LMFDB - Embedded newform 37.9.g.a.8.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,9,Mod(8,37)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("37.8");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	37.g (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.0730085723$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$25$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			8.5
Character	$\chi$	$=$	37.8
Dual form			37.9.g.a.14.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-22.4552 - 6.01684i) q^{2} +(-2.68847 - 1.55219i) q^{3} +(246.329 + 142.218i) q^{4} +(152.334 - 40.8178i) q^{5} +(51.0307 + 51.0307i) q^{6} +(-434.094 + 751.872i) q^{7} +(-467.444 - 467.444i) q^{8} +(-3275.68 - 5673.65i) q^{9} +O(q^{10})$	\(q+(-22.4552 - 6.01684i) q^{2} +(-2.68847 - 1.55219i) q^{3} +(246.329 + 142.218i) q^{4} +(152.334 - 40.8178i) q^{5} +(51.0307 + 51.0307i) q^{6} +(-434.094 + 751.872i) q^{7} +(-467.444 - 467.444i) q^{8} +(-3275.68 - 5673.65i) q^{9} -3666.28 q^{10} -19422.6i q^{11} +(-441.498 - 764.697i) q^{12} +(-33825.5 + 9063.52i) q^{13} +(14271.5 - 14271.5i) q^{14} +(-472.903 - 126.714i) q^{15} +(-28723.9 - 49751.2i) q^{16} +(-29472.0 + 109991. i) q^{17} +(39418.5 + 147112. i) q^{18} +(224205. - 60075.4i) q^{19} +(43329.4 + 11610.1i) q^{20} +(2334.09 - 1347.59i) q^{21} +(-116863. + 436138. i) q^{22} +(285996. + 285996. i) q^{23} +(531.147 + 1982.27i) q^{24} +(-316752. + 182877. i) q^{25} +814091. q^{26} +40705.7i q^{27} +(-213860. + 123472. i) q^{28} +(-369886. + 369886. i) q^{29} +(9856.68 + 5690.76i) q^{30} +(-364142. + 364142. i) q^{31} +(389454. + 1.45346e6i) q^{32} +(-30147.5 + 52217.1i) q^{33} +(1.32360e6 - 2.29253e6i) q^{34} +(-35437.5 + 132255. i) q^{35} -1.86344e6i q^{36} +(1.87398e6 + 25792.3i) q^{37} -5.39601e6 q^{38} +(105007. + 28136.6i) q^{39} +(-90287.7 - 52127.6i) q^{40} +(-1.30794e6 - 755138. i) q^{41} +(-60520.6 + 16216.5i) q^{42} +(1.33615e6 + 1.33615e6i) q^{43} +(2.76225e6 - 4.78436e6i) q^{44} +(-730584. - 730584. i) q^{45} +(-4.70129e6 - 8.14287e6i) q^{46} -5.62296e6 q^{47} +178339. i q^{48} +(2.50553e6 + 4.33970e6i) q^{49} +(8.21304e6 - 2.20068e6i) q^{50} +(249961. - 249961. i) q^{51} +(-9.62120e6 - 2.57799e6i) q^{52} +(6.82022e6 + 1.18130e7i) q^{53} +(244920. - 914052. i) q^{54} +(-792789. - 2.95873e6i) q^{55} +(554372. - 148544. i) q^{56} +(-696015. - 186497. i) q^{57} +(1.05314e7 - 6.08031e6i) q^{58} +(-3.89451e6 + 1.45345e7i) q^{59} +(-98468.6 - 98468.6i) q^{60} +(3.55971e6 + 1.32850e7i) q^{61} +(1.03679e7 - 5.98589e6i) q^{62} +5.68781e6 q^{63} -2.02744e7i q^{64} +(-4.78283e6 + 2.76137e6i) q^{65} +(991150. - 991150. i) q^{66} +(-1.19960e7 - 6.92592e6i) q^{67} +(-2.29025e7 + 2.29025e7i) q^{68} +(-324971. - 1.21281e6i) q^{69} +(1.59151e6 - 2.75658e6i) q^{70} +(-1.09837e7 + 1.90243e7i) q^{71} +(-1.12091e6 + 4.18331e6i) q^{72} -5.43094e7i q^{73} +(-4.19254e7 - 1.18546e7i) q^{74} +1.13543e6 q^{75} +(6.37719e7 + 1.70876e7i) q^{76} +(1.46033e7 + 8.43124e6i) q^{77} +(-2.18866e6 - 1.26362e6i) q^{78} +(-6.83745e6 + 1.83209e6i) q^{79} +(-6.40636e6 - 6.40636e6i) q^{80} +(-2.14286e7 + 3.71154e7i) q^{81} +(2.48264e7 + 2.48264e7i) q^{82} +(3.07779e7 + 5.33089e7i) q^{83} +766606. q^{84} +1.79584e7i q^{85} +(-2.19641e7 - 3.80430e7i) q^{86} +(1.56856e6 - 420295. i) q^{87} +(-9.07898e6 + 9.07898e6i) q^{88} +(1.88463e7 + 5.04985e6i) q^{89} +(1.20096e7 + 2.08012e7i) q^{90} +(7.86883e6 - 2.93669e7i) q^{91} +(2.97753e7 + 1.11123e8i) q^{92} +(1.54420e6 - 413768. i) q^{93} +(1.26265e8 + 3.38325e7i) q^{94} +(3.17019e7 - 1.83031e7i) q^{95} +(1.20901e6 - 4.51209e6i) q^{96} +(-3.93976e7 - 3.93976e7i) q^{97} +(-3.01507e7 - 1.12524e8i) q^{98} +(-1.10197e8 + 6.36223e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 10 q^{2} - 6 q^{3} + 552 q^{4} - 1642 q^{5} - 516 q^{6} - 2 q^{7} - 7440 q^{8} + 117258 q^{9}+O(q^{10}) $ 100 * q - 10 * q^2 - 6 * q^3 + 552 * q^4 - 1642 * q^5 - 516 * q^6 - 2 * q^7 - 7440 * q^8 + 117258 * q^9	\( 100 q - 10 q^{2} - 6 q^{3} + 552 q^{4} - 1642 q^{5} - 516 q^{6} - 2 q^{7} - 7440 q^{8} + 117258 q^{9} + 10744 q^{10} - 62086 q^{12} - 63598 q^{13} - 62648 q^{14} + 53318 q^{15} + 1056692 q^{16} - 53050 q^{17} - 150954 q^{18} - 161388 q^{19} - 922330 q^{20} + 589656 q^{21} - 713044 q^{22} + 32888 q^{23} - 1193742 q^{24} + 1859250 q^{25} + 900088 q^{26} - 7001094 q^{28} + 2288858 q^{29} + 9620658 q^{30} + 5782072 q^{31} - 4920832 q^{32} - 719444 q^{33} - 5308306 q^{34} - 10575422 q^{35} + 14052530 q^{37} - 10994096 q^{38} + 3417088 q^{39} + 9928698 q^{40} + 16320936 q^{41} + 39067848 q^{42} - 9546800 q^{43} - 19056984 q^{44} - 12333970 q^{45} - 15608210 q^{46} - 844736 q^{47} - 54639310 q^{49} - 52548004 q^{50} + 25866216 q^{51} + 31025896 q^{52} - 17856728 q^{53} + 8699372 q^{54} - 14191504 q^{55} - 23168766 q^{56} + 74736160 q^{57} + 109856484 q^{58} + 499856 q^{59} - 286204560 q^{60} - 34778024 q^{61} + 6537756 q^{62} + 154042660 q^{63} - 107386782 q^{65} - 14426072 q^{66} + 84112848 q^{67} + 247473908 q^{68} - 74383808 q^{69} - 55414618 q^{70} - 57046730 q^{71} - 172153588 q^{72} + 315393932 q^{74} + 164078200 q^{75} - 141128756 q^{76} + 272235456 q^{77} + 655339260 q^{78} + 18584140 q^{79} + 43263824 q^{80} - 337954862 q^{81} - 363936872 q^{82} - 86956118 q^{83} - 505940536 q^{84} + 41750098 q^{86} + 195776154 q^{87} + 425134052 q^{88} + 253234298 q^{89} - 139130828 q^{90} - 327702612 q^{91} - 572151958 q^{92} - 608615132 q^{93} - 502568260 q^{94} - 115562040 q^{95} + 1165361934 q^{96} - 123302218 q^{97} + 537492294 q^{98} + 533594376 q^{99}+O(q^{100}) \) 100 * q - 10 * q^2 - 6 * q^3 + 552 * q^4 - 1642 * q^5 - 516 * q^6 - 2 * q^7 - 7440 * q^8 + 117258 * q^9 + 10744 * q^10 - 62086 * q^12 - 63598 * q^13 - 62648 * q^14 + 53318 * q^15 + 1056692 * q^16 - 53050 * q^17 - 150954 * q^18 - 161388 * q^19 - 922330 * q^20 + 589656 * q^21 - 713044 * q^22 + 32888 * q^23 - 1193742 * q^24 + 1859250 * q^25 + 900088 * q^26 - 7001094 * q^28 + 2288858 * q^29 + 9620658 * q^30 + 5782072 * q^31 - 4920832 * q^32 - 719444 * q^33 - 5308306 * q^34 - 10575422 * q^35 + 14052530 * q^37 - 10994096 * q^38 + 3417088 * q^39 + 9928698 * q^40 + 16320936 * q^41 + 39067848 * q^42 - 9546800 * q^43 - 19056984 * q^44 - 12333970 * q^45 - 15608210 * q^46 - 844736 * q^47 - 54639310 * q^49 - 52548004 * q^50 + 25866216 * q^51 + 31025896 * q^52 - 17856728 * q^53 + 8699372 * q^54 - 14191504 * q^55 - 23168766 * q^56 + 74736160 * q^57 + 109856484 * q^58 + 499856 * q^59 - 286204560 * q^60 - 34778024 * q^61 + 6537756 * q^62 + 154042660 * q^63 - 107386782 * q^65 - 14426072 * q^66 + 84112848 * q^67 + 247473908 * q^68 - 74383808 * q^69 - 55414618 * q^70 - 57046730 * q^71 - 172153588 * q^72 + 315393932 * q^74 + 164078200 * q^75 - 141128756 * q^76 + 272235456 * q^77 + 655339260 * q^78 + 18584140 * q^79 + 43263824 * q^80 - 337954862 * q^81 - 363936872 * q^82 - 86956118 * q^83 - 505940536 * q^84 + 41750098 * q^86 + 195776154 * q^87 + 425134052 * q^88 + 253234298 * q^89 - 139130828 * q^90 - 327702612 * q^91 - 572151958 * q^92 - 608615132 * q^93 - 502568260 * q^94 - 115562040 * q^95 + 1165361934 * q^96 - 123302218 * q^97 + 537492294 * q^98 + 533594376 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−22.4552	−	6.01684i	−1.40345	−	0.376052i	−0.523866	−	0.851801i	$-0.675511\pi$
$2$	−22.4552	−	6.01684i	−1.40345	−	0.376052i	−0.879581	+	0.475748i	$0.842177\pi$
$3$	−2.68847	−	1.55219i	−0.0331910	−	0.0191628i	0.483313	−	0.875448i	$-0.339433\pi$
$3$	−2.68847	−	1.55219i	−0.0331910	−	0.0191628i	−0.516504	+	0.856285i	$0.672767\pi$
$4$	246.329	+	142.218i	0.962223	+	0.555540i
$5$	152.334	−	40.8178i	0.243735	−	0.0653085i	−0.134883	−	0.990861i	$-0.543066\pi$
$5$	152.334	−	40.8178i	0.243735	−	0.0653085i	0.378618	+	0.925553i	$0.376399\pi$
$6$	51.0307	+	51.0307i	0.0393755	+	0.0393755i
$7$	−434.094	+	751.872i	−0.180797	+	0.313150i	−0.942152	−	0.335185i	$-0.891201\pi$
$7$	−434.094	+	751.872i	−0.180797	+	0.313150i	0.761355	+	0.648335i	$0.224534\pi$
$8$	−467.444	−	467.444i	−0.114122	−	0.114122i
$9$	−3275.68	−	5673.65i	−0.499266	−	0.864753i
$10$	−3666.28			−0.366628
$11$		−	19422.6i		−	1.32659i	−0.748357	−	0.663296i	$-0.769157\pi$
$11$		−	19422.6i		−	1.32659i	0.748357	−	0.663296i	$-0.230843\pi$
$12$	−441.498	−	764.697i	−0.0212914	−	0.0368778i
$13$	−33825.5	+	9063.52i	−1.18433	+	0.317339i	−0.796641	−	0.604453i	$-0.793392\pi$
$13$	−33825.5	+	9063.52i	−1.18433	+	0.317339i	−0.387685	+	0.921792i	$0.626725\pi$
$14$	14271.5	−	14271.5i	0.371500	−	0.371500i
$15$	−472.903	−	126.714i	−0.00934129	−	0.00250299i
$16$	−28723.9	−	49751.2i	−0.438291	−	0.759143i
$17$	−29472.0	+	109991.i	−0.352869	+	1.31692i	0.530276	+	0.847825i	$0.322088\pi$
$17$	−29472.0	+	109991.i	−0.352869	+	1.31692i	−0.883145	+	0.469100i	$0.844578\pi$
$18$	39418.5	+	147112.i	0.375500	+	1.40139i
$19$	224205.	−	60075.4i	1.72040	−	0.460981i	0.742466	−	0.669883i	$-0.233656\pi$
$19$	224205.	−	60075.4i	1.72040	−	0.460981i	0.977936	+	0.208903i	$0.0669892\pi$
$20$	43329.4	+	11610.1i	0.270809	+	0.0725629i
$21$	2334.09	−	1347.59i	0.0120016	−	0.00692916i
$22$	−116863.	+	436138.i	−0.498868	+	1.86180i
$23$	285996.	+	285996.i	1.02199	+	1.02199i	0.999753	+	0.0222408i	$0.00708006\pi$
$23$	285996.	+	285996.i	1.02199	+	1.02199i	0.0222408	+	0.999753i	$0.492920\pi$
$24$	531.147	+	1982.27i	0.00160092	+	0.00597471i
$25$	−316752.	+	182877.i	−0.810884	+	0.468164i
$26$	814091.			1.78147
$27$			40705.7i			0.0765949i
$28$	−213860.	+	123472.i	−0.347934	+	0.200880i
$29$	−369886.	+	369886.i	−0.522970	+	0.522970i	−0.918467	−	0.395497i	$-0.870572\pi$
$29$	−369886.	+	369886.i	−0.522970	+	0.522970i	0.395497	+	0.918467i	$0.370572\pi$
$30$	9856.68	+	5690.76i	0.0121687	+	0.00702563i
$31$	−364142.	+	364142.i	−0.394298	+	0.394298i	−0.876216	−	0.481918i	$-0.839940\pi$
$31$	−364142.	+	364142.i	−0.394298	+	0.394298i	0.481918	+	0.876216i	$0.339940\pi$
$32$	389454.	+	1.45346e6i	0.371413	+	1.38613i
$33$	−30147.5	+	52217.1i	−0.0254212	+	0.0440308i
$34$	1.32360e6	−	2.29253e6i	0.990466	−	1.71554i
$35$	−35437.5	+	132255.i	−0.0236152	+	0.0881330i
$36$		−	1.86344e6i		−	1.10945i
$37$	1.87398e6	+	25792.3i	0.999905	+	0.0137621i
$37$	1.87398e6	+	25792.3i	0.999905	+	0.0137621i
$38$	−5.39601e6			−2.58785
$39$	105007.	+	28136.6i	0.0453900	+	0.0121622i
$40$	−90287.7	−	52127.6i	−0.0352686	−	0.0203624i
$41$	−1.30794e6	−	755138.i	−0.462862	−	0.267233i	0.250385	−	0.968146i	$-0.419443\pi$
$41$	−1.30794e6	−	755138.i	−0.462862	−	0.267233i	−0.713247	+	0.700913i	$0.752776\pi$
$42$	−60520.6	+	16216.5i	−0.0194494	+	0.00521145i
