LMFDB - Embedded newform 360.2.w.e.163.1

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			163.1
Character	$\chi$	$=$	360.163
Dual form			360.2.w.e.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31581 + 0.518298i) q^{2} +(1.46273 - 1.36397i) q^{4} +(2.22965 + 0.169312i) q^{5} +(0.645414 + 0.645414i) q^{7} +(-1.21775 + 2.55286i) q^{8} +O(q^{10})$	\(q+(-1.31581 + 0.518298i) q^{2} +(1.46273 - 1.36397i) q^{4} +(2.22965 + 0.169312i) q^{5} +(0.645414 + 0.645414i) q^{7} +(-1.21775 + 2.55286i) q^{8} +(-3.02156 + 0.932839i) q^{10} +2.11990 q^{11} +(-1.65437 + 1.65437i) q^{13} +(-1.18376 - 0.514728i) q^{14} +(0.279184 - 3.99025i) q^{16} +(4.23698 - 4.23698i) q^{17} -2.18966i q^{19} +(3.49232 - 2.79351i) q^{20} +(-2.78940 + 1.09874i) q^{22} +(-6.05433 + 6.05433i) q^{23} +(4.94267 + 0.755014i) q^{25} +(1.31938 - 3.03429i) q^{26} +(1.82439 + 0.0637454i) q^{28} +7.93585 q^{29} -0.574128i q^{31} +(1.70078 + 5.39512i) q^{32} +(-3.37906 + 7.77109i) q^{34} +(1.32977 + 1.54832i) q^{35} +(6.90775 + 6.90775i) q^{37} +(1.13490 + 2.88118i) q^{38} +(-3.14737 + 5.48580i) q^{40} -2.99799 q^{41} +(3.18765 + 3.18765i) q^{43} +(3.10085 - 2.89148i) q^{44} +(4.82843 - 11.1043i) q^{46} +(-5.04999 - 5.04999i) q^{47} -6.16688i q^{49} +(-6.89495 + 1.56832i) q^{50} +(-0.163396 + 4.67640i) q^{52} +(-1.19626 + 1.19626i) q^{53} +(4.72664 + 0.358925i) q^{55} +(-2.43360 + 0.861702i) q^{56} +(-10.4421 + 4.11314i) q^{58} +11.5919i q^{59} -2.35096i q^{61} +(0.297570 + 0.755446i) q^{62} +(-5.03419 - 6.21747i) q^{64} +(-3.96876 + 3.40855i) q^{65} +(4.99799 - 4.99799i) q^{67} +(0.418473 - 11.9767i) q^{68} +(-2.55222 - 1.34809i) q^{70} -5.01557i q^{71} +(-6.18765 - 6.18765i) q^{73} +(-12.6696 - 5.50904i) q^{74} +(-2.98662 - 3.20289i) q^{76} +(1.36821 + 1.36821i) q^{77} -10.1700 q^{79} +(1.29808 - 8.84958i) q^{80} +(3.94480 - 1.55385i) q^{82} +(-11.7654 - 11.7654i) q^{83} +(10.1643 - 8.72960i) q^{85} +(-5.84651 - 2.54221i) q^{86} +(-2.58150 + 5.41181i) q^{88} -8.65485i q^{89} -2.13550 q^{91} +(-0.597967 + 17.1138i) q^{92} +(9.26225 + 4.02745i) q^{94} +(0.370736 - 4.88217i) q^{95} +(-8.06823 + 8.06823i) q^{97} +(3.19628 + 8.11447i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.31581	+	0.518298i	−0.930421	+	0.366492i
$2$	−1.31581	+	0.518298i	−0.930421	+	0.366492i
$3$		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	0.818479	−	0.574536i	$-0.194817\pi$
$7$	0.645414	+	0.645414i	0.243943	+	0.243943i	−0.574536	+	0.818479i	$0.694817\pi$
$8$	−1.21775	+	2.55286i	−0.430538	+	0.902572i
$9$		0			0
$10$	−3.02156	+	0.932839i	−0.955500	+	0.294990i
$11$	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	−0.898274	−	0.439435i	$-0.855179\pi$
$13$	−1.65437	+	1.65437i	−0.458839	+	0.458839i	0.439435	+	0.898274i	$0.355179\pi$
$14$	−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	$-0.0808157\pi$
$20$	3.49232	−	2.79351i	0.780907	−	0.624648i
$21$		0			0
$22$	−2.78940	+	1.09874i	−0.594701	+	0.234252i
$23$	−6.05433	+	6.05433i	−1.26242	+	1.26242i	−0.312496	+	0.949919i	$0.601165\pi$
$23$	−6.05433	+	6.05433i	−1.26242	+	1.26242i	−0.949919	+	0.312496i	$0.898835\pi$
$24$		0			0
$25$	4.94267	+	0.755014i	0.988533	+	0.151003i
$26$	1.31938	−	3.03429i	0.258753	−	0.595074i
$27$		0			0
$28$	1.82439	+	0.0637454i	0.344778	+	0.0120468i
$29$	7.93585			1.47365			0.736825	−	0.676083i	$-0.236324\pi$
$29$	7.93585			1.47365			0.736825	+	0.676083i	$0.236324\pi$
$30$		0			0
$31$		−	0.574128i		−	0.103116i	−0.998670	−	0.0515582i	$-0.983581\pi$
$31$		−	0.574128i		−	0.103116i	0.998670	−	0.0515582i	$-0.0164188\pi$
$32$	1.70078	+	5.39512i	0.300658	+	0.953732i
$33$		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	$0.0467692\pi$
$37$	6.90775	+	6.90775i	1.13563	+	1.13563i	0.146402	+	0.989225i	$0.453231\pi$
$38$	1.13490	+	2.88118i	0.184104	+	0.467390i
$39$		0			0
$40$	−3.14737	+	5.48580i	−0.497644	+	0.867382i
$41$	−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	0.235305	−	0.971922i	$-0.424391\pi$
$47$	−5.04999	−	5.04999i	−0.736617	−	0.736617i	−0.971922	+	0.235305i	$0.924391\pi$
$48$		0			0
$49$		−	6.16688i		−	0.880983i
$50$	−6.89495	+	1.56832i	−0.975094	+	0.221793i
$51$		0			0
$52$	−0.163396	+	4.67640i	−0.0226590	+	0.648500i
$53$	−1.19626	+	1.19626i	−0.164319	+	0.164319i	−0.784477	−	0.620158i	$-0.787068\pi$
$53$	−1.19626	+	1.19626i	−0.164319	+	0.164319i	0.620158	+	0.784477i	$0.287068\pi$
$54$		0			0
$55$	4.72664	+	0.358925i	0.637340	+	0.0483975i
$56$	−2.43360	+	0.861702i	−0.325204	+	0.115150i
