LMFDB - Embedded newform 29.13.c.a.12.12

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			12.12
Character	$\chi$	$=$	29.12
Dual form			29.13.c.a.17.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15.4217 - 15.4217i) q^{2} +(-236.320 - 236.320i) q^{3} -3620.34i q^{4} +24342.5i q^{5} +7288.92i q^{6} +119306. q^{7} +(-118999. + 118999. i) q^{8} -419746. i q^{9} +O(q^{10})$	\(q+(-15.4217 - 15.4217i) q^{2} +(-236.320 - 236.320i) q^{3} -3620.34i q^{4} +24342.5i q^{5} +7288.92i q^{6} +119306. q^{7} +(-118999. + 118999. i) q^{8} -419746. i q^{9} +(375403. - 375403. i) q^{10} +(-1.77799e6 - 1.77799e6i) q^{11} +(-855561. + 855561. i) q^{12} -626657. i q^{13} +(-1.83990e6 - 1.83990e6i) q^{14} +(5.75263e6 - 5.75263e6i) q^{15} -1.11586e7 q^{16} +(6.88086e6 + 6.88086e6i) q^{17} +(-6.47320e6 + 6.47320e6i) q^{18} +(2.20348e7 + 2.20348e7i) q^{19} +8.81282e7 q^{20} +(-2.81944e7 - 2.81944e7i) q^{21} +5.48391e7i q^{22} -2.08304e8 q^{23} +5.62438e7 q^{24} -3.48417e8 q^{25} +(-9.66412e6 + 9.66412e6i) q^{26} +(-2.24785e8 + 2.24785e8i) q^{27} -4.31929e8i q^{28} +(2.77987e8 + 5.25869e8i) q^{29} -1.77431e8 q^{30} +(9.57761e7 + 9.57761e7i) q^{31} +(6.59505e8 + 6.59505e8i) q^{32} +8.40348e8i q^{33} -2.12229e8i q^{34} +2.90421e9i q^{35} -1.51963e9 q^{36} +(-2.91189e9 + 2.91189e9i) q^{37} -6.79628e8i q^{38} +(-1.48092e8 + 1.48092e8i) q^{39} +(-2.89674e9 - 2.89674e9i) q^{40} +(-4.16527e7 + 4.16527e7i) q^{41} +8.69612e8i q^{42} +(-5.02447e9 - 5.02447e9i) q^{43} +(-6.43692e9 + 6.43692e9i) q^{44} +1.02177e10 q^{45} +(3.21240e9 + 3.21240e9i) q^{46} +(-9.68896e9 + 9.68896e9i) q^{47} +(2.63700e9 + 2.63700e9i) q^{48} +3.92639e8 q^{49} +(5.37318e9 + 5.37318e9i) q^{50} -3.25217e9i q^{51} -2.26871e9 q^{52} -9.89509e9 q^{53} +6.93313e9 q^{54} +(4.32806e10 - 4.32806e10i) q^{55} +(-1.41973e10 + 1.41973e10i) q^{56} -1.04145e10i q^{57} +(3.82277e9 - 1.23968e10i) q^{58} -1.12175e10 q^{59} +(-2.08265e10 - 2.08265e10i) q^{60} +(1.92196e9 + 1.92196e9i) q^{61} -2.95406e9i q^{62} -5.00783e10i q^{63} +2.53642e10i q^{64} +1.52544e10 q^{65} +(1.29596e10 - 1.29596e10i) q^{66} -4.49785e10i q^{67} +(2.49111e10 - 2.49111e10i) q^{68} +(4.92264e10 + 4.92264e10i) q^{69} +(4.47878e10 - 4.47878e10i) q^{70} +2.24645e11i q^{71} +(4.99495e10 + 4.99495e10i) q^{72} +(1.44688e11 - 1.44688e11i) q^{73} +8.98127e10 q^{74} +(8.23380e10 + 8.23380e10i) q^{75} +(7.97735e10 - 7.97735e10i) q^{76} +(-2.12124e11 - 2.12124e11i) q^{77} +4.56766e9 q^{78} +(-1.08437e11 - 1.08437e11i) q^{79} -2.71628e11i q^{80} -1.16828e11 q^{81} +1.28471e9 q^{82} -4.90368e11 q^{83} +(-1.02074e11 + 1.02074e11i) q^{84} +(-1.67497e11 + 1.67497e11i) q^{85} +1.54972e11i q^{86} +(5.85797e10 - 1.89967e11i) q^{87} +4.23157e11 q^{88} +(2.68102e11 + 2.68102e11i) q^{89} +(-1.57574e11 - 1.57574e11i) q^{90} -7.47640e10i q^{91} +7.54130e11i q^{92} -4.52677e10i q^{93} +2.98841e11 q^{94} +(-5.36382e11 + 5.36382e11i) q^{95} -3.11709e11i q^{96} +(5.71214e10 - 5.71214e10i) q^{97} +(-6.05516e9 - 6.05516e9i) q^{98} +(-7.46303e11 + 7.46303e11i) 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 $

$2$	−15.4217	−	15.4217i	−0.240964	−	0.240964i	0.576285	−	0.817249i	$-0.304502\pi$
$2$	−15.4217	−	15.4217i	−0.240964	−	0.240964i	−0.817249	+	0.576285i	$0.804502\pi$
$3$	−236.320	−	236.320i	−0.324171	−	0.324171i	0.526194	−	0.850365i	$-0.323619\pi$
$3$	−236.320	−	236.320i	−0.324171	−	0.324171i	−0.850365	+	0.526194i	$0.823619\pi$
$4$		−	3620.34i		−	0.883873i
$5$			24342.5i			1.55792i	0.627074	+	0.778960i	$0.284253\pi$
$5$			24342.5i			1.55792i	−0.627074	+	0.778960i	$0.715747\pi$
$6$			7288.92i			0.156227i
$7$	119306.			1.01408			0.507042	−	0.861921i	$-0.330739\pi$
$7$	119306.			1.01408			0.507042	+	0.861921i	$0.330739\pi$
$8$	−118999.	+	118999.i	−0.453946	+	0.453946i
$9$		−	419746.i		−	0.789827i
$10$	375403.	−	375403.i	0.375403	−	0.375403i
$11$	−1.77799e6	−	1.77799e6i	−1.00363	−	1.00363i	−0.999993	−	0.00363323i	$-0.998844\pi$
$11$	−1.77799e6	−	1.77799e6i	−1.00363	−	1.00363i	−0.00363323	−	0.999993i	$-0.501156\pi$
$12$	−855561.	+	855561.i	−0.286525	+	0.286525i
$13$		−	626657.i		−	0.129828i	−0.997891	−	0.0649142i	$-0.979323\pi$
$13$		−	626657.i		−	0.129828i	0.997891	−	0.0649142i	$-0.0206774\pi$
$14$	−1.83990e6	−	1.83990e6i	−0.244358	−	0.244358i
$15$	5.75263e6	−	5.75263e6i	0.505032	−	0.505032i
$16$	−1.11586e7			−0.665103
$17$	6.88086e6	+	6.88086e6i	0.285068	+	0.285068i	0.835126	−	0.550058i	$-0.185394\pi$
$17$	6.88086e6	+	6.88086e6i	0.285068	+	0.285068i	−0.550058	+	0.835126i	$0.685394\pi$
$18$	−6.47320e6	+	6.47320e6i	−0.190320	+	0.190320i
$19$	2.20348e7	+	2.20348e7i	0.468368	+	0.468368i	0.901386	−	0.433017i	$-0.142551\pi$
$19$	2.20348e7	+	2.20348e7i	0.468368	+	0.468368i	−0.433017	+	0.901386i	$0.642551\pi$
$20$	8.81282e7			1.37700
$21$	−2.81944e7	−	2.81944e7i	−0.328736	−	0.328736i
$22$			5.48391e7i			0.483676i
$23$	−2.08304e8			−1.40712			−0.703558	−	0.710638i	$-0.748406\pi$
$23$	−2.08304e8			−1.40712			−0.703558	+	0.710638i	$0.748406\pi$
$24$	5.62438e7			0.294312
$25$	−3.48417e8			−1.42712
$26$	−9.66412e6	+	9.66412e6i	−0.0312840	+	0.0312840i
$27$	−2.24785e8	+	2.24785e8i	−0.580209	+	0.580209i
$28$		−	4.31929e8i		−	0.896321i
$29$	2.77987e8	+	5.25869e8i	0.467343	+	0.884076i
$29$	2.77987e8	+	5.25869e8i	0.467343	+	0.884076i
$30$	−1.77431e8			−0.243389
$31$	9.57761e7	+	9.57761e7i	0.107916	+	0.107916i	0.759003	−	0.651087i	$-0.225687\pi$
$31$	9.57761e7	+	9.57761e7i	0.107916	+	0.107916i	−0.651087	+	0.759003i	$0.725687\pi$
$32$	6.59505e8	+	6.59505e8i	0.614212	+	0.614212i
$33$			8.40348e8i			0.650692i
$34$		−	2.12229e8i		−	0.137382i
$35$			2.90421e9i			1.57986i
$36$	−1.51963e9			−0.698106
$37$	−2.91189e9	+	2.91189e9i	−1.13492	+	1.13492i	−0.145573	+	0.989348i	$0.546502\pi$
$37$	−2.91189e9	+	2.91189e9i	−1.13492	+	1.13492i	−0.989348	+	0.145573i	$0.953498\pi$
$38$		−	6.79628e8i		−	0.225720i
$39$	−1.48092e8	+	1.48092e8i	−0.0420866	+	0.0420866i
$40$	−2.89674e9	−	2.89674e9i	−0.707211	−	0.707211i
$41$	−4.16527e7	+	4.16527e7i	−0.00876879	+	0.00876879i	−0.711478	−	0.702709i	$-0.751974\pi$
$41$	−4.16527e7	+	4.16527e7i	−0.00876879	+	0.00876879i	0.702709	+	0.711478i	$0.251974\pi$
$42$			8.69612e8i			0.158427i
$43$	−5.02447e9	−	5.02447e9i	−0.794840	−	0.794840i	0.187437	−	0.982277i	$-0.439982\pi$
$43$	−5.02447e9	−	5.02447e9i	−0.794840	−	0.794840i	−0.982277	+	0.187437i	$0.939982\pi$
$44$	−6.43692e9	+	6.43692e9i	−0.887078	+	0.887078i
$45$	1.02177e10			1.23049
$46$	3.21240e9	+	3.21240e9i	0.339064	+	0.339064i
$47$	−9.68896e9	+	9.68896e9i	−0.898856	+	0.898856i	−0.995335	−	0.0964791i	$-0.969242\pi$
$47$	−9.68896e9	+	9.68896e9i	−0.898856	+	0.898856i	0.0964791	+	0.995335i	$0.469242\pi$
$48$	2.63700e9	+	2.63700e9i	0.215607	+	0.215607i
$49$	3.92639e8			0.0283672
$50$	5.37318e9	+	5.37318e9i	0.343883	+	0.343883i
$51$		−	3.25217e9i		−	0.184821i
$52$	−2.26871e9			−0.114752
$53$	−9.89509e9			−0.446442			−0.223221	−	0.974768i	$-0.571657\pi$
$53$	−9.89509e9			−0.446442			−0.223221	+	0.974768i	$0.571657\pi$
$54$	6.93313e9			0.279619
$55$	4.32806e10	−	4.32806e10i	1.56357	−	1.56357i
$56$	−1.41973e10	+	1.41973e10i	−0.460339	+	0.460339i
$57$		−	1.04145e10i		−	0.303662i
$58$	3.82277e9	−	1.23968e10i	0.100418	−	0.325643i
$59$	−1.12175e10			−0.265939			−0.132970	−	0.991120i	$-0.542451\pi$
$59$	−1.12175e10			−0.265939			−0.132970	+	0.991120i	$0.542451\pi$
$60$	−2.08265e10	−	2.08265e10i	−0.446384	−	0.446384i
$61$	1.92196e9	+	1.92196e9i	0.0373048	+	0.0373048i	0.725513	−	0.688208i	$-0.241602\pi$
$61$	1.92196e9	+	1.92196e9i	0.0373048	+	0.0373048i	−0.688208	+	0.725513i	$0.741602\pi$
$62$		−	2.95406e9i		−	0.0520079i
$63$		−	5.00783e10i		−	0.800951i
$64$			2.53642e10i			0.369098i
$65$	1.52544e10			0.202262
$66$	1.29596e10	−	1.29596e10i	0.156793	−	0.156793i
$67$		−	4.49785e10i		−	0.497228i	−0.968603	−	0.248614i	$-0.920025\pi$
$67$		−	4.49785e10i		−	0.497228i	0.968603	−	0.248614i	$-0.0799751\pi$
$68$	2.49111e10	−	2.49111e10i	0.251964	−	0.251964i
$69$	4.92264e10	+	4.92264e10i	0.456145	+	0.456145i
$70$	4.47878e10	−	4.47878e10i	0.380690	−	0.380690i
$71$			2.24645e11i			1.75367i	0.480794	+	0.876834i	$0.340349\pi$
$71$			2.24645e11i			1.75367i	−0.480794	+	0.876834i	$0.659651\pi$
$72$	4.99495e10	+	4.99495e10i	0.358538	+	0.358538i
$73$	1.44688e11	−	1.44688e11i	0.956080	−	0.956080i	−0.0429949	−	0.999075i	$-0.513690\pi$
$73$	1.44688e11	−	1.44688e11i	0.956080	−	0.956080i	0.999075	+	0.0429949i	$0.0136899\pi$
$74$	8.98127e10			0.546950
$75$	8.23380e10	+	8.23380e10i	0.462629	+	0.462629i
$76$	7.97735e10	−	7.97735e10i	0.413978	−	0.413978i
$77$	−2.12124e11	−	2.12124e11i	−1.01776	−	1.01776i
