LMFDB - Embedded newform 37.8.f.a.7.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,8,Mod(7,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("37.7");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	37.f (of order $9$, degree $6$, 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:	$11.5582459429$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			7.20
Character	$\chi$	$=$	37.7
Dual form			37.8.f.a.16.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(16.4964 - 6.00419i) q^{2} +(64.3192 + 23.4103i) q^{3} +(138.026 - 115.818i) q^{4} +(23.4987 + 133.267i) q^{5} +1201.59 q^{6} +(-96.3778 - 546.586i) q^{7} +(458.016 - 793.306i) q^{8} +(1913.58 + 1605.68i) q^{9} +O(q^{10})$	\(q+(16.4964 - 6.00419i) q^{2} +(64.3192 + 23.4103i) q^{3} +(138.026 - 115.818i) q^{4} +(23.4987 + 133.267i) q^{5} +1201.59 q^{6} +(-96.3778 - 546.586i) q^{7} +(458.016 - 793.306i) q^{8} +(1913.58 + 1605.68i) q^{9} +(1187.81 + 2057.34i) q^{10} +(1368.96 - 2371.10i) q^{11} +(11589.1 - 4218.07i) q^{12} +(-4632.81 + 3887.39i) q^{13} +(-4871.69 - 8438.01i) q^{14} +(-1608.41 + 9121.76i) q^{15} +(-1212.43 + 6876.03i) q^{16} +(-2262.74 - 1898.66i) q^{17} +(41207.9 + 14998.4i) q^{18} +(-18878.4 - 6871.16i) q^{19} +(18678.2 + 15672.8i) q^{20} +(6596.78 - 37412.2i) q^{21} +(8346.27 - 47334.0i) q^{22} +(-31572.3 - 54684.8i) q^{23} +(48030.7 - 40302.5i) q^{24} +(56205.4 - 20457.1i) q^{25} +(-53084.0 + 91944.2i) q^{26} +(10643.4 + 18434.9i) q^{27} +(-76607.0 - 64280.9i) q^{28} +(-21304.9 + 36901.2i) q^{29} +(28235.8 + 160133. i) q^{30} -42681.3 q^{31} +(41644.9 + 236180. i) q^{32} +(143558. - 120460. i) q^{33} +(-48726.9 - 17735.2i) q^{34} +(70577.4 - 25688.1i) q^{35} +450090. q^{36} +(303528. - 52940.5i) q^{37} -352680. q^{38} +(-388984. + 141578. i) q^{39} +(116485. + 42397.0i) q^{40} +(-516084. + 433046. i) q^{41} +(-115807. - 656773. i) q^{42} -966988. q^{43} +(-85663.8 - 485824. i) q^{44} +(-169019. + 292749. i) q^{45} +(-849166. - 712535. i) q^{46} +(226274. + 391918. i) q^{47} +(-238952. + 413877. i) q^{48} +(484410. - 176311. i) q^{49} +(804357. - 674936. i) q^{50} +(-101089. - 175092. i) q^{51} +(-189221. + 1.07312e6i) q^{52} +(-211704. + 1.20063e6i) q^{53} +(286264. + 240204. i) q^{54} +(348159. + 126720. i) q^{55} +(-477752. - 173888. i) q^{56} +(-1.05339e6 - 883895. i) q^{57} +(-129892. + 736654. i) q^{58} +(187829. - 1.06523e6i) q^{59} +(834459. + 1.44533e6i) q^{60} +(1.75373e6 - 1.47156e6i) q^{61} +(-704086. + 256266. i) q^{62} +(693216. - 1.20069e6i) q^{63} +(1.65820e6 + 2.87209e6i) q^{64} +(-626928. - 526055. i) q^{65} +(1.64493e6 - 2.84910e6i) q^{66} +(367637. + 2.08497e6i) q^{67} -532216. q^{68} +(-750518. - 4.25640e6i) q^{69} +(1.01003e6 - 847520. i) q^{70} +(5.14406e6 + 1.87229e6i) q^{71} +(2.15024e6 - 782625. i) q^{72} +5.11369e6 q^{73} +(4.68924e6 - 2.69576e6i) q^{74} +4.09399e6 q^{75} +(-3.40151e6 + 1.23805e6i) q^{76} +(-1.42795e6 - 519731. i) q^{77} +(-5.56675e6 + 4.67106e6i) q^{78} +(282809. + 1.60389e6i) q^{79} -944842. q^{80} +(-695652. - 3.94524e6i) q^{81} +(-5.91342e6 + 1.02424e7i) q^{82} +(-4.01567e6 - 3.36955e6i) q^{83} +(-3.42247e6 - 5.92789e6i) q^{84} +(199859. - 346166. i) q^{85} +(-1.59518e7 + 5.80597e6i) q^{86} +(-2.23418e6 + 1.87470e6i) q^{87} +(-1.25401e6 - 2.17200e6i) q^{88} +(1.56085e6 - 8.85201e6i) q^{89} +(-1.03047e6 + 5.84411e6i) q^{90} +(2.57129e6 + 2.15757e6i) q^{91} +(-1.06913e7 - 3.89131e6i) q^{92} +(-2.74523e6 - 999180. i) q^{93} +(6.08585e6 + 5.10663e6i) q^{94} +(472087. - 2.67734e6i) q^{95} +(-2.85047e6 + 1.61658e7i) q^{96} +(-2.92526e6 - 5.06670e6i) q^{97} +(6.93240e6 - 5.81697e6i) q^{98} +(6.42684e6 - 2.33918e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 15 q^{2} + 33 q^{3} - 279 q^{4} + 576 q^{5} - 12 q^{6} - 597 q^{7} - 3750 q^{8} - 3243 q^{9}+O(q^{10}) $ 132 * q + 15 * q^2 + 33 * q^3 - 279 * q^4 + 576 * q^5 - 12 * q^6 - 597 * q^7 - 3750 * q^8 - 3243 * q^9	\( 132 q + 15 q^{2} + 33 q^{3} - 279 q^{4} + 576 q^{5} - 12 q^{6} - 597 q^{7} - 3750 q^{8} - 3243 q^{9} - 6003 q^{10} - 15975 q^{11} - 4635 q^{12} - 15981 q^{13} - 13491 q^{14} + 38493 q^{15} - 74151 q^{16} + 37698 q^{17} - 20100 q^{18} - 66102 q^{19} - 176184 q^{20} - 142530 q^{21} + 132783 q^{22} + 140631 q^{23} - 38793 q^{24} - 544092 q^{25} - 423147 q^{26} + 130557 q^{27} + 603813 q^{28} + 22890 q^{29} - 319860 q^{30} - 1288044 q^{31} - 217866 q^{32} + 112344 q^{33} + 812019 q^{34} + 1479252 q^{35} + 8118132 q^{36} - 1664550 q^{37} + 305010 q^{38} - 1580340 q^{39} - 4681425 q^{40} - 2956593 q^{41} - 3553029 q^{42} - 1023528 q^{43} + 6409524 q^{44} + 1803336 q^{45} + 10219434 q^{46} - 2607204 q^{47} - 2984043 q^{48} - 6819531 q^{49} + 5724015 q^{50} - 1675833 q^{51} + 11768451 q^{52} + 2280177 q^{53} - 7803897 q^{54} - 3542196 q^{55} + 12168843 q^{56} - 85203 q^{57} - 12425487 q^{58} - 7014600 q^{59} + 2356788 q^{60} + 10840332 q^{61} + 6334368 q^{62} - 3331359 q^{63} - 26175624 q^{64} - 573195 q^{65} - 36720249 q^{66} + 6642918 q^{67} - 25277742 q^{68} - 1236438 q^{69} - 27401982 q^{70} + 20311041 q^{71} + 40093005 q^{72} + 38643780 q^{73} - 9531 q^{74} + 16639446 q^{75} + 5787405 q^{76} - 316971 q^{77} + 9363381 q^{78} + 17712534 q^{79} - 74410128 q^{80} - 10355109 q^{81} - 16702371 q^{82} - 31021176 q^{83} - 61626192 q^{84} + 23576445 q^{85} + 18579072 q^{86} + 104996631 q^{87} + 57279702 q^{88} - 13471320 q^{89} + 56306910 q^{90} - 2335911 q^{91} - 178133436 q^{92} + 24366258 q^{93} + 77086020 q^{94} - 26254407 q^{95} + 152523921 q^{96} + 14408415 q^{97} - 521205 q^{98} + 58375668 q^{99}+O(q^{100}) \) 132 * q + 15 * q^2 + 33 * q^3 - 279 * q^4 + 576 * q^5 - 12 * q^6 - 597 * q^7 - 3750 * q^8 - 3243 * q^9 - 6003 * q^10 - 15975 * q^11 - 4635 * q^12 - 15981 * q^13 - 13491 * q^14 + 38493 * q^15 - 74151 * q^16 + 37698 * q^17 - 20100 * q^18 - 66102 * q^19 - 176184 * q^20 - 142530 * q^21 + 132783 * q^22 + 140631 * q^23 - 38793 * q^24 - 544092 * q^25 - 423147 * q^26 + 130557 * q^27 + 603813 * q^28 + 22890 * q^29 - 319860 * q^30 - 1288044 * q^31 - 217866 * q^32 + 112344 * q^33 + 812019 * q^34 + 1479252 * q^35 + 8118132 * q^36 - 1664550 * q^37 + 305010 * q^38 - 1580340 * q^39 - 4681425 * q^40 - 2956593 * q^41 - 3553029 * q^42 - 1023528 * q^43 + 6409524 * q^44 + 1803336 * q^45 + 10219434 * q^46 - 2607204 * q^47 - 2984043 * q^48 - 6819531 * q^49 + 5724015 * q^50 - 1675833 * q^51 + 11768451 * q^52 + 2280177 * q^53 - 7803897 * q^54 - 3542196 * q^55 + 12168843 * q^56 - 85203 * q^57 - 12425487 * q^58 - 7014600 * q^59 + 2356788 * q^60 + 10840332 * q^61 + 6334368 * q^62 - 3331359 * q^63 - 26175624 * q^64 - 573195 * q^65 - 36720249 * q^66 + 6642918 * q^67 - 25277742 * q^68 - 1236438 * q^69 - 27401982 * q^70 + 20311041 * q^71 + 40093005 * q^72 + 38643780 * q^73 - 9531 * q^74 + 16639446 * q^75 + 5787405 * q^76 - 316971 * q^77 + 9363381 * q^78 + 17712534 * q^79 - 74410128 * q^80 - 10355109 * q^81 - 16702371 * q^82 - 31021176 * q^83 - 61626192 * q^84 + 23576445 * q^85 + 18579072 * q^86 + 104996631 * q^87 + 57279702 * q^88 - 13471320 * q^89 + 56306910 * q^90 - 2335911 * q^91 - 178133436 * q^92 + 24366258 * q^93 + 77086020 * q^94 - 26254407 * q^95 + 152523921 * q^96 + 14408415 * q^97 - 521205 * q^98 + 58375668 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	16.4964	−	6.00419i	1.45809	−	0.530700i	0.513249	−	0.858240i	$-0.328442\pi$
$2$	16.4964	−	6.00419i	1.45809	−	0.530700i	0.944838	+	0.327539i	$0.106219\pi$
$3$	64.3192	+	23.4103i	1.37536	+	0.500590i	0.920768	−	0.390111i	$-0.127563\pi$
$3$	64.3192	+	23.4103i	1.37536	+	0.500590i	0.454591	+	0.890700i	$0.349785\pi$
$4$	138.026	−	115.818i	1.07833	−	0.904826i
$5$	23.4987	+	133.267i	0.0840713	+	0.476792i	0.997553	+	0.0699126i	$0.0222720\pi$
$5$	23.4987	+	133.267i	0.0840713	+	0.476792i	−0.913482	+	0.406880i	$0.866617\pi$
$6$	1201.59			2.27106
$7$	−96.3778	−	546.586i	−0.106202	−	0.602303i	−0.990733	−	0.135822i	$-0.956633\pi$
$7$	−96.3778	−	546.586i	−0.106202	−	0.602303i	0.884531	−	0.466481i	$-0.154479\pi$
$8$	458.016	−	793.306i	0.316275	−	0.547805i
$9$	1913.58	+	1605.68i	0.874978	+	0.734194i
$10$	1187.81	+	2057.34i	0.375617	+	0.650588i
$11$	1368.96	−	2371.10i	0.310110	−	0.537126i	−0.668276	−	0.743913i	$-0.732968\pi$
$11$	1368.96	−	2371.10i	0.310110	−	0.537126i	0.978386	+	0.206788i	$0.0663009\pi$
$12$	11589.1	−	4218.07i	1.93604	−	0.704660i
$13$	−4632.81	+	3887.39i	−0.584848	+	0.490746i	−0.886535	−	0.462661i	$-0.846895\pi$
$13$	−4632.81	+	3887.39i	−0.584848	+	0.490746i	0.301687	+	0.953407i	$0.402450\pi$
$14$	−4871.69	−	8438.01i	−0.474495	−	0.821849i
$15$	−1608.41	+	9121.76i	−0.123049	+	0.697846i
$16$	−1212.43	+	6876.03i	−0.0740009	+	0.419680i
$17$	−2262.74	−	1898.66i	−0.111703	−	0.0937296i	0.585226	−	0.810871i	$-0.301006\pi$
$17$	−2262.74	−	1898.66i	−0.111703	−	0.0937296i	−0.696928	+	0.717141i	$0.745450\pi$
$18$	41207.9	+	14998.4i	1.66543	+	0.606167i
$19$	−18878.4	−	6871.16i	−0.631432	−	0.229823i	0.00642224	−	0.999979i	$-0.497956\pi$
$19$	−18878.4	−	6871.16i	−0.631432	−	0.229823i	−0.637855	+	0.770157i	$0.720178\pi$
$20$	18678.2	+	15672.8i	0.522071	+	0.438069i
$21$	6596.78	−	37412.2i	0.155441	−	0.881547i
$22$	8346.27	−	47334.0i	0.167114	−	0.947751i
$23$	−31572.3	−	54684.8i	−0.541076	−	0.937172i	−0.998843	−	0.0480991i	$-0.984684\pi$
$23$	−31572.3	−	54684.8i	−0.541076	−	0.937172i	0.457766	−	0.889073i	$-0.348650\pi$
$24$	48030.7	−	40302.5i	0.709218	−	0.595104i
$25$	56205.4	−	20457.1i	0.719430	−	0.261851i
$26$	−53084.0	+	91944.2i	−0.592320	+	1.02593i
$27$	10643.4	+	18434.9i	0.104066	+	0.180247i
$28$	−76607.0	−	64280.9i	−0.659501	−	0.553387i
$29$	−21304.9	+	36901.2i	−0.162213	+	0.280962i	−0.935662	−	0.352897i	$-0.885197\pi$
$29$	−21304.9	+	36901.2i	−0.162213	+	0.280962i	0.773449	+	0.633859i	$0.218530\pi$
$30$	28235.8	+	160133.i	0.190931	+	1.08282i
$31$	−42681.3			−0.257319			−0.128659	−	0.991689i	$-0.541067\pi$
$31$	−42681.3			−0.257319			−0.128659	+	0.991689i	$0.541067\pi$
$32$	41644.9	+	236180.i	0.224666	+	1.27414i
$33$	143558.	−	120460.i	0.695392	−	0.583503i
$34$	−48726.9	−	17735.2i	−0.212614	−	0.0773853i
$35$	70577.4	−	25688.1i	0.278245	−	0.101273i
$36$	450090.			1.60783
$37$	303528.	−	52940.5i	0.985128	−	0.171823i
$37$	303528.	−	52940.5i	0.985128	−	0.171823i
$38$	−352680.			−1.04265
$39$	−388984.	+	141578.i	−1.05004	+	0.382183i
$40$	116485.	+	42397.0i	0.287779	+	0.104743i
$41$	−516084.	+	433046.i	−1.16944	+	0.981275i	−0.999991	−	0.00426478i	$-0.998642\pi$
$41$	−516084.	+	433046.i	−1.16944	+	0.981275i	−0.169447	+	0.985539i	$0.554198\pi$