$57$		0			0
$58$	−10.4421	+	4.11314i	−1.37112	+	0.540081i
$59$			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	$-0.951910\pi$
$61$		−	2.35096i		−	0.301009i	0.988609	−	0.150505i	$-0.0480898\pi$
$62$	0.297570	+	0.755446i	0.0377914	+	0.0959418i
$63$		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	$0.107892\pi$
$68$	0.418473	−	11.9767i	0.0507473	−	1.45239i
$69$		0			0
$70$	−2.55222	−	1.34809i	−0.305049	−	0.161127i
$71$		−	5.01557i		−	0.595239i	−0.954685	−	0.297619i	$-0.903807\pi$
$71$		−	5.01557i		−	0.595239i	0.954685	−	0.297619i	$-0.0961926\pi$
$72$		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	$-0.693873\pi$
$79$	−10.1700			−1.14421			−0.572106	+	0.820180i	$0.693873\pi$
$80$	1.29808	−	8.84958i	0.145130	−	0.989413i
$81$		0			0
$82$	3.94480	−	1.55385i	0.435631	−	0.171594i
$83$	−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
$88$	−2.58150	+	5.41181i	−0.275189	+	0.576901i
$89$		−	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
$92$	−0.597967	+	17.1138i	−0.0623423	+	1.78424i
$93$		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	$0.446660\pi$
$98$	3.19628	+	8.11447i	0.322873	+	0.819685i
$99$		0			0
$100$	8.25962	−	5.63725i	0.825962	−	0.563725i
$101$			2.83542i			0.282135i	0.990000	+	0.141067i	$0.0450534\pi$
$101$			2.83542i			0.282135i	−0.990000	+	0.141067i	$0.954947\pi$
$102$		0			0
$103$	−7.52594	+	7.52594i	−0.741553	+	0.741553i	−0.972877	−	0.231324i	$-0.925694\pi$
$103$	−7.52594	+	7.52594i	−0.741553	+	0.741553i	0.231324	+	0.972877i	$0.425694\pi$
$104$	−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	$-0.556613\pi$
$109$	−3.69420			−0.353840			−0.176920	+	0.984225i	$0.556613\pi$
$110$	−6.40541	+	1.97753i	−0.610732	+	0.188550i
$111$		0			0
$112$	2.75555	−	2.39517i	0.260375	−	0.226322i
$113$	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
$118$	−6.00803	−	15.2527i	−0.553084	−	1.40413i
$119$	5.46921			0.501362
$120$		0			0
$121$	−6.50602			−0.591456
$122$	1.21850	+	3.09342i	0.110317	+	0.280065i
$123$		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	$-0.973115\pi$
$127$	−12.1799	−	12.1799i	−1.08080	−	1.08080i	−0.0843601	−	0.996435i	$-0.526885\pi$
$128$	9.84656	+	5.57182i	0.870321	+	0.492484i
$129$		0			0
$130$	3.45551	−	6.54202i	0.303068	−	0.573773i
$131$	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	$0.820190\pi$
$140$	4.05696	+	0.451022i	0.342876	+	0.0381183i
$141$		0			0
$142$	2.59956	+	6.59956i	0.218150	+	0.553823i
$143$	−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
$148$	19.5262	+	0.682256i	1.60504	+	0.0560811i
$149$	−18.4367			−1.51039			−0.755195	−	0.655500i	$-0.772458\pi$
$149$	−18.4367			−1.51039			−0.755195	+	0.655500i	$0.772458\pi$
$150$		0			0
$151$		−	0.00374102i		−	0.000304440i	−1.00000		0.000152220i	$-0.999952\pi$
$151$		−	0.00374102i		−	0.000304440i	1.00000		0.000152220i	$-4.84532e-5\pi$
$152$	5.58989	+	2.66645i	0.453400	+	0.216277i
$153$		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	0.0926688	−	0.995697i	$-0.470460\pi$
$157$	−11.3149	−	11.3149i	−0.903028	−	0.903028i	−0.995697	+	0.0926688i	$0.970460\pi$
$158$	13.3818	−	5.27108i	1.06460	−	0.419344i
$159$		0			0
$160$	2.87868	+	12.3172i	0.227580	+	0.973759i
$161$	−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	0.616229	−	0.787567i	$-0.288660\pi$
$167$	−2.21418	−	2.21418i	−0.171339	−	0.171339i	−0.787567	+	0.616229i	$0.788660\pi$
$168$		0			0
$169$			7.52614i			0.578934i
$170$	−8.84986	+	16.7547i	−0.678753	+	1.28503i
$171$		0			0
$172$	9.01055	+	0.314834i	0.687048	+	0.0240059i
$173$	7.02012	−	7.02012i	0.533730	−	0.533730i	−0.387951	−	0.921680i	$-0.626817\pi$
$173$	7.02012	−	7.02012i	0.533730	−	0.533730i	0.921680	+	0.387951i	$0.126817\pi$
$174$		0			0
$175$	2.70277	+	3.67736i	0.204310	+	0.277982i
$176$	0.591843	−	8.45893i	0.0446119	−	0.637616i
$177$		0			0
$178$	4.48579	+	11.3882i	0.336224	+	0.853580i
$179$			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	$0.0868137\pi$
$181$			7.24786i			0.538729i	−0.963038	+	0.269365i	$0.913186\pi$
$182$	2.80992	−	1.10683i	0.208285	−	0.0820434i
$183$		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
$188$	−14.2748	−	0.498771i	−1.04110	−	0.0363766i
$189$		0			0
$190$	2.04260	+	6.61618i	0.148186	+	0.479988i
$191$			4.60879i			0.333480i	0.986001	+	0.166740i	$0.0533241\pi$
$191$			4.60879i			0.333480i	−0.986001	+	0.166740i	$0.946676\pi$
$192$		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	0.0469844	−	0.998896i	$-0.485039\pi$
