LMFDB - Embedded newform 920.2.bv.a.217.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.35
Character	$\chi$	$=$	920.217
Dual form			920.2.bv.a.513.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.15820 - 0.687024i) q^{3} +(-0.353687 - 2.20792i) q^{5} +(-2.17642 + 1.18841i) q^{7} +(6.77333 - 3.09327i) q^{9} +O(q^{10})$	\(q+(3.15820 - 0.687024i) q^{3} +(-0.353687 - 2.20792i) q^{5} +(-2.17642 + 1.18841i) q^{7} +(6.77333 - 3.09327i) q^{9} +(3.54029 + 3.06768i) q^{11} +(3.30985 - 6.06154i) q^{13} +(-2.63391 - 6.73006i) q^{15} +(-2.11464 - 1.58300i) q^{17} +(-0.781908 + 5.43829i) q^{19} +(-6.05709 + 5.24850i) q^{21} +(-4.27284 - 2.17781i) q^{23} +(-4.74981 + 1.56182i) q^{25} +(11.5042 - 8.61191i) q^{27} +(2.86256 - 0.411573i) q^{29} +(-5.61108 + 3.60602i) q^{31} +(13.2885 + 7.25608i) q^{33} +(3.39369 + 4.38503i) q^{35} +(4.79273 + 1.78760i) q^{37} +(6.28874 - 21.4175i) q^{39} +(1.93264 - 4.23189i) q^{41} +(-1.78435 - 8.20252i) q^{43} +(-9.22534 - 13.8609i) q^{45} +(-0.664657 - 0.664657i) q^{47} +(-0.460018 + 0.715801i) q^{49} +(-7.76602 - 3.54662i) q^{51} +(2.19966 + 4.02838i) q^{53} +(5.52103 - 8.90167i) q^{55} +(1.26682 + 17.7124i) q^{57} +(2.47466 + 8.42793i) q^{59} +(1.51538 + 2.35798i) q^{61} +(-11.0655 + 14.7818i) q^{63} +(-14.5540 - 5.16399i) q^{65} +(4.30526 + 0.307918i) q^{67} +(-14.9907 - 3.94242i) q^{69} +(6.78762 + 7.83333i) q^{71} +(-2.67228 - 3.56975i) q^{73} +(-13.9278 + 8.19579i) q^{75} +(-11.3508 - 2.46922i) q^{77} +(0.0960215 - 0.0281945i) q^{79} +(15.7871 - 18.2193i) q^{81} +(-3.10217 + 8.31723i) q^{83} +(-2.74722 + 5.22884i) q^{85} +(8.75776 - 3.26648i) q^{87} +(-5.99269 - 3.85127i) q^{89} +17.1259i q^{91} +(-15.2435 + 15.2435i) q^{93} +(12.2839 - 0.197063i) q^{95} +(1.63053 + 4.37163i) q^{97} +(33.4687 + 9.82730i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q+O(q^{10}) $ 720 * q	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{3}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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			0
$2$		0			0
$3$	3.15820	−	0.687024i	1.82339	−	0.396654i	0.835205	−	0.549938i	$-0.185349\pi$
$3$	3.15820	−	0.687024i	1.82339	−	0.396654i	0.988182	+	0.153285i	$0.0489852\pi$
$4$		0			0
$5$	−0.353687	−	2.20792i	−0.158174	−	0.987411i
$5$	−0.353687	−	2.20792i	−0.158174	−	0.987411i
$6$		0			0
$7$	−2.17642	+	1.18841i	−0.822609	+	0.449178i	−0.834671	−	0.550749i	$-0.814342\pi$
$7$	−2.17642	+	1.18841i	−0.822609	+	0.449178i	0.0120622	+	0.999927i	$0.496160\pi$
$8$		0			0
$9$	6.77333	−	3.09327i	2.25778	−	1.03109i
$10$		0			0
$11$	3.54029	+	3.06768i	1.06744	+	0.924940i	0.997361	−	0.0726013i	$-0.0231301\pi$
$11$	3.54029	+	3.06768i	1.06744	+	0.924940i	0.0700770	+	0.997542i	$0.477676\pi$
$12$		0			0
$13$	3.30985	−	6.06154i	0.917987	−	1.68117i	0.206527	−	0.978441i	$-0.433784\pi$
$13$	3.30985	−	6.06154i	0.917987	−	1.68117i	0.711460	−	0.702727i	$-0.248034\pi$
$14$		0			0
$15$	−2.63391	−	6.73006i	−0.680072	−	1.73769i
$16$		0			0
$17$	−2.11464	−	1.58300i	−0.512876	−	0.383934i	0.311261	−	0.950324i	$-0.399249\pi$
$17$	−2.11464	−	1.58300i	−0.512876	−	0.383934i	−0.824137	+	0.566390i	$0.808339\pi$
$18$		0			0
$19$	−0.781908	+	5.43829i	−0.179382	+	1.24763i	0.678815	+	0.734309i	$0.262494\pi$
$19$	−0.781908	+	5.43829i	−0.179382	+	1.24763i	−0.858197	+	0.513320i	$0.828415\pi$
$20$		0			0
$21$	−6.05709	+	5.24850i	−1.32177	+	1.14532i
$22$		0			0
$23$	−4.27284	−	2.17781i	−0.890948	−	0.454105i
$23$	−4.27284	−	2.17781i	−0.890948	−	0.454105i
$24$		0			0
$25$	−4.74981	+	1.56182i	−0.949962	+	0.312365i
$26$		0			0
$27$	11.5042	−	8.61191i	2.21398	−	1.65736i
$28$		0			0
$29$	2.86256	−	0.411573i	0.531563	−	0.0764272i	0.128693	−	0.991684i	$-0.458922\pi$
$29$	2.86256	−	0.411573i	0.531563	−	0.0764272i	0.402870	+	0.915257i	$0.368013\pi$
$30$		0			0
$31$	−5.61108	+	3.60602i	−1.00778	+	0.647660i	−0.936817	−	0.349819i	$-0.886243\pi$
$31$	−5.61108	+	3.60602i	−1.00778	+	0.647660i	−0.0709615	+	0.997479i	$0.522607\pi$
$32$		0			0
$33$	13.2885	+	7.25608i	2.31323	+	1.26312i
$34$		0			0
$35$	3.39369	+	4.38503i	0.573639	+	0.741205i
$36$		0			0
$37$	4.79273	+	1.78760i	0.787920	+	0.293879i	0.711031	−	0.703161i	$-0.248229\pi$
$37$	4.79273	+	1.78760i	0.787920	+	0.293879i	0.0768891	+	0.997040i	$0.475501\pi$
$38$		0			0
$39$	6.28874	−	21.4175i	1.00700	−	3.42954i
$40$		0			0
$41$	1.93264	−	4.23189i	0.301827	−	0.660910i	−0.696571	−	0.717488i	$-0.745292\pi$
$41$	1.93264	−	4.23189i	0.301827	−	0.660910i	0.998398	+	0.0565785i	$0.0180191\pi$
$42$		0			0
$43$	−1.78435	−	8.20252i	−0.272111	−	1.25087i	−0.886819	−	0.462117i	$-0.847090\pi$
$43$	−1.78435	−	8.20252i	−0.272111	−	1.25087i	0.614708	−	0.788755i	$-0.289274\pi$
$44$		0			0
$45$	−9.22534	−	13.8609i	−1.37523	−	2.06626i
$46$		0			0
$47$	−0.664657	−	0.664657i	−0.0969502	−	0.0969502i	0.656968	−	0.753918i	$-0.271839\pi$
$47$	−0.664657	−	0.664657i	−0.0969502	−	0.0969502i	−0.753918	+	0.656968i	$0.771839\pi$
$48$		0			0
$49$	−0.460018	+	0.715801i	−0.0657168	+	0.102257i
$50$		0			0
$51$	−7.76602	−	3.54662i	−1.08746	−	0.496626i
$52$		0			0
$53$	2.19966	+	4.02838i	0.302147	+	0.553341i	0.984004	−	0.178144i	$-0.0570093\pi$
$53$	2.19966	+	4.02838i	0.302147	+	0.553341i	−0.681857	+	0.731485i	$0.738828\pi$
$54$		0			0
$55$	5.52103	−	8.90167i	0.744456	−	1.20030i
$56$		0			0
$57$	1.26682	+	17.7124i	0.167794	+	2.34606i
$58$		0			0
$59$	2.47466	+	8.42793i	0.322174	+	1.09722i	0.948267	+	0.317475i	$0.102835\pi$
$59$	2.47466	+	8.42793i	0.322174	+	1.09722i	−0.626093	+	0.779749i	$0.715347\pi$
$60$		0			0
$61$	1.51538	+	2.35798i	0.194025	+	0.301909i	0.924612	−	0.380911i	$-0.124390\pi$
$61$	1.51538	+	2.35798i	0.194025	+	0.301909i	−0.730587	+	0.682820i	$0.760753\pi$
$62$		0			0
$63$	−11.0655	+	14.7818i	−1.39412	+	1.86233i
$64$		0			0
$65$	−14.5540	−	5.16399i	−1.80521	−	0.640514i
$66$		0			0
$67$	4.30526	+	0.307918i	0.525971	+	0.0376182i	0.331800	−	0.943350i	$-0.392344\pi$
$67$	4.30526	+	0.307918i	0.525971	+	0.0376182i	0.194170	+	0.980968i	$0.437799\pi$
$68$		0			0
$69$	−14.9907	−	3.94242i	−1.80467	−	0.474611i
$70$		0			0
$71$	6.78762	+	7.83333i	0.805543	+	0.929646i	0.998672	−	0.0515277i	$-0.0164090\pi$
$71$	6.78762	+	7.83333i	0.805543	+	0.929646i	−0.193129	+	0.981173i	$0.561864\pi$
$72$		0			0
$73$	−2.67228	−	3.56975i	−0.312767	−	0.417808i	0.616420	−	0.787418i	$-0.288582\pi$
$73$	−2.67228	−	3.56975i	−0.312767	−	0.417808i	−0.929187	+	0.369609i	$0.879491\pi$
$74$		0			0
$75$	−13.9278	+	8.19579i	−1.60825	+	0.946368i
$76$		0			0
$77$	−11.3508	−	2.46922i	−1.29355	−	0.281394i
$78$		0			0
$79$	0.0960215	−	0.0281945i	0.0108033	−	0.00317212i	−0.276326	−	0.961064i	$-0.589117\pi$
$79$	0.0960215	−	0.0281945i	0.0108033	−	0.00317212i	0.287130	+	0.957892i	$0.407299\pi$
$80$		0			0
$81$	15.7871	−	18.2193i	1.75413	−	2.02437i
$82$		0			0
