LMFDB - Embedded newform 600.2.v.b.307.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,2,Mod(43,600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("600.43"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.v (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.79102412128$
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			307.1
Character	$\chi$	$=$	600.307
Dual form			600.2.v.b.43.1

$q$-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} +(-0.707107 + 0.707107i) q^{3} +(1.46273 + 1.36397i) q^{4} +(1.29691 - 0.563929i) q^{6} +(-0.645414 + 0.645414i) q^{7} +(-1.21775 - 2.55286i) q^{8} -1.00000i q^{9} -2.11990 q^{11} +(-1.99878 + 0.0698387i) q^{12} +(1.65437 + 1.65437i) q^{13} +(1.18376 - 0.514728i) q^{14} +(0.279184 + 3.99025i) q^{16} +(4.23698 + 4.23698i) q^{17} +(-0.518298 + 1.31581i) q^{18} +2.18966i q^{19} -0.912753i q^{21} +(2.78940 + 1.09874i) q^{22} +(-6.05433 - 6.05433i) q^{23} +(2.66622 + 0.944069i) q^{24} +(-1.31938 - 3.03429i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-1.82439 + 0.0637454i) q^{28} -7.93585 q^{29} +0.574128i q^{31} +(1.70078 - 5.39512i) q^{32} +(1.49900 - 1.49900i) q^{33} +(-3.37906 - 7.77109i) q^{34} +(1.36397 - 1.46273i) q^{36} +(-6.90775 + 6.90775i) q^{37} +(1.13490 - 2.88118i) q^{38} -2.33963 q^{39} +2.99799 q^{41} +(-0.473078 + 1.20101i) q^{42} +(-3.18765 + 3.18765i) q^{43} +(-3.10085 - 2.89148i) q^{44} +(4.82843 + 11.1043i) q^{46} +(-5.04999 + 5.04999i) q^{47} +(-3.01894 - 2.62412i) q^{48} +6.16688i q^{49} -5.99199 q^{51} +(0.163396 + 4.67640i) q^{52} +(-1.19626 - 1.19626i) q^{53} +(-0.563929 - 1.29691i) q^{54} +(2.43360 + 0.861702i) q^{56} +(-1.54832 - 1.54832i) q^{57} +(10.4421 + 4.11314i) q^{58} +11.5919i q^{59} +2.35096i q^{61} +(0.297570 - 0.755446i) q^{62} +(0.645414 + 0.645414i) q^{63} +(-5.03419 + 6.21747i) q^{64} +(-2.74933 + 1.19547i) q^{66} +(-4.99799 - 4.99799i) q^{67} +(0.418473 + 11.9767i) q^{68} +8.56212 q^{69} -5.01557i q^{71} +(-2.55286 + 1.21775i) q^{72} +(6.18765 - 6.18765i) q^{73} +(12.6696 - 5.50904i) q^{74} +(-2.98662 + 3.20289i) q^{76} +(1.36821 - 1.36821i) q^{77} +(3.07852 + 1.21262i) q^{78} -10.1700 q^{79} -1.00000 q^{81} +(-3.94480 - 1.55385i) q^{82} +(-11.7654 + 11.7654i) q^{83} +(1.24497 - 1.33512i) q^{84} +(5.84651 - 2.54221i) q^{86} +(5.61149 - 5.61149i) q^{87} +(2.58150 + 5.41181i) q^{88} -8.65485i q^{89} -2.13550 q^{91} +(-0.597967 - 17.1138i) q^{92} +(-0.405970 - 0.405970i) q^{93} +(9.26225 - 4.02745i) q^{94} +(2.61229 + 5.01756i) q^{96} +(8.06823 + 8.06823i) q^{97} +(3.19628 - 8.11447i) q^{98} +2.11990i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{6} + 12 q^{8} + 8 q^{12} - 20 q^{16} - 8 q^{17} + 28 q^{22} - 16 q^{26} - 4 q^{28} - 20 q^{32} + 4 q^{36} - 40 q^{38} - 20 q^{42} + 32 q^{43} + 48 q^{46} - 16 q^{48} - 16 q^{51} + 48 q^{52}+ \cdots + 88 q^{98}+O(q^{100}) $ 24 * q + 4 * q^6 + 12 * q^8 + 8 * q^12 - 20 * q^16 - 8 * q^17 + 28 * q^22 - 16 * q^26 - 4 * q^28 - 20 * q^32 + 4 * q^36 - 40 * q^38 - 20 * q^42 + 32 * q^43 + 48 * q^46 - 16 * q^48 - 16 * q^51 + 48 * q^52 - 32 * q^56 + 12 * q^58 + 16 * q^62 - 24 * q^66 - 48 * q^67 - 72 * q^68 - 12 * q^72 + 40 * q^73 + 48 * q^76 + 24 * q^78 - 24 * q^81 - 24 * q^82 - 80 * q^83 - 32 * q^86 - 12 * q^88 + 64 * q^91 - 16 * q^92 - 44 * q^96 + 24 * q^97 + 88 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.46273	+	1.36397i	0.731367	+	0.681984i
$5$		0			0
$5$		0			0
$6$	1.29691	−	0.563929i	0.529463	−	0.230223i
$7$	−0.645414	+	0.645414i	−0.243943	+	0.243943i	−0.818479	−	0.574536i	$-0.805183\pi$
$7$	−0.645414	+	0.645414i	−0.243943	+	0.243943i	0.574536	+	0.818479i	$0.305183\pi$
$8$	−1.21775	−	2.55286i	−0.430538	−	0.902572i
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−2.11990			−0.639174			−0.319587	−	0.947557i	$-0.603544\pi$
$11$	−2.11990			−0.639174			−0.319587	+	0.947557i	$0.603544\pi$
$12$	−1.99878	+	0.0698387i	−0.576998	+	0.0201607i
$13$	1.65437	+	1.65437i	0.458839	+	0.458839i	0.898274	−	0.439435i	$-0.144821\pi$
$13$	1.65437	+	1.65437i	0.458839	+	0.458839i	−0.439435	+	0.898274i	$0.644821\pi$
$14$	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	0.999608	+	0.0280106i	$0.00891721\pi$
$17$	4.23698	+	4.23698i	1.02762	+	1.02762i	0.0280106	+	0.999608i	$0.491083\pi$
$18$	−0.518298	+	1.31581i	−0.122164	+	0.310140i
$19$			2.18966i			0.502342i	0.967943	+	0.251171i	$0.0808157\pi$
$19$			2.18966i			0.502342i	−0.967943	+	0.251171i	$0.919184\pi$
$20$		0			0
$21$		−	0.912753i		−	0.199179i
$22$	2.78940	+	1.09874i	0.594701	+	0.234252i
$23$	−6.05433	−	6.05433i	−1.26242	−	1.26242i	−0.949919	−	0.312496i	$-0.898835\pi$
$23$	−6.05433	−	6.05433i	−1.26242	−	1.26242i	−0.312496	−	0.949919i	$-0.601165\pi$
$24$	2.66622	+	0.944069i	0.544240	+	0.192707i
$25$		0			0
$26$	−1.31938	−	3.03429i	−0.258753	−	0.595074i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−1.82439	+	0.0637454i	−0.344778	+	0.0120468i
$29$	−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	$0.983581\pi$
$32$	1.70078	−	5.39512i	0.300658	−	0.953732i
$33$	1.49900	−	1.49900i	0.260942	−	0.260942i
$34$	−3.37906	−	7.77109i	−0.579504	−	1.33273i
$35$		0			0
$36$	1.36397	−	1.46273i	0.227328	−	0.243789i
$37$	−6.90775	+	6.90775i	−1.13563	+	1.13563i	−0.146402	+	0.989225i	$0.546769\pi$
$37$	−6.90775	+	6.90775i	−1.13563	+	1.13563i	−0.989225	+	0.146402i	$0.953231\pi$
$38$	1.13490	−	2.88118i	0.184104	−	0.467390i
$39$	−2.33963			−0.374640
$40$		0			0
$41$	2.99799			0.468208			0.234104	−	0.972212i	$-0.424784\pi$
$41$	2.99799			0.468208			0.234104	+	0.972212i	$0.424784\pi$
$42$	−0.473078	+	1.20101i	−0.0729975	+	0.185320i
$43$	−3.18765	+	3.18765i	−0.486112	+	0.486112i	−0.907077	−	0.420965i	$-0.861692\pi$
$43$	−3.18765	+	3.18765i	−0.486112	+	0.486112i	0.420965	+	0.907077i	$0.361692\pi$
$44$	−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	$-0.924391\pi$
$47$	−5.04999	+	5.04999i	−0.736617	+	0.736617i	0.235305	+	0.971922i	$0.424391\pi$
$48$	−3.01894	−	2.62412i	−0.435747	−	0.378759i
$49$			6.16688i			0.880983i
$50$		0			0
$51$	−5.99199			−0.839047
$52$	0.163396	+	4.67640i	0.0226590	+	0.648500i
$53$	−1.19626	−	1.19626i	−0.164319	−	0.164319i	0.620158	−	0.784477i	$-0.287068\pi$
$53$	−1.19626	−	1.19626i	−0.164319	−	0.164319i	−0.784477	+	0.620158i	$0.787068\pi$
$54$	−0.563929	−	1.29691i	−0.0767410	−	0.176488i
$55$		0			0
$56$	2.43360	+	0.861702i	0.325204	+	0.115150i
$57$	−1.54832	−	1.54832i	−0.205080	−	0.205080i
$58$	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	$0.0480898\pi$
$61$			2.35096i			0.301009i	−0.988609	+	0.150505i	$0.951910\pi$
$62$	0.297570	−	0.755446i	0.0377914	−	0.0959418i
$63$	0.645414	+	0.645414i	0.0813145	+	0.0813145i
$64$	−5.03419	+	6.21747i	−0.629274	+	0.777183i
$65$		0			0
