LMFDB - Embedded newform 735.2.j.e.638.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("735.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			638.6
Character	$\chi$	$=$	735.638
Dual form			735.2.j.e.197.6

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.218381 - 0.218381i) q^{2} +(-0.354425 + 1.69540i) 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} +(3.22909 + 0.675045i) q^{12} +(2.27077 + 2.27077i) q^{13} +(1.71870 - 3.47074i) q^{15} -3.43682 q^{16} +(3.43677 + 3.43677i) q^{17} +(0.337831 + 0.862724i) 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} +(3.01174 - 4.23432i) q^{27} +4.94251 q^{29} +(-1.13328 + 0.382613i) q^{30} +5.92827 q^{31} +(2.45592 + 2.45592i) q^{32} +(-1.29269 - 0.270237i) 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} +(5.27515 + 4.14401i) q^{45} -2.36283 q^{46} +(3.03177 + 3.03177i) q^{47} +(1.21809 - 5.82678i) 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} +(-2.77522 - 0.580162i) q^{57} +(-1.07935 - 1.07935i) q^{58} -7.69002 q^{59} +(-6.61045 - 3.27347i) 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} +(3.36861 - 1.31910i) q^{72} +(-0.981264 - 0.981264i) q^{73} +1.09216 q^{74} +(-5.66808 + 6.54774i) q^{75} +3.11769 q^{76} +(1.68147 + 0.351513i) 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} +(-1.75175 + 8.37953i) q^{87} +(-0.650150 - 0.650150i) q^{88} +0.907199 q^{89} +(-0.247020 - 2.05696i) q^{90} +(-10.3038 - 10.3038i) q^{92} +(-2.10113 + 10.0508i) 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	0.625670	−	0.780088i	$-0.284826\pi$
$2$	−0.218381	−	0.218381i	−0.154419	−	0.154419i	−0.780088	+	0.625670i	$0.784826\pi$
$3$	−0.354425	+	1.69540i	−0.204628	+	0.978840i
$3$	−0.354425	+	1.69540i	−0.204628	+	0.978840i
$4$		−	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	$0.963330\pi$
$12$	3.22909	+	0.675045i	0.932159	+	0.194869i
$13$	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
$15$	1.71870	−	3.47074i	0.443767	−	0.896142i
$16$	−3.43682			−0.859204
$17$	3.43677	+	3.43677i	0.833539	+	0.833539i	0.987999	−	0.154460i	$-0.0493638\pi$
$17$	3.43677	+	3.43677i	0.833539	+	0.833539i	−0.154460	+	0.987999i	$0.549364\pi$
$18$	0.337831	+	0.862724i	0.0796275	+	0.203346i
$19$			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	$-0.456080\pi$
$23$	5.40988	−	5.40988i	1.12804	−	1.12804i	0.990496	−	0.137542i	$-0.0439201\pi$
$24$	−1.14344	−	1.74787i	−0.233404	−	0.356783i
$25$	4.36998	+	2.42966i	0.873997	+	0.485932i
$26$		−	0.991783i		−	0.194505i
$27$	3.01174	−	4.23432i	0.579610	−	0.814894i
$28$		0			0
$29$	4.94251			0.917801			0.458900	−	0.888488i	$-0.348243\pi$
$29$	4.94251			0.917801			0.458900	+	0.888488i	$0.348243\pi$
$30$	−1.13328	+	0.382613i	−0.206907	+	0.0698552i
$31$	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
$33$	−1.29269	−	0.270237i	−0.225028	−	0.0470423i
$34$		−	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	$0.110573\pi$
$41$			4.35963i			0.680860i	−0.940270	+	0.340430i	$0.889427\pi$
$42$		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
$45$	5.27515	+	4.14401i	0.786373	+	0.617752i
$46$	−2.36283			−0.348380
$47$	3.03177	+	3.03177i	0.442230	+	0.442230i	0.892761	−	0.450531i	$-0.148765\pi$
$47$	3.03177	+	3.03177i	0.442230	+	0.442230i	−0.450531	+	0.892761i	$0.648765\pi$
$48$	1.21809	−	5.82678i	0.175817	−	0.841023i
$49$		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	$-0.591596\pi$
$53$	4.91465	−	4.91465i	0.675080	−	0.675080i	0.958883	+	0.283803i	$0.0915961\pi$
$54$	−1.58240	+	0.266987i	−0.215337	+	0.0363323i
$55$	0.427939	−	1.65035i	0.0577032	−	0.222533i
$56$		0			0
$57$	−2.77522	−	0.580162i	−0.367587	−	0.0768444i
$58$	−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	$0.666879\pi$
$60$	−6.61045	−	3.27347i	−0.853405	−	0.422603i
$61$	−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	$0.263676\pi$
$71$			12.4172i			1.47365i	−0.676082	+	0.736826i	$0.736324\pi$
