LMFDB - Embedded newform 414.3.k.b.71.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,3,Mod(35,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 20]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("414.35");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	414.k (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.2806829445$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			71.5
Character	$\chi$	$=$	414.71
Dual form			414.3.k.b.35.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.764582 - 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(-2.05853 + 7.01070i) q^{5} +(4.13834 - 4.77590i) q^{7} +(-2.79964 - 0.402527i) q^{8} +O(q^{10})$	\(q+(0.764582 - 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(-2.05853 + 7.01070i) q^{5} +(4.13834 - 4.77590i) q^{7} +(-2.79964 - 0.402527i) q^{8} +(6.76681 + 7.80931i) q^{10} +(0.672913 + 1.04707i) q^{11} +(-3.82404 - 4.41318i) q^{13} +(-2.51784 - 8.57499i) q^{14} +(-2.61944 + 3.02300i) q^{16} +(25.7355 + 11.7530i) q^{17} +(10.9154 + 23.9013i) q^{19} +(14.4646 - 2.07970i) q^{20} +1.76021 q^{22} +(13.1668 + 18.8583i) q^{23} +(-23.8811 - 15.3474i) q^{25} +(-8.17420 + 1.17527i) q^{26} +(-12.1269 - 3.56077i) q^{28} +(34.5666 + 15.7860i) q^{29} +(-3.16533 + 22.0154i) q^{31} +(1.59372 + 5.42771i) q^{32} +(33.6596 - 21.6317i) q^{34} +(24.9635 + 38.8440i) q^{35} +(29.7771 - 8.74336i) q^{37} +(36.7813 + 5.28836i) q^{38} +(8.58513 - 18.7988i) q^{40} +(6.39567 - 21.7817i) q^{41} +(-6.56335 - 45.6491i) q^{43} +(1.34583 - 2.09414i) q^{44} +(32.5030 - 1.24608i) q^{46} +40.0654i q^{47} +(1.29008 + 8.97272i) q^{49} +(-36.5181 + 16.6772i) q^{50} +(-4.85161 + 10.6235i) q^{52} +(-70.6820 - 61.2463i) q^{53} +(-8.72592 + 2.56216i) q^{55} +(-13.5083 + 11.7050i) q^{56} +(45.2098 - 29.0546i) q^{58} +(-66.2497 + 57.4057i) q^{59} +(10.3306 - 71.8509i) q^{61} +(23.7718 + 20.5984i) q^{62} +(7.67594 + 2.25386i) q^{64} +(38.8114 - 17.7246i) q^{65} +(-61.7638 - 39.6932i) q^{67} -56.5845i q^{68} +65.2998 q^{70} +(27.0487 - 42.0886i) q^{71} +(-21.2481 - 46.5267i) q^{73} +(12.3650 - 42.1112i) q^{74} +(34.4140 - 39.7158i) q^{76} +(7.78545 + 1.11938i) q^{77} +(39.9157 + 46.0652i) q^{79} +(-15.8011 - 24.5871i) q^{80} +(-21.0239 - 24.2629i) q^{82} +(26.3120 + 89.6103i) q^{83} +(-135.374 + 156.230i) q^{85} +(-59.3275 - 27.0940i) q^{86} +(-1.46244 - 3.20229i) q^{88} +(27.5898 - 3.96681i) q^{89} -36.9020 q^{91} +(23.3687 - 39.6220i) q^{92} +(47.6663 + 30.6333i) q^{94} +(-190.034 + 27.3228i) q^{95} +(11.5638 + 3.39544i) q^{97} +(11.6613 + 5.32555i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{4} + 16 q^{7}+O(q^{10}) $ 80 * q + 16 * q^4 + 16 * q^7	$ 80 q + 16 q^{4} + 16 q^{7} - 8 q^{10} - 24 q^{13} - 32 q^{16} + 208 q^{19} + 64 q^{22} + 256 q^{25} - 32 q^{28} + 268 q^{34} - 256 q^{37} + 16 q^{40} - 524 q^{43} - 48 q^{46} + 144 q^{49} + 48 q^{52} + 396 q^{55} + 456 q^{58} + 376 q^{61} + 64 q^{64} + 44 q^{67} - 520 q^{70} - 188 q^{73} - 64 q^{76} + 164 q^{79} - 924 q^{82} - 1524 q^{85} + 48 q^{88} + 128 q^{91} - 176 q^{94} - 1144 q^{97}+O(q^{100}) $ 80 * q + 16 * q^4 + 16 * q^7 - 8 * q^10 - 24 * q^13 - 32 * q^16 + 208 * q^19 + 64 * q^22 + 256 * q^25 - 32 * q^28 + 268 * q^34 - 256 * q^37 + 16 * q^40 - 524 * q^43 - 48 * q^46 + 144 * q^49 + 48 * q^52 + 396 * q^55 + 456 * q^58 + 376 * q^61 + 64 * q^64 + 44 * q^67 - 520 * q^70 - 188 * q^73 - 64 * q^76 + 164 * q^79 - 924 * q^82 - 1524 * q^85 + 48 * q^88 + 128 * q^91 - 176 * q^94 - 1144 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$-1$	$e\left(\frac{1}{11}\right)$

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 $

$2$	0.764582	−	1.18971i	0.382291	−	0.594856i
$2$	0.764582	−	1.18971i	0.382291	−	0.594856i
$3$		0			0
$3$		0			0
$4$	−0.830830	−	1.81926i	−0.207708	−	0.454816i
$5$	−2.05853	+	7.01070i	−0.411706	+	1.40214i	0.449225	+	0.893419i	$0.351700\pi$
$5$	−2.05853	+	7.01070i	−0.411706	+	1.40214i	−0.860931	+	0.508722i	$0.830118\pi$
$6$		0			0
$7$	4.13834	−	4.77590i	0.591191	−	0.682271i	−0.378781	−	0.925486i	$-0.623657\pi$
$7$	4.13834	−	4.77590i	0.591191	−	0.682271i	0.969972	+	0.243215i	$0.0782022\pi$
$8$	−2.79964	−	0.402527i	−0.349955	−	0.0503159i
$9$		0			0
$10$	6.76681	+	7.80931i	0.676681	+	0.780931i
$11$	0.672913	+	1.04707i	0.0611739	+	0.0951884i	0.870493	−	0.492181i	$-0.163800\pi$
$11$	0.672913	+	1.04707i	0.0611739	+	0.0951884i	−0.809319	+	0.587369i	$0.800164\pi$
$12$		0			0
$13$	−3.82404	−	4.41318i	−0.294157	−	0.339475i	0.589363	−	0.807868i	$-0.299379\pi$
$13$	−3.82404	−	4.41318i	−0.294157	−	0.339475i	−0.883520	+	0.468393i	$0.844833\pi$
$14$	−2.51784	−	8.57499i	−0.179846	−	0.612499i
$15$		0			0
$16$	−2.61944	+	3.02300i	−0.163715	+	0.188937i
$17$	25.7355	+	11.7530i	1.51386	+	0.691355i	0.987312	−	0.158793i	$-0.0507603\pi$
$17$	25.7355	+	11.7530i	1.51386	+	0.691355i	0.526544	+	0.850148i	$0.323488\pi$
$18$		0			0
$19$	10.9154	+	23.9013i	0.574492	+	1.25796i	0.944371	+	0.328883i	$0.106672\pi$
$19$	10.9154	+	23.9013i	0.574492	+	1.25796i	−0.369879	+	0.929080i	$0.620601\pi$
$20$	14.4646	−	2.07970i	0.723230	−	0.103985i
$21$		0			0
$22$	1.76021			0.0800096
$23$	13.1668	+	18.8583i	0.572472	+	0.819925i
$23$	13.1668	+	18.8583i	0.572472	+	0.819925i
$24$		0			0
$25$	−23.8811	−	15.3474i	−0.955243	−	0.613898i
$26$	−8.17420	+	1.17527i	−0.314392	+	0.0452028i
$27$		0			0
$28$	−12.1269	−	3.56077i	−0.433102	−	0.127170i
$29$	34.5666	+	15.7860i	1.19195	+	0.544346i	0.909809	−	0.415027i	$-0.136228\pi$
$29$	34.5666	+	15.7860i	1.19195	+	0.544346i	0.282142	+	0.959373i	$0.408955\pi$
$30$		0			0
$31$	−3.16533	+	22.0154i	−0.102107	+	0.710173i	0.872884	+	0.487929i	$0.162247\pi$
$31$	−3.16533	+	22.0154i	−0.102107	+	0.710173i	−0.974991	+	0.222244i	$0.928662\pi$
$32$	1.59372	+	5.42771i	0.0498038	+	0.169616i
$33$		0			0
$34$	33.6596	−	21.6317i	0.989990	−	0.636228i
$35$	24.9635	+	38.8440i	0.713243	+	1.10983i
$36$		0			0
$37$	29.7771	−	8.74336i	0.804788	−	0.236307i	0.146634	−	0.989191i	$-0.453156\pi$
$37$	29.7771	−	8.74336i	0.804788	−	0.236307i	0.658153	+	0.752884i	$0.271338\pi$
$38$	36.7813	+	5.28836i	0.967930	+	0.139167i
$39$		0			0
$40$	8.58513	−	18.7988i	0.214628	−	0.469970i
$41$	6.39567	−	21.7817i	0.155992	−	0.531260i	−0.843995	−	0.536351i	$-0.819802\pi$
$41$	6.39567	−	21.7817i	0.155992	−	0.531260i	0.999987	+	0.00509090i	$0.00162049\pi$
$42$		0			0
$43$	−6.56335	−	45.6491i	−0.152636	−	1.06161i	−0.911778	−	0.410682i	$-0.865290\pi$
$43$	−6.56335	−	45.6491i	−0.152636	−	1.06161i	0.759142	−	0.650925i	$-0.225619\pi$
$44$	1.34583	−	2.09414i	0.0305869	−	0.0475942i
$45$		0			0
$46$	32.5030	−	1.24608i	0.706588	−	0.0270886i
$47$			40.0654i			0.852456i	0.904616	+	0.426228i	$0.140158\pi$
$47$			40.0654i			0.852456i	−0.904616	+	0.426228i	$0.859842\pi$
$48$		0			0
$49$	1.29008	+	8.97272i	0.0263282	+	0.183117i
$50$	−36.5181	+	16.6772i	−0.730362	+	0.333545i
$51$		0			0
$52$	−4.85161	+	10.6235i	−0.0933001	+	0.204299i
$53$	−70.6820	−	61.2463i	−1.33362	−	1.15559i	−0.975024	−	0.222098i	$-0.928710\pi$
$53$	−70.6820	−	61.2463i	−1.33362	−	1.15559i	−0.358598	−	0.933492i	$-0.616745\pi$
$54$		0			0
$55$	−8.72592	+	2.56216i	−0.158653	+	0.0465848i
$56$	−13.5083	+	11.7050i	−0.241219	+	0.209018i
$57$		0			0
$58$	45.2098	−	29.0546i	0.779479	−	0.500941i
$59$	−66.2497	+	57.4057i	−1.12288	+	0.972978i	−0.999811	−	0.0194202i	$-0.993818\pi$
$59$	−66.2497	+	57.4057i	−1.12288	+	0.972978i	−0.123065	+	0.992399i	$0.539273\pi$
$60$		0			0
$61$	10.3306	−	71.8509i	0.169354	−	1.17788i	−0.710869	−	0.703324i	$-0.751698\pi$
$61$	10.3306	−	71.8509i	0.169354	−	1.17788i	0.880223	−	0.474560i	$-0.157393\pi$
$62$	23.7718	+	20.5984i	0.383416	+	0.332232i
$63$		0			0
$64$	7.67594	+	2.25386i	0.119937	+	0.0352166i
$65$	38.8114	−	17.7246i	0.597098	−	0.272686i
$66$		0			0
