LMFDB - Embedded newform 507.2.f.g.239.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(239,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("507.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.f (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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.16
Character	$\chi$	$=$	507.239
Dual form			507.2.f.g.437.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.540287 + 0.540287i) q^{2} +(0.0858391 + 1.72992i) q^{3} -1.41618i q^{4} +(-0.996141 - 0.996141i) q^{5} +(-0.888277 + 0.981032i) q^{6} +(-1.80254 - 1.80254i) q^{7} +(1.84572 - 1.84572i) q^{8} +(-2.98526 + 0.296990i) q^{9} +O(q^{10})$	\(q+(0.540287 + 0.540287i) q^{2} +(0.0858391 + 1.72992i) q^{3} -1.41618i q^{4} +(-0.996141 - 0.996141i) q^{5} +(-0.888277 + 0.981032i) q^{6} +(-1.80254 - 1.80254i) q^{7} +(1.84572 - 1.84572i) q^{8} +(-2.98526 + 0.296990i) q^{9} -1.07640i q^{10} +(3.35957 - 3.35957i) q^{11} +(2.44988 - 0.121564i) q^{12} -1.94778i q^{14} +(1.63774 - 1.80876i) q^{15} -0.837927 q^{16} +5.80420 q^{17} +(-1.77336 - 1.45244i) q^{18} +(2.39843 - 2.39843i) q^{19} +(-1.41072 + 1.41072i) q^{20} +(2.96353 - 3.27298i) q^{21} +3.63026 q^{22} -3.39759 q^{23} +(3.35138 + 3.03451i) q^{24} -3.01541i q^{25} +(-0.770022 - 5.13878i) q^{27} +(-2.55272 + 2.55272i) q^{28} +6.57944i q^{29} +(1.86210 - 0.0923975i) q^{30} +(0.386730 - 0.386730i) q^{31} +(-4.14416 - 4.14416i) q^{32} +(6.10017 + 5.52341i) q^{33} +(3.13593 + 3.13593i) q^{34} +3.59117i q^{35} +(0.420591 + 4.22767i) q^{36} +(-5.93729 - 5.93729i) q^{37} +2.59169 q^{38} -3.67719 q^{40} +(0.734507 + 0.734507i) q^{41} +(3.36950 - 0.167195i) q^{42} +7.56816i q^{43} +(-4.75775 - 4.75775i) q^{44} +(3.26959 + 2.67790i) q^{45} +(-1.83567 - 1.83567i) q^{46} +(-0.243559 + 0.243559i) q^{47} +(-0.0719269 - 1.44955i) q^{48} -0.501699i q^{49} +(1.62918 - 1.62918i) q^{50} +(0.498228 + 10.0408i) q^{51} +2.07223i q^{53} +(2.36038 - 3.19245i) q^{54} -6.69321 q^{55} -6.65396 q^{56} +(4.35499 + 3.94323i) q^{57} +(-3.55478 + 3.55478i) q^{58} +(3.56074 - 3.56074i) q^{59} +(-2.56152 - 2.31933i) q^{60} +7.04831 q^{61} +0.417890 q^{62} +(5.91639 + 4.84572i) q^{63} -2.80221i q^{64} +(0.311618 + 6.28007i) q^{66} +(-4.54045 + 4.54045i) q^{67} -8.21980i q^{68} +(-0.291646 - 5.87756i) q^{69} +(-1.94026 + 1.94026i) q^{70} +(6.79242 + 6.79242i) q^{71} +(-4.96179 + 6.05811i) q^{72} +(-6.04700 - 6.04700i) q^{73} -6.41568i q^{74} +(5.21642 - 0.258840i) q^{75} +(-3.39662 - 3.39662i) q^{76} -12.1115 q^{77} +8.77426 q^{79} +(0.834694 + 0.834694i) q^{80} +(8.82359 - 1.77319i) q^{81} +0.793689i q^{82} +(8.31849 + 8.31849i) q^{83} +(-4.63513 - 4.19689i) q^{84} +(-5.78181 - 5.78181i) q^{85} +(-4.08898 + 4.08898i) q^{86} +(-11.3819 + 0.564773i) q^{87} -12.4016i q^{88} +(-9.62559 + 9.62559i) q^{89} +(0.319681 + 