$72$	3.36861	−	1.31910i	0.396995	−	0.155457i
$73$	−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
$75$	−5.66808	+	6.54774i	−0.654493	+	0.756068i
$76$	3.11769			0.357624
$77$		0			0
$78$	1.68147	+	0.351513i	0.190389	+	0.0398010i
$79$			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	−0.927792	−	0.373097i	$-0.878296\pi$
$83$	−5.05351	+	5.05351i	−0.554695	+	0.554695i	0.373097	+	0.927792i	$0.378296\pi$
$84$		0			0
$85$	−5.50993	−	9.36774i	−0.597635	−	1.01607i
$86$		−	1.17505i		−	0.126709i
$87$	−1.75175	+	8.37953i	−0.187807	+	0.898380i
$88$	−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	$0.484689\pi$
$90$	−0.247020	−	2.05696i	−0.0260382	−	0.216823i
$91$		0			0
$92$	−10.3038	−	10.3038i	−1.07424	−	1.07424i
$93$	−2.10113	+	10.0508i	−0.217877	+	1.04222i
$94$		−	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	$-0.606345\pi$
$101$		−	18.9884i		−	1.88942i	0.327913	−	0.944708i	$-0.393655\pi$
$102$	2.54488	+	0.532010i	0.251981	+	0.0526768i
$103$	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	0.777701	−	0.628634i	$-0.216386\pi$
$107$	1.54196	+	1.54196i	0.149066	+	0.149066i	−0.628634	+	0.777701i	$0.716386\pi$
$108$	−8.06476	−	5.73622i	−0.776032	−	0.551968i
$109$			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	$-0.457920\pi$
$113$	11.9386	−	11.9386i	1.12309	−	1.12309i	0.991274	−	0.131814i	$-0.0420801\pi$
$114$	0.479358	+	0.732751i	0.0448960	+	0.0686284i
$115$	−14.7459	+	8.67327i	−1.37506	+	0.808787i
$116$		−	9.41360i		−	0.874031i
$117$	−3.51283	−	8.97077i	−0.324761	−	0.829348i
$118$	1.67935	+	1.67935i	0.154597	+	0.154597i
$119$		0			0
$120$	1.49396	+	4.42501i	0.136379	+	0.403946i
$121$	10.4186			0.947150
$122$	0.959560	+	0.959560i	0.0868744	+	0.0868744i
$123$	−7.39132	−	1.54516i	−0.666453	−	0.139323i
$124$		−	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	$0.0299334\pi$
$131$			2.14947i			0.187800i	−0.995582	+	0.0938999i	$0.970067\pi$
$132$	−0.514699	+	2.46207i	−0.0447988	+	0.214296i
$133$		0			0
$134$	−0.0150704			−0.00130188
$135$	−8.89540	+	7.47475i	−0.765594	+	0.643324i
$136$	−5.86102			−0.502579
$137$	−6.23472	−	6.23472i	−0.532668	−	0.532668i	0.388698	−	0.921365i	$-0.372925\pi$
$137$	−6.23472	−	6.23472i	−0.532668	−	0.532668i	−0.921365	+	0.388698i	$0.872925\pi$
$138$	0.837446	−	4.00594i	0.0712881	−	0.341008i
$139$		−	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	$-0.246446\pi$
$149$	17.4543			1.42991			0.714957	+	0.699169i	$0.246446\pi$
$150$	2.66770	−	0.192101i	0.217817	−	0.0156850i
$151$	−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
$153$	−5.31661	−	13.5771i	−0.429823	−	1.09765i
$154$		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
$162$	0.108192	−	2.77743i	0.00850040	−	0.218215i
$163$	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
$165$	2.64632	+	1.31045i	0.206016	+	0.102018i
$166$	2.20718			0.171310
$167$	3.85551	+	3.85551i	0.298348	+	0.298348i	0.840367	−	0.542018i	$-0.182340\pi$
$167$	3.85551	+	3.85551i	0.298348	+	0.298348i	−0.542018	+	0.840367i	$0.682340\pi$
$168$		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	−0.741781	−	0.670643i	$-0.766018\pi$
$173$	−0.935674	+	0.935674i	−0.0711380	+	0.0711380i	0.670643	+	0.741781i	$0.266018\pi$
$174$	2.21248	−	1.44738i	0.167727	−	0.109726i
$175$		0			0
$176$		−	2.62045i		−	0.197524i
$177$	2.72554	−	13.0377i	0.204864	−	0.979970i
$178$	−0.198115	−	0.198115i	−0.0148493	−	0.0148493i
$179$	0.241671			0.0180634			0.00903168	−	0.999959i	$-0.497125\pi$
$179$	0.241671			0.0180634			0.00903168	+	0.999959i	$0.497125\pi$
$180$	7.89276	−	10.0472i	0.588291	−	0.748871i
$181$	−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
$183$	1.55734	−	7.44955i	0.115122	−	0.550686i
$184$			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	$0.827710\pi$
$192$	−9.83498	−	2.05601i	−0.709779	−	0.148380i
$193$	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
$195$	11.7840	−	3.97848i	0.843871	−	0.284905i
