LMFDB - Embedded newform 1440.2.cc.a.1391.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1440,2,Mod(911,1440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1440, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("1440.911");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1440 = 2^{5} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1440.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:	$11.4984578911$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 360)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1391.9
Character	$\chi$	$=$	1440.1391
Dual form			1440.2.cc.a.911.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.801968 - 1.53520i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-4.07138 + 2.35061i) q^{7} +(-1.71369 + 2.46237i) q^{9} +O(q^{10})$	\(q+(-0.801968 - 1.53520i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-4.07138 + 2.35061i) q^{7} +(-1.71369 + 2.46237i) q^{9} +(3.19675 - 1.84565i) q^{11} +(2.94278 + 1.69902i) q^{13} +(1.73051 + 0.0730766i) q^{15} -3.19988i q^{17} +0.184741 q^{19} +(6.87379 + 4.36528i) q^{21} +(-1.68941 + 2.92615i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(5.15456 + 0.656128i) q^{27} +(-4.71642 - 8.16907i) q^{29} +(-1.31877 - 0.761389i) q^{31} +(-5.39713 - 3.42751i) q^{33} -4.70123i q^{35} -2.21087i q^{37} +(0.248316 - 5.88032i) q^{39} +(7.97131 + 4.60224i) q^{41} +(-5.05231 - 8.75086i) q^{43} +(-1.27563 - 2.71529i) q^{45} +(-3.20071 - 5.54379i) q^{47} +(7.55077 - 13.0783i) q^{49} +(-4.91246 + 2.56620i) q^{51} +0.652400 q^{53} +3.69129i q^{55} +(-0.148157 - 0.283616i) q^{57} +(-7.25989 - 4.19150i) q^{59} +(5.59632 - 3.23103i) q^{61} +(1.18903 - 14.0535i) q^{63} +(-2.94278 + 1.69902i) q^{65} +(0.725538 - 1.25667i) q^{67} +(5.84709 + 0.246913i) q^{69} +11.5995 q^{71} -15.3080 q^{73} +(-0.928540 + 1.46213i) q^{75} +(-8.67680 + 15.0287i) q^{77} +(-2.19259 + 1.26589i) q^{79} +(-3.12650 - 8.43949i) q^{81} +(3.86408 - 2.23093i) q^{83} +(2.77118 + 1.59994i) q^{85} +(-8.75877 + 13.7920i) q^{87} -4.32981i q^{89} -15.9749 q^{91} +(-0.111279 + 2.63518i) q^{93} +(-0.0923707 + 0.159991i) q^{95} +(-8.59159 - 14.8811i) q^{97} +(-0.933599 + 11.0345i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{5}+O(q^{10}) $ 48 * q - 24 * q^5	$ 48 q - 24 q^{5} - 4 q^{21} - 24 q^{25} - 12 q^{27} - 8 q^{33} - 16 q^{39} + 12 q^{41} - 12 q^{47} + 24 q^{49} + 20 q^{51} + 4 q^{57} + 36 q^{59} + 12 q^{61} - 56 q^{63} - 40 q^{69} - 8 q^{81} + 60 q^{83} - 36 q^{87} + 16 q^{99}+O(q^{100}) $ 48 * q - 24 * q^5 - 4 * q^21 - 24 * q^25 - 12 * q^27 - 8 * q^33 - 16 * q^39 + 12 * q^41 - 12 * q^47 + 24 * q^49 + 20 * q^51 + 4 * q^57 + 36 * q^59 + 12 * q^61 - 56 * q^63 - 40 * q^69 - 8 * q^81 + 60 * q^83 - 36 * q^87 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$991$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.801968	−	1.53520i	−0.463017	−	0.886350i
$3$	−0.801968	−	1.53520i	−0.463017	−	0.886350i
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−4.07138	+	2.35061i	−1.53884	+	0.888449i	−0.539931	+	0.841709i	$0.681550\pi$
$7$	−4.07138	+	2.35061i	−1.53884	+	0.888449i	−0.998907	+	0.0467391i	$0.985117\pi$
$8$		0			0
$9$	−1.71369	+	2.46237i	−0.571231	+	0.820789i
$10$		0			0
$11$	3.19675	−	1.84565i	0.963857	−	0.556483i	0.0664992	−	0.997786i	$-0.478817\pi$
$11$	3.19675	−	1.84565i	0.963857	−	0.556483i	0.897358	+	0.441303i	$0.145484\pi$
$12$		0			0
$13$	2.94278	+	1.69902i	0.816181	+	0.471222i	0.849098	−	0.528236i	$-0.177146\pi$
$13$	2.94278	+	1.69902i	0.816181	+	0.471222i	−0.0329169	+	0.999458i	$0.510480\pi$
$14$		0			0
$15$	1.73051	+	0.0730766i	0.446815	+	0.0188683i
$16$		0			0
$17$		−	3.19988i		−	0.776084i	−0.921642	−	0.388042i	$-0.873151\pi$
$17$		−	3.19988i		−	0.776084i	0.921642	−	0.388042i	$-0.126849\pi$
$18$		0			0
$19$	0.184741			0.0423826			0.0211913	−	0.999775i	$-0.493254\pi$
$19$	0.184741			0.0423826			0.0211913	+	0.999775i	$0.493254\pi$
$20$		0			0
$21$	6.87379	+	4.36528i	1.49998	+	0.952582i
$22$		0			0
$23$	−1.68941	+	2.92615i	−0.352267	+	0.610145i	−0.986646	−	0.162877i	$-0.947923\pi$
$23$	−1.68941	+	2.92615i	−0.352267	+	0.610145i	0.634379	+	0.773022i	$0.281256\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	5.15456	+	0.656128i	0.991996	+	0.126272i
$28$		0			0
$29$	−4.71642	−	8.16907i	−0.875817	−	1.51696i	−0.855890	−	0.517157i	$-0.826990\pi$
$29$	−4.71642	−	8.16907i	−0.875817	−	1.51696i	−0.0199263	−	0.999801i	$-0.506343\pi$
$30$		0			0
$31$	−1.31877	−	0.761389i	−0.236857	−	0.136750i	0.376874	−	0.926264i	$-0.376999\pi$
$31$	−1.31877	−	0.761389i	−0.236857	−	0.136750i	−0.613731	+	0.789515i	$0.710332\pi$
$32$		0			0
$33$	−5.39713	−	3.42751i	−0.939521	−	0.596654i
$34$		0			0
$35$		−	4.70123i		−	0.794653i
$36$		0			0
$37$		−	2.21087i		−	0.363465i	−0.983348	−	0.181732i	$-0.941830\pi$
$37$		−	2.21087i		−	0.363465i	0.983348	−	0.181732i	$-0.0581704\pi$
$38$		0			0
$39$	0.248316	−	5.88032i	0.0397625	−	0.941605i
$40$		0			0
$41$	7.97131	+	4.60224i	1.24491	+	0.718749i	0.970090	−	0.242746i	$-0.0780483\pi$
$41$	7.97131	+	4.60224i	1.24491	+	0.718749i	0.274820	+	0.961496i	$0.411382\pi$
$42$		0			0
$43$	−5.05231	−	8.75086i	−0.770470	−	1.33449i	−0.937306	−	0.348509i	$-0.886688\pi$
$43$	−5.05231	−	8.75086i	−0.770470	−	1.33449i	0.166836	−	0.985985i	$-0.446645\pi$
$44$		0			0
$45$	−1.27563	−	2.71529i	−0.190159	−	0.404771i
$46$		0			0
$47$	−3.20071	−	5.54379i	−0.466872	−	0.808645i	0.532412	−	0.846485i	$-0.321286\pi$
$47$	−3.20071	−	5.54379i	−0.466872	−	0.808645i	−0.999284	+	0.0378398i	$0.987952\pi$
$48$		0			0
$49$	7.55077	−	13.0783i	1.07868	−	1.86833i
$50$		0			0
$51$	−4.91246	+	2.56620i	−0.687882	+	0.359340i
$52$		0			0
$53$	0.652400			0.0896140			0.0448070	−	0.998996i	$-0.485733\pi$
$53$	0.652400			0.0896140			0.0448070	+	0.998996i	$0.485733\pi$
$54$		0			0
$55$			3.69129i			0.497734i
$56$		0			0
$57$	−0.148157	−	0.283616i	−0.0196238	−	0.0375658i
$58$		0			0
$59$	−7.25989	−	4.19150i	−0.945157	−	0.545687i	−0.0535842	−	0.998563i	$-0.517065\pi$
$59$	−7.25989	−	4.19150i	−0.945157	−	0.545687i	−0.891573	+	0.452876i	$0.850398\pi$
$60$		0			0
$61$	5.59632	−	3.23103i	0.716535	−	0.413692i	−0.0969412	−	0.995290i	$-0.530906\pi$
$61$	5.59632	−	3.23103i	0.716535	−	0.413692i	0.813476	+	0.581599i	$0.197573\pi$
$62$		0			0
$63$	1.18903	−	14.0535i	0.149804	−	1.77057i
$64$		0			0
$65$	−2.94278	+	1.69902i	−0.365007	+	0.210737i
$66$		0			0
$67$	0.725538	−	1.25667i	0.0886386	−	0.153527i	−0.818297	−	0.574795i	$-0.805082\pi$
$67$	0.725538	−	1.25667i	0.0886386	−	0.153527i	0.906936	+	0.421269i	$0.138415\pi$
$68$		0			0
$69$	5.84709	+	0.246913i	0.703907	+	0.0297249i
$70$		0			0
$71$	11.5995			1.37661			0.688306	−	0.725421i	$-0.258355\pi$
$71$	11.5995			1.37661			0.688306	+	0.725421i	$0.258355\pi$