$66$	−2.74933	+	1.19547i	−0.338419	+	0.147153i
$67$	−4.99799	−	4.99799i	−0.610602	−	0.610602i	0.332501	−	0.943103i	$-0.392108\pi$
$67$	−4.99799	−	4.99799i	−0.610602	−	0.610602i	−0.943103	+	0.332501i	$0.892108\pi$
$68$	0.418473	+	11.9767i	0.0507473	+	1.45239i
$69$	8.56212			1.03076
$70$		0			0
$71$		−	5.01557i		−	0.595239i	−0.954685	−	0.297619i	$-0.903807\pi$
$71$		−	5.01557i		−	0.595239i	0.954685	−	0.297619i	$-0.0961926\pi$
$72$	−2.55286	+	1.21775i	−0.300857	+	0.143513i
$73$	6.18765	−	6.18765i	0.724210	−	0.724210i	−0.245250	−	0.969460i	$-0.578870\pi$
$73$	6.18765	−	6.18765i	0.724210	−	0.724210i	0.969460	+	0.245250i	$0.0788700\pi$
$74$	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
$78$	3.07852	+	1.21262i	0.348573	+	0.137303i
$79$	−10.1700			−1.14421			−0.572106	−	0.820180i	$-0.693873\pi$
$79$	−10.1700			−1.14421			−0.572106	+	0.820180i	$0.693873\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	−3.94480	−	1.55385i	−0.435631	−	0.171594i
$83$	−11.7654	+	11.7654i	−1.29142	+	1.29142i	−0.357517	+	0.933906i	$0.616377\pi$
$83$	−11.7654	+	11.7654i	−1.29142	+	1.29142i	−0.933906	+	0.357517i	$0.883623\pi$
$84$	1.24497	−	1.33512i	0.135837	−	0.145673i
$85$		0			0
$86$	5.84651	−	2.54221i	0.630446	−	0.274133i
$87$	5.61149	−	5.61149i	0.601615	−	0.601615i
$88$	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
$93$	−0.405970	−	0.405970i	−0.0420971	−	0.0420971i
$94$	9.26225	−	4.02745i	0.955328	−	0.415400i
$95$		0			0
$96$	2.61229	+	5.01756i	0.266616	+	0.512103i
$97$	8.06823	+	8.06823i	0.819205	+	0.819205i	0.985993	−	0.166788i	$-0.0533396\pi$
$97$	8.06823	+	8.06823i	0.819205	+	0.819205i	−0.166788	+	0.985993i	$0.553340\pi$
$98$	3.19628	−	8.11447i	0.322873	−	0.819685i
$99$			2.11990i			0.213058i
$100$		0			0
$101$			2.83542i			0.282135i	0.990000	+	0.141067i	$0.0450534\pi$
$101$			2.83542i			0.282135i	−0.990000	+	0.141067i	$0.954947\pi$
$102$	7.88435	+	3.10564i	0.780667	+	0.307504i
$103$	7.52594	+	7.52594i	0.741553	+	0.741553i	0.972877	−	0.231324i	$-0.0743057\pi$
$103$	7.52594	+	7.52594i	0.741553	+	0.741553i	−0.231324	+	0.972877i	$0.574306\pi$
$104$	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	0.813055	−	0.582187i	$-0.197803\pi$
$107$	2.38812	+	2.38812i	0.230868	+	0.230868i	−0.582187	+	0.813055i	$0.697803\pi$
$108$	0.0698387	+	1.99878i	0.00672023	+	0.192333i
$109$	−3.69420			−0.353840			−0.176920	−	0.984225i	$-0.556613\pi$
$109$	−3.69420			−0.353840			−0.176920	+	0.984225i	$0.556613\pi$
$110$		0			0
$111$		−	9.76903i		−	0.927236i
$112$	−2.75555	−	2.39517i	−0.260375	−	0.226322i
$113$	3.14033	−	3.14033i	0.295418	−	0.295418i	−0.543798	−	0.839216i	$-0.683014\pi$
$113$	3.14033	−	3.14033i	0.295418	−	0.295418i	0.839216	+	0.543798i	$0.183014\pi$
$114$	1.23481	+	2.83980i	0.115651	+	0.265971i
$115$		0			0
$116$	−11.6080	−	10.8242i	−1.07778	−	1.00501i
$117$	1.65437	−	1.65437i	0.152946	−	0.152946i
$118$	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
$123$	−2.11990	+	2.11990i	−0.191145	+	0.191145i
$124$	−0.783093	+	0.839797i	−0.0703238	+	0.0754160i
$125$		0			0
$126$	−0.514728	−	1.18376i	−0.0458556	−	0.105458i
$127$	12.1799	−	12.1799i	1.08080	−	1.08080i	0.0843601	−	0.996435i	$-0.473115\pi$
$127$	12.1799	−	12.1799i	1.08080	−	1.08080i	0.996435	−	0.0843601i	$-0.0268846\pi$
$128$	9.84656	−	5.57182i	0.870321	−	0.492484i
$129$		−	4.50802i		−	0.396909i
$130$		0			0
$131$	−0.440307			−0.0384698			−0.0192349	−	0.999815i	$-0.506123\pi$
$131$	−0.440307			−0.0384698			−0.0192349	+	0.999815i	$0.506123\pi$
$132$	4.23722	−	0.148051i	0.368802	−	0.0128862i
$133$	−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	0.771300	−	0.636472i	$-0.219607\pi$
$137$	1.57812	+	1.57812i	0.134828	+	0.134828i	−0.636472	+	0.771300i	$0.719607\pi$
$138$	−11.2662	−	4.43773i	−0.959039	−	0.377764i
$139$		−	12.6228i		−	1.07065i	−0.844647	−	0.535324i	$-0.820190\pi$
$139$		−	12.6228i		−	1.07065i	0.844647	−	0.535324i	$-0.179810\pi$
$140$		0			0
$141$		−	7.14177i		−	0.601445i
$142$	−2.59956	+	6.59956i	−0.218150	+	0.553823i
$143$	−3.50709	−	3.50709i	−0.293278	−	0.293278i
$144$	3.99025	−	0.279184i	0.332520	−	0.0232654i
$145$		0			0
$146$	−11.3488	+	4.93475i	−0.939237	+	0.408403i
$147$	−4.36064	−	4.36064i	−0.359660	−	0.359660i
$148$	−19.5262	+	0.682256i	−1.60504	+	0.0560811i
$149$	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	$0.999952\pi$
$152$	5.58989	−	2.66645i	0.453400	−	0.216277i
$153$	4.23698	−	4.23698i	0.342539	−	0.342539i
$154$	−2.50946	+	1.09117i	−0.202218	+	0.0879292i
$155$		0			0
$156$	−3.42225	−	3.19118i	−0.274000	−	0.255499i
$157$	11.3149	−	11.3149i	0.903028	−	0.903028i	−0.0926688	−	0.995697i	$-0.529540\pi$
$157$	11.3149	−	11.3149i	0.903028	−	0.903028i	0.995697	+	0.0926688i	$0.0295398\pi$
$158$	13.3818	+	5.27108i	1.06460	+	0.419344i
$159$	1.69177			0.134166
$160$		0			0
$161$	7.81510			0.615916
$162$	1.31581	+	0.518298i	0.103380	+	0.0407213i
$163$	5.79433	−	5.79433i	0.453847	−	0.453847i	−0.442782	−	0.896629i	$-0.646009\pi$
$163$	5.79433	−	5.79433i	0.453847	−	0.453847i	0.896629	+	0.442782i	$0.146009\pi$
$164$	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	$-0.788660\pi$
$167$	−2.21418	+	2.21418i	−0.171339	+	0.171339i	0.616229	+	0.787567i	$0.288660\pi$
$168$	−2.33013	+	1.11150i	−0.179774	+	0.0857541i
$169$		−	7.52614i		−	0.578934i
$170$		0			0
$171$	2.18966			0.167447
$172$	−9.01055	+	0.314834i	−0.687048	+	0.0240059i
$173$	7.02012	+	7.02012i	0.533730	+	0.533730i	0.921680	−	0.387951i	$-0.126817\pi$
$173$	7.02012	+	7.02012i	0.533730	+	0.533730i	−0.387951	+	0.921680i	$0.626817\pi$
$174$	−10.2921	+	4.47526i	−0.780243	+	0.339268i
$175$		0			0
$176$	−0.591843	−	8.45893i	−0.0446119	−	0.637616i
$177$	−8.19668	−	8.19668i	−0.616100	−	0.616100i
$178$	−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	$-0.913186\pi$
$181$		−	7.24786i		−	0.538729i	0.963038	−	0.269365i	$-0.0868137\pi$
$182$	2.80992	+	1.10683i	0.208285	+	0.0820434i
$183$	−1.66238	−	1.66238i	−0.122887	−	0.122887i
$184$	−8.08323	+	22.8285i	−0.595903	+	1.68294i
$185$		0			0
$186$	0.323768	+	0.744595i	0.0237398	+	0.0545963i
$187$	−8.98198	−	8.98198i	−0.656827	−	0.656827i
$188$	−14.2748	+	0.498771i	−1.04110	+	0.0363766i
$189$	−0.912753			−0.0663930
$190$		0			0
$191$			4.60879i			0.333480i	0.986001	+	0.166740i	$0.0533241\pi$
$191$			4.60879i			0.333480i	−0.986001	+	0.166740i	$0.946676\pi$
$192$	−0.836701	−	7.95613i	−0.0603837	−	0.574184i
$193$	−2.88058	+	2.88058i	−0.207349	+	0.207349i	−0.803140	−	0.595791i	$-0.796839\pi$
$193$	−2.88058	+	2.88058i	−0.207349	+	0.207349i	0.595791	+	0.803140i	$0.296839\pi$
$194$	−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	$-0.985039\pi$
$197$	−13.3607	+	13.3607i	−0.951911	+	0.951911i	0.0469844	+	0.998896i	$0.485039\pi$
