LMFDB - Embedded newform 414.3.k.b.35.5

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			35.5
Character	$\chi$	$=$	414.35
Dual form			414.3.k.b.71.5

$q$-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 $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$-1$	$e\left(\frac{10}{11}\right)$

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	−0.860931	−	0.508722i	$-0.830118\pi$
$5$	−2.05853	−	7.01070i	−0.411706	−	1.40214i	0.449225	−	0.893419i	$-0.351700\pi$
$6$		0			0
$7$	4.13834	+	4.77590i	0.591191	+	0.682271i	0.969972	−	0.243215i	$-0.0782022\pi$
$7$	4.13834	+	4.77590i	0.591191	+	0.682271i	−0.378781	+	0.925486i	$0.623657\pi$
$8$	−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	−0.809319	−	0.587369i	$-0.800164\pi$
$11$	0.672913	−	1.04707i	0.0611739	−	0.0951884i	0.870493	+	0.492181i	$0.163800\pi$
$12$		0			0
$13$	−3.82404	+	4.41318i	−0.294157	+	0.339475i	−0.883520	−	0.468393i	$-0.844833\pi$
$13$	−3.82404	+	4.41318i	−0.294157	+	0.339475i	0.589363	+	0.807868i	$0.299379\pi$
$14$	−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	0.526544	−	0.850148i	$-0.323488\pi$
$17$	25.7355	−	11.7530i	1.51386	−	0.691355i	0.987312	+	0.158793i	$0.0507603\pi$
$18$		0			0
$19$	10.9154	−	23.9013i	0.574492	−	1.25796i	−0.369879	−	0.929080i	$-0.620601\pi$
$19$	10.9154	−	23.9013i	0.574492	−	1.25796i	0.944371	−	0.328883i	$-0.106672\pi$
$20$	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	0.282142	−	0.959373i	$-0.408955\pi$
$29$	34.5666	−	15.7860i	1.19195	−	0.544346i	0.909809	+	0.415027i	$0.136228\pi$
$30$		0			0
$31$	−3.16533	−	22.0154i	−0.102107	−	0.710173i	−0.974991	−	0.222244i	$-0.928662\pi$
$31$	−3.16533	−	22.0154i	−0.102107	−	0.710173i	0.872884	−	0.487929i	$-0.162247\pi$
$32$	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	0.658153	−	0.752884i	$-0.271338\pi$
$37$	29.7771	+	8.74336i	0.804788	+	0.236307i	0.146634	+	0.989191i	$0.453156\pi$
$38$	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	0.999987	−	0.00509090i	$-0.00162049\pi$
$41$	6.39567	+	21.7817i	0.155992	+	0.531260i	−0.843995	+	0.536351i	$0.819802\pi$
$42$		0			0
$43$	−6.56335	+	45.6491i	−0.152636	+	1.06161i	0.759142	+	0.650925i	$0.225619\pi$
$43$	−6.56335	+	45.6491i	−0.152636	+	1.06161i	−0.911778	+	0.410682i	$0.865290\pi$
$44$	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	$-0.859842\pi$
$47$		−	40.0654i		−	0.852456i	0.904616	−	0.426228i	$-0.140158\pi$
$48$		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	−0.358598	+	0.933492i	$0.616745\pi$
$53$	−70.6820	+	61.2463i	−1.33362	+	1.15559i	−0.975024	+	0.222098i	$0.928710\pi$
$54$		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	−0.123065	−	0.992399i	$-0.539273\pi$
$59$	−66.2497	−	57.4057i	−1.12288	−	0.972978i	−0.999811	+	0.0194202i	$0.993818\pi$
$60$		0			0
$61$	10.3306	+	71.8509i	0.169354	+	1.17788i	0.880223	+	0.474560i	$0.157393\pi$
$61$	10.3306	+	71.8509i	0.169354	+	1.17788i	−0.710869	+	0.703324i	$0.751698\pi$
$62$	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	−0.913193	−	0.407527i	$-0.866391\pi$
$67$	−61.7638	+	39.6932i	−0.921848	+	0.592436i	−0.00865461	+	0.999963i	$0.502755\pi$
$68$			56.5845i			0.832125i
$69$		0			0
$70$	65.2998			0.932854
$71$	27.0487	+	42.0886i	0.380967	+	0.592796i	0.977793	−	0.209575i	$-0.0672079\pi$
$71$	27.0487	+	42.0886i	0.380967	+	0.592796i	−0.596825	+	0.802371i	$0.703572\pi$
$72$		0			0
$73$	−21.2481	+	46.5267i	−0.291069	+	0.637353i	−0.997518	−	0.0704115i	$-0.977569\pi$
$73$	−21.2481	+	46.5267i	−0.291069	+	0.637353i	0.706449	+	0.707764i	$0.250296\pi$
$74$	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	−0.444617	−	0.895721i	$-0.646660\pi$
