LMFDB - Embedded newform 1008.2.v.d.323.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(323,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))

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

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

chi := DirichletCharacter("1008.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.v (of order $4$, degree $2$, 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.6
Character	$\chi$	$=$	1008.323
Dual form			1008.2.v.d.827.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.575817 - 1.29168i) q^{2} +(-1.33687 + 1.48754i) q^{4} +(0.270063 + 0.270063i) q^{5} -1.00000 q^{7} +(2.69122 + 0.870254i) q^{8} +O(q^{10})$	\(q+(-0.575817 - 1.29168i) q^{2} +(-1.33687 + 1.48754i) q^{4} +(0.270063 + 0.270063i) q^{5} -1.00000 q^{7} +(2.69122 + 0.870254i) q^{8} +(0.193328 - 0.504342i) q^{10} +(3.03491 - 3.03491i) q^{11} +(1.28727 + 1.28727i) q^{13} +(0.575817 + 1.29168i) q^{14} +(-0.425561 - 3.97730i) q^{16} +5.15741i q^{17} +(-5.55077 + 5.55077i) q^{19} +(-0.762769 + 0.0406911i) q^{20} +(-5.66768 - 2.17258i) q^{22} +5.69943i q^{23} -4.85413i q^{25} +(0.921508 - 2.40397i) q^{26} +(1.33687 - 1.48754i) q^{28} +(1.94351 - 1.94351i) q^{29} +0.936219i q^{31} +(-4.89235 + 2.83988i) q^{32} +(6.66172 - 2.96973i) q^{34} +(-0.270063 - 0.270063i) q^{35} +(-1.52927 + 1.52927i) q^{37} +(10.3660 + 3.97359i) q^{38} +(0.491775 + 0.961822i) q^{40} +12.4273 q^{41} +(-0.346427 - 0.346427i) q^{43} +(0.457277 + 8.57183i) q^{44} +(7.36183 - 3.28183i) q^{46} +9.71825 q^{47} +1.00000 q^{49} +(-6.26998 + 2.79509i) q^{50} +(-3.63578 + 0.193956i) q^{52} +(7.69522 + 7.69522i) q^{53} +1.63923 q^{55} +(-2.69122 - 0.870254i) q^{56} +(-3.62949 - 1.39128i) q^{58} +(-2.03405 + 2.03405i) q^{59} +(5.86902 + 5.86902i) q^{61} +(1.20929 - 0.539091i) q^{62} +(6.48532 + 4.68409i) q^{64} +0.695288i q^{65} +(10.7316 - 10.7316i) q^{67} +(-7.67187 - 6.89479i) q^{68} +(-0.193328 + 0.504342i) q^{70} -12.5046i q^{71} +7.37743i q^{73} +(2.85591 + 1.09475i) q^{74} +(-0.836349 - 15.6777i) q^{76} +(-3.03491 + 3.03491i) q^{77} +13.0724i q^{79} +(0.959193 - 1.18905i) q^{80} +(-7.15587 - 16.0521i) q^{82} +(-2.53806 - 2.53806i) q^{83} +(-1.39283 + 1.39283i) q^{85} +(-0.247994 + 0.646951i) q^{86} +(10.8087 - 5.52646i) q^{88} -7.04518 q^{89} +(-1.28727 - 1.28727i) q^{91} +(-8.47814 - 7.61939i) q^{92} +(-5.59594 - 12.5529i) q^{94} -2.99812 q^{95} +0.334289 q^{97} +(-0.575817 - 1.29168i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 8 q^{4} - 36 q^{7}+O(q^{10}) $ 36 * q - 8 * q^4 - 36 * q^7	$ 36 q - 8 q^{4} - 36 q^{7} - 8 q^{10} - 16 q^{13} - 16 q^{19} + 32 q^{22} + 8 q^{28} + 40 q^{34} + 20 q^{37} - 24 q^{40} + 36 q^{43} - 64 q^{46} + 36 q^{49} - 48 q^{52} + 32 q^{55} + 112 q^{61} - 32 q^{64} - 36 q^{67} + 8 q^{70} + 8 q^{76} - 48 q^{82} - 96 q^{85} + 8 q^{88} + 16 q^{91} - 16 q^{94} + 56 q^{97}+O(q^{100}) $ 36 * q - 8 * q^4 - 36 * q^7 - 8 * q^10 - 16 * q^13 - 16 * q^19 + 32 * q^22 + 8 * q^28 + 40 * q^34 + 20 * q^37 - 24 * q^40 + 36 * q^43 - 64 * q^46 + 36 * q^49 - 48 * q^52 + 32 * q^55 + 112 * q^61 - 32 * q^64 - 36 * q^67 + 8 * q^70 + 8 * q^76 - 48 * q^82 - 96 * q^85 + 8 * q^88 + 16 * q^91 - 16 * q^94 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.575817	−	1.29168i	−0.407164	−	0.913355i
$2$	−0.575817	−	1.29168i	−0.407164	−	0.913355i
$3$		0			0
$3$		0			0
$4$	−1.33687	+	1.48754i	−0.668435	+	0.743771i
$5$	0.270063	+	0.270063i	0.120776	+	0.120776i	0.764911	−	0.644136i	$-0.222783\pi$
$5$	0.270063	+	0.270063i	0.120776	+	0.120776i	−0.644136	+	0.764911i	$0.722783\pi$
$6$		0			0
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	2.69122	+	0.870254i	0.951490	+	0.307681i
$9$		0			0
$10$	0.193328	−	0.504342i	0.0611356	−	0.159487i
$11$	3.03491	−	3.03491i	0.915060	−	0.915060i	−0.0816051	−	0.996665i	$-0.526005\pi$
$11$	3.03491	−	3.03491i	0.915060	−	0.915060i	0.996665	+	0.0816051i	$0.0260046\pi$
$12$		0			0
$13$	1.28727	+	1.28727i	0.357025	+	0.357025i	0.862715	−	0.505690i	$-0.168762\pi$
$13$	1.28727	+	1.28727i	0.357025	+	0.357025i	−0.505690	+	0.862715i	$0.668762\pi$
$14$	0.575817	+	1.29168i	0.153894	+	0.345216i
$15$		0			0
$16$	−0.425561	−	3.97730i	−0.106390	−	0.994324i
$17$			5.15741i			1.25086i	0.780282	+	0.625428i	$0.215076\pi$
$17$			5.15741i			1.25086i	−0.780282	+	0.625428i	$0.784924\pi$
$18$		0			0
$19$	−5.55077	+	5.55077i	−1.27343	+	1.27343i	−0.329161	+	0.944274i	$0.606766\pi$
$19$	−5.55077	+	5.55077i	−1.27343	+	1.27343i	−0.944274	+	0.329161i	$0.893234\pi$
$20$	−0.762769	+	0.0406911i	−0.170560	+	0.00909880i
$21$		0			0
$22$	−5.66768	−	2.17258i	−1.20835	−	0.463195i
$23$			5.69943i			1.18841i	0.804313	+	0.594206i	$0.202534\pi$
$23$			5.69943i			1.18841i	−0.804313	+	0.594206i	$0.797466\pi$
$24$		0			0
$25$		−	4.85413i		−	0.970826i
$26$	0.921508	−	2.40397i	0.180723	−	0.471458i
$27$		0			0
$28$	1.33687	−	1.48754i	0.252645	−	0.281119i
$29$	1.94351	−	1.94351i	0.360900	−	0.360900i	−0.503244	−	0.864144i	$-0.667860\pi$
$29$	1.94351	−	1.94351i	0.360900	−	0.360900i	0.864144	+	0.503244i	$0.167860\pi$
$30$		0			0
$31$			0.936219i			0.168150i	0.996459	+	0.0840750i	$0.0267935\pi$
$31$			0.936219i			0.168150i	−0.996459	+	0.0840750i	$0.973206\pi$
$32$	−4.89235	+	2.83988i	−0.864853	+	0.502025i
$33$		0			0
$34$	6.66172	−	2.96973i	1.14248	−	0.509304i
$35$	−0.270063	−	0.270063i	−0.0456490	−	0.0456490i
$36$		0			0
$37$	−1.52927	+	1.52927i	−0.251411	+	0.251411i	−0.821549	−	0.570138i	$-0.806890\pi$
$37$	−1.52927	+	1.52927i	−0.251411	+	0.251411i	0.570138	+	0.821549i	$0.306890\pi$
$38$	10.3660	+	3.97359i	1.68159	+	0.644601i
$39$		0			0
$40$	0.491775	+	0.961822i	0.0777565	+	0.152077i
$41$	12.4273			1.94082			0.970412	−	0.241457i	$-0.0776251\pi$
$41$	12.4273			1.94082			0.970412	+	0.241457i	$0.0776251\pi$
$42$		0			0
$43$	−0.346427	−	0.346427i	−0.0528296	−	0.0528296i	0.680198	−	0.733028i	$-0.261894\pi$
$43$	−0.346427	−	0.346427i	−0.0528296	−	0.0528296i	−0.733028	+	0.680198i	$0.761894\pi$
$44$	0.457277	+	8.57183i	0.0689372	+	1.29225i
$45$		0			0
$46$	7.36183	−	3.28183i	1.08544	−	0.483879i
$47$	9.71825			1.41755			0.708776	−	0.705433i	$-0.249248\pi$
$47$	9.71825			1.41755			0.708776	+	0.705433i	$0.249248\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	−6.26998	+	2.79509i	−0.886709	+	0.395286i
$51$		0			0
$52$	−3.63578	+	0.193956i	−0.504192	+	0.0268969i
$53$	7.69522	+	7.69522i	1.05702	+	1.05702i	0.998273	+	0.0587471i	$0.0187105\pi$
$53$	7.69522	+	7.69522i	1.05702	+	1.05702i	0.0587471	+	0.998273i	$0.481289\pi$
$54$		0			0
$55$	1.63923			0.221034
$56$	−2.69122	−	0.870254i	−0.359629	−	0.116293i
$57$		0			0
$58$	−3.62949	−	1.39128i	−0.476575	−	0.182684i
$59$	−2.03405	+	2.03405i	−0.264810	+	0.264810i	−0.827005	−	0.562195i	$-0.809957\pi$
$59$	−2.03405	+	2.03405i	−0.264810	+	0.264810i	0.562195	+	0.827005i	$0.309957\pi$
$60$		0			0
$61$	5.86902	+	5.86902i	0.751451	+	0.751451i	0.974750	−	0.223299i	$-0.0716826\pi$
$61$	5.86902	+	5.86902i	0.751451	+	0.751451i	−0.223299	+	0.974750i	$0.571683\pi$
$62$	1.20929	−	0.539091i	0.153581	−	0.0684646i
$63$		0			0
$64$	6.48532	+	4.68409i	0.810665	+	0.585511i
$65$			0.695288i			0.0862399i
$66$		0			0
$67$	10.7316	−	10.7316i	1.31107	−	1.31107i	0.390439	−	0.920629i	$-0.372323\pi$
$67$	10.7316	−	10.7316i	1.31107	−	1.31107i	0.920629	−	0.390439i	$-0.127677\pi$
