LMFDB - Embedded newform 416.2.bk.a.175.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [416,2,Mod(15,416)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("416.15"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(416, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bk (of order $12$, degree $4$, not 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			175.7
Character	$\chi$	$=$	416.175
Dual form			416.2.bk.a.271.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.223033 - 0.386304i) q^{3} +(-0.612771 - 0.612771i) q^{5} +(2.00697 + 0.537767i) q^{7} +(1.40051 + 2.42576i) q^{9} +(3.04671 - 0.816364i) q^{11} +(-3.45772 - 1.02185i) q^{13} +(-0.373384 + 0.100048i) q^{15} +(2.68659 - 1.55110i) q^{17} +(3.53955 + 0.948419i) q^{19} +(0.655362 - 0.655362i) q^{21} +(1.56087 - 2.70351i) q^{23} -4.24902i q^{25} +2.58764 q^{27} +(6.13693 + 3.54316i) q^{29} +(-2.77530 - 2.77530i) q^{31} +(0.364152 - 1.35903i) q^{33} +(-0.900287 - 1.55934i) q^{35} +(-0.155585 - 0.580652i) q^{37} +(-1.16593 + 1.10782i) q^{39} +(1.60304 + 5.98263i) q^{41} +(-5.34113 + 3.08370i) q^{43} +(0.628242 - 2.34463i) q^{45} +(-6.19352 + 6.19352i) q^{47} +(-2.32343 - 1.34143i) q^{49} -1.38379i q^{51} +2.19261i q^{53} +(-2.36718 - 1.36669i) q^{55} +(1.15581 - 1.15581i) q^{57} +(-1.67691 + 6.25832i) q^{59} +(0.346176 - 0.199865i) q^{61} +(1.50630 + 5.62158i) q^{63} +(1.49263 + 2.74495i) q^{65} +(-2.40698 - 8.98296i) q^{67} +(-0.696252 - 1.20594i) q^{69} +(4.33338 - 16.1724i) q^{71} +(-6.53734 - 6.53734i) q^{73} +(-1.64142 - 0.947672i) q^{75} +6.55368 q^{77} +12.9134i q^{79} +(-3.62441 + 6.27766i) q^{81} +(-9.22816 + 9.22816i) q^{83} +(-2.59674 - 0.695794i) q^{85} +(2.73747 - 1.58048i) q^{87} +(-6.08135 + 1.62949i) q^{89} +(-6.39003 - 3.91028i) q^{91} +(-1.69109 + 0.453127i) q^{93} +(-1.58777 - 2.75010i) q^{95} +(-15.1972 - 4.07209i) q^{97} +(6.24726 + 6.24726i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{3} - 20 q^{9} + 8 q^{11} - 12 q^{17} + 8 q^{19} - 8 q^{27} + 4 q^{33} + 4 q^{35} + 12 q^{43} - 60 q^{49} + 36 q^{57} + 64 q^{59} - 16 q^{65} + 8 q^{67} - 12 q^{73} - 24 q^{75} - 8 q^{81} + 48 q^{83}+ \cdots - 168 q^{99}+O(q^{100}) $ 48 * q + 4 * q^3 - 20 * q^9 + 8 * q^11 - 12 * q^17 + 8 * q^19 - 8 * q^27 + 4 * q^33 + 4 * q^35 + 12 * q^43 - 60 * q^49 + 36 * q^57 + 64 * q^59 - 16 * q^65 + 8 * q^67 - 12 * q^73 - 24 * q^75 - 8 * q^81 + 48 * q^83 + 12 * q^89 - 104 * q^91 + 4 * q^97 - 168 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{12}\right)$

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
$3$	0.223033	−	0.386304i	0.128768	−	0.223033i	−0.794431	−	0.607354i	$-0.792231\pi$
$3$	0.223033	−	0.386304i	0.128768	−	0.223033i	0.923200	+	0.384321i	$0.125564\pi$
$4$		0			0
$5$	−0.612771	−	0.612771i	−0.274040	−	0.274040i	0.556684	−	0.830724i	$-0.312073\pi$
$5$	−0.612771	−	0.612771i	−0.274040	−	0.274040i	−0.830724	+	0.556684i	$0.812073\pi$
$6$		0			0
$7$	2.00697	+	0.537767i	0.758564	+	0.203257i	0.617314	−	0.786717i	$-0.288221\pi$
$7$	2.00697	+	0.537767i	0.758564	+	0.203257i	0.141251	+	0.989974i	$0.454888\pi$
$8$		0			0
$9$	1.40051	+	2.42576i	0.466838	+	0.808586i
$10$		0			0
$11$	3.04671	−	0.816364i	0.918618	−	0.246143i	0.231623	−	0.972806i	$-0.425596\pi$
$11$	3.04671	−	0.816364i	0.918618	−	0.246143i	0.686995	+	0.726663i	$0.258930\pi$
$12$		0			0
$13$	−3.45772	−	1.02185i	−0.958999	−	0.283411i
$13$	−3.45772	−	1.02185i	−0.958999	−	0.283411i
$14$		0			0
$15$	−0.373384	+	0.100048i	−0.0964074	+	0.0258323i
$16$		0			0
$17$	2.68659	−	1.55110i	0.651594	−	0.376198i	−0.137473	−	0.990506i	$-0.543898\pi$
$17$	2.68659	−	1.55110i	0.651594	−	0.376198i	0.789067	+	0.614308i	$0.210565\pi$
$18$		0			0
$19$	3.53955	+	0.948419i	0.812028	+	0.217582i	0.640858	−	0.767659i	$-0.278579\pi$
$19$	3.53955	+	0.948419i	0.812028	+	0.217582i	0.171170	+	0.985242i	$0.445245\pi$
$20$		0			0
$21$	0.655362	−	0.655362i	0.143012	−	0.143012i
$22$		0			0
$23$	1.56087	−	2.70351i	0.325464	−	0.563721i	−0.656142	−	0.754638i	$-0.727813\pi$
$23$	1.56087	−	2.70351i	0.325464	−	0.563721i	0.981606	+	0.190917i	$0.0611460\pi$
$24$		0			0
$25$		−	4.24902i		−	0.849805i
$26$		0			0
$27$	2.58764			0.497991
$28$		0			0
$29$	6.13693	+	3.54316i	1.13960	+	0.657948i	0.946331	−	0.323198i	$-0.104758\pi$
$29$	6.13693	+	3.54316i	1.13960	+	0.657948i	0.193268	+	0.981146i	$0.438091\pi$
$30$		0			0
$31$	−2.77530	−	2.77530i	−0.498459	−	0.498459i	0.412499	−	0.910958i	$-0.364656\pi$
$31$	−2.77530	−	2.77530i	−0.498459	−	0.498459i	−0.910958	+	0.412499i	$0.864656\pi$
$32$		0			0
$33$	0.364152	−	1.35903i	0.0633907	−	0.236577i
$34$		0			0
$35$	−0.900287	−	1.55934i	−0.152176	−	0.263577i
$36$		0			0
$37$	−0.155585	−	0.580652i	−0.0255781	−	0.0954586i	0.951957	−	0.306232i	$-0.0990684\pi$
$37$	−0.155585	−	0.580652i	−0.0255781	−	0.0954586i	−0.977535	+	0.210774i	$0.932402\pi$
$38$		0			0
$39$	−1.16593	+	1.10782i	−0.186698	+	0.177394i
$40$		0			0
$41$	1.60304	+	5.98263i	0.250353	+	0.934330i	0.970617	+	0.240630i	$0.0773540\pi$
$41$	1.60304	+	5.98263i	0.250353	+	0.934330i	−0.720264	+	0.693700i	$0.755979\pi$
$42$		0			0
$43$	−5.34113	+	3.08370i	−0.814514	+	0.470260i	−0.848521	−	0.529162i	$-0.822507\pi$
$43$	−5.34113	+	3.08370i	−0.814514	+	0.470260i	0.0340068	+	0.999422i	$0.489173\pi$
$44$		0			0
$45$	0.628242	−	2.34463i	0.0936527	−	0.349517i
$46$		0			0
$47$	−6.19352	+	6.19352i	−0.903418	+	0.903418i	−0.995730	−	0.0923122i	$-0.970574\pi$
$47$	−6.19352	+	6.19352i	−0.903418	+	0.903418i	0.0923122	+	0.995730i	$0.470574\pi$
$48$		0			0
$49$	−2.32343	−	1.34143i	−0.331919	−	0.191633i
$50$		0			0
$51$		−	1.38379i		−	0.193769i
$52$		0			0
$53$			2.19261i			0.301178i	0.988596	+	0.150589i	$0.0481170\pi$
$53$			2.19261i			0.301178i	−0.988596	+	0.150589i	$0.951883\pi$
$54$		0			0
$55$	−2.36718	−	1.36669i	−0.319191	−	0.184285i
$56$		0			0
$57$	1.15581	−	1.15581i	0.153091	−	0.153091i
$58$		0			0
$59$	−1.67691	+	6.25832i	−0.218315	+	0.814764i	0.766658	+	0.642056i	$0.221918\pi$
$59$	−1.67691	+	6.25832i	−0.218315	+	0.814764i	−0.984973	+	0.172708i	$0.944748\pi$
$60$		0			0
$61$	0.346176	−	0.199865i	0.0443234	−	0.0255901i	−0.477675	−	0.878537i	$-0.658520\pi$
$61$	0.346176	−	0.199865i	0.0443234	−	0.0255901i	0.521998	+	0.852947i	$0.325187\pi$
$62$		0			0
$63$	1.50630	+	5.62158i	0.189776	+	0.708253i
$64$		0			0
$65$	1.49263	+	2.74495i	0.185138	+	0.340469i
$66$		0			0
$67$	−2.40698	−	8.98296i	−0.294059	−	1.09744i	−0.941962	−	0.335720i	$-0.891020\pi$
$67$	−2.40698	−	8.98296i	−0.294059	−	1.09744i	0.647903	−	0.761723i	$-0.275646\pi$
$68$		0			0
$69$	−0.696252	−	1.20594i	−0.0838189	−	0.145179i
$70$		0			0
$71$	4.33338	−	16.1724i	0.514277	−	1.91931i	0.147246	−	0.989100i	$-0.452959\pi$
$71$	4.33338	−	16.1724i	0.514277	−	1.91931i	0.367031	−	0.930209i	$-0.380374\pi$
$72$		0			0
$73$	−6.53734	−	6.53734i	−0.765137	−	0.765137i	0.212109	−	0.977246i	$-0.431967\pi$