$79$	39.9157	−	46.0652i	0.505262	−	0.583103i	0.949879	+	0.312617i	$0.101206\pi$
$80$	−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	−0.634728	−	0.772736i	$-0.718888\pi$
$83$	26.3120	−	89.6103i	0.317012	−	1.07964i	0.951740	−	0.306907i	$-0.0992940\pi$
$84$		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	0.295558	−	0.955325i	$-0.404494\pi$
$89$	27.5898	+	3.96681i	0.309998	+	0.0445709i	0.0144396	+	0.999896i	$0.495404\pi$
$90$		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	−0.221581	−	0.975142i	$-0.571122\pi$
$97$	11.5638	−	3.39544i	0.119214	−	0.0350045i	0.340796	+	0.940137i	$0.389304\pi$
$98$	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	−0.555680	−	0.831396i	$-0.687542\pi$
$101$	36.4887	−	124.269i	0.361275	−	1.23039i	0.916954	−	0.398992i	$-0.130640\pi$
$102$		0			0
$103$	46.8171	+	30.0875i	0.454535	+	0.292112i	0.747806	−	0.663918i	$-0.231107\pi$
$103$	46.8171	+	30.0875i	0.454535	+	0.292112i	−0.293271	+	0.956029i	$0.594744\pi$
$104$	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	−0.270390	−	0.962751i	$-0.587153\pi$
$107$	−27.6690	+	3.97820i	−0.258589	+	0.0371794i	0.0118012	+	0.999930i	$0.496243\pi$
$108$		0			0
$109$	−47.5683	−	104.160i	−0.436406	−	0.955597i	−0.992244	−	0.124306i	$-0.960330\pi$
$109$	−47.5683	−	104.160i	−0.436406	−	0.955597i	0.555837	−	0.831291i	$-0.312398\pi$
$110$	−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	0.909448	−	0.415817i	$-0.136504\pi$
$113$	17.3353	+	26.9743i	0.153410	+	0.238710i	−0.756039	+	0.654527i	$0.772868\pi$
$114$		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	0.641624	−	0.767019i	$-0.278261\pi$
$127$	26.7284	+	17.1773i	0.210460	+	0.135254i	−0.431165	+	0.902273i	$0.641897\pi$
$128$	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	−0.866484	−	0.499204i	$-0.833626\pi$
$131$	−64.9334	+	56.2651i	−0.495675	+	0.429504i	0.370810	+	0.928709i	$0.379080\pi$
$132$		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	$0.253574\pi$
$137$			195.910i			1.43000i	−0.699123	+	0.715002i	$0.746426\pi$
$138$		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	−0.776952	−	0.629559i	$-0.783235\pi$
$149$	17.6524	−	27.4677i	0.118473	−	0.184347i	0.895425	+	0.445212i	$0.146872\pi$
$150$		0			0
$151$	−103.274	+	119.185i	−0.683934	+	0.789302i	−0.986489	−	0.163830i	$-0.947615\pi$
$151$	−103.274	+	119.185i	−0.683934	+	0.789302i	0.302554	+	0.953132i	$0.402161\pi$
$152$	−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	−0.273168	−	0.961966i	$-0.588071\pi$
$157$	99.3378	−	217.519i	0.632725	−	1.38547i	0.905893	−	0.423508i	$-0.139201\pi$
$158$	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	−0.788435	−	0.615119i	$-0.789108\pi$
$163$	−90.6982	+	58.2882i	−0.556431	+	0.357596i	0.232004	+	0.972715i	$0.425472\pi$
$164$	−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	−0.951151	−	0.308726i	$-0.900097\pi$
$167$	−223.897	+	102.251i	−1.34070	+	0.612278i	−0.389552	+	0.921005i	$0.627370\pi$
$168$		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	0.310836	+	0.950464i	$0.399391\pi$
$173$	−118.135	+	183.822i	−0.682862	+	1.06255i	−0.993698	+	0.112091i	$0.964245\pi$
$174$		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	−0.976208	−	0.216834i	$-0.930427\pi$
$179$	−48.7236	−	165.937i	−0.272199	−	0.927025i	0.704010	−	0.710191i	$-0.251391\pi$
$180$		0			0
$181$	42.0028	−	292.136i	0.232060	−	1.61401i	−0.457110	−	0.889410i	$-0.651116\pi$
$181$	42.0028	−	292.136i	0.232060	−	1.61401i	0.689170	−	0.724600i	$-0.257975\pi$
$182$	−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	−0.249201	+	0.968452i	$0.580168\pi$
$191$	−237.463	+	205.763i	−1.24326	+	1.07729i	−0.994059	+	0.108840i	$0.965286\pi$
