LMFDB - Embedded newform 768.2.s.a.143.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(47,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 11, 8]))

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

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

chi := DirichletCharacter("768.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.s (of order $16$, degree $8$, 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:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 192)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			143.22
Character	$\chi$	$=$	768.143
Dual form			768.2.s.a.623.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12690 + 1.31533i) q^{3} +(-0.193910 + 0.974852i) q^{5} +(-3.70761 - 1.53574i) q^{7} +(-0.460173 + 2.96450i) q^{9} +O(q^{10})$	\(q+(1.12690 + 1.31533i) q^{3} +(-0.193910 + 0.974852i) q^{5} +(-3.70761 - 1.53574i) q^{7} +(-0.460173 + 2.96450i) q^{9} +(-2.91108 - 4.35674i) q^{11} +(-4.94964 + 0.984544i) q^{13} +(-1.50077 + 0.843510i) q^{15} +(0.683765 + 0.683765i) q^{17} +(-2.19880 + 0.437368i) q^{19} +(-2.15812 - 6.60736i) q^{21} +(-5.93261 + 2.45737i) q^{23} +(3.70666 + 1.53535i) q^{25} +(-4.41786 + 2.73543i) q^{27} +(-3.04078 - 2.03178i) q^{29} +6.01645 q^{31} +(2.45003 - 8.73866i) q^{33} +(2.21607 - 3.31658i) q^{35} +(-1.17177 + 5.89086i) q^{37} +(-6.87277 - 5.40091i) q^{39} +(-2.28094 - 5.50667i) q^{41} +(4.39265 + 6.57407i) q^{43} +(-2.80071 - 1.02345i) q^{45} +(0.410028 - 0.410028i) q^{47} +(6.43813 + 6.43813i) q^{49} +(-0.128837 + 1.66991i) q^{51} +(3.47118 - 2.31937i) q^{53} +(4.81167 - 1.99306i) q^{55} +(-3.05311 - 2.39927i) q^{57} +(0.669452 + 0.133162i) q^{59} +(-1.32504 - 0.885363i) q^{61} +(6.25885 - 10.2845i) q^{63} -5.01608i q^{65} +(-5.83232 + 8.72868i) q^{67} +(-9.91773 - 5.03411i) q^{69} +(2.48885 - 6.00860i) q^{71} +(-0.0562858 - 0.135886i) q^{73} +(2.15757 + 6.60567i) q^{75} +(4.10233 + 20.6238i) q^{77} +(-0.732784 + 0.732784i) q^{79} +(-8.57648 - 2.72836i) q^{81} +(-1.38633 - 6.96953i) q^{83} +(-0.799159 + 0.533981i) q^{85} +(-0.754205 - 6.28924i) q^{87} +(-3.52518 + 8.51054i) q^{89} +(19.8633 + 3.95106i) q^{91} +(6.77997 + 7.91361i) q^{93} -2.22831i q^{95} -7.20955i q^{97} +(14.2552 - 6.62504i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 8 q^{3} + 16 q^{7} - 8 q^{9}+O(q^{10}) $ 240 * q + 8 * q^3 + 16 * q^7 - 8 * q^9	$ 240 q + 8 q^{3} + 16 q^{7} - 8 q^{9} - 16 q^{13} + 8 q^{15} + 16 q^{19} - 8 q^{21} - 16 q^{25} + 8 q^{27} + 32 q^{31} - 16 q^{37} + 8 q^{39} + 16 q^{43} - 8 q^{45} - 16 q^{49} + 8 q^{51} + 80 q^{55} - 8 q^{57} - 16 q^{61} + 144 q^{67} - 8 q^{69} - 16 q^{73} + 8 q^{75} + 48 q^{79} - 8 q^{81} - 16 q^{85} + 8 q^{87} + 16 q^{91} - 32 q^{93} + 8 q^{99}+O(q^{100}) $ 240 * q + 8 * q^3 + 16 * q^7 - 8 * q^9 - 16 * q^13 + 8 * q^15 + 16 * q^19 - 8 * q^21 - 16 * q^25 + 8 * q^27 + 32 * q^31 - 16 * q^37 + 8 * q^39 + 16 * q^43 - 8 * q^45 - 16 * q^49 + 8 * q^51 + 80 * q^55 - 8 * q^57 - 16 * q^61 + 144 * q^67 - 8 * q^69 - 16 * q^73 + 8 * q^75 + 48 * q^79 - 8 * q^81 - 16 * q^85 + 8 * q^87 + 16 * q^91 - 32 * q^93 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{16}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.12690	+	1.31533i	0.650619	+	0.759405i
$3$	1.12690	+	1.31533i	0.650619	+	0.759405i
$4$		0			0
$5$	−0.193910	+	0.974852i	−0.0867193	+	0.435967i	0.912895	+	0.408194i	$0.133841\pi$
$5$	−0.193910	+	0.974852i	−0.0867193	+	0.435967i	−0.999614	+	0.0277727i	$0.991159\pi$
$6$		0			0
$7$	−3.70761	−	1.53574i	−1.40135	−	0.580456i	−0.451245	−	0.892400i	$-0.649020\pi$
$7$	−3.70761	−	1.53574i	−1.40135	−	0.580456i	−0.950100	+	0.311944i	$0.899020\pi$
$8$		0			0
$9$	−0.460173	+	2.96450i	−0.153391	+	0.988166i
$10$		0			0
$11$	−2.91108	−	4.35674i	−0.877724	−	1.31361i	−0.948716	−	0.316130i	$-0.897616\pi$
$11$	−2.91108	−	4.35674i	−0.877724	−	1.31361i	0.0709914	−	0.997477i	$-0.477384\pi$
$12$		0			0
$13$	−4.94964	+	0.984544i	−1.37278	+	0.273063i	−0.825745	−	0.564044i	$-0.809245\pi$
$13$	−4.94964	+	0.984544i	−1.37278	+	0.273063i	−0.547038	+	0.837108i	$0.684245\pi$
$14$		0			0
$15$	−1.50077	+	0.843510i	−0.387497	+	0.217793i
$16$		0			0
$17$	0.683765	+	0.683765i	0.165837	+	0.165837i	0.785147	−	0.619310i	$-0.212587\pi$
$17$	0.683765	+	0.683765i	0.165837	+	0.165837i	−0.619310	+	0.785147i	$0.712587\pi$
$18$		0			0
$19$	−2.19880	+	0.437368i	−0.504438	+	0.100339i	−0.440748	−	0.897631i	$-0.645287\pi$
$19$	−2.19880	+	0.437368i	−0.504438	+	0.100339i	−0.0636900	+	0.997970i	$0.520287\pi$
$20$		0			0
$21$	−2.15812	−	6.60736i	−0.470940	−	1.44184i
$22$		0			0
$23$	−5.93261	+	2.45737i	−1.23704	+	0.512397i	−0.902787	−	0.430088i	$-0.858482\pi$
$23$	−5.93261	+	2.45737i	−1.23704	+	0.512397i	−0.334248	+	0.942485i	$0.608482\pi$
$24$		0			0
$25$	3.70666	+	1.53535i	0.741332	+	0.307070i
$26$		0			0
$27$	−4.41786	+	2.73543i	−0.850217	+	0.526433i
$28$		0			0
$29$	−3.04078	−	2.03178i	−0.564658	−	0.377292i	0.240233	−	0.970715i	$-0.422776\pi$
$29$	−3.04078	−	2.03178i	−0.564658	−	0.377292i	−0.804891	+	0.593423i	$0.797776\pi$
$30$		0			0
$31$	6.01645			1.08059			0.540294	−	0.841477i	$-0.318313\pi$
$31$	6.01645			1.08059			0.540294	+	0.841477i	$0.318313\pi$
$32$		0			0
$33$	2.45003	−	8.73866i	0.426496	−	1.52121i
$34$		0			0
$35$	2.21607	−	3.31658i	0.374584	−	0.560604i
$36$		0			0
$37$	−1.17177	+	5.89086i	−0.192637	+	0.968452i	0.756597	+	0.653881i	$0.226860\pi$
$37$	−1.17177	+	5.89086i	−0.192637	+	0.968452i	−0.949234	+	0.314570i	$0.898140\pi$
$38$		0			0
$39$	−6.87277	−	5.40091i	−1.10052	−	0.864838i
$40$		0			0
$41$	−2.28094	−	5.50667i	−0.356222	−	0.859997i	−0.995824	−	0.0912906i	$-0.970901\pi$
$41$	−2.28094	−	5.50667i	−0.356222	−	0.859997i	0.639602	−	0.768706i	$-0.279099\pi$
$42$		0			0
$43$	4.39265	+	6.57407i	0.669873	+	1.00254i	0.998316	+	0.0580124i	$0.0184763\pi$
$43$	4.39265	+	6.57407i	0.669873	+	1.00254i	−0.328442	+	0.944524i	$0.606524\pi$
$44$		0			0
$45$	−2.80071	−	1.02345i	−0.417506	−	0.152566i
$46$		0			0
$47$	0.410028	−	0.410028i	0.0598087	−	0.0598087i	−0.676570	−	0.736379i	$-0.736534\pi$
$47$	0.410028	−	0.410028i	0.0598087	−	0.0598087i	0.736379	+	0.676570i	$0.236534\pi$
$48$		0			0
$49$	6.43813	+	6.43813i	0.919732	+	0.919732i
$50$		0			0
$51$	−0.128837	+	1.66991i	−0.0180408	+	0.233834i
$52$		0			0
$53$	3.47118	−	2.31937i	0.476803	−	0.318590i	−0.293842	−	0.955854i	$-0.594934\pi$
$53$	3.47118	−	2.31937i	0.476803	−	0.318590i	0.770645	+	0.637264i	$0.219934\pi$
$54$		0			0
$55$	4.81167	−	1.99306i	0.648805	−	0.268744i
$56$		0			0
$57$	−3.05311	−	2.39927i	−0.404395	−	0.317790i
$58$		0			0
$59$	0.669452	+	0.133162i	0.0871552	+	0.0173363i	0.238475	−	0.971149i	$-0.423352\pi$
$59$	0.669452	+	0.133162i	0.0871552	+	0.0173363i	−0.151320	+	0.988485i	$0.548352\pi$
$60$		0			0
$61$	−1.32504	−	0.885363i	−0.169654	−	0.113359i	0.467845	−	0.883811i	$-0.345031\pi$
$61$	−1.32504	−	0.885363i	−0.169654	−	0.113359i	−0.637498	+	0.770452i	$0.720031\pi$
$62$		0			0
$63$	6.25885	−	10.2845i	0.788541	−	1.29572i
$64$		0			0
$65$		−	5.01608i		−	0.622168i
