LMFDB - Embedded newform 98.8.c.g.67.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,8,Mod(67,98)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("98.67"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-16,-70,-128,-126,1120,0,2048,-2014] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$30.6137324974$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{1969})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 493x^{2} + 492x + 242064 $ x^4 - x^3 + 493x^2 + 492x + 242064
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.2
Root			$-10.8434 + 18.7812i$ of defining polynomial
Character	$\chi$	$=$	98.67
Dual form			98.8.c.g.79.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.00000 - 6.92820i) q^{2} +(4.68671 - 8.11762i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-231.180 - 400.416i) q^{5} -74.9873 q^{6} +512.000 q^{8} +(1049.57 + 1817.91i) q^{9} +(-1849.44 + 3203.33i) q^{10} +(-1940.53 + 3361.09i) q^{11} +(299.949 + 519.527i) q^{12} -11585.6 q^{13} -4333.90 q^{15} +(-2048.00 - 3547.24i) q^{16} +(7621.20 - 13200.3i) q^{17} +(8396.56 - 14543.3i) q^{18} +(16230.9 + 28112.7i) q^{19} +29591.1 q^{20} +31048.4 q^{22} +(-28073.1 - 48623.9i) q^{23} +(2399.59 - 4156.22i) q^{24} +(-67826.2 + 117478. i) q^{25} +(46342.3 + 80267.2i) q^{26} +40175.8 q^{27} -26442.0 q^{29} +(17335.6 + 30026.1i) q^{30} +(22724.1 - 39359.3i) q^{31} +(-16384.0 + 28377.9i) q^{32} +(18189.3 + 31504.9i) q^{33} -121939. q^{34} -134345. q^{36} +(277622. + 480856. i) q^{37} +(129847. - 224902. i) q^{38} +(-54298.2 + 94047.3i) q^{39} +(-118364. - 205013. i) q^{40} +306385. q^{41} +780755. q^{43} +(-124194. - 215110. i) q^{44} +(485280. - 840529. i) q^{45} +(-224584. + 388992. i) q^{46} +(265622. + 460070. i) q^{47} -38393.5 q^{48} +1.08522e6 q^{50} +(-71436.6 - 123732. i) q^{51} +(370738. - 642138. i) q^{52} +(181796. - 314880. i) q^{53} +(-160703. - 278346. i) q^{54} +1.79445e6 q^{55} +304277. q^{57} +(105768. + 183195. i) q^{58} +(1.07048e6 - 1.85412e6i) q^{59} +(138685. - 240209. i) q^{60} +(-444412. - 769744. i) q^{61} -363586. q^{62} +262144. q^{64} +(2.67836e6 + 4.63905e6i) q^{65} +(145515. - 252039. i) q^{66} +(-2.17270e6 + 3.76323e6i) q^{67} +(487757. + 844819. i) q^{68} -526281. q^{69} +663207. q^{71} +(537380. + 930769. i) q^{72} +(-671009. + 1.16222e6i) q^{73} +(2.22098e6 - 3.84685e6i) q^{74} +(635763. + 1.10117e6i) q^{75} -2.07755e6 q^{76} +868771. q^{78} +(-3.52917e6 - 6.11270e6i) q^{79} +(-946915. + 1.64010e6i) q^{80} +(-2.10712e6 + 3.64963e6i) q^{81} +(-1.22554e6 - 2.12270e6i) q^{82} +6.60874e6 q^{83} -7.04748e6 q^{85} +(-3.12302e6 - 5.40923e6i) q^{86} +(-123926. + 214646. i) q^{87} +(-993549. + 1.72088e6i) q^{88} +(2.66499e6 + 4.61590e6i) q^{89} -7.76448e6 q^{90} +3.59335e6 q^{92} +(-213002. - 368931. i) q^{93} +(2.12497e6 - 3.68056e6i) q^{94} +(7.50452e6 - 1.29982e7i) q^{95} +(153574. + 265998. i) q^{96} -2.09810e6 q^{97} -8.14686e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} - 70 q^{3} - 128 q^{4} - 126 q^{5} + 1120 q^{6} + 2048 q^{8} - 2014 q^{9} - 1008 q^{10} + 3420 q^{11} - 4480 q^{12} - 12796 q^{13} - 62064 q^{15} - 8192 q^{16} + 38472 q^{17} - 16112 q^{18}+ \cdots - 76354200 q^{99}+O(q^{100}) $ 4 * q - 16 * q^2 - 70 * q^3 - 128 * q^4 - 126 * q^5 + 1120 * q^6 + 2048 * q^8 - 2014 * q^9 - 1008 * q^10 + 3420 * q^11 - 4480 * q^12 - 12796 * q^13 - 62064 * q^15 - 8192 * q^16 + 38472 * q^17 - 16112 * q^18 + 43358 * q^19 + 16128 * q^20 - 54720 * q^22 - 89928 * q^23 - 35840 * q^24 - 170666 * q^25 + 51184 * q^26 + 386120 * q^27 + 319152 * q^29 + 248256 * q^30 + 143612 * q^31 - 65536 * q^32 + 615888 * q^33 - 615552 * q^34 + 257792 * q^36 + 271832 * q^37 + 346864 * q^38 - 520352 * q^39 - 64512 * q^40 + 129696 * q^41 + 3055928 * q^43 + 218880 * q^44 + 2354058 * q^45 - 719424 * q^46 - 485436 * q^47 + 573440 * q^48 + 2730656 * q^50 + 1700940 * q^51 + 409472 * q^52 + 145716 * q^53 - 1544480 * q^54 + 8500464 * q^55 - 1121192 * q^57 - 1276608 * q^58 + 4183662 * q^59 + 1986048 * q^60 + 280658 * q^61 - 2297792 * q^62 + 1048576 * q^64 + 7101612 * q^65 + 4927104 * q^66 - 5671648 * q^67 + 2462208 * q^68 + 4310208 * q^69 - 1238544 * q^71 - 1031168 * q^72 - 3939628 * q^73 + 2174656 * q^74 - 1507618 * q^75 - 5549824 * q^76 + 8325632 * q^78 - 4656616 * q^79 - 516096 * q^80 - 7353742 * q^81 - 518784 * q^82 + 2471700 * q^83 + 1532088 * q^85 - 12223712 * q^86 - 15012732 * q^87 + 1751040 * q^88 + 17241420 * q^89 - 37664928 * q^90 + 11510784 * q^92 + 7365592 * q^93 - 3883488 * q^94 + 11343960 * q^95 - 2293760 * q^96 - 1481872 * q^97 - 76354200 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−4.00000	−	6.92820i	−0.353553	−	0.612372i
$2$	−4.00000	−	6.92820i	−0.353553	−	0.612372i
$3$	4.68671	−	8.11762i	0.100217	−	0.173582i	−0.811557	−	0.584274i	$-0.801379\pi$
$3$	4.68671	−	8.11762i	0.100217	−	0.173582i	0.911774	+	0.410692i	$0.134713\pi$
$4$	−32.0000	+	55.4256i	−0.250000	+	0.433013i
$5$	−231.180	−	400.416i	−0.827096	−	1.43257i	−0.900307	−	0.435256i	$-0.856658\pi$
$5$	−231.180	−	400.416i	−0.827096	−	1.43257i	0.0732108	−	0.997316i	$-0.476675\pi$
$6$	−74.9873			−0.141729
$7$		0			0
$7$		0			0
$8$	512.000			0.353553
$9$	1049.57	+	1817.91i	0.479913	+	0.831234i
$10$	−1849.44	+	3203.33i	−0.584845	+	1.01298i
$11$	−1940.53	+	3361.09i	−0.439587	+	0.761387i	−0.997658	−	0.0684065i	$-0.978209\pi$
$11$	−1940.53	+	3361.09i	−0.439587	+	0.761387i	0.558070	+	0.829794i	$0.311542\pi$
$12$	299.949	+	519.527i	0.0501087	+	0.0867909i
$13$	−11585.6			−1.46257			−0.731284	−	0.682073i	$-0.761078\pi$
$13$	−11585.6			−1.46257			−0.731284	+	0.682073i	$0.761078\pi$
$14$		0			0
$15$	−4333.90			−0.331558
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	7621.20	−	13200.3i	0.376229	−	0.651647i	−0.614281	−	0.789087i	$-0.710554\pi$
$17$	7621.20	−	13200.3i	0.376229	−	0.651647i	0.990510	+	0.137440i	$0.0438874\pi$
$18$	8396.56	−	14543.3i	0.339350	−	0.587771i
$19$	16230.9	+	28112.7i	0.542880	+	0.940297i	0.998737	+	0.0502433i	$0.0159997\pi$
$19$	16230.9	+	28112.7i	0.542880	+	0.940297i	−0.455857	+	0.890053i	$0.650667\pi$
$20$	29591.1			0.827096
$21$		0			0
$22$	31048.4			0.621670
$23$	−28073.1	−	48623.9i	−0.481108	−	0.833303i	0.518657	−	0.854982i	$-0.326432\pi$
$23$	−28073.1	−	48623.9i	−0.481108	−	0.833303i	−0.999765	+	0.0216794i	$0.993099\pi$
$24$	2399.59	−	4156.22i	0.0354322	−	0.0613704i
$25$	−67826.2	+	117478.i	−0.868176	+	1.50372i
$26$	46342.3	+	80267.2i	0.517096	+	0.895636i
$27$	40175.8			0.392818
$28$		0			0
$29$	−26442.0			−0.201326			−0.100663	−	0.994921i	$-0.532096\pi$
$29$	−26442.0			−0.201326			−0.100663	+	0.994921i	$0.532096\pi$
$30$	17335.6	+	30026.1i	0.117223	+	0.203037i
$31$	22724.1	−	39359.3i	0.137000	−	0.237291i	−0.789360	−	0.613931i	$-0.789587\pi$
$31$	22724.1	−	39359.3i	0.137000	−	0.237291i	0.926360	+	0.376640i	$0.122921\pi$
$32$	−16384.0	+	28377.9i	−0.0883883	+	0.153093i
$33$	18189.3	+	31504.9i	0.0881086	+	0.152609i
$34$	−121939.			−0.532068
$35$		0			0
$36$	−134345.			−0.479913
$37$	277622.	+	480856.i	0.901049	+	1.56066i	0.826135	+	0.563473i	$0.190535\pi$
$37$	277622.	+	480856.i	0.901049	+	1.56066i	0.0749145	+	0.997190i	$0.476132\pi$
$38$	129847.	−	224902.i	0.383874	−	0.664890i
$39$	−54298.2	+	94047.3i	−0.146575	+	0.253875i
$40$	−118364.	−	205013.i	−0.292423	−	0.506491i
$41$	306385.			0.694264			0.347132	−	0.937816i	$-0.387156\pi$
$41$	306385.			0.694264			0.347132	+	0.937816i	$0.387156\pi$
$42$		0			0
$43$	780755.			1.49753			0.748765	−	0.662836i	$-0.230647\pi$
$43$	780755.			1.49753			0.748765	+	0.662836i	$0.230647\pi$
$44$	−124194.	−	215110.i	−0.219794	−	0.380694i
$45$	485280.	−	840529.i	0.793868	−	1.37502i
$46$	−224584.	+	388992.i	−0.340194	+	0.589234i
$47$	265622.	+	460070.i	0.373182	+	0.646370i	0.990053	−	0.140694i	$-0.0449333\pi$
$47$	265622.	+	460070.i	0.373182	+	0.646370i	−0.616871	+	0.787064i	$0.711600\pi$
$48$	−38393.5			−0.0501087
$49$		0			0
$50$	1.08522e6			1.22779
$51$	−71436.6	−	123732.i	−0.0754094	−	0.130613i
$52$	370738.	−	642138.i	0.365642	−	0.633310i
$53$	181796.	−	314880.i	0.167733	−	0.290523i	−0.769889	−	0.638178i	$-0.779689\pi$
$53$	181796.	−	314880.i	0.167733	−	0.290523i	0.937623	+	0.347655i	$0.113022\pi$
$54$	−160703.	−	278346.i	−0.138882	−	0.240551i
$55$	1.79445e6			1.45432
$56$		0			0
$57$	304277.			0.217624
$58$	105768.	+	183195.i	0.0711796	+	0.123287i
$59$	1.07048e6	−	1.85412e6i	0.678570	−	1.17532i	−0.296841	−	0.954927i	$-0.595933\pi$
$59$	1.07048e6	−	1.85412e6i	0.678570	−	1.17532i	0.975411	−	0.220392i	$-0.0707335\pi$
$60$	138685.	−	240209.i	0.0828895	−	0.143569i