$83$	−3.10217	+	8.31723i	−0.340507	+	0.912934i	0.647984	+	0.761654i	$0.275612\pi$
$83$	−3.10217	+	8.31723i	−0.340507	+	0.912934i	−0.988491	+	0.151280i	$0.951660\pi$
$84$		0			0
$85$	−2.74722	+	5.22884i	−0.297977	+	0.567148i
$86$		0			0
$87$	8.75776	−	3.26648i	0.938930	−	0.350203i
$88$		0			0
$89$	−5.99269	−	3.85127i	−0.635224	−	0.408233i	0.183017	−	0.983110i	$-0.441414\pi$
$89$	−5.99269	−	3.85127i	−0.635224	−	0.408233i	−0.818240	+	0.574876i	$0.805050\pi$
$90$		0			0
$91$			17.1259i			1.79528i
$92$		0			0
$93$	−15.2435	+	15.2435i	−1.58067	+	1.58067i
$94$		0			0
$95$	12.2839	−	0.197063i	1.26030	−	0.0202182i
$96$		0			0
$97$	1.63053	+	4.37163i	0.165556	+	0.443872i	0.993063	−	0.117583i	$-0.0375146\pi$
$97$	1.63053	+	4.37163i	0.165556	+	0.443872i	−0.827507	+	0.561455i	$0.810242\pi$
$98$		0			0
$99$	33.4687	+	9.82730i	3.36373	+	0.987681i
$100$		0			0
$101$	1.35283	+	2.96229i	0.134612	+	0.294759i	0.964919	−	0.262547i	$-0.0845624\pi$
$101$	1.35283	+	2.96229i	0.134612	+	0.294759i	−0.830307	+	0.557306i	$0.811835\pi$
$102$		0			0
$103$	−15.3108	+	1.09505i	−1.50862	+	0.107899i	−0.800986	−	0.598683i	$-0.795691\pi$
$103$	−15.3108	+	1.09505i	−1.50862	+	0.107899i	−0.707632	+	0.706581i	$0.750237\pi$
$104$		0			0
$105$	13.7306	+	11.5172i	1.33997	+	1.12397i
$106$		0			0
$107$	−1.87411	+	8.61516i	−0.181177	+	0.832859i	0.793381	+	0.608725i	$0.208319\pi$
$107$	−1.87411	+	8.61516i	−0.181177	+	0.832859i	−0.974558	+	0.224134i	$0.928045\pi$
$108$		0			0
$109$	−1.21986	−	8.48433i	−0.116842	−	0.812651i	−0.960998	−	0.276554i	$-0.910807\pi$
$109$	−1.21986	−	8.48433i	−0.116842	−	0.812651i	0.844157	−	0.536097i	$-0.180102\pi$
$110$		0			0
$111$	16.3645	+	2.35286i	1.55325	+	0.223324i
$112$		0			0
$113$	−0.264191	+	3.69387i	−0.0248530	+	0.347490i	0.969777	+	0.243994i	$0.0784576\pi$
$113$	−0.264191	+	3.69387i	−0.0248530	+	0.347490i	−0.994630	+	0.103497i	$0.966997\pi$
$114$		0			0
$115$	−3.29718	+	10.2043i	−0.307464	+	0.951560i
$116$		0			0
$117$	3.66869	−	51.2950i	0.339171	−	4.74223i
$118$		0			0
$119$	6.48360	+	0.932201i	0.594351	+	0.0854548i
$120$		0			0
$121$	1.55754	+	10.8329i	0.141595	+	0.984812i
$122$		0			0
$123$	3.19625	−	14.6929i	0.288196	−	1.32481i
$124$		0			0
$125$	5.12833	+	9.93480i	0.458692	+	0.888596i
$126$		0			0
$127$	−7.74540	+	0.553962i	−0.687293	+	0.0491562i	−0.410618	−	0.911807i	$-0.634687\pi$
$127$	−7.74540	+	0.553962i	−0.687293	+	0.0491562i	−0.276675	+	0.960964i	$0.589233\pi$
$128$		0			0
$129$	−11.2707	−	24.6793i	−0.992326	−	2.17289i
$130$		0			0
$131$	−7.90968	−	2.32249i	−0.691072	−	0.202917i	−0.0827062	−	0.996574i	$-0.526356\pi$
$131$	−7.90968	−	2.32249i	−0.691072	−	0.202917i	−0.608365	+	0.793657i	$0.708174\pi$
$132$		0			0
$133$	−4.76118	−	12.7652i	−0.412847	−	1.10689i
$134$		0			0
$135$	−23.0833	−	22.3543i	−1.98669	−	1.92395i
$136$		0			0
$137$	−9.56209	+	9.56209i	−0.816945	+	0.816945i	−0.985664	−	0.168719i	$-0.946037\pi$
$137$	−9.56209	+	9.56209i	−0.816945	+	0.816945i	0.168719	+	0.985664i	$0.446037\pi$
$138$		0			0
$139$			3.40481i			0.288792i	0.989520	+	0.144396i	$0.0461240\pi$
$139$			3.40481i			0.288792i	−0.989520	+	0.144396i	$0.953876\pi$
$140$		0			0
$141$	−2.55575	−	1.64248i	−0.215233	−	0.138322i
$142$		0			0
$143$	30.3127	−	11.3060i	2.53487	−	0.945459i
$144$		0			0
$145$	−1.92117	−	6.17472i	−0.159544	−	0.512783i
$146$		0			0
$147$	−0.961054	+	2.57669i	−0.0792664	+	0.212522i
$148$		0			0
$149$	−1.83820	+	2.12140i	−0.150591	+	0.173791i	−0.826033	−	0.563622i	$-0.809408\pi$
$149$	−1.83820	+	2.12140i	−0.150591	+	0.173791i	0.675442	+	0.737413i	$0.263953\pi$
$150$		0			0
$151$	−8.25794	+	2.42475i	−0.672022	+	0.197323i	−0.599903	−	0.800073i	$-0.704794\pi$
$151$	−8.25794	+	2.42475i	−0.672022	+	0.197323i	−0.0721187	+	0.997396i	$0.522976\pi$
$152$		0			0
$153$	−19.2198	−	4.18101i	−1.55383	−	0.338015i
$154$		0			0
$155$	9.94636	+	11.1134i	0.798911	+	0.892649i
$156$		0			0
$157$	7.31264	+	9.76855i	0.583612	+	0.779615i	0.991032	−	0.133626i	$-0.0426622\pi$
$157$	7.31264	+	9.76855i	0.583612	+	0.779615i	−0.407419	+	0.913241i	$0.633571\pi$
$158$		0			0
$159$	9.71458	+	11.2112i	0.770416	+	0.889107i
$160$		0			0
$161$	11.8876	−	0.338074i	0.936876	−	0.0266439i
$162$		0			0
$163$	12.8431	+	0.918559i	1.00595	+	0.0719471i	0.564581	−	0.825378i	$-0.309038\pi$
$163$	12.8431	+	0.918559i	1.00595	+	0.0719471i	0.441371	+	0.897325i	$0.354492\pi$
$164$		0			0
$165$	11.3209	−	31.9063i	0.881328	−	2.48391i
$166$		0			0
$167$	10.1449	−	13.5520i	0.785038	−	1.04869i	−0.212402	−	0.977182i	$-0.568129\pi$
$167$	10.1449	−	13.5520i	0.785038	−	1.04869i	0.997440	−	0.0715061i	$-0.0227805\pi$
$168$		0			0
$169$	−18.7588	−	29.1892i	−1.44298	−	2.24533i
$170$		0			0
$171$	11.5260	+	39.2540i	0.881415	+	3.00183i
$172$		0			0
$173$	1.56932	+	21.9419i	0.119313	+	1.66821i	0.606628	+	0.794986i	$0.292522\pi$
$173$	1.56932	+	21.9419i	0.119313	+	1.66821i	−0.487315	+	0.873226i	$0.662024\pi$
$174$		0			0
$175$	8.48148	−	9.04393i	0.641140	−	0.683657i
$176$		0			0
$177$	13.6057	+	24.9169i	1.02267	+	1.87287i
$178$		0			0
$179$	3.33290	+	1.52208i	0.249112	+	0.113766i	0.536058	−	0.844181i	$-0.319913\pi$
$179$	3.33290	+	1.52208i	0.249112	+	0.113766i	−0.286946	+	0.957947i	$0.592640\pi$
$180$		0			0
$181$	−0.665830	+	1.03605i	−0.0494908	+	0.0770091i	−0.865117	−	0.501570i	$-0.832756\pi$
$181$	−0.665830	+	1.03605i	−0.0494908	+	0.0770091i	0.815627	+	0.578579i	$0.196392\pi$
$182$		0			0
$183$	6.40588	+	6.40588i	0.473536	+	0.473536i
$184$		0			0
$185$	2.25174	−	11.2142i	0.165551	−	0.824485i
$186$		0			0
$187$	−2.63031	−	12.0913i	−0.192347	−	0.884205i
$188$		0			0
$189$	−14.8034	+	32.4148i	−1.07679	+	2.35783i
$190$		0			0
$191$	−6.15512	+	20.9624i	−0.445369	+	1.51679i	0.365080	+	0.930976i	$0.381042\pi$
$191$	−6.15512	+	20.9624i	−0.445369	+	1.51679i	−0.810448	+	0.585810i	$0.800776\pi$
$192$		0			0
$193$	16.3236	+	6.08839i	1.17500	+	0.438252i	0.859729	−	0.510750i	$-0.170632\pi$
$193$	16.3236	+	6.08839i	1.17500	+	0.438252i	0.315270	+	0.949002i	$0.397905\pi$
$194$		0			0
$195$	−49.5123	−	6.30994i	−3.54565	−	0.451864i
$196$		0			0
$197$	−3.34645	−	1.82730i	−0.238425	−	0.130190i	0.355595	−	0.934640i	$-0.384278\pi$
$197$	−3.34645	−	1.82730i	−0.238425	−	0.130190i	−0.594020	+	0.804450i	$0.702460\pi$
$198$		0			0
$199$	−2.18728	+	1.40568i	−0.155052	+	0.0996458i	−0.615866	−	0.787851i	$-0.711194\pi$
$199$	−2.18728	+	1.40568i	−0.155052	+	0.0996458i	0.460814	+	0.887497i	$0.347557\pi$
$200$		0			0
$201$	13.8084	−	1.98535i	0.973970	−	0.140036i
$202$		0			0
$203$	−5.74100	+	4.29766i	−0.402939	+	0.301636i
$204$		0			0
$205$	−10.0272	−	2.77034i	−0.700331	−	0.193489i
$206$		0			0
$207$	−35.6779	−	1.53396i	−2.47978	−	0.106618i
$208$		0			0
$209$	−19.4511	+	16.8545i	−1.34546	+	1.16585i
$210$		0			0