$67$	−61.7638	−	39.6932i	−0.921848	−	0.592436i	−0.00865461	−	0.999963i	$-0.502755\pi$
$67$	−61.7638	−	39.6932i	−0.921848	−	0.592436i	−0.913193	+	0.407527i	$0.866391\pi$
$68$		−	56.5845i		−	0.832125i
$69$		0			0
$70$	65.2998			0.932854
$71$	27.0487	−	42.0886i	0.380967	−	0.592796i	−0.596825	−	0.802371i	$-0.703572\pi$
$71$	27.0487	−	42.0886i	0.380967	−	0.592796i	0.977793	+	0.209575i	$0.0672079\pi$
$72$		0			0
$73$	−21.2481	−	46.5267i	−0.291069	−	0.637353i	0.706449	−	0.707764i	$-0.250296\pi$
$73$	−21.2481	−	46.5267i	−0.291069	−	0.637353i	−0.997518	+	0.0704115i	$0.977569\pi$
$74$	12.3650	−	42.1112i	0.167094	−	0.569071i
$75$		0			0
$76$	34.4140	−	39.7158i	0.452815	−	0.522577i
$77$	7.78545	+	1.11938i	0.101110	+	0.0145374i
$78$		0			0
$79$	39.9157	+	46.0652i	0.505262	+	0.583103i	0.949879	−	0.312617i	$-0.101206\pi$
$79$	39.9157	+	46.0652i	0.505262	+	0.583103i	−0.444617	+	0.895721i	$0.646660\pi$
$80$	−15.8011	−	24.5871i	−0.197514	−	0.307338i
$81$		0			0
$82$	−21.0239	−	24.2629i	−0.256389	−	0.295889i
$83$	26.3120	+	89.6103i	0.317012	+	1.07964i	0.951740	+	0.306907i	$0.0992940\pi$
$83$	26.3120	+	89.6103i	0.317012	+	1.07964i	−0.634728	+	0.772736i	$0.718888\pi$
$84$		0			0
$85$	−135.374	+	156.230i	−1.59264	+	1.83800i
$86$	−59.3275	−	27.0940i	−0.689855	−	0.315046i
$87$		0			0
$88$	−1.46244	−	3.20229i	−0.0166186	−	0.0363897i
$89$	27.5898	−	3.96681i	0.309998	−	0.0445709i	0.0144396	−	0.999896i	$-0.495404\pi$
$89$	27.5898	−	3.96681i	0.309998	−	0.0445709i	0.295558	+	0.955325i	$0.404494\pi$
$90$		0			0
$91$	−36.9020			−0.405517
$92$	23.3687	−	39.6220i	0.254008	−	0.430674i
$93$		0			0
$94$	47.6663	+	30.6333i	0.507088	+	0.325886i
$95$	−190.034	+	27.3228i	−2.00036	+	0.287609i
$96$		0			0
$97$	11.5638	+	3.39544i	0.119214	+	0.0350045i	0.340796	−	0.940137i	$-0.389304\pi$
$97$	11.5638	+	3.39544i	0.119214	+	0.0350045i	−0.221581	+	0.975142i	$0.571122\pi$
$98$	11.6613	+	5.32555i	0.118993	+	0.0543423i
$99$		0			0
$100$	−8.07993	+	56.1971i	−0.0807993	+	0.561971i
$101$	36.4887	+	124.269i	0.361275	+	1.23039i	0.916954	+	0.398992i	$0.130640\pi$
$101$	36.4887	+	124.269i	0.361275	+	1.23039i	−0.555680	+	0.831396i	$0.687542\pi$
$102$		0			0
$103$	46.8171	−	30.0875i	0.454535	−	0.292112i	−0.293271	−	0.956029i	$-0.594744\pi$
$103$	46.8171	−	30.0875i	0.454535	−	0.292112i	0.747806	+	0.663918i	$0.231107\pi$
$104$	8.92950	+	13.8946i	0.0858606	+	0.133602i
$105$		0			0
$106$	−126.908	+	37.2634i	−1.19724	+	0.351542i
$107$	−27.6690	−	3.97820i	−0.258589	−	0.0371794i	0.0118012	−	0.999930i	$-0.496243\pi$
$107$	−27.6690	−	3.97820i	−0.258589	−	0.0371794i	−0.270390	+	0.962751i	$0.587153\pi$
$108$		0			0
$109$	−47.5683	+	104.160i	−0.436406	+	0.955597i	0.555837	+	0.831291i	$0.312398\pi$
$109$	−47.5683	+	104.160i	−0.436406	+	0.955597i	−0.992244	+	0.124306i	$0.960330\pi$
$110$	−3.62345	+	12.3403i	−0.0329404	+	0.112185i
$111$		0			0
$112$	3.59739	+	25.0204i	0.0321195	+	0.223396i
$113$	17.3353	−	26.9743i	0.153410	−	0.238710i	−0.756039	−	0.654527i	$-0.772868\pi$
$113$	17.3353	−	26.9743i	0.153410	−	0.238710i	0.909448	+	0.415817i	$0.136504\pi$
$114$		0			0
$115$	−159.314	+	53.4886i	−1.38534	+	0.465118i
$116$		−	76.0012i		−	0.655183i
$117$		0			0
$118$	17.6430	+	122.709i	0.149517	+	1.03991i
$119$	162.634	−	74.2723i	1.36667	−	0.624137i
$120$		0			0
$121$	49.6217	−	108.656i	0.410096	−	0.897986i
$122$	−77.5833	−	67.2263i	−0.635929	−	0.551036i
$123$		0			0
$124$	42.6816	−	12.5324i	0.344206	−	0.101068i
$125$	18.7058	−	16.2087i	0.149647	−	0.129670i
$126$		0			0
$127$	26.7284	−	17.1773i	0.210460	−	0.135254i	−0.431165	−	0.902273i	$-0.641897\pi$
$127$	26.7284	−	17.1773i	0.210460	−	0.135254i	0.641624	+	0.767019i	$0.278261\pi$
$128$	8.55033	−	7.40890i	0.0667995	−	0.0578821i
$129$		0			0
$130$	8.58733	−	59.7262i	0.0660564	−	0.459433i
$131$	−64.9334	−	56.2651i	−0.495675	−	0.429504i	0.370810	−	0.928709i	$-0.379080\pi$
$131$	−64.9334	−	56.2651i	−0.495675	−	0.429504i	−0.866484	+	0.499204i	$0.833626\pi$
$132$		0			0
$133$	159.321	+	46.7810i	1.19791	+	0.351737i
$134$	−94.4469	+	43.1325i	−0.704828	+	0.321884i
$135$		0			0
$136$	−67.3193	−	43.2635i	−0.494995	−	0.318114i
$137$		−	195.910i		−	1.43000i	−0.699123	−	0.715002i	$-0.746426\pi$
$137$		−	195.910i		−	1.43000i	0.699123	−	0.715002i	$-0.253574\pi$
$138$		0			0
$139$	34.2281			0.246245			0.123122	−	0.992391i	$-0.460709\pi$
$139$	34.2281			0.246245			0.123122	+	0.992391i	$0.460709\pi$
$140$	49.9270	−	77.6879i	0.356621	−	0.554914i
$141$		0			0
$142$	−29.3923	−	64.3603i	−0.206988	−	0.453241i
$143$	2.04767	−	6.97373i	0.0143194	−	0.0487673i
$144$		0			0
$145$	−181.827	+	209.840i	−1.25398	+	1.44717i
$146$	−71.5993	−	10.2944i	−0.490406	−	0.0705098i
$147$		0			0
$148$	−40.6462	−	46.9082i	−0.274637	−	0.316948i
$149$	17.6524	+	27.4677i	0.118473	+	0.184347i	0.895425	−	0.445212i	$-0.146872\pi$
$149$	17.6524	+	27.4677i	0.118473	+	0.184347i	−0.776952	+	0.629559i	$0.783235\pi$
$150$		0			0
$151$	−103.274	−	119.185i	−0.683934	−	0.789302i	0.302554	−	0.953132i	$-0.402161\pi$
$151$	−103.274	−	119.185i	−0.683934	−	0.789302i	−0.986489	+	0.163830i	$0.947615\pi$
$152$	−20.9381	−	71.3087i	−0.137751	−	0.469136i
$153$		0			0
$154$	7.28435	−	8.40659i	0.0473010	−	0.0545882i
$155$	−147.827	−	67.5104i	−0.953724	−	0.435551i
$156$		0			0
$157$	99.3378	+	217.519i	0.632725	+	1.38547i	0.905893	+	0.423508i	$0.139201\pi$
$157$	99.3378	+	217.519i	0.632725	+	1.38547i	−0.273168	+	0.961966i	$0.588071\pi$
$158$	85.3231	−	12.2676i	0.540019	−	0.0776431i
$159$		0			0
$160$	−41.3328			−0.258330
$161$	144.554	+	15.1584i	0.897851	+	0.0941514i
$162$		0			0
$163$	−90.6982	−	58.2882i	−0.556431	−	0.357596i	0.232004	−	0.972715i	$-0.425472\pi$
$163$	−90.6982	−	58.2882i	−0.556431	−	0.357596i	−0.788435	+	0.615119i	$0.789108\pi$
$164$	−44.9403	+	6.46144i	−0.274026	+	0.0393990i
$165$		0			0
$166$	126.728	+	37.2107i	0.763423	+	0.224161i
$167$	−223.897	−	102.251i	−1.34070	−	0.612278i	−0.389552	−	0.921005i	$-0.627370\pi$
$167$	−223.897	−	102.251i	−1.34070	−	0.612278i	−0.951151	+	0.308726i	$0.900097\pi$
$168$		0			0
$169$	19.1984	−	133.527i	0.113600	−	0.790104i
$170$	82.3644	+	280.507i	0.484496	+	1.65004i
$171$		0			0
$172$	−77.5947	+	49.8671i	−0.451132	+	0.289925i
$173$	−118.135	−	183.822i	−0.682862	−	1.06255i	−0.993698	−	0.112091i	$-0.964245\pi$
$173$	−118.135	−	183.822i	−0.682862	−	1.06255i	0.310836	−	0.950464i	$-0.399391\pi$
$174$		0			0
$175$	−172.126	+	50.5407i	−0.983576	+	0.288804i
$176$	−4.92795	−	0.708533i	−0.0279997	−	0.00402576i
$177$		0			0
$178$	16.3753	−	35.8568i	0.0919959	−	0.201443i
$179$	−48.7236	+	165.937i	−0.272199	+	0.927025i	0.704010	+	0.710191i	$0.251391\pi$
$179$	−48.7236	+	165.937i	−0.272199	+	0.927025i	−0.976208	+	0.216834i	$0.930427\pi$
$180$		0			0
$181$	42.0028	+	292.136i	0.232060	+	1.61401i	0.689170	+	0.724600i	$0.257975\pi$
$181$	42.0028	+	292.136i	0.232060	+	1.61401i	−0.457110	+	0.889410i	$0.651116\pi$
$182$	−28.2146	+	43.9028i	−0.155025	+	0.241224i
$183$		0			0
$184$	−29.2714	−	58.0963i	−0.159084	−	0.315741i
$185$			226.757i			1.22571i
$186$		0			0
$187$	5.01150	+	34.8557i	0.0267995	+	0.186394i
$188$	72.8896	−	33.2876i	0.387710	−	0.177061i
$189$		0			0
$190$	−112.791	+	246.977i	−0.593634	+	1.29988i
$191$	−237.463	−	205.763i	−1.24326	−	1.07729i	−0.994059	−	0.108840i	$-0.965286\pi$
$191$	−237.463	−	205.763i	−1.24326	−	1.07729i	−0.249201	−	0.968452i	$-0.580168\pi$
$192$		0			0
$193$	164.503	−	48.3023i	0.852345	−	0.250271i	0.173755	−	0.984789i	$-0.444410\pi$
$193$	164.503	−	48.3023i	0.852345	−	0.250271i	0.678589	+	0.734518i	$0.262592\pi$
$194$	12.8811	−	11.1615i	0.0663972	−	0.0575335i
$195$		0			0
$196$	15.2519	−	9.80180i	0.0778158	−	0.0500092i
$197$	−52.5374	+	45.5239i	−0.266687	+	0.231086i	−0.777931	−	0.628350i	$-0.783731\pi$
$197$	−52.5374	+	45.5239i	−0.266687	+	0.231086i	0.511243	+	0.859436i	$0.329185\pi$
