LMFDB - Embedded newform 820.2.bq.a.49.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(49,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 10, 19])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bq (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			49.10
Character	$\chi$	$=$	820.49
Dual form			820.2.bq.a.569.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.341338 + 0.341338i) q^{3} +(-0.760852 - 2.10264i) q^{5} +(0.0854014 - 0.539203i) q^{7} +2.76698i q^{9} +(-1.98214 + 1.00995i) q^{11} +(4.21907 - 0.668235i) q^{13} +(0.977418 + 0.458003i) q^{15} +(2.48447 - 1.26590i) q^{17} +(0.450296 - 2.84306i) q^{19} +(0.154900 + 0.213201i) q^{21} +(3.82670 - 5.26700i) q^{23} +(-3.84221 + 3.19960i) q^{25} +(-1.96849 - 1.96849i) q^{27} +(1.54344 - 3.02917i) q^{29} +(2.98497 - 9.18678i) q^{31} +(0.331845 - 1.02131i) q^{33} +(-1.19873 + 0.230685i) q^{35} +(5.19622 - 1.68835i) q^{37} +(-1.21203 + 1.66822i) q^{39} +(-6.40132 - 0.151843i) q^{41} +(-7.14003 - 5.18753i) q^{43} +(5.81796 - 2.10526i) q^{45} +(-0.266460 - 1.68236i) q^{47} +(6.37395 + 2.07102i) q^{49} +(-0.415943 + 1.28014i) q^{51} +(-9.96147 - 5.07562i) q^{53} +(3.63168 + 3.39931i) q^{55} +(0.816739 + 1.12414i) q^{57} +(3.87648 + 2.81643i) q^{59} +(3.47423 + 4.78187i) q^{61} +(1.49196 + 0.236304i) q^{63} +(-4.61515 - 8.36277i) q^{65} +(2.13947 - 4.19894i) q^{67} +(0.491629 + 3.10402i) q^{69} +(0.557185 - 0.283900i) q^{71} +17.0188 q^{73} +(0.219346 - 2.40363i) q^{75} +(0.375292 + 1.15503i) q^{77} +(9.91802 + 9.91802i) q^{79} -6.95710 q^{81} -0.647608i q^{83} +(-4.55204 - 4.26078i) q^{85} +(0.507135 + 1.56080i) q^{87} +(15.3360 + 2.42898i) q^{89} -2.33200i q^{91} +(2.11691 + 4.15468i) q^{93} +(-6.32054 + 1.21633i) q^{95} +(-3.34906 + 6.57290i) q^{97} +(-2.79451 - 5.48454i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 4 q^{11} - 10 q^{15} - 4 q^{19} + 12 q^{25} + 8 q^{29} - 8 q^{31} - 6 q^{35} + 40 q^{39} + 28 q^{41} - 4 q^{45} + 20 q^{49} - 32 q^{51} - 50 q^{55} + 12 q^{59} + 40 q^{61} - 10 q^{65} - 28 q^{69}+ \cdots + 4 q^{99}+O(q^{100}) $ 176 * q + 4 * q^11 - 10 * q^15 - 4 * q^19 + 12 * q^25 + 8 * q^29 - 8 * q^31 - 6 * q^35 + 40 * q^39 + 28 * q^41 - 4 * q^45 + 20 * q^49 - 32 * q^51 - 50 * q^55 + 12 * q^59 + 40 * q^61 - 10 * q^65 - 28 * q^69 - 108 * q^71 + 52 * q^75 + 48 * q^79 - 328 * q^81 + 98 * q^85 - 16 * q^89 + 26 * q^95 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$	$-1$

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
$3$	−0.341338	+	0.341338i	−0.197071	+	0.197071i	−0.798743	−	0.601672i	$-0.794501\pi$
$3$	−0.341338	+	0.341338i	−0.197071	+	0.197071i	0.601672	+	0.798743i	$0.294501\pi$
$4$		0			0
$5$	−0.760852	−	2.10264i	−0.340263	−	0.940330i
$5$	−0.760852	−	2.10264i	−0.340263	−	0.940330i
$6$		0			0
$7$	0.0854014	−	0.539203i	0.0322787	−	0.203800i	−0.966278	−	0.257500i	$-0.917101\pi$
$7$	0.0854014	−	0.539203i	0.0322787	−	0.203800i	0.998557	+	0.0536999i	$0.0171014\pi$
$8$		0			0
$9$			2.76698i			0.922326i
$10$		0			0
$11$	−1.98214	+	1.00995i	−0.597638	+	0.304512i	−0.726517	−	0.687148i	$-0.758862\pi$
$11$	−1.98214	+	1.00995i	−0.597638	+	0.304512i	0.128879	+	0.991660i	$0.458862\pi$
$12$		0			0
$13$	4.21907	−	0.668235i	1.17016	−	0.185335i	0.459046	−	0.888412i	$-0.348191\pi$
$13$	4.21907	−	0.668235i	1.17016	−	0.185335i	0.711113	+	0.703077i	$0.248191\pi$
$14$		0			0
$15$	0.977418	+	0.458003i	0.252368	+	0.118256i
$16$		0			0
$17$	2.48447	−	1.26590i	0.602572	−	0.307026i	−0.125963	−	0.992035i	$-0.540202\pi$
$17$	2.48447	−	1.26590i	0.602572	−	0.307026i	0.728534	+	0.685009i	$0.240202\pi$
$18$		0			0
$19$	0.450296	−	2.84306i	0.103305	−	0.652242i	−0.880642	−	0.473782i	$-0.842889\pi$
$19$	0.450296	−	2.84306i	0.103305	−	0.652242i	0.983947	−	0.178460i	$-0.0571115\pi$
$20$		0			0
$21$	0.154900	+	0.213201i	0.0338019	+	0.0465243i
$22$		0			0
$23$	3.82670	−	5.26700i	0.797923	−	1.09825i	−0.195153	−	0.980773i	$-0.562520\pi$
$23$	3.82670	−	5.26700i	0.797923	−	1.09825i	0.993076	−	0.117474i	$-0.0374796\pi$
$24$		0			0
$25$	−3.84221	+	3.19960i	−0.768442	+	0.639920i
$26$		0			0
$27$	−1.96849	−	1.96849i	−0.378835	−	0.378835i
$28$		0			0
$29$	1.54344	−	3.02917i	0.286609	−	0.562502i	−0.702148	−	0.712031i	$-0.747776\pi$
$29$	1.54344	−	3.02917i	0.286609	−	0.562502i	0.988757	+	0.149529i	$0.0477757\pi$
$30$		0			0
$31$	2.98497	−	9.18678i	0.536116	−	1.65000i	−0.205109	−	0.978739i	$-0.565755\pi$
$31$	2.98497	−	9.18678i	0.536116	−	1.65000i	0.741225	−	0.671256i	$-0.234245\pi$
$32$		0			0
$33$	0.331845	−	1.02131i	0.0577668	−	0.177788i
$34$		0			0
$35$	−1.19873	+	0.230685i	−0.202622	+	0.0389929i
$36$		0			0
$37$	5.19622	−	1.68835i	0.854253	−	0.277564i	0.151027	−	0.988530i	$-0.451742\pi$
$37$	5.19622	−	1.68835i	0.854253	−	0.277564i	0.703226	+	0.710966i	$0.251742\pi$
$38$		0			0
$39$	−1.21203	+	1.66822i	−0.194081	+	0.267129i
$40$		0			0
$41$	−6.40132	−	0.151843i	−0.999719	−	0.0237139i
$41$	−6.40132	−	0.151843i	−0.999719	−	0.0237139i
$42$		0			0
$43$	−7.14003	−	5.18753i	−1.08884	−	0.791091i	−0.109640	−	0.993971i	$-0.534970\pi$
$43$	−7.14003	−	5.18753i	−1.08884	−	0.791091i	−0.979204	+	0.202880i	$0.934970\pi$
$44$		0			0
$45$	5.81796	−	2.10526i	0.867291	−	0.313834i
$46$		0			0
$47$	−0.266460	−	1.68236i	−0.0388672	−	0.245398i	0.960604	−	0.277921i	$-0.0896455\pi$
$47$	−0.266460	−	1.68236i	−0.0388672	−	0.245398i	−0.999471	+	0.0325239i	$0.989646\pi$
$48$		0			0
$49$	6.37395	+	2.07102i	0.910564	+	0.295860i
$50$		0			0
$51$	−0.415943	+	1.28014i	−0.0582436	+	0.179256i
$52$		0			0
$53$	−9.96147	−	5.07562i	−1.36831	−	0.697190i	−0.393315	−	0.919404i	$-0.628672\pi$
$53$	−9.96147	−	5.07562i	−1.36831	−	0.697190i	−0.974998	+	0.222213i	$0.928672\pi$
$54$		0			0
$55$	3.63168	+	3.39931i	0.489696	+	0.458363i
$56$		0			0
$57$	0.816739	+	1.12414i	0.108180	+	0.148897i
$58$		0			0
$59$	3.87648	+	2.81643i	0.504675	+	0.366668i	0.810800	−	0.585324i	$-0.199033\pi$
$59$	3.87648	+	2.81643i	0.504675	+	0.366668i	−0.306125	+	0.951991i	$0.599033\pi$
$60$		0			0
$61$	3.47423	+	4.78187i	0.444830	+	0.612255i	0.971277	−	0.237952i	$-0.0764762\pi$
$61$	3.47423	+	4.78187i	0.444830	+	0.612255i	−0.526447	+	0.850208i	$0.676476\pi$
$62$		0			0
$63$	1.49196	+	0.236304i	0.187970	+	0.0297715i
$64$		0			0
$65$	−4.61515	−	8.36277i	−0.572439	−	1.03727i
$66$		0			0
$67$	2.13947	−	4.19894i	0.261377	−	0.512982i	−0.722602	−	0.691264i	$-0.757054\pi$
$67$	2.13947	−	4.19894i	0.261377	−	0.512982i	0.983979	+	0.178282i	$0.0570540\pi$
$68$		0			0
$69$	0.491629	+	3.10402i	0.0591852	+	0.373681i
$70$		0			0
$71$	0.557185	−	0.283900i	0.0661257	−	0.0336927i	−0.420615	−	0.907239i	$-0.638186\pi$
$71$	0.557185	−	0.283900i	0.0661257	−	0.0336927i	0.486741	+	0.873547i	$0.338186\pi$
$72$		0			0
$73$	17.0188			1.99190			0.995949	−	0.0899155i	$-0.0286597\pi$
$73$	17.0188			1.99190			0.995949	+	0.0899155i	$0.0286597\pi$
$74$		0			0
