LMFDB - Embedded newform 1456.2.cc.g.673.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(225,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

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

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

chi := DirichletCharacter("1456.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.cc (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 728)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.2
Character	$\chi$	$=$	1456.673
Dual form			1456.2.cc.g.225.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41211 - 2.44584i) q^{3} +4.08885i q^{5} +(-0.866025 - 0.500000i) q^{7} +(-2.48810 + 4.30952i) q^{9} +O(q^{10})$	\(q+(-1.41211 - 2.44584i) q^{3} +4.08885i q^{5} +(-0.866025 - 0.500000i) q^{7} +(-2.48810 + 4.30952i) q^{9} +(0.331079 - 0.191148i) q^{11} +(2.36169 - 2.72441i) q^{13} +(10.0007 - 5.77390i) q^{15} +(2.13018 - 3.68959i) q^{17} +(-5.59985 - 3.23308i) q^{19} +2.82422i q^{21} +(2.08763 + 3.61588i) q^{23} -11.7187 q^{25} +5.58125 q^{27} +(0.997018 + 1.72689i) q^{29} +9.98911i q^{31} +(-0.935039 - 0.539845i) q^{33} +(2.04442 - 3.54105i) q^{35} +(1.96323 - 1.13347i) q^{37} +(-9.99845 - 1.92917i) q^{39} +(-3.13172 + 1.80810i) q^{41} +(-4.59232 + 7.95413i) q^{43} +(-17.6210 - 10.1735i) q^{45} +0.162342i q^{47} +(0.500000 + 0.866025i) q^{49} -12.0322 q^{51} -12.4678 q^{53} +(0.781577 + 1.35373i) q^{55} +18.2618i q^{57} +(0.759723 + 0.438626i) q^{59} +(-6.25809 + 10.8393i) q^{61} +(4.30952 - 2.48810i) q^{63} +(11.1397 + 9.65660i) q^{65} +(-7.65760 + 4.42112i) q^{67} +(5.89592 - 10.2120i) q^{69} +(2.05567 + 1.18684i) q^{71} -6.58886i q^{73} +(16.5481 + 28.6621i) q^{75} -0.382297 q^{77} -8.34960 q^{79} +(-0.417016 - 0.722292i) q^{81} -10.8740i q^{83} +(15.0862 + 8.71000i) q^{85} +(2.81580 - 4.87710i) q^{87} +(1.75178 - 1.01139i) q^{89} +(-3.40749 + 1.17856i) q^{91} +(24.4318 - 14.1057i) q^{93} +(13.2196 - 22.8969i) q^{95} +(4.91317 + 2.83662i) q^{97} +1.90239i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{3} - 18 q^{9}+O(q^{10}) $ 24 * q + 2 * q^3 - 18 * q^9	$ 24 q + 2 q^{3} - 18 q^{9} - 12 q^{11} + 8 q^{17} + 12 q^{19} - 2 q^{23} - 28 q^{25} + 20 q^{27} + 2 q^{29} - 18 q^{33} + 8 q^{35} + 60 q^{37} - 18 q^{39} - 6 q^{41} - 24 q^{43} - 72 q^{45} + 12 q^{49} + 72 q^{51} - 48 q^{53} + 44 q^{55} + 12 q^{59} - 30 q^{61} - 12 q^{63} + 10 q^{65} - 78 q^{67} + 36 q^{69} + 36 q^{71} - 22 q^{75} + 4 q^{77} - 20 q^{79} - 40 q^{81} - 6 q^{85} + 20 q^{87} + 108 q^{89} - 6 q^{91} + 30 q^{93} - 18 q^{95} - 54 q^{97}+O(q^{100}) $ 24 * q + 2 * q^3 - 18 * q^9 - 12 * q^11 + 8 * q^17 + 12 * q^19 - 2 * q^23 - 28 * q^25 + 20 * q^27 + 2 * q^29 - 18 * q^33 + 8 * q^35 + 60 * q^37 - 18 * q^39 - 6 * q^41 - 24 * q^43 - 72 * q^45 + 12 * q^49 + 72 * q^51 - 48 * q^53 + 44 * q^55 + 12 * q^59 - 30 * q^61 - 12 * q^63 + 10 * q^65 - 78 * q^67 + 36 * q^69 + 36 * q^71 - 22 * q^75 + 4 * q^77 - 20 * q^79 - 40 * q^81 - 6 * q^85 + 20 * q^87 + 108 * q^89 - 6 * q^91 + 30 * q^93 - 18 * q^95 - 54 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.41211	−	2.44584i	−0.815282	−	1.41211i	−0.909126	−	0.416522i	$-0.863249\pi$
$3$	−1.41211	−	2.44584i	−0.815282	−	1.41211i	0.0938439	−	0.995587i	$-0.470085\pi$
$4$		0			0
$5$			4.08885i			1.82859i	0.405051	+	0.914294i	$0.367254\pi$
$5$			4.08885i			1.82859i	−0.405051	+	0.914294i	$0.632746\pi$
$6$		0			0
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$		0			0
$9$	−2.48810	+	4.30952i	−0.829368	+	1.43651i
$10$		0			0
$11$	0.331079	−	0.191148i	0.0998240	−	0.0576334i	−0.449257	−	0.893403i	$-0.648311\pi$
$11$	0.331079	−	0.191148i	0.0998240	−	0.0576334i	0.549081	+	0.835769i	$0.314978\pi$
$12$		0			0
$13$	2.36169	−	2.72441i	0.655015	−	0.755616i
$13$	2.36169	−	2.72441i	0.655015	−	0.755616i
$14$		0			0
$15$	10.0007	−	5.77390i	2.58217	−	1.49081i
$16$		0			0
$17$	2.13018	−	3.68959i	0.516646	−	0.894857i	−0.483167	−	0.875528i	$-0.660514\pi$
$17$	2.13018	−	3.68959i	0.516646	−	0.894857i	0.999813	−	0.0193287i	$-0.00615290\pi$
$18$		0			0
$19$	−5.59985	−	3.23308i	−1.28469	−	0.741719i	−0.306991	−	0.951712i	$-0.599322\pi$
$19$	−5.59985	−	3.23308i	−1.28469	−	0.741719i	−0.977703	+	0.209994i	$0.932656\pi$
$20$		0			0
$21$			2.82422i			0.616295i
$22$		0			0
$23$	2.08763	+	3.61588i	0.435300	+	0.753962i	0.997320	−	0.0731615i	$-0.0233088\pi$
$23$	2.08763	+	3.61588i	0.435300	+	0.753962i	−0.562020	+	0.827124i	$0.689976\pi$
$24$		0			0
$25$	−11.7187			−2.34374
$26$		0			0
$27$	5.58125			1.07411
$28$		0			0
$29$	0.997018	+	1.72689i	0.185142	+	0.320675i	0.943624	−	0.331019i	$-0.107392\pi$
$29$	0.997018	+	1.72689i	0.185142	+	0.320675i	−0.758483	+	0.651693i	$0.774059\pi$
$30$		0			0
$31$			9.98911i			1.79410i	0.441932	+	0.897049i	$0.354293\pi$
$31$			9.98911i			1.79410i	−0.441932	+	0.897049i	$0.645707\pi$
$32$		0			0
$33$	−0.935039	−	0.539845i	−0.162769	−	0.0939749i
$34$		0			0
$35$	2.04442	−	3.54105i	0.345571	−	0.598546i
$36$		0			0
$37$	1.96323	−	1.13347i	0.322753	−	0.186342i	−0.329866	−	0.944028i	$-0.607004\pi$
$37$	1.96323	−	1.13347i	0.322753	−	0.186342i	0.652619	+	0.757686i	$0.273670\pi$
$38$		0			0
$39$	−9.99845	−	1.92917i	−1.60103	−	0.308914i
$40$		0			0
$41$	−3.13172	+	1.80810i	−0.489092	+	0.282378i	−0.724198	−	0.689592i	$-0.757790\pi$
$41$	−3.13172	+	1.80810i	−0.489092	+	0.282378i	0.235106	+	0.971970i	$0.424456\pi$
$42$		0			0
$43$	−4.59232	+	7.95413i	−0.700322	+	1.21299i	0.268031	+	0.963410i	$0.413627\pi$
$43$	−4.59232	+	7.95413i	−0.700322	+	1.21299i	−0.968353	+	0.249583i	$0.919706\pi$
$44$		0			0
$45$	−17.6210	−	10.1735i	−2.62678	−	1.51657i
$46$		0			0
$47$			0.162342i			0.0236800i	0.999930	+	0.0118400i	$0.00376888\pi$
$47$			0.162342i			0.0236800i	−0.999930	+	0.0118400i	$0.996231\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$		0			0
$51$	−12.0322			−1.68485
$52$		0			0
$53$	−12.4678			−1.71258			−0.856292	−	0.516492i	$-0.827238\pi$
$53$	−12.4678			−1.71258			−0.856292	+	0.516492i	$0.827238\pi$
$54$		0			0
$55$	0.781577	+	1.35373i	0.105388	+	0.182537i
$56$		0			0
$57$			18.2618i			2.41884i
$58$		0			0
$59$	0.759723	+	0.438626i	0.0989075	+	0.0571043i	0.548638	−	0.836060i	$-0.315147\pi$
$59$	0.759723	+	0.438626i	0.0989075	+	0.0571043i	−0.449730	+	0.893164i	$0.648480\pi$
$60$		0			0
$61$	−6.25809	+	10.8393i	−0.801267	+	1.38783i	0.117516	+	0.993071i	$0.462507\pi$
$61$	−6.25809	+	10.8393i	−0.801267	+	1.38783i	−0.918783	+	0.394763i	$0.870827\pi$
$62$		0			0
$63$	4.30952	−	2.48810i	0.542949	−	0.313472i
$64$		0			0
$65$	11.1397	+	9.65660i	1.38171	+	1.19775i
$66$		0			0
