LMFDB - Embedded newform 735.2.j.h.197.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(197,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("735.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.j (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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.4
Character	$\chi$	$=$	735.197
Dual form			735.2.j.h.638.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.800553 + 0.800553i) q^{2} +(1.34285 - 1.09397i) q^{3} +0.718229i q^{4} +(2.10480 + 0.754855i) q^{5} +(-0.199242 + 1.95080i) q^{6} +(-2.17609 - 2.17609i) q^{8} +(0.606476 - 2.93806i) q^{9} +O(q^{10})$	\(q+(-0.800553 + 0.800553i) q^{2} +(1.34285 - 1.09397i) q^{3} +0.718229i q^{4} +(2.10480 + 0.754855i) q^{5} +(-0.199242 + 1.95080i) q^{6} +(-2.17609 - 2.17609i) q^{8} +(0.606476 - 2.93806i) q^{9} +(-2.28931 + 1.08070i) q^{10} +5.20191i q^{11} +(0.785718 + 0.964471i) q^{12} +(3.24693 - 3.24693i) q^{13} +(3.65221 - 1.28893i) q^{15} +2.04769 q^{16} +(0.844232 - 0.844232i) q^{17} +(1.86656 + 2.83759i) q^{18} +1.32025i q^{19} +(-0.542159 + 1.51173i) q^{20} +(-4.16440 - 4.16440i) q^{22} +(5.62910 + 5.62910i) q^{23} +(-5.30272 - 0.541586i) q^{24} +(3.86039 + 3.17764i) q^{25} +5.19868i q^{26} +(-2.39973 - 4.60883i) q^{27} -4.38282 q^{29} +(-1.89194 + 3.95565i) q^{30} +1.70499 q^{31} +(2.71289 - 2.71289i) q^{32} +(5.69071 + 6.98536i) q^{33} +1.35170i q^{34} +(2.11020 + 0.435588i) q^{36} +(-1.71171 - 1.71171i) q^{37} +(-1.05693 - 1.05693i) q^{38} +(0.808099 - 7.91217i) q^{39} +(-2.93760 - 6.22286i) q^{40} -1.82176i q^{41} +(-0.281771 + 0.281771i) q^{43} -3.73616 q^{44} +(3.49432 - 5.72623i) q^{45} -9.01279 q^{46} +(-3.39588 + 3.39588i) q^{47} +(2.74973 - 2.24010i) q^{48} +(-5.63432 + 0.546575i) q^{50} +(0.210113 - 2.05723i) q^{51} +(2.33204 + 2.33204i) q^{52} +(-3.51059 - 3.51059i) q^{53} +(5.61073 + 1.76850i) q^{54} +(-3.92668 + 10.9490i) q^{55} +(1.44431 + 1.77289i) q^{57} +(3.50868 - 3.50868i) q^{58} +1.81772 q^{59} +(0.925745 + 2.62313i) q^{60} +2.47514 q^{61} +(-1.36494 + 1.36494i) q^{62} +8.43900i q^{64} +(9.28511 - 4.38319i) q^{65} +(-10.1479 - 1.03644i) q^{66} +(7.92132 + 7.92132i) q^{67} +(0.606352 + 0.606352i) q^{68} +(13.7171 + 1.40098i) q^{69} -9.06358i q^{71} +(-7.71322 + 5.07373i) q^{72} +(1.33856 - 1.33856i) q^{73} +2.74064 q^{74} +(8.66014 + 0.0439525i) q^{75} -0.948239 q^{76} +(5.68718 + 6.98104i) q^{78} +11.5015i q^{79} +(4.30998 + 1.54571i) q^{80} +(-8.26437 - 3.56372i) q^{81} +(1.45841 + 1.45841i) q^{82} +(-5.46196 - 5.46196i) q^{83} +(2.41421 - 1.13967i) q^{85} -0.451146i q^{86} +(-5.88546 + 4.79466i) q^{87} +(11.3198 - 11.3198i) q^{88} -9.43116 q^{89} +(1.78676 + 7.38154i) q^{90} +(-4.04298 + 4.04298i) q^{92} +(2.28954 - 1.86520i) q^{93} -5.43717i q^{94} +(-0.996595 + 2.77886i) q^{95} +(0.675186 - 6.61080i) q^{96} +(3.06315 + 3.06315i) q^{97} +(15.2835 + 3.15483i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3}+O(q^{10}) $ 24 * q + 4 * q^3	$ 24 q + 4 q^{3} + 16 q^{10} - 16 q^{12} + 8 q^{13} - 16 q^{15} - 16 q^{16} - 20 q^{18} + 8 q^{22} - 16 q^{25} + 16 q^{27} + 20 q^{30} - 28 q^{33} + 16 q^{36} - 16 q^{37} - 64 q^{40} - 40 q^{43} - 20 q^{45} - 64 q^{46} - 16 q^{48} - 20 q^{51} - 40 q^{55} + 4 q^{57} + 40 q^{58} + 32 q^{60} - 32 q^{61} + 16 q^{66} + 24 q^{67} - 8 q^{72} - 32 q^{73} + 60 q^{75} - 32 q^{76} + 60 q^{78} + 52 q^{81} + 80 q^{82} + 24 q^{85} - 4 q^{87} + 96 q^{88} + 24 q^{90} - 76 q^{93} + 96 q^{96} - 24 q^{97}+O(q^{100}) $ 24 * q + 4 * q^3 + 16 * q^10 - 16 * q^12 + 8 * q^13 - 16 * q^15 - 16 * q^16 - 20 * q^18 + 8 * q^22 - 16 * q^25 + 16 * q^27 + 20 * q^30 - 28 * q^33 + 16 * q^36 - 16 * q^37 - 64 * q^40 - 40 * q^43 - 20 * q^45 - 64 * q^46 - 16 * q^48 - 20 * q^51 - 40 * q^55 + 4 * q^57 + 40 * q^58 + 32 * q^60 - 32 * q^61 + 16 * q^66 + 24 * q^67 - 8 * q^72 - 32 * q^73 + 60 * q^75 - 32 * q^76 + 60 * q^78 + 52 * q^81 + 80 * q^82 + 24 * q^85 - 4 * q^87 + 96 * q^88 + 24 * q^90 - 76 * q^93 + 96 * q^96 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.800553	+	0.800553i	−0.566077	+	0.566077i	−0.931027	−	0.364950i	$-0.881086\pi$
$2$	−0.800553	+	0.800553i	−0.566077	+	0.566077i	0.364950	+	0.931027i	$0.381086\pi$
$3$	1.34285	−	1.09397i	0.775293	−	0.631602i
$3$	1.34285	−	1.09397i	0.775293	−	0.631602i
$4$			0.718229i			0.359114i
$5$	2.10480	+	0.754855i	0.941296	+	0.337581i
$5$	2.10480	+	0.754855i	0.941296	+	0.337581i
$6$	−0.199242	+	1.95080i	−0.0813403	+	0.796410i
$7$		0			0
$7$		0			0
$8$	−2.17609	−	2.17609i	−0.769363	−	0.769363i
$9$	0.606476	−	2.93806i	0.202159	−	0.979353i
$10$	−2.28931	+	1.08070i	−0.723943	+	0.341749i
$11$			5.20191i			1.56843i	0.620487	+	0.784217i	$0.286935\pi$
$11$			5.20191i			1.56843i	−0.620487	+	0.784217i	$0.713065\pi$
$12$	0.785718	+	0.964471i	0.226817	+	0.278419i
$13$	3.24693	−	3.24693i	0.900537	−	0.900537i	−0.0949456	−	0.995482i	$-0.530268\pi$
$13$	3.24693	−	3.24693i	0.900537	−	0.900537i	0.995482	+	0.0949456i	$0.0302677\pi$
$14$		0			0
$15$	3.65221	−	1.28893i	0.942997	−	0.332800i
$16$	2.04769			0.511922
$17$	0.844232	−	0.844232i	0.204756	−	0.204756i	−0.597278	−	0.802034i	$-0.703751\pi$
$17$	0.844232	−	0.844232i	0.204756	−	0.204756i	0.802034	+	0.597278i	$0.203751\pi$
$18$	1.86656	+	2.83759i	0.439951	+	0.668826i
$19$			1.32025i			0.302885i	0.988466	+	0.151443i	$0.0483919\pi$
$19$			1.32025i			0.302885i	−0.988466	+	0.151443i	$0.951608\pi$
$20$	−0.542159	+	1.51173i	−0.121230	+	0.338033i
$21$		0			0
$22$	−4.16440	−	4.16440i	−0.887854	−	0.887854i
$23$	5.62910	+	5.62910i	1.17375	+	1.17375i	0.981309	+	0.192440i	$0.0616401\pi$
$23$	5.62910	+	5.62910i	1.17375	+	1.17375i	0.192440	+	0.981309i	$0.438360\pi$
$24$	−5.30272	−	0.541586i	−1.08241	−	0.110551i
$25$	3.86039	+	3.17764i	0.772078	+	0.635528i
$26$			5.19868i			1.01955i
$27$	−2.39973	−	4.60883i	−0.461829	−	0.886969i
$28$		0			0
$29$	−4.38282			−0.813870			−0.406935	−	0.913457i	$-0.633402\pi$
$29$	−4.38282			−0.813870			−0.406935	+	0.913457i	$0.633402\pi$
$30$	−1.89194	+	3.95565i	−0.345419	+	0.722199i
$31$	1.70499			0.306225			0.153113	−	0.988209i	$-0.451070\pi$
$31$	1.70499			0.306225			0.153113	+	0.988209i	$0.451070\pi$
$32$	2.71289	−	2.71289i	0.479576	−	0.479576i
$33$	5.69071	+	6.98536i	0.990625	+	1.21600i
$34$			1.35170i			0.231815i
$35$		0			0
$36$	2.11020	+	0.435588i	0.351700	+	0.0725981i
$37$	−1.71171	−	1.71171i	−0.281404	−	0.281404i	0.552265	−	0.833669i	$-0.313764\pi$
$37$	−1.71171	−	1.71171i	−0.281404	−	0.281404i	−0.833669	+	0.552265i	$0.813764\pi$
$38$	−1.05693	−	1.05693i	−0.171456	−	0.171456i
$39$	0.808099	−	7.91217i	0.129399	−	1.26696i
$40$	−2.93760	−	6.22286i	−0.464476	−	0.983921i
$41$		−	1.82176i		−	0.284511i	−0.989830	−	0.142255i	$-0.954565\pi$
$41$		−	1.82176i		−	0.284511i	0.989830	−	0.142255i	$-0.0454354\pi$
$42$		0			0
$43$	−0.281771	+	0.281771i	−0.0429697	+	0.0429697i	−0.728265	−	0.685295i	$-0.759673\pi$
$43$	−0.281771	+	0.281771i	−0.0429697	+	0.0429697i	0.685295	+	0.728265i	$0.259673\pi$
$44$	−3.73616			−0.563247
$45$	3.49432	−	5.72623i	0.520902	−	0.853616i
$46$	−9.01279			−1.32886
$47$	−3.39588	+	3.39588i	−0.495340	+	0.495340i	−0.909984	−	0.414644i	$-0.863906\pi$
$47$	−3.39588	+	3.39588i	−0.495340	+	0.495340i	0.414644	+	0.909984i	$0.363906\pi$
$48$	2.74973	−	2.24010i	0.396890	−	0.323331i
$49$		0			0
$50$	−5.63432	+	0.546575i	−0.796813	+	0.0772973i
$51$	0.210113	−	2.05723i	0.0294217	−	0.288071i
$52$	2.33204	+	2.33204i	0.323396	+	0.323396i
$53$	−3.51059	−	3.51059i	−0.482216	−	0.482216i	0.423623	−	0.905839i	$-0.360758\pi$
$53$	−3.51059	−	3.51059i	−0.482216	−	0.482216i	−0.905839	+	0.423623i	$0.860758\pi$
$54$	5.61073	+	1.76850i	0.763523	+	0.240662i
$55$	−3.92668	+	10.9490i	−0.529474	+	1.47636i
$56$		0			0
$57$	1.44431	+	1.77289i	0.191303	+	0.234825i
$58$	3.50868	−	3.50868i	0.460713	−	0.460713i
$59$	1.81772			0.236647			0.118323	−	0.992975i	$-0.462248\pi$
$59$	1.81772			0.236647			0.118323	+	0.992975i	$0.462248\pi$
$60$	0.925745	+	2.62313i	0.119513	+	0.338644i
$61$	2.47514			0.316909			0.158455	−	0.987366i	$-0.449349\pi$
$61$	2.47514			0.316909			0.158455	+	0.987366i	$0.449349\pi$
$62$	−1.36494	+	1.36494i	−0.173347	+	0.173347i
$63$		0			0
$64$			8.43900i			1.05488i
$65$	9.28511	−	4.38319i	1.15168	−	0.543668i
$66$	−10.1479	−	1.03644i	−1.24912	−	0.127577i
$67$	7.92132	+	7.92132i	0.967743	+	0.967743i	0.999496	−	0.0317530i	$-0.0101090\pi$