$192$		0			0
$193$	164.503	+	48.3023i	0.852345	+	0.250271i	0.678589	−	0.734518i	$-0.262592\pi$
$193$	164.503	+	48.3023i	0.852345	+	0.250271i	0.173755	+	0.984789i	$0.444410\pi$
$194$	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	0.511243	−	0.859436i	$-0.329185\pi$
$197$	−52.5374	−	45.5239i	−0.266687	−	0.231086i	−0.777931	+	0.628350i	$0.783731\pi$
$198$		0			0
$199$	39.3416	+	273.627i	0.197696	+	1.37501i	0.810947	+	0.585120i	$0.198953\pi$
$199$	39.3416	+	273.627i	0.197696	+	1.37501i	−0.613251	+	0.789888i	$0.710138\pi$
$200$	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	−0.952034	−	0.305993i	$-0.901012\pi$
$211$	−20.5367	+	44.9691i	−0.0973304	+	0.213124i	0.854703	+	0.519117i	$0.173739\pi$
$212$	−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	0.962049	−	0.272877i	$-0.0879751\pi$
$223$	123.773	+	142.842i	0.555036	+	0.640546i	−0.407013	+	0.913422i	$0.633430\pi$
$224$	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	0.167911	−	0.985802i	$-0.446298\pi$
$227$	11.6422	+	1.67389i	0.0512872	+	0.00737398i	−0.116623	+	0.993176i	$0.537207\pi$
$228$		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	0.110982	−	0.993822i	$-0.464600\pi$
$233$	−14.5679	−	2.09455i	−0.0625232	−	0.00898948i	−0.173505	+	0.984833i	$0.555509\pi$
$234$		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	−0.192373	−	0.981322i	$-0.561618\pi$
$239$	119.501	−	406.983i	0.500004	−	1.70286i	0.692377	−	0.721536i	$-0.256564\pi$
$240$		0			0
$241$	275.909	+	177.316i	1.14485	+	0.735751i	0.968607	−	0.248595i	$-0.0799689\pi$
$241$	275.909	+	177.316i	1.14485	+	0.735751i	0.176244	+	0.984347i	$0.443605\pi$
$242$	−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	0.893701	+	0.448663i	$0.148100\pi$
$251$	233.571	+	363.444i	0.930562	+	1.44798i	0.0368614	+	0.999320i	$0.488264\pi$
$252$		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	0.754529	−	0.656267i	$-0.227866\pi$
$257$	193.435	+	88.3389i	0.752666	+	0.343731i	−0.00186242	+	0.999998i	$0.500593\pi$
$258$		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	−0.998855	−	0.0478459i	$-0.984764\pi$
$263$	−312.540	−	270.818i	−1.18837	−	1.02972i	−0.189511	−	0.981879i	$-0.560690\pi$
$264$		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	−0.926214	−	0.376997i	$-0.876957\pi$
$269$	−184.230	+	159.636i	−0.684869	+	0.593442i	0.241346	+	0.970439i	$0.422411\pi$
$270$		0			0
$271$	222.933	−	65.4590i	0.822631	−	0.241546i	0.156782	−	0.987633i	$-0.449888\pi$
$271$	222.933	−	65.4590i	0.822631	−	0.241546i	0.665849	+	0.746087i	$0.268070\pi$
$272$	−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	−0.961898	−	0.273409i	$-0.911849\pi$
$281$	−84.4445	−	287.591i	−0.300514	−	1.02346i	0.661384	−	0.750048i	$-0.269970\pi$
$282$		0			0
$283$	294.007	+	339.302i	1.03889	+	1.19895i	0.979652	+	0.200704i	$0.0643229\pi$
$283$	294.007	+	339.302i	1.03889	+	1.19895i	0.0592420	+	0.998244i	$0.481132\pi$
$284$	−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	−0.401979	−	0.915649i	$-0.631678\pi$
$293$	7.84685	−	3.58353i	0.0267810	−	0.0122305i	0.428761	+	0.903418i	$0.358950\pi$
$294$		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	−0.963942	−	0.266113i	$-0.914261\pi$
$307$	−35.0039	−	243.457i	−0.114019	−	0.793021i	0.849923	−	0.526907i	$-0.176649\pi$
$308$	−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	−0.568992	−	0.822343i	$-0.692666\pi$
$311$	129.191	−	201.025i	0.415406	−	0.646384i	0.984397	+	0.175959i	$0.0563028\pi$
$312$		0			0
$313$	192.404	+	56.4949i	0.614709	+	0.180495i	0.574241	−	0.818686i	$-0.305297\pi$
$313$	192.404	+	56.4949i	0.614709	+	0.180495i	0.0404674	+	0.999181i	$0.487115\pi$
