LMFDB - Embedded newform 756.2.bi.c.307.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(307,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("756.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bi (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			307.22
Character	$\chi$	$=$	756.307
Dual form			756.2.bi.c.559.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.161186 + 1.40500i) q^{2} +(-1.94804 + 0.452933i) q^{4} +(1.43245 + 0.827025i) q^{5} +(0.0302588 - 2.64558i) q^{7} +(-0.950366 - 2.66398i) q^{8} +O(q^{10})$	\(q+(0.161186 + 1.40500i) q^{2} +(-1.94804 + 0.452933i) q^{4} +(1.43245 + 0.827025i) q^{5} +(0.0302588 - 2.64558i) q^{7} +(-0.950366 - 2.66398i) q^{8} +(-0.931077 + 2.14589i) q^{10} +(4.24842 - 2.45282i) q^{11} +(0.876334 + 0.505952i) q^{13} +(3.72191 - 0.383917i) q^{14} +(3.58970 - 1.76466i) q^{16} -7.66107i q^{17} -2.85119 q^{19} +(-3.16505 - 0.962273i) q^{20} +(4.13100 + 5.57365i) q^{22} +(1.98118 + 1.14384i) q^{23} +(-1.13206 - 1.96079i) q^{25} +(-0.569608 + 1.31280i) q^{26} +(1.13932 + 5.16739i) q^{28} +(4.19857 + 7.27213i) q^{29} +(0.348784 - 0.604112i) q^{31} +(3.05795 + 4.75909i) q^{32} +(10.7638 - 1.23486i) q^{34} +(2.23130 - 3.76463i) q^{35} +3.97490 q^{37} +(-0.459573 - 4.00592i) q^{38} +(0.841829 - 4.60200i) q^{40} +(6.69947 + 3.86794i) q^{41} +(-6.70811 + 3.87293i) q^{43} +(-7.16511 + 6.70244i) q^{44} +(-1.28775 + 2.96793i) q^{46} +(-3.70722 - 6.42109i) q^{47} +(-6.99817 - 0.160104i) q^{49} +(2.57243 - 1.90659i) q^{50} +(-1.93629 - 0.588693i) q^{52} +8.61878 q^{53} +8.11418 q^{55} +(-7.07653 + 2.43366i) q^{56} +(-9.54058 + 7.07115i) q^{58} +(-2.54378 + 4.40596i) q^{59} +(-5.12759 + 2.96042i) q^{61} +(0.904996 + 0.392667i) q^{62} +(-6.19361 + 5.06352i) q^{64} +(0.836869 + 1.44950i) q^{65} +(2.18590 + 1.26203i) q^{67} +(3.46995 + 14.9241i) q^{68} +(5.64895 + 2.52817i) q^{70} -1.00362i q^{71} -5.89658i q^{73} +(0.640700 + 5.58473i) q^{74} +(5.55423 - 1.29140i) q^{76} +(-6.36058 - 11.3137i) q^{77} +(4.90752 - 2.83336i) q^{79} +(6.60149 + 0.440989i) q^{80} +(-4.35458 + 10.0362i) q^{82} +(1.20736 + 2.09120i) q^{83} +(6.33589 - 10.9741i) q^{85} +(-6.52272 - 8.80062i) q^{86} +(-10.5718 - 8.98662i) q^{88} +8.19734i q^{89} +(1.36505 - 2.30310i) q^{91} +(-4.37750 - 1.33089i) q^{92} +(8.42407 - 6.24363i) q^{94} +(-4.08418 - 2.35800i) q^{95} +(8.82136 - 5.09301i) q^{97} +(-0.903062 - 9.85822i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8}+O(q^{10}) $ 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8	$ 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8} - 10 q^{14} - 18 q^{16} - 14 q^{22} + 32 q^{25} + 28 q^{28} - 8 q^{29} + 16 q^{32} - 16 q^{37} + 84 q^{44} + 24 q^{46} - 24 q^{49} + 12 q^{50} + 48 q^{53} - 32 q^{56} - 14 q^{58} - 8 q^{64} + 40 q^{65} - 22 q^{70} - 64 q^{74} + 12 q^{77} + 40 q^{85} + 52 q^{86} + 6 q^{88} - 30 q^{92} - 20 q^{98}+O(q^{100}) $ 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8 - 10 * q^14 - 18 * q^16 - 14 * q^22 + 32 * q^25 + 28 * q^28 - 8 * q^29 + 16 * q^32 - 16 * q^37 + 84 * q^44 + 24 * q^46 - 24 * q^49 + 12 * q^50 + 48 * q^53 - 32 * q^56 - 14 * q^58 - 8 * q^64 + 40 * q^65 - 22 * q^70 - 64 * q^74 + 12 * q^77 + 40 * q^85 + 52 * q^86 + 6 * q^88 - 30 * q^92 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.161186	+	1.40500i	0.113976	+	0.993484i
$2$	0.161186	+	1.40500i	0.113976	+	0.993484i
$3$		0			0
$3$		0			0
$4$	−1.94804	+	0.452933i	−0.974019	+	0.226466i
$5$	1.43245	+	0.827025i	0.640611	+	0.369857i	0.784850	−	0.619686i	$-0.212740\pi$
$5$	1.43245	+	0.827025i	0.640611	+	0.369857i	−0.144239	+	0.989543i	$0.546073\pi$
$6$		0			0
$7$	0.0302588	−	2.64558i	0.0114368	−	0.999935i
$7$	0.0302588	−	2.64558i	0.0114368	−	0.999935i
$8$	−0.950366	−	2.66398i	−0.336005	−	0.941860i
$9$		0			0
$10$	−0.931077	+	2.14589i	−0.294432	+	0.678591i
$11$	4.24842	−	2.45282i	1.28095	−	0.739554i	0.303924	−	0.952696i	$-0.401703\pi$
$11$	4.24842	−	2.45282i	1.28095	−	0.739554i	0.977021	+	0.213142i	$0.0683697\pi$
$12$		0			0
$13$	0.876334	+	0.505952i	0.243051	+	0.140326i	0.616578	−	0.787294i	$-0.288518\pi$
$13$	0.876334	+	0.505952i	0.243051	+	0.140326i	−0.373527	+	0.927619i	$0.621852\pi$
$14$	3.72191	−	0.383917i	0.994722	−	0.102606i
$15$		0			0
$16$	3.58970	−	1.76466i	0.897426	−	0.441165i
$17$		−	7.66107i		−	1.85808i	−0.369976	−	0.929041i	$-0.620634\pi$
$17$		−	7.66107i		−	1.85808i	0.369976	−	0.929041i	$-0.379366\pi$
$18$		0			0
$19$	−2.85119			−0.654108			−0.327054	−	0.945006i	$-0.606056\pi$
$19$	−2.85119			−0.654108			−0.327054	+	0.945006i	$0.606056\pi$
$20$	−3.16505	−	0.962273i	−0.707727	−	0.215171i
$21$		0			0
$22$	4.13100	+	5.57365i	0.880732	+	1.18831i
$23$	1.98118	+	1.14384i	0.413105	+	0.238506i	0.692123	−	0.721780i	$-0.256676\pi$
$23$	1.98118	+	1.14384i	0.413105	+	0.238506i	−0.279018	+	0.960286i	$0.590009\pi$
$24$		0			0
$25$	−1.13206	−	1.96079i	−0.226412	−	0.392157i
$26$	−0.569608	+	1.31280i	−0.111709	+	0.257461i
$27$		0			0
$28$	1.13932	+	5.16739i	0.215312	+	0.976545i
$29$	4.19857	+	7.27213i	0.779654	+	1.35040i	0.932141	+	0.362096i	$0.117939\pi$
$29$	4.19857	+	7.27213i	0.779654	+	1.35040i	−0.152486	+	0.988306i	$0.548728\pi$
$30$		0			0
$31$	0.348784	−	0.604112i	0.0626435	−	0.108502i	−0.833003	−	0.553269i	$-0.813380\pi$
$31$	0.348784	−	0.604112i	0.0626435	−	0.108502i	0.895646	+	0.444767i	$0.146714\pi$
$32$	3.05795	+	4.75909i	0.540575	+	0.841296i
$33$		0			0
$34$	10.7638	−	1.23486i	1.84597	−	0.211777i
$35$	2.23130	−	3.76463i	0.377159	−	0.636339i
$36$		0			0
$37$	3.97490			0.653470			0.326735	−	0.945116i	$-0.394051\pi$
$37$	3.97490			0.653470			0.326735	+	0.945116i	$0.394051\pi$
$38$	−0.459573	−	4.00592i	−0.0745525	−	0.649845i
$39$		0			0
$40$	0.841829	−	4.60200i	0.133105	−	0.727639i
$41$	6.69947	+	3.86794i	1.04628	+	0.604071i	0.921606	−	0.388127i	$-0.126878\pi$
$41$	6.69947	+	3.86794i	1.04628	+	0.604071i	0.124675	+	0.992198i	$0.460211\pi$
$42$		0			0
$43$	−6.70811	+	3.87293i	−1.02298	+	0.590617i	−0.914965	−	0.403533i	$-0.867782\pi$
$43$	−6.70811	+	3.87293i	−1.02298	+	0.590617i	−0.108013	+	0.994150i	$0.534449\pi$
$44$	−7.16511	+	6.70244i	−1.08018	+	1.01043i
$45$		0			0
$46$	−1.28775	+	2.96793i	−0.189868	+	0.437597i
$47$	−3.70722	−	6.42109i	−0.540754	−	0.936613i	−0.998861	−	0.0477158i	$-0.984806\pi$
$47$	−3.70722	−	6.42109i	−0.540754	−	0.936613i	0.458107	−	0.888897i	$-0.348528\pi$
$48$		0			0
$49$	−6.99817	−	0.160104i	−0.999738	−	0.0228720i
$50$	2.57243	−	1.90659i	0.363796	−	0.269633i
$51$		0			0
$52$	−1.93629	−	0.588693i	−0.268516	−	0.0816370i
$53$	8.61878			1.18388			0.591940	−	0.805982i	$-0.298362\pi$
$53$	8.61878			1.18388			0.591940	+	0.805982i	$0.298362\pi$
$54$		0			0
$55$	8.11418			1.09412
$56$	−7.07653	+	2.43366i	−0.945641	+	0.325211i
$57$		0			0
$58$	−9.54058	+	7.07115i	−1.25274	+	0.928487i
$59$	−2.54378	+	4.40596i	−0.331172	+	0.573607i	−0.982742	−	0.184981i	$-0.940778\pi$
$59$	−2.54378	+	4.40596i	−0.331172	+	0.573607i	0.651570	+	0.758589i	$0.274111\pi$
$60$		0			0
$61$	−5.12759	+	2.96042i	−0.656521	+	0.379042i	−0.790950	−	0.611881i	$-0.790413\pi$
$61$	−5.12759	+	2.96042i	−0.656521	+	0.379042i	0.134429	+	0.990923i	$0.457080\pi$
$62$	0.904996	+	0.392667i	0.114935	+	0.0498687i
$63$		0			0
$64$	−6.19361	+	5.06352i	−0.774201	+	0.632940i
$65$	0.836869	+	1.44950i	0.103801	+	0.179788i
$66$		0			0
$67$	2.18590	+	1.26203i	0.267051	+	0.154182i	0.627547	−	0.778579i	$-0.284059\pi$
$67$	2.18590	+	1.26203i	0.267051	+	0.154182i	−0.360496	+	0.932761i	$0.617393\pi$
$68$	3.46995	+	14.9241i	0.420793	+	1.80981i
$69$		0			0
$70$	5.64895	+	2.52817i	0.675179	+	0.302174i
$71$		−	1.00362i		−	0.119108i	−0.998225	−	0.0595539i	$-0.981032\pi$