$66$		0			0
$67$	−5.83232	+	8.72868i	−0.712531	+	1.06638i	0.281740	+	0.959491i	$0.409088\pi$
$67$	−5.83232	+	8.72868i	−0.712531	+	1.06638i	−0.994271	+	0.106887i	$0.965912\pi$
$68$		0			0
$69$	−9.91773	−	5.03411i	−1.19395	−	0.606036i
$70$		0			0
$71$	2.48885	−	6.00860i	0.295372	−	0.713090i	−0.704622	−	0.709583i	$-0.748884\pi$
$71$	2.48885	−	6.00860i	0.295372	−	0.713090i	0.999994	−	0.00350749i	$-0.00111647\pi$
$72$		0			0
$73$	−0.0562858	−	0.135886i	−0.00658776	−	0.0159043i	0.920551	−	0.390621i	$-0.127740\pi$
$73$	−0.0562858	−	0.135886i	−0.00658776	−	0.0159043i	−0.927139	+	0.374717i	$0.877740\pi$
$74$		0			0
$75$	2.15757	+	6.60567i	0.249134	+	0.762757i
$76$		0			0
$77$	4.10233	+	20.6238i	0.467503	+	2.35030i
$78$		0			0
$79$	−0.732784	+	0.732784i	−0.0824446	+	0.0824446i	−0.747127	−	0.664682i	$-0.768567\pi$
$79$	−0.732784	+	0.732784i	−0.0824446	+	0.0824446i	0.664682	+	0.747127i	$0.268567\pi$
$80$		0			0
$81$	−8.57648	−	2.72836i	−0.952942	−	0.303152i
$82$		0			0
$83$	−1.38633	−	6.96953i	−0.152169	−	0.765006i	−0.979208	−	0.202860i	$-0.934976\pi$
$83$	−1.38633	−	6.96953i	−0.152169	−	0.765006i	0.827039	−	0.562145i	$-0.190024\pi$
$84$		0			0
$85$	−0.799159	+	0.533981i	−0.0866809	+	0.0579183i
$86$		0			0
$87$	−0.754205	−	6.28924i	−0.0808593	−	0.674277i
$88$		0			0
$89$	−3.52518	+	8.51054i	−0.373669	+	0.902116i	0.619454	+	0.785033i	$0.287354\pi$
$89$	−3.52518	+	8.51054i	−0.373669	+	0.902116i	−0.993122	+	0.117083i	$0.962646\pi$
$90$		0			0
$91$	19.8633	+	3.95106i	2.08224	+	0.414184i
$92$		0			0
$93$	6.77997	+	7.91361i	0.703050	+	0.820603i
$94$		0			0
$95$		−	2.22831i		−	0.228620i
$96$		0			0
$97$		−	7.20955i		−	0.732019i	−0.930611	−	0.366009i	$-0.880724\pi$
$97$		−	7.20955i		−	0.732019i	0.930611	−	0.366009i	$-0.119276\pi$
$98$		0			0
$99$	14.2552	−	6.62504i	1.43270	−	0.665841i
$100$		0			0
$101$	−10.0719	−	2.00343i	−1.00219	−	0.199349i	−0.333390	−	0.942789i	$-0.608193\pi$
$101$	−10.0719	−	2.00343i	−1.00219	−	0.199349i	−0.668802	+	0.743440i	$0.733193\pi$
$102$		0			0
$103$	−3.84510	+	9.28290i	−0.378869	+	0.914672i	0.613309	+	0.789843i	$0.289838\pi$
$103$	−3.84510	+	9.28290i	−0.378869	+	0.914672i	−0.992178	+	0.124828i	$0.960162\pi$
$104$		0			0
$105$	6.85968	−	0.822612i	0.669436	−	0.0802787i
$106$		0			0
$107$	−15.0307	+	10.0432i	−1.45307	+	0.970911i	−0.456367	+	0.889792i	$0.650849\pi$
$107$	−15.0307	+	10.0432i	−1.45307	+	0.970911i	−0.996704	+	0.0811191i	$0.974151\pi$
$108$		0			0
$109$	−1.13131	−	5.68748i	−0.108360	−	0.544762i	−0.996384	−	0.0849650i	$-0.972922\pi$
$109$	−1.13131	−	5.68748i	−0.108360	−	0.544762i	0.888024	−	0.459797i	$-0.152078\pi$
$110$		0			0
$111$	−9.06888	+	5.09718i	−0.860780	+	0.483803i
$112$		0			0
$113$	7.57068	−	7.57068i	0.712190	−	0.712190i	−0.254803	−	0.966993i	$-0.582011\pi$
$113$	7.57068	−	7.57068i	0.712190	−	0.712190i	0.966993	+	0.254803i	$0.0820107\pi$
$114$		0			0
$115$	−1.24518	−	6.25993i	−0.116113	−	0.583741i
$116$		0			0
$117$	−0.640987	−	15.1262i	−0.0592592	−	1.39842i
$118$		0			0
$119$	−1.48505	−	3.58522i	−0.136134	−	0.328657i
$120$		0			0
$121$	−6.29729	+	15.2030i	−0.572481	+	1.38209i
$122$		0			0
$123$	4.67267	−	9.20566i	0.421321	−	0.830047i
$124$		0			0
$125$	−4.97655	+	7.44793i	−0.445116	+	0.666163i
$126$		0			0
$127$			4.30331i			0.381857i	0.981604	+	0.190928i	$0.0611498\pi$
$127$			4.30331i			0.381857i	−0.981604	+	0.190928i	$0.938850\pi$
$128$		0			0
$129$	−3.69696	+	13.1861i	−0.325499	+	1.16097i
$130$		0			0
$131$	0.418316	+	0.279510i	0.0365484	+	0.0244209i	0.573710	−	0.819058i	$-0.305504\pi$
$131$	0.418316	+	0.279510i	0.0365484	+	0.0244209i	−0.537162	+	0.843479i	$0.680504\pi$
$132$		0			0
$133$	8.82396	+	1.75520i	0.765135	+	0.152195i
$134$		0			0
$135$	−1.80997	−	4.83718i	−0.155777	−	0.416318i
$136$		0			0
$137$	4.55661	−	1.88741i	0.389298	−	0.161252i	−0.179445	−	0.983768i	$-0.557430\pi$
$137$	4.55661	−	1.88741i	0.389298	−	0.161252i	0.568742	+	0.822516i	$0.307430\pi$
$138$		0			0
$139$	−18.9938	+	12.6912i	−1.61103	+	1.07646i	−0.667792	+	0.744348i	$0.732760\pi$
$139$	−18.9938	+	12.6912i	−1.61103	+	1.07646i	−0.943241	+	0.332109i	$0.892240\pi$
$140$		0			0
$141$	1.00138	+	0.0772588i	0.0843317	+	0.00650637i
$142$		0			0
$143$	18.6982	+	18.6982i	1.56362	+	1.56362i
$144$		0			0
$145$	2.57033	−	2.57033i	0.213454	−	0.213454i
$146$		0			0
$147$	−1.21309	+	15.7234i	−0.100054	+	1.29684i
$148$		0			0
$149$	0.484782	+	0.725528i	0.0397149	+	0.0594375i	0.850796	−	0.525496i	$-0.176120\pi$
$149$	0.484782	+	0.725528i	0.0397149	+	0.0594375i	−0.811081	+	0.584934i	$0.801120\pi$
$150$		0			0
$151$	−6.03653	−	14.5735i	−0.491246	−	1.18597i	−0.954086	−	0.299531i	$-0.903170\pi$
$151$	−6.03653	−	14.5735i	−0.491246	−	1.18597i	0.462840	−	0.886442i	$-0.346830\pi$
$152$		0			0
$153$	−2.34167	+	1.71237i	−0.189313	+	0.138437i
$154$		0			0
$155$	−1.16665	+	5.86515i	−0.0937077	+	0.471101i
$156$		0			0
$157$	−0.607206	+	0.908748i	−0.0484603	+	0.0725260i	−0.854909	−	0.518779i	$-0.826387\pi$
$157$	−0.607206	+	0.908748i	−0.0484603	+	0.0725260i	0.806448	+	0.591305i	$0.201387\pi$
$158$		0			0
$159$	6.96242	+	1.95203i	0.552156	+	0.154806i
$160$		0			0
$161$	25.7697			2.03094
$162$		0			0
$163$	0.673986	+	0.450343i	0.0527906	+	0.0352736i	0.581686	−	0.813414i	$-0.302393\pi$
$163$	0.673986	+	0.450343i	0.0527906	+	0.0352736i	−0.528895	+	0.848687i	$0.677393\pi$
$164$		0			0
$165$	8.04382	+	4.08293i	0.626210	+	0.317856i
$166$		0			0
$167$	7.64654	+	3.16730i	0.591707	+	0.245093i	0.658385	−	0.752681i	$-0.271240\pi$
$167$	7.64654	+	3.16730i	0.591707	+	0.245093i	−0.0666777	+	0.997775i	$0.521240\pi$
$168$		0			0
$169$	11.5192	−	4.77139i	0.886090	−	0.367030i
$170$		0			0
$171$	−0.284748	−	6.71959i	−0.0217752	−	0.513860i
$172$		0			0
$173$	4.87296	−	0.969292i	0.370484	−	0.0736939i	−0.00633687	−	0.999980i	$-0.502017\pi$
$173$	4.87296	−	0.969292i	0.370484	−	0.0736939i	0.376821	+	0.926286i	$0.377017\pi$
$174$		0			0
$175$	−11.3850	−	11.3850i	−0.860622	−	0.860622i
$176$		0			0
$177$	0.579256	+	1.03061i	0.0435396	+	0.0774654i
$178$		0			0
$179$	7.27280	−	1.44665i	0.543595	−	0.108128i	0.0843477	−	0.996436i	$-0.473119\pi$
$179$	7.27280	−	1.44665i	0.543595	−	0.108128i	0.459247	+	0.888309i	$0.348119\pi$
$180$		0			0
$181$	−5.17210	−	7.74060i	−0.384439	−	0.575354i	0.587898	−	0.808935i	$-0.299956\pi$
$181$	−5.17210	−	7.74060i	−0.384439	−	0.575354i	−0.972337	+	0.233581i	$0.924956\pi$
$182$		0			0
$183$	−0.328650	−	2.74058i	−0.0242945	−	0.202589i
$184$		0			0
$185$	−5.51550	−	2.28460i	−0.405508	−	0.167967i
$186$		0			0
$187$	0.988492	−	4.96948i	0.0722857	−	0.363405i
$188$		0			0
$189$	20.5806	−	3.35720i	1.49702	−	0.244201i
$190$		0			0
$191$	18.7379			1.35583			0.677915	−	0.735140i	$-0.262884\pi$
$191$	18.7379			1.35583			0.677915	+	0.735140i	$0.262884\pi$
$192$		0			0
$193$	10.3487			0.744917			0.372458	−	0.928049i	$-0.378515\pi$
$193$	10.3487			0.744917			0.372458	+	0.928049i	$0.378515\pi$
$194$		0			0
$195$	6.59779	−	5.65264i	0.472477	−	0.404794i
$196$		0			0
$197$	0.499551	−	2.51141i	0.0355916	−	0.178931i	−0.958901	−	0.283742i	$-0.908424\pi$
