LMFDB - Embedded newform 400.2.y.c.369.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(129,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("400.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.y (of order $10$, degree $4$, not 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			369.1
Root			$1.17421 - 0.0566033i$ of defining polynomial
Character	$\chi$	$=$	400.369
Dual form			400.2.y.c.129.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29224 - 1.77862i) q^{3} +(-1.22570 - 1.87020i) q^{5} +0.992398i q^{7} +(-0.566541 + 1.74363i) q^{9} +O(q^{10})$	\(q+(-1.29224 - 1.77862i) q^{3} +(-1.22570 - 1.87020i) q^{5} +0.992398i q^{7} +(-0.566541 + 1.74363i) q^{9} +(-0.618034 - 1.90211i) q^{11} +(-3.20892 - 1.04264i) q^{13} +(-1.74248 + 4.59680i) q^{15} +(-1.70135 + 2.34171i) q^{17} +(2.09089 + 1.51912i) q^{19} +(1.76510 - 1.28242i) q^{21} +(-4.32696 + 1.40591i) q^{23} +(-1.99532 + 4.58462i) q^{25} +(-2.43930 + 0.792578i) q^{27} +(-4.35599 + 3.16481i) q^{29} +(0.110461 + 0.0802548i) q^{31} +(-2.58448 + 3.55723i) q^{33} +(1.85599 - 1.21638i) q^{35} +(2.04392 + 0.664110i) q^{37} +(2.29224 + 7.05479i) q^{39} +(2.66780 - 8.21064i) q^{41} -4.64398i q^{43} +(3.95536 - 1.07763i) q^{45} +(-5.83453 - 8.03054i) q^{47} +6.01515 q^{49} +6.36356 q^{51} +(-4.44672 - 6.12038i) q^{53} +(-2.79981 + 3.48727i) q^{55} -5.68196i q^{57} +(1.51967 - 4.67706i) q^{59} +(-0.855890 - 2.63416i) q^{61} +(-1.73038 - 0.562235i) q^{63} +(1.98322 + 7.27931i) q^{65} +(1.28477 - 1.76833i) q^{67} +(8.09205 + 5.87922i) q^{69} +(7.80098 - 5.66774i) q^{71} +(-0.737953 + 0.239775i) q^{73} +(10.7327 - 2.37552i) q^{75} +(1.88765 - 0.613336i) q^{77} +(-12.8236 + 9.31689i) q^{79} +(9.01153 + 6.54726i) q^{81} +(1.04103 - 1.43285i) q^{83} +(6.46482 + 0.311640i) q^{85} +(11.2580 + 3.65794i) q^{87} +(-4.48322 - 13.7979i) q^{89} +(1.03472 - 3.18453i) q^{91} -0.300177i q^{93} +(0.278260 - 5.77237i) q^{95} +(-10.0095 - 13.7768i) q^{97} +3.66673 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{3} + q^{9}+O(q^{10}) $ 8 * q + 5 * q^3 + q^9	$ 8 q + 5 q^{3} + q^{9} + 4 q^{11} - 5 q^{13} - 15 q^{15} - 10 q^{17} + 5 q^{19} - 4 q^{21} - 5 q^{23} - 10 q^{25} + 5 q^{27} - 5 q^{29} + 9 q^{31} + 10 q^{33} - 15 q^{35} + 30 q^{37} + 3 q^{39} - 4 q^{41} - 15 q^{45} + 14 q^{49} + 4 q^{51} - 10 q^{53} + 10 q^{55} - 9 q^{61} - 10 q^{63} + 5 q^{65} - 20 q^{67} + 17 q^{69} - 6 q^{71} + 15 q^{73} + 10 q^{75} + 10 q^{77} - 15 q^{79} + 28 q^{81} + 45 q^{83} - 15 q^{85} + 20 q^{87} - 25 q^{89} - 6 q^{91} - 15 q^{95} - 60 q^{97} + 8 q^{99}+O(q^{100}) $ 8 * q + 5 * q^3 + q^9 + 4 * q^11 - 5 * q^13 - 15 * q^15 - 10 * q^17 + 5 * q^19 - 4 * q^21 - 5 * q^23 - 10 * q^25 + 5 * q^27 - 5 * q^29 + 9 * q^31 + 10 * q^33 - 15 * q^35 + 30 * q^37 + 3 * q^39 - 4 * q^41 - 15 * q^45 + 14 * q^49 + 4 * q^51 - 10 * q^53 + 10 * q^55 - 9 * q^61 - 10 * q^63 + 5 * q^65 - 20 * q^67 + 17 * q^69 - 6 * q^71 + 15 * q^73 + 10 * q^75 + 10 * q^77 - 15 * q^79 + 28 * q^81 + 45 * q^83 - 15 * q^85 + 20 * q^87 - 25 * q^89 - 6 * q^91 - 15 * q^95 - 60 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$	$1$

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			0
$2$		0			0
$3$	−1.29224	−	1.77862i	−0.746076	−	1.02689i	−0.998246	−	0.0592022i	$-0.981144\pi$
$3$	−1.29224	−	1.77862i	−0.746076	−	1.02689i	0.252170	−	0.967683i	$-0.418856\pi$
$4$		0			0
$5$	−1.22570	−	1.87020i	−0.548150	−	0.836380i
$5$	−1.22570	−	1.87020i	−0.548150	−	0.836380i
$6$		0			0
$7$			0.992398i			0.375091i	0.982256	+	0.187546i	$0.0600533\pi$
$7$			0.992398i			0.375091i	−0.982256	+	0.187546i	$0.939947\pi$
$8$		0			0
$9$	−0.566541	+	1.74363i	−0.188847	+	0.581211i
$10$		0			0
$11$	−0.618034	−	1.90211i	−0.186344	−	0.573509i	0.813625	−	0.581390i	$-0.197491\pi$
$11$	−0.618034	−	1.90211i	−0.186344	−	0.573509i	−0.999969	+	0.00788181i	$0.997491\pi$
$12$		0			0
$13$	−3.20892	−	1.04264i	−0.889995	−	0.289177i	−0.171894	−	0.985115i	$-0.554989\pi$
$13$	−3.20892	−	1.04264i	−0.889995	−	0.289177i	−0.718101	+	0.695938i	$0.754989\pi$
$14$		0			0
$15$	−1.74248	+	4.59680i	−0.449905	+	1.18689i
$16$		0			0
$17$	−1.70135	+	2.34171i	−0.412638	+	0.567948i	−0.963859	−	0.266411i	$-0.914162\pi$
$17$	−1.70135	+	2.34171i	−0.412638	+	0.567948i	0.551221	+	0.834359i	$0.314162\pi$
$18$		0			0
$19$	2.09089	+	1.51912i	0.479683	+	0.348510i	0.801203	−	0.598393i	$-0.204194\pi$
$19$	2.09089	+	1.51912i	0.479683	+	0.348510i	−0.321520	+	0.946903i	$0.604194\pi$
$20$		0			0
$21$	1.76510	−	1.28242i	0.385176	−	0.279847i
$22$		0			0
$23$	−4.32696	+	1.40591i	−0.902233	+	0.293153i	−0.723158	−	0.690682i	$-0.757310\pi$
$23$	−4.32696	+	1.40591i	−0.902233	+	0.293153i	−0.179075	+	0.983835i	$0.557310\pi$
$24$		0			0
$25$	−1.99532	+	4.58462i	−0.399064	+	0.916923i
$26$		0			0
$27$	−2.43930	+	0.792578i	−0.469444	+	0.152532i
$28$		0			0
$29$	−4.35599	+	3.16481i	−0.808886	+	0.587690i	−0.913508	−	0.406822i	$-0.866637\pi$
$29$	−4.35599	+	3.16481i	−0.808886	+	0.587690i	0.104621	+	0.994512i	$0.466637\pi$
$30$		0			0
$31$	0.110461	+	0.0802548i	0.0198394	+	0.0144142i	0.597661	−	0.801749i	$-0.296097\pi$
$31$	0.110461	+	0.0802548i	0.0198394	+	0.0144142i	−0.577821	+	0.816163i	$0.696097\pi$
$32$		0			0
$33$	−2.58448	+	3.55723i	−0.449901	+	0.619235i
$34$		0			0
$35$	1.85599	−	1.21638i	0.313719	−	0.205606i
$36$		0			0
$37$	2.04392	+	0.664110i	0.336018	+	0.109179i	0.472166	−	0.881510i	$-0.343472\pi$
$37$	2.04392	+	0.664110i	0.336018	+	0.109179i	−0.136148	+	0.990689i	$0.543472\pi$
$38$		0			0
$39$	2.29224	+	7.05479i	0.367052	+	1.12967i
$40$		0			0
$41$	2.66780	−	8.21064i	0.416640	−	1.28229i	−0.494135	−	0.869385i	$-0.664515\pi$
$41$	2.66780	−	8.21064i	0.416640	−	1.28229i	0.910776	−	0.412902i	$-0.135485\pi$
$42$		0			0
$43$		−	4.64398i		−	0.708200i	−0.935208	−	0.354100i	$-0.884787\pi$
$43$		−	4.64398i		−	0.708200i	0.935208	−	0.354100i	$-0.115213\pi$
$44$		0			0
$45$	3.95536	−	1.07763i	0.589630	−	0.160643i
$46$		0			0
$47$	−5.83453	−	8.03054i	−0.851054	−	1.17137i	−0.983630	−	0.180202i	$-0.942325\pi$
$47$	−5.83453	−	8.03054i	−0.851054	−	1.17137i	0.132576	−	0.991173i	$-0.457675\pi$
$48$		0			0
$49$	6.01515			0.859306
$50$		0			0
$51$	6.36356			0.891077
$52$		0			0
$53$	−4.44672	−	6.12038i	−0.610804	−	0.840699i	0.385839	−	0.922566i	$-0.373912\pi$
$53$	−4.44672	−	6.12038i	−0.610804	−	0.840699i	−0.996643	+	0.0818665i	$0.973912\pi$
$54$		0			0
$55$	−2.79981	+	3.48727i	−0.377527	+	0.470223i
$56$		0			0
$57$		−	5.68196i		−	0.752594i
$58$		0			0
$59$	1.51967	−	4.67706i	0.197844	−	0.608901i	−0.802088	−	0.597206i	$-0.796277\pi$
$59$	1.51967	−	4.67706i	0.197844	−	0.608901i	0.999932	−	0.0116948i	$-0.00372266\pi$
$60$		0			0
$61$	−0.855890	−	2.63416i	−0.109585	−	0.337269i	0.881194	−	0.472755i	$-0.156740\pi$
$61$	−0.855890	−	2.63416i	−0.109585	−	0.337269i	−0.990779	+	0.135486i	$0.956740\pi$
$62$		0			0
$63$	−1.73038	−	0.562235i	−0.218007	−	0.0708349i
$64$		0			0
$65$	1.98322	+	7.27931i	0.245989	+	0.902887i
$66$		0			0
$67$	1.28477	−	1.76833i	0.156959	−	0.216036i	−0.723294	−	0.690540i	$-0.757373\pi$
$67$	1.28477	−	1.76833i	0.156959	−	0.216036i	0.880253	+	0.474505i	$0.157373\pi$