$71$		−	1.00362i		−	0.119108i	0.998225	−	0.0595539i	$-0.0189678\pi$
$72$		0			0
$73$		−	5.89658i		−	0.690142i	−0.938577	−	0.345071i	$-0.887855\pi$
$73$		−	5.89658i		−	0.690142i	0.938577	−	0.345071i	$-0.112145\pi$
$74$	0.640700	+	5.58473i	0.0744799	+	0.649212i
$75$		0			0
$76$	5.55423	−	1.29140i	0.637113	−	0.148133i
$77$	−6.36058	−	11.3137i	−0.724856	−	1.28932i
$78$		0			0
$79$	4.90752	−	2.83336i	0.552139	−	0.318778i	−0.197845	−	0.980233i	$-0.563394\pi$
$79$	4.90752	−	2.83336i	0.552139	−	0.318778i	0.749984	+	0.661456i	$0.230061\pi$
$80$	6.60149	+	0.440989i	0.738069	+	0.0493041i
$81$		0			0
$82$	−4.35458	+	10.0362i	−0.480883	+	1.10831i
$83$	1.20736	+	2.09120i	0.132525	+	0.229539i	0.924649	−	0.380820i	$-0.124358\pi$
$83$	1.20736	+	2.09120i	0.132525	+	0.229539i	−0.792125	+	0.610359i	$0.791025\pi$
$84$		0			0
$85$	6.33589	−	10.9741i	0.687224	−	1.19031i
$86$	−6.52272	−	8.80062i	−0.703363	−	0.948996i
$87$		0			0
$88$	−10.5718	−	8.98662i	−1.12696	−	0.957977i
$89$			8.19734i			0.868916i	0.900692	+	0.434458i	$0.143060\pi$
$89$			8.19734i			0.868916i	−0.900692	+	0.434458i	$0.856940\pi$
$90$		0			0
$91$	1.36505	−	2.30310i	0.143096	−	0.241431i
$92$	−4.37750	−	1.33089i	−0.456386	−	0.138755i
$93$		0			0
$94$	8.42407	−	6.24363i	0.868876	−	0.643981i
$95$	−4.08418	−	2.35800i	−0.419028	−	0.241926i
$96$		0			0
$97$	8.82136	−	5.09301i	0.895673	−	0.517117i	0.0198794	−	0.999802i	$-0.493672\pi$
$97$	8.82136	−	5.09301i	0.895673	−	0.517117i	0.875794	+	0.482685i	$0.160338\pi$
$98$	−0.903062	−	9.85822i	−0.0912231	−	0.995830i
$99$		0			0
$100$	3.09340	+	3.30694i	0.309340	+	0.330694i
$101$	0.846450	−	0.488698i	0.0842249	−	0.0486273i	−0.457296	−	0.889315i	$-0.651182\pi$
$101$	0.846450	−	0.488698i	0.0842249	−	0.0486273i	0.541521	+	0.840687i	$0.317849\pi$
$102$		0			0
$103$	−6.53514	+	11.3192i	−0.643926	+	1.11531i	0.340622	+	0.940200i	$0.389362\pi$
$103$	−6.53514	+	11.3192i	−0.643926	+	1.11531i	−0.984548	+	0.175113i	$0.943971\pi$
$104$	0.515008	−	2.81538i	0.0505007	−	0.276071i
$105$		0			0
$106$	1.38923	+	12.1094i	0.134934	+	1.17617i
$107$		−	1.03143i		−	0.0997116i	−0.998756	−	0.0498558i	$-0.984124\pi$
$107$		−	1.03143i		−	0.0997116i	0.998756	−	0.0498558i	$-0.0158762\pi$
$108$		0			0
$109$	−0.842410			−0.0806882			−0.0403441	−	0.999186i	$-0.512845\pi$
$109$	−0.842410			−0.0806882			−0.0403441	+	0.999186i	$0.512845\pi$
$110$	1.30789	+	11.4004i	0.124703	+	1.08699i
$111$		0			0
$112$	−4.55993	−	9.55024i	−0.430872	−	0.902413i
$113$	−3.19162	+	5.52804i	−0.300242	+	0.520035i	−0.976191	−	0.216914i	$-0.930401\pi$
$113$	−3.19162	+	5.52804i	−0.300242	+	0.520035i	0.675949	+	0.736949i	$0.263734\pi$
$114$		0			0
$115$	1.89196	+	3.27697i	0.176426	+	0.305579i
$116$	−11.4728	−	12.2647i	−1.06522	−	1.13875i
$117$		0			0
$118$	−6.60039	−	2.86383i	−0.607615	−	0.263637i
$119$	−20.2680	−	0.231815i	−1.85796	−	0.0212505i
$120$		0			0
$121$	6.53269	−	11.3149i	0.593881	−	1.02863i
$122$	−4.98587	−	6.72707i	−0.451400	−	0.609041i
$123$		0			0
$124$	−0.405823	+	1.33481i	−0.0364440	+	0.119869i
$125$		−	12.0152i		−	1.07467i
$126$		0			0
$127$		−	17.9070i		−	1.58899i	−0.607272	−	0.794494i	$-0.707736\pi$
$127$		−	17.9070i		−	1.58899i	0.607272	−	0.794494i	$-0.292264\pi$
$128$	−8.11256	−	7.88584i	−0.717056	−	0.697016i
$129$		0			0
$130$	−1.90165	+	1.40944i	−0.166786	+	0.123616i
$131$	−5.02346	+	8.70089i	−0.438902	+	0.760200i	−0.997605	−	0.0691675i	$-0.977966\pi$
$131$	−5.02346	+	8.70089i	−0.438902	+	0.760200i	0.558703	+	0.829368i	$0.311299\pi$
$132$		0			0
$133$	−0.0862737	+	7.54305i	−0.00748088	+	0.654065i
$134$	−1.42081	+	3.27461i	−0.122740	+	0.282883i
$135$		0			0
$136$	−20.4090	+	7.28082i	−1.75005	+	0.624325i
$137$	−1.97707	−	3.42439i	−0.168913	−	0.292566i	0.769125	−	0.639098i	$-0.220692\pi$
$137$	−1.97707	−	3.42439i	−0.168913	−	0.292566i	−0.938038	+	0.346533i	$0.887359\pi$
$138$		0			0
$139$	−4.85060	+	8.40148i	−0.411422	+	0.712605i	−0.995046	−	0.0994201i	$-0.968301\pi$
$139$	−4.85060	+	8.40148i	−0.411422	+	0.712605i	0.583623	+	0.812025i	$0.301635\pi$
$140$	−2.64154	+	8.34427i	−0.223251	+	0.705220i
$141$		0			0
$142$	1.41008	−	0.161770i	0.118332	−	0.0135754i
$143$	4.96404			0.415114
$144$		0			0
$145$			13.8893i			1.15344i
$146$	8.28468	−	0.950447i	0.685645	−	0.0786596i
$147$		0			0
$148$	−7.74327	+	1.80036i	−0.636493	+	0.147989i
$149$	3.46856	−	6.00773i	0.284156	−	0.492172i	−0.688248	−	0.725475i	$-0.741620\pi$
$149$	3.46856	−	6.00773i	0.284156	−	0.492172i	0.972404	+	0.233303i	$0.0749534\pi$
$150$		0			0
$151$	−10.8500	+	6.26427i	−0.882964	+	0.509779i	−0.871635	−	0.490156i	$-0.836940\pi$
$151$	−10.8500	+	6.26427i	−0.882964	+	0.509779i	−0.0113294	+	0.999936i	$0.503606\pi$
$152$	2.70967	+	7.59552i	0.219784	+	0.616078i
$153$		0			0
$154$	14.8705	−	10.7602i	1.19830	−	0.867084i
$155$	0.999232	−	0.576907i	0.0802602	−	0.0463383i
$156$		0			0
$157$	−1.44619	−	0.834956i	−0.115418	−	0.0666367i	0.441180	−	0.897419i	$-0.354560\pi$
$157$	−1.44619	−	0.834956i	−0.115418	−	0.0666367i	−0.556598	+	0.830782i	$0.687894\pi$
$158$	4.77189	+	6.43836i	0.379631	+	0.512208i
$159$		0			0
$160$	0.444480	+	9.34615i	0.0351392	+	0.738878i
$161$	3.08606	−	5.20676i	0.243215	−	0.410350i
$162$		0			0
$163$			7.06914i			0.553698i	0.960913	+	0.276849i	$0.0892901\pi$
$163$			7.06914i			0.553698i	−0.960913	+	0.276849i	$0.910710\pi$
$164$	−14.8027	−	4.50048i	−1.15590	−	0.351429i
$165$		0			0
$166$	−2.74352	+	2.03341i	−0.212939	+	0.157823i
$167$	0.578614	−	1.00219i	0.0447745	−	0.0775518i	−0.842770	−	0.538274i	$-0.819076\pi$
$167$	0.578614	−	1.00219i	0.0447745	−	0.0775518i	0.887544	+	0.460723i	$0.152410\pi$
$168$		0			0
$169$	−5.98803	−	10.3716i	−0.460617	−	0.797813i
$170$	16.4398	+	7.13305i	1.26088	+	0.547080i
$171$		0			0
$172$	11.3135	−	10.5829i	0.862645	−	0.806942i
$173$	−1.30347	+	0.752561i	−0.0991013	+	0.0572162i	−0.548732	−	0.835999i	$-0.684889\pi$
$173$	−1.30347	+	0.752561i	−0.0991013	+	0.0572162i	0.449630	+	0.893215i	$0.351556\pi$
$174$		0			0
$175$	−5.22167	+	2.93562i	−0.394721	+	0.221912i
$176$	10.9222	−	16.3019i	0.823288	−	1.22880i
$177$		0			0
$178$	−11.5172	+	1.32130i	−0.863254	+	0.0990355i
$179$		−	1.28088i		−	0.0957374i	−0.998854	−	0.0478687i	$-0.984757\pi$
$179$		−	1.28088i		−	0.0957374i	0.998854	−	0.0478687i	$-0.0152429\pi$
$180$		0			0
$181$		−	26.6202i		−	1.97866i	−0.145683	−	0.989331i	$-0.546538\pi$
$181$		−	26.6202i		−	1.97866i	0.145683	−	0.989331i	$-0.453462\pi$
$182$	3.45588	+	1.54667i	0.256167	+	0.114647i
$183$		0			0
$184$	1.16431	−	6.36490i	0.0858341	−	0.469227i
$185$	5.69385	+	3.28734i	0.418620	+	0.241690i
$186$		0			0
$187$	−18.7913	−	32.5474i	−1.37415	−	2.38010i
$188$	10.1301	+	10.8294i	0.738815	+	0.789816i
$189$		0			0
$190$	2.65468	−	6.11835i	0.192591	−	0.443872i
$191$	7.44229	−	4.29681i	0.538506	−	0.310906i	−0.205968	−	0.978559i	$-0.566034\pi$
$191$	7.44229	−	4.29681i	0.538506	−	0.310906i	0.744473	+	0.667653i	$0.232701\pi$
$192$		0			0
$193$	−3.80654	+	6.59312i	−0.274001	+	0.474583i	−0.969882	−	0.243573i	$-0.921680\pi$
$193$	−3.80654	+	6.59312i	−0.274001	+	0.474583i	0.695882	+	0.718156i	$0.255014\pi$
$194$	8.57756	+	11.5731i	0.615833	+	0.830898i
$195$		0			0
$196$	13.7052	−	2.85781i	0.978944	−	0.204129i
$197$	−14.3946			−1.02557			−0.512786	−	0.858517i	$-0.671386\pi$
$197$	−14.3946			−1.02557			−0.512786	+	0.858517i	$0.671386\pi$
$198$		0			0
$199$	21.9194			1.55382			0.776911	−	0.629610i	$-0.216785\pi$
$199$	21.9194			1.55382			0.776911	+	0.629610i	$0.216785\pi$
$200$	−4.14763	+	4.87925i	−0.293282	+	0.345015i
$201$		0			0
$202$	0.823056	+	1.11049i	0.0579100	+	0.0781337i
$203$	19.3660	−	10.8876i	1.35923	−	0.764159i
$204$		0			0