$42$	−115807.	−	656773.i	−0.241191	−	1.36786i
$43$	−966988.			−1.85473			−0.927366	−	0.374155i	$-0.877933\pi$
$43$	−966988.			−1.85473			−0.927366	+	0.374155i	$0.877933\pi$
$44$	−85663.8	−	485824.i	−0.151605	−	0.859794i
$45$	−169019.	+	292749.i	−0.276497	+	0.478907i
$46$	−849166.	−	712535.i	−1.28629	−	1.07933i
$47$	226274.	+	391918.i	0.317901	+	0.550621i	0.980050	−	0.198751i	$-0.0636886\pi$
$47$	226274.	+	391918.i	0.317901	+	0.550621i	−0.662149	+	0.749373i	$0.730355\pi$
$48$	−238952.	+	413877.i	−0.311865	+	0.540166i
$49$	484410.	−	176311.i	0.588202	−	0.214088i
$50$	804357.	−	674936.i	0.910027	−	0.763603i
$51$	−101089.	−	175092.i	−0.106711	−	0.184829i
$52$	−189221.	+	1.07312e6i	−0.186620	+	1.05837i
$53$	−211704.	+	1.20063e6i	−0.195327	+	1.10776i	0.716624	+	0.697459i	$0.245686\pi$
$53$	−211704.	+	1.20063e6i	−0.195327	+	1.10776i	−0.911952	+	0.410298i	$0.865425\pi$
$54$	286264.	+	240204.i	0.247394	+	0.207588i
$55$	348159.	+	126720.i	0.282169	+	0.102701i
$56$	−477752.	−	173888.i	−0.363534	−	0.132316i
$57$	−1.05339e6	−	883895.i	−0.753399	−	0.632177i
$58$	−129892.	+	736654.i	−0.0874147	+	0.495753i
$59$	187829.	−	1.06523e6i	0.119064	−	0.675245i	−0.865594	−	0.500747i	$-0.833059\pi$
$59$	187829.	−	1.06523e6i	0.119064	−	0.675245i	0.984658	−	0.174498i	$-0.0558302\pi$
$60$	834459.	+	1.44533e6i	0.498742	+	0.863846i
$61$	1.75373e6	−	1.47156e6i	0.989256	−	0.830085i	0.00379653	−	0.999993i	$-0.498792\pi$
$61$	1.75373e6	−	1.47156e6i	0.989256	−	0.830085i	0.985460	+	0.169908i	$0.0543471\pi$
$62$	−704086.	+	256266.i	−0.375193	+	0.136559i
$63$	693216.	−	1.20069e6i	0.349283	−	0.604975i
$64$	1.65820e6	+	2.87209e6i	0.790693	+	1.36952i
$65$	−626928.	−	526055.i	−0.283153	−	0.237593i
$66$	1.64493e6	−	2.84910e6i	0.704276	−	1.21984i
$67$	367637.	+	2.08497e6i	0.149333	+	0.846912i	0.963785	+	0.266680i	$0.0859268\pi$
$67$	367637.	+	2.08497e6i	0.149333	+	0.846912i	−0.814452	+	0.580231i	$0.802962\pi$
$68$	−532216.			−0.205261
$69$	−750518.	−	4.25640e6i	−0.275036	−	1.55980i
$70$	1.01003e6	−	847520.i	0.351960	−	0.295329i
$71$	5.14406e6	+	1.87229e6i	1.70570	+	0.620823i	0.996454	−	0.0841395i	$-0.0268142\pi$
$71$	5.14406e6	+	1.87229e6i	1.70570	+	0.620823i	0.709244	+	0.704963i	$0.249036\pi$
$72$	2.15024e6	−	782625.i	0.678929	−	0.247110i
$73$	5.11369e6			1.53852			0.769262	−	0.638934i	$-0.220624\pi$
$73$	5.11369e6			1.53852			0.769262	+	0.638934i	$0.220624\pi$
$74$	4.68924e6	−	2.69576e6i	1.34522	−	0.773341i
$75$	4.09399e6			1.12055
$76$	−3.40151e6	+	1.23805e6i	−0.888842	+	0.323512i
$77$	−1.42795e6	−	519731.i	−0.356447	−	0.129736i
$78$	−5.56675e6	+	4.67106e6i	−1.32822	+	1.11451i
$79$	282809.	+	1.60389e6i	0.0645355	+	0.365999i	0.999923	+	0.0123756i	$0.00393936\pi$
$79$	282809.	+	1.60389e6i	0.0645355	+	0.365999i	−0.935388	+	0.353623i	$0.884950\pi$
$80$	−944842.			−0.206321
$81$	−695652.	−	3.94524e6i	−0.145444	−	0.824851i
$82$	−5.91342e6	+	1.02424e7i	−1.18438	+	2.05140i
$83$	−4.01567e6	−	3.36955e6i	−0.770877	−	0.646842i	0.170057	−	0.985434i	$-0.445605\pi$
$83$	−4.01567e6	−	3.36955e6i	−0.770877	−	0.646842i	−0.940933	+	0.338592i	$0.890049\pi$
$84$	−3.42247e6	−	5.92789e6i	−0.630031	−	1.09125i
$85$	199859.	−	346166.i	0.0352986	−	0.0611389i
$86$	−1.59518e7	+	5.80597e6i	−2.70436	+	0.984307i
$87$	−2.23418e6	+	1.87470e6i	−0.363748	+	0.305221i
$88$	−1.25401e6	−	2.17200e6i	−0.196160	−	0.339759i
$89$	1.56085e6	−	8.85201e6i	0.234690	−	1.33100i	−0.608574	−	0.793497i	$-0.708258\pi$
$89$	1.56085e6	−	8.85201e6i	0.234690	−	1.33100i	0.843264	−	0.537499i	$-0.180631\pi$
$90$	−1.03047e6	+	5.84411e6i	−0.149001	+	0.845026i
$91$	2.57129e6	+	2.15757e6i	0.357690	+	0.300138i
$92$	−1.06913e7	−	3.89131e6i	−1.43144	−	0.521000i
$93$	−2.74523e6	−	999180.i	−0.353906	−	0.128811i
$94$	6.08585e6	+	5.10663e6i	0.755742	+	0.634143i
$95$	472087.	−	2.67734e6i	0.0564923	−	0.320384i
$96$	−2.85047e6	+	1.61658e7i	−0.328827	+	1.86487i
$97$	−2.92526e6	−	5.06670e6i	−0.325435	−	0.563669i	0.656166	−	0.754617i	$-0.272177\pi$
$97$	−2.92526e6	−	5.06670e6i	−0.325435	−	0.563669i	−0.981600	+	0.190948i	$0.938844\pi$
$98$	6.93240e6	−	5.81697e6i	0.744033	−	0.624318i
$99$	6.42684e6	−	2.33918e6i	0.665693	−	0.242293i
$100$	5.38853e6	−	9.33321e6i	0.538853	−	0.933321i
$101$	−2.15284e6	−	3.72883e6i	−0.207916	−	0.360121i	0.743142	−	0.669134i	$-0.233335\pi$
$101$	−2.15284e6	−	3.72883e6i	−0.207916	−	0.360121i	−0.951058	+	0.309013i	$0.900001\pi$
$102$	−2.71889e6	−	2.28142e6i	−0.253683	−	0.212865i
$103$	266144.	−	460975.i	0.0239986	−	0.0415668i	−0.853777	−	0.520639i	$-0.825694\pi$
$103$	266144.	−	460975.i	0.0239986	−	0.0415668i	0.877775	+	0.479073i	$0.159027\pi$
$104$	961992.	+	5.45573e6i	0.0838600	+	0.475594i
$105$	5.14084e6			0.433383
$106$	3.71648e6	+	2.10772e7i	0.303082	+	1.71887i
$107$	−1.40223e6	+	1.17661e6i	−0.110656	+	0.0928514i	−0.696437	−	0.717618i	$-0.745232\pi$
$107$	−1.40223e6	+	1.17661e6i	−0.110656	+	0.0928514i	0.585781	+	0.810469i	$0.300788\pi$
$108$	3.60416e6	+	1.31181e6i	0.275309	+	0.100204i
$109$	2.67230e6	−	972636.i	0.197648	−	0.0719379i	−0.241300	−	0.970451i	$-0.577574\pi$
$109$	2.67230e6	−	972636.i	0.197648	−	0.0719379i	0.438947	+	0.898513i	$0.355351\pi$
$110$	6.50422e6			0.465930
$111$	2.07620e7	+	3.70058e6i	1.44092	+	0.256826i
$112$	3.87519e6			0.260634
$113$	1.12598e7	−	4.09823e6i	0.734102	−	0.267191i	0.0522016	−	0.998637i	$-0.483376\pi$
$113$	1.12598e7	−	4.09823e6i	0.734102	−	0.267191i	0.681900	+	0.731445i	$0.261154\pi$
$114$	−2.26841e7	−	8.25634e6i	−1.43402	−	0.521940i
$115$	6.54580e6	−	5.49258e6i	0.401347	−	0.336770i
$116$	1.33318e6	+	7.56081e6i	0.0793020	+	0.449744i
$117$	−1.51072e7			−0.872032
$118$	−3.29735e6	−	1.87002e7i	−0.184747	−	1.04775i
$119$	−819705.	+	1.41977e6i	−0.0445906	+	0.0772332i
$120$	6.49967e6	+	5.45387e6i	0.343366	+	0.288118i
$121$	5.99550e6	+	1.03845e7i	0.307664	+	0.532890i
$122$	2.00947e7	−	3.48051e7i	1.00190	−	1.73533i
$123$	−4.33318e7	+	1.57715e7i	−2.09961	+	0.764196i
$124$	−5.89114e6	+	4.94325e6i	−0.277475	+	0.232829i
$125$	9.33309e6	+	1.61654e7i	0.427406	+	0.740288i
$126$	4.22641e6	−	2.39692e7i	0.188224	−	1.06747i
$127$	−2.72844e6	+	1.54738e7i	−0.118196	+	0.670321i	0.866922	+	0.498443i	$0.166095\pi$
$127$	−2.72844e6	+	1.54738e7i	−0.118196	+	0.670321i	−0.985118	+	0.171878i	$0.945016\pi$
$128$	2.10833e7	+	1.76910e7i	0.888596	+	0.745621i
$129$	−6.21958e7	−	2.26374e7i	−2.55092	−	0.928460i
$130$	−1.35006e7	−	4.91380e6i	−0.538952	−	0.196163i
$131$	1.94635e7	+	1.63318e7i	0.756435	+	0.634724i	0.937196	−	0.348803i	$-0.113412\pi$
$131$	1.94635e7	+	1.63318e7i	0.756435	+	0.634724i	−0.180761	+	0.983527i	$0.557856\pi$
$132$	5.86344e6	−	3.32532e7i	0.221893	−	1.25842i
$133$	−1.93622e6	+	1.09809e7i	−0.0713633	+	0.404722i
$134$	1.85832e7	+	3.21871e7i	0.667197	+	1.15562i
$135$	−2.20667e6	+	1.85162e6i	−0.0771914	+	0.0647713i
$136$	−2.54259e6	+	925428.i	−0.0866743	+	0.0315469i
$137$	−1.95979e7	+	3.39446e7i	−0.651161	+	1.12784i	0.331681	+	0.943392i	$0.392384\pi$
$137$	−1.95979e7	+	3.39446e7i	−0.651161	+	1.12784i	−0.982842	+	0.184452i	$0.940949\pi$
$138$	−3.79370e7	−	6.57088e7i	−1.22881	−	2.12837i
$139$	−2.28450e7	−	1.91693e7i	−0.721506	−	0.605416i	0.206295	−	0.978490i	$-0.433859\pi$
$139$	−2.28450e7	−	1.91693e7i	−0.721506	−	0.605416i	−0.927802	+	0.373074i	$0.878304\pi$
$140$	6.76639e6	−	1.17197e7i	0.208406	−	0.360969i
$141$	5.37885e6	+	3.05050e7i	0.161593	+	0.916440i
$142$	9.60999e7			2.81653
$143$	2.87528e6	+	1.63065e7i	0.0822251	+	0.466322i
$144$	−1.33608e7	+	1.12110e7i	−0.372875	+	0.312880i
$145$	−5.41836e6	−	1.97212e6i	−0.147598	−	0.0537212i
$146$	8.43573e7	−	3.07035e7i	2.24330	−	0.816495i
$147$	3.52843e7			0.916160
$148$	3.57634e7	−	4.24611e7i	0.906823	−	1.07665i
$149$	3.59457e7			0.890215			0.445107	−	0.895477i	$-0.353165\pi$
$149$	3.59457e7			0.890215			0.445107	+	0.895477i	$0.353165\pi$
$150$	6.75360e7	−	2.45811e7i	1.63387	−	0.594678i
$151$	−1.84106e7	−	6.70091e6i	−0.435159	−	0.158385i	0.115146	−	0.993349i	$-0.463266\pi$
$151$	−1.84106e7	−	6.70091e6i	−0.435159	−	0.158385i	−0.550305	+	0.834964i	$0.685489\pi$
$152$	−1.40975e7	+	1.18292e7i	−0.325604	+	0.273215i
$153$	−1.28128e6	−	7.26648e6i	−0.0289216	−	0.164023i
$154$	−2.66765e7			−0.588581
$155$	−1.00295e6	−	5.68803e6i	−0.0216331	−	0.122688i
$156$	−3.72926e7	+	6.45928e7i	−0.786479	+	1.36222i
$157$	−4.21536e7	−	3.53711e7i	−0.869333	−	0.729457i	0.0946244	−	0.995513i	$-0.469835\pi$
$157$	−4.21536e7	−	3.53711e7i	−0.869333	−	0.729457i	−0.963958	+	0.266056i	$0.914279\pi$
$158$	1.42954e7	+	2.47603e7i	0.288334	+	0.499409i
$159$	−4.17237e7	+	7.22676e7i	−0.823177	+	1.42578i
$160$	−3.04965e7	+	1.10998e7i	−0.588613	+	0.214238i
$161$	−2.68471e7	+	2.25274e7i	−0.506998	+	0.425422i
$162$	−3.51637e7	−	6.09053e7i	−0.649818	−	1.12552i
$163$	8.79656e6	−	4.98878e7i	0.159095	−	0.902272i	−0.795851	−	0.605492i	$-0.792976\pi$
$163$	8.79656e6	−	4.98878e7i	0.159095	−	0.902272i	0.954946	−	0.296780i	$-0.0959127\pi$
$164$	−2.10787e7	+	1.19543e8i	−0.373156	+	2.11628i
$165$	1.94268e7	+	1.63010e7i	0.336672	+	0.282501i
$166$	−8.64754e7	−	3.14745e7i	−1.46728	−	0.534048i
$167$	4.69070e7	+	1.70728e7i	0.779346	+	0.283659i	0.700900	−	0.713260i	$-0.252782\pi$
$167$	4.69070e7	+	1.70728e7i	0.779346	+	0.283659i	0.0784459	+	0.996918i	$0.475004\pi$
$168$	−2.66579e7	−	2.23686e7i	−0.433754	−	0.363963i
$169$	−4.54502e6	+	2.57761e7i	−0.0724323	+	0.410784i
$170$	1.21850e6	−	6.91047e6i	0.0190219	−	0.107879i
$171$	−2.50923e7	−	4.34611e7i	−0.383755	−	0.664683i
$172$	−1.33470e8	+	1.11994e8i	−2.00001	+	1.67821i
$173$	6.37754e7	−	2.32123e7i	0.936465	−	0.340845i	0.171696	−	0.985150i	$-0.445075\pi$
$173$	6.37754e7	−	2.32123e7i	0.936465	−	0.340845i	0.764769	+	0.644305i	$0.222853\pi$
$174$	−2.55998e7	+	4.43402e7i	−0.368395	+	0.638080i
$175$	−1.65985e7	−	2.87495e7i	−0.234119	−	0.405506i
$176$	1.46440e7	+	1.22878e7i	0.202472	+	0.169894i
$177$	3.70183e7	−	6.41176e7i	0.501776	−	0.869102i
$178$	−2.74008e7	−	1.55398e8i	−0.364161	−	2.06526i
$179$	−1.06628e8			−1.38959			−0.694796	−	0.719207i	$-0.744505\pi$
$179$	−1.06628e8			−1.38959			−0.694796	+	0.719207i	$0.744505\pi$
$180$	1.05765e7	+	5.99824e7i	0.135173	+	0.766602i
$181$	4.98984e6	−	4.18697e6i	0.0625477	−	0.0524838i	−0.610978	−	0.791648i	$-0.709224\pi$
$181$	4.98984e6	−	4.18697e6i	0.0625477	−	0.0524838i	0.673526	+	0.739164i	$0.264779\pi$
$182$	5.53715e7	+	2.01536e7i	0.680826	+	0.247801i
$183$	1.47248e8	−	5.35939e7i	1.77611	−	0.646453i
$184$	−5.78424e7			−0.684516
$185$	1.41877e7	+	3.92064e7i	0.164745	+	0.455256i
$186$	−5.12855e7			−0.584385
