LMFDB - Embedded newform 756.2.be.c.107.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(107,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.107"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.be (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,0,-4,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.13
Character	$\chi$	$=$	756.107
Dual form			756.2.be.c.431.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.38410 + 0.290278i) q^{2} +(1.83148 + 0.803549i) q^{4} +(-2.75822 - 1.59246i) q^{5} +(-0.944233 + 2.47152i) q^{7} +(2.30170 + 1.64383i) q^{8} +(-3.35540 - 3.00478i) q^{10} +(1.24831 + 2.16213i) q^{11} +6.61093 q^{13} +(-2.02434 + 3.14675i) q^{14} +(2.70862 + 2.94336i) q^{16} +(2.67612 - 1.54506i) q^{17} +(4.40292 + 2.54203i) q^{19} +(-3.77200 - 5.13292i) q^{20} +(1.10017 + 3.35497i) q^{22} +(-2.53877 + 4.39728i) q^{23} +(2.57186 + 4.45459i) q^{25} +(9.15020 + 1.91901i) q^{26} +(-3.71533 + 3.76780i) q^{28} +1.59554i q^{29} +(-7.31098 + 4.22099i) q^{31} +(2.89461 + 4.86017i) q^{32} +(4.15252 - 1.36170i) q^{34} +(6.54021 - 5.31335i) q^{35} +(-0.357491 + 0.619192i) q^{37} +(5.35619 + 4.79649i) q^{38} +(-3.73086 - 8.19942i) q^{40} -12.2607i q^{41} -3.72407i q^{43} +(0.548869 + 4.96297i) q^{44} +(-4.79036 + 5.34934i) q^{46} +(2.51371 - 4.35388i) q^{47} +(-5.21685 - 4.66739i) q^{49} +(2.26665 + 6.91216i) q^{50} +(12.1078 + 5.31220i) q^{52} +(-7.21991 + 4.16842i) q^{53} -7.95152i q^{55} +(-6.23611 + 4.13654i) q^{56} +(-0.463151 + 2.20840i) q^{58} +(-5.36835 - 9.29825i) q^{59} +(0.997571 - 1.72784i) q^{61} +(-11.3444 + 3.72007i) q^{62} +(2.59564 + 7.56721i) q^{64} +(-18.2344 - 10.5276i) q^{65} +(-0.00277185 + 0.00160033i) q^{67} +(6.14278 - 0.679346i) q^{68} +(10.5947 - 5.45575i) q^{70} +12.4088 q^{71} +(0.957657 + 1.65871i) q^{73} +(-0.674541 + 0.753253i) q^{74} +(6.02120 + 8.19362i) q^{76} +(-6.52245 + 1.04366i) q^{77} +(6.11304 + 3.52937i) q^{79} +(-2.78378 - 12.4318i) q^{80} +(3.55901 - 16.9701i) q^{82} -7.93317 q^{83} -9.84177 q^{85} +(1.08102 - 5.15449i) q^{86} +(-0.680951 + 7.02859i) q^{88} +(-0.482940 - 0.278825i) q^{89} +(-6.24226 + 16.3391i) q^{91} +(-8.18314 + 6.01350i) q^{92} +(4.74307 - 5.29653i) q^{94} +(-8.09615 - 14.0229i) q^{95} +0.127151 q^{97} +(-5.86581 - 7.97448i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{4} - 2 q^{7} - 20 q^{10} + 8 q^{13} + 12 q^{16} + 42 q^{19} + 4 q^{22} + 6 q^{25} - 28 q^{28} - 30 q^{31} + 24 q^{34} + 12 q^{37} + 36 q^{40} - 12 q^{46} - 14 q^{49} + 84 q^{52} + 28 q^{58}+ \cdots - 4 q^{97}+O(q^{100}) $ 28 * q - 4 * q^4 - 2 * q^7 - 20 * q^10 + 8 * q^13 + 12 * q^16 + 42 * q^19 + 4 * q^22 + 6 * q^25 - 28 * q^28 - 30 * q^31 + 24 * q^34 + 12 * q^37 + 36 * q^40 - 12 * q^46 - 14 * q^49 + 84 * q^52 + 28 * q^58 + 6 * q^61 + 8 * q^64 - 24 * q^67 + 128 * q^70 - 22 * q^73 - 48 * q^79 - 36 * q^82 - 24 * q^85 - 16 * q^88 - 16 * q^91 - 12 * q^94 - 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.38410	+	0.290278i	0.978708	+	0.205258i
$2$	1.38410	+	0.290278i	0.978708	+	0.205258i
$3$		0			0
$3$		0			0
$4$	1.83148	+	0.803549i	0.915739	+	0.401774i
$5$	−2.75822	−	1.59246i	−1.23351	−	0.712170i	−0.265754	−	0.964041i	$-0.585621\pi$
$5$	−2.75822	−	1.59246i	−1.23351	−	0.712170i	−0.967761	+	0.251871i	$0.918954\pi$
$6$		0			0
$7$	−0.944233	+	2.47152i	−0.356887	+	0.934148i
$7$	−0.944233	+	2.47152i	−0.356887	+	0.934148i
$8$	2.30170	+	1.64383i	0.813774	+	0.581182i
$9$		0			0
$10$	−3.35540	−	3.00478i	−1.06107	−	0.950194i
$11$	1.24831	+	2.16213i	0.376379	+	0.651907i	0.990532	−	0.137279i	$-0.0438357\pi$
$11$	1.24831	+	2.16213i	0.376379	+	0.651907i	−0.614153	+	0.789187i	$0.710502\pi$
$12$		0			0
$13$	6.61093			1.83354			0.916771	−	0.399414i	$-0.130786\pi$
$13$	6.61093			1.83354			0.916771	+	0.399414i	$0.130786\pi$
$14$	−2.02434	+	3.14675i	−0.541029	+	0.841004i
$15$		0			0
$16$	2.70862	+	2.94336i	0.677155	+	0.735841i
$17$	2.67612	−	1.54506i	0.649054	−	0.374731i	−0.139040	−	0.990287i	$-0.544402\pi$
$17$	2.67612	−	1.54506i	0.649054	−	0.374731i	0.788094	+	0.615555i	$0.211068\pi$
$18$		0			0
$19$	4.40292	+	2.54203i	1.01010	+	0.583181i	0.911220	−	0.411919i	$-0.135141\pi$
$19$	4.40292	+	2.54203i	1.01010	+	0.583181i	0.0988779	+	0.995100i	$0.468475\pi$
$20$	−3.77200	−	5.13292i	−0.843445	−	1.14776i
$21$		0			0
$22$	1.10017	+	3.35497i	0.234556	+	0.715282i
$23$	−2.53877	+	4.39728i	−0.529371	+	0.916897i	0.470042	+	0.882644i	$0.344239\pi$
$23$	−2.53877	+	4.39728i	−0.529371	+	0.916897i	−0.999413	+	0.0342533i	$0.989095\pi$
$24$		0			0
$25$	2.57186	+	4.45459i	0.514372	+	0.890918i
$26$	9.15020	+	1.91901i	1.79450	+	0.376348i
$27$		0			0
$28$	−3.71533	+	3.76780i	−0.702131	+	0.712047i
$29$			1.59554i			0.296285i	0.988966	+	0.148143i	$0.0473294\pi$
$29$			1.59554i			0.296285i	−0.988966	+	0.148143i	$0.952671\pi$
$30$		0			0
$31$	−7.31098	+	4.22099i	−1.31309	+	0.758113i	−0.982607	−	0.185699i	$-0.940545\pi$
$31$	−7.31098	+	4.22099i	−1.31309	+	0.758113i	−0.330483	+	0.943812i	$0.607212\pi$
$32$	2.89461	+	4.86017i	0.511700	+	0.859164i
$33$		0			0
$34$	4.15252	−	1.36170i	0.712151	−	0.233529i
$35$	6.54021	−	5.31335i	1.10550	−	0.898121i
$36$		0			0
$37$	−0.357491	+	0.619192i	−0.0587711	+	0.101795i	−0.893914	−	0.448238i	$-0.852052\pi$
$37$	−0.357491	+	0.619192i	−0.0587711	+	0.101795i	0.835143	+	0.550033i	$0.185385\pi$
$38$	5.35619	+	4.79649i	0.868889	+	0.778094i
$39$		0			0
$40$	−3.73086	−	8.19942i	−0.589901	−	1.29644i
$41$		−	12.2607i		−	1.91480i	−0.288763	−	0.957401i	$-0.593244\pi$
$41$		−	12.2607i		−	1.91480i	0.288763	−	0.957401i	$-0.406756\pi$
$42$		0			0
$43$		−	3.72407i		−	0.567915i	−0.958837	−	0.283958i	$-0.908352\pi$
$43$		−	3.72407i		−	0.567915i	0.958837	−	0.283958i	$-0.0916475\pi$
$44$	0.548869	+	4.96297i	0.0827451	+	0.748196i
$45$		0			0
$46$	−4.79036	+	5.34934i	−0.706300	+	0.788717i
$47$	2.51371	−	4.35388i	0.366663	−	0.635078i	−0.622379	−	0.782716i	$-0.713834\pi$
$47$	2.51371	−	4.35388i	0.366663	−	0.635078i	0.989041	+	0.147638i	$0.0471670\pi$
$48$		0			0
$49$	−5.21685	−	4.66739i	−0.745264	−	0.666770i
$50$	2.26665	+	6.91216i	0.320552	+	0.977527i
$51$		0			0
$52$	12.1078	+	5.31220i	1.67904	+	0.736670i
$53$	−7.21991	+	4.16842i	−0.991732	+	0.572576i	−0.905791	−	0.423724i	$-0.860723\pi$
$53$	−7.21991	+	4.16842i	−0.991732	+	0.572576i	−0.0859401	+	0.996300i	$0.527389\pi$
$54$		0			0
$55$		−	7.95152i		−	1.07218i
$56$	−6.23611	+	4.13654i	−0.833335	+	0.552769i
$57$		0			0
$58$	−0.463151	+	2.20840i	−0.0608147	+	0.289977i
$59$	−5.36835	−	9.29825i	−0.698899	−	1.21053i	−0.968848	−	0.247654i	$-0.920340\pi$
$59$	−5.36835	−	9.29825i	−0.698899	−	1.21053i	0.269949	−	0.962875i	$-0.412993\pi$
$60$		0			0
$61$	0.997571	−	1.72784i	0.127726	−	0.221228i	−0.795069	−	0.606519i	$-0.792566\pi$
$61$	0.997571	−	1.72784i	0.127726	−	0.221228i	0.922795	+	0.385291i	$0.125899\pi$
$62$	−11.3444	+	3.72007i	−1.44074	+	0.472450i
$63$		0			0
$64$	2.59564	+	7.56721i	0.324455	+	0.945901i
$65$	−18.2344	−	10.5276i	−2.26170	−	1.30579i
$66$		0			0
$67$	−0.00277185	+	0.00160033i	−0.000338635	+	0.000195511i	−0.500169	−	0.865928i	$-0.666729\pi$
$67$	−0.00277185	+	0.00160033i	−0.000338635	+	0.000195511i	0.499831	+	0.866123i	$0.333396\pi$
$68$	6.14278	−	0.679346i	0.744921	−	0.0823828i
$69$		0			0
$70$	10.5947	−	5.45575i	1.26630	−	0.652086i
$71$	12.4088			1.47265			0.736324	−	0.676629i	$-0.236560\pi$
$71$	12.4088			1.47265			0.736324	+	0.676629i	$0.236560\pi$
$72$		0			0
$73$	0.957657	+	1.65871i	0.112085	+	0.194137i	0.916611	−	0.399781i	$-0.130914\pi$