$75$	0.219346	−	2.40363i	0.0253279	−	0.277548i
$76$		0			0
$77$	0.375292	+	1.15503i	0.0427684	+	0.131628i
$78$		0			0
$79$	9.91802	+	9.91802i	1.11586	+	1.11586i	0.992342	+	0.123522i	$0.0394191\pi$
$79$	9.91802	+	9.91802i	1.11586	+	1.11586i	0.123522	+	0.992342i	$0.460581\pi$
$80$		0			0
$81$	−6.95710			−0.773011
$82$		0			0
$83$		−	0.647608i		−	0.0710842i	−0.999368	−	0.0355421i	$-0.988684\pi$
$83$		−	0.647608i		−	0.0710842i	0.999368	−	0.0355421i	$-0.0113158\pi$
$84$		0			0
$85$	−4.55204	−	4.26078i	−0.493739	−	0.462147i
$86$		0			0
$87$	0.507135	+	1.56080i	0.0543706	+	0.167335i
$88$		0			0
$89$	15.3360	+	2.42898i	1.62561	+	0.257471i	0.901680	−	0.432404i	$-0.142334\pi$
$89$	15.3360	+	2.42898i	1.62561	+	0.257471i	0.723929	+	0.689875i	$0.242334\pi$
$90$		0			0
$91$		−	2.33200i		−	0.244460i
$92$		0			0
$93$	2.11691	+	4.15468i	0.219514	+	0.430820i
$94$		0			0
$95$	−6.32054	+	1.21633i	−0.648474	+	0.124793i
$96$		0			0
$97$	−3.34906	+	6.57290i	−0.340045	+	0.667377i	−0.996185	−	0.0872625i	$-0.972188\pi$
$97$	−3.34906	+	6.57290i	−0.340045	+	0.667377i	0.656140	+	0.754639i	$0.272188\pi$
$98$		0			0
$99$	−2.79451	−	5.48454i	−0.280859	−	0.551217i
$100$		0			0
$101$	−2.07914	+	13.1272i	−0.206882	+	1.30620i	0.637496	+	0.770454i	$0.279970\pi$
$101$	−2.07914	+	13.1272i	−0.206882	+	1.30620i	−0.844378	+	0.535748i	$0.820030\pi$
$102$		0			0
$103$	−14.4632	+	10.5081i	−1.42510	+	1.03540i	−0.434199	+	0.900817i	$0.642969\pi$
$103$	−14.4632	+	10.5081i	−1.42510	+	1.03540i	−0.990903	+	0.134580i	$0.957031\pi$
$104$		0			0
$105$	0.330430	−	0.487913i	0.0322466	−	0.0476154i
$106$		0			0
$107$	−7.41650	−	10.2079i	−0.716980	−	0.986839i	−0.999619	−	0.0276124i	$-0.991210\pi$
$107$	−7.41650	−	10.2079i	−0.716980	−	0.986839i	0.282638	−	0.959227i	$-0.408790\pi$
$108$		0			0
$109$	11.4300	−	11.4300i	1.09480	−	1.09480i	0.0997879	−	0.995009i	$-0.468184\pi$
$109$	11.4300	−	11.4300i	1.09480	−	1.09480i	0.995009	−	0.0997879i	$-0.0318164\pi$
$110$		0			0
$111$	−1.19737	+	2.34996i	−0.113649	+	0.223049i
$112$		0			0
$113$	−5.56639	−	1.80863i	−0.523642	−	0.170141i	0.0352557	−	0.999378i	$-0.488775\pi$
$113$	−5.56639	−	1.80863i	−0.523642	−	0.170141i	−0.558897	+	0.829237i	$0.688775\pi$
$114$		0			0
$115$	−13.9862	−	4.03877i	−1.30422	−	0.376618i
$116$		0			0
$117$	1.84899	+	11.6741i	0.170939	+	1.07927i
$118$		0			0
$119$	−0.470400	−	1.44774i	−0.0431215	−	0.132714i
$120$		0			0
$121$	−3.55675	+	4.89545i	−0.323341	+	0.445041i
$122$		0			0
$123$	2.23684	−	2.13318i	0.201689	−	0.192343i
$124$		0			0
$125$	9.65097	+	5.64436i	0.863209	+	0.504847i
$126$		0			0
$127$	3.05652	−	0.993122i	0.271222	−	0.0881254i	−0.170248	−	0.985401i	$-0.554457\pi$
$127$	3.05652	−	0.993122i	0.271222	−	0.0881254i	0.441470	+	0.897276i	$0.354457\pi$
$128$		0			0
$129$	4.20786	−	0.666459i	0.370481	−	0.0586785i
$130$		0			0
$131$	−9.44817	−	3.06990i	−0.825491	−	0.268218i	−0.134346	−	0.990935i	$-0.542893\pi$
$131$	−9.44817	−	3.06990i	−0.825491	−	0.268218i	−0.691145	+	0.722716i	$0.742893\pi$
$132$		0			0
$133$	−1.49453	−	0.485602i	−0.129592	−	0.0421070i
$134$		0			0
$135$	−2.64129	+	5.63675i	−0.227326	+	0.485134i
$136$		0			0
$137$	3.47860	+	3.47860i	0.297196	+	0.297196i	0.839915	−	0.542718i	$-0.182605\pi$
$137$	3.47860	+	3.47860i	0.297196	+	0.297196i	−0.542718	+	0.839915i	$0.682605\pi$
$138$		0			0
$139$	−12.2680	+	8.91321i	−1.04056	+	0.756008i	−0.970394	−	0.241527i	$-0.922352\pi$
$139$	−12.2680	+	8.91321i	−1.04056	+	0.756008i	−0.0701623	+	0.997536i	$0.522352\pi$
$140$		0			0
$141$	0.665206	+	0.483300i	0.0560204	+	0.0407012i
$142$		0			0
$143$	−7.68791	+	5.58560i	−0.642896	+	0.467091i
$144$		0			0
$145$	−7.54358	−	0.940548i	−0.626460	−	0.0781083i
$146$		0			0
$147$	−2.88259	+	1.46875i	−0.237752	+	0.121141i
$148$		0			0
$149$	−6.29366	−	3.20678i	−0.515597	−	0.262710i	0.176774	−	0.984251i	$-0.443434\pi$
$149$	−6.29366	−	3.20678i	−0.515597	−	0.262710i	−0.692371	+	0.721542i	$0.743434\pi$
$150$		0			0
$151$	−2.23715	−	14.1248i	−0.182057	−	1.14946i	−0.894280	−	0.447508i	$-0.852312\pi$
$151$	−2.23715	−	14.1248i	−0.182057	−	1.14946i	0.712224	−	0.701953i	$-0.247688\pi$
$152$		0			0
$153$	3.50271	+	6.87446i	0.283178	+	0.555767i
$154$		0			0
$155$	−21.5876	+	0.713468i	−1.73396	+	0.0573071i
$156$		0			0
$157$	0.772593	−	4.87796i	0.0616597	−	0.389304i	−0.937488	−	0.348018i	$-0.886855\pi$
$157$	0.772593	−	4.87796i	0.0616597	−	0.389304i	0.999147	−	0.0412855i	$-0.0131453\pi$
$158$		0			0
$159$	5.13272	−	1.66772i	0.407051	−	0.132259i
$160$		0			0
$161$	−2.51318	−	2.51318i	−0.198066	−	0.198066i
$162$		0			0
$163$			1.81166i			0.141900i	0.997480	+	0.0709500i	$0.0226031\pi$
$163$			1.81166i			0.141900i	−0.997480	+	0.0709500i	$0.977397\pi$
$164$		0			0
$165$	−2.39994	+	0.0793177i	−0.186835	+	0.00617487i
$166$		0			0
$167$	−10.8777	+	10.8777i	−0.841741	+	0.841741i	−0.989085	−	0.147344i	$-0.952928\pi$
$167$	−10.8777	+	10.8777i	−0.841741	+	0.841741i	0.147344	+	0.989085i	$0.452928\pi$
$168$		0			0
$169$	4.99028	−	1.62144i	0.383868	−	0.124726i
$170$		0			0
$171$	7.86667	+	1.24596i	0.601579	+	0.0952808i
$172$		0			0
$173$	10.1507			0.771747			0.385873	−	0.922552i	$-0.373900\pi$
$173$	10.1507			0.771747			0.385873	+	0.922552i	$0.373900\pi$
$174$		0			0
$175$	1.39710	+	2.34498i	0.105611	+	0.177264i
$176$		0			0
$177$	−2.28454	+	0.361836i	−0.171717	+	0.0271972i
$178$		0			0
$179$	16.5134	+	8.41397i	1.23427	+	0.628890i	0.944596	−	0.328237i	$-0.106454\pi$
$179$	16.5134	+	8.41397i	1.23427	+	0.628890i	0.289670	+	0.957126i	$0.406454\pi$
$180$		0			0
$181$	−7.89882	−	15.5023i	−0.587115	−	1.15228i	−0.973231	−	0.229828i	$-0.926184\pi$
$181$	−7.89882	−	15.5023i	−0.587115	−	1.15228i	0.386116	−	0.922450i	$-0.373816\pi$
$182$		0			0
$183$	−2.81812	−	0.446346i	−0.208321	−	0.0329948i
$184$		0			0
$185$	−7.50356	−	9.64120i	−0.551672	−	0.708835i
$186$		0			0
$187$	−3.64607	+	5.01838i	−0.266627	+	0.366981i
$188$		0			0
$189$	−1.22953	+	0.893302i	−0.0894348	+	0.0649782i
$190$		0			0
$191$	−5.22062	+	5.22062i	−0.377751	+	0.377751i	−0.870290	−	0.492539i	$-0.836069\pi$
$191$	−5.22062	+	5.22062i	−0.377751	+	0.377751i	0.492539	+	0.870290i	$0.336069\pi$
$192$		0			0
$193$	13.3111	+	6.78235i	0.958155	+	0.488204i	0.861859	−	0.507148i	$-0.169300\pi$
$193$	13.3111	+	6.78235i	0.958155	+	0.488204i	0.0962963	+	0.995353i	$0.469300\pi$
$194$		0			0
$195$	4.42985	+	1.27920i	0.317228	+	0.0916056i
$196$		0			0
$197$	−1.76099	+	5.41976i	−0.125465	+	0.386142i	−0.993986	−	0.109511i	$-0.965071\pi$
$197$	−1.76099	+	5.41976i	−0.125465	+	0.386142i	0.868520	+	0.495653i	$0.165071\pi$
$198$		0			0
$199$	16.1577	−	2.55912i	1.14539	−	0.181412i	0.445241	−	0.895411i	$-0.353118\pi$
$199$	16.1577	−	2.55912i	1.14539	−	0.181412i	0.700146	+	0.713999i	$0.253118\pi$
$200$		0			0
$201$	0.702975	+	2.16354i	0.0495840	+	0.152604i
$202$		0			0
$203$	−1.50152	−	1.09092i	−0.105386	−	0.0765676i