$67$	7.92132	+	7.92132i	0.967743	+	0.967743i	−0.0317530	+	0.999496i	$0.510109\pi$
$68$	0.606352	+	0.606352i	0.0735309	+	0.0735309i
$69$	13.7171	+	1.40098i	1.65134	+	0.168658i
$70$		0			0
$71$		−	9.06358i		−	1.07565i	−0.843057	−	0.537825i	$-0.819246\pi$
$71$		−	9.06358i		−	1.07565i	0.843057	−	0.537825i	$-0.180754\pi$
$72$	−7.71322	+	5.07373i	−0.909011	+	0.597944i
$73$	1.33856	−	1.33856i	0.156666	−	0.156666i	−0.624422	−	0.781088i	$-0.714665\pi$
$73$	1.33856	−	1.33856i	0.156666	−	0.156666i	0.781088	+	0.624422i	$0.214665\pi$
$74$	2.74064			0.318592
$75$	8.66014	+	0.0439525i	0.999987	+	0.00507520i
$76$	−0.948239			−0.108771
$77$		0			0
$78$	5.68718	+	6.98104i	0.643947	+	0.790447i
$79$			11.5015i			1.29402i	0.762481	+	0.647011i	$0.223981\pi$
$79$			11.5015i			1.29402i	−0.762481	+	0.647011i	$0.776019\pi$
$80$	4.30998	+	1.54571i	0.481871	+	0.172815i
$81$	−8.26437	−	3.56372i	−0.918264	−	0.395969i
$82$	1.45841	+	1.45841i	0.161055	+	0.161055i
$83$	−5.46196	−	5.46196i	−0.599528	−	0.599528i	0.340659	−	0.940187i	$-0.389350\pi$
$83$	−5.46196	−	5.46196i	−0.599528	−	0.599528i	−0.940187	+	0.340659i	$0.889350\pi$
$84$		0			0
$85$	2.41421	−	1.13967i	0.261858	−	0.123614i
$86$		−	0.451146i		−	0.0486483i
$87$	−5.88546	+	4.79466i	−0.630988	+	0.514041i
$88$	11.3198	−	11.3198i	1.20669	−	1.20669i
$89$	−9.43116			−0.999701			−0.499850	−	0.866112i	$-0.666612\pi$
$89$	−9.43116			−0.999701			−0.499850	+	0.866112i	$0.666612\pi$
$90$	1.78676	+	7.38154i	0.188341	+	0.778083i
$91$		0			0
$92$	−4.04298	+	4.04298i	−0.421510	+	0.421510i
$93$	2.28954	−	1.86520i	0.237414	−	0.193412i
$94$		−	5.43717i		−	0.560801i
$95$	−0.996595	+	2.77886i	−0.102248	+	0.285105i
$96$	0.675186	−	6.61080i	0.0689109	−	0.674712i
$97$	3.06315	+	3.06315i	0.311016	+	0.311016i	0.845303	−	0.534287i	$-0.179420\pi$
$97$	3.06315	+	3.06315i	0.311016	+	0.311016i	−0.534287	+	0.845303i	$0.679420\pi$
$98$		0			0
$99$	15.2835	+	3.15483i	1.53605	+	0.317072i
$100$	−2.28227	+	2.77264i	−0.228227	+	0.277264i
$101$		−	3.71640i		−	0.369796i	−0.982758	−	0.184898i	$-0.940805\pi$
$101$		−	3.71640i		−	0.369796i	0.982758	−	0.184898i	$-0.0591954\pi$
$102$	1.47872	+	1.81513i	0.146415	+	0.179725i
$103$	−1.18049	+	1.18049i	−0.116317	+	0.116317i	−0.762869	−	0.646553i	$-0.776210\pi$
$103$	−1.18049	+	1.18049i	−0.116317	+	0.116317i	0.646553	+	0.762869i	$0.276210\pi$
$104$	−14.1312			−1.38568
$105$		0			0
$106$	5.62082			0.545943
$107$	1.38009	−	1.38009i	0.133418	−	0.133418i	−0.637244	−	0.770662i	$-0.719926\pi$
$107$	1.38009	−	1.38009i	0.133418	−	0.133418i	0.770662	+	0.637244i	$0.219926\pi$
$108$	3.31019	−	1.72356i	0.318523	−	0.165849i
$109$		−	5.93506i		−	0.568475i	−0.958754	−	0.284238i	$-0.908260\pi$
$109$		−	5.93506i		−	0.568475i	0.958754	−	0.284238i	$-0.0917405\pi$
$110$	−5.62173	−	11.9088i	−0.536011	−	1.13546i
$111$	−4.17113	−	0.426013i	−0.395906	−	0.0404353i
$112$		0			0
$113$	−0.240664	−	0.240664i	−0.0226398	−	0.0226398i	0.695696	−	0.718336i	$-0.255096\pi$
$113$	−0.240664	−	0.240664i	−0.0226398	−	0.0226398i	−0.718336	+	0.695696i	$0.755096\pi$
$114$	−2.57554	−	0.263049i	−0.241221	−	0.0246368i
$115$	7.59899	+	16.0973i	0.708610	+	1.50108i
$116$		−	3.14787i		−	0.292272i
$117$	−7.57049	−	11.5089i	−0.699892	−	1.06399i
$118$	−1.45518	+	1.45518i	−0.133960	+	0.133960i
$119$		0			0
$120$	−10.7524	−	5.14271i	−0.981551	−	0.469463i
$121$	−16.0598			−1.45998
$122$	−1.98148	+	1.98148i	−0.179395	+	0.179395i
$123$	−1.99294	−	2.44634i	−0.179697	−	0.220579i
$124$			1.22457i			0.109970i
$125$	5.72670	+	9.60234i	0.512211	+	0.858860i
$126$		0			0
$127$	−4.55939	−	4.55939i	−0.404581	−	0.404581i	0.475263	−	0.879844i	$-0.342353\pi$
$127$	−4.55939	−	4.55939i	−0.404581	−	0.404581i	−0.879844	+	0.475263i	$0.842353\pi$
$128$	−1.33009	−	1.33009i	−0.117565	−	0.117565i
$129$	−0.0701274	+	0.686624i	−0.00617437	+	0.0604538i
$130$	−3.92425	+	10.9422i	−0.344180	+	0.959695i
$131$		−	13.6784i		−	1.19509i	−0.801837	−	0.597543i	$-0.796144\pi$
$131$		−	13.6784i		−	1.19509i	0.801837	−	0.597543i	$-0.203856\pi$
$132$	−5.01709	+	4.08723i	−0.436682	+	0.355748i
$133$		0			0
$134$	−12.6829			−1.09563
$135$	−1.57197	−	11.5121i	−0.135293	−	0.990806i
$136$	−3.67424			−0.315064
$137$	−10.0232	+	10.0232i	−0.856337	+	0.856337i	−0.990904	−	0.134567i	$-0.957036\pi$
$137$	−10.0232	+	10.0232i	−0.856337	+	0.856337i	0.134567	+	0.990904i	$0.457036\pi$
$138$	−12.1028	+	9.85969i	−1.03026	+	0.839313i
$139$		−	15.8262i		−	1.34236i	−0.741292	−	0.671182i	$-0.765787\pi$
$139$		−	15.8262i		−	1.34236i	0.741292	−	0.671182i	$-0.234213\pi$
$140$		0			0
$141$	−0.845170	+	8.27513i	−0.0711761	+	0.696892i
$142$	7.25588	+	7.25588i	0.608900	+	0.608900i
$143$	16.8902	+	16.8902i	1.41243	+	1.41243i
$144$	1.24187	−	6.01623i	0.103490	−	0.501353i
$145$	−9.22498	−	3.30840i	−0.766093	−	0.274747i
$146$			2.14317i			0.177370i
$147$		0			0
$148$	1.22940	−	1.22940i	0.101056	−	0.101056i
$149$	−9.30594			−0.762373			−0.381186	−	0.924498i	$-0.624484\pi$
$149$	−9.30594			−0.762373			−0.381186	+	0.924498i	$0.624484\pi$
$150$	−6.96809	+	6.89772i	−0.568942	+	0.563196i
$151$	−16.8274			−1.36939			−0.684697	−	0.728827i	$-0.740066\pi$
$151$	−16.8274			−1.36939			−0.684697	+	0.728827i	$0.740066\pi$
$152$	2.87297	−	2.87297i	0.233029	−	0.233029i
$153$	−1.96840	−	2.99241i	−0.159135	−	0.241922i
$154$		0			0
$155$	3.58867	+	1.28702i	0.288249	+	0.103376i
$156$	5.68275	+	0.580400i	0.454984	+	0.0464692i
$157$	−6.80647	−	6.80647i	−0.543216	−	0.543216i	0.381255	−	0.924470i	$-0.375492\pi$
$157$	−6.80647	−	6.80647i	−0.543216	−	0.543216i	−0.924470	+	0.381255i	$0.875492\pi$
$158$	−9.20757	−	9.20757i	−0.732515	−	0.732515i
$159$	−8.55464	−	0.873717i	−0.678427	−	0.0692903i
$160$	7.75793	−	3.66226i	0.613319	−	0.289527i
$161$		0			0
$162$	9.46902	−	3.76312i	0.743957	−	0.295659i
$163$	8.77966	−	8.77966i	0.687676	−	0.687676i	−0.274042	−	0.961718i	$-0.588361\pi$
$163$	8.77966	−	8.77966i	0.687676	−	0.687676i	0.961718	+	0.274042i	$0.0883607\pi$
$164$	1.30844			0.102172
$165$	6.70488	+	18.9985i	0.521974	+	1.47903i
$166$	8.74519			0.678758
$167$	12.4516	−	12.4516i	0.963532	−	0.963532i	−0.0358258	−	0.999358i	$-0.511406\pi$
$167$	12.4516	−	12.4516i	0.963532	−	0.963532i	0.999358	+	0.0358258i	$0.0114062\pi$
$168$		0			0
$169$		−	8.08513i		−	0.621933i
$170$	−1.02034	+	2.84507i	−0.0782566	+	0.218207i
$171$	3.87896	+	0.800698i	0.296632	+	0.0612309i
$172$	−0.202376	−	0.202376i	−0.0154310	−	0.0154310i
$173$	−13.7966	−	13.7966i	−1.04894	−	1.04894i	−0.998739	−	0.0501977i	$-0.984015\pi$
$173$	−13.7966	−	13.7966i	−1.04894	−	1.04894i	−0.0501977	−	0.998739i	$-0.515985\pi$
$174$	0.873244	−	8.55000i	0.0662004	−	0.648174i
$175$		0			0
$176$			10.6519i			0.802916i
$177$	2.44092	−	1.98852i	0.183471	−	0.149466i
$178$	7.55015	−	7.55015i	0.565907	−	0.565907i
$179$	−7.03160			−0.525567			−0.262783	−	0.964855i	$-0.584640\pi$
$179$	−7.03160			−0.525567			−0.262783	+	0.964855i	$0.584640\pi$
$180$	4.11274	+	2.50972i	0.306546	+	0.187064i
$181$	−14.1873			−1.05454			−0.527268	−	0.849699i	$-0.676784\pi$
$181$	−14.1873			−1.05454			−0.527268	+	0.849699i	$0.676784\pi$
$182$		0			0
$183$	3.32374	−	2.70772i	0.245698	−	0.200161i
$184$		−	24.4988i		−	1.80608i
$185$	−2.31072	−	4.89492i	−0.169888	−	0.359881i
$186$	−0.339706	+	3.32609i	−0.0249085	+	0.243881i
$187$	4.39161	+	4.39161i	0.321147	+	0.321147i
$188$	−2.43902	−	2.43902i	−0.177884	−	0.177884i
$189$		0			0
$190$	−1.42680	−	3.02245i	−0.103511	−	0.219272i
$191$		−	15.6450i		−	1.13203i	−0.824394	−	0.566017i	$-0.808484\pi$
$191$		−	15.6450i		−	1.13203i	0.824394	−	0.566017i	$-0.191516\pi$
$192$	9.23199	+	11.3323i	0.666261	+	0.817838i
$193$	9.00959	−	9.00959i	0.648525	−	0.648525i	−0.304112	−	0.952636i	$-0.598360\pi$
$193$	9.00959	−	9.00959i	0.648525	−	0.648525i	0.952636	+	0.304112i	$0.0983596\pi$
$194$	−4.90443			−0.352118
$195$	7.67343	−	16.0436i	0.549506	−	1.14890i
$196$		0			0
$197$	−2.78986	+	2.78986i	−0.198769	+	0.198769i	−0.799472	−	0.600703i	$-0.794887\pi$
$197$	−2.78986	+	2.78986i	−0.198769	+	0.198769i	0.600703	+	0.799472i	$0.294887\pi$
$198$	−14.7609	+	9.70965i	−1.04901	+	0.690035i
$199$		−	14.4320i		−	1.02306i	−0.859266	−	0.511528i	$-0.829080\pi$
$199$		−	14.4320i		−	1.02306i	0.859266	−	0.511528i	$-0.170920\pi$
$200$	−1.48572	−	15.3154i	−0.105056	−	1.08296i
$201$	19.3028	+	1.97146i	1.36151	+	0.139056i
$202$	2.97518	+	2.97518i	0.209333	+	0.209333i
$203$		0			0