$78$	4.56766e9			0.0202827
$79$	−1.08437e11	−	1.08437e11i	−0.446084	−	0.446084i	0.447967	−	0.894050i	$-0.352148\pi$
$79$	−1.08437e11	−	1.08437e11i	−0.446084	−	0.446084i	−0.894050	+	0.447967i	$0.852148\pi$
$80$		−	2.71628e11i		−	1.03618i
$81$	−1.16828e11			−0.413653
$82$	1.28471e9			0.00422593
$83$	−4.90368e11			−1.49987			−0.749935	−	0.661511i	$-0.769915\pi$
$83$	−4.90368e11			−1.49987			−0.749935	+	0.661511i	$0.769915\pi$
$84$	−1.02074e11	+	1.02074e11i	−0.290561	+	0.290561i
$85$	−1.67497e11	+	1.67497e11i	−0.444114	+	0.444114i
$86$			1.54972e11i			0.383056i
$87$	5.85797e10	−	1.89967e11i	0.135093	−	0.438090i
$88$	4.23157e11			0.911184
$89$	2.68102e11	+	2.68102e11i	0.539461	+	0.539461i	0.923371	−	0.383909i	$-0.125423\pi$
$89$	2.68102e11	+	2.68102e11i	0.539461	+	0.539461i	−0.383909	+	0.923371i	$0.625423\pi$
$90$	−1.57574e11	−	1.57574e11i	−0.296503	−	0.296503i
$91$		−	7.47640e10i		−	0.131657i
$92$			7.54130e11i			1.24371i
$93$		−	4.52677e10i		−	0.0699665i
$94$	2.98841e11			0.433184
$95$	−5.36382e11	+	5.36382e11i	−0.729681	+	0.729681i
$96$		−	3.11709e11i		−	0.398219i
$97$	5.71214e10	−	5.71214e10i	0.0685754	−	0.0685754i	−0.671987	−	0.740563i	$-0.734559\pi$
$97$	5.71214e10	−	5.71214e10i	0.0685754	−	0.0685754i	0.740563	+	0.671987i	$0.234559\pi$
$98$	−6.05516e9	−	6.05516e9i	−0.00683548	−	0.00683548i
$99$	−7.46303e11	+	7.46303e11i	−0.792691	+	0.792691i
$100$			1.26139e12i			1.26139i
$101$	3.36529e11	+	3.36529e11i	0.317026	+	0.317026i	0.847624	−	0.530598i	$-0.178033\pi$
$101$	3.36529e11	+	3.36529e11i	0.317026	+	0.317026i	−0.530598	+	0.847624i	$0.678033\pi$
$102$	−5.01540e10	+	5.01540e10i	−0.0445353	+	0.0445353i
$103$	−1.43175e12			−1.19907			−0.599534	−	0.800349i	$-0.704648\pi$
$103$	−1.43175e12			−1.19907			−0.599534	+	0.800349i	$0.704648\pi$
$104$	7.45717e10	+	7.45717e10i	0.0589351	+	0.0589351i
$105$	6.86323e11	−	6.86323e11i	0.512145	−	0.512145i
$106$	1.52599e11	+	1.52599e11i	0.107576	+	0.107576i
$107$	−1.81948e12			−1.21240			−0.606198	−	0.795314i	$-0.707306\pi$
$107$	−1.81948e12			−1.21240			−0.606198	+	0.795314i	$0.707306\pi$
$108$	8.13798e11	+	8.13798e11i	0.512831	+	0.512831i
$109$			9.99926e11i			0.596223i	0.954531	+	0.298112i	$0.0963568\pi$
$109$			9.99926e11i			0.596223i	−0.954531	+	0.298112i	$0.903643\pi$
$110$	−1.33492e12			−0.753528
$111$	1.37628e12			0.735815
$112$	−1.33129e12			−0.674471
$113$	2.06378e12	−	2.06378e12i	0.991271	−	0.991271i	−0.00869103	−	0.999962i	$-0.502766\pi$
$113$	2.06378e12	−	2.06378e12i	0.991271	−	0.991271i	0.999962	+	0.00869103i	$0.00276648\pi$
$114$	−1.60610e11	+	1.60610e11i	−0.0731718	+	0.0731718i
$115$		−	5.07063e12i		−	2.19217i
$116$	1.90383e12	−	1.00641e12i	0.781411	−	0.413072i
$117$	−2.63037e11			−0.102542
$118$	1.72992e11	+	1.72992e11i	0.0640819	+	0.0640819i
$119$	8.20927e11	+	8.20927e11i	0.289083	+	0.289083i
$120$			1.36912e12i			0.458514i
$121$			3.18404e12i			1.01453i
$122$		−	5.92797e10i		−	0.0179782i
$123$	1.96868e10			0.00568517
$124$	3.46742e11	−	3.46742e11i	0.0953842	−	0.0953842i
$125$		−	2.53834e12i		−	0.665411i
$126$	−7.72292e11	+	7.72292e11i	−0.193000	+	0.193000i
$127$	−3.42070e12	−	3.42070e12i	−0.815254	−	0.815254i	0.170162	−	0.985416i	$-0.445571\pi$
$127$	−3.42070e12	−	3.42070e12i	−0.815254	−	0.815254i	−0.985416	+	0.170162i	$0.945571\pi$
$128$	3.09249e12	−	3.09249e12i	0.703151	−	0.703151i
$129$			2.37477e12i			0.515327i
$130$	−2.35249e11	−	2.35249e11i	−0.0487380	−	0.0487380i
$131$	6.51106e12	−	6.51106e12i	1.28832	−	1.28832i	0.352515	−	0.935806i	$-0.385326\pi$
$131$	6.51106e12	−	6.51106e12i	1.28832	−	1.28832i	0.935806	−	0.352515i	$-0.114674\pi$
$132$	3.04235e12			0.575129
$133$	2.62888e12	+	2.62888e12i	0.474965	+	0.474965i
$134$	−6.93645e11	+	6.93645e11i	−0.119814	+	0.119814i
$135$	−5.47183e12	−	5.47183e12i	−0.903920	−	0.903920i
$136$	−1.63763e12			−0.258811
$137$	3.04111e12	+	3.04111e12i	0.459948	+	0.459948i	0.898638	−	0.438690i	$-0.144557\pi$
$137$	3.04111e12	+	3.04111e12i	0.459948	+	0.459948i	−0.438690	+	0.898638i	$0.644557\pi$
$138$		−	1.51831e12i		−	0.219829i
$139$	−8.15535e12			−1.13072			−0.565359	−	0.824845i	$-0.691262\pi$
$139$	−8.15535e12			−1.13072			−0.565359	+	0.824845i	$0.691262\pi$
$140$	1.05142e13			1.39640
$141$	4.57940e12			0.582765
$142$	3.46441e12	−	3.46441e12i	0.422571	−	0.422571i
$143$	−1.11419e12	+	1.11419e12i	−0.130299	+	0.130299i
$144$			4.68378e12i			0.525317i
$145$	−1.28010e13	+	6.76689e12i	−1.37732	+	0.728083i
$146$	−4.46266e12			−0.460762
$147$	−9.27886e10	−	9.27886e10i	−0.00919582	−	0.00919582i
$148$	1.05421e13	+	1.05421e13i	1.00312	+	1.00312i
$149$		−	2.21419e12i		−	0.202347i	−0.994869	−	0.101173i	$-0.967740\pi$
$149$		−	2.21419e12i		−	0.202347i	0.994869	−	0.101173i	$-0.0322597\pi$
$150$		−	2.53958e12i		−	0.222954i
$151$		−	1.39790e13i		−	1.17928i	−0.807668	−	0.589638i	$-0.799270\pi$
$151$		−	1.39790e13i		−	1.17928i	0.807668	−	0.589638i	$-0.200730\pi$
$152$	−5.24424e12			−0.425228
$153$	2.88821e12	−	2.88821e12i	0.225155	−	0.225155i
$154$			6.54264e12i			0.490488i
$155$	−2.33143e12	+	2.33143e12i	−0.168125	+	0.168125i
$156$	5.36143e11	+	5.36143e11i	0.0371992	+	0.0371992i
$157$	1.19559e12	−	1.19559e12i	0.0798330	−	0.0798330i	−0.666063	−	0.745896i	$-0.732022\pi$
$157$	1.19559e12	−	1.19559e12i	0.0798330	−	0.0798330i	0.745896	+	0.666063i	$0.232022\pi$
$158$			3.34458e12i			0.214980i
$159$	2.33841e12	+	2.33841e12i	0.144723	+	0.144723i
$160$	−1.60540e13	+	1.60540e13i	−0.956893	+	0.956893i
$161$	−2.48519e13			−1.42693
$162$	1.80169e12	+	1.80169e12i	0.0996756	+	0.0996756i
$163$	5.10742e12	−	5.10742e12i	0.272318	−	0.272318i	−0.557715	−	0.830033i	$-0.688322\pi$
$163$	5.10742e12	−	5.10742e12i	0.272318	−	0.272318i	0.830033	+	0.557715i	$0.188322\pi$
$164$	1.50797e11	+	1.50797e11i	0.00775050	+	0.00775050i
$165$	−2.04562e13			−1.01373
$166$	7.56231e12	+	7.56231e12i	0.361415	+	0.361415i
$167$		−	1.37408e13i		−	0.633450i	−0.948517	−	0.316725i	$-0.897417\pi$
$167$		−	1.37408e13i		−	0.633450i	0.948517	−	0.316725i	$-0.102583\pi$
$168$	6.71023e12			0.298457
$169$	2.29054e13			0.983145
$170$	5.16618e12			0.214031
$171$	9.24903e12	−	9.24903e12i	0.369930	−	0.369930i
$172$	−1.81903e13	+	1.81903e13i	−0.702537	+	0.702537i
$173$			4.28814e13i			1.59953i	0.600314	+	0.799765i	$0.295042\pi$
$173$			4.28814e13i			1.59953i	−0.600314	+	0.799765i	$0.704958\pi$
$174$	−3.83302e12	+	2.02622e12i	−0.138116	+	0.0730116i
$175$	−4.15682e13			−1.44722
$176$	1.98398e13	+	1.98398e13i	0.667516	+	0.667516i
$177$	2.65092e12	+	2.65092e12i	0.0862098	+	0.0862098i
$178$		−	8.26918e12i		−	0.259982i
$179$			5.31911e13i			1.61704i	0.588469	+	0.808520i	$0.299731\pi$
$179$			5.31911e13i			1.61704i	−0.588469	+	0.808520i	$0.700269\pi$
$180$		−	3.69915e13i		−	1.08759i
$181$	2.51901e13			0.716404			0.358202	−	0.933644i	$-0.383390\pi$
$181$	2.51901e13			0.716404			0.358202	+	0.933644i	$0.383390\pi$
$182$	−1.15299e12	+	1.15299e12i	−0.0317246	+	0.0317246i
$183$		−	9.08395e11i		−	0.0241862i
$184$	2.47879e13	−	2.47879e13i	0.638754	−	0.638754i
$185$	−7.08828e13	−	7.08828e13i	−1.76812	−	1.76812i
$186$	−6.98104e11	+	6.98104e11i	−0.0168594	+	0.0168594i
$187$		−	2.44681e13i		−	0.572204i
$188$	3.50774e13	+	3.50774e13i	0.794474	+	0.794474i
$189$	−2.68182e13	+	2.68182e13i	−0.588381	+	0.588381i
$190$	1.65439e13			0.351654
$191$	−1.84970e13	−	1.84970e13i	−0.380979	−	0.380979i	0.490476	−	0.871455i	$-0.336823\pi$
$191$	−1.84970e13	−	1.84970e13i	−0.380979	−	0.380979i	−0.871455	+	0.490476i	$0.836823\pi$
$192$	5.99407e12	−	5.99407e12i	0.119651	−	0.119651i
$193$	−6.93903e13	−	6.93903e13i	−1.34262	−	1.34262i	−0.893438	−	0.449187i	$-0.851714\pi$
$193$	−6.93903e13	−	6.93903e13i	−1.34262	−	1.34262i	−0.449187	−	0.893438i	$-0.648286\pi$
$194$	−1.76182e12			−0.0330484
$195$	−3.60493e12	−	3.60493e12i	−0.0655675	−	0.0655675i
$196$		−	1.42149e12i		−	0.0250730i
$197$	6.90692e13			1.18164			0.590822	−	0.806802i	$-0.298803\pi$
$197$	6.90692e13			1.18164			0.590822	+	0.806802i	$0.298803\pi$
$198$	2.30185e13			0.382020
$199$	7.79561e13			1.25525			0.627627	−	0.778514i	$-0.284026\pi$
$199$	7.79561e13			1.25525			0.627627	+	0.778514i	$0.284026\pi$
$200$	4.14613e13	−	4.14613e13i	0.647833	−	0.647833i
$201$	−1.06293e13	+	1.06293e13i	−0.161187	+	0.161187i
$202$		−	1.03797e13i		−	0.152784i
$203$	3.31655e13	+	6.27393e13i	0.473925	+	0.896528i
$204$	−1.17740e13			−0.163359
$205$	−1.01393e12	−	1.01393e12i	−0.0136611	−	0.0136611i
$206$	2.20800e13	+	2.20800e13i	0.288932	+	0.288932i
$207$			8.74347e13i			1.11138i
$208$			6.99261e12i			0.0863494i
$209$		−	7.83551e13i		−	0.940134i
$210$	−2.11685e13			−0.246817
$211$	−3.14897e13	+	3.14897e13i	−0.356840	+	0.356840i	−0.862647	−	0.505807i	$-0.831195\pi$