$73$	−6.53734	−	6.53734i	−0.765137	−	0.765137i	−0.977246	+	0.212109i	$0.931967\pi$
$74$		0			0
$75$	−1.64142	−	0.947672i	−0.189534	−	0.109428i
$76$		0			0
$77$	6.55368			0.746861
$78$		0			0
$79$			12.9134i			1.45287i	0.687234	+	0.726436i	$0.258825\pi$
$79$			12.9134i			1.45287i	−0.687234	+	0.726436i	$0.741175\pi$
$80$		0			0
$81$	−3.62441	+	6.27766i	−0.402712	+	0.697518i
$82$		0			0
$83$	−9.22816	+	9.22816i	−1.01292	+	1.01292i	−0.0130073	+	0.999915i	$0.504140\pi$
$83$	−9.22816	+	9.22816i	−1.01292	+	1.01292i	−0.999915	+	0.0130073i	$0.995860\pi$
$84$		0			0
$85$	−2.59674	−	0.695794i	−0.281656	−	0.0754694i
$86$		0			0
$87$	2.73747	−	1.58048i	0.293488	−	0.169445i
$88$		0			0
$89$	−6.08135	+	1.62949i	−0.644622	+	0.172726i	−0.566296	−	0.824202i	$-0.691624\pi$
$89$	−6.08135	+	1.62949i	−0.644622	+	0.172726i	−0.0783258	+	0.996928i	$0.524957\pi$
$90$		0			0
$91$	−6.39003	−	3.91028i	−0.669857	−	0.409908i
$92$		0			0
$93$	−1.69109	+	0.453127i	−0.175358	+	0.0469871i
$94$		0			0
$95$	−1.58777	−	2.75010i	−0.162902	−	0.282154i
$96$		0			0
$97$	−15.1972	−	4.07209i	−1.54305	−	0.413458i	−0.615798	−	0.787904i	$-0.711166\pi$
$97$	−15.1972	−	4.07209i	−1.54305	−	0.413458i	−0.927249	+	0.374446i	$0.877833\pi$
$98$		0			0
$99$	6.24726	+	6.24726i	0.627873	+	0.627873i
$100$		0			0
$101$	−8.35641	+	14.4737i	−0.831493	+	1.44019i	0.0653604	+	0.997862i	$0.479180\pi$
$101$	−8.35641	+	14.4737i	−0.831493	+	1.44019i	−0.896854	+	0.442327i	$0.854153\pi$
$102$		0			0
$103$	15.3368			1.51118			0.755590	−	0.655044i	$-0.227350\pi$
$103$	15.3368			1.51118			0.755590	+	0.655044i	$0.227350\pi$
$104$		0			0
$105$	−0.803175			−0.0783818
$106$		0			0
$107$	4.67529	−	8.09785i	0.451978	−	0.782848i	−0.546531	−	0.837439i	$-0.684052\pi$
$107$	4.67529	−	8.09785i	0.451978	−	0.782848i	0.998509	+	0.0545904i	$0.0173853\pi$
$108$		0			0
$109$	−7.59869	−	7.59869i	−0.727822	−	0.727822i	0.242363	−	0.970186i	$-0.422077\pi$
$109$	−7.59869	−	7.59869i	−0.727822	−	0.727822i	−0.970186	+	0.242363i	$0.922077\pi$
$110$		0			0
$111$	−0.259009	−	0.0694012i	−0.0245840	−	0.00658727i
$112$		0			0
$113$	4.50930	+	7.81034i	0.424200	+	0.734735i	0.996345	−	0.0854166i	$-0.0272221\pi$
$113$	4.50930	+	7.81034i	0.424200	+	0.734735i	−0.572146	+	0.820152i	$0.693889\pi$
$114$		0			0
$115$	−2.61309	+	0.700176i	−0.243672	+	0.0652917i
$116$		0			0
$117$	−2.36381	−	9.81871i	−0.218534	−	0.907740i
$118$		0			0
$119$	6.22605	−	1.66826i	0.570741	−	0.152930i
$120$		0			0
$121$	−0.910281	+	0.525551i	−0.0827528	+	0.0477774i
$122$		0			0
$123$	2.66865	+	0.715062i	0.240624	+	0.0644749i
$124$		0			0
$125$	−5.66754	+	5.66754i	−0.506920	+	0.506920i
$126$		0			0
$127$	−8.27984	+	14.3411i	−0.734717	+	1.27257i	0.220130	+	0.975471i	$0.429352\pi$
$127$	−8.27984	+	14.3411i	−0.734717	+	1.27257i	−0.954847	+	0.297097i	$0.903982\pi$
$128$		0			0
$129$			2.75107i			0.242218i
$130$		0			0
$131$	−6.74450			−0.589270			−0.294635	−	0.955610i	$-0.595198\pi$
$131$	−6.74450			−0.589270			−0.294635	+	0.955610i	$0.595198\pi$
$132$		0			0
$133$	6.59375	+	3.80690i	0.571751	+	0.330100i
$134$		0			0
$135$	−1.58563	−	1.58563i	−0.136469	−	0.136469i
$136$		0			0
$137$	2.22488	−	8.30336i	0.190084	−	0.709404i	−0.803401	−	0.595439i	$-0.796978\pi$
$137$	2.22488	−	8.30336i	0.190084	−	0.709404i	0.993485	−	0.113965i	$-0.0363552\pi$
$138$		0			0
$139$	−6.82393	−	11.8194i	−0.578798	−	1.00251i	−0.995618	−	0.0935188i	$-0.970188\pi$
$139$	−6.82393	−	11.8194i	−0.578798	−	1.00251i	0.416819	−	0.908989i	$-0.363145\pi$
$140$		0			0
$141$	1.01122	+	3.77394i	0.0851605	+	0.317823i
$142$		0			0
$143$	−11.3689	−	0.290534i	−0.950713	−	0.0242956i
$144$		0			0
$145$	−1.58939	−	5.93168i	−0.131992	−	0.492599i
$146$		0			0
$147$	−1.03640	+	0.598367i	−0.0854811	+	0.0493525i
$148$		0			0
$149$	4.11452	−	15.3556i	0.337074	−	1.25798i	−0.564529	−	0.825414i	$-0.690942\pi$
$149$	4.11452	−	15.3556i	0.337074	−	1.25798i	0.901603	−	0.432565i	$-0.142391\pi$
$150$		0			0
$151$	2.00046	−	2.00046i	0.162795	−	0.162795i	−0.621009	−	0.783804i	$-0.713277\pi$
$151$	2.00046	−	2.00046i	0.162795	−	0.162795i	0.783804	+	0.621009i	$0.213277\pi$
$152$		0			0
$153$	7.52521	+	4.34468i	0.608377	+	0.351247i
$154$		0			0
$155$			3.40125i			0.273195i
$156$		0			0
$157$			7.48330i			0.597233i	0.954373	+	0.298616i	$0.0965251\pi$
$157$			7.48330i			0.597233i	−0.954373	+	0.298616i	$0.903475\pi$
$158$		0			0
$159$	0.847015	+	0.489024i	0.0671726	+	0.0387821i
$160$		0			0
$161$	4.58649	−	4.58649i	0.361466	−	0.361466i
$162$		0			0
$163$	0.915854	−	3.41801i	0.0717352	−	0.267720i	−0.920738	−	0.390181i	$-0.872412\pi$
$163$	0.915854	−	3.41801i	0.0717352	−	0.267720i	0.992473	+	0.122462i	$0.0390789\pi$
$164$		0			0
$165$	−1.05592	+	0.609635i	−0.0822031	+	0.0474600i
$166$		0			0
$167$	−0.664336	−	2.47934i	−0.0514079	−	0.191857i	0.935447	−	0.353468i	$-0.114998\pi$
$167$	−0.664336	−	2.47934i	−0.0514079	−	0.191857i	−0.986855	+	0.161611i	$0.948331\pi$
$168$		0			0
$169$	10.9116	+	7.06656i	0.839357	+	0.543581i
$170$		0			0
$171$	2.65655	+	9.91437i	0.203151	+	0.758171i
$172$		0			0
$173$	−2.80779	−	4.86324i	−0.213473	−	0.369745i	0.739326	−	0.673347i	$-0.235144\pi$
$173$	−2.80779	−	4.86324i	−0.213473	−	0.369745i	−0.952799	+	0.303602i	$0.901811\pi$
$174$		0			0
$175$	2.28498	−	8.52767i	0.172728	−	0.644631i
$176$		0			0
$177$	2.04361	+	2.04361i	0.153607	+	0.153607i
$178$		0			0
$179$	13.4278	+	7.75255i	1.00364	+	0.579453i	0.909324	−	0.416089i	$-0.136600\pi$
$179$	13.4278	+	7.75255i	1.00364	+	0.579453i	0.0943183	+	0.995542i	$0.469933\pi$
$180$		0			0
$181$	24.7729			1.84136			0.920678	−	0.390323i	$-0.127637\pi$
$181$	24.7729			1.84136			0.920678	+	0.390323i	$0.127637\pi$
$182$		0			0
$183$		−	0.178306i		−	0.0131808i
$184$		0			0
$185$	−0.260469	+	0.451145i	−0.0191500	+	0.0331688i
$186$		0			0
$187$	6.91900	−	6.91900i	0.505967	−	0.505967i
$188$		0			0
$189$	5.19332	+	1.39155i	0.377758	+	0.101220i
$190$		0			0
$191$	−7.56637	+	4.36844i	−0.547483	+	0.316090i	−0.748106	−	0.663579i	$-0.769037\pi$
$191$	−7.56637	+	4.36844i	−0.547483	+	0.316090i	0.200623	+	0.979669i	$0.435703\pi$
$192$		0			0
$193$	7.59913	−	2.03618i	0.546997	−	0.146567i	0.0252713	−	0.999681i	$-0.491955\pi$
$193$	7.59913	−	2.03618i	0.546997	−	0.146567i	0.521726	+	0.853113i	$0.325288\pi$
$194$		0			0
$195$	1.39329	+	0.0356058i	0.0997757	+	0.00254979i
$196$		0			0
$197$	6.71320	−	1.79880i	0.478296	−	0.128159i	−0.0116133	−	0.999933i	$-0.503697\pi$
$197$	6.71320	−	1.79880i	0.478296	−	0.128159i	0.489909	+	0.871774i	$0.337030\pi$
$198$		0			0
$199$	−6.11321	−	10.5884i	−0.433354	−	0.750591i	0.563806	−	0.825907i	$-0.309337\pi$
$199$	−6.11321	−	10.5884i	−0.433354	−	0.750591i	−0.997160	+	0.0753164i	$0.976003\pi$
$200$		0			0
$201$	−4.00699	−	1.07367i	−0.282631	−	0.0757308i
$202$		0			0
$203$	10.4113	+	10.4113i	0.730727	+	0.730727i