$198$	1.09874	−	2.78940i	0.0780841	−	0.198234i
$199$	21.3015			1.51002			0.755010	−	0.655713i	$-0.227632\pi$
$199$	21.3015			1.51002			0.755010	+	0.655713i	$0.227632\pi$
$200$		0			0
$201$	7.06823			0.498555
$202$	1.46959	−	3.73088i	0.103400	−	0.262504i
$203$	5.12191	−	5.12191i	0.359487	−	0.359487i
$204$	−8.76469	−	8.17288i	−0.613651	−	0.572216i
$205$		0			0
$206$	−6.00206	−	13.8034i	−0.418183	−	0.961730i
$207$	−6.05433	+	6.05433i	−0.420805	+	0.420805i
$208$	−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
$213$	3.54654	+	3.54654i	0.243005	+	0.243005i
$214$	−1.90456	−	4.38008i	−0.130193	−	0.299416i
$215$		0			0
$216$	0.944069	−	2.66622i	0.0642358	−	0.181413i
$217$	−0.370550	−	0.370550i	−0.0251546	−	0.0251546i
$218$	4.86088	+	1.91470i	0.329221	+	0.129680i
$219$			8.75066i			0.591315i
$220$		0			0
$221$			14.0190i			0.943022i
$222$	−5.06327	+	12.8542i	−0.339824	+	0.862720i
$223$	−8.17006	−	8.17006i	−0.547108	−	0.547108i	0.378495	−	0.925603i	$-0.376442\pi$
$223$	−8.17006	−	8.17006i	−0.547108	−	0.547108i	−0.925603	+	0.378495i	$0.876442\pi$
$224$	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	0.859935	−	0.510404i	$-0.170504\pi$
$227$	5.26621	+	5.26621i	0.349531	+	0.349531i	−0.510404	+	0.859935i	$0.670504\pi$
$228$	−0.152923	−	4.37665i	−0.0101276	−	0.289851i
$229$	3.12556			0.206543			0.103271	−	0.994653i	$-0.467069\pi$
$229$	3.12556			0.206543			0.103271	+	0.994653i	$0.467069\pi$
$230$		0			0
$231$			1.93495i			0.127310i
$232$	9.66384	+	20.2591i	0.634463	+	1.33008i
$233$	2.41787	−	2.41787i	0.158400	−	0.158400i	−0.623457	−	0.781857i	$-0.714273\pi$
$233$	2.41787	−	2.41787i	0.158400	−	0.158400i	0.781857	+	0.623457i	$0.214273\pi$
$234$	−3.03429	+	1.31938i	−0.198358	+	0.0862508i
$235$		0			0
$236$	−15.8109	+	16.9558i	−1.02920	+	1.10373i
$237$	7.19126	−	7.19126i	0.467122	−	0.467122i
$238$	7.19646	+	2.83468i	0.466477	+	0.183745i
$239$	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	$0.670539\pi$
$242$	8.56071	+	3.37205i	0.550303	+	0.216764i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−3.20663	+	3.43883i	−0.205283	+	0.220148i
$245$		0			0
$246$	3.88814	−	1.69066i	0.247899	−	0.107792i
$247$	−3.62250	+	3.62250i	−0.230494	+	0.230494i
$248$	1.46567	−	0.699142i	0.0930701	−	0.0443956i
$249$		−	16.6388i		−	1.05444i
$250$		0			0
$251$	4.25540			0.268599			0.134299	−	0.990941i	$-0.457122\pi$
$251$	4.25540			0.268599			0.134299	+	0.990941i	$0.457122\pi$
$252$	0.0637454	+	1.82439i	0.00401559	+	0.114926i
$253$	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	0.601704	−	0.798719i	$-0.294489\pi$
$257$	−3.15838	−	3.15838i	−0.197015	−	0.197015i	−0.798719	+	0.601704i	$0.794489\pi$
$258$	−2.33650	+	5.93172i	−0.145464	+	0.369293i
$259$		−	8.91671i		−	0.554058i
$260$		0			0
$261$			7.93585i			0.491217i
$262$	0.579363	+	0.228210i	0.0357931	+	0.0140989i
$263$	9.25036	+	9.25036i	0.570402	+	0.570402i	0.932241	−	0.361839i	$-0.117851\pi$
$263$	9.25036	+	9.25036i	0.570402	+	0.570402i	−0.361839	+	0.932241i	$0.617851\pi$
$264$	−5.65213	−	2.00133i	−0.347864	−	0.123174i
$265$		0			0
$266$	1.12708	+	2.59203i	0.0691056	+	0.158928i
$267$	6.11990	+	6.11990i	0.374532	+	0.374532i
$268$	−0.493636	−	14.1278i	−0.0301536	−	0.862995i
$269$	−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	$0.740345\pi$
$272$	−15.7237	+	18.0895i	−0.953388	+	1.09684i
$273$	1.51003	−	1.51003i	0.0913910	−	0.0913910i
$274$	−1.25857	−	2.89445i	−0.0760333	−	0.174860i
$275$		0			0
$276$	12.5241	+	11.6784i	0.753862	+	0.702960i
$277$	0.392928	−	0.392928i	0.0236087	−	0.0236087i	−0.695204	−	0.718813i	$-0.744686\pi$
$277$	0.392928	−	0.392928i	0.0236087	−	0.0236087i	0.718813	+	0.695204i	$0.244686\pi$
$278$	−6.54235	+	16.6092i	−0.392384	+	0.996154i
$279$	0.574128			0.0343722
$280$		0			0
$281$	24.8077			1.47990			0.739952	−	0.672659i	$-0.234848\pi$
$281$	24.8077			1.47990			0.739952	+	0.672659i	$0.234848\pi$
$282$	−3.70156	+	9.39724i	−0.220425	+	0.559597i
$283$	9.23780	−	9.23780i	0.549130	−	0.549130i	−0.377059	−	0.926189i	$-0.623065\pi$
$283$	9.23780	−	9.23780i	0.549130	−	0.549130i	0.926189	+	0.377059i	$0.123065\pi$
$284$	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
$288$	−5.39512	−	1.70078i	−0.317911	−	0.100219i
$289$			18.9040i			1.11200i
$290$		0			0
$291$	−11.4102			−0.668878
$292$	17.4907	−	0.611134i	1.02356	−	0.0357639i
$293$	−11.1431	−	11.1431i	−0.650987	−	0.650987i	0.302244	−	0.953231i	$-0.402264\pi$
$293$	−11.1431	−	11.1431i	−0.650987	−	0.650987i	−0.953231	+	0.302244i	$0.902264\pi$
$294$	3.47768	+	7.99791i	0.202823	+	0.466448i
$295$		0			0
$296$	26.0464	+	9.22264i	1.51392	+	0.536055i
$297$	−1.49900	−	1.49900i	−0.0869806	−	0.0869806i
$298$	−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
$303$	−2.00494	−	2.00494i	−0.115181	−	0.115181i
$304$	−8.73728	+	0.611318i	−0.501117	+	0.0350615i
$305$		0			0
$306$	−7.77109	+	3.37906i	−0.444244	+	0.193168i
$307$	−12.0381	−	12.0381i	−0.687053	−	0.687053i	0.274527	−	0.961580i	$-0.411479\pi$
$307$	−12.0381	−	12.0381i	−0.687053	−	0.687053i	−0.961580	+	0.274527i	$0.911479\pi$
$308$	3.86753	−	0.135134i	0.220373	−	0.00769998i
$309$	−10.6433			−0.605475
$310$		0			0
$311$			30.9541i			1.75525i	0.479350	+	0.877624i	$0.340872\pi$
$311$			30.9541i			1.75525i	−0.479350	+	0.877624i	$0.659128\pi$
$312$	2.84907	+	5.97274i	0.161297	+	0.338140i
$313$	−8.62544	+	8.62544i	−0.487539	+	0.487539i	−0.907529	−	0.419990i	$-0.862034\pi$
$313$	−8.62544	+	8.62544i	−0.487539	+	0.487539i	0.419990	+	0.907529i	$0.362034\pi$
$314$	−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	$-0.779711\pi$
$317$	−2.34682	+	2.34682i	−0.131811	+	0.131811i	0.638123	+	0.769934i	$0.279711\pi$
$318$	−2.22605	−	0.876839i	−0.124831	−	0.0491707i
$319$	16.8232			0.941920
$320$		0			0
$321$	−3.37731			−0.188503
$322$	−10.2832	−	4.05055i	−0.573061	−	0.225728i
$323$	−9.27754	+	9.27754i	−0.516216	+	0.516216i
$324$	−1.46273	−	1.36397i	−0.0812630	−	0.0757760i
$325$		0			0
$326$	−10.6274	+	4.62107i	−0.588600	+	0.255937i
$327$	2.61220	−	2.61220i	0.144455	−	0.144455i
$328$	−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
$333$	6.90775	+	6.90775i	0.378542	+	0.378542i
$334$	4.06106	−	1.76585i	0.222211	−	0.0966229i
$335$		0			0
$336$	3.64211	−	0.254826i	0.198693	−	0.0139019i
$337$	8.63207	+	8.63207i	0.470219	+	0.470219i	0.901985	−	0.431767i	$-0.142110\pi$
$337$	8.63207	+	8.63207i	0.470219	+	0.470219i	−0.431767	+	0.901985i	$0.642110\pi$
$338$	−3.90079	+	9.90301i	−0.212175	+	0.538653i
$339$			4.44110i			0.241208i
$340$		0			0
$341$		−	1.21710i		−	0.0659094i
$342$	−2.88118	−	1.13490i	−0.155797	−	0.0613681i
$343$	−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	0.875404	−	0.483392i	$-0.160595\pi$
$347$	7.30238	+	7.30238i	0.392013	+	0.392013i	−0.483392	+	0.875404i	$0.660595\pi$
