LMFDB - Embedded newform 735.2.j.e.638.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(197,735)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("735.197"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [24,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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.e.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+(0.218381 + 0.218381i) q^{2} +(1.69540 - 0.354425i) q^{3} -1.90462i q^{4} +(2.16448 + 0.561256i) q^{5} +(0.447643 + 0.292843i) q^{6} +(0.852694 - 0.852694i) q^{8} +(2.74877 - 1.20179i) q^{9} +(0.350114 + 0.595249i) q^{10} -0.762466i q^{11} +(-0.675045 - 3.22909i) q^{12} +(2.27077 + 2.27077i) q^{13} +(3.86859 + 0.184406i) q^{15} -3.43682 q^{16} +(-3.43677 - 3.43677i) q^{17} +(0.862724 + 0.337831i) q^{18} +1.63691i q^{19} +(1.06898 - 4.12252i) q^{20} +(0.166508 - 0.166508i) q^{22} +(-5.40988 + 5.40988i) q^{23} +(1.14344 - 1.74787i) q^{24} +(4.36998 + 2.42966i) q^{25} +0.991783i q^{26} +(4.23432 - 3.01174i) q^{27} -4.94251 q^{29} +(0.804555 + 0.885097i) q^{30} +5.92827 q^{31} +(-2.45592 - 2.45592i) q^{32} +(-0.270237 - 1.29269i) q^{33} -1.50105i q^{34} +(-2.28894 - 5.23535i) q^{36} +(-2.50059 + 2.50059i) q^{37} +(-0.357470 + 0.357470i) q^{38} +(4.65467 + 3.04504i) q^{39} +(2.32422 - 1.36706i) q^{40} -4.35963i q^{41} +(2.69037 + 2.69037i) q^{43} -1.45221 q^{44} +(6.62417 - 1.05849i) q^{45} -2.36283 q^{46} +(-3.03177 - 3.03177i) q^{47} +(-5.82678 + 1.21809i) q^{48} +(0.423730 + 1.48491i) q^{50} +(-7.04478 - 4.60862i) q^{51} +(4.32494 - 4.32494i) q^{52} +(-4.91465 + 4.91465i) q^{53} +(1.58240 + 0.266987i) q^{54} +(0.427939 - 1.65035i) q^{55} +(0.580162 + 2.77522i) q^{57} +(-1.07935 - 1.07935i) q^{58} +7.69002 q^{59} +(0.351222 - 7.36819i) q^{60} -4.39397 q^{61} +(1.29462 + 1.29462i) q^{62} +5.80098i q^{64} +(3.64056 + 6.18952i) q^{65} +(0.223283 - 0.341312i) q^{66} +(0.0345049 - 0.0345049i) q^{67} +(-6.54574 + 6.54574i) q^{68} +(-7.25451 + 11.0893i) q^{69} -12.4172i q^{71} +(1.31910 - 3.36861i) q^{72} +(-0.981264 - 0.981264i) q^{73} -1.09216 q^{74} +(8.27000 + 2.57041i) q^{75} +3.11769 q^{76} +(0.351513 + 1.68147i) q^{78} +4.23554i q^{79} +(-7.43893 - 1.92893i) q^{80} +(6.11142 - 6.60685i) q^{81} +(0.952060 - 0.952060i) q^{82} +(5.05351 - 5.05351i) q^{83} +(-5.50993 - 9.36774i) q^{85} +1.17505i q^{86} +(-8.37953 + 1.75175i) q^{87} +(-0.650150 - 0.650150i) q^{88} -0.907199 q^{89} +(1.67774 + 1.21544i) q^{90} +(10.3038 + 10.3038i) q^{92} +(10.0508 - 2.10113i) q^{93} -1.32416i q^{94} +(-0.918726 + 3.54307i) q^{95} +(-5.03421 - 3.29333i) q^{96} +(-3.73061 + 3.73061i) q^{97} +(-0.916321 - 2.09584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{3} + 12 q^{6} - 8 q^{10} - 10 q^{12} + 8 q^{13} + 2 q^{15} + 8 q^{16} - 14 q^{18} - 4 q^{22} - 4 q^{25} - 20 q^{27} - 40 q^{30} - 24 q^{31} - 4 q^{33} + 4 q^{36} - 4 q^{37} - 16 q^{40} + 8 q^{43}+ \cdots + 60 q^{97}+O(q^{100}) $ 24 * q - 2 * q^3 + 12 * q^6 - 8 * q^10 - 10 * q^12 + 8 * q^13 + 2 * q^15 + 8 * q^16 - 14 * q^18 - 4 * q^22 - 4 * q^25 - 20 * q^27 - 40 * q^30 - 24 * q^31 - 4 * q^33 + 4 * q^36 - 4 * q^37 - 16 * q^40 + 8 * q^43 + 40 * q^45 + 32 * q^46 - 22 * q^48 - 8 * q^51 + 36 * q^52 + 20 * q^55 - 44 * q^57 - 56 * q^58 + 50 * q^60 - 8 * q^61 + 76 * q^66 - 12 * q^67 + 34 * q^72 + 52 * q^73 + 6 * q^75 - 32 * q^76 - 60 * q^78 - 20 * q^81 + 104 * q^82 - 12 * q^85 - 46 * q^87 + 42 * q^90 + 44 * q^93 + 12 * q^96 + 60 * q^97

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 $

$2$	0.218381	+	0.218381i	0.154419	+	0.154419i	0.780088	−	0.625670i	$-0.215174\pi$
$2$	0.218381	+	0.218381i	0.154419	+	0.154419i	−0.625670	+	0.780088i	$0.715174\pi$
$3$	1.69540	−	0.354425i	0.978840	−	0.204628i
$3$	1.69540	−	0.354425i	0.978840	−	0.204628i
$4$		−	1.90462i		−	0.952310i
$5$	2.16448	+	0.561256i	0.967987	+	0.251001i
$5$	2.16448	+	0.561256i	0.967987	+	0.251001i
$6$	0.447643	+	0.292843i	0.182749	+	0.119553i
$7$		0			0
$7$		0			0
$8$	0.852694	−	0.852694i	0.301473	−	0.301473i
$9$	2.74877	−	1.20179i	0.916255	−	0.400595i
$10$	0.350114	+	0.595249i	0.110716	+	0.188234i
$11$		−	0.762466i		−	0.229892i	−0.993372	−	0.114946i	$-0.963330\pi$
$11$		−	0.762466i		−	0.229892i	0.993372	−	0.114946i	$-0.0366695\pi$
$12$	−0.675045	−	3.22909i	−0.194869	−	0.932159i
$13$	2.27077	+	2.27077i	0.629797	+	0.629797i	0.948017	−	0.318220i	$-0.103085\pi$
$13$	2.27077	+	2.27077i	0.629797	+	0.629797i	−0.318220	+	0.948017i	$0.603085\pi$
$14$		0			0
$15$	3.86859	+	0.184406i	0.998866	+	0.0476133i
$16$	−3.43682			−0.859204
$17$	−3.43677	−	3.43677i	−0.833539	−	0.833539i	0.154460	−	0.987999i	$-0.450636\pi$
$17$	−3.43677	−	3.43677i	−0.833539	−	0.833539i	−0.987999	+	0.154460i	$0.950636\pi$
$18$	0.862724	+	0.337831i	0.203346	+	0.0796275i
$19$			1.63691i			0.375533i	0.982214	+	0.187767i	$0.0601248\pi$
$19$			1.63691i			0.375533i	−0.982214	+	0.187767i	$0.939875\pi$
$20$	1.06898	−	4.12252i	0.239031	−	0.921823i
$21$		0			0
$22$	0.166508	−	0.166508i	0.0354996	−	0.0354996i
$23$	−5.40988	+	5.40988i	−1.12804	+	1.12804i	−0.137542	+	0.990496i	$0.543920\pi$
$23$	−5.40988	+	5.40988i	−1.12804	+	1.12804i	−0.990496	+	0.137542i	$0.956080\pi$
$24$	1.14344	−	1.74787i	0.233404	−	0.356783i
$25$	4.36998	+	2.42966i	0.873997	+	0.485932i
$26$			0.991783i			0.194505i
$27$	4.23432	−	3.01174i	0.814894	−	0.579610i
$28$		0			0
$29$	−4.94251			−0.917801			−0.458900	−	0.888488i	$-0.651757\pi$
$29$	−4.94251			−0.917801			−0.458900	+	0.888488i	$0.651757\pi$
$30$	0.804555	+	0.885097i	0.146891	+	0.161596i
$31$	5.92827			1.06475			0.532374	−	0.846509i	$-0.321300\pi$
$31$	5.92827			1.06475			0.532374	+	0.846509i	$0.321300\pi$
$32$	−2.45592	−	2.45592i	−0.434150	−	0.434150i
$33$	−0.270237	−	1.29269i	−0.0470423	−	0.225028i
$34$		−	1.50105i		−	0.257428i
$35$		0			0
$36$	−2.28894	−	5.23535i	−0.381491	−	0.872559i
$37$	−2.50059	+	2.50059i	−0.411095	+	0.411095i	−0.882120	−	0.471025i	$-0.843884\pi$
$37$	−2.50059	+	2.50059i	−0.411095	+	0.411095i	0.471025	+	0.882120i	$0.343884\pi$
$38$	−0.357470	+	0.357470i	−0.0579893	+	0.0579893i
$39$	4.65467	+	3.04504i	0.745344	+	0.487597i
$40$	2.32422	−	1.36706i	0.367492	−	0.216152i
$41$		−	4.35963i		−	0.680860i	−0.940270	−	0.340430i	$-0.889427\pi$
$41$		−	4.35963i		−	0.680860i	0.940270	−	0.340430i	$-0.110573\pi$
$42$		0			0
$43$	2.69037	+	2.69037i	0.410277	+	0.410277i	0.881835	−	0.471558i	$-0.156308\pi$
$43$	2.69037	+	2.69037i	0.410277	+	0.410277i	−0.471558	+	0.881835i	$0.656308\pi$
$44$	−1.45221			−0.218929
$45$	6.62417	−	1.05849i	0.987473	−	0.157790i
$46$	−2.36283			−0.348380
$47$	−3.03177	−	3.03177i	−0.442230	−	0.442230i	0.450531	−	0.892761i	$-0.351235\pi$
$47$	−3.03177	−	3.03177i	−0.442230	−	0.442230i	−0.892761	+	0.450531i	$0.851235\pi$
$48$	−5.82678	+	1.21809i	−0.841023	+	0.175817i
$49$		0			0
$50$	0.423730	+	1.48491i	0.0599244	+	0.209998i
$51$	−7.04478	−	4.60862i	−0.986466	−	0.645336i
$52$	4.32494	−	4.32494i	0.599762	−	0.599762i
$53$	−4.91465	+	4.91465i	−0.675080	+	0.675080i	−0.958883	−	0.283803i	$-0.908404\pi$
$53$	−4.91465	+	4.91465i	−0.675080	+	0.675080i	0.283803	+	0.958883i	$0.408404\pi$
$54$	1.58240	+	0.266987i	0.215337	+	0.0363323i
$55$	0.427939	−	1.65035i	0.0577032	−	0.222533i
$56$		0			0
$57$	0.580162	+	2.77522i	0.0768444	+	0.367587i
$58$	−1.07935	−	1.07935i	−0.141725	−	0.141725i
$59$	7.69002			1.00115			0.500577	−	0.865692i	$-0.333121\pi$
$59$	7.69002			1.00115			0.500577	+	0.865692i	$0.333121\pi$
$60$	0.351222	−	7.36819i	0.0453426	−	0.951230i
$61$	−4.39397			−0.562591			−0.281295	−	0.959621i	$-0.590764\pi$
$61$	−4.39397			−0.562591			−0.281295	+	0.959621i	$0.590764\pi$
$62$	1.29462	+	1.29462i	0.164417	+	0.164417i
$63$		0			0
$64$			5.80098i			0.725122i
$65$	3.64056	+	6.18952i	0.451555	+	0.767715i
$66$	0.223283	−	0.341312i	0.0274842	−	0.0420126i
$67$	0.0345049	−	0.0345049i	0.00421544	−	0.00421544i	−0.704996	−	0.709211i	$-0.749051\pi$
$67$	0.0345049	−	0.0345049i	0.00421544	−	0.00421544i	0.709211	+	0.704996i	$0.249051\pi$
$68$	−6.54574	+	6.54574i	−0.793787	+	0.793787i
$69$	−7.25451	+	11.0893i	−0.873341	+	1.33500i
$70$		0			0
$71$		−	12.4172i		−	1.47365i	−0.676082	−	0.736826i	$-0.736324\pi$
$71$		−	12.4172i		−	1.47365i	0.676082	−	0.736826i	$-0.263676\pi$
$72$	1.31910	−	3.36861i	0.155457	−	0.396995i
$73$	−0.981264	−	0.981264i	−0.114848	−	0.114848i	0.647347	−	0.762195i	$-0.275878\pi$