$68$		0			0
$69$	8.09205	+	5.87922i	0.974169	+	0.707775i
$70$		0			0
$71$	7.80098	−	5.66774i	0.925806	−	0.672637i	−0.0191565	−	0.999816i	$-0.506098\pi$
$71$	7.80098	−	5.66774i	0.925806	−	0.672637i	0.944962	+	0.327179i	$0.106098\pi$
$72$		0			0
$73$	−0.737953	+	0.239775i	−0.0863708	+	0.0280636i	−0.351884	−	0.936044i	$-0.614459\pi$
$73$	−0.737953	+	0.239775i	−0.0863708	+	0.0280636i	0.265513	+	0.964107i	$0.414459\pi$
$74$		0			0
$75$	10.7327	−	2.37552i	1.23931	−	0.274301i
$76$		0			0
$77$	1.88765	−	0.613336i	0.215118	−	0.0698961i
$78$		0			0
$79$	−12.8236	+	9.31689i	−1.44277	+	1.04823i	−0.455313	+	0.890332i	$0.650473\pi$
$79$	−12.8236	+	9.31689i	−1.44277	+	1.04823i	−0.987455	+	0.157900i	$0.949527\pi$
$80$		0			0
$81$	9.01153	+	6.54726i	1.00128	+	0.727474i
$82$		0			0
$83$	1.04103	−	1.43285i	0.114268	−	0.157276i	−0.748052	−	0.663640i	$-0.769011\pi$
$83$	1.04103	−	1.43285i	0.114268	−	0.157276i	0.862320	+	0.506364i	$0.169011\pi$
$84$		0			0
$85$	6.46482	+	0.311640i	0.701208	+	0.0338021i
$86$		0			0
$87$	11.2580	+	3.65794i	1.20698	+	0.392172i
$88$		0			0
$89$	−4.48322	−	13.7979i	−0.475221	−	1.46258i	−0.845660	−	0.533722i	$-0.820793\pi$
$89$	−4.48322	−	13.7979i	−0.475221	−	1.46258i	0.370439	−	0.928857i	$-0.379207\pi$
$90$		0			0
$91$	1.03472	−	3.18453i	0.108468	−	0.333830i
$92$		0			0
$93$		−	0.300177i		−	0.0311269i
$94$		0			0
$95$	0.278260	−	5.77237i	0.0285489	−	0.592233i
$96$		0			0
$97$	−10.0095	−	13.7768i	−1.01631	−	1.39883i	−0.914761	−	0.403995i	$-0.867621\pi$
$97$	−10.0095	−	13.7768i	−1.01631	−	1.39883i	−0.101545	−	0.994831i	$-0.532379\pi$
$98$		0			0
$99$	3.66673			0.368520
$100$		0			0
$101$	−2.54716			−0.253452			−0.126726	−	0.991938i	$-0.540447\pi$
$101$	−2.54716			−0.253452			−0.126726	+	0.991938i	$0.540447\pi$
$102$		0			0
$103$	5.97509	+	8.22400i	0.588743	+	0.810335i	0.994620	−	0.103593i	$-0.0330338\pi$
$103$	5.97509	+	8.22400i	0.588743	+	0.810335i	−0.405877	+	0.913928i	$0.633034\pi$
$104$		0			0
$105$	−4.56186	−	1.72923i	−0.445192	−	0.168756i
$106$		0			0
$107$		−	4.81720i		−	0.465697i	−0.972513	−	0.232848i	$-0.925195\pi$
$107$		−	4.81720i		−	0.465697i	0.972513	−	0.232848i	$-0.0748046\pi$
$108$		0			0
$109$	−5.02903	+	15.4778i	−0.481694	+	1.48250i	0.355019	+	0.934859i	$0.384474\pi$
$109$	−5.02903	+	15.4778i	−0.481694	+	1.48250i	−0.836713	+	0.547642i	$0.815526\pi$
$110$		0			0
$111$	−1.46004	−	4.49354i	−0.138581	−	0.426508i
$112$		0			0
$113$	6.42633	+	2.08804i	0.604538	+	0.196426i	0.595264	−	0.803531i	$-0.297048\pi$
$113$	6.42633	+	2.08804i	0.604538	+	0.196426i	0.00927487	+	0.999957i	$0.497048\pi$
$114$		0			0
$115$	7.93290	+	6.36906i	0.739746	+	0.593918i
$116$		0			0
$117$	3.63597	−	5.00449i	0.336146	−	0.462665i
$118$		0			0
$119$	−2.32391	−	1.68842i	−0.213032	−	0.154777i
$120$		0			0
$121$	5.66312	−	4.11450i	0.514829	−	0.374045i
$122$		0			0
$123$	−18.0510	+	5.86513i	−1.62761	+	0.528841i
$124$		0			0
$125$	11.0198	−	1.88771i	0.985643	−	0.168842i
$126$		0			0
$127$	1.41785	−	0.460687i	0.125814	−	0.0408793i	−0.245433	−	0.969413i	$-0.578930\pi$
$127$	1.41785	−	0.460687i	0.125814	−	0.0408793i	0.371247	+	0.928534i	$0.378930\pi$
$128$		0			0
$129$	−8.25985	+	6.00114i	−0.727240	+	0.528370i
$130$		0			0
$131$	11.4190	+	8.29640i	0.997684	+	0.724860i	0.961590	−	0.274489i	$-0.0885086\pi$
$131$	11.4190	+	8.29640i	0.997684	+	0.724860i	0.0360934	+	0.999348i	$0.488509\pi$
$132$		0			0
$133$	−1.50757	+	2.07500i	−0.130723	+	0.179925i
$134$		0			0
$135$	4.47214	+	3.59053i	0.384900	+	0.309024i
$136$		0			0
$137$	0.655703	+	0.213051i	0.0560205	+	0.0182022i	0.336893	−	0.941543i	$-0.390624\pi$
$137$	0.655703	+	0.213051i	0.0560205	+	0.0182022i	−0.280873	+	0.959745i	$0.590624\pi$
$138$		0			0
$139$	−5.12099	−	15.7608i	−0.434356	−	1.33681i	−0.893745	−	0.448576i	$-0.851931\pi$
$139$	−5.12099	−	15.7608i	−0.434356	−	1.33681i	0.459388	−	0.888236i	$-0.348069\pi$
$140$		0			0
$141$	−6.74364	+	20.7548i	−0.567917	+	1.74787i
$142$		0			0
$143$			6.74812i			0.564307i
$144$		0			0
$145$	11.2580	+	4.26747i	0.934923	+	0.354394i
$146$		0			0
$147$	−7.77302	−	10.6986i	−0.641108	−	0.882409i
$148$		0			0
$149$	−3.21156			−0.263101			−0.131551	−	0.991309i	$-0.541996\pi$
$149$	−3.21156			−0.263101			−0.131551	+	0.991309i	$0.541996\pi$
$150$		0			0
$151$	−17.6863			−1.43929			−0.719647	−	0.694340i	$-0.755696\pi$
$151$	−17.6863			−1.43929			−0.719647	+	0.694340i	$0.755696\pi$
$152$		0			0
$153$	−3.11920	−	4.29321i	−0.252172	−	0.347085i
$154$		0			0
$155$	0.0147004	−	0.304953i	0.00118077	−	0.0244944i
$156$		0			0
$157$		−	1.65512i		−	0.132093i	−0.997817	−	0.0660465i	$-0.978961\pi$
$157$		−	1.65512i		−	0.132093i	0.997817	−	0.0660465i	$-0.0210386\pi$
$158$		0			0
$159$	−5.13959	+	15.8180i	−0.407596	+	1.25445i
$160$		0			0
$161$	−1.39523	−	4.29407i	−0.109959	−	0.338420i
$162$		0			0
$163$	−0.849231	−	0.275932i	−0.0665169	−	0.0216127i	0.275570	−	0.961281i	$-0.411134\pi$
$163$	−0.849231	−	0.275932i	−0.0665169	−	0.0216127i	−0.342086	+	0.939668i	$0.611134\pi$
$164$		0			0
$165$	9.82055	+	0.473405i	0.764529	+	0.0368545i
$166$		0			0
$167$	3.05388	−	4.20331i	0.236317	−	0.325262i	−0.674344	−	0.738417i	$-0.735573\pi$
$167$	3.05388	−	4.20331i	0.236317	−	0.325262i	0.910660	+	0.413156i	$0.135573\pi$
$168$		0			0
$169$	−1.30713	−	0.949687i	−0.100549	−	0.0730529i
$170$		0			0
$171$	−3.83337	+	2.78510i	−0.293145	+	0.212982i
$172$		0			0
$173$	5.48250	−	1.78137i	0.416827	−	0.135435i	−0.0930924	−	0.995657i	$-0.529675\pi$
$173$	5.48250	−	1.78137i	0.416827	−	0.135435i	0.509919	+	0.860222i	$0.329675\pi$
$174$		0			0
$175$	−4.54977	−	1.98015i	−0.343930	−	0.149685i
$176$		0			0
$177$	−10.2825	+	3.34098i	−0.772878	+	0.251123i
$178$		0			0
$179$	−7.01326	+	5.09543i	−0.524196	+	0.380850i	−0.818182	−	0.574959i	$-0.805018\pi$
$179$	−7.01326	+	5.09543i	−0.524196	+	0.380850i	0.293986	+	0.955810i	$0.405018\pi$
$180$		0			0
$181$	−11.5616	−	8.39996i	−0.859363	−	0.624364i	0.0683483	−	0.997662i	$-0.478227\pi$
$181$	−11.5616	−	8.39996i	−0.859363	−	0.624364i	−0.927712	+	0.373297i	$0.878227\pi$
$182$		0			0
$183$	−3.57914	+	4.92627i	−0.264578	+	0.364160i
$184$		0			0
$185$	−1.26321	−	4.63655i	−0.0928732	−	0.340886i
$186$		0			0
$187$	5.50569	+	1.78891i	0.402616	+	0.130818i
$188$		0			0
$189$	−0.786553	−	2.42076i	−0.0572133	−	0.176084i
$190$		0			0
$191$	0.391326	−	1.20438i	0.0283154	−	0.0871458i	−0.935900	−	0.352265i	$-0.885411\pi$
$191$	0.391326	−	1.20438i	0.0283154	−	0.0871458i	0.964216	+	0.265120i	$0.0854114\pi$
$192$		0			0
$193$			21.1730i			1.52406i	0.647540	+	0.762031i	$0.275798\pi$
$193$			21.1730i			1.52406i	−0.647540	+	0.762031i	$0.724202\pi$
$194$		0			0
$195$	10.3843	−	12.9340i	0.743635	−	0.926224i
$196$		0			0
$197$	−7.17176	−	9.87108i	−0.510967	−	0.703285i	0.473115	−	0.881001i	$-0.343129\pi$
$197$	−7.17176	−	9.87108i	−0.510967	−	0.703285i	−0.984082	+	0.177715i	$0.943129\pi$
$198$		0			0
$199$	10.4065			0.737695			0.368848	−	0.929490i	$-0.379752\pi$
$199$	10.4065			0.737695			0.368848	+	0.929490i	$0.379752\pi$
$200$		0			0
$201$	−4.80540			−0.338947