$72$		0			0
$73$	−15.3080			−1.79166			−0.895832	−	0.444393i	$-0.853419\pi$
$73$	−15.3080			−1.79166			−0.895832	+	0.444393i	$0.853419\pi$
$74$		0			0
$75$	−0.928540	+	1.46213i	−0.107219	+	0.168832i
$76$		0			0
$77$	−8.67680	+	15.0287i	−0.988813	+	1.71268i
$78$		0			0
$79$	−2.19259	+	1.26589i	−0.246686	+	0.142424i	−0.618246	−	0.785985i	$-0.712156\pi$
$79$	−2.19259	+	1.26589i	−0.246686	+	0.142424i	0.371560	+	0.928409i	$0.378823\pi$
$80$		0			0
$81$	−3.12650	−	8.43949i	−0.347389	−	0.937721i
$82$		0			0
$83$	3.86408	−	2.23093i	0.424138	−	0.244876i	−0.272708	−	0.962097i	$-0.587919\pi$
$83$	3.86408	−	2.23093i	0.424138	−	0.244876i	0.696846	+	0.717221i	$0.254586\pi$
$84$		0			0
$85$	2.77118	+	1.59994i	0.300576	+	0.173538i
$86$		0			0
$87$	−8.75877	+	13.7920i	−0.939038	+	1.47866i
$88$		0			0
$89$		−	4.32981i		−	0.458959i	−0.973313	−	0.229480i	$-0.926298\pi$
$89$		−	4.32981i		−	0.458959i	0.973313	−	0.229480i	$-0.0737024\pi$
$90$		0			0
$91$	−15.9749			−1.67463
$92$		0			0
$93$	−0.111279	+	2.63518i	−0.0115391	+	0.273256i
$94$		0			0
$95$	−0.0923707	+	0.159991i	−0.00947703	+	0.0164147i
$96$		0			0
$97$	−8.59159	−	14.8811i	−0.872344	−	1.51094i	−0.859565	−	0.511026i	$-0.829266\pi$
$97$	−8.59159	−	14.8811i	−0.872344	−	1.51094i	−0.0127789	−	0.999918i	$-0.504068\pi$
$98$		0			0
$99$	−0.933599	+	11.0345i	−0.0938302	+	1.10900i
$100$		0			0
$101$	1.01593	+	1.75965i	0.101089	+	0.175091i	0.912134	−	0.409893i	$-0.134434\pi$
$101$	1.01593	+	1.75965i	0.101089	+	0.175091i	−0.811045	+	0.584984i	$0.801101\pi$
$102$		0			0
$103$	−1.17647	−	0.679237i	−0.115921	−	0.0669272i	0.440918	−	0.897547i	$-0.354653\pi$
$103$	−1.17647	−	0.679237i	−0.115921	−	0.0669272i	−0.556840	+	0.830620i	$0.687986\pi$
$104$		0			0
$105$	−7.21734	+	3.77023i	−0.704340	+	0.367937i
$106$		0			0
$107$			10.2120i			0.987227i	0.869681	+	0.493614i	$0.164324\pi$
$107$			10.2120i			0.987227i	−0.869681	+	0.493614i	$0.835676\pi$
$108$		0			0
$109$		−	11.9528i		−	1.14487i	−0.819950	−	0.572435i	$-0.805999\pi$
$109$		−	11.9528i		−	1.14487i	0.819950	−	0.572435i	$-0.194001\pi$
$110$		0			0
$111$	−3.39413	+	1.77305i	−0.322157	+	0.168290i
$112$		0			0
$113$	8.07593	+	4.66264i	0.759720	+	0.438625i	0.829195	−	0.558959i	$-0.188799\pi$
$113$	8.07593	+	4.66264i	0.759720	+	0.438625i	−0.0694752	+	0.997584i	$0.522132\pi$
$114$		0			0
$115$	−1.68941	−	2.92615i	−0.157539	−	0.272865i
$116$		0			0
$117$	−9.22663	+	4.33462i	−0.853002	+	0.400735i
$118$		0			0
$119$	7.52168	+	13.0279i	0.689511	+	1.19427i
$120$		0			0
$121$	1.31282	−	2.27387i	0.119347	−	0.206715i
$122$		0			0
$123$	0.672632	−	15.9284i	0.0606492	−	1.43622i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$			3.88163i			0.344439i	0.985059	+	0.172220i	$0.0550939\pi$
$127$			3.88163i			0.344439i	−0.985059	+	0.172220i	$0.944906\pi$
$128$		0			0
$129$	−9.38255	+	14.7742i	−0.826087	+	1.30080i
$130$		0			0
$131$	9.59245	+	5.53820i	0.838096	+	0.483875i	0.856617	−	0.515953i	$-0.172562\pi$
$131$	9.59245	+	5.53820i	0.838096	+	0.483875i	−0.0185204	+	0.999828i	$0.505896\pi$
$132$		0			0
$133$	−0.752153	+	0.434256i	−0.0652199	+	0.0376547i
$134$		0			0
$135$	−3.14550	+	4.13592i	−0.270722	+	0.355963i
$136$		0			0
$137$	3.98251	−	2.29930i	0.340249	−	0.196443i	−0.320133	−	0.947373i	$-0.603728\pi$
$137$	3.98251	−	2.29930i	0.340249	−	0.196443i	0.660382	+	0.750930i	$0.270394\pi$
$138$		0			0
$139$	5.91862	−	10.2514i	0.502011	−	0.869508i	−0.497986	−	0.867185i	$-0.665927\pi$
$139$	5.91862	−	10.2514i	0.502011	−	0.869508i	0.999997	−	0.00232356i	$-0.000739612\pi$
$140$		0			0
$141$	−5.94398	+	9.35969i	−0.500573	+	0.788228i
$142$		0			0
$143$	12.5431			1.04891
$144$		0			0
$145$	9.43283			0.783354
$146$		0			0
$147$	−26.1333	−	1.10357i	−2.15544	−	0.0910208i
$148$		0			0
$149$	3.42256	−	5.92805i	0.280387	−	0.485645i	−0.691093	−	0.722766i	$-0.742870\pi$
$149$	3.42256	−	5.92805i	0.280387	−	0.485645i	0.971480	+	0.237121i	$0.0762038\pi$
$150$		0			0
$151$	14.5652	−	8.40923i	1.18530	−	0.684333i	0.228065	−	0.973646i	$-0.426760\pi$
$151$	14.5652	−	8.40923i	1.18530	−	0.684333i	0.957235	+	0.289313i	$0.0934268\pi$
$152$		0			0
$153$	7.87927	+	5.48361i	0.637002	+	0.443324i
$154$		0			0
$155$	1.31877	−	0.761389i	0.105926	−	0.0611563i
$156$		0			0
$157$	−13.8050	−	7.97033i	−1.10176	−	0.636102i	−0.165077	−	0.986281i	$-0.552787\pi$
$157$	−13.8050	−	7.97033i	−1.10176	−	0.636102i	−0.936683	+	0.350179i	$0.886121\pi$
$158$		0			0
$159$	−0.523204	−	1.00157i	−0.0414928	−	0.0794293i
$160$		0			0
$161$		−	15.8846i		−	1.25189i
$162$		0			0
$163$	5.41232			0.423925			0.211963	−	0.977278i	$-0.432014\pi$
$163$	5.41232			0.423925			0.211963	+	0.977278i	$0.432014\pi$
$164$		0			0
$165$	5.66688	−	2.96030i	0.441166	−	0.230459i
$166$		0			0
$167$	1.12519	−	1.94888i	0.0870697	−	0.150809i	−0.819202	−	0.573506i	$-0.805583\pi$
$167$	1.12519	−	1.94888i	0.0870697	−	0.150809i	0.906271	+	0.422697i	$0.138916\pi$
$168$		0			0
$169$	−0.726690	−	1.25866i	−0.0558992	−	0.0968203i
$170$		0			0
$171$	−0.316590	+	0.454901i	−0.0242103	+	0.0347872i
$172$		0			0
$173$	−2.58385	−	4.47535i	−0.196446	−	0.340255i	0.750927	−	0.660385i	$-0.229607\pi$
$173$	−2.58385	−	4.47535i	−0.196446	−	0.340255i	−0.947374	+	0.320130i	$0.896273\pi$
$174$		0			0
$175$	4.07138	+	2.35061i	0.307768	+	0.177690i
$176$		0			0
$177$	−0.612601	+	14.5069i	−0.0460459	+	1.09040i
$178$		0			0
$179$		−	15.9037i		−	1.18870i	−0.804207	−	0.594349i	$-0.797410\pi$
$179$		−	15.9037i		−	1.18870i	0.804207	−	0.594349i	$-0.202590\pi$
$180$		0			0
$181$		−	15.1761i		−	1.12803i	−0.825763	−	0.564017i	$-0.809255\pi$
$181$		−	15.1761i		−	1.12803i	0.825763	−	0.564017i	$-0.190745\pi$
$182$		0			0
$183$	−9.44836	−	6.00029i	−0.698443	−	0.443554i
$184$		0			0
$185$	1.91467	+	1.10543i	0.140769	+	0.0812732i
$186$		0			0
$187$	−5.90584	−	10.2292i	−0.431878	−	0.748034i
$188$		0			0
$189$	−22.5285	+	9.44503i	−1.63871	+	0.687025i
$190$		0			0
$191$	−3.74786	−	6.49149i	−0.271186	−	0.469708i	0.697980	−	0.716117i	$-0.254082\pi$
$191$	−3.74786	−	6.49149i	−0.271186	−	0.469708i	−0.969166	+	0.246410i	$0.920749\pi$
$192$		0			0
$193$	−9.69314	+	16.7890i	−0.697728	+	1.20850i	0.271525	+	0.962431i	$0.412472\pi$
$193$	−9.69314	+	16.7890i	−0.697728	+	1.20850i	−0.969252	+	0.246069i	$0.920861\pi$
$194$		0			0
$195$	4.96835	+	3.15521i	0.355791	+	0.225949i
$196$		0			0
$197$	0.617357			0.0439849			0.0219924	−	0.999758i	$-0.492999\pi$
$197$	0.617357			0.0439849			0.0219924	+	0.999758i	$0.492999\pi$
$198$		0			0
$199$			0.851922i			0.0603912i	0.999544	+	0.0301956i	$0.00961301\pi$
$199$			0.851922i			0.0603912i	−0.999544	+	0.0301956i	$0.990387\pi$
$200$		0			0
$201$	−2.51110	−	0.106040i	−0.177119	−	0.00747946i
$202$		0			0
$203$	38.4047	+	22.1729i	2.69548	+	1.55624i