$204$		0			0
$205$	4.55119	+	13.5752i	0.317869	+	0.948135i
$206$		0			0
$207$	14.5737	+	10.5884i	1.01294	+	0.735945i
$208$		0			0
$209$	1.97880	+	6.09012i	0.136876	+	0.421262i
$210$		0			0
$211$	−10.0839	+	1.59714i	−0.694207	+	0.109952i	−0.493560	−	0.869712i	$-0.664305\pi$
$211$	−10.0839	+	1.59714i	−0.694207	+	0.109952i	−0.200647	+	0.979664i	$0.564305\pi$
$212$		0			0
$213$	−0.0932825	+	0.287094i	−0.00639161	+	0.0196714i
$214$		0			0
$215$	−5.47502	+	18.9599i	−0.373393	+	1.29305i
$216$		0			0
$217$	−4.69862	−	2.39407i	−0.318963	−	0.162520i
$218$		0			0
$219$	−5.80915	+	5.80915i	−0.392546	+	0.392546i
$220$		0			0
$221$	9.63622	−	7.00113i	0.648202	−	0.470947i
$222$		0			0
$223$	−14.8978	+	20.5050i	−0.997629	+	1.37312i	−0.0708605	+	0.997486i	$0.522575\pi$
$223$	−14.8978	+	20.5050i	−0.997629	+	1.37312i	−0.926769	+	0.375633i	$0.877425\pi$
$224$		0			0
$225$	−8.85322	−	10.6313i	−0.590215	−	0.708753i
$226$		0			0
$227$	−21.0347	−	3.33156i	−1.39612	−	0.221124i	−0.587390	−	0.809304i	$-0.699845\pi$
$227$	−21.0347	−	3.33156i	−1.39612	−	0.221124i	−0.808730	+	0.588180i	$0.799845\pi$
$228$		0			0
$229$	6.53496	+	12.8256i	0.431842	+	0.847538i	0.999702	+	0.0244125i	$0.00777152\pi$
$229$	6.53496	+	12.8256i	0.431842	+	0.847538i	−0.567860	+	0.823125i	$0.692228\pi$
$230$		0			0
$231$	−0.522356	−	0.266153i	−0.0343685	−	0.0175116i
$232$		0			0
$233$	−7.81653	+	1.23802i	−0.512078	+	0.0811052i	−0.407126	−	0.913372i	$-0.633469\pi$
$233$	−7.81653	+	1.23802i	−0.512078	+	0.0811052i	−0.104952	+	0.994477i	$0.533469\pi$
$234$		0			0
$235$	−3.33467	+	1.84030i	−0.217530	+	0.120048i
$236$		0			0
$237$	−6.77078			−0.439810
$238$		0			0
$239$	8.58525	+	1.35977i	0.555333	+	0.0879562i	0.427792	−	0.903877i	$-0.359291\pi$
$239$	8.58525	+	1.35977i	0.555333	+	0.0879562i	0.127541	+	0.991833i	$0.459291\pi$
$240$		0			0
$241$	8.23556	−	2.67590i	0.530499	−	0.172370i	−0.0315057	−	0.999504i	$-0.510030\pi$
$241$	8.23556	−	2.67590i	0.530499	−	0.172370i	0.562005	+	0.827134i	$0.310030\pi$
$242$		0			0
$243$	8.28018	−	8.28018i	0.531173	−	0.531173i
$244$		0			0
$245$	−0.495016	−	14.9779i	−0.0316254	−	0.956901i
$246$		0			0
$247$		−	12.2960i		−	0.782373i
$248$		0			0
$249$	0.221053	+	0.221053i	0.0140087	+	0.0140087i
$250$		0			0
$251$	21.0132	−	6.82761i	1.32634	−	0.430955i	0.441674	−	0.897175i	$-0.354385\pi$
$251$	21.0132	−	6.82761i	1.32634	−	0.430955i	0.884669	+	0.466221i	$0.154385\pi$
$252$		0			0
$253$	−2.26565	+	14.3047i	−0.142440	+	0.899331i
$254$		0			0
$255$	3.00815	−	0.0994188i	0.188378	−	0.00622585i
$256$		0			0
$257$	−4.36110	−	8.55913i	−0.272038	−	0.533904i	0.714057	−	0.700087i	$-0.246856\pi$
$257$	−4.36110	−	8.55913i	−0.272038	−	0.533904i	−0.986095	+	0.166183i	$0.946856\pi$
$258$		0			0
$259$	−0.466601	−	2.94600i	−0.0289932	−	0.183056i
$260$		0			0
$261$	8.38163	+	4.27065i	0.518810	+	0.264347i
$262$		0			0
$263$	−17.1881	+	8.75776i	−1.05986	+	0.540027i	−0.894897	−	0.446273i	$-0.852751\pi$
$263$	−17.1881	+	8.75776i	−1.05986	+	0.540027i	−0.164965	+	0.986299i	$0.552751\pi$
$264$		0			0
$265$	−3.09301	+	24.8072i	−0.190002	+	1.52389i
$266$		0			0
$267$	−6.06384	+	4.40564i	−0.371101	+	0.269621i
$268$		0			0
$269$	−9.75564	−	7.08789i	−0.594812	−	0.432156i	0.249222	−	0.968446i	$-0.419825\pi$
$269$	−9.75564	−	7.08789i	−0.594812	−	0.432156i	−0.844034	+	0.536290i	$0.819825\pi$
$270$		0			0
$271$	−15.1792	+	11.0283i	−0.922072	+	0.669924i	−0.944039	−	0.329834i	$-0.893007\pi$
$271$	−15.1792	+	11.0283i	−0.922072	+	0.669924i	0.0219669	+	0.999759i	$0.493007\pi$
$272$		0			0
$273$	0.796001	+	0.796001i	0.0481761	+	0.0481761i
$274$		0			0
$275$	4.38436	−	10.2225i	0.264387	−	0.616440i
$276$		0			0
$277$	15.8105	+	5.13715i	0.949962	+	0.308661i	0.742700	−	0.669624i	$-0.233545\pi$
$277$	15.8105	+	5.13715i	0.949962	+	0.308661i	0.207262	+	0.978286i	$0.433545\pi$
$278$		0			0
$279$	25.4196	+	8.25934i	1.52183	+	0.494474i
$280$		0			0
$281$	−15.7223	+	2.49016i	−0.937911	+	0.148551i	−0.606632	−	0.794982i	$-0.707480\pi$
$281$	−15.7223	+	2.49016i	−0.937911	+	0.148551i	−0.331279	+	0.943533i	$0.607480\pi$
$282$		0			0
$283$	25.6442	−	8.33229i	1.52439	−	0.495303i	0.577369	−	0.816483i	$-0.304079\pi$
$283$	25.6442	−	8.33229i	1.52439	−	0.495303i	0.947018	+	0.321180i	$0.104079\pi$
$284$		0			0
$285$	1.74226	−	2.57262i	0.103202	−	0.152389i
$286$		0			0
$287$	−0.628556	+	3.43865i	−0.0371025	+	0.202977i
$288$		0			0
$289$	−5.42228	+	7.46312i	−0.318957	+	0.439007i
$290$		0			0
$291$	−1.10042	−	3.38674i	−0.0645076	−	0.198534i
$292$		0			0
$293$	−4.09921	−	25.8814i	−0.239479	−	1.51201i	−0.755338	−	0.655335i	$-0.772527\pi$
$293$	−4.09921	−	25.8814i	−0.239479	−	1.51201i	0.515860	−	0.856673i	$-0.327473\pi$
$294$		0			0
$295$	2.97251	−	10.2937i	0.173066	−	0.599325i
$296$		0			0
$297$	5.88989	+	1.91374i	0.341766	+	0.111047i
$298$		0			0
$299$	12.6255	−	24.7790i	0.730153	−	1.43301i
$300$		0			0
$301$	−3.40690	+	3.40690i	−0.196371	+	0.196371i
$302$		0			0
$303$	−3.77111	−	5.19048i	−0.216644	−	0.298185i
$304$		0			0
$305$	7.41118	−	10.9434i	0.424363	−	0.626615i
$306$		0			0
$307$	12.2490	−	8.89944i	0.699089	−	0.507918i	−0.180547	−	0.983566i	$-0.557787\pi$
$307$	12.2490	−	8.89944i	0.699089	−	0.507918i	0.879635	+	0.475649i	$0.157787\pi$
$308$		0			0
$309$	1.35001	−	8.52366i	0.0767996	−	0.484894i
$310$		0			0
$311$	−11.0458	−	21.6785i	−0.626347	−	1.22928i	−0.958242	−	0.285959i	$-0.907688\pi$
$311$	−11.0458	−	21.6785i	−0.626347	−	1.22928i	0.331894	−	0.943317i	$-0.392312\pi$
$312$		0			0
$313$	−5.82546	+	11.4331i	−0.329274	+	0.646237i	−0.994991	−	0.0999676i	$-0.968126\pi$
$313$	−5.82546	+	11.4331i	−0.329274	+	0.646237i	0.665716	+	0.746205i	$0.268126\pi$
$314$		0			0
$315$	−0.638301	−	3.31686i	−0.0359642	−	0.186884i
$316$		0			0
$317$	−3.30556	−	6.48754i	−0.185659	−	0.364376i	0.779352	−	0.626587i	$-0.215549\pi$
$317$	−3.30556	−	6.48754i	−0.185659	−	0.364376i	−0.965011	+	0.262210i	$0.915549\pi$
$318$		0			0
$319$			7.56303i			0.423449i
$320$		0			0
$321$	6.01588	+	0.952822i	0.335774	+	0.0531814i
$322$		0			0
$323$	−2.48028	−	7.63351i	−0.138006	−	0.424740i
$324$		0			0
$325$	−14.0725	+	16.0668i	−0.780600	+	0.891228i
$326$		0			0
$327$			7.80298i			0.431506i
$328$		0			0
$329$	−0.929890			−0.0512665
$330$		0			0
$331$	−8.32046	−	8.32046i	−0.457334	−	0.457334i	0.440446	−	0.897779i	$-0.354820\pi$
$331$	−8.32046	−	8.32046i	−0.457334	−	0.457334i	−0.897779	+	0.440446i	$0.854820\pi$
$332$		0			0
$333$	4.67164	+	14.3778i	0.256004	+	0.787899i
$334$		0			0
$335$	−10.4567	−	1.30376i	−0.571310	−	0.0712320i
$336$		0			0
$337$	22.0474			1.20100			0.600498	−	0.799626i	$-0.294969\pi$
$337$	22.0474			1.20100			0.600498	+	0.799626i	$0.294969\pi$
$338$		0			0
$339$	2.51737	−	1.28266i	0.136725	−	0.0696647i
$340$		0			0
$341$	3.36158	+	21.2242i	0.182040	+	1.14935i
$342$		0			0
$343$	3.39596	−	6.66494i	0.183364	−	0.359873i
