LMFDB - Embedded newform 936.2.dg.e.829.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(829,936)] 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("936.829"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.dg (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			829.18
Character	$\chi$	$=$	936.829
Dual form			936.2.dg.e.901.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.939983 - 1.05661i) q^{2} +(-0.232865 - 1.98640i) q^{4} +4.32865 q^{5} +(1.87318 + 1.08148i) q^{7} +(-2.31774 - 1.62113i) q^{8} +(4.06885 - 4.57371i) q^{10} +(-2.57249 - 4.45568i) q^{11} +(-2.72749 + 2.35814i) q^{13} +(2.90347 - 0.962655i) q^{14} +(-3.89155 + 0.925127i) q^{16} +(2.79961 - 4.84906i) q^{17} +(-0.963361 + 1.66859i) q^{19} +(-1.00799 - 8.59842i) q^{20} +(-7.12602 - 1.47013i) q^{22} +(1.01290 + 1.75439i) q^{23} +13.7372 q^{25} +(-0.0721467 + 5.09851i) q^{26} +(1.71205 - 3.97272i) q^{28} +(0.171090 - 0.0987787i) q^{29} +7.11414i q^{31} +(-2.68049 + 4.98147i) q^{32} +(-2.49200 - 7.51614i) q^{34} +(8.10834 + 4.68135i) q^{35} +(0.231065 + 0.400217i) q^{37} +(0.857513 + 2.58635i) q^{38} +(-10.0327 - 7.01730i) q^{40} +(1.21570 - 0.701886i) q^{41} +(-2.55733 - 1.47647i) q^{43} +(-8.25170 + 6.14755i) q^{44} +(2.80582 + 0.578856i) q^{46} +2.20506i q^{47} +(-1.16080 - 2.01056i) q^{49} +(12.9127 - 14.5149i) q^{50} +(5.31934 + 4.86874i) q^{52} +2.10538i q^{53} +(-11.1354 - 19.2871i) q^{55} +(-2.58833 - 5.54327i) q^{56} +(0.0564504 - 0.273626i) q^{58} +(-2.18299 + 3.78104i) q^{59} +(10.6432 + 6.14485i) q^{61} +(7.51690 + 6.68717i) q^{62} +(2.74388 + 7.51473i) q^{64} +(-11.8063 + 10.2076i) q^{65} +(-5.50969 - 9.54306i) q^{67} +(-10.2841 - 4.43195i) q^{68} +(12.5681 - 4.16700i) q^{70} +(-5.01087 - 2.89303i) q^{71} +10.1096i q^{73} +(0.640072 + 0.132050i) q^{74} +(3.53882 + 1.52506i) q^{76} -11.1284i q^{77} -7.37163 q^{79} +(-16.8451 + 4.00455i) q^{80} +(0.401116 - 1.94429i) q^{82} -2.04171 q^{83} +(12.1185 - 20.9899i) q^{85} +(-3.96390 + 1.31425i) q^{86} +(-1.26087 + 14.4975i) q^{88} +(4.34987 - 2.51140i) q^{89} +(-7.65936 + 1.46750i) q^{91} +(3.24905 - 2.42056i) q^{92} +(2.32990 + 2.07272i) q^{94} +(-4.17005 + 7.22274i) q^{95} +(-7.41183 - 4.27922i) q^{97} +(-3.21551 - 0.663376i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{4} - 12 q^{7} - 4 q^{10} + 36 q^{14} - 2 q^{16} - 12 q^{17} - 54 q^{20} - 14 q^{22} - 20 q^{23} + 48 q^{25} + 42 q^{26} + 6 q^{28} + 28 q^{38} - 8 q^{40} + 12 q^{41} - 30 q^{46} + 16 q^{49}+ \cdots - 24 q^{98}+O(q^{100}) $ 48 * q - 2 * q^4 - 12 * q^7 - 4 * q^10 + 36 * q^14 - 2 * q^16 - 12 * q^17 - 54 * q^20 - 14 * q^22 - 20 * q^23 + 48 * q^25 + 42 * q^26 + 6 * q^28 + 28 * q^38 - 8 * q^40 + 12 * q^41 - 30 * q^46 + 16 * q^49 + 84 * q^50 - 28 * q^52 - 68 * q^55 - 18 * q^56 - 24 * q^58 - 24 * q^62 - 68 * q^64 - 12 * q^65 - 4 * q^68 + 12 * q^71 - 54 * q^74 - 54 * q^76 - 192 * q^79 - 78 * q^80 - 6 * q^82 - 10 * q^88 + 48 * q^89 + 12 * q^92 + 54 * q^94 + 20 * q^95 + 144 * q^97 - 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

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 $

$2$	0.939983	−	1.05661i	0.664668	−	0.747139i
$2$	0.939983	−	1.05661i	0.664668	−	0.747139i
$3$		0			0
$3$		0			0
$4$	−0.232865	−	1.98640i	−0.116433	−	0.993199i
$5$	4.32865			1.93583			0.967915	−	0.251276i	$-0.0808503\pi$
$5$	4.32865			1.93583			0.967915	+	0.251276i	$0.0808503\pi$
$6$		0			0
$7$	1.87318	+	1.08148i	0.707996	+	0.408762i	0.810319	−	0.585990i	$-0.199294\pi$
$7$	1.87318	+	1.08148i	0.707996	+	0.408762i	−0.102323	+	0.994751i	$0.532627\pi$
$8$	−2.31774	−	1.62113i	−0.819446	−	0.573156i
$9$		0			0
$10$	4.06885	−	4.57371i	1.28668	−	1.44633i
$11$	−2.57249	−	4.45568i	−0.775634	−	1.34344i	−0.934438	−	0.356127i	$-0.884097\pi$
$11$	−2.57249	−	4.45568i	−0.775634	−	1.34344i	0.158804	−	0.987310i	$-0.449236\pi$
$12$		0			0
$13$	−2.72749	+	2.35814i	−0.756468	+	0.654030i
$13$	−2.72749	+	2.35814i	−0.756468	+	0.654030i
$14$	2.90347	−	0.962655i	0.775984	−	0.257280i
$15$		0			0
$16$	−3.89155	+	0.925127i	−0.972887	+	0.231282i
$17$	2.79961	−	4.84906i	0.679005	−	1.17607i	−0.296276	−	0.955102i	$-0.595745\pi$
$17$	2.79961	−	4.84906i	0.679005	−	1.17607i	0.975281	−	0.220968i	$-0.0709217\pi$
$18$		0			0
$19$	−0.963361	+	1.66859i	−0.221010	+	0.382801i	−0.955115	−	0.296235i	$-0.904269\pi$
$19$	−0.963361	+	1.66859i	−0.221010	+	0.382801i	0.734105	+	0.679036i	$0.237602\pi$
$20$	−1.00799	−	8.59842i	−0.225394	−	1.92266i
$21$		0			0
$22$	−7.12602	−	1.47013i	−1.51927	−	0.313434i
$23$	1.01290	+	1.75439i	0.211204	+	0.365816i	0.952092	−	0.305813i	$-0.0989282\pi$
$23$	1.01290	+	1.75439i	0.211204	+	0.365816i	−0.740887	+	0.671629i	$0.765595\pi$
$24$		0			0
$25$	13.7372			2.74744
$26$	−0.0721467	+	5.09851i	−0.0141491	+	0.999900i
$27$		0			0
$28$	1.71205	−	3.97272i	0.323548	−	0.750774i
$29$	0.171090	−	0.0987787i	0.0317706	−	0.0183427i	−0.484031	−	0.875051i	$-0.660828\pi$
$29$	0.171090	−	0.0987787i	0.0317706	−	0.0183427i	0.515801	+	0.856708i	$0.327494\pi$
$30$		0			0
$31$			7.11414i			1.27774i	0.769316	+	0.638869i	$0.220597\pi$
$31$			7.11414i			1.27774i	−0.769316	+	0.638869i	$0.779403\pi$
$32$	−2.68049	+	4.98147i	−0.473847	+	0.880607i
$33$		0			0
$34$	−2.49200	−	7.51614i	−0.427375	−	1.28901i
$35$	8.10834	+	4.68135i	1.37056	+	0.791293i
$36$		0			0
$37$	0.231065	+	0.400217i	0.0379869	+	0.0657952i	0.884394	−	0.466742i	$-0.154572\pi$
$37$	0.231065	+	0.400217i	0.0379869	+	0.0657952i	−0.846407	+	0.532537i	$0.821239\pi$
$38$	0.857513	+	2.58635i	0.139107	+	0.419561i
$39$		0			0
$40$	−10.0327	−	7.01730i	−1.58631	−	1.10953i
$41$	1.21570	−	0.701886i	0.189861	−	0.109616i	−0.402057	−	0.915615i	$-0.631705\pi$
$41$	1.21570	−	0.701886i	0.189861	−	0.109616i	0.591917	+	0.805999i	$0.298371\pi$
$42$		0			0
$43$	−2.55733	−	1.47647i	−0.389989	−	0.225160i	0.292167	−	0.956367i	$-0.405624\pi$
$43$	−2.55733	−	1.47647i	−0.389989	−	0.225160i	−0.682155	+	0.731207i	$0.738957\pi$
$44$	−8.25170	+	6.14755i	−1.24399	+	0.926778i
$45$		0			0
$46$	2.80582	+	0.578856i	0.413696	+	0.0853476i
$47$			2.20506i			0.321641i	0.986984	+	0.160821i	$0.0514141\pi$
$47$			2.20506i			0.321641i	−0.986984	+	0.160821i	$0.948586\pi$
$48$		0			0
$49$	−1.16080	−	2.01056i	−0.165828	−	0.287222i
$50$	12.9127	−	14.5149i	1.82614	−	2.05272i
$51$		0			0
$52$	5.31934	+	4.86874i	0.737660	+	0.675173i
$53$			2.10538i			0.289196i	0.989490	+	0.144598i	$0.0461890\pi$
$53$			2.10538i			0.289196i	−0.989490	+	0.144598i	$0.953811\pi$
$54$		0			0
$55$	−11.1354	−	19.2871i	−1.50150	−	2.60067i
$56$	−2.58833	−	5.54327i	−0.345880	−	0.740750i
$57$		0			0
$58$	0.0564504	−	0.273626i	0.00741230	−	0.0359288i
$59$	−2.18299	+	3.78104i	−0.284200	+	0.492250i	−0.972415	−	0.233258i	$-0.925061\pi$
$59$	−2.18299	+	3.78104i	−0.284200	+	0.492250i	0.688215	+	0.725507i	$0.258395\pi$
$60$		0			0
$61$	10.6432	+	6.14485i	1.36272	+	0.786767i	0.989985	−	0.141171i	$-0.0450867\pi$
$61$	10.6432	+	6.14485i	1.36272	+	0.786767i	0.372735	+	0.927938i	$0.378420\pi$
$62$	7.51690	+	6.68717i	0.954647	+	0.849271i
$63$		0			0
$64$	2.74388	+	7.51473i	0.342984	+	0.939341i
$65$	−11.8063	+	10.2076i	−1.46439	+	1.26609i
$66$		0			0
$67$	−5.50969	−	9.54306i	−0.673115	−	1.16587i	−0.977016	−	0.213166i	$-0.931622\pi$
$67$	−5.50969	−	9.54306i	−0.673115	−	1.16587i	0.303901	−	0.952704i	$-0.401711\pi$
$68$	−10.2841	−	4.43195i	−1.24713	−	0.537453i
$69$		0			0
$70$	12.5681	−	4.16700i	1.50217	−	0.498051i
$71$	−5.01087	−	2.89303i	−0.594680	−	0.343339i	0.172266	−	0.985051i	$-0.444891\pi$
$71$	−5.01087	−	2.89303i	−0.594680	−	0.343339i	−0.766946	+	0.641712i	$0.778225\pi$