$68$	−7.67187	−	6.89479i	−0.930350	−	0.836116i
$69$		0			0
$70$	−0.193328	+	0.504342i	−0.0231071	+	0.0602804i
$71$		−	12.5046i		−	1.48402i	−0.670389	−	0.742010i	$-0.733873\pi$
$71$		−	12.5046i		−	1.48402i	0.670389	−	0.742010i	$-0.266127\pi$
$72$		0			0
$73$			7.37743i			0.863463i	0.902002	+	0.431732i	$0.142097\pi$
$73$			7.37743i			0.863463i	−0.902002	+	0.431732i	$0.857903\pi$
$74$	2.85591	+	1.09475i	0.331993	+	0.127262i
$75$		0			0
$76$	−0.836349	−	15.6777i	−0.0959358	−	1.79835i
$77$	−3.03491	+	3.03491i	−0.345860	+	0.345860i
$78$		0			0
$79$			13.0724i			1.47076i	0.677658	+	0.735378i	$0.262995\pi$
$79$			13.0724i			1.47076i	−0.677658	+	0.735378i	$0.737005\pi$
$80$	0.959193	−	1.18905i	0.107241	−	0.132940i
$81$		0			0
$82$	−7.15587	−	16.0521i	−0.790234	−	1.77266i
$83$	−2.53806	−	2.53806i	−0.278588	−	0.278588i	0.553957	−	0.832545i	$-0.313117\pi$
$83$	−2.53806	−	2.53806i	−0.278588	−	0.278588i	−0.832545	+	0.553957i	$0.813117\pi$
$84$		0			0
$85$	−1.39283	+	1.39283i	−0.151073	+	0.151073i
$86$	−0.247994	+	0.646951i	−0.0267419	+	0.0697625i
$87$		0			0
$88$	10.8087	−	5.52646i	1.15222	−	0.589123i
$89$	−7.04518			−0.746787			−0.373394	−	0.927673i	$-0.621806\pi$
$89$	−7.04518			−0.746787			−0.373394	+	0.927673i	$0.621806\pi$
$90$		0			0
$91$	−1.28727	−	1.28727i	−0.134943	−	0.134943i
$92$	−8.47814	−	7.61939i	−0.883907	−	0.794376i
$93$		0			0
$94$	−5.59594	−	12.5529i	−0.577177	−	1.29473i
$95$	−2.99812			−0.307600
$96$		0			0
$97$	0.334289			0.0339419			0.0169710	−	0.999856i	$-0.494598\pi$
$97$	0.334289			0.0339419			0.0169710	+	0.999856i	$0.494598\pi$
$98$	−0.575817	−	1.29168i	−0.0581663	−	0.130479i
$99$		0			0
$100$	7.22072	+	6.48934i	0.722072	+	0.648934i
$101$	7.38370	+	7.38370i	0.734706	+	0.734706i	0.971548	−	0.236842i	$-0.0761124\pi$
$101$	7.38370	+	7.38370i	0.734706	+	0.734706i	−0.236842	+	0.971548i	$0.576112\pi$
$102$		0			0
$103$	−14.6297			−1.44151			−0.720755	−	0.693190i	$-0.756205\pi$
$103$	−14.6297			−1.44151			−0.720755	+	0.693190i	$0.756205\pi$
$104$	2.34407	+	4.58458i	0.229855	+	0.449555i
$105$		0			0
$106$	5.50872	−	14.3708i	0.535054	−	1.39582i
$107$	4.13731	−	4.13731i	0.399969	−	0.399969i	−0.478253	−	0.878222i	$-0.658730\pi$
$107$	4.13731	−	4.13731i	0.399969	−	0.399969i	0.878222	+	0.478253i	$0.158730\pi$
$108$		0			0
$109$	10.4525	+	10.4525i	1.00117	+	1.00117i	0.999999	+	0.00116943i	$0.000372243\pi$
$109$	10.4525	+	10.4525i	1.00117	+	1.00117i	0.00116943	+	0.999999i	$0.499628\pi$
$110$	−0.943899	−	2.11736i	−0.0899972	−	0.201883i
$111$		0			0
$112$	0.425561	+	3.97730i	0.0402117	+	0.375819i
$113$			8.90575i			0.837782i	0.908036	+	0.418891i	$0.137581\pi$
$113$			8.90575i			0.837782i	−0.908036	+	0.418891i	$0.862419\pi$
$114$		0			0
$115$	−1.53920	+	1.53920i	−0.143532	+	0.143532i
$116$	0.292833	+	5.48926i	0.0271889	+	0.509665i
$117$		0			0
$118$	3.79858	+	1.45610i	0.349687	+	0.134045i
$119$		−	5.15741i		−	0.472779i
$120$		0			0
$121$		−	7.42135i		−	0.674668i
$122$	4.20141	−	10.9604i	0.380378	−	0.992305i
$123$		0			0
$124$	−1.39267	−	1.25160i	−0.125065	−	0.112397i
$125$	2.66124	−	2.66124i	0.238028	−	0.238028i
$126$		0			0
$127$			13.8060i			1.22509i	0.790437	+	0.612543i	$0.209853\pi$
$127$			13.8060i			1.22509i	−0.790437	+	0.612543i	$0.790147\pi$
$128$	2.31598	−	11.0741i	0.204706	−	0.978824i
$129$		0			0
$130$	0.898089	−	0.400359i	0.0787676	−	0.0351138i
$131$	−8.53288	−	8.53288i	−0.745521	−	0.745521i	0.228113	−	0.973635i	$-0.426744\pi$
$131$	−8.53288	−	8.53288i	−0.745521	−	0.745521i	−0.973635	+	0.228113i	$0.926744\pi$
$132$		0			0
$133$	5.55077	−	5.55077i	0.481313	−	0.481313i
$134$	−20.0411	−	7.68231i	−1.73129	−	0.663650i
$135$		0			0
$136$	−4.48826	+	13.8797i	−0.384865	+	1.19018i
$137$	−4.08397			−0.348917			−0.174459	−	0.984664i	$-0.555818\pi$
$137$	−4.08397			−0.348917			−0.174459	+	0.984664i	$0.555818\pi$
$138$		0			0
$139$	−2.52222	−	2.52222i	−0.213932	−	0.213932i	0.592003	−	0.805935i	$-0.298337\pi$
$139$	−2.52222	−	2.52222i	−0.213932	−	0.213932i	−0.805935	+	0.592003i	$0.798337\pi$
$140$	0.762769	−	0.0406911i	0.0644657	−	0.00343902i
$141$		0			0
$142$	−16.1519	+	7.20035i	−1.35544	+	0.604240i
$143$	7.81350			0.653397
$144$		0			0
$145$	1.04974			0.0871760
$146$	9.52928	−	4.24805i	0.788649	−	0.351571i
$147$		0			0
$148$	−0.230419	−	4.31929i	−0.0189403	−	0.355044i
$149$	−4.47402	−	4.47402i	−0.366526	−	0.366526i	0.499683	−	0.866208i	$-0.333450\pi$
$149$	−4.47402	−	4.47402i	−0.366526	−	0.366526i	−0.866208	+	0.499683i	$0.833450\pi$
$150$		0			0
$151$	−18.6642			−1.51887			−0.759434	−	0.650584i	$-0.774524\pi$
$151$	−18.6642			−1.51887			−0.759434	+	0.650584i	$0.774524\pi$
$152$	−19.7689	+	10.1078i	−1.60347	+	0.819848i
$153$		0			0
$154$	5.66768	+	2.17258i	0.456715	+	0.175071i
$155$	−0.252838	+	0.252838i	−0.0203085	+	0.0203085i
$156$		0			0
$157$	−0.517468	−	0.517468i	−0.0412985	−	0.0412985i	0.686156	−	0.727454i	$-0.259297\pi$
$157$	−0.517468	−	0.517468i	−0.0412985	−	0.0412985i	−0.727454	+	0.686156i	$0.759297\pi$
$158$	16.8853	−	7.52729i	1.34332	−	0.598839i
$159$		0			0
$160$	−2.08819	−	0.554294i	−0.165086	−	0.0438208i
$161$		−	5.69943i		−	0.449178i
$162$		0			0
$163$	2.16031	−	2.16031i	0.169209	−	0.169209i	−0.617423	−	0.786632i	$-0.711823\pi$
$163$	2.16031	−	2.16031i	0.169209	−	0.169209i	0.786632	+	0.617423i	$0.211823\pi$
$164$	−16.6137	+	18.4862i	−1.29731	+	1.44353i
$165$		0			0
$166$	−1.81690	+	4.73981i	−0.141019	+	0.367881i
$167$		−	1.45631i		−	0.112693i	−0.998411	−	0.0563465i	$-0.982055\pi$
$167$		−	1.45631i		−	0.112693i	0.998411	−	0.0563465i	$-0.0179451\pi$
$168$		0			0
$169$		−	9.68587i		−	0.745067i
$170$	2.60110	+	0.997071i	0.199495	+	0.0764719i
$171$		0			0
$172$	0.978452	−	0.0521970i	0.0746062	−	0.00397998i
$173$	15.6519	−	15.6519i	1.18999	−	1.18999i	0.212922	−	0.977069i	$-0.431702\pi$
$173$	15.6519	−	15.6519i	1.18999	−	1.18999i	0.977069	−	0.212922i	$-0.0682980\pi$
$174$		0			0
$175$			4.85413i			0.366938i
$176$	−13.3623	−	10.7792i	−1.00722	−	0.812513i
$177$		0			0
$178$	4.05673	+	9.10010i	0.304065	+	0.682082i
$179$	−10.3258	−	10.3258i	−0.771788	−	0.771788i	0.206631	−	0.978419i	$-0.433750\pi$
$179$	−10.3258	−	10.3258i	−0.771788	−	0.771788i	−0.978419	+	0.206631i	$0.933750\pi$
$180$		0			0
$181$	9.01856	−	9.01856i	0.670344	−	0.670344i	−0.287451	−	0.957795i	$-0.592808\pi$
$181$	9.01856	−	9.01856i	0.670344	−	0.670344i	0.957795	+	0.287451i	$0.0928078\pi$
$182$	−0.921508	+	2.40397i	−0.0683067	+	0.178194i
$183$		0			0
$184$	−4.95995	+	15.3384i	−0.365652	+	1.13076i
$185$	−0.825999			−0.0607287
$186$		0			0
$187$	15.6523	+	15.6523i	1.14461	+	1.14461i
$188$	−12.9920	+	14.4563i	−0.947541	+	1.05433i
$189$		0			0
$190$	1.72637	+	3.87260i	0.125244	+	0.280948i
$191$	−9.73439			−0.704356			−0.352178	−	0.935933i	$-0.614559\pi$
$191$	−9.73439			−0.704356			−0.352178	+	0.935933i	$0.614559\pi$
$192$		0			0
$193$	−3.44692			−0.248115			−0.124057	−	0.992275i	$-0.539591\pi$
$193$	−3.44692			−0.248115			−0.124057	+	0.992275i	$0.539591\pi$
$194$	−0.192489	−	0.431794i	−0.0138199	−	0.0310010i
$195$		0			0
$196$	−1.33687	+	1.48754i	−0.0954907	+	0.106253i
$197$	0.585435	+	0.585435i	0.0417105	+	0.0417105i	0.727654	−	0.685944i	$-0.240610\pi$
$197$	0.585435	+	0.585435i	0.0417105	+	0.0417105i	−0.685944	+	0.727654i	$0.740610\pi$
$198$		0			0
$199$	−2.57428			−0.182486			−0.0912429	−	0.995829i	$-0.529084\pi$