$67$	−7.65760	+	4.42112i	−0.935525	+	0.540126i	−0.888555	−	0.458771i	$-0.848290\pi$
$67$	−7.65760	+	4.42112i	−0.935525	+	0.540126i	−0.0469702	+	0.998896i	$0.514957\pi$
$68$		0			0
$69$	5.89592	−	10.2120i	0.709785	−	1.22938i
$70$		0			0
$71$	2.05567	+	1.18684i	0.243963	+	0.140852i	0.616997	−	0.786966i	$-0.288349\pi$
$71$	2.05567	+	1.18684i	0.243963	+	0.140852i	−0.373034	+	0.927818i	$0.621682\pi$
$72$		0			0
$73$		−	6.58886i		−	0.771167i	−0.922673	−	0.385584i	$-0.874000\pi$
$73$		−	6.58886i		−	0.771167i	0.922673	−	0.385584i	$-0.126000\pi$
$74$		0			0
$75$	16.5481	+	28.6621i	1.91080	+	3.30961i
$76$		0			0
$77$	−0.382297			−0.0435668
$78$		0			0
$79$	−8.34960			−0.939403			−0.469702	−	0.882825i	$-0.655638\pi$
$79$	−8.34960			−0.939403			−0.469702	+	0.882825i	$0.655638\pi$
$80$		0			0
$81$	−0.417016	−	0.722292i	−0.0463351	−	0.0802547i
$82$		0			0
$83$		−	10.8740i		−	1.19358i	−0.802397	−	0.596790i	$-0.796442\pi$
$83$		−	10.8740i		−	1.19358i	0.802397	−	0.596790i	$-0.203558\pi$
$84$		0			0
$85$	15.0862	+	8.71000i	1.63632	+	0.944732i
$86$		0			0
$87$	2.81580	−	4.87710i	0.301885	−	0.522880i
$88$		0			0
$89$	1.75178	−	1.01139i	0.185689	−	0.107207i	−0.404274	−	0.914638i	$-0.632476\pi$
$89$	1.75178	−	1.01139i	0.185689	−	0.107207i	0.589963	+	0.807431i	$0.299142\pi$
$90$		0			0
$91$	−3.40749	+	1.17856i	−0.357202	+	0.123547i
$92$		0			0
$93$	24.4318	−	14.1057i	2.53346	−	1.46269i
$94$		0			0
$95$	13.2196	−	22.8969i	1.35630	−	2.34918i
$96$		0			0
$97$	4.91317	+	2.83662i	0.498856	+	0.288015i	0.728241	−	0.685321i	$-0.240338\pi$
$97$	4.91317	+	2.83662i	0.498856	+	0.288015i	−0.229385	+	0.973336i	$0.573671\pi$
$98$		0			0
$99$			1.90239i			0.191197i
$100$		0			0
$101$	−0.786982	−	1.36309i	−0.0783076	−	0.135633i	0.824212	−	0.566281i	$-0.191618\pi$
$101$	−0.786982	−	1.36309i	−0.0783076	−	0.135633i	−0.902520	+	0.430648i	$0.858285\pi$
$102$		0			0
$103$	16.1089			1.58726			0.793630	−	0.608401i	$-0.208189\pi$
$103$	16.1089			1.58726			0.793630	+	0.608401i	$0.208189\pi$
$104$		0			0
$105$	−11.5478			−1.12695
$106$		0			0
$107$	2.53794	+	4.39585i	0.245352	+	0.424963i	0.962231	−	0.272236i	$-0.0877630\pi$
$107$	2.53794	+	4.39585i	0.245352	+	0.424963i	−0.716878	+	0.697198i	$0.754430\pi$
$108$		0			0
$109$			4.89392i			0.468752i	0.972146	+	0.234376i	$0.0753047\pi$
$109$			4.89392i			0.468752i	−0.972146	+	0.234376i	$0.924695\pi$
$110$		0			0
$111$	−5.54459	−	3.20117i	−0.526269	−	0.303842i
$112$		0			0
$113$	−9.86038	+	17.0787i	−0.927587	+	1.60663i	−0.140239	+	0.990118i	$0.544787\pi$
$113$	−9.86038	+	17.0787i	−0.927587	+	1.60663i	−0.787347	+	0.616510i	$0.788546\pi$
$114$		0			0
$115$	−14.7848	+	8.53599i	−1.37869	+	0.795985i
$116$		0			0
$117$	5.86478	+	16.9564i	0.542199	+	1.56762i
$118$		0			0
$119$	−3.68959	+	2.13018i	−0.338224	+	0.195274i
$120$		0			0
$121$	−5.42692	+	9.39971i	−0.493357	+	0.854519i
$122$		0			0
$123$	8.84466	+	5.10646i	0.797496	+	0.460434i
$124$		0			0
$125$		−	27.4717i		−	2.45714i
$126$		0			0
$127$	−0.0645326	−	0.111774i	−0.00572634	−	0.00991832i	0.863148	−	0.504951i	$-0.168489\pi$
$127$	−0.0645326	−	0.111774i	−0.00572634	−	0.00991832i	−0.868874	+	0.495033i	$0.835156\pi$
$128$		0			0
$129$	25.9394			2.28384
$130$		0			0
$131$	−14.3494			−1.25372			−0.626858	−	0.779133i	$-0.715660\pi$
$131$	−14.3494			−1.25372			−0.626858	+	0.779133i	$0.715660\pi$
$132$		0			0
$133$	3.23308	+	5.59985i	0.280343	+	0.485569i
$134$		0			0
$135$			22.8209i			1.96411i
$136$		0			0
$137$	9.39528	+	5.42437i	0.802693	+	0.463435i	0.844412	−	0.535694i	$-0.179950\pi$
$137$	9.39528	+	5.42437i	0.802693	+	0.463435i	−0.0417187	+	0.999129i	$0.513283\pi$
$138$		0			0
$139$	−3.36411	+	5.82680i	−0.285340	+	0.494223i	−0.972692	−	0.232102i	$-0.925440\pi$
$139$	−3.36411	+	5.82680i	−0.285340	+	0.494223i	0.687352	+	0.726325i	$0.258773\pi$
$140$		0			0
$141$	0.397064	−	0.229245i	0.0334388	−	0.0193059i
$142$		0			0
$143$	0.261139	−	1.35343i	0.0218376	−	0.113179i
$144$		0			0
$145$	−7.06097	+	4.07665i	−0.586382	+	0.338548i
$146$		0			0
$147$	1.41211	−	2.44584i	0.116469	−	0.201730i
$148$		0			0
$149$	−17.4324	−	10.0646i	−1.42812	−	0.824524i	−0.431145	−	0.902283i	$-0.641890\pi$
$149$	−17.4324	−	10.0646i	−1.42812	−	0.824524i	−0.996972	+	0.0777587i	$0.975224\pi$
$150$		0			0
$151$			3.05895i			0.248934i	0.992224	+	0.124467i	$0.0397221\pi$
$151$			3.05895i			0.248934i	−0.992224	+	0.124467i	$0.960278\pi$
$152$		0			0
$153$	10.6002	+	18.3602i	0.856979	+	1.48433i
$154$		0			0
$155$	−40.8440			−3.28067
$156$		0			0
$157$	−10.6969			−0.853707			−0.426853	−	0.904321i	$-0.640378\pi$
$157$	−10.6969			−0.853707			−0.426853	+	0.904321i	$0.640378\pi$
$158$		0			0
$159$	17.6059	+	30.4943i	1.39624	+	2.41836i
$160$		0			0
$161$		−	4.17525i		−	0.329056i
$162$		0			0
$163$	−5.72177	−	3.30347i	−0.448164	−	0.258748i	0.258891	−	0.965907i	$-0.416643\pi$
$163$	−5.72177	−	3.30347i	−0.448164	−	0.258748i	−0.707054	+	0.707159i	$0.749976\pi$
$164$		0			0
$165$	2.20734	−	3.82323i	0.171841	−	0.297638i
$166$		0			0
$167$	−9.32836	+	5.38573i	−0.721850	+	0.416760i	−0.815433	−	0.578851i	$-0.803501\pi$
$167$	−9.32836	+	5.38573i	−0.721850	+	0.416760i	0.0935831	+	0.995611i	$0.470168\pi$
$168$		0			0
$169$	−1.84483	−	12.8684i	−0.141910	−	0.989880i
$170$		0			0
$171$	27.8660	−	16.0885i	2.13097	−	1.23032i
$172$		0			0
$173$	4.69082	−	8.12474i	0.356636	−	0.617712i	−0.630760	−	0.775978i	$-0.717257\pi$
$173$	4.69082	−	8.12474i	0.356636	−	0.617712i	0.987397	+	0.158265i	$0.0505902\pi$
$174$		0			0
$175$	10.1487	+	5.85934i	0.767168	+	0.442924i
$176$		0			0
$177$		−	2.47755i		−	0.186224i
$178$		0			0
$179$	−5.37150	−	9.30372i	−0.401485	−	0.695393i	0.592420	−	0.805629i	$-0.298172\pi$
$179$	−5.37150	−	9.30372i	−0.401485	−	0.695393i	−0.993905	+	0.110237i	$0.964839\pi$
$180$		0			0
$181$	−13.8998			−1.03316			−0.516581	−	0.856238i	$-0.672796\pi$
$181$	−13.8998			−1.03316			−0.516581	+	0.856238i	$0.672796\pi$
$182$		0			0
$183$	35.3484			2.61303
$184$		0			0
$185$	4.63459	+	8.02735i	0.340742	+	0.590183i
$186$		0			0
$187$		−	1.62873i		−	0.119104i
$188$		0			0
$189$	−4.83350	−	2.79062i	−0.351585	−	0.202988i
$190$		0			0
$191$	−2.72559	+	4.72086i	−0.197217	+	0.341589i	−0.947625	−	0.319385i	$-0.896524\pi$
$191$	−2.72559	+	4.72086i	−0.197217	+	0.341589i	0.750408	+	0.660975i	$0.229857\pi$
$192$		0			0
$193$	12.4736	−	7.20164i	0.897870	−	0.518386i	0.0213615	−	0.999772i	$-0.493200\pi$
$193$	12.4736	−	7.20164i	0.897870	−	0.518386i	0.876509	+	0.481386i	$0.159867\pi$
$194$		0			0
$195$	7.88807	−	40.8822i	0.564876	−	2.92763i
$196$		0			0
$197$	0.591869	−	0.341716i	0.0421690	−	0.0243463i	−0.478767	−	0.877942i	$-0.658916\pi$