3.21335i) q^{90} +4.81159i q^{92} +(0.702209 + 0.635816i) q^{93} -0.263183 q^{94} -4.77836 q^{95} +(6.81334 - 7.52480i) q^{96} +(-1.34200 + 1.34200i) q^{97} +(0.271062 - 0.271062i) q^{98} +(-9.03143 + 11.0270i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{9}+O(q^{10}) $ 48 * q - 24 * q^9	$ 48 q - 24 q^{9} - 8 q^{16} + 112 q^{22} - 84 q^{27} + 128 q^{40} - 56 q^{42} - 188 q^{48} + 8 q^{55} + 56 q^{61} - 92 q^{66} - 72 q^{81} - 112 q^{87} + 296 q^{94}+O(q^{100}) $ 48 * q - 24 * q^9 - 8 * q^16 + 112 * q^22 - 84 * q^27 + 128 * q^40 - 56 * q^42 - 188 * q^48 + 8 * q^55 + 56 * q^61 - 92 * q^66 - 72 * q^81 - 112 * q^87 + 296 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.540287	+	0.540287i	0.382040	+	0.382040i	0.871837	−	0.489796i	$-0.162929\pi$
$2$	0.540287	+	0.540287i	0.382040	+	0.382040i	−0.489796	+	0.871837i	$0.662929\pi$
$3$	0.0858391	+	1.72992i	0.0495592	+	0.998771i
$3$	0.0858391	+	1.72992i	0.0495592	+	0.998771i
$4$		−	1.41618i		−	0.708090i
$5$	−0.996141	−	0.996141i	−0.445488	−	0.445488i	0.448363	−	0.893851i	$-0.352007\pi$
$5$	−0.996141	−	0.996141i	−0.445488	−	0.445488i	−0.893851	+	0.448363i	$0.852007\pi$
$6$	−0.888277	+	0.981032i	−0.362637	+	0.400505i
$7$	−1.80254	−	1.80254i	−0.681296	−	0.681296i	0.278996	−	0.960292i	$-0.409998\pi$
$7$	−1.80254	−	1.80254i	−0.681296	−	0.681296i	−0.960292	+	0.278996i	$0.909998\pi$
$8$	1.84572	−	1.84572i	0.652560	−	0.652560i
$9$	−2.98526	+	0.296990i	−0.995088	+	0.0989967i
$10$		−	1.07640i		−	0.340389i
$11$	3.35957	−	3.35957i	1.01295	−	1.01295i	0.0130325	−	0.999915i	$-0.495852\pi$
$11$	3.35957	−	3.35957i	1.01295	−	1.01295i	0.999915	−	0.0130325i	$-0.00414850\pi$
$12$	2.44988	−	0.121564i	0.707220	−	0.0350924i
$13$		0			0
$13$		0			0
$14$		−	1.94778i		−	0.520565i
$15$	1.63774	−	1.80876i	0.422862	−	0.467019i
$16$	−0.837927			−0.209482
$17$	5.80420			1.40773			0.703863	−	0.710336i	$-0.251457\pi$
$17$	5.80420			1.40773			0.703863	+	0.710336i	$0.251457\pi$
$18$	−1.77336	−	1.45244i	−0.417985	−	0.342343i
$19$	2.39843	−	2.39843i	0.550239	−	0.550239i	−0.376271	−	0.926510i	$-0.622794\pi$
$19$	2.39843	−	2.39843i	0.550239	−	0.550239i	0.926510	+	0.376271i	$0.122794\pi$
$20$	−1.41072	+	1.41072i	−0.315446	+	0.315446i
$21$	2.96353	−	3.27298i	0.646694	−	0.714223i
$22$	3.63026			0.773974
$23$	−3.39759			−0.708446			−0.354223	−	0.935161i	$-0.615255\pi$
$23$	−3.39759			−0.708446			−0.354223	+	0.935161i	$0.615255\pi$
$24$	3.35138	+	3.03451i	0.684098	+	0.619417i
$25$		−	3.01541i		−	0.603081i
$26$		0			0
$27$	−0.770022	−	5.13878i	−0.148191	−	0.988959i
$28$	−2.55272	+	2.55272i	−0.482419	+	0.482419i
$29$			6.57944i			1.22177i	0.791719	+	0.610885i	$0.209186\pi$
$29$			6.57944i			1.22177i	−0.791719	+	0.610885i	$0.790814\pi$
$30$	1.86210	−	0.0923975i	0.339971	−	0.0168694i
$31$	0.386730	−	0.386730i	0.0694587	−	0.0694587i	−0.671524	−	0.740983i	$-0.734360\pi$