$43$	1.33615e6	+	1.33615e6i	0.390825	+	0.390825i	0.874982	−	0.484156i	$-0.160873\pi$
$43$	1.33615e6	+	1.33615e6i	0.390825	+	0.390825i	−0.484156	+	0.874982i	$0.660873\pi$
$44$	2.76225e6	−	4.78436e6i	0.736974	−	1.27648i
$45$	−730584.	−	730584.i	−0.178164	−	0.178164i
$46$	−4.70129e6	−	8.14287e6i	−1.04999	−	1.81864i
$47$	−5.62296e6			−1.15232			−0.576161	−	0.817336i	$-0.695450\pi$
$47$	−5.62296e6			−1.15232			−0.576161	+	0.817336i	$0.695450\pi$
$48$			178339.i			0.0335956i
$49$	2.50553e6	+	4.33970e6i	0.434625	+	0.752792i
$50$	8.21304e6	−	2.20068e6i	1.31409	−	0.352109i
$51$	249961.	−	249961.i	0.0369480	−	0.0369480i
$52$	−9.62120e6	−	2.57799e6i	−1.31588	−	0.352589i
$53$	6.82022e6	+	1.18130e7i	0.864360	+	1.49712i	0.867681	+	0.497122i	$0.165610\pi$
$53$	6.82022e6	+	1.18130e7i	0.864360	+	1.49712i	−0.00332053	+	0.999994i	$0.501057\pi$
$54$	244920.	−	914052.i	0.0288037	−	0.107497i
$55$	−792789.	−	2.95873e6i	−0.0866377	−	0.323336i
$56$	554372.	−	148544.i	0.0563702	−	0.0151043i
$57$	−696015.	−	186497.i	−0.0659355	−	0.0176674i
$58$	1.05314e7	−	6.08031e6i	0.930624	−	0.537296i
$59$	−3.89451e6	+	1.45345e7i	−0.321399	+	1.19948i	0.596483	+	0.802626i	$0.296564\pi$
$59$	−3.89451e6	+	1.45345e7i	−0.321399	+	1.19948i	−0.917882	+	0.396853i	$0.870102\pi$
$60$	−98468.6	−	98468.6i	−0.00759789	−	0.00759789i
$61$	3.55971e6	+	1.32850e7i	0.257096	+	0.959497i	0.966912	+	0.255109i	$0.0821115\pi$
$61$	3.55971e6	+	1.32850e7i	0.257096	+	0.959497i	−0.709816	+	0.704387i	$0.751222\pi$
$62$	1.03679e7	−	5.98589e6i	0.701653	−	0.405099i
$63$	5.68781e6			0.361063
$64$		−	2.02744e7i		−	1.20845i
$65$	−4.78283e6	+	2.76137e6i	−0.267936	+	0.154693i
$66$	991150.	−	991150.i	0.0522352	−	0.0522352i
$67$	−1.19960e7	−	6.92592e6i	−0.595304	−	0.343699i	0.171888	−	0.985116i	$-0.445013\pi$
$67$	−1.19960e7	−	6.92592e6i	−0.595304	−	0.343699i	−0.767192	+	0.641418i	$0.778347\pi$
$68$	−2.29025e7	+	2.29025e7i	−1.07114	+	1.07114i
$69$	−324971.	−	1.21281e6i	−0.0143367	−	0.0535052i
$70$	1.59151e6	−	2.75658e6i	0.0662853	−	0.114809i
$71$	−1.09837e7	+	1.90243e7i	−0.432230	+	0.748645i	−0.997065	−	0.0765592i	$-0.975607\pi$
$71$	−1.09837e7	+	1.90243e7i	−0.432230	+	0.748645i	0.564835	+	0.825204i	$0.308940\pi$
$72$	−1.12091e6	+	4.18331e6i	−0.0417102	+	0.155665i
$73$		−	5.43094e7i		−	1.91242i	−0.292678	−	0.956211i	$-0.594546\pi$
$73$		−	5.43094e7i		−	1.91242i	0.292678	−	0.956211i	$-0.405454\pi$
$74$	−4.19254e7	−	1.18546e7i	−1.39814	−	0.395331i
$75$	1.13543e6			0.0358853
$76$	6.37719e7	+	1.70876e7i	1.91150	+	0.512186i
$77$	1.46033e7	+	8.43124e6i	0.415421	+	0.239844i
$78$	−2.18866e6	−	1.26362e6i	−0.0591288	−	0.0341380i
$79$	−6.83745e6	+	1.83209e6i	−0.175544	+	0.0470369i	−0.345520	−	0.938411i	$-0.612298\pi$
$79$	−6.83745e6	+	1.83209e6i	−0.175544	+	0.0470369i	0.169976	+	0.985448i	$0.445631\pi$
$80$	−6.40636e6	−	6.40636e6i	−0.156405	−	0.156405i
$81$	−2.14286e7	+	3.71154e7i	−0.497798	+	0.862211i
$82$	2.48264e7	+	2.48264e7i	0.549108	+	0.549108i
$83$	3.07779e7	+	5.33089e7i	0.648525	+	1.12328i	0.983475	+	0.181043i	$0.0579473\pi$
$83$	3.07779e7	+	5.33089e7i	0.648525	+	1.12328i	−0.334950	+	0.942236i	$0.608719\pi$
$84$	766606.			0.0153977
$85$			1.79584e7i			0.344026i
$86$	−2.19641e7	−	3.80430e7i	−0.401532	−	0.695473i
$87$	1.56856e6	−	420295.i	0.0273794	−	0.00733630i
$88$	−9.07898e6	+	9.07898e6i	−0.151393	+	0.151393i
$89$	1.88463e7	+	5.04985e6i	0.300377	+	0.0804857i	0.405860	−	0.913935i	$-0.366972\pi$
$89$	1.88463e7	+	5.04985e6i	0.300377	+	0.0804857i	−0.105483	+	0.994421i	$0.533639\pi$
$90$	1.20096e7	+	2.08012e7i	0.183045	+	0.317043i
$91$	7.86883e6	−	2.93669e7i	0.114748	−	0.428245i
$92$	2.97753e7	+	1.11123e8i	0.415628	+	1.55114i
$93$	1.54420e6	−	413768.i	0.0206430	−	0.00553127i
$94$	1.26265e8	+	3.38325e7i	1.61722	+	0.433334i
$95$	3.17019e7	−	1.83031e7i	0.389216	−	0.224714i
$96$	1.20901e6	−	4.51209e6i	0.0142346	−	0.0531243i
$97$	−3.93976e7	−	3.93976e7i	−0.445024	−	0.445024i	0.448672	−	0.893696i	$-0.351897\pi$
$97$	−3.93976e7	−	3.93976e7i	−0.445024	−	0.445024i	−0.893696	+	0.448672i	$0.851897\pi$
$98$	−3.01507e7	−	1.12524e8i	−0.326884	−	1.21995i
$99$	−1.10197e8	+	6.36223e7i	−1.14717	+	0.662321i
$100$	−1.04033e8			−1.04033
$101$			4.39284e7i			0.422143i	0.977471	+	0.211072i	$0.0676953\pi$
$101$			4.39284e7i			0.422143i	−0.977471	+	0.211072i	$0.932305\pi$
$102$	−7.11688e6	+	4.10893e6i	−0.0657490	+	0.0379602i
$103$	3.19435e7	−	3.19435e7i	0.283814	−	0.283814i	−0.550814	−	0.834628i	$-0.685683\pi$
$103$	3.19435e7	−	3.19435e7i	0.283814	−	0.283814i	0.834628	+	0.550814i	$0.185683\pi$
$104$	2.00482e7	+	1.15748e7i	0.171373	+	0.0989422i
$105$	300557.	−	300557.i	0.00247269	−	0.00247269i
$106$	−8.20723e7	−	3.06298e8i	−0.650090	−	2.42617i
$107$	1.15152e7	−	1.99449e7i	0.0878488	−	0.152159i	−0.818753	−	0.574146i	$-0.805334\pi$
$107$	1.15152e7	−	1.99449e7i	0.0878488	−	0.152159i	0.906602	+	0.421988i	$0.138667\pi$
$108$	−5.78909e6	+	1.00270e7i	−0.0425515	+	0.0737014i
$109$	5.31043e7	−	1.98188e8i	0.376204	−	1.40401i	−0.475374	−	0.879784i	$-0.657687\pi$
$109$	5.31043e7	−	1.98188e8i	0.376204	−	1.40401i	0.851578	−	0.524228i	$-0.175646\pi$
$110$			7.12088e7i			0.486366i
$111$	−4.99811e6	−	2.97812e6i	−0.0329241	−	0.0196178i
$112$	4.98754e7			0.316967
$113$	−2.21919e8	−	5.94631e7i	−1.36107	−	0.364699i	−0.496863	−	0.867829i	$-0.665515\pi$
$113$	−2.21919e8	−	5.94631e7i	−1.36107	−	0.364699i	−0.864210	+	0.503130i	$0.832182\pi$
$114$	1.45070e7	+	8.37562e6i	0.0858931	+	0.0495904i
$115$	5.52407e7	+	3.18932e7i	0.315840	+	0.182350i
$116$	−1.43718e8	+	3.85092e7i	−0.793744	+	0.212683i
$117$	1.62225e8	+	1.62225e8i	0.865713	+	0.865713i
$118$	1.74904e8	−	3.02942e8i	0.902134	−	1.56254i
$119$	−6.99055e7	−	6.99055e7i	−0.348597	−	0.348597i
$120$	161824.	+	280287.i	0.000780400	+	0.00135169i
$121$	−1.62879e8			−0.759844
$122$		−	3.19736e8i		−	1.44328i
$123$	2.34423e6	+	4.06033e6i	0.0102419	+	0.0177395i
$124$	−1.41486e8	+	3.79112e7i	−0.598450	+	0.160354i
$125$	−8.43486e7	+	8.43486e7i	−0.345492	+	0.345492i
$126$	−1.27721e8	−	3.42226e7i	−0.506733	−	0.135779i
$127$	1.22630e8	+	2.12401e8i	0.471390	+	0.816472i	0.999464	−	0.0327266i	$-0.0104191\pi$
$127$	1.22630e8	+	2.12401e8i	0.471390	+	0.816472i	−0.528074	+	0.849198i	$0.677086\pi$
$128$	−2.22876e7	+	8.31784e7i	−0.0830277	+	0.309864i
$129$	−1.51824e6	−	5.66617e6i	−0.00548255	−	0.0204612i
$130$	1.24014e8	−	3.32294e7i	0.434207	−	0.116345i
$131$	−1.30785e8	−	3.50437e7i	−0.444091	−	0.118994i	0.0298423	−	0.999555i	$-0.490499\pi$
$131$	−1.30785e8	−	3.50437e7i	−0.444091	−	0.118994i	−0.473933	+	0.880561i	$0.657166\pi$
$132$	−1.48524e7	+	8.57505e6i	−0.0489217	+	0.0282450i
$133$	−5.21567e7	+	1.94652e8i	−0.166688	+	0.622087i
$134$	2.27701e8	+	2.27701e8i	0.706229	+	0.706229i
$135$	1.66152e6	+	6.20087e6i	0.00500230	+	0.0186688i
$136$	6.51910e7	−	3.76381e7i	0.190560	−	0.110020i
$137$	3.28278e8			0.931880			0.465940	−	0.884816i	$-0.345716\pi$
$137$	3.28278e8			0.931880			0.465940	+	0.884816i	$0.345716\pi$
$138$			2.91891e7i			0.0804831i
$139$	1.39888e8	−	8.07644e7i	0.374732	−	0.216352i	−0.300792	−	0.953690i	$-0.597251\pi$
$139$	1.39888e8	−	8.07644e7i	0.374732	−	0.216352i	0.675524	+	0.737338i	$0.263918\pi$
$140$	−2.75383e7	+	2.75383e7i	−0.0716844	+	0.0716844i
$141$	1.51172e7	+	8.72789e6i	0.0382467	+	0.0220817i
$142$	3.61107e8	−	3.61107e8i	0.888142	−	0.888142i
$143$	1.76037e8	+	6.56980e8i	0.420979	+	1.57112i
$144$	−1.88180e8	+	3.25938e8i	−0.437647	+	0.758028i
$145$	−4.12484e7	+	7.14443e7i	−0.0933115	+	0.161620i
$146$	−3.26771e8	+	1.21953e9i	−0.719171	+	2.68398i
$147$		−	1.55562e7i		−	0.0333145i
$148$	4.57948e8	+	2.72868e8i	0.954486	+	0.568729i
$149$	−1.53505e8			−0.311442			−0.155721	−	0.987801i	$-0.549770\pi$
$149$	−1.53505e8			−0.311442			−0.155721	+	0.987801i	$0.549770\pi$
$150$	−2.54964e7	−	6.83173e6i	−0.0503632	−	0.0134948i
$151$	2.67579e7	+	1.54487e7i	0.0514689	+	0.0297156i	0.525514	−	0.850785i	$-0.323873\pi$
$151$	2.67579e7	+	1.54487e7i	0.0514689	+	0.0297156i	−0.474045	+	0.880501i	$0.657207\pi$
$152$	−1.32885e8	−	7.67211e7i	−0.248944	−	0.143728i
$153$	7.20590e8	−	1.93082e8i	1.31499	−	0.352351i
$154$	−2.77191e8	−	2.77191e8i	−0.492828	−	0.492828i
$155$	−4.06078e7	+	7.03349e7i	−0.0703531	+	0.121855i
$156$	2.18648e7	+	2.18648e7i	0.0369187	+	0.0369187i
$157$	4.11124e8	+	7.12088e8i	0.676666	+	1.17202i	0.975979	+	0.217866i	$0.0699094\pi$
$157$	4.11124e8	+	7.12088e8i	0.676666	+	1.17202i	−0.299312	+	0.954155i	$0.596757\pi$
$158$	1.64559e8			0.264055
$159$		−	4.23450e7i		−	0.0662543i
$160$	1.18654e8	+	2.05516e8i	0.181052	+	0.313592i
$161$	−3.39181e8	+	9.08833e7i	−0.504810	+	0.135263i
$162$	7.04499e8	−	7.04499e8i	1.02287	−	1.02287i
$163$	−1.06841e9	−	2.86280e8i	−1.51352	−	0.405547i	−0.595919	−	0.803045i	$-0.703212\pi$
$163$	−1.06841e9	−	2.86280e8i	−1.51352	−	0.405547i	−0.917603	+	0.397498i	$0.869879\pi$
$164$	−2.14789e8	−	3.72025e8i	−0.296917	−	0.514276i
$165$	−2.46112e6	+	9.18501e6i	−0.00332044	+	0.0123921i
$166$	−3.70372e8	−	1.38225e9i	−0.487759	−	1.82034i
$167$	−3.41149e8	+	9.14107e7i	−0.438610	+	0.117525i	−0.471365	−	0.881938i	$-0.656239\pi$
$167$	−3.41149e8	+	9.14107e7i	−0.438610	+	0.117525i	0.0327549	+	0.999463i	$0.489572\pi$
$168$	−1.72098e6	−	461135.i	−0.00216042	−	0.000578883i
$169$	3.55575e8	−	2.05291e8i	0.435897	−	0.251665i
$170$	1.08053e8	−	4.03258e8i	0.129372	−	0.482822i
$171$	−1.07527e9	−	1.07527e9i	−1.25757	−	1.25757i
$172$	1.39108e8	+	5.19159e8i	0.158942	+	0.593180i
$173$	−9.19045e8	+	5.30611e8i	−1.02601	+	0.592368i	−0.915840	−	0.401544i	$-0.868474\pi$
$173$	−9.19045e8	+	5.30611e8i	−1.02601	+	0.592368i	−0.110172	+	0.993912i	$0.535140\pi$
$174$	−3.77511e7			−0.0411844
$175$		−	3.17542e8i		−	0.338571i
$176$	−9.66298e8	+	5.57893e8i	−1.00707	+	0.581433i
$177$	3.30305e7	−	3.30305e7i	0.0336529	−	0.0336529i
$178$	−3.92812e8	−	2.26790e8i	−0.391296	−	0.225915i
$179$	7.82073e8	−	7.82073e8i	0.761790	−	0.761790i	−0.214856	−	0.976646i	$-0.568928\pi$
$179$	7.82073e8	−	7.82073e8i	0.761790	−	0.761790i	0.976646	+	0.214856i	$0.0689282\pi$
$180$	−7.60618e7	−	2.83866e8i	−0.0724564	−	0.270411i
$181$	9.59579e8	−	1.66204e9i	0.894060	−	1.54856i	0.0590960	−	0.998252i	$-0.481178\pi$
$181$	9.59579e8	−	1.66204e9i	0.894060	−	1.54856i	0.834964	−	0.550305i	$-0.185488\pi$
$182$	−3.53392e8	+	6.12092e8i	−0.322085	+	0.557868i
$183$	1.10507e7	−	4.12417e7i	0.00985337	−	0.0367733i
$184$		−	2.67374e8i		−	0.233264i
$185$	2.86525e8	−	7.25629e7i	0.244610	−	0.0619481i
$186$	−3.71649e7			−0.0310514
$187$	2.13631e9	+	5.72423e8i	1.74702	+	0.468113i
$188$	−1.38510e9	−	7.99687e8i	−1.10879	−	0.640160i
