LMFDB - Embedded newform 126.6.g.j.109.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,6,Mod(37,126)] 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("126.37"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	126.g (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,8,0,-32,70] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$20.2083612964$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{79})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 79x^{2} + 6241 $ x^4 + 79*x^2 + 6241
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
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			109.1
Root			$-4.44410 - 7.69740i$ of defining polynomial
Character	$\chi$	$=$	126.109
Dual form			126.6.g.j.37.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.00000 + 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(-18.0528 - 31.2683i) q^{5} +(-124.435 + 36.3731i) q^{7} -64.0000 q^{8} +(72.2111 - 125.073i) q^{10} +(77.7174 - 134.610i) q^{11} +1158.87 q^{13} +(-374.869 - 358.308i) q^{14} +(-128.000 - 221.703i) q^{16} +(619.040 - 1072.21i) q^{17} +(140.140 + 242.729i) q^{19} +577.689 q^{20} +621.739 q^{22} +(-1741.20 - 3015.84i) q^{23} +(910.694 - 1577.37i) q^{25} +(2317.74 + 4014.44i) q^{26} +(491.478 - 2015.20i) q^{28} +5656.78 q^{29} +(1157.35 - 2004.59i) q^{31} +(512.000 - 886.810i) q^{32} +4952.32 q^{34} +(3383.72 + 3234.23i) q^{35} +(1166.59 + 2020.59i) q^{37} +(-560.558 + 970.916i) q^{38} +(1155.38 + 2001.17i) q^{40} -3812.61 q^{41} +3925.73 q^{43} +(1243.48 + 2153.77i) q^{44} +(6964.78 - 12063.4i) q^{46} +(-5558.23 - 9627.13i) q^{47} +(14161.0 - 9052.14i) q^{49} +7285.56 q^{50} +(-9270.96 + 16057.8i) q^{52} +(-5593.10 + 9687.54i) q^{53} -5612.06 q^{55} +(7963.82 - 2327.88i) q^{56} +(11313.6 + 19595.7i) q^{58} +(-3005.18 + 5205.12i) q^{59} +(7419.36 + 12850.7i) q^{61} +9258.81 q^{62} +4096.00 q^{64} +(-20920.8 - 36235.9i) q^{65} +(21491.9 - 37225.1i) q^{67} +(9904.64 + 17155.3i) q^{68} +(-4436.27 + 18190.0i) q^{70} +19962.4 q^{71} +(-22775.3 + 39448.0i) q^{73} +(-4666.35 + 8082.36i) q^{74} -4484.47 q^{76} +(-4774.54 + 19577.0i) q^{77} +(-54496.0 - 94389.9i) q^{79} +(-4621.51 + 8004.69i) q^{80} +(-7625.22 - 13207.3i) q^{82} -55829.0 q^{83} -44701.6 q^{85} +(7851.47 + 13599.1i) q^{86} +(-4973.91 + 8615.07i) q^{88} +(-47772.9 - 82745.1i) q^{89} +(-144204. + 42151.6i) q^{91} +55718.2 q^{92} +(22232.9 - 38508.5i) q^{94} +(5059.82 - 8763.86i) q^{95} +15004.9 q^{97} +(59679.5 + 30950.9i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} - 32 q^{4} + 70 q^{5} - 256 q^{8} - 280 q^{10} + 62 q^{11} + 3640 q^{13} - 504 q^{14} - 512 q^{16} + 1694 q^{17} - 826 q^{19} - 2240 q^{20} + 496 q^{22} - 2734 q^{23} - 6312 q^{25} + 7280 q^{26}+ \cdots + 113288 q^{98}+O(q^{100}) $ 4 * q + 8 * q^2 - 32 * q^4 + 70 * q^5 - 256 * q^8 - 280 * q^10 + 62 * q^11 + 3640 * q^13 - 504 * q^14 - 512 * q^16 + 1694 * q^17 - 826 * q^19 - 2240 * q^20 + 496 * q^22 - 2734 * q^23 - 6312 * q^25 + 7280 * q^26 - 2016 * q^28 + 5704 * q^29 + 2674 * q^31 + 2048 * q^32 + 13552 * q^34 + 13286 * q^35 + 9146 * q^37 + 3304 * q^38 - 4480 * q^40 - 12264 * q^41 - 32080 * q^43 + 992 * q^44 + 10936 * q^46 - 25326 * q^47 + 56644 * q^49 - 50496 * q^50 - 29120 * q^52 + 14958 * q^53 - 31052 * q^55 + 11408 * q^58 - 1106 * q^59 + 28042 * q^61 + 21392 * q^62 + 16384 * q^64 + 28308 * q^65 + 102642 * q^67 + 27104 * q^68 - 88424 * q^70 + 22112 * q^71 - 35070 * q^73 - 36584 * q^74 + 26432 * q^76 - 27062 * q^77 - 101762 * q^79 + 17920 * q^80 - 24528 * q^82 + 89264 * q^83 + 7348 * q^85 - 64160 * q^86 - 3968 * q^88 - 75474 * q^89 - 123872 * q^91 + 87488 * q^92 + 101304 * q^94 + 127502 * q^95 - 16632 * q^97 + 113288 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.00000	+	3.46410i	0.353553	+	0.612372i
$2$	2.00000	+	3.46410i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	−18.0528	−	31.2683i	−0.322938	−	0.559345i	0.658155	−	0.752883i	$-0.271337\pi$
$5$	−18.0528	−	31.2683i	−0.322938	−	0.559345i	−0.981093	+	0.193538i	$0.938004\pi$
$6$		0			0
$7$	−124.435	+	36.3731i	−0.959835	+	0.280566i
$7$	−124.435	+	36.3731i	−0.959835	+	0.280566i
$8$	−64.0000			−0.353553
$9$		0			0
$10$	72.2111	−	125.073i	0.228352	−	0.395517i
$11$	77.7174	−	134.610i	0.193658	−	0.335426i	−0.752801	−	0.658248i	$-0.771298\pi$
$11$	77.7174	−	134.610i	0.193658	−	0.335426i	0.946460	+	0.322821i	$0.104631\pi$
$12$		0			0
$13$	1158.87			1.90185			0.950925	−	0.309422i	$-0.100136\pi$
$13$	1158.87			1.90185			0.950925	+	0.309422i	$0.100136\pi$
$14$	−374.869	−	358.308i	−0.511164	−	0.488581i
$15$		0			0
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	619.040	−	1072.21i	0.519513	−	0.899823i	−0.480230	−	0.877143i	$-0.659447\pi$
$17$	619.040	−	1072.21i	0.519513	−	0.899823i	0.999743	−	0.0226804i	$-0.00722003\pi$
$18$		0			0
$19$	140.140	+	242.729i	0.0890588	+	0.154254i	0.907114	−	0.420886i	$-0.138281\pi$
$19$	140.140	+	242.729i	0.0890588	+	0.154254i	−0.818055	+	0.575140i	$0.804947\pi$
$20$	577.689			0.322938
$21$		0			0
$22$	621.739			0.273874
$23$	−1741.20	−	3015.84i	−0.686322	−	1.18874i	−0.973019	−	0.230723i	$-0.925891\pi$
$23$	−1741.20	−	3015.84i	−0.686322	−	1.18874i	0.286698	−	0.958021i	$-0.407443\pi$
$24$		0			0
$25$	910.694	−	1577.37i	0.291422	−	0.504758i
$26$	2317.74	+	4014.44i	0.672405	+	1.16464i
$27$		0			0
$28$	491.478	−	2015.20i	0.118470	−	0.485762i
$29$	5656.78			1.24903			0.624517	−	0.781011i	$-0.285296\pi$
$29$	5656.78			1.24903			0.624517	+	0.781011i	$0.285296\pi$
$30$		0			0
$31$	1157.35	−	2004.59i	0.216302	−	0.374646i	−0.737372	−	0.675486i	$-0.763934\pi$
$31$	1157.35	−	2004.59i	0.216302	−	0.374646i	0.953675	+	0.300840i	$0.0972671\pi$
$32$	512.000	−	886.810i	0.0883883	−	0.153093i
$33$		0			0
$34$	4952.32			0.734703
$35$	3383.72	+	3234.23i	0.466900	+	0.446273i
$36$		0			0
$37$	1166.59	+	2020.59i	0.140092	+	0.242646i	0.927531	−	0.373746i	$-0.121927\pi$
$37$	1166.59	+	2020.59i	0.140092	+	0.242646i	−0.787439	+	0.616392i	$0.788594\pi$
$38$	−560.558	+	970.916i	−0.0629741	+	0.109074i
$39$		0			0
$40$	1155.38	+	2001.17i	0.114176	+	0.197758i
$41$	−3812.61			−0.354211			−0.177106	−	0.984192i	$-0.556673\pi$
$41$	−3812.61			−0.354211			−0.177106	+	0.984192i	$0.556673\pi$
$42$		0			0
$43$	3925.73			0.323780			0.161890	−	0.986809i	$-0.448241\pi$
$43$	3925.73			0.323780			0.161890	+	0.986809i	$0.448241\pi$
$44$	1243.48	+	2153.77i	0.0968292	+	0.167713i
$45$		0			0
$46$	6964.78	−	12063.4i	0.485303	−	0.840569i
$47$	−5558.23	−	9627.13i	−0.367022	−	0.635700i	0.622077	−	0.782956i	$-0.286289\pi$
$47$	−5558.23	−	9627.13i	−0.367022	−	0.635700i	−0.989098	+	0.147256i	$0.952956\pi$
$48$		0			0
$49$	14161.0	−	9052.14i	0.842566	−	0.538594i
$50$	7285.56			0.412133
$51$		0			0
$52$	−9270.96	+	16057.8i	−0.475462	+	0.823525i
$53$	−5593.10	+	9687.54i	−0.273504	+	0.473722i	−0.969757	−	0.244074i	$-0.921516\pi$
$53$	−5593.10	+	9687.54i	−0.273504	+	0.473722i	0.696253	+	0.717797i	$0.254849\pi$
$54$		0			0
$55$	−5612.06			−0.250159
$56$	7963.82	−	2327.88i	0.339353	−	0.0991950i
$57$		0			0
$58$	11313.6	+	19595.7i	0.441600	+	0.764874i
$59$	−3005.18	+	5205.12i	−0.112393	+	0.194671i	−0.916735	−	0.399497i	$-0.869185\pi$
$59$	−3005.18	+	5205.12i	−0.112393	+	0.194671i	0.804342	+	0.594167i	$0.202518\pi$
$60$		0			0
$61$	7419.36	+	12850.7i	0.255295	+	0.442183i	0.964975	−	0.262340i	$-0.0844942\pi$
$61$	7419.36	+	12850.7i	0.255295	+	0.442183i	−0.709681	+	0.704523i	$0.751161\pi$
$62$	9258.81			0.305897
$63$		0			0
$64$	4096.00			0.125000
$65$	−20920.8	−	36235.9i	−0.614179	−	1.06379i
$66$		0			0
