LMFDB - Embedded newform 735.2.j.h.197.6

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			197.6
Character	$\chi$	$=$	735.197
Dual form			735.2.j.h.638.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.260263 + 0.260263i) q^{2} +(1.52191 + 0.826909i) q^{3} +1.86453i q^{4} +(-0.895238 - 2.04904i) q^{5} +(-0.611312 + 0.180884i) q^{6} +(-1.00579 - 1.00579i) q^{8} +(1.63244 + 2.51697i) q^{9} +O(q^{10})$	\(q+(-0.260263 + 0.260263i) q^{2} +(1.52191 + 0.826909i) 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} +(-1.54179 + 2.83765i) q^{12} +(-1.59420 + 1.59420i) q^{13} +(0.331892 - 3.85874i) q^{15} -3.20551 q^{16} +(0.140684 - 0.140684i) q^{17} +(-1.07994 - 0.230209i) 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} +(0.403134 + 5.18049i) q^{27} +9.49165 q^{29} +(0.917908 + 1.09067i) q^{30} -0.922582 q^{31} +(2.84586 - 2.84586i) q^{32} +(-2.80115 + 5.15548i) 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} +(3.69593 - 5.59822i) q^{45} +1.15267 q^{46} +(0.651346 - 0.651346i) q^{47} +(-4.87851 - 2.65066i) 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} +(-6.07522 + 11.1814i) q^{57} +(-2.47033 + 2.47033i) q^{58} -6.25032 q^{59} +(7.19471 + 0.618821i) 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} +(0.889650 - 4.17345i) q^{72} +(4.80768 - 4.80768i) q^{73} -3.07921 q^{74} +(-8.20381 + 2.77443i) q^{75} -13.6985 q^{76} +(0.686187 - 1.26292i) 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} +(14.4455 + 7.84873i) q^{87} +(3.40712 - 3.40712i) q^{88} +12.3767 q^{89} +(0.495095 + 2.41893i) q^{90} +(4.12888 - 4.12888i) q^{92} +(-1.40409 - 0.762891i) 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 $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.260263	+	0.260263i	−0.184034	+	0.184034i	−0.793111	−	0.609077i	$-0.791540\pi$
$2$	−0.260263	+	0.260263i	−0.184034	+	0.184034i	0.609077	+	0.793111i	$0.291540\pi$
$3$	1.52191	+	0.826909i	0.878677	+	0.477416i
$3$	1.52191	+	0.826909i	0.878677	+	0.477416i
$4$			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	$0.829392\pi$
$12$	−1.54179	+	2.83765i	−0.445077	+	0.819158i
$13$	−1.59420	+	1.59420i	−0.442151	+	0.442151i	−0.892734	−	0.450583i	$-0.851216\pi$
$13$	−1.59420	+	1.59420i	−0.442151	+	0.442151i	0.450583	+	0.892734i	$0.351216\pi$
$14$		0			0
$15$	0.331892	−	3.85874i	0.0856941	−	0.996321i
$16$	−3.20551			−0.801377
$17$	0.140684	−	0.140684i	0.0341210	−	0.0341210i	−0.689840	−	0.723961i	$-0.742319\pi$
$17$	0.140684	−	0.140684i	0.0341210	−	0.0341210i	0.723961	+	0.689840i	$0.242319\pi$
$18$	−1.07994	−	0.230209i	−0.254544	−	0.0542609i
$19$			7.34691i			1.68550i	0.538308	+	0.842748i	$0.319064\pi$
$19$			7.34691i			1.68550i	−0.538308	+	0.842748i	$0.680936\pi$
$20$	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	$-0.355870\pi$
$23$	−2.21444	−	2.21444i	−0.461742	−	0.461742i	−0.899226	+	0.437484i	$0.855870\pi$
$24$	−0.699032	−	2.36243i	−0.142689	−	0.482229i
$25$	−3.39710	+	3.66875i	−0.679420	+	0.733750i
$26$		−	0.829822i		−	0.162741i
$27$	0.403134	+	5.18049i	0.0775831	+	0.996986i
$28$		0			0
$29$	9.49165			1.76256			0.881278	−	0.472598i	$-0.156684\pi$
$29$	9.49165			1.76256			0.881278	+	0.472598i	$0.156684\pi$
$30$	0.917908	+	1.09067i	0.167586	+	0.199128i
$31$	−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
$33$	−2.80115	+	5.15548i	−0.487618	+	0.897454i
$34$			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	0.999632	−	0.0271173i	$-0.00863275\pi$
$37$	5.91558	+	5.91558i	0.972515	+	0.972515i	−0.0271173	+	0.999632i	$0.508633\pi$
$38$	−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	−0.638108	−	0.769947i	$-0.720283\pi$
$43$	0.864526	−	0.864526i	0.131839	−	0.131839i	0.769947	+	0.638108i	$0.220283\pi$
$44$	−6.31608			−0.952184
$45$	3.69593	−	5.59822i	0.550957	−	0.834533i
$46$	1.15267			0.169952
$47$	0.651346	−	0.651346i	0.0950085	−	0.0950085i	−0.658005	−	0.753014i	$-0.728599\pi$
$47$	0.651346	−	0.651346i	0.0950085	−	0.0950085i	0.753014	+	0.658005i	$0.228599\pi$
$48$	−4.87851	−	2.65066i	−0.704152	−	0.382591i
$49$		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	$-0.469134\pi$
$53$	−6.54108	−	6.54108i	−0.898486	−	0.898486i	−0.995302	+	0.0968158i	$0.969134\pi$
$54$	−1.45321	−	1.24337i	−0.197757	−	0.169201i
$55$	6.94110	−	3.03262i	0.935938	−	0.408918i
$56$		0			0
$57$	−6.07522	+	11.1814i	−0.804683	+	1.48101i
$58$	−2.47033	+	2.47033i	−0.324370	+	0.324370i
$59$	−6.25032			−0.813722			−0.406861	−	0.913490i	$-0.633377\pi$
$59$	−6.25032			−0.813722			−0.406861	+	0.913490i	$0.633377\pi$
$60$	7.19471	+	0.618821i	0.928834	+	0.0798894i
$61$	−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	0.655535	−	0.755165i	$-0.272443\pi$
$67$	−0.815500	−	0.815500i	−0.0996292	−	0.0996292i	−0.755165	+	0.655535i	$0.772443\pi$
$68$	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	$-0.196998\pi$
$72$	0.889650	−	4.17345i	0.104846	−	0.491846i
$73$	4.80768	−	4.80768i	0.562697	−	0.562697i	−0.367376	−	0.930073i	$-0.619744\pi$
$73$	4.80768	−	4.80768i	0.562697	−	0.562697i	0.930073	+	0.367376i	$0.119744\pi$
$74$	−3.07921			−0.357951
$75$	−8.20381	+	2.77443i	−0.947295	+	0.320363i
$76$	−13.6985			−1.57133
$77$		0			0
$78$	0.686187	−	1.26292i	0.0776954	−	0.142997i
$79$		−	3.41711i		−	0.384455i	−0.981350	−	0.192228i	$-0.938429\pi$
$79$		−	3.41711i		−	0.384455i	0.981350	−	0.192228i	$-0.0615712\pi$
$80$	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	$-0.411755\pi$