$204$		0			0
$205$	2.68369	−	4.64828i	0.187437	−	0.324650i
$206$		0			0
$207$	8.74409			0.607756
$208$		0			0
$209$	11.5582			0.799500
$210$		0			0
$211$	6.18515	−	10.7130i	0.425803	−	0.737513i	−0.570692	−	0.821164i	$-0.693325\pi$
$211$	6.18515	−	10.7130i	0.425803	−	0.737513i	0.996495	+	0.0836516i	$0.0266583\pi$
$212$		0			0
$213$	−5.28097	−	5.28097i	−0.361846	−	0.361846i
$214$		0			0
$215$	5.16249	+	1.38329i	0.352079	+	0.0943393i
$216$		0			0
$217$	−4.07749	−	7.06242i	−0.276798	−	0.479428i
$218$		0			0
$219$	−3.98344	+	1.06736i	−0.269176	+	0.0721255i
$220$		0			0
$221$	−10.8745	+	2.61798i	−0.731496	+	0.176104i
$222$		0			0
$223$	−17.8596	+	4.78547i	−1.19597	+	0.320459i	−0.801242	−	0.598340i	$-0.795827\pi$
$223$	−17.8596	+	4.78547i	−1.19597	+	0.320459i	−0.394726	+	0.918799i	$0.629160\pi$
$224$		0			0
$225$	10.3071	−	5.95081i	0.687140	−	0.396721i
$226$		0			0
$227$	9.38417	+	2.51448i	0.622849	+	0.166892i	0.556423	−	0.830899i	$-0.312174\pi$
$227$	9.38417	+	2.51448i	0.622849	+	0.166892i	0.0664264	+	0.997791i	$0.478840\pi$
$228$		0			0
$229$	−18.0244	+	18.0244i	−1.19109	+	1.19109i	−0.214324	+	0.976763i	$0.568755\pi$
$229$	−18.0244	+	18.0244i	−1.19109	+	1.19109i	−0.976763	+	0.214324i	$0.931245\pi$
$230$		0			0
$231$	1.46169	−	2.53171i	0.0961719	−	0.166575i
$232$		0			0
$233$			0.0680880i			0.00446059i	0.999998	+	0.00223030i	$0.000709926\pi$
$233$			0.0680880i			0.00446059i	−0.999998	+	0.00223030i	$0.999290\pi$
$234$		0			0
$235$	7.59042			0.495145
$236$		0			0
$237$	4.98850	+	2.88011i	0.324038	+	0.187084i
$238$		0			0
$239$	−5.90861	−	5.90861i	−0.382196	−	0.382196i	0.489697	−	0.871893i	$-0.337108\pi$
$239$	−5.90861	−	5.90861i	−0.382196	−	0.382196i	−0.871893	+	0.489697i	$0.837108\pi$
$240$		0			0
$241$	0.964885	−	3.60100i	0.0621537	−	0.231961i	−0.927861	−	0.372927i	$-0.878354\pi$
$241$	0.964885	−	3.60100i	0.0621537	−	0.231961i	0.990014	+	0.140966i	$0.0450209\pi$
$242$		0			0
$243$	5.49818	+	9.52313i	0.352709	+	0.610909i
$244$		0			0
$245$	0.601740	+	2.24572i	0.0384437	+	0.143474i
$246$		0			0
$247$	−11.2696	−	6.89626i	−0.717069	−	0.438799i
$248$		0			0
$249$	1.50670	+	5.62306i	0.0954829	+	0.356347i
$250$		0			0
$251$	5.43844	−	3.13989i	0.343271	−	0.198188i	−0.318446	−	0.947941i	$-0.603161\pi$
$251$	5.43844	−	3.13989i	0.343271	−	0.198188i	0.661718	+	0.749753i	$0.269828\pi$
$252$		0			0
$253$	2.54848	−	9.51106i	0.160222	−	0.597955i
$254$		0			0
$255$	−0.847946	+	0.847946i	−0.0531004	+	0.0531004i
$256$		0			0
$257$	−5.81970	−	3.36000i	−0.363023	−	0.209591i	0.307383	−	0.951586i	$-0.400547\pi$
$257$	−5.81970	−	3.36000i	−0.363023	−	0.209591i	−0.670406	+	0.741995i	$0.733880\pi$
$258$		0			0
$259$		−	1.24902i		−	0.0776104i
$260$		0			0
$261$			19.8490i			1.22862i
$262$		0			0
$263$	25.0990	+	14.4909i	1.54767	+	0.893548i	0.998319	+	0.0579570i	$0.0184586\pi$
$263$	25.0990	+	14.4909i	1.54767	+	0.893548i	0.549352	+	0.835591i	$0.314875\pi$
$264$		0			0
$265$	1.34357	−	1.34357i	0.0825348	−	0.0825348i
$266$		0			0
$267$	−0.726861	+	2.71268i	−0.0444832	+	0.166013i
$268$		0			0
$269$	15.9192	−	9.19093i	0.970608	−	0.560381i	0.0711868	−	0.997463i	$-0.477321\pi$
$269$	15.9192	−	9.19093i	0.970608	−	0.560381i	0.899422	+	0.437082i	$0.143988\pi$
$270$		0			0
$271$	−0.415837	−	1.55192i	−0.0252603	−	0.0942727i	0.952145	−	0.305647i	$-0.0988728\pi$
$271$	−0.415837	−	1.55192i	−0.0252603	−	0.0942727i	−0.977405	+	0.211374i	$0.932206\pi$
$272$		0			0
$273$	−2.93574	+	1.59637i	−0.177679	+	0.0966170i
$274$		0			0
$275$	−3.46875	−	12.9455i	−0.209173	−	0.780646i
$276$		0			0
$277$	−14.7809	−	25.6013i	−0.888100	−	1.53823i	−0.842119	−	0.539291i	$-0.818692\pi$
$277$	−14.7809	−	25.6013i	−0.888100	−	1.53823i	−0.0459802	−	0.998942i	$-0.514641\pi$
$278$		0			0
$279$	2.84537	−	10.6191i	0.170348	−	0.635746i
$280$		0			0
$281$	14.2859	+	14.2859i	0.852225	+	0.852225i	0.990407	−	0.138182i	$-0.0441260\pi$
$281$	14.2859	+	14.2859i	0.852225	+	0.852225i	−0.138182	+	0.990407i	$0.544126\pi$
$282$		0			0
$283$	−1.72953	−	0.998544i	−0.102810	−	0.0593573i	0.447713	−	0.894177i	$-0.352238\pi$
$283$	−1.72953	−	0.998544i	−0.102810	−	0.0593573i	−0.550523	+	0.834820i	$0.685572\pi$
$284$		0			0
$285$	−1.41650			−0.0839062
$286$		0			0
$287$			12.8690i			0.759635i
$288$		0			0
$289$	−3.68815	+	6.38807i	−0.216950	+	0.375769i
$290$		0			0
$291$	−4.96255	+	4.96255i	−0.290910	+	0.290910i
$292$		0			0
$293$	8.32527	+	2.23075i	0.486367	+	0.130322i	0.493666	−	0.869652i	$-0.335657\pi$
$293$	8.32527	+	2.23075i	0.486367	+	0.130322i	−0.00729863	+	0.999973i	$0.502323\pi$
$294$		0			0
$295$	4.86248	−	2.80736i	0.283105	−	0.163451i
$296$		0			0
$297$	7.88379	−	2.11245i	0.457464	−	0.122577i
$298$		0			0
$299$	−8.15965	+	7.75300i	−0.471885	+	0.448367i
$300$		0			0
$301$	−12.3778	+	3.31662i	−0.713445	+	0.191167i
$302$		0			0
$303$	3.72751	+	6.45623i	0.214140	+	0.370901i
$304$		0			0
$305$	−0.334599	−	0.0896554i	−0.0191591	−	0.00513365i
$306$		0			0
$307$	−20.6396	−	20.6396i	−1.17797	−	1.17797i	−0.980262	−	0.197703i	$-0.936652\pi$
$307$	−20.6396	−	20.6396i	−1.17797	−	1.17797i	−0.197703	−	0.980262i	$-0.563348\pi$
$308$		0			0
$309$	3.42061	−	5.92467i	0.194592	−	0.337043i
$310$		0			0
$311$	18.1641			1.02999			0.514995	−	0.857193i	$-0.327794\pi$
$311$	18.1641			1.02999			0.514995	+	0.857193i	$0.327794\pi$
$312$		0			0
$313$	−13.0914			−0.739968			−0.369984	−	0.929038i	$-0.620637\pi$
$313$	−13.0914			−0.739968			−0.369984	+	0.929038i	$0.620637\pi$
$314$		0			0
$315$	2.52173	−	4.36776i	0.142083	−	0.246095i
$316$		0			0
$317$	−16.6920	−	16.6920i	−0.937519	−	0.937519i	0.0606409	−	0.998160i	$-0.480686\pi$
$317$	−16.6920	−	16.6920i	−0.937519	−	0.937519i	−0.998160	+	0.0606409i	$0.980686\pi$
$318$		0			0
$319$	21.5900	+	5.78501i	1.20881	+	0.323899i
$320$		0			0
$321$	−2.08549	−	3.61217i	−0.116401	−	0.201612i
$322$		0			0
$323$	10.9804	−	2.94219i	0.610967	−	0.163708i
$324$		0			0
$325$	−4.34187	+	14.6919i	−0.240844	+	0.814961i
$326$		0			0
$327$	−4.63016	+	1.24065i	−0.256049	+	0.0686080i
$328$		0			0
$329$	−15.7609	+	9.09956i	−0.868926	+	0.501675i
$330$		0			0
$331$	−23.0936	−	6.18790i	−1.26934	−	0.340118i	−0.439560	−	0.898213i	$-0.644866\pi$
$331$	−23.0936	−	6.18790i	−1.26934	−	0.340118i	−0.829777	+	0.558095i	$0.811532\pi$
$332$		0			0
$333$	1.19062	−	1.19062i	0.0652457	−	0.0652457i
$334$		0			0
$335$	−4.02957	+	6.97943i	−0.220159	+	0.381327i
$336$		0			0
$337$		−	10.3450i		−	0.563530i	−0.959483	−	0.281765i	$-0.909080\pi$
$337$		−	10.3450i		−	0.563530i	0.959483	−	0.281765i	$-0.0909198\pi$
$338$		0			0
$339$	4.02289			0.218493
$340$		0			0
$341$	−10.7212	−	6.18989i	−0.580585	−	0.335201i
$342$		0			0
$343$	−14.2261	−	14.2261i	−0.768139	−	0.768139i
$344$		0			0
$345$	−0.312324	+	1.16561i	−0.0168150	+	0.0627544i
$346$		0			0
$347$	−3.70616	−	6.41927i	−0.198957	−	0.344604i	0.749233	−	0.662306i	$-0.230422\pi$
