LMFDB - Embedded newform 735.2.j.g.197.7

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			197.7
Character	$\chi$	$=$	735.197
Dual form			735.2.j.g.638.7

$q$-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 $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.218381	−	0.218381i	0.154419	−	0.154419i	−0.625670	−	0.780088i	$-0.715174\pi$
$2$	0.218381	−	0.218381i	0.154419	−	0.154419i	0.780088	+	0.625670i	$0.215174\pi$
$3$	−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	$0.0366695\pi$
$11$			0.762466i			0.229892i	−0.993372	+	0.114946i	$0.963330\pi$
$12$	0.675045	−	3.22909i	0.194869	−	0.932159i
$13$	−2.27077	+	2.27077i	−0.629797	+	0.629797i	−0.948017	−	0.318220i	$-0.896915\pi$
$13$	−2.27077	+	2.27077i	−0.629797	+	0.629797i	0.318220	+	0.948017i	$0.396915\pi$
$14$		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	$-0.549364\pi$
$17$	3.43677	−	3.43677i	0.833539	−	0.833539i	0.987999	+	0.154460i	$0.0493638\pi$
$18$	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	−0.990496	−	0.137542i	$-0.956080\pi$
$23$	−5.40988	−	5.40988i	−1.12804	−	1.12804i	−0.137542	−	0.990496i	$-0.543920\pi$
$24$	−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	$-0.678700\pi$
$31$	−5.92827			−1.06475			−0.532374	+	0.846509i	$0.678700\pi$
$32$	−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	0.471025	−	0.882120i	$-0.343884\pi$
$37$	−2.50059	−	2.50059i	−0.411095	−	0.411095i	−0.882120	+	0.471025i	$0.843884\pi$
$38$	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	−0.471558	−	0.881835i	$-0.656308\pi$
$43$	2.69037	−	2.69037i	0.410277	−	0.410277i	0.881835	+	0.471558i	$0.156308\pi$
$44$	−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	$-0.648765\pi$
$47$	3.03177	−	3.03177i	0.442230	−	0.442230i	0.892761	+	0.450531i	$0.148765\pi$
$48$	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	0.283803	−	0.958883i	$-0.408404\pi$
$53$	−4.91465	−	4.91465i	−0.675080	−	0.675080i	−0.958883	+	0.283803i	$0.908404\pi$
$54$	−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	$-0.666879\pi$
$59$	−7.69002			−1.00115			−0.500577	+	0.865692i	$0.666879\pi$
$60$	0.351222	+	7.36819i	0.0453426	+	0.951230i
$61$	4.39397			0.562591			0.281295	−	0.959621i	$-0.409236\pi$
$61$	4.39397			0.562591			0.281295	+	0.959621i	$0.409236\pi$
$62$	−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	0.709211	−	0.704996i	$-0.249051\pi$
$67$	0.0345049	+	0.0345049i	0.00421544	+	0.00421544i	−0.704996	+	0.709211i	$0.749051\pi$
$68$	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	$0.263676\pi$
$71$			12.4172i			1.47365i	−0.676082	+	0.736826i	$0.736324\pi$
$72$	1.31910	+	3.36861i	0.155457	+	0.396995i
$73$	0.981264	−	0.981264i	0.114848	−	0.114848i	−0.647347	−	0.762195i	$-0.724122\pi$
$73$	0.981264	−	0.981264i	0.114848	−	0.114848i	0.762195	+	0.647347i	$0.224122\pi$
$74$	−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	$-0.923420\pi$
$79$		−	4.23554i		−	0.476535i	0.971200	−	0.238268i	$-0.0765795\pi$
$80$	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	$-0.378296\pi$
$83$	−5.05351	−	5.05351i	−0.554695	−	0.554695i	−0.927792	+	0.373097i	$0.878296\pi$
$84$		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	$-0.484689\pi$
$89$	0.907199			0.0961629			0.0480815	+	0.998843i	$0.484689\pi$
$90$	−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	$-0.163689\pi$