$204$	1.47757	+	0.150909i	0.103450	+	0.0105658i
$205$	1.37516	−	3.83444i	0.0960455	−	0.267809i
$206$		−	1.89009i		−	0.131689i
$207$	19.9525	−	13.1247i	1.38680	−	0.912231i
$208$	6.64871	−	6.64871i	0.461005	−	0.461005i
$209$	−6.86780			−0.475056
$210$		0			0
$211$	11.9845			0.825049			0.412524	−	0.910947i	$-0.364647\pi$
$211$	11.9845			0.825049			0.412524	+	0.910947i	$0.364647\pi$
$212$	2.52140	−	2.52140i	0.173171	−	0.173171i
$213$	−9.91525	−	12.1710i	−0.679382	−	0.833943i
$214$			2.20967i			0.151050i
$215$	−0.805769	+	0.380376i	−0.0549530	+	0.0259414i
$216$	−4.80718	+	15.2512i	−0.327087	+	1.03772i
$217$		0			0
$218$	4.75133	+	4.75133i	0.321801	+	0.321801i
$219$	0.333141	−	3.26181i	0.0225116	−	0.220413i
$220$	−7.86388	−	2.82026i	−0.530182	−	0.190142i
$221$		−	5.48233i		−	0.368781i
$222$	3.68025	−	2.99816i	0.247003	−	0.201224i
$223$	12.1834	−	12.1834i	0.815858	−	0.815858i	−0.169647	−	0.985505i	$-0.554263\pi$
$223$	12.1834	−	12.1834i	0.815858	−	0.815858i	0.985505	+	0.169647i	$0.0542628\pi$
$224$		0			0
$225$	11.6773	−	9.41488i	0.778489	−	0.627659i
$226$	0.385328			0.0256317
$227$	4.17335	−	4.17335i	0.276995	−	0.276995i	−0.554913	−	0.831908i	$-0.687249\pi$
$227$	4.17335	−	4.17335i	0.276995	−	0.276995i	0.831908	+	0.554913i	$0.187249\pi$
$228$	−1.27334	+	1.03734i	−0.0843290	+	0.0686996i
$229$			27.2705i			1.80209i	0.433730	+	0.901043i	$0.357197\pi$
$229$			27.2705i			1.80209i	−0.433730	+	0.901043i	$0.642803\pi$
$230$	−18.9701	−	6.80335i	−1.25085	−	0.448600i
$231$		0			0
$232$	9.53740	+	9.53740i	0.626161	+	0.626161i
$233$	−1.96791	−	1.96791i	−0.128922	−	0.128922i	0.639701	−	0.768624i	$-0.279058\pi$
$233$	−1.96791	−	1.96791i	−0.128922	−	0.128922i	−0.768624	+	0.639701i	$0.779058\pi$
$234$	15.2740	+	3.15288i	0.998495	+	0.206110i
$235$	−9.71106	+	4.58426i	−0.633480	+	0.299044i
$236$			1.30554i			0.0849832i
$237$	12.5823	+	15.4448i	0.817306	+	1.00325i
$238$		0			0
$239$	1.42942			0.0924613			0.0462307	−	0.998931i	$-0.485279\pi$
$239$	1.42942			0.0924613			0.0462307	+	0.998931i	$0.485279\pi$
$240$	7.47860	−	2.63932i	0.482742	−	0.170368i
$241$	−29.1319			−1.87655			−0.938274	−	0.345893i	$-0.887576\pi$
$241$	−29.1319			−1.87655			−0.938274	+	0.345893i	$0.887576\pi$
$242$	12.8567	−	12.8567i	0.826463	−	0.826463i
$243$	−14.9964	+	4.25541i	−0.962018	+	0.272985i
$244$			1.77772i			0.113807i
$245$		0			0
$246$	3.55388	+	0.362971i	0.226587	+	0.0231422i
$247$	4.28675	+	4.28675i	0.272759	+	0.272759i
$248$	−3.71021	−	3.71021i	−0.235598	−	0.235598i
$249$	−13.3098	−	1.35938i	−0.843473	−	0.0861470i
$250$	−12.2717	−	3.10266i	−0.776131	−	0.196230i
$251$		−	12.3977i		−	0.782538i	−0.920276	−	0.391269i	$-0.872036\pi$
$251$		−	12.3977i		−	0.782538i	0.920276	−	0.391269i	$-0.127964\pi$
$252$		0			0
$253$	−29.2821	+	29.2821i	−1.84095	+	1.84095i
$254$	7.30007			0.458047
$255$	1.99516	−	4.17147i	0.124942	−	0.261227i
$256$	−14.7484			−0.921774
$257$	−13.8717	+	13.8717i	−0.865290	+	0.865290i	−0.991947	−	0.126657i	$-0.959575\pi$
$257$	−13.8717	+	13.8717i	−0.865290	+	0.865290i	0.126657	+	0.991947i	$0.459575\pi$
$258$	−0.493538	−	0.605820i	−0.0307263	−	0.0377167i
$259$		0			0
$260$	3.14813	+	6.66884i	0.195239	+	0.413584i
$261$	−2.65808	+	12.8770i	−0.164531	+	0.797066i
$262$	10.9503	+	10.9503i	0.676511	+	0.676511i
$263$	12.2912	+	12.2912i	0.757909	+	0.757909i	0.975942	−	0.218032i	$-0.0699639\pi$
$263$	12.2912	+	12.2912i	0.757909	+	0.757909i	−0.218032	+	0.975942i	$0.569964\pi$
$264$	2.81728	−	27.5842i	0.173392	−	1.69769i
$265$	−4.73911	−	10.0391i	−0.291121	−	0.616695i
$266$		0			0
$267$	−12.6646	+	10.3174i	−0.775061	+	0.631413i
$268$	−5.68932	+	5.68932i	−0.347530	+	0.347530i
$269$	−19.1535			−1.16781			−0.583906	−	0.811822i	$-0.698476\pi$
$269$	−19.1535			−1.16781			−0.583906	+	0.811822i	$0.698476\pi$
$270$	10.4745	+	7.95762i	0.637458	+	0.484286i
$271$	−18.4629			−1.12154			−0.560771	−	0.827971i	$-0.689495\pi$
$271$	−18.4629			−1.12154			−0.560771	+	0.827971i	$0.689495\pi$
$272$	1.72872	−	1.72872i	0.104819	−	0.104819i
$273$		0			0
$274$		−	16.0482i		−	0.969505i
$275$	−16.5298	+	20.0814i	−0.996784	+	1.21095i
$276$	−1.00622	+	9.85200i	−0.0605674	+	0.593020i
$277$	−7.66076	−	7.66076i	−0.460290	−	0.460290i	0.438460	−	0.898751i	$-0.355524\pi$
$277$	−7.66076	−	7.66076i	−0.460290	−	0.460290i	−0.898751	+	0.438460i	$0.855524\pi$
$278$	12.6698	+	12.6698i	0.759881	+	0.759881i
$279$	1.03404	−	5.00936i	0.0619061	−	0.299903i
$280$		0			0
$281$		−	20.4646i		−	1.22082i	−0.792087	−	0.610408i	$-0.791005\pi$
$281$		−	20.4646i		−	1.22082i	0.792087	−	0.610408i	$-0.208995\pi$
$282$	−5.94808	−	7.30129i	−0.354203	−	0.434785i
$283$	−8.24528	+	8.24528i	−0.490131	+	0.490131i	−0.908347	−	0.418216i	$-0.862655\pi$
$283$	−8.24528	+	8.24528i	−0.490131	+	0.490131i	0.418216	+	0.908347i	$0.362655\pi$
$284$	6.50972			0.386281
$285$	1.70170	+	4.82182i	0.100800	+	0.285620i
$286$	−27.0431			−1.59909
$287$		0			0
$288$	−6.32533	−	9.61593i	−0.372723	−	0.566624i
$289$			15.5745i			0.916150i
$290$	10.0336	−	4.73654i	0.589195	−	0.278139i
$291$	7.46433	+	0.762360i	0.437567	+	0.0446903i
$292$	0.961389	+	0.961389i	0.0562610	+	0.0562610i
$293$	19.7225	+	19.7225i	1.15220	+	1.15220i	0.986111	+	0.166088i	$0.0531135\pi$
$293$	19.7225	+	19.7225i	1.15220	+	1.15220i	0.166088	+	0.986111i	$0.446886\pi$
$294$		0			0
$295$	3.82594	+	1.37211i	0.222755	+	0.0798875i
$296$			7.44968i			0.433004i
$297$	23.9747	−	12.4832i	1.39115	−	0.724348i
$298$	7.44990	−	7.44990i	0.431561	−	0.431561i
$299$	36.5546			2.11401
$300$	−0.0315680	+	6.21996i	−0.00182258	+	0.359110i
$301$		0			0
$302$	13.4712	−	13.4712i	0.775182	−	0.775182i
$303$	−4.06562	−	4.99056i	−0.233564	−	0.286700i
$304$			2.70346i			0.155054i
$305$	5.20968	+	1.86837i	0.298306	+	0.106983i
$306$	3.97139	+	0.819776i	0.227029	+	0.0468635i
$307$	13.2997	+	13.2997i	0.759057	+	0.759057i	0.976151	−	0.217094i	$-0.0696578\pi$
$307$	13.2997	+	13.2997i	0.759057	+	0.759057i	−0.217094	+	0.976151i	$0.569658\pi$
$308$		0			0
$309$	−0.293801	+	2.87663i	−0.0167137	+	0.163646i
$310$	−3.90325	+	1.84259i	−0.221690	+	0.104652i
$311$			23.8049i			1.34985i	0.737885	+	0.674926i	$0.235824\pi$
$311$			23.8049i			1.34985i	−0.737885	+	0.674926i	$0.764176\pi$
$312$	−18.9761	+	15.4591i	−1.07431	+	0.875197i
$313$	18.9352	−	18.9352i	1.07028	−	1.07028i	0.0729475	−	0.997336i	$-0.476759\pi$
$313$	18.9352	−	18.9352i	1.07028	−	1.07028i	0.997336	−	0.0729475i	$-0.0232406\pi$
$314$	10.8979			0.615003
$315$		0			0
$316$	−8.26072			−0.464702
$317$	11.6929	−	11.6929i	0.656739	−	0.656739i	−0.297868	−	0.954607i	$-0.596275\pi$
$317$	11.6929	−	11.6929i	0.656739	−	0.656739i	0.954607	+	0.297868i	$0.0962755\pi$
$318$	7.54790	−	6.14899i	0.423265	−	0.344818i
$319$		−	22.7990i		−	1.27650i
$320$	−6.37022	+	17.7624i	−0.356106	+	0.992950i
$321$	0.343478	−	3.36302i	0.0191711	−	0.187706i
$322$		0			0
$323$	1.11459	+	1.11459i	0.0620177	+	0.0620177i
$324$	2.55957	−	5.93571i	0.142198	−	0.329762i
$325$	22.8520	−	2.21683i	1.26760	−	0.122968i
$326$			14.0572i			0.778555i
$327$	−6.49275	−	7.96987i	−0.359050	−	0.440735i
$328$	−3.96430	+	3.96430i	−0.218892	+	0.218892i
$329$		0			0
$330$	−20.5769	−	9.84167i	−1.13272	−	0.541766i
$331$	−11.5898			−0.637031			−0.318516	−	0.947918i	$-0.603184\pi$
$331$	−11.5898			−0.637031			−0.318516	+	0.947918i	$0.603184\pi$
$332$	3.92294	−	3.92294i	0.215299	−	0.215299i
$333$	−6.06723	+	3.99100i	−0.332482	+	0.218706i
$334$			19.9363i			1.09087i
$335$	10.6934	+	22.6523i	0.584241	+	1.23762i
$336$		0			0
$337$	−5.46127	−	5.46127i	−0.297494	−	0.297494i	0.542537	−	0.840032i	$-0.317464\pi$
$337$	−5.46127	−	5.46127i	−0.297494	−	0.297494i	−0.840032	+	0.542537i	$0.817464\pi$
$338$	6.47258	+	6.47258i	0.352062	+	0.352062i
$339$	−0.586453	−	0.0598966i	−0.0318517	−	0.00325314i
$340$	0.818543	+	1.73396i	0.0443917	+	0.0940371i
$341$			8.86920i			0.480294i
$342$	−3.74632	+	2.46431i	−0.202578	+	0.133255i
$343$		0			0
$344$	1.22632			0.0661186
$345$	27.8142	+	13.3032i	1.49747	+	0.716219i
$346$	22.0898			1.18756
$347$	−20.1982	+	20.1982i	−1.08430	+	1.08430i	−0.0881938	+	0.996103i	$0.528109\pi$
$347$	−20.1982	+	20.1982i	−1.08430	+	1.08430i	−0.996103	+	0.0881938i	$0.971891\pi$
$348$	−3.44366	−	4.22711i	−0.184600	−	0.226597i
$349$			11.9748i			0.640997i	0.947249	+	0.320498i	$0.103850\pi$
$349$			11.9748i			0.640997i	−0.947249	+	0.320498i	$0.896150\pi$
$350$		0			0
$351$	−22.7563	−	7.17278i	−1.21464	−	0.382855i