$314$	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	0.992447	+	0.122674i	$0.0391468\pi$
$317$	70.9667	+	241.690i	0.223870	+	0.762430i	−0.768577	+	0.639757i	$0.779035\pi$
$318$		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	0.340867	−	0.940112i	$-0.389279\pi$
$331$	39.5081	+	11.6006i	0.119360	+	0.0350472i	−0.221507	+	0.975159i	$0.571098\pi$
$332$	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	0.981314	+	0.192413i	$0.0616315\pi$
$337$	31.6643	+	220.230i	0.0939593	+	0.653501i	−0.887355	+	0.461087i	$0.847459\pi$
$338$	−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	0.805413	−	0.592714i	$-0.201943\pi$
$347$	−23.7066	−	36.8882i	−0.0683187	−	0.106306i	−0.873732	+	0.486408i	$0.838307\pi$
$348$		0			0
$349$	158.634	−	347.360i	0.454539	−	0.995301i	−0.534160	−	0.845383i	$-0.679372\pi$
$349$	158.634	−	347.360i	0.454539	−	0.995301i	0.988699	−	0.149917i	$-0.0479007\pi$
$350$	−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	0.139980	−	0.990154i	$-0.455296\pi$
$353$	195.297	−	28.0794i	0.553248	−	0.0795451i	0.413268	+	0.910609i	$0.364387\pi$
$354$		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	−0.970366	−	0.241642i	$-0.922314\pi$
$359$	−8.40090	+	28.6108i	−0.0234008	+	0.0796959i	0.946965	+	0.321337i	$0.104132\pi$
$360$		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	−0.583535	−	0.812088i	$-0.698331\pi$
$373$	−237.000	+	69.5895i	−0.635389	+	0.186567i	−0.0518535	+	0.998655i	$0.516513\pi$
$374$	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	−0.239651	−	0.970859i	$-0.577033\pi$
$379$	−463.263	−	297.721i	−1.22233	−	0.785544i	−0.982679	+	0.185315i	$0.940669\pi$
$380$	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	−0.864581	−	0.502494i	$-0.832416\pi$
$383$	−594.635	+	85.4956i	−1.55257	+	0.223226i	−0.687990	+	0.725720i	$0.741507\pi$
$384$		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	0.991946	+	0.126664i	$0.0404268\pi$
$389$	270.391	+	420.737i	0.695094	+	1.08159i	−0.296852	+	0.954924i	$0.595937\pi$
$390$		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	0.986641	−	0.162912i	$-0.0520886\pi$
$397$	86.3110	+	188.995i	0.217408	+	0.476057i	−0.769233	+	0.638969i	$0.779361\pi$
$398$	−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	0.983258	−	0.182221i	$-0.0583285\pi$
$401$	378.072	+	327.602i	0.942824	+	0.816962i	−0.0404337	+	0.999182i	$0.512874\pi$
$402$		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	−0.235667	−	0.971834i	$-0.575728\pi$
$409$	37.4193	−	10.9873i	0.0914897	−	0.0268638i	0.327157	+	0.944970i	$0.393909\pi$
$410$	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	0.939633	−	0.342184i	$-0.111167\pi$
$419$	−15.0150	−	51.1365i	−0.0358354	−	0.122044i	−0.975468	+	0.220140i	$0.929349\pi$
$420$		0			0
$421$	−123.594	−	142.635i	−0.293573	−	0.338801i	0.589733	−	0.807598i	$-0.299233\pi$
$421$	−123.594	−	142.635i	−0.293573	−	0.338801i	−0.883306	+	0.468797i	$0.844688\pi$
$422$	−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	−0.765121	−	0.643886i	$-0.777321\pi$
$431$	−335.987	+	153.440i	−0.779552	+	0.356010i	−0.0144311	+	0.999896i	$0.504594\pi$
$432$		0			0
$433$	−290.499	+	636.105i	−0.670899	+	1.46906i	0.201106	+	0.979569i	$0.435546\pi$
$433$	−290.499	+	636.105i	−0.670899	+	1.46906i	−0.872006	+	0.489495i	$0.837181\pi$
$434$	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	−0.254705	−	0.967019i	$-0.581978\pi$
$439$	227.893	−	146.458i	0.519119	−	0.333617i	0.773823	+	0.633402i	$0.218342\pi$
$440$	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	0.142747	−	0.989759i	$-0.454407\pi$
$443$	436.017	−	199.122i	0.984236	−	0.449486i	0.841489	+	0.540274i	$0.181679\pi$
