LMFDB - Embedded newform 29.13.c.a.12.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,13,Mod(12,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("29.12");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	29.c (of order $4$, degree $2$, 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:	$26.5058207010$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.19
Character	$\chi$	$=$	29.12
Dual form			29.13.c.a.17.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(33.1274 + 33.1274i) q^{2} +(-631.679 - 631.679i) q^{3} -1901.16i q^{4} -13469.1i q^{5} -41851.7i q^{6} +113718. q^{7} +(198670. - 198670. i) q^{8} +266596. i q^{9} +O(q^{10})$	\(q+(33.1274 + 33.1274i) q^{2} +(-631.679 - 631.679i) q^{3} -1901.16i q^{4} -13469.1i q^{5} -41851.7i q^{6} +113718. q^{7} +(198670. - 198670. i) q^{8} +266596. i q^{9} +(446197. - 446197. i) q^{10} +(979737. + 979737. i) q^{11} +(-1.20092e6 + 1.20092e6i) q^{12} -7.13138e6i q^{13} +(3.76717e6 + 3.76717e6i) q^{14} +(-8.50818e6 + 8.50818e6i) q^{15} +5.37569e6 q^{16} +(-1.36053e7 - 1.36053e7i) q^{17} +(-8.83162e6 + 8.83162e6i) q^{18} +(7.00389e6 + 7.00389e6i) q^{19} -2.56069e7 q^{20} +(-7.18331e7 - 7.18331e7i) q^{21} +6.49122e7i q^{22} -2.39819e8 q^{23} -2.50991e8 q^{24} +6.27227e7 q^{25} +(2.36244e8 - 2.36244e8i) q^{26} +(-1.67297e8 + 1.67297e8i) q^{27} -2.16195e8i q^{28} +(5.39336e8 - 2.50861e8i) q^{29} -5.63707e8 q^{30} +(8.35541e8 + 8.35541e8i) q^{31} +(-6.35670e8 - 6.35670e8i) q^{32} -1.23776e9i q^{33} -9.01413e8i q^{34} -1.53168e9i q^{35} +5.06840e8 q^{36} +(1.44922e8 - 1.44922e8i) q^{37} +4.64041e8i q^{38} +(-4.50474e9 + 4.50474e9i) q^{39} +(-2.67592e9 - 2.67592e9i) q^{40} +(-1.87652e9 + 1.87652e9i) q^{41} -4.75928e9i q^{42} +(-6.36642e9 - 6.36642e9i) q^{43} +(1.86263e9 - 1.86263e9i) q^{44} +3.59082e9 q^{45} +(-7.94457e9 - 7.94457e9i) q^{46} +(-1.30500e10 + 1.30500e10i) q^{47} +(-3.39571e9 - 3.39571e9i) q^{48} -9.09557e8 q^{49} +(2.07784e9 + 2.07784e9i) q^{50} +1.71883e10i q^{51} -1.35579e10 q^{52} +2.13746e10 q^{53} -1.10842e10 q^{54} +(1.31962e10 - 1.31962e10i) q^{55} +(2.25923e10 - 2.25923e10i) q^{56} -8.84842e9i q^{57} +(2.61771e10 + 9.55643e9i) q^{58} +4.45578e10 q^{59} +(1.61754e10 + 1.61754e10i) q^{60} +(2.78164e10 + 2.78164e10i) q^{61} +5.53586e10i q^{62} +3.03167e10i q^{63} -6.41350e10i q^{64} -9.60536e10 q^{65} +(4.10037e10 - 4.10037e10i) q^{66} +6.17243e10i q^{67} +(-2.58657e10 + 2.58657e10i) q^{68} +(1.51489e11 + 1.51489e11i) q^{69} +(5.07406e10 - 5.07406e10i) q^{70} -1.59859e11i q^{71} +(5.29646e10 + 5.29646e10i) q^{72} +(-6.16978e10 + 6.16978e10i) q^{73} +9.60179e9 q^{74} +(-3.96206e10 - 3.96206e10i) q^{75} +(1.33155e10 - 1.33155e10i) q^{76} +(1.11414e11 + 1.11414e11i) q^{77} -2.98461e11 q^{78} +(1.44571e11 + 1.44571e11i) q^{79} -7.24060e10i q^{80} +3.53036e11 q^{81} -1.24328e11 q^{82} -9.68340e10 q^{83} +(-1.36566e11 + 1.36566e11i) q^{84} +(-1.83251e11 + 1.83251e11i) q^{85} -4.21805e11i q^{86} +(-4.99151e11 - 1.82224e11i) q^{87} +3.89289e11 q^{88} +(-1.93556e10 - 1.93556e10i) q^{89} +(1.18954e11 + 1.18954e11i) q^{90} -8.10965e11i q^{91} +4.55933e11i q^{92} -1.05559e12i q^{93} -8.64623e11 q^{94} +(9.43364e10 - 9.43364e10i) q^{95} +8.03078e11i q^{96} +(-3.96346e10 + 3.96346e10i) q^{97} +(-3.01312e10 - 3.01312e10i) q^{98} +(-2.61194e11 + 2.61194e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q + 88 q^{2} - 2 q^{3} - 4 q^{7} + 79650 q^{8}+O(q^{10}) $ 58 * q + 88 * q^2 - 2 * q^3 - 4 * q^7 + 79650 * q^8	\( 58 q + 88 q^{2} - 2 q^{3} - 4 q^{7} + 79650 q^{8} - 1957890 q^{10} + 4120990 q^{11} + 2920062 q^{12} - 1824520 q^{14} - 8383600 q^{15} - 133743512 q^{16} + 33971578 q^{17} - 122384158 q^{18} + 65838718 q^{19} - 59408388 q^{20} + 200896236 q^{21} + 104539676 q^{23} + 163907064 q^{24} - 3086882294 q^{25} + 607848030 q^{26} - 1190867840 q^{27} + 817714294 q^{29} + 5793833612 q^{30} - 1059975938 q^{31} + 2323254598 q^{32} + 517001400 q^{36} - 864725342 q^{37} + 18048639408 q^{39} - 22547920086 q^{40} - 17292603926 q^{41} - 3344004962 q^{43} - 53750811886 q^{44} - 16067938640 q^{45} + 43310099300 q^{46} - 15159905282 q^{47} - 4602803862 q^{48} + 32036753022 q^{49} - 16057299278 q^{50} + 81167587800 q^{52} - 69552844564 q^{53} + 38996274808 q^{54} + 3944882736 q^{55} - 156397031424 q^{56} + 107434998568 q^{58} + 82613255468 q^{59} - 147410252946 q^{60} + 128229759922 q^{61} + 125938412928 q^{65} + 364716671994 q^{66} - 141670411468 q^{68} + 529640675916 q^{69} + 518962441956 q^{70} - 180699442320 q^{72} - 428225274062 q^{73} + 307721180948 q^{74} - 617987210610 q^{75} - 455232145048 q^{76} - 963484794004 q^{77} + 688403957040 q^{78} - 183006289538 q^{79} + 1001949265154 q^{81} - 1176460419184 q^{82} + 361042835756 q^{83} - 402324805420 q^{84} + 832273178976 q^{85} - 1065344596322 q^{87} - 1836857960940 q^{88} + 1922736257242 q^{89} - 1170237151648 q^{90} - 2759662014220 q^{94} + 5518358548560 q^{95} + 1356111950818 q^{97} - 2518255928616 q^{98} + 3259343912178 q^{99}+O(q^{100}) \) 58 * q + 88 * q^2 - 2 * q^3 - 4 * q^7 + 79650 * q^8 - 1957890 * q^10 + 4120990 * q^11 + 2920062 * q^12 - 1824520 * q^14 - 8383600 * q^15 - 133743512 * q^16 + 33971578 * q^17 - 122384158 * q^18 + 65838718 * q^19 - 59408388 * q^20 + 200896236 * q^21 + 104539676 * q^23 + 163907064 * q^24 - 3086882294 * q^25 + 607848030 * q^26 - 1190867840 * q^27 + 817714294 * q^29 + 5793833612 * q^30 - 1059975938 * q^31 + 2323254598 * q^32 + 517001400 * q^36 - 864725342 * q^37 + 18048639408 * q^39 - 22547920086 * q^40 - 17292603926 * q^41 - 3344004962 * q^43 - 53750811886 * q^44 - 16067938640 * q^45 + 43310099300 * q^46 - 15159905282 * q^47 - 4602803862 * q^48 + 32036753022 * q^49 - 16057299278 * q^50 + 81167587800 * q^52 - 69552844564 * q^53 + 38996274808 * q^54 + 3944882736 * q^55 - 156397031424 * q^56 + 107434998568 * q^58 + 82613255468 * q^59 - 147410252946 * q^60 + 128229759922 * q^61 + 125938412928 * q^65 + 364716671994 * q^66 - 141670411468 * q^68 + 529640675916 * q^69 + 518962441956 * q^70 - 180699442320 * q^72 - 428225274062 * q^73 + 307721180948 * q^74 - 617987210610 * q^75 - 455232145048 * q^76 - 963484794004 * q^77 + 688403957040 * q^78 - 183006289538 * q^79 + 1001949265154 * q^81 - 1176460419184 * q^82 + 361042835756 * q^83 - 402324805420 * q^84 + 832273178976 * q^85 - 1065344596322 * q^87 - 1836857960940 * q^88 + 1922736257242 * q^89 - 1170237151648 * q^90 - 2759662014220 * q^94 + 5518358548560 * q^95 + 1356111950818 * q^97 - 2518255928616 * q^98 + 3259343912178 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	33.1274	+	33.1274i	0.517615	+	0.517615i	0.916849	−	0.399234i	$-0.130724\pi$
$2$	33.1274	+	33.1274i	0.517615	+	0.517615i	−0.399234	+	0.916849i	$0.630724\pi$
$3$	−631.679	−	631.679i	−0.866501	−	0.866501i	0.125582	−	0.992083i	$-0.459920\pi$
$3$	−631.679	−	631.679i	−0.866501	−	0.866501i	−0.992083	+	0.125582i	$0.959920\pi$
$4$		−	1901.16i		−	0.464149i
$5$		−	13469.1i		−	0.862026i	−0.902346	−	0.431013i	$-0.858156\pi$
$5$		−	13469.1i		−	0.862026i	0.902346	−	0.431013i	$-0.141844\pi$
$6$		−	41851.7i		−	0.897028i
$7$	113718.			0.966585			0.483293	−	0.875459i	$-0.339441\pi$
$7$	113718.			0.966585			0.483293	+	0.875459i	$0.339441\pi$
$8$	198670.	−	198670.i	0.757866	−	0.757866i
$9$			266596.i			0.501647i
$10$	446197.	−	446197.i	0.446197	−	0.446197i
$11$	979737.	+	979737.i	0.553036	+	0.553036i	0.927316	−	0.374280i	$-0.122110\pi$
$11$	979737.	+	979737.i	0.553036	+	0.553036i	−0.374280	+	0.927316i	$0.622110\pi$
$12$	−1.20092e6	+	1.20092e6i	−0.402186	+	0.402186i
$13$		−	7.13138e6i		−	1.47745i	−0.674006	−	0.738726i	$-0.735428\pi$
$13$		−	7.13138e6i		−	1.47745i	0.674006	−	0.738726i	$-0.264572\pi$
$14$	3.76717e6	+	3.76717e6i	0.500319	+	0.500319i
$15$	−8.50818e6	+	8.50818e6i	−0.746946	+	0.746946i
$16$	5.37569e6			0.320416
$17$	−1.36053e7	−	1.36053e7i	−0.563655	−	0.563655i	0.366688	−	0.930344i	$-0.380491\pi$
$17$	−1.36053e7	−	1.36053e7i	−0.563655	−	0.563655i	−0.930344	+	0.366688i	$0.880491\pi$
$18$	−8.83162e6	+	8.83162e6i	−0.259660	+	0.259660i
$19$	7.00389e6	+	7.00389e6i	0.148874	+	0.148874i	0.777615	−	0.628741i	$-0.216429\pi$
$19$	7.00389e6	+	7.00389e6i	0.148874	+	0.148874i	−0.628741	+	0.777615i	$0.716429\pi$
$20$	−2.56069e7			−0.400108
$21$	−7.18331e7	−	7.18331e7i	−0.837547	−	0.837547i
$22$			6.49122e7i			0.572520i
$23$	−2.39819e8			−1.62001			−0.810003	−	0.586426i	$-0.800534\pi$
$23$	−2.39819e8			−1.62001			−0.810003	+	0.586426i	$0.800534\pi$
$24$	−2.50991e8			−1.31338
$25$	6.27227e7			0.256912
$26$	2.36244e8	−	2.36244e8i	0.764752	−	0.764752i
$27$	−1.67297e8	+	1.67297e8i	−0.431823	+	0.431823i
$28$		−	2.16195e8i		−	0.448640i
$29$	5.39336e8	−	2.50861e8i	0.906717	−	0.421740i
$29$	5.39336e8	−	2.50861e8i	0.906717	−	0.421740i
$30$	−5.63707e8			−0.773261
$31$	8.35541e8	+	8.35541e8i	0.941451	+	0.941451i	0.998378	−	0.0569271i	$-0.0181303\pi$
$31$	8.35541e8	+	8.35541e8i	0.941451	+	0.941451i	−0.0569271	+	0.998378i	$0.518130\pi$
$32$	−6.35670e8	−	6.35670e8i	−0.592013	−	0.592013i
$33$		−	1.23776e9i		−	0.958413i
$34$		−	9.01413e8i		−	0.583513i
$35$		−	1.53168e9i		−	0.833221i
$36$	5.06840e8			0.232839
$37$	1.44922e8	−	1.44922e8i	0.0564840	−	0.0564840i	−0.678301	−	0.734785i	$-0.737283\pi$
$37$	1.44922e8	−	1.44922e8i	0.0564840	−	0.0564840i	0.734785	+	0.678301i	$0.237283\pi$
$38$			4.64041e8i			0.154118i
$39$	−4.50474e9	+	4.50474e9i	−1.28021	+	1.28021i
$40$	−2.67592e9	−	2.67592e9i	−0.653300	−	0.653300i