$196$		0			0
$197$	7.65626	+	7.65626i	0.545486	+	0.545486i	0.925132	−	0.379646i	$-0.123954\pi$
$197$	7.65626	+	7.65626i	0.545486	+	0.545486i	−0.379646	+	0.925132i	$0.623954\pi$
$198$	−0.657798	+	0.257584i	−0.0467477	+	0.0183057i
$199$		−	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
$207$	−21.3720	+	8.36897i	−1.48546	+	0.581684i
$208$	−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
$213$	−21.0522	−	4.40097i	−1.44247	−	0.301550i
$214$		−	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
$222$	−0.387090	+	1.85165i	−0.0259798	+	0.124275i
$223$	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
$225$	−9.09213	−	11.9303i	−0.606142	−	0.795356i
$226$	−5.21432			−0.346851
$227$	−9.08481	−	9.08481i	−0.602980	−	0.602980i	0.338122	−	0.941102i	$-0.390208\pi$
$227$	−9.08481	−	9.08481i	−0.602980	−	0.602980i	−0.941102	+	0.338122i	$0.890208\pi$
$228$	−1.10499	+	5.28574i	−0.0731797	+	0.350056i
$229$			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	$-0.822157\pi$
$233$	−4.85174	+	4.85174i	−0.317848	+	0.317848i	0.530092	+	0.847940i	$0.322157\pi$
$234$	−1.19191	+	2.72618i	−0.0779176	+	0.178216i
$235$	−4.86062	−	8.26382i	−0.317072	−	0.539072i
$236$			14.6466i			0.953410i
$237$	−7.18093	−	1.50118i	−0.466452	−	0.0975122i
$238$		0			0
$239$	18.7082			1.21013			0.605067	−	0.796174i	$-0.293146\pi$
$239$	18.7082			1.21013			0.605067	+	0.796174i	$0.293146\pi$
$240$	−5.90686	+	11.9283i	−0.381286	+	0.769969i
$241$	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
$243$	−13.3673	+	8.01967i	−0.857513	+	0.514462i
$244$			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	$0.191112\pi$
$251$			17.9016i			1.12994i	−0.825112	+	0.564970i	$0.808888\pi$
$252$		0			0
$253$	4.12485	+	4.12485i	0.259327	+	0.259327i
$254$	−1.94851			−0.122260
$255$	17.8349	−	6.02137i	1.11687	−	0.377073i
$256$	8.90335			0.556460
$257$	−13.9432	−	13.9432i	−0.869756	−	0.869756i	0.122689	−	0.992445i	$-0.460848\pi$
$257$	−13.9432	−	13.9432i	−0.869756	−	0.869756i	−0.992445	+	0.122689i	$0.960848\pi$
$258$	1.99218	+	0.416467i	0.124028	+	0.0259281i
$259$		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	$-0.695278\pi$
$263$	3.92341	−	3.92341i	0.241928	−	0.241928i	0.817647	+	0.575719i	$0.195278\pi$
$264$	1.33269	−	0.871835i	0.0820217	−	0.0536577i
$265$	−13.3961	+	7.87931i	−0.822914	+	0.484022i
$266$		0			0
$267$	−0.321534	+	1.53807i	−0.0196776	+	0.0941281i
$268$	−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	$0.599081\pi$
$270$	3.57493	+	0.310242i	0.217563	+	0.0188807i
$271$	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	$0.0183183\pi$
$281$			1.92831i			0.115033i	−0.998345	+	0.0575167i	$0.981682\pi$
$282$	2.24498	+	0.469316i	0.133687	+	0.0279474i
$283$	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
$285$	5.68130	+	2.81336i	0.336531	+	0.166649i
$286$	0.756201			0.0447151
$287$		0			0
$288$	−3.79926	−	9.70225i	−0.223874	−	0.571710i
$289$			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	−0.440249	−	0.897876i	$-0.645110\pi$
$293$	7.83332	−	7.83332i	0.457627	−	0.457627i	0.897876	+	0.440249i	$0.145110\pi$
$294$		0			0
$295$	16.6449	+	4.31607i	0.969105	+	0.251291i
$296$		−	4.26448i		−	0.247868i
$297$	3.22852	+	2.29635i	0.187338	+	0.133248i
$298$	−3.81169	−	3.81169i	−0.220805	−	0.220805i
$299$	24.5691			1.42087
$300$	12.4710	+	10.7955i	0.720011	+	0.623280i
$301$		0			0
$302$	3.32282	+	3.32282i	0.191207	+	0.191207i
$303$	32.1929	+	6.72997i	1.84944	+	0.386627i
$304$		−	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	$0.233910\pi$
$311$			23.6479i			1.34095i	−0.741932	+	0.670475i	$0.766090\pi$
$312$	1.37252	−	6.56550i	0.0777039	−	0.371698i
$313$	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	0.614484	−	0.788929i	$-0.289364\pi$
$317$	−3.10591	−	3.10591i	−0.174445	−	0.174445i	−0.788929	+	0.614484i	$0.789364\pi$
$318$	0.760785	−	3.63923i	0.0426627	−	0.204078i
