LMFDB - Embedded newform 735.2.j.h.638.7

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			638.7
Character	$\chi$	$=$	735.638
Dual form			735.2.j.h.197.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.260263 + 0.260263i) q^{2} +(-0.826909 + 1.52191i) q^{3} -1.86453i q^{4} +(0.895238 - 2.04904i) q^{5} +(-0.611312 + 0.180884i) q^{6} +(1.00579 - 1.00579i) q^{8} +(-1.63244 - 2.51697i) q^{9} +O(q^{10})$	\(q+(0.260263 + 0.260263i) q^{2} +(-0.826909 + 1.52191i) q^{3} -1.86453i q^{4} +(0.895238 - 2.04904i) q^{5} +(-0.611312 + 0.180884i) q^{6} +(1.00579 - 1.00579i) q^{8} +(-1.63244 - 2.51697i) q^{9} +(0.766286 - 0.300291i) q^{10} +3.38750i q^{11} +(2.83765 + 1.54179i) q^{12} +(-1.59420 - 1.59420i) q^{13} +(2.37818 + 3.05684i) q^{15} -3.20551 q^{16} +(-0.140684 - 0.140684i) q^{17} +(0.230209 - 1.07994i) q^{18} -7.34691i q^{19} +(-3.82048 - 1.66919i) q^{20} +(-0.881641 + 0.881641i) q^{22} +(2.21444 - 2.21444i) q^{23} +(0.699032 + 2.36243i) q^{24} +(-3.39710 - 3.66875i) q^{25} -0.829822i q^{26} +(5.18049 - 0.403134i) q^{27} -9.49165 q^{29} +(-0.176632 + 1.41454i) q^{30} -0.922582 q^{31} +(-2.84586 - 2.84586i) q^{32} +(-5.15548 - 2.80115i) q^{33} -0.0732300i q^{34} +(-4.69295 + 3.04373i) q^{36} +(5.91558 - 5.91558i) q^{37} +(1.91213 - 1.91213i) q^{38} +(3.74449 - 1.10797i) q^{39} +(-1.16048 - 2.96133i) q^{40} +1.39256i q^{41} +(0.864526 + 0.864526i) q^{43} +6.31608 q^{44} +(-6.61878 + 1.09165i) q^{45} +1.15267 q^{46} +(-0.651346 - 0.651346i) q^{47} +(2.65066 - 4.87851i) q^{48} +(0.0707006 - 1.83898i) q^{50} +(0.330443 - 0.0977764i) q^{51} +(-2.97242 + 2.97242i) q^{52} +(6.54108 - 6.54108i) q^{53} +(1.45321 + 1.24337i) q^{54} +(6.94110 + 3.03262i) q^{55} +(11.1814 + 6.07522i) q^{57} +(-2.47033 - 2.47033i) q^{58} +6.25032 q^{59} +(5.69956 - 4.43417i) q^{60} -1.83261 q^{61} +(-0.240114 - 0.240114i) q^{62} +4.92967i q^{64} +(-4.69375 + 1.83938i) q^{65} +(-0.612745 - 2.07082i) q^{66} +(-0.815500 + 0.815500i) q^{67} +(-0.262310 + 0.262310i) q^{68} +(1.53904 + 5.20132i) q^{69} -9.77651i q^{71} +(-4.17345 - 0.889650i) q^{72} +(4.80768 + 4.80768i) q^{73} +3.07921 q^{74} +(8.39261 - 2.13637i) q^{75} -13.6985 q^{76} +(1.26292 + 0.686187i) q^{78} +3.41711i q^{79} +(-2.86969 + 6.56821i) q^{80} +(-3.67026 + 8.21761i) q^{81} +(-0.362432 + 0.362432i) q^{82} +(6.26911 - 6.26911i) q^{83} +(-0.414214 + 0.162321i) q^{85} +0.450009i q^{86} +(7.84873 - 14.4455i) q^{87} +(3.40712 + 3.40712i) q^{88} -12.3767 q^{89} +(-2.00674 - 1.43851i) q^{90} +(-4.12888 - 4.12888i) q^{92} +(0.762891 - 1.40409i) q^{93} -0.339043i q^{94} +(-15.0541 - 6.57723i) q^{95} +(6.68443 - 1.97789i) q^{96} +(6.71326 - 6.71326i) q^{97} +(8.52622 - 5.52990i) 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 $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	0.260263	+	0.260263i	0.184034	+	0.184034i	0.793111	−	0.609077i	$-0.208460\pi$
$2$	0.260263	+	0.260263i	0.184034	+	0.184034i	−0.609077	+	0.793111i	$0.708460\pi$
$3$	−0.826909	+	1.52191i	−0.477416	+	0.878677i
$3$	−0.826909	+	1.52191i	−0.477416	+	0.878677i
$4$		−	1.86453i		−	0.932263i
$5$	0.895238	−	2.04904i	0.400362	−	0.916357i
$5$	0.895238	−	2.04904i	0.400362	−	0.916357i
$6$	−0.611312	+	0.180884i	−0.249567	+	0.0738457i
$7$		0			0
$7$		0			0
$8$	1.00579	−	1.00579i	0.355602	−	0.355602i
$9$	−1.63244	−	2.51697i	−0.544148	−	0.838989i
$10$	0.766286	−	0.300291i	0.242321	−	0.0949605i
$11$			3.38750i			1.02137i	0.859768	+	0.510684i	$0.170608\pi$
$11$			3.38750i			1.02137i	−0.859768	+	0.510684i	$0.829392\pi$
$12$	2.83765	+	1.54179i	0.819158	+	0.445077i
$13$	−1.59420	−	1.59420i	−0.442151	−	0.442151i	0.450583	−	0.892734i	$-0.351216\pi$
$13$	−1.59420	−	1.59420i	−0.442151	−	0.442151i	−0.892734	+	0.450583i	$0.851216\pi$
$14$		0			0
$15$	2.37818	+	3.05684i	0.614042	+	0.789273i
$16$	−3.20551			−0.801377
$17$	−0.140684	−	0.140684i	−0.0341210	−	0.0341210i	0.689840	−	0.723961i	$-0.257681\pi$
$17$	−0.140684	−	0.140684i	−0.0341210	−	0.0341210i	−0.723961	+	0.689840i	$0.757681\pi$
$18$	0.230209	−	1.07994i	0.0542609	−	0.254544i
$19$		−	7.34691i		−	1.68550i	−0.538308	−	0.842748i	$-0.680936\pi$
$19$		−	7.34691i		−	1.68550i	0.538308	−	0.842748i	$-0.319064\pi$
$20$	−3.82048	−	1.66919i	−0.854286	−	0.373243i
$21$		0			0
$22$	−0.881641	+	0.881641i	−0.187966	+	0.187966i
$23$	2.21444	−	2.21444i	0.461742	−	0.461742i	−0.437484	−	0.899226i	$-0.644130\pi$
$23$	2.21444	−	2.21444i	0.461742	−	0.461742i	0.899226	+	0.437484i	$0.144130\pi$
$24$	0.699032	+	2.36243i	0.142689	+	0.482229i
$25$	−3.39710	−	3.66875i	−0.679420	−	0.733750i
$26$		−	0.829822i		−	0.162741i
$27$	5.18049	−	0.403134i	0.996986	−	0.0775831i
$28$		0			0
$29$	−9.49165			−1.76256			−0.881278	−	0.472598i	$-0.843316\pi$
$29$	−9.49165			−1.76256			−0.881278	+	0.472598i	$0.843316\pi$
$30$	−0.176632	+	1.41454i	−0.0322484	+	0.258258i
$31$	−0.922582			−0.165701			−0.0828503	−	0.996562i	$-0.526402\pi$
$31$	−0.922582			−0.165701			−0.0828503	+	0.996562i	$0.526402\pi$
$32$	−2.84586	−	2.84586i	−0.503083	−	0.503083i
$33$	−5.15548	−	2.80115i	−0.897454	−	0.487618i
$34$		−	0.0732300i		−	0.0125588i
$35$		0			0
$36$	−4.69295	+	3.04373i	−0.782159	+	0.507289i
$37$	5.91558	−	5.91558i	0.972515	−	0.972515i	−0.0271173	−	0.999632i	$-0.508633\pi$
$37$	5.91558	−	5.91558i	0.972515	−	0.972515i	0.999632	+	0.0271173i	$0.00863275\pi$
$38$	1.91213	−	1.91213i	0.310188	−	0.310188i
$39$	3.74449	−	1.10797i	0.599598	−	0.177418i
$40$	−1.16048	−	2.96133i	−0.183489	−	0.468228i
$41$			1.39256i			0.217481i	0.994070	+	0.108741i	$0.0346818\pi$
$41$			1.39256i			0.217481i	−0.994070	+	0.108741i	$0.965318\pi$
$42$		0			0
$43$	0.864526	+	0.864526i	0.131839	+	0.131839i	0.769947	−	0.638108i	$-0.220283\pi$
$43$	0.864526	+	0.864526i	0.131839	+	0.131839i	−0.638108	+	0.769947i	$0.720283\pi$
$44$	6.31608			0.952184
$45$	−6.61878	+	1.09165i	−0.986670	+	0.162734i
$46$	1.15267			0.169952
$47$	−0.651346	−	0.651346i	−0.0950085	−	0.0950085i	0.658005	−	0.753014i	$-0.271401\pi$
$47$	−0.651346	−	0.651346i	−0.0950085	−	0.0950085i	−0.753014	+	0.658005i	$0.771401\pi$
$48$	2.65066	−	4.87851i	0.382591	−	0.704152i
$49$		0			0
$50$	0.0707006	−	1.83898i	0.00999858	−	0.260071i
$51$	0.330443	−	0.0977764i	0.0462713	−	0.0136914i
$52$	−2.97242	+	2.97242i	−0.412201	+	0.412201i
$53$	6.54108	−	6.54108i	0.898486	−	0.898486i	−0.0968158	−	0.995302i	$-0.530866\pi$
$53$	6.54108	−	6.54108i	0.898486	−	0.898486i	0.995302	+	0.0968158i	$0.0308658\pi$
$54$	1.45321	+	1.24337i	0.197757	+	0.169201i
$55$	6.94110	+	3.03262i	0.935938	+	0.408918i
$56$		0			0
$57$	11.1814	+	6.07522i	1.48101	+	0.804683i
$58$	−2.47033	−	2.47033i	−0.324370	−	0.324370i
$59$	6.25032			0.813722			0.406861	−	0.913490i	$-0.366623\pi$
$59$	6.25032			0.813722			0.406861	+	0.913490i	$0.366623\pi$
$60$	5.69956	−	4.43417i	0.735810	−	0.572449i
$61$	−1.83261			−0.234642			−0.117321	−	0.993094i	$-0.537431\pi$
$61$	−1.83261			−0.234642			−0.117321	+	0.993094i	$0.537431\pi$
$62$	−0.240114	−	0.240114i	−0.0304945	−	0.0304945i
$63$		0			0
$64$			4.92967i			0.616209i
$65$	−4.69375	+	1.83938i	−0.582189	+	0.228147i
$66$	−0.612745	−	2.07082i	−0.0754237	−	0.254900i
$67$	−0.815500	+	0.815500i	−0.0996292	+	0.0996292i	−0.755165	−	0.655535i	$-0.772443\pi$
$67$	−0.815500	+	0.815500i	−0.0996292	+	0.0996292i	0.655535	+	0.755165i	$0.272443\pi$
$68$	−0.262310	+	0.262310i	−0.0318097	+	0.0318097i
$69$	1.53904	+	5.20132i	0.185279	+	0.626166i
$70$		0			0
$71$		−	9.77651i		−	1.16026i	−0.814524	−	0.580129i	$-0.803002\pi$
$71$		−	9.77651i		−	1.16026i	0.814524	−	0.580129i	$-0.196998\pi$
$72$	−4.17345	−	0.889650i	−0.491846	−	0.104846i
$73$	4.80768	+	4.80768i	0.562697	+	0.562697i	0.930073	−	0.367376i	$-0.119744\pi$
$73$	4.80768	+	4.80768i	0.562697	+	0.562697i	−0.367376	+	0.930073i	$0.619744\pi$
$74$	3.07921			0.357951
$75$	8.39261	−	2.13637i	0.969095	−	0.246687i
$76$	−13.6985			−1.57133
$77$		0			0
$78$	1.26292	+	0.686187i	0.142997	+	0.0776954i
$79$			3.41711i			0.384455i	0.981350	+	0.192228i	$0.0615712\pi$
$79$			3.41711i			0.384455i	−0.981350	+	0.192228i	$0.938429\pi$
$80$	−2.86969	+	6.56821i	−0.320841	+	0.734348i
$81$	−3.67026	+	8.21761i	−0.407807	+	0.913068i