$41$	−1.87652e9	+	1.87652e9i	−0.395048	+	0.395048i	−0.876482	−	0.481434i	$-0.840116\pi$
$41$	−1.87652e9	+	1.87652e9i	−0.395048	+	0.395048i	0.481434	+	0.876482i	$0.340116\pi$
$42$		−	4.75928e9i		−	0.867054i
$43$	−6.36642e9	−	6.36642e9i	−1.00713	−	1.00713i	−0.999974	−	0.00715326i	$-0.997723\pi$
$43$	−6.36642e9	−	6.36642e9i	−1.00713	−	1.00713i	−0.00715326	−	0.999974i	$-0.502277\pi$
$44$	1.86263e9	−	1.86263e9i	0.256691	−	0.256691i
$45$	3.59082e9			0.432433
$46$	−7.94457e9	−	7.94457e9i	−0.838539	−	0.838539i
$47$	−1.30500e10	+	1.30500e10i	−1.21066	+	1.21066i	−0.239852	+	0.970809i	$0.577099\pi$
$47$	−1.30500e10	+	1.30500e10i	−1.21066	+	1.21066i	−0.970809	+	0.239852i	$0.922901\pi$
$48$	−3.39571e9	−	3.39571e9i	−0.277641	−	0.277641i
$49$	−9.09557e8			−0.0657133
$50$	2.07784e9	+	2.07784e9i	0.132982	+	0.132982i
$51$			1.71883e10i			0.976815i
$52$	−1.35579e10			−0.685758
$53$	2.13746e10			0.964370			0.482185	−	0.876069i	$-0.339843\pi$
$53$	2.13746e10			0.964370			0.482185	+	0.876069i	$0.339843\pi$
$54$	−1.10842e10			−0.447036
$55$	1.31962e10	−	1.31962e10i	0.476731	−	0.476731i
$56$	2.25923e10	−	2.25923e10i	0.732542	−	0.732542i
$57$		−	8.84842e9i		−	0.257998i
$58$	2.61771e10	+	9.55643e9i	0.687629	+	0.251031i
$59$	4.45578e10			1.05636			0.528179	−	0.849133i	$-0.322875\pi$
$59$	4.45578e10			1.05636			0.528179	+	0.849133i	$0.322875\pi$
$60$	1.61754e10	+	1.61754e10i	0.346694	+	0.346694i
$61$	2.78164e10	+	2.78164e10i	0.539911	+	0.539911i	0.923503	−	0.383592i	$-0.125313\pi$
$61$	2.78164e10	+	2.78164e10i	0.539911	+	0.539911i	−0.383592	+	0.923503i	$0.625313\pi$
$62$			5.53586e10i			0.974619i
$63$			3.03167e10i			0.484885i
$64$		−	6.41350e10i		−	0.933286i
$65$	−9.60536e10			−1.27360
$66$	4.10037e10	−	4.10037e10i	0.496089	−	0.496089i
$67$			6.17243e10i			0.682350i	0.940000	+	0.341175i	$0.110825\pi$
$67$			6.17243e10i			0.682350i	−0.940000	+	0.341175i	$0.889175\pi$
$68$	−2.58657e10	+	2.58657e10i	−0.261620	+	0.261620i
$69$	1.51489e11	+	1.51489e11i	1.40374	+	1.40374i
$70$	5.07406e10	−	5.07406e10i	0.431288	−	0.431288i
$71$		−	1.59859e11i		−	1.24792i	−0.781456	−	0.623961i	$-0.785523\pi$
$71$		−	1.59859e11i		−	1.24792i	0.781456	−	0.623961i	$-0.214477\pi$
$72$	5.29646e10	+	5.29646e10i	0.380181	+	0.380181i
$73$	−6.16978e10	+	6.16978e10i	−0.407692	+	0.407692i	−0.880933	−	0.473241i	$-0.843084\pi$
$73$	−6.16978e10	+	6.16978e10i	−0.407692	+	0.407692i	0.473241	+	0.880933i	$0.343084\pi$
$74$	9.60179e9			0.0584739
$75$	−3.96206e10	−	3.96206e10i	−0.222614	−	0.222614i
$76$	1.33155e10	−	1.33155e10i	0.0690996	−	0.0690996i
$77$	1.11414e11	+	1.11414e11i	0.534557	+	0.534557i
$78$	−2.98461e11			−1.32532
$79$	1.44571e11	+	1.44571e11i	0.594727	+	0.594727i	0.938905	−	0.344177i	$-0.111842\pi$
$79$	1.44571e11	+	1.44571e11i	0.594727	+	0.594727i	−0.344177	+	0.938905i	$0.611842\pi$
$80$		−	7.24060e10i		−	0.276207i
$81$	3.53036e11			1.25000
$82$	−1.24328e11			−0.408966
$83$	−9.68340e10			−0.296182			−0.148091	−	0.988974i	$-0.547313\pi$
$83$	−9.68340e10			−0.296182			−0.148091	+	0.988974i	$0.547313\pi$
$84$	−1.36566e11	+	1.36566e11i	−0.388747	+	0.388747i
$85$	−1.83251e11	+	1.83251e11i	−0.485885	+	0.485885i
$86$		−	4.21805e11i		−	1.04261i
$87$	−4.99151e11	−	1.82224e11i	−1.15111	−	0.420233i
$88$	3.89289e11			0.838254
$89$	−1.93556e10	−	1.93556e10i	−0.0389464	−	0.0389464i	0.687365	−	0.726312i	$-0.258767\pi$
$89$	−1.93556e10	−	1.93556e10i	−0.0389464	−	0.0389464i	−0.726312	+	0.687365i	$0.758767\pi$
$90$	1.18954e11	+	1.18954e11i	0.223834	+	0.223834i
$91$		−	8.10965e11i		−	1.42808i
$92$			4.55933e11i			0.751924i
$93$		−	1.05559e12i		−	1.63154i
$94$	−8.64623e11			−1.25331
$95$	9.43364e10	−	9.43364e10i	0.128333	−	0.128333i
$96$			8.03078e11i			1.02596i
$97$	−3.96346e10	+	3.96346e10i	−0.0475821	+	0.0475821i	−0.730498	−	0.682915i	$-0.760712\pi$
$97$	−3.96346e10	+	3.96346e10i	−0.0475821	+	0.0475821i	0.682915	+	0.730498i	$0.260712\pi$
$98$	−3.01312e10	−	3.01312e10i	−0.0340142	−	0.0340142i
$99$	−2.61194e11	+	2.61194e11i	−0.277429	+	0.277429i
$100$		−	1.19246e11i		−	0.119246i
$101$	−6.06070e11	−	6.06070e11i	−0.570945	−	0.570945i	0.361447	−	0.932393i	$-0.382283\pi$
$101$	−6.06070e11	−	6.06070e11i	−0.570945	−	0.570945i	−0.932393	+	0.361447i	$0.882283\pi$
$102$	−5.69404e11	+	5.69404e11i	−0.505614	+	0.505614i
$103$	5.01935e10			0.0420363			0.0210181	−	0.999779i	$-0.493309\pi$
$103$	5.01935e10			0.0420363			0.0210181	+	0.999779i	$0.493309\pi$
$104$	−1.41679e12	−	1.41679e12i	−1.11971	−	1.11971i
$105$	−9.67531e11	+	9.67531e11i	−0.721987	+	0.721987i
$106$	7.08086e11	+	7.08086e11i	0.499172	+	0.499172i
$107$	1.13112e12			0.753711			0.376856	−	0.926272i	$-0.377005\pi$
$107$	1.13112e12			0.753711			0.376856	+	0.926272i	$0.377005\pi$
$108$	3.18058e11	+	3.18058e11i	0.200430	+	0.200430i
$109$		−	2.01069e12i		−	1.19891i	−0.800410	−	0.599453i	$-0.795385\pi$
$109$		−	2.01069e12i		−	1.19891i	0.800410	−	0.599453i	$-0.204615\pi$
$110$	8.74313e11			0.493527
$111$	−1.83089e11			−0.0978868
$112$	6.11312e11			0.309710
$113$	1.91849e12	−	1.91849e12i	0.921487	−	0.921487i	−0.0756479	−	0.997135i	$-0.524103\pi$
$113$	1.91849e12	−	1.91849e12i	0.921487	−	0.921487i	0.997135	+	0.0756479i	$0.0241025\pi$
$114$	2.93125e11	−	2.93125e11i	0.133544	−	0.133544i
$115$			3.23016e12i			1.39649i
$116$	−4.76925e11	−	1.02536e12i	−0.195750	−	0.420852i
$117$	1.90120e12			0.741160
$118$	1.47608e12	+	1.47608e12i	0.546787	+	0.546787i
$119$	−1.54716e12	−	1.54716e12i	−0.544821	−	0.544821i
$120$			3.38064e12i			1.13217i
$121$		−	1.21866e12i		−	0.388302i
$122$			1.84297e12i			0.558932i
$123$	2.37072e12			0.684619
$124$	1.58849e12	−	1.58849e12i	0.436974	−	0.436974i
$125$		−	4.13319e12i		−	1.08349i
$126$	−1.00431e12	+	1.00431e12i	−0.250984	+	0.250984i
$127$	−5.20089e11	−	5.20089e11i	−0.123952	−	0.123952i	0.642409	−	0.766362i	$-0.277935\pi$
$127$	−5.20089e11	−	5.20089e11i	−0.123952	−	0.123952i	−0.766362	+	0.642409i	$0.777935\pi$
$128$	−4.79081e11	+	4.79081e11i	−0.108930	+	0.108930i
$129$			8.04307e12i			1.74535i
$130$	−3.18200e12	−	3.18200e12i	−0.659235	−	0.659235i
$131$	−4.86083e12	+	4.86083e12i	−0.961795	+	0.961795i	−0.999297	−	0.0375017i	$-0.988060\pi$
$131$	−4.86083e12	+	4.86083e12i	−0.961795	+	0.961795i	0.0375017	+	0.999297i	$0.488060\pi$
$132$	−2.35317e12			−0.444847
$133$	7.96467e11	+	7.96467e11i	0.143899	+	0.143899i
$134$	−2.04476e12	+	2.04476e12i	−0.353195	+	0.353195i
$135$	2.25335e12	+	2.25335e12i	0.372243	+	0.372243i
$136$	−5.40592e12			−0.854350
$137$	−5.41758e10	−	5.41758e10i	−0.00819374	−	0.00819374i	0.702998	−	0.711192i	$-0.251844\pi$
$137$	−5.41758e10	−	5.41758e10i	−0.00819374	−	0.00819374i	−0.711192	+	0.702998i	$0.751844\pi$
$138$			1.00368e13i			1.45319i
$139$	9.41829e12			1.30582			0.652910	−	0.757435i	$-0.273548\pi$
$139$	9.41829e12			1.30582			0.652910	+	0.757435i	$0.273548\pi$
$140$	−2.91196e12			−0.386739
$141$	1.64868e13			2.09808
$142$	5.29571e12	−	5.29571e12i	0.645943	−	0.645943i
$143$	6.98688e12	−	6.98688e12i	0.817085	−	0.817085i
$144$			1.43314e12i			0.160736i
$145$	−3.37888e12	−	7.26440e12i	−0.363551	−	0.781613i
$146$	−4.08777e12			−0.422055
$147$	5.74548e11	+	5.74548e11i	0.0569406	+	0.0569406i
$148$	−2.75520e11	−	2.75520e11i	−0.0262170	−	0.0262170i
$149$		−	1.88486e13i		−	1.72251i	−0.508172	−	0.861256i	$-0.669678\pi$
$149$		−	1.88486e13i		−	1.72251i	0.508172	−	0.861256i	$-0.330322\pi$
$150$		−	2.62505e12i		−	0.230457i
$151$			2.56247e12i			0.216171i	0.994142	+	0.108085i	$0.0344719\pi$
$151$			2.56247e12i			0.216171i	−0.994142	+	0.108085i	$0.965528\pi$
$152$	2.78293e12			0.225652
$153$	3.62711e12	−	3.62711e12i	0.282756	−	0.282756i
$154$			7.38168e12i			0.553389i
$155$	1.12540e13	−	1.12540e13i	0.811555	−	0.811555i
$156$	8.56422e12	+	8.56422e12i	0.594210	+	0.594210i
$157$	−1.47762e13	+	1.47762e13i	−0.986657	+	0.986657i	−0.999912	−	0.0132553i	$-0.995781\pi$
$157$	−1.47762e13	+	1.47762e13i	−0.986657	+	0.986657i	0.0132553	+	0.999912i	$0.495781\pi$
$158$			9.57850e12i			0.615680i
$159$	−1.35019e13	−	1.35019e13i	−0.835627	−	0.835627i
$160$	−8.56193e12	+	8.56193e12i	−0.510331	+	0.510331i
$161$	−2.72717e13			−1.56587
$162$	1.16952e13	+	1.16952e13i	0.647017	+	0.647017i
$163$	2.38907e13	−	2.38907e13i	1.27380	−	1.27380i	0.329729	−	0.944076i	$-0.393043\pi$
$163$	2.38907e13	−	2.38907e13i	1.27380	−	1.27380i	0.944076	−	0.329729i	$-0.106957\pi$
$164$	3.56755e12	+	3.56755e12i	0.183361	+	0.183361i
$165$	−1.66716e13			−0.826176
$166$	−3.20786e12	−	3.20786e12i	−0.153308	−	0.153308i
$167$		−	2.28148e11i		−	0.0105176i	−0.999986	−	0.00525881i	$-0.998326\pi$
$167$		−	2.28148e11i		−	0.0105176i	0.999986	−	0.00525881i	$-0.00167394\pi$
$168$	−2.85422e13			−1.26950
$169$	−2.75585e13			−1.18287
$170$	−1.21413e13			−0.503003
$171$	−1.86721e12	+	1.86721e12i	−0.0746820	+	0.0746820i
$172$	−1.21036e13	+	1.21036e13i	−0.467458	+	0.467458i
$173$		−	1.93616e13i		−	0.722213i	−0.932525	−	0.361107i	$-0.882399\pi$
$173$		−	1.93616e13i		−	0.722213i	0.932525	−	0.361107i	$-0.117601\pi$
$174$	−1.04990e13	−	2.25722e13i	−0.378313	−	0.813350i
$175$	7.13268e12			0.248327
$176$	5.26677e12	+	5.26677e12i	0.177202	+	0.177202i
$177$	−2.81462e13	−	2.81462e13i	−0.915336	−	0.915336i
$178$		−	1.28240e12i		−	0.0403184i
$179$			2.42531e13i			0.737307i	0.929567	+	0.368653i	$0.120181\pi$
$179$			2.42531e13i			0.737307i	−0.929567	+	0.368653i	$0.879819\pi$
$180$		−	6.82670e12i		−	0.200713i
$181$	1.58356e13			0.450363			0.225181	−	0.974317i	$-0.427703\pi$