$347$	−3.70616	−	6.41927i	−0.198957	−	0.344604i	−0.948191	+	0.317702i	$0.897089\pi$
$348$		0			0
$349$	4.31088	+	16.0884i	0.230756	+	0.861193i	0.980016	+	0.198917i	$0.0637425\pi$
$349$	4.31088	+	16.0884i	0.230756	+	0.861193i	−0.749260	+	0.662276i	$0.769591\pi$
$350$		0			0
$351$	−8.94733	−	2.64418i	−0.477573	−	0.141136i
$352$		0			0
$353$	1.99348	+	7.43976i	0.106102	+	0.395978i	0.998468	−	0.0553346i	$-0.0176225\pi$
$353$	1.99348	+	7.43976i	0.106102	+	0.395978i	−0.892366	+	0.451313i	$0.850956\pi$
$354$		0			0
$355$	−12.5653	+	7.25460i	−0.666899	+	0.385034i
$356$		0			0
$357$	0.744155	−	2.77723i	0.0393849	−	0.146986i
$358$		0			0
$359$	−11.7450	+	11.7450i	−0.619878	+	0.619878i	−0.945500	−	0.325622i	$-0.894426\pi$
$359$	−11.7450	+	11.7450i	−0.619878	+	0.619878i	0.325622	+	0.945500i	$0.394426\pi$
$360$		0			0
$361$	−4.82557	−	2.78605i	−0.253978	−	0.146634i
$362$		0			0
$363$			0.468860i			0.0246088i
$364$		0			0
$365$			8.01178i			0.419356i
$366$		0			0
$367$	5.54625	+	3.20213i	0.289512	+	0.167150i	0.637722	−	0.770267i	$-0.279877\pi$
$367$	5.54625	+	3.20213i	0.289512	+	0.167150i	−0.348210	+	0.937417i	$0.613210\pi$
$368$		0			0
$369$	−12.2673	+	12.2673i	−0.638612	+	0.638612i
$370$		0			0
$371$	−1.17911	+	4.40051i	−0.0612165	+	0.228463i
$372$		0			0
$373$	4.49235	−	2.59366i	0.232605	−	0.134295i	−0.379168	−	0.925328i	$-0.623790\pi$
$373$	4.49235	−	2.59366i	0.232605	−	0.134295i	0.611773	+	0.791033i	$0.290456\pi$
$374$		0			0
$375$	0.925346	+	3.45344i	0.0477847	+	0.178335i
$376$		0			0
$377$	−17.5992	−	18.5223i	−0.906405	−	0.953946i
$378$		0			0
$379$	7.15495	+	26.7026i	0.367525	+	1.37162i	0.863965	+	0.503551i	$0.167974\pi$
$379$	7.15495	+	26.7026i	0.367525	+	1.37162i	−0.496440	+	0.868071i	$0.665360\pi$
$380$		0			0
$381$	3.69335	+	6.39708i	0.189216	+	0.327732i
$382$		0			0
$383$	2.27219	−	8.47994i	0.116104	−	0.433305i	−0.883263	−	0.468877i	$-0.844659\pi$
$383$	2.27219	−	8.47994i	0.116104	−	0.433305i	0.999367	+	0.0355723i	$0.0113254\pi$
$384$		0			0
$385$	−4.01591	−	4.01591i	−0.204670	−	0.204670i
$386$		0			0
$387$	−14.9606	−	8.63753i	−0.760492	−	0.439070i
$388$		0			0
$389$	1.89321			0.0959896			0.0479948	−	0.998848i	$-0.484717\pi$
$389$	1.89321			0.0959896			0.0479948	+	0.998848i	$0.484717\pi$
$390$		0			0
$391$		−	9.68430i		−	0.489756i
$392$		0			0
$393$	−1.50425	+	2.60543i	−0.0758791	+	0.131427i
$394$		0			0
$395$	7.91297	−	7.91297i	0.398145	−	0.398145i
$396$		0			0
$397$	3.02242	+	0.809855i	0.151691	+	0.0406455i	0.333865	−	0.942621i	$-0.391647\pi$
$397$	3.02242	+	0.809855i	0.151691	+	0.0406455i	−0.182174	+	0.983266i	$0.558314\pi$
$398$		0			0
$399$	2.94125	−	1.69813i	0.147246	−	0.0850128i
$400$		0			0
$401$	−14.5581	+	3.90083i	−0.726997	+	0.194798i	−0.603292	−	0.797521i	$-0.706145\pi$
$401$	−14.5581	+	3.90083i	−0.726997	+	0.194798i	−0.123706	+	0.992319i	$0.539478\pi$
$402$		0			0
$403$	6.76026	+	12.4322i	0.336753	+	0.619290i
$404$		0			0
$405$	6.06771	−	1.62584i	0.301507	−	0.0807885i
$406$		0			0
$407$	−0.948046	−	1.64206i	−0.0469929	−	0.0813941i
$408$		0			0
$409$	16.6323	+	4.45660i	0.822412	+	0.220365i	0.645401	−	0.763844i	$-0.276690\pi$
$409$	16.6323	+	4.45660i	0.822412	+	0.220365i	0.177011	+	0.984209i	$0.443357\pi$
$410$		0			0
$411$	−2.71140	−	2.71140i	−0.133744	−	0.133744i
$412$		0			0
$413$	−6.73103	+	11.6585i	−0.331213	+	0.573677i
$414$		0			0
$415$	11.3095			0.555162
$416$		0			0
$417$	−6.08784			−0.298123
$418$		0			0
$419$	−15.2221	+	26.3654i	−0.743647	+	1.28803i	0.207178	+	0.978303i	$0.433572\pi$
$419$	−15.2221	+	26.3654i	−0.743647	+	1.28803i	−0.950824	+	0.309730i	$0.899761\pi$
$420$		0			0
$421$	14.5609	+	14.5609i	0.709654	+	0.709654i	0.966462	−	0.256809i	$-0.0826710\pi$
$421$	14.5609	+	14.5609i	0.709654	+	0.709654i	−0.256809	+	0.966462i	$0.582671\pi$
$422$		0			0
$423$	−23.6981	−	6.34989i	−1.15224	−	0.308742i
$424$		0			0
$425$	−6.59068	−	11.4154i	−0.319695	−	0.553727i
$426$		0			0
$427$	0.802247	−	0.214962i	0.0388235	−	0.0104027i
$428$		0			0
$429$	−2.64787	+	4.32704i	−0.127840	+	0.208912i
$430$		0			0
$431$	0.530842	−	0.142239i	0.0255697	−	0.00685139i	−0.246012	−	0.969267i	$-0.579120\pi$
$431$	0.530842	−	0.142239i	0.0255697	−	0.00685139i	0.271581	+	0.962416i	$0.412453\pi$
$432$		0			0
$433$	−8.21876	+	4.74511i	−0.394969	+	0.228035i	−0.684311	−	0.729191i	$-0.739897\pi$
$433$	−8.21876	+	4.74511i	−0.394969	+	0.228035i	0.289342	+	0.957226i	$0.406563\pi$
$434$		0			0
$435$	−2.64592	−	0.708972i	−0.126862	−	0.0339926i
$436$		0			0
$437$	8.08885	−	8.08885i	0.386942	−	0.386942i
$438$		0			0
$439$	−15.4192	+	26.7068i	−0.735916	+	1.27464i	0.218404	+	0.975858i	$0.429915\pi$
$439$	−15.4192	+	26.7068i	−0.735916	+	1.27464i	−0.954320	+	0.298786i	$0.903418\pi$
$440$		0			0
$441$		−	7.51478i		−	0.357847i
$442$		0			0
$443$	−27.9824			−1.32949			−0.664743	−	0.747072i	$-0.731459\pi$
$443$	−27.9824			−1.32949			−0.664743	+	0.747072i	$0.731459\pi$
$444$		0			0
$445$	4.72498	+	2.72797i	0.223986	+	0.129318i
$446$		0			0
$447$	−5.01425	−	5.01425i	−0.237166	−	0.237166i
$448$		0			0
$449$	−4.57532	+	17.0753i	−0.215923	+	0.805835i	0.769917	+	0.638144i	$0.220298\pi$
$449$	−4.57532	+	17.0753i	−0.215923	+	0.805835i	−0.985840	+	0.167690i	$0.946369\pi$
$450$		0			0
$451$	9.76801	+	16.9187i	0.459958	+	0.796670i
$452$		0			0
$453$	−0.326618	−	1.21895i	−0.0153458	−	0.0572715i
$454$		0			0
$455$	1.51952	+	6.31173i	0.0712362	+	0.295899i
$456$		0			0
$457$	−4.64267	−	17.3267i	−0.217175	−	0.810508i	−0.985390	−	0.170315i	$-0.945521\pi$
$457$	−4.64267	−	17.3267i	−0.217175	−	0.810508i	0.768215	−	0.640192i	$-0.221145\pi$
$458$		0			0
$459$	6.95192	−	4.01370i	0.324488	−	0.187343i
$460$		0			0
$461$	4.87396	−	18.1899i	0.227003	−	0.847186i	−0.754589	−	0.656197i	$-0.772164\pi$
$461$	4.87396	−	18.1899i	0.227003	−	0.847186i	0.981592	−	0.190989i	$-0.0611695\pi$
$462$		0			0
$463$	9.12291	−	9.12291i	0.423978	−	0.423978i	−0.462593	−	0.886571i	$-0.653081\pi$
$463$	9.12291	−	9.12291i	0.423978	−	0.423978i	0.886571	+	0.462593i	$0.153081\pi$
$464$		0			0
$465$	1.31392	+	0.758590i	0.0609314	+	0.0351788i
$466$		0			0
$467$		−	32.7960i		−	1.51762i	−0.651313	−	0.758809i	$-0.725781\pi$
$467$		−	32.7960i		−	1.51762i	0.651313	−	0.758809i	$-0.274219\pi$
$468$		0			0
$469$		−	19.3229i		−	0.892251i
$470$		0			0
$471$	2.89083	+	1.66902i	0.133202	+	0.0769045i
$472$		0			0
$473$	−13.7554	+	13.7554i	−0.632476	+	0.632476i
$474$		0			0
$475$	4.02986	−	15.0396i	0.184902	−	0.690065i
$476$		0			0
$477$	−5.31875	+	3.07078i	−0.243529	+	0.140601i
$478$		0			0
$479$	−2.37037	−	8.84634i	−0.108305	−	0.404200i	0.890394	−	0.455190i	$-0.150429\pi$
$479$	−2.37037	−	8.84634i	−0.108305	−	0.404200i	−0.998699	+	0.0509907i	$0.983762\pi$
$480$		0			0
$481$	−0.0553708	+	2.16672i	−0.00252469	+	0.0987937i
$482$		0			0