$204$		0			0
$205$	−7.97131	+	4.60224i	−0.556741	+	0.321434i
$206$		0			0
$207$	−4.31012	−	9.17449i	−0.299574	−	0.637671i
$208$		0			0
$209$	0.590573	−	0.340967i	0.0408508	−	0.0235852i
$210$		0			0
$211$	3.16321	−	5.47885i	0.217765	−	0.377179i	−0.736360	−	0.676590i	$-0.763457\pi$
$211$	3.16321	−	5.47885i	0.217765	−	0.377179i	0.954124	+	0.299411i	$0.0967902\pi$
$212$		0			0
$213$	−9.30246	−	17.8076i	−0.637394	−	1.22016i
$214$		0			0
$215$	10.1046			0.689129
$216$		0			0
$217$	7.15893			0.485980
$218$		0			0
$219$	12.2765	+	23.5009i	0.829570	+	1.58804i
$220$		0			0
$221$	5.43664	−	9.41654i	0.365708	−	0.633425i
$222$		0			0
$223$	−12.4436	+	7.18433i	−0.833286	+	0.481098i	−0.854977	−	0.518667i	$-0.826429\pi$
$223$	−12.4436	+	7.18433i	−0.833286	+	0.481098i	0.0216902	+	0.999765i	$0.493095\pi$
$224$		0			0
$225$	2.98932	+	0.252919i	0.199288	+	0.0168613i
$226$		0			0
$227$	8.80058	−	5.08102i	0.584115	−	0.337239i	−0.178652	−	0.983912i	$-0.557174\pi$
$227$	8.80058	−	5.08102i	0.584115	−	0.337239i	0.762767	+	0.646673i	$0.223840\pi$
$228$		0			0
$229$	19.4053	+	11.2037i	1.28234	+	0.740359i	0.977275	−	0.211974i	$-0.0679891\pi$
$229$	19.4053	+	11.2037i	1.28234	+	0.740359i	0.305063	+	0.952332i	$0.401322\pi$
$230$		0			0
$231$	30.0306	+	1.26814i	1.97587	+	0.0834376i
$232$		0			0
$233$			3.15942i			0.206981i	0.994630	+	0.103490i	$0.0330011\pi$
$233$			3.15942i			0.206981i	−0.994630	+	0.103490i	$0.966999\pi$
$234$		0			0
$235$	6.40142			0.417583
$236$		0			0
$237$	3.70179	+	2.35087i	0.240457	+	0.152705i
$238$		0			0
$239$	7.27012	−	12.5922i	0.470265	−	0.814523i	−0.529157	−	0.848524i	$-0.677492\pi$
$239$	7.27012	−	12.5922i	0.470265	−	0.814523i	0.999422	+	0.0340013i	$0.0108250\pi$
$240$		0			0
$241$	−3.13622	−	5.43210i	−0.202022	−	0.349912i	0.747158	−	0.664647i	$-0.231418\pi$
$241$	−3.13622	−	5.43210i	−0.202022	−	0.349912i	−0.949180	+	0.314734i	$0.898085\pi$
$242$		0			0
$243$	−10.4490	+	11.5680i	−0.670302	+	0.742089i
$244$		0			0
$245$	7.55077	+	13.0783i	0.482401	+	0.835543i
$246$		0			0
$247$	0.543654	+	0.313879i	0.0345919	+	0.0199716i
$248$		0			0
$249$	−6.52380	−	4.14301i	−0.413429	−	0.262553i
$250$		0			0
$251$			18.7861i			1.18577i	0.805287	+	0.592885i	$0.202011\pi$
$251$			18.7861i			1.18577i	−0.805287	+	0.592885i	$0.797989\pi$
$252$		0			0
$253$			12.4722i			0.784123i
$254$		0			0
$255$	0.233836	−	5.53742i	0.0146434	−	0.346766i
$256$		0			0
$257$	22.7852	+	13.1551i	1.42130	+	0.820590i	0.996410	−	0.0846537i	$-0.0269784\pi$
$257$	22.7852	+	13.1551i	1.42130	+	0.820590i	0.424893	+	0.905244i	$0.360312\pi$
$258$		0			0
$259$	5.19690	+	9.00129i	0.322920	+	0.559313i
$260$		0			0
$261$	28.1978	+	2.38574i	1.74540	+	0.147674i
$262$		0			0
$263$	3.46251	+	5.99725i	0.213508	+	0.369806i	0.952810	−	0.303568i	$-0.0981778\pi$
$263$	3.46251	+	5.99725i	0.213508	+	0.369806i	−0.739302	+	0.673374i	$0.764844\pi$
$264$		0			0
$265$	−0.326200	+	0.564995i	−0.0200383	+	0.0347073i
$266$		0			0
$267$	−6.64714	+	3.47237i	−0.406798	+	0.212506i
$268$		0			0
$269$	−21.6782			−1.32174			−0.660871	−	0.750500i	$-0.729813\pi$
$269$	−21.6782			−1.32174			−0.660871	+	0.750500i	$0.729813\pi$
$270$		0			0
$271$			2.04312i			0.124111i	0.998073	+	0.0620554i	$0.0197656\pi$
$271$			2.04312i			0.124111i	−0.998073	+	0.0620554i	$0.980234\pi$
$272$		0			0
$273$	12.8114	+	24.5247i	0.775380	+	1.48430i
$274$		0			0
$275$	−3.19675	−	1.84565i	−0.192771	−	0.111297i
$276$		0			0
$277$	−19.0765	+	11.0138i	−1.14619	+	0.661755i	−0.947957	−	0.318399i	$-0.896855\pi$
$277$	−19.0765	+	11.0138i	−1.14619	+	0.661755i	−0.198237	+	0.980154i	$0.563521\pi$
$278$		0			0
$279$	4.13478	−	1.94250i	0.247543	−	0.116294i
$280$		0			0
$281$	−7.10884	+	4.10429i	−0.424078	+	0.244842i	−0.696821	−	0.717246i	$-0.745403\pi$
$281$	−7.10884	+	4.10429i	−0.424078	+	0.244842i	0.272743	+	0.962087i	$0.412069\pi$
$282$		0			0
$283$	10.4458	−	18.0927i	0.620939	−	1.07550i	−0.368372	−	0.929679i	$-0.620085\pi$
$283$	10.4458	−	18.0927i	0.620939	−	1.07550i	0.989311	−	0.145820i	$-0.0465821\pi$
$284$		0			0
$285$	0.319697	+	0.0135003i	0.0189372	+	0.000799687i
$286$		0			0
$287$	−43.2724			−2.55429
$288$		0			0
$289$	6.76078			0.397693
$290$		0			0
$291$	−15.9553	+	25.1240i	−0.935315	+	1.47279i
$292$		0			0
$293$	0.921400	−	1.59591i	0.0538288	−	0.0932342i	−0.837855	−	0.545892i	$-0.816191\pi$
$293$	0.921400	−	1.59591i	0.0538288	−	0.0932342i	0.891684	+	0.452658i	$0.149524\pi$
$294$		0			0
$295$	7.25989	−	4.19150i	0.422687	−	0.244039i
$296$		0			0
$297$	17.6888	−	7.41602i	1.02641	−	0.430321i
$298$		0			0
$299$	−9.94316	+	5.74068i	−0.575028	+	0.331992i
$300$		0			0
$301$	41.1398	+	23.7521i	2.37126	+	1.36905i
$302$		0			0
$303$	1.88667	−	2.97084i	0.108386	−	0.170670i
$304$		0			0
$305$			6.46207i			0.370017i
$306$		0			0
$307$	10.1957			0.581899			0.290949	−	0.956738i	$-0.406029\pi$
$307$	10.1957			0.581899			0.290949	+	0.956738i	$0.406029\pi$
$308$		0			0
$309$	−0.0992725	+	2.35085i	−0.00564742	+	0.133735i
$310$		0			0
$311$	−10.2923	+	17.8267i	−0.583621	+	1.01086i	0.411425	+	0.911444i	$0.365031\pi$
$311$	−10.2923	+	17.8267i	−0.583621	+	1.01086i	−0.995046	+	0.0994177i	$0.968302\pi$
$312$		0			0
$313$	2.71867	+	4.70888i	0.153668	+	0.266161i	0.932573	−	0.360981i	$-0.117558\pi$
$313$	2.71867	+	4.70888i	0.153668	+	0.266161i	−0.778905	+	0.627142i	$0.784225\pi$
$314$		0			0
$315$	11.5761	+	8.05647i	0.652242	+	0.453930i
$316$		0			0
$317$	−9.98948	−	17.3023i	−0.561065	−	0.971793i	−0.997404	−	0.0720107i	$-0.977058\pi$
$317$	−9.98948	−	17.3023i	−0.561065	−	0.971793i	0.436339	−	0.899782i	$-0.356275\pi$
$318$		0			0
$319$	−30.1544	−	17.4097i	−1.68832	−	0.974755i
$320$		0			0
$321$	15.6774	−	8.18966i	0.875028	−	0.457102i
$322$		0			0
$323$		−	0.591150i		−	0.0328925i
$324$		0			0
$325$		−	3.39803i		−	0.188489i
$326$		0			0
$327$	−18.3500	+	9.58576i	−1.01475	+	0.530094i
$328$		0			0
$329$	26.0626	+	15.0473i	1.43688	+	0.829583i
$330$		0			0
$331$	−0.711679	−	1.23266i	−0.0391174	−	0.0677534i	0.845804	−	0.533494i	$-0.179121\pi$
$331$	−0.711679	−	1.23266i	−0.0391174	−	0.0677534i	−0.884921	+	0.465741i	$0.845788\pi$
$332$		0			0
$333$	5.44397	+	3.78875i	0.298328	+	0.207622i
$334$		0			0
$335$	0.725538	+	1.25667i	0.0396404	+	0.0686592i
$336$		0			0
$337$	−10.3266	+	17.8863i	−0.562528	+	0.974327i	0.434747	+	0.900553i	$0.356838\pi$
$337$	−10.3266	+	17.8863i	−0.562528	+	0.974327i	−0.997275	+	0.0737746i	$0.976495\pi$
$338$		0			0
$339$	0.681460	−	16.1375i	0.0370118	−	0.876468i
$340$		0			0
$341$	−5.62102			−0.304395
$342$		0			0
$343$			38.0872i			2.05652i
$344$		0			0
$345$	−3.13738	+	4.94027i	−0.168911	+	0.265975i
$346$		0			0
$347$	7.00513	+	4.04441i	0.376055	+	0.217115i	0.676100	−	0.736809i	$-0.263669\pi$