$198$		0			0
$199$	39.3416	−	273.627i	0.197696	−	1.37501i	−0.613251	−	0.789888i	$-0.710138\pi$
$199$	39.3416	−	273.627i	0.197696	−	1.37501i	0.810947	−	0.585120i	$-0.198953\pi$
$200$	60.6806	+	52.5801i	0.303403	+	0.262900i
$201$		0			0
$202$	175.743	+	51.6029i	0.870016	+	0.255460i
$203$	218.441	−	99.7584i	1.07606	−	0.491421i
$204$		0			0
$205$	139.539	+	89.6764i	0.680679	+	0.437446i
$206$		−	78.7032i		−	0.382054i
$207$		0			0
$208$	23.3579			0.112297
$209$	−17.6813	+	27.5126i	−0.0845995	+	0.131639i
$210$		0			0
$211$	−20.5367	−	44.9691i	−0.0973304	−	0.213124i	0.854703	−	0.519117i	$-0.173739\pi$
$211$	−20.5367	−	44.9691i	−0.0973304	−	0.213124i	−0.952034	+	0.305993i	$0.901012\pi$
$212$	−52.6984	+	179.474i	−0.248578	+	0.846577i
$213$		0			0
$214$	−25.8881	+	29.8765i	−0.120972	+	0.139610i
$215$	333.543	+	47.9563i	1.55136	+	0.223052i
$216$		0			0
$217$	92.0439	+	106.224i	0.424165	+	0.489513i
$218$	87.5506	+	136.231i	0.401608	+	0.624915i
$219$		0			0
$220$	11.9110	+	13.7460i	0.0541410	+	0.0624820i
$221$	−46.5455	−	158.520i	−0.210613	−	0.717283i
$222$		0			0
$223$	123.773	−	142.842i	0.555036	−	0.640546i	−0.407013	−	0.913422i	$-0.633430\pi$
$223$	123.773	−	142.842i	0.555036	−	0.640546i	0.962049	+	0.272877i	$0.0879751\pi$
$224$	32.5175	+	14.8503i	0.145168	+	0.0662958i
$225$		0			0
$226$	−18.8374	−	41.2480i	−0.0833511	−	0.182513i
$227$	11.6422	−	1.67389i	0.0512872	−	0.00737398i	−0.116623	−	0.993176i	$-0.537207\pi$
$227$	11.6422	−	1.67389i	0.0512872	−	0.00737398i	0.167911	+	0.985802i	$0.446298\pi$
$228$		0			0
$229$	−344.710			−1.50528			−0.752641	−	0.658431i	$-0.771221\pi$
$229$	−344.710			−1.50528			−0.752641	+	0.658431i	$0.771221\pi$
$230$	−58.1725	+	230.434i	−0.252924	+	1.00189i
$231$		0			0
$232$	−90.4196	−	58.1091i	−0.389740	−	0.250470i
$233$	−14.5679	+	2.09455i	−0.0625232	+	0.00898948i	−0.173505	−	0.984833i	$-0.555509\pi$
$233$	−14.5679	+	2.09455i	−0.0625232	+	0.00898948i	0.110982	+	0.993822i	$0.464600\pi$
$234$		0			0
$235$	−280.887	−	82.4758i	−1.19526	−	0.350961i
$236$	159.478	+	72.8314i	0.675756	+	0.308607i
$237$		0			0
$238$	35.9840	−	250.274i	0.151193	−	1.05157i
$239$	119.501	+	406.983i	0.500004	+	1.70286i	0.692377	+	0.721536i	$0.256564\pi$
$239$	119.501	+	406.983i	0.500004	+	1.70286i	−0.192373	+	0.981322i	$0.561618\pi$
$240$		0			0
$241$	275.909	−	177.316i	1.14485	−	0.735751i	0.176244	−	0.984347i	$-0.443605\pi$
$241$	275.909	−	177.316i	1.14485	−	0.735751i	0.968607	+	0.248595i	$0.0799689\pi$
$242$	−91.3299	−	142.112i	−0.377396	−	0.587240i
$243$		0			0
$244$	−139.299	+	40.9018i	−0.570897	+	0.167630i
$245$	−65.5607	−	9.42621i	−0.267595	−	0.0384743i
$246$		0			0
$247$	63.7399	−	139.571i	0.258056	−	0.565064i
$248$	17.7236	−	60.3609i	0.0714660	−	0.243391i
$249$		0			0
$250$	−4.98155	−	34.6475i	−0.0199262	−	0.138590i
$251$	233.571	−	363.444i	0.930562	−	1.44798i	0.0368614	−	0.999320i	$-0.488264\pi$
$251$	233.571	−	363.444i	0.930562	−	1.44798i	0.893701	−	0.448663i	$-0.148100\pi$
$252$		0			0
$253$	−10.8858	+	26.4766i	−0.0430270	+	0.104651i
$254$		−	44.9326i		−	0.176900i
$255$		0			0
$256$	−2.27704	−	15.8371i	−0.00889468	−	0.0618638i
$257$	193.435	−	88.3389i	0.752666	−	0.343731i	−0.00186242	−	0.999998i	$-0.500593\pi$
$257$	193.435	−	88.3389i	0.752666	−	0.343731i	0.754529	+	0.656267i	$0.227866\pi$
$258$		0			0
$259$	81.4705	−	178.395i	0.314558	−	0.688786i
$260$	−64.4913	−	55.8820i	−0.248043	−	0.214931i
$261$		0			0
$262$	−116.586	+	34.2328i	−0.444985	+	0.130659i
$263$	−312.540	+	270.818i	−1.18837	+	1.02972i	−0.189511	+	0.981879i	$0.560690\pi$
$263$	−312.540	+	270.818i	−1.18837	+	1.02972i	−0.998855	+	0.0478459i	$0.984764\pi$
$264$		0			0
$265$	574.880	−	369.453i	2.16936	−	1.39416i
$266$	177.470	−	153.779i	0.667181	−	0.578116i
$267$		0			0
$268$	−20.8972	+	145.343i	−0.0779745	+	0.542324i
$269$	−184.230	−	159.636i	−0.684869	−	0.593442i	0.241346	−	0.970439i	$-0.422411\pi$
$269$	−184.230	−	159.636i	−0.684869	−	0.593442i	−0.926214	+	0.376997i	$0.876957\pi$
$270$		0			0
$271$	222.933	+	65.4590i	0.822631	+	0.241546i	0.665849	−	0.746087i	$-0.268070\pi$
$271$	222.933	+	65.4590i	0.822631	+	0.241546i	0.156782	+	0.987633i	$0.449888\pi$
$272$	−102.942	+	47.0121i	−0.378464	+	0.172839i
$273$		0			0
$274$	−233.077	−	149.790i	−0.850646	−	0.546677i
$275$		−	35.3327i		−	0.128483i
$276$		0			0
$277$	334.733			1.20842			0.604212	−	0.796824i	$-0.293488\pi$
$277$	334.733			1.20842			0.604212	+	0.796824i	$0.293488\pi$
$278$	26.1701	−	40.7215i	0.0941372	−	0.146480i
$279$		0			0
$280$	−54.2530	−	118.798i	−0.193761	−	0.424277i
$281$	−84.4445	+	287.591i	−0.300514	+	1.02346i	0.661384	+	0.750048i	$0.269970\pi$
$281$	−84.4445	+	287.591i	−0.300514	+	1.02346i	−0.961898	+	0.273409i	$0.911849\pi$
$282$		0			0
$283$	294.007	−	339.302i	1.03889	−	1.19895i	0.0592420	−	0.998244i	$-0.481132\pi$
$283$	294.007	−	339.302i	1.03889	−	1.19895i	0.979652	−	0.200704i	$-0.0643229\pi$
$284$	−99.0430	−	14.2402i	−0.348743	−	0.0501417i
$285$		0			0
$286$	−6.73112	−	7.76812i	−0.0235354	−	0.0271613i
$287$	−77.5595	−	120.685i	−0.270242	−	0.420505i
$288$		0			0
$289$	334.930	+	386.530i	1.15893	+	1.33747i
$290$	110.627	+	376.762i	0.381473	+	1.29918i
$291$		0			0
$292$	−66.9909	+	77.3116i	−0.229421	+	0.264766i
$293$	7.84685	+	3.58353i	0.0267810	+	0.0122305i	0.428761	−	0.903418i	$-0.358950\pi$
$293$	7.84685	+	3.58353i	0.0267810	+	0.0122305i	−0.401979	+	0.915649i	$0.631678\pi$
$294$		0			0
$295$	−266.078	−	582.629i	−0.901958	−	1.97501i
$296$	−86.8846	+	12.4921i	−0.293529	+	0.0422031i
$297$		0			0
$298$	46.1754			0.154951
$299$	32.8743	−	130.222i	0.109948	−	0.435526i
$300$		0			0
$301$	−245.177	−	157.566i	−0.814541	−	0.523473i
$302$	−220.757	+	31.7400i	−0.730983	+	0.105099i
$303$		0			0
$304$	−100.846	−	29.6110i	−0.331729	−	0.0974045i
$305$	482.460	+	220.332i	1.58184	+	0.722400i
$306$		0			0
$307$	−35.0039	+	243.457i	−0.114019	+	0.793021i	0.849923	+	0.526907i	$0.176649\pi$
$307$	−35.0039	+	243.457i	−0.114019	+	0.793021i	−0.963942	+	0.266113i	$0.914261\pi$
$308$	−4.43194	−	15.0938i	−0.0143894	−	0.0490058i
$309$		0			0
$310$	−193.344	+	124.255i	−0.623690	+	0.400821i
$311$	129.191	+	201.025i	0.415406	+	0.646384i	0.984397	−	0.175959i	$-0.0563028\pi$
$311$	129.191	+	201.025i	0.415406	+	0.646384i	−0.568992	+	0.822343i	$0.692666\pi$
$312$		0			0
$313$	192.404	−	56.4949i	0.614709	−	0.180495i	0.0404674	−	0.999181i	$-0.487115\pi$
$313$	192.404	−	56.4949i	0.614709	−	0.180495i	0.574241	+	0.818686i	$0.305297\pi$
$314$	334.737	+	48.1280i	1.06604	+	0.153274i
$315$		0			0
$316$	50.6415	−	110.889i	0.160258	−	0.350916i
$317$	70.9667	−	241.690i	0.223870	−	0.762430i	−0.768577	−	0.639757i	$-0.779035\pi$
$317$	70.9667	−	241.690i	0.223870	−	0.762430i	0.992447	−	0.122674i	$-0.0391468\pi$
$318$		0			0
$319$	6.73117	+	46.8163i	0.0211008	+	0.146760i
$320$	−31.6023	+	49.1741i	−0.0987572	+	0.153669i
$321$		0			0
$322$	128.557	−	160.388i	0.399247	−	0.498099i
$323$			743.401i			2.30155i
$324$		0			0
$325$	23.5912	+	164.081i	0.0725884	+	0.504864i
$326$	−138.692	+	63.3387i	−0.425437	+	0.194290i
$327$		0			0
$328$	−26.6733	+	58.4063i	−0.0813210	+	0.178068i
$329$	191.348	+	165.804i	0.581606	+	0.503964i
$330$		0			0
$331$	39.5081	−	11.6006i	0.119360	−	0.0350472i	−0.221507	−	0.975159i	$-0.571098\pi$
$331$	39.5081	−	11.6006i	0.119360	−	0.0350472i	0.340867	+	0.940112i	$0.389279\pi$
$332$	141.164	−	122.319i	0.425193	−	0.368432i
$333$		0			0
$334$	−292.836	+	188.195i	−0.876756	+	0.563457i
$335$	405.420	−	351.298i	1.21021	−	1.04865i
$336$		0			0
$337$	31.6643	−	220.230i	0.0939593	−	0.653501i	−0.887355	−	0.461087i	$-0.847459\pi$
$337$	31.6643	−	220.230i	0.0939593	−	0.653501i	0.981314	−	0.192413i	$-0.0616315\pi$
$338$	−144.181	−	124.933i	−0.426570	−	0.369625i
$339$		0			0