$189$	−3.06055e7	−	1.76701e7i	−0.0239857	−	0.0138481i
$190$	−8.21998e8	+	2.20254e8i	−0.630748	+	0.169009i
$191$	1.39377e9	+	1.39377e9i	1.04727	+	1.04727i	0.998826	+	0.0484390i	$0.0154246\pi$
$191$	1.39377e9	+	1.39377e9i	1.04727	+	1.04727i	0.0484390	+	0.998826i	$0.484575\pi$
$192$	−3.14697e7	+	5.45071e7i	−0.0231573	+	0.0401096i
$193$	−1.16795e9	−	1.16795e9i	−0.841775	−	0.841775i	0.147315	−	0.989090i	$-0.452937\pi$
$193$	−1.16795e9	−	1.16795e9i	−0.841775	−	0.841775i	−0.989090	+	0.147315i	$0.952937\pi$
$194$	6.47631e8	+	1.12173e9i	0.457215	+	0.791920i
$195$	1.71446e7			0.0118574
$196$			1.42532e9i			0.965805i
$197$	4.22888e8	+	7.32464e8i	0.280777	+	0.486319i	0.971576	−	0.236727i	$-0.0760747\pi$
$197$	4.22888e8	+	7.32464e8i	0.280777	+	0.486319i	−0.690800	+	0.723046i	$0.742741\pi$
$198$	2.85730e9	−	7.65611e8i	1.85907	−	0.498135i
$199$	−1.84238e9	+	1.84238e9i	−1.17481	+	1.17481i	−0.193756	+	0.981050i	$0.562067\pi$
$199$	−1.84238e9	+	1.84238e9i	−1.17481	+	1.17481i	−0.981050	+	0.193756i	$0.937933\pi$
$200$	2.33548e8	+	6.25790e7i	0.145967	+	0.0391119i
$201$	2.15006e7	+	3.72402e7i	0.0131725	+	0.0228154i
$202$	2.64310e8	−	9.86419e8i	0.158748	−	0.592456i
$203$	−1.17542e8	−	4.38673e8i	−0.0692164	−	0.258319i
$204$	9.71216e7	−	2.60236e7i	0.0560783	−	0.0150261i
$205$	−2.30067e8	−	6.16462e7i	−0.130268	−	0.0349052i
$206$	−9.09495e8	+	5.25097e8i	−0.505047	+	0.291589i
$207$	6.85808e8	−	2.55947e9i	0.373526	−	1.39402i
$208$	1.42252e9	+	1.42252e9i	0.759985	+	0.759985i
$209$	−1.16682e9	−	4.35464e9i	−0.611533	−	2.28227i
$210$	−8.55744e6	+	4.94064e6i	−0.00440014	+	0.00254042i
$211$	−1.16075e9			−0.585609			−0.292804	−	0.956172i	$-0.594588\pi$
$211$	−1.16075e9			−0.585609			−0.292804	+	0.956172i	$0.594588\pi$
$212$			3.87983e9i			1.92075i
$213$	5.90586e7	−	3.40975e7i	0.0286923	−	0.0165655i
$214$	−3.78580e8	+	3.78580e8i	−0.180511	+	0.180511i
$215$	2.58081e8	+	1.49003e8i	0.120782	+	0.0697335i
$216$	1.90276e7	−	1.90276e7i	0.00874116	−	0.00874116i
$217$	−1.15717e8	−	4.31860e8i	−0.0521863	−	0.194762i
$218$	−2.38493e9	+	4.13082e9i	−1.05596	+	1.82898i
$219$	−8.42984e7	+	1.46009e8i	−0.0366474	+	0.0634751i
$220$	2.25498e8	−	8.41570e8i	0.0962614	−	0.359252i
$221$		−	3.98762e9i		−	1.67165i
$222$	9.43145e7	+	9.69469e7i	0.0388299	+	0.0399137i
$223$	−1.56578e9			−0.633158			−0.316579	−	0.948566i	$-0.602534\pi$
$223$	−1.56578e9			−0.633158			−0.316579	+	0.948566i	$0.602534\pi$
$224$	−1.26188e9	−	3.38119e8i	−0.501216	−	0.134301i
$225$	2.07515e9	+	1.19809e9i	0.809693	+	0.467476i
$226$	4.62545e9	+	2.67051e9i	1.77305	+	1.02367i
$227$	3.21623e9	−	8.61786e8i	1.21128	−	0.324561i	0.404014	−	0.914753i	$-0.367615\pi$
$227$	3.21623e9	−	8.61786e8i	1.21128	−	0.324561i	0.807263	+	0.590192i	$0.200948\pi$
$228$	−1.44925e8	−	1.44925e8i	−0.0536297	−	0.0536297i
$229$	−1.51653e9	+	2.62670e9i	−0.551452	+	0.955144i	0.446718	+	0.894675i	$0.352593\pi$
$229$	−1.51653e9	+	2.62670e9i	−0.551452	+	0.955144i	−0.998170	+	0.0604687i	$0.980740\pi$
$230$	−1.04854e9	−	1.04854e9i	−0.374692	−	0.374692i
$231$	−2.61737e7	−	4.53342e7i	−0.00919216	−	0.0159213i
$232$	3.45802e8			0.119365
$233$		−	2.06096e9i		−	0.699271i	−0.936886	−	0.349636i	$-0.886305\pi$
$233$		−	2.06096e9i		−	0.699271i	0.936886	−	0.349636i	$-0.113695\pi$
$234$	−2.66670e9	−	4.61886e9i	−0.889429	−	1.54054i
$235$	−8.56570e8	+	2.29517e8i	−0.280861	+	0.0752565i
$236$	−3.02640e9	+	3.02640e9i	−0.975615	+	0.975615i
$237$	2.12260e7	+	5.68749e6i	0.00672783	+	0.00180272i
$238$	1.14913e9	+	1.99035e9i	0.358146	+	0.620328i
$239$	−1.82657e8	+	6.81685e8i	−0.0559815	+	0.208926i	−0.988251	−	0.152838i	$-0.951159\pi$
$239$	−1.82657e8	+	6.81685e8i	−0.0559815	+	0.208926i	0.932270	+	0.361764i	$0.117825\pi$
$240$	7.27942e6	+	2.71672e7i	0.00219408	+	0.00818841i
$241$	2.96173e9	−	7.93593e8i	0.877965	−	0.235250i	0.208436	−	0.978036i	$-0.433163\pi$
$241$	2.96173e9	−	7.93593e8i	0.877965	−	0.235250i	0.669529	+	0.742786i	$0.266496\pi$
$242$	3.65748e9	+	9.80019e8i	1.06640	+	0.285741i
$243$	3.46509e8	−	2.00057e8i	0.0993779	−	0.0573759i
$244$	−1.01251e9	+	3.77875e9i	−0.285654	+	1.06608i
$245$	5.58815e8	+	5.58815e8i	0.155097	+	0.155097i
$246$	−2.82097e7	−	1.05280e8i	−0.00770297	−	0.0287479i
$247$	−7.03934e9	+	4.06417e9i	−1.89123	+	1.09190i
$248$	3.40432e8			0.0899961
$249$		−	1.91092e8i		−	0.0497103i
$250$	2.40157e9	−	1.38655e9i	0.614802	−	0.354956i
$251$	9.52590e8	−	9.52590e8i	0.240000	−	0.240000i	−0.576850	−	0.816850i	$-0.695718\pi$
$251$	9.52590e8	−	9.52590e8i	0.240000	−	0.240000i	0.816850	+	0.576850i	$0.195718\pi$
$252$	1.40107e9	+	8.08909e8i	0.347423	+	0.200585i
$253$	5.55479e9	−	5.55479e9i	1.35577	−	1.35577i
$254$	−1.47569e9	−	5.50733e9i	−0.354535	−	1.32314i
$255$	2.78747e7	−	4.82805e7i	0.00659250	−	0.0114185i
$256$	−1.59418e9	+	2.76121e9i	−0.371175	+	0.642893i
$257$	−2.00053e9	+	7.46609e9i	−0.458578	+	1.71144i	0.218771	+	0.975776i	$0.429795\pi$
$257$	−2.00053e9	+	7.46609e9i	−0.458578	+	1.71144i	−0.677350	+	0.735661i	$0.736872\pi$
$258$			1.36370e8i			0.0307779i
$259$	−8.32877e8	+	1.39780e9i	−0.185089	+	0.310632i
$260$	−1.57087e9			−0.343753
$261$	3.31024e9	+	8.86975e8i	0.713340	+	0.191139i
$262$	2.72594e9	+	1.57382e9i	0.578510	+	0.334003i
$263$	−6.67580e9	−	3.85427e9i	−1.39534	−	0.805600i	−0.401440	−	0.915885i	$-0.631490\pi$
$263$	−6.67580e9	−	3.85427e9i	−1.39534	−	0.805600i	−0.993900	+	0.110285i	$0.964824\pi$
$264$	3.85008e7	−	1.03163e7i	0.00792600	−	0.00212377i
$265$	1.52113e9	+	1.52113e9i	0.308449	+	0.308449i
$266$	2.34237e9	−	4.05711e9i	0.467875	−	0.810383i
$267$	−4.28294e7	−	4.28294e7i	−0.00842746	−	0.00842746i
$268$	−1.96998e9	−	3.41211e9i	−0.381877	−	0.661430i
$269$	7.94672e8			0.151767			0.0758837	−	0.997117i	$-0.475822\pi$
$269$	7.94672e8			0.151767			0.0758837	+	0.997117i	$0.475822\pi$
$270$		−	1.49239e8i		−	0.0280819i
$271$	−3.37511e7	−	5.84586e7i	−0.00625764	−	0.0108386i	0.862880	−	0.505409i	$-0.168659\pi$
$271$	−3.37511e7	−	5.84586e7i	−0.00625764	−	0.0108386i	−0.869137	+	0.494571i	$0.835325\pi$
$272$	6.31872e9	−	1.69310e9i	1.15439	−	0.309319i
$273$	−6.67380e7	+	6.67380e7i	−0.0120150	+	0.0120150i
$274$	−7.37154e9	−	1.97520e9i	−1.30784	−	0.350436i
$275$	3.55194e9	+	6.15215e9i	0.621062	+	1.07571i
$276$	9.24336e7	−	3.44967e8i	0.0159292	−	0.0594485i
$277$	−9.89907e7	−	3.69438e8i	−0.0168142	−	0.0627513i	0.957009	−	0.290058i	$-0.0936746\pi$
$277$	−9.89907e7	−	3.69438e8i	−0.0168142	−	0.0627513i	−0.973823	+	0.227307i	$0.927008\pi$
$278$	−3.62715e9	+	9.71892e8i	−0.607277	+	0.162719i
$279$	3.25883e9	+	8.73201e8i	0.537830	+	0.144111i
$280$	7.83866e7	−	4.52565e7i	0.0127529	−	0.00736291i
$281$	−1.75399e9	+	6.54599e9i	−0.281321	+	1.04991i	0.670165	+	0.742212i	$0.266223\pi$
$281$	−1.75399e9	+	6.54599e9i	−0.281321	+	1.04991i	−0.951486	+	0.307693i	$0.900443\pi$
$282$	−2.86944e8	−	2.86944e8i	−0.0453733	−	0.0453733i
$283$	1.37300e9	+	5.12412e9i	0.214055	+	0.798865i	0.986497	+	0.163780i	$0.0523686\pi$
$283$	1.37300e9	+	5.12412e9i	0.214055	+	0.798865i	−0.772442	+	0.635086i	$0.780965\pi$
$284$	−5.41121e9	+	3.12416e9i	−0.831804	+	0.480242i
$285$	−1.13639e8			−0.0172246
$286$		−	1.58118e10i		−	2.36329i
$287$	1.13553e9	−	6.55601e8i	0.167368	−	0.0966300i
$288$	6.97071e9	−	6.97071e9i	1.01323	−	1.01323i
$289$	−5.18821e9	−	2.99542e9i	−0.743749	−	0.429404i
$290$	1.35611e9	−	1.35611e9i	0.191735	−	0.191735i
$291$	4.47667e7	+	1.67072e8i	0.00624286	+	0.0232987i
$292$	7.72378e9	−	1.33780e10i	1.06243	−	1.84018i
$293$	−1.81603e9	+	3.14546e9i	−0.246407	+	0.426789i	−0.962526	−	0.271189i	$-0.912583\pi$
$293$	−1.81603e9	+	3.14546e9i	−0.246407	+	0.426789i	0.716119	+	0.697978i	$0.245917\pi$
$294$	−9.35991e7	+	3.49316e8i	−0.0125280	+	0.0467552i
$295$			2.37307e9i			0.313345i
$296$	−8.63925e8	−	8.88038e8i	−0.112541	−	0.115682i
$297$	7.90611e8			0.101610
$298$	3.44697e9	+	9.23614e8i	0.437092	+	0.117118i
$299$	−1.22661e10	−	7.08182e9i	−1.53469	−	0.886054i
$300$	2.79691e8	+	1.61479e8i	0.0345297	+	0.0199357i
$301$	−1.58463e9	+	4.24601e8i	−0.193047	+	0.0517267i
$302$	−5.07901e8	−	5.07901e8i	−0.0610592	−	0.0610592i
$303$	6.81851e7	−	1.18100e8i	0.00808945	−	0.0140113i
$304$	−9.42884e9	−	9.42884e9i	−1.10399	−	1.10399i
$305$	1.08453e9	+	1.87847e9i	0.125327	+	0.217072i
$306$	−1.73427e10			−1.97802
$307$			1.81350e9i			0.204157i	0.994776	+	0.102078i	$0.0325492\pi$
$307$			1.81350e9i			0.204157i	−0.994776	+	0.102078i	$0.967451\pi$
$308$	2.39815e9	+	4.15372e9i	0.266485	+	0.461566i
$309$	−1.35461e8	+	3.62968e7i	−0.0148587	+	0.00398138i
$310$	1.33505e9	−	1.33505e9i	0.144561	−	0.144561i
$311$	−5.54922e8	−	1.48691e8i	−0.0593185	−	0.0158944i	0.229038	−	0.973418i	$-0.426442\pi$
$311$	−5.54922e8	−	1.48691e8i	−0.0593185	−	0.0158944i	−0.288356	+	0.957523i	$0.593109\pi$
$312$	−3.59326e7	−	6.22371e7i	−0.00379202	−	0.00656797i
$313$	−1.81678e8	+	6.78030e8i	−0.0189288	+	0.0706434i	−0.974744	−	0.223324i	$-0.928309\pi$
$313$	−1.81678e8	+	6.78030e8i	−0.0189288	+	0.0706434i	0.955815	+	0.293968i	$0.0949758\pi$
$314$	−4.94734e9	−	1.84637e10i	−0.508924	−	1.89933i
$315$	8.66448e8	−	2.32164e8i	0.0880036	−	0.0235805i
$316$	−1.94482e9	−	5.21113e8i	−0.195043	−	0.0522617i
$317$	5.48453e9	−	3.16650e9i	0.543128	−	0.313575i	−0.203218	−	0.979134i	$-0.565140\pi$
$317$	5.48453e9	−	3.16650e9i	0.543128	−	0.313575i	0.746346	+	0.665558i	$0.231807\pi$
$318$	−2.54783e8	+	9.50864e8i	−0.0249151	+	0.0929844i
$319$	7.18417e9	+	7.18417e9i	0.693767	+	0.693767i
$320$	−8.27558e8	−	3.08849e9i	−0.0789220	−	0.294541i
$321$	−6.19164e7	+	3.57474e7i	−0.00583157	+	0.00336686i
$322$	8.16319e9			0.759341
$323$			2.64310e10i			2.42831i
$324$	−1.05570e10	+	6.09506e9i	−0.957985	+	0.553093i
$325$	9.05678e9	−	9.05678e9i	0.811784	−	0.811784i
$326$	2.22689e10	+	1.28569e10i	1.97164	+	1.13833i
$327$	−4.50394e8	+	4.50394e8i	−0.0393914	+	0.0393914i
$328$	2.58402e8	+	9.64371e8i	0.0223255	+	0.0833199i
$329$	2.44089e9	−	4.22775e9i	0.208336	−	0.360849i
$330$	1.10529e8	−	1.91443e8i	0.00932014	−	0.0161429i
$331$	−5.05719e9	+	1.88737e10i	−0.421305	+	1.57233i	0.350556	+	0.936542i	$0.385993\pi$
$331$	−5.05719e9	+	1.88737e10i	−0.421305	+	1.57233i	−0.771861	+	0.635791i	$0.780674\pi$
$332$			1.75087e10i			1.44113i
$333$	−5.99224e9	−	1.07168e10i	−0.487317	−	0.871542i
$334$	8.21056e9			0.659762
$335$	−2.11011e9	−	5.65402e8i	−0.167543	−	0.0448929i
$336$	−1.34088e8	−	7.74159e7i	−0.0105204	−	0.00607398i
$337$	9.39936e8	+	5.42672e8i	0.0728750	+	0.0420744i	0.535995	−	0.844221i	$-0.319937\pi$
$337$	9.39936e8	+	5.42672e8i	0.0728750	+	0.0420744i	−0.463120	+	0.886296i	$0.653270\pi$
$338$	−9.21969e9	+	2.47041e9i	−0.706398	+	0.189279i
