LMFDB - Embedded newform 360.2.w.e.163.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(163,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("360.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.6
Character	$\chi$	$=$	360.163
Dual form			360.2.w.e.307.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.518298 + 1.31581i) q^{2} +(-1.46273 - 1.36397i) q^{4} +(-2.22965 - 0.169312i) q^{5} +(-0.645414 - 0.645414i) q^{7} +(2.55286 - 1.21775i) q^{8} +O(q^{10})$	\(q+(-0.518298 + 1.31581i) q^{2} +(-1.46273 - 1.36397i) q^{4} +(-2.22965 - 0.169312i) q^{5} +(-0.645414 - 0.645414i) q^{7} +(2.55286 - 1.21775i) q^{8} +(1.37841 - 2.84605i) q^{10} +2.11990 q^{11} +(1.65437 - 1.65437i) q^{13} +(1.18376 - 0.514728i) q^{14} +(0.279184 + 3.99025i) q^{16} +(4.23698 - 4.23698i) q^{17} -2.18966i q^{19} +(3.03045 + 3.28883i) q^{20} +(-1.09874 + 2.78940i) q^{22} +(6.05433 - 6.05433i) q^{23} +(4.94267 + 0.755014i) q^{25} +(1.31938 + 3.03429i) q^{26} +(0.0637454 + 1.82439i) q^{28} -7.93585 q^{29} +0.574128i q^{31} +(-5.39512 - 1.70078i) q^{32} +(3.37906 + 7.77109i) q^{34} +(1.32977 + 1.54832i) q^{35} +(-6.90775 - 6.90775i) q^{37} +(2.88118 + 1.13490i) q^{38} +(-5.89816 + 2.28291i) q^{40} -2.99799 q^{41} +(3.18765 + 3.18765i) q^{43} +(-3.10085 - 2.89148i) q^{44} +(4.82843 + 11.1043i) q^{46} +(5.04999 + 5.04999i) q^{47} -6.16688i q^{49} +(-3.55523 + 6.11231i) q^{50} +(-4.67640 + 0.163396i) q^{52} +(1.19626 - 1.19626i) q^{53} +(-4.72664 - 0.358925i) q^{55} +(-2.43360 - 0.861702i) q^{56} +(4.11314 - 10.4421i) q^{58} +11.5919i q^{59} +2.35096i q^{61} +(-0.755446 - 0.297570i) q^{62} +(5.03419 - 6.21747i) q^{64} +(-3.96876 + 3.40855i) q^{65} +(4.99799 - 4.99799i) q^{67} +(-11.9767 + 0.418473i) q^{68} +(-2.72652 + 0.947237i) q^{70} +5.01557i q^{71} +(-6.18765 - 6.18765i) q^{73} +(12.6696 - 5.50904i) q^{74} +(-2.98662 + 3.20289i) q^{76} +(-1.36821 - 1.36821i) q^{77} +10.1700 q^{79} +(0.0531148 - 8.94411i) q^{80} +(1.55385 - 3.94480i) q^{82} +(-11.7654 - 11.7654i) q^{83} +(-10.1643 + 8.72960i) q^{85} +(-5.84651 + 2.54221i) q^{86} +(5.41181 - 2.58150i) q^{88} -8.65485i q^{89} -2.13550 q^{91} +(-17.1138 + 0.597967i) q^{92} +(-9.26225 + 4.02745i) q^{94} +(-0.370736 + 4.88217i) q^{95} +(-8.06823 + 8.06823i) q^{97} +(8.11447 + 3.19628i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{8}+O(q^{10}) $ 24 * q + 12 * q^8	$ 24 q + 12 q^{8} + 8 q^{10} - 20 q^{16} - 8 q^{17} + 20 q^{20} - 28 q^{22} - 8 q^{25} + 16 q^{26} + 4 q^{28} - 20 q^{32} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 32 q^{43} + 48 q^{46} - 56 q^{50} - 48 q^{52} + 32 q^{56} - 12 q^{58} + 16 q^{62} + 8 q^{65} + 48 q^{67} - 72 q^{68} + 4 q^{70} - 40 q^{73} + 48 q^{76} - 76 q^{80} + 24 q^{82} - 80 q^{83} + 32 q^{86} + 12 q^{88} + 64 q^{91} - 16 q^{92} - 24 q^{97} + 88 q^{98}+O(q^{100}) $ 24 * q + 12 * q^8 + 8 * q^10 - 20 * q^16 - 8 * q^17 + 20 * q^20 - 28 * q^22 - 8 * q^25 + 16 * q^26 + 4 * q^28 - 20 * q^32 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 32 * q^43 + 48 * q^46 - 56 * q^50 - 48 * q^52 + 32 * q^56 - 12 * q^58 + 16 * q^62 + 8 * q^65 + 48 * q^67 - 72 * q^68 + 4 * q^70 - 40 * q^73 + 48 * q^76 - 76 * q^80 + 24 * q^82 - 80 * q^83 + 32 * q^86 + 12 * q^88 + 64 * q^91 - 16 * q^92 - 24 * q^97 + 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−0.518298	+	1.31581i	−0.366492	+	0.930421i
$2$	−0.518298	+	1.31581i	−0.366492	+	0.930421i
$3$		0			0
$3$		0			0
$4$	−1.46273	−	1.36397i	−0.731367	−	0.681984i
$5$	−2.22965	−	0.169312i	−0.997129	−	0.0757188i
$5$	−2.22965	−	0.169312i	−0.997129	−	0.0757188i
$6$		0			0
$7$	−0.645414	−	0.645414i	−0.243943	−	0.243943i	0.574536	−	0.818479i	$-0.305183\pi$
$7$	−0.645414	−	0.645414i	−0.243943	−	0.243943i	−0.818479	+	0.574536i	$0.805183\pi$
$8$	2.55286	−	1.21775i	0.902572	−	0.430538i
$9$		0			0
$10$	1.37841	−	2.84605i	0.435890	−	0.900000i
$11$	2.11990			0.639174			0.319587	−	0.947557i	$-0.396456\pi$
$11$	2.11990			0.639174			0.319587	+	0.947557i	$0.396456\pi$
$12$		0			0
$13$	1.65437	−	1.65437i	0.458839	−	0.458839i	−0.439435	−	0.898274i	$-0.644821\pi$
$13$	1.65437	−	1.65437i	0.458839	−	0.458839i	0.898274	+	0.439435i	$0.144821\pi$
$14$	1.18376	−	0.514728i	0.316374	−	0.137567i
$15$		0			0
$16$	0.279184	+	3.99025i	0.0697961	+	0.997561i
$17$	4.23698	−	4.23698i	1.02762	−	1.02762i	0.0280106	−	0.999608i	$-0.491083\pi$
$17$	4.23698	−	4.23698i	1.02762	−	1.02762i	0.999608	−	0.0280106i	$-0.00891721\pi$
$18$		0			0
$19$		−	2.18966i		−	0.502342i	−0.967943	−	0.251171i	$-0.919184\pi$
$19$		−	2.18966i		−	0.502342i	0.967943	−	0.251171i	$-0.0808157\pi$
$20$	3.03045	+	3.28883i	0.677629	+	0.735404i
$21$		0			0
$22$	−1.09874	+	2.78940i	−0.234252	+	0.594701i
$23$	6.05433	−	6.05433i	1.26242	−	1.26242i	0.312496	−	0.949919i	$-0.398835\pi$
$23$	6.05433	−	6.05433i	1.26242	−	1.26242i	0.949919	−	0.312496i	$-0.101165\pi$
$24$		0			0
$25$	4.94267	+	0.755014i	0.988533	+	0.151003i
$26$	1.31938	+	3.03429i	0.258753	+	0.595074i
$27$		0			0
$28$	0.0637454	+	1.82439i	0.0120468	+	0.344778i
$29$	−7.93585			−1.47365			−0.736825	−	0.676083i	$-0.763676\pi$
$29$	−7.93585			−1.47365			−0.736825	+	0.676083i	$0.763676\pi$
$30$		0			0
$31$			0.574128i			0.103116i	0.998670	+	0.0515582i	$0.0164188\pi$
$31$			0.574128i			0.103116i	−0.998670	+	0.0515582i	$0.983581\pi$
$32$	−5.39512	−	1.70078i	−0.953732	−	0.300658i
$33$		0			0
$34$	3.37906	+	7.77109i	0.579504	+	1.33273i
$35$	1.32977	+	1.54832i	0.224772	+	0.261714i
$36$		0			0
$37$	−6.90775	−	6.90775i	−1.13563	−	1.13563i	−0.989225	−	0.146402i	$-0.953231\pi$
$37$	−6.90775	−	6.90775i	−1.13563	−	1.13563i	−0.146402	−	0.989225i	$-0.546769\pi$
$38$	2.88118	+	1.13490i	0.467390	+	0.184104i
$39$		0			0
$40$	−5.89816	+	2.28291i	−0.932581	+	0.360960i
$41$	−2.99799			−0.468208			−0.234104	−	0.972212i	$-0.575216\pi$
$41$	−2.99799			−0.468208			−0.234104	+	0.972212i	$0.575216\pi$
$42$		0			0
$43$	3.18765	+	3.18765i	0.486112	+	0.486112i	0.907077	−	0.420965i	$-0.138308\pi$
$43$	3.18765	+	3.18765i	0.486112	+	0.486112i	−0.420965	+	0.907077i	$0.638308\pi$
$44$	−3.10085	−	2.89148i	−0.467471	−	0.435907i
$45$		0			0
$46$	4.82843	+	11.1043i	0.711913	+	1.63724i
$47$	5.04999	+	5.04999i	0.736617	+	0.736617i	0.971922	−	0.235305i	$-0.0756088\pi$
$47$	5.04999	+	5.04999i	0.736617	+	0.736617i	−0.235305	+	0.971922i	$0.575609\pi$
$48$		0			0
$49$		−	6.16688i		−	0.880983i
$50$	−3.55523	+	6.11231i	−0.502786	+	0.864411i
$51$		0			0
$52$	−4.67640	+	0.163396i	−0.648500	+	0.0226590i
$53$	1.19626	−	1.19626i	0.164319	−	0.164319i	−0.620158	−	0.784477i	$-0.712932\pi$
$53$	1.19626	−	1.19626i	0.164319	−	0.164319i	0.784477	+	0.620158i	$0.212932\pi$
$54$		0			0
$55$	−4.72664	−	0.358925i	−0.637340	−	0.0483975i
$56$	−2.43360	−	0.861702i	−0.325204	−	0.115150i
$57$		0			0
$58$	4.11314	−	10.4421i	0.540081	−	1.37112i
$59$			11.5919i			1.50913i	0.656225	+	0.754565i	$0.272152\pi$
$59$			11.5919i			1.50913i	−0.656225	+	0.754565i	$0.727848\pi$
$60$		0			0
$61$			2.35096i			0.301009i	0.988609	+	0.150505i	$0.0480898\pi$
$61$			2.35096i			0.301009i	−0.988609	+	0.150505i	$0.951910\pi$
$62$	−0.755446	−	0.297570i	−0.0959418	−	0.0377914i
$63$		0			0
$64$	5.03419	−	6.21747i	0.629274	−	0.777183i
$65$	−3.96876	+	3.40855i	−0.492264	+	0.422779i
$66$		0			0
$67$	4.99799	−	4.99799i	0.610602	−	0.610602i	−0.332501	−	0.943103i	$-0.607892\pi$
$67$	4.99799	−	4.99799i	0.610602	−	0.610602i	0.943103	+	0.332501i	$0.107892\pi$
$68$	−11.9767	+	0.418473i	−1.45239	+	0.0507473i
$69$		0			0
$70$	−2.72652	+	0.947237i	−0.325882	+	0.113217i
$71$			5.01557i			0.595239i	0.954685	+	0.297619i	$0.0961926\pi$