$67$	21491.9	−	37225.1i	0.584909	−	1.01309i	−0.409977	−	0.912096i	$-0.634463\pi$
$67$	21491.9	−	37225.1i	0.584909	−	1.01309i	0.994887	−	0.100997i	$-0.0322032\pi$
$68$	9904.64	+	17155.3i	0.259757	+	0.449912i
$69$		0			0
$70$	−4436.27	+	18190.0i	−0.108211	+	0.443698i
$71$	19962.4			0.469967			0.234984	−	0.971999i	$-0.424496\pi$
$71$	19962.4			0.469967			0.234984	+	0.971999i	$0.424496\pi$
$72$		0			0
$73$	−22775.3	+	39448.0i	−0.500215	+	0.866398i	0.499785	+	0.866150i	$0.333412\pi$
$73$	−22775.3	+	39448.0i	−0.500215	+	0.866398i	−1.00000		0.000248463i	$0.999921\pi$
$74$	−4666.35	+	8082.36i	−0.0990599	+	0.171577i
$75$		0			0
$76$	−4484.47			−0.0890588
$77$	−4774.54	+	19577.0i	−0.0917709	+	0.376288i
$78$		0			0
$79$	−54496.0	−	94389.9i	−0.982419	−	1.70160i	−0.652885	−	0.757457i	$-0.726442\pi$
$79$	−54496.0	−	94389.9i	−0.982419	−	1.70160i	−0.329534	−	0.944144i	$-0.606892\pi$
$80$	−4621.51	+	8004.69i	−0.0807345	+	0.139836i
$81$		0			0
$82$	−7625.22	−	13207.3i	−0.125233	−	0.216909i
$83$	−55829.0			−0.889538			−0.444769	−	0.895645i	$-0.646714\pi$
$83$	−55829.0			−0.889538			−0.444769	+	0.895645i	$0.646714\pi$
$84$		0			0
$85$	−44701.6			−0.671082
$86$	7851.47	+	13599.1i	0.114473	+	0.198274i
$87$		0			0
$88$	−4973.91	+	8615.07i	−0.0684686	+	0.118591i
$89$	−47772.9	−	82745.1i	−0.639303	−	1.10731i	−0.985586	−	0.169175i	$-0.945890\pi$
$89$	−47772.9	−	82745.1i	−0.639303	−	1.10731i	0.346283	−	0.938130i	$-0.387444\pi$
$90$		0			0
$91$	−144204.	+	42151.6i	−1.82546	+	0.533594i
$92$	55718.2			0.686322
$93$		0			0
$94$	22232.9	−	38508.5i	0.259523	−	0.449508i
$95$	5059.82	−	8763.86i	0.0575209	−	0.0996292i
$96$		0			0
$97$	15004.9			0.161922			0.0809609	−	0.996717i	$-0.474201\pi$
$97$	15004.9			0.161922			0.0809609	+	0.996717i	$0.474201\pi$
$98$	59679.5	+	30950.9i	0.627712	+	0.325542i
$99$		0			0
$100$	14571.1	+	25237.9i	0.145711	+	0.252379i
$101$	13438.1	−	23275.4i	0.131079	−	0.227036i	−0.793014	−	0.609204i	$-0.791489\pi$
$101$	13438.1	−	23275.4i	0.131079	−	0.227036i	0.924093	+	0.382168i	$0.124822\pi$
$102$		0			0
$103$	25957.6	+	44959.9i	0.241086	+	0.417573i	0.961024	−	0.276466i	$-0.0891632\pi$
$103$	25957.6	+	44959.9i	0.241086	+	0.417573i	−0.719938	+	0.694038i	$0.755830\pi$
$104$	−74167.6			−0.672405
$105$		0			0
$106$	−44744.8			−0.386793
$107$	−12487.4	−	21628.8i	−0.105442	−	0.182630i	0.808477	−	0.588528i	$-0.200292\pi$
$107$	−12487.4	−	21628.8i	−0.105442	−	0.182630i	−0.913919	+	0.405898i	$0.866959\pi$
$108$		0			0
$109$	1818.07	−	3148.99i	0.0146570	−	0.0253867i	−0.858604	−	0.512640i	$-0.828668\pi$
$109$	1818.07	−	3148.99i	0.0146570	−	0.0253867i	0.873261	+	0.487253i	$0.162001\pi$
$110$	−11224.1	−	19440.7i	−0.0884444	−	0.153190i
$111$		0			0
$112$	23991.6	+	22931.7i	0.180724	+	0.172740i
$113$	−62175.0			−0.458057			−0.229028	−	0.973420i	$-0.573555\pi$
$113$	−62175.0			−0.458057			−0.229028	+	0.973420i	$0.573555\pi$
$114$		0			0
$115$	−62866.8	+	108889.i	−0.443279	+	0.767781i
$116$	−45254.2	+	78382.7i	−0.312259	+	0.540848i
$117$		0			0
$118$	−24041.4			−0.158948
$119$	−38030.6	+	155936.i	−0.246187	+	1.00944i
$120$		0			0
$121$	68445.5	+	118551.i	0.424993	+	0.736109i
$122$	−29677.4	+	51402.8i	−0.180521	+	0.312671i
$123$		0			0
$124$	18517.6	+	32073.4i	0.108151	+	0.187323i
$125$	−178592.			−1.02232
$126$		0			0
$127$	63550.3			0.349630			0.174815	−	0.984601i	$-0.444067\pi$
$127$	63550.3			0.349630			0.174815	+	0.984601i	$0.444067\pi$
$128$	8192.00	+	14189.0i	0.0441942	+	0.0765466i
$129$		0			0
$130$	83683.2	−	144944.i	0.434290	−	0.752213i
$131$	68148.5	+	118037.i	0.346959	+	0.600950i	0.985708	−	0.168465i	$-0.0538810\pi$
$131$	68148.5	+	118037.i	0.346959	+	0.600950i	−0.638749	+	0.769415i	$0.720548\pi$
$132$		0			0
$133$	−26267.0	−	25106.6i	−0.128760	−	0.123072i
$134$	171935.			0.827187
$135$		0			0
$136$	−39618.6	+	68621.4i	−0.183676	+	0.318136i
$137$	167652.	−	290381.i	0.763144	−	1.32180i	−0.178078	−	0.984016i	$-0.556988\pi$
$137$	167652.	−	290381.i	0.763144	−	1.32180i	0.941222	−	0.337788i	$-0.109679\pi$
$138$		0			0
$139$	58195.2			0.255476			0.127738	−	0.991808i	$-0.459228\pi$
$139$	58195.2			0.255476			0.127738	+	0.991808i	$0.459228\pi$
$140$	−71884.6	+	21012.3i	−0.309967	+	0.0906054i
$141$		0			0
$142$	39924.9	+	69151.9i	0.166158	+	0.287795i
$143$	90064.3	−	155996.i	0.368309	−	0.637930i
$144$		0			0
$145$	−102121.	−	176878.i	−0.403360	−	0.698641i
$146$	−182202.			−0.707411
$147$		0			0
$148$	−37330.8			−0.140092
$149$	141529.	+	245135.i	0.522251	+	0.904566i	0.999665	+	0.0258870i	$0.00824101\pi$
$149$	141529.	+	245135.i	0.522251	+	0.904566i	−0.477414	+	0.878679i	$0.658426\pi$
$150$		0			0
$151$	120779.	−	209195.i	0.431071	−	0.746637i	−0.565895	−	0.824477i	$-0.691469\pi$
$151$	120779.	−	209195.i	0.431071	−	0.746637i	0.996966	+	0.0778407i	$0.0248026\pi$
$152$	−8968.93	−	15534.6i	−0.0314870	−	0.0545372i
$153$		0			0
$154$	−77365.9	+	22614.6i	−0.262874	+	0.0768398i
$155$	−83573.6			−0.279409
$156$		0			0
$157$	107014.	−	185354.i	0.346492	−	0.600142i	−0.639132	−	0.769097i	$-0.720706\pi$
$157$	107014.	−	185354.i	0.346492	−	0.600142i	0.985624	+	0.168956i	$0.0540394\pi$
$158$	217984.	−	377559.i	0.694675	−	1.20321i
$159$		0			0
$160$	−36972.1			−0.114176
$161$	326360.	+	311942.i	0.992277	+	0.948440i
$162$		0			0
$163$	−32233.0	−	55829.2i	−0.0950237	−	0.164586i	0.814595	−	0.580030i	$-0.196959\pi$
$163$	−32233.0	−	55829.2i	−0.0950237	−	0.164586i	−0.909619	+	0.415445i	$0.863626\pi$
$164$	30500.9	−	52829.1i	0.0885529	−	0.153378i
$165$		0			0
$166$	−111658.	−	193397.i	−0.314499	−	0.544729i
$167$	442694.			1.22832			0.614162	−	0.789180i	$-0.289494\pi$
$167$	442694.			1.22832			0.614162	+	0.789180i	$0.289494\pi$
$168$		0			0
$169$	971685.			2.61703
$170$	−89403.2	−	154851.i	−0.237263	−	0.410952i
$171$		0			0
$172$	−31405.9	+	54396.6i	−0.0809449	+	0.140201i
$173$	−39299.5	−	68068.8i	−0.0998325	−	0.172915i	0.811783	−	0.583960i	$-0.198497\pi$
$173$	−39299.5	−	68068.8i	−0.0998325	−	0.172915i	−0.911615	+	0.411045i	$0.865164\pi$
$174$		0			0
$175$	−55948.3	+	229404.i	−0.138099	+	0.566247i
$176$	−39791.3			−0.0968292
$177$		0			0
$178$	191092.	−	330980.i	0.452055	−	0.782983i
$179$	−255214.	+	442043.i	−0.595348	+	1.03117i	0.398149	+	0.917321i	$0.369653\pi$
$179$	−255214.	+	442043.i	−0.595348	+	1.03117i	−0.993498	+	0.113853i	$0.963681\pi$
$180$		0			0
$181$	−22051.8			−0.0500319			−0.0250160	−	0.999687i	$-0.507964\pi$
$181$	−22051.8			−0.0500319			−0.0250160	+	0.999687i	$0.507964\pi$
$182$	−434425.	−	415233.i	−0.972156	−	0.929208i
$183$		0			0
$184$	111436.	+	193014.i	0.242651	+	0.420285i
$185$	42120.3	−	72954.5i	0.0904820	−	0.156719i
$186$		0			0
$187$	−96220.4	−	166659.i	−0.201216	−	0.348517i
$188$	177863.			0.367022
$189$		0			0
$190$	40478.5			0.0813469
$191$	−279076.	−	483374.i	−0.553528	−	0.958738i	−0.998016	−	0.0629535i	$-0.979948\pi$
$191$	−279076.	−	483374.i	−0.553528	−	0.958738i	0.444489	−	0.895784i	$-0.353385\pi$
$192$		0			0
$193$	24658.1	−	42709.1i	0.0476504	−	0.0825330i	−0.841216	−	0.540699i	$-0.818160\pi$
$193$	24658.1	−	42709.1i	0.0476504	−	0.0825330i	0.888867	+	0.458166i	$0.151493\pi$
$194$	30009.9	+	51978.7i	0.0572480	+	0.0991564i
$195$		0			0
$196$	12142.2	+	268638.i	0.0225765	+	0.499490i
$197$	941509.			1.72846			0.864229	−	0.503099i	$-0.167807\pi$
$197$	941509.			1.72846			0.864229	+	0.503099i	$0.167807\pi$
$198$		0			0
$199$	−320006.	+	554267.i	−0.572830	+	0.992170i	0.423444	+	0.905922i	$0.360821\pi$
$199$	−320006.	+	554267.i	−0.572830	+	0.992170i	−0.996274	+	0.0862477i	$0.972512\pi$
$200$	−58284.4	+	100952.i	−0.103033	+	0.178459i