$339$	5.04325e8	+	5.04325e8i	0.0381867	+	0.0381867i
$340$	−2.55400e9	+	4.42366e9i	−0.191120	+	0.331029i
$341$	7.07260e9	+	7.07260e9i	0.523072	+	0.523072i
$342$	1.76756e10	+	3.06151e10i	1.29202	+	2.23785i
$343$	−9.35546e9			−0.675909
$344$		−	1.24915e9i		−	0.0892035i
$345$	−9.90085e7	−	1.71488e8i	−0.00698869	−	0.0121048i
$346$	2.38299e10	−	6.38520e9i	1.66272	−	0.445523i
$347$	−3.92795e9	+	3.92795e9i	−0.270924	+	0.270924i	−0.829472	−	0.558548i	$-0.811359\pi$
$347$	−3.92795e9	+	3.92795e9i	−0.270924	+	0.270924i	0.558548	+	0.829472i	$0.311359\pi$
$348$	4.46156e8	+	1.19547e8i	0.0304207	+	0.00815120i
$349$	−4.70717e9	−	8.15305e9i	−0.317291	−	0.549564i	0.662631	−	0.748946i	$-0.269440\pi$
$349$	−4.70717e9	−	8.15305e9i	−0.317291	−	0.549564i	−0.979922	+	0.199382i	$0.936107\pi$
$350$	−1.91060e9	+	7.13046e9i	−0.127320	+	0.475166i
$351$	−3.68937e8	−	1.37689e9i	−0.0243066	−	0.0907133i
$352$	2.82301e10	−	7.56422e9i	1.83883	−	0.492713i
$353$	3.13515e9	+	8.40061e8i	0.201911	+	0.0541018i	0.358357	−	0.933585i	$-0.383337\pi$
$353$	3.13515e9	+	8.40061e8i	0.201911	+	0.0541018i	−0.156446	+	0.987686i	$0.550004\pi$
$354$	−9.40445e8	+	5.42966e8i	−0.0598853	+	0.0345748i
$355$	−8.96662e8	+	3.34639e9i	−0.0564567	+	0.210699i
$356$	3.92421e9	+	3.92421e9i	0.244316	+	0.244316i
$357$	7.94322e7	+	2.96445e8i	0.00489017	+	0.0182504i
$358$	−2.22672e10	+	1.28560e10i	−1.35560	+	0.782659i
$359$	−1.55910e9			−0.0938633			−0.0469316	−	0.998898i	$-0.514944\pi$
$359$	−1.55910e9			−0.0938633			−0.0469316	+	0.998898i	$0.514944\pi$
$360$			6.83014e8i			0.0406649i
$361$	3.19505e10	−	1.84466e10i	1.88126	−	1.08614i
$362$	−3.15477e10	+	3.15477e10i	−1.83710	+	1.83710i
$363$	4.37896e8	+	2.52819e8i	0.0252200	+	0.0145608i
$364$	6.11482e9	−	6.11482e9i	0.348320	−	0.348320i
$365$	−2.21679e9	−	8.27319e9i	−0.124898	−	0.466124i
$366$	−4.96290e8	+	8.59599e8i	−0.0276574	+	0.0479040i
$367$	2.61902e8	−	4.53628e8i	0.0144369	−	0.0250055i	−0.858717	−	0.512451i	$-0.828738\pi$
$367$	2.61902e8	−	4.53628e8i	0.0144369	−	0.0250055i	0.873154	+	0.487445i	$0.162071\pi$
$368$	6.01372e9	−	2.24435e10i	0.327908	−	1.22377i
$369$			9.89436e9i			0.533682i
$370$	−6.87055e9	−	9.45620e7i	−0.366594	−	0.00504557i
$371$	−1.18425e10			−0.625095
$372$	4.39227e8	+	1.17691e8i	0.0229360	+	0.00614568i
$373$	−2.89555e10	−	1.67175e10i	−1.49588	−	0.863646i	−0.495890	−	0.868386i	$-0.665158\pi$
$373$	−2.89555e10	−	1.67175e10i	−1.49588	−	0.863646i	−0.999989	+	0.00473968i	$0.998491\pi$
$374$	−4.45270e10	−	2.57077e10i	−2.27582	−	1.31394i
$375$	3.57693e8	−	9.58436e7i	0.0180878	−	0.00484661i
$376$	2.62842e9	+	2.62842e9i	0.131505	+	0.131505i
$377$	9.15913e9	−	1.58641e10i	0.453408	−	0.785325i
$378$	5.80932e8	+	5.80932e8i	0.0284550	+	0.0284550i
$379$	−1.07494e10	−	1.86186e10i	−0.520990	−	0.902381i	−0.999702	−	0.0244091i	$-0.992230\pi$
$379$	−1.07494e10	−	1.86186e10i	−0.520990	−	0.902381i	0.478712	−	0.877972i	$-0.341104\pi$
$380$	1.04121e10			0.499350
$381$		−	7.61377e8i		−	0.0361326i
$382$	−2.29112e10	−	3.96833e10i	−1.07595	−	1.86361i
$383$	2.07407e10	−	5.55745e9i	0.963892	−	0.258274i	0.257645	−	0.966240i	$-0.417053\pi$
$383$	2.07407e10	−	5.55745e9i	0.963892	−	0.258274i	0.706247	+	0.707966i	$0.250387\pi$
$384$	1.89028e8	−	1.89028e8i	0.00869362	−	0.00869362i
$385$	2.56873e9	+	6.88290e8i	0.116917	+	0.0313277i
$386$	1.91992e10	+	3.32539e10i	0.864835	+	1.49794i
$387$	3.20405e9	−	1.19577e10i	0.142842	−	0.533093i
$388$	−4.10172e9	−	1.53078e10i	−0.180984	−	0.675440i
$389$	9.58650e9	−	2.56870e9i	0.418660	−	0.112180i	−0.0433381	−	0.999060i	$-0.513799\pi$
$389$	9.58650e9	−	2.56870e9i	0.418660	−	0.112180i	0.461998	+	0.886881i	$0.347133\pi$
$390$	−3.84986e8	−	1.03157e8i	−0.0166413	−	0.00445901i
$391$	−3.98858e10	+	2.30281e10i	−1.70652	+	0.985259i
$392$	8.57372e8	−	3.19976e9i	0.0363099	−	0.135510i
$393$	2.97216e8	+	2.97216e8i	0.0124595	+	0.0124595i
$394$	−5.08890e9	−	1.89920e10i	−0.211173	−	0.788110i
$395$	−9.66796e8	+	5.58180e8i	−0.0397143	+	0.0229290i
$396$	−3.61930e10			−1.47178
$397$			2.39571e10i			0.964433i	0.876052	+	0.482216i	$0.160168\pi$
$397$			2.39571e10i			0.964433i	−0.876052	+	0.482216i	$0.839832\pi$
$398$	5.24561e10	−	3.02856e10i	2.09057	−	1.20699i
$399$	4.42357e8	−	4.42357e8i	0.0174535	−	0.0174535i
$400$	1.81966e10	+	1.05058e10i	0.710807	+	0.410384i
$401$	2.50445e10	−	2.50445e10i	0.968578	−	0.968578i	−0.0309432	−	0.999521i	$-0.509851\pi$
$401$	2.50445e10	−	2.50445e10i	0.968578	−	0.968578i	0.999521	+	0.0309432i	$0.00985110\pi$
$402$	−2.58732e8	−	9.65600e8i	−0.00990708	−	0.0369737i
$403$	9.01689e9	−	1.56177e10i	0.341851	−	0.592103i
$404$	−6.24741e9	+	1.08208e10i	−0.234517	+	0.406196i
$405$	−1.74934e9	+	6.52861e9i	−0.0650209	+	0.242661i
$406$			1.05577e10i			0.388566i
$407$	5.00955e8	−	3.63977e10i	0.0182567	−	1.32647i
$408$	−2.33685e8			−0.00843317
$409$	−8.58556e9	−	2.30049e9i	−0.306814	−	0.0822106i	0.102127	−	0.994771i	$-0.467435\pi$
$409$	−8.58556e9	−	2.30049e9i	−0.306814	−	0.0822106i	−0.408941	+	0.912561i	$0.634102\pi$
$410$	4.79527e9	+	2.76855e9i	0.169698	+	0.0979753i
$411$	−8.82565e8	−	5.09549e8i	−0.0309300	−	0.0178574i
$412$	1.24116e10	−	3.32567e9i	0.430762	−	0.115422i
$413$	−9.23751e9	−	9.23751e9i	−0.317508	−	0.317508i
$414$	−3.07998e10	+	5.33469e10i	−1.04845	+	1.81597i
$415$	6.86449e9	+	6.86449e9i	0.231428	+	0.231428i
$416$	−2.63470e10	−	4.56343e10i	−0.879747	−	1.52377i
$417$	−5.01446e8			−0.0165836
$418$			1.04805e11i			3.43302i
$419$	−1.81961e10	−	3.15166e10i	−0.590367	−	1.02255i	−0.994183	−	0.107705i	$-0.965650\pi$
$419$	−1.81961e10	−	3.15166e10i	−0.590367	−	1.02255i	0.403816	−	0.914840i	$-0.367684\pi$
$420$	1.16780e8	−	3.12912e7i	0.00375295	−	0.00100560i
$421$	−1.20624e10	+	1.20624e10i	−0.383977	+	0.383977i	−0.872533	−	0.488555i	$-0.837524\pi$
$421$	−1.20624e10	+	1.20624e10i	−0.383977	+	0.383977i	0.488555	+	0.872533i	$0.337524\pi$
$422$	2.60647e10	+	6.98402e9i	0.821871	+	0.220220i
$423$	1.84190e10	+	3.19027e10i	0.575315	+	0.996474i
$424$	2.33383e9	−	8.70996e9i	0.0722113	−	0.269496i
$425$	−1.07795e10	−	4.02295e10i	−0.330401	−	1.23307i
$426$	−1.53133e9	+	4.10319e8i	−0.0464976	+	0.0124590i
$427$	−1.15339e10	−	3.09050e9i	−0.346948	−	0.0929645i
$428$	5.67305e9	−	3.27534e9i	0.169060	−	0.0976069i
$429$	5.46486e8	−	2.03951e9i	0.0161343	−	0.0602140i
$430$	−4.89872e9	−	4.89872e9i	−0.143288	−	0.143288i
$431$	−7.82559e9	−	2.92055e10i	−0.226782	−	0.846361i	−0.981683	−	0.190522i	$-0.938982\pi$
$431$	−7.82559e9	−	2.92055e10i	−0.226782	−	0.846361i	0.754901	−	0.655838i	$-0.227685\pi$
$432$	2.02516e9	−	1.16922e9i	0.0581465	−	0.0335709i
$433$	1.24927e10			0.355391			0.177695	−	0.984086i	$-0.443136\pi$
$433$	1.24927e10			0.355391			0.177695	+	0.984086i	$0.443136\pi$
$434$			1.03937e10i			0.292963i
$435$	2.21790e8	−	1.28051e8i	0.00619420	−	0.00357622i
$436$	4.12670e10	−	4.12670e10i	1.14198	−	1.14198i
$437$	8.13029e10	+	4.69402e10i	2.22936	+	1.28712i
$438$	2.77145e9	−	2.77145e9i	0.0753026	−	0.0753026i
$439$	7.76817e9	+	2.89912e10i	0.209151	+	0.780563i	0.988144	+	0.153530i	$0.0490642\pi$
$439$	7.76817e9	+	2.89912e10i	0.209151	+	0.780563i	−0.778993	+	0.627033i	$0.784269\pi$
$440$	−1.01246e9	+	1.75362e9i	−0.0270125	+	0.0467871i
$441$	1.64146e10	−	2.84309e10i	0.433986	−	0.751687i
$442$	−2.39929e10	+	8.95426e10i	−0.628627	+	2.34607i
$443$			5.54902e10i			1.44079i	0.693563	+	0.720396i	$0.256040\pi$
$443$			5.54902e10i			1.44079i	−0.693563	+	0.720396i	$0.743960\pi$
$444$	−8.07637e8	−	1.44442e9i	−0.0207819	−	0.0371673i
$445$	3.07706e9			0.0784686
$446$	3.51599e10	+	9.42106e9i	0.888603	+	0.238101i
$447$	4.12693e8	+	2.38268e8i	0.0103370	+	0.00596810i
$448$	1.52438e10	+	8.80099e9i	0.378425	+	0.218484i
$449$	−5.96034e10	+	1.59707e10i	−1.46651	+	0.392951i	−0.901734	−	0.432291i	$-0.857705\pi$
$449$	−5.96034e10	+	1.59707e10i	−1.46651	+	0.392951i	−0.564779	+	0.825242i	$0.691039\pi$
$450$	−3.93892e10	−	3.93892e10i	−0.960565	−	0.960565i
$451$	−1.46668e10	+	2.54036e10i	−0.354510	+	0.614029i
$452$	−4.62085e10	−	4.62085e10i	−1.10705	−	1.10705i
$453$	−4.79585e7	−	8.30666e7i	−0.00113887	−	0.00197258i
$454$	−7.74061e10			−1.82201
$455$		−	4.79477e9i		−	0.111872i
$456$	2.38171e8	+	4.12524e8i	0.00550845	+	0.00954092i
$457$	3.99919e10	−	1.07158e10i	0.916869	−	0.245674i	0.230622	−	0.973043i	$-0.425924\pi$
$457$	3.99919e10	−	1.07158e10i	0.916869	−	0.245674i	0.686246	+	0.727369i	$0.259257\pi$
$458$	4.98583e10	−	4.98583e10i	1.13312	−	1.13312i
$459$	−4.47725e9	−	1.19968e9i	−0.100870	−	0.0270280i
$460$	9.07158e9	+	1.57124e10i	0.202606	+	0.350923i
$461$	4.64233e9	−	1.73254e10i	0.102786	−	0.383601i	−0.895299	−	0.445466i	$-0.853038\pi$
$461$	4.64233e9	−	1.73254e10i	0.102786	−	0.383601i	0.998085	+	0.0618648i	$0.0197048\pi$
$462$	3.14966e8	+	1.17547e9i	0.00691347	+	0.0258014i
$463$	−1.05818e10	+	2.83537e9i	−0.230268	+	0.0617002i	−0.372108	−	0.928189i	$-0.621365\pi$
$463$	−1.05818e10	+	2.83537e9i	−0.230268	+	0.0617002i	0.141840	+	0.989890i	$0.454698\pi$
$464$	2.90269e10	+	7.77772e9i	0.626222	+	0.167796i
$465$	2.18346e8	−	1.26062e8i	0.00467017	−	0.00269633i
$466$	−1.24005e10	+	4.62791e10i	−0.262963	+	0.981390i
$467$	3.82590e10	+	3.82590e10i	0.804390	+	0.804390i	0.983778	−	0.179389i	$-0.0574119\pi$
$467$	3.82590e10	+	3.82590e10i	0.804390	+	0.804390i	−0.179389	+	0.983778i	$0.557412\pi$
$468$	1.68894e10	+	6.30320e10i	0.352071	+	1.31395i
$469$	1.04148e10	−	6.01299e9i	0.215258	−	0.124279i
$470$	2.06154e10			0.422474
$471$		−	2.55257e9i		−	0.0518673i
$472$	8.61453e9	−	4.97360e9i	0.173566	−	0.100208i
$473$	2.59516e10	−	2.59516e10i	0.518465	−	0.518465i
$474$	−4.42413e8	−	2.55427e8i	−0.00876424	−	0.00506003i
$475$	−6.00308e10	+	6.00308e10i	−1.17923	+	1.17923i
$476$	−7.27792e9	−	2.71616e10i	−0.141768	−	0.529087i
$477$	4.46817e10	−	7.73910e10i	0.863091	−	1.49492i
$478$	8.20318e9	−	1.42083e10i	0.157134	−	0.272164i
$479$	−2.91183e9	+	1.08671e10i	−0.0553126	+	0.206429i	−0.988052	−	0.154123i	$-0.950745\pi$
$479$	−2.91183e9	+	1.08671e10i	−0.0553126	+	0.206429i	0.932739	+	0.360552i	$0.117412\pi$
$480$		−	7.36696e8i		−	0.0138779i
$481$	−6.36222e10	+	1.61124e10i	−1.18858	+	0.301010i
$482$	−7.12810e10			−1.32064
$483$	1.05295e9	+	2.82136e8i	0.0193472	+	0.00518406i
$484$	−4.01219e10	−	2.31644e10i	−0.731139	−	0.422124i
$485$	−7.60974e9	−	4.39348e9i	−0.137532	−	0.0794039i
$486$	−8.98463e9	+	2.40743e9i	−0.161048	+	0.0431527i
$487$	1.08409e10	+	1.08409e10i	0.192729	+	0.192729i	0.796874	−	0.604145i	$-0.206485\pi$
$487$	1.08409e10	+	1.08409e10i	0.192729	+	0.192729i	−0.604145	+	0.796874i	$0.706485\pi$
$488$	4.54604e9	−	7.87397e9i	0.0801593	−	0.138840i