$202$		0			0
$203$	−3.14075	−	4.32287i	−0.220438	−	0.303406i
$204$		0			0
$205$	−18.6255	+	5.07446i	−1.30086	+	0.354415i
$206$		0			0
$207$		−	8.34114i		−	0.579749i
$208$		0			0
$209$	1.59730	−	4.91598i	0.110487	−	0.340045i
$210$		0			0
$211$	2.67537	+	8.23395i	0.184180	+	0.566848i	0.999933	−	0.0115520i	$-0.00367718\pi$
$211$	2.67537	+	8.23395i	0.184180	+	0.566848i	−0.815753	+	0.578400i	$0.803677\pi$
$212$		0			0
$213$	−20.1615	−	6.55086i	−1.38144	−	0.448858i
$214$		0			0
$215$	−8.68518	+	5.69212i	−0.592324	+	0.388199i
$216$		0			0
$217$	−0.0796448	+	0.109622i	−0.00540664	+	0.00744160i
$218$		0			0
$219$	1.38008	+	1.00269i	0.0932573	+	0.0677554i
$220$		0			0
$221$	7.90107	−	5.74046i	0.531484	−	0.386145i
$222$		0			0
$223$	26.9562	−	8.75859i	1.80512	−	0.586518i	0.805139	−	0.593086i	$-0.202091\pi$
$223$	26.9562	−	8.75859i	1.80512	−	0.586518i	0.999978	+	0.00656747i	$0.00209051\pi$
$224$		0			0
$225$	−6.86346	−	6.07648i	−0.457564	−	0.405099i
$226$		0			0
$227$	−21.1529	+	6.87299i	−1.40397	+	0.456176i	−0.910471	−	0.413572i	$-0.864281\pi$
$227$	−21.1529	+	6.87299i	−1.40397	+	0.456176i	−0.493495	+	0.869749i	$0.664281\pi$
$228$		0			0
$229$	2.00280	−	1.45512i	0.132348	−	0.0961568i	−0.519641	−	0.854384i	$-0.673934\pi$
$229$	2.00280	−	1.45512i	0.132348	−	0.0961568i	0.651990	+	0.758228i	$0.273934\pi$
$230$		0			0
$231$	−3.53019	−	2.56484i	−0.232270	−	0.168754i
$232$		0			0
$233$	3.50088	−	4.81854i	0.229350	−	0.315673i	−0.678796	−	0.734327i	$-0.737498\pi$
$233$	3.50088	−	4.81854i	0.229350	−	0.315673i	0.908146	+	0.418654i	$0.137498\pi$
$234$		0			0
$235$	−7.86736	+	20.7548i	−0.513210	+	1.35389i
$236$		0			0
$237$	33.1424	+	10.7686i	2.15283	+	0.699496i
$238$		0			0
$239$	−2.17314	−	6.68823i	−0.140569	−	0.432626i	0.855846	−	0.517231i	$-0.173037\pi$
$239$	−2.17314	−	6.68823i	−0.140569	−	0.432626i	−0.996415	+	0.0846050i	$0.973037\pi$
$240$		0			0
$241$	0.364567	−	1.12202i	0.0234838	−	0.0722758i	−0.938628	−	0.344932i	$-0.887902\pi$
$241$	0.364567	−	1.12202i	0.0234838	−	0.0722758i	0.962112	+	0.272656i	$0.0879021\pi$
$242$		0			0
$243$		−	16.7942i		−	1.07735i
$244$		0			0
$245$	−7.37276	−	11.2495i	−0.471029	−	0.718707i
$246$		0			0
$247$	−5.12561	−	7.05479i	−0.326135	−	0.448886i
$248$		0			0
$249$	−3.89375			−0.246757
$250$		0			0
$251$	−4.60867			−0.290897			−0.145448	−	0.989366i	$-0.546462\pi$
$251$	−4.60867			−0.290897			−0.145448	+	0.989366i	$0.546462\pi$
$252$		0			0
$253$	5.34841	+	7.36146i	0.336252	+	0.462811i
$254$		0			0
$255$	−7.79981	−	11.9011i	−0.488443	−	0.745279i
$256$		0			0
$257$			9.75542i			0.608526i	0.952588	+	0.304263i	$0.0984102\pi$
$257$			9.75542i			0.608526i	−0.952588	+	0.304263i	$0.901590\pi$
$258$		0			0
$259$	−0.659062	+	2.02838i	−0.0409521	+	0.126038i
$260$		0			0
$261$	−3.05043	−	9.38824i	−0.188817	−	0.581118i
$262$		0			0
$263$	−0.947088	−	0.307728i	−0.0584000	−	0.0189753i	0.279671	−	0.960096i	$-0.409775\pi$
$263$	−0.947088	−	0.307728i	−0.0584000	−	0.0189753i	−0.338071	+	0.941121i	$0.609775\pi$
$264$		0			0
$265$	−5.99602	+	15.8180i	−0.368333	+	0.971693i
$266$		0			0
$267$	−18.7479	+	25.8042i	−1.14735	+	1.57919i
$268$		0			0
$269$	−2.66048	−	1.93295i	−0.162212	−	0.117854i	0.503718	−	0.863868i	$-0.331965\pi$
$269$	−2.66048	−	1.93295i	−0.162212	−	0.117854i	−0.665930	+	0.746014i	$0.731965\pi$
$270$		0			0
$271$	9.82960	−	7.14162i	0.597105	−	0.433823i	−0.247745	−	0.968825i	$-0.579689\pi$
$271$	9.82960	−	7.14162i	0.597105	−	0.433823i	0.844850	+	0.535003i	$0.179689\pi$
$272$		0			0
$273$	−7.00116	+	2.27482i	−0.423730	+	0.137678i
$274$		0			0
$275$	9.95363	+	0.961876i	0.600227	+	0.0580033i
$276$		0			0
$277$	−11.2858	+	3.66697i	−0.678096	+	0.220327i	−0.627762	−	0.778406i	$-0.716029\pi$
$277$	−11.2858	+	3.66697i	−0.678096	+	0.220327i	−0.0503346	+	0.998732i	$0.516029\pi$
$278$		0			0
$279$	−0.202516	+	0.147136i	−0.0121243	+	0.00880883i
$280$		0			0
$281$	19.9355	+	14.4840i	1.18925	+	0.864041i	0.993185	−	0.116549i	$-0.0371833\pi$
$281$	19.9355	+	14.4840i	1.18925	+	0.864041i	0.196066	+	0.980591i	$0.437183\pi$
$282$		0			0
$283$	1.97697	−	2.72107i	0.117519	−	0.161751i	−0.746205	−	0.665716i	$-0.768126\pi$
$283$	1.97697	−	2.72107i	0.117519	−	0.161751i	0.863724	+	0.503965i	$0.168126\pi$
$284$		0			0
$285$	−10.6264	+	6.96438i	−0.629455	+	0.412534i
$286$		0			0
$287$	8.14823	+	2.64752i	0.480975	+	0.156278i
$288$		0			0
$289$	2.66428	+	8.19982i	0.156723	+	0.482342i
$290$		0			0
$291$	−11.5691	+	35.6060i	−0.678192	+	2.08726i
$292$		0			0
$293$		−	8.96340i		−	0.523647i	−0.965116	−	0.261824i	$-0.915676\pi$
$293$		−	8.96340i		−	0.523647i	0.965116	−	0.261824i	$-0.0843239\pi$
$294$		0			0
$295$	−10.6097	+	2.89058i	−0.617721	+	0.168296i
$296$		0			0
$297$	3.01515	+	4.14999i	0.174956	+	0.240807i
$298$		0			0
$299$	15.3507			0.887756
$300$		0			0
$301$	4.60867			0.265640
$302$		0			0
$303$	3.29155	+	4.53042i	0.189094	+	0.260266i
$304$		0			0
$305$	−3.87735	+	4.82937i	−0.222016	+	0.276529i
$306$		0			0
$307$			9.48133i			0.541128i	0.962702	+	0.270564i	$0.0872102\pi$
$307$			9.48133i			0.541128i	−0.962702	+	0.270564i	$0.912790\pi$
$308$		0			0
$309$	6.90610	−	21.2548i	0.392874	−	1.20914i
$310$		0			0
$311$	−9.06409	−	27.8964i	−0.513978	−	1.58186i	−0.785135	−	0.619325i	$-0.787406\pi$
$311$	−9.06409	−	27.8964i	−0.513978	−	1.58186i	0.271157	−	0.962535i	$-0.412594\pi$
$312$		0			0
$313$	17.9655	+	5.83735i	1.01547	+	0.329947i	0.769031	−	0.639212i	$-0.220739\pi$
$313$	17.9655	+	5.83735i	1.01547	+	0.329947i	0.246440	+	0.969158i	$0.420739\pi$
$314$		0			0
$315$	1.06943	+	3.92529i	0.0602558	+	0.221165i
$316$		0			0
$317$	−13.3952	+	18.4369i	−0.752351	+	1.03552i	0.245461	+	0.969406i	$0.421061\pi$
$317$	−13.3952	+	18.4369i	−0.752351	+	1.03552i	−0.997812	+	0.0661157i	$0.978939\pi$
$318$		0			0
$319$	8.71197	+	6.32962i	0.487777	+	0.354391i
$320$		0			0
$321$	−8.56796	+	6.22499i	−0.478217	+	0.347445i
$322$		0			0
$323$	−7.11468	+	2.31170i	−0.395871	+	0.128626i
$324$		0			0
$325$	11.1829	−	12.6313i	0.620318	−	0.700657i
$326$		0			0
$327$	34.0277	−	11.0563i	1.88174	−	0.611414i
$328$		0			0
$329$	7.96950	−	5.79018i	0.439373	−	0.319223i
$330$		0			0
$331$	2.39711	+	1.74160i	0.131757	+	0.0957272i	0.651712	−	0.758467i	$-0.274051\pi$
$331$	2.39711	+	1.74160i	0.131757	+	0.0957272i	−0.519955	+	0.854194i	$0.674051\pi$
$332$		0			0
$333$	−2.31593	+	3.18760i	−0.126912	+	0.174680i
$334$		0			0
$335$	−4.88187	−	0.235333i	−0.266725	−	0.0128576i
$336$		0			0
$337$	17.8916	+	5.81332i	0.974615	+	0.316672i	0.752678	−	0.658389i	$-0.228762\pi$
$337$	17.8916	+	5.81332i	0.974615	+	0.316672i	0.221937	+	0.975061i	$0.428762\pi$
$338$		0			0
$339$	−4.59054	−	14.1282i	−0.249324	−	0.767340i
$340$		0			0
$341$	0.0843849	−	0.259710i	0.00456970	−	0.0140641i
$342$		0			0
$343$			12.9162i			0.697410i
$344$		0			0
$345$	1.07691	−	22.3399i	0.0579788	−	1.20274i
$346$		0			0
$347$	13.3652	+	18.3956i	0.717480	+	0.987526i	0.999604	+	0.0281483i	$0.00896108\pi$
$347$	13.3652	+	18.3956i	0.717480	+	0.987526i	−0.282124	+	0.959378i	$0.591039\pi$
$348$		0			0
$349$	−1.93849			−0.103765			−0.0518824	−	0.998653i	$-0.516522\pi$