$347$	7.00513	+	4.04441i	0.376055	+	0.217115i	−0.300046	+	0.953925i	$0.597002\pi$
$348$		0			0
$349$	−5.62169	+	3.24568i	−0.300922	+	0.173737i	−0.642857	−	0.765986i	$-0.722251\pi$
$349$	−5.62169	+	3.24568i	−0.300922	+	0.173737i	0.341935	+	0.939724i	$0.388918\pi$
$350$		0			0
$351$	14.0540	+	10.6885i	0.750146	+	0.570511i
$352$		0			0
$353$	8.32842	−	4.80842i	0.443277	−	0.255926i	−0.261710	−	0.965147i	$-0.584286\pi$
$353$	8.32842	−	4.80842i	0.443277	−	0.255926i	0.704987	+	0.709220i	$0.250953\pi$
$354$		0			0
$355$	−5.79977	+	10.0455i	−0.307820	+	0.533159i
$356$		0			0
$357$	13.9684	−	21.9953i	0.739284	−	1.16411i
$358$		0			0
$359$	−33.0939			−1.74663			−0.873314	−	0.487157i	$-0.838034\pi$
$359$	−33.0939			−1.74663			−0.873314	+	0.487157i	$0.838034\pi$
$360$		0			0
$361$	−18.9659			−0.998204
$362$		0			0
$363$	−4.54369	−	0.191873i	−0.238482	−	0.0100707i
$364$		0			0
$365$	7.65399	−	13.2571i	0.400628	−	0.693908i
$366$		0			0
$367$	27.3961	−	15.8172i	1.43007	−	0.825649i	0.432942	−	0.901422i	$-0.357476\pi$
$367$	27.3961	−	15.8172i	1.43007	−	0.825649i	0.997125	+	0.0757725i	$0.0241423\pi$
$368$		0			0
$369$	−24.9928	+	11.7415i	−1.30107	+	0.611237i
$370$		0			0
$371$	−2.65617	+	1.53354i	−0.137901	+	0.0796174i
$372$		0			0
$373$	−22.6518	−	13.0780i	−1.17287	−	0.677155i	−0.218513	−	0.975834i	$-0.570121\pi$
$373$	−22.6518	−	13.0780i	−1.17287	−	0.677155i	−0.954353	+	0.298679i	$0.903454\pi$
$374$		0			0
$375$	−0.801968	−	1.53520i	−0.0414135	−	0.0792775i
$376$		0			0
$377$		−	32.0531i		−	1.65082i
$378$		0			0
$379$	−31.6890			−1.62776			−0.813878	−	0.581036i	$-0.802647\pi$
$379$	−31.6890			−1.62776			−0.813878	+	0.581036i	$0.802647\pi$
$380$		0			0
$381$	5.95909	−	3.11295i	0.305294	−	0.159481i
$382$		0			0
$383$	3.82550	−	6.62596i	0.195474	−	0.338571i	−0.751582	−	0.659640i	$-0.770709\pi$
$383$	3.82550	−	6.62596i	0.195474	−	0.338571i	0.947056	+	0.321069i	$0.104042\pi$
$384$		0			0
$385$	−8.67680	−	15.0287i	−0.442211	−	0.765932i
$386$		0			0
$387$	30.2059	+	2.55565i	1.53545	+	0.129911i
$388$		0			0
$389$	13.7167	+	23.7581i	0.695466	+	1.20458i	0.970023	+	0.243011i	$0.0781352\pi$
$389$	13.7167	+	23.7581i	0.695466	+	1.20458i	−0.274558	+	0.961571i	$0.588531\pi$
$390$		0			0
$391$	9.36333	+	5.40592i	0.473524	+	0.273389i
$392$		0			0
$393$	0.809426	−	19.1678i	0.0408301	−	0.966889i
$394$		0			0
$395$		−	2.53179i		−	0.127388i
$396$		0			0
$397$			0.681061i			0.0341815i	0.999854	+	0.0170907i	$0.00544042\pi$
$397$			0.681061i			0.0341815i	−0.999854	+	0.0170907i	$0.994560\pi$
$398$		0			0
$399$	1.26987	+	0.806448i	0.0635732	+	0.0403729i
$400$		0			0
$401$	9.45372	+	5.45811i	0.472096	+	0.272565i	0.717117	−	0.696953i	$-0.245461\pi$
$401$	9.45372	+	5.45811i	0.472096	+	0.272565i	−0.245020	+	0.969518i	$0.578795\pi$
$402$		0			0
$403$	−2.58723	−	4.48121i	−0.128879	−	0.223225i
$404$		0			0
$405$	8.87206	+	1.51211i	0.440856	+	0.0751375i
$406$		0			0
$407$	−4.08048	−	7.06760i	−0.202262	−	0.350328i
$408$		0			0
$409$	14.9762	−	25.9395i	0.740525	−	1.28263i	−0.211731	−	0.977328i	$-0.567910\pi$
$409$	14.9762	−	25.9395i	0.740525	−	1.28263i	0.952256	−	0.305299i	$-0.0987565\pi$
$410$		0			0
$411$	−6.72374	−	4.26999i	−0.331658	−	0.210623i
$412$		0			0
$413$	39.4104			1.93926
$414$		0			0
$415$			4.46186i			0.219024i
$416$		0			0
$417$	−20.4844	−	0.865025i	−1.00313	−	0.0423605i
$418$		0			0
$419$	24.3390	+	14.0521i	1.18904	+	0.686492i	0.958088	−	0.286474i	$-0.0924831\pi$
$419$	24.3390	+	14.0521i	1.18904	+	0.686492i	0.230950	+	0.972966i	$0.425816\pi$
$420$		0			0
$421$	3.81125	−	2.20043i	0.185749	−	0.107242i	−0.404242	−	0.914652i	$-0.632465\pi$
$421$	3.81125	−	2.20043i	0.185749	−	0.107242i	0.589991	+	0.807410i	$0.299131\pi$
$422$		0			0
$423$	19.1359	+	1.61904i	0.930419	+	0.0787205i
$424$		0			0
$425$	−2.77118	+	1.59994i	−0.134422	+	0.0776084i
$426$		0			0
$427$	−15.1898	+	26.3096i	−0.735087	+	1.27321i
$428$		0			0
$429$	−10.0592	−	19.2562i	−0.485662	−	0.929700i
$430$		0			0
$431$	−16.9022			−0.814149			−0.407074	−	0.913395i	$-0.633451\pi$
$431$	−16.9022			−0.814149			−0.407074	+	0.913395i	$0.633451\pi$
$432$		0			0
$433$	2.10526			0.101172			0.0505862	−	0.998720i	$-0.483891\pi$
$433$	2.10526			0.101172			0.0505862	+	0.998720i	$0.483891\pi$
$434$		0			0
$435$	−7.56483	−	14.4813i	−0.362706	−	0.694326i
$436$		0			0
$437$	−0.312105	+	0.540581i	−0.0149300	+	0.0258595i
$438$		0			0
$439$	−15.4910	+	8.94370i	−0.739343	+	0.426860i	−0.821830	−	0.569732i	$-0.807047\pi$
$439$	−15.4910	+	8.94370i	−0.739343	+	0.426860i	0.0824875	+	0.996592i	$0.473714\pi$
$440$		0			0
$441$	19.2639	+	41.0050i	0.917329	+	1.95262i
$442$		0			0
$443$	−29.8821	+	17.2525i	−1.41974	+	0.819689i	−0.996276	−	0.0862217i	$-0.972521\pi$
$443$	−29.8821	+	17.2525i	−1.41974	+	0.819689i	−0.423468	+	0.905911i	$0.639187\pi$
$444$		0			0
$445$	3.74973	+	2.16491i	0.177754	+	0.102626i
$446$		0			0
$447$	−11.8455	−	0.500218i	−0.560275	−	0.0236595i
$448$		0			0
$449$			39.3197i			1.85561i	0.373063	+	0.927806i	$0.378308\pi$
$449$			39.3197i			1.85561i	−0.373063	+	0.927806i	$0.621692\pi$
$450$		0			0
$451$	33.9764			1.59989
$452$		0			0
$453$	−24.5907	−	15.6166i	−1.15537	−	0.733732i
$454$		0			0
$455$	7.98746	−	13.8347i	0.374458	−	0.648580i
$456$		0			0
$457$	3.25936	+	5.64538i	0.152467	+	0.264080i	0.932134	−	0.362114i	$-0.117945\pi$
$457$	3.25936	+	5.64538i	0.152467	+	0.264080i	−0.779667	+	0.626194i	$0.784612\pi$
$458$		0			0
$459$	2.09953	−	16.4940i	0.0979976	−	0.769872i
$460$		0			0
$461$	2.23638	+	3.87352i	0.104158	+	0.180408i	0.913394	−	0.407077i	$-0.133452\pi$
$461$	2.23638	+	3.87352i	0.104158	+	0.180408i	−0.809236	+	0.587484i	$0.800118\pi$
$462$		0			0
$463$	−30.0244	−	17.3346i	−1.39535	−	0.805608i	−0.401452	−	0.915880i	$-0.631494\pi$
$463$	−30.0244	−	17.3346i	−1.39535	−	0.805608i	−0.993901	+	0.110273i	$0.964828\pi$
$464$		0			0
$465$	−2.22649	−	1.41396i	−0.103251	−	0.0655709i
$466$		0			0
$467$		−	11.4074i		−	0.527874i	−0.964540	−	0.263937i	$-0.914979\pi$
$467$		−	11.4074i		−	0.527874i	0.964540	−	0.263937i	$-0.0850211\pi$
$468$		0			0
$469$			6.82184i			0.315003i
$470$		0			0
$471$	−1.16489	+	27.5854i	−0.0536752	+	1.27107i
$472$		0			0
$473$	−32.3020	−	18.6496i	−1.48525	−	0.857507i
$474$		0			0
$475$	−0.0923707	−	0.159991i	−0.00423826	−	0.00734088i
$476$		0			0
$477$	−1.11801	+	1.60645i	−0.0511903	+	0.0735542i
$478$		0			0
$479$	−5.73970	−	9.94145i	−0.262254	−	0.454237i	0.704587	−	0.709618i	$-0.251132\pi$
$479$	−5.73970	−	9.94145i	−0.262254	−	0.454237i	−0.966840	+	0.255381i	$0.917799\pi$
$480$		0			0
$481$	3.75630	−	6.50610i	0.171273	−	0.296653i
$482$		0			0
$483$	−24.3862	+	12.7390i	−1.10961	+	0.579644i
$484$		0			0
$485$	17.1832			0.780248
$486$		0			0
$487$		−	35.6160i		−	1.61391i	−0.590610	−	0.806957i	$-0.701113\pi$