$201$		0			0
$202$	107505.			0.185374
$203$	−703900.	+	205754.i	−1.19887	+	0.350436i
$204$		0			0
$205$	68828.2	+	119214.i	0.114388	+	0.198126i
$206$	−103830.	+	179840.i	−0.170473	+	0.295268i
$207$		0			0
$208$	−148335.	−	256924.i	−0.237731	−	0.411762i
$209$	43565.1			0.0689879
$210$		0			0
$211$	921869.			1.42549			0.712743	−	0.701425i	$-0.247452\pi$
$211$	921869.			1.42549			0.712743	+	0.701425i	$0.247452\pi$
$212$	−89489.7	−	155001.i	−0.136752	−	0.236861i
$213$		0			0
$214$	49949.5	−	86515.1i	0.0745585	−	0.129139i
$215$	−70870.4	−	122751.i	−0.104561	−	0.181105i
$216$		0			0
$217$	−71101.5	+	291537.i	−0.102501	+	0.420285i
$218$	14544.6			0.0207281
$219$		0			0
$220$	44896.5	−	77762.9i	0.0625396	−	0.108322i
$221$	717387.	−	1.24255e6i	0.988036	−	1.71133i
$222$		0			0
$223$	−837700.			−1.12805			−0.564023	−	0.825759i	$-0.690747\pi$
$223$	−837700.			−1.12805			−0.564023	+	0.825759i	$0.690747\pi$
$224$	−31454.6	+	128973.i	−0.0418855	+	0.171743i
$225$		0			0
$226$	−124350.	−	215380.i	−0.161948	−	0.280501i
$227$	−665344.	+	1.15241e6i	−0.857002	+	1.48437i	0.0177731	+	0.999842i	$0.494342\pi$
$227$	−665344.	+	1.15241e6i	−0.857002	+	1.48437i	−0.874775	+	0.484529i	$0.838991\pi$
$228$		0			0
$229$	−505317.	−	875234.i	−0.636759	−	1.10290i	−0.986140	−	0.165918i	$-0.946941\pi$
$229$	−505317.	−	875234.i	−0.636759	−	1.10290i	0.349381	−	0.936981i	$-0.386392\pi$
$230$	−502935.			−0.626891
$231$		0			0
$232$	−362034.			−0.441600
$233$	743050.	+	1.28700e6i	0.896661	+	1.55306i	0.831736	+	0.555172i	$0.187347\pi$
$233$	743050.	+	1.28700e6i	0.896661	+	1.55306i	0.0649249	+	0.997890i	$0.479319\pi$
$234$		0			0
$235$	−200683.	+	347593.i	−0.237050	+	0.410583i
$236$	−48082.8	−	83281.9i	−0.0561966	−	0.0973353i
$237$		0			0
$238$	−616241.	+	180131.i	−0.705193	+	0.206132i
$239$	−875637.			−0.991584			−0.495792	−	0.868441i	$-0.665122\pi$
$239$	−875637.			−0.991584			−0.495792	+	0.868441i	$0.665122\pi$
$240$		0			0
$241$	−726472.	+	1.25829e6i	−0.805706	+	1.39552i	0.110108	+	0.993920i	$0.464880\pi$
$241$	−726472.	+	1.25829e6i	−0.805706	+	1.39552i	−0.915814	+	0.401604i	$0.868453\pi$
$242$	−273782.	+	474204.i	−0.300515	+	0.520508i
$243$		0			0
$244$	−237419.			−0.255295
$245$	−538691.	−	279374.i	−0.573356	−	0.297352i
$246$		0			0
$247$	162403.	+	281291.i	0.169376	+	0.293369i
$248$	−74070.4	+	128294.i	−0.0764743	+	0.132457i
$249$		0			0
$250$	−357184.	−	618661.i	−0.361445	−	0.626041i
$251$	198384.			0.198757			0.0993786	−	0.995050i	$-0.468315\pi$
$251$	198384.			0.198757			0.0993786	+	0.995050i	$0.468315\pi$
$252$		0			0
$253$	−541284.			−0.531648
$254$	127101.	+	220145.i	0.123613	+	0.214104i
$255$		0			0
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	239786.	+	415321.i	0.226460	+	0.392240i	0.956756	−	0.290890i	$-0.0939515\pi$
$257$	239786.	+	415321.i	0.226460	+	0.392240i	−0.730297	+	0.683130i	$0.760618\pi$
$258$		0			0
$259$	−218659.	−	208999.i	−0.202543	−	0.193595i
$260$	669466.			0.614179
$261$		0			0
$262$	−272594.	+	472147.i	−0.245337	+	0.424936i
$263$	227471.	−	393992.i	0.202786	−	0.351235i	−0.746639	−	0.665229i	$-0.768334\pi$
$263$	227471.	−	393992.i	0.202786	−	0.351235i	0.949425	+	0.313994i	$0.101667\pi$
$264$		0			0
$265$	403884.			0.353299
$266$	34437.7	−	141205.i	0.0298422	−	0.122362i
$267$		0			0
$268$	343871.	+	595602.i	0.292455	+	0.506546i
$269$	−430068.	+	744900.i	−0.362374	+	0.627650i	−0.988351	−	0.152192i	$-0.951367\pi$
$269$	−430068.	+	744900.i	−0.362374	+	0.627650i	0.625977	+	0.779841i	$0.284700\pi$
$270$		0			0
$271$	−652790.	−	1.13067e6i	−0.539946	−	0.935214i	−0.998906	−	0.0467569i	$-0.985111\pi$
$271$	−652790.	−	1.13067e6i	−0.539946	−	0.935214i	0.458960	−	0.888457i	$-0.348222\pi$
$272$	−316949.			−0.259757
$273$		0			0
$274$	1.34121e6			1.07925
$275$	−141554.	−	245178.i	−0.112873	−	0.195501i
$276$		0			0
$277$	271554.	−	470346.i	0.212646	−	0.368314i	−0.739896	−	0.672721i	$-0.765125\pi$
$277$	271554.	−	470346.i	0.212646	−	0.368314i	0.952542	+	0.304408i	$0.0984586\pi$
$278$	116390.	+	201594.i	0.0903245	+	0.156447i
$279$		0			0
$280$	−216558.	−	206991.i	−0.165074	−	0.157781i
$281$	−998089.			−0.754055			−0.377028	−	0.926202i	$-0.623054\pi$
$281$	−998089.			−0.754055			−0.377028	+	0.926202i	$0.623054\pi$
$282$		0			0
$283$	−888660.	+	1.53920e6i	−0.659583	+	1.14243i	0.321140	+	0.947032i	$0.395934\pi$
$283$	−888660.	+	1.53920e6i	−0.659583	+	1.14243i	−0.980724	+	0.195400i	$0.937399\pi$
$284$	−159699.	+	276608.i	−0.117492	+	0.203502i
$285$		0			0
$286$	720514.			0.520868
$287$	474421.	−	138676.i	0.339984	−	0.0993796i
$288$		0			0
$289$	−56493.2	−	97849.1i	−0.0397880	−	0.0689148i
$290$	408482.	−	707512.i	0.285219	−	0.494014i
$291$		0			0
$292$	−364405.	−	631167.i	−0.250108	−	0.433199i
$293$	1.63987e6			1.11594			0.557969	−	0.829862i	$-0.311581\pi$
$293$	1.63987e6			1.11594			0.557969	+	0.829862i	$0.311581\pi$
$294$		0			0
$295$	217007.			0.145184
$296$	−74661.6	−	129318.i	−0.0495300	−	0.0857884i
$297$		0			0
$298$	−566116.	+	980541.i	−0.369287	+	0.639625i
$299$	−2.01782e6	−	3.49496e6i	−1.30528	−	2.26081i
$300$		0			0
$301$	−488498.	+	142791.i	−0.310775	+	0.0908415i
$302$	966231.			0.609626
$303$		0			0
$304$	35875.7	−	62138.6i	0.0222647	−	0.0385636i
$305$	267880.	−	463982.i	0.164889	−	0.285595i
$306$		0			0
$307$	2.38130e6			1.44201			0.721006	−	0.692928i	$-0.243680\pi$
$307$	2.38130e6			1.44201			0.721006	+	0.692928i	$0.243680\pi$
$308$	−233071.	−	222774.i	−0.139995	−	0.133810i
$309$		0			0
$310$	−167147.	−	289507.i	−0.0987859	−	0.171102i
$311$	−622564.	+	1.07831e6i	−0.364992	+	0.632184i	−0.988775	−	0.149413i	$-0.952262\pi$
$311$	−622564.	+	1.07831e6i	−0.364992	+	0.632184i	0.623783	+	0.781597i	$0.285595\pi$
$312$		0			0
$313$	−831495.	−	1.44019e6i	−0.479732	−	0.830921i	0.519997	−	0.854168i	$-0.325933\pi$
$313$	−831495.	−	1.44019e6i	−0.479732	−	0.830921i	−0.999730	+	0.0232470i	$0.992600\pi$
$314$	856115.			0.490014
$315$		0			0
$316$	1.74387e6			0.982419
$317$	−1.31243e6	−	2.27319e6i	−0.733547	−	1.27054i	−0.955358	−	0.295450i	$-0.904530\pi$
$317$	−1.31243e6	−	2.27319e6i	−0.733547	−	1.27054i	0.221812	−	0.975090i	$-0.428803\pi$
$318$		0			0
$319$	439630.	−	761462.i	0.241886	−	0.418959i
$320$	−73944.2	−	128075.i	−0.0403672	−	0.0699181i
$321$		0			0
$322$	−427879.	+	1.75443e6i	−0.229976	+	0.942967i
$323$	347008.			0.185069
$324$		0			0
$325$	1.05538e6	−	1.82796e6i	0.554241	−	0.959974i
$326$	128932.	−	223317.i	0.0671919	−	0.116380i
$327$		0			0
$328$	244007.			0.125233
$329$	1.04180e6	+	995780.i	0.530636	+	0.507193i
$330$		0			0
$331$	−869428.	−	1.50589e6i	−0.436178	−	0.755482i	0.561213	−	0.827671i	$-0.310335\pi$
$331$	−869428.	−	1.50589e6i	−0.436178	−	0.755482i	−0.997391	+	0.0721894i	$0.977001\pi$
$332$	446632.	−	773589.i	0.222385	−	0.385181i
$333$		0			0
$334$	885389.	+	1.53354e6i	0.434278	+	0.752191i
$335$	−1.55196e6			−0.755558
$336$		0			0
$337$	853564.			0.409413			0.204706	−	0.978823i	$-0.434376\pi$
$337$	853564.			0.409413			0.204706	+	0.978823i	$0.434376\pi$
$338$	1.94337e6	+	3.36602e6i	0.925260	+	1.60260i
$339$		0			0
$340$	357613.	−	619403.i	0.167771	−	0.290587i
$341$	−179892.	−	311583.i	−0.0837774	−	0.145107i
$342$		0			0
$343$	−1.43287e6	+	1.64148e6i	−0.657613	+	0.753356i
$344$	−251247.			−0.114473
$345$		0			0
$346$	157198.	−	272275.i	0.0705922	−	0.122269i
$347$	−1.49250e6	+	2.58508e6i	−0.665411	+	1.15253i	0.313763	+	0.949501i	$0.398410\pi$
$347$	−1.49250e6	+	2.58508e6i	−0.665411	+	1.15253i	−0.979174	+	0.203024i	$0.934923\pi$
$348$		0			0
$349$	2.87467e6			1.26335			0.631676	−	0.775233i	$-0.282367\pi$