$444$		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	0.0965650	+	0.995327i	$0.469214\pi$
$449$	−381.170	+	593.112i	−0.848931	+	1.32096i	−0.945496	+	0.325635i	$0.894422\pi$
$450$		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	−0.965441	−	0.260622i	$-0.916072\pi$
$457$	15.6836	−	109.082i	0.0343185	−	0.238690i	0.999759	+	0.0219313i	$0.00698152\pi$
$458$	−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	$0.236499\pi$
$461$			623.723i			1.35298i	−0.736453	+	0.676489i	$0.763501\pi$
$462$		0			0
$463$	−55.0608	+	382.956i	−0.118922	+	0.827119i	0.839825	+	0.542857i	$0.182658\pi$
$463$	−55.0608	+	382.956i	−0.118922	+	0.827119i	−0.958747	+	0.284262i	$0.908251\pi$
$464$	−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	−0.700068	−	0.714076i	$-0.746847\pi$
$467$	−43.3797	+	37.5887i	−0.0928901	+	0.0804898i	0.607178	+	0.794566i	$0.292302\pi$
$468$		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	0.353731	−	0.935347i	$-0.384913\pi$
$479$	−58.2050	−	26.5813i	−0.121513	−	0.0554933i	−0.475244	+	0.879854i	$0.657640\pi$
$480$		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	−0.190849	−	0.981619i	$-0.561124\pi$
$487$	329.207	−	720.862i	0.675989	−	1.48021i	0.866838	−	0.498590i	$-0.166149\pi$
$488$	−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	−0.453399	−	0.891308i	$-0.649789\pi$
$491$	−312.925	+	44.9918i	−0.637321	+	0.0916330i	−0.183923	+	0.982941i	$0.558880\pi$
$492$		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	0.997194	+	0.0748556i	$0.0238496\pi$
$499$	463.757	+	535.204i	0.929372	+	1.07255i	−0.0678219	+	0.997697i	$0.521605\pi$
$500$	−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	0.258379	−	0.966044i	$-0.416812\pi$
$503$	117.765	+	16.9320i	0.234125	+	0.0336621i	−0.0242535	+	0.999706i	$0.507721\pi$
$504$		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	0.559071	−	0.829120i	$-0.311158\pi$
$509$	438.710	+	63.0770i	0.861905	+	0.123923i	0.302835	+	0.953043i	$0.402067\pi$
$510$		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	−0.545200	−	0.838306i	$-0.683546\pi$
$521$	−433.544	+	62.3342i	−0.832138	+	0.119643i	−0.286938	+	0.957949i	$0.592637\pi$
$522$		0			0
$523$	80.9466	+	177.248i	0.154774	+	0.338907i	0.971096	−	0.238690i	$-0.0767179\pi$
$523$	80.9466	+	177.248i	0.154774	+	0.338907i	−0.816322	+	0.577597i	$0.803991\pi$
$524$	−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	−0.409954	−	0.912106i	$-0.634455\pi$
$541$	−762.776	−	490.206i	−1.40994	−	0.906111i	−0.999982	+	0.00599483i	$0.998092\pi$
$542$	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	−0.757370	−	0.652986i	$-0.773516\pi$
$547$	−569.689	+	167.276i	−1.04148	+	0.305806i	−0.284110	+	0.958792i	$0.591698\pi$
$548$	−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	−0.740333	−	0.672240i	$-0.765332\pi$
$557$	−267.898	−	912.376i	−0.480966	−	1.63802i	0.259368	−	0.965779i	$-0.416486\pi$
$558$		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	−0.899204	−	0.437530i	$-0.855853\pi$
$563$	−71.8780	+	111.844i	−0.127670	+	0.198658i	0.771534	+	0.636188i	$0.219490\pi$
$564$		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	−0.0427414	−	0.999086i	$-0.513609\pi$
$569$	389.383	−	177.825i	0.684328	−	0.312522i	0.727069	+	0.686564i	$0.240882\pi$
$570$		0			0
$571$	99.4070	−	217.671i	0.174093	−	0.381210i	−0.802392	−	0.596798i	$-0.796439\pi$
$571$	99.4070	−	217.671i	0.174093	−	0.381210i	0.976484	+	0.215588i	$0.0691667\pi$
$572$	−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	0.107900	−	0.994162i	$-0.465587\pi$
$577$	609.915	−	391.968i	1.05704	−	0.679321i	0.949145	+	0.314840i	$0.101951\pi$