$181$	1.58356e13			0.450363			0.225181	+	0.974317i	$0.427703\pi$
$182$	2.68651e13	−	2.68651e13i	0.739198	−	0.739198i
$183$		−	3.51421e13i		−	0.935666i
$184$	−4.76448e13	+	4.76448e13i	−1.22775	+	1.22775i
$185$	−1.95198e12	−	1.95198e12i	−0.0486906	−	0.0486906i
$186$	3.49689e13	−	3.49689e13i	0.844508	−	0.844508i
$187$		−	2.66592e13i		−	0.623444i
$188$	2.48100e13	+	2.48100e13i	0.561928	+	0.561928i
$189$	−1.90247e13	+	1.90247e13i	−0.417394	+	0.417394i
$190$	6.25024e12			0.132854
$191$	4.49335e13	+	4.49335e13i	0.925486	+	0.925486i	0.997410	−	0.0719239i	$-0.0229139\pi$
$191$	4.49335e13	+	4.49335e13i	0.925486	+	0.925486i	−0.0719239	+	0.997410i	$0.522914\pi$
$192$	−4.05127e13	+	4.05127e13i	−0.808693	+	0.808693i
$193$	5.19362e13	+	5.19362e13i	1.00491	+	1.00491i	0.999988	+	0.00491969i	$0.00156599\pi$
$193$	5.19362e13	+	5.19362e13i	1.00491	+	1.00491i	0.00491969	+	0.999988i	$0.498434\pi$
$194$	−2.62598e12			−0.0492585
$195$	6.06751e13	+	6.06751e13i	1.10358	+	1.10358i
$196$			1.72921e12i			0.0305008i
$197$	−1.14842e13			−0.196473			−0.0982363	−	0.995163i	$-0.531320\pi$
$197$	−1.14842e13			−0.196473			−0.0982363	+	0.995163i	$0.531320\pi$
$198$	−1.73053e13			−0.287203
$199$	6.58966e13			1.06107			0.530536	−	0.847662i	$-0.321991\pi$
$199$	6.58966e13			1.06107			0.530536	+	0.847662i	$0.321991\pi$
$200$	1.24611e13	−	1.24611e13i	0.194705	−	0.194705i
$201$	3.89900e13	−	3.89900e13i	0.591257	−	0.591257i
$202$		−	4.01550e13i		−	0.591060i
$203$	6.13321e13	−	2.85273e13i	0.876419	−	0.407648i
$204$	3.26777e13			0.453388
$205$	2.52751e13	+	2.52751e13i	0.340541	+	0.340541i
$206$	1.66278e12	+	1.66278e12i	0.0217586	+	0.0217586i
$207$		−	6.39347e13i		−	0.812671i
$208$		−	3.83361e13i		−	0.473400i
$209$			1.37239e13i			0.164665i
$210$	−6.41035e13			−0.747422
$211$	3.76858e13	−	3.76858e13i	0.427054	−	0.427054i	−0.460570	−	0.887624i	$-0.652355\pi$
$211$	3.76858e13	−	3.76858e13i	0.427054	−	0.427054i	0.887624	+	0.460570i	$0.152355\pi$
$212$		−	4.06365e13i		−	0.447612i
$213$	−1.00980e14	+	1.00980e14i	−1.08132	+	1.08132i
$214$	3.74709e13	+	3.74709e13i	0.390132	+	0.390132i
$215$	−8.57503e13	+	8.57503e13i	−0.868170	+	0.868170i
$216$			6.64738e13i			0.654528i
$217$	9.50159e13	+	9.50159e13i	0.909993	+	0.909993i
$218$	6.66087e13	−	6.66087e13i	0.620572	−	0.620572i
$219$	7.79464e13			0.706531
$220$	−2.50881e13	−	2.50881e13i	−0.221275	−	0.221275i
$221$	−9.70244e13	+	9.70244e13i	−0.832774	+	0.832774i
$222$	−6.06525e12	−	6.06525e12i	−0.0506677	−	0.0506677i
$223$	−1.15647e14			−0.940387			−0.470194	−	0.882563i	$-0.655816\pi$
$223$	−1.15647e14			−0.940387			−0.470194	+	0.882563i	$0.655816\pi$
$224$	−7.22869e13	−	7.22869e13i	−0.572231	−	0.572231i
$225$			1.67216e13i			0.128879i
$226$	1.27109e14			0.953951
$227$	−7.90193e13			−0.577535			−0.288767	−	0.957399i	$-0.593245\pi$
$227$	−7.90193e13			−0.577535			−0.288767	+	0.957399i	$0.593245\pi$
$228$	−1.68222e13			−0.119750
$229$	−3.61995e13	+	3.61995e13i	−0.251009	+	0.251009i	−0.821384	−	0.570375i	$-0.806798\pi$
$229$	−3.61995e13	+	3.61995e13i	−0.251009	+	0.251009i	0.570375	+	0.821384i	$0.306798\pi$
$230$	−1.07007e14	+	1.07007e14i	−0.722842	+	0.722842i
$231$		−	1.40755e14i		−	0.926387i
$232$	5.73114e13	−	1.56988e14i	0.367547	−	1.00679i
$233$	−2.21371e14			−1.38352			−0.691759	−	0.722129i	$-0.743164\pi$
$233$	−2.21371e14			−1.38352			−0.691759	+	0.722129i	$0.743164\pi$
$234$	6.29816e13	+	6.29816e13i	0.383635	+	0.383635i
$235$	1.75772e14	+	1.75772e14i	1.04362	+	1.04362i
$236$		−	8.47113e13i		−	0.490308i
$237$		−	1.82645e14i		−	1.03066i
$238$		−	1.02507e14i		−	0.564015i
$239$	−2.68358e14			−1.43988			−0.719941	−	0.694035i	$-0.755831\pi$
$239$	−2.68358e14			−1.43988			−0.719941	+	0.694035i	$0.755831\pi$
$240$	−4.57374e13	+	4.57374e13i	−0.239334	+	0.239334i
$241$			2.62031e12i			0.0133737i	0.999978	+	0.00668683i	$0.00212850\pi$
$241$			2.62031e12i			0.0133737i	−0.999978	+	0.00668683i	$0.997871\pi$
$242$	4.03709e13	−	4.03709e13i	0.200991	−	0.200991i
$243$	−1.34097e14	−	1.34097e14i	−0.651300	−	0.651300i
$244$	5.28833e13	−	5.28833e13i	0.250599	−	0.250599i
$245$			1.22510e13i			0.0566466i
$246$	7.85356e13	+	7.85356e13i	0.354369	+	0.354369i
$247$	4.99474e13	−	4.99474e13i	0.219954	−	0.219954i
$248$	3.31994e14			1.42699
$249$	6.11680e13	+	6.11680e13i	0.256642	+	0.256642i
$250$	1.36922e14	−	1.36922e14i	0.560831	−	0.560831i
$251$	1.20113e14	+	1.20113e14i	0.480340	+	0.480340i	0.905240	−	0.424900i	$-0.139691\pi$
$251$	1.20113e14	+	1.20113e14i	0.480340	+	0.480340i	−0.424900	+	0.905240i	$0.639691\pi$
$252$	5.76367e13			0.225059
$253$	−2.34960e14	−	2.34960e14i	−0.895922	−	0.895922i
$254$		−	3.44583e13i		−	0.128319i
$255$	2.31512e14			0.842040
$256$	−2.94438e14			−1.04605
$257$	−1.77546e14			−0.616187			−0.308093	−	0.951356i	$-0.599691\pi$
$257$	−1.77546e14			−0.616187			−0.308093	+	0.951356i	$0.599691\pi$
$258$	−2.66446e14	+	2.66446e14i	−0.903421	+	0.903421i
$259$	1.64802e13	−	1.64802e13i	0.0545966	−	0.0545966i
$260$			1.82613e14i			0.591141i
$261$	6.68785e13	+	1.43785e14i	0.211565	+	0.454852i
$262$	−3.22053e14			−0.995679
$263$	−1.98893e14	−	1.98893e14i	−0.601013	−	0.601013i	0.339568	−	0.940581i	$-0.389719\pi$
$263$	−1.98893e14	−	1.98893e14i	−0.601013	−	0.601013i	−0.940581	+	0.339568i	$0.889719\pi$
$264$	−2.45906e14	−	2.45906e14i	−0.726348	−	0.726348i
$265$		−	2.87898e14i		−	0.831311i
$266$			5.27697e13i			0.148969i
$267$			2.44531e13i			0.0674941i
$268$	1.17348e14			0.316712
$269$	1.48962e14	−	1.48962e14i	0.393153	−	0.393153i	−0.482656	−	0.875810i	$-0.660328\pi$
$269$	1.48962e14	−	1.48962e14i	0.393153	−	0.393153i	0.875810	+	0.482656i	$0.160328\pi$
$270$			1.49295e14i			0.385357i
$271$	4.62210e14	−	4.62210e14i	1.16687	−	1.16687i	0.183935	−	0.982938i	$-0.441117\pi$
$271$	4.62210e14	−	4.62210e14i	1.16687	−	1.16687i	0.982938	−	0.183935i	$-0.0588835\pi$
$272$	−7.31377e13	−	7.31377e13i	−0.180604	−	0.180604i
$273$	−5.12269e14	+	5.12269e14i	−1.23744	+	1.23744i
$274$		−	3.58941e12i		−	0.00848241i
$275$	6.14517e13	+	6.14517e13i	0.142082	+	0.142082i
$276$	2.88003e14	−	2.88003e14i	0.651543	−	0.651543i
$277$	−3.28537e14			−0.727286			−0.363643	−	0.931538i	$-0.618467\pi$
$277$	−3.28537e14			−0.727286			−0.363643	+	0.931538i	$0.618467\pi$
$278$	3.12003e14	+	3.12003e14i	0.675912	+	0.675912i
$279$	−2.22752e14	+	2.22752e14i	−0.472276	+	0.472276i
$280$	−3.04299e14	−	3.04299e14i	−0.631470	−	0.631470i
$281$	7.21532e14			1.46561			0.732804	−	0.680440i	$-0.238211\pi$
$281$	7.21532e14			1.46561			0.732804	+	0.680440i	$0.238211\pi$
$282$	5.46164e14	+	5.46164e14i	1.08600	+	1.08600i
$283$			6.64003e14i			1.29256i	0.763099	+	0.646281i	$0.223677\pi$
$283$			6.64003e14i			1.29256i	−0.763099	+	0.646281i	$0.776323\pi$
$284$	−3.03917e14			−0.579222
$285$	−1.19181e14			−0.222401
$286$	4.62914e14			0.845871
$287$	−2.13394e14	+	2.13394e14i	−0.381847	+	0.381847i
$288$	1.69467e14	−	1.69467e14i	0.296982	−	0.296982i
$289$		−	2.12416e14i		−	0.364585i
$290$	1.28717e14	−	3.52584e14i	0.216395	−	0.592754i
$291$	5.00727e13			0.0824599
$292$	1.17297e14	+	1.17297e14i	0.189230	+	0.189230i
$293$	4.95250e14	+	4.95250e14i	0.782743	+	0.782743i	0.980293	−	0.197550i	$-0.0632984\pi$
$293$	4.95250e14	+	4.95250e14i	0.782743	+	0.782743i	−0.197550	+	0.980293i	$0.563298\pi$
$294$			3.80665e13i			0.0589467i
$295$		−	6.00155e14i		−	0.910608i
$296$		−	5.75834e13i		−	0.0856145i
$297$	−3.27815e14			−0.477628
$298$	6.24405e14	−	6.24405e14i	0.891598	−	0.891598i
$299$			1.71024e15i			2.39348i
$300$	−7.53249e13	+	7.53249e13i	−0.103326	+	0.103326i
$301$	−7.23975e14	−	7.23975e14i	−0.973475	−	0.973475i
$302$	−8.48878e13	+	8.48878e13i	−0.111893	+	0.111893i
$303$			7.65683e14i			0.989449i
$304$	3.76508e13	+	3.76508e13i	0.0477015	+	0.0477015i
$305$	3.74663e14	−	3.74663e14i	0.465417	−	0.465417i
$306$	2.40313e14			0.292718
$307$	−8.47905e14	−	8.47905e14i	−1.01278	−	1.01278i	−0.999917	−	0.0128665i	$-0.995904\pi$
$307$	−8.47905e14	−	8.47905e14i	−1.01278	−	1.01278i	−0.0128665	−	0.999917i	$-0.504096\pi$
$308$	2.11814e14	−	2.11814e14i	0.248114	−	0.248114i
$309$	−3.17062e13	−	3.17062e13i	−0.0364244	−	0.0364244i
$310$	7.45633e14			0.840146
$311$	3.27260e14	+	3.27260e14i	0.361685	+	0.361685i	0.864433	−	0.502748i	$-0.167678\pi$
$311$	3.27260e14	+	3.27260e14i	0.361685	+	0.361685i	−0.502748	+	0.864433i	$0.667678\pi$
$312$			1.78991e15i			1.94046i
$313$	1.72727e15			1.83694			0.918470	−	0.395491i	$-0.129426\pi$
$313$	1.72727e15			1.83694			0.918470	+	0.395491i	$0.129426\pi$
$314$	−9.78996e14			−1.02142
$315$	4.08340e14			0.417983
$316$	2.74851e14	−	2.74851e14i	0.276042	−	0.276042i
$317$	−8.39493e14	+	8.39493e14i	−0.827298	+	0.827298i	−0.987142	−	0.159845i	$-0.948901\pi$
$317$	−8.39493e14	+	8.39493e14i	−0.827298	+	0.827298i	0.159845	+	0.987142i	$0.448901\pi$
$318$		−	8.94566e14i		−	0.865066i
$319$	7.74186e14	+	2.82630e14i	0.734685	+	0.268210i
$320$	−8.63843e14			−0.804517
$321$	−7.14503e14	−	7.14503e14i	−0.653091	−	0.653091i
$322$	−9.03439e14	−	9.03439e14i	−0.810519	−	0.810519i
$323$		−	1.90580e14i		−	0.167827i
$324$		−	6.71177e14i		−	0.580185i
$325$		−	4.47299e14i		−	0.379575i
$326$	1.58287e15			1.31868
$327$	−1.27011e15	+	1.27011e15i	−1.03885	+	1.03885i
$328$			7.45616e14i			0.598787i
$329$	−1.48401e15	+	1.48401e15i	−1.17021	+	1.17021i
$330$	−5.52285e14	−	5.52285e14i	−0.427641	−	0.427641i
$331$	1.44897e15	−	1.44897e15i	1.10177	−	1.10177i	0.107578	−	0.994197i	$-0.465690\pi$