$211$	3.30633	−	22.9961i	0.227617	−	1.58311i	−0.480484	−	0.877003i	$-0.659539\pi$
$211$	3.30633	−	22.9961i	0.227617	−	1.58311i	0.708102	−	0.706110i	$-0.249552\pi$
$212$		0			0
$213$	26.8184	+	20.0760i	1.83756	+	1.37558i
$214$		0			0
$215$	−17.4794	+	6.84082i	−1.19208	+	0.466540i
$216$		0			0
$217$	7.92660	−	14.5165i	0.538093	−	0.985443i
$218$		0			0
$219$	−10.8921	−	9.43807i	−0.736021	−	0.637766i
$220$		0			0
$221$	−16.5946	+	7.57848i	−1.11627	+	0.509784i
$222$		0			0
$223$	−8.89619	+	4.85769i	−0.595733	+	0.325295i	−0.748672	−	0.662941i	$-0.769308\pi$
$223$	−8.89619	+	4.85769i	−0.595733	+	0.325295i	0.152939	+	0.988236i	$0.451126\pi$
$224$		0			0
$225$	−27.3409	+	25.2712i	−1.82272	+	1.68475i
$226$		0			0
$227$	19.9047	−	4.33001i	1.32112	−	0.287393i	0.503924	−	0.863748i	$-0.331889\pi$
$227$	19.9047	−	4.33001i	1.32112	−	0.287393i	0.817199	+	0.576356i	$0.195526\pi$
$228$		0			0
$229$	8.28112			0.547232			0.273616	−	0.961839i	$-0.411780\pi$
$229$	8.28112			0.547232			0.273616	+	0.961839i	$0.411780\pi$
$230$		0			0
$231$	−37.5446			−2.47025
$232$		0			0
$233$	6.44488	−	1.40200i	0.422218	−	0.0918479i	0.00356381	−	0.999994i	$-0.498866\pi$
$233$	6.44488	−	1.40200i	0.422218	−	0.0918479i	0.418654	+	0.908146i	$0.362502\pi$
$234$		0			0
$235$	−1.23243	+	1.70259i	−0.0803947	+	0.111065i
$236$		0			0
$237$	0.283885	−	0.155013i	0.0184403	−	0.0100692i
$238$		0			0
$239$	−0.484553	+	0.221288i	−0.0313431	+	0.0143139i	−0.431025	−	0.902340i	$-0.641848\pi$
$239$	−0.484553	+	0.221288i	−0.0313431	+	0.0143139i	0.399682	+	0.916654i	$0.369121\pi$
$240$		0			0
$241$	1.36075	+	1.17910i	0.0876538	+	0.0759525i	0.697586	−	0.716501i	$-0.254258\pi$
$241$	1.36075	+	1.17910i	0.0876538	+	0.0759525i	−0.609932	+	0.792454i	$0.708803\pi$
$242$		0			0
$243$	16.6807	−	30.5484i	1.07007	−	1.95968i
$244$		0			0
$245$	1.74313	+	0.762512i	0.111365	+	0.0487151i
$246$		0			0
$247$	30.3764	+	22.7395i	1.93280	+	1.44688i
$248$		0			0
$249$	−4.08312	+	28.3987i	−0.258757	+	1.79970i
$250$		0			0
$251$	15.3416	−	13.2936i	0.968354	−	0.839084i	−0.0186421	−	0.999826i	$-0.505934\pi$
$251$	15.3416	−	13.2936i	0.968354	−	0.839084i	0.986996	+	0.160742i	$0.0513888\pi$
$252$		0			0
$253$	−8.44626	−	20.8178i	−0.531012	−	1.30880i
$254$		0			0
$255$	−5.08391	+	18.4011i	−0.318367	+	1.15232i
$256$		0			0
$257$	5.95875	−	4.46066i	0.371697	−	0.278249i	−0.397057	−	0.917794i	$-0.629968\pi$
$257$	5.95875	−	4.46066i	0.371697	−	0.278249i	0.768753	+	0.639546i	$0.220877\pi$
$258$		0			0
$259$	−12.5554	+	1.80519i	−0.780154	+	0.112169i
$260$		0			0
$261$	18.1159	−	11.6424i	1.12135	−	0.720646i
$262$		0			0
$263$	−7.16312	−	3.91136i	−0.441697	−	0.241185i	0.242980	−	0.970031i	$-0.421875\pi$
$263$	−7.16312	−	3.91136i	−0.441697	−	0.241185i	−0.684677	+	0.728847i	$0.740057\pi$
$264$		0			0
$265$	8.11635	−	6.28147i	0.498584	−	0.385867i
$266$		0			0
$267$	−21.5720	−	8.04595i	−1.32019	−	0.492404i
$268$		0			0
$269$	−6.98034	+	23.7729i	−0.425599	+	1.44946i	0.416005	+	0.909362i	$0.363430\pi$
$269$	−6.98034	+	23.7729i	−0.425599	+	1.44946i	−0.841604	+	0.540095i	$0.818388\pi$
$270$		0			0
$271$	3.72211	−	8.15028i	0.226102	−	0.495094i	−0.762249	−	0.647283i	$-0.775905\pi$
$271$	3.72211	−	8.15028i	0.226102	−	0.495094i	0.988351	+	0.152189i	$0.0486323\pi$
$272$		0			0
$273$	11.7659	+	54.0870i	0.712106	+	3.27350i
$274$		0			0
$275$	−21.6069	−	9.04159i	−1.30294	−	0.545228i
$276$		0			0
$277$	−20.4386	−	20.4386i	−1.22804	−	1.22804i	−0.964706	−	0.263331i	$-0.915179\pi$
$277$	−20.4386	−	20.4386i	−1.22804	−	1.22804i	−0.263331	−	0.964706i	$-0.584821\pi$
$278$		0			0
$279$	−26.8512	+	41.7813i	−1.60754	+	2.50138i
$280$		0			0
$281$	−25.9924	−	11.8703i	−1.55058	−	0.708124i	−0.558010	−	0.829834i	$-0.688435\pi$
$281$	−25.9924	−	11.8703i	−1.55058	−	0.708124i	−0.992566	+	0.121710i	$0.961162\pi$
$282$		0			0
$283$	−12.4249	−	22.7545i	−0.738584	−	1.35262i	−0.928692	−	0.370853i	$-0.879065\pi$
$283$	−12.4249	−	22.7545i	−0.738584	−	1.35262i	0.190107	−	0.981763i	$-0.439116\pi$
$284$		0			0
$285$	38.6595	−	9.06167i	2.28999	−	0.536767i
$286$		0			0
$287$	0.823006	+	11.5071i	0.0485805	+	0.679244i
$288$		0			0
$289$	−2.82364	−	9.61643i	−0.166096	−	0.565672i
$290$		0			0
$291$	8.15297	+	12.6863i	0.477935	+	0.743682i
$292$		0			0
$293$	5.19880	−	6.94478i	0.303717	−	0.405718i	−0.622554	−	0.782577i	$-0.713905\pi$
$293$	5.19880	−	6.94478i	0.303717	−	0.405718i	0.926271	+	0.376859i	$0.122996\pi$
$294$		0			0
$295$	17.7329	−	8.44471i	1.03245	−	0.491670i
$296$		0			0
$297$	67.1467	+	4.80242i	3.89624	+	0.278665i
$298$		0			0
$299$	−27.3433	+	18.6917i	−1.58131	+	1.08097i
$300$		0			0
$301$	13.6315	+	15.7316i	0.785705	+	0.906752i
$302$		0			0
$303$	6.30769	+	8.42608i	0.362367	+	0.484066i
$304$		0			0
$305$	4.67026	−	4.17983i	0.267419	−	0.239336i
$306$		0			0
$307$	15.1108	+	3.28714i	0.862417	+	0.187607i	0.621957	−	0.783052i	$-0.286338\pi$
$307$	15.1108	+	3.28714i	0.862417	+	0.187607i	0.240460	+	0.970659i	$0.422702\pi$
$308$		0			0
$309$	−47.6022	+	13.9773i	−2.70800	+	0.795140i
$310$		0			0
$311$	−13.8457	+	15.9788i	−0.785120	+	0.906077i	−0.997468	−	0.0711172i	$-0.977344\pi$
$311$	−13.8457	+	15.9788i	−0.785120	+	0.906077i	0.212348	+	0.977194i	$0.431889\pi$
$312$		0			0
$313$	6.41824	−	17.2080i	0.362780	−	0.972651i	−0.619461	−	0.785028i	$-0.712649\pi$
$313$	6.41824	−	17.2080i	0.362780	−	0.972651i	0.982241	−	0.187624i	$-0.0600786\pi$
$314$		0			0
$315$	36.5507	+	19.2036i	2.05940	+	1.08200i
$316$		0			0
$317$	−21.4850	+	8.01347i	−1.20672	+	0.450081i	−0.870719	−	0.491782i	$-0.836346\pi$
$317$	−21.4850	+	8.01347i	−1.20672	+	0.450081i	−0.335997	+	0.941863i	$0.609073\pi$
$318$		0			0
$319$	11.3969	+	7.32431i	0.638101	+	0.410083i
$320$		0			0
$321$			28.4960i			1.59049i
$322$		0			0
$323$	10.2623	−	10.2623i	0.571008	−	0.571008i
$324$		0			0
$325$	−6.25410	+	33.9606i	−0.346915	+	1.88379i
$326$		0			0
$327$	−9.68150	−	25.9571i	−0.535388	−	1.43543i
$328$		0			0
$329$	2.23646	+	0.656684i	0.123300	+	0.0362041i
$330$		0			0
$331$	−9.26942	−	20.2972i	−0.509493	−	1.11563i	−0.973266	−	0.229680i	$-0.926232\pi$
$331$	−9.26942	−	20.2972i	−0.509493	−	1.11563i	0.463773	−	0.885954i	$-0.346495\pi$
$332$		0			0
$333$	37.9923	−	2.71726i	2.08196	−	0.148905i
$334$		0			0
$335$	−0.842855	−	9.61456i	−0.0460501	−	0.525300i
$336$		0			0
$337$	−0.692225	+	3.18211i	−0.0377079	+	0.173340i	−0.992150	−	0.125057i	$-0.960089\pi$
$337$	−0.692225	+	3.18211i	−0.0377079	+	0.173340i	0.954442	+	0.298398i	$0.0964522\pi$
$338$		0			0
$339$	1.70341	+	11.8475i	0.0925166	+	0.643467i
$340$		0			0
$341$	−30.9270	−	4.44662i	−1.67479	−	0.240798i
$342$		0			0
$343$	1.38884	−	19.4185i	0.0749904	−	1.04850i
$344$		0			0
$345$	−3.40253	+	34.4926i	−0.183186	+	1.85702i
$346$		0			0
$347$	0.985701	−	13.7819i	0.0529152	−	0.739851i	−0.899861	−	0.436177i	$-0.856332\pi$