$352$	14.1122	+	14.1122i	0.752183	+	0.752183i
$353$	−24.3423	−	24.3423i	−1.29561	−	1.29561i	−0.931264	−	0.364345i	$-0.881293\pi$
$353$	−24.3423	−	24.3423i	−1.29561	−	1.29561i	−0.364345	−	0.931264i	$-0.618707\pi$
$354$	−0.362166	+	3.54600i	−0.0192489	+	0.188468i
$355$	6.84169	−	19.0770i	0.363119	−	1.01250i
$356$		−	6.77373i		−	0.359007i
$357$		0			0
$358$	5.62917	−	5.62917i	0.297511	−	0.297511i
$359$	14.2164			0.750314			0.375157	−	0.926961i	$-0.377589\pi$
$359$	14.2164			0.750314			0.375157	+	0.926961i	$0.377589\pi$
$360$	−20.0647	+	4.85683i	−1.05750	+	0.255978i
$361$	17.2569			0.908260
$362$	11.3577	−	11.3577i	0.596948	−	0.596948i
$363$	−21.5659	+	17.5689i	−1.13192	+	0.922129i
$364$		0			0
$365$	3.82781	−	1.80698i	0.200357	−	0.0945816i
$366$	−0.493153	+	4.82850i	−0.0257775	+	0.252390i
$367$	−16.7024	−	16.7024i	−0.871859	−	0.871859i	0.120816	−	0.992675i	$-0.461449\pi$
$367$	−16.7024	−	16.7024i	−0.871859	−	0.871859i	−0.992675	+	0.120816i	$0.961449\pi$
$368$	11.5267	+	11.5267i	0.600868	+	0.600868i
$369$	−5.35243	−	1.10485i	−0.278636	−	0.0575163i
$370$	5.76850	+	2.06878i	0.299890	+	0.107551i
$371$		0			0
$372$	1.33964	+	1.64441i	0.0694572	+	0.0852589i
$373$	4.57877	−	4.57877i	0.237080	−	0.237080i	−0.578560	−	0.815640i	$-0.696385\pi$
$373$	4.57877	−	4.57877i	0.237080	−	0.237080i	0.815640	+	0.578560i	$0.196385\pi$
$374$	−7.03144			−0.363587
$375$	18.1947	+	6.62966i	0.939571	+	0.342354i
$376$	14.7795			0.762193
$377$	−14.2307	+	14.2307i	−0.732920	+	0.732920i
$378$		0			0
$379$			12.6506i			0.649816i	0.945746	+	0.324908i	$0.105333\pi$
$379$			12.6506i			0.649816i	−0.945746	+	0.324908i	$0.894667\pi$
$380$	−1.99586	−	0.715783i	−0.102385	−	0.0367189i
$381$	−11.1104	−	1.13474i	−0.569202	−	0.0581347i
$382$	12.5247	+	12.5247i	0.640818	+	0.640818i
$383$	18.0165	+	18.0165i	0.920601	+	0.920601i	0.997072	−	0.0764705i	$-0.0243651\pi$
$383$	18.0165	+	18.0165i	0.920601	+	0.920601i	−0.0764705	+	0.997072i	$0.524365\pi$
$384$	−3.24119	−	0.331035i	−0.165401	−	0.0168930i
$385$		0			0
$386$			14.4253i			0.734229i
$387$	0.656973	+	0.998748i	0.0333958	+	0.0507692i
$388$	−2.20004	+	2.20004i	−0.111690	+	0.111690i
$389$	17.7215			0.898517			0.449259	−	0.893402i	$-0.351688\pi$
$389$	17.7215			0.898517			0.449259	+	0.893402i	$0.351688\pi$
$390$	6.70073	+	18.9867i	0.339305	+	0.961429i
$391$	9.50453			0.480665
$392$		0			0
$393$	−14.9637	−	18.3680i	−0.754819	−	0.926543i
$394$		−	4.46686i		−	0.225037i
$395$	−8.68197	+	24.2084i	−0.436838	+	1.21806i
$396$	−2.26589	+	10.9771i	−0.113865	+	0.551618i
$397$	−4.43035	−	4.43035i	−0.222353	−	0.222353i	0.587136	−	0.809489i	$-0.300255\pi$
$397$	−4.43035	−	4.43035i	−0.222353	−	0.222353i	−0.809489	+	0.587136i	$0.800255\pi$
$398$	11.5536	+	11.5536i	0.579128	+	0.579128i
$399$		0			0
$400$	7.90488	+	6.50682i	0.395244	+	0.325341i
$401$			34.4780i			1.72175i	0.508818	+	0.860874i	$0.330082\pi$
$401$			34.4780i			1.72175i	−0.508818	+	0.860874i	$0.669918\pi$
$402$	−17.0312	+	13.8746i	−0.849437	+	0.692004i
$403$	5.53599	−	5.53599i	0.275767	−	0.275767i
$404$	2.66923			0.132799
$405$	−14.7048	−	13.7393i	−0.730686	−	0.682713i
$406$		0			0
$407$	8.90417	−	8.90417i	0.441364	−	0.441364i
$408$	−4.93395	+	4.01950i	−0.244267	+	0.198995i
$409$			19.5663i			0.967490i	0.875209	+	0.483745i	$0.160724\pi$
$409$			19.5663i			0.967490i	−0.875209	+	0.483745i	$0.839276\pi$
$410$	1.96878	+	4.17056i	0.0972312	+	0.205969i
$411$	−2.49457	+	24.4246i	−0.123048	+	1.20478i
$412$	−0.847860	−	0.847860i	−0.0417711	−	0.0417711i
$413$		0			0
$414$	−5.46604	+	26.4801i	−0.268641	+	1.30143i
$415$	−7.37336	−	15.6193i	−0.361944	−	0.766723i
$416$		−	17.6171i		−	0.863751i
$417$	−17.3134	−	21.2522i	−0.847840	−	1.04073i
$418$	5.49804	−	5.49804i	0.268918	−	0.268918i
$419$	−17.0209			−0.831524			−0.415762	−	0.909474i	$-0.636485\pi$
$419$	−17.0209			−0.831524			−0.415762	+	0.909474i	$0.636485\pi$
$420$		0			0
$421$	21.7474			1.05990			0.529951	−	0.848028i	$-0.322210\pi$
$421$	21.7474			1.05990			0.529951	+	0.848028i	$0.322210\pi$
$422$	−9.59425	+	9.59425i	−0.467041	+	0.467041i
$423$	7.91778	+	12.0368i	0.384976	+	0.585250i
$424$			15.2787i			0.741998i
$425$	5.94173	−	0.576396i	0.288216	−	0.0279593i
$426$	17.6812	+	1.80585i	0.856658	+	0.0874936i
$427$		0			0
$428$	0.991221	+	0.991221i	0.0479125	+	0.0479125i
$429$	41.1583	+	4.20365i	1.98714	+	0.202954i
$430$	0.340550	−	0.949573i	0.0164228	−	0.0457925i
$431$			10.7912i			0.519796i	0.965636	+	0.259898i	$0.0836889\pi$
$431$			10.7912i			0.519796i	−0.965636	+	0.259898i	$0.916311\pi$
$432$	−4.91391	−	9.43745i	−0.236420	−	0.454059i
$433$	−0.466927	+	0.466927i	−0.0224391	+	0.0224391i	−0.718237	−	0.695798i	$-0.755051\pi$
$433$	−0.466927	+	0.466927i	−0.0224391	+	0.0224391i	0.695798	+	0.718237i	$0.255051\pi$
$434$		0			0
$435$	−16.0070	+	5.64914i	−0.767477	+	0.270856i
$436$	4.26273			0.204148
$437$	−7.43180	+	7.43180i	−0.355511	+	0.355511i
$438$	2.34456	+	2.87795i	0.112027	+	0.137514i
$439$		−	9.43662i		−	0.450385i	−0.974314	−	0.225193i	$-0.927699\pi$
$439$		−	9.43662i		−	0.450385i	0.974314	−	0.225193i	$-0.0723011\pi$
$440$	32.3708	−	15.2811i	1.54322	−	0.728500i
$441$		0			0
$442$	4.38889	+	4.38889i	0.208758	+	0.208758i
$443$	−16.8956	−	16.8956i	−0.802734	−	0.802734i	0.180788	−	0.983522i	$-0.442135\pi$
$443$	−16.8956	−	16.8956i	−0.802734	−	0.802734i	−0.983522	+	0.180788i	$0.942135\pi$
$444$	0.305975	−	2.99582i	0.0145209	−	0.142175i
$445$	−19.8507	−	7.11916i	−0.941015	−	0.337480i
$446$			19.5068i			0.923676i
$447$	−12.4965	+	10.1804i	−0.591062	+	0.481516i
$448$		0			0
$449$	11.5643			0.545753			0.272876	−	0.962049i	$-0.412025\pi$
$449$	11.5643			0.545753			0.272876	+	0.962049i	$0.412025\pi$
$450$	−1.81121	+	16.8854i	−0.0853812	+	0.795987i
$451$	9.47661			0.446236
$452$	0.172852	−	0.172852i	0.00813026	−	0.00813026i
$453$	−22.5966	+	18.4086i	−1.06168	+	0.864912i
$454$			6.68197i			0.313601i
$455$		0			0
$456$	0.715027	−	7.00090i	0.0334842	−	0.327847i
$457$	−17.8413	−	17.8413i	−0.834580	−	0.834580i	0.153560	−	0.988139i	$-0.450926\pi$
$457$	−17.8413	−	17.8413i	−0.834580	−	0.834580i	−0.988139	+	0.153560i	$0.950926\pi$
$458$	−21.8315	−	21.8315i	−1.02012	−	1.02012i
$459$	−5.91685	−	1.86499i	−0.276175	−	0.0870502i
$460$	−11.5615	+	5.45782i	−0.539060	+	0.254472i
$461$			13.0571i			0.608129i	0.952651	+	0.304064i	$0.0983438\pi$
$461$			13.0571i			0.608129i	−0.952651	+	0.304064i	$0.901656\pi$
$462$		0			0
$463$	17.3925	−	17.3925i	0.808298	−	0.808298i	−0.176079	−	0.984376i	$-0.556341\pi$
$463$	17.3925	−	17.3925i	0.808298	−	0.808298i	0.984376	+	0.176079i	$0.0563413\pi$
$464$	−8.97466			−0.416638
$465$	6.22699	−	2.19761i	0.288770	−	0.101912i
$466$	3.15084			0.145960
$467$	9.40605	−	9.40605i	0.435260	−	0.435260i	−0.455153	−	0.890413i	$-0.650415\pi$
$467$	9.40605	−	9.40605i	0.435260	−	0.435260i	0.890413	+	0.455153i	$0.150415\pi$
$468$	8.26600	−	5.43734i	0.382096	−	0.251341i
$469$		0			0
$470$	4.10427	−	11.4442i	0.189316	−	0.527880i
$471$	−16.5861	−	1.69400i	−0.764247	−	0.0780554i
$472$	−3.95551	−	3.95551i	−0.182067	−	0.182067i
$473$	−1.46575	−	1.46575i	−0.0673951	−	0.0673951i
$474$	−22.4371	−	2.29159i	−1.03057	−	0.105256i
$475$	−4.19527	+	5.09667i	−0.192492	+	0.233851i
$476$		0			0
$477$	−12.4434	+	8.18522i	−0.569744	+	0.374776i
$478$	−1.14432	+	1.14432i	−0.0523402	+	0.0523402i
$479$	38.8689			1.77596			0.887982	−	0.459879i	$-0.152107\pi$
$479$	38.8689			1.77596			0.887982	+	0.459879i	$0.152107\pi$
$480$	6.41133	−	13.4048i	0.292636	−	0.611841i
$481$	−11.1156			−0.506829
$482$	23.3216	−	23.3216i	1.06227	−	1.06227i
$483$		0			0
$484$		−	11.5346i		−	0.524301i
$485$	4.13509	+	8.75957i	0.187765	+	0.397751i
$486$	8.59872	−	15.4121i	0.390046	−	0.699106i
$487$	23.9549	+	23.9549i	1.08550	+	1.08550i	0.995985	+	0.0895148i	$0.0285316\pi$
$487$	23.9549	+	23.9549i	1.08550	+	1.08550i	0.0895148	+	0.995985i	$0.471468\pi$
$488$	−5.38612	−	5.38612i	−0.243818	−	0.243818i
$489$	2.18509	−	21.3944i	0.0988131	−	0.967488i
$490$		0			0
$491$			25.6453i			1.15736i	0.815556	+	0.578678i	$0.196431\pi$
$491$			25.6453i			1.15736i	−0.815556	+	0.578678i	$0.803569\pi$
$492$	1.75703	−	1.43139i	0.0792132	−	0.0645319i
$493$	−3.70012	+	3.70012i	−0.166645	+	0.166645i
$494$	−6.86355			−0.308806
$495$	29.7873	+	18.1771i	1.33884	+	0.817001i
$496$	3.49129			0.156764
$497$		0			0
$498$	11.7434	−	9.56694i	0.526236	−	0.428705i