$348$	15.8620	−	0.554229i	0.850294	−	0.0297098i
$349$	−14.2003			−0.760124			−0.380062	−	0.924961i	$-0.624097\pi$
$349$	−14.2003			−0.760124			−0.380062	+	0.924961i	$0.624097\pi$
$350$		0			0
$351$			2.33963i			0.124880i
$352$	−3.60549	+	11.4371i	−0.192173	+	0.609601i
$353$	−4.21893	+	4.21893i	−0.224551	+	0.224551i	−0.810412	−	0.585861i	$-0.800757\pi$
$353$	−4.21893	+	4.21893i	−0.224551	+	0.224551i	0.585861	+	0.810412i	$0.300757\pi$
$354$	6.53698	+	15.0336i	0.347437	+	0.799028i
$355$		0			0
$356$	11.8049	−	12.6597i	0.625660	−	0.670965i
$357$	3.86731	−	3.86731i	0.204680	−	0.204680i
$358$	6.85011	−	17.3905i	0.362040	−	0.919118i
$359$	−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
$362$	−3.75655	+	9.53684i	−0.197440	+	0.501245i
$363$	4.60045	−	4.60045i	0.241461	−	0.241461i
$364$	−3.12367	−	2.91276i	−0.163725	−	0.152670i
$365$		0			0
$366$	1.32577	+	3.04899i	0.0692993	+	0.159373i
$367$	3.79229	−	3.79229i	0.197956	−	0.197956i	−0.601167	−	0.799123i	$-0.705297\pi$
$367$	3.79229	−	3.79229i	0.197956	−	0.197956i	0.799123	+	0.601167i	$0.205297\pi$
$368$	22.4680	−	25.8485i	1.17122	−	1.34745i
$369$		−	2.99799i		−	0.156069i
$370$		0			0
$371$	1.54417			0.0801691
$372$	−0.0400964	−	1.14756i	−0.00207890	−	0.0594980i
$373$	−15.0702	−	15.0702i	−0.780305	−	0.780305i	0.199577	−	0.979882i	$-0.436043\pi$
$373$	−15.0702	−	15.0702i	−0.780305	−	0.780305i	−0.979882	+	0.199577i	$0.936043\pi$
$374$	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
$378$	1.20101	+	0.473078i	0.0617735	+	0.0243325i
$379$		−	25.4415i		−	1.30684i	−0.756995	−	0.653421i	$-0.773333\pi$
$379$		−	25.4415i		−	1.30684i	0.756995	−	0.653421i	$-0.226667\pi$
$380$		0			0
$381$			17.2250i			0.882466i
$382$	2.38872	−	6.06431i	0.122218	−	0.310277i
$383$	5.40762	+	5.40762i	0.276317	+	0.276317i	0.831637	−	0.555320i	$-0.187404\pi$
$383$	5.40762	+	5.40762i	0.276317	+	0.276317i	−0.555320	+	0.831637i	$0.687404\pi$
$384$	−3.02270	+	10.9024i	−0.154252	+	0.556363i
$385$		0			0
$386$	5.28330	−	2.29731i	0.268913	−	0.116930i
$387$	3.18765	+	3.18765i	0.162037	+	0.162037i
$388$	0.796873	+	22.8065i	0.0404551	+	1.15782i
$389$	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
$392$	15.7432	−	7.50969i	0.795151	−	0.379297i
$393$	0.311344	−	0.311344i	0.0157052	−	0.0157052i
$394$	24.5050	−	10.6554i	1.23455	−	0.536811i
$395$		0			0
$396$	−2.89148	+	3.10085i	−0.145302	+	0.155824i
$397$	−12.1053	+	12.1053i	−0.607550	+	0.607550i	−0.942305	−	0.334755i	$-0.891346\pi$
$397$	−12.1053	+	12.1053i	−0.607550	+	0.607550i	0.334755	+	0.942305i	$0.391346\pi$
$398$	−28.0288	−	11.0405i	−1.40496	−	0.553410i
$399$	1.99862			0.100056
$400$		0			0
$401$	−26.5884			−1.32776			−0.663880	−	0.747839i	$-0.731091\pi$
$401$	−26.5884			−1.32776			−0.663880	+	0.747839i	$0.731091\pi$
$402$	−9.30048	−	3.66345i	−0.463866	−	0.182716i
$403$	−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
$408$	7.29672	+	15.2967i	0.361241	+	0.757300i
$409$			9.14423i			0.452153i	0.974110	+	0.226077i	$0.0725900\pi$
$409$			9.14423i			0.452153i	−0.974110	+	0.226077i	$0.927410\pi$
$410$		0			0
$411$	−2.23180			−0.110086
$412$	0.743313	+	21.2736i	0.0366204	+	1.04807i
$413$	−7.48154	−	7.48154i	−0.368143	−	0.368143i
$414$	11.1043	−	4.82843i	0.545748	−	0.237304i
$415$		0			0
$416$	11.7392	−	6.11179i	0.575563	−	0.299655i
$417$	8.92563	+	8.92563i	0.437090	+	0.437090i
$418$	−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	$-0.933607\pi$
$421$		−	8.49742i		−	0.414139i	0.978326	−	0.207069i	$-0.0663926\pi$
$422$	−13.5261	−	5.32790i	−0.658438	−	0.259358i
$423$	5.04999	+	5.04999i	0.245539	+	0.245539i
$424$	−1.59714	+	4.51062i	−0.0775642	+	0.219055i
$425$		0			0
$426$	−2.82843	−	6.50476i	−0.137038	−	0.315157i
$427$	−1.51734	−	1.51734i	−0.0734293	−	0.0734293i
$428$	0.235867	+	6.75050i	0.0114011	+	0.326298i
$429$	4.95978			0.239460
$430$		0			0
$431$		−	25.8697i		−	1.24610i	−0.782182	−	0.623050i	$-0.785893\pi$
$431$		−	25.8697i		−	1.24610i	0.782182	−	0.623050i	$-0.214107\pi$
$432$	−2.62412	+	3.01894i	−0.126253	+	0.145249i
$433$	−18.1990	+	18.1990i	−0.874590	+	0.874590i	−0.992969	−	0.118378i	$-0.962230\pi$
$433$	−18.1990	+	18.1990i	−0.874590	+	0.874590i	0.118378	+	0.992969i	$0.462230\pi$
$434$	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
$438$	4.53545	−	11.5142i	0.216712	−	0.550172i
$439$	16.7069			0.797377			0.398688	−	0.917086i	$-0.369465\pi$
$439$	16.7069			0.797377			0.398688	+	0.917086i	$0.369465\pi$
$440$		0			0
$441$	6.16688			0.293661
$442$	7.26603	−	18.4464i	0.345610	−	0.877408i
$443$	4.25017	−	4.25017i	0.201932	−	0.201932i	−0.598896	−	0.800827i	$-0.704394\pi$
$443$	4.25017	−	4.25017i	0.201932	−	0.201932i	0.800827	+	0.598896i	$0.204394\pi$
$444$	13.3246	−	14.2895i	0.632360	−	0.678150i
$445$		0			0
$446$	6.51576	+	14.9848i	0.308530	+	0.709551i
$447$	−13.0367	+	13.0367i	−0.616614	+	0.616614i
$448$	−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
$453$	−0.00264530	−	0.00264530i	−0.000124287	−	0.000124287i
$454$	−4.19989	−	9.65882i	−0.197111	−	0.453311i
$455$		0			0
$456$	−2.06719	+	5.83811i	−0.0968050	+	0.273395i
$457$	−19.5101	−	19.5101i	−0.912645	−	0.912645i	0.0838344	−	0.996480i	$-0.473283\pi$
$457$	−19.5101	−	19.5101i	−0.912645	−	0.912645i	−0.996480	+	0.0838344i	$0.973283\pi$
$458$	−4.11266	−	1.61997i	−0.192172	−	0.0756963i
$459$			5.99199i			0.279682i
$460$		0			0
$461$			5.42713i			0.252767i	0.991981	+	0.126383i	$0.0403370\pi$
$461$			5.42713i			0.252767i	−0.991981	+	0.126383i	$0.959663\pi$
$462$	1.00288	−	2.54603i	0.0466582	−	0.118452i
$463$	24.1397	+	24.1397i	1.12187	+	1.12187i	0.991461	+	0.130407i	$0.0416285\pi$
$463$	24.1397	+	24.1397i	1.12187	+	1.12187i	0.130407	+	0.991461i	$0.458372\pi$
$464$	−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	0.996275	−	0.0862361i	$-0.0274839\pi$
$467$	19.6661	+	19.6661i	0.910039	+	0.910039i	−0.0862361	+	0.996275i	$0.527484\pi$
$468$	4.67640	−	0.163396i	0.216167	−	0.00755300i
$469$	6.45155			0.297905
$470$		0			0
$471$			16.0017i			0.737319i
$472$	29.5924	−	14.1159i	1.36210	−	0.649738i
$473$	6.75751	−	6.75751i	0.310711	−	0.310711i
$474$	−13.1896	+	5.73514i	−0.605817	+	0.263424i
$475$		0			0
$476$	−8.00000	−	7.45982i	−0.366679	−	0.341920i
$477$	−1.19626	+	1.19626i	−0.0547730	+	0.0547730i
$478$	−8.79793	−	3.46550i	−0.402408	−	0.158508i
$479$	−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
$482$	20.8558	+	8.21510i	0.949958	+	0.374187i
$483$	−5.52611	+	5.52611i	−0.251447	+	0.251447i
$484$	−9.51657	−	8.87400i	−0.432572	−	0.403363i
$485$		0			0
$486$	−1.29691	+	0.563929i	−0.0588292	+	0.0255803i
$487$	−17.0261	+	17.0261i	−0.771525	+	0.771525i	−0.978373	−	0.206848i	$-0.933679\pi$