$349$	−1.93849			−0.103765			−0.0518824	+	0.998653i	$0.516522\pi$
$350$		0			0
$351$	8.65392			0.461912
$352$		0			0
$353$	−3.08555	−	4.24689i	−0.164227	−	0.226039i	0.718970	−	0.695041i	$-0.244614\pi$
$353$	−3.08555	−	4.24689i	−0.164227	−	0.226039i	−0.883197	+	0.469002i	$0.844614\pi$
$354$		0			0
$355$	−20.1615	−	7.64246i	−1.07006	−	0.405620i
$356$		0			0
$357$			6.31519i			0.334235i
$358$		0			0
$359$	6.98184	−	21.4879i	0.368488	−	1.13409i	−0.579281	−	0.815128i	$-0.696666\pi$
$359$	6.98184	−	21.4879i	0.368488	−	1.13409i	0.947768	−	0.318960i	$-0.103334\pi$
$360$		0			0
$361$	−3.80723	−	11.7174i	−0.200380	−	0.616708i
$362$		0			0
$363$	−14.6362	−	4.75560i	−0.768203	−	0.249604i
$364$		0			0
$365$	1.35294	+	1.08623i	0.0708160	+	0.0568558i
$366$		0			0
$367$	−4.29008	+	5.90479i	−0.223940	+	0.308228i	−0.906173	−	0.422908i	$-0.861009\pi$
$367$	−4.29008	+	5.90479i	−0.223940	+	0.308228i	0.682232	+	0.731136i	$0.261009\pi$
$368$		0			0
$369$	12.8049	+	9.30333i	0.666598	+	0.484312i
$370$		0			0
$371$	6.07386	−	4.41292i	0.315339	−	0.229107i
$372$		0			0
$373$	21.2156	−	6.89335i	1.09850	−	0.356924i	0.296975	−	0.954885i	$-0.404022\pi$
$373$	21.2156	−	6.89335i	1.09850	−	0.356924i	0.801525	+	0.597961i	$0.204022\pi$
$374$		0			0
$375$	−17.5978	−	17.1607i	−0.908746	−	0.886173i
$376$		0			0
$377$	17.2778	−	5.61390i	0.889852	−	0.289130i
$378$		0			0
$379$	26.6544	−	19.3655i	1.36914	−	0.994740i	0.371339	−	0.928497i	$-0.378899\pi$
$379$	26.6544	−	19.3655i	1.36914	−	0.994740i	0.997804	−	0.0662429i	$-0.0211012\pi$
$380$		0			0
$381$	−2.65159	−	1.92649i	−0.135845	−	0.0986971i
$382$		0			0
$383$	12.1673	−	16.7468i	0.621719	−	0.855722i	−0.375758	−	0.926718i	$-0.622618\pi$
$383$	12.1673	−	16.7468i	0.621719	−	0.855722i	0.997477	+	0.0709955i	$0.0226176\pi$
$384$		0			0
$385$	−3.46076	−	2.77853i	−0.176377	−	0.141607i
$386$		0			0
$387$	8.09739	+	2.63100i	0.411614	+	0.133741i
$388$		0			0
$389$	0.353657	+	1.08844i	0.0179311	+	0.0551863i	0.959622	−	0.281294i	$-0.0907635\pi$
$389$	0.353657	+	1.08844i	0.0179311	+	0.0551863i	−0.941691	+	0.336480i	$0.890764\pi$
$390$		0			0
$391$	4.06943	−	12.5244i	0.205800	−	0.633388i
$392$		0			0
$393$		−	31.0310i		−	1.56531i
$394$		0			0
$395$	33.1424	+	12.5630i	1.66757	+	0.632114i
$396$		0			0
$397$	−2.75385	−	3.79035i	−0.138212	−	0.190232i	0.734300	−	0.678825i	$-0.237510\pi$
$397$	−2.75385	−	3.79035i	−0.138212	−	0.190232i	−0.872512	+	0.488593i	$0.837510\pi$
$398$		0			0
$399$	5.63877			0.282292
$400$		0			0
$401$	−24.0851			−1.20275			−0.601376	−	0.798966i	$-0.705381\pi$
$401$	−24.0851			−1.20275			−0.601376	+	0.798966i	$0.705381\pi$
$402$		0			0
$403$	−0.270785	−	0.372703i	−0.0134888	−	0.0185657i
$404$		0			0
$405$	1.19928	−	24.8784i	0.0595925	−	1.23622i
$406$		0			0
$407$		−	4.29821i		−	0.213054i
$408$		0			0
$409$	0.586930	−	1.80638i	0.0290218	−	0.0893199i	−0.935496	−	0.353336i	$-0.885047\pi$
$409$	0.586930	−	1.80638i	0.0290218	−	0.0893199i	0.964518	+	0.264016i	$0.0850472\pi$
$410$		0			0
$411$	−0.468391	−	1.44156i	−0.0231040	−	0.0711068i
$412$		0			0
$413$	4.64151	+	1.50812i	0.228394	+	0.0742096i
$414$		0			0
$415$	−3.95571	−	0.190687i	−0.194178	−	0.00936047i
$416$		0			0
$417$	−21.4148	+	29.4750i	−1.04869	+	1.44340i
$418$		0			0
$419$	1.88344	+	1.36840i	0.0920120	+	0.0668507i	0.632840	−	0.774283i	$-0.281889\pi$
$419$	1.88344	+	1.36840i	0.0920120	+	0.0668507i	−0.540828	+	0.841133i	$0.681889\pi$
$420$		0			0
$421$	19.3760	−	14.0775i	0.944329	−	0.686095i	−0.00513010	−	0.999987i	$-0.501633\pi$
$421$	19.3760	−	14.0775i	0.944329	−	0.686095i	0.949459	+	0.313892i	$0.101633\pi$
$422$		0			0
$423$	17.3078	−	5.62366i	0.841536	−	0.273431i
$424$		0			0
$425$	−7.34110	−	12.4725i	−0.356095	−	0.605005i
$426$		0			0
$427$	2.61413	−	0.849384i	0.126507	−	0.0411045i
$428$		0			0
$429$	12.0023	−	8.72020i	0.579478	−	0.421015i
$430$		0			0
$431$	0.964563	+	0.700796i	0.0464614	+	0.0337562i	0.610774	−	0.791805i	$-0.290859\pi$
$431$	0.964563	+	0.700796i	0.0464614	+	0.0337562i	−0.564312	+	0.825561i	$0.690859\pi$
$432$		0			0
$433$	15.0554	−	20.7220i	0.723518	−	0.995837i	−0.275882	−	0.961192i	$-0.588970\pi$
$433$	15.0554	−	20.7220i	0.723518	−	0.995837i	0.999400	−	0.0346454i	$-0.0110302\pi$
$434$		0			0
$435$	−6.95781	−	25.5382i	−0.333601	−	1.22446i
$436$		0			0
$437$	−11.1829	−	3.63356i	−0.534953	−	0.173817i
$438$		0			0
$439$	5.98693	+	18.4259i	0.285741	+	0.879420i	0.986176	+	0.165703i	$0.0529894\pi$
$439$	5.98693	+	18.4259i	0.285741	+	0.879420i	−0.700435	+	0.713716i	$0.747011\pi$
$440$		0			0
$441$	−3.40783	+	10.4882i	−0.162277	+	0.499439i
$442$		0			0
$443$			2.46263i			0.117003i	0.998287	+	0.0585016i	$0.0186323\pi$
$443$			2.46263i			0.117003i	−0.998287	+	0.0585016i	$0.981368\pi$
$444$		0			0
$445$	−20.3099	+	25.2967i	−0.962780	+	1.19918i
$446$		0			0
$447$	4.15011	+	5.71214i	0.196294	+	0.270175i
$448$		0			0
$449$	14.3585			0.677618			0.338809	−	0.940855i	$-0.389976\pi$
$449$	14.3585			0.677618			0.338809	+	0.940855i	$0.389976\pi$
$450$		0			0
$451$	−17.2664			−0.813041
$452$		0			0
$453$	22.8550	+	31.4572i	1.07382	+	1.47799i
$454$		0			0
$455$	−7.22397	+	1.96815i	−0.338665	+	0.0922682i
$456$		0			0
$457$		−	25.1964i		−	1.17864i	−0.807901	−	0.589319i	$-0.799396\pi$
$457$		−	25.1964i		−	1.17864i	0.807901	−	0.589319i	$-0.200604\pi$
$458$		0			0
$459$	2.29413	−	7.06059i	0.107081	−	0.329560i
$460$		0			0
$461$	8.90758	+	27.4147i	0.414867	+	1.27683i	0.912370	+	0.409367i	$0.134251\pi$
$461$	8.90758	+	27.4147i	0.414867	+	1.27683i	−0.497502	+	0.867463i	$0.665749\pi$
$462$		0			0
$463$	30.3193	+	9.85134i	1.40906	+	0.457831i	0.912108	−	0.409949i	$-0.134453\pi$
$463$	30.3193	+	9.85134i	1.40906	+	0.457831i	0.496949	+	0.867780i	$0.334453\pi$
$464$		0			0
$465$	−0.561392	+	0.367927i	−0.0260339	+	0.0170622i
$466$		0			0
$467$	−25.3333	+	34.8683i	−1.17229	+	1.61351i	−0.525706	+	0.850666i	$0.676199\pi$
$467$	−25.3333	+	34.8683i	−1.17229	+	1.61351i	−0.646580	+	0.762847i	$0.723801\pi$
$468$		0			0
$469$	1.75489	+	1.27500i	0.0810331	+	0.0588740i
$470$		0			0
$471$	−2.94383	+	2.13882i	−0.135644	+	0.0985514i
$472$		0			0
$473$	−8.83337	+	2.87013i	−0.406159	+	0.131969i
$474$		0			0
$475$	−11.1366	+	6.55479i	−0.510981	+	0.300755i
$476$		0			0
$477$	13.1910	−	4.28600i	0.603973	−	0.196243i
$478$		0			0
$479$	−17.0107	+	12.3590i	−0.777237	+	0.564696i	−0.904148	−	0.427218i	$-0.859494\pi$
$479$	−17.0107	+	12.3590i	−0.777237	+	0.564696i	0.126912	+	0.991914i	$0.459494\pi$
$480$		0			0
$481$	−5.86635	−	4.26216i	−0.267483	−	0.194338i
$482$		0			0
$483$	−5.83453	+	8.03054i	−0.265480	+	0.365402i
$484$		0			0
$485$	−13.4969	+	35.6060i	−0.612862	+	1.61678i
$486$		0			0
$487$	26.5525	+	8.62744i	1.20321	+	0.390947i	0.840941	−	0.541127i	$-0.182002\pi$
$487$	26.5525	+	8.62744i	1.20321	+	0.390947i	0.362269	+	0.932073i	$0.382002\pi$
$488$		0			0
$489$	0.606634	+	1.86703i	0.0274329	+	0.0844299i
$490$		0			0
$491$	−4.62322	+	14.2288i	−0.208643	+	0.642137i	0.790901	+	0.611944i	$0.209612\pi$
$491$	−4.62322	+	14.2288i	−0.208643	+	0.642137i	−0.999544	+	0.0301930i	$0.990388\pi$