$61$	−444412.	−	769744.i	−0.250687	−	0.434202i	0.713028	−	0.701135i	$-0.247323\pi$
$61$	−444412.	−	769744.i	−0.250687	−	0.434202i	−0.963715	+	0.266933i	$0.913990\pi$
$62$	−363586.			−0.193747
$63$		0			0
$64$	262144.			0.125000
$65$	2.67836e6	+	4.63905e6i	1.20968	+	2.09523i
$66$	145515.	−	252039.i	0.0623022	−	0.107911i
$67$	−2.17270e6	+	3.76323e6i	−0.882549	+	1.52862i	−0.0340512	+	0.999420i	$0.510841\pi$
$67$	−2.17270e6	+	3.76323e6i	−0.882549	+	1.52862i	−0.848498	+	0.529199i	$0.822492\pi$
$68$	487757.	+	844819.i	0.188114	+	0.325824i
$69$	−526281.			−0.192862
$70$		0			0
$71$	663207.			0.219910			0.109955	−	0.993937i	$-0.464929\pi$
$71$	663207.			0.219910			0.109955	+	0.993937i	$0.464929\pi$
$72$	537380.	+	930769.i	0.169675	+	0.293885i
$73$	−671009.	+	1.16222e6i	−0.201882	+	0.349671i	−0.949135	−	0.314870i	$-0.898039\pi$
$73$	−671009.	+	1.16222e6i	−0.201882	+	0.349671i	0.747252	+	0.664540i	$0.231373\pi$
$74$	2.22098e6	−	3.84685e6i	0.637138	−	1.10356i
$75$	635763.	+	1.10117e6i	0.174013	+	0.301399i
$76$	−2.07755e6			−0.542880
$77$		0			0
$78$	868771.			0.207288
$79$	−3.52917e6	−	6.11270e6i	−0.805337	−	1.39488i	−0.916063	−	0.401033i	$-0.868651\pi$
$79$	−3.52917e6	−	6.11270e6i	−0.805337	−	1.39488i	0.110727	−	0.993851i	$-0.464682\pi$
$80$	−946915.	+	1.64010e6i	−0.206774	+	0.358143i
$81$	−2.10712e6	+	3.64963e6i	−0.440546	+	0.763048i
$82$	−1.22554e6	−	2.12270e6i	−0.245459	−	0.425148i
$83$	6.60874e6			1.26866			0.634330	−	0.773063i	$-0.281276\pi$
$83$	6.60874e6			1.26866			0.634330	+	0.773063i	$0.281276\pi$
$84$		0			0
$85$	−7.04748e6			−1.24471
$86$	−3.12302e6	−	5.40923e6i	−0.529456	−	0.917046i
$87$	−123926.	+	214646.i	−0.0201764	+	0.0349466i
$88$	−993549.	+	1.72088e6i	−0.155417	+	0.269191i
$89$	2.66499e6	+	4.61590e6i	0.400710	+	0.694050i	0.993812	−	0.111077i	$-0.0354301\pi$
$89$	2.66499e6	+	4.61590e6i	0.400710	+	0.694050i	−0.593102	+	0.805128i	$0.702097\pi$
$90$	−7.76448e6			−1.12270
$91$		0			0
$92$	3.59335e6			0.481108
$93$	−213002.	−	368931.i	−0.0274596	−	0.0475614i
$94$	2.12497e6	−	3.68056e6i	0.263880	−	0.457053i
$95$	7.50452e6	−	1.29982e7i	0.898029	−	1.55543i
$96$	153574.	+	265998.i	0.0177161	+	0.0306852i
$97$	−2.09810e6			−0.233413			−0.116707	−	0.993166i	$-0.537234\pi$
$97$	−2.09810e6			−0.233413			−0.116707	+	0.993166i	$0.537234\pi$
$98$		0			0
$99$	−8.14686e6			−0.843854
$100$	−4.34088e6	−	7.51862e6i	−0.434088	−	0.751862i
$101$	−9.77690e6	+	1.69341e7i	−0.944227	+	1.63545i	−0.186936	+	0.982372i	$0.559856\pi$
$101$	−9.77690e6	+	1.69341e7i	−0.944227	+	1.63545i	−0.757291	+	0.653078i	$0.773478\pi$
$102$	−571493.	+	989855.i	−0.0533225	+	0.0923573i
$103$	4.47546e6	+	7.75173e6i	0.403560	+	0.698986i	0.994153	−	0.107984i	$-0.0344394\pi$
$103$	4.47546e6	+	7.75173e6i	0.403560	+	0.698986i	−0.590593	+	0.806970i	$0.701106\pi$
$104$	−5.93181e6			−0.517096
$105$		0			0
$106$	−2.90874e6			−0.237211
$107$	6.97547e6	+	1.20819e7i	0.550466	+	0.953435i	0.998241	+	0.0592886i	$0.0188832\pi$
$107$	6.97547e6	+	1.20819e7i	0.550466	+	0.953435i	−0.447775	+	0.894146i	$0.647783\pi$
$108$	−1.28562e6	+	2.22677e6i	−0.0982044	+	0.170095i
$109$	−2.92147e6	+	5.06014e6i	−0.216077	+	0.374257i	−0.953605	−	0.301060i	$-0.902660\pi$
$109$	−2.92147e6	+	5.06014e6i	−0.216077	+	0.374257i	0.737528	+	0.675317i	$0.235993\pi$
$110$	−7.17778e6	−	1.24323e7i	−0.514181	−	0.890587i
$111$	5.20454e6			0.361203
$112$		0			0
$113$	−1.20951e7			−0.788562			−0.394281	−	0.918990i	$-0.629006\pi$
$113$	−1.20951e7			−0.788562			−0.394281	+	0.918990i	$0.629006\pi$
$114$	−1.21711e6	−	2.10810e6i	−0.0769419	−	0.133267i
$115$	−1.29799e7	+	2.24818e7i	−0.795844	+	1.37844i
$116$	846143.	−	1.46556e6i	0.0503316	−	0.0871769i
$117$	−1.21599e7	−	2.10615e7i	−0.701905	−	1.21574i
$118$	−1.71276e7			−0.959644
$119$		0			0
$120$	−2.21896e6			−0.117223
$121$	2.21231e6	+	3.83183e6i	0.113526	+	0.196634i
$122$	−3.55529e6	+	6.15795e6i	−0.177262	+	0.307027i
$123$	1.43594e6	−	2.48712e6i	0.0695774	−	0.120512i
$124$	1.45434e6	+	2.51899e6i	0.0685000	+	0.118646i
$125$	2.65984e7			1.21807
$126$		0			0
$127$	−325760.			−0.0141119			−0.00705594	−	0.999975i	$-0.502246\pi$
$127$	−325760.			−0.0141119			−0.00705594	+	0.999975i	$0.502246\pi$
$128$	−1.04858e6	−	1.81619e6i	−0.0441942	−	0.0765466i
$129$	3.65917e6	−	6.33787e6i	0.150079	−	0.259944i
$130$	2.14269e7	−	3.71124e7i	0.855376	−	1.48155i
$131$	−3.19024e6	−	5.52566e6i	−0.123986	−	0.214751i	0.797350	−	0.603517i	$-0.206235\pi$
$131$	−3.19024e6	−	5.52566e6i	−0.123986	−	0.214751i	−0.921336	+	0.388767i	$0.872901\pi$
$132$	−2.32824e6			−0.0881086
$133$		0			0
$134$	3.47633e7			1.24811
$135$	−9.28785e6	−	1.60870e7i	−0.324898	−	0.562740i
$136$	3.90205e6	−	6.75855e6i	0.133017	−	0.230392i
$137$	−2.31162e6	+	4.00384e6i	−0.0768059	+	0.133032i	−0.901870	−	0.432007i	$-0.857806\pi$
$137$	−2.31162e6	+	4.00384e6i	−0.0768059	+	0.133032i	0.825064	+	0.565039i	$0.191139\pi$
$138$	2.10512e6	+	3.64618e6i	0.0681869	+	0.118103i
$139$	−3.55394e7			−1.12243			−0.561214	−	0.827671i	$-0.689665\pi$
$139$	−3.55394e7			−1.12243			−0.561214	+	0.827671i	$0.689665\pi$
$140$		0			0
$141$	4.97956e6			0.149597
$142$	−2.65283e6	−	4.59483e6i	−0.0777499	−	0.134667i
$143$	2.24821e7	−	3.89401e7i	0.642926	−	1.11358i
$144$	4.29904e6	−	7.44615e6i	0.119978	−	0.207808i
$145$	6.11286e6	+	1.05878e7i	0.166516	+	0.288415i
$146$	1.07362e7			0.285505
$147$		0			0
$148$	−3.55357e7			−0.901049
$149$	−5.08540e6	−	8.80816e6i	−0.125943	−	0.218139i	0.796158	−	0.605088i	$-0.206862\pi$
$149$	−5.08540e6	−	8.80816e6i	−0.125943	−	0.218139i	−0.922101	+	0.386949i	$0.873529\pi$
$150$	5.08611e6	−	8.80940e6i	0.123046	−	0.213121i
$151$	−1.22636e7	+	2.12412e7i	−0.289867	+	0.502065i	−0.973778	−	0.227501i	$-0.926945\pi$
$151$	−1.22636e7	+	2.12412e7i	−0.289867	+	0.502065i	0.683911	+	0.729566i	$0.260278\pi$
$152$	8.31021e6	+	1.43937e7i	0.191937	+	0.332445i
$153$	3.19959e7			0.722228
$154$		0			0
$155$	−2.10135e7			−0.453249
$156$	−3.47509e6	−	6.01902e6i	−0.0732874	−	0.126938i
$157$	6.36893e6	−	1.10313e7i	0.131346	−	0.227498i	−0.792849	−	0.609418i	$-0.791403\pi$
$157$	6.36893e6	−	1.10313e7i	0.131346	−	0.227498i	0.924196	+	0.381919i	$0.124737\pi$
$158$	−2.82333e7	+	4.89016e7i	−0.569459	+	0.986332i
$159$	−1.70405e6	−	2.95151e6i	−0.0336196	−	0.0582309i
$160$	1.51506e7			0.292423
$161$		0			0
$162$	3.37139e7			0.623026
$163$	4.25765e7	+	7.37447e7i	0.770041	+	1.33375i	0.937540	+	0.347878i	$0.113098\pi$
$163$	4.25765e7	+	7.37447e7i	0.770041	+	1.33375i	−0.167499	+	0.985872i	$0.553569\pi$
$164$	−9.80433e6	+	1.69816e7i	−0.173566	+	0.300625i
$165$	8.41004e6	−	1.45666e7i	0.145749	−	0.252444i
$166$	−2.64349e7	−	4.57867e7i	−0.448539	−	0.776892i
$167$	−3.74260e6			−0.0621822			−0.0310911	−	0.999517i	$-0.509898\pi$
$167$	−3.74260e6			−0.0621822			−0.0310911	+	0.999517i	$0.509898\pi$
$168$		0			0
$169$	7.14770e7			1.13910
$170$	2.81899e7	+	4.88264e7i	0.440071	+	0.762226i
$171$	−3.40709e7	+	5.90124e7i	−0.521071	+	0.902521i
$172$	−2.49842e7	+	4.32738e7i	−0.374382	+	0.648449i
$173$	3.63432e7	+	6.29483e7i	0.533657	+	0.924321i	0.999227	+	0.0393101i	$0.0125160\pi$
$173$	3.63432e7	+	6.29483e7i	0.533657	+	0.924321i	−0.465570	+	0.885011i	$0.654151\pi$
$174$	1.98281e6			0.0285338
$175$		0			0
$176$	1.58968e7			0.219794
$177$	−1.00340e7	−	1.73794e7i	−0.136009	−	0.235575i
$178$	2.13199e7	−	3.69272e7i	0.283345	−	0.490768i
$179$	−5.12224e7	+	8.87198e7i	−0.667536	+	1.15621i	0.311056	+	0.950392i	$0.399317\pi$
$179$	−5.12224e7	+	8.87198e7i	−0.667536	+	1.15621i	−0.978591	+	0.205814i	$0.934016\pi$
$180$	3.10579e7	+	5.37939e7i	0.396934	+	0.687510i
$181$	4.79161e6			0.0600630			0.0300315	−	0.999549i	$-0.490439\pi$
$181$	4.79161e6			0.0600630			0.0300315	+	0.999549i	$0.490439\pi$
$182$		0			0
$183$	−8.33131e6			−0.100493
$184$	−1.43734e7	−	2.48955e7i	−0.170097	−	0.294617i
$185$	1.28362e8	−	2.22329e8i	1.49051	−	2.58164i
$186$	−1.70402e6	+	2.95145e6i	−0.0194169	+	0.0336310i
$187$	2.95782e7	+	5.12310e7i	0.330771	+	0.572911i
$188$	−3.39996e7			−0.373182
$189$		0			0
$190$	−1.20072e8			−1.27000
$191$	−1.30086e7	−	2.25316e7i	−0.135087	−	0.233978i	0.790543	−	0.612406i	$-0.209798\pi$
$191$	−1.30086e7	−	2.25316e7i	−0.135087	−	0.233978i	−0.925631	+	0.378428i	$0.876465\pi$
$192$	1.22859e6	−	2.12798e6i	0.0125272	−	0.0216977i
$193$	3.79163e7	−	6.56730e7i	0.379643	−	0.657561i	−0.611367	−	0.791347i	$-0.709380\pi$
$193$	3.79163e7	−	6.56730e7i	0.379643	−	0.657561i	0.991010	+	0.133786i	$0.0427134\pi$
$194$	8.39241e6	+	1.45361e7i	0.0825241	+	0.142936i
$195$	5.02107e7			0.484926
$196$		0			0
$197$	1.19192e8			1.11075			0.555374	−	0.831601i	$-0.312575\pi$
$197$	1.19192e8			1.11075			0.555374	+	0.831601i	$0.312575\pi$