$83$	−6.26911	−	6.26911i	−0.688124	−	0.688124i	−0.961817	+	0.273693i	$0.911755\pi$
$84$		0			0
$85$	−0.414214	−	0.162321i	−0.0449278	−	0.0176062i
$86$			0.450009i			0.0485257i
$87$	14.4455	+	7.84873i	1.54872	+	0.841473i
$88$	3.40712	−	3.40712i	0.363201	−	0.363201i
$89$	12.3767			1.31192			0.655962	−	0.754794i	$-0.272263\pi$
$89$	12.3767			1.31192			0.655962	+	0.754794i	$0.272263\pi$
$90$	0.495095	+	2.41893i	0.0521876	+	0.254977i
$91$		0			0
$92$	4.12888	−	4.12888i	0.430465	−	0.430465i
$93$	−1.40409	−	0.762891i	−0.145597	−	0.0791082i
$94$			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	0.960367	−	0.278739i	$-0.0899164\pi$
$97$	6.71326	+	6.71326i	0.681628	+	0.681628i	−0.278739	+	0.960367i	$0.589916\pi$
$98$		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	$0.787325\pi$
$102$	−0.0605545	+	0.111450i	−0.00599579	+	0.0110352i
$103$	9.78924	−	9.78924i	0.964563	−	0.964563i	−0.0348303	−	0.999393i	$-0.511089\pi$
$103$	9.78924	−	9.78924i	0.964563	−	0.964563i	0.999393	+	0.0348303i	$0.0110891\pi$
$104$	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	$-0.866112\pi$
$107$	−5.21866	+	5.21866i	−0.504507	+	0.504507i	0.408328	+	0.912835i	$0.366112\pi$
$108$	−9.65916	+	0.751653i	−0.929453	+	0.0723279i
$109$		−	6.67661i		−	0.639504i	−0.947501	−	0.319752i	$-0.896400\pi$
$109$		−	6.67661i		−	0.639504i	0.947501	−	0.319752i	$-0.103600\pi$
$110$	−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	$-0.0654841\pi$
$113$	8.23451	+	8.23451i	0.774637	+	0.774637i	−0.204276	+	0.978913i	$0.565484\pi$
$114$	−1.32894	−	4.49125i	−0.124467	−	0.420644i
$115$	−2.55501	+	6.51991i	−0.238256	+	0.607985i
$116$			17.6974i			1.64317i
$117$	−6.61498	−	1.41011i	−0.611555	−	0.130365i
$118$	1.62673	−	1.62673i	0.149752	−	0.149752i
$119$		0			0
$120$	−4.21491	+	3.54728i	−0.384767	+	0.323821i
$121$	−0.475134			−0.0431940
$122$	0.476962	−	0.476962i	0.0431821	−	0.0431821i
$123$	−1.15152	+	2.11936i	−0.103829	+	0.191096i
$124$		−	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	0.785652	−	0.618669i	$-0.212328\pi$
$127$	1.88180	+	1.88180i	0.166983	+	0.166983i	−0.618669	+	0.785652i	$0.712328\pi$
$128$	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	$-0.128179\pi$
$132$	−9.61252	−	5.22282i	−0.836663	−	0.454588i
$133$		0			0
$134$	0.424489			0.0366703
$135$	10.2541	−	5.46381i	0.882533	−	0.470250i
$136$	−0.282999			−0.0242670
$137$	6.49538	−	6.49538i	0.554938	−	0.554938i	−0.372924	−	0.927862i	$-0.621645\pi$
$137$	6.49538	−	6.49538i	0.554938	−	0.554938i	0.927862	+	0.372924i	$0.121645\pi$
$138$	1.75427	+	0.953156i	0.149333	+	0.0811380i
$139$		−	1.83916i		−	0.155995i	−0.996954	−	0.0779976i	$-0.975147\pi$
$139$		−	1.83916i		−	0.155995i	0.996954	−	0.0779976i	$-0.0248526\pi$
$140$		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	$-0.487125\pi$
$149$	0.987227			0.0808768			0.0404384	+	0.999182i	$0.487125\pi$
$150$	1.41307	−	2.85723i	0.115377	−	0.233292i
$151$	−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
$153$	0.583758	+	0.124439i	0.0471940	+	0.0100603i
$154$		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	0.465179	−	0.885217i	$-0.345990\pi$
$157$	−5.26306	−	5.26306i	−0.420038	−	0.420038i	−0.885217	+	0.465179i	$0.845990\pi$
$158$	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
$162$	−1.18351	−	3.09398i	−0.0929853	−	0.243086i
$163$	14.1511	−	14.1511i	1.10840	−	1.10840i	0.115041	−	0.993361i	$-0.463300\pi$
$163$	14.1511	−	14.1511i	1.10840	−	1.10840i	0.993361	−	0.115041i	$-0.0367000\pi$
$164$	−2.59646			−0.202750
$165$	13.0715	+	1.12428i	1.01761	+	0.0875253i
$166$	3.26324			0.253276
$167$	17.4876	−	17.4876i	1.35323	−	1.35323i	0.471215	−	0.882018i	$-0.343816\pi$
$167$	17.4876	−	17.4876i	1.35323	−	1.35323i	0.882018	−	0.471215i	$-0.156184\pi$
$168$		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	$-0.0511979\pi$
$173$	10.8767	+	10.8767i	0.826942	+	0.826942i	−0.160150	+	0.987093i	$0.551198\pi$
$174$	−5.80236	+	1.71689i	−0.439876	+	0.130157i
$175$		0			0
$176$		−	10.8587i		−	0.818502i
$177$	−9.51244	−	5.16844i	−0.714999	−	0.388484i
$178$	−3.22119	+	3.22119i	−0.241439	+	0.241439i
$179$	−17.6524			−1.31941			−0.659703	−	0.751527i	$-0.729318\pi$
$179$	−17.6524			−1.31941			−0.659703	+	0.751527i	$0.729318\pi$
$180$	10.4380	+	6.89117i	0.778005	+	0.513637i
$181$	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
$183$	−2.78908	−	1.51541i	−0.206175	−	0.112022i
$184$			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	$0.777509\pi$
$192$	4.07639	−	7.50253i	0.294188	−	0.541449i
$193$	14.3394	−	14.3394i	1.03217	−	1.03217i	0.0327052	−	0.999465i	$-0.489588\pi$
$193$	14.3394	−	14.3394i	1.03217	−	1.03217i	0.999465	−	0.0327052i	$-0.0104123\pi$
$194$	−3.49443			−0.250885
$195$	5.62249	+	6.68069i	0.402635	+	0.478414i
$196$		0			0
$197$	4.10678	−	4.10678i	0.292596	−	0.292596i	−0.545509	−	0.838105i	$-0.683664\pi$
$197$	4.10678	−	4.10678i	0.292596	−	0.292596i	0.838105	+	0.545509i	$0.183664\pi$
$198$	0.779834	−	3.65829i	0.0554204	−	0.259983i
$199$			13.4148i			0.950949i	0.879730	+	0.475474i	$0.157724\pi$
$199$			13.4148i			0.950949i	−0.879730	+	0.475474i	$0.842276\pi$
$200$	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
$207$	1.95873	−	9.18861i	0.136141	−	0.638653i
$208$	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
$213$	8.08429	−	14.8790i	0.553926	−	1.01949i
$214$		−	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
$222$	−4.68630	−	2.54623i	−0.314524	−	0.170892i