$331$	1.44897e15	−	1.44897e15i	1.10177	−	1.10177i	0.994197	−	0.107578i	$-0.0343095\pi$
$332$			1.84096e14i			0.137473i
$333$	3.86357e13	+	3.86357e13i	0.0283350	+	0.0283350i
$334$	7.55793e12	−	7.55793e12i	0.00544408	−	0.00544408i
$335$	8.31374e14			0.588204
$336$	−3.86153e14	−	3.86153e14i	−0.268364	−	0.268364i
$337$	1.89040e15	−	1.89040e15i	1.29055	−	1.29055i	0.356099	−	0.934448i	$-0.384107\pi$
$337$	1.89040e15	−	1.89040e15i	1.29055	−	1.29055i	0.934448	−	0.356099i	$-0.115893\pi$
$338$	−9.12941e14	−	9.12941e14i	−0.612269	−	0.612269i
$339$	−2.42374e15			−1.59694
$340$	3.48389e14	+	3.48389e14i	0.225523	+	0.225523i
$341$			1.63722e15i			1.04131i
$342$	−1.23711e14			−0.0773131
$343$	−1.67743e15			−1.03010
$344$	−2.52963e15			−1.52654
$345$	2.04042e15	−	2.04042e15i	1.21006	−	1.21006i
$346$	6.41400e14	−	6.41400e14i	0.373828	−	0.373828i
$347$			6.64235e14i			0.380491i	0.981737	+	0.190246i	$0.0609285\pi$
$347$			6.64235e14i			0.380491i	−0.981737	+	0.190246i	$0.939072\pi$
$348$	−3.46436e14	+	9.48963e14i	−0.195051	+	0.534286i
$349$	2.11913e15			1.17275			0.586374	−	0.810041i	$-0.300555\pi$
$349$	2.11913e15			1.17275			0.586374	+	0.810041i	$0.300555\pi$
$350$	2.36287e14	+	2.36287e14i	0.128538	+	0.128538i
$351$	1.19306e15	+	1.19306e15i	0.637998	+	0.637998i
$352$		−	1.24558e15i		−	0.654810i
$353$		−	1.57963e13i		−	0.00816410i	−0.999992	−	0.00408205i	$-0.998701\pi$
$353$		−	1.57963e13i		−	0.00816410i	0.999992	−	0.00408205i	$-0.00129936\pi$
$354$		−	1.86482e15i		−	0.947583i
$355$	−2.15317e15			−1.07574
$356$	−3.67980e13	+	3.67980e13i	−0.0180769	+	0.0180769i
$357$			1.95462e15i			0.944175i
$358$	−8.03440e14	+	8.03440e14i	−0.381641	+	0.381641i
$359$	−1.61662e15	−	1.61662e15i	−0.755164	−	0.755164i	0.220274	−	0.975438i	$-0.429305\pi$
$359$	−1.61662e15	−	1.61662e15i	−0.755164	−	0.755164i	−0.975438	+	0.220274i	$0.929305\pi$
$360$	7.13388e14	−	7.13388e14i	0.327726	−	0.327726i
$361$		−	2.11521e15i		−	0.955673i
$362$	5.24591e14	+	5.24591e14i	0.233114	+	0.233114i
$363$	−7.69800e14	+	7.69800e14i	−0.336464	+	0.336464i
$364$	−1.54177e15			−0.662844
$365$	8.31017e14	+	8.31017e14i	0.351441	+	0.351441i
$366$	1.16416e15	−	1.16416e15i	0.484315	−	0.484315i
$367$	−1.37748e14	−	1.37748e14i	−0.0563753	−	0.0563753i	0.678357	−	0.734732i	$-0.262692\pi$
$367$	−1.37748e14	−	1.37748e14i	−0.0563753	−	0.0563753i	−0.734732	+	0.678357i	$0.762692\pi$
$368$	−1.28919e15			−0.519076
$369$	−5.00272e14	−	5.00272e14i	−0.198175	−	0.198175i
$370$		−	1.29328e14i		−	0.0504060i
$371$	2.43068e15			0.932146
$372$	−2.00684e15			−0.757276
$373$	7.98554e13			0.0296518			0.0148259	−	0.999890i	$-0.495281\pi$
$373$	7.98554e13			0.0296518			0.0148259	+	0.999890i	$0.495281\pi$
$374$	8.83149e14	−	8.83149e14i	0.322704	−	0.322704i
$375$	−2.61085e15	+	2.61085e15i	−0.938845	+	0.938845i
$376$			5.18528e15i			1.83504i
$377$	−1.78898e15	−	3.84621e15i	−0.623101	−	1.33963i
$378$	−1.26047e15			−0.432099
$379$	−6.98200e14	−	6.98200e14i	−0.235583	−	0.235583i	0.579435	−	0.815018i	$-0.303273\pi$
$379$	−6.98200e14	−	6.98200e14i	−0.235583	−	0.235583i	−0.815018	+	0.579435i	$0.803273\pi$
$380$	−1.79348e14	−	1.79348e14i	−0.0595656	−	0.0595656i
$381$			6.57058e14i			0.214810i
$382$			2.97706e15i			0.958091i
$383$		−	5.38533e15i		−	1.70616i	−0.521780	−	0.853080i	$-0.674732\pi$
$383$		−	5.38533e15i		−	1.70616i	0.521780	−	0.853080i	$-0.325268\pi$
$384$	6.05250e14			0.188776
$385$	1.50065e15	−	1.50065e15i	0.460801	−	0.460801i
$386$			3.44102e15i			1.04031i
$387$	1.69726e15	−	1.69726e15i	0.505223	−	0.505223i
$388$	7.53515e13	+	7.53515e13i	0.0220852	+	0.0220852i
$389$	−3.93341e15	+	3.93341e15i	−1.13520	+	1.13520i	−0.145900	+	0.989299i	$0.546608\pi$
$389$	−3.93341e15	+	3.93341e15i	−1.13520	+	1.13520i	−0.989299	+	0.145900i	$0.953392\pi$
$390$			4.02001e15i			1.14246i
$391$	3.26280e15	+	3.26280e15i	0.913125	+	0.913125i
$392$	−1.80702e14	+	1.80702e14i	−0.0498019	+	0.0498019i
$393$	6.14097e15			1.66679
$394$	−3.80440e14	−	3.80440e14i	−0.101697	−	0.101697i
$395$	1.94725e15	−	1.94725e15i	0.512670	−	0.512670i
$396$	4.96570e14	+	4.96570e14i	0.128768	+	0.128768i
$397$	1.20451e14			0.0307658			0.0153829	−	0.999882i	$-0.495103\pi$
$397$	1.20451e14			0.0307658			0.0153829	+	0.999882i	$0.495103\pi$
$398$	2.18298e15	+	2.18298e15i	0.549227	+	0.549227i
$399$		−	1.00622e15i		−	0.249377i
$400$	3.37178e14			0.0823188
$401$	−2.44145e15			−0.587195			−0.293597	−	0.955929i	$-0.594852\pi$
$401$	−2.44145e15			−0.587195			−0.293597	+	0.955929i	$0.594852\pi$
$402$	2.58327e15			0.612087
$403$	5.95856e15	−	5.95856e15i	1.39095	−	1.39095i
$404$	−1.15223e15	+	1.15223e15i	−0.265004	+	0.265004i
$405$		−	4.75510e15i		−	1.07753i
$406$	2.97681e15	+	1.08674e15i	0.664652	+	0.242643i
$407$	2.83972e14			0.0624754
$408$	3.41480e15	+	3.41480e15i	0.740295	+	0.740295i
$409$	3.11859e15	+	3.11859e15i	0.666220	+	0.666220i	0.956839	−	0.290619i	$-0.0938611\pi$
$409$	3.11859e15	+	3.11859e15i	0.666220	+	0.666220i	−0.290619	+	0.956839i	$0.593861\pi$
$410$			1.67460e15i			0.352539i
$411$			6.84435e13i			0.0141998i
$412$		−	9.54256e13i		−	0.0195111i
$413$	5.06701e15			1.02106
$414$	2.11799e15	−	2.11799e15i	0.420651	−	0.420651i
$415$			1.30427e15i			0.255317i
$416$	−4.53320e15	+	4.53320e15i	−0.874672	+	0.874672i
$417$	−5.94934e15	−	5.94934e15i	−1.13149	−	1.13149i
$418$	−4.54638e14	+	4.54638e14i	−0.0852331	+	0.0852331i
$419$			4.04006e15i			0.746627i	0.927705	+	0.373313i	$0.121778\pi$
$419$			4.04006e15i			0.746627i	−0.927705	+	0.373313i	$0.878222\pi$
$420$	1.83943e15	+	1.83943e15i	0.335110	+	0.335110i
$421$	3.94209e15	−	3.94209e15i	0.708001	−	0.708001i	−0.258114	−	0.966115i	$-0.583101\pi$
$421$	3.94209e15	−	3.94209e15i	0.708001	−	0.708001i	0.966115	+	0.258114i	$0.0831009\pi$
$422$	2.49686e15			0.442099
$423$	−3.47907e15	−	3.47907e15i	−0.607325	−	0.607325i
$424$	4.24650e15	−	4.24650e15i	0.730863	−	0.730863i
$425$	−8.53359e14	−	8.53359e14i	−0.144810	−	0.144810i
$426$	−6.69038e15			−1.11942
$427$	3.16322e15	+	3.16322e15i	0.521870	+	0.521870i
$428$		−	2.15043e15i		−	0.349835i
$429$	−8.82693e15			−1.41601
$430$	−5.68136e15			−0.898756
$431$	9.93185e15			1.54941			0.774705	−	0.632322i	$-0.217898\pi$
$431$	9.93185e15			1.54941			0.774705	+	0.632322i	$0.217898\pi$
$432$	−8.99338e14	+	8.99338e14i	−0.138363	+	0.138363i
$433$	−3.32587e15	+	3.32587e15i	−0.504636	+	0.504636i	−0.912875	−	0.408239i	$-0.866143\pi$
$433$	−3.32587e15	+	3.32587e15i	−0.504636	+	0.504636i	0.408239	+	0.912875i	$0.366143\pi$
$434$			6.29525e15i			0.942052i
$435$	−2.45440e15	+	6.72314e15i	−0.362251	+	0.992285i
$436$	−3.82262e15			−0.556471
$437$	−1.67967e15	−	1.67967e15i	−0.241176	−	0.241176i
$438$	2.58216e15	+	2.58216e15i	0.365711	+	0.365711i
$439$		−	9.43741e15i		−	1.31846i	−0.751943	−	0.659228i	$-0.770883\pi$
$439$		−	9.43741e15i		−	1.31846i	0.751943	−	0.659228i	$-0.229117\pi$
$440$		−	5.24339e15i		−	0.722597i
$441$		−	2.42484e14i		−	0.0329649i
$442$	−6.42832e15			−0.862113
$443$	1.05125e15	−	1.05125e15i	0.139086	−	0.139086i	−0.634136	−	0.773222i	$-0.718644\pi$
$443$	1.05125e15	−	1.05125e15i	0.139086	−	0.139086i	0.773222	+	0.634136i	$0.218644\pi$
$444$			3.48080e14i			0.0454341i
$445$	−2.60704e14	+	2.60704e14i	−0.0335728	+	0.0335728i
$446$	−3.83109e15	−	3.83109e15i	−0.486759	−	0.486759i
$447$	−1.19063e16	+	1.19063e16i	−1.49256	+	1.49256i
$448$		−	7.29328e15i		−	0.902101i
$449$	−3.87605e15	−	3.87605e15i	−0.473054	−	0.473054i	0.429847	−	0.902902i	$-0.358567\pi$
$449$	−3.87605e15	−	3.87605e15i	−0.473054	−	0.473054i	−0.902902	+	0.429847i	$0.858567\pi$
$450$	−5.53943e14	+	5.53943e14i	−0.0667098	+	0.0667098i
$451$	−3.67699e15			−0.436952
$452$	−3.64735e15	−	3.64735e15i	−0.427707	−	0.427707i
$453$	1.61866e15	−	1.61866e15i	0.187312	−	0.187312i
$454$	−2.61770e15	−	2.61770e15i	−0.298941	−	0.298941i
$455$	−1.09230e16			−1.23104
$456$	−1.75792e15	−	1.75792e15i	−0.195528	−	0.195528i
$457$			1.47283e16i			1.61680i	0.588635	+	0.808399i	$0.299666\pi$
$457$			1.47283e16i			1.61680i	−0.588635	+	0.808399i	$0.700334\pi$
$458$	−2.39839e15			−0.259852
$459$	4.55225e15			0.486799
$460$	6.14103e15			0.648178
$461$	−1.38407e15	+	1.38407e15i	−0.144196	+	0.144196i	−0.775520	−	0.631323i	$-0.782512\pi$
$461$	−1.38407e15	+	1.38407e15i	−0.144196	+	0.144196i	0.631323	+	0.775520i	$0.282512\pi$
$462$	4.66285e15	−	4.66285e15i	0.479512	−	0.479512i
$463$		−	9.14037e15i		−	0.927851i	−0.885874	−	0.463925i	$-0.846441\pi$
$463$		−	9.14037e15i		−	0.927851i	0.885874	−	0.463925i	$-0.153559\pi$
$464$	2.89931e15	−	1.34855e15i	0.290527	−	0.135132i
$465$	−1.42179e16			−1.40643
$466$	−7.33343e15	−	7.33343e15i	−0.716129	−	0.716129i
$467$	5.66084e15	+	5.66084e15i	0.545732	+	0.545732i	0.925203	−	0.379472i	$-0.123894\pi$
$467$	5.66084e15	+	5.66084e15i	0.545732	+	0.545732i	−0.379472	+	0.925203i	$0.623894\pi$
$468$		−	3.61447e15i		−	0.344009i
$469$			7.01915e15i			0.659550i
$470$			1.16457e16i			1.08039i
$471$	1.86677e16			1.70988
$472$	8.85229e15	−	8.85229e15i	0.800578	−	0.800578i
$473$		−	1.24748e16i		−	1.11396i
$474$	6.05054e15	−	6.05054e15i	0.533487	−	0.533487i
$475$	4.39303e14	+	4.39303e14i	0.0382474	+	0.0382474i
$476$	−2.94139e15	+	2.94139e15i	−0.252878	+	0.252878i
$477$			5.69839e15i			0.483773i
$478$	−8.88999e15	−	8.88999e15i	−0.745305	−	0.745305i
$479$	1.15323e16	−	1.15323e16i	0.954781	−	0.954781i	−0.0442404	−	0.999021i	$-0.514087\pi$
$479$	1.15323e16	−	1.15323e16i	0.954781	−	0.954781i	0.999021	+	0.0442404i	$0.0140868\pi$
$480$	1.08168e16			0.884404