$197$	0.591869	−	0.341716i	0.0421690	−	0.0243463i	0.520936	+	0.853596i	$0.325583\pi$
$198$		0			0
$199$	−0.482139	+	0.835089i	−0.0341779	+	0.0591979i	−0.882608	−	0.470109i	$-0.844215\pi$
$199$	−0.482139	+	0.835089i	−0.0341779	+	0.0591979i	0.848430	+	0.529307i	$0.177548\pi$
$200$		0			0
$201$	21.6267	+	12.4862i	1.52543	+	0.880709i
$202$		0			0
$203$		−	1.99404i		−	0.139954i
$204$		0			0
$205$	−7.39304	−	12.8051i	−0.516352	−	0.894348i
$206$		0			0
$207$	−20.7769			−1.44410
$208$		0			0
$209$	−2.47199			−0.170991
$210$		0			0
$211$	11.6491	+	20.1768i	0.801955	+	1.38903i	0.918328	+	0.395821i	$0.129540\pi$
$211$	11.6491	+	20.1768i	0.801955	+	1.38903i	−0.116373	+	0.993206i	$0.537127\pi$
$212$		0			0
$213$		−	6.70379i		−	0.459336i
$214$		0			0
$215$	−32.5232	−	18.7773i	−2.21807	−	1.28060i
$216$		0			0
$217$	4.99456	−	8.65082i	0.339052	−	0.587256i
$218$		0			0
$219$	−16.1153	+	9.30419i	−1.08897	+	0.628719i
$220$		0			0
$221$	−5.02111	−	14.5172i	−0.337757	−	0.976530i
$222$		0			0
$223$	−9.79161	+	5.65319i	−0.655695	+	0.378566i	−0.790635	−	0.612288i	$-0.790249\pi$
$223$	−9.79161	+	5.65319i	−0.655695	+	0.378566i	0.134940	+	0.990854i	$0.456916\pi$
$224$		0			0
$225$	29.1573	−	50.5019i	1.94382	−	3.36679i
$226$		0			0
$227$	3.23042	+	1.86508i	0.214410	+	0.123790i	0.603359	−	0.797469i	$-0.293828\pi$
$227$	3.23042	+	1.86508i	0.214410	+	0.123790i	−0.388949	+	0.921259i	$0.627162\pi$
$228$		0			0
$229$		−	23.5767i		−	1.55799i	−0.627028	−	0.778996i	$-0.715729\pi$
$229$		−	23.5767i		−	1.55799i	0.627028	−	0.778996i	$-0.284271\pi$
$230$		0			0
$231$	0.539845	+	0.935039i	0.0355192	+	0.0615210i
$232$		0			0
$233$	24.5749			1.60996			0.804978	−	0.593304i	$-0.202177\pi$
$233$	24.5749			1.60996			0.804978	+	0.593304i	$0.202177\pi$
$234$		0			0
$235$	−0.663793			−0.0433011
$236$		0			0
$237$	11.7905	+	20.4218i	0.765878	+	1.32654i
$238$		0			0
$239$		−	2.68748i		−	0.173839i	−0.996215	−	0.0869193i	$-0.972298\pi$
$239$		−	2.68748i		−	0.173839i	0.996215	−	0.0869193i	$-0.0277022\pi$
$240$		0			0
$241$	−12.4846	−	7.20796i	−0.804201	−	0.464306i	0.0407371	−	0.999170i	$-0.487029\pi$
$241$	−12.4846	−	7.20796i	−0.804201	−	0.464306i	−0.844938	+	0.534864i	$0.820363\pi$
$242$		0			0
$243$	7.19413	−	12.4606i	0.461503	−	0.799347i
$244$		0			0
$245$	−3.54105	+	2.04442i	−0.226229	+	0.130613i
$246$		0			0
$247$	−22.0334	+	7.62077i	−1.40195	+	0.484898i
$248$		0			0
$249$	−26.5962	+	15.3553i	−1.68547	+	0.973104i
$250$		0			0
$251$	7.51621	−	13.0185i	0.474419	−	0.821718i	−0.525152	−	0.851009i	$-0.675991\pi$
$251$	7.51621	−	13.0185i	0.474419	−	0.821718i	0.999571	+	0.0292904i	$0.00932476\pi$
$252$		0			0
$253$	1.38234	+	0.798093i	0.0869068	+	0.0501757i
$254$		0			0
$255$		−	49.1979i		−	3.08089i
$256$		0			0
$257$	3.03093	+	5.24973i	0.189064	+	0.327469i	0.944939	−	0.327248i	$-0.106121\pi$
$257$	3.03093	+	5.24973i	0.189064	+	0.327469i	−0.755874	+	0.654717i	$0.772788\pi$
$258$		0			0
$259$	−2.26694			−0.140861
$260$		0			0
$261$	−9.92274			−0.614202
$262$		0			0
$263$	14.5238	+	25.1560i	0.895577	+	1.55118i	0.833089	+	0.553138i	$0.186570\pi$
$263$	14.5238	+	25.1560i	0.895577	+	1.55118i	0.0624870	+	0.998046i	$0.480097\pi$
$264$		0			0
$265$		−	50.9789i		−	3.13161i
$266$		0			0
$267$	−4.94742	−	2.85639i	−0.302777	−	0.174808i
$268$		0			0
$269$	1.18602	−	2.05425i	0.0723130	−	0.125250i	−0.827602	−	0.561316i	$-0.810295\pi$
$269$	1.18602	−	2.05425i	0.0723130	−	0.125250i	0.899915	+	0.436066i	$0.143629\pi$
$270$		0			0
$271$	13.8552	−	7.99931i	0.841644	−	0.485923i	−0.0161786	−	0.999869i	$-0.505150\pi$
$271$	13.8552	−	7.99931i	0.841644	−	0.485923i	0.857823	+	0.513946i	$0.171817\pi$
$272$		0			0
$273$	7.69433	+	6.66993i	0.465682	+	0.403683i
$274$		0			0
$275$	−3.87981	+	2.24001i	−0.233961	+	0.135077i
$276$		0			0
$277$	−14.3491	+	24.8533i	−0.862153	+	1.49329i	0.00769363	+	0.999970i	$0.497551\pi$
$277$	−14.3491	+	24.8533i	−0.862153	+	1.49329i	−0.869847	+	0.493322i	$0.835782\pi$
$278$		0			0
$279$	−43.0483	−	24.8540i	−2.57723	−	1.48797i
$280$		0			0
$281$			4.55311i			0.271616i	0.990735	+	0.135808i	$0.0433630\pi$
$281$			4.55311i			0.271616i	−0.990735	+	0.135808i	$0.956637\pi$
$282$		0			0
$283$	8.11116	+	14.0489i	0.482158	+	0.835123i	0.999790	−	0.0204806i	$-0.00651965\pi$
$283$	8.11116	+	14.0489i	0.482158	+	0.835123i	−0.517632	+	0.855603i	$0.673186\pi$
$284$		0			0
$285$	−74.6698			−4.42306
$286$		0			0
$287$	3.61620			0.213457
$288$		0			0
$289$	−0.575376	−	0.996581i	−0.0338457	−	0.0586224i
$290$		0			0
$291$		−	16.0225i		−	0.939253i
$292$		0			0
$293$	3.15477	+	1.82141i	0.184304	+	0.106408i	0.589313	−	0.807905i	$-0.299398\pi$
$293$	3.15477	+	1.82141i	0.184304	+	0.106408i	−0.405010	+	0.914312i	$0.632732\pi$
$294$		0			0
$295$	−1.79348	+	3.10639i	−0.104420	+	0.180861i
$296$		0			0
$297$	1.84783	−	1.06685i	0.107222	−	0.0619047i
$298$		0			0
$299$	14.7815	+	2.85203i	0.854834	+	0.164937i
$300$		0			0
$301$	7.95413	−	4.59232i	0.458468	−	0.264697i
$302$		0			0
$303$	−2.22261	+	3.84967i	−0.127685	+	0.221158i
$304$		0			0
$305$	−44.3204	−	25.5884i	−2.53778	−	1.46519i
$306$		0			0
$307$		−	15.5964i		−	0.890134i	−0.895497	−	0.445067i	$-0.853180\pi$
$307$		−	15.5964i		−	0.890134i	0.895497	−	0.445067i	$-0.146820\pi$
$308$		0			0
$309$	−22.7476	−	39.3999i	−1.29406	−	2.24138i
$310$		0			0
$311$	31.7711			1.80157			0.900786	−	0.434263i	$-0.142991\pi$
$311$	31.7711			1.80157			0.900786	+	0.434263i	$0.142991\pi$
$312$		0			0
$313$	−5.80891			−0.328339			−0.164169	−	0.986432i	$-0.552494\pi$
$313$	−5.80891			−0.328339			−0.164169	+	0.986432i	$0.552494\pi$
$314$		0			0
$315$	10.1735	+	17.6210i	0.573211	+	0.992830i
$316$		0			0
$317$			26.8461i			1.50783i	0.656973	+	0.753914i	$0.271836\pi$
$317$			26.8461i			1.50783i	−0.656973	+	0.753914i	$0.728164\pi$
$318$		0			0
$319$	0.660183	+	0.381157i	0.0369631	+	0.0213407i
$320$		0			0
$321$	7.16771	−	12.4148i	0.400062	−	0.692929i
$322$		0			0
$323$	−23.8574	+	13.7741i	−1.32746	+	0.766411i
$324$		0			0
$325$	−27.6759	+	31.9265i	−1.53518	+	1.77096i
$326$		0			0
$327$	11.9698	−	6.91074i	0.661929	−	0.382165i
$328$		0			0
$329$	0.0811711	−	0.140592i	0.00447511	−	0.00775111i
$330$		0			0
$331$	−12.6112	−	7.28106i	−0.693172	−	0.400203i	0.111627	−	0.993750i	$-0.464394\pi$
$331$	−12.6112	−	7.28106i	−0.693172	−	0.400203i	−0.804799	+	0.593547i	$0.797727\pi$
$332$		0			0
$333$			11.2808i			0.618183i
$334$		0			0
$335$	−18.0773	−	31.3108i	−0.987667	−	1.71069i
$336$		0			0
$337$	−17.7870			−0.968922			−0.484461	−	0.874813i	$-0.660984\pi$
$337$	−17.7870			−0.968922			−0.484461	+	0.874813i	$0.660984\pi$
$338$		0			0