$319$			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
$327$	−4.00066	−	0.836342i	−0.221237	−	0.0462498i
$328$	−3.71743	−	3.71743i	−0.205261	−	0.205261i
$329$		0			0
$330$	−0.291729	−	0.864084i	−0.0160592	−	0.0475662i
$331$	−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
$333$	9.87871	−	3.86836i	0.541350	−	0.211985i
$334$		−	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
$342$	−1.41220	+	0.552999i	−0.0763632	+	0.0299027i
$343$		0			0
$344$	−4.58812			−0.247375
$345$	−9.47834	−	28.0743i	−0.510297	−	1.51147i
$346$	0.408667			0.0219701
$347$	13.6203	+	13.6203i	0.731178	+	0.731178i	0.970853	−	0.239675i	$-0.0770409\pi$
$347$	13.6203	+	13.6203i	0.731178	+	0.731178i	−0.239675	+	0.970853i	$0.577041\pi$
$348$	15.9598	+	3.33642i	0.855536	+	0.178851i
$349$		−	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	−0.893505	−	0.449053i	$-0.851761\pi$
$353$	−8.35049	+	8.35049i	−0.444452	+	0.444452i	0.449053	+	0.893505i	$0.351761\pi$
$354$	−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	$-0.620114\pi$
$359$	−13.9626			−0.736917			−0.368459	+	0.929644i	$0.620114\pi$
$360$	−8.03166	+	0.964519i	−0.423306	+	0.0508346i
$361$	16.3205			0.858975
$362$	4.08075	+	4.08075i	0.214480	+	0.214480i
$363$	−3.69263	+	17.6638i	−0.193813	+	0.927108i
$364$		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
$372$	19.1429	+	4.00185i	0.992515	+	0.207486i
$373$	−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
$375$	15.9434	−	10.9912i	0.823315	−	0.567585i
$376$	−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	−0.866366	−	0.499410i	$-0.833550\pi$
$383$	−7.18147	+	7.18147i	−0.366956	+	0.366956i	0.499410	+	0.866366i	$0.333550\pi$
$384$	8.28544	+	12.6652i	0.422815	+	0.646318i
$385$		0			0
$386$		−	2.10507i		−	0.107145i
$387$	−4.16194	−	10.6284i	−0.211564	−	0.540274i
$388$	7.10540	+	7.10540i	0.360722	+	0.360722i
$389$	−37.2580			−1.88906			−0.944528	−	0.328431i	$-0.893480\pi$
$389$	−37.2580			−1.88906			−0.944528	+	0.328431i	$0.893480\pi$
$390$	−3.44222	−	1.70458i	−0.174304	−	0.0863147i
$391$	37.1850			1.88053
$392$		0			0
$393$	−3.64421	−	0.761825i	−0.183826	−	0.0384290i
$394$		−	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	$0.0370529\pi$
$401$			4.65150i			0.232285i	−0.993233	+	0.116142i	$0.962947\pi$
$402$	0.00534133	−	0.0255504i	0.000266401	−	0.00127434i
$403$	13.4617	+	13.4617i	0.670575	+	0.670575i
$404$	−36.1657			−1.79931
$405$	−9.51994	−	17.7305i	−0.473050	−	0.881036i
$406$		0			0
$407$	−1.90662	−	1.90662i	−0.0945074	−	0.0945074i
$408$	2.07729	−	9.93678i	0.102841	−	0.491944i
$409$		−	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
$417$	17.5687	+	3.67275i	0.860343	+	0.179856i
$418$	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
$423$	−4.69009	−	11.9772i	−0.228040	−	0.582350i
$424$			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	$0.871488\pi$
$432$	−10.3508	+	14.5526i	−0.498003	+	0.700160i
$433$	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
$435$	8.49470	−	17.1542i	0.407290	−	0.822480i
$436$	4.49436			0.215241
$437$	8.85549	+	8.85549i	0.423615	+	0.423615i
$438$	−0.726612	−	0.151899i	−0.0347189	−	0.00725802i
$439$		−	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	$-0.819555\pi$
$443$	−6.45258	+	6.45258i	−0.306572	+	0.306572i	0.537007	+	0.843578i	$0.319555\pi$
$444$	−9.76265	+	6.38663i	−0.463315	+	0.303096i
$445$	−1.96362	−	0.509171i	−0.0930845	−	0.0241370i
$446$		−	6.74996i		−	0.319620i
$447$	−6.18625	+	29.5921i	−0.292600	+	1.39966i
$448$		0			0
$449$	−9.40891			−0.444034			−0.222017	−	0.975043i	$-0.571264\pi$
$449$	−9.40891			−0.444034			−0.222017	+	0.975043i	$0.571264\pi$
$450$	−0.619811	+	4.59091i	−0.0292182	+	0.216417i
$451$	−3.32407			−0.156524
$452$	−22.7385	−	22.7385i	−1.06953	−	1.06953i
$453$	5.39284	−	25.7967i	0.253378	−	1.21204i
$454$			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	$-0.670426\pi$