$205$	6.39776	+	11.0813i	0.446839	+	0.773948i
$206$	−16.9568	−	7.35736i	−1.18144	−	0.512611i
$207$		0			0
$208$	4.03861	+	0.269785i	0.280027	+	0.0187062i
$209$	−12.1130	+	6.99347i	−0.837876	+	0.483748i
$210$		0			0
$211$	1.45464	+	0.839838i	0.100142	+	0.0578168i	0.549234	−	0.835668i	$-0.314919\pi$
$211$	1.45464	+	0.839838i	0.100142	+	0.0578168i	−0.449093	+	0.893485i	$0.648253\pi$
$212$	−16.7897	+	3.90373i	−1.15312	+	0.268109i
$213$		0			0
$214$	1.44915	−	0.166252i	0.0990619	−	0.0113647i
$215$	−12.8120			−0.873774
$216$		0			0
$217$	−1.58767	−	0.941016i	−0.107778	−	0.0638803i
$218$	−0.135785	−	1.18358i	−0.00919651	−	0.0801624i
$219$		0			0
$220$	−15.8067	+	3.67518i	−1.06569	+	0.247780i
$221$	3.87613	−	6.71366i	0.260737	−	0.451609i
$222$		0			0
$223$	4.09002	+	7.08413i	0.273888	+	0.474388i	0.969854	−	0.243687i	$-0.0783568\pi$
$223$	4.09002	+	7.08413i	0.273888	+	0.474388i	−0.695966	+	0.718075i	$0.745023\pi$
$224$	12.6831	−	7.94605i	0.847423	−	0.530918i
$225$		0			0
$226$	−8.28133	−	3.59317i	−0.550866	−	0.239014i
$227$	13.5064	+	23.3937i	0.896450	+	1.55270i	0.832000	+	0.554776i	$0.187196\pi$
$227$	13.5064	+	23.3937i	0.896450	+	1.55270i	0.0644498	+	0.997921i	$0.479471\pi$
$228$		0			0
$229$	10.4216	+	6.01689i	0.688677	+	0.397608i	0.803116	−	0.595823i	$-0.203174\pi$
$229$	10.4216	+	6.01689i	0.688677	+	0.397608i	−0.114439	+	0.993430i	$0.536507\pi$
$230$	−4.29918	+	3.18640i	−0.283480	+	0.210105i
$231$		0			0
$232$	15.3827	−	18.0961i	1.00992	−	1.18807i
$233$	−12.9746			−0.849992			−0.424996	−	0.905195i	$-0.639724\pi$
$233$	−12.9746			−0.849992			−0.424996	+	0.905195i	$0.639724\pi$
$234$		0			0
$235$		−	12.2639i		−	0.800005i
$236$	2.95978	−	9.73514i	0.192665	−	0.633704i
$237$		0			0
$238$	−2.94122	−	28.5138i	−0.190651	−	1.84828i
$239$	5.65067	+	3.26242i	0.365512	+	0.211028i	0.671496	−	0.741008i	$-0.265652\pi$
$239$	5.65067	+	3.26242i	0.365512	+	0.211028i	−0.305984	+	0.952037i	$0.598985\pi$
$240$		0			0
$241$	−20.0162	+	11.5564i	−1.28936	+	0.744410i	−0.978539	−	0.206059i	$-0.933936\pi$
$241$	−20.0162	+	11.5564i	−1.28936	+	0.744410i	−0.310817	+	0.950470i	$0.600603\pi$
$242$	16.9505	+	7.35460i	1.08962	+	0.472772i
$243$		0			0
$244$	8.64787	−	8.08945i	0.553623	−	0.517874i
$245$	−9.89211	−	6.01700i	−0.631984	−	0.384412i
$246$		0			0
$247$	−2.49859	−	1.44256i	−0.158982	−	0.0917881i
$248$	−1.94082	−	0.355028i	−0.123242	−	0.0225443i
$249$		0			0
$250$	16.8814	−	1.93669i	1.06767	−	0.122487i
$251$	5.55147			0.350406			0.175203	−	0.984532i	$-0.443942\pi$
$251$	5.55147			0.350406			0.175203	+	0.984532i	$0.443942\pi$
$252$		0			0
$253$	11.2225			0.705553
$254$	25.1593	−	2.88636i	1.57863	−	0.181106i
$255$		0			0
$256$	9.77195	−	12.6692i	0.610747	−	0.791826i
$257$	16.9652	+	9.79486i	1.05826	+	0.610987i	0.924950	−	0.380088i	$-0.124106\pi$
$257$	16.9652	+	9.79486i	1.05826	+	0.610987i	0.133309	+	0.991074i	$0.457440\pi$
$258$		0			0
$259$	0.120276	−	10.5159i	0.00747359	−	0.653428i
$260$	−2.28678	−	2.44464i	−0.141820	−	0.151610i
$261$		0			0
$262$	−13.0344	−	5.65549i	−0.805270	−	0.349397i
$263$	−11.4745	+	6.62480i	−0.707548	+	0.408503i	−0.810152	−	0.586219i	$-0.800616\pi$
$263$	−11.4745	+	6.62480i	−0.707548	+	0.408503i	0.102605	+	0.994722i	$0.467282\pi$
$264$		0			0
$265$	12.3460	+	7.12794i	0.758406	+	0.437866i
$266$	−10.6119	+	1.09462i	−0.650655	+	0.0671155i
$267$		0			0
$268$	−4.82984	−	1.46842i	−0.295029	−	0.0896980i
$269$			23.5318i			1.43476i	0.696683	+	0.717379i	$0.254658\pi$
$269$			23.5318i			1.43476i	−0.696683	+	0.717379i	$0.745342\pi$
$270$		0			0
$271$	−20.2947			−1.23281			−0.616406	−	0.787428i	$-0.711412\pi$
$271$	−20.2947			−1.23281			−0.616406	+	0.787428i	$0.711412\pi$
$272$	−13.5192	−	27.5010i	−0.819721	−	1.66749i
$273$		0			0
$274$	4.49259	−	3.32975i	0.271407	−	0.201157i
$275$	−9.61892	−	5.55349i	−0.580043	−	0.334888i
$276$		0			0
$277$	9.44902	+	16.3662i	0.567736	+	0.983348i	0.996789	+	0.0800689i	$0.0255140\pi$
$277$	9.44902	+	16.3662i	0.567736	+	0.983348i	−0.429053	+	0.903279i	$0.641153\pi$
$278$	−12.5859	−	5.46088i	−0.754853	−	0.327522i
$279$		0			0
$280$	−12.1495	−	2.36637i	−0.726070	−	0.141418i
$281$	1.06714	+	1.84834i	0.0636602	+	0.110263i	0.896099	−	0.443854i	$-0.146389\pi$
$281$	1.06714	+	1.84834i	0.0636602	+	0.110263i	−0.832439	+	0.554117i	$0.813056\pi$
$282$		0			0
$283$	−0.122715	+	0.212549i	−0.00729468	+	0.0126347i	−0.869650	−	0.493669i	$-0.835655\pi$
$283$	−0.122715	+	0.212549i	−0.00729468	+	0.0126347i	0.862355	+	0.506304i	$0.168989\pi$
$284$	0.454572	+	1.95509i	0.0269739	+	0.116013i
$285$		0			0
$286$	0.800135	+	6.97447i	0.0473130	+	0.412409i
$287$	10.4357	−	17.6069i	0.615997	−	1.03930i
$288$		0			0
$289$	−41.6920			−2.45247
$290$	−19.5144	+	2.23876i	−1.14593	+	0.131465i
$291$		0			0
$292$	2.67075	+	11.4868i	0.156294	+	0.672212i
$293$	−9.64296	−	5.56736i	−0.563347	−	0.325249i	0.191141	−	0.981563i	$-0.438781\pi$
$293$	−9.64296	−	5.56736i	−0.563347	−	0.325249i	−0.754488	+	0.656314i	$0.772115\pi$
$294$		0			0
$295$	−7.28768	+	4.20754i	−0.424305	+	0.244973i
$296$	−3.77762	−	10.5891i	−0.219569	−	0.615478i
$297$		0			0
$298$	8.99993	+	3.90496i	0.521352	+	0.226208i
$299$	1.15745	+	2.00476i	0.0669371	+	0.115939i
$300$		0			0
$301$	10.0432	+	17.8640i	0.578878	+	1.02967i
$302$	−10.5502	−	14.2346i	−0.607094	−	0.819108i
$303$		0			0
$304$	−10.2349	+	5.03138i	−0.587013	+	0.288569i
$305$	−9.79335			−0.560765
$306$		0			0
$307$	23.3864			1.33473			0.667366	−	0.744730i	$-0.267422\pi$
$307$	23.3864			1.33473			0.667366	+	0.744730i	$0.267422\pi$
$308$	17.5150	+	19.1587i	0.998011	+	1.09167i
$309$		0			0
$310$	0.971615	+	1.31093i	0.0551840	+	0.0744558i
$311$	−15.3325	+	26.5567i	−0.869428	+	1.50589i	−0.00684678	+	0.999977i	$0.502179\pi$
$311$	−15.3325	+	26.5567i	−0.869428	+	1.50589i	−0.862582	+	0.505918i	$0.831154\pi$
$312$		0			0
$313$	−13.6566	+	7.88467i	−0.771919	+	0.445668i	−0.833559	−	0.552431i	$-0.813700\pi$
$313$	−13.6566	+	7.88467i	−0.771919	+	0.445668i	0.0616396	+	0.998098i	$0.480367\pi$
$314$	0.940006	−	2.16647i	0.0530476	−	0.122261i
$315$		0			0
$316$	−8.27672	+	7.74227i	−0.465602	+	0.435537i
$317$	3.31354	+	5.73923i	0.186107	+	0.322347i	0.943949	−	0.330091i	$-0.107080\pi$
$317$	3.31354	+	5.73923i	0.186107	+	0.322347i	−0.757842	+	0.652438i	$0.773746\pi$
$318$		0			0
$319$	35.6745	+	20.5967i	1.99739	+	1.15319i
$320$	−13.0597	+	2.13096i	−0.730058	+	0.119125i
$321$		0			0
$322$	7.81292	+	3.49664i	0.435397	+	0.194860i
$323$			21.8432i			1.21539i
$324$		0			0
$325$		−	2.29107i		−	0.127086i
$326$	−9.93212	+	1.13945i	−0.550089	+	0.0631082i
$327$		0			0
$328$	3.93718	−	21.5232i	0.217394	−	1.18842i
$329$	−17.0997	+	9.61345i	−0.942736	+	0.530006i
$330$		0			0
$331$	−6.89178	+	3.97897i	−0.378807	+	0.218704i	−0.677299	−	0.735708i	$-0.736850\pi$
$331$	−6.89178	+	3.97897i	−0.378807	+	0.218704i	0.298492	+	0.954412i	$0.403516\pi$
$332$	−3.29915	−	3.52689i	−0.181064	−	0.193563i
$333$		0			0
$334$	1.50134	+	0.651413i	0.0821496	+	0.0356437i
$335$	2.08746	+	3.61559i	0.114050	+	0.197541i
$336$		0			0
$337$	−16.0246	+	27.7555i	−0.872918	+	1.51194i	−0.0139542	+	0.999903i	$0.504442\pi$
$337$	−16.0246	+	27.7555i	−0.872918	+	1.51194i	−0.858964	+	0.512036i	$0.828891\pi$
$338$	13.6068	−	10.0849i	0.740114	−	0.548547i
$339$		0			0
$340$	−7.37204	+	24.2477i	−0.399805	+	1.31502i
$341$		−	3.42203i		−	0.185313i
$342$		0			0
$343$	−0.635325	+	18.5094i	−0.0343043	+	0.999411i
$344$	16.6926	+	14.1896i	0.900004	+	0.765052i
$345$		0			0
$346$	−1.26745	−	1.71008i	−0.0681385	−	0.0919343i
$347$	2.35072	+	1.35719i	0.126193	+	0.0728576i	0.561768	−	0.827295i	$-0.310121\pi$
$347$	2.35072	+	1.35719i	0.126193	+	0.0728576i	−0.435575	+	0.900153i	$0.643455\pi$