$73$	−0.981264	−	0.981264i	−0.114848	−	0.114848i	−0.762195	+	0.647347i	$0.775878\pi$
$74$	−1.09216			−0.126961
$75$	8.27000	+	2.57041i	0.954938	+	0.296806i
$76$	3.11769			0.357624
$77$		0			0
$78$	0.351513	+	1.68147i	0.0398010	+	0.190389i
$79$			4.23554i			0.476535i	0.971200	+	0.238268i	$0.0765795\pi$
$79$			4.23554i			0.476535i	−0.971200	+	0.238268i	$0.923420\pi$
$80$	−7.43893	−	1.92893i	−0.831698	−	0.215661i
$81$	6.11142	−	6.60685i	0.679047	−	0.734095i
$82$	0.952060	−	0.952060i	0.105137	−	0.105137i
$83$	5.05351	−	5.05351i	0.554695	−	0.554695i	−0.373097	−	0.927792i	$-0.621704\pi$
$83$	5.05351	−	5.05351i	0.554695	−	0.554695i	0.927792	+	0.373097i	$0.121704\pi$
$84$		0			0
$85$	−5.50993	−	9.36774i	−0.597635	−	1.01607i
$86$			1.17505i			0.126709i
$87$	−8.37953	+	1.75175i	−0.898380	+	0.187807i
$88$	−0.650150	−	0.650150i	−0.0693062	−	0.0693062i
$89$	−0.907199			−0.0961629			−0.0480815	−	0.998843i	$-0.515311\pi$
$89$	−0.907199			−0.0961629			−0.0480815	+	0.998843i	$0.515311\pi$
$90$	1.67774	+	1.21544i	0.176850	+	0.128118i
$91$		0			0
$92$	10.3038	+	10.3038i	1.07424	+	1.07424i
$93$	10.0508	−	2.10113i	1.04222	−	0.217877i
$94$		−	1.32416i		−	0.136577i
$95$	−0.918726	+	3.54307i	−0.0942593	+	0.363511i
$96$	−5.03421	−	3.29333i	−0.513802	−	0.336124i
$97$	−3.73061	+	3.73061i	−0.378786	+	0.378786i	−0.870664	−	0.491878i	$-0.836311\pi$
$97$	−3.73061	+	3.73061i	−0.378786	+	0.378786i	0.491878	+	0.870664i	$0.336311\pi$
$98$		0			0
$99$	−0.916321	−	2.09584i	−0.0920937	−	0.210640i
$100$	4.62758	−	8.32316i	0.462758	−	0.832316i
$101$			18.9884i			1.88942i	0.327913	+	0.944708i	$0.393655\pi$
$101$			18.9884i			1.88942i	−0.327913	+	0.944708i	$0.606345\pi$
$102$	−0.532010	−	2.54488i	−0.0526768	−	0.251981i
$103$	8.93165	+	8.93165i	0.880061	+	0.880061i	0.993540	−	0.113479i	$-0.0361995\pi$
$103$	8.93165	+	8.93165i	0.880061	+	0.880061i	−0.113479	+	0.993540i	$0.536200\pi$
$104$	3.87254			0.379733
$105$		0			0
$106$	−2.14653			−0.208490
$107$	−1.54196	−	1.54196i	−0.149066	−	0.149066i	0.628634	−	0.777701i	$-0.283614\pi$
$107$	−1.54196	−	1.54196i	−0.149066	−	0.149066i	−0.777701	+	0.628634i	$0.783614\pi$
$108$	−5.73622	−	8.06476i	−0.551968	−	0.776032i
$109$			2.35971i			0.226020i	0.993594	+	0.113010i	$0.0360491\pi$
$109$			2.35971i			0.226020i	−0.993594	+	0.113010i	$0.963951\pi$
$110$	0.453857	−	0.266950i	0.0432736	−	0.0254527i
$111$	−3.35323	+	5.12578i	−0.318275	+	0.486517i
$112$		0			0
$113$	−11.9386	+	11.9386i	−1.12309	+	1.12309i	−0.131814	+	0.991274i	$0.542080\pi$
$113$	−11.9386	+	11.9386i	−1.12309	+	1.12309i	−0.991274	+	0.131814i	$0.957920\pi$
$114$	−0.479358	+	0.732751i	−0.0448960	+	0.0686284i
$115$	−14.7459	+	8.67327i	−1.37506	+	0.808787i
$116$			9.41360i			0.874031i
$117$	8.97077	+	3.51283i	0.829348	+	0.324761i
$118$	1.67935	+	1.67935i	0.154597	+	0.154597i
$119$		0			0
$120$	3.45597	−	3.14148i	0.315485	−	0.286777i
$121$	10.4186			0.947150
$122$	−0.959560	−	0.959560i	−0.0868744	−	0.0868744i
$123$	−1.54516	−	7.39132i	−0.139323	−	0.666453i
$124$		−	11.2911i		−	1.01397i
$125$	8.09510	+	7.71164i	0.724048	+	0.689750i
$126$		0			0
$127$	4.46126	−	4.46126i	0.395873	−	0.395873i	−0.480901	−	0.876775i	$-0.659691\pi$
$127$	4.46126	−	4.46126i	0.395873	−	0.395873i	0.876775	+	0.480901i	$0.159691\pi$
$128$	−6.17867	+	6.17867i	−0.546122	+	0.546122i
$129$	5.51478	+	3.60772i	0.485550	+	0.317642i
$130$	−0.556644	+	2.14670i	−0.0488209	+	0.188278i
$131$		−	2.14947i		−	0.187800i	−0.995582	−	0.0938999i	$-0.970067\pi$
$131$		−	2.14947i		−	0.187800i	0.995582	−	0.0938999i	$-0.0299334\pi$
$132$	−2.46207	+	0.514699i	−0.214296	+	0.0447988i
$133$		0			0
$134$	0.0150704			0.00130188
$135$	10.8555	−	4.14233i	0.934290	−	0.356515i
$136$	−5.86102			−0.502579
$137$	6.23472	+	6.23472i	0.532668	+	0.532668i	0.921365	−	0.388698i	$-0.127075\pi$
$137$	6.23472	+	6.23472i	0.532668	+	0.532668i	−0.388698	+	0.921365i	$0.627075\pi$
$138$	−4.00594	+	0.837446i	−0.341008	+	0.0712881i
$139$		−	10.3626i		−	0.878941i	−0.898257	−	0.439471i	$-0.855166\pi$
$139$		−	10.3626i		−	0.878941i	0.898257	−	0.439471i	$-0.144834\pi$
$140$		0			0
$141$	−6.21461	−	4.06553i	−0.523364	−	0.342380i
$142$	2.71168	−	2.71168i	0.227559	−	0.227559i
$143$	1.73138	−	1.73138i	0.144785	−	0.144785i
$144$	−9.44700	+	4.13031i	−0.787250	+	0.344193i
$145$	−10.6980	−	2.77401i	−0.888419	−	0.230369i
$146$		−	0.428578i		−	0.0354694i
$147$		0			0
$148$	4.76267	+	4.76267i	0.391489	+	0.391489i
$149$	−17.4543			−1.42991			−0.714957	−	0.699169i	$-0.753554\pi$
$149$	−17.4543			−1.42991			−0.714957	+	0.699169i	$0.753554\pi$
$150$	1.24468	+	2.36734i	0.101628	+	0.193292i
$151$	−15.2157			−1.23824			−0.619119	−	0.785297i	$-0.712510\pi$
$151$	−15.2157			−1.23824			−0.619119	+	0.785297i	$0.712510\pi$
$152$	1.39578	+	1.39578i	0.113213	+	0.113213i
$153$	−13.5771	−	5.31661i	−1.09765	−	0.429823i
$154$		0			0
$155$	12.8316	+	3.32727i	1.03066	+	0.267253i
$156$	5.79964	−	8.86538i	0.464343	−	0.709799i
$157$	−6.46046	+	6.46046i	−0.515601	+	0.515601i	−0.916237	−	0.400636i	$-0.868789\pi$
$157$	−6.46046	+	6.46046i	−0.515601	+	0.515601i	0.400636	+	0.916237i	$0.368789\pi$
$158$	−0.924960	+	0.924960i	−0.0735859	+	0.0735859i
$159$	−6.59043	+	10.0742i	−0.522655	+	0.798935i
$160$	−3.93740	−	6.69421i	−0.311279	−	0.529223i
$161$		0			0
$162$	2.77743	−	0.108192i	0.218215	−	0.00850040i
$163$	1.91437	+	1.91437i	0.149945	+	0.149945i	0.778094	−	0.628148i	$-0.216187\pi$
$163$	1.91437	+	1.91437i	0.149945	+	0.149945i	−0.628148	+	0.778094i	$0.716187\pi$
$164$	−8.30344			−0.648390
$165$	0.140603	−	2.94967i	0.0109459	−	0.229631i
$166$	2.20718			0.171310
$167$	−3.85551	−	3.85551i	−0.298348	−	0.298348i	0.542018	−	0.840367i	$-0.317660\pi$
$167$	−3.85551	−	3.85551i	−0.298348	−	0.298348i	−0.840367	+	0.542018i	$0.817660\pi$
$168$		0			0
$169$		−	2.68725i		−	0.206712i
$170$	0.842472	−	3.24900i	0.0646147	−	0.249187i
$171$	1.96722	+	4.49948i	0.150437	+	0.344084i
$172$	5.12413	−	5.12413i	0.390711	−	0.390711i
$173$	0.935674	−	0.935674i	0.0711380	−	0.0711380i	−0.670643	−	0.741781i	$-0.733982\pi$
$173$	0.935674	−	0.935674i	0.0711380	−	0.0711380i	0.741781	+	0.670643i	$0.233982\pi$
$174$	−2.21248	−	1.44738i	−0.167727	−	0.109726i
$175$		0			0
$176$			2.62045i			0.197524i
$177$	13.0377	−	2.72554i	0.979970	−	0.204864i
$178$	−0.198115	−	0.198115i	−0.0148493	−	0.0148493i
$179$	−0.241671			−0.0180634			−0.00903168	−	0.999959i	$-0.502875\pi$
$179$	−0.241671			−0.0180634			−0.00903168	+	0.999959i	$0.502875\pi$
$180$	−2.01601	−	12.6165i	−0.150265	−	0.940380i
$181$	−18.6864			−1.38895			−0.694475	−	0.719517i	$-0.744363\pi$
$181$	−18.6864			−1.38895			−0.694475	+	0.719517i	$0.744363\pi$
$182$		0			0
$183$	−7.44955	+	1.55734i	−0.550686	+	0.115122i
$184$			9.22594i			0.680145i
$185$	−6.81596	+	4.00902i	−0.501119	+	0.294749i
$186$	2.65374	+	1.73605i	0.194582	+	0.127294i
$187$	−2.62042	+	2.62042i	−0.191624	+	0.191624i
$188$	−5.77437	+	5.77437i	−0.421140	+	0.421140i
$189$		0			0
$190$	−0.974370	+	0.573106i	−0.0706882	+	0.0415775i
$191$		−	14.2410i		−	1.03044i	−0.857058	−	0.515220i	$-0.827710\pi$
$191$		−	14.2410i		−	1.03044i	0.857058	−	0.515220i	$-0.172290\pi$
$192$	2.05601	+	9.83498i	0.148380	+	0.709779i
$193$	4.81971	+	4.81971i	0.346931	+	0.346931i	0.858965	−	0.512034i	$-0.171108\pi$
$193$	4.81971	+	4.81971i	0.346931	+	0.346931i	−0.512034	+	0.858965i	$0.671108\pi$
$194$	−1.62939			−0.116983
$195$	8.36592	+	9.20340i	0.599096	+	0.659069i
$196$		0			0
$197$	−7.65626	−	7.65626i	−0.545486	−	0.545486i	0.379646	−	0.925132i	$-0.376046\pi$
$197$	−7.65626	−	7.65626i	−0.545486	−	0.545486i	−0.925132	+	0.379646i	$0.876046\pi$
$198$	0.257584	−	0.657798i	0.0183057	−	0.0467477i
$199$		−	16.3800i		−	1.16115i	−0.814208	−	0.580573i	$-0.802828\pi$
$199$		−	16.3800i		−	1.16115i	0.814208	−	0.580573i	$-0.197172\pi$
$200$	5.79801	−	1.65450i	0.409981	−	0.116991i
$201$	0.0462702	−	0.0707289i	0.00326365	−	0.00498884i
$202$	−4.14670	+	4.14670i	−0.291761	+	0.291761i
$203$		0			0
$204$	−8.77767	+	13.4176i	−0.614560	+	0.939421i
$205$	2.44687	−	9.43636i	0.170897	−	0.659064i
$206$			3.90100i			0.271796i
$207$	−8.36897	+	21.3720i	−0.581684	+	1.48546i
$208$	−7.80420	−	7.80420i	−0.541124	−	0.541124i
$209$	1.24809			0.0863321
$210$		0			0
$211$	−25.5028			−1.75568			−0.877842	−	0.478950i	$-0.841018\pi$
$211$	−25.5028			−1.75568			−0.877842	+	0.478950i	$0.841018\pi$