$198$	3.25875e7	+	5.64431e7i	0.298347	+	0.516753i
$199$	−3.36331e7	+	5.82543e7i	−0.302539	+	0.524013i	−0.976710	−	0.214562i	$-0.931168\pi$
$199$	−3.36331e7	+	5.82543e7i	−0.302539	+	0.524013i	0.674171	+	0.738575i	$0.264501\pi$
$200$	−3.47270e7	+	6.01490e7i	−0.306946	+	0.531647i
$201$	2.03657e7	+	3.52743e7i	0.176894	+	0.306389i
$202$	1.56430e8			1.33534
$203$		0			0
$204$	9.14389e6			0.0754094
$205$	−7.08303e7	−	1.22682e8i	−0.574223	−	0.994583i
$206$	3.58037e7	−	6.20139e7i	0.285360	−	0.494258i
$207$	5.89292e7	−	1.02068e8i	0.461779	−	0.799825i
$208$	2.37273e7	+	4.10968e7i	0.182821	+	0.316655i
$209$	−1.25986e8			−0.954573
$210$		0			0
$211$	2.32421e8			1.70328			0.851641	−	0.524126i	$-0.175608\pi$
$211$	2.32421e8			1.70328			0.851641	+	0.524126i	$0.175608\pi$
$212$	1.16350e7	+	2.01523e7i	0.0838667	+	0.145261i
$213$	3.10826e6	−	5.38366e6i	0.0220388	−	0.0381723i
$214$	5.58038e7	−	9.66550e7i	0.389238	−	0.674180i
$215$	−1.80495e8	−	3.12627e8i	−1.23860	−	2.14532i
$216$	2.05700e7			0.138882
$217$		0			0
$218$	4.67436e7			0.305580
$219$	6.28965e6	+	1.08940e7i	0.0404643	+	0.0700862i
$220$	−5.74222e7	+	9.94583e7i	−0.363581	+	0.629740i
$221$	−8.82959e7	+	1.52933e8i	−0.550260	+	0.953078i
$222$	−2.08182e7	−	3.60581e7i	−0.127705	−	0.221191i
$223$	−2.53319e8			−1.52968			−0.764840	−	0.644221i	$-0.777182\pi$
$223$	−2.53319e8			−1.52968			−0.764840	+	0.644221i	$0.777182\pi$
$224$		0			0
$225$	−2.84753e8			−1.66659
$226$	4.83805e7	+	8.37975e7i	0.278799	+	0.482894i
$227$	−2.25062e7	+	3.89819e7i	−0.127706	+	0.221194i	−0.922788	−	0.385309i	$-0.874095\pi$
$227$	−2.25062e7	+	3.89819e7i	−0.127706	+	0.221194i	0.795081	+	0.606503i	$0.207428\pi$
$228$	−9.73688e6	+	1.68648e7i	−0.0544061	+	0.0942341i
$229$	−9.34866e7	−	1.61924e8i	−0.514429	−	0.891017i	−0.999860	−	0.0167418i	$-0.994671\pi$
$229$	−9.34866e7	−	1.61924e8i	−0.514429	−	0.891017i	0.485431	−	0.874275i	$-0.338663\pi$
$230$	2.07678e8			1.12549
$231$		0			0
$232$	−1.35383e7			−0.0711796
$233$	1.28794e8	+	2.23078e8i	0.667038	+	1.15534i	0.978729	+	0.205159i	$0.0657713\pi$
$233$	1.28794e8	+	2.23078e8i	0.667038	+	1.15534i	−0.311691	+	0.950184i	$0.600895\pi$
$234$	−9.72789e7	+	1.68492e8i	−0.496322	+	0.859655i
$235$	1.22813e8	−	2.12718e8i	0.617315	−	1.06922i
$236$	6.85105e7	+	1.18664e8i	0.339285	+	0.587659i
$237$	−6.61607e7			−0.322835
$238$		0			0
$239$	−3.15071e8			−1.49285			−0.746425	−	0.665469i	$-0.768231\pi$
$239$	−3.15071e8			−1.49285			−0.746425	+	0.665469i	$0.768231\pi$
$240$	8.87583e6	+	1.53734e7i	0.0414447	+	0.0717844i
$241$	−4.19950e7	+	7.27374e7i	−0.193258	+	0.334733i	−0.946328	−	0.323208i	$-0.895239\pi$
$241$	−4.19950e7	+	7.27374e7i	−0.193258	+	0.334733i	0.753070	+	0.657940i	$0.228572\pi$
$242$	1.76985e7	−	3.06547e7i	0.0802753	−	0.139041i
$243$	6.36831e7	+	1.10302e8i	0.284710	+	0.493131i
$244$	5.68847e7			0.250687
$245$		0			0
$246$	−2.29750e7			−0.0983973
$247$	−1.88044e8	−	3.25702e8i	−0.793999	−	1.37525i
$248$	1.16347e7	−	2.01520e7i	0.0484368	−	0.0838950i
$249$	3.09732e7	−	5.36472e7i	0.127142	−	0.220216i
$250$	−1.06394e8	−	1.84279e8i	−0.430652	−	0.745910i
$251$	−5.33130e6			−0.0212802			−0.0106401	−	0.999943i	$-0.503387\pi$
$251$	−5.33130e6			−0.0212802			−0.0106401	+	0.999943i	$0.503387\pi$
$252$		0			0
$253$	2.17906e8			0.845955
$254$	1.30304e6	+	2.25693e6i	0.00498930	+	0.00864173i
$255$	−3.30295e7	+	5.72088e7i	−0.124742	+	0.216059i
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	1.04971e8	+	1.81815e8i	0.385747	+	0.668134i	0.991873	−	0.127235i	$-0.0406103\pi$
$257$	1.04971e8	+	1.81815e8i	0.385747	+	0.668134i	−0.606125	+	0.795369i	$0.707277\pi$
$258$	−5.85467e7			−0.212243
$259$		0			0
$260$	−3.42830e8			−1.20968
$261$	−2.77527e7	−	4.80690e7i	−0.0966191	−	0.167349i
$262$	−2.55219e7	+	4.42053e7i	−0.0876717	+	0.151852i
$263$	1.25403e8	−	2.17204e8i	0.425071	−	0.736245i	−0.571356	−	0.820703i	$-0.693582\pi$
$263$	1.25403e8	−	2.17204e8i	0.425071	−	0.736245i	0.996427	+	0.0844572i	$0.0269156\pi$
$264$	9.31295e6	+	1.61305e7i	0.0311511	+	0.0539553i
$265$	−1.68111e8			−0.554926
$266$		0			0
$267$	4.99601e7			0.160633
$268$	−1.39053e8	−	2.40847e8i	−0.441274	−	0.764310i
$269$	−1.69599e8	+	2.93753e8i	−0.531238	+	0.920131i	0.468097	+	0.883677i	$0.344940\pi$
$269$	−1.69599e8	+	2.93753e8i	−0.531238	+	0.920131i	−0.999335	+	0.0364542i	$0.988394\pi$
$270$	−7.43028e7	+	1.28696e8i	−0.229738	+	0.397917i
$271$	−3.79787e7	−	6.57810e7i	−0.115917	−	0.200774i	0.802229	−	0.597017i	$-0.203647\pi$
$271$	−3.79787e7	−	6.57810e7i	−0.115917	−	0.200774i	−0.918146	+	0.396242i	$0.870314\pi$
$272$	−6.24328e7			−0.188114
$273$		0			0
$274$	3.69859e7			0.108620
$275$	−2.63237e8	−	4.55940e8i	−0.763278	−	1.32204i
$276$	1.68410e7	−	2.91694e7i	0.0482154	−	0.0835115i
$277$	2.50442e7	−	4.33778e7i	0.0707990	−	0.122628i	−0.828453	−	0.560059i	$-0.810778\pi$
$277$	2.50442e7	−	4.33778e7i	0.0707990	−	0.122628i	0.899252	+	0.437432i	$0.144112\pi$
$278$	1.42158e8	+	2.46224e8i	0.396838	+	0.687344i
$279$	9.54021e7			0.262992
$280$		0			0
$281$	3.41917e8			0.919283			0.459641	−	0.888105i	$-0.347978\pi$
$281$	3.41917e8			0.919283			0.459641	+	0.888105i	$0.347978\pi$
$282$	−1.99182e7	−	3.44994e7i	−0.0528907	−	0.0916094i
$283$	−1.84539e8	+	3.19630e8i	−0.483988	+	0.838293i	−0.999831	−	0.0183909i	$-0.994146\pi$
$283$	−1.84539e8	+	3.19630e8i	−0.483988	+	0.838293i	0.515842	+	0.856683i	$0.327479\pi$
$284$	−2.12226e7	+	3.67586e7i	−0.0549775	+	0.0952238i
$285$	−7.03430e7	−	1.21838e8i	−0.179996	−	0.311763i
$286$	−3.59714e8			−0.909234
$287$		0			0
$288$	−6.87846e7			−0.169675
$289$	8.90041e7	+	1.54160e8i	0.216904	+	0.375689i
$290$	4.89029e7	−	8.47023e7i	0.117745	−	0.203940i
$291$	−9.83319e6	+	1.70316e7i	−0.0233921	+	0.0405163i
$292$	−4.29446e7	−	7.43822e7i	−0.100941	−	0.174835i
$293$	5.92780e8			1.37676			0.688378	−	0.725352i	$-0.258323\pi$
$293$	5.92780e8			1.37676			0.688378	+	0.725352i	$0.258323\pi$
$294$		0			0
$295$	−9.89892e8			−2.24497
$296$	1.42143e8	+	2.46198e8i	0.318569	+	0.551778i
$297$	−7.79621e7	+	1.35034e8i	−0.172678	+	0.299086i
$298$	−4.06832e7	+	7.04653e7i	−0.0890549	+	0.154248i
$299$	3.25242e8	+	5.63336e8i	0.703652	+	1.21876i
$300$	−8.13777e7			−0.174013
$301$		0			0
$302$	1.96218e8			0.409934
$303$	9.16430e7	+	1.58730e8i	0.189256	+	0.327801i
$304$	6.64816e7	−	1.15150e8i	0.135720	−	0.235074i
$305$	−2.05479e8	+	3.55899e8i	−0.414684	+	0.718253i
$306$	−1.27984e8	−	2.21674e8i	−0.255346	−	0.442273i
$307$	−9.43846e8			−1.86173			−0.930865	−	0.365363i	$-0.880945\pi$
$307$	−9.43846e8			−1.86173			−0.930865	+	0.365363i	$0.880945\pi$
$308$		0			0
$309$	8.39008e7			0.161775
$310$	8.40538e7	+	1.45586e8i	0.160248	+	0.277557i
$311$	8.20325e7	−	1.42085e8i	0.154641	−	0.267846i	−0.778287	−	0.627908i	$-0.783911\pi$
$311$	8.20325e7	−	1.42085e8i	0.154641	−	0.267846i	0.932928	+	0.360062i	$0.117245\pi$
$312$	−2.78007e7	+	4.81522e7i	−0.0518220	+	0.0897584i
$313$	−1.73006e8	−	2.99655e8i	−0.318901	−	0.552352i	0.661358	−	0.750070i	$-0.269980\pi$
$313$	−1.73006e8	−	2.99655e8i	−0.318901	−	0.552352i	−0.980259	+	0.197718i	$0.936647\pi$
$314$	−1.01903e8			−0.185752
$315$		0			0
$316$	4.51734e8			0.805337
$317$	4.76620e8	+	8.25530e8i	0.840359	+	1.45554i	0.889591	+	0.456758i	$0.150989\pi$
$317$	4.76620e8	+	8.25530e8i	0.840359	+	1.45554i	−0.0492320	+	0.998787i	$0.515677\pi$
$318$	−1.36324e7	+	2.36120e7i	−0.0237727	+	0.0411755i
$319$	5.13113e7	−	8.88737e7i	0.0885004	−	0.153287i
$320$	−6.06025e7	−	1.04967e8i	−0.103387	−	0.179072i
$321$	1.30768e8			0.220665
$322$		0			0
$323$	4.94795e8			0.816989
$324$	−1.34855e8	−	2.33577e8i	−0.220273	−	0.381524i
$325$	7.85806e8	−	1.36106e9i	1.26977	−	2.19930i
$326$	3.40612e8	−	5.89958e8i	0.544501	−	0.943104i
$327$	2.73842e7	+	4.74308e7i	0.0433095	+	0.0750142i
$328$	1.56869e8			0.245459
$329$		0			0
$330$	−1.34561e8			−0.206120
$331$	−1.12131e8	−	1.94217e8i	−0.169953	−	0.294367i	0.768450	−	0.639910i	$-0.221028\pi$
$331$	−1.12131e8	−	1.94217e8i	−0.169953	−	0.294367i	−0.938403	+	0.345542i	$0.887695\pi$
$332$	−2.11480e8	+	3.66293e8i	−0.317165	+	0.549346i
$333$	−5.82768e8	+	1.00938e9i	−0.864850	+	1.49796i
$334$	1.49704e7	+	2.59295e7i	0.0219847	+	0.0380787i
$335$	2.00915e9			2.91981
$336$		0			0
$337$	3.56750e8			0.507761			0.253880	−	0.967236i	$-0.418293\pi$
$337$	3.56750e8			0.507761			0.253880	+	0.967236i	$0.418293\pi$
$338$	−2.85908e8	−	4.95207e8i	−0.402734	−	0.697555i
$339$	−5.66863e7	+	9.81836e7i	−0.0790277	+	0.136880i
$340$	2.25519e8	−	3.90611e8i	0.311177	−	0.538975i
$341$	8.81934e7	+	1.52755e8i	0.120447	+	0.208620i
$342$	5.45134e8			0.736905
$343$		0			0
$344$	3.99747e8			0.529456
$345$	1.21666e8	+	2.10731e8i	0.159515	+	0.276288i