$197$	−13.3607	−	13.3607i	−0.951911	−	0.951911i	−0.998896	+	0.0469844i	$0.985039\pi$
$198$		0			0
$199$	21.3015			1.51002			0.755010	−	0.655713i	$-0.227632\pi$
$199$	21.3015			1.51002			0.755010	+	0.655713i	$0.227632\pi$
$200$	−7.94635	+	11.6985i	−0.561892	+	0.827211i
$201$		0			0
$202$	−1.46959	−	3.73088i	−0.103400	−	0.262504i
$203$	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
$208$	6.13945	+	7.06320i	0.425695	+	0.489745i
$209$		−	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	$0.384876\pi$
$212$	−0.118151	+	3.38147i	−0.00811463	+	0.232240i
$213$		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
$218$	4.86088	−	1.91470i	0.329221	−	0.129680i
$219$		0			0
$220$	7.40338	−	5.92197i	0.499136	−	0.399259i
$221$			14.0190i			0.943022i
$222$		0			0
$223$	8.17006	−	8.17006i	0.547108	−	0.547108i	−0.378495	−	0.925603i	$-0.623558\pi$
$223$	8.17006	−	8.17006i	0.547108	−	0.547108i	0.925603	+	0.378495i	$0.123558\pi$
$224$	−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	$-0.467069\pi$
$229$	3.12556			0.206543			0.103271	+	0.994653i	$0.467069\pi$
$230$	12.6458	−	23.9412i	0.833839	−	1.57864i
$231$		0			0
$232$	−9.66384	+	20.2591i	−0.634463	+	1.33008i
$233$	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
$238$	−7.19646	+	2.83468i	−0.466477	+	0.183745i
$239$	−6.68630			−0.432501			−0.216251	−	0.976338i	$-0.569383\pi$
$239$	−6.68630			−0.432501			−0.216251	+	0.976338i	$0.569383\pi$
$240$		0			0
$241$	−15.8501			−1.02100			−0.510499	−	0.859878i	$-0.670539\pi$
$241$	−15.8501			−1.02100			−0.510499	+	0.859878i	$0.670539\pi$
$242$	8.56071	−	3.37205i	0.550303	−	0.216764i
$243$		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
$248$	1.46567	+	0.699142i	0.0930701	+	0.0443956i
$249$		0			0
$250$	−15.6389	+	2.32939i	−0.989088	+	0.147324i
$251$	−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
$260$	−1.15609	+	10.3991i	−0.0716976	+	0.644923i
$261$		0			0
$262$	−0.579363	+	0.228210i	−0.0357931	+	0.0140989i
$263$	9.25036	−	9.25036i	0.570402	−	0.570402i	−0.361839	−	0.932241i	$-0.617851\pi$
$263$	9.25036	−	9.25036i	0.570402	−	0.570402i	0.932241	+	0.361839i	$0.117851\pi$
$264$		0			0
$265$	−2.86978	+	2.46470i	−0.176289	+	0.151405i
$266$	−1.12708	+	2.59203i	−0.0691056	+	0.158928i
$267$		0			0
$268$	0.493636	−	14.1278i	0.0301536	−	0.862995i
$269$	2.69801			0.164501			0.0822504	−	0.996612i	$-0.473789\pi$
$269$	2.69801			0.164501			0.0822504	+	0.996612i	$0.473789\pi$
$270$		0			0
$271$		−	23.9762i		−	1.45645i	−0.685336	−	0.728227i	$-0.740345\pi$
$271$		−	23.9762i		−	1.45645i	0.685336	−	0.728227i	$-0.259655\pi$
$272$	−15.7237	−	18.0895i	−0.953388	−	1.09684i
$273$		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	0.695204	−	0.718813i	$-0.255314\pi$
$277$	−0.392928	−	0.392928i	−0.0236087	−	0.0236087i	−0.718813	+	0.695204i	$0.755314\pi$
$278$	−6.54235	−	16.6092i	−0.392384	−	0.996154i
$279$		0			0
$280$	−5.57197	+	1.50925i	−0.332989	+	0.0901952i
$281$	−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
$290$	−23.9786	+	7.40287i	−1.40807	+	0.434711i
$291$		0			0
$292$	−17.4907	−	0.611134i	−1.02356	−	0.0357639i
$293$	−11.1431	+	11.1431i	−0.650987	+	0.650987i	−0.953231	−	0.302244i	$-0.902264\pi$
$293$	−11.1431	+	11.1431i	−0.650987	+	0.650987i	0.302244	+	0.953231i	$0.402264\pi$
$294$		0			0
$295$	−1.96264	+	25.8458i	−0.114270	+	1.50480i
$296$	−26.0464	+	9.22264i	−1.51392	+	0.536055i
$297$		0			0
$298$	24.2592	−	9.55568i	1.40530	−	0.553546i
$299$		−	20.0322i		−	1.15849i
$300$		0			0
$301$			4.11471i			0.237168i
$302$	0.00193897	+	0.00492249i	0.000111575	+	0.000283258i
$303$		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	$0.0885211\pi$
$308$	3.86753	+	0.135134i	0.220373	+	0.00769998i
$309$		0			0
$310$	0.535569	+	1.73476i	0.0304183	+	0.0985279i
$311$			30.9541i			1.75525i	0.479350	+	0.877624i	$0.340872\pi$
$311$			30.9541i			1.75525i	−0.479350	+	0.877624i	$0.659128\pi$
$312$		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	0.638123	−	0.769934i	$-0.279711\pi$
$317$	−2.34682	−	2.34682i	−0.131811	−	0.131811i	−0.769934	+	0.638123i	$0.779711\pi$
$318$		0			0
$319$	16.8232			0.941920
$320$	−10.1718	−	14.7151i	−0.568620	−	0.822600i
$321$		0			0
$322$	10.2832	−	4.05055i	0.573061	−	0.225728i
$323$	−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
$328$	3.65079	−	7.65346i	0.201581	−	0.422592i
$329$		−	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	$0.391300\pi$