$461$		−	36.9326i		−	1.72012i	0.510192	−	0.860061i	$-0.329574\pi$
$462$		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
$465$	10.1889	−	20.5755i	0.472500	−	0.954166i
$466$	2.11906			0.0981633
$467$	7.21204	+	7.21204i	0.333733	+	0.333733i	0.854002	−	0.520269i	$-0.174168\pi$
$467$	7.21204	+	7.21204i	0.333733	+	0.333733i	−0.520269	+	0.854002i	$0.674168\pi$
$468$	−17.0859	+	6.69060i	−0.789797	+	0.309273i
$469$		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
$477$	−19.4156	+	7.60287i	−0.888979	+	0.348112i
$478$	−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	$0.601382\pi$
$480$	12.7449	−	4.30288i	0.581721	−	0.196399i
$481$	−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	$0.180012\pi$
$491$			23.7476i			1.07172i	−0.844308	+	0.535858i	$0.819988\pi$
$492$	−2.94295	+	14.0777i	−0.132678	+	0.634670i
$493$	16.9863	+	16.9863i	0.765023	+	0.765023i
$494$	1.62346			0.0730429
$495$	−3.15966	+	4.02212i	−0.142016	+	0.180781i
$496$	−20.3744			−0.914836
$497$		0			0
$498$	−0.782280	+	3.74205i	−0.0350548	+	0.167685i
$499$		−	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	−0.763274	−	0.646075i	$-0.776409\pi$
$503$	−2.62851	+	2.62851i	−0.117199	+	0.117199i	0.646075	+	0.763274i	$0.276409\pi$
$504$		0			0
$505$	−10.6573	+	41.1001i	−0.474246	+	1.82893i
$506$		−	1.80158i		−	0.0800898i
$507$	4.55597	+	0.952430i	0.202338	+	0.0422989i
$508$	−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	$0.599113\pi$
$510$	−5.20976	−	2.57985i	−0.230692	−	0.114238i
$511$		0			0
$512$	−14.3017	−	14.3017i	−0.632050	−	0.632050i
$513$	6.93120	+	4.92995i	0.306020	+	0.217663i
$514$			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	$-0.922826\pi$
$521$		−	10.9599i		−	0.480162i	0.970753	−	0.240081i	$-0.0771741\pi$
$522$	1.66973	+	4.26402i	0.0730822	+	0.186631i
$523$	−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
$528$	4.44272	+	0.928755i	0.193345	+	0.0404189i
$529$		−	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
$537$	−0.0856544	+	0.409730i	−0.00369626	+	0.0176811i
$538$	2.19394	+	2.19394i	0.0945876	+	0.0945876i
$539$		0			0
$540$	14.2366	+	16.9423i	0.612644	+	0.729083i
$541$	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
$543$	6.62293	−	31.6809i	0.284217	−	1.35956i
$544$			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
$552$	−15.6417	−	3.26991i	−0.665753	−	0.139176i
$553$		0			0
$554$	−3.47282			−0.147546
$555$	4.38114	+	12.9767i	0.185969	+	0.550829i
$556$	−19.7367			−0.837024
$557$	30.9586	+	30.9586i	1.31176	+	1.31176i	0.920119	+	0.391638i	$0.128092\pi$
$557$	30.9586	+	30.9586i	1.31176	+	1.31176i	0.391638	+	0.920119i	$0.371908\pi$
$558$	2.00275	+	5.11446i	0.0847832	+	0.216512i
$559$			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	−0.522224	−	0.852808i	$-0.674897\pi$
$563$	7.84399	−	7.84399i	0.330585	−	0.330585i	0.852808	+	0.522224i	$0.174897\pi$
$564$	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	$-0.593455\pi$
$569$	−13.8064			−0.578793			−0.289396	+	0.957209i	$0.593455\pi$
$570$	−0.626302	−	1.85507i	−0.0262329	−	0.0777003i
$571$	−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
$573$	−24.1442	−	5.04736i	−1.00864	−	0.210857i
$574$		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
$582$	−0.577496	+	2.76247i	−0.0239380	+	0.114508i
$583$	3.74726	+	3.74726i	0.155196	+	0.155196i
$584$	1.67344			0.0692473
$585$	2.56856	+	21.3887i	0.106197	+	0.884314i
$586$	−3.42129			−0.141332
$587$	−5.54217	−	5.54217i	−0.228750	−	0.228750i	0.583421	−	0.812170i	$-0.301714\pi$
$587$	−5.54217	−	5.54217i	−0.228750	−	0.228750i	−0.812170	+	0.583421i	$0.801714\pi$
$588$		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	−0.569872	−	0.821733i	$-0.693007\pi$
$593$	6.13323	−	6.13323i	0.251861	−	0.251861i	0.821733	+	0.569872i	$0.193007\pi$
$594$	−0.203568	−	1.20653i	−0.00835252	−	0.0495043i
$595$		0			0
$596$		−	33.2438i		−	1.36172i
$597$	27.7706	+	5.80548i	1.13658	+	0.237603i