$199$	−2.57428			−0.182486			−0.0912429	+	0.995829i	$0.529084\pi$
$200$	4.22433	−	13.0635i	0.298705	−	0.923731i
$201$		0			0
$202$	5.28571	−	13.7890i	0.371901	−	0.970193i
$203$	−1.94351	+	1.94351i	−0.136407	+	0.136407i
$204$		0			0
$205$	3.35616	+	3.35616i	0.234405	+	0.234405i
$206$	8.42405	+	18.8969i	0.586931	+	1.31661i
$207$		0			0
$208$	4.57204	−	5.66767i	0.317014	−	0.392982i
$209$			33.6922i			2.33054i
$210$		0			0
$211$	−11.3783	+	11.3783i	−0.783317	+	0.783317i	−0.980389	−	0.197072i	$-0.936857\pi$
$211$	−11.3783	+	11.3783i	−0.783317	+	0.783317i	0.197072	+	0.980389i	$0.436857\pi$
$212$	−21.7345	+	1.15946i	−1.49273	+	0.0796319i
$213$		0			0
$214$	−7.72641	−	2.96174i	−0.528166	−	0.202461i
$215$		−	0.187114i		−	0.0127611i
$216$		0			0
$217$		−	0.936219i		−	0.0635547i
$218$	7.48255	−	19.5200i	0.506782	−	1.32206i
$219$		0			0
$220$	−2.19144	+	2.43843i	−0.147747	+	0.164399i
$221$	−6.63898	+	6.63898i	−0.446586	+	0.446586i
$222$		0			0
$223$		−	6.26410i		−	0.419475i	−0.977758	−	0.209738i	$-0.932739\pi$
$223$		−	6.26410i		−	0.419475i	0.977758	−	0.209738i	$-0.0672610\pi$
$224$	4.89235	−	2.83988i	0.326884	−	0.189748i
$225$		0			0
$226$	11.5034	−	5.12808i	0.765193	−	0.341115i
$227$	4.38594	+	4.38594i	0.291105	+	0.291105i	0.837517	−	0.546412i	$-0.184007\pi$
$227$	4.38594	+	4.38594i	0.291105	+	0.291105i	−0.546412	+	0.837517i	$0.684007\pi$
$228$		0			0
$229$	−17.8540	+	17.8540i	−1.17982	+	1.17982i	−0.200034	+	0.979789i	$0.564105\pi$
$229$	−17.8540	+	17.8540i	−1.17982	+	1.17982i	−0.979789	+	0.200034i	$0.935895\pi$
$230$	2.87446	+	1.10186i	0.189536	+	0.0726544i
$231$		0			0
$232$	6.92174	−	3.53906i	0.454435	−	0.232350i
$233$	−15.0142			−0.983614			−0.491807	−	0.870704i	$-0.663664\pi$
$233$	−15.0142			−0.983614			−0.491807	+	0.870704i	$0.663664\pi$
$234$		0			0
$235$	2.62454	+	2.62454i	0.171206	+	0.171206i
$236$	−0.306475	−	5.74499i	−0.0199498	−	0.373967i
$237$		0			0
$238$	−6.66172	+	2.96973i	−0.431815	+	0.192499i
$239$	1.62807			0.105311			0.0526554	−	0.998613i	$-0.483232\pi$
$239$	1.62807			0.105311			0.0526554	+	0.998613i	$0.483232\pi$
$240$		0			0
$241$	−22.7132			−1.46308			−0.731542	−	0.681797i	$-0.761199\pi$
$241$	−22.7132			−1.46308			−0.731542	+	0.681797i	$0.761199\pi$
$242$	−9.58600	+	4.27334i	−0.616211	+	0.274701i
$243$		0			0
$244$	−16.5765	+	0.884300i	−1.06120	+	0.0566115i
$245$	0.270063	+	0.270063i	0.0172537	+	0.0172537i
$246$		0			0
$247$	−14.2907			−0.909295
$248$	−0.814748	+	2.51957i	−0.0517366	+	0.159993i
$249$		0			0
$250$	−4.96985	−	1.90508i	−0.314321	−	0.120488i
$251$	16.1734	−	16.1734i	1.02085	−	1.02085i	0.0210767	−	0.999778i	$-0.493291\pi$
$251$	16.1734	−	16.1734i	1.02085	−	1.02085i	0.999778	−	0.0210767i	$-0.00670942\pi$
$252$		0			0
$253$	17.2972	+	17.2972i	1.08747	+	1.08747i
$254$	17.8329	−	7.94974i	1.11894	−	0.498811i
$255$		0			0
$256$	−15.6378	+	3.38517i	−0.977362	+	0.211573i
$257$			23.1675i			1.44515i	0.691293	+	0.722574i	$0.257041\pi$
$257$			23.1675i			1.44515i	−0.691293	+	0.722574i	$0.742959\pi$
$258$		0			0
$259$	1.52927	−	1.52927i	0.0950243	−	0.0950243i
$260$	−1.03427	−	0.929509i	−0.0641427	−	0.0576457i
$261$		0			0
$262$	−6.10836	+	15.9351i	−0.377376	+	0.984475i
$263$			0.643221i			0.0396627i	0.999803	+	0.0198314i	$0.00631293\pi$
$263$			0.643221i			0.0396627i	−0.999803	+	0.0198314i	$0.993687\pi$
$264$		0			0
$265$			4.15639i			0.255325i
$266$	−10.3660	−	3.97359i	−0.635583	−	0.243636i
$267$		0			0
$268$	1.61695	+	30.3103i	0.0987709	+	1.85150i
$269$	7.72444	−	7.72444i	0.470967	−	0.470967i	−0.431260	−	0.902228i	$-0.641931\pi$
$269$	7.72444	−	7.72444i	0.470967	−	0.470967i	0.902228	+	0.431260i	$0.141931\pi$
$270$		0			0
$271$			20.3731i			1.23758i	0.785558	+	0.618788i	$0.212376\pi$
$271$			20.3731i			1.23758i	−0.785558	+	0.618788i	$0.787624\pi$
$272$	20.5126	−	2.19479i	1.24376	−	0.133079i
$273$		0			0
$274$	2.35162	+	5.27518i	0.142067	+	0.318685i
$275$	−14.7319	−	14.7319i	−0.888364	−	0.888364i
$276$		0			0
$277$	21.6135	−	21.6135i	1.29863	−	1.29863i	0.369336	−	0.929296i	$-0.379585\pi$
$277$	21.6135	−	21.6135i	1.29863	−	1.29863i	0.929296	−	0.369336i	$-0.120415\pi$
$278$	−1.80556	+	4.71024i	−0.108290	+	0.282501i
$279$		0			0
$280$	−0.491775	−	0.961822i	−0.0293892	−	0.0574799i
$281$	−7.42826			−0.443133			−0.221566	−	0.975145i	$-0.571117\pi$
$281$	−7.42826			−0.443133			−0.221566	+	0.975145i	$0.571117\pi$
$282$		0			0
$283$	−8.92425	−	8.92425i	−0.530492	−	0.530492i	0.390227	−	0.920719i	$-0.372397\pi$
$283$	−8.92425	−	8.92425i	−0.530492	−	0.530492i	−0.920719	+	0.390227i	$0.872397\pi$
$284$	18.6011	+	16.7170i	1.10377	+	0.991970i
$285$		0			0
$286$	−4.49915	−	10.0925i	−0.266040	−	0.596784i
$287$	−12.4273			−0.733562
$288$		0			0
$289$	−9.59890			−0.564641
$290$	−0.604457	−	1.35592i	−0.0354950	−	0.0796226i
$291$		0			0
$292$	−10.9742	−	9.86267i	−0.642219	−	0.577169i
$293$	9.06945	+	9.06945i	0.529843	+	0.529843i	0.920526	−	0.390682i	$-0.127761\pi$
$293$	9.06945	+	9.06945i	0.529843	+	0.529843i	−0.390682	+	0.920526i	$0.627761\pi$
$294$		0			0
$295$	−1.09864			−0.0639654
$296$	−5.44646	+	2.78475i	−0.316569	+	0.161860i
$297$		0			0
$298$	−3.20278	+	8.35521i	−0.185532	+	0.484004i
$299$	−7.33670	+	7.33670i	−0.424293	+	0.424293i
$300$		0			0
$301$	0.346427	+	0.346427i	0.0199677	+	0.0199677i
$302$	10.7471	+	24.1081i	0.618429	+	1.38727i
$303$		0			0
$304$	24.4393	+	19.7149i	1.40169	+	1.13073i
$305$			3.17001i			0.181514i
$306$		0			0
$307$	15.2349	−	15.2349i	0.869504	−	0.869504i	−0.122913	−	0.992417i	$-0.539224\pi$
$307$	15.2349	−	15.2349i	0.869504	−	0.869504i	0.992417	+	0.122913i	$0.0392237\pi$
$308$	−0.457277	−	8.57183i	−0.0260558	−	0.488425i
$309$		0			0
$310$	0.472174	+	0.180997i	0.0268177	+	0.0102800i
$311$			21.1899i			1.20157i	0.799410	+	0.600785i	$0.205145\pi$
$311$			21.1899i			1.20157i	−0.799410	+	0.600785i	$0.794855\pi$
$312$		0			0
$313$			15.4334i			0.872347i	0.899863	+	0.436173i	$0.143667\pi$
$313$			15.4334i			0.872347i	−0.899863	+	0.436173i	$0.856333\pi$
$314$	−0.370436	+	0.966370i	−0.0209049	+	0.0545354i
$315$		0			0
$316$	−19.4457	−	17.4760i	−1.09390	−	0.983104i
$317$	−8.23380	+	8.23380i	−0.462456	+	0.462456i	−0.899460	−	0.437003i	$-0.856040\pi$
$317$	−8.23380	+	8.23380i	−0.462456	+	0.462456i	0.437003	+	0.899460i	$0.356040\pi$
$318$		0			0
$319$		−	11.7967i		−	0.660490i
$320$	0.486445	+	3.01644i	0.0271931	+	0.168624i
$321$		0			0
$322$	−7.36183	+	3.28183i	−0.410259	+	0.182889i
$323$	−28.6276	−	28.6276i	−1.59288	−	1.59288i
$324$		0			0
$325$	6.24858	−	6.24858i	0.346609	−	0.346609i
$326$	−4.03438	−	1.54649i	−0.223444	−	0.0856520i
$327$		0			0
$328$	33.4447	+	10.8149i	1.84667	+	0.597155i
$329$	−9.71825			−0.535784
$330$		0			0
$331$	−18.1815	−	18.1815i	−0.999344	−	0.999344i	0.000656172	−	1.00000i	$-0.499791\pi$
$331$	−18.1815	−	18.1815i	−0.999344	−	0.999344i	−1.00000		0.000656172i	$0.999791\pi$
$332$	7.16852	−	0.382415i	0.393423	−	0.0209878i
$333$		0			0
$334$	−1.88109	+	0.838570i	−0.102929	+	0.0458845i
$335$	5.79639			0.316691
$336$		0			0
$337$	20.4267			1.11271			0.556357	−	0.830943i	$-0.312199\pi$
$337$	20.4267			1.11271			0.556357	+	0.830943i	$0.312199\pi$
$338$	−12.5110	+	5.57729i	−0.680511	+	0.303365i
$339$		0			0
$340$	−0.209861	−	3.93391i	−0.0113813	−	0.213346i