$71$			5.01557i			0.595239i	−0.954685	+	0.297619i	$0.903807\pi$
$72$		0			0
$73$	−6.18765	−	6.18765i	−0.724210	−	0.724210i	0.245250	−	0.969460i	$-0.421130\pi$
$73$	−6.18765	−	6.18765i	−0.724210	−	0.724210i	−0.969460	+	0.245250i	$0.921130\pi$
$74$	12.6696	−	5.50904i	1.47281	−	0.640413i
$75$		0			0
$76$	−2.98662	+	3.20289i	−0.342589	+	0.367397i
$77$	−1.36821	−	1.36821i	−0.155922	−	0.155922i
$78$		0			0
$79$	10.1700			1.14421			0.572106	−	0.820180i	$-0.306127\pi$
$79$	10.1700			1.14421			0.572106	+	0.820180i	$0.306127\pi$
$80$	0.0531148	−	8.94411i	0.00593841	−	0.999982i
$81$		0			0
$82$	1.55385	−	3.94480i	0.171594	−	0.435631i
$83$	−11.7654	−	11.7654i	−1.29142	−	1.29142i	−0.933906	−	0.357517i	$-0.883623\pi$
$83$	−11.7654	−	11.7654i	−1.29142	−	1.29142i	−0.357517	−	0.933906i	$-0.616377\pi$
$84$		0			0
$85$	−10.1643	+	8.72960i	−1.10248	+	0.946858i
$86$	−5.84651	+	2.54221i	−0.630446	+	0.274133i
$87$		0			0
$88$	5.41181	−	2.58150i	0.576901	−	0.275189i
$89$		−	8.65485i		−	0.917412i	−0.888588	−	0.458706i	$-0.848313\pi$
$89$		−	8.65485i		−	0.917412i	0.888588	−	0.458706i	$-0.151687\pi$
$90$		0			0
$91$	−2.13550			−0.223861
$92$	−17.1138	+	0.597967i	−1.78424	+	0.0623423i
$93$		0			0
$94$	−9.26225	+	4.02745i	−0.955328	+	0.415400i
$95$	−0.370736	+	4.88217i	−0.0380367	+	0.500900i
$96$		0			0
$97$	−8.06823	+	8.06823i	−0.819205	+	0.819205i	−0.985993	−	0.166788i	$-0.946660\pi$
$97$	−8.06823	+	8.06823i	−0.819205	+	0.819205i	0.166788	+	0.985993i	$0.446660\pi$
$98$	8.11447	+	3.19628i	0.819685	+	0.322873i
$99$		0			0
$100$	−6.19999	−	7.84602i	−0.619999	−	0.784602i
$101$		−	2.83542i		−	0.282135i	−0.990000	−	0.141067i	$-0.954947\pi$
$101$		−	2.83542i		−	0.282135i	0.990000	−	0.141067i	$-0.0450534\pi$
$102$		0			0
$103$	7.52594	−	7.52594i	0.741553	−	0.741553i	−0.231324	−	0.972877i	$-0.574306\pi$
$103$	7.52594	−	7.52594i	0.741553	−	0.741553i	0.972877	+	0.231324i	$0.0743057\pi$
$104$	2.20877	−	6.23796i	0.216588	−	0.611683i
$105$		0			0
$106$	0.954037	+	2.19408i	0.0926643	+	0.213107i
$107$	2.38812	−	2.38812i	0.230868	−	0.230868i	−0.582187	−	0.813055i	$-0.697803\pi$
$107$	2.38812	−	2.38812i	0.230868	−	0.230868i	0.813055	+	0.582187i	$0.197803\pi$
$108$		0			0
$109$	3.69420			0.353840			0.176920	−	0.984225i	$-0.443387\pi$
$109$	3.69420			0.353840			0.176920	+	0.984225i	$0.443387\pi$
$110$	2.92209	−	6.03335i	0.278610	−	0.575257i
$111$		0			0
$112$	2.39517	−	2.75555i	0.226322	−	0.260375i
$113$	3.14033	+	3.14033i	0.295418	+	0.295418i	0.839216	−	0.543798i	$-0.183014\pi$
$113$	3.14033	+	3.14033i	0.295418	+	0.295418i	−0.543798	+	0.839216i	$0.683014\pi$
$114$		0			0
$115$	−14.5241	+	12.4740i	−1.35438	+	1.16320i
$116$	11.6080	+	10.8242i	1.07778	+	1.00501i
$117$		0			0
$118$	−15.2527	−	6.00803i	−1.40413	−	0.553084i
$119$	−5.46921			−0.501362
$120$		0			0
$121$	−6.50602			−0.591456
$122$	−3.09342	−	1.21850i	−0.280065	−	0.110317i
$123$		0			0
$124$	0.783093	−	0.839797i	0.0703238	−	0.0754160i
$125$	−10.8926	−	2.52027i	−0.974262	−	0.225420i
$126$		0			0
$127$	12.1799	+	12.1799i	1.08080	+	1.08080i	0.996435	+	0.0843601i	$0.0268846\pi$
$127$	12.1799	+	12.1799i	1.08080	+	1.08080i	0.0843601	+	0.996435i	$0.473115\pi$
$128$	5.57182	+	9.84656i	0.492484	+	0.870321i
$129$		0			0
$130$	−2.42802	−	6.98880i	−0.212951	−	0.612958i
$131$	0.440307			0.0384698			0.0192349	−	0.999815i	$-0.493877\pi$
$131$	0.440307			0.0384698			0.0192349	+	0.999815i	$0.493877\pi$
$132$		0			0
$133$	−1.41324	+	1.41324i	−0.122543	+	0.122543i
$134$	3.98598	+	9.16688i	0.344336	+	0.791898i
$135$		0			0
$136$	5.65685	−	15.9760i	0.485071	−	1.36993i
$137$	1.57812	−	1.57812i	0.134828	−	0.134828i	−0.636472	−	0.771300i	$-0.719607\pi$
$137$	1.57812	−	1.57812i	0.134828	−	0.134828i	0.771300	+	0.636472i	$0.219607\pi$
$138$		0			0
$139$			12.6228i			1.07065i	0.844647	+	0.535324i	$0.179810\pi$
$139$			12.6228i			1.07065i	−0.844647	+	0.535324i	$0.820190\pi$
$140$	0.166762	−	4.07855i	0.0140940	−	0.344700i
$141$		0			0
$142$	−6.59956	−	2.59956i	−0.553823	−	0.218150i
$143$	3.50709	−	3.50709i	0.293278	−	0.293278i
$144$		0			0
$145$	17.6942	+	1.34364i	1.46942	+	0.111583i
$146$	11.3488	−	4.93475i	0.939237	−	0.408403i
$147$		0			0
$148$	0.682256	+	19.5262i	0.0560811	+	1.60504i
$149$	18.4367			1.51039			0.755195	−	0.655500i	$-0.227542\pi$
$149$	18.4367			1.51039			0.755195	+	0.655500i	$0.227542\pi$
$150$		0			0
$151$			0.00374102i			0.000304440i	1.00000		0.000152220i	$4.84532e-5\pi$
$151$			0.00374102i			0.000304440i	−1.00000		0.000152220i	$0.999952\pi$
$152$	−2.66645	−	5.58989i	−0.216277	−	0.453400i
$153$		0			0
$154$	2.50946	−	1.09117i	0.202218	−	0.0879292i
$155$	0.0972070	−	1.28010i	0.00780785	−	0.102820i
$156$		0			0
$157$	11.3149	+	11.3149i	0.903028	+	0.903028i	0.995697	−	0.0926688i	$-0.0295398\pi$
$157$	11.3149	+	11.3149i	0.903028	+	0.903028i	−0.0926688	+	0.995697i	$0.529540\pi$
$158$	−5.27108	+	13.3818i	−0.419344	+	1.06460i
$159$		0			0
$160$	11.7413	+	4.70561i	0.928228	+	0.372011i
$161$	−7.81510			−0.615916
$162$		0			0
$163$	−5.79433	−	5.79433i	−0.453847	−	0.453847i	0.442782	−	0.896629i	$-0.353991\pi$
$163$	−5.79433	−	5.79433i	−0.453847	−	0.453847i	−0.896629	+	0.442782i	$0.853991\pi$
$164$	4.38527	+	4.08917i	0.342432	+	0.319310i
$165$		0			0
$166$	21.5791	−	9.38312i	1.67486	−	0.728272i
$167$	2.21418	+	2.21418i	0.171339	+	0.171339i	0.787567	−	0.616229i	$-0.211340\pi$
$167$	2.21418	+	2.21418i	0.171339	+	0.171339i	−0.616229	+	0.787567i	$0.711340\pi$
$168$		0			0
$169$			7.52614i			0.578934i
$170$	−6.21837	−	17.8989i	−0.476927	−	1.37278i
$171$		0			0
$172$	−0.314834	−	9.01055i	−0.0240059	−	0.687048i
$173$	−7.02012	+	7.02012i	−0.533730	+	0.533730i	−0.921680	−	0.387951i	$-0.873183\pi$
$173$	−7.02012	+	7.02012i	−0.533730	+	0.533730i	0.387951	+	0.921680i	$0.373183\pi$
$174$		0			0
$175$	−2.70277	−	3.67736i	−0.204310	−	0.277982i
$176$	0.591843	+	8.45893i	0.0446119	+	0.637616i
$177$		0			0
$178$	11.3882	+	4.48579i	0.853580	+	0.336224i
$179$			13.2165i			0.987851i	0.869504	+	0.493926i	$0.164438\pi$
$179$			13.2165i			0.987851i	−0.869504	+	0.493926i	$0.835562\pi$
$180$		0			0
$181$		−	7.24786i		−	0.538729i	−0.963038	−	0.269365i	$-0.913186\pi$
$181$		−	7.24786i		−	0.538729i	0.963038	−	0.269365i	$-0.0868137\pi$
$182$	1.10683	−	2.80992i	0.0820434	−	0.208285i
$183$		0			0
$184$	8.08323	−	22.8285i	0.595903	−	1.68294i
$185$	14.2323	+	16.5714i	1.04638	+	1.21836i
$186$		0			0
$187$	8.98198	−	8.98198i	0.656827	−	0.656827i
$188$	−0.498771	−	14.2748i	−0.0363766	−	1.04110i
$189$		0			0
$190$	−6.23188	−	3.01824i	−0.452108	−	0.218966i
$191$		−	4.60879i		−	0.333480i	−0.986001	−	0.166740i	$-0.946676\pi$
$191$		−	4.60879i		−	0.333480i	0.986001	−	0.166740i	$-0.0533241\pi$
$192$		0			0
$193$	2.88058	+	2.88058i	0.207349	+	0.207349i	0.803140	−	0.595791i	$-0.203161\pi$
$193$	2.88058	+	2.88058i	0.207349	+	0.207349i	−0.595791	+	0.803140i	$0.703161\pi$
$194$	−6.43455	−	14.7980i	−0.461973	−	1.06244i
$195$		0			0
$196$	−8.41143	+	9.02051i	−0.600816	+	0.644322i
$197$	13.3607	+	13.3607i	0.951911	+	0.951911i	0.998896	−	0.0469844i	$-0.0149611\pi$
$197$	13.3607	+	13.3607i	0.951911	+	0.951911i	−0.0469844	+	0.998896i	$0.514961\pi$
$198$		0			0
$199$	−21.3015			−1.51002			−0.755010	−	0.655713i	$-0.772368\pi$
$199$	−21.3015			−1.51002			−0.755010	+	0.655713i	$0.772368\pi$
$200$	13.5374	−	4.09146i	0.957235	−	0.289310i
$201$		0			0
$202$	3.73088	+	1.46959i	0.262504	+	0.103400i
$203$	5.12191	+	5.12191i	0.359487	+	0.359487i
$204$		0			0
$205$	6.68447	+	0.507597i	0.466864	+	0.0354521i
$206$	6.00206	+	13.8034i	0.418183	+	0.961730i
$207$		0			0