$72$		0			0
$73$			10.1096i			1.18324i	0.806217	+	0.591619i	$0.201511\pi$
$73$			10.1096i			1.18324i	−0.806217	+	0.591619i	$0.798489\pi$
$74$	0.640072	+	0.132050i	0.0744068	+	0.0153505i
$75$		0			0
$76$	3.53882	+	1.52506i	0.405930	+	0.174936i
$77$		−	11.1284i		−	1.26820i
$78$		0			0
$79$	−7.37163			−0.829373			−0.414687	−	0.909964i	$-0.636109\pi$
$79$	−7.37163			−0.829373			−0.414687	+	0.909964i	$0.636109\pi$
$80$	−16.8451	+	4.00455i	−1.88334	+	0.447722i
$81$		0			0
$82$	0.401116	−	1.94429i	0.0442959	−	0.214711i
$83$	−2.04171			−0.224106			−0.112053	−	0.993702i	$-0.535743\pi$
$83$	−2.04171			−0.224106			−0.112053	+	0.993702i	$0.535743\pi$
$84$		0			0
$85$	12.1185	−	20.9899i	1.31444	−	2.27667i
$86$	−3.96390	+	1.31425i	−0.427439	+	0.141719i
$87$		0			0
$88$	−1.26087	+	14.4975i	−0.134409	+	1.54543i
$89$	4.34987	−	2.51140i	0.461085	−	0.266208i	−0.251415	−	0.967879i	$-0.580896\pi$
$89$	4.34987	−	2.51140i	0.461085	−	0.266208i	0.712501	+	0.701672i	$0.247563\pi$
$90$		0			0
$91$	−7.65936	+	1.46750i	−0.802919	+	0.153835i
$92$	3.24905	−	2.42056i	0.338737	−	0.252361i
$93$		0			0
$94$	2.32990	+	2.07272i	0.240311	+	0.213785i
$95$	−4.17005	+	7.22274i	−0.427838	+	0.741038i
$96$		0			0
$97$	−7.41183	−	4.27922i	−0.752557	−	0.434489i	0.0740599	−	0.997254i	$-0.476404\pi$
$97$	−7.41183	−	4.27922i	−0.752557	−	0.434489i	−0.826617	+	0.562765i	$0.809738\pi$
$98$	−3.21551	−	0.663376i	−0.324816	−	0.0670111i
$99$		0			0
$100$	−3.19892	−	27.2875i	−0.319892	−	2.72875i
$101$	−3.09840	+	1.78886i	−0.308303	+	0.177999i	−0.646167	−	0.763196i	$-0.723629\pi$
$101$	−3.09840	+	1.78886i	−0.308303	+	0.177999i	0.337864	+	0.941195i	$0.390296\pi$
$102$		0			0
$103$	−4.69498			−0.462610			−0.231305	−	0.972881i	$-0.574300\pi$
$103$	−4.69498			−0.462610			−0.231305	+	0.972881i	$0.574300\pi$
$104$	10.1445	−	1.04395i	0.994747	−	0.102368i
$105$		0			0
$106$	2.22458	+	1.97902i	0.216070	+	0.192220i
$107$	−1.85628	+	1.07172i	−0.179453	+	0.103607i	−0.587036	−	0.809561i	$-0.699705\pi$
$107$	−1.85628	+	1.07172i	−0.179453	+	0.103607i	0.407583	+	0.913168i	$0.366372\pi$
$108$		0			0
$109$	9.31589			0.892300			0.446150	−	0.894958i	$-0.352795\pi$
$109$	9.31589			0.892300			0.446150	+	0.894958i	$0.352795\pi$
$110$	−30.8460	−	6.36369i	−2.94105	−	0.606754i
$111$		0			0
$112$	−8.29008	−	2.47571i	−0.783339	−	0.233932i
$113$	−9.68859	+	16.7811i	−0.911426	+	1.57864i	−0.0993747	+	0.995050i	$0.531684\pi$
$113$	−9.68859	+	16.7811i	−0.911426	+	1.57864i	−0.812051	+	0.583586i	$0.801649\pi$
$114$		0			0
$115$	4.38449	+	7.59415i	0.408856	+	0.708159i
$116$	−0.236055	−	0.316850i	−0.0219171	−	0.0294188i
$117$		0			0
$118$	1.94313	+	5.86068i	0.178880	+	0.539520i
$119$	10.4883	−	6.05545i	0.961465	−	0.555102i
$120$		0			0
$121$	−7.73537	+	13.3980i	−0.703215	+	1.21800i
$122$	16.4971	−	5.46969i	1.49358	−	0.495202i
$123$		0			0
$124$	14.1315	−	1.65664i	1.26905	−	0.148771i
$125$	37.8203			3.38275
$126$		0			0
$127$	3.32924	+	5.76642i	0.295423	+	0.511687i	0.975083	−	0.221840i	$-0.0712062\pi$
$127$	3.32924	+	5.76642i	0.295423	+	0.511687i	−0.679661	+	0.733527i	$0.737873\pi$
$128$	10.5194	+	4.16450i	0.929789	+	0.368093i
$129$		0			0
$130$	−0.312298	+	22.0697i	−0.0273903	+	1.93564i
$131$		−	10.3800i		−	0.906905i	−0.891280	−	0.453453i	$-0.850192\pi$
$131$		−	10.3800i		−	0.906905i	0.891280	−	0.453453i	$-0.149808\pi$
$132$		0			0
$133$	−3.60910	+	2.08371i	−0.312949	+	0.180681i
$134$	−15.2623	−	3.14870i	−1.31846	−	0.272006i
$135$		0			0
$136$	−14.3497	+	6.70036i	−1.23048	+	0.574551i
$137$	−2.55242	−	1.47364i	−0.218068	−	0.125902i	0.386987	−	0.922085i	$-0.373516\pi$
$137$	−2.55242	−	1.47364i	−0.218068	−	0.125902i	−0.605056	+	0.796183i	$0.706849\pi$
$138$		0			0
$139$	17.1010	+	9.87324i	1.45048	+	0.837437i	0.998509	−	0.0545929i	$-0.0173861\pi$
$139$	17.1010	+	9.87324i	1.45048	+	0.837437i	0.451976	+	0.892030i	$0.350719\pi$
$140$	7.41087	−	17.1965i	0.626333	−	1.45337i
$141$		0			0
$142$	−7.76694	+	2.57516i	−0.651787	+	0.216102i
$143$	17.5235	+	6.08651i	1.46539	+	0.508980i
$144$		0			0
$145$	0.740587	−	0.427578i	0.0615024	−	0.0355084i
$146$	10.6819	+	9.50285i	0.884044	+	0.786461i
$147$		0			0
$148$	0.741182	−	0.552184i	0.0609248	−	0.0453892i
$149$	−3.78459	+	6.55509i	−0.310045	+	0.537014i	−0.978372	−	0.206854i	$-0.933678\pi$
$149$	−3.78459	+	6.55509i	−0.310045	+	0.537014i	0.668327	+	0.743868i	$0.267011\pi$
$150$		0			0
$151$			2.09922i			0.170832i	0.996345	+	0.0854161i	$0.0272220\pi$
$151$			2.09922i			0.170832i	−0.996345	+	0.0854161i	$0.972778\pi$
$152$	4.93783	−	2.30563i	0.400511	−	0.187011i
$153$		0			0
$154$	−11.7584	−	10.4605i	−0.947519	−	0.842930i
$155$			30.7946i			2.47348i
$156$		0			0
$157$			8.35087i			0.666472i	0.942843	+	0.333236i	$0.108141\pi$
$157$			8.35087i			0.666472i	−0.942843	+	0.333236i	$0.891859\pi$
$158$	−6.92921	+	7.78897i	−0.551258	+	0.619657i
$159$		0			0
$160$	−11.6029	+	21.5630i	−0.917288	+	1.70471i
$161$			4.38173i			0.345329i
$162$		0			0
$163$	−3.81101	+	6.60086i	−0.298501	+	0.517019i	−0.975793	−	0.218695i	$-0.929820\pi$
$163$	−3.81101	+	6.60086i	−0.298501	+	0.517019i	0.677292	+	0.735714i	$0.263153\pi$
$164$	−1.67732	−	2.25142i	−0.130977	−	0.175807i
$165$		0			0
$166$	−1.91917	+	2.15729i	−0.148956	+	0.167438i
$167$	10.4948	−	6.05915i	0.812109	−	0.468871i	−0.0355788	−	0.999367i	$-0.511327\pi$
$167$	10.4948	−	6.05915i	0.812109	−	0.468871i	0.847688	+	0.530496i	$0.177994\pi$
$168$		0			0
$169$	1.87836	−	12.8636i	0.144489	−	0.989506i
$170$	−10.7870	−	32.5347i	−0.827326	−	2.49530i
$171$		0			0
$172$	−2.33735	+	5.42368i	−0.178221	+	0.413552i
$173$	−4.95047	−	2.85815i	−0.376377	−	0.217301i	0.299864	−	0.953982i	$-0.403059\pi$
$173$	−4.95047	−	2.85815i	−0.376377	−	0.217301i	−0.676241	+	0.736681i	$0.736392\pi$
$174$		0			0
$175$	25.7323	+	14.8565i	1.94518	+	1.12305i
$176$	14.1330	+	14.9596i	1.06532	+	1.12762i
$177$		0			0
$178$	1.43522	−	6.95680i	0.107575	−	0.521435i
$179$	−6.10323	+	3.52370i	−0.456177	+	0.263374i	−0.710435	−	0.703762i	$-0.751502\pi$
$179$	−6.10323	+	3.52370i	−0.456177	+	0.263374i	0.254258	+	0.967136i	$0.418169\pi$
$180$		0			0
$181$		−	7.85231i		−	0.583658i	−0.956471	−	0.291829i	$-0.905736\pi$
$181$		−	7.85231i		−	0.583658i	0.956471	−	0.291829i	$-0.0942638\pi$
$182$	−5.64909	+	9.47240i	−0.418738	+	0.702141i
$183$		0			0
$184$	0.496458	−	5.70828i	0.0365993	−	0.420820i
$185$	1.00020	+	1.73240i	0.0735362	+	0.127368i
$186$		0			0
$187$	−28.8078			−2.10664
$188$	4.38013	−	0.513483i	0.319454	−	0.0374496i
$189$		0			0
$190$	3.71187	+	11.1954i	0.269288	+	0.812199i
$191$	−10.1668	+	17.6094i	−0.735644	+	1.27417i	0.218796	+	0.975771i	$0.429787\pi$
$191$	−10.1668	+	17.6094i	−0.735644	+	1.27417i	−0.954440	+	0.298403i	$0.903546\pi$
$192$		0			0
$193$	−6.49899	+	3.75219i	−0.467808	+	0.270089i	−0.715322	−	0.698795i	$-0.753720\pi$
$193$	−6.49899	+	3.75219i	−0.467808	+	0.270089i	0.247514	+	0.968884i	$0.420386\pi$
$194$	−11.4885	+	3.80905i	−0.824824	+	0.273474i
$195$		0			0
$196$	−3.72346	+	2.77399i	−0.265961	+	0.198142i
$197$	−2.25982	−	3.91412i	−0.161005	−	0.278869i	0.774224	−	0.632911i	$-0.218140\pi$
$197$	−2.25982	−	3.91412i	−0.161005	−	0.278869i	−0.935229	+	0.354042i	$0.884807\pi$
$198$		0			0
$199$	12.5909	−	21.8080i	0.892543	−	1.54593i	0.0557276	−	0.998446i	$-0.482252\pi$
$199$	12.5909	−	21.8080i	0.892543	−	1.54593i	0.836816	−	0.547484i	$-0.184414\pi$
$200$	−31.8393	−	22.2698i	−2.25138	−	1.57471i
$201$		0			0
$202$	−1.02231	+	4.95532i	−0.0719292	+	0.348655i
$203$	0.427309			0.0299912
$204$		0			0