$332$	−33.2574	−	1.16203i	−1.82524	−	0.0637749i
$333$		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	$0.357890\pi$
$338$	−3.90079	−	9.90301i	−0.212175	−	0.538653i
$339$		0			0
$340$	2.96085	−	26.6329i	0.160574	−	1.44437i
$341$		−	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	$-0.624097\pi$
$349$	−14.2003			−0.760124			−0.380062	+	0.924961i	$0.624097\pi$
$350$	−5.46231	−	3.43789i	−0.291973	−	0.183763i
$351$		0			0
$352$	3.60549	+	11.4371i	0.192173	+	0.609601i
$353$	−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
$358$	−6.85011	−	17.3905i	−0.362040	−	0.919118i
$359$	34.5078			1.82125			0.910626	−	0.413232i	$-0.135600\pi$
$359$	34.5078			1.82125			0.910626	+	0.413232i	$0.135600\pi$
$360$		0			0
$361$	14.2054			0.747652
$362$	−3.75655	−	9.53684i	−0.197440	−	0.501245i
$363$		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	0.601167	−	0.799123i	$-0.294703\pi$
$367$	−3.79229	−	3.79229i	−0.197956	−	0.197956i	−0.799123	+	0.601167i	$0.794703\pi$
$368$	22.4680	+	25.8485i	1.17122	+	1.34745i
$369$		0			0
$370$	−27.3160	−	14.4283i	−1.42009	−	0.750094i
$371$	−1.54417			−0.0801691
$372$		0			0
$373$	15.0702	−	15.0702i	0.780305	−	0.780305i	−0.199577	−	0.979882i	$-0.563957\pi$
$373$	15.0702	−	15.0702i	0.780305	−	0.780305i	0.979882	+	0.199577i	$0.0639568\pi$
$374$	−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	$0.773333\pi$
$380$	−6.11683	−	7.64699i	−0.313787	−	0.392282i
$381$		0			0
$382$	−2.38872	−	6.06431i	−0.122218	−	0.310277i
$383$	5.40762	−	5.40762i	0.276317	−	0.276317i	−0.555320	−	0.831637i	$-0.687404\pi$
$383$	5.40762	−	5.40762i	0.276317	−	0.276317i	0.831637	+	0.555320i	$0.187404\pi$
$384$		0			0
$385$	2.81898	+	3.28229i	0.143669	+	0.167281i
$386$	−5.28330	−	2.29731i	−0.268913	−	0.116930i
$387$		0			0
$388$	−0.796873	+	22.8065i	−0.0404551	+	1.15782i
$389$	−4.35502			−0.220809			−0.110404	−	0.993887i	$-0.535215\pi$
$389$	−4.35502			−0.220809			−0.110404	+	0.993887i	$0.535215\pi$
$390$		0			0
$391$			51.3041i			2.59456i
$392$	15.7432	+	7.50969i	0.795151	+	0.379297i
$393$		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	0.942305	−	0.334755i	$-0.108654\pi$
$397$	12.1053	+	12.1053i	0.607550	+	0.607550i	−0.334755	+	0.942305i	$0.608654\pi$
$398$	−28.0288	+	11.0405i	−1.40496	+	0.553410i
$399$		0			0
$400$	4.39261	−	19.5117i	0.219630	−	0.975583i
$401$	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	$-0.0725900\pi$
$410$	9.05861	−	2.79665i	0.447373	−	0.138116i
$411$		0			0
$412$	−0.743313	+	21.2736i	−0.0366204	+	1.04807i
$413$	−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
$418$	2.40587	+	6.10783i	0.117675	+	0.298744i
$419$			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	$0.0663926\pi$
$421$			8.49742i			0.414139i	−0.978326	+	0.207069i	$0.933607\pi$
$422$	−13.5261	+	5.32790i	−0.658438	+	0.259358i
$423$		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
$428$	0.235867	−	6.75050i	0.0114011	−	0.326298i
$429$		0			0
$430$	−12.6052	−	6.65811i	−0.607879	−	0.321083i
$431$		−	25.8697i		−	1.24610i	−0.782182	−	0.623050i	$-0.785893\pi$
$431$		−	25.8697i		−	1.24610i	0.782182	−	0.623050i	$-0.214107\pi$
$432$		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	$-0.369465\pi$
$439$	16.7069			0.797377			0.398688	+	0.917086i	$0.369465\pi$
$440$	−6.67213	+	11.6294i	−0.318081	+	0.554408i
$441$		0			0
$442$	−7.26603	−	18.4464i	−0.345610	−	0.877408i
$443$	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
$448$	0.763702	−	7.26198i	0.0360815	−	0.343096i
$449$			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
$452$	8.87679	+	0.310161i	0.417529	+	0.0145887i
$453$		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	$0.0267167\pi$
$458$	−4.11266	+	1.61997i	−0.192172	+	0.0756963i
$459$		0			0
$460$	−4.23083	+	38.0565i	−0.197263	+	1.77439i
$461$			5.42713i			0.252767i	0.991981	+	0.126383i	$0.0403370\pi$
$461$			5.42713i			0.252767i	−0.991981	+	0.126383i	$0.959663\pi$
$462$		0			0
$463$	−24.1397	+	24.1397i	−1.12187	+	1.12187i	−0.130407	+	0.991461i	$0.541628\pi$
$463$	−24.1397	+	24.1397i	−1.12187	+	1.12187i	−0.991461	+	0.130407i	$0.958372\pi$
$464$	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
$470$	19.9697	+	10.5480i	0.921132	+	0.486544i
$471$		0			0
$472$	−29.5924	−	14.1159i	−1.36210	−	0.649738i
$473$	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
$478$	8.79793	−	3.46550i	0.402408	−	0.158508i
$479$	4.12247			0.188360			0.0941802	−	0.995555i	$-0.469977\pi$
$479$	4.12247			0.188360			0.0941802	+	0.995555i	$0.469977\pi$