$208$	7.06320	+	6.13945i	0.489745	+	0.425695i
$209$		−	4.64186i		−	0.321084i
$210$		0			0
$211$	10.2796			0.707677			0.353839	−	0.935306i	$-0.384876\pi$
$211$	10.2796			0.707677			0.353839	+	0.935306i	$0.384876\pi$
$212$	−3.38147	+	0.118151i	−0.232240	+	0.00811463i
$213$		0			0
$214$	1.90456	+	4.38008i	0.130193	+	0.299416i
$215$	−6.56764	−	7.64705i	−0.447909	−	0.521525i
$216$		0			0
$217$	0.370550	−	0.370550i	0.0251546	−	0.0251546i
$218$	−1.91470	+	4.86088i	−0.129680	+	0.329221i
$219$		0			0
$220$	6.42425	+	6.97199i	0.433123	+	0.470052i
$221$		−	14.0190i		−	0.943022i
$222$		0			0
$223$	−8.17006	+	8.17006i	−0.547108	+	0.547108i	−0.925603	−	0.378495i	$-0.876442\pi$
$223$	−8.17006	+	8.17006i	−0.547108	+	0.547108i	0.378495	+	0.925603i	$0.376442\pi$
$224$	2.38438	+	4.57979i	0.159313	+	0.306000i
$225$		0			0
$226$	−5.75972	+	2.50447i	−0.383131	+	0.166595i
$227$	5.26621	−	5.26621i	0.349531	−	0.349531i	−0.510404	−	0.859935i	$-0.670504\pi$
$227$	5.26621	−	5.26621i	0.349531	−	0.349531i	0.859935	+	0.510404i	$0.170504\pi$
$228$		0			0
$229$	−3.12556			−0.206543			−0.103271	−	0.994653i	$-0.532931\pi$
$229$	−3.12556			−0.206543			−0.103271	+	0.994653i	$0.532931\pi$
$230$	−8.88560	−	25.5762i	−0.585899	−	1.68645i
$231$		0			0
$232$	−20.2591	+	9.66384i	−1.33008	+	0.634463i
$233$	2.41787	+	2.41787i	0.158400	+	0.158400i	0.781857	−	0.623457i	$-0.214273\pi$
$233$	2.41787	+	2.41787i	0.158400	+	0.158400i	−0.623457	+	0.781857i	$0.714273\pi$
$234$		0			0
$235$	−10.4047	−	12.1147i	−0.678726	−	0.790278i
$236$	15.8109	−	16.9558i	1.02920	−	1.10373i
$237$		0			0
$238$	2.83468	−	7.19646i	0.183745	−	0.466477i
$239$	6.68630			0.432501			0.216251	−	0.976338i	$-0.430617\pi$
$239$	6.68630			0.432501			0.216251	+	0.976338i	$0.430617\pi$
$240$		0			0
$241$	−15.8501			−1.02100			−0.510499	−	0.859878i	$-0.670539\pi$
$241$	−15.8501			−1.02100			−0.510499	+	0.859878i	$0.670539\pi$
$242$	3.37205	−	8.56071i	0.216764	−	0.550303i
$243$		0			0
$244$	3.20663	−	3.43883i	0.205283	−	0.220148i
$245$	−1.04413	+	13.7500i	−0.0667070	+	0.878454i
$246$		0			0
$247$	−3.62250	−	3.62250i	−0.230494	−	0.230494i
$248$	0.699142	+	1.46567i	0.0443956	+	0.0930701i
$249$		0			0
$250$	8.96181	−	13.0264i	0.566794	−	0.823859i
$251$	−4.25540			−0.268599			−0.134299	−	0.990941i	$-0.542878\pi$
$251$	−4.25540			−0.268599			−0.134299	+	0.990941i	$0.542878\pi$
$252$		0			0
$253$	12.8346	−	12.8346i	0.806904	−	0.806904i
$254$	−22.3394	+	9.71371i	−1.40170	+	0.609492i
$255$		0			0
$256$	−15.8441	+	2.22803i	−0.990257	+	0.139252i
$257$	−3.15838	+	3.15838i	−0.197015	+	0.197015i	−0.798719	−	0.601704i	$-0.794489\pi$
$257$	−3.15838	+	3.15838i	−0.197015	+	0.197015i	0.601704	+	0.798719i	$0.294489\pi$
$258$		0			0
$259$			8.91671i			0.554058i
$260$	10.4544	+	0.427456i	0.648354	+	0.0265097i
$261$		0			0
$262$	−0.228210	+	0.579363i	−0.0140989	+	0.0357931i
$263$	−9.25036	+	9.25036i	−0.570402	+	0.570402i	−0.932241	−	0.361839i	$-0.882149\pi$
$263$	−9.25036	+	9.25036i	−0.570402	+	0.570402i	0.361839	+	0.932241i	$0.382149\pi$
$264$		0			0
$265$	−2.86978	+	2.46470i	−0.176289	+	0.151405i
$266$	−1.12708	−	2.59203i	−0.0691056	−	0.158928i
$267$		0			0
$268$	−14.1278	+	0.493636i	−0.862995	+	0.0301536i
$269$	−2.69801			−0.164501			−0.0822504	−	0.996612i	$-0.526211\pi$
$269$	−2.69801			−0.164501			−0.0822504	+	0.996612i	$0.526211\pi$
$270$		0			0
$271$			23.9762i			1.45645i	0.685336	+	0.728227i	$0.259655\pi$
$271$			23.9762i			1.45645i	−0.685336	+	0.728227i	$0.740345\pi$
$272$	18.0895	+	15.7237i	1.09684	+	0.953388i
$273$		0			0
$274$	1.25857	+	2.89445i	0.0760333	+	0.174860i
$275$	10.4780	+	1.60056i	0.631845	+	0.0965171i
$276$		0			0
$277$	0.392928	+	0.392928i	0.0236087	+	0.0236087i	0.718813	−	0.695204i	$-0.244686\pi$
$277$	0.392928	+	0.392928i	0.0236087	+	0.0236087i	−0.695204	+	0.718813i	$0.744686\pi$
$278$	−16.6092	−	6.54235i	−0.996154	−	0.392384i
$279$		0			0
$280$	5.28018	+	2.33333i	0.315551	+	0.139443i
$281$	−24.8077			−1.47990			−0.739952	−	0.672659i	$-0.765152\pi$
$281$	−24.8077			−1.47990			−0.739952	+	0.672659i	$0.765152\pi$
$282$		0			0
$283$	−9.23780	−	9.23780i	−0.549130	−	0.549130i	0.377059	−	0.926189i	$-0.376935\pi$
$283$	−9.23780	−	9.23780i	−0.549130	−	0.549130i	−0.926189	+	0.377059i	$0.876935\pi$
$284$	6.84108	−	7.33645i	0.405943	−	0.435338i
$285$		0			0
$286$	2.79697	+	6.43240i	0.165388	+	0.380356i
$287$	1.93495	+	1.93495i	0.114216	+	0.114216i
$288$		0			0
$289$		−	18.9040i		−	1.11200i
$290$	−10.9388	+	22.5858i	−0.642350	+	1.32629i
$291$		0			0
$292$	0.611134	+	17.4907i	0.0357639	+	1.02356i
$293$	11.1431	−	11.1431i	0.650987	−	0.650987i	−0.302244	−	0.953231i	$-0.597736\pi$
$293$	11.1431	−	11.1431i	0.650987	−	0.650987i	0.953231	+	0.302244i	$0.0977357\pi$
$294$		0			0
$295$	1.96264	−	25.8458i	0.114270	−	1.50480i
$296$	−26.0464	−	9.22264i	−1.51392	−	0.536055i
$297$		0			0
$298$	−9.55568	+	24.2592i	−0.553546	+	1.40530i
$299$		−	20.0322i		−	1.15849i
$300$		0			0
$301$		−	4.11471i		−	0.237168i
$302$	−0.00492249	−	0.00193897i	−0.000283258	−	0.000111575i
$303$		0			0
$304$	8.73728	−	0.611318i	0.501117	−	0.0350615i
$305$	0.398046	−	5.24181i	0.0227921	−	0.300145i
$306$		0			0
$307$	12.0381	−	12.0381i	0.687053	−	0.687053i	−0.274527	−	0.961580i	$-0.588521\pi$
$307$	12.0381	−	12.0381i	0.687053	−	0.687053i	0.961580	+	0.274527i	$0.0885211\pi$
$308$	0.135134	+	3.86753i	0.00769998	+	0.220373i
$309$		0			0
$310$	1.63400	+	0.791382i	0.0928048	+	0.0449475i
$311$		−	30.9541i		−	1.75525i	−0.479350	−	0.877624i	$-0.659128\pi$
$311$		−	30.9541i		−	1.75525i	0.479350	−	0.877624i	$-0.340872\pi$
$312$		0			0
$313$	8.62544	+	8.62544i	0.487539	+	0.487539i	0.907529	−	0.419990i	$-0.137966\pi$
$313$	8.62544	+	8.62544i	0.487539	+	0.487539i	−0.419990	+	0.907529i	$0.637966\pi$
$314$	−20.7528	+	9.02383i	−1.17115	+	0.509244i
$315$		0			0
$316$	−14.8760	−	13.8715i	−0.836839	−	0.780334i
$317$	2.34682	+	2.34682i	0.131811	+	0.131811i	0.769934	−	0.638123i	$-0.220289\pi$
$317$	2.34682	+	2.34682i	0.131811	+	0.131811i	−0.638123	+	0.769934i	$0.720289\pi$
$318$		0			0
$319$	−16.8232			−0.941920
$320$	−12.2772	+	13.0104i	−0.686315	+	0.727304i
$321$		0			0
$322$	4.05055	−	10.2832i	0.225728	−	0.573061i
$323$	−9.27754	−	9.27754i	−0.516216	−	0.516216i
$324$		0			0
$325$	9.42605	−	6.92791i	0.522863	−	0.384291i
$326$	10.6274	−	4.62107i	0.588600	−	0.255937i
$327$		0			0
$328$	−7.65346	+	3.65079i	−0.422592	+	0.201581i
$329$		−	6.51867i		−	0.359386i
$330$		0			0
$331$	12.1856			0.669784			0.334892	−	0.942257i	$-0.391300\pi$
$331$	12.1856			0.669784			0.334892	+	0.942257i	$0.391300\pi$
$332$	1.16203	+	33.2574i	0.0637749	+	1.82524i
$333$		0			0
$334$	−4.06106	+	1.76585i	−0.222211	+	0.0966229i
$335$	−11.9900	+	10.2975i	−0.655083	+	0.562615i
$336$		0			0
$337$	−8.63207	+	8.63207i	−0.470219	+	0.470219i	−0.901985	−	0.431767i	$-0.857890\pi$
$337$	−8.63207	+	8.63207i	−0.470219	+	0.470219i	0.431767	+	0.901985i	$0.357890\pi$
$338$	−9.90301	−	3.90079i	−0.538653	−	0.212175i
$339$		0			0
$340$	26.7746	+	1.09475i	1.45206	+	0.0593712i
$341$			1.21710i			0.0659094i
$342$		0			0
$343$	−8.49809	+	8.49809i	−0.458854	+	0.458854i
$344$	12.0194	+	4.25588i	0.648042	+	0.229462i
$345$		0			0
$346$	−5.59866	−	12.8757i	−0.300986	−	0.692201i
$347$	7.30238	−	7.30238i	0.392013	−	0.392013i	−0.483392	−	0.875404i	$-0.660595\pi$
$347$	7.30238	−	7.30238i	0.392013	−	0.392013i	0.875404	+	0.483392i	$0.160595\pi$
$348$		0			0
$349$	14.2003			0.760124			0.380062	−	0.924961i	$-0.375903\pi$
$349$	14.2003			0.760124			0.380062	+	0.924961i	$0.375903\pi$
$350$	6.23956	−	1.65037i	0.333519	−	0.0882161i