$212$	9.36055	+	9.36055i	0.642885	+	0.642885i
$213$	−4.40097	−	21.0522i	−0.301550	−	1.44247i
$214$		−	0.673467i		−	0.0460372i
$215$	4.31327	+	7.33324i	0.294163	+	0.500123i
$216$	1.04248	−	6.17867i	0.0709320	−	0.420405i
$217$		0			0
$218$	−0.515316	+	0.515316i	−0.0349016	+	0.0349016i
$219$	−2.01142	−	1.31585i	−0.135919	−	0.0889170i
$220$	−3.14328	−	0.815060i	−0.211920	−	0.0549513i
$221$		−	15.6082i		−	1.04992i
$222$	−1.85165	+	0.387090i	−0.124275	+	0.0259798i
$223$	15.4546	+	15.4546i	1.03491	+	1.03491i	0.999368	+	0.0355465i	$0.0113172\pi$
$223$	15.4546	+	15.4546i	1.03491	+	1.03491i	0.0355465	+	0.999368i	$0.488683\pi$
$224$		0			0
$225$	14.9320	+	1.42678i	0.995466	+	0.0951186i
$226$	−5.21432			−0.346851
$227$	9.08481	+	9.08481i	0.602980	+	0.602980i	0.941102	−	0.338122i	$-0.109792\pi$
$227$	9.08481	+	9.08481i	0.602980	+	0.602980i	−0.338122	+	0.941102i	$0.609792\pi$
$228$	5.28574	−	1.10499i	0.350056	−	0.0731797i
$229$			15.3008i			1.01110i	0.862797	+	0.505551i	$0.168711\pi$
$229$			15.3008i			1.01110i	−0.862797	+	0.505551i	$0.831289\pi$
$230$	−5.11430	−	1.32615i	−0.337227	−	0.0874438i
$231$		0			0
$232$	−4.21445	+	4.21445i	−0.276692	+	0.276692i
$233$	4.85174	−	4.85174i	0.317848	−	0.317848i	−0.530092	−	0.847940i	$-0.677843\pi$
$233$	4.85174	−	4.85174i	0.317848	−	0.317848i	0.847940	+	0.530092i	$0.177843\pi$
$234$	1.19191	+	2.72618i	0.0779176	+	0.178216i
$235$	−4.86062	−	8.26382i	−0.317072	−	0.539072i
$236$		−	14.6466i		−	0.953410i
$237$	1.50118	+	7.18093i	0.0975122	+	0.466452i
$238$		0			0
$239$	−18.7082			−1.21013			−0.605067	−	0.796174i	$-0.706854\pi$
$239$	−18.7082			−1.21013			−0.605067	+	0.796174i	$0.706854\pi$
$240$	−13.2956	−	0.633768i	−0.858229	−	0.0409095i
$241$	1.97213			0.127036			0.0635179	−	0.997981i	$-0.479768\pi$
$241$	1.97213			0.127036			0.0635179	+	0.997981i	$0.479768\pi$
$242$	2.27523	+	2.27523i	0.146257	+	0.146257i
$243$	8.01967	−	13.3673i	0.514462	−	0.857513i
$244$			8.36885i			0.535761i
$245$		0			0
$246$	1.27669	−	1.95156i	0.0813987	−	0.124427i
$247$	−3.71704	+	3.71704i	−0.236510	+	0.236510i
$248$	5.05500	−	5.05500i	0.320993	−	0.320993i
$249$	6.77663	−	10.3588i	0.429452	−	0.656463i
$250$	0.0837410	+	3.45189i	0.00529625	+	0.218317i
$251$		−	17.9016i		−	1.12994i	−0.825112	−	0.564970i	$-0.808888\pi$
$251$		−	17.9016i		−	1.12994i	0.825112	−	0.564970i	$-0.191112\pi$
$252$		0			0
$253$	4.12485	+	4.12485i	0.259327	+	0.259327i
$254$	1.94851			0.122260
$255$	−12.6617	−	13.9292i	−0.792906	−	0.872281i
$256$	8.90335			0.556460
$257$	13.9432	+	13.9432i	0.869756	+	0.869756i	0.992445	−	0.122689i	$-0.0391519\pi$
$257$	13.9432	+	13.9432i	0.869756	+	0.869756i	−0.122689	+	0.992445i	$0.539152\pi$
$258$	0.416467	+	1.99218i	0.0259281	+	0.124028i
$259$		0			0
$260$	11.7887	−	6.93387i	0.731102	−	0.430021i
$261$	−13.5858	+	5.93984i	−0.840940	+	0.367667i
$262$	0.469402	−	0.469402i	0.0289998	−	0.0289998i
$263$	−3.92341	+	3.92341i	−0.241928	+	0.241928i	−0.817647	−	0.575719i	$-0.804722\pi$
$263$	−3.92341	+	3.92341i	−0.241928	+	0.241928i	0.575719	+	0.817647i	$0.304722\pi$
$264$	−1.33269	−	0.871835i	−0.0820217	−	0.0536577i
$265$	−13.3961	+	7.87931i	−0.822914	+	0.484022i
$266$		0			0
$267$	−1.53807	+	0.321534i	−0.0941281	+	0.0196776i
$268$	−0.0657186	−	0.0657186i	−0.00401440	−	0.00401440i
$269$	10.0464			0.612541			0.306270	−	0.951945i	$-0.400919\pi$
$269$	10.0464			0.612541			0.306270	+	0.951945i	$0.400919\pi$
$270$	3.27523	+	1.46602i	0.199324	+	0.0892191i
$271$	5.64055			0.342639			0.171320	−	0.985216i	$-0.445197\pi$
$271$	5.64055			0.342639			0.171320	+	0.985216i	$0.445197\pi$
$272$	11.8115	+	11.8115i	0.716180	+	0.716180i
$273$		0			0
$274$			2.72309i			0.164508i
$275$	1.85253	−	3.33196i	0.111712	−	0.200925i
$276$	21.1209	+	13.8171i	1.27133	+	0.831691i
$277$	7.95130	−	7.95130i	0.477747	−	0.477747i	−0.426663	−	0.904411i	$-0.640311\pi$
$277$	7.95130	−	7.95130i	0.477747	−	0.477747i	0.904411	+	0.426663i	$0.140311\pi$
$278$	2.26299	−	2.26299i	0.135725	−	0.135725i
$279$	16.2954	−	7.12451i	0.975581	−	0.426533i
$280$		0			0
$281$		−	1.92831i		−	0.115033i	−0.998345	−	0.0575167i	$-0.981682\pi$
$281$		−	1.92831i		−	0.115033i	0.998345	−	0.0575167i	$-0.0183183\pi$
$282$	−0.469316	−	2.24498i	−0.0279474	−	0.133687i
$283$	18.6429	+	18.6429i	1.10821	+	1.10821i	0.993386	+	0.114822i	$0.0366298\pi$
$283$	18.6429	+	18.6429i	1.10821	+	1.10821i	0.114822	+	0.993386i	$0.463370\pi$
$284$	−23.6501			−1.40337
$285$	−0.301855	+	6.33254i	−0.0178804	+	0.375107i
$286$	0.756201			0.0447151
$287$		0			0
$288$	−9.70225	−	3.79926i	−0.571710	−	0.223874i
$289$			6.62276i			0.389574i
$290$	−1.73044	−	2.94203i	−0.101615	−	0.172762i
$291$	−5.00266	+	7.64711i	−0.293261	+	0.448281i
$292$	−1.86894	+	1.86894i	−0.109371	+	0.109371i
$293$	−7.83332	+	7.83332i	−0.457627	+	0.457627i	−0.897876	−	0.440249i	$-0.854890\pi$
$293$	−7.83332	+	7.83332i	−0.457627	+	0.457627i	0.440249	+	0.897876i	$0.354890\pi$
$294$		0			0
$295$	16.6449	+	4.31607i	0.969105	+	0.251291i
$296$			4.26448i			0.247868i
$297$	−2.29635	−	3.22852i	−0.133248	−	0.187338i
$298$	−3.81169	−	3.81169i	−0.220805	−	0.220805i
$299$	−24.5691			−1.42087
$300$	4.89566	−	15.7512i	0.282651	−	0.909397i
$301$		0			0
$302$	−3.32282	−	3.32282i	−0.191207	−	0.191207i
$303$	6.72997	+	32.1929i	0.386627	+	1.84944i
$304$		−	5.62576i		−	0.322659i
$305$	−9.51069	−	2.46614i	−0.544580	−	0.141211i
$306$	−1.80394	−	4.12603i	−0.103124	−	0.235869i
$307$	17.0769	−	17.0769i	0.974628	−	0.974628i	−0.0250576	−	0.999686i	$-0.507977\pi$
$307$	17.0769	−	17.0769i	0.974628	−	0.974628i	0.999686	+	0.0250576i	$0.00797691\pi$
$308$		0			0
$309$	18.3083	+	11.9771i	1.04152	+	0.681354i
$310$	2.07557	+	3.52880i	0.117885	+	0.200422i
$311$		−	23.6479i		−	1.34095i	−0.741932	−	0.670475i	$-0.766090\pi$
$311$		−	23.6479i		−	1.34095i	0.741932	−	0.670475i	$-0.233910\pi$
$312$	6.56550	−	1.37252i	0.371698	−	0.0777039i
$313$	8.75372	+	8.75372i	0.494790	+	0.494790i	0.909812	−	0.415022i	$-0.136226\pi$
$313$	8.75372	+	8.75372i	0.494790	+	0.494790i	−0.415022	+	0.909812i	$0.636226\pi$
$314$	−2.82168			−0.159237
$315$		0			0
$316$	8.06709			0.453809
$317$	3.10591	+	3.10591i	0.174445	+	0.174445i	0.788929	−	0.614484i	$-0.210636\pi$
$317$	3.10591	+	3.10591i	0.174445	+	0.174445i	−0.614484	+	0.788929i	$0.710636\pi$
$318$	−3.63923	+	0.760785i	−0.204078	+	0.0426627i
$319$			3.76850i			0.210995i
$320$	−3.25583	+	12.5561i	−0.182007	+	0.701909i
$321$	−3.16074	−	2.06772i	−0.176415	−	0.115409i
$322$		0			0
$323$	5.62568	−	5.62568i	0.313021	−	0.313021i
$324$	−12.5835	−	11.6399i	−0.699086	−	0.646663i
$325$	4.40602	+	15.4404i	0.244402	+	0.856479i
$326$			0.836125i			0.0463087i
$327$	0.836342	+	4.00066i	0.0462498	+	0.221237i
$328$	−3.71743	−	3.71743i	−0.205261	−	0.205261i
$329$		0			0
$330$	0.674856	−	0.613446i	0.0371496	−	0.0337691i
$331$	−6.21866			−0.341808			−0.170904	−	0.985288i	$-0.554669\pi$
$331$	−6.21866			−0.341808			−0.170904	+	0.985288i	$0.554669\pi$
$332$	−9.62501	−	9.62501i	−0.528241	−	0.528241i
$333$	−3.86836	+	9.87871i	−0.211985	+	0.541350i
$334$		−	1.68394i		−	0.0921411i
$335$	0.0940513	−	0.0553192i	0.00513857	−	0.00302241i
$336$		0			0
$337$	15.0501	−	15.0501i	0.819833	−	0.819833i	−0.166250	−	0.986084i	$-0.553166\pi$
$337$	15.0501	−	15.0501i	0.819833	−	0.819833i	0.986084	+	0.166250i	$0.0531659\pi$
$338$	0.586844	−	0.586844i	0.0319201	−	0.0319201i
$339$	−16.0094	+	24.4720i	−0.869509	+	1.32914i
$340$	−17.8420	+	10.4943i	−0.967617	+	0.569134i
$341$		−	4.52010i		−	0.244777i
$342$	−0.552999	+	1.41220i	−0.0299027	+	0.0763632i
$343$		0			0
$344$	4.58812			0.247375
$345$	−21.9262	+	19.9310i	−1.18047	+	1.07305i
$346$	0.408667			0.0219701
$347$	−13.6203	−	13.6203i	−0.731178	−	0.731178i	0.239675	−	0.970853i	$-0.422959\pi$
$347$	−13.6203	−	13.6203i	−0.731178	−	0.731178i	−0.970853	+	0.239675i	$0.922959\pi$
$348$	3.33642	+	15.9598i	0.178851	+	0.855536i
$349$		−	9.24369i		−	0.494803i	−0.968913	−	0.247402i	$-0.920423\pi$
$349$		−	9.24369i		−	0.494803i	0.968913	−	0.247402i	$-0.0795767\pi$
$350$		0			0
$351$	16.4541	+	2.77618i	0.878254	+	0.148182i
$352$	−1.87256	+	1.87256i	−0.0998076	+	0.0998076i
$353$	8.35049	−	8.35049i	0.444452	−	0.444452i	−0.449053	−	0.893505i	$-0.648239\pi$
$353$	8.35049	−	8.35049i	0.444452	−	0.444452i	0.893505	+	0.449053i	$0.148239\pi$