$483$	−0.748842	−	2.79472i	−0.0340735	−	0.127164i
$484$		0			0
$485$	6.81718	+	11.8077i	0.309552	+	0.536160i
$486$		0			0
$487$	−4.31509	+	16.1041i	−0.195535	+	0.729748i	0.796592	+	0.604517i	$0.206634\pi$
$487$	−4.31509	+	16.1041i	−0.195535	+	0.729748i	−0.992128	+	0.125231i	$0.960033\pi$
$488$		0			0
$489$	−1.11613	−	1.11613i	−0.0504730	−	0.0504730i
$490$		0			0
$491$	10.6955	+	6.17507i	0.482683	+	0.278677i	0.721534	−	0.692379i	$-0.243437\pi$
$491$	10.6955	+	6.17507i	0.482683	+	0.278677i	−0.238851	+	0.971056i	$0.576771\pi$
$492$		0			0
$493$	21.9832			0.990075
$494$		0			0
$495$		−	7.65628i		−	0.344124i
$496$		0			0
$497$	17.3939	−	30.1272i	0.780225	−	1.35139i
$498$		0			0
$499$	−3.14337	+	3.14337i	−0.140717	+	0.140717i	−0.773956	−	0.633239i	$-0.781725\pi$
$499$	−3.14337	+	3.14337i	−0.140717	+	0.140717i	0.633239	+	0.773956i	$0.281725\pi$
$500$		0			0
$501$	−1.10595	−	0.296338i	−0.0494101	−	0.0132394i
$502$		0			0
$503$	−1.32816	+	0.766812i	−0.0592196	+	0.0341905i	−0.529317	−	0.848424i	$-0.677552\pi$
$503$	−1.32816	+	0.766812i	−0.0592196	+	0.0341905i	0.470098	+	0.882614i	$0.344219\pi$
$504$		0			0
$505$	13.9896	−	3.74851i	0.622531	−	0.166807i
$506$		0			0
$507$	5.16349	−	2.63914i	0.229319	−	0.117208i
$508$		0			0
$509$	2.31792	−	0.621084i	0.102740	−	0.0275291i	−0.207083	−	0.978323i	$-0.566397\pi$
$509$	2.31792	−	0.621084i	0.102740	−	0.0275291i	0.309823	+	0.950794i	$0.399730\pi$
$510$		0			0
$511$	−9.60469	−	16.6358i	−0.424887	−	0.735925i
$512$		0			0
$513$	9.15907	+	2.45417i	0.404383	+	0.108354i
$514$		0			0
$515$	−9.39796	−	9.39796i	−0.414123	−	0.414123i
$516$		0			0
$517$	−13.8137	+	23.9260i	−0.607526	+	1.05227i
$518$		0			0
$519$	−2.50492			−0.109954
$520$		0			0
$521$	33.5565			1.47014			0.735069	−	0.677992i	$-0.237150\pi$
$521$	33.5565			1.47014			0.735069	+	0.677992i	$0.237150\pi$
$522$		0			0
$523$	−10.9193	+	18.9129i	−0.477469	+	0.827001i	−0.999667	−	0.0258235i	$-0.991779\pi$
$523$	−10.9193	+	18.9129i	−0.477469	+	0.827001i	0.522197	+	0.852825i	$0.325113\pi$
$524$		0			0
$525$	−2.78465	−	2.78465i	−0.121532	−	0.121532i
$526$		0			0
$527$	−11.7609	−	3.15132i	−0.512312	−	0.137274i
$528$		0			0
$529$	6.62735	+	11.4789i	0.288146	+	0.499083i
$530$		0			0
$531$	−17.5297	+	4.69707i	−0.760725	+	0.203836i
$532$		0			0
$533$	0.570502	−	22.3243i	0.0247112	−	0.966974i
$534$		0			0
$535$	−7.82701	+	2.09724i	−0.338391	+	0.0906717i
$536$		0			0
$537$	5.98969	−	3.45815i	0.258474	−	0.149230i
$538$		0			0
$539$	−8.17392	−	2.19020i	−0.352076	−	0.0943384i
$540$		0			0
$541$	−2.04526	+	2.04526i	−0.0879326	+	0.0879326i	−0.749705	−	0.661772i	$-0.769805\pi$
$541$	−2.04526	+	2.04526i	−0.0879326	+	0.0879326i	0.661772	+	0.749705i	$0.269805\pi$
$542$		0			0
$543$	5.52517	−	9.56988i	0.237108	−	0.410683i
$544$		0			0
$545$			9.31252i			0.398904i
$546$		0			0
$547$	43.0237			1.83956			0.919781	−	0.392432i	$-0.128366\pi$
$547$	43.0237			1.83956			0.919781	+	0.392432i	$0.128366\pi$
$548$		0			0
$549$	0.969649	+	0.559827i	0.0413836	+	0.0238928i
$550$		0			0
$551$	18.3616	+	18.3616i	0.782229	+	0.782229i
$552$		0			0
$553$	−6.94440	+	25.9169i	−0.295306	+	1.10210i
$554$		0			0
$555$	0.116186	+	0.201240i	0.00493183	+	0.00854217i
$556$		0			0
$557$	−2.27626	−	8.49514i	−0.0964484	−	0.359950i	0.900787	−	0.434262i	$-0.142991\pi$
$557$	−2.27626	−	8.49514i	−0.0964484	−	0.359950i	−0.997235	+	0.0743115i	$0.976324\pi$
$558$		0			0
$559$	21.6192	−	5.20473i	0.914395	−	0.220136i
$560$		0			0
$561$	−1.12967	−	4.21600i	−0.0476949	−	0.178000i
$562$		0			0
$563$	14.9276	−	8.61848i	0.629125	−	0.363226i	−0.151288	−	0.988490i	$-0.548342\pi$
$563$	14.9276	−	8.61848i	0.629125	−	0.363226i	0.780413	+	0.625264i	$0.215009\pi$
$564$		0			0
$565$	2.02278	−	7.54913i	0.0850991	−	0.317594i
$566$		0			0
$567$	−10.6500	+	10.6500i	−0.447258	+	0.447258i
$568$		0			0
$569$	−2.01113	−	1.16112i	−0.0843108	−	0.0486769i	0.457252	−	0.889337i	$-0.348834\pi$
$569$	−2.01113	−	1.16112i	−0.0843108	−	0.0486769i	−0.541563	+	0.840660i	$0.682167\pi$
$570$		0			0
$571$			19.3989i			0.811819i	0.913913	+	0.405909i	$0.133045\pi$
$571$			19.3989i			0.811819i	−0.913913	+	0.405909i	$0.866955\pi$
$572$		0			0
$573$			3.89723i			0.162809i
$574$		0			0
$575$	−11.4873	−	6.63218i	−0.479053	−	0.276581i
$576$		0			0
$577$	9.26086	−	9.26086i	0.385535	−	0.385535i	−0.487557	−	0.873091i	$-0.662112\pi$
$577$	9.26086	−	9.26086i	0.385535	−	0.385535i	0.873091	+	0.487557i	$0.162112\pi$
$578$		0			0
$579$	0.908270	−	3.38971i	0.0377464	−	0.140872i
$580$		0			0
$581$	−23.4833	+	13.5581i	−0.974250	+	0.562484i
$582$		0			0
$583$	1.78997	+	6.68025i	0.0741329	+	0.276668i
$584$		0			0
$585$	−4.56815	+	7.46510i	−0.188870	+	0.308644i
$586$		0			0
$587$	−4.05069	−	15.1174i	−0.167190	−	0.623961i	−0.997751	−	0.0670334i	$-0.978647\pi$
$587$	−4.05069	−	15.1174i	−0.167190	−	0.623961i	0.830561	−	0.556928i	$-0.188020\pi$
$588$		0			0
$589$	−7.19116	−	12.4555i	−0.296307	−	0.513218i
$590$		0			0
$591$	0.802381	−	2.99453i	0.0330056	−	0.123178i
$592$		0			0
$593$	−1.40502	−	1.40502i	−0.0576975	−	0.0576975i	0.677669	−	0.735367i	$-0.262990\pi$
$593$	−1.40502	−	1.40502i	−0.0576975	−	0.0576975i	−0.735367	+	0.677669i	$0.762990\pi$
$594$		0			0
$595$	−4.83741	−	2.79288i	−0.198314	−	0.114497i
$596$		0			0
$597$	−5.45379			−0.223209
$598$		0			0
$599$			26.5849i			1.08623i	0.839658	+	0.543115i	$0.182755\pi$
$599$			26.5849i			1.08623i	−0.839658	+	0.543115i	$0.817245\pi$
$600$		0			0
$601$	12.4968	−	21.6452i	0.509757	−	0.882925i	−0.490179	−	0.871622i	$-0.663069\pi$
$601$	12.4968	−	21.6452i	0.509757	−	0.882925i	0.999936	−	0.0113032i	$-0.00359799\pi$
$602$		0			0
$603$	18.4195	−	18.4195i	0.750100	−	0.750100i
$604$		0			0
$605$	0.879836	+	0.235751i	0.0357704	+	0.00958466i
$606$		0			0
$607$	38.1595	−	22.0314i	1.54885	−	0.894227i	0.550617	−	0.834758i	$-0.314392\pi$
$607$	38.1595	−	22.0314i	1.54885	−	0.894227i	0.998230	−	0.0594694i	$-0.0189409\pi$
$608$		0			0
$609$	6.34397	−	1.69986i	0.257071	−	0.0688819i
$610$		0			0
$611$	27.7443	−	15.0866i	1.12241	−	0.610338i
$612$		0			0
$613$	−25.5592	+	6.84856i	−1.03232	+	0.276611i	−0.734929	−	0.678144i	$-0.762785\pi$
$613$	−25.5592	+	6.84856i	−1.03232	+	0.276611i	−0.297396	+	0.954754i	$0.596118\pi$
$614$		0			0
$615$	−1.19710	−	2.07344i	−0.0482718	−	0.0836091i
$616$		0			0
$617$	11.8300	+	3.16985i	0.476260	+	0.127613i	0.488960	−	0.872306i	$-0.337376\pi$
$617$	11.8300	+	3.16985i	0.476260	+	0.127613i	−0.0127008	+	0.999919i	$0.504043\pi$
$618$		0			0
$619$	20.6210	+	20.6210i	0.828828	+	0.828828i	0.987355	−	0.158526i	$-0.0506743\pi$
$619$	20.6210	+	20.6210i	0.828828	+	0.828828i	−0.158526	+	0.987355i	$0.550674\pi$
$620$		0			0
$621$	4.03897	−	6.99571i	0.162078	−	0.280728i
$622$		0			0
$623$	−13.0814			−0.524095
$624$		0			0
$625$	−14.2993			−0.571972
$626$		0			0
$627$	2.57787	−	4.46500i	0.102950	−	0.178315i