$211$	−3.14897e13	+	3.14897e13i	−0.356840	+	0.356840i	0.505807	+	0.862647i	$0.331195\pi$
$212$			3.58236e13i			0.394598i
$213$	5.30883e13	−	5.30883e13i	0.568487	−	0.568487i
$214$	2.80595e13	+	2.80595e13i	0.292144	+	0.292144i
$215$	1.22308e14	−	1.22308e14i	1.23830	−	1.23830i
$216$		−	5.34984e13i		−	0.526767i
$217$	1.14267e13	+	1.14267e13i	0.109436	+	0.109436i
$218$	1.54206e13	−	1.54206e13i	0.143668	−	0.143668i
$219$	−6.83853e13			−0.619866
$220$	−1.56691e14	−	1.56691e14i	−1.38200	−	1.38200i
$221$	4.31194e12	−	4.31194e12i	0.0370100	−	0.0370100i
$222$	−2.12246e13	−	2.12246e13i	−0.177305	−	0.177305i
$223$	−2.46632e13			−0.200549			−0.100274	−	0.994960i	$-0.531972\pi$
$223$	−2.46632e13			−0.200549			−0.100274	+	0.994960i	$0.531972\pi$
$224$	7.86829e13	+	7.86829e13i	0.622862	+	0.622862i
$225$			1.46247e14i			1.12717i
$226$	−6.36540e13			−0.477721
$227$	6.95149e13			0.508069			0.254034	−	0.967195i	$-0.418242\pi$
$227$	6.95149e13			0.508069			0.254034	+	0.967195i	$0.418242\pi$
$228$	−3.77042e13			−0.268399
$229$	1.97448e14	−	1.97448e14i	1.36912	−	1.36912i	0.507415	−	0.861702i	$-0.330601\pi$
$229$	1.97448e14	−	1.97448e14i	1.36912	−	1.36912i	0.861702	−	0.507415i	$-0.169399\pi$
$230$	−7.81977e13	+	7.81977e13i	−0.528235	+	0.528235i
$231$			1.00259e14i			0.659857i
$232$	−9.56581e13	−	2.94978e13i	−0.613471	−	0.189174i
$233$	−2.46838e14			−1.54269			−0.771343	−	0.636420i	$-0.780414\pi$
$233$	−2.46838e14			−1.54269			−0.771343	+	0.636420i	$0.780414\pi$
$234$	4.05648e12	+	4.05648e12i	0.0247089	+	0.0247089i
$235$	−2.35854e14	−	2.35854e14i	−1.40035	−	1.40035i
$236$			4.06111e13i			0.235057i
$237$			5.12519e13i			0.289214i
$238$		−	2.53202e13i		−	0.139317i
$239$	3.23452e14			1.73549			0.867746	−	0.497007i	$-0.165568\pi$
$239$	3.23452e14			1.73549			0.867746	+	0.497007i	$0.165568\pi$
$240$	−6.41912e13	+	6.41912e13i	−0.335898	+	0.335898i
$241$			3.65761e14i			1.86679i	0.358855	+	0.933393i	$0.383167\pi$
$241$			3.65761e14i			1.86679i	−0.358855	+	0.933393i	$0.616833\pi$
$242$	4.91033e13	−	4.91033e13i	0.244466	−	0.244466i
$243$	1.47069e14	+	1.47069e14i	0.714303	+	0.714303i
$244$	6.95814e12	−	6.95814e12i	0.0329727	−	0.0329727i
$245$			9.55782e12i			0.0441939i
$246$	−3.03603e11	−	3.03603e11i	−0.00136992	−	0.00136992i
$247$	1.38083e13	−	1.38083e13i	0.0608076	−	0.0608076i
$248$	−2.27945e13			−0.0979762
$249$	1.15884e14	+	1.15884e14i	0.486214	+	0.486214i
$250$	−3.91456e13	+	3.91456e13i	−0.160340	+	0.160340i
$251$	−2.19201e14	−	2.19201e14i	−0.876597	−	0.876597i	0.116584	−	0.993181i	$-0.462806\pi$
$251$	−2.19201e14	−	2.19201e14i	−0.876597	−	0.876597i	−0.993181	+	0.116584i	$0.962806\pi$
$252$	−1.81300e14			−0.707939
$253$	3.70361e14	+	3.70361e14i	1.41222	+	1.41222i
$254$			1.05506e14i			0.392894i
$255$	7.91660e13			0.287937
$256$	8.50881e12			0.0302294
$257$	−4.18598e14			−1.45278			−0.726388	−	0.687285i	$-0.758803\pi$
$257$	−4.18598e14			−1.45278			−0.726388	+	0.687285i	$0.758803\pi$
$258$	3.66230e13	−	3.66230e13i	0.124175	−	0.124175i
$259$	−3.47407e14	+	3.47407e14i	−1.15091	+	1.15091i
$260$		−	5.52262e13i		−	0.178774i
$261$	2.20732e14	−	1.16684e14i	0.698267	−	0.369120i
$262$	−2.00823e14			−0.620878
$263$	−1.26098e14	−	1.26098e14i	−0.381041	−	0.381041i	0.490436	−	0.871477i	$-0.336838\pi$
$263$	−1.26098e14	−	1.26098e14i	−0.381041	−	0.381041i	−0.871477	+	0.490436i	$0.836838\pi$
$264$	−1.00001e14	−	1.00001e14i	−0.295379	−	0.295379i
$265$		−	2.40871e14i		−	0.695520i
$266$		−	8.10838e13i		−	0.228899i
$267$		−	1.26716e14i		−	0.349755i
$268$	−1.62838e14			−0.439487
$269$	−3.81746e14	+	3.81746e14i	−1.00754	+	1.00754i	−0.00756389	+	0.999971i	$0.502408\pi$
$269$	−3.81746e14	+	3.81746e14i	−1.00754	+	1.00754i	−0.999971	+	0.00756389i	$0.997592\pi$
$270$			1.68770e14i			0.435624i
$271$	1.94357e14	−	1.94357e14i	0.490665	−	0.490665i	−0.417851	−	0.908516i	$-0.637217\pi$
$271$	1.94357e14	−	1.94357e14i	0.490665	−	0.490665i	0.908516	+	0.417851i	$0.137217\pi$
$272$	−7.67806e13	−	7.67806e13i	−0.189600	−	0.189600i
$273$	−1.76683e13	+	1.76683e13i	−0.0426793	+	0.0426793i
$274$		−	9.37982e13i		−	0.221662i
$275$	6.19480e14	+	6.19480e14i	1.43229	+	1.43229i
$276$	1.78216e14	−	1.78216e14i	0.403174	−	0.403174i
$277$	−7.39558e13			−0.163717			−0.0818585	−	0.996644i	$-0.526086\pi$
$277$	−7.39558e13			−0.163717			−0.0818585	+	0.996644i	$0.526086\pi$
$278$	1.25769e14	+	1.25769e14i	0.272462	+	0.272462i
$279$	4.02017e13	−	4.02017e13i	0.0852351	−	0.0852351i
$280$	−3.45598e14	−	3.45598e14i	−0.717172	−	0.717172i
$281$	3.38715e14			0.688014			0.344007	−	0.938967i	$-0.388216\pi$
$281$	3.38715e14			0.688014			0.344007	+	0.938967i	$0.388216\pi$
$282$	−7.06221e13	−	7.06221e13i	−0.140425	−	0.140425i
$283$			2.76019e14i			0.537305i	0.963237	+	0.268653i	$0.0865783\pi$
$283$			2.76019e14i			0.537305i	−0.963237	+	0.268653i	$0.913422\pi$
$284$	8.13293e14			1.55002
$285$	2.53516e14			0.473082
$286$	3.43653e13			0.0627949
$287$	−4.96942e12	+	4.96942e12i	−0.00889230	+	0.00889230i
$288$	2.76825e14	−	2.76825e14i	0.485121	−	0.485121i
$289$		−	4.87930e14i		−	0.837472i
$290$	3.01770e14	+	9.30558e13i	0.507326	+	0.156443i
$291$	−2.69979e13			−0.0444603
$292$	−5.23819e14	−	5.23819e14i	−0.845053	−	0.845053i
$293$	4.07369e13	+	4.07369e13i	0.0643846	+	0.0643846i	0.738566	−	0.674181i	$-0.235503\pi$
$293$	4.07369e13	+	4.07369e13i	0.0643846	+	0.0643846i	−0.674181	+	0.738566i	$0.735503\pi$
$294$			2.86192e12i			0.00443173i
$295$		−	2.73061e14i		−	0.414312i
$296$		−	6.93026e14i		−	1.03038i
$297$	7.99329e14			1.16463
$298$	−3.41465e13	+	3.41465e13i	−0.0487583	+	0.0487583i
$299$			1.30535e14i			0.182684i
$300$	2.98092e14	−	2.98092e14i	0.408905	−	0.408905i
$301$	−5.99450e14	−	5.99450e14i	−0.806035	−	0.806035i
$302$	−2.15580e14	+	2.15580e14i	−0.284163	+	0.284163i
$303$		−	1.59057e14i		−	0.205541i
$304$	−2.45877e14	−	2.45877e14i	−0.311513	−	0.311513i
$305$	−4.67852e13	+	4.67852e13i	−0.0581179	+	0.0581179i
$306$	−8.90823e13			−0.108508
$307$	−2.85349e14	−	2.85349e14i	−0.340837	−	0.340837i	0.515845	−	0.856682i	$-0.327478\pi$
$307$	−2.85349e14	−	2.85349e14i	−0.340837	−	0.340837i	−0.856682	+	0.515845i	$0.827478\pi$
$308$	−7.67963e14	+	7.67963e14i	−0.899572	+	0.899572i
$309$	3.38352e14	+	3.38352e14i	0.388703	+	0.388703i
$310$	7.19092e13			0.0810241
$311$	−4.13952e14	−	4.13952e14i	−0.457497	−	0.457497i	0.440336	−	0.897833i	$-0.354859\pi$
$311$	−4.13952e14	−	4.13952e14i	−0.457497	−	0.457497i	−0.897833	+	0.440336i	$0.854859\pi$
$312$		−	3.52456e13i		−	0.0382100i
$313$	−6.84250e13			−0.0727694			−0.0363847	−	0.999338i	$-0.511584\pi$
$313$	−6.84250e13			−0.0727694			−0.0363847	+	0.999338i	$0.511584\pi$
$314$	−3.68759e13			−0.0384738
$315$	1.21903e15			1.24782
$316$	−3.92580e14	+	3.92580e14i	−0.394281	+	0.394281i
$317$	1.95677e14	−	1.95677e14i	0.192834	−	0.192834i	−0.604085	−	0.796920i	$-0.706461\pi$
$317$	1.95677e14	−	1.95677e14i	0.192834	−	0.192834i	0.796920	+	0.604085i	$0.206461\pi$
$318$		−	7.21246e13i		−	0.0697462i
$319$	4.40732e14	−	1.42924e15i	0.418244	−	1.35632i
$320$	−6.17428e14			−0.575025
$321$	4.29980e14	+	4.29980e14i	0.393023	+	0.393023i
$322$	3.83258e14	+	3.83258e14i	0.343840	+	0.343840i
$323$			3.03237e14i			0.267034i
$324$			4.22957e14i			0.365617i
$325$			2.18338e14i			0.185280i
$326$	−1.57530e14			−0.131238
$327$	2.36303e14	−	2.36303e14i	0.193278	−	0.193278i
$328$		−	9.91327e12i		−	0.00796111i
$329$	−1.15595e15	+	1.15595e15i	−0.911516	+	0.911516i
$330$	3.15469e14	+	3.15469e14i	0.244272	+	0.244272i
$331$	1.67423e14	−	1.67423e14i	0.127305	−	0.127305i	−0.640583	−	0.767889i	$-0.721307\pi$
$331$	1.67423e14	−	1.67423e14i	0.127305	−	0.127305i	0.767889	+	0.640583i	$0.221307\pi$
$332$			1.77530e15i			1.32569i
$333$	1.22226e15	+	1.22226e15i	0.896391	+	0.896391i
$334$	−2.11906e14	+	2.11906e14i	−0.152639	+	0.152639i
$335$	1.09489e15			0.774642
$336$	3.14610e14	+	3.14610e14i	0.218644	+	0.218644i
$337$	−5.81604e14	+	5.81604e14i	−0.397053	+	0.397053i	−0.877192	−	0.480139i	$-0.840586\pi$
$337$	−5.81604e14	+	5.81604e14i	−0.397053	+	0.397053i	0.480139	+	0.877192i	$0.340586\pi$
$338$	−3.53240e14	−	3.53240e14i	−0.236903	−	0.236903i
$339$	−9.75426e14			−0.642682
$340$	6.06397e14	+	6.06397e14i	0.392540	+	0.392540i
$341$		−	3.40577e14i		−	0.216615i
$342$	−2.85272e14			−0.178280
$343$	−1.60450e15			−0.985318
$344$	1.19582e15			0.721628
$345$	−1.19829e15	+	1.19829e15i	−0.710638	+	0.710638i
$346$	6.61304e14	−	6.61304e14i	0.385429	−	0.385429i
$347$			1.11494e15i			0.638665i	0.947643	+	0.319332i	$0.103459\pi$
$347$			1.11494e15i			0.638665i	−0.947643	+	0.319332i	$0.896541\pi$