$487$		−	35.6160i		−	1.61391i	0.590610	−	0.806957i	$-0.298887\pi$
$488$		0			0
$489$	−4.34050	−	8.30900i	−0.196284	−	0.375746i
$490$		0			0
$491$	−4.58796	−	2.64886i	−0.207052	−	0.119541i	0.392889	−	0.919586i	$-0.371476\pi$
$491$	−4.58796	−	2.64886i	−0.207052	−	0.119541i	−0.599940	+	0.800045i	$0.704809\pi$
$492$		0			0
$493$	−26.1400	+	15.0920i	−1.17729	+	0.679708i
$494$		0			0
$495$	−9.08932	−	6.32575i	−0.408534	−	0.284321i
$496$		0			0
$497$	−47.2262	+	27.2660i	−2.11838	+	1.22305i
$498$		0			0
$499$	−18.4386	+	31.9366i	−0.825426	+	1.42968i	0.0761666	+	0.997095i	$0.475732\pi$
$499$	−18.4386	+	31.9366i	−0.825426	+	1.42968i	−0.901593	+	0.432585i	$0.857601\pi$
$500$		0			0
$501$	−3.89430	−	0.164450i	−0.173984	−	0.00734707i
$502$		0			0
$503$	26.6354			1.18761			0.593807	−	0.804608i	$-0.297624\pi$
$503$	26.6354			1.18761			0.593807	+	0.804608i	$0.297624\pi$
$504$		0			0
$505$	−2.03186			−0.0904168
$506$		0			0
$507$	−1.34952	+	2.12503i	−0.0599344	+	0.0943757i
$508$		0			0
$509$	−3.16205	+	5.47683i	−0.140155	+	0.242756i	−0.927555	−	0.373687i	$-0.878093\pi$
$509$	−3.16205	+	5.47683i	−0.140155	+	0.242756i	0.787400	+	0.616443i	$0.211427\pi$
$510$		0			0
$511$	62.3246	−	35.9832i	2.75708	−	1.59180i
$512$		0			0
$513$	0.952261	+	0.121214i	0.0420433	+	0.00535173i
$514$		0			0
$515$	1.17647	−	0.679237i	0.0518416	−	0.0299307i
$516$		0			0
$517$	−20.4638	−	11.8148i	−0.899995	−	0.519613i
$518$		0			0
$519$	−4.79841	+	7.55582i	−0.210627	+	0.331664i
$520$		0			0
$521$		−	3.86881i		−	0.169496i	−0.996402	−	0.0847478i	$-0.972992\pi$
$521$		−	3.86881i		−	0.169496i	0.996402	−	0.0847478i	$-0.0270085\pi$
$522$		0			0
$523$	−7.06854			−0.309086			−0.154543	−	0.987986i	$-0.549390\pi$
$523$	−7.06854			−0.309086			−0.154543	+	0.987986i	$0.549390\pi$
$524$		0			0
$525$	0.343550	−	8.13551i	0.0149937	−	0.355063i
$526$		0			0
$527$	−2.43635	+	4.21989i	−0.106129	+	0.183821i
$528$		0			0
$529$	5.79176	+	10.0316i	0.251815	+	0.436157i
$530$		0			0
$531$	22.7622	−	10.6936i	0.987798	−	0.464061i
$532$		0			0
$533$	15.6386	+	27.0868i	0.677381	+	1.17326i
$534$		0			0
$535$	−8.84381	−	5.10598i	−0.382351	−	0.220751i
$536$		0			0
$537$	−24.4154	+	12.7543i	−1.05360	+	0.550387i
$538$		0			0
$539$		−	55.7442i		−	2.40107i
$540$		0			0
$541$		−	25.3091i		−	1.08812i	−0.839045	−	0.544062i	$-0.816886\pi$
$541$		−	25.3091i		−	1.08812i	0.839045	−	0.544062i	$-0.183114\pi$
$542$		0			0
$543$	−23.2985	+	12.1708i	−0.999832	+	0.522298i
$544$		0			0
$545$	10.3514	+	5.97639i	0.443406	+	0.256001i
$546$		0			0
$547$	−5.74111	−	9.94389i	−0.245472	−	0.425170i	0.716792	−	0.697287i	$-0.245610\pi$
$547$	−5.74111	−	9.94389i	−0.245472	−	0.425170i	−0.962264	+	0.272117i	$0.912276\pi$
$548$		0			0
$549$	−1.63438	+	19.3172i	−0.0697537	+	0.824437i
$550$		0			0
$551$	−0.871318	−	1.50917i	−0.0371194	−	0.0642926i
$552$		0			0
$553$	5.95125	−	10.3079i	0.253073	−	0.438335i
$554$		0			0
$555$	0.161563	−	3.82593i	0.00685795	−	0.162402i
$556$		0			0
$557$	−11.9398			−0.505907			−0.252953	−	0.967478i	$-0.581402\pi$
$557$	−11.9398			−0.505907			−0.252953	+	0.967478i	$0.581402\pi$
$558$		0			0
$559$		−	34.3358i		−	1.45225i
$560$		0			0
$561$	−10.9676	+	17.2702i	−0.463054	+	0.729147i
$562$		0			0
$563$	−20.7893	−	12.0027i	−0.876166	−	0.505855i	−0.00677354	−	0.999977i	$-0.502156\pi$
$563$	−20.7893	−	12.0027i	−0.876166	−	0.505855i	−0.869392	+	0.494122i	$0.835489\pi$
$564$		0			0
$565$	−8.07593	+	4.66264i	−0.339757	+	0.196159i
$566$		0			0
$567$	32.5672	+	27.0112i	1.36769	+	1.13436i
$568$		0			0
$569$	−2.19323	+	1.26626i	−0.0919449	+	0.0530844i	−0.545267	−	0.838262i	$-0.683572\pi$
$569$	−2.19323	+	1.26626i	−0.0919449	+	0.0530844i	0.453323	+	0.891347i	$0.350239\pi$
$570$		0			0
$571$	11.7630	−	20.3742i	0.492267	−	0.852632i	−0.507693	−	0.861538i	$-0.669502\pi$
$571$	11.7630	−	20.3742i	0.492267	−	0.852632i	0.999960	+	0.00890626i	$0.00283499\pi$
$572$		0			0
$573$	−6.96008	+	10.9597i	−0.290762	+	0.457848i
$574$		0			0
$575$	3.37883			0.140907
$576$		0			0
$577$	17.3679			0.723037			0.361519	−	0.932365i	$-0.382258\pi$
$577$	17.3679			0.723037			0.361519	+	0.932365i	$0.382258\pi$
$578$		0			0
$579$	33.5481	+	1.41668i	1.39421	+	0.0588753i
$580$		0			0
$581$	−10.4881	+	18.1659i	−0.435120	+	0.753649i
$582$		0			0
$583$	2.08556	−	1.20410i	0.0863751	−	0.0498687i
$584$		0			0
$585$	0.859427	−	10.1578i	0.0355330	−	0.419973i
$586$		0			0
$587$	3.86272	−	2.23014i	0.159431	−	0.0920478i	−0.418162	−	0.908373i	$-0.637325\pi$
$587$	3.86272	−	2.23014i	0.159431	−	0.0920478i	0.577593	+	0.816325i	$0.303992\pi$
$588$		0			0
$589$	−0.243631	−	0.140660i	−0.0100386	−	0.00579580i
$590$		0			0
$591$	−0.495101	−	0.947768i	−0.0203657	−	0.0389860i
$592$		0			0
$593$		−	33.8336i		−	1.38938i	−0.719310	−	0.694689i	$-0.755542\pi$
$593$		−	33.8336i		−	1.38938i	0.719310	−	0.694689i	$-0.244458\pi$
$594$		0			0
$595$	−15.0434			−0.616717
$596$		0			0
$597$	1.30787	−	0.683214i	0.0535277	−	0.0279621i
$598$		0			0
$599$	−17.5171	+	30.3406i	−0.715731	+	1.23968i	0.246946	+	0.969029i	$0.420573\pi$
$599$	−17.5171	+	30.3406i	−0.715731	+	1.23968i	−0.962677	+	0.270653i	$0.912760\pi$
$600$		0			0
$601$	17.6687	+	30.6032i	0.720723	+	1.24833i	0.960710	+	0.277553i	$0.0895235\pi$
$601$	17.6687	+	30.6032i	0.720723	+	1.24833i	−0.239987	+	0.970776i	$0.577143\pi$
$602$		0			0
$603$	1.85103	+	3.94009i	0.0753798	+	0.160453i
$604$		0			0
$605$	1.31282	+	2.27387i	0.0533737	+	0.0924459i
$606$		0			0
$607$	9.95148	+	5.74549i	0.403918	+	0.233202i	0.688173	−	0.725547i	$-0.258413\pi$
$607$	9.95148	+	5.74549i	0.403918	+	0.233202i	−0.284255	+	0.958749i	$0.591746\pi$
$608$		0			0
$609$	3.24065	−	76.7410i	0.131318	−	3.10970i
$610$		0			0
$611$		−	21.7522i		−	0.880001i
$612$		0			0
$613$			29.1512i			1.17741i	0.808349	+	0.588704i	$0.200362\pi$
$613$			29.1512i			1.17741i	−0.808349	+	0.588704i	$0.799638\pi$
$614$		0			0
$615$	13.4581	+	8.54673i	0.542683	+	0.344638i
$616$		0			0
$617$	13.1438	+	7.58860i	0.529151	+	0.305506i	0.740671	−	0.671868i	$-0.234508\pi$
$617$	13.1438	+	7.58860i	0.529151	+	0.305506i	−0.211520	+	0.977374i	$0.567841\pi$
$618$		0			0
$619$	14.6309	+	25.3414i	0.588064	+	1.01856i	0.994486	+	0.104872i	$0.0334432\pi$
$619$	14.6309	+	25.3414i	0.588064	+	1.01856i	−0.406421	+	0.913686i	$0.633223\pi$
$620$		0			0
$621$	−10.6281	+	13.9746i	−0.426492	+	0.560780i
$622$		0			0
$623$	10.1777	+	17.6283i	0.407762	+	0.706264i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−0.997074	−	0.633204i	−0.0398193	−	0.0252877i
$628$		0			0
$629$	−7.07451			−0.282079
$630$		0			0
$631$			17.6089i			0.700998i	0.936563	+	0.350499i	$0.113988\pi$
$631$			17.6089i			0.700998i	−0.936563	+	0.350499i	$0.886012\pi$
$632$		0			0