$578$	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	−0.0362259	+	0.999344i	$0.511534\pi$
$587$	−546.034	+	849.646i	−0.930212	+	1.44744i	−0.893986	+	0.448095i	$0.852103\pi$
$588$		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	0.936593	−	0.350418i	$-0.113961\pi$
$593$	−24.1764	−	82.3371i	−0.0407696	−	0.138848i	−0.977363	+	0.211570i	$0.932142\pi$
$594$		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	$-0.880175\pi$
$599$		−	440.400i		−	0.735226i	0.929979	−	0.367613i	$-0.119825\pi$
$600$		0			0
$601$	−153.986	+	1070.99i	−0.256216	+	1.78202i	0.302994	+	0.952992i	$0.402014\pi$
$601$	−153.986	+	1070.99i	−0.256216	+	1.78202i	−0.559210	+	0.829026i	$0.688895\pi$
$602$	−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	0.0169274	−	0.999857i	$-0.494612\pi$
$607$	−309.203	−	90.7902i	−0.509396	−	0.149572i	−0.526323	+	0.850285i	$0.676430\pi$
$608$	−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	0.783513	+	0.621375i	$0.213426\pi$
$613$	126.768	+	881.691i	0.206799	+	1.43832i	−0.576713	+	0.816947i	$0.695665\pi$
$614$	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	0.990123	−	0.140205i	$-0.0447760\pi$
$617$	945.587	+	431.835i	1.53256	+	0.699895i	0.542433	+	0.840099i	$0.317503\pi$
$618$		0			0
$619$	−755.801	+	485.724i	−1.22100	+	0.784691i	−0.982466	−	0.186442i	$-0.940304\pi$
$619$	−755.801	+	485.724i	−1.22100	+	0.784691i	−0.238538	+	0.971133i	$0.576668\pi$
$620$		−	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	−0.113831	+	0.993500i	$0.536312\pi$
$631$	−682.123	+	787.212i	−1.08102	+	1.24756i	−0.967188	+	0.254063i	$0.918233\pi$
$632$	−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	−0.499468	−	0.866332i	$-0.666471\pi$
$641$	−783.800	−	112.693i	−1.22278	−	0.175809i	−0.723310	+	0.690524i	$0.757380\pi$
$642$		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	0.168673	−	0.985672i	$-0.446052\pi$
$647$	34.1732	+	4.91337i	0.0528179	+	0.00759407i	−0.115855	+	0.993266i	$0.536961\pi$
$648$		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	0.0469657	−	0.998897i	$-0.485045\pi$
$653$	357.517	−	1217.59i	0.547500	−	1.86461i	0.500534	−	0.865717i	$-0.333137\pi$
$654$		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	−0.723095	−	0.690749i	$-0.757281\pi$
$659$	−805.491	+	115.812i	−1.22229	+	0.175739i	−0.499198	+	0.866488i	$0.666372\pi$
$660$		0			0
$661$	−275.873	−	604.077i	−0.417357	−	0.913884i	−0.995212	−	0.0977444i	$-0.968837\pi$
$661$	−275.873	−	604.077i	−0.417357	−	0.913884i	0.577855	−	0.816140i	$-0.303890\pi$
$662$	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	0.891927	−	0.452179i	$-0.149353\pi$
$673$	−22.8111	−	49.9493i	−0.0338947	−	0.0742189i	−0.925822	+	0.377960i	$0.876626\pi$
$674$	−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	0.999078	+	0.0429347i	$0.0136707\pi$
$677$	801.405	+	694.421i	1.18376	+	1.02573i	0.184681	+	0.982798i	$0.440875\pi$
$678$		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	−0.717590	−	0.696465i	$-0.754755\pi$
$683$	−89.0206	+	77.1368i	−0.130338	+	0.112938i	0.587253	+	0.809404i	$0.300209\pi$
$684$		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	−0.996598	−	0.0824125i	$-0.973738\pi$
$701$	−355.850	+	553.713i	−0.507631	+	0.789890i	0.488967	+	0.872302i	$0.337374\pi$
$702$		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	−0.985029	−	0.172388i	$-0.944852\pi$
$709$	−148.670	+	325.543i	−0.209690	+	0.459157i	0.775339	+	0.631545i	$0.217579\pi$
$710$	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	0.250625	−	0.968084i	$-0.419364\pi$
$719$	824.246	−	376.420i	1.14638	−	0.523533i	0.895754	+	0.444551i	$0.146637\pi$