$339$	55.6957			3.02498
$340$		0			0
$341$	1.90940	+	3.30718i	0.103400	+	0.179094i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$	41.7554	+	24.1075i	2.24804	+	1.29790i
$346$		0			0
$347$	−2.03659	+	3.52748i	−0.109330	+	0.189365i	−0.915499	−	0.402320i	$-0.868204\pi$
$347$	−2.03659	+	3.52748i	−0.109330	+	0.189365i	0.806169	+	0.591685i	$0.201537\pi$
$348$		0			0
$349$	30.3923	−	17.5470i	1.62686	−	0.939268i	0.641838	−	0.766840i	$-0.278172\pi$
$349$	30.3923	−	17.5470i	1.62686	−	0.939268i	0.985022	−	0.172428i	$-0.0551614\pi$
$350$		0			0
$351$	13.1812	−	15.2056i	0.703559	−	0.811615i
$352$		0			0
$353$	5.49803	−	3.17429i	0.292630	−	0.168950i	−0.346497	−	0.938051i	$-0.612629\pi$
$353$	5.49803	−	3.17429i	0.292630	−	0.168950i	0.639127	+	0.769101i	$0.279296\pi$
$354$		0			0
$355$	−4.85281	+	8.40532i	−0.257560	+	0.446108i
$356$		0			0
$357$	10.4202	+	6.01611i	0.551496	+	0.318406i
$358$		0			0
$359$		−	22.9526i		−	1.21139i	−0.795696	−	0.605697i	$-0.792894\pi$
$359$		−	22.9526i		−	1.21139i	0.795696	−	0.605697i	$-0.207106\pi$
$360$		0			0
$361$	11.4056	+	19.7550i	0.600293	+	1.03974i
$362$		0			0
$363$	30.6536			1.60890
$364$		0			0
$365$	26.9408			1.41015
$366$		0			0
$367$	−11.6782	−	20.2272i	−0.609596	−	1.05585i	−0.991307	−	0.131570i	$-0.957998\pi$
$367$	−11.6782	−	20.2272i	−0.609596	−	1.05585i	0.381711	−	0.924282i	$-0.375335\pi$
$368$		0			0
$369$		−	17.9950i		−	0.936780i
$370$		0			0
$371$	10.7974	+	6.23390i	0.560575	+	0.323648i
$372$		0			0
$373$	−3.51692	+	6.09148i	−0.182099	+	0.315405i	−0.942595	−	0.333938i	$-0.891623\pi$
$373$	−3.51692	+	6.09148i	−0.182099	+	0.315405i	0.760496	+	0.649343i	$0.224956\pi$
$374$		0			0
$375$	−67.1914	+	38.7930i	−3.46975	+	2.00326i
$376$		0			0
$377$	7.05939	+	1.36208i	0.363577	+	0.0701509i
$378$		0			0
$379$	19.8720	−	11.4731i	1.02076	−	0.589335i	0.106435	−	0.994320i	$-0.466056\pi$
$379$	19.8720	−	11.4731i	1.02076	−	0.589335i	0.914323	+	0.404985i	$0.132723\pi$
$380$		0			0
$381$	−0.182254	+	0.315673i	−0.00933716	+	0.0161724i
$382$		0			0
$383$	−28.5865	−	16.5044i	−1.46070	−	0.843336i	−0.461658	−	0.887058i	$-0.652745\pi$
$383$	−28.5865	−	16.5044i	−1.46070	−	0.843336i	−0.999044	+	0.0437219i	$0.986078\pi$
$384$		0			0
$385$		−	1.56315i		−	0.0796657i
$386$		0			0
$387$	−22.8523	−	39.5814i	−1.16165	−	2.01204i
$388$		0			0
$389$	−7.95326			−0.403246			−0.201623	−	0.979463i	$-0.564622\pi$
$389$	−7.95326			−0.403246			−0.201623	+	0.979463i	$0.564622\pi$
$390$		0			0
$391$	17.7881			0.899584
$392$		0			0
$393$	20.2630	+	35.0965i	1.02213	+	1.77039i
$394$		0			0
$395$		−	34.1402i		−	1.71778i
$396$		0			0
$397$	−2.06619	−	1.19292i	−0.103699	−	0.0598708i	0.447253	−	0.894407i	$-0.352402\pi$
$397$	−2.06619	−	1.19292i	−0.103699	−	0.0598708i	−0.550953	+	0.834536i	$0.685736\pi$
$398$		0			0
$399$	9.13091	−	15.8152i	0.457117	−	0.791751i
$400$		0			0
$401$	−4.11624	+	2.37651i	−0.205555	+	0.118677i	−0.599244	−	0.800566i	$-0.704532\pi$
$401$	−4.11624	+	2.37651i	−0.205555	+	0.118677i	0.393689	+	0.919244i	$0.371199\pi$
$402$		0			0
$403$	27.2144	+	23.5912i	1.35565	+	1.17516i
$404$		0			0
$405$	2.95334	−	1.70511i	0.146753	−	0.0847278i
$406$		0			0
$407$	0.433323	−	0.750537i	0.0214790	−	0.0372027i
$408$		0			0
$409$	1.39079	+	0.802973i	0.0687701	+	0.0397045i	0.533991	−	0.845490i	$-0.320692\pi$
$409$	1.39079	+	0.802973i	0.0687701	+	0.0397045i	−0.465221	+	0.885195i	$0.654025\pi$
$410$		0			0
$411$		−	30.6392i		−	1.51132i
$412$		0			0
$413$	−0.438626	−	0.759723i	−0.0215834	−	0.0373835i
$414$		0			0
$415$	44.4623			2.18257
$416$		0			0
$417$	19.0019			0.930529
$418$		0			0
$419$	17.0797	+	29.5829i	0.834396	+	1.44522i	0.894521	+	0.447026i	$0.147517\pi$
$419$	17.0797	+	29.5829i	0.834396	+	1.44522i	−0.0601245	+	0.998191i	$0.519150\pi$
$420$		0			0
$421$			31.9086i			1.55513i	0.628802	+	0.777566i	$0.283546\pi$
$421$			31.9086i			1.55513i	−0.628802	+	0.777566i	$0.716454\pi$
$422$		0			0
$423$	−0.699618	−	0.403924i	−0.0340166	−	0.0196395i
$424$		0			0
$425$	−24.9630	+	43.2371i	−1.21088	+	2.09731i
$426$		0			0
$427$	10.8393	−	6.25809i	0.524552	−	0.302850i
$428$		0			0
$429$	−3.67903	+	1.27248i	−0.177625	+	0.0614360i
$430$		0			0
$431$	−5.22985	+	3.01945i	−0.251913	+	0.145442i	−0.620640	−	0.784096i	$-0.713127\pi$
$431$	−5.22985	+	3.01945i	−0.251913	+	0.145442i	0.368727	+	0.929538i	$0.379794\pi$
$432$		0			0
$433$	8.46103	−	14.6549i	0.406611	−	0.704271i	−0.587896	−	0.808936i	$-0.700044\pi$
$433$	8.46103	−	14.6549i	0.406611	−	0.704271i	0.994508	+	0.104665i	$0.0333771\pi$
$434$		0			0
$435$	19.9417	+	11.5134i	0.956133	+	0.552023i
$436$		0			0
$437$		−	26.9978i		−	1.29148i
$438$		0			0
$439$	0.722824	+	1.25197i	0.0344985	+	0.0597532i	0.882759	−	0.469826i	$-0.155683\pi$
$439$	0.722824	+	1.25197i	0.0344985	+	0.0597532i	−0.848261	+	0.529579i	$0.822350\pi$
$440$		0			0
$441$	−4.97621			−0.236962
$442$		0			0
$443$	−3.19732			−0.151909			−0.0759546	−	0.997111i	$-0.524200\pi$
$443$	−3.19732			−0.151909			−0.0759546	+	0.997111i	$0.524200\pi$
$444$		0			0
$445$	4.13543	+	7.16277i	0.196038	+	0.339548i
$446$		0			0
$447$			56.8492i			2.68888i
$448$		0			0
$449$	−32.3770	−	18.6929i	−1.52796	−	0.882170i	−0.999447	−	0.0332473i	$-0.989415\pi$
$449$	−32.3770	−	18.6929i	−1.52796	−	0.882170i	−0.528517	−	0.848923i	$-0.677252\pi$
$450$		0			0
$451$	−0.691230	+	1.19725i	−0.0325488	+	0.0563761i
$452$		0			0
$453$	7.48173	−	4.31958i	0.351522	−	0.202951i
$454$		0			0
$455$	−4.81897	−	13.9327i	−0.225917	−	0.653175i
$456$		0			0
$457$	12.6834	−	7.32278i	0.593305	−	0.342545i	−0.173098	−	0.984905i	$-0.555378\pi$
$457$	12.6834	−	7.32278i	0.593305	−	0.342545i	0.766403	+	0.642360i	$0.222044\pi$
$458$		0			0
$459$	11.8891	−	20.5925i	0.554935	−	0.961176i
$460$		0			0
$461$	−2.73915	−	1.58145i	−0.127575	−	0.0736554i	0.434854	−	0.900501i	$-0.356800\pi$
$461$	−2.73915	−	1.58145i	−0.127575	−	0.0736554i	−0.562429	+	0.826845i	$0.690133\pi$
$462$		0			0
$463$			0.522002i			0.0242595i	0.999926	+	0.0121297i	$0.00386111\pi$
$463$			0.522002i			0.0242595i	−0.999926	+	0.0121297i	$0.996139\pi$
$464$		0			0
$465$	57.6761	+	99.8980i	2.67467	+	4.63266i
$466$		0			0
$467$	−18.8169			−0.870744			−0.435372	−	0.900251i	$-0.643383\pi$
$467$	−18.8169			−0.870744			−0.435372	+	0.900251i	$0.643383\pi$
$468$		0			0
$469$	8.84224			0.408297
$470$		0			0
$471$	15.1052	+	26.1630i	0.696011	+	1.20553i
$472$		0			0
$473$			3.51126i			0.161448i
$474$		0			0
$475$	65.6229	+	37.8874i	3.01098	+	1.73839i
$476$		0			0
$477$	31.0212	−	53.7303i	1.42036	−	2.46014i
$478$		0			0
$479$	17.1067	−	9.87654i	0.781624	−	0.451271i	−0.0553816	−	0.998465i	$-0.517638\pi$