$223$	11.5431	−	11.5431i	0.772984	−	0.772984i	−0.205643	−	0.978627i	$-0.565928\pi$
$223$	11.5431	−	11.5431i	0.772984	−	0.772984i	0.978627	+	0.205643i	$0.0659285\pi$
$224$		0			0
$225$	−14.7797	−	2.56137i	−0.985313	−	0.170758i
$226$	−4.28628			−0.285119
$227$	−7.04578	+	7.04578i	−0.467645	+	0.467645i	−0.901151	−	0.433506i	$-0.857276\pi$
$227$	−7.04578	+	7.04578i	−0.467645	+	0.467645i	0.433506	+	0.901151i	$0.357276\pi$
$228$	−20.8479	−	11.3274i	−1.38069	−	0.750176i
$229$			4.80117i			0.317270i	0.987337	+	0.158635i	$0.0507093\pi$
$229$			4.80117i			0.317270i	−0.987337	+	0.158635i	$0.949291\pi$
$230$	−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	$-0.480066\pi$
$233$	−14.2791	−	14.2791i	−0.935455	−	0.935455i	−0.998040	+	0.0625851i	$0.980066\pi$
$234$	2.08864	−	1.35464i	0.136538	−	0.0885554i
$235$	−1.91774	−	0.751522i	−0.125100	−	0.0490239i
$236$		−	11.6539i		−	0.758603i
$237$	2.82564	−	5.20055i	0.183545	−	0.337812i
$238$		0			0
$239$	−12.8618			−0.831961			−0.415981	−	0.909373i	$-0.636562\pi$
$239$	−12.8618			−0.831961			−0.415981	+	0.909373i	$0.636562\pi$
$240$	−1.06388	+	12.3692i	−0.0686733	+	0.798430i
$241$	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
$243$	−12.3810	+	9.47153i	−0.794244	+	0.607599i
$244$		−	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
$255$	−0.496172	−	0.589556i	−0.0310715	−	0.0369194i
$256$	6.22880			0.389300
$257$	−16.6108	+	16.6108i	−1.03615	+	1.03615i	−0.0368323	+	0.999321i	$0.511727\pi$
$257$	−16.6108	+	16.6108i	−1.03615	+	1.03615i	−0.999321	+	0.0368323i	$0.988273\pi$
$258$	−0.372116	+	0.684874i	−0.0231669	+	0.0426384i
$259$		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	$-0.456142\pi$
$263$	−13.8361	−	13.8361i	−0.853173	−	0.853173i	−0.990523	+	0.137350i	$0.956142\pi$
$264$	8.00273	−	2.36797i	0.492534	−	0.145738i
$265$	−7.54709	+	19.2587i	−0.463614	+	1.18305i
$266$		0			0
$267$	18.8362	+	10.2344i	1.15276	+	0.626334i
$268$	1.52052	−	1.52052i	0.0928806	−	0.0928806i
$269$	−11.4632			−0.698925			−0.349463	−	0.936950i	$-0.613636\pi$
$269$	−11.4632			−0.698925			−0.349463	+	0.936950i	$0.613636\pi$
$270$	−1.24674	+	4.09080i	−0.0758742	+	0.248958i
$271$	−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	0.977206	−	0.212293i	$-0.0680930\pi$
$277$	12.7307	+	12.7307i	0.764914	+	0.764914i	−0.212293	+	0.977206i	$0.568093\pi$
$278$	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	$0.957984\pi$
$282$	−0.280357	+	0.515994i	−0.0166950	+	0.0307270i
$283$	−2.07246	+	2.07246i	−0.123195	+	0.123195i	−0.766016	−	0.642821i	$-0.777764\pi$
$283$	−2.07246	+	2.07246i	−0.123195	+	0.123195i	0.642821	+	0.766016i	$0.277764\pi$
$284$	18.2286			1.08167
$285$	28.3498	+	2.43838i	1.67930	+	0.144437i
$286$	2.81102			0.166219
$287$		0			0
$288$	11.8087	+	2.51724i	0.695832	+	0.148330i
$289$			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	$-0.151445\pi$
$293$	7.37595	+	7.37595i	0.430908	+	0.430908i	−0.458029	+	0.888937i	$0.651445\pi$
$294$		0			0
$295$	5.59552	+	12.8071i	0.325784	+	0.745660i
$296$		−	11.8997i		−	0.691656i
$297$	−17.5489	+	1.36561i	−1.01829	+	0.0792410i
$298$	−0.256939	+	0.256939i	−0.0148841	+	0.0148841i
$299$	7.06050			0.408319
$300$	−5.17299	−	15.2962i	−0.298663	−	0.883128i
$301$		0			0
$302$	2.26711	−	2.26711i	0.130458	−	0.130458i
$303$	−10.2969	+	18.9513i	−0.591543	+	1.08873i
$304$		−	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	0.304209	−	0.952605i	$-0.401608\pi$
$307$	−11.3608	−	11.3608i	−0.648396	−	0.648396i	−0.952605	+	0.304209i	$0.901608\pi$
$308$		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	$-0.0815992\pi$
$312$	4.88058	+	2.65179i	0.276308	+	0.150128i
$313$	−4.52473	+	4.52473i	−0.255753	+	0.255753i	−0.823324	−	0.567571i	$-0.807883\pi$
$313$	−4.52473	+	4.52473i	−0.255753	+	0.255753i	0.567571	+	0.823324i	$0.307883\pi$
$314$	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	$-0.727422\pi$
$317$	1.78453	−	1.78453i	0.100229	−	0.100229i	0.755443	+	0.655214i	$0.227422\pi$
$318$	5.18182	+	2.81546i	0.290582	+	0.157883i
$319$			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
$327$	5.52095	−	10.1612i	0.305309	−	0.561917i
$328$	1.40063	−	1.40063i	0.0773368	−	0.0773368i
$329$		0			0
$330$	−3.69463	+	3.10941i	−0.203383	+	0.171167i
$331$	−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
$333$	−5.23248	+	24.5462i	−0.286738	+	1.34512i
$334$			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	0.0666042	−	0.997779i	$-0.478784\pi$
$337$	−17.0941	−	17.0941i	−0.931175	−	0.931175i	−0.997779	+	0.0666042i	$0.978784\pi$
$338$	−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
$342$	1.69133	−	7.93421i	0.0914565	−	0.429033i
$343$		0			0
$344$	−1.73907			−0.0937644
$345$	−9.27989	+	7.80998i	−0.499612	+	0.420475i
$346$	−5.66162			−0.304371
$347$	−5.48573	+	5.48573i	−0.294489	+	0.294489i	−0.838851	−	0.544361i	$-0.816772\pi$
$347$	−5.48573	+	5.48573i	−0.294489	+	0.294489i	0.544361	+	0.838851i	$0.316772\pi$
$348$	−14.6342	+	26.9340i	−0.784474	+	1.44381i
$349$			14.8272i			0.793681i	0.917888	+	0.396841i	$0.129893\pi$
$349$			14.8272i			0.793681i	−0.917888	+	0.396841i	$0.870107\pi$
$350$		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	$-0.158218\pi$
$353$	7.55570	+	7.55570i	0.402149	+	0.402149i	−0.476841	+	0.878990i	$0.658218\pi$
$354$	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	$-0.448579\pi$
$359$	6.09504			0.321684			0.160842	+	0.986980i	$0.448579\pi$
$360$	−9.34801	+	1.91331i	−0.492683	+	0.100840i
$361$	−34.9770			−1.84090