$187$	−7.59952e6	+	2.76600e6i	−0.0849847	+	0.0309319i
$188$	7.66228e7	+	2.78884e7i	0.841019	+	0.306106i
$189$	9.05048e6	−	7.59425e6i	0.0975114	−	0.0818217i
$190$	−8.28751e6	−	4.70008e7i	−0.0876570	−	0.497128i
$191$	−3.42851e6			−0.0356032			−0.0178016	−	0.999842i	$-0.505667\pi$
$191$	−3.42851e6			−0.0356032			−0.0178016	+	0.999842i	$0.505667\pi$
$192$	3.94178e7	+	2.23550e8i	0.401919	+	2.27939i
$193$	−5.48743e7	+	9.50451e7i	−0.549438	+	0.951654i	0.448875	+	0.893594i	$0.351825\pi$
$193$	−5.48743e7	+	9.50451e7i	−0.549438	+	0.951654i	−0.998313	+	0.0580597i	$0.981509\pi$
$194$	−7.86776e7	−	6.60184e7i	−0.773651	−	0.649171i
$195$	−2.80084e7	−	4.85120e7i	−0.270500	−	0.468520i
$196$	4.64413e7	−	8.04388e7i	0.440564	−	0.763078i
$197$	6.52672e7	−	2.37553e7i	0.608223	−	0.221375i	−0.0195023	−	0.999810i	$-0.506208\pi$
$197$	6.52672e7	−	2.37553e7i	0.608223	−	0.221375i	0.627726	+	0.778435i	$0.283986\pi$
$198$	9.19746e7	−	7.71759e7i	0.842054	−	0.706567i
$199$	−8.45525e7	−	1.46449e8i	−0.760573	−	1.31735i	−0.942556	−	0.334049i	$-0.891585\pi$
$199$	−8.45525e7	−	1.46449e8i	−0.760573	−	1.31735i	0.181983	−	0.983302i	$-0.441749\pi$
$200$	9.51422e6	−	5.39578e7i	0.0840946	−	0.476924i
$201$	−2.51636e7	+	1.42710e8i	−0.218568	+	1.23956i
$202$	−5.79027e7	−	4.85861e7i	−0.494275	−	0.414746i
$203$	2.22230e7	+	8.08850e6i	0.186452	+	0.0678628i
$204$	−3.42317e7	−	1.24593e7i	−0.282308	−	0.102752i
$205$	−6.98382e7	−	5.86012e7i	−0.566180	−	0.475082i
$206$	1.62263e6	−	9.20238e6i	0.0129325	−	0.0733441i
$207$	2.73904e7	−	1.55339e8i	0.214636	−	1.21726i
$208$	−2.11129e7	−	3.65686e7i	−0.162677	−	0.281765i
$209$	−4.21359e7	+	3.53562e7i	−0.319257	+	0.267888i
$210$	8.48052e7	−	3.08666e7i	0.631910	−	0.229996i
$211$	−9.06588e7	+	1.57026e8i	−0.664387	+	1.15075i	0.315064	+	0.949071i	$0.397974\pi$
$211$	−9.06588e7	+	1.57026e8i	−0.664387	+	1.15075i	−0.979451	+	0.201682i	$0.935359\pi$
$212$	1.09834e8	+	1.90238e8i	0.791700	+	1.37126i
$213$	2.87031e8	+	2.40848e8i	2.03517	+	1.70771i
$214$	−1.60671e7	+	2.78290e7i	−0.112070	+	0.194111i
$215$	−2.27229e7	−	1.28868e8i	−0.155930	−	0.884322i
$216$	1.94994e7			0.131654
$217$	4.11353e6	+	2.33290e7i	0.0273279	+	0.154984i
$218$	3.82433e7	−	3.20899e7i	0.250010	−	0.209783i
$219$	3.28908e8	+	1.19713e8i	2.11602	+	0.770169i
$220$	6.27315e7	−	2.28324e7i	0.397197	−	0.144568i
$221$	1.78637e7			0.111327
$222$	3.64717e8	−	6.36129e7i	2.23728	−	0.390220i
$223$	−1.34378e8			−0.811451			−0.405726	−	0.913995i	$-0.632981\pi$
$223$	−1.34378e8			−0.811451			−0.405726	+	0.913995i	$0.632981\pi$
$224$	1.25079e8	−	4.55250e7i	0.743560	−	0.270634i
$225$	1.40401e8	+	5.11018e7i	0.821734	+	0.299087i
$226$	1.61139e8	−	1.35212e8i	0.928585	−	0.779176i
$227$	−3.41116e7	−	1.93456e8i	−0.193558	−	1.09772i	−0.914457	−	0.404682i	$-0.867382\pi$
$227$	−3.41116e7	−	1.93456e8i	−0.193558	−	1.09772i	0.720899	−	0.693040i	$-0.243729\pi$
$228$	−2.47766e8			−1.38442
$229$	3.15794e7	+	1.79096e8i	0.173772	+	0.985510i	0.939552	+	0.342407i	$0.111242\pi$
$229$	3.15794e7	+	1.79096e8i	0.173772	+	0.985510i	−0.765780	+	0.643103i	$0.777647\pi$
$230$	7.50035e7	−	1.29910e8i	0.406475	−	0.704035i
$231$	−7.96774e7	−	6.68573e7i	−0.425298	−	0.356867i
$232$	1.95159e7	+	3.38026e7i	0.102608	+	0.177722i
$233$	−1.62629e8	+	2.81682e8i	−0.842272	+	1.45886i	0.0456969	+	0.998955i	$0.485449\pi$
$233$	−1.62629e8	+	2.81682e8i	−0.842272	+	1.45886i	−0.887969	+	0.459903i	$0.847884\pi$
$234$	−2.49213e8	+	9.07062e7i	−1.27150	+	0.462787i
$235$	−4.69128e7	+	3.93645e7i	−0.235806	+	0.197864i
$236$	−9.74472e7	−	1.68784e8i	−0.482589	−	0.835869i
$237$	−1.93574e7	+	1.09781e8i	−0.0944558	+	0.535685i
$238$	−4.99759e6	+	2.83427e7i	−0.0240293	+	0.136277i
$239$	−1.86275e8	−	1.56303e8i	−0.882595	−	0.740585i	0.0841163	−	0.996456i	$-0.473193\pi$
$239$	−1.86275e8	−	1.56303e8i	−0.882595	−	0.740585i	−0.966711	+	0.255871i	$0.917638\pi$
$240$	−6.07715e7	−	2.21190e7i	−0.283766	−	0.103282i
$241$	−3.73691e7	−	1.36012e7i	−0.171970	−	0.0625920i	0.254600	−	0.967046i	$-0.418056\pi$
$241$	−3.73691e7	−	1.36012e7i	−0.171970	−	0.0625920i	−0.426570	+	0.904454i	$0.640278\pi$
$242$	1.61255e8	+	1.35309e8i	0.731406	+	0.613722i
$243$	5.56994e7	−	3.15887e8i	0.249017	−	1.41224i
$244$	7.16287e7	−	4.06227e8i	0.315662	−	1.79021i
$245$	3.48795e7	+	6.04130e7i	0.151527	+	0.262452i
$246$	−6.20123e8	+	5.20345e8i	−2.65586	+	2.22853i
$247$	1.14171e8	−	4.15548e7i	0.482077	−	0.175462i
$248$	−1.95487e7	+	3.38593e7i	−0.0813836	+	0.140961i
$249$	−1.79403e8	−	3.10735e8i	−0.736429	−	1.27553i
$250$	2.51022e8	+	2.10633e8i	1.01607	+	0.852580i
$251$	2.20684e7	−	3.82236e7i	0.0880873	−	0.152572i	−0.818615	−	0.574342i	$-0.805258\pi$
$251$	2.20684e7	−	3.82236e7i	0.0880873	−	0.152572i	0.906703	+	0.421771i	$0.138591\pi$
$252$	−4.33787e7	−	2.46013e8i	−0.170756	−	0.968403i
$253$	−1.72884e8			−0.671172
$254$	4.78980e7	+	2.71643e8i	0.183400	+	1.04011i
$255$	2.09586e7	−	1.75863e7i	0.0791537	−	0.0664179i
$256$	5.51192e7	+	2.00618e7i	0.205335	+	0.0747359i
$257$	2.77344e8	−	1.00945e8i	1.01919	−	0.370953i	0.222232	−	0.974994i	$-0.428666\pi$
$257$	2.77344e8	−	1.00945e8i	1.01919	−	0.370953i	0.796954	+	0.604040i	$0.206443\pi$
$258$	−1.16192e9			−4.21220
$259$	−5.81899e7	−	1.60802e8i	−0.208113	−	0.575098i
$260$	−1.47459e8			−0.520313
$261$	−1.00020e8	+	3.64043e7i	−0.348213	+	0.126739i
$262$	4.19137e8	+	1.52553e8i	1.43980	+	0.524043i
$263$	−1.76857e8	+	1.48400e8i	−0.599482	+	0.503025i	−0.891279	−	0.453455i	$-0.850191\pi$
$263$	−1.76857e8	+	1.48400e8i	−0.599482	+	0.503025i	0.291797	+	0.956480i	$0.405747\pi$
$264$	−2.98095e7	−	1.69058e8i	−0.0997105	−	0.565486i
$265$	−1.64980e8			−0.544591
$266$	3.39906e7	+	1.92770e8i	0.110732	+	0.627992i
$267$	3.07620e8	−	5.32814e8i	0.989067	−	1.71311i
$268$	2.92220e8	+	2.45202e8i	0.927339	+	0.778130i
$269$	1.13299e8	+	1.96239e8i	0.354888	+	0.614684i	0.987099	−	0.160112i	$-0.0511856\pi$
$269$	1.13299e8	+	1.96239e8i	0.354888	+	0.614684i	−0.632211	+	0.774797i	$0.717852\pi$
$270$	−2.52846e7	+	4.37942e7i	−0.0781777	+	0.135408i
$271$	−3.85368e8	+	1.40263e8i	−1.17621	+	0.428104i	−0.854861	−	0.518858i	$-0.826357\pi$
$271$	−3.85368e8	+	1.40263e8i	−1.17621	+	0.428104i	−0.321346	+	0.946962i	$0.604135\pi$
$272$	1.57987e7	−	1.32567e7i	0.0476025	−	0.0399433i
$273$	1.14874e8	+	1.98968e8i	0.341707	+	0.591853i
$274$	−1.19485e8	+	6.77633e8i	−0.350902	+	1.99007i
$275$	2.84369e7	−	1.61274e8i	0.0824552	−	0.467627i
$276$	−5.96557e8	−	5.00571e8i	−1.70793	−	1.43312i
$277$	4.45634e8	+	1.62198e8i	1.25979	+	0.458527i	0.883700	−	0.468055i	$-0.155045\pi$
$277$	4.45634e8	+	1.62198e8i	1.25979	+	0.458527i	0.376093	+	0.926582i	$0.377267\pi$
$278$	−4.91956e8	−	1.79057e8i	−1.37331	−	0.499845i
$279$	−8.16739e7	−	6.85326e7i	−0.225148	−	0.188922i
$280$	1.19470e7	−	6.77550e7i	0.0325242	−	0.184454i
$281$	−6.60210e7	+	3.74423e8i	−0.177505	+	1.00668i	0.757708	+	0.652593i	$0.226319\pi$
$281$	−6.60210e7	+	3.74423e8i	−0.177505	+	1.00668i	−0.935213	+	0.354086i	$0.884792\pi$
$282$	2.71889e8	+	4.70926e8i	0.721972	+	1.25049i
$283$	−3.47282e8	+	2.91404e8i	−0.910814	+	0.764263i	−0.972274	−	0.233846i	$-0.924869\pi$
$283$	−3.47282e8	+	2.91404e8i	−0.910814	+	0.764263i	0.0614599	+	0.998110i	$0.480424\pi$
$284$	9.26860e8	−	3.37349e8i	2.40104	−	0.873908i
$285$	9.30414e7	−	1.61152e8i	0.238078	−	0.412363i
$286$	1.45339e8	+	2.51735e8i	0.367369	+	0.636301i
$287$	2.86436e8	+	2.40348e8i	0.715222	+	0.600142i
$288$	−2.99539e8	+	5.18817e8i	−0.738890	+	1.27979i
$289$	−6.97395e7	−	3.95512e8i	−0.169956	−	0.963868i
$290$	−1.01224e8			−0.243720
$291$	−6.95376e7	−	3.94367e8i	−0.165422	−	0.938157i
$292$	7.05823e8	−	5.92256e8i	1.65904	−	1.39210i
$293$	−2.13248e8	−	7.76160e7i	−0.495278	−	0.180266i	0.0822910	−	0.996608i	$-0.473776\pi$
$293$	−2.13248e8	−	7.76160e7i	−0.495278	−	0.180266i	−0.577569	+	0.816342i	$0.695999\pi$
$294$	5.82063e8	−	2.11854e8i	1.33584	−	0.486206i
$295$	1.46374e8			0.331961
$296$	9.70225e7	−	2.65038e8i	0.217446	−	0.594001i
$297$	5.82814e7			0.129087
$298$	5.92973e8	−	2.15825e8i	1.29801	−	0.472437i
$299$	3.58850e8	+	1.30611e8i	0.776361	+	0.282572i
$300$	5.65079e8	−	4.74157e8i	1.20833	−	1.01391i
$301$	9.31962e7	+	5.28542e8i	0.196977	+	1.11711i
$302$	−3.43941e8			−0.718555
$303$	−5.11761e7	−	2.90234e8i	−0.105686	−	0.599376i
$304$	7.01351e7	−	1.21477e8i	0.143178	−	0.247992i
$305$	2.37321e8	+	1.99136e8i	0.478946	+	0.401883i
$306$	−6.47657e7	−	1.12177e8i	−0.129217	−	0.223811i
$307$	2.27196e8	−	3.93515e8i	0.448143	−	0.776206i	−0.550122	−	0.835084i	$-0.685419\pi$
$307$	2.27196e8	−	3.93515e8i	0.448143	−	0.776206i	0.998265	+	0.0588779i	$0.0187523\pi$
$308$	−2.57288e8	+	9.36453e7i	−0.501756	+	0.182624i
$309$	2.79097e7	−	2.34190e7i	0.0538146	−	0.0451558i
$310$	−5.06971e7	−	8.78099e7i	−0.0966533	−	0.167409i
$311$	−1.97636e7	+	1.12085e8i	−0.0372568	+	0.211294i	−0.997753	−	0.0669992i	$-0.978657\pi$
$311$	−1.97636e7	+	1.12085e8i	−0.0372568	+	0.211294i	0.960496	+	0.278293i	$0.0897686\pi$
$312$	−6.58455e7	+	3.73428e8i	−0.122740	+	0.696091i
$313$	−7.29151e8	−	6.11830e8i	−1.34404	−	1.12778i	−0.980568	−	0.196178i	$-0.937147\pi$
$313$	−7.29151e8	−	6.11830e8i	−1.34404	−	1.12778i	−0.363472	−	0.931605i	$-0.618409\pi$
$314$	−9.07757e8	−	3.30396e8i	−1.65469	−	0.602257i
$315$	1.76302e8	+	6.41687e7i	0.317812	+	0.115674i
$316$	2.24794e8	+	1.88624e8i	0.400756	+	0.336274i
$317$	1.86888e8	−	1.05989e9i	0.329514	−	1.86877i	−0.146327	−	0.989236i	$-0.546745\pi$
$317$	1.86888e8	−	1.05989e9i	0.329514	−	1.86877i	0.475841	−	0.879531i	$-0.342144\pi$
$318$	−2.54382e8	+	1.44267e9i	−0.443600	+	2.51578i
$319$	5.83310e7	+	1.01032e8i	0.100608	+	0.174258i
$320$	−3.43791e8	+	2.88475e8i	−0.586502	+	0.492134i
$321$	−1.17735e8	+	4.28519e7i	−0.198672	+	0.0723108i
$322$	−3.07621e8	+	5.32815e8i	−0.513476	+	0.889366i
$323$	2.96708e7	+	5.13913e7i	0.0489915	+	0.0848557i
$324$	−5.52947e8	−	4.63977e8i	−0.903183	−	0.757861i
$325$	−1.80865e8	+	3.13267e8i	−0.292255	+	0.506200i
$326$	−1.54424e8	−	8.75783e8i	−0.246862	−	1.40002i
$327$	1.94650e8			0.307848
$328$	1.07164e8	+	6.07755e8i	0.167683	+	0.950976i
$329$	1.92409e8	−	1.61450e8i	0.297879	−	0.249950i
$330$	4.18346e8	+	1.52265e8i	0.640821	+	0.233240i
$331$	3.42221e8	−	1.24558e8i	0.518692	−	0.188788i	−0.0693905	−	0.997590i	$-0.522105\pi$
$331$	3.42221e8	−	1.24558e8i	0.518692	−	0.188788i	0.588082	+	0.808801i	$0.299883\pi$
$332$	−9.44521e8			−1.41654
$333$	6.65829e8	+	3.86063e8i	0.988117	+	0.572933i
$334$	8.76303e8			1.28689
$335$	−2.69220e8	+	9.79880e7i	−0.391246	+	0.142402i
$336$	2.49249e8	+	9.07193e7i	0.358465	+	0.130470i
$337$	−5.00853e8	+	4.20266e8i	−0.712863	+	0.598163i	−0.925401	−	0.378990i	$-0.876271\pi$