$348$	−6.87747e14	−	2.12078e14i	−0.387216	−	0.119405i
$349$	−2.94562e15			−1.63014			−0.815069	−	0.579364i	$-0.803301\pi$
$349$	−2.94562e15			−1.63014			−0.815069	+	0.579364i	$0.803301\pi$
$350$	6.41053e14	+	6.41053e14i	0.348727	+	0.348727i
$351$	1.40863e14	+	1.40863e14i	0.0753277	+	0.0753277i
$352$		−	2.34518e15i		−	1.23288i
$353$		−	2.90551e15i		−	1.50167i	−0.660492	−	0.750833i	$-0.729652\pi$
$353$		−	2.90551e15i		−	1.50167i	0.660492	−	0.750833i	$-0.270348\pi$
$354$		−	8.17633e13i		−	0.0415469i
$355$	−5.46843e15			−2.73207
$356$	9.70622e14	−	9.70622e14i	0.476815	−	0.476815i
$357$		−	3.88004e14i		−	0.187425i
$358$	8.20297e14	−	8.20297e14i	0.389649	−	0.389649i
$359$	−1.34840e15	−	1.34840e15i	−0.629870	−	0.629870i	0.318165	−	0.948035i	$-0.396933\pi$
$359$	−1.34840e15	−	1.34840e15i	−0.629870	−	0.629870i	−0.948035	+	0.318165i	$0.896933\pi$
$360$	−1.21589e15	+	1.21589e15i	−0.558574	+	0.558574i
$361$		−	1.24225e15i		−	0.561262i
$362$	−3.88474e14	−	3.88474e14i	−0.172628	−	0.172628i
$363$	7.52453e14	−	7.52453e14i	0.328882	−	0.328882i
$364$	−2.70671e14			−0.116368
$365$	3.52206e15	+	3.52206e15i	1.48950	+	1.48950i
$366$	−1.40090e13	+	1.40090e13i	−0.00582801	+	0.00582801i
$367$	3.06294e15	+	3.06294e15i	1.25355	+	1.25355i	0.954117	+	0.299433i	$0.0967976\pi$
$367$	3.06294e15	+	3.06294e15i	1.25355	+	1.25355i	0.299433	+	0.954117i	$0.403202\pi$
$368$	2.32437e15			0.935877
$369$	1.74836e13	+	1.74836e13i	0.00692583	+	0.00692583i
$370$			2.18627e15i			0.852104i
$371$	−1.18054e15			−0.452730
$372$	−1.63884e14			−0.0618415
$373$	−2.09682e15			−0.778590			−0.389295	−	0.921113i	$-0.627281\pi$
$373$	−2.09682e15			−0.778590			−0.389295	+	0.921113i	$0.627281\pi$
$374$	−3.77340e14	+	3.77340e14i	−0.137881	+	0.137881i
$375$	−5.99862e14	+	5.99862e14i	−0.215707	+	0.215707i
$376$		−	2.30596e15i		−	0.816063i
$377$	3.29540e14	−	1.74202e14i	0.114778	−	0.0606744i
$378$	8.27164e14			0.283557
$379$	1.36400e15	+	1.36400e15i	0.460235	+	0.460235i	0.898732	−	0.438497i	$-0.144489\pi$
$379$	1.36400e15	+	1.36400e15i	0.460235	+	0.460235i	−0.438497	+	0.898732i	$0.644489\pi$
$380$	1.94189e15	+	1.94189e15i	0.644945	+	0.644945i
$381$			1.61676e15i			0.528563i
$382$			5.70510e14i			0.183604i
$383$		−	2.68319e15i		−	0.850079i	−0.905175	−	0.425039i	$-0.860260\pi$
$383$		−	2.68319e15i		−	0.850079i	0.905175	−	0.425039i	$-0.139740\pi$
$384$	−1.46164e15			−0.455882
$385$	5.16364e15	−	5.16364e15i	1.58559	−	1.58559i
$386$			2.14023e15i			0.647049i
$387$	−2.10900e15	+	2.10900e15i	−0.627786	+	0.627786i
$388$	−2.06799e14	−	2.06799e14i	−0.0606119	−	0.0606119i
$389$	2.43572e15	−	2.43572e15i	0.702960	−	0.702960i	−0.262085	−	0.965045i	$-0.584410\pi$
$389$	2.43572e15	−	2.43572e15i	0.702960	−	0.702960i	0.965045	+	0.262085i	$0.0844100\pi$
$390$			1.11188e14i			0.0315988i
$391$	−1.43331e15	−	1.43331e15i	−0.401124	−	0.401124i
$392$	−4.67237e13	+	4.67237e13i	−0.0128772	+	0.0128772i
$393$	−3.07739e15			−0.835272
$394$	−1.06516e15	−	1.06516e15i	−0.284734	−	0.284734i
$395$	2.63964e15	−	2.63964e15i	0.694963	−	0.694963i
$396$	2.70187e15	+	2.70187e15i	0.700638	+	0.700638i
$397$	−1.43080e14			−0.0365457			−0.0182729	−	0.999833i	$-0.505817\pi$
$397$	−1.43080e14			−0.0365457			−0.0182729	+	0.999833i	$0.505817\pi$
$398$	−1.20222e15	−	1.20222e15i	−0.302471	−	0.302471i
$399$		−	1.24252e15i		−	0.307939i
$400$	3.88784e15			0.949179
$401$	−7.17939e15			−1.72672			−0.863359	−	0.504591i	$-0.831643\pi$
$401$	−7.17939e15			−1.72672			−0.863359	+	0.504591i	$0.831643\pi$
$402$	3.27845e14			0.0776805
$403$	6.00188e13	−	6.00188e13i	0.0140106	−	0.0140106i
$404$	1.21835e15	−	1.21835e15i	0.280210	−	0.280210i
$405$		−	2.84388e15i		−	0.644439i
$406$	4.56079e14	−	1.47902e15i	0.101832	−	0.330230i
$407$	1.03546e16			2.27807
$408$	3.87006e14	+	3.87006e14i	0.0838989	+	0.0838989i
$409$	−5.48763e15	−	5.48763e15i	−1.17232	−	1.17232i	−0.981656	−	0.190662i	$-0.938937\pi$
$409$	−5.48763e15	−	5.48763e15i	−1.17232	−	1.17232i	−0.190662	−	0.981656i	$-0.561063\pi$
$410$			3.12731e13i			0.00658366i
$411$		−	1.43735e15i		−	0.298203i
$412$			5.18343e15i			1.05982i
$413$	−1.33831e15			−0.269685
$414$	1.34839e15	−	1.34839e15i	0.267802	−	0.267802i
$415$		−	1.19368e16i		−	2.33668i
$416$	4.13283e14	−	4.13283e14i	0.0797422	−	0.0797422i
$417$	1.92728e15	+	1.92728e15i	0.366545	+	0.366545i
$418$	−1.20837e15	+	1.20837e15i	−0.226539	+	0.226539i
$419$			8.89870e15i			1.64453i	0.569104	+	0.822266i	$0.307290\pi$
$419$			8.89870e15i			1.64453i	−0.569104	+	0.822266i	$0.692710\pi$
$420$	−2.48472e15	−	2.48472e15i	−0.452671	−	0.452671i
$421$	−4.98882e15	+	4.98882e15i	−0.895994	+	0.895994i	−0.995079	−	0.0990847i	$-0.968409\pi$
$421$	−4.98882e15	+	4.98882e15i	−0.895994	+	0.895994i	0.0990847	+	0.995079i	$0.468409\pi$
$422$	9.71249e14			0.171971
$423$	4.06691e15	+	4.06691e15i	0.709941	+	0.709941i
$424$	1.17751e15	−	1.17751e15i	0.202660	−	0.202660i
$425$	−2.39741e15	−	2.39741e15i	−0.406825	−	0.406825i
$426$	−1.63742e15			−0.273970
$427$	2.29301e14	+	2.29301e14i	0.0378302	+	0.0378302i
$428$			6.58714e15i			1.07160i
$429$	5.26610e14			0.0844784
$430$	−3.77240e15			−0.596770
$431$	2.76924e15			0.432014			0.216007	−	0.976392i	$-0.430697\pi$
$431$	2.76924e15			0.432014			0.216007	+	0.976392i	$0.430697\pi$
$432$	2.50828e15	−	2.50828e15i	0.385899	−	0.385899i
$433$	2.26676e15	−	2.26676e15i	0.343937	−	0.343937i	−0.513908	−	0.857845i	$-0.671803\pi$
$433$	2.26676e15	−	2.26676e15i	0.343937	−	0.343937i	0.857845	+	0.513908i	$0.171803\pi$
$434$		−	3.52437e14i		−	0.0527404i
$435$	4.62428e15	+	1.42598e15i	0.682510	+	0.210463i
$436$	3.62007e15			0.526985
$437$	−4.58993e15	−	4.58993e15i	−0.659048	−	0.659048i
$438$	1.05462e15	+	1.05462e15i	0.149365	+	0.149365i
$439$		−	3.47578e15i		−	0.485585i	−0.970078	−	0.242793i	$-0.921937\pi$
$439$		−	3.47578e15i		−	0.485585i	0.970078	−	0.242793i	$-0.0780634\pi$
$440$			1.03007e16i			1.41955i
$441$		−	1.64809e14i		−	0.0224052i
$442$	−1.32995e14			−0.0178362
$443$	−4.43359e14	+	4.43359e14i	−0.0586589	+	0.0586589i	−0.735828	−	0.677169i	$-0.763207\pi$
$443$	−4.43359e14	+	4.43359e14i	−0.0586589	+	0.0586589i	0.677169	+	0.735828i	$0.263207\pi$
$444$		−	4.98260e15i		−	0.650367i
$445$	−6.52628e15	+	6.52628e15i	−0.840438	+	0.840438i
$446$	3.80348e14	+	3.80348e14i	0.0483251	+	0.0483251i
$447$	−5.23257e14	+	5.23257e14i	−0.0655949	+	0.0655949i
$448$			3.02610e15i			0.374296i
$449$	2.19052e15	+	2.19052e15i	0.267343	+	0.267343i	0.828029	−	0.560686i	$-0.189462\pi$
$449$	2.19052e15	+	2.19052e15i	0.267343	+	0.267343i	−0.560686	+	0.828029i	$0.689462\pi$
$450$	2.25537e15	−	2.25537e15i	0.271608	−	0.271608i
$451$	1.48116e14			0.0176012
$452$	−7.47159e15	−	7.47159e15i	−0.876157	−	0.876157i
$453$	−3.30353e15	+	3.30353e15i	−0.382287	+	0.382287i
$454$	−1.07204e15	−	1.07204e15i	−0.122426	−	0.122426i
$455$	1.81994e15			0.205111
$456$	1.23932e15	+	1.23932e15i	0.137846	+	0.137846i
$457$			2.91370e15i			0.319851i	0.987129	+	0.159926i	$0.0511254\pi$
$457$			2.91370e15i			0.319851i	−0.987129	+	0.159926i	$0.948875\pi$
$458$	−6.08998e15			−0.659816
$459$	−3.09343e15			−0.330798
$460$	−1.83574e16			−1.93760
$461$	−2.25392e15	+	2.25392e15i	−0.234819	+	0.234819i	−0.814701	−	0.579882i	$-0.803099\pi$
$461$	−2.25392e15	+	2.25392e15i	−0.234819	+	0.234819i	0.579882	+	0.814701i	$0.303099\pi$
$462$	1.54616e15	−	1.54616e15i	0.159002	−	0.159002i
$463$			1.77985e16i			1.80675i	0.428850	+	0.903376i	$0.358919\pi$
$463$			1.77985e16i			1.80675i	−0.428850	+	0.903376i	$0.641081\pi$
$464$	−3.10194e15	−	5.86795e15i	−0.310831	−	0.588002i
$465$	1.10193e15			0.109002
$466$	3.80667e15	+	3.80667e15i	0.371732	+	0.371732i
$467$	−6.08863e14	−	6.08863e14i	−0.0586973	−	0.0586973i	0.677149	−	0.735846i	$-0.263215\pi$
$467$	−6.08863e14	−	6.08863e14i	−0.0586973	−	0.0586973i	−0.735846	+	0.677149i	$0.763215\pi$
$468$			9.52285e14i			0.0906341i
$469$		−	5.36620e15i		−	0.504232i
$470$			7.27453e15i			0.674866i
$471$	−5.65082e14			−0.0517590
$472$	1.33487e15	−	1.33487e15i	0.120722	−	0.120722i
$473$			1.78669e16i			1.59544i
$474$	7.90392e14	−	7.90392e14i	0.0696903	−	0.0696903i
$475$	−7.67730e15	−	7.67730e15i	−0.668416	−	0.668416i
$476$	2.97204e15	−	2.97204e15i	0.255513	−	0.255513i
$477$			4.15343e15i			0.352612i
$478$	−4.98818e15	−	4.98818e15i	−0.418191	−	0.418191i
$479$	7.17199e15	−	7.17199e15i	0.593782	−	0.593782i	−0.344869	−	0.938651i	$-0.612077\pi$
$479$	7.17199e15	−	7.17199e15i	0.593782	−	0.593782i	0.938651	+	0.344869i	$0.112077\pi$
$480$	7.58777e15			0.620393
$481$	1.82476e15	+	1.82476e15i	0.147345	+	0.147345i
$482$	5.64065e15	−	5.64065e15i	0.449828	−	0.449828i
$483$	5.87300e15	+	5.87300e15i	0.462570	+	0.462570i