$341$	2.84134	+	2.84134i	0.153867	+	0.153867i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	−0.630831	−	1.23379i	−0.0340121	−	0.0665215i
$345$		0			0
$346$	−29.2298	−	11.2046i	−1.57141	−	0.602363i
$347$	1.37130	−	1.37130i	0.0736154	−	0.0736154i	−0.669340	−	0.742956i	$-0.733423\pi$
$347$	1.37130	−	1.37130i	0.0736154	−	0.0736154i	0.742956	+	0.669340i	$0.233423\pi$
$348$		0			0
$349$	5.10409	+	5.10409i	0.273216	+	0.273216i	0.830393	−	0.557178i	$-0.188116\pi$
$349$	5.10409	+	5.10409i	0.273216	+	0.273216i	−0.557178	+	0.830393i	$0.688116\pi$
$350$	6.26998	−	2.79509i	0.335145	−	0.149404i
$351$		0			0
$352$	−6.22904	+	23.4666i	−0.332009	+	1.25078i
$353$		−	32.0190i		−	1.70420i	−0.523378	−	0.852101i	$-0.675328\pi$
$353$		−	32.0190i		−	1.70420i	0.523378	−	0.852101i	$-0.324672\pi$
$354$		0			0
$355$	3.37702	−	3.37702i	0.179234	−	0.179234i
$356$	9.41848	−	10.4800i	0.499178	−	0.555438i
$357$		0			0
$358$	−7.39186	+	19.2834i	−0.390672	+	1.01916i
$359$		−	10.8950i		−	0.575018i	−0.957778	−	0.287509i	$-0.907173\pi$
$359$		−	10.8950i		−	0.575018i	0.957778	−	0.287509i	$-0.0928272\pi$
$360$		0			0
$361$		−	42.6222i		−	2.24327i
$362$	−16.8421	−	6.45605i	−0.885203	−	0.339322i
$363$		0			0
$364$	3.63578	−	0.193956i	0.190567	−	0.0101661i
$365$	−1.99237	+	1.99237i	−0.104286	+	0.104286i
$366$		0			0
$367$		−	3.57323i		−	0.186521i	−0.995642	−	0.0932605i	$-0.970271\pi$
$367$		−	3.57323i		−	0.186521i	0.995642	−	0.0932605i	$-0.0297290\pi$
$368$	22.6683	−	2.42546i	1.18167	−	0.126436i
$369$		0			0
$370$	0.475625	+	1.06693i	0.0247265	+	0.0554668i
$371$	−7.69522	−	7.69522i	−0.399516	−	0.399516i
$372$		0			0
$373$	−8.40095	+	8.40095i	−0.434985	+	0.434985i	−0.890320	−	0.455335i	$-0.849519\pi$
$373$	−8.40095	+	8.40095i	−0.434985	+	0.434985i	0.455335	+	0.890320i	$0.349519\pi$
$374$	11.2049	−	29.2306i	0.579390	−	1.51148i
$375$		0			0
$376$	26.1539	+	8.45735i	1.34879	+	0.436154i
$377$	5.00363			0.257700
$378$		0			0
$379$	−7.51287	−	7.51287i	−0.385910	−	0.385910i	0.487316	−	0.873226i	$-0.337976\pi$
$379$	−7.51287	−	7.51287i	−0.385910	−	0.385910i	−0.873226	+	0.487316i	$0.837976\pi$
$380$	4.00809	−	4.45982i	0.205611	−	0.228784i
$381$		0			0
$382$	5.60523	+	12.5737i	0.286789	+	0.643327i
$383$	28.9165			1.47757			0.738783	−	0.673944i	$-0.235401\pi$
$383$	28.9165			1.47757			0.738783	+	0.673944i	$0.235401\pi$
$384$		0			0
$385$	−1.63923			−0.0835431
$386$	1.98480	+	4.45232i	0.101023	+	0.226617i
$387$		0			0
$388$	−0.446901	+	0.497269i	−0.0226880	+	0.0252450i
$389$	1.26758	+	1.26758i	0.0642689	+	0.0642689i	0.738511	−	0.674242i	$-0.235529\pi$
$389$	1.26758	+	1.26758i	0.0642689	+	0.0642689i	−0.674242	+	0.738511i	$0.735529\pi$
$390$		0			0
$391$	−29.3943			−1.48653
$392$	2.69122	+	0.870254i	0.135927	+	0.0439545i
$393$		0			0
$394$	0.419090	−	1.09330i	0.0211135	−	0.0550795i
$395$	−3.53036	+	3.53036i	−0.177632	+	0.177632i
$396$		0			0
$397$	−2.08140	−	2.08140i	−0.104463	−	0.104463i	0.652944	−	0.757406i	$-0.273534\pi$
$397$	−2.08140	−	2.08140i	−0.104463	−	0.104463i	−0.757406	+	0.652944i	$0.773534\pi$
$398$	1.48231	+	3.32514i	0.0743017	+	0.166674i
$399$		0			0
$400$	−19.3063	+	2.06573i	−0.965316	+	0.103287i
$401$		−	7.64862i		−	0.381954i	−0.981595	−	0.190977i	$-0.938834\pi$
$401$		−	7.64862i		−	0.381954i	0.981595	−	0.190977i	$-0.0611656\pi$
$402$		0			0
$403$	−1.20517	+	1.20517i	−0.0600336	+	0.0600336i
$404$	−20.8546	+	1.11252i	−1.03756	+	0.0553500i
$405$		0			0
$406$	3.62949	+	1.39128i	0.180129	+	0.0690482i
$407$			9.28240i			0.460111i
$408$		0			0
$409$		−	36.0331i		−	1.78172i	−0.454275	−	0.890862i	$-0.650102\pi$
$409$		−	36.0331i		−	1.78172i	0.454275	−	0.890862i	$-0.349898\pi$
$410$	2.40255	−	6.26762i	0.118653	−	0.309536i
$411$		0			0
$412$	19.5580	−	21.7623i	0.963555	−	1.07215i
$413$	2.03405	−	2.03405i	0.100089	−	0.100089i
$414$		0			0
$415$		−	1.37087i		−	0.0672934i
$416$	−9.95347	−	2.64207i	−0.488009	−	0.129538i
$417$		0			0
$418$	43.5195	−	19.4005i	2.12861	−	0.948911i
$419$	4.27031	+	4.27031i	0.208618	+	0.208618i	0.803680	−	0.595062i	$-0.202872\pi$
$419$	4.27031	+	4.27031i	0.208618	+	0.208618i	−0.595062	+	0.803680i	$0.702872\pi$
$420$		0			0
$421$	−6.30843	+	6.30843i	−0.307454	+	0.307454i	−0.843921	−	0.536467i	$-0.819759\pi$
$421$	−6.30843	+	6.30843i	−0.307454	+	0.307454i	0.536467	+	0.843921i	$0.319759\pi$
$422$	21.2490	+	8.14532i	1.03439	+	0.396508i
$423$		0			0
$424$	14.0127	+	27.4063i	0.680518	+	1.33097i
$425$	25.0348			1.21436
$426$		0			0
$427$	−5.86902	−	5.86902i	−0.284022	−	0.284022i
$428$	0.623379	+	11.6855i	0.0301322	+	0.564838i
$429$		0			0
$430$	−0.241691	+	0.107744i	−0.0116554	+	0.00519585i
$431$	−12.7409			−0.613708			−0.306854	−	0.951757i	$-0.599276\pi$
$431$	−12.7409			−0.613708			−0.306854	+	0.951757i	$0.599276\pi$
$432$		0			0
$433$	2.89975			0.139353			0.0696764	−	0.997570i	$-0.477803\pi$
$433$	2.89975			0.139353			0.0696764	+	0.997570i	$0.477803\pi$
$434$	−1.20929	+	0.539091i	−0.0580480	+	0.0258772i
$435$		0			0
$436$	−29.5222	+	1.57491i	−1.41386	+	0.0754243i
$437$	−31.6362	−	31.6362i	−1.51337	−	1.51337i
$438$		0			0
$439$	18.1968			0.868487			0.434243	−	0.900796i	$-0.357016\pi$
$439$	18.1968			0.868487			0.434243	+	0.900796i	$0.357016\pi$
$440$	4.41154	+	1.42655i	0.210312	+	0.0680081i
$441$		0			0
$442$	12.3983	+	4.75259i	0.589726	+	0.226058i
$443$	−5.90248	+	5.90248i	−0.280435	+	0.280435i	−0.833283	−	0.552847i	$-0.813541\pi$
$443$	−5.90248	+	5.90248i	−0.280435	+	0.280435i	0.552847	+	0.833283i	$0.313541\pi$
$444$		0			0
$445$	−1.90264	−	1.90264i	−0.0901938	−	0.0901938i
$446$	−8.09121	+	3.60698i	−0.383130	+	0.170795i
$447$		0			0
$448$	−6.48532	−	4.68409i	−0.306402	−	0.221302i
$449$			13.5014i			0.637172i	0.947894	+	0.318586i	$0.103208\pi$
$449$			13.5014i			0.637172i	−0.947894	+	0.318586i	$0.896792\pi$
$450$		0			0
$451$	37.7158	−	37.7158i	1.77597	−	1.77597i
$452$	−13.2477	−	11.9058i	−0.623118	−	0.560003i
$453$		0			0
$454$	3.13973	−	8.19072i	0.147355	−	0.384410i
$455$		−	0.695288i		−	0.0325956i
$456$		0			0
$457$		−	24.4732i		−	1.14481i	−0.819972	−	0.572403i	$-0.806011\pi$
$457$		−	24.4732i		−	1.14481i	0.819972	−	0.572403i	$-0.193989\pi$
$458$	33.3422	+	12.7810i	1.55798	+	0.597216i
$459$		0			0
$460$	−0.231916	−	4.34735i	−0.0108131	−	0.202696i
$461$	5.52778	−	5.52778i	0.257455	−	0.257455i	−0.566563	−	0.824018i	$-0.691727\pi$
$461$	5.52778	−	5.52778i	0.257455	−	0.257455i	0.824018	+	0.566563i	$0.191727\pi$
$462$		0			0
$463$			8.48501i			0.394332i	0.980370	+	0.197166i	$0.0631738\pi$
$463$			8.48501i			0.394332i	−0.980370	+	0.197166i	$0.936826\pi$
$464$	−8.55698	−	6.90282i	−0.397248	−	0.320455i
$465$		0			0
$466$	8.64545	+	19.3936i	0.400493	+	0.898389i
$467$	1.61601	+	1.61601i	0.0747800	+	0.0747800i	0.743508	−	0.668728i	$-0.233161\pi$
$467$	1.61601	+	1.61601i	0.0747800	+	0.0747800i	−0.668728	+	0.743508i	$0.733161\pi$
$468$		0			0
$469$	−10.7316	+	10.7316i	−0.495537	+	0.495537i
$470$	1.87881	−	4.90132i	0.0866630	−	0.226081i
$471$		0			0
$472$	−7.24421	+	3.70393i	−0.333442	+	0.170487i
$473$	−2.10275			−0.0966844
$474$		0			0
$475$	26.9442	+	26.9442i	1.23628	+	1.23628i
$476$	7.67187	+	6.89479i	0.351639	+	0.316022i
$477$		0			0
$478$	−0.937468	−	2.10294i	−0.0428788	−	0.0961862i
$479$	−16.9452			−0.774247			−0.387123	−	0.922028i	$-0.626531\pi$
$479$	−16.9452			−0.774247			−0.387123	+	0.922028i	$0.626531\pi$
$480$		0			0
$481$	−3.93717			−0.179520