$97$	3.73061	+	3.73061i	0.378786	+	0.378786i	−0.491878	+	0.870664i	$0.663689\pi$
$98$		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	$-0.963800\pi$
$103$	−8.93165	+	8.93165i	−0.880061	+	0.880061i	0.113479	+	0.993540i	$0.463800\pi$
$104$	−3.87254			−0.379733
$105$		0			0
$106$	−2.14653			−0.208490
$107$	−1.54196	+	1.54196i	−0.149066	+	0.149066i	−0.777701	−	0.628634i	$-0.783614\pi$
$107$	−1.54196	+	1.54196i	−0.149066	+	0.149066i	0.628634	+	0.777701i	$0.283614\pi$
$108$	5.73622	−	8.06476i	0.551968	−	0.776032i
$109$		−	2.35971i		−	0.226020i	−0.993594	−	0.113010i	$-0.963951\pi$
$109$		−	2.35971i		−	0.226020i	0.993594	−	0.113010i	$-0.0360491\pi$
$110$	−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	−0.991274	−	0.131814i	$-0.957920\pi$
$113$	−11.9386	−	11.9386i	−1.12309	−	1.12309i	−0.131814	−	0.991274i	$-0.542080\pi$
$114$	−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	0.876775	−	0.480901i	$-0.159691\pi$
$127$	4.46126	+	4.46126i	0.395873	+	0.395873i	−0.480901	+	0.876775i	$0.659691\pi$
$128$	−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	−0.388698	−	0.921365i	$-0.627075\pi$
$137$	6.23472	−	6.23472i	0.532668	−	0.532668i	0.921365	+	0.388698i	$0.127075\pi$
$138$	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	$-0.131211\pi$
$157$	6.46046	+	6.46046i	0.515601	+	0.515601i	−0.400636	+	0.916237i	$0.631211\pi$
$158$	−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	−0.628148	−	0.778094i	$-0.716187\pi$
$163$	1.91437	−	1.91437i	0.149945	−	0.149945i	0.778094	+	0.628148i	$0.216187\pi$
$164$	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	$-0.682340\pi$
$167$	3.85551	−	3.85551i	0.298348	−	0.298348i	0.840367	+	0.542018i	$0.182340\pi$
$168$		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	$-0.266018\pi$
$173$	−0.935674	−	0.935674i	−0.0711380	−	0.0711380i	−0.741781	+	0.670643i	$0.766018\pi$
$174$	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	$-0.255637\pi$
$181$	18.6864			1.38895			0.694475	+	0.719517i	$0.255637\pi$
$182$		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	$0.172290\pi$
$191$			14.2410i			1.03044i	−0.857058	+	0.515220i	$0.827710\pi$
$192$	−2.05601	+	9.83498i	−0.148380	+	0.709779i
$193$	4.81971	−	4.81971i	0.346931	−	0.346931i	−0.512034	−	0.858965i	$-0.671108\pi$
$193$	4.81971	−	4.81971i	0.346931	−	0.346931i	0.858965	+	0.512034i	$0.171108\pi$
$194$	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	−0.925132	−	0.379646i	$-0.876046\pi$
$197$	−7.65626	+	7.65626i	−0.545486	+	0.545486i	0.379646	+	0.925132i	$0.376046\pi$
$198$	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	−0.0355465	+	0.999368i	$0.511317\pi$
$223$	−15.4546	+	15.4546i	−1.03491	+	1.03491i	−0.999368	+	0.0355465i	$0.988683\pi$
$224$		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	$-0.890208\pi$
$227$	−9.08481	+	9.08481i	−0.602980	+	0.602980i	0.338122	+	0.941102i	$0.390208\pi$
$228$	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	0.847940	−	0.530092i	$-0.177843\pi$
$233$	4.85174	+	4.85174i	0.317848	+	0.317848i	−0.530092	+	0.847940i	$0.677843\pi$
$234$	−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	$-0.520232\pi$
$241$	−1.97213			−0.127036			−0.0635179	+	0.997981i	$0.520232\pi$
$242$	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	$-0.960848\pi$
$257$	−13.9432	+	13.9432i	−0.869756	+	0.869756i	0.122689	+	0.992445i	$0.460848\pi$