$484$	1.15273e16			0.896718
$485$	1.39048e15	+	1.39048e15i	0.106835	+	0.106835i
$486$		−	4.53610e15i		−	0.344243i
$487$	6.10839e13			0.00457882			0.00228941	−	0.999997i	$-0.499271\pi$
$487$	6.10839e13			0.00457882			0.00228941	+	0.999997i	$0.499271\pi$
$488$	−4.57422e14			−0.0338687
$489$	−2.41398e15			−0.176555
$490$	1.47398e14	−	1.47398e14i	0.0106491	−	0.0106491i
$491$	1.07260e16	−	1.07260e16i	0.765509	−	0.765509i	−0.211803	−	0.977312i	$-0.567934\pi$
$491$	1.07260e16	−	1.07260e16i	0.765509	−	0.765509i	0.977312	+	0.211803i	$0.0679336\pi$
$492$		−	7.12728e13i		−	0.00502497i
$493$	−1.70564e15	+	5.53121e15i	−0.118797	+	0.385247i
$494$	−4.25894e14			−0.0293049
$495$	−1.81669e16	−	1.81669e16i	−1.23495	−	1.23495i
$496$	−1.06873e15	−	1.06873e15i	−0.0717755	−	0.0717755i
$497$			2.68015e16i			1.77837i
$498$		−	3.57426e15i		−	0.234320i
$499$			5.89975e15i			0.382147i	0.981576	+	0.191073i	$0.0611968\pi$
$499$			5.89975e15i			0.382147i	−0.981576	+	0.191073i	$0.938803\pi$
$500$	−9.18967e15			−0.588139
$501$	−3.24722e15	+	3.24722e15i	−0.205346	+	0.205346i
$502$			6.76090e15i			0.422457i
$503$	1.39676e16	−	1.39676e16i	0.862409	−	0.862409i	−0.129208	−	0.991617i	$-0.541244\pi$
$503$	1.39676e16	−	1.39676e16i	0.862409	−	0.862409i	0.991617	+	0.129208i	$0.0412436\pi$
$504$	5.95927e15	+	5.95927e15i	0.363588	+	0.363588i
$505$	−8.19196e15	+	8.19196e15i	−0.493901	+	0.493901i
$506$		−	1.14232e16i		−	0.680588i
$507$	−5.41301e15	−	5.41301e15i	−0.318707	−	0.318707i
$508$	−1.23841e16	+	1.23841e16i	−0.720581	+	0.720581i
$509$	8.35825e14			0.0480628			0.0240314	−	0.999711i	$-0.492350\pi$
$509$	8.35825e14			0.0480628			0.0240314	+	0.999711i	$0.492350\pi$
$510$	−1.22087e15	−	1.22087e15i	−0.0693825	−	0.0693825i
$511$	1.72621e16	−	1.72621e16i	0.969546	−	0.969546i
$512$	−1.27981e16	−	1.27981e16i	−0.710435	−	0.710435i
$513$	−9.90618e15			−0.543503
$514$	6.45550e15	+	6.45550e15i	0.350067	+	0.350067i
$515$		−	3.48524e16i		−	1.86805i
$516$	8.59748e15			0.455484
$517$	3.44537e16			1.80423
$518$	1.07152e16			0.554654
$519$	1.01337e16	−	1.01337e16i	0.518520	−	0.518520i
$520$	−1.81526e15	+	1.81526e15i	−0.0918161	+	0.0918161i
$521$			2.54783e16i			1.27393i	0.770894	+	0.636964i	$0.219810\pi$
$521$			2.54783e16i			1.27393i	−0.770894	+	0.636964i	$0.780190\pi$
$522$	−5.20352e15	−	1.60459e15i	−0.257202	−	0.0793126i
$523$	5.29334e15			0.258654			0.129327	−	0.991602i	$-0.458718\pi$
$523$	5.29334e15			0.258654			0.129327	+	0.991602i	$0.458718\pi$
$524$	−2.35723e16	−	2.35723e16i	−1.13871	−	1.13871i
$525$	9.82342e15	+	9.82342e15i	0.469145	+	0.469145i
$526$			3.88928e15i			0.183635i
$527$			1.31804e15i			0.0615270i
$528$		−	9.37710e15i		−	0.432778i
$529$	2.14758e16			0.979974
$530$	−3.71465e15	+	3.71465e15i	−0.167595	+	0.167595i
$531$			4.70849e15i			0.210046i
$532$	9.51746e15	−	9.51746e15i	0.419809	−	0.419809i
$533$	2.61020e13	+	2.61020e13i	0.00113844	+	0.00113844i
$534$	−1.95418e15	+	1.95418e15i	−0.0842784	+	0.0842784i
$535$		−	4.42907e16i		−	1.88882i
$536$	5.35240e15	+	5.35240e15i	0.225715	+	0.225715i
$537$	1.25701e16	−	1.25701e16i	0.524197	−	0.524197i
$538$	1.17743e16			0.485560
$539$	−6.98107e14	−	6.98107e14i	−0.0284701	−	0.0284701i
$540$	−1.98099e16	+	1.98099e16i	−0.798950	+	0.798950i
$541$	1.37568e16	+	1.37568e16i	0.548700	+	0.548700i	0.926065	−	0.377365i	$-0.123170\pi$
$541$	1.37568e16	+	1.37568e16i	0.548700	+	0.548700i	−0.377365	+	0.926065i	$0.623170\pi$
$542$	−5.99464e15			−0.236465
$543$	−5.95293e15	−	5.95293e15i	−0.232237	−	0.232237i
$544$			9.07591e15i			0.350185i
$545$	−2.43407e16			−0.928868
$546$	5.44949e14			0.0205684
$547$	−1.48319e16			−0.553697			−0.276849	−	0.960914i	$-0.589290\pi$
$547$	−1.48319e16			−0.553697			−0.276849	+	0.960914i	$0.589290\pi$
$548$	1.10099e16	−	1.10099e16i	0.406535	−	0.406535i
$549$	8.06734e14	−	8.06734e14i	0.0294643	−	0.0294643i
$550$		−	1.91069e16i		−	0.690261i
$551$	−5.46204e15	+	1.77128e16i	−0.195185	+	0.632962i
$552$	−1.17158e16			−0.414130
$553$	−1.29372e16	−	1.29372e16i	−0.452367	−	0.452367i
$554$	1.14052e15	+	1.14052e15i	0.0394499	+	0.0394499i
$555$			3.35021e16i			1.14634i
$556$			2.95252e16i			0.999410i
$557$		−	3.07077e16i		−	1.02829i	−0.857703	−	0.514146i	$-0.828109\pi$
$557$		−	3.07077e16i		−	1.02829i	0.857703	−	0.514146i	$-0.171891\pi$
$558$	−1.23996e15			−0.0410772
$559$	−3.14862e15	+	3.14862e15i	−0.103193	+	0.103193i
$560$		−	3.24068e16i		−	1.05077i
$561$	−5.78232e15	+	5.78232e15i	−0.185492	+	0.185492i
$562$	−5.22357e15	−	5.22357e15i	−0.165787	−	0.165787i
$563$	−1.83628e16	+	1.83628e16i	−0.576619	+	0.576619i	−0.933970	−	0.357351i	$-0.883680\pi$
$563$	−1.83628e16	+	1.83628e16i	−0.576619	+	0.576619i	0.357351	+	0.933970i	$0.383680\pi$
$564$		−	1.65790e16i		−	0.515090i
$565$	5.02375e16	+	5.02375e16i	1.54432	+	1.54432i
$566$	4.25669e15	−	4.25669e15i	0.129471	−	0.129471i
$567$	−1.39383e16			−0.419480
$568$	−2.67326e16	−	2.67326e16i	−0.796070	−	0.796070i
$569$	−1.66156e16	+	1.66156e16i	−0.489601	+	0.489601i	−0.908180	−	0.418580i	$-0.862528\pi$
$569$	−1.66156e16	+	1.66156e16i	−0.489601	+	0.489601i	0.418580	+	0.908180i	$0.362528\pi$
$570$	−3.90965e15	−	3.90965e15i	−0.113996	−	0.113996i
$571$	6.79007e15			0.195910			0.0979552	−	0.995191i	$-0.468770\pi$
$571$	6.79007e15			0.195910			0.0979552	+	0.995191i	$0.468770\pi$
$572$	4.03374e15	+	4.03374e15i	0.115168	+	0.115168i
$573$			8.74243e15i			0.247004i
$574$	1.53274e14			0.00428545
$575$	7.25765e16			2.00812
$576$	1.06465e16			0.291523
$577$	−3.83951e16	+	3.83951e16i	−1.04045	+	1.04045i	−0.0413017	+	0.999147i	$0.513150\pi$
$577$	−3.83951e16	+	3.83951e16i	−1.04045	+	1.04045i	−0.999147	+	0.0413017i	$0.986850\pi$
$578$	−7.52471e15	+	7.52471e15i	−0.201801	+	0.201801i
$579$			3.27967e16i			0.870479i
$580$	2.44985e16	+	4.63439e16i	0.643533	+	1.21738i
$581$	−5.85039e16			−1.52099
$582$	4.16353e14	+	4.16353e14i	0.0107133	+	0.0107133i
$583$	1.75933e16	+	1.75933e16i	0.448061	+	0.448061i
$584$			3.44354e16i			0.868017i
$585$		−	6.40298e15i		−	0.159752i
$586$		−	1.25646e15i		−	0.0310287i
$587$	1.49630e16			0.365756			0.182878	−	0.983136i	$-0.441459\pi$
$587$	1.49630e16			0.365756			0.182878	+	0.983136i	$0.441459\pi$
$588$	−3.35926e14	+	3.35926e14i	−0.00812794	+	0.00812794i
$589$			4.22081e15i			0.101089i
$590$	−4.21107e15	+	4.21107e15i	−0.0998344	+	0.0998344i
$591$	−1.63224e16	−	1.63224e16i	−0.383054	−	0.383054i
$592$	3.24926e16	−	3.24926e16i	0.754839	−	0.754839i
$593$			5.12948e15i			0.117963i	0.998259	+	0.0589814i	$0.0187853\pi$
$593$			5.12948e15i			0.117963i	−0.998259	+	0.0589814i	$0.981215\pi$
$594$	−1.23270e16	−	1.23270e16i	−0.280633	−	0.280633i
$595$	−1.99834e16	+	1.99834e16i	−0.450369	+	0.450369i
$596$	−8.01611e15			−0.178849
$597$	−1.84226e16	−	1.84226e16i	−0.406916	−	0.406916i
$598$	2.01307e15	−	2.01307e15i	0.0440202	−	0.0440202i
$599$	−4.66323e16	−	4.66323e16i	−1.00955	−	1.00955i	−0.999954	−	0.00959123i	$-0.996947\pi$
$599$	−4.66323e16	−	4.66323e16i	−1.00955	−	1.00955i	−0.00959123	−	0.999954i	$-0.503053\pi$
$600$	−1.95963e16			−0.420017
$601$	4.80516e16	+	4.80516e16i	1.01967	+	1.01967i	0.999803	+	0.0198697i	$0.00632514\pi$
$601$	4.80516e16	+	4.80516e16i	1.01967	+	1.01967i	0.0198697	+	0.999803i	$0.493675\pi$
$602$			1.84891e16i			0.388451i
$603$	−1.88796e16			−0.392724
$604$	−5.06089e16			−1.04233
$605$	−7.75075e16			−1.58056
$606$	−2.45294e15	+	2.45294e15i	−0.0495280	+	0.0495280i
$607$	2.24607e16	−	2.24607e16i	0.449046	−	0.449046i	−0.445991	−	0.895037i	$-0.647149\pi$
$607$	2.24607e16	−	2.24607e16i	0.449046	−	0.449046i	0.895037	+	0.445991i	$0.147149\pi$
$608$			2.90641e16i			0.575355i
$609$	6.98891e15	−	2.26643e16i	0.136995	−	0.444261i
$610$	1.44302e15			0.0280086
$611$	6.07166e15	+	6.07166e15i	0.116697	+	0.116697i
$612$	−1.04563e16	−	1.04563e16i	−0.199008	−	0.199008i
$613$		−	1.31483e16i		−	0.247803i	−0.992294	−	0.123902i	$-0.960459\pi$
$613$		−	1.31483e16i		−	0.247803i	0.992294	−	0.123902i	$-0.0395408\pi$
$614$			8.80114e15i			0.164259i
$615$			4.79225e14i			0.00885704i
$616$	5.04852e16			0.924017
$617$	−1.81553e15	+	1.81553e15i	−0.0329073	+	0.0329073i	−0.723369	−	0.690462i	$-0.757407\pi$
$617$	−1.81553e15	+	1.81553e15i	−0.0329073	+	0.0329073i	0.690462	+	0.723369i	$0.257407\pi$
$618$		−	1.04359e16i		−	0.187327i
$619$	3.94587e16	−	3.94587e16i	0.701454	−	0.701454i	−0.263269	−	0.964723i	$-0.584801\pi$
$619$	3.94587e16	−	3.94587e16i	0.701454	−	0.701454i	0.964723	+	0.263269i	$0.0848005\pi$
$620$	8.44057e15	+	8.44057e15i	0.148601	+	0.148601i
$621$	4.68235e16	−	4.68235e16i	0.816421	−	0.816421i
$622$			1.27677e16i			0.220480i
$623$	3.19862e16	+	3.19862e16i	0.547059	+	0.547059i