$31$	0.386730	−	0.386730i	0.0694587	−	0.0694587i	0.740983	+	0.671524i	$0.234360\pi$
$32$	−4.14416	−	4.14416i	−0.732590	−	0.732590i
$33$	6.10017	+	5.52341i	1.06190	+	0.961502i
$34$	3.13593	+	3.13593i	0.537808	+	0.537808i
$35$			3.59117i			0.607018i
$36$	0.420591	+	4.22767i	0.0700986	+	0.704612i
$37$	−5.93729	−	5.93729i	−0.976084	−	0.976084i	0.0236364	−	0.999721i	$-0.492476\pi$
$37$	−5.93729	−	5.93729i	−0.976084	−	0.976084i	−0.999721	+	0.0236364i	$0.992476\pi$
$38$	2.59169			0.420427
$39$		0			0
$40$	−3.67719			−0.581415
$41$	0.734507	+	0.734507i	0.114711	+	0.114711i	0.762132	−	0.647421i	$-0.224153\pi$
$41$	0.734507	+	0.734507i	0.114711	+	0.114711i	−0.647421	+	0.762132i	$0.724153\pi$
$42$	3.36950	−	0.167195i	0.519926	−	0.0257988i
$43$			7.56816i			1.15413i	0.816697	+	0.577067i	$0.195803\pi$
$43$			7.56816i			1.15413i	−0.816697	+	0.577067i	$0.804197\pi$
$44$	−4.75775	−	4.75775i	−0.717258	−	0.717258i
$45$	3.26959	+	2.67790i	0.487401	+	0.399198i
$46$	−1.83567	−	1.83567i	−0.270655	−	0.270655i
$47$	−0.243559	+	0.243559i	−0.0355267	+	0.0355267i	−0.724647	−	0.689120i	$-0.757997\pi$
$47$	−0.243559	+	0.243559i	−0.0355267	+	0.0355267i	0.689120	+	0.724647i	$0.257997\pi$
$48$	−0.0719269	−	1.44955i	−0.0103818	−	0.209224i
$49$		−	0.501699i		−	0.0716713i
$50$	1.62918	−	1.62918i	0.230401	−	0.230401i
$51$	0.498228	+	10.0408i	0.0697658	+	1.40600i
$52$		0			0
$53$			2.07223i			0.284642i	0.989821	+	0.142321i	$0.0454566\pi$
$53$			2.07223i			0.284642i	−0.989821	+	0.142321i	$0.954543\pi$
$54$	2.36038	−	3.19245i	0.321207	−	0.434437i
$55$	−6.69321			−0.902512
$56$	−6.65396			−0.889173
$57$	4.35499	+	3.94323i	0.576832	+	0.522293i
$58$	−3.55478	+	3.55478i	−0.466766	+	0.466766i
$59$	3.56074	−	3.56074i	0.463569	−	0.463569i	−0.436254	−	0.899823i	$-0.643695\pi$
$59$	3.56074	−	3.56074i	0.463569	−	0.463569i	0.899823	+	0.436254i	$0.143695\pi$
$60$	−2.56152	−	2.31933i	−0.330691	−	0.299425i
$61$	7.04831			0.902443			0.451222	−	0.892412i	$-0.350988\pi$
$61$	7.04831			0.902443			0.451222	+	0.892412i	$0.350988\pi$
$62$	0.417890			0.0530721
$63$	5.91639	+	4.84572i	0.745395	+	0.610503i
$64$		−	2.80221i		−	0.350276i
$65$		0			0
$66$	0.311618	+	6.28007i	0.0383575	+	0.773023i
$67$	−4.54045	+	4.54045i	−0.554704	+	0.554704i	−0.927795	−	0.373091i	$-0.878298\pi$
$67$	−4.54045	+	4.54045i	−0.554704	+	0.554704i	0.373091	+	0.927795i	$0.378298\pi$
$68$		−	8.21980i		−	0.996797i
$69$	−0.291646	−	5.87756i	−0.0351100	−	0.707575i
$70$	−1.94026	+	1.94026i	−0.231906	+	0.231906i
$71$	6.79242	+	6.79242i	0.806112	+	0.806112i	0.984043	−	0.177931i	$-0.0569404\pi$
$71$	6.79242	+	6.79242i	0.806112	+	0.806112i	−0.177931	+	0.984043i	$0.556940\pi$
$72$	−4.96179	+	6.05811i	−0.584753	+	0.713955i
$73$	−6.04700	−	6.04700i	−0.707748	−	0.707748i	0.258313	−	0.966061i	$-0.416833\pi$