$362$	−3.10330	+	3.10330i	−0.163106	+	0.163106i
$363$	−0.723114	−	0.392893i	−0.0379536	−	0.0206215i
$364$		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	0.609019	−	0.793155i	$-0.291563\pi$
$367$	−3.52753	−	3.52753i	−0.184136	−	0.184136i	−0.793155	+	0.609019i	$0.791563\pi$
$368$	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
$372$	1.42243	−	2.61796i	0.0737496	−	0.135735i
$373$	−7.07089	+	7.07089i	−0.366117	+	0.366117i	−0.866059	−	0.499942i	$-0.833355\pi$
$373$	−7.07089	+	7.07089i	−0.366117	+	0.366117i	0.499942	+	0.866059i	$0.333355\pi$
$374$	−0.248066			−0.0128272
$375$	13.0293	+	14.3261i	0.672828	+	0.739799i
$376$	−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	$-0.814071\pi$
$379$		−	21.4715i		−	1.10292i	0.834202	−	0.551459i	$-0.185929\pi$
$380$	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	$-0.427635\pi$
$383$	−14.6559	−	14.6559i	−0.748882	−	0.748882i	−0.974269	+	0.225388i	$0.927635\pi$
$384$	4.84748	+	16.3824i	0.247372	+	0.836012i
$385$		0			0
$386$			7.46402i			0.379909i
$387$	3.58727	+	0.764695i	0.182351	+	0.0388716i
$388$	−12.5170	+	12.5170i	−0.635457	+	0.635457i
$389$	−13.6323			−0.691185			−0.345592	−	0.938385i	$-0.612322\pi$
$389$	−13.6323			−0.691185			−0.345592	+	0.938385i	$0.612322\pi$
$390$	−3.20206	−	0.275411i	−0.162143	−	0.0139460i
$391$	−0.623074			−0.0315102
$392$		0			0
$393$	7.41804	−	13.6528i	0.374190	−	0.688692i
$394$			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	0.962886	+	0.269907i	$0.0869929\pi$
$397$	24.5632	+	24.5632i	1.23279	+	1.23279i	0.269907	+	0.962886i	$0.413007\pi$
$398$	−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	$-0.126504\pi$
$402$	0.646036	+	0.351014i	0.0322214	+	0.0175070i
$403$	1.47078	−	1.47078i	0.0732647	−	0.0732647i
$404$	−23.2177			−1.15512
$405$	20.1239	+	0.163776i	0.999967	+	0.00813810i
$406$		0			0
$407$	−20.0390	+	20.0390i	−0.993296	+	0.993296i
$408$	−0.430700	−	0.234015i	−0.0213228	−	0.0115854i
$409$		−	32.0414i		−	1.58434i	−0.610298	−	0.792172i	$-0.708950\pi$
$409$		−	32.0414i		−	1.58434i	0.610298	−	0.792172i	$-0.291050\pi$
$410$	−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
$417$	1.52081	−	2.79904i	0.0744746	−	0.137069i
$418$	6.47733	−	6.47733i	0.316817	−	0.316817i
$419$	−5.95062			−0.290707			−0.145353	−	0.989380i	$-0.546432\pi$
$419$	−5.95062			−0.290707			−0.145353	+	0.989380i	$0.546432\pi$
$420$		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
$423$	2.70270	+	0.576132i	0.131410	+	0.0280125i
$424$			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	$-0.0875271\pi$
$432$	−1.29225	−	16.6061i	−0.0621733	−	0.798962i
$433$	−9.75098	+	9.75098i	−0.468602	+	0.468602i	−0.901462	−	0.432859i	$-0.857505\pi$
$433$	−9.75098	+	9.75098i	−0.468602	+	0.468602i	0.432859	+	0.901462i	$0.357505\pi$
$434$		0			0
$435$	3.15020	−	36.6258i	0.151041	−	1.75607i
$436$	12.4487			0.596185
$437$	16.2693	−	16.2693i	0.778265	−	0.778265i
$438$	−2.06936	+	3.80863i	−0.0988779	+	0.181983i
$439$			28.4375i			1.35725i	0.734485	+	0.678625i	$0.237424\pi$
$439$			28.4375i			1.35725i	−0.734485	+	0.678625i	$0.762576\pi$
$440$	−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	$-0.0266723\pi$
$443$	19.2121	+	19.2121i	0.912796	+	0.912796i	−0.0836955	+	0.996491i	$0.526672\pi$
$444$	−25.9069	+	7.66573i	−1.22949	+	0.363799i
$445$	−11.0801	−	25.3602i	−0.525245	−	1.20219i
$446$			6.00850i			0.284511i
$447$	1.50247	+	0.816347i	0.0710646	+	0.0386119i
$448$		0			0
$449$	2.40628			0.113559			0.0567796	−	0.998387i	$-0.481917\pi$
$449$	2.40628			0.113559			0.0567796	+	0.998387i	$0.481917\pi$
$450$	4.51324	−	3.17998i	0.212756	−	0.149906i
$451$	−4.71729			−0.222129
$452$	−15.3534	+	15.3534i	−0.722166	+	0.722166i
$453$	−13.2572	−	7.20307i	−0.622875	−	0.338430i
$454$		−	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	0.837383	−	0.546617i	$-0.184084\pi$
$457$	6.21588	+	6.21588i	0.290767	+	0.290767i	−0.546617	+	0.837383i	$0.684084\pi$
$458$	−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	−0.997924	−	0.0644045i	$-0.979485\pi$
$463$	−20.0869	+	20.0869i	−0.933519	+	0.933519i	0.0644045	+	0.997924i	$0.479485\pi$
$464$	−30.4256			−1.41247
$465$	−0.306197	+	3.56000i	−0.0141996	+	0.165091i
$466$	7.43265			0.344311
$467$	−5.80567	+	5.80567i	−0.268654	+	0.268654i	−0.828558	−	0.559903i	$-0.810838\pi$
$467$	−5.80567	+	5.80567i	−0.268654	+	0.268654i	0.559903	+	0.828558i	$0.310838\pi$
$468$	2.62918	−	12.3338i	0.121534	−	0.570130i
$469$		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
$477$	5.78575	−	27.1416i	0.264911	−	1.24273i
$478$	3.34746	−	3.34746i	0.153109	−	0.153109i
$479$	40.3829			1.84514			0.922571	−	0.385828i	$-0.126084\pi$
$479$	40.3829			1.84514			0.922571	+	0.385828i	$0.126084\pi$
$480$	−10.0369	−	11.9260i	−0.458121	−	0.544343i
$481$	−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	0.995183	−	0.0980363i	$-0.0312561\pi$
$487$	19.7983	+	19.7983i	0.897147	+	0.897147i	−0.0980363	+	0.995183i	$0.531256\pi$
$488$	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	$0.689506\pi$
$492$	−3.95159	−	2.14704i	−0.178152	−	0.0967960i
$493$	1.33533	−	1.33533i	0.0601402	−	0.0601402i
$494$	6.09662			0.274300
$495$	18.9640	+	12.5200i	0.852366	+	0.562731i
$496$	2.95735			0.132789
$497$		0			0
$498$	4.96636	+	2.69840i	0.222548	+	0.120918i
$499$			7.62548i			0.341363i	0.985326	+	0.170682i	$0.0545970\pi$
$499$			7.62548i			0.341363i	−0.985326	+	0.170682i	$0.945403\pi$