$82$	−0.362432	+	0.362432i	−0.0400239	+	0.0400239i
$83$	6.26911	−	6.26911i	0.688124	−	0.688124i	−0.273693	−	0.961817i	$-0.588245\pi$
$83$	6.26911	−	6.26911i	0.688124	−	0.688124i	0.961817	+	0.273693i	$0.0882453\pi$
$84$		0			0
$85$	−0.414214	+	0.162321i	−0.0449278	+	0.0176062i
$86$			0.450009i			0.0485257i
$87$	7.84873	−	14.4455i	0.841473	−	1.54872i
$88$	3.40712	+	3.40712i	0.363201	+	0.363201i
$89$	−12.3767			−1.31192			−0.655962	−	0.754794i	$-0.727737\pi$
$89$	−12.3767			−1.31192			−0.655962	+	0.754794i	$0.727737\pi$
$90$	−2.00674	−	1.43851i	−0.211529	−	0.151632i
$91$		0			0
$92$	−4.12888	−	4.12888i	−0.430465	−	0.430465i
$93$	0.762891	−	1.40409i	0.0791082	−	0.145597i
$94$		−	0.339043i		−	0.0349696i
$95$	−15.0541	−	6.57723i	−1.54452	−	0.674809i
$96$	6.68443	−	1.97789i	0.682227	−	0.201867i
$97$	6.71326	−	6.71326i	0.681628	−	0.681628i	−0.278739	−	0.960367i	$-0.589916\pi$
$97$	6.71326	−	6.71326i	0.681628	−	0.681628i	0.960367	+	0.278739i	$0.0899164\pi$
$98$		0			0
$99$	8.52622	−	5.52990i	0.856918	−	0.555775i
$100$	−6.84048	+	6.33398i	−0.684048	+	0.633398i
$101$			12.4523i			1.23905i	0.784976	+	0.619526i	$0.212675\pi$
$101$			12.4523i			1.23905i	−0.784976	+	0.619526i	$0.787325\pi$
$102$	0.111450	+	0.0605545i	0.0110352	+	0.00599579i
$103$	9.78924	+	9.78924i	0.964563	+	0.964563i	0.999393	−	0.0348303i	$-0.0110891\pi$
$103$	9.78924	+	9.78924i	0.964563	+	0.964563i	−0.0348303	+	0.999393i	$0.511089\pi$
$104$	−3.20687			−0.314459
$105$		0			0
$106$	3.40481			0.330704
$107$	5.21866	+	5.21866i	0.504507	+	0.504507i	0.912835	−	0.408328i	$-0.133888\pi$
$107$	5.21866	+	5.21866i	0.504507	+	0.504507i	−0.408328	+	0.912835i	$0.633888\pi$
$108$	−0.751653	−	9.65916i	−0.0723279	−	0.929453i
$109$			6.67661i			0.639504i	0.947501	+	0.319752i	$0.103600\pi$
$109$			6.67661i			0.639504i	−0.947501	+	0.319752i	$0.896400\pi$
$110$	1.01724	+	2.59579i	0.0969896	+	0.247499i
$111$	4.11135	+	13.8946i	0.390233	+	1.31882i
$112$		0			0
$113$	−8.23451	+	8.23451i	−0.774637	+	0.774637i	−0.978913	−	0.204276i	$-0.934516\pi$
$113$	−8.23451	+	8.23451i	−0.774637	+	0.774637i	0.204276	+	0.978913i	$0.434516\pi$
$114$	1.32894	+	4.49125i	0.124467	+	0.420644i
$115$	−2.55501	−	6.51991i	−0.238256	−	0.607985i
$116$			17.6974i			1.64317i
$117$	−1.41011	+	6.61498i	−0.130365	+	0.611555i
$118$	1.62673	+	1.62673i	0.149752	+	0.149752i
$119$		0			0
$120$	5.46651	+	0.682597i	0.499022	+	0.0623123i
$121$	−0.475134			−0.0431940
$122$	−0.476962	−	0.476962i	−0.0431821	−	0.0431821i
$123$	−2.11936	−	1.15152i	−0.191096	−	0.103829i
$124$			1.72018i			0.154477i
$125$	−10.5586	+	3.67638i	−0.944391	+	0.328825i
$126$		0			0
$127$	1.88180	−	1.88180i	0.166983	−	0.166983i	−0.618669	−	0.785652i	$-0.712328\pi$
$127$	1.88180	−	1.88180i	0.166983	−	0.166983i	0.785652	+	0.618669i	$0.212328\pi$
$128$	−6.97474	+	6.97474i	−0.616486	+	0.616486i
$129$	−2.03062	+	0.600850i	−0.178786	+	0.0529019i
$130$	−1.70034	−	0.742888i	−0.149129	−	0.0651556i
$131$		−	8.97080i		−	0.783783i	−0.920012	−	0.391891i	$-0.871821\pi$
$131$		−	8.97080i		−	0.783783i	0.920012	−	0.391891i	$-0.128179\pi$
$132$	−5.22282	+	9.61252i	−0.454588	+	0.836663i
$133$		0			0
$134$	−0.424489			−0.0366703
$135$	3.81174	−	10.9759i	0.328062	−	0.944656i
$136$	−0.282999			−0.0242670
$137$	−6.49538	−	6.49538i	−0.554938	−	0.554938i	0.372924	−	0.927862i	$-0.378355\pi$
$137$	−6.49538	−	6.49538i	−0.554938	−	0.554938i	−0.927862	+	0.372924i	$0.878355\pi$
$138$	−0.953156	+	1.75427i	−0.0811380	+	0.149333i
$139$			1.83916i			0.155995i	0.996954	+	0.0779976i	$0.0248526\pi$
$139$			1.83916i			0.155995i	−0.996954	+	0.0779976i	$0.975147\pi$
$140$		0			0
$141$	1.52990	−	0.452688i	0.128840	−	0.0381232i
$142$	2.54447	−	2.54447i	0.213527	−	0.213527i
$143$	5.40034	−	5.40034i	0.451599	−	0.451599i
$144$	5.23281	+	8.06817i	0.436068	+	0.672347i
$145$	−8.49729	+	19.4487i	−0.705661	+	1.61513i
$146$			2.50253i			0.207110i
$147$		0			0
$148$	−11.0297	−	11.0297i	−0.906640	−	0.906640i
$149$	−0.987227			−0.0808768			−0.0404384	−	0.999182i	$-0.512875\pi$
$149$	−0.987227			−0.0808768			−0.0404384	+	0.999182i	$0.512875\pi$
$150$	2.74031	+	1.62827i	0.223745	+	0.132948i
$151$	−8.71084			−0.708878			−0.354439	−	0.935079i	$-0.615328\pi$
$151$	−8.71084			−0.708878			−0.354439	+	0.935079i	$0.615328\pi$
$152$	−7.38948	−	7.38948i	−0.599366	−	0.599366i
$153$	−0.124439	+	0.583758i	−0.0100603	+	0.0471940i
$154$		0			0
$155$	−0.825930	+	1.89040i	−0.0663403	+	0.151841i
$156$	−2.06585	−	6.98169i	−0.165400	−	0.558983i
$157$	−5.26306	+	5.26306i	−0.420038	+	0.420038i	−0.885217	−	0.465179i	$-0.845990\pi$
$157$	−5.26306	+	5.26306i	−0.420038	+	0.420038i	0.465179	+	0.885217i	$0.345990\pi$
$158$	−0.889349	+	0.889349i	−0.0707528	+	0.0707528i
$159$	4.54608	+	15.3638i	0.360528	+	1.21843i
$160$	−8.37901	+	3.28355i	−0.662419	+	0.259588i
$161$		0			0
$162$	−3.09398	+	1.18351i	−0.243086	+	0.0929853i
$163$	14.1511	+	14.1511i	1.10840	+	1.10840i	0.993361	+	0.115041i	$0.0367000\pi$
$163$	14.1511	+	14.1511i	1.10840	+	1.10840i	0.115041	+	0.993361i	$0.463300\pi$
$164$	2.59646			0.202750
$165$	−10.3550	+	8.05606i	−0.806139	+	0.627164i
$166$	3.26324			0.253276
$167$	−17.4876	−	17.4876i	−1.35323	−	1.35323i	−0.882018	−	0.471215i	$-0.843816\pi$
$167$	−17.4876	−	17.4876i	−1.35323	−	1.35323i	−0.471215	−	0.882018i	$-0.656184\pi$
$168$		0			0
$169$		−	7.91707i		−	0.609005i
$170$	−0.150051	−	0.0655582i	−0.0115084	−	0.00502809i
$171$	−18.4919	+	11.9934i	−1.41411	+	0.917159i
$172$	1.61193	−	1.61193i	0.122909	−	0.122909i
$173$	−10.8767	+	10.8767i	−0.826942	+	0.826942i	−0.987093	−	0.160150i	$-0.948802\pi$
$173$	−10.8767	+	10.8767i	−0.826942	+	0.826942i	0.160150	+	0.987093i	$0.448802\pi$
$174$	5.80236	−	1.71689i	0.439876	−	0.130157i
$175$		0			0
$176$		−	10.8587i		−	0.818502i
$177$	−5.16844	+	9.51244i	−0.388484	+	0.714999i
$178$	−3.22119	−	3.22119i	−0.241439	−	0.241439i
$179$	17.6524			1.31941			0.659703	−	0.751527i	$-0.270682\pi$
$179$	17.6524			1.31941			0.659703	+	0.751527i	$0.270682\pi$
$180$	2.03541	+	12.3409i	0.151710	+	0.919836i
$181$	11.9237			0.886282			0.443141	−	0.896452i	$-0.353864\pi$
$181$	11.9237			0.886282			0.443141	+	0.896452i	$0.353864\pi$
$182$		0			0
$183$	1.51541	−	2.78908i	0.112022	−	0.206175i
$184$		−	4.45454i		−	0.328393i
$185$	−6.82538	−	17.4171i	−0.501812	−	1.28053i
$186$	0.563986	−	0.166881i	0.0413534	−	0.0122363i
$187$	0.476568	−	0.476568i	0.0348501	−	0.0348501i
$188$	−1.21445	+	1.21445i	−0.0885729	+	0.0885729i
$189$		0			0
$190$	−2.20621	−	5.62983i	−0.160055	−	0.408431i
$191$			17.7849i			1.28687i	0.765501	+	0.643435i	$0.222491\pi$
$191$			17.7849i			1.28687i	−0.765501	+	0.643435i	$0.777509\pi$
$192$	−7.50253	−	4.07639i	−0.541449	−	0.294188i
$193$	14.3394	+	14.3394i	1.03217	+	1.03217i	0.999465	+	0.0327052i	$0.0104123\pi$
$193$	14.3394	+	14.3394i	1.03217	+	1.03217i	0.0327052	+	0.999465i	$0.489588\pi$
$194$	3.49443			0.250885
$195$	1.08193	−	8.66449i	0.0774783	−	0.620477i
$196$		0			0
$197$	−4.10678	−	4.10678i	−0.292596	−	0.292596i	0.545509	−	0.838105i	$-0.316336\pi$
$197$	−4.10678	−	4.10678i	−0.292596	−	0.292596i	−0.838105	+	0.545509i	$0.816336\pi$
$198$	3.65829	+	0.779834i	0.259983	+	0.0554204i
$199$		−	13.4148i		−	0.950949i	−0.879730	−	0.475474i	$-0.842276\pi$
$199$		−	13.4148i		−	0.950949i	0.879730	−	0.475474i	$-0.157724\pi$
$200$	−7.10679	−	0.273224i	−0.502526	−	0.0193199i
$201$	−0.566776	−	1.91547i	−0.0399773	−	0.135107i
$202$	−3.24088	+	3.24088i	−0.228027	+	0.228027i
$203$		0			0
$204$	−0.182307	−	0.616119i	−0.0127640	−	0.0431370i
$205$	2.85341	+	1.24667i	0.199290	+	0.0870714i
$206$			5.09556i			0.355025i
$207$	−9.18861	−	1.95873i	−0.638653	−	0.136141i
$208$	5.11022	+	5.11022i	0.354330	+	0.354330i
$209$	24.8876			1.72151
$210$		0			0
$211$	8.11525			0.558677			0.279338	−	0.960193i	$-0.409885\pi$
$211$	8.11525			0.558677			0.279338	+	0.960193i	$0.409885\pi$
$212$	−12.1960	−	12.1960i	−0.837626	−	0.837626i
$213$	14.8790	+	8.08429i	1.01949	+	0.553926i
$214$			2.71645i			0.185693i
$215$	2.54540	−	0.997489i	0.173595	−	0.0680282i
$216$	4.80504	−	5.61598i	0.326941	−	0.382119i
$217$		0			0
$218$	−1.73768	+	1.73768i	−0.117690	+	0.117690i
$219$	−11.2924	+	3.34136i	−0.763069	+	0.225788i