$492$		0			0
$493$		−	15.5849i		−	0.701909i
$494$		0			0
$495$	−4.49431	−	6.85753i	−0.202004	−	0.308223i
$496$		0			0
$497$	5.62466	+	7.74168i	0.252300	+	0.347262i
$498$		0			0
$499$	−44.3253			−1.98427			−0.992137	−	0.125160i	$-0.960056\pi$
$499$	−44.3253			−1.98427			−0.992137	+	0.125160i	$0.960056\pi$
$500$		0			0
$501$	−11.4224			−0.510316
$502$		0			0
$503$	−13.8842	−	19.1100i	−0.619066	−	0.852071i	0.378219	−	0.925716i	$-0.376537\pi$
$503$	−13.8842	−	19.1100i	−0.619066	−	0.852071i	−0.997284	+	0.0736453i	$0.976537\pi$
$504$		0			0
$505$	3.12205	+	4.76371i	0.138930	+	0.211982i
$506$		0			0
$507$			3.55211i			0.157755i
$508$		0			0
$509$	8.25552	−	25.4079i	0.365920	−	1.12618i	−0.583484	−	0.812125i	$-0.698311\pi$
$509$	8.25552	−	25.4079i	0.365920	−	1.12618i	0.949403	−	0.314060i	$-0.101689\pi$
$510$		0			0
$511$	−0.237953	−	0.732343i	−0.0105264	−	0.0323970i
$512$		0			0
$513$	−6.30434	−	2.04840i	−0.278343	−	0.0904392i
$514$		0			0
$515$	8.05689	−	21.2548i	0.355029	−	0.936598i
$516$		0			0
$517$	−11.6691	+	16.0611i	−0.513205	+	0.706366i
$518$		0			0
$519$	−10.2531	−	7.44931i	−0.450061	−	0.326988i
$520$		0			0
$521$	−26.4607	+	19.2249i	−1.15927	+	0.842256i	−0.989685	−	0.143260i	$-0.954241\pi$
$521$	−26.4607	+	19.2249i	−1.15927	+	0.842256i	−0.169581	+	0.985516i	$0.554241\pi$
$522$		0			0
$523$	0.224417	−	0.0729175i	0.00981307	−	0.00318846i	−0.304106	−	0.952638i	$-0.598358\pi$
$523$	0.224417	−	0.0729175i	0.00981307	−	0.00318846i	0.313919	+	0.949450i	$0.398358\pi$
$524$		0			0
$525$	2.35746	+	10.6511i	0.102888	+	0.464853i
$526$		0			0
$527$	−0.375867	+	0.122127i	−0.0163730	+	0.00531992i
$528$		0			0
$529$	−1.86142	+	1.35240i	−0.0809313	+	0.0588001i
$530$		0			0
$531$	7.29413	+	5.29949i	0.316538	+	0.229978i
$532$		0			0
$533$	−17.1215	+	23.5658i	−0.741616	+	1.02075i
$534$		0			0
$535$	−9.00915	+	5.90445i	−0.389499	+	0.255271i
$536$		0			0
$537$	18.1256	+	5.88938i	0.782179	+	0.254145i
$538$		0			0
$539$	−3.71756	−	11.4415i	−0.160127	−	0.492820i
$540$		0			0
$541$	−10.3698	+	31.9148i	−0.445830	+	1.37213i	0.435740	+	0.900073i	$0.356487\pi$
$541$	−10.3698	+	31.9148i	−0.445830	+	1.37213i	−0.881570	+	0.472053i	$0.843513\pi$
$542$		0			0
$543$			31.4183i			1.34829i
$544$		0			0
$545$	35.1106	−	9.56578i	1.50397	−	0.409753i
$546$		0			0
$547$	−22.6371	−	31.1573i	−0.967892	−	1.33219i	−0.943105	−	0.332496i	$-0.892109\pi$
$547$	−22.6371	−	31.1573i	−0.967892	−	1.33219i	−0.0247869	−	0.999693i	$-0.507891\pi$
$548$		0			0
$549$	5.07790			0.216720
$550$		0			0
$551$	−13.9156			−0.592825
$552$		0			0
$553$	−9.24607	−	12.7261i	−0.393183	−	0.541170i
$554$		0			0
$555$	−6.61426	+	8.23830i	−0.280760	+	0.349697i
$556$		0			0
$557$		−	4.33445i		−	0.183657i	−0.995775	−	0.0918283i	$-0.970729\pi$
$557$		−	4.33445i		−	0.183657i	0.995775	−	0.0918283i	$-0.0292711\pi$
$558$		0			0
$559$	−4.84201	+	14.9022i	−0.204795	+	0.630294i
$560$		0			0
$561$	−3.93290	−	12.1042i	−0.166047	−	0.511040i
$562$		0			0
$563$	33.1936	+	10.7853i	1.39894	+	0.454544i	0.908849	−	0.417125i	$-0.136962\pi$
$563$	33.1936	+	10.7853i	1.39894	+	0.454544i	0.490094	+	0.871669i	$0.336962\pi$
$564$		0			0
$565$	−3.97169	−	14.5779i	−0.167090	−	0.613295i
$566$		0			0
$567$	−6.49749	+	8.94303i	−0.272869	+	0.375572i
$568$		0			0
$569$	−33.9501	−	24.6662i	−1.42326	−	1.03406i	−0.991223	−	0.132204i	$-0.957795\pi$
$569$	−33.9501	−	24.6662i	−1.42326	−	1.03406i	−0.432038	−	0.901855i	$-0.642205\pi$
$570$		0			0
$571$	−11.1913	+	8.13093i	−0.468340	+	0.340269i	−0.796794	−	0.604251i	$-0.793472\pi$
$571$	−11.1913	+	8.13093i	−0.468340	+	0.340269i	0.328454	+	0.944520i	$0.393472\pi$
$572$		0			0
$573$	−2.64782	+	0.860328i	−0.110614	+	0.0359407i
$574$		0			0
$575$	2.18809	−	22.6427i	0.0912497	−	0.944265i
$576$		0			0
$577$	12.1538	−	3.94902i	0.505970	−	0.164400i	−0.0448986	−	0.998992i	$-0.514296\pi$
$577$	12.1538	−	3.94902i	0.505970	−	0.164400i	0.550869	+	0.834592i	$0.314296\pi$
$578$		0			0
$579$	37.6586	−	27.3606i	1.56504	−	1.13707i
$580$		0			0
$581$	1.42196	+	1.03311i	0.0589928	+	0.0428608i
$582$		0			0
$583$	−8.89344	+	12.2408i	−0.368329	+	0.506961i
$584$		0			0
$585$	−13.8160	−	0.666009i	−0.571222	−	0.0275361i
$586$		0			0
$587$	11.5905	+	3.76597i	0.478390	+	0.155438i	0.538279	−	0.842767i	$-0.319075\pi$
$587$	11.5905	+	3.76597i	0.478390	+	0.155438i	−0.0598889	+	0.998205i	$0.519075\pi$
$588$		0			0
$589$	0.109046	+	0.335608i	0.00449315	+	0.0138285i
$590$		0			0
$591$	−8.28923	+	25.5116i	−0.340973	+	1.04941i
$592$		0			0
$593$			31.2580i			1.28361i	0.766866	+	0.641807i	$0.221815\pi$
$593$			31.2580i			1.28361i	−0.766866	+	0.641807i	$0.778185\pi$
$594$		0			0
$595$	−0.309271	+	6.41567i	−0.0126789	+	0.263017i
$596$		0			0
$597$	−13.4477	−	18.5091i	−0.550376	−	0.757528i
$598$		0			0
$599$	−33.3707			−1.36349			−0.681746	−	0.731589i	$-0.738779\pi$
$599$	−33.3707			−1.36349			−0.681746	+	0.731589i	$0.738779\pi$
$600$		0			0
$601$	−46.8052			−1.90922			−0.954611	−	0.297854i	$-0.903729\pi$
$601$	−46.8052			−1.90922			−0.954611	+	0.297854i	$0.903729\pi$
$602$		0			0
$603$	2.35544	+	3.24199i	0.0959211	+	0.132024i
$604$		0			0
$605$	−14.6362	−	5.54805i	−0.595047	−	0.225560i
$606$		0			0
$607$		−	30.7401i		−	1.24770i	−0.781543	−	0.623851i	$-0.785567\pi$
$607$		−	30.7401i		−	1.24770i	0.781543	−	0.623851i	$-0.214433\pi$
$608$		0			0
$609$	−3.63013	+	11.1724i	−0.147100	+	0.452728i
$610$		0			0
$611$	10.3496	+	31.8527i	0.418699	+	1.28862i
$612$		0			0
$613$	36.4154	+	11.8321i	1.47081	+	0.477894i	0.931352	−	0.364121i	$-0.118631\pi$
$613$	36.4154	+	11.8321i	1.47081	+	0.477894i	0.539454	+	0.842015i	$0.318631\pi$
$614$		0			0
$615$	33.0941	+	26.5702i	1.33448	+	1.07141i
$616$		0			0
$617$	0.249989	−	0.344080i	0.0100642	−	0.0138521i	−0.803955	−	0.594690i	$-0.797275\pi$
$617$	0.249989	−	0.344080i	0.0100642	−	0.0138521i	0.814019	+	0.580838i	$0.197275\pi$
$618$		0			0
$619$	−6.07691	−	4.41513i	−0.244252	−	0.177459i	0.458924	−	0.888476i	$-0.348235\pi$
$619$	−6.07691	−	4.41513i	−0.244252	−	0.177459i	−0.703175	+	0.711016i	$0.748235\pi$
$620$		0			0
$621$	9.44047	−	6.85890i	0.378833	−	0.275238i
$622$		0			0
$623$	13.6931	−	4.44914i	0.548601	−	0.178251i
$624$		0			0
$625$	−17.0374	−	18.2955i	−0.681496	−	0.731822i
$626$		0			0
$627$	−10.8077	+	3.51165i	−0.431619	+	0.140242i
$628$		0			0
$629$	−5.03258	+	3.65638i	−0.200662	+	0.145789i
$630$		0			0
$631$	−9.11889	−	6.62526i	−0.363017	−	0.263747i	0.391292	−	0.920266i	$-0.372028\pi$
$631$	−9.11889	−	6.62526i	−0.363017	−	0.263747i	−0.754309	+	0.656519i	$0.772028\pi$
$632$		0			0
$633$	11.1878	−	15.3987i	0.444676	−	0.612044i
$634$		0			0
$635$	−2.59943	−	2.08700i	−0.103155	−	0.0828201i
$636$		0			0
$637$	−19.3021	−	6.27165i	−0.764779	−	0.248492i
$638$		0			0
$639$	5.46290	+	16.8131i	0.216109	+	0.665115i
$640$		0			0
$641$	8.05994	−	24.8060i	0.318349	−	0.979776i	−0.656006	−	0.754756i	$-0.727755\pi$
$641$	8.05994	−	24.8060i	0.318349	−	0.979776i	0.974354	−	0.225020i	$-0.0722448\pi$
$642$		0			0
$643$		−	31.9492i		−	1.25995i	−0.776614	−	0.629977i	$-0.783064\pi$