$628$		0			0
$629$	−1.31865	−	1.31865i	−0.0525778	−	0.0525778i
$630$		0			0
$631$	15.4030	+	4.12723i	0.613185	+	0.164302i	0.552028	−	0.833826i	$-0.313854\pi$
$631$	15.4030	+	4.12723i	0.613185	+	0.164302i	0.0611571	+	0.998128i	$0.480521\pi$
$632$		0			0
$633$	−2.75898	−	4.77870i	−0.109660	−	0.189936i
$634$		0			0
$635$	13.8615	−	3.71417i	0.550076	−	0.147392i
$636$		0			0
$637$	6.66302	+	7.01250i	0.263999	+	0.277846i
$638$		0			0
$639$	45.2993	−	12.1379i	1.79201	−	0.480168i
$640$		0			0
$641$	−12.4266	+	7.17450i	−0.490821	+	0.283376i	−0.724915	−	0.688838i	$-0.758121\pi$
$641$	−12.4266	+	7.17450i	−0.490821	+	0.283376i	0.234094	+	0.972214i	$0.424788\pi$
$642$		0			0
$643$	4.87873	+	1.30725i	0.192398	+	0.0515529i	0.353731	−	0.935347i	$-0.384913\pi$
$643$	4.87873	+	1.30725i	0.192398	+	0.0515529i	−0.161333	+	0.986900i	$0.551579\pi$
$644$		0			0
$645$	1.68577	−	1.68577i	0.0663773	−	0.0663773i
$646$		0			0
$647$	9.63239	−	16.6838i	0.378688	−	0.655907i	−0.612183	−	0.790716i	$-0.709709\pi$
$647$	9.63239	−	16.6838i	0.378688	−	0.655907i	0.990872	+	0.134809i	$0.0430419\pi$
$648$		0			0
$649$			20.4363i			0.802194i
$650$		0			0
$651$	−3.63766			−0.142571
$652$		0			0
$653$	−8.45370	−	4.88075i	−0.330819	−	0.190998i	0.325386	−	0.945581i	$-0.394506\pi$
$653$	−8.45370	−	4.88075i	−0.330819	−	0.190998i	−0.656205	+	0.754583i	$0.727839\pi$
$654$		0			0
$655$	4.13284	+	4.13284i	0.161483	+	0.161483i
$656$		0			0
$657$	6.70238	−	25.0136i	0.261485	−	0.975874i
$658$		0			0
$659$	18.8285	+	32.6119i	0.733454	+	1.27038i	0.955398	+	0.295320i	$0.0954262\pi$
$659$	18.8285	+	32.6119i	0.733454	+	1.27038i	−0.221945	+	0.975059i	$0.571241\pi$
$660$		0			0
$661$	−9.10613	−	33.9845i	−0.354187	−	1.32184i	−0.881504	−	0.472176i	$-0.843469\pi$
$661$	−9.10613	−	33.9845i	−0.354187	−	1.32184i	0.527317	−	0.849669i	$-0.323198\pi$
$662$		0			0
$663$	−1.41403	+	4.78475i	−0.0549163	+	0.185824i
$664$		0			0
$665$	−1.70770	−	6.37322i	−0.0662218	−	0.247143i
$666$		0			0
$667$	19.1579	−	11.0608i	0.741799	−	0.428278i
$668$		0			0
$669$	−2.13463	+	7.96656i	−0.0825297	+	0.308005i
$670$		0			0
$671$	0.891537	−	0.891537i	0.0344174	−	0.0344174i
$672$		0			0
$673$	44.3178	+	25.5869i	1.70833	+	0.986303i	0.936635	+	0.350308i	$0.113923\pi$
$673$	44.3178	+	25.5869i	1.70833	+	0.986303i	0.771693	+	0.635995i	$0.219410\pi$
$674$		0			0
$675$		−	10.9949i		−	0.423195i
$676$		0			0
$677$			10.0607i			0.386664i	0.981133	+	0.193332i	$0.0619295\pi$
$677$			10.0607i			0.386664i	−0.981133	+	0.193332i	$0.938070\pi$
$678$		0			0
$679$	−28.3106	−	16.3451i	−1.08646	−	0.627269i
$680$		0			0
$681$	3.06433	−	3.06433i	0.117425	−	0.117425i
$682$		0			0
$683$	9.91535	−	37.0046i	0.379400	−	1.41594i	−0.467407	−	0.884042i	$-0.654812\pi$
$683$	9.91535	−	37.0046i	0.379400	−	1.41594i	0.846807	−	0.531900i	$-0.178522\pi$
$684$		0			0
$685$	−6.45140	+	3.72472i	−0.246495	+	0.142314i
$686$		0			0
$687$	2.94287	+	10.9829i	0.112278	+	0.419025i
$688$		0			0
$689$	2.24053	−	7.58143i	0.0853572	−	0.288830i
$690$		0			0
$691$	5.45532	+	20.3595i	0.207530	+	0.774512i	0.988663	+	0.150148i	$0.0479752\pi$
$691$	5.45532	+	20.3595i	0.207530	+	0.774512i	−0.781133	+	0.624364i	$0.785358\pi$
$692$		0			0
$693$	9.17851	+	15.8976i	0.348663	+	0.603902i
$694$		0			0
$695$	−3.06108	+	11.4241i	−0.116113	+	0.433341i
$696$		0			0
$697$	13.5864	+	13.5864i	0.514622	+	0.514622i
$698$		0			0
$699$	0.0263027	+	0.0151859i	0.000994859	+	0.000574382i
$700$		0			0
$701$	−10.2387			−0.386709			−0.193355	−	0.981129i	$-0.561937\pi$
$701$	−10.2387			−0.386709			−0.193355	+	0.981129i	$0.561937\pi$
$702$		0			0
$703$		−	2.20281i		−	0.0830804i
$704$		0			0
$705$	1.69291	−	2.93221i	0.0637588	−	0.110434i
$706$		0			0
$707$	−24.5546	+	24.5546i	−0.923469	+	0.923469i
$708$		0			0
$709$	5.65808	+	1.51608i	0.212494	+	0.0569375i	0.363495	−	0.931596i	$-0.381583\pi$
$709$	5.65808	+	1.51608i	0.212494	+	0.0569375i	−0.151002	+	0.988534i	$0.548250\pi$
$710$		0			0
$711$	−31.3248	+	18.0854i	−1.17477	+	0.678255i
$712$		0			0
$713$	−11.8349	+	3.17117i	−0.443222	+	0.118761i
$714$		0			0
$715$	6.78849	+	7.14455i	0.253875	+	0.267191i
$716$		0			0
$717$	−3.60034	+	0.964707i	−0.134457	+	0.0360277i
$718$		0			0
$719$	−8.07264	−	13.9822i	−0.301059	−	0.521449i	0.675317	−	0.737527i	$-0.264007\pi$
$719$	−8.07264	−	13.9822i	−0.301059	−	0.521449i	−0.976376	+	0.216078i	$0.930673\pi$
$720$		0			0
$721$	30.7806	+	8.24763i	1.14633	+	0.307158i
$722$		0			0
$723$	−1.17588	−	1.17588i	−0.0437315	−	0.0437315i
$724$		0			0
$725$	15.0550	−	26.0760i	0.559127	−	0.968437i
$726$		0			0
$727$	−36.8561			−1.36692			−0.683459	−	0.729989i	$-0.739525\pi$
$727$	−36.8561			−1.36692			−0.683459	+	0.729989i	$0.739525\pi$
$728$		0			0
$729$	−16.8414			−0.623754
$730$		0			0
$731$	−9.56628	+	16.5693i	−0.353822	+	0.612837i
$732$		0			0
$733$	31.9929	+	31.9929i	1.18168	+	1.18168i	0.979308	+	0.202377i	$0.0648667\pi$
$733$	31.9929	+	31.9929i	1.18168	+	1.18168i	0.202377	+	0.979308i	$0.435133\pi$
$734$		0			0
$735$	1.00174	+	0.268416i	0.0369497	+	0.00990065i
$736$		0			0
$737$	−14.6667	−	25.4035i	−0.540256	−	0.935751i
$738$		0			0
$739$	−18.9049	+	5.06556i	−0.695429	+	0.186340i	−0.589182	−	0.808000i	$-0.700550\pi$
$739$	−18.9049	+	5.06556i	−0.695429	+	0.186340i	−0.106247	+	0.994340i	$0.533883\pi$
$740$		0			0
$741$	−5.17755	+	2.81541i	−0.190202	+	0.103427i
$742$		0			0
$743$	2.10402	−	0.563770i	0.0771889	−	0.0206827i	−0.220018	−	0.975496i	$-0.570612\pi$
$743$	2.10402	−	0.563770i	0.0771889	−	0.0206827i	0.297207	+	0.954813i	$0.403945\pi$
$744$		0			0
$745$	−11.9307	+	6.88820i	−0.437108	+	0.252364i
$746$		0			0
$747$	−35.3095	−	9.46114i	−1.29191	−	0.346165i
$748$		0			0
$749$	13.7379	−	13.7379i	0.501973	−	0.501973i
$750$		0			0
$751$	14.1395	−	24.4904i	0.515959	−	0.893667i	−0.483869	−	0.875140i	$-0.660769\pi$
$751$	14.1395	−	24.4904i	0.515959	−	0.893667i	0.999828	−	0.0185271i	$-0.00589770\pi$
$752$		0			0
$753$		−	2.80119i		−	0.102081i
$754$		0			0
$755$	−2.45165			−0.0892246
$756$		0			0
$757$	2.32506	+	1.34238i	0.0845058	+	0.0487895i	0.541657	−	0.840599i	$-0.317797\pi$
$757$	2.32506	+	1.34238i	0.0845058	+	0.0487895i	−0.457152	+	0.889389i	$0.651130\pi$
$758$		0			0
$759$	−3.10577	−	3.10577i	−0.112732	−	0.112732i
$760$		0			0
$761$	−3.52566	+	13.1579i	−0.127805	+	0.476975i	−0.999924	−	0.0123189i	$-0.996079\pi$
$761$	−3.52566	+	13.1579i	−0.127805	+	0.476975i	0.872119	+	0.489294i	$0.162745\pi$
$762$		0			0
$763$	−11.1640	−	19.3367i	−0.404165	−	0.700035i
$764$		0			0
$765$	−1.94894	−	7.27353i	−0.0704639	−	0.262975i
$766$		0			0
$767$	12.1934	−	19.9260i	0.440277	−	0.719485i
$768$		0			0
$769$	1.32057	+	4.92844i	0.0476210	+	0.177724i	0.985640	−	0.168859i	$-0.0540084\pi$
$769$	1.32057	+	4.92844i	0.0476210	+	0.177724i	−0.938019	+	0.346584i	$0.887342\pi$
$770$		0			0