$480$		0			0
$481$	−22.8559			−1.04214
$482$	20.8558	−	8.21510i	0.949958	−	0.374187i
$483$		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	0.978373	−	0.206848i	$-0.0663207\pi$
$487$	17.0261	+	17.0261i	0.771525	+	0.771525i	−0.206848	+	0.978373i	$0.566321\pi$
$488$	6.00167	+	2.86287i	0.271683	+	0.129596i
$489$		0			0
$490$	5.75271	+	18.6336i	0.259881	+	0.841780i
$491$	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	$0.874966\pi$
$500$	19.3705	−	11.1706i	0.866276	−	0.499566i
$501$		0			0
$502$	5.59932	−	2.20557i	0.249910	−	0.0984393i
$503$	−7.10917	+	7.10917i	−0.316982	+	0.316982i	−0.847607	−	0.530625i	$-0.821957\pi$
$503$	−7.10917	+	7.10917i	−0.316982	+	0.316982i	0.530625	+	0.847607i	$0.321957\pi$
$504$		0			0
$505$	−0.480071	+	6.32198i	−0.0213629	+	0.281325i
$506$	10.2358	−	23.5401i	0.455036	−	1.04648i
$507$		0			0
$508$	−34.4291	−	1.20297i	−1.52754	−	0.0533733i
$509$	−16.3100			−0.722927			−0.361464	−	0.932386i	$-0.617723\pi$
$509$	−16.3100			−0.722927			−0.361464	+	0.932386i	$0.617723\pi$
$510$		0			0
$511$		−	7.98719i		−	0.353333i
$512$	22.0027	−	5.28030i	0.972391	−	0.233359i
$513$		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
$518$	−4.62151	−	11.7327i	−0.203058	−	0.515507i
$519$		0			0
$520$	−3.86862	−	14.2824i	−0.169650	−	0.626326i
$521$	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
$530$	2.49865	−	4.73049i	0.108534	−	0.205479i
$531$		0			0
$532$	0.139581	−	3.99480i	0.00605159	−	0.173196i
$533$	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
$538$	−3.55009	+	1.39838i	−0.153055	+	0.0602882i
$539$		−	13.0732i		−	0.563102i
$540$		0			0
$541$			32.5138i			1.39788i	0.715182	+	0.698938i	$0.246344\pi$
$541$			32.5138i			1.39788i	−0.715182	+	0.698938i	$0.753656\pi$
$542$	12.4268	+	31.5483i	0.533778	+	1.35511i
$543$		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	$0.232186\pi$
$548$	0.155866	−	4.46087i	0.00665825	−	0.190559i
$549$		0			0
$550$	−14.6166	+	3.32468i	−0.623255	+	0.141765i
$551$		−	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	0.797073	−	0.603883i	$-0.206381\pi$
$557$	4.55944	+	4.55944i	0.193190	+	0.193190i	−0.603883	+	0.797073i	$0.706381\pi$
$558$		0			0
$559$	−10.5471			−0.446094
$560$	6.54944	−	4.87384i	0.276764	−	0.205957i
$561$		0			0
$562$	32.6424	−	12.8578i	1.37693	−	0.542373i
$563$	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
$568$	12.8041	+	6.10769i	0.537246	+	0.256273i
$569$		−	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	$0.280451\pi$
$572$	−0.346384	+	9.91351i	−0.0144831	+	0.414505i
$573$		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	$0.467570\pi$
$578$	9.79789	+	24.8741i	0.407538	+	1.03463i
$579$		0			0
$580$	27.7145	−	22.1689i	1.15078	−	0.920513i
$581$		−	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
$590$	−10.8133	−	35.0255i	−0.445178	−	1.44198i
$591$		0			0
$592$	29.4921	−	25.6351i	1.21212	−	1.05360i
$593$	−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
$598$	10.3826	+	26.3586i	0.424577	+	1.07788i
$599$	−28.7818			−1.17599			−0.587997	−	0.808863i	$-0.700083\pi$
$599$	−28.7818			−1.17599			−0.587997	+	0.808863i	$0.700083\pi$
$600$		0			0
$601$	−23.8948			−0.974691			−0.487346	−	0.873209i	$-0.662035\pi$
$601$	−23.8948			−0.974691			−0.487346	+	0.873209i	$0.662035\pi$
$602$	−2.13265	−	5.41419i	−0.0869202	−	0.220666i
$603$		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	0.0254522	−	0.999676i	$-0.491897\pi$
$607$	−24.0023	−	24.0023i	−0.974224	−	0.974224i	−0.999676	+	0.0254522i	$0.991897\pi$
$608$	11.8135	−	3.72413i	0.479100	−	0.151033i
$609$		0			0
$610$	2.19306	+	7.10355i	0.0887946	+	0.287615i
$611$	16.7091			0.675977
$612$		0			0
$613$	−33.6909	+	33.6909i	−1.36076	+	1.36076i	−0.487816	+	0.872946i	$0.662206\pi$
$613$	−33.6909	+	33.6909i	−1.36076	+	1.36076i	−0.872946	+	0.487816i	$0.837794\pi$
$614$	−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	$-0.139245\pi$
$620$	−1.60383	−	2.00504i	−0.0644115	−	0.0805244i
$621$		0			0
$622$	−16.0435	−	40.7299i	−0.643284	−	1.63312i
$623$	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
$628$	−31.9839	−	1.11754i	−1.27630	−	0.0445946i
$629$	58.5360			2.33398
$630$		0			0
$631$		−	42.6546i		−	1.69805i	−0.528351	−	0.849026i	$-0.677190\pi$
$631$		−	42.6546i		−	1.69805i	0.528351	−	0.849026i	$-0.322810\pi$
$632$	12.3844	−	25.9625i	0.492626	−	1.03273i
$633$		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