$479$	17.1067	−	9.87654i	0.781624	−	0.451271i	0.837005	+	0.547195i	$0.184304\pi$
$480$		0			0
$481$	1.54850	−	8.02556i	0.0706056	−	0.365934i
$482$		0			0
$483$	−10.2120	+	5.89592i	−0.464663	+	0.268273i
$484$		0			0
$485$	−11.5985	+	20.0892i	−0.526661	+	0.912203i
$486$		0			0
$487$	17.0401	+	9.83813i	0.772163	+	0.445808i	0.833646	−	0.552300i	$-0.186250\pi$
$487$	17.0401	+	9.83813i	0.772163	+	0.445808i	−0.0614829	+	0.998108i	$0.519583\pi$
$488$		0			0
$489$			18.6594i			0.843809i
$490$		0			0
$491$	−14.8951	−	25.7992i	−0.672209	−	1.16430i	−0.977276	−	0.211969i	$-0.932012\pi$
$491$	−14.8951	−	25.7992i	−0.672209	−	1.16430i	0.305068	−	0.952331i	$-0.401321\pi$
$492$		0			0
$493$	8.49533			0.382610
$494$		0			0
$495$	−7.77858			−0.349621
$496$		0			0
$497$	−1.18684	−	2.05567i	−0.0532371	−	0.0922093i
$498$		0			0
$499$		−	6.80364i		−	0.304573i	−0.988336	−	0.152286i	$-0.951336\pi$
$499$		−	6.80364i		−	0.304573i	0.988336	−	0.152286i	$-0.0486636\pi$
$500$		0			0
$501$	26.3453	+	15.2105i	1.17702	+	0.679554i
$502$		0			0
$503$	−3.52877	+	6.11202i	−0.157340	+	0.272521i	−0.933909	−	0.357512i	$-0.883625\pi$
$503$	−3.52877	+	6.11202i	−0.157340	+	0.272521i	0.776568	+	0.630033i	$0.216959\pi$
$504$		0			0
$505$	5.57348	−	3.21785i	0.248016	−	0.143192i
$506$		0			0
$507$	−28.8691	+	22.6838i	−1.28212	+	1.00742i
$508$		0			0
$509$	28.9747	−	16.7286i	1.28428	−	0.741480i	0.306654	−	0.951821i	$-0.400791\pi$
$509$	28.9747	−	16.7286i	1.28428	−	0.741480i	0.977628	+	0.210341i	$0.0674573\pi$
$510$		0			0
$511$	−3.29443	+	5.70612i	−0.145737	+	0.252424i
$512$		0			0
$513$	−31.2542	−	18.0446i	−1.37990	−	0.796688i
$514$		0			0
$515$			65.8669i			2.90244i
$516$		0			0
$517$	0.0310314	+	0.0537480i	0.00136476	+	0.00236384i
$518$		0			0
$519$	−26.4958			−1.16304
$520$		0			0
$521$	−9.15972			−0.401295			−0.200647	−	0.979664i	$-0.564305\pi$
$521$	−9.15972			−0.401295			−0.200647	+	0.979664i	$0.564305\pi$
$522$		0			0
$523$	2.17134	+	3.76086i	0.0949459	+	0.164451i	0.909586	−	0.415516i	$-0.136399\pi$
$523$	2.17134	+	3.76086i	0.0949459	+	0.164451i	−0.814640	+	0.579967i	$0.803066\pi$
$524$		0			0
$525$		−	33.0961i		−	1.44443i
$526$		0			0
$527$	36.8557	+	21.2787i	1.60546	+	0.926913i
$528$		0			0
$529$	2.78362	−	4.82138i	0.121027	−	0.209625i
$530$		0			0
$531$	−3.78054	+	2.18270i	−0.164062	+	0.0947210i
$532$		0			0
$533$	−2.47015	+	12.8023i	−0.106994	+	0.554527i
$534$		0			0
$535$	−17.9740	+	10.3773i	−0.777082	+	0.448648i
$536$		0			0
$537$	−15.1703	+	26.2757i	−0.654647	+	1.13388i
$538$		0			0
$539$	0.331079	+	0.191148i	0.0142606	+	0.00823334i
$540$		0			0
$541$			8.37148i			0.359918i	0.983674	+	0.179959i	$0.0575965\pi$
$541$			8.37148i			0.359918i	−0.983674	+	0.179959i	$0.942403\pi$
$542$		0			0
$543$	19.6280	+	33.9967i	0.842319	+	1.45894i
$544$		0			0
$545$	−20.0105			−0.857155
$546$		0			0
$547$	2.97036			0.127003			0.0635017	−	0.997982i	$-0.479773\pi$
$547$	2.97036			0.127003			0.0635017	+	0.997982i	$0.479773\pi$
$548$		0			0
$549$	−31.1416	−	53.9388i	−1.32909	−	2.30205i
$550$		0			0
$551$		−	12.8937i		−	0.549292i
$552$		0			0
$553$	7.23096	+	4.17480i	0.307492	+	0.177530i
$554$		0			0
$555$	13.0891	−	22.6710i	0.555601	−	0.962330i
$556$		0			0
$557$	14.8421	−	8.56909i	0.628880	−	0.363084i	−0.151438	−	0.988467i	$-0.548390\pi$
$557$	14.8421	−	8.56909i	0.628880	−	0.363084i	0.780318	+	0.625383i	$0.215057\pi$
$558$		0			0
$559$	10.8247	+	31.2966i	0.457835	+	1.32370i
$560$		0			0
$561$	−3.98361	+	2.29994i	−0.168188	+	0.0971035i
$562$		0			0
$563$	0.179546	−	0.310982i	0.00756695	−	0.0131063i	−0.862217	−	0.506539i	$-0.830925\pi$
$563$	0.179546	−	0.310982i	0.00756695	−	0.0131063i	0.869784	+	0.493433i	$0.164258\pi$
$564$		0			0
$565$	−69.8321	−	40.3176i	−2.93786	−	1.69617i
$566$		0			0
$567$			0.834031i			0.0350260i
$568$		0			0
$569$	−3.33252	−	5.77210i	−0.139707	−	0.241979i	0.787679	−	0.616086i	$-0.211283\pi$
$569$	−3.33252	−	5.77210i	−0.139707	−	0.241979i	−0.927386	+	0.374107i	$0.877949\pi$
$570$		0			0
$571$	9.08603			0.380238			0.190119	−	0.981761i	$-0.439113\pi$
$571$	9.08603			0.380238			0.190119	+	0.981761i	$0.439113\pi$
$572$		0			0
$573$	15.3953			0.643148
$574$		0			0
$575$	−24.4642	−	42.3733i	−1.02023	−	1.76709i
$576$		0			0
$577$			28.9966i			1.20715i	0.797308	+	0.603573i	$0.206257\pi$
$577$			28.9966i			1.20715i	−0.797308	+	0.603573i	$0.793743\pi$
$578$		0			0
$579$	−35.2282	−	20.3390i	−1.46403	−	0.845260i
$580$		0			0
$581$	−5.43702	+	9.41719i	−0.225566	+	0.390691i
$582$		0			0
$583$	−4.12782	+	2.38320i	−0.170957	+	0.0987020i
$584$		0			0
$585$	−69.3321	+	23.9802i	−2.86653	+	0.991458i
$586$		0			0
$587$	9.46179	−	5.46277i	0.390530	−	0.225473i	−0.291860	−	0.956461i	$-0.594274\pi$
$587$	9.46179	−	5.46277i	0.390530	−	0.225473i	0.682390	+	0.730989i	$0.260941\pi$
$588$		0			0
$589$	32.2956	−	55.9375i	1.33072	−	2.30487i
$590$		0			0
$591$	−1.67157	−	0.965081i	−0.0687591	−	0.0396981i
$592$		0			0
$593$		−	15.0205i		−	0.616817i	−0.951254	−	0.308408i	$-0.900204\pi$
$593$		−	15.0205i		−	0.616817i	0.951254	−	0.308408i	$-0.0997963\pi$
$594$		0			0
$595$	−8.71000	−	15.0862i	−0.357075	−	0.618473i
$596$		0			0
$597$	2.72333			0.111459
$598$		0			0
$599$	−43.8866			−1.79316			−0.896579	−	0.442885i	$-0.853955\pi$
$599$	−43.8866			−1.79316			−0.896579	+	0.442885i	$0.853955\pi$
$600$		0			0
$601$	−20.1567	−	34.9124i	−0.822208	−	1.42411i	−0.904035	−	0.427459i	$-0.859409\pi$
$601$	−20.1567	−	34.9124i	−0.822208	−	1.42411i	0.0818270	−	0.996647i	$-0.473925\pi$
$602$		0			0
$603$		−	44.0008i		−	1.79185i
$604$		0			0
$605$	−38.4340	−	22.1899i	−1.56256	−	0.902147i
$606$		0			0
$607$	−12.4453	+	21.5559i	−0.505140	+	0.874927i	0.494843	+	0.868983i	$0.335226\pi$
$607$	−12.4453	+	21.5559i	−0.505140	+	0.874927i	−0.999982	+	0.00594489i	$0.998108\pi$
$608$		0			0
$609$	−4.87710	+	2.81580i	−0.197630	+	0.114102i
$610$		0			0
$611$	0.442287	+	0.383402i	0.0178930	+	0.0155108i
$612$		0			0
$613$	30.9473	−	17.8674i	1.24995	−	0.721658i	0.278849	−	0.960335i	$-0.410047\pi$
$613$	30.9473	−	17.8674i	1.24995	−	0.721658i	0.971099	+	0.238677i	$0.0767137\pi$
$614$		0			0
$615$	−20.8796	+	36.1645i	−0.841945	+	1.45829i
$616$		0			0
$617$	−27.7049	−	15.9954i	−1.11536	−	0.643952i	−0.175145	−	0.984543i	$-0.556040\pi$
$617$	−27.7049	−	15.9954i	−1.11536	−	0.643952i	−0.940212	+	0.340591i	$0.889373\pi$
$618$		0			0
$619$			25.5705i			1.02777i	0.857860	+	0.513883i	$0.171793\pi$
$619$			25.5705i			1.02777i	−0.857860	+	0.513883i	$0.828207\pi$
$620$		0			0
$621$	11.6516	+	20.1811i	0.467561	+	0.809840i
$622$		0			0
$623$	−2.02278			−0.0810412