$354$	3.44238	+	2.25197i	0.182960	+	0.119691i
$355$	6.96923	−	26.8769i	0.369889	−	1.42648i
$356$			1.72787i			0.0915769i
$357$		0			0
$358$	−0.0527764	−	0.0527764i	−0.00278932	−	0.00278932i
$359$	13.9626			0.736917			0.368459	−	0.929644i	$-0.379886\pi$
$359$	13.9626			0.736917			0.368459	+	0.929644i	$0.379886\pi$
$360$	4.74582	−	6.55095i	0.250127	−	0.345265i
$361$	16.3205			0.858975
$362$	−4.08075	−	4.08075i	−0.214480	−	0.214480i
$363$	17.6638	−	3.69263i	0.927108	−	0.193813i
$364$		0			0
$365$	−1.57319	−	2.67467i	−0.0823446	−	0.139999i
$366$	−1.96693	−	1.28675i	−0.102813	−	0.0672593i
$367$	10.6651	−	10.6651i	0.556714	−	0.556714i	−0.371657	−	0.928370i	$-0.621210\pi$
$367$	10.6651	−	10.6651i	0.556714	−	0.556714i	0.928370	+	0.371657i	$0.121210\pi$
$368$	18.5928	−	18.5928i	0.969214	−	0.969214i
$369$	−5.23934	−	11.9836i	−0.272749	−	0.623842i
$370$	−2.36397	−	0.612982i	−0.122897	−	0.0318674i
$371$		0			0
$372$	−4.00185	−	19.1429i	−0.207486	−	0.992515i
$373$	−24.6331	−	24.6331i	−1.27545	−	1.27545i	−0.943184	−	0.332271i	$-0.892185\pi$
$373$	−24.6331	−	24.6331i	−1.27545	−	1.27545i	−0.332271	−	0.943184i	$-0.607815\pi$
$374$	−1.14450			−0.0591806
$375$	16.4576	+	10.2052i	0.849869	+	0.526995i
$376$	−5.17035			−0.266640
$377$	−11.2233	−	11.2233i	−0.578028	−	0.578028i
$378$		0			0
$379$		−	19.0602i		−	0.979056i	−0.871988	−	0.489528i	$-0.837169\pi$
$379$		−	19.0602i		−	0.979056i	0.871988	−	0.489528i	$-0.162831\pi$
$380$	6.74820	+	1.74982i	0.346175	+	0.0897640i
$381$	5.98244	−	9.14481i	0.306490	−	0.468503i
$382$	3.10996	−	3.10996i	0.159119	−	0.159119i
$383$	7.18147	−	7.18147i	0.366956	−	0.366956i	−0.499410	−	0.866366i	$-0.666450\pi$
$383$	7.18147	−	7.18147i	0.366956	−	0.366956i	0.866366	+	0.499410i	$0.166450\pi$
$384$	−8.28544	+	12.6652i	−0.422815	+	0.646318i
$385$		0			0
$386$			2.10507i			0.107145i
$387$	10.6284	+	4.16194i	0.540274	+	0.211564i
$388$	7.10540	+	7.10540i	0.360722	+	0.360722i
$389$	37.2580			1.88906			0.944528	−	0.328431i	$-0.106520\pi$
$389$	37.2580			1.88906			0.944528	+	0.328431i	$0.106520\pi$
$390$	−0.182890	+	3.83680i	−0.00926101	+	0.194284i
$391$	37.1850			1.88053
$392$		0			0
$393$	−0.761825	−	3.64421i	−0.0384290	−	0.183826i
$394$		−	3.34396i		−	0.168466i
$395$	−2.37722	+	9.16776i	−0.119611	+	0.461280i
$396$	−3.99178	+	1.74524i	−0.200594	+	0.0877017i
$397$	6.28581	−	6.28581i	0.315476	−	0.315476i	−0.531551	−	0.847027i	$-0.678390\pi$
$397$	6.28581	−	6.28581i	0.315476	−	0.315476i	0.847027	+	0.531551i	$0.178390\pi$
$398$	3.57708	−	3.57708i	0.179303	−	0.179303i
$399$		0			0
$400$	−15.0188	−	8.35029i	−0.750941	−	0.417514i
$401$		−	4.65150i		−	0.232285i	−0.993233	−	0.116142i	$-0.962947\pi$
$401$		−	4.65150i		−	0.232285i	0.993233	−	0.116142i	$-0.0370529\pi$
$402$	0.0255504	−	0.00534133i	0.00127434	−	0.000266401i
$403$	13.4617	+	13.4617i	0.670575	+	0.670575i
$404$	36.1657			1.79931
$405$	16.9362	−	10.8704i	0.841567	−	0.540152i
$406$		0			0
$407$	1.90662	+	1.90662i	0.0945074	+	0.0945074i
$408$	−9.93678	+	2.07729i	−0.491944	+	0.102841i
$409$		−	26.5589i		−	1.31325i	−0.754217	−	0.656626i	$-0.771983\pi$
$409$		−	26.5589i		−	1.31325i	0.754217	−	0.656626i	$-0.228017\pi$
$410$	2.59507	−	1.52637i	0.128161	−	0.0753820i
$411$	12.7801	+	8.36060i	0.630395	+	0.412398i
$412$	17.0114	−	17.0114i	0.838091	−	0.838091i
$413$		0			0
$414$	−6.49486	+	2.83961i	−0.319205	+	0.139559i
$415$	13.7746	−	8.10193i	0.676166	−	0.397708i
$416$		−	11.1536i		−	0.546852i
$417$	−3.67275	−	17.5687i	−0.179856	−	0.860343i
$418$	0.272559	+	0.272559i	0.0133313	+	0.0133313i
$419$	−25.8278			−1.26177			−0.630885	−	0.775876i	$-0.717308\pi$
$419$	−25.8278			−1.26177			−0.630885	+	0.775876i	$0.717308\pi$
$420$		0			0
$421$	0.432430			0.0210753			0.0105377	−	0.999944i	$-0.496646\pi$
$421$	0.432430			0.0210753			0.0105377	+	0.999944i	$0.496646\pi$
$422$	−5.56932	−	5.56932i	−0.271110	−	0.271110i
$423$	−11.9772	−	4.69009i	−0.582350	−	0.228040i
$424$			8.38139i			0.407036i
$425$	−6.66845	−	23.3688i	−0.323467	−	1.13355i
$426$	3.63630	−	5.55847i	0.176179	−	0.269309i
$427$		0			0
$428$	−2.93684	+	2.93684i	−0.141957	+	0.141957i
$429$	2.32174	−	3.54903i	0.112095	−	0.171349i
$430$	−0.659503	+	2.54338i	−0.0318041	+	0.122652i
$431$		−	16.3117i		−	0.785708i	−0.919601	−	0.392854i	$-0.871488\pi$
$431$		−	16.3117i		−	0.785708i	0.919601	−	0.392854i	$-0.128512\pi$
$432$	−14.5526	+	10.3508i	−0.700160	+	0.498003i
$433$	0.514238	+	0.514238i	0.0247127	+	0.0247127i	0.719355	−	0.694642i	$-0.244437\pi$
$433$	0.514238	+	0.514238i	0.0247127	+	0.0247127i	−0.694642	+	0.719355i	$0.744437\pi$
$434$		0			0
$435$	−19.1205	−	0.911426i	−0.916760	−	0.0436995i
$436$	4.49436			0.215241
$437$	−8.85549	−	8.85549i	−0.423615	−	0.423615i
$438$	−0.151899	−	0.726612i	−0.00725802	−	0.0347189i
$439$		−	15.2983i		−	0.730150i	−0.930978	−	0.365075i	$-0.881043\pi$
$439$		−	15.2983i		−	0.730150i	0.930978	−	0.365075i	$-0.118957\pi$
$440$	−1.04234	−	1.77214i	−0.0496916	−	0.0844835i
$441$		0			0
$442$	3.40853	−	3.40853i	0.162127	−	0.162127i
$443$	6.45258	−	6.45258i	0.306572	−	0.306572i	−0.537007	−	0.843578i	$-0.680445\pi$
$443$	6.45258	−	6.45258i	0.306572	−	0.306572i	0.843578	+	0.537007i	$0.180445\pi$
$444$	9.76265	+	6.38663i	0.463315	+	0.303096i
$445$	−1.96362	−	0.509171i	−0.0930845	−	0.0241370i
$446$			6.74996i			0.319620i
$447$	−29.5921	+	6.18625i	−1.39966	+	0.292600i
$448$		0			0
$449$	9.40891			0.444034			0.222017	−	0.975043i	$-0.428736\pi$
$449$	9.40891			0.444034			0.222017	+	0.975043i	$0.428736\pi$
$450$	2.94928	+	3.57244i	0.139030	+	0.168406i
$451$	−3.32407			−0.156524
$452$	22.7385	+	22.7385i	1.06953	+	1.06953i
$453$	−25.7967	+	5.39284i	−1.21204	+	0.253378i
$454$			3.96789i			0.186222i
$455$		0			0
$456$	2.86111	+	1.87171i	0.133984	+	0.0876509i
$457$	−24.4154	+	24.4154i	−1.14210	+	1.14210i	−0.154038	+	0.988065i	$0.549228\pi$
$457$	−24.4154	+	24.4154i	−1.14210	+	1.14210i	−0.988065	+	0.154038i	$0.950772\pi$
$458$	−3.34139	+	3.34139i	−0.156133	+	0.156133i
$459$	−24.9030	−	4.20171i	−1.16237	−	0.196119i
$460$	16.5193	+	28.0854i	0.770216	+	1.30949i
$461$			36.9326i			1.72012i	0.510192	+	0.860061i	$0.329574\pi$
$461$			36.9326i			1.72012i	−0.510192	+	0.860061i	$0.670426\pi$
$462$		0			0
$463$	26.3687	+	26.3687i	1.22546	+	1.22546i	0.965664	+	0.259794i	$0.0836548\pi$
$463$	26.3687	+	26.3687i	1.22546	+	1.22546i	0.259794	+	0.965664i	$0.416345\pi$
$464$	16.9865			0.788578
$465$	22.9340	+	1.09321i	1.06354	+	0.0506962i
$466$	2.11906			0.0981633
$467$	−7.21204	−	7.21204i	−0.333733	−	0.333733i	0.520269	−	0.854002i	$-0.325832\pi$
$467$	−7.21204	−	7.21204i	−0.333733	−	0.333733i	−0.854002	+	0.520269i	$0.825832\pi$
$468$	6.69060	−	17.0859i	0.309273	−	0.789797i
$469$		0			0
$470$	0.743194	−	2.86613i	0.0342810	−	0.132205i
$471$	−8.66332	+	13.2428i	−0.399185	+	0.610197i
$472$	6.55723	−	6.55723i	0.301821	−	0.301821i
$473$	2.05131	−	2.05131i	0.0943195	−	0.0943195i
$474$	−1.24035	+	1.89601i	−0.0569711	+	0.0870865i
$475$	−3.97713	+	7.15327i	−0.182483	+	0.328215i
$476$		0			0
$477$	−7.60287	+	19.4156i	−0.348112	+	0.888979i
$478$	−4.08552	−	4.08552i	−0.186867	−	0.186867i
$479$	13.7070			0.626289			0.313144	−	0.949706i	$-0.398618\pi$
$479$	13.7070			0.626289			0.313144	+	0.949706i	$0.398618\pi$
$480$	−9.04807	−	9.95384i	−0.412986	−	0.454329i
$481$	−11.3565			−0.517812
$482$	0.430674	+	0.430674i	0.0196167	+	0.0196167i
$483$		0			0
$484$		−	19.8436i		−	0.901980i
$485$	−10.1687	+	5.98102i	−0.461736	+	0.271584i
$486$	4.67051	−	1.16782i	0.211858	−	0.0529734i
$487$	−16.1645	+	16.1645i	−0.732484	+	0.732484i	−0.971111	−	0.238627i	$-0.923303\pi$
$487$	−16.1645	+	16.1645i	−0.732484	+	0.732484i	0.238627	+	0.971111i	$0.423303\pi$
$488$	−3.74672	+	3.74672i	−0.169606	+	0.169606i
$489$	3.92413	+	2.56713i	0.177455	+	0.116090i
$490$		0			0
$491$		−	23.7476i		−	1.07172i	−0.844308	−	0.535858i	$-0.819988\pi$
$491$		−	23.7476i		−	1.07172i	0.844308	−	0.535858i	$-0.180012\pi$
$492$	−14.0777	+	2.94295i	−0.634670	+	0.132678i
$493$	16.9863	+	16.9863i	0.765023	+	0.765023i
$494$	−1.62346			−0.0730429
$495$	−0.807059	−	5.05070i	−0.0362746	−	0.227012i
$496$	−20.3744			−0.914836
$497$		0			0
$498$	3.74205	−	0.782280i	0.167685	−	0.0350548i
$499$		−	3.23532i		−	0.144833i	−0.997374	−	0.0724165i	$-0.976929\pi$
$499$		−	3.23532i		−	0.144833i	0.997374	−	0.0724165i	$-0.0230711\pi$
$500$	14.6877	−	15.4181i	0.656856	−	0.689518i