$489$	2.42803e9	+	2.42803e9i	0.0424638	+	0.0424638i
$490$	−9.18597e9	−	1.59106e10i	−0.159346	−	0.275995i
$491$	−2.20214e10			−0.378894			−0.189447	−	0.981891i	$-0.560670\pi$
$491$	−2.20214e10			−0.378894			−0.189447	+	0.981891i	$0.560670\pi$
$492$			1.33357e9i			0.0227591i
$493$	−2.97829e10	−	5.15854e10i	−0.504172	−	0.873251i
$494$	1.82523e11	−	4.89069e10i	3.06485	−	0.821225i
$495$	−1.41899e10	+	1.41899e10i	−0.236351	+	0.236351i
$496$	2.85761e10	+	7.65694e9i	0.472146	+	0.126511i
$497$	−9.53591e9	−	1.65167e10i	−0.156292	−	0.270705i
$498$	−1.14977e9	+	4.29101e9i	−0.0186937	+	0.0697657i
$499$	−2.09120e10	−	7.80447e10i	−0.337282	−	1.25875i	−0.901374	−	0.433042i	$-0.857440\pi$
$499$	−2.09120e10	−	7.80447e10i	−0.337282	−	1.25875i	0.564091	−	0.825712i	$-0.309227\pi$
$500$	−3.27734e10	+	8.78160e9i	−0.524374	+	0.140506i
$501$	1.05906e9	+	2.83773e8i	0.0168100	+	0.00450423i
$502$	−2.71221e10	+	1.56590e10i	−0.427080	+	0.246575i
$503$	−2.47524e10	+	9.23771e10i	−0.386674	+	1.44309i	0.448837	+	0.893614i	$0.351838\pi$
$503$	−2.47524e10	+	9.23771e10i	−0.386674	+	1.44309i	−0.835511	+	0.549474i	$0.814828\pi$
$504$	−2.65873e9	−	2.65873e9i	−0.0412052	−	0.0412052i
$505$	1.79306e9	+	6.69180e9i	0.0275696	+	0.102891i
$506$	−1.58156e11	+	9.13113e10i	−2.41259	+	1.39291i
$507$	−1.27460e9			−0.0192905
$508$			6.97606e10i			1.04750i
$509$	5.12812e10	−	2.96072e10i	0.763988	−	0.441089i	−0.0667376	−	0.997771i	$-0.521259\pi$
$509$	5.12812e10	−	2.96072e10i	0.763988	−	0.441089i	0.830726	+	0.556682i	$0.187926\pi$
$510$	−9.16427e8	+	9.16427e8i	−0.0135462	+	0.0135462i
$511$	4.08337e10	+	2.35754e10i	0.598874	+	0.345760i
$512$	6.79994e10	−	6.79994e10i	0.989521	−	0.989521i
$513$	2.44541e9	+	9.12640e9i	0.0353088	+	0.131774i
$514$	8.98446e10	−	1.55615e11i	1.28718	−	2.22946i
$515$	3.56222e9	−	6.16995e9i	0.0506398	−	0.0877108i
$516$	4.31844e8	−	1.61166e9i	0.00609155	−	0.0227340i
$517$			1.09213e11i			1.52866i
$518$	2.71127e10	−	2.63765e10i	0.376577	−	0.366352i
$519$	3.29443e9			0.0454058
$520$	3.52649e9	+	9.44920e8i	0.0482313	+	0.0129235i
$521$	−2.27538e10	−	1.31369e10i	−0.308818	−	0.178296i	0.337580	−	0.941297i	$-0.390392\pi$
$521$	−2.27538e10	−	1.31369e10i	−0.308818	−	0.178296i	−0.646397	+	0.763001i	$0.723725\pi$
$522$	−6.89951e10	−	3.98343e10i	−0.929257	−	0.536507i
$523$	1.55564e9	−	4.16832e8i	0.0207923	−	0.00557128i	−0.248408	−	0.968656i	$-0.579907\pi$
$523$	1.55564e9	−	4.16832e8i	0.0207923	−	0.00557128i	0.269200	+	0.963084i	$0.413241\pi$
$524$	−2.72322e10	−	2.72322e10i	−0.361208	−	0.361208i
$525$	−4.92885e8	+	8.53702e8i	−0.00648796	+	0.0112375i
$526$	1.26716e11	+	1.26716e11i	1.65534	+	1.65534i
$527$	−2.93203e10	−	5.07843e10i	−0.380125	−	0.658396i
$528$	3.46382e9			0.0445676
$529$			8.52761e10i			1.08894i
$530$	−2.50049e10	−	4.33097e10i	−0.316899	−	0.548885i
$531$	9.52209e10	−	2.55144e10i	1.19772	−	0.320927i
$532$	−4.05307e10	+	4.05307e10i	−0.505985	+	0.505985i
$533$	5.10858e10	+	1.36884e10i	0.632983	+	0.169607i
$534$	7.04042e8	+	1.21944e9i	0.00865832	+	0.0149967i
$535$	9.40050e8	−	3.50831e9i	0.0114746	−	0.0428236i
$536$	2.37000e9	+	8.84495e9i	0.0287137	+	0.107161i
$537$	−3.31650e9	+	8.88654e8i	−0.0398826	+	0.0106865i
$538$	−1.78445e10	−	4.78141e9i	−0.212998	−	0.0570725i
$539$	8.42883e10	−	4.86639e10i	0.998648	−	0.576570i
$540$	−4.72596e8	+	1.76375e9i	−0.00555795	+	0.0207426i
$541$	−4.52801e10	−	4.52801e10i	−0.528590	−	0.528590i	0.391562	−	0.920152i	$-0.371935\pi$
$541$	−4.52801e10	−	4.52801e10i	−0.528590	−	0.528590i	−0.920152	+	0.391562i	$0.871935\pi$
$542$	4.06150e8	+	1.51577e9i	0.00470640	+	0.0175645i
$543$	−5.15960e9	+	2.97889e9i	−0.0593494	+	0.0342654i
$544$	−1.71346e11			−1.95649
$545$		−	3.23584e10i		−	0.366776i
$546$	1.90016e9	−	1.09706e9i	0.0213806	−	0.0123441i
$547$	−3.62038e10	+	3.62038e10i	−0.404394	+	0.404394i	−0.879778	−	0.475384i	$-0.842309\pi$
$547$	−3.62038e10	+	3.62038e10i	−0.404394	+	0.404394i	0.475384	+	0.879778i	$0.342309\pi$
$548$	8.08645e10	+	4.66871e10i	0.896676	+	0.517696i
$549$	6.37141e10	−	6.37141e10i	0.701368	−	0.701368i
$550$	−4.27429e10	−	1.59519e11i	−0.467104	−	1.74326i
$551$	−6.07092e10	+	1.05151e11i	−0.658640	+	1.14080i
$552$	−4.15014e8	+	7.18825e8i	−0.00446999	+	0.00774225i
$553$	1.59060e9	−	5.93619e9i	0.0170082	−	0.0634756i
$554$			8.89141e9i			0.0943912i
$555$	−8.82943e8	−	2.49657e8i	−0.00930595	−	0.00263131i
$556$	4.59446e10			0.480768
$557$	−4.10992e10	−	1.10125e10i	−0.426985	−	0.114410i	0.0389254	−	0.999242i	$-0.487607\pi$
$557$	−4.10992e10	−	1.10125e10i	−0.426985	−	0.114410i	−0.465911	+	0.884832i	$0.654273\pi$
$558$	−6.79236e10	−	3.92157e10i	−0.700622	−	0.404504i
$559$	−5.73063e10	−	3.30858e10i	−0.586888	−	0.338840i
$560$	7.59773e9	−	2.03580e9i	0.0772559	−	0.0207006i
$561$	−4.85490e9	−	4.85490e9i	−0.0490149	−	0.0490149i
$562$	7.87723e10	−	1.36438e11i	0.789639	−	1.36769i
$563$	−7.43490e10	−	7.43490e10i	−0.740017	−	0.740017i	0.232564	−	0.972581i	$-0.425288\pi$
$563$	−7.43490e10	−	7.43490e10i	−0.740017	−	0.740017i	−0.972581	+	0.232564i	$0.925288\pi$
$564$	2.48253e9	+	4.29987e9i	0.0245345	+	0.0424951i
$565$	−3.62331e10			−0.355559
$566$		−	1.23324e11i		−	1.20166i
$567$	−1.86040e10	−	3.22231e10i	−0.180001	−	0.311770i
$568$	1.40271e10	−	3.75854e9i	0.134764	−	0.0361098i
$569$	1.40382e10	−	1.40382e10i	0.133925	−	0.133925i	−0.636967	−	0.770891i	$-0.719811\pi$
$569$	1.40382e10	−	1.40382e10i	0.133925	−	0.133925i	0.770891	+	0.636967i	$0.219811\pi$
$570$	2.55179e9	+	6.83750e8i	0.0241738	+	0.00647735i
$571$	2.11707e10	+	3.66688e10i	0.199155	+	0.344947i	0.948255	−	0.317511i	$-0.102847\pi$
$571$	2.11707e10	+	3.66688e10i	0.199155	+	0.344947i	−0.749100	+	0.662457i	$0.769514\pi$
$572$	−5.00714e10	+	1.86869e11i	−0.467741	+	1.74563i
$573$	−1.58371e9	−	5.91048e9i	−0.0146912	−	0.0548283i
$574$	−2.94432e10	+	7.88929e9i	−0.271230	+	0.0726759i
$575$	−1.42891e11	−	3.82877e10i	−1.30718	−	0.350257i
$576$	−1.15030e11	+	6.64125e10i	−1.04501	+	0.603337i
$577$	1.03497e10	−	3.86255e10i	0.0933733	−	0.348474i	−0.903394	−	0.428810i	$-0.858933\pi$
$577$	1.03497e10	−	3.86255e10i	0.0933733	−	0.348474i	0.996768	+	0.0803365i	$0.0255995\pi$
$578$	9.84792e10	+	9.84792e10i	0.882334	+	0.882334i
$579$	1.32712e9	+	4.95288e9i	0.0118085	+	0.0440701i
$580$	−2.03214e10	+	1.17325e10i	−0.179573	+	0.103676i
$581$	−5.34420e10			−0.469006
$582$		−	4.02098e9i		−	0.0350461i
$583$	2.29439e11	−	1.32467e11i	1.98606	−	1.14665i
$584$	−2.53866e10	+	2.53866e10i	−0.218249	+	0.218249i
$585$	3.13341e10	+	1.80907e10i	0.267543	+	0.154466i
$586$	5.97049e10	−	5.97049e10i	0.506314	−	0.506314i
$587$	−4.58170e8	−	1.70991e9i	−0.00385899	−	0.0144020i	0.963969	−	0.266013i	$-0.0857064\pi$
$587$	−4.58170e8	−	1.70991e9i	−0.00385899	−	0.0144020i	−0.967828	+	0.251611i	$0.919040\pi$
$588$	2.21237e9	−	3.83194e9i	0.0185075	−	0.0320560i
$589$	−5.97664e10	+	1.03518e11i	−0.496587	+	0.860115i
$590$	1.42784e10	−	5.32876e10i	0.117834	−	0.439763i
$591$		−	2.62561e9i		−	0.0215219i
$592$	−5.25448e10	−	9.39737e10i	−0.427802	−	0.765103i
$593$	5.64389e10			0.456415			0.228208	−	0.973613i	$-0.426714\pi$
$593$	5.64389e10			0.456415			0.228208	+	0.973613i	$0.426714\pi$
$594$	−1.77533e10	−	4.75698e9i	−0.142604	−	0.0382108i
$595$	−1.35024e10	−	7.79561e9i	−0.107732	−	0.0621988i
$596$	−3.78127e10	−	2.18312e10i	−0.299676	−	0.173018i
$597$	7.81288e9	−	2.09346e9i	0.0615055	−	0.0164803i
$598$	2.32826e11	+	2.32826e11i	1.82065	+	1.82065i
$599$	−4.89175e10	+	8.47276e10i	−0.379977	+	0.658139i	−0.991058	−	0.133429i	$-0.957401\pi$
$599$	−4.89175e10	+	8.47276e10i	−0.379977	+	0.658139i	0.611082	+	0.791567i	$0.290735\pi$
$600$	−5.30752e8	−	5.30752e8i	−0.00409531	−	0.00409531i
$601$	1.14664e11	+	1.98604e11i	0.878878	+	1.52226i	0.852573	+	0.522607i	$0.175041\pi$
$601$	1.14664e11	+	1.98604e11i	0.878878	+	1.52226i	0.0263045	+	0.999654i	$0.491626\pi$
$602$	3.81379e10			0.290383
$603$			9.07484e10i			0.686388i
$604$	4.39417e9	+	7.61092e9i	0.0330163	+	0.0571860i
$605$	−2.48121e10	+	6.64838e9i	−0.185201	+	0.0496243i
$606$	−2.24170e9	+	2.24170e9i	−0.0166221	+	0.0166221i
$607$	−2.60007e11	−	6.96686e10i	−1.91527	−	0.513195i	−0.991474	−	0.130308i	$-0.958403\pi$
$607$	−2.60007e11	−	6.96686e10i	−1.91527	−	0.513195i	−0.923795	−	0.382887i	$-0.874930\pi$
$608$	1.74635e11	+	3.02477e11i	1.27796	+	2.21349i
$609$	−3.64894e8	+	1.36180e9i	−0.00265276	+	0.00990024i
$610$	−1.30509e10	−	4.87067e10i	−0.0942588	−	0.351779i
$611$	1.90200e11	−	5.09638e10i	1.36472	−	0.365677i
$612$	2.04962e11	+	5.49194e10i	1.46106	+	0.391489i
$613$	−3.08079e10	+	1.77869e10i	−0.218182	+	0.125968i	−0.605108	−	0.796143i	$-0.706870\pi$
$613$	−3.08079e10	+	1.77869e10i	−0.218182	+	0.125968i	0.386926	+	0.922111i	$0.373537\pi$
$614$	1.09115e10	−	4.07224e10i	0.0767736	−	0.286523i
$615$	5.22840e8	+	5.22840e8i	0.00365484	+	0.00365484i
$616$	−2.88511e9	−	1.07674e10i	−0.0200373	−	0.0747802i
$617$	−1.45698e11	+	8.41189e10i	−1.00534	+	0.580434i	−0.909824	−	0.414994i	$-0.863784\pi$
$617$	−1.45698e11	+	8.41189e10i	−1.00534	+	0.580434i	−0.0955171	+	0.995428i	$0.530450\pi$
$618$	3.26020e9			0.0223506
$619$			1.17050e11i			0.797277i	0.917108	+	0.398639i	$0.130517\pi$
$619$			1.17050e11i			0.797277i	−0.917108	+	0.398639i	$0.869483\pi$
$620$	−2.00058e10	+	1.15503e10i	−0.135391	+	0.0781678i
$621$	−1.16417e10	+	1.16417e10i	−0.0782795	+	0.0782795i
$622$	1.15662e10	+	6.67775e9i	0.0772733	+	0.0446138i
$623$	−1.19779e10	+	1.19779e10i	−0.0795112	+	0.0795112i
$624$	−1.61638e9	−	6.03242e9i	−0.0106612	−	0.0397881i
$625$	6.20299e10	−	1.07439e11i	0.406519	−	0.704112i
$626$	8.15919e9	−	1.41321e10i	0.0531312	−	0.0920260i
$627$	−3.62225e9	+	1.35184e10i	−0.0234374	+	0.0874694i
$628$			2.33877e11i			1.50366i
$629$	−5.80669e10	+	2.05361e11i	−0.370959	+	1.31194i
$630$	−2.08531e10			−0.132376
$631$	2.60040e11	+	6.96775e10i	1.64030	+	0.439516i	0.956873	−	0.290506i	$-0.0938236\pi$
$631$	2.60040e11	+	6.96775e10i	1.64030	+	0.439516i	0.683424	+	0.730022i	$0.260490\pi$
$632$	4.05252e9	+	2.33972e9i	0.0254014	+	0.0146655i
$633$	3.12063e9	+	1.80170e9i	0.0194369	+	0.0112219i
$634$	−1.42208e11	+	3.81046e10i	−0.880172	+	0.235842i
$635$	2.73504e10	+	2.73504e10i	0.168217	+	0.168217i
$636$	6.02223e9	−	1.04308e10i	0.0368069	−	0.0637514i
$637$	−1.24084e11	−	1.24084e11i	−0.753628	−	0.753628i
$638$	−1.18096e11	−	2.04548e11i	−0.712772	−	1.23456i
$639$	1.43916e11			0.863191
$640$			1.35806e10i			0.0809469i
$641$	6.85923e10	+	1.18805e11i	0.406296	+	0.703726i	0.994471	−	0.105008i	$-0.0334867\pi$
$641$	6.85923e10	+	1.18805e11i	0.406296	+	0.703726i	−0.588175	+	0.808734i	$0.700153\pi$
$642$	1.60543e9	−	4.30173e8i	0.00945042	−	0.00253223i