$482$	13.0786	+	29.3381i	0.595715	+	1.33631i
$483$		0			0
$484$	11.0396	+	9.92137i	0.501799	+	0.450972i
$485$	0.0902791	+	0.0902791i	0.00409936	+	0.00409936i
$486$		0			0
$487$	6.48781			0.293991			0.146995	−	0.989137i	$-0.453040\pi$
$487$	6.48781			0.293991			0.146995	+	0.989137i	$0.453040\pi$
$488$	10.6873	+	20.9024i	0.483790	+	0.946205i
$489$		0			0
$490$	0.193328	−	0.504342i	0.00873366	−	0.0227838i
$491$	−3.03691	+	3.03691i	−0.137054	+	0.137054i	−0.772305	−	0.635251i	$-0.780896\pi$
$491$	−3.03691	+	3.03691i	−0.137054	+	0.137054i	0.635251	+	0.772305i	$0.280896\pi$
$492$		0			0
$493$	10.0235	+	10.0235i	0.451434	+	0.451434i
$494$	8.22882	+	18.4590i	0.370232	+	0.830509i
$495$		0			0
$496$	3.72362	−	0.398419i	0.167196	−	0.0178895i
$497$			12.5046i			0.560907i
$498$		0			0
$499$	29.0548	−	29.0548i	1.30067	−	1.30067i	0.372735	−	0.927938i	$-0.378420\pi$
$499$	29.0548	−	29.0548i	1.30067	−	1.30067i	0.927938	−	0.372735i	$-0.121580\pi$
$500$	0.400975	+	7.51643i	0.0179322	+	0.336145i
$501$		0			0
$502$	−30.2037	−	11.5779i	−1.34806	−	0.516747i
$503$			24.3803i			1.08706i	0.839388	+	0.543532i	$0.182913\pi$
$503$			24.3803i			1.08706i	−0.839388	+	0.543532i	$0.817087\pi$
$504$		0			0
$505$			3.98813i			0.177469i
$506$	12.3824	−	32.3025i	0.550467	−	1.43602i
$507$		0			0
$508$	−20.5370	−	18.4568i	−0.911184	−	0.818890i
$509$	−6.39973	+	6.39973i	−0.283663	+	0.283663i	−0.834568	−	0.550905i	$-0.814283\pi$
$509$	−6.39973	+	6.39973i	−0.283663	+	0.283663i	0.550905	+	0.834568i	$0.314283\pi$
$510$		0			0
$511$		−	7.37743i		−	0.326359i
$512$	13.3771	+	18.2498i	0.591188	+	0.806534i
$513$		0			0
$514$	29.9250	−	13.3402i	1.31993	−	0.588413i
$515$	−3.95095	−	3.95095i	−0.174100	−	0.174100i
$516$		0			0
$517$	29.4940	−	29.4940i	1.29715	−	1.29715i
$518$	−2.85591	−	1.09475i	−0.125481	−	0.0481004i
$519$		0			0
$520$	−0.605077	+	1.87117i	−0.0265344	+	0.0820563i
$521$	−24.3522			−1.06689			−0.533444	−	0.845835i	$-0.679103\pi$
$521$	−24.3522			−1.06689			−0.533444	+	0.845835i	$0.679103\pi$
$522$		0			0
$523$	−13.4483	−	13.4483i	−0.588054	−	0.588054i	0.349050	−	0.937104i	$-0.386504\pi$
$523$	−13.4483	−	13.4483i	−0.588054	−	0.588054i	−0.937104	+	0.349050i	$0.886504\pi$
$524$	24.1004	−	1.28567i	1.05283	−	0.0561648i
$525$		0			0
$526$	0.830835	−	0.370378i	0.0362261	−	0.0161492i
$527$	−4.82847			−0.210331
$528$		0			0
$529$	−9.48348			−0.412325
$530$	5.36872	−	2.39332i	0.233202	−	0.103959i
$531$		0			0
$532$	0.836349	+	15.6777i	0.0362603	+	0.679713i
$533$	15.9973	+	15.9973i	0.692921	+	0.692921i
$534$		0			0
$535$	2.23467			0.0966131
$536$	38.2201	−	19.5418i	1.65086	−	0.844076i
$537$		0			0
$538$	−14.4254	−	5.52963i	−0.621921	−	0.238399i
$539$	3.03491	−	3.03491i	0.130723	−	0.130723i
$540$		0			0
$541$	2.15117	+	2.15117i	0.0924861	+	0.0924861i	0.751836	−	0.659350i	$-0.229168\pi$
$541$	2.15117	+	2.15117i	0.0924861	+	0.0924861i	−0.659350	+	0.751836i	$0.729168\pi$
$542$	26.3155	−	11.7312i	1.13035	−	0.503896i
$543$		0			0
$544$	−14.6465	−	25.2318i	−0.627962	−	1.08181i
$545$			5.64567i			0.241834i
$546$		0			0
$547$	5.10155	−	5.10155i	0.218126	−	0.218126i	−0.589582	−	0.807708i	$-0.700708\pi$
$547$	5.10155	−	5.10155i	0.218126	−	0.218126i	0.807708	+	0.589582i	$0.200708\pi$
$548$	5.45974	−	6.07508i	0.233228	−	0.259515i
$549$		0			0
$550$	−10.5460	+	27.5117i	−0.449682	+	1.17310i
$551$			21.5759i			0.919165i
$552$		0			0
$553$		−	13.0724i		−	0.555893i
$554$	−40.3632	−	15.4723i	−1.71487	−	0.657355i
$555$		0			0
$556$	7.12379	−	0.380030i	0.302116	−	0.0161168i
$557$	16.0391	−	16.0391i	0.679599	−	0.679599i	−0.280310	−	0.959909i	$-0.590437\pi$
$557$	16.0391	−	16.0391i	0.679599	−	0.679599i	0.959909	+	0.280310i	$0.0904374\pi$
$558$		0			0
$559$		−	0.891890i		−	0.0377229i
$560$	−0.959193	+	1.18905i	−0.0405333	+	0.0502465i
$561$		0			0
$562$	4.27732	+	9.59493i	0.180428	+	0.404738i
$563$	20.3434	+	20.3434i	0.857370	+	0.857370i	0.991028	−	0.133657i	$-0.0426721\pi$
$563$	20.3434	+	20.3434i	0.857370	+	0.857370i	−0.133657	+	0.991028i	$0.542672\pi$
$564$		0			0
$565$	−2.40511	+	2.40511i	−0.101184	+	0.101184i
$566$	−6.38853	+	16.6660i	−0.268530	+	0.700524i
$567$		0			0
$568$	10.8822	−	33.6525i	0.456605	−	1.41203i
$569$	−34.6243			−1.45152			−0.725762	−	0.687945i	$-0.758513\pi$
$569$	−34.6243			−1.45152			−0.725762	+	0.687945i	$0.758513\pi$
$570$		0			0
$571$	−30.1046	−	30.1046i	−1.25984	−	1.25984i	−0.951170	−	0.308667i	$-0.900117\pi$
$571$	−30.1046	−	30.1046i	−1.25984	−	1.25984i	−0.308667	−	0.951170i	$-0.599883\pi$
$572$	−10.4456	+	11.6229i	−0.436753	+	0.485978i
$573$		0			0
$574$	7.15587	+	16.0521i	0.298680	+	0.670003i
$575$	27.6658			1.15374
$576$		0			0
$577$	−4.97393			−0.207067			−0.103534	−	0.994626i	$-0.533015\pi$
$577$	−4.97393			−0.207067			−0.103534	+	0.994626i	$0.533015\pi$
$578$	5.52721	+	12.3987i	0.229902	+	0.515718i
$579$		0			0
$580$	−1.40336	+	1.56153i	−0.0582715	+	0.0648390i
$581$	2.53806	+	2.53806i	0.105296	+	0.105296i
$582$		0			0
$583$	46.7086			1.93447
$584$	−6.42024	+	19.8543i	−0.265671	+	0.821576i
$585$		0			0
$586$	6.49248	−	16.9372i	0.268202	−	0.699668i
$587$	4.50154	−	4.50154i	0.185798	−	0.185798i	−0.608079	−	0.793877i	$-0.708059\pi$
$587$	4.50154	−	4.50154i	0.185798	−	0.185798i	0.793877	+	0.608079i	$0.208059\pi$
$588$		0			0
$589$	−5.19674	−	5.19674i	−0.214128	−	0.214128i
$590$	0.632617	+	1.41909i	0.0260444	+	0.0584231i
$591$		0			0
$592$	6.73317	+	5.43157i	0.276731	+	0.223236i
$593$		−	38.9459i		−	1.59931i	−0.600457	−	0.799657i	$-0.705015\pi$
$593$		−	38.9459i		−	1.59931i	0.600457	−	0.799657i	$-0.294985\pi$
$594$		0			0
$595$	1.39283	−	1.39283i	0.0571003	−	0.0571003i
$596$	12.6365	−	0.674111i	0.517609	−	0.0276127i
$597$		0			0
$598$	13.7013	+	5.25207i	0.560286	+	0.214773i
$599$		−	12.5162i		−	0.511398i	−0.966756	−	0.255699i	$-0.917694\pi$
$599$		−	12.5162i		−	0.511398i	0.966756	−	0.255699i	$-0.0823056\pi$
$600$		0			0
$601$		−	25.5234i		−	1.04112i	−0.853825	−	0.520561i	$-0.825723\pi$
$601$		−	25.5234i		−	1.04112i	0.853825	−	0.520561i	$-0.174277\pi$
$602$	0.247994	−	0.646951i	0.0101075	−	0.0263677i
$603$		0			0
$604$	24.9516	−	27.7637i	1.01526	−	1.12969i
$605$	2.00423	−	2.00423i	0.0814836	−	0.0814836i
$606$		0			0
$607$			14.1652i			0.574949i	0.957788	+	0.287475i	$0.0928157\pi$
$607$			14.1652i			0.574949i	−0.957788	+	0.287475i	$0.907184\pi$
$608$	11.3928	−	42.9199i	0.462037	−	1.74063i
$609$		0			0
$610$	4.09464	−	1.82535i	0.165787	−	0.0739061i
$611$	12.5100	+	12.5100i	0.506101	+	0.506101i
$612$		0			0
$613$	28.9735	−	28.9735i	1.17023	−	1.17023i	0.188071	−	0.982155i	$-0.439776\pi$
$613$	28.9735	−	28.9735i	1.17023	−	1.17023i	0.982155	−	0.188071i	$-0.0602236\pi$
$614$	−28.4512	−	10.9061i	−1.14820	−	0.440135i
$615$		0			0
$616$	−10.8087	+	5.52646i	−0.435497	+	0.222668i
$617$	−5.73722			−0.230972			−0.115486	−	0.993309i	$-0.536843\pi$
$617$	−5.73722			−0.230972			−0.115486	+	0.993309i	$0.536843\pi$
$618$		0			0
$619$	27.3596	+	27.3596i	1.09968	+	1.09968i	0.994448	+	0.105229i	$0.0335575\pi$
$619$	27.3596	+	27.3596i	1.09968	+	1.09968i	0.105229	+	0.994448i	$0.466442\pi$
$620$	−0.0380958	−	0.714119i	−0.00152996	−	0.0286797i
$621$		0			0
$622$	27.3706	−	12.2015i	1.09746	−	0.489237i
$623$	7.04518			0.282259
$624$		0			0
$625$	−22.8333			−0.913330
$626$	19.9350	−	8.88681i	0.796762	−	0.355188i
$627$		0			0