$344$		0			0
$345$	6.15259	−	3.39542i	0.331244	−	0.182803i
$346$		0			0
$347$	4.77551	+	0.756367i	0.256363	+	0.0406039i	0.283293	−	0.959033i	$-0.408573\pi$
$347$	4.77551	+	0.756367i	0.256363	+	0.0406039i	−0.0269300	+	0.999637i	$0.508573\pi$
$348$		0			0
$349$	8.29485	+	11.4169i	0.444013	+	0.611132i	0.971098	−	0.238681i	$-0.0767150\pi$
$349$	8.29485	+	11.4169i	0.444013	+	0.611132i	−0.527085	+	0.849813i	$0.676715\pi$
$350$		0			0
$351$	−9.62059	−	6.98977i	−0.513509	−	0.373086i
$352$		0			0
$353$	−11.9419	−	16.4366i	−0.635601	−	0.874830i	0.362770	−	0.931879i	$-0.381831\pi$
$353$	−11.9419	−	16.4366i	−0.635601	−	0.874830i	−0.998371	+	0.0570486i	$0.981831\pi$
$354$		0			0
$355$	−1.02088	−	0.955555i	−0.0541825	−	0.0507156i
$356$		0			0
$357$	0.654734	+	0.333603i	0.0346522	+	0.0176562i
$358$		0			0
$359$	−2.66014	+	8.18706i	−0.140397	+	0.432097i	−0.996390	−	0.0848896i	$-0.972946\pi$
$359$	−2.66014	+	8.18706i	−0.140397	+	0.432097i	0.855994	+	0.516986i	$0.172946\pi$
$360$		0			0
$361$	10.1899	+	3.31089i	0.536309	+	0.174257i
$362$		0			0
$363$	−0.456948	−	2.88505i	−0.0239835	−	0.151426i
$364$		0			0
$365$	−12.9488	−	35.7844i	−0.677770	−	1.87304i
$366$		0			0
$367$	11.1033	+	8.06704i	0.579589	+	0.421096i	0.838576	−	0.544785i	$-0.183389\pi$
$367$	11.1033	+	8.06704i	0.579589	+	0.421096i	−0.258987	+	0.965881i	$0.583389\pi$
$368$		0			0
$369$	0.420147	−	17.7123i	0.0218720	−	0.922066i
$370$		0			0
$371$	−3.58751	+	4.93779i	−0.186254	+	0.256357i
$372$		0			0
$373$	8.53605	−	2.77353i	0.441980	−	0.143608i	−0.0795690	−	0.996829i	$-0.525354\pi$
$373$	8.53605	−	2.77353i	0.441980	−	0.143608i	0.521549	+	0.853221i	$0.325354\pi$
$374$		0			0
$375$	−5.22087	+	1.36760i	−0.269605	+	0.0706227i
$376$		0			0
$377$	4.48767	−	13.8116i	0.231127	−	0.711336i
$378$		0			0
$379$	−3.82286	+	11.7656i	−0.196367	+	0.604356i	0.803591	+	0.595182i	$0.202920\pi$
$379$	−3.82286	+	11.7656i	−0.196367	+	0.604356i	−0.999958	+	0.00917387i	$0.997080\pi$
$380$		0			0
$381$	−0.704314	+	1.38229i	−0.0360831	+	0.0708170i
$382$		0			0
$383$	7.42978	+	7.42978i	0.379644	+	0.379644i	0.870974	−	0.491330i	$-0.163489\pi$
$383$	7.42978	+	7.42978i	0.379644	+	0.379644i	−0.491330	+	0.870974i	$0.663489\pi$
$384$		0			0
$385$	2.14307	−	1.66791i	0.109221	−	0.0850046i
$386$		0			0
$387$	14.3538	−	19.7563i	0.729644	−	1.00427i
$388$		0			0
$389$	4.79177	+	6.59531i	0.242953	+	0.334396i	0.913028	−	0.407898i	$-0.133738\pi$
$389$	4.79177	+	6.59531i	0.242953	+	0.334396i	−0.670075	+	0.742293i	$0.733738\pi$
$390$		0			0
$391$	2.83982	−	17.9299i	0.143616	−	0.906755i
$392$		0			0
$393$	4.27289	−	2.17714i	0.215539	−	0.109822i
$394$		0			0
$395$	13.3079	−	28.4002i	0.669593	−	1.42897i
$396$		0			0
$397$	−23.1071	+	3.65980i	−1.15971	+	0.183680i	−0.706494	−	0.707719i	$-0.749724\pi$
$397$	−23.1071	+	3.65980i	−1.15971	+	0.183680i	−0.453218	+	0.891400i	$0.649724\pi$
$398$		0			0
$399$	0.675893	−	0.344385i	0.0338370	−	0.0172408i
$400$		0			0
$401$			15.2382i			0.760961i	0.924789	+	0.380480i	$0.124241\pi$
$401$			15.2382i			0.760961i	−0.924789	+	0.380480i	$0.875759\pi$
$402$		0			0
$403$	6.45486	−	40.7544i	0.321539	−	2.03012i
$404$		0			0
$405$	5.29332	+	14.6283i	0.263027	+	0.726885i
$406$		0			0
$407$	−8.59449	+	8.59449i	−0.426013	+	0.426013i
$408$		0			0
$409$	−16.3900			−0.810433			−0.405216	−	0.914221i	$-0.632804\pi$
$409$	−16.3900			−0.810433			−0.405216	+	0.914221i	$0.632804\pi$
$410$		0			0
$411$	−2.37475			−0.117138
$412$		0			0
$413$	1.84968	−	1.84968i	0.0910170	−	0.0910170i
$414$		0			0
$415$	−1.36169	+	0.492734i	−0.0668426	+	0.0241874i
$416$		0			0
$417$	1.14511	−	7.22993i	0.0560762	−	0.354051i
$418$		0			0
$419$			22.8901i			1.11826i	0.829081	+	0.559128i	$0.188864\pi$
$419$			22.8901i			1.11826i	−0.829081	+	0.559128i	$0.811136\pi$
$420$		0			0
$421$	−25.5890	+	13.0383i	−1.24713	+	0.635446i	−0.947849	−	0.318718i	$-0.896748\pi$
$421$	−25.5890	+	13.0383i	−1.24713	+	0.635446i	−0.299283	+	0.954164i	$0.596748\pi$
$422$		0			0
$423$	4.65506	−	0.737288i	0.226337	−	0.0358482i
$424$		0			0
$425$	−5.49547	+	12.8131i	−0.266569	+	0.621529i
$426$		0			0
$427$	2.87510	−	1.46494i	0.139136	−	0.0708933i
$428$		0			0
$429$	0.717600	−	4.53075i	0.0346460	−	0.218746i
$430$		0			0
$431$	2.57857	+	3.54909i	0.124205	+	0.170954i	0.866591	−	0.499018i	$-0.166306\pi$
$431$	2.57857	+	3.54909i	0.124205	+	0.170954i	−0.742386	+	0.669972i	$0.766306\pi$
$432$		0			0
$433$	4.64539	−	6.39383i	0.223243	−	0.307268i	−0.682674	−	0.730723i	$-0.739183\pi$
$433$	4.64539	−	6.39383i	0.223243	−	0.307268i	0.905917	+	0.423455i	$0.139183\pi$
$434$		0			0
$435$	2.89595	−	2.25386i	0.138850	−	0.108064i
$436$		0			0
$437$	−13.2512	−	13.2512i	−0.633893	−	0.633893i
$438$		0			0
$439$	2.67759	−	5.25507i	0.127795	−	0.250811i	−0.818240	−	0.574877i	$-0.805050\pi$
$439$	2.67759	−	5.25507i	0.127795	−	0.250811i	0.946035	+	0.324066i	$0.105050\pi$
$440$		0			0
$441$	−5.73047	+	17.6366i	−0.272880	+	0.839837i
$442$		0			0
$443$	−1.24548	+	3.83319i	−0.0591745	+	0.182120i	−0.976274	−	0.216537i	$-0.930524\pi$
$443$	−1.24548	+	3.83319i	−0.0591745	+	0.182120i	0.917100	+	0.398657i	$0.130524\pi$
$444$		0			0
$445$	−6.56113	−	34.0941i	−0.311027	−	1.61622i
$446$		0			0
$447$	3.24286	−	1.05367i	0.153382	−	0.0498368i
$448$		0			0
$449$	5.10920	−	7.03221i	0.241118	−	0.331871i	−0.671258	−	0.741224i	$-0.734246\pi$
$449$	5.10920	−	7.03221i	0.241118	−	0.331871i	0.912376	+	0.409353i	$0.134246\pi$
$450$		0			0
$451$	12.8417	−	6.16405i	0.604691	−	0.290254i
$452$		0			0
$453$	5.58495	+	4.05770i	0.262404	+	0.190648i
$454$		0			0
$455$	−4.90337	+	1.77431i	−0.229874	+	0.0831810i
$456$		0			0
$457$	−0.223899	−	1.41364i	−0.0104735	−	0.0661274i	0.981898	−	0.189410i	$-0.0606577\pi$
$457$	−0.223899	−	1.41364i	−0.0104735	−	0.0661274i	−0.992372	+	0.123283i	$0.960658\pi$
$458$		0			0
$459$	−7.38254	−	2.39873i	−0.344588	−	0.111963i
$460$		0			0
$461$	−1.33891	+	4.12076i	−0.0623595	+	0.191923i	−0.977383	−	0.211479i	$-0.932172\pi$
$461$	−1.33891	+	4.12076i	−0.0623595	+	0.191923i	0.915023	+	0.403401i	$0.132172\pi$
$462$		0			0
$463$	19.9966	+	10.1888i	0.929319	+	0.473512i	0.852028	−	0.523497i	$-0.175373\pi$
$463$	19.9966	+	10.1888i	0.929319	+	0.473512i	0.0772914	+	0.997009i	$0.475373\pi$
$464$		0			0
$465$	7.12514	−	7.61220i	0.330420	−	0.353008i
$466$		0			0
$467$	−15.7043	−	21.6152i	−0.726710	−	1.00023i	−0.999274	−	0.0380925i	$-0.987872\pi$
$467$	−15.7043	−	21.6152i	−0.726710	−	1.00023i	0.272565	−	0.962137i	$-0.412128\pi$
$468$		0			0
$469$	−2.08137	−	1.51220i	−0.0961086	−	0.0698270i
$470$		0			0
$471$	1.40132	+	1.92875i	0.0645693	+	0.0888720i
$472$		0			0
$473$	19.3917	+	3.07134i	0.891632	+	0.141221i
$474$		0			0
$475$	7.36651	+	12.3644i	0.337999	+	0.567317i
$476$		0			0
$477$	14.0441	−	27.5632i	0.643037	−	1.26203i
$478$		0			0
$479$	−4.17044	−	26.3311i	−0.190552	−	1.20310i	−0.878645	−	0.477476i	$-0.841552\pi$
