LMFDB - Embedded newform 1674.2.q.a.557.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1674,2,Mod(557,1674)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1674.557"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1674, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1674 = 2 \cdot 3^{3} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1674.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$13.3669572984$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 558)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			557.20
Character	$\chi$	$=$	1674.557
Dual form			1674.2.q.a.1115.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.53994 - 1.46644i) q^{5} +(2.03804 + 3.52999i) q^{7} -1.00000i q^{8} -2.93287 q^{10} +(1.42757 + 2.47262i) q^{11} +(0.887117 + 0.512177i) q^{13} +(3.52999 + 2.03804i) q^{14} +(-0.500000 - 0.866025i) q^{16} -5.67253 q^{17} -7.01983 q^{19} +(-2.53994 + 1.46644i) q^{20} +(2.47262 + 1.42757i) q^{22} +(-4.35174 + 7.53743i) q^{23} +(1.80087 + 3.11920i) q^{25} +1.02435 q^{26} +4.07608 q^{28} +(3.19560 + 5.53494i) q^{29} +(1.41782 - 5.38422i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.91256 + 2.83627i) q^{34} -11.9546i q^{35} +5.63967i q^{37} +(-6.07935 + 3.50991i) q^{38} +(-1.46644 + 2.53994i) q^{40} +(-3.22261 - 1.86058i) q^{41} +(3.66962 - 2.11866i) q^{43} +2.85513 q^{44} +8.70347i q^{46} +(-2.99058 + 1.72661i) q^{47} +(-4.80721 + 8.32632i) q^{49} +(3.11920 + 1.80087i) q^{50} +(0.887117 - 0.512177i) q^{52} +10.5738 q^{53} -8.37374i q^{55} +(3.52999 - 2.03804i) q^{56} +(5.53494 + 3.19560i) q^{58} +(4.81405 + 2.77939i) q^{59} +(-10.8811 + 6.28219i) q^{61} +(-1.46424 - 5.37178i) q^{62} -1.00000 q^{64} +(-1.50215 - 2.60180i) q^{65} +(-0.327613 + 0.567442i) q^{67} +(-2.83627 + 4.91256i) q^{68} +(-5.97731 - 10.3530i) q^{70} +1.41846i q^{71} +12.9850i q^{73} +(2.81984 + 4.88410i) q^{74} +(-3.50991 + 6.07935i) q^{76} +(-5.81887 + 10.0786i) q^{77} +(3.28967 - 1.89929i) q^{79} +2.93287i q^{80} -3.72115 q^{82} +(2.20366 + 3.81685i) q^{83} +(14.4079 + 8.31841i) q^{85} +(2.11866 - 3.66962i) q^{86} +(2.47262 - 1.42757i) q^{88} +2.33927 q^{89} +4.17535i q^{91} +(4.35174 + 7.53743i) q^{92} +(-1.72661 + 2.99058i) q^{94} +(17.8300 + 10.2941i) q^{95} +(2.69419 + 4.66648i) q^{97} +9.61441i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} - 12 q^{5} - 4 q^{7} - 32 q^{16} - 8 q^{19} - 12 q^{20} + 44 q^{25} - 8 q^{28} + 8 q^{31} - 36 q^{38} - 24 q^{41} + 48 q^{47} - 36 q^{49} + 12 q^{59} - 64 q^{64} + 16 q^{67} - 12 q^{70}+ \cdots - 16 q^{97}+O(q^{100}) $ 64 * q + 32 * q^4 - 12 * q^5 - 4 * q^7 - 32 * q^16 - 8 * q^19 - 12 * q^20 + 44 * q^25 - 8 * q^28 + 8 * q^31 - 36 * q^38 - 24 * q^41 + 48 * q^47 - 36 * q^49 + 12 * q^59 - 64 * q^64 + 16 * q^67 - 12 * q^70 - 4 * q^76 + 180 * q^95 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1674\mathbb{Z}\right)^\times$.

$n$	$1055$	$1243$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.53994	−	1.46644i	−1.13590	−	0.655810i	−0.190486	−	0.981690i	$-0.561006\pi$
$5$	−2.53994	−	1.46644i	−1.13590	−	0.655810i	−0.945411	+	0.325879i	$0.894340\pi$
$6$		0			0
$7$	2.03804	+	3.52999i	0.770306	+	1.33421i	0.937395	+	0.348268i	$0.113230\pi$
$7$	2.03804	+	3.52999i	0.770306	+	1.33421i	−0.167089	+	0.985942i	$0.553437\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−2.93287			−0.927456
$11$	1.42757	+	2.47262i	0.430428	+	0.745522i	0.996910	−	0.0785514i	$-0.0250295\pi$
$11$	1.42757	+	2.47262i	0.430428	+	0.745522i	−0.566483	+	0.824074i	$0.691696\pi$
$12$		0			0
$13$	0.887117	+	0.512177i	0.246042	+	0.142052i	0.617951	−	0.786217i	$-0.287963\pi$
$13$	0.887117	+	0.512177i	0.246042	+	0.142052i	−0.371909	+	0.928269i	$0.621297\pi$
$14$	3.52999	+	2.03804i	0.943429	+	0.544689i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.67253			−1.37579			−0.687896	−	0.725810i	$-0.741465\pi$
$17$	−5.67253			−1.37579			−0.687896	+	0.725810i	$0.741465\pi$
$18$		0			0
$19$	−7.01983			−1.61046			−0.805229	−	0.592964i	$-0.797958\pi$
$19$	−7.01983			−1.61046			−0.805229	+	0.592964i	$0.797958\pi$
$20$	−2.53994	+	1.46644i	−0.567949	+	0.327905i
$21$		0			0
$22$	2.47262	+	1.42757i	0.527164	+	0.304358i
$23$	−4.35174	+	7.53743i	−0.907400	+	1.57166i	−0.0897370	+	0.995965i	$0.528603\pi$
$23$	−4.35174	+	7.53743i	−0.907400	+	1.57166i	−0.817663	+	0.575697i	$0.804731\pi$
$24$		0			0
$25$	1.80087	+	3.11920i	0.360175	+	0.623841i
$26$	1.02435			0.200892
$27$		0			0
$28$	4.07608			0.770306
$29$	3.19560	+	5.53494i	0.593408	+	1.02781i	0.993769	+	0.111456i	$0.0355513\pi$
$29$	3.19560	+	5.53494i	0.593408	+	1.02781i	−0.400361	+	0.916357i	$0.631115\pi$
$30$		0			0
$31$	1.41782	−	5.38422i	0.254649	−	0.967034i
$31$	1.41782	−	5.38422i	0.254649	−	0.967034i
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−4.91256	+	2.83627i	−0.842497	+	0.486416i
$35$		−	11.9546i		−	2.02070i
$36$		0			0
$37$			5.63967i			0.927157i	0.886056	+	0.463578i	$0.153435\pi$
$37$			5.63967i			0.927157i	−0.886056	+	0.463578i	$0.846565\pi$
$38$	−6.07935	+	3.50991i	−0.986200	+	0.569383i
$39$		0			0
$40$	−1.46644	+	2.53994i	−0.231864	+	0.401600i
$41$	−3.22261	−	1.86058i	−0.503288	−	0.290573i	0.226783	−	0.973945i	$-0.427179\pi$
$41$	−3.22261	−	1.86058i	−0.503288	−	0.290573i	−0.730070	+	0.683372i	$0.760513\pi$
$42$		0			0
$43$	3.66962	−	2.11866i	0.559612	−	0.323092i	−0.193378	−	0.981124i	$-0.561944\pi$
$43$	3.66962	−	2.11866i	0.559612	−	0.323092i	0.752990	+	0.658032i	$0.228611\pi$
$44$	2.85513			0.430428
$45$		0			0
$46$			8.70347i			1.28326i
$47$	−2.99058	+	1.72661i	−0.436221	+	0.251852i	−0.701993	−	0.712184i	$-0.747706\pi$
$47$	−2.99058	+	1.72661i	−0.436221	+	0.251852i	0.265773	+	0.964036i	$0.414373\pi$
$48$		0			0
$49$	−4.80721	+	8.32632i	−0.686744	+	1.18947i
$50$	3.11920	+	1.80087i	0.441122	+	0.254682i
$51$		0			0
$52$	0.887117	−	0.512177i	0.123021	−	0.0710262i
$53$	10.5738			1.45242			0.726211	−	0.687472i	$-0.241279\pi$
$53$	10.5738			1.45242			0.726211	+	0.687472i	$0.241279\pi$
$54$		0			0
$55$		−	8.37374i		−	1.12912i
$56$	3.52999	−	2.03804i	0.471714	−	0.272344i
$57$		0			0
$58$	5.53494	+	3.19560i	0.726773	+	0.419603i
$59$	4.81405	+	2.77939i	0.626736	+	0.361846i	0.779487	−	0.626419i	$-0.215480\pi$
$59$	4.81405	+	2.77939i	0.626736	+	0.361846i	−0.152751	+	0.988265i	$0.548813\pi$
$60$		0			0
$61$	−10.8811	+	6.28219i	−1.39318	+	0.804352i	−0.993666	−	0.112376i	$-0.964154\pi$
$61$	−10.8811	+	6.28219i	−1.39318	+	0.804352i	−0.399512	+	0.916728i	$0.630821\pi$
$62$	−1.46424	−	5.37178i	−0.185958	−	0.682217i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.50215	−	2.60180i	−0.186319	−	0.322714i
$66$		0			0
$67$	−0.327613	+	0.567442i	−0.0400242	+	0.0693240i	−0.885344	−	0.464937i	$-0.846077\pi$
$67$	−0.327613	+	0.567442i	−0.0400242	+	0.0693240i	0.845319	+	0.534261i	$0.179410\pi$
$68$	−2.83627	+	4.91256i	−0.343948	+	0.595735i
$69$		0			0
$70$	−5.97731	−	10.3530i	−0.714425	−	1.23742i
$71$			1.41846i			0.168340i	0.996451	+	0.0841701i	$0.0268239\pi$
$71$			1.41846i			0.168340i	−0.996451	+	0.0841701i	$0.973176\pi$
$72$		0			0
$73$			12.9850i			1.51978i	0.650052	+	0.759890i	$0.274747\pi$