$628$	1.46154	−	0.0779682i	0.0583219	−	0.00311127i
$629$	−7.88708	−	7.88708i	−0.314479	−	0.314479i
$630$		0			0
$631$	−39.5537			−1.57461			−0.787303	−	0.616566i	$-0.788523\pi$
$631$	−39.5537			−1.57461			−0.787303	+	0.616566i	$0.788523\pi$
$632$	−11.3763	+	35.1806i	−0.452524	+	1.39941i
$633$		0			0
$634$	15.3766	+	5.89426i	0.610683	+	0.234091i
$635$	−3.72850	+	3.72850i	−0.147961	+	0.147961i
$636$		0			0
$637$	1.28727	+	1.28727i	0.0510035	+	0.0510035i
$638$	−15.2376	+	6.79276i	−0.603262	+	0.268928i
$639$		0			0
$640$	3.61617	−	2.36525i	0.142942	−	0.0934947i
$641$			42.5474i			1.68052i	0.542182	+	0.840261i	$0.317598\pi$
$641$			42.5474i			1.68052i	−0.542182	+	0.840261i	$0.682402\pi$
$642$		0			0
$643$	−13.6174	+	13.6174i	−0.537017	+	0.537017i	−0.922652	−	0.385635i	$-0.873983\pi$
$643$	−13.6174	+	13.6174i	−0.537017	+	0.537017i	0.385635	+	0.922652i	$0.373983\pi$
$644$	8.47814	+	7.61939i	0.334085	+	0.300246i
$645$		0			0
$646$	−20.4934	+	53.4620i	−0.806303	+	2.10343i
$647$			29.7806i			1.17080i	0.810746	+	0.585398i	$0.199062\pi$
$647$			29.7806i			1.17080i	−0.810746	+	0.585398i	$0.800938\pi$
$648$		0			0
$649$			12.3463i			0.484635i
$650$	−11.6692	−	4.47312i	−0.457704	−	0.175450i
$651$		0			0
$652$	0.325500	+	6.10162i	0.0127476	+	0.238958i
$653$	13.9493	−	13.9493i	0.545880	−	0.545880i	−0.379367	−	0.925246i	$-0.623858\pi$
$653$	13.9493	−	13.9493i	0.545880	−	0.545880i	0.925246	+	0.379367i	$0.123858\pi$
$654$		0			0
$655$		−	4.60883i		−	0.180082i
$656$	−5.28859	−	49.4272i	−0.206485	−	1.92981i
$657$		0			0
$658$	5.59594	+	12.5529i	0.218152	+	0.489361i
$659$	12.9096	+	12.9096i	0.502888	+	0.502888i	0.912334	−	0.409446i	$-0.134278\pi$
$659$	12.9096	+	12.9096i	0.502888	+	0.502888i	−0.409446	+	0.912334i	$0.634278\pi$
$660$		0			0
$661$	−19.0427	+	19.0427i	−0.740674	+	0.740674i	−0.972708	−	0.232033i	$-0.925462\pi$
$661$	−19.0427	+	19.0427i	−0.740674	+	0.740674i	0.232033	+	0.972708i	$0.425462\pi$
$662$	−13.0154	+	33.9538i	−0.505859	+	1.31965i
$663$		0			0
$664$	−4.62171	−	9.03922i	−0.179357	−	0.350790i
$665$	2.99812			0.116262
$666$		0			0
$667$	11.0769	+	11.0769i	0.428898	+	0.428898i
$668$	2.16633	+	1.94690i	0.0838177	+	0.0753279i
$669$		0			0
$670$	−3.33766	−	7.48708i	−0.128945	−	0.289251i
$671$	35.6239			1.37524
$672$		0			0
$673$	−20.4420			−0.787983			−0.393991	−	0.919114i	$-0.628906\pi$
$673$	−20.4420			−0.787983			−0.393991	+	0.919114i	$0.628906\pi$
$674$	−11.7621	−	26.3848i	−0.453057	−	1.01630i
$675$		0			0
$676$	14.4081	+	12.9487i	0.554159	+	0.498029i
$677$	4.78059	+	4.78059i	0.183733	+	0.183733i	0.792980	−	0.609247i	$-0.208528\pi$
$677$	4.78059	+	4.78059i	0.183733	+	0.183733i	−0.609247	+	0.792980i	$0.708528\pi$
$678$		0			0
$679$	−0.334289			−0.0128288
$680$	−4.96051	+	2.53629i	−0.190227	+	0.0972622i
$681$		0			0
$682$	2.03401	−	5.30619i	0.0778862	−	0.203185i
$683$	1.19706	−	1.19706i	0.0458041	−	0.0458041i	−0.683834	−	0.729638i	$-0.739689\pi$
$683$	1.19706	−	1.19706i	0.0458041	−	0.0458041i	0.729638	+	0.683834i	$0.239689\pi$
$684$		0			0
$685$	−1.10293	−	1.10293i	−0.0421408	−	0.0421408i
$686$	0.575817	+	1.29168i	0.0219848	+	0.0493165i
$687$		0			0
$688$	−1.23042	+	1.52527i	−0.0469092	+	0.0581503i
$689$			19.8117i			0.754764i
$690$		0			0
$691$	−2.98198	+	2.98198i	−0.113440	+	0.113440i	−0.761548	−	0.648108i	$-0.775560\pi$
$691$	−2.98198	+	2.98198i	−0.113440	+	0.113440i	0.648108	+	0.761548i	$0.275560\pi$
$692$	2.35831	+	44.2074i	0.0896495	+	1.68051i
$693$		0			0
$694$	−2.56090	−	0.981663i	−0.0972105	−	0.0372634i
$695$		−	1.36232i		−	0.0516757i
$696$		0			0
$697$			64.0929i			2.42769i
$698$	3.65383	−	9.53187i	0.138299	−	0.360787i
$699$		0			0
$700$	−7.22072	−	6.48934i	−0.272918	−	0.245274i
$701$	25.9008	−	25.9008i	0.978261	−	0.978261i	−0.0215079	−	0.999769i	$-0.506847\pi$
$701$	25.9008	−	25.9008i	0.978261	−	0.978261i	0.999769	+	0.0215079i	$0.00684670\pi$
$702$		0			0
$703$		−	16.9773i		−	0.640310i
$704$	33.8981	−	5.46657i	1.27758	−	0.206029i
$705$		0			0
$706$	−41.3583	+	18.4371i	−1.55654	+	0.693890i
$707$	−7.38370	−	7.38370i	−0.277693	−	0.277693i
$708$		0			0
$709$	−2.86472	+	2.86472i	−0.107587	+	0.107587i	−0.758851	−	0.651264i	$-0.774239\pi$
$709$	−2.86472	+	2.86472i	−0.107587	+	0.107587i	0.651264	+	0.758851i	$0.274239\pi$
$710$	−6.30657	−	2.41748i	−0.236682	−	0.0907264i
$711$		0			0
$712$	−18.9601	−	6.13109i	−0.710560	−	0.229772i
$713$	−5.33591			−0.199832
$714$		0			0
$715$	2.11014	+	2.11014i	0.0789146	+	0.0789146i
$716$	29.1643	−	1.55582i	1.08992	−	0.0581436i
$717$		0			0
$718$	−14.0729	+	6.27355i	−0.525196	+	0.234127i
$719$	−1.64941			−0.0615126			−0.0307563	−	0.999527i	$-0.509792\pi$
$719$	−1.64941			−0.0615126			−0.0307563	+	0.999527i	$0.509792\pi$
$720$		0			0
$721$	14.6297			0.544839
$722$	−55.0541	+	24.5426i	−2.04890	+	0.913380i
$723$		0			0
$724$	1.35885	+	25.4721i	0.0505012	+	0.946664i
$725$	−9.43403	−	9.43403i	−0.350371	−	0.350371i
$726$		0			0
$727$	−30.5976			−1.13480			−0.567400	−	0.823442i	$-0.692051\pi$
$727$	−30.5976			−1.13480			−0.567400	+	0.823442i	$0.692051\pi$
$728$	−2.34407	−	4.58458i	−0.0868772	−	0.169916i
$729$		0			0
$730$	3.72075	+	1.42626i	0.137711	+	0.0527884i
$731$	1.78667	−	1.78667i	0.0660822	−	0.0660822i
$732$		0			0
$733$	36.9502	+	36.9502i	1.36479	+	1.36479i	0.867704	+	0.497082i	$0.165595\pi$
$733$	36.9502	+	36.9502i	1.36479	+	1.36479i	0.497082	+	0.867704i	$0.334405\pi$
$734$	−4.61547	+	2.05753i	−0.170360	+	0.0759447i
$735$		0			0
$736$	−16.1857	−	27.8836i	−0.596613	−	1.02780i
$737$		−	65.1386i		−	2.39941i
$738$		0			0
$739$	−16.0208	+	16.0208i	−0.589335	+	0.589335i	−0.937451	−	0.348116i	$-0.886821\pi$
$739$	−16.0208	+	16.0208i	−0.589335	+	0.589335i	0.348116	+	0.937451i	$0.386821\pi$
$740$	1.10425	−	1.22871i	0.0405931	−	0.0451682i
$741$		0			0
$742$	−5.50872	+	14.3708i	−0.202231	+	0.527569i
$743$		−	34.0911i		−	1.25068i	−0.780352	−	0.625341i	$-0.784960\pi$
$743$		−	34.0911i		−	1.25068i	0.780352	−	0.625341i	$-0.215040\pi$
$744$		0			0
$745$		−	2.41653i		−	0.0885349i
$746$	15.6887	+	6.01392i	0.574405	+	0.220185i
$747$		0			0
$748$	−44.2085	+	2.35837i	−1.61642	+	0.0862305i
$749$	−4.13731	+	4.13731i	−0.151174	+	0.151174i
$750$		0			0
$751$		−	37.9956i		−	1.38648i	−0.720708	−	0.693239i	$-0.756183\pi$
$751$		−	37.9956i		−	1.38648i	0.720708	−	0.693239i	$-0.243817\pi$
$752$	−4.13571	−	38.6524i	−0.150814	−	1.40951i
$753$		0			0
$754$	−2.88118	−	6.46309i	−0.104926	−	0.235372i
$755$	−5.04050	−	5.04050i	−0.183443	−	0.183443i
$756$		0			0
$757$	−36.2650	+	36.2650i	−1.31807	+	1.31807i	−0.402774	+	0.915300i	$0.631954\pi$
$757$	−36.2650	+	36.2650i	−1.31807	+	1.31807i	−0.915300	+	0.402774i	$0.868046\pi$
$758$	−5.37818	+	14.0303i	−0.195344	+	0.509602i
$759$		0			0
$760$	−8.06859	−	2.60912i	−0.292678	−	0.0946428i
$761$	−16.8705			−0.611556			−0.305778	−	0.952103i	$-0.598916\pi$
$761$	−16.8705			−0.611556			−0.305778	+	0.952103i	$0.598916\pi$
$762$		0			0
$763$	−10.4525	−	10.4525i	−0.378406	−	0.378406i
$764$	13.0136	−	14.4803i	0.470816	−	0.523880i
$765$		0			0
$766$	−16.6506	−	37.3509i	−0.601612	−	1.34954i
$767$	−5.23674			−0.189088
$768$		0			0
$769$	−46.7971			−1.68755			−0.843774	−	0.536698i	$-0.819671\pi$
$769$	−46.7971			−1.68755			−0.843774	+	0.536698i	$0.819671\pi$
$770$	0.943899	+	2.11736i	0.0340157	+	0.0763045i
$771$		0			0
$772$	4.60808	−	5.12744i	0.165849	−	0.184541i