$220$	5.65439	−	12.9419i	0.381219	−	0.872541i
$221$			0.448558i			0.0301732i
$222$	−2.54623	+	4.68630i	−0.170892	+	0.314524i
$223$	11.5431	+	11.5431i	0.772984	+	0.772984i	0.978627	−	0.205643i	$-0.0659285\pi$
$223$	11.5431	+	11.5431i	0.772984	+	0.772984i	−0.205643	+	0.978627i	$0.565928\pi$
$224$		0			0
$225$	−3.68856	+	14.5394i	−0.245904	+	0.969294i
$226$	−4.28628			−0.285119
$227$	7.04578	+	7.04578i	0.467645	+	0.467645i	0.901151	−	0.433506i	$-0.142724\pi$
$227$	7.04578	+	7.04578i	0.467645	+	0.467645i	−0.433506	+	0.901151i	$0.642724\pi$
$228$	11.3274	−	20.8479i	0.750176	−	1.38069i
$229$		−	4.80117i		−	0.317270i	−0.987337	−	0.158635i	$-0.949291\pi$
$229$		−	4.80117i		−	0.317270i	0.987337	−	0.158635i	$-0.0507093\pi$
$230$	1.03192	−	2.36187i	0.0680426	−	0.155737i
$231$		0			0
$232$	−9.54665	+	9.54665i	−0.626768	+	0.626768i
$233$	14.2791	−	14.2791i	0.935455	−	0.935455i	−0.0625851	−	0.998040i	$-0.519934\pi$
$233$	14.2791	−	14.2791i	0.935455	−	0.935455i	0.998040	+	0.0625851i	$0.0199345\pi$
$234$	−2.08864	+	1.35464i	−0.136538	+	0.0885554i
$235$	−1.91774	+	0.751522i	−0.125100	+	0.0490239i
$236$		−	11.6539i		−	0.758603i
$237$	−5.20055	−	2.82564i	−0.337812	−	0.183545i
$238$		0			0
$239$	12.8618			0.831961			0.415981	−	0.909373i	$-0.363438\pi$
$239$	12.8618			0.831961			0.415981	+	0.909373i	$0.363438\pi$
$240$	−7.62327	−	9.79873i	−0.492080	−	0.632506i
$241$	16.1856			1.04261			0.521304	−	0.853371i	$-0.325446\pi$
$241$	16.1856			1.04261			0.521304	+	0.853371i	$0.325446\pi$
$242$	−0.123660	−	0.123660i	−0.00794917	−	0.00794917i
$243$	−9.47153	−	12.3810i	−0.607599	−	0.794244i
$244$			3.41696i			0.218748i
$245$		0			0
$246$	−0.251892	−	0.851289i	−0.0160601	−	0.0542762i
$247$	−11.7124	+	11.7124i	−0.745243	+	0.745243i
$248$	−0.927928	+	0.927928i	−0.0589235	+	0.0589235i
$249$	4.35706	+	14.7250i	0.276117	+	0.933160i
$250$	−3.70484	−	1.79119i	−0.234315	−	0.113285i
$251$			8.02862i			0.506762i	0.967367	+	0.253381i	$0.0815426\pi$
$251$			8.02862i			0.506762i	−0.967367	+	0.253381i	$0.918457\pi$
$252$		0			0
$253$	7.50140	+	7.50140i	0.471609	+	0.471609i
$254$	0.979525			0.0614609
$255$	0.0954776	−	0.764622i	0.00597904	−	0.0478825i
$256$	6.22880			0.389300
$257$	16.6108	+	16.6108i	1.03615	+	1.03615i	0.999321	+	0.0368323i	$0.0117267\pi$
$257$	16.6108	+	16.6108i	1.03615	+	1.03615i	0.0368323	+	0.999321i	$0.488273\pi$
$258$	−0.684874	−	0.372116i	−0.0426384	−	0.0231669i
$259$		0			0
$260$	3.42958	+	8.75163i	0.212693	+	0.542753i
$261$	15.4946	+	23.8902i	0.959091	+	1.47877i
$262$	2.33477	−	2.33477i	0.144243	−	0.144243i
$263$	13.8361	−	13.8361i	0.853173	−	0.853173i	−0.137350	−	0.990523i	$-0.543858\pi$
$263$	13.8361	−	13.8361i	0.853173	−	0.853173i	0.990523	+	0.137350i	$0.0438584\pi$
$264$	−8.00273	+	2.36797i	−0.492534	+	0.145738i
$265$	−7.54709	−	19.2587i	−0.463614	−	1.18305i
$266$		0			0
$267$	10.2344	−	18.8362i	0.626334	−	1.15276i
$268$	1.52052	+	1.52052i	0.0928806	+	0.0928806i
$269$	11.4632			0.698925			0.349463	−	0.936950i	$-0.386364\pi$
$269$	11.4632			0.698925			0.349463	+	0.936950i	$0.386364\pi$
$270$	3.84868	−	1.86457i	0.234223	−	0.113474i
$271$	−8.42276			−0.511646			−0.255823	−	0.966724i	$-0.582346\pi$
$271$	−8.42276			−0.511646			−0.255823	+	0.966724i	$0.582346\pi$
$272$	0.450965	+	0.450965i	0.0273438	+	0.0273438i
$273$		0			0
$274$		−	3.38102i		−	0.204255i
$275$	12.4279	−	11.5077i	0.749429	−	0.693938i
$276$	9.69800	−	2.86959i	0.583751	−	0.172729i
$277$	12.7307	−	12.7307i	0.764914	−	0.764914i	−0.212293	−	0.977206i	$-0.568093\pi$
$277$	12.7307	−	12.7307i	0.764914	−	0.764914i	0.977206	+	0.212293i	$0.0680930\pi$
$278$	−0.478665	+	0.478665i	−0.0287084	+	0.0287084i
$279$	1.50606	+	2.32211i	0.0901656	+	0.139021i
$280$		0			0
$281$			4.41251i			0.263228i	0.991301	+	0.131614i	$0.0420160\pi$
$281$			4.41251i			0.263228i	−0.991301	+	0.131614i	$0.957984\pi$
$282$	0.515994	+	0.280357i	0.0307270	+	0.0166950i
$283$	−2.07246	−	2.07246i	−0.123195	−	0.123195i	0.642821	−	0.766016i	$-0.277764\pi$
$283$	−2.07246	−	2.07246i	−0.123195	−	0.123195i	−0.766016	+	0.642821i	$0.777764\pi$
$284$	−18.2286			−1.08167
$285$	22.4583	−	17.4722i	1.33032	−	1.03497i
$286$	2.81102			0.166219
$287$		0			0
$288$	−2.51724	+	11.8087i	−0.148330	+	0.695832i
$289$		−	16.9604i		−	0.997672i
$290$	−7.27332	+	2.85026i	−0.427104	+	0.167373i
$291$	4.66575	+	15.7683i	0.273511	+	0.924352i
$292$	8.96405	−	8.96405i	0.524581	−	0.524581i
$293$	−7.37595	+	7.37595i	−0.430908	+	0.430908i	−0.888937	−	0.458029i	$-0.848555\pi$
$293$	−7.37595	+	7.37595i	−0.430908	+	0.430908i	0.458029	+	0.888937i	$0.348555\pi$
$294$		0			0
$295$	5.59552	−	12.8071i	0.325784	−	0.745660i
$296$		−	11.8997i		−	0.691656i
$297$	1.36561	+	17.5489i	0.0792410	+	1.01829i
$298$	−0.256939	−	0.256939i	−0.0148841	−	0.0148841i
$299$	−7.06050			−0.408319
$300$	−3.98332	−	15.6482i	−0.229977	−	0.903452i
$301$		0			0
$302$	−2.26711	−	2.26711i	−0.130458	−	0.130458i
$303$	−18.9513	−	10.2969i	−1.08873	−	0.591543i
$304$			23.5506i			1.35072i
$305$	−1.64063	+	3.75509i	−0.0939420	+	0.215016i
$306$	−0.184318	+	0.119544i	−0.0105367	+	0.00683386i
$307$	−11.3608	+	11.3608i	−0.648396	+	0.648396i	−0.952605	−	0.304209i	$-0.901608\pi$
$307$	−11.3608	+	11.3608i	−0.648396	+	0.648396i	0.304209	+	0.952605i	$0.401608\pi$
$308$		0			0
$309$	−22.9932	+	6.80357i	−1.30804	+	0.387042i
$310$	−0.706962	+	0.277043i	−0.0401527	+	0.0157350i
$311$		−	8.94291i		−	0.507106i	−0.967322	−	0.253553i	$-0.918401\pi$
$311$		−	8.94291i		−	0.507106i	0.967322	−	0.253553i	$-0.0815992\pi$
$312$	2.65179	−	4.88058i	0.150128	−	0.276308i
$313$	−4.52473	−	4.52473i	−0.255753	−	0.255753i	0.567571	−	0.823324i	$-0.307883\pi$
$313$	−4.52473	−	4.52473i	−0.255753	−	0.255753i	−0.823324	+	0.567571i	$0.807883\pi$
$314$	−2.73956			−0.154602
$315$		0			0
$316$	6.37130			0.358414
$317$	−1.78453	−	1.78453i	−0.100229	−	0.100229i	0.655214	−	0.755443i	$-0.272578\pi$
$317$	−1.78453	−	1.78453i	−0.100229	−	0.100229i	−0.755443	+	0.655214i	$0.772578\pi$
$318$	−2.81546	+	5.18182i	−0.157883	+	0.290582i
$319$		−	32.1529i		−	1.80022i
$320$	10.1011	+	4.41323i	0.564667	+	0.246707i
$321$	−12.2577	+	3.62699i	−0.684158	+	0.202439i
$322$		0			0
$323$	−1.03360	+	1.03360i	−0.0575108	+	0.0575108i
$324$	15.3220	+	6.84330i	0.851220	+	0.380183i
$325$	−0.433064	+	11.2644i	−0.0240221	+	0.624834i
$326$			7.36604i			0.407967i
$327$	−10.1612	−	5.52095i	−0.561917	−	0.305309i
$328$	1.40063	+	1.40063i	0.0773368	+	0.0773368i
$329$		0			0
$330$	−4.79173	−	0.598339i	−0.263776	−	0.0329375i
$331$	−3.61857			−0.198895			−0.0994474	−	0.995043i	$-0.531707\pi$
$331$	−3.61857			−0.198895			−0.0994474	+	0.995043i	$0.531707\pi$
$332$	−11.6889	−	11.6889i	−0.641512	−	0.641512i
$333$	−24.5462	−	5.23248i	−1.34512	−	0.286738i
$334$		−	9.10277i		−	0.498082i
$335$	0.940923	+	2.40106i	0.0514081	+	0.131184i
$336$		0			0
$337$	−17.0941	+	17.0941i	−0.931175	+	0.931175i	−0.997779	−	0.0666042i	$-0.978784\pi$
$337$	−17.0941	+	17.0941i	−0.931175	+	0.931175i	0.0666042	+	0.997779i	$0.478784\pi$
$338$	2.06052	−	2.06052i	0.112078	−	0.112078i
$339$	−5.72302	−	19.3414i	−0.310832	−	1.05048i
$340$	0.302653	+	0.772312i	0.0164136	+	0.0418845i
$341$		−	3.12524i		−	0.169241i
$342$	−7.93421	−	1.69133i	−0.429033	−	0.0914565i
$343$		0			0
$344$	1.73907			0.0937644
$345$	12.0355	+	1.50286i	0.647970	+	0.0809113i
$346$	−5.66162			−0.304371
$347$	5.48573	+	5.48573i	0.294489	+	0.294489i	0.838851	−	0.544361i	$-0.183228\pi$
$347$	5.48573	+	5.48573i	0.294489	+	0.294489i	−0.544361	+	0.838851i	$0.683228\pi$
$348$	−26.9340	−	14.6342i	−1.44381	−	0.784474i
$349$		−	14.8272i		−	0.793681i	−0.917888	−	0.396841i	$-0.870107\pi$
$349$		−	14.8272i		−	0.793681i	0.917888	−	0.396841i	$-0.129893\pi$
$350$		0			0
$351$	−8.90140	−	7.61605i	−0.475122	−	0.406515i
$352$	9.64036	−	9.64036i	0.513833	−	0.513833i
$353$	−7.55570	+	7.55570i	−0.402149	+	0.402149i	−0.878990	−	0.476841i	$-0.841782\pi$
$353$	−7.55570	+	7.55570i	−0.402149	+	0.402149i	0.476841	+	0.878990i	$0.341782\pi$
$354$	−3.82089	+	1.13058i	−0.203078	+	0.0600898i
$355$	−20.0324	−	8.75231i	−1.06321	−	0.464524i
$356$			23.0766i			1.22306i
$357$		0			0