$500$	−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	$-0.415446\pi$
$503$	−15.7533	−	15.7533i	−0.702406	−	0.702406i	−0.964926	+	0.262521i	$0.915446\pi$
$504$		0			0
$505$	25.5152	−	11.1478i	1.13541	−	0.496070i
$506$			3.90468i			0.173584i
$507$	−6.54670	+	12.0491i	−0.290749	+	0.535119i
$508$	−3.50866	+	3.50866i	−0.155672	+	0.155672i
$509$	14.4091			0.638673			0.319336	−	0.947641i	$-0.396540\pi$
$509$	14.4091			0.638673			0.319336	+	0.947641i	$0.396540\pi$
$510$	0.282575	+	0.0243044i	0.0125126	+	0.00107622i
$511$		0			0
$512$	−15.5706	+	15.5706i	−0.688130	+	0.688130i
$513$	−38.0606	+	2.96178i	−1.68042	+	0.130766i
$514$		−	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	$-0.187691\pi$
$522$	−10.2504	−	2.18507i	−0.448648	−	0.0956378i
$523$	16.0464	−	16.0464i	0.701661	−	0.701661i	−0.263106	−	0.964767i	$-0.584747\pi$
$523$	16.0464	−	16.0464i	0.701661	−	0.701661i	0.964767	+	0.263106i	$0.0847470\pi$
$524$	16.7263			0.730692
$525$		0			0
$526$	7.20208			0.314026
$527$	−0.129793	+	0.129793i	−0.00565387	+	0.00565387i
$528$	8.97912	−	16.5259i	0.390766	−	0.719199i
$529$		−	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
$537$	−26.8655	−	14.5970i	−1.15933	−	0.629905i
$538$	2.98346	−	2.98346i	0.128626	−	0.128626i
$539$		0			0
$540$	10.1874	+	19.1191i	0.438396	+	0.822753i
$541$	−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
$543$	18.1468	+	9.85981i	0.778756	+	0.423125i
$544$		−	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	0.977501	−	0.210929i	$-0.0676489\pi$
$547$	17.9286	+	17.9286i	0.766572	+	0.766572i	−0.210929	+	0.977501i	$0.567649\pi$
$548$	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
$552$	−3.68350	+	6.77942i	−0.156780	+	0.288551i
$553$		0			0
$554$	−6.62667			−0.281540
$555$	24.7900	−	20.8633i	1.05228	−	0.885599i
$556$	3.42915			0.145428
$557$	5.15944	−	5.15944i	0.218613	−	0.218613i	−0.589301	−	0.807914i	$-0.700597\pi$
$557$	5.15944	−	5.15944i	0.218613	−	0.218613i	0.807914	+	0.589301i	$0.200597\pi$
$558$	0.996333	+	0.212387i	0.0421781	+	0.00899106i
$559$			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	$-0.493718\pi$
$563$	−23.2548	−	23.2548i	−0.980072	−	0.980072i	−0.999805	+	0.0197332i	$0.993718\pi$
$564$	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	$-0.103839\pi$
$569$	45.1914			1.89452			0.947260	+	0.320466i	$0.103839\pi$
$570$	−8.01302	+	6.74378i	−0.335629	+	0.282466i
$571$	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
$573$	−14.7065	+	27.0671i	−0.614372	+	1.13074i
$574$		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	0.822957	−	0.568104i	$-0.192323\pi$
$577$	6.12177	+	6.12177i	0.254853	+	0.254853i	−0.568104	+	0.822957i	$0.692323\pi$
$578$	−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
$582$	−5.31822	−	2.88958i	−0.220447	−	0.119777i
$583$	22.1579	−	22.1579i	0.917686	−	0.917686i
$584$	−9.67107			−0.400192
$585$	3.03262	+	14.8167i	0.125383	+	0.612596i
$586$	−3.83938			−0.158603
$587$	−3.77086	+	3.77086i	−0.155640	+	0.155640i	−0.780632	−	0.624992i	$-0.785102\pi$
$587$	−3.77086	+	3.77086i	−0.155640	+	0.155640i	0.624992	+	0.780632i	$0.285102\pi$
$588$		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	$-0.328242\pi$
$593$	−8.38017	−	8.38017i	−0.344132	−	0.344132i	−0.857918	+	0.513786i	$0.828242\pi$
$594$	4.21191	−	4.92275i	0.172817	−	0.201983i
$595$		0			0
$596$			1.84071i			0.0753985i
$597$	−11.0928	+	20.4161i	−0.453998	+	0.835577i
$598$	−1.83759	+	1.83759i	−0.0751446	+	0.0751446i
$599$	6.75588			0.276038			0.138019	−	0.990430i	$-0.455927\pi$
$599$	6.75588			0.276038			0.138019	+	0.990430i	$0.455927\pi$
$600$	11.0419	+	5.46084i	0.450782	+	0.222938i
$601$	−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
$603$	0.721331	−	3.38385i	0.0293749	−	0.137801i
$604$		−	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	0.649641	−	0.760241i	$-0.274919\pi$
$607$	−2.72491	−	2.72491i	−0.110601	−	0.110601i	−0.760241	+	0.649641i	$0.774919\pi$
$608$	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
$612$	−0.232020	+	1.08843i	−0.00937884	+	0.0439972i
$613$	15.6232	−	15.6232i	0.631017	−	0.631017i	−0.317306	−	0.948323i	$-0.602778\pi$
$613$	15.6232	−	15.6232i	0.631017	−	0.631017i	0.948323	+	0.317306i	$0.102778\pi$
$614$	5.91361			0.238654
$615$	5.37352	+	0.462179i	0.216681	+	0.0186369i
$616$		0			0
$617$	−5.47009	+	5.47009i	−0.220218	+	0.220218i	−0.808590	−	0.588373i	$-0.799769\pi$
$617$	−5.47009	+	5.47009i	−0.220218	+	0.220218i	0.588373	+	0.808590i	$0.299769\pi$
$618$	−4.21357	+	7.75500i	−0.169494	+	0.311952i
$619$			42.9951i			1.72812i	0.503389	+	0.864060i	$0.332086\pi$
$619$			42.9951i			1.72812i	−0.503389	+	0.864060i	$0.667914\pi$
$620$	−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
$627$	−37.8768	−	20.5798i	−1.51265	−	0.821878i
$628$	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
$633$	12.3507	+	6.71057i	0.490897	+	0.266721i
$634$			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	$-0.208141\pi$
$642$	2.24626	−	4.13420i	0.0886527	−	0.163164i
$643$	6.17366	−	6.17366i	0.243465	−	0.243465i	−0.574817	−	0.818282i	$-0.694927\pi$
$643$	6.17366	−	6.17366i	0.243465	−	0.243465i	0.818282	+	0.574817i	$0.194927\pi$
$644$		0			0
$645$	−3.04905	−	3.62291i	−0.120056	−	0.142652i
$646$	−0.538014			−0.0211679
$647$	−23.4296	+	23.4296i	−0.921112	+	0.921112i	−0.997108	−	0.0759964i	$-0.975786\pi$
$647$	−23.4296	+	23.4296i	−0.921112	+	0.921112i	0.0759964	+	0.997108i	$0.475786\pi$
$648$	11.9568	−	4.57370i	0.469706	−	0.179672i