$349$	2.87467e6			1.26335			0.631676	+	0.775233i	$0.282367\pi$
$350$	−906576.	+	264998.i	−0.395580	+	0.115631i
$351$		0			0
$352$	−79582.6	−	137841.i	−0.0342343	−	0.0592955i
$353$	735546.	−	1.27400e6i	0.314176	−	0.544169i	−0.665086	−	0.746767i	$-0.731605\pi$
$353$	735546.	−	1.27400e6i	0.314176	−	0.544169i	0.979262	+	0.202598i	$0.0649384\pi$
$354$		0			0
$355$	−360377.	−	624192.i	−0.151770	−	0.262874i
$356$	1.52873e6			0.639303
$357$		0			0
$358$	−2.04171e6			−0.841950
$359$	1.53900e6	+	2.66562e6i	0.630233	+	1.09160i	0.987504	+	0.157595i	$0.0503741\pi$
$359$	1.53900e6	+	2.66562e6i	0.630233	+	1.09160i	−0.357270	+	0.934001i	$0.616293\pi$
$360$		0			0
$361$	1.19877e6	−	2.07633e6i	0.484137	−	0.838550i
$362$	−44103.6	−	76389.6i	−0.0176890	−	0.0306382i
$363$		0			0
$364$	569559.	−	2.33536e6i	0.225312	−	0.923846i
$365$	1.64463e6			0.646154
$366$		0			0
$367$	−808349.	+	1.40010e6i	−0.313281	+	0.542618i	−0.979071	−	0.203521i	$-0.934761\pi$
$367$	−808349.	+	1.40010e6i	−0.313281	+	0.542618i	0.665790	+	0.746139i	$0.268095\pi$
$368$	−445746.	+	772055.i	−0.171580	+	0.297186i
$369$		0			0
$370$	336962.			0.127961
$371$	343611.	−	1.40890e6i	0.129608	−	0.531431i
$372$		0			0
$373$	2.38059e6	+	4.12331e6i	0.885958	+	1.53452i	0.844612	+	0.535379i	$0.179831\pi$
$373$	2.38059e6	+	4.12331e6i	0.885958	+	1.53452i	0.0413462	+	0.999145i	$0.486835\pi$
$374$	384881.	−	666634.i	0.142281	−	0.246439i
$375$		0			0
$376$	355727.	+	616136.i	0.129762	+	0.224754i
$377$	6.55547e6			2.37548
$378$		0			0
$379$	1.00193e6			0.358294			0.179147	−	0.983822i	$-0.442666\pi$
$379$	1.00193e6			0.358294			0.179147	+	0.983822i	$0.442666\pi$
$380$	80957.1	+	140222.i	0.0287605	+	0.0498146i
$381$		0			0
$382$	1.11630e6	−	1.93350e6i	0.391403	−	0.677930i
$383$	−1.41076e6	−	2.44351e6i	−0.491424	−	0.851172i	0.508527	−	0.861046i	$-0.330190\pi$
$383$	−1.41076e6	−	2.44351e6i	−0.491424	−	0.851172i	−0.999951	+	0.00987425i	$0.996857\pi$
$384$		0			0
$385$	698335.	−	204128.i	0.240111	−	0.0701859i
$386$	197265.			0.0673879
$387$		0			0
$388$	−120040.	+	207915.i	−0.0404804	+	0.0701142i
$389$	−621198.	+	1.07595e6i	−0.208140	+	0.360510i	−0.951129	−	0.308795i	$-0.900074\pi$
$389$	−621198.	+	1.07595e6i	−0.208140	+	0.360510i	0.742988	+	0.669304i	$0.233408\pi$
$390$		0			0
$391$	−4.31148e6			−1.42621
$392$	−906304.	+	579337.i	−0.297892	+	0.190422i
$393$		0			0
$394$	1.88302e6	+	3.26148e6i	0.611102	+	1.05846i
$395$	−1.96761e6	+	3.40800e6i	−0.634521	+	1.09902i
$396$		0			0
$397$	−1.37281e6	−	2.37778e6i	−0.437154	−	0.757173i	0.560315	−	0.828280i	$-0.310680\pi$
$397$	−1.37281e6	−	2.37778e6i	−0.437154	−	0.757173i	−0.997469	+	0.0711068i	$0.977347\pi$
$398$	−2.56005e6			−0.810103
$399$		0			0
$400$	−466276.			−0.145711
$401$	−1.85668e6	−	3.21586e6i	−0.576601	−	0.998702i	−0.995866	−	0.0908378i	$-0.971046\pi$
$401$	−1.85668e6	−	3.21586e6i	−0.576601	−	0.998702i	0.419265	−	0.907864i	$-0.362288\pi$
$402$		0			0
$403$	1.34122e6	−	2.32306e6i	0.411374	−	0.712521i
$404$	215009.	+	372407.i	0.0655396	+	0.113518i
$405$		0			0
$406$	−2.12055e6	−	2.02687e6i	−0.638461	−	0.610255i
$407$	362656.			0.108520
$408$		0			0
$409$	−1.87970e6	+	3.25574e6i	−0.555623	+	0.962367i	0.442232	+	0.896901i	$0.354187\pi$
$409$	−1.87970e6	+	3.25574e6i	−0.555623	+	0.962367i	−0.997855	+	0.0654664i	$0.979146\pi$
$410$	−275313.	+	476856.i	−0.0808847	+	0.140096i
$411$		0			0
$412$	−830643.			−0.241086
$413$	184622.	−	757005.i	0.0532609	−	0.218385i
$414$		0			0
$415$	1.00787e6	+	1.74568e6i	0.287266	+	0.497559i
$416$	593341.	−	1.02770e6i	0.168101	−	0.291160i
$417$		0			0
$418$	87130.2	+	150914.i	0.0243909	+	0.0422463i
$419$	−4.60027e6			−1.28011			−0.640056	−	0.768328i	$-0.721089\pi$
$419$	−4.60027e6			−1.28011			−0.640056	+	0.768328i	$0.721089\pi$
$420$		0			0
$421$	−404864.			−0.111328			−0.0556639	−	0.998450i	$-0.517728\pi$
$421$	−404864.			−0.111328			−0.0556639	+	0.998450i	$0.517728\pi$
$422$	1.84374e6	+	3.19345e6i	0.503986	+	0.872929i
$423$		0			0
$424$	357959.	−	620003.i	0.0966982	−	0.167486i
$425$	−1.12751e6	−	1.95291e6i	−0.302795	−	0.524457i
$426$		0			0
$427$	−1.39065e6	−	1.32921e6i	−0.369102	−	0.352796i
$428$	399596.			0.105442
$429$		0			0
$430$	283482.	−	491004.i	0.0739356	−	0.128060i
$431$	47379.2	−	82063.2i	0.0122856	−	0.0212792i	−0.859817	−	0.510602i	$-0.829423\pi$
$431$	47379.2	−	82063.2i	0.0122856	−	0.0212792i	0.872103	+	0.489323i	$0.162756\pi$
$432$		0			0
$433$	4.31727e6			1.10660			0.553298	−	0.832983i	$-0.313369\pi$
$433$	4.31727e6			1.10660			0.553298	+	0.832983i	$0.313369\pi$
$434$	−1.15212e6	+	336771.i	−0.293611	+	0.0858244i
$435$		0			0
$436$	29089.2	+	50383.9i	0.00732850	+	0.0126933i
$437$	488021.	−	845277.i	0.122246	−	0.211736i
$438$		0			0
$439$	1.11184e6	+	1.92576e6i	0.275346	+	0.476914i	0.970222	−	0.242216i	$-0.0778741\pi$
$439$	1.11184e6	+	1.92576e6i	0.275346	+	0.476914i	−0.694876	+	0.719130i	$0.744541\pi$
$440$	359172.			0.0884444
$441$		0			0
$442$	5.73909e6			1.39729
$443$	−2.34213e6	−	4.05668e6i	−0.567024	−	0.982114i	−0.996858	−	0.0792062i	$-0.974761\pi$
$443$	−2.34213e6	−	4.05668e6i	−0.567024	−	0.982114i	0.429835	−	0.902908i	$-0.358572\pi$
$444$		0			0
$445$	−1.72487e6	+	2.98756e6i	−0.412910	+	0.715182i
$446$	−1.67540e6	−	2.90188e6i	−0.398824	−	0.690784i
$447$		0			0
$448$	−509685.	+	148984.i	−0.119979	+	0.0350707i
$449$	−897932.			−0.210198			−0.105099	−	0.994462i	$-0.533516\pi$
$449$	−897932.			−0.210198			−0.105099	+	0.994462i	$0.533516\pi$
$450$		0			0
$451$	−296306.	+	513217.i	−0.0685960	+	0.118812i
$452$	497400.	−	861522.i	0.114514	−	0.198344i
$453$		0			0
$454$	−5.32276e6			−1.21198
$455$	3.92129e6	+	3.74805e6i	0.887974	+	0.848745i
$456$		0			0
$457$	−2.99091e6	−	5.18040e6i	−0.669903	−	1.16031i	−0.977931	−	0.208929i	$-0.933002\pi$
$457$	−2.99091e6	−	5.18040e6i	−0.669903	−	1.16031i	0.308027	−	0.951377i	$-0.400331\pi$
$458$	2.02127e6	−	3.50094e6i	0.450256	−	0.779867i
$459$		0			0
$460$	−1.00587e6	−	1.74222e6i	−0.221639	−	0.383891i
$461$	−1.62507e6			−0.356138			−0.178069	−	0.984018i	$-0.556985\pi$
$461$	−1.62507e6			−0.356138			−0.178069	+	0.984018i	$0.556985\pi$
$462$		0			0
$463$	−8.46295e6			−1.83472			−0.917359	−	0.398060i	$-0.869683\pi$
$463$	−8.46295e6			−1.83472			−0.917359	+	0.398060i	$0.869683\pi$
$464$	−724068.	−	1.25412e6i	−0.156129	−	0.270424i
$465$		0			0
$466$	−2.97220e6	+	5.14800e6i	−0.634035	+	1.09818i
$467$	3.83297e6	+	6.63890e6i	0.813286	+	1.40865i	0.910552	+	0.413395i	$0.135657\pi$
$467$	3.83297e6	+	6.63890e6i	0.813286	+	1.40865i	−0.0972658	+	0.995258i	$0.531010\pi$
$468$		0			0
$469$	−1.32035e6	+	5.41383e6i	−0.277177	+	1.13651i
$470$	−1.60546e6			−0.335240
$471$		0			0
$472$	192331.	−	333127.i	0.0397370	−	0.0688265i
$473$	305098.	−	528445.i	0.0627027	−	0.108604i
$474$		0			0
$475$	510497.			0.103815
$476$	−1.85647e6	−	1.77446e6i	−0.375553	−	0.358962i
$477$		0			0
$478$	−1.75127e6	−	3.03330e6i	−0.350578	−	0.607219i
$479$	−1.20146e6	+	2.08099e6i	−0.239261	+	0.414412i	−0.960502	−	0.278272i	$-0.910238\pi$
$479$	−1.20146e6	+	2.08099e6i	−0.239261	+	0.414412i	0.721242	+	0.692683i	$0.243572\pi$
$480$		0			0
$481$	1.35192e6	+	2.34160e6i	0.266434	+	0.461477i
$482$	−5.81178e6			−1.13944
$483$		0			0
$484$	−2.19026e6			−0.424993
$485$	−270881.	−	469180.i	−0.0522907	−	0.0905701i
$486$		0			0
$487$	85150.8	−	147486.i	0.0162692	−	0.0281791i	−0.857776	−	0.514023i	$-0.828154\pi$
$487$	85150.8	−	147486.i	0.0162692	−	0.0281791i	0.874045	+	0.485844i	$0.161488\pi$
$488$	−474839.	−	822445.i	−0.0902603	−	0.156335i
$489$		0			0
$490$	−109600.	−	2.42483e6i	−0.0206215	−	0.456237i