$197$	0.499551	−	2.51141i	0.0355916	−	0.178931i	0.994492	+	0.104812i	$0.0334239\pi$
$198$		0			0
$199$	21.9191	+	9.07919i	1.55380	+	0.643606i	0.983999	−	0.178174i	$-0.0570190\pi$
$199$	21.9191	+	9.07919i	1.55380	+	0.643606i	0.569804	+	0.821780i	$0.307019\pi$
$200$		0			0
$201$	−18.0535	+	2.16498i	−1.27340	+	0.152706i
$202$		0			0
$203$	8.15372	+	12.2029i	0.572279	+	0.856476i
$204$		0			0
$205$	5.81048	−	1.15578i	0.405822	−	0.0807230i
$206$		0			0
$207$	−4.55483	−	18.7180i	−0.316583	−	1.30099i
$208$		0			0
$209$	8.30637	+	8.30637i	0.574564	+	0.574564i
$210$		0			0
$211$	−5.82420	+	1.15850i	−0.400954	+	0.0797547i	−0.391448	−	0.920200i	$-0.628026\pi$
$211$	−5.82420	+	1.15850i	−0.400954	+	0.0797547i	−0.00950579	+	0.999955i	$0.503026\pi$
$212$		0			0
$213$	10.7080	−	3.49747i	0.733698	−	0.239643i
$214$		0			0
$215$	−7.26053	+	3.00741i	−0.495164	+	0.205104i
$216$		0			0
$217$	−22.3067	−	9.23973i	−1.51428	−	0.627234i
$218$		0			0
$219$	0.115306	−	0.227165i	0.00779165	−	0.0153504i
$220$		0			0
$221$	−4.05759	−	2.71119i	−0.272943	−	0.182375i
$222$		0			0
$223$	3.73785			0.250305			0.125152	−	0.992138i	$-0.460058\pi$
$223$	3.73785			0.250305			0.125152	+	0.992138i	$0.460058\pi$
$224$		0			0
$225$	−6.25725	+	10.2819i	−0.417150	+	0.685457i
$226$		0			0
$227$	1.99547	−	2.98643i	0.132444	−	0.198216i	−0.759320	−	0.650717i	$-0.774468\pi$
$227$	1.99547	−	2.98643i	0.132444	−	0.198216i	0.891764	+	0.452501i	$0.149468\pi$
$228$		0			0
$229$	−5.43450	+	27.3211i	−0.359122	+	1.80543i	0.203908	+	0.978990i	$0.434636\pi$
$229$	−5.43450	+	27.3211i	−0.359122	+	1.80543i	−0.563030	+	0.826437i	$0.690364\pi$
$230$		0			0
$231$	−22.5041	+	28.6369i	−1.48066	+	1.88417i
$232$		0			0
$233$	−9.69909	−	23.4157i	−0.635408	−	1.53401i	−0.832734	−	0.553674i	$-0.813226\pi$
$233$	−9.69909	−	23.4157i	−0.635408	−	1.53401i	0.197325	−	0.980338i	$-0.436774\pi$
$234$		0			0
$235$	0.320208	+	0.479225i	0.0208881	+	0.0312612i
$236$		0			0
$237$	−1.78963	−	0.138074i	−0.116249	−	0.00896884i
$238$		0			0
$239$	0.877531	−	0.877531i	0.0567628	−	0.0567628i	−0.678156	−	0.734918i	$-0.737220\pi$
$239$	0.877531	−	0.877531i	0.0567628	−	0.0567628i	0.734918	+	0.678156i	$0.237220\pi$
$240$		0			0
$241$	1.37915	+	1.37915i	0.0888390	+	0.0888390i	0.750130	−	0.661291i	$-0.229991\pi$
$241$	1.37915	+	1.37915i	0.0888390	+	0.0888390i	−0.661291	+	0.750130i	$0.729991\pi$
$242$		0			0
$243$	−6.07618	−	14.3555i	−0.389787	−	0.920905i
$244$		0			0
$245$	−7.52464	+	5.02780i	−0.480732	+	0.321215i
$246$		0			0
$247$	10.4526	−	4.32962i	0.665085	−	0.275487i
$248$		0			0
$249$	7.60496	−	9.67747i	0.481945	−	0.613285i
$250$		0			0
$251$	−21.1556	−	4.20812i	−1.33533	−	0.265614i	−0.524759	−	0.851251i	$-0.675845\pi$
$251$	−21.1556	−	4.20812i	−1.33533	−	0.265614i	−0.810574	+	0.585637i	$0.800845\pi$
$252$		0			0
$253$	27.9764	+	18.6933i	1.75886	+	1.17524i
$254$		0			0
$255$	−1.60293	−	0.449410i	−0.100380	−	0.0281432i
$256$		0			0
$257$		−	11.0021i		−	0.686292i	−0.939282	−	0.343146i	$-0.888507\pi$
$257$		−	11.0021i		−	0.686292i	0.939282	−	0.343146i	$-0.111493\pi$
$258$		0			0
$259$	13.3913	−	20.0415i	0.832095	−	1.24532i
$260$		0			0
$261$	7.42250	−	8.07940i	0.459441	−	0.500102i
$262$		0			0
$263$	−3.70327	+	8.94049i	−0.228354	+	0.551294i	−0.995977	−	0.0896065i	$-0.971439\pi$
$263$	−3.70327	+	8.94049i	−0.228354	+	0.551294i	0.767624	+	0.640901i	$0.221439\pi$
$264$		0			0
$265$	1.58794	+	3.83364i	0.0975467	+	0.235498i
$266$		0			0
$267$	−15.1667	+	4.95380i	−0.928187	+	0.303168i
$268$		0			0
$269$	−2.23837	−	11.2530i	−0.136476	−	0.686109i	−0.987070	−	0.160287i	$-0.948758\pi$
$269$	−2.23837	−	11.2530i	−0.136476	−	0.686109i	0.850595	−	0.525822i	$-0.176242\pi$
$270$		0			0
$271$	−19.6396	+	19.6396i	−1.19302	+	1.19302i	−0.216808	+	0.976214i	$0.569565\pi$
$271$	−19.6396	+	19.6396i	−1.19302	+	1.19302i	−0.976214	+	0.216808i	$0.930435\pi$
$272$		0			0
$273$	17.1871	+	30.5793i	1.04021	+	1.85074i
$274$		0			0
$275$	−4.10127	−	20.6185i	−0.247316	−	1.24334i
$276$		0			0
$277$	4.66619	−	3.11785i	0.280364	−	0.187334i	−0.407435	−	0.913234i	$-0.633577\pi$
$277$	4.66619	−	3.11785i	0.280364	−	0.187334i	0.687800	+	0.725901i	$0.258577\pi$
$278$		0			0
$279$	−2.76861	+	17.8358i	−0.165752	+	1.06780i
$280$		0			0
$281$	−7.24049	+	17.4801i	−0.431931	+	1.04277i	0.546733	+	0.837307i	$0.315871\pi$
$281$	−7.24049	+	17.4801i	−0.431931	+	1.04277i	−0.978664	+	0.205467i	$0.934129\pi$
$282$		0			0
$283$	−0.419792	−	0.0835019i	−0.0249541	−	0.00496367i	0.182598	−	0.983188i	$-0.441549\pi$
$283$	−0.419792	−	0.0835019i	−0.0249541	−	0.00496367i	−0.207552	+	0.978224i	$0.566549\pi$
$284$		0			0
$285$	2.93096	−	2.51109i	0.173615	−	0.148744i
$286$		0			0
$287$			23.9195i			1.41192i
$288$		0			0
$289$		−	16.0649i		−	0.944996i
$290$		0			0
$291$	9.48292	−	8.12447i	0.555898	−	0.476265i
$292$		0			0
$293$	8.13084	+	1.61732i	0.475009	+	0.0944851i	0.426788	−	0.904352i	$-0.359645\pi$
$293$	8.13084	+	1.61732i	0.475009	+	0.0944851i	0.0482204	+	0.998837i	$0.484645\pi$
$294$		0			0
$295$	−0.259627	+	0.626795i	−0.0151161	+	0.0364934i
$296$		0			0
$297$	24.7783	+	11.2844i	1.43778	+	0.654788i
$298$		0			0
$299$	26.9449	−	18.0040i	1.55826	−	1.04120i
$300$		0			0
$301$	−6.19017	−	31.1201i	−0.356795	−	1.79373i
$302$		0			0
$303$	−8.71492	−	15.5055i	−0.500659	−	0.890770i
$304$		0			0
$305$	1.12004	−	1.12004i	0.0641331	−	0.0641331i
$306$		0			0
$307$	−3.00071	−	15.0856i	−0.171260	−	0.860981i	−0.966889	−	0.255197i	$-0.917860\pi$
$307$	−3.00071	−	15.0856i	−0.171260	−	0.860981i	0.795629	−	0.605784i	$-0.207140\pi$
$308$		0			0
$309$	−16.5431	+	5.40337i	−0.941105	+	0.307387i
$310$		0			0
$311$	−3.32454	−	8.02614i	−0.188517	−	0.455121i	0.801157	−	0.598454i	$-0.204218\pi$
$311$	−3.32454	−	8.02614i	−0.188517	−	0.455121i	−0.989674	+	0.143333i	$0.954218\pi$
$312$		0			0
$313$	−5.93757	+	14.3346i	−0.335611	+	0.810238i	0.662515	+	0.749049i	$0.269489\pi$
$313$	−5.93757	+	14.3346i	−0.335611	+	0.810238i	−0.998126	+	0.0611888i	$0.980511\pi$
$314$		0			0
$315$	8.81221	+	8.09572i	0.496512	+	0.456142i
$316$		0			0
$317$	−4.58817	+	6.86668i	−0.257697	+	0.385671i	−0.937648	−	0.347587i	$-0.887001\pi$
$317$	−4.58817	+	6.86668i	−0.257697	+	0.385671i	0.679951	+	0.733258i	$0.262001\pi$
$318$		0			0
$319$			19.1626i			1.07290i
$320$		0			0
$321$	−30.1482	−	8.45257i	−1.68271	−	0.471776i
$322$		0			0
$323$	−1.80252	−	1.20440i	−0.100295	−	0.0670147i
$324$		0			0
$325$	−19.8583	−	3.95005i	−1.10154	−	0.219110i
$326$		0			0
$327$	6.20602	−	7.89729i	0.343194	−	0.436721i
$328$		0			0
$329$	−2.14992	+	0.890527i	−0.118529	+	0.0490963i
$330$		0			0
$331$	16.8218	−	11.2399i	0.924607	−	0.617803i	0.000526305	−	1.00000i	$-0.499832\pi$
$331$	16.8218	−	11.2399i	0.924607	−	0.617803i	0.924081	+	0.382197i	$0.124832\pi$
$332$		0			0
$333$	−16.9242	−	6.18451i	−0.927442	−	0.338909i
$334$		0			0
$335$	−7.37823	−	7.37823i	−0.403116	−	0.403116i
$336$		0			0
$337$	−10.4562	+	10.4562i	−0.569588	+	0.569588i	−0.932013	−	0.362425i	$-0.881949\pi$