$205$	5.26235	−	3.03822i	0.367538	−	0.212198i
$206$	−4.41320	+	4.96078i	−0.307482	+	0.345634i
$207$		0			0
$208$	8.43256	−	11.7001i	0.584693	−	0.811255i
$209$	9.91293			0.685692
$210$		0			0
$211$	−13.5839	+	7.84264i	−0.935151	+	0.539910i	−0.888437	−	0.458999i	$-0.848208\pi$
$211$	−13.5839	+	7.84264i	−0.935151	+	0.539910i	−0.0467141	+	0.998908i	$0.514875\pi$
$212$	4.18213	−	0.490271i	0.287230	−	0.0336719i
$213$		0			0
$214$	−0.612472	+	2.96877i	−0.0418678	+	0.202941i
$215$	−11.0698	−	6.39113i	−0.754952	−	0.435872i
$216$		0			0
$217$	−7.69381	+	13.3261i	−0.522290	+	0.904633i
$218$	8.75677	−	9.84329i	0.593083	−	0.666672i
$219$		0			0
$220$	−35.7187	+	26.6106i	−2.40816	+	1.79409i
$221$	3.79887	+	19.8276i	0.255540	+	1.33375i
$222$		0			0
$223$	−19.7231	+	11.3871i	−1.32076	+	0.762540i	−0.983849	−	0.178998i	$-0.942715\pi$
$223$	−19.7231	+	11.3871i	−1.32076	+	0.762540i	−0.336908	+	0.941538i	$0.609381\pi$
$224$	−10.4084	+	6.43229i	−0.695440	+	0.429776i
$225$		0			0
$226$	8.62407	+	26.0111i	0.573665	+	1.73023i
$227$	2.14767	−	3.71988i	0.142546	−	0.246897i	−0.785909	−	0.618343i	$-0.787804\pi$
$227$	2.14767	−	3.71988i	0.142546	−	0.246897i	0.928455	+	0.371446i	$0.121138\pi$
$228$		0			0
$229$	20.0355			1.32398			0.661991	−	0.749512i	$-0.269712\pi$
$229$	20.0355			1.32398			0.661991	+	0.749512i	$0.269712\pi$
$230$	12.1454	+	2.50566i	0.800846	+	0.165219i
$231$		0			0
$232$	−0.556675	−	0.0484149i	−0.0365475	−	0.00317859i
$233$	7.21901			0.472933			0.236467	−	0.971640i	$-0.424011\pi$
$233$	7.21901			0.472933			0.236467	+	0.971640i	$0.424011\pi$
$234$		0			0
$235$			9.54494i			0.622643i
$236$	8.01899	+	3.45580i	0.521992	+	0.224954i
$237$		0			0
$238$	3.46059	−	16.7741i	0.224317	−	1.08731i
$239$		−	1.40644i		−	0.0909750i	−0.998965	−	0.0454875i	$-0.985516\pi$
$239$		−	1.40644i		−	0.0909750i	0.998965	−	0.0454875i	$-0.0144841\pi$
$240$		0			0
$241$	4.79595	+	2.76894i	0.308934	+	0.178363i	0.646449	−	0.762957i	$-0.276253\pi$
$241$	4.79595	+	2.76894i	0.308934	+	0.178363i	−0.337515	+	0.941320i	$0.609586\pi$
$242$	6.88545	+	20.7672i	0.442614	+	1.33497i
$243$		0			0
$244$	9.72767	−	22.5725i	0.622751	−	1.44506i
$245$	−5.02468	−	8.70300i	−0.321015	−	0.556014i
$246$		0			0
$247$	−1.30721	−	6.82280i	−0.0831761	−	0.434124i
$248$	11.5329	−	16.4888i	0.732343	−	1.04704i
$249$		0			0
$250$	35.5504	−	39.9614i	2.24841	−	2.52738i
$251$	19.6157	+	11.3251i	1.23813	+	0.714836i	0.968712	−	0.248187i	$-0.0798346\pi$
$251$	19.6157	+	11.3251i	1.23813	+	0.714836i	0.269420	+	0.963023i	$0.413168\pi$
$252$		0			0
$253$	5.21134	−	9.02631i	0.327634	−	0.567479i
$254$	9.22231	+	1.90261i	0.578659	+	0.119380i
$255$		0			0
$256$	14.2883	−	7.20035i	0.893018	−	0.450022i
$257$	−9.24512	−	16.0130i	−0.576695	−	0.998865i	−0.995855	−	0.0909525i	$-0.971009\pi$
$257$	−9.24512	−	16.0130i	−0.576695	−	0.998865i	0.419160	−	0.907912i	$-0.362324\pi$
$258$		0			0
$259$			0.999571i			0.0621103i
$260$	23.0255	+	21.0751i	1.42798	+	1.30702i
$261$		0			0
$262$	−10.9677	−	9.75702i	−0.677584	−	0.602791i
$263$	−13.1764	−	22.8222i	−0.812493	−	1.40728i	−0.911114	−	0.412154i	$-0.864776\pi$
$263$	−13.1764	−	22.8222i	−0.812493	−	1.40728i	0.0986208	−	0.995125i	$-0.468557\pi$
$264$		0			0
$265$			9.11346i			0.559835i
$266$	−1.19081	+	5.77208i	−0.0730132	+	0.353909i
$267$		0			0
$268$	−17.6733	+	13.1667i	−1.07957	+	0.804283i
$269$	−27.2381	−	15.7259i	−1.66073	−	0.958825i	−0.972365	−	0.233464i	$-0.924994\pi$
$269$	−27.2381	−	15.7259i	−1.66073	−	0.958825i	−0.688369	−	0.725361i	$-0.741673\pi$
$270$		0			0
$271$	17.1939	−	9.92693i	1.04446	−	0.603018i	0.123365	−	0.992361i	$-0.460631\pi$
$271$	17.1939	−	9.92693i	1.04446	−	0.603018i	0.921093	+	0.389343i	$0.127298\pi$
$272$	−6.40881	+	21.4603i	−0.388591	+	1.30122i
$273$		0			0
$274$	−3.95631	+	1.31173i	−0.239009	+	0.0792444i
$275$	−35.3388	−	61.2085i	−2.13101	−	3.69101i
$276$		0			0
$277$	11.0151	+	6.35956i	0.661832	+	0.382109i	0.792975	−	0.609254i	$-0.208531\pi$
$277$	11.0151	+	6.35956i	0.661832	+	0.382109i	−0.131142	+	0.991364i	$0.541865\pi$
$278$	26.5068	−	8.78843i	1.58977	−	0.527095i
$279$		0			0
$280$	−11.2040	−	23.9949i	−0.669566	−	1.43397i
$281$		−	20.9908i		−	1.25221i	−0.779740	−	0.626103i	$-0.784649\pi$
$281$		−	20.9908i		−	1.25221i	0.779740	−	0.626103i	$-0.215351\pi$
$282$		0			0
$283$	20.0094	−	11.5524i	1.18944	−	0.686721i	0.231257	−	0.972893i	$-0.425716\pi$
$283$	20.0094	−	11.5524i	1.18944	−	0.686721i	0.958178	+	0.286172i	$0.0923828\pi$
$284$	−4.57984	+	10.6273i	−0.271763	+	0.630612i
$285$		0			0
$286$	22.9029	−	12.7944i	1.35428	−	0.756548i
$287$	3.03631			0.179227
$288$		0			0
$289$	−7.17561	−	12.4285i	−0.422094	−	0.731089i
$290$	0.244354	−	1.18443i	0.0143490	−	0.0695522i
$291$		0			0
$292$	20.0817	−	2.35418i	1.17519	−	0.137768i
$293$	−5.32829	+	9.22886i	−0.311282	+	0.539156i	−0.978640	−	0.205581i	$-0.934092\pi$
$293$	−5.32829	+	9.22886i	−0.311282	+	0.539156i	0.667358	+	0.744737i	$0.267425\pi$
$294$		0			0
$295$	−9.44938	+	16.3668i	−0.550164	+	0.952912i
$296$	0.113253	−	1.30219i	0.00658270	−	0.0756880i
$297$		0			0
$298$	3.36876	+	10.1605i	0.195147	+	0.588583i
$299$	−6.89977	−	2.39653i	−0.399024	−	0.138595i
$300$		0			0
$301$	−3.19356	−	5.53140i	−0.184073	−	0.318825i
$302$	2.21807	+	1.97323i	0.127635	+	0.113547i
$303$		0			0
$304$	2.20531	−	7.38463i	0.126483	−	0.423538i
$305$	46.0706	+	26.5989i	2.63800	+	1.52305i
$306$		0			0
$307$	7.50490			0.428327			0.214164	−	0.976798i	$-0.431297\pi$
$307$	7.50490			0.428327			0.214164	+	0.976798i	$0.431297\pi$
$308$	−22.1054	+	2.59142i	−1.25957	+	0.147660i
$309$		0			0
$310$	32.5380	+	28.9464i	1.84804	+	1.64405i
$311$	−23.1457			−1.31247			−0.656237	−	0.754555i	$-0.727853\pi$
$311$	−23.1457			−1.31247			−0.656237	+	0.754555i	$0.727853\pi$
$312$		0			0
$313$	−20.9965			−1.18679			−0.593397	−	0.804910i	$-0.702213\pi$
$313$	−20.9965			−1.18679			−0.593397	+	0.804910i	$0.702213\pi$
$314$	8.82365	+	7.84967i	0.497947	+	0.442983i
$315$		0			0
$316$	1.71660	+	14.6430i	0.0965662	+	0.823733i
$317$	1.12069			0.0629444			0.0314722	−	0.999505i	$-0.489980\pi$
$317$	1.12069			0.0629444			0.0314722	+	0.999505i	$0.489980\pi$
$318$		0			0
$319$	−0.880252	−	0.508213i	−0.0492846	−	0.0284545i
$320$	11.8773	+	32.5286i	0.663960	+	1.81841i
$321$		0			0
$322$	4.62979	+	4.11875i	0.258008	+	0.229529i
$323$	5.39407	+	9.34280i	0.300134	+	0.519847i
$324$		0			0
$325$	−37.4680	+	32.3942i	−2.07835	+	1.79691i
$326$	3.39228	+	10.2315i	0.187881	+	0.566668i
$327$		0			0
$328$	−3.95553	−	0.344019i	−0.218408	−	0.0189953i
$329$	−2.38473	+	4.13048i	−0.131475	+	0.227721i
$330$		0			0
$331$	−0.633917	+	1.09798i	−0.0348432	+	0.0603503i	−0.882921	−	0.469521i	$-0.844427\pi$
$331$	−0.633917	+	1.09798i	−0.0348432	+	0.0603503i	0.848078	+	0.529872i	$0.177760\pi$
$332$	0.475443	+	4.05564i	0.0260933	+	0.222582i
$333$		0			0
$334$	3.46271	−	16.7844i	0.189471	−	0.918402i
$335$	−23.8495	−	41.3085i	−1.30304	−	2.25693i
$336$		0			0
$337$	10.2889			0.560475			0.280237	−	0.959931i	$-0.409587\pi$
$337$	10.2889			0.560475			0.280237	+	0.959931i	$0.409587\pi$
$338$	−11.8262	−	14.0762i	−0.643261	−	0.765647i
$339$		0			0
$340$	−44.5162	−	19.1844i	−2.41423	−	1.04042i
$341$	31.6983	−	18.3010i	1.71656	−	0.991056i
$342$		0			0
$343$		−	20.1623i		−	1.08866i
$344$	3.53367	+	7.56784i	0.190523	+	0.408031i
$345$		0			0
$346$	−7.67332	+	2.54412i	−0.412520	+	0.136773i
$347$	10.8544	+	6.26678i	0.582694	+	0.336418i	0.762203	−	0.647338i	$-0.224118\pi$
$347$	10.8544	+	6.26678i	0.582694	+	0.336418i	−0.179509	+	0.983756i	$0.557451\pi$