$501$	−7.90313	−	5.17015i	−0.353086	−	0.230985i
$502$	3.90937	−	3.90937i	0.174484	−	0.174484i
$503$	2.62851	−	2.62851i	0.117199	−	0.117199i	−0.646075	−	0.763274i	$-0.723591\pi$
$503$	2.62851	−	2.62851i	0.117199	−	0.117199i	0.763274	+	0.646075i	$0.223591\pi$
$504$		0			0
$505$	−10.6573	+	41.1001i	−0.474246	+	1.82893i
$506$			1.80158i			0.0800898i
$507$	−0.952430	−	4.55597i	−0.0422989	−	0.202338i
$508$	−8.49701	−	8.49701i	−0.376994	−	0.376994i
$509$	13.8238			0.612728			0.306364	−	0.951914i	$-0.400887\pi$
$509$	13.8238			0.612728			0.306364	+	0.951914i	$0.400887\pi$
$510$	0.276802	−	5.80694i	0.0122570	−	0.257136i
$511$		0			0
$512$	14.3017	+	14.3017i	0.632050	+	0.632050i
$513$	4.92995	+	6.93120i	0.217663	+	0.306020i
$514$			6.08987i			0.268613i
$515$	14.3195	+	24.3453i	0.630991	+	1.07278i
$516$	6.87133	−	10.5036i	0.302493	−	0.462394i
$517$	−2.31162	+	2.31162i	−0.101665	+	0.101665i
$518$		0			0
$519$	1.25472	−	1.91797i	0.0550759	−	0.0841895i
$520$	8.38204	+	2.17348i	0.367577	+	0.0953135i
$521$			10.9599i			0.480162i	0.970753	+	0.240081i	$0.0771741\pi$
$521$			10.9599i			0.480162i	−0.970753	+	0.240081i	$0.922826\pi$
$522$	−4.26402	−	1.66973i	−0.186631	−	0.0730822i
$523$	−9.69371	−	9.69371i	−0.423876	−	0.423876i	0.462660	−	0.886536i	$-0.346895\pi$
$523$	−9.69371	−	9.69371i	−0.423876	−	0.423876i	−0.886536	+	0.462660i	$0.846895\pi$
$524$	−4.09392			−0.178844
$525$		0			0
$526$	−1.71360			−0.0747163
$527$	−20.3741	−	20.3741i	−0.887509	−	0.887509i
$528$	0.928755	+	4.44272i	0.0404189	+	0.193345i
$529$		−	35.5336i		−	1.54494i
$530$	−4.64614	−	1.20475i	−0.201815	−	0.0523312i
$531$	21.1381	−	9.24175i	0.917313	−	0.401058i
$532$		0			0
$533$	9.89970	−	9.89970i	0.428804	−	0.428804i
$534$	−0.406101	−	0.265667i	−0.0175737	−	0.0114965i
$535$	−2.47211	−	4.20297i	−0.106878	−	0.181710i
$536$		−	0.0588442i		−	0.00254168i
$537$	−0.409730	+	0.0856544i	−0.0176811	+	0.00369626i
$538$	2.19394	+	2.19394i	0.0945876	+	0.0945876i
$539$		0			0
$540$	−7.88956	−	20.6755i	−0.339513	−	0.889733i
$541$	7.06552			0.303770			0.151885	−	0.988398i	$-0.451466\pi$
$541$	7.06552			0.303770			0.151885	+	0.988398i	$0.451466\pi$
$542$	1.23179	+	1.23179i	0.0529098	+	0.0529098i
$543$	−31.6809	+	6.62293i	−1.35956	+	0.284217i
$544$			16.8809i			0.723762i
$545$	−1.32440	+	5.10756i	−0.0567312	+	0.218784i
$546$		0			0
$547$	−19.7665	+	19.7665i	−0.845154	+	0.845154i	−0.989524	−	0.144370i	$-0.953885\pi$
$547$	−19.7665	+	19.7665i	−0.845154	+	0.845154i	0.144370	+	0.989524i	$0.453885\pi$
$548$	11.8748	−	11.8748i	0.507265	−	0.507265i
$549$	−12.0780	+	5.28061i	−0.515477	+	0.225371i
$550$	1.13219	−	0.323079i	0.0482769	−	0.0137762i
$551$		−	8.09045i		−	0.344665i
$552$	3.26991	+	15.6417i	0.139176	+	0.665753i
$553$		0			0
$554$	3.47282			0.147546
$555$	−10.1349	+	9.21264i	−0.430202	+	0.391055i
$556$	−19.7367			−0.837024
$557$	−30.9586	−	30.9586i	−1.31176	−	1.31176i	−0.920119	−	0.391638i	$-0.871908\pi$
$557$	−30.9586	−	30.9586i	−1.31176	−	1.31176i	−0.391638	−	0.920119i	$-0.628092\pi$
$558$	5.11446	+	2.00275i	0.216512	+	0.0847832i
$559$			12.2184i			0.516783i
$560$		0			0
$561$	−3.51392	+	5.37140i	−0.148358	+	0.226781i
$562$	0.421106	−	0.421106i	0.0177633	−	0.0177633i
$563$	−7.84399	+	7.84399i	−0.330585	+	0.330585i	−0.852808	−	0.522224i	$-0.825103\pi$
$563$	−7.84399	+	7.84399i	−0.330585	+	0.330585i	0.522224	+	0.852808i	$0.325103\pi$
$564$	−7.74329	+	11.8365i	−0.326051	+	0.498405i
$565$	−32.5415	+	19.1403i	−1.36903	+	0.805238i
$566$			8.14252i			0.342256i
$567$		0			0
$568$	−10.5881	−	10.5881i	−0.444266	−	0.444266i
$569$	13.8064			0.578793			0.289396	−	0.957209i	$-0.406545\pi$
$569$	13.8064			0.578793			0.289396	+	0.957209i	$0.406545\pi$
$570$	−1.44882	+	1.31699i	−0.0606846	+	0.0551624i
$571$	−13.1252			−0.549272			−0.274636	−	0.961548i	$-0.588557\pi$
$571$	−13.1252			−0.549272			−0.274636	+	0.961548i	$0.588557\pi$
$572$	−3.29762	−	3.29762i	−0.137881	−	0.137881i
$573$	−5.04736	−	24.1442i	−0.210857	−	1.00864i
$574$		0			0
$575$	−36.7852	+	10.4969i	−1.53405	+	0.437752i
$576$	6.97153	+	15.9455i	0.290480	+	0.664397i
$577$	10.7854	−	10.7854i	0.449001	−	0.449001i	−0.446021	−	0.895022i	$-0.647159\pi$
$577$	10.7854	−	10.7854i	0.449001	−	0.449001i	0.895022	+	0.446021i	$0.147159\pi$
$578$	−1.44628	+	1.44628i	−0.0601575	+	0.0601575i
$579$	9.87957	+	6.46312i	0.410581	+	0.268598i
$580$	−5.28344	+	20.3756i	−0.219383	+	0.846050i
$581$		0			0
$582$	−2.76247	+	0.577496i	−0.114508	+	0.0239380i
$583$	3.74726	+	3.74726i	0.155196	+	0.155196i
$584$	−1.67344			−0.0692473
$585$	17.4455	+	12.6384i	0.721283	+	0.522532i
$586$	−3.42129			−0.141332
$587$	5.54217	+	5.54217i	0.228750	+	0.228750i	0.812170	−	0.583421i	$-0.198286\pi$
$587$	5.54217	+	5.54217i	0.228750	+	0.228750i	−0.583421	+	0.812170i	$0.698286\pi$
$588$		0			0
$589$			9.70404i			0.399848i
$590$	2.69238	+	4.57748i	0.110844	+	0.188452i
$591$	−15.6940	−	10.2669i	−0.645565	−	0.422322i
$592$	8.59407	−	8.59407i	0.353214	−	0.353214i
$593$	−6.13323	+	6.13323i	−0.251861	+	0.251861i	−0.821733	−	0.569872i	$-0.806993\pi$
$593$	−6.13323	+	6.13323i	−0.251861	+	0.251861i	0.569872	+	0.821733i	$0.306993\pi$
$594$	0.203568	−	1.20653i	0.00835252	−	0.0495043i
$595$		0			0
$596$			33.2438i			1.36172i
$597$	−5.80548	−	27.7706i	−0.237603	−	1.13658i
$598$	−5.36543	−	5.36543i	−0.219409	−	0.219409i
$599$	15.8774			0.648732			0.324366	−	0.945932i	$-0.394849\pi$
$599$	15.8774			0.648732			0.324366	+	0.945932i	$0.394849\pi$
$600$	9.24356	−	4.86001i	0.377367	−	0.198409i
$601$	−41.5249			−1.69384			−0.846919	−	0.531722i	$-0.821545\pi$
$601$	−41.5249			−1.69384			−0.846919	+	0.531722i	$0.821545\pi$
$602$		0			0
$603$	0.0533783	−	0.136313i	0.00217373	−	0.00555110i
$604$			28.9802i			1.17919i
$605$	22.5510	+	5.84753i	0.916828	+	0.237736i
$606$	−5.56062	+	8.50001i	−0.225885	+	0.345289i
$607$	10.8110	−	10.8110i	0.438805	−	0.438805i	−0.452805	−	0.891610i	$-0.649577\pi$
$607$	10.8110	−	10.8110i	0.438805	−	0.438805i	0.891610	+	0.452805i	$0.149577\pi$
$608$	4.02013	−	4.02013i	0.163038	−	0.163038i
$609$		0			0
$610$	−1.53839	−	2.61551i	−0.0622877	−	0.105899i
$611$		−	13.7689i		−	0.557030i
$612$	−10.1261	+	25.8593i	−0.409324	+	1.04530i
$613$	21.8063	+	21.8063i	0.880747	+	0.880747i	0.993611	−	0.112863i	$-0.0360022\pi$
$613$	21.8063	+	21.8063i	0.880747	+	0.880747i	−0.112863	+	0.993611i	$0.536002\pi$
$614$	7.45852			0.301001
$615$	0.803941	−	16.8656i	0.0324180	−	0.680088i
$616$		0			0
$617$	−13.2098	−	13.2098i	−0.531808	−	0.531808i	0.389302	−	0.921110i	$-0.372716\pi$
$617$	−13.2098	−	13.2098i	−0.531808	−	0.531808i	−0.921110	+	0.389302i	$0.872716\pi$
$618$	1.38261	+	6.61376i	0.0556168	+	0.266044i
$619$		−	17.0312i		−	0.684542i	−0.939601	−	0.342271i	$-0.888804\pi$
$619$		−	17.0312i		−	0.684542i	0.939601	−	0.342271i	$-0.111196\pi$
$620$	6.33719	−	24.4394i	0.254508	−	0.981510i
$621$	−6.61399	+	39.2003i	−0.265410	+	1.57305i
$622$	5.16425	−	5.16425i	0.207068	−	0.207068i
$623$		0			0
$624$	−15.9973	−	10.4652i	−0.640403	−	0.418945i
$625$	13.1935	+	21.2351i	0.527741	+	0.849406i
$626$			3.82329i			0.152809i
$627$	2.11601	−	0.442354i	0.0845053	−	0.0176659i
$628$	12.3047	+	12.3047i	0.491012	+	0.491012i
$629$	17.1879			0.685327
$630$		0			0
$631$	6.51082			0.259191			0.129596	−	0.991567i	$-0.458632\pi$
$631$	6.51082			0.259191			0.129596	+	0.991567i	$0.458632\pi$
$632$	3.61162	+	3.61162i	0.143662	+	0.143662i
$633$	−43.2374	+	9.03883i	−1.71853	+	0.359261i
$634$			1.35654i			0.0538752i
$635$	12.1602	−	7.15242i	0.482565	−	0.283835i
$636$	19.1875	+	12.5523i	0.760834	+	0.497730i
$637$		0			0
$638$	−0.822967	+	0.822967i	−0.0325816	+	0.0325816i
$639$	−14.9228	−	34.1320i	−0.590338	−	1.35024i
$640$	−16.8414	+	9.90581i	−0.665716	+	0.391562i
$641$			42.3545i			1.67290i	0.548042	+	0.836451i	$0.315374\pi$
$641$			42.3545i			1.67290i	−0.548042	+	0.836451i	$0.684626\pi$
$642$	−0.238694	−	1.14180i	−0.00942049	−	0.0450631i
$643$	−11.2098	−	11.2098i	−0.442072	−	0.442072i	0.450636	−	0.892708i	$-0.351197\pi$
$643$	−11.2098	−	11.2098i	−0.442072	−	0.442072i	−0.892708	+	0.450636i	$0.851197\pi$
$644$		0			0
$645$	9.91181	+	10.9040i	0.390277	+	0.429347i
$646$	2.45708			0.0966726
$647$	16.8086	+	16.8086i	0.660814	+	0.660814i	0.955572	−	0.294758i	$-0.0952390\pi$
$647$	16.8086	+	16.8086i	0.660814	+	0.660814i	−0.294758	+	0.955572i	$0.595239\pi$