$347$	0.985701	−	13.7819i	0.0529152	−	0.739851i	0.952776	−	0.303674i	$-0.0982134\pi$
$348$		0			0
$349$	9.21229	+	1.32453i	0.493123	+	0.0709004i	0.384390	−	0.923171i	$-0.374412\pi$
$349$	9.21229	+	1.32453i	0.493123	+	0.0709004i	0.108733	+	0.994071i	$0.465321\pi$
$350$		0			0
$351$	−14.1243	−	98.2370i	−0.753902	−	5.24350i
$352$		0			0
$353$	−2.87125	+	13.1989i	−0.152821	+	0.702507i	0.835421	+	0.549610i	$0.185224\pi$
$353$	−2.87125	+	13.1989i	−0.152821	+	0.702507i	−0.988242	+	0.152897i	$0.951140\pi$
$354$		0			0
$355$	14.8947	−	17.7571i	0.790527	−	0.942447i
$356$		0			0
$357$	21.1170	−	1.51031i	1.11763	−	0.0799343i
$358$		0			0
$359$	−5.24185	−	11.4781i	−0.276654	−	0.605789i	0.719394	−	0.694602i	$-0.244420\pi$
$359$	−5.24185	−	11.4781i	−0.276654	−	0.605789i	−0.996048	+	0.0888138i	$0.971692\pi$
$360$		0			0
$361$	−10.7332	−	3.15156i	−0.564907	−	0.165872i
$362$		0			0
$363$	12.3615	+	33.1425i	0.648811	+	1.73953i
$364$		0			0
$365$	−6.93657	+	7.16276i	−0.363077	+	0.374916i
$366$		0			0
$367$	3.85401	−	3.85401i	0.201178	−	0.201178i	−0.599327	−	0.800505i	$-0.704565\pi$
$367$	3.85401	−	3.85401i	0.201178	−	0.201178i	0.800505	+	0.599327i	$0.204565\pi$
$368$		0			0
$369$		−	34.6421i		−	1.80340i
$370$		0			0
$371$	−9.57478	−	6.15334i	−0.497098	−	0.319465i
$372$		0			0
$373$	4.85030	−	1.80907i	0.251139	−	0.0936700i	−0.220742	−	0.975332i	$-0.570848\pi$
$373$	4.85030	−	1.80907i	0.251139	−	0.0936700i	0.471881	+	0.881662i	$0.343575\pi$
$374$		0			0
$375$	23.0217	+	27.8528i	1.18884	+	1.43831i
$376$		0			0
$377$	6.97986	−	18.7137i	0.359481	−	0.963806i
$378$		0			0
$379$	6.68533	−	7.71528i	0.343402	−	0.396307i	−0.557609	−	0.830104i	$-0.688281\pi$
$379$	6.68533	−	7.71528i	0.343402	−	0.396307i	0.901011	+	0.433797i	$0.142826\pi$
$380$		0			0
$381$	−24.0809	+	7.07080i	−1.23370	+	0.362248i
$382$		0			0
$383$	−9.10164	−	1.97994i	−0.465072	−	0.101170i	−0.0260776	−	0.999660i	$-0.508302\pi$
$383$	−9.10164	−	1.97994i	−0.465072	−	0.101170i	−0.438995	+	0.898490i	$0.644665\pi$
$384$		0			0
$385$	−1.43720	+	25.9350i	−0.0732465	+	1.32177i
$386$		0			0
$387$	−37.4586	−	50.0388i	−1.90413	−	2.54362i
$388$		0			0
$389$	−15.7248	−	18.1474i	−0.797280	−	0.920111i	0.200948	−	0.979602i	$-0.435598\pi$
$389$	−15.7248	−	18.1474i	−0.797280	−	0.920111i	−0.998229	+	0.0594912i	$0.981052\pi$
$390$		0			0
$391$	5.58804	+	11.3692i	0.282599	+	0.574965i
$392$		0			0
$393$	−26.5759	−	1.90075i	−1.34058	−	0.0958801i
$394$		0			0
$395$	−0.0962126	−	0.202036i	−0.00484098	−	0.0101655i
$396$		0			0
$397$	11.9177	−	15.9202i	0.598132	−	0.799011i	−0.394664	−	0.918825i	$-0.629139\pi$
$397$	11.9177	−	15.9202i	0.598132	−	0.799011i	0.992796	+	0.119814i	$0.0382299\pi$
$398$		0			0
$399$	−23.8068	−	37.0441i	−1.19183	−	1.85452i
$400$		0			0
$401$	7.08909	+	24.1432i	0.354012	+	1.20566i	0.923482	+	0.383643i	$0.125331\pi$
$401$	7.08909	+	24.1432i	0.354012	+	1.20566i	−0.569469	+	0.822013i	$0.692851\pi$
$402$		0			0
$403$	3.28620	+	45.9471i	0.163697	+	2.28879i
$404$		0			0
$405$	−45.8105	−	28.4128i	−2.27634	−	1.41184i
$406$		0			0
$407$	11.4839	+	21.0312i	0.569235	+	1.04248i
$408$		0			0
$409$	3.84414	+	1.75556i	0.190081	+	0.0868069i	0.508182	−	0.861250i	$-0.330318\pi$
$409$	3.84414	+	1.75556i	0.190081	+	0.0868069i	−0.318101	+	0.948057i	$0.603045\pi$
$410$		0			0
$411$	−23.6296	+	36.7684i	−1.16556	+	1.81365i
$412$		0			0
$413$	−15.4018	−	15.4018i	−0.757872	−	0.757872i
$414$		0			0
$415$	19.4610	+	3.90763i	0.955301	+	0.191818i
$416$		0			0
$417$	2.33919	+	10.7531i	0.114551	+	0.526580i
$418$		0			0
$419$	2.52568	−	5.53047i	0.123388	−	0.270181i	−0.837851	−	0.545899i	$-0.816188\pi$
$419$	2.52568	−	5.53047i	0.123388	−	0.270181i	0.961239	+	0.275718i	$0.0889156\pi$
$420$		0			0
$421$	6.08401	−	20.7202i	0.296517	−	1.00984i	−0.667635	−	0.744489i	$-0.732693\pi$
$421$	6.08401	−	20.7202i	0.296517	−	1.00984i	0.964151	−	0.265354i	$-0.0854887\pi$
$422$		0			0
$423$	−6.55790	−	2.44597i	−0.318856	−	0.118927i
$424$		0			0
$425$	12.5165	+	4.21625i	0.607140	+	0.204518i
$426$		0			0
$427$	−6.10037	−	3.33105i	−0.295218	−	0.161201i
$428$		0			0
$429$	87.9660	−	56.5323i	4.24704	−	2.72940i
$430$		0			0
$431$	−9.64547	+	1.38681i	−0.464606	+	0.0668002i	−0.370643	−	0.928775i	$-0.620863\pi$
$431$	−9.64547	+	1.38681i	−0.464606	+	0.0668002i	−0.0939629	+	0.995576i	$0.529954\pi$
$432$		0			0
$433$	9.43308	−	7.06152i	0.453325	−	0.339355i	−0.348092	−	0.937460i	$-0.613170\pi$
$433$	9.43308	−	7.06152i	0.453325	−	0.339355i	0.801418	+	0.598105i	$0.204080\pi$
$434$		0			0
$435$	−10.3096	−	18.1811i	−0.494308	−	0.871718i
$436$		0			0
$437$	15.1845	−	21.5341i	0.726375	−	1.03011i
$438$		0			0
$439$	25.0126	−	21.6736i	1.19379	−	1.03442i	0.195229	−	0.980758i	$-0.437455\pi$
$439$	25.0126	−	21.6736i	1.19379	−	1.03442i	0.998559	−	0.0536655i	$-0.0170905\pi$
$440$		0			0
$441$	−0.901679	+	6.27132i	−0.0429371	+	0.298634i
$442$		0			0
$443$	−29.5291	−	22.1052i	−1.40297	−	1.05025i	−0.990237	−	0.139397i	$-0.955484\pi$
$443$	−29.5291	−	22.1052i	−1.40297	−	1.05025i	−0.412732	−	0.910852i	$-0.635426\pi$
$444$		0			0
$445$	−6.38375	+	14.5935i	−0.302619	+	0.691799i
$446$		0			0
$447$	−4.34795	+	7.96268i	−0.205651	+	0.376622i
$448$		0			0
$449$	12.5444	+	10.8698i	0.592006	+	0.512976i	0.898545	−	0.438882i	$-0.144626\pi$
$449$	12.5444	+	10.8698i	0.592006	+	0.512976i	−0.306539	+	0.951858i	$0.599171\pi$
$450$		0			0
$451$	19.8242	−	9.05340i	0.933484	−	0.426308i
$452$		0			0
$453$	−24.4144	+	13.3313i	−1.14709	+	0.626357i
$454$		0			0
$455$	37.8126	−	6.05721i	1.77268	−	0.283966i
$456$		0			0
$457$	−13.3610	+	2.90650i	−0.625000	+	0.135960i	−0.513902	−	0.857849i	$-0.671800\pi$
$457$	−13.3610	+	2.90650i	−0.625000	+	0.135960i	−0.111098	+	0.993809i	$0.535437\pi$
$458$		0			0
$459$	−37.9598			−1.77181
$460$		0			0
$461$	12.3968			0.577378			0.288689	−	0.957423i	$-0.406781\pi$
$461$	12.3968			0.577378			0.288689	+	0.957423i	$0.406781\pi$
$462$		0			0
$463$	−16.4647	+	3.58168i	−0.765181	+	0.166455i	−0.578185	−	0.815906i	$-0.696239\pi$
$463$	−16.4647	+	3.58168i	−0.765181	+	0.166455i	−0.186996	+	0.982361i	$0.559875\pi$
$464$		0			0
$465$	39.0478	+	28.2649i	1.81080	+	1.31075i
$466$		0			0
$467$	23.9894	−	13.0992i	1.11010	−	0.606158i	0.183803	−	0.982963i	$-0.441159\pi$
$467$	23.9894	−	13.0992i	1.11010	−	0.606158i	0.926293	+	0.376805i	$0.122977\pi$
$468$		0			0
$469$	−9.73597	+	4.44627i	−0.449565	+	0.205310i
$470$		0			0
$471$	29.8060	+	25.8271i	1.37339	+	1.19005i
$472$		0			0
$473$	18.8456	−	34.5131i	0.866521	−	1.58691i
$474$		0			0
$475$	−4.77974	−	27.0520i	−0.219309	−	1.24123i
$476$		0			0
$477$	27.3599	+	20.4814i	1.25273	+	0.937779i
$478$		0			0
$479$	0.601020	−	4.18019i	0.0274613	−	0.190998i	−0.971473	−	0.237150i	$-0.923787\pi$
$479$	0.601020	−	4.18019i	0.0274613	−	0.190998i	0.998934	+	0.0461521i	$0.0146959\pi$