$348$		0			0
$349$	−12.8044	−	22.1779i	−0.685404	−	1.18715i	−0.973310	−	0.229496i	$-0.926292\pi$
$349$	−12.8044	−	22.1779i	−0.685404	−	1.18715i	0.287906	−	0.957659i	$-0.407041\pi$
$350$	39.8855	−	13.2242i	2.13197	−	0.706863i
$351$		0			0
$352$	29.0913	−	0.871376i	1.55057	−	0.0464445i
$353$	−14.9054	+	8.60561i	−0.793332	+	0.458031i	−0.841134	−	0.540826i	$-0.818112\pi$
$353$	−14.9054	+	8.60561i	−0.793332	+	0.458031i	0.0478020	+	0.998857i	$0.484778\pi$
$354$		0			0
$355$	−21.6903	−	12.5229i	−1.15120	−	0.664646i
$356$	−6.00157	−	8.05575i	−0.318083	−	0.426954i
$357$		0			0
$358$	−2.01374	+	9.76098i	−0.106429	+	0.515884i
$359$			15.0466i			0.794128i	0.917791	+	0.397064i	$0.129971\pi$
$359$			15.0466i			0.794128i	−0.917791	+	0.397064i	$0.870029\pi$
$360$		0			0
$361$	7.64387	+	13.2396i	0.402309	+	0.696820i
$362$	−8.29686	−	7.38103i	−0.436073	−	0.387939i
$363$		0			0
$364$	4.69863	+	14.8728i	0.246275	+	0.779546i
$365$			43.7609i			2.29055i
$366$		0			0
$367$	10.3822	+	17.9826i	0.541949	+	0.938683i	0.998792	+	0.0491356i	$0.0156466\pi$
$367$	10.3822	+	17.9826i	0.541949	+	0.938683i	−0.456843	+	0.889547i	$0.651020\pi$
$368$	−5.56478	−	5.89025i	−0.290084	−	0.307050i
$369$		0			0
$370$	2.77064	+	0.571598i	0.144039	+	0.0297160i
$371$	−2.27693	+	3.94376i	−0.118212	+	0.204750i
$372$		0			0
$373$	−0.716227	−	0.413514i	−0.0370848	−	0.0214109i	0.481343	−	0.876532i	$-0.340149\pi$
$373$	−0.716227	−	0.413514i	−0.0370848	−	0.0214109i	−0.518428	+	0.855121i	$0.673483\pi$
$374$	−27.0788	+	30.4387i	−1.40021	+	1.57395i
$375$		0			0
$376$	3.57469	−	5.11077i	0.184351	−	0.263568i
$377$	−0.233711	+	0.672871i	−0.0120367	+	0.0346546i
$378$		0			0
$379$	−4.60242	−	7.97163i	−0.236410	−	0.409475i	0.723271	−	0.690564i	$-0.242638\pi$
$379$	−4.60242	−	7.97163i	−0.236410	−	0.409475i	−0.959682	+	0.281089i	$0.909304\pi$
$380$	15.3183	+	6.60145i	0.785812	+	0.338647i
$381$		0			0
$382$	9.04974	+	27.2949i	0.463025	+	1.39653i
$383$	18.2780	+	10.5528i	0.933964	+	0.539225i	0.888063	−	0.459721i	$-0.152051\pi$
$383$	18.2780	+	10.5528i	0.933964	+	0.539225i	0.0459012	+	0.998946i	$0.485384\pi$
$384$		0			0
$385$		−	48.1709i		−	2.45501i
$386$	−2.14432	+	10.3939i	−0.109143	+	0.529037i
$387$		0			0
$388$	−6.77427	+	15.7193i	−0.343912	+	0.798028i
$389$		−	23.7270i		−	1.20301i	−0.798871	−	0.601503i	$-0.794569\pi$
$389$		−	23.7270i		−	1.20301i	0.798871	−	0.601503i	$-0.205431\pi$
$390$		0			0
$391$	11.3429			0.573634
$392$	−0.568947	+	6.54176i	−0.0287362	+	0.330409i
$393$		0			0
$394$	−6.25990	−	1.29145i	−0.315369	−	0.0650622i
$395$	−31.9092			−1.60553
$396$		0			0
$397$	−3.36607	+	5.83020i	−0.168938	+	0.292609i	−0.938047	−	0.346509i	$-0.887367\pi$
$397$	−3.36607	+	5.83020i	−0.168938	+	0.292609i	0.769109	+	0.639118i	$0.220700\pi$
$398$	−11.2075	−	33.8029i	−0.561780	−	1.69438i
$399$		0			0
$400$	−53.4590	+	12.7087i	−2.67295	+	0.635433i
$401$	−3.32956	+	1.92232i	−0.166270	+	0.0959962i	−0.580826	−	0.814028i	$-0.697270\pi$
$401$	−3.32956	+	1.92232i	−0.166270	+	0.0959962i	0.414556	+	0.910024i	$0.363937\pi$
$402$		0			0
$403$	−16.7761	−	19.4037i	−0.835679	−	0.966568i
$404$	4.27490	+	5.73809i	0.212684	+	0.285481i
$405$		0			0
$406$	0.401663	−	0.451501i	0.0199342	−	0.0224076i
$407$	1.18882	−	2.05910i	0.0589278	−	0.102066i
$408$		0			0
$409$	28.4778	+	16.4417i	1.40814	+	0.812988i	0.995208	−	0.0977760i	$-0.0311729\pi$
$409$	28.4778	+	16.4417i	1.40814	+	0.812988i	0.412928	+	0.910764i	$0.364506\pi$
$410$	1.73629	−	8.41614i	0.0857494	−	0.415644i
$411$		0			0
$412$	1.09330	+	9.32610i	0.0538630	+	0.459464i
$413$	−8.17825	+	4.72172i	−0.402425	+	0.232340i
$414$		0			0
$415$	−8.83783			−0.433832
$416$	−4.43600	−	19.9078i	−0.217493	−	0.976062i
$417$		0			0
$418$	9.31798	−	10.4741i	0.455758	−	0.512307i
$419$	2.46615	−	1.42383i	0.120480	−	0.0695589i	−0.438549	−	0.898707i	$-0.644507\pi$
$419$	2.46615	−	1.42383i	0.120480	−	0.0695589i	0.559029	+	0.829148i	$0.311174\pi$
$420$		0			0
$421$	−1.04860			−0.0511058			−0.0255529	−	0.999673i	$-0.508135\pi$
$421$	−1.04860			−0.0511058			−0.0255529	+	0.999673i	$0.508135\pi$
$422$	−4.48194	+	21.7248i	−0.218178	+	1.05755i
$423$		0			0
$424$	3.41310	−	4.87974i	0.165755	−	0.236981i
$425$	38.4588	−	66.6126i	1.86552	−	3.23118i
$426$		0			0
$427$	13.2911	+	23.0208i	0.643200	+	1.11406i
$428$	2.56113	+	3.43774i	0.123797	+	0.166169i
$429$		0			0
$430$	−17.1583	+	5.68891i	−0.827449	+	0.274344i
$431$	−19.1618	+	11.0631i	−0.922994	+	0.532891i	−0.884589	−	0.466372i	$-0.845561\pi$
$431$	−19.1618	+	11.0631i	−0.922994	+	0.532891i	−0.0384048	+	0.999262i	$0.512228\pi$
$432$		0			0
$433$	8.37706	−	14.5095i	0.402576	−	0.697281i	−0.591460	−	0.806334i	$-0.701448\pi$
$433$	8.37706	−	14.5095i	0.402576	−	0.697281i	0.994036	+	0.109053i	$0.0347817\pi$
$434$	6.84847	+	20.6557i	0.328737	+	0.991504i
$435$		0			0
$436$	−2.16935	−	18.5050i	−0.103893	−	0.886231i
$437$	−3.90315			−0.186713
$438$		0			0
$439$	−3.46657	−	6.00428i	−0.165451	−	0.286569i	0.771365	−	0.636393i	$-0.219574\pi$
$439$	−3.46657	−	6.00428i	−0.165451	−	0.286569i	−0.936815	+	0.349825i	$0.886241\pi$
$440$	−5.45785	+	62.7544i	−0.260193	+	2.99170i
$441$		0			0
$442$	24.5210	+	14.6237i	1.16635	+	0.695577i
$443$		−	22.9404i		−	1.08993i	−0.838458	−	0.544966i	$-0.816543\pi$
$443$		−	22.9404i		−	1.08993i	0.838458	−	0.544966i	$-0.183457\pi$
$444$		0			0
$445$	18.8291	−	10.8710i	0.892583	−	0.515333i
$446$	−6.50757	+	31.5434i	−0.308142	+	1.49363i
$447$		0			0
$448$	−2.98726	+	17.0439i	−0.141135	+	0.805248i
$449$	−25.8804	−	14.9420i	−1.22137	−	0.705159i	−0.256161	−	0.966634i	$-0.582458\pi$
$449$	−25.8804	−	14.9420i	−1.22137	−	0.705159i	−0.965210	+	0.261475i	$0.915791\pi$
$450$		0			0
$451$	−6.25475	−	3.61118i	−0.294525	−	0.170044i
$452$	35.5901	+	15.3376i	1.67402	+	0.721422i
$453$		0			0
$454$	−1.91170	−	5.76588i	−0.0897205	−	0.270606i
$455$	−33.1547	+	6.35227i	−1.55432	+	0.297799i
$456$		0			0
$457$	−3.45008	+	1.99190i	−0.161388	+	0.0931773i	−0.578519	−	0.815669i	$-0.696369\pi$
$457$	−3.45008	+	1.99190i	−0.161388	+	0.0931773i	0.417131	+	0.908846i	$0.363036\pi$
$458$	18.8330	−	21.1698i	0.880009	−	0.989198i
$459$		0			0
$460$	14.0640	−	10.4777i	0.655738	−	0.488528i
$461$	−0.328552	+	0.569069i	−0.0153022	+	0.0265042i	−0.873575	−	0.486689i	$-0.838204\pi$
$461$	−0.328552	+	0.569069i	−0.0153022	+	0.0265042i	0.858273	+	0.513194i	$0.171538\pi$
$462$		0			0
$463$		−	8.60871i		−	0.400081i	−0.979788	−	0.200040i	$-0.935893\pi$
$463$		−	8.60871i		−	0.400081i	0.979788	−	0.200040i	$-0.0641073\pi$
$464$	−0.574421	+	0.542681i	−0.0266668	+	0.0251934i
$465$		0			0
$466$	6.78575	−	7.62771i	0.314344	−	0.353347i
$467$			19.4449i			0.899804i	0.893078	+	0.449902i	$0.148541\pi$
$467$			19.4449i			0.899804i	−0.893078	+	0.449902i	$0.851459\pi$
$468$		0			0
$469$		−	23.8345i		−	1.10057i
$470$	10.0853	+	8.97208i	0.465201	+	0.413851i
$471$		0			0
$472$	11.1892	−	5.22458i	0.515023	−	0.240481i
$473$			15.1928i			0.698567i
$474$		0			0
$475$	−13.2339	+	22.9218i	−0.607212	+	1.05172i
$476$	−14.4709	−	19.4239i	−0.663272	−	0.890293i
$477$		0			0
$478$	−1.48606	−	1.32203i	−0.0679710	−	0.0604682i
$479$	1.92596	−	1.11196i	0.0879995	−	0.0508066i	−0.455354	−	0.890310i	$-0.650487\pi$
$479$	1.92596	−	1.11196i	0.0879995	−	0.0508066i	0.543354	+	0.839504i	$0.317154\pi$
$480$		0			0
$481$	−1.57399	−	0.546701i	−0.0717679	−	0.0249274i
$482$	7.43381	−	2.46471i	0.338601	−	0.112264i
$483$		0			0
$484$	28.4151	+	12.2456i	1.29160	+	0.556617i
$485$	−32.0832	−	18.5232i	−1.45682	−	0.841097i
$486$		0			0