$351$		0			0
$352$	−11.4371	−	3.60549i	−0.609601	−	0.192173i
$353$	−4.21893	−	4.21893i	−0.224551	−	0.224551i	0.585861	−	0.810412i	$-0.300757\pi$
$353$	−4.21893	−	4.21893i	−0.224551	−	0.224551i	−0.810412	+	0.585861i	$0.800757\pi$
$354$		0			0
$355$	0.849198	−	11.1830i	0.0450707	−	0.593530i
$356$	−11.8049	+	12.6597i	−0.625660	+	0.670965i
$357$		0			0
$358$	−17.3905	−	6.85011i	−0.919118	−	0.362040i
$359$	−34.5078			−1.82125			−0.910626	−	0.413232i	$-0.864400\pi$
$359$	−34.5078			−1.82125			−0.910626	+	0.413232i	$0.864400\pi$
$360$		0			0
$361$	14.2054			0.747652
$362$	9.53684	+	3.75655i	0.501245	+	0.197440i
$363$		0			0
$364$	3.12367	+	2.91276i	0.163725	+	0.152670i
$365$	12.7486	+	14.8439i	0.667295	+	0.776967i
$366$		0			0
$367$	3.79229	+	3.79229i	0.197956	+	0.197956i	0.799123	−	0.601167i	$-0.205297\pi$
$367$	3.79229	+	3.79229i	0.197956	+	0.197956i	−0.601167	+	0.799123i	$0.705297\pi$
$368$	25.8485	+	22.4680i	1.34745	+	1.17122i
$369$		0			0
$370$	−29.1815	+	10.1381i	−1.51707	+	0.527055i
$371$	−1.54417			−0.0801691
$372$		0			0
$373$	−15.0702	+	15.0702i	−0.780305	+	0.780305i	−0.979882	−	0.199577i	$-0.936043\pi$
$373$	−15.0702	+	15.0702i	−0.780305	+	0.780305i	0.199577	+	0.979882i	$0.436043\pi$
$374$	7.16327	+	16.4740i	0.370404	+	0.851848i
$375$		0			0
$376$	19.0415	+	6.74232i	0.981992	+	0.347709i
$377$	−13.1288	+	13.1288i	−0.676168	+	0.676168i
$378$		0			0
$379$			25.4415i			1.30684i	0.756995	+	0.653421i	$0.226667\pi$
$379$			25.4415i			1.30684i	−0.756995	+	0.653421i	$0.773333\pi$
$380$	7.20141	−	6.63565i	0.369425	−	0.340401i
$381$		0			0
$382$	6.06431	+	2.38872i	0.310277	+	0.122218i
$383$	−5.40762	+	5.40762i	−0.276317	+	0.276317i	−0.831637	−	0.555320i	$-0.812596\pi$
$383$	−5.40762	+	5.40762i	−0.276317	+	0.276317i	0.555320	+	0.831637i	$0.312596\pi$
$384$		0			0
$385$	2.81898	+	3.28229i	0.143669	+	0.167281i
$386$	−5.28330	+	2.29731i	−0.268913	+	0.116930i
$387$		0			0
$388$	22.8065	−	0.796873i	1.15782	−	0.0404551i
$389$	4.35502			0.220809			0.110404	−	0.993887i	$-0.464785\pi$
$389$	4.35502			0.220809			0.110404	+	0.993887i	$0.464785\pi$
$390$		0			0
$391$		−	51.3041i		−	2.59456i
$392$	−7.50969	−	15.7432i	−0.379297	−	0.795151i
$393$		0			0
$394$	−24.5050	+	10.6554i	−1.23455	+	0.536811i
$395$	−22.6755	−	1.72190i	−1.14093	−	0.0866383i
$396$		0			0
$397$	−12.1053	−	12.1053i	−0.607550	−	0.607550i	0.334755	−	0.942305i	$-0.391346\pi$
$397$	−12.1053	−	12.1053i	−0.607550	−	0.607550i	−0.942305	+	0.334755i	$0.891346\pi$
$398$	11.0405	−	28.0288i	0.553410	−	1.40496i
$399$		0			0
$400$	−1.63278	+	19.9332i	−0.0816388	+	0.996662i
$401$	26.5884			1.32776			0.663880	−	0.747839i	$-0.268909\pi$
$401$	26.5884			1.32776			0.663880	+	0.747839i	$0.268909\pi$
$402$		0			0
$403$	0.949819	+	0.949819i	0.0473138	+	0.0473138i
$404$	−3.86742	+	4.14746i	−0.192411	+	0.206344i
$405$		0			0
$406$	−9.39415	+	4.08481i	−0.466224	+	0.202725i
$407$	−14.6438	−	14.6438i	−0.725864	−	0.725864i
$408$		0			0
$409$		−	9.14423i		−	0.452153i	−0.974110	−	0.226077i	$-0.927410\pi$
$409$		−	9.14423i		−	0.452153i	0.974110	−	0.226077i	$-0.0725900\pi$
$410$	−4.13245	+	8.53244i	−0.204087	+	0.421387i
$411$		0			0
$412$	−21.2736	+	0.743313i	−1.04807	+	0.0366204i
$413$	7.48154	−	7.48154i	0.368143	−	0.368143i
$414$		0			0
$415$	24.2407	+	28.2248i	1.18993	+	1.38550i
$416$	−11.7392	+	6.11179i	−0.575563	+	0.299655i
$417$		0			0
$418$	6.10783	+	2.40587i	0.298744	+	0.117675i
$419$			4.32353i			0.211218i	0.994408	+	0.105609i	$0.0336793\pi$
$419$			4.32353i			0.211218i	−0.994408	+	0.105609i	$0.966321\pi$
$420$		0			0
$421$		−	8.49742i		−	0.414139i	−0.978326	−	0.207069i	$-0.933607\pi$
$421$		−	8.49742i		−	0.414139i	0.978326	−	0.207069i	$-0.0663926\pi$
$422$	−5.32790	+	13.5261i	−0.259358	+	0.658438i
$423$		0			0
$424$	1.59714	−	4.51062i	0.0775642	−	0.219055i
$425$	24.1409	−	17.7430i	1.17101	−	0.860662i
$426$		0			0
$427$	1.51734	−	1.51734i	0.0734293	−	0.0734293i
$428$	−6.75050	+	0.235867i	−0.326298	+	0.0114011i
$429$		0			0
$430$	13.4661	−	4.67834i	0.649393	−	0.225609i
$431$			25.8697i			1.24610i	0.782182	+	0.623050i	$0.214107\pi$
$431$			25.8697i			1.24610i	−0.782182	+	0.623050i	$0.785893\pi$
$432$		0			0
$433$	18.1990	+	18.1990i	0.874590	+	0.874590i	0.992969	−	0.118378i	$-0.0377696\pi$
$433$	18.1990	+	18.1990i	0.874590	+	0.874590i	−0.118378	+	0.992969i	$0.537770\pi$
$434$	0.295520	+	0.679631i	0.0141854	+	0.0326233i
$435$		0			0
$436$	−5.40364	−	5.03877i	−0.258787	−	0.241313i
$437$	−13.2569	−	13.2569i	−0.634164	−	0.634164i
$438$		0			0
$439$	−16.7069			−0.797377			−0.398688	−	0.917086i	$-0.630535\pi$
$439$	−16.7069			−0.797377			−0.398688	+	0.917086i	$0.630535\pi$
$440$	−12.5035	+	4.83955i	−0.596082	+	0.230717i
$441$		0			0
$442$	18.4464	+	7.26603i	0.877408	+	0.345610i
$443$	4.25017	+	4.25017i	0.201932	+	0.201932i	0.800827	−	0.598896i	$-0.204394\pi$
$443$	4.25017	+	4.25017i	0.201932	+	0.201932i	−0.598896	+	0.800827i	$0.704394\pi$
$444$		0			0
$445$	−1.46537	+	19.2973i	−0.0694653	+	0.914778i
$446$	−6.51576	−	14.9848i	−0.308530	−	0.709551i
$447$		0			0
$448$	−7.26198	+	0.763702i	−0.343096	+	0.0360815i
$449$			36.7452i			1.73412i	0.498208	+	0.867058i	$0.333992\pi$
$449$			36.7452i			1.73412i	−0.498208	+	0.867058i	$0.666008\pi$
$450$		0			0
$451$	−6.35545			−0.299267
$452$	−0.310161	−	8.87679i	−0.0145887	−	0.417529i
$453$		0			0
$454$	4.19989	+	9.65882i	0.197111	+	0.453311i
$455$	4.76142	+	0.361567i	0.223219	+	0.0169505i
$456$		0			0
$457$	19.5101	−	19.5101i	0.912645	−	0.912645i	−0.0838344	−	0.996480i	$-0.526717\pi$
$457$	19.5101	−	19.5101i	0.912645	−	0.912645i	0.996480	+	0.0838344i	$0.0267167\pi$
$458$	1.61997	−	4.11266i	0.0756963	−	0.192172i
$459$		0			0
$460$	38.2590	+	1.56432i	1.78383	+	0.0729368i
$461$		−	5.42713i		−	0.252767i	−0.991981	−	0.126383i	$-0.959663\pi$
$461$		−	5.42713i		−	0.252767i	0.991981	−	0.126383i	$-0.0403370\pi$
$462$		0			0
$463$	24.1397	−	24.1397i	1.12187	−	1.12187i	0.130407	−	0.991461i	$-0.458372\pi$
$463$	24.1397	−	24.1397i	1.12187	−	1.12187i	0.991461	−	0.130407i	$-0.0416285\pi$
$464$	−2.21556	−	31.6660i	−0.102855	−	1.47006i
$465$		0			0
$466$	−4.43464	+	1.92829i	−0.205431	+	0.0893263i
$467$	19.6661	−	19.6661i	0.910039	−	0.910039i	−0.0862361	−	0.996275i	$-0.527484\pi$
$467$	19.6661	−	19.6661i	0.910039	−	0.910039i	0.996275	+	0.0862361i	$0.0274839\pi$
$468$		0			0
$469$	−6.45155			−0.297905
$470$	21.3335	−	7.41159i	0.984039	−	0.341871i
$471$		0			0
$472$	14.1159	+	29.5924i	0.649738	+	1.36210i
$473$	6.75751	+	6.75751i	0.310711	+	0.310711i
$474$		0			0
$475$	1.65322	−	10.8228i	0.0758551	−	0.496582i
$476$	8.00000	+	7.45982i	0.366679	+	0.341920i
$477$		0			0
$478$	−3.46550	+	8.79793i	−0.158508	+	0.402408i
$479$	−4.12247			−0.188360			−0.0941802	−	0.995555i	$-0.530023\pi$
$479$	−4.12247			−0.188360			−0.0941802	+	0.995555i	$0.530023\pi$
$480$		0			0
$481$	−22.8559			−1.04214
$482$	8.21510	−	20.8558i	0.374187	−	0.949958i
$483$		0			0
$484$	9.51657	+	8.87400i	0.432572	+	0.403363i
$485$	19.3554	−	16.6233i	0.878882	−	0.754824i
$486$		0			0
$487$	−17.0261	−	17.0261i	−0.771525	−	0.771525i	0.206848	−	0.978373i	$-0.433679\pi$
$487$	−17.0261	−	17.0261i	−0.771525	−	0.771525i	−0.978373	+	0.206848i	$0.933679\pi$
$488$	2.86287	+	6.00167i	0.129596	+	0.271683i
$489$		0			0
$490$	−17.5513	−	8.50047i	−0.792885	−	0.384012i
$491$	6.33601			0.285940			0.142970	−	0.989727i	$-0.454335\pi$
$491$	6.33601			0.285940			0.142970	+	0.989727i	$0.454335\pi$
$492$		0			0
$493$	−33.6240	+	33.6240i	−1.51435	+	1.51435i
$494$	6.64407	−	2.88900i	0.298931	−	0.129982i
$495$		0			0