$648$	−0.422450	−	10.8448i	−0.0165954	−	0.426024i
$649$		−	5.86338i		−	0.230158i
$650$	−2.40969	+	4.33408i	−0.0945160	+	0.169996i
$651$		0			0
$652$	3.64616	−	3.64616i	0.142794	−	0.142794i
$653$	15.4100	−	15.4100i	0.603041	−	0.603041i	−0.338078	−	0.941118i	$-0.609777\pi$
$653$	15.4100	−	15.4100i	0.603041	−	0.603041i	0.941118	+	0.338078i	$0.109777\pi$
$654$	−0.691026	+	1.05631i	−0.0270213	+	0.0413049i
$655$	1.20640	−	4.65249i	0.0471380	−	0.181788i
$656$			14.9833i			0.584998i
$657$	−3.87653	−	1.51800i	−0.151238	−	0.0592227i
$658$		0			0
$659$	42.6184			1.66018			0.830088	−	0.557632i	$-0.188290\pi$
$659$	42.6184			1.66018			0.830088	+	0.557632i	$0.188290\pi$
$660$	−5.61800	−	0.267795i	−0.218680	−	0.0104239i
$661$	−45.4934			−1.76949			−0.884744	−	0.466076i	$-0.845667\pi$
$661$	−45.4934			−1.76949			−0.884744	+	0.466076i	$0.845667\pi$
$662$	−1.35804	−	1.35804i	−0.0527816	−	0.0527816i
$663$	−5.53194	−	26.4621i	−0.214843	−	1.02770i
$664$		−	8.61819i		−	0.334451i
$665$		0			0
$666$	−3.00210	+	1.31254i	−0.116329	+	0.0508601i
$667$	26.7384	−	26.7384i	1.03531	−	1.03531i
$668$	−7.34328	+	7.34328i	−0.284120	+	0.284120i
$669$	31.6792	+	20.7242i	1.22479	+	0.801244i
$670$	0.0326196	+	0.00845835i	0.00126021	+	0.000326774i
$671$			3.35026i			0.129335i
$672$		0			0
$673$	−32.1249	−	32.1249i	−1.23832	−	1.23832i	−0.960686	−	0.277636i	$-0.910449\pi$
$673$	−32.1249	−	32.1249i	−1.23832	−	1.23832i	−0.277636	−	0.960686i	$-0.589551\pi$
$674$	6.57332			0.253195
$675$	25.8214	−	2.87331i	0.993866	−	0.110594i
$676$	−5.11819			−0.196854
$677$	−30.1078	−	30.1078i	−1.15714	−	1.15714i	−0.985088	−	0.172049i	$-0.944961\pi$
$677$	−30.1078	−	30.1078i	−1.15714	−	1.15714i	−0.172049	−	0.985088i	$-0.555039\pi$
$678$	−8.84036	+	1.84809i	−0.339512	+	0.0709753i
$679$		0			0
$680$	−12.6861	−	3.28953i	−0.486489	−	0.126148i
$681$	18.6223	+	12.1825i	0.713607	+	0.466834i
$682$	0.987103	−	0.987103i	0.0377981	−	0.0377981i
$683$	1.64841	−	1.64841i	0.0630747	−	0.0630747i	−0.674866	−	0.737940i	$-0.735798\pi$
$683$	1.64841	−	1.64841i	0.0630747	−	0.0630747i	0.737940	+	0.674866i	$0.235798\pi$
$684$	8.56980	−	3.74680i	0.327675	−	0.143262i
$685$	9.99568	+	16.9942i	0.381915	+	0.649316i
$686$		0			0
$687$	5.42298	+	25.9409i	0.206899	+	0.989708i
$688$	−9.24630	−	9.24630i	−0.352512	−	0.352512i
$689$	−22.3201			−0.850326
$690$	−9.14081	−	0.435718i	−0.347985	−	0.0165875i
$691$	16.5565			0.629838			0.314919	−	0.949119i	$-0.398023\pi$
$691$	16.5565			0.629838			0.314919	+	0.949119i	$0.398023\pi$
$692$	−1.78210	−	1.78210i	−0.0677454	−	0.0677454i
$693$		0			0
$694$		−	5.94884i		−	0.225815i
$695$	5.81605	−	22.4296i	0.220615	−	0.850804i
$696$	−5.65147	+	8.63888i	−0.214218	+	0.327456i
$697$	−14.9831	+	14.9831i	−0.567524	+	0.567524i
$698$	2.01864	−	2.01864i	0.0764068	−	0.0764068i
$699$	6.50607	−	9.94523i	0.246082	−	0.376163i
$700$		0			0
$701$			26.5973i			1.00457i	0.864703	+	0.502284i	$0.167507\pi$
$701$			26.5973i			1.00457i	−0.864703	+	0.502284i	$0.832493\pi$
$702$	2.98699	+	4.19952i	0.112737	+	0.158501i
$703$	−4.09324	−	4.09324i	−0.154380	−	0.154380i
$704$	4.42305			0.166700
$705$	−11.1696	−	12.2878i	−0.420672	−	0.462784i
$706$	3.64717			0.137263
$707$		0			0
$708$	−5.19111	−	24.8318i	−0.195094	−	0.933235i
$709$		−	15.9176i		−	0.597798i	−0.954285	−	0.298899i	$-0.903381\pi$
$709$		−	15.9176i		−	0.597798i	0.954285	−	0.298899i	$-0.0966194\pi$
$710$	7.39134	−	4.34744i	0.277392	−	0.163157i
$711$	5.09021	+	11.6425i	0.190898	+	0.436628i
$712$	−0.773563	+	0.773563i	−0.0289905	+	0.0289905i
$713$	−32.0712	+	32.0712i	−1.20108	+	1.20108i
$714$		0			0
$715$	4.71930	−	2.77580i	0.176492	−	0.103809i
$716$			0.460292i			0.0172019i
$717$	−31.7179	+	6.63067i	−1.18453	+	0.247627i
$718$	3.04916	+	3.04916i	0.113794	+	0.113794i
$719$	−21.3813			−0.797388			−0.398694	−	0.917084i	$-0.630536\pi$
$719$	−21.3813			−0.797388			−0.398694	+	0.917084i	$0.630536\pi$
$720$	−22.7660	+	3.63782i	−0.848440	+	0.135573i
$721$		0			0
$722$	3.56409	+	3.56409i	0.132642	+	0.132642i
$723$	3.34354	−	0.698971i	0.124348	−	0.0259950i
$724$			35.5905i			1.32271i
$725$	−21.5987	−	12.0086i	−0.802155	−	0.445989i
$726$	4.66383	+	3.05103i	0.173091	+	0.113234i
$727$	−7.43836	+	7.43836i	−0.275873	+	0.275873i	−0.831459	−	0.555586i	$-0.812494\pi$
$727$	−7.43836	+	7.43836i	−0.275873	+	0.275873i	0.555586	+	0.831459i	$0.312494\pi$
$728$		0			0
$729$	8.85885	−	25.5053i	0.328106	−	0.944641i
$730$	0.240542	−	0.927651i	0.00890287	−	0.0343339i
$731$		−	18.4923i		−	0.683964i
$732$	2.96613	+	14.1886i	0.109631	+	0.524424i
$733$	−25.8200	−	25.8200i	−0.953683	−	0.953683i	0.0452905	−	0.998974i	$-0.485579\pi$
$733$	−25.8200	−	25.8200i	−0.953683	−	0.953683i	−0.998974	+	0.0452905i	$0.985579\pi$
$734$	4.65810			0.171934
$735$		0			0
$736$	26.5725			0.979475
$737$	−0.0263088	−	0.0263088i	−0.000969096	−	0.000969096i
$738$	1.47282	−	3.76116i	0.0542152	−	0.138450i
$739$		−	38.3589i		−	1.41105i	−0.708683	−	0.705527i	$-0.750710\pi$
$739$		−	38.3589i		−	1.41105i	0.708683	−	0.705527i	$-0.249290\pi$
$740$	7.63566	+	12.9818i	0.280692	+	0.477221i
$741$	−4.98446	+	7.61928i	−0.183109	+	0.279901i
$742$		0			0
$743$	30.8182	−	30.8182i	1.13061	−	1.13061i	0.140534	−	0.990076i	$-0.455118\pi$
$743$	30.8182	−	30.8182i	1.13061	−	1.13061i	0.990076	−	0.140534i	$-0.0448819\pi$
$744$	6.77863	−	10.3619i	0.248516	−	0.379884i
$745$	−37.7796	−	9.79634i	−1.38414	−	0.358910i
$746$		−	10.7588i		−	0.393908i
$747$	7.81768	−	19.9641i	0.286034	−	0.730450i
$748$	4.99090	+	4.99090i	0.182485	+	0.182485i
$749$		0			0
$750$	1.36541	+	5.82265i	0.0498578	+	0.212613i
$751$	39.8711			1.45492			0.727459	−	0.686151i	$-0.240701\pi$
$751$	39.8711			1.45492			0.727459	+	0.686151i	$0.240701\pi$
$752$	10.4196	+	10.4196i	0.379965	+	0.379965i
$753$	−6.34478	−	30.3504i	−0.231217	−	1.10603i
$754$		−	4.90190i		−	0.178517i
$755$	−32.9342	−	8.53991i	−1.19860	−	0.310799i
$756$		0			0
$757$	0.798673	−	0.798673i	0.0290283	−	0.0290283i	−0.692444	−	0.721472i	$-0.743466\pi$
$757$	0.798673	−	0.798673i	0.0290283	−	0.0290283i	0.721472	+	0.692444i	$0.243466\pi$
$758$	4.16238	−	4.16238i	0.151184	−	0.151184i
$759$	8.45522	+	5.53132i	0.306905	+	0.200774i
$760$	2.23776	+	3.80454i	0.0811721	+	0.138005i
$761$			43.1790i			1.56524i	0.622500	+	0.782619i	$0.286117\pi$
$761$			43.1790i			1.56524i	−0.622500	+	0.782619i	$0.713883\pi$
$762$	3.30350	−	0.690601i	0.119673	−	0.0250178i
$763$		0			0
$764$	−27.1236			−0.981299
$765$	−26.4035	−	19.1280i	−0.954621	−	0.691573i
$766$	3.13659			0.113330
$767$	17.4622	+	17.4622i	0.630524	+	0.630524i
$768$	15.0947	−	3.15557i	0.544685	−	0.113867i
$769$		−	44.1875i		−	1.59344i	−0.604348	−	0.796720i	$-0.706566\pi$
$769$		−	44.1875i		−	1.59344i	0.604348	−	0.796720i	$-0.293434\pi$
$770$		0			0
$771$	28.5812	+	18.6975i	1.02933	+	0.673376i
$772$	9.17972	−	9.17972i	0.330385	−	0.330385i
$773$	−15.4692	+	15.4692i	−0.556390	+	0.556390i	−0.928278	−	0.371888i	$-0.878711\pi$
$773$	−15.4692	+	15.4692i	−0.556390	+	0.556390i	0.371888	+	0.928278i	$0.378711\pi$
$774$	1.41216	+	3.22993i	0.0507589	+	0.116098i
$775$	25.9064	+	14.4037i	0.930586	+	0.517395i
$776$			6.36214i			0.228388i
$777$		0			0
$778$	8.13643	+	8.13643i	0.291705	+	0.291705i
$779$	7.13633			0.255686
$780$	17.5290	−	15.9339i	0.627638	−	0.570525i
$781$	−9.46770			−0.338781
$782$	8.12049	+	8.12049i	0.290388	+	0.290388i
$783$	−20.9281	+	14.8856i	−0.747911	+	0.531966i
$784$		0			0
$785$	−17.6095	+	10.3576i	−0.628512	+	0.369679i
$786$	0.629457	−	0.962193i	0.0224520	−	0.0343203i
$787$	−0.213202	+	0.213202i	−0.00759982	+	0.00759982i	−0.710896	−	0.703297i	$-0.751711\pi$
$787$	−0.213202	+	0.213202i	−0.00759982	+	0.00759982i	0.703297	+	0.710896i	$0.251711\pi$
$788$	−14.5823	+	14.5823i	−0.519472	+	0.519472i
$789$	−5.26120	+	8.04231i	−0.187304	+	0.286314i
$790$	−2.52120	+	1.48292i	−0.0897003	+	0.0527600i
$791$		0			0
$792$	−2.56845	−	1.00577i	−0.0912659	−	0.0357385i
$793$	−9.97768	−	9.97768i	−0.354318	−	0.354318i
$794$	2.74540			0.0974306
$795$	−19.9191	+	18.1065i	−0.706457	+	0.642171i
$796$	−31.1977			−1.10577
$797$	−8.45240	−	8.45240i	−0.299399	−	0.299399i	0.541379	−	0.840779i	$-0.317902\pi$
$797$	−8.45240	−	8.45240i	−0.299399	−	0.299399i	−0.840779	+	0.541379i	$0.817902\pi$
$798$		0			0
$799$			20.8390i			0.737231i
$800$	−4.76529	−	16.6994i	−0.168478	−	0.590413i