$499$			29.1057i			1.30295i	0.758669	+	0.651476i	$0.225850\pi$
$499$			29.1057i			1.30295i	−0.758669	+	0.651476i	$0.774150\pi$
$500$	−6.89668	+	4.11308i	−0.308429	+	0.183942i
$501$	3.09896	−	30.3422i	0.138451	−	1.35559i
$502$	9.92505	+	9.92505i	0.442976	+	0.442976i
$503$	−10.1763	−	10.1763i	−0.453738	−	0.453738i	0.442855	−	0.896593i	$-0.353965\pi$
$503$	−10.1763	−	10.1763i	−0.453738	−	0.453738i	−0.896593	+	0.442855i	$0.853965\pi$
$504$		0			0
$505$	2.80534	−	7.82229i	0.124836	−	0.348087i
$506$		−	46.8837i		−	2.08423i
$507$	−8.84486	−	10.8571i	−0.392814	−	0.482181i
$508$	3.27469	−	3.27469i	0.145291	−	0.145291i
$509$	31.2970			1.38721			0.693607	−	0.720354i	$-0.256021\pi$
$509$	31.2970			1.38721			0.693607	+	0.720354i	$0.256021\pi$
$510$	1.74225	+	4.93672i	0.0771481	+	0.218601i
$511$		0			0
$512$	14.4671	−	14.4671i	0.639360	−	0.639360i
$513$	6.08479	−	3.16824i	0.268650	−	0.139881i
$514$		−	22.2100i		−	0.979641i
$515$	−3.37579	+	1.59360i	−0.148755	+	0.0702222i
$516$	−0.493153	−	0.0503675i	−0.0217098	−	0.00221731i
$517$	−17.6651	−	17.6651i	−0.776908	−	0.776908i
$518$		0			0
$519$	−33.6198	−	3.43371i	−1.47574	−	0.150723i
$520$	−29.7434	−	10.6670i	−1.30433	−	0.467780i
$521$		−	24.4644i		−	1.07180i	−0.844280	−	0.535902i	$-0.819972\pi$
$521$		−	24.4644i		−	1.07180i	0.844280	−	0.535902i	$-0.180028\pi$
$522$	−8.18078	−	12.4366i	−0.358063	−	0.544337i
$523$	−1.82790	+	1.82790i	−0.0799284	+	0.0799284i	−0.745941	−	0.666012i	$-0.768000\pi$
$523$	−1.82790	+	1.82790i	−0.0799284	+	0.0799284i	0.666012	+	0.745941i	$0.268000\pi$
$524$	9.82422			0.429173
$525$		0			0
$526$	−19.6796			−0.858069
$527$	1.43941	−	1.43941i	0.0627015	−	0.0627015i
$528$	11.6528	+	14.3039i	0.507123	+	0.622495i
$529$			40.3736i			1.75537i
$530$	11.8307	+	4.24291i	0.513894	+	0.184300i
$531$	1.10240	−	5.34056i	0.0478402	−	0.231761i
$532$		0			0
$533$	−5.91512	−	5.91512i	−0.256212	−	0.256212i
$534$	1.87909	−	18.3983i	0.0813160	−	0.796172i
$535$	3.94659	−	1.86305i	0.170626	−	0.0805467i
$536$		−	34.4749i		−	1.48909i
$537$	−9.44237	+	7.69234i	−0.407468	+	0.331949i
$538$	15.3334	−	15.3334i	0.661071	−	0.661071i
$539$		0			0
$540$	8.26834	−	1.12903i	0.355813	−	0.0485858i
$541$	41.8839			1.80073			0.900364	−	0.435137i	$-0.143300\pi$
$541$	41.8839			1.80073			0.900364	+	0.435137i	$0.143300\pi$
$542$	14.7805	−	14.7805i	0.634879	−	0.634879i
$543$	−19.0514	+	15.5205i	−0.817575	+	0.666047i
$544$		−	4.58061i		−	0.196392i
$545$	4.48011	−	12.4921i	0.191907	−	0.535104i
$546$		0			0
$547$	−21.6813	−	21.6813i	−0.927024	−	0.927024i	0.0704885	−	0.997513i	$-0.477544\pi$
$547$	−21.6813	−	21.6813i	−0.927024	−	0.927024i	−0.997513	+	0.0704885i	$0.977544\pi$
$548$	−7.19893	−	7.19893i	−0.307523	−	0.307523i
$549$	1.50111	−	7.27211i	0.0640660	−	0.310366i
$550$	−2.84323	−	29.3092i	−0.121236	−	1.24975i
$551$		−	5.78641i		−	0.246509i
$552$	−26.8009	−	32.8982i	−1.14072	−	1.40024i
$553$		0			0
$554$	12.2657			0.521119
$555$	−8.45782	−	4.04527i	−0.359014	−	0.171712i
$556$	11.3669			0.482063
$557$	13.1204	−	13.1204i	0.555929	−	0.555929i	−0.372217	−	0.928146i	$-0.621402\pi$
$557$	13.1204	−	13.1204i	0.555929	−	0.555929i	0.928146	+	0.372217i	$0.121402\pi$
$558$	3.18246	+	4.83806i	0.134724	+	0.204811i
$559$			1.82978i			0.0773916i
$560$		0			0
$561$	10.7015	+	1.09299i	0.451819	+	0.0461460i
$562$	16.3830	+	16.3830i	0.691076	+	0.691076i
$563$	15.9166	+	15.9166i	0.670804	+	0.670804i	0.957901	−	0.287097i	$-0.0926903\pi$
$563$	15.9166	+	15.9166i	0.670804	+	0.670804i	−0.287097	+	0.957901i	$0.592690\pi$
$564$	−5.94344	−	0.607025i	−0.250264	−	0.0255604i
$565$	−0.324884	−	0.688216i	−0.0136680	−	0.0289535i
$566$		−	13.2016i		−	0.554903i
$567$		0			0
$568$	−19.7231	+	19.7231i	−0.827565	+	0.827565i
$569$	−27.8303			−1.16671			−0.583354	−	0.812218i	$-0.698260\pi$
$569$	−27.8303			−1.16671			−0.583354	+	0.812218i	$0.698260\pi$
$570$	−5.22243	−	2.49782i	−0.218744	−	0.104622i
$571$	−4.11555			−0.172230			−0.0861151	−	0.996285i	$-0.527445\pi$
$571$	−4.11555			−0.172230			−0.0861151	+	0.996285i	$0.527445\pi$
$572$	−12.1311	+	12.1311i	−0.507225	+	0.507225i
$573$	−17.1151	−	21.0089i	−0.714994	−	0.877658i
$574$		0			0
$575$	3.84325	+	39.6178i	0.160275	+	1.65218i
$576$	24.7943	+	5.11805i	1.03310	+	0.213252i
$577$	15.3143	+	15.3143i	0.637542	+	0.637542i	0.949949	−	0.312406i	$-0.101135\pi$
$577$	15.3143	+	15.3143i	0.637542	+	0.637542i	−0.312406	+	0.949949i	$0.601135\pi$
$578$	−12.4683	−	12.4683i	−0.518611	−	0.518611i
$579$	2.24231	−	21.9547i	0.0931874	−	0.912406i
$580$	2.37619	−	6.62564i	0.0986657	−	0.275115i
$581$		0			0
$582$	−6.58590	+	5.36528i	−0.272994	+	0.222398i
$583$	18.2617	−	18.2617i	0.756324	−	0.756324i
$584$	−5.82563			−0.241066
$585$	−7.24686	−	29.9385i	−0.299621	−	1.23780i
$586$	−31.5778			−1.30447
$587$	−23.2211	+	23.2211i	−0.958439	+	0.958439i	−0.999170	−	0.0407314i	$-0.987031\pi$
$587$	−23.2211	+	23.2211i	−0.958439	+	0.958439i	0.0407314	+	0.999170i	$0.487031\pi$
$588$		0			0
$589$			2.25101i			0.0927512i
$590$	−4.16132	+	1.96442i	−0.171319	+	0.0808737i
$591$	−0.694342	+	6.79837i	−0.0285614	+	0.279647i
$592$	−3.50506	−	3.50506i	−0.144057	−	0.144057i
$593$	−24.2941	−	24.2941i	−0.997641	−	0.997641i	0.00235668	−	0.999997i	$-0.499250\pi$
$593$	−24.2941	−	24.2941i	−0.997641	−	0.997641i	−0.999997	+	0.00235668i	$0.999250\pi$
$594$	−9.19956	+	29.1865i	−0.377463	+	1.19754i
$595$		0			0
$596$		−	6.68380i		−	0.273779i
$597$	−15.7881	−	19.3799i	−0.646164	−	0.793169i
$598$	−29.2639	+	29.2639i	−1.19669	+	1.19669i
$599$	22.7865			0.931029			0.465515	−	0.885040i	$-0.345869\pi$
$599$	22.7865			0.931029			0.465515	+	0.885040i	$0.345869\pi$
$600$	−18.7496	−	18.9409i	−0.765448	−	0.773258i
$601$	41.7276			1.70210			0.851052	−	0.525082i	$-0.175965\pi$
$601$	41.7276			1.70210			0.851052	+	0.525082i	$0.175965\pi$
$602$		0			0
$603$	28.0774	−	18.4692i	1.14340	−	0.752124i
$604$		−	12.0859i		−	0.491769i
$605$	−33.8028	−	12.1228i	−1.37428	−	0.492864i
$606$	7.24995	+	0.740464i	0.294509	+	0.0300793i
$607$	17.5164	+	17.5164i	0.710968	+	0.710968i	0.966738	−	0.255770i	$-0.0823289\pi$
$607$	17.5164	+	17.5164i	0.710968	+	0.710968i	−0.255770	+	0.966738i	$0.582329\pi$
$608$	3.58168	+	3.58168i	0.145256	+	0.145256i
$609$		0			0
$610$	−5.66636	+	2.67490i	−0.229424	+	0.108303i
$611$			22.0524i			0.892144i
$612$	2.14923	−	1.41376i	0.0868776	−	0.0571478i
$613$	−25.9860	+	25.9860i	−1.04956	+	1.04956i	−0.0508591	+	0.998706i	$0.516196\pi$
$613$	−25.9860	+	25.9860i	−1.04956	+	1.04956i	−0.998706	+	0.0508591i	$0.983804\pi$
$614$	−21.2943			−0.859369
$615$	−2.34811	−	6.65345i	−0.0946851	−	0.268293i
$616$		0			0
$617$	−8.12737	+	8.12737i	−0.327196	+	0.327196i	−0.851519	−	0.524323i	$-0.824318\pi$
$617$	−8.12737	+	8.12737i	−0.327196	+	0.327196i	0.524323	+	0.851519i	$0.324318\pi$
$618$	−2.06769	−	2.53810i	−0.0831747	−	0.102097i
$619$			7.20599i			0.289633i	0.989459	+	0.144817i	$0.0462592\pi$
$619$			7.20599i			0.289633i	−0.989459	+	0.144817i	$0.953741\pi$
$620$	−0.924375	+	2.57748i	−0.0371238	+	0.103514i
$621$	12.4352	−	39.4519i	0.499008	−	1.58315i
$622$	−19.0571	−	19.0571i	−0.764120	−	0.764120i
$623$		0			0
$624$	1.65474	−	16.2017i	0.0662424	−	0.648586i
$625$	4.80519	+	24.5339i	0.192208	+	0.981354i
$626$			30.3173i			1.21172i
$627$	−9.22241	+	7.51314i	−0.368307	+	0.300046i
$628$	4.88860	−	4.88860i	0.195077	−	0.195077i
$629$	−2.89017			−0.115238
$630$		0			0
$631$	−29.8770			−1.18938			−0.594692	−	0.803954i	$-0.702726\pi$
$631$	−29.8770			−1.18938			−0.594692	+	0.803954i	$0.702726\pi$
$632$	25.0283	−	25.0283i	0.995572	−	0.995572i
$633$	16.0934	−	13.1107i	0.639655	−	0.521102i
$634$			18.7216i			0.743530i
$635$	−6.15494	−	13.0383i	−0.244251	−	0.517409i
$636$	0.627529	−	6.14419i	0.0248831	−	0.243633i
$637$		0			0
$638$	18.2518	+	18.2518i	0.722597	+	0.722597i
$639$	−26.6293	−	5.49684i	−1.05344	−	0.217452i
$640$	−1.79556	−	3.80361i	−0.0709756	−	0.150351i
$641$			19.3661i			0.764917i	0.923973	+	0.382458i	$0.124922\pi$
$641$			19.3661i			0.764917i	−0.923973	+	0.382458i	$0.875078\pi$
$642$	2.41731	+	2.96725i	0.0954035	+	0.117108i
$643$	−11.6091	+	11.6091i	−0.457819	+	0.457819i	−0.897939	−	0.440120i	$-0.854936\pi$
$643$	−11.6091	+	11.6091i	−0.457819	+	0.457819i	0.440120	+	0.897939i	$0.354936\pi$
$644$		0			0
$645$	−0.665906	+	1.39227i	−0.0262200	+	0.0548206i
$646$	−1.78458			−0.0702135