$340$	396.697	+	116.481i	1.16676	+	0.342591i
$341$	−25.1817	+	11.5001i	−0.0738465	+	0.0337246i
$342$		0			0
$343$	308.687	+	198.381i	0.899962	+	0.578370i
$344$			130.443i			0.379194i
$345$		0			0
$346$	−309.019			−0.893119
$347$	−23.7066	+	36.8882i	−0.0683187	+	0.106306i	−0.873732	−	0.486408i	$-0.838307\pi$
$347$	−23.7066	+	36.8882i	−0.0683187	+	0.106306i	0.805413	+	0.592714i	$0.201943\pi$
$348$		0			0
$349$	158.634	+	347.360i	0.454539	+	0.995301i	0.988699	+	0.149917i	$0.0479007\pi$
$349$	158.634	+	347.360i	0.454539	+	0.995301i	−0.534160	+	0.845383i	$0.679372\pi$
$350$	−71.4753	+	243.423i	−0.204215	+	0.695493i
$351$		0			0
$352$	−4.61077	+	5.32112i	−0.0130988	+	0.0151168i
$353$	195.297	+	28.0794i	0.553248	+	0.0795451i	0.413268	−	0.910609i	$-0.364387\pi$
$353$	195.297	+	28.0794i	0.553248	+	0.0795451i	0.139980	+	0.990154i	$0.455296\pi$
$354$		0			0
$355$	239.390	+	276.271i	0.674338	+	0.778227i
$356$	−30.1391	−	46.8973i	−0.0846604	−	0.131734i
$357$		0			0
$358$	160.165	+	184.840i	0.447387	+	0.516312i
$359$	−8.40090	−	28.6108i	−0.0234008	−	0.0796959i	0.946965	−	0.321337i	$-0.104132\pi$
$359$	−8.40090	−	28.6108i	−0.0234008	−	0.0796959i	−0.970366	+	0.241642i	$0.922314\pi$
$360$		0			0
$361$	−215.722	+	248.957i	−0.597568	+	0.689630i
$362$	379.672	+	173.390i	1.04882	+	0.478979i
$363$		0			0
$364$	30.6593	+	67.1345i	0.0842289	+	0.184436i
$365$	369.925	−	53.1872i	1.01349	−	0.145718i
$366$		0			0
$367$	−507.550			−1.38297			−0.691485	−	0.722390i	$-0.743043\pi$
$367$	−507.550			−1.38297			−0.691485	+	0.722390i	$0.743043\pi$
$368$	−91.4983	−	9.59479i	−0.248637	−	0.0260728i
$369$		0			0
$370$	269.776	+	173.374i	0.729124	+	0.468579i
$371$	−585.012	+	84.1120i	−1.57685	+	0.226717i
$372$		0			0
$373$	−237.000	−	69.5895i	−0.635389	−	0.186567i	−0.0518535	−	0.998655i	$-0.516513\pi$
$373$	−237.000	−	69.5895i	−0.635389	−	0.186567i	−0.583535	+	0.812088i	$0.698331\pi$
$374$	45.3000	+	20.6878i	0.121123	+	0.0553150i
$375$		0			0
$376$	16.1274	−	112.169i	0.0428921	−	0.298321i
$377$	−62.5174	−	212.915i	−0.165829	−	0.564761i
$378$		0			0
$379$	−463.263	+	297.721i	−1.22233	+	0.785544i	−0.982679	−	0.185315i	$-0.940669\pi$
$379$	−463.263	+	297.721i	−1.22233	+	0.785544i	−0.239651	+	0.970859i	$0.577033\pi$
$380$	207.594	+	323.022i	0.546299	+	0.850058i
$381$		0			0
$382$	−426.358	+	125.190i	−1.11612	+	0.327723i
$383$	−594.635	−	85.4956i	−1.55257	−	0.223226i	−0.687990	−	0.725720i	$-0.741507\pi$
$383$	−594.635	−	85.4956i	−1.55257	−	0.223226i	−0.864581	+	0.502494i	$0.832416\pi$
$384$		0			0
$385$	−23.8742	+	52.2772i	−0.0620109	+	0.135785i
$386$	68.3098	−	232.642i	0.176968	−	0.602699i
$387$		0			0
$388$	−3.43035	−	23.8586i	−0.00884112	−	0.0614913i
$389$	270.391	−	420.737i	0.695094	−	1.08159i	−0.296852	−	0.954924i	$-0.595937\pi$
$389$	270.391	−	420.737i	0.695094	−	1.08159i	0.991946	−	0.126664i	$-0.0404268\pi$
$390$		0			0
$391$	117.214	+	640.078i	0.299781	+	1.63703i
$392$		−	25.6397i		−	0.0654073i
$393$		0			0
$394$	13.9912	+	97.3111i	0.0355107	+	0.246983i
$395$	−405.117	+	185.011i	−1.02561	+	0.468381i
$396$		0			0
$397$	86.3110	−	188.995i	0.217408	−	0.476057i	−0.769233	−	0.638969i	$-0.779361\pi$
$397$	86.3110	−	188.995i	0.217408	−	0.476057i	0.986641	+	0.162912i	$0.0520886\pi$
$398$	−295.457	−	256.015i	−0.742355	−	0.643254i
$399$		0			0
$400$	108.950	−	31.9907i	0.272376	−	0.0799768i
$401$	378.072	−	327.602i	0.942824	−	0.816962i	−0.0404337	−	0.999182i	$-0.512874\pi$
$401$	378.072	−	327.602i	0.942824	−	0.816962i	0.983258	+	0.182221i	$0.0583285\pi$
$402$		0			0
$403$	109.262	−	70.2184i	0.271122	−	0.174239i
$404$	195.763	−	169.629i	0.484561	−	0.419874i
$405$		0			0
$406$	48.3318	−	336.155i	0.119044	−	0.827967i
$407$	29.1923	+	25.2953i	0.0717257	+	0.0621506i
$408$		0			0
$409$	37.4193	+	10.9873i	0.0914897	+	0.0268638i	0.327157	−	0.944970i	$-0.393909\pi$
$409$	37.4193	+	10.9873i	0.0914897	+	0.0268638i	−0.235667	+	0.971834i	$0.575728\pi$
$410$	213.378	−	97.4465i	0.520434	−	0.237674i
$411$		0			0
$412$	−93.6342	−	60.1750i	−0.227267	−	0.146056i
$413$			553.966i			1.34132i
$414$		0			0
$415$	−682.395			−1.64433
$416$	17.8590	−	27.7892i	0.0429303	−	0.0668008i
$417$		0			0
$418$	19.2133	+	42.0713i	0.0459649	+	0.100649i
$419$	−15.0150	+	51.1365i	−0.0358354	+	0.122044i	−0.975468	−	0.220140i	$-0.929349\pi$
$419$	−15.0150	+	51.1365i	−0.0358354	+	0.122044i	0.939633	+	0.342184i	$0.111167\pi$
$420$		0			0
$421$	−123.594	+	142.635i	−0.293573	+	0.338801i	−0.883306	−	0.468797i	$-0.844688\pi$
$421$	−123.594	+	142.635i	−0.293573	+	0.338801i	0.589733	+	0.807598i	$0.299233\pi$
$422$	−69.2023	−	9.94979i	−0.163987	−	0.0235777i
$423$		0			0
$424$	173.231	+	199.919i	0.408563	+	0.471507i
$425$	−434.214	−	675.650i	−1.02168	−	1.58976i
$426$		0			0
$427$	−300.401	−	346.681i	−0.703515	−	0.811900i
$428$	15.7508	+	53.6424i	0.0368010	+	0.125333i
$429$		0			0
$430$	312.075	−	360.154i	0.725756	−	0.837567i
$431$	−335.987	−	153.440i	−0.779552	−	0.356010i	−0.0144311	−	0.999896i	$-0.504594\pi$
$431$	−335.987	−	153.440i	−0.779552	−	0.356010i	−0.765121	+	0.643886i	$0.777321\pi$
$432$		0			0
$433$	−290.499	−	636.105i	−0.670899	−	1.46906i	−0.872006	−	0.489495i	$-0.837181\pi$
$433$	−290.499	−	636.105i	−0.670899	−	1.46906i	0.201106	−	0.979569i	$-0.435546\pi$
$434$	196.751	−	28.2886i	0.453344	−	0.0651810i
$435$		0			0
$436$	229.016			0.525266
$437$	−307.016	+	520.549i	−0.702554	+	1.19119i
$438$		0			0
$439$	227.893	+	146.458i	0.519119	+	0.333617i	0.773823	−	0.633402i	$-0.218342\pi$
$439$	227.893	+	146.458i	0.519119	+	0.333617i	−0.254705	+	0.967019i	$0.581978\pi$
$440$	25.4608	−	3.66071i	0.0578654	−	0.00831979i
$441$		0			0
$442$	−224.181	−	65.8253i	−0.507196	−	0.148926i
$443$	436.017	+	199.122i	0.984236	+	0.449486i	0.841489	−	0.540274i	$-0.181679\pi$
$443$	436.017	+	199.122i	0.984236	+	0.449486i	0.142747	+	0.989759i	$0.454407\pi$
$444$		0			0
$445$	−28.9842	+	201.590i	−0.0651330	+	0.453010i
$446$	−75.3059	−	256.468i	−0.168847	−	0.575041i
$447$		0			0
$448$	42.5298	−	27.3323i	0.0949327	−	0.0610095i
$449$	−381.170	−	593.112i	−0.848931	−	1.32096i	−0.945496	−	0.325635i	$-0.894422\pi$
$449$	−381.170	−	593.112i	−0.848931	−	1.32096i	0.0965650	−	0.995327i	$-0.469214\pi$
$450$		0			0
$451$	27.1107	−	7.96042i	0.0601124	−	0.0176506i
$452$	−63.4760	−	9.12647i	−0.140434	−	0.0201913i
$453$		0			0
$454$	6.90995	−	15.1307i	0.0152202	−	0.0333275i
$455$	75.9639	−	258.709i	0.166954	−	0.568592i
$456$		0			0
$457$	15.6836	+	109.082i	0.0343185	+	0.238690i	0.999759	−	0.0219313i	$-0.00698152\pi$
$457$	15.6836	+	109.082i	0.0343185	+	0.238690i	−0.965441	+	0.260622i	$0.916072\pi$
$458$	−263.559	+	410.105i	−0.575456	+	0.895427i
$459$		0			0
$460$	229.673	+	245.394i	0.499289	+	0.533466i
$461$		−	623.723i		−	1.35298i	−0.736453	−	0.676489i	$-0.763501\pi$
$461$		−	623.723i		−	1.35298i	0.736453	−	0.676489i	$-0.236499\pi$
$462$		0			0
$463$	−55.0608	−	382.956i	−0.118922	−	0.827119i	−0.958747	−	0.284262i	$-0.908251\pi$
$463$	−55.0608	−	382.956i	−0.118922	−	0.827119i	0.839825	−	0.542857i	$-0.182658\pi$
$464$	−138.266	+	63.1441i	−0.297988	+	0.136086i
$465$		0			0
$466$	−8.64644	+	18.9331i	−0.0185546	+	0.0406289i
$467$	−43.3797	−	37.5887i	−0.0928901	−	0.0804898i	0.607178	−	0.794566i	$-0.292302\pi$
$467$	−43.3797	−	37.5887i	−0.0928901	−	0.0804898i	−0.700068	+	0.714076i	$0.746847\pi$
$468$		0			0
$469$	−445.170	+	130.714i	−0.949190	+	0.278707i
$470$	−312.883	+	271.115i	−0.665709	+	0.576840i
$471$		0			0
$472$	208.583	−	134.048i	0.441912	−	0.284000i
$473$	43.3814	−	37.5902i	0.0917153	−	0.0794718i
$474$		0			0
$475$	106.153	−	738.312i	0.223480	−	1.55434i
$476$	−270.242	−	234.166i	−0.567735	−	0.491945i
$477$		0			0
$478$	575.561	+	169.000i	1.20410	+	0.353556i
$479$	−58.2050	+	26.5813i	−0.121513	+	0.0554933i	−0.475244	−	0.879854i	$-0.657640\pi$