$633$	−10.9479	−	0.462313i	−0.435141	−	0.0183753i
$634$		0			0
$635$	−3.36159	−	1.94082i	−0.133401	−	0.0770190i
$636$		0			0
$637$	44.4405	−	25.6578i	1.76080	−	1.01660i
$638$		0			0
$639$	−19.8781	+	28.5623i	−0.786364	+	1.12991i
$640$		0			0
$641$	5.78399	−	3.33939i	0.228454	−	0.131898i	−0.381405	−	0.924408i	$-0.624560\pi$
$641$	5.78399	−	3.33939i	0.228454	−	0.131898i	0.609859	+	0.792510i	$0.291226\pi$
$642$		0			0
$643$	17.7601	−	30.7613i	0.700389	−	1.21311i	−0.267941	−	0.963435i	$-0.586343\pi$
$643$	17.7601	−	30.7613i	0.700389	−	1.21311i	0.968330	−	0.249674i	$-0.0803234\pi$
$644$		0			0
$645$	−8.10358	−	15.5126i	−0.319078	−	0.610810i
$646$		0			0
$647$	21.1567			0.831755			0.415877	−	0.909421i	$-0.363475\pi$
$647$	21.1567			0.831755			0.415877	+	0.909421i	$0.363475\pi$
$648$		0			0
$649$	−30.9441			−1.21466
$650$		0			0
$651$	−5.74123	−	10.9904i	−0.225017	−	0.430748i
$652$		0			0
$653$	16.9536	−	29.3645i	0.663445	−	1.14912i	−0.316260	−	0.948673i	$-0.602427\pi$
$653$	16.9536	−	29.3645i	0.663445	−	1.14912i	0.979705	−	0.200447i	$-0.0642395\pi$
$654$		0			0
$655$	−9.59245	+	5.53820i	−0.374808	+	0.216396i
$656$		0			0
$657$	26.2332	−	37.6939i	1.02345	−	1.47058i
$658$		0			0
$659$	−7.53060	+	4.34779i	−0.293350	+	0.169366i	−0.639452	−	0.768831i	$-0.720839\pi$
$659$	−7.53060	+	4.34779i	−0.293350	+	0.169366i	0.346101	+	0.938197i	$0.387505\pi$
$660$		0			0
$661$	−27.5930	−	15.9308i	−1.07324	−	0.619638i	−0.144178	−	0.989552i	$-0.546054\pi$
$661$	−27.5930	−	15.9308i	−1.07324	−	0.619638i	−0.929066	+	0.369914i	$0.879387\pi$
$662$		0			0
$663$	−18.8163	−	0.794582i	−0.730765	−	0.0308590i
$664$		0			0
$665$		−	0.868511i		−	0.0336794i
$666$		0			0
$667$	31.8719			1.23409
$668$		0			0
$669$	21.0088	+	13.3419i	0.812247	+	0.515827i
$670$		0			0
$671$	11.9267	−	20.6576i	0.460425	−	0.797479i
$672$		0			0
$673$	−4.39045	−	7.60448i	−0.169239	−	0.293131i	0.768913	−	0.639353i	$-0.220798\pi$
$673$	−4.39045	−	7.60448i	−0.169239	−	0.293131i	−0.938153	+	0.346222i	$0.887464\pi$
$674$		0			0
$675$	−2.00906	−	4.79204i	−0.0773286	−	0.184446i
$676$		0			0
$677$	8.38094	+	14.5162i	0.322106	+	0.557903i	0.980922	−	0.194400i	$-0.0622760\pi$
$677$	8.38094	+	14.5162i	0.322106	+	0.557903i	−0.658817	+	0.752304i	$0.728943\pi$
$678$		0			0
$679$	69.9593	+	40.3910i	2.68479	+	1.55007i
$680$		0			0
$681$	−14.8582	−	9.43586i	−0.569366	−	0.361583i
$682$		0			0
$683$		−	29.5084i		−	1.12911i	−0.825397	−	0.564553i	$-0.809048\pi$
$683$		−	29.5084i		−	1.12911i	0.825397	−	0.564553i	$-0.190952\pi$
$684$		0			0
$685$			4.59861i			0.175704i
$686$		0			0
$687$	1.63745	−	38.7761i	0.0624726	−	1.47940i
$688$		0			0
$689$	1.91987	+	1.10844i	0.0731412	+	0.0422281i
$690$		0			0
$691$	2.98412	+	5.16864i	0.113521	+	0.196624i	0.917188	−	0.398456i	$-0.130454\pi$
$691$	2.98412	+	5.16864i	0.113521	+	0.196624i	−0.803667	+	0.595080i	$0.797120\pi$
$692$		0			0
$693$	−22.1367	−	47.1200i	−0.840904	−	1.78994i
$694$		0			0
$695$	5.91862	+	10.2514i	0.224506	+	0.388856i
$696$		0			0
$697$	14.7266	−	25.5072i	0.557810	−	0.966155i
$698$		0			0
$699$	4.85035	−	2.53376i	0.183457	−	0.0958354i
$700$		0			0
$701$	−13.9632			−0.527383			−0.263692	−	0.964607i	$-0.584940\pi$
$701$	−13.9632			−0.527383			−0.263692	+	0.964607i	$0.584940\pi$
$702$		0			0
$703$		−	0.408439i		−	0.0154046i
$704$		0			0
$705$	−5.13374	−	9.82748i	−0.193348	−	0.370124i
$706$		0			0
$707$	−8.27250	−	4.77613i	−0.311119	−	0.179625i
$708$		0			0
$709$	−28.0403	+	16.1891i	−1.05308	+	0.607993i	−0.923509	−	0.383578i	$-0.874692\pi$
$709$	−28.0403	+	16.1891i	−1.05308	+	0.607993i	−0.129566	+	0.991571i	$0.541359\pi$
$710$		0			0
$711$	0.640338	−	7.56832i	0.0240145	−	0.283834i
$712$		0			0
$713$	4.45588	−	2.57260i	0.166874	−	0.0963448i
$714$		0			0
$715$	−6.27156	+	10.8627i	−0.234543	+	0.406241i
$716$		0			0
$717$	−25.1620	−	1.06255i	−0.939692	−	0.0396817i
$718$		0			0
$719$	42.2991			1.57749			0.788745	−	0.614721i	$-0.210731\pi$
$719$	42.2991			1.57749			0.788745	+	0.614721i	$0.210731\pi$
$720$		0			0
$721$	6.38649			0.237845
$722$		0			0
$723$	−5.82422	+	9.17111i	−0.216605	+	0.341077i
$724$		0			0
$725$	−4.71642	+	8.16907i	−0.175163	+	0.303392i
$726$		0			0
$727$	−33.2203	+	19.1797i	−1.23207	+	0.711337i	−0.967461	−	0.253019i	$-0.918577\pi$
$727$	−33.2203	+	19.1797i	−1.23207	+	0.711337i	−0.264610	+	0.964355i	$0.585243\pi$
$728$		0			0
$729$	26.1390	+	6.76410i	0.968111	+	0.250522i
$730$		0			0
$731$	−28.0017	+	16.1668i	−1.03568	+	0.597950i
$732$		0			0
$733$	12.7323	+	7.35097i	0.470277	+	0.271514i	0.716356	−	0.697735i	$-0.245809\pi$
$733$	12.7323	+	7.35097i	0.470277	+	0.271514i	−0.246079	+	0.969250i	$0.579142\pi$
$734$		0			0
$735$	14.0224	−	22.0804i	0.517224	−	0.814446i
$736$		0			0
$737$		−	5.35635i		−	0.197304i
$738$		0			0
$739$	−50.4167			−1.85461			−0.927304	−	0.374310i	$-0.877880\pi$
$739$	−50.4167			−1.85461			−0.927304	+	0.374310i	$0.877880\pi$
$740$		0			0
$741$	0.0458743	−	1.08634i	0.00168524	−	0.0399077i
$742$		0			0
$743$	−7.23945	+	12.5391i	−0.265590	+	0.460015i	−0.967718	−	0.252036i	$-0.918900\pi$
$743$	−7.23945	+	12.5391i	−0.265590	+	0.460015i	0.702128	+	0.712051i	$0.252233\pi$
$744$		0			0
$745$	3.42256	+	5.92805i	0.125393	+	0.217187i
$746$		0			0
$747$	−1.12849	+	13.3379i	−0.0412893	+	0.488009i
$748$		0			0
$749$	−24.0044	−	41.5768i	−0.877101	−	1.51918i
$750$		0			0
$751$	−39.0021	−	22.5179i	−1.42321	−	0.821690i	−0.426636	−	0.904423i	$-0.640302\pi$
$751$	−39.0021	−	22.5179i	−1.42321	−	0.821690i	−0.996572	+	0.0827337i	$0.973635\pi$
$752$		0			0
$753$	28.8405	−	15.0659i	1.05101	−	0.549031i
$754$		0			0
$755$			16.8185i			0.612086i
$756$		0			0
$757$		−	5.56940i		−	0.202423i	−0.994865	−	0.101212i	$-0.967728\pi$
$757$		−	5.56940i		−	0.202423i	0.994865	−	0.101212i	$-0.0322719\pi$
$758$		0			0
$759$	19.1474	−	10.0023i	0.695008	−	0.363062i
$760$		0			0
$761$	−35.9383	−	20.7490i	−1.30276	−	0.752149i	−0.321884	−	0.946779i	$-0.604316\pi$
$761$	−35.9383	−	20.7490i	−1.30276	−	0.752149i	−0.980877	+	0.194630i	$0.937649\pi$
$762$		0			0
$763$	28.0964	+	48.6644i	1.01716	+	1.76177i
$764$		0			0
$765$	−8.68858	+	4.08185i	−0.314136	+	0.147579i
$766$		0			0
$767$	−14.2429	−	24.6693i	−0.514280	−	0.890758i
$768$		0			0
$769$	−8.42654	+	14.5952i	−0.303869	+	0.526316i	−0.977009	−	0.213199i	$-0.931612\pi$
$769$	−8.42654	+	14.5952i	−0.303869	+	0.526316i	0.673140	+	0.739515i	$0.264945\pi$
$770$		0			0
$771$	1.92265	−	45.5299i	0.0692426	−	1.63972i
$772$		0			0
$773$	19.6992			0.708530			0.354265	−	0.935145i	$-0.384731\pi$
$773$	19.6992			0.708530			0.354265	+	0.935145i	$0.384731\pi$
$774$		0			0
$775$			1.52278i			0.0546998i
$776$		0			0
$777$	9.65106	−	15.1970i	0.346230	−	0.545191i
$778$		0			0
$779$	1.47263	+	0.850224i	0.0527625	+	0.0304625i