$496$	−2.29091	+	0.160288i	−0.102865	+	0.00719713i
$497$	3.23712	−	3.23712i	0.145205	−	0.145205i
$498$		0			0
$499$			17.1014i			0.765564i	0.923839	+	0.382782i	$0.125034\pi$
$499$			17.1014i			0.765564i	−0.923839	+	0.382782i	$0.874966\pi$
$500$	12.4954	+	18.5436i	0.558810	+	0.829295i
$501$		0			0
$502$	2.20557	−	5.59932i	0.0984393	−	0.249910i
$503$	7.10917	−	7.10917i	0.316982	−	0.316982i	−0.530625	−	0.847607i	$-0.678043\pi$
$503$	7.10917	−	7.10917i	0.316982	−	0.316982i	0.847607	+	0.530625i	$0.178043\pi$
$504$		0			0
$505$	−0.480071	+	6.32198i	−0.0213629	+	0.281325i
$506$	10.2358	+	23.5401i	0.455036	+	1.04648i
$507$		0			0
$508$	−1.20297	−	34.4291i	−0.0533733	−	1.52754i
$509$	16.3100			0.722927			0.361464	−	0.932386i	$-0.382277\pi$
$509$	16.3100			0.722927			0.361464	+	0.932386i	$0.382277\pi$
$510$		0			0
$511$			7.98719i			0.353333i
$512$	5.28030	−	22.0027i	0.233359	−	0.972391i
$513$		0			0
$514$	−2.51886	−	5.79283i	−0.111102	−	0.255511i
$515$	−18.0544	+	15.5060i	−0.795574	+	0.683275i
$516$		0			0
$517$	10.7055	+	10.7055i	0.470827	+	0.470827i
$518$	−11.7327	−	4.62151i	−0.515507	−	0.203058i
$519$		0			0
$520$	−5.98094	+	13.5345i	−0.262282	+	0.593527i
$521$	5.97735			0.261872			0.130936	−	0.991391i	$-0.458202\pi$
$521$	5.97735			0.261872			0.130936	+	0.991391i	$0.458202\pi$
$522$		0			0
$523$	−15.8757	−	15.8757i	−0.694195	−	0.694195i	0.268957	−	0.963152i	$-0.413321\pi$
$523$	−15.8757	−	15.8757i	−0.694195	−	0.694195i	−0.963152	+	0.268957i	$0.913321\pi$
$524$	−0.644053	−	0.600565i	−0.0281356	−	0.0262358i
$525$		0			0
$526$	−7.37731	−	16.9662i	−0.321666	−	0.739761i
$527$	2.43257	+	2.43257i	0.105964	+	0.105964i
$528$		0			0
$529$		−	50.3098i		−	2.18738i
$530$	−1.75568	−	5.05355i	−0.0762620	−	0.219512i
$531$		0			0
$532$	3.99480	−	0.139581i	0.173196	−	0.00605159i
$533$	−4.95978	+	4.95978i	−0.214832	+	0.214832i
$534$		0			0
$535$	−5.72901	+	4.92033i	−0.247687	+	0.212724i
$536$	6.67290	−	18.8455i	0.288225	−	0.814000i
$537$		0			0
$538$	1.39838	−	3.55009i	0.0602882	−	0.153055i
$539$		−	13.0732i		−	0.563102i
$540$		0			0
$541$		−	32.5138i		−	1.39788i	−0.715182	−	0.698938i	$-0.753656\pi$
$541$		−	32.5138i		−	1.39788i	0.715182	−	0.698938i	$-0.246344\pi$
$542$	−31.5483	−	12.4268i	−1.35511	−	0.533778i
$543$		0			0
$544$	−30.0652	+	15.6528i	−1.28903	+	0.671110i
$545$	−8.23677	−	0.625474i	−0.352825	−	0.0267924i
$546$		0			0
$547$	1.85008	−	1.85008i	0.0791037	−	0.0791037i	−0.666448	−	0.745552i	$-0.732186\pi$
$547$	1.85008	−	1.85008i	0.0791037	−	0.0791037i	0.745552	+	0.666448i	$0.232186\pi$
$548$	−4.46087	+	0.155866i	−0.190559	+	0.00665825i
$549$		0			0
$550$	−7.53674	+	12.9575i	−0.321368	+	0.552509i
$551$			17.3768i			0.740277i
$552$		0			0
$553$	−6.56384	−	6.56384i	−0.279123	−	0.279123i
$554$	−0.720674	+	0.313366i	−0.0306185	+	0.0133137i
$555$		0			0
$556$	17.2170	−	18.4637i	0.730165	−	0.783037i
$557$	−4.55944	−	4.55944i	−0.193190	−	0.193190i	0.603883	−	0.797073i	$-0.293619\pi$
$557$	−4.55944	−	4.55944i	−0.193190	−	0.193190i	−0.797073	+	0.603883i	$0.793619\pi$
$558$		0			0
$559$	10.5471			0.446094
$560$	−5.80694	+	5.73837i	−0.245388	+	0.242491i
$561$		0			0
$562$	12.8578	−	32.6424i	0.542373	−	1.37693i
$563$	28.3506	+	28.3506i	1.19483	+	1.19483i	0.975693	+	0.219142i	$0.0703257\pi$
$563$	28.3506	+	28.3506i	1.19483	+	1.19483i	0.219142	+	0.975693i	$0.429674\pi$
$564$		0			0
$565$	−6.47014	−	7.53354i	−0.272201	−	0.316938i
$566$	16.9432	−	7.36729i	0.712174	−	0.309670i
$567$		0			0
$568$	6.10769	+	12.8041i	0.256273	+	0.537246i
$569$		−	23.9629i		−	1.00458i	−0.864700	−	0.502289i	$-0.832491\pi$
$569$		−	23.9629i		−	1.00458i	0.864700	−	0.502289i	$-0.167509\pi$
$570$		0			0
$571$	30.4111			1.27266			0.636332	−	0.771415i	$-0.280451\pi$
$571$	30.4111			1.27266			0.636332	+	0.771415i	$0.280451\pi$
$572$	−9.91351	+	0.346384i	−0.414505	+	0.0144831i
$573$		0			0
$574$	−3.54891	+	1.54315i	−0.148129	+	0.0644099i
$575$	34.4956	−	25.3534i	1.43857	−	1.05731i
$576$		0			0
$577$	−21.4532	+	21.4532i	−0.893108	+	0.893108i	−0.994814	−	0.101707i	$-0.967570\pi$
$577$	−21.4532	+	21.4532i	−0.893108	+	0.893108i	0.101707	+	0.994814i	$0.467570\pi$
$578$	24.8741	+	9.79789i	1.03463	+	0.407538i
$579$		0			0
$580$	−24.0492	−	26.0996i	−0.998588	−	1.08373i
$581$			15.1871i			0.630069i
$582$		0			0
$583$	2.53595	−	2.53595i	0.105028	−	0.105028i
$584$	−23.3312	−	8.26123i	−0.965452	−	0.341852i
$585$		0			0
$586$	8.88680	+	20.4377i	0.367110	+	0.844273i
$587$	−20.9607	+	20.9607i	−0.865142	+	0.865142i	−0.991930	−	0.126788i	$-0.959533\pi$
$587$	−20.9607	+	20.9607i	−0.865142	+	0.865142i	0.126788	+	0.991930i	$0.459533\pi$
$588$		0			0
$589$	1.25715			0.0517998
$590$	32.9910	+	15.9783i	1.35822	+	0.657815i
$591$		0			0
$592$	25.6351	−	29.4921i	1.05360	−	1.21212i
$593$	−16.7528	−	16.7528i	−0.687953	−	0.687953i	0.273826	−	0.961779i	$-0.411711\pi$
$593$	−16.7528	−	16.7528i	−0.687953	−	0.687953i	−0.961779	+	0.273826i	$0.911711\pi$
$594$		0			0
$595$	12.1944	+	0.926004i	0.499922	+	0.0379625i
$596$	−26.9679	−	25.1470i	−1.10465	−	1.03006i
$597$		0			0
$598$	26.3586	+	10.3826i	1.07788	+	0.424577i
$599$	28.7818			1.17599			0.587997	−	0.808863i	$-0.299917\pi$
$599$	28.7818			1.17599			0.587997	+	0.808863i	$0.299917\pi$
$600$		0			0
$601$	−23.8948			−0.974691			−0.487346	−	0.873209i	$-0.662035\pi$
$601$	−23.8948			−0.974691			−0.487346	+	0.873209i	$0.662035\pi$
$602$	5.41419	+	2.13265i	0.220666	+	0.0869202i
$603$		0			0
$604$	0.00510264	−	0.00547213i	0.000207623	−	0.000222658i
$605$	14.5061	+	1.10155i	0.589758	+	0.0447843i
$606$		0			0
$607$	24.0023	+	24.0023i	0.974224	+	0.974224i	0.999676	−	0.0254522i	$-0.00810257\pi$
$607$	24.0023	+	24.0023i	0.974224	+	0.974224i	−0.0254522	+	0.999676i	$0.508103\pi$
$608$	−3.72413	+	11.8135i	−0.151033	+	0.479100i
$609$		0			0
$610$	6.69094	+	3.24057i	0.270908	+	0.131207i
$611$	16.7091			0.675977
$612$		0			0
$613$	33.6909	−	33.6909i	1.36076	−	1.36076i	0.487816	−	0.872946i	$-0.337794\pi$
$613$	33.6909	−	33.6909i	1.36076	−	1.36076i	0.872946	−	0.487816i	$-0.162206\pi$
$614$	9.60061	+	22.0793i	0.387449	+	0.891048i
$615$		0			0
$616$	−5.15900	−	1.82672i	−0.207862	−	0.0736008i
$617$	−22.5125	+	22.5125i	−0.906319	+	0.906319i	−0.995973	−	0.0896535i	$-0.971424\pi$
$617$	−22.5125	+	22.5125i	−0.906319	+	0.906319i	0.0896535	+	0.995973i	$0.471424\pi$
$618$		0			0
$619$		−	21.0797i		−	0.847265i	−0.905834	−	0.423633i	$-0.860755\pi$
$619$		−	21.0797i		−	0.847265i	0.905834	−	0.423633i	$-0.139245\pi$
$620$	−1.88821	+	1.73987i	−0.0758323	+	0.0698747i
$621$		0			0
$622$	40.7299	+	16.0435i	1.63312	+	0.643284i
$623$	−5.58596	+	5.58596i	−0.223797	+	0.223797i
$624$		0			0
$625$	23.8599	+	7.46356i	0.954396	+	0.298543i
$626$	−15.8200	+	6.87893i	−0.632295	+	0.274937i
$627$		0			0
$628$	−1.11754	−	31.9839i	−0.0445946	−	1.27630i
$629$	−58.5360			−2.33398
$630$		0			0
$631$			42.6546i			1.69805i	0.528351	+	0.849026i	$0.322810\pi$
$631$			42.6546i			1.69805i	−0.528351	+	0.849026i	$0.677190\pi$
$632$	25.9625	−	12.3844i	1.03273	−	0.492626i
$633$		0			0
$634$	−4.30434	+	1.87163i	−0.170947	+	0.0743320i
$635$	−25.0948	−	29.2192i	−0.995856	−	1.15953i
$636$		0			0
$637$	−10.2023	−	10.2023i	−0.404229	−	0.404229i
$638$	8.71944	−	22.1362i	0.345206	−	0.876382i
$639$		0			0
$640$	−10.7561	−	22.8978i	−0.425171	−	0.905113i
$641$	−0.687931			−0.0271716			−0.0135858	−	0.999908i	$-0.504325\pi$
$641$	−0.687931			−0.0271716			−0.0135858	+	0.999908i	$0.504325\pi$
$642$		0			0
$643$	9.24755	+	9.24755i	0.364688	+	0.364688i	0.865535	−	0.500848i	$-0.166978\pi$
$643$	9.24755	+	9.24755i	0.364688	+	0.364688i	−0.500848	+	0.865535i	$0.666978\pi$