$73$	0.957657	+	1.65871i	0.112085	+	0.194137i	−0.804526	+	0.593918i	$0.797580\pi$
$74$	−0.674541	+	0.753253i	−0.0784139	+	0.0875639i
$75$		0			0
$76$	6.02120	+	8.19362i	0.690679	+	0.939873i
$77$	−6.52245	+	1.04366i	−0.743302	+	0.118936i
$78$		0			0
$79$	6.11304	+	3.52937i	0.687771	+	0.397085i	0.802776	−	0.596280i	$-0.203355\pi$
$79$	6.11304	+	3.52937i	0.687771	+	0.397085i	−0.115005	+	0.993365i	$0.536689\pi$
$80$	−2.78378	−	12.4318i	−0.311237	−	1.38992i
$81$		0			0
$82$	3.55901	−	16.9701i	0.393027	−	1.87403i
$83$	−7.93317			−0.870778			−0.435389	−	0.900242i	$-0.643389\pi$
$83$	−7.93317			−0.870778			−0.435389	+	0.900242i	$0.643389\pi$
$84$		0			0
$85$	−9.84177			−1.06749
$86$	1.08102	−	5.15449i	0.116569	−	0.555823i
$87$		0			0
$88$	−0.680951	+	7.02859i	−0.0725897	+	0.749250i
$89$	−0.482940	−	0.278825i	−0.0511915	−	0.0295554i	0.474186	−	0.880425i	$-0.342742\pi$
$89$	−0.482940	−	0.278825i	−0.0511915	−	0.0295554i	−0.525377	+	0.850869i	$0.676076\pi$
$90$		0			0
$91$	−6.24226	+	16.3391i	−0.654366	+	1.71280i
$92$	−8.18314	+	6.01350i	−0.853151	+	0.626951i
$93$		0			0
$94$	4.74307	−	5.29653i	0.489210	−	0.546296i
$95$	−8.09615	−	14.0229i	−0.830647	−	1.43872i
$96$		0			0
$97$	0.127151			0.0129103			0.00645513	−	0.999979i	$-0.497945\pi$
$97$	0.127151			0.0129103			0.00645513	+	0.999979i	$0.497945\pi$
$98$	−5.86581	−	7.97448i	−0.592536	−	0.805544i
$99$		0			0
$100$	1.13082	+	10.2251i	0.113082	+	1.02251i
$101$	−2.78771	+	1.60949i	−0.277388	+	0.160150i	−0.632240	−	0.774772i	$-0.717864\pi$
$101$	−2.78771	+	1.60949i	−0.277388	+	0.160150i	0.354852	+	0.934922i	$0.384531\pi$
$102$		0			0
$103$	−1.60433	−	0.926260i	−0.158079	−	0.0912671i	0.418874	−	0.908045i	$-0.362425\pi$
$103$	−1.60433	−	0.926260i	−0.158079	−	0.0912671i	−0.576953	+	0.816777i	$0.695758\pi$
$104$	15.2164	+	10.8672i	1.49209	+	1.06562i
$105$		0			0
$106$	−11.2031	+	3.67374i	−1.08814	+	0.356825i
$107$	−1.34472	+	2.32912i	−0.129999	+	0.225165i	−0.923676	−	0.383175i	$-0.874831\pi$
$107$	−1.34472	+	2.32912i	−0.129999	+	0.225165i	0.793677	+	0.608340i	$0.208164\pi$
$108$		0			0
$109$	−1.16374	−	2.01566i	−0.111466	−	0.193065i	0.804895	−	0.593417i	$-0.202221\pi$
$109$	−1.16374	−	2.01566i	−0.111466	−	0.193065i	−0.916362	+	0.400352i	$0.868888\pi$
$110$	2.30815	−	11.0057i	0.220074	−	1.04935i
$111$		0			0
$112$	−9.83216	+	3.91519i	−0.929051	+	0.369951i
$113$			3.19262i			0.300336i	0.988660	+	0.150168i	$0.0479815\pi$
$113$			3.19262i			0.300336i	−0.988660	+	0.150168i	$0.952019\pi$
$114$		0			0
$115$	14.0050	−	8.08579i	1.30597	−	0.754004i
$116$	−1.28210	+	2.92220i	−0.119040	+	0.271320i
$117$		0			0
$118$	−4.73126	−	14.4280i	−0.435548	−	1.32821i
$119$	1.29176	+	8.07298i	0.118416	+	0.740049i
$120$		0			0
$121$	2.38346	−	4.12827i	0.216678	−	0.375297i
$122$	1.88230	−	2.10194i	0.170415	−	0.190301i
$123$		0			0
$124$	−16.7817	+	1.85593i	−1.50704	+	0.166667i
$125$		−	0.457730i		−	0.0409406i
$126$		0			0
$127$		−	16.3682i		−	1.45244i	−0.687463	−	0.726220i	$-0.741275\pi$
$127$		−	16.3682i		−	1.45244i	0.687463	−	0.726220i	$-0.258725\pi$
$128$	1.39604	+	11.2272i	0.123393	+	0.992358i
$129$		0			0
$130$	−22.1823	−	19.8644i	−1.94552	−	1.74222i
$131$	−6.73046	+	11.6575i	−0.588043	+	1.01852i	0.406445	+	0.913675i	$0.366768\pi$
$131$	−6.73046	+	11.6575i	−0.588043	+	1.01852i	−0.994489	+	0.104845i	$0.966565\pi$
$132$		0			0
$133$	−10.4401	+	8.48164i	−0.905267	+	0.735452i
$134$	−0.00430106	+	0.00141041i	−0.000371555	+	0.000121841i
$135$		0			0
$136$	8.69943	+	0.842828i	0.745970	+	0.0722719i
$137$	17.8601	−	10.3115i	1.52589	−	0.880974i	0.526363	−	0.850260i	$-0.323555\pi$
$137$	17.8601	−	10.3115i	1.52589	−	0.880974i	0.999528	−	0.0307143i	$-0.00977821\pi$
$138$		0			0
$139$		−	1.68786i		−	0.143163i	−0.997435	−	0.0715813i	$-0.977195\pi$
$139$		−	1.68786i		−	0.143163i	0.997435	−	0.0715813i	$-0.0228045\pi$
$140$	16.2478	−	4.47591i	1.37319	−	0.378284i
$141$		0			0
$142$	17.1750	+	3.60199i	1.44129	+	0.302272i
$143$	8.25247	+	14.2937i	0.690106	+	1.19530i
$144$		0			0
$145$	2.54084	−	4.40086i	0.211005	−	0.365472i
$146$	0.844008	+	2.57381i	0.0698506	+	0.213010i
$147$		0			0
$148$	−1.15229	+	0.846775i	−0.0947174	+	0.0696045i
$149$	1.78690	+	1.03167i	0.146389	+	0.0845175i	0.571405	−	0.820668i	$-0.306398\pi$
$149$	1.78690	+	1.03167i	0.146389	+	0.0845175i	−0.425017	+	0.905186i	$0.639732\pi$
$150$		0			0
$151$	3.42476	−	1.97728i	0.278703	−	0.160909i	−0.354133	−	0.935195i	$-0.615224\pi$
$151$	3.42476	−	1.97728i	0.278703	−	0.160909i	0.632836	+	0.774286i	$0.281891\pi$
$152$	5.95553	+	13.0886i	0.483057	+	1.06163i
$153$		0			0
$154$	−9.33069	−	0.448788i	−0.751889	−	0.0361643i
$155$	26.8871			2.15962
$156$		0			0
$157$	0.964497	+	1.67056i	0.0769753	+	0.133325i	0.901944	−	0.431854i	$-0.142140\pi$
$157$	0.964497	+	1.67056i	0.0769753	+	0.133325i	−0.824968	+	0.565179i	$0.808807\pi$
$158$	7.43658	+	6.65949i	0.591622	+	0.529800i
$159$		0			0
$160$	−0.244360	−	18.0150i	−0.0193183	−	1.42421i
$161$	−8.47079	−	10.4267i	−0.667592	−	0.821739i
$162$		0			0
$163$	−3.87357	−	2.23640i	−0.303401	−	0.175169i	0.340569	−	0.940220i	$-0.389380\pi$
$163$	−3.87357	−	2.23640i	−0.303401	−	0.175169i	−0.643970	+	0.765051i	$0.722714\pi$
$164$	9.85208	−	22.4552i	0.769318	−	1.75346i
$165$		0			0
$166$	−10.9803	−	2.30282i	−0.852237	−	0.178734i
$167$	−10.5654			−0.817573			−0.408787	−	0.912630i	$-0.634048\pi$
$167$	−10.5654			−0.817573			−0.408787	+	0.912630i	$0.634048\pi$
$168$		0			0
$169$	30.7044			2.36187
$170$	−13.6220	−	2.85685i	−1.04476	−	0.219110i
$171$		0			0
$172$	2.99247	−	6.82055i	0.228174	−	0.520062i
$173$	0.942299	+	0.544036i	0.0716417	+	0.0413623i	0.535393	−	0.844603i	$-0.320164\pi$
$173$	0.942299	+	0.544036i	0.0716417	+	0.0413623i	−0.463751	+	0.885965i	$0.653497\pi$
$174$		0			0
$175$	−13.4381	+	2.15023i	−1.01582	+	0.162542i
$176$	−2.98275	+	9.53061i	−0.224833	+	0.718397i
$177$		0			0
$178$	−0.587501	−	0.526109i	−0.0440350	−	0.0394336i
$179$	−7.75422	−	13.4307i	−0.579578	−	1.00386i	−0.995528	−	0.0944707i	$-0.969884\pi$
$179$	−7.75422	−	13.4307i	−0.579578	−	1.00386i	0.415950	−	0.909388i	$-0.363449\pi$
$180$		0			0
$181$	−6.30027			−0.468295			−0.234148	−	0.972201i	$-0.575230\pi$
$181$	−6.30027			−0.468295			−0.234148	+	0.972201i	$0.575230\pi$
$182$	−13.3828	+	20.8029i	−0.991998	+	1.54202i
$183$		0			0
$184$	−13.0719	+	5.94791i	−0.963672	+	0.438486i
$185$	1.97208	−	1.13858i	0.144990	−	0.0837100i
$186$		0			0
$187$	6.68124	+	3.85741i	0.488580	+	0.282082i
$188$	8.10236	−	5.95414i	0.590925	−	0.434250i
$189$		0			0
$190$	−7.13535	−	21.7593i	−0.517652	−	1.57859i
$191$	7.84498	−	13.5879i	0.567643	−	0.983186i	−0.429156	−	0.903231i	$-0.641189\pi$
$191$	7.84498	−	13.5879i	0.567643	−	0.983186i	0.996798	−	0.0799556i	$-0.0254779\pi$
$192$		0			0
$193$	−9.09152	−	15.7470i	−0.654422	−	1.13349i	−0.982038	−	0.188681i	$-0.939579\pi$
$193$	−9.09152	−	15.7470i	−0.654422	−	1.13349i	0.327617	−	0.944811i	$-0.393755\pi$
$194$	0.175990	+	0.0369092i	0.0126354	+	0.00264993i
$195$		0			0
$196$	−5.80406	−	12.7402i	−0.414576	−	0.910015i
$197$			15.1305i			1.07801i	0.842304	+	0.539003i	$0.181199\pi$
$197$			15.1305i			1.07801i	−0.842304	+	0.539003i	$0.818801\pi$
$198$		0			0
$199$	−12.7163	+	7.34175i	−0.901434	+	0.520443i	−0.877665	−	0.479275i	$-0.840900\pi$
$199$	−12.7163	+	7.34175i	−0.901434	+	0.520443i	−0.0237685	+	0.999717i	$0.507566\pi$
$200$	−1.40295	+	14.4808i	−0.0992034	+	1.02395i
$201$		0			0
$202$	−4.32568	+	1.41848i	−0.304354	+	0.0998041i