$773$	−28.7793	−	28.7793i	−1.03512	−	1.03512i	−0.999360	−	0.0357608i	$-0.988615\pi$
$773$	−28.7793	−	28.7793i	−1.03512	−	1.03512i	−0.0357608	−	0.999360i	$-0.511385\pi$
$774$		0			0
$775$	4.54453			0.163244
$776$	0.899645	+	0.290916i	0.0322954	+	0.0104433i
$777$		0			0
$778$	0.907413	−	2.36720i	0.0325323	−	0.0848683i
$779$	−68.9813	+	68.9813i	−2.47151	+	2.47151i
$780$		0			0
$781$	−37.9502	−	37.9502i	−1.35797	−	1.35797i
$782$	16.9257	+	37.9680i	0.605263	+	1.35773i
$783$		0			0
$784$	−0.425561	−	3.97730i	−0.0151986	−	0.142046i
$785$		−	0.279498i		−	0.00997571i
$786$		0			0
$787$	29.7259	−	29.7259i	1.05961	−	1.05961i	0.0615057	−	0.998107i	$-0.480410\pi$
$787$	29.7259	−	29.7259i	1.05961	−	1.05961i	0.998107	−	0.0615057i	$-0.0195902\pi$
$788$	−1.65351	+	0.0882089i	−0.0589038	+	0.00314231i
$789$		0			0
$790$	6.59293	+	2.52725i	0.234566	+	0.0899155i
$791$		−	8.90575i		−	0.316652i
$792$		0			0
$793$			15.1100i			0.536573i
$794$	−1.49000	+	3.88701i	−0.0528780	+	0.137945i
$795$		0			0
$796$	3.44147	−	3.82935i	0.121980	−	0.135728i
$797$	21.6739	−	21.6739i	0.767728	−	0.767728i	−0.209978	−	0.977706i	$-0.567339\pi$
$797$	21.6739	−	21.6739i	0.767728	−	0.767728i	0.977706	+	0.209978i	$0.0673393\pi$
$798$		0			0
$799$			50.1210i			1.77315i
$800$	13.7852	+	23.7481i	0.487380	+	0.839622i
$801$		0			0
$802$	−9.87956	+	4.40421i	−0.348859	+	0.155518i
$803$	22.3898	+	22.3898i	0.790121	+	0.790121i
$804$		0			0
$805$	1.53920	−	1.53920i	0.0542498	−	0.0542498i
$806$	2.25064	+	0.862733i	0.0792756	+	0.0303885i
$807$		0			0
$808$	13.4455	+	26.2969i	0.473010	+	0.925120i
$809$	27.6371			0.971669			0.485834	−	0.874051i	$-0.338516\pi$
$809$	27.6371			0.971669			0.485834	+	0.874051i	$0.338516\pi$
$810$		0			0
$811$	20.6941	+	20.6941i	0.726668	+	0.726668i	0.969955	−	0.243286i	$-0.0782254\pi$
$811$	20.6941	+	20.6941i	0.726668	+	0.726668i	−0.243286	+	0.969955i	$0.578225\pi$
$812$	−0.292833	−	5.48926i	−0.0102764	−	0.192635i
$813$		0			0
$814$	11.9899	−	5.34496i	0.420245	−	0.187341i
$815$	1.16684			0.0408727
$816$		0			0
$817$	3.84587			0.134550
$818$	−46.5432	+	20.7485i	−1.62735	+	0.725454i
$819$		0			0
$820$	−9.47918	+	0.505682i	−0.331027	+	0.0176592i
$821$	−8.30451	−	8.30451i	−0.289829	−	0.289829i	0.547183	−	0.837013i	$-0.315700\pi$
$821$	−8.30451	−	8.30451i	−0.289829	−	0.289829i	−0.837013	+	0.547183i	$0.815700\pi$
$822$		0			0
$823$	5.77989			0.201474			0.100737	−	0.994913i	$-0.467880\pi$
$823$	5.77989			0.201474			0.100737	+	0.994913i	$0.467880\pi$
$824$	−39.3718	−	12.7316i	−1.37158	−	0.443525i
$825$		0			0
$826$	−3.79858	−	1.45610i	−0.132169	−	0.0506641i
$827$	8.49162	−	8.49162i	0.295282	−	0.295282i	−0.543880	−	0.839163i	$-0.683045\pi$
$827$	8.49162	−	8.49162i	0.295282	−	0.295282i	0.839163	+	0.543880i	$0.183045\pi$
$828$		0			0
$829$	−22.2746	−	22.2746i	−0.773629	−	0.773629i	0.205110	−	0.978739i	$-0.434245\pi$
$829$	−22.2746	−	22.2746i	−0.773629	−	0.773629i	−0.978739	+	0.205110i	$0.934245\pi$
$830$	−1.77072	+	0.789371i	−0.0614628	+	0.0273995i
$831$		0			0
$832$	2.31867	+	14.3780i	0.0803854	+	0.498469i
$833$			5.15741i			0.178694i
$834$		0			0
$835$	0.393296	−	0.393296i	0.0136106	−	0.0136106i
$836$	−50.1185	−	45.0420i	−1.73339	−	1.55781i
$837$		0			0
$838$	3.05695	−	7.97479i	0.105601	−	0.275485i
$839$			31.0889i			1.07331i	0.843803	+	0.536653i	$0.180312\pi$
$839$			31.0889i			1.07331i	−0.843803	+	0.536653i	$0.819688\pi$
$840$		0			0
$841$			21.4456i			0.739502i
$842$	11.7810	+	4.51596i	0.405999	+	0.155630i
$843$		0			0
$844$	−1.71440	−	32.1371i	−0.0590122	−	1.10621i
$845$	2.61580	−	2.61580i	0.0899861	−	0.0899861i
$846$		0			0
$847$			7.42135i			0.255001i
$848$	27.3314	−	33.8810i	0.938564	−	1.16348i
$849$		0			0
$850$	−14.4154	−	32.3369i	−0.494446	−	1.10915i
$851$	−8.71597	−	8.71597i	−0.298780	−	0.298780i
$852$		0			0
$853$	−13.2899	+	13.2899i	−0.455037	+	0.455037i	−0.897022	−	0.441985i	$-0.854274\pi$
$853$	−13.2899	+	13.2899i	−0.455037	+	0.455037i	0.441985	+	0.897022i	$0.354274\pi$
$854$	−4.20141	+	10.9604i	−0.143769	+	0.375056i
$855$		0			0
$856$	14.7349	−	7.53389i	0.503629	−	0.257503i
$857$	−19.3573			−0.661234			−0.330617	−	0.943765i	$-0.607257\pi$
$857$	−19.3573			−0.661234			−0.330617	+	0.943765i	$0.607257\pi$
$858$		0			0
$859$	−1.21680	−	1.21680i	−0.0415165	−	0.0415165i	0.686044	−	0.727560i	$-0.259346\pi$
$859$	−1.21680	−	1.21680i	−0.0415165	−	0.0415165i	−0.727560	+	0.686044i	$0.759346\pi$
$860$	0.278340	+	0.250147i	0.00949132	+	0.00852995i
$861$		0			0
$862$	7.33643	+	16.4572i	0.249880	+	0.560533i
$863$	34.8956			1.18786			0.593929	−	0.804517i	$-0.297576\pi$
$863$	34.8956			1.18786			0.593929	+	0.804517i	$0.297576\pi$
$864$		0			0
$865$	8.45399			0.287444
$866$	−1.66972	−	3.74554i	−0.0567395	−	0.127279i
$867$		0			0
$868$	1.39267	+	1.25160i	0.0472701	+	0.0424822i
$869$	39.6734	+	39.6734i	1.34583	+	1.34583i
$870$		0			0
$871$	27.6288			0.936167
$872$	19.0337	+	37.2263i	0.644561	+	1.26064i
$873$		0			0
$874$	−22.6472	+	59.0805i	−0.766052	+	1.99843i
$875$	−2.66124	+	2.66124i	−0.0899662	+	0.0899662i
$876$		0			0
$877$	−11.2180	−	11.2180i	−0.378804	−	0.378804i	0.491866	−	0.870671i	$-0.336315\pi$
$877$	−11.2180	−	11.2180i	−0.378804	−	0.378804i	−0.870671	+	0.491866i	$0.836315\pi$
$878$	−10.4780	−	23.5045i	−0.353617	−	0.793237i
$879$		0			0
$880$	−0.697594	−	6.51972i	−0.0235159	−	0.219780i
$881$		−	3.79230i		−	0.127766i	−0.997957	−	0.0638829i	$-0.979652\pi$
$881$		−	3.79230i		−	0.127766i	0.997957	−	0.0638829i	$-0.0203484\pi$
$882$		0			0
$883$	7.66911	−	7.66911i	0.258086	−	0.258086i	−0.566189	−	0.824275i	$-0.691583\pi$
$883$	7.66911	−	7.66911i	0.258086	−	0.258086i	0.824275	+	0.566189i	$0.191583\pi$
$884$	−1.00031	−	18.7512i	−0.0336441	−	0.630672i
$885$		0			0
$886$	11.0229	+	4.22536i	0.370320	+	0.141954i
$887$		−	15.3130i		−	0.514161i	−0.966390	−	0.257081i	$-0.917239\pi$
$887$		−	15.3130i		−	0.514161i	0.966390	−	0.257081i	$-0.0827606\pi$
$888$		0			0
$889$		−	13.8060i		−	0.463039i
$890$	−1.36203	+	3.55318i	−0.0456553	+	0.119103i
$891$		0			0
$892$	9.31811	+	8.37428i	0.311993	+	0.280392i
$893$	−53.9438	+	53.9438i	−1.80516	+	1.80516i
$894$		0			0
$895$		−	5.57724i		−	0.186427i
$896$	−2.31598	+	11.0741i	−0.0773715	+	0.369961i
$897$		0			0
$898$	17.4395	−	7.77435i	0.581964	−	0.259433i
$899$	1.81955	+	1.81955i	0.0606853	+	0.0606853i
$900$		0			0
$901$	−39.6874	+	39.6874i	−1.32218	+	1.32218i
$902$	−70.4342	−	26.9993i	−2.34520	−	0.898979i
$903$		0			0
$904$	−7.75026	+	23.9673i	−0.257770	+	0.797141i
$905$	4.87116			0.161923
$906$		0			0
$907$	32.8167	+	32.8167i	1.08966	+	1.08966i	0.995563	+	0.0940982i	$0.0299968\pi$
$907$	32.8167	+	32.8167i	1.08966	+	1.08966i	0.0940982	+	0.995563i	$0.470003\pi$
$908$	−12.3877	+	0.660840i	−0.411100	+	0.0219308i
$909$		0			0
$910$	−0.898089	+	0.400359i	−0.0297714	+	0.0132718i
$911$	−26.8385			−0.889200			−0.444600	−	0.895729i	$-0.646654\pi$
$911$	−26.8385			−0.889200			−0.444600	+	0.895729i	$0.646654\pi$
$912$		0			0
$913$	−15.4055			−0.509849
$914$	−31.6115	+	14.0921i	−1.04561	+	0.466124i
$915$		0			0
$916$	−2.69010	−	50.4269i	−0.0888835	−	1.66615i
$917$	8.53288	+	8.53288i	0.281781	+	0.281781i
$918$		0			0
$919$	19.8195			0.653785			0.326893	−	0.945061i	$-0.393998\pi$
$919$	19.8195			0.653785			0.326893	+	0.945061i	$0.393998\pi$
$920$	−5.48184	+	2.80284i	−0.180731	+	0.0924068i