$337$	−5.00853e8	+	4.20266e8i	−0.712863	+	0.598163i	0.212538	+	0.977153i	$0.431827\pi$
$338$	7.97881e7	+	4.52501e8i	0.112391	+	0.637399i
$339$	8.20162e8			1.14341
$340$	−1.25064e7	−	7.09272e7i	−0.0172566	−	0.0978670i
$341$	−5.84288e7	+	1.01202e8i	−0.0797970	+	0.138213i
$342$	−6.74881e8	−	5.66292e8i	−0.912296	−	0.765507i
$343$	−3.71596e8	−	6.43623e8i	−0.497212	−	0.861196i
$344$	−4.42895e8	+	7.67117e8i	−0.586606	+	1.01603i
$345$	5.49603e8	−	2.00039e8i	0.720580	−	0.262270i
$346$	9.12691e8	−	7.65838e8i	1.18456	−	0.993964i
$347$	−284749.	−	493200.i	−0.000365855	−	0.000633680i	0.865842	−	0.500317i	$-0.166783\pi$
$347$	−284749.	−	493200.i	−0.000365855	−	0.000633680i	−0.866208	+	0.499683i	$0.833450\pi$
$348$	−9.12519e7	+	5.17515e8i	−0.116069	+	0.658258i
$349$	−2.15734e8	+	1.22349e9i	−0.271663	+	1.54068i	0.477703	+	0.878521i	$0.341469\pi$
$349$	−2.15734e8	+	1.22349e9i	−0.271663	+	1.54068i	−0.749366	+	0.662156i	$0.769642\pi$
$350$	−4.46433e8	−	3.74602e8i	−0.556568	−	0.467016i
$351$	−1.20973e8	−	4.40305e7i	−0.149318	−	0.0543473i
$352$	6.17017e8	+	2.24576e8i	0.754046	+	0.274450i
$353$	−8.36067e8	−	7.01544e8i	−1.01165	−	0.848874i	−0.0230936	−	0.999733i	$-0.507352\pi$
$353$	−8.36067e8	−	7.01544e8i	−1.01165	−	0.848874i	−0.988555	+	0.150859i	$0.951796\pi$
$354$	2.25694e8	−	1.27997e9i	0.270401	−	1.53352i
$355$	−1.28636e8	+	7.29533e8i	−0.152603	+	0.865457i
$356$	−8.09782e8	−	1.40258e9i	−0.951246	−	1.64761i
$357$	−8.59600e7	+	7.21290e7i	−0.0999902	+	0.0839017i
$358$	−1.75898e9	+	6.40217e8i	−2.02615	+	0.737457i
$359$	5.09662e8	−	8.82760e8i	0.581368	−	1.00696i	−0.413949	−	0.910300i	$-0.635851\pi$
$359$	5.09662e8	−	8.82760e8i	0.581368	−	1.00696i	0.995318	−	0.0966595i	$-0.0308158\pi$
$360$	1.54826e8	+	2.68167e8i	0.174899	+	0.302933i
$361$	−3.75566e8	−	3.15137e8i	−0.420156	−	0.352553i
$362$	5.71748e7	−	9.90297e7i	0.0633468	−	0.109720i
$363$	1.42522e8	+	8.08280e8i	0.156389	+	0.886928i
$364$	6.04791e8			0.657280
$365$	1.20165e8	+	6.81488e8i	0.129346	+	0.733556i
$366$	2.10727e9	−	1.76821e9i	2.24666	−	1.88517i
$367$	4.32865e8	+	1.57550e8i	0.457110	+	0.166374i	0.560304	−	0.828287i	$-0.310684\pi$
$367$	4.32865e8	+	1.57550e8i	0.457110	+	0.166374i	−0.103194	+	0.994661i	$0.532906\pi$
$368$	4.14294e8	−	1.50791e8i	0.433352	−	0.157727i
$369$	−1.68290e9			−1.74368
$370$	4.69449e8	+	5.61577e8i	0.481817	+	0.576372i
$371$	6.76652e8			0.687950
$372$	−4.94636e8	+	1.80033e8i	−0.498179	+	0.181322i
$373$	1.60216e9	+	5.83138e8i	1.59854	+	0.581822i	0.979129	−	0.203241i	$-0.0651475\pi$
$373$	1.60216e9	+	5.83138e8i	1.59854	+	0.581822i	0.619415	+	0.785064i	$0.287370\pi$
$374$	−1.08757e8	+	9.12579e7i	−0.107499	+	0.0902027i
$375$	2.21861e8	+	1.25823e9i	0.217256	+	1.23212i
$376$	4.14548e8			0.402177
$377$	−4.47477e7	−	2.53777e8i	−0.0430106	−	0.243925i
$378$	1.03703e8	−	1.79618e8i	0.0987572	−	0.171052i
$379$	−1.03878e9	−	8.71641e8i	−0.980137	−	0.822432i	0.00397317	−	0.999992i	$-0.498735\pi$
$379$	−1.03878e9	−	8.71641e8i	−0.980137	−	0.822432i	−0.984110	+	0.177560i	$0.943180\pi$
$380$	−2.44923e8	−	4.24219e8i	−0.228974	−	0.396595i
$381$	−5.37736e8	+	9.31386e8i	−0.498117	+	0.862765i
$382$	−5.65580e7	+	2.05854e7i	−0.0519125	+	0.0188946i
$383$	−8.52088e8	+	7.14987e8i	−0.774977	+	0.650283i	−0.941978	−	0.335674i	$-0.891036\pi$
$383$	−8.52088e8	+	7.14987e8i	−0.774977	+	0.650283i	0.167002	+	0.985957i	$0.446592\pi$
$384$	9.41911e8	+	1.63144e9i	0.848889	+	1.47032i
$385$	3.57083e7	−	2.02512e8i	0.0318902	−	0.180858i
$386$	−3.34558e8	+	1.89737e9i	−0.296085	+	1.67918i
$387$	−1.85040e9	−	1.55267e9i	−1.62285	−	1.36173i
$388$	−9.90577e8	−	3.60541e8i	−0.860949	−	0.313360i
$389$	1.37303e9	+	4.99741e8i	1.18265	+	0.430449i	0.857136	−	0.515089i	$-0.172241\pi$
$389$	1.37303e9	+	4.99741e8i	1.18265	+	0.430449i	0.325512	+	0.945538i	$0.394463\pi$
$390$	−7.53312e8	−	6.32104e8i	−0.643056	−	0.539588i
$391$	−3.23882e7	+	1.83683e8i	−0.0274011	+	0.155399i
$392$	8.19988e7	−	4.65038e8i	0.0687553	−	0.389931i
$393$	8.69545e8	+	1.50610e9i	0.722633	+	1.25164i
$394$	9.34040e8	−	7.83753e8i	0.769359	−	0.645569i
$395$	−2.07101e8	+	7.53785e7i	−0.169080	+	0.0615400i
$396$	6.16154e8	−	1.06721e9i	0.498604	−	0.863608i
$397$	−5.37580e8	−	9.31116e8i	−0.431198	−	0.746857i	0.565779	−	0.824557i	$-0.308576\pi$
$397$	−5.37580e8	−	9.31116e8i	−0.431198	−	0.746857i	−0.996977	+	0.0777004i	$0.975242\pi$
$398$	−2.27412e9	−	1.90821e9i	−1.80810	−	1.51718i
$399$	−3.81602e8	+	6.60953e8i	−0.300750	+	0.520914i
$400$	7.25186e7	+	4.11273e8i	0.0566551	+	0.321307i
$401$	3.31623e8			0.256826			0.128413	−	0.991721i	$-0.459012\pi$
$401$	3.31623e8			0.256826			0.128413	+	0.991721i	$0.459012\pi$
$402$	4.41749e8	+	2.50529e9i	0.339145	+	1.92338i
$403$	1.97734e8	−	1.65919e8i	0.150492	−	0.126278i
$404$	−7.29014e8	−	2.65339e8i	−0.550048	−	0.200201i
$405$	5.09425e8	−	1.85416e8i	0.381055	−	0.138693i
$406$	4.15163e8			0.307877
$407$	2.89989e8	−	7.92169e8i	0.213207	−	0.582421i
$408$	−1.85202e8			−0.135000
$409$	−2.11382e9	+	7.69367e8i	−1.52769	+	0.556035i	−0.963055	−	0.269305i	$-0.913206\pi$
$409$	−2.11382e9	+	7.69367e8i	−1.52769	+	0.556035i	−0.564637	+	0.825339i	$0.690984\pi$
$410$	−1.50393e9	−	5.47386e8i	−1.07767	−	0.392238i
$411$	−2.05518e9	+	1.72450e9i	−1.46017	+	1.22523i
$412$	−1.66542e7	−	9.44507e7i	−0.0117323	−	0.0665373i
$413$	−6.00342e8			−0.419347
$414$	−4.80840e8	−	2.72698e9i	−0.333042	−	1.88878i
$415$	3.54688e8	−	6.14338e8i	0.243601	−	0.421929i
$416$	−1.11106e9	−	9.32288e8i	−0.756676	−	0.634926i
$417$	−1.02062e9	−	1.76776e9i	−0.689265	−	1.19384i
$418$	−4.82804e8	+	8.36241e8i	−0.323336	+	0.560034i
$419$	5.50298e8	−	2.00292e8i	0.365467	−	0.133019i	−0.152757	−	0.988264i	$-0.548815\pi$
$419$	5.50298e8	−	2.00292e8i	0.365467	−	0.133019i	0.518225	+	0.855245i	$0.326593\pi$
$420$	7.09571e8	−	5.95401e8i	0.467330	−	0.392136i
$421$	−5.08564e8	−	8.80859e8i	−0.332169	−	0.575333i	0.650768	−	0.759276i	$-0.274447\pi$
$421$	−5.08564e8	−	8.80859e8i	−0.332169	−	0.575333i	−0.982937	+	0.183944i	$0.941114\pi$
$422$	−5.52730e8	+	3.13469e9i	−0.358030	+	2.03049i
$423$	−1.96303e8	+	1.11329e9i	−0.126106	+	0.715182i
$424$	8.55505e8	+	7.17854e8i	0.545057	+	0.457357i
$425$	−1.66020e8	−	6.04262e7i	−0.104905	−	0.0381824i
$426$	6.18107e9	+	2.24973e9i	3.87374	+	1.40992i
$427$	−9.73353e8	−	8.16740e8i	−0.605024	−	0.507676i
$428$	−5.72720e7	+	3.24805e8i	−0.0353093	+	0.200249i
$429$	−1.96805e8	+	1.11613e9i	−0.120347	+	0.682521i
$430$	−1.14859e9	−	1.98942e9i	−0.696669	−	1.20667i
$431$	1.96591e9	−	1.64960e9i	1.18275	−	0.992447i	0.182795	−	0.983151i	$-0.441485\pi$
$431$	1.96591e9	−	1.64960e9i	1.18275	−	0.992447i	0.999957	−	0.00929581i	$-0.00295899\pi$
$432$	−1.39663e8	+	5.08334e7i	−0.0833470	+	0.0303358i
$433$	1.38437e9	−	2.39781e9i	0.819494	−	1.41941i	−0.0865617	−	0.996246i	$-0.527588\pi$
$433$	1.38437e9	−	2.39781e9i	0.819494	−	1.41941i	0.906056	−	0.423159i	$-0.139079\pi$
$434$	2.07930e8	+	3.60145e8i	0.122096	+	0.211477i
$435$	−3.02337e8	−	2.53691e8i	−0.176108	−	0.147772i
$436$	2.56198e8	−	4.43749e8i	0.148038	−	0.256410i
$437$	2.20285e8	+	1.24930e9i	0.126270	+	0.716112i
$438$	6.14457e9			3.49407
$439$	−2.95363e7	−	1.67509e8i	−0.0166621	−	0.0944957i	0.975343	−	0.220696i	$-0.0708329\pi$
$439$	−2.95363e7	−	1.67509e8i	−0.0166621	−	0.0944957i	−0.992005	+	0.126200i	$0.959722\pi$
$440$	2.59990e8	−	2.18157e8i	0.145503	−	0.122092i
$441$	1.21005e9	+	4.40424e8i	0.671846	+	0.244532i
$442$	2.94686e8	−	1.07257e8i	0.162324	−	0.0590810i
$443$	2.66594e9			1.45693			0.728464	−	0.685084i	$-0.240235\pi$
$443$	2.66594e9			1.45693			0.728464	+	0.685084i	$0.240235\pi$
$444$	3.29430e9	−	1.89383e9i	1.78617	−	1.02684i
$445$	1.21636e9			0.654339
$446$	−2.21676e9	+	8.06833e8i	−1.18317	+	0.430637i
$447$	2.31200e9	+	8.41498e8i	1.22436	+	0.445632i
$448$	1.41003e9	−	1.18316e9i	0.740893	−	0.621683i
$449$	2.49246e8	+	1.41355e9i	0.129947	+	0.736966i	0.978246	+	0.207449i	$0.0665160\pi$
$449$	2.49246e8	+	1.41355e9i	0.129947	+	0.736966i	−0.848299	+	0.529518i	$0.822373\pi$
$450$	2.62293e9			1.35689
$451$	3.20300e8	+	1.81651e9i	0.164414	+	0.932438i
$452$	1.07950e9	−	1.86975e9i	0.549842	−	0.952355i
$453$	−1.02728e9	−	8.61993e8i	−0.519214	−	0.435673i
$454$	−1.72426e9	−	2.98651e9i	−0.864785	−	1.49785i
$455$	−2.27112e8	+	3.93370e8i	−0.113032	+	0.195777i
$456$	−1.18367e9	+	4.30819e8i	−0.584591	+	0.212774i
$457$	−1.88876e9	+	1.58486e9i	−0.925701	+	0.776755i	−0.975041	−	0.222027i	$-0.928733\pi$
$457$	−1.88876e9	+	1.58486e9i	−0.925701	+	0.776755i	0.0493395	+	0.998782i	$0.484288\pi$
$458$	1.59627e9	+	2.76482e9i	0.776385	+	1.34474i
$459$	1.09185e7	−	6.19217e7i	0.00527008	−	0.0298881i
$460$	2.67354e8	−	1.51624e9i	0.128066	−	0.726299i
$461$	6.91941e8	+	5.80607e8i	0.328939	+	0.276013i	0.792267	−	0.610174i	$-0.208900\pi$
$461$	6.91941e8	+	5.80607e8i	0.328939	+	0.276013i	−0.463328	+	0.886187i	$0.653345\pi$
$462$	−1.71581e9	−	6.24504e8i	−0.809511	−	0.294638i
$463$	−2.97424e9	−	1.08253e9i	−1.39265	−	0.506883i	−0.466662	−	0.884436i	$-0.654544\pi$
$463$	−2.97424e9	−	1.08253e9i	−1.39265	−	0.506883i	−0.925988	+	0.377552i	$0.876766\pi$
$464$	−2.27903e8	−	1.91233e8i	−0.105910	−	0.0888690i
$465$	6.86491e7	−	3.89329e8i	0.0316628	−	0.179569i
$466$	−9.91519e8	+	5.62318e9i	−0.453890	+	2.57414i
$467$	−6.12382e8	−	1.06068e9i	−0.278236	−	0.481919i	0.692711	−	0.721216i	$-0.256416\pi$
$467$	−6.12382e8	−	1.06068e9i	−0.278236	−	0.481919i	−0.970946	+	0.239297i	$0.923083\pi$
$468$	−2.08518e9	+	1.74968e9i	−0.940338	+	0.789037i
$469$	1.10418e9	−	4.01890e8i	0.494238	−	0.179888i
$470$	−5.37539e8	+	9.31045e8i	−0.238818	+	0.413645i
$471$	−1.88324e9	−	3.26187e9i	−0.830486	−	1.43844i
$472$	−7.59025e8	−	6.36897e8i	−0.332245	−	0.278787i
$473$	−1.32376e9	+	2.29283e9i	−0.575170	+	0.996224i
$474$	3.39821e8	+	1.92722e9i	0.146564	+	0.831204i
$475$	−1.20163e9			−0.514451
$476$	5.12939e7	+	2.90902e8i	0.0217992	+	0.123630i
$477$	−2.33294e9	+	1.95757e9i	−0.984215	+	0.825855i
$478$	−4.01133e9	−	1.46000e9i	−1.67993	−	0.611444i
$479$	2.43759e9	−	8.87210e8i	1.01341	−	0.368852i	0.218670	−	0.975799i	$-0.429828\pi$
$479$	2.43759e9	−	8.87210e8i	1.01341	−	0.368852i	0.794742	+	0.606947i	$0.207606\pi$
$480$	−2.22136e9			−0.916800
$481$	−1.20039e9	+	1.42520e9i	−0.491829	+	0.583938i
$482$	−6.98119e8			−0.283965
$483$	−2.25415e9	+	8.20445e8i	−0.910266	+	0.331310i
$484$	2.03025e9	+	7.38950e8i	0.813936	+	0.296248i
$485$	6.06487e8	−	5.08903e8i	0.241393	−	0.202553i
$486$	−9.77806e8	−	5.54542e9i	−0.386390	−	2.19133i
$487$	5.91998e8			0.232257			0.116128	−	0.993234i	$-0.462952\pi$