$73$			12.9850i			1.51978i	−0.650052	+	0.759890i	$0.725253\pi$
$74$	2.81984	+	4.88410i	0.327799	+	0.567765i
$75$		0			0
$76$	−3.50991	+	6.07935i	−0.402615	+	0.697349i
$77$	−5.81887	+	10.0786i	−0.663122	+	1.14856i
$78$		0			0
$79$	3.28967	−	1.89929i	0.370117	−	0.213687i	−0.303393	−	0.952866i	$-0.598119\pi$
$79$	3.28967	−	1.89929i	0.370117	−	0.213687i	0.673510	+	0.739178i	$0.264786\pi$
$80$			2.93287i			0.327905i
$81$		0			0
$82$	−3.72115			−0.410933
$83$	2.20366	+	3.81685i	0.241883	+	0.418954i	0.961251	−	0.275676i	$-0.0889015\pi$
$83$	2.20366	+	3.81685i	0.241883	+	0.418954i	−0.719367	+	0.694630i	$0.755568\pi$
$84$		0			0
$85$	14.4079	+	8.31841i	1.56276	+	0.902258i
$86$	2.11866	−	3.66962i	0.228460	−	0.395705i
$87$		0			0
$88$	2.47262	−	1.42757i	0.263582	−	0.152179i
$89$	2.33927			0.247962			0.123981	−	0.992285i	$-0.460434\pi$
$89$	2.33927			0.247962			0.123981	+	0.992285i	$0.460434\pi$
$90$		0			0
$91$			4.17535i			0.437696i
$92$	4.35174	+	7.53743i	0.453700	+	0.785831i
$93$		0			0
$94$	−1.72661	+	2.99058i	−0.178086	+	0.308455i
$95$	17.8300	+	10.2941i	1.82932	+	1.05616i
$96$		0			0
$97$	2.69419	+	4.66648i	0.273554	+	0.473809i	0.969769	−	0.244024i	$-0.0784675\pi$
$97$	2.69419	+	4.66648i	0.273554	+	0.473809i	−0.696215	+	0.717833i	$0.745134\pi$
$98$			9.61441i			0.971202i
$99$		0			0
$100$	3.60175			0.360175
$101$	−16.1150	+	9.30400i	−1.60350	+	0.925782i	−0.612722	+	0.790298i	$0.709926\pi$
$101$	−16.1150	+	9.30400i	−1.60350	+	0.925782i	−0.990780	+	0.135484i	$0.956741\pi$
$102$		0			0
$103$	0.824711	−	1.42844i	0.0812612	−	0.140748i	−0.822531	−	0.568721i	$-0.807439\pi$
$103$	0.824711	−	1.42844i	0.0812612	−	0.140748i	0.903792	+	0.427972i	$0.140772\pi$
$104$	0.512177	−	0.887117i	0.0502231	−	0.0869890i
$105$		0			0
$106$	9.15718	−	5.28690i	0.889423	−	0.513509i
$107$		−	9.92203i		−	0.959199i	−0.877488	−	0.479599i	$-0.840782\pi$
$107$		−	9.92203i		−	0.959199i	0.877488	−	0.479599i	$-0.159218\pi$
$108$		0			0
$109$	18.8530			1.80579			0.902897	−	0.429857i	$-0.141436\pi$
$109$	18.8530			1.80579			0.902897	+	0.429857i	$0.141436\pi$
$110$	−4.18687	−	7.25188i	−0.399203	−	0.691439i
$111$		0			0
$112$	2.03804	−	3.52999i	0.192577	−	0.333552i
$113$	−8.43172	−	4.86805i	−0.793189	−	0.457948i	0.0478950	−	0.998852i	$-0.484749\pi$
$113$	−8.43172	−	4.86805i	−0.793189	−	0.457948i	−0.841084	+	0.540904i	$0.818082\pi$
$114$		0			0
$115$	22.1063	−	12.7631i	2.06143	−	1.19016i
$116$	6.39120			0.593408
$117$		0			0
$118$	5.55879			0.511728
$119$	−11.5608	−	20.0240i	−1.05978	−	1.83559i
$120$		0			0
$121$	1.42411	−	2.46663i	0.129464	−	0.224239i
$122$	−6.28219	+	10.8811i	−0.568763	+	0.985126i
$123$		0			0
$124$	−3.95396	−	3.91998i	−0.355076	−	0.352025i
$125$			4.10090i			0.366795i
$126$		0			0
$127$		−	9.65404i		−	0.856657i	−0.903623	−	0.428329i	$-0.859103\pi$
$127$		−	9.65404i		−	0.856657i	0.903623	−	0.428329i	$-0.140897\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−2.60180	−	1.50215i	−0.228193	−	0.131747i
$131$	0.961641	+	0.555203i	0.0840189	+	0.0485084i	0.541421	−	0.840752i	$-0.317887\pi$
$131$	0.961641	+	0.555203i	0.0840189	+	0.0485084i	−0.457402	+	0.889260i	$0.651220\pi$
$132$		0			0
$133$	−14.3067	−	24.7799i	−1.24055	−	2.14869i
$134$			0.655225i			0.0566028i
$135$		0			0
$136$			5.67253i			0.486416i
$137$	1.18927	+	2.05988i	0.101606	+	0.175987i	0.912347	−	0.409419i	$-0.134268\pi$
$137$	1.18927	+	2.05988i	0.101606	+	0.175987i	−0.810740	+	0.585406i	$0.800935\pi$
$138$		0			0
$139$	−15.1170	−	8.72781i	−1.28221	−	0.740283i	−0.304956	−	0.952366i	$-0.598642\pi$
$139$	−15.1170	−	8.72781i	−1.28221	−	0.740283i	−0.977252	+	0.212084i	$0.931975\pi$
$140$	−10.3530	−	5.97731i	−0.874989	−	0.505175i
$141$		0			0
$142$	0.709229	+	1.22842i	0.0595172	+	0.103087i
$143$			2.92467i			0.244573i
$144$		0			0
$145$		−	18.7446i		−	1.55665i
$146$	6.49250	+	11.2453i	0.537323	+	0.930671i
$147$		0			0
$148$	4.88410	+	2.81984i	0.401471	+	0.231789i
$149$	−1.94748	−	1.12438i	−0.159544	−	0.0921129i	0.418102	−	0.908400i	$-0.362695\pi$
$149$	−1.94748	−	1.12438i	−0.159544	−	0.0921129i	−0.577646	+	0.816287i	$0.696029\pi$
$150$		0			0
$151$	0.945284	−	0.545760i	0.0769261	−	0.0444133i	−0.461044	−	0.887378i	$-0.652525\pi$
$151$	0.945284	−	0.545760i	0.0769261	−	0.0444133i	0.537970	+	0.842964i	$0.319191\pi$
$152$			7.01983i			0.569383i
$153$		0			0
$154$			11.6377i			0.937796i
$155$	−11.4968	+	11.5965i	−0.923445	+	0.931449i
$156$		0			0
$157$	−3.28221	+	5.68495i	−0.261949	+	0.453708i	−0.966760	−	0.255687i	$-0.917698\pi$
$157$	−3.28221	+	5.68495i	−0.261949	+	0.453708i	0.704811	+	0.709395i	$0.251032\pi$
$158$	1.89929	−	3.28967i	0.151100	−	0.261712i
$159$		0			0
$160$	1.46644	+	2.53994i	0.115932	+	0.200800i
$161$	−35.4760			−2.79590
$162$		0			0
$163$	9.26680			0.725832			0.362916	−	0.931822i	$-0.381781\pi$
$163$	9.26680			0.725832			0.362916	+	0.931822i	$0.381781\pi$
$164$	−3.22261	+	1.86058i	−0.251644	+	0.145287i
$165$		0			0
$166$	3.81685	+	2.20366i	0.296245	+	0.171037i
$167$	0.313267	−	0.542595i	0.0242414	−	0.0419873i	−0.853650	−	0.520847i	$-0.825616\pi$
$167$	0.313267	−	0.542595i	0.0242414	−	0.0419873i	0.877892	+	0.478859i	$0.158950\pi$
$168$		0			0
$169$	−5.97535	−	10.3496i	−0.459642	−	0.796124i
$170$	16.6368			1.27599
$171$		0			0
$172$		−	4.23731i		−	0.323092i
$173$	20.4999	−	11.8356i	1.55857	−	0.899844i	0.561181	−	0.827693i	$-0.310347\pi$
$173$	20.4999	−	11.8356i	1.55857	−	0.899844i	0.997394	−	0.0721506i	$-0.0229862\pi$
$174$		0			0
$175$	−7.34050	+	12.7141i	−0.554890	+	0.961097i
$176$	1.42757	−	2.47262i	0.107607	−	0.186381i
$177$		0			0
$178$	2.02587	−	1.16963i	0.151845	−	0.0876678i
$179$	−1.55169			−0.115979			−0.0579894	−	0.998317i	$-0.518469\pi$
$179$	−1.55169			−0.115979			−0.0579894	+	0.998317i	$0.518469\pi$
$180$		0			0
$181$			12.3884i			0.920822i	0.887706	+	0.460411i	$0.152298\pi$
$181$			12.3884i			0.920822i	−0.887706	+	0.460411i	$0.847702\pi$
$182$	2.08767	+	3.61596i	0.154749	+	0.268033i
$183$		0			0
$184$	7.53743	+	4.35174i	0.555667	+	0.320814i
$185$	8.27022	−	14.3244i	0.608039	−	1.05315i
$186$		0			0
$187$	−8.09792	−	14.0260i	−0.592178	−	1.02568i
$188$			3.45322i			0.251852i
$189$		0			0
$190$	20.5883			1.49363
$191$	−2.87262	+	1.65851i	−0.207855	+	0.120005i	−0.600314	−	0.799764i	$-0.704958\pi$
$191$	−2.87262	+	1.65851i	−0.207855	+	0.120005i	0.392459	+	0.919770i	$0.371625\pi$
$192$		0			0
$193$	0.0584452	−	0.101230i	0.00420698	−	0.00728670i	−0.863914	−	0.503639i	$-0.831994\pi$
$193$	0.0584452	−	0.101230i	0.00420698	−	0.00728670i	0.868121	+	0.496352i	$0.165328\pi$
$194$	4.66648	+	2.69419i	0.335034	+	0.193432i
$195$		0			0
$196$	4.80721	+	8.32632i	0.343372	+	0.594737i
$197$	−15.1370			−1.07847			−0.539233	−	0.842157i	$-0.681286\pi$
$197$	−15.1370			−1.07847			−0.539233	+	0.842157i	$0.681286\pi$
$198$		0			0
$199$		−	11.8299i		−	0.838598i	−0.907848	−	0.419299i	$-0.862276\pi$
$199$		−	11.8299i		−	0.838598i	0.907848	−	0.419299i	$-0.137724\pi$
$200$	3.11920	−	1.80087i	0.220561	−	0.127341i
$201$		0			0
$202$	−9.30400	+	16.1150i	−0.654627	+	1.13385i
$203$	−13.0255	+	22.5609i	−0.914212	+	1.58346i
$204$		0			0
$205$	5.45684	+	9.45152i	0.381122	+	0.660123i