$638$	−22.1362	+	8.71944i	−0.876382	+	0.345206i
$639$		0			0
$640$	21.0110	+	14.0903i	0.830533	+	0.556970i
$641$	−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	0.288429	−	0.957501i	$-0.406867\pi$
$647$	−17.0187	−	17.0187i	−0.669073	−	0.669073i	−0.957501	+	0.288429i	$0.906867\pi$
$648$		0			0
$649$			24.5736i			0.964598i
$650$	8.81221	−	14.0013i	0.345643	−	0.549178i
$651$		0			0
$652$	−16.3788	−	0.572287i	−0.641445	−	0.0224125i
$653$	11.9095	−	11.9095i	0.466056	−	0.466056i	−0.434578	−	0.900634i	$-0.643102\pi$
$653$	11.9095	−	11.9095i	0.466056	−	0.466056i	0.900634	+	0.434578i	$0.143102\pi$
$654$		0			0
$655$	0.981730	+	0.0745494i	0.0383594	+	0.00291289i
$656$	−0.836993	+	11.9627i	−0.0326791	+	0.467066i
$657$		0			0
$658$	3.37861	+	8.57736i	0.131712	+	0.334380i
$659$			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	$-0.724594\pi$
$661$		−	39.1425i		−	1.52247i	0.648478	−	0.761233i	$-0.275406\pi$
$662$	−16.0340	+	6.31580i	−0.623181	+	0.245470i
$663$		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
$668$	−6.25884	−	0.218688i	−0.242162	−	0.00846128i
$669$		0			0
$670$	−10.4394	+	19.7641i	−0.403309	+	0.763552i
$671$		−	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	0.989443	−	0.144921i	$-0.0462928\pi$
$677$	21.9738	+	21.9738i	0.844522	+	0.844522i	−0.144921	+	0.989443i	$0.546293\pi$
$678$		0			0
$679$	−10.4147			−0.399679
$680$	9.90787	+	36.5786i	0.379949	+	1.40272i
$681$		0			0
$682$	0.630818	+	1.60147i	0.0241553	+	0.0613235i
$683$	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
$688$	13.6095	−	11.8296i	0.518856	−	0.450998i
$689$		−	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	$0.601887\pi$
$692$	0.693354	−	19.8438i	0.0263574	−	0.754347i
$693$		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
$698$	18.6850	−	7.35998i	0.707236	−	0.278580i
$699$		0			0
$700$	8.96924	+	1.69251i	0.339005	+	0.0639710i
$701$		−	35.1981i		−	1.32941i	−0.747105	−	0.664707i	$-0.768557\pi$
$701$		−	35.1981i		−	1.32941i	0.747105	−	0.664707i	$-0.231443\pi$
$702$		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	$-0.825328\pi$
$709$	−45.4352			−1.70636			−0.853178	+	0.521620i	$0.825328\pi$
$710$	4.67872	+	15.1548i	0.175589	+	0.568751i
$711$		0			0
$712$	22.0946	+	10.5394i	0.828031	+	0.394981i
$713$	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
$718$	−45.4058	+	17.8853i	−1.69453	+	0.667474i
$719$	−16.1926			−0.603880			−0.301940	−	0.953327i	$-0.597634\pi$
$719$	−16.1926			−0.603880			−0.301940	+	0.953327i	$0.597634\pi$
$720$		0			0
$721$	−9.71469			−0.361794
$722$	−18.6917	+	7.36263i	−0.695632	+	0.274009i
$723$		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	0.874505	−	0.485017i	$-0.161187\pi$
$727$	10.5017	+	10.5017i	0.389488	+	0.389488i	−0.485017	+	0.874505i	$0.661187\pi$
$728$	2.60050	−	5.45164i	0.0963808	−	0.202051i
$729$		0			0
$730$	24.4684	+	12.9243i	0.905617	+	0.478349i
$731$	27.0120			0.999076
$732$		0			0
$733$	10.0752	−	10.0752i	0.372134	−	0.372134i	−0.496120	−	0.868254i	$-0.665242\pi$
$733$	10.0752	−	10.0752i	0.372134	−	0.372134i	0.868254	+	0.496120i	$0.165242\pi$
$734$	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	$0.838108\pi$
$740$	43.4209	+	4.82721i	1.59619	+	0.177452i
$741$		0			0
$742$	2.03184	−	0.800338i	0.0745910	−	0.0293813i
$743$	6.15658	−	6.15658i	0.225863	−	0.225863i	−0.585099	−	0.810962i	$-0.698944\pi$
$743$	6.15658	−	6.15658i	0.225863	−	0.225863i	0.810962	+	0.585099i	$0.198944\pi$
$744$		0			0
$745$	−41.1073	−	3.12155i	−1.50605	−	0.114365i
$746$	−12.0187	+	27.6404i	−0.440037	+	1.01199i
$747$		0			0
$748$	0.887121	−	25.3894i	0.0324364	−	0.928328i
$749$	3.08265			0.112638
$750$		0			0
$751$		−	13.9490i		−	0.509008i	−0.967072	−	0.254504i	$-0.918088\pi$
$751$		−	13.9490i		−	0.509008i	0.967072	−	0.254504i	$-0.0819122\pi$
$752$	−21.5606	+	18.7408i	−0.786233	+	0.683408i
$753$		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	0.831815	−	0.555053i	$-0.187302\pi$
$757$	7.61475	+	7.61475i	0.276763	+	0.276763i	−0.555053	+	0.831815i	$0.687302\pi$
$758$	−13.1863	−	33.4763i	−0.478947	−	1.21591i
$759$		0			0
$760$	12.0120	+	6.89168i	0.435722	+	0.249987i
$761$	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	$-0.0303639\pi$
$770$	−5.41046	−	2.85781i	−0.194979	−	0.102988i
$771$		0			0
$772$	8.14254	+	0.284505i	0.293056	+	0.0102396i
$773$	19.4982	−	19.4982i	0.701302	−	0.701302i	−0.263388	−	0.964690i	$-0.584840\pi$
$773$	19.4982	−	19.4982i	0.701302	−	0.701302i	0.964690	+	0.263388i	$0.0848398\pi$