$487$	5.91998e8			0.232257			0.116128	+	0.993234i	$0.462952\pi$
$488$	−3.64158e8	−	2.06524e9i	−0.141847	−	0.804455i
$489$	1.73367e9	−	3.00281e9i	0.670481	−	1.16131i
$490$	9.38116e8	+	7.87173e8i	0.360222	+	0.302262i
$491$	−1.02182e9	−	1.76984e9i	−0.389572	−	0.674758i	0.602820	−	0.797877i	$-0.294044\pi$
$491$	−1.02182e9	−	1.76984e9i	−0.389572	−	0.674758i	−0.992392	+	0.123119i	$0.960710\pi$
$492$	−4.15431e9	+	7.19547e9i	−1.57261	+	2.72384i
$493$	1.18270e8	−	4.30469e7i	0.0444541	−	0.0161800i
$494$	1.63390e9	−	1.37101e9i	0.609792	−	0.511676i
$495$	4.62758e8	+	8.01521e8i	0.171489	+	0.297028i
$496$	5.17481e7	−	2.93478e8i	0.0190418	−	0.107992i
$497$	5.27591e8	−	2.99212e9i	0.192775	−	1.09328i
$498$	−4.82520e9	−	4.04882e9i	−1.75070	−	1.46901i
$499$	−1.69626e9	−	6.17389e8i	−0.611141	−	0.222437i	0.0178617	−	0.999840i	$-0.494314\pi$
$499$	−1.69626e9	−	6.17389e8i	−0.611141	−	0.222437i	−0.629002	+	0.777403i	$0.716536\pi$
$500$	3.16045e9	+	1.15031e9i	1.13072	+	0.411547i
$501$	2.61734e9	+	2.19621e9i	0.929884	+	0.780265i
$502$	1.34547e8	−	7.63054e8i	0.0474691	−	0.269211i
$503$	−6.52125e8	+	3.69839e9i	−0.228477	+	1.29576i	0.627447	+	0.778659i	$0.284100\pi$
$503$	−6.52125e8	+	3.69839e9i	−0.228477	+	1.29576i	−0.855925	+	0.517100i	$0.827011\pi$
$504$	−6.35008e8	−	1.09987e9i	−0.220939	−	0.382677i
$505$	4.46343e8	−	3.74526e8i	0.154223	−	0.129408i
$506$	−2.85196e9	+	1.03803e9i	−0.978627	+	0.356191i
$507$	−8.95757e8	+	1.55150e9i	−0.305255	+	0.528717i
$508$	1.41554e9	+	2.45179e9i	0.479070	+	0.829774i
$509$	3.20798e9	+	2.69182e9i	1.07825	+	0.904760i	0.995774	−	0.0918333i	$-0.0292727\pi$
$509$	3.20798e9	+	2.69182e9i	1.07825	+	0.904760i	0.0824763	+	0.996593i	$0.473717\pi$
$510$	2.40149e8	−	4.15950e8i	0.0801650	−	0.138850i
$511$	−4.92846e8	−	2.79507e9i	−0.163395	−	0.926658i
$512$	−2.49314e9			−0.820921
$513$	−7.42608e7	−	4.21154e8i	−0.0242856	−	0.137730i
$514$	3.96908e9	−	3.33046e9i	1.28920	−	1.08176i
$515$	6.76869e7	+	2.46360e7i	0.0218363	+	0.00794777i
$516$	−1.12065e10	+	4.07882e9i	−3.59083	+	1.30696i
$517$	1.23904e9			0.394337
$518$	−1.92541e9	−	2.30326e9i	−0.608651	−	0.728097i
$519$	4.64539e9			1.45860
$520$	−7.04466e8	+	2.56404e8i	−0.219709	+	0.0799676i
$521$	4.02777e9	+	1.46599e9i	1.24776	+	0.454149i	0.879645	−	0.475630i	$-0.157780\pi$
$521$	4.02777e9	+	1.46599e9i	1.24776	+	0.454149i	0.368118	+	0.929779i	$0.380002\pi$
$522$	−1.43139e9	+	1.20108e9i	−0.440465	+	0.369594i
$523$	2.07025e8	+	1.17410e9i	0.0632801	+	0.358879i	0.999962	+	0.00869833i	$0.00276880\pi$
$523$	2.07025e8	+	1.17410e9i	0.0632801	+	0.358879i	−0.936682	+	0.350181i	$0.886120\pi$
$524$	4.57799e9			1.39000
$525$	−3.94570e8	−	2.23772e9i	−0.119005	−	0.674913i
$526$	−2.02647e9	+	3.50995e9i	−0.607141	+	1.05160i
$527$	9.65767e7	+	8.10374e7i	0.0287432	+	0.0241184i
$528$	6.54230e8	+	1.13316e9i	0.193425	+	0.335021i
$529$	−2.91205e8	+	5.04382e8i	−0.0855272	+	0.148137i
$530$	−2.72157e9	+	9.90571e8i	−0.794061	+	0.289015i
$531$	2.06984e9	−	1.73681e9i	0.599939	−	0.503408i
$532$	1.00453e9	+	1.73990e9i	0.289249	+	0.500995i
$533$	7.07502e8	−	4.01244e9i	0.202387	−	1.14779i
$534$	1.87550e9	−	1.06365e10i	0.532995	−	3.02277i
$535$	−1.89754e8	−	1.59223e8i	−0.0535738	−	0.0449538i
$536$	1.82240e9	+	6.63301e8i	0.511173	+	0.186052i
$537$	−6.85825e9	−	2.49620e9i	−1.91119	−	0.695616i
$538$	3.04727e9	+	2.55696e9i	0.843671	+	0.707924i
$539$	2.45085e8	−	1.38995e9i	0.0674150	−	0.382329i
$540$	−9.01283e7	+	5.11143e8i	−0.0246311	+	0.139690i
$541$	3.96648e8	+	6.87014e8i	0.107700	+	0.186542i	0.914838	−	0.403821i	$-0.132318\pi$
$541$	3.96648e8	+	6.87014e8i	0.107700	+	0.186542i	−0.807138	+	0.590362i	$0.798985\pi$
$542$	−5.51502e9	+	4.62765e9i	−1.48782	+	1.24843i
$543$	4.18960e8	−	1.52489e8i	0.112298	−	0.0408733i
$544$	3.54195e8	−	6.13483e8i	0.0943292	−	0.163383i
$545$	1.92416e8	+	3.33275e8i	0.0509159	+	0.0881890i
$546$	3.08965e9	+	2.59252e9i	0.812334	+	0.681629i
$547$	2.50034e9	−	4.33072e9i	0.653197	−	1.13137i	−0.329146	−	0.944279i	$-0.606761\pi$
$547$	2.50034e9	−	4.33072e9i	0.653197	−	1.13137i	0.982343	−	0.187091i	$-0.0599059\pi$
$548$	1.22636e9	+	6.95504e9i	0.318336	+	1.80537i
$549$	5.71875e9			1.47502
$550$	−4.99212e8	−	2.83117e9i	−0.127943	−	0.725599i
$551$	6.55756e8	−	5.50244e8i	0.166998	−	0.140128i
$552$	−3.72037e9	−	1.35411e9i	−0.941456	−	0.342662i
$553$	8.49407e8	−	3.09159e8i	0.213588	−	0.0777398i
$554$	8.32521e9			2.08023
$555$	−5.28751e6	+	2.85386e9i	−0.00131288	+	0.708610i
$556$	−5.37336e9			−1.32582
$557$	2.43989e9	−	8.88047e8i	0.598242	−	0.217742i	−0.0251086	−	0.999685i	$-0.507993\pi$
$557$	2.43989e9	−	8.88047e8i	0.598242	−	0.217742i	0.623351	+	0.781942i	$0.285771\pi$
$558$	−1.75881e9	−	6.40153e8i	−0.428547	−	0.155978i
$559$	4.47987e9	−	3.75906e9i	1.08474	−	0.910202i
$560$	9.10618e7	+	5.16437e8i	0.0219118	+	0.124268i
$561$	−5.53548e8			−0.132369
$562$	1.15900e9	+	6.57303e9i	0.275427	+	1.56203i
$563$	2.67321e9	−	4.63013e9i	0.631326	−	1.09349i	−0.355955	−	0.934503i	$-0.615844\pi$
$563$	2.67321e9	−	4.63013e9i	0.631326	−	1.09349i	0.987281	−	0.158985i	$-0.0508222\pi$
$564$	4.27544e9	+	3.58752e9i	1.00347	+	0.842011i
$565$	8.10751e8	+	1.40426e9i	0.189112	+	0.327551i
$566$	−3.97924e9	+	6.89225e9i	−0.922451	+	1.59773i
$567$	−2.08937e9	+	7.60467e8i	−0.481364	+	0.175202i
$568$	3.84136e9	−	3.22328e9i	0.879560	−	0.738039i
$569$	−1.81273e9	−	3.13973e9i	−0.412514	−	0.714496i	0.582649	−	0.812724i	$-0.302016\pi$
$569$	−1.81273e9	−	3.13973e9i	−0.412514	−	0.714496i	−0.995164	+	0.0982275i	$0.968683\pi$
$570$	5.67256e8	−	3.21707e9i	0.128297	−	0.727609i
$571$	4.16205e8	−	2.36041e9i	0.0935579	−	0.530593i	−0.901622	−	0.432525i	$-0.857623\pi$
$571$	4.16205e8	−	2.36041e9i	0.0935579	−	0.530593i	0.995180	−	0.0980680i	$-0.0312663\pi$
$572$	2.28545e9	+	1.91772e9i	0.510606	+	0.428449i
$573$	−2.20519e8	−	8.02623e7i	−0.0489671	−	0.0178226i
$574$	6.16825e9	+	2.24506e9i	1.36135	+	0.495491i
$575$	−2.89323e9	−	2.42771e9i	−0.634666	−	0.532548i
$576$	−1.43857e9	+	8.15851e9i	−0.313654	+	1.77882i
$577$	−5.00448e8	+	2.83818e9i	−0.108454	+	0.615071i	0.881331	+	0.472500i	$0.156648\pi$
$577$	−5.00448e8	+	2.83818e9i	−0.108454	+	0.615071i	−0.989785	+	0.142571i	$0.954463\pi$
$578$	−3.52518e9	−	6.10579e9i	−0.759335	−	1.31521i
$579$	−5.75450e9	+	4.82860e9i	−1.23206	+	1.03382i
$580$	−9.76283e8	+	3.55338e8i	−0.207768	+	0.0756212i
$581$	−1.45473e9	+	2.51966e9i	−0.307726	+	0.532998i
$582$	−3.51497e9	−	6.08811e9i	−0.739080	−	1.28012i
$583$	2.55701e9	+	2.14558e9i	0.534432	+	0.448441i
$584$	2.34215e9	−	4.05672e9i	0.486597	−	0.842811i
$585$	−3.54998e8	−	2.01329e9i	−0.0733129	−	0.415778i
$586$	−3.98384e9			−0.817826
$587$	−8.58698e8	−	4.86992e9i	−0.175229	−	0.993776i	−0.937879	−	0.346963i	$-0.887213\pi$
$587$	−8.58698e8	−	4.86992e9i	−0.175229	−	0.993776i	0.762649	−	0.646812i	$-0.223898\pi$
$588$	4.87016e9	−	4.08655e9i	0.987922	−	0.828965i
$589$	8.05753e8	+	2.93270e8i	0.162479	+	0.0591377i
$590$	2.41464e9	−	8.78858e8i	0.484028	−	0.176172i
$591$	4.75405e9			0.947344
$592$	−3.98575e6	+	2.15125e9i	−0.000789559	+	0.426153i
$593$	−4.45258e9			−0.876841			−0.438420	−	0.898770i	$-0.644462\pi$
$593$	−4.45258e9			−0.876841			−0.438420	+	0.898770i	$0.644462\pi$
$594$	9.61432e8	−	3.49933e8i	0.188220	−	0.0685065i
$595$	−2.08471e8	−	7.58773e7i	−0.0405730	−	0.0147674i
$596$	4.96145e9	−	4.16315e9i	0.959945	−	0.805490i
$597$	−2.00993e9	−	1.13989e10i	−0.386609	−	2.19257i
$598$	6.70393e9			1.28196
$599$	1.22033e9	+	6.92081e9i	0.231997	+	1.31572i	0.848847	+	0.528638i	$0.177297\pi$
$599$	1.22033e9	+	6.92081e9i	0.231997	+	1.31572i	−0.616850	+	0.787080i	$0.711592\pi$
$600$	1.87511e9	−	3.24779e9i	0.354404	−	0.613845i
$601$	−4.66100e9	−	3.91105e9i	−0.875828	−	0.734907i	0.0894889	−	0.995988i	$-0.471477\pi$
$601$	−4.66100e9	−	3.91105e9i	−0.875828	−	0.734907i	−0.965317	+	0.261081i	$0.915921\pi$
$602$	4.71086e9	+	8.15945e9i	0.880061	+	1.52431i
$603$	−2.64430e9	+	4.58006e9i	−0.491134	+	0.850669i
$604$	−3.31723e9	+	1.20737e9i	−0.612556	+	0.222952i
$605$	−1.24303e9	+	1.04303e9i	−0.228212	+	0.191493i
$606$	−2.58684e9	−	4.48054e9i	−0.472188	−	0.817854i
$607$	−1.88222e9	+	1.06746e10i	−0.341593	+	1.93727i	0.00694589	+	0.999976i	$0.497789\pi$
$607$	−1.88222e9	+	1.06746e10i	−0.341593	+	1.93727i	−0.348539	+	0.937294i	$0.613322\pi$
$608$	8.36643e8	−	4.74484e9i	0.150966	−	0.856168i
$609$	1.24001e9	+	1.04049e9i	0.222466	+	0.186672i
$610$	5.11058e9	+	1.86010e9i	0.911625	+	0.331804i
$611$	−2.57183e9	−	9.36068e8i	−0.456139	−	0.166021i
$612$	−1.01844e9	−	8.54570e8i	−0.179599	−	0.150702i
$613$	−1.13912e9	+	6.46026e9i	−0.199736	+	1.13276i	0.705774	+	0.708437i	$0.250599\pi$
$613$	−1.13912e9	+	6.46026e9i	−0.199736	+	1.13276i	−0.905510	+	0.424324i	$0.860512\pi$
$614$	1.38517e9	−	7.85570e9i	0.241498	−	1.36961i
$615$	−3.12007e9	−	5.40412e9i	−0.540880	−	0.936832i
$616$	−1.06633e9	+	8.94755e8i	−0.183805	+	0.154231i
$617$	2.10745e9	−	7.67049e8i	0.361210	−	0.131470i	−0.155039	−	0.987908i	$-0.549550\pi$
$617$	2.10745e9	−	7.67049e8i	0.361210	−	0.131470i	0.516249	+	0.856439i	$0.327328\pi$
$618$	3.19796e8	−	5.53903e8i	0.0545022	−	0.0944005i
$619$	2.12680e9	+	3.68372e9i	0.360420	+	0.624266i	0.988030	−	0.154262i	$-0.0492999\pi$
$619$	2.12680e9	+	3.68372e9i	0.360420	+	0.624266i	−0.627610	+	0.778528i	$0.715967\pi$
$620$	−7.97208e8	−	6.68937e8i	−0.134339	−	0.112724i
$621$	6.72073e8	−	1.16406e9i	0.112615	−	0.195055i
$622$	3.46952e8	+	1.96766e9i	0.0578100	+	0.327857i
$623$	−4.98881e9			−0.826588
$624$	−5.01883e8	−	2.84632e9i	−0.0826906	−	0.468962i
$625$	1.64461e9	−	1.37999e9i	0.269453	−	0.226098i
$626$	−1.57019e10	−	5.71502e9i	−2.55824	−	0.931124i
$627$	−3.53784e9	+	1.28767e9i	−0.573195	+	0.208626i
$628$	−9.91491e9			−1.59746
$629$	−7.87321e8	−	4.56507e8i	−0.126146	−	0.0731426i
$630$	3.29362e9			0.524786
$631$	−5.62438e9	+	2.04711e9i	−0.891193	+	0.324368i	−0.746718	−	0.665141i	$-0.768371\pi$
$631$	−5.62438e9	+	2.04711e9i	−0.891193	+	0.324368i	−0.144475	+	0.989508i	$0.546149\pi$
$632$	1.40191e9	+	5.10252e8i	0.220907	+	0.0804035i
$633$	−9.50711e9	+	7.97741e9i	−1.48983	+	1.25011i
$634$	−3.28083e9	−	1.86065e10i	−0.511295	−	2.89970i
$635$	−2.12626e9			−0.329541
$636$	2.61091e9	+	1.48072e10i	0.402431	+	2.28230i
$637$	−1.55879e9	+	2.69991e9i	−0.238946	+	0.413867i
$638$	1.56887e9	+	1.31643e9i	0.239174	+	0.200690i
$639$	6.83727e9	+	1.18425e10i	1.03664	+	1.79552i
$640$	−1.86221e9	+	3.22544e9i	−0.280801	+	0.486361i
$641$	1.82991e9	−	6.66033e8i	0.274427	−	0.0998833i	−0.201141	−	0.979562i	$-0.564465\pi$
$641$	1.82991e9	−	6.66033e8i	0.274427	−	0.0998833i	0.475568	+	0.879679i	$0.342243\pi$