$358$	4.59428	+	4.59428i	0.242815	+	0.242815i
$359$	−6.09504			−0.321684			−0.160842	−	0.986980i	$-0.551421\pi$
$359$	−6.09504			−0.321684			−0.160842	+	0.986980i	$0.551421\pi$
$360$	−5.55916	+	7.75511i	−0.292993	+	0.408730i
$361$	−34.9770			−1.84090
$362$	3.10330	+	3.10330i	0.163106	+	0.163106i
$363$	0.392893	−	0.723114i	0.0206215	−	0.0379536i
$364$		0			0
$365$	14.1551	−	5.54710i	0.740913	−	0.290348i
$366$	1.12030	−	0.331491i	0.0585590	−	0.0173273i
$367$	−3.52753	+	3.52753i	−0.184136	+	0.184136i	−0.793155	−	0.609019i	$-0.791563\pi$
$367$	−3.52753	+	3.52753i	−0.184136	+	0.184136i	0.609019	+	0.793155i	$0.291563\pi$
$368$	−7.09840	+	7.09840i	−0.370030	+	0.370030i
$369$	3.50503	−	2.27327i	0.182465	−	0.118342i
$370$	2.75663	−	6.30942i	0.143310	−	0.328011i
$371$		0			0
$372$	−2.61796	−	1.42243i	−0.135735	−	0.0737496i
$373$	−7.07089	−	7.07089i	−0.366117	−	0.366117i	0.499942	−	0.866059i	$-0.333355\pi$
$373$	−7.07089	−	7.07089i	−0.366117	−	0.366117i	−0.866059	+	0.499942i	$0.833355\pi$
$374$	0.248066			0.0128272
$375$	3.13588	−	19.1093i	0.161936	−	0.986801i
$376$	−1.31024			−0.0675704
$377$	15.1316	+	15.1316i	0.779315	+	0.779315i
$378$		0			0
$379$			21.4715i			1.10292i	0.834202	+	0.551459i	$0.185929\pi$
$379$			21.4715i			1.10292i	−0.834202	+	0.551459i	$0.814071\pi$
$380$	−12.2634	+	28.0687i	−0.629100	+	1.43989i
$381$	1.30786	+	4.42001i	0.0670036	+	0.226444i
$382$	−4.62875	+	4.62875i	−0.236828	+	0.236828i
$383$	14.6559	−	14.6559i	0.748882	−	0.748882i	−0.225388	−	0.974269i	$-0.572365\pi$
$383$	14.6559	−	14.6559i	0.748882	−	0.748882i	0.974269	+	0.225388i	$0.0723648\pi$
$384$	−4.84748	−	16.3824i	−0.247372	−	0.836012i
$385$		0			0
$386$			7.46402i			0.379909i
$387$	0.764695	−	3.58727i	0.0388716	−	0.182351i
$388$	−12.5170	−	12.5170i	−0.635457	−	0.635457i
$389$	13.6323			0.691185			0.345592	−	0.938385i	$-0.387678\pi$
$389$	13.6323			0.691185			0.345592	+	0.938385i	$0.387678\pi$
$390$	2.53663	−	1.97346i	0.128447	−	0.0999302i
$391$	−0.623074			−0.0315102
$392$		0			0
$393$	13.6528	+	7.41804i	0.688692	+	0.374190i
$394$		−	2.13769i		−	0.107695i
$395$	7.00179	+	3.05913i	0.352298	+	0.153922i
$396$	−10.3106	−	15.8974i	−0.518129	−	0.798873i
$397$	24.5632	−	24.5632i	1.23279	−	1.23279i	0.269907	−	0.962886i	$-0.413007\pi$
$397$	24.5632	−	24.5632i	1.23279	−	1.23279i	0.962886	−	0.269907i	$-0.0869929\pi$
$398$	3.49137	−	3.49137i	0.175007	−	0.175007i
$399$		0			0
$400$	10.8894	+	11.7602i	0.544472	+	0.588011i
$401$		−	15.5011i		−	0.774088i	−0.922061	−	0.387044i	$-0.873496\pi$
$401$		−	15.5011i		−	0.774088i	0.922061	−	0.387044i	$-0.126504\pi$
$402$	0.351014	−	0.646036i	0.0175070	−	0.0322214i
$403$	1.47078	+	1.47078i	0.0732647	+	0.0732647i
$404$	23.2177			1.15512
$405$	13.5524	+	14.8772i	0.673426	+	0.739255i
$406$		0			0
$407$	20.0390	+	20.0390i	0.993296	+	0.993296i
$408$	0.234015	−	0.430700i	0.0115854	−	0.0213228i
$409$			32.0414i			1.58434i	0.610298	+	0.792172i	$0.291050\pi$
$409$			32.0414i			1.58434i	−0.610298	+	0.792172i	$0.708950\pi$
$410$	0.418174	+	1.06710i	0.0206521	+	0.0527003i
$411$	15.2565	−	4.51432i	0.752547	−	0.222675i
$412$	18.2523	−	18.2523i	0.899226	−	0.899226i
$413$		0			0
$414$	−1.88167	−	2.90124i	−0.0924792	−	0.142588i
$415$	−7.23329	−	18.4580i	−0.355068	−	0.906066i
$416$			9.07374i			0.444877i
$417$	−2.79904	−	1.52081i	−0.137069	−	0.0744746i
$418$	6.47733	+	6.47733i	0.316817	+	0.316817i
$419$	5.95062			0.290707			0.145353	−	0.989380i	$-0.453568\pi$
$419$	5.95062			0.290707			0.145353	+	0.989380i	$0.453568\pi$
$420$		0			0
$421$	−10.6388			−0.518504			−0.259252	−	0.965810i	$-0.583476\pi$
$421$	−10.6388			−0.518504			−0.259252	+	0.965810i	$0.583476\pi$
$422$	2.11210	+	2.11210i	0.102816	+	0.102816i
$423$	−0.576132	+	2.70270i	−0.0280125	+	0.131410i
$424$		−	13.1580i		−	0.639007i
$425$	−0.0382170	+	0.994055i	−0.00185380	+	0.0482187i
$426$	1.76842	+	5.97650i	0.0856801	+	0.289563i
$427$		0			0
$428$	9.73032	−	9.73032i	0.470333	−	0.470333i
$429$	3.75326	+	12.6844i	0.181209	+	0.612410i
$430$	0.922084	+	0.402865i	0.0444668	+	0.0194279i
$431$		−	11.2739i		−	0.543045i	−0.962432	−	0.271523i	$-0.912473\pi$
$431$		−	11.2739i		−	0.543045i	0.962432	−	0.271523i	$-0.0875271\pi$
$432$	−16.6061	+	1.29225i	−0.798962	+	0.0621733i
$433$	−9.75098	−	9.75098i	−0.468602	−	0.468602i	0.432859	−	0.901462i	$-0.357505\pi$
$433$	−9.75098	−	9.75098i	−0.468602	−	0.468602i	−0.901462	+	0.432859i	$0.857505\pi$
$434$		0			0
$435$	−22.5728	−	29.0145i	−1.08228	−	1.39114i
$436$	12.4487			0.596185
$437$	−16.2693	−	16.2693i	−0.778265	−	0.778265i
$438$	−3.80863	−	2.06936i	−0.181983	−	0.0988779i
$439$		−	28.4375i		−	1.35725i	−0.734485	−	0.678625i	$-0.762576\pi$
$439$		−	28.4375i		−	1.35725i	0.734485	−	0.678625i	$-0.237424\pi$
$440$	10.0315	−	3.93113i	0.478233	−	0.187409i
$441$		0			0
$442$	−0.116743	+	0.116743i	−0.00555290	+	0.00555290i
$443$	−19.2121	+	19.2121i	−0.912796	+	0.912796i	−0.996491	−	0.0836955i	$-0.973328\pi$
$443$	−19.2121	+	19.2121i	−0.912796	+	0.912796i	0.0836955	+	0.996491i	$0.473328\pi$
$444$	25.9069	−	7.66573i	1.22949	−	0.363799i
$445$	−11.0801	+	25.3602i	−0.525245	+	1.20219i
$446$			6.00850i			0.284511i
$447$	0.816347	−	1.50247i	0.0386119	−	0.0710646i
$448$		0			0
$449$	−2.40628			−0.113559			−0.0567796	−	0.998387i	$-0.518083\pi$
$449$	−2.40628			−0.113559			−0.0567796	+	0.998387i	$0.518083\pi$
$450$	−4.74407	+	2.82408i	−0.223638	+	0.133128i
$451$	−4.71729			−0.222129
$452$	15.3534	+	15.3534i	0.722166	+	0.722166i
$453$	7.20307	−	13.2572i	0.338430	−	0.622875i
$454$			3.66752i			0.172125i
$455$		0			0
$456$	17.3566	−	5.13572i	0.812796	−	0.240502i
$457$	6.21588	−	6.21588i	0.290767	−	0.290767i	−0.546617	−	0.837383i	$-0.684084\pi$
$457$	6.21588	−	6.21588i	0.290767	−	0.290767i	0.837383	+	0.546617i	$0.184084\pi$
$458$	1.24957	−	1.24957i	0.0583884	−	0.0583884i
$459$	−0.785529	−	0.672100i	−0.0366654	−	0.0313709i
$460$	−12.1565	+	4.76389i	−0.566802	+	0.222118i
$461$		−	35.4227i		−	1.64980i	−0.565278	−	0.824900i	$-0.691231\pi$
$461$		−	35.4227i		−	1.64980i	0.565278	−	0.824900i	$-0.308769\pi$
$462$		0			0
$463$	−20.0869	−	20.0869i	−0.933519	−	0.933519i	0.0644045	−	0.997924i	$-0.479485\pi$
$463$	−20.0869	−	20.0869i	−0.933519	−	0.933519i	−0.997924	+	0.0644045i	$0.979485\pi$
$464$	30.4256			1.41247
$465$	−2.19406	−	2.82019i	−0.101747	−	0.130783i
$466$	7.43265			0.344311
$467$	5.80567	+	5.80567i	0.268654	+	0.268654i	0.828558	−	0.559903i	$-0.189162\pi$
$467$	5.80567	+	5.80567i	0.268654	+	0.268654i	−0.559903	+	0.828558i	$0.689162\pi$
$468$	12.3338	+	2.62918i	0.570130	+	0.121534i
$469$		0			0
$470$	−0.694711	−	0.303524i	−0.0320446	−	0.0140005i
$471$	−3.65785	−	12.3620i	−0.168545	−	0.569610i
$472$	6.28653	−	6.28653i	0.289361	−	0.289361i
$473$	−2.92858	+	2.92858i	−0.134656	+	0.134656i
$474$	−0.618102	−	2.08892i	−0.0283904	−	0.0959475i
$475$	−26.9540	+	24.9582i	−1.23673	+	1.14516i
$476$		0			0
$477$	−27.1416	−	5.78575i	−1.24273	−	0.264911i
$478$	3.34746	+	3.34746i	0.153109	+	0.153109i
$479$	−40.3829			−1.84514			−0.922571	−	0.385828i	$-0.873916\pi$
$479$	−40.3829			−1.84514			−0.922571	+	0.385828i	$0.873916\pi$
$480$	1.93139	−	15.4673i	0.0881554	−	0.705984i
$481$	−18.8612			−0.859997
$482$	4.21252	+	4.21252i	0.191875	+	0.191875i
$483$		0			0
$484$			0.885900i			0.0402682i
$485$	−7.74575	−	19.7657i	−0.351716	−	0.897513i
$486$	0.757238	−	5.68742i	0.0343490	−	0.257987i
$487$	19.7983	−	19.7983i	0.897147	−	0.897147i	−0.0980363	−	0.995183i	$-0.531256\pi$
$487$	19.7983	−	19.7983i	0.897147	−	0.897147i	0.995183	+	0.0980363i	$0.0312561\pi$
$488$	−1.84323	+	1.84323i	−0.0834393	+	0.0834393i
$489$	−33.2385	+	9.83510i	−1.50310	+	0.444759i
$490$		0			0
$491$			36.6924i			1.65590i	0.560798	+	0.827952i	$0.310494\pi$
$491$			36.6924i			1.65590i	−0.560798	+	0.827952i	$0.689506\pi$
$492$	−2.14704	+	3.95159i	−0.0967960	+	0.178152i
$493$	1.33533	+	1.33533i	0.0601402	+	0.0601402i
$494$	−6.09662			−0.274300
$495$	−3.69796	−	22.4211i	−0.166211	−	1.00775i
$496$	2.95735			0.132789
$497$		0			0
$498$	−2.69840	+	4.96636i	−0.120918	+	0.222548i
$499$		−	7.62548i		−	0.341363i	−0.985326	−	0.170682i	$-0.945403\pi$
$499$		−	7.62548i		−	0.341363i	0.985326	−	0.170682i	$-0.0545970\pi$