$337$	−10.4562	+	10.4562i	−0.569588	+	0.569588i	0.362425	+	0.932013i	$0.381949\pi$
$338$		0			0
$339$	18.4894	+	1.42649i	1.00420	+	0.0774764i
$340$		0			0
$341$	−17.5144	−	26.2121i	−0.948458	−	1.41947i
$342$		0			0
$343$	−3.23256	−	7.80410i	−0.174542	−	0.421382i
$344$		0			0
$345$	6.83066	−	8.69216i	0.367751	−	0.467970i
$346$		0			0
$347$	−0.0191071	+	0.0960581i	−0.00102573	+	0.00515667i	−0.981295	−	0.192511i	$-0.938337\pi$
$347$	−0.0191071	+	0.0960581i	−0.00102573	+	0.00515667i	0.980269	+	0.197668i	$0.0633368\pi$
$348$		0			0
$349$	12.5311	−	18.7541i	0.670773	−	1.00388i	−0.327483	−	0.944857i	$-0.606201\pi$
$349$	12.5311	−	18.7541i	0.670773	−	1.00388i	0.998256	−	0.0590258i	$-0.0187994\pi$
$350$		0			0
$351$	19.1736	−	17.8889i	1.02341	−	0.954841i
$352$		0			0
$353$	−29.0761			−1.54757			−0.773783	−	0.633450i	$-0.781638\pi$
$353$	−29.0761			−1.54757			−0.773783	+	0.633450i	$0.781638\pi$
$354$		0			0
$355$	5.37489	+	3.59139i	0.285269	+	0.190611i
$356$		0			0
$357$	3.04223	−	5.99352i	0.161012	−	0.317211i
$358$		0			0
$359$	15.5113	+	6.42500i	0.818656	+	0.339099i	0.752402	−	0.658704i	$-0.228895\pi$
$359$	15.5113	+	6.42500i	0.818656	+	0.339099i	0.0662543	+	0.997803i	$0.478895\pi$
$360$		0			0
$361$	−12.9103	+	5.34762i	−0.679489	+	0.281454i
$362$		0			0
$363$	−27.0934	+	8.84933i	−1.42203	+	0.464469i
$364$		0			0
$365$	0.143383	−	0.0285207i	0.00750502	−	0.00149284i
$366$		0			0
$367$	17.7815	+	17.7815i	0.928188	+	0.928188i	0.997589	−	0.0694007i	$-0.0221087\pi$
$367$	17.7815	+	17.7815i	0.928188	+	0.928188i	−0.0694007	+	0.997589i	$0.522109\pi$
$368$		0			0
$369$	17.3741	−	4.22781i	0.904461	−	0.220091i
$370$		0			0
$371$	−16.4317	+	3.26848i	−0.853093	+	0.169691i
$372$		0			0
$373$	14.2133	+	21.2718i	0.735939	+	1.10141i	0.990919	+	0.134464i	$0.0429311\pi$
$373$	14.2133	+	21.2718i	0.735939	+	1.10141i	−0.254980	+	0.966946i	$0.582069\pi$
$374$		0			0
$375$	−15.4046	+	1.84731i	−0.795488	+	0.0953948i
$376$		0			0
$377$	17.0511	+	7.06281i	0.878178	+	0.363753i
$378$		0			0
$379$	6.08068	−	30.5696i	0.312343	−	1.57026i	−0.431632	−	0.902050i	$-0.642062\pi$
$379$	6.08068	−	30.5696i	0.312343	−	1.57026i	0.743975	−	0.668207i	$-0.232938\pi$
$380$		0			0
$381$	−5.66026	+	4.84941i	−0.289984	+	0.248443i
$382$		0			0
$383$	−36.2148			−1.85049			−0.925244	−	0.379371i	$-0.876140\pi$
$383$	−36.2148			−1.85049			−0.925244	+	0.379371i	$0.876140\pi$
$384$		0			0
$385$	−20.9006			−1.06519
$386$		0			0
$387$	−21.5102	+	9.99680i	−1.09342	+	0.508166i
$388$		0			0
$389$	−3.80380	+	19.1230i	−0.192861	+	0.969575i	0.756166	+	0.654380i	$0.227070\pi$
$389$	−3.80380	+	19.1230i	−0.192861	+	0.969575i	−0.949027	+	0.315196i	$0.897930\pi$
$390$		0			0
$391$	−5.73677	−	2.37625i	−0.290121	−	0.120172i
$392$		0			0
$393$	0.103755	+	0.865204i	0.00523375	+	0.0436437i
$394$		0			0
$395$	−0.572262	−	0.856450i	−0.0287936	−	0.0430927i
$396$		0			0
$397$	−21.5746	+	4.29146i	−1.08280	+	0.215382i	−0.704074	−	0.710127i	$-0.748638\pi$
$397$	−21.5746	+	4.29146i	−1.08280	+	0.215382i	−0.378726	+	0.925509i	$0.623638\pi$
$398$		0			0
$399$	7.63511	+	13.5843i	0.382233	+	0.680068i
$400$		0			0
$401$	−24.9191	−	24.9191i	−1.24440	−	1.24440i	−0.958157	−	0.286245i	$-0.907593\pi$
$401$	−24.9191	−	24.9191i	−1.24440	−	1.24440i	−0.286245	−	0.958157i	$-0.592407\pi$
$402$		0			0
$403$	−29.7793	+	5.92347i	−1.48341	+	0.295069i
$404$		0			0
$405$	4.32282	−	7.83174i	0.214803	−	0.389163i
$406$		0			0
$407$	29.0761	−	12.0437i	1.44125	−	0.596984i
$408$		0			0
$409$	−32.8827	−	13.6204i	−1.62594	−	0.673488i	−0.631175	−	0.775641i	$-0.717427\pi$
$409$	−32.8827	−	13.6204i	−1.62594	−	0.673488i	−0.994769	+	0.102153i	$0.967427\pi$
$410$		0			0
$411$	7.61743	+	3.86651i	0.375740	+	0.190721i
$412$		0			0
$413$	−2.27757	−	1.52182i	−0.112072	−	0.0748839i
$414$		0			0
$415$	7.06309			0.346713
$416$		0			0
$417$	−38.0973	−	10.6812i	−1.86563	−	0.523063i
$418$		0			0
$419$	−21.0879	+	31.5602i	−1.03021	+	1.54182i	−0.203592	+	0.979056i	$0.565261\pi$
$419$	−21.0879	+	31.5602i	−1.03021	+	1.54182i	−0.826619	+	0.562763i	$0.809739\pi$
$420$		0			0
$421$	0.323711	−	1.62741i	0.0157767	−	0.0793149i	−0.972095	−	0.234588i	$-0.924626\pi$
$421$	0.323711	−	1.62741i	0.0157767	−	0.0793149i	0.987872	+	0.155273i	$0.0496258\pi$
$422$		0			0
$423$	1.02684	+	1.40421i	0.0499268	+	0.0682751i
$424$		0			0
$425$	1.48467	+	3.58430i	0.0720169	+	0.173864i
$426$		0			0
$427$	3.55304	+	5.31750i	0.171944	+	0.257332i
$428$		0			0
$429$	−3.52318	+	45.6654i	−0.170101	+	2.20474i
$430$		0			0
$431$	8.48020	−	8.48020i	0.408477	−	0.408477i	−0.472730	−	0.881207i	$-0.656732\pi$
$431$	8.48020	−	8.48020i	0.408477	−	0.408477i	0.881207	+	0.472730i	$0.156732\pi$
$432$		0			0
$433$	7.39431	+	7.39431i	0.355348	+	0.355348i	0.862095	−	0.506747i	$-0.169152\pi$
$433$	7.39431	+	7.39431i	0.355348	+	0.355348i	−0.506747	+	0.862095i	$0.669152\pi$
$434$		0			0
$435$	6.27733	+	0.484309i	0.300975	+	0.0232208i
$436$		0			0
$437$	11.9698	−	7.99798i	0.572595	−	0.382596i
$438$		0			0
$439$	−15.1087	+	6.25824i	−0.721100	+	0.298689i	−0.712889	−	0.701277i	$-0.752614\pi$
$439$	−15.1087	+	6.25824i	−0.721100	+	0.298689i	−0.00821108	+	0.999966i	$0.502614\pi$
$440$		0			0
$441$	−22.0485	+	16.1232i	−1.04993	+	0.767769i
$442$		0			0
$443$	−35.7076	−	7.10267i	−1.69652	−	0.337458i	−0.750326	−	0.661067i	$-0.770104\pi$
$443$	−35.7076	−	7.10267i	−1.69652	−	0.337458i	−0.946191	+	0.323609i	$0.895104\pi$
$444$		0			0
$445$	−7.61295	−	5.08681i	−0.360889	−	0.241138i
$446$		0			0
$447$	−0.408004	+	1.45525i	−0.0192979	+	0.0688309i
$448$		0			0
$449$			29.1190i			1.37421i	0.726559	+	0.687104i	$0.241118\pi$
$449$			29.1190i			1.37421i	−0.726559	+	0.687104i	$0.758882\pi$
$450$		0			0
$451$	−17.3511	+	25.9678i	−0.817033	+	1.22278i
$452$		0			0
$453$	12.3663	−	24.3629i	0.581020	−	1.14467i
$454$		0			0
$455$	−7.70341	+	18.5977i	−0.361141	+	0.871872i
$456$		0			0
$457$	0.159700	+	0.385549i	0.00747044	+	0.0180352i	0.927571	−	0.373648i	$-0.121893\pi$
$457$	0.159700	+	0.385549i	0.00747044	+	0.0180352i	−0.920100	+	0.391683i	$0.871893\pi$
$458$		0			0
$459$	−4.89116	−	1.15039i	−0.228300	−	0.0536954i
$460$		0			0
$461$	3.45947	+	17.3919i	0.161124	+	0.810023i	0.973817	+	0.227332i	$0.0730003\pi$
$461$	3.45947	+	17.3919i	0.161124	+	0.810023i	−0.812694	+	0.582691i	$0.802000\pi$
$462$		0			0
$463$	−10.9564	+	10.9564i	−0.509187	+	0.509187i	−0.914277	−	0.405090i	$-0.867240\pi$
$463$	−10.9564	+	10.9564i	−0.509187	+	0.509187i	0.405090	+	0.914277i	$0.367240\pi$
$464$		0			0
$465$	−9.02930	+	5.07494i	−0.418724	+	0.235345i
$466$		0			0
$467$	−0.465826	−	2.34187i	−0.0215559	−	0.108369i	0.968509	−	0.248977i	$-0.0800943\pi$
$467$	−0.465826	−	2.34187i	−0.0215559	−	0.108369i	−0.990065	+	0.140608i	$0.955094\pi$
$468$		0			0
$469$	35.0290	−	23.4056i	1.61749	−	1.08077i
$470$		0			0
$471$	−1.87956	+	0.225397i	−0.0866058	+	0.0103858i
$472$		0			0
$473$	15.8542	−	38.2753i	0.728975	−	1.75990i
$474$		0			0
$475$	−8.82170	−	1.75475i	−0.404768	−	0.0805133i
$476$		0			0
$477$	5.27842	+	11.3576i	0.241682	+	0.520029i
$478$		0			0