$203$	−3.94342	−	1.50657i	−0.276774	−	0.105740i
$204$		0			0
$205$	−19.5247	+	33.8178i	−1.36366	+	2.36193i
$206$	−1.95168	−	1.74774i	−0.135980	−	0.121771i
$207$		0			0
$208$	17.9065	+	19.4584i	1.24159	+	1.34919i
$209$			12.6929i			0.877988i
$210$		0			0
$211$		−	12.6913i		−	0.873707i	−0.899533	−	0.436853i	$-0.856093\pi$
$211$		−	12.6913i		−	0.873707i	0.899533	−	0.436853i	$-0.143907\pi$
$212$	−16.5726	+	1.83281i	−1.13821	+	0.125878i
$213$		0			0
$214$	−2.53732	+	2.83340i	−0.173448	+	0.193687i
$215$	−5.93043	+	10.2718i	−0.404452	+	0.700532i
$216$		0			0
$217$	−3.52901	−	22.0548i	−0.239565	−	1.49718i
$218$	−1.02564	−	3.12769i	−0.0694648	−	0.211834i
$219$		0			0
$220$	6.38943	−	14.5630i	0.430776	−	0.981839i
$221$	17.6916	−	10.2143i	1.19007	−	0.687086i
$222$		0			0
$223$		−	26.9731i		−	1.80625i	−0.429377	−	0.903125i	$-0.641267\pi$
$223$		−	26.9731i		−	1.80625i	0.429377	−	0.903125i	$-0.358733\pi$
$224$	−14.7452	+	2.56497i	−0.985205	+	0.171379i
$225$		0			0
$226$	−0.926747	+	4.41891i	−0.0616463	+	0.293941i
$227$	10.4418	+	18.0857i	0.693045	+	1.20039i	0.970835	+	0.239748i	$0.0770648\pi$
$227$	10.4418	+	18.0857i	0.693045	+	1.20039i	−0.277790	+	0.960642i	$0.589602\pi$
$228$		0			0
$229$	−10.3698	+	17.9611i	−0.685258	+	1.18690i	0.288097	+	0.957601i	$0.406977\pi$
$229$	−10.3698	+	17.9611i	−0.685258	+	1.18690i	−0.973356	+	0.229301i	$0.926356\pi$
$230$	21.7315	−	7.12622i	1.43293	−	0.469889i
$231$		0			0
$232$	−2.62280	+	3.67246i	−0.172196	+	0.241109i
$233$	14.4007	+	8.31426i	0.943422	+	0.544685i	0.891031	−	0.453942i	$-0.149983\pi$
$233$	14.4007	+	8.31426i	0.943422	+	0.544685i	0.0523907	+	0.998627i	$0.483316\pi$
$234$		0			0
$235$	−13.8668	+	8.00597i	−0.904567	+	0.522252i
$236$	−2.36041	−	21.3433i	−0.153650	−	1.38933i
$237$		0			0
$238$	−0.555474	+	11.5488i	−0.0360060	+	0.748597i
$239$	−20.5645			−1.33021			−0.665104	−	0.746751i	$-0.731613\pi$
$239$	−20.5645			−1.33021			−0.665104	+	0.746751i	$0.731613\pi$
$240$		0			0
$241$	−11.2591	−	19.5013i	−0.725262	−	1.25619i	−0.958866	−	0.283859i	$-0.908385\pi$
$241$	−11.2591	−	19.5013i	−0.725262	−	1.25619i	0.233604	−	0.972332i	$-0.424948\pi$
$242$	4.49729	−	5.02208i	0.289097	−	0.322831i
$243$		0			0
$244$	3.21544	−	2.36291i	0.205847	−	0.151270i
$245$	6.95659	+	21.1813i	0.444440	+	1.35322i
$246$		0			0
$247$	29.1074	+	16.8051i	1.85206	+	1.06929i
$248$	−23.7663	−	2.30255i	−1.50916	−	0.146212i
$249$		0			0
$250$	0.132869	−	0.633545i	0.00840336	−	0.0400689i
$251$	5.03762			0.317972			0.158986	−	0.987281i	$-0.449178\pi$
$251$	5.03762			0.317972			0.158986	+	0.987281i	$0.449178\pi$
$252$		0			0
$253$	−12.6767			−0.796976
$254$	4.75132	−	22.6552i	0.298124	−	1.42151i
$255$		0			0
$256$	−1.32677	+	15.9449i	−0.0829230	+	0.996556i
$257$	2.41622	+	1.39501i	0.150720	+	0.0870182i	0.573463	−	0.819231i	$-0.305600\pi$
$257$	2.41622	+	1.39501i	0.150720	+	0.0870182i	−0.422743	+	0.906249i	$0.638933\pi$
$258$		0			0
$259$	−1.19279	−	1.46821i	−0.0741165	−	0.0912300i
$260$	−24.9364	−	33.9334i	−1.54649	−	2.10446i
$261$		0			0
$262$	−12.6996	+	14.1815i	−0.784582	+	0.876134i
$263$	−14.2092	−	24.6110i	−0.876176	−	1.51758i	−0.855504	−	0.517796i	$-0.826753\pi$
$263$	−14.2092	−	24.6110i	−0.876176	−	1.51758i	−0.0206722	−	0.999786i	$-0.506581\pi$
$264$		0			0
$265$	26.5522			1.63109
$266$	−16.9121	+	8.70894i	−1.03695	+	0.533980i
$267$		0			0
$268$	−0.00636252		0.000703648i	−0.000388653		4.29822e-5i
$269$	6.30707	−	3.64139i	0.384549	−	0.222019i	−0.295247	−	0.955421i	$-0.595402\pi$
$269$	6.30707	−	3.64139i	0.384549	−	0.222019i	0.679796	+	0.733402i	$0.262068\pi$
$270$		0			0
$271$	3.46120	+	1.99832i	0.210253	+	0.121390i	0.601429	−	0.798926i	$-0.294598\pi$
$271$	3.46120	+	1.99832i	0.210253	+	0.121390i	−0.391176	+	0.920316i	$0.627932\pi$
$272$	11.7962	+	3.69181i	0.715252	+	0.223849i
$273$		0			0
$274$	27.7134	−	9.08782i	1.67423	−	0.549016i
$275$	−6.42094	+	11.1214i	−0.387197	+	0.670646i
$276$		0			0
$277$	−9.96864	−	17.2662i	−0.598958	−	1.03743i	−0.992975	−	0.118322i	$-0.962248\pi$
$277$	−9.96864	−	17.2662i	−0.598958	−	1.03743i	0.394018	−	0.919103i	$-0.371085\pi$
$278$	0.489949	−	2.33617i	0.0293852	−	0.140114i
$279$		0			0
$280$	23.7878	−	1.47875i	1.42160	−	0.0883721i
$281$			13.3615i			0.797082i	0.917150	+	0.398541i	$0.130483\pi$
$281$			13.3615i			0.797082i	−0.917150	+	0.398541i	$0.869517\pi$
$282$		0			0
$283$	18.4457	−	10.6496i	1.09648	−	0.633054i	0.161187	−	0.986924i	$-0.448468\pi$
$283$	18.4457	−	10.6496i	1.09648	−	0.633054i	0.935295	+	0.353870i	$0.115134\pi$
$284$	22.7264	+	9.97104i	1.34856	+	0.591673i
$285$		0			0
$286$	7.27312	+	22.1795i	0.430068	+	1.31150i
$287$	30.3026	+	11.5770i	1.78871	+	0.683367i
$288$		0			0
$289$	−3.72560	+	6.45293i	−0.219153	+	0.379584i
$290$	4.79426	−	5.35370i	0.281528	−	0.314380i
$291$		0			0
$292$	0.421072	+	3.80741i	0.0246414	+	0.222812i
$293$		−	0.551006i		−	0.0321901i	−0.999870	−	0.0160951i	$-0.994877\pi$
$293$		−	0.551006i		−	0.0321901i	0.999870	−	0.0160951i	$-0.00512344\pi$
$294$		0			0
$295$			34.1955i			1.99094i
$296$	−1.84068	+	0.837540i	−0.106988	+	0.0486810i
$297$		0			0
$298$	2.17378	+	1.94663i	0.125924	+	0.112765i
$299$	−16.7836	+	29.0701i	−0.970623	+	1.68117i
$300$		0			0
$301$	9.20412	+	3.51639i	0.530517	+	0.202681i
$302$	5.31417	−	1.74263i	0.305796	−	0.100277i
$303$		0			0
$304$	4.44372	+	19.8448i	0.254865	+	1.13817i
$305$	−5.50305	+	3.17719i	−0.315104	+	0.181925i
$306$		0			0
$307$		−	3.49188i		−	0.199292i	−0.995023	−	0.0996460i	$-0.968229\pi$
$307$		−	3.49188i		−	0.199292i	0.995023	−	0.0996460i	$-0.0317710\pi$
$308$	−12.7844	−	3.32966i	−0.728456	−	0.189725i
$309$		0			0
$310$	37.2144	+	7.80472i	2.11364	+	0.443278i
$311$	−6.52568	−	11.3028i	−0.370037	−	0.640924i	0.619533	−	0.784970i	$-0.287322\pi$
$311$	−6.52568	−	11.3028i	−0.370037	−	0.640924i	−0.989571	+	0.144047i	$0.953988\pi$
$312$		0			0
$313$	10.0472	−	17.4022i	0.567899	−	0.983630i	−0.428875	−	0.903364i	$-0.641090\pi$
$313$	10.0472	−	17.4022i	0.567899	−	0.983630i	0.996774	−	0.0802656i	$-0.0255768\pi$
$314$	0.850036	+	2.59220i	0.0479703	+	0.146286i
$315$		0			0
$316$	8.35988	+	11.3761i	0.470280	+	0.639955i
$317$	18.4393	+	10.6459i	1.03565	+	0.597935i	0.918599	−	0.395190i	$-0.129321\pi$
$317$	18.4393	+	10.6459i	1.03565	+	0.597935i	0.117055	+	0.993125i	$0.462655\pi$
$318$		0			0
$319$	−3.44978	+	1.99173i	−0.193150	+	0.111515i
$320$	4.89113	−	25.0055i	0.273423	−	1.39785i
$321$		0			0
$322$	−8.69780	−	16.8905i	−0.484710	−	0.941271i
$323$	15.7103			0.874144
$324$		0			0
$325$	17.0024	+	29.4490i	0.943122	+	1.63354i
$326$	−4.71223	−	4.21982i	−0.260986	−	0.233714i
$327$		0			0
$328$	20.1545	−	28.2205i	1.11285	−	1.55821i
$329$	8.38717	+	10.3238i	0.462400	+	0.569168i
$330$		0			0
$331$	−4.03493	−	2.32957i	−0.221780	−	0.128045i	0.384994	−	0.922919i	$-0.374203\pi$
$331$	−4.03493	−	2.32957i	−0.221780	−	0.128045i	−0.606774	+	0.794874i	$0.707537\pi$
$332$	−14.5294	−	6.37469i	−0.797405	−	0.349856i
$333$		0			0
$334$	−14.6236	−	3.06690i	−0.800165	−	0.167813i
$335$	0.0101938			0.000556948
$336$		0			0
$337$	−7.41763			−0.404064			−0.202032	−	0.979379i	$-0.564754\pi$
$337$	−7.41763			−0.404064			−0.202032	+	0.979379i	$0.564754\pi$
$338$	42.4980	+	8.91280i	2.31159	+	0.484793i
$339$		0			0
$340$	−18.0250	−	7.90834i	−0.977541	−	0.428890i
$341$	−18.2527	−	10.5382i	−0.988439	−	0.570675i
$342$		0			0
$343$	16.4615	−	8.48645i	0.888836	−	0.458225i
$344$	6.12174	−	8.57169i	0.330062	−	0.462154i
$345$		0			0