$491$	5.77628e6			1.08130			0.540648	−	0.841249i	$-0.318179\pi$
$491$	5.77628e6			1.08130			0.540648	+	0.841249i	$0.318179\pi$
$492$		0			0
$493$	3.50177e6	−	6.06525e6i	0.648890	−	1.12391i
$494$	−649614.	+	1.12516e6i	−0.119767	+	0.207443i
$495$		0			0
$496$	−592564.			−0.108151
$497$	−2.48402e6	+	726095.i	−0.451091	+	0.131857i
$498$		0			0
$499$	−271801.	−	470773.i	−0.0488652	−	0.0846369i	0.840558	−	0.541721i	$-0.182227\pi$
$499$	−271801.	−	470773.i	−0.0488652	−	0.0846369i	−0.889423	+	0.457084i	$0.848894\pi$
$500$	1.42874e6	−	2.47464e6i	0.255580	−	0.442678i
$501$		0			0
$502$	396769.	+	687223.i	0.0702713	+	0.121713i
$503$	5.40086e6			0.951794			0.475897	−	0.879501i	$-0.342124\pi$
$503$	5.40086e6			0.951794			0.475897	+	0.879501i	$0.342124\pi$
$504$		0			0
$505$	−970378.			−0.169322
$506$	−1.08257e6	−	1.87506e6i	−0.187966	−	0.325567i
$507$		0			0
$508$	−508402.	+	880579.i	−0.0874074	+	0.151394i
$509$	4.17209e6	+	7.22628e6i	0.713772	+	1.23629i	0.963431	+	0.267955i	$0.0863480\pi$
$509$	4.17209e6	+	7.22628e6i	0.713772	+	1.23629i	−0.249659	+	0.968334i	$0.580319\pi$
$510$		0			0
$511$	1.39919e6	−	5.73710e6i	0.237042	−	0.971942i
$512$	−262144.			−0.0441942
$513$		0			0
$514$	−959144.	+	1.66129e6i	−0.160131	+	0.277355i
$515$	937213.	−	1.62330e6i	0.155711	−	0.269700i
$516$		0			0
$517$	−1.72788e6			−0.284307
$518$	286676.	−	1.17546e6i	0.0469426	−	0.192478i
$519$		0			0
$520$	1.33893e6	+	2.31910e6i	0.217145	+	0.376106i
$521$	−5.73919e6	+	9.94057e6i	−0.926310	+	1.60442i	−0.136870	+	0.990589i	$0.543704\pi$
$521$	−5.73919e6	+	9.94057e6i	−0.926310	+	1.60442i	−0.789441	+	0.613827i	$0.789629\pi$
$522$		0			0
$523$	2.19367e6	+	3.79955e6i	0.350685	+	0.607404i	0.986370	−	0.164545i	$-0.0526155\pi$
$523$	2.19367e6	+	3.79955e6i	0.350685	+	0.607404i	−0.635685	+	0.771949i	$0.719282\pi$
$524$	−2.18075e6			−0.346959
$525$		0			0
$526$	1.81977e6			0.286782
$527$	−1.43289e6	−	2.48184e6i	−0.224744	−	0.389267i
$528$		0			0
$529$	−2.84535e6	+	4.92829e6i	−0.442075	+	0.765697i
$530$	807769.	+	1.39910e6i	0.124910	+	0.216350i
$531$		0			0
$532$	558023.	−	163114.i	0.0854817	−	0.0249869i
$533$	−4.41832e6			−0.673657
$534$		0			0
$535$	−450864.	+	780919.i	−0.0681022	+	0.117956i
$536$	−1.37548e6	+	2.38241e6i	−0.206797	+	0.358182i
$537$		0			0
$538$	−3.44055e6			−0.512474
$539$	−117957.	−	2.60973e6i	−0.0174885	−	0.386922i
$540$		0			0
$541$	−3.61153e6	−	6.25535e6i	−0.530515	−	0.918879i	−0.999366	−	0.0356020i	$-0.988665\pi$
$541$	−3.61153e6	−	6.25535e6i	−0.530515	−	0.918879i	0.468851	−	0.883277i	$-0.344668\pi$
$542$	2.61116e6	−	4.52266e6i	0.381799	−	0.661296i
$543$		0			0
$544$	−633897.	−	1.09794e6i	−0.0918378	−	0.159068i
$545$	−131285.			−0.0189332
$546$		0			0
$547$	3.54529e6			0.506622			0.253311	−	0.967385i	$-0.418480\pi$
$547$	3.54529e6			0.506622			0.253311	+	0.967385i	$0.418480\pi$
$548$	2.68243e6	+	4.64610e6i	0.381572	+	0.660902i
$549$		0			0
$550$	566214.	−	980712.i	0.0798131	−	0.138240i
$551$	792739.	+	1.37306e6i	0.111237	+	0.192669i
$552$		0			0
$553$	1.02144e7	+	9.76319e6i	1.42037	+	1.35762i
$554$	2.17243e6			0.300727
$555$		0			0
$556$	−465562.	+	806377.i	−0.0638691	+	0.110624i
$557$	5.18314e6	−	8.97747e6i	0.707873	−	1.22607i	−0.257772	−	0.966206i	$-0.582988\pi$
$557$	5.18314e6	−	8.97747e6i	0.707873	−	1.22607i	0.965645	−	0.259866i	$-0.0836783\pi$
$558$		0			0
$559$	4.54941e6			0.615780
$560$	283921.	−	1.16416e6i	0.0382585	−	0.156871i
$561$		0			0
$562$	−1.99618e6	−	3.45748e6i	−0.266599	−	0.461763i
$563$	−2.24141e6	+	3.88223e6i	−0.298023	+	0.516191i	−0.975684	−	0.219184i	$-0.929661\pi$
$563$	−2.24141e6	+	3.88223e6i	−0.298023	+	0.516191i	0.677660	+	0.735375i	$0.262994\pi$
$564$		0			0
$565$	1.12243e6	+	1.94411e6i	0.147924	+	0.256212i
$566$	−7.10928e6			−0.932792
$567$		0			0
$568$	−1.27760e6			−0.166158
$569$	3.24668e6	+	5.62341e6i	0.420396	+	0.728147i	0.995978	−	0.0895969i	$-0.0285579\pi$
$569$	3.24668e6	+	5.62341e6i	0.420396	+	0.728147i	−0.575582	+	0.817744i	$0.695225\pi$
$570$		0			0
$571$	248754.	−	430854.i	0.0319286	−	0.0553019i	−0.849620	−	0.527396i	$-0.823168\pi$
$571$	248754.	−	430854.i	0.0319286	−	0.0553019i	0.881548	+	0.472094i	$0.156502\pi$
$572$	1.44103e6	+	2.49593e6i	0.184155	+	0.318965i
$573$		0			0
$574$	1.42923e6	+	1.36609e6i	0.181060	+	0.173061i
$575$	−6.34279e6			−0.800038
$576$		0			0
$577$	3.27561e6	−	5.67353e6i	0.409594	−	0.709437i	−0.585250	−	0.810853i	$-0.699004\pi$
$577$	3.27561e6	−	5.67353e6i	0.409594	−	0.709437i	0.994844	+	0.101416i	$0.0323372\pi$
$578$	225973.	−	391397.i	0.0281343	−	0.0487301i
$579$		0			0
$580$	3.26786e6			0.403360
$581$	6.94707e6	−	2.03067e6i	0.853810	−	0.249574i
$582$		0			0
$583$	869363.	+	1.50578e6i	0.105933	+	0.183481i
$584$	1.45762e6	−	2.52467e6i	0.176853	−	0.306318i
$585$		0			0
$586$	3.27974e6	+	5.68067e6i	0.394543	+	0.683369i
$587$	30793.5			0.00368862			0.00184431	−	0.999998i	$-0.499413\pi$
$587$	30793.5			0.00368862			0.00184431	+	0.999998i	$0.499413\pi$
$588$		0			0
$589$	648763.			0.0770544
$590$	434014.	+	751735.i	0.0513303	+	0.0889067i
$591$		0			0
$592$	298646.	−	517271.i	0.0350230	−	0.0606616i
$593$	285468.	+	494446.i	0.0333366	+	0.0577407i	0.882212	−	0.470852i	$-0.156053\pi$
$593$	285468.	+	494446.i	0.0333366	+	0.0577407i	−0.848876	+	0.528592i	$0.822720\pi$
$594$		0			0
$595$	5.56243e6	−	1.62593e6i	0.644128	−	0.188283i
$596$	−4.52893e6			−0.522251
$597$		0			0
$598$	8.07127e6	−	1.39799e7i	0.922973	−	1.59864i
$599$	4.53555e6	−	7.85581e6i	0.516492	−	0.894590i	−0.483325	−	0.875441i	$-0.660571\pi$
$599$	4.53555e6	−	7.85581e6i	0.516492	−	0.894590i	0.999817	−	0.0191488i	$-0.00609561\pi$
$600$		0			0
$601$	−1.36309e7			−1.53936			−0.769679	−	0.638431i	$-0.779584\pi$
$601$	−1.36309e7			−1.53936			−0.769679	+	0.638431i	$0.779584\pi$
$602$	−1.47164e6	−	1.40662e6i	−0.165504	−	0.158193i
$603$		0			0
$604$	1.93246e6	+	3.34712e6i	0.215535	+	0.373318i
$605$	2.47126e6	−	4.28035e6i	0.274493	−	0.475435i
$606$		0			0
$607$	1.97825e6	+	3.42644e6i	0.217927	+	0.377460i	0.954174	−	0.299253i	$-0.0967373\pi$
$607$	1.97825e6	+	3.42644e6i	0.217927	+	0.377460i	−0.736247	+	0.676713i	$0.763404\pi$
$608$	287006.			0.0314870
$609$		0			0
$610$	2.14304e6			0.233188
$611$	−6.44126e6	−	1.11566e7i	−0.698020	−	1.20901i
$612$		0			0
$613$	−661552.	+	1.14584e6i	−0.0711070	+	0.123161i	−0.899387	−	0.437154i	$-0.855987\pi$
$613$	−661552.	+	1.14584e6i	−0.0711070	+	0.123161i	0.828280	+	0.560315i	$0.189320\pi$
$614$	4.76261e6	+	8.24908e6i	0.509828	+	0.883049i
$615$		0			0
$616$	305571.	−	1.25293e6i	0.0324459	−	0.133038i
$617$	−9.26370e6			−0.979651			−0.489826	−	0.871820i	$-0.662940\pi$
$617$	−9.26370e6			−0.979651			−0.489826	+	0.871820i	$0.662940\pi$
$618$		0			0
$619$	−334693.	+	579705.i	−0.0351091	+	0.0608107i	−0.883046	−	0.469286i	$-0.844511\pi$
$619$	−334693.	+	579705.i	−0.0351091	+	0.0608107i	0.847937	+	0.530097i	$0.177845\pi$
$620$	668589.	−	1.15803e6i	0.0698521	−	0.120987i
$621$		0			0
$622$	−4.98051e6			−0.516176
$623$	8.95430e6	+	8.55872e6i	0.924297	+	0.883463i
$624$		0			0
$625$	378164.	+	654999.i	0.0387240	+	0.0670719i
$626$	3.32598e6	−	5.76077e6i	0.339222	−	0.587550i
$627$		0			0
$628$	1.71223e6	+	2.96567e6i	0.173246	+	0.300071i
$629$	2.88866e6			0.291118
$630$		0			0
$631$	−666246.			−0.0666133			−0.0333067	−	0.999445i	$-0.510604\pi$
$631$	−666246.			−0.0666133			−0.0333067	+	0.999445i	$0.510604\pi$
$632$	3.48774e6	+	6.04095e6i	0.347338	+	0.601607i
$633$		0			0
$634$	5.24972e6	−	9.09277e6i	0.518696	−	0.898407i
$635$	−1.14726e6	−	1.98711e6i	−0.112909	−	0.195564i
$636$		0			0