$348$		0			0
$349$	−0.192902	+	0.111372i	−0.0103258	+	0.00596160i	−0.505154	−	0.863029i	$-0.668564\pi$
$349$	−0.192902	+	0.111372i	−0.0103258	+	0.00596160i	0.494828	+	0.868991i	$0.335231\pi$
$350$	−4.96620	−	6.86325i	−0.265455	−	0.366856i
$351$		0			0
$352$	24.6647	+	12.7180i	1.31463	+	0.677869i
$353$	24.5385	−	14.1673i	1.30605	−	0.754049i	0.324617	−	0.945846i	$-0.394765\pi$
$353$	24.5385	−	14.1673i	1.30605	−	0.754049i	0.981435	+	0.191796i	$0.0614312\pi$
$354$		0			0
$355$	0.830019	−	1.43763i	0.0440528	−	0.0763017i
$356$	−3.71284	−	15.9687i	−0.196780	−	0.846341i
$357$		0			0
$358$	1.79963	−	0.206460i	0.0951135	−	0.0109117i
$359$			21.8680i			1.15415i	0.816691	+	0.577075i	$0.195806\pi$
$359$			21.8680i			1.15415i	−0.816691	+	0.577075i	$0.804194\pi$
$360$		0			0
$361$	−10.8707			−0.572143
$362$	37.4013	−	4.29081i	1.96577	−	0.225520i
$363$		0			0
$364$	−1.61602	+	5.10480i	−0.0847026	+	0.267564i
$365$	4.87662	−	8.44655i	0.255254	−	0.442113i
$366$		0			0
$367$	3.75833	+	6.50962i	0.196183	+	0.339800i	0.947288	−	0.320384i	$-0.103812\pi$
$367$	3.75833	+	6.50962i	0.196183	+	0.339800i	−0.751104	+	0.660183i	$0.770479\pi$
$368$	9.13034	+	0.609920i	0.475952	+	0.0317943i
$369$		0			0
$370$	−3.70094	+	8.52972i	−0.192403	+	0.443439i
$371$	0.260794	−	22.8017i	0.0135398	−	1.18380i
$372$		0			0
$373$	5.04377	−	8.73606i	0.261156	−	0.452336i	−0.705393	−	0.708816i	$-0.749230\pi$
$373$	5.04377	−	8.73606i	0.261156	−	0.452336i	0.966549	+	0.256480i	$0.0825629\pi$
$374$	42.7001	−	31.6479i	2.20797	−	1.63647i
$375$		0			0
$376$	−13.5825	+	15.9784i	−0.700462	+	0.824021i
$377$			8.49709i			0.437622i
$378$		0			0
$379$			20.7129i			1.06395i	0.846761	+	0.531974i	$0.178550\pi$
$379$			20.7129i			1.06395i	−0.846761	+	0.531974i	$0.821450\pi$
$380$	9.02416	+	2.74362i	0.462930	+	0.140745i
$381$		0			0
$382$	7.23661	+	9.76382i	0.370257	+	0.499561i
$383$	12.6923	−	21.9837i	0.648545	−	1.12331i	−0.334926	−	0.942245i	$-0.608711\pi$
$383$	12.6923	−	21.9837i	0.648545	−	1.12331i	0.983471	−	0.181068i	$-0.0579555\pi$
$384$		0			0
$385$	0.245526	−	21.4667i	0.0125132	−	1.09404i
$386$	−9.87688	−	4.28546i	−0.502720	−	0.218124i
$387$		0			0
$388$	−14.8776	+	13.9169i	−0.755293	+	0.706522i
$389$	−15.9336	−	27.5978i	−0.807865	−	1.39926i	−0.914340	−	0.404947i	$-0.867290\pi$
$389$	−15.9336	−	27.5978i	−0.807865	−	1.39926i	0.106475	−	0.994315i	$-0.466043\pi$
$390$		0			0
$391$	8.76301	−	15.1780i	0.443164	−	0.767583i
$392$	6.22431	+	18.7952i	0.314375	+	0.949299i
$393$		0			0
$394$	−2.32021	−	20.2244i	−0.116890	−	1.01889i
$395$	9.37303			0.471608
$396$		0			0
$397$			10.3571i			0.519806i	0.965635	+	0.259903i	$0.0836906\pi$
$397$			10.3571i			0.519806i	−0.965635	+	0.259903i	$0.916309\pi$
$398$	3.53310	+	30.7967i	0.177098	+	1.54370i
$399$		0			0
$400$	−7.52388	−	5.04094i	−0.376194	−	0.252047i
$401$	−9.69923	+	16.7996i	−0.484356	+	0.838930i	−0.999839	−	0.0179704i	$-0.994280\pi$
$401$	−9.69923	+	16.7996i	−0.484356	+	0.838930i	0.515482	+	0.856900i	$0.327613\pi$
$402$		0			0
$403$	0.611303	−	0.352936i	0.0304512	−	0.0175810i
$404$	−1.42757	+	1.33539i	−0.0710242	+	0.0664380i
$405$		0			0
$406$	18.4186	+	25.4543i	0.914099	+	1.26328i
$407$	16.8870	−	9.74974i	0.837060	−	0.483277i
$408$		0			0
$409$	14.1825	+	8.18830i	0.701282	+	0.404885i	0.807825	−	0.589423i	$-0.200645\pi$
$409$	14.1825	+	8.18830i	0.701282	+	0.404885i	−0.106543	+	0.994308i	$0.533978\pi$
$410$	−14.5379	+	10.7750i	−0.717976	+	0.532139i
$411$		0			0
$412$	7.60387	−	25.0102i	0.374616	−	1.23216i
$413$	11.5793	+	6.86310i	0.569782	+	0.337711i
$414$		0			0
$415$			3.99405i			0.196060i
$416$	0.271921	+	5.71773i	0.0133320	+	0.280335i
$417$		0			0
$418$	−11.7783	−	15.8915i	−0.576093	−	0.777281i
$419$	10.4437	−	18.0890i	0.510209	−	0.883707i	−0.489722	−	0.871879i	$-0.662902\pi$
$419$	10.4437	−	18.0890i	0.510209	−	0.883707i	0.999930	−	0.0118282i	$-0.00376511\pi$
$420$		0			0
$421$	−2.68795	−	4.65567i	−0.131003	−	0.226904i	0.793061	−	0.609143i	$-0.208486\pi$
$421$	−2.68795	−	4.65567i	−0.131003	−	0.226904i	−0.924063	+	0.382239i	$0.875153\pi$
$422$	−0.945502	+	2.17914i	−0.0460263	+	0.106079i
$423$		0			0
$424$	−8.19100	−	22.9603i	−0.397790	−	1.11505i
$425$	−15.0217	+	8.67279i	−0.728660	+	0.420692i
$426$		0			0
$427$	7.67685	+	13.6550i	0.371509	+	0.660813i
$428$	0.467166	+	2.00926i	0.0225813	+	0.0971210i
$429$		0			0
$430$	−2.06512	−	18.0009i	−0.0995892	−	0.868080i
$431$			0.569062i			0.0274108i	0.999906	+	0.0137054i	$0.00436270\pi$
$431$			0.569062i			0.0274108i	−0.999906	+	0.0137054i	$0.995637\pi$
$432$		0			0
$433$			29.1119i			1.39903i	0.714619	+	0.699514i	$0.246600\pi$
$433$			29.1119i			1.39903i	−0.714619	+	0.699514i	$0.753400\pi$
$434$	1.06621	−	2.38236i	0.0511799	−	0.114357i
$435$		0			0
$436$	1.64105	−	0.381555i	0.0785919	−	0.0182732i
$437$	−5.64873	−	3.26129i	−0.270215	−	0.156009i
$438$		0			0
$439$	0.679870	+	1.17757i	0.0324484	+	0.0562023i	0.881794	−	0.471636i	$-0.156336\pi$
$439$	0.679870	+	1.17757i	0.0324484	+	0.0562023i	−0.849345	+	0.527838i	$0.823003\pi$
$440$	−7.71145	−	21.6160i	−0.367629	−	1.03050i
$441$		0			0
$442$	10.0575	+	4.36381i	0.478384	+	0.207565i
$443$	3.04716	−	1.75928i	0.144775	−	0.0835858i	−0.425863	−	0.904788i	$-0.640029\pi$
$443$	3.04716	−	1.75928i	0.144775	−	0.0835858i	0.570638	+	0.821202i	$0.306696\pi$
$444$		0			0
$445$	−6.77940	+	11.7423i	−0.321374	+	0.556637i
$446$	−9.29393	+	6.88834i	−0.440080	+	0.326172i
$447$		0			0
$448$	13.2085	+	16.5389i	0.624044	+	0.781389i
$449$	−13.2772			−0.626591			−0.313295	−	0.949656i	$-0.601433\pi$
$449$	−13.2772			−0.626591			−0.313295	+	0.949656i	$0.601433\pi$
$450$		0			0
$451$	37.9495			1.78697
$452$	3.71356	−	12.2144i	0.174671	−	0.574518i
$453$		0			0
$454$	−30.6911	+	22.7472i	−1.44040	+	1.06758i
$455$	3.86009	−	2.17014i	0.180964	−	0.101738i
$456$		0			0
$457$	11.7494	+	20.3506i	0.549614	+	0.951959i	0.998301	+	0.0582701i	$0.0185584\pi$
$457$	11.7494	+	20.3506i	0.549614	+	0.951959i	−0.448687	+	0.893689i	$0.648108\pi$
$458$	−6.77391	+	15.6121i	−0.316524	+	0.729507i
$459$		0			0
$460$	−5.16986	−	5.52674i	−0.241046	−	0.257685i
$461$	13.3984	−	7.73555i	0.624024	−	0.360280i	−0.154410	−	0.988007i	$-0.549348\pi$
$461$	13.3984	−	7.73555i	0.624024	−	0.360280i	0.778434	+	0.627726i	$0.216014\pi$
$462$		0			0
$463$	18.2044	+	10.5103i	0.846031	+	0.488456i	0.859310	−	0.511456i	$-0.170894\pi$
$463$	18.2044	+	10.5103i	0.846031	+	0.488456i	−0.0132786	+	0.999912i	$0.504227\pi$
$464$	27.9045	+	18.6958i	1.29543	+	0.867929i
$465$		0			0
$466$	−2.09132	−	18.2292i	−0.0968786	−	0.844453i
$467$	−29.6578			−1.37240			−0.686199	−	0.727414i	$-0.740722\pi$
$467$	−29.6578			−1.37240			−0.686199	+	0.727414i	$0.740722\pi$
$468$		0			0
$469$	3.40495	−	5.74479i	0.157226	−	0.265270i
$470$	17.2307	−	1.97676i	0.794792	−	0.0911813i
$471$		0			0
$472$	14.1549	+	2.58932i	0.651534	+	0.119183i
$473$	−18.9992	+	32.9076i	−0.873586	+	1.51310i
$474$		0			0
$475$	3.22772	+	5.59057i	0.148098	+	0.256513i
$476$	39.5878	−	8.72844i	1.81450	−	0.400067i
$477$		0			0
$478$	−3.67288	+	8.46504i	−0.167994	+	0.387182i
$479$	2.16539	+	3.75057i	0.0989393	+	0.171368i	0.911246	−	0.411863i	$-0.135122\pi$
$479$	2.16539	+	3.75057i	0.0989393	+	0.171368i	−0.812307	+	0.583231i	$0.801788\pi$
$480$		0			0
$481$	3.48334	+	2.01111i	0.158827	+	0.0916987i
$482$	−19.4630	−	26.2600i	−0.886515	−	1.19611i
$483$		0			0
$484$	−7.60102	+	25.0008i	−0.345501	+	1.13640i
$485$	16.8482			0.765037
$486$		0			0
$487$		−	33.3117i		−	1.50950i	−0.656015	−	0.754748i	$-0.727759\pi$
$487$		−	33.3117i		−	1.50950i	0.656015	−	0.754748i	$-0.272241\pi$
$488$	12.7596	+	10.8463i	0.577599	+	0.490990i
$489$		0			0