$643$	9.67436e10	−	9.67436e10i	0.565950	−	0.565950i	−0.365041	−	0.930991i	$-0.618945\pi$
$643$	9.67436e10	−	9.67436e10i	0.565950	−	0.565950i	0.930991	+	0.365041i	$0.118945\pi$
$644$	−9.64754e10	−	2.58505e10i	−0.560884	−	0.150288i
$645$	−4.62561e8	−	8.01180e8i	−0.00267258	−	0.00462904i
$646$	1.59031e11	−	5.93512e11i	0.913171	−	3.40800i
$647$	−4.27020e8	−	1.59366e9i	−0.00243686	−	0.00909450i	0.964697	−	0.263363i	$-0.0848318\pi$
$647$	−4.27020e8	−	1.59366e9i	−0.00243686	−	0.00909450i	−0.967134	+	0.254269i	$0.918165\pi$
$648$	2.73660e10	−	7.33269e9i	0.155207	−	0.0415876i
$649$	2.82298e11	+	7.56416e10i	1.59122	+	0.426365i
$650$	−2.57865e11	+	1.48878e11i	−1.44457	+	0.834022i
$651$	−3.59228e8	+	1.34066e9i	−0.00200007	+	0.00746438i
$652$	−2.22467e11	−	2.22467e11i	−1.23105	−	1.23105i
$653$	2.57064e10	+	9.59377e10i	0.141380	+	0.527638i	0.999890	+	0.0148409i	$0.00472417\pi$
$653$	2.57064e10	+	9.59377e10i	0.141380	+	0.527638i	−0.858510	+	0.512797i	$0.828609\pi$
$654$	1.28236e10	−	7.40371e9i	0.0700969	−	0.0404705i
$655$	−2.13534e10			−0.116012
$656$			8.67619e10i			0.468504i
$657$	−3.08132e11	+	1.77900e11i	−1.65377	+	0.954807i
$658$	−8.02483e10	+	8.02483e10i	−0.428087	+	0.428087i
$659$	−2.64471e11	−	1.52692e11i	−1.40229	−	0.809610i	−0.407658	−	0.913135i	$-0.633655\pi$
$659$	−2.64471e11	−	1.52692e11i	−1.40229	−	0.809610i	−0.994627	+	0.103525i	$0.966988\pi$
$660$	−1.91252e9	+	1.91252e9i	−0.0100793	+	0.0100793i
$661$	−5.66999e10	−	2.11607e11i	−0.297013	−	1.10847i	−0.939605	−	0.342261i	$-0.888807\pi$
$661$	−5.66999e10	−	2.11607e11i	−0.297013	−	1.10847i	0.642592	−	0.766209i	$-0.277859\pi$
$662$	2.27120e11	−	3.93383e11i	1.18256	−	2.04825i
$663$	−6.18953e9	+	1.07206e10i	−0.0320334	+	0.0554835i
$664$	1.05320e10	−	3.93059e10i	0.0541798	−	0.202202i
$665$			3.17810e10i			0.162510i
$666$	7.00753e10	+	2.76702e11i	0.356179	+	1.40642i
$667$	−2.11572e11			−1.06894
$668$	−9.70352e10	−	2.60005e10i	−0.487331	−	0.130580i
$669$	4.20955e9	+	2.43039e9i	0.0210151	+	0.0121331i
$670$	4.39809e10	+	2.53924e10i	0.218255	+	0.126010i
$671$	2.58030e11	−	6.91390e10i	1.27286	−	0.341062i
$672$	2.86769e9	+	2.86769e9i	0.0140623	+	0.0140623i
$673$	7.06478e10	−	1.22366e11i	0.344380	−	0.596484i	−0.640861	−	0.767657i	$-0.721422\pi$
$673$	7.06478e10	−	1.22366e11i	0.344380	−	0.596484i	0.985241	+	0.171173i	$0.0547557\pi$
$674$	−1.78412e10	−	1.78412e10i	−0.0864541	−	0.0864541i
$675$	−7.44412e9	−	1.28936e10i	−0.0358590	−	0.0621096i
$676$	1.16784e11			0.559240
$677$			2.13428e11i			1.01601i	0.861355	+	0.508003i	$0.169616\pi$
$677$			2.13428e11i			1.01601i	−0.861355	+	0.508003i	$0.830384\pi$
$678$	−8.29026e9	−	1.43591e10i	−0.0392328	−	0.0679532i
$679$	4.67242e10	−	1.25197e10i	0.219818	−	0.0589000i
$680$	8.39452e9	−	8.39452e9i	0.0392609	−	0.0392609i
$681$	−9.98438e9	−	2.67531e9i	−0.0464229	−	0.0124390i
$682$	−1.16262e11	−	2.01371e11i	−0.537401	−	0.930807i
$683$	−5.42958e9	+	2.02635e10i	−0.0249507	+	0.0931174i	−0.977278	−	0.211960i	$-0.932016\pi$
$683$	−5.42958e9	+	2.02635e10i	−0.0249507	+	0.0931174i	0.952328	+	0.305077i	$0.0986822\pi$
$684$	−1.11947e11	−	4.17793e11i	−0.511433	−	1.90870i
$685$	5.00080e10	−	1.33996e10i	0.227132	−	0.0608597i
$686$	2.10078e11	+	5.62903e10i	0.948603	+	0.254177i
$687$	8.15426e9	−	4.70787e9i	0.0366065	−	0.0211348i
$688$	2.80957e10	−	1.04855e11i	0.125397	−	0.467987i
$689$	−3.37764e11	−	3.37764e11i	−1.49878	−	1.49878i
$690$	1.19144e9	+	4.44650e9i	0.00525623	+	0.0196165i
$691$	−2.21491e11	+	1.27878e11i	−0.971502	+	0.560897i	−0.899694	−	0.436521i	$-0.856210\pi$
$691$	−2.21491e11	+	1.27878e11i	−0.971502	+	0.560897i	−0.0718083	+	0.997418i	$0.522877\pi$
$692$	−3.01850e11			−1.31634
$693$		−	1.10472e11i		−	0.478983i
$694$	1.11837e11	−	6.45689e10i	0.482110	−	0.278346i
$695$	1.80131e10	−	1.80131e10i	0.0772057	−	0.0772057i
$696$	−9.29678e8	−	5.36750e8i	−0.00396183	−	0.00228736i
$697$	1.21606e11	−	1.21606e11i	0.515256	−	0.515256i
$698$	5.66445e10	+	2.11400e11i	0.238636	+	0.890602i
$699$	−3.19899e9	+	5.54082e9i	−0.0134000	+	0.0232095i
$700$	4.51603e10	−	7.82199e10i	0.188089	−	0.325780i
$701$	−4.01297e10	+	1.49766e11i	−0.166186	+	0.620214i	0.831700	+	0.555225i	$0.187368\pi$
$701$	−4.01297e10	+	1.49766e11i	−0.166186	+	0.620214i	−0.997886	+	0.0649890i	$0.979299\pi$
$702$			3.31381e10i			0.136452i
$703$	4.21705e11	−	1.06798e11i	1.72658	−	0.437261i
$704$	−3.93782e11			−1.60312
$705$	2.65911e9	+	7.12508e8i	0.0107642	+	0.00288425i
$706$	−6.53458e10	−	3.77274e10i	−0.263026	−	0.151858i
$707$	−3.30285e10	−	1.90690e10i	−0.132194	−	0.0763222i
$708$	1.28339e10	−	3.43884e9i	0.0510771	−	0.0136861i
$709$	−1.18967e11	−	1.18967e11i	−0.470805	−	0.470805i	0.431370	−	0.902175i	$-0.358030\pi$
$709$	−1.18967e11	−	1.18967e11i	−0.470805	−	0.470805i	−0.902175	+	0.431370i	$0.858030\pi$
$710$	4.02693e10	−	6.97485e10i	0.158468	−	0.274474i
$711$	3.27919e10	+	3.27919e10i	0.128318	+	0.128318i
$712$	−6.44906e9	−	1.11701e10i	−0.0250944	−	0.0434648i
$713$	−2.08286e11			−0.805940
$714$		−	7.13465e9i		−	0.0274524i
$715$	5.36330e10	+	9.28951e10i	0.205215	+	0.355442i
$716$	3.03872e11	−	8.14223e10i	1.15622	−	0.309807i
$717$	1.54917e9	−	1.54917e9i	0.00586168	−	0.00586168i
$718$	3.50098e10	+	9.38085e9i	0.131732	+	0.0352975i
$719$	1.62036e11	+	2.80655e11i	0.606313	+	1.05017i	0.991842	+	0.127470i	$0.0406856\pi$
$719$	1.62036e11	+	2.80655e11i	0.606313	+	1.05017i	−0.385529	+	0.922696i	$0.625981\pi$
$720$	−1.53622e10	+	5.73326e10i	−0.0571642	+	0.213340i
$721$	1.01510e10	+	3.78839e10i	0.0375635	+	0.140189i
$722$	−8.28443e11	+	2.21980e11i	−3.04869	+	0.816895i
$723$	−9.19432e9	−	2.46361e9i	−0.0336486	−	0.00901610i
$724$	4.72744e11	−	2.72939e11i	1.72057	−	0.993371i
$725$	4.95185e10	−	1.84806e11i	0.179232	−	0.668903i
$726$	−8.31185e9	−	8.31185e9i	−0.0299193	−	0.0299193i
$727$	4.05254e10	+	1.51243e11i	0.145074	+	0.541423i	0.999752	+	0.0222649i	$0.00708774\pi$
$727$	4.05254e10	+	1.51243e11i	0.145074	+	0.541423i	−0.854678	+	0.519158i	$0.826246\pi$
$728$	−1.74056e10	+	1.00491e10i	−0.0619674	+	0.0357769i
$729$	2.79943e11			0.991198
$730$			1.99114e11i			0.701148i
$731$	−1.86344e11	+	1.07586e11i	−0.652597	+	0.376777i
$732$	8.58743e9	−	8.58743e9i	0.0299102	−	0.0299102i
$733$	1.70510e10	+	9.84438e9i	0.0590654	+	0.0341014i	0.529242	−	0.848471i	$-0.322476\pi$
$733$	1.70510e10	+	9.84438e9i	0.0590654	+	0.0341014i	−0.470176	+	0.882572i	$0.655810\pi$
$734$	−8.61047e9	+	8.61047e9i	−0.0296649	+	0.0296649i
$735$	−6.34970e8	−	2.36974e9i	−0.00217572	−	0.00811991i
$736$	−3.04302e11	+	5.27066e11i	−1.03704	+	1.79620i
$737$	−1.34519e11	+	2.32995e11i	−0.455948	+	0.789725i
$738$	5.95328e10	−	2.22179e11i	0.200692	−	0.748994i
$739$		−	3.73259e11i		−	1.25151i	−0.780022	−	0.625753i	$-0.784792\pi$
$739$		−	3.73259e11i		−	1.25151i	0.780022	−	0.625753i	$-0.215208\pi$
$740$	8.08991e10	+	2.28746e10i	0.269784	+	0.0762830i
$741$	2.52334e10			0.0836956
$742$	2.65924e11	+	7.12541e10i	0.877288	+	0.235069i
$743$	2.72205e11	+	1.57158e11i	0.893184	+	0.515680i	0.874983	−	0.484154i	$-0.160873\pi$
$743$	2.72205e11	+	1.57158e11i	0.893184	+	0.515680i	0.0182016	+	0.999834i	$0.494206\pi$
$744$	−9.15240e8	−	5.28414e8i	−0.00298706	−	0.00172458i
$745$	−2.33840e10	+	6.26573e9i	−0.0759092	+	0.0203398i
$746$	5.49615e11	+	5.49615e11i	1.77461	+	1.77461i
$747$	2.01637e11	−	3.49246e11i	0.647573	−	1.12163i
$748$	4.44827e11	+	4.44827e11i	1.42097	+	1.42097i
$749$	9.99734e9	+	1.73159e10i	0.0317656	+	0.0550196i
$750$	−8.60873e9			−0.0272078
$751$		−	5.09736e11i		−	1.60245i	−0.598360	−	0.801227i	$-0.704181\pi$
$751$		−	5.09736e11i		−	1.60245i	0.598360	−	0.801227i	$-0.295819\pi$
$752$	1.61513e11	+	2.79749e11i	0.505053	+	0.874777i
$753$	−4.03960e9	+	1.08241e9i	−0.0125649	+	0.00336675i
$754$	−3.01121e11	+	3.01121e11i	−0.931657	+	0.931657i
$755$	4.70673e9	+	1.26116e9i	0.0144854	+	0.00388136i
$756$	−5.02601e9	−	8.70530e9i	−0.0153864	−	0.0266500i
$757$	−6.24248e10	+	2.32972e11i	−0.190096	+	0.709449i	0.803386	+	0.595459i	$0.203030\pi$
$757$	−6.24248e10	+	2.32972e11i	−0.190096	+	0.709449i	−0.993482	+	0.113990i	$0.963637\pi$
$758$	1.29355e11	+	4.82761e11i	0.391839	+	1.46236i
$759$	−2.35559e10	+	6.31179e9i	−0.0709795	+	0.0190189i
$760$	−2.33745e10	−	6.26318e9i	−0.0700629	−	0.0187733i
$761$	−3.12392e11	+	1.80359e11i	−0.931453	+	0.537775i	−0.887271	−	0.461249i	$-0.847401\pi$
$761$	−3.12392e11	+	1.80359e11i	−0.931453	+	0.537775i	−0.0441820	+	0.999023i	$0.514068\pi$
$762$	−4.58108e9	+	1.70968e10i	−0.0135878	+	0.0507102i
$763$	1.25960e11	+	1.25960e11i	0.371649	+	0.371649i
$764$	1.45106e11	+	5.41544e11i	0.425905	+	1.58950i
$765$	1.01889e11	−	5.88259e10i	0.297497	−	0.171760i
$766$	−4.99174e11			−1.44990
$767$		−	5.26935e11i		−	1.52256i
$768$	8.57182e9	−	4.94894e9i	0.0246393	−	0.0142255i
$769$	−2.20845e11	+	2.20845e11i	−0.631512	+	0.631512i	−0.948447	−	0.316935i	$-0.897346\pi$
$769$	−2.20845e11	+	2.20845e11i	−0.631512	+	0.631512i	0.316935	+	0.948447i	$0.397346\pi$
$770$	−5.35399e10	−	3.09113e10i	−0.152305	−	0.0879335i
$771$	1.69671e10	−	1.69671e10i	0.0480166	−	0.0480166i
$772$	−1.21597e11	−	4.53804e11i	−0.342336	−	1.27761i
$773$	−2.85517e10	+	4.94530e10i	−0.0799676	+	0.138508i	−0.903236	−	0.429145i	$-0.858815\pi$
$773$	−2.85517e10	+	4.94530e10i	−0.0799676	+	0.138508i	0.823268	+	0.567653i	$0.192148\pi$
$774$	−1.43895e11	+	2.49233e11i	−0.400942	+	0.694452i
$775$	4.87495e10	−	1.81936e11i	0.135134	−	0.504326i
$776$			3.68323e10i			0.101574i
$777$	4.40881e9	−	2.46516e9i	0.0120959	−	0.00676333i
$778$	−2.30722e11			−0.629753
$779$	−3.38611e11	−	9.07305e10i	−0.919498	−	0.246379i
$780$	4.22322e9	+	2.43828e9i	0.0114095	+	0.00658726i
$781$	3.69502e11	+	2.13332e11i	0.993146	+	0.573393i
$782$	1.03420e12	−	2.77112e11i	2.76552	−	0.741018i
$783$	−1.50565e10	−	1.50565e10i	−0.0400568	−	0.0400568i
$784$	1.43937e11	−	2.49306e11i	0.380985	−	0.659885i
$785$	9.16942e10	+	9.16942e10i	0.241470	+	0.241470i
$786$	−4.88573e9	−	8.46233e9i	−0.0128009	−	0.0221717i
$787$	3.29883e11			0.859926			0.429963	−	0.902847i	$-0.358527\pi$
$787$	3.29883e11			0.859926			0.429963	+	0.902847i	$0.358527\pi$
$788$			2.40570e11i			0.623930i
$789$	1.19651e10	+	2.07242e10i	0.0308751	+	0.0534773i
$790$	2.50680e10	−	6.71696e9i	0.0643594	−	0.0172450i
$791$	1.41042e11	−	1.41042e11i	0.360283	−	0.360283i
$792$	8.12508e10	+	2.17711e10i	0.206503	+	0.0553324i
$793$	−2.40818e11	−	4.17110e11i	−0.608971	−	1.05477i
$794$	1.44146e11	−	5.37960e11i	0.362677	−	1.35353i
$795$	−1.72843e9	−	6.45060e9i	−0.00432697	−	0.0161485i
$796$	−7.15850e11	+	1.91811e11i	−1.78308	+	0.477774i