$649$		−	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	$-0.407821\pi$
$653$	−17.1928	−	17.1928i	−0.672805	−	0.672805i	−0.958362	+	0.285557i	$0.907821\pi$
$654$	1.20769	+	4.08150i	0.0472246	+	0.159599i
$655$	−18.3815	+	8.03100i	−0.718225	+	0.313797i
$656$		−	4.46386i		−	0.174285i
$657$	19.9490	+	4.25252i	0.778286	+	0.165906i
$658$		0			0
$659$	−0.0375362			−0.00146220			−0.000731101	−	1.00000i	$-0.500233\pi$
$659$	−0.0375362			−0.00146220			−0.000731101		1.00000i	$0.500233\pi$
$660$	−2.09625	+	24.3721i	−0.0815966	+	0.948682i
$661$	−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
$663$	−0.370916	+	0.682666i	−0.0144052	+	0.0265125i
$664$			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	−0.785666	−	0.618651i	$-0.787680\pi$
$673$	−4.33276	+	4.33276i	−0.167016	+	0.167016i	0.618651	+	0.785666i	$0.287680\pi$
$674$	8.89793			0.342736
$675$	−20.3754	−	16.1196i	−0.784250	−	0.620445i
$676$	−14.7616			−0.567753
$677$	3.64637	−	3.64637i	0.140142	−	0.140142i	−0.633556	−	0.773697i	$-0.718405\pi$
$677$	3.64637	−	3.64637i	0.140142	−	0.140142i	0.773697	+	0.633556i	$0.218405\pi$
$678$	−6.52335	−	3.54436i	−0.250528	−	0.136120i
$679$		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	0.933830	+	0.357718i	$0.116445\pi$
$683$	33.7536	+	33.7536i	1.29155	+	1.29155i	0.357718	+	0.933830i	$0.383555\pi$
$684$	−22.3620	−	34.4787i	−0.855033	−	1.31833i
$685$	−19.1242	−	7.49436i	−0.730697	−	0.286345i
$686$		0			0
$687$	−3.97013	+	7.30696i	−0.151470	+	0.278778i
$688$	−2.77125	+	2.77125i	−0.105653	+	0.105653i
$689$	20.8555			0.794533
$690$	0.382563	−	4.44786i	0.0145639	−	0.169327i
$691$	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	$-0.134999\pi$
$702$	4.29889	−	0.334529i	0.162251	−	0.0126260i
$703$	−43.4612	+	43.4612i	−1.63917	+	1.63917i
$704$	16.6992			0.629377
$705$	−2.29719	−	2.72955i	−0.0865174	−	0.102801i
$706$	−3.93294			−0.148018
$707$		0			0
$708$	9.63670	−	17.7362i	0.362169	−	0.666567i
$709$			14.1622i			0.531874i	0.963990	+	0.265937i	$0.0856814\pi$
$709$			14.1622i			0.531874i	−0.963990	+	0.265937i	$0.914319\pi$
$710$	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
$717$	−19.5746	−	10.6355i	−0.731026	−	0.397192i
$718$	−1.58632	+	1.58632i	−0.0592008	+	0.0592008i
$719$	−39.3153			−1.46621			−0.733106	−	0.680114i	$-0.761930\pi$
$719$	−39.3153			−1.46621			−0.733106	+	0.680114i	$0.761930\pi$
$720$	−11.8474	+	17.9451i	−0.441525	+	0.668776i
$721$		0			0
$722$	9.10324	−	9.10324i	0.338787	−	0.338787i
$723$	24.6331	+	13.3840i	0.916115	+	0.497757i
$724$			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	0.496585	−	0.867988i	$-0.334587\pi$
$727$	−10.0141	−	10.0141i	−0.371403	−	0.371403i	−0.867988	+	0.496585i	$0.834587\pi$
$728$		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
$732$	2.82551	−	5.20032i	0.104434	−	0.192209i
$733$	30.5737	−	30.5737i	1.12926	−	1.12926i	0.138967	−	0.990297i	$-0.455622\pi$
$733$	30.5737	−	30.5737i	1.12926	−	1.12926i	0.990297	−	0.138967i	$-0.0443783\pi$
$734$	1.83618			0.0677745
$735$		0			0
$736$	−12.6040			−0.464589
$737$	2.76250	−	2.76250i	0.101758	−	0.101758i
$738$	0.320580	−	1.50388i	0.0118007	−	0.0553586i
$739$		−	16.1095i		−	0.592598i	−0.955095	−	0.296299i	$-0.904247\pi$
$739$		−	16.1095i		−	0.592598i	0.955095	−	0.296299i	$-0.0957525\pi$
$740$	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	$-0.455232\pi$
$743$	−23.1679	−	23.1679i	−0.849946	−	0.849946i	−0.990126	+	0.140180i	$0.955232\pi$
$744$	0.644914	+	2.17954i	0.0236437	+	0.0799057i
$745$	−0.883803	−	2.02286i	−0.0323800	−	0.0741120i
$746$		−	3.68059i		−	0.134756i
$747$	5.54518	−	26.0131i	0.202888	−	0.951770i
$748$	−0.888574	+	0.888574i	−0.0324895	+	0.0324895i
$749$		0			0
$750$	−7.11961	−	0.337528i	−0.259971	−	0.0123248i
$751$	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
$753$	−6.63894	+	12.2189i	−0.241936	+	0.445280i
$754$		−	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	0.683270	−	0.730166i	$-0.260557\pi$
$757$	−1.29026	−	1.29026i	−0.0468952	−	0.0468952i	−0.730166	+	0.683270i	$0.760557\pi$
$758$	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	$-0.211326\pi$
$762$	−1.49075	−	0.809978i	−0.0540043	−	0.0293424i
$763$		0			0
$764$	−33.1604			−1.19970
$765$	−0.267622	−	1.30754i	−0.00967589	−	0.0472743i
$766$	7.62879			0.275639
$767$	9.96424	−	9.96424i	0.359788	−	0.359788i
$768$	9.47970	+	5.15065i	0.342069	+	0.185858i
$769$		−	21.4206i		−	0.772448i	−0.922405	−	0.386224i	$-0.873779\pi$
$769$		−	21.4206i		−	0.772448i	0.922405	−	0.386224i	$-0.126221\pi$
$770$		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	$-0.172279\pi$
$773$	9.50533	+	9.50533i	0.341883	+	0.341883i	−0.515192	+	0.857075i	$0.672279\pi$
$774$	−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
$780$	−12.4563	+	10.4833i	−0.446008	+	0.375361i
$781$	33.1179			1.18505
$782$	0.162163	−	0.162163i	0.00579895	−	0.00579895i
$783$	3.82640	+	49.1714i	0.136745	+	1.75724i
$784$		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	0.598015	−	0.801485i	$-0.295956\pi$
$787$	−5.70807	−	5.70807i	−0.203471	−	0.203471i	−0.801485	+	0.598015i	$0.795956\pi$
$788$	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
$792$	14.1376	+	3.01369i	0.502356	+	0.107087i
$793$	2.92155	−	2.92155i	0.103747	−	0.103747i
$794$	−12.7858			−0.453752
$795$	−27.4112	+	23.0694i	−0.972176	+	0.818186i
$796$	−25.0122			−0.886534
$797$	−7.78096	+	7.78096i	−0.275616	+	0.275616i	−0.831356	−	0.555740i	$-0.812435\pi$