$480$		0			0
$481$	26.6988	−	23.1346i	1.21736	−	1.05485i
$482$		0			0
$483$	37.3112	−	9.23479i	1.69772	−	0.420197i
$484$		0			0
$485$	9.07551	−	5.14628i	0.412098	−	0.233680i
$486$		0			0
$487$	8.51702	−	6.37576i	0.385943	−	0.288913i	−0.388635	−	0.921392i	$-0.627053\pi$
$487$	8.51702	−	6.37576i	0.385943	−	0.288913i	0.774578	+	0.632479i	$0.217962\pi$
$488$		0			0
$489$	41.1923	−	5.92255i	1.86278	−	0.267827i
$490$		0			0
$491$	−10.3372	+	6.64334i	−0.466513	+	0.299810i	−0.752700	−	0.658364i	$-0.771249\pi$
$491$	−10.3372	+	6.64334i	−0.466513	+	0.299810i	0.286186	+	0.958174i	$0.407612\pi$
$492$		0			0
$493$	−6.70480	−	3.66110i	−0.301969	−	0.164887i
$494$		0			0
$495$	9.86044	−	77.3720i	0.443194	−	3.47761i
$496$		0			0
$497$	−24.0820	−	8.98210i	−1.08022	−	0.402902i
$498$		0			0
$499$	0.989776	−	3.37087i	0.0443085	−	0.150901i	−0.934368	−	0.356311i	$-0.884035\pi$
$499$	0.989776	−	3.37087i	0.0443085	−	0.150901i	0.978676	+	0.205410i	$0.0658527\pi$
$500$		0			0
$501$	22.7291	−	49.7699i	1.01546	−	2.22355i
$502$		0			0
$503$	1.00199	+	4.60606i	0.0446764	+	0.205374i	0.994074	−	0.108701i	$-0.0346692\pi$
$503$	1.00199	+	4.60606i	0.0446764	+	0.205374i	−0.949398	+	0.314075i	$0.898306\pi$
$504$		0			0
$505$	6.06202	−	4.03467i	0.269756	−	0.179541i
$506$		0			0
$507$	−79.2977	−	79.2977i	−3.52173	−	3.52173i
$508$		0			0
$509$	18.1689	−	28.2714i	0.805322	−	1.25311i	−0.158711	−	0.987325i	$-0.550734\pi$
$509$	18.1689	−	28.2714i	0.805322	−	1.25311i	0.964033	−	0.265781i	$-0.0856299\pi$
$510$		0			0
$511$	10.0584	+	4.59350i	0.444955	+	0.203204i
$512$		0			0
$513$	37.8388	+	69.2967i	1.67063	+	3.05952i
$514$		0			0
$515$	7.83301	+	33.4177i	0.345164	+	1.47256i
$516$		0			0
$517$	−0.314124	−	4.39203i	−0.0138152	−	0.193161i
$518$		0			0
$519$	20.0308	+	68.2187i	0.879256	+	2.99447i
$520$		0			0
$521$	12.0391	+	18.7331i	0.527441	+	0.820714i	0.998101	−	0.0616009i	$-0.0196206\pi$
$521$	12.0391	+	18.7331i	0.527441	+	0.820714i	−0.470660	+	0.882315i	$0.655984\pi$
$522$		0			0
$523$	4.72424	−	6.31084i	0.206576	−	0.275954i	−0.685273	−	0.728286i	$-0.740317\pi$
$523$	4.72424	−	6.31084i	0.206576	−	0.275954i	0.891849	+	0.452333i	$0.149408\pi$
$524$		0			0
$525$	20.5728	−	34.3895i	0.897871	−	1.50088i
$526$		0			0
$527$	17.5737	+	1.25690i	0.765524	+	0.0547514i
$528$		0			0
$529$	13.5143	+	18.6109i	0.587577	+	0.809168i
$530$		0			0
$531$	42.8316	+	49.4303i	1.85873	+	2.14509i
$532$		0			0
$533$	−19.2550	−	25.7217i	−0.834026	−	1.11413i
$534$		0			0
$535$	19.6844	+	1.09082i	0.851032	+	0.0471602i
$536$		0			0
$537$	11.5717	+	2.51726i	0.499354	+	0.108628i
$538$		0			0
$539$	−3.82445	+	1.12296i	−0.164731	+	0.0483692i
$540$		0			0
$541$	0.641592	−	0.740436i	0.0275842	−	0.0318338i	−0.741790	−	0.670632i	$-0.766023\pi$
$541$	0.641592	−	0.740436i	0.0275842	−	0.0318338i	0.769374	+	0.638799i	$0.220568\pi$
$542$		0			0
$543$	−1.39103	+	3.72950i	−0.0596949	+	0.160048i
$544$		0			0
$545$	−18.3013	+	5.69415i	−0.783940	+	0.243911i
$546$		0			0
$547$	−22.8288	+	8.51469i	−0.976088	+	0.364062i	−0.786356	−	0.617774i	$-0.788035\pi$
$547$	−22.8288	+	8.51469i	−0.976088	+	0.364062i	−0.189732	+	0.981836i	$0.560762\pi$
$548$		0			0
$549$	17.5581	+	11.2839i	0.749360	+	0.481585i
$550$		0			0
$551$			15.8892i			0.676903i
$552$		0			0
$553$	−0.175476	+	0.175476i	−0.00746201	+	0.00746201i
$554$		0			0
$555$	−0.592989	−	36.9637i	−0.0251710	−	1.56902i
$556$		0			0
$557$	−6.62371	−	17.7588i	−0.280656	−	0.752467i	−0.998421	−	0.0561812i	$-0.982108\pi$
$557$	−6.62371	−	17.7588i	−0.280656	−	0.752467i	0.717765	−	0.696285i	$-0.245165\pi$
$558$		0			0
$559$	−55.6258	−	16.3332i	−2.35272	−	0.690821i
$560$		0			0
$561$	−16.6141	−	36.3797i	−0.701446	−	1.53595i
$562$		0			0
$563$	19.2486	−	1.37668i	0.811230	−	0.0580203i	0.340441	−	0.940266i	$-0.389424\pi$
$563$	19.2486	−	1.37668i	0.811230	−	0.0580203i	0.470790	+	0.882246i	$0.343969\pi$
$564$		0			0
$565$	8.24921	−	0.723162i	0.347047	−	0.0304237i
$566$		0			0
$567$	−12.7073	+	58.4145i	−0.533656	+	2.45318i
$568$		0			0
$569$	3.66749	+	25.5080i	0.153749	+	1.06935i	0.909863	+	0.414910i	$0.136187\pi$
$569$	3.66749	+	25.5080i	0.153749	+	1.06935i	−0.756113	+	0.654441i	$0.772904\pi$
$570$		0			0
$571$	−0.0236381	−	0.00339865i	−0.000989224	−	0.000142229i	0.141820	−	0.989892i	$-0.454705\pi$
$571$	−0.0236381	−	0.00339865i	−0.000989224	−	0.000142229i	−0.142809	+	0.989750i	$0.545614\pi$
$572$		0			0
$573$	−5.03741	+	70.4322i	−0.210441	+	2.94235i
$574$		0			0
$575$	23.6965	+	3.67077i	0.988214	+	0.153082i
$576$		0			0
$577$	1.61480	−	22.5779i	0.0672251	−	0.939930i	−0.846185	−	0.532889i	$-0.821106\pi$
$577$	1.61480	−	22.5779i	0.0672251	−	0.939930i	0.913410	−	0.407041i	$-0.133439\pi$
$578$		0			0
$579$	55.7361	+	8.01364i	2.31631	+	0.333036i
$580$		0			0
$581$	−3.13270	−	21.7884i	−0.129966	−	0.903936i
$582$		0			0
$583$	−4.57034	+	21.0095i	−0.189284	+	0.870125i
$584$		0			0
$585$	−114.553	+	10.0422i	−4.73618	+	0.415194i
$586$		0			0
$587$	38.4813	−	2.75224i	1.58829	−	0.113597i	0.750983	−	0.660322i	$-0.229580\pi$
$587$	38.4813	−	2.75224i	1.58829	−	0.113597i	0.837312	+	0.546725i	$0.184126\pi$
$588$		0			0
$589$	−15.2232	−	33.3342i	−0.627262	−	1.37351i
$590$		0			0
$591$	−11.8242	−	3.47189i	−0.486381	−	0.142814i
$592$		0			0
$593$	−2.75740	−	7.39287i	−0.113233	−	0.303589i	0.867956	−	0.496642i	$-0.165434\pi$
$593$	−2.75740	−	7.39287i	−0.113233	−	0.303589i	−0.981188	+	0.193053i	$0.938161\pi$
$594$		0			0
$595$	−0.234941	−	14.6450i	−0.00963165	−	0.600386i
$596$		0			0
$597$	−5.94212	+	5.94212i	−0.243195	+	0.243195i
$598$		0			0
$599$		−	0.648284i		−	0.0264882i	−0.999912	−	0.0132441i	$-0.995784\pi$
$599$		−	0.648284i		−	0.0264882i	0.999912	−	0.0132441i	$-0.00421585\pi$
$600$		0			0
$601$	−16.6792	−	10.7191i	−0.680358	−	0.437239i	0.154289	−	0.988026i	$-0.450691\pi$
$601$	−16.6792	−	10.7191i	−0.680358	−	0.437239i	−0.834646	+	0.550787i	$0.814328\pi$
$602$		0			0
$603$	30.1134	−	11.2317i	1.22631	−	0.457390i
$604$		0			0
$605$	23.3673	−	7.27039i	0.950018	−	0.295583i
$606$		0			0
$607$	−8.13768	+	21.8180i	−0.330298	+	0.885564i	0.660574	+	0.750761i	$0.270313\pi$
$607$	−8.13768	+	21.8180i	−0.330298	+	0.885564i	−0.990872	+	0.134803i	$0.956960\pi$
$608$		0			0
$609$	−15.1786	+	17.5171i	−0.615069	+	0.709827i
$610$		0			0
$611$	−6.22875	+	1.82893i	−0.251988	+	0.0739905i
$612$		0			0
$613$	−20.6463	−	4.49133i	−0.833897	−	0.181403i	−0.224706	−	0.974427i	$-0.572142\pi$
$613$	−20.6463	−	4.49133i	−0.833897	−	0.181403i	−0.609191	+	0.793024i	$0.708506\pi$
$614$		0			0
$615$	−33.5712	−	1.86036i	−1.35372	−	0.0750170i
$616$		0			0
$617$	−0.144219	−	0.192654i	−0.00580605	−	0.00775597i	0.797629	−	0.603149i	$-0.206087\pi$
$617$	−0.144219	−	0.192654i	−0.00580605	−	0.00775597i	−0.803435	+	0.595393i	$0.796997\pi$
$618$		0			0