$479$	−4.17044	−	26.3311i	−0.190552	−	1.20310i	0.688093	−	0.725623i	$-0.258448\pi$
$480$		0			0
$481$	20.7950	−	10.5956i	0.948170	−	0.483117i
$482$		0			0
$483$	1.71569			0.0780664
$484$		0			0
$485$	16.3686	+	2.04087i	0.743260	+	0.0926711i
$486$		0			0
$487$	8.37211	+	25.7667i	0.379377	+	1.16760i	0.940478	+	0.339854i	$0.110378\pi$
$487$	8.37211	+	25.7667i	0.379377	+	1.16760i	−0.561102	+	0.827747i	$0.689622\pi$
$488$		0			0
$489$	−0.618387	−	0.618387i	−0.0279644	−	0.0279644i
$490$		0			0
$491$	29.9081			1.34973			0.674867	−	0.737940i	$-0.264201\pi$
$491$	29.9081			1.34973			0.674867	+	0.737940i	$0.264201\pi$
$492$		0			0
$493$		−	9.47970i		−	0.426944i
$494$		0			0
$495$	−9.40582	+	10.0488i	−0.422760	+	0.451659i
$496$		0			0
$497$	−0.105495	−	0.324682i	−0.00473212	−	0.0145640i
$498$		0			0
$499$	4.85417	+	0.768825i	0.217302	+	0.0344173i	0.264136	−	0.964485i	$-0.414913\pi$
$499$	4.85417	+	0.768825i	0.217302	+	0.0344173i	−0.0468338	+	0.998903i	$0.514913\pi$
$500$		0			0
$501$		−	7.42593i		−	0.331766i
$502$		0			0
$503$	2.77755	+	5.45124i	0.123845	+	0.243059i	0.944602	−	0.328218i	$-0.106448\pi$
$503$	2.77755	+	5.45124i	0.123845	+	0.243059i	−0.820757	+	0.571277i	$0.806448\pi$
$504$		0			0
$505$	29.1837	−	5.61615i	1.29866	−	0.249915i
$506$		0			0
$507$	−1.14991	+	2.25683i	−0.0510694	+	0.100229i
$508$		0			0
$509$	4.86459	+	9.54729i	0.215619	+	0.423176i	0.973329	−	0.229416i	$-0.0736815\pi$
$509$	4.86459	+	9.54729i	0.215619	+	0.423176i	−0.757709	+	0.652592i	$0.773682\pi$
$510$		0			0
$511$	1.45343	−	9.17659i	0.0642959	−	0.405948i
$512$		0			0
$513$	−6.48292	+	4.71011i	−0.286228	+	0.207957i
$514$		0			0
$515$	33.0992	+	22.4158i	1.45853	+	0.987759i
$516$		0			0
$517$	2.22726	+	3.06557i	0.0979550	+	0.134823i
$518$		0			0
$519$	−3.46483	+	3.46483i	−0.152089	+	0.152089i
$520$		0			0
$521$	−13.8331	+	27.1490i	−0.606040	+	1.18942i	0.360466	+	0.932773i	$0.382618\pi$
$521$	−13.8331	+	27.1490i	−0.606040	+	1.18942i	−0.966505	+	0.256647i	$0.917382\pi$
$522$		0			0
$523$	−8.46331	−	2.74990i	−0.370075	−	0.120245i	0.118074	−	0.993005i	$-0.462328\pi$
$523$	−8.46331	−	2.74990i	−0.370075	−	0.120245i	−0.488149	+	0.872760i	$0.662328\pi$
$524$		0			0
$525$	−1.27731	−	0.323546i	−0.0557466	−	0.0141207i
$526$		0			0
$527$	−4.21349	−	26.6029i	−0.183542	−	1.15884i
$528$		0			0
$529$	−5.99029	−	18.4362i	−0.260447	−	0.801575i
$530$		0			0
$531$	−7.79299	+	10.7261i	−0.338187	+	0.465475i
$532$		0			0
$533$	−27.1091	+	3.63695i	−1.17423	+	0.157534i
$534$		0			0
$535$	−15.8208	+	23.3610i	−0.683992	+	1.00998i
$536$		0			0
$537$	−8.50863	+	2.76462i	−0.367175	+	0.119302i
$538$		0			0
$539$	−14.7257	+	2.33232i	−0.634281	+	0.100460i
$540$		0			0
$541$	19.4498	+	6.31962i	0.836211	+	0.271702i	0.695659	−	0.718372i	$-0.255112\pi$
$541$	19.4498	+	6.31962i	0.836211	+	0.271702i	0.140552	+	0.990073i	$0.455112\pi$
$542$		0			0
$543$	7.98768	+	2.59536i	0.342784	+	0.111377i
$544$		0			0
$545$	−32.7298	−	15.3367i	−1.40199	−	0.656951i
$546$		0			0
$547$	−1.11972	−	1.11972i	−0.0478757	−	0.0478757i	0.682764	−	0.730639i	$-0.260778\pi$
$547$	−1.11972	−	1.11972i	−0.0478757	−	0.0478757i	−0.730639	+	0.682764i	$0.760778\pi$
$548$		0			0
$549$	−13.2313	+	9.61312i	−0.564699	+	0.410278i
$550$		0			0
$551$	−7.91708	−	5.75210i	−0.337279	−	0.245048i
$552$		0			0
$553$	6.19484	−	4.50081i	0.263431	−	0.191394i
$554$		0			0
$555$	5.85215	+	0.729657i	0.248410	+	0.0309722i
$556$		0			0
$557$	19.9754	−	10.1780i	0.846386	−	0.431255i	0.0236782	−	0.999720i	$-0.492462\pi$
$557$	19.9754	−	10.1780i	0.846386	−	0.431255i	0.822708	+	0.568464i	$0.192462\pi$
$558$		0			0
$559$	−33.5908	−	17.1154i	−1.42074	−	0.723902i
$560$		0			0
$561$	−0.468422	−	2.95750i	−0.0197768	−	0.124866i
$562$		0			0
$563$	17.0788	+	33.5190i	0.719785	+	1.41266i	0.903024	+	0.429589i	$0.141342\pi$
$563$	17.0788	+	33.5190i	0.719785	+	1.41266i	−0.183240	+	0.983068i	$0.558658\pi$
$564$		0			0
$565$	0.432299	+	13.0802i	0.0181870	+	0.550289i
$566$		0			0
$567$	−0.594146	+	3.75129i	−0.0249518	+	0.157539i
$568$		0			0
$569$	23.8827	−	7.75995i	1.00121	−	0.325314i	0.237864	−	0.971299i	$-0.423553\pi$
$569$	23.8827	−	7.75995i	1.00121	−	0.325314i	0.763351	+	0.645984i	$0.223553\pi$
$570$		0			0
$571$	−6.35444	−	6.35444i	−0.265925	−	0.265925i	0.561531	−	0.827456i	$-0.310213\pi$
$571$	−6.35444	−	6.35444i	−0.265925	−	0.265925i	−0.827456	+	0.561531i	$0.810213\pi$
$572$		0			0
$573$		−	3.56399i		−	0.148888i
$574$		0			0
$575$	2.14932	+	32.4808i	0.0896329	+	1.35454i
$576$		0			0
$577$	−31.2029	+	31.2029i	−1.29899	+	1.29899i	−0.369937	+	0.929057i	$0.620621\pi$
$577$	−31.2029	+	31.2029i	−1.29899	+	1.29899i	−0.929057	+	0.369937i	$0.879379\pi$
$578$		0			0
$579$	−6.85866	+	2.22851i	−0.285036	+	0.0926138i
$580$		0			0
$581$	−0.349192	−	0.0553066i	−0.0144869	−	0.00229450i
$582$		0			0
$583$	24.8712			1.03006
$584$		0			0
$585$	23.1396	−	12.7700i	0.956704	−	0.527975i
$586$		0			0
$587$	40.8188	−	6.46506i	1.68477	−	0.266842i	0.760712	−	0.649089i	$-0.224850\pi$
$587$	40.8188	−	6.46506i	1.68477	−	0.266842i	0.924060	+	0.382248i	$0.124850\pi$
$588$		0			0
$589$	−24.7744	−	12.6232i	−1.02081	−	0.520130i
$590$		0			0
$591$	−1.24888	−	2.45106i	−0.0513719	−	0.100823i
$592$		0			0
$593$	−27.9457	−	4.42617i	−1.14759	−	0.181761i	−0.446468	−	0.894799i	$-0.647318\pi$
$593$	−27.9457	−	4.42617i	−1.14759	−	0.181761i	−0.701125	+	0.713038i	$0.747318\pi$
$594$		0			0
$595$	−2.68618	+	2.09060i	−0.110123	+	0.0857062i
$596$		0			0
$597$	−4.64170	+	6.38875i	−0.189972	+	0.261474i
$598$		0			0
$599$	−6.32193	+	4.59315i	−0.258307	+	0.187671i	−0.709400	−	0.704806i	$-0.751034\pi$
$599$	−6.32193	+	4.59315i	−0.258307	+	0.187671i	0.451093	+	0.892477i	$0.351034\pi$
$600$		0			0
$601$	7.26733	−	7.26733i	0.296441	−	0.296441i	−0.543177	−	0.839618i	$-0.682779\pi$
$601$	7.26733	−	7.26733i	0.296441	−	0.296441i	0.839618	+	0.543177i	$0.182779\pi$
$602$		0			0
$603$	11.6184	+	5.91985i	0.473136	+	0.241075i
$604$		0			0
$605$	12.9995	+	3.75386i	0.528507	+	0.152616i
$606$		0			0
$607$	0.0423159	−	0.130235i	0.00171755	−	0.00528608i	−0.950194	−	0.311659i	$-0.899115\pi$
$607$	0.0423159	−	0.130235i	0.00171755	−	0.00528608i	0.951912	+	0.306373i	$0.0991154\pi$
$608$		0			0
$609$	0.884899	−	0.140154i	0.0358579	−	0.00567933i
$610$		0			0
$611$	−2.24843	−	6.91994i	−0.0909616	−	0.279951i
$612$		0			0
$613$	−20.4146	−	14.8321i	−0.824538	−	0.599062i	0.0934709	−	0.995622i	$-0.470204\pi$
$613$	−20.4146	−	14.8321i	−0.824538	−	0.599062i	−0.918009	+	0.396560i	$0.870204\pi$
$614$		0			0
$615$	−6.18722	−	3.08024i	−0.249493	−	0.124207i
$616$		0			0
$617$	−16.9469	−	12.3127i	−0.682258	−	0.495689i	0.191848	−	0.981425i	$-0.438552\pi$
$617$	−16.9469	−	12.3127i	−0.682258	−	0.495689i	−0.874106	+	0.485735i	$0.838552\pi$
$618$		0			0
$619$	12.4786	+	38.4053i	0.501559	+	1.54364i	0.806480	+	0.591262i	$0.201370\pi$