$644$	11.4314	+	10.6595i	0.450461	+	0.420045i
$645$		0			0
$646$	17.0160	−	7.39899i	0.669487	−	0.291109i
$647$	17.0187	+	17.0187i	0.669073	+	0.669073i	0.957501	−	0.288429i	$-0.0931328\pi$
$647$	17.0187	+	17.0187i	0.669073	+	0.669073i	−0.288429	+	0.957501i	$0.593133\pi$
$648$		0			0
$649$			24.5736i			0.964598i
$650$	4.23034	+	15.9937i	0.165928	+	0.627323i
$651$		0			0
$652$	0.572287	+	16.3788i	0.0224125	+	0.641445i
$653$	−11.9095	+	11.9095i	−0.466056	+	0.466056i	−0.900634	−	0.434578i	$-0.856898\pi$
$653$	−11.9095	+	11.9095i	−0.466056	+	0.466056i	0.434578	+	0.900634i	$0.356898\pi$
$654$		0			0
$655$	−0.981730	−	0.0745494i	−0.0383594	−	0.00291289i
$656$	−0.836993	−	11.9627i	−0.0326791	−	0.467066i
$657$		0			0
$658$	8.57736	+	3.37861i	0.334380	+	0.131712i
$659$			27.4244i			1.06830i	0.845389	+	0.534151i	$0.179369\pi$
$659$			27.4244i			1.06830i	−0.845389	+	0.534151i	$0.820631\pi$
$660$		0			0
$661$			39.1425i			1.52247i	0.648478	+	0.761233i	$0.275406\pi$
$661$			39.1425i			1.52247i	−0.648478	+	0.761233i	$0.724594\pi$
$662$	−6.31580	+	16.0340i	−0.245470	+	0.623181i
$663$		0			0
$664$	−44.3628	−	15.7082i	−1.72161	−	0.609597i
$665$	3.39030	−	2.91174i	0.131470	−	0.112912i
$666$		0			0
$667$	−48.0463	+	48.0463i	−1.86036	+	1.86036i
$668$	−0.218688	−	6.25884i	−0.00846128	−	0.242162i
$669$		0			0
$670$	−7.33527	−	21.1138i	−0.283386	−	0.815697i
$671$			4.98380i			0.192397i
$672$		0			0
$673$	23.5686	+	23.5686i	0.908503	+	0.908503i	0.996151	−	0.0876488i	$-0.0279353\pi$
$673$	23.5686	+	23.5686i	0.908503	+	0.908503i	−0.0876488	+	0.996151i	$0.527935\pi$
$674$	−6.88422	−	15.8322i	−0.265170	−	0.609833i
$675$		0			0
$676$	10.2654	−	11.0088i	0.394824	−	0.423413i
$677$	−21.9738	−	21.9738i	−0.844522	−	0.844522i	0.144921	−	0.989443i	$-0.453707\pi$
$677$	−21.9738	−	21.9738i	−0.844522	−	0.844522i	−0.989443	+	0.144921i	$0.953707\pi$
$678$		0			0
$679$	10.4147			0.399679
$680$	−15.3177	+	34.6630i	−0.587408	+	1.32927i
$681$		0			0
$682$	−1.60147	−	0.630818i	−0.0613235	−	0.0241553i
$683$	6.94901	+	6.94901i	0.265896	+	0.265896i	0.827444	−	0.561548i	$-0.189794\pi$
$683$	6.94901	+	6.94901i	0.265896	+	0.265896i	−0.561548	+	0.827444i	$0.689794\pi$
$684$		0			0
$685$	−3.78584	+	3.25145i	−0.144650	+	0.124232i
$686$	−6.77736	−	15.5864i	−0.258761	−	0.595093i
$687$		0			0
$688$	−11.8296	+	13.6095i	−0.450998	+	0.518856i
$689$		−	3.95810i		−	0.150792i
$690$		0			0
$691$	−16.5423			−0.629299			−0.314650	−	0.949208i	$-0.601887\pi$
$691$	−16.5423			−0.629299			−0.314650	+	0.949208i	$0.601887\pi$
$692$	19.8438	−	0.693354i	0.754347	−	0.0263574i
$693$		0			0
$694$	5.82377	+	13.3934i	0.221067	+	0.508406i
$695$	2.13719	−	28.1443i	0.0810681	−	1.06757i
$696$		0			0
$697$	−12.7024	+	12.7024i	−0.481139	+	0.481139i
$698$	−7.35998	+	18.6850i	−0.278580	+	0.707236i
$699$		0			0
$700$	−1.06237	+	9.06549i	−0.0401538	+	0.342643i
$701$			35.1981i			1.32941i	0.747105	+	0.664707i	$0.231443\pi$
$701$			35.1981i			1.32941i	−0.747105	+	0.664707i	$0.768557\pi$
$702$		0			0
$703$	−15.1256	+	15.1256i	−0.570473	+	0.570473i
$704$	10.6720	−	13.1804i	0.402216	−	0.496756i
$705$		0			0
$706$	7.73799	−	3.36466i	0.291223	−	0.126631i
$707$	−1.83002	+	1.83002i	−0.0688249	+	0.0688249i
$708$		0			0
$709$	45.4352			1.70636			0.853178	−	0.521620i	$-0.174672\pi$
$709$	45.4352			1.70636			0.853178	+	0.521620i	$0.174672\pi$
$710$	14.2746	+	6.91349i	0.535715	+	0.259459i
$711$		0			0
$712$	−10.5394	−	22.0946i	−0.394981	−	0.828031i
$713$	3.47596	+	3.47596i	0.130176	+	0.130176i
$714$		0			0
$715$	−8.41338	+	7.22579i	−0.314643	+	0.270229i
$716$	18.0269	−	19.3323i	0.673698	−	0.722482i
$717$		0			0
$718$	17.8853	−	45.4058i	0.667474	−	1.69453i
$719$	16.1926			0.603880			0.301940	−	0.953327i	$-0.402366\pi$
$719$	16.1926			0.603880			0.301940	+	0.953327i	$0.402366\pi$
$720$		0			0
$721$	−9.71469			−0.361794
$722$	−7.36263	+	18.6917i	−0.274009	+	0.695632i
$723$		0			0
$724$	−9.88585	+	10.6017i	−0.367405	+	0.394009i
$725$	−39.2243	−	5.99168i	−1.45675	−	0.222525i
$726$		0			0
$727$	−10.5017	−	10.5017i	−0.389488	−	0.389488i	0.485017	−	0.874505i	$-0.338813\pi$
$727$	−10.5017	−	10.5017i	−0.389488	−	0.389488i	−0.874505	+	0.485017i	$0.838813\pi$
$728$	−5.45164	+	2.60050i	−0.202051	+	0.0963808i
$729$		0			0
$730$	−26.1395	+	9.08127i	−0.967465	+	0.336113i
$731$	27.0120			0.999076
$732$		0			0
$733$	−10.0752	+	10.0752i	−0.372134	+	0.372134i	−0.868254	−	0.496120i	$-0.834758\pi$
$733$	−10.0752	+	10.0752i	−0.372134	+	0.372134i	0.496120	+	0.868254i	$0.334758\pi$
$734$	−6.95548	+	3.02441i	−0.256732	+	0.111633i
$735$		0			0
$736$	−42.9609	+	22.3668i	−1.58356	+	0.824450i
$737$	10.5953	−	10.5953i	0.390281	−	0.390281i
$738$		0			0
$739$			26.4753i			0.973909i	0.873427	+	0.486955i	$0.161892\pi$
$739$			26.4753i			0.973909i	−0.873427	+	0.486955i	$0.838108\pi$
$740$	1.78483	−	43.6520i	0.0656115	−	1.60468i
$741$		0			0
$742$	0.800338	−	2.03184i	0.0293813	−	0.0745910i
$743$	−6.15658	+	6.15658i	−0.225863	+	0.225863i	−0.810962	−	0.585099i	$-0.801056\pi$
$743$	−6.15658	+	6.15658i	−0.225863	+	0.225863i	0.585099	+	0.810962i	$0.301056\pi$
$744$		0			0
$745$	−41.1073	−	3.12155i	−1.50605	−	0.114365i
$746$	−12.0187	−	27.6404i	−0.440037	−	1.01199i
$747$		0			0
$748$	−25.3894	+	0.887121i	−0.928328	+	0.0324364i
$749$	−3.08265			−0.112638
$750$		0			0
$751$			13.9490i			0.509008i	0.967072	+	0.254504i	$0.0819122\pi$
$751$			13.9490i			0.509008i	−0.967072	+	0.254504i	$0.918088\pi$
$752$	−18.7408	+	21.5606i	−0.683408	+	0.786233i
$753$		0			0
$754$	−10.4704	−	24.0797i	−0.381311	−	0.876931i
$755$	0.000633401	−	0.00834117i	2.30518e−5	−	0.000303566i
$756$		0			0
$757$	−7.61475	−	7.61475i	−0.276763	−	0.276763i	0.555053	−	0.831815i	$-0.312698\pi$
$757$	−7.61475	−	7.61475i	−0.276763	−	0.276763i	−0.831815	+	0.555053i	$0.812698\pi$
$758$	−33.4763	−	13.1863i	−1.21591	−	0.478947i
$759$		0			0
$760$	4.99880	+	12.9150i	0.181326	+	0.468475i
$761$	2.57254			0.0932543			0.0466272	−	0.998912i	$-0.485153\pi$
$761$	2.57254			0.0932543			0.0466272	+	0.998912i	$0.485153\pi$
$762$		0			0
$763$	−2.38429	−	2.38429i	−0.0863171	−	0.0863171i
$764$	−6.28624	+	6.74143i	−0.227428	+	0.243896i
$765$		0			0
$766$	−4.31267	−	9.91818i	−0.155823	−	0.358359i
$767$	19.1772	+	19.1772i	0.692448	+	0.692448i
$768$		0			0
$769$		−	5.28253i		−	0.190493i	−0.995454	−	0.0952465i	$-0.969636\pi$
$769$		−	5.28253i		−	0.190493i	0.995454	−	0.0952465i	$-0.0303639\pi$
$770$	−5.77996	+	2.00805i	−0.208295	+	0.0723651i
$771$		0			0
$772$	−0.284505	−	8.14254i	−0.0102396	−	0.293056i
$773$	−19.4982	+	19.4982i	−0.701302	+	0.701302i	−0.964690	−	0.263388i	$-0.915160\pi$
$773$	−19.4982	+	19.4982i	−0.701302	+	0.701302i	0.263388	+	0.964690i	$0.415160\pi$
$774$		0			0
$775$	−0.433475	+	2.83773i	−0.0155709	+	0.101934i
$776$	−10.7720	+	30.4221i	−0.386693	+	1.09209i
$777$		0			0
$778$	−2.25720	+	5.73040i	−0.0809246	+	0.205445i
$779$			6.56458i			0.235201i
$780$		0			0
$781$			10.6325i			0.380461i
$782$	67.5067	+	26.5908i	2.41403	+	0.950886i
$783$		0			0
$784$	24.6074	−	1.72170i	0.878835	−	0.0614892i
$785$	−23.3125	−	27.1440i	−0.832060	−	0.968812i
$786$		0			0
$787$	−3.02573	+	3.02573i	−0.107856	+	0.107856i	−0.758975	−	0.651120i	$-0.774300\pi$
$787$	−3.02573	+	3.02573i	−0.107856	+	0.107856i	0.651120	+	0.758975i	$0.274300\pi$
$788$	−1.31959	−	37.7668i	−0.0470086	−	1.34538i
$789$		0			0
$790$	14.0183	−	28.9442i	0.498751	−	1.02979i
$791$		−	4.05363i		−	0.144130i
$792$		0			0
$793$	3.88935	+	3.88935i	0.138115	+	0.138115i
$794$	22.2026	−	9.65421i	0.787939	−	0.342615i
$795$		0			0