$490$	6.85940	−	14.8683i	0.309876	−	0.671679i
$491$	−27.8604	−	16.0852i	−1.25732	−	0.725916i	−0.284770	−	0.958596i	$-0.591917\pi$
$491$	−27.8604	−	16.0852i	−1.25732	−	0.725916i	−0.972553	+	0.232680i	$0.925250\pi$
$492$		0			0
$493$	55.7123	−	32.1655i	2.50916	−	1.44866i
$494$	1.62406	−	3.74304i	0.0730699	−	0.168407i
$495$		0			0
$496$	0.185980	−	2.78407i	0.00835075	−	0.125008i
$497$	−2.65516	−	0.0303684i	−0.119100	−	0.00136221i
$498$		0			0
$499$	−29.5577	−	17.0652i	−1.32319	−	0.763941i	−0.338950	−	0.940805i	$-0.610072\pi$
$499$	−29.5577	−	17.0652i	−1.32319	−	0.763941i	−0.984235	+	0.176863i	$0.943405\pi$
$500$	5.44208	+	23.4061i	0.243377	+	1.04675i
$501$		0			0
$502$	0.894821	+	7.79980i	0.0399378	+	0.348122i
$503$	9.76180			0.435257			0.217629	−	0.976032i	$-0.430168\pi$
$503$	9.76180			0.435257			0.217629	+	0.976032i	$0.430168\pi$
$504$		0			0
$505$	1.61666			0.0719405
$506$	1.80891	+	15.7676i	0.0804161	+	0.700956i
$507$		0			0
$508$	8.11066	+	34.8835i	0.359852	+	1.54770i
$509$	−12.0256	−	6.94300i	−0.533027	−	0.307743i	0.209221	−	0.977868i	$-0.432907\pi$
$509$	−12.0256	−	6.94300i	−0.533027	−	0.307743i	−0.742248	+	0.670125i	$0.766240\pi$
$510$		0			0
$511$	−15.5999	−	0.178424i	−0.690097	−	0.00789300i
$512$	19.3753	+	11.6875i	0.856276	+	0.516518i
$513$		0			0
$514$	−11.0272	+	25.4149i	−0.486389	+	1.12100i
$515$	−18.7225	+	10.8094i	−0.825012	+	0.476321i
$516$		0			0
$517$	−31.4996	−	18.1863i	−1.38535	−	0.799833i
$518$	14.7942	−	1.52603i	0.650021	−	0.0670501i
$519$		0			0
$520$	3.06611	−	3.60696i	0.134458	−	0.158176i
$521$			15.9160i			0.697291i	0.937255	+	0.348646i	$0.113358\pi$
$521$			15.9160i			0.697291i	−0.937255	+	0.348646i	$0.886642\pi$
$522$		0			0
$523$	−28.0511			−1.22659			−0.613294	−	0.789855i	$-0.710156\pi$
$523$	−28.0511			−1.22659			−0.613294	+	0.789855i	$0.710156\pi$
$524$	5.84497	−	19.2249i	0.255339	−	0.839846i
$525$		0			0
$526$	−11.1574	−	15.0538i	−0.486484	−	0.656378i
$527$	−4.62815	−	2.67206i	−0.201605	−	0.116397i
$528$		0			0
$529$	−8.88328	−	15.3863i	−0.386229	−	0.668969i
$530$	−8.02475	+	18.4950i	−0.348573	+	0.803370i
$531$		0			0
$532$	−3.24843	−	14.7332i	−0.140837	−	0.638766i
$533$	3.91398	+	6.77921i	0.169533	+	0.293640i
$534$		0			0
$535$	0.853014	−	1.47746i	0.0368790	−	0.0638763i
$536$	1.28462	−	7.02260i	0.0554872	−	0.303330i
$537$		0			0
$538$	−33.0621	+	3.79300i	−1.42541	+	0.163528i
$539$	−30.1238	+	16.4851i	−1.29753	+	0.710063i
$540$		0			0
$541$	4.98478			0.214313			0.107156	−	0.994242i	$-0.465825\pi$
$541$	4.98478			0.214313			0.107156	+	0.994242i	$0.465825\pi$
$542$	−3.27122	−	28.5140i	−0.140511	−	1.22478i
$543$		0			0
$544$	36.4597	−	23.4272i	1.56320	−	1.00443i
$545$	−1.20671	−	0.696694i	−0.0516897	−	0.0298431i
$546$		0			0
$547$	24.9146	−	14.3844i	1.06527	−	0.615034i	0.138384	−	0.990379i	$-0.455809\pi$
$547$	24.9146	−	14.3844i	1.06527	−	0.615034i	0.926885	+	0.375345i	$0.122476\pi$
$548$	5.40243	+	5.77536i	0.230780	+	0.246711i
$549$		0			0
$550$	6.25220	−	14.4097i	0.266595	−	0.614432i
$551$	−11.9709	−	20.7342i	−0.509978	−	0.883308i
$552$		0			0
$553$	−7.34738	−	13.0690i	−0.312442	−	0.555749i
$554$	−21.4714	+	15.9139i	−0.912232	+	0.676115i
$555$		0			0
$556$	5.64384	−	18.5634i	0.239352	−	0.787264i
$557$	24.8923			1.05472			0.527360	−	0.849642i	$-0.323182\pi$
$557$	24.8923			1.05472			0.527360	+	0.849642i	$0.323182\pi$
$558$		0			0
$559$	−7.83806			−0.331515
$560$	1.36642	−	17.4514i	0.0577420	−	0.737456i
$561$		0			0
$562$	−2.42491	+	1.79726i	−0.102289	+	0.0758127i
$563$	−5.94575	+	10.2983i	−0.250584	+	0.434024i	−0.963687	−	0.267036i	$-0.913956\pi$
$563$	−5.94575	+	10.2983i	−0.250584	+	0.434024i	0.713103	+	0.701059i	$0.247289\pi$
$564$		0			0
$565$	−9.14366	+	5.27909i	−0.384677	+	0.222093i
$566$	−0.318411	−	0.138155i	−0.0133838	−	0.00580708i
$567$		0			0
$568$	−2.67363	+	0.953807i	−0.112183	+	0.0400208i
$569$	−2.96159	−	5.12962i	−0.124156	−	0.215045i	0.797247	−	0.603654i	$-0.206289\pi$
$569$	−2.96159	−	5.12962i	−0.124156	−	0.215045i	−0.921403	+	0.388609i	$0.872956\pi$
$570$		0			0
$571$	−28.8922	−	16.6809i	−1.20910	−	0.698074i	−0.246537	−	0.969133i	$-0.579293\pi$
$571$	−28.8922	−	16.6809i	−1.20910	−	0.698074i	−0.962563	+	0.271059i	$0.912626\pi$
$572$	−9.67014	+	2.24838i	−0.404329	+	0.0940093i
$573$		0			0
$574$	26.4198	+	11.8241i	1.10274	+	0.493527i
$575$		−	5.17956i		−	0.216003i
$576$		0			0
$577$		−	29.0803i		−	1.21063i	−0.795987	−	0.605314i	$-0.793048\pi$
$577$		−	29.0803i		−	1.21063i	0.795987	−	0.605314i	$-0.206952\pi$
$578$	−6.72017	−	58.5772i	−0.279522	−	2.43649i
$579$		0			0
$580$	−6.29091	−	27.0568i	−0.261216	−	1.12347i
$581$	5.56897	−	3.13088i	0.231040	−	0.129891i
$582$		0			0
$583$	36.6162	−	21.1403i	1.51649	−	0.875544i
$584$	−15.7084	+	5.60391i	−0.650018	+	0.231891i
$585$		0			0
$586$	6.26782	−	14.4457i	0.258921	−	0.596747i
$587$	7.47781	+	12.9519i	0.308642	+	0.534584i	0.978066	−	0.208297i	$-0.0667921\pi$
$587$	7.47781	+	12.9519i	0.308642	+	0.534584i	−0.669423	+	0.742881i	$0.733459\pi$
$588$		0			0
$589$	−0.994450	+	1.72244i	−0.0409756	+	0.0709718i
$590$	−7.08626	−	9.56098i	−0.291737	−	0.393619i
$591$		0			0
$592$	14.2687	−	7.01436i	0.586441	−	0.288288i
$593$			15.6604i			0.643096i	0.946893	+	0.321548i	$0.104203\pi$
$593$			15.6604i			0.643096i	−0.946893	+	0.321548i	$0.895797\pi$
$594$		0			0
$595$	−28.8411	−	17.0942i	−1.18237	−	0.700793i
$596$	−4.03580	+	13.2743i	−0.165313	+	0.543737i
$597$		0			0
$598$	−2.63012	+	1.94936i	−0.107554	+	0.0797151i
$599$	33.5225	+	19.3542i	1.36969	+	0.790791i	0.990888	−	0.134686i	$-0.0430026\pi$
$599$	33.5225	+	19.3542i	1.36969	+	0.790791i	0.378803	+	0.925477i	$0.376336\pi$
$600$		0			0
$601$	−22.3109	+	12.8812i	−0.910081	+	0.525435i	−0.880457	−	0.474126i	$-0.842764\pi$
$601$	−22.3109	+	12.8812i	−0.910081	+	0.525435i	−0.0296235	+	0.999561i	$0.509431\pi$
$602$	−23.4801	+	16.9901i	−0.956978	+	0.692463i
$603$		0			0
$604$	18.2990	−	17.1174i	0.744576	−	0.696496i
$605$	18.7155	−	10.8054i	0.760893	−	0.439302i
$606$		0			0
$607$	−3.14595	+	5.44895i	−0.127690	+	0.221166i	−0.922781	−	0.385324i	$-0.874090\pi$
$607$	−3.14595	+	5.44895i	−0.127690	+	0.221166i	0.795091	+	0.606490i	$0.207423\pi$
$608$	−8.71881	−	13.5691i	−0.353594	−	0.550298i
$609$		0			0
$610$	−1.57855	−	13.7596i	−0.0639137	−	0.557111i
$611$		−	7.50270i		−	0.303527i
$612$		0			0
$613$	22.1645			0.895217			0.447608	−	0.894230i	$-0.352276\pi$
$613$	22.1645			0.895217			0.447608	+	0.894230i	$0.352276\pi$
$614$	3.76957	+	32.8579i	0.152127	+	1.32604i
$615$		0			0
$616$	−24.0947	+	27.6967i	−0.970803	+	1.11593i
$617$	20.1769	−	34.9474i	0.812291	−	1.40693i	−0.0989666	−	0.995091i	$-0.531554\pi$
$617$	20.1769	−	34.9474i	0.812291	−	1.40693i	0.911257	−	0.411838i	$-0.135113\pi$
$618$		0			0
$619$	19.4800	+	33.7403i	0.782966	+	1.35614i	0.930207	+	0.367035i	$0.119627\pi$
$619$	19.4800	+	33.7403i	0.782966	+	1.35614i	−0.147241	+	0.989101i	$0.547039\pi$
$620$	−1.68524	+	1.57642i	−0.0676809	+	0.0633106i
$621$		0			0
$622$	−39.7836	−	17.2616i	−1.59518	−	0.692127i
$623$	21.6867	+	0.248042i	0.868859	+	0.00993759i
$624$		0			0
$625$	4.27658	−	7.40725i	0.171063	−	0.296290i
$626$	−13.2792	−	17.9167i	−0.530744	−	0.716094i
$627$		0			0
$628$	3.19540	+	0.971501i	0.127510	+	0.0387671i
$629$		−	30.4520i		−	1.21420i
$630$		0			0
$631$		−	1.06032i		−	0.0422108i	−0.999777	−	0.0211054i	$-0.993281\pi$
$631$		−	1.06032i		−	0.0422108i	0.999777	−	0.0211054i	$-0.00671856\pi$
$632$	−12.2120	−	10.3808i	−0.485766	−	0.412927i
$633$		0			0
$634$	−7.52950	+	5.58061i	−0.299035	+	0.221634i
$635$	14.8095	−	25.6508i	0.587698	−	1.01792i
$636$		0			0
$637$	−6.05173	−	3.68104i	−0.239778	−	0.145848i