$487$	−18.3856	−	10.6149i	−0.833129	−	0.481007i	0.0217938	−	0.999762i	$-0.493062\pi$
$487$	−18.3856	−	10.6149i	−0.833129	−	0.481007i	−0.854923	+	0.518755i	$0.826396\pi$
$488$	−14.7066	−	31.4962i	−0.665736	−	1.42576i
$489$		0			0
$490$	−13.9188	−	2.87152i	−0.628788	−	0.129722i
$491$	10.8716	−	6.27672i	0.490628	−	0.283264i	−0.234207	−	0.972187i	$-0.575249\pi$
$491$	10.8716	−	6.27672i	0.490628	−	0.283264i	0.724835	+	0.688922i	$0.241916\pi$
$492$		0			0
$493$		−	1.10617i		−	0.0498192i
$494$	−8.43782	−	5.03209i	−0.379636	−	0.226404i
$495$		0			0
$496$	−6.58148	−	27.6850i	−0.295517	−	1.24309i
$497$	−6.25751	−	10.8383i	−0.280688	−	0.486165i
$498$		0			0
$499$	−21.0316			−0.941506			−0.470753	−	0.882265i	$-0.656018\pi$
$499$	−21.0316			−0.941506			−0.470753	+	0.882265i	$0.656018\pi$
$500$	−8.80704	−	75.1261i	−0.393863	−	3.35974i
$501$		0			0
$502$	30.4047	−	10.0808i	1.35703	−	0.449928i
$503$	13.5799	−	23.5210i	0.605496	−	1.04875i	−0.386477	−	0.922299i	$-0.626308\pi$
$503$	13.5799	−	23.5210i	0.605496	−	1.04875i	0.991973	−	0.126450i	$-0.0403584\pi$
$504$		0			0
$505$	−13.4119	+	7.74336i	−0.596822	+	0.344575i
$506$	−4.63875	−	13.9909i	−0.206218	−	0.621973i
$507$		0			0
$508$	10.6791	−	7.95600i	0.473810	−	0.352990i
$509$	−9.37387	−	16.2360i	−0.415489	−	0.719649i	0.579990	−	0.814623i	$-0.303056\pi$
$509$	−9.37387	−	16.2360i	−0.415489	−	0.719649i	−0.995480	+	0.0949746i	$0.969723\pi$
$510$		0			0
$511$	−10.9333	+	18.9371i	−0.483663	+	0.837728i
$512$	5.82275	−	21.8654i	0.257332	−	0.966323i
$513$		0			0
$514$	−25.6098	−	5.28344i	−1.12960	−	0.233042i
$515$	−20.3229			−0.895536
$516$		0			0
$517$	9.82504	−	5.67249i	0.432105	−	0.249476i
$518$	1.05616	+	0.939579i	0.0464050	+	0.0412827i
$519$		0			0
$520$	43.9118	−	4.51891i	1.92566	−	0.198167i
$521$	−22.1856			−0.971969			−0.485985	−	0.873967i	$-0.661539\pi$
$521$	−22.1856			−0.971969			−0.485985	+	0.873967i	$0.661539\pi$
$522$		0			0
$523$	19.8524	−	11.4618i	0.868084	−	0.501188i	0.00137276	−	0.999999i	$-0.499563\pi$
$523$	19.8524	−	11.4618i	0.868084	−	0.501188i	0.866711	+	0.498811i	$0.166230\pi$
$524$	−20.6188	+	2.41714i	−0.900737	+	0.105593i
$525$		0			0
$526$	−36.4999	−	7.53011i	−1.59147	−	0.328329i
$527$	34.4969	+	19.9168i	1.50271	+	0.867590i
$528$		0			0
$529$	9.44807	−	16.3645i	0.410786	−	0.711502i
$530$	9.62941	+	8.56649i	0.418275	+	0.372105i
$531$		0			0
$532$	4.97952	+	6.68388i	0.215890	+	0.289783i
$533$	−1.66067	+	4.78118i	−0.0719314	+	0.207096i
$534$		0			0
$535$	−8.03518	+	4.63911i	−0.347391	+	0.200566i
$536$	−2.70049	+	31.0503i	−0.116643	+	1.34117i
$537$		0			0
$538$	−42.2195	+	13.9980i	−1.82021	+	0.603498i
$539$	−5.97226	+	10.3443i	−0.257244	+	0.445559i
$540$		0			0
$541$	−14.3408			−0.616560			−0.308280	−	0.951296i	$-0.599753\pi$
$541$	−14.3408			−0.616560			−0.308280	+	0.951296i	$0.599753\pi$
$542$	5.67308	−	27.4985i	0.243680	−	1.18116i
$543$		0			0
$544$	16.6511	+	26.9440i	0.713911	+	1.15521i
$545$	40.3252			1.72734
$546$		0			0
$547$			22.9812i			0.982605i	0.870989	+	0.491302i	$0.163479\pi$
$547$			22.9812i			0.982605i	−0.870989	+	0.491302i	$0.836521\pi$
$548$	−2.33287	+	5.41329i	−0.0996552	+	0.231244i
$549$		0			0
$550$	−97.8916	−	20.1955i	−4.17411	−	0.861140i
$551$			0.380638i			0.0162157i
$552$		0			0
$553$	−13.8084	−	7.97228i	−0.587193	−	0.339016i
$554$	17.0736	−	5.66081i	0.725387	−	0.240505i
$555$		0			0
$556$	15.6300	−	36.2684i	0.662858	−	1.53812i
$557$	−1.79684	−	3.11221i	−0.0761344	−	0.131869i	0.825445	−	0.564483i	$-0.190924\pi$
$557$	−1.79684	−	3.11221i	−0.0761344	−	0.131869i	−0.901579	+	0.432614i	$0.857591\pi$
$558$		0			0
$559$	10.4568	−	2.00347i	0.442275	−	0.0847378i
$560$	−35.8848	−	10.7165i	−1.51641	−	0.452853i
$561$		0			0
$562$	−22.1792	−	19.7310i	−0.935572	−	0.832301i
$563$	37.1235	+	21.4332i	1.56457	+	0.903303i	0.996785	+	0.0801243i	$0.0255317\pi$
$563$	37.1235	+	21.4332i	1.56457	+	0.903303i	0.567782	+	0.823179i	$0.307802\pi$
$564$		0			0
$565$	−41.9385	+	72.6396i	−1.76437	+	3.05597i
$566$	6.60203	−	32.0013i	0.277504	−	1.34512i
$567$		0			0
$568$	6.92394	+	14.8286i	0.290522	+	0.622192i
$569$	1.88614	+	3.26690i	0.0790712	+	0.136955i	0.902849	−	0.429957i	$-0.141471\pi$
$569$	1.88614	+	3.26690i	0.0790712	+	0.136955i	−0.823778	+	0.566912i	$0.808138\pi$
$570$		0			0
$571$		−	33.2710i		−	1.39235i	−0.717872	−	0.696175i	$-0.754884\pi$
$571$		−	33.2710i		−	1.39235i	0.717872	−	0.696175i	$-0.245116\pi$
$572$	8.00961	−	36.2260i	0.334899	−	1.51469i
$573$		0			0
$574$	2.85407	−	3.20820i	0.119127	−	0.133908i
$575$	13.9144	+	24.1005i	0.580271	+	1.00506i
$576$		0			0
$577$			35.1086i			1.46159i	0.682596	+	0.730796i	$0.260851\pi$
$577$			35.1086i			1.46159i	−0.682596	+	0.730796i	$0.739149\pi$
$578$	−19.8771	−	4.10074i	−0.826778	−	0.170568i
$579$		0			0
$580$	−1.02180	−	1.37153i	−0.0424278	−	0.0569498i
$581$	−3.82448	−	2.20807i	−0.158666	−	0.0916060i
$582$		0			0
$583$	9.38090	−	5.41607i	0.388517	−	0.224311i
$584$	16.3890	−	23.4315i	0.678180	−	0.969601i
$585$		0			0
$586$	4.74285	+	14.3049i	0.195925	+	0.590930i
$587$	−0.0738353	−	0.127887i	−0.00304751	−	0.00527844i	0.864498	−	0.502637i	$-0.167637\pi$
$587$	−0.0738353	−	0.127887i	−0.00304751	−	0.00527844i	−0.867545	+	0.497358i	$0.834303\pi$
$588$		0			0
$589$	−11.8706	−	6.85349i	−0.489119	−	0.282393i
$590$	8.41114	+	25.3688i	0.346281	+	1.04442i
$591$		0			0
$592$	−1.26945	−	1.34370i	−0.0521741	−	0.0552256i
$593$			17.5025i			0.718742i	0.933195	+	0.359371i	$0.117009\pi$
$593$			17.5025i			0.718742i	−0.933195	+	0.359371i	$0.882991\pi$
$594$		0			0
$595$	45.4004	−	26.2119i	1.86123	−	1.07458i
$596$	13.9023	+	5.99123i	0.569461	+	0.245411i
$597$		0			0
$598$	−9.01787	+	5.03770i	−0.368768	+	0.206007i
$599$	41.9746			1.71504			0.857518	−	0.514454i	$-0.172005\pi$
$599$	41.9746			1.71504			0.857518	+	0.514454i	$0.172005\pi$
$600$		0			0
$601$	−20.7461	−	35.9333i	−0.846250	−	1.46575i	−0.884531	−	0.466481i	$-0.845521\pi$
$601$	−20.7461	−	35.9333i	−0.846250	−	1.46575i	0.0382808	−	0.999267i	$-0.487812\pi$
$602$	−8.84644	−	1.82507i	−0.360554	−	0.0743841i
$603$		0			0
$604$	4.16989	−	0.488836i	0.169670	−	0.0198905i
$605$	−33.4837	+	57.9955i	−1.36131	+	2.35785i
$606$		0			0
$607$	4.37951	−	7.58553i	0.177759	−	0.307887i	−0.763354	−	0.645981i	$-0.776449\pi$
$607$	4.37951	−	7.58553i	0.177759	−	0.307887i	0.941113	+	0.338094i	$0.109782\pi$
$608$	−5.72975	−	9.27158i	−0.232372	−	0.376012i
$609$		0			0
$610$	71.4103	−	23.6764i	2.89132	−	0.958628i
$611$	−5.19984	−	6.01427i	−0.210363	−	0.243311i
$612$		0			0
$613$	−3.97286	−	6.88119i	−0.160462	−	0.277929i	0.774572	−	0.632485i	$-0.217965\pi$
$613$	−3.97286	−	6.88119i	−0.160462	−	0.277929i	−0.935035	+	0.354557i	$0.884632\pi$
$614$	7.05447	−	7.92978i	0.284695	−	0.320020i
$615$		0			0
$616$	−18.0406	+	25.7927i	−0.726875	+	1.03922i
$617$	−29.8107	−	17.2112i	−1.20013	−	0.692898i	−0.239550	−	0.970884i	$-0.577000\pi$
$617$	−29.8107	−	17.2112i	−1.20013	−	0.692898i	−0.960585	+	0.277986i	$0.910333\pi$
$618$		0			0
$619$	−31.7543			−1.27631			−0.638157	−	0.769906i	$-0.720303\pi$
$619$	−31.7543			−1.27631			−0.638157	+	0.769906i	$0.720303\pi$
$620$	61.1704	−	7.17101i	2.45666	−	0.287995i
$621$		0			0
$622$	−21.7566	+	24.4561i	−0.872360	+	0.980600i
$623$	10.8641			0.435262
$624$		0			0
$625$	95.0247			3.80099
$626$	−19.7364	+	22.1852i	−0.788823	+	0.886699i
$627$		0			0
$628$	16.5881	−	1.94463i	0.661939	−	0.0775992i
$629$	2.58757			0.103173
$630$		0			0
$631$	−1.82187	−	1.05185i	−0.0725273	−	0.0418737i	0.463298	−	0.886203i	$-0.346666\pi$
$631$	−1.82187	−	1.05185i	−0.0725273	−	0.0418737i	−0.535825	+	0.844329i	$0.679999\pi$