$619$	12.4786	+	38.4053i	0.501559	+	1.54364i	−0.304921	+	0.952378i	$0.598630\pi$
$620$		0			0
$621$	−17.9008	+	2.83521i	−0.718336	+	0.113773i
$622$		0			0
$623$	2.61943	−	8.06176i	0.104945	−	0.322988i
$624$		0			0
$625$	4.52512	−	24.5871i	0.181005	−	0.983482i
$626$		0			0
$627$	−2.75422	−	1.40335i	−0.109993	−	0.0560443i
$628$		0			0
$629$	10.7725	−	10.7725i	0.429529	−	0.429529i
$630$		0			0
$631$	35.3430	−	25.6782i	1.40698	−	1.02223i	0.413228	−	0.910628i	$-0.364401\pi$
$631$	35.3430	−	25.6782i	1.40698	−	1.02223i	0.993753	−	0.111604i	$-0.0355987\pi$
$632$		0			0
$633$	2.89686	−	3.98719i	0.115140	−	0.158477i
$634$		0			0
$635$	−4.41374	−	5.67114i	−0.175154	−	0.225052i
$636$		0			0
$637$	28.2761	+	4.47849i	1.12034	+	0.177444i
$638$		0			0
$639$	0.785545	+	1.54172i	0.0310757	+	0.0609895i
$640$		0			0
$641$	7.95937	+	4.05550i	0.314376	+	0.160183i	0.604058	−	0.796940i	$-0.293549\pi$
$641$	7.95937	+	4.05550i	0.314376	+	0.160183i	−0.289682	+	0.957123i	$0.593549\pi$
$642$		0			0
$643$	−24.1314	+	3.82204i	−0.951651	+	0.150727i	−0.612910	−	0.790153i	$-0.710001\pi$
$643$	−24.1314	+	3.82204i	−0.951651	+	0.150727i	−0.338741	+	0.940880i	$0.610001\pi$
$644$		0			0
$645$	−4.60288	−	8.34054i	−0.181238	−	0.328409i
$646$		0			0
$647$	2.93270			0.115296			0.0576482	−	0.998337i	$-0.481640\pi$
$647$	2.93270			0.115296			0.0576482	+	0.998337i	$0.481640\pi$
$648$		0			0
$649$	−10.5282	−	1.66750i	−0.413268	−	0.0654552i
$650$		0			0
$651$	2.42100	−	0.786631i	0.0948865	−	0.0308305i
$652$		0			0
$653$	1.04447	−	1.04447i	0.0408733	−	0.0408733i	−0.686375	−	0.727248i	$-0.740799\pi$
$653$	1.04447	−	1.04447i	0.0408733	−	0.0408733i	0.727248	+	0.686375i	$0.240799\pi$
$654$		0			0
$655$	0.733768	+	22.2019i	0.0286707	+	0.867499i
$656$		0			0
$657$			47.0906i			1.83718i
$658$		0			0
$659$	−17.7979	−	17.7979i	−0.693310	−	0.693310i	0.269649	−	0.962959i	$-0.413092\pi$
$659$	−17.7979	−	17.7979i	−0.693310	−	0.693310i	−0.962959	+	0.269649i	$0.913092\pi$
$660$		0			0
$661$	16.7708	−	5.44916i	0.652308	−	0.211948i	0.0358764	−	0.999356i	$-0.488578\pi$
$661$	16.7708	−	5.44916i	0.652308	−	0.211948i	0.616432	+	0.787409i	$0.288578\pi$
$662$		0			0
$663$	−0.899457	+	5.67895i	−0.0349320	+	0.220552i
$664$		0			0
$665$	0.116069	+	3.51193i	0.00450095	+	0.136187i
$666$		0			0
$667$	−10.0484	−	19.7210i	−0.389074	−	0.763600i
$668$		0			0
$669$	−1.91397	−	12.0843i	−0.0739982	−	0.467206i
$670$		0			0
$671$	−11.7159	−	5.96954i	−0.452286	−	0.230451i
$672$		0			0
$673$	−31.4887	+	16.0443i	−1.21380	+	0.618462i	−0.939291	−	0.343122i	$-0.888516\pi$
$673$	−31.4887	+	16.0443i	−1.21380	+	0.618462i	−0.274510	+	0.961584i	$0.588516\pi$
$674$		0			0
$675$	13.8617	+	1.26496i	0.533537	+	0.0486885i
$676$		0			0
$677$	−20.7505	+	15.0762i	−0.797508	+	0.579424i	−0.910182	−	0.414208i	$-0.864058\pi$
$677$	−20.7505	+	15.0762i	−0.797508	+	0.579424i	0.112674	+	0.993632i	$0.464058\pi$
$678$		0			0
$679$	3.25811	+	2.36716i	0.125035	+	0.0908432i
$680$		0			0
$681$	8.31711	−	6.04273i	0.318712	−	0.231558i
$682$		0			0
$683$	−31.0457	−	31.0457i	−1.18793	−	1.18793i	−0.977639	−	0.210291i	$-0.932559\pi$
$683$	−31.0457	−	31.0457i	−1.18793	−	1.18793i	−0.210291	−	0.977639i	$-0.567441\pi$
$684$		0			0
$685$	4.66754	−	9.96094i	0.178338	−	0.380588i
$686$		0			0
$687$	−6.60847	−	2.14722i	−0.252129	−	0.0819217i
$688$		0			0
$689$	−45.4199	−	14.7578i	−1.73036	−	0.562228i
$690$		0			0
$691$	28.5218	−	4.51740i	1.08502	−	0.171850i	0.411786	−	0.911281i	$-0.364905\pi$
$691$	28.5218	−	4.51740i	1.08502	−	0.171850i	0.673233	+	0.739431i	$0.264905\pi$
$692$		0			0
$693$	−3.19594	+	1.03842i	−0.121404	+	0.0394464i
$694$		0			0
$695$	28.0754	+	19.0135i	1.06496	+	0.721224i
$696$		0			0
$697$	−16.0961	+	7.72618i	−0.609683	+	0.292650i
$698$		0			0
$699$	2.24549	−	3.09066i	0.0849324	−	0.116899i
$700$		0			0
$701$	−0.680789	−	2.09525i	−0.0257130	−	0.0791366i	0.937377	−	0.348318i	$-0.113247\pi$
$701$	−0.680789	−	2.09525i	−0.0257130	−	0.0791366i	−0.963090	+	0.269181i	$0.913247\pi$
$702$		0			0
$703$	−2.46025	−	15.5334i	−0.0927900	−	0.585853i
$704$		0			0
$705$	0.510084	−	1.76641i	0.0192109	−	0.0665268i
$706$		0			0
$707$	6.90065	+	2.24216i	0.259526	+	0.0843250i
$708$		0			0
$709$	−3.19872	+	6.27784i	−0.120130	+	0.235769i	−0.943239	−	0.332115i	$-0.892238\pi$
$709$	−3.19872	+	6.27784i	−0.120130	+	0.235769i	0.823109	+	0.567884i	$0.192238\pi$
$710$		0			0
$711$	−27.4429	+	27.4429i	−1.02919	+	1.02919i
$712$		0			0
$713$	−36.9643	−	50.8769i	−1.38432	−	1.90536i
$714$		0			0
$715$	17.5939	+	11.9151i	0.657974	+	0.445600i
$716$		0			0
$717$	−3.39461	+	2.46633i	−0.126774	+	0.0921066i
$718$		0			0
$719$	−4.85040	+	30.6242i	−0.180889	+	1.14209i	0.715431	+	0.698684i	$0.246230\pi$
$719$	−4.85040	+	30.6242i	−0.180889	+	1.14209i	−0.896320	+	0.443407i	$0.853770\pi$
$720$		0			0
$721$	4.43084	+	8.69602i	0.165013	+	0.323857i
$722$		0			0
$723$	−1.89772	+	3.72449i	−0.0705771	+	0.138515i
$724$		0			0
$725$	3.76191	+	16.5771i	0.139714	+	0.615657i
$726$		0			0
$727$	22.8238	+	44.7943i	0.846489	+	1.66133i	0.745563	+	0.666435i	$0.232181\pi$
$727$	22.8238	+	44.7943i	0.846489	+	1.66133i	0.100927	+	0.994894i	$0.467819\pi$
$728$		0			0
$729$		−	15.2186i		−	0.563653i
$730$		0			0
$731$	−24.3061	−	3.84970i	−0.898992	−	0.142386i
$732$		0			0
$733$	6.47352	+	19.9234i	0.239105	+	0.735889i	0.996550	+	0.0829905i	$0.0264471\pi$
$733$	6.47352	+	19.9234i	0.239105	+	0.735889i	−0.757446	+	0.652898i	$0.773553\pi$
$734$		0			0
$735$	5.28148	+	4.94354i	0.194810	+	0.182345i
$736$		0			0
$737$			10.4836i			0.386170i
$738$		0			0
$739$	−39.3132			−1.44616			−0.723080	−	0.690764i	$-0.757274\pi$
$739$	−39.3132			−1.44616			−0.723080	+	0.690764i	$0.757274\pi$
$740$		0			0
$741$	4.19707	+	4.19707i	0.154183	+	0.154183i
$742$		0			0
$743$	15.1852	+	46.7352i	0.557090	+	1.71455i	0.690359	+	0.723467i	$0.257452\pi$
$743$	15.1852	+	46.7352i	0.557090	+	1.71455i	−0.133270	+	0.991080i	$0.542548\pi$
$744$		0			0
$745$	−1.95417	+	15.6732i	−0.0715951	+	0.574222i
$746$		0			0
$747$	1.79192			0.0655628
$748$		0			0
$749$	−6.13753	+	3.12723i	−0.224261	+	0.114266i
$750$		0			0
$751$	−5.98183	−	37.7678i	−0.218280	−	1.37817i	−0.816736	−	0.577011i	$-0.804219\pi$
$751$	−5.98183	−	37.7678i	−0.218280	−	1.37817i	0.598456	−	0.801156i	$-0.295781\pi$
$752$		0			0
$753$	−4.84208	+	9.50312i	−0.176455	+	0.346313i
$754$		0			0
$755$	−27.9973	+	15.4508i	−1.01892	+	0.562313i
$756$		0			0
$757$	−30.0588	−	4.76085i	−1.09251	−	0.173036i	−0.415921	−	0.909401i	$-0.636541\pi$
$757$	−30.0588	−	4.76085i	−1.09251	−	0.173036i	−0.676585	+	0.736365i	$0.736541\pi$
$758$		0			0
$759$	−4.10939	−	5.65609i	−0.149162	−	0.205303i
$760$		0			0
$761$	10.7709	+	7.82549i	0.390444	+	0.283674i	0.765637	−	0.643273i	$-0.222424\pi$
$761$	10.7709	+	7.82549i	0.390444	+	0.283674i	−0.375194	+	0.926946i	$0.622424\pi$