$637$	1.64108e7	−	1.04903e7i	1.60243	−	1.02432i
$638$	3.51704e6			0.342078
$639$		0			0
$640$	295777.	−	512300.i	0.0285439	−	0.0494396i
$641$	−1.05439e6	+	1.82625e6i	−0.101357	+	0.175556i	−0.912244	−	0.409647i	$-0.865652\pi$
$641$	−1.05439e6	+	1.82625e6i	−0.101357	+	0.175556i	0.810887	+	0.585203i	$0.198985\pi$
$642$		0			0
$643$	1.25977e7			1.20161			0.600806	−	0.799395i	$-0.294846\pi$
$643$	1.25977e7			1.20161			0.600806	+	0.799395i	$0.294846\pi$
$644$	−6.93328e6	+	2.02664e6i	−0.658756	+	0.192558i
$645$		0			0
$646$	694016.	+	1.20207e6i	0.0654317	+	0.113331i
$647$	8.56496e6	−	1.48349e7i	0.804386	−	1.39324i	−0.112319	−	0.993672i	$-0.535828\pi$
$647$	8.56496e6	−	1.48349e7i	0.804386	−	1.39324i	0.916705	−	0.399565i	$-0.130839\pi$
$648$		0			0
$649$	467109.	+	809056.i	0.0435318	+	0.0753992i
$650$	8.44301e6			0.783815
$651$		0			0
$652$	1.03146e6			0.0950237
$653$	−4.12762e6	−	7.14925e6i	−0.378806	−	0.656112i	0.612083	−	0.790794i	$-0.290332\pi$
$653$	−4.12762e6	−	7.14925e6i	−0.378806	−	0.656112i	−0.990889	+	0.134682i	$0.956999\pi$
$654$		0			0
$655$	2.46054e6	−	4.26178e6i	0.224092	−	0.388139i
$656$	488014.	+	845265.i	0.0442764	+	0.0766890i
$657$		0			0
$658$	−1.36587e6	+	5.60048e6i	−0.122983	+	0.504267i
$659$	1.05417e7			0.945581			0.472790	−	0.881175i	$-0.343247\pi$
$659$	1.05417e7			0.945581			0.472790	+	0.881175i	$0.343247\pi$
$660$		0			0
$661$	−2.23820e6	+	3.87668e6i	−0.199249	+	0.345109i	−0.948285	−	0.317420i	$-0.897184\pi$
$661$	−2.23820e6	+	3.87668e6i	−0.199249	+	0.345109i	0.749036	+	0.662529i	$0.230517\pi$
$662$	3.47771e6	−	6.02357e6i	0.308424	−	0.534206i
$663$		0			0
$664$	3.57306e6			0.314499
$665$	−310848.	+	1.27457e6i	−0.0272580	+	0.111766i
$666$		0			0
$667$	−9.84956e6	−	1.70599e7i	−0.857240	−	1.48478i
$668$	−3.54155e6	+	6.13415e6i	−0.307081	+	0.531880i
$669$		0			0
$670$	−3.10391e6	−	5.37614e6i	−0.267130	−	0.462683i
$671$	2.30645e6			0.197760
$672$		0			0
$673$	−1.87165e7			−1.59289			−0.796447	−	0.604708i	$-0.793290\pi$
$673$	−1.87165e7			−1.59289			−0.796447	+	0.604708i	$0.793290\pi$
$674$	1.70713e6	+	2.95683e6i	0.144749	+	0.250713i
$675$		0			0
$676$	−7.77348e6	+	1.34641e7i	−0.654258	+	1.13321i
$677$	2.08116e6	+	3.60467e6i	0.174515	+	0.302270i	0.939993	−	0.341192i	$-0.110831\pi$
$677$	2.08116e6	+	3.60467e6i	0.174515	+	0.302270i	−0.765478	+	0.643462i	$0.777497\pi$
$678$		0			0
$679$	−1.86714e6	+	545776.i	−0.155418	+	0.0454297i
$680$	2.86090e6			0.237263
$681$		0			0
$682$	719570.	−	1.24633e6i	0.0592396	−	0.102606i
$683$	−6.43455e6	+	1.11450e7i	−0.527796	+	0.914170i	0.471679	+	0.881770i	$0.343648\pi$
$683$	−6.43455e6	+	1.11450e7i	−0.527796	+	0.914170i	−0.999475	+	0.0323992i	$0.989685\pi$
$684$		0			0
$685$	−1.21063e7			−0.985793
$686$	−8.55199e6	−	1.68063e6i	−0.693836	−	0.136352i
$687$		0			0
$688$	−502494.	−	870345.i	−0.0404725	−	0.0701004i
$689$	−6.48168e6	+	1.12266e7i	−0.520163	+	0.900949i
$690$		0			0
$691$	4.64518e6	+	8.04569e6i	0.370090	+	0.641015i	0.989579	−	0.143990i	$-0.0459934\pi$
$691$	4.64518e6	+	8.04569e6i	0.370090	+	0.641015i	−0.619489	+	0.785006i	$0.712660\pi$
$692$	1.25758e6			0.0998325
$693$		0			0
$694$	−1.19400e7			−0.941033
$695$	−1.05059e6	−	1.81967e6i	−0.0825029	−	0.142899i
$696$		0			0
$697$	−2.36016e6	+	4.08791e6i	−0.184018	+	0.318728i
$698$	5.74934e6	+	9.95815e6i	0.446662	+	0.773642i
$699$		0			0
$700$	−2.73113e6	−	2.61048e6i	−0.210668	−	0.201361i
$701$	−2.50809e7			−1.92774			−0.963870	−	0.266375i	$-0.914174\pi$
$701$	−2.50809e7			−1.92774			−0.963870	+	0.266375i	$0.914174\pi$
$702$		0			0
$703$	−326970.	+	566329.i	−0.0249528	+	0.0432196i
$704$	318330.	−	551364.i	0.0242073	−	0.0419283i
$705$		0			0
$706$	5.88437e6			0.444312
$707$	−825564.	+	3.38505e6i	−0.0621158	+	0.254693i
$708$		0			0
$709$	−4.96890e6	−	8.60639e6i	−0.371231	−	0.642991i	0.618524	−	0.785766i	$-0.287731\pi$
$709$	−4.96890e6	−	8.60639e6i	−0.371231	−	0.642991i	−0.989755	+	0.142774i	$0.954398\pi$
$710$	1.44151e6	−	2.49677e6i	0.107318	−	0.185880i
$711$		0			0
$712$	3.05747e6	+	5.29569e6i	0.226028	+	0.391491i
$713$	−8.06069e6			−0.593811
$714$		0			0
$715$	−6.50364e6			−0.475764
$716$	−4.08342e6	−	7.07269e6i	−0.297674	−	0.515587i
$717$		0			0
$718$	−6.15598e6	+	1.06625e7i	−0.445642	+	0.771875i
$719$	−7.00047e6	−	1.21252e7i	−0.505016	−	0.874713i	−0.999983	−	0.00580117i	$-0.998153\pi$
$719$	−7.00047e6	−	1.21252e7i	−0.505016	−	0.874713i	0.494968	−	0.868911i	$-0.335180\pi$
$720$		0			0
$721$	−4.86536e6	−	4.65041e6i	−0.348559	−	0.333160i
$722$	9.59017e6			0.684673
$723$		0			0
$724$	176414.	−	305559.i	0.0125080	−	0.0216645i
$725$	5.15160e6	−	8.92283e6i	0.363996	−	0.630460i
$726$		0			0
$727$	8.27315e6			0.580544			0.290272	−	0.956944i	$-0.406254\pi$
$727$	8.27315e6			0.580544			0.290272	+	0.956944i	$0.406254\pi$
$728$	9.22903e6	−	2.69770e6i	0.645398	−	0.188654i
$729$		0			0
$730$	3.28926e6	+	5.69716e6i	0.228450	+	0.395687i
$731$	2.43019e6	−	4.20921e6i	0.168208	−	0.291345i
$732$		0			0
$733$	1.64295e6	+	2.84568e6i	0.112945	+	0.195626i	0.916956	−	0.398988i	$-0.130638\pi$
$733$	1.64295e6	+	2.84568e6i	0.112945	+	0.195626i	−0.804012	+	0.594614i	$0.797305\pi$
$734$	−6.46679e6			−0.443046
$735$		0			0
$736$	−3.56597e6			−0.242651
$737$	−3.34059e6	−	5.78608e6i	−0.226545	−	0.392388i
$738$		0			0
$739$	−5.04564e6	+	8.73930e6i	−0.339864	+	0.588662i	−0.984407	−	0.175907i	$-0.943714\pi$
$739$	−5.04564e6	+	8.73930e6i	−0.339864	+	0.588662i	0.644543	+	0.764568i	$0.277048\pi$
$740$	673925.	+	1.16727e6i	0.0452410	+	0.0783597i
$741$		0			0
$742$	5.56781e6	−	1.62751e6i	0.371257	−	0.108521i
$743$	−1.73443e7			−1.15261			−0.576307	−	0.817233i	$-0.695507\pi$
$743$	−1.73443e7			−1.15261			−0.576307	+	0.817233i	$0.695507\pi$
$744$		0			0
$745$	5.10998e6	−	8.85074e6i	0.337309	−	0.584237i
$746$	−9.52237e6	+	1.64932e7i	−0.626467	+	1.08507i
$747$		0			0
$748$	3.07905e6			0.201216
$749$	2.34057e6	+	2.23717e6i	0.152446	+	0.145711i
$750$		0			0
$751$	8.79857e6	+	1.52396e7i	0.569262	+	0.985990i	0.996639	+	0.0819170i	$0.0261042\pi$
$751$	8.79857e6	+	1.52396e7i	0.569262	+	0.985990i	−0.427377	+	0.904073i	$0.640562\pi$
$752$	−1.42291e6	+	2.46455e6i	−0.0917554	+	0.158925i
$753$		0			0
$754$	1.31109e7	+	2.27088e7i	0.839857	+	1.45468i
$755$	−8.72158e6			−0.556836
$756$		0			0
$757$	−4.66480e6			−0.295865			−0.147932	−	0.988997i	$-0.547262\pi$
$757$	−4.66480e6			−0.295865			−0.147932	+	0.988997i	$0.547262\pi$
$758$	2.00386e6	+	3.47079e6i	0.126676	+	0.219409i
$759$		0			0
$760$	−323828.	+	560887.i	−0.0203367	+	0.0352242i
$761$	9.13585e6	+	1.58238e7i	0.571857	+	0.990485i	0.996375	+	0.0850658i	$0.0271101\pi$
$761$	9.13585e6	+	1.58238e7i	0.571857	+	0.990485i	−0.424518	+	0.905419i	$0.639557\pi$
$762$		0			0
$763$	−111693.	+	457973.i	−0.00694566	+	0.0284792i
$764$	8.93044e6			0.553528
$765$		0			0
$766$	5.64305e6	−	9.77404e6i	0.347489	−	0.601869i
$767$	−3.48261e6	+	6.03205e6i	−0.213755	+	0.370234i
$768$		0			0
$769$	−2.31895e7			−1.41409			−0.707043	−	0.707171i	$-0.749971\pi$
$769$	−2.31895e7			−1.41409			−0.707043	+	0.707171i	$0.749971\pi$
$770$	2.10379e6	+	2.01085e6i	0.127872	+	0.122223i
$771$		0			0
$772$	394530.	+	683346.i	0.0238252	+	0.0412665i
$773$	1.01074e6	−	1.75066e6i	0.0608405	−	0.105379i	−0.834001	−	0.551763i	$-0.813955\pi$
$773$	1.01074e6	−	1.75066e6i	0.0608405	−	0.105379i	0.894841	+	0.446384i	$0.147289\pi$
$774$		0			0
$775$	−2.10799e6	−	3.65114e6i	−0.126070	−	0.218360i
$776$	−960317.			−0.0572480
$777$		0			0
$778$	−4.96959e6			−0.294355
$779$	−534297.	−	925430.i	−0.0315456	−	0.0546387i
$780$		0			0
$781$	1.55143e6	−	2.68715e6i	0.0910131	−	0.157639i