$774$		0			0
$775$	0.433475	−	2.83773i	0.0155709	−	0.101934i
$776$	−10.7720	−	30.4221i	−0.386693	−	1.09209i
$777$		0			0
$778$	5.73040	−	2.25720i	0.205445	−	0.0809246i
$779$			6.56458i			0.235201i
$780$		0			0
$781$		−	10.6325i		−	0.380461i
$782$	−26.5908	−	67.5067i	−0.950886	−	2.41403i
$783$		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	$0.274300\pi$
$788$	−37.7668	−	1.31959i	−1.34538	−	0.0470086i
$789$		0			0
$790$	30.7292	−	9.48694i	1.09329	−	0.337530i
$791$			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	0.795529	−	0.605915i	$-0.207193\pi$
$797$	5.35305	+	5.35305i	0.189615	+	0.189615i	−0.605915	+	0.795529i	$0.707193\pi$
$798$		0			0
$799$	−42.7934			−1.51392
$800$	4.33300	+	27.9504i	0.153195	+	0.988196i
$801$		0			0
$802$	−34.9853	+	13.7807i	−1.23538	+	0.486613i
$803$	−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
$808$	−7.23842	−	3.45282i	−0.254647	−	0.121470i
$809$		−	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	$0.506520\pi$
$812$	14.4781	+	0.505874i	0.508082	+	0.0177527i
$813$		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
$818$	4.73944	+	12.0321i	0.165711	+	0.420693i
$819$		0			0
$820$	−10.4700	+	8.37493i	−0.365627	+	0.292465i
$821$		−	13.4087i		−	0.467968i	−0.972240	−	0.233984i	$-0.924824\pi$
$821$		−	13.4087i		−	0.467968i	0.972240	−	0.233984i	$-0.0751763\pi$
$822$		0			0
$823$	−1.36211	+	1.36211i	−0.0474803	+	0.0474803i	−0.730448	−	0.682968i	$-0.760689\pi$
$823$	−1.36211	+	1.36211i	−0.0474803	+	0.0474803i	0.682968	+	0.730448i	$0.260689\pi$
$824$	−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	$-0.436403\pi$
$829$	11.4288			0.396940			0.198470	+	0.980107i	$0.436403\pi$
$830$	46.5252	+	24.5747i	1.61491	+	0.853000i
$831$		0			0
$832$	18.6144	+	1.95757i	0.645337	+	0.0678665i
$833$	−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
$838$	−2.24088	−	5.68897i	−0.0774099	−	0.196522i
$839$	−47.7970			−1.65014			−0.825069	−	0.565032i	$-0.808864\pi$
$839$	−47.7970			−1.65014			−0.825069	+	0.565032i	$0.808864\pi$
$840$		0			0
$841$	33.9777			1.17165
$842$	−4.40419	−	11.1810i	−0.151779	−	0.385323i
$843$		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
$848$	4.43939	+	5.10735i	0.152449	+	0.175387i
$849$		0			0
$850$	−22.5688	+	35.8587i	−0.774105	+	1.22994i
$851$	−83.6436			−2.86727
$852$		0			0
$853$	22.3165	−	22.3165i	0.764103	−	0.764103i	−0.212959	−	0.977061i	$-0.568310\pi$
$853$	22.3165	−	22.3165i	0.764103	−	0.764103i	0.977061	+	0.212959i	$0.0683099\pi$
$854$	−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	$-0.219235\pi$
$860$	20.0370	+	2.22757i	0.683258	+	0.0759594i
$861$		0			0
$862$	13.4082	+	34.0397i	0.456686	+	1.15940i
$863$	−10.5386	+	10.5386i	−0.358738	+	0.358738i	−0.863348	−	0.504610i	$-0.831636\pi$
$863$	−10.5386	+	10.5386i	−0.358738	+	0.358738i	0.504610	+	0.863348i	$0.331636\pi$
$864$		0			0
$865$	16.8410	−	14.4638i	0.572611	−	0.491784i
$866$	−33.3791	−	14.5140i	−1.13427	−	0.493207i
$867$		0			0
$868$	0.0365981	−	1.04744i	0.00124222	−	0.0355523i
$869$	−21.5593			−0.731351
$870$		0			0
$871$			16.5370i			0.560336i
$872$	4.49860	−	9.43078i	0.152342	−	0.319367i
$873$		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	0.932506	−	0.361153i	$-0.117617\pi$
$877$	16.9202	+	16.9202i	0.571353	+	0.571353i	−0.361153	+	0.932506i	$0.617617\pi$
$878$	−21.9832	+	8.65915i	−0.741896	+	0.292232i
$879$		0			0
$880$	2.75180	−	18.7602i	0.0927633	−	0.632407i
$881$	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	0.999147	−	0.0412884i	$-0.0131463\pi$
$887$	28.5275	+	28.5275i	0.957859	+	0.957859i	−0.0412884	+	0.999147i	$0.513146\pi$
$888$		0			0
$889$		−	15.7222i		−	0.527306i
$890$	8.07358	+	26.1511i	0.270627	+	0.876588i
$891$		0			0
$892$	0.806930	−	23.0943i	0.0270180	−	0.773255i
$893$	−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
$898$	−19.0450	−	48.3499i	−0.635539	−	1.61346i
$899$		−	4.55620i		−	0.151958i
$900$		0			0
$901$			10.1371i			0.337714i
$902$	8.36260	−	3.29402i	0.278444	−	0.109679i
$903$		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	$0.135339\pi$
$908$	0.520127	−	14.8860i	0.0172610	−	0.494010i
$909$		0			0
$910$	6.45254	−	1.99208i	0.213900	−	0.0660368i
$911$		−	17.5986i		−	0.583068i	−0.956560	−	0.291534i	$-0.905834\pi$
$911$		−	17.5986i		−	0.583068i	0.956560	−	0.291534i	$-0.0941657\pi$
$912$		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	$-0.531204\pi$
$919$	−5.93406			−0.195747			−0.0978733	+	0.995199i	$0.531204\pi$