$346$	1.14632	+	1.02653i	0.0616263	+	0.0551866i
$347$	−6.28113	−	10.8792i	−0.337188	−	0.584028i	0.646714	−	0.762732i	$-0.276143\pi$
$347$	−6.28113	−	10.8792i	−0.337188	−	0.584028i	−0.983903	+	0.178705i	$0.942809\pi$
$348$		0			0
$349$	−16.6865			−0.893208			−0.446604	−	0.894732i	$-0.647367\pi$
$349$	−16.6865			−0.893208			−0.446604	+	0.894732i	$0.647367\pi$
$350$	−19.2238	−	0.924626i	−1.02756	−	0.0494234i
$351$		0			0
$352$	−6.89496	+	12.3255i	−0.367502	+	0.656952i
$353$	9.31826	−	5.37990i	0.495961	−	0.286343i	−0.231083	−	0.972934i	$-0.574227\pi$
$353$	9.31826	−	5.37990i	0.495961	−	0.286343i	0.727044	+	0.686591i	$0.240894\pi$
$354$		0			0
$355$	−34.2261	−	19.7605i	−1.81653	−	1.04878i
$356$	−0.660443	−	0.898728i	−0.0350034	−	0.0476325i
$357$		0			0
$358$	−6.83400	−	20.8404i	−0.361188	−	1.10145i
$359$	−13.8374	+	23.9670i	−0.730309	+	1.26493i	0.226442	+	0.974025i	$0.427291\pi$
$359$	−13.8374	+	23.9670i	−0.730309	+	1.26493i	−0.956751	+	0.290908i	$0.906043\pi$
$360$		0			0
$361$	3.42378	+	5.93017i	0.180199	+	0.312114i
$362$	−8.72022	−	1.82883i	−0.458324	−	0.0961212i
$363$		0			0
$364$	−24.5618	+	24.9087i	−1.28739	+	1.30557i
$365$		−	6.10012i		−	0.319295i
$366$		0			0
$367$	2.00186	−	1.15577i	0.104496	−	0.0603308i	−0.446841	−	0.894613i	$-0.647451\pi$
$367$	2.00186	−	1.15577i	0.104496	−	0.0603308i	0.551337	+	0.834282i	$0.314118\pi$
$368$	−19.8194	+	4.43804i	−1.03316	+	0.231349i
$369$		0			0
$370$	3.06006	−	1.00346i	0.159085	−	0.0521674i
$371$	−3.48506	−	21.7801i	−0.180935	−	1.13077i
$372$		0			0
$373$	4.61557	−	7.99441i	0.238985	−	0.413935i	−0.721438	−	0.692479i	$-0.756519\pi$
$373$	4.61557	−	7.99441i	0.238985	−	0.413935i	0.960423	+	0.278544i	$0.0898519\pi$
$374$	8.12779	+	7.27847i	0.420278	+	0.376361i
$375$		0			0
$376$	12.9428	−	5.88920i	0.667476	−	0.303712i
$377$			10.5480i			0.543251i
$378$		0			0
$379$			9.38441i			0.482045i	0.970520	+	0.241022i	$0.0774827\pi$
$379$			9.38441i			0.482045i	−0.970520	+	0.241022i	$0.922517\pi$
$380$	−3.55980	−	32.1883i	−0.182614	−	1.65123i
$381$		0			0
$382$	14.8025	−	16.5298i	0.757363	−	0.845739i
$383$	−5.31186	+	9.20042i	−0.271424	+	0.470119i	−0.969227	−	0.246170i	$-0.920828\pi$
$383$	−5.31186	+	9.20042i	−0.271424	+	0.470119i	0.697803	+	0.716290i	$0.254161\pi$
$384$		0			0
$385$	19.6524	+	7.50809i	1.00158	+	0.382648i
$386$	−8.01259	−	24.4345i	−0.407830	−	1.24368i
$387$		0			0
$388$	0.232875	+	0.102172i	0.0118224	+	0.00518701i
$389$	−15.4666	+	8.92965i	−0.784188	+	0.452751i	−0.837912	−	0.545805i	$-0.816224\pi$
$389$	−15.4666	+	8.92965i	−0.784188	+	0.452751i	0.0537245	+	0.998556i	$0.482891\pi$
$390$		0			0
$391$			15.6902i			0.793487i
$392$	−4.33522	−	19.3185i	−0.218962	−	0.975733i
$393$		0			0
$394$	−4.39206	+	20.9422i	−0.221269	+	1.05505i
$395$	−11.2408	−	19.4696i	−0.565584	−	0.979620i
$396$		0			0
$397$	3.96912	−	6.87472i	0.199204	−	0.345032i	−0.749066	−	0.662495i	$-0.769498\pi$
$397$	3.96912	−	6.87472i	0.199204	−	0.345032i	0.948271	+	0.317463i	$0.102831\pi$
$398$	−19.7318	+	6.47047i	−0.989065	+	0.324336i
$399$		0			0
$400$	−6.14529	+	19.6357i	−0.307264	+	0.981785i
$401$	5.23636	+	3.02322i	0.261491	+	0.150972i	0.625015	−	0.780613i	$-0.285093\pi$
$401$	5.23636	+	3.02322i	0.261491	+	0.150972i	−0.363523	+	0.931585i	$0.618426\pi$
$402$		0			0
$403$	−48.3323	+	27.9047i	−2.40761	+	1.39003i
$404$	−6.39893	+	0.707675i	−0.318359	+	0.0352082i
$405$		0			0
$406$	−5.02078	−	3.22993i	−0.249177	−	0.160299i
$407$	−1.78503			−0.0884808
$408$		0			0
$409$	14.4850	+	25.0887i	0.716237	+	1.24056i	0.962481	+	0.271351i	$0.0874703\pi$
$409$	14.4850	+	25.0887i	0.716237	+	1.24056i	−0.246244	+	0.969208i	$0.579196\pi$
$410$	−36.8407	+	41.1396i	−1.81943	+	2.03174i
$411$		0			0
$412$	−2.19400	−	2.98558i	−0.108091	−	0.147089i
$413$	28.0498	−	4.48827i	1.38024	−	0.220854i
$414$		0			0
$415$	21.8814	+	12.6333i	1.07412	+	0.620142i
$416$	19.1361	+	32.1302i	0.938223	+	1.57531i
$417$		0			0
$418$	−3.68447	+	17.5683i	−0.180214	+	0.859293i
$419$	−23.3784			−1.14211			−0.571054	−	0.820913i	$-0.693465\pi$
$419$	−23.3784			−1.14211			−0.571054	+	0.820913i	$0.693465\pi$
$420$		0			0
$421$	19.0596			0.928910			0.464455	−	0.885597i	$-0.346250\pi$
$421$	19.0596			0.928910			0.464455	+	0.885597i	$0.346250\pi$
$422$	3.68401	−	17.5661i	0.179335	−	0.855104i
$423$		0			0
$424$	−23.4702	−	2.27387i	−1.13982	−	0.110429i
$425$	13.7652	+	7.94734i	0.667710	+	0.385502i
$426$		0			0
$427$	3.32847	+	4.09701i	0.161076	+	0.198268i
$428$	−4.33439	+	3.18519i	−0.209511	+	0.153962i
$429$		0			0
$430$	−11.1900	+	12.4958i	−0.539630	+	0.602599i
$431$	−6.24488	−	10.8164i	−0.300805	−	0.521010i	0.675513	−	0.737348i	$-0.263922\pi$
$431$	−6.24488	−	10.8164i	−0.300805	−	0.521010i	−0.976319	+	0.216338i	$0.930589\pi$
$432$		0			0
$433$	21.0419			1.01121			0.505604	−	0.862766i	$-0.331270\pi$
$433$	21.0419			1.01121			0.505604	+	0.862766i	$0.331270\pi$
$434$	1.51752	−	31.5506i	0.0728432	−	1.51447i
$435$		0			0
$436$	−0.511686	−	4.62676i	−0.0245053	−	0.221582i
$437$	−22.3560	+	12.9073i	−1.06943	+	0.617438i
$438$		0			0
$439$	−27.9142	−	16.1163i	−1.33227	−	0.769189i	−0.346626	−	0.938003i	$-0.612673\pi$
$439$	−27.9142	−	16.1163i	−1.33227	−	0.769189i	−0.985648	+	0.168815i	$0.946006\pi$
$440$	13.0710	−	18.3020i	0.623133	−	0.872514i
$441$		0			0
$442$	27.4520	−	9.00209i	1.30576	−	0.428186i
$443$	1.90658	−	3.30230i	0.0905844	−	0.156897i	−0.817173	−	0.576393i	$-0.804460\pi$
$443$	1.90658	−	3.30230i	0.0905844	−	0.156897i	0.907757	+	0.419496i	$0.137793\pi$
$444$		0			0
$445$	0.888036	+	1.53812i	0.0420970	+	0.0729141i
$446$	7.82969	−	37.3335i	0.370746	−	1.76779i
$447$		0			0
$448$	−21.1534	−	0.730030i	−0.999405	−	0.0344907i
$449$			33.6975i			1.59028i	0.606425	+	0.795141i	$0.292603\pi$
$449$			33.6975i			1.59028i	−0.606425	+	0.795141i	$0.707397\pi$
$450$		0			0
$451$	26.5093	−	15.3051i	1.24827	−	0.720691i
$452$	−2.56542	+	5.84721i	−0.120667	+	0.275030i
$453$		0			0
$454$	9.20261	+	28.0635i	0.431900	+	1.31708i
$455$	43.2368	−	35.1262i	2.02697	−	1.64674i
$456$		0			0
$457$	12.8270	−	22.2171i	0.600023	−	1.03927i	−0.392794	−	0.919626i	$-0.628491\pi$
$457$	12.8270	−	22.2171i	0.600023	−	1.03927i	0.992817	−	0.119644i	$-0.0381752\pi$
$458$	−19.5666	+	21.8498i	−0.914289	+	1.02098i
$459$		0			0
$460$	32.1472	−	3.55524i	1.49887	−	0.165764i
$461$		−	12.8586i		−	0.598884i	−0.954115	−	0.299442i	$-0.903200\pi$
$461$		−	12.8586i		−	0.598884i	0.954115	−	0.299442i	$-0.0968005\pi$
$462$		0			0
$463$			15.0540i			0.699619i	0.936821	+	0.349809i	$0.113754\pi$
$463$			15.0540i			0.699619i	−0.936821	+	0.349809i	$0.886246\pi$
$464$	−4.69626	+	4.32172i	−0.218019	+	0.200631i
$465$		0			0
$466$	17.5186	+	15.6880i	0.811534	+	0.726732i
$467$	−5.85210	+	10.1361i	−0.270803	+	0.469044i	−0.969068	−	0.246795i	$-0.920622\pi$
$467$	−5.85210	+	10.1361i	−0.270803	+	0.469044i	0.698265	+	0.715840i	$0.253956\pi$
$468$		0			0
$469$	−0.00133797	−	0.00836177i	−6.17819e−5	−	0.000386111i
$470$	−21.5170	+	7.05587i	−0.992503	+	0.325463i
$471$		0			0
$472$	2.92843	−	30.2264i	0.134792	−	1.39128i
$473$	8.05193	−	4.64878i	0.370228	−	0.213751i
$474$		0			0
$475$			26.1509i			1.19989i
$476$	−4.12119	+	15.8235i	−0.188895	+	0.725268i
$477$		0			0
$478$	−28.4634	−	5.96943i	−1.30189	−	0.273035i
$479$	15.5454	+	26.9254i	0.710287	+	1.23025i	0.964749	+	0.263170i	$0.0847682\pi$
$479$	15.5454	+	26.9254i	0.710287	+	1.23025i	−0.254462	+	0.967083i	$0.581898\pi$
$480$		0			0
$481$	−2.36335	+	4.09343i	−0.107759	+	0.186645i