$481$	−1.03350e15	−	1.03350e15i	−0.0834524	−	0.0834524i
$482$	−8.68040e13	+	8.68040e13i	−0.00692241	+	0.00692241i
$483$	1.72269e16	+	1.72269e16i	1.35683	+	1.35683i
$484$	−2.31686e15			−0.180230
$485$	5.33844e14	+	5.33844e14i	0.0410170	+	0.0410170i
$486$		−	8.88456e15i		−	0.674246i
$487$	1.77844e16			1.33311			0.666554	−	0.745456i	$-0.267768\pi$
$487$	1.77844e16			1.33311			0.666554	+	0.745456i	$0.267768\pi$
$488$	1.10526e16			0.818360
$489$	−3.01825e16			−2.20751
$490$	−4.05842e14	+	4.05842e14i	−0.0293211	+	0.0293211i
$491$	4.21644e15	−	4.21644e15i	0.300924	−	0.300924i	−0.540451	−	0.841375i	$-0.681747\pi$
$491$	4.21644e15	−	4.21644e15i	0.300924	−	0.300924i	0.841375	+	0.540451i	$0.181747\pi$
$492$		−	4.50710e15i		−	0.317765i
$493$	−1.07508e16	−	3.92479e15i	−0.748792	−	0.273360i
$494$	3.30925e15			0.227703
$495$	3.51806e15	+	3.51806e15i	0.239151	+	0.239151i
$496$	4.49161e15	+	4.49161e15i	0.301656	+	0.301656i
$497$		−	1.81788e16i		−	1.20622i
$498$			4.05267e15i			0.265684i
$499$			2.57397e16i			1.66725i	0.552330	+	0.833625i	$0.313739\pi$
$499$			2.57397e16i			1.66725i	−0.552330	+	0.833625i	$0.686261\pi$
$500$	−7.85783e15			−0.502901
$501$	−1.44116e14	+	1.44116e14i	−0.00911352	+	0.00911352i
$502$			7.95808e15i			0.497263i
$503$	−1.80359e16	+	1.80359e16i	−1.11360	+	1.11360i	−0.120944	+	0.992659i	$0.538592\pi$
$503$	−1.80359e16	+	1.80359e16i	−1.11360	+	1.11360i	−0.992659	+	0.120944i	$0.961408\pi$
$504$	6.02301e15	+	6.02301e15i	0.367477	+	0.367477i
$505$	−8.16325e15	+	8.16325e15i	−0.492169	+	0.492169i
$506$		−	1.55672e16i		−	0.927485i
$507$	1.74081e16	+	1.74081e16i	1.02495	+	1.02495i
$508$	−9.88770e14	+	9.88770e14i	−0.0575325	+	0.0575325i
$509$	−9.77423e14			−0.0562051			−0.0281026	−	0.999605i	$-0.508947\pi$
$509$	−9.77423e14			−0.0562051			−0.0281026	+	0.999605i	$0.508947\pi$
$510$	7.66939e15	+	7.66939e15i	0.435853	+	0.435853i
$511$	−7.01613e15	+	7.01613e15i	−0.394069	+	0.394069i
$512$	−7.79165e15	−	7.79165e15i	−0.432523	−	0.432523i
$513$	−2.34346e15			−0.128574
$514$	−5.88163e15	−	5.88163e15i	−0.318947	−	0.318947i
$515$		−	6.76064e14i		−	0.0362363i
$516$	1.52911e16			0.810105
$517$	−2.55711e16			−1.33908
$518$	1.09189e15			0.0565200
$519$	−1.22303e16	+	1.22303e16i	−0.625798	+	0.625798i
$520$	−1.90830e16	+	1.90830e16i	−0.965219	+	0.965219i
$521$		−	8.42794e15i		−	0.421400i	−0.977551	−	0.210700i	$-0.932426\pi$
$521$		−	8.42794e15i		−	0.421400i	0.977551	−	0.210700i	$-0.0675744\pi$
$522$	−2.54770e15	+	6.97872e15i	−0.125929	+	0.344947i
$523$	1.81826e16			0.888478			0.444239	−	0.895908i	$-0.353474\pi$
$523$	1.81826e16			0.888478			0.444239	+	0.895908i	$0.353474\pi$
$524$	9.24119e15	+	9.24119e15i	0.446416	+	0.446416i
$525$	−4.50557e15	−	4.50557e15i	−0.215176	−	0.215176i
$526$		−	1.31776e16i		−	0.622187i
$527$		−	2.27355e16i		−	1.06131i
$528$		−	6.65381e15i		−	0.307091i
$529$	3.55985e16			1.62442
$530$	9.53731e15	−	9.53731e15i	0.430299	−	0.430299i
$531$			1.18789e16i			0.529919i
$532$	1.51421e15	−	1.51421e15i	0.0667906	−	0.0667906i
$533$	1.33822e16	+	1.33822e16i	0.583665	+	0.583665i
$534$	−8.10066e14	+	8.10066e14i	−0.0349360	+	0.0349360i
$535$		−	1.52352e16i		−	0.649718i
$536$	1.22628e16	+	1.22628e16i	0.517130	+	0.517130i
$537$	1.53201e16	−	1.53201e16i	0.638877	−	0.638877i
$538$	9.86944e15			0.407004
$539$	−8.91127e14	−	8.91127e14i	−0.0363419	−	0.0363419i
$540$	4.28397e15	−	4.28397e15i	0.172776	−	0.172776i
$541$	−1.45010e16	−	1.45010e16i	−0.578383	−	0.578383i	0.356075	−	0.934457i	$-0.384115\pi$
$541$	−1.45010e16	−	1.45010e16i	−0.578383	−	0.578383i	−0.934457	+	0.356075i	$0.884115\pi$
$542$	3.06236e16			1.20798
$543$	−1.00030e16	−	1.00030e16i	−0.390239	−	0.390239i
$544$			1.72969e16i			0.667383i
$545$	−2.70822e16			−1.03349
$546$	−3.39403e16			−1.28103
$547$	1.60959e16			0.600883			0.300442	−	0.953800i	$-0.402866\pi$
$547$	1.60959e16			0.600883			0.300442	+	0.953800i	$0.402866\pi$
$548$	−1.02997e14	+	1.02997e14i	−0.00380312	+	0.00380312i
$549$	−7.41574e15	+	7.41574e15i	−0.270845	+	0.270845i
$550$			4.07147e15i			0.147087i
$551$	5.53445e15	+	2.02045e15i	0.197772	+	0.0722002i
$552$	6.01925e16			2.12769
$553$	1.64403e16	+	1.64403e16i	0.574855	+	0.574855i
$554$	−1.08836e16	−	1.08836e16i	−0.376454	−	0.376454i
$555$			2.46605e15i			0.0843809i
$556$		−	1.79056e16i		−	0.606095i
$557$			3.60176e16i			1.20610i	0.797703	+	0.603050i	$0.206048\pi$
$557$			3.60176e16i			1.20610i	−0.797703	+	0.603050i	$0.793952\pi$
$558$	−1.47584e16			−0.488915
$559$	−4.54014e16	+	4.54014e16i	−1.48798	+	1.48798i
$560$		−	8.23385e15i		−	0.266978i
$561$	−1.68400e16	+	1.68400e16i	−0.540214	+	0.540214i
$562$	2.39025e16	+	2.39025e16i	0.758621	+	0.758621i
$563$	−7.20035e15	+	7.20035e15i	−0.226101	+	0.226101i	−0.811062	−	0.584960i	$-0.801110\pi$
$563$	−7.20035e15	+	7.20035e15i	−0.226101	+	0.226101i	0.584960	+	0.811062i	$0.301110\pi$
$564$		−	3.13440e16i		−	0.973821i
$565$	−2.58404e16	−	2.58404e16i	−0.794345	−	0.794345i
$566$	−2.19967e16	+	2.19967e16i	−0.669050	+	0.669050i
$567$	4.01465e16			1.20823
$568$	−3.17592e16	−	3.17592e16i	−0.945757	−	0.945757i
$569$	1.37583e16	−	1.37583e16i	0.405406	−	0.405406i	−0.474727	−	0.880133i	$-0.657453\pi$
$569$	1.37583e16	−	1.37583e16i	0.405406	−	0.405406i	0.880133	+	0.474727i	$0.157453\pi$
$570$	−3.94814e15	−	3.94814e15i	−0.115118	−	0.115118i
$571$	9.56194e15			0.275886			0.137943	−	0.990440i	$-0.455951\pi$
$571$	9.56194e15			0.275886			0.137943	+	0.990440i	$0.455951\pi$
$572$	−1.32831e16	−	1.32831e16i	−0.379249	−	0.379249i
$573$		−	5.67671e16i		−	1.60387i
$574$	−1.41383e16			−0.395300
$575$	−1.50421e16			−0.416199
$576$	1.70981e16			0.468180
$577$	1.17349e16	−	1.17349e16i	0.317999	−	0.317999i	−0.529999	−	0.847998i	$-0.677808\pi$
$577$	1.17349e16	−	1.17349e16i	0.317999	−	0.317999i	0.847998	+	0.529999i	$0.177808\pi$
$578$	7.03677e15	−	7.03677e15i	0.188715	−	0.188715i
$579$		−	6.56140e16i		−	1.74151i
$580$	−1.38108e16	+	6.42378e15i	−0.362785	+	0.168742i
$581$	−1.10117e16			−0.286286
$582$	1.65878e15	+	1.65878e15i	0.0426825	+	0.0426825i
$583$	2.09415e16	+	2.09415e16i	0.533332	+	0.533332i
$584$			2.45150e16i			0.617952i
$585$		−	2.56075e16i		−	0.638899i
$586$			3.28127e16i			0.810319i
$587$	9.48894e14			0.0231947			0.0115974	−	0.999933i	$-0.496308\pi$
$587$	9.48894e14			0.0231947			0.0115974	+	0.999933i	$0.496308\pi$
$588$	1.09231e15	−	1.09231e15i	0.0264290	−	0.0264290i
$589$			1.17041e16i			0.280315i
$590$	1.98816e16	−	1.98816e16i	0.471345	−	0.471345i
$591$	7.25431e15	+	7.25431e15i	0.170244	+	0.170244i
$592$	7.79058e14	−	7.79058e14i	0.0180984	−	0.0180984i
$593$			1.63472e16i			0.375937i	0.982175	+	0.187968i	$0.0601902\pi$
$593$			1.63472e16i			0.375937i	−0.982175	+	0.187968i	$0.939810\pi$
$594$	−1.08596e16	−	1.08596e16i	−0.247227	−	0.247227i
$595$	−2.08389e16	+	2.08389e16i	−0.469649	+	0.469649i
$596$	−3.58342e16			−0.799502
$597$	−4.16255e16	−	4.16255e16i	−0.919420	−	0.919420i
$598$	−5.66557e16	+	5.66557e16i	−1.23890	+	1.23890i
$599$	8.25108e15	+	8.25108e15i	0.178628	+	0.178628i	0.790758	−	0.612129i	$-0.209687\pi$
$599$	8.25108e15	+	8.25108e15i	0.178628	+	0.178628i	−0.612129	+	0.790758i	$0.709687\pi$
$600$	−1.57428e16			−0.337424
$601$	−5.71089e16	−	5.71089e16i	−1.21187	−	1.21187i	−0.970410	−	0.241463i	$-0.922373\pi$
$601$	−5.71089e16	−	5.71089e16i	−1.21187	−	1.21187i	−0.241463	−	0.970410i	$-0.577627\pi$
$602$		−	4.79668e16i		−	1.00777i
$603$	−1.64554e16			−0.342299
$604$	4.87165e15			0.100335
$605$	−1.64143e16			−0.334726
$606$	−2.53651e16	+	2.53651e16i	−0.512154	+	0.512154i
$607$	5.08524e16	−	5.08524e16i	1.01667	−	1.01667i	0.0168101	−	0.999859i	$-0.494649\pi$
$607$	5.08524e16	−	5.08524e16i	1.01667	−	1.01667i	0.999859	−	0.0168101i	$-0.00535106\pi$
$608$		−	8.90432e15i		−	0.176270i
$609$	−5.67623e16	−	2.07221e16i	−1.11264	−	0.406191i
$610$	2.48232e16			0.481814
$611$	9.30644e16	+	9.30644e16i	1.78869	+	1.78869i
$612$	−6.89569e15	−	6.89569e15i	−0.131241	−	0.131241i
$613$			8.33450e16i			1.57078i	0.618998	+	0.785392i	$0.287539\pi$
$613$			8.33450e16i			1.57078i	−0.618998	+	0.785392i	$0.712461\pi$
$614$		−	5.61777e16i		−	1.04846i
$615$		−	3.19315e16i		−	0.590159i
$616$	4.42691e16			0.810244
$617$	−3.19932e16	+	3.19932e16i	−0.579891	+	0.579891i	−0.934873	−	0.354982i	$-0.884487\pi$
$617$	−3.19932e16	+	3.19932e16i	−0.579891	+	0.579891i	0.354982	+	0.934873i	$0.384487\pi$
$618$		−	2.10068e15i		−	0.0377077i
$619$	2.83352e16	−	2.83352e16i	0.503712	−	0.503712i	−0.408877	−	0.912589i	$-0.634080\pi$
$619$	2.83352e16	−	2.83352e16i	0.503712	−	0.503712i	0.912589	+	0.408877i	$0.134080\pi$
$620$	−2.13957e16	−	2.13957e16i	−0.376683	−	0.376683i
$621$	4.01210e16	−	4.01210e16i	0.699556	−	0.699556i
$622$			2.16825e16i			0.374427i
$623$	−2.20108e15	−	2.20108e15i	−0.0376450	−	0.0376450i
$624$	−2.42161e16	+	2.42161e16i	−0.410201	+	0.410201i
$625$	−4.03574e16			−0.677084
$626$	5.72200e16	+	5.72200e16i	0.950827	+	0.950827i
$627$	8.66913e15	−	8.66913e15i	0.142682	−	0.142682i
$628$	2.80919e16	+	2.80919e16i	0.457956	+	0.457956i
$629$	−3.94342e15			−0.0636750
$630$	1.35272e16	+	1.35272e16i	0.216354	+	0.216354i
$631$			7.63135e16i			1.20900i	0.796606	+	0.604499i	$0.206627\pi$
$631$			7.63135e16i			1.20900i	−0.796606	+	0.604499i	$0.793373\pi$
$632$	5.74437e16			0.901447
$633$	−4.76106e16			−0.740085
$634$	−5.56204e16			−0.856443
$635$	−7.00515e15	+	7.00515e15i	−0.106850	+	0.106850i
$636$	−2.56692e16	+	2.56692e16i	−0.387856	+	0.387856i
$637$			6.48640e15i			0.0970883i