$479$	−58.2050	+	26.5813i	−0.121513	+	0.0554933i	0.353731	+	0.935347i	$0.384913\pi$
$480$		0			0
$481$	−152.455	−	97.9768i	−0.316954	−	0.203694i
$482$		−	463.825i		−	0.962293i
$483$		0			0
$484$	−238.902			−0.493598
$485$	−47.6088	+	74.0808i	−0.0981625	+	0.152744i
$486$		0			0
$487$	329.207	+	720.862i	0.675989	+	1.48021i	0.866838	+	0.498590i	$0.166149\pi$
$487$	329.207	+	720.862i	0.675989	+	1.48021i	−0.190849	+	0.981619i	$0.561124\pi$
$488$	−57.8439	+	196.998i	−0.118533	+	0.403685i
$489$		0			0
$490$	−61.3410	+	70.7913i	−0.125186	+	0.144472i
$491$	−312.925	−	44.9918i	−0.637321	−	0.0916330i	−0.183923	−	0.982941i	$-0.558880\pi$
$491$	−312.925	−	44.9918i	−0.637321	−	0.0916330i	−0.453399	+	0.891308i	$0.649789\pi$
$492$		0			0
$493$	704.056	+	812.524i	1.42811	+	1.64812i
$494$	−117.315	−	182.545i	−0.237479	−	0.369525i
$495$		0			0
$496$	−58.2610	−	67.2368i	−0.117462	−	0.135558i
$497$	−89.0740	−	303.358i	−0.179223	−	0.610379i
$498$		0			0
$499$	463.757	−	535.204i	0.929372	−	1.07255i	−0.0678219	−	0.997697i	$-0.521605\pi$
$499$	463.757	−	535.204i	0.929372	−	1.07255i	0.997194	−	0.0748556i	$-0.0238496\pi$
$500$	−45.0293	−	20.5642i	−0.0900586	−	0.0411284i
$501$		0			0
$502$	−253.809	−	555.765i	−0.505596	−	1.10710i
$503$	117.765	−	16.9320i	0.234125	−	0.0336621i	−0.0242535	−	0.999706i	$-0.507721\pi$
$503$	117.765	−	16.9320i	0.234125	−	0.0336621i	0.258379	+	0.966044i	$0.416812\pi$
$504$		0			0
$505$	−946.328			−1.87392
$506$	23.1764	+	33.1945i	0.0458032	+	0.0656018i
$507$		0			0
$508$	−53.4568	−	34.3546i	−0.105230	−	0.0676272i
$509$	438.710	−	63.0770i	0.861905	−	0.123923i	0.302835	−	0.953043i	$-0.402067\pi$
$509$	438.710	−	63.0770i	0.861905	−	0.123923i	0.559071	+	0.829120i	$0.311158\pi$
$510$		0			0
$511$	−310.138	−	91.0649i	−0.606925	−	0.178209i
$512$	−20.5826	−	9.39977i	−0.0402004	−	0.0183589i
$513$		0			0
$514$	42.7991	−	297.675i	0.0832668	−	0.579133i
$515$	114.560	+	390.157i	0.222447	+	0.757586i
$516$		0			0
$517$	−41.9514	+	26.9605i	−0.0811439	+	0.0521480i
$518$	−149.948	−	233.324i	−0.289476	−	0.450433i
$519$		0			0
$520$	−115.792	+	33.9997i	−0.222678	+	0.0653841i
$521$	−433.544	−	62.3342i	−0.832138	−	0.119643i	−0.286938	−	0.957949i	$-0.592637\pi$
$521$	−433.544	−	62.3342i	−0.832138	−	0.119643i	−0.545200	+	0.838306i	$0.683546\pi$
$522$		0			0
$523$	80.9466	−	177.248i	0.154774	−	0.338907i	−0.816322	−	0.577597i	$-0.803991\pi$
$523$	80.9466	−	177.248i	0.154774	−	0.338907i	0.971096	+	0.238690i	$0.0767179\pi$
$524$	−48.4125	+	164.878i	−0.0923902	+	0.314652i
$525$		0			0
$526$	83.2325	+	578.895i	0.158237	+	1.10056i
$527$	−340.209	+	529.375i	−0.645557	+	1.00451i
$528$		0			0
$529$	−182.268	+	496.608i	−0.344552	+	0.938767i
$530$		−	966.419i		−	1.82343i
$531$		0			0
$532$	−47.2621	−	328.715i	−0.0888385	−	0.617885i
$533$	−120.584	+	55.0687i	−0.226236	+	0.103318i
$534$		0			0
$535$	84.8474	−	185.790i	0.158593	−	0.347271i
$536$	156.939	+	135.988i	0.292796	+	0.253709i
$537$		0			0
$538$	−330.779	+	97.1256i	−0.614832	+	0.180531i
$539$	−8.52697	+	7.38867i	−0.0158200	+	0.0137081i
$540$		0			0
$541$	−762.776	+	490.206i	−1.40994	+	0.906111i	−0.999982	−	0.00599483i	$-0.998092\pi$
$541$	−762.776	+	490.206i	−1.40994	+	0.906111i	−0.409954	+	0.912106i	$0.634455\pi$
$542$	248.328	−	215.177i	0.458170	−	0.397006i
$543$		0			0
$544$	−22.7768	+	158.416i	−0.0418691	+	0.291206i
$545$	−632.315	−	547.904i	−1.16021	−	1.00533i
$546$		0			0
$547$	−569.689	−	167.276i	−1.04148	−	0.305806i	−0.284110	−	0.958792i	$-0.591698\pi$
$547$	−569.689	−	167.276i	−1.04148	−	0.305806i	−0.757370	+	0.652986i	$0.773516\pi$
$548$	−356.413	+	162.768i	−0.650389	+	0.297022i
$549$		0			0
$550$	−42.0358	−	27.0147i	−0.0764287	−	0.0491177i
$551$			998.496i			1.81215i
$552$		0			0
$553$	385.187			0.696541
$554$	255.931	−	398.236i	0.461969	−	0.718838i
$555$		0			0
$556$	−28.4377	−	62.2699i	−0.0511469	−	0.111996i
$557$	−267.898	+	912.376i	−0.480966	+	1.63802i	0.259368	+	0.965779i	$0.416486\pi$
$557$	−267.898	+	912.376i	−0.480966	+	1.63802i	−0.740333	+	0.672240i	$0.765332\pi$
$558$		0			0
$559$	−176.359	+	203.529i	−0.315490	+	0.364095i
$560$	−182.816	−	26.2849i	−0.326457	−	0.0469374i
$561$		0			0
$562$	277.586	+	320.352i	0.493926	+	0.570021i
$563$	−71.8780	−	111.844i	−0.127670	−	0.198658i	0.771534	−	0.636188i	$-0.219490\pi$
$563$	−71.8780	−	111.844i	−0.127670	−	0.198658i	−0.899204	+	0.437530i	$0.855853\pi$
$564$		0			0
$565$	153.423	+	177.060i	0.271546	+	0.313380i
$566$	−178.880	−	609.208i	−0.316042	−	1.07634i
$567$		0			0
$568$	−92.6683	+	106.945i	−0.163148	+	0.188283i
$569$	389.383	+	177.825i	0.684328	+	0.312522i	0.727069	−	0.686564i	$-0.240882\pi$
$569$	389.383	+	177.825i	0.684328	+	0.312522i	−0.0427414	+	0.999086i	$0.513609\pi$
$570$		0			0
$571$	99.4070	+	217.671i	0.174093	+	0.381210i	0.976484	−	0.215588i	$-0.0691667\pi$
$571$	99.4070	+	217.671i	0.174093	+	0.381210i	−0.802392	+	0.596798i	$0.796439\pi$
$572$	−14.3883	+	2.06873i	−0.0251544	+	0.00361666i
$573$		0			0
$574$	−202.881			−0.353451
$575$	−25.0125	−	652.433i	−0.0435000	−	1.13467i
$576$		0			0
$577$	609.915	+	391.968i	1.05704	+	0.679321i	0.949145	−	0.314840i	$-0.101951\pi$
$577$	609.915	+	391.968i	1.05704	+	0.679321i	0.107900	+	0.994162i	$0.465587\pi$
$578$	715.940	−	102.937i	1.23865	−	0.178091i
$579$		0			0
$580$	532.822	+	156.451i	0.918659	+	0.269742i
$581$	536.857	+	245.175i	0.924023	+	0.421987i
$582$		0			0
$583$	16.5665	−	115.223i	0.0284160	−	0.197637i
$584$	40.7586	+	138.811i	0.0697921	+	0.237690i
$585$		0			0
$586$	10.2629	−	6.59558i	0.0175135	−	0.0112553i
$587$	−546.034	−	849.646i	−0.930212	−	1.44744i	−0.893986	−	0.448095i	$-0.852103\pi$
$587$	−546.034	−	849.646i	−0.930212	−	1.44744i	−0.0362259	−	0.999344i	$-0.511534\pi$
$588$		0			0
$589$	−560.746	+	164.650i	−0.952031	+	0.279542i
$590$	−896.598	−	128.911i	−1.51966	−	0.218494i
$591$		0			0
$592$	−51.5684	+	112.919i	−0.0871087	+	0.190742i
$593$	−24.1764	+	82.3371i	−0.0407696	+	0.138848i	−0.977363	−	0.211570i	$-0.932142\pi$
$593$	−24.1764	+	82.3371i	−0.0407696	+	0.138848i	0.936593	+	0.350418i	$0.113961\pi$
$594$		0			0
$595$	185.915	+	1293.07i	0.312462	+	2.17322i
$596$	35.3049	−	54.9355i	0.0592364	−	0.0921736i
$597$		0			0
$598$	−129.792	−	138.677i	−0.217044	−	0.231901i
$599$			440.400i			0.735226i	0.929979	+	0.367613i	$0.119825\pi$
$599$			440.400i			0.735226i	−0.929979	+	0.367613i	$0.880175\pi$
$600$		0			0
$601$	−153.986	−	1070.99i	−0.256216	−	1.78202i	−0.559210	−	0.829026i	$-0.688895\pi$
$601$	−153.986	−	1070.99i	−0.256216	−	1.78202i	0.302994	−	0.952992i	$-0.402014\pi$
$602$	−374.915	+	171.218i	−0.622783	+	0.284415i
$603$		0			0
$604$	−131.025	+	286.905i	−0.216929	+	0.475008i
$605$	659.609	+	571.555i	1.09026	+	0.944719i
$606$		0			0
$607$	−309.203	+	90.7902i	−0.509396	+	0.149572i	−0.526323	−	0.850285i	$-0.676430\pi$
$607$	−309.203	+	90.7902i	−0.509396	+	0.149572i	0.0169274	+	0.999857i	$0.494612\pi$
$608$	−112.333	+	97.3374i	−0.184759	+	0.160094i
$609$		0			0
$610$	631.011	−	405.526i	1.03445	−	0.664797i
$611$	176.816	−	153.212i	0.289388	−	0.250756i
$612$		0			0
$613$	126.768	−	881.691i	0.206799	−	1.43832i	−0.576713	−	0.816947i	$-0.695665\pi$
$613$	126.768	−	881.691i	0.206799	−	1.43832i	0.783513	−	0.621375i	$-0.213426\pi$
$614$	262.881	+	227.788i	0.428145	+	0.370989i
$615$		0			0
$616$	−21.3459	−	6.26771i	−0.0346524	−	0.0101749i
$617$	945.587	−	431.835i	1.53256	−	0.699895i	0.542433	−	0.840099i	$-0.317503\pi$
$617$	945.587	−	431.835i	1.53256	−	0.699895i	0.990123	+	0.140205i	$0.0447760\pi$
$618$		0			0
$619$	−755.801	−	485.724i	−1.22100	−	0.784691i	−0.238538	−	0.971133i	$-0.576668\pi$
$619$	−755.801	−	485.724i	−1.22100	−	0.784691i	−0.982466	+	0.186442i	$0.940304\pi$
$620$			325.026i			0.524236i
$621$		0			0