$771$	−2.59597	+	1.49878i	−0.0934915	+	0.0539773i
$772$		0			0
$773$	−10.1248	+	37.7861i	−0.364162	+	1.35907i	0.504391	+	0.863475i	$0.331717\pi$
$773$	−10.1248	+	37.7861i	−0.364162	+	1.35907i	−0.868553	+	0.495596i	$0.834950\pi$
$774$		0			0
$775$	−11.7923	+	11.7923i	−0.423593	+	0.423593i
$776$		0			0
$777$	−0.482502	−	0.278573i	−0.0173097	−	0.00999374i
$778$		0			0
$779$			22.6962i			0.813175i
$780$		0			0
$781$		−	52.8102i		−	1.88970i
$782$		0			0
$783$	15.8802	+	9.16842i	0.567511	+	0.327652i
$784$		0			0
$785$	4.58555	−	4.58555i	0.163665	−	0.163665i
$786$		0			0
$787$	−1.85344	+	6.91712i	−0.0660679	+	0.246569i	−0.991060	−	0.133418i	$-0.957405\pi$
$787$	−1.85344	+	6.91712i	−0.0660679	+	0.246569i	0.924992	+	0.379987i	$0.124071\pi$
$788$		0			0
$789$	11.1958	−	6.46390i	0.398581	−	0.230121i
$790$		0			0
$791$	4.84991	+	18.1001i	0.172443	+	0.643566i
$792$		0			0
$793$	−1.40121	+	0.337336i	−0.0497585	+	0.0119791i
$794$		0			0
$795$	−0.219366	−	0.818686i	−0.00778012	−	0.0290358i
$796$		0			0
$797$	19.2443	+	33.3321i	0.681667	+	1.18068i	0.974472	+	0.224510i	$0.0720782\pi$
$797$	19.2443	+	33.3321i	0.681667	+	1.18068i	−0.292804	+	0.956172i	$0.594588\pi$
$798$		0			0
$799$	−7.03266	+	26.2462i	−0.248798	+	0.928526i
$800$		0			0
$801$	−12.4698	−	12.4698i	−0.440598	−	0.440598i
$802$		0			0
$803$	−25.2542	−	14.5805i	−0.891202	−	0.514536i
$804$		0			0
$805$	−5.62094			−0.198112
$806$		0			0
$807$		−	8.19952i		−	0.288637i
$808$		0			0
$809$	15.1785	−	26.2900i	0.533648	−	0.924306i	−0.465579	−	0.885006i	$-0.654154\pi$
$809$	15.1785	−	26.2900i	0.533648	−	0.924306i	0.999227	−	0.0392997i	$-0.0125127\pi$
$810$		0			0
$811$	14.3976	−	14.3976i	0.505568	−	0.505568i	−0.407595	−	0.913163i	$-0.633632\pi$
$811$	14.3976	−	14.3976i	0.505568	−	0.505568i	0.913163	+	0.407595i	$0.133632\pi$
$812$		0			0
$813$	−0.692260	−	0.185491i	−0.0242786	−	0.00650544i
$814$		0			0
$815$	−2.65567	+	1.53325i	−0.0930241	+	0.0537075i
$816$		0			0
$817$	−21.8298	+	5.84928i	−0.763729	+	0.204641i
$818$		0			0
$819$	0.536072	−	20.9771i	0.0187319	−	0.732998i
$820$		0			0
$821$	20.7868	−	5.56981i	0.725465	−	0.194388i	0.122856	−	0.992425i	$-0.460795\pi$
$821$	20.7868	−	5.56981i	0.725465	−	0.194388i	0.602609	+	0.798037i	$0.294128\pi$
$822$		0			0
$823$	4.31762	+	7.47834i	0.150503	+	0.260679i	0.931412	−	0.363966i	$-0.118577\pi$
$823$	4.31762	+	7.47834i	0.150503	+	0.260679i	−0.780910	+	0.624644i	$0.785244\pi$
$824$		0			0
$825$	−5.77456	−	1.54729i	−0.201044	−	0.0538697i
$826$		0			0
$827$	−0.967256	−	0.967256i	−0.0336348	−	0.0336348i	0.690089	−	0.723724i	$-0.257571\pi$
$827$	−0.967256	−	0.967256i	−0.0336348	−	0.0336348i	−0.723724	+	0.690089i	$0.757571\pi$
$828$		0			0
$829$	8.27244	−	14.3283i	0.287314	−	0.497642i	−0.685854	−	0.727739i	$-0.740571\pi$
$829$	8.27244	−	14.3283i	0.287314	−	0.497642i	0.973168	+	0.230097i	$0.0739044\pi$
$830$		0			0
$831$	−13.1865			−0.457435
$832$		0			0
$833$	−8.32281			−0.288368
$834$		0			0
$835$	−1.11218	+	1.92635i	−0.0384886	+	0.0666642i
$836$		0			0
$837$	−7.18148	−	7.18148i	−0.248228	−	0.248228i
$838$		0			0
$839$	−26.2626	−	7.03704i	−0.906686	−	0.242946i	−0.224800	−	0.974405i	$-0.572173\pi$
$839$	−26.2626	−	7.03704i	−0.906686	−	0.242946i	−0.681885	+	0.731459i	$0.738840\pi$
$840$		0			0
$841$	10.6080	+	18.3735i	0.365792	+	0.633570i
$842$		0			0
$843$	8.70492	−	2.33248i	0.299813	−	0.0803348i
$844$		0			0
$845$	−2.35615	−	11.0165i	−0.0810541	−	0.378980i
$846$		0			0
$847$	−2.10953	+	0.565248i	−0.0724844	+	0.0194221i
$848$		0			0
$849$	−0.771484	+	0.445416i	−0.0264772	+	0.0152866i
$850$		0			0
$851$	−1.81265	−	0.485697i	−0.0621368	−	0.0166495i
$852$		0			0
$853$	23.3124	−	23.3124i	0.798201	−	0.798201i	−0.184611	−	0.982812i	$-0.559102\pi$
$853$	23.3124	−	23.3124i	0.798201	−	0.798201i	0.982812	+	0.184611i	$0.0591025\pi$
$854$		0			0
$855$	4.44738	−	7.70309i	0.152097	−	0.263440i
$856$		0			0
$857$			15.0760i			0.514985i	0.966280	+	0.257493i	$0.0828963\pi$
$857$			15.0760i			0.514985i	−0.966280	+	0.257493i	$0.917104\pi$
$858$		0			0
$859$	−23.0423			−0.786192			−0.393096	−	0.919497i	$-0.628596\pi$
$859$	−23.0423			−0.786192			−0.393096	+	0.919497i	$0.628596\pi$
$860$		0			0
$861$	4.97136	+	2.87022i	0.169424	+	0.0978168i
$862$		0			0
$863$	−7.80375	−	7.80375i	−0.265643	−	0.265643i	0.561699	−	0.827342i	$-0.310148\pi$
$863$	−7.80375	−	7.80375i	−0.265643	−	0.265643i	−0.827342	+	0.561699i	$0.810148\pi$
$864$		0			0
$865$	−1.25952	+	4.70059i	−0.0428249	+	0.159825i
$866$		0			0
$867$	1.64516	+	2.84950i	0.0558725	+	0.0967741i
$868$		0			0
$869$	10.5420	+	39.3434i	0.357614	+	1.33463i
$870$		0			0
$871$	−0.856613	+	33.5201i	−0.0290252	+	1.13579i
$872$		0			0
$873$	−11.4060	−	42.5679i	−0.386035	−	1.44070i
$874$		0			0
$875$	−14.4224	+	8.32678i	−0.487566	+	0.281496i
$876$		0			0
$877$	−11.4299	+	42.6571i	−0.385961	+	1.44043i	0.450685	+	0.892683i	$0.351180\pi$
$877$	−11.4299	+	42.6571i	−0.385961	+	1.44043i	−0.836646	+	0.547744i	$0.815487\pi$
$878$		0			0
$879$	2.71856	−	2.71856i	0.0916946	−	0.0916946i
$880$		0			0
$881$	−39.3183	−	22.7004i	−1.32467	−	0.764796i	−0.340197	−	0.940354i	$-0.610494\pi$
$881$	−39.3183	−	22.7004i	−1.32467	−	0.764796i	−0.984469	+	0.175558i	$0.943827\pi$
$882$		0			0
$883$			11.5891i			0.390003i	0.980803	+	0.195001i	$0.0624711\pi$
$883$			11.5891i			0.390003i	−0.980803	+	0.195001i	$0.937529\pi$
$884$		0			0
$885$		−	2.50453i		−	0.0841889i
$886$		0			0
$887$	−11.5755	−	6.68314i	−0.388669	−	0.224398i	0.292915	−	0.956139i	$-0.405375\pi$
$887$	−11.5755	−	6.68314i	−0.388669	−	0.224398i	−0.681583	+	0.731741i	$0.738708\pi$
$888$		0			0
$889$	−24.3296	+	24.3296i	−0.815988	+	0.815988i
$890$		0			0
$891$	−5.91767	+	22.0851i	−0.198250	+	0.739877i
$892$		0			0
$893$	−27.7963	+	16.0482i	−0.930169	+	0.537033i
$894$		0			0
$895$	−3.47764	−	12.9787i	−0.116245	−	0.433831i
$896$		0			0
$897$	1.17515	+	4.88128i	0.0392370	+	0.162981i
$898$		0			0
$899$	−7.19850	−	26.8652i	−0.240083	−	0.896004i
$900$		0			0
$901$	3.40097	+	5.89065i	0.113303	+	0.196246i
$902$		0			0
$903$	−1.47943	+	5.52132i	−0.0492324	+	0.183738i
$904$		0			0
$905$	−15.1801	−	15.1801i	−0.504605	−	0.504605i
$906$		0			0
$907$	11.0043	+	6.35332i	0.365391	+	0.210959i	0.671443	−	0.741056i	$-0.265675\pi$
$907$	11.0043	+	6.35332i	0.365391	+	0.210959i	−0.306052	+	0.952015i	$0.599008\pi$
$908$		0			0
$909$	−46.8130			−1.55269
$910$		0			0
$911$		−	38.0656i		−	1.26117i	−0.776121	−	0.630585i	$-0.782815\pi$
$911$		−	38.0656i		−	1.26117i	0.776121	−	0.630585i	$-0.217185\pi$
$912$		0			0
$913$	−20.5820	+	35.6491i	−0.681165	+	1.17981i
$914$		0			0
$915$	−0.109261	+	0.109261i	−0.00361205	+	0.00361205i
$916$		0			0
$917$	−13.5360	−	3.62697i	−0.446999	−	0.119773i
$918$		0			0
$919$	4.00602	−	2.31288i	0.132146	−	0.0762948i	−0.432469	−	0.901649i	$-0.642358\pi$
$919$	4.00602	−	2.31288i	0.132146	−	0.0762948i	0.564616	+	0.825354i	$0.309024\pi$