$796$	31.1584	+	29.0545i	1.10438	+	1.02981i
$797$	−5.35305	−	5.35305i	−0.189615	−	0.189615i	0.605915	−	0.795529i	$-0.292807\pi$
$797$	−5.35305	−	5.35305i	−0.189615	−	0.189615i	−0.795529	+	0.605915i	$0.792807\pi$
$798$		0			0
$799$	42.7934			1.51392
$800$	−25.3822	−	12.4798i	−0.897395	−	0.441227i
$801$		0			0
$802$	−13.7807	+	34.9853i	−0.486613	+	1.23538i
$803$	−13.1172	−	13.1172i	−0.462897	−	0.462897i
$804$		0			0
$805$	17.4249	+	1.32319i	0.614148	+	0.0466364i
$806$	−1.74207	+	0.757496i	−0.0613619	+	0.0266817i
$807$		0			0
$808$	−3.45282	−	7.23842i	−0.121470	−	0.254647i
$809$		−	25.2432i		−	0.887504i	−0.896150	−	0.443752i	$-0.853647\pi$
$809$		−	25.2432i		−	0.887504i	0.896150	−	0.443752i	$-0.146353\pi$
$810$		0			0
$811$	−1.16655			−0.0409632			−0.0204816	−	0.999790i	$-0.506520\pi$
$811$	−1.16655			−0.0409632			−0.0204816	+	0.999790i	$0.506520\pi$
$812$	−0.505874	−	14.4781i	−0.0177527	−	0.508082i
$813$		0			0
$814$	26.8583	−	11.6786i	0.941382	−	0.409336i
$815$	11.9383	+	13.9004i	0.418179	+	0.486908i
$816$		0			0
$817$	6.97987	−	6.97987i	0.244195	−	0.244195i
$818$	12.0321	+	4.73944i	0.420693	+	0.165711i
$819$		0			0
$820$	−9.08526	−	9.85989i	−0.317271	−	0.344322i
$821$			13.4087i			0.467968i	0.972240	+	0.233984i	$0.0751763\pi$
$821$			13.4087i			0.467968i	−0.972240	+	0.233984i	$0.924824\pi$
$822$		0			0
$823$	1.36211	−	1.36211i	0.0474803	−	0.0474803i	−0.682968	−	0.730448i	$-0.739311\pi$
$823$	1.36211	−	1.36211i	0.0474803	−	0.0474803i	0.730448	+	0.682968i	$0.239311\pi$
$824$	10.0480	−	28.3774i	0.350039	−	0.988572i
$825$		0			0
$826$	5.96665	+	13.7220i	0.207606	+	0.477449i
$827$	−25.7402	+	25.7402i	−0.895073	+	0.895073i	−0.994995	−	0.0999219i	$-0.968141\pi$
$827$	−25.7402	+	25.7402i	−0.895073	+	0.895073i	0.0999219	+	0.994995i	$0.468141\pi$
$828$		0			0
$829$	−11.4288			−0.396940			−0.198470	−	0.980107i	$-0.563597\pi$
$829$	−11.4288			−0.396940			−0.198470	+	0.980107i	$0.563597\pi$
$830$	−49.7025	+	17.2675i	−1.72520	+	0.599362i
$831$		0			0
$832$	−1.95757	−	18.6144i	−0.0678665	−	0.645337i
$833$	−26.1289	−	26.1289i	−0.905314	−	0.905314i
$834$		0			0
$835$	−4.56196	−	5.31174i	−0.157873	−	0.183820i
$836$	−6.33135	+	6.78981i	−0.218974	+	0.234831i
$837$		0			0
$838$	−5.68897	−	2.24088i	−0.196522	−	0.0774099i
$839$	47.7970			1.65014			0.825069	−	0.565032i	$-0.191136\pi$
$839$	47.7970			1.65014			0.825069	+	0.565032i	$0.191136\pi$
$840$		0			0
$841$	33.9777			1.17165
$842$	11.1810	+	4.40419i	0.385323	+	0.151779i
$843$		0			0
$844$	−15.0363	−	14.0211i	−0.517572	−	0.482625i
$845$	1.27427	−	16.7807i	0.0438362	−	0.577272i
$846$		0			0
$847$	4.19907	+	4.19907i	0.144282	+	0.144282i
$848$	5.10735	+	4.43939i	0.175387	+	0.152449i
$849$		0			0
$850$	10.8343	+	40.9612i	0.371613	+	1.40496i
$851$	−83.6436			−2.86727
$852$		0			0
$853$	−22.3165	+	22.3165i	−0.764103	+	0.764103i	−0.977061	−	0.212959i	$-0.931690\pi$
$853$	−22.3165	+	22.3165i	−0.764103	+	0.764103i	0.212959	+	0.977061i	$0.431690\pi$
$854$	1.21010	+	2.78297i	0.0414089	+	0.0952314i
$855$		0			0
$856$	3.18842	−	9.00466i	0.108978	−	0.307773i
$857$	−8.47209	+	8.47209i	−0.289401	+	0.289401i	−0.836843	−	0.547442i	$-0.815602\pi$
$857$	−8.47209	+	8.47209i	−0.289401	+	0.289401i	0.547442	+	0.836843i	$0.315602\pi$
$858$		0			0
$859$		−	37.2555i		−	1.27114i	−0.772042	−	0.635571i	$-0.780765\pi$
$859$		−	37.2555i		−	1.27114i	0.772042	−	0.635571i	$-0.219235\pi$
$860$	−0.823626	+	20.1437i	−0.0280854	+	0.686893i
$861$		0			0
$862$	−34.0397	−	13.4082i	−1.15940	−	0.456686i
$863$	10.5386	−	10.5386i	0.358738	−	0.358738i	−0.504610	−	0.863348i	$-0.668364\pi$
$863$	10.5386	−	10.5386i	0.358738	−	0.358738i	0.863348	+	0.504610i	$0.168364\pi$
$864$		0			0
$865$	16.8410	−	14.4638i	0.572611	−	0.491784i
$866$	−33.3791	+	14.5140i	−1.13427	+	0.493207i
$867$		0			0
$868$	−1.04744	+	0.0365981i	−0.0355523	+	0.00124222i
$869$	21.5593			0.731351
$870$		0			0
$871$		−	16.5370i		−	0.560336i
$872$	9.43078	−	4.49860i	0.319367	−	0.152342i
$873$		0			0
$874$	24.3147	−	10.5726i	0.822456	−	0.357624i
$875$	5.40360	+	8.65684i	0.182675	+	0.292654i
$876$		0			0
$877$	−16.9202	−	16.9202i	−0.571353	−	0.571353i	0.361153	−	0.932506i	$-0.382383\pi$
$877$	−16.9202	−	16.9202i	−0.571353	−	0.571353i	−0.932506	+	0.361153i	$0.882383\pi$
$878$	8.65915	−	21.9832i	0.292232	−	0.741896i
$879$		0			0
$880$	0.112598	−	18.9606i	0.00379568	−	0.639163i
$881$	34.6268			1.16661			0.583304	−	0.812254i	$-0.301760\pi$
$881$	34.6268			1.16661			0.583304	+	0.812254i	$0.301760\pi$
$882$		0			0
$883$	−23.6485	−	23.6485i	−0.795835	−	0.795835i	0.186601	−	0.982436i	$-0.440253\pi$
$883$	−23.6485	−	23.6485i	−0.795835	−	0.795835i	−0.982436	+	0.186601i	$0.940253\pi$
$884$	−19.1215	+	20.5061i	−0.643126	+	0.689695i
$885$		0			0
$886$	−7.79529	+	3.38958i	−0.261888	+	0.113875i
$887$	−28.5275	−	28.5275i	−0.957859	−	0.957859i	0.0412884	−	0.999147i	$-0.486854\pi$
$887$	−28.5275	−	28.5275i	−0.957859	−	0.957859i	−0.999147	+	0.0412884i	$0.986854\pi$
$888$		0			0
$889$		−	15.7222i		−	0.527306i
$890$	−24.6321	−	11.9299i	−0.825671	−	0.399891i
$891$		0			0
$892$	23.0943	−	0.806930i	0.773255	−	0.0270180i
$893$	11.0578	−	11.0578i	0.370034	−	0.370034i
$894$		0			0
$895$	2.23772	−	29.4683i	0.0747989	−	0.985015i
$896$	2.75898	−	9.95124i	0.0921710	−	0.332448i
$897$		0			0
$898$	−48.3499	−	19.0450i	−1.61346	−	0.635539i
$899$		−	4.55620i		−	0.151958i
$900$		0			0
$901$		−	10.1371i		−	0.337714i
$902$	3.29402	−	8.36260i	0.109679	−	0.278444i
$903$		0			0
$904$	11.8410	+	4.19271i	0.393824	+	0.139447i
$905$	−1.22715	+	16.1602i	−0.0407919	+	0.537183i
$906$		0			0
$907$	15.0125	−	15.0125i	0.498481	−	0.498481i	−0.412484	−	0.910965i	$-0.635339\pi$
$907$	15.0125	−	15.0125i	0.498481	−	0.498481i	0.910965	+	0.412484i	$0.135339\pi$
$908$	−14.8860	+	0.520127i	−0.494010	+	0.0172610i
$909$		0			0
$910$	−2.94359	+	6.07774i	−0.0975790	+	0.201475i
$911$			17.5986i			0.583068i	0.956560	+	0.291534i	$0.0941657\pi$
$911$			17.5986i			0.583068i	−0.956560	+	0.291534i	$0.905834\pi$
$912$		0			0
$913$	−24.9416	−	24.9416i	−0.825445	−	0.825445i
$914$	15.5596	+	35.7838i	0.514667	+	1.18362i
$915$		0			0
$916$	4.57186	+	4.26316i	0.151059	+	0.140859i
$917$	−0.284180	−	0.284180i	−0.00938446	−	0.00938446i
$918$		0			0
$919$	5.93406			0.195747			0.0978733	−	0.995199i	$-0.468796\pi$
$919$	5.93406			0.195747			0.0978733	+	0.995199i	$0.468796\pi$
$920$	−21.8879	+	49.5309i	−0.721623	+	1.63299i
$921$		0			0
$922$	7.14110	+	2.81287i	0.235180	+	0.0926370i
$923$	8.29759	+	8.29759i	0.273119	+	0.273119i
$924$		0			0
$925$	−28.9273	−	39.3581i	−0.951122	−	1.29409i
$926$	19.2518	+	44.2749i	0.632654	+	1.45497i
$927$		0			0
$928$	42.8149	+	13.4971i	1.40547	+	0.443066i
$929$			43.1598i			1.41603i	0.706198	+	0.708014i	$0.250409\pi$
$929$			43.1598i			1.41603i	−0.706198	+	0.708014i	$0.749591\pi$
$930$		0			0
$931$	−13.5034			−0.442555
$932$	−0.238805	−	6.83460i	−0.00782232	−	0.223875i
$933$		0			0
$934$	15.6840	+	36.0698i	0.513197	+	1.18024i
$935$	−21.5474	+	18.5059i	−0.704676	+	0.605208i
$936$		0			0
$937$	12.4605	−	12.4605i	0.407068	−	0.407068i	−0.473647	−	0.880715i	$-0.657063\pi$
$937$	12.4605	−	12.4605i	0.407068	−	0.407068i	0.880715	+	0.473647i	$0.157063\pi$
$938$	3.34382	−	8.48904i	0.109180	−	0.277177i
$939$		0			0
$940$	−1.30482	+	31.9123i	−0.0425585	+	1.04086i
$941$		−	18.6088i		−	0.606630i	−0.952890	−	0.303315i	$-0.901907\pi$
$941$		−	18.6088i		−	0.606630i	0.952890	−	0.303315i	$-0.0980934\pi$
$942$		0			0
$943$	−18.1508	+	18.1508i	−0.591073	+	0.591073i
$944$	−46.2543	+	3.23626i	−1.50545	+	0.105331i
$945$		0			0