$479$		−	27.3126i		−	1.24794i	−0.781447	−	0.623971i	$-0.785518\pi$
$479$		−	27.3126i		−	1.24794i	0.781447	−	0.623971i	$-0.214482\pi$
$480$		0			0
$481$		−	30.3113i		−	1.38208i
$482$		0			0
$483$	29.0400	+	33.8956i	1.32137	+	1.54230i
$484$		0			0
$485$	7.02824	+	1.39800i	0.319136	+	0.0634801i
$486$		0			0
$487$	11.7515	−	28.3705i	0.532510	−	1.28559i	−0.397346	−	0.917669i	$-0.630069\pi$
$487$	11.7515	−	28.3705i	0.532510	−	1.28559i	0.929856	−	0.367924i	$-0.119931\pi$
$488$		0			0
$489$	0.167169	+	1.39401i	0.00755964	+	0.0630391i
$490$		0			0
$491$	7.62054	−	5.09188i	0.343910	−	0.229793i	−0.371605	−	0.928391i	$-0.621192\pi$
$491$	7.62054	−	5.09188i	0.343910	−	0.229793i	0.715515	+	0.698598i	$0.246192\pi$
$492$		0			0
$493$	−0.689915	−	3.46844i	−0.0310722	−	0.156211i
$494$		0			0
$495$	3.69421	+	15.1813i	0.166043	+	0.682350i
$496$		0			0
$497$	−18.4553	+	18.4553i	−0.827835	+	0.827835i
$498$		0			0
$499$	−7.60310	−	38.2234i	−0.340361	−	1.71111i	−0.649726	−	0.760169i	$-0.725116\pi$
$499$	−7.60310	−	38.2234i	−0.340361	−	1.71111i	0.309364	−	0.950944i	$-0.399884\pi$
$500$		0			0
$501$	4.45088	+	13.6270i	0.198851	+	0.608807i
$502$		0			0
$503$	−4.74830	−	11.4634i	−0.211716	−	0.511129i	0.781971	−	0.623315i	$-0.214215\pi$
$503$	−4.74830	−	11.4634i	−0.211716	−	0.511129i	−0.993687	+	0.112186i	$0.964215\pi$
$504$		0			0
$505$	3.90609	−	9.43014i	0.173819	−	0.419636i
$506$		0			0
$507$	19.2569	+	9.77457i	0.855231	+	0.434104i
$508$		0			0
$509$	19.2360	−	28.7886i	0.852619	−	1.27603i	−0.106866	−	0.994273i	$-0.534082\pi$
$509$	19.2360	−	28.7886i	0.852619	−	1.27603i	0.959485	−	0.281761i	$-0.0909184\pi$
$510$		0			0
$511$			0.590253i			0.0261113i
$512$		0			0
$513$	8.51758	−	7.94687i	0.376060	−	0.350863i
$514$		0			0
$515$	−8.30385	−	5.54846i	−0.365912	−	0.244494i
$516$		0			0
$517$	−2.98001	−	0.592761i	−0.131061	−	0.0260696i
$518$		0			0
$519$	6.76630	+	5.31724i	0.297008	+	0.233401i
$520$		0			0
$521$	24.9630	−	10.3400i	1.09365	−	0.453004i	0.238372	−	0.971174i	$-0.423386\pi$
$521$	24.9630	−	10.3400i	1.09365	−	0.453004i	0.855278	+	0.518170i	$0.173386\pi$
$522$		0			0
$523$	10.8065	−	7.22068i	0.472536	−	0.315738i	−0.296401	−	0.955064i	$-0.595786\pi$
$523$	10.8065	−	7.22068i	0.472536	−	0.315738i	0.768936	+	0.639326i	$0.220786\pi$
$524$		0			0
$525$	2.14519	−	27.8047i	0.0936238	−	1.21350i
$526$		0			0
$527$	4.11384	+	4.11384i	0.179202	+	0.179202i
$528$		0			0
$529$	12.8938	−	12.8938i	0.560599	−	0.560599i
$530$		0			0
$531$	−0.702823	+	1.92331i	−0.0304999	+	0.0834646i
$532$		0			0
$533$	16.7114	+	25.0103i	0.723850	+	1.08332i
$534$		0			0
$535$	−6.87602	−	16.6002i	−0.297276	−	0.717688i
$536$		0			0
$537$	10.0986	+	7.93588i	0.435785	+	0.342458i
$538$		0			0
$539$	9.30734	−	46.7912i	0.400896	−	2.01544i
$540$		0			0
$541$	1.36985	−	2.05013i	0.0588947	−	0.0881421i	−0.800853	−	0.598860i	$-0.795620\pi$
$541$	1.36985	−	2.05013i	0.0588947	−	0.0881421i	0.859748	+	0.510718i	$0.170620\pi$
$542$		0			0
$543$	4.35296	−	15.5259i	0.186803	−	0.666281i
$544$		0			0
$545$	5.76383			0.246895
$546$		0			0
$547$	−1.11688	−	0.746278i	−0.0477545	−	0.0319086i	0.531464	−	0.847081i	$-0.321642\pi$
$547$	−1.11688	−	0.746278i	−0.0477545	−	0.0319086i	−0.579218	+	0.815172i	$0.696642\pi$
$548$		0			0
$549$	3.23440	−	3.52065i	0.138041	−	0.150258i
$550$		0			0
$551$	7.57468	+	3.13754i	0.322692	+	0.133664i
$552$		0			0
$553$	3.84225	−	1.59151i	0.163389	−	0.0676779i
$554$		0			0
$555$	−3.21045	−	9.82921i	−0.136276	−	0.417227i
$556$		0			0
$557$	−32.1153	+	6.38814i	−1.36077	+	0.270674i	−0.820899	−	0.571074i	$-0.806527\pi$
$557$	−32.1153	+	6.38814i	−1.36077	+	0.270674i	−0.539871	+	0.841748i	$0.681527\pi$
$558$		0			0
$559$	−28.2145	−	28.2145i	−1.19335	−	1.19335i
$560$		0			0
$561$	7.65043	−	4.29994i	0.323002	−	0.181544i
$562$		0			0
$563$	3.24723	−	0.645913i	0.136854	−	0.0272220i	−0.126188	−	0.992006i	$-0.540274\pi$
$563$	3.24723	−	0.645913i	0.136854	−	0.0272220i	0.263042	+	0.964784i	$0.415274\pi$
$564$		0			0
$565$	5.91226	+	8.84833i	0.248731	+	0.372252i
$566$		0			0
$567$	27.6082	+	23.2870i	1.15943	+	0.977961i
$568$		0			0
$569$	13.6962	+	5.67316i	0.574175	+	0.237831i	0.650826	−	0.759227i	$-0.274423\pi$
$569$	13.6962	+	5.67316i	0.574175	+	0.237831i	−0.0766510	+	0.997058i	$0.524423\pi$
$570$		0			0
$571$	−3.79750	+	19.0913i	−0.158920	+	0.798947i	0.816286	+	0.577649i	$0.196030\pi$
$571$	−3.79750	+	19.0913i	−0.158920	+	0.798947i	−0.975206	+	0.221299i	$0.928970\pi$
$572$		0			0
$573$	21.1159	+	24.6465i	0.882128	+	1.02962i
$574$		0			0
$575$	−25.7631			−1.07440
$576$		0			0
$577$	38.2782			1.59354			0.796771	−	0.604281i	$-0.206540\pi$
$577$	38.2782			1.59354			0.796771	+	0.604281i	$0.206540\pi$
$578$		0			0
$579$	11.6620	+	13.6120i	0.484657	+	0.565693i
$580$		0			0
$581$	−5.56345	+	27.9694i	−0.230811	+	1.16036i
$582$		0			0
$583$	−20.2098	−	8.37117i	−0.837004	−	0.346698i
$584$		0			0
$585$	14.8702	+	2.30827i	0.614805	+	0.0954351i
$586$		0			0
$587$	20.6062	+	30.8394i	0.850511	+	1.27288i	0.960313	+	0.278926i	$0.0899784\pi$
$587$	20.6062	+	30.8394i	0.850511	+	1.27288i	−0.109802	+	0.993954i	$0.535022\pi$
$588$		0			0
$589$	−13.2290	+	2.63140i	−0.545090	+	0.108425i
$590$		0			0
$591$	3.86628	−	2.17305i	0.159037	−	0.0893873i
$592$		0			0
$593$	−1.60218	−	1.60218i	−0.0657938	−	0.0657938i	0.673444	−	0.739238i	$-0.264814\pi$
$593$	−1.60218	−	1.60218i	−0.0657938	−	0.0657938i	−0.739238	+	0.673444i	$0.764814\pi$
$594$		0			0
$595$	3.78303	−	0.752491i	0.155089	−	0.0308491i
$596$		0			0
$597$	12.7586	+	39.0622i	0.522175	+	1.59871i
$598$		0			0
$599$	−2.19472	+	0.909083i	−0.0896738	+	0.0371441i	−0.427069	−	0.904219i	$-0.640454\pi$
$599$	−2.19472	+	0.909083i	−0.0896738	+	0.0371441i	0.337396	+	0.941363i	$0.390454\pi$
$600$		0			0
$601$	17.3626	+	7.19182i	0.708235	+	0.293360i	0.707574	−	0.706639i	$-0.249790\pi$
$601$	17.3626	+	7.19182i	0.708235	+	0.293360i	0.000660854		1.00000i	$0.499790\pi$
$602$		0			0
$603$	−23.1923	−	21.3066i	−0.944462	−	0.867672i
$604$		0			0
$605$	−13.5996	−	9.08694i	−0.552901	−	0.369437i
$606$		0			0
$607$	−5.07416			−0.205954			−0.102977	−	0.994684i	$-0.532837\pi$
$607$	−5.07416			−0.205954			−0.102977	+	0.994684i	$0.532837\pi$
$608$		0			0
$609$	−6.86236	+	24.4763i	−0.278077	+	0.991831i
$610$		0			0
$611$	−1.62580	+	2.43318i	−0.0657728	+	0.0984360i
$612$		0			0
$613$	2.85290	−	14.3425i	0.115227	−	0.579287i	−0.879428	−	0.476033i	$-0.842074\pi$
$613$	2.85290	−	14.3425i	0.115227	−	0.579287i	0.994655	−	0.103255i	$-0.0329256\pi$
$614$		0			0
$615$	8.06808	+	6.34024i	0.325337	+	0.255663i
$616$		0			0
$617$	8.24754	+	19.9113i	0.332033	+	0.801599i	0.998431	+	0.0560025i	$0.0178355\pi$
$617$	8.24754	+	19.9113i	0.332033	+	0.801599i	−0.666397	+	0.745597i	$0.732165\pi$
$618$		0			0
$619$	4.96359	+	7.42854i	0.199504	+	0.298578i	0.917709	−	0.397253i	$-0.130036\pi$
$619$	4.96359	+	7.42854i	0.199504	+	0.298578i	−0.718206	+	0.695831i	$0.755036\pi$
$620$		0			0
$621$	19.4875	−	27.0845i	0.782006	−	1.08686i
$622$		0			0
$623$	26.1400	−	26.1400i	1.04728	−	1.04728i