$487$	−17.0261	+	17.0261i	−0.771525	+	0.771525i	0.206848	+	0.978373i	$0.433679\pi$
$488$	6.00167	−	2.86287i	0.271683	−	0.129596i
$489$			8.19441i			0.370564i
$490$		0			0
$491$	−6.33601			−0.285940			−0.142970	−	0.989727i	$-0.545665\pi$
$491$	−6.33601			−0.285940			−0.142970	+	0.989727i	$0.545665\pi$
$492$	−5.99233	+	0.209376i	−0.270155	+	0.00943939i
$493$	−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
$498$	−8.62387	+	21.8936i	−0.386445	+	0.981076i
$499$		−	17.1014i		−	0.765564i	−0.923839	−	0.382782i	$-0.874966\pi$
$499$		−	17.1014i		−	0.765564i	0.923839	−	0.382782i	$-0.125034\pi$
$500$		0			0
$501$		−	3.13133i		−	0.139897i
$502$	−5.59932	−	2.20557i	−0.249910	−	0.0984393i
$503$	−7.10917	−	7.10917i	−0.316982	−	0.316982i	0.530625	−	0.847607i	$-0.321957\pi$
$503$	−7.10917	−	7.10917i	−0.316982	−	0.316982i	−0.847607	+	0.530625i	$0.821957\pi$
$504$	0.861702	−	2.43360i	0.0383832	−	0.108401i
$505$		0			0
$506$	−10.2358	−	23.5401i	−0.455036	−	1.04648i
$507$	5.32179	+	5.32179i	0.236349	+	0.236349i
$508$	34.4291	−	1.20297i	1.52754	−	0.0533733i
$509$	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
$512$	22.0027	+	5.28030i	0.972391	+	0.233359i
$513$	−1.54832	+	1.54832i	−0.0683601	+	0.0683601i
$514$	2.51886	+	5.79283i	0.111102	+	0.255511i
$515$		0			0
$516$	6.14880	−	6.59404i	0.270686	−	0.290286i
$517$	10.7055	−	10.7055i	0.470827	−	0.470827i
$518$	−4.62151	+	11.7327i	−0.203058	+	0.515507i
$519$	−9.92794			−0.435788
$520$		0			0
$521$	−5.97735			−0.261872			−0.130936	−	0.991391i	$-0.541798\pi$
$521$	−5.97735			−0.261872			−0.130936	+	0.991391i	$0.541798\pi$
$522$	4.11314	−	10.4421i	0.180027	−	0.457039i
$523$	15.8757	−	15.8757i	0.694195	−	0.694195i	−0.268957	−	0.963152i	$-0.586679\pi$
$523$	15.8757	−	15.8757i	0.694195	−	0.694195i	0.963152	+	0.268957i	$0.0866791\pi$
$524$	−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
$528$	6.39986	+	5.56287i	0.278518	+	0.242093i
$529$			50.3098i			2.18738i
$530$		0			0
$531$	11.5919			0.503044
$532$	−0.139581	−	3.99480i	−0.00605159	−	0.173196i
$533$	4.95978	+	4.95978i	0.214832	+	0.214832i
$534$	−4.88072	−	11.2246i	−0.211209	−	0.485735i
$535$		0			0
$536$	−6.67290	+	18.8455i	−0.288225	+	0.814000i
$537$	−9.34551	−	9.34551i	−0.403289	−	0.403289i
$538$	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	$-0.753656\pi$
$541$		−	32.5138i		−	1.39788i	0.715182	−	0.698938i	$-0.246344\pi$
$542$	12.4268	−	31.5483i	0.533778	−	1.35511i
$543$	5.12501	+	5.12501i	0.219935	+	0.219935i
$544$	30.0652	−	15.6528i	1.28903	−	0.671110i
$545$		0			0
$546$	−2.76956	+	1.20427i	−0.118526	+	0.0515381i
$547$	−1.85008	−	1.85008i	−0.0791037	−	0.0791037i	0.666448	−	0.745552i	$-0.267814\pi$
$547$	−1.85008	−	1.85008i	−0.0791037	−	0.0791037i	−0.745552	+	0.666448i	$0.767814\pi$
$548$	0.155866	+	4.46087i	0.00665825	+	0.190559i
$549$	2.35096			0.100336
$550$		0			0
$551$		−	17.3768i		−	0.740277i
$552$	−10.4265	−	21.8579i	−0.443780	−	0.930333i
$553$	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	$-0.706381\pi$
$557$	4.55944	−	4.55944i	0.193190	−	0.193190i	0.797073	+	0.603883i	$0.206381\pi$
$558$	−0.755446	−	0.297570i	−0.0319806	−	0.0125971i
$559$	−10.5471			−0.446094
$560$		0			0
$561$	12.7024			0.536297
$562$	−32.6424	−	12.8578i	−1.37693	−	0.542373i
$563$	28.3506	−	28.3506i	1.19483	−	1.19483i	0.219142	−	0.975693i	$-0.429674\pi$
$563$	28.3506	−	28.3506i	1.19483	−	1.19483i	0.975693	−	0.219142i	$-0.0703257\pi$
$564$	9.74114	−	10.4465i	0.410176	−	0.439877i
$565$		0			0
$566$	−16.9432	+	7.36729i	−0.712174	+	0.309670i
$567$	0.645414	−	0.645414i	0.0271048	−	0.0271048i
$568$	−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
$573$	−3.25890	−	3.25890i	−0.136143	−	0.136143i
$574$	3.54891	−	1.54315i	0.148129	−	0.0644099i
$575$		0			0
$576$	6.21747	+	5.03419i	0.259061	+	0.209758i
$577$	21.4532	+	21.4532i	0.893108	+	0.893108i	0.994814	−	0.101707i	$-0.0324303\pi$
$577$	21.4532	+	21.4532i	0.893108	+	0.893108i	−0.101707	+	0.994814i	$0.532430\pi$
$578$	9.79789	−	24.8741i	0.407538	−	1.03463i
$579$		−	4.07375i		−	0.169299i
$580$		0			0
$581$		−	15.1871i		−	0.630069i
$582$	15.0137	+	5.91388i	0.622338	+	0.245138i
$583$	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	0.126788	−	0.991930i	$-0.459533\pi$
$587$	−20.9607	−	20.9607i	−0.865142	−	0.865142i	−0.991930	+	0.126788i	$0.959533\pi$
$588$	−0.430687	−	12.3262i	−0.0177612	−	0.508326i
$589$	−1.25715			−0.0517998
$590$		0			0
$591$		−	18.8949i		−	0.777232i
$592$	−29.4921	−	25.6351i	−1.21212	−	1.05360i
$593$	−16.7528	+	16.7528i	−0.687953	+	0.687953i	−0.961779	−	0.273826i	$-0.911711\pi$
$593$	−16.7528	+	16.7528i	−0.687953	+	0.687953i	0.273826	+	0.961779i	$0.411711\pi$
$594$	1.19547	+	2.74933i	0.0490509	+	0.112806i
$595$		0			0
$596$	26.9679	+	25.1470i	1.10465	+	1.03006i
$597$	−15.0624	+	15.0624i	−0.616463	+	0.616463i
$598$	−10.3826	+	26.3586i	−0.424577	+	1.07788i
$599$	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	$0.662035\pi$
$602$	−2.13265	+	5.41419i	−0.0869202	+	0.220666i
$603$	−4.99799	+	4.99799i	−0.203534	+	0.203534i
$604$	−0.00510264	+	0.00547213i	−0.000207623	+	0.000222658i
$605$		0			0
$606$	1.59897	+	3.67729i	0.0649539	+	0.149380i
$607$	24.0023	−	24.0023i	0.974224	−	0.974224i	−0.0254522	−	0.999676i	$-0.508103\pi$
$607$	24.0023	−	24.0023i	0.974224	−	0.974224i	0.999676	+	0.0254522i	$0.00810257\pi$
$608$	11.8135	+	3.72413i	0.479100	+	0.151033i
$609$			7.24347i			0.293520i
$610$		0			0
$611$	−16.7091			−0.675977
$612$	11.9767	−	0.418473i	0.484128	−	0.0169158i
$613$	33.6909	+	33.6909i	1.36076	+	1.36076i	0.872946	+	0.487816i	$0.162206\pi$
$613$	33.6909	+	33.6909i	1.36076	+	1.36076i	0.487816	+	0.872946i	$0.337794\pi$
$614$	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	0.0896535	−	0.995973i	$-0.471424\pi$
$617$	−22.5125	−	22.5125i	−0.906319	−	0.906319i	−0.995973	+	0.0896535i	$0.971424\pi$
$618$	14.0046	+	5.51639i	0.563347	+	0.221902i
$619$			21.0797i			0.847265i	0.905834	+	0.423633i	$0.139245\pi$
$619$			21.0797i			0.847265i	−0.905834	+	0.423633i	$0.860755\pi$
$620$		0			0
$621$		−	8.56212i		−	0.343586i
$622$	16.0435	−	40.7299i	0.643284	−	1.63312i
$623$	5.58596	+	5.58596i	0.223797	+	0.223797i
$624$	−0.653187	−	9.33569i	−0.0261484	−	0.373727i
$625$		0			0
$626$	15.8200	−	6.87893i	0.632295	−	0.274937i
$627$	3.28229	+	3.28229i	0.131082	+	0.131082i
$628$	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	$0.322810\pi$
$631$			42.6546i			1.69805i	−0.528351	+	0.849026i	$0.677190\pi$
$632$	12.3844	+	25.9625i	0.492626	+	1.03273i
$633$	−7.26878	+	7.26878i	−0.288908	+	0.288908i
$634$	4.30434	−	1.87163i	0.170947	−	0.0743320i
$635$		0			0
$636$	2.47461	+	2.30752i	0.0981245	+	0.0914990i
$637$	−10.2023	+	10.2023i	−0.404229	+	0.404229i
$638$	−22.1362	−	8.71944i	−0.876382	−	0.345206i