$780$		0			0
$781$	37.0809	−	21.4086i	1.32686	−	0.766061i
$782$		0			0
$783$	−18.9511	−	45.2026i	−0.677257	−	1.61541i
$784$		0			0
$785$	13.8050	−	7.97033i	0.492722	−	0.284473i
$786$		0			0
$787$	5.29184	−	9.16574i	0.188634	−	0.326723i	−0.756161	−	0.654385i	$-0.772927\pi$
$787$	5.29184	−	9.16574i	0.188634	−	0.326723i	0.944795	+	0.327662i	$0.106261\pi$
$788$		0			0
$789$	6.43017	−	10.1253i	0.228920	−	0.360469i
$790$		0			0
$791$	−43.8403			−1.55878
$792$		0			0
$793$	21.9583			0.779763
$794$		0			0
$795$	1.12898	+	0.0476751i	0.0400409	+	0.00169086i
$796$		0			0
$797$	7.01916	−	12.1575i	0.248631	−	0.430642i	−0.714515	−	0.699620i	$-0.753353\pi$
$797$	7.01916	−	12.1575i	0.248631	−	0.430642i	0.963146	+	0.268978i	$0.0866859\pi$
$798$		0			0
$799$	−17.7395	+	10.2419i	−0.627577	+	0.362332i
$800$		0			0
$801$	10.6616	+	7.41997i	0.376709	+	0.262172i
$802$		0			0
$803$	−48.9358	+	28.2531i	−1.72691	+	0.997031i
$804$		0			0
$805$	13.7565	+	7.94232i	0.484853	+	0.279930i
$806$		0			0
$807$	17.3852	+	33.2804i	0.611988	+	1.17153i
$808$		0			0
$809$			13.5081i			0.474919i	0.971397	+	0.237459i	$0.0763147\pi$
$809$			13.5081i			0.474919i	−0.971397	+	0.237459i	$0.923685\pi$
$810$		0			0
$811$	−1.04752			−0.0367835			−0.0183918	−	0.999831i	$-0.505855\pi$
$811$	−1.04752			−0.0367835			−0.0183918	+	0.999831i	$0.505855\pi$
$812$		0			0
$813$	3.13661	−	1.63852i	0.110006	−	0.0574654i
$814$		0			0
$815$	−2.70616	+	4.68720i	−0.0947926	+	0.164186i
$816$		0			0
$817$	−0.933371	−	1.61665i	−0.0326545	−	0.0565593i
$818$		0			0
$819$	27.3761	−	39.3361i	0.956599	−	1.37452i
$820$		0			0
$821$	−22.1991	−	38.4500i	−0.774755	−	1.34192i	−0.934932	−	0.354827i	$-0.884540\pi$
$821$	−22.1991	−	38.4500i	−0.774755	−	1.34192i	0.160176	−	0.987088i	$-0.448794\pi$
$822$		0			0
$823$	13.9621	+	8.06104i	0.486689	+	0.280990i	0.723200	−	0.690639i	$-0.242671\pi$
$823$	13.9621	+	8.06104i	0.486689	+	0.280990i	−0.236511	+	0.971629i	$0.576004\pi$
$824$		0			0
$825$	−0.269747	+	6.38781i	−0.00939138	+	0.222395i
$826$		0			0
$827$		−	11.7598i		−	0.408930i	−0.978874	−	0.204465i	$-0.934455\pi$
$827$		−	11.7598i		−	0.408930i	0.978874	−	0.204465i	$-0.0655454\pi$
$828$		0			0
$829$			10.9353i			0.379798i	0.981804	+	0.189899i	$0.0608161\pi$
$829$			10.9353i			0.379798i	−0.981804	+	0.189899i	$0.939184\pi$
$830$		0			0
$831$	32.2071	+	20.4535i	1.11725	+	0.709525i
$832$		0			0
$833$	−41.8490	−	24.1615i	−1.44998	−	0.837148i
$834$		0			0
$835$	1.12519	+	1.94888i	0.0389387	+	0.0674439i
$836$		0			0
$837$	−6.29809	−	4.78991i	−0.217694	−	0.165563i
$838$		0			0
$839$	−10.0450	−	17.3985i	−0.346793	−	0.600663i	0.638885	−	0.769302i	$-0.279396\pi$
$839$	−10.0450	−	17.3985i	−0.346793	−	0.600663i	−0.985678	+	0.168639i	$0.946063\pi$
$840$		0			0
$841$	−29.9892	+	51.9428i	−1.03411	+	1.79113i
$842$		0			0
$843$	12.0020	+	7.62200i	0.413370	+	0.262516i
$844$		0			0
$845$	1.45338			0.0499978
$846$		0			0
$847$			12.3437i			0.424135i
$848$		0			0
$849$	−36.1532	−	1.52669i	−1.24077	−	0.0523958i
$850$		0			0
$851$	6.46934	+	3.73507i	0.221766	+	0.128037i
$852$		0			0
$853$	−25.3701	+	14.6474i	−0.868654	+	0.501518i	−0.866901	−	0.498481i	$-0.833891\pi$
$853$	−25.3701	+	14.6474i	−0.868654	+	0.501518i	−0.00175348	+	0.999998i	$0.500558\pi$
$854$		0			0
$855$	−0.235661	−	0.501626i	−0.00805943	−	0.0171552i
$856$		0			0
$857$	−20.4040	+	11.7802i	−0.696987	+	0.402406i	−0.806224	−	0.591610i	$-0.798493\pi$
$857$	−20.4040	+	11.7802i	−0.696987	+	0.402406i	0.109237	+	0.994016i	$0.465159\pi$
$858$		0			0
$859$	−2.37008	+	4.10510i	−0.0808660	+	0.140064i	−0.903622	−	0.428330i	$-0.859102\pi$
$859$	−2.37008	+	4.10510i	−0.0808660	+	0.140064i	0.822756	+	0.568395i	$0.192435\pi$
$860$		0			0
$861$	34.7031	+	66.4318i	1.18268	+	2.26399i
$862$		0			0
$863$	15.5711			0.530046			0.265023	−	0.964242i	$-0.414620\pi$
$863$	15.5711			0.530046			0.265023	+	0.964242i	$0.414620\pi$
$864$		0			0
$865$	5.16769			0.175707
$866$		0			0
$867$	−5.42193	−	10.3792i	−0.184138	−	0.352495i
$868$		0			0
$869$	−4.67278	+	8.09350i	−0.158513	+	0.274553i
$870$		0			0
$871$	4.27020	−	2.46540i	0.144690	−	0.0835370i
$872$		0			0
$873$	51.3660	+	4.34596i	1.73848	+	0.147088i
$874$		0			0
$875$	−4.07138	+	2.35061i	−0.137638	+	0.0794653i
$876$		0			0
$877$	34.1807	+	19.7342i	1.15420	+	0.666378i	0.949907	−	0.312532i	$-0.101177\pi$
$877$	34.1807	+	19.7342i	1.15420	+	0.666378i	0.204293	+	0.978910i	$0.434511\pi$
$878$		0			0
$879$	−3.18898	−	0.134666i	−0.107562	−	0.00454215i
$880$		0			0
$881$		−	40.8421i		−	1.37601i	−0.725708	−	0.688003i	$-0.758488\pi$
$881$		−	40.8421i		−	1.37601i	0.725708	−	0.688003i	$-0.241512\pi$
$882$		0			0
$883$	6.63432			0.223263			0.111631	−	0.993750i	$-0.464392\pi$
$883$	6.63432			0.223263			0.111631	+	0.993750i	$0.464392\pi$
$884$		0			0
$885$	−12.2570	−	7.78396i	−0.412015	−	0.261655i
$886$		0			0
$887$	8.69428	−	15.0589i	0.291925	−	0.505629i	−0.682340	−	0.731035i	$-0.739037\pi$
$887$	8.69428	−	15.0589i	0.291925	−	0.505629i	0.974265	+	0.225406i	$0.0723708\pi$
$888$		0			0
$889$	−9.12422	−	15.8036i	−0.306017	−	0.530036i
$890$		0			0
$891$	−25.5710	−	21.2085i	−0.856660	−	0.710513i
$892$		0			0
$893$	−0.591304	−	1.02417i	−0.0197872	−	0.0342725i
$894$		0			0
$895$	13.7730	+	7.95185i	0.460381	+	0.265801i
$896$		0			0
$897$	16.7872	+	10.6609i	0.560509	+	0.355958i
$898$		0			0
$899$			14.3641i			0.479070i
$900$		0			0
$901$		−	2.08760i		−	0.0695480i
$902$		0			0
$903$	3.47144	−	82.2063i	0.115522	−	2.73565i
$904$		0			0
$905$	13.1429	+	7.58807i	0.436886	+	0.252236i
$906$		0			0
$907$	−18.1322	−	31.4059i	−0.602071	−	1.04282i	−0.992507	−	0.122187i	$-0.961009\pi$
$907$	−18.1322	−	31.4059i	−0.602071	−	1.04282i	0.390436	−	0.920630i	$-0.372324\pi$
$908$		0			0
$909$	−6.07389	−	0.513898i	−0.201458	−	0.0170449i
$910$		0			0
$911$	−4.34808	−	7.53110i	−0.144058	−	0.249517i	0.784963	−	0.619543i	$-0.212682\pi$
$911$	−4.34808	−	7.53110i	−0.144058	−	0.249517i	−0.929021	+	0.370026i	$0.879349\pi$
$912$		0			0
$913$	8.23501	−	14.2635i	0.272539	−	0.472051i
$914$		0			0
$915$	9.92058	−	5.18237i	0.327964	−	0.171324i
$916$		0			0
$917$	−52.0727			−1.71959
$918$		0			0
$919$		−	8.35467i		−	0.275595i	−0.990460	−	0.137798i	$-0.955998\pi$
$919$		−	8.35467i		−	0.275595i	0.990460	−	0.137798i	$-0.0440023\pi$
$920$		0			0
$921$	−8.17662	−	15.6524i	−0.269429	−	0.515766i
$922$		0			0
$923$	34.1349	+	19.7078i	1.12356	+	0.648690i
$924$		0			0
$925$	−1.91467	+	1.10543i	−0.0629539	+	0.0363465i
$926$		0			0
$927$	3.68864	−	1.73290i	0.121151	−	0.0569160i
$928$		0			0
$929$	0.0492053	−	0.0284087i	0.00161437	−	0.000932059i	−0.499193	−	0.866491i	$-0.666370\pi$
$929$	0.0492053	−	0.0284087i	0.00161437	−	0.000932059i	0.500807	+	0.865559i	$0.333037\pi$
$930$		0			0