$638$	1.62839e16	+	3.50095e16i	0.241455	+	0.519113i
$639$	4.26178e16			0.626016
$640$	6.45281e15	+	6.45281e15i	0.0939007	+	0.0939007i
$641$	3.66752e16	+	3.66752e16i	0.528718	+	0.528718i	0.920190	−	0.391472i	$-0.128034\pi$
$641$	3.66752e16	+	3.66752e16i	0.528718	+	0.528718i	−0.391472	+	0.920190i	$0.628034\pi$
$642$		−	4.73392e16i		−	0.676100i
$643$		−	5.75449e16i		−	0.814219i	−0.913379	−	0.407110i	$-0.866537\pi$
$643$		−	5.75449e16i		−	0.814219i	0.913379	−	0.407110i	$-0.133463\pi$
$644$			5.18477e16i			0.726799i
$645$	1.08333e17			1.50454
$646$	6.31340e15	−	6.31340e15i	0.0868697	−	0.0868697i
$647$			3.38041e16i			0.460834i	0.973092	+	0.230417i	$0.0740089\pi$
$647$			3.38041e16i			0.460834i	−0.973092	+	0.230417i	$0.925991\pi$
$648$	7.01377e16	−	7.01377e16i	0.947330	−	0.947330i
$649$	4.36549e16	+	4.36549e16i	0.584205	+	0.584205i
$650$	1.48178e16	−	1.48178e16i	0.196474	−	0.196474i
$651$		−	1.20039e17i		−	1.57702i
$652$	−4.54199e16	−	4.54199e16i	−0.591235	−	0.591235i
$653$	9.95509e16	−	9.95509e16i	1.28400	−	1.28400i	0.345635	−	0.938369i	$-0.387664\pi$
$653$	9.95509e16	−	9.95509e16i	1.28400	−	1.28400i	0.938369	−	0.345635i	$-0.112336\pi$
$654$	−8.41506e16			−1.07545
$655$	6.54712e16	+	6.54712e16i	0.829092	+	0.829092i
$656$	−1.00876e16	+	1.00876e16i	−0.126580	+	0.126580i
$657$	−1.64484e16	−	1.64484e16i	−0.204518	−	0.204518i
$658$	−9.83230e16			−1.21143
$659$	−1.58220e16	−	1.58220e16i	−0.193174	−	0.193174i	0.603892	−	0.797066i	$-0.293616\pi$
$659$	−1.58220e16	−	1.58220e16i	−0.193174	−	0.193174i	−0.797066	+	0.603892i	$0.793616\pi$
$660$			3.16952e16i			0.383469i
$661$	−1.15076e17			−1.37968			−0.689838	−	0.723964i	$-0.742318\pi$
$661$	−1.15076e17			−1.37968			−0.689838	+	0.723964i	$0.742318\pi$
$662$	9.60014e16			1.14059
$663$	1.22577e17			1.44320
$664$	−1.92380e16	+	1.92380e16i	−0.224467	+	0.224467i
$665$	1.07277e16	−	1.07277e16i	0.124045	−	0.124045i
$666$			2.55980e15i			0.0293333i
$667$	−1.29343e17	+	6.01612e16i	−1.46889	+	0.683221i
$668$	−4.33744e14			−0.00488174
$669$	7.30520e16	+	7.30520e16i	0.814846	+	0.814846i
$670$	2.75412e16	+	2.75412e16i	0.304463	+	0.304463i
$671$			5.45056e16i			0.597181i
$672$			9.13243e16i			0.991678i
$673$		−	9.46879e16i		−	1.01907i	−0.860450	−	0.509535i	$-0.829817\pi$
$673$		−	9.46879e16i		−	1.01907i	0.860450	−	0.509535i	$-0.170183\pi$
$674$	1.25248e17			1.33601
$675$	−1.04933e16	+	1.04933e16i	−0.110941	+	0.110941i
$676$			5.23930e16i			0.549026i
$677$	−5.51443e16	+	5.51443e16i	−0.572755	+	0.572755i	−0.932897	−	0.360142i	$-0.882728\pi$
$677$	−5.51443e16	+	5.51443e16i	−0.572755	+	0.572755i	0.360142	+	0.932897i	$0.382728\pi$
$678$	−8.02921e16	−	8.02921e16i	−0.826599	−	0.826599i
$679$	−4.50716e15	+	4.50716e15i	−0.0459922	+	0.0459922i
$680$			7.28131e16i			0.736472i
$681$	4.99149e16	+	4.99149e16i	0.500434	+	0.500434i
$682$	−5.42369e16	+	5.42369e16i	−0.539000	+	0.539000i
$683$	−1.21077e17			−1.19272			−0.596358	−	0.802719i	$-0.703386\pi$
$683$	−1.21077e17			−1.19272			−0.596358	+	0.802719i	$0.703386\pi$
$684$	3.54985e15	+	3.54985e15i	0.0346636	+	0.0346636i
$685$	−7.29703e14	+	7.29703e14i	−0.00706321	+	0.00706321i
$686$	−5.55689e16	−	5.55689e16i	−0.533197	−	0.533197i
$687$	4.57329e16			0.434999
$688$	−3.42239e16	−	3.42239e16i	−0.322700	−	0.322700i
$689$		−	1.52431e17i		−	1.42481i
$690$	1.35188e17			1.25269
$691$	1.61878e17			1.48702			0.743512	−	0.668722i	$-0.233158\pi$
$691$	1.61878e17			1.48702			0.743512	+	0.668722i	$0.233158\pi$
$692$	−3.68095e16			−0.335215
$693$	−2.97024e16	+	2.97024e16i	−0.268159	+	0.268159i
$694$	−2.20044e16	+	2.20044e16i	−0.196948	+	0.196948i
$695$		−	1.26856e17i		−	1.12565i
$696$	−1.35369e17	+	6.29639e16i	−1.19087	+	0.553906i
$697$	5.10611e16			0.445342
$698$	7.02011e16	+	7.02011e16i	0.607032	+	0.607032i
$699$	1.39835e17	+	1.39835e17i	1.19882	+	1.19882i
$700$		−	1.35603e16i		−	0.115261i
$701$		−	1.34793e17i		−	1.13595i	−0.823047	−	0.567973i	$-0.807728\pi$
$701$		−	1.34793e17i		−	1.13595i	0.823047	−	0.567973i	$-0.192272\pi$
$702$			7.90459e16i			0.660475i
$703$	2.03004e15			0.0168179
$704$	6.28354e16	−	6.28354e16i	0.516141	−	0.516141i
$705$		−	2.22063e17i		−	1.80860i
$706$	5.23291e14	−	5.23291e14i	0.00422586	−	0.00422586i
$707$	−6.89209e16	−	6.89209e16i	−0.551867	−	0.551867i
$708$	−5.35103e16	+	5.35103e16i	−0.424852	+	0.424852i
$709$			4.19311e16i			0.330110i	0.986284	+	0.165055i	$0.0527802\pi$
$709$			4.19311e16i			0.330110i	−0.986284	+	0.165055i	$0.947220\pi$
$710$	−7.13287e16	−	7.13287e16i	−0.556819	−	0.556819i
$711$	−3.85420e16	+	3.85420e16i	−0.298343	+	0.298343i
$712$	−7.69076e15			−0.0590322
$713$	−2.00379e17	−	2.00379e17i	−1.52516	−	1.52516i
$714$	−6.47513e16	+	6.47513e16i	−0.488719	+	0.488719i
$715$	−9.41073e16	−	9.41073e16i	−0.704348	−	0.704348i
$716$	4.61088e16			0.342220
$717$	1.69516e17	+	1.69516e17i	1.24766	+	1.24766i
$718$		−	1.07109e17i		−	0.781768i
$719$	−1.60768e17			−1.16366			−0.581829	−	0.813311i	$-0.697663\pi$
$719$	−1.60768e17			−1.16366			−0.581829	+	0.813311i	$0.697663\pi$
$720$	1.93031e16			0.138558
$721$	5.70789e15			0.0406316
$722$	7.00712e16	−	7.00712e16i	0.494671	−	0.494671i
$723$	1.65520e15	−	1.65520e15i	0.0115883	−	0.0115883i
$724$		−	3.01059e16i		−	0.209035i
$725$	3.38286e16	−	1.57347e16i	0.232946	−	0.108350i
$726$	−5.10029e16			−0.348317
$727$	−1.03512e17	−	1.03512e17i	−0.701105	−	0.701105i	0.263543	−	0.964648i	$-0.415109\pi$
$727$	−1.03512e17	−	1.03512e17i	−0.701105	−	0.701105i	−0.964648	+	0.263543i	$0.915109\pi$
$728$	−1.61114e17	−	1.61114e17i	−1.08230	−	1.08230i
$729$		−	1.82054e16i		−	0.121293i
$730$			5.50588e16i			0.363822i
$731$			1.73234e17i			1.13535i
$732$	−6.68106e16			−0.434289
$733$	−4.13094e16	+	4.13094e16i	−0.266333	+	0.266333i	−0.827621	−	0.561288i	$-0.810306\pi$
$733$	−4.13094e16	+	4.13094e16i	−0.266333	+	0.266333i	0.561288	+	0.827621i	$0.310306\pi$
$734$		−	9.12646e15i		−	0.0583615i
$735$	7.73867e15	−	7.73867e15i	0.0490843	−	0.0490843i
$736$	1.52446e17	+	1.52446e17i	0.959065	+	0.959065i
$737$	−6.04736e16	+	6.04736e16i	−0.377365	+	0.377365i
$738$		−	3.31454e16i		−	0.205156i
$739$	2.13827e17	+	2.13827e17i	1.31279	+	1.31279i	0.919348	+	0.393445i	$0.128717\pi$
$739$	2.13827e17	+	2.13827e17i	1.31279	+	1.31279i	0.393445	+	0.919348i	$0.371283\pi$
$740$	−3.71102e15	+	3.71102e15i	−0.0225997	+	0.0225997i
$741$	−6.31015e16			−0.381180
$742$	8.05219e16	+	8.05219e16i	0.482493	+	0.482493i
$743$	−2.34881e17	+	2.34881e17i	−1.39609	+	1.39609i	−0.585215	+	0.810878i	$0.698990\pi$
$743$	−2.34881e17	+	2.34881e17i	−1.39609	+	1.39609i	−0.810878	+	0.585215i	$0.801010\pi$
$744$	−2.09714e17	−	2.09714e17i	−1.23649	−	1.23649i
$745$	−2.53875e17			−1.48485
$746$	2.64540e15	+	2.64540e15i	0.0153482	+	0.0153482i
$747$		−	2.58155e16i		−	0.148579i
$748$	−5.06832e16			−0.289371
$749$	1.28628e17			0.728526
$750$	−1.72981e17			−0.971921
$751$	1.44316e17	−	1.44316e17i	0.804405	−	0.804405i	−0.179376	−	0.983781i	$-0.557408\pi$
$751$	1.44316e17	−	1.44316e17i	0.804405	−	0.804405i	0.983781	+	0.179376i	$0.0574079\pi$
$752$	−7.01527e16	+	7.01527e16i	−0.387916	+	0.387916i
$753$		−	1.51746e17i		−	0.832430i
$754$	6.81505e16	−	1.86679e17i	0.370887	−	1.01594i
$755$	3.45142e16			0.186345
$756$	3.61688e16	+	3.61688e16i	0.193733	+	0.193733i
$757$	6.16634e16	+	6.16634e16i	0.327682	+	0.327682i	0.851704	−	0.524023i	$-0.175569\pi$
$757$	6.16634e16	+	6.16634e16i	0.327682	+	0.327682i	−0.524023	+	0.851704i	$0.675569\pi$
$758$		−	4.62590e16i		−	0.243883i
$759$			2.96838e17i			1.55263i
$760$		−	3.74836e16i		−	0.194518i
$761$	−1.31593e17			−0.677524			−0.338762	−	0.940872i	$-0.610008\pi$
$761$	−1.31593e17			−0.677524			−0.338762	+	0.940872i	$0.610008\pi$
$762$	−2.17666e16	+	2.17666e16i	−0.111189	+	0.111189i
$763$		−	2.28651e17i		−	1.15884i
$764$	8.54255e16	−	8.54255e16i	0.429564	−	0.429564i
$765$	−4.88541e16	−	4.88541e16i	−0.243743	−	0.243743i
$766$	1.78402e17	−	1.78402e17i	0.883134	−	0.883134i
$767$		−	3.17759e17i		−	1.56072i
$768$	1.85990e17	+	1.85990e17i	0.906407	+	0.906407i
$769$	−3.00543e16	+	3.00543e16i	−0.145328	+	0.145328i	−0.776027	−	0.630699i	$-0.782768\pi$
$769$	−3.00543e16	+	3.00543e16i	−0.145328	+	0.145328i	0.630699	+	0.776027i	$0.282768\pi$
$770$	9.94249e16			0.477036
$771$	1.12152e17	+	1.12152e17i	0.533926	+	0.533926i
$772$	9.87387e16	−	9.87387e16i	0.466427	−	0.466427i
$773$	−1.12788e16	−	1.12788e16i	−0.0528669	−	0.0528669i	0.680179	−	0.733046i	$-0.261902\pi$
$773$	−1.12788e16	−	1.12788e16i	−0.0528669	−	0.0528669i	−0.733046	+	0.680179i	$0.761902\pi$
$774$	1.12452e17			0.523022
$775$	5.24074e16	+	5.24074e16i	0.241870	+	0.241870i
$776$			1.57484e16i			0.0721218i
$777$	−2.08205e16			−0.0946159
$778$	−2.60607e17			−1.17519
$779$	−2.62859e16			−0.117624
$780$	1.15353e17	−	1.15353e17i	0.512224	−	0.512224i
$781$	1.56620e17	−	1.56620e17i	0.690146	−	0.690146i
$782$			2.16176e17i			0.945294i
$783$	−4.82611e16	+	1.32198e17i	−0.209424	+	0.573658i
$784$	−4.88950e15			−0.0210556
$785$	1.99023e17	+	1.99023e17i	0.850523	+	0.850523i
$786$	2.03434e17	+	2.03434e17i	0.862757	+	0.862757i
$787$			3.70290e17i			1.55845i	0.626744	+	0.779226i	$0.284387\pi$
$787$			3.70290e17i			1.55845i	−0.626744	+	0.779226i	$0.715613\pi$
$788$			2.18332e16i			0.0911926i
$789$			2.51273e17i			1.04156i
$790$	1.29014e17			0.530732
$791$	2.18166e17	−	2.18166e17i	0.890695	−	0.890695i
$792$			1.03783e17i			0.420508i
$793$	1.98369e17	−	1.98369e17i	0.797693	−	0.797693i