$346$	2.90746e8	−	5.03587e8i	0.377353	−	0.653594i
$347$	−8.09193e6	+	1.40156e7i	−0.0103968	+	0.0180077i	−0.871177	−	0.490969i	$-0.836643\pi$
$347$	−8.09193e6	+	1.40156e7i	−0.0103968	+	0.0180077i	0.860780	+	0.508977i	$0.169976\pi$
$348$	−7.93125e6	−	1.37373e7i	−0.0100882	−	0.0174733i
$349$	2.07780e8			0.261647			0.130823	−	0.991406i	$-0.458238\pi$
$349$	2.07780e8			0.261647			0.130823	+	0.991406i	$0.458238\pi$
$350$		0			0
$351$	−4.65459e8			−0.574522
$352$	−6.35871e7	−	1.10136e8i	−0.0777087	−	0.134595i
$353$	6.58118e8	−	1.13989e9i	0.796328	−	1.37928i	−0.125664	−	0.992073i	$-0.540106\pi$
$353$	6.58118e8	−	1.13989e9i	0.796328	−	1.37928i	0.921992	−	0.387208i	$-0.126560\pi$
$354$	−8.02721e7	+	1.39035e8i	−0.0961731	+	0.166577i
$355$	−1.53320e8	−	2.65559e8i	−0.181887	−	0.315037i
$356$	−3.41119e8			−0.400710
$357$		0			0
$358$	8.19559e8			0.944038
$359$	3.09636e8	+	5.36305e8i	0.353200	+	0.611760i	0.986808	−	0.161894i	$-0.0517603\pi$
$359$	3.09636e8	+	5.36305e8i	0.353200	+	0.611760i	−0.633608	+	0.773654i	$0.718427\pi$
$360$	2.48463e8	−	4.30351e8i	0.280675	−	0.486143i
$361$	−7.99464e7	+	1.38471e8i	−0.0894383	+	0.154912i
$362$	−1.91665e7	−	3.31973e7i	−0.0212355	−	0.0367809i
$363$	4.14738e7			0.0455093
$364$		0			0
$365$	6.20497e8			0.667905
$366$	3.33253e7	+	5.77210e7i	0.0355295	+	0.0615390i
$367$	−1.39314e8	+	2.41299e8i	−0.147117	+	0.254815i	−0.930161	−	0.367152i	$-0.880333\pi$
$367$	−1.39314e8	+	2.41299e8i	−0.147117	+	0.254815i	0.783043	+	0.621967i	$0.213666\pi$
$368$	−1.14987e8	+	1.99164e8i	−0.120277	+	0.208326i
$369$	3.21573e8	+	5.56981e8i	0.333186	+	0.577096i
$370$	−2.05379e9			−2.10790
$371$		0			0
$372$	2.72643e7			0.0274596
$373$	8.25282e7	+	1.42943e8i	0.0823420	+	0.142621i	0.904256	−	0.426992i	$-0.140427\pi$
$373$	8.25282e7	+	1.42943e8i	0.0823420	+	0.142621i	−0.821913	+	0.569612i	$0.807093\pi$
$374$	2.36626e8	−	4.09848e8i	0.233890	−	0.405110i
$375$	1.24659e8	−	2.15916e8i	0.122072	−	0.211434i
$376$	1.35998e8	+	2.35556e8i	0.131940	+	0.228526i
$377$	3.06345e8			0.294453
$378$		0			0
$379$	4.29433e8			0.405190			0.202595	−	0.979263i	$-0.435063\pi$
$379$	4.29433e8			0.405190			0.202595	+	0.979263i	$0.435063\pi$
$380$	4.80289e8	+	8.31885e8i	0.449014	+	0.777716i
$381$	−1.52674e6	+	2.64440e6i	−0.00141426	+	0.00244957i
$382$	−1.04069e8	+	1.80253e8i	−0.0955213	+	0.165448i
$383$	−6.71888e8	−	1.16374e9i	−0.611084	−	1.05843i	−0.991058	−	0.133432i	$-0.957400\pi$
$383$	−6.71888e8	−	1.16374e9i	−0.611084	−	1.05843i	0.379974	−	0.924997i	$-0.375933\pi$
$384$	−1.96575e7			−0.0177161
$385$		0			0
$386$	−6.06661e8			−0.536897
$387$	8.19457e8	+	1.41934e9i	0.718684	+	1.24480i
$388$	6.71393e7	−	1.16289e8i	0.0583533	−	0.101071i
$389$	5.39354e7	−	9.34189e7i	0.0464569	−	0.0804658i	−0.841862	−	0.539693i	$-0.818540\pi$
$389$	5.39354e7	−	9.34189e7i	0.0464569	−	0.0804658i	0.888319	+	0.459227i	$0.151874\pi$
$390$	−2.00843e8	−	3.47870e8i	−0.171447	−	0.296955i
$391$	−8.55801e8			−0.724026
$392$		0			0
$393$	−5.98070e7			−0.0497024
$394$	−4.76768e8	−	8.25787e8i	−0.392709	−	0.680192i
$395$	−1.63175e9	+	2.82627e9i	−1.33218	+	2.30741i
$396$	2.60700e8	−	4.51545e8i	0.210963	−	0.365399i
$397$	9.32624e8	+	1.61535e9i	0.748066	+	1.29569i	0.948749	+	0.316031i	$0.102350\pi$
$397$	9.32624e8	+	1.61535e9i	0.748066	+	1.29569i	−0.200683	+	0.979656i	$0.564316\pi$
$398$	5.38130e8			0.427855
$399$		0			0
$400$	5.55632e8			0.434088
$401$	−4.97362e6	−	8.61456e6i	−0.00385183	−	0.00667157i	0.864093	−	0.503332i	$-0.167893\pi$
$401$	−4.97362e6	−	8.61456e6i	−0.00385183	−	0.00667157i	−0.867945	+	0.496661i	$0.834559\pi$
$402$	1.62925e8	−	2.82195e8i	0.125083	−	0.216650i
$403$	−2.63272e8	+	4.56000e8i	−0.200372	+	0.347054i
$404$	−6.25722e8	−	1.08378e9i	−0.472114	−	0.817725i
$405$	1.94850e9			1.45749
$406$		0			0
$407$	−2.15493e9			−1.58436
$408$	−3.65756e7	−	6.33507e7i	−0.0266612	−	0.0461786i
$409$	4.38188e8	−	7.58964e8i	0.316686	−	0.548517i	−0.663108	−	0.748523i	$-0.730763\pi$
$409$	4.38188e8	−	7.58964e8i	0.316686	−	0.548517i	0.979794	+	0.200007i	$0.0640965\pi$
$410$	−5.66642e8	+	9.81454e8i	−0.406037	+	0.703277i
$411$	2.16678e7	+	3.75297e7i	0.0153946	+	0.0266642i
$412$	−5.72859e8			−0.403560
$413$		0			0
$414$	−9.42868e8			−0.653055
$415$	−1.52781e9	−	2.64624e9i	−1.04930	−	1.81745i
$416$	1.89818e8	−	3.28775e8i	0.129274	−	0.223909i
$417$	−1.66563e8	+	2.88495e8i	−0.112487	+	0.194833i
$418$	5.03943e8	+	8.72854e8i	0.337492	+	0.584554i
$419$	−2.01605e9			−1.33891			−0.669457	−	0.742851i	$-0.733473\pi$
$419$	−2.01605e9			−1.33891			−0.669457	+	0.742851i	$0.733473\pi$
$420$		0			0
$421$	5.69546e8			0.371999			0.186000	−	0.982550i	$-0.440448\pi$
$421$	5.69546e8			0.371999			0.186000	+	0.982550i	$0.440448\pi$
$422$	−9.29683e8	−	1.61026e9i	−0.602201	−	1.04304i
$423$	−5.57577e8	+	9.65751e8i	−0.358190	+	0.620403i
$424$	9.30797e7	−	1.61219e8i	0.0593027	−	0.102715i
$425$	1.03383e9	+	1.79065e9i	0.653265	+	1.13149i
$426$	−4.97321e7			−0.0311676
$427$		0			0
$428$	−8.92860e8			−0.550466
$429$	−2.10734e8	−	3.65002e8i	−0.128865	−	0.223200i
$430$	−1.44396e9	+	2.50102e9i	−0.875823	+	1.51697i
$431$	3.85970e8	−	6.68519e8i	0.232211	−	0.402201i	−0.726247	−	0.687433i	$-0.758737\pi$
$431$	3.85970e8	−	6.68519e8i	0.232211	−	0.402201i	0.958459	+	0.285232i	$0.0920706\pi$
$432$	−8.22800e7	−	1.42513e8i	−0.0491022	−	0.0850475i
$433$	1.24002e9			0.734043			0.367021	−	0.930213i	$-0.380378\pi$
$433$	1.24002e9			0.734043			0.367021	+	0.930213i	$0.380378\pi$
$434$		0			0
$435$	1.14597e8			0.0667513
$436$	−1.86974e8	−	3.23849e8i	−0.108039	−	0.187129i
$437$	9.11300e8	−	1.57842e9i	0.522368	−	0.904768i
$438$	5.03172e7	−	8.71520e7i	0.0286126	−	0.0495585i
$439$	−9.53106e8	−	1.65083e9i	−0.537669	−	0.931271i	−0.999029	−	0.0440574i	$-0.985972\pi$
$439$	−9.53106e8	−	1.65083e9i	−0.537669	−	0.931271i	0.461360	−	0.887213i	$-0.347362\pi$
$440$	9.18756e8			0.514181
$441$		0			0
$442$	1.41274e9			0.778185
$443$	2.52369e8	+	4.37116e8i	0.137919	+	0.238882i	0.926709	−	0.375781i	$-0.122625\pi$
$443$	2.52369e8	+	4.37116e8i	0.137919	+	0.238882i	−0.788790	+	0.614663i	$0.789292\pi$
$444$	−1.66545e8	+	2.88465e8i	−0.0903009	+	0.156406i
$445$	1.23219e9	−	2.13421e9i	0.662852	−	1.14809i
$446$	1.01328e9	+	1.75504e9i	0.540823	+	0.936733i
$447$	−9.53351e7			−0.0504866
$448$		0			0
$449$	−2.02721e9			−1.05691			−0.528453	−	0.848962i	$-0.677228\pi$
$449$	−2.02721e9			−1.05691			−0.528453	+	0.848962i	$0.677228\pi$
$450$	1.13901e9	+	1.97283e9i	0.589230	+	1.02058i
$451$	−5.94549e8	+	1.02979e9i	−0.305189	+	0.528604i
$452$	3.87044e8	−	6.70380e8i	0.197141	−	0.341457i
$453$	1.14952e8	+	1.99103e8i	0.0580995	+	0.100631i
$454$	3.60100e8			0.180604
$455$		0			0
$456$	1.55790e8			0.0769419
$457$	−1.01984e9	−	1.76642e9i	−0.499836	−	0.865741i	0.500164	−	0.865931i	$-0.333273\pi$
$457$	−1.01984e9	−	1.76642e9i	−0.499836	−	0.865741i	−1.00000		0.000189507i	$0.999940\pi$
$458$	−7.47893e8	+	1.29539e9i	−0.363756	+	0.630044i
$459$	3.06187e8	−	5.30332e8i	0.147789	−	0.255979i
$460$	−8.30712e8	−	1.43884e9i	−0.397922	−	0.689221i
$461$	−3.41390e9			−1.62292			−0.811461	−	0.584406i	$-0.801327\pi$
$461$	−3.41390e9			−1.62292			−0.811461	+	0.584406i	$0.801327\pi$
$462$		0			0
$463$	−1.97893e9			−0.926608			−0.463304	−	0.886199i	$-0.653336\pi$
$463$	−1.97893e9			−0.926608			−0.463304	+	0.886199i	$0.653336\pi$
$464$	5.41531e7	+	9.37960e7i	0.0251658	+	0.0435884i
$465$	−9.84839e7	+	1.70579e8i	−0.0454234	+	0.0786757i
$466$	1.03035e9	−	1.78462e9i	0.471667	−	0.816951i
$467$	−9.32108e8	−	1.61446e9i	−0.423504	−	0.733530i	0.572776	−	0.819712i	$-0.305867\pi$
$467$	−9.32108e8	−	1.61446e9i	−0.423504	−	0.733530i	−0.996279	+	0.0861822i	$0.972533\pi$
$468$	1.55646e9			0.701905
$469$		0			0
$470$	−1.96501e9			−0.873015
$471$	−5.96986e7	−	1.03401e8i	−0.0263264	−	0.0455986i
$472$	5.48084e8	−	9.49309e8i	0.239911	−	0.415538i
$473$	−1.51508e9	+	2.62419e9i	−0.658294	+	1.14020i
$474$	2.64643e8	+	4.58375e8i	0.114140	+	0.197695i
$475$	−4.40351e9			−1.88526
$476$		0			0
$477$	7.63231e8			0.321990
$478$	1.26029e9	+	2.18288e9i	0.527802	+	0.914181i
$479$	−1.85914e9	+	3.22013e9i	−0.772926	+	1.33875i	0.163027	+	0.986622i	$0.447874\pi$
$479$	−1.85914e9	+	3.22013e9i	−0.772926	+	1.33875i	−0.935953	+	0.352125i	$0.885459\pi$
$480$	7.10066e7	−	1.22987e8i	0.0293059	−	0.0507592i
$481$	−3.21642e9	−	5.57099e9i	−1.31784	−	2.28257i
$482$	6.71920e8			0.273308
$483$		0			0
$484$	−2.83176e8			−0.113526
$485$	4.85040e8	+	8.40114e8i	0.193055	+	0.334381i
$486$	5.09465e8	−	8.82419e8i	0.201320	−	0.348697i
$487$	1.08171e9	−	1.87357e9i	0.424383	−	0.735053i	−0.571979	−	0.820268i	$-0.693824\pi$