$643$		−	31.9492i		−	1.25995i	0.776614	−	0.629977i	$-0.216936\pi$
$644$		0			0
$645$	21.3474	+	8.09201i	0.840555	+	0.318623i
$646$		0			0
$647$	−4.34628	−	5.98214i	−0.170870	−	0.235182i	0.714990	−	0.699134i	$-0.246431\pi$
$647$	−4.34628	−	5.98214i	−0.170870	−	0.235182i	−0.885860	+	0.463952i	$0.846431\pi$
$648$		0			0
$649$	−9.83550			−0.386077
$650$		0			0
$651$	0.297895			0.0116754
$652$		0			0
$653$	10.9829	+	15.1167i	0.429796	+	0.591563i	0.967906	−	0.251311i	$-0.0808618\pi$
$653$	10.9829	+	15.1167i	0.429796	+	0.591563i	−0.538111	+	0.842874i	$0.680862\pi$
$654$		0			0
$655$	1.51967	−	31.5248i	0.0593784	−	1.23177i
$656$		0			0
$657$		−	1.42256i		−	0.0554994i
$658$		0			0
$659$	3.02885	−	9.32184i	0.117987	−	0.363128i	−0.874571	−	0.484897i	$-0.838857\pi$
$659$	3.02885	−	9.32184i	0.117987	−	0.363128i	0.992558	+	0.121770i	$0.0388570\pi$
$660$		0			0
$661$	−8.70145	−	26.7803i	−0.338447	−	1.04163i	−0.964999	−	0.262253i	$-0.915534\pi$
$661$	−8.70145	−	26.7803i	−0.338447	−	1.04163i	0.626552	−	0.779380i	$-0.284466\pi$
$662$		0			0
$663$	−20.4202	−	6.63492i	−0.793054	−	0.257679i
$664$		0			0
$665$	5.72850	+	0.276145i	0.222142	+	0.0107085i
$666$		0			0
$667$	14.3987	−	19.8181i	0.557521	−	0.767361i
$668$		0			0
$669$	−50.4120	−	36.6265i	−1.94904	−	1.41606i
$670$		0			0
$671$	−4.48150	+	3.25600i	−0.173006	+	0.125696i
$672$		0			0
$673$	−37.1153	+	12.0595i	−1.43069	+	0.464859i	−0.918981	−	0.394301i	$-0.870987\pi$
$673$	−37.1153	+	12.0595i	−1.43069	+	0.464859i	−0.511707	+	0.859160i	$0.670987\pi$
$674$		0			0
$675$	1.23353	−	12.7647i	0.0474785	−	0.491314i
$676$		0			0
$677$	−4.78888	+	1.55600i	−0.184052	+	0.0598020i	−0.399593	−	0.916693i	$-0.630848\pi$
$677$	−4.78888	+	1.55600i	−0.184052	+	0.0598020i	0.215541	+	0.976495i	$0.430848\pi$
$678$		0			0
$679$	13.6721	−	9.93337i	0.524687	−	0.381208i
$680$		0			0
$681$	39.5590	+	28.7413i	1.51591	+	1.10137i
$682$		0			0
$683$	−17.8282	+	24.5384i	−0.682178	+	0.938937i	−0.999957	−	0.00922734i	$-0.997063\pi$
$683$	−17.8282	+	24.5384i	−0.682178	+	0.938937i	0.317780	+	0.948165i	$0.397063\pi$
$684$		0			0
$685$	−0.405247	−	1.48743i	−0.0154837	−	0.0568320i
$686$		0			0
$687$	−5.17619	−	1.68185i	−0.197484	−	0.0641664i
$688$		0			0
$689$	7.88781	+	24.2762i	0.300502	+	0.924849i
$690$		0			0
$691$	6.56134	−	20.1937i	0.249605	−	0.768205i	−0.745240	−	0.666796i	$-0.767665\pi$
$691$	6.56134	−	20.1937i	0.249605	−	0.768205i	0.994845	−	0.101409i	$-0.0323349\pi$
$692$		0			0
$693$			3.63886i			0.138229i
$694$		0			0
$695$	−23.1991	+	28.8953i	−0.879991	+	1.09606i
$696$		0			0
$697$	14.6881	+	20.2164i	0.556350	+	0.765751i
$698$		0			0
$699$	−13.0943			−0.495273
$700$		0			0
$701$	32.7698			1.23770			0.618849	−	0.785510i	$-0.287599\pi$
$701$	32.7698			1.23770			0.618849	+	0.785510i	$0.287599\pi$
$702$		0			0
$703$	3.26475	+	4.49354i	0.123132	+	0.169477i
$704$		0			0
$705$	47.0814	−	12.8272i	1.77319	−	0.483099i
$706$		0			0
$707$		−	2.52780i		−	0.0950676i
$708$		0			0
$709$	−6.13273	+	18.8746i	−0.230320	+	0.708851i	0.767388	+	0.641183i	$0.221556\pi$
$709$	−6.13273	+	18.8746i	−0.230320	+	0.708851i	−0.997708	+	0.0676683i	$0.978444\pi$
$710$		0			0
$711$	−8.98015	−	27.6381i	−0.336782	−	1.03651i
$712$		0			0
$713$	−0.590793	−	0.191960i	−0.0221254	−	0.00718897i
$714$		0			0
$715$	12.6204	−	8.27117i	0.471975	−	0.309324i
$716$		0			0
$717$	−9.08759	+	12.5080i	−0.339382	+	0.467120i
$718$		0			0
$719$	−19.5945	−	14.2362i	−0.730751	−	0.530922i	0.159050	−	0.987271i	$-0.449157\pi$
$719$	−19.5945	−	14.2362i	−0.730751	−	0.530922i	−0.889801	+	0.456349i	$0.849157\pi$
$720$		0			0
$721$	−8.16149	+	5.92967i	−0.303950	+	0.220832i
$722$		0			0
$723$	−2.46676	+	0.801498i	−0.0917397	+	0.0298080i
$724$		0			0
$725$	−5.81785	−	26.2853i	−0.216069	−	0.976213i
$726$		0			0
$727$	−5.57804	+	1.81242i	−0.206878	+	0.0672188i	−0.410623	−	0.911805i	$-0.634689\pi$
$727$	−5.57804	+	1.81242i	−0.206878	+	0.0672188i	0.203745	+	0.979024i	$0.434689\pi$
$728$		0			0
$729$	−2.83585	+	2.06037i	−0.105032	+	0.0763099i
$730$		0			0
$731$	10.8748	+	7.90103i	0.402220	+	0.292230i
$732$		0			0
$733$	20.2795	−	27.9123i	0.749039	−	1.03096i	−0.249008	−	0.968501i	$-0.580105\pi$
$733$	20.2795	−	27.9123i	0.749039	−	1.03096i	0.998047	−	0.0624625i	$-0.0198954\pi$
$734$		0			0
$735$	−10.4812	+	27.6504i	−0.386607	+	1.01990i
$736$		0			0
$737$	−4.15759	−	1.35088i	−0.153147	−	0.0497604i
$738$		0			0
$739$	12.2282	+	37.6345i	0.449821	+	1.38441i	0.877109	+	0.480291i	$0.159469\pi$
$739$	12.2282	+	37.6345i	0.449821	+	1.38441i	−0.427288	+	0.904116i	$0.640531\pi$
$740$		0			0
$741$	−5.92426	+	18.2330i	−0.217633	+	0.669805i
$742$		0			0
$743$			29.7058i			1.08980i	0.838501	+	0.544900i	$0.183433\pi$
$743$			29.7058i			1.08980i	−0.838501	+	0.544900i	$0.816567\pi$
$744$		0			0
$745$	3.93641	+	6.00627i	0.144219	+	0.220053i
$746$		0			0
$747$	1.90858	+	2.62694i	0.0698314	+	0.0961147i
$748$		0			0
$749$	4.78058			0.174679
$750$		0			0
$751$	−26.8870			−0.981122			−0.490561	−	0.871407i	$-0.663208\pi$
$751$	−26.8870			−0.981122			−0.490561	+	0.871407i	$0.663208\pi$
$752$		0			0
$753$	5.95552	+	8.19707i	0.217031	+	0.298718i
$754$		0			0
$755$	21.6781	+	33.0771i	0.788949	+	1.20380i
$756$		0			0
$757$		−	44.6792i		−	1.62389i	−0.583731	−	0.811947i	$-0.698408\pi$
$757$		−	44.6792i		−	1.62389i	0.583731	−	0.811947i	$-0.301592\pi$
$758$		0			0
$759$	6.18178	−	19.0256i	0.224384	−	0.690584i
$760$		0			0
$761$	6.27550	+	19.3140i	0.227487	+	0.700132i	0.998030	+	0.0627441i	$0.0199852\pi$
$761$	6.27550	+	19.3140i	0.227487	+	0.700132i	−0.770543	+	0.637388i	$0.780015\pi$
$762$		0			0
$763$	−15.3601	−	4.99080i	−0.556073	−	0.180679i
$764$		0			0
$765$	−4.20597	+	11.0957i	−0.152067	+	0.401167i
$766$		0			0
$767$	−9.75300	+	13.4239i	−0.352160	+	0.484707i
$768$		0			0
$769$	21.0811	+	15.3163i	0.760205	+	0.552321i	0.898973	−	0.438004i	$-0.144314\pi$
$769$	21.0811	+	15.3163i	0.760205	+	0.552321i	−0.138768	+	0.990325i	$0.544314\pi$
$770$		0			0
$771$	17.3511	−	12.6063i	0.624886	−	0.454007i
$772$		0			0
$773$	−13.0585	+	4.24295i	−0.469680	+	0.152608i	−0.534288	−	0.845302i	$-0.679420\pi$
$773$	−13.0585	+	4.24295i	−0.469680	+	0.152608i	0.0646079	+	0.997911i	$0.479420\pi$
$774$		0			0
$775$	−0.588343	+	0.346289i	−0.0211339	+	0.0124391i
$776$		0			0
$777$	4.45938	−	1.44894i	0.159979	−	0.0519805i
$778$		0			0
$779$	18.0510	−	13.1148i	0.646745	−	0.469888i
$780$		0			0
$781$	−15.6020	−	11.3355i	−0.558282	−	0.405616i
$782$		0			0
$783$	8.11722	−	11.1724i	0.290086	−	0.399269i
$784$		0			0
$785$	−3.09541	+	2.02868i	−0.110480	+	0.0724068i
$786$		0			0
$787$	−18.7035	−	6.07714i	−0.666708	−	0.216627i	−0.0439412	−	0.999034i	$-0.513991\pi$
$787$	−18.7035	−	6.07714i	−0.666708	−	0.216627i	−0.622767	+	0.782408i	$0.713991\pi$
$788$		0			0
$789$	0.676537	+	2.08217i	0.0240853	+	0.0741271i
$790$		0			0
$791$	−2.07217	+	6.37748i	−0.0736779	+	0.226757i
$792$		0			0
$793$			9.34520i			0.331858i
$794$		0			0
$795$	35.8825	−	9.77608i	1.27262	−	0.346722i
$796$		0			0
$797$	6.43278	+	8.85396i	0.227861	+	0.313623i	0.907604	−	0.419826i	$-0.137909\pi$