$797$	2.02145e11	+	5.41647e10i	0.500992	+	0.134240i	0.500460	−	0.865759i	$-0.333164\pi$
$797$	2.02145e11	+	5.41647e10i	0.500992	+	0.134240i	0.000531633		1.00000i	$0.499831\pi$
$798$	−1.25948e10	+	7.27161e9i	−0.0310584	+	0.0179316i
$799$	1.65720e11	−	6.18475e11i	0.406619	−	1.51752i
$800$	−3.89165e11	−	3.89165e11i	−0.950109	−	0.950109i
$801$	−3.30834e10	−	1.23469e11i	−0.0803675	−	0.299935i
$802$	−7.13066e11	+	4.11689e11i	−1.72358	+	0.995112i
$803$	−1.05483e12			−2.53700
$804$			1.22311e10i			0.0292713i
$805$	−4.79592e10	+	2.76893e10i	−0.114206	+	0.0659368i
$806$	−2.96445e11	+	2.96445e11i	−0.702431	+	0.702431i
$807$	−2.13645e9	−	1.23348e9i	−0.00503731	−	0.00290829i
$808$	2.05341e10	−	2.05341e10i	0.0481758	−	0.0481758i
$809$	−9.97366e10	−	3.72222e11i	−0.232841	−	0.868976i	−0.979110	−	0.203331i	$-0.934823\pi$
$809$	−9.97366e10	−	3.72222e11i	−0.232841	−	0.868976i	0.746269	−	0.665645i	$-0.231843\pi$
$810$	7.85632e10	−	1.36075e11i	0.182507	−	0.316111i
$811$	2.19068e11	−	3.79437e11i	0.506402	−	0.877115i	−0.493570	−	0.869706i	$-0.664308\pi$
$811$	2.19068e11	−	3.79437e11i	0.506402	−	0.877115i	0.999973	−	0.00740863i	$-0.00235826\pi$
$812$	3.34332e10	−	1.24774e11i	0.0769049	−	0.287013i
$813$			2.09552e8i			0.000479656i
$814$	−2.30248e11	+	8.14301e11i	−0.524443	+	1.85476i
$815$	−1.74441e11			−0.395384
$816$	−1.96157e10	−	5.25601e9i	−0.0442428	−	0.0118548i
$817$	3.79842e11	+	2.19302e11i	0.852540	+	0.492214i
$818$	1.78948e11	+	1.03316e11i	0.399682	+	0.230756i
$819$	−1.92393e11	+	5.15516e10i	−0.427616	+	0.114579i
$820$	−4.79049e10	−	4.79049e10i	−0.105956	−	0.105956i
$821$	1.56702e10	−	2.71416e10i	0.0344907	−	0.0597397i	−0.848265	−	0.529572i	$-0.822352\pi$
$821$	1.56702e10	−	2.71416e10i	0.0344907	−	0.0597397i	0.882756	+	0.469833i	$0.155686\pi$
$822$	1.67523e10	+	1.67523e10i	0.0366933	+	0.0366933i
$823$	−3.58322e11	−	6.20631e11i	−0.781041	−	1.35280i	−0.931336	−	0.364161i	$-0.881356\pi$
$823$	−3.58322e11	−	6.20631e11i	−0.781041	−	1.35280i	0.150296	−	0.988641i	$-0.451977\pi$
$824$	−2.98636e10			−0.0647788
$825$		−	2.20531e10i		−	0.0476052i
$826$	1.51849e11	+	2.63010e11i	0.326206	+	0.565005i
$827$	3.55838e11	−	9.53466e10i	0.760731	−	0.203837i	0.142458	−	0.989801i	$-0.454499\pi$
$827$	3.55838e11	−	9.53466e10i	0.760731	−	0.203837i	0.618273	+	0.785964i	$0.287833\pi$
$828$	5.32937e11	−	5.32937e11i	1.13385	−	1.13385i
$829$	3.38528e11	+	9.07082e10i	0.716764	+	0.192056i	0.598727	−	0.800953i	$-0.295673\pi$
$829$	3.38528e11	+	9.07082e10i	0.716764	+	0.192056i	0.118037	+	0.993009i	$0.462340\pi$
$830$	−1.12841e11	−	1.95446e11i	−0.237768	−	0.411826i
$831$	−3.07304e8	+	1.14688e9i	−0.000644413	+	0.00240498i
$832$	1.83758e11	+	6.85792e11i	0.383488	+	1.43120i
$833$	−5.51170e11	+	1.47686e11i	−1.14474	+	0.306731i
$834$	1.12600e10	+	3.01712e9i	0.0232742	+	0.00623632i
$835$	−4.82375e10	+	2.78500e10i	−0.0992291	+	0.0572900i
$836$	3.31887e11	−	1.23862e12i	0.679461	−	2.53578i
$837$	−1.48227e10	−	1.48227e10i	−0.0302012	−	0.0302012i
$838$	2.18966e11	+	8.17192e11i	0.444018	+	1.65710i
$839$	−1.49084e10	+	8.60738e9i	−0.0300873	+	0.0173709i	−0.514968	−	0.857209i	$-0.672196\pi$
$839$	−1.49084e10	+	8.60738e9i	−0.0300873	+	0.0173709i	0.484881	+	0.874580i	$0.338863\pi$
$840$	−2.80987e8			−0.000564376
$841$			2.26614e11i			0.453006i
$842$	3.43441e11	−	1.98286e11i	0.683288	−	0.394496i
$843$	1.48762e10	−	1.48762e10i	0.0294564	−	0.0294564i
$844$	−2.85925e11	−	1.65079e11i	−0.563486	−	0.325329i
$845$	4.57866e10	−	4.57866e10i	0.0898074	−	0.0898074i
$846$	−2.21649e11	−	8.27205e11i	−0.432697	−	1.61485i
$847$	7.07049e10	−	1.22464e11i	0.137378	−	0.237945i
$848$	3.91806e11	−	6.78628e11i	0.757683	−	1.31235i
$849$	4.26232e9	−	1.59072e10i	0.00820380	−	0.0306170i
$850$			9.68218e11i			1.85480i
$851$	5.28575e11	+	5.43328e11i	1.00783	+	1.03596i
$852$	1.93971e10			0.0368111
$853$	−4.43593e11	−	1.18860e11i	−0.837893	−	0.224513i	−0.185739	−	0.982599i	$-0.559468\pi$
$853$	−4.43593e11	−	1.18860e11i	−0.837893	−	0.224513i	−0.652154	+	0.758086i	$0.726135\pi$
$854$	2.40400e11	+	1.38795e11i	0.451964	+	0.260941i
$855$	−2.07691e11	−	1.19910e11i	−0.388644	−	0.224384i
$856$	−1.47058e10	+	3.94041e9i	−0.0273901	+	0.00733916i
$857$	2.79665e11	+	2.79665e11i	0.518459	+	0.518459i	0.917105	−	0.398646i	$-0.130520\pi$
$857$	2.79665e11	+	2.79665e11i	0.518459	+	0.518459i	−0.398646	+	0.917105i	$0.630520\pi$
$858$	−2.45428e10	+	4.25095e10i	−0.0452872	+	0.0784398i
$859$	3.24755e11	+	3.24755e11i	0.596462	+	0.596462i	0.939369	−	0.342907i	$-0.111412\pi$
$859$	3.24755e11	+	3.24755e11i	0.596462	+	0.596462i	−0.342907	+	0.939369i	$0.611412\pi$
$860$	4.23819e10	+	7.34075e10i	0.0774794	+	0.134198i
$861$	−4.07046e9			−0.00740681
$862$			7.02899e11i			1.27310i
$863$	2.58990e11	+	4.48584e11i	0.466917	+	0.808724i	0.999286	−	0.0377888i	$-0.0120314\pi$
$863$	2.58990e11	+	4.48584e11i	0.466917	+	0.808724i	−0.532369	+	0.846512i	$0.678698\pi$
$864$	−5.91642e10	+	1.58530e10i	−0.106171	+	0.0284483i
$865$	−1.18344e11	+	1.18344e11i	−0.211388	+	0.211388i
$866$	−2.80526e11	−	7.51668e10i	−0.498772	−	0.133645i
$867$	9.29890e9	+	1.61062e10i	0.0164572	+	0.0285046i
$868$	3.29140e10	−	1.22837e11i	0.0579831	−	0.216396i
$869$	3.55840e10	+	1.32801e11i	0.0623987	+	0.232875i
$870$	−5.75079e9	+	1.54092e9i	−0.0100381	+	0.00268969i
$871$	4.68545e11	+	1.25546e11i	0.814103	+	0.218138i
$872$	−1.17465e11	+	6.78184e10i	−0.203162	+	0.117295i
$873$	−9.44742e10	+	3.52582e11i	−0.162651	+	0.607021i
$874$	−1.54324e12	−	1.54324e12i	−2.64476	−	2.64476i
$875$	−2.68042e10	−	1.00035e11i	−0.0457267	−	0.170654i
$876$	−4.15303e10	+	2.39775e10i	−0.0705259	+	0.0407181i
$877$	8.35043e11			1.41160			0.705798	−	0.708413i	$-0.250588\pi$
$877$	8.35043e11			1.41160			0.705798	+	0.708413i	$0.250588\pi$
$878$		−	6.97742e11i		−	1.17413i
$879$	9.76467e9	−	5.63764e9i	0.0163569	−	0.00944369i
$880$	−1.24428e11	+	1.24428e11i	−0.207486	+	0.207486i
$881$	−8.53963e11	−	4.93036e11i	−1.41754	−	0.818417i	−0.421458	−	0.906848i	$-0.638481\pi$
$881$	−8.53963e11	−	4.93036e11i	−1.41754	−	0.818417i	−0.996082	+	0.0884311i	$0.971815\pi$
$882$	−5.39657e11	+	5.39657e11i	−0.891751	+	0.891751i
$883$	2.10047e11	+	7.83907e11i	0.345521	+	1.28950i	0.892003	+	0.452030i	$0.149300\pi$
$883$	2.10047e11	+	7.83907e11i	0.345521	+	1.28950i	−0.546482	+	0.837471i	$0.684033\pi$
$884$	5.67112e11	−	9.82266e11i	0.928666	−	1.60850i
$885$	3.68345e9	−	6.37992e9i	0.00600456	−	0.0104002i
$886$	3.33875e11	−	1.24604e12i	0.541813	−	2.02207i
$887$			1.68502e11i			0.272214i	0.990694	+	0.136107i	$0.0434591\pi$
$887$			1.68502e11i			0.272214i	−0.990694	+	0.136107i	$0.956541\pi$
$888$	9.44233e8	+	3.72843e9i	0.00151854	+	0.00599618i
$889$	−2.12931e11			−0.340904
$890$	−6.90959e10	−	1.85142e10i	−0.110127	−	0.0295083i
$891$	7.20878e11	+	4.16199e11i	1.14380	+	0.660374i
$892$	−3.85698e11	−	2.22683e11i	−0.609239	−	0.351744i
$893$	−1.26069e12	+	3.37802e11i	−1.98246	+	0.531198i
$894$	−7.83345e9	−	7.83345e9i	−0.0122632	−	0.0122632i
$895$	8.72139e10	−	1.51059e11i	0.135923	−	0.235426i
$896$	−5.28646e10	−	5.28646e10i	−0.0820225	−	0.0820225i
$897$	2.19846e10	+	3.80785e10i	0.0339586	+	0.0588180i
$898$	1.43450e12			2.20594
$899$		−	2.69383e11i		−	0.412412i
$900$	3.40780e11	+	5.90249e11i	0.519403	+	0.899633i
$901$	−1.50032e12	+	4.02011e11i	−2.27660	+	0.610012i
$902$	4.82193e11	−	4.82193e11i	0.728442	−	0.728442i
$903$	4.91929e9	+	1.31812e9i	0.00739864	+	0.00198246i
$904$	7.59392e10	+	1.31530e11i	0.113708	+	0.196949i
$905$	7.83359e10	−	2.92354e11i	0.116779	−	0.435827i
$906$	5.77118e8	+	2.15383e9i	0.000856548	+	0.00319668i
$907$	−3.28607e11	+	8.80499e10i	−0.485565	+	0.130107i	−0.493293	−	0.869863i	$-0.664207\pi$
$907$	−3.28607e11	+	8.80499e10i	−0.485565	+	0.130107i	0.00772773	+	0.999970i	$0.497540\pi$
$908$	9.14812e11	+	2.45123e11i	1.34582	+	0.360613i
$909$	2.49234e11	−	1.43895e11i	0.365050	−	0.210762i
$910$	−2.88494e10	+	1.07667e11i	−0.0420698	+	0.157007i
$911$	−8.68937e10	−	8.68937e10i	−0.126158	−	0.126158i	0.641209	−	0.767367i	$-0.278433\pi$
$911$	−8.68937e10	−	8.68937e10i	−0.126158	−	0.126158i	−0.767367	+	0.641209i	$0.778433\pi$
$912$	1.07138e10	+	3.99845e10i	0.0154869	+	0.0577979i
$913$	1.03540e12	−	5.97788e11i	1.49013	−	0.860328i
$914$	−9.62499e11			−1.37916
$915$		−	6.73359e9i		−	0.00960644i
$916$	−7.47129e11	+	4.31355e11i	−1.06124	+	0.612707i
$917$	8.31211e10	−	8.31211e10i	0.117553	−	0.117553i
$918$	9.33192e10	+	5.38778e10i	0.131401	+	0.0758647i
$919$	−7.60305e11	+	7.60305e11i	−1.06592	+	1.06592i	−0.0682544	+	0.997668i	$0.521743\pi$
$919$	−7.60305e11	+	7.60305e11i	−1.06592	+	1.06592i	−0.997668	+	0.0682544i	$0.978257\pi$
$920$	−1.09136e10	−	4.07302e10i	−0.0152341	−	0.0568545i
$921$	2.81489e9	−	4.87553e9i	0.00391221	−	0.00677615i
$922$	−2.08488e11	+	3.61113e11i	−0.288508	+	0.499711i
$923$	1.99102e11	−	7.43058e11i	0.274327	−	1.02380i
$924$		−	1.48895e10i		−	0.0204264i
$925$	−5.98304e11	+	3.34538e11i	−0.817250	+	0.456960i
$926$	2.54675e11			0.346372
$927$	−2.85873e11	−	7.65994e10i	−0.387127	−	0.103730i
$928$	−6.81670e11	−	3.93563e11i	−0.919142	−	0.530667i
$929$	2.62941e11	+	1.51809e11i	0.353017	+	0.203815i	0.666013	−	0.745940i	$-0.267999\pi$
$929$	2.62941e11	+	1.51809e11i	0.353017	+	0.203815i	−0.312996	+	0.949754i	$0.601333\pi$
$930$	−5.66148e9	+	1.51699e9i	−0.00756830	+	0.00202792i
$931$	8.22460e11	+	8.22460e11i	1.09475	+	1.09475i
$932$	2.93106e11	−	5.07674e11i	0.388473	−	0.672854i
$933$	1.26109e9	+	1.26109e9i	0.00166426	+	0.00166426i
$934$	−6.28914e11	−	1.08931e12i	−0.826426	−	1.43141i
$935$	3.48798e11			0.456382
$936$		−	1.51662e11i		−	0.197594i
$937$	1.91987e11	+	3.32532e11i	0.249066	+	0.431394i	0.963267	−	0.268546i	$-0.0865432\pi$
$937$	1.91987e11	+	3.32532e11i	0.249066	+	0.431394i	−0.714201	+	0.699940i	$0.753210\pi$
$938$	−2.70045e11	+	7.23584e10i	−0.348839	+	0.0934712i
$939$	1.54086e9	−	1.54086e9i	0.00198199	−	0.00198199i
$940$	−2.43640e11	−	6.52830e10i	−0.312059	−	0.0836159i
$941$	3.38624e11	+	5.86514e11i	0.431876	+	0.748031i	0.997035	−	0.0769509i	$-0.0245185\pi$
$941$	3.38624e11	+	5.86514e11i	0.431876	+	0.748031i	−0.565159	+	0.824982i	$0.691185\pi$
$942$	−1.53584e10	+	5.73183e10i	−0.0195048	+	0.0727930i
$943$	−1.58098e11	−	5.90030e11i	−0.199931	−	0.746153i
$944$	8.34974e11	−	2.23731e11i	1.05144	−	0.281733i
$945$	−5.38352e9	−	1.44251e9i	−0.00675054	−	0.00180880i
$946$	−7.38894e11	+	4.26601e11i	−0.922609	+	0.532668i
$947$	−1.70376e11	+	6.35853e11i	−0.211841	+	0.790600i	0.775414	+	0.631453i	$0.217541\pi$
$947$	−1.70376e11	+	6.35853e11i	−0.211841	+	0.790600i	−0.987255	+	0.159147i	$0.949126\pi$
$948$	4.41972e9	+	4.41972e9i	0.00547219	+	0.00547219i