$598$	−5.36543	−	5.36543i	−0.219409	−	0.219409i
$599$	−15.8774			−0.648732			−0.324366	−	0.945932i	$-0.605151\pi$
$599$	−15.8774			−0.648732			−0.324366	+	0.945932i	$0.605151\pi$
$600$	−0.750083	−	10.4164i	−0.0306220	−	0.425246i
$601$	−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
$603$	−0.136313	+	0.0533783i	−0.00555110	+	0.00217373i
$604$			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
$612$	−25.8593	+	10.1261i	−1.04530	+	0.409324i
$613$	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
$615$	15.1312	+	7.49291i	0.610148	+	0.302143i
$616$		0			0
$617$	13.2098	+	13.2098i	0.531808	+	0.531808i	0.921110	−	0.389302i	$-0.127284\pi$
$617$	13.2098	+	13.2098i	0.531808	+	0.531808i	−0.389302	+	0.921110i	$0.627284\pi$
$618$	6.61376	+	1.38261i	0.266044	+	0.0556168i
$619$		−	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
$627$	0.442354	−	2.11601i	0.0176659	−	0.0845053i
$628$	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
$633$	9.03883	−	43.2374i	0.359261	−	1.71853i
$634$			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	$-0.315374\pi$
$642$	1.14180	+	0.238694i	0.0450631	+	0.00942049i
$643$	−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
$645$	13.9615	−	4.71364i	0.549734	−	0.185599i
$646$	2.45708			0.0966726
$647$	−16.8086	−	16.8086i	−0.660814	−	0.660814i	0.294758	−	0.955572i	$-0.404761\pi$
$647$	−16.8086	−	16.8086i	−0.660814	−	0.660814i	−0.955572	+	0.294758i	$0.904761\pi$
$648$	−10.8448	−	0.422450i	−0.426024	−	0.0165954i
$649$		−	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	$-0.890223\pi$
$653$	−15.4100	+	15.4100i	−0.603041	+	0.603041i	0.338078	+	0.941118i	$0.390223\pi$
$654$	0.691026	+	1.05631i	0.0270213	+	0.0413049i
$655$	1.20640	−	4.65249i	0.0471380	−	0.181788i
$656$		−	14.9833i		−	0.584998i
$657$	1.51800	+	3.87653i	0.0592227	+	0.151238i
$658$		0			0
$659$	−42.6184			−1.66018			−0.830088	−	0.557632i	$-0.811710\pi$
$659$	−42.6184			−1.66018			−0.830088	+	0.557632i	$0.811710\pi$
$660$	2.49591	−	5.04024i	0.0971532	−	0.196191i
$661$	−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
$663$	−26.4621	−	5.53194i	−1.02770	−	0.214843i
$664$		−	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
$675$	23.4492	−	11.1864i	0.902560	−	0.430564i
$676$	−5.11819			−0.196854
$677$	30.1078	+	30.1078i	1.15714	+	1.15714i	0.985088	+	0.172049i	$0.0550388\pi$
$677$	30.1078	+	30.1078i	1.15714	+	1.15714i	0.172049	+	0.985088i	$0.444961\pi$
$678$	1.84809	−	8.84036i	0.0709753	−	0.339512i
$679$		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	$-0.764202\pi$
$683$	−1.64841	+	1.64841i	−0.0630747	+	0.0630747i	0.674866	+	0.737940i	$0.264202\pi$
$684$	−8.56980	−	3.74680i	−0.327675	−	0.143262i
$685$	9.99568	+	16.9942i	0.381915	+	0.649316i
$686$		0			0
$687$	−25.9409	−	5.42298i	−0.989708	−	0.206899i
$688$	−9.24630	−	9.24630i	−0.352512	−	0.352512i
$689$	22.3201			0.850326
$690$	−4.06099	+	8.20077i	−0.154599	+	0.312198i
$691$	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	$-0.832493\pi$
$701$		−	26.5973i		−	1.00457i	0.864703	−	0.502284i	$-0.167507\pi$
$702$	−4.19952	−	2.98699i	−0.158501	−	0.112737i
$703$	−4.09324	−	4.09324i	−0.154380	−	0.154380i
$704$	−4.42305			−0.166700
$705$	15.7332	−	5.31180i	0.592547	−	0.200054i
$706$	3.64717			0.137263
$707$		0			0
$708$	−24.8318	−	5.19111i	−0.933235	−	0.195094i
$709$		−	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
$717$	−6.63067	+	31.7179i	−0.247627	+	1.18453i
$718$	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	$0.369464\pi$
$720$	−18.1297	−	14.2422i	−0.675655	−	0.530775i
$721$		0			0
$722$	−3.56409	−	3.56409i	−0.132642	−	0.132642i
$723$	−0.698971	+	3.34354i	−0.0259950	+	0.124348i
$724$			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
$732$	−14.1886	−	2.96613i	−0.524424	−	0.109631i
$733$	−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
$738$	−3.76116	+	1.47282i	−0.138450	+	0.0542152i