$921$		0			0
$922$	−10.3231	−	3.95713i	−0.339974	−	0.130321i
$923$	16.0968	−	16.0968i	0.529831	−	0.529831i
$924$		0			0
$925$	7.42329	+	7.42329i	0.244076	+	0.244076i
$926$	10.9599	−	4.88582i	0.360165	−	0.160558i
$927$		0			0
$928$	−3.98897	+	15.0276i	−0.130944	+	0.493306i
$929$		−	38.2590i		−	1.25524i	−0.778521	−	0.627619i	$-0.784030\pi$
$929$		−	38.2590i		−	1.25524i	0.778521	−	0.627619i	$-0.215970\pi$
$930$		0			0
$931$	−5.55077	+	5.55077i	−0.181919	+	0.181919i
$932$	20.0721	−	22.3343i	0.657482	−	0.731584i
$933$		0			0
$934$	1.15684	−	3.01789i	0.0378529	−	0.0987484i
$935$			8.45420i			0.276482i
$936$		0			0
$937$			41.1963i			1.34582i	0.739722	+	0.672912i	$0.234957\pi$
$937$			41.1963i			1.34582i	−0.739722	+	0.672912i	$0.765043\pi$
$938$	20.0411	+	7.68231i	0.654366	+	0.250836i
$939$		0			0
$940$	−7.41278	+	0.395446i	−0.241778	+	0.0128980i
$941$	14.9904	−	14.9904i	0.488673	−	0.488673i	−0.419214	−	0.907887i	$-0.637694\pi$
$941$	14.9904	−	14.9904i	0.488673	−	0.488673i	0.907887	+	0.419214i	$0.137694\pi$
$942$		0			0
$943$			70.8287i			2.30650i
$944$	8.95563	+	7.22440i	0.291481	+	0.235134i
$945$		0			0
$946$	1.21080	+	2.71608i	0.0393664	+	0.0883072i
$947$	2.55196	+	2.55196i	0.0829275	+	0.0829275i	0.747354	−	0.664426i	$-0.231324\pi$
$947$	2.55196	+	2.55196i	0.0829275	+	0.0829275i	−0.664426	+	0.747354i	$0.731324\pi$
$948$		0			0
$949$	−9.49675	+	9.49675i	−0.308278	+	0.308278i
$950$	19.2883	−	50.3182i	0.625796	−	1.63254i
$951$		0			0
$952$	4.48826	−	13.8797i	0.145465	−	0.449844i
$953$	16.1058			0.521719			0.260859	−	0.965377i	$-0.415994\pi$
$953$	16.1058			0.521719			0.260859	+	0.965377i	$0.415994\pi$
$954$		0			0
$955$	−2.62890	−	2.62890i	−0.0850692	−	0.0850692i
$956$	−2.17651	+	2.42182i	−0.0703934	+	0.0783271i
$957$		0			0
$958$	9.75735	+	21.8878i	0.315246	+	0.707162i
$959$	4.08397			0.131878
$960$		0			0
$961$	30.1235			0.971726
$962$	2.26709	+	5.08556i	0.0730939	+	0.163965i
$963$		0			0
$964$	30.3645	−	33.7868i	0.977976	−	1.08820i
$965$	−0.930886	−	0.930886i	−0.0299663	−	0.0299663i
$966$		0			0
$967$	21.1491			0.680110			0.340055	−	0.940406i	$-0.389554\pi$
$967$	21.1491			0.680110			0.340055	+	0.940406i	$0.389554\pi$
$968$	6.45846	−	19.9725i	0.207583	−	0.641940i
$969$		0			0
$970$	0.0646274	−	0.168596i	0.00207506	−	0.00541329i
$971$	43.0192	−	43.0192i	1.38055	−	1.38055i	0.536915	−	0.843636i	$-0.319590\pi$
$971$	43.0192	−	43.0192i	1.38055	−	1.38055i	0.843636	−	0.536915i	$-0.180410\pi$
$972$		0			0
$973$	2.52222	+	2.52222i	0.0808587	+	0.0808587i
$974$	−3.73579	−	8.38016i	−0.119702	−	0.268518i
$975$		0			0
$976$	20.8452	−	25.8405i	0.667239	−	0.827133i
$977$			2.96367i			0.0948161i	0.998876	+	0.0474081i	$0.0150961\pi$
$977$			2.96367i			0.0948161i	−0.998876	+	0.0474081i	$0.984904\pi$
$978$		0			0
$979$	−21.3815	+	21.3815i	−0.683355	+	0.683355i
$980$	−0.762769	+	0.0406911i	−0.0243658	+	0.00129983i
$981$		0			0
$982$	5.67143	+	2.17401i	0.180982	+	0.0693755i
$983$			29.5904i			0.943787i	0.881655	+	0.471894i	$0.156429\pi$
$983$			29.5904i			0.943787i	−0.881655	+	0.471894i	$0.843571\pi$
$984$		0			0
$985$			0.316209i			0.0100752i
$986$	7.17541	−	18.7188i	0.228512	−	0.596127i
$987$		0			0
$988$	19.1048	−	21.2580i	0.607804	−	0.676307i
$989$	1.97443	−	1.97443i	0.0627834	−	0.0627834i
$990$		0			0
$991$		−	25.3741i		−	0.806035i	−0.915192	−	0.403017i	$-0.867961\pi$
$991$		−	25.3741i		−	0.806035i	0.915192	−	0.403017i	$-0.132039\pi$
$992$	−2.65875	−	4.58031i	−0.0844155	−	0.145425i
$993$		0			0
$994$	16.1519	−	7.20035i	0.512307	−	0.228381i
$995$	−0.695217	−	0.695217i	−0.0220399	−	0.0220399i
$996$		0			0
$997$	−3.08066	+	3.08066i	−0.0975654	+	0.0975654i	−0.754205	−	0.656639i	$-0.771977\pi$
$997$	−3.08066	+	3.08066i	−0.0975654	+	0.0975654i	0.656639	+	0.754205i	$0.271977\pi$
$998$	−54.2598	−	20.7992i	−1.71756	−	0.658389i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.v.d.323.6	✓	36
3.2	odd	2	inner	1008.2.v.d.323.13	yes	36
4.3	odd	2		4032.2.v.d.1583.10		36
12.11	even	2		4032.2.v.d.1583.9		36
16.5	even	4		4032.2.v.d.3599.9		36
16.11	odd	4	inner	1008.2.v.d.827.13	yes	36
48.5	odd	4		4032.2.v.d.3599.10		36
48.11	even	4	inner	1008.2.v.d.827.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.v.d.323.6	✓	36	1.1	even	1	trivial
1008.2.v.d.323.13	yes	36	3.2	odd	2	inner
1008.2.v.d.827.6	yes	36	48.11	even	4	inner
1008.2.v.d.827.13	yes	36	16.11	odd	4	inner
4032.2.v.d.1583.9		36	12.11	even	2
4032.2.v.d.1583.10		36	4.3	odd	2
4032.2.v.d.3599.9		36	16.5	even	4
4032.2.v.d.3599.10		36	48.5	odd	4

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.575817 - 1.29168i) q^{2} +(-1.33687 + 1.48754i) q^{4} +(0.270063 + 0.270063i) q^{5} -1.00000 q^{7} +(2.69122 + 0.870254i) q^{8} +O(q^{10})\)	\(q+(-0.575817 - 1.29168i) q^{2} +(-1.33687 + 1.48754i) q^{4} +(0.270063 + 0.270063i) q^{5} -1.00000 q^{7} +(2.69122 + 0.870254i) q^{8} +(0.193328 - 0.504342i) q^{10} +(3.03491 - 3.03491i) q^{11} +(1.28727 + 1.28727i) q^{13} +(0.575817 + 1.29168i) q^{14} +(-0.425561 - 3.97730i) q^{16} +5.15741i q^{17} +(-5.55077 + 5.55077i) q^{19} +(-0.762769 + 0.0406911i) q^{20} +(-5.66768 - 2.17258i) q^{22} +5.69943i q^{23} -4.85413i q^{25} +(0.921508 - 2.40397i) q^{26} +(1.33687 - 1.48754i) q^{28} +(1.94351 - 1.94351i) q^{29} +0.936219i q^{31} +(-4.89235 + 2.83988i) q^{32} +(6.66172 - 2.96973i) q^{34} +(-0.270063 - 0.270063i) q^{35} +(-1.52927 + 1.52927i) q^{37} +(10.3660 + 3.97359i) q^{38} +(0.491775 + 0.961822i) q^{40} +12.4273 q^{41} +(-0.346427 - 0.346427i) q^{43} +(0.457277 + 8.57183i) q^{44} +(7.36183 - 3.28183i) q^{46} +9.71825 q^{47} +1.00000 q^{49} +(-6.26998 + 2.79509i) q^{50} +(-3.63578 + 0.193956i) q^{52} +(7.69522 + 7.69522i) q^{53} +1.63923 q^{55} +(-2.69122 - 0.870254i) q^{56} +(-3.62949 - 1.39128i) q^{58} +(-2.03405 + 2.03405i) q^{59} +(5.86902 + 5.86902i) q^{61} +(1.20929 - 0.539091i) q^{62} +(6.48532 + 4.68409i) q^{64} +0.695288i q^{65} +(10.7316 - 10.7316i) q^{67} +(-7.67187 - 6.89479i) q^{68} +(-0.193328 + 0.504342i) q^{70} -12.5046i q^{71} +7.37743i q^{73} +(2.85591 + 1.09475i) q^{74} +(-0.836349 - 15.6777i) q^{76} +(-3.03491 + 3.03491i) q^{77} +13.0724i q^{79} +(0.959193 - 1.18905i) q^{80} +(-7.15587 - 16.0521i) q^{82} +(-2.53806 - 2.53806i) q^{83} +(-1.39283 + 1.39283i) q^{85} +(-0.247994 + 0.646951i) q^{86} +(10.8087 - 5.52646i) q^{88} -7.04518 q^{89} +(-1.28727 - 1.28727i) q^{91} +(-8.47814 - 7.61939i) q^{92} +(-5.59594 - 12.5529i) q^{94} -2.99812 q^{95} +0.334289 q^{97} +(-0.575817 - 1.29168i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 8 q^{4} - 36 q^{7}+O(q^{10}) \) 36 * q - 8 * q^4 - 36 * q^7	\( 36 q - 8 q^{4} - 36 q^{7} - 8 q^{10} - 16 q^{13} - 16 q^{19} + 32 q^{22} + 8 q^{28} + 40 q^{34} + 20 q^{37} - 24 q^{40} + 36 q^{43} - 64 q^{46} + 36 q^{49} - 48 q^{52} + 32 q^{55} + 112 q^{61} - 32 q^{64} - 36 q^{67} + 8 q^{70} + 8 q^{76} - 48 q^{82} - 96 q^{85} + 8 q^{88} + 16 q^{91} - 16 q^{94} + 56 q^{97}+O(q^{100}) \) 36 * q - 8 * q^4 - 36 * q^7 - 8 * q^10 - 16 * q^13 - 16 * q^19 + 32 * q^22 + 8 * q^28 + 40 * q^34 + 20 * q^37 - 24 * q^40 + 36 * q^43 - 64 * q^46 + 36 * q^49 - 48 * q^52 + 32 * q^55 + 112 * q^61 - 32 * q^64 - 36 * q^67 + 8 * q^70 + 8 * q^76 - 48 * q^82 - 96 * q^85 + 8 * q^88 + 16 * q^91 - 16 * q^94 + 56 * q^97

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