$258$	−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	0.575719	−	0.817647i	$-0.304722\pi$
$263$	−3.92341	−	3.92341i	−0.241928	−	0.241928i	−0.817647	+	0.575719i	$0.804722\pi$
$264$	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	$-0.599081\pi$
$269$	−10.0464			−0.612541			−0.306270	+	0.951945i	$0.599081\pi$
$270$	3.27523	−	1.46602i	0.199324	−	0.0892191i
$271$	−5.64055			−0.342639			−0.171320	−	0.985216i	$-0.554803\pi$
$271$	−5.64055			−0.342639			−0.171320	+	0.985216i	$0.554803\pi$
$272$	−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	0.904411	−	0.426663i	$-0.140311\pi$
$277$	7.95130	+	7.95130i	0.477747	+	0.477747i	−0.426663	+	0.904411i	$0.640311\pi$
$278$	−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	$0.0183183\pi$
$281$			1.92831i			0.115033i	−0.998345	+	0.0575167i	$0.981682\pi$
$282$	−0.469316	+	2.24498i	−0.0279474	+	0.133687i
$283$	−18.6429	+	18.6429i	−1.10821	+	1.10821i	−0.114822	+	0.993386i	$0.536630\pi$
$283$	−18.6429	+	18.6429i	−1.10821	+	1.10821i	−0.993386	+	0.114822i	$0.963370\pi$
$284$	−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	$-0.145110\pi$
$293$	7.83332	+	7.83332i	0.457627	+	0.457627i	−0.440249	+	0.897876i	$0.645110\pi$
$294$		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	$-0.492023\pi$
$307$	−17.0769	−	17.0769i	−0.974628	−	0.974628i	−0.999686	+	0.0250576i	$0.992023\pi$
$308$		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	$-0.863774\pi$
$313$	−8.75372	+	8.75372i	−0.494790	+	0.494790i	0.415022	+	0.909812i	$0.363774\pi$
$314$	2.82168			0.159237
$315$		0			0
$316$	8.06709			0.453809
$317$	3.10591	−	3.10591i	0.174445	−	0.174445i	−0.614484	−	0.788929i	$-0.710636\pi$
$317$	3.10591	−	3.10591i	0.174445	−	0.174445i	0.788929	+	0.614484i	$0.210636\pi$
$318$	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	0.986084	−	0.166250i	$-0.0531659\pi$
$337$	15.0501	+	15.0501i	0.819833	+	0.819833i	−0.166250	+	0.986084i	$0.553166\pi$
$338$	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	−0.970853	−	0.239675i	$-0.922959\pi$
$347$	−13.6203	+	13.6203i	−0.731178	+	0.731178i	0.239675	+	0.970853i	$0.422959\pi$
$348$	−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	$-0.351761\pi$
$353$	−8.35049	−	8.35049i	−0.444452	−	0.444452i	−0.893505	+	0.449053i	$0.851761\pi$
$354$	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	$-0.378790\pi$
$367$	−10.6651	−	10.6651i	−0.556714	−	0.556714i	−0.928370	+	0.371657i	$0.878790\pi$
$368$	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	−0.332271	+	0.943184i	$0.607815\pi$
$373$	−24.6331	+	24.6331i	−1.27545	+	1.27545i	−0.943184	+	0.332271i	$0.892185\pi$
$374$	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	$0.162831\pi$
$379$			19.0602i			0.979056i	−0.871988	+	0.489528i	$0.837169\pi$
$380$	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	$-0.333550\pi$
$383$	−7.18147	−	7.18147i	−0.366956	−	0.366956i	−0.866366	+	0.499410i	$0.833550\pi$
$384$	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	$-0.321610\pi$
$397$	−6.28581	−	6.28581i	−0.315476	−	0.315476i	−0.847027	+	0.531551i	$0.821610\pi$
$398$	−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	$0.0370529\pi$
$401$			4.65150i			0.232285i	−0.993233	+	0.116142i	$0.962947\pi$
$402$	−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	$-0.282692\pi$