$639$	−5.01557			−0.198413
$640$		0			0
$641$	0.687931			0.0271716			0.0135858	−	0.999908i	$-0.495675\pi$
$641$	0.687931			0.0271716			0.0135858	+	0.999908i	$0.495675\pi$
$642$	4.44391	+	1.75045i	0.175387	+	0.0690849i
$643$	−9.24755	+	9.24755i	−0.364688	+	0.364688i	−0.865535	−	0.500848i	$-0.833022\pi$
$643$	−9.24755	+	9.24755i	−0.364688	+	0.364688i	0.500848	+	0.865535i	$0.333022\pi$
$644$	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	$-0.906867\pi$
$647$	−17.0187	+	17.0187i	−0.669073	+	0.669073i	0.288429	+	0.957501i	$0.406867\pi$
$648$	1.21775	+	2.55286i	0.0478376	+	0.100286i
$649$		−	24.5736i		−	0.964598i
$650$		0			0
$651$	0.524037			0.0205386
$652$	16.3788	−	0.572287i	0.641445	−	0.0224125i
$653$	11.9095	+	11.9095i	0.466056	+	0.466056i	0.900634	−	0.434578i	$-0.143102\pi$
$653$	11.9095	+	11.9095i	0.466056	+	0.466056i	−0.434578	+	0.900634i	$0.643102\pi$
$654$	−4.79106	+	2.08327i	−0.187345	+	0.0814623i
$655$		0			0
$656$	0.836993	+	11.9627i	0.0326791	+	0.467066i
$657$	−6.18765	−	6.18765i	−0.241403	−	0.241403i
$658$	−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	$0.275406\pi$
$661$			39.1425i			1.52247i	−0.648478	+	0.761233i	$0.724594\pi$
$662$	−16.0340	−	6.31580i	−0.623181	−	0.245470i
$663$	−9.91295	−	9.91295i	−0.384987	−	0.384987i
$664$	44.3628	+	15.7082i	1.72161	+	0.609597i
$665$		0			0
$666$	−5.50904	−	12.6696i	−0.213471	−	0.490937i
$667$	48.0463	+	48.0463i	1.86036	+	1.86036i
$668$	−6.25884	+	0.218688i	−0.242162	+	0.00846128i
$669$	11.5542			0.446712
$670$		0			0
$671$		−	4.98380i		−	0.192397i
$672$	−4.92441	−	1.55239i	−0.189963	−	0.0598849i
$673$	−23.5686	+	23.5686i	−0.908503	+	0.908503i	−0.996151	−	0.0876488i	$-0.972065\pi$
$673$	−23.5686	+	23.5686i	−0.908503	+	0.908503i	0.0876488	+	0.996151i	$0.472065\pi$
$674$	−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	$-0.546293\pi$
$677$	21.9738	−	21.9738i	0.844522	−	0.844522i	0.989443	+	0.144921i	$0.0462928\pi$
$678$	2.30181	−	5.84367i	0.0884006	−	0.224425i
$679$	−10.4147			−0.399679
$680$		0			0
$681$	−7.44755			−0.285391
$682$	−0.630818	+	1.60147i	−0.0241553	+	0.0613235i
$683$	6.94901	−	6.94901i	0.265896	−	0.265896i	−0.561548	−	0.827444i	$-0.689794\pi$
$683$	6.94901	−	6.94901i	0.265896	−	0.265896i	0.827444	+	0.561548i	$0.189794\pi$
$684$	3.20289	+	2.98662i	0.122466	+	0.114196i
$685$		0			0
$686$	6.77736	+	15.5864i	0.258761	+	0.595093i
$687$	−2.21010	+	2.21010i	−0.0843208	+	0.0843208i
$688$	−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
$693$	−1.36821	−	1.36821i	−0.0519742	−	0.0519742i
$694$	−5.82377	−	13.3934i	−0.221067	−	0.508406i
$695$		0			0
$696$	−21.1587	−	7.49199i	−0.802020	−	0.283983i
$697$	12.7024	+	12.7024i	0.481139	+	0.481139i
$698$	18.6850	+	7.35998i	0.707236	+	0.278580i
$699$			3.41938i			0.129333i
$700$		0			0
$701$		−	35.1981i		−	1.32941i	−0.747105	−	0.664707i	$-0.768557\pi$
$701$		−	35.1981i		−	1.32941i	0.747105	−	0.664707i	$-0.231443\pi$
$702$	1.21262	−	3.07852i	0.0457675	−	0.116191i
$703$	−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
$708$	−0.809559	−	23.1696i	−0.0304251	−	0.870766i
$709$	−45.4352			−1.70636			−0.853178	−	0.521620i	$-0.825328\pi$
$709$	−45.4352			−1.70636			−0.853178	+	0.521620i	$0.825328\pi$
$710$		0			0
$711$			10.1700i			0.381404i
$712$	−22.0946	+	10.5394i	−0.828031	+	0.394981i
$713$	3.47596	−	3.47596i	0.130176	−	0.130176i
$714$	−7.09309	+	3.08425i	−0.265452	+	0.115425i
$715$		0			0
$716$	−18.0269	+	19.3323i	−0.673698	+	0.722482i
$717$	−4.72793	+	4.72793i	−0.176568	+	0.176568i
$718$	45.4058	+	17.8853i	1.69453	+	0.667474i
$719$	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
$722$	−18.6917	−	7.36263i	−0.695632	−	0.274009i
$723$	11.2077	−	11.2077i	0.416821	−	0.416821i
$724$	9.88585	−	10.6017i	0.367405	−	0.394009i
$725$		0			0
$726$	−8.43774	+	3.66893i	−0.313154	+	0.136167i
$727$	−10.5017	+	10.5017i	−0.389488	+	0.389488i	−0.874505	−	0.485017i	$-0.838813\pi$
$727$	−10.5017	+	10.5017i	−0.389488	+	0.389488i	0.485017	+	0.874505i	$0.338813\pi$
$728$	2.60050	+	5.45164i	0.0963808	+	0.202051i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−27.0120			−0.999076
$732$	−0.164188	−	4.69905i	−0.00606855	−	0.173682i
$733$	−10.0752	−	10.0752i	−0.372134	−	0.372134i	0.496120	−	0.868254i	$-0.334758\pi$
$733$	−10.0752	−	10.0752i	−0.372134	−	0.372134i	−0.868254	+	0.496120i	$0.834758\pi$
$734$	−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
$738$	−1.55385	+	3.94480i	−0.0571982	+	0.145210i
$739$		−	26.4753i		−	0.973909i	−0.873427	−	0.486955i	$-0.838108\pi$
$739$		−	26.4753i		−	0.973909i	0.873427	−	0.486955i	$-0.161892\pi$
$740$		0			0
$741$		−	5.12299i		−	0.188198i
$742$	−2.03184	−	0.800338i	−0.0745910	−	0.0293813i
$743$	6.15658	+	6.15658i	0.225863	+	0.225863i	0.810962	−	0.585099i	$-0.198944\pi$
$743$	6.15658	+	6.15658i	0.225863	+	0.225863i	−0.585099	+	0.810962i	$0.698944\pi$
$744$	−0.542017	+	1.53075i	−0.0198713	+	0.0561201i
$745$		0			0
$746$	12.0187	+	27.6404i	0.440037	+	1.01199i
$747$	11.7654	+	11.7654i	0.430475	+	0.430475i
$748$	−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	$0.0819122\pi$
$751$			13.9490i			0.509008i	−0.967072	+	0.254504i	$0.918088\pi$
$752$	−21.5606	−	18.7408i	−0.786233	−	0.683408i
$753$	−3.00902	+	3.00902i	−0.109655	+	0.109655i
$754$	10.4704	+	24.0797i	0.381311	+	0.876931i
$755$		0			0
$756$	−1.33512	−	1.24497i	−0.0485577	−	0.0452790i
$757$	−7.61475	+	7.61475i	−0.276763	+	0.276763i	−0.831815	−	0.555053i	$-0.812698\pi$
$757$	−7.61475	+	7.61475i	−0.276763	+	0.276763i	0.555053	+	0.831815i	$0.312698\pi$
$758$	−13.1863	+	33.4763i	−0.478947	+	1.21591i
$759$	−18.1508			−0.658834
$760$		0			0
$761$	−2.57254			−0.0932543			−0.0466272	−	0.998912i	$-0.514847\pi$
$761$	−2.57254			−0.0932543			−0.0466272	+	0.998912i	$0.514847\pi$
$762$	8.92771	−	22.6650i	0.323417	−	0.821065i
$763$	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
$768$	9.62803	−	12.7789i	0.347421	−	0.461120i
$769$			5.28253i			0.190493i	0.995454	+	0.0952465i	$0.0303639\pi$
$769$			5.28253i			0.190493i	−0.995454	+	0.0952465i	$0.969636\pi$
$770$		0			0
$771$	4.46663			0.160862
$772$	−8.14254	+	0.284505i	−0.293056	+	0.0102396i
$773$	19.4982	+	19.4982i	0.701302	+	0.701302i	0.964690	−	0.263388i	$-0.0848398\pi$
$773$	19.4982	+	19.4982i	0.701302	+	0.701302i	−0.263388	+	0.964690i	$0.584840\pi$
$774$	−2.54221	−	5.84651i	−0.0913777	−	0.210149i
$775$		0			0
$776$	10.7720	−	30.4221i	0.386693	−	1.09209i
$777$	6.30507	+	6.30507i	0.226193	+	0.226193i
$778$	−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
$783$	−5.61149	−	5.61149i	−0.200538	−	0.200538i
$784$	−24.6074	+	1.72170i	−0.878835	+	0.0614892i
$785$		0			0
$786$	−0.571040	+	0.248302i	−0.0203683	+	0.00885664i