$946$	−12.3940	+	5.38923i	−0.402965	+	0.175219i
$947$	14.1917	−	14.1917i	0.461168	−	0.461168i	−0.437870	−	0.899038i	$-0.644267\pi$
$947$	14.1917	−	14.1917i	0.461168	−	0.461168i	0.899038	+	0.437870i	$0.144267\pi$
$948$		0			0
$949$	−20.4733			−0.664591
$950$	13.3839	+	7.78475i	0.434230	+	0.252570i
$951$		0			0
$952$	−13.9621	+	6.66010i	−0.452515	+	0.215855i
$953$	25.0919	+	25.0919i	0.812806	+	0.812806i	0.985054	−	0.172248i	$-0.0551029\pi$
$953$	25.0919	+	25.0919i	0.812806	+	0.812806i	−0.172248	+	0.985054i	$0.555103\pi$
$954$		0			0
$955$	−0.780324	+	10.2760i	−0.0252507	+	0.332523i
$956$	−9.78029	−	9.11990i	−0.316317	−	0.294959i
$957$		0			0
$958$	2.13667	−	5.42440i	0.0690326	−	0.175254i
$959$	−2.03708			−0.0657807
$960$		0			0
$961$	30.6704			0.989367
$962$	11.8462	−	30.0741i	0.381936	−	0.969628i
$963$		0			0
$964$	23.1846	+	21.6191i	0.746724	+	0.696304i
$965$	−5.93496	−	6.91039i	−0.191053	−	0.222453i
$966$		0			0
$967$	−41.2729	−	41.2729i	−1.32725	−	1.32725i	−0.907764	−	0.419482i	$-0.862212\pi$
$967$	−41.2729	−	41.2729i	−1.32725	−	1.32725i	−0.419482	−	0.907764i	$-0.637788\pi$
$968$	−16.6090	+	7.92267i	−0.533832	+	0.254644i
$969$		0			0
$970$	11.8413	+	34.0839i	0.380201	+	1.09437i
$971$	47.1256			1.51233			0.756166	−	0.654380i	$-0.227070\pi$
$971$	47.1256			1.51233			0.756166	+	0.654380i	$0.227070\pi$
$972$		0			0
$973$	8.14690	−	8.14690i	0.261178	−	0.261178i
$974$	31.2277	−	13.5786i	1.00060	−	0.435085i
$975$		0			0
$976$	−9.38090	+	0.656350i	−0.300275	+	0.0210093i
$977$	−2.70084	+	2.70084i	−0.0864074	+	0.0864074i	−0.748989	−	0.662582i	$-0.769461\pi$
$977$	−2.70084	+	2.70084i	−0.0864074	+	0.0864074i	0.662582	+	0.748989i	$0.269461\pi$
$978$		0			0
$979$		−	18.3474i		−	0.586386i
$980$	20.2818	−	18.6884i	0.647879	−	0.596979i
$981$		0			0
$982$	−3.28394	+	8.33701i	−0.104795	+	0.266045i
$983$	17.7831	−	17.7831i	0.567192	−	0.567192i	−0.364149	−	0.931341i	$-0.618640\pi$
$983$	17.7831	−	17.7831i	0.567192	−	0.567192i	0.931341	+	0.364149i	$0.118640\pi$
$984$		0			0
$985$	−27.5276	−	32.0518i	−0.877101	−	1.02126i
$986$	−26.8157	−	61.6702i	−0.853986	−	1.96398i
$987$		0			0
$988$	0.357782	+	10.2397i	0.0113826	+	0.325769i
$989$	38.5982			1.22735
$990$		0			0
$991$			20.7223i			0.658267i	0.944283	+	0.329134i	$0.106757\pi$
$991$			20.7223i			0.658267i	−0.944283	+	0.329134i	$0.893243\pi$
$992$	0.976467	−	3.09749i	0.0310029	−	0.0983455i
$993$		0			0
$994$	2.58166	+	5.93724i	0.0818851	+	0.188318i
$995$	47.4948	+	3.60660i	1.50569	+	0.114337i
$996$		0			0
$997$	12.9685	+	12.9685i	0.410715	+	0.410715i	0.881988	−	0.471273i	$-0.156205\pi$
$997$	12.9685	+	12.9685i	0.410715	+	0.410715i	−0.471273	+	0.881988i	$0.656205\pi$
$998$	−22.5023	−	8.86362i	−0.712297	−	0.280573i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.w.e.163.6		24
3.2	odd	2		120.2.v.a.43.7	✓	24
4.3	odd	2		1440.2.bi.e.1423.1		24
5.2	odd	4	inner	360.2.w.e.307.1		24
8.3	odd	2	inner	360.2.w.e.163.1		24
8.5	even	2		1440.2.bi.e.1423.12		24
12.11	even	2		480.2.bh.a.463.6		24
15.2	even	4		120.2.v.a.67.12	yes	24
15.8	even	4		600.2.v.b.307.1		24
15.14	odd	2		600.2.v.b.43.6		24
20.7	even	4		1440.2.bi.e.847.12		24
24.5	odd	2		480.2.bh.a.463.1		24
24.11	even	2		120.2.v.a.43.12	yes	24
40.27	even	4	inner	360.2.w.e.307.6		24
40.37	odd	4		1440.2.bi.e.847.1		24
60.23	odd	4		2400.2.bh.b.1807.12		24
60.47	odd	4		480.2.bh.a.367.1		24
60.59	even	2		2400.2.bh.b.943.11		24
120.29	odd	2		2400.2.bh.b.943.12		24
120.53	even	4		2400.2.bh.b.1807.11		24
120.59	even	2		600.2.v.b.43.1		24
120.77	even	4		480.2.bh.a.367.6		24
120.83	odd	4		600.2.v.b.307.6		24
120.107	odd	4		120.2.v.a.67.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.v.a.43.7	✓	24	3.2	odd	2
120.2.v.a.43.12	yes	24	24.11	even	2
120.2.v.a.67.7	yes	24	120.107	odd	4
120.2.v.a.67.12	yes	24	15.2	even	4
360.2.w.e.163.1		24	8.3	odd	2	inner
360.2.w.e.163.6		24	1.1	even	1	trivial
360.2.w.e.307.1		24	5.2	odd	4	inner
360.2.w.e.307.6		24	40.27	even	4	inner
480.2.bh.a.367.1		24	60.47	odd	4
480.2.bh.a.367.6		24	120.77	even	4
480.2.bh.a.463.1		24	24.5	odd	2
480.2.bh.a.463.6		24	12.11	even	2
600.2.v.b.43.1		24	120.59	even	2
600.2.v.b.43.6		24	15.14	odd	2
600.2.v.b.307.1		24	15.8	even	4
600.2.v.b.307.6		24	120.83	odd	4
1440.2.bi.e.847.1		24	40.37	odd	4
1440.2.bi.e.847.12		24	20.7	even	4
1440.2.bi.e.1423.1		24	4.3	odd	2
1440.2.bi.e.1423.12		24	8.5	even	2
2400.2.bh.b.943.11		24	60.59	even	2
2400.2.bh.b.943.12		24	120.29	odd	2
2400.2.bh.b.1807.11		24	120.53	even	4
2400.2.bh.b.1807.12		24	60.23	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.518298 + 1.31581i) q^{2} +(-1.46273 - 1.36397i) q^{4} +(-2.22965 - 0.169312i) q^{5} +(-0.645414 - 0.645414i) q^{7} +(2.55286 - 1.21775i) q^{8} +O(q^{10})\)	\(q+(-0.518298 + 1.31581i) q^{2} +(-1.46273 - 1.36397i) q^{4} +(-2.22965 - 0.169312i) q^{5} +(-0.645414 - 0.645414i) q^{7} +(2.55286 - 1.21775i) q^{8} +(1.37841 - 2.84605i) q^{10} +2.11990 q^{11} +(1.65437 - 1.65437i) q^{13} +(1.18376 - 0.514728i) q^{14} +(0.279184 + 3.99025i) q^{16} +(4.23698 - 4.23698i) q^{17} -2.18966i q^{19} +(3.03045 + 3.28883i) q^{20} +(-1.09874 + 2.78940i) q^{22} +(6.05433 - 6.05433i) q^{23} +(4.94267 + 0.755014i) q^{25} +(1.31938 + 3.03429i) q^{26} +(0.0637454 + 1.82439i) q^{28} -7.93585 q^{29} +0.574128i q^{31} +(-5.39512 - 1.70078i) q^{32} +(3.37906 + 7.77109i) q^{34} +(1.32977 + 1.54832i) q^{35} +(-6.90775 - 6.90775i) q^{37} +(2.88118 + 1.13490i) q^{38} +(-5.89816 + 2.28291i) q^{40} -2.99799 q^{41} +(3.18765 + 3.18765i) q^{43} +(-3.10085 - 2.89148i) q^{44} +(4.82843 + 11.1043i) q^{46} +(5.04999 + 5.04999i) q^{47} -6.16688i q^{49} +(-3.55523 + 6.11231i) q^{50} +(-4.67640 + 0.163396i) q^{52} +(1.19626 - 1.19626i) q^{53} +(-4.72664 - 0.358925i) q^{55} +(-2.43360 - 0.861702i) q^{56} +(4.11314 - 10.4421i) q^{58} +11.5919i q^{59} +2.35096i q^{61} +(-0.755446 - 0.297570i) q^{62} +(5.03419 - 6.21747i) q^{64} +(-3.96876 + 3.40855i) q^{65} +(4.99799 - 4.99799i) q^{67} +(-11.9767 + 0.418473i) q^{68} +(-2.72652 + 0.947237i) q^{70} +5.01557i q^{71} +(-6.18765 - 6.18765i) q^{73} +(12.6696 - 5.50904i) q^{74} +(-2.98662 + 3.20289i) q^{76} +(-1.36821 - 1.36821i) q^{77} +10.1700 q^{79} +(0.0531148 - 8.94411i) q^{80} +(1.55385 - 3.94480i) q^{82} +(-11.7654 - 11.7654i) q^{83} +(-10.1643 + 8.72960i) q^{85} +(-5.84651 + 2.54221i) q^{86} +(5.41181 - 2.58150i) q^{88} -8.65485i q^{89} -2.13550 q^{91} +(-17.1138 + 0.597967i) q^{92} +(-9.26225 + 4.02745i) q^{94} +(-0.370736 + 4.88217i) q^{95} +(-8.06823 + 8.06823i) q^{97} +(8.11447 + 3.19628i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{8}+O(q^{10}) \) 24 * q + 12 * q^8	\( 24 q + 12 q^{8} + 8 q^{10} - 20 q^{16} - 8 q^{17} + 20 q^{20} - 28 q^{22} - 8 q^{25} + 16 q^{26} + 4 q^{28} - 20 q^{32} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 32 q^{43} + 48 q^{46} - 56 q^{50} - 48 q^{52} + 32 q^{56} - 12 q^{58} + 16 q^{62} + 8 q^{65} + 48 q^{67} - 72 q^{68} + 4 q^{70} - 40 q^{73} + 48 q^{76} - 76 q^{80} + 24 q^{82} - 80 q^{83} + 32 q^{86} + 12 q^{88} + 64 q^{91} - 16 q^{92} - 24 q^{97} + 88 q^{98}+O(q^{100}) \) 24 * q + 12 * q^8 + 8 * q^10 - 20 * q^16 - 8 * q^17 + 20 * q^20 - 28 * q^22 - 8 * q^25 + 16 * q^26 + 4 * q^28 - 20 * q^32 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 32 * q^43 + 48 * q^46 - 56 * q^50 - 48 * q^52 + 32 * q^56 - 12 * q^58 + 16 * q^62 + 8 * q^65 + 48 * q^67 - 72 * q^68 + 4 * q^70 - 40 * q^73 + 48 * q^76 - 76 * q^80 + 24 * q^82 - 80 * q^83 + 32 * q^86 + 12 * q^88 + 64 * q^91 - 16 * q^92 - 24 * q^97 + 88 * q^98

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