$206$		−	1.64942i		−	0.114921i
$207$		0			0
$208$		−	1.02435i		−	0.0710262i
$209$	−10.0213	−	17.3573i	−0.693186	−	1.20063i
$210$		0			0
$211$	−2.95666	+	5.12109i	−0.203545	+	0.352550i	−0.949668	−	0.313258i	$-0.898580\pi$
$211$	−2.95666	+	5.12109i	−0.203545	+	0.352550i	0.746123	+	0.665808i	$0.231913\pi$
$212$	5.28690	−	9.15718i	0.363106	−	0.628917i
$213$		0			0
$214$	−4.96101	−	8.59273i	−0.339128	−	0.587387i
$215$	−12.4275			−0.847548
$216$		0			0
$217$	21.8958	−	5.96834i	1.48638	−	0.405157i
$218$	16.3272	−	9.42652i	1.10582	−	0.638445i
$219$		0			0
$220$	−7.25188	−	4.18687i	−0.488921	−	0.282279i
$221$	−5.03220	−	2.90534i	−0.338502	−	0.195434i
$222$		0			0
$223$	−20.5760	+	11.8796i	−1.37787	+	0.795514i	−0.991903	−	0.126999i	$-0.959465\pi$
$223$	−20.5760	+	11.8796i	−1.37787	+	0.795514i	−0.385967	+	0.922513i	$0.626132\pi$
$224$		−	4.07608i		−	0.272344i
$225$		0			0
$226$	−9.73611			−0.647636
$227$	6.15389	−	3.55295i	0.408448	−	0.235818i	−0.281675	−	0.959510i	$-0.590890\pi$
$227$	6.15389	−	3.55295i	0.408448	−	0.235818i	0.690123	+	0.723692i	$0.257557\pi$
$228$		0			0
$229$	−11.7189	−	6.76589i	−0.774405	−	0.447103i	0.0600390	−	0.998196i	$-0.480877\pi$
$229$	−11.7189	−	6.76589i	−0.774405	−	0.447103i	−0.834444	+	0.551093i	$0.814211\pi$
$230$	12.7631	−	22.1063i	0.841574	−	1.45765i
$231$		0			0
$232$	5.53494	−	3.19560i	0.363387	−	0.209801i
$233$		−	4.43140i		−	0.290311i	−0.989409	−	0.145155i	$-0.953632\pi$
$233$		−	4.43140i		−	0.290311i	0.989409	−	0.145155i	$-0.0463682\pi$
$234$		0			0
$235$	10.1279			0.660669
$236$	4.81405	−	2.77939i	0.313368	−	0.180923i
$237$		0			0
$238$	−20.0240	−	11.5608i	−1.29796	−	0.749378i
$239$	15.1818	−	26.2956i	0.982028	−	1.70092i	0.327562	−	0.944830i	$-0.393773\pi$
$239$	15.1818	−	26.2956i	0.982028	−	1.70092i	0.654465	−	0.756092i	$-0.272894\pi$
$240$		0			0
$241$	6.71197	−	3.87516i	0.432356	−	0.249621i	−0.267994	−	0.963421i	$-0.586361\pi$
$241$	6.71197	−	3.87516i	0.432356	−	0.249621i	0.700350	+	0.713800i	$0.253027\pi$
$242$		−	2.84821i		−	0.183090i
$243$		0			0
$244$			12.5644i			0.804352i
$245$	24.4201	−	14.0989i	1.56014	−	0.900747i
$246$		0			0
$247$	−6.22741	−	3.59540i	−0.396240	−	0.228770i
$248$	−5.38422	−	1.41782i	−0.341898	−	0.0900319i
$249$		0			0
$250$	2.05045	+	3.55148i	0.129682	+	0.224615i
$251$	−8.86796			−0.559740			−0.279870	−	0.960038i	$-0.590291\pi$
$251$	−8.86796			−0.559740			−0.279870	+	0.960038i	$0.590291\pi$
$252$		0			0
$253$	−24.8496			−1.56228
$254$	−4.82702	−	8.36064i	−0.302874	−	0.524593i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	23.6507	+	13.6547i	1.47529	+	0.851759i	0.999612	−	0.0278599i	$-0.00886922\pi$
$257$	23.6507	+	13.6547i	1.47529	+	0.851759i	0.475679	+	0.879619i	$0.342203\pi$
$258$		0			0
$259$	−19.9080	+	11.4939i	−1.23702	+	0.714195i
$260$	−3.00430			−0.186319
$261$		0			0
$262$	1.11041			0.0686012
$263$	−6.96217	−	12.0588i	−0.429306	−	0.743580i	0.567506	−	0.823369i	$-0.307908\pi$
$263$	−6.96217	−	12.0588i	−0.429306	−	0.743580i	−0.996812	+	0.0797897i	$0.974575\pi$
$264$		0			0
$265$	−26.8568	−	15.5058i	−1.64980	−	0.952514i
$266$	−24.7799	−	14.3067i	−1.51935	−	0.877199i
$267$		0			0
$268$	0.327613	+	0.567442i	0.0200121	+	0.0346620i
$269$	11.4048			0.695365			0.347683	−	0.937612i	$-0.386969\pi$
$269$	11.4048			0.695365			0.347683	+	0.937612i	$0.386969\pi$
$270$		0			0
$271$		−	2.56098i		−	0.155568i	−0.996970	−	0.0777842i	$-0.975215\pi$
$271$		−	2.56098i		−	0.155568i	0.996970	−	0.0777842i	$-0.0247845\pi$
$272$	2.83627	+	4.91256i	0.171974	+	0.297868i
$273$		0			0
$274$	2.05988	+	1.18927i	0.124442	+	0.0718466i
$275$	−5.14173	+	8.90575i	−0.310058	+	0.537037i
$276$		0			0
$277$	26.5465	−	15.3266i	1.59502	−	0.920888i	0.602599	−	0.798044i	$-0.294132\pi$
$277$	26.5465	−	15.3266i	1.59502	−	0.920888i	0.992426	−	0.122844i	$-0.0392014\pi$
$278$	−17.4556			−1.04692
$279$		0			0
$280$	−11.9546			−0.714425
$281$	−11.1689	+	6.44836i	−0.666279	+	0.384677i	−0.794665	−	0.607048i	$-0.792354\pi$
$281$	−11.1689	+	6.44836i	−0.666279	+	0.384677i	0.128386	+	0.991724i	$0.459020\pi$
$282$		0			0
$283$	1.29250	−	2.23868i	0.0768312	−	0.133076i	−0.825050	−	0.565060i	$-0.808853\pi$
$283$	1.29250	−	2.23868i	0.0768312	−	0.133076i	0.901881	+	0.431984i	$0.142186\pi$
$284$	1.22842	+	0.709229i	0.0728934	+	0.0420850i
$285$		0			0
$286$	1.46233	+	2.53284i	0.0864697	+	0.149770i
$287$		−	15.1677i		−	0.895322i
$288$		0			0
$289$	15.1776			0.892801
$290$	−9.37229	−	16.2333i	−0.550360	−	0.953251i
$291$		0			0
$292$	11.2453	+	6.49250i	0.658084	+	0.379945i
$293$	−1.12509	−	0.649569i	−0.0657282	−	0.0379482i	0.466776	−	0.884376i	$-0.345416\pi$
$293$	−1.12509	−	0.649569i	−0.0657282	−	0.0379482i	−0.532504	+	0.846428i	$0.678749\pi$
$294$		0			0
$295$	−8.15161	−	14.1190i	−0.474605	−	0.822040i
$296$	5.63967			0.327799
$297$		0			0
$298$	−2.24876			−0.130267
$299$	−7.72100	+	4.45772i	−0.446517	+	0.257797i
$300$		0			0
$301$	14.9577	+	8.63580i	0.862145	+	0.497759i
$302$	0.545760	−	0.945284i	0.0314050	−	0.0543950i
$303$		0			0
$304$	3.50991	+	6.07935i	0.201307	+	0.348674i
$305$	36.8497			2.11001
$306$		0			0
$307$	−2.15765			−0.123144			−0.0615718	−	0.998103i	$-0.519611\pi$
$307$	−2.15765			−0.123144			−0.0615718	+	0.998103i	$0.519611\pi$
$308$	5.81887	+	10.0786i	0.331561	+	0.574281i
$309$		0			0
$310$	−4.15830	+	15.7912i	−0.236175	+	0.896881i
$311$	11.9653	+	6.90814i	0.678487	+	0.391725i	0.799285	−	0.600952i	$-0.205212\pi$
$311$	11.9653	+	6.90814i	0.678487	+	0.391725i	−0.120798	+	0.992677i	$0.538545\pi$
$312$		0			0
$313$	15.1750	−	8.76129i	0.857741	−	0.495217i	−0.00551388	−	0.999985i	$-0.501755\pi$
$313$	15.1750	−	8.76129i	0.857741	−	0.495217i	0.863255	+	0.504768i	$0.168422\pi$
$314$			6.56441i			0.370451i
$315$		0			0
$316$		−	3.79859i		−	0.213687i
$317$	−13.8613	+	8.00281i	−0.778527	+	0.449483i	−0.835908	−	0.548870i	$-0.815058\pi$
$317$	−13.8613	+	8.00281i	−0.778527	+	0.449483i	0.0573812	+	0.998352i	$0.481725\pi$
$318$		0			0
$319$	−9.12386	+	15.8030i	−0.510838	+	0.884798i
$320$	2.53994	+	1.46644i	0.141987	+	0.0819763i
$321$		0			0
$322$	−30.7232	+	17.7380i	−1.71213	+	0.988501i
$323$	39.8202			2.21565
$324$		0			0
$325$			3.68947i			0.204655i
$326$	8.02529	−	4.63340i	0.444479	−	0.256620i
$327$		0			0
$328$	−1.86058	+	3.22261i	−0.102733	+	0.177939i
$329$	−12.1898	−	7.03780i	−0.672047	−	0.388006i
$330$		0			0
$331$	−30.6325	+	17.6857i	−1.68371	+	0.972093i	−0.724559	+	0.689213i	$0.757957\pi$
$331$	−30.6325	+	17.6857i	−1.68371	+	0.972093i	−0.959155	+	0.282880i	$0.908710\pi$
$332$	4.40732			0.241883
$333$		0			0
$334$		−	0.626535i		−	0.0342824i
$335$	1.66423	−	0.960846i	0.0909268	−	0.0524966i
$336$		0			0
$337$	13.3807	+	7.72535i	0.728893	+	0.420827i	0.818017	−	0.575194i	$-0.195073\pi$
$337$	13.3807	+	7.72535i	0.728893	+	0.420827i	−0.0891240	+	0.996021i	$0.528407\pi$
$338$	−10.3496	−	5.97535i	−0.562944	−	0.325016i
$339$		0			0
$340$	14.4079	−	8.31841i	0.781379	−	0.451129i
$341$	15.3371	−	4.18059i	0.830553	−	0.226392i
$342$		0			0
$343$	−10.6565			−0.575399
$344$	−2.11866	−	3.66962i	−0.114230	−	0.197853i
$345$		0			0
$346$	11.8356	−	20.4999i	0.636286	−	1.10208i