$482$	−9.92293	−	30.2601i	−0.451977	−	1.37831i
$483$		0			0
$484$	7.68251	−	5.64560i	0.349205	−	0.256618i
$485$	−0.350712	−	0.202483i	−0.0159250	−	0.00919430i
$486$		0			0
$487$	4.79848	−	2.77040i	0.217440	−	0.125539i	−0.387324	−	0.921943i	$-0.626601\pi$
$487$	4.79848	−	2.77040i	0.217440	−	0.125539i	0.604764	+	0.796405i	$0.293267\pi$
$488$	5.13639	−	2.33714i	0.232514	−	0.105797i
$489$		0			0
$490$	3.48017	+	31.3364i	0.157218	+	1.41564i
$491$	30.3204			1.36834			0.684171	−	0.729321i	$-0.260164\pi$
$491$	30.3204			1.36834			0.684171	+	0.729321i	$0.260164\pi$
$492$		0			0
$493$	2.46521	+	4.26986i	0.111027	+	0.192305i
$494$	35.4094	+	31.7093i	1.59314	+	1.42667i
$495$		0			0
$496$	−32.2266	−	10.0858i	−1.44702	−	0.452865i
$497$	−11.7168	+	30.6685i	−0.525569	+	1.37567i
$498$		0			0
$499$	11.9203	+	6.88217i	0.533624	+	0.308088i	0.742491	−	0.669856i	$-0.233644\pi$
$499$	11.9203	+	6.88217i	0.533624	+	0.308088i	−0.208867	+	0.977944i	$0.566978\pi$
$500$	0.367808	−	0.838321i	0.0164489	−	0.0374909i
$501$		0			0
$502$	6.97258	+	1.46231i	0.311201	+	0.0652661i
$503$	−5.66994			−0.252810			−0.126405	−	0.991979i	$-0.540344\pi$
$503$	−5.66994			−0.252810			−0.126405	+	0.991979i	$0.540344\pi$
$504$		0			0
$505$	10.2522			0.456216
$506$	−17.5458	−	3.67976i	−0.780007	−	0.163585i
$507$		0			0
$508$	13.1526	−	29.9779i	0.583553	−	1.33006i
$509$	23.9698	+	13.8390i	1.06244	+	0.613401i	0.926107	−	0.377262i	$-0.123134\pi$
$509$	23.9698	+	13.8390i	1.06244	+	0.613401i	0.136335	+	0.990663i	$0.456468\pi$
$510$		0			0
$511$	−5.00379	+	0.800661i	−0.221355	+	0.0354192i
$512$	−6.46483	+	21.6842i	−0.285708	+	0.958317i
$513$		0			0
$514$	2.93936	+	2.63221i	0.129650	+	0.116102i
$515$	2.95006	+	5.10966i	0.129995	+	0.225159i
$516$		0			0
$517$	12.5515			0.552016
$518$	−1.22476	−	2.37839i	−0.0538128	−	0.104501i
$519$		0			0
$520$	−24.6645	−	54.2057i	−1.08161	−	2.37708i
$521$	−4.14916	+	2.39552i	−0.181778	+	0.104950i	−0.588128	−	0.808768i	$-0.700135\pi$
$521$	−4.14916	+	2.39552i	−0.181778	+	0.104950i	0.406350	+	0.913718i	$0.366801\pi$
$522$		0			0
$523$	6.54438	+	3.77840i	0.286166	+	0.165218i	0.636211	−	0.771515i	$-0.280501\pi$
$523$	6.54438	+	3.77840i	0.286166	+	0.165218i	−0.350046	+	0.936733i	$0.613834\pi$
$524$	−21.6941	+	15.9422i	−0.947709	+	0.696438i
$525$		0			0
$526$	−12.5229	−	38.1888i	−0.546026	−	1.66511i
$527$	−13.0434	+	22.5917i	−0.568177	+	0.984112i
$528$		0			0
$529$	−1.39074	−	2.40883i	−0.0604670	−	0.104732i
$530$	36.7509	+	7.70751i	1.59636	+	0.334793i
$531$		0			0
$532$	−25.9361	+	7.14485i	−1.12447	+	0.309768i
$533$		−	81.0547i		−	3.51087i
$534$		0			0
$535$	7.41808	−	4.28283i	0.320711	−	0.185163i
$536$	−0.00901063		0.000872978i	−0.000389200		3.77069e-5i
$537$		0			0
$538$	9.78665	−	3.20925i	0.421932	−	0.138361i
$539$	3.57928	−	17.1058i	0.154170	−	0.736801i
$540$		0			0
$541$	−10.7589	+	18.6349i	−0.462560	+	0.801177i	−0.999088	−	0.0427053i	$-0.986402\pi$
$541$	−10.7589	+	18.6349i	−0.462560	+	0.801177i	0.536528	+	0.843883i	$0.319736\pi$
$542$	4.21058	+	3.77059i	0.180860	+	0.161961i
$543$		0			0
$544$	15.2556	+	8.53404i	0.654077	+	0.365894i
$545$			7.41285i			0.317532i
$546$		0			0
$547$		−	10.1856i		−	0.435505i	−0.976004	−	0.217752i	$-0.930128\pi$
$547$		−	10.1856i		−	0.435505i	0.976004	−	0.217752i	$-0.0698725\pi$
$548$	40.9962	−	4.53388i	1.75127	−	0.193678i
$549$		0			0
$550$	−12.1155	+	13.5293i	−0.516608	+	0.576891i
$551$	−4.05591	+	7.02505i	−0.172788	+	0.299277i
$552$		0			0
$553$	−14.4950	+	11.7760i	−0.616392	+	0.500765i
$554$	−8.78562	−	26.7919i	−0.373265	−	1.13828i
$555$		0			0
$556$	1.35628	−	3.09128i	0.0575191	−	0.131100i
$557$	32.7379	−	18.9012i	1.38715	−	0.800871i	0.394156	−	0.919044i	$-0.371037\pi$
$557$	32.7379	−	18.9012i	1.38715	−	0.800871i	0.992993	+	0.118173i	$0.0377038\pi$
$558$		0			0
$559$		−	24.6196i		−	1.04130i
$560$	33.3541	+	4.85835i	1.40947	+	0.205303i
$561$		0			0
$562$	−3.87856	+	18.4937i	−0.163607	+	0.780111i
$563$	10.9769	+	19.0126i	0.462623	+	0.801286i	0.999091	−	0.0426347i	$-0.0135752\pi$
$563$	10.9769	+	19.0126i	0.462623	+	0.801286i	−0.536468	+	0.843921i	$0.680242\pi$
$564$		0			0
$565$	5.08412	−	8.80595i	0.213890	−	0.370469i
$566$	28.6221	−	9.38579i	1.20307	−	0.394514i
$567$		0			0
$568$	28.5612	+	20.3979i	1.19840	+	0.855877i
$569$	−11.2711	−	6.50737i	−0.472509	−	0.272803i	0.244781	−	0.969578i	$-0.421284\pi$
$569$	−11.2711	−	6.50737i	−0.472509	−	0.272803i	−0.717289	+	0.696775i	$0.754617\pi$
$570$		0			0
$571$	24.3678	−	14.0688i	1.01976	−	0.588760i	0.105727	−	0.994395i	$-0.466283\pi$
$571$	24.3678	−	14.0688i	1.01976	−	0.588760i	0.914035	+	0.405635i	$0.132950\pi$
$572$	3.62853	+	32.8099i	0.151717	+	1.37185i
$573$		0			0
$574$	38.5814	+	24.8199i	1.61036	+	1.03596i
$575$	−26.1175			−1.08917
$576$		0			0
$577$	−9.72878	−	16.8507i	−0.405014	−	0.701505i	0.589309	−	0.807908i	$-0.299400\pi$
$577$	−9.72878	−	16.8507i	−0.405014	−	0.701505i	−0.994323	+	0.106403i	$0.966067\pi$
$578$	−7.02975	+	7.85005i	−0.292399	+	0.326519i
$579$		0			0
$580$	8.18980	−	6.01840i	0.340063	−	0.249900i
$581$	7.49076	−	19.6070i	0.310769	−	0.813435i
$582$		0			0
$583$	−18.0253	−	10.4069i	−0.746534	−	0.431011i
$584$	−0.522401	+	5.39208i	−0.0216171	+	0.223126i
$585$		0			0
$586$	0.159945	−	0.762649i	0.00660727	−	0.0315047i
$587$	−17.0416			−0.703384			−0.351692	−	0.936116i	$-0.614393\pi$
$587$	−17.0416			−0.703384			−0.351692	+	0.936116i	$0.614393\pi$
$588$		0			0
$589$	−42.9195			−1.76847
$590$	−9.92620	+	47.3301i	−0.408655	+	1.94855i
$591$		0			0
$592$	−2.79081	+	0.624931i	−0.114702	+	0.0256845i
$593$	−34.0062	−	19.6335i	−1.39647	−	0.806251i	−0.402448	−	0.915443i	$-0.631840\pi$
$593$	−34.0062	−	19.6335i	−1.39647	−	0.806251i	−0.994021	+	0.109192i	$0.965174\pi$
$594$		0			0
$595$	9.29292	−	24.3241i	0.380973	−	0.997193i
$596$	2.44367	+	3.32534i	0.100097	+	0.136211i
$597$		0			0
$598$	−31.6687	+	35.3641i	−1.29503	+	1.44615i
$599$	2.41297	+	4.17938i	0.0985912	+	0.170765i	0.911102	−	0.412182i	$-0.135233\pi$
$599$	2.41297	+	4.17938i	0.0985912	+	0.170765i	−0.812511	+	0.582946i	$0.801900\pi$
$600$		0			0
$601$	−17.5618			−0.716363			−0.358181	−	0.933652i	$-0.616603\pi$
$601$	−17.5618			−0.716363			−0.358181	+	0.933652i	$0.616603\pi$
$602$	11.7187	+	7.53880i	0.477619	+	0.307258i
$603$		0			0
$604$	7.86121	−	0.869392i	0.319868	−	0.0353751i
$605$	−13.1482	+	7.59112i	−0.534550	+	0.308623i
$606$		0			0
$607$	0.967882	+	0.558807i	0.0392851	+	0.0226813i	0.519514	−	0.854462i	$-0.326113\pi$
$607$	0.967882	+	0.558807i	0.0392851	+	0.0226813i	−0.480229	+	0.877143i	$0.659446\pi$
$608$	0.390068	+	28.7571i	0.0158194	+	1.16625i
$609$		0			0
$610$	−8.53905	+	2.80014i	−0.345736	+	0.113374i
$611$	16.6180	−	28.7832i	0.672291	−	1.16444i
$612$		0			0
$613$	21.2827	+	36.8627i	0.859599	+	1.48887i	0.872312	+	0.488950i	$0.162620\pi$
$613$	21.2827	+	36.8627i	0.859599	+	1.48887i	−0.0127126	+	0.999919i	$0.504047\pi$
$614$	1.01362	−	4.83312i	0.0409062	−	0.195049i
$615$		0			0
$616$	−16.7283	−	8.31961i	−0.674004	−	0.335207i
$617$		−	13.9753i		−	0.562625i	−0.959616	−	0.281313i	$-0.909230\pi$
$617$		−	13.9753i		−	0.562625i	0.959616	−	0.281313i	$-0.0907698\pi$
$618$		0			0
$619$	−26.7181	+	15.4257i	−1.07389	+	0.620012i	−0.929242	−	0.369470i	$-0.879539\pi$
$619$	−26.7181	+	15.4257i	−1.07389	+	0.620012i	−0.144650	+	0.989483i	$0.546206\pi$
$620$	49.2430	+	21.6051i	1.97765	+	0.867680i
$621$		0			0
$622$	−5.75125	−	17.5385i	−0.230604	−	0.703230i
$623$	1.14513	−	0.930320i	0.0458787	−	0.0372725i
$624$		0			0