$619$	−28.0746	−	32.3998i	−1.12841	−	1.30226i	−0.947858	−	0.318693i	$-0.896756\pi$
$619$	−28.0746	−	32.3998i	−1.12841	−	1.30226i	−0.180555	−	0.983565i	$-0.557789\pi$
$620$		0			0
$621$	−67.9105	+	11.7434i	−2.72516	+	0.471246i
$622$		0			0
$623$	17.6195	+	1.26017i	0.705910	+	0.0504877i
$624$		0			0
$625$	20.1214	−	14.8367i	0.804856	−	0.593470i
$626$		0			0
$627$	−49.8511	+	66.5932i	−1.99086	+	2.65948i
$628$		0			0
$629$	−7.30514	−	11.3670i	−0.291275	−	0.453233i
$630$		0			0
$631$	2.01136	+	6.85008i	0.0800711	+	0.272697i	0.989791	−	0.142525i	$-0.0455221\pi$
$631$	2.01136	+	6.85008i	0.0800711	+	0.272697i	−0.909720	+	0.415222i	$0.863704\pi$
$632$		0			0
$633$	−5.35679	−	74.8977i	−0.212913	−	2.97691i
$634$		0			0
$635$	3.96255	+	16.9053i	0.157249	+	0.670866i
$636$		0			0
$637$	2.81627	+	5.15761i	0.111585	+	0.204352i
$638$		0			0
$639$	70.2054	+	32.0617i	2.77728	+	1.26834i
$640$		0			0
$641$	−18.7400	+	29.1599i	−0.740184	+	1.15175i	0.243159	+	0.969987i	$0.421816\pi$
$641$	−18.7400	+	29.1599i	−0.740184	+	1.15175i	−0.983343	+	0.181762i	$0.941820\pi$
$642$		0			0
$643$	−19.3841	−	19.3841i	−0.764434	−	0.764434i	0.212686	−	0.977120i	$-0.431779\pi$
$643$	−19.3841	−	19.3841i	−0.764434	−	0.764434i	−0.977120	+	0.212686i	$0.931779\pi$
$644$		0			0
$645$	−50.5036	+	33.6134i	−1.98858	+	1.32353i
$646$		0			0
$647$	7.84748	+	36.0743i	0.308516	+	1.41823i	0.826549	+	0.562865i	$0.190301\pi$
$647$	7.84748	+	36.0743i	0.308516	+	1.41823i	−0.518032	+	0.855361i	$0.673335\pi$
$648$		0			0
$649$	−17.0932	+	37.4288i	−0.670966	+	1.46921i
$650$		0			0
$651$	15.0606	−	51.2917i	0.590272	−	2.01028i
$652$		0			0
$653$	−16.8650	−	6.29032i	−0.659978	−	0.246159i	−0.00291639	−	0.999996i	$-0.500928\pi$
$653$	−16.8650	−	6.29032i	−0.659978	−	0.246159i	−0.657062	+	0.753837i	$0.728201\pi$
$654$		0			0
$655$	−2.33032	+	18.2854i	−0.0910532	+	0.714468i
$656$		0			0
$657$	−29.1425	−	15.9130i	−1.13696	−	0.620825i
$658$		0			0
$659$	10.4359	−	6.70677i	0.406527	−	0.261259i	−0.321359	−	0.946957i	$-0.604140\pi$
$659$	10.4359	−	6.70677i	0.406527	−	0.261259i	0.727885	+	0.685699i	$0.240503\pi$
$660$		0			0
$661$	7.19498	−	1.03448i	0.279852	−	0.0402367i	−0.000959531	−	1.00000i	$-0.500305\pi$
$661$	7.19498	−	1.03448i	0.279852	−	0.0402367i	0.280812	+	0.959763i	$0.409396\pi$
$662$		0			0
$663$	−47.2023	+	35.3352i	−1.83319	+	1.37231i
$664$		0			0
$665$	−26.5006	+	15.0272i	−1.02765	+	0.582730i
$666$		0			0
$667$	−13.1276	−	4.47552i	−0.508301	−	0.173293i
$668$		0			0
$669$	−24.7586	+	21.4534i	−0.957223	+	0.829438i
$670$		0			0
$671$	−1.86864	+	12.9967i	−0.0721379	+	0.501730i
$672$		0			0
$673$	−23.7363	−	17.7687i	−0.914966	−	0.684935i	0.0342995	−	0.999412i	$-0.489080\pi$
$673$	−23.7363	−	17.7687i	−0.914966	−	0.684935i	−0.949265	+	0.314477i	$0.898171\pi$
$674$		0			0
$675$	−41.1923	+	58.8724i	−1.58549	+	2.26600i
$676$		0			0
$677$	−3.52093	+	6.44811i	−0.135321	+	0.247821i	−0.936548	−	0.350538i	$-0.885999\pi$
$677$	−3.52093	+	6.44811i	−0.135321	+	0.247821i	0.801228	+	0.598359i	$0.204180\pi$
$678$		0			0
$679$	−8.74403	−	7.57675i	−0.335565	−	0.290769i
$680$		0			0
$681$	59.8883	−	27.3500i	2.29492	−	1.04806i
$682$		0			0
$683$	−11.0006	+	6.00676i	−0.420925	+	0.229842i	−0.675729	−	0.737150i	$-0.736171\pi$
$683$	−11.0006	+	6.00676i	−0.420925	+	0.229842i	0.254804	+	0.966993i	$0.417989\pi$
$684$		0			0
$685$	24.4943	+	17.7303i	0.935880	+	0.677441i
$686$		0			0
$687$	26.1534	−	5.68933i	0.997816	−	0.217062i
$688$		0			0
$689$	31.6987			1.20763
$690$		0			0
$691$	−22.2170			−0.845175			−0.422587	−	0.906322i	$-0.638878\pi$
$691$	−22.2170			−0.845175			−0.422587	+	0.906322i	$0.638878\pi$
$692$		0			0
$693$	−84.5209	+	18.3864i	−3.21068	+	0.698441i
$694$		0			0
$695$	7.51755	−	1.20424i	0.285157	−	0.0456793i
$696$		0			0
$697$	−10.7859	+	5.88955i	−0.408546	+	0.223083i
$698$		0			0
$699$	19.3910	−	8.85557i	0.733435	−	0.334949i
$700$		0			0
$701$	6.72283	+	5.82537i	0.253918	+	0.220021i	0.772513	−	0.634999i	$-0.218999\pi$
$701$	6.72283	+	5.82537i	0.253918	+	0.220021i	−0.518595	+	0.855020i	$0.673545\pi$
$702$		0			0
$703$	−13.4689	+	24.6665i	−0.507991	+	0.930315i
$704$		0			0
$705$	−2.72253	+	6.22382i	−0.102537	+	0.234403i
$706$		0			0
$707$	−6.46476	−	4.83946i	−0.243132	−	0.182007i
$708$		0			0
$709$	−2.24883	+	15.6410i	−0.0844567	+	0.587409i	0.903015	+	0.429610i	$0.141349\pi$
$709$	−2.24883	+	15.6410i	−0.0844567	+	0.587409i	−0.987471	+	0.157799i	$0.949560\pi$
$710$		0			0
$711$	0.563172	−	0.487991i	0.0211206	−	0.0183011i
$712$		0			0
$713$	31.8284	−	3.18807i	1.19198	−	0.119394i
$714$		0			0
$715$	−35.6840	−	62.9291i	−1.33451	−	2.35342i
$716$		0			0
$717$	−1.37828	+	1.03177i	−0.0514730	+	0.0385322i
$718$		0			0
$719$	9.69917	−	1.39453i	0.361718	−	0.0520072i	0.0409400	−	0.999162i	$-0.486965\pi$
$719$	9.69917	−	1.39453i	0.361718	−	0.0520072i	0.320778	+	0.947154i	$0.396056\pi$
$720$		0			0
$721$	32.0213	−	20.5789i	1.19254	−	0.766397i
$722$		0			0
$723$	5.10760	+	2.78896i	0.189954	+	0.103723i
$724$		0			0
$725$	−12.9538	+	6.42570i	−0.481092	+	0.238645i
$726$		0			0
$727$	−14.1346	−	5.27195i	−0.524225	−	0.195526i	0.0733985	−	0.997303i	$-0.476615\pi$
$727$	−14.1346	−	5.27195i	−0.524225	−	0.195526i	−0.597623	+	0.801777i	$0.703888\pi$
$728$		0			0
$729$	11.3177	−	38.5446i	0.419175	−	1.42758i
$730$		0			0
$731$	−9.21133	+	20.1700i	−0.340693	+	0.746014i
$732$		0			0
$733$	−7.79513	−	35.8336i	−0.287920	−	1.32354i	−0.862899	−	0.505377i	$-0.831354\pi$
$733$	−7.79513	−	35.8336i	−0.287920	−	1.32354i	0.574979	−	0.818168i	$-0.305010\pi$
$734$		0			0
$735$	6.02903	+	1.21059i	0.222384	+	0.0446533i
$736$		0			0
$737$	14.2973	+	14.2973i	0.526647	+	0.526647i
$738$		0			0
$739$	−8.39429	+	13.0618i	−0.308789	+	0.480485i	−0.960615	−	0.277884i	$-0.910367\pi$
$739$	−8.39429	+	13.0618i	−0.308789	+	0.480485i	0.651826	+	0.758369i	$0.274003\pi$
$740$		0			0
$741$	111.557	+	50.9465i	4.09816	+	1.87157i
$742$		0			0
$743$	−14.1919	−	25.9904i	−0.520649	−	0.953497i	−0.997231	−	0.0743669i	$-0.976306\pi$
$743$	−14.1919	−	25.9904i	−0.520649	−	0.953497i	0.476582	−	0.879130i	$-0.341875\pi$
$744$		0			0
$745$	5.33402	+	3.30829i	0.195423	+	0.121206i
$746$		0			0
$747$	4.71549	+	65.9312i	0.172531	+	2.41229i
$748$		0			0
$749$	−6.15952	−	20.9774i	−0.225064	−	0.766498i
$750$		0			0
$751$	−12.4512	−	19.3745i	−0.454351	−	0.706984i	0.536206	−	0.844087i	$-0.319857\pi$
$751$	−12.4512	−	19.3745i	−0.454351	−	0.706984i	−0.990557	+	0.137103i	$0.956221\pi$
$752$		0			0
$753$	39.3189	−	52.5239i	1.43286	−	1.91408i
$754$		0			0
$755$	8.27438	+	17.3753i	0.301136	+	0.632351i
$756$		0			0
$757$	41.8693	+	2.99455i	1.52176	+	0.108839i	0.807010	−	0.590537i	$-0.201084\pi$
$757$	41.8693	+	2.99455i	1.52176	+	0.108839i	0.714754	+	0.699376i	$0.246539\pi$
$758$		0			0
$759$	−40.9773	−	59.9439i	−1.48738	−	2.17583i