$797$	6.43278	+	8.85396i	0.227861	+	0.313623i	−0.679744	+	0.733450i	$0.737909\pi$
$798$		0			0
$799$	28.7318			1.01646
$800$		0			0
$801$	26.5985			0.939812
$802$		0			0
$803$	0.912160	+	1.25548i	0.0321894	+	0.0443049i
$804$		0			0
$805$	−6.32065	+	7.87259i	−0.222774	+	0.277472i
$806$		0			0
$807$			7.22982i			0.254502i
$808$		0			0
$809$	−5.08109	+	15.6380i	−0.178641	+	0.549802i	−0.999781	−	0.0209255i	$-0.993339\pi$
$809$	−5.08109	+	15.6380i	−0.178641	+	0.549802i	0.821140	+	0.570727i	$0.193339\pi$
$810$		0			0
$811$	−6.99839	−	21.5388i	−0.245747	−	0.756331i	−0.995513	−	0.0946276i	$-0.969834\pi$
$811$	−6.99839	−	21.5388i	−0.245747	−	0.756331i	0.749766	−	0.661703i	$-0.230166\pi$
$812$		0			0
$813$	−25.4044	−	8.25439i	−0.890972	−	0.289494i
$814$		0			0
$815$	0.524854	+	1.92644i	0.0183848	+	0.0674804i
$816$		0			0
$817$	7.05476	−	9.71004i	0.246815	−	0.339711i
$818$		0			0
$819$	4.96645	+	3.60834i	0.173542	+	0.126085i
$820$		0			0
$821$	32.1820	−	23.3816i	1.12316	−	0.816024i	0.138475	−	0.990366i	$-0.455780\pi$
$821$	32.1820	−	23.3816i	1.12316	−	0.816024i	0.984685	+	0.174342i	$0.0557800\pi$
$822$		0			0
$823$	15.7497	−	5.11738i	0.548999	−	0.178381i	−0.0213662	−	0.999772i	$-0.506802\pi$
$823$	15.7497	−	5.11738i	0.548999	−	0.178381i	0.570365	+	0.821391i	$0.306802\pi$
$824$		0			0
$825$	−11.1517	−	18.9467i	−0.388252	−	0.659639i
$826$		0			0
$827$	24.7618	−	8.04561i	0.861053	−	0.279773i	0.154985	−	0.987917i	$-0.450467\pi$
$827$	24.7618	−	8.04561i	0.861053	−	0.279773i	0.706068	+	0.708144i	$0.250467\pi$
$828$		0			0
$829$	4.16123	−	3.02331i	0.144526	−	0.105004i	−0.513173	−	0.858285i	$-0.671530\pi$
$829$	4.16123	−	3.02331i	0.144526	−	0.105004i	0.657699	+	0.753281i	$0.271530\pi$
$830$		0			0
$831$	21.1061	+	15.3345i	0.732162	+	0.531947i
$832$		0			0
$833$	−10.2339	+	14.0857i	−0.354583	+	0.488041i
$834$		0			0
$835$	−11.6042	−	0.559386i	−0.401579	−	0.0193584i
$836$		0			0
$837$	−0.333057	−	0.108217i	−0.0115121	−	0.00374052i
$838$		0			0
$839$	11.9177	+	36.6788i	0.411444	+	1.26629i	0.915393	+	0.402560i	$0.131880\pi$
$839$	11.9177	+	36.6788i	0.411444	+	1.26629i	−0.503950	+	0.863733i	$0.668120\pi$
$840$		0			0
$841$	−0.00289251	+	0.00890222i	−9.97416e−5	+	0.000306973i
$842$		0			0
$843$		−	54.1744i		−	1.86586i
$844$		0			0
$845$	−0.173956	+	3.60863i	−0.00598427	+	0.124141i
$846$		0			0
$847$	4.08322	+	5.62007i	0.140301	+	0.193108i
$848$		0			0
$849$	−7.39447			−0.253777
$850$		0			0
$851$	−9.77764			−0.335173
$852$		0			0
$853$	−5.37684	−	7.40059i	−0.184100	−	0.253391i	0.706985	−	0.707228i	$-0.250055\pi$
$853$	−5.37684	−	7.40059i	−0.184100	−	0.253391i	−0.891085	+	0.453837i	$0.850055\pi$
$854$		0			0
$855$	9.90726	+	3.75547i	0.338821	+	0.128434i
$856$		0			0
$857$			13.6712i			0.466998i	0.972357	+	0.233499i	$0.0750176\pi$
$857$			13.6712i			0.466998i	−0.972357	+	0.233499i	$0.924982\pi$
$858$		0			0
$859$	−11.0182	+	33.9105i	−0.375936	+	1.15701i	0.566909	+	0.823780i	$0.308139\pi$
$859$	−11.0182	+	33.9105i	−0.375936	+	1.15701i	−0.942845	+	0.333232i	$0.891861\pi$
$860$		0			0
$861$	−5.82055	−	17.9138i	−0.198364	−	0.610501i
$862$		0			0
$863$	−32.2725	−	10.4860i	−1.09857	−	0.356947i	−0.297017	−	0.954872i	$-0.595992\pi$
$863$	−32.2725	−	10.4860i	−1.09857	−	0.356947i	−0.801552	+	0.597926i	$0.795992\pi$
$864$		0			0
$865$	−10.0514	−	8.06997i	−0.341759	−	0.274387i
$866$		0			0
$867$	11.1414	−	15.3349i	0.378383	−	0.520800i
$868$		0			0
$869$	25.6472	+	18.6338i	0.870022	+	0.632108i
$870$		0			0
$871$	−5.96645	+	4.33488i	−0.202165	+	0.146882i
$872$		0			0
$873$	29.6925	−	9.64769i	1.00494	−	0.326525i
$874$		0			0
$875$	1.87336	+	10.9361i	0.0633311	+	0.369706i
$876$		0			0
$877$	27.2945	−	8.86851i	0.921668	−	0.299468i	0.190517	−	0.981684i	$-0.438983\pi$
$877$	27.2945	−	8.86851i	0.921668	−	0.299468i	0.731151	+	0.682216i	$0.238983\pi$
$878$		0			0
$879$	−15.9425	+	11.5829i	−0.537726	+	0.390680i
$880$		0			0
$881$	−6.73943	−	4.89648i	−0.227057	−	0.164967i	0.468441	−	0.883495i	$-0.344816\pi$
$881$	−6.73943	−	4.89648i	−0.227057	−	0.164967i	−0.695498	+	0.718528i	$0.744816\pi$
$882$		0			0
$883$	29.5753	−	40.7069i	0.995289	−	1.36990i	0.0671169	−	0.997745i	$-0.478620\pi$
$883$	29.5753	−	40.7069i	0.995289	−	1.36990i	0.928172	−	0.372152i	$-0.121380\pi$
$884$		0			0
$885$	18.8515	+	15.1353i	0.633687	+	0.508767i
$886$		0			0
$887$	11.5255	+	3.74486i	0.386988	+	0.125740i	0.496048	−	0.868295i	$-0.334784\pi$
$887$	11.5255	+	3.74486i	0.386988	+	0.125740i	−0.109060	+	0.994035i	$0.534784\pi$
$888$		0			0
$889$	0.457185	+	1.40707i	0.0153335	+	0.0471916i
$890$		0			0
$891$	6.88420	−	21.1874i	0.230629	−	0.709804i
$892$		0			0
$893$		−	25.6543i		−	0.858490i
$894$		0			0
$895$	18.1256	+	6.87075i	0.605874	+	0.229664i
$896$		0			0
$897$	−19.8369	−	27.3031i	−0.662333	−	0.911624i
$898$		0			0
$899$	−0.735159			−0.0245189
$900$		0			0
$901$	21.8976			0.729514
$902$		0			0
$903$	−5.95552	−	8.19707i	−0.198187	−	0.272781i
$904$		0			0
$905$	−1.53864	+	31.9183i	−0.0511461	+	1.06100i
$906$		0			0
$907$		−	31.9105i		−	1.05957i	−0.848132	−	0.529786i	$-0.822272\pi$
$907$		−	31.9105i		−	1.05957i	0.848132	−	0.529786i	$-0.177728\pi$
$908$		0			0
$909$	1.44307	−	4.44132i	0.0478637	−	0.147309i
$910$		0			0
$911$	7.62900	+	23.4797i	0.252760	+	0.777916i	0.994263	+	0.106966i	$0.0341135\pi$
$911$	7.62900	+	23.4797i	0.252760	+	0.777916i	−0.741503	+	0.670950i	$0.765886\pi$
$912$		0			0
$913$	−3.36884	−	1.09460i	−0.111492	−	0.0362260i
$914$		0			0
$915$	13.6001	+	0.655599i	0.449605	+	0.0216734i
$916$		0			0
$917$	−8.23333	+	11.3322i	−0.271889	+	0.374223i
$918$		0			0
$919$	15.7637	+	11.4530i	0.519997	+	0.377800i	0.816603	−	0.577200i	$-0.195855\pi$
$919$	15.7637	+	11.4530i	0.519997	+	0.377800i	−0.296606	+	0.955000i	$0.595855\pi$
$920$		0			0
$921$	16.8637	−	12.2522i	0.555676	−	0.403723i
$922$		0			0
$923$	−30.9422	+	10.0537i	−1.01847	+	0.330922i
$924$		0			0
$925$	−7.12296	+	8.04548i	−0.234202	+	0.264534i
$926$		0			0
$927$	−17.7248	+	5.75913i	−0.582158	+	0.189155i
$928$		0			0
$929$	9.51748	−	6.91485i	0.312258	−	0.226869i	−0.420607	−	0.907243i	$-0.638183\pi$
$929$	9.51748	−	6.91485i	0.312258	−	0.226869i	0.732865	+	0.680374i	$0.238183\pi$
$930$		0			0
$931$	12.5770	+	9.13773i	0.412195	+	0.299477i
$932$		0			0
$933$	−37.9040	+	52.1704i	−1.24092	+	1.70798i
$934$		0			0
$935$	−3.40270	−	12.4894i	−0.111280	−	0.408448i
$936$		0			0
$937$	20.0371	+	6.51046i	0.654585	+	0.212688i	0.617435	−	0.786622i	$-0.288172\pi$
$937$	20.0371	+	6.51046i	0.654585	+	0.212688i	0.0371502	+	0.999310i	$0.488172\pi$
$938$		0			0
$939$	−12.8334	−	39.4970i	−0.418801	−	1.28894i
$940$		0			0
$941$	−0.694380	+	2.13708i	−0.0226362	+	0.0696669i	−0.961736	−	0.273976i	$-0.911661\pi$
$941$	−0.694380	+	2.13708i	−0.0226362	+	0.0696669i	0.939100	+	0.343643i	$0.111661\pi$
$942$		0			0
$943$			39.2778i			1.27906i
$944$		0			0
$945$	−3.56324	+	4.43814i	−0.115912	+	0.144373i
$946$		0			0
$947$	3.97122	+	5.46592i	0.129047	+	0.177619i	0.868651	−	0.495424i	$-0.164987\pi$
$947$	3.97122	+	5.46592i	0.129047	+	0.177619i	−0.739604	+	0.673042i	$0.764987\pi$
$948$		0			0