$642$	−1.68490e9	+	1.41380e9i	−0.251306	+	0.210871i
$643$	2.44433e9	+	4.23371e9i	0.362595	+	0.628033i	0.988387	−	0.151957i	$-0.0485575\pi$
$643$	2.44433e9	+	4.23371e9i	0.362595	+	0.628033i	−0.625792	+	0.779990i	$0.715224\pi$
$644$	−1.09653e9	+	6.21873e9i	−0.161778	+	0.917490i
$645$	1.55532e9	−	8.82063e9i	0.228223	−	1.29432i
$646$	7.98024e8	+	6.69621e8i	0.116467	+	0.0977272i
$647$	7.30226e9	+	2.65780e9i	1.05997	+	0.385796i	0.812416	−	0.583079i	$-0.198152\pi$
$647$	7.30226e9	+	2.65780e9i	1.05997	+	0.385796i	0.247551	+	0.968875i	$0.420374\pi$
$648$	−3.44840e9	−	1.25512e9i	−0.497858	−	0.181205i
$649$	−2.26864e9	−	1.90361e9i	−0.325768	−	0.273352i
$650$	−1.10270e9	+	6.25371e9i	−0.157492	+	0.893184i
$651$	−2.81559e8	+	1.59680e9i	−0.0399978	+	0.226839i
$652$	−4.56373e9	−	7.90462e9i	−0.644843	−	1.11690i
$653$	−7.08345e8	+	5.94372e8i	−0.0995516	+	0.0835337i	−0.691205	−	0.722659i	$-0.742920\pi$
$653$	−7.08345e8	+	5.94372e8i	−0.0995516	+	0.0835337i	0.591653	+	0.806192i	$0.298475\pi$
$654$	3.21101e9	−	1.16871e9i	0.448869	−	0.163375i
$655$	−1.71914e9	+	2.97763e9i	−0.239037	+	0.414025i
$656$	−2.35192e9	−	4.07365e9i	−0.325282	−	0.563404i
$657$	9.78543e9	+	8.21095e9i	1.34617	+	1.12957i
$658$	2.20467e9	−	3.81861e9i	0.301685	−	0.522534i
$659$	7.08084e8	+	4.01574e9i	0.0963798	+	0.546597i	0.994316	+	0.106471i	$0.0339551\pi$
$659$	7.08084e8	+	4.01574e9i	0.0963798	+	0.546597i	−0.897936	+	0.440126i	$0.854934\pi$
$660$	4.56935e9			0.618658
$661$	−9.51401e8	−	5.39566e9i	−0.128132	−	0.726674i	−0.979398	−	0.201939i	$-0.935276\pi$
$661$	−9.51401e8	−	5.39566e9i	−0.128132	−	0.726674i	0.851266	−	0.524735i	$-0.175835\pi$
$662$	4.89754e9	−	4.10952e9i	0.656107	−	0.550539i
$663$	1.14898e9	+	4.18194e8i	0.153114	+	0.0557289i
$664$	−4.51232e9	+	1.64235e9i	−0.598153	+	0.217710i
$665$	−1.50889e9			−0.198968
$666$	1.33018e10	+	2.37088e9i	1.74482	+	0.310992i
$667$	2.69058e9			0.351079
$668$	8.45173e9	−	3.07618e9i	1.09705	−	0.399295i
$669$	−8.64311e9	−	3.14583e9i	−1.11604	−	0.406204i
$670$	−3.85281e9	+	3.23289e9i	−0.494898	+	0.415269i
$671$	−1.08843e9	−	6.17277e9i	−0.139082	−	0.788772i
$672$	9.11073e9			1.15814
$673$	−1.65640e8	−	9.39388e8i	−0.0209465	−	0.118793i	0.972542	−	0.232729i	$-0.0747654\pi$
$673$	−1.65640e8	−	9.39388e8i	−0.0209465	−	0.118793i	−0.993488	+	0.113935i	$0.963654\pi$
$674$	−5.73891e9	+	9.94008e9i	−0.721971	+	1.25049i
$675$	9.75343e8	+	8.18410e8i	0.122066	+	0.102425i
$676$	2.35800e9	+	4.08417e9i	0.293582	+	0.508499i
$677$	2.27490e9	−	3.94023e9i	0.281774	−	0.488047i	−0.690048	−	0.723764i	$-0.742410\pi$
$677$	2.27490e9	−	3.94023e9i	0.281774	−	0.488047i	0.971822	+	0.235717i	$0.0757438\pi$
$678$	1.35297e10	−	4.92441e9i	1.66719	−	0.606806i
$679$	−2.48746e9	+	2.08722e9i	−0.304938	+	0.255873i
$680$	−1.83077e8	−	3.17099e8i	−0.0223281	−	0.0386735i
$681$	2.33483e9	−	1.32415e10i	0.283297	−	1.60665i
$682$	−3.56230e8	+	2.02028e9i	−0.0430016	+	0.243874i
$683$	9.23164e9	+	7.74627e9i	1.10868	+	0.930294i	0.997978	−	0.0635599i	$-0.0202454\pi$
$683$	9.23164e9	+	7.74627e9i	1.10868	+	0.930294i	0.110703	+	0.993854i	$0.464690\pi$
$684$	−8.49697e9	−	3.09264e9i	−1.01524	−	0.369516i
$685$	−4.98424e9	−	1.81411e9i	−0.592491	−	0.215649i
$686$	−9.99441e9	−	8.38631e9i	−1.18201	−	0.991828i
$687$	−2.16152e9	+	1.22586e10i	−0.254337	+	1.44242i
$688$	1.17240e9	−	6.64904e9i	0.137252	−	0.778394i
$689$	−3.68654e9	−	6.38528e9i	−0.429390	−	0.743726i
$690$	7.86538e9	−	6.59984e9i	0.911482	−	0.764824i
$691$	4.88957e9	−	1.77966e9i	0.563764	−	0.205193i	−0.0443871	−	0.999014i	$-0.514134\pi$
$691$	4.88957e9	−	1.77966e9i	0.563764	−	0.205193i	0.608152	+	0.793821i	$0.291911\pi$
$692$	6.11427e9	−	1.05902e10i	0.701412	−	1.21488i
$693$	−1.89797e9	−	3.28737e9i	−0.216632	−	0.375217i
$694$	−7.65859e6	−	6.42632e6i	−0.000869743	−	0.000729801i
$695$	2.01781e9	−	3.49495e9i	0.228000	−	0.394907i
$696$	4.63922e8	+	2.63103e9i	0.0521570	+	0.295797i
$697$	1.98997e9			0.222604
$698$	3.78723e9	+	2.14785e10i	0.421529	+	2.39061i
$699$	−1.70544e10	+	1.43104e10i	−1.88872	+	1.58482i
$700$	−5.62073e9	−	2.04578e9i	−0.619370	−	0.225432i
$701$	3.59308e9	−	1.30777e9i	0.393961	−	0.143390i	−0.137441	−	0.990510i	$-0.543888\pi$
$701$	3.59308e9	−	1.30777e9i	0.393961	−	0.143390i	0.531402	+	0.847120i	$0.321665\pi$
$702$	−2.25998e9			−0.246561
$703$	−6.09387e9	−	1.08616e9i	−0.661530	−	0.117910i
$704$	9.08003e9			0.980806
$705$	−3.93893e9	+	1.43365e9i	−0.423366	+	0.154093i
$706$	−1.80043e10	−	6.55302e9i	−1.92557	−	0.700850i
$707$	−1.83064e9	+	1.53609e9i	−0.194821	+	0.163474i
$708$	−2.31646e9	−	1.31373e10i	−0.245306	−	1.39120i
$709$	−1.76868e9			−0.186375			−0.0931873	−	0.995649i	$-0.529706\pi$
$709$	−1.76868e9			−0.186375			−0.0931873	+	0.995649i	$0.529706\pi$
$710$	2.25822e9	+	1.28070e10i	0.236789	+	1.34290i
$711$	−2.03416e9	+	3.52327e9i	−0.212247	+	0.367622i
$712$	−6.30746e9	−	5.29259e9i	−0.654899	−	0.549526i
$713$	1.34755e9	+	2.33402e9i	0.139229	+	0.241152i
$714$	−9.84951e8	+	1.70599e9i	−0.101268	+	0.175401i
$715$	−2.10557e9	+	7.66364e8i	−0.215426	+	0.0784086i
$716$	−1.47175e10	+	1.23495e10i	−1.49844	+	1.25734i
$717$	−8.32194e9	−	1.44140e10i	−0.843155	−	1.46039i
$718$	3.10731e9	−	1.76224e10i	0.313292	−	1.77677i
$719$	−2.62238e9	+	1.48723e10i	−0.263115	+	1.49220i	0.511236	+	0.859441i	$0.329188\pi$
$719$	−2.62238e9	+	1.48723e10i	−0.263115	+	1.49220i	−0.774350	+	0.632757i	$0.781923\pi$
$720$	−1.80803e9	−	1.51712e9i	−0.180527	−	0.151480i
$721$	−2.77613e8	−	1.01043e8i	−0.0275845	−	0.0100399i
$722$	−8.08761e9	−	2.94365e9i	−0.799724	−	0.291076i
$723$	−2.08514e9	−	1.74964e9i	−0.205188	−	0.172173i
$724$	2.03803e8	−	1.15582e9i	0.0199584	−	0.113190i
$725$	−4.42560e8	+	2.50988e9i	−0.0431310	+	0.244608i
$726$	7.20415e9	+	1.24780e10i	0.698722	+	1.21022i
$727$	2.57090e9	−	2.15724e9i	0.248150	−	0.208223i	−0.510225	−	0.860041i	$-0.670438\pi$
$727$	2.57090e9	−	2.15724e9i	0.248150	−	0.208223i	0.758375	+	0.651818i	$0.225993\pi$
$728$	2.88931e9	−	1.05162e9i	0.277545	−	0.101018i
$729$	6.59686e9	−	1.14261e10i	0.630654	−	1.09232i
$730$	6.07407e9	+	1.05206e10i	0.577896	+	1.00094i
$731$	2.18804e9	+	1.83598e9i	0.207179	+	0.173843i
$732$	1.41170e10	−	2.44513e10i	1.33031	−	2.30416i
$733$	1.68294e9	+	9.54441e9i	0.157835	+	0.895128i	0.956148	+	0.292884i	$0.0946151\pi$
$733$	1.68294e9	+	9.54441e9i	0.157835	+	0.895128i	−0.798313	+	0.602243i	$0.794274\pi$
$734$	8.08665e9			0.754801
$735$	8.29134e8	+	4.70225e9i	0.0770228	+	0.436818i
$736$	1.16006e10	−	9.73408e9i	1.07253	−	0.899959i
$737$	5.44696e9	+	1.98253e9i	0.501208	+	0.182425i
$738$	−2.77617e10	+	1.01044e10i	−2.54243	+	0.925370i
$739$	9.43550e9			0.860022			0.430011	−	0.902824i	$-0.358510\pi$
$739$	9.43550e9			0.860022			0.430011	+	0.902824i	$0.358510\pi$
$740$	6.49907e9	+	3.76831e9i	0.589577	+	0.341850i
$741$	8.31619e9			0.750863
$742$	1.11623e10	−	4.06275e9i	1.00309	−	0.365095i
$743$	8.00606e9	+	2.91397e9i	0.716075	+	0.260630i	0.674258	−	0.738496i	$-0.264463\pi$
$743$	8.00606e9	+	2.91397e9i	0.716075	+	0.260630i	0.0418161	+	0.999125i	$0.486686\pi$
$744$	−2.05001e9	+	1.72016e9i	−0.182495	+	0.153132i
$745$	8.44675e8	+	4.79039e9i	0.0748416	+	0.424448i
$746$	2.99311e10			2.63959
$747$	−2.27387e9	−	1.28958e10i	−0.199592	−	1.13195i
$748$	−7.28581e8	+	1.26194e9i	−0.0636535	+	0.110251i
$749$	7.78261e8	+	6.53038e8i	0.0676766	+	0.0567874i
$750$	1.12146e10	+	1.94242e10i	0.970662	+	1.68124i
$751$	8.57374e9	−	1.48502e10i	0.738636	−	1.27936i	−0.214473	−	0.976730i	$-0.568804\pi$
$751$	8.57374e9	−	1.48502e10i	0.738636	−	1.27936i	0.953110	−	0.302626i	$-0.0978632\pi$
$752$	−2.96918e9	+	1.08069e9i	−0.254610	+	0.0926703i
$753$	2.31425e9	−	1.94189e9i	0.197528	−	0.165745i
$754$	−2.26190e9	−	3.91772e9i	−0.192165	−	0.332839i
$755$	4.60389e8	−	2.61099e9i	0.0389323	−	0.220796i
$756$	3.69654e8	−	2.09641e9i	0.0311150	−	0.176462i
$757$	4.91922e9	+	4.12772e9i	0.412155	+	0.345839i	0.825169	−	0.564885i	$-0.191080\pi$
$757$	4.91922e9	+	4.12772e9i	0.412155	+	0.345839i	−0.413014	+	0.910725i	$0.635524\pi$
$758$	−2.23696e10	−	8.14187e9i	−1.86559	−	0.679019i
$759$	−1.11198e10	−	4.04727e9i	−0.923102	−	0.335982i
$760$	−1.90772e9	−	1.60077e9i	−0.157641	−	0.132276i
$761$	−1.90125e9	+	1.07825e10i	−0.156384	+	0.886899i	0.801125	+	0.598497i	$0.204235\pi$
$761$	−1.90125e9	+	1.07825e10i	−0.156384	+	0.886899i	−0.957509	+	0.288402i	$0.906876\pi$
$762$	−3.27848e9	+	1.85932e10i	−0.268429	+	1.52234i
$763$	−7.89179e8	−	1.36690e9i	−0.0643191	−	0.111404i
$764$	−4.73224e8	+	3.97082e8i	−0.0383920	+	0.0322147i
$765$	9.38277e8	−	3.41505e8i	0.0757733	−	0.0275792i
$766$	−9.76344e9	+	1.69108e10i	−0.784878	+	1.35945i
$767$	3.27079e9	+	5.66518e9i	0.261739	+	0.453346i
$768$	3.07557e9	+	2.58071e9i	0.244997	+	0.205577i
$769$	9.52173e9	−	1.64921e10i	0.755046	−	1.30778i	−0.190305	−	0.981725i	$-0.560948\pi$
$769$	9.52173e9	−	1.64921e10i	0.755046	−	1.30778i	0.945351	−	0.326054i	$-0.105719\pi$
$770$	−6.26862e8	−	3.55511e9i	−0.0494828	−	0.280631i
$771$	2.02017e10			1.58744
$772$	3.43382e9	+	1.94741e10i	0.268606	+	1.52334i
$773$	−9.38705e8	+	7.87667e8i	−0.0730972	+	0.0613358i	−0.678604	−	0.734504i	$-0.737415\pi$
$773$	−9.38705e8	+	7.87667e8i	−0.0730972	+	0.0613358i	0.605507	+	0.795840i	$0.292970\pi$
$774$	−3.98475e10	−	1.45033e10i	−3.08893	−	1.12428i
$775$	−2.39892e9	+	8.73136e8i	−0.185123	+	0.0673792i
$776$	−5.35926e9			−0.411708
$777$	2.16863e7	−	1.17049e10i	0.00165849	−	0.895145i
$778$	2.56505e10			1.95284
$779$	1.27184e10	−	4.62910e9i	0.963940	−	0.350845i
$780$	−9.48444e9	−	3.45205e9i	−0.715617	−	0.260463i
$781$	1.14814e10	−	9.63402e9i	0.862414	−	0.723651i
$782$	5.68577e8	+	3.22456e9i	0.0425173	+	0.241128i
$783$	−9.07027e8			−0.0675233
$784$	6.25006e8	+	3.54458e9i	0.0463210	+	0.262699i
$785$	3.72326e9	−	6.44888e9i	0.274714	−	0.475818i
$786$	2.33872e10	+	1.96242e10i	1.71791	+	1.44149i
$787$	−7.82500e9	−	1.35533e10i	−0.572233	−	0.991137i	−0.996336	−	0.0855229i	$-0.972744\pi$
$787$	−7.82500e9	−	1.35533e10i	−0.572233	−	0.991137i	0.424103	−	0.905614i	$-0.360589\pi$
$788$	6.25730e9	−	1.08380e10i	0.455559	−	0.789052i
$789$	−1.48494e10	+	5.40472e9i	−1.07631	+	0.391746i
$790$	−2.96382e9	+	2.48694e9i	−0.213874	+	0.179461i
$791$	−3.32523e9	−	5.75947e9i	−0.238893	−	0.413775i
$792$	1.08791e9	−	6.16983e9i	0.0778133	−	0.441301i
$793$	−2.40420e9	+	1.36349e10i	−0.171204	+	0.970947i
$794$	−1.44587e10	−	1.21323e10i	−1.02508	−	0.860145i
$795$	−1.06114e10	−	3.86223e9i	−0.749009	−	0.272617i
$796$	−2.86319e10	−	1.04212e10i	−2.01212	−	0.732353i