$638$	−23.1881	+	53.4425i	−0.918024	+	2.11581i
$639$		0			0
$640$	−5.09904	−	18.0053i	−0.201557	−	0.711724i
$641$	13.7294	+	23.7800i	0.542278	+	0.939253i	0.998773	+	0.0495272i	$0.0157714\pi$
$641$	13.7294	+	23.7800i	0.542278	+	0.939253i	−0.456495	+	0.889726i	$0.650895\pi$
$642$		0			0
$643$	0.0203966	−	0.0353280i	0.000804364	−	0.00139320i	−0.865623	−	0.500696i	$-0.833077\pi$
$643$	0.0203966	−	0.0353280i	0.000804364	−	0.00139320i	0.866427	+	0.499303i	$0.166411\pi$
$644$	−3.65344	+	11.5407i	−0.143966	+	0.454769i
$645$		0			0
$646$	−30.6896	+	3.52082i	−1.20747	+	0.138525i
$647$	−12.6901			−0.498899			−0.249449	−	0.968388i	$-0.580250\pi$
$647$	−12.6901			−0.498899			−0.249449	+	0.968388i	$0.580250\pi$
$648$		0			0
$649$			24.9578i			0.979680i
$650$	3.21895	−	0.369289i	0.126258	−	0.0144847i
$651$		0			0
$652$	−3.20184	−	13.7709i	−0.125394	−	0.539312i
$653$	3.40787	−	5.90260i	0.133360	−	0.230987i	−0.791610	−	0.611027i	$-0.790757\pi$
$653$	3.40787	−	5.90260i	0.133360	−	0.230987i	0.924970	+	0.380041i	$0.124090\pi$
$654$		0			0
$655$	−14.3917	+	8.30905i	−0.562330	+	0.324661i
$656$	30.8747	+	2.06248i	1.20545	+	0.0805261i
$657$		0			0
$658$	−16.2631	−	22.4755i	−0.634002	−	0.876185i
$659$	21.9583	−	12.6776i	0.855375	−	0.493851i	−0.00708581	−	0.999975i	$-0.502256\pi$
$659$	21.9583	−	12.6776i	0.855375	−	0.493851i	0.862461	+	0.506124i	$0.168922\pi$
$660$		0			0
$661$	−27.4120	−	15.8263i	−1.06620	−	0.615572i	−0.139061	−	0.990284i	$-0.544408\pi$
$661$	−27.4120	−	15.8263i	−1.06620	−	0.615572i	−0.927141	+	0.374712i	$0.877742\pi$
$662$	−6.70131	−	9.04158i	−0.260454	−	0.351411i
$663$		0			0
$664$	4.42349	−	5.20378i	0.171665	−	0.201946i
$665$	−6.36187	+	10.7337i	−0.246703	+	0.416234i
$666$		0			0
$667$			19.2099i			0.743810i
$668$	−0.673239	+	2.21438i	−0.0260484	+	0.0856768i
$669$		0			0
$670$	−4.74343	+	3.51566i	−0.183255	+	0.135822i
$671$	−14.5228	+	25.1541i	−0.560645	+	0.971065i
$672$		0			0
$673$	−2.22066	−	3.84630i	−0.0856002	−	0.148264i	0.820047	−	0.572297i	$-0.193947\pi$
$673$	−2.22066	−	3.84630i	−0.0856002	−	0.148264i	−0.905647	+	0.424033i	$0.860614\pi$
$674$	−41.5794	−	18.0408i	−1.60158	−	0.694905i
$675$		0			0
$676$	16.3625	+	17.4920i	0.629328	+	0.672770i
$677$	−5.61421	+	3.24137i	−0.215772	+	0.124576i	−0.603991	−	0.796991i	$-0.706424\pi$
$677$	−5.61421	+	3.24137i	−0.215772	+	0.124576i	0.388219	+	0.921567i	$0.373090\pi$
$678$		0			0
$679$	−13.2070	−	23.4917i	−0.506840	−	0.901529i
$680$	−35.2562	−	6.44931i	−1.35201	−	0.247320i
$681$		0			0
$682$	4.80794	−	0.551583i	0.184106	−	0.0211212i
$683$		−	28.5921i		−	1.09405i	−0.837117	−	0.547024i	$-0.815761\pi$
$683$		−	28.5921i		−	1.09405i	0.837117	−	0.547024i	$-0.184239\pi$
$684$		0			0
$685$		−	6.54035i		−	0.249894i
$686$	−26.1080	+	2.09082i	−0.996809	+	0.0798280i
$687$		0			0
$688$	−17.2457	+	25.7402i	−0.657488	+	0.981337i
$689$	7.55293	+	4.36069i	0.287744	+	0.166129i
$690$		0			0
$691$	4.98156	+	8.62831i	0.189507	+	0.328236i	0.945086	−	0.326822i	$-0.105978\pi$
$691$	4.98156	+	8.62831i	0.189507	+	0.328236i	−0.755579	+	0.655058i	$0.772644\pi$
$692$	2.19836	−	2.05640i	0.0835690	−	0.0781728i
$693$		0			0
$694$	−1.52794	+	3.52151i	−0.0579999	+	0.133675i
$695$	−13.8965	+	8.02313i	−0.527123	+	0.304335i
$696$		0			0
$697$	29.6326	−	51.3251i	1.12241	−	1.94408i
$698$	−0.187570	−	0.253075i	−0.00709964	−	0.00957902i
$699$		0			0
$700$	8.84236	−	8.08377i	0.334210	−	0.305538i
$701$	13.0365			0.492382			0.246191	−	0.969221i	$-0.420821\pi$
$701$	13.0365			0.492382			0.246191	+	0.969221i	$0.420821\pi$
$702$		0			0
$703$	−11.3332			−0.427440
$704$	−13.8931	+	36.7038i	−0.523616	+	1.38332i
$705$		0			0
$706$	23.8603	+	32.1929i	0.897994	+	1.21160i
$707$	−1.26728	−	2.25414i	−0.0476608	−	0.0847755i
$708$		0			0
$709$	−1.46945	−	2.54516i	−0.0551862	−	0.0955853i	0.837113	−	0.547031i	$-0.184242\pi$
$709$	−1.46945	−	2.54516i	−0.0551862	−	0.0955853i	−0.892299	+	0.451445i	$0.850909\pi$
$710$	2.15366	+	0.934447i	0.0808254	+	0.0350692i
$711$		0			0
$712$	21.8376	−	7.79047i	0.818397	−	0.291960i
$713$	1.38201	−	0.797904i	0.0517567	−	0.0298817i
$714$		0			0
$715$	7.11073	+	4.10538i	0.265926	+	0.153533i
$716$	0.580152	+	2.49520i	0.0216813	+	0.0932500i
$717$		0			0
$718$	−30.7245	+	3.52482i	−1.14663	+	0.131545i
$719$	52.8108			1.96951			0.984754	−	0.173951i	$-0.0556534\pi$
$719$	52.8108			1.96951			0.984754	+	0.173951i	$0.0556534\pi$
$720$		0			0
$721$	29.7481	+	17.6317i	1.10788	+	0.656640i
$722$	−1.75221	−	15.2733i	−0.0652105	−	0.568415i
$723$		0			0
$724$	12.0571	+	51.8571i	0.448100	+	1.92726i
$725$	9.50606	−	16.4650i	0.353046	−	0.611494i
$726$		0			0
$727$	−13.3309	−	23.0897i	−0.494414	−	0.856351i	0.505565	−	0.862789i	$-0.331284\pi$
$727$	−13.3309	−	23.0897i	−0.494414	−	0.856351i	−0.999979	+	0.00643778i	$0.997951\pi$
$728$	−7.43272	−	1.44768i	−0.275475	−	0.0536548i
$729$		0			0
$730$	12.6534	+	5.49017i	0.468324	+	0.203200i
$731$	29.6708	+	51.3913i	1.09741	+	1.90078i
$732$		0			0
$733$	−23.6033	−	13.6274i	−0.871807	−	0.503338i	−0.00385894	−	0.999993i	$-0.501228\pi$
$733$	−23.6033	−	13.6274i	−0.871807	−	0.503338i	−0.867948	+	0.496654i	$0.834562\pi$
$734$	−8.54021	+	6.32971i	−0.315225	+	0.233634i
$735$		0			0
$736$	0.614749	+	12.9264i	0.0226599	+	0.476474i
$737$	12.3822			0.456103
$738$		0			0
$739$			42.7029i			1.57085i	0.618957	+	0.785425i	$0.287556\pi$
$739$			42.7029i			1.57085i	−0.618957	+	0.785425i	$0.712444\pi$
$740$	−12.5808	−	3.82494i	−0.462479	−	0.140608i
$741$		0			0
$742$	32.0783	−	3.30890i	1.17763	−	0.121473i
$743$	−31.9011	−	18.4181i	−1.17034	−	0.675695i	−0.216578	−	0.976265i	$-0.569490\pi$
$743$	−31.9011	−	18.4181i	−1.17034	−	0.675695i	−0.953760	+	0.300571i	$0.902823\pi$
$744$		0			0
$745$	9.93708	−	5.73718i	0.364067	−	0.210194i
$746$	13.0871	+	5.67835i	0.479154	+	0.207899i
$747$		0			0
$748$	51.3479	+	54.8924i	1.87746	+	2.00707i
$749$	−2.72872	−	0.0312097i	−0.0997051	−	0.00114038i
$750$		0			0
$751$	−20.8062	−	12.0125i	−0.759228	−	0.438341i	0.0697904	−	0.997562i	$-0.477767\pi$
$751$	−20.8062	−	12.0125i	−0.759228	−	0.438341i	−0.829019	+	0.559221i	$0.811100\pi$
$752$	−24.6389	−	16.5078i	−0.898487	−	0.601979i
$753$		0			0
$754$	−11.9384	+	1.36961i	−0.434771	+	0.0498784i
$755$	−20.7228			−0.754181
$756$		0			0
$757$	45.4741			1.65279			0.826393	−	0.563094i	$-0.190389\pi$
$757$	45.4741			1.65279			0.826393	+	0.563094i	$0.190389\pi$
$758$	−29.1015	+	3.33863i	−1.05701	+	0.121264i
$759$		0			0
$760$	−2.40021	+	13.1212i	−0.0870649	+	0.475955i
$761$	−33.8844	−	19.5632i	−1.22831	−	0.709164i	−0.261633	−	0.965167i	$-0.584261\pi$
$761$	−33.8844	−	19.5632i	−1.22831	−	0.709164i	−0.966676	+	0.256003i	$0.917594\pi$
$762$		0			0
$763$	−0.0254903	+	2.22866i	−0.000922812	+	0.0806829i
$764$	−12.5517	+	11.7412i	−0.454105	+	0.424782i
$765$		0			0
$766$	32.9328	+	14.2892i	1.18991	+	0.516288i
$767$	−4.45841	+	2.57406i	−0.160984	+	0.0929440i
$768$		0			0
$769$	−14.2130	−	8.20587i	−0.512534	−	0.295911i	0.221341	−	0.975196i	$-0.428957\pi$
$769$	−14.2130	−	8.20587i	−0.512534	−	0.295911i	−0.733874	+	0.679285i	$0.762290\pi$
$770$	30.2003	−	3.11517i	1.08834	−	0.112263i
$771$		0			0
$772$	4.42904	−	14.5677i	0.159405	−	0.524305i
$773$		−	43.6024i		−	1.56827i	−0.620591	−	0.784134i	$-0.713107\pi$
$773$		−	43.6024i		−	1.56827i	0.620591	−	0.784134i	$-0.286893\pi$
$774$		0			0
$775$	−1.57938			−0.0567330
$776$	−21.9512	−	18.6597i	−0.788003	−	0.669845i
$777$		0			0
$778$	36.2065	−	26.8350i	1.29807	−	0.962082i
$779$	−19.1015	−	11.0282i	−0.684380	−	0.395127i
$780$		0			0
$781$	−2.46170	−	4.26379i	−0.0880866	−	0.152571i
$782$	22.7375	+	9.86553i	0.813091	+	0.352790i
$783$		0			0
$784$	−25.4039	+	11.7747i	−0.907282	+	0.420524i