$949$	2.61803			0.0849850
$950$		0			0
$951$	50.1021			1.62467
$952$		0			0
$953$	−35.2397	−	48.5033i	−1.14153	−	1.57118i	−0.764051	−	0.645156i	$-0.776793\pi$
$953$	−35.2397	−	48.5033i	−1.14153	−	1.57118i	−0.377475	−	0.926020i	$-0.623207\pi$
$954$		0			0
$955$	−2.73208	+	0.744347i	−0.0884081	+	0.0240865i
$956$		0			0
$957$		−	23.6747i		−	0.765293i
$958$		0			0
$959$	−0.211431	+	0.650719i	−0.00682748	+	0.0210128i
$960$		0			0
$961$	−9.57377	−	29.4650i	−0.308831	−	0.950485i
$962$		0			0
$963$	8.39944	+	2.72914i	0.270668	+	0.0879454i
$964$		0			0
$965$	39.5977	−	25.9517i	1.27470	−	0.835414i
$966$		0			0
$967$	−5.32298	+	7.32645i	−0.171175	+	0.235603i	−0.885982	−	0.463719i	$-0.846515\pi$
$967$	−5.32298	+	7.32645i	−0.171175	+	0.235603i	0.714807	+	0.699322i	$0.246515\pi$
$968$		0			0
$969$	13.3055	+	9.66701i	0.427434	+	0.310549i
$970$		0			0
$971$	38.3076	−	27.8321i	1.22935	−	0.893175i	0.232509	−	0.972594i	$-0.425307\pi$
$971$	38.3076	−	27.8321i	1.22935	−	0.893175i	0.996841	+	0.0794192i	$0.0253066\pi$
$972$		0			0
$973$	15.6410	−	5.08206i	0.501426	−	0.162923i
$974$		0			0
$975$	−36.9173	−	3.56752i	−1.18230	−	0.114252i
$976$		0			0
$977$	−4.51245	+	1.46618i	−0.144366	+	0.0469074i	−0.380309	−	0.924860i	$-0.624182\pi$
$977$	−4.51245	+	1.46618i	−0.144366	+	0.0469074i	0.235943	+	0.971767i	$0.424182\pi$
$978$		0			0
$979$	−23.4745	+	17.0552i	−0.750247	+	0.545086i
$980$		0			0
$981$	−24.1384	−	17.5376i	−0.770680	−	0.559932i
$982$		0			0
$983$	−10.9126	+	15.0199i	−0.348057	+	0.479059i	−0.946773	−	0.321902i	$-0.895678\pi$
$983$	−10.9126	+	15.0199i	−0.348057	+	0.479059i	0.598716	+	0.800961i	$0.295678\pi$
$984$		0			0
$985$	−9.67050	+	25.5116i	−0.308128	+	0.812868i
$986$		0			0
$987$	−20.5970	−	6.69238i	−0.655610	−	0.213021i
$988$		0			0
$989$	6.52903	+	20.0943i	0.207611	+	0.638961i
$990$		0			0
$991$	12.2741	−	37.7758i	0.389900	−	1.19999i	−0.542963	−	0.839757i	$-0.682698\pi$
$991$	12.2741	−	37.7758i	0.389900	−	1.19999i	0.932863	−	0.360232i	$-0.117302\pi$
$992$		0			0
$993$		−	6.51411i		−	0.206719i
$994$		0			0
$995$	−12.7552	−	19.4622i	−0.404367	−	0.616994i
$996$		0			0
$997$	17.8048	+	24.5063i	0.563885	+	0.776121i	0.991814	−	0.127691i	$-0.0407567\pi$
$997$	17.8048	+	24.5063i	0.563885	+	0.776121i	−0.427929	+	0.903812i	$0.640757\pi$
$998$		0			0
$999$	−5.51210			−0.174395

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.y.c.369.1		8
4.3	odd	2		25.2.e.a.19.1	yes	8
12.11	even	2		225.2.m.a.19.2		8
20.3	even	4		125.2.d.b.26.4		16
20.7	even	4		125.2.d.b.26.1		16
20.19	odd	2		125.2.e.b.99.2		8
25.2	odd	20		10000.2.a.bj.1.7		8
25.4	even	10	inner	400.2.y.c.129.1		8
25.23	odd	20		10000.2.a.bj.1.2		8
100.3	even	20		125.2.d.b.101.4		16
100.11	odd	10		625.2.b.c.624.7		8
100.19	odd	10		625.2.e.a.249.1		8
100.23	even	20		625.2.a.f.1.7		8
100.27	even	20		625.2.a.f.1.2		8
100.31	odd	10		625.2.e.i.249.2		8
100.39	odd	10		625.2.b.c.624.2		8
100.47	even	20		125.2.d.b.101.1		16
100.59	odd	10		625.2.e.i.374.2		8
100.63	even	20		625.2.d.o.251.1		16
100.67	even	20		625.2.d.o.376.4		16
100.71	odd	10		125.2.e.b.24.2		8
100.79	odd	10		25.2.e.a.4.1	✓	8
100.83	even	20		625.2.d.o.376.1		16
100.87	even	20		625.2.d.o.251.4		16
100.91	odd	10		625.2.e.a.374.1		8
300.23	odd	20		5625.2.a.x.1.2		8
300.179	even	10		225.2.m.a.154.2		8
300.227	odd	20		5625.2.a.x.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.4.1	✓	8	100.79	odd	10
25.2.e.a.19.1	yes	8	4.3	odd	2
125.2.d.b.26.1		16	20.7	even	4
125.2.d.b.26.4		16	20.3	even	4
125.2.d.b.101.1		16	100.47	even	20
125.2.d.b.101.4		16	100.3	even	20
125.2.e.b.24.2		8	100.71	odd	10
125.2.e.b.99.2		8	20.19	odd	2
225.2.m.a.19.2		8	12.11	even	2
225.2.m.a.154.2		8	300.179	even	10
400.2.y.c.129.1		8	25.4	even	10	inner
400.2.y.c.369.1		8	1.1	even	1	trivial
625.2.a.f.1.2		8	100.27	even	20
625.2.a.f.1.7		8	100.23	even	20
625.2.b.c.624.2		8	100.39	odd	10
625.2.b.c.624.7		8	100.11	odd	10
625.2.d.o.251.1		16	100.63	even	20
625.2.d.o.251.4		16	100.87	even	20
625.2.d.o.376.1		16	100.83	even	20
625.2.d.o.376.4		16	100.67	even	20
625.2.e.a.249.1		8	100.19	odd	10
625.2.e.a.374.1		8	100.91	odd	10
625.2.e.i.249.2		8	100.31	odd	10
625.2.e.i.374.2		8	100.59	odd	10
5625.2.a.x.1.2		8	300.23	odd	20
5625.2.a.x.1.7		8	300.227	odd	20
10000.2.a.bj.1.2		8	25.23	odd	20
10000.2.a.bj.1.7		8	25.2	odd	20

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.y (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.29224 - 1.77862i) q^{3} +(-1.22570 - 1.87020i) q^{5} +0.992398i q^{7} +(-0.566541 + 1.74363i) q^{9} +O(q^{10})\)	\(q+(-1.29224 - 1.77862i) q^{3} +(-1.22570 - 1.87020i) q^{5} +0.992398i q^{7} +(-0.566541 + 1.74363i) q^{9} +(-0.618034 - 1.90211i) q^{11} +(-3.20892 - 1.04264i) q^{13} +(-1.74248 + 4.59680i) q^{15} +(-1.70135 + 2.34171i) q^{17} +(2.09089 + 1.51912i) q^{19} +(1.76510 - 1.28242i) q^{21} +(-4.32696 + 1.40591i) q^{23} +(-1.99532 + 4.58462i) q^{25} +(-2.43930 + 0.792578i) q^{27} +(-4.35599 + 3.16481i) q^{29} +(0.110461 + 0.0802548i) q^{31} +(-2.58448 + 3.55723i) q^{33} +(1.85599 - 1.21638i) q^{35} +(2.04392 + 0.664110i) q^{37} +(2.29224 + 7.05479i) q^{39} +(2.66780 - 8.21064i) q^{41} -4.64398i q^{43} +(3.95536 - 1.07763i) q^{45} +(-5.83453 - 8.03054i) q^{47} +6.01515 q^{49} +6.36356 q^{51} +(-4.44672 - 6.12038i) q^{53} +(-2.79981 + 3.48727i) q^{55} -5.68196i q^{57} +(1.51967 - 4.67706i) q^{59} +(-0.855890 - 2.63416i) q^{61} +(-1.73038 - 0.562235i) q^{63} +(1.98322 + 7.27931i) q^{65} +(1.28477 - 1.76833i) q^{67} +(8.09205 + 5.87922i) q^{69} +(7.80098 - 5.66774i) q^{71} +(-0.737953 + 0.239775i) q^{73} +(10.7327 - 2.37552i) q^{75} +(1.88765 - 0.613336i) q^{77} +(-12.8236 + 9.31689i) q^{79} +(9.01153 + 6.54726i) q^{81} +(1.04103 - 1.43285i) q^{83} +(6.46482 + 0.311640i) q^{85} +(11.2580 + 3.65794i) q^{87} +(-4.48322 - 13.7979i) q^{89} +(1.03472 - 3.18453i) q^{91} -0.300177i q^{93} +(0.278260 - 5.77237i) q^{95} +(-10.0095 - 13.7768i) q^{97} +3.66673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{3} + q^{9}+O(q^{10}) \) 8 * q + 5 * q^3 + q^9	\( 8 q + 5 q^{3} + q^{9} + 4 q^{11} - 5 q^{13} - 15 q^{15} - 10 q^{17} + 5 q^{19} - 4 q^{21} - 5 q^{23} - 10 q^{25} + 5 q^{27} - 5 q^{29} + 9 q^{31} + 10 q^{33} - 15 q^{35} + 30 q^{37} + 3 q^{39} - 4 q^{41} - 15 q^{45} + 14 q^{49} + 4 q^{51} - 10 q^{53} + 10 q^{55} - 9 q^{61} - 10 q^{63} + 5 q^{65} - 20 q^{67} + 17 q^{69} - 6 q^{71} + 15 q^{73} + 10 q^{75} + 10 q^{77} - 15 q^{79} + 28 q^{81} + 45 q^{83} - 15 q^{85} + 20 q^{87} - 25 q^{89} - 6 q^{91} - 15 q^{95} - 60 q^{97} + 8 q^{99}+O(q^{100}) \) 8 * q + 5 * q^3 + q^9 + 4 * q^11 - 5 * q^13 - 15 * q^15 - 10 * q^17 + 5 * q^19 - 4 * q^21 - 5 * q^23 - 10 * q^25 + 5 * q^27 - 5 * q^29 + 9 * q^31 + 10 * q^33 - 15 * q^35 + 30 * q^37 + 3 * q^39 - 4 * q^41 - 15 * q^45 + 14 * q^49 + 4 * q^51 - 10 * q^53 + 10 * q^55 - 9 * q^61 - 10 * q^63 + 5 * q^65 - 20 * q^67 + 17 * q^69 - 6 * q^71 + 15 * q^73 + 10 * q^75 + 10 * q^77 - 15 * q^79 + 28 * q^81 + 45 * q^83 - 15 * q^85 + 20 * q^87 - 25 * q^89 - 6 * q^91 - 15 * q^95 - 60 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more