$500$	6.85470	+	19.6868i	0.306551	+	0.880421i
$501$	41.0753	−	12.1540i	1.83511	−	0.543000i
$502$	−2.08955	+	2.08955i	−0.0932614	+	0.0932614i
$503$	15.7533	−	15.7533i	0.702406	−	0.702406i	−0.262521	−	0.964926i	$-0.584554\pi$
$503$	15.7533	−	15.7533i	0.702406	−	0.702406i	0.964926	+	0.262521i	$0.0845538\pi$
$504$		0			0
$505$	25.5152	+	11.1478i	1.13541	+	0.496070i
$506$			3.90468i			0.173584i
$507$	12.0491	+	6.54670i	0.535119	+	0.290749i
$508$	−3.50866	−	3.50866i	−0.155672	−	0.155672i
$509$	−14.4091			−0.638673			−0.319336	−	0.947641i	$-0.603460\pi$
$509$	−14.4091			−0.638673			−0.319336	+	0.947641i	$0.603460\pi$
$510$	0.223852	−	0.174154i	0.00991235	−	0.00771166i
$511$		0			0
$512$	15.5706	+	15.5706i	0.688130	+	0.688130i
$513$	−2.96178	−	38.0606i	−0.130766	−	1.68042i
$514$			8.64637i			0.381375i
$515$	28.8222	−	11.2948i	1.27006	−	0.497709i
$516$	1.12030	+	3.78614i	0.0493185	+	0.166676i
$517$	2.20643	−	2.20643i	0.0970387	−	0.0970387i
$518$		0			0
$519$	−7.55938	−	25.5475i	−0.331820	−	1.12141i
$520$	−2.87091	+	6.57099i	−0.125898	+	0.288157i
$521$		−	25.3850i		−	1.11214i	−0.831136	−	0.556069i	$-0.812309\pi$
$521$		−	25.3850i		−	1.11214i	0.831136	−	0.556069i	$-0.187691\pi$
$522$	−2.18507	+	10.2504i	−0.0956378	+	0.448648i
$523$	16.0464	+	16.0464i	0.701661	+	0.701661i	0.964767	−	0.263106i	$-0.0847470\pi$
$523$	16.0464	+	16.0464i	0.701661	+	0.701661i	−0.263106	+	0.964767i	$0.584747\pi$
$524$	−16.7263			−0.730692
$525$		0			0
$526$	7.20208			0.314026
$527$	0.129793	+	0.129793i	0.00565387	+	0.00565387i
$528$	16.5259	+	8.97912i	0.719199	+	0.390766i
$529$			13.1925i			0.573588i
$530$	3.04811	−	6.97657i	0.132401	−	0.303043i
$531$	−10.2033	−	15.7318i	−0.442785	−	0.682704i
$532$		0			0
$533$	2.22002	−	2.22002i	0.0961595	−	0.0961595i
$534$	7.56601	−	2.23874i	0.327413	−	0.0968799i
$535$	15.3652	−	6.02128i	0.664294	−	0.260323i
$536$			1.64045i			0.0708567i
$537$	−14.5970	+	26.8655i	−0.629905	+	1.15933i
$538$	2.98346	+	2.98346i	0.128626	+	0.128626i
$539$		0			0
$540$	−20.4649	−	7.10708i	−0.880668	−	0.305840i
$541$	−26.9427			−1.15836			−0.579178	−	0.815201i	$-0.696626\pi$
$541$	−26.9427			−1.15836			−0.579178	+	0.815201i	$0.696626\pi$
$542$	−2.19213	−	2.19213i	−0.0941602	−	0.0941602i
$543$	−9.85981	+	18.1468i	−0.423125	+	0.778756i
$544$			0.800738i			0.0343313i
$545$	13.6806	+	5.97716i	0.586013	+	0.256033i
$546$		0			0
$547$	17.9286	−	17.9286i	0.766572	−	0.766572i	−0.210929	−	0.977501i	$-0.567649\pi$
$547$	17.9286	−	17.9286i	0.766572	−	0.766572i	0.977501	+	0.210929i	$0.0676489\pi$
$548$	−12.1108	+	12.1108i	−0.517348	+	0.517348i
$549$	2.99164	+	4.61263i	0.127680	+	0.196862i
$550$	6.22954	+	0.239498i	0.265629	+	0.0102122i
$551$			69.7343i			2.97078i
$552$	6.77942	+	3.68350i	0.288551	+	0.156780i
$553$		0			0
$554$	6.62667			0.281540
$555$	32.1513	+	4.01470i	1.36475	+	0.170414i
$556$	3.42915			0.145428
$557$	−5.15944	−	5.15944i	−0.218613	−	0.218613i	0.589301	−	0.807914i	$-0.299403\pi$
$557$	−5.15944	−	5.15944i	−0.218613	−	0.218613i	−0.807914	+	0.589301i	$0.799403\pi$
$558$	−0.212387	+	0.996333i	−0.00899106	+	0.0421781i
$559$		−	2.75645i		−	0.116585i
$560$		0			0
$561$	0.331217	+	1.11937i	0.0139840	+	0.0472600i
$562$	−1.14841	+	1.14841i	−0.0484429	+	0.0484429i
$563$	23.2548	−	23.2548i	0.980072	−	0.980072i	−0.0197332	−	0.999805i	$-0.506282\pi$
$563$	23.2548	−	23.2548i	0.980072	−	0.980072i	0.999805	+	0.0197332i	$0.00628169\pi$
$564$	−0.844049	−	2.85253i	−0.0355409	−	0.120113i
$565$	9.50096	+	24.2446i	0.399708	+	1.01998i
$566$		−	1.07877i		−	0.0453442i
$567$		0			0
$568$	−9.83316	−	9.83316i	−0.412590	−	0.412590i
$569$	−45.1914			−1.89452			−0.947260	−	0.320466i	$-0.896161\pi$
$569$	−45.1914			−1.89452			−0.947260	+	0.320466i	$0.896161\pi$
$570$	10.3925	+	1.29770i	0.435292	+	0.0543545i
$571$	15.2468			0.638059			0.319029	−	0.947745i	$-0.396643\pi$
$571$	15.2468			0.638059			0.319029	+	0.947745i	$0.396643\pi$
$572$	−10.0691	−	10.0691i	−0.421009	−	0.421009i
$573$	−27.0671	−	14.7065i	−1.13074	−	0.614372i
$574$		0			0
$575$	−15.6469	−	0.601553i	−0.652520	−	0.0250865i
$576$	12.4078	−	8.04741i	0.516993	−	0.335309i
$577$	6.12177	−	6.12177i	0.254853	−	0.254853i	−0.568104	−	0.822957i	$-0.692323\pi$
$577$	6.12177	−	6.12177i	0.254853	−	0.254853i	0.822957	+	0.568104i	$0.192323\pi$
$578$	4.41417	−	4.41417i	0.183605	−	0.183605i
$579$	−33.6806	+	9.96593i	−1.39972	+	0.414170i
$580$	36.2627	+	15.8434i	1.50573	+	0.657862i
$581$		0			0
$582$	−2.88958	+	5.31822i	−0.119777	+	0.220447i
$583$	22.1579	+	22.1579i	0.917686	+	0.917686i
$584$	9.67107			0.400192
$585$	12.2920	+	8.81134i	0.508210	+	0.364304i
$586$	−3.83938			−0.158603
$587$	3.77086	+	3.77086i	0.155640	+	0.155640i	0.780632	−	0.624992i	$-0.214898\pi$
$587$	3.77086	+	3.77086i	0.155640	+	0.155640i	−0.624992	+	0.780632i	$0.714898\pi$
$588$		0			0
$589$			6.77812i			0.279288i
$590$	4.78953	−	1.87692i	0.197182	−	0.0772714i
$591$	9.64610	−	2.85423i	0.396787	−	0.117407i
$592$	−18.9624	+	18.9624i	−0.779352	+	0.779352i
$593$	8.38017	−	8.38017i	0.344132	−	0.344132i	−0.513786	−	0.857918i	$-0.671758\pi$
$593$	8.38017	−	8.38017i	0.344132	−	0.344132i	0.857918	+	0.513786i	$0.171758\pi$
$594$	−4.21191	+	4.92275i	−0.172817	+	0.201983i
$595$		0			0
$596$			1.84071i			0.0753985i
$597$	20.4161	+	11.0928i	0.835577	+	0.453998i
$598$	−1.83759	−	1.83759i	−0.0751446	−	0.0751446i
$599$	−6.75588			−0.276038			−0.138019	−	0.990430i	$-0.544073\pi$
$599$	−6.75588			−0.276038			−0.138019	+	0.990430i	$0.544073\pi$
$600$	6.29249	−	10.5900i	0.256890	−	0.432334i
$601$	−21.2564			−0.867068			−0.433534	−	0.901137i	$-0.642734\pi$
$601$	−21.2564			−0.867068			−0.433534	+	0.901137i	$0.642734\pi$
$602$		0			0
$603$	3.38385	+	0.721331i	0.137801	+	0.0293749i
$604$			16.2416i			0.660861i
$605$	−0.425358	+	0.973568i	−0.0172933	+	0.0395812i
$606$	−2.25243	−	7.61225i	−0.0914986	−	0.309227i
$607$	−2.72491	+	2.72491i	−0.110601	+	0.110601i	−0.760241	−	0.649641i	$-0.774919\pi$
$607$	−2.72491	+	2.72491i	−0.110601	+	0.110601i	0.649641	+	0.760241i	$0.274919\pi$
$608$	−20.9083	+	20.9083i	−0.847944	+	0.847944i
$609$		0			0
$610$	−1.40431	+	0.550318i	−0.0568588	+	0.0222817i
$611$			2.07675i			0.0840162i
$612$	1.08843	+	0.232020i	0.0439972	+	0.00937884i
$613$	15.6232	+	15.6232i	0.631017	+	0.631017i	0.948323	−	0.317306i	$-0.102778\pi$
$613$	15.6232	+	15.6232i	0.631017	+	0.631017i	−0.317306	+	0.948323i	$0.602778\pi$
$614$	−5.91361			−0.238654
$615$	−4.25683	+	3.31175i	−0.171652	+	0.133543i
$616$		0			0
$617$	5.47009	+	5.47009i	0.220218	+	0.220218i	0.808590	−	0.588373i	$-0.200231\pi$
$617$	5.47009	+	5.47009i	0.220218	+	0.220218i	−0.588373	+	0.808590i	$0.700231\pi$
$618$	−7.75500	−	4.21357i	−0.311952	−	0.169494i
$619$		−	42.9951i		−	1.72812i	−0.503389	−	0.864060i	$-0.667914\pi$
$619$		−	42.9951i		−	1.72812i	0.503389	−	0.864060i	$-0.332086\pi$
$620$	3.52471	+	1.53997i	0.141556	+	0.0618466i
$621$	10.5792	−	12.3646i	0.424527	−	0.496174i
$622$	2.32751	−	2.32751i	0.0933247	−	0.0933247i
$623$		0			0
$624$	−12.0030	+	3.55162i	−0.480504	+	0.142179i
$625$	−1.91944	+	24.9262i	−0.0767776	+	0.997048i
$626$		−	2.35524i		−	0.0941344i
$627$	−20.5798	+	37.8768i	−0.821878	+	1.51265i
$628$	9.81311	+	9.81311i	0.391586	+	0.391586i
$629$	−1.66446			−0.0663664
$630$		0			0
$631$	−38.0091			−1.51312			−0.756560	−	0.653925i	$-0.773121\pi$
$631$	−38.0091			−1.51312			−0.756560	+	0.653925i	$0.773121\pi$
$632$	3.43691	+	3.43691i	0.136713	+	0.136713i
$633$	−6.71057	+	12.3507i	−0.266721	+	0.490897i
$634$		−	0.928896i		−	0.0368912i
$635$	−2.17121	−	5.54053i	−0.0861620	−	0.219869i
$636$	28.6463	−	8.47629i	1.13590	−	0.336107i
$637$		0			0
$638$	8.36823	−	8.36823i	0.331301	−	0.331301i
$639$	−24.6072	+	15.9596i	−0.973445	+	0.631352i
$640$	8.04745	+	20.5355i	0.318103	+	0.811739i
$641$		−	30.8009i		−	1.21656i	−0.793721	−	0.608282i	$-0.791859\pi$
$641$		−	30.8009i		−	1.21656i	0.793721	−	0.608282i	$-0.208141\pi$
$642$	−4.13420	−	2.24626i	−0.163164	−	0.0886527i
$643$	6.17366	+	6.17366i	0.243465	+	0.243465i	0.818282	−	0.574817i	$-0.194927\pi$
$643$	6.17366	+	6.17366i	0.243465	+	0.243465i	−0.574817	+	0.818282i	$0.694927\pi$
$644$		0			0