$347$	−14.6770	+	25.4213i	−0.787902	+	1.36469i	0.139348	+	0.990244i	$0.455499\pi$
$347$	−14.6770	+	25.4213i	−0.787902	+	1.36469i	−0.927250	+	0.374443i	$0.877834\pi$
$348$		0			0
$349$	5.36076	+	9.28512i	0.286955	+	0.497021i	0.973081	−	0.230462i	$-0.0740236\pi$
$349$	5.36076	+	9.28512i	0.286955	+	0.497021i	−0.686126	+	0.727482i	$0.740690\pi$
$350$			14.6810i			0.784733i
$351$		0			0
$352$		−	2.85513i		−	0.152179i
$353$	−1.65198	−	2.86131i	−0.0879258	−	0.152292i	0.818708	−	0.574210i	$-0.194691\pi$
$353$	−1.65198	−	2.86131i	−0.0879258	−	0.152292i	−0.906634	+	0.421918i	$0.861357\pi$
$354$		0			0
$355$	2.08008	−	3.60280i	0.110399	−	0.191217i
$356$	1.16963	−	2.02587i	0.0619905	−	0.107371i
$357$		0			0
$358$	−1.34380	+	0.775846i	−0.0710223	+	0.0410047i
$359$		−	15.3585i		−	0.810589i	−0.914186	−	0.405295i	$-0.867169\pi$
$359$		−	15.3585i		−	0.810589i	0.914186	−	0.405295i	$-0.132831\pi$
$360$		0			0
$361$	30.2780			1.59358
$362$	6.19420	+	10.7287i	0.325560	+	0.563886i
$363$		0			0
$364$	3.61596	+	2.08767i	0.189528	+	0.109424i
$365$	19.0417	−	32.9812i	0.996687	−	1.72631i
$366$		0			0
$367$	−9.12269	+	5.26699i	−0.476200	+	0.274934i	−0.718832	−	0.695184i	$-0.755323\pi$
$367$	−9.12269	+	5.26699i	−0.476200	+	0.274934i	0.242631	+	0.970119i	$0.421989\pi$
$368$	8.70347			0.453700
$369$		0			0
$370$		−	16.5404i		−	0.859897i
$371$	21.5498	+	37.3254i	1.11881	+	1.93784i
$372$		0			0
$373$	−14.7654	+	25.5743i	−0.764521	+	1.32419i	0.175978	+	0.984394i	$0.443691\pi$
$373$	−14.7654	+	25.5743i	−0.764521	+	1.32419i	−0.940499	+	0.339796i	$0.889642\pi$
$374$	−14.0260	−	8.09792i	−0.725267	−	0.418733i
$375$		0			0
$376$	1.72661	+	2.99058i	0.0890432	+	0.154227i
$377$			6.54686i			0.337180i
$378$		0			0
$379$	−7.54595			−0.387609			−0.193805	−	0.981040i	$-0.562083\pi$
$379$	−7.54595			−0.387609			−0.193805	+	0.981040i	$0.562083\pi$
$380$	17.8300	−	10.2941i	0.914658	−	0.528078i
$381$		0			0
$382$	−1.65851	+	2.87262i	−0.0848566	+	0.146976i
$383$	0.603701	−	1.04564i	0.0308477	−	0.0534297i	−0.850189	−	0.526477i	$-0.823513\pi$
$383$	0.603701	−	1.04564i	0.0308477	−	0.0534297i	0.881037	+	0.473047i	$0.156846\pi$
$384$		0			0
$385$	29.5592	−	17.0660i	1.50648	−	0.869765i
$386$		−	0.116890i		−	0.00594957i
$387$		0			0
$388$	5.38838			0.273554
$389$	5.74579	+	9.95201i	0.291323	+	0.504587i	0.974123	−	0.226019i	$-0.0725711\pi$
$389$	5.74579	+	9.95201i	0.291323	+	0.504587i	−0.682800	+	0.730606i	$0.739238\pi$
$390$		0			0
$391$	24.6854	−	42.7563i	1.24839	−	2.16228i
$392$	8.32632	+	4.80721i	0.420543	+	0.242801i
$393$		0			0
$394$	−13.1090	+	7.56850i	−0.660423	+	0.381295i
$395$	−11.1408			−0.560553
$396$		0			0
$397$	−17.4608			−0.876333			−0.438167	−	0.898894i	$-0.644372\pi$
$397$	−17.4608			−0.876333			−0.438167	+	0.898894i	$0.644372\pi$
$398$	−5.91494	−	10.2450i	−0.296489	−	0.513534i
$399$		0			0
$400$	1.80087	−	3.11920i	0.0900437	−	0.155960i
$401$	−9.37877	+	16.2445i	−0.468354	+	0.811212i	−0.999346	−	0.0361645i	$-0.988486\pi$
$401$	−9.37877	+	16.2445i	−0.468354	+	0.811212i	0.530992	+	0.847377i	$0.321819\pi$
$402$		0			0
$403$	4.01545	−	4.05025i	0.200024	−	0.201757i
$404$			18.6080i			0.925782i
$405$		0			0
$406$			26.0510i			1.29289i
$407$	−13.9448	+	8.05101i	−0.691216	+	0.399074i
$408$		0			0
$409$	−12.5445	−	7.24259i	−0.620287	−	0.358123i	0.156693	−	0.987647i	$-0.449917\pi$
$409$	−12.5445	−	7.24259i	−0.620287	−	0.358123i	−0.776981	+	0.629524i	$0.783250\pi$
$410$	9.45152	+	5.45684i	0.466777	+	0.269494i
$411$		0			0
$412$	−0.824711	−	1.42844i	−0.0406306	−	0.0703742i
$413$			22.6580i			1.11493i
$414$		0			0
$415$		−	12.9261i		−	0.634518i
$416$	−0.512177	−	0.887117i	−0.0251116	−	0.0434945i
$417$		0			0
$418$	−17.3573	−	10.0213i	−0.848976	−	0.490156i
$419$	22.1910	+	12.8120i	1.08410	+	0.625906i	0.932000	−	0.362459i	$-0.118063\pi$
$419$	22.1910	+	12.8120i	1.08410	+	0.625906i	0.152101	+	0.988365i	$0.451396\pi$
$420$		0			0
$421$	15.0985	+	26.1513i	0.735854	+	1.27454i	0.954348	+	0.298698i	$0.0965522\pi$
$421$	15.0985	+	26.1513i	0.735854	+	1.27454i	−0.218494	+	0.975838i	$0.570114\pi$
$422$			5.91332i			0.287856i
$423$		0			0
$424$		−	10.5738i		−	0.513509i
$425$	−10.2155	−	17.6938i	−0.495525	−	0.858275i
$426$		0			0
$427$	−44.3521	−	25.6067i	−2.14635	−	1.23919i
$428$	−8.59273	−	4.96101i	−0.415345	−	0.239800i
$429$		0			0
$430$	−10.7625	+	6.21375i	−0.519015	+	0.299654i
$431$			22.9545i			1.10568i	0.833287	+	0.552840i	$0.186456\pi$
$431$			22.9545i			1.10568i	−0.833287	+	0.552840i	$0.813544\pi$
$432$		0			0
$433$			15.5286i			0.746257i	0.927780	+	0.373129i	$0.121715\pi$
$433$			15.5286i			0.746257i	−0.927780	+	0.373129i	$0.878285\pi$
$434$	15.9781	−	16.1166i	0.766975	−	0.773623i
$435$		0			0
$436$	9.42652	−	16.3272i	0.451449	−	0.781932i
$437$	30.5484	−	52.9114i	1.46133	−	2.53110i
$438$		0			0
$439$	−4.51078	−	7.81290i	−0.215288	−	0.372889i	0.738074	−	0.674720i	$-0.235736\pi$
$439$	−4.51078	−	7.81290i	−0.215288	−	0.372889i	−0.953362	+	0.301831i	$0.902402\pi$
$440$	−8.37374			−0.399203
$441$		0			0
$442$	−5.81068			−0.276386
$443$	−26.8128	+	15.4804i	−1.27392	+	0.735496i	−0.975723	−	0.219009i	$-0.929718\pi$
$443$	−26.8128	+	15.4804i	−1.27392	+	0.735496i	−0.298194	+	0.954505i	$0.596384\pi$
$444$		0			0
$445$	−5.94161	−	3.43039i	−0.281659	−	0.162616i
$446$	−11.8796	+	20.5760i	−0.562513	+	0.974301i
$447$		0			0
$448$	−2.03804	−	3.52999i	−0.0962883	−	0.166776i
$449$	−0.114241			−0.00539135			−0.00269568	−	0.999996i	$-0.500858\pi$
$449$	−0.114241			−0.00539135			−0.00269568	+	0.999996i	$0.500858\pi$
$450$		0			0
$451$		−	10.6244i		−	0.500283i
$452$	−8.43172	+	4.86805i	−0.396595	+	0.228974i
$453$		0			0
$454$	3.55295	−	6.15389i	0.166748	−	0.288816i
$455$	6.12289	−	10.6051i	0.287045	−	0.497177i
$456$		0			0
$457$	14.0698	−	8.12321i	0.658158	−	0.379988i	−0.133417	−	0.991060i	$-0.542595\pi$
$457$	14.0698	−	8.12321i	0.658158	−	0.379988i	0.791575	+	0.611072i	$0.209261\pi$
$458$	−13.5318			−0.632299
$459$		0			0
$460$		−	25.5262i		−	1.19016i
$461$	−12.0624	−	20.8926i	−0.561800	−	0.973066i	−0.997340	−	0.0728965i	$-0.976776\pi$
$461$	−12.0624	−	20.8926i	−0.561800	−	0.973066i	0.435540	−	0.900170i	$-0.356558\pi$
$462$		0			0
$463$	2.07227	+	1.19642i	0.0963065	+	0.0556026i	0.547380	−	0.836884i	$-0.315625\pi$
$463$	2.07227	+	1.19642i	0.0963065	+	0.0556026i	−0.451073	+	0.892487i	$0.648959\pi$
$464$	3.19560	−	5.53494i	0.148352	−	0.256953i
$465$		0			0
$466$	−2.21570	−	3.83770i	−0.102640	−	0.177778i
$467$		−	13.5383i		−	0.626476i	−0.949675	−	0.313238i	$-0.898586\pi$
$467$		−	13.5383i		−	0.626476i	0.949675	−	0.313238i	$-0.101414\pi$
$468$		0			0
$469$	−2.67075			−0.123324
$470$	8.77099	−	5.06393i	0.404575	−	0.233582i
$471$		0			0
$472$	2.77939	−	4.81405i	0.127932	−	0.221585i
$473$	10.4772	+	6.04904i	0.481744	+	0.278135i
$474$		0			0
$475$	−12.6418	−	21.8963i	−0.580046	−	1.00467i
$476$	−23.1217			−1.05978
$477$		0			0
$478$		−	30.3636i		−	1.38880i
$479$	21.6971	−	12.5268i	0.991364	−	0.572364i	0.0856824	−	0.996323i	$-0.472693\pi$
$479$	21.6971	−	12.5268i	0.991364	−	0.572364i	0.905682	+	0.423958i	$0.139360\pi$
$480$		0			0