$762$		0			0
$763$	−5.18696	−	7.13924i	−0.187781	−	0.258458i
$764$		0			0
$765$	11.7895	−	12.5954i	0.426250	−	0.455388i
$766$		0			0
$767$	18.2372	+	9.29231i	0.658506	+	0.335526i
$768$		0			0
$769$	−3.70408	+	11.4000i	−0.133572	+	0.411094i	−0.995365	−	0.0961669i	$-0.969342\pi$
$769$	−3.70408	+	11.4000i	−0.133572	+	0.411094i	0.861793	+	0.507260i	$0.169342\pi$
$770$		0			0
$771$	4.41016	+	1.43295i	0.158828	+	0.0516063i
$772$		0			0
$773$	2.77010	+	17.4897i	0.0996337	+	0.629062i	0.986085	+	0.166241i	$0.0531629\pi$
$773$	2.77010	+	17.4897i	0.0996337	+	0.629062i	−0.886451	+	0.462822i	$0.846837\pi$
$774$		0			0
$775$	17.9252	+	44.8482i	0.643891	+	1.61100i
$776$		0			0
$777$	1.16485	+	0.846313i	0.0417888	+	0.0303613i
$778$		0			0
$779$	−3.31419	+	18.1309i	−0.118743	+	0.649609i
$780$		0			0
$781$	−0.817695	+	1.12546i	−0.0292594	+	0.0402722i
$782$		0			0
$783$	−9.00110	+	2.92464i	−0.321673	+	0.104518i
$784$		0			0
$785$	−10.8444	+	2.08692i	−0.387055	+	0.0744854i
$786$		0			0
$787$	9.59451	−	29.5289i	0.342007	−	1.05259i	−0.621159	−	0.783684i	$-0.713338\pi$
$787$	9.59451	−	29.5289i	0.342007	−	1.05259i	0.963167	−	0.268906i	$-0.0866620\pi$
$788$		0			0
$789$	2.87758	−	8.85629i	0.102445	−	0.315292i
$790$		0			0
$791$	−1.45060	+	2.84695i	−0.0515772	+	0.101226i
$792$		0			0
$793$	17.8534	+	17.8534i	0.633994	+	0.633994i
$794$		0			0
$795$	−7.41187	−	9.52339i	−0.262872	−	0.337760i
$796$		0			0
$797$	−4.40018	+	6.05633i	−0.155862	+	0.214526i	−0.879806	−	0.475333i	$-0.842328\pi$
$797$	−4.40018	+	6.05633i	−0.155862	+	0.214526i	0.723944	+	0.689859i	$0.242328\pi$
$798$		0			0
$799$	−2.79171	−	3.84246i	−0.0987636	−	0.135936i
$800$		0			0
$801$	−6.72093	+	42.4343i	−0.237472	+	1.49934i
$802$		0			0
$803$	−33.7337	+	17.1882i	−1.19044	+	0.606557i
$804$		0			0
$805$	−3.37216	+	7.19648i	−0.118853	+	0.253642i
$806$		0			0
$807$	5.74933	−	0.910604i	0.202386	−	0.0320548i
$808$		0			0
$809$	3.63117	−	1.85017i	0.127665	−	0.0650486i	−0.388991	−	0.921241i	$-0.627176\pi$
$809$	3.63117	−	1.85017i	0.127665	−	0.0650486i	0.516656	+	0.856193i	$0.327176\pi$
$810$		0			0
$811$		−	10.3939i		−	0.364978i	−0.983208	−	0.182489i	$-0.941585\pi$
$811$		−	10.3939i		−	0.364978i	0.983208	−	0.182489i	$-0.0584154\pi$
$812$		0			0
$813$	1.41685	−	8.94563i	0.0496910	−	0.313737i
$814$		0			0
$815$	3.80927	−	1.37840i	0.133433	−	0.0482834i
$816$		0			0
$817$	−17.9636	+	17.9636i	−0.628466	+	0.628466i
$818$		0			0
$819$	6.45260			0.225472
$820$		0			0
$821$	41.6424			1.45333			0.726665	−	0.686992i	$-0.241069\pi$
$821$	41.6424			1.45333			0.726665	+	0.686992i	$0.241069\pi$
$822$		0			0
$823$	15.0402	−	15.0402i	0.524267	−	0.524267i	−0.394590	−	0.918857i	$-0.629113\pi$
$823$	15.0402	−	15.0402i	0.524267	−	0.524267i	0.918857	+	0.394590i	$0.129113\pi$
$824$		0			0
$825$	1.99278	+	4.98587i	0.0693796	+	0.173586i
$826$		0			0
$827$	−8.10241	+	51.1566i	−0.281749	+	1.77889i	0.288562	+	0.957461i	$0.406823\pi$
$827$	−8.10241	+	51.1566i	−0.281749	+	1.77889i	−0.570311	+	0.821429i	$0.693177\pi$
$828$		0			0
$829$			5.10655i			0.177358i	0.996060	+	0.0886789i	$0.0282645\pi$
$829$			5.10655i			0.177358i	−0.996060	+	0.0886789i	$0.971736\pi$
$830$		0			0
$831$	−7.15022	+	3.64322i	−0.248038	+	0.126382i
$832$		0			0
$833$	18.4576	−	2.92339i	0.639517	−	0.101290i
$834$		0			0
$835$	31.1482	+	14.5956i	1.07793	+	0.505101i
$836$		0			0
$837$	−23.9599	+	12.2082i	−0.828176	+	0.421977i
$838$		0			0
$839$	1.75279	−	11.0667i	0.0605129	−	0.382063i	−0.938782	−	0.344512i	$-0.888044\pi$
$839$	1.75279	−	11.0667i	0.0605129	−	0.382063i	0.999295	−	0.0375510i	$-0.0119557\pi$
$840$		0			0
$841$	10.2521	+	14.1108i	0.353522	+	0.486581i
$842$		0			0
$843$	4.51661	−	6.21658i	0.155560	−	0.214110i
$844$		0			0
$845$	−7.20618	−	9.25910i	−0.247900	−	0.318523i
$846$		0			0
$847$	2.33589	+	2.33589i	0.0802622	+	0.0802622i
$848$		0			0
$849$	−5.90919	+	11.5974i	−0.202803	+	0.398023i
$850$		0			0
$851$	10.9918	−	33.8293i	0.376795	−	1.15965i
$852$		0			0
$853$	−9.37925	+	28.8664i	−0.321140	+	0.988366i	0.652014	+	0.758207i	$0.273924\pi$
$853$	−9.37925	+	28.8664i	−0.321140	+	0.988366i	−0.973153	+	0.230159i	$0.926076\pi$
$854$		0			0
$855$	−3.36557	−	17.4888i	−0.115100	−	0.598104i
$856$		0			0
$857$	40.2005	−	13.0619i	1.37322	−	0.446187i	0.472788	−	0.881176i	$-0.343248\pi$
$857$	40.2005	−	13.0619i	1.37322	−	0.446187i	0.900436	+	0.434989i	$0.143248\pi$
$858$		0			0
$859$	4.56719	−	6.28620i	0.155831	−	0.214482i	−0.723962	−	0.689839i	$-0.757681\pi$
$859$	4.56719	−	6.28620i	0.155831	−	0.214482i	0.879793	+	0.475357i	$0.157681\pi$
$860$		0			0
$861$	−0.959189	−	1.38829i	−0.0326891	−	0.0473128i
$862$		0			0
$863$	33.6103	+	24.4193i	1.14411	+	0.831244i	0.987686	−	0.156447i	$-0.0500040\pi$
$863$	33.6103	+	24.4193i	1.14411	+	0.831244i	0.156422	+	0.987690i	$0.450004\pi$
$864$		0			0
$865$	−7.72322	−	21.3434i	−0.262597	−	0.725697i
$866$		0			0
$867$	−0.696617	−	4.39827i	−0.0236584	−	0.149373i
$868$		0			0
$869$	−29.6756	−	9.64220i	−1.00668	−	0.327089i
$870$		0			0
$871$	6.22068	−	19.1453i	0.210780	−	0.648713i
$872$		0			0
$873$	−18.1871	−	9.26677i	−0.615539	−	0.313633i
$874$		0			0
$875$	3.86767	−	4.72179i	0.130751	−	0.159626i
$876$		0			0
$877$	−17.1232	−	23.5681i	−0.578210	−	0.795838i	0.415287	−	0.909690i	$-0.363681\pi$
$877$	−17.1232	−	23.5681i	−0.578210	−	0.795838i	−0.993498	+	0.113852i	$0.963681\pi$
$878$		0			0
$879$	10.2335	+	7.43508i	0.345168	+	0.250779i
$880$		0			0
$881$	15.2724	+	21.0207i	0.514541	+	0.708205i	0.984677	−	0.174389i	$-0.0557950\pi$
$881$	15.2724	+	21.0207i	0.514541	+	0.708205i	−0.470136	+	0.882594i	$0.655795\pi$
$882$		0			0
$883$	9.07270	+	1.43697i	0.305321	+	0.0483581i	0.307215	−	0.951640i	$-0.400603\pi$
$883$	9.07270	+	1.43697i	0.305321	+	0.0483581i	−0.00189421	+	0.999998i	$0.500603\pi$
$884$		0			0
$885$	2.49901	+	4.52827i	0.0840033	+	0.152216i
$886$		0			0
$887$	−16.8193	+	33.0097i	−0.564736	+	1.10836i	0.415328	+	0.909672i	$0.363667\pi$
$887$	−16.8193	+	33.0097i	−0.564736	+	1.10836i	−0.980064	+	0.198684i	$0.936333\pi$
$888$		0			0
$889$	−0.274464	−	1.73290i	−0.00920523	−	0.0581195i
$890$		0			0
$891$	13.7900	−	7.02633i	0.461981	−	0.235391i
$892$		0			0
$893$	−4.90303			−0.164074
$894$		0			0
$895$	5.12735	−	41.1235i	0.171389	−	1.37461i
$896$		0			0
$897$	4.14844	+	12.7676i	0.138512	+	0.426297i
$898$		0			0
$899$	−23.2212	−	23.2212i	−0.774470	−	0.774470i
$900$		0			0
$901$	−31.1742			−1.03856
$902$		0			0
$903$		−	2.32581i		−	0.0773980i
$904$		0			0
$905$	−26.5860	+	28.4034i	−0.883748	+	0.944160i
$906$		0			0
$907$	−1.60103	−	4.92745i	−0.0531612	−	0.163613i	0.920951	−	0.389678i	$-0.127414\pi$
$907$	−1.60103	−	4.92745i	−0.0531612	−	0.163613i	−0.974112	+	0.226065i	$0.927414\pi$
$908$		0			0
$909$	−36.3226	−	5.75293i	−1.20474	−	0.190813i
$910$		0			0
$911$			22.5784i			0.748055i	0.927418	+	0.374027i	$0.122023\pi$