$760$		0			0
$761$	−19.6709	−	22.7014i	−0.713070	−	0.822927i	0.277386	−	0.960759i	$-0.410532\pi$
$761$	−19.6709	−	22.7014i	−0.713070	−	0.822927i	−0.990456	+	0.137832i	$0.955987\pi$
$762$		0			0
$763$	12.7378	+	17.0157i	0.461140	+	0.616011i
$764$		0			0
$765$	−2.43354	+	43.9145i	−0.0879849	+	1.58773i
$766$		0			0
$767$	59.2770	+	12.8949i	2.14037	+	0.465608i
$768$		0			0
$769$	−4.63473	+	1.36088i	−0.167133	+	0.0490746i	−0.364228	−	0.931310i	$-0.618667\pi$
$769$	−4.63473	+	1.36088i	−0.167133	+	0.0490746i	0.197096	+	0.980384i	$0.436849\pi$
$770$		0			0
$771$	15.7543	−	18.1815i	0.567378	−	0.654790i
$772$		0			0
$773$	−9.61337	+	25.7744i	−0.345769	+	0.927042i	0.641378	+	0.767225i	$0.278363\pi$
$773$	−9.61337	+	25.7744i	−0.345769	+	0.927042i	−0.987147	+	0.159817i	$0.948910\pi$
$774$		0			0
$775$	21.0196	−	25.8914i	0.755045	−	0.930047i
$776$		0			0
$777$	−38.4122	+	14.3270i	−1.37803	+	0.513979i
$778$		0			0
$779$	21.5031	+	13.8192i	0.770427	+	0.495124i
$780$		0			0
$781$			48.5545i			1.73742i
$782$		0			0
$783$	29.3869	−	29.3869i	1.05020	−	1.05020i
$784$		0			0
$785$	18.9818	−	19.6007i	0.677488	−	0.699580i
$786$		0			0
$787$	5.23345	+	14.0314i	0.186552	+	0.500166i	0.996234	−	0.0867028i	$-0.0276330\pi$
$787$	5.23345	+	14.0314i	0.186552	+	0.500166i	−0.809682	+	0.586869i	$0.800360\pi$
$788$		0			0
$789$	−25.3097	−	7.43161i	−0.901051	−	0.264572i
$790$		0			0
$791$	−3.81486	−	8.35338i	−0.135641	−	0.297012i
$792$		0			0
$793$	19.3087	−	1.38098i	0.685672	−	0.0490402i
$794$		0			0
$795$	21.3175	−	25.4143i	0.756055	−	0.901351i
$796$		0			0
$797$	1.82944	−	8.40980i	0.0648021	−	0.297890i	−0.933327	−	0.359027i	$-0.883109\pi$
$797$	1.82944	−	8.40980i	0.0648021	−	0.297890i	0.998129	+	0.0611361i	$0.0194724\pi$
$798$		0			0
$799$	0.353358	+	2.45766i	0.0125009	+	0.0869458i
$800$		0			0
$801$	−52.5034	−	7.54886i	−1.85512	−	0.266726i
$802$		0			0
$803$	1.49020	−	20.8357i	0.0525879	−	0.735275i
$804$		0			0
$805$	−4.95094	−	26.1273i	−0.174498	−	0.920868i
$806$		0			0
$807$	−5.71278	+	79.8751i	−0.201099	+	2.81174i
$808$		0			0
$809$	0.394958	+	0.0567863i	0.0138860	+	0.00199650i	0.149254	−	0.988799i	$-0.452313\pi$
$809$	0.394958	+	0.0567863i	0.0138860	+	0.00199650i	−0.135368	+	0.990795i	$0.543222\pi$
$810$		0			0
$811$	3.68219	+	25.6102i	0.129299	+	0.899295i	0.946445	+	0.322864i	$0.104646\pi$
$811$	3.68219	+	25.6102i	0.129299	+	0.899295i	−0.817146	+	0.576430i	$0.804445\pi$
$812$		0			0
$813$	6.15572	−	28.2974i	0.215891	−	0.992433i
$814$		0			0
$815$	−2.51435	−	28.6815i	−0.0880737	−	1.00467i
$816$		0			0
$817$	46.0028	−	3.29019i	1.60944	−	0.115109i
$818$		0			0
$819$	52.9751	+	115.999i	1.85110	+	4.05335i
$820$		0			0
$821$	4.77661	+	1.40254i	0.166705	+	0.0489490i	0.364020	−	0.931391i	$-0.381404\pi$
$821$	4.77661	+	1.40254i	0.166705	+	0.0489490i	−0.197315	+	0.980340i	$0.563222\pi$
$822$		0			0
$823$	5.87749	+	15.7582i	0.204877	+	0.549295i	0.998230	−	0.0594655i	$-0.0189396\pi$
$823$	5.87749	+	15.7582i	0.204877	+	0.549295i	−0.793354	+	0.608761i	$0.791667\pi$
$824$		0			0
$825$	−74.4507	−	13.7107i	−2.59204	−	0.477344i
$826$		0			0
$827$	−10.9046	+	10.9046i	−0.379189	+	0.379189i	−0.870809	−	0.491621i	$-0.836405\pi$
$827$	−10.9046	+	10.9046i	−0.379189	+	0.379189i	0.491621	+	0.870809i	$0.336405\pi$
$828$		0			0
$829$			44.1655i			1.53393i	0.641687	+	0.766966i	$0.278235\pi$
$829$			44.1655i			1.53393i	−0.641687	+	0.766966i	$0.721765\pi$
$830$		0			0
$831$	−78.5910	−	50.5074i	−2.72629	−	1.75208i
$832$		0			0
$833$	2.10589	−	0.785455i	0.0729646	−	0.0272144i
$834$		0			0
$835$	−33.5099	−	17.6060i	−1.15966	−	0.609281i
$836$		0			0
$837$	−33.4960	+	89.8063i	−1.15779	+	3.10416i
$838$		0			0
$839$	1.91461	−	2.20957i	0.0660996	−	0.0762830i	−0.721737	−	0.692168i	$-0.756656\pi$
$839$	1.91461	−	2.20957i	0.0660996	−	0.0762830i	0.787836	+	0.615885i	$0.211201\pi$
$840$		0			0
$841$	−19.8005	+	5.81394i	−0.682775	+	0.200481i
$842$		0			0
$843$	−90.2443	−	19.6315i	−3.10818	−	0.676143i
$844$		0			0
$845$	−57.8127	+	51.7417i	−1.98882	+	1.77997i
$846$		0			0
$847$	−16.2639	−	21.7260i	−0.558833	−	0.746513i
$848$		0			0
$849$	−54.8733	−	63.3271i	−1.88325	−	2.17338i
$850$		0			0
$851$	−16.5855	−	18.0758i	−0.568544	−	0.619629i
$852$		0			0
$853$	24.1613	+	1.72805i	0.827267	+	0.0591673i	0.478549	−	0.878061i	$-0.341163\pi$
$853$	24.1613	+	1.72805i	0.827267	+	0.0591673i	0.348717	+	0.937228i	$0.386617\pi$
$854$		0			0
$855$	82.5930	−	39.3321i	2.82462	−	1.34513i
$856$		0			0
$857$	29.4489	−	39.3392i	1.00596	−	1.34380i	0.0677591	−	0.997702i	$-0.478415\pi$
$857$	29.4489	−	39.3392i	1.00596	−	1.34380i	0.938198	−	0.346099i	$-0.112494\pi$
$858$		0			0
$859$	−8.30715	−	12.9262i	−0.283436	−	0.441036i	0.670119	−	0.742254i	$-0.266243\pi$
$859$	−8.30715	−	12.9262i	−0.283436	−	0.441036i	−0.953555	+	0.301218i	$0.902607\pi$
$860$		0			0
$861$	10.5049	+	35.7764i	0.358006	+	1.21926i
$862$		0			0
$863$	−1.33489	−	18.6643i	−0.0454403	−	0.635339i	−0.968234	−	0.250045i	$-0.919555\pi$
$863$	−1.33489	−	18.6643i	−0.0454403	−	0.635339i	0.922794	−	0.385294i	$-0.125900\pi$
$864$		0			0
$865$	47.8909	−	11.2255i	1.62834	−	0.381678i
$866$		0			0
$867$	−15.5243	−	28.4307i	−0.527234	−	0.965557i
$868$		0			0
$869$	0.426436	+	0.194747i	0.0144658	+	0.00660633i
$870$		0			0
$871$	16.1162	−	25.0773i	0.546077	−	0.849712i
$872$		0			0
$873$	24.5668	+	24.5668i	0.831460	+	0.831460i
$874$		0			0
$875$	−22.9680	−	15.5277i	−0.776462	−	0.524932i
$876$		0			0
$877$	11.5288	+	52.9969i	0.389299	+	1.78958i	0.587294	+	0.809374i	$0.300193\pi$
$877$	11.5288	+	52.9969i	0.389299	+	1.78958i	−0.197995	+	0.980203i	$0.563443\pi$
$878$		0			0
$879$	11.6476	−	25.5047i	0.392864	−	0.860252i
$880$		0			0
$881$	−9.58579	+	32.6462i	−0.322953	+	1.09988i	0.624776	+	0.780804i	$0.285190\pi$
$881$	−9.58579	+	32.6462i	−0.322953	+	1.09988i	−0.947730	+	0.319075i	$0.896628\pi$
$882$		0			0
$883$	−3.09503	−	1.15439i	−0.104156	−	0.0388482i	0.296846	−	0.954925i	$-0.404065\pi$
$883$	−3.09503	−	1.15439i	−0.104156	−	0.0388482i	−0.401002	+	0.916077i	$0.631338\pi$
$884$		0			0
$885$	50.2024	−	38.8530i	1.68754	−	1.30603i
$886$		0			0
$887$	−0.313220	−	0.171031i	−0.0105169	−	0.00574266i	0.473982	−	0.880535i	$-0.342816\pi$
$887$	−0.313220	−	0.171031i	−0.0105169	−	0.00574266i	−0.484499	+	0.874792i	$0.660998\pi$
$888$		0			0
$889$	16.1989	−	10.4104i	0.543293	−	0.349153i
$890$		0			0
$891$	111.782	−	16.0718i	3.74484	−	0.538427i
$892$		0			0
$893$	4.13430	−	3.09489i	0.138349	−	0.103567i
$894$		0			0
$895$	2.18183	−	7.89711i	0.0729307	−	0.263971i
$896$		0			0
$897$	−73.5140	+	77.8177i	−2.45456	+	2.59826i
$898$		0			0
$899$	−14.5779	+	12.6318i	−0.486199	+	0.421294i
$900$		0			0
$901$	1.72543	−	12.0007i	0.0574825	−	0.399800i
$902$		0			0
$903$	53.8589	+	40.3183i	1.79231	+	1.34171i