$949$	4.92235e11	+	1.83704e12i	0.606886	+	2.26493i
$950$	1.70920e12	−	9.86804e11i	2.09844	−	1.21154i
$951$	−1.96600e10			−0.0240359
$952$			6.53537e10i			0.0795651i
$953$	−3.85347e11	+	2.22480e11i	−0.467175	+	0.269724i	−0.715057	−	0.699067i	$-0.753599\pi$
$953$	−3.85347e11	+	2.22480e11i	−0.467175	+	0.269724i	0.247881	+	0.968790i	$0.420266\pi$
$954$	−1.46898e12	+	1.46898e12i	−1.77347	+	1.77347i
$955$	2.69209e11	+	1.55428e11i	0.323650	+	0.186860i
$956$	−1.41942e11	+	1.41942e11i	−0.169933	+	0.169933i
$957$	−8.16322e9	−	3.04656e10i	−0.00973227	−	0.0363213i
$958$	1.30771e11	−	2.26502e11i	0.155257	−	0.268912i
$959$	−1.42503e11	+	2.46823e11i	−0.168481	+	0.291818i
$960$	−2.56905e9	+	9.58782e9i	−0.00302474	+	0.0112885i
$961$			5.87692e11i			0.689058i
$962$	1.52559e12	+	2.09973e10i	1.78131	+	0.0245168i
$963$	−1.50880e11			−0.175440
$964$	8.42423e11	+	2.25727e11i	0.975489	+	0.261381i
$965$	−2.25592e11	−	1.30246e11i	−0.260145	−	0.150195i
$966$	−2.19465e10	−	1.26708e10i	−0.0252032	−	0.0145511i
$967$	1.56014e12	−	4.18038e11i	1.78426	−	0.478090i	0.792906	−	0.609344i	$-0.208567\pi$
$967$	1.56014e12	−	4.18038e11i	1.78426	−	0.478090i	0.991349	+	0.131254i	$0.0419003\pi$
$968$	7.61369e10	+	7.61369e10i	0.0867149	+	0.0867149i
$969$	4.10259e10	−	7.10589e10i	0.0465332	−	0.0805978i
$970$	1.44443e11	+	1.44443e11i	0.163158	+	0.163158i
$971$	−6.60511e11	−	1.14404e12i	−0.743024	−	1.28696i	−0.951112	−	0.308846i	$-0.900057\pi$
$971$	−6.60511e11	−	1.14404e12i	−0.743024	−	1.28696i	0.208088	−	0.978110i	$-0.433276\pi$
$972$	1.13807e11			0.127498
$973$			1.40237e11i			0.156463i
$974$	−1.78205e11	−	3.08661e11i	−0.198009	−	0.342962i
$975$	−3.84067e10	+	1.02910e10i	−0.0424999	+	0.0113878i
$976$	5.58697e11	−	5.58697e11i	0.615712	−	0.615712i
$977$	1.43438e11	+	3.84340e10i	0.157429	+	0.0421830i	0.336673	−	0.941622i	$-0.390698\pi$
$977$	1.43438e11	+	3.84340e10i	0.157429	+	0.0421830i	−0.179244	+	0.983805i	$0.557365\pi$
$978$	−3.99128e10	−	6.91309e10i	−0.0436271	−	0.0755644i
$979$	9.80814e10	−	3.66045e11i	0.106772	−	0.398477i
$980$	5.81787e10	+	2.17126e11i	0.0630753	+	0.235400i
$981$	−1.29840e12	+	3.47905e11i	−1.40195	+	0.375651i
$982$	4.94493e11	+	1.32499e11i	0.531758	+	0.142484i
$983$	−7.29130e11	+	4.20963e11i	−0.780892	+	0.450848i	−0.836746	−	0.547591i	$-0.815545\pi$
$983$	−7.29130e11	+	4.20963e11i	−0.780892	+	0.450848i	0.0558543	+	0.998439i	$0.482212\pi$
$984$	8.02178e8	−	2.99377e9i	0.000855639	−	0.00319329i
$985$	9.43180e10	+	9.43180e10i	0.100196	+	0.100196i
$986$	3.58397e11	+	1.33756e12i	0.379190	+	1.41516i
$987$	−1.31245e10	+	7.57745e9i	−0.0138298	+	0.00798462i
$988$	−2.31199e12			−2.42638
$989$			7.64268e11i			0.798842i
$990$	4.04014e11	−	2.33257e11i	0.420587	−	0.242826i
$991$	−2.20198e11	+	2.20198e11i	−0.228306	+	0.228306i	−0.811985	−	0.583679i	$-0.801613\pi$
$991$	−2.20198e11	+	2.20198e11i	−0.228306	+	0.228306i	0.583679	+	0.811985i	$0.301613\pi$
$992$	−6.71084e11	−	3.87451e11i	−0.692995	−	0.400101i
$993$	4.28916e10	−	4.28916e10i	0.0441138	−	0.0441138i
$994$	1.14752e11	+	4.28260e11i	0.117548	+	0.438695i
$995$	−2.05455e11	+	3.55859e11i	−0.209616	+	0.363066i
$996$	2.71768e10	−	4.70716e10i	0.0276160	−	0.0478323i
$997$	3.02423e11	−	1.12866e12i	0.306079	−	1.14230i	−0.625933	−	0.779877i	$-0.715282\pi$
$997$	3.02423e11	−	1.12866e12i	0.306079	−	1.14230i	0.932012	−	0.362426i	$-0.118052\pi$
$998$			1.87833e12i			1.89343i
$999$	−1.04990e9	+	7.62818e10i	−0.00105411	+	0.0765877i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.9.g.a.8.5	✓	100
37.14	odd	12	inner	37.9.g.a.14.5	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.9.g.a.8.5	✓	100	1.1	even	1	trivial
37.9.g.a.14.5	yes	100	37.14	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	37.g (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-22.4552 - 6.01684i) q^{2} +(-2.68847 - 1.55219i) q^{3} +(246.329 + 142.218i) q^{4} +(152.334 - 40.8178i) q^{5} +(51.0307 + 51.0307i) q^{6} +(-434.094 + 751.872i) q^{7} +(-467.444 - 467.444i) q^{8} +(-3275.68 - 5673.65i) q^{9} +O(q^{10})\)	\(q+(-22.4552 - 6.01684i) q^{2} +(-2.68847 - 1.55219i) q^{3} +(246.329 + 142.218i) q^{4} +(152.334 - 40.8178i) q^{5} +(51.0307 + 51.0307i) q^{6} +(-434.094 + 751.872i) q^{7} +(-467.444 - 467.444i) q^{8} +(-3275.68 - 5673.65i) q^{9} -3666.28 q^{10} -19422.6i q^{11} +(-441.498 - 764.697i) q^{12} +(-33825.5 + 9063.52i) q^{13} +(14271.5 - 14271.5i) q^{14} +(-472.903 - 126.714i) q^{15} +(-28723.9 - 49751.2i) q^{16} +(-29472.0 + 109991. i) q^{17} +(39418.5 + 147112. i) q^{18} +(224205. - 60075.4i) q^{19} +(43329.4 + 11610.1i) q^{20} +(2334.09 - 1347.59i) q^{21} +(-116863. + 436138. i) q^{22} +(285996. + 285996. i) q^{23} +(531.147 + 1982.27i) q^{24} +(-316752. + 182877. i) q^{25} +814091. q^{26} +40705.7i q^{27} +(-213860. + 123472. i) q^{28} +(-369886. + 369886. i) q^{29} +(9856.68 + 5690.76i) q^{30} +(-364142. + 364142. i) q^{31} +(389454. + 1.45346e6i) q^{32} +(-30147.5 + 52217.1i) q^{33} +(1.32360e6 - 2.29253e6i) q^{34} +(-35437.5 + 132255. i) q^{35} -1.86344e6i q^{36} +(1.87398e6 + 25792.3i) q^{37} -5.39601e6 q^{38} +(105007. + 28136.6i) q^{39} +(-90287.7 - 52127.6i) q^{40} +(-1.30794e6 - 755138. i) q^{41} +(-60520.6 + 16216.5i) q^{42} +(1.33615e6 + 1.33615e6i) q^{43} +(2.76225e6 - 4.78436e6i) q^{44} +(-730584. - 730584. i) q^{45} +(-4.70129e6 - 8.14287e6i) q^{46} -5.62296e6 q^{47} +178339. i q^{48} +(2.50553e6 + 4.33970e6i) q^{49} +(8.21304e6 - 2.20068e6i) q^{50} +(249961. - 249961. i) q^{51} +(-9.62120e6 - 2.57799e6i) q^{52} +(6.82022e6 + 1.18130e7i) q^{53} +(244920. - 914052. i) q^{54} +(-792789. - 2.95873e6i) q^{55} +(554372. - 148544. i) q^{56} +(-696015. - 186497. i) q^{57} +(1.05314e7 - 6.08031e6i) q^{58} +(-3.89451e6 + 1.45345e7i) q^{59} +(-98468.6 - 98468.6i) q^{60} +(3.55971e6 + 1.32850e7i) q^{61} +(1.03679e7 - 5.98589e6i) q^{62} +5.68781e6 q^{63} -2.02744e7i q^{64} +(-4.78283e6 + 2.76137e6i) q^{65} +(991150. - 991150. i) q^{66} +(-1.19960e7 - 6.92592e6i) q^{67} +(-2.29025e7 + 2.29025e7i) q^{68} +(-324971. - 1.21281e6i) q^{69} +(1.59151e6 - 2.75658e6i) q^{70} +(-1.09837e7 + 1.90243e7i) q^{71} +(-1.12091e6 + 4.18331e6i) q^{72} -5.43094e7i q^{73} +(-4.19254e7 - 1.18546e7i) q^{74} +1.13543e6 q^{75} +(6.37719e7 + 1.70876e7i) q^{76} +(1.46033e7 + 8.43124e6i) q^{77} +(-2.18866e6 - 1.26362e6i) q^{78} +(-6.83745e6 + 1.83209e6i) q^{79} +(-6.40636e6 - 6.40636e6i) q^{80} +(-2.14286e7 + 3.71154e7i) q^{81} +(2.48264e7 + 2.48264e7i) q^{82} +(3.07779e7 + 5.33089e7i) q^{83} +766606. q^{84} +1.79584e7i q^{85} +(-2.19641e7 - 3.80430e7i) q^{86} +(1.56856e6 - 420295. i) q^{87} +(-9.07898e6 + 9.07898e6i) q^{88} +(1.88463e7 + 5.04985e6i) q^{89} +(1.20096e7 + 2.08012e7i) q^{90} +(7.86883e6 - 2.93669e7i) q^{91} +(2.97753e7 + 1.11123e8i) q^{92} +(1.54420e6 - 413768. i) q^{93} +(1.26265e8 + 3.38325e7i) q^{94} +(3.17019e7 - 1.83031e7i) q^{95} +(1.20901e6 - 4.51209e6i) q^{96} +(-3.93976e7 - 3.93976e7i) q^{97} +(-3.01507e7 - 1.12524e8i) q^{98} +(-1.10197e8 + 6.36223e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 10 q^{2} - 6 q^{3} + 552 q^{4} - 1642 q^{5} - 516 q^{6} - 2 q^{7} - 7440 q^{8} + 117258 q^{9}+O(q^{10}) \) 100 * q - 10 * q^2 - 6 * q^3 + 552 * q^4 - 1642 * q^5 - 516 * q^6 - 2 * q^7 - 7440 * q^8 + 117258 * q^9	\( 100 q - 10 q^{2} - 6 q^{3} + 552 q^{4} - 1642 q^{5} - 516 q^{6} - 2 q^{7} - 7440 q^{8} + 117258 q^{9} + 10744 q^{10} - 62086 q^{12} - 63598 q^{13} - 62648 q^{14} + 53318 q^{15} + 1056692 q^{16} - 53050 q^{17} - 150954 q^{18} - 161388 q^{19} - 922330 q^{20} + 589656 q^{21} - 713044 q^{22} + 32888 q^{23} - 1193742 q^{24} + 1859250 q^{25} + 900088 q^{26} - 7001094 q^{28} + 2288858 q^{29} + 9620658 q^{30} + 5782072 q^{31} - 4920832 q^{32} - 719444 q^{33} - 5308306 q^{34} - 10575422 q^{35} + 14052530 q^{37} - 10994096 q^{38} + 3417088 q^{39} + 9928698 q^{40} + 16320936 q^{41} + 39067848 q^{42} - 9546800 q^{43} - 19056984 q^{44} - 12333970 q^{45} - 15608210 q^{46} - 844736 q^{47} - 54639310 q^{49} - 52548004 q^{50} + 25866216 q^{51} + 31025896 q^{52} - 17856728 q^{53} + 8699372 q^{54} - 14191504 q^{55} - 23168766 q^{56} + 74736160 q^{57} + 109856484 q^{58} + 499856 q^{59} - 286204560 q^{60} - 34778024 q^{61} + 6537756 q^{62} + 154042660 q^{63} - 107386782 q^{65} - 14426072 q^{66} + 84112848 q^{67} + 247473908 q^{68} - 74383808 q^{69} - 55414618 q^{70} - 57046730 q^{71} - 172153588 q^{72} + 315393932 q^{74} + 164078200 q^{75} - 141128756 q^{76} + 272235456 q^{77} + 655339260 q^{78} + 18584140 q^{79} + 43263824 q^{80} - 337954862 q^{81} - 363936872 q^{82} - 86956118 q^{83} - 505940536 q^{84} + 41750098 q^{86} + 195776154 q^{87} + 425134052 q^{88} + 253234298 q^{89} - 139130828 q^{90} - 327702612 q^{91} - 572151958 q^{92} - 608615132 q^{93} - 502568260 q^{94} - 115562040 q^{95} + 1165361934 q^{96} - 123302218 q^{97} + 537492294 q^{98} + 533594376 q^{99}+O(q^{100}) \) 100 * q - 10 * q^2 - 6 * q^3 + 552 * q^4 - 1642 * q^5 - 516 * q^6 - 2 * q^7 - 7440 * q^8 + 117258 * q^9 + 10744 * q^10 - 62086 * q^12 - 63598 * q^13 - 62648 * q^14 + 53318 * q^15 + 1056692 * q^16 - 53050 * q^17 - 150954 * q^18 - 161388 * q^19 - 922330 * q^20 + 589656 * q^21 - 713044 * q^22 + 32888 * q^23 - 1193742 * q^24 + 1859250 * q^25 + 900088 * q^26 - 7001094 * q^28 + 2288858 * q^29 + 9620658 * q^30 + 5782072 * q^31 - 4920832 * q^32 - 719444 * q^33 - 5308306 * q^34 - 10575422 * q^35 + 14052530 * q^37 - 10994096 * q^38 + 3417088 * q^39 + 9928698 * q^40 + 16320936 * q^41 + 39067848 * q^42 - 9546800 * q^43 - 19056984 * q^44 - 12333970 * q^45 - 15608210 * q^46 - 844736 * q^47 - 54639310 * q^49 - 52548004 * q^50 + 25866216 * q^51 + 31025896 * q^52 - 17856728 * q^53 + 8699372 * q^54 - 14191504 * q^55 - 23168766 * q^56 + 74736160 * q^57 + 109856484 * q^58 + 499856 * q^59 - 286204560 * q^60 - 34778024 * q^61 + 6537756 * q^62 + 154042660 * q^63 - 107386782 * q^65 - 14426072 * q^66 + 84112848 * q^67 + 247473908 * q^68 - 74383808 * q^69 - 55414618 * q^70 - 57046730 * q^71 - 172153588 * q^72 + 315393932 * q^74 + 164078200 * q^75 - 141128756 * q^76 + 272235456 * q^77 + 655339260 * q^78 + 18584140 * q^79 + 43263824 * q^80 - 337954862 * q^81 - 363936872 * q^82 - 86956118 * q^83 - 505940536 * q^84 + 41750098 * q^86 + 195776154 * q^87 + 425134052 * q^88 + 253234298 * q^89 - 139130828 * q^90 - 327702612 * q^91 - 572151958 * q^92 - 608615132 * q^93 - 502568260 * q^94 - 115562040 * q^95 + 1165361934 * q^96 - 123302218 * q^97 + 537492294 * q^98 + 533594376 * q^99

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