$487$	1.08171e9	−	1.87357e9i	0.424383	−	0.735053i	0.996363	+	0.0852146i	$0.0271576\pi$
$488$	−2.27539e8	−	3.94109e8i	−0.0886311	−	0.153514i
$489$	7.98175e8			0.308686
$490$		0			0
$491$	2.37608e8			0.0905890			0.0452945	−	0.998974i	$-0.485577\pi$
$491$	2.37608e8			0.0905890			0.0452945	+	0.998974i	$0.485577\pi$
$492$	9.19001e7	+	1.59176e8i	0.0347887	+	0.0602558i
$493$	−2.01519e8	+	3.49042e8i	−0.0757447	+	0.131194i
$494$	−1.50435e9	+	2.60561e9i	−0.561442	+	0.972446i
$495$	1.88340e9	+	3.26214e9i	0.697948	+	1.20888i
$496$	−1.86156e8			−0.0685000
$497$		0			0
$498$	−4.95571e8			−0.179806
$499$	−1.32583e9	−	2.29641e9i	−0.477679	−	0.827364i	0.521994	−	0.852949i	$-0.325188\pi$
$499$	−1.32583e9	−	2.29641e9i	−0.477679	−	0.827364i	−0.999673	+	0.0255852i	$0.991855\pi$
$500$	−8.51150e8	+	1.47423e9i	−0.304517	+	0.527438i
$501$	−1.75405e7	+	3.03810e7i	−0.00623174	+	0.0107937i
$502$	2.13252e7	+	3.69363e7i	0.00752368	+	0.0130314i
$503$	2.15865e9			0.756300			0.378150	−	0.925744i	$-0.376560\pi$
$503$	2.15865e9			0.756300			0.378150	+	0.925744i	$0.376560\pi$
$504$		0			0
$505$	9.04091e9			3.12387
$506$	−8.71623e8	−	1.50970e9i	−0.299090	−	0.518039i
$507$	3.34992e8	−	5.80223e8i	0.114158	−	0.197728i
$508$	1.04243e7	−	1.80555e7i	0.00352797	−	0.00611062i
$509$	−1.23916e9	−	2.14628e9i	−0.416499	−	0.721398i	0.579085	−	0.815267i	$-0.303410\pi$
$509$	−1.23916e9	−	2.14628e9i	−0.416499	−	0.721398i	−0.995585	+	0.0938693i	$0.970076\pi$
$510$	5.28472e8			0.176411
$511$		0			0
$512$	1.34218e8			0.0441942
$513$	6.52088e8	+	1.12945e9i	0.213253	+	0.369365i
$514$	8.39767e8	−	1.45452e9i	0.272765	−	0.472442i
$515$	2.06928e9	−	3.58410e9i	0.667565	−	1.15626i
$516$	2.34187e8	+	4.05624e8i	0.0750393	+	0.129972i
$517$	−2.06178e9			−0.656184
$518$		0			0
$519$	6.81321e8			0.213927
$520$	1.37132e9	+	2.37519e9i	0.427688	+	0.740777i
$521$	1.99867e9	−	3.46181e9i	0.619170	−	1.07243i	−0.370467	−	0.928846i	$-0.620802\pi$
$521$	1.99867e9	−	3.46181e9i	0.619170	−	1.07243i	0.989637	−	0.143589i	$-0.0458643\pi$
$522$	−2.22021e8	+	3.84552e8i	−0.0683200	+	0.118334i
$523$	1.96566e9	+	3.40462e9i	0.600831	+	1.04067i	0.992696	+	0.120647i	$0.0384968\pi$
$523$	1.96566e9	+	3.40462e9i	0.600831	+	1.04067i	−0.391865	+	0.920023i	$0.628170\pi$
$524$	4.08351e8			0.123986
$525$		0			0
$526$	−2.00644e9			−0.601142
$527$	−3.46370e8	−	5.99930e8i	−0.103087	−	0.178551i
$528$	7.45036e7	−	1.29044e8i	0.0220272	−	0.0381521i
$529$	1.26220e8	−	2.18620e8i	0.0370710	−	0.0642089i
$530$	6.72444e8	+	1.16471e9i	0.196196	+	0.339822i
$531$	4.49416e9			1.30262
$532$		0			0
$533$	−3.54965e9			−1.01541
$534$	−1.99840e8	−	3.46134e8i	−0.0567922	−	0.0983670i
$535$	3.22518e9	−	5.58618e9i	0.910576	−	1.57716i
$536$	−1.11242e9	+	1.92678e9i	−0.312028	+	0.540449i
$537$	4.80129e8	+	8.31608e8i	0.133797	+	0.231744i
$538$	2.71358e9			0.751284
$539$		0			0
$540$	1.18884e9			0.324898
$541$	1.37383e9	+	2.37954e9i	0.373028	+	0.646104i	0.990030	−	0.140858i	$-0.0449861\pi$
$541$	1.37383e9	+	2.37954e9i	0.373028	+	0.646104i	−0.617001	+	0.786962i	$0.711653\pi$
$542$	−3.03830e8	+	5.26248e8i	−0.0819658	+	0.141969i
$543$	2.24569e7	−	3.88965e7i	0.00601936	−	0.0104258i
$544$	2.49731e8	+	4.32547e8i	0.0665085	+	0.115196i
$545$	2.70155e9			0.714867
$546$		0			0
$547$	−1.40581e9			−0.367258			−0.183629	−	0.982996i	$-0.558784\pi$
$547$	−1.40581e9			−0.367258			−0.183629	+	0.982996i	$0.558784\pi$
$548$	−1.47944e8	−	2.56246e8i	−0.0384029	−	0.0665159i
$549$	9.32882e8	−	1.61580e9i	0.240616	−	0.416758i
$550$	−2.10590e9	+	3.64752e9i	−0.539719	+	0.934820i
$551$	−4.29176e8	−	7.43355e8i	−0.109296	−	0.189306i
$552$	−2.69456e8			−0.0681869
$553$		0			0
$554$	−4.00707e8			−0.100125
$555$	−1.20319e9	−	2.08398e9i	−0.298750	−	0.517450i
$556$	1.13726e9	−	1.96979e9i	0.280607	−	0.486025i
$557$	−4.93902e8	+	8.55464e8i	−0.121101	+	0.209753i	−0.920202	−	0.391443i	$-0.871976\pi$
$557$	−4.93902e8	+	8.55464e8i	−0.121101	+	0.209753i	0.799101	+	0.601197i	$0.205309\pi$
$558$	−3.81608e8	−	6.60965e8i	−0.0929818	−	0.161049i
$559$	−9.04550e9			−2.19024
$560$		0			0
$561$	5.54498e8			0.132596
$562$	−1.36767e9	−	2.36887e9i	−0.325016	−	0.562943i
$563$	−9.40576e8	+	1.62913e9i	−0.222134	+	0.384747i	−0.955456	−	0.295135i	$-0.904636\pi$
$563$	−9.40576e8	+	1.62913e9i	−0.222134	+	0.384747i	0.733322	+	0.679882i	$0.237969\pi$
$564$	−1.59346e8	+	2.75995e8i	−0.0373994	+	0.0647776i
$565$	2.79616e9	+	4.84309e9i	0.652217	+	1.12967i
$566$	2.95262e9			0.684463
$567$		0			0
$568$	3.39562e8			0.0777499
$569$	1.94266e9	+	3.36478e9i	0.442082	+	0.765708i	0.997844	−	0.0656331i	$-0.0209067\pi$
$569$	1.94266e9	+	3.36478e9i	0.442082	+	0.765708i	−0.555762	+	0.831342i	$0.687573\pi$
$570$	−5.62744e8	+	9.74701e8i	−0.127277	+	0.220450i
$571$	−1.22450e9	+	2.12089e9i	−0.275253	+	0.476752i	−0.970199	−	0.242310i	$-0.922095\pi$
$571$	−1.22450e9	+	2.12089e9i	−0.275253	+	0.476752i	0.694946	+	0.719062i	$0.255428\pi$
$572$	1.43885e9	+	2.49217e9i	0.321463	+	0.556790i
$573$	−2.43871e8			−0.0541525
$574$		0			0
$575$	7.61636e9			1.67074
$576$	2.75138e8	+	4.76554e8i	0.0599891	+	0.103904i
$577$	−1.44109e9	+	2.49604e9i	−0.312303	+	0.540924i	−0.978860	−	0.204529i	$-0.934434\pi$
$577$	−1.44109e9	+	2.49604e9i	−0.312303	+	0.540924i	0.666558	+	0.745453i	$0.267767\pi$
$578$	7.12033e8	−	1.23328e9i	0.153374	−	0.265652i
$579$	−3.55405e8	−	6.15580e8i	−0.0760938	−	0.131798i
$580$	−7.82446e8			−0.166516
$581$		0			0
$582$	1.57331e8			0.0330814
$583$	7.05561e8	+	1.22207e9i	0.147467	+	0.255420i
$584$	−3.43557e8	+	5.95058e8i	−0.0713762	+	0.123627i
$585$	−5.62225e9	+	9.73801e9i	−1.16109	+	2.01106i
$586$	−2.37112e9	−	4.10690e9i	−0.486757	−	0.843087i
$587$	4.72250e9			0.963692			0.481846	−	0.876256i	$-0.339966\pi$
$587$	4.72250e9			0.963692			0.481846	+	0.876256i	$0.339966\pi$
$588$		0			0
$589$	1.47533e9			0.297499
$590$	3.95957e9	+	6.85818e9i	0.793717	+	1.37476i
$591$	5.58618e8	−	9.67556e8i	0.111316	−	0.192806i
$592$	1.13714e9	−	1.96959e9i	0.225262	−	0.390166i
$593$	−6.15833e7	−	1.06665e8i	−0.0121275	−	0.0210055i	0.859898	−	0.510466i	$-0.170527\pi$
$593$	−6.15833e7	−	1.06665e8i	−0.0121275	−	0.0210055i	−0.872025	+	0.489460i	$0.837194\pi$
$594$	1.24739e9			0.244203
$595$		0			0
$596$	6.50931e8			0.125943
$597$	3.15257e8	+	5.46041e8i	0.0606394	+	0.105031i
$598$	2.60194e9	−	4.50669e9i	0.497557	−	0.861794i
$599$	−6.77485e8	+	1.17344e9i	−0.128797	+	0.223083i	−0.923211	−	0.384294i	$-0.874445\pi$
$599$	−6.77485e8	+	1.17344e9i	−0.128797	+	0.223083i	0.794414	+	0.607377i	$0.207778\pi$
$600$	3.25511e8	+	5.63801e8i	0.0615228	+	0.106561i
$601$	−5.25107e9			−0.986704			−0.493352	−	0.869830i	$-0.664228\pi$
$601$	−5.25107e9			−0.986704			−0.493352	+	0.869830i	$0.664228\pi$
$602$		0			0
$603$	−9.12161e9			−1.69419
$604$	−7.84871e8	−	1.35944e9i	−0.144934	−	0.251032i
$605$	1.02289e9	−	1.77169e9i	0.187795	−	0.325270i
$606$	7.33144e8	−	1.26984e9i	0.133824	−	0.231791i
$607$	−2.49506e9	−	4.32157e9i	−0.452815	−	0.784298i	0.545745	−	0.837951i	$-0.316247\pi$
$607$	−2.49506e9	−	4.32157e9i	−0.452815	−	0.784298i	−0.998560	+	0.0536532i	$0.982913\pi$
$608$	−1.06371e9			−0.191937
$609$		0			0
$610$	3.28766e9			0.586452
$611$	−3.07738e9	−	5.33018e9i	−0.545804	−	0.945360i
$612$	−1.02387e9	+	1.77339e9i	−0.180557	+	0.312734i
$613$	1.23014e9	−	2.13067e9i	0.215696	−	0.373597i	−0.737791	−	0.675029i	$-0.764131\pi$
$613$	1.23014e9	−	2.13067e9i	0.215696	−	0.373597i	0.953488	+	0.301432i	$0.0974645\pi$
$614$	3.77538e9	+	6.53916e9i	0.658221	+	1.14007i
$615$	−1.32784e9			−0.230189
$616$		0			0
$617$	−1.93223e9			−0.331178			−0.165589	−	0.986195i	$-0.552953\pi$
$617$	−1.93223e9			−0.331178			−0.165589	+	0.986195i	$0.552953\pi$
$618$	−3.35603e8	−	5.81282e8i	−0.0571961	−	0.0990665i
$619$	4.06849e9	−	7.04684e9i	0.689472	−	1.19420i	−0.282538	−	0.959256i	$-0.591176\pi$
$619$	4.06849e9	−	7.04684e9i	0.689472	−	1.19420i	0.972009	−	0.234943i	$-0.0754905\pi$
$620$	6.72431e8	−	1.16468e9i	0.113312	−	0.196262i
$621$	−1.12786e9	−	1.95350e9i	−0.188988	−	0.327336i
$622$	−1.31252e9			−0.218695
$623$		0			0
$624$	4.44811e8			0.0732874
$625$	−8.50112e8	−	1.47244e9i	−0.139282	−	0.241244i
$626$	−1.38405e9	+	2.39724e9i	−0.225497	+	0.390572i
$627$	−5.90458e8	+	1.02270e9i	−0.0956649	+	0.165696i
$628$	4.07612e8	+	7.06004e8i	0.0656731	+	0.113749i
$629$	8.46326e9			1.35600
$630$		0			0
$631$	8.83737e9			1.40030			0.700149	−	0.713997i	$-0.253117\pi$
$631$	8.83737e9			1.40030			0.700149	+	0.713997i	$0.253117\pi$
$632$	−1.80693e9	−	3.12970e9i	−0.284730	−	0.493166i
$633$	1.08929e9	−	1.88670e9i	0.170699	−	0.295659i
$634$	3.81296e9	−	6.60424e9i	0.594224	−	1.02923i
$635$	7.53093e7	+	1.30440e8i	0.0116719	+	0.0202163i
$636$	2.18119e8			0.0336196