$794$	3.99023e15	+	3.99023e15i	0.0159248	+	0.0159248i
$795$	−1.81859e17	+	1.81859e17i	−0.720332	+	0.720332i
$796$		−	1.25280e17i		−	0.492496i
$797$	1.63158e17	+	1.63158e17i	0.636589	+	0.636589i	0.949712	−	0.313123i	$-0.101375\pi$
$797$	1.63158e17	+	1.63158e17i	0.636589	+	0.636589i	−0.313123	+	0.949712i	$0.601375\pi$
$798$	3.33335e16	−	3.33335e16i	0.129081	−	0.129081i
$799$	3.55097e17			1.36479
$800$	−3.98709e16	−	3.98709e16i	−0.152095	−	0.152095i
$801$	5.16012e15	−	5.16012e15i	0.0195373	−	0.0195373i
$802$	−8.08789e16	−	8.08789e16i	−0.303941	−	0.303941i
$803$	−1.20895e17			−0.450937
$804$	−7.41260e16	−	7.41260e16i	−0.274432	−	0.274432i
$805$			3.67326e17i			1.34982i
$806$	3.94783e17			1.43995
$807$	−1.88192e17			−0.681335
$808$	−2.40816e17			−0.865400
$809$	1.57946e17	−	1.57946e17i	0.563402	−	0.563402i	−0.366870	−	0.930272i	$-0.619571\pi$
$809$	1.57946e17	−	1.57946e17i	0.563402	−	0.563402i	0.930272	+	0.366870i	$0.119571\pi$
$810$	1.57524e17	−	1.57524e17i	0.557746	−	0.557746i
$811$			3.89729e16i			0.136974i	0.997652	+	0.0684869i	$0.0218171\pi$
$811$			3.89729e16i			0.136974i	−0.997652	+	0.0684869i	$0.978183\pi$
$812$	−5.42349e16	−	1.16602e17i	−0.189209	−	0.406789i
$813$	−5.83937e17			−2.02219
$814$	9.40724e15	+	9.40724e15i	0.0323382	+	0.0323382i
$815$	−3.21787e17	−	3.21787e17i	−1.09805	−	1.09805i
$816$			9.23992e16i			0.312988i
$817$		−	8.91794e16i		−	0.299869i
$818$			2.06621e17i			0.689692i
$819$	2.16200e17			0.716394
$820$	4.80519e16	−	4.80519e16i	0.158062	−	0.158062i
$821$			4.14831e17i			1.35460i	0.735706	+	0.677301i	$0.236851\pi$
$821$			4.14831e17i			1.35460i	−0.735706	+	0.677301i	$0.763149\pi$
$822$	−2.26735e15	+	2.26735e15i	−0.00735001	+	0.00735001i
$823$	−4.97681e16	−	4.97681e16i	−0.160159	−	0.160159i	0.622478	−	0.782637i	$-0.286126\pi$
$823$	−4.97681e16	−	4.97681e16i	−0.160159	−	0.160159i	−0.782637	+	0.622478i	$0.786126\pi$
$824$	9.97194e15	−	9.97194e15i	0.0318578	−	0.0318578i
$825$		−	7.76356e16i		−	0.246228i
$826$	1.67857e17	+	1.67857e17i	0.528516	+	0.528516i
$827$	6.71785e16	−	6.71785e16i	0.209989	−	0.209989i	−0.594274	−	0.804263i	$-0.702560\pi$
$827$	6.71785e16	−	6.71785e16i	0.209989	−	0.209989i	0.804263	+	0.594274i	$0.202560\pi$
$828$	−1.21550e17			−0.377201
$829$	−1.31948e17	−	1.31948e17i	−0.406515	−	0.406515i	0.474007	−	0.880521i	$-0.342807\pi$
$829$	−1.31948e17	−	1.31948e17i	−0.406515	−	0.406515i	−0.880521	+	0.474007i	$0.842807\pi$
$830$	−4.32071e16	+	4.32071e16i	−0.132156	+	0.132156i
$831$	2.07530e17	+	2.07530e17i	0.630194	+	0.630194i
$832$	−4.57371e17			−1.37889
$833$	1.23748e16	+	1.23748e16i	0.0370397	+	0.0370397i
$834$		−	3.94172e17i		−	1.17136i
$835$	−3.07295e15			−0.00906645
$836$	2.60914e16			0.0764291
$837$	−2.79567e17			−0.813081
$838$	−1.33837e17	+	1.33837e17i	−0.386465	+	0.386465i
$839$	−3.89300e17	+	3.89300e17i	−1.11612	+	1.11612i	−0.123820	+	0.992305i	$0.539515\pi$
$839$	−3.89300e17	+	3.89300e17i	−1.11612	+	1.11612i	−0.992305	+	0.123820i	$0.960485\pi$
$840$			3.84439e17i			1.09434i
$841$	2.27952e17	−	2.70597e17i	0.644271	−	0.764798i
$842$	2.61182e17			0.732944
$843$	−4.55777e17	−	4.55777e17i	−1.26995	−	1.26995i
$844$	−7.16465e16	−	7.16465e16i	−0.198217	−	0.198217i
$845$			3.71190e17i			1.01966i
$846$		−	2.30505e17i		−	0.628721i
$847$		−	1.38583e17i		−	0.375327i
$848$	1.14904e17			0.309000
$849$	4.19437e17	−	4.19437e17i	1.12001	−	1.12001i
$850$		−	5.65391e16i		−	0.149912i
$851$	−3.47551e16	+	3.47551e16i	−0.0915043	+	0.0915043i
$852$	1.91978e17	+	1.91978e17i	0.501896	+	0.501896i
$853$	−3.28646e17	+	3.28646e17i	−0.853167	+	0.853167i	−0.990522	−	0.137355i	$-0.956140\pi$
$853$	−3.28646e17	+	3.28646e17i	−0.853167	+	0.853167i	0.137355	+	0.990522i	$0.456140\pi$
$854$			2.09578e17i			0.540255i
$855$	2.51497e16	+	2.51497e16i	0.0643778	+	0.0643778i
$856$	2.24719e17	−	2.24719e17i	0.571212	−	0.571212i
$857$	−4.44115e17			−1.12101			−0.560506	−	0.828151i	$-0.689393\pi$
$857$	−4.44115e17			−1.12101			−0.560506	+	0.828151i	$0.689393\pi$
$858$	−2.92413e17	−	2.92413e17i	−0.732948	−	0.732948i
$859$	3.77031e16	−	3.77031e16i	0.0938465	−	0.0938465i	−0.658625	−	0.752471i	$-0.728862\pi$
$859$	3.77031e16	−	3.77031e16i	0.0938465	−	0.0938465i	0.752471	+	0.658625i	$0.228862\pi$
$860$	1.63025e17	+	1.63025e17i	0.402960	+	0.402960i
$861$	2.69592e17			0.661742
$862$	3.29016e17	+	3.29016e17i	0.801998	+	0.801998i
$863$			1.13075e17i			0.273717i	0.990591	+	0.136858i	$0.0437005\pi$
$863$			1.13075e17i			0.273717i	−0.990591	+	0.136858i	$0.956299\pi$
$864$	2.12691e17			0.511290
$865$	−2.60785e17			−0.622566
$866$	−2.20355e17			−0.522414
$867$	−1.34178e17	+	1.34178e17i	−0.315914	+	0.315914i
$868$	1.80640e17	−	1.80640e17i	0.422372	−	0.422372i
$869$			2.83283e17i			0.657812i
$870$	−3.04028e17	+	1.41412e17i	−0.701128	+	0.326115i
$871$	4.40180e17			1.00814
$872$	−3.99463e17	−	3.99463e17i	−0.908610	−	0.908610i
$873$	−1.05664e16	−	1.05664e16i	−0.0238694	−	0.0238694i
$874$		−	1.11286e17i		−	0.249673i
$875$		−	4.70017e17i		−	1.04729i
$876$		−	1.48188e17i		−	0.327936i
$877$	−8.74221e16			−0.192143			−0.0960713	−	0.995374i	$-0.530628\pi$
$877$	−8.74221e16			−0.192143			−0.0960713	+	0.995374i	$0.530628\pi$
$878$	3.12636e17	−	3.12636e17i	0.682452	−	0.682452i
$879$		−	6.25679e17i		−	1.35649i
$880$	7.09389e16	−	7.09389e16i	0.152752	−	0.152752i
$881$	−4.00861e17	−	4.00861e17i	−0.857312	−	0.857312i	0.133709	−	0.991021i	$-0.457311\pi$
$881$	−4.00861e17	−	4.00861e17i	−0.857312	−	0.857312i	−0.991021	+	0.133709i	$0.957311\pi$
$882$	8.03286e15	−	8.03286e15i	0.0170631	−	0.0170631i
$883$		−	4.95907e17i		−	1.04625i	−0.852256	−	0.523125i	$-0.824766\pi$
$883$		−	4.95907e17i		−	1.04625i	0.852256	−	0.523125i	$-0.175234\pi$
$884$	1.84458e17	+	1.84458e17i	0.386531	+	0.386531i
$885$	−3.79106e17	+	3.79106e17i	−0.789043	+	0.789043i
$886$	6.96501e16			0.143986
$887$	4.67860e17	+	4.67860e17i	0.960670	+	0.960670i	0.999255	−	0.0385854i	$-0.0122852\pi$
$887$	4.67860e17	+	4.67860e17i	0.960670	+	0.960670i	−0.0385854	+	0.999255i	$0.512285\pi$
$888$	−3.63743e16	+	3.63743e16i	−0.0741850	+	0.0741850i
$889$	−5.91433e16	−	5.91433e16i	−0.119811	−	0.119811i
$890$	−1.72728e16			−0.0347555
$891$	3.45883e17	+	3.45883e17i	0.691294	+	0.691294i
$892$			2.19864e17i			0.436480i
$893$	−1.82801e17			−0.360471
$894$	−7.88848e17			−1.54514
$895$	3.26668e17			0.635577
$896$	−5.44800e16	+	5.44800e16i	−0.105290	+	0.105290i
$897$	1.08032e18	−	1.08032e18i	2.07395	−	2.07395i
$898$		−	2.56806e17i		−	0.489720i
$899$	6.60242e17	+	2.41033e17i	1.25068	+	0.456582i
$900$	3.17904e16			0.0598192
$901$	−2.90808e17	−	2.90808e17i	−0.543572	−	0.543572i
$902$	−1.21809e17	−	1.21809e17i	−0.226173	−	0.226173i
$903$			9.14640e17i			1.68703i
$904$		−	7.62293e17i		−	1.39673i
$905$		−	2.13292e17i		−	0.388224i
$906$	1.07244e17			0.193911
$907$	2.20888e16	−	2.20888e16i	0.0396760	−	0.0396760i	−0.686990	−	0.726666i	$-0.741069\pi$
$907$	2.20888e16	−	2.20888e16i	0.0396760	−	0.0396760i	0.726666	+	0.686990i	$0.241069\pi$
$908$			1.50228e17i			0.268062i
$909$	1.61576e17	−	1.61576e17i	0.286413	−	0.286413i
$910$	−3.61850e17	−	3.61850e17i	−0.637207	−	0.637207i
$911$	−2.20126e17	+	2.20126e17i	−0.385089	+	0.385089i	−0.872932	−	0.487843i	$-0.837784\pi$
$911$	−2.20126e17	+	2.20126e17i	−0.385089	+	0.385089i	0.487843	+	0.872932i	$0.337784\pi$
$912$		−	4.75664e16i		−	0.0826668i
$913$	−9.48719e16	−	9.48719e16i	−0.163800	−	0.163800i
$914$	−4.87910e17	+	4.87910e17i	−0.836879	+	0.836879i
$915$	−4.73334e17			−0.806568
$916$	6.88208e16	+	6.88208e16i	0.116506	+	0.116506i
$917$	−5.52762e17	+	5.52762e17i	−0.929657	+	0.929657i
$918$	1.50804e17	+	1.50804e17i	0.251974	+	0.251974i
$919$	3.24521e17			0.538704			0.269352	−	0.963042i	$-0.413191\pi$
$919$	3.24521e17			0.538704			0.269352	+	0.963042i	$0.413191\pi$
$920$	6.41735e17	+	6.41735e17i	1.05835	+	1.05835i
$921$			1.07121e18i			1.75516i
$922$	−9.17015e16			−0.149276
$923$	−1.14002e18			−1.84374
$924$	−2.67598e17			−0.429982
$925$	9.08992e15	−	9.08992e15i	0.0145114	−	0.0145114i
$926$	3.02797e17	−	3.02797e17i	0.480269	−	0.480269i
$927$			1.33814e16i			0.0210874i
$928$	−5.02304e17	−	1.83375e17i	−0.786464	−	0.287113i
$929$	−2.33271e17			−0.362882			−0.181441	−	0.983402i	$-0.558076\pi$
$929$	−2.33271e17			−0.362882			−0.181441	+	0.983402i	$0.558076\pi$
$930$	−4.71001e17	−	4.71001e17i	−0.727987	−	0.727987i
$931$	−6.37044e15	−	6.37044e15i	−0.00978298	−	0.00978298i
$932$			4.20860e17i			0.642159i
$933$		−	4.13446e17i		−	0.626800i
$934$			3.75057e17i			0.564958i
$935$	−3.59077e17			−0.537424
$936$	3.77711e17	−	3.77711e17i	0.561700	−	0.561700i
$937$			4.21036e17i			0.622131i	0.950388	+	0.311066i	$0.100686\pi$
$937$			4.21036e17i			0.622131i	−0.950388	+	0.311066i	$0.899314\pi$
$938$	−2.32526e17	+	2.32526e17i	−0.341393	+	0.341393i
$939$	−1.09108e18	−	1.09108e18i	−1.59171	−	1.59171i
$940$	3.34170e17	−	3.34170e17i	0.484396	−	0.484396i
$941$			8.13705e17i			1.17200i	0.810309	+	0.586002i	$0.199299\pi$
$941$			8.13705e17i			1.17200i	−0.810309	+	0.586002i	$0.800701\pi$
$942$	6.18411e17	+	6.18411e17i	0.885059	+	0.885059i
$943$	4.50025e17	−	4.50025e17i	0.639980	−	0.639980i
$944$	2.39529e17			0.338475
$945$	2.56246e17	+	2.56246e17i	0.359804	+	0.359804i
$946$	4.13259e17	−	4.13259e17i	0.576601	−	0.576601i
$947$	−2.05757e17	−	2.05757e17i	−0.285269	−	0.285269i	0.549937	−	0.835206i	$-0.314652\pi$
$947$	−2.05757e17	−	2.05757e17i	−0.285269	−	0.285269i	−0.835206	+	0.549937i	$0.814652\pi$
$948$	−3.47236e17			−0.478382