$622$	337.939			0.543311
$623$	95.2307	−	148.182i	0.152858	−	0.237852i
$624$		0			0
$625$	−219.687	−	481.047i	−0.351499	−	0.769676i
$626$	79.8958	−	272.100i	0.127629	−	0.434665i
$627$		0			0
$628$	313.192	−	361.443i	0.498714	−	0.575547i
$629$	869.092	+	124.957i	1.38170	+	0.198659i
$630$		0			0
$631$	−682.123	−	787.212i	−1.08102	−	1.24756i	−0.967188	−	0.254063i	$-0.918233\pi$
$631$	−682.123	−	787.212i	−1.08102	−	1.24756i	−0.113831	−	0.993500i	$-0.536312\pi$
$632$	−93.2070	−	145.033i	−0.147479	−	0.229482i
$633$		0			0
$634$	−233.282	−	269.222i	−0.367953	−	0.424640i
$635$	65.4038	+	222.745i	0.102998	+	0.350779i
$636$		0			0
$637$	34.6649	−	40.0054i	0.0544190	−	0.0628028i
$638$	60.8445	+	27.7867i	0.0953675	+	0.0435529i
$639$		0			0
$640$	34.3405	+	75.1953i	0.0536571	+	0.117493i
$641$	−783.800	+	112.693i	−1.22278	+	0.175809i	−0.723310	−	0.690524i	$-0.757380\pi$
$641$	−783.800	+	112.693i	−1.22278	+	0.175809i	−0.499468	+	0.866332i	$0.666471\pi$
$642$		0			0
$643$	958.176			1.49016			0.745082	−	0.666972i	$-0.232410\pi$
$643$	958.176			1.49016			0.745082	+	0.666972i	$0.232410\pi$
$644$	−92.5227	−	275.576i	−0.143669	−	0.427913i
$645$		0			0
$646$	884.434	+	568.391i	1.36909	+	0.879862i
$647$	34.1732	−	4.91337i	0.0528179	−	0.00759407i	−0.115855	−	0.993266i	$-0.536961\pi$
$647$	34.1732	−	4.91337i	0.0528179	−	0.00759407i	0.168673	+	0.985672i	$0.446052\pi$
$648$		0			0
$649$	−104.688	−	30.7392i	−0.161307	−	0.0473640i
$650$	213.246	+	97.3863i	0.328071	+	0.149825i
$651$		0			0
$652$	−30.6868	+	213.432i	−0.0470657	+	0.327349i
$653$	357.517	+	1217.59i	0.547500	+	1.86461i	0.500534	+	0.865717i	$0.333137\pi$
$653$	357.517	+	1217.59i	0.547500	+	1.86461i	0.0469657	+	0.998897i	$0.485045\pi$
$654$		0			0
$655$	528.125	−	339.405i	0.806298	−	0.518176i
$656$	49.0928	+	76.3899i	0.0748366	+	0.116448i
$657$		0			0
$658$	343.561	−	100.878i	0.522129	−	0.153311i
$659$	−805.491	−	115.812i	−1.22229	−	0.175739i	−0.499198	−	0.866488i	$-0.666372\pi$
$659$	−805.491	−	115.812i	−1.22229	−	0.175739i	−0.723095	+	0.690749i	$0.757281\pi$
$660$		0			0
$661$	−275.873	+	604.077i	−0.417357	+	0.913884i	0.577855	+	0.816140i	$0.303890\pi$
$661$	−275.873	+	604.077i	−0.417357	+	0.913884i	−0.995212	+	0.0977444i	$0.968837\pi$
$662$	16.4057	−	55.8728i	0.0247821	−	0.0844001i
$663$		0			0
$664$	−37.5934	−	261.468i	−0.0566166	−	0.393777i
$665$	−655.936	+	1020.66i	−0.986369	+	1.53482i
$666$		0			0
$667$	157.436	+	859.718i	0.236036	+	1.28893i
$668$			492.281i			0.736948i
$669$		0			0
$670$	−107.967	−	750.929i	−0.161145	−	1.12079i
$671$	82.1847	−	37.5325i	0.122481	−	0.0559352i
$672$		0			0
$673$	−22.8111	+	49.9493i	−0.0338947	+	0.0742189i	−0.925822	−	0.377960i	$-0.876626\pi$
$673$	−22.8111	+	49.9493i	−0.0338947	+	0.0742189i	0.891927	+	0.452179i	$0.149353\pi$
$674$	−237.800	−	206.055i	−0.352819	−	0.305720i
$675$		0			0
$676$	−258.872	+	76.0118i	−0.382947	+	0.112443i
$677$	801.405	−	694.421i	1.18376	−	1.02573i	0.184681	−	0.982798i	$-0.440875\pi$
$677$	801.405	−	694.421i	1.18376	−	1.02573i	0.999078	−	0.0429347i	$-0.0136707\pi$
$678$		0			0
$679$	64.0712	−	41.1760i	0.0943611	−	0.0606422i
$680$	441.886	−	382.897i	0.649833	−	0.563083i
$681$		0			0
$682$	−5.57165	+	38.7517i	−0.00816958	+	0.0568207i
$683$	−89.0206	−	77.1368i	−0.130338	−	0.112938i	0.587253	−	0.809404i	$-0.300209\pi$
$683$	−89.0206	−	77.1368i	−0.130338	−	0.112938i	−0.717590	+	0.696465i	$0.754755\pi$
$684$		0			0
$685$	1373.47	+	403.287i	2.00507	+	0.588741i
$686$	472.033	−	215.570i	0.688094	−	0.314242i
$687$		0			0
$688$	155.189	+	99.7342i	0.225566	+	0.144963i
$689$			546.140i			0.792656i
$690$		0			0
$691$	−723.240			−1.04666			−0.523329	−	0.852131i	$-0.675310\pi$
$691$	−723.240			−1.04666			−0.523329	+	0.852131i	$0.675310\pi$
$692$	−236.270	+	367.644i	−0.341431	+	0.531277i
$693$		0			0
$694$	25.7607	+	56.4080i	0.0371191	+	0.0812795i
$695$	−70.4594	+	239.963i	−0.101380	+	0.345270i
$696$		0			0
$697$	420.597	−	485.395i	0.603439	−	0.696405i
$698$	534.547	+	76.8563i	0.765827	+	0.110109i
$699$		0			0
$700$	234.954	+	271.151i	0.335649	+	0.387359i
$701$	−355.850	−	553.713i	−0.507631	−	0.789890i	0.488967	−	0.872302i	$-0.337374\pi$
$701$	−355.850	−	553.713i	−0.507631	−	0.789890i	−0.996598	+	0.0824125i	$0.973738\pi$
$702$		0			0
$703$	534.006	+	616.275i	0.759610	+	0.876636i
$704$	2.80528	+	9.55392i	0.00398478	+	0.0135709i
$705$		0			0
$706$	182.727	−	210.878i	0.258820	−	0.298694i
$707$	744.500	+	340.002i	1.05304	+	0.480907i
$708$		0			0
$709$	−148.670	−	325.543i	−0.209690	−	0.459157i	0.775339	−	0.631545i	$-0.217579\pi$
$709$	−148.670	−	325.543i	−0.209690	−	0.459157i	−0.985029	+	0.172388i	$0.944852\pi$
$710$	511.716	−	73.5736i	0.720726	−	0.103625i
$711$		0			0
$712$	−78.8381			−0.110728
$713$	−456.849	+	230.180i	−0.640742	+	0.322833i
$714$		0			0
$715$	44.6756	+	28.7112i	0.0624833	+	0.0401556i
$716$	342.365	−	49.2247i	0.478163	−	0.0687495i
$717$		0			0
$718$	−40.4618	−	11.8807i	−0.0563535	−	0.0165469i
$719$	824.246	+	376.420i	1.14638	+	0.523533i	0.895754	−	0.444551i	$-0.146637\pi$
$719$	824.246	+	376.420i	1.14638	+	0.523533i	0.250625	+	0.968084i	$0.419364\pi$
$720$		0			0
$721$	50.0500	−	348.106i	0.0694175	−	0.482810i
$722$	131.249	+	446.995i	0.181786	+	0.619106i
$723$		0			0
$724$	496.575	−	319.129i	0.685877	−	0.440786i
$725$	−583.212	−	907.496i	−0.804431	−	1.25172i
$726$		0			0
$727$	−1182.45	+	347.198i	−1.62648	+	0.477577i	−0.962749	−	0.270398i	$-0.912845\pi$
$727$	−1182.45	+	347.198i	−1.62648	+	0.477577i	−0.663728	+	0.747974i	$0.731027\pi$
$728$	103.312	+	14.8541i	0.141913	+	0.0204039i
$729$		0			0
$730$	219.560	−	480.770i	0.300768	−	0.658589i
$731$	367.604	−	1251.94i	0.502878	−	1.71265i
$732$		0			0
$733$	14.3777	+	99.9993i	0.0196149	+	0.136425i	0.997276	−	0.0737642i	$-0.0235012\pi$
$733$	14.3777	+	99.9993i	0.0196149	+	0.136425i	−0.977661	+	0.210189i	$0.932592\pi$
$734$	−388.064	+	603.839i	−0.528697	+	0.822669i
$735$		0			0
$736$	−81.3730	+	101.521i	−0.110561	+	0.137936i
$737$		−	91.3812i		−	0.123991i
$738$		0			0
$739$	−118.023	−	820.866i	−0.159706	−	1.11078i	−0.899175	−	0.437589i	$-0.855833\pi$
$739$	−118.023	−	820.866i	−0.159706	−	1.11078i	0.739469	−	0.673190i	$-0.235077\pi$
$740$	412.531	−	188.397i	0.557474	−	0.254590i
$741$		0			0
$742$	−347.220	+	760.306i	−0.467952	+	1.02467i
$743$	918.167	+	795.597i	1.23576	+	1.07079i	0.994966	+	0.100212i	$0.0319522\pi$
$743$	918.167	+	795.597i	1.23576	+	1.07079i	0.240791	+	0.970577i	$0.422593\pi$
$744$		0			0
$745$	−228.906	+	67.2129i	−0.307257	+	0.0902187i
$746$	−263.997	+	228.755i	−0.353884	+	0.306642i
$747$		0			0
$748$	59.2481	−	38.0764i	0.0792087	−	0.0509043i
$749$	−133.503	+	115.681i	−0.178242	+	0.154447i
$750$		0			0
$751$	102.116	−	710.231i	0.135973	−	0.945714i	−0.801584	−	0.597882i	$-0.796009\pi$
$751$	102.116	−	710.231i	0.135973	−	0.945714i	0.937557	−	0.347832i	$-0.113082\pi$
$752$	−121.118	−	104.949i	−0.161061	−	0.139560i
$753$		0			0
$754$	−301.107	−	88.4130i	−0.399346	−	0.117259i
$755$	1048.16	−	478.679i	1.38829	−	0.634012i
$756$		0			0
$757$	−485.548	−	312.043i	−0.641411	−	0.412210i	0.179108	−	0.983829i	$-0.442679\pi$
$757$	−485.548	−	312.043i	−0.641411	−	0.412210i	−0.820519	+	0.571620i	$0.806315\pi$
$758$			778.782i			1.02742i
$759$		0			0
$760$	543.026			0.714508
$761$	−45.7891	+	71.2493i	−0.0601697	+	0.0936258i	−0.870035	−	0.492990i	$-0.835904\pi$
$761$	−45.7891	+	71.2493i	−0.0601697	+	0.0936258i	0.809865	+	0.586616i	$0.199540\pi$
$762$		0			0
$763$	300.604	+	658.231i	0.393976	+	0.862688i
$764$	−177.045	+	602.961i	−0.231735	+	0.789216i
$765$		0			0
$766$	−556.362	+	642.076i	−0.726321	+	0.838219i
$767$	506.683	+	72.8500i	0.660604	+	0.0949805i
$768$		0			0
$769$	146.105	+	168.614i	0.189994	+	0.219264i	0.842752	−	0.538302i	$-0.180934\pi$