$920$		0			0
$921$	−12.5765	+	3.36986i	−0.414409	+	0.111041i
$922$		0			0
$923$	−31.5094	+	51.4915i	−1.03714	+	1.69486i
$924$		0			0
$925$	−2.46720	+	0.661085i	−0.0811211	+	0.0217363i
$926$		0			0
$927$	21.4794	+	37.2034i	0.705476	+	1.22192i
$928$		0			0
$929$	−28.2064	−	7.55789i	−0.925423	−	0.247966i	−0.235521	−	0.971869i	$-0.575680\pi$
$929$	−28.2064	−	7.55789i	−0.925423	−	0.247966i	−0.689902	+	0.723903i	$0.742346\pi$
$930$		0			0
$931$	−6.95166	−	6.95166i	−0.227831	−	0.227831i
$932$		0			0
$933$	4.05119	−	7.01686i	0.132630	−	0.229722i
$934$		0			0
$935$	−8.47953			−0.277310
$936$		0			0
$937$	−16.4032			−0.535870			−0.267935	−	0.963437i	$-0.586341\pi$
$937$	−16.4032			−0.535870			−0.267935	+	0.963437i	$0.586341\pi$
$938$		0			0
$939$	−2.91981	+	5.05725i	−0.0952843	+	0.165037i
$940$		0			0
$941$	14.6711	+	14.6711i	0.478264	+	0.478264i	0.904576	−	0.426312i	$-0.140187\pi$
$941$	14.6711	+	14.6711i	0.478264	+	0.478264i	−0.426312	+	0.904576i	$0.640187\pi$
$942$		0			0
$943$	18.6763	+	5.00429i	0.608183	+	0.162962i
$944$		0			0
$945$	−2.32962	−	4.03502i	−0.0757825	−	0.131259i
$946$		0			0
$947$	−20.8148	+	5.57731i	−0.676391	+	0.181238i	−0.580632	−	0.814166i	$-0.697194\pi$
$947$	−20.8148	+	5.57731i	−0.676391	+	0.181238i	−0.0957588	+	0.995405i	$0.530528\pi$
$948$		0			0
$949$	15.9241	+	29.2845i	0.516917	+	0.950614i
$950$		0			0
$951$	−10.1711	+	2.72533i	−0.329820	+	0.0883750i
$952$		0			0
$953$	46.8688	−	27.0597i	1.51823	−	0.876550i	0.518459	−	0.855103i	$-0.326506\pi$
$953$	46.8688	−	27.0597i	1.51823	−	0.876550i	0.999770	−	0.0214470i	$-0.00682733\pi$
$954$		0			0
$955$	7.31331	+	1.95960i	0.236653	+	0.0634110i
$956$		0			0
$957$	7.05005	−	7.05005i	0.227896	−	0.227896i
$958$		0			0
$959$	8.93054	−	15.4682i	0.288382	−	0.499493i
$960$		0			0
$961$		−	15.5954i		−	0.503078i
$962$		0			0
$963$	26.1912			0.844001
$964$		0			0
$965$	−5.90424	−	3.40882i	−0.190064	−	0.109734i
$966$		0			0
$967$	6.56401	+	6.56401i	0.211084	+	0.211084i	0.804728	−	0.593644i	$-0.202311\pi$
$967$	6.56401	+	6.56401i	0.211084	+	0.211084i	−0.593644	+	0.804728i	$0.702311\pi$
$968$		0			0
$969$	1.31241	−	4.89799i	0.0421607	−	0.157346i
$970$		0			0
$971$	−25.6280	−	44.3889i	−0.822440	−	1.42451i	−0.903860	−	0.427829i	$-0.859279\pi$
$971$	−25.6280	−	44.3889i	−0.822440	−	1.42451i	0.0814193	−	0.996680i	$-0.474055\pi$
$972$		0			0
$973$	−7.33937	−	27.3909i	−0.235289	−	0.878112i
$974$		0			0
$975$	4.70717	+	4.95407i	0.150750	+	0.158657i
$976$		0			0
$977$	11.3765	+	42.4576i	0.363966	+	1.35834i	0.868817	+	0.495133i	$0.164881\pi$
$977$	11.3765	+	42.4576i	0.363966	+	1.35834i	−0.504851	+	0.863206i	$0.668453\pi$
$978$		0			0
$979$	−17.1979	+	9.92919i	−0.549646	+	0.317338i
$980$		0			0
$981$	7.79053	−	29.0747i	0.248732	−	0.928282i
$982$		0			0
$983$	26.2621	−	26.2621i	0.837632	−	0.837632i	−0.150915	−	0.988547i	$-0.548222\pi$
$983$	26.2621	−	26.2621i	0.837632	−	0.837632i	0.988547	+	0.150915i	$0.0482219\pi$
$984$		0			0
$985$	−5.21591	−	3.01140i	−0.166193	−	0.0959513i
$986$		0			0
$987$			8.11800i			0.258399i
$988$		0			0
$989$			19.2531i			0.612212i
$990$		0			0
$991$	−2.40594	−	1.38907i	−0.0764273	−	0.0441253i	0.461299	−	0.887245i	$-0.347383\pi$
$991$	−2.40594	−	1.38907i	−0.0764273	−	0.0441253i	−0.537727	+	0.843119i	$0.680717\pi$
$992$		0			0
$993$	−7.54104	+	7.54104i	−0.239308	+	0.239308i
$994$		0			0
$995$	−2.74226	+	10.2343i	−0.0869355	+	0.324448i
$996$		0			0
$997$	23.5492	−	13.5962i	0.745812	−	0.430595i	−0.0783668	−	0.996925i	$-0.524971\pi$
$997$	23.5492	−	13.5962i	0.745812	−	0.430595i	0.824179	+	0.566330i	$0.191637\pi$
$998$		0			0
$999$	−0.402598	−	1.50252i	−0.0127376	−	0.0475375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bk.a.175.7		48
4.3	odd	2		104.2.u.a.19.12	yes	48
8.3	odd	2	inner	416.2.bk.a.175.8		48
8.5	even	2		104.2.u.a.19.2	yes	48
12.11	even	2		936.2.ed.d.19.1		48
13.11	odd	12	inner	416.2.bk.a.271.8		48
24.5	odd	2		936.2.ed.d.19.11		48
52.11	even	12		104.2.u.a.11.2	✓	48
104.11	even	12	inner	416.2.bk.a.271.7		48
104.37	odd	12		104.2.u.a.11.12	yes	48
156.11	odd	12		936.2.ed.d.739.11		48
312.245	even	12		936.2.ed.d.739.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.u.a.11.2	✓	48	52.11	even	12
104.2.u.a.11.12	yes	48	104.37	odd	12
104.2.u.a.19.2	yes	48	8.5	even	2
104.2.u.a.19.12	yes	48	4.3	odd	2
416.2.bk.a.175.7		48	1.1	even	1	trivial
416.2.bk.a.175.8		48	8.3	odd	2	inner
416.2.bk.a.271.7		48	104.11	even	12	inner
416.2.bk.a.271.8		48	13.11	odd	12	inner
936.2.ed.d.19.1		48	12.11	even	2
936.2.ed.d.19.11		48	24.5	odd	2
936.2.ed.d.739.1		48	312.245	even	12
936.2.ed.d.739.11		48	156.11	odd	12

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bk (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.223033 - 0.386304i) q^{3} +(-0.612771 - 0.612771i) q^{5} +(2.00697 + 0.537767i) q^{7} +(1.40051 + 2.42576i) q^{9} +(3.04671 - 0.816364i) q^{11} +(-3.45772 - 1.02185i) q^{13} +(-0.373384 + 0.100048i) q^{15} +(2.68659 - 1.55110i) q^{17} +(3.53955 + 0.948419i) q^{19} +(0.655362 - 0.655362i) q^{21} +(1.56087 - 2.70351i) q^{23} -4.24902i q^{25} +2.58764 q^{27} +(6.13693 + 3.54316i) q^{29} +(-2.77530 - 2.77530i) q^{31} +(0.364152 - 1.35903i) q^{33} +(-0.900287 - 1.55934i) q^{35} +(-0.155585 - 0.580652i) q^{37} +(-1.16593 + 1.10782i) q^{39} +(1.60304 + 5.98263i) q^{41} +(-5.34113 + 3.08370i) q^{43} +(0.628242 - 2.34463i) q^{45} +(-6.19352 + 6.19352i) q^{47} +(-2.32343 - 1.34143i) q^{49} -1.38379i q^{51} +2.19261i q^{53} +(-2.36718 - 1.36669i) q^{55} +(1.15581 - 1.15581i) q^{57} +(-1.67691 + 6.25832i) q^{59} +(0.346176 - 0.199865i) q^{61} +(1.50630 + 5.62158i) q^{63} +(1.49263 + 2.74495i) q^{65} +(-2.40698 - 8.98296i) q^{67} +(-0.696252 - 1.20594i) q^{69} +(4.33338 - 16.1724i) q^{71} +(-6.53734 - 6.53734i) q^{73} +(-1.64142 - 0.947672i) q^{75} +6.55368 q^{77} +12.9134i q^{79} +(-3.62441 + 6.27766i) q^{81} +(-9.22816 + 9.22816i) q^{83} +(-2.59674 - 0.695794i) q^{85} +(2.73747 - 1.58048i) q^{87} +(-6.08135 + 1.62949i) q^{89} +(-6.39003 - 3.91028i) q^{91} +(-1.69109 + 0.453127i) q^{93} +(-1.58777 - 2.75010i) q^{95} +(-15.1972 - 4.07209i) q^{97} +(6.24726 + 6.24726i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{3} - 20 q^{9} + 8 q^{11} - 12 q^{17} + 8 q^{19} - 8 q^{27} + 4 q^{33} + 4 q^{35} + 12 q^{43} - 60 q^{49} + 36 q^{57} + 64 q^{59} - 16 q^{65} + 8 q^{67} - 12 q^{73} - 24 q^{75} - 8 q^{81} + 48 q^{83}+ \cdots - 168 q^{99}+O(q^{100}) \) 48 * q + 4 * q^3 - 20 * q^9 + 8 * q^11 - 12 * q^17 + 8 * q^19 - 8 * q^27 + 4 * q^33 + 4 * q^35 + 12 * q^43 - 60 * q^49 + 36 * q^57 + 64 * q^59 - 16 * q^65 + 8 * q^67 - 12 * q^73 - 24 * q^75 - 8 * q^81 + 48 * q^83 + 12 * q^89 - 104 * q^91 + 4 * q^97 - 168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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