$785$	−1.38106	−	2.39206i	−0.0492921	−	0.0853764i
$786$		0			0
$787$	−2.89125	+	5.00779i	−0.103062	+	0.178508i	−0.912945	−	0.408083i	$-0.866197\pi$
$787$	−2.89125	+	5.00779i	−0.103062	+	0.178508i	0.809883	+	0.586592i	$0.199531\pi$
$788$	28.0412	−	6.51978i	0.998926	−	0.232257i
$789$		0			0
$790$	1.51080	+	13.1691i	0.0537520	+	0.468535i
$791$	14.5283	+	8.61095i	0.516567	+	0.306170i
$792$		0			0
$793$	−5.99131			−0.212758
$794$	−14.5517	+	1.66942i	−0.516419	+	0.0592454i
$795$		0			0
$796$	−42.6997	+	9.92799i	−1.51345	+	0.351888i
$797$	−11.1404	−	6.43191i	−0.394613	−	0.227830i	0.289544	−	0.957165i	$-0.406496\pi$
$797$	−11.1404	−	6.43191i	−0.394613	−	0.227830i	−0.684157	+	0.729335i	$0.739830\pi$
$798$		0			0
$799$	−49.1924	+	28.4013i	−1.74030	+	1.00476i
$800$	5.86976	−	11.3836i	0.207527	−	0.402470i
$801$		0			0
$802$	−25.1667	−	10.9195i	−0.888668	−	0.385582i
$803$	−14.4633	−	25.0511i	−0.510398	−	0.884035i
$804$		0			0
$805$	8.72674	−	4.90617i	0.307577	−	0.172920i
$806$	0.594408	+	0.801991i	0.0209371	+	0.0282489i
$807$		0			0
$808$	−2.10632	−	1.79049i	−0.0741001	−	0.0629890i
$809$	−11.6895			−0.410980			−0.205490	−	0.978659i	$-0.565879\pi$
$809$	−11.6895			−0.410980			−0.205490	+	0.978659i	$0.565879\pi$
$810$		0			0
$811$	−23.0355			−0.808885			−0.404443	−	0.914563i	$-0.632534\pi$
$811$	−23.0355			−0.808885			−0.404443	+	0.914563i	$0.632534\pi$
$812$	−32.7944	+	29.9810i	−1.15086	+	1.05213i
$813$		0			0
$814$	16.4203	+	22.1547i	0.575532	+	0.776523i
$815$	−5.84635	+	10.1262i	−0.204789	+	0.354705i
$816$		0			0
$817$	19.1261	−	11.0425i	0.669138	−	0.386327i
$818$	−9.21851	+	21.2463i	−0.322318	+	0.742859i
$819$		0			0
$820$	−17.4821	−	18.6889i	−0.610503	−	0.652646i
$821$	−5.85488	−	10.1410i	−0.204337	−	0.353922i	0.745584	−	0.666411i	$-0.232170\pi$
$821$	−5.85488	−	10.1410i	−0.204337	−	0.353922i	−0.949921	+	0.312489i	$0.898837\pi$
$822$		0			0
$823$	−30.7319	−	17.7431i	−1.07125	−	0.618484i	−0.142724	−	0.989763i	$-0.545586\pi$
$823$	−30.7319	−	17.7431i	−1.07125	−	0.618484i	−0.928521	+	0.371279i	$0.878919\pi$
$824$	36.3649	+	6.65212i	1.26683	+	0.231737i
$825$		0			0
$826$	−7.77621	+	17.3752i	−0.270569	+	0.604560i
$827$			28.8739i			1.00405i	0.864854	+	0.502023i	$0.167411\pi$
$827$			28.8739i			1.00405i	−0.864854	+	0.502023i	$0.832589\pi$
$828$		0			0
$829$			31.4981i			1.09397i	0.837141	+	0.546987i	$0.184225\pi$
$829$			31.4981i			1.09397i	−0.837141	+	0.546987i	$0.815775\pi$
$830$	−5.61164	+	0.643786i	−0.194783	+	0.0223461i
$831$		0			0
$832$	−7.98956	+	1.30367i	−0.276988	+	0.0451965i
$833$	−1.22657	+	53.6135i	−0.0424981	+	1.85760i
$834$		0			0
$835$	1.65767	−	0.957057i	0.0573661	−	0.0331203i
$836$	20.4291	−	19.1099i	0.706555	−	0.660931i
$837$		0			0
$838$	27.0984	+	11.7577i	0.936100	+	0.406162i
$839$	7.70959	+	13.3534i	0.266165	+	0.461011i	0.967868	−	0.251458i	$-0.0809102\pi$
$839$	7.70959	+	13.3534i	0.266165	+	0.461011i	−0.701703	+	0.712469i	$0.747577\pi$
$840$		0			0
$841$	−20.7559	+	35.9503i	−0.715722	+	1.23967i
$842$	6.10795	−	4.52700i	0.210494	−	0.156011i
$843$		0			0
$844$	−3.21409	−	0.977182i	−0.110633	−	0.0336360i
$845$		−	19.8090i		−	0.681450i
$846$		0			0
$847$	−29.7369	−	17.6251i	−1.02177	−	0.605606i
$848$	30.9389	−	15.2092i	1.06245	−	0.522287i
$849$		0			0
$850$	−14.6065	−	19.7075i	−0.501000	−	0.675963i
$851$	7.87501	+	4.54664i	0.269952	+	0.155857i
$852$		0			0
$853$	9.82218	−	5.67084i	0.336305	−	0.194166i	−0.322332	−	0.946627i	$-0.604467\pi$
$853$	9.82218	−	5.67084i	0.336305	−	0.194166i	0.658637	+	0.752461i	$0.271133\pi$
$854$	−17.9479	+	12.9870i	−0.614163	+	0.444405i
$855$		0			0
$856$	−2.74770	+	0.980232i	−0.0939144	+	0.0335036i
$857$	0.268417	−	0.154971i	0.00916895	−	0.00529370i	−0.495409	−	0.868660i	$-0.664982\pi$
$857$	0.268417	−	0.154971i	0.00916895	−	0.00529370i	0.504577	+	0.863366i	$0.331648\pi$
$858$		0			0
$859$	9.88124	−	17.1148i	0.337144	−	0.583950i	−0.646751	−	0.762702i	$-0.723873\pi$
$859$	9.88124	−	17.1148i	0.337144	−	0.583950i	0.983894	+	0.178752i	$0.0572059\pi$
$860$	24.9583	−	5.80299i	0.851073	−	0.197880i
$861$		0			0
$862$	−0.799531	+	0.0917250i	−0.0272321	+	0.00312417i
$863$		−	23.9730i		−	0.816051i	−0.912970	−	0.408026i	$-0.866217\pi$
$863$		−	23.9730i		−	0.816051i	0.912970	−	0.408026i	$-0.133783\pi$
$864$		0			0
$865$	−2.48955			−0.0846472
$866$	−40.9021	+	4.69244i	−1.38991	+	0.159455i
$867$		0			0
$868$	3.51906	+	1.11403i	0.119445	+	0.0378125i
$869$	13.8995	−	24.0746i	0.471507	−	0.816674i
$870$		0			0
$871$	1.27705	+	2.21192i	0.0432713	+	0.0749481i
$872$	0.800598	+	2.24416i	0.0271117	+	0.0759970i
$873$		0			0
$874$	3.67161	−	8.46212i	0.124194	−	0.286236i
$875$	−31.7872	−	0.363567i	−1.07460	−	0.0122908i
$876$		0			0
$877$	15.6916	−	27.1787i	0.529868	−	0.917759i	−0.469524	−	0.882919i	$-0.655575\pi$
$877$	15.6916	−	27.1787i	0.529868	−	0.917759i	0.999393	−	0.0348396i	$-0.0110920\pi$
$878$	−1.54490	+	1.14502i	−0.0521377	+	0.0386427i
$879$		0			0
$880$	29.1275	−	14.3188i	0.981888	−	0.482686i
$881$		−	2.85106i		−	0.0960548i	−0.998846	−	0.0480274i	$-0.984707\pi$
$881$		−	2.85106i		−	0.0960548i	0.998846	−	0.0480274i	$-0.0152935\pi$
$882$		0			0
$883$		−	58.5844i		−	1.97152i	−0.168153	−	0.985761i	$-0.553780\pi$
$883$		−	58.5844i		−	1.97152i	0.168153	−	0.985761i	$-0.446220\pi$
$884$	−4.51002	+	14.8341i	−0.151688	+	0.498924i
$885$		0			0
$886$	2.96294	+	3.99768i	0.0995419	+	0.134305i
$887$	−11.7716	+	20.3891i	−0.395253	+	0.684598i	−0.993133	−	0.116987i	$-0.962676\pi$
$887$	−11.7716	+	20.3891i	−0.395253	+	0.684598i	0.597881	+	0.801585i	$0.296010\pi$
$888$		0			0
$889$	−47.3743	−	0.541845i	−1.58888	−	0.0181729i
$890$	−17.5906	−	7.63235i	−0.589638	−	0.255837i
$891$		0			0
$892$	−11.1762	−	11.9476i	−0.374205	−	0.400037i
$893$	10.5700	+	18.3078i	0.353711	+	0.612646i
$894$		0			0
$895$	1.05932	−	1.83479i	0.0354091	−	0.0613304i
$896$	−21.1081	+	21.2238i	−0.705171	+	0.709037i
$897$		0			0
$898$	−2.14010	−	18.6545i	−0.0714162	−	0.622508i
$899$	5.85758			0.195361
$900$		0			0
$901$		−	66.0291i		−	2.19975i
$902$	6.11694	+	53.3190i	0.203672	+	1.77533i
$903$		0			0
$904$	17.7598	+	3.24875i	0.590683	+	0.108052i
$905$	22.0156	−	38.1321i	0.731822	−	1.26755i
$906$		0			0
$907$	16.2312	−	9.37107i	0.538947	−	0.311161i	−0.205705	−	0.978614i	$-0.565949\pi$
$907$	16.2312	−	9.37107i	0.538947	−	0.311161i	0.744652	+	0.667453i	$0.232615\pi$
$908$	−36.9067	−	39.4544i	−1.22479	−	1.30934i
$909$		0			0
$910$	3.67124	+	5.07362i	0.121700	+	0.168189i
$911$	−27.7633	+	16.0291i	−0.919838	+	0.531069i	−0.883583	−	0.468274i	$-0.844876\pi$
$911$	−27.7633	+	16.0291i	−0.919838	+	0.531069i	−0.0362544	+	0.999343i	$0.511543\pi$
$912$		0			0
$913$	10.2587	+	5.92286i	0.339513	+	0.196018i
$914$	−26.6987	+	19.7881i	−0.883113	+	0.654533i
$915$		0			0
$916$	−23.0269	−	7.00087i	−0.760829	−	0.231315i
$917$	22.8669	+	13.5532i	0.755131	+	0.447567i
$918$		0			0
$919$			40.9560i			1.35101i	0.737354	+	0.675507i	$0.236075\pi$
$919$			40.9560i			1.35101i	−0.737354	+	0.675507i	$0.763925\pi$
$920$	6.93174	−	8.15448i	0.228533	−	0.268845i
$921$		0			0
$922$	13.0281	+	17.5778i	0.429056	+	0.578894i
$923$	0.507783	−	0.879506i	0.0167139	−	0.0289493i
$924$		0			0
$925$	−4.49983	−	7.79394i	−0.147954	−	0.256263i
$926$	−11.8327	+	27.2713i	−0.388846	+	0.896190i
$927$		0			0
$928$	−21.7697	+	42.2192i	−0.714625	+	1.38591i
$929$	20.6442	−	11.9189i	0.677314	−	0.391047i	−0.121528	−	0.992588i	$-0.538779\pi$
$929$	20.6442	−	11.9189i	0.677314	−	0.391047i	0.798842	+	0.601540i	$0.205446\pi$
$930$		0			0
$931$	19.9531	+	0.456488i	0.653937	+	0.0149608i
$932$	25.2749	−	5.87660i	0.827908	−	0.192495i
$933$		0			0