$797$	−7.78096	+	7.78096i	−0.275616	+	0.275616i	0.555740	+	0.831356i	$0.312435\pi$
$798$		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
$807$	−17.4460	−	9.47905i	−0.614130	−	0.333678i
$808$	12.5245	−	12.5245i	0.440609	−	0.440609i
$809$	28.7871			1.01210			0.506051	−	0.862504i	$-0.331105\pi$
$809$	28.7871			1.01210			0.506051	+	0.862504i	$0.331105\pi$
$810$	−5.28015	+	5.19490i	−0.185526	+	0.182530i
$811$	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
$813$	−12.8187	−	6.96485i	−0.449572	−	0.244268i
$814$		−	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	$0.794062\pi$
$822$	−2.79579	+	5.14561i	−0.0975145	+	0.179474i
$823$	−11.9459	+	11.9459i	−0.416409	+	0.416409i	−0.883964	−	0.467555i	$-0.845135\pi$
$823$	−11.9459	+	11.9459i	−0.416409	+	0.416409i	0.467555	+	0.883964i	$0.345135\pi$
$824$	−19.6919			−0.686001
$825$	−9.39837	−	27.7904i	−0.327209	−	0.967537i
$826$		0			0
$827$	20.8624	−	20.8624i	0.725457	−	0.725457i	−0.244254	−	0.969711i	$-0.578543\pi$
$827$	20.8624	−	20.8624i	0.725457	−	0.725457i	0.969711	+	0.244254i	$0.0785431\pi$
$828$	17.1324	+	3.65210i	0.595392	+	0.126919i
$829$		−	34.6491i		−	1.20341i	−0.798717	−	0.601706i	$-0.794488\pi$
$829$		−	34.6491i		−	1.20341i	0.798717	−	0.601706i	$-0.205512\pi$
$830$	−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
$837$	−0.371924	−	4.77943i	−0.0128556	−	0.165201i
$838$	1.54873	−	1.54873i	0.0534999	−	0.0534999i
$839$	10.9282			0.377283			0.188642	−	0.982046i	$-0.439592\pi$
$839$	10.9282			0.377283			0.188642	+	0.982046i	$0.439592\pi$
$840$		0			0
$841$	61.0915			2.10660
$842$	2.76889	−	2.76889i	0.0954223	−	0.0954223i
$843$	−3.64874	+	6.71546i	−0.125669	+	0.231293i
$844$			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
$852$	27.7423	+	15.0734i	0.950436	+	0.516405i
$853$	8.08267	−	8.08267i	0.276745	−	0.276745i	−0.555063	−	0.831808i	$-0.687306\pi$
$853$	8.08267	−	8.08267i	0.276745	−	0.276745i	0.831808	+	0.555063i	$0.187306\pi$
$854$		0			0
$855$	41.1296	+	27.1537i	1.40660	+	0.928636i
$856$	10.4978			0.358807
$857$	−14.3191	+	14.3191i	−0.489131	+	0.489131i	−0.908032	−	0.418901i	$-0.862415\pi$
$857$	−14.3191	+	14.3191i	−0.489131	+	0.489131i	0.418901	+	0.908032i	$0.362415\pi$
$858$	4.27813	+	2.32446i	0.146053	+	0.0793557i
$859$			25.0614i			0.855084i	0.903995	+	0.427542i	$0.140620\pi$
$859$			25.0614i			0.855084i	−0.903995	+	0.427542i	$0.859380\pi$
$860$	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	−0.992170	−	0.124896i	$-0.960140\pi$
$863$	−32.8159	−	32.8159i	−1.11707	−	1.11707i	−0.124896	−	0.992170i	$-0.539860\pi$
$864$	15.8902	+	13.5957i	0.540597	+	0.462535i
$865$	12.5496	−	32.0241i	0.426698	−	1.08885i
$866$		−	5.07564i		−	0.172477i
$867$	−14.0247	+	25.8123i	−0.476304	+	0.876631i
$868$		0			0
$869$	11.5755			0.392671
$870$	8.71247	+	10.3522i	0.295380	+	0.350973i
$871$	2.60014			0.0881023
$872$	−6.71530	+	6.71530i	−0.227409	+	0.227409i
$873$	−5.93805	+	27.8561i	−0.200972	+	0.942785i
$874$			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	0.916441	−	0.400170i	$-0.131049\pi$
$877$	15.2890	+	15.2890i	0.516271	+	0.516271i	−0.400170	+	0.916441i	$0.631049\pi$
$878$	−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	−0.988115	−	0.153718i	$-0.950875\pi$
$883$	−24.7944	+	24.7944i	−0.834397	+	0.834397i	0.153718	+	0.988115i	$0.450875\pi$
$884$	−0.836347			−0.0281294
$885$	−2.07443	+	24.1183i	−0.0697312	+	0.810729i
$886$	−10.0004			−0.335971
$887$	18.5532	−	18.5532i	0.622956	−	0.622956i	−0.323331	−	0.946286i	$-0.604803\pi$
$887$	18.5532	−	18.5532i	0.622956	−	0.622956i	0.946286	+	0.323331i	$0.104803\pi$
$888$	9.83997	−	18.1103i	0.330208	−	0.607743i
$889$		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
$897$	10.7455	+	5.83839i	0.358781	+	0.194938i
$898$	−0.626265	+	0.626265i	−0.0208987	+	0.0208987i
$899$	−8.75683			−0.292057
$900$	4.77573	−	27.5571i	0.159191	−	0.918571i
$901$	−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	0.761177	−	0.648545i	$-0.224622\pi$
$907$	3.39207	+	3.39207i	0.112632	+	0.112632i	−0.648545	+	0.761177i	$0.724622\pi$
$908$	−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	$0.913441\pi$
$912$	19.4742	−	35.8419i	0.644855	−	1.18685i
$913$	21.2366	−	21.2366i	0.702828	−	0.702828i
$914$	−3.23553			−0.107022
$915$	−0.608230	+	7.07158i	−0.0201075	+	0.233779i
$916$	−8.95190			−0.295779
$917$		0			0
$918$	−0.379367	+	0.0295215i	−0.0125210	+	0.000974354i
$919$			5.54658i			0.182965i	0.995807	+	0.0914823i	$0.0291605\pi$
$919$			5.54658i			0.182965i	−0.995807	+	0.0914823i	$0.970839\pi$
$920$	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
$927$	40.6196	+	8.65884i	1.33412	+	0.284393i
$928$	27.0120	−	27.0120i	0.886711	−	0.886711i
$929$	12.7978			0.419884			0.209942	−	0.977714i	$-0.432673\pi$
$929$	12.7978			0.419884			0.209942	+	0.977714i	$0.432673\pi$
$930$	−0.846846	−	1.00623i	−0.0277692	−	0.0329956i
$931$		0			0
$932$	26.6237	−	26.6237i	0.872090	−	0.872090i
$933$	7.39497	−	13.6103i	0.242100	−	0.445582i
$934$		−	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	0.185119	−	0.982716i	$-0.440733\pi$
$937$	−24.4148	−	24.4148i	−0.797598	−	0.797598i	−0.982716	+	0.185119i	$0.940733\pi$
$938$		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	$0.980665\pi$
$942$	4.16938	+	2.26537i	0.135846	+	0.0738097i
$943$	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	−0.124186	+	0.992259i	$0.539632\pi$
$947$	−34.3568	+	34.3568i	−1.11644	+	1.11644i	−0.992259	+	0.124186i	$0.960368\pi$