$73$	−6.04700	−	6.04700i	−0.707748	−	0.707748i	−0.966061	+	0.258313i	$0.916833\pi$
$74$		−	6.41568i		−	0.745807i
$75$	5.21642	−	0.258840i	0.602340	−	0.0298882i
$76$	−3.39662	−	3.39662i	−0.389619	−	0.389619i
$77$	−12.1115			−1.38023
$78$		0			0
$79$	8.77426			0.987182			0.493591	−	0.869694i	$-0.335684\pi$
$79$	8.77426			0.987182			0.493591	+	0.869694i	$0.335684\pi$
$80$	0.834694	+	0.834694i	0.0933216	+	0.0933216i
$81$	8.82359	−	1.77319i	0.980399	−	0.197021i
$82$			0.793689i			0.0876483i
$83$	8.31849	+	8.31849i	0.913073	+	0.913073i	0.996513	−	0.0834395i	$-0.0265905\pi$
$83$	8.31849	+	8.31849i	0.913073	+	0.913073i	−0.0834395	+	0.996513i	$0.526591\pi$
$84$	−4.63513	−	4.19689i	−0.505735	−	0.457918i
$85$	−5.78181	−	5.78181i	−0.627125	−	0.627125i
$86$	−4.08898	+	4.08898i	−0.440926	+	0.440926i
$87$	−11.3819	+	0.564773i	−1.22027	+	0.0605500i
$88$		−	12.4016i		−	1.32202i
$89$	−9.62559	+	9.62559i	−1.02031	+	1.02031i	−0.0205215	+	0.999789i	$0.506533\pi$
$89$	−9.62559	+	9.62559i	−1.02031	+	1.02031i	−0.999789	+	0.0205215i	$0.993467\pi$
$90$	0.319681	+	3.21335i	0.0336974	+	0.338717i
$91$		0			0
$92$			4.81159i			0.501643i
$93$	0.702209	+	0.635816i	0.0728157	+	0.0659311i
$94$	−0.263183			−0.0271453
$95$	−4.77836			−0.490249
$96$	6.81334	−	7.52480i	0.695383	−	0.767996i
$97$	−1.34200	+	1.34200i	−0.136260	+	0.136260i	−0.771947	−	0.635687i	$-0.780717\pi$
$97$	−1.34200	+	1.34200i	−0.136260	+	0.136260i	0.635687	+	0.771947i	$0.280717\pi$
$98$	0.271062	−	0.271062i	0.0273813	−	0.0273813i
$99$	−9.03143	+	11.0270i	−0.907693	+	1.10825i
$100$	−4.27036			−0.427036
$101$	2.06768			0.205742			0.102871	−	0.994695i	$-0.467197\pi$
$101$	2.06768			0.205742			0.102871	+	0.994695i	$0.467197\pi$
$102$	−5.15574	+	5.69411i	−0.510494	+	0.563801i
$103$		−	13.3818i		−	1.31854i	−0.751905	−	0.659272i	$-0.770865\pi$
$103$		−	13.3818i		−	1.31854i	0.751905	−	0.659272i	$-0.229135\pi$
$104$		0			0
$105$	−6.21244	+	0.308263i	−0.606272	+	0.0300834i
$106$	−1.11960	+	1.11960i	−0.108745	+	0.108745i
$107$		−	7.52219i		−	0.727197i	−0.931556	−	0.363599i	$-0.881548\pi$
$107$		−	7.52219i		−	0.727197i	0.931556	−	0.363599i	$-0.118452\pi$
$108$	−7.27744	+	1.09049i	−0.700272	+	0.104932i
$109$	−2.10533	+	2.10533i	−0.201654	+	0.201654i	−0.800709	−	0.599054i	$-0.795543\pi$
$109$	−2.10533	+	2.10533i	−0.201654	+	0.201654i	0.599054	+	0.800709i	$0.295543\pi$
$110$	−3.61625	−	3.61625i	−0.344796	−	0.344796i
$111$	9.76140	−	10.7807i	0.926511	−	1.02326i
$112$	1.51040	+	1.51040i	0.142719	+	0.142719i
$113$			1.89573i			0.178335i	0.996017	+	0.0891677i	$0.0284207\pi$
$113$			1.89573i			0.178335i	−0.996017	+	0.0891677i	$0.971579\pi$
$114$	0.222468	+	4.48341i	0.0208360	+	0.419910i
$115$	3.38448	+	3.38448i	0.315604	+	0.315604i
$116$	9.31767			0.865124
$117$		0			0
$118$	3.84764			0.354204
$119$	−10.4623	−	10.4623i	−0.959078	−	0.959078i