$949$	4.39990e17	+	4.39990e17i	0.602346	+	0.602346i
$950$			2.91059e16i			0.0395949i
$951$	1.06058e18			1.43371
$952$	−6.14749e17			−0.825802
$953$	−1.06208e18			−1.41775			−0.708875	−	0.705334i	$-0.750797\pi$
$953$	−1.06208e18			−1.41775			−0.708875	+	0.705334i	$0.750797\pi$
$954$	−1.88773e17	+	1.88773e17i	−0.250408	+	0.250408i
$955$	6.05216e17	−	6.05216e17i	0.797793	−	0.797793i
$956$			5.10190e17i			0.668320i
$957$	−3.10505e17	−	6.67568e17i	−0.404201	−	0.869009i
$958$	7.64071e17			0.988418
$959$	−6.16076e15	−	6.16076e15i	−0.00791995	−	0.00791995i
$960$	5.45672e17	+	5.45672e17i	0.697114	+	0.697114i
$961$			6.08596e17i			0.772661i
$962$		−	6.84740e16i		−	0.0863924i
$963$			3.01551e17i			0.378097i
$964$	4.98162e15			0.00620738
$965$	6.99536e17	−	6.99536e17i	0.866256	−	0.866256i
$966$			1.14137e18i			1.40463i
$967$	1.03201e17	−	1.03201e17i	0.126219	−	0.126219i	−0.641175	−	0.767394i	$-0.721553\pi$
$967$	1.03201e17	−	1.03201e17i	0.126219	−	0.126219i	0.767394	+	0.641175i	$0.221553\pi$
$968$	−2.42111e17	−	2.42111e17i	−0.294281	−	0.294281i
$969$	−1.20385e17	+	1.20385e17i	−0.145422	+	0.145422i
$970$			3.53697e16i			0.0424621i
$971$	7.71670e17	+	7.71670e17i	0.920695	+	0.920695i	0.997079	−	0.0763831i	$-0.0243372\pi$
$971$	7.71670e17	+	7.71670e17i	0.920695	+	0.920695i	−0.0763831	+	0.997079i	$0.524337\pi$
$972$	−2.54939e17	+	2.54939e17i	−0.302301	+	0.302301i
$973$	1.07103e18			1.26219
$974$	5.89151e17	+	5.89151e17i	0.690037	+	0.690037i
$975$	−2.82550e17	+	2.82550e17i	−0.328902	+	0.328902i
$976$	1.49532e17	+	1.49532e17i	0.172996	+	0.172996i
$977$	1.00989e18			1.16120			0.580599	−	0.814189i	$-0.302818\pi$
$977$	1.00989e18			1.16120			0.580599	+	0.814189i	$0.302818\pi$
$978$	−9.99866e17	−	9.99866e17i	−1.14264	−	1.14264i
$979$		−	3.79268e16i		−	0.0430775i
$980$	2.32910e16			0.0262925
$981$	5.36040e17			0.601428
$982$	2.79359e17			0.311525
$983$	1.10254e18	−	1.10254e18i	1.22201	−	1.22201i	0.255088	−	0.966918i	$-0.417896\pi$
$983$	1.10254e18	−	1.10254e18i	1.22201	−	1.22201i	0.966918	−	0.255088i	$-0.0821044\pi$
$984$	4.70990e17	−	4.70990e17i	0.518849	−	0.518849i
$985$			1.54682e17i			0.169364i
$986$	−2.26129e17	−	4.86165e17i	−0.246091	−	0.529081i
$987$	1.87484e18			2.02797
$988$	−9.49578e16	−	9.49578e16i	−0.102091	−	0.102091i
$989$	1.52679e18	+	1.52679e18i	1.63155	+	1.63155i
$990$			2.33088e17i			0.247576i
$991$			1.63141e18i			1.72235i	0.508306	+	0.861177i	$0.330272\pi$
$991$			1.63141e18i			1.72235i	−0.508306	+	0.861177i	$0.669728\pi$
$992$		−	1.06226e18i		−	1.11470i
$993$	−1.83057e18			−1.90938
$994$	6.02216e17	−	6.02216e17i	0.624359	−	0.624359i
$995$		−	8.87572e17i		−	0.914671i
$996$	1.16290e17	−	1.16290e17i	0.119120	−	0.119120i
$997$	−8.72865e16	−	8.72865e16i	−0.0888743	−	0.0888743i	0.661272	−	0.750146i	$-0.270017\pi$
$997$	−8.72865e16	−	8.72865e16i	−0.0888743	−	0.0888743i	−0.750146	+	0.661272i	$0.770017\pi$
$998$	−8.52690e17	+	8.52690e17i	−0.862994	+	0.862994i
$999$			4.84902e16i			0.0487822i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.13.c.a.12.19	✓	58
29.17	odd	4	inner	29.13.c.a.17.19	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.13.c.a.12.19	✓	58	1.1	even	1	trivial
29.13.c.a.17.19	yes	58	29.17	odd	4	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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(33.1274 + 33.1274i) q^{2} +(-631.679 - 631.679i) q^{3} -1901.16i q^{4} -13469.1i q^{5} -41851.7i q^{6} +113718. q^{7} +(198670. - 198670. i) q^{8} +266596. i q^{9} +O(q^{10})\)	\(q+(33.1274 + 33.1274i) q^{2} +(-631.679 - 631.679i) q^{3} -1901.16i q^{4} -13469.1i q^{5} -41851.7i q^{6} +113718. q^{7} +(198670. - 198670. i) q^{8} +266596. i q^{9} +(446197. - 446197. i) q^{10} +(979737. + 979737. i) q^{11} +(-1.20092e6 + 1.20092e6i) q^{12} -7.13138e6i q^{13} +(3.76717e6 + 3.76717e6i) q^{14} +(-8.50818e6 + 8.50818e6i) q^{15} +5.37569e6 q^{16} +(-1.36053e7 - 1.36053e7i) q^{17} +(-8.83162e6 + 8.83162e6i) q^{18} +(7.00389e6 + 7.00389e6i) q^{19} -2.56069e7 q^{20} +(-7.18331e7 - 7.18331e7i) q^{21} +6.49122e7i q^{22} -2.39819e8 q^{23} -2.50991e8 q^{24} +6.27227e7 q^{25} +(2.36244e8 - 2.36244e8i) q^{26} +(-1.67297e8 + 1.67297e8i) q^{27} -2.16195e8i q^{28} +(5.39336e8 - 2.50861e8i) q^{29} -5.63707e8 q^{30} +(8.35541e8 + 8.35541e8i) q^{31} +(-6.35670e8 - 6.35670e8i) q^{32} -1.23776e9i q^{33} -9.01413e8i q^{34} -1.53168e9i q^{35} +5.06840e8 q^{36} +(1.44922e8 - 1.44922e8i) q^{37} +4.64041e8i q^{38} +(-4.50474e9 + 4.50474e9i) q^{39} +(-2.67592e9 - 2.67592e9i) q^{40} +(-1.87652e9 + 1.87652e9i) q^{41} -4.75928e9i q^{42} +(-6.36642e9 - 6.36642e9i) q^{43} +(1.86263e9 - 1.86263e9i) q^{44} +3.59082e9 q^{45} +(-7.94457e9 - 7.94457e9i) q^{46} +(-1.30500e10 + 1.30500e10i) q^{47} +(-3.39571e9 - 3.39571e9i) q^{48} -9.09557e8 q^{49} +(2.07784e9 + 2.07784e9i) q^{50} +1.71883e10i q^{51} -1.35579e10 q^{52} +2.13746e10 q^{53} -1.10842e10 q^{54} +(1.31962e10 - 1.31962e10i) q^{55} +(2.25923e10 - 2.25923e10i) q^{56} -8.84842e9i q^{57} +(2.61771e10 + 9.55643e9i) q^{58} +4.45578e10 q^{59} +(1.61754e10 + 1.61754e10i) q^{60} +(2.78164e10 + 2.78164e10i) q^{61} +5.53586e10i q^{62} +3.03167e10i q^{63} -6.41350e10i q^{64} -9.60536e10 q^{65} +(4.10037e10 - 4.10037e10i) q^{66} +6.17243e10i q^{67} +(-2.58657e10 + 2.58657e10i) q^{68} +(1.51489e11 + 1.51489e11i) q^{69} +(5.07406e10 - 5.07406e10i) q^{70} -1.59859e11i q^{71} +(5.29646e10 + 5.29646e10i) q^{72} +(-6.16978e10 + 6.16978e10i) q^{73} +9.60179e9 q^{74} +(-3.96206e10 - 3.96206e10i) q^{75} +(1.33155e10 - 1.33155e10i) q^{76} +(1.11414e11 + 1.11414e11i) q^{77} -2.98461e11 q^{78} +(1.44571e11 + 1.44571e11i) q^{79} -7.24060e10i q^{80} +3.53036e11 q^{81} -1.24328e11 q^{82} -9.68340e10 q^{83} +(-1.36566e11 + 1.36566e11i) q^{84} +(-1.83251e11 + 1.83251e11i) q^{85} -4.21805e11i q^{86} +(-4.99151e11 - 1.82224e11i) q^{87} +3.89289e11 q^{88} +(-1.93556e10 - 1.93556e10i) q^{89} +(1.18954e11 + 1.18954e11i) q^{90} -8.10965e11i q^{91} +4.55933e11i q^{92} -1.05559e12i q^{93} -8.64623e11 q^{94} +(9.43364e10 - 9.43364e10i) q^{95} +8.03078e11i q^{96} +(-3.96346e10 + 3.96346e10i) q^{97} +(-3.01312e10 - 3.01312e10i) q^{98} +(-2.61194e11 + 2.61194e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q + 88 q^{2} - 2 q^{3} - 4 q^{7} + 79650 q^{8}+O(q^{10}) \) 58 * q + 88 * q^2 - 2 * q^3 - 4 * q^7 + 79650 * q^8	\( 58 q + 88 q^{2} - 2 q^{3} - 4 q^{7} + 79650 q^{8} - 1957890 q^{10} + 4120990 q^{11} + 2920062 q^{12} - 1824520 q^{14} - 8383600 q^{15} - 133743512 q^{16} + 33971578 q^{17} - 122384158 q^{18} + 65838718 q^{19} - 59408388 q^{20} + 200896236 q^{21} + 104539676 q^{23} + 163907064 q^{24} - 3086882294 q^{25} + 607848030 q^{26} - 1190867840 q^{27} + 817714294 q^{29} + 5793833612 q^{30} - 1059975938 q^{31} + 2323254598 q^{32} + 517001400 q^{36} - 864725342 q^{37} + 18048639408 q^{39} - 22547920086 q^{40} - 17292603926 q^{41} - 3344004962 q^{43} - 53750811886 q^{44} - 16067938640 q^{45} + 43310099300 q^{46} - 15159905282 q^{47} - 4602803862 q^{48} + 32036753022 q^{49} - 16057299278 q^{50} + 81167587800 q^{52} - 69552844564 q^{53} + 38996274808 q^{54} + 3944882736 q^{55} - 156397031424 q^{56} + 107434998568 q^{58} + 82613255468 q^{59} - 147410252946 q^{60} + 128229759922 q^{61} + 125938412928 q^{65} + 364716671994 q^{66} - 141670411468 q^{68} + 529640675916 q^{69} + 518962441956 q^{70} - 180699442320 q^{72} - 428225274062 q^{73} + 307721180948 q^{74} - 617987210610 q^{75} - 455232145048 q^{76} - 963484794004 q^{77} + 688403957040 q^{78} - 183006289538 q^{79} + 1001949265154 q^{81} - 1176460419184 q^{82} + 361042835756 q^{83} - 402324805420 q^{84} + 832273178976 q^{85} - 1065344596322 q^{87} - 1836857960940 q^{88} + 1922736257242 q^{89} - 1170237151648 q^{90} - 2759662014220 q^{94} + 5518358548560 q^{95} + 1356111950818 q^{97} - 2518255928616 q^{98} + 3259343912178 q^{99}+O(q^{100}) \) 58 * q + 88 * q^2 - 2 * q^3 - 4 * q^7 + 79650 * q^8 - 1957890 * q^10 + 4120990 * q^11 + 2920062 * q^12 - 1824520 * q^14 - 8383600 * q^15 - 133743512 * q^16 + 33971578 * q^17 - 122384158 * q^18 + 65838718 * q^19 - 59408388 * q^20 + 200896236 * q^21 + 104539676 * q^23 + 163907064 * q^24 - 3086882294 * q^25 + 607848030 * q^26 - 1190867840 * q^27 + 817714294 * q^29 + 5793833612 * q^30 - 1059975938 * q^31 + 2323254598 * q^32 + 517001400 * q^36 - 864725342 * q^37 + 18048639408 * q^39 - 22547920086 * q^40 - 17292603926 * q^41 - 3344004962 * q^43 - 53750811886 * q^44 - 16067938640 * q^45 + 43310099300 * q^46 - 15159905282 * q^47 - 4602803862 * q^48 + 32036753022 * q^49 - 16057299278 * q^50 + 81167587800 * q^52 - 69552844564 * q^53 + 38996274808 * q^54 + 3944882736 * q^55 - 156397031424 * q^56 + 107434998568 * q^58 + 82613255468 * q^59 - 147410252946 * q^60 + 128229759922 * q^61 + 125938412928 * q^65 + 364716671994 * q^66 - 141670411468 * q^68 + 529640675916 * q^69 + 518962441956 * q^70 - 180699442320 * q^72 - 428225274062 * q^73 + 307721180948 * q^74 - 617987210610 * q^75 - 455232145048 * q^76 - 963484794004 * q^77 + 688403957040 * q^78 - 183006289538 * q^79 + 1001949265154 * q^81 - 1176460419184 * q^82 + 361042835756 * q^83 - 402324805420 * q^84 + 832273178976 * q^85 - 1065344596322 * q^87 - 1836857960940 * q^88 + 1922736257242 * q^89 - 1170237151648 * q^90 - 2759662014220 * q^94 + 5518358548560 * q^95 + 1356111950818 * q^97 - 2518255928616 * q^98 + 3259343912178 * q^99

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