$647$	−10.6517	+	10.6517i	−0.418760	+	0.418760i	−0.884776	−	0.466016i	$-0.845689\pi$
$647$	−10.6517	+	10.6517i	−0.418760	+	0.418760i	0.466016	+	0.884776i	$0.345689\pi$
$648$	10.2290	+	25.7390i	0.401834	+	1.01112i
$649$			9.45560i			0.371165i
$650$	−16.5196	+	20.0689i	−0.647950	+	0.787168i
$651$		0			0
$652$	6.30580	+	6.30580i	0.246954	+	0.246954i
$653$	3.67307	+	3.67307i	0.143738	+	0.143738i	0.775314	−	0.631576i	$-0.217592\pi$
$653$	3.67307	+	3.67307i	0.143738	+	0.143738i	−0.631576	+	0.775314i	$0.717592\pi$
$654$	11.5781	+	1.18251i	0.452740	+	0.0462400i
$655$	10.3252	−	28.7903i	0.403439	−	1.12493i
$656$		−	3.73039i		−	0.145647i
$657$	−3.12095	−	4.74456i	−0.121760	−	0.185103i
$658$		0			0
$659$	45.6844			1.77961			0.889807	−	0.456338i	$-0.150839\pi$
$659$	45.6844			1.77961			0.889807	+	0.456338i	$0.150839\pi$
$660$	−13.6453	+	4.81564i	−0.531141	+	0.187449i
$661$	21.8518			0.849935			0.424968	−	0.905209i	$-0.360285\pi$
$661$	21.8518			0.849935			0.424968	+	0.905209i	$0.360285\pi$
$662$	9.27823	−	9.27823i	0.360609	−	0.360609i
$663$	−5.99748	−	7.36192i	−0.232923	−	0.285913i
$664$			23.7714i			0.922510i
$665$		0			0
$666$	1.66213	−	8.05215i	0.0644062	−	0.312014i
$667$	−24.6714	−	24.6714i	−0.955279	−	0.955279i
$668$	8.94308	+	8.94308i	0.346018	+	0.346018i
$669$	3.03220	−	29.6886i	0.117232	−	1.14783i
$670$	−26.6949	−	9.57373i	−1.03132	−	0.369865i
$671$			12.8755i			0.497051i
$672$		0			0
$673$	12.1963	−	12.1963i	0.470132	−	0.470132i	−0.431825	−	0.901957i	$-0.642130\pi$
$673$	12.1963	−	12.1963i	0.470132	−	0.470132i	0.901957	+	0.431825i	$0.142130\pi$
$674$	8.74408			0.336809
$675$	5.38130	−	25.4173i	0.207126	−	0.978314i
$676$	5.80698			0.223345
$677$	30.0858	−	30.0858i	1.15629	−	1.15629i	0.171025	−	0.985267i	$-0.445292\pi$
$677$	30.0858	−	30.0858i	1.15629	−	1.15629i	0.985267	−	0.171025i	$-0.0547080\pi$
$678$	0.517437	−	0.421536i	0.0198721	−	0.0161890i
$679$		0			0
$680$	−7.73356	−	2.77352i	−0.296568	−	0.106360i
$681$	1.03867	−	10.1697i	0.0398018	−	0.389703i
$682$	−7.10027	−	7.10027i	−0.271883	−	0.271883i
$683$	1.48486	+	1.48486i	0.0568166	+	0.0568166i	0.734944	−	0.678128i	$-0.237208\pi$
$683$	1.48486	+	1.48486i	0.0568166	+	0.0568166i	−0.678128	+	0.734944i	$0.737208\pi$
$684$	−0.575084	+	2.78598i	−0.0219889	+	0.106525i
$685$	−28.6628	+	13.5308i	−1.09515	+	0.516984i
$686$		0			0
$687$	29.8330	+	36.6201i	1.13820	+	1.39714i
$688$	−0.576980	+	0.576980i	−0.0219972	+	0.0219972i
$689$	−22.7973			−0.868507
$690$	−32.9166	+	11.6168i	−1.25312	+	0.442246i
$691$	−42.2833			−1.60853			−0.804267	−	0.594269i	$-0.797442\pi$
$691$	−42.2833			−1.60853			−0.804267	+	0.594269i	$0.797442\pi$
$692$	9.90912	−	9.90912i	0.376688	−	0.376688i
$693$		0			0
$694$		−	32.3395i		−	1.22759i
$695$	11.9465	−	33.3111i	0.453157	−	1.26356i
$696$	23.2409	+	2.37368i	0.880943	+	0.0899740i
$697$	−1.53799	−	1.53799i	−0.0582553	−	0.0582553i
$698$	−9.58647	−	9.58647i	−0.362853	−	0.362853i
$699$	−4.79544	−	0.489776i	−0.181380	−	0.0185250i
$700$		0			0
$701$		−	42.8399i		−	1.61804i	−0.587781	−	0.809020i	$-0.699998\pi$
$701$		−	42.8399i		−	1.61804i	0.587781	−	0.809020i	$-0.300002\pi$
$702$	23.9598	−	12.4755i	0.904306	−	0.470856i
$703$	2.25988	−	2.25988i	0.0852332	−	0.0852332i
$704$	−43.8989			−1.65450
$705$	−8.02544	+	16.7795i	−0.302255	+	0.631954i
$706$	38.9746			1.46683
$707$		0			0
$708$	1.42821	+	1.75314i	0.0536756	+	0.0658869i
$709$			21.7856i			0.818175i	0.912495	+	0.409087i	$0.134153\pi$
$709$			21.7856i			0.818175i	−0.912495	+	0.409087i	$0.865847\pi$
$710$	9.79506	+	20.7493i	0.367602	+	0.778708i
$711$	33.7921	+	6.97539i	1.26730	+	0.261598i
$712$	20.5230	+	20.5230i	0.769133	+	0.769133i
$713$	9.59756	+	9.59756i	0.359432	+	0.359432i
$714$		0			0
$715$	22.8009	+	48.3003i	0.852706	+	1.80633i
$716$		−	5.05030i		−	0.188739i
$717$	1.91949	−	1.56373i	0.0716846	−	0.0583987i
$718$	−11.3810	+	11.3810i	−0.424735	+	0.424735i
$719$	−45.9617			−1.71408			−0.857041	−	0.515249i	$-0.827699\pi$
$719$	−45.9617			−1.71408			−0.857041	+	0.515249i	$0.827699\pi$
$720$	7.15528	−	11.7255i	0.266662	−	0.436985i
$721$		0			0
$722$	−13.8151	+	13.8151i	−0.514145	+	0.514145i
$723$	−39.1196	+	31.8693i	−1.45487	+	1.18523i
$724$		−	10.1898i		−	0.378699i
$725$	−16.9194	−	13.9270i	−0.628371	−	0.517237i
$726$	3.19980	−	31.3295i	0.118756	−	1.16275i
$727$	4.37251	+	4.37251i	0.162168	+	0.162168i	0.783526	−	0.621359i	$-0.213419\pi$
$727$	4.37251	+	4.37251i	0.162168	+	0.162168i	−0.621359	+	0.783526i	$0.713419\pi$
$728$		0			0
$729$	−15.4826	+	22.1199i	−0.573428	+	0.819256i
$730$	−1.61778	+	4.51095i	−0.0598768	+	0.166958i
$731$			0.475760i			0.0175966i
$732$	1.94476	+	2.38720i	0.0718805	+	0.0882336i
$733$	32.0267	−	32.0267i	1.18293	−	1.18293i	0.203952	−	0.978981i	$-0.434621\pi$
$733$	32.0267	−	32.0267i	1.18293	−	1.18293i	0.978981	−	0.203952i	$-0.0653787\pi$
$734$	26.7423			0.987078
$735$		0			0
$736$	30.5423			1.12580
$737$	−41.2059	+	41.2059i	−1.51784	+	1.51784i
$738$	5.16940	−	3.40041i	0.190288	−	0.125171i
$739$			19.8100i			0.728722i	0.931258	+	0.364361i	$0.118713\pi$
$739$			19.8100i			0.728722i	−0.931258	+	0.364361i	$0.881287\pi$
$740$	3.51567	−	1.65963i	0.129239	−	0.0610092i
$741$	10.4460	+	1.06689i	0.383744	+	0.0391932i
$742$		0			0
$743$	14.6828	+	14.6828i	0.538660	+	0.538660i	0.923135	−	0.384475i	$-0.125618\pi$
$743$	14.6828	+	14.6828i	0.538660	+	0.538660i	−0.384475	+	0.923135i	$0.625618\pi$
$744$	−9.04108	−	0.923399i	−0.331462	−	0.0338535i
$745$	−19.5872	−	7.02464i	−0.717619	−	0.257363i
$746$			7.33110i			0.268411i
$747$	−19.3601	+	12.7350i	−0.708350	+	0.465950i
$748$	−3.15418	+	3.15418i	−0.115328	+	0.115328i
$749$		0			0
$750$	−19.8732	+	9.25844i	−0.725668	+	0.338070i
$751$	−26.6832			−0.973682			−0.486841	−	0.873491i	$-0.661851\pi$
$751$	−26.6832			−0.973682			−0.486841	+	0.873491i	$0.661851\pi$
$752$	−6.95371	+	6.95371i	−0.253576	+	0.253576i
$753$	−13.5627	−	16.6483i	−0.494252	−	0.606696i
$754$		−	22.7849i		−	0.829777i
$755$	−35.4184	−	12.7023i	−1.28901	−	0.462282i
$756$		0			0
$757$	−4.11078	−	4.11078i	−0.149409	−	0.149409i	0.628445	−	0.777854i	$-0.283692\pi$
$757$	−4.11078	−	4.11078i	−0.149409	−	0.149409i	−0.777854	+	0.628445i	$0.783692\pi$
$758$	−10.1275	−	10.1275i	−0.367846	−	0.367846i
$759$	−7.28774	+	71.3549i	−0.264528	+	2.59002i
$760$	8.21572	−	3.87836i	0.298015	−	0.140683i
$761$		−	22.2859i		−	0.807862i	−0.914789	−	0.403931i	$-0.867644\pi$
$761$		−	22.2859i		−	0.807862i	0.914789	−	0.403931i	$-0.132356\pi$
$762$	9.80288	−	7.98603i	0.355121	−	0.289303i
$763$		0			0
$764$	11.2367			0.406530
$765$	−1.88425	−	7.78428i	−0.0681252	−	0.281441i
$766$	−28.8464			−1.04226
$767$	5.90201	−	5.90201i	0.213109	−	0.213109i
$768$	−19.8048	+	16.1342i	−0.714645	+	0.582194i
$769$			37.7021i			1.35957i	0.733410	+	0.679786i	$0.237927\pi$
$769$			37.7021i			1.35957i	−0.733410	+	0.679786i	$0.762073\pi$
$770$		0			0
$771$	−3.45239	+	33.8026i	−0.124335	+	1.21737i
$772$	6.47095	+	6.47095i	0.232895	+	0.232895i
$773$	20.5564	+	20.5564i	0.739362	+	0.739362i	0.972455	−	0.233093i	$-0.0748845\pi$
$773$	20.5564	+	20.5564i	0.739362	+	0.739362i	−0.233093	+	0.972455i	$0.574884\pi$
$774$	−1.32549	−	0.273609i	−0.0476438	−	0.00983467i
$775$	6.58192	+	5.41785i	0.236430	+	0.194615i
$776$		−	13.3314i		−	0.478568i
$777$		0			0
$778$	−14.1870	+	14.1870i	−0.508630	+	0.508630i
$779$	2.40517			0.0861741
$780$	11.5229	+	5.51128i	0.412587	+	0.197335i
$781$	47.1479			1.68708
$782$	−7.60888	+	7.60888i	−0.272093	+	0.272093i
$783$	10.5176	+	20.1997i	0.375868	+	0.721877i
$784$		0			0
$785$	−9.18838	−	19.4642i	−0.327947	−	0.694706i
$786$	26.6838	+	2.72531i	0.951779	+	0.0972088i
$787$	−9.45113	−	9.45113i	−0.336896	−	0.336896i	0.518302	−	0.855198i	$-0.326564\pi$
$787$	−9.45113	−	9.45113i	−0.336896	−	0.336896i	−0.855198	+	0.518302i	$0.826564\pi$
$788$	−2.00376	−	2.00376i	−0.0713809	−	0.0713809i
$789$	29.9514	+	3.05905i	1.06630	+	0.108905i
$790$	−12.4297	−	26.3305i	−0.442230	−	0.936797i
$791$		0			0
$792$	−26.3930	−	40.1234i	−0.937836	−	1.42572i
$793$	8.03662	−	8.03662i	0.285389	−	0.285389i
$794$	7.09346			0.251737
$795$	−17.3463	−	8.29652i	−0.615210	−	0.294247i
$796$	10.3655			0.367394
$797$	5.16008	−	5.16008i	0.182779	−	0.182779i	−0.609786	−	0.792566i	$-0.708745\pi$
$797$	5.16008	−	5.16008i	0.182779	−	0.182779i	0.792566	+	0.609786i	$0.208745\pi$
$798$		0			0
$799$			5.73382i			0.202848i
$800$	19.0934	−	1.85221i	0.675053	−	0.0654857i