$797$	−1.13738e10	−	9.54374e9i	−0.795794	−	0.667751i	0.151378	−	0.988476i	$-0.451629\pi$
$797$	−1.13738e10	−	9.54374e9i	−0.795794	−	0.667751i	−0.947172	+	0.320725i	$0.896073\pi$
$798$	−2.32655e9	+	1.31945e10i	−0.162070	+	0.919145i
$799$	2.32122e8	−	1.31643e9i	0.0160991	−	0.0913026i
$800$	7.17223e9	+	1.24227e10i	0.495267	+	0.857827i
$801$	1.72003e10	−	1.44328e10i	1.18256	−	0.992284i
$802$	5.47058e9	−	1.99113e9i	0.374475	−	0.136298i
$803$	7.00042e9	−	1.21251e10i	0.477111	−	0.826381i
$804$	1.30551e10	+	2.26121e10i	0.885900	+	1.53442i
$805$	−3.63304e9	−	3.04848e9i	−0.245462	−	0.205967i
$806$	2.26569e9	−	3.92429e9i	0.152415	−	0.263991i
$807$	2.69327e9	+	1.52743e10i	0.180394	+	1.02307i
$808$	−3.94414e9			−0.263034
$809$	3.53282e9	+	2.00356e10i	0.234586	+	1.33040i	0.843484	+	0.537154i	$0.180501\pi$
$809$	3.53282e9	+	2.00356e10i	0.234586	+	1.33040i	−0.608898	+	0.793248i	$0.708388\pi$
$810$	7.29039e9	−	6.11737e9i	0.482007	−	0.404452i
$811$	−2.56227e10	−	9.32592e9i	−1.68676	−	0.613930i	−0.692546	−	0.721373i	$-0.743511\pi$
$811$	−2.56227e10	−	9.32592e9i	−1.68676	−	0.613930i	−0.994211	+	0.107444i	$0.965733\pi$
$812$	4.00415e9	−	1.45739e9i	0.262460	−	0.0955278i
$813$	−2.80702e10			−1.83201
$814$	2.74376e7	−	1.48091e10i	0.00178304	−	0.962370i
$815$	6.85513e9			0.443572
$816$	1.32650e9	−	4.82807e8i	0.0854657	−	0.0311070i
$817$	1.82551e10	+	6.64433e9i	1.17114	+	0.426259i
$818$	−3.02509e10	+	2.53835e10i	−1.93242	+	1.62149i
$819$	1.45600e9	+	8.25736e9i	0.0926118	+	0.525228i
$820$	−1.64266e10			−1.04040
$821$	−4.93327e9	−	2.79780e10i	−0.311124	−	1.76447i	−0.593174	−	0.805074i	$-0.702126\pi$
$821$	−4.93327e9	−	2.79780e10i	−0.311124	−	1.76447i	0.282050	−	0.959400i	$-0.408986\pi$
$822$	−2.35487e10	+	4.07876e10i	−1.47882	+	2.56140i
$823$	1.13448e10	+	9.51938e9i	0.709407	+	0.595263i	0.924433	−	0.381345i	$-0.124539\pi$
$823$	1.13448e10	+	9.51938e9i	0.709407	+	0.595263i	−0.215026	+	0.976608i	$0.568983\pi$
$824$	−2.43796e8	−	4.22267e8i	−0.0151803	−	0.0262931i
$825$	5.60450e9	−	9.70728e9i	0.347495	−	0.601878i
$826$	−9.90346e9	+	3.60457e9i	−0.611444	+	0.222548i
$827$	1.77825e9	−	1.49213e9i	0.109326	−	0.0917356i	−0.586486	−	0.809959i	$-0.699489\pi$
$827$	1.77825e9	−	1.49213e9i	0.109326	−	0.0917356i	0.695812	+	0.718224i	$0.255045\pi$
$828$	−1.42104e10	−	2.46131e10i	−0.869960	−	1.50681i
$829$	−1.52771e9	+	8.66409e9i	−0.0931324	+	0.528180i	0.902171	+	0.431378i	$0.141973\pi$
$829$	−1.52771e9	+	8.66409e9i	−0.0931324	+	0.528180i	−0.995304	+	0.0968022i	$0.969139\pi$
$830$	2.16247e9	−	1.22640e10i	0.131273	−	0.744488i
$831$	2.48657e10	+	2.08648e10i	1.50313	+	1.26128i
$832$	−1.88471e10	−	6.85978e9i	−1.13452	−	0.412932i
$833$	−1.43085e9	−	5.20786e8i	−0.0857702	−	0.0312178i
$834$	−2.74504e10	−	2.30336e10i	−1.63858	−	1.37493i
$835$	−1.17299e9	+	6.65237e9i	−0.0697256	+	0.395434i
$836$	−1.72098e9	+	9.76017e9i	−0.101872	+	0.577744i
$837$	−4.54274e8	−	7.86826e8i	−0.0267781	−	0.0463810i
$838$	7.87532e9	−	6.60818e9i	0.462290	−	0.387907i
$839$	−1.67092e10	+	6.08165e9i	−0.976762	+	0.355512i	−0.780581	−	0.625055i	$-0.785076\pi$
$839$	−1.67092e10	+	6.08165e9i	−0.976762	+	0.355512i	−0.196182	+	0.980568i	$0.562854\pi$
$840$	2.35459e9	−	4.07826e9i	0.137068	−	0.237409i
$841$	7.71714e9	+	1.33665e10i	0.447374	+	0.774874i
$842$	−1.36783e10	−	1.14775e10i	−0.789660	−	0.662603i
$843$	−1.30118e10	+	2.25370e10i	−0.748066	+	1.29569i
$844$	5.67307e9	+	3.21736e10i	0.324802	+	1.84205i
$845$	−3.54192e9			−0.201948
$846$	3.44611e9	+	1.95439e10i	0.195674	+	1.10972i
$847$	5.09819e9	−	4.27789e9i	0.288287	−	0.241901i
$848$	−7.99891e9	−	2.91137e9i	−0.450449	−	0.163950i
$849$	−2.91587e10	+	1.06129e10i	−1.63528	+	0.595193i
$850$	−3.10153e9			−0.173225
$851$	−1.24781e10	−	1.49269e10i	−0.694057	−	0.830264i
$852$	6.75123e10			3.73976
$853$	−2.87038e10	+	1.04473e10i	−1.58350	+	0.576346i	−0.975961	−	0.217946i	$-0.930064\pi$
$853$	−2.87038e10	+	1.04473e10i	−1.58350	+	0.576346i	−0.607536	+	0.794292i	$0.707842\pi$
$854$	−2.09606e10	−	7.62905e9i	−1.15160	−	0.419149i
$855$	5.20232e9	−	4.36527e9i	0.284653	−	0.238852i
$856$	2.91169e8	+	1.65130e9i	0.0158667	+	0.0899845i
$857$	−1.58640e10			−0.860953			−0.430477	−	0.902602i	$-0.641654\pi$
$857$	−1.58640e10			−0.860953			−0.430477	+	0.902602i	$0.641654\pi$
$858$	3.45492e9	+	1.95938e10i	0.186738	+	1.05904i
$859$	8.94869e9	−	1.54996e10i	0.481707	−	0.834341i	−0.518072	−	0.855337i	$-0.673350\pi$
$859$	8.94869e9	−	1.54996e10i	0.481707	−	0.834341i	0.999780	+	0.0209953i	$0.00668352\pi$
$860$	−1.80616e10	−	1.51554e10i	−0.968302	−	0.812502i
$861$	1.27967e10	+	2.21645e10i	0.683262	+	1.18344i
$862$	2.25259e10	−	3.90161e10i	1.19786	−	2.07476i
$863$	−3.68673e9	+	1.34186e9i	−0.195256	+	0.0710672i	−0.437797	−	0.899074i	$-0.644241\pi$
$863$	−3.68673e9	+	1.34186e9i	−0.195256	+	0.0710672i	0.242541	+	0.970141i	$0.422019\pi$
$864$	−3.91071e9	+	3.28148e9i	−0.206280	+	0.173090i
$865$	4.59208e9	+	7.95372e9i	0.241242	+	0.417844i
$866$	8.44027e9	−	4.78671e10i	0.441615	−	2.50452i
$867$	4.77346e9	−	2.70716e10i	0.248752	−	1.41074i
$868$	3.26969e9	+	2.74359e9i	0.169702	+	0.142397i
$869$	4.19014e9	+	1.52509e9i	0.216600	+	0.0788361i
$870$	−6.51066e9	−	2.36969e9i	−0.335203	−	0.122004i
$871$	−9.80829e9	−	8.23014e9i	−0.502956	−	0.422030i
$872$	4.52355e8	−	2.56543e9i	0.0231032	−	0.131025i
$873$	2.53780e9	−	1.43926e10i	0.129094	−	0.732130i
$874$	1.11349e10	+	1.92862e10i	0.564153	+	0.977142i
$875$	7.93627e9	−	6.65932e9i	0.400487	−	0.336048i
$876$	5.92628e10	−	2.15699e10i	2.97864	−	1.08414i
$877$	−5.30576e9	+	9.18985e9i	−0.265613	+	0.460055i	−0.967724	−	0.252012i	$-0.918908\pi$
$877$	−5.30576e9	+	9.18985e9i	−0.265613	+	0.460055i	0.702111	+	0.712067i	$0.252241\pi$
$878$	−1.49300e9	−	2.58595e9i	−0.0744438	−	0.128940i
$879$	−1.18989e10	−	9.98440e9i	−0.590945	−	0.495862i
$880$	−1.29345e9	+	2.24032e9i	−0.0639823	+	0.110821i
$881$	4.13745e9	+	2.34646e10i	0.203853	+	1.15611i	0.899235	+	0.437467i	$0.144124\pi$
$881$	4.13745e9	+	2.34646e10i	0.203853	+	1.15611i	−0.695382	+	0.718641i	$0.744765\pi$
$882$	2.26059e10			1.10938
$883$	4.12007e9	+	2.33661e10i	0.201392	+	1.14215i	0.903018	+	0.429604i	$0.141347\pi$
$883$	4.12007e9	+	2.33661e10i	0.201392	+	1.14215i	−0.701626	+	0.712546i	$0.747542\pi$
$884$	2.46566e9	−	2.06893e9i	0.120047	−	0.100731i
$885$	9.41467e9	+	3.42666e9i	0.456566	+	0.166176i
$886$	4.39784e10	−	1.60068e10i	2.12433	−	0.773192i
$887$	1.57608e10			0.758310			0.379155	−	0.925333i	$-0.376215\pi$
$887$	1.57608e10			0.758310			0.379155	+	0.925333i	$0.376215\pi$
$888$	1.24450e10	−	1.47757e10i	0.596417	−	0.708114i
$889$	8.72070e9			0.416289
$890$	2.00656e10	−	7.30327e9i	0.954083	−	0.347258i
$891$	−1.03069e10	−	3.75140e9i	−0.488152	−	0.177673i
$892$	−1.85477e10	+	1.55634e10i	−0.875012	+	0.734222i
$893$	−1.57875e9	−	8.95354e9i	−0.0741880	−	0.420741i
$894$	4.31921e10			2.02173
$895$	−2.50562e9	−	1.42101e10i	−0.116825	−	0.662547i
$896$	7.63769e9	−	1.32289e10i	0.354719	−	0.614391i
$897$	2.00233e10	+	1.68015e10i	0.926322	+	0.777276i
$898$	1.25988e10	+	2.18218e10i	0.580582	+	1.00560i
$899$	9.09321e8	−	1.57499e9i	0.0417405	−	0.0722967i
$900$	2.52975e10	−	9.20754e9i	1.15672	−	0.421013i
$901$	2.75863e9	−	2.31476e9i	0.125648	−	0.105431i
$902$	1.61904e10	+	2.80427e10i	0.734574	+	1.27232i
$903$	−6.37900e9	+	3.61771e10i	−0.288301	+	1.63503i
$904$	1.90601e9	−	1.08095e10i	0.0858096	−	0.486650i
$905$	6.75241e8	+	5.66595e8i	0.0302823	+	0.0254099i
$906$	−2.21220e10	−	8.05176e9i	−0.988271	−	0.359701i
$907$	−6.66590e9	−	2.42619e9i	−0.296642	−	0.107969i	0.189412	−	0.981898i	$-0.439342\pi$
$907$	−6.66590e9	−	2.42619e9i	−0.296642	−	0.107969i	−0.486054	+	0.873929i	$0.661564\pi$
$908$	−2.71140e10	−	2.27513e10i	−1.20197	−	1.00857i
$909$	1.86769e9	−	1.05922e10i	0.0824766	−	0.467748i
$910$	−1.38466e9	+	7.85280e9i	−0.0609114	+	0.345446i
$911$	−6.78856e9	−	1.17581e10i	−0.297484	−	0.515257i	0.678076	−	0.734992i	$-0.262814\pi$
$911$	−6.78856e9	−	1.17581e10i	−0.297484	−	0.515257i	−0.975560	+	0.219735i	$0.929481\pi$
$912$	7.35485e9	−	6.17145e9i	0.321064	−	0.269405i
$913$	−1.34868e10	+	4.90880e9i	−0.586492	+	0.213466i
$914$	−2.16419e10	+	3.74849e10i	−0.937528	+	1.62385i
$915$	1.06025e10	+	1.83640e10i	0.457544	+	0.792490i
$916$	2.51013e10	+	2.10625e10i	1.07910	+	0.905472i
$917$	7.05089e9	−	1.22125e10i	0.301961	−	0.523013i
$918$	−1.91674e8	−	1.08704e9i	−0.00817739	−	0.0463763i
$919$	8.25888e9			0.351008			0.175504	−	0.984479i	$-0.443844\pi$
$919$	8.25888e9			0.351008			0.175504	+	0.984479i	$0.443844\pi$
$920$	−1.35922e9	−	7.70851e9i	−0.0575482	−	0.326372i
$921$	2.38254e10	−	1.99918e10i	1.00492	−	0.843226i
$922$	1.49006e10	+	5.42337e9i	0.626102	+	0.227882i
$923$	−3.11098e10	+	1.13230e10i	−1.30224	+	0.473977i
$924$	−1.87408e10			−0.781514
$925$	1.59769e10	−	9.18485e9i	0.663738	−	0.381571i
$926$	−5.55638e10			−2.29961
$927$	1.24946e9	−	4.54768e8i	0.0515163	−	0.0187504i
$928$	−9.60255e9	−	3.49504e9i	−0.394429	−	0.143560i
$929$	−2.10631e9	+	1.76740e9i	−0.0861921	+	0.0723237i	−0.684866	−	0.728669i	$-0.740139\pi$
$929$	−2.10631e9	+	1.76740e9i	−0.0861921	+	0.0723237i	0.598674	+	0.800993i	$0.295695\pi$
$930$	−1.20514e9	−	6.83469e9i	−0.0491301	−	0.278630i
$931$	−1.03563e10			−0.420612
$932$	1.01767e10	+	5.77148e10i	0.411766	+	2.33524i
$933$	−3.89512e9	+	6.74655e9i	−0.157013	+	0.271954i
$934$	−1.64706e10	−	1.38205e10i	−0.661446	−	0.555019i
$935$	−5.47196e8	−	9.47772e8i	−0.0218929	−	0.0379195i
$936$	−6.91931e9	+	1.19846e10i	−0.275802	+	0.477703i
$937$	2.84906e10	−	1.03697e10i	1.13139	−	0.411794i	0.292595	−	0.956236i	$-0.405481\pi$
$937$	2.84906e10	−	1.03697e10i	1.13139	−	0.411794i	0.838798	+	0.544443i	$0.183259\pi$
$938$	1.58020e10	−	1.32595e10i	0.625176	−	0.524585i
$939$	−3.25753e10	−	5.64220e10i	−1.28398	−	2.22392i
$940$	−1.91609e9	+	1.08667e10i	−0.0752433	+	0.426726i
$941$	−3.28085e9	+	1.86066e10i	−0.128358	+	0.727954i	0.850899	+	0.525330i	$0.176058\pi$
$941$	−3.28085e9	+	1.86066e10i	−0.128358	+	0.727954i	−0.979257	+	0.202624i	$0.935053\pi$
$942$	−5.06515e10	−	4.25016e10i	−1.97430	−	1.65664i
$943$	3.99750e10	+	1.45497e10i	1.55238	+	0.565019i
$944$	7.09682e9	+	2.58303e9i	0.274576	+	0.0999374i
$945$	1.22474e9	+	1.02768e9i	0.0472099	+	0.0396138i
$946$	−8.07074e9	+	4.57714e10i	−0.309952	+	1.75782i
$947$	6.29989e9	−	3.57284e10i	0.241050	−	1.36706i	−0.588439	−	0.808542i	$-0.700257\pi$
$947$	6.29989e9	−	3.57284e10i	0.241050	−	1.36706i	0.829489	−	0.558523i	$-0.188632\pi$
$948$	1.00428e10	+	1.73947e10i	0.382848	+	0.663112i
$949$	−2.36908e10	+	1.98789e10i	−0.899803	+	0.755024i
$950$	−1.98226e10	+	7.21482e9i	−0.750114	+	0.273019i