$624$		0			0
$625$	7.88915	+	7.88915i	0.315566	+	0.315566i
$626$		0			0
$627$	−1.56511	+	20.2861i	−0.0625046	+	0.810148i
$628$		0			0
$629$	−4.82918	+	3.22675i	−0.192552	+	0.128659i
$630$		0			0
$631$	30.3756	−	12.5820i	1.20923	−	0.500881i	0.315262	−	0.949005i	$-0.397908\pi$
$631$	30.3756	−	12.5820i	1.20923	−	0.500881i	0.893971	+	0.448124i	$0.147908\pi$
$632$		0			0
$633$	−8.08712	−	6.35520i	−0.321434	−	0.252597i
$634$		0			0
$635$	−4.19509	−	0.834455i	−0.166477	−	0.0331143i
$636$		0			0
$637$	−38.2050	−	25.5278i	−1.51374	−	1.01145i
$638$		0			0
$639$	16.6672	+	10.1432i	0.659344	+	0.401258i
$640$		0			0
$641$		−	13.2130i		−	0.521881i	−0.965355	−	0.260940i	$-0.915967\pi$
$641$		−	13.2130i		−	0.521881i	0.965355	−	0.260940i	$-0.0840326\pi$
$642$		0			0
$643$	8.38907	−	12.5551i	0.330832	−	0.495126i	−0.628343	−	0.777936i	$-0.716267\pi$
$643$	8.38907	−	12.5551i	0.330832	−	0.495126i	0.959176	+	0.282810i	$0.0912667\pi$
$644$		0			0
$645$	−12.1376	−	6.16091i	−0.477919	−	0.242586i
$646$		0			0
$647$	−6.02373	+	14.5426i	−0.236817	+	0.571727i	−0.996950	−	0.0780403i	$-0.975134\pi$
$647$	−6.02373	+	14.5426i	−0.236817	+	0.571727i	0.760133	+	0.649767i	$0.225134\pi$
$648$		0			0
$649$	−1.36868	−	3.30428i	−0.0537252	−	0.129704i
$650$		0			0
$651$	−12.9842	−	39.7529i	−0.508892	−	1.55804i
$652$		0			0
$653$	−3.44866	−	17.3376i	−0.134957	−	0.678472i	−0.987727	−	0.156187i	$-0.950080\pi$
$653$	−3.44866	−	17.3376i	−0.134957	−	0.678472i	0.852771	−	0.522285i	$-0.174920\pi$
$654$		0			0
$655$	−0.353597	+	0.353597i	−0.0138162	+	0.0138162i
$656$		0			0
$657$	0.428735	−	0.104328i	0.0167265	−	0.00407022i
$658$		0			0
$659$	9.02750	+	45.3843i	0.351661	+	1.76792i	0.600746	+	0.799440i	$0.294870\pi$
$659$	9.02750	+	45.3843i	0.351661	+	1.76792i	−0.249085	+	0.968482i	$0.580130\pi$
$660$		0			0
$661$	−17.0665	+	11.4035i	−0.663809	+	0.443543i	−0.841292	−	0.540581i	$-0.818205\pi$
$661$	−17.0665	+	11.4035i	−0.663809	+	0.443543i	0.177483	+	0.984124i	$0.443205\pi$
$662$		0			0
$663$	−1.00641	−	8.39231i	−0.0390855	−	0.325930i
$664$		0			0
$665$	−3.42211	+	8.26171i	−0.132704	+	0.320375i
$666$		0			0
$667$	23.0326	+	4.58147i	0.891825	+	0.177395i
$668$		0			0
$669$	4.21220	+	4.91650i	0.162853	+	0.190083i
$670$		0			0
$671$			8.35022i			0.322357i
$672$		0			0
$673$			39.9401i			1.53958i	0.638300	+	0.769788i	$0.279638\pi$
$673$			39.9401i			1.53958i	−0.638300	+	0.769788i	$0.720362\pi$
$674$		0			0
$675$	−20.5753	+	3.35634i	−0.791945	+	0.129186i
$676$		0			0
$677$	−4.42850	−	0.880884i	−0.170201	−	0.0338551i	0.109254	−	0.994014i	$-0.465154\pi$
$677$	−4.42850	−	0.880884i	−0.170201	−	0.0338551i	−0.279455	+	0.960159i	$0.590154\pi$
$678$		0			0
$679$	−11.0720	+	26.7302i	−0.424905	+	1.02581i
$680$		0			0
$681$	6.17683	−	0.740725i	0.236697	−	0.0283846i
$682$		0			0
$683$	12.1355	−	8.10869i	0.464352	−	0.310270i	−0.301295	−	0.953531i	$-0.597419\pi$
$683$	12.1355	−	8.10869i	0.464352	−	0.310270i	0.765647	+	0.643261i	$0.222419\pi$
$684$		0			0
$685$	0.956373	+	4.80801i	0.0365411	+	0.183705i
$686$		0			0
$687$	−42.0603	+	23.6401i	−1.60470	+	0.901925i
$688$		0			0
$689$	−14.8976	+	14.8976i	−0.567552	+	0.567552i
$690$		0			0
$691$	6.14932	+	30.9147i	0.233931	+	1.17605i	0.901928	+	0.431887i	$0.142152\pi$
$691$	6.14932	+	30.9147i	0.233931	+	1.17605i	−0.667996	+	0.744165i	$0.732848\pi$
$692$		0			0
$693$	−63.0269	+	2.67082i	−2.39419	+	0.101456i
$694$		0			0
$695$	−8.68900	−	20.9771i	−0.329593	−	0.795707i
$696$		0			0
$697$	2.20564	−	5.32489i	0.0835446	−	0.201695i
$698$		0			0
$699$	19.8693	−	39.1447i	0.751527	−	1.48059i
$700$		0			0
$701$	6.98670	−	10.4563i	0.263884	−	0.394931i	−0.675739	−	0.737141i	$-0.736175\pi$
$701$	6.98670	−	10.4563i	0.263884	−	0.394931i	0.939623	+	0.342210i	$0.111175\pi$
$702$		0			0
$703$		−	13.4653i		−	0.507853i
$704$		0			0
$705$	−0.269494	+	0.961220i	−0.0101497	+	0.0362016i
$706$		0			0
$707$	34.2660	+	22.8958i	1.28870	+	0.861085i
$708$		0			0
$709$	43.9099	+	8.73421i	1.64907	+	0.328020i	0.930180	−	0.367104i	$-0.119651\pi$
$709$	43.9099	+	8.73421i	1.64907	+	0.328020i	0.718889	+	0.695125i	$0.244651\pi$
$710$		0			0
$711$	−1.83513	−	2.50954i	−0.0688227	−	0.0941152i
$712$		0			0
$713$	−35.6933	+	14.7846i	−1.33672	+	0.553689i
$714$		0			0
$715$	−21.8538	+	14.6022i	−0.817285	+	0.546092i
$716$		0			0
$717$	2.14313	+	0.165347i	0.0800368	+	0.00617501i
$718$		0			0
$719$	−24.3513	−	24.3513i	−0.908150	−	0.908150i	0.0879732	−	0.996123i	$-0.471961\pi$
$719$	−24.3513	−	24.3513i	−0.908150	−	0.908150i	−0.996123	+	0.0879732i	$0.971961\pi$
$720$		0			0
$721$	28.5123	−	28.5123i	1.06185	−	1.06185i
$722$		0			0
$723$	−0.259864	+	3.36821i	−0.00966446	+	0.125265i
$724$		0			0
$725$	−8.15164	−	12.1998i	−0.302744	−	0.453089i
$726$		0			0
$727$	−2.78741	−	6.72940i	−0.103379	−	0.249580i	0.863723	−	0.503966i	$-0.168126\pi$
$727$	−2.78741	−	6.72940i	−0.103379	−	0.249580i	−0.967103	+	0.254387i	$0.918126\pi$
$728$		0			0
$729$	12.0349	−	24.1694i	0.445737	−	0.895164i
$730$		0			0
$731$	−1.49158	+	7.49866i	−0.0551679	+	0.277348i
$732$		0			0
$733$	−4.59999	+	6.88437i	−0.169904	+	0.254280i	−0.906644	−	0.421897i	$-0.861364\pi$
$733$	−4.59999	+	6.88437i	−0.169904	+	0.254280i	0.736739	+	0.676177i	$0.236364\pi$
$734$		0			0
$735$	−15.0928	−	4.23151i	−0.556705	−	0.156082i
$736$		0			0
$737$	55.0070			2.02621
$738$		0			0
$739$	−9.60076	−	6.41502i	−0.353170	−	0.235980i	0.366312	−	0.930492i	$-0.380620\pi$
$739$	−9.60076	−	6.41502i	−0.353170	−	0.235980i	−0.719481	+	0.694512i	$0.755620\pi$
$740$		0			0
$741$	17.4740	+	8.86957i	0.641923	+	0.325832i
$742$		0			0
$743$	22.3975	+	9.27734i	0.821684	+	0.340353i	0.753605	−	0.657327i	$-0.228313\pi$
$743$	22.3975	+	9.27734i	0.821684	+	0.340353i	0.0680787	+	0.997680i	$0.478313\pi$
$744$		0			0
$745$	−0.801287	+	0.331904i	−0.0293569	+	0.0121600i
$746$		0			0
$747$	21.2991	−	0.902566i	0.779294	−	0.0330232i
$748$		0			0
$749$	71.1517	−	14.1529i	2.59983	−	0.517137i
$750$		0			0
$751$	5.97994	+	5.97994i	0.218211	+	0.218211i	0.807744	−	0.589533i	$-0.200688\pi$
$751$	5.97994	+	5.97994i	0.218211	+	0.218211i	−0.589533	+	0.807744i	$0.700688\pi$
$752$		0			0
$753$	−18.3053	−	32.5688i	−0.667083	−	1.18687i
$754$		0			0
$755$	15.3775	−	3.05878i	0.559646	−	0.111320i
$756$		0			0
$757$	−13.3796	−	20.0239i	−0.486288	−	0.727782i	0.504469	−	0.863430i	$-0.331688\pi$
$757$	−13.3796	−	20.0239i	−0.486288	−	0.727782i	−0.990757	+	0.135648i	$0.956688\pi$
$758$		0			0
$759$	6.93901	+	57.8637i	0.251870	+	2.10032i
$760$		0			0
$761$	41.9677	+	17.3836i	1.52133	+	0.630155i	0.977857	−	0.209273i	$-0.0671097\pi$
$761$	41.9677	+	17.3836i	1.52133	+	0.630155i	0.543471	+	0.839428i	$0.317110\pi$
$762$		0			0
$763$	−4.54005	+	22.8244i	−0.164361	+	0.826298i
$764$		0			0
$765$	−1.21523	−	2.61483i	−0.0439368	−	0.0945393i
$766$		0			0
$767$	−3.44465			−0.124379
$768$		0			0
$769$	−17.5017			−0.631126			−0.315563	−	0.948905i	$-0.602193\pi$
$769$	−17.5017			−0.631126			−0.315563	+	0.948905i	$0.602193\pi$
$770$		0			0
$771$	14.4714	−	12.3983i	0.521174	−	0.446514i