$624$		0			0
$625$	53.7340			2.14936
$626$		0			0
$627$	3.49072	+	6.04610i	0.139406	+	0.241458i
$628$		0			0
$629$		−	9.65802i		−	0.385090i
$630$		0			0
$631$	8.52063	+	4.91939i	0.339201	+	0.195838i	0.659919	−	0.751337i	$-0.270591\pi$
$631$	8.52063	+	4.91939i	0.339201	+	0.195838i	−0.320718	+	0.947175i	$0.603924\pi$
$632$		0			0
$633$	32.8995	−	56.9836i	1.30764	−	2.26490i
$634$		0			0
$635$	0.457026	−	0.263864i	0.0181365	−	0.0104711i
$636$		0			0
$637$	3.54025	+	0.683080i	0.140270	+	0.0270646i
$638$		0			0
$639$	−10.2294	+	5.90597i	−0.404670	+	0.233636i
$640$		0			0
$641$	−3.15099	+	5.45768i	−0.124457	+	0.215565i	−0.921520	−	0.388330i	$-0.873052\pi$
$641$	−3.15099	+	5.45768i	−0.124457	+	0.215565i	0.797064	+	0.603895i	$0.206385\pi$
$642$		0			0
$643$	−15.7251	−	9.07889i	−0.620138	−	0.358037i	0.156785	−	0.987633i	$-0.449887\pi$
$643$	−15.7251	−	9.07889i	−0.620138	−	0.358037i	−0.776923	+	0.629596i	$0.783220\pi$
$644$		0			0
$645$			106.062i			4.17620i
$646$		0			0
$647$	6.16059	+	10.6704i	0.242198	+	0.419499i	0.961340	−	0.275364i	$-0.0887984\pi$
$647$	6.16059	+	10.6704i	0.242198	+	0.419499i	−0.719142	+	0.694863i	$0.755465\pi$
$648$		0			0
$649$	0.335371			0.0131645
$650$		0			0
$651$	−28.2114			−1.10569
$652$		0			0
$653$	−22.0571	−	38.2041i	−0.863162	−	1.49504i	−0.868861	−	0.495057i	$-0.835147\pi$
$653$	−22.0571	−	38.2041i	−0.863162	−	1.49504i	0.00569838	−	0.999984i	$-0.498186\pi$
$654$		0			0
$655$		−	58.6727i		−	2.29253i
$656$		0			0
$657$	28.3948	+	16.3938i	1.10779	+	0.639582i
$658$		0			0
$659$	7.96359	−	13.7933i	0.310217	−	0.537312i	−0.668192	−	0.743989i	$-0.732931\pi$
$659$	7.96359	−	13.7933i	0.310217	−	0.537312i	0.978409	+	0.206677i	$0.0662648\pi$
$660$		0			0
$661$	7.38234	−	4.26220i	0.287140	−	0.165780i	−0.349511	−	0.936932i	$-0.613652\pi$
$661$	7.38234	−	4.26220i	0.287140	−	0.165780i	0.636651	+	0.771152i	$0.280319\pi$
$662$		0			0
$663$	−28.4164	+	32.7807i	−1.10360	+	1.27310i
$664$		0			0
$665$	−22.8969	+	13.2196i	−0.887905	+	0.512632i
$666$		0			0
$667$	−4.16280	+	7.21019i	−0.161184	+	0.279180i
$668$		0			0
$669$	27.6537	+	15.9658i	1.06915	+	0.617275i
$670$		0			0
$671$			4.78490i			0.184719i
$672$		0			0
$673$	8.21719	+	14.2326i	0.316749	+	0.548626i	0.979808	−	0.199942i	$-0.0640753\pi$
$673$	8.21719	+	14.2326i	0.316749	+	0.548626i	−0.663059	+	0.748568i	$0.730742\pi$
$674$		0			0
$675$	−65.4048			−2.51743
$676$		0			0
$677$	3.26825			0.125609			0.0628045	−	0.998026i	$-0.479996\pi$
$677$	3.26825			0.125609			0.0628045	+	0.998026i	$0.479996\pi$
$678$		0			0
$679$	−2.83662	−	4.91317i	−0.108859	−	0.188550i
$680$		0			0
$681$		−	10.5348i		−	0.403695i
$682$		0			0
$683$	9.68708	+	5.59284i	0.370666	+	0.214004i	0.673749	−	0.738960i	$-0.264683\pi$
$683$	9.68708	+	5.59284i	0.370666	+	0.214004i	−0.303083	+	0.952964i	$0.598016\pi$
$684$		0			0
$685$	−22.1794	+	38.4159i	−0.847432	+	1.46780i
$686$		0			0
$687$	−57.6650	+	33.2929i	−2.20006	+	1.27020i
$688$		0			0
$689$	−29.4451	+	33.9674i	−1.12177	+	1.29405i
$690$		0			0
$691$	−34.4498	+	19.8896i	−1.31053	+	0.756636i	−0.982184	−	0.187920i	$-0.939825\pi$
$691$	−34.4498	+	19.8896i	−1.31053	+	0.756636i	−0.328348	+	0.944557i	$0.606492\pi$
$692$		0			0
$693$	0.951194	−	1.64752i	0.0361329	−	0.0625840i
$694$		0			0
$695$	−23.8249	−	13.7553i	−0.903731	−	0.521769i
$696$		0			0
$697$			15.4063i			0.583557i
$698$		0			0
$699$	−34.7025	−	60.1065i	−1.31257	−	2.27343i
$700$		0			0
$701$	11.4338			0.431847			0.215924	−	0.976410i	$-0.430724\pi$
$701$	11.4338			0.431847			0.215924	+	0.976410i	$0.430724\pi$
$702$		0			0
$703$	−14.6584			−0.552852
$704$		0			0
$705$	0.937348	+	1.62353i	0.0353026	+	0.0611458i
$706$		0			0
$707$			1.57396i			0.0591950i
$708$		0			0
$709$	39.9889	+	23.0876i	1.50182	+	0.867074i	0.999998	+	0.00210074i	$0.000668686\pi$
$709$	39.9889	+	23.0876i	1.50182	+	0.867074i	0.501818	+	0.864973i	$0.332665\pi$
$710$		0			0
$711$	20.7747	−	35.9828i	0.779111	−	1.34946i
$712$		0			0
$713$	−36.1194	+	20.8535i	−1.35268	+	0.780971i
$714$		0			0
$715$	5.53396	+	1.06776i	0.206958	+	0.0399319i
$716$		0			0
$717$	−6.57316	+	3.79501i	−0.245479	+	0.141727i
$718$		0			0
$719$	−4.35110	+	7.53633i	−0.162269	+	0.281058i	−0.935682	−	0.352844i	$-0.885214\pi$
$719$	−4.35110	+	7.53633i	−0.162269	+	0.281058i	0.773413	+	0.633902i	$0.218548\pi$
$720$		0			0
$721$	−13.9507	−	8.05446i	−0.519553	−	0.299964i
$722$		0			0
$723$			40.7137i			1.51416i
$724$		0			0
$725$	−11.6837	−	20.2368i	−0.433923	−	0.751576i
$726$		0			0
$727$	−4.64525			−0.172283			−0.0861414	−	0.996283i	$-0.527454\pi$
$727$	−4.64525			−0.172283			−0.0861414	+	0.996283i	$0.527454\pi$
$728$		0			0
$729$	−43.1377			−1.59769
$730$		0			0
$731$	19.5650	+	33.8875i	0.723637	+	1.25338i
$732$		0			0
$733$			24.1498i			0.891994i	0.895034	+	0.445997i	$0.147151\pi$
$733$			24.1498i			0.891994i	−0.895034	+	0.445997i	$0.852849\pi$
$734$		0			0
$735$	10.0007	+	5.77390i	0.368881	+	0.212974i
$736$		0			0
$737$	−1.69018	+	2.92748i	−0.0622586	+	0.107835i
$738$		0			0
$739$	14.0044	−	8.08546i	0.515161	−	0.297428i	−0.219791	−	0.975547i	$-0.570538\pi$
$739$	14.0044	−	8.08546i	0.515161	−	0.297428i	0.734953	+	0.678118i	$0.237204\pi$
$740$		0			0
$741$	49.7527	+	43.1288i	1.82771	+	1.58438i
$742$		0			0
$743$	17.7990	−	10.2763i	0.652982	−	0.376999i	−0.136616	−	0.990624i	$-0.543623\pi$
$743$	17.7990	−	10.2763i	0.652982	−	0.376999i	0.789598	+	0.613625i	$0.210289\pi$
$744$		0			0
$745$	41.1526	−	71.2784i	1.50771	−	2.61144i
$746$		0			0
$747$	46.8619	+	27.0557i	1.71459	+	0.989918i
$748$		0			0
$749$		−	5.07589i		−	0.185469i
$750$		0			0
$751$	−6.57490	−	11.3881i	−0.239922	−	0.415556i	0.720770	−	0.693174i	$-0.243788\pi$
$751$	−6.57490	−	11.3881i	−0.239922	−	0.415556i	−0.960692	+	0.277618i	$0.910455\pi$
$752$		0			0
$753$	−42.4549			−1.54714
$754$		0			0
$755$	−12.5076			−0.455198
$756$		0			0
$757$	3.75689	+	6.50712i	0.136547	+	0.236505i	0.926187	−	0.377064i	$-0.123066\pi$
$757$	3.75689	+	6.50712i	0.136547	+	0.236505i	−0.789641	+	0.613570i	$0.789733\pi$
$758$		0			0
$759$		−	4.50798i		−	0.163629i
$760$		0			0
$761$	−4.12126	−	2.37941i	−0.149396	−	0.0862536i	0.423439	−	0.905925i	$-0.360823\pi$
$761$	−4.12126	−	2.37941i	−0.149396	−	0.0862536i	−0.572834	+	0.819671i	$0.694156\pi$
$762$		0			0
$763$	2.44696	−	4.23826i	0.0885858	−	0.153435i
$764$		0			0
$765$	−75.0719	+	43.3428i	−2.71423	+	1.56706i
$766$		0			0
$767$	2.98923	−	1.03390i	0.107935	−	0.0373319i
$768$		0			0
$769$	−18.5057	+	10.6843i	−0.667334	+	0.385285i	−0.795066	−	0.606523i	$-0.792564\pi$
$769$	−18.5057	+	10.6843i	−0.667334	+	0.385285i	0.127732	+	0.991809i	$0.459230\pi$