$625$	12.1304	−	21.0104i	0.485215	−	0.840417i
$626$	18.9578	−	21.1699i	0.757704	−	0.846121i
$627$		0			0
$628$	0.424080	+	3.83461i	0.0169226	+	0.153018i
$629$			2.20937i			0.0880935i
$630$		0			0
$631$			27.5528i			1.09686i	0.836197	+	0.548429i	$0.184774\pi$
$631$			27.5528i			1.09686i	−0.836197	+	0.548429i	$0.815226\pi$
$632$	8.26870	+	18.1724i	0.328911	+	0.722857i
$633$		0			0
$634$	22.4316	+	20.0876i	0.890873	+	0.797780i
$635$	−26.0656	+	45.1470i	−1.03438	+	1.79161i
$636$		0			0
$637$	−34.4882	−	30.8558i	−1.36647	−	1.22255i
$638$	−5.35300	+	1.75536i	−0.211927	+	0.0694955i
$639$		0			0
$640$	14.0284	−	33.1904i	0.554520	−	1.31196i
$641$	−15.1145	+	8.72634i	−0.596986	+	0.344670i	−0.767855	−	0.640624i	$-0.778676\pi$
$641$	−15.1145	+	8.72634i	−0.596986	+	0.344670i	0.170869	+	0.985294i	$0.445342\pi$
$642$		0			0
$643$			18.1663i			0.716409i	0.933643	+	0.358205i	$0.116611\pi$
$643$			18.1663i			0.716409i	−0.933643	+	0.358205i	$0.883389\pi$
$644$	−7.13571	−	25.9030i	−0.281186	−	1.02072i
$645$		0			0
$646$	21.7447	+	4.56035i	0.855532	+	0.179425i
$647$	23.0188	+	39.8697i	0.904961	+	1.56744i	0.820969	+	0.570973i	$0.193434\pi$
$647$	23.0188	+	39.8697i	0.904961	+	1.56744i	0.0839921	+	0.996466i	$0.473233\pi$
$648$		0			0
$649$	13.4027	−	23.2142i	0.526102	−	0.911235i
$650$	14.9846	+	45.6958i	0.587746	+	1.79234i
$651$		0			0
$652$	−5.29729	−	7.20852i	−0.207458	−	0.282308i
$653$	−26.5274	−	15.3156i	−1.03810	−	0.599345i	−0.118803	−	0.992918i	$-0.537906\pi$
$653$	−26.5274	−	15.3156i	−1.03810	−	0.599345i	−0.919293	+	0.393573i	$0.871239\pi$
$654$		0			0
$655$	37.1282	−	21.4360i	1.45072	−	0.837573i
$656$	36.0877	−	33.2096i	1.40899	−	1.29662i
$657$		0			0
$658$	8.61194	+	16.7238i	0.335728	+	0.651960i
$659$	23.5790			0.918508			0.459254	−	0.888305i	$-0.348117\pi$
$659$	23.5790			0.918508			0.459254	+	0.888305i	$0.348117\pi$
$660$		0			0
$661$	−8.01914	−	13.8896i	−0.311908	−	0.540241i	0.666867	−	0.745177i	$-0.267635\pi$
$661$	−8.01914	−	13.8896i	−0.311908	−	0.540241i	−0.978775	+	0.204936i	$0.934302\pi$
$662$	−4.90854	−	4.39562i	−0.190776	−	0.170840i
$663$		0			0
$664$	−18.2598	−	13.0408i	−0.708616	−	0.506081i
$665$	42.3027	−	6.76889i	1.64043	−	0.262486i
$666$		0			0
$667$	−7.01606	−	4.05072i	−0.271663	−	0.156845i
$668$	−19.3502	−	8.48979i	−0.748683	−	0.328480i
$669$		0			0
$670$	0.0141093	+	0.00295904i	0.000545090	+	0.000114318i
$671$	4.98110			0.192293
$672$		0			0
$673$	−44.4724			−1.71429			−0.857143	−	0.515079i	$-0.827763\pi$
$673$	−44.4724			−1.71429			−0.857143	+	0.515079i	$0.827763\pi$
$674$	−10.2668	−	2.15317i	−0.395461	−	0.0829372i
$675$		0			0
$676$	56.2344	+	24.6725i	2.16286	+	0.948941i
$677$	−9.48306	−	5.47505i	−0.364464	−	0.210423i	0.306573	−	0.951847i	$-0.400818\pi$
$677$	−9.48306	−	5.47505i	−0.364464	−	0.210423i	−0.671037	+	0.741424i	$0.734151\pi$
$678$		0			0
$679$	−0.120061	+	0.314257i	−0.00460750	+	0.0120601i
$680$	−22.6528	−	16.1782i	−0.868695	−	0.620406i
$681$		0			0
$682$	−22.2046	−	19.8843i	−0.850258	−	0.761409i
$683$	−4.06412	−	7.03927i	−0.155509	−	0.269350i	0.777735	−	0.628592i	$-0.216369\pi$
$683$	−4.06412	−	7.03927i	−0.155509	−	0.269350i	−0.933244	+	0.359242i	$0.883035\pi$
$684$		0			0
$685$	−65.6828			−2.50961
$686$	25.2478	−	6.96771i	0.963965	−	0.266029i
$687$		0			0
$688$	10.9613	−	10.0871i	0.417895	−	0.384567i
$689$	−47.7303	+	27.5571i	−1.81838	+	1.04984i
$690$		0			0
$691$	8.95759	+	5.17166i	0.340763	+	0.196739i	0.660609	−	0.750730i	$-0.270298\pi$
$691$	8.95759	+	5.17166i	0.340763	+	0.196739i	−0.319847	+	0.947469i	$0.603631\pi$
$692$	1.28864	+	1.75357i	0.0489867	+	0.0666609i
$693$		0			0
$694$	−5.53572	−	16.8812i	−0.210133	−	0.640803i
$695$	−2.68785	+	4.65550i	−0.101956	+	0.176593i
$696$		0			0
$697$	−18.9435	−	32.8111i	−0.717536	−	1.24281i
$698$	−23.0958	−	4.84373i	−0.874190	−	0.183338i
$699$		0			0
$700$	−26.3393	−	6.86002i	−0.995532	−	0.259285i
$701$			36.9229i			1.39456i	0.716800	+	0.697279i	$0.245606\pi$
$701$			36.9229i			1.39456i	−0.716800	+	0.697279i	$0.754394\pi$
$702$		0			0
$703$	−3.14800	+	1.81750i	−0.118729	+	0.0685483i
$704$	−13.1212	+	15.0583i	−0.494522	+	0.567532i
$705$		0			0
$706$	14.4591	−	4.74145i	0.544175	−	0.178447i
$707$	−1.34563	−	8.40963i	−0.0506077	−	0.316277i
$708$		0			0
$709$	−15.4835	+	26.8182i	−0.581494	+	1.00718i	0.413808	+	0.910364i	$0.364198\pi$
$709$	−15.4835	+	26.8182i	−0.581494	+	1.00718i	−0.995303	+	0.0968137i	$0.969135\pi$
$710$	−41.6364	−	37.2856i	−1.56259	−	1.39930i
$711$		0			0
$712$	−0.653240	−	1.43564i	−0.0244812	−	0.0538030i
$713$		−	42.8646i		−	1.60529i
$714$		0			0
$715$		−	52.5669i		−	1.96589i
$716$	−3.40946	−	30.8289i	−0.127417	−	1.15213i
$717$		0			0
$718$	−26.1095	+	29.1562i	−0.974396	+	1.08810i
$719$	23.5411	−	40.7744i	0.877936	−	1.52063i	0.0243332	−	0.999704i	$-0.492254\pi$
$719$	23.5411	−	40.7744i	0.877936	−	1.52063i	0.853602	−	0.520925i	$-0.174413\pi$
$720$		0			0
$721$	3.80413	−	3.09053i	0.141673	−	0.115097i
$722$	3.01747	+	9.20181i	0.112299	+	0.342456i
$723$		0			0
$724$	−11.5388	−	5.06257i	−0.428836	−	0.188149i
$725$	−7.10750	+	4.10351i	−0.263966	+	0.152401i
$726$		0			0
$727$		−	23.8977i		−	0.886317i	−0.896443	−	0.443158i	$-0.853858\pi$
$727$		−	23.8977i		−	0.886317i	0.896443	−	0.443158i	$-0.146142\pi$
$728$	−41.2265	+	27.3464i	−1.52795	+	1.01352i
$729$		0			0
$730$	1.77073	−	8.44319i	0.0655377	−	0.312496i
$731$	−5.75390	−	9.96605i	−0.212816	−	0.368608i
$732$		0			0
$733$	−19.4989	+	33.7731i	−0.720210	+	1.24744i	0.240706	+	0.970598i	$0.422621\pi$
$733$	−19.4989	+	33.7731i	−0.720210	+	1.24744i	−0.960916	+	0.276842i	$0.910712\pi$
$734$	3.10627	−	1.01861i	0.114654	−	0.0375977i
$735$		0			0
$736$	−28.7203	+	0.389569i	−1.05864	+	0.0143597i
$737$	−0.00692024	−	0.00399540i	−0.000254910	−	0.000147173i
$738$		0			0
$739$	−19.5445	+	11.2840i	−0.718957	+	0.415090i	−0.814369	−	0.580348i	$-0.802917\pi$
$739$	−19.5445	+	11.2840i	−0.718957	+	0.415090i	0.0954118	+	0.995438i	$0.469583\pi$
$740$	4.52672	−	0.500622i	0.166406	−	0.0184032i
$741$		0			0
$742$	1.49862	−	31.1576i	0.0550160	−	1.14383i
$743$	25.8493			0.948319			0.474159	−	0.880439i	$-0.342752\pi$
$743$	25.8493			0.948319			0.474159	+	0.880439i	$0.342752\pi$
$744$		0			0
$745$	−3.28578	−	5.69114i	−0.120382	−	0.208507i
$746$	8.70903	−	9.72528i	0.318860	−	0.356068i
$747$		0			0
$748$	9.13691	+	12.4335i	0.334079	+	0.454612i
$749$	−4.48675	−	5.52274i	−0.163942	−	0.201797i
$750$		0			0
$751$	−37.3627	−	21.5714i	−1.36339	−	0.787151i	−0.373313	−	0.927706i	$-0.621778\pi$
$751$	−37.3627	−	21.5714i	−1.36339	−	0.787151i	−0.990073	+	0.140555i	$0.955111\pi$
$752$	19.6237	−	4.39423i	0.715604	−	0.160241i
$753$		0			0
$754$	−3.06186	+	14.5995i	−0.111506	+	0.531684i
$755$	−12.5950			−0.458378
$756$		0			0
$757$	0.176821			0.00642668			0.00321334	−	0.999995i	$-0.498977\pi$
$757$	0.176821			0.00642668			0.00321334	+	0.999995i	$0.498977\pi$
$758$	−2.72409	+	12.9890i	−0.0989433	+	0.471781i
$759$		0			0
$760$	4.41645	−	45.5853i	0.160201	−	1.65355i
$761$	−26.2278	−	15.1426i	−0.950758	−	0.548920i	−0.0574416	−	0.998349i	$-0.518294\pi$
$761$	−26.2278	−	15.1426i	−0.950758	−	0.548920i	−0.893316	+	0.449429i	$0.851628\pi$
$762$		0			0
$763$	6.08059	−	0.972961i	0.220132	−	0.0352235i
$764$	25.2864	−	18.5821i	0.914832	−	0.672277i
$765$		0			0
$766$	−10.0228	+	11.1924i	−0.362140	+	0.404398i
$767$	−35.4898	−	61.4701i	−1.28146	−	2.21956i
$768$		0			0
$769$	48.5276			1.74995			0.874974	−	0.484169i	$-0.160878\pi$