$419$	25.8278			1.26177			0.630885	+	0.775876i	$0.282692\pi$
$420$		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	$0.128512\pi$
$431$			16.3117i			0.785708i	−0.919601	+	0.392854i	$0.871488\pi$
$432$	14.5526	+	10.3508i	0.700160	+	0.498003i
$433$	−0.514238	+	0.514238i	−0.0247127	+	0.0247127i	−0.719355	−	0.694642i	$-0.755563\pi$
$433$	−0.514238	+	0.514238i	−0.0247127	+	0.0247127i	0.694642	+	0.719355i	$0.255563\pi$
$434$		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	0.843578	−	0.537007i	$-0.180445\pi$
$443$	6.45258	+	6.45258i	0.306572	+	0.306572i	−0.537007	+	0.843578i	$0.680445\pi$
$444$	−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	−0.988065	−	0.154038i	$-0.950772\pi$
$457$	−24.4154	−	24.4154i	−1.14210	−	1.14210i	−0.154038	−	0.988065i	$-0.549228\pi$
$458$	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	0.259794	−	0.965664i	$-0.416345\pi$
$463$	26.3687	−	26.3687i	1.22546	−	1.22546i	0.965664	−	0.259794i	$-0.0836548\pi$
$464$	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	$-0.674168\pi$
$467$	7.21204	−	7.21204i	0.333733	−	0.333733i	0.854002	+	0.520269i	$0.174168\pi$
$468$	−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	$-0.601382\pi$
$479$	−13.7070			−0.626289			−0.313144	+	0.949706i	$0.601382\pi$
$480$	−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	0.238627	−	0.971111i	$-0.423303\pi$
$487$	−16.1645	−	16.1645i	−0.732484	−	0.732484i	−0.971111	+	0.238627i	$0.923303\pi$
$488$	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	$0.180012\pi$
$491$			23.7476i			1.07172i	−0.844308	+	0.535858i	$0.819988\pi$
$492$	−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	$0.0230711\pi$
$499$			3.23532i			0.144833i	−0.997374	+	0.0724165i	$0.976929\pi$
$500$	−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	$-0.276409\pi$
$503$	−2.62851	−	2.62851i	−0.117199	−	0.117199i	−0.763274	+	0.646075i	$0.776409\pi$
$504$		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	$-0.599113\pi$
$509$	−13.8238			−0.612728			−0.306364	+	0.951914i	$0.599113\pi$
$510$	−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	$-0.653105\pi$
$523$	9.69371	−	9.69371i	0.423876	−	0.423876i	0.886536	+	0.462660i	$0.153105\pi$
$524$	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	0.144370	−	0.989524i	$-0.453885\pi$
$547$	−19.7665	−	19.7665i	−0.845154	−	0.845154i	−0.989524	+	0.144370i	$0.953885\pi$
$548$	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	−0.391638	+	0.920119i	$0.628092\pi$
$557$	−30.9586	+	30.9586i	−1.31176	+	1.31176i	−0.920119	+	0.391638i	$0.871908\pi$
$558$	−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	$-0.174897\pi$
$563$	7.84399	+	7.84399i	0.330585	+	0.330585i	−0.522224	+	0.852808i	$0.674897\pi$
$564$	−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	$-0.352841\pi$
$577$	−10.7854	−	10.7854i	−0.449001	−	0.449001i	−0.895022	+	0.446021i	$0.852841\pi$
$578$	−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	$-0.801714\pi$
$587$	−5.54217	+	5.54217i	−0.228750	+	0.228750i	0.583421	+	0.812170i	$0.301714\pi$
$588$		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	$-0.193007\pi$
$593$	6.13323	+	6.13323i	0.251861	+	0.251861i	−0.569872	+	0.821733i	$0.693007\pi$
$594$	−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	$-0.178455\pi$
$601$	41.5249			1.69384			0.846919	+	0.531722i	$0.178455\pi$