$931$	1.39494	−	2.41611i	0.0457173	−	0.0791847i
$932$		0			0
$933$	35.6217	+	1.50425i	1.16620	+	0.0492469i
$934$		0			0
$935$	11.8117			0.386283
$936$		0			0
$937$	−8.91661			−0.291293			−0.145646	−	0.989337i	$-0.546526\pi$
$937$	−8.91661			−0.291293			−0.145646	+	0.989337i	$0.546526\pi$
$938$		0			0
$939$	5.04879	−	7.95008i	0.164761	−	0.259441i
$940$		0			0
$941$	−11.9913	+	20.7695i	−0.390904	+	0.677065i	−0.992569	−	0.121683i	$-0.961171\pi$
$941$	−11.9913	+	20.7695i	−0.390904	+	0.677065i	0.601665	+	0.798748i	$0.294504\pi$
$942$		0			0
$943$	−26.9337	+	15.5502i	−0.877082	+	0.506384i
$944$		0			0
$945$	3.08461	−	24.2328i	0.100342	−	0.788292i
$946$		0			0
$947$	−15.8908	+	9.17457i	−0.516382	+	0.298133i	−0.735453	−	0.677576i	$-0.763031\pi$
$947$	−15.8908	+	9.17457i	−0.516382	+	0.298133i	0.219071	+	0.975709i	$0.429697\pi$
$948$		0			0
$949$	−45.0480	−	26.0085i	−1.46232	−	0.844272i
$950$		0			0
$951$	−18.5513	+	29.2118i	−0.601566	+	0.947256i
$952$		0			0
$953$		−	6.04509i		−	0.195820i	−0.995195	−	0.0979099i	$-0.968784\pi$
$953$		−	6.04509i		−	0.195820i	0.995195	−	0.0979099i	$-0.0312157\pi$
$954$		0			0
$955$	7.49572			0.242556
$956$		0			0
$957$	−2.54448	+	60.2552i	−0.0822513	+	1.94777i
$958$		0			0
$959$	−10.8095	+	18.7227i	−0.349058	+	0.604587i
$960$		0			0
$961$	−14.3406	−	24.8386i	−0.462599	−	0.801245i
$962$		0			0
$963$	−25.1456	−	17.5002i	−0.810305	−	0.563935i
$964$		0			0
$965$	−9.69314	−	16.7890i	−0.312033	−	0.540458i
$966$		0			0
$967$	−27.9898	−	16.1599i	−0.900091	−	0.519668i	−0.0228612	−	0.999739i	$-0.507278\pi$
$967$	−27.9898	−	16.1599i	−0.900091	−	0.519668i	−0.877230	+	0.480071i	$0.840611\pi$
$968$		0			0
$969$	−0.907535	+	0.474083i	−0.0291542	+	0.0152298i
$970$		0			0
$971$		−	51.1694i		−	1.64210i	−0.570854	−	0.821052i	$-0.693388\pi$
$971$		−	51.1694i		−	1.64210i	0.570854	−	0.821052i	$-0.306612\pi$
$972$		0			0
$973$			55.6496i			1.78404i
$974$		0			0
$975$	−5.21667	+	2.72511i	−0.167067	+	0.0872735i
$976$		0			0
$977$	−28.6240	−	16.5261i	−0.915762	−	0.528715i	−0.0334814	−	0.999439i	$-0.510659\pi$
$977$	−28.6240	−	16.5261i	−0.915762	−	0.528715i	−0.882281	+	0.470724i	$0.843993\pi$
$978$		0			0
$979$	−7.99130	−	13.8413i	−0.255403	−	0.442371i
$980$		0			0
$981$	29.4322	+	20.4834i	0.939696	+	0.653985i
$982$		0			0
$983$	−1.80025	−	3.11812i	−0.0574189	−	0.0994525i	0.835887	−	0.548901i	$-0.184954\pi$
$983$	−1.80025	−	3.11812i	−0.0574189	−	0.0994525i	−0.893306	+	0.449449i	$0.851620\pi$
$984$		0			0
$985$	−0.308679	+	0.534647i	−0.00983532	+	0.0170353i
$986$		0			0
$987$	2.19921	−	52.0789i	0.0700015	−	1.65769i
$988$		0			0
$989$	34.1418			1.08565
$990$		0			0
$991$		−	2.89979i		−	0.0921149i	−0.998939	−	0.0460575i	$-0.985334\pi$
$991$		−	2.89979i		−	0.0921149i	0.998939	−	0.0460575i	$-0.0146657\pi$
$992$		0			0
$993$	−1.32165	+	2.08113i	−0.0419412	+	0.0660426i
$994$		0			0
$995$	−0.737786	−	0.425961i	−0.0233894	−	0.0135039i
$996$		0			0
$997$	37.0402	−	21.3851i	1.17307	−	0.677274i	0.218671	−	0.975799i	$-0.429828\pi$
$997$	37.0402	−	21.3851i	1.17307	−	0.677274i	0.954402	+	0.298524i	$0.0964944\pi$
$998$		0			0
$999$	1.45061	−	11.3961i	0.0458954	−	0.360555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1440.2.cc.a.1391.9		48
3.2	odd	2		4320.2.cc.b.3311.1		48
4.3	odd	2		360.2.bm.a.131.17	yes	48
8.3	odd	2		1440.2.cc.b.1391.9		48
8.5	even	2		360.2.bm.b.131.9	yes	48
9.2	odd	6		1440.2.cc.b.911.9		48
9.7	even	3		4320.2.cc.a.1871.24		48
12.11	even	2		1080.2.bm.b.611.8		48
24.5	odd	2		1080.2.bm.a.611.16		48
24.11	even	2		4320.2.cc.a.3311.24		48
36.7	odd	6		1080.2.bm.a.251.16		48
36.11	even	6		360.2.bm.b.11.9	yes	48
72.11	even	6	inner	1440.2.cc.a.911.9		48
72.29	odd	6		360.2.bm.a.11.17	✓	48
72.43	odd	6		4320.2.cc.b.1871.1		48
72.61	even	6		1080.2.bm.b.251.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.17	✓	48	72.29	odd	6
360.2.bm.a.131.17	yes	48	4.3	odd	2
360.2.bm.b.11.9	yes	48	36.11	even	6
360.2.bm.b.131.9	yes	48	8.5	even	2
1080.2.bm.a.251.16		48	36.7	odd	6
1080.2.bm.a.611.16		48	24.5	odd	2
1080.2.bm.b.251.8		48	72.61	even	6
1080.2.bm.b.611.8		48	12.11	even	2
1440.2.cc.a.911.9		48	72.11	even	6	inner
1440.2.cc.a.1391.9		48	1.1	even	1	trivial
1440.2.cc.b.911.9		48	9.2	odd	6
1440.2.cc.b.1391.9		48	8.3	odd	2
4320.2.cc.a.1871.24		48	9.7	even	3
4320.2.cc.a.3311.24		48	24.11	even	2
4320.2.cc.b.1871.1		48	72.43	odd	6
4320.2.cc.b.3311.1		48	3.2	odd	2

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:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.801968 - 1.53520i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-4.07138 + 2.35061i) q^{7} +(-1.71369 + 2.46237i) q^{9} +O(q^{10})\)	\(q+(-0.801968 - 1.53520i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-4.07138 + 2.35061i) q^{7} +(-1.71369 + 2.46237i) q^{9} +(3.19675 - 1.84565i) q^{11} +(2.94278 + 1.69902i) q^{13} +(1.73051 + 0.0730766i) q^{15} -3.19988i q^{17} +0.184741 q^{19} +(6.87379 + 4.36528i) q^{21} +(-1.68941 + 2.92615i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(5.15456 + 0.656128i) q^{27} +(-4.71642 - 8.16907i) q^{29} +(-1.31877 - 0.761389i) q^{31} +(-5.39713 - 3.42751i) q^{33} -4.70123i q^{35} -2.21087i q^{37} +(0.248316 - 5.88032i) q^{39} +(7.97131 + 4.60224i) q^{41} +(-5.05231 - 8.75086i) q^{43} +(-1.27563 - 2.71529i) q^{45} +(-3.20071 - 5.54379i) q^{47} +(7.55077 - 13.0783i) q^{49} +(-4.91246 + 2.56620i) q^{51} +0.652400 q^{53} +3.69129i q^{55} +(-0.148157 - 0.283616i) q^{57} +(-7.25989 - 4.19150i) q^{59} +(5.59632 - 3.23103i) q^{61} +(1.18903 - 14.0535i) q^{63} +(-2.94278 + 1.69902i) q^{65} +(0.725538 - 1.25667i) q^{67} +(5.84709 + 0.246913i) q^{69} +11.5995 q^{71} -15.3080 q^{73} +(-0.928540 + 1.46213i) q^{75} +(-8.67680 + 15.0287i) q^{77} +(-2.19259 + 1.26589i) q^{79} +(-3.12650 - 8.43949i) q^{81} +(3.86408 - 2.23093i) q^{83} +(2.77118 + 1.59994i) q^{85} +(-8.75877 + 13.7920i) q^{87} -4.32981i q^{89} -15.9749 q^{91} +(-0.111279 + 2.63518i) q^{93} +(-0.0923707 + 0.159991i) q^{95} +(-8.59159 - 14.8811i) q^{97} +(-0.933599 + 11.0345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{5}+O(q^{10}) \) 48 * q - 24 * q^5	\( 48 q - 24 q^{5} - 4 q^{21} - 24 q^{25} - 12 q^{27} - 8 q^{33} - 16 q^{39} + 12 q^{41} - 12 q^{47} + 24 q^{49} + 20 q^{51} + 4 q^{57} + 36 q^{59} + 12 q^{61} - 56 q^{63} - 40 q^{69} - 8 q^{81} + 60 q^{83} - 36 q^{87} + 16 q^{99}+O(q^{100}) \) 48 * q - 24 * q^5 - 4 * q^21 - 24 * q^25 - 12 * q^27 - 8 * q^33 - 16 * q^39 + 12 * q^41 - 12 * q^47 + 24 * q^49 + 20 * q^51 + 4 * q^57 + 36 * q^59 + 12 * q^61 - 56 * q^63 - 40 * q^69 - 8 * q^81 + 60 * q^83 - 36 * q^87 + 16 * q^99

Introduction

L-functions

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Database

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