$632$	17.0856	+	11.9504i	0.679627	+	0.475360i
$633$		0			0
$634$	1.05343	−	1.18414i	0.0418371	−	0.0470282i
$635$	14.4111	+	24.9608i	0.571888	+	0.990539i
$636$		0			0
$637$	7.90723	+	2.74645i	0.313296	+	0.108818i
$638$	−1.36441	+	0.452374i	−0.0540174	+	0.0179097i
$639$		0			0
$640$	45.5346	+	18.0266i	1.79991	+	0.712566i
$641$	−4.71373	+	8.16441i	−0.186181	+	0.322475i	−0.943974	−	0.330020i	$-0.892944\pi$
$641$	−4.71373	+	8.16441i	−0.186181	+	0.322475i	0.757793	+	0.652495i	$0.226278\pi$
$642$		0			0
$643$	21.6550	−	37.5076i	0.853991	−	1.47916i	−0.0235861	−	0.999722i	$-0.507508\pi$
$643$	21.6550	−	37.5076i	0.853991	−	1.47916i	0.877578	−	0.479435i	$-0.159158\pi$
$644$	8.70385	−	1.02035i	0.342980	−	0.0402076i
$645$		0			0
$646$	14.9421	+	3.08262i	0.587887	+	0.121284i
$647$	6.58305	+	11.4022i	0.258807	+	0.448266i	0.965922	−	0.258832i	$-0.0833375\pi$
$647$	6.58305	+	11.4022i	0.258807	+	0.448266i	−0.707116	+	0.707098i	$0.750004\pi$
$648$		0			0
$649$	22.4628			0.881742
$650$	−0.991094	+	70.0393i	−0.0388739	+	2.74717i
$651$		0			0
$652$	13.9994	+	6.03307i	0.548258	+	0.236273i
$653$	31.8783	−	18.4049i	1.24749	−	0.720240i	0.276884	−	0.960903i	$-0.410698\pi$
$653$	31.8783	−	18.4049i	1.24749	−	0.720240i	0.970609	+	0.240663i	$0.0773649\pi$
$654$		0			0
$655$		−	44.9314i		−	1.75562i
$656$	−4.08163	+	3.85610i	−0.159361	+	0.150555i
$657$		0			0
$658$	2.12271	+	6.40232i	0.0827520	+	0.249588i
$659$	−36.8969	−	21.3024i	−1.43730	−	0.829824i	−0.439636	−	0.898176i	$-0.644893\pi$
$659$	−36.8969	−	21.3024i	−1.43730	−	0.829824i	−0.997661	+	0.0683515i	$0.978226\pi$
$660$		0			0
$661$	−4.76553	−	8.25413i	−0.185357	−	0.321049i	0.758339	−	0.651860i	$-0.226011\pi$
$661$	−4.76553	−	8.25413i	−0.185357	−	0.321049i	−0.943697	+	0.330811i	$0.892678\pi$
$662$	0.564266	+	1.70188i	0.0219308	+	0.0661456i
$663$		0			0
$664$	4.73215	+	3.30987i	0.183643	+	0.128448i
$665$	−15.6225	+	9.01967i	−0.605816	+	0.349768i
$666$		0			0
$667$	0.346593	+	0.200106i	0.0134201	+	0.00774813i
$668$	−14.4798	−	19.4358i	−0.560238	−	0.751993i
$669$		0			0
$670$	−66.0653	−	13.6296i	−2.55232	−	0.526557i
$671$		−	63.2301i		−	2.44097i
$672$		0			0
$673$	−11.8396	−	20.5068i	−0.456383	−	0.790478i	0.542384	−	0.840131i	$-0.317522\pi$
$673$	−11.8396	−	20.5068i	−0.456383	−	0.790478i	−0.998767	+	0.0496527i	$0.984189\pi$
$674$	9.67143	−	10.8714i	0.372530	−	0.418752i
$675$		0			0
$676$	−25.9896	−	0.735681i	−0.999600	−	0.0282954i
$677$			21.0758i			0.810007i	0.914315	+	0.405004i	$0.132730\pi$
$677$			21.0758i			0.810007i	−0.914315	+	0.405004i	$0.867270\pi$
$678$		0			0
$679$	−9.25580	−	16.0315i	−0.355205	−	0.615233i
$680$	−62.1150	+	29.0035i	−2.38200	+	1.11223i
$681$		0			0
$682$	10.4587	−	50.6955i	0.400486	−	1.94123i
$683$	5.53695	−	9.59027i	0.211865	−	0.366962i	−0.740433	−	0.672130i	$-0.765379\pi$
$683$	5.53695	−	9.59027i	0.211865	−	0.366962i	0.952298	+	0.305169i	$0.0987128\pi$
$684$		0			0
$685$	−11.0486	−	6.37888i	−0.422143	−	0.243725i
$686$	−21.3037	−	18.9522i	−0.813380	−	0.723597i
$687$		0			0
$688$	11.3179	+	3.37991i	0.431490	+	0.128858i
$689$	−4.96478	−	5.74240i	−0.189143	−	0.218768i
$690$		0			0
$691$	17.4252	+	30.1813i	0.662885	+	1.14815i	0.979854	+	0.199714i	$0.0640013\pi$
$691$	17.4252	+	30.1813i	0.662885	+	1.14815i	−0.316970	+	0.948436i	$0.602665\pi$
$692$	−4.52464	+	10.4992i	−0.172001	+	0.399118i
$693$		0			0
$694$	16.8245	−	5.57823i	0.638649	−	0.211747i
$695$	74.0240	+	42.7378i	2.80789	+	1.62114i
$696$		0			0
$697$		−	7.86002i		−	0.297719i
$698$	−35.4694	−	7.31751i	−1.34254	−	0.276972i
$699$		0			0
$700$	23.5188	−	54.5741i	0.888928	−	2.06271i
$701$		−	35.7266i		−	1.34937i	−0.738104	−	0.674687i	$-0.764279\pi$
$701$		−	35.7266i		−	1.34937i	0.738104	−	0.674687i	$-0.235721\pi$
$702$		0			0
$703$	−0.890397			−0.0335819
$704$	26.4246	−	31.5574i	0.995915	−	1.18936i
$705$		0			0
$706$	−4.91797	+	23.8383i	−0.185090	+	0.897168i
$707$	−7.73849			−0.291036
$708$		0			0
$709$	11.0711	−	19.1758i	0.415785	−	0.720160i	−0.579726	−	0.814812i	$-0.696840\pi$
$709$	11.0711	−	19.1758i	0.415785	−	0.720160i	0.995510	+	0.0946513i	$0.0301736\pi$
$710$	−33.6203	+	11.1470i	−1.26175	+	0.418338i
$711$		0			0
$712$	−14.1532	−	1.23092i	−0.530413	−	0.0461309i
$713$	−12.4810	+	7.20591i	−0.467417	+	0.269864i
$714$		0			0
$715$	75.8532	+	26.3464i	2.83675	+	0.985299i
$716$	8.42070	+	11.3029i	0.314697	+	0.422409i
$717$		0			0
$718$	15.8984	+	14.1435i	0.593324	+	0.527832i
$719$	20.9483	−	36.2834i	0.781238	−	1.35314i	−0.149983	−	0.988689i	$-0.547922\pi$
$719$	20.9483	−	36.2834i	0.781238	−	1.35314i	0.931221	−	0.364455i	$-0.118745\pi$
$720$		0			0
$721$	−8.79455	−	5.07754i	−0.327526	−	0.189097i
$722$	21.1742	+	4.36835i	0.788023	+	0.162573i
$723$		0			0
$724$	−15.5978	+	1.82853i	−0.579688	+	0.0679569i
$725$	2.35029	−	1.35694i	0.0872877	−	0.0503956i
$726$		0			0
$727$	−26.1552			−0.970042			−0.485021	−	0.874503i	$-0.661188\pi$
$727$	−26.1552			−0.970042			−0.485021	+	0.874503i	$0.661188\pi$
$728$	20.1314	+	9.01553i	0.746121	+	0.334138i
$729$		0			0
$730$	46.2384	+	41.1345i	1.71136	+	1.52246i
$731$	−14.3190	+	8.26709i	−0.529608	+	0.305769i
$732$		0			0
$733$	−23.0609			−0.851774			−0.425887	−	0.904776i	$-0.640038\pi$
$733$	−23.0609			−0.851774			−0.425887	+	0.904776i	$0.640038\pi$
$734$	28.7598	+	5.93328i	1.06154	+	0.219002i
$735$		0			0
$736$	−11.4545	+	0.343099i	−0.422219	+	0.0126468i
$737$	−28.3472	+	49.0988i	−1.04418	+	1.80858i
$738$		0			0
$739$	6.46731	+	11.2017i	0.237904	+	0.412061i	0.960113	−	0.279614i	$-0.0902064\pi$
$739$	6.46731	+	11.2017i	0.237904	+	0.412061i	−0.722209	+	0.691675i	$0.756873\pi$
$740$	3.20832	−	2.39021i	0.117940	−	0.0878659i
$741$		0			0
$742$	2.02676	+	6.11290i	0.0744046	+	0.224412i
$743$	19.2118	−	11.0919i	0.704813	−	0.406924i	−0.104324	−	0.994543i	$-0.533268\pi$
$743$	19.2118	−	11.0919i	0.704813	−	0.406924i	0.809138	+	0.587619i	$0.199935\pi$
$744$		0			0
$745$	−16.3821	+	28.3747i	−0.600195	+	1.03957i
$746$	−1.11017	+	0.368080i	−0.0406460	+	0.0134763i
$747$		0			0
$748$	6.70834	+	57.2237i	0.245281	+	2.09231i
$749$	−4.63619			−0.169403
$750$		0			0
$751$	5.27970	+	9.14471i	0.192659	+	0.333695i	0.946131	−	0.323785i	$-0.104956\pi$
$751$	5.27970	+	9.14471i	0.192659	+	0.333695i	−0.753472	+	0.657480i	$0.771622\pi$
$752$	−2.03996	−	8.58110i	−0.0743897	−	0.312921i
$753$		0			0
$754$	0.491280	+	0.879429i	0.0178914	+	0.0320269i
$755$			9.08679i			0.330702i
$756$		0			0
$757$	31.1972	−	18.0117i	1.13388	−	0.654647i	0.188973	−	0.981982i	$-0.439484\pi$
$757$	31.1972	−	18.0117i	1.13388	−	0.654647i	0.944908	+	0.327336i	$0.106151\pi$
$758$	−12.7491	−	2.63021i	−0.463069	−	0.0955335i
$759$		0			0
$760$	21.3741	−	9.98027i	0.775321	−	0.362023i
$761$	−6.84148	−	3.94993i	−0.248004	−	0.143185i	0.370846	−	0.928694i	$-0.379068\pi$
$761$	−6.84148	−	3.94993i	−0.248004	−	0.143185i	−0.618850	+	0.785509i	$0.712401\pi$
$762$		0			0
$763$	17.4503	+	10.0750i	0.631745	+	0.364738i
$764$	37.3468	+	16.0947i	1.35116	+	0.582286i
$765$		0			0
$766$	28.3313	−	9.39335i	1.02365	−	0.339396i
$767$	−2.96216	−	15.4605i	−0.106957	−	0.558247i
$768$		0			0
$769$	−38.3137	+	22.1204i	−1.38163	+	0.797682i	−0.992352	−	0.123440i	$-0.960607\pi$
$769$	−38.3137	+	22.1204i	−1.38163	+	0.797682i	−0.389274	+	0.921122i	$0.627274\pi$
$770$	−50.8980	−	45.2798i	−1.83424	−	1.63177i
$771$		0			0
$772$	8.96674	+	12.0358i	0.322720	+	0.433179i
$773$	−0.173392	+	0.300323i	−0.00623647	+	0.0108019i	−0.869127	−	0.494589i	$-0.835318\pi$