$645$	−0.586724	+	4.69871i	−0.0231022	+	0.185012i
$646$	−0.538014			−0.0211679
$647$	23.4296	+	23.4296i	0.921112	+	0.921112i	0.997108	−	0.0759964i	$-0.0242137\pi$
$647$	23.4296	+	23.4296i	0.921112	+	0.921112i	−0.0759964	+	0.997108i	$0.524214\pi$
$648$	4.57370	+	11.9568i	0.179672	+	0.469706i
$649$			21.1729i			0.831110i
$650$	−3.04441	+	2.81899i	−0.119412	+	0.110570i
$651$		0			0
$652$	26.3851	−	26.3851i	1.03332	−	1.03332i
$653$	17.1928	−	17.1928i	0.672805	−	0.672805i	−0.285557	−	0.958362i	$-0.592179\pi$
$653$	17.1928	−	17.1928i	0.672805	−	0.672805i	0.958362	+	0.285557i	$0.0921786\pi$
$654$	−1.20769	−	4.08150i	−0.0472246	−	0.159599i
$655$	−18.3815	−	8.03100i	−0.718225	−	0.313797i
$656$		−	4.46386i		−	0.174285i
$657$	4.25252	−	19.9490i	0.165906	−	0.778286i
$658$		0			0
$659$	0.0375362			0.00146220			0.000731101	−	1.00000i	$-0.499767\pi$
$659$	0.0375362			0.00146220			0.000731101		1.00000i	$0.499767\pi$
$660$	15.0207	+	19.3072i	0.584682	+	0.751533i
$661$	−19.6937			−0.765995			−0.382998	−	0.923749i	$-0.625108\pi$
$661$	−19.6937			−0.765995			−0.382998	+	0.923749i	$0.625108\pi$
$662$	−0.941782	−	0.941782i	−0.0366034	−	0.0366034i
$663$	−0.682666	−	0.370916i	−0.0265125	−	0.0144052i
$664$		−	12.6109i		−	0.489396i
$665$		0			0
$666$	−5.02664	−	7.75029i	−0.194778	−	0.300318i
$667$	−21.0187	+	21.0187i	−0.813846	+	0.813846i
$668$	−32.6061	+	32.6061i	−1.26157	+	1.26157i
$669$	−27.1127	+	8.02252i	−1.04824	+	0.310169i
$670$	−0.380019	+	0.869794i	−0.0146814	+	0.0336031i
$671$		−	6.20798i		−	0.239656i
$672$		0			0
$673$	−4.33276	−	4.33276i	−0.167016	−	0.167016i	0.618651	−	0.785666i	$-0.287680\pi$
$673$	−4.33276	−	4.33276i	−0.167016	−	0.167016i	−0.785666	+	0.618651i	$0.787680\pi$
$674$	−8.89793			−0.342736
$675$	−19.0776	−	17.6364i	−0.734298	−	0.678827i
$676$	−14.7616			−0.567753
$677$	−3.64637	−	3.64637i	−0.140142	−	0.140142i	0.633556	−	0.773697i	$-0.281595\pi$
$677$	−3.64637	−	3.64637i	−0.140142	−	0.140142i	−0.773697	+	0.633556i	$0.781595\pi$
$678$	3.54436	−	6.52335i	0.136120	−	0.250528i
$679$		0			0
$680$	−0.253352	+	0.579876i	−0.00971559	+	0.0222372i
$681$	−16.5493	+	4.89685i	−0.634170	+	0.187648i
$682$	0.813386	−	0.813386i	0.0311462	−	0.0311462i
$683$	−33.7536	+	33.7536i	−1.29155	+	1.29155i	−0.357718	+	0.933830i	$0.616445\pi$
$683$	−33.7536	+	33.7536i	−1.29155	+	1.29155i	−0.933830	+	0.357718i	$0.883555\pi$
$684$	22.3620	+	34.4787i	0.855033	+	1.31833i
$685$	−19.1242	+	7.49436i	−0.730697	+	0.286345i
$686$		0			0
$687$	7.30696	+	3.97013i	0.278778	+	0.151470i
$688$	−2.77125	−	2.77125i	−0.105653	−	0.105653i
$689$	−20.8555			−0.794533
$690$	2.74126	+	3.52354i	0.104358	+	0.134139i
$691$	12.2184			0.464812			0.232406	−	0.972619i	$-0.425340\pi$
$691$	12.2184			0.464812			0.232406	+	0.972619i	$0.425340\pi$
$692$	20.2799	+	20.2799i	0.770928	+	0.770928i
$693$		0			0
$694$			2.85547i			0.108392i
$695$	3.76850	+	1.64648i	0.142947	+	0.0624546i
$696$	−6.63497	−	22.4234i	−0.251498	−	0.849956i
$697$	0.195912	−	0.195912i	0.00742068	−	0.00742068i
$698$	3.85897	−	3.85897i	0.146064	−	0.146064i
$699$	9.92404	+	33.5391i	0.375362	+	1.26856i
$700$		0			0
$701$		−	21.7907i		−	0.823024i	−0.911404	−	0.411512i	$-0.865001\pi$
$701$		−	21.7907i		−	0.823024i	0.911404	−	0.411512i	$-0.134999\pi$
$702$	−0.334529	−	4.29889i	−0.0126260	−	0.162251i
$703$	−43.4612	−	43.4612i	−1.63917	−	1.63917i
$704$	−16.6992			−0.629377
$705$	0.442045	−	3.54007i	0.0166484	−	0.133327i
$706$	−3.93294			−0.148018
$707$		0			0
$708$	17.7362	+	9.63670i	0.666567	+	0.362169i
$709$		−	14.1622i		−	0.531874i	−0.963990	−	0.265937i	$-0.914319\pi$
$709$		−	14.1622i		−	0.531874i	0.963990	−	0.265937i	$-0.0856814\pi$
$710$	−2.93580	−	7.49161i	−0.110179	−	0.281155i
$711$	8.60077	−	5.57825i	0.322554	−	0.209201i
$712$	−12.4484	+	12.4484i	−0.466523	+	0.466523i
$713$	−2.04300	+	2.04300i	−0.0765110	+	0.0765110i
$714$		0			0
$715$	−6.23090	−	15.9001i	−0.233023	−	0.594629i
$716$		−	32.9134i		−	1.23003i
$717$	−10.6355	+	19.5746i	−0.397192	+	0.731026i
$718$	−1.58632	−	1.58632i	−0.0592008	−	0.0592008i
$719$	39.3153			1.46621			0.733106	−	0.680114i	$-0.238070\pi$
$719$	39.3153			1.46621			0.733106	+	0.680114i	$0.238070\pi$
$720$	21.2166	−	3.49929i	0.790695	−	0.130411i
$721$		0			0
$722$	−9.10324	−	9.10324i	−0.338787	−	0.338787i
$723$	−13.3840	+	24.6331i	−0.497757	+	0.916115i
$724$		−	22.2320i		−	0.826248i
$725$	32.2441	+	34.8225i	1.19752	+	1.29328i
$726$	0.290455	−	0.0859443i	0.0107798	−	0.00318969i
$727$	−10.0141	+	10.0141i	−0.371403	+	0.371403i	−0.867988	−	0.496585i	$-0.834587\pi$
$727$	−10.0141	+	10.0141i	−0.371403	+	0.371403i	0.496585	+	0.867988i	$0.334587\pi$
$728$		0			0
$729$	26.6750	−	4.17686i	0.987962	−	0.154699i
$730$	5.12777	+	2.24036i	0.189787	+	0.0829193i
$731$		−	0.243251i		−	0.00899695i
$732$	−5.20032	−	2.82551i	−0.192209	−	0.104434i
$733$	30.5737	+	30.5737i	1.12926	+	1.12926i	0.990297	+	0.138967i	$0.0443783\pi$
$733$	30.5737	+	30.5737i	1.12926	+	1.12926i	0.138967	+	0.990297i	$0.455622\pi$
$734$	−1.83618			−0.0677745
$735$		0			0
$736$	−12.6040			−0.464589
$737$	−2.76250	−	2.76250i	−0.101758	−	0.101758i
$738$	1.50388	+	0.320580i	0.0553586	+	0.0118007i
$739$			16.1095i			0.592598i	0.955095	+	0.296299i	$0.0957525\pi$
$739$			16.1095i			0.592598i	−0.955095	+	0.296299i	$0.904247\pi$
$740$	−32.4746	+	12.7261i	−1.19379	+	0.467821i
$741$	−8.14019	−	27.5104i	−0.299037	−	1.01062i
$742$		0			0
$743$	23.1679	−	23.1679i	0.849946	−	0.849946i	−0.140180	−	0.990126i	$-0.544768\pi$
$743$	23.1679	−	23.1679i	0.849946	−	0.849946i	0.990126	+	0.140180i	$0.0447681\pi$
$744$	−0.644914	−	2.17954i	−0.0236437	−	0.0799057i
$745$	−0.883803	+	2.02286i	−0.0323800	+	0.0741120i
$746$		−	3.68059i		−	0.134756i
$747$	−26.0131	−	5.54518i	−0.951770	−	0.202888i
$748$	−0.888574	−	0.888574i	−0.0324895	−	0.0324895i
$749$		0			0
$750$	5.78961	−	4.15730i	0.211407	−	0.151803i
$751$	28.7540			1.04925			0.524625	−	0.851334i	$-0.324206\pi$
$751$	28.7540			1.04925			0.524625	+	0.851334i	$0.324206\pi$
$752$	2.08789	+	2.08789i	0.0761377	+	0.0761377i
$753$	−12.2189	−	6.63894i	−0.445280	−	0.241936i
$754$			7.87638i			0.286841i
$755$	−7.79827	+	17.8488i	−0.283808	+	0.649585i
$756$		0			0
$757$	−1.29026	+	1.29026i	−0.0468952	+	0.0468952i	−0.730166	−	0.683270i	$-0.760557\pi$
$757$	−1.29026	+	1.29026i	−0.0468952	+	0.0468952i	0.683270	+	0.730166i	$0.260557\pi$
$758$	−5.58825	+	5.58825i	−0.202974	+	0.202974i
$759$	−17.6195	+	5.21351i	−0.639546	+	0.189238i
$760$	−21.7566	+	8.52596i	−0.789196	+	0.309269i
$761$		−	33.9969i		−	1.23239i	−0.787596	−	0.616193i	$-0.788674\pi$
$761$		−	33.9969i		−	1.23239i	0.787596	−	0.616193i	$-0.211326\pi$
$762$	−0.809978	+	1.49075i	−0.0293424	+	0.0540043i
$763$		0			0
$764$	33.1604			1.19970
$765$	1.08474	+	0.777582i	0.0392188	+	0.0281135i
$766$	7.62879			0.275639
$767$	−9.96424	−	9.96424i	−0.359788	−	0.359788i
$768$	−5.15065	+	9.47970i	−0.185858	+	0.342069i
$769$			21.4206i			0.772448i	0.922405	+	0.386224i	$0.126221\pi$
$769$			21.4206i			0.772448i	−0.922405	+	0.386224i	$0.873779\pi$
$770$		0			0
$771$	−39.0158	+	11.5446i	−1.40512	+	0.415768i
$772$	26.7361	−	26.7361i	0.962254	−	0.962254i
$773$	−9.50533	+	9.50533i	−0.341883	+	0.341883i	−0.857075	−	0.515192i	$-0.827721\pi$
$773$	−9.50533	+	9.50533i	−0.341883	+	0.341883i	0.515192	+	0.857075i	$0.327721\pi$
$774$	1.13266	−	0.734614i	0.0407125	−	0.0264051i
$775$	3.13410	+	3.38472i	0.112580	+	0.121583i
$776$		−	13.5043i		−	0.484777i
$777$		0			0
$778$	3.54798	+	3.54798i	0.127201	+	0.127201i
$779$	10.2310			0.366564
$780$	−16.1552	−	2.01728i	−0.578448	−	0.0722302i
$781$	33.1179			1.18505
$782$	−0.162163	−	0.162163i	−0.00579895	−	0.00579895i
$783$	−49.1714	+	3.82640i	−1.75724	+	0.136745i
$784$		0			0
$785$	6.07251	+	15.4959i	0.216737	+	0.553072i
$786$	1.62268	+	5.48396i	0.0578789	+	0.195606i
$787$	−5.70807	+	5.70807i	−0.203471	+	0.203471i	−0.801485	−	0.598015i	$-0.795956\pi$
$787$	−5.70807	+	5.70807i	−0.203471	+	0.203471i	0.598015	+	0.801485i	$0.295956\pi$
$788$	−7.65720	+	7.65720i	−0.272776	+	0.272776i
$789$	9.61618	+	32.4986i	0.342345	+	1.15698i
$790$	1.02613	+	2.61849i	0.0365081	+	0.0931616i
$791$		0			0