$602$		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	$-0.350423\pi$
$607$	−10.8110	−	10.8110i	−0.438805	−	0.438805i	−0.891610	+	0.452805i	$0.850423\pi$
$608$	−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	−0.112863	−	0.993611i	$-0.536002\pi$
$613$	21.8063	−	21.8063i	0.880747	−	0.880747i	0.993611	+	0.112863i	$0.0360022\pi$
$614$	−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	−0.921110	−	0.389302i	$-0.872716\pi$
$617$	−13.2098	+	13.2098i	−0.531808	+	0.531808i	0.389302	+	0.921110i	$0.372716\pi$
$618$	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	$-0.684626\pi$
$641$		−	42.3545i		−	1.67290i	0.548042	−	0.836451i	$-0.315374\pi$
$642$	0.238694	−	1.14180i	0.00942049	−	0.0450631i
$643$	11.2098	−	11.2098i	0.442072	−	0.442072i	−0.450636	−	0.892708i	$-0.648803\pi$
$643$	11.2098	−	11.2098i	0.442072	−	0.442072i	0.892708	+	0.450636i	$0.148803\pi$
$644$		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	$-0.904761\pi$
$647$	−16.8086	+	16.8086i	−0.660814	+	0.660814i	0.294758	+	0.955572i	$0.404761\pi$
$648$	−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	0.941118	−	0.338078i	$-0.109777\pi$
$653$	15.4100	+	15.4100i	0.603041	+	0.603041i	−0.338078	+	0.941118i	$0.609777\pi$
$654$	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	$-0.154333\pi$
$661$	45.4934			1.76949			0.884744	+	0.466076i	$0.154333\pi$
$662$	−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	−0.277636	+	0.960686i	$0.589551\pi$
$673$	−32.1249	+	32.1249i	−1.23832	+	1.23832i	−0.960686	+	0.277636i	$0.910449\pi$
$674$	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	0.172049	−	0.985088i	$-0.444961\pi$
$677$	30.1078	−	30.1078i	1.15714	−	1.15714i	0.985088	−	0.172049i	$-0.0550388\pi$
$678$	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	0.737940	−	0.674866i	$-0.235798\pi$
$683$	1.64841	+	1.64841i	0.0630747	+	0.0630747i	−0.674866	+	0.737940i	$0.735798\pi$
$684$	−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	$-0.601977\pi$
$691$	−16.5565			−0.629838			−0.314919	+	0.949119i	$0.601977\pi$
$692$	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	$-0.832493\pi$
$701$		−	26.5973i		−	1.00457i	0.864703	−	0.502284i	$-0.167507\pi$
$702$	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	$0.0966194\pi$
$709$			15.9176i			0.597798i	−0.954285	+	0.298899i	$0.903381\pi$
$710$	−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	$-0.369464\pi$
$719$	21.3813			0.797388			0.398694	+	0.917084i	$0.369464\pi$
$720$	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	$-0.187506\pi$
$727$	7.43836	+	7.43836i	0.275873	+	0.275873i	−0.555586	+	0.831459i	$0.687506\pi$
$728$		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	$-0.514421\pi$
$733$	25.8200	−	25.8200i	0.953683	−	0.953683i	0.998974	+	0.0452905i	$0.0144214\pi$
$734$	−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	$0.249290\pi$
$739$			38.3589i			1.41105i	−0.708683	+	0.705527i	$0.750710\pi$
$740$	−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	0.990076	+	0.140534i	$0.0448819\pi$
$743$	30.8182	+	30.8182i	1.13061	+	1.13061i	0.140534	+	0.990076i	$0.455118\pi$
$744$	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	0.721472	−	0.692444i	$-0.243466\pi$
$757$	0.798673	+	0.798673i	0.0290283	+	0.0290283i	−0.692444	+	0.721472i	$0.743466\pi$