$769$	48.5276			1.74995			0.874974	+	0.484169i	$0.160878\pi$
$770$	25.0214	+	16.0966i	0.901710	+	0.580082i
$771$		0			0
$772$	−3.99745	−	36.1457i	−0.143871	−	1.30091i
$773$	3.70357	−	2.13826i	0.133208	−	0.0769078i	−0.431915	−	0.901914i	$-0.642162\pi$
$773$	3.70357	−	2.13826i	0.133208	−	0.0769078i	0.565123	+	0.825007i	$0.308829\pi$
$774$		0			0
$775$	−37.6056	−	21.7116i	−1.35083	−	0.779904i
$776$	0.292664	+	0.209015i	0.0105060	+	0.00750321i
$777$		0			0
$778$	−23.9994	+	7.86993i	−0.860422	+	0.282151i
$779$	31.1670	−	53.9829i	1.11667	−	1.93414i
$780$		0			0
$781$	15.4900	+	26.8294i	0.554274	+	0.960031i
$782$	−4.55452	+	21.7168i	−0.162869	+	0.776592i
$783$		0			0
$784$	−0.392637	−	27.9972i	−0.0140228	−	0.999902i
$785$		−	6.14369i		−	0.219278i
$786$		0			0
$787$	11.2769	−	6.51073i	0.401979	−	0.232083i	−0.285359	−	0.958421i	$-0.592113\pi$
$787$	11.2769	−	6.51073i	0.401979	−	0.232083i	0.687337	+	0.726338i	$0.258779\pi$
$788$	−12.1581	+	27.7112i	−0.433115	+	0.987171i
$789$		0			0
$790$	−9.90677	−	30.2108i	−0.352467	−	1.07485i
$791$	−7.89063	−	3.01458i	−0.280558	−	0.107186i
$792$		0			0
$793$	6.59487	−	11.4227i	0.234191	−	0.405630i
$794$	7.48924	−	8.36316i	0.265783	−	0.296797i
$795$		0			0
$796$	−29.1890	+	3.22810i	−1.03458	+	0.114417i
$797$		−	14.3145i		−	0.507044i	−0.967330	−	0.253522i	$-0.918411\pi$
$797$		−	14.3145i		−	0.507044i	0.967330	−	0.253522i	$-0.0815891\pi$
$798$		0			0
$799$		−	15.5353i		−	0.549600i
$800$	−14.2055	+	25.3940i	−0.502241	+	0.897813i
$801$		0			0
$802$	6.37009	+	5.70444i	0.224936	+	0.201431i
$803$	−2.39090	+	4.14116i	−0.0843730	+	0.146138i
$804$		0			0
$805$	6.76023	+	42.2485i	0.238267	+	1.48907i
$806$	−74.9970	+	24.5931i	−2.64166	+	0.866256i
$807$		0			0
$808$	−9.06220	−	0.877974i	−0.318807	−	0.0308870i
$809$	−27.1605	+	15.6811i	−0.954911	+	0.551318i	−0.894603	−	0.446862i	$-0.852542\pi$
$809$	−27.1605	+	15.6811i	−0.954911	+	0.551318i	−0.0603080	+	0.998180i	$0.519208\pi$
$810$		0			0
$811$		−	6.06315i		−	0.212906i	−0.994318	−	0.106453i	$-0.966051\pi$
$811$		−	6.06315i		−	0.212906i	0.994318	−	0.106453i	$-0.0339493\pi$
$812$	−6.01169	−	5.92797i	−0.210969	−	0.208031i
$813$		0			0
$814$	−2.47067	−	0.518156i	−0.0865969	−	0.0181614i
$815$	7.12277	+	12.3370i	0.249500	+	0.432146i
$816$		0			0
$817$	9.46668	−	16.3968i	0.331197	−	0.573650i
$818$	12.7660	+	38.9301i	0.446353	+	1.36116i
$819$		0			0
$820$	−62.9333	+	46.2474i	−2.19772	+	1.61503i
$821$	−14.9421	−	8.62681i	−0.521482	−	0.301078i	0.216059	−	0.976380i	$-0.430680\pi$
$821$	−14.9421	−	8.62681i	−0.521482	−	0.301078i	−0.737541	+	0.675303i	$0.764013\pi$
$822$		0			0
$823$	15.6910	−	9.05923i	0.546955	−	0.315785i	−0.200938	−	0.979604i	$-0.564399\pi$
$823$	15.6910	−	9.05923i	0.546955	−	0.315785i	0.747893	+	0.663819i	$0.231066\pi$
$824$	−2.17007	−	4.76922i	−0.0755979	−	0.166144i
$825$		0			0
$826$	40.1266	+	1.93001i	1.39618	+	0.0671537i
$827$	−30.9864			−1.07750			−0.538751	−	0.842465i	$-0.681104\pi$
$827$	−30.9864			−1.07750			−0.538751	+	0.842465i	$0.681104\pi$
$828$		0			0
$829$	−21.8585	−	37.8601i	−0.759178	−	1.31493i	−0.943270	−	0.332026i	$-0.892268\pi$
$829$	−21.8585	−	37.8601i	−0.759178	−	1.31493i	0.184092	−	0.982909i	$-0.441065\pi$
$830$	26.6190	+	23.8374i	0.923958	+	0.827408i
$831$		0			0
$832$	17.1596	+	50.0263i	0.594901	+	1.73435i
$833$	−21.1723	−	4.43015i	−0.733576	−	0.153496i
$834$		0			0
$835$	29.1416	+	16.8249i	1.00849	+	0.582251i
$836$	−10.1994	+	23.2468i	−0.352753	+	0.804007i
$837$		0			0
$838$	−32.3580	−	6.78622i	−1.11779	−	0.234426i
$839$	−35.4628			−1.22431			−0.612156	−	0.790737i	$-0.709698\pi$
$839$	−35.4628			−1.22431			−0.612156	+	0.790737i	$0.709698\pi$
$840$		0			0
$841$	26.4542			0.912215
$842$	26.3805	+	5.53259i	0.909131	+	0.190666i
$843$		0			0
$844$	10.1981	−	23.2439i	0.351033	−	0.800087i
$845$	−84.6895	−	48.8955i	−2.91341	−	1.68206i
$846$		0			0
$847$	7.95257	+	9.78881i	0.273253	+	0.336348i
$848$	−31.8252	−	9.96017i	−1.09288	−	0.342034i
$849$		0			0
$850$	16.7455	+	14.9957i	0.574366	+	0.514347i
$851$	−1.81518	−	3.14398i	−0.0622234	−	0.107774i
$852$		0			0
$853$	31.1730			1.06734			0.533672	−	0.845692i	$-0.320812\pi$
$853$	31.1730			1.06734			0.533672	+	0.845692i	$0.320812\pi$
$854$	3.41767	+	6.63686i	0.116950	+	0.227109i
$855$		0			0
$856$	−6.92383	+	3.15045i	−0.236652	+	0.107680i
$857$	−6.55908	+	3.78689i	−0.224054	+	0.129358i	−0.607826	−	0.794070i	$-0.707958\pi$
$857$	−6.55908	+	3.78689i	−0.224054	+	0.129358i	0.383772	+	0.923428i	$0.374625\pi$
$858$		0			0
$859$	35.8209	+	20.6812i	1.22219	+	0.705633i	0.965385	−	0.260830i	$-0.0839962\pi$
$859$	35.8209	+	20.6812i	1.22219	+	0.705633i	0.256807	+	0.966463i	$0.417330\pi$
$860$	−19.1154	+	14.0472i	−0.651828	+	0.479005i
$861$		0			0
$862$	−5.50377	−	16.7838i	−0.187459	−	0.571659i
$863$	5.01544	−	8.68700i	0.170728	−	0.295709i	−0.767947	−	0.640514i	$-0.778721\pi$
$863$	5.01544	−	8.68700i	0.170728	−	0.295709i	0.938674	+	0.344805i	$0.112055\pi$
$864$		0			0
$865$	−1.73271	−	3.00115i	−0.0589140	−	0.102042i
$866$	29.1241	+	6.10799i	0.989677	+	0.207558i
$867$		0			0
$868$	11.2588	−	43.2287i	0.382150	−	1.46728i
$869$			17.6229i			0.597817i
$870$		0			0
$871$	−0.0183245	+	0.0105796i	−0.000620902	+	0.000358478i
$872$	0.634821	−	6.55244i	0.0214977	−	0.221894i
$873$		0			0
$874$	−34.6897	+	11.3755i	−1.17340	+	0.384782i
$875$	1.13129	+	0.432204i	0.0382446	+	0.0146111i
$876$		0			0
$877$	−2.63052	+	4.55619i	−0.0888263	+	0.153852i	−0.907015	−	0.421098i	$-0.861645\pi$
$877$	−2.63052	+	4.55619i	−0.0888263	+	0.153852i	0.818189	+	0.574949i	$0.194978\pi$
$878$	−33.9580	−	30.4095i	−1.14603	−	1.02627i
$879$		0			0
$880$	23.4042	−	21.5376i	0.788956	−	0.726034i
$881$		−	29.4366i		−	0.991746i	−0.868395	−	0.495873i	$-0.834848\pi$
$881$		−	29.4366i		−	0.991746i	0.868395	−	0.495873i	$-0.165152\pi$
$882$		0			0
$883$			46.4470i			1.56307i	0.623864	+	0.781533i	$0.285562\pi$
$883$			46.4470i			1.56307i	−0.623864	+	0.781533i	$0.714438\pi$
$884$	40.6095	−	4.49111i	1.36584	−	0.151052i
$885$		0			0
$886$	3.59749	−	4.01728i	0.120860	−	0.134963i
$887$	21.0703	−	36.4948i	0.707471	−	1.22538i	−0.258322	−	0.966059i	$-0.583169\pi$
$887$	21.0703	−	36.4948i	0.707471	−	1.22538i	0.965792	−	0.259316i	$-0.0834972\pi$
$888$		0			0
$889$	40.4543	+	15.4554i	1.35679	+	0.518356i
$890$	0.782649	+	2.38670i	0.0262345	+	0.0800023i
$891$		0			0
$892$	21.6742	−	49.4006i	0.725705	−	1.65405i
$893$	22.1353	−	12.7798i	0.740731	−	0.427661i
$894$		0			0
$895$			49.3932i			1.65103i
$896$	−29.0666	−	7.15081i	−0.971046	−	0.238892i
$897$		0			0
$898$	−9.78163	+	46.6407i	−0.326417	+	1.55642i
$899$	−6.73478	−	11.6650i	−0.224618	−	0.389049i
$900$		0			0
$901$	−12.8809	+	22.3104i	−0.429125	+	0.743266i
$902$	41.1343	−	13.4888i	1.36962	−	0.449128i
$903$		0			0
$904$	−5.24812	+	7.34845i	−0.174550	+	0.244406i
$905$	17.3775	+	10.0329i	0.577649	+	0.333506i
$906$		0			0
$907$	23.5846	−	13.6166i	0.783115	−	0.452132i	−0.0544183	−	0.998518i	$-0.517330\pi$
$907$	23.5846	−	13.6166i	0.783115	−	0.452132i	0.837533	+	0.546387i	$0.183997\pi$
$908$	4.59115	+	41.5140i	0.152363	+	1.37769i
$909$		0			0
$910$	70.0406	−	36.0675i	2.32182	−	1.19563i
$911$	34.1346			1.13093			0.565466	−	0.824772i	$-0.308697\pi$
$911$	34.1346			1.13093			0.565466	+	0.824772i	$0.308697\pi$
$912$		0			0
$913$	−9.90303	−	17.1526i	−0.327743	−	0.567667i
$914$	24.2030	−	27.0273i	0.800565	−	0.893983i
$915$		0			0
$916$	−33.4247	+	24.5627i	−1.10438	+	0.811573i
$917$	−22.4567	−	27.6419i	−0.741584	−	0.912815i
$918$		0			0