$792$	3.01369	−	14.1376i	0.107087	−	0.502356i
$793$	2.92155	+	2.92155i	0.103747	+	0.103747i
$794$	12.7858			0.453752
$795$	35.5509	+	4.43920i	1.26086	+	0.157442i
$796$	−25.0122			−0.886534
$797$	7.78096	+	7.78096i	0.275616	+	0.275616i	0.831356	−	0.555740i	$-0.187565\pi$
$797$	7.78096	+	7.78096i	0.275616	+	0.275616i	−0.555740	+	0.831356i	$0.687565\pi$
$798$		0			0
$799$			0.183268i			0.00648357i
$800$	−0.773080	+	20.1084i	−0.0273325	+	0.710941i
$801$	20.2042	+	31.1517i	0.713881	+	1.10069i
$802$	4.03437	−	4.03437i	0.142458	−	0.142458i
$803$	−16.2860	+	16.2860i	−0.574721	+	0.574721i
$804$	−3.57144	+	1.05677i	−0.125955	+	0.0372694i
$805$		0			0
$806$			0.765579i			0.0269664i
$807$	−9.47905	+	17.4460i	−0.333678	+	0.614130i
$808$	12.5245	+	12.5245i	0.440609	+	0.440609i
$809$	−28.7871			−1.01210			−0.506051	−	0.862504i	$-0.668895\pi$
$809$	−28.7871			−1.01210			−0.506051	+	0.862504i	$0.668895\pi$
$810$	−0.344791	+	7.39919i	−0.0121147	+	0.259981i
$811$	9.83136			0.345226			0.172613	−	0.984990i	$-0.444779\pi$
$811$	9.83136			0.345226			0.172613	+	0.984990i	$0.444779\pi$
$812$		0			0
$813$	6.96485	−	12.8187i	0.244268	−	0.449572i
$814$			10.4308i			0.365600i
$815$	41.6648	−	16.3276i	1.45945	−	0.571929i
$816$	−1.05924	+	0.313423i	−0.0370807	+	0.0109720i
$817$	6.35159	−	6.35159i	0.222214	−	0.222214i
$818$	−8.33920	+	8.33920i	−0.291573	+	0.291573i
$819$		0			0
$820$	2.32445	−	5.32025i	0.0811734	−	0.185791i
$821$			34.5427i			1.20555i	0.797911	+	0.602775i	$0.205938\pi$
$821$			34.5427i			1.20555i	−0.797911	+	0.602775i	$0.794062\pi$
$822$	5.14561	+	2.79579i	0.179474	+	0.0975145i
$823$	−11.9459	−	11.9459i	−0.416409	−	0.416409i	0.467555	−	0.883964i	$-0.345135\pi$
$823$	−11.9459	−	11.9459i	−0.416409	−	0.416409i	−0.883964	+	0.467555i	$0.845135\pi$
$824$	19.6919			0.686001
$825$	7.23695	+	28.4299i	0.251958	+	0.989804i
$826$		0			0
$827$	−20.8624	−	20.8624i	−0.725457	−	0.725457i	0.244254	−	0.969711i	$-0.421457\pi$
$827$	−20.8624	−	20.8624i	−0.725457	−	0.725457i	−0.969711	+	0.244254i	$0.921457\pi$
$828$	−3.65210	+	17.1324i	−0.126919	+	0.595392i
$829$			34.6491i			1.20341i	0.798717	+	0.601706i	$0.205512\pi$
$829$			34.6491i			1.20341i	−0.798717	+	0.601706i	$0.794488\pi$
$830$	2.92137	−	6.68649i	0.101402	−	0.232091i
$831$	8.84790	+	29.9022i	0.306930	+	1.03729i
$832$	7.85887	−	7.85887i	0.272457	−	0.272457i
$833$		0			0
$834$	−0.332674	−	1.12430i	−0.0115196	−	0.0389313i
$835$	−51.4884	+	20.1772i	−1.78183	+	0.698261i
$836$		−	46.4036i		−	1.60490i
$837$	−4.77943	+	0.371924i	−0.165201	+	0.0128556i
$838$	1.54873	+	1.54873i	0.0534999	+	0.0534999i
$839$	−10.9282			−0.377283			−0.188642	−	0.982046i	$-0.560408\pi$
$839$	−10.9282			−0.377283			−0.188642	+	0.982046i	$0.560408\pi$
$840$		0			0
$841$	61.0915			2.10660
$842$	−2.76889	−	2.76889i	−0.0954223	−	0.0954223i
$843$	−6.71546	−	3.64874i	−0.231293	−	0.125669i
$844$		−	15.1311i		−	0.520834i
$845$	−16.2224	−	7.08766i	−0.558066	−	0.243823i
$846$	−0.853360	+	0.553468i	−0.0293391	+	0.0190286i
$847$		0			0
$848$	−20.9675	+	20.9675i	−0.720027	+	0.720027i
$849$	4.86785	−	1.44037i	0.167064	−	0.0494335i
$850$	−0.268662	+	0.248769i	−0.00921505	+	0.00853272i
$851$		−	26.1994i		−	0.898102i
$852$	15.0734	−	27.7423i	0.516405	−	0.950436i
$853$	8.08267	+	8.08267i	0.276745	+	0.276745i	0.831808	−	0.555063i	$-0.187306\pi$
$853$	8.08267	+	8.08267i	0.276745	+	0.276745i	−0.555063	+	0.831808i	$0.687306\pi$
$854$		0			0
$855$	8.02025	+	48.6276i	0.274287	+	1.66303i
$856$	10.4978			0.358807
$857$	14.3191	+	14.3191i	0.489131	+	0.489131i	0.908032	−	0.418901i	$-0.137585\pi$
$857$	14.3191	+	14.3191i	0.489131	+	0.489131i	−0.418901	+	0.908032i	$0.637585\pi$
$858$	−2.32446	+	4.27813i	−0.0793557	+	0.146053i
$859$		−	25.0614i		−	0.855084i	−0.903995	−	0.427542i	$-0.859380\pi$
$859$		−	25.0614i		−	0.855084i	0.903995	−	0.427542i	$-0.140620\pi$
$860$	−1.85984	−	4.74597i	−0.0634202	−	0.161836i
$861$		0			0
$862$	2.93418	−	2.93418i	0.0999387	−	0.0999387i
$863$	32.8159	−	32.8159i	1.11707	−	1.11707i	0.124896	−	0.992170i	$-0.460140\pi$
$863$	32.8159	−	32.8159i	1.11707	−	1.11707i	0.992170	−	0.124896i	$-0.0398598\pi$
$864$	−15.8902	−	13.5957i	−0.540597	−	0.462535i
$865$	12.5496	+	32.0241i	0.426698	+	1.08885i
$866$		−	5.07564i		−	0.172477i
$867$	25.8123	+	14.0247i	0.876631	+	0.476304i
$868$		0			0
$869$	−11.5755			−0.392671
$870$	1.67653	−	13.4263i	0.0568395	−	0.455194i
$871$	2.60014			0.0881023
$872$	6.71530	+	6.71530i	0.227409	+	0.227409i
$873$	−27.8561	−	5.93805i	−0.942785	−	0.200972i
$874$		−	8.46858i		−	0.286454i
$875$		0			0
$876$	6.23006	+	21.0550i	0.210494	+	0.711381i
$877$	15.2890	−	15.2890i	0.516271	−	0.516271i	−0.400170	−	0.916441i	$-0.631049\pi$
$877$	15.2890	−	15.2890i	0.516271	−	0.516271i	0.916441	+	0.400170i	$0.131049\pi$
$878$	7.40125	−	7.40125i	0.249780	−	0.249780i
$879$	−5.12632	−	17.3248i	−0.172906	−	0.584351i
$880$	−22.2498	−	9.72108i	−0.750040	−	0.327697i
$881$		−	29.1988i		−	0.983734i	−0.870670	−	0.491867i	$-0.836315\pi$
$881$		−	29.1988i		−	0.983734i	0.870670	−	0.491867i	$-0.163685\pi$
$882$		0			0
$883$	−24.7944	−	24.7944i	−0.834397	−	0.834397i	0.153718	−	0.988115i	$-0.450875\pi$
$883$	−24.7944	−	24.7944i	−0.834397	−	0.834397i	−0.988115	+	0.153718i	$0.950875\pi$
$884$	0.836347			0.0281294
$885$	14.8644	+	19.1062i	0.499660	+	0.642249i
$886$	−10.0004			−0.335971
$887$	−18.5532	−	18.5532i	−0.622956	−	0.622956i	0.323331	−	0.946286i	$-0.395197\pi$
$887$	−18.5532	−	18.5532i	−0.622956	−	0.622956i	−0.946286	+	0.323331i	$0.895197\pi$
$888$	18.1103	+	9.83997i	0.607743	+	0.330208i
$889$		0			0
$890$	−9.48407	+	3.71661i	−0.317907	+	0.124581i
$891$	−27.8371	−	12.4330i	−0.932579	−	0.416521i
$892$	21.5224	−	21.5224i	0.720625	−	0.720625i
$893$	−4.78537	+	4.78537i	−0.160136	+	0.160136i
$894$	0.603504	−	0.178574i	0.0201842	−	0.00597240i
$895$	15.8031	−	36.1705i	0.528240	−	1.20905i
$896$		0			0
$897$	5.83839	−	10.7455i	0.194938	−	0.358781i
$898$	−0.626265	−	0.626265i	−0.0208987	−	0.0208987i
$899$	8.75683			0.292057
$900$	27.1091	+	6.87741i	0.903637	+	0.229247i
$901$	−1.84046			−0.0613145
$902$	−1.22774	−	1.22774i	−0.0408792	−	0.0408792i
$903$		0			0
$904$			16.5644i			0.550925i
$905$	10.6745	−	24.4321i	0.354834	−	0.812150i
$906$	5.32504	−	1.57565i	0.176913	−	0.0523476i
$907$	3.39207	−	3.39207i	0.112632	−	0.112632i	−0.648545	−	0.761177i	$-0.724622\pi$
$907$	3.39207	−	3.39207i	0.112632	−	0.112632i	0.761177	+	0.648545i	$0.224622\pi$
$908$	13.1370	−	13.1370i	0.435968	−	0.435968i
$909$	31.3421	−	20.3277i	1.03955	−	0.674227i
$910$		0			0
$911$			16.2139i			0.537190i	0.963253	+	0.268595i	$0.0865592\pi$
$911$			16.2139i			0.537190i	−0.963253	+	0.268595i	$0.913441\pi$
$912$	−35.8419	−	19.4742i	−1.18685	−	0.644855i
$913$	21.2366	+	21.2366i	0.702828	+	0.702828i
$914$	3.23553			0.107022
$915$	−4.35828	−	5.60201i	−0.144080	−	0.185197i
$916$	−8.95190			−0.295779
$917$		0			0
$918$	−0.0295215	−	0.379367i	−0.000974354	−	0.0125210i
$919$		−	5.54658i		−	0.182965i	−0.995807	−	0.0914823i	$-0.970839\pi$
$919$		−	5.54658i		−	0.182965i	0.995807	−	0.0914823i	$-0.0291605\pi$
$920$	−9.12751	−	3.98787i	−0.300925	−	0.131476i
$921$	−7.89582	−	26.6845i	−0.260176	−	0.879286i
$922$	9.21923	−	9.21923i	0.303619	−	0.303619i
$923$	−15.5857	+	15.5857i	−0.513009	+	0.513009i
$924$		0			0
$925$	−41.7986	−	1.60697i	−1.37433	−	0.0528368i
$926$		−	10.4558i		−	0.343598i
$927$	8.65884	−	40.6196i	0.284393	−	1.33412i
$928$	27.0120	+	27.0120i	0.886711	+	0.886711i
$929$	−12.7978			−0.419884			−0.209942	−	0.977714i	$-0.567327\pi$
$929$	−12.7978			−0.419884			−0.209942	+	0.977714i	$0.567327\pi$
$930$	0.162957	−	1.30503i	0.00534357	−	0.0427935i
$931$		0			0
$932$	−26.6237	−	26.6237i	−0.872090	−	0.872090i
$933$	13.6103	+	7.39497i	0.445582	+	0.242100i
$934$			3.02201i			0.0988830i
$935$	−0.549864	−	1.40315i	−0.0179825	−	0.0458878i
$936$	5.23503	+	8.07159i	0.171112	+	0.263828i
$937$	−24.4148	+	24.4148i	−0.797598	+	0.797598i	−0.982716	−	0.185119i	$-0.940733\pi$
$937$	−24.4148	+	24.4148i	−0.797598	+	0.797598i	0.185119	+	0.982716i	$0.440733\pi$
$938$		0			0
$939$	10.6278	−	3.14471i	0.346825	−	0.102624i
$940$	1.40123	+	3.57568i	0.0457031	+	0.116626i