$769$	146.105	+	168.614i	0.189994	+	0.219264i	−0.652759	+	0.757566i	$0.726388\pi$
$770$	43.9410	+	68.3736i	0.0570663	+	0.0887969i
$771$		0			0
$772$	−224.548	−	259.143i	−0.290866	−	0.335677i
$773$	207.821	+	707.773i	0.268850	+	0.915619i	0.977655	+	0.210215i	$0.0674163\pi$
$773$	207.821	+	707.773i	0.268850	+	0.915619i	−0.708805	+	0.705404i	$0.750766\pi$
$774$		0			0
$775$	413.471	−	477.171i	0.533511	−	0.615705i
$776$	−31.0077	−	14.1607i	−0.0399584	−	0.0182484i
$777$		0			0
$778$	−293.820	−	643.376i	−0.377661	−	0.826962i
$779$	590.421	−	84.8897i	0.757922	−	0.108973i
$780$		0			0
$781$	62.2712			0.0797326
$782$	851.129	+	349.941i	1.08840	+	0.447495i
$783$		0			0
$784$	−30.5038	−	19.6036i	−0.0389079	−	0.0250046i
$785$	−1729.45	+	248.658i	−2.20313	+	0.316762i
$786$		0			0
$787$	21.1350	+	6.20578i	0.0268551	+	0.00788537i	0.295133	−	0.955456i	$-0.404636\pi$
$787$	21.1350	+	6.20578i	0.0268551	+	0.00788537i	−0.268277	+	0.963342i	$0.586454\pi$
$788$	126.470	+	57.7568i	0.160495	+	0.0732954i
$789$		0			0
$790$	−89.6354	+	623.428i	−0.113463	+	0.789149i
$791$	−57.0869	−	194.420i	−0.0721706	−	0.245790i
$792$		0			0
$793$	−356.596	+	229.170i	−0.449679	+	0.288991i
$794$	−158.857	−	247.187i	−0.200072	−	0.311319i
$795$		0			0
$796$	−530.485	+	155.765i	−0.666439	+	0.195684i
$797$	965.079	+	138.757i	1.21089	+	0.174100i	0.718032	−	0.696010i	$-0.245043\pi$
$797$	965.079	+	138.757i	1.21089	+	0.174100i	0.492858	+	0.870110i	$0.335952\pi$
$798$		0			0
$799$	−470.890	+	1031.11i	−0.589349	+	1.29049i
$800$	45.2417	−	154.079i	0.0565522	−	0.192599i
$801$		0			0
$802$	−100.684	−	700.276i	−0.125542	−	0.873162i
$803$	34.4188	−	53.5567i	0.0428628	−	0.0666957i
$804$		0			0
$805$	−403.839	+	982.221i	−0.501664	+	1.22015i
$806$		−	183.678i		−	0.227888i
$807$		0			0
$808$	−52.1335	−	362.597i	−0.0645217	−	0.448758i
$809$	−727.982	+	332.458i	−0.899855	+	0.410950i	−0.810967	−	0.585092i	$-0.801058\pi$
$809$	−727.982	+	332.458i	−0.899855	+	0.410950i	−0.0888875	+	0.996042i	$0.528331\pi$
$810$		0			0
$811$	−226.966	+	496.986i	−0.279859	+	0.612806i	−0.996403	−	0.0847356i	$-0.972995\pi$
$811$	−226.966	+	496.986i	−0.279859	+	0.612806i	0.716544	+	0.697541i	$0.245723\pi$
$812$	−362.974	−	314.519i	−0.447012	−	0.387338i
$813$		0			0
$814$	52.4141	−	15.3902i	0.0643907	−	0.0189068i
$815$	595.346	−	515.870i	0.730486	−	0.632970i
$816$		0			0
$817$	1019.43	−	655.149i	1.24777	−	0.801896i
$818$	41.6818	−	36.1175i	0.0509558	−	0.0441534i
$819$		0			0
$820$	47.2117	−	328.364i	0.0575752	−	0.400444i
$821$	593.639	+	514.392i	0.723069	+	0.626543i	0.936603	−	0.350393i	$-0.113952\pi$
$821$	593.639	+	514.392i	0.723069	+	0.626543i	−0.213534	+	0.976936i	$0.568497\pi$
$822$		0			0
$823$	1155.80	+	339.375i	1.40438	+	0.412363i	0.894186	−	0.447696i	$-0.147755\pi$
$823$	1155.80	+	339.375i	1.40438	+	0.412363i	0.510194	+	0.860059i	$0.329574\pi$
$824$	−143.182	+	65.3890i	−0.173764	+	0.0793556i
$825$		0			0
$826$	659.060	+	423.552i	0.797894	+	0.512775i
$827$		−	517.170i		−	0.625356i	−0.949859	−	0.312678i	$-0.898774\pi$
$827$		−	517.170i		−	0.625356i	0.949859	−	0.312678i	$-0.101226\pi$
$828$		0			0
$829$	−171.042			−0.206323			−0.103162	−	0.994665i	$-0.532896\pi$
$829$	−171.042			−0.206323			−0.103162	+	0.994665i	$0.532896\pi$
$830$	−521.747	+	811.854i	−0.628611	+	0.978138i
$831$		0			0
$832$	−19.4064	−	42.4941i	−0.0233250	−	0.0510747i
$833$	−72.2557	+	246.080i	−0.0867415	+	0.295414i
$834$		0			0
$835$	1177.75	−	1359.19i	1.41048	−	1.62778i
$836$	64.7429	+	9.30863i	0.0774437	+	0.0111347i
$837$		0			0
$838$	49.3575	+	56.9616i	0.0588992	+	0.0679733i
$839$	64.7164	+	100.701i	0.0771351	+	0.120025i	0.877678	−	0.479251i	$-0.159092\pi$
$839$	64.7164	+	100.701i	0.0771351	+	0.120025i	−0.800543	+	0.599276i	$0.795455\pi$
$840$		0			0
$841$	394.911	+	455.752i	0.469573	+	0.541917i
$842$	75.1972	+	256.098i	0.0893078	+	0.304154i
$843$		0			0
$844$	−64.7482	+	74.7234i	−0.0767159	+	0.0885348i
$845$	896.601	+	409.464i	1.06107	+	0.484573i
$846$		0			0
$847$	−313.580	−	686.644i	−0.370224	−	0.810678i
$848$	370.295	−	53.2404i	0.436668	−	0.0627834i
$849$		0			0
$850$	−1135.82			−1.33626
$851$	556.956	+	446.423i	0.654472	+	0.524586i
$852$		0			0
$853$	399.292	+	256.609i	0.468103	+	0.300831i	0.753347	−	0.657624i	$-0.228438\pi$
$853$	399.292	+	256.609i	0.468103	+	0.300831i	−0.285244	+	0.958455i	$0.592075\pi$
$854$	−642.132	+	92.3246i	−0.751911	+	0.108108i
$855$		0			0
$856$	75.8618	+	22.2750i	0.0886236	+	0.0260222i
$857$	−1332.66	−	608.607i	−1.55503	−	0.710160i	−0.561907	−	0.827200i	$-0.689932\pi$
$857$	−1332.66	−	608.607i	−1.55503	−	0.710160i	−0.993127	+	0.117040i	$0.962659\pi$
$858$		0			0
$859$	−171.341	+	1191.70i	−0.199466	+	1.38731i	0.606373	+	0.795180i	$0.292624\pi$
$859$	−171.341	+	1191.70i	−0.199466	+	1.38731i	−0.805839	+	0.592135i	$0.798285\pi$
$860$	−189.873	−	646.647i	−0.220782	−	0.751915i
$861$		0			0
$862$	−439.439	+	282.410i	−0.509790	+	0.327622i
$863$	46.7278	+	72.7099i	0.0541458	+	0.0842525i	0.867271	−	0.497836i	$-0.165872\pi$
$863$	46.7278	+	72.7099i	0.0541458	+	0.0842525i	−0.813125	+	0.582089i	$0.802236\pi$
$864$		0			0
$865$	1531.91	−	449.808i	1.77099	−	0.520009i
$866$	−978.892	−	140.743i	−1.13036	−	0.162521i
$867$		0			0
$868$	116.777	−	255.706i	0.134536	−	0.294593i
$869$	−21.3738	+	72.7924i	−0.0245958	+	0.0837658i
$870$		0			0
$871$	61.0142	+	424.363i	0.0700507	+	0.487213i
$872$	175.101	−	272.463i	0.200804	−	0.312457i
$873$		0			0
$874$	384.565	+	763.263i	0.440006	+	0.873299i
$875$		−	156.414i		−	0.178759i
$876$		0			0
$877$	−136.808	−	951.520i	−0.155995	−	1.08497i	−0.905920	−	0.423448i	$-0.860819\pi$
$877$	−136.808	−	951.520i	−0.155995	−	1.08497i	0.749925	−	0.661523i	$-0.230090\pi$
$878$	348.486	−	159.148i	0.396908	−	0.181262i
$879$		0			0
$880$	15.1116	−	33.0899i	0.0171723	−	0.0376022i
$881$	−145.784	−	126.322i	−0.165475	−	0.143385i	0.568187	−	0.822900i	$-0.307645\pi$
$881$	−145.784	−	126.322i	−0.165475	−	0.143385i	−0.733662	+	0.679514i	$0.762191\pi$
$882$		0			0
$883$	749.104	−	219.957i	0.848363	−	0.249102i	0.171476	−	0.985188i	$-0.445147\pi$
$883$	749.104	−	219.957i	0.848363	−	0.249102i	0.676887	+	0.736087i	$0.263328\pi$
$884$	−249.718	+	216.381i	−0.282486	+	0.244775i
$885$		0			0
$886$	570.268	−	366.489i	0.643644	−	0.413645i
$887$	−261.360	+	226.470i	−0.294656	+	0.255321i	−0.789625	−	0.613590i	$-0.789725\pi$
$887$	−261.360	+	226.470i	−0.294656	+	0.255321i	0.494969	+	0.868911i	$0.335180\pi$
$888$		0			0
$889$	28.5741	−	198.738i	0.0321419	−	0.223552i
$890$	217.673	+	188.615i	0.244576	+	0.211926i
$891$		0			0
$892$	−362.701	−	106.499i	−0.406616	−	0.119393i
$893$	−957.615	+	437.328i	−1.07236	+	0.489729i
$894$		0			0
$895$	−1063.04	−	683.174i	−1.18775	−	0.763322i
$896$		−	71.4960i		−	0.0797947i
$897$		0			0
$898$	−997.068			−1.11032
$899$	−456.950	+	711.027i	−0.508287	+	0.790909i
$900$		0			0
$901$	−1099.21	−	2406.93i	−1.21999	−	2.67140i
$902$	11.2577	−	38.3403i	0.0124809	−	0.0425059i
$903$		0			0
$904$	−59.3905	+	68.5402i	−0.0656974	+	0.0758188i
$905$	−2134.54	−	306.901i	−2.35861	−	0.339117i
$906$		0			0
$907$	944.552	+	1090.07i	1.04140	+	1.20184i	0.979014	+	0.203791i	$0.0653262\pi$
$907$	944.552	+	1090.07i	1.04140	+	1.20184i	0.0623880	+	0.998052i	$0.480128\pi$
$908$	−12.7179	−	19.7895i	−0.0140065	−	0.0217946i
$909$		0			0
$910$	−249.709	−	288.179i	−0.274405	−	0.316681i
$911$	−324.070	−	1103.68i	−0.355730	−	1.21150i	−0.921969	−	0.387264i	$-0.873420\pi$
$911$	−324.070	−	1103.68i	−0.355730	−	1.21150i	0.566239	−	0.824241i	$-0.308398\pi$
$912$		0			0
$913$	−76.1229	+	87.8505i	−0.0833766	+	0.0962218i
$914$	141.767	+	64.7428i	0.155106	+	0.0708346i
$915$		0			0
$916$	286.395	+	627.118i	0.312659	+	0.684627i
$917$	−537.432	+	77.2711i	−0.586077	+	0.0842651i
$918$		0			0