$782$	−8.62296e6	−	1.49354e7i	−0.504243	−	0.873374i
$783$		0			0
$784$	−3.81949e6	−	1.98085e6i	−0.221930	−	0.115097i
$785$	−7.72763e6			−0.447582
$786$		0			0
$787$	−7.88722e6	+	1.36611e7i	−0.453928	+	0.786227i	−0.998626	−	0.0524059i	$-0.983311\pi$
$787$	−7.88722e6	+	1.36611e7i	−0.453928	+	0.786227i	0.544698	+	0.838632i	$0.316644\pi$
$788$	−7.53207e6	+	1.30459e7i	−0.432114	+	0.748444i
$789$		0			0
$790$	−1.57409e7			−0.897348
$791$	7.73672e6	−	2.26149e6i	0.439659	−	0.128515i
$792$		0			0
$793$	8.59807e6	+	1.48923e7i	0.485532	+	0.840966i
$794$	5.49124e6	−	9.51111e6i	0.309115	−	0.535402i
$795$		0			0
$796$	−5.12010e6	−	8.86827e6i	−0.286415	−	0.496085i
$797$	−1.22436e6			−0.0682750			−0.0341375	−	0.999417i	$-0.510868\pi$
$797$	−1.22436e6			−0.0682750			−0.0341375	+	0.999417i	$0.510868\pi$
$798$		0			0
$799$	−1.37631e7			−0.762690
$800$	−932551.	−	1.61523e6i	−0.0515167	−	0.0892295i
$801$		0			0
$802$	7.42670e6	−	1.28634e7i	0.407718	−	0.706189i
$803$	3.54007e6	+	6.13158e6i	0.193742	+	0.335571i
$804$		0			0
$805$	3.86221e6	−	1.58362e7i	0.210061	−	0.861312i
$806$	1.07297e7			0.581771
$807$		0			0
$808$	−860037.	+	1.48963e6i	−0.0463435	+	0.0802692i
$809$	−1.38662e7	+	2.40170e7i	−0.744882	+	1.29017i	0.205368	+	0.978685i	$0.434161\pi$
$809$	−1.38662e7	+	2.40170e7i	−0.744882	+	1.29017i	−0.950250	+	0.311489i	$0.899172\pi$
$810$		0			0
$811$	−1.19246e7			−0.636636			−0.318318	−	0.947984i	$-0.603118\pi$
$811$	−1.19246e7			−0.636636			−0.318318	+	0.947984i	$0.603118\pi$
$812$	2.78018e6	−	1.13996e7i	0.147973	−	0.606734i
$813$		0			0
$814$	725313.	+	1.25628e6i	0.0383676	+	0.0664546i
$815$	−1.16379e6	+	2.01575e6i	−0.0613735	+	0.106302i
$816$		0			0
$817$	550151.	+	952889.i	0.0288354	+	0.0499444i
$818$	−1.50376e7			−0.785770
$819$		0			0
$820$	−2.20250e6			−0.114388
$821$	8.02312e6	+	1.38965e7i	0.415418	+	0.719525i	0.995472	−	0.0950526i	$-0.0303019\pi$
$821$	8.02312e6	+	1.38965e7i	0.415418	+	0.719525i	−0.580054	+	0.814578i	$0.696969\pi$
$822$		0			0
$823$	5.61533e6	−	9.72603e6i	0.288985	−	0.500537i	−0.684583	−	0.728935i	$-0.740016\pi$
$823$	5.61533e6	−	9.72603e6i	0.288985	−	0.500537i	0.973568	+	0.228398i	$0.0733489\pi$
$824$	−1.66129e6	−	2.87743e6i	−0.0852367	−	0.147634i
$825$		0			0
$826$	2.99159e6	−	874460.i	0.152564	−	0.0445954i
$827$	2.68427e7			1.36478			0.682389	−	0.730989i	$-0.260941\pi$
$827$	2.68427e7			1.36478			0.682389	+	0.730989i	$0.260941\pi$
$828$		0			0
$829$	−1.40210e7	+	2.42850e7i	−0.708584	+	1.22730i	0.256798	+	0.966465i	$0.417332\pi$
$829$	−1.40210e7	+	2.42850e7i	−0.708584	+	1.22730i	−0.965382	+	0.260839i	$0.916001\pi$
$830$	−4.03147e6	+	6.98272e6i	−0.203127	+	0.351827i
$831$		0			0
$832$	4.74673e6			0.237731
$833$	−939564.	−	2.07872e7i	−0.0469152	−	1.03797i
$834$		0			0
$835$	−7.99186e6	−	1.38423e7i	−0.396672	−	0.687056i
$836$	−348521.	+	603656.i	−0.0172470	+	0.0298727i
$837$		0			0
$838$	−9.20054e6	−	1.59358e7i	−0.452588	−	0.783905i
$839$	3.30603e7			1.62145			0.810723	−	0.585430i	$-0.199074\pi$
$839$	3.30603e7			1.62145			0.810723	+	0.585430i	$0.199074\pi$
$840$		0			0
$841$	1.14880e7			0.560086
$842$	−809728.	−	1.40249e6i	−0.0393604	−	0.0681741i
$843$		0			0
$844$	−7.37495e6	+	1.27738e7i	−0.356372	+	0.617254i
$845$	−1.75416e7	−	3.03830e7i	−0.845139	−	1.46382i
$846$		0			0
$847$	−1.28291e7	−	1.22623e7i	−0.614450	−	0.587305i
$848$	2.86367e6			0.136752
$849$		0			0
$850$	4.51005e6	−	7.81164e6i	0.214109	−	0.370847i
$851$	4.06251e6	−	7.03648e6i	0.192296	−	0.333067i
$852$		0			0
$853$	2.73897e7			1.28889			0.644444	−	0.764652i	$-0.277089\pi$
$853$	2.73897e7			1.28889			0.644444	+	0.764652i	$0.277089\pi$
$854$	1.82322e6	−	7.47575e6i	0.0855452	−	0.350760i
$855$		0			0
$856$	799192.	+	1.38424e6i	0.0372792	+	0.0645695i
$857$	−1.48360e6	+	2.56968e6i	−0.0690027	+	0.119516i	−0.898463	−	0.439050i	$-0.855315\pi$
$857$	−1.48360e6	+	2.56968e6i	−0.0690027	+	0.119516i	0.829460	+	0.558566i	$0.188648\pi$
$858$		0			0
$859$	1.98980e7	+	3.44643e7i	0.920081	+	1.59363i	0.799287	+	0.600949i	$0.205211\pi$
$859$	1.98980e7	+	3.44643e7i	0.920081	+	1.59363i	0.120794	+	0.992678i	$0.461456\pi$
$860$	2.26785e6			0.104561
$861$		0			0
$862$	379034.			0.0173744
$863$	3.59799e6	+	6.23190e6i	0.164450	+	0.284835i	0.936460	−	0.350775i	$-0.114082\pi$
$863$	3.59799e6	+	6.23190e6i	0.164450	+	0.284835i	−0.772010	+	0.635610i	$0.780749\pi$
$864$		0			0
$865$	−1.41893e6	+	2.45766e6i	−0.0644794	+	0.111682i
$866$	8.63453e6	+	1.49554e7i	0.391241	+	0.677649i
$867$		0			0
$868$	−3.47084e6	−	3.31751e6i	−0.156364	−	0.149456i
$869$	−1.69411e7			−0.761015
$870$		0			0
$871$	2.49063e7	−	4.31391e7i	1.11241	−	1.92675i
$872$	−116357.	+	201536.i	−0.00518203	+	0.00897554i
$873$		0			0
$874$	3.90417e6			0.172882
$875$	2.22231e7	−	6.49594e6i	0.981259	−	0.286828i
$876$		0			0
$877$	−1.25621e7	−	2.17582e7i	−0.551523	−	0.955266i	−0.998165	−	0.0605532i	$-0.980714\pi$
$877$	−1.25621e7	−	2.17582e7i	−0.551523	−	0.955266i	0.446642	−	0.894713i	$-0.352620\pi$
$878$	−4.44734e6	+	7.70303e6i	−0.194699	+	0.337229i
$879$		0			0
$880$	718343.	+	1.24421e6i	0.0312698	+	0.0541609i
$881$	−120262.			−0.00522022			−0.00261011	−	0.999997i	$-0.500831\pi$
$881$	−120262.			−0.00522022			−0.00261011	+	0.999997i	$0.500831\pi$
$882$		0			0
$883$	2.43497e7			1.05097			0.525487	−	0.850802i	$-0.323883\pi$
$883$	2.43497e7			1.05097			0.525487	+	0.850802i	$0.323883\pi$
$884$	1.14782e7	+	1.98808e7i	0.494018	+	0.855664i
$885$		0			0
$886$	9.36851e6	−	1.62267e7i	0.400946	−	0.694459i
$887$	−1.41383e7	−	2.44883e7i	−0.603377	−	1.04508i	−0.992306	−	0.123812i	$-0.960488\pi$
$887$	−1.41383e7	−	2.44883e7i	−0.603377	−	1.04508i	0.388929	−	0.921268i	$-0.372845\pi$
$888$		0			0
$889$	−7.90786e6	+	2.31152e6i	−0.335587	+	0.0980941i
$890$	−1.37989e7			−0.583943
$891$		0			0
$892$	6.70160e6	−	1.16075e7i	0.282011	−	0.488458i
$893$	1.55786e6	−	2.69828e6i	0.0653730	−	0.113229i
$894$		0			0
$895$	1.84293e7			0.769042
$896$	−1.53547e6	−	1.46763e6i	−0.0638955	−	0.0610727i
$897$		0			0
$898$	−1.79586e6	−	3.11053e6i	−0.0743161	−	0.128719i
$899$	6.54688e6	−	1.13395e7i	0.270169	−	0.467946i
$900$		0			0
$901$	6.92471e6	+	1.19940e7i	0.284178	+	0.492210i
$902$	−2.37045e6			−0.0970094
$903$		0			0
$904$	3.97920e6			0.161948
$905$	398096.	+	689523.i	0.0161572	+	0.0279851i
$906$		0			0
$907$	1.21584e7	−	2.10590e7i	0.490748	−	0.850000i	−0.509195	−	0.860651i	$-0.670057\pi$
$907$	1.21584e7	−	2.10590e7i	0.490748	−	0.850000i	0.999943	+	0.0106507i	$0.00339029\pi$
$908$	−1.06455e7	−	1.84386e7i	−0.428501	−	0.742186i
$909$		0			0
$910$	−5.14106e6	+	2.10798e7i	−0.205802	+	0.843847i
$911$	3.36224e7			1.34225			0.671123	−	0.741346i	$-0.265812\pi$
$911$	3.36224e7			1.34225			0.671123	+	0.741346i	$0.265812\pi$
$912$		0			0
$913$	−4.33888e6	+	7.51517e6i	−0.172267	+	0.298374i
$914$	1.19636e7	−	2.07216e7i	0.473693	−	0.820461i
$915$		0			0
$916$	1.61701e7			0.636759
$917$	−1.27734e7	−	1.22091e7i	−0.501629	−	0.479468i
$918$		0			0
$919$	4.06874e6	+	7.04727e6i	0.158917	+	0.275253i	0.934479	−	0.356019i	$-0.115866\pi$
$919$	4.06874e6	+	7.04727e6i	0.158917	+	0.275253i	−0.775561	+	0.631272i	$0.782533\pi$
$920$	4.02348e6	−	6.96887e6i	0.156723	−	0.271452i
$921$		0			0
$922$	−3.25013e6	−	5.62939e6i	−0.125914	−	0.218089i
$923$	2.31338e7			0.893807
$924$		0			0
$925$	4.24962e6			0.163304
$926$	−1.69259e7	−	2.93165e7i	−0.648671	−	1.12353i
$927$		0			0
$928$	2.89627e6	−	5.01649e6i	0.110400	−	0.191219i
$929$	1.79027e7	+	3.10084e7i	0.680580	+	1.17880i	0.974804	+	0.223063i	$0.0716054\pi$
$929$	1.79027e7	+	3.10084e7i	0.680580	+	1.17880i	−0.294224	+	0.955736i	$0.595061\pi$