$758$	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	$-0.121289\pi$
$773$	15.4692	+	15.4692i	0.556390	+	0.556390i	−0.371888	+	0.928278i	$0.621289\pi$
$774$	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	$-0.248289\pi$
$787$	0.213202	+	0.213202i	0.00759982	+	0.00759982i	−0.703297	+	0.710896i	$0.748289\pi$
$788$	−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	$-0.682098\pi$
$797$	8.45240	−	8.45240i	0.299399	−	0.299399i	0.840779	+	0.541379i	$0.182098\pi$
$798$		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	$-0.364320\pi$
$811$	23.5491			0.826921			0.413461	+	0.910522i	$0.364320\pi$
$812$		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	$-0.746287\pi$
$821$		−	40.9914i		−	1.43061i	0.698812	−	0.715306i	$-0.253713\pi$
$822$	−0.965130	+	4.61672i	−0.0336628	+	0.161027i
$823$	−18.2198	+	18.2198i	−0.635104	+	0.635104i	−0.949344	−	0.314240i	$-0.898250\pi$
$823$	−18.2198	+	18.2198i	−0.635104	+	0.635104i	0.314240	+	0.949344i	$0.398250\pi$
$824$	−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	−0.960091	−	0.279687i	$-0.909769\pi$
$827$	−19.5668	+	19.5668i	−0.680404	+	0.680404i	0.279687	+	0.960091i	$0.409769\pi$
$828$	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	$-0.839807\pi$
$839$	−50.7484			−1.75203			−0.876014	+	0.482286i	$0.839807\pi$
$840$		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	$-0.900807\pi$
$853$	−18.8448	+	18.8448i	−0.645233	+	0.645233i	0.306604	+	0.951837i	$0.400807\pi$
$854$		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	$-0.681819\pi$
$857$	8.80014	−	8.80014i	0.300607	−	0.300607i	0.841251	+	0.540644i	$0.181819\pi$
$858$	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	−0.973732	−	0.227695i	$-0.926881\pi$
$863$	−35.2942	−	35.2942i	−1.20143	−	1.20143i	−0.227695	−	0.973732i	$-0.573119\pi$
$864$	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	−0.996551	−	0.0829852i	$-0.973555\pi$
$877$	−31.9696	−	31.9696i	−1.07954	−	1.07954i	−0.0829852	−	0.996551i	$-0.526445\pi$
$878$	−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	−0.905463	−	0.424424i	$-0.860476\pi$
$883$	−14.2942	+	14.2942i	−0.481039	+	0.481039i	0.424424	+	0.905463i	$0.360476\pi$
$884$	−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	$-0.976597\pi$
$887$	−27.5143	+	27.5143i	−0.923840	+	0.923840i	0.0734580	+	0.997298i	$0.476597\pi$
$888$	−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	0.734831	−	0.678250i	$-0.237261\pi$
$907$	1.70404	+	1.70404i	0.0565816	+	0.0565816i	−0.678250	+	0.734831i	$0.737261\pi$
$908$	−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	$-0.896043\pi$
$911$		−	19.3662i		−	0.641631i	0.947142	−	0.320815i	$-0.103957\pi$
$912$	−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	$-0.809665\pi$
$919$		−	34.1319i		−	1.12591i	0.826489	−	0.562953i	$-0.190335\pi$
$920$	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	$-0.395116\pi$
$929$	19.7246			0.647144			0.323572	+	0.946204i	$0.395116\pi$
$930$	−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	$-0.380895\pi$
$937$	−17.3041	−	17.3041i	−0.565300	−	0.565300i	−0.930808	+	0.365508i	$0.880895\pi$
$938$		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	−0.513448	−	0.858121i	$-0.671632\pi$
$947$	10.6067	−	10.6067i	0.344673	−	0.344673i	0.858121	+	0.513448i	$0.171632\pi$
$948$	−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	0.264193	−	0.964470i	$-0.414895\pi$