$739$		−	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	$0.544882\pi$
$743$	−30.8182	+	30.8182i	−1.13061	+	1.13061i	−0.990076	+	0.140534i	$0.955118\pi$
$744$	−6.77863	−	10.3619i	−0.248516	−	0.379884i
$745$	−37.7796	−	9.79634i	−1.38414	−	0.358910i
$746$			10.7588i			0.393908i
$747$	19.9641	−	7.81768i	0.730450	−	0.286034i
$748$	4.99090	+	4.99090i	0.182485	+	0.182485i
$749$		0			0
$750$	−5.88201	−	1.08146i	−0.214781	−	0.0394894i
$751$	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
$753$	−30.3504	−	6.34478i	−1.10603	−	0.231217i
$754$		−	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	$-0.713883\pi$
$761$		−	43.1790i		−	1.56524i	0.622500	−	0.782619i	$-0.286117\pi$
$762$	0.690601	−	3.30350i	0.0250178	−	0.119673i
$763$		0			0
$764$	27.1236			0.981299
$765$	3.88748	+	32.3715i	0.140552	+	1.17039i
$766$	3.13659			0.113330
$767$	−17.4622	−	17.4622i	−0.630524	−	0.630524i
$768$	−3.15557	+	15.0947i	−0.113867	+	0.544685i
$769$		−	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	−0.371888	−	0.928278i	$-0.621289\pi$
$773$	15.4692	−	15.4692i	0.556390	−	0.556390i	0.928278	+	0.371888i	$0.121289\pi$
$774$	−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
$780$	−7.57749	−	22.4441i	−0.271318	−	0.803626i
$781$	−9.46770			−0.338781
$782$	−8.12049	−	8.12049i	−0.290388	−	0.290388i
$783$	14.8856	−	20.9281i	0.531966	−	0.747911i
$784$		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
$792$	1.00577	+	2.56845i	0.0357385	+	0.0912659i
$793$	−9.97768	−	9.97768i	−0.354318	−	0.354318i
$794$	−2.74540			−0.0974306
$795$	−8.61069	−	25.5043i	−0.305390	−	0.904546i
$796$	−31.1977			−1.10577
$797$	8.45240	+	8.45240i	0.299399	+	0.299399i	0.840779	−	0.541379i	$-0.182098\pi$
$797$	8.45240	+	8.45240i	0.299399	+	0.299399i	−0.541379	+	0.840779i	$0.682098\pi$
$798$		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
$807$	3.56070	−	17.0327i	0.125343	−	0.599579i
$808$	16.1913	+	16.1913i	0.569608	+	0.569608i
$809$	37.1351			1.30560			0.652801	−	0.757530i	$-0.273594\pi$
$809$	37.1351			1.30560			0.652801	+	0.757530i	$0.273594\pi$
$810$	−1.79303	+	5.95097i	−0.0630006	+	0.209096i
$811$	−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
$813$	−1.99915	+	9.56300i	−0.0701134	+	0.335389i
$814$			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	$-0.253713\pi$
$822$	−4.61672	−	0.965130i	−0.161027	−	0.0336628i
$823$	−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
$825$	−4.99243	−	4.32172i	−0.173814	−	0.150463i
$826$		0			0
$827$	19.5668	+	19.5668i	0.680404	+	0.680404i	0.960091	−	0.279687i	$-0.0902308\pi$
$827$	19.5668	+	19.5668i	0.680404	+	0.680404i	−0.279687	+	0.960091i	$0.590231\pi$
$828$	15.9397	+	40.7055i	0.553943	+	1.41462i
$829$			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
$837$	17.8544	−	25.1022i	0.617138	−	0.867657i
$838$	−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
$843$	−3.26926	−	0.683443i	−0.112599	−	0.0235390i
$844$			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
$852$	−8.38218	+	40.0963i	−0.287169	+	1.37368i
$853$	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
$855$	−6.78337	+	8.63495i	−0.231986	+	0.295309i
$856$	−2.62963			−0.0898790
$857$	8.80014	+	8.80014i	0.300607	+	0.300607i	0.841251	−	0.540644i	$-0.181819\pi$
$857$	8.80014	+	8.80014i	0.300607	+	0.300607i	−0.540644	+	0.841251i	$0.681819\pi$
$858$	−0.268017	+	1.28206i	−0.00914994	+	0.0437689i
$859$		−	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	$-0.426881\pi$
$863$	35.2942	−	35.2942i	1.20143	−	1.20143i	0.973732	−	0.227695i	$-0.0731190\pi$
$864$	17.7957	−	3.00255i	0.605424	−	0.102149i
$865$	2.55040	−	1.50010i	0.0867164	−	0.0510049i
$866$		−	0.224599i		−	0.00763219i
$867$	−11.2282	−	2.34727i	−0.381331	−	0.0797176i
$868$		0			0
$869$	−3.22945			−0.109552
$870$	−5.60122	+	1.89107i	−0.189899	+	0.0641131i
$871$	0.156705			0.00530974
$872$	−2.01211	−	2.01211i	−0.0681387	−	0.0681387i