$948$	9.69657	+	5.26849i	0.314930	+	0.171112i
$949$			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	$-0.0842497\pi$
$953$	21.7199	+	21.7199i	0.703578	+	0.703578i	−0.261599	+	0.965177i	$0.584250\pi$
$954$	5.55815	+	8.56979i	0.179952	+	0.277457i
$955$	36.4419	−	15.9217i	1.17923	−	0.515214i
$956$		−	23.9812i		−	0.775607i
$957$	−26.5876	+	48.9340i	−0.859454	+	1.58181i
$958$	−10.5102	+	10.5102i	−0.339569	+	0.339569i
$959$		0			0
$960$	−19.0223	−	1.63612i	−0.613942	−	0.0528055i
$961$	−30.1488			−0.972543
$962$	4.90888	−	4.90888i	0.158269	−	0.158269i
$963$	−21.6544	−	4.61604i	−0.697802	−	0.148750i
$964$			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	−0.880616	−	0.473831i	$-0.842871\pi$
$967$	−42.1187	−	42.1187i	−1.35445	−	1.35445i	−0.473831	−	0.880616i	$-0.657129\pi$
$968$	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	$0.854865\pi$
$972$	−17.6599	−	23.0848i	−0.566442	−	0.740444i
$973$		0			0
$974$	−10.3055			−0.330211
$975$	8.65551	−	17.5015i	0.277198	−	0.560496i
$976$	5.87447			0.188037
$977$	−40.5573	+	40.5573i	−1.29754	+	1.29754i	−0.367531	+	0.930011i	$0.619797\pi$
$977$	−40.5573	+	40.5573i	−1.29754	+	1.29754i	−0.930011	+	0.367531i	$0.880203\pi$
$978$	−6.09104	+	11.2105i	−0.194770	+	0.358471i
$979$			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	$-0.124495\pi$
$983$	17.0329	+	17.0329i	0.543267	+	0.543267i	−0.381218	+	0.924485i	$0.624495\pi$
$984$	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
$990$	−8.19411	+	1.67713i	−0.260426	+	0.0533028i
$991$	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
$993$	−5.50716	−	2.99223i	−0.174764	−	0.0949556i
$994$		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	−0.999967	−	0.00814356i	$-0.997408\pi$
$997$	−31.8314	−	31.8314i	−1.00811	−	1.00811i	−0.00814356	−	0.999967i	$-0.502592\pi$
$998$	−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.197.6		24
3.2	odd	2	inner	735.2.j.h.197.7		24
5.3	odd	4	inner	735.2.j.h.638.7		24
7.2	even	3		735.2.y.g.557.7		48
7.3	odd	6		735.2.y.j.422.6		48
7.4	even	3		735.2.y.g.422.6		48
7.5	odd	6		735.2.y.j.557.7		48
7.6	odd	2		105.2.j.a.92.6	yes	24
15.8	even	4	inner	735.2.j.h.638.6		24
21.2	odd	6		735.2.y.g.557.6		48
21.5	even	6		735.2.y.j.557.6		48
21.11	odd	6		735.2.y.g.422.7		48
21.17	even	6		735.2.y.j.422.7		48
21.20	even	2		105.2.j.a.92.7	yes	24
35.3	even	12		735.2.y.j.128.6		48
35.13	even	4		105.2.j.a.8.7	yes	24
35.18	odd	12		735.2.y.g.128.6		48
35.23	odd	12		735.2.y.g.263.7		48
35.27	even	4		525.2.j.b.218.6		24
35.33	even	12		735.2.y.j.263.7		48
35.34	odd	2		525.2.j.b.407.7		24
105.23	even	12		735.2.y.g.263.6		48
105.38	odd	12		735.2.y.j.128.7		48
105.53	even	12		735.2.y.g.128.7		48
105.62	odd	4		525.2.j.b.218.7		24
105.68	odd	12		735.2.y.j.263.6		48
105.83	odd	4		105.2.j.a.8.6	✓	24
105.104	even	2		525.2.j.b.407.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.6	✓	24	105.83	odd	4
105.2.j.a.8.7	yes	24	35.13	even	4
105.2.j.a.92.6	yes	24	7.6	odd	2
105.2.j.a.92.7	yes	24	21.20	even	2
525.2.j.b.218.6		24	35.27	even	4
525.2.j.b.218.7		24	105.62	odd	4
525.2.j.b.407.6		24	105.104	even	2
525.2.j.b.407.7		24	35.34	odd	2
735.2.j.h.197.6		24	1.1	even	1	trivial
735.2.j.h.197.7		24	3.2	odd	2	inner
735.2.j.h.638.6		24	15.8	even	4	inner
735.2.j.h.638.7		24	5.3	odd	4	inner
735.2.y.g.128.6		48	35.18	odd	12
735.2.y.g.128.7		48	105.53	even	12
735.2.y.g.263.6		48	105.23	even	12
735.2.y.g.263.7		48	35.23	odd	12
735.2.y.g.422.6		48	7.4	even	3
735.2.y.g.422.7		48	21.11	odd	6
735.2.y.g.557.6		48	21.2	odd	6
735.2.y.g.557.7		48	7.2	even	3
735.2.y.j.128.6		48	35.3	even	12
735.2.y.j.128.7		48	105.38	odd	12
735.2.y.j.263.6		48	105.68	odd	12
735.2.y.j.263.7		48	35.33	even	12
735.2.y.j.422.6		48	7.3	odd	6
735.2.y.j.422.7		48	21.17	even	6
735.2.y.j.557.6		48	21.5	even	6
735.2.y.j.557.7		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)

\(f(q)\)	\(=\)	\(q+(-0.260263 + 0.260263i) q^{2} +(1.52191 + 0.826909i) q^{3} +1.86453i q^{4} +(-0.895238 - 2.04904i) q^{5} +(-0.611312 + 0.180884i) q^{6} +(-1.00579 - 1.00579i) q^{8} +(1.63244 + 2.51697i) q^{9} +O(q^{10})\)	\(q+(-0.260263 + 0.260263i) q^{2} +(1.52191 + 0.826909i) 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} +(-1.54179 + 2.83765i) q^{12} +(-1.59420 + 1.59420i) q^{13} +(0.331892 - 3.85874i) q^{15} -3.20551 q^{16} +(0.140684 - 0.140684i) q^{17} +(-1.07994 - 0.230209i) 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} +(0.403134 + 5.18049i) q^{27} +9.49165 q^{29} +(0.917908 + 1.09067i) q^{30} -0.922582 q^{31} +(2.84586 - 2.84586i) q^{32} +(-2.80115 + 5.15548i) 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} +(3.69593 - 5.59822i) q^{45} +1.15267 q^{46} +(0.651346 - 0.651346i) q^{47} +(-4.87851 - 2.65066i) 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} +(-6.07522 + 11.1814i) q^{57} +(-2.47033 + 2.47033i) q^{58} -6.25032 q^{59} +(7.19471 + 0.618821i) 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} +(0.889650 - 4.17345i) q^{72} +(4.80768 - 4.80768i) q^{73} -3.07921 q^{74} +(-8.20381 + 2.77443i) q^{75} -13.6985 q^{76} +(0.686187 - 1.26292i) 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} +(14.4455 + 7.84873i) q^{87} +(3.40712 - 3.40712i) q^{88} +12.3767 q^{89} +(0.495095 + 2.41893i) q^{90} +(4.12888 - 4.12888i) q^{92} +(-1.40409 - 0.762891i) 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

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