$953$	−21.6181	−	21.6181i	−0.700277	−	0.700277i	−0.964470	+	0.264193i	$0.914895\pi$
$954$	−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	0.917774	−	0.397102i	$-0.129984\pi$
$967$	16.1911	+	16.1911i	0.520672	+	0.520672i	−0.397102	+	0.917774i	$0.629984\pi$
$968$	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	−0.855289	−	0.518151i	$-0.826621\pi$
$977$	−10.5379	+	10.5379i	−0.337139	+	0.337139i	0.518151	+	0.855289i	$0.326621\pi$
$978$	−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	$-0.189951\pi$
$983$	8.31506	+	8.31506i	0.265209	+	0.265209i	−0.561957	+	0.827166i	$0.689951\pi$
$984$	−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	$-0.321546\pi$
$997$	−9.95260	−	9.95260i	−0.315202	−	0.315202i	−0.846921	+	0.531719i	$0.821546\pi$
$998$	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.g.197.7		24
3.2	odd	2	inner	735.2.j.g.197.6		24
5.3	odd	4	inner	735.2.j.g.638.6		24
7.2	even	3		105.2.x.a.32.6	yes	48
7.3	odd	6		735.2.y.i.422.7		48
7.4	even	3		105.2.x.a.2.7	yes	48
7.5	odd	6		735.2.y.i.557.6		48
7.6	odd	2		735.2.j.e.197.7		24
15.8	even	4	inner	735.2.j.g.638.7		24
21.2	odd	6		105.2.x.a.32.7	yes	48
21.5	even	6		735.2.y.i.557.7		48
21.11	odd	6		105.2.x.a.2.6	✓	48
21.17	even	6		735.2.y.i.422.6		48
21.20	even	2		735.2.j.e.197.6		24
35.2	odd	12		525.2.bf.f.368.7		48
35.3	even	12		735.2.y.i.128.7		48
35.4	even	6		525.2.bf.f.107.6		48
35.9	even	6		525.2.bf.f.32.7		48
35.13	even	4		735.2.j.e.638.6		24
35.18	odd	12		105.2.x.a.23.7	yes	48
35.23	odd	12		105.2.x.a.53.6	yes	48
35.32	odd	12		525.2.bf.f.443.6		48
35.33	even	12		735.2.y.i.263.6		48
105.2	even	12		525.2.bf.f.368.6		48
105.23	even	12		105.2.x.a.53.7	yes	48
105.32	even	12		525.2.bf.f.443.7		48
105.38	odd	12		735.2.y.i.128.6		48
105.44	odd	6		525.2.bf.f.32.6		48
105.53	even	12		105.2.x.a.23.6	yes	48
105.68	odd	12		735.2.y.i.263.7		48
105.74	odd	6		525.2.bf.f.107.7		48
105.83	odd	4		735.2.j.e.638.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.x.a.2.6	✓	48	21.11	odd	6
105.2.x.a.2.7	yes	48	7.4	even	3
105.2.x.a.23.6	yes	48	105.53	even	12
105.2.x.a.23.7	yes	48	35.18	odd	12
105.2.x.a.32.6	yes	48	7.2	even	3
105.2.x.a.32.7	yes	48	21.2	odd	6
105.2.x.a.53.6	yes	48	35.23	odd	12
105.2.x.a.53.7	yes	48	105.23	even	12
525.2.bf.f.32.6		48	105.44	odd	6
525.2.bf.f.32.7		48	35.9	even	6
525.2.bf.f.107.6		48	35.4	even	6
525.2.bf.f.107.7		48	105.74	odd	6
525.2.bf.f.368.6		48	105.2	even	12
525.2.bf.f.368.7		48	35.2	odd	12
525.2.bf.f.443.6		48	35.32	odd	12
525.2.bf.f.443.7		48	105.32	even	12
735.2.j.e.197.6		24	21.20	even	2
735.2.j.e.197.7		24	7.6	odd	2
735.2.j.e.638.6		24	35.13	even	4
735.2.j.e.638.7		24	105.83	odd	4
735.2.j.g.197.6		24	3.2	odd	2	inner
735.2.j.g.197.7		24	1.1	even	1	trivial
735.2.j.g.638.6		24	5.3	odd	4	inner
735.2.j.g.638.7		24	15.8	even	4	inner
735.2.y.i.128.6		48	105.38	odd	12
735.2.y.i.128.7		48	35.3	even	12
735.2.y.i.263.6		48	35.33	even	12
735.2.y.i.263.7		48	105.68	odd	12
735.2.y.i.422.6		48	21.17	even	6
735.2.y.i.422.7		48	7.3	odd	6
735.2.y.i.557.6		48	7.5	odd	6
735.2.y.i.557.7		48	21.5	even	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 $\F_{q}$
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

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Representations

Groups

Database

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