$772$		0			0
$773$	−5.07740	+	25.5258i	−0.182621	+	0.918100i	0.775415	+	0.631452i	$0.217541\pi$
$773$	−5.07740	+	25.5258i	−0.182621	+	0.918100i	−0.958036	+	0.286647i	$0.907459\pi$
$774$		0			0
$775$	22.3010	+	9.23736i	0.801074	+	0.331816i
$776$		0			0
$777$	41.4518	−	4.97090i	1.48708	−	0.178330i
$778$		0			0
$779$	7.42375	+	11.1104i	0.265983	+	0.398072i
$780$		0			0
$781$	−33.4232	+	6.64828i	−1.19598	+	0.237894i
$782$		0			0
$783$	18.9915	+	0.658302i	0.678701	+	0.0235258i
$784$		0			0
$785$	−0.768152	−	0.768152i	−0.0274165	−	0.0274165i
$786$		0			0
$787$	−4.24897	+	0.845172i	−0.151459	+	0.0301271i	−0.270238	−	0.962794i	$-0.587102\pi$
$787$	−4.24897	+	0.845172i	−0.151459	+	0.0301271i	0.118778	+	0.992921i	$0.462102\pi$
$788$		0			0
$789$	−15.9329	+	5.20406i	−0.567227	+	0.185270i
$790$		0			0
$791$	−39.6958	+	16.4425i	−1.41142	+	0.584629i
$792$		0			0
$793$	7.43014	+	3.07767i	0.263852	+	0.109291i
$794$		0			0
$795$	−3.25303	+	6.40881i	−0.115373	+	0.227297i
$796$		0			0
$797$	5.95920	+	3.98181i	0.211086	+	0.141043i	0.656619	−	0.754222i	$-0.271986\pi$
$797$	5.95920	+	3.98181i	0.211086	+	0.141043i	−0.445533	+	0.895265i	$0.646986\pi$
$798$		0			0
$799$	0.560726			0.0198370
$800$		0			0
$801$	−23.6073	−	14.3667i	−0.834122	−	0.507623i
$802$		0			0
$803$	−0.428168	+	0.640798i	−0.0151097	+	0.0226133i
$804$		0			0
$805$	−4.99701	+	25.1217i	−0.176121	+	0.885422i
$806$		0			0
$807$	12.2790	−	15.6253i	0.432241	−	0.550036i
$808$		0			0
$809$	4.18595	+	10.1058i	0.147170	+	0.355300i	0.980224	−	0.197892i	$-0.0634096\pi$
$809$	4.18595	+	10.1058i	0.147170	+	0.355300i	−0.833054	+	0.553192i	$0.813410\pi$
$810$		0			0
$811$	−8.10301	−	12.1270i	−0.284535	−	0.425837i	0.661478	−	0.749964i	$-0.269929\pi$
$811$	−8.10301	−	12.1270i	−0.284535	−	0.425837i	−0.946013	+	0.324127i	$0.894929\pi$
$812$		0			0
$813$	−47.9645	−	3.70056i	−1.68219	−	0.129784i
$814$		0			0
$815$	−0.569710	+	0.569710i	−0.0199561	+	0.0199561i
$816$		0			0
$817$	−12.5338	−	12.5338i	−0.438503	−	0.438503i
$818$		0			0
$819$	−20.8535	+	57.0666i	−0.728680	+	1.99407i
$820$		0			0
$821$	43.7273	−	29.2177i	1.52609	−	1.01970i	0.542346	−	0.840155i	$-0.317536\pi$
$821$	43.7273	−	29.2177i	1.52609	−	1.01970i	0.983749	−	0.179548i	$-0.0574637\pi$
$822$		0			0
$823$	9.51214	−	3.94006i	0.331572	−	0.137342i	−0.210686	−	0.977554i	$-0.567570\pi$
$823$	9.51214	−	3.94006i	0.331572	−	0.137342i	0.542258	+	0.840212i	$0.317570\pi$
$824$		0			0
$825$	22.4983	−	28.6296i	0.783292	−	0.996755i
$826$		0			0
$827$	51.3042	+	10.2050i	1.78402	+	0.354864i	0.973116	−	0.230315i	$-0.0739755\pi$
$827$	51.3042	+	10.2050i	1.78402	+	0.354864i	0.810905	+	0.585178i	$0.198976\pi$
$828$		0			0
$829$	−33.9311	−	22.6720i	−1.17847	−	0.787431i	−0.197260	−	0.980351i	$-0.563204\pi$
$829$	−33.9311	−	22.6720i	−1.17847	−	0.787431i	−0.981215	+	0.192920i	$0.938204\pi$
$830$		0			0
$831$	9.35935	+	2.62405i	0.324672	+	0.0910274i
$832$		0			0
$833$			8.80433i			0.305052i
$834$		0			0
$835$	−4.57039	+	6.84008i	−0.158165	+	0.236711i
$836$		0			0
$837$	−26.5798	+	16.4576i	−0.918733	+	0.568857i
$838$		0			0
$839$	−3.41574	+	8.24632i	−0.117924	+	0.284695i	−0.971810	−	0.235767i	$-0.924240\pi$
$839$	−3.41574	+	8.24632i	−0.117924	+	0.284695i	0.853885	+	0.520461i	$0.174240\pi$
$840$		0			0
$841$	−5.97963	−	14.4361i	−0.206194	−	0.497797i
$842$		0			0
$843$	−31.1514	+	10.1748i	−1.07291	+	0.350438i
$844$		0			0
$845$	2.41772	+	12.1547i	0.0831721	+	0.418135i
$846$		0			0
$847$	46.6958	−	46.6958i	1.60449	−	1.60449i
$848$		0			0
$849$	−0.363233	−	0.646263i	−0.0124661	−	0.0221797i
$850$		0			0
$851$	−7.52439	−	37.8277i	−0.257933	−	1.29672i
$852$		0			0
$853$	−39.4858	+	26.3836i	−1.35197	+	0.903356i	−0.999473	−	0.0324574i	$-0.989667\pi$
$853$	−39.4858	+	26.3836i	−1.35197	+	0.903356i	−0.352495	+	0.935814i	$0.614667\pi$
$854$		0			0
$855$	6.60582	+	1.02541i	0.225914	+	0.0350683i
$856$		0			0
$857$	−10.9630	+	26.4671i	−0.374490	+	0.904098i	0.618488	+	0.785794i	$0.287746\pi$
$857$	−10.9630	+	26.4671i	−0.374490	+	0.904098i	−0.992977	+	0.118303i	$0.962254\pi$
$858$		0			0
$859$	21.7921	+	4.33472i	0.743538	+	0.147899i	0.552301	−	0.833645i	$-0.313750\pi$
$859$	21.7921	+	4.33472i	0.743538	+	0.147899i	0.191237	+	0.981544i	$0.438750\pi$
$860$		0			0
$861$	−31.4620	+	26.9550i	−1.07222	+	0.918624i
$862$		0			0
$863$			38.8721i			1.32322i	0.749847	+	0.661611i	$0.230127\pi$
$863$			38.8721i			1.32322i	−0.749847	+	0.661611i	$0.769873\pi$
$864$		0			0
$865$			4.93837i			0.167910i
$866$		0			0
$867$	21.1306	−	18.1036i	0.717634	−	0.614832i
$868$		0			0
$869$	5.32574	+	1.05936i	0.180664	+	0.0359362i
$870$		0			0
$871$	20.2741	−	48.9460i	0.686961	−	1.65847i
$872$		0			0
$873$	21.3727	+	3.31764i	0.723356	+	0.112285i
$874$		0			0
$875$	29.8892	−	19.9713i	1.01044	−	0.675154i
$876$		0			0
$877$	1.77370	+	8.91702i	0.0598938	+	0.301106i	0.999108	−	0.0422250i	$-0.0134446\pi$
$877$	1.77370	+	8.91702i	0.0598938	+	0.301106i	−0.939214	+	0.343331i	$0.888445\pi$
$878$		0			0
$879$	7.03536	+	12.5173i	0.237297	+	0.422198i
$880$		0			0
$881$	−31.0693	+	31.0693i	−1.04675	+	1.04675i	−0.0479003	+	0.998852i	$0.515253\pi$
$881$	−31.0693	+	31.0693i	−1.04675	+	1.04675i	−0.998852	+	0.0479003i	$0.984747\pi$
$882$		0			0
$883$	1.53518	+	7.71788i	0.0516630	+	0.259727i	0.997981	−	0.0635089i	$-0.0202291\pi$
$883$	1.53518	+	7.71788i	0.0516630	+	0.259727i	−0.946318	+	0.323236i	$0.895229\pi$
$884$		0			0
$885$	−1.11702	+	0.364844i	−0.0375481	+	0.0122641i
$886$		0			0
$887$	−0.656614	−	1.58521i	−0.0220469	−	0.0532260i	0.912473	−	0.409138i	$-0.134170\pi$
$887$	−0.656614	−	1.58521i	−0.0220469	−	0.0532260i	−0.934520	+	0.355912i	$0.884170\pi$
$888$		0			0
$889$	6.60877	−	15.9550i	0.221651	−	0.535113i
$890$		0			0
$891$	13.0801	+	45.3080i	0.438198	+	1.51788i
$892$		0			0
$893$	−0.722235	+	1.08090i	−0.0241687	+	0.0361710i
$894$		0			0
$895$			7.37043i			0.246366i
$896$		0			0
$897$	54.0455	+	15.1526i	1.80453	+	0.505930i
$898$		0			0
$899$	−18.2947	−	12.2241i	−0.610162	−	0.407697i
$900$		0			0
$901$	3.95937	+	0.787568i	0.131906	+	0.0262377i
$902$		0			0
$903$	33.9574	−	43.2115i	1.13003	−	1.43799i
$904$		0			0
$905$	8.54886	−	3.54105i	0.284174	−	0.117709i
$906$		0			0
$907$	7.16595	−	4.78814i	0.237942	−	0.158987i	−0.430883	−	0.902408i	$-0.641798\pi$
$907$	7.16595	−	4.78814i	0.237942	−	0.158987i	0.668824	+	0.743420i	$0.266798\pi$
$908$		0			0
$909$	10.5740	−	28.9362i	0.350717	−	0.959754i
$910$		0			0
$911$	−33.5714	−	33.5714i	−1.11227	−	1.11227i	−0.992843	−	0.119428i	$-0.961894\pi$
$911$	−33.5714	−	33.5714i	−1.11227	−	1.11227i	−0.119428	−	0.992843i	$-0.538106\pi$
$912$		0			0
$913$	−26.3287	+	26.3287i	−0.871354	+	0.871354i
$914$		0			0
$915$	2.73539	+	0.211041i	0.0904291	+	0.00697680i
$916$		0			0
$917$	−1.12170	−	1.67874i	−0.0370417	−	0.0554369i
$918$		0			0
$919$	2.63731	+	6.36703i	0.0869968	+	0.210029i	0.961390	−	0.275189i	$-0.0887404\pi$
$919$	2.63731	+	6.36703i	0.0869968	+	0.210029i	−0.874393	+	0.485218i	$0.838740\pi$
$920$		0			0
$921$	16.4610	−	20.9470i	0.542408	−	0.690226i