$934$	−4.78042	−	41.6691i	−0.156420	−	1.36345i
$935$		−	62.1633i		−	2.03296i
$936$		0			0
$937$		−	28.7675i		−	0.939794i	−0.882721	−	0.469897i	$-0.844291\pi$
$937$		−	28.7675i		−	0.939794i	0.882721	−	0.469897i	$-0.155709\pi$
$938$	8.62025	+	3.85796i	0.281461	+	0.125967i
$939$		0			0
$940$	5.55470	+	23.8904i	0.181174	+	0.779220i
$941$	35.9743	+	20.7698i	1.17273	+	0.677075i	0.954321	−	0.298783i	$-0.0965807\pi$
$941$	35.9743	+	20.7698i	1.17273	+	0.677075i	0.218407	+	0.975858i	$0.429914\pi$
$942$		0			0
$943$	8.84858	+	15.3262i	0.288149	+	0.499089i
$944$	−1.35640	+	20.3050i	−0.0441472	+	0.660872i
$945$		0			0
$946$	−49.2976	−	21.3896i	−1.60280	−	0.695437i
$947$	11.5666	−	6.67800i	0.375865	−	0.217006i	−0.300152	−	0.953891i	$-0.597038\pi$
$947$	11.5666	−	6.67800i	0.375865	−	0.217006i	0.676018	+	0.736885i	$0.263704\pi$
$948$		0			0
$949$	2.98338	−	5.16737i	0.0968447	−	0.167740i
$950$	−7.33448	+	5.43606i	−0.237962	+	0.176369i
$951$		0			0
$952$	18.6444	+	54.2138i	0.604270	+	1.75708i
$953$	6.70188			0.217095			0.108548	−	0.994091i	$-0.465380\pi$
$953$	6.70188			0.217095			0.108548	+	0.994091i	$0.465380\pi$
$954$		0			0
$955$	14.2143			0.459963
$956$	−12.4854	−	3.79594i	−0.403806	−	0.122769i
$957$		0			0
$958$	−4.92051	+	3.64691i	−0.158975	+	0.117826i
$959$	−9.11932	+	5.12688i	−0.294478	+	0.165556i
$960$		0			0
$961$	15.2567	+	26.4254i	0.492152	+	0.852432i
$962$	−2.26414	+	5.21825i	−0.0729987	+	0.168243i
$963$		0			0
$964$	33.7581	−	31.5782i	1.08727	−	1.01707i
$965$	−10.9053	+	6.29620i	−0.351055	+	0.202682i
$966$		0			0
$967$	−18.7298	−	10.8137i	−0.602311	−	0.347744i	0.167639	−	0.985848i	$-0.446386\pi$
$967$	−18.7298	−	10.8137i	−0.602311	−	0.347744i	−0.769950	+	0.638104i	$0.779719\pi$
$968$	−36.3513	−	6.64962i	−1.16837	−	0.213727i
$969$		0			0
$970$	2.71570	+	23.6717i	0.0871958	+	0.760052i
$971$	−25.7885			−0.827592			−0.413796	−	0.910370i	$-0.635797\pi$
$971$	−25.7885			−0.827592			−0.413796	+	0.910370i	$0.635797\pi$
$972$		0			0
$973$	22.0800	+	13.0869i	0.707853	+	0.419545i
$974$	46.8028	−	5.36938i	1.49966	−	0.172046i
$975$		0			0
$976$	−13.1824	+	19.6755i	−0.421958	+	0.629796i
$977$	−18.8498	+	32.6488i	−0.603058	+	1.04453i	0.389298	+	0.921112i	$0.372718\pi$
$977$	−18.8498	+	32.6488i	−0.603058	+	1.04453i	−0.992355	+	0.123414i	$0.960616\pi$
$978$		0			0
$979$	20.1066	+	34.8257i	0.642610	+	1.11303i
$980$	21.9955	+	7.24089i	0.702620	+	0.231302i
$981$		0			0
$982$	18.1090	−	41.7365i	0.577881	−	1.33187i
$983$	−23.1492	−	40.0956i	−0.738345	−	1.27885i	−0.953240	−	0.302214i	$-0.902274\pi$
$983$	−23.1492	−	40.0956i	−0.738345	−	1.27885i	0.214895	−	0.976637i	$-0.431059\pi$
$984$		0			0
$985$	−20.6195	−	11.9047i	−0.656992	−	0.379315i
$986$	54.1725	+	73.0910i	1.72521	+	2.32769i
$987$		0			0
$988$	5.52074	+	1.67847i	0.175638	+	0.0533994i
$989$	−17.7200			−0.563463
$990$		0			0
$991$			12.6519i			0.401900i	0.979602	+	0.200950i	$0.0644028\pi$
$991$			12.6519i			0.401900i	−0.979602	+	0.200950i	$0.935597\pi$
$992$	3.94159	−	0.187452i	0.125146	−	0.00595162i
$993$		0			0
$994$	−0.385307	−	3.73538i	−0.0122212	−	0.118479i
$995$	31.3984	+	18.1279i	0.995395	+	0.574692i
$996$		0			0
$997$	−12.9778	+	7.49276i	−0.411012	+	0.237298i	−0.691225	−	0.722640i	$-0.742928\pi$
$997$	−12.9778	+	7.49276i	−0.411012	+	0.237298i	0.280212	+	0.959938i	$0.409595\pi$
$998$	19.2122	−	44.2792i	0.608152	−	1.40163i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bi.c.307.22		80
3.2	odd	2		252.2.bi.c.139.19	yes	80
4.3	odd	2	inner	756.2.bi.c.307.32		80
7.6	odd	2	inner	756.2.bi.c.307.21		80
9.2	odd	6		252.2.bi.c.223.9	yes	80
9.7	even	3	inner	756.2.bi.c.559.31		80
12.11	even	2		252.2.bi.c.139.10	yes	80
21.20	even	2		252.2.bi.c.139.20	yes	80
28.27	even	2	inner	756.2.bi.c.307.31		80
36.7	odd	6	inner	756.2.bi.c.559.21		80
36.11	even	6		252.2.bi.c.223.20	yes	80
63.20	even	6		252.2.bi.c.223.10	yes	80
63.34	odd	6	inner	756.2.bi.c.559.32		80
84.83	odd	2		252.2.bi.c.139.9	✓	80
252.83	odd	6		252.2.bi.c.223.19	yes	80
252.223	even	6	inner	756.2.bi.c.559.22		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.9	✓	80	84.83	odd	2
252.2.bi.c.139.10	yes	80	12.11	even	2
252.2.bi.c.139.19	yes	80	3.2	odd	2
252.2.bi.c.139.20	yes	80	21.20	even	2
252.2.bi.c.223.9	yes	80	9.2	odd	6
252.2.bi.c.223.10	yes	80	63.20	even	6
252.2.bi.c.223.19	yes	80	252.83	odd	6
252.2.bi.c.223.20	yes	80	36.11	even	6
756.2.bi.c.307.21		80	7.6	odd	2	inner
756.2.bi.c.307.22		80	1.1	even	1	trivial
756.2.bi.c.307.31		80	28.27	even	2	inner
756.2.bi.c.307.32		80	4.3	odd	2	inner
756.2.bi.c.559.21		80	36.7	odd	6	inner
756.2.bi.c.559.22		80	252.223	even	6	inner
756.2.bi.c.559.31		80	9.7	even	3	inner
756.2.bi.c.559.32		80	63.34	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.161186 + 1.40500i) q^{2} +(-1.94804 + 0.452933i) q^{4} +(1.43245 + 0.827025i) q^{5} +(0.0302588 - 2.64558i) q^{7} +(-0.950366 - 2.66398i) q^{8} +O(q^{10})\)	\(q+(0.161186 + 1.40500i) q^{2} +(-1.94804 + 0.452933i) q^{4} +(1.43245 + 0.827025i) q^{5} +(0.0302588 - 2.64558i) q^{7} +(-0.950366 - 2.66398i) q^{8} +(-0.931077 + 2.14589i) q^{10} +(4.24842 - 2.45282i) q^{11} +(0.876334 + 0.505952i) q^{13} +(3.72191 - 0.383917i) q^{14} +(3.58970 - 1.76466i) q^{16} -7.66107i q^{17} -2.85119 q^{19} +(-3.16505 - 0.962273i) q^{20} +(4.13100 + 5.57365i) q^{22} +(1.98118 + 1.14384i) q^{23} +(-1.13206 - 1.96079i) q^{25} +(-0.569608 + 1.31280i) q^{26} +(1.13932 + 5.16739i) q^{28} +(4.19857 + 7.27213i) q^{29} +(0.348784 - 0.604112i) q^{31} +(3.05795 + 4.75909i) q^{32} +(10.7638 - 1.23486i) q^{34} +(2.23130 - 3.76463i) q^{35} +3.97490 q^{37} +(-0.459573 - 4.00592i) q^{38} +(0.841829 - 4.60200i) q^{40} +(6.69947 + 3.86794i) q^{41} +(-6.70811 + 3.87293i) q^{43} +(-7.16511 + 6.70244i) q^{44} +(-1.28775 + 2.96793i) q^{46} +(-3.70722 - 6.42109i) q^{47} +(-6.99817 - 0.160104i) q^{49} +(2.57243 - 1.90659i) q^{50} +(-1.93629 - 0.588693i) q^{52} +8.61878 q^{53} +8.11418 q^{55} +(-7.07653 + 2.43366i) q^{56} +(-9.54058 + 7.07115i) q^{58} +(-2.54378 + 4.40596i) q^{59} +(-5.12759 + 2.96042i) q^{61} +(0.904996 + 0.392667i) q^{62} +(-6.19361 + 5.06352i) q^{64} +(0.836869 + 1.44950i) q^{65} +(2.18590 + 1.26203i) q^{67} +(3.46995 + 14.9241i) q^{68} +(5.64895 + 2.52817i) q^{70} -1.00362i q^{71} -5.89658i q^{73} +(0.640700 + 5.58473i) q^{74} +(5.55423 - 1.29140i) q^{76} +(-6.36058 - 11.3137i) q^{77} +(4.90752 - 2.83336i) q^{79} +(6.60149 + 0.440989i) q^{80} +(-4.35458 + 10.0362i) q^{82} +(1.20736 + 2.09120i) q^{83} +(6.33589 - 10.9741i) q^{85} +(-6.52272 - 8.80062i) q^{86} +(-10.5718 - 8.98662i) q^{88} +8.19734i q^{89} +(1.36505 - 2.30310i) q^{91} +(-4.37750 - 1.33089i) q^{92} +(8.42407 - 6.24363i) q^{94} +(-4.08418 - 2.35800i) q^{95} +(8.82136 - 5.09301i) q^{97} +(-0.903062 - 9.85822i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8}+O(q^{10}) \) 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8	\( 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8} - 10 q^{14} - 18 q^{16} - 14 q^{22} + 32 q^{25} + 28 q^{28} - 8 q^{29} + 16 q^{32} - 16 q^{37} + 84 q^{44} + 24 q^{46} - 24 q^{49} + 12 q^{50} + 48 q^{53} - 32 q^{56} - 14 q^{58} - 8 q^{64} + 40 q^{65} - 22 q^{70} - 64 q^{74} + 12 q^{77} + 40 q^{85} + 52 q^{86} + 6 q^{88} - 30 q^{92} - 20 q^{98}+O(q^{100}) \) 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8 - 10 * q^14 - 18 * q^16 - 14 * q^22 + 32 * q^25 + 28 * q^28 - 8 * q^29 + 16 * q^32 - 16 * q^37 + 84 * q^44 + 24 * q^46 - 24 * q^49 + 12 * q^50 + 48 * q^53 - 32 * q^56 - 14 * q^58 - 8 * q^64 + 40 * q^65 - 22 * q^70 - 64 * q^74 + 12 * q^77 + 40 * q^85 + 52 * q^86 + 6 * q^88 - 30 * q^92 - 20 * q^98

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