$801$	−5.71977	+	27.7093i	−0.202098	+	0.979060i
$802$	−27.6015	−	27.6015i	−0.974641	−	0.974641i
$803$	6.96304	+	6.96304i	0.245720	+	0.245720i
$804$	−1.41596	+	13.8638i	−0.0499371	+	0.488939i
$805$		0			0
$806$			8.86371i			0.312211i
$807$	−25.7203	+	20.9533i	−0.905396	+	0.737592i
$808$	−8.08721	+	8.08721i	−0.284507	+	0.284507i
$809$	−12.8615			−0.452187			−0.226093	−	0.974106i	$-0.572595\pi$
$809$	−12.8615			−0.452187			−0.226093	+	0.974106i	$0.572595\pi$
$810$	22.7710	−	0.772890i	0.800093	−	0.0271566i
$811$	−0.485057			−0.0170327			−0.00851633	−	0.999964i	$-0.502711\pi$
$811$	−0.485057			−0.0170327			−0.00851633	+	0.999964i	$0.502711\pi$
$812$		0			0
$813$	−24.7929	+	20.1978i	−0.869524	+	0.708368i
$814$			14.2565i			0.499691i
$815$	25.1068	−	11.8521i	0.879454	−	0.415160i
$816$	0.430246	−	4.21258i	0.0150616	−	0.147470i
$817$	−0.372008	−	0.372008i	−0.0130149	−	0.0130149i
$818$	−15.6638	−	15.6638i	−0.547673	−	0.547673i
$819$		0			0
$820$	2.75401	+	0.987682i	0.0961740	+	0.0344913i
$821$		−	28.1679i		−	0.983066i	−0.870859	−	0.491533i	$-0.836437\pi$
$821$		−	28.1679i		−	0.983066i	0.870859	−	0.491533i	$-0.163563\pi$
$822$	−17.5562	−	21.5502i	−0.612341	−	0.751651i
$823$	7.62024	−	7.62024i	0.265625	−	0.265625i	−0.561710	−	0.827334i	$-0.689856\pi$
$823$	7.62024	−	7.62024i	0.265625	−	0.265625i	0.827334	+	0.561710i	$0.189856\pi$
$824$	5.13769			0.178980
$825$	−0.228637	+	45.0492i	−0.00796012	+	1.56841i
$826$		0			0
$827$	−24.0314	+	24.0314i	−0.835652	+	0.835652i	−0.988283	−	0.152631i	$-0.951225\pi$
$827$	−24.0314	+	24.0314i	−0.835652	+	0.835652i	0.152631	+	0.988283i	$0.451225\pi$
$828$	9.42655	+	14.3305i	0.327595	+	0.498019i
$829$			18.7082i			0.649763i	0.945755	+	0.324881i	$0.105324\pi$
$829$			18.7082i			0.649763i	−0.945755	+	0.324881i	$0.894676\pi$
$830$	18.4069	+	6.60135i	0.638912	+	0.229136i
$831$	−18.6678	−	1.90661i	−0.647580	−	0.0661397i
$832$	27.4009	+	27.4009i	0.949954	+	0.949954i
$833$		0			0
$834$	30.8738	+	3.15326i	1.06907	+	0.109188i
$835$	35.6073	−	16.8090i	1.23224	−	0.581699i
$836$		−	4.93265i		−	0.170599i
$837$	−4.09152	−	7.85801i	−0.141424	−	0.271612i
$838$	13.6261	−	13.6261i	0.470706	−	0.470706i
$839$	−1.64172			−0.0566785			−0.0283392	−	0.999598i	$-0.509022\pi$
$839$	−1.64172			−0.0566785			−0.0283392	+	0.999598i	$0.509022\pi$
$840$		0			0
$841$	−9.79087			−0.337616
$842$	−17.4099	+	17.4099i	−0.599986	+	0.599986i
$843$	−22.3876	−	27.4809i	−0.771070	−	0.946491i
$844$			8.60763i			0.296287i
$845$	6.10310	−	17.0176i	0.209953	−	0.585424i
$846$	−15.9747	−	3.29751i	−0.549222	−	0.113371i
$847$		0			0
$848$	−7.18859	−	7.18859i	−0.246857	−	0.246857i
$849$	−2.05209	+	20.0922i	−0.0704276	+	0.689563i
$850$	−4.29523	+	5.21811i	−0.147325	+	0.178980i
$851$		−	19.2708i		−	0.660595i
$852$	8.74156	−	7.12142i	0.299481	−	0.243976i
$853$	−3.77850	+	3.77850i	−0.129373	+	0.129373i	−0.768828	−	0.639455i	$-0.779160\pi$
$853$	−3.77850	+	3.77850i	−0.129373	+	0.129373i	0.639455	+	0.768828i	$0.279160\pi$
$854$		0			0
$855$	7.56004	+	4.61337i	0.258548	+	0.157774i
$856$	−6.00639			−0.205294
$857$	−8.38908	+	8.38908i	−0.286566	+	0.286566i	−0.835721	−	0.549155i	$-0.814950\pi$
$857$	−8.38908	+	8.38908i	−0.286566	+	0.286566i	0.549155	+	0.835721i	$0.314950\pi$
$858$	−36.3147	+	29.5842i	−1.23976	+	1.00999i
$859$			12.4393i			0.424424i	0.977224	+	0.212212i	$0.0680668\pi$
$859$			12.4393i			0.424424i	−0.977224	+	0.212212i	$0.931933\pi$
$860$	−0.273197	−	0.578727i	−0.00931595	−	0.0197344i
$861$		0			0
$862$	−8.63896	−	8.63896i	−0.294244	−	0.294244i
$863$	8.43057	+	8.43057i	0.286980	+	0.286980i	0.835885	−	0.548905i	$-0.184955\pi$
$863$	8.43057	+	8.43057i	0.286980	+	0.286980i	−0.548905	+	0.835885i	$0.684955\pi$
$864$	−19.0134	−	5.99303i	−0.646851	−	0.203887i
$865$	−18.6247	−	39.4536i	−0.633259	−	1.34146i
$866$		−	0.747600i		−	0.0254045i
$867$	17.0380	+	20.9142i	0.578642	+	0.710285i
$868$		0			0
$869$	−59.8298			−2.02959
$870$	8.29202	−	17.3369i	0.281126	−	0.587776i
$871$	51.4399			1.74298
$872$	−12.9152	+	12.9152i	−0.437364	+	0.437364i
$873$	10.8574	−	7.14199i	0.367469	−	0.241720i
$874$		−	11.8991i		−	0.402493i
$875$		0			0
$876$	2.34273	+	0.239271i	0.0791534	+	0.00808423i
$877$	−2.56130	−	2.56130i	−0.0864889	−	0.0864889i	0.662539	−	0.749028i	$-0.269479\pi$
$877$	−2.56130	−	2.56130i	−0.0864889	−	0.0864889i	−0.749028	+	0.662539i	$0.769479\pi$
$878$	7.55451	+	7.55451i	0.254953	+	0.254953i
$879$	48.0600	+	4.90854i	1.62102	+	0.165561i
$880$	−8.04063	+	22.4201i	−0.271050	+	0.755782i
$881$			16.9744i			0.571882i	0.958247	+	0.285941i	$0.0923061\pi$
$881$			16.9744i			0.571882i	−0.958247	+	0.285941i	$0.907694\pi$
$882$		0			0
$883$	21.2023	−	21.2023i	0.713513	−	0.713513i	−0.253756	−	0.967268i	$-0.581666\pi$
$883$	21.2023	−	21.2023i	0.713513	−	0.713513i	0.967268	+	0.253756i	$0.0816660\pi$
$884$	3.93756			0.132435
$885$	6.63869	−	2.34291i	0.223157	−	0.0787560i
$886$	27.0517			0.908818
$887$	−12.5527	+	12.5527i	−0.421480	+	0.421480i	−0.885713	−	0.464233i	$-0.846330\pi$
$887$	−12.5527	+	12.5527i	−0.421480	+	0.421480i	0.464233	+	0.885713i	$0.346330\pi$
$888$	8.14969	+	10.0038i	0.273486	+	0.335705i
$889$		0			0
$890$	21.5908	−	10.1923i	0.723726	−	0.341647i
$891$	18.5382	−	42.9905i	0.621051	−	1.44024i
$892$	8.75044	+	8.75044i	0.292986	+	0.292986i
$893$	−4.48340	−	4.48340i	−0.150031	−	0.150031i
$894$	1.85414	−	18.1540i	0.0620116	−	0.607161i
$895$	−14.8001	−	5.30784i	−0.494714	−	0.177422i
$896$		0			0
$897$	49.0873	−	39.9895i	1.63898	−	1.33521i
$898$	−9.25783	+	9.25783i	−0.308938	+	0.308938i
$899$	−7.47267			−0.249227
$900$	6.76204	+	8.38699i	0.225401	+	0.279566i
$901$	−5.92750			−0.197474
$902$	−7.58653	+	7.58653i	−0.252604	+	0.252604i
$903$		0			0
$904$			1.04741i			0.0348364i
$905$	−29.8615	−	10.7094i	−0.992631	−	0.355992i
$906$	3.35273	−	32.8269i	0.111387	−	1.09060i
$907$	−8.60959	−	8.60959i	−0.285877	−	0.285877i	0.549571	−	0.835447i	$-0.314791\pi$
$907$	−8.60959	−	8.60959i	−0.285877	−	0.285877i	−0.835447	+	0.549571i	$0.814791\pi$
$908$	2.99742	+	2.99742i	0.0994728	+	0.0994728i
$909$	−10.9190	−	2.25391i	−0.362160	−	0.0747574i
$910$		0			0
$911$			23.0151i			0.762525i	0.924467	+	0.381263i	$0.124511\pi$
$911$			23.0151i			0.762525i	−0.924467	+	0.381263i	$0.875489\pi$
$912$	2.95749	+	3.63033i	0.0979323	+	0.120212i
$913$	28.4126	−	28.4126i	0.940320	−	0.940320i
$914$	28.5658			0.944872
$915$	9.03975	−	3.19028i	0.298845	−	0.105467i
$916$	−19.5865			−0.647155
$917$		0			0
$918$	6.22977	−	3.24373i	0.205613	−	0.107059i
$919$			22.0977i			0.728935i	0.931216	+	0.364468i	$0.118749\pi$
$919$			22.0977i			0.728935i	−0.931216	+	0.364468i	$0.881251\pi$
$920$	18.4931	−	51.5652i	0.609698	−	1.70005i
$921$	32.4090	+	3.31005i	1.06791	+	0.109070i
$922$	−10.4529	−	10.4529i	−0.344248	−	0.344248i
$923$	−29.4288	−	29.4288i	−0.968662	−	0.968662i
$924$		0			0
$925$	−1.16867	−	12.0471i	−0.0384255	−	0.396106i
$926$			27.8472i			0.915117i
$927$	2.75240	+	4.18428i	0.0904008	+	0.137430i
$928$	−11.8901	+	11.8901i	−0.390312	+	0.390312i
$929$	−51.7684			−1.69846			−0.849232	−	0.528019i	$-0.822935\pi$
$929$	−51.7684			−1.69846			−0.849232	+	0.528019i	$0.822935\pi$
$930$	−3.22573	+	6.74434i	−0.105776	+	0.221156i
$931$		0			0
$932$	1.41341	−	1.41341i	0.0462979	−	0.0462979i
$933$	26.0418	+	31.9663i	0.852569	+	1.04653i
$934$			15.0601i			0.492781i
$935$	5.92845	+	12.5585i	0.193881	+	0.410707i
$936$	−8.57024	+	41.5183i	−0.280127	+	1.35707i
$937$	−32.8470	−	32.8470i	−1.07307	−	1.07307i	−0.997111	−	0.0759541i	$-0.975800\pi$
$937$	−32.8470	−	32.8470i	−1.07307	−	1.07307i	−0.0759541	−	0.997111i	$-0.524200\pi$
$938$		0			0
$939$	4.71262	−	46.1417i	0.153790	−	1.50578i
$940$	−3.29255	−	6.97476i	−0.107391	−	0.227492i
$941$		−	15.0930i		−	0.492018i	−0.969268	−	0.246009i	$-0.920881\pi$
$941$		−	15.0930i		−	0.492018i	0.969268	−	0.246009i	$-0.0791193\pi$
$942$	14.6342	−	11.9219i	0.476808	−	0.388437i
$943$	10.2549	−	10.2549i	0.333944	−	0.333944i
$944$	3.72212			0.121145
$945$		0			0
$946$	2.34682			0.0763016
$947$	27.9272	−	27.9272i	0.907512	−	0.907512i	−0.0885587	−	0.996071i	$-0.528226\pi$
$947$	27.9272	−	27.9272i	0.907512	−	0.907512i	0.996071	+	0.0885587i	$0.0282261\pi$
$948$	−11.0929	+	9.03695i	−0.360280	+	0.293506i
$949$		−	8.69240i		−	0.282167i
$950$	−0.721614	−	7.43869i	−0.0234122	−	0.241343i
$951$	2.91014	−	28.4934i	0.0943678	−	0.923963i
$952$		0			0