$930$		0			0
$931$	4.18173e6	+	2.16872e6i	0.158118	+	0.0820029i
$932$	−2.37776e7			−0.896661
$933$		0			0
$934$	−1.53319e7	+	2.65556e7i	−0.575080	+	0.996068i
$935$	−3.47409e6	+	6.01730e6i	−0.129961	+	0.225098i
$936$		0			0
$937$	4.65849e7			1.73339			0.866694	−	0.498840i	$-0.166241\pi$
$937$	4.65849e7			1.73339			0.866694	+	0.498840i	$0.166241\pi$
$938$	−2.13947e7	+	6.25382e6i	−0.793963	+	0.232080i
$939$		0			0
$940$	−3.21093e6	−	5.56149e6i	−0.118525	−	0.205292i
$941$	−1.03362e6	+	1.79029e6i	−0.0380529	+	0.0659096i	−0.884425	−	0.466683i	$-0.845449\pi$
$941$	−1.03362e6	+	1.79029e6i	−0.0380529	+	0.0659096i	0.846372	+	0.532593i	$0.178782\pi$
$942$		0			0
$943$	6.63850e6	+	1.14982e7i	0.243103	+	0.421067i
$944$	1.53865e6			0.0561966
$945$		0			0
$946$	2.44078e6			0.0886750
$947$	1.18386e7	+	2.05051e7i	0.428970	+	0.742998i	0.996782	−	0.0801602i	$-0.0255432\pi$
$947$	1.18386e7	+	2.05051e7i	0.428970	+	0.742998i	−0.567812	+	0.823158i	$0.692210\pi$
$948$		0			0
$949$	−2.63936e7	+	4.57150e7i	−0.951334	+	1.64776i
$950$	1.02099e6	+	1.76841e6i	0.0367041	+	0.0635734i
$951$		0			0
$952$	2.43396e6	−	9.97993e6i	0.0870403	−	0.356891i
$953$	3.40521e6			0.121454			0.0607270	−	0.998154i	$-0.480658\pi$
$953$	3.40521e6			0.121454			0.0607270	+	0.998154i	$0.480658\pi$
$954$		0			0
$955$	−1.00762e7	+	1.74525e7i	−0.357510	+	0.619226i
$956$	7.00510e6	−	1.21332e7i	0.247896	−	0.429368i
$957$		0			0
$958$	−9.61170e6			−0.338366
$959$	−1.02996e7	+	4.22315e7i	−0.361639	+	1.48283i
$960$		0			0
$961$	1.16357e7	+	2.01535e7i	0.406427	+	0.703952i
$962$	−5.40769e6	+	9.36639e6i	−0.188397	+	0.326313i
$963$		0			0
$964$	−1.16236e7	−	2.01326e7i	−0.402853	−	0.697762i
$965$	−1.78059e6			−0.0615525
$966$		0			0
$967$	1.44238e6			0.0496036			0.0248018	−	0.999692i	$-0.492105\pi$
$967$	1.44238e6			0.0496036			0.0248018	+	0.999692i	$0.492105\pi$
$968$	−4.38051e6	−	7.58727e6i	−0.150258	−	0.260254i
$969$		0			0
$970$	1.08352e6	−	1.87672e6i	0.0369751	−	0.0640427i
$971$	−2.57977e6	−	4.46830e6i	−0.0878078	−	0.152088i	0.818776	−	0.574113i	$-0.194653\pi$
$971$	−2.57977e6	−	4.46830e6i	−0.0878078	−	0.152088i	−0.906584	+	0.422025i	$0.861319\pi$
$972$		0			0
$973$	−7.24151e6	+	2.11674e6i	−0.245215	+	0.0716779i
$974$	681206.			0.0230081
$975$		0			0
$976$	1.89936e6	−	3.28978e6i	0.0638237	−	0.110546i
$977$	−3.48825e6	+	6.04183e6i	−0.116915	+	0.202503i	−0.918544	−	0.395319i	$-0.870634\pi$
$977$	−3.48825e6	+	6.04183e6i	−0.116915	+	0.202503i	0.801628	+	0.597823i	$0.203967\pi$
$978$		0			0
$979$	−1.48511e7			−0.495225
$980$	8.18065e6	−	5.22932e6i	0.272096	−	0.173932i
$981$		0			0
$982$	1.15526e7	+	2.00096e7i	0.382296	+	0.662156i
$983$	−1.40784e7	+	2.43845e7i	−0.464696	+	0.804878i	−0.999188	−	0.0402961i	$-0.987170\pi$
$983$	−1.40784e7	+	2.43845e7i	−0.464696	+	0.804878i	0.534491	+	0.845174i	$0.320503\pi$
$984$		0			0
$985$	−1.69968e7	−	2.94394e7i	−0.558184	−	0.966804i
$986$	2.80142e7			0.917669
$987$		0			0
$988$	−5.19691e6			−0.169376
$989$	−6.83547e6	−	1.18394e7i	−0.222217	−	0.384891i
$990$		0			0
$991$	1.17022e7	−	2.02687e7i	0.378514	−	0.655606i	−0.612332	−	0.790601i	$-0.709768\pi$
$991$	1.17022e7	−	2.02687e7i	0.378514	−	0.655606i	0.990846	+	0.134995i	$0.0431018\pi$
$992$	−1.18513e6	−	2.05270e6i	−0.0382372	−	0.0662287i
$993$		0			0
$994$	−7.48330e6	−	7.15271e6i	−0.240230	−	0.229617i
$995$	2.31080e7			0.739954
$996$		0			0
$997$	2.15142e7	−	3.72637e7i	0.685468	−	1.18727i	−0.287822	−	0.957684i	$-0.592931\pi$
$997$	2.15142e7	−	3.72637e7i	0.685468	−	1.18727i	0.973290	−	0.229581i	$-0.0737356\pi$
$998$	1.08720e6	−	1.88309e6i	0.0345529	−	0.0598474i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.6.g.j.109.1		4
3.2	odd	2		14.6.c.a.11.1	yes	4
7.2	even	3	inner	126.6.g.j.37.1		4
7.3	odd	6		882.6.a.bi.1.1		2
7.4	even	3		882.6.a.ba.1.2		2
12.11	even	2		112.6.i.d.81.2		4
21.2	odd	6		14.6.c.a.9.1	✓	4
21.5	even	6		98.6.c.e.79.2		4
21.11	odd	6		98.6.a.h.1.2		2
21.17	even	6		98.6.a.g.1.1		2
21.20	even	2		98.6.c.e.67.2		4
84.11	even	6		784.6.a.s.1.1		2
84.23	even	6		112.6.i.d.65.2		4
84.59	odd	6		784.6.a.bb.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.6.c.a.9.1	✓	4	21.2	odd	6
14.6.c.a.11.1	yes	4	3.2	odd	2
98.6.a.g.1.1		2	21.17	even	6
98.6.a.h.1.2		2	21.11	odd	6
98.6.c.e.67.2		4	21.20	even	2
98.6.c.e.79.2		4	21.5	even	6
112.6.i.d.65.2		4	84.23	even	6
112.6.i.d.81.2		4	12.11	even	2
126.6.g.j.37.1		4	7.2	even	3	inner
126.6.g.j.109.1		4	1.1	even	1	trivial
784.6.a.s.1.1		2	84.11	even	6
784.6.a.bb.1.2		2	84.59	odd	6
882.6.a.ba.1.2		2	7.4	even	3
882.6.a.bi.1.1		2	7.3	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 3.46410i) q^{2} +(-8.00000 + 13.8564i) q^{4} +(-18.0528 - 31.2683i) q^{5} +(-124.435 + 36.3731i) q^{7} -64.0000 q^{8} +(72.2111 - 125.073i) q^{10} +(77.7174 - 134.610i) q^{11} +1158.87 q^{13} +(-374.869 - 358.308i) q^{14} +(-128.000 - 221.703i) q^{16} +(619.040 - 1072.21i) q^{17} +(140.140 + 242.729i) q^{19} +577.689 q^{20} +621.739 q^{22} +(-1741.20 - 3015.84i) q^{23} +(910.694 - 1577.37i) q^{25} +(2317.74 + 4014.44i) q^{26} +(491.478 - 2015.20i) q^{28} +5656.78 q^{29} +(1157.35 - 2004.59i) q^{31} +(512.000 - 886.810i) q^{32} +4952.32 q^{34} +(3383.72 + 3234.23i) q^{35} +(1166.59 + 2020.59i) q^{37} +(-560.558 + 970.916i) q^{38} +(1155.38 + 2001.17i) q^{40} -3812.61 q^{41} +3925.73 q^{43} +(1243.48 + 2153.77i) q^{44} +(6964.78 - 12063.4i) q^{46} +(-5558.23 - 9627.13i) q^{47} +(14161.0 - 9052.14i) q^{49} +7285.56 q^{50} +(-9270.96 + 16057.8i) q^{52} +(-5593.10 + 9687.54i) q^{53} -5612.06 q^{55} +(7963.82 - 2327.88i) q^{56} +(11313.6 + 19595.7i) q^{58} +(-3005.18 + 5205.12i) q^{59} +(7419.36 + 12850.7i) q^{61} +9258.81 q^{62} +4096.00 q^{64} +(-20920.8 - 36235.9i) q^{65} +(21491.9 - 37225.1i) q^{67} +(9904.64 + 17155.3i) q^{68} +(-4436.27 + 18190.0i) q^{70} +19962.4 q^{71} +(-22775.3 + 39448.0i) q^{73} +(-4666.35 + 8082.36i) q^{74} -4484.47 q^{76} +(-4774.54 + 19577.0i) q^{77} +(-54496.0 - 94389.9i) q^{79} +(-4621.51 + 8004.69i) q^{80} +(-7625.22 - 13207.3i) q^{82} -55829.0 q^{83} -44701.6 q^{85} +(7851.47 + 13599.1i) q^{86} +(-4973.91 + 8615.07i) q^{88} +(-47772.9 - 82745.1i) q^{89} +(-144204. + 42151.6i) q^{91} +55718.2 q^{92} +(22232.9 - 38508.5i) q^{94} +(5059.82 - 8763.86i) q^{95} +15004.9 q^{97} +(59679.5 + 30950.9i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} - 32 q^{4} + 70 q^{5} - 256 q^{8} - 280 q^{10} + 62 q^{11} + 3640 q^{13} - 504 q^{14} - 512 q^{16} + 1694 q^{17} - 826 q^{19} - 2240 q^{20} + 496 q^{22} - 2734 q^{23} - 6312 q^{25} + 7280 q^{26}+ \cdots + 113288 q^{98}+O(q^{100}) \) 4 * q + 8 * q^2 - 32 * q^4 + 70 * q^5 - 256 * q^8 - 280 * q^10 + 62 * q^11 + 3640 * q^13 - 504 * q^14 - 512 * q^16 + 1694 * q^17 - 826 * q^19 - 2240 * q^20 + 496 * q^22 - 2734 * q^23 - 6312 * q^25 + 7280 * q^26 - 2016 * q^28 + 5704 * q^29 + 2674 * q^31 + 2048 * q^32 + 13552 * q^34 + 13286 * q^35 + 9146 * q^37 + 3304 * q^38 - 4480 * q^40 - 12264 * q^41 - 32080 * q^43 + 992 * q^44 + 10936 * q^46 - 25326 * q^47 + 56644 * q^49 - 50496 * q^50 - 29120 * q^52 + 14958 * q^53 - 31052 * q^55 + 11408 * q^58 - 1106 * q^59 + 28042 * q^61 + 21392 * q^62 + 16384 * q^64 + 28308 * q^65 + 102642 * q^67 + 27104 * q^68 - 88424 * q^70 + 22112 * q^71 - 35070 * q^73 - 36584 * q^74 + 26432 * q^76 - 27062 * q^77 - 101762 * q^79 + 17920 * q^80 - 24528 * q^82 + 89264 * q^83 + 7348 * q^85 - 64160 * q^86 - 3968 * q^88 - 75474 * q^89 - 123872 * q^91 + 87488 * q^92 + 101304 * q^94 + 127502 * q^95 - 16632 * q^97 + 113288 * q^98

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