$770$		0			0
$771$	8.56001	−	14.8264i	0.308281	−	0.533959i
$772$		0			0
$773$	32.7649	+	18.9168i	1.17847	+	0.680391i	0.955661	−	0.294471i	$-0.0951433\pi$
$773$	32.7649	+	18.9168i	1.17847	+	0.680391i	0.222811	+	0.974862i	$0.428477\pi$
$774$		0			0
$775$		−	117.059i		−	4.20489i
$776$		0			0
$777$	3.20117	+	5.54459i	0.114841	+	0.198911i
$778$		0			0
$779$	23.3829			0.837779
$780$		0			0
$781$	0.907451			0.0324711
$782$		0			0
$783$	5.56460	+	9.63817i	0.198863	+	0.344440i
$784$		0			0
$785$		−	43.7380i		−	1.56108i
$786$		0			0
$787$	37.5066	+	21.6545i	1.33697	+	0.771899i	0.986357	−	0.164623i	$-0.0526407\pi$
$787$	37.5066	+	21.6545i	1.33697	+	0.771899i	0.350611	+	0.936521i	$0.385974\pi$
$788$		0			0
$789$	41.0184	−	71.0460i	1.46029	−	2.52930i
$790$		0			0
$791$	17.0787	−	9.86038i	0.607248	−	0.350595i
$792$		0			0
$793$	14.7511	+	42.6488i	0.523827	+	1.51450i
$794$		0			0
$795$	−124.687	+	71.9878i	−4.42218	+	2.55314i
$796$		0			0
$797$	4.49226	−	7.78082i	0.159124	−	0.275611i	−0.775429	−	0.631435i	$-0.782466\pi$
$797$	4.49226	−	7.78082i	0.159124	−	0.275611i	0.934553	+	0.355824i	$0.115800\pi$
$798$		0			0
$799$	0.598976	+	0.345819i	0.0211902	+	0.0122342i
$800$		0			0
$801$			10.0658i			0.355658i
$802$		0			0
$803$	−1.25945	−	2.18143i	−0.0444450	−	0.0769810i
$804$		0			0
$805$	17.0720			0.601708
$806$		0			0
$807$	−6.69917			−0.235822
$808$		0			0
$809$	7.59444	+	13.1539i	0.267006	+	0.462468i	0.968087	−	0.250613i	$-0.0806323\pi$
$809$	7.59444	+	13.1539i	0.267006	+	0.462468i	−0.701081	+	0.713082i	$0.747299\pi$
$810$		0			0
$811$			35.9705i			1.26309i	0.775337	+	0.631547i	$0.217580\pi$
$811$			35.9705i			1.26309i	−0.775337	+	0.631547i	$0.782420\pi$
$812$		0			0
$813$	−39.1301	−	22.5918i	−1.37235	−	0.792329i
$814$		0			0
$815$	13.5074	−	23.3955i	0.473143	−	0.819507i
$816$		0			0
$817$	51.4326	−	29.6946i	1.79940	−	1.03888i
$818$		0			0
$819$	3.39915	−	17.6170i	0.118776	−	0.615589i
$820$		0			0
$821$	18.8182	−	10.8647i	0.656761	−	0.379181i	−0.134281	−	0.990943i	$-0.542872\pi$
$821$	18.8182	−	10.8647i	0.656761	−	0.379181i	0.791042	+	0.611762i	$0.209539\pi$
$822$		0			0
$823$	−11.3241	+	19.6140i	−0.394735	+	0.683700i	−0.993067	−	0.117547i	$-0.962497\pi$
$823$	−11.3241	+	19.6140i	−0.394735	+	0.683700i	0.598333	+	0.801248i	$0.295830\pi$
$824$		0			0
$825$	10.9574	+	6.32627i	0.381488	+	0.220252i
$826$		0			0
$827$		−	54.1772i		−	1.88393i	−0.335717	−	0.941963i	$-0.608979\pi$
$827$		−	54.1772i		−	1.88393i	0.335717	−	0.941963i	$-0.391021\pi$
$828$		0			0
$829$	−14.9986	−	25.9784i	−0.520924	−	0.902266i	−0.999704	−	0.0243316i	$-0.992254\pi$
$829$	−14.9986	−	25.9784i	−0.520924	−	0.902266i	0.478780	−	0.877935i	$-0.341079\pi$
$830$		0			0
$831$	81.0499			2.81159
$832$		0			0
$833$	4.26037			0.147613
$834$		0			0
$835$	−22.0214	−	38.1422i	−0.762083	−	1.31997i
$836$		0			0
$837$			55.7517i			1.92706i
$838$		0			0
$839$	−2.99341	−	1.72825i	−0.103344	−	0.0596657i	0.447437	−	0.894315i	$-0.352337\pi$
$839$	−2.99341	−	1.72825i	−0.103344	−	0.0596657i	−0.550781	+	0.834650i	$0.685670\pi$
$840$		0			0
$841$	12.5119	−	21.6713i	0.431445	−	0.747285i
$842$		0			0
$843$	11.1362	−	6.42948i	0.383551	−	0.221443i
$844$		0			0
$845$	52.6171	−	7.54321i	1.81008	−	0.259494i
$846$		0			0
$847$	9.39971	−	5.42692i	0.322978	−	0.186471i
$848$		0			0
$849$	22.9077	−	39.6773i	0.786190	−	1.36172i
$850$		0			0
$851$	8.19699	+	4.73253i	0.280989	+	0.162229i
$852$		0			0
$853$			55.6739i			1.90624i	0.302598	+	0.953118i	$0.402146\pi$
$853$			55.6739i			1.90624i	−0.302598	+	0.953118i	$0.597854\pi$
$854$		0			0
$855$	65.7833	+	113.940i	2.24974	+	3.89667i
$856$		0			0
$857$	25.7094			0.878215			0.439107	−	0.898435i	$-0.355295\pi$
$857$	25.7094			0.878215			0.439107	+	0.898435i	$0.355295\pi$
$858$		0			0
$859$	−29.6248			−1.01079			−0.505393	−	0.862889i	$-0.668653\pi$
$859$	−29.6248			−1.01079			−0.505393	+	0.862889i	$0.668653\pi$
$860$		0			0
$861$	−5.10646	−	8.84466i	−0.174028	−	0.301425i
$862$		0			0
$863$		−	20.0127i		−	0.681240i	−0.940201	−	0.340620i	$-0.889363\pi$
$863$		−	20.0127i		−	0.681240i	0.940201	−	0.340620i	$-0.110637\pi$
$864$		0			0
$865$	33.2208	+	19.1800i	1.12954	+	0.652141i
$866$		0			0
$867$	−1.62499	+	2.81456i	−0.0551875	+	0.0955875i
$868$		0			0
$869$	−2.76437	+	1.59601i	−0.0937750	+	0.0541410i
$870$		0			0
$871$	−6.03995	+	31.3038i	−0.204656	+	1.06069i
$872$		0			0
$873$	−24.4489	+	14.1156i	−0.827471	+	0.477741i
$874$		0			0
$875$	−13.7358	+	23.7912i	−0.464356	+	0.804288i
$876$		0			0
$877$	−17.5974	−	10.1599i	−0.594222	−	0.343074i	0.172543	−	0.985002i	$-0.444802\pi$
$877$	−17.5974	−	10.1599i	−0.594222	−	0.343074i	−0.766765	+	0.641928i	$0.778135\pi$
$878$		0			0
$879$		−	10.2881i		−	0.347009i
$880$		0			0
$881$	2.79510	+	4.84125i	0.0941693	+	0.163106i	0.909262	−	0.416225i	$-0.136647\pi$
$881$	2.79510	+	4.84125i	0.0941693	+	0.163106i	−0.815092	+	0.579331i	$0.803314\pi$
$882$		0			0
$883$	−3.77692			−0.127103			−0.0635517	−	0.997979i	$-0.520243\pi$
$883$	−3.77692			−0.127103			−0.0635517	+	0.997979i	$0.520243\pi$
$884$		0			0
$885$	10.1303			0.340528
$886$		0			0
$887$	5.39436	+	9.34331i	0.181125	+	0.313718i	0.942264	−	0.334871i	$-0.108693\pi$
$887$	5.39436	+	9.34331i	0.181125	+	0.313718i	−0.761139	+	0.648589i	$0.775359\pi$
$888$		0			0
$889$			0.129065i			0.00432871i
$890$		0			0
$891$	−0.276130	−	0.159424i	−0.00925070	−	0.00534090i
$892$		0			0
$893$	0.524865	−	0.909092i	0.0175639	−	0.0304216i
$894$		0			0
$895$	38.0415	−	21.9633i	1.27159	−	0.734151i
$896$		0			0
$897$	−13.8974	−	40.1805i	−0.464021	−	1.34159i
$898$		0			0
$899$	−17.2500	+	9.95932i	−0.575321	+	0.332162i
$900$		0			0
$901$	−26.5587	+	46.0010i	−0.884799	+	1.53252i
$902$		0			0
$903$	−22.4642	−	12.9697i	−0.747562	−	0.431605i
$904$		0			0
$905$		−	56.8341i		−	1.88923i
$906$		0			0
$907$	11.5627	+	20.0272i	0.383934	+	0.664993i	0.991621	−	0.129184i	$-0.0412358\pi$
$907$	11.5627	+	20.0272i	0.383934	+	0.664993i	−0.607687	+	0.794177i	$0.707902\pi$
$908$		0			0
$909$	7.83237			0.259783
$910$		0			0
$911$	57.4207			1.90243			0.951217	−	0.308524i	$-0.0998349\pi$
$911$	57.4207			1.90243			0.951217	+	0.308524i	$0.0998349\pi$
$912$		0			0
$913$	−2.07855	−	3.60016i	−0.0687901	−	0.119148i
$914$		0			0
$915$			144.534i			4.77816i
$916$		0			0
$917$	12.4270	+	7.17472i	0.410375	+	0.236930i
$918$		0			0
$919$	−9.79173	+	16.9598i	−0.322999	+	0.559452i	−0.981105	−	0.193474i	$-0.938025\pi$
$919$	−9.79173	+	16.9598i	−0.322999	+	0.559452i	0.658106	+	0.752925i	$0.271358\pi$
$920$		0			0
$921$	−38.1464	+	22.0238i	−1.25697	+	0.725709i
$922$		0			0