$919$	−33.2306	−	19.1857i	−1.09618	−	0.632878i	−0.160962	−	0.986961i	$-0.551460\pi$
$919$	−33.2306	−	19.1857i	−1.09618	−	0.632878i	−0.935214	+	0.354083i	$0.884793\pi$
$920$	45.5270	+	4.41080i	1.50098	+	0.145420i
$921$		0			0
$922$	3.73256	−	17.7976i	0.122925	−	0.586132i
$923$	82.0334			2.70016
$924$		0			0
$925$	−3.67766			−0.120921
$926$	−4.36985	+	20.8363i	−0.143602	+	0.684723i
$927$		0			0
$928$	−7.75461	+	4.61848i	−0.254558	+	0.151609i
$929$	39.0507	+	22.5459i	1.28121	+	0.739708i	0.977070	−	0.212919i	$-0.0682971\pi$
$929$	39.0507	+	22.5459i	1.28121	+	0.739708i	0.304142	+	0.952627i	$0.401630\pi$
$930$		0			0
$931$	−11.1047	−	33.8115i	−0.363943	−	1.10813i
$932$	19.6937	+	26.7990i	0.645088	+	0.877832i
$933$		0			0
$934$	−11.0422	+	12.3307i	−0.361312	+	0.403473i
$935$	−12.2856	−	21.2792i	−0.401781	−	0.695904i
$936$		0			0
$937$	−14.4277			−0.471333			−0.235667	−	0.971834i	$-0.575727\pi$
$937$	−14.4277			−0.471333			−0.235667	+	0.971834i	$0.575727\pi$
$938$	0.000575345	−	0.0119619i	1.87857e−5	−	0.000390571i
$939$		0			0
$940$	−31.8298	+	3.52015i	−1.03817	+	0.114815i
$941$	35.1619	−	20.3007i	1.14624	−	0.661784i	0.198275	−	0.980147i	$-0.436466\pi$
$941$	35.1619	−	20.3007i	1.14624	−	0.661784i	0.947969	+	0.318362i	$0.103133\pi$
$942$		0			0
$943$	53.9138	+	31.1272i	1.75568	+	1.01364i
$944$	12.8273	−	40.9864i	0.417494	−	1.33399i
$945$		0			0
$946$	12.4941	−	4.09709i	0.406219	−	0.133208i
$947$	−7.38792	+	12.7963i	−0.240075	+	0.415822i	−0.960735	−	0.277466i	$-0.910505\pi$
$947$	−7.38792	+	12.7963i	−0.240075	+	0.415822i	0.720660	+	0.693288i	$0.243839\pi$
$948$		0			0
$949$	6.33100	+	10.9656i	0.205513	+	0.355959i
$950$	−7.59104	+	36.1955i	−0.246286	+	1.17434i
$951$		0			0
$952$	−10.2974	+	20.7050i	−0.333739	+	0.671053i
$953$		−	31.2092i		−	1.01097i	−0.862836	−	0.505483i	$-0.831314\pi$
$953$		−	31.2092i		−	1.01097i	0.862836	−	0.505483i	$-0.168686\pi$
$954$		0			0
$955$	−43.2764	+	24.9856i	−1.40039	+	0.808516i
$956$	−37.6635	−	16.5246i	−1.21812	−	0.534444i
$957$		0			0
$958$	13.7006	+	41.7800i	0.442645	+	1.34985i
$959$	8.62109	+	53.8781i	0.278390	+	1.73982i
$960$		0			0
$961$	20.1336	−	34.8724i	0.649470	−	1.12492i
$962$	−4.45935	+	4.97970i	−0.143775	+	0.160552i
$963$		0			0
$964$	−4.95051	−	44.7635i	−0.159445	−	1.44173i
$965$			57.9115i			1.86424i
$966$		0			0
$967$			39.3749i			1.26621i	0.774065	+	0.633106i	$0.218220\pi$
$967$			39.3749i			1.26621i	−0.774065	+	0.633106i	$0.781780\pi$
$968$	12.2722	−	5.58403i	0.394443	−	0.179477i
$969$		0			0
$970$	−0.426644	−	0.382062i	−0.0136987	−	0.0122673i
$971$	−30.0829	+	52.1052i	−0.965407	+	1.67213i	−0.256890	+	0.966441i	$0.582698\pi$
$971$	−30.0829	+	52.1052i	−0.965407	+	1.67213i	−0.708517	+	0.705694i	$0.750635\pi$
$972$		0			0
$973$	4.17159	+	1.59374i	0.133735	+	0.0510928i
$974$	7.44577	−	2.44163i	0.238578	−	0.0782348i
$975$		0			0
$976$	7.78771	−	1.74386i	0.249279	−	0.0558195i
$977$	12.5257	−	7.23172i	0.400733	−	0.231363i	−0.286067	−	0.958209i	$-0.592348\pi$
$977$	12.5257	−	7.23172i	0.400733	−	0.231363i	0.686800	+	0.726846i	$0.259015\pi$
$978$		0			0
$979$		−	1.39224i		−	0.0444961i
$980$	−4.27937	+	44.3831i	−0.136700	+	1.41776i
$981$		0			0
$982$	41.9666	+	8.80136i	1.33921	+	0.280863i
$983$	−0.291450	−	0.504806i	−0.00929582	−	0.0161008i	0.861340	−	0.508029i	$-0.169626\pi$
$983$	−0.291450	−	0.504806i	−0.00929582	−	0.0161008i	−0.870636	+	0.491928i	$0.836292\pi$
$984$		0			0
$985$	24.0948	−	41.7333i	0.767723	−	1.32973i
$986$	2.17265	+	6.62552i	0.0691913	+	0.211000i
$987$		0			0
$988$	39.8057	+	54.1674i	1.26639	+	1.72330i
$989$	16.3758	+	9.45457i	0.520720	+	0.300638i
$990$		0			0
$991$	−6.69703	+	3.86653i	−0.212738	+	0.122824i	−0.602583	−	0.798056i	$-0.705862\pi$
$991$	−6.69703	+	3.86653i	−0.212738	+	0.122824i	0.389845	+	0.920880i	$0.372529\pi$
$992$	−41.6772	−	23.3144i	−1.32325	−	0.740234i
$993$		0			0
$994$	−25.1196	+	39.0473i	−0.796745	+	1.23850i
$995$	46.7658			1.48257
$996$		0			0
$997$	12.6526	+	21.9150i	0.400713	+	0.694055i	0.993812	−	0.111074i	$-0.0354291\pi$
$997$	12.6526	+	21.9150i	0.400713	+	0.694055i	−0.593099	+	0.805130i	$0.702096\pi$
$998$	14.5011	+	12.9858i	0.459025	+	0.411059i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.be.c.107.13	yes	28
3.2	odd	2	inner	756.2.be.c.107.2	✓	28
4.3	odd	2		756.2.be.d.107.11	yes	28
7.4	even	3		756.2.be.d.431.4	yes	28
12.11	even	2		756.2.be.d.107.4	yes	28
21.11	odd	6		756.2.be.d.431.11	yes	28
28.11	odd	6	inner	756.2.be.c.431.2	yes	28
84.11	even	6	inner	756.2.be.c.431.13	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.c.107.2	✓	28	3.2	odd	2	inner
756.2.be.c.107.13	yes	28	1.1	even	1	trivial
756.2.be.c.431.2	yes	28	28.11	odd	6	inner
756.2.be.c.431.13	yes	28	84.11	even	6	inner
756.2.be.d.107.4	yes	28	12.11	even	2
756.2.be.d.107.11	yes	28	4.3	odd	2
756.2.be.d.431.4	yes	28	7.4	even	3
756.2.be.d.431.11	yes	28	21.11	odd	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38410 + 0.290278i) q^{2} +(1.83148 + 0.803549i) q^{4} +(-2.75822 - 1.59246i) q^{5} +(-0.944233 + 2.47152i) q^{7} +(2.30170 + 1.64383i) q^{8} +(-3.35540 - 3.00478i) q^{10} +(1.24831 + 2.16213i) q^{11} +6.61093 q^{13} +(-2.02434 + 3.14675i) q^{14} +(2.70862 + 2.94336i) q^{16} +(2.67612 - 1.54506i) q^{17} +(4.40292 + 2.54203i) q^{19} +(-3.77200 - 5.13292i) q^{20} +(1.10017 + 3.35497i) q^{22} +(-2.53877 + 4.39728i) q^{23} +(2.57186 + 4.45459i) q^{25} +(9.15020 + 1.91901i) q^{26} +(-3.71533 + 3.76780i) q^{28} +1.59554i q^{29} +(-7.31098 + 4.22099i) q^{31} +(2.89461 + 4.86017i) q^{32} +(4.15252 - 1.36170i) q^{34} +(6.54021 - 5.31335i) q^{35} +(-0.357491 + 0.619192i) q^{37} +(5.35619 + 4.79649i) q^{38} +(-3.73086 - 8.19942i) q^{40} -12.2607i q^{41} -3.72407i q^{43} +(0.548869 + 4.96297i) q^{44} +(-4.79036 + 5.34934i) q^{46} +(2.51371 - 4.35388i) q^{47} +(-5.21685 - 4.66739i) q^{49} +(2.26665 + 6.91216i) q^{50} +(12.1078 + 5.31220i) q^{52} +(-7.21991 + 4.16842i) q^{53} -7.95152i q^{55} +(-6.23611 + 4.13654i) q^{56} +(-0.463151 + 2.20840i) q^{58} +(-5.36835 - 9.29825i) q^{59} +(0.997571 - 1.72784i) q^{61} +(-11.3444 + 3.72007i) q^{62} +(2.59564 + 7.56721i) q^{64} +(-18.2344 - 10.5276i) q^{65} +(-0.00277185 + 0.00160033i) q^{67} +(6.14278 - 0.679346i) q^{68} +(10.5947 - 5.45575i) q^{70} +12.4088 q^{71} +(0.957657 + 1.65871i) q^{73} +(-0.674541 + 0.753253i) q^{74} +(6.02120 + 8.19362i) q^{76} +(-6.52245 + 1.04366i) q^{77} +(6.11304 + 3.52937i) q^{79} +(-2.78378 - 12.4318i) q^{80} +(3.55901 - 16.9701i) q^{82} -7.93317 q^{83} -9.84177 q^{85} +(1.08102 - 5.15449i) q^{86} +(-0.680951 + 7.02859i) q^{88} +(-0.482940 - 0.278825i) q^{89} +(-6.24226 + 16.3391i) q^{91} +(-8.18314 + 6.01350i) q^{92} +(4.74307 - 5.29653i) q^{94} +(-8.09615 - 14.0229i) q^{95} +0.127151 q^{97} +(-5.86581 - 7.97448i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{4} - 2 q^{7} - 20 q^{10} + 8 q^{13} + 12 q^{16} + 42 q^{19} + 4 q^{22} + 6 q^{25} - 28 q^{28} - 30 q^{31} + 24 q^{34} + 12 q^{37} + 36 q^{40} - 12 q^{46} - 14 q^{49} + 84 q^{52} + 28 q^{58}+ \cdots - 4 q^{97}+O(q^{100}) \) 28 * q - 4 * q^4 - 2 * q^7 - 20 * q^10 + 8 * q^13 + 12 * q^16 + 42 * q^19 + 4 * q^22 + 6 * q^25 - 28 * q^28 - 30 * q^31 + 24 * q^34 + 12 * q^37 + 36 * q^40 - 12 * q^46 - 14 * q^49 + 84 * q^52 + 28 * q^58 + 6 * q^61 + 8 * q^64 - 24 * q^67 + 128 * q^70 - 22 * q^73 - 48 * q^79 - 36 * q^82 - 24 * q^85 - 16 * q^88 - 16 * q^91 - 12 * q^94 - 4 * q^97

Introduction

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