$787$	3.02573	+	3.02573i	0.107856	+	0.107856i	0.758975	−	0.651120i	$-0.225700\pi$
$787$	3.02573	+	3.02573i	0.107856	+	0.107856i	−0.651120	+	0.758975i	$0.725700\pi$
$788$	−37.7668	+	1.31959i	−1.34538	+	0.0470086i
$789$	−13.0820			−0.465731
$790$		0			0
$791$			4.05363i			0.144130i
$792$	5.41181	−	2.58150i	0.192300	−	0.0917296i
$793$	−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	$-0.707193\pi$
$797$	5.35305	−	5.35305i	0.189615	−	0.189615i	0.795529	+	0.605915i	$0.207193\pi$
$798$	−2.62981	−	1.03588i	−0.0930942	−	0.0366697i
$799$	−42.7934			−1.51392
$800$		0			0
$801$	−8.65485			−0.305804
$802$	34.9853	+	13.7807i	1.23538	+	0.486613i
$803$	−13.1172	+	13.1172i	−0.462897	+	0.462897i
$804$	10.3389	+	9.64084i	0.364626	+	0.340006i
$805$		0			0
$806$	1.74207	−	0.757496i	0.0613619	−	0.0266817i
$807$	1.90778	−	1.90778i	0.0671572	−	0.0671572i
$808$	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
$813$	−16.9538	−	16.9538i	−0.594595	−	0.594595i
$814$	−26.8583	+	11.6786i	−0.941382	+	0.409336i
$815$		0			0
$816$	−1.67287	−	23.9095i	−0.0585622	−	0.837001i
$817$	−6.97987	−	6.97987i	−0.244195	−	0.244195i
$818$	4.73944	−	12.0321i	0.165711	−	0.420693i
$819$			2.13550i			0.0746205i
$820$		0			0
$821$		−	13.4087i		−	0.467968i	−0.972240	−	0.233984i	$-0.924824\pi$
$821$		−	13.4087i		−	0.467968i	0.972240	−	0.233984i	$-0.0751763\pi$
$822$	2.93663	+	1.15674i	0.102427	+	0.0403458i
$823$	1.36211	+	1.36211i	0.0474803	+	0.0474803i	0.730448	−	0.682968i	$-0.239311\pi$
$823$	1.36211	+	1.36211i	0.0474803	+	0.0474803i	−0.682968	+	0.730448i	$0.739311\pi$
$824$	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	0.0999219	−	0.994995i	$-0.468141\pi$
$827$	−25.7402	−	25.7402i	−0.895073	−	0.895073i	−0.994995	+	0.0999219i	$0.968141\pi$
$828$	−17.1138	+	0.597967i	−0.594745	+	0.0207808i
$829$	11.4288			0.396940			0.198470	−	0.980107i	$-0.436403\pi$
$829$	11.4288			0.396940			0.198470	+	0.980107i	$0.436403\pi$
$830$		0			0
$831$			0.555684i			0.0192765i
$832$	−18.6144	+	1.95757i	−0.645337	+	0.0678665i
$833$	−26.1289	+	26.1289i	−0.905314	+	0.905314i
$834$	−7.11834	−	16.3706i	−0.246488	−	0.566868i
$835$		0			0
$836$	6.33135	−	6.78981i	0.218974	−	0.234831i
$837$	−0.405970	+	0.405970i	−0.0140324	+	0.0140324i
$838$	2.24088	−	5.68897i	0.0774099	−	0.196522i
$839$	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
$842$	−4.40419	+	11.1810i	−0.151779	+	0.385323i
$843$	−17.5417	+	17.5417i	−0.604169	+	0.604169i
$844$	15.0363	+	14.0211i	0.517572	+	0.482625i
$845$		0			0
$846$	−4.02745	−	9.26225i	−0.138467	−	0.318443i
$847$	4.19907	−	4.19907i	0.144282	−	0.144282i
$848$	4.43939	−	5.10735i	0.152449	−	0.175387i
$849$			13.0642i			0.448363i
$850$		0			0
$851$	83.6436			2.86727
$852$	0.350281	+	10.0250i	0.0120004	+	0.343452i
$853$	−22.3165	−	22.3165i	−0.764103	−	0.764103i	0.212959	−	0.977061i	$-0.431690\pi$
$853$	−22.3165	−	22.3165i	−0.764103	−	0.764103i	−0.977061	+	0.212959i	$0.931690\pi$
$854$	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	0.547442	−	0.836843i	$-0.315602\pi$
$857$	−8.47209	−	8.47209i	−0.289401	−	0.289401i	−0.836843	+	0.547442i	$0.815602\pi$
$858$	−6.52615	−	2.57064i	−0.222799	−	0.0877603i
$859$			37.2555i			1.27114i	0.772042	+	0.635571i	$0.219235\pi$
$859$			37.2555i			1.27114i	−0.772042	+	0.635571i	$0.780765\pi$
$860$		0			0
$861$		−	2.73643i		−	0.0932572i
$862$	−13.4082	+	34.0397i	−0.456686	+	1.15940i
$863$	−10.5386	−	10.5386i	−0.358738	−	0.358738i	0.504610	−	0.863348i	$-0.331636\pi$
$863$	−10.5386	−	10.5386i	−0.358738	−	0.358738i	−0.863348	+	0.504610i	$0.831636\pi$
$864$	5.01756	−	2.61229i	0.170701	−	0.0888720i
$865$		0			0
$866$	33.3791	−	14.5140i	1.13427	−	0.493207i
$867$	−13.3671	−	13.3671i	−0.453971	−	0.453971i
$868$	−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
$873$	8.06823	−	8.06823i	0.273068	−	0.273068i
$874$	−24.3147	+	10.5726i	−0.822456	+	0.357624i
$875$		0			0
$876$	−11.9356	+	12.7999i	−0.403267	+	0.432468i
$877$	−16.9202	+	16.9202i	−0.571353	+	0.571353i	−0.932506	−	0.361153i	$-0.882383\pi$
$877$	−16.9202	+	16.9202i	−0.571353	+	0.571353i	0.361153	+	0.932506i	$0.382383\pi$
$878$	−21.9832	−	8.65915i	−0.741896	−	0.292232i
$879$	15.7587			0.531528
$880$		0			0
$881$	−34.6268			−1.16661			−0.583304	−	0.812254i	$-0.698240\pi$
$881$	−34.6268			−1.16661			−0.583304	+	0.812254i	$0.698240\pi$
$882$	−8.11447	−	3.19628i	−0.273228	−	0.107624i
$883$	23.6485	−	23.6485i	0.795835	−	0.795835i	−0.186601	−	0.982436i	$-0.559747\pi$
$883$	23.6485	−	23.6485i	0.795835	−	0.795835i	0.982436	+	0.186601i	$0.0597472\pi$
$884$	−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	$-0.513146\pi$
$887$	28.5275	−	28.5275i	0.957859	−	0.957859i	0.999147	+	0.0412884i	$0.0131463\pi$
$888$	−24.9390	+	11.8962i	−0.836897	+	0.399210i
$889$			15.7222i			0.527306i
$890$		0			0
$891$	2.11990			0.0710194
$892$	−0.806930	−	23.0943i	−0.0270180	−	0.773255i
$893$	−11.0578	−	11.0578i	−0.370034	−	0.370034i
$894$	23.9107	−	10.3970i	0.799695	−	0.347727i
$895$		0			0
$896$	−2.75898	+	9.95124i	−0.0921710	+	0.332448i
$897$	14.1649	+	14.1649i	0.472951	+	0.472951i
$898$	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
$903$	2.90954	+	2.90954i	0.0968234	+	0.0968234i
$904$	−11.8410	−	4.19271i	−0.393824	−	0.139447i
$905$		0			0
$906$	0.00210967	+	0.00485178i	7.00892e−5	+	0.000161190i
$907$	−15.0125	−	15.0125i	−0.498481	−	0.498481i	0.412484	−	0.910965i	$-0.364661\pi$
$907$	−15.0125	−	15.0125i	−0.498481	−	0.498481i	−0.910965	+	0.412484i	$0.864661\pi$
$908$	0.520127	+	14.8860i	0.0172610	+	0.494010i
$909$	2.83542			0.0940449
$910$		0			0
$911$		−	17.5986i		−	0.583068i	−0.956560	−	0.291534i	$-0.905834\pi$
$911$		−	17.5986i		−	0.583068i	0.956560	−	0.291534i	$-0.0941657\pi$
$912$	5.74592	−	6.61045i	0.190266	−	0.218894i
$913$	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
$918$	3.10564	−	7.88435i	0.102501	−	0.260222i
$919$	−5.93406			−0.195747			−0.0978733	−	0.995199i	$-0.531204\pi$
$919$	−5.93406			−0.195747			−0.0978733	+	0.995199i	$0.531204\pi$
$920$		0			0
$921$	17.0245			0.560976
$922$	2.81287	−	7.14110i	0.0926370	−	0.235180i
$923$	8.29759	−	8.29759i	0.273119	−	0.273119i
$924$	−2.63920	+	2.83031i	−0.0868235	+	0.0931105i
$925$		0			0
$926$	−19.2518	−	44.2749i	−0.632654	−	1.45497i
$927$	7.52594	−	7.52594i	0.247184	−	0.247184i
$928$	−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
$933$	−21.8879	−	21.8879i	−0.716577	−	0.716577i
$934$	−15.6840	−	36.0698i	−0.513197	−	1.18024i
$935$		0			0
$936$	−6.23796	−	2.20877i	−0.203894	−	0.0721959i
$937$	−12.4605	−	12.4605i	−0.407068	−	0.407068i	0.473647	−	0.880715i	$-0.342937\pi$
$937$	−12.4605	−	12.4605i	−0.407068	−	0.407068i	−0.880715	+	0.473647i	$0.842937\pi$
$938$	−8.48904	−	3.34382i	−0.277177	−	0.109180i
$939$		−	12.1982i		−	0.398074i