$953$	−11.2553	−	11.2553i	−0.364595	−	0.364595i	0.500906	−	0.865501i	$-0.333000\pi$
$953$	−11.2553	−	11.2553i	−0.364595	−	0.364595i	−0.865501	+	0.500906i	$0.833000\pi$
$954$	3.40889	−	16.5143i	0.110367	−	0.534670i
$955$	11.8097	−	32.9297i	0.382153	−	1.06558i
$956$			1.02665i			0.0332042i
$957$	−24.9414	−	30.6156i	−0.806240	−	0.989662i
$958$	−31.1166	+	31.1166i	−1.00533	+	1.00533i
$959$		0			0
$960$	10.8773	+	30.8210i	0.351062	+	0.994745i
$961$	−28.0930			−0.906226
$962$	8.89866	−	8.89866i	0.286904	−	0.286904i
$963$	−3.21779	−	4.89178i	−0.103692	−	0.157635i
$964$		−	20.9233i		−	0.673896i
$965$	25.7643	−	12.1625i	0.829384	−	0.391524i
$966$		0			0
$967$	21.6914	+	21.6914i	0.697548	+	0.697548i	0.963881	−	0.266333i	$-0.0858122\pi$
$967$	21.6914	+	21.6914i	0.697548	+	0.697548i	−0.266333	+	0.963881i	$0.585812\pi$
$968$	34.9476	+	34.9476i	1.12326	+	1.12326i
$969$	2.71606	+	0.277401i	0.0872524	+	0.00891141i
$970$	−10.3229	−	3.70214i	−0.331447	−	0.118868i
$971$			57.5902i			1.84816i	0.382201	+	0.924079i	$0.375166\pi$
$971$			57.5902i			1.84816i	−0.382201	+	0.924079i	$0.624834\pi$
$972$	−3.05636	−	10.7708i	−0.0980328	−	0.345475i
$973$		0			0
$974$	−38.3544			−1.22895
$975$	28.2616	−	27.9762i	0.905096	−	0.895955i
$976$	5.06832			0.162233
$977$	7.49722	−	7.49722i	0.239857	−	0.239857i	−0.576934	−	0.816791i	$-0.695751\pi$
$977$	7.49722	−	7.49722i	0.239857	−	0.239857i	0.816791	+	0.576934i	$0.195751\pi$
$978$	15.3781	+	18.8766i	0.491736	+	0.603608i
$979$		−	49.0600i		−	1.56796i
$980$		0			0
$981$	−17.4375	−	3.59947i	−0.556738	−	0.114922i
$982$	−20.5304	−	20.5304i	−0.655152	−	0.655152i
$983$	−1.92238	−	1.92238i	−0.0613143	−	0.0613143i	0.675785	−	0.737099i	$-0.263805\pi$
$983$	−1.92238	−	1.92238i	−0.0613143	−	0.0613143i	−0.737099	+	0.675785i	$0.763805\pi$
$984$	−0.986639	+	9.66026i	−0.0314529	+	0.307958i
$985$	−7.97804	+	3.76616i	−0.254202	+	0.120000i
$986$		−	5.92428i		−	0.188668i
$987$		0			0
$988$	−3.07887	+	3.07887i	−0.0979519	+	0.0979519i
$989$	−3.17224			−0.100871
$990$	−38.3981	+	9.29458i	−1.22037	+	0.295401i
$991$	−31.7442			−1.00839			−0.504194	−	0.863591i	$-0.668210\pi$
$991$	−31.7442			−1.00839			−0.504194	+	0.863591i	$0.668210\pi$
$992$	4.62545	−	4.62545i	0.146858	−	0.146858i
$993$	−15.5633	+	12.6788i	−0.493886	+	0.402350i
$994$		0			0
$995$	10.8941	−	30.3765i	0.345365	−	0.962999i
$996$	0.976344	−	9.55947i	0.0309366	−	0.302903i
$997$	−12.7289	−	12.7289i	−0.403128	−	0.403128i	0.476206	−	0.879334i	$-0.342012\pi$
$997$	−12.7289	−	12.7289i	−0.403128	−	0.403128i	−0.879334	+	0.476206i	$0.842012\pi$
$998$	−23.3007	−	23.3007i	−0.737571	−	0.737571i
$999$	−3.78134	+	11.9966i	−0.119636	+	0.379557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.j.h.197.4		24
3.2	odd	2	inner	735.2.j.h.197.9		24
5.3	odd	4	inner	735.2.j.h.638.9		24
7.2	even	3		735.2.y.g.557.9		48
7.3	odd	6		735.2.y.j.422.4		48
7.4	even	3		735.2.y.g.422.4		48
7.5	odd	6		735.2.y.j.557.9		48
7.6	odd	2		105.2.j.a.92.4	yes	24
15.8	even	4	inner	735.2.j.h.638.4		24
21.2	odd	6		735.2.y.g.557.4		48
21.5	even	6		735.2.y.j.557.4		48
21.11	odd	6		735.2.y.g.422.9		48
21.17	even	6		735.2.y.j.422.9		48
21.20	even	2		105.2.j.a.92.9	yes	24
35.3	even	12		735.2.y.j.128.4		48
35.13	even	4		105.2.j.a.8.9	yes	24
35.18	odd	12		735.2.y.g.128.4		48
35.23	odd	12		735.2.y.g.263.9		48
35.27	even	4		525.2.j.b.218.4		24
35.33	even	12		735.2.y.j.263.9		48
35.34	odd	2		525.2.j.b.407.9		24
105.23	even	12		735.2.y.g.263.4		48
105.38	odd	12		735.2.y.j.128.9		48
105.53	even	12		735.2.y.g.128.9		48
105.62	odd	4		525.2.j.b.218.9		24
105.68	odd	12		735.2.y.j.263.4		48
105.83	odd	4		105.2.j.a.8.4	✓	24
105.104	even	2		525.2.j.b.407.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.4	✓	24	105.83	odd	4
105.2.j.a.8.9	yes	24	35.13	even	4
105.2.j.a.92.4	yes	24	7.6	odd	2
105.2.j.a.92.9	yes	24	21.20	even	2
525.2.j.b.218.4		24	35.27	even	4
525.2.j.b.218.9		24	105.62	odd	4
525.2.j.b.407.4		24	105.104	even	2
525.2.j.b.407.9		24	35.34	odd	2
735.2.j.h.197.4		24	1.1	even	1	trivial
735.2.j.h.197.9		24	3.2	odd	2	inner
735.2.j.h.638.4		24	15.8	even	4	inner
735.2.j.h.638.9		24	5.3	odd	4	inner
735.2.y.g.128.4		48	35.18	odd	12
735.2.y.g.128.9		48	105.53	even	12
735.2.y.g.263.4		48	105.23	even	12
735.2.y.g.263.9		48	35.23	odd	12
735.2.y.g.422.4		48	7.4	even	3
735.2.y.g.422.9		48	21.11	odd	6
735.2.y.g.557.4		48	21.2	odd	6
735.2.y.g.557.9		48	7.2	even	3
735.2.y.j.128.4		48	35.3	even	12
735.2.y.j.128.9		48	105.38	odd	12
735.2.y.j.263.4		48	105.68	odd	12
735.2.y.j.263.9		48	35.33	even	12
735.2.y.j.422.4		48	7.3	odd	6
735.2.y.j.422.9		48	21.17	even	6
735.2.y.j.557.4		48	21.5	even	6
735.2.y.j.557.9		48	7.5	odd	6

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.800553 + 0.800553i) q^{2} +(1.34285 - 1.09397i) q^{3} +0.718229i q^{4} +(2.10480 + 0.754855i) q^{5} +(-0.199242 + 1.95080i) q^{6} +(-2.17609 - 2.17609i) q^{8} +(0.606476 - 2.93806i) q^{9} +O(q^{10})\)	\(q+(-0.800553 + 0.800553i) q^{2} +(1.34285 - 1.09397i) q^{3} +0.718229i q^{4} +(2.10480 + 0.754855i) q^{5} +(-0.199242 + 1.95080i) q^{6} +(-2.17609 - 2.17609i) q^{8} +(0.606476 - 2.93806i) q^{9} +(-2.28931 + 1.08070i) q^{10} +5.20191i q^{11} +(0.785718 + 0.964471i) q^{12} +(3.24693 - 3.24693i) q^{13} +(3.65221 - 1.28893i) q^{15} +2.04769 q^{16} +(0.844232 - 0.844232i) q^{17} +(1.86656 + 2.83759i) q^{18} +1.32025i q^{19} +(-0.542159 + 1.51173i) q^{20} +(-4.16440 - 4.16440i) q^{22} +(5.62910 + 5.62910i) q^{23} +(-5.30272 - 0.541586i) q^{24} +(3.86039 + 3.17764i) q^{25} +5.19868i q^{26} +(-2.39973 - 4.60883i) q^{27} -4.38282 q^{29} +(-1.89194 + 3.95565i) q^{30} +1.70499 q^{31} +(2.71289 - 2.71289i) q^{32} +(5.69071 + 6.98536i) q^{33} +1.35170i q^{34} +(2.11020 + 0.435588i) q^{36} +(-1.71171 - 1.71171i) q^{37} +(-1.05693 - 1.05693i) q^{38} +(0.808099 - 7.91217i) q^{39} +(-2.93760 - 6.22286i) q^{40} -1.82176i q^{41} +(-0.281771 + 0.281771i) q^{43} -3.73616 q^{44} +(3.49432 - 5.72623i) q^{45} -9.01279 q^{46} +(-3.39588 + 3.39588i) q^{47} +(2.74973 - 2.24010i) q^{48} +(-5.63432 + 0.546575i) q^{50} +(0.210113 - 2.05723i) q^{51} +(2.33204 + 2.33204i) q^{52} +(-3.51059 - 3.51059i) q^{53} +(5.61073 + 1.76850i) q^{54} +(-3.92668 + 10.9490i) q^{55} +(1.44431 + 1.77289i) q^{57} +(3.50868 - 3.50868i) q^{58} +1.81772 q^{59} +(0.925745 + 2.62313i) q^{60} +2.47514 q^{61} +(-1.36494 + 1.36494i) q^{62} +8.43900i q^{64} +(9.28511 - 4.38319i) q^{65} +(-10.1479 - 1.03644i) q^{66} +(7.92132 + 7.92132i) q^{67} +(0.606352 + 0.606352i) q^{68} +(13.7171 + 1.40098i) q^{69} -9.06358i q^{71} +(-7.71322 + 5.07373i) q^{72} +(1.33856 - 1.33856i) q^{73} +2.74064 q^{74} +(8.66014 + 0.0439525i) q^{75} -0.948239 q^{76} +(5.68718 + 6.98104i) q^{78} +11.5015i q^{79} +(4.30998 + 1.54571i) q^{80} +(-8.26437 - 3.56372i) q^{81} +(1.45841 + 1.45841i) q^{82} +(-5.46196 - 5.46196i) q^{83} +(2.41421 - 1.13967i) q^{85} -0.451146i q^{86} +(-5.88546 + 4.79466i) q^{87} +(11.3198 - 11.3198i) q^{88} -9.43116 q^{89} +(1.78676 + 7.38154i) q^{90} +(-4.04298 + 4.04298i) q^{92} +(2.28954 - 1.86520i) q^{93} -5.43717i q^{94} +(-0.996595 + 2.77886i) q^{95} +(0.675186 - 6.61080i) q^{96} +(3.06315 + 3.06315i) q^{97} +(15.2835 + 3.15483i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3}+O(q^{10}) \) 24 * q + 4 * q^3	\( 24 q + 4 q^{3} + 16 q^{10} - 16 q^{12} + 8 q^{13} - 16 q^{15} - 16 q^{16} - 20 q^{18} + 8 q^{22} - 16 q^{25} + 16 q^{27} + 20 q^{30} - 28 q^{33} + 16 q^{36} - 16 q^{37} - 64 q^{40} - 40 q^{43} - 20 q^{45} - 64 q^{46} - 16 q^{48} - 20 q^{51} - 40 q^{55} + 4 q^{57} + 40 q^{58} + 32 q^{60} - 32 q^{61} + 16 q^{66} + 24 q^{67} - 8 q^{72} - 32 q^{73} + 60 q^{75} - 32 q^{76} + 60 q^{78} + 52 q^{81} + 80 q^{82} + 24 q^{85} - 4 q^{87} + 96 q^{88} + 24 q^{90} - 76 q^{93} + 96 q^{96} - 24 q^{97}+O(q^{100}) \) 24 * q + 4 * q^3 + 16 * q^10 - 16 * q^12 + 8 * q^13 - 16 * q^15 - 16 * q^16 - 20 * q^18 + 8 * q^22 - 16 * q^25 + 16 * q^27 + 20 * q^30 - 28 * q^33 + 16 * q^36 - 16 * q^37 - 64 * q^40 - 40 * q^43 - 20 * q^45 - 64 * q^46 - 16 * q^48 - 20 * q^51 - 40 * q^55 + 4 * q^57 + 40 * q^58 + 32 * q^60 - 32 * q^61 + 16 * q^66 + 24 * q^67 - 8 * q^72 - 32 * q^73 + 60 * q^75 - 32 * q^76 + 60 * q^78 + 52 * q^81 + 80 * q^82 + 24 * q^85 - 4 * q^87 + 96 * q^88 + 24 * q^90 - 76 * q^93 + 96 * q^96 - 24 * q^97

Introduction

L-functions

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