$720$		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	−0.663728	−	0.747974i	$-0.731027\pi$
$727$	−1182.45	−	347.198i	−1.62648	−	0.477577i	−0.962749	+	0.270398i	$0.912845\pi$
$728$	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	−0.977661	−	0.210189i	$-0.932592\pi$
$733$	14.3777	−	99.9993i	0.0196149	−	0.136425i	0.997276	+	0.0737642i	$0.0235012\pi$
$734$	−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	0.739469	+	0.673190i	$0.235077\pi$
$739$	−118.023	+	820.866i	−0.159706	+	1.11078i	−0.899175	+	0.437589i	$0.855833\pi$
$740$	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	0.240791	−	0.970577i	$-0.422593\pi$
$743$	918.167	−	795.597i	1.23576	−	1.07079i	0.994966	−	0.100212i	$-0.0319522\pi$
$744$		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	0.937557	+	0.347832i	$0.113082\pi$
$751$	102.116	+	710.231i	0.135973	+	0.945714i	−0.801584	+	0.597882i	$0.796009\pi$
$752$	−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	−0.820519	−	0.571620i	$-0.806315\pi$
$757$	−485.548	+	312.043i	−0.641411	+	0.412210i	0.179108	+	0.983829i	$0.442679\pi$
$758$		−	778.782i		−	1.02742i
$759$		0			0
$760$	543.026			0.714508
$761$	−45.7891	−	71.2493i	−0.0601697	−	0.0936258i	0.809865	−	0.586616i	$-0.199540\pi$
$761$	−45.7891	−	71.2493i	−0.0601697	−	0.0936258i	−0.870035	+	0.492990i	$0.835904\pi$
$762$		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	−0.652759	−	0.757566i	$-0.726388\pi$
$769$	146.105	−	168.614i	0.189994	−	0.219264i	0.842752	+	0.538302i	$0.180934\pi$
$770$	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	−0.708805	−	0.705404i	$-0.750766\pi$
$773$	207.821	−	707.773i	0.268850	−	0.915619i	0.977655	−	0.210215i	$-0.0674163\pi$
$774$		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	−0.268277	−	0.963342i	$-0.586454\pi$
$787$	21.1350	−	6.20578i	0.0268551	−	0.00788537i	0.295133	+	0.955456i	$0.404636\pi$
$788$	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	0.492858	−	0.870110i	$-0.335952\pi$
$797$	965.079	−	138.757i	1.21089	−	0.174100i	0.718032	+	0.696010i	$0.245043\pi$
$798$		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	−0.0888875	−	0.996042i	$-0.528331\pi$
$809$	−727.982	−	332.458i	−0.899855	−	0.410950i	−0.810967	+	0.585092i	$0.801058\pi$
$810$		0			0
$811$	−226.966	−	496.986i	−0.279859	−	0.612806i	0.716544	−	0.697541i	$-0.245723\pi$
$811$	−226.966	−	496.986i	−0.279859	−	0.612806i	−0.996403	+	0.0847356i	$0.972995\pi$
$812$	−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	−0.213534	−	0.976936i	$-0.568497\pi$
$821$	593.639	−	514.392i	0.723069	−	0.626543i	0.936603	+	0.350393i	$0.113952\pi$
$822$		0			0
$823$	1155.80	−	339.375i	1.40438	−	0.412363i	0.510194	−	0.860059i	$-0.329574\pi$
$823$	1155.80	−	339.375i	1.40438	−	0.412363i	0.894186	+	0.447696i	$0.147755\pi$
$824$	−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	$0.101226\pi$
$827$			517.170i			0.625356i	−0.949859	+	0.312678i	$0.898774\pi$
$828$		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	−0.800543	−	0.599276i	$-0.795455\pi$
$839$	64.7164	−	100.701i	0.0771351	−	0.120025i	0.877678	+	0.479251i	$0.159092\pi$
$840$		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	−0.285244	−	0.958455i	$-0.592075\pi$
$853$	399.292	−	256.609i	0.468103	−	0.300831i	0.753347	+	0.657624i	$0.228438\pi$
$854$	−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	−0.993127	−	0.117040i	$-0.962659\pi$
$857$	−1332.66	+	608.607i	−1.55503	+	0.710160i	−0.561907	+	0.827200i	$0.689932\pi$
$858$		0			0
$859$	−171.341	−	1191.70i	−0.199466	−	1.38731i	−0.805839	−	0.592135i	$-0.798285\pi$
$859$	−171.341	−	1191.70i	−0.199466	−	1.38731i	0.606373	−	0.795180i	$-0.292624\pi$