$624$	1.65250e15	−	1.65250e15i	0.0279919	−	0.0279919i
$625$	−2.32731e16			−0.390458
$626$	1.05523e15	+	1.05523e15i	0.0175348	+	0.0175348i
$627$	−1.85169e16	+	1.85169e16i	−0.304764	+	0.304764i
$628$	−4.32843e15	−	4.32843e15i	−0.0705622	−	0.0705622i
$629$	−4.00727e16			−0.647060
$630$	−1.87995e16	−	1.87995e16i	−0.300679	−	0.300679i
$631$		−	1.15107e17i		−	1.82358i	−0.410652	−	0.911792i	$-0.634699\pi$
$631$		−	1.15107e17i		−	1.82358i	0.410652	−	0.911792i	$-0.365301\pi$
$632$	2.58079e16			0.404996
$633$	1.48833e16			0.231354
$634$	−6.03534e15			−0.0929323
$635$	8.32684e16	−	8.32684e16i	1.27010	−	1.27010i
$636$	8.46585e15	−	8.46585e15i	0.127917	−	0.127917i
$637$		−	2.46050e14i		−	0.00368288i
$638$	−2.88382e16	+	1.52445e16i	−0.427606	+	0.226043i
$639$	9.42941e16			1.38509
$640$	7.52790e16	+	7.52790e16i	1.09545	+	1.09545i
$641$	−7.94468e16	−	7.94468e16i	−1.14532	−	1.14532i	−0.987461	−	0.157862i	$-0.949540\pi$
$641$	−7.94468e16	−	7.94468e16i	−1.14532	−	1.14532i	−0.157862	−	0.987461i	$-0.550460\pi$
$642$		−	1.32620e16i		−	0.189409i
$643$			4.03472e16i			0.570883i	0.958396	+	0.285442i	$0.0921403\pi$
$643$			4.03472e16i			0.570883i	−0.958396	+	0.285442i	$0.907860\pi$
$644$			8.99723e16i			1.26123i
$645$	−5.78078e16			−0.802839
$646$	4.67642e15	−	4.67642e15i	0.0643456	−	0.0643456i
$647$		−	6.02400e16i		−	0.821219i	−0.911811	−	0.410610i	$-0.865316\pi$
$647$		−	6.02400e16i		−	0.821219i	0.911811	−	0.410610i	$-0.134684\pi$
$648$	1.39024e16	−	1.39024e16i	0.187776	−	0.187776i
$649$	1.99445e16	+	1.99445e16i	0.266904	+	0.266904i
$650$	3.36714e15	−	3.36714e15i	0.0446459	−	0.0446459i
$651$		−	5.40070e15i		−	0.0709520i
$652$	−1.84906e16	−	1.84906e16i	−0.240694	−	0.240694i
$653$	−3.03642e15	+	3.03642e15i	−0.0391636	+	0.0391636i	−0.726417	−	0.687254i	$-0.758816\pi$
$653$	−3.03642e15	+	3.03642e15i	−0.0391636	+	0.0391636i	0.687254	+	0.726417i	$0.258816\pi$
$654$	−7.28838e15			−0.0931461
$655$	1.58496e17	+	1.58496e17i	2.00710	+	2.00710i
$656$	4.64785e14	−	4.64785e14i	0.00583216	−	0.00583216i
$657$	−6.07321e16	−	6.07321e16i	−0.755138	−	0.755138i
$658$	3.56535e16			0.439285
$659$	−2.42178e15	−	2.42178e15i	−0.0295681	−	0.0295681i	0.692168	−	0.721736i	$-0.256656\pi$
$659$	−2.42178e15	−	2.42178e15i	−0.0295681	−	0.0295681i	−0.721736	+	0.692168i	$0.756656\pi$
$660$			7.40584e16i			0.896005i
$661$	1.82728e15			0.0219077			0.0109539	−	0.999940i	$-0.496513\pi$
$661$	1.82728e15			0.0219077			0.0109539	+	0.999940i	$0.496513\pi$
$662$	−5.16389e15			−0.0613520
$663$	−2.03800e15			−0.0239951
$664$	5.83534e16	−	5.83534e16i	0.680859	−	0.680859i
$665$	−6.39936e16	+	6.39936e16i	−0.739958	+	0.739958i
$666$		−	3.76986e16i		−	0.431996i
$667$	−5.79056e16	−	1.09540e17i	−0.657606	−	1.24400i
$668$	−4.97463e16			−0.559889
$669$	5.82841e15	+	5.82841e15i	0.0650120	+	0.0650120i
$670$	−1.68850e16	−	1.68850e16i	−0.186661	−	0.186661i
$671$		−	6.83442e15i		−	0.0748802i
$672$		−	3.71887e16i		−	0.403827i
$673$			8.95750e16i			0.964043i	0.876159	+	0.482021i	$0.160097\pi$
$673$			8.95750e16i			0.964043i	−0.876159	+	0.482021i	$0.839903\pi$
$674$	1.79387e16			0.191351
$675$	7.83188e16	−	7.83188e16i	0.828025	−	0.828025i
$676$		−	8.29253e16i		−	0.868975i
$677$	8.04476e16	−	8.04476e16i	0.835567	−	0.835567i	−0.152705	−	0.988272i	$-0.548798\pi$
$677$	8.04476e16	−	8.04476e16i	0.835567	−	0.835567i	0.988272	+	0.152705i	$0.0487984\pi$
$678$	1.50427e16	+	1.50427e16i	0.154863	+	0.154863i
$679$	6.81493e15	−	6.81493e15i	0.0695413	−	0.0695413i
$680$		−	3.98640e16i		−	0.403207i
$681$	−1.64278e16	−	1.64278e16i	−0.164701	−	0.164701i
$682$	−5.25228e15	+	5.25228e15i	−0.0521965	+	0.0521965i
$683$	−1.59000e17			−1.56629			−0.783146	−	0.621838i	$-0.786386\pi$
$683$	−1.59000e17			−1.56629			−0.783146	+	0.621838i	$0.786386\pi$
$684$	−3.34847e16	−	3.34847e16i	−0.326971	−	0.326971i
$685$	−7.40282e16	+	7.40282e16i	−0.716562	+	0.716562i
$686$	2.47442e16	+	2.47442e16i	0.237426	+	0.237426i
$687$	−9.33221e16			−0.887655
$688$	5.60660e16	+	5.60660e16i	0.528651	+	0.528651i
$689$			6.20083e15i			0.0579608i
$690$	3.69594e16			0.342476
$691$	9.91020e15			0.0910362			0.0455181	−	0.998964i	$-0.485506\pi$
$691$	9.91020e15			0.0910362			0.0455181	+	0.998964i	$0.485506\pi$
$692$	1.55245e17			1.41378
$693$	−8.90385e16	+	8.90385e16i	−0.803856	+	0.803856i
$694$	1.71942e16	−	1.71942e16i	0.153895	−	0.153895i
$695$		−	1.98522e17i		−	1.76157i
$696$	1.56350e16	+	2.95769e16i	0.137544	+	0.260194i
$697$	−5.73212e14			−0.00499941
$698$	4.54265e16	+	4.54265e16i	0.392805	+	0.392805i
$699$	5.83329e16	+	5.83329e16i	0.500093	+	0.500093i
$700$			1.50491e17i			1.27915i
$701$		−	4.23345e16i		−	0.356768i	−0.983961	−	0.178384i	$-0.942913\pi$
$701$		−	4.23345e16i		−	0.356768i	0.983961	−	0.178384i	$-0.0570869\pi$
$702$		−	4.34470e15i		−	0.0363025i
$703$	−1.28326e17			−1.06312
$704$	4.50972e16	−	4.50972e16i	0.370436	−	0.370436i
$705$			1.11474e17i			0.907902i
$706$	−4.48078e16	+	4.48078e16i	−0.361848	+	0.361848i
$707$	4.01500e16	+	4.01500e16i	0.321491	+	0.321491i
$708$	9.59722e15	−	9.59722e15i	0.0761984	−	0.0761984i
$709$			2.05043e17i			1.61424i	0.590390	+	0.807118i	$0.298974\pi$
$709$			2.05043e17i			1.61424i	−0.590390	+	0.807118i	$0.701026\pi$
$710$	8.43325e16	+	8.43325e16i	0.658332	+	0.658332i
$711$	−4.55162e16	+	4.55162e16i	−0.352329	+	0.352329i
$712$	−6.38079e16			−0.489772
$713$	−1.99505e16	−	1.99505e16i	−0.151851	−	0.151851i
$714$	−5.98368e15	+	5.98368e15i	−0.0451626	+	0.0451626i
$715$	−2.71221e16	−	2.71221e16i	−0.202996	−	0.202996i
$716$	1.92570e17			1.42926
$717$	−7.64383e16	−	7.64383e16i	−0.562596	−	0.562596i
$718$			4.15891e16i			0.303552i
$719$	7.03479e16			0.509188			0.254594	−	0.967048i	$-0.418058\pi$
$719$	7.03479e16			0.509188			0.254594	+	0.967048i	$0.418058\pi$
$720$	−1.14015e17			−0.818401
$721$	−1.70816e17			−1.21596
$722$	−1.91576e16	+	1.91576e16i	−0.135244	+	0.135244i
$723$	8.64367e16	−	8.64367e16i	0.605157	−	0.605157i
$724$		−	9.11968e16i		−	0.633210i
$725$	−9.68552e16	−	1.83222e17i	−0.666952	−	1.26168i
$726$	−2.32082e16			−0.158497
$727$	9.36826e16	+	9.36826e16i	0.634531	+	0.634531i	0.949201	−	0.314670i	$-0.101894\pi$
$727$	9.36826e16	+	9.36826e16i	0.634531	+	0.634531i	−0.314670	+	0.949201i	$0.601894\pi$
$728$	8.89685e15	+	8.89685e15i	0.0597651	+	0.0597651i
$729$		−	7.42351e15i		−	0.0494589i
$730$		−	1.08632e17i		−	0.717831i
$731$		−	6.91453e16i		−	0.453167i
$732$	−3.28870e15			−0.0213775
$733$	−3.27201e16	+	3.27201e16i	−0.210955	+	0.210955i	−0.804673	−	0.593718i	$-0.797660\pi$
$733$	−3.27201e16	+	3.27201e16i	−0.210955	+	0.210955i	0.593718	+	0.804673i	$0.297660\pi$
$734$		−	9.44714e16i		−	0.604121i
$735$	2.25871e15	−	2.25871e15i	0.0143264	−	0.0143264i
$736$	−1.37377e17	−	1.37377e17i	−0.864267	−	0.864267i
$737$	−7.99711e16	+	7.99711e16i	−0.499032	+	0.499032i
$738$		−	5.39253e14i		−	0.00333775i
$739$	−4.60164e16	−	4.60164e16i	−0.282518	−	0.282518i	0.551594	−	0.834113i	$-0.314020\pi$
$739$	−4.60164e16	−	4.60164e16i	−0.282518	−	0.282518i	−0.834113	+	0.551594i	$0.814020\pi$
$740$	−2.56620e17	+	2.56620e17i	−1.56279	+	1.56279i
$741$	−6.52635e15			−0.0394240
$742$	1.82060e16	+	1.82060e16i	0.109092	+	0.109092i
$743$	−1.48798e17	+	1.48798e17i	−0.884430	+	0.884430i	−0.993981	−	0.109551i	$-0.965059\pi$
$743$	−1.48798e17	+	1.48798e17i	−0.884430	+	0.884430i	0.109551	+	0.993981i	$0.465059\pi$
$744$	5.38681e15	+	5.38681e15i	0.0317610	+	0.0317610i
$745$	5.38988e16			0.315240
$746$	3.23366e16	+	3.23366e16i	0.187612	+	0.187612i
$747$			2.05830e17i			1.18464i
$748$	−8.85830e16			−0.505756
$749$	−2.17075e17			−1.22947
$750$	1.85018e16			0.103955
$751$	−5.17960e16	+	5.17960e16i	−0.288706	+	0.288706i	−0.836569	−	0.547862i	$-0.815442\pi$
$751$	−5.17960e16	+	5.17960e16i	−0.288706	+	0.288706i	0.547862	+	0.836569i	$0.315442\pi$
$752$	1.08115e17	−	1.08115e17i	0.597832	−	0.597832i
$753$			1.03603e17i			0.568334i
$754$	−7.76856e15	−	2.39557e15i	−0.0422778	−	0.0130371i
$755$	3.40285e17			1.83722
$756$	9.70910e16	+	9.70910e16i	0.520054	+	0.520054i
$757$	5.16002e16	+	5.16002e16i	0.274205	+	0.274205i	0.830791	−	0.556585i	$-0.187889\pi$
$757$	5.16002e16	+	5.16002e16i	0.274205	+	0.274205i	−0.556585	+	0.830791i	$0.687889\pi$
$758$		−	4.20704e16i		−	0.221800i
$759$		−	1.75048e17i		−	0.915599i
$760$		−	1.27658e17i		−	0.662471i
$761$	2.24798e17			1.15740			0.578701	−	0.815540i	$-0.303560\pi$
$761$	2.24798e17			1.15740			0.578701	+	0.815540i	$0.303560\pi$
$762$	2.49332e16	−	2.49332e16i	0.127365	−	0.127365i
$763$			1.19297e17i			0.604621i
$764$	−6.69654e16	+	6.69654e16i	−0.336737	+	0.336737i
$765$	7.03064e16	+	7.03064e16i	0.350773	+	0.350773i