$940$		0			0
$941$			18.6088i			0.606630i	0.952890	+	0.303315i	$0.0980934\pi$
$941$			18.6088i			0.606630i	−0.952890	+	0.303315i	$0.901907\pi$
$942$	8.29365	−	21.0553i	0.270222	−	0.686018i
$943$	−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	0.899038	−	0.437870i	$-0.144267\pi$
$947$	14.1917	+	14.1917i	0.461168	+	0.461168i	−0.437870	+	0.899038i	$0.644267\pi$
$948$	20.3275	−	0.710257i	0.660208	−	0.0230681i
$949$	20.4733			0.664591
$950$		0			0
$951$		−	3.31891i		−	0.107623i
$952$	6.66010	+	13.9621i	0.215855	+	0.452515i
$953$	25.0919	−	25.0919i	0.812806	−	0.812806i	−0.172248	−	0.985054i	$-0.555103\pi$
$953$	25.0919	−	25.0919i	0.812806	−	0.812806i	0.985054	+	0.172248i	$0.0551029\pi$
$954$	2.19408	−	0.954037i	0.0710358	−	0.0308881i
$955$		0			0
$956$	9.78029	+	9.11990i	0.316317	+	0.294959i
$957$	−11.8958	+	11.8958i	−0.384537	+	0.384537i
$958$	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
$963$	2.38812	−	2.38812i	0.0769561	−	0.0769561i
$964$	−23.1846	−	21.6191i	−0.746724	−	0.696304i
$965$		0			0
$966$	10.1355	−	4.40716i	0.326104	−	0.141798i
$967$	−41.2729	+	41.2729i	−1.32725	+	1.32725i	−0.419482	+	0.907764i	$0.637788\pi$
$967$	−41.2729	+	41.2729i	−1.32725	+	1.32725i	−0.907764	+	0.419482i	$0.862212\pi$
$968$	7.92267	+	16.6090i	0.254644	+	0.533832i
$969$		−	13.1204i		−	0.421489i
$970$		0			0
$971$	−47.1256			−1.51233			−0.756166	−	0.654380i	$-0.772930\pi$
$971$	−47.1256			−1.51233			−0.756166	+	0.654380i	$0.772930\pi$
$972$	1.99878	−	0.0698387i	0.0641109	−	0.00224008i
$973$	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	0.662582	−	0.748989i	$-0.269461\pi$
$977$	−2.70084	−	2.70084i	−0.0864074	−	0.0864074i	−0.748989	+	0.662582i	$0.769461\pi$
$978$	4.24715	−	10.7823i	0.135809	−	0.344781i
$979$			18.3474i			0.586386i
$980$		0			0
$981$			3.69420i			0.117947i
$982$	8.33701	+	3.28394i	0.266045	+	0.104795i
$983$	−17.7831	−	17.7831i	−0.567192	−	0.567192i	0.364149	−	0.931341i	$-0.381360\pi$
$983$	−17.7831	−	17.7831i	−0.567192	−	0.567192i	−0.931341	+	0.364149i	$0.881360\pi$
$984$	7.99331	+	2.83031i	0.254818	+	0.0902271i
$985$		0			0
$986$	26.8157	+	61.6702i	0.853986	+	1.96398i
$987$	4.60939	+	4.60939i	0.146719	+	0.146719i
$988$	−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	$0.106757\pi$
$991$			20.7223i			0.658267i	−0.944283	+	0.329134i	$0.893243\pi$
$992$	3.09749	+	0.976467i	0.0983455	+	0.0310029i
$993$	−8.61655	+	8.61655i	−0.273438	+	0.273438i
$994$	−2.58166	−	5.93724i	−0.0818851	−	0.188318i
$995$		0			0
$996$	22.6948	−	24.3382i	0.719113	−	0.771185i
$997$	12.9685	−	12.9685i	0.410715	−	0.410715i	−0.471273	−	0.881988i	$-0.656205\pi$
$997$	12.9685	−	12.9685i	0.410715	−	0.410715i	0.881988	+	0.471273i	$0.156205\pi$
$998$	−8.86362	+	22.5023i	−0.280573	+	0.712297i
$999$	−9.76903			−0.309079

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.v.a.43.7	✓	24	5.2	odd	4
120.2.v.a.43.12	yes	24	40.27	even	4
120.2.v.a.67.7	yes	24	40.19	odd	2
120.2.v.a.67.12	yes	24	5.4	even	2
360.2.w.e.163.1		24	120.107	odd	4
360.2.w.e.163.6		24	15.2	even	4
360.2.w.e.307.1		24	15.14	odd	2
360.2.w.e.307.6		24	120.59	even	2
480.2.bh.a.367.1		24	20.19	odd	2
480.2.bh.a.367.6		24	40.29	even	2
480.2.bh.a.463.1		24	40.37	odd	4
480.2.bh.a.463.6		24	20.7	even	4
600.2.v.b.43.1		24	40.3	even	4	inner
600.2.v.b.43.6		24	5.3	odd	4	inner
600.2.v.b.307.1		24	1.1	even	1	trivial
600.2.v.b.307.6		24	8.3	odd	2	inner
1440.2.bi.e.847.1		24	120.29	odd	2
1440.2.bi.e.847.12		24	60.59	even	2
1440.2.bi.e.1423.1		24	60.47	odd	4
1440.2.bi.e.1423.12		24	120.77	even	4
2400.2.bh.b.943.11		24	20.3	even	4
2400.2.bh.b.943.12		24	40.13	odd	4
2400.2.bh.b.1807.11		24	8.5	even	2
2400.2.bh.b.1807.12		24	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31581 - 0.518298i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.46273 + 1.36397i) q^{4} +(1.29691 - 0.563929i) q^{6} +(-0.645414 + 0.645414i) q^{7} +(-1.21775 - 2.55286i) q^{8} -1.00000i q^{9} -2.11990 q^{11} +(-1.99878 + 0.0698387i) q^{12} +(1.65437 + 1.65437i) q^{13} +(1.18376 - 0.514728i) q^{14} +(0.279184 + 3.99025i) q^{16} +(4.23698 + 4.23698i) q^{17} +(-0.518298 + 1.31581i) q^{18} +2.18966i q^{19} -0.912753i q^{21} +(2.78940 + 1.09874i) q^{22} +(-6.05433 - 6.05433i) q^{23} +(2.66622 + 0.944069i) q^{24} +(-1.31938 - 3.03429i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-1.82439 + 0.0637454i) q^{28} -7.93585 q^{29} +0.574128i q^{31} +(1.70078 - 5.39512i) q^{32} +(1.49900 - 1.49900i) q^{33} +(-3.37906 - 7.77109i) q^{34} +(1.36397 - 1.46273i) q^{36} +(-6.90775 + 6.90775i) q^{37} +(1.13490 - 2.88118i) q^{38} -2.33963 q^{39} +2.99799 q^{41} +(-0.473078 + 1.20101i) q^{42} +(-3.18765 + 3.18765i) q^{43} +(-3.10085 - 2.89148i) q^{44} +(4.82843 + 11.1043i) q^{46} +(-5.04999 + 5.04999i) q^{47} +(-3.01894 - 2.62412i) q^{48} +6.16688i q^{49} -5.99199 q^{51} +(0.163396 + 4.67640i) q^{52} +(-1.19626 - 1.19626i) q^{53} +(-0.563929 - 1.29691i) q^{54} +(2.43360 + 0.861702i) q^{56} +(-1.54832 - 1.54832i) q^{57} +(10.4421 + 4.11314i) q^{58} +11.5919i q^{59} +2.35096i q^{61} +(0.297570 - 0.755446i) q^{62} +(0.645414 + 0.645414i) q^{63} +(-5.03419 + 6.21747i) q^{64} +(-2.74933 + 1.19547i) q^{66} +(-4.99799 - 4.99799i) q^{67} +(0.418473 + 11.9767i) q^{68} +8.56212 q^{69} -5.01557i q^{71} +(-2.55286 + 1.21775i) q^{72} +(6.18765 - 6.18765i) q^{73} +(12.6696 - 5.50904i) q^{74} +(-2.98662 + 3.20289i) q^{76} +(1.36821 - 1.36821i) q^{77} +(3.07852 + 1.21262i) q^{78} -10.1700 q^{79} -1.00000 q^{81} +(-3.94480 - 1.55385i) q^{82} +(-11.7654 + 11.7654i) q^{83} +(1.24497 - 1.33512i) q^{84} +(5.84651 - 2.54221i) q^{86} +(5.61149 - 5.61149i) q^{87} +(2.58150 + 5.41181i) q^{88} -8.65485i q^{89} -2.13550 q^{91} +(-0.597967 - 17.1138i) q^{92} +(-0.405970 - 0.405970i) q^{93} +(9.26225 - 4.02745i) q^{94} +(2.61229 + 5.01756i) q^{96} +(8.06823 + 8.06823i) q^{97} +(3.19628 - 8.11447i) q^{98} +2.11990i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{6} + 12 q^{8} + 8 q^{12} - 20 q^{16} - 8 q^{17} + 28 q^{22} - 16 q^{26} - 4 q^{28} - 20 q^{32} + 4 q^{36} - 40 q^{38} - 20 q^{42} + 32 q^{43} + 48 q^{46} - 16 q^{48} - 16 q^{51} + 48 q^{52}+ \cdots + 88 q^{98}+O(q^{100}) \) 24 * q + 4 * q^6 + 12 * q^8 + 8 * q^12 - 20 * q^16 - 8 * q^17 + 28 * q^22 - 16 * q^26 - 4 * q^28 - 20 * q^32 + 4 * q^36 - 40 * q^38 - 20 * q^42 + 32 * q^43 + 48 * q^46 - 16 * q^48 - 16 * q^51 + 48 * q^52 - 32 * q^56 + 12 * q^58 + 16 * q^62 - 24 * q^66 - 48 * q^67 - 72 * q^68 - 12 * q^72 + 40 * q^73 + 48 * q^76 + 24 * q^78 - 24 * q^81 - 24 * q^82 - 80 * q^83 - 32 * q^86 - 12 * q^88 + 64 * q^91 - 16 * q^92 - 44 * q^96 + 24 * q^97 + 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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