$481$	−2.88851	+	5.00305i	−0.131705	+	0.228119i
$482$	3.87516	−	6.71197i	0.176509	−	0.305722i
$483$		0			0
$484$	−1.42411	−	2.46663i	−0.0647321	−	0.112119i
$485$		−	15.8035i		−	0.717598i
$486$		0			0
$487$			2.48634i			0.112667i	0.998412	+	0.0563335i	$0.0179410\pi$
$487$			2.48634i			0.112667i	−0.998412	+	0.0563335i	$0.982059\pi$
$488$	6.28219	+	10.8811i	0.284381	+	0.492563i
$489$		0			0
$490$	14.0989	−	24.4201i	0.636925	−	1.10319i
$491$	−10.5582	+	18.2873i	−0.476484	+	0.825294i	−0.999637	−	0.0269445i	$-0.991422\pi$
$491$	−10.5582	+	18.2873i	−0.476484	+	0.825294i	0.523153	+	0.852239i	$0.324756\pi$
$492$		0			0
$493$	−18.1271	−	31.3971i	−0.816406	−	1.41406i
$494$	−7.19079			−0.323529
$495$		0			0
$496$	−5.37178	+	1.46424i	−0.241200	+	0.0657462i
$497$	−5.00714	+	2.89087i	−0.224601	+	0.129673i
$498$		0			0
$499$	9.97074	+	5.75661i	0.446352	+	0.257701i	0.706288	−	0.707925i	$-0.250368\pi$
$499$	9.97074	+	5.75661i	0.446352	+	0.257701i	−0.259937	+	0.965626i	$0.583702\pi$
$500$	3.55148	+	2.05045i	0.158827	+	0.0916989i
$501$		0			0
$502$	−7.67988	+	4.43398i	−0.342770	+	0.197898i
$503$		−	39.6468i		−	1.76776i	−0.467710	−	0.883882i	$-0.654921\pi$
$503$		−	39.6468i		−	1.76776i	0.467710	−	0.883882i	$-0.345079\pi$
$504$		0			0
$505$	54.5749			2.42855
$506$	−21.5204	+	12.4248i	−0.956697	+	0.552349i
$507$		0			0
$508$	−8.36064	−	4.82702i	−0.370944	−	0.214164i
$509$	11.2188	−	19.4315i	0.497265	−	0.861288i	−0.502730	−	0.864443i	$-0.667671\pi$
$509$	11.2188	−	19.4315i	0.497265	−	0.861288i	0.999995	+	0.00315565i	$0.00100448\pi$
$510$		0			0
$511$	−45.8369	+	26.4639i	−2.02770	+	1.17070i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	27.3095			1.20457
$515$	−4.18944	+	2.41877i	−0.184609	+	0.106584i
$516$		0			0
$517$	−8.53850	−	4.92970i	−0.375523	−	0.216808i
$518$	−11.4939	+	19.9080i	−0.505012	+	0.874706i
$519$		0			0
$520$	−2.60180	+	1.50215i	−0.114097	+	0.0658737i
$521$			20.4636i			0.896526i	0.893902	+	0.448263i	$0.147957\pi$
$521$			20.4636i			0.896526i	−0.893902	+	0.448263i	$0.852043\pi$
$522$		0			0
$523$			24.0253i			1.05055i	0.850931	+	0.525277i	$0.176038\pi$
$523$			24.0253i			1.05055i	−0.850931	+	0.525277i	$0.823962\pi$
$524$	0.961641	−	0.555203i	0.0420095	−	0.0242542i
$525$		0			0
$526$	−12.0588	−	6.96217i	−0.525790	−	0.303565i
$527$	−8.04265	+	30.5421i	−0.350343	+	1.33044i
$528$		0			0
$529$	−26.3752	−	45.6832i	−1.14675	−	1.98623i
$530$	−31.0116			−1.34706
$531$		0			0
$532$	−28.6134			−1.24055
$533$	−1.90589	−	3.30110i	−0.0825533	−	0.142986i
$534$		0			0
$535$	−14.5500	+	25.2014i	−0.629052	+	1.08955i
$536$	0.567442	+	0.327613i	0.0245097	+	0.0141507i
$537$		0			0
$538$	9.87688	−	5.70242i	0.425822	−	0.245849i
$539$	−27.4504			−1.18237
$540$		0			0
$541$	4.82179			0.207305			0.103653	−	0.994614i	$-0.466947\pi$
$541$	4.82179			0.207305			0.103653	+	0.994614i	$0.466947\pi$
$542$	−1.28049	−	2.21787i	−0.0550018	−	0.0952658i
$543$		0			0
$544$	4.91256	+	2.83627i	0.210624	+	0.121604i
$545$	−47.8857	−	27.6468i	−2.05120	−	1.18426i
$546$		0			0
$547$	10.7763	+	18.6651i	0.460761	+	0.798061i	0.998999	−	0.0447319i	$-0.0142434\pi$
$547$	10.7763	+	18.6651i	0.460761	+	0.798061i	−0.538238	+	0.842793i	$0.680910\pi$
$548$	2.37854			0.101606
$549$		0			0
$550$			10.2835i			0.438489i
$551$	−22.4326	−	38.8543i	−0.955659	−	1.65525i
$552$		0			0
$553$	13.4090	+	7.74167i	0.570207	+	0.329209i
$554$	15.3266	−	26.5465i	0.651166	−	1.12785i
$555$		0			0
$556$	−15.1170	+	8.72781i	−0.641104	+	0.370141i
$557$	29.6046			1.25439			0.627194	−	0.778863i	$-0.284203\pi$
$557$	29.6046			1.25439			0.627194	+	0.778863i	$0.284203\pi$
$558$		0			0
$559$	4.34051			0.183584
$560$	−10.3530	+	5.97731i	−0.437494	+	0.252587i
$561$		0			0
$562$	−6.44836	+	11.1689i	−0.272007	+	0.471131i
$563$	35.1826	+	20.3127i	1.48277	+	0.856079i	0.999809	−	0.0195620i	$-0.00622716\pi$
$563$	35.1826	+	20.3127i	1.48277	+	0.856079i	0.482963	+	0.875641i	$0.339560\pi$
$564$		0			0
$565$	14.2774	+	24.7292i	0.600654	+	1.04036i
$566$		−	2.58500i		−	0.108656i
$567$		0			0
$568$	1.41846			0.0595172
$569$	−0.258866	−	0.448369i	−0.0108522	−	0.0187966i	0.860548	−	0.509369i	$-0.170121\pi$
$569$	−0.258866	−	0.448369i	−0.0108522	−	0.0187966i	−0.871401	+	0.490572i	$0.836788\pi$
$570$		0			0
$571$	37.4562	+	21.6254i	1.56749	+	0.904993i	0.996460	+	0.0840671i	$0.0267910\pi$
$571$	37.4562	+	21.6254i	1.56749	+	0.904993i	0.571034	+	0.820926i	$0.306542\pi$
$572$	2.53284	+	1.46233i	0.105903	+	0.0611433i
$573$		0			0
$574$	−7.58386	−	13.1356i	−0.316544	−	0.548270i
$575$	−31.3477			−1.30729
$576$		0			0
$577$	−24.4727			−1.01881			−0.509405	−	0.860527i	$-0.670135\pi$
$577$	−24.4727			−1.01881			−0.509405	+	0.860527i	$0.670135\pi$
$578$	13.1442	−	7.58881i	0.546727	−	0.315653i
$579$		0			0
$580$	−16.2333	−	9.37229i	−0.674050	−	0.389163i
$581$	−8.98230	+	15.5578i	−0.372648	+	0.645446i
$582$		0			0
$583$	15.0948	+	26.1450i	0.625163	+	1.08281i
$584$	12.9850			0.537323
$585$		0			0
$586$	−1.29914			−0.0536669
$587$	5.84891	+	10.1306i	0.241410	+	0.418135i	0.961116	−	0.276144i	$-0.0890568\pi$
$587$	5.84891	+	10.1306i	0.241410	+	0.418135i	−0.719706	+	0.694279i	$0.755723\pi$
$588$		0			0
$589$	−9.95287	+	37.7963i	−0.410101	+	1.55737i
$590$	−14.1190	−	8.15161i	−0.581270	−	0.335596i
$591$		0			0
$592$	4.88410	−	2.81984i	0.200735	−	0.115895i
$593$		−	13.5891i		−	0.558039i	−0.960285	−	0.279020i	$-0.909991\pi$
$593$		−	13.5891i		−	0.558039i	0.960285	−	0.279020i	$-0.0900094\pi$
$594$		0			0
$595$			67.8130i			2.78006i
$596$	−1.94748	+	1.12438i	−0.0797721	+	0.0460564i
$597$		0			0
$598$	−4.45772	+	7.72100i	−0.182290	+	0.315735i
$599$	−10.1957	−	5.88651i	−0.416587	−	0.240516i	0.277029	−	0.960861i	$-0.410650\pi$
$599$	−10.1957	−	5.88651i	−0.416587	−	0.240516i	−0.693616	+	0.720345i	$0.743983\pi$
$600$		0			0
$601$	−4.87209	+	2.81290i	−0.198737	+	0.114741i	−0.596066	−	0.802935i	$-0.703270\pi$
$601$	−4.87209	+	2.81290i	−0.198737	+	0.114741i	0.397329	+	0.917676i	$0.369937\pi$
$602$	17.2716			0.703938
$603$		0			0
$604$		−	1.09152i		−	0.0444133i
$605$	−7.23430	+	4.17673i	−0.294116	+	0.169808i
$606$		0			0
$607$	17.5127	−	30.3328i	0.710817	−	1.23117i	−0.253734	−	0.967274i	$-0.581659\pi$
$607$	17.5127	−	30.3328i	0.710817	−	1.23117i	0.964551	−	0.263897i	$-0.0850079\pi$
$608$	6.07935	+	3.50991i	0.246550	+	0.142346i
$609$		0			0
$610$	31.9128	−	18.4249i	1.29211	−	0.746001i
$611$	−3.53732			−0.143105
$612$		0			0
$613$		−	41.6914i		−	1.68390i	−0.539555	−	0.841950i	$-0.681408\pi$
$613$		−	41.6914i		−	1.68390i	0.539555	−	0.841950i	$-0.318592\pi$
$614$	−1.86858	+	1.07883i	−0.0754098	+	0.0435379i
$615$		0			0
$616$	10.0786	+	5.81887i	0.406078	+	0.234449i
$617$	24.1663	+	13.9524i	0.972900	+	0.561704i	0.900119	−	0.435644i	$-0.143479\pi$
$617$	24.1663	+	13.9524i	0.972900	+	0.561704i	0.0727809	+	0.997348i	$0.476813\pi$
$618$		0			0
$619$	11.3385	−	6.54630i	0.455734	−	0.263118i	−0.254515	−	0.967069i	$-0.581916\pi$
$619$	11.3385	−	6.54630i	0.455734	−	0.263118i	0.710249	+	0.703951i	$0.248582\pi$
$620$	4.29442	+	15.7547i	0.172468	+	0.632726i
$621$		0			0
$622$	13.8163			0.553982
$623$	4.76752	+	8.25759i	0.191007	+	0.330833i
$624$		0			0