$766$	−4.13794e16	+	4.13794e16i	−0.204838	+	0.204838i
$767$			7.02951e15i			0.0345265i
$768$	−2.01080e15	−	2.01080e15i	−0.00979947	−	0.00979947i
$769$	2.33335e17	−	2.33335e17i	1.12829	−	1.12829i	0.137839	−	0.990455i	$-0.455984\pi$
$769$	2.33335e17	−	2.33335e17i	1.12829	−	1.12829i	0.990455	−	0.137839i	$-0.0440157\pi$
$770$	−1.59264e17			−0.764141
$771$	9.89233e16	+	9.89233e16i	0.470947	+	0.470947i
$772$	−2.51217e17	+	2.51217e17i	−1.18671	+	1.18671i
$773$	1.68103e17	+	1.68103e17i	0.787951	+	0.787951i	0.981158	−	0.193207i	$-0.0618888\pi$
$773$	1.68103e17	+	1.68103e17i	0.787951	+	0.787951i	−0.193207	+	0.981158i	$0.561889\pi$
$774$	6.50488e16			0.302548
$775$	−3.33700e16	−	3.33700e16i	−0.154009	−	0.154009i
$776$			1.35948e16i			0.0622590i
$777$	1.64198e17			0.746179
$778$	−7.51260e16			−0.338776
$779$	−1.83562e15			−0.00821405
$780$	−1.30511e16	+	1.30511e16i	−0.0579533	+	0.0579533i
$781$	3.99416e17	−	3.99416e17i	1.76003	−	1.76003i
$782$			4.42081e16i			0.193313i
$783$	−1.80695e17	−	5.57202e16i	−0.784106	−	0.241792i
$784$	−4.38130e15			−0.0188671
$785$	2.91035e16	+	2.91035e16i	0.124373	+	0.124373i
$786$	4.74586e16	+	4.74586e16i	0.201270	+	0.201270i
$787$			2.23122e16i			0.0939062i	0.998897	+	0.0469531i	$0.0149511\pi$
$787$			2.23122e16i			0.0939062i	−0.998897	+	0.0469531i	$0.985049\pi$
$788$		−	2.50054e17i		−	1.04442i
$789$			5.95988e16i			0.247045i
$790$	−8.14154e16			−0.334922
$791$	2.46221e17	−	2.46221e17i	1.00523	−	1.00523i
$792$		−	1.77619e17i		−	0.719678i
$793$	1.20441e15	−	1.20441e15i	0.00484322	−	0.00484322i
$794$	2.20654e15	+	2.20654e15i	0.00880621	+	0.00880621i
$795$	−5.69228e16	+	5.69228e16i	−0.225467	+	0.225467i
$796$		−	2.82228e17i		−	1.10948i
$797$	2.80855e17	+	2.80855e17i	1.09580	+	1.09580i	0.994896	+	0.100906i	$0.0321741\pi$
$797$	2.80855e17	+	2.80855e17i	1.09580	+	1.09580i	0.100906	+	0.994896i	$0.467826\pi$
$798$	−1.91617e16	+	1.91617e16i	−0.0742023	+	0.0742023i
$799$	−1.33337e17			−0.512471
$800$	−2.29783e17	−	2.29783e17i	−0.876551	−	0.876551i
$801$	1.12535e17	−	1.12535e17i	0.426081	−	0.426081i
$802$	1.10718e17	+	1.10718e17i	0.416077	+	0.416077i
$803$	−5.14505e17			−1.91910
$804$	3.84818e16	+	3.84818e16i	0.142469	+	0.142469i
$805$		−	6.04957e17i		−	2.22305i
$806$	−1.85118e15			−0.00675210
$807$	1.80428e17			0.653227
$808$	−8.00934e16			−0.287825
$809$	−3.15267e17	+	3.15267e17i	−1.12457	+	1.12457i	−0.133529	+	0.991045i	$0.542631\pi$
$809$	−3.15267e17	+	3.15267e17i	−1.12457	+	1.12457i	−0.991045	+	0.133529i	$0.957369\pi$
$810$	−4.38575e16	+	4.38575e16i	−0.155287	+	0.155287i
$811$		−	4.88348e17i		−	1.71635i	−0.513361	−	0.858173i	$-0.671600\pi$
$811$		−	4.88348e17i		−	1.71635i	0.513361	−	0.858173i	$-0.328400\pi$
$812$	2.27138e17	−	1.20070e17i	0.792416	−	0.418890i
$813$	−9.18611e16			−0.318118
$814$	−1.59686e17	−	1.59686e17i	−0.548934	−	0.548934i
$815$	1.24327e17	+	1.24327e17i	0.424250	+	0.424250i
$816$			3.62896e16i			0.122925i
$817$		−	2.21426e17i		−	0.744556i
$818$			1.69257e17i			0.564973i
$819$	−3.13819e16			−0.103986
$820$	−3.67078e15	+	3.67078e15i	−0.0120747	+	0.0120747i
$821$			3.39183e17i			1.10758i	0.832656	+	0.553791i	$0.186819\pi$
$821$			3.39183e17i			1.10758i	−0.832656	+	0.553791i	$0.813181\pi$
$822$	−2.21664e16	+	2.21664e16i	−0.0718562	+	0.0718562i
$823$	−1.53656e17	−	1.53656e17i	−0.494482	−	0.494482i	0.415233	−	0.909715i	$-0.363700\pi$
$823$	−1.53656e17	−	1.53656e17i	−0.494482	−	0.494482i	−0.909715	+	0.415233i	$0.863700\pi$
$824$	1.70377e17	−	1.70377e17i	0.544312	−	0.544312i
$825$		−	2.92791e17i		−	0.928613i
$826$	2.06390e16	+	2.06390e16i	0.0649844	+	0.0649844i
$827$	1.27844e17	−	1.27844e17i	0.399621	−	0.399621i	−0.478478	−	0.878099i	$-0.658811\pi$
$827$	1.27844e17	−	1.27844e17i	0.399621	−	0.399621i	0.878099	+	0.478478i	$0.158811\pi$
$828$	3.16543e17			0.982316
$829$	4.31658e17	+	4.31658e17i	1.32988	+	1.32988i	0.905470	+	0.424411i	$0.139519\pi$
$829$	4.31658e17	+	4.31658e17i	1.32988	+	1.32988i	0.424411	+	0.905470i	$0.360481\pi$
$830$	−1.84086e17	+	1.84086e17i	−0.563055	+	0.563055i
$831$	1.74773e16	+	1.74773e16i	0.0530722	+	0.0530722i
$832$	1.58947e16			0.0479194
$833$	2.70169e15	+	2.70169e15i	0.00808660	+	0.00808660i
$834$		−	5.94437e16i		−	0.176648i
$835$	3.34485e17			0.986864
$836$	−2.83672e17			−0.830959
$837$	−4.30580e16			−0.125228
$838$	1.37233e17	−	1.37233e17i	0.396273	−	0.396273i
$839$	−3.13151e17	+	3.13151e17i	−0.897806	+	0.897806i	−0.995242	−	0.0974357i	$-0.968936\pi$
$839$	−3.13151e17	+	3.13151e17i	−0.897806	+	0.897806i	0.0974357	+	0.995242i	$0.468936\pi$
$840$			1.63344e17i			0.464972i
$841$	−1.99262e17	+	2.92369e17i	−0.563181	+	0.826334i
$842$	1.53872e17			0.431805
$843$	−8.00454e16	−	8.00454e16i	−0.223034	−	0.223034i
$844$	1.14003e17	+	1.14003e17i	0.315401	+	0.315401i
$845$			5.57574e17i			1.53166i
$846$		−	1.25437e17i		−	0.342140i
$847$			3.79875e17i			1.02882i
$848$	1.10415e17			0.296930
$849$	6.52290e16	−	6.52290e16i	0.174178	−	0.174178i
$850$			7.39441e16i			0.196061i
$851$	6.06558e17	−	6.06558e17i	1.59696	−	1.59696i
$852$	−1.92198e17	−	1.92198e17i	−0.502470	−	0.502470i
$853$	−3.85787e17	+	3.85787e17i	−1.00151	+	1.00151i	−0.00150694	+	0.999999i	$0.500480\pi$
$853$	−3.85787e17	+	3.85787e17i	−1.00151	+	1.00151i	−0.999999	+	0.00150694i	$0.999520\pi$
$854$		−	7.07242e15i		−	0.0182314i
$855$	2.25145e17	+	2.25145e17i	0.576321	+	0.576321i
$856$	2.16516e17	−	2.16516e17i	0.550362	−	0.550362i
$857$	4.94233e17			1.24752			0.623759	−	0.781617i	$-0.285605\pi$
$857$	4.94233e17			1.24752			0.623759	+	0.781617i	$0.285605\pi$
$858$	−8.12123e15	−	8.12123e15i	−0.0203563	−	0.0203563i
$859$	1.43111e17	−	1.43111e17i	0.356217	−	0.356217i	−0.506199	−	0.862416i	$-0.668950\pi$
$859$	1.43111e17	−	1.43111e17i	0.356217	−	0.356217i	0.862416	+	0.506199i	$0.168950\pi$
$860$	−4.42798e17	−	4.42798e17i	−1.09450	−	1.09450i
$861$	2.34875e15			0.00576524
$862$	−4.27064e16	−	4.27064e16i	−0.104100	−	0.104100i
$863$			5.91807e17i			1.43257i	0.697808	+	0.716284i	$0.254159\pi$
$863$			5.91807e17i			1.43257i	−0.697808	+	0.716284i	$0.745841\pi$
$864$	−2.96493e17			−0.712742
$865$	−1.04384e18			−2.49194
$866$	−6.99147e16			−0.165753
$867$	−1.15308e17	+	1.15308e17i	−0.271484	+	0.271484i
$868$	4.13684e16	−	4.13684e16i	0.0967276	−	0.0967276i
$869$			3.85600e17i			0.895403i
$870$	−4.93233e16	−	9.33053e16i	−0.113746	−	0.215174i
$871$	−2.81861e16			−0.0645544
$872$	−1.18990e17	−	1.18990e17i	−0.270653	−	0.270653i
$873$	−2.39765e16	−	2.39765e16i	−0.0541627	−	0.0541627i
$874$			1.41569e17i			0.317614i
$875$		−	3.02840e17i		−	0.674783i
$876$			2.47578e17i			0.547883i
$877$	3.23873e17			0.711831			0.355915	−	0.934518i	$-0.384169\pi$
$877$	3.23873e17			0.711831			0.355915	+	0.934518i	$0.384169\pi$
$878$	−5.36025e16	+	5.36025e16i	−0.117009	+	0.117009i
$879$		−	1.92539e16i		−	0.0417432i
$880$	−4.82950e17	+	4.82950e17i	−1.03994	+	1.03994i
$881$	−7.63726e16	−	7.63726e16i	−0.163336	−	0.163336i	0.620707	−	0.784043i	$-0.286846\pi$
$881$	−7.63726e16	−	7.63726e16i	−0.163336	−	0.163336i	−0.784043	+	0.620707i	$0.786846\pi$
$882$	−2.54163e15	+	2.54163e15i	−0.00539885	+	0.00539885i
$883$		−	2.28579e17i		−	0.482250i	−0.970494	−	0.241125i	$-0.922484\pi$
$883$		−	2.28579e17i		−	0.482250i	0.970494	−	0.241125i	$-0.0775164\pi$
$884$	−1.56107e16	−	1.56107e16i	−0.0327121	−	0.0327121i
$885$	−6.45299e16	+	6.45299e16i	−0.134308	+	0.134308i
$886$	1.36747e16			0.0282694
$887$	−7.60433e15	−	7.60433e15i	−0.0156142	−	0.0156142i	0.699257	−	0.714871i	$-0.253514\pi$
$887$	−7.60433e15	−	7.60433e15i	−0.0156142	−	0.0156142i	−0.714871	+	0.699257i	$0.753514\pi$
$888$	−1.63776e17	+	1.63776e17i	−0.334020	+	0.334020i
$889$	−4.08110e17	−	4.08110e17i	−0.826736	−	0.826736i
$890$	2.01293e17			0.405031
$891$	2.07718e17	+	2.07718e17i	0.415154	+	0.415154i
$892$			8.92892e16i			0.177260i
$893$	−4.26989e17			−0.841991
$894$	1.61390e16			0.0316120
$895$	−1.29480e18			−2.51922
$896$	3.68953e17	−	3.68953e17i	0.713054	−	0.713054i
$897$	3.08481e16	−	3.08481e16i	0.0592207	−	0.0592207i
$898$		−	6.75631e16i		−	0.128840i
$899$	−2.37412e16	+	7.69901e16i	−0.0449723	+	0.145840i
$900$	5.29463e17			0.996278
$901$	−6.80867e16	−	6.80867e16i	−0.127266	−	0.127266i
$902$	−2.28420e15	−	2.28420e15i	−0.00424125	−	0.00424125i
$903$			2.83324e17i			0.522585i
$904$			4.91176e17i			0.899966i
$905$			6.13190e17i			1.11610i
$906$	1.01892e17			0.184235
$907$	1.55820e17	−	1.55820e17i	0.279885	−	0.279885i	−0.553178	−	0.833063i	$-0.686585\pi$
$907$	1.55820e17	−	1.55820e17i	0.279885	−	0.279885i	0.833063	+	0.553178i	$0.186585\pi$
$908$		−	2.51668e17i		−	0.449068i
$909$	1.41257e17	−	1.41257e17i	0.250395	−	0.250395i