$911$			22.5784i			0.748055i	−0.927418	+	0.374027i	$0.877977\pi$
$912$		0			0
$913$	0.654053	+	1.28365i	0.0216460	+	0.0424826i
$914$		0			0
$915$	1.20566	+	6.26509i	0.0398580	+	0.207118i
$916$		0			0
$917$	−2.46219	+	4.83231i	−0.0813085	+	0.159577i
$918$		0			0
$919$	−1.39741	−	2.74257i	−0.0460964	−	0.0904692i	0.866809	−	0.498640i	$-0.166167\pi$
$919$	−1.39741	−	2.74257i	−0.0460964	−	0.0904692i	−0.912906	+	0.408170i	$0.866167\pi$
$920$		0			0
$921$	−1.14334	+	7.21876i	−0.0376743	+	0.237866i
$922$		0			0
$923$	2.16109	−	1.57013i	0.0711332	−	0.0516813i
$924$		0			0
$925$	−14.5629	+	23.1128i	−0.478825	+	0.759945i
$926$		0			0
$927$	−29.0758	−	40.0194i	−0.954974	−	1.31441i
$928$		0			0
$929$	−6.11571	+	6.11571i	−0.200650	+	0.200650i	−0.800278	−	0.599629i	$-0.795315\pi$
$929$	−6.11571	+	6.11571i	−0.200650	+	0.200650i	0.599629	+	0.800278i	$0.295315\pi$
$930$		0			0
$931$	8.75819	−	17.1889i	0.287038	−	0.563344i
$932$		0			0
$933$	11.1700	+	3.62936i	0.365690	+	0.118820i
$934$		0			0
$935$	13.3260	+	3.84813i	0.435806	+	0.125847i
$936$		0			0
$937$	−6.84261	−	43.2025i	−0.223538	−	1.41137i	−0.802812	−	0.596232i	$-0.796664\pi$
$937$	−6.84261	−	43.2025i	−0.223538	−	1.41137i	0.579274	−	0.815133i	$-0.303336\pi$
$938$		0			0
$939$	−1.91410	−	5.89100i	−0.0624643	−	0.192245i
$940$		0			0
$941$	−14.7334	+	20.2788i	−0.480295	+	0.661070i	−0.978562	−	0.205954i	$-0.933970\pi$
$941$	−14.7334	+	20.2788i	−0.480295	+	0.661070i	0.498266	+	0.867024i	$0.333970\pi$
$942$		0			0
$943$	−25.2957	+	33.1347i	−0.823742	+	1.07902i
$944$		0			0
$945$	2.81378	+	1.90558i	0.0915323	+	0.0619885i
$946$		0			0
$947$	−0.918992	+	0.298598i	−0.0298632	+	0.00970315i	−0.323911	−	0.946088i	$-0.604998\pi$
$947$	−0.918992	+	0.298598i	−0.0298632	+	0.00970315i	0.294047	+	0.955791i	$0.404998\pi$
$948$		0			0
$949$	71.8035	−	11.3726i	2.33084	−	0.369169i
$950$		0			0
$951$	3.34275	+	1.08613i	0.108396	+	0.0352201i
$952$		0			0
$953$	34.1721	+	11.1032i	1.10694	+	0.359668i	0.804771	−	0.593585i	$-0.202288\pi$
$953$	34.1721	+	11.1032i	1.10694	+	0.359668i	0.302173	+	0.953253i	$0.402288\pi$
$954$		0			0
$955$	14.9492	+	7.00498i	0.483746	+	0.226676i
$956$		0			0
$957$	−2.58155	−	2.58155i	−0.0834496	−	0.0834496i
$958$		0			0
$959$	2.17275	−	1.57859i	0.0701617	−	0.0509754i
$960$		0			0
$961$	−50.4075	−	36.6232i	−1.62605	−	1.18139i
$962$		0			0
$963$	28.2451	−	20.5213i	0.910187	−	0.661290i
$964$		0			0
$965$	4.13307	−	33.1489i	0.133048	−	1.06710i
$966$		0			0
$967$	−3.14458	+	1.60224i	−0.101123	+	0.0515247i	−0.503820	−	0.863808i	$-0.668073\pi$
$967$	−3.14458	+	1.60224i	−0.101123	+	0.0515247i	0.402697	+	0.915333i	$0.368073\pi$
$968$		0			0
$969$	3.45221	+	1.75899i	0.110901	+	0.0565069i
$970$		0			0
$971$	−0.260837	−	1.64686i	−0.00837066	−	0.0528503i	0.983149	−	0.182804i	$-0.0585172\pi$
$971$	−0.260837	−	1.64686i	−0.00837066	−	0.0528503i	−0.991520	+	0.129953i	$0.958517\pi$
$972$		0			0
$973$	3.75833	+	7.37613i	0.120486	+	0.236468i
$974$		0			0
$975$	−0.680755	−	10.2877i	−0.0218016	−	0.329469i
$976$		0			0
$977$	9.17888	−	57.9532i	0.293659	−	1.85409i	−0.193933	−	0.981015i	$-0.562124\pi$
$977$	9.17888	−	57.9532i	0.293659	−	1.85409i	0.487591	−	0.873072i	$-0.337876\pi$
$978$		0			0
$979$	−32.8512	+	10.6740i	−1.04993	+	0.341143i
$980$		0			0
$981$	31.6266	+	31.6266i	1.00976	+	1.00976i
$982$		0			0
$983$		−	7.75638i		−	0.247390i	−0.992320	−	0.123695i	$-0.960526\pi$
$983$		−	7.75638i		−	0.247390i	0.992320	−	0.123695i	$-0.0394745\pi$
$984$		0			0
$985$	12.7357	−	0.420912i	0.405792	−	0.0134114i
$986$		0			0
$987$	0.317406	−	0.317406i	0.0101032	−	0.0101032i
$988$		0			0
$989$	−54.6455	+	17.7554i	−1.73763	+	0.564589i
$990$		0			0
$991$	15.9770	+	2.53050i	0.507525	+	0.0803840i	0.404946	−	0.914341i	$-0.367290\pi$
$991$	15.9770	+	2.53050i	0.507525	+	0.0803840i	0.102579	+	0.994725i	$0.467290\pi$
$992$		0			0
$993$	5.68017			0.180255
$994$		0			0
$995$	−17.6745	−	32.0267i	−0.560320	−	1.01531i
$996$		0			0
$997$	−13.3585	+	2.11578i	−0.423068	+	0.0670074i	−0.364339	−	0.931267i	$-0.618705\pi$
$997$	−13.3585	+	2.11578i	−0.423068	+	0.0670074i	−0.0587293	+	0.998274i	$0.518705\pi$
$998$		0			0
$999$	−13.5522	−	6.90518i	−0.428772	−	0.218470i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bq.a.49.10	✓	176
5.4	even	2	inner	820.2.bq.a.49.13	yes	176
41.36	even	20	inner	820.2.bq.a.569.13	yes	176
205.159	even	20	inner	820.2.bq.a.569.10	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bq.a.49.10	✓	176	1.1	even	1	trivial
820.2.bq.a.49.13	yes	176	5.4	even	2	inner
820.2.bq.a.569.10	yes	176	205.159	even	20	inner
820.2.bq.a.569.13	yes	176	41.36	even	20	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bq (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.341338 + 0.341338i) q^{3} +(-0.760852 - 2.10264i) q^{5} +(0.0854014 - 0.539203i) q^{7} +2.76698i q^{9} +(-1.98214 + 1.00995i) q^{11} +(4.21907 - 0.668235i) q^{13} +(0.977418 + 0.458003i) q^{15} +(2.48447 - 1.26590i) q^{17} +(0.450296 - 2.84306i) q^{19} +(0.154900 + 0.213201i) q^{21} +(3.82670 - 5.26700i) q^{23} +(-3.84221 + 3.19960i) q^{25} +(-1.96849 - 1.96849i) q^{27} +(1.54344 - 3.02917i) q^{29} +(2.98497 - 9.18678i) q^{31} +(0.331845 - 1.02131i) q^{33} +(-1.19873 + 0.230685i) q^{35} +(5.19622 - 1.68835i) q^{37} +(-1.21203 + 1.66822i) q^{39} +(-6.40132 - 0.151843i) q^{41} +(-7.14003 - 5.18753i) q^{43} +(5.81796 - 2.10526i) q^{45} +(-0.266460 - 1.68236i) q^{47} +(6.37395 + 2.07102i) q^{49} +(-0.415943 + 1.28014i) q^{51} +(-9.96147 - 5.07562i) q^{53} +(3.63168 + 3.39931i) q^{55} +(0.816739 + 1.12414i) q^{57} +(3.87648 + 2.81643i) q^{59} +(3.47423 + 4.78187i) q^{61} +(1.49196 + 0.236304i) q^{63} +(-4.61515 - 8.36277i) q^{65} +(2.13947 - 4.19894i) q^{67} +(0.491629 + 3.10402i) q^{69} +(0.557185 - 0.283900i) q^{71} +17.0188 q^{73} +(0.219346 - 2.40363i) q^{75} +(0.375292 + 1.15503i) q^{77} +(9.91802 + 9.91802i) q^{79} -6.95710 q^{81} -0.647608i q^{83} +(-4.55204 - 4.26078i) q^{85} +(0.507135 + 1.56080i) q^{87} +(15.3360 + 2.42898i) q^{89} -2.33200i q^{91} +(2.11691 + 4.15468i) q^{93} +(-6.32054 + 1.21633i) q^{95} +(-3.34906 + 6.57290i) q^{97} +(-2.79451 - 5.48454i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 4 q^{11} - 10 q^{15} - 4 q^{19} + 12 q^{25} + 8 q^{29} - 8 q^{31} - 6 q^{35} + 40 q^{39} + 28 q^{41} - 4 q^{45} + 20 q^{49} - 32 q^{51} - 50 q^{55} + 12 q^{59} + 40 q^{61} - 10 q^{65} - 28 q^{69}+ \cdots + 4 q^{99}+O(q^{100}) \) 176 * q + 4 * q^11 - 10 * q^15 - 4 * q^19 + 12 * q^25 + 8 * q^29 - 8 * q^31 - 6 * q^35 + 40 * q^39 + 28 * q^41 - 4 * q^45 + 20 * q^49 - 32 * q^51 - 50 * q^55 + 12 * q^59 + 40 * q^61 - 10 * q^65 - 28 * q^69 - 108 * q^71 + 52 * q^75 + 48 * q^79 - 328 * q^81 + 98 * q^85 - 16 * q^89 + 26 * q^95 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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