$637$		0			0
$638$	−8.20981e8			−0.125159
$639$	6.96082e8	+	1.20565e9i	0.105538	+	0.182796i
$640$	−4.84820e8	+	8.39734e8i	−0.0731057	+	0.126623i
$641$	6.29527e9	−	1.09037e10i	0.944086	−	1.63520i	0.186514	−	0.982452i	$-0.440281\pi$
$641$	6.29527e9	−	1.09037e10i	0.944086	−	1.63520i	0.757572	−	0.652752i	$-0.226386\pi$
$642$	−5.23072e8	−	9.05987e8i	−0.0780169	−	0.135129i
$643$	6.47578e9			0.960625			0.480312	−	0.877098i	$-0.340523\pi$
$643$	6.47578e9			0.960625			0.480312	+	0.877098i	$0.340523\pi$
$644$		0			0
$645$	−3.38371e9			−0.496518
$646$	−1.97918e9	−	3.42804e9i	−0.288849	−	0.500301i
$647$	−4.34760e9	+	7.53027e9i	−0.631081	+	1.09306i	0.356251	+	0.934390i	$0.384055\pi$
$647$	−4.34760e9	+	7.53027e9i	−0.631081	+	1.09306i	−0.987331	+	0.158673i	$0.949278\pi$
$648$	−1.07884e9	+	1.86861e9i	−0.155756	+	0.269778i
$649$	4.15457e9	+	7.19593e9i	0.596582	+	1.03331i
$650$	−1.25729e10			−1.79572
$651$		0			0
$652$	−5.44980e9			−0.770041
$653$	1.93949e9	+	3.35929e9i	0.272578	+	0.472119i	0.969521	−	0.245007i	$-0.0787904\pi$
$653$	1.93949e9	+	3.35929e9i	0.272578	+	0.472119i	−0.696943	+	0.717126i	$0.745457\pi$
$654$	2.19074e8	−	3.79447e8i	0.0306244	−	0.0530430i
$655$	−1.47504e9	+	2.55485e9i	−0.205097	+	0.355239i
$656$	−6.27477e8	−	1.08682e9i	−0.0867830	−	0.150313i
$657$	−2.81708e9			−0.387544
$658$		0			0
$659$	−1.30333e9			−0.177400			−0.0887000	−	0.996058i	$-0.528271\pi$
$659$	−1.30333e9			−0.177400			−0.0887000	+	0.996058i	$0.528271\pi$
$660$	5.38243e8	+	9.32264e8i	0.0728743	+	0.126222i
$661$	−3.42944e9	+	5.93996e9i	−0.461868	+	0.799979i	−0.999054	−	0.0434848i	$-0.986154\pi$
$661$	−3.42944e9	+	5.93996e9i	−0.461868	+	0.799979i	0.537186	+	0.843464i	$0.319487\pi$
$662$	−8.97051e8	+	1.55374e9i	−0.120175	+	0.208149i
$663$	8.27635e8	+	1.43351e9i	0.110291	+	0.191030i
$664$	3.38367e9			0.448539
$665$		0			0
$666$	9.32429e9			1.22308
$667$	7.42306e8	+	1.28571e9i	0.0968596	+	0.167766i
$668$	1.19763e8	−	2.07436e8i	0.0155455	−	0.0269257i
$669$	−1.18723e9	+	2.05634e9i	−0.153301	+	0.265524i
$670$	−8.03658e9	−	1.39198e10i	−1.03231	−	1.78801i
$671$	3.44957e9			0.440794
$672$		0			0
$673$	−6.44953e9			−0.815596			−0.407798	−	0.913072i	$-0.633703\pi$
$673$	−6.44953e9			−0.815596			−0.407798	+	0.913072i	$0.633703\pi$
$674$	−1.42700e9	−	2.47163e9i	−0.179520	−	0.310939i
$675$	−2.72497e9	+	4.71979e9i	−0.341035	+	0.590689i
$676$	−2.28727e9	+	3.96166e9i	−0.284776	+	0.493246i
$677$	−1.91513e9	−	3.31711e9i	−0.237213	−	0.410865i	0.722700	−	0.691161i	$-0.242901\pi$
$677$	−1.91513e9	−	3.31711e9i	−0.237213	−	0.410865i	−0.959914	+	0.280296i	$0.909567\pi$
$678$	9.06981e8			0.111762
$679$		0			0
$680$	−3.60831e9			−0.440071
$681$	2.10960e8	+	3.65394e8i	0.0255968	+	0.0443349i
$682$	7.05547e8	−	1.22204e9i	0.0851688	−	0.147517i
$683$	9.89178e8	−	1.71331e9i	0.118796	−	0.205761i	−0.800495	−	0.599340i	$-0.795430\pi$
$683$	9.89178e8	−	1.71331e9i	0.118796	−	0.205761i	0.919291	+	0.393579i	$0.128763\pi$
$684$	−2.18053e9	−	3.77680e9i	−0.260535	−	0.451260i
$685$	2.13761e9			0.254103
$686$		0			0
$687$	−1.75258e9			−0.206219
$688$	−1.59899e9	−	2.76953e9i	−0.187191	−	0.324225i
$689$	−2.10621e9	+	3.64807e9i	−0.245321	+	0.424909i
$690$	9.73326e8	−	1.68585e9i	0.112794	−	0.195365i
$691$	−5.01275e9	−	8.68233e9i	−0.577967	−	1.00107i	−0.995712	−	0.0925035i	$-0.970513\pi$
$691$	−5.01275e9	−	8.68233e9i	−0.577967	−	1.00107i	0.417746	−	0.908564i	$-0.362820\pi$
$692$	−4.65193e9			−0.533657
$693$		0			0
$694$	1.29471e8			0.0147033
$695$	8.21601e9	+	1.42305e10i	0.928355	+	1.60796i
$696$	−6.34500e7	+	1.09899e8i	−0.00713344	+	0.0123555i
$697$	2.33502e9	−	4.04438e9i	0.261202	−	0.452415i
$698$	−8.31122e8	−	1.43955e9i	−0.0925062	−	0.160225i
$699$	2.41448e9			0.267395
$700$		0			0
$701$	1.21616e9			0.133345			0.0666727	−	0.997775i	$-0.478762\pi$
$701$	1.21616e9			0.133345			0.0666727	+	0.997775i	$0.478762\pi$
$702$	1.86184e9	+	3.22480e9i	0.203124	+	0.351822i
$703$	−9.01211e9	+	1.56094e10i	−0.978324	+	1.69451i
$704$	−5.08697e8	+	8.81089e8i	−0.0549484	+	0.0951734i
$705$	−1.15118e9	−	1.99390e9i	−0.123731	−	0.214309i
$706$	−1.05299e10			−1.12618
$707$		0			0
$708$	1.28435e9			0.136009
$709$	−5.23530e9	−	9.06781e9i	−0.551671	−	0.955522i	−0.998154	−	0.0607300i	$-0.980657\pi$
$709$	−5.23530e9	−	9.06781e9i	−0.551671	−	0.955522i	0.446483	−	0.894792i	$-0.352676\pi$
$710$	−1.22656e9	+	2.12447e9i	−0.128613	+	0.222765i
$711$	7.40822e9	−	1.28314e10i	0.772983	−	1.33885i
$712$	1.36447e9	+	2.36334e9i	0.141672	+	0.245384i
$713$	−2.55174e9			−0.263647
$714$		0			0
$715$	−2.07897e10			−2.12705
$716$	−3.27823e9	−	5.67807e9i	−0.333768	−	0.578103i
$717$	−1.47665e9	+	2.55763e9i	−0.149610	+	0.259132i
$718$	2.47709e9	−	4.29044e9i	0.249750	−	0.432580i
$719$	1.49793e9	+	2.59449e9i	0.150294	+	0.260316i	0.931335	−	0.364163i	$-0.118645\pi$
$719$	1.49793e9	+	2.59449e9i	0.150294	+	0.260316i	−0.781042	+	0.624479i	$0.785311\pi$
$720$	−3.97541e9			−0.396934
$721$		0			0
$722$	1.27914e9			0.126485
$723$	3.93636e8	+	6.81798e8i	0.0387357	+	0.0670922i
$724$	−1.53332e8	+	2.65578e8i	−0.0150157	+	0.0260080i
$725$	1.79346e9	−	3.10636e9i	0.174787	−	0.302739i
$726$	−1.65895e8	−	2.87339e8i	−0.0160900	−	0.0278687i
$727$	−6.52469e9			−0.629781			−0.314890	−	0.949128i	$-0.601968\pi$
$727$	−6.52469e9			−0.629781			−0.314890	+	0.949128i	$0.601968\pi$
$728$		0			0
$729$	−8.02267e9			−0.766960
$730$	−2.48199e9	−	4.29893e9i	−0.236140	−	0.409006i
$731$	5.95029e9	−	1.03062e10i	0.563413	−	0.975861i
$732$	2.66602e8	−	4.61768e8i	0.0251232	−	0.0435146i
$733$	5.99282e9	+	1.03799e10i	0.562040	+	0.973482i	0.997318	+	0.0731862i	$0.0233167\pi$
$733$	5.99282e9	+	1.03799e10i	0.562040	+	0.973482i	−0.435278	+	0.900296i	$0.643350\pi$
$734$	2.22903e9			0.208056
$735$		0			0
$736$	1.83980e9			0.170097
$737$	−8.43237e9	−	1.46053e10i	−0.775914	−	1.34392i
$738$	2.57258e9	−	4.45584e9i	0.235598	−	0.408068i
$739$	−9.09217e9	+	1.57481e10i	−0.828728	+	1.43540i	0.0703080	+	0.997525i	$0.477602\pi$
$739$	−9.09217e9	+	1.57481e10i	−0.828728	+	1.43540i	−0.899036	+	0.437874i	$0.855732\pi$
$740$	8.21515e9	+	1.42291e10i	0.745254	+	1.29082i
$741$	−3.52523e9			−0.318290
$742$		0			0
$743$	6.10111e9			0.545692			0.272846	−	0.962058i	$-0.412035\pi$
$743$	6.10111e9			0.545692			0.272846	+	0.962058i	$0.412035\pi$
$744$	−1.09057e8	−	1.88893e8i	−0.00970843	−	0.0168155i
$745$	−2.35129e9	+	4.07255e9i	−0.208333	+	0.360844i
$746$	6.60226e8	−	1.14354e9i	0.0582246	−	0.100848i
$747$	6.93633e9	+	1.20141e10i	0.608846	+	1.05455i
$748$	−3.78602e9			−0.330771
$749$		0			0
$750$	−1.99455e9			−0.172635
$751$	1.84692e9	+	3.19896e9i	0.159114	+	0.275594i	0.934549	−	0.355833i	$-0.115803\pi$
$751$	1.84692e9	+	3.19896e9i	0.159114	+	0.275594i	−0.775435	+	0.631427i	$0.782470\pi$
$752$	1.08799e9	−	1.88445e9i	0.0932955	−	0.161593i
$753$	−2.49862e7	+	4.32775e7i	−0.00213265	+	0.00369385i
$754$	−1.22538e9	−	2.12242e9i	−0.104105	−	0.180315i
$755$	1.13404e10			0.958992
$756$		0			0
$757$	1.35894e10			1.13858			0.569292	−	0.822135i	$-0.307217\pi$
$757$	1.35894e10			1.13858			0.569292	+	0.822135i	$0.307217\pi$
$758$	−1.71773e9	−	2.97520e9i	−0.143256	−	0.248127i
$759$	1.02126e9	−	1.76888e9i	0.0847794	−	0.146842i
$760$	3.84231e9	−	6.65508e9i	0.317501	−	0.549928i
$761$	−8.99970e9	−	1.55879e10i	−0.740255	−	1.28216i	−0.952379	−	0.304917i	$-0.901371\pi$
$761$	−8.99970e9	−	1.55879e10i	−0.740255	−	1.28216i	0.212123	−	0.977243i	$-0.431962\pi$
$762$	2.44279e7			0.00200006
$763$		0			0
$764$	1.66511e9			0.135087
$765$	−7.39682e9	−	1.28117e10i	−0.597352	−	1.03464i
$766$	−5.37510e9	+	9.30995e9i	−0.432102	+	0.748422i
$767$	−1.24021e10	+	2.14810e10i	−0.992455	+	1.71898i
$768$	7.86299e7	+	1.36191e8i	0.00626359	+	0.0108489i
$769$	1.41340e10			1.12079			0.560394	−	0.828226i	$-0.310650\pi$
$769$	1.41340e10			1.12079			0.560394	+	0.828226i	$0.310650\pi$
$770$		0			0
$771$	1.96787e9			0.154634
$772$	2.42664e9	+	4.20307e9i	0.189822	+	0.328781i
$773$	3.69742e9	−	6.40412e9i	0.287919	−	0.498691i	−0.685394	−	0.728173i	$-0.740370\pi$
$773$	3.69742e9	−	6.40412e9i	0.287919	−	0.498691i	0.973313	+	0.229482i	$0.0737032\pi$
$774$	6.55565e9	−	1.13547e10i	0.508186	−	0.880204i
$775$	3.08258e9	+	5.33918e9i	0.237880	+	0.412021i
$776$	−1.07423e9			−0.0825241
$777$		0			0
$778$	−8.62967e8			−0.0657000
$779$	4.97290e9	+	8.61332e9i	0.376902	+	0.652814i
$780$	−1.60674e9	+	2.78296e9i	−0.121231	+	0.209979i
$781$	−1.28697e9	+	2.22910e9i	−0.0966695	+	0.167437i
$782$	3.42320e9	+	5.92916e9i	0.255982	+	0.443373i
$783$	−1.06233e9			−0.0790845
$784$		0			0
$785$	−5.88949e9			−0.434544
$786$	2.39228e8	+	4.14355e8i	0.0175725	+	0.0304364i