$923$	8.08830	−	2.79753i	0.266230	−	0.0920819i
$924$		0			0
$925$	−23.0065	+	13.2828i	−0.756448	+	0.436735i
$926$		0			0
$927$	−40.0807	+	69.4218i	−1.31642	+	2.28011i
$928$		0			0
$929$	29.5758	+	17.0756i	0.970351	+	0.560232i	0.899343	−	0.437243i	$-0.144045\pi$
$929$	29.5758	+	17.0756i	0.970351	+	0.560232i	0.0710077	+	0.997476i	$0.477379\pi$
$930$		0			0
$931$		−	6.46615i		−	0.211920i
$932$		0			0
$933$	−44.8642	−	77.7071i	−1.46879	−	2.54402i
$934$		0			0
$935$	6.65961			0.217793
$936$		0			0
$937$	−38.4914			−1.25746			−0.628729	−	0.777624i	$-0.716425\pi$
$937$	−38.4914			−1.25746			−0.628729	+	0.777624i	$0.716425\pi$
$938$		0			0
$939$	8.20281	+	14.2077i	0.267689	+	0.463651i
$940$		0			0
$941$			14.0111i			0.456748i	0.973574	+	0.228374i	$0.0733409\pi$
$941$			14.0111i			0.456748i	−0.973574	+	0.228374i	$0.926659\pi$
$942$		0			0
$943$	−13.0757	−	7.54927i	−0.425804	−	0.245838i
$944$		0			0
$945$	11.4104	−	19.7635i	0.371181	−	0.642905i
$946$		0			0
$947$	−12.3370	+	7.12278i	−0.400899	+	0.231459i	−0.686872	−	0.726778i	$-0.741017\pi$
$947$	−12.3370	+	7.12278i	−0.400899	+	0.231459i	0.285973	+	0.958238i	$0.407683\pi$
$948$		0			0
$949$	−17.9508	−	15.5608i	−0.582706	−	0.505127i
$950$		0			0
$951$	65.6614	−	37.9096i	2.12922	−	1.22930i
$952$		0			0
$953$	−15.2257	+	26.3716i	−0.493208	+	0.854261i	−0.999969	−	0.00782534i	$-0.997509\pi$
$953$	−15.2257	+	26.3716i	−0.493208	+	0.854261i	0.506762	+	0.862086i	$0.330842\pi$
$954$		0			0
$955$	−19.3029	−	11.1445i	−0.624626	−	0.360628i
$956$		0			0
$957$		−	2.15294i		−	0.0695946i
$958$		0			0
$959$	−5.42437	−	9.39528i	−0.175162	−	0.303390i
$960$		0			0
$961$	−68.7823			−2.21878
$962$		0			0
$963$	−25.2587			−0.813950
$964$		0			0
$965$	29.4464	+	51.0027i	0.947914	+	1.64183i
$966$		0			0
$967$			2.49838i			0.0803425i	0.999193	+	0.0401713i	$0.0127903\pi$
$967$			2.49838i			0.0803425i	−0.999193	+	0.0401713i	$0.987210\pi$
$968$		0			0
$969$	67.3786	+	38.9011i	2.16451	+	1.24968i
$970$		0			0
$971$	0.870872	−	1.50839i	0.0279476	−	0.0484067i	−0.851713	−	0.524008i	$-0.824436\pi$
$971$	0.870872	−	1.50839i	0.0279476	−	0.0484067i	0.879661	+	0.475601i	$0.157770\pi$
$972$		0			0
$973$	5.82680	−	3.36411i	0.186799	−	0.107848i
$974$		0			0
$975$	117.169	+	22.6073i	3.75240	+	0.724012i
$976$		0			0
$977$	−22.3903	+	12.9270i	−0.716328	+	0.413572i	−0.813400	−	0.581705i	$-0.802386\pi$
$977$	−22.3903	+	12.9270i	−0.716328	+	0.413572i	0.0970715	+	0.995277i	$0.469052\pi$
$978$		0			0
$979$	0.386652	−	0.669701i	0.0123575	−	0.0214037i
$980$		0			0
$981$	−21.0904	−	12.1766i	−0.673366	−	0.388768i
$982$		0			0
$983$		−	5.96972i		−	0.190405i	−0.995458	−	0.0952023i	$-0.969650\pi$
$983$		−	5.96972i		−	0.190405i	0.995458	−	0.0952023i	$-0.0303498\pi$
$984$		0			0
$985$	1.39722	+	2.42006i	0.0445193	+	0.0771097i
$986$		0			0
$987$	−0.458490			−0.0145939
$988$		0			0
$989$	−38.3482			−1.21940
$990$		0			0
$991$	2.35598	+	4.08068i	0.0748402	+	0.129627i	0.901017	−	0.433784i	$-0.142822\pi$
$991$	2.35598	+	4.08068i	0.0748402	+	0.129627i	−0.826177	+	0.563411i	$0.809489\pi$
$992$		0			0
$993$			41.1266i			1.30511i
$994$		0			0
$995$	−3.41455	−	1.97139i	−0.108249	−	0.0624974i
$996$		0			0
$997$	20.4509	−	35.4219i	0.647685	−	1.12182i	−0.335989	−	0.941866i	$-0.609071\pi$
$997$	20.4509	−	35.4219i	0.647685	−	1.12182i	0.983674	−	0.179958i	$-0.0575961\pi$
$998$		0			0
$999$	10.9573	−	6.32618i	0.346673	−	0.200152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.g.673.2		24
4.3	odd	2		728.2.bm.c.673.11	yes	24
13.4	even	6	inner	1456.2.cc.g.225.2		24
52.11	even	12		9464.2.a.bl.1.2		12
52.15	even	12		9464.2.a.bm.1.2		12
52.43	odd	6		728.2.bm.c.225.11	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.bm.c.225.11	✓	24	52.43	odd	6
728.2.bm.c.673.11	yes	24	4.3	odd	2
1456.2.cc.g.225.2		24	13.4	even	6	inner
1456.2.cc.g.673.2		24	1.1	even	1	trivial
9464.2.a.bl.1.2		12	52.11	even	12
9464.2.a.bm.1.2		12	52.15	even	12

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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.41211 - 2.44584i) q^{3} +4.08885i q^{5} +(-0.866025 - 0.500000i) q^{7} +(-2.48810 + 4.30952i) q^{9} +O(q^{10})\)	\(q+(-1.41211 - 2.44584i) q^{3} +4.08885i q^{5} +(-0.866025 - 0.500000i) q^{7} +(-2.48810 + 4.30952i) q^{9} +(0.331079 - 0.191148i) q^{11} +(2.36169 - 2.72441i) q^{13} +(10.0007 - 5.77390i) q^{15} +(2.13018 - 3.68959i) q^{17} +(-5.59985 - 3.23308i) q^{19} +2.82422i q^{21} +(2.08763 + 3.61588i) q^{23} -11.7187 q^{25} +5.58125 q^{27} +(0.997018 + 1.72689i) q^{29} +9.98911i q^{31} +(-0.935039 - 0.539845i) q^{33} +(2.04442 - 3.54105i) q^{35} +(1.96323 - 1.13347i) q^{37} +(-9.99845 - 1.92917i) q^{39} +(-3.13172 + 1.80810i) q^{41} +(-4.59232 + 7.95413i) q^{43} +(-17.6210 - 10.1735i) q^{45} +0.162342i q^{47} +(0.500000 + 0.866025i) q^{49} -12.0322 q^{51} -12.4678 q^{53} +(0.781577 + 1.35373i) q^{55} +18.2618i q^{57} +(0.759723 + 0.438626i) q^{59} +(-6.25809 + 10.8393i) q^{61} +(4.30952 - 2.48810i) q^{63} +(11.1397 + 9.65660i) q^{65} +(-7.65760 + 4.42112i) q^{67} +(5.89592 - 10.2120i) q^{69} +(2.05567 + 1.18684i) q^{71} -6.58886i q^{73} +(16.5481 + 28.6621i) q^{75} -0.382297 q^{77} -8.34960 q^{79} +(-0.417016 - 0.722292i) q^{81} -10.8740i q^{83} +(15.0862 + 8.71000i) q^{85} +(2.81580 - 4.87710i) q^{87} +(1.75178 - 1.01139i) q^{89} +(-3.40749 + 1.17856i) q^{91} +(24.4318 - 14.1057i) q^{93} +(13.2196 - 22.8969i) q^{95} +(4.91317 + 2.83662i) q^{97} +1.90239i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{3} - 18 q^{9}+O(q^{10}) \) 24 * q + 2 * q^3 - 18 * q^9	\( 24 q + 2 q^{3} - 18 q^{9} - 12 q^{11} + 8 q^{17} + 12 q^{19} - 2 q^{23} - 28 q^{25} + 20 q^{27} + 2 q^{29} - 18 q^{33} + 8 q^{35} + 60 q^{37} - 18 q^{39} - 6 q^{41} - 24 q^{43} - 72 q^{45} + 12 q^{49} + 72 q^{51} - 48 q^{53} + 44 q^{55} + 12 q^{59} - 30 q^{61} - 12 q^{63} + 10 q^{65} - 78 q^{67} + 36 q^{69} + 36 q^{71} - 22 q^{75} + 4 q^{77} - 20 q^{79} - 40 q^{81} - 6 q^{85} + 20 q^{87} + 108 q^{89} - 6 q^{91} + 30 q^{93} - 18 q^{95} - 54 q^{97}+O(q^{100}) \) 24 * q + 2 * q^3 - 18 * q^9 - 12 * q^11 + 8 * q^17 + 12 * q^19 - 2 * q^23 - 28 * q^25 + 20 * q^27 + 2 * q^29 - 18 * q^33 + 8 * q^35 + 60 * q^37 - 18 * q^39 - 6 * q^41 - 24 * q^43 - 72 * q^45 + 12 * q^49 + 72 * q^51 - 48 * q^53 + 44 * q^55 + 12 * q^59 - 30 * q^61 - 12 * q^63 + 10 * q^65 - 78 * q^67 + 36 * q^69 + 36 * q^71 - 22 * q^75 + 4 * q^77 - 20 * q^79 - 40 * q^81 - 6 * q^85 + 20 * q^87 + 108 * q^89 - 6 * q^91 + 30 * q^93 - 18 * q^95 - 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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