$773$	−0.173392	+	0.300323i	−0.00623647	+	0.0108019i	0.862890	+	0.505391i	$0.168652\pi$
$774$		0			0
$775$			97.7284i			3.51051i
$776$	10.2416	+	21.9337i	0.367650	+	0.787373i
$777$		0			0
$778$	−25.0703	−	22.3030i	−0.898812	−	0.799600i
$779$			2.70468i			0.0969052i
$780$		0			0
$781$			29.7691i			1.06522i
$782$	10.6621	−	11.9850i	0.381276	−	0.428584i
$783$		0			0
$784$	6.37731	+	6.75030i	0.227761	+	0.241082i
$785$			36.1480i			1.29018i
$786$		0			0
$787$	19.9378	−	34.5333i	0.710706	−	1.23098i	−0.253887	−	0.967234i	$-0.581709\pi$
$787$	19.9378	−	34.5333i	0.710706	−	1.23098i	0.964593	−	0.263744i	$-0.0849576\pi$
$788$	−7.24875	+	5.40035i	−0.258226	+	0.192380i
$789$		0			0
$790$	−29.9941	+	33.7157i	−1.06714	+	1.19955i
$791$	−36.2970	+	20.9561i	−1.29057	+	0.745112i
$792$		0			0
$793$	−43.5195	+	8.33813i	−1.54542	+	0.296096i
$794$	2.99622	+	9.03691i	0.106332	+	0.320708i
$795$		0			0
$796$	−46.2514	−	19.9321i	−1.63934	−	0.706476i
$797$	−29.9292	−	17.2796i	−1.06015	−	0.612076i	−0.134674	−	0.990890i	$-0.542999\pi$
$797$	−29.9292	−	17.2796i	−1.06015	−	0.612076i	−0.925473	+	0.378814i	$0.876332\pi$
$798$		0			0
$799$	10.6925	+	6.17331i	0.378273	+	0.218396i
$800$	−36.8224	+	68.4314i	−1.30187	+	2.41942i
$801$		0			0
$802$	−1.09858	+	5.32501i	−0.0387921	+	0.188033i
$803$	45.0451	−	26.0068i	1.58961	−	0.917760i
$804$		0			0
$805$			18.9670i			0.668498i
$806$	−36.2715	−	0.513262i	−1.27761	−	0.0180789i
$807$		0			0
$808$	10.0813	+	0.876785i	0.354658	+	0.0308452i
$809$	2.06348	+	3.57406i	0.0725483	+	0.125657i	0.900017	−	0.435854i	$-0.143554\pi$
$809$	2.06348	+	3.57406i	0.0725483	+	0.125657i	−0.827469	+	0.561511i	$0.810220\pi$
$810$		0			0
$811$	−29.5522			−1.03772			−0.518859	−	0.854860i	$-0.673643\pi$
$811$	−29.5522			−1.03772			−0.518859	+	0.854860i	$0.673643\pi$
$812$	−0.0995056	−	0.848806i	−0.00349196	−	0.0297872i
$813$		0			0
$814$	−1.05820	−	3.19165i	−0.0370900	−	0.111867i
$815$	−16.4965	+	28.5728i	−0.577848	+	1.00086i
$816$		0			0
$817$	4.92726	−	2.84475i	0.172383	−	0.0995253i
$818$	44.1411	−	14.6352i	1.54336	−	0.511706i
$819$		0			0
$820$	−7.26053	−	9.74562i	−0.253549	−	0.340332i
$821$	20.9185	+	36.2319i	0.730061	+	1.26450i	0.956857	+	0.290560i	$0.0938416\pi$
$821$	20.9185	+	36.2319i	0.730061	+	1.26450i	−0.226796	+	0.973942i	$0.572825\pi$
$822$		0			0
$823$	13.3260	−	23.0813i	0.464515	−	0.804563i	−0.534665	−	0.845064i	$-0.679562\pi$
$823$	13.3260	−	23.0813i	0.464515	−	0.804563i	0.999179	+	0.0405014i	$0.0128955\pi$
$824$	10.8818	+	7.61118i	0.379084	+	0.265148i
$825$		0			0
$826$	−2.69838	+	13.0796i	−0.0938888	+	0.455097i
$827$	45.2843			1.57469			0.787344	−	0.616514i	$-0.211456\pi$
$827$	45.2843			1.57469			0.787344	+	0.616514i	$0.211456\pi$
$828$		0			0
$829$	−40.4769	+	23.3693i	−1.40582	+	0.811651i	−0.994982	−	0.100057i	$-0.968097\pi$
$829$	−40.4769	+	23.3693i	−1.40582	+	0.811651i	−0.410839	+	0.911708i	$0.634764\pi$
$830$	−8.30740	+	9.33817i	−0.288354	+	0.324133i
$831$		0			0
$832$	−25.2047	−	14.0259i	−0.873814	−	0.486260i
$833$	−12.9991			−0.450392
$834$		0			0
$835$	45.4281	−	26.2279i	1.57211	−	0.907655i
$836$	−2.30838	−	19.6910i	−0.0798370	−	0.681028i
$837$		0			0
$838$	0.813698	−	3.94415i	0.0281087	−	0.136248i
$839$	7.87045	+	4.54401i	0.271718	+	0.156877i	0.629668	−	0.776864i	$-0.283191\pi$
$839$	7.87045	+	4.54401i	0.271718	+	0.156877i	−0.357950	+	0.933741i	$0.616524\pi$
$840$		0			0
$841$	−14.4805	+	25.0809i	−0.499327	+	0.864860i
$842$	−0.985670	+	1.10797i	−0.0339684	+	0.0381832i
$843$		0			0
$844$	18.7418	+	25.1566i	0.645120	+	0.865928i
$845$	8.13075	−	55.6819i	0.279706	−	1.91552i
$846$		0			0
$847$	−28.9795	+	16.7313i	−0.995747	+	0.574895i
$848$	−1.94775	−	8.19319i	−0.0668858	−	0.281355i
$849$		0			0
$850$	−34.2332	−	103.251i	−1.17419	−	3.54147i
$851$	−0.468092	+	0.810758i	−0.0160460	+	0.0277924i
$852$		0			0
$853$	−42.5016			−1.45523			−0.727613	−	0.685988i	$-0.759370\pi$
$853$	−42.5016			−1.45523			−0.727613	+	0.685988i	$0.759370\pi$
$854$	36.8175	+	7.59563i	1.25987	+	0.259917i
$855$		0			0
$856$	6.03978	+	0.525289i	0.206435	+	0.0179540i
$857$	−44.3414			−1.51467			−0.757337	−	0.653024i	$-0.773500\pi$
$857$	−44.3414			−1.51467			−0.757337	+	0.653024i	$0.773500\pi$
$858$		0			0
$859$		−	43.6352i		−	1.48881i	−0.667727	−	0.744406i	$-0.732733\pi$
$859$		−	43.6352i		−	1.48881i	0.667727	−	0.744406i	$-0.267267\pi$
$860$	−10.1176	+	23.4772i	−0.345006	+	0.800567i
$861$		0			0
$862$	−6.32238	+	30.6458i	−0.215341	+	1.04380i
$863$			35.7395i			1.21659i	0.793712	+	0.608293i	$0.208146\pi$
$863$			35.7395i			1.21659i	−0.793712	+	0.608293i	$0.791854\pi$
$864$		0			0
$865$	−21.4288	−	12.3719i	−0.728603	−	0.420659i
$866$	−7.45664	−	22.4900i	−0.253387	−	0.764240i
$867$		0			0
$868$	28.2625	+	12.1798i	0.959292	+	0.413409i
$869$	18.9634	+	32.8456i	0.643290	+	1.11421i
$870$		0			0
$871$	37.5314	+	13.0359i	1.27170	+	0.441706i
$872$	−21.5918	−	15.1023i	−0.731192	−	0.511427i
$873$		0			0
$874$	−3.66890	+	4.12413i	−0.124102	+	0.139501i
$875$	70.8442	+	40.9019i	2.39497	+	1.38274i
$876$		0			0
$877$	−5.98460	+	10.3656i	−0.202085	+	0.350022i	−0.949200	−	0.314673i	$-0.898105\pi$
$877$	−5.98460	+	10.3656i	−0.202085	+	0.350022i	0.747115	+	0.664695i	$0.231439\pi$
$878$	−9.60273	−	1.98109i	−0.324076	−	0.0668586i
$879$		0			0
$880$	61.1769	+	64.7549i	2.06227	+	2.18289i
$881$	−4.67299	−	8.09386i	−0.157437	−	0.272689i	0.776507	−	0.630109i	$-0.216990\pi$
$881$	−4.67299	−	8.09386i	−0.157437	−	0.272689i	−0.933944	+	0.357420i	$0.883656\pi$
$882$		0			0
$883$		−	12.2815i		−	0.413307i	−0.978414	−	0.206653i	$-0.933743\pi$
$883$		−	12.2815i		−	0.413307i	0.978414	−	0.206653i	$-0.0662573\pi$
$884$	38.5009	−	12.1632i	1.29493	−	0.409094i
$885$		0			0
$886$	−24.2392	−	21.5636i	−0.814330	−	0.724443i
$887$	5.70155	+	9.87537i	0.191439	+	0.331582i	0.945727	−	0.324961i	$-0.105351\pi$
$887$	5.70155	+	9.87537i	0.191439	+	0.331582i	−0.754288	+	0.656543i	$0.772018\pi$
$888$		0			0
$889$			14.4021i			0.483030i
$890$	6.21258	−	30.1136i	0.208246	−	1.00941i
$891$		0			0
$892$	27.2122	+	36.5263i	0.911133	+	1.22299i
$893$	−3.67935	−	2.12427i	−0.123125	−	0.0710860i
$894$		0			0
$895$	−26.4187	+	15.2529i	−0.883081	+	0.509847i
$896$	15.2008	+	19.1773i	0.507824	+	0.640670i
$897$		0			0
$898$	−40.1151	+	13.3003i	−1.33866	+	0.443837i
$899$	0.702726	+	1.21716i	0.0234372	+	0.0405944i
$900$		0			0
$901$	10.2091	+	5.89424i	0.340115	+	0.196366i
$902$	−9.69498	+	3.21441i	−0.322808	+	0.107028i
$903$		0			0
$904$	49.6601	−	23.1879i	1.65167	−	0.771218i
$905$		−	33.9899i		−	1.12986i
$906$		0			0
$907$	−4.78402	+	2.76206i	−0.158851	+	0.0917126i	−0.577318	−	0.816519i	$-0.695901\pi$
$907$	−4.78402	+	2.76206i	−0.158851	+	0.0917126i	0.418467	+	0.908232i	$0.362567\pi$
$908$	−7.88927	−	3.39990i	−0.261815	−	0.112830i
$909$		0			0
$910$	−24.4529	+	41.0027i	−0.810606	+	1.35923i
$911$	−33.5295			−1.11088			−0.555441	−	0.831556i	$-0.687451\pi$
$911$	−33.5295			−1.11088			−0.555441	+	0.831556i	$0.687451\pi$
$912$		0			0
$913$	5.25226	+	9.09718i	0.173824	+	0.301073i
$914$	−1.13834	+	5.51775i	−0.0376530	+	0.182511i
$915$		0			0
$916$	−4.66557	−	39.7984i	−0.154155	−	1.31498i
$917$	11.2258	−	19.4436i	0.370708	−	0.642085i
$918$		0			0
$919$	13.6169	−	23.5851i	0.449179	−	0.778001i	−0.549154	−	0.835721i	$-0.685050\pi$
$919$	13.6169	−	23.5851i	0.449179	−	0.778001i	0.998333	+	0.0577205i	$0.0183832\pi$
$920$	2.14899	−	24.7091i	0.0708501	−	0.814636i
$921$		0			0
$922$	0.292453	+	0.882068i	0.00963143	+	0.0290494i
$923$	20.4892	−	3.92564i	0.674411	−	0.129214i
$924$		0			0
$925$	3.17419	+	5.49786i	0.104367	+	0.180768i