$787$	4.74573e9	−	8.21985e9i	0.347050	−	0.601107i	−0.638674	−	0.769477i	$-0.720517\pi$
$787$	4.74573e9	−	8.21985e9i	0.347050	−	0.601107i	0.985724	+	0.168370i	$0.0538502\pi$
$788$	−3.81415e9	+	6.60630e9i	−0.277687	+	0.480968i
$789$	−1.17545e9	−	2.03594e9i	−0.0851992	−	0.147569i
$790$	2.61080e10			1.88399
$791$		0			0
$792$	−4.17119e9			−0.298347
$793$	5.14877e9	+	8.91793e9i	0.366646	+	0.635050i
$794$	7.46099e9	−	1.29228e10i	0.528962	−	0.916189i
$795$	−7.87887e8	+	1.36466e9i	−0.0556133	+	0.0963251i
$796$	−2.15252e9	−	3.72827e9i	−0.151269	−	0.262006i
$797$	−8.83350e9			−0.618057			−0.309029	−	0.951053i	$-0.600004\pi$
$797$	−8.83350e9			−0.618057			−0.309029	+	0.951053i	$0.600004\pi$
$798$		0			0
$799$	8.09742e9			0.561607
$800$	−2.22253e9	−	3.84953e9i	−0.153473	−	0.265823i
$801$	−5.59418e9	+	9.68941e9i	−0.384612	+	0.666167i
$802$	−3.97890e7	+	6.89165e7i	−0.00272366	+	0.00471751i
$803$	−2.60422e9	−	4.51064e9i	−0.177490	−	0.307421i
$804$	−2.60680e9			−0.176894
$805$		0			0
$806$	4.21235e9			0.283368
$807$	1.58972e9	+	2.75347e9i	0.106479	+	0.184426i
$808$	−5.00578e9	+	8.67026e9i	−0.333835	+	0.578219i
$809$	−3.07811e9	+	5.33144e9i	−0.204392	+	0.354018i	−0.949939	−	0.312436i	$-0.898855\pi$
$809$	−3.07811e9	+	5.33144e9i	−0.204392	+	0.354018i	0.745547	+	0.666453i	$0.232188\pi$
$810$	−7.79398e9	−	1.34996e10i	−0.515302	−	0.892529i
$811$	−1.53945e10			−1.01343			−0.506715	−	0.862114i	$-0.669140\pi$
$811$	−1.53945e10			−1.01343			−0.506715	+	0.862114i	$0.669140\pi$
$812$		0			0
$813$	−7.11980e8			−0.0464677
$814$	8.61973e9	+	1.49298e10i	0.560155	+	0.970217i
$815$	1.96857e10	−	3.40967e10i	1.27380	−	2.20628i
$816$	−2.92604e8	+	5.06806e8i	−0.0188523	+	0.0326532i
$817$	1.26723e10	+	2.19491e10i	0.812979	+	1.40812i
$818$	−7.01101e9			−0.447862
$819$		0			0
$820$	9.06628e9			0.574223
$821$	1.37453e10	+	2.38076e10i	0.866871	+	1.50146i	0.865177	+	0.501466i	$0.167206\pi$
$821$	1.37453e10	+	2.38076e10i	0.866871	+	1.50146i	0.00169374	+	0.999999i	$0.499461\pi$
$822$	1.73342e8	−	3.00238e8i	0.0108856	−	0.0188544i
$823$	−8.06498e8	+	1.39690e9i	−0.0504318	+	0.0873504i	−0.890139	−	0.455689i	$-0.849393\pi$
$823$	−8.06498e8	+	1.39690e9i	−0.0504318	+	0.0873504i	0.839708	+	0.543039i	$0.182726\pi$
$824$	2.29144e9	+	3.96889e9i	0.142680	+	0.247129i
$825$	−4.93486e9			−0.305975
$826$		0			0
$827$	9.03950e9			0.555745			0.277872	−	0.960618i	$-0.410371\pi$
$827$	9.03950e9			0.555745			0.277872	+	0.960618i	$0.410371\pi$
$828$	3.77147e9	+	6.53238e9i	0.230890	+	0.399913i
$829$	−1.23163e10	+	2.13324e10i	−0.750826	+	1.30047i	0.196597	+	0.980484i	$0.437011\pi$
$829$	−1.23163e10	+	2.13324e10i	−0.750826	+	1.30047i	−0.947423	+	0.319984i	$0.896323\pi$
$830$	−1.22225e10	+	2.11700e10i	−0.741969	+	1.28513i
$831$	−2.34749e8	−	4.06598e8i	−0.0141906	−	0.0245788i
$832$	−3.03709e9			−0.182821
$833$		0			0
$834$	2.66500e9			0.159080
$835$	8.65216e8	+	1.49860e9i	0.0514306	+	0.0890805i
$836$	4.03154e9	−	6.98283e9i	0.238643	−	0.413342i
$837$	9.12958e8	−	1.58129e9i	0.0538160	−	0.0932121i
$838$	8.06421e9	+	1.39676e10i	0.473378	+	0.819914i
$839$	−6.84347e9			−0.400046			−0.200023	−	0.979791i	$-0.564102\pi$
$839$	−6.84347e9			−0.400046			−0.200023	+	0.979791i	$0.564102\pi$
$840$		0			0
$841$	−1.65507e10			−0.959468
$842$	−2.27819e9	−	3.94593e9i	−0.131522	−	0.227802i
$843$	1.60247e9	−	2.77555e9i	0.0921282	−	0.159571i
$844$	−7.43747e9	+	1.28821e10i	−0.425820	+	0.737543i
$845$	−1.65241e10	−	2.86206e10i	−0.942148	−	1.63185i
$846$	8.92123e9			0.506557
$847$		0			0
$848$	−1.48928e9			−0.0838667
$849$	1.72976e9	+	2.99603e9i	0.0970082	+	0.168023i
$850$	8.27067e9	−	1.43252e10i	0.461928	−	0.800083i
$851$	1.55874e10	−	2.69982e10i	0.867003	−	1.50169i
$852$	1.98928e8	+	3.44554e8i	0.0110194	+	0.0190862i
$853$	3.54072e10			1.95330			0.976652	−	0.214826i	$-0.0689185\pi$
$853$	3.54072e10			1.95330			0.976652	+	0.214826i	$0.0689185\pi$
$854$		0			0
$855$	3.15061e10			1.72390
$856$	3.57144e9	+	6.18592e9i	0.194619	+	0.337090i
$857$	9.36496e9	−	1.62206e10i	0.508245	−	0.880306i	−0.491710	−	0.870759i	$-0.663628\pi$
$857$	9.36496e9	−	1.62206e10i	0.508245	−	0.880306i	0.999954	−	0.00954671i	$-0.00303886\pi$
$858$	−1.68587e9	+	2.92002e9i	−0.0911212	+	0.157826i
$859$	2.69136e9	+	4.66157e9i	0.144876	+	0.250932i	0.929327	−	0.369259i	$-0.120388\pi$
$859$	2.69136e9	+	4.66157e9i	0.144876	+	0.250932i	−0.784451	+	0.620191i	$0.787055\pi$
$860$	2.31034e10			1.23860
$861$		0			0
$862$	−6.17552e9			−0.328396
$863$	−3.64722e9	−	6.31717e9i	−0.193163	−	0.334568i	0.753134	−	0.657868i	$-0.228541\pi$
$863$	−3.64722e9	−	6.31717e9i	−0.193163	−	0.334568i	−0.946297	+	0.323299i	$0.895208\pi$
$864$	−6.58240e8	+	1.14010e9i	−0.0347205	+	0.0601377i
$865$	1.68037e10	−	2.91048e10i	0.882771	−	1.52900i
$866$	−4.96008e9	−	8.59111e9i	−0.259523	−	0.449507i
$867$	1.66854e9			0.0869503
$868$		0			0
$869$	2.73938e10			1.41606
$870$	−4.58387e8	−	7.93950e8i	−0.0236002	−	0.0408767i
$871$	2.51720e10	−	4.35992e10i	1.29079	−	2.23571i
$872$	−1.49579e9	+	2.59079e9i	−0.0763949	+	0.132320i
$873$	−2.20210e9	−	3.81416e9i	−0.112018	−	0.194021i
$874$	−1.45808e10			−0.738740
$875$		0			0
$876$	−8.05075e8			−0.0404643
$877$	−1.52811e10	−	2.64677e10i	−0.764992	−	1.32501i	−0.940251	−	0.340483i	$-0.889409\pi$
$877$	−1.52811e10	−	2.64677e10i	−0.764992	−	1.32501i	0.175258	−	0.984522i	$-0.443924\pi$
$878$	−7.62485e9	+	1.32066e10i	−0.380190	+	0.658508i
$879$	2.77819e9	−	4.81196e9i	0.137975	−	0.238980i
$880$	−3.67502e9	−	6.36533e9i	−0.181790	−	0.314870i
$881$	−3.10736e10			−1.53100			−0.765500	−	0.643436i	$-0.777508\pi$
$881$	−3.10736e10			−1.53100			−0.765500	+	0.643436i	$0.777508\pi$
$882$		0			0
$883$	9.10432e9			0.445026			0.222513	−	0.974930i	$-0.428574\pi$
$883$	9.10432e9			0.445026			0.222513	+	0.974930i	$0.428574\pi$
$884$	−5.65094e9	−	9.78772e9i	−0.275130	−	0.476539i
$885$	−4.63934e9	+	8.03557e9i	−0.224985	+	0.389686i
$886$	2.01895e9	−	3.49693e9i	0.0975232	−	0.168915i
$887$	2.51708e8	+	4.35972e8i	0.0121106	+	0.0209761i	0.872017	−	0.489475i	$-0.162812\pi$
$887$	2.51708e8	+	4.35972e8i	0.0121106	+	0.0209761i	−0.859907	+	0.510451i	$0.829478\pi$
$888$	2.66472e9			0.127705
$889$		0			0
$890$	−1.97150e10			−0.937414
$891$	−8.17783e9	−	1.41644e10i	−0.387316	−	0.670852i
$892$	8.10620e9	−	1.40404e10i	0.382420	−	0.662370i
$893$	−8.62254e9	+	1.49347e10i	−0.405187	+	0.701804i
$894$	3.81340e8	+	6.60501e8i	0.0178497	+	0.0309166i
$895$	4.73665e10			2.20846
$896$		0			0
$897$	6.09727e9			0.282073
$898$	8.10884e9	+	1.40449e10i	0.373673	+	0.647221i
$899$	−6.00870e8	+	1.04074e9i	−0.0275817	+	0.0477729i
$900$	9.11211e9	−	1.57826e10i	0.416649	−	0.721657i
$901$	−2.77101e9	−	4.79953e9i	−0.126212	−	0.218606i
$902$	9.51278e9			0.431603
$903$		0			0
$904$	−6.19271e9			−0.278799
$905$	−1.10773e9	−	1.91864e9i	−0.0496778	−	0.0860445i
$906$	9.19616e8	−	1.59282e9i	0.0410826	−	0.0711571i
$907$	−1.77696e10	+	3.07779e10i	−0.790774	+	1.36966i	0.134715	+	0.990884i	$0.456988\pi$
$907$	−1.77696e10	+	3.07779e10i	−0.790774	+	1.36966i	−0.925488	+	0.378776i	$0.876345\pi$
$908$	−1.44040e9	−	2.49484e9i	−0.0638531	−	0.110597i
$909$	−4.10462e10			−1.81259
$910$		0			0
$911$	3.60841e10			1.58125			0.790627	−	0.612299i	$-0.209755\pi$
$911$	3.60841e10			1.58125			0.790627	+	0.612299i	$0.209755\pi$
$912$	−6.23160e8	−	1.07934e9i	−0.0272031	−	0.0471171i
$913$	−1.28244e10	+	2.22125e10i	−0.557686	+	0.965941i
$914$	−8.15876e9	+	1.41314e10i	−0.353437	+	0.612171i
$915$	1.92604e9	+	3.33599e9i	0.0831171	+	0.143963i
$916$	1.19663e10			0.514429
$917$		0			0
$918$	−4.89900e9			−0.209006
$919$	3.53488e9	+	6.12259e9i	0.150235	+	0.260214i	0.931314	−	0.364218i	$-0.118664\pi$
$919$	3.53488e9	+	6.12259e9i	0.150235	+	0.260214i	−0.781079	+	0.624432i	$0.785330\pi$
$920$	−6.64570e9	+	1.15107e10i	−0.281373	+	0.487353i
$921$	−4.42353e9	+	7.66178e9i	−0.186578	+	0.323162i
$922$	1.36556e10	+	2.36522e10i	0.573790	+	0.993833i
$923$	−7.68363e9			−0.321633
$924$		0			0
$925$	−7.53203e10			−3.12908
$926$	7.91571e9	+	1.37104e10i	0.327606	+	0.567429i
$927$	−9.39462e9	+	1.62720e10i	−0.387347	+	0.670905i
$928$	4.33225e8	−	7.50368e8i	0.0177949	−	0.0308217i
$929$	7.75510e9	+	1.34322e10i	0.317345	+	0.549659i	0.979933	−	0.199326i	$-0.0638752\pi$
$929$	7.75510e9	+	1.34322e10i	0.317345	+	0.549659i	−0.662588	+	0.748984i	$0.730542\pi$
$930$	1.57574e9			0.0642385
$931$		0			0
$932$	−1.64856e10			−0.667038
$933$	−7.68925e8	−	1.33182e9i	−0.0309955	−	0.0536857i
$934$	−7.45687e9	+	1.29157e10i	−0.299462	+	0.518684i
$935$	1.36758e10	−	2.36872e10i	0.547158	−	0.947705i
$936$	−6.22585e9	−	1.07835e10i	−0.248161	−	0.429827i
$937$	−3.61814e10			−1.43680			−0.718400	−	0.695630i	$-0.755125\pi$