$904$		0			0
$905$	2.52301	+	1.10366i	0.0838678	+	0.0366869i
$906$		0			0
$907$	19.9594	−	36.5529i	0.662740	−	1.21372i	−0.302698	−	0.953087i	$-0.597887\pi$
$907$	19.9594	−	36.5529i	0.662740	−	1.21372i	0.965438	−	0.260632i	$-0.0839309\pi$
$908$		0			0
$909$	18.3264	+	15.8799i	0.607847	+	0.526703i
$910$		0			0
$911$	−24.9773	+	11.4068i	−0.827536	+	0.377923i	−0.783718	−	0.621117i	$-0.786679\pi$
$911$	−24.9773	+	11.4068i	−0.827536	+	0.377923i	−0.0438176	+	0.999040i	$0.513952\pi$
$912$		0			0
$913$	−36.4972	+	19.9290i	−1.20788	+	0.659552i
$914$		0			0
$915$	11.8780	−	16.4093i	0.392674	−	0.542476i
$916$		0			0
$917$	19.9748	−	4.34526i	0.659627	−	0.143493i
$918$		0			0
$919$	−8.31301			−0.274221			−0.137110	−	0.990556i	$-0.543782\pi$
$919$	−8.31301			−0.274221			−0.137110	+	0.990556i	$0.543782\pi$
$920$		0			0
$921$	49.9811			1.64693
$922$		0			0
$923$	69.9480	−	15.2163i	2.30237	−	0.500849i
$924$		0			0
$925$	−25.5565	−	1.00534i	−0.840292	−	0.0330554i
$926$		0			0
$927$	−100.318	+	54.7776i	−3.29487	+	1.79913i
$928$		0			0
$929$	40.6319	−	18.5560i	1.33309	−	0.608802i	0.383861	−	0.923391i	$-0.374594\pi$
$929$	40.6319	−	18.5560i	1.33309	−	0.608802i	0.949228	+	0.314589i	$0.101867\pi$
$930$		0			0
$931$	−3.53304	−	3.06140i	−0.115791	−	0.100333i
$932$		0			0
$933$	−32.7498	+	59.9767i	−1.07218	+	1.96355i
$934$		0			0
$935$	−25.7664	+	10.0840i	−0.842650	+	0.329784i
$936$		0			0
$937$	−47.8587	−	35.8266i	−1.56348	−	1.17040i	−0.910861	−	0.412713i	$-0.864581\pi$
$937$	−47.8587	−	35.8266i	−1.56348	−	1.17040i	−0.652614	−	0.757690i	$-0.726328\pi$
$938$		0			0
$939$	8.44779	−	58.7557i	0.275683	−	1.91742i
$940$		0			0
$941$	9.27155	−	8.03384i	0.302244	−	0.261896i	−0.490513	−	0.871434i	$-0.663191\pi$
$941$	9.27155	−	8.03384i	0.302244	−	0.261896i	0.792757	+	0.609538i	$0.208645\pi$
$942$		0			0
$943$	−17.4741	+	13.8732i	−0.569035	+	0.451775i
$944$		0			0
$945$	76.8051	+	21.2199i	2.49847	+	0.690283i
$946$		0			0
$947$	−25.3585	+	18.9831i	−0.824040	+	0.616869i	−0.925831	−	0.377937i	$-0.876634\pi$
$947$	−25.3585	+	18.9831i	−0.824040	+	0.616869i	0.101791	+	0.994806i	$0.467543\pi$
$948$		0			0
$949$	−30.4830	+	4.38280i	−0.989522	+	0.142272i
$950$		0			0
$951$	−62.3483	+	40.0688i	−2.02178	+	1.29932i
$952$		0			0
$953$	−37.1569	−	20.2892i	−1.20363	−	0.657232i	−0.252972	−	0.967473i	$-0.581408\pi$
$953$	−37.1569	−	20.2892i	−1.20363	−	0.657232i	−0.950658	+	0.310242i	$0.899590\pi$
$954$		0			0
$955$	48.4603	+	6.17587i	1.56814	+	0.199846i
$956$		0			0
$957$	41.0255	+	15.3017i	1.32617	+	0.494635i
$958$		0			0
$959$	9.44739	−	32.1748i	0.305072	−	1.03898i
$960$		0			0
$961$	5.60292	−	12.2687i	0.180740	−	0.395764i
$962$		0			0
$963$	13.9551	+	64.1504i	0.449696	+	2.06722i
$964$		0			0
$965$	7.66923	−	38.1946i	0.246881	−	1.22953i
$966$		0			0
$967$	9.51598	+	9.51598i	0.306013	+	0.306013i	0.843361	−	0.537348i	$-0.180574\pi$
$967$	9.51598	+	9.51598i	0.306013	+	0.306013i	−0.537348	+	0.843361i	$0.680574\pi$
$968$		0			0
$969$	25.3599	−	39.4607i	0.814676	−	1.26766i
$970$		0			0
$971$	−3.30522	−	1.50944i	−0.106070	−	0.0484404i	0.361674	−	0.932305i	$-0.382206\pi$
$971$	−3.30522	−	1.50944i	−0.106070	−	0.0484404i	−0.467743	+	0.883864i	$0.654933\pi$
$972$		0			0
$973$	−4.04633	−	7.41029i	−0.129719	−	0.237563i
$974$		0			0
$975$	3.58002	+	111.551i	0.114652	+	3.57249i
$976$		0			0
$977$	3.75055	+	52.4395i	0.119991	+	1.67769i	0.599672	+	0.800246i	$0.295298\pi$
$977$	3.75055	+	52.4395i	0.119991	+	1.67769i	−0.479681	+	0.877443i	$0.659248\pi$
$978$		0			0
$979$	−9.40141	−	32.0182i	−0.300470	−	1.02331i
$980$		0			0
$981$	−34.5069	−	53.6937i	−1.10172	−	1.71431i
$982$		0			0
$983$	26.1466	−	34.9278i	0.833948	−	1.11402i	−0.158007	−	0.987438i	$-0.550507\pi$
$983$	26.1466	−	34.9278i	0.833948	−	1.11402i	0.991956	−	0.126587i	$-0.0404022\pi$
$984$		0			0
$985$	−2.85094	+	8.03499i	−0.0908384	+	0.256016i
$986$		0			0
$987$	7.51434	+	0.537436i	0.239184	+	0.0171068i
$988$		0			0
$989$	−10.2393	+	38.9340i	−0.325591	+	1.23803i
$990$		0			0
$991$	0.940126	+	1.08496i	0.0298641	+	0.0344650i	0.770485	−	0.637458i	$-0.220014\pi$
$991$	0.940126	+	1.08496i	0.0298641	+	0.0344650i	−0.740621	+	0.671923i	$0.765469\pi$
$992$		0			0
$993$	−43.2193	−	57.7343i	−1.37152	−	1.83214i
$994$		0			0
$995$	3.87723	+	4.33216i	0.122917	+	0.137339i
$996$		0			0
$997$	−25.8448	−	5.62220i	−0.818514	−	0.178057i	−0.216234	−	0.976342i	$-0.569377\pi$
$997$	−25.8448	−	5.62220i	−0.818514	−	0.178057i	−0.602280	+	0.798285i	$0.705741\pi$
$998$		0			0
$999$	70.5310	−	20.7098i	2.23150	−	0.655228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.217.35	yes	720
5.3	odd	4	inner	920.2.bv.a.33.35	✓	720
23.7	odd	22	inner	920.2.bv.a.697.35	yes	720
115.53	even	44	inner	920.2.bv.a.513.35	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.33.35	✓	720	5.3	odd	4	inner
920.2.bv.a.217.35	yes	720	1.1	even	1	trivial
920.2.bv.a.513.35	yes	720	115.53	even	44	inner
920.2.bv.a.697.35	yes	720	23.7	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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(3.15820 - 0.687024i) q^{3} +(-0.353687 - 2.20792i) q^{5} +(-2.17642 + 1.18841i) q^{7} +(6.77333 - 3.09327i) q^{9} +O(q^{10})\)	\(q+(3.15820 - 0.687024i) q^{3} +(-0.353687 - 2.20792i) q^{5} +(-2.17642 + 1.18841i) q^{7} +(6.77333 - 3.09327i) q^{9} +(3.54029 + 3.06768i) q^{11} +(3.30985 - 6.06154i) q^{13} +(-2.63391 - 6.73006i) q^{15} +(-2.11464 - 1.58300i) q^{17} +(-0.781908 + 5.43829i) q^{19} +(-6.05709 + 5.24850i) q^{21} +(-4.27284 - 2.17781i) q^{23} +(-4.74981 + 1.56182i) q^{25} +(11.5042 - 8.61191i) q^{27} +(2.86256 - 0.411573i) q^{29} +(-5.61108 + 3.60602i) q^{31} +(13.2885 + 7.25608i) q^{33} +(3.39369 + 4.38503i) q^{35} +(4.79273 + 1.78760i) q^{37} +(6.28874 - 21.4175i) q^{39} +(1.93264 - 4.23189i) q^{41} +(-1.78435 - 8.20252i) q^{43} +(-9.22534 - 13.8609i) q^{45} +(-0.664657 - 0.664657i) q^{47} +(-0.460018 + 0.715801i) q^{49} +(-7.76602 - 3.54662i) q^{51} +(2.19966 + 4.02838i) q^{53} +(5.52103 - 8.90167i) q^{55} +(1.26682 + 17.7124i) q^{57} +(2.47466 + 8.42793i) q^{59} +(1.51538 + 2.35798i) q^{61} +(-11.0655 + 14.7818i) q^{63} +(-14.5540 - 5.16399i) q^{65} +(4.30526 + 0.307918i) q^{67} +(-14.9907 - 3.94242i) q^{69} +(6.78762 + 7.83333i) q^{71} +(-2.67228 - 3.56975i) q^{73} +(-13.9278 + 8.19579i) q^{75} +(-11.3508 - 2.46922i) q^{77} +(0.0960215 - 0.0281945i) q^{79} +(15.7871 - 18.2193i) q^{81} +(-3.10217 + 8.31723i) q^{83} +(-2.74722 + 5.22884i) q^{85} +(8.75776 - 3.26648i) q^{87} +(-5.99269 - 3.85127i) q^{89} +17.1259i q^{91} +(-15.2435 + 15.2435i) q^{93} +(12.2839 - 0.197063i) q^{95} +(1.63053 + 4.37163i) q^{97} +(33.4687 + 9.82730i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q+O(q^{10}) \) 720 * q	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more