$625$	15.0181	−	26.0121i	0.600723	−	1.04048i
$626$	8.76129	−	15.1750i	0.350171	−	0.606515i
$627$		0			0
$628$	3.28221	+	5.68495i	0.130974	+	0.226854i
$629$		−	31.9912i		−	1.27557i
$630$		0			0
$631$			10.9471i			0.435796i	0.975972	+	0.217898i	$0.0699200\pi$
$631$			10.9471i			0.435796i	−0.975972	+	0.217898i	$0.930080\pi$
$632$	−1.89929	−	3.28967i	−0.0755498	−	0.130856i
$633$		0			0
$634$	−8.00281	+	13.8613i	−0.317832	+	0.550502i
$635$	−14.1570	+	24.5207i	−0.561805	+	0.973075i
$636$		0			0
$637$	−8.52911	+	4.92428i	−0.337936	+	0.195107i
$638$			18.2477i			0.722434i
$639$		0			0
$640$	2.93287			0.115932
$641$	−12.6285	−	21.8732i	−0.498796	−	0.863939i	0.501203	−	0.865329i	$-0.332891\pi$
$641$	−12.6285	−	21.8732i	−0.498796	−	0.863939i	−0.999999	+	0.00139021i	$0.999557\pi$
$642$		0			0
$643$	−5.65600	−	3.26550i	−0.223051	−	0.128779i	0.384311	−	0.923204i	$-0.374439\pi$
$643$	−5.65600	−	3.26550i	−0.223051	−	0.128779i	−0.607362	+	0.794425i	$0.707772\pi$
$644$	−17.7380	+	30.7232i	−0.698976	+	1.21066i
$645$		0			0
$646$	34.4853	−	19.9101i	1.35681	−	0.783352i
$647$	30.8555			1.21306			0.606528	−	0.795062i	$-0.292562\pi$
$647$	30.8555			1.21306			0.606528	+	0.795062i	$0.292562\pi$
$648$		0			0
$649$			15.8711i			0.622994i
$650$	1.84473	+	3.19517i	0.0723564	+	0.125325i
$651$		0			0
$652$	4.63340	−	8.02529i	0.181458	−	0.314294i
$653$	21.0077	+	12.1288i	0.822095	+	0.474637i	0.851139	−	0.524941i	$-0.175913\pi$
$653$	21.0077	+	12.1288i	0.822095	+	0.474637i	−0.0290431	+	0.999578i	$0.509246\pi$
$654$		0			0
$655$	−1.62834	−	2.82037i	−0.0636246	−	0.110201i
$656$			3.72115i			0.145287i
$657$		0			0
$658$	−14.0756			−0.548724
$659$	12.9132	−	7.45542i	0.503026	−	0.290422i	−0.226937	−	0.973910i	$-0.572871\pi$
$659$	12.9132	−	7.45542i	0.503026	−	0.290422i	0.729962	+	0.683488i	$0.239538\pi$
$660$		0			0
$661$	−5.59524	+	9.69123i	−0.217629	+	0.376945i	−0.954083	−	0.299543i	$-0.903166\pi$
$661$	−5.59524	+	9.69123i	−0.217629	+	0.376945i	0.736453	+	0.676488i	$0.236499\pi$
$662$	−17.6857	+	30.6325i	−0.687373	+	1.19057i
$663$		0			0
$664$	3.81685	−	2.20366i	0.148123	−	0.0855187i
$665$			83.9194i			3.25425i
$666$		0			0
$667$	−55.6256			−2.15383
$668$	−0.313267	−	0.542595i	−0.0121207	−	0.0209936i
$669$		0			0
$670$	0.960846	−	1.66423i	0.0371207	−	0.0642950i
$671$	−31.0669	−	17.9365i	−1.19932	−	0.692430i
$672$		0			0
$673$	−32.2169	+	18.6004i	−1.24187	+	0.716993i	−0.969474	−	0.245192i	$-0.921149\pi$
$673$	−32.2169	+	18.6004i	−1.24187	+	0.716993i	−0.272395	+	0.962186i	$0.587816\pi$
$674$	15.4507			0.595139
$675$		0			0
$676$	−11.9507			−0.459642
$677$	15.6341	+	27.0790i	0.600867	+	1.04073i	0.992690	+	0.120692i	$0.0385112\pi$
$677$	15.6341	+	27.0790i	0.600867	+	1.04073i	−0.391823	+	0.920041i	$0.628155\pi$
$678$		0			0
$679$	−10.9817	+	19.0209i	−0.421440	+	0.729956i
$680$	8.31841	−	14.4079i	0.318996	−	0.552518i
$681$		0			0
$682$	11.1921	−	11.2891i	0.428566	−	0.432281i
$683$			13.5166i			0.517199i	0.965985	+	0.258600i	$0.0832610\pi$
$683$			13.5166i			0.517199i	−0.965985	+	0.258600i	$0.916739\pi$
$684$		0			0
$685$		−	6.97597i		−	0.266538i
$686$	−9.22884	+	5.32827i	−0.352359	+	0.203434i
$687$		0			0
$688$	−3.66962	−	2.11866i	−0.139903	−	0.0807730i
$689$	9.38019	+	5.41566i	0.357357	+	0.206320i
$690$		0			0
$691$	−0.917897	−	1.58984i	−0.0349185	−	0.0604805i	0.848038	−	0.529935i	$-0.177784\pi$
$691$	−0.917897	−	1.58984i	−0.0349185	−	0.0604805i	−0.882956	+	0.469455i	$0.844450\pi$
$692$		−	23.6712i		−	0.899844i
$693$		0			0
$694$			29.3540i			1.11426i
$695$	25.5976	+	44.3363i	0.970970	+	1.68177i
$696$		0			0
$697$	18.2804	+	10.5542i	0.692419	+	0.399768i
$698$	9.28512	+	5.36076i	0.351447	+	0.202908i
$699$		0			0
$700$	7.34050	+	12.7141i	0.277445	+	0.480549i
$701$		−	32.7034i		−	1.23519i	−0.786496	−	0.617595i	$-0.788107\pi$
$701$		−	32.7034i		−	1.23519i	0.786496	−	0.617595i	$-0.211893\pi$
$702$		0			0
$703$		−	39.5895i		−	1.49315i
$704$	−1.42757	−	2.47262i	−0.0538034	−	0.0931903i
$705$		0			0
$706$	−2.86131	−	1.65198i	−0.107687	−	0.0621729i
$707$	−65.6860	−	37.9238i	−2.47038	−	1.42627i
$708$		0			0
$709$	31.9531	−	18.4481i	1.20002	−	0.692833i	0.239462	−	0.970906i	$-0.423029\pi$
$709$	31.9531	−	18.4481i	1.20002	−	0.692833i	0.960560	+	0.278073i	$0.0896956\pi$
$710$		−	4.16016i		−	0.156128i
$711$		0			0
$712$		−	2.33927i		−	0.0876678i
$713$	34.4132	+	34.1174i	1.28878	+	1.27771i
$714$		0			0
$715$	4.28884	−	7.42849i	0.160394	−	0.277810i
$716$	−0.775846	+	1.34380i	−0.0289947	+	0.0502203i
$717$		0			0
$718$	−7.67923	−	13.3008i	−0.286587	−	0.496382i
$719$	16.0983			0.600367			0.300183	−	0.953881i	$-0.402952\pi$
$719$	16.0983			0.600367			0.300183	+	0.953881i	$0.402952\pi$
$720$		0			0
$721$	6.72317			0.250384
$722$	26.2215	−	15.1390i	0.975862	−	0.563414i
$723$		0			0
$724$	10.7287	+	6.19420i	0.398728	+	0.230206i
$725$	−11.5097	+	19.9355i	−0.427461	+	0.740384i
$726$		0			0
$727$	−0.646145	−	1.11916i	−0.0239642	−	0.0415072i	0.853795	−	0.520610i	$-0.174295\pi$
$727$	−0.646145	−	1.11916i	−0.0239642	−	0.0415072i	−0.877759	+	0.479103i	$0.840962\pi$
$728$	4.17535			0.154749
$729$		0			0
$730$		−	38.0834i		−	1.40953i
$731$	−20.8160	+	12.0181i	−0.769909	+	0.444507i
$732$		0			0
$733$	6.61585	−	11.4590i	0.244362	−	0.423247i	−0.717590	−	0.696466i	$-0.754755\pi$
$733$	6.61585	−	11.4590i	0.244362	−	0.423247i	0.961952	+	0.273218i	$0.0880882\pi$
$734$	−5.26699	+	9.12269i	−0.194408	+	0.336725i
$735$		0			0
$736$	7.53743	−	4.35174i	0.277833	−	0.160407i
$737$	−1.87075			−0.0689101
$738$		0			0
$739$			14.0404i			0.516483i	0.966080	+	0.258242i	$0.0831431\pi$
$739$			14.0404i			0.516483i	−0.966080	+	0.258242i	$0.916857\pi$
$740$	−8.27022	−	14.3244i	−0.304020	−	0.526577i
$741$		0			0
$742$	37.3254	+	21.5498i	1.37026	+	0.791118i
$743$	12.3917	−	21.4630i	0.454606	−	0.787401i	−0.544059	−	0.839047i	$-0.683113\pi$
$743$	12.3917	−	21.4630i	0.454606	−	0.787401i	0.998665	+	0.0516459i	$0.0164467\pi$
$744$		0			0
$745$	3.29767	+	5.71173i	0.120817	+	0.209261i
$746$			29.5307i			1.08120i
$747$		0			0
$748$	−16.1958			−0.592178
$749$	35.0246	−	20.2215i	1.27977	−	0.738877i
$750$		0			0
$751$	−1.28802	+	2.23091i	−0.0470004	+	0.0814071i	−0.888569	−	0.458744i	$-0.848300\pi$
$751$	−1.28802	+	2.23091i	−0.0470004	+	0.0814071i	0.841568	+	0.540151i	$0.181633\pi$
$752$	2.99058	+	1.72661i	0.109055	+	0.0629630i
$753$		0			0
$754$	3.27343	+	5.66974i	0.119211	+	0.206480i
$755$	−3.20129			−0.116507
$756$		0			0
$757$			29.0801i			1.05693i	0.848954	+	0.528466i	$0.177233\pi$
$757$			29.0801i			1.05693i	−0.848954	+	0.528466i	$0.822767\pi$
$758$	−6.53498	+	3.77297i	−0.237361	+	0.137041i
$759$		0			0
$760$	10.2941	−	17.8300i	0.373407	−	0.646761i
$761$	−0.248473	+	0.430368i	−0.00900715	+	0.0156008i	−0.870494	−	0.492179i	$-0.836200\pi$
$761$	−0.248473	+	0.430368i	−0.00900715	+	0.0156008i	0.861487	+	0.507780i	$0.169534\pi$
$762$		0			0
$763$	38.4232	+	66.5510i	1.39101	+	2.40931i
$764$			3.31701i			0.120005i
$765$		0			0
$766$		−	1.20740i		−	0.0436252i
$767$	2.84708	+	4.93129i	0.102802	+	0.178059i
$768$		0			0
$769$	7.63741	−	13.2284i	0.275412	−	0.477028i	−0.694827	−	0.719177i	$-0.744519\pi$