$937$	−3.61814e10			−1.43680			−0.718400	+	0.695630i	$0.755125\pi$
$938$		0			0
$939$	−3.24331e9			−0.127838
$940$	7.86003e9	+	1.36140e10i	0.308657	+	0.534610i
$941$	−9.32588e9	+	1.61529e10i	−0.364860	+	0.631956i	−0.988754	−	0.149553i	$-0.952216\pi$
$941$	−9.32588e9	+	1.61529e10i	−0.364860	+	0.631956i	0.623894	+	0.781509i	$0.285550\pi$
$942$	−4.77589e8	+	8.27209e8i	−0.0186156	+	0.0322431i
$943$	−8.60117e9	−	1.48977e10i	−0.334016	−	0.578532i
$944$	−8.76934e9			−0.339285
$945$		0			0
$946$	2.42412e10			0.930969
$947$	−4.27815e9	−	7.40997e9i	−0.163693	−	0.283525i	0.772497	−	0.635018i	$-0.219007\pi$
$947$	−4.27815e9	−	7.40997e9i	−0.163693	−	0.283525i	−0.936190	+	0.351493i	$0.885674\pi$
$948$	2.11714e9	−	3.66700e9i	0.0807088	−	0.139792i
$949$	7.77403e9	−	1.34650e10i	0.295267	−	0.511417i
$950$	1.76141e10	+	3.05084e10i	0.666541	+	1.15448i
$951$	8.93512e9			0.336875
$952$		0			0
$953$	−5.92820e8			−0.0221870			−0.0110935	−	0.999938i	$-0.503531\pi$
$953$	−5.92820e8			−0.0221870			−0.0110935	+	0.999938i	$0.503531\pi$
$954$	−3.05293e9	−	5.28782e9i	−0.113841	−	0.197178i
$955$	−6.01468e9	+	1.04177e10i	−0.223461	+	0.387045i
$956$	1.00823e10	−	1.74630e10i	0.373213	−	0.646423i
$957$	−4.80962e8	−	8.33051e8i	−0.0177386	−	0.0307241i
$958$	2.97462e10			1.09308
$959$		0			0
$960$	−1.13611e9			−0.0414447
$961$	1.27235e10	+	2.20378e10i	0.462462	+	0.801008i
$962$	−2.57313e10	+	4.45680e10i	−0.931857	+	1.61402i
$963$	−1.46425e10	+	2.53615e10i	−0.528351	+	0.915131i
$964$	−2.68768e9	−	4.65520e9i	−0.0966291	−	0.167366i
$965$	−3.50620e10			−1.25601
$966$		0			0
$967$	−5.25393e10			−1.86849			−0.934247	−	0.356626i	$-0.883927\pi$
$967$	−5.25393e10			−1.86849			−0.934247	+	0.356626i	$0.883927\pi$
$968$	1.13270e9	+	1.96190e9i	0.0401377	+	0.0695205i
$969$	2.31896e9	−	4.01655e9i	0.0818766	−	0.141814i
$970$	3.88032e9	−	6.72091e9i	0.136511	−	0.236443i
$971$	4.58288e9	+	7.93778e9i	0.160647	+	0.278248i	0.935101	−	0.354382i	$-0.115309\pi$
$971$	4.58288e9	+	7.93778e9i	0.160647	+	0.278248i	−0.774454	+	0.632630i	$0.781975\pi$
$972$	−8.15143e9			−0.284710
$973$		0			0
$974$	−1.73073e10			−0.600169
$975$	−7.36568e9	−	1.27577e10i	−0.254505	−	0.440816i
$976$	−1.82031e9	+	3.15287e9i	−0.0626717	+	0.108550i
$977$	1.00802e10	−	1.74594e10i	0.345809	−	0.598959i	−0.639691	−	0.768632i	$-0.720938\pi$
$977$	1.00802e10	−	1.74594e10i	0.345809	−	0.598959i	0.985500	+	0.169673i	$0.0542711\pi$
$978$	−3.19270e9	−	5.52992e9i	−0.109137	−	0.189031i
$979$	−2.06859e10			−0.704588
$980$		0			0
$981$	−1.22652e10			−0.414793
$982$	−9.50432e8	−	1.64620e9i	−0.0320281	−	0.0554742i
$983$	5.94946e8	−	1.03048e9i	0.0199775	−	0.0346020i	−0.855864	−	0.517201i	$-0.826974\pi$
$983$	5.94946e8	−	1.03048e9i	0.0199775	−	0.0346020i	0.875841	+	0.482599i	$0.160307\pi$
$984$	7.35201e8	−	1.27341e9i	0.0245993	−	0.0426073i
$985$	−2.75549e10	−	4.77264e10i	−0.918695	−	1.59123i
$986$	3.22431e9			0.107119
$987$		0			0
$988$	2.40696e10			0.793999
$989$	−2.19182e10	−	3.79634e10i	−0.720473	−	1.24790i
$990$	1.50672e10	−	2.60971e10i	0.493524	−	0.854809i
$991$	−1.04993e10	+	1.81853e10i	−0.342691	+	0.593558i	−0.984931	−	0.172945i	$-0.944672\pi$
$991$	−1.04993e10	+	1.81853e10i	−0.342691	+	0.593558i	0.642240	+	0.766503i	$0.278005\pi$
$992$	7.44623e8	+	1.28973e9i	0.0242184	+	0.0419475i
$993$	−2.10211e9			−0.0681291
$994$		0			0
$995$	3.11013e10			1.00092
$996$	1.98229e9	+	3.43342e9i	0.0635709	+	0.110108i
$997$	−1.60829e10	+	2.78563e10i	−0.513961	+	0.890206i	0.485908	+	0.874010i	$0.338489\pi$
$997$	−1.60829e10	+	2.78563e10i	−0.513961	+	0.890206i	−0.999869	+	0.0161963i	$0.994844\pi$
$998$	−1.06066e10	+	1.83712e10i	−0.337770	+	0.585035i
$999$	1.11537e10	+	1.93188e10i	0.353948	+	0.613056i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.8.c.g.67.2		4
7.2	even	3	inner	98.8.c.g.79.2		4
7.3	odd	6		98.8.a.g.1.2		2
7.4	even	3		14.8.a.c.1.1	✓	2
7.5	odd	6		98.8.c.k.79.1		4
7.6	odd	2		98.8.c.k.67.1		4
21.11	odd	6		126.8.a.i.1.1		2
28.11	odd	6		112.8.a.g.1.2		2
35.4	even	6		350.8.a.j.1.2		2
35.18	odd	12		350.8.c.k.99.1		4
35.32	odd	12		350.8.c.k.99.4		4
56.11	odd	6		448.8.a.s.1.1		2
56.53	even	6		448.8.a.l.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.8.a.c.1.1	✓	2	7.4	even	3
98.8.a.g.1.2		2	7.3	odd	6
98.8.c.g.67.2		4	1.1	even	1	trivial
98.8.c.g.79.2		4	7.2	even	3	inner
98.8.c.k.67.1		4	7.6	odd	2
98.8.c.k.79.1		4	7.5	odd	6
112.8.a.g.1.2		2	28.11	odd	6
126.8.a.i.1.1		2	21.11	odd	6
350.8.a.j.1.2		2	35.4	even	6
350.8.c.k.99.1		4	35.18	odd	12
350.8.c.k.99.4		4	35.32	odd	12
448.8.a.l.1.2		2	56.53	even	6
448.8.a.s.1.1		2	56.11	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 - 6.92820i) q^{2} +(4.68671 - 8.11762i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-231.180 - 400.416i) q^{5} -74.9873 q^{6} +512.000 q^{8} +(1049.57 + 1817.91i) q^{9} +(-1849.44 + 3203.33i) q^{10} +(-1940.53 + 3361.09i) q^{11} +(299.949 + 519.527i) q^{12} -11585.6 q^{13} -4333.90 q^{15} +(-2048.00 - 3547.24i) q^{16} +(7621.20 - 13200.3i) q^{17} +(8396.56 - 14543.3i) q^{18} +(16230.9 + 28112.7i) q^{19} +29591.1 q^{20} +31048.4 q^{22} +(-28073.1 - 48623.9i) q^{23} +(2399.59 - 4156.22i) q^{24} +(-67826.2 + 117478. i) q^{25} +(46342.3 + 80267.2i) q^{26} +40175.8 q^{27} -26442.0 q^{29} +(17335.6 + 30026.1i) q^{30} +(22724.1 - 39359.3i) q^{31} +(-16384.0 + 28377.9i) q^{32} +(18189.3 + 31504.9i) q^{33} -121939. q^{34} -134345. q^{36} +(277622. + 480856. i) q^{37} +(129847. - 224902. i) q^{38} +(-54298.2 + 94047.3i) q^{39} +(-118364. - 205013. i) q^{40} +306385. q^{41} +780755. q^{43} +(-124194. - 215110. i) q^{44} +(485280. - 840529. i) q^{45} +(-224584. + 388992. i) q^{46} +(265622. + 460070. i) q^{47} -38393.5 q^{48} +1.08522e6 q^{50} +(-71436.6 - 123732. i) q^{51} +(370738. - 642138. i) q^{52} +(181796. - 314880. i) q^{53} +(-160703. - 278346. i) q^{54} +1.79445e6 q^{55} +304277. q^{57} +(105768. + 183195. i) q^{58} +(1.07048e6 - 1.85412e6i) q^{59} +(138685. - 240209. i) q^{60} +(-444412. - 769744. i) q^{61} -363586. q^{62} +262144. q^{64} +(2.67836e6 + 4.63905e6i) q^{65} +(145515. - 252039. i) q^{66} +(-2.17270e6 + 3.76323e6i) q^{67} +(487757. + 844819. i) q^{68} -526281. q^{69} +663207. q^{71} +(537380. + 930769. i) q^{72} +(-671009. + 1.16222e6i) q^{73} +(2.22098e6 - 3.84685e6i) q^{74} +(635763. + 1.10117e6i) q^{75} -2.07755e6 q^{76} +868771. q^{78} +(-3.52917e6 - 6.11270e6i) q^{79} +(-946915. + 1.64010e6i) q^{80} +(-2.10712e6 + 3.64963e6i) q^{81} +(-1.22554e6 - 2.12270e6i) q^{82} +6.60874e6 q^{83} -7.04748e6 q^{85} +(-3.12302e6 - 5.40923e6i) q^{86} +(-123926. + 214646. i) q^{87} +(-993549. + 1.72088e6i) q^{88} +(2.66499e6 + 4.61590e6i) q^{89} -7.76448e6 q^{90} +3.59335e6 q^{92} +(-213002. - 368931. i) q^{93} +(2.12497e6 - 3.68056e6i) q^{94} +(7.50452e6 - 1.29982e7i) q^{95} +(153574. + 265998. i) q^{96} -2.09810e6 q^{97} -8.14686e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} - 70 q^{3} - 128 q^{4} - 126 q^{5} + 1120 q^{6} + 2048 q^{8} - 2014 q^{9} - 1008 q^{10} + 3420 q^{11} - 4480 q^{12} - 12796 q^{13} - 62064 q^{15} - 8192 q^{16} + 38472 q^{17} - 16112 q^{18}+ \cdots - 76354200 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 - 70 * q^3 - 128 * q^4 - 126 * q^5 + 1120 * q^6 + 2048 * q^8 - 2014 * q^9 - 1008 * q^10 + 3420 * q^11 - 4480 * q^12 - 12796 * q^13 - 62064 * q^15 - 8192 * q^16 + 38472 * q^17 - 16112 * q^18 + 43358 * q^19 + 16128 * q^20 - 54720 * q^22 - 89928 * q^23 - 35840 * q^24 - 170666 * q^25 + 51184 * q^26 + 386120 * q^27 + 319152 * q^29 + 248256 * q^30 + 143612 * q^31 - 65536 * q^32 + 615888 * q^33 - 615552 * q^34 + 257792 * q^36 + 271832 * q^37 + 346864 * q^38 - 520352 * q^39 - 64512 * q^40 + 129696 * q^41 + 3055928 * q^43 + 218880 * q^44 + 2354058 * q^45 - 719424 * q^46 - 485436 * q^47 + 573440 * q^48 + 2730656 * q^50 + 1700940 * q^51 + 409472 * q^52 + 145716 * q^53 - 1544480 * q^54 + 8500464 * q^55 - 1121192 * q^57 - 1276608 * q^58 + 4183662 * q^59 + 1986048 * q^60 + 280658 * q^61 - 2297792 * q^62 + 1048576 * q^64 + 7101612 * q^65 + 4927104 * q^66 - 5671648 * q^67 + 2462208 * q^68 + 4310208 * q^69 - 1238544 * q^71 - 1031168 * q^72 - 3939628 * q^73 + 2174656 * q^74 - 1507618 * q^75 - 5549824 * q^76 + 8325632 * q^78 - 4656616 * q^79 - 516096 * q^80 - 7353742 * q^81 - 518784 * q^82 + 2471700 * q^83 + 1532088 * q^85 - 12223712 * q^86 - 15012732 * q^87 + 1751040 * q^88 + 17241420 * q^89 - 37664928 * q^90 + 11510784 * q^92 + 7365592 * q^93 - 3883488 * q^94 + 11343960 * q^95 - 2293760 * q^96 - 1481872 * q^97 - 76354200 * q^99

Introduction

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