$941$			3.72437i			0.121411i	0.998156	+	0.0607055i	$0.0193351\pi$
$941$			3.72437i			0.121411i	−0.998156	+	0.0607055i	$0.980665\pi$
$942$	2.26537	−	4.16938i	0.0738097	−	0.135846i
$943$	3.08374	+	3.08374i	0.100420	+	0.100420i
$944$	−20.0354			−0.652098
$945$		0			0
$946$	−1.52440			−0.0495626
$947$	34.3568	+	34.3568i	1.11644	+	1.11644i	0.992259	+	0.124186i	$0.0396318\pi$
$947$	34.3568	+	34.3568i	1.11644	+	1.11644i	0.124186	+	0.992259i	$0.460368\pi$
$948$	−5.26849	+	9.69657i	−0.171112	+	0.314930i
$949$		−	15.3288i		−	0.497593i
$950$	−13.5108	−	0.519431i	−0.438349	−	0.0168526i
$951$	4.19155	−	1.24026i	0.135920	−	0.0402181i
$952$		0			0
$953$	−21.7199	+	21.7199i	−0.703578	+	0.703578i	−0.965177	−	0.261599i	$-0.915750\pi$
$953$	−21.7199	+	21.7199i	−0.703578	+	0.703578i	0.261599	+	0.965177i	$0.415750\pi$
$954$	−5.55815	−	8.56979i	−0.179952	−	0.277457i
$955$	36.4419	+	15.9217i	1.17923	+	0.515214i
$956$		−	23.9812i		−	0.775607i
$957$	48.9340	+	26.5876i	1.58181	+	0.859454i
$958$	−10.5102	−	10.5102i	−0.339569	−	0.339569i
$959$		0			0
$960$	−15.0692	+	11.7236i	−0.486357	+	0.378378i
$961$	−30.1488			−0.972543
$962$	−4.90888	−	4.90888i	−0.158269	−	0.158269i
$963$	4.61604	−	21.6544i	0.148750	−	0.697802i
$964$		−	30.1785i		−	0.971984i
$965$	42.2190	−	16.5447i	1.35908	−	0.532594i
$966$		0			0
$967$	−42.1187	+	42.1187i	−1.35445	+	1.35445i	−0.473831	+	0.880616i	$0.657129\pi$
$967$	−42.1187	+	42.1187i	−1.35445	+	1.35445i	−0.880616	+	0.473831i	$0.842871\pi$
$968$	−0.477887	+	0.477887i	−0.0153599	+	0.0153599i
$969$	−0.718354	−	2.42773i	−0.0230768	−	0.0779900i
$970$	3.12835	−	7.16021i	0.100445	−	0.229901i
$971$			27.4414i			0.880638i	0.897841	+	0.440319i	$0.145135\pi$
$971$			27.4414i			0.880638i	−0.897841	+	0.440319i	$0.854865\pi$
$972$	−23.0848	+	17.6599i	−0.740444	+	0.566442i
$973$		0			0
$974$	10.3055			0.330211
$975$	−16.7853	−	9.97368i	−0.537559	−	0.319414i
$976$	5.87447			0.188037
$977$	40.5573	+	40.5573i	1.29754	+	1.29754i	0.930011	+	0.367531i	$0.119797\pi$
$977$	40.5573	+	40.5573i	1.29754	+	1.29754i	0.367531	+	0.930011i	$0.380203\pi$
$978$	−11.2105	−	6.09104i	−0.358471	−	0.194770i
$979$		−	41.9259i		−	1.33996i
$980$		0			0
$981$	16.8048	−	10.8992i	0.536537	−	0.347984i
$982$	−9.54968	+	9.54968i	−0.304743	+	0.304743i
$983$	−17.0329	+	17.0329i	−0.543267	+	0.543267i	−0.924485	−	0.381218i	$-0.875505\pi$
$983$	−17.0329	+	17.0329i	−0.543267	+	0.543267i	0.381218	+	0.924485i	$0.375505\pi$
$984$	−3.28983	+	0.973443i	−0.104876	+	0.0310322i
$985$	−12.0915	+	4.73840i	−0.385267	+	0.150978i
$986$			0.695074i			0.0221357i
$987$		0			0
$988$	21.8381	+	21.8381i	0.694763	+	0.694763i
$989$	3.82888			0.121751
$990$	4.87295	−	6.79783i	0.154872	−	0.216049i
$991$	22.4760			0.713973			0.356986	−	0.934110i	$-0.383804\pi$
$991$	22.4760			0.713973			0.356986	+	0.934110i	$0.383804\pi$
$992$	2.62554	+	2.62554i	0.0833611	+	0.0833611i
$993$	2.99223	−	5.50716i	0.0949556	−	0.174764i
$994$		0			0
$995$	−27.4874	−	12.0094i	−0.871408	−	0.380724i
$996$	27.4552	−	8.12385i	0.869951	−	0.257414i
$997$	−31.8314	+	31.8314i	−1.00811	+	1.00811i	−0.00814356	+	0.999967i	$0.502592\pi$
$997$	−31.8314	+	31.8314i	−1.00811	+	1.00811i	−0.999967	+	0.00814356i	$0.997408\pi$
$998$	1.98463	−	1.98463i	0.0628224	−	0.0628224i
$999$	28.2608	−	33.0304i	0.894133	−	1.04503i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.j.h.638.7		24
3.2	odd	2	inner	735.2.j.h.638.6		24
5.2	odd	4	inner	735.2.j.h.197.6		24
7.2	even	3		735.2.y.g.263.7		48
7.3	odd	6		735.2.y.j.128.6		48
7.4	even	3		735.2.y.g.128.6		48
7.5	odd	6		735.2.y.j.263.7		48
7.6	odd	2		105.2.j.a.8.7	yes	24
15.2	even	4	inner	735.2.j.h.197.7		24
21.2	odd	6		735.2.y.g.263.6		48
21.5	even	6		735.2.y.j.263.6		48
21.11	odd	6		735.2.y.g.128.7		48
21.17	even	6		735.2.y.j.128.7		48
21.20	even	2		105.2.j.a.8.6	✓	24
35.2	odd	12		735.2.y.g.557.7		48
35.12	even	12		735.2.y.j.557.7		48
35.13	even	4		525.2.j.b.407.7		24
35.17	even	12		735.2.y.j.422.6		48
35.27	even	4		105.2.j.a.92.6	yes	24
35.32	odd	12		735.2.y.g.422.6		48
35.34	odd	2		525.2.j.b.218.6		24
105.2	even	12		735.2.y.g.557.6		48
105.17	odd	12		735.2.y.j.422.7		48
105.32	even	12		735.2.y.g.422.7		48
105.47	odd	12		735.2.y.j.557.6		48
105.62	odd	4		105.2.j.a.92.7	yes	24
105.83	odd	4		525.2.j.b.407.6		24
105.104	even	2		525.2.j.b.218.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.6	✓	24	21.20	even	2
105.2.j.a.8.7	yes	24	7.6	odd	2
105.2.j.a.92.6	yes	24	35.27	even	4
105.2.j.a.92.7	yes	24	105.62	odd	4
525.2.j.b.218.6		24	35.34	odd	2
525.2.j.b.218.7		24	105.104	even	2
525.2.j.b.407.6		24	105.83	odd	4
525.2.j.b.407.7		24	35.13	even	4
735.2.j.h.197.6		24	5.2	odd	4	inner
735.2.j.h.197.7		24	15.2	even	4	inner
735.2.j.h.638.6		24	3.2	odd	2	inner
735.2.j.h.638.7		24	1.1	even	1	trivial
735.2.y.g.128.6		48	7.4	even	3
735.2.y.g.128.7		48	21.11	odd	6
735.2.y.g.263.6		48	21.2	odd	6
735.2.y.g.263.7		48	7.2	even	3
735.2.y.g.422.6		48	35.32	odd	12
735.2.y.g.422.7		48	105.32	even	12
735.2.y.g.557.6		48	105.2	even	12
735.2.y.g.557.7		48	35.2	odd	12
735.2.y.j.128.6		48	7.3	odd	6
735.2.y.j.128.7		48	21.17	even	6
735.2.y.j.263.6		48	21.5	even	6
735.2.y.j.263.7		48	7.5	odd	6
735.2.y.j.422.6		48	35.17	even	12
735.2.y.j.422.7		48	105.17	odd	12
735.2.y.j.557.6		48	105.47	odd	12
735.2.y.j.557.7		48	35.12	even	12

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)

\(f(q)\)	\(=\)	\(q+(0.260263 + 0.260263i) q^{2} +(-0.826909 + 1.52191i) q^{3} -1.86453i q^{4} +(0.895238 - 2.04904i) q^{5} +(-0.611312 + 0.180884i) q^{6} +(1.00579 - 1.00579i) q^{8} +(-1.63244 - 2.51697i) q^{9} +O(q^{10})\)	\(q+(0.260263 + 0.260263i) q^{2} +(-0.826909 + 1.52191i) q^{3} -1.86453i q^{4} +(0.895238 - 2.04904i) q^{5} +(-0.611312 + 0.180884i) q^{6} +(1.00579 - 1.00579i) q^{8} +(-1.63244 - 2.51697i) q^{9} +(0.766286 - 0.300291i) q^{10} +3.38750i q^{11} +(2.83765 + 1.54179i) q^{12} +(-1.59420 - 1.59420i) q^{13} +(2.37818 + 3.05684i) q^{15} -3.20551 q^{16} +(-0.140684 - 0.140684i) q^{17} +(0.230209 - 1.07994i) q^{18} -7.34691i q^{19} +(-3.82048 - 1.66919i) q^{20} +(-0.881641 + 0.881641i) q^{22} +(2.21444 - 2.21444i) q^{23} +(0.699032 + 2.36243i) q^{24} +(-3.39710 - 3.66875i) q^{25} -0.829822i q^{26} +(5.18049 - 0.403134i) q^{27} -9.49165 q^{29} +(-0.176632 + 1.41454i) q^{30} -0.922582 q^{31} +(-2.84586 - 2.84586i) q^{32} +(-5.15548 - 2.80115i) q^{33} -0.0732300i q^{34} +(-4.69295 + 3.04373i) q^{36} +(5.91558 - 5.91558i) q^{37} +(1.91213 - 1.91213i) q^{38} +(3.74449 - 1.10797i) q^{39} +(-1.16048 - 2.96133i) q^{40} +1.39256i q^{41} +(0.864526 + 0.864526i) q^{43} +6.31608 q^{44} +(-6.61878 + 1.09165i) q^{45} +1.15267 q^{46} +(-0.651346 - 0.651346i) q^{47} +(2.65066 - 4.87851i) q^{48} +(0.0707006 - 1.83898i) q^{50} +(0.330443 - 0.0977764i) q^{51} +(-2.97242 + 2.97242i) q^{52} +(6.54108 - 6.54108i) q^{53} +(1.45321 + 1.24337i) q^{54} +(6.94110 + 3.03262i) q^{55} +(11.1814 + 6.07522i) q^{57} +(-2.47033 - 2.47033i) q^{58} +6.25032 q^{59} +(5.69956 - 4.43417i) q^{60} -1.83261 q^{61} +(-0.240114 - 0.240114i) q^{62} +4.92967i q^{64} +(-4.69375 + 1.83938i) q^{65} +(-0.612745 - 2.07082i) q^{66} +(-0.815500 + 0.815500i) q^{67} +(-0.262310 + 0.262310i) q^{68} +(1.53904 + 5.20132i) q^{69} -9.77651i q^{71} +(-4.17345 - 0.889650i) q^{72} +(4.80768 + 4.80768i) q^{73} +3.07921 q^{74} +(8.39261 - 2.13637i) q^{75} -13.6985 q^{76} +(1.26292 + 0.686187i) q^{78} +3.41711i q^{79} +(-2.86969 + 6.56821i) q^{80} +(-3.67026 + 8.21761i) q^{81} +(-0.362432 + 0.362432i) q^{82} +(6.26911 - 6.26911i) q^{83} +(-0.414214 + 0.162321i) q^{85} +0.450009i q^{86} +(7.84873 - 14.4455i) q^{87} +(3.40712 + 3.40712i) q^{88} -12.3767 q^{89} +(-2.00674 - 1.43851i) q^{90} +(-4.12888 - 4.12888i) q^{92} +(0.762891 - 1.40409i) q^{93} -0.339043i q^{94} +(-15.0541 - 6.57723i) q^{95} +(6.68443 - 1.97789i) q^{96} +(6.71326 - 6.71326i) q^{97} +(8.52622 - 5.52990i) 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

Modular forms

Varieties

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Representations

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Database

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