$919$	730.277			0.794643			0.397321	−	0.917679i	$-0.369940\pi$
$919$	730.277			0.794643			0.397321	+	0.917679i	$0.369940\pi$
$920$	467.552	−	85.6205i	0.508209	−	0.0930657i
$921$		0			0
$922$	−742.050	−	476.887i	−0.804827	−	0.517231i
$923$	−289.179	+	41.5777i	−0.313304	+	0.0450463i
$924$		0			0
$925$	−845.299	−	248.202i	−0.913836	−	0.268327i
$926$	−497.706	−	227.295i	−0.537480	−	0.245459i
$927$		0			0
$928$	−30.5926	+	212.776i	−0.0329661	+	0.229284i
$929$	−149.079	−	507.718i	−0.160473	−	0.546521i	−0.999995	−	0.00319494i	$-0.998983\pi$
$929$	−149.079	−	507.718i	−0.160473	−	0.546521i	0.839522	−	0.543326i	$-0.182835\pi$
$930$		0			0
$931$	−200.378	+	128.775i	−0.215229	+	0.138319i
$932$	15.9140	+	24.7627i	0.0170751	+	0.0265694i
$933$		0			0
$934$	−77.8871	+	22.8697i	−0.0833909	+	0.0244858i
$935$	−254.680	−	36.6174i	−0.272385	−	0.0391630i
$936$		0			0
$937$	621.380	−	1360.63i	0.663159	−	1.45212i	−0.216389	−	0.976307i	$-0.569428\pi$
$937$	621.380	−	1360.63i	0.663159	−	1.45212i	0.879549	−	0.475809i	$-0.157845\pi$
$938$	−184.857	+	629.565i	−0.197076	+	0.671178i
$939$		0			0
$940$	83.3239	+	579.531i	0.0886425	+	0.616522i
$941$	586.869	−	913.186i	0.623665	−	0.970442i	−0.375385	−	0.926869i	$-0.622489\pi$
$941$	586.869	−	913.186i	0.623665	−	0.970442i	0.999050	−	0.0435732i	$-0.0138742\pi$
$942$		0			0
$943$	494.975	−	166.185i	0.524894	−	0.176230i
$944$		−	350.644i		−	0.371445i
$945$		0			0
$946$	−11.5529	−	80.3521i	−0.0122124	−	0.0849388i
$947$	−230.981	+	105.485i	−0.243908	+	0.111389i	−0.533619	−	0.845725i	$-0.679168\pi$
$947$	−230.981	+	105.485i	−0.243908	+	0.111389i	0.289711	+	0.957114i	$0.406441\pi$
$948$		0			0
$949$	−124.077	+	271.692i	−0.130745	+	0.286292i
$950$	−797.215	−	690.791i	−0.839174	−	0.727149i
$951$		0			0
$952$	−485.212	+	142.471i	−0.509676	+	0.149654i
$953$	582.926	−	505.109i	0.611675	−	0.530020i	−0.293005	−	0.956111i	$-0.594655\pi$
$953$	582.926	−	505.109i	0.611675	−	0.530020i	0.904680	+	0.426091i	$0.140110\pi$
$954$		0			0
$955$	1931.36	−	1241.21i	2.02237	−	1.29970i
$956$	641.125	−	555.538i	0.670632	−	0.581106i
$957$		0			0
$958$	−12.8783	+	89.5707i	−0.0134429	+	0.0934976i
$959$	−935.648	−	810.744i	−0.975650	−	0.845405i
$960$		0			0
$961$	447.416	+	131.373i	0.465573	+	0.136705i
$962$	−233.128	+	106.466i	−0.242337	+	0.110672i
$963$		0			0
$964$	−551.818	−	354.632i	−0.572426	−	0.367876i
$965$			1252.71i			1.29815i
$966$		0			0
$967$	582.234			0.602104			0.301052	−	0.953608i	$-0.402662\pi$
$967$	582.234			0.602104			0.301052	+	0.953608i	$0.402662\pi$
$968$	−182.660	+	284.224i	−0.188698	+	0.293620i
$969$		0			0
$970$	51.7340	+	113.282i	0.0533340	+	0.116785i
$971$	288.496	−	982.528i	0.297112	−	1.01187i	−0.666708	−	0.745319i	$-0.732297\pi$
$971$	288.496	−	982.528i	0.297112	−	1.01187i	0.963820	−	0.266553i	$-0.0858847\pi$
$972$		0			0
$973$	141.647	−	163.470i	0.145578	−	0.168006i
$974$	1109.32	+	159.497i	1.13894	+	0.163754i
$975$		0			0
$976$	190.145	+	219.439i	0.194821	+	0.224835i
$977$	194.391	+	302.478i	0.198967	+	0.309599i	0.926372	−	0.376610i	$-0.122910\pi$
$977$	194.391	+	302.478i	0.198967	+	0.309599i	−0.727405	+	0.686208i	$0.759274\pi$
$978$		0			0
$979$	22.7190	+	26.2192i	0.0232064	+	0.0267816i
$980$	37.3211	+	127.104i	0.0380827	+	0.129698i
$981$		0			0
$982$	−292.784	+	337.891i	−0.298151	+	0.344084i
$983$	−1293.58	−	590.758i	−1.31595	−	0.600974i	−0.371136	−	0.928579i	$-0.621031\pi$
$983$	−1293.58	−	590.758i	−1.31595	−	0.600974i	−0.944815	+	0.327604i	$0.893759\pi$
$984$		0			0
$985$	−211.005	−	462.036i	−0.214218	−	0.469073i
$986$	1504.98	−	216.383i	1.52635	−	0.219456i
$987$		0			0
$988$	−306.873			−0.310600
$989$	774.444	−	724.828i	0.783058	−	0.732890i
$990$		0			0
$991$	−1056.14	−	678.743i	−1.06574	−	0.684907i	−0.114517	−	0.993421i	$-0.536532\pi$
$991$	−1056.14	−	678.743i	−1.06574	−	0.684907i	−0.951220	+	0.308514i	$0.900168\pi$
$992$	−124.538	+	17.9058i	−0.125542	+	0.0180502i
$993$		0			0
$994$	−429.013	−	125.970i	−0.431603	−	0.126730i
$995$	1837.33	+	839.080i	1.84656	+	0.843297i
$996$		0			0
$997$	−42.9551	+	298.759i	−0.0430844	+	0.299658i	0.956874	+	0.290504i	$0.0938230\pi$
$997$	−42.9551	+	298.759i	−0.0430844	+	0.299658i	−0.999958	+	0.00915419i	$0.997086\pi$
$998$	−282.159	−	960.944i	−0.282724	−	0.962870i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.3.k.b.71.5	yes	80
3.2	odd	2	inner	414.3.k.b.71.4	yes	80
23.12	even	11	inner	414.3.k.b.35.4	✓	80
69.35	odd	22	inner	414.3.k.b.35.5	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.3.k.b.35.4	✓	80	23.12	even	11	inner
414.3.k.b.35.5	yes	80	69.35	odd	22	inner
414.3.k.b.71.4	yes	80	3.2	odd	2	inner
414.3.k.b.71.5	yes	80	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	414.k (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.764582 - 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(-2.05853 + 7.01070i) q^{5} +(4.13834 - 4.77590i) q^{7} +(-2.79964 - 0.402527i) q^{8} +O(q^{10})\)	\(q+(0.764582 - 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(-2.05853 + 7.01070i) q^{5} +(4.13834 - 4.77590i) q^{7} +(-2.79964 - 0.402527i) q^{8} +(6.76681 + 7.80931i) q^{10} +(0.672913 + 1.04707i) q^{11} +(-3.82404 - 4.41318i) q^{13} +(-2.51784 - 8.57499i) q^{14} +(-2.61944 + 3.02300i) q^{16} +(25.7355 + 11.7530i) q^{17} +(10.9154 + 23.9013i) q^{19} +(14.4646 - 2.07970i) q^{20} +1.76021 q^{22} +(13.1668 + 18.8583i) q^{23} +(-23.8811 - 15.3474i) q^{25} +(-8.17420 + 1.17527i) q^{26} +(-12.1269 - 3.56077i) q^{28} +(34.5666 + 15.7860i) q^{29} +(-3.16533 + 22.0154i) q^{31} +(1.59372 + 5.42771i) q^{32} +(33.6596 - 21.6317i) q^{34} +(24.9635 + 38.8440i) q^{35} +(29.7771 - 8.74336i) q^{37} +(36.7813 + 5.28836i) q^{38} +(8.58513 - 18.7988i) q^{40} +(6.39567 - 21.7817i) q^{41} +(-6.56335 - 45.6491i) q^{43} +(1.34583 - 2.09414i) q^{44} +(32.5030 - 1.24608i) q^{46} +40.0654i q^{47} +(1.29008 + 8.97272i) q^{49} +(-36.5181 + 16.6772i) q^{50} +(-4.85161 + 10.6235i) q^{52} +(-70.6820 - 61.2463i) q^{53} +(-8.72592 + 2.56216i) q^{55} +(-13.5083 + 11.7050i) q^{56} +(45.2098 - 29.0546i) q^{58} +(-66.2497 + 57.4057i) q^{59} +(10.3306 - 71.8509i) q^{61} +(23.7718 + 20.5984i) q^{62} +(7.67594 + 2.25386i) q^{64} +(38.8114 - 17.7246i) q^{65} +(-61.7638 - 39.6932i) q^{67} -56.5845i q^{68} +65.2998 q^{70} +(27.0487 - 42.0886i) q^{71} +(-21.2481 - 46.5267i) q^{73} +(12.3650 - 42.1112i) q^{74} +(34.4140 - 39.7158i) q^{76} +(7.78545 + 1.11938i) q^{77} +(39.9157 + 46.0652i) q^{79} +(-15.8011 - 24.5871i) q^{80} +(-21.0239 - 24.2629i) q^{82} +(26.3120 + 89.6103i) q^{83} +(-135.374 + 156.230i) q^{85} +(-59.3275 - 27.0940i) q^{86} +(-1.46244 - 3.20229i) q^{88} +(27.5898 - 3.96681i) q^{89} -36.9020 q^{91} +(23.3687 - 39.6220i) q^{92} +(47.6663 + 30.6333i) q^{94} +(-190.034 + 27.3228i) q^{95} +(11.5638 + 3.39544i) q^{97} +(11.6613 + 5.32555i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{4} + 16 q^{7}+O(q^{10}) \) 80 * q + 16 * q^4 + 16 * q^7	\( 80 q + 16 q^{4} + 16 q^{7} - 8 q^{10} - 24 q^{13} - 32 q^{16} + 208 q^{19} + 64 q^{22} + 256 q^{25} - 32 q^{28} + 268 q^{34} - 256 q^{37} + 16 q^{40} - 524 q^{43} - 48 q^{46} + 144 q^{49} + 48 q^{52} + 396 q^{55} + 456 q^{58} + 376 q^{61} + 64 q^{64} + 44 q^{67} - 520 q^{70} - 188 q^{73} - 64 q^{76} + 164 q^{79} - 924 q^{82} - 1524 q^{85} + 48 q^{88} + 128 q^{91} - 176 q^{94} - 1144 q^{97}+O(q^{100}) \) 80 * q + 16 * q^4 + 16 * q^7 - 8 * q^10 - 24 * q^13 - 32 * q^16 + 208 * q^19 + 64 * q^22 + 256 * q^25 - 32 * q^28 + 268 * q^34 - 256 * q^37 + 16 * q^40 - 524 * q^43 - 48 * q^46 + 144 * q^49 + 48 * q^52 + 396 * q^55 + 456 * q^58 + 376 * q^61 + 64 * q^64 + 44 * q^67 - 520 * q^70 - 188 * q^73 - 64 * q^76 + 164 * q^79 - 924 * q^82 - 1524 * q^85 + 48 * q^88 + 128 * q^91 - 176 * q^94 - 1144 * q^97

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