$873$	14.7380	−	5.77118i	0.498805	−	0.195325i
$874$		−	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	$0.139584\pi$
$881$			25.2055i			0.849195i	−0.905382	+	0.424597i	$0.860416\pi$
$882$		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
$885$	−13.2168	+	26.6901i	−0.444279	+	0.897177i
$886$	2.81824			0.0946806
$887$	−27.5143	−	27.5143i	−0.923840	−	0.923840i	0.0734580	−	0.997298i	$-0.476597\pi$
$887$	−27.5143	−	27.5143i	−0.923840	−	0.923840i	−0.997298	+	0.0734580i	$0.976597\pi$
$888$	7.23000	+	1.51144i	0.242623	+	0.0507206i
$889$		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
$897$	−8.70792	+	41.6545i	−0.290749	+	1.39080i
$898$	2.05472	+	2.05472i	0.0685670	+	0.0685670i
$899$	29.3005			0.977227
$900$	−22.7228	+	17.3171i	−0.757426	+	0.577235i
$901$	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	$-0.896043\pi$
$911$		−	19.3662i		−	0.641631i	0.947142	−	0.320815i	$-0.103957\pi$
$912$	9.53792	+	1.99391i	0.315832	+	0.0660250i
$913$	−3.85313	−	3.85313i	−0.127520	−	0.127520i
$914$	10.6637			0.352724
$915$	−7.55193	+	15.2504i	−0.249659	+	0.504161i
$916$	29.1421			0.962883
$917$		0			0
$918$	−6.35591	−	4.52077i	−0.209776	−	0.149208i
$919$			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
$927$	−13.8171	−	35.2849i	−0.453812	−	1.15891i
$928$	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	$0.395116\pi$
$930$	−6.71836	+	2.26823i	−0.220304	+	0.0743782i
$931$		0			0
$932$	9.24073	+	9.24073i	0.302690	+	0.302690i
$933$	−40.0927	−	8.38142i	−1.31258	−	0.274395i
$934$		−	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	$0.0233418\pi$
$941$			4.49489i			0.146529i	−0.997313	+	0.0732646i	$0.976658\pi$
$942$	−1.00008	+	4.78388i	−0.0325842	+	0.155867i
$943$	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	$-0.328368\pi$
$947$	−10.6067	−	10.6067i	−0.344673	−	0.344673i	−0.858121	+	0.513448i	$0.828368\pi$
$948$	−2.85918	+	13.6769i	−0.0928619	+	0.444207i
$949$		−	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	$-0.585105\pi$
$953$	21.6181	−	21.6181i	0.700277	−	0.700277i	0.964470	+	0.264193i	$0.0851054\pi$
$954$	5.90031	+	2.57967i	0.191030	+	0.0835199i
$955$	7.99283	−	30.8244i	0.258642	−	0.997453i
$956$		−	35.6321i		−	1.15242i
$957$	−6.38911	−	1.33565i	−0.206531	−	0.0431754i
$958$	2.99334	+	2.99334i	0.0967106	+	0.0967106i
$959$		0			0
$960$	20.1337	+	9.97015i	0.649813	+	0.321785i
$961$	4.14435			0.133689
$962$	2.48004	+	2.48004i	0.0799598	+	0.0799598i
$963$	−2.38537	−	6.09157i	−0.0768676	−	0.196298i
$964$		−	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	$-0.905162\pi$
$971$		−	18.2948i		−	0.587107i	0.955943	−	0.293553i	$-0.0948379\pi$
$972$	15.2744	+	25.4596i	0.489928	+	0.816618i
$973$		0			0
$974$	7.06004			0.226218
$975$	−27.7393	+	1.99751i	−0.888367	+	0.0639714i
$976$	15.1013			0.483380
$977$	10.5379	+	10.5379i	0.337139	+	0.337139i	0.855289	−	0.518151i	$-0.173379\pi$
$977$	10.5379	+	10.5379i	0.337139	+	0.337139i	−0.518151	+	0.855289i	$0.673379\pi$
$978$	1.41757	+	0.296344i	0.0453288	+	0.00947603i
$979$			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	−0.561957	−	0.827166i	$-0.689951\pi$
$983$	8.31506	−	8.31506i	0.265209	−	0.265209i	0.827166	+	0.561957i	$0.189951\pi$
$984$	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
$990$	1.56836	−	0.188344i	0.0498459	−	0.00598598i
$991$	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
$993$	2.20405	−	10.5431i	0.0699434	−	0.334576i
$994$		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

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

)

Twists

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

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

Overview	Random
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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	735.2.j.e.638.6

Level	$735$
Weight	$2$
Character	735.638
Analytic conductor	$5.869$
Analytic rank	$0$
Dimension	$24$
Inner twists	$4$