$801$	−2.49368	+	1.09026i	−0.0881098	+	0.0385224i
$802$	1.01580	−	1.01580i	0.0358691	−	0.0358691i
$803$	−0.748181	+	0.748181i	−0.0264027	+	0.0264027i
$804$	−0.134712	−	0.0881271i	−0.00475092	−	0.00310800i
$805$		0			0
$806$			5.87955i			0.207098i
$807$	17.0327	−	3.56070i	0.599579	−	0.125343i
$808$	16.1913	+	16.1913i	0.569608	+	0.569608i
$809$	−37.1351			−1.30560			−0.652801	−	0.757530i	$-0.726406\pi$
$809$	−37.1351			−1.30560			−0.652801	+	0.757530i	$0.726406\pi$
$810$	6.07242	+	1.32467i	0.213363	+	0.0465440i
$811$	−23.5491			−0.826921			−0.413461	−	0.910522i	$-0.635680\pi$
$811$	−23.5491			−0.826921			−0.413461	+	0.910522i	$0.635680\pi$
$812$		0			0
$813$	9.56300	−	1.99915i	0.335389	−	0.0701134i
$814$			0.832736i			0.0291874i
$815$	3.06918	+	5.21809i	0.107509	+	0.182782i
$816$	24.2116	+	15.8390i	0.847576	+	0.554475i
$817$	−4.40389	+	4.40389i	−0.154073	+	0.154073i
$818$	5.79994	−	5.79994i	0.202790	−	0.202790i
$819$		0			0
$820$	−17.9727	−	4.66036i	−0.627633	−	0.162747i
$821$			40.9914i			1.43061i	0.698812	+	0.715306i	$0.253713\pi$
$821$			40.9914i			1.43061i	−0.698812	+	0.715306i	$0.746287\pi$
$822$	0.965130	+	4.61672i	0.0336628	+	0.161027i
$823$	−18.2198	−	18.2198i	−0.635104	−	0.635104i	0.314240	−	0.949344i	$-0.398250\pi$
$823$	−18.2198	−	18.2198i	−0.635104	−	0.635104i	−0.949344	+	0.314240i	$0.898250\pi$
$824$	15.2319			0.530629
$825$	1.95985	−	6.30560i	0.0682333	−	0.219533i
$826$		0			0
$827$	−19.5668	−	19.5668i	−0.680404	−	0.680404i	0.279687	−	0.960091i	$-0.409769\pi$
$827$	−19.5668	−	19.5668i	−0.680404	−	0.680404i	−0.960091	+	0.279687i	$0.909769\pi$
$828$	40.7055	+	15.9397i	1.41462	+	0.553943i
$829$			25.3202i			0.879406i	0.898143	+	0.439703i	$0.144916\pi$
$829$			25.3202i			0.879406i	−0.898143	+	0.439703i	$0.855084\pi$
$830$	4.77740	+	1.23879i	0.165826	+	0.0429991i
$831$	10.6625	−	16.2988i	0.369878	−	0.565398i
$832$	−13.1727	+	13.1727i	−0.456680	+	0.456680i
$833$		0			0
$834$	3.03461	−	4.63873i	0.105080	−	0.160626i
$835$	−6.18127	−	10.5091i	−0.213912	−	0.363683i
$836$		−	2.37713i		−	0.0822149i
$837$	25.1022	−	17.8544i	0.867657	−	0.617138i
$838$	−5.64030	−	5.64030i	−0.194841	−	0.194841i
$839$	50.7484			1.75203			0.876014	−	0.482286i	$-0.160193\pi$
$839$	50.7484			1.75203			0.876014	+	0.482286i	$0.160193\pi$
$840$		0			0
$841$	−4.57160			−0.157641
$842$	0.0944344	+	0.0944344i	0.00325442	+	0.00325442i
$843$	−0.683443	−	3.26926i	−0.0235390	−	0.112599i
$844$			48.5731i			1.67196i
$845$	1.50824	−	5.81651i	0.0518849	−	0.200094i
$846$	−1.59136	−	3.63981i	−0.0547120	−	0.125139i
$847$		0			0
$848$	16.8908	−	16.8908i	0.580031	−	0.580031i
$849$	38.2148	+	24.9997i	1.31153	+	0.857989i
$850$	3.64704	−	6.55956i	0.125092	−	0.224991i
$851$		−	27.0558i		−	0.927460i
$852$	−40.0963	+	8.38218i	−1.37368	+	0.287169i
$853$	18.8448	+	18.8448i	0.645233	+	0.645233i	0.951837	−	0.306604i	$-0.0991928\pi$
$853$	18.8448	+	18.8448i	0.645233	+	0.645233i	−0.306604	+	0.951837i	$0.599193\pi$
$854$		0			0
$855$	1.73265	+	10.8432i	0.0592552	+	0.370829i
$856$	−2.62963			−0.0898790
$857$	−8.80014	−	8.80014i	−0.300607	−	0.300607i	0.540644	−	0.841251i	$-0.318181\pi$
$857$	−8.80014	−	8.80014i	−0.300607	−	0.300607i	−0.841251	+	0.540644i	$0.818181\pi$
$858$	1.28206	−	0.268017i	0.0437689	−	0.00914994i
$859$		−	3.85330i		−	0.131473i	−0.997837	−	0.0657364i	$-0.979060\pi$
$859$		−	3.85330i		−	0.131473i	0.997837	−	0.0657364i	$-0.0209397\pi$
$860$	13.9670	−	8.21515i	0.476272	−	0.280134i
$861$		0			0
$862$	3.56217	−	3.56217i	0.121328	−	0.121328i
$863$	−35.2942	+	35.2942i	−1.20143	+	1.20143i	−0.227695	+	0.973732i	$0.573119\pi$
$863$	−35.2942	+	35.2942i	−1.20143	+	1.20143i	−0.973732	+	0.227695i	$0.926881\pi$
$864$	−17.7957	−	3.00255i	−0.605424	−	0.102149i
$865$	2.55040	−	1.50010i	0.0867164	−	0.0510049i
$866$			0.224599i			0.00763219i
$867$	2.34727	+	11.2282i	0.0797176	+	0.381331i
$868$		0			0
$869$	3.22945			0.109552
$870$	−3.97652	−	4.37460i	−0.134817	−	0.148313i
$871$	0.156705			0.00530974
$872$	2.01211	+	2.01211i	0.0681387	+	0.0681387i
$873$	−5.77118	+	14.7380i	−0.195325	+	0.498805i
$874$		−	3.86774i		−	0.130828i
$875$		0			0
$876$	−2.50620	+	3.83099i	−0.0846765	+	0.129437i
$877$	−31.9696	+	31.9696i	−1.07954	+	1.07954i	−0.0829852	+	0.996551i	$0.526445\pi$
$877$	−31.9696	+	31.9696i	−1.07954	+	1.07954i	−0.996551	+	0.0829852i	$0.973555\pi$
$878$	3.34086	−	3.34086i	0.112749	−	0.112749i
$879$	−10.5043	+	16.0569i	−0.354301	+	0.541587i
$880$	−1.47075	+	5.67193i	−0.0495788	+	0.191201i
$881$		−	25.2055i		−	0.849195i	−0.905382	−	0.424597i	$-0.860416\pi$
$881$		−	25.2055i		−	0.849195i	0.905382	−	0.424597i	$-0.139584\pi$
$882$		0			0
$883$	−14.2942	−	14.2942i	−0.481039	−	0.481039i	0.424424	−	0.905463i	$-0.360476\pi$
$883$	−14.2942	−	14.2942i	−0.481039	−	0.481039i	−0.905463	+	0.424424i	$0.860476\pi$
$884$	−29.7277			−0.999850
$885$	29.7495	+	1.41808i	1.00002	+	0.0476683i
$886$	2.81824			0.0946806
$887$	27.5143	+	27.5143i	0.923840	+	0.923840i	0.997298	−	0.0734580i	$-0.0234035\pi$
$887$	27.5143	+	27.5143i	0.923840	+	0.923840i	−0.0734580	+	0.997298i	$0.523403\pi$
$888$	1.51144	+	7.23000i	0.0507206	+	0.242623i
$889$		0			0
$890$	−0.317623	−	0.540010i	−0.0106468	−	0.0181012i
$891$	−5.03750	−	4.65975i	−0.168763	−	0.156108i
$892$	29.4351	−	29.4351i	0.985559	−	0.985559i
$893$	4.96274	−	4.96274i	0.166072	−	0.166072i
$894$	−7.81330	−	5.11138i	−0.261316	−	0.170950i
$895$	−0.523094	−	0.135639i	−0.0174851	−	0.00453393i
$896$		0			0
$897$	−41.6545	+	8.70792i	−1.39080	+	0.290749i
$898$	2.05472	+	2.05472i	0.0685670	+	0.0685670i
$899$	−29.3005			−0.977227
$900$	2.71747	−	28.4398i	0.0905824	−	0.947992i
$901$	33.7811			1.12541
$902$	−0.725914	−	0.725914i	−0.0241703	−	0.0241703i
$903$		0			0
$904$			20.3599i			0.677161i
$905$	−40.4464	−	10.4879i	−1.34448	−	0.348628i
$906$	−6.81120	−	4.45582i	−0.226287	−	0.148035i
$907$	1.70404	−	1.70404i	0.0565816	−	0.0565816i	−0.678250	−	0.734831i	$-0.737261\pi$
$907$	1.70404	−	1.70404i	0.0565816	−	0.0565816i	0.734831	+	0.678250i	$0.237261\pi$
$908$	17.3031	−	17.3031i	0.574224	−	0.574224i
$909$	22.8200	+	52.1946i	0.756891	+	1.73119i
$910$		0			0
$911$			19.3662i			0.641631i	0.947142	+	0.320815i	$0.103957\pi$
$911$			19.3662i			0.641631i	−0.947142	+	0.320815i	$0.896043\pi$
$912$	−1.99391	−	9.53792i	−0.0660250	−	0.315832i
$913$	−3.85313	−	3.85313i	−0.127520	−	0.127520i
$914$	−10.6637			−0.352724
$915$	−16.9985	−	0.810273i	−0.561953	−	0.0267868i
$916$	29.1421			0.962883
$917$		0			0
$918$	−4.52077	−	6.35591i	−0.149208	−	0.209776i
$919$			34.1319i			1.12591i	0.826489	+	0.562953i	$0.190335\pi$
$919$			34.1319i			1.12591i	−0.826489	+	0.562953i	$0.809665\pi$
$920$	−5.17811	+	19.9694i	−0.170717	+	0.658372i
$921$	22.8997	−	35.0046i	0.754569	−	1.15344i
$922$	−8.06536	+	8.06536i	−0.265619	+	0.265619i
$923$	28.1966	−	28.1966i	0.928102	−	0.928102i
$924$		0			0
$925$	−17.0031	+	4.85196i	−0.559059	+	0.159531i
$926$			11.5168i			0.378467i
$927$	35.2849	+	13.8171i	1.15891	+	0.453812i
$928$	12.1384	+	12.1384i	0.398463	+	0.398463i
$929$	−19.7246			−0.647144			−0.323572	−	0.946204i	$-0.604884\pi$
$929$	−19.7246			−0.647144			−0.323572	+	0.946204i	$0.604884\pi$
$930$	4.76962	+	5.24709i	0.156402	+	0.172059i
$931$		0			0
$932$	−9.24073	−	9.24073i	−0.302690	−	0.302690i
$933$	−8.38142	−	40.0927i	−0.274395	−	1.31258i
$934$		−	3.14994i		−	0.103069i
$935$	−7.14258	+	4.20113i	−0.233587	+	0.137392i
$936$	10.6447	−	4.65396i	0.347933	−	0.152119i
$937$	17.3041	−	17.3041i	0.565300	−	0.565300i	−0.365508	−	0.930808i	$-0.619105\pi$
$937$	17.3041	−	17.3041i	0.565300	−	0.565300i	0.930808	+	0.365508i	$0.119105\pi$
$938$		0			0
$939$	17.9436	+	11.7385i	0.585568	+	0.383072i
$940$	−15.7394	+	9.25764i	−0.513364	+	0.301951i
$941$		−	4.49489i		−	0.146529i	−0.997313	−	0.0732646i	$-0.976658\pi$
$941$		−	4.49489i		−	0.146529i	0.997313	−	0.0732646i	$-0.0233418\pi$
$942$	−4.78388	+	1.00008i	−0.155867	+	0.0325842i
$943$	23.5851	+	23.5851i	0.768036	+	0.768036i
$944$	−26.4292			−0.860196
$945$		0			0
$946$	0.895935			0.0291294
$947$	10.6067	+	10.6067i	0.344673	+	0.344673i	0.858121	−	0.513448i	$-0.171632\pi$
$947$	10.6067	+	10.6067i	0.344673	+	0.344673i	−0.513448	+	0.858121i	$0.671632\pi$
$948$	13.6769	−	2.85918i	0.444207	−	0.0928619i
$949$		−	4.45644i		−	0.144662i
$950$	−2.43067	+	0.693608i	−0.0788613	+	0.0225036i