$920$	−14.1576	−	52.2681i	−0.466763	−	1.72323i
$921$		0			0
$922$	−2.81287	−	7.14110i	−0.0926370	−	0.235180i
$923$	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
$928$	13.4971	+	42.8149i	0.443066	+	1.40547i
$929$			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
$932$	6.83460	+	0.238805i	0.223875	+	0.00782232i
$933$		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	$0.157063\pi$
$938$	−8.48904	+	3.34382i	−0.277177	+	0.109180i
$939$		0			0
$940$	−31.7434	−	3.52899i	−1.03536	−	0.115103i
$941$			18.6088i			0.606630i	0.952890	+	0.303315i	$0.0980934\pi$
$941$			18.6088i			0.606630i	−0.952890	+	0.303315i	$0.901907\pi$
$942$		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
$950$	3.43408	+	15.0976i	0.111416	+	0.489831i
$951$		0			0
$952$	−6.66010	+	13.9621i	−0.215855	+	0.452515i
$953$	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
$958$	−5.42440	+	2.13667i	−0.175254	+	0.0690326i
$959$	2.03708			0.0657807
$960$		0			0
$961$	30.6704			0.989367
$962$	30.0741	−	11.8462i	0.969628	−	0.381936i
$963$		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	$0.137788\pi$
$967$	41.2729	+	41.2729i	1.32725	+	1.32725i	0.419482	+	0.907764i	$0.362212\pi$
$968$	7.92267	−	16.6090i	0.254644	−	0.533832i
$969$		0			0
$970$	16.8523	−	31.9050i	0.541094	−	1.02441i
$971$	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
$980$	−17.2272	−	21.5367i	−0.550304	−	0.687966i
$981$		0			0
$982$	−8.33701	+	3.28394i	−0.266045	+	0.104795i
$983$	−17.7831	+	17.7831i	−0.567192	+	0.567192i	−0.931341	−	0.364149i	$-0.881360\pi$
$983$	−17.7831	+	17.7831i	−0.567192	+	0.567192i	0.364149	+	0.931341i	$0.381360\pi$
$984$		0			0
$985$	−27.5276	−	32.0518i	−0.877101	−	1.02126i
$986$	−26.8157	+	61.6702i	−0.853986	+	1.96398i
$987$		0			0
$988$	10.2397	+	0.357782i	0.325769	+	0.0113826i
$989$	−38.5982			−1.22735
$990$		0			0
$991$		−	20.7223i		−	0.658267i	−0.944283	−	0.329134i	$-0.893243\pi$
$991$		−	20.7223i		−	0.658267i	0.944283	−	0.329134i	$-0.106757\pi$
$992$	3.09749	−	0.976467i	0.0983455	−	0.0310029i
$993$		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	0.471273	−	0.881988i	$-0.343795\pi$
$997$	−12.9685	−	12.9685i	−0.410715	−	0.410715i	−0.881988	+	0.471273i	$0.843795\pi$
$998$	−8.86362	−	22.5023i	−0.280573	−	0.712297i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.31581 + 0.518298i) q^{2} +(1.46273 - 1.36397i) q^{4} +(2.22965 + 0.169312i) q^{5} +(0.645414 + 0.645414i) q^{7} +(-1.21775 + 2.55286i) q^{8} +O(q^{10})\)	\(q+(-1.31581 + 0.518298i) q^{2} +(1.46273 - 1.36397i) q^{4} +(2.22965 + 0.169312i) q^{5} +(0.645414 + 0.645414i) q^{7} +(-1.21775 + 2.55286i) q^{8} +(-3.02156 + 0.932839i) q^{10} +2.11990 q^{11} +(-1.65437 + 1.65437i) q^{13} +(-1.18376 - 0.514728i) q^{14} +(0.279184 - 3.99025i) q^{16} +(4.23698 - 4.23698i) q^{17} -2.18966i q^{19} +(3.49232 - 2.79351i) q^{20} +(-2.78940 + 1.09874i) q^{22} +(-6.05433 + 6.05433i) q^{23} +(4.94267 + 0.755014i) q^{25} +(1.31938 - 3.03429i) q^{26} +(1.82439 + 0.0637454i) q^{28} +7.93585 q^{29} -0.574128i q^{31} +(1.70078 + 5.39512i) q^{32} +(-3.37906 + 7.77109i) q^{34} +(1.32977 + 1.54832i) q^{35} +(6.90775 + 6.90775i) q^{37} +(1.13490 + 2.88118i) q^{38} +(-3.14737 + 5.48580i) q^{40} -2.99799 q^{41} +(3.18765 + 3.18765i) q^{43} +(3.10085 - 2.89148i) q^{44} +(4.82843 - 11.1043i) q^{46} +(-5.04999 - 5.04999i) q^{47} -6.16688i q^{49} +(-6.89495 + 1.56832i) q^{50} +(-0.163396 + 4.67640i) q^{52} +(-1.19626 + 1.19626i) q^{53} +(4.72664 + 0.358925i) q^{55} +(-2.43360 + 0.861702i) q^{56} +(-10.4421 + 4.11314i) q^{58} +11.5919i q^{59} -2.35096i q^{61} +(0.297570 + 0.755446i) q^{62} +(-5.03419 - 6.21747i) q^{64} +(-3.96876 + 3.40855i) q^{65} +(4.99799 - 4.99799i) q^{67} +(0.418473 - 11.9767i) q^{68} +(-2.55222 - 1.34809i) q^{70} -5.01557i q^{71} +(-6.18765 - 6.18765i) q^{73} +(-12.6696 - 5.50904i) q^{74} +(-2.98662 - 3.20289i) q^{76} +(1.36821 + 1.36821i) q^{77} -10.1700 q^{79} +(1.29808 - 8.84958i) q^{80} +(3.94480 - 1.55385i) q^{82} +(-11.7654 - 11.7654i) q^{83} +(10.1643 - 8.72960i) q^{85} +(-5.84651 - 2.54221i) q^{86} +(-2.58150 + 5.41181i) q^{88} -8.65485i q^{89} -2.13550 q^{91} +(-0.597967 + 17.1138i) q^{92} +(9.26225 + 4.02745i) q^{94} +(0.370736 - 4.88217i) q^{95} +(-8.06823 + 8.06823i) q^{97} +(3.19628 + 8.11447i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{8}+O(q^{10}) \) 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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