$926$	−9.09608	−	8.09204i	−0.298916	−	0.265921i
$927$		0			0
$928$	0.0334592	+	1.11705i	0.00109835	+	0.0366690i
$929$	−28.3942	−	16.3934i	−0.931582	−	0.537849i	−0.0442707	−	0.999020i	$-0.514096\pi$
$929$	−28.3942	−	16.3934i	−0.931582	−	0.537849i	−0.887312	+	0.461170i	$0.847430\pi$
$930$		0			0
$931$	4.47306			0.146599
$932$	−1.68106	−	14.3398i	−0.0550649	−	0.469717i
$933$		0			0
$934$	20.5458	+	18.2779i	0.672279	+	0.598071i
$935$	−124.699			−4.07809
$936$		0			0
$937$	39.0993			1.27732			0.638659	−	0.769490i	$-0.279489\pi$
$937$	39.0993			1.27732			0.638659	+	0.769490i	$0.279489\pi$
$938$	−25.1839	−	22.4040i	−0.822282	−	0.731517i
$939$		0			0
$940$	18.9600	−	2.22269i	0.618408	−	0.0724960i
$941$	16.6878			0.544007			0.272003	−	0.962296i	$-0.412314\pi$
$941$	16.6878			0.544007			0.272003	+	0.962296i	$0.412314\pi$
$942$		0			0
$943$	2.46277	+	1.42188i	0.0801988	+	0.0463028i
$944$	4.99725	−	16.7336i	0.162647	−	0.544634i
$945$		0			0
$946$	16.0529	+	14.2810i	0.521926	+	0.464315i
$947$	−12.4326	−	21.5339i	−0.404005	−	0.699758i	0.590200	−	0.807257i	$-0.299049\pi$
$947$	−12.4326	−	21.5339i	−0.404005	−	0.699758i	−0.994205	+	0.107499i	$0.965716\pi$
$948$		0			0
$949$	−23.8398	−	27.5738i	−0.773874	−	0.895083i
$950$	11.7798	+	35.5292i	0.382188	+	1.15272i
$951$		0			0
$952$	−34.1260	−	2.96799i	−1.10603	−	0.0961930i
$953$	28.8903	−	50.0395i	0.935850	−	1.62094i	0.162739	−	0.986669i	$-0.447967\pi$
$953$	28.8903	−	50.0395i	0.935850	−	1.62094i	0.773111	−	0.634270i	$-0.218699\pi$
$954$		0			0
$955$	−44.0085	+	76.2250i	−1.42408	+	2.46658i
$956$	−2.79375	+	0.327511i	−0.0903563	+	0.0105925i
$957$		0			0
$958$	0.635465	−	3.08022i	0.0205309	−	0.0995174i
$959$	−3.18744	−	5.52080i	−0.102928	−	0.178276i
$960$		0			0
$961$	−19.6110			−0.632614
$962$	−2.05718	+	1.14921i	−0.0663261	+	0.0370521i
$963$		0			0
$964$	4.38340	−	10.1714i	0.141180	−	0.327600i
$965$	−28.1319	+	16.2419i	−0.905596	+	0.522846i
$966$		0			0
$967$			38.2787i			1.23096i	0.788153	+	0.615480i	$0.211038\pi$
$967$			38.2787i			1.23096i	−0.788153	+	0.615480i	$0.788962\pi$
$968$	39.6486	−	18.5132i	1.27435	−	0.595037i
$969$		0			0
$970$	−49.7296	+	16.4880i	−1.59672	+	0.529399i
$971$	27.6258	+	15.9498i	0.886554	+	0.511852i	0.872814	−	0.488053i	$-0.162293\pi$
$971$	27.6258	+	15.9498i	0.886554	+	0.511852i	0.0137404	+	0.999906i	$0.495626\pi$
$972$		0			0
$973$	21.3555	+	36.9887i	0.684625	+	1.18580i
$974$	−28.4980	+	9.44861i	−0.913133	+	0.302753i
$975$		0			0
$976$	−47.1032	−	14.0667i	−1.50774	−	0.450263i
$977$	35.5820	−	20.5433i	1.13837	−	0.657237i	0.192342	−	0.981328i	$-0.438392\pi$
$977$	35.5820	−	20.5433i	1.13837	−	0.657237i	0.946026	+	0.324091i	$0.105058\pi$
$978$		0			0
$979$	−22.3800	−	12.9211i	−0.715267	−	0.412959i
$980$	−16.1175	+	12.0076i	−0.514856	+	0.383570i
$981$		0			0
$982$	3.58704	−	17.3871i	0.114467	−	0.554844i
$983$			31.6606i			1.00982i	0.863173	+	0.504909i	$0.168474\pi$
$983$			31.6606i			1.00982i	−0.863173	+	0.504909i	$0.831526\pi$
$984$		0			0
$985$	−9.78195	−	16.9428i	−0.311679	−	0.539844i
$986$	−1.16879	−	1.03978i	−0.0372219	−	0.0331132i
$987$		0			0
$988$	−13.2484	+	4.18544i	−0.421487	+	0.133157i
$989$		−	5.98207i		−	0.190219i
$990$		0			0
$991$	15.5004	+	26.8476i	0.492388	+	0.852841i	0.999962	−	0.00876746i	$-0.00279080\pi$
$991$	15.5004	+	26.8476i	0.492388	+	0.852841i	−0.507574	+	0.861608i	$0.669457\pi$
$992$	−35.4389	−	19.0694i	−1.12518	−	0.605453i
$993$		0			0
$994$	−17.3339	−	3.57606i	−0.549797	−	0.113426i
$995$	54.5015	−	94.3993i	1.72781	−	2.99266i
$996$		0			0
$997$	23.2481	+	13.4223i	0.736273	+	0.425088i	0.820713	−	0.571341i	$-0.193577\pi$
$997$	23.2481	+	13.4223i	0.736273	+	0.425088i	−0.0844395	+	0.996429i	$0.526910\pi$
$998$	−19.7694	+	22.2223i	−0.625789	+	0.703436i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.dg.e.829.18		48
3.2	odd	2		312.2.bk.b.205.7	yes	48
8.5	even	2	inner	936.2.dg.e.829.24		48
12.11	even	2		1248.2.ca.b.49.1		48
13.4	even	6	inner	936.2.dg.e.901.24		48
24.5	odd	2		312.2.bk.b.205.1	✓	48
24.11	even	2		1248.2.ca.b.49.24		48
39.17	odd	6		312.2.bk.b.277.1	yes	48
104.69	even	6	inner	936.2.dg.e.901.18		48
156.95	even	6		1248.2.ca.b.433.24		48
312.173	odd	6		312.2.bk.b.277.7	yes	48
312.251	even	6		1248.2.ca.b.433.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bk.b.205.1	✓	48	24.5	odd	2
312.2.bk.b.205.7	yes	48	3.2	odd	2
312.2.bk.b.277.1	yes	48	39.17	odd	6
312.2.bk.b.277.7	yes	48	312.173	odd	6
936.2.dg.e.829.18		48	1.1	even	1	trivial
936.2.dg.e.829.24		48	8.5	even	2	inner
936.2.dg.e.901.18		48	104.69	even	6	inner
936.2.dg.e.901.24		48	13.4	even	6	inner
1248.2.ca.b.49.1		48	12.11	even	2
1248.2.ca.b.49.24		48	24.11	even	2
1248.2.ca.b.433.1		48	312.251	even	6
1248.2.ca.b.433.24		48	156.95	even	6

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.dg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939983 - 1.05661i) q^{2} +(-0.232865 - 1.98640i) q^{4} +4.32865 q^{5} +(1.87318 + 1.08148i) q^{7} +(-2.31774 - 1.62113i) q^{8} +(4.06885 - 4.57371i) q^{10} +(-2.57249 - 4.45568i) q^{11} +(-2.72749 + 2.35814i) q^{13} +(2.90347 - 0.962655i) q^{14} +(-3.89155 + 0.925127i) q^{16} +(2.79961 - 4.84906i) q^{17} +(-0.963361 + 1.66859i) q^{19} +(-1.00799 - 8.59842i) q^{20} +(-7.12602 - 1.47013i) q^{22} +(1.01290 + 1.75439i) q^{23} +13.7372 q^{25} +(-0.0721467 + 5.09851i) q^{26} +(1.71205 - 3.97272i) q^{28} +(0.171090 - 0.0987787i) q^{29} +7.11414i q^{31} +(-2.68049 + 4.98147i) q^{32} +(-2.49200 - 7.51614i) q^{34} +(8.10834 + 4.68135i) q^{35} +(0.231065 + 0.400217i) q^{37} +(0.857513 + 2.58635i) q^{38} +(-10.0327 - 7.01730i) q^{40} +(1.21570 - 0.701886i) q^{41} +(-2.55733 - 1.47647i) q^{43} +(-8.25170 + 6.14755i) q^{44} +(2.80582 + 0.578856i) q^{46} +2.20506i q^{47} +(-1.16080 - 2.01056i) q^{49} +(12.9127 - 14.5149i) q^{50} +(5.31934 + 4.86874i) q^{52} +2.10538i q^{53} +(-11.1354 - 19.2871i) q^{55} +(-2.58833 - 5.54327i) q^{56} +(0.0564504 - 0.273626i) q^{58} +(-2.18299 + 3.78104i) q^{59} +(10.6432 + 6.14485i) q^{61} +(7.51690 + 6.68717i) q^{62} +(2.74388 + 7.51473i) q^{64} +(-11.8063 + 10.2076i) q^{65} +(-5.50969 - 9.54306i) q^{67} +(-10.2841 - 4.43195i) q^{68} +(12.5681 - 4.16700i) q^{70} +(-5.01087 - 2.89303i) q^{71} +10.1096i q^{73} +(0.640072 + 0.132050i) q^{74} +(3.53882 + 1.52506i) q^{76} -11.1284i q^{77} -7.37163 q^{79} +(-16.8451 + 4.00455i) q^{80} +(0.401116 - 1.94429i) q^{82} -2.04171 q^{83} +(12.1185 - 20.9899i) q^{85} +(-3.96390 + 1.31425i) q^{86} +(-1.26087 + 14.4975i) q^{88} +(4.34987 - 2.51140i) q^{89} +(-7.65936 + 1.46750i) q^{91} +(3.24905 - 2.42056i) q^{92} +(2.32990 + 2.07272i) q^{94} +(-4.17005 + 7.22274i) q^{95} +(-7.41183 - 4.27922i) q^{97} +(-3.21551 - 0.663376i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} - 12 q^{7} - 4 q^{10} + 36 q^{14} - 2 q^{16} - 12 q^{17} - 54 q^{20} - 14 q^{22} - 20 q^{23} + 48 q^{25} + 42 q^{26} + 6 q^{28} + 28 q^{38} - 8 q^{40} + 12 q^{41} - 30 q^{46} + 16 q^{49}+ \cdots - 24 q^{98}+O(q^{100}) \) 48 * q - 2 * q^4 - 12 * q^7 - 4 * q^10 + 36 * q^14 - 2 * q^16 - 12 * q^17 - 54 * q^20 - 14 * q^22 - 20 * q^23 + 48 * q^25 + 42 * q^26 + 6 * q^28 + 28 * q^38 - 8 * q^40 + 12 * q^41 - 30 * q^46 + 16 * q^49 + 84 * q^50 - 28 * q^52 - 68 * q^55 - 18 * q^56 - 24 * q^58 - 24 * q^62 - 68 * q^64 - 12 * q^65 - 4 * q^68 + 12 * q^71 - 54 * q^74 - 54 * q^76 - 192 * q^79 - 78 * q^80 - 6 * q^82 - 10 * q^88 + 48 * q^89 + 12 * q^92 + 54 * q^94 + 20 * q^95 + 144 * q^97 - 24 * q^98

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