$769$	7.63741	−	13.2284i	0.275412	−	0.477028i	0.970239	+	0.242149i	$0.0778524\pi$
$770$	17.0660	−	29.5592i	0.615017	−	1.06524i
$771$		0			0
$772$	−0.0584452	−	0.101230i	−0.00210349	−	0.00364335i
$773$	40.0384			1.44008			0.720040	−	0.693932i	$-0.244123\pi$
$773$	40.0384			1.44008			0.720040	+	0.693932i	$0.244123\pi$
$774$		0			0
$775$	19.3478	−	5.27381i	0.694993	−	0.189441i
$776$	4.66648	−	2.69419i	0.167517	−	0.0967159i
$777$		0			0
$778$	9.95201	+	5.74579i	0.356797	+	0.205997i
$779$	22.6222	+	13.0609i	0.810524	+	0.467956i
$780$		0			0
$781$	−3.50731	+	2.02494i	−0.125501	+	0.0724582i
$782$		−	49.3707i		−	1.76549i
$783$		0			0
$784$	9.61441			0.343372
$785$	16.6732	−	9.62629i	0.595093	−	0.343577i
$786$		0			0
$787$	15.8897	+	9.17391i	0.566406	+	0.327015i	0.755713	−	0.654903i	$-0.227291\pi$
$787$	15.8897	+	9.17391i	0.566406	+	0.327015i	−0.189307	+	0.981918i	$0.560624\pi$
$788$	−7.56850	+	13.1090i	−0.269616	+	0.466989i
$789$		0			0
$790$	−9.64819	+	5.57039i	−0.343267	+	0.198185i
$791$		−	39.6851i		−	1.41104i
$792$		0			0
$793$	−12.8704			−0.457040
$794$	−15.1215	+	8.73041i	−0.536642	+	0.309831i
$795$		0			0
$796$	−10.2450	−	5.91494i	−0.363123	−	0.209649i
$797$	3.44226	−	5.96217i	0.121931	−	0.211191i	−0.798598	−	0.601865i	$-0.794425\pi$
$797$	3.44226	−	5.96217i	0.121931	−	0.211191i	0.920529	+	0.390674i	$0.127758\pi$
$798$		0			0
$799$	16.9641	−	9.79426i	0.600148	−	0.346496i
$800$		−	3.60175i		−	0.127341i
$801$		0			0
$802$			18.7575i			0.662352i
$803$	−32.1069	+	18.5370i	−1.13303	+	0.654155i
$804$		0			0
$805$	90.1071	+	52.0234i	3.17586	+	1.83358i
$806$	1.45235	−	5.51535i	0.0511570	−	0.194270i
$807$		0			0
$808$	9.30400	+	16.1150i	0.327313	+	0.566924i
$809$	−4.22765			−0.148636			−0.0743182	−	0.997235i	$-0.523678\pi$
$809$	−4.22765			−0.148636			−0.0743182	+	0.997235i	$0.523678\pi$
$810$		0			0
$811$	−5.17461			−0.181705			−0.0908525	−	0.995864i	$-0.528959\pi$
$811$	−5.17461			−0.181705			−0.0908525	+	0.995864i	$0.528959\pi$
$812$	13.0255	+	22.5609i	0.457106	+	0.791731i
$813$		0			0
$814$	−8.05101	+	13.9448i	−0.282188	+	0.488763i
$815$	−23.5371	−	13.5892i	−0.824470	−	0.476008i
$816$		0			0
$817$	−25.7601	+	14.8726i	−0.901231	+	0.520326i
$818$	−14.4852			−0.506463
$819$		0			0
$820$	10.9137			0.381122
$821$	7.94452	+	13.7603i	0.277266	+	0.480238i	0.970704	−	0.240278i	$-0.0772385\pi$
$821$	7.94452	+	13.7603i	0.277266	+	0.480238i	−0.693439	+	0.720516i	$0.743905\pi$
$822$		0			0
$823$	−30.1165	−	17.3878i	−1.04979	−	0.606099i	−0.127203	−	0.991877i	$-0.540600\pi$
$823$	−30.1165	−	17.3878i	−1.04979	−	0.606099i	−0.922592	+	0.385778i	$0.873933\pi$
$824$	−1.42844	−	0.824711i	−0.0497621	−	0.0287302i
$825$		0			0
$826$	11.3290	+	19.6224i	0.394187	+	0.682752i
$827$	−41.8701			−1.45597			−0.727983	−	0.685595i	$-0.759542\pi$
$827$	−41.8701			−1.45597			−0.727983	+	0.685595i	$0.759542\pi$
$828$		0			0
$829$			8.11598i			0.281880i	0.990018	+	0.140940i	$0.0450124\pi$
$829$			8.11598i			0.281880i	−0.990018	+	0.140940i	$0.954988\pi$
$830$	−6.46306	−	11.1944i	−0.224336	−	0.388562i
$831$		0			0
$832$	−0.887117	−	0.512177i	−0.0307553	−	0.0177566i
$833$	27.2690	−	47.2313i	0.944816	−	1.63647i
$834$		0			0
$835$	−1.59136	+	0.918773i	−0.0550714	+	0.0317955i
$836$	−20.0425			−0.693186
$837$		0			0
$838$	25.6239			0.885165
$839$	9.44010	−	5.45024i	0.325908	−	0.188163i	−0.328115	−	0.944638i	$-0.606413\pi$
$839$	9.44010	−	5.45024i	0.325908	−	0.188163i	0.654023	+	0.756475i	$0.273080\pi$
$840$		0			0
$841$	−5.92372	+	10.2602i	−0.204266	+	0.353800i
$842$	26.1513	+	15.0985i	0.901233	+	0.520327i
$843$		0			0
$844$	2.95666	+	5.12109i	0.101772	+	0.176275i
$845$			35.0499i			1.20575i
$846$		0			0
$847$	11.6095			0.398909
$848$	−5.28690	−	9.15718i	−0.181553	−	0.314459i
$849$		0			0
$850$	−17.6938	−	10.2155i	−0.606892	−	0.350389i
$851$	−42.5086	−	24.5424i	−1.45718	−	0.841302i
$852$		0			0
$853$	26.0774	+	45.1673i	0.892872	+	1.54650i	0.836417	+	0.548094i	$0.184646\pi$
$853$	26.0774	+	45.1673i	0.892872	+	1.54650i	0.0564553	+	0.998405i	$0.482020\pi$
$854$	−51.2134			−1.75249
$855$		0			0
$856$	−9.92203			−0.339128
$857$	−7.31813	+	4.22512i	−0.249982	+	0.144327i	−0.619756	−	0.784794i	$-0.712769\pi$
$857$	−7.31813	+	4.22512i	−0.249982	+	0.144327i	0.369774	+	0.929122i	$0.379435\pi$
$858$		0			0
$859$	−2.65979	−	1.53563i	−0.0907510	−	0.0523951i	0.453938	−	0.891033i	$-0.350019\pi$
$859$	−2.65979	−	1.53563i	−0.0907510	−	0.0523951i	−0.544689	+	0.838638i	$0.683352\pi$
$860$	−6.21375	+	10.7625i	−0.211887	+	0.366999i
$861$		0			0
$862$	11.4773	+	19.8792i	0.390917	+	0.677088i
$863$	−10.0748			−0.342949			−0.171475	−	0.985189i	$-0.554853\pi$
$863$	−10.0748			−0.342949			−0.171475	+	0.985189i	$0.554853\pi$
$864$		0			0
$865$	−69.4246			−2.36051
$866$	7.76430	+	13.4482i	0.263842	+	0.456987i
$867$		0			0
$868$	5.77916	−	21.9465i	0.196157	−	0.744912i
$869$	9.39245	+	5.42273i	0.318617	+	0.183954i
$870$		0			0
$871$	−0.581261	+	0.335591i	−0.0196953	+	0.0113711i
$872$		−	18.8530i		−	0.638445i
$873$		0			0
$874$		−	61.0969i		−	2.06663i
$875$	−14.4761	+	8.35779i	−0.489382	+	0.282545i
$876$		0			0
$877$	−3.27797	+	5.67761i	−0.110689	+	0.191719i	−0.916048	−	0.401068i	$-0.868639\pi$
$877$	−3.27797	+	5.67761i	−0.110689	+	0.191719i	0.805359	+	0.592787i	$0.201972\pi$
$878$	−7.81290	−	4.51078i	−0.263673	−	0.152231i
$879$		0			0
$880$	−7.25188	+	4.18687i	−0.244461	+	0.141139i
$881$	−3.02318			−0.101854			−0.0509268	−	0.998702i	$-0.516218\pi$
$881$	−3.02318			−0.101854			−0.0509268	+	0.998702i	$0.516218\pi$
$882$		0			0
$883$			20.0772i			0.675653i	0.941208	+	0.337826i	$0.109692\pi$
$883$			20.0772i			0.675653i	−0.941208	+	0.337826i	$0.890308\pi$
$884$	−5.03220	+	2.90534i	−0.169251	+	0.0977172i
$885$		0			0
$886$	−15.4804	+	26.8128i	−0.520074	+	0.900795i
$887$	28.6270	+	16.5278i	0.961202	+	0.554950i	0.896543	−	0.442957i	$-0.146071\pi$
$887$	28.6270	+	16.5278i	0.961202	+	0.554950i	0.0646591	+	0.997907i	$0.479404\pi$
$888$		0			0
$889$	34.0786	−	19.6753i	1.14296	−	0.659889i
$890$	−6.86078			−0.229974
$891$		0			0
$892$			23.7591i			0.795514i
$893$	20.9933	−	12.1205i	0.702515	−	0.405597i
$894$		0			0
$895$	3.94121	+	2.27546i	0.131740	+	0.0760602i
$896$	−3.52999	−	2.03804i	−0.117929	−	0.0680861i
$897$		0			0
$898$	−0.0989353	+	0.0571203i	−0.00330151	+	0.00190613i
$899$	34.3321	−	9.35823i	1.14504	−	0.312114i
$900$		0			0
$901$	−59.9802			−1.99823
$902$	−5.31219	−	9.20099i	−0.176877	−	0.306359i
$903$		0			0
$904$	−4.86805	+	8.43172i	−0.161909	+	0.280435i
$905$	18.1668	−	31.4658i	0.603885	−	1.04596i
$906$		0			0
$907$	−18.6969	−	32.3839i	−0.620820	−	1.07529i	−0.989333	−	0.145669i	$-0.953467\pi$
$907$	−18.6969	−	32.3839i	−0.620820	−	1.07529i	0.368514	−	0.929622i	$-0.379867\pi$
$908$		−	7.10590i		−	0.235818i
$909$		0			0
$910$		−	12.2458i		−	0.405943i
$911$	1.50507	+	2.60685i	0.0498651	+	0.0863689i	0.889881	−	0.456194i	$-0.150788\pi$
$911$	1.50507	+	2.60685i	0.0498651	+	0.0863689i	−0.840015	+	0.542562i	$0.817454\pi$
$912$		0			0
$913$	−6.29175	+	10.8976i	−0.208226	+	0.360659i
$914$	8.12321	−	14.0698i	0.268692	−	0.465388i
$915$		0			0