$922$		0			0
$923$	−6.40315	+	32.1908i	−0.210762	+	1.05957i
$924$		0			0
$925$	−13.3879	+	20.0364i	−0.440190	+	0.658792i
$926$		0			0
$927$	−25.7497	−	15.6705i	−0.845732	−	0.514688i
$928$		0			0
$929$	−32.0105			−1.05023			−0.525115	−	0.851031i	$-0.675978\pi$
$929$	−32.0105			−1.05023			−0.525115	+	0.851031i	$0.675978\pi$
$930$		0			0
$931$	−16.9720	−	11.3403i	−0.556233	−	0.371663i
$932$		0			0
$933$	6.81057	−	13.4175i	0.222968	−	0.439271i
$934$		0			0
$935$	4.65283	+	1.92727i	0.152164	+	0.0630284i
$936$		0			0
$937$	7.59876	−	3.14751i	0.248241	−	0.102825i	−0.255094	−	0.966916i	$-0.582106\pi$
$937$	7.59876	−	3.14751i	0.248241	−	0.102825i	0.503334	+	0.864092i	$0.332106\pi$
$938$		0			0
$939$	−25.5457	+	8.34383i	−0.833653	+	0.272291i
$940$		0			0
$941$	−32.1872	+	6.40243i	−1.04927	+	0.208713i	−0.689469	−	0.724315i	$-0.742156\pi$
$941$	−32.1872	+	6.40243i	−1.04927	+	0.208713i	−0.359803	+	0.933028i	$0.617156\pi$
$942$		0			0
$943$	27.0638	+	27.0638i	0.881319	+	0.881319i
$944$		0			0
$945$	−0.718010	+	20.7140i	−0.0233569	+	0.673828i
$946$		0			0
$947$	14.8826	−	2.96033i	0.483619	−	0.0961978i	0.0527413	−	0.998608i	$-0.483204\pi$
$947$	14.8826	−	2.96033i	0.483619	−	0.0961978i	0.430877	+	0.902410i	$0.358204\pi$
$948$		0			0
$949$	0.412380	+	0.617171i	0.0133864	+	0.0200342i
$950$		0			0
$951$	−14.2024	+	1.70315i	−0.460543	+	0.0552283i
$952$		0			0
$953$	−30.2146	−	12.5153i	−0.978748	−	0.405411i	−0.164786	−	0.986329i	$-0.552693\pi$
$953$	−30.2146	−	12.5153i	−0.978748	−	0.405411i	−0.813962	+	0.580919i	$0.802693\pi$
$954$		0			0
$955$	−3.63348	+	18.2667i	−0.117577	+	0.591097i
$956$		0			0
$957$	−25.2051	+	21.5944i	−0.814764	+	0.698047i
$958$		0			0
$959$	−19.7927			−0.639140
$960$		0			0
$961$	5.19773			0.167669
$962$		0			0
$963$	−22.8563	−	49.1800i	−0.736533	−	1.58480i
$964$		0			0
$965$	−2.00672	+	10.0885i	−0.0645986	+	0.324759i
$966$		0			0
$967$	−31.2373	−	12.9389i	−1.00452	−	0.416088i	−0.181070	−	0.983470i	$-0.557956\pi$
$967$	−31.2373	−	12.9389i	−1.00452	−	0.416088i	−0.823454	+	0.567382i	$0.807956\pi$
$968$		0			0
$969$	−0.447079	−	3.72815i	−0.0143622	−	0.119765i
$970$		0			0
$971$	−18.9299	−	28.3306i	−0.607489	−	0.909171i	0.392455	−	0.919771i	$-0.371626\pi$
$971$	−18.9299	−	28.3306i	−0.607489	−	0.909171i	−0.999944	+	0.0106000i	$0.996626\pi$
$972$		0			0
$973$	89.9121	−	17.8846i	2.88245	−	0.573355i
$974$		0			0
$975$	−17.1827	−	30.5714i	−0.550288	−	0.979070i
$976$		0			0
$977$	−16.1554	−	16.1554i	−0.516857	−	0.516857i	0.399762	−	0.916619i	$-0.369093\pi$
$977$	−16.1554	−	16.1554i	−0.516857	−	0.516857i	−0.916619	+	0.399762i	$0.869093\pi$
$978$		0			0
$979$	47.3403	−	9.41658i	1.51300	−	0.300955i
$980$		0			0
$981$	17.3811	−	0.736539i	0.554937	−	0.0235159i
$982$		0			0
$983$	35.1998	−	14.5803i	1.12270	−	0.465038i	0.257407	−	0.966303i	$-0.417132\pi$
$983$	35.1998	−	14.5803i	1.12270	−	0.465038i	0.865294	+	0.501265i	$0.167132\pi$
$984$		0			0
$985$	2.35139	+	0.973978i	0.0749215	+	0.0310335i
$986$		0			0
$987$	−3.59409	−	1.82431i	−0.114401	−	0.0580685i
$988$		0			0
$989$	−42.2148	−	28.2070i	−1.34235	−	0.896932i
$990$		0			0
$991$	−32.4796			−1.03175			−0.515874	−	0.856664i	$-0.672533\pi$
$991$	−32.4796			−1.03175			−0.515874	+	0.856664i	$0.672533\pi$
$992$		0			0
$993$	33.7407	+	9.45978i	1.07073	+	0.300197i
$994$		0			0
$995$	−13.1012	+	19.6073i	−0.415336	+	0.621594i
$996$		0			0
$997$	7.69284	−	38.6745i	0.243635	−	1.22483i	−0.644267	−	0.764801i	$-0.722837\pi$
$997$	7.69284	−	38.6745i	0.243635	−	1.22483i	0.887901	−	0.460034i	$-0.152163\pi$
$998$		0			0
$999$	−10.9373	−	29.2303i	−0.346042	−	0.924804i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.s.a.143.22		240
3.2	odd	2	inner	768.2.s.a.143.3		240
4.3	odd	2		192.2.s.a.59.13	✓	240
12.11	even	2		192.2.s.a.59.18	yes	240
64.13	even	16		192.2.s.a.179.18	yes	240
64.51	odd	16	inner	768.2.s.a.623.3		240
192.77	odd	16		192.2.s.a.179.13	yes	240
192.179	even	16	inner	768.2.s.a.623.22		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.59.13	✓	240	4.3	odd	2
192.2.s.a.59.18	yes	240	12.11	even	2
192.2.s.a.179.13	yes	240	192.77	odd	16
192.2.s.a.179.18	yes	240	64.13	even	16
768.2.s.a.143.3		240	3.2	odd	2	inner
768.2.s.a.143.22		240	1.1	even	1	trivial
768.2.s.a.623.3		240	64.51	odd	16	inner
768.2.s.a.623.22		240	192.179	even	16	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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.s (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.12690 + 1.31533i) q^{3} +(-0.193910 + 0.974852i) q^{5} +(-3.70761 - 1.53574i) q^{7} +(-0.460173 + 2.96450i) q^{9} +O(q^{10})\)	\(q+(1.12690 + 1.31533i) q^{3} +(-0.193910 + 0.974852i) q^{5} +(-3.70761 - 1.53574i) q^{7} +(-0.460173 + 2.96450i) q^{9} +(-2.91108 - 4.35674i) q^{11} +(-4.94964 + 0.984544i) q^{13} +(-1.50077 + 0.843510i) q^{15} +(0.683765 + 0.683765i) q^{17} +(-2.19880 + 0.437368i) q^{19} +(-2.15812 - 6.60736i) q^{21} +(-5.93261 + 2.45737i) q^{23} +(3.70666 + 1.53535i) q^{25} +(-4.41786 + 2.73543i) q^{27} +(-3.04078 - 2.03178i) q^{29} +6.01645 q^{31} +(2.45003 - 8.73866i) q^{33} +(2.21607 - 3.31658i) q^{35} +(-1.17177 + 5.89086i) q^{37} +(-6.87277 - 5.40091i) q^{39} +(-2.28094 - 5.50667i) q^{41} +(4.39265 + 6.57407i) q^{43} +(-2.80071 - 1.02345i) q^{45} +(0.410028 - 0.410028i) q^{47} +(6.43813 + 6.43813i) q^{49} +(-0.128837 + 1.66991i) q^{51} +(3.47118 - 2.31937i) q^{53} +(4.81167 - 1.99306i) q^{55} +(-3.05311 - 2.39927i) q^{57} +(0.669452 + 0.133162i) q^{59} +(-1.32504 - 0.885363i) q^{61} +(6.25885 - 10.2845i) q^{63} -5.01608i q^{65} +(-5.83232 + 8.72868i) q^{67} +(-9.91773 - 5.03411i) q^{69} +(2.48885 - 6.00860i) q^{71} +(-0.0562858 - 0.135886i) q^{73} +(2.15757 + 6.60567i) q^{75} +(4.10233 + 20.6238i) q^{77} +(-0.732784 + 0.732784i) q^{79} +(-8.57648 - 2.72836i) q^{81} +(-1.38633 - 6.96953i) q^{83} +(-0.799159 + 0.533981i) q^{85} +(-0.754205 - 6.28924i) q^{87} +(-3.52518 + 8.51054i) q^{89} +(19.8633 + 3.95106i) q^{91} +(6.77997 + 7.91361i) q^{93} -2.22831i q^{95} -7.20955i q^{97} +(14.2552 - 6.62504i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 8 q^{3} + 16 q^{7} - 8 q^{9}+O(q^{10}) \) 240 * q + 8 * q^3 + 16 * q^7 - 8 * q^9	\( 240 q + 8 q^{3} + 16 q^{7} - 8 q^{9} - 16 q^{13} + 8 q^{15} + 16 q^{19} - 8 q^{21} - 16 q^{25} + 8 q^{27} + 32 q^{31} - 16 q^{37} + 8 q^{39} + 16 q^{43} - 8 q^{45} - 16 q^{49} + 8 q^{51} + 80 q^{55} - 8 q^{57} - 16 q^{61} + 144 q^{67} - 8 q^{69} - 16 q^{73} + 8 q^{75} + 48 q^{79} - 8 q^{81} - 16 q^{85} + 8 q^{87} + 16 q^{91} - 32 q^{93} + 8 q^{99}+O(q^{100}) \) 240 * q + 8 * q^3 + 16 * q^7 - 8 * q^9 - 16 * q^13 + 8 * q^15 + 16 * q^19 - 8 * q^21 - 16 * q^25 + 8 * q^27 + 32 * q^31 - 16 * q^37 + 8 * q^39 + 16 * q^43 - 8 * q^45 - 16 * q^49 + 8 * q^51 + 80 * q^55 - 8 * q^57 - 16 * q^61 + 144 * q^67 - 8 * q^69 - 16 * q^73 + 8 * q^75 + 48 * q^79 - 8 * q^81 - 16 * q^85 + 8 * q^87 + 16 * q^91 - 32 * q^93 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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