$860$	−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	−0.813125	−	0.582089i	$-0.802236\pi$
$863$	46.7278	−	72.7099i	0.0541458	−	0.0842525i	0.867271	+	0.497836i	$0.165872\pi$
$864$		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	0.749925	+	0.661523i	$0.230090\pi$
$877$	−136.808	+	951.520i	−0.155995	+	1.08497i	−0.905920	+	0.423448i	$0.860819\pi$
$878$	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	−0.733662	−	0.679514i	$-0.762191\pi$
$881$	−145.784	+	126.322i	−0.165475	+	0.143385i	0.568187	+	0.822900i	$0.307645\pi$
$882$		0			0
$883$	749.104	+	219.957i	0.848363	+	0.249102i	0.676887	−	0.736087i	$-0.263328\pi$
$883$	749.104	+	219.957i	0.848363	+	0.249102i	0.171476	+	0.985188i	$0.445147\pi$
$884$	−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	0.494969	−	0.868911i	$-0.335180\pi$
$887$	−261.360	−	226.470i	−0.294656	−	0.255321i	−0.789625	+	0.613590i	$0.789725\pi$
$888$		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	0.0623880	−	0.998052i	$-0.480128\pi$
$907$	944.552	−	1090.07i	1.04140	−	1.20184i	0.979014	−	0.203791i	$-0.0653262\pi$
$908$	−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	0.566239	+	0.824241i	$0.308398\pi$
$911$	−324.070	+	1103.68i	−0.355730	+	1.21150i	−0.921969	+	0.387264i	$0.873420\pi$
$912$		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	0.839522	+	0.543326i	$0.182835\pi$
$929$	−149.079	+	507.718i	−0.160473	+	0.546521i	−0.999995	+	0.00319494i	$0.998983\pi$
$930$		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	0.879549	+	0.475809i	$0.157845\pi$
$937$	621.380	+	1360.63i	0.663159	+	1.45212i	−0.216389	+	0.976307i	$0.569428\pi$
$938$	−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	0.999050	+	0.0435732i	$0.0138742\pi$
$941$	586.869	+	913.186i	0.623665	+	0.970442i	−0.375385	+	0.926869i	$0.622489\pi$
$942$		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	0.289711	−	0.957114i	$-0.406441\pi$
$947$	−230.981	−	105.485i	−0.243908	−	0.111389i	−0.533619	+	0.845725i	$0.679168\pi$
$948$		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	0.904680	−	0.426091i	$-0.140110\pi$
$953$	582.926	+	505.109i	0.611675	+	0.530020i	−0.293005	+	0.956111i	$0.594655\pi$
$954$		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	0.963820	+	0.266553i	$0.0858847\pi$
$971$	288.496	+	982.528i	0.297112	+	1.01187i	−0.666708	+	0.745319i	$0.732297\pi$
$972$		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	−0.727405	−	0.686208i	$-0.759274\pi$
$977$	194.391	−	302.478i	0.198967	−	0.309599i	0.926372	+	0.376610i	$0.122910\pi$
$978$		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	−0.944815	−	0.327604i	$-0.893759\pi$
$983$	−1293.58	+	590.758i	−1.31595	+	0.600974i	−0.371136	+	0.928579i	$0.621031\pi$
$984$		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	−0.951220	−	0.308514i	$-0.900168\pi$
$991$	−1056.14	+	678.743i	−1.06574	+	0.684907i	−0.114517	+	0.993421i	$0.536532\pi$
$992$	−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	−0.999958	−	0.00915419i	$-0.997086\pi$
$997$	−42.9551	−	298.759i	−0.0430844	−	0.299658i	0.956874	−	0.290504i	$-0.0938230\pi$
$998$	−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.35.5	yes	80
3.2	odd	2	inner	414.3.k.b.35.4	✓	80
23.2	even	11	inner	414.3.k.b.71.4	yes	80
69.2	odd	22	inner	414.3.k.b.71.5	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.3.k.b.35.4	✓	80	3.2	odd	2	inner
414.3.k.b.35.5	yes	80	1.1	even	1	trivial
414.3.k.b.71.4	yes	80	23.2	even	11	inner
414.3.k.b.71.5	yes	80	69.2	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
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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