$916$	−11.7189	+	6.76589i	−0.387202	+	0.223551i
$917$			4.52611i			0.149465i
$918$		0			0
$919$	3.34394			0.110306			0.0551532	−	0.998478i	$-0.482435\pi$
$919$	3.34394			0.110306			0.0551532	+	0.998478i	$0.482435\pi$
$920$	−12.7631	−	22.1063i	−0.420787	−	0.728824i
$921$		0			0
$922$	−20.8926	−	12.0624i	−0.688062	−	0.397253i
$923$	−0.726503	+	1.25834i	−0.0239131	+	0.0414187i
$924$		0			0
$925$	−17.5913	+	10.1563i	−0.578398	+	0.333938i
$926$	2.39285			0.0786339
$927$		0			0
$928$		−	6.39120i		−	0.209801i
$929$	13.0827	+	22.6599i	0.429229	+	0.743447i	0.996805	−	0.0798745i	$-0.0254520\pi$
$929$	13.0827	+	22.6599i	0.429229	+	0.743447i	−0.567576	+	0.823321i	$0.692119\pi$
$930$		0			0
$931$	33.7457	−	58.4493i	1.10597	−	1.91560i
$932$	−3.83770	−	2.21570i	−0.125708	−	0.0725777i
$933$		0			0
$934$	−6.76913	−	11.7245i	−0.221493	−	0.383637i
$935$			47.5003i			1.55343i
$936$		0			0
$937$	−6.83244			−0.223206			−0.111603	−	0.993753i	$-0.535599\pi$
$937$	−6.83244			−0.223206			−0.111603	+	0.993753i	$0.535599\pi$
$938$	−2.31294	+	1.33537i	−0.0755200	+	0.0436015i
$939$		0			0
$940$	5.06393	−	8.77099i	0.165167	−	0.286078i
$941$	−23.4056	+	40.5397i	−0.763002	+	1.32156i	0.178295	+	0.983977i	$0.442942\pi$
$941$	−23.4056	+	40.5397i	−0.763002	+	1.32156i	−0.941297	+	0.337580i	$0.890392\pi$
$942$		0			0
$943$	28.0479	−	16.1935i	0.913366	−	0.527332i
$944$		−	5.55879i		−	0.180923i
$945$		0			0
$946$	12.0981			0.393343
$947$	−17.1034	−	29.6240i	−0.555786	−	0.962649i	−0.997842	−	0.0656618i	$-0.979084\pi$
$947$	−17.1034	−	29.6240i	−0.555786	−	0.962649i	0.442056	−	0.896987i	$-0.354249\pi$
$948$		0			0
$949$	−6.65062	+	11.5192i	−0.215888	+	0.373930i
$950$	−21.8963	−	12.6418i	−0.710409	−	0.410155i
$951$		0			0
$952$	−20.0240	+	11.5608i	−0.648980	+	0.374689i
$953$	9.49649			0.307621			0.153811	−	0.988100i	$-0.450845\pi$
$953$	9.49649			0.307621			0.153811	+	0.988100i	$0.450845\pi$
$954$		0			0
$955$	9.72838			0.314803
$956$	−15.1818	−	26.2956i	−0.491014	−	0.850461i
$957$		0			0
$958$	12.5268	−	21.6971i	0.404723	−	0.701000i
$959$	−4.84757	+	8.39623i	−0.156536	+	0.271128i
$960$		0			0
$961$	−26.9796	−	15.2677i	−0.870308	−	0.492508i
$962$			5.77703i			0.186259i
$963$		0			0
$964$		−	7.75032i		−	0.249621i
$965$	−0.296895	+	0.171412i	−0.00955739	+	0.00551796i
$966$		0			0
$967$	26.2672	+	15.1654i	0.844696	+	0.487686i	0.858858	−	0.512214i	$-0.171175\pi$
$967$	26.2672	+	15.1654i	0.844696	+	0.487686i	−0.0141616	+	0.999900i	$0.504508\pi$
$968$	−2.46663	−	1.42411i	−0.0792804	−	0.0457725i
$969$		0			0
$970$	−7.90173	−	13.6862i	−0.253709	−	0.439437i
$971$		−	14.1371i		−	0.453682i	−0.973932	−	0.226841i	$-0.927160\pi$
$971$		−	14.1371i		−	0.453682i	0.973932	−	0.226841i	$-0.0728397\pi$
$972$		0			0
$973$		−	71.1504i		−	2.28098i
$974$	1.24317	+	2.15324i	0.0398338	+	0.0689942i
$975$		0			0
$976$	10.8811	+	6.28219i	0.348295	+	0.201088i
$977$	31.3324	+	18.0898i	1.00241	+	0.578744i	0.908962	−	0.416880i	$-0.136876\pi$
$977$	31.3324	+	18.0898i	1.00241	+	0.578744i	0.0934521	+	0.995624i	$0.470210\pi$
$978$		0			0
$979$	3.33946	+	5.78412i	0.106730	+	0.184861i
$980$		−	28.1979i		−	0.900747i
$981$		0			0
$982$			21.1164i			0.673850i
$983$	−19.6881	−	34.1009i	−0.627954	−	1.08765i	−0.987962	−	0.154699i	$-0.950559\pi$
$983$	−19.6881	−	34.1009i	−0.627954	−	1.08765i	0.360008	−	0.932949i	$-0.382774\pi$
$984$		0			0
$985$	38.4471	+	22.1974i	1.22503	+	0.707269i
$986$	−31.3971	−	18.1271i	−0.999889	−	0.577286i
$987$		0			0
$988$	−6.22741	+	3.59540i	−0.198120	+	0.114385i
$989$			36.8793i			1.17269i
$990$		0			0
$991$		−	16.6544i		−	0.529045i	−0.964379	−	0.264523i	$-0.914786\pi$
$991$		−	16.6544i		−	0.529045i	0.964379	−	0.264523i	$-0.0852144\pi$
$992$	−3.91998	+	3.95396i	−0.124459	+	0.125538i
$993$		0			0
$994$	−2.89087	+	5.00714i	−0.0916930	+	0.158817i
$995$	−17.3478	+	30.0472i	−0.549961	+	0.952560i
$996$		0			0
$997$	24.8521	+	43.0450i	0.787073	+	1.36325i	0.927753	+	0.373195i	$0.121738\pi$
$997$	24.8521	+	43.0450i	0.787073	+	1.36325i	−0.140680	+	0.990055i	$0.544929\pi$
$998$	11.5132			0.364445
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1674.2.q.a.557.20		64
3.2	odd	2		558.2.q.a.185.12	yes	64
9.2	odd	6	inner	1674.2.q.a.1115.25		64
9.7	even	3		558.2.q.a.371.5	yes	64
31.30	odd	2	inner	1674.2.q.a.557.25		64
93.92	even	2		558.2.q.a.185.5	✓	64
279.61	odd	6		558.2.q.a.371.12	yes	64
279.92	even	6	inner	1674.2.q.a.1115.20		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.q.a.185.5	✓	64	93.92	even	2
558.2.q.a.185.12	yes	64	3.2	odd	2
558.2.q.a.371.5	yes	64	9.7	even	3
558.2.q.a.371.12	yes	64	279.61	odd	6
1674.2.q.a.557.20		64	1.1	even	1	trivial
1674.2.q.a.557.25		64	31.30	odd	2	inner
1674.2.q.a.1115.20		64	279.92	even	6	inner
1674.2.q.a.1115.25		64	9.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1674 = 2 \cdot 3^{3} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1674.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.53994 - 1.46644i) q^{5} +(2.03804 + 3.52999i) q^{7} -1.00000i q^{8} -2.93287 q^{10} +(1.42757 + 2.47262i) q^{11} +(0.887117 + 0.512177i) q^{13} +(3.52999 + 2.03804i) q^{14} +(-0.500000 - 0.866025i) q^{16} -5.67253 q^{17} -7.01983 q^{19} +(-2.53994 + 1.46644i) q^{20} +(2.47262 + 1.42757i) q^{22} +(-4.35174 + 7.53743i) q^{23} +(1.80087 + 3.11920i) q^{25} +1.02435 q^{26} +4.07608 q^{28} +(3.19560 + 5.53494i) q^{29} +(1.41782 - 5.38422i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.91256 + 2.83627i) q^{34} -11.9546i q^{35} +5.63967i q^{37} +(-6.07935 + 3.50991i) q^{38} +(-1.46644 + 2.53994i) q^{40} +(-3.22261 - 1.86058i) q^{41} +(3.66962 - 2.11866i) q^{43} +2.85513 q^{44} +8.70347i q^{46} +(-2.99058 + 1.72661i) q^{47} +(-4.80721 + 8.32632i) q^{49} +(3.11920 + 1.80087i) q^{50} +(0.887117 - 0.512177i) q^{52} +10.5738 q^{53} -8.37374i q^{55} +(3.52999 - 2.03804i) q^{56} +(5.53494 + 3.19560i) q^{58} +(4.81405 + 2.77939i) q^{59} +(-10.8811 + 6.28219i) q^{61} +(-1.46424 - 5.37178i) q^{62} -1.00000 q^{64} +(-1.50215 - 2.60180i) q^{65} +(-0.327613 + 0.567442i) q^{67} +(-2.83627 + 4.91256i) q^{68} +(-5.97731 - 10.3530i) q^{70} +1.41846i q^{71} +12.9850i q^{73} +(2.81984 + 4.88410i) q^{74} +(-3.50991 + 6.07935i) q^{76} +(-5.81887 + 10.0786i) q^{77} +(3.28967 - 1.89929i) q^{79} +2.93287i q^{80} -3.72115 q^{82} +(2.20366 + 3.81685i) q^{83} +(14.4079 + 8.31841i) q^{85} +(2.11866 - 3.66962i) q^{86} +(2.47262 - 1.42757i) q^{88} +2.33927 q^{89} +4.17535i q^{91} +(4.35174 + 7.53743i) q^{92} +(-1.72661 + 2.99058i) q^{94} +(17.8300 + 10.2941i) q^{95} +(2.69419 + 4.66648i) q^{97} +9.61441i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 12 q^{5} - 4 q^{7} - 32 q^{16} - 8 q^{19} - 12 q^{20} + 44 q^{25} - 8 q^{28} + 8 q^{31} - 36 q^{38} - 24 q^{41} + 48 q^{47} - 36 q^{49} + 12 q^{59} - 64 q^{64} + 16 q^{67} - 12 q^{70}+ \cdots - 16 q^{97}+O(q^{100}) \) 64 * q + 32 * q^4 - 12 * q^5 - 4 * q^7 - 32 * q^16 - 8 * q^19 - 12 * q^20 + 44 * q^25 - 8 * q^28 + 8 * q^31 - 36 * q^38 - 24 * q^41 + 48 * q^47 - 36 * q^49 + 12 * q^59 - 64 * q^64 + 16 * q^67 - 12 * q^70 - 4 * q^76 + 180 * q^95 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more