$951$	6.36658	+	4.16495i	0.206451	+	0.135058i
$952$		0			0
$953$	−21.6181	+	21.6181i	−0.700277	+	0.700277i	−0.964470	−	0.264193i	$-0.914895\pi$
$953$	−21.6181	+	21.6181i	−0.700277	+	0.700277i	0.264193	+	0.964470i	$0.414895\pi$
$954$	−5.90031	+	2.57967i	−0.191030	+	0.0835199i
$955$	7.99283	−	30.8244i	0.258642	−	0.997453i
$956$			35.6321i			1.15242i
$957$	1.33565	+	6.38911i	0.0431754	+	0.206531i
$958$	2.99334	+	2.99334i	0.0967106	+	0.0967106i
$959$		0			0
$960$	−1.06973	+	22.4416i	−0.0345255	+	0.724300i
$961$	4.14435			0.133689
$962$	−2.48004	−	2.48004i	−0.0799598	−	0.0799598i
$963$	−6.09157	−	2.38537i	−0.196298	−	0.0768676i
$964$		−	3.75615i		−	0.120977i
$965$	7.72710	+	13.1373i	0.248744	+	0.422904i
$966$		0			0
$967$	16.1911	−	16.1911i	0.520672	−	0.520672i	−0.397102	−	0.917774i	$-0.629984\pi$
$967$	16.1911	−	16.1911i	0.520672	−	0.520672i	0.917774	+	0.397102i	$0.129984\pi$
$968$	8.88392	−	8.88392i	0.285540	−	0.285540i
$969$	7.54390	−	11.5317i	0.242345	−	0.370451i
$970$	−3.52678	−	0.914504i	−0.113238	−	0.0293629i
$971$			18.2948i			0.587107i	0.955943	+	0.293553i	$0.0948379\pi$
$971$			18.2948i			0.587107i	−0.955943	+	0.293553i	$0.905162\pi$
$972$	−25.4596	−	15.2744i	−0.816618	−	0.489928i
$973$		0			0
$974$	−7.06004			−0.226218
$975$	12.9424	+	24.6160i	0.414490	+	0.788344i
$976$	15.1013			0.483380
$977$	−10.5379	−	10.5379i	−0.337139	−	0.337139i	0.518151	−	0.855289i	$-0.326621\pi$
$977$	−10.5379	−	10.5379i	−0.337139	−	0.337139i	−0.855289	+	0.518151i	$0.826621\pi$
$978$	0.296344	+	1.41757i	0.00947603	+	0.0453288i
$979$			0.691709i			0.0221071i
$980$		0			0
$981$	2.83587	+	6.48630i	0.0905423	+	0.207092i
$982$	5.18603	−	5.18603i	0.165493	−	0.165493i
$983$	−8.31506	+	8.31506i	−0.265209	+	0.265209i	−0.827166	−	0.561957i	$-0.810049\pi$
$983$	−8.31506	+	8.31506i	−0.265209	+	0.265209i	0.561957	+	0.827166i	$0.310049\pi$
$984$	−7.62009	−	4.98499i	−0.242920	−	0.158916i
$985$	−12.2747	−	20.8690i	−0.391106	−	0.664941i
$986$			7.41895i			0.236267i
$987$		0			0
$988$	7.07955	+	7.07955i	0.225230	+	0.225230i
$989$	−29.1091			−0.925616
$990$	0.926730	−	1.27922i	0.0294534	−	0.0406564i
$991$	10.0401			0.318933			0.159467	−	0.987203i	$-0.449023\pi$
$991$	10.0401			0.318933			0.159467	+	0.987203i	$0.449023\pi$
$992$	−14.5594	−	14.5594i	−0.462260	−	0.462260i
$993$	−10.5431	+	2.20405i	−0.334576	+	0.0699434i
$994$		0			0
$995$	9.19337	−	35.4542i	0.291449	−	1.12397i
$996$	−19.7296	−	12.9069i	−0.625156	−	0.408971i
$997$	9.95260	−	9.95260i	0.315202	−	0.315202i	−0.531719	−	0.846921i	$-0.678454\pi$
$997$	9.95260	−	9.95260i	0.315202	−	0.315202i	0.846921	+	0.531719i	$0.178454\pi$
$998$	0.706533	−	0.706533i	0.0223649	−	0.0223649i
$999$	−3.05716	+	18.1194i	−0.0967243	+	0.573273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.j.e.638.7		24
3.2	odd	2	inner	735.2.j.e.638.6		24
5.2	odd	4	inner	735.2.j.e.197.6		24
7.2	even	3		735.2.y.i.263.7		48
7.3	odd	6		105.2.x.a.23.6	yes	48
7.4	even	3		735.2.y.i.128.6		48
7.5	odd	6		105.2.x.a.53.7	yes	48
7.6	odd	2		735.2.j.g.638.7		24
15.2	even	4	inner	735.2.j.e.197.7		24
21.2	odd	6		735.2.y.i.263.6		48
21.5	even	6		105.2.x.a.53.6	yes	48
21.11	odd	6		735.2.y.i.128.7		48
21.17	even	6		105.2.x.a.23.7	yes	48
21.20	even	2		735.2.j.g.638.6		24
35.2	odd	12		735.2.y.i.557.7		48
35.3	even	12		525.2.bf.f.107.7		48
35.12	even	12		105.2.x.a.32.7	yes	48
35.17	even	12		105.2.x.a.2.6	✓	48
35.19	odd	6		525.2.bf.f.368.6		48
35.24	odd	6		525.2.bf.f.443.7		48
35.27	even	4		735.2.j.g.197.6		24
35.32	odd	12		735.2.y.i.422.6		48
35.33	even	12		525.2.bf.f.32.6		48
105.2	even	12		735.2.y.i.557.6		48
105.17	odd	12		105.2.x.a.2.7	yes	48
105.32	even	12		735.2.y.i.422.7		48
105.38	odd	12		525.2.bf.f.107.6		48
105.47	odd	12		105.2.x.a.32.6	yes	48
105.59	even	6		525.2.bf.f.443.6		48
105.62	odd	4		735.2.j.g.197.7		24
105.68	odd	12		525.2.bf.f.32.7		48
105.89	even	6		525.2.bf.f.368.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.x.a.2.6	✓	48	35.17	even	12
105.2.x.a.2.7	yes	48	105.17	odd	12
105.2.x.a.23.6	yes	48	7.3	odd	6
105.2.x.a.23.7	yes	48	21.17	even	6
105.2.x.a.32.6	yes	48	105.47	odd	12
105.2.x.a.32.7	yes	48	35.12	even	12
105.2.x.a.53.6	yes	48	21.5	even	6
105.2.x.a.53.7	yes	48	7.5	odd	6
525.2.bf.f.32.6		48	35.33	even	12
525.2.bf.f.32.7		48	105.68	odd	12
525.2.bf.f.107.6		48	105.38	odd	12
525.2.bf.f.107.7		48	35.3	even	12
525.2.bf.f.368.6		48	35.19	odd	6
525.2.bf.f.368.7		48	105.89	even	6
525.2.bf.f.443.6		48	105.59	even	6
525.2.bf.f.443.7		48	35.24	odd	6
735.2.j.e.197.6		24	5.2	odd	4	inner
735.2.j.e.197.7		24	15.2	even	4	inner
735.2.j.e.638.6		24	3.2	odd	2	inner
735.2.j.e.638.7		24	1.1	even	1	trivial
735.2.j.g.197.6		24	35.27	even	4
735.2.j.g.197.7		24	105.62	odd	4
735.2.j.g.638.6		24	21.20	even	2
735.2.j.g.638.7		24	7.6	odd	2
735.2.y.i.128.6		48	7.4	even	3
735.2.y.i.128.7		48	21.11	odd	6
735.2.y.i.263.6		48	21.2	odd	6
735.2.y.i.263.7		48	7.2	even	3
735.2.y.i.422.6		48	35.32	odd	12
735.2.y.i.422.7		48	105.32	even	12
735.2.y.i.557.6		48	105.2	even	12
735.2.y.i.557.7		48	35.2	odd	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 $\F_{q}$
Belyi maps

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+(0.218381 + 0.218381i) q^{2} +(1.69540 - 0.354425i) q^{3} -1.90462i q^{4} +(2.16448 + 0.561256i) q^{5} +(0.447643 + 0.292843i) q^{6} +(0.852694 - 0.852694i) q^{8} +(2.74877 - 1.20179i) q^{9} +(0.350114 + 0.595249i) q^{10} -0.762466i q^{11} +(-0.675045 - 3.22909i) q^{12} +(2.27077 + 2.27077i) q^{13} +(3.86859 + 0.184406i) q^{15} -3.43682 q^{16} +(-3.43677 - 3.43677i) q^{17} +(0.862724 + 0.337831i) q^{18} +1.63691i q^{19} +(1.06898 - 4.12252i) q^{20} +(0.166508 - 0.166508i) q^{22} +(-5.40988 + 5.40988i) q^{23} +(1.14344 - 1.74787i) q^{24} +(4.36998 + 2.42966i) q^{25} +0.991783i q^{26} +(4.23432 - 3.01174i) q^{27} -4.94251 q^{29} +(0.804555 + 0.885097i) q^{30} +5.92827 q^{31} +(-2.45592 - 2.45592i) q^{32} +(-0.270237 - 1.29269i) q^{33} -1.50105i q^{34} +(-2.28894 - 5.23535i) q^{36} +(-2.50059 + 2.50059i) q^{37} +(-0.357470 + 0.357470i) q^{38} +(4.65467 + 3.04504i) q^{39} +(2.32422 - 1.36706i) q^{40} -4.35963i q^{41} +(2.69037 + 2.69037i) q^{43} -1.45221 q^{44} +(6.62417 - 1.05849i) q^{45} -2.36283 q^{46} +(-3.03177 - 3.03177i) q^{47} +(-5.82678 + 1.21809i) q^{48} +(0.423730 + 1.48491i) q^{50} +(-7.04478 - 4.60862i) q^{51} +(4.32494 - 4.32494i) q^{52} +(-4.91465 + 4.91465i) q^{53} +(1.58240 + 0.266987i) q^{54} +(0.427939 - 1.65035i) q^{55} +(0.580162 + 2.77522i) q^{57} +(-1.07935 - 1.07935i) q^{58} +7.69002 q^{59} +(0.351222 - 7.36819i) q^{60} -4.39397 q^{61} +(1.29462 + 1.29462i) q^{62} +5.80098i q^{64} +(3.64056 + 6.18952i) q^{65} +(0.223283 - 0.341312i) q^{66} +(0.0345049 - 0.0345049i) q^{67} +(-6.54574 + 6.54574i) q^{68} +(-7.25451 + 11.0893i) q^{69} -12.4172i q^{71} +(1.31910 - 3.36861i) q^{72} +(-0.981264 - 0.981264i) q^{73} -1.09216 q^{74} +(8.27000 + 2.57041i) q^{75} +3.11769 q^{76} +(0.351513 + 1.68147i) q^{78} +4.23554i q^{79} +(-7.43893 - 1.92893i) q^{80} +(6.11142 - 6.60685i) q^{81} +(0.952060 - 0.952060i) q^{82} +(5.05351 - 5.05351i) q^{83} +(-5.50993 - 9.36774i) q^{85} +1.17505i q^{86} +(-8.37953 + 1.75175i) q^{87} +(-0.650150 - 0.650150i) q^{88} -0.907199 q^{89} +(1.67774 + 1.21544i) q^{90} +(10.3038 + 10.3038i) q^{92} +(10.0508 - 2.10113i) q^{93} -1.32416i q^{94} +(-0.918726 + 3.54307i) q^{95} +(-5.03421 - 3.29333i) q^{96} +(-3.73061 + 3.73061i) q^{97} +(-0.916321 - 2.09584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{3} + 12 q^{6} - 8 q^{10} - 10 q^{12} + 8 q^{13} + 2 q^{15} + 8 q^{16} - 14 q^{18} - 4 q^{22} - 4 q^{25} - 20 q^{27} - 40 q^{30} - 24 q^{31} - 4 q^{33} + 4 q^{36} - 4 q^{37} - 16 q^{40} + 8 q^{43}+ \cdots + 60 q^{97}+O(q^{100}) \) 24 * q - 2 * q^3 + 12 * q^6 - 8 * q^10 - 10 * q^12 + 8 * q^13 + 2 * q^15 + 8 * q^16 - 14 * q^18 - 4 * q^22 - 4 * q^25 - 20 * q^27 - 40 * q^30 - 24 * q^31 - 4 * q^33 + 4 * q^36 - 4 * q^37 - 16 * q^40 + 8 * q^43 + 40 * q^45 + 32 * q^46 - 22 * q^48 - 8 * q^51 + 36 * q^52 + 20 * q^55 - 44 * q^57 - 56 * q^58 + 50 * q^60 - 8 * q^61 + 76 * q^66 - 12 * q^67 + 34 * q^72 + 52 * q^73 + 6 * q^75 - 32 * q^76 - 60 * q^78 - 20 * q^81 + 104 * q^82 - 12 * q^85 - 46 * q^87 + 42 * q^90 + 44 * q^93 + 12 * q^96 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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