$910$	−2.80666e16	−	2.80666e16i	−0.0494244	−	0.0494244i
$911$	−1.15429e17	+	1.15429e17i	−0.201931	+	0.201931i	−0.800827	−	0.598896i	$-0.795606\pi$
$911$	−1.15429e17	+	1.15429e17i	−0.201931	+	0.201931i	0.598896	+	0.800827i	$0.295606\pi$
$912$			1.16212e17i			0.201967i
$913$	8.71867e17	+	8.71867e17i	1.50531	+	1.50531i
$914$	4.49342e16	−	4.49342e16i	0.0770726	−	0.0770726i
$915$	2.21126e16			0.0376802
$916$	−7.14830e17	−	7.14830e17i	−1.21012	−	1.21012i
$917$	7.76809e17	−	7.76809e17i	1.30647	−	1.30647i
$918$	4.77059e16	+	4.77059e16i	0.0797105	+	0.0797105i
$919$	−5.86448e17			−0.973501			−0.486751	−	0.873541i	$-0.661818\pi$
$919$	−5.86448e17			−0.973501			−0.486751	+	0.873541i	$0.661818\pi$
$920$	6.03401e17	+	6.03401e17i	0.995127	+	0.995127i
$921$			1.34868e17i			0.220979i
$922$	6.95186e16			0.113166
$923$	1.40776e17			0.227676
$924$	3.62971e17			0.583230
$925$	1.01455e18	−	1.01455e18i	1.61966	−	1.61966i
$926$	2.74484e17	−	2.74484e17i	0.435362	−	0.435362i
$927$			6.00972e17i			0.947057i
$928$	−1.63480e17	+	5.30147e17i	−0.255962	+	0.830057i
$929$	−3.95318e17			−0.614968			−0.307484	−	0.951553i	$-0.599487\pi$
$929$	−3.95318e17			−0.614968			−0.307484	+	0.951553i	$0.599487\pi$
$930$	−1.69936e16	−	1.69936e16i	−0.0262656	−	0.0262656i
$931$	8.65173e15	+	8.65173e15i	0.0132863	+	0.0132863i
$932$			8.93640e17i			1.36354i
$933$			1.95651e17i			0.296614i
$934$			1.87794e16i			0.0282879i
$935$	5.95615e17			0.891448
$936$	3.13012e16	−	3.13012e16i	0.0465485	−	0.0465485i
$937$		−	7.98842e17i		−	1.18038i	−0.807263	−	0.590192i	$-0.799052\pi$
$937$		−	7.98842e17i		−	1.18038i	0.807263	−	0.590192i	$-0.200948\pi$
$938$	−8.27560e16	+	8.27560e16i	−0.121502	+	0.121502i
$939$	1.61702e16	+	1.61702e16i	0.0235897	+	0.0235897i
$940$	−8.53871e17	+	8.53871e17i	−1.23773	+	1.23773i
$941$		−	7.57139e17i		−	1.09053i	−0.838264	−	0.545265i	$-0.816429\pi$
$941$		−	7.57139e17i		−	1.09053i	0.838264	−	0.545265i	$-0.183571\pi$
$942$	8.71453e15	+	8.71453e15i	0.0124721	+	0.0124721i
$943$	8.67640e15	−	8.67640e15i	0.0123387	−	0.0123387i
$944$	1.25171e17			0.176877
$945$	−6.52822e17	−	6.52822e17i	−0.916651	−	0.916651i
$946$	2.75538e17	−	2.75538e17i	0.384445	−	0.384445i
$947$	−7.33746e17	−	7.33746e17i	−1.01729	−	1.01729i	−0.999848	−	0.0174441i	$-0.994447\pi$
$947$	−7.33746e17	−	7.33746e17i	−1.01729	−	1.01729i	−0.0174441	−	0.999848i	$-0.505553\pi$
$948$	1.85549e17			0.255629
$949$	−9.06696e16	−	9.06696e16i	−0.124126	−	0.124126i
$950$			2.36794e17i			0.322128i
$951$	−9.24849e16			−0.125022
$952$	−1.95379e17			−0.262456
$953$	−1.26869e18			−1.69355			−0.846777	−	0.531949i	$-0.821460\pi$
$953$	−1.26869e18			−1.69355			−0.846777	+	0.531949i	$0.821460\pi$
$954$	6.40530e16	−	6.40530e16i	0.0849667	−	0.0849667i
$955$	4.50263e17	−	4.50263e17i	0.593535	−	0.593535i
$956$		−	1.17101e18i		−	1.53395i
$957$	−4.41913e17	+	2.33606e17i	−0.575262	+	0.304097i
$958$	−2.21209e17			−0.286160
$959$	3.62823e17	+	3.62823e17i	0.466426	+	0.466426i
$960$	1.45911e17	+	1.45911e17i	0.186406	+	0.186406i
$961$		−	7.69317e17i		−	0.976708i
$962$		−	5.62818e16i		−	0.0710097i
$963$			7.63720e17i			0.957583i
$964$	1.32418e18			1.65000
$965$	1.68913e18	−	1.68913e18i	2.09170	−	2.09170i
$966$		−	1.81143e17i		−	0.222925i
$967$	3.08860e17	−	3.08860e17i	0.377749	−	0.377749i	−0.492540	−	0.870290i	$-0.663932\pi$
$967$	3.08860e17	−	3.08860e17i	0.377749	−	0.377749i	0.870290	+	0.492540i	$0.163932\pi$
$968$	−3.78898e17	−	3.78898e17i	−0.460543	−	0.460543i
$969$	7.16610e16	−	7.16610e16i	0.0865645	−	0.0865645i
$970$		−	4.28871e16i		−	0.0514868i
$971$	4.27878e17	+	4.27878e17i	0.510511	+	0.510511i	0.914683	−	0.404172i	$-0.132440\pi$
$971$	4.27878e17	+	4.27878e17i	0.510511	+	0.510511i	−0.404172	+	0.914683i	$0.632440\pi$
$972$	5.32439e17	−	5.32439e17i	0.631353	−	0.631353i
$973$	−9.72983e17			−1.14664
$974$	−9.42018e14	−	9.42018e14i	−0.00110333	−	0.00110333i
$975$	5.15977e16	−	5.15977e16i	0.0600624	−	0.0600624i
$976$	−2.14463e16	−	2.14463e16i	−0.0248115	−	0.0248115i
$977$	−9.51723e17			−1.09432			−0.547158	−	0.837029i	$-0.684290\pi$
$977$	−9.51723e17			−1.09432			−0.547158	+	0.837029i	$0.684290\pi$
$978$	3.72276e16	+	3.72276e16i	0.0425434	+	0.0425434i
$979$		−	9.53364e17i		−	1.08284i
$980$	3.46026e16			0.0390618
$981$	4.19715e17			0.470913
$982$	−3.30828e17			−0.368920
$983$	1.18293e17	−	1.18293e17i	0.131111	−	0.131111i	−0.638506	−	0.769617i	$-0.720447\pi$
$983$	1.18293e17	−	1.18293e17i	0.131111	−	0.131111i	0.769617	+	0.638506i	$0.220447\pi$
$984$	−2.34271e15	+	2.34271e15i	−0.00258076	+	0.00258076i
$985$			1.68132e18i			1.84091i
$986$	1.11605e17	−	5.89968e16i	0.121457	−	0.0642047i
$987$	5.46350e17			0.590973
$988$	−4.99907e16	−	4.99907e16i	−0.0537461	−	0.0537461i
$989$	1.04662e18	+	1.04662e18i	1.11843	+	1.11843i
$990$			5.60329e17i			0.595157i
$991$			9.01994e17i			0.952274i	0.879371	+	0.476137i	$0.157963\pi$
$991$			9.01994e17i			0.952274i	−0.879371	+	0.476137i	$0.842037\pi$
$992$			1.26330e17i			0.132567i
$993$	−7.91308e16			−0.0825373
$994$	4.13325e17	−	4.13325e17i	0.428523	−	0.428523i
$995$			1.89765e18i			1.95559i
$996$	4.19540e17	−	4.19540e17i	0.429751	−	0.429751i
$997$	−1.21331e18	−	1.21331e18i	−1.23538	−	1.23538i	−0.961870	−	0.273507i	$-0.911816\pi$
$997$	−1.21331e18	−	1.21331e18i	−1.23538	−	1.23538i	−0.273507	−	0.961870i	$-0.588184\pi$
$998$	9.09841e16	−	9.09841e16i	0.0920836	−	0.0920836i
$999$		−	1.30910e18i		−	1.31698i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.13.c.a.12.12	✓	58
29.17	odd	4	inner	29.13.c.a.17.12	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.13.c.a.12.12	✓	58	1.1	even	1	trivial
29.13.c.a.17.12	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)

\(f(q)\)	\(=\)	\(q+(-15.4217 - 15.4217i) q^{2} +(-236.320 - 236.320i) q^{3} -3620.34i q^{4} +24342.5i q^{5} +7288.92i q^{6} +119306. q^{7} +(-118999. + 118999. i) q^{8} -419746. i q^{9} +O(q^{10})\)	\(q+(-15.4217 - 15.4217i) q^{2} +(-236.320 - 236.320i) q^{3} -3620.34i q^{4} +24342.5i q^{5} +7288.92i q^{6} +119306. q^{7} +(-118999. + 118999. i) q^{8} -419746. i q^{9} +(375403. - 375403. i) q^{10} +(-1.77799e6 - 1.77799e6i) q^{11} +(-855561. + 855561. i) q^{12} -626657. i q^{13} +(-1.83990e6 - 1.83990e6i) q^{14} +(5.75263e6 - 5.75263e6i) q^{15} -1.11586e7 q^{16} +(6.88086e6 + 6.88086e6i) q^{17} +(-6.47320e6 + 6.47320e6i) q^{18} +(2.20348e7 + 2.20348e7i) q^{19} +8.81282e7 q^{20} +(-2.81944e7 - 2.81944e7i) q^{21} +5.48391e7i q^{22} -2.08304e8 q^{23} +5.62438e7 q^{24} -3.48417e8 q^{25} +(-9.66412e6 + 9.66412e6i) q^{26} +(-2.24785e8 + 2.24785e8i) q^{27} -4.31929e8i q^{28} +(2.77987e8 + 5.25869e8i) q^{29} -1.77431e8 q^{30} +(9.57761e7 + 9.57761e7i) q^{31} +(6.59505e8 + 6.59505e8i) q^{32} +8.40348e8i q^{33} -2.12229e8i q^{34} +2.90421e9i q^{35} -1.51963e9 q^{36} +(-2.91189e9 + 2.91189e9i) q^{37} -6.79628e8i q^{38} +(-1.48092e8 + 1.48092e8i) q^{39} +(-2.89674e9 - 2.89674e9i) q^{40} +(-4.16527e7 + 4.16527e7i) q^{41} +8.69612e8i q^{42} +(-5.02447e9 - 5.02447e9i) q^{43} +(-6.43692e9 + 6.43692e9i) q^{44} +1.02177e10 q^{45} +(3.21240e9 + 3.21240e9i) q^{46} +(-9.68896e9 + 9.68896e9i) q^{47} +(2.63700e9 + 2.63700e9i) q^{48} +3.92639e8 q^{49} +(5.37318e9 + 5.37318e9i) q^{50} -3.25217e9i q^{51} -2.26871e9 q^{52} -9.89509e9 q^{53} +6.93313e9 q^{54} +(4.32806e10 - 4.32806e10i) q^{55} +(-1.41973e10 + 1.41973e10i) q^{56} -1.04145e10i q^{57} +(3.82277e9 - 1.23968e10i) q^{58} -1.12175e10 q^{59} +(-2.08265e10 - 2.08265e10i) q^{60} +(1.92196e9 + 1.92196e9i) q^{61} -2.95406e9i q^{62} -5.00783e10i q^{63} +2.53642e10i q^{64} +1.52544e10 q^{65} +(1.29596e10 - 1.29596e10i) q^{66} -4.49785e10i q^{67} +(2.49111e10 - 2.49111e10i) q^{68} +(4.92264e10 + 4.92264e10i) q^{69} +(4.47878e10 - 4.47878e10i) q^{70} +2.24645e11i q^{71} +(4.99495e10 + 4.99495e10i) q^{72} +(1.44688e11 - 1.44688e11i) q^{73} +8.98127e10 q^{74} +(8.23380e10 + 8.23380e10i) q^{75} +(7.97735e10 - 7.97735e10i) q^{76} +(-2.12124e11 - 2.12124e11i) q^{77} +4.56766e9 q^{78} +(-1.08437e11 - 1.08437e11i) q^{79} -2.71628e11i q^{80} -1.16828e11 q^{81} +1.28471e9 q^{82} -4.90368e11 q^{83} +(-1.02074e11 + 1.02074e11i) q^{84} +(-1.67497e11 + 1.67497e11i) q^{85} +1.54972e11i q^{86} +(5.85797e10 - 1.89967e11i) q^{87} +4.23157e11 q^{88} +(2.68102e11 + 2.68102e11i) q^{89} +(-1.57574e11 - 1.57574e11i) q^{90} -7.47640e10i q^{91} +7.54130e11i q^{92} -4.52677e10i q^{93} +2.98841e11 q^{94} +(-5.36382e11 + 5.36382e11i) q^{95} -3.11709e11i q^{96} +(5.71214e10 - 5.71214e10i) q^{97} +(-6.05516e9 - 6.05516e9i) q^{98} +(-7.46303e11 + 7.46303e11i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more