$951$	3.68329e10	−	6.37964e10i	1.38869	−	2.40527i
$952$	7.50875e8	+	1.30055e9i	0.0282058	+	0.0488539i
$953$	6.50390e9	+	5.45742e9i	0.243416	+	0.204250i	0.756331	−	0.654189i	$-0.226990\pi$
$953$	6.50390e9	+	5.45742e9i	0.243416	+	0.204250i	−0.512915	+	0.858439i	$0.671434\pi$
$954$	−2.67315e10	+	4.63003e10i	−0.996790	+	1.72649i
$955$	−8.05654e7	−	4.56909e8i	−0.00299321	−	0.0169753i
$956$	−4.38135e10			−1.62183
$957$	1.38661e9	+	7.86385e9i	0.0511402	+	0.290030i
$958$	3.48844e10	−	2.92715e10i	1.28189	−	1.07564i
$959$	2.04425e10	+	7.44044e9i	0.748459	+	0.272417i
$960$	−2.88656e10	+	1.05062e10i	−1.05301	+	0.383263i
$961$	−2.56909e10			−0.933787
$962$	−1.12449e10	+	3.07179e10i	−0.407233	+	1.11245i
$963$	−4.57253e9			−0.164992
$964$	−6.73318e9	+	2.45068e9i	−0.242076	+	0.0881083i
$965$	−1.39559e10	−	5.07953e9i	−0.499933	−	0.181961i
$966$	−3.22592e10	+	2.70687e10i	−1.15142	+	0.966157i
$967$	−4.63135e9	−	2.62657e10i	−0.164708	−	0.934106i	−0.949365	−	0.314175i	$-0.898272\pi$
$967$	−4.63135e9	−	2.62657e10i	−0.164708	−	0.934106i	0.784657	−	0.619930i	$-0.212839\pi$
$968$	1.09841e10			0.389226
$969$	7.05317e8	+	4.00005e9i	0.0249030	+	0.141232i
$970$	6.94929e9	−	1.20365e10i	0.244478	−	0.423448i
$971$	−2.06096e10	−	1.72935e10i	−0.722440	−	0.606199i	0.205619	−	0.978632i	$-0.434079\pi$
$971$	−2.06096e10	−	1.72935e10i	−0.722440	−	0.606199i	−0.928059	+	0.372433i	$0.878524\pi$
$972$	−2.88973e10	−	5.00516e10i	−1.00931	−	1.74818i
$973$	−8.27589e9	+	1.43343e10i	−0.288018	+	0.498862i
$974$	9.76581e9	−	3.55446e9i	0.338651	−	0.123259i
$975$	−1.89667e10	+	1.59150e10i	−0.655354	+	0.549907i
$976$	7.99219e9	+	1.38429e10i	0.275164	+	0.476598i
$977$	−3.25255e8	+	1.84461e9i	−0.0111582	+	0.0632811i	−0.989878	−	0.141918i	$-0.954673\pi$
$977$	−3.25255e8	+	1.84461e9i	−0.0111582	+	0.0632811i	0.978720	+	0.205199i	$0.0657842\pi$
$978$	1.05699e10	−	5.99448e10i	0.361313	−	2.04911i
$979$	−1.88523e10	−	1.58189e10i	−0.642132	−	0.538813i
$980$	1.18112e10	+	4.29892e9i	0.400869	+	0.145904i
$981$	6.67539e9	+	2.42964e9i	0.225754	+	0.0821676i
$982$	−2.74827e10	−	2.30607e10i	−0.926124	−	0.777110i
$983$	6.12259e9	−	3.47229e10i	0.205588	−	1.16595i	−0.690924	−	0.722927i	$-0.742796\pi$
$983$	6.12259e9	−	3.47229e10i	0.205588	−	1.16595i	0.896512	−	0.443020i	$-0.146093\pi$
$984$	−7.33503e9	+	4.15990e10i	−0.245425	+	1.39187i
$985$	4.69950e9	+	8.13978e9i	0.156684	+	0.271385i
$986$	1.69257e9	−	1.42023e9i	0.0562312	−	0.0471836i
$987$	1.61552e10	−	5.88001e9i	0.534813	−	0.194656i
$988$	1.09458e10	−	1.89587e10i	0.361075	−	0.625401i
$989$	3.05300e10	+	5.28795e10i	1.00355	+	1.73820i
$990$	1.24463e10	+	1.04437e10i	0.407678	+	0.342083i
$991$	−7.13998e9	+	1.23668e10i	−0.233045	+	0.403645i	−0.958703	−	0.284410i	$-0.908202\pi$
$991$	−7.13998e9	+	1.23668e10i	−0.233045	+	0.403645i	0.725658	+	0.688056i	$0.241535\pi$
$992$	−1.77746e9	−	1.00805e10i	−0.0578107	−	0.327861i
$993$	2.49273e10			0.807893
$994$	−9.26190e9	−	5.25269e10i	−0.299122	−	1.69640i
$995$	1.75301e10	−	1.47095e10i	0.564160	−	0.473387i
$996$	−6.07508e10	−	2.21115e10i	−1.94825	−	0.709105i
$997$	−2.89682e10	+	1.05436e10i	−0.925739	+	0.336942i	−0.760519	−	0.649315i	$-0.775056\pi$
$997$	−2.89682e10	+	1.05436e10i	−0.925739	+	0.336942i	−0.165220	+	0.986257i	$0.552833\pi$
$998$	−3.16891e10			−1.00914
$999$	4.20652e9	+	5.03205e9i	0.133489	+	0.159685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.8.f.a.7.20	✓	132
37.16	even	9	inner	37.8.f.a.16.20	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.8.f.a.7.20	✓	132	1.1	even	1	trivial
37.8.f.a.16.20	yes	132	37.16	even	9	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	37.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(16.4964 - 6.00419i) q^{2} +(64.3192 + 23.4103i) q^{3} +(138.026 - 115.818i) q^{4} +(23.4987 + 133.267i) q^{5} +1201.59 q^{6} +(-96.3778 - 546.586i) q^{7} +(458.016 - 793.306i) q^{8} +(1913.58 + 1605.68i) q^{9} +O(q^{10})\)	\(q+(16.4964 - 6.00419i) q^{2} +(64.3192 + 23.4103i) q^{3} +(138.026 - 115.818i) q^{4} +(23.4987 + 133.267i) q^{5} +1201.59 q^{6} +(-96.3778 - 546.586i) q^{7} +(458.016 - 793.306i) q^{8} +(1913.58 + 1605.68i) q^{9} +(1187.81 + 2057.34i) q^{10} +(1368.96 - 2371.10i) q^{11} +(11589.1 - 4218.07i) q^{12} +(-4632.81 + 3887.39i) q^{13} +(-4871.69 - 8438.01i) q^{14} +(-1608.41 + 9121.76i) q^{15} +(-1212.43 + 6876.03i) q^{16} +(-2262.74 - 1898.66i) q^{17} +(41207.9 + 14998.4i) q^{18} +(-18878.4 - 6871.16i) q^{19} +(18678.2 + 15672.8i) q^{20} +(6596.78 - 37412.2i) q^{21} +(8346.27 - 47334.0i) q^{22} +(-31572.3 - 54684.8i) q^{23} +(48030.7 - 40302.5i) q^{24} +(56205.4 - 20457.1i) q^{25} +(-53084.0 + 91944.2i) q^{26} +(10643.4 + 18434.9i) q^{27} +(-76607.0 - 64280.9i) q^{28} +(-21304.9 + 36901.2i) q^{29} +(28235.8 + 160133. i) q^{30} -42681.3 q^{31} +(41644.9 + 236180. i) q^{32} +(143558. - 120460. i) q^{33} +(-48726.9 - 17735.2i) q^{34} +(70577.4 - 25688.1i) q^{35} +450090. q^{36} +(303528. - 52940.5i) q^{37} -352680. q^{38} +(-388984. + 141578. i) q^{39} +(116485. + 42397.0i) q^{40} +(-516084. + 433046. i) q^{41} +(-115807. - 656773. i) q^{42} -966988. q^{43} +(-85663.8 - 485824. i) q^{44} +(-169019. + 292749. i) q^{45} +(-849166. - 712535. i) q^{46} +(226274. + 391918. i) q^{47} +(-238952. + 413877. i) q^{48} +(484410. - 176311. i) q^{49} +(804357. - 674936. i) q^{50} +(-101089. - 175092. i) q^{51} +(-189221. + 1.07312e6i) q^{52} +(-211704. + 1.20063e6i) q^{53} +(286264. + 240204. i) q^{54} +(348159. + 126720. i) q^{55} +(-477752. - 173888. i) q^{56} +(-1.05339e6 - 883895. i) q^{57} +(-129892. + 736654. i) q^{58} +(187829. - 1.06523e6i) q^{59} +(834459. + 1.44533e6i) q^{60} +(1.75373e6 - 1.47156e6i) q^{61} +(-704086. + 256266. i) q^{62} +(693216. - 1.20069e6i) q^{63} +(1.65820e6 + 2.87209e6i) q^{64} +(-626928. - 526055. i) q^{65} +(1.64493e6 - 2.84910e6i) q^{66} +(367637. + 2.08497e6i) q^{67} -532216. q^{68} +(-750518. - 4.25640e6i) q^{69} +(1.01003e6 - 847520. i) q^{70} +(5.14406e6 + 1.87229e6i) q^{71} +(2.15024e6 - 782625. i) q^{72} +5.11369e6 q^{73} +(4.68924e6 - 2.69576e6i) q^{74} +4.09399e6 q^{75} +(-3.40151e6 + 1.23805e6i) q^{76} +(-1.42795e6 - 519731. i) q^{77} +(-5.56675e6 + 4.67106e6i) q^{78} +(282809. + 1.60389e6i) q^{79} -944842. q^{80} +(-695652. - 3.94524e6i) q^{81} +(-5.91342e6 + 1.02424e7i) q^{82} +(-4.01567e6 - 3.36955e6i) q^{83} +(-3.42247e6 - 5.92789e6i) q^{84} +(199859. - 346166. i) q^{85} +(-1.59518e7 + 5.80597e6i) q^{86} +(-2.23418e6 + 1.87470e6i) q^{87} +(-1.25401e6 - 2.17200e6i) q^{88} +(1.56085e6 - 8.85201e6i) q^{89} +(-1.03047e6 + 5.84411e6i) q^{90} +(2.57129e6 + 2.15757e6i) q^{91} +(-1.06913e7 - 3.89131e6i) q^{92} +(-2.74523e6 - 999180. i) q^{93} +(6.08585e6 + 5.10663e6i) q^{94} +(472087. - 2.67734e6i) q^{95} +(-2.85047e6 + 1.61658e7i) q^{96} +(-2.92526e6 - 5.06670e6i) q^{97} +(6.93240e6 - 5.81697e6i) q^{98} +(6.42684e6 - 2.33918e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 15 q^{2} + 33 q^{3} - 279 q^{4} + 576 q^{5} - 12 q^{6} - 597 q^{7} - 3750 q^{8} - 3243 q^{9}+O(q^{10}) \) 132 * q + 15 * q^2 + 33 * q^3 - 279 * q^4 + 576 * q^5 - 12 * q^6 - 597 * q^7 - 3750 * q^8 - 3243 * q^9	\( 132 q + 15 q^{2} + 33 q^{3} - 279 q^{4} + 576 q^{5} - 12 q^{6} - 597 q^{7} - 3750 q^{8} - 3243 q^{9} - 6003 q^{10} - 15975 q^{11} - 4635 q^{12} - 15981 q^{13} - 13491 q^{14} + 38493 q^{15} - 74151 q^{16} + 37698 q^{17} - 20100 q^{18} - 66102 q^{19} - 176184 q^{20} - 142530 q^{21} + 132783 q^{22} + 140631 q^{23} - 38793 q^{24} - 544092 q^{25} - 423147 q^{26} + 130557 q^{27} + 603813 q^{28} + 22890 q^{29} - 319860 q^{30} - 1288044 q^{31} - 217866 q^{32} + 112344 q^{33} + 812019 q^{34} + 1479252 q^{35} + 8118132 q^{36} - 1664550 q^{37} + 305010 q^{38} - 1580340 q^{39} - 4681425 q^{40} - 2956593 q^{41} - 3553029 q^{42} - 1023528 q^{43} + 6409524 q^{44} + 1803336 q^{45} + 10219434 q^{46} - 2607204 q^{47} - 2984043 q^{48} - 6819531 q^{49} + 5724015 q^{50} - 1675833 q^{51} + 11768451 q^{52} + 2280177 q^{53} - 7803897 q^{54} - 3542196 q^{55} + 12168843 q^{56} - 85203 q^{57} - 12425487 q^{58} - 7014600 q^{59} + 2356788 q^{60} + 10840332 q^{61} + 6334368 q^{62} - 3331359 q^{63} - 26175624 q^{64} - 573195 q^{65} - 36720249 q^{66} + 6642918 q^{67} - 25277742 q^{68} - 1236438 q^{69} - 27401982 q^{70} + 20311041 q^{71} + 40093005 q^{72} + 38643780 q^{73} - 9531 q^{74} + 16639446 q^{75} + 5787405 q^{76} - 316971 q^{77} + 9363381 q^{78} + 17712534 q^{79} - 74410128 q^{80} - 10355109 q^{81} - 16702371 q^{82} - 31021176 q^{83} - 61626192 q^{84} + 23576445 q^{85} + 18579072 q^{86} + 104996631 q^{87} + 57279702 q^{88} - 13471320 q^{89} + 56306910 q^{90} - 2335911 q^{91} - 178133436 q^{92} + 24366258 q^{93} + 77086020 q^{94} - 26254407 q^{95} + 152523921 q^{96} + 14408415 q^{97} - 521205 q^{98} + 58375668 q^{99}+O(q^{100}) \) 132 * q + 15 * q^2 + 33 * q^3 - 279 * q^4 + 576 * q^5 - 12 * q^6 - 597 * q^7 - 3750 * q^8 - 3243 * q^9 - 6003 * q^10 - 15975 * q^11 - 4635 * q^12 - 15981 * q^13 - 13491 * q^14 + 38493 * q^15 - 74151 * q^16 + 37698 * q^17 - 20100 * q^18 - 66102 * q^19 - 176184 * q^20 - 142530 * q^21 + 132783 * q^22 + 140631 * q^23 - 38793 * q^24 - 544092 * q^25 - 423147 * q^26 + 130557 * q^27 + 603813 * q^28 + 22890 * q^29 - 319860 * q^30 - 1288044 * q^31 - 217866 * q^32 + 112344 * q^33 + 812019 * q^34 + 1479252 * q^35 + 8118132 * q^36 - 1664550 * q^37 + 305010 * q^38 - 1580340 * q^39 - 4681425 * q^40 - 2956593 * q^41 - 3553029 * q^42 - 1023528 * q^43 + 6409524 * q^44 + 1803336 * q^45 + 10219434 * q^46 - 2607204 * q^47 - 2984043 * q^48 - 6819531 * q^49 + 5724015 * q^50 - 1675833 * q^51 + 11768451 * q^52 + 2280177 * q^53 - 7803897 * q^54 - 3542196 * q^55 + 12168843 * q^56 - 85203 * q^57 - 12425487 * q^58 - 7014600 * q^59 + 2356788 * q^60 + 10840332 * q^61 + 6334368 * q^62 - 3331359 * q^63 - 26175624 * q^64 - 573195 * q^65 - 36720249 * q^66 + 6642918 * q^67 - 25277742 * q^68 - 1236438 * q^69 - 27401982 * q^70 + 20311041 * q^71 + 40093005 * q^72 + 38643780 * q^73 - 9531 * q^74 + 16639446 * q^75 + 5787405 * q^76 - 316971 * q^77 + 9363381 * q^78 + 17712534 * q^79 - 74410128 * q^80 - 10355109 * q^81 - 16702371 * q^82 - 31021176 * q^83 - 61626192 * q^84 + 23576445 * q^85 + 18579072 * q^86 + 104996631 * q^87 + 57279702 * q^88 - 13471320 * q^89 + 56306910 * q^90 - 2335911 * q^91 - 178133436 * q^92 + 24366258 * q^93 + 77086020 * q^94 - 26254407 * q^95 + 152523921 * q^96 + 14408415 * q^97 - 521205 * q^98 + 58375668 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more