$120$	−0.315647	−	6.36125i	−0.0288145	−	0.580700i
$121$		−	11.5734i		−	1.05213i
$122$	3.80811	+	3.80811i	0.344770	+	0.344770i
$123$	−1.20759	+	1.33369i	−0.108885	+	0.120255i
$124$	−0.547679	−	0.547679i	−0.0491831	−	0.0491831i
$125$	−7.98448	+	7.98448i	−0.714153	+	0.714153i
$126$	0.578470	+	5.81463i	0.0515342	+	0.518008i
$127$			7.11474i			0.631331i	0.948871	+	0.315665i	$0.102228\pi$
$127$			7.11474i			0.631331i	−0.948871	+	0.315665i	$0.897772\pi$
$128$	−6.77431	+	6.77431i	−0.598770	+	0.598770i
$129$	−13.0923	+	0.649644i	−1.15272	+	0.0571980i
$130$		0			0
$131$			5.36072i			0.468368i	0.972192	+	0.234184i	$0.0752419\pi$
$131$			5.36072i			0.468368i	−0.972192	+	0.234184i	$0.924758\pi$
$132$	7.82214	−	8.63894i	0.680830	−	0.751924i
$133$	−8.64655			−0.749751
$134$	−4.90629			−0.423839
$135$	−4.35190	+	5.88600i	−0.374552	+	0.506586i
$136$	10.7129	−	10.7129i	0.918625	−	0.918625i
$137$	−3.42266	+	3.42266i	−0.292417	+	0.292417i	−0.838035	−	0.545617i	$-0.816295\pi$
$137$	−3.42266	+	3.42266i	−0.292417	+	0.292417i	0.545617	+	0.838035i	$0.316295\pi$
$138$	3.01800	−	3.33314i	0.256909	−	0.283736i
$139$	11.7881			0.999851			0.499926	−	0.866068i	$-0.333361\pi$
$139$	11.7881			0.999851			0.499926	+	0.866068i	$0.333361\pi$
$140$	5.08574			0.429824
$141$	−0.442245	−	0.400431i	−0.0372437	−	0.0337224i
$142$			7.33971i			0.615935i
$143$		0			0
$144$	2.50143	−	0.248856i	0.208453	−	0.0207380i
$145$	6.55405	−	6.55405i	0.544284	−	0.544284i
$146$		−	6.53423i		−	0.540777i
$147$	0.867901	−	0.0430654i	0.0715833	−	0.00355198i
$148$	−8.40827	+	8.40827i	−0.691156	+	0.691156i
$149$	4.87047	+	4.87047i	0.399004	+	0.399004i	0.877882	−	0.478877i	$-0.158956\pi$
$149$	4.87047	+	4.87047i	0.399004	+	0.399004i	−0.478877	+	0.877882i	$0.658956\pi$
$150$	2.95821	+	2.67851i	0.241537	+	0.218700i
$151$	12.2053	+	12.2053i	0.993251	+	0.993251i	0.999977	−	0.00672628i	$-0.00214106\pi$
$151$	12.2053	+	12.2053i	0.993251	+	0.993251i	−0.00672628	+	0.999977i	$0.502141\pi$
$152$		−	8.85366i		−	0.718127i
$153$	−17.3271	+	1.72379i	−1.40081	+	0.139360i
$154$	−6.54369	−	6.54369i	−0.527305	−	0.527305i
$155$	−0.770475			−0.0618861
$156$		0			0
$157$	−13.4410			−1.07271			−0.536355	−	0.843993i	$-0.680199\pi$
$157$	−13.4410			−1.07271			−0.536355	+	0.843993i	$0.680199\pi$
$158$	4.74062	+	4.74062i	0.377143	+	0.377143i
$159$	−3.58479	+	0.177878i	−0.284293	+	0.0141067i
$160$			8.25633i			0.652720i
$161$	6.12428	+	6.12428i	0.482661	+	0.482661i
$162$	5.72530	+	3.80924i	0.449822	+	0.299282i
$163$	4.50040	+	4.50040i	0.352498	+	0.352498i	0.861038	−	0.508540i	$-0.169815\pi$
$163$	4.50040	+	4.50040i	0.352498	+	0.352498i	−0.508540	+	0.861038i	$0.669815\pi$
$164$	1.04019	−	1.04019i	0.0812256	−	0.0812256i
$165$	−0.574539	−	11.5787i	−0.0447278	−	0.901403i
$166$			8.98875i			0.697662i
$167$	3.09828	−	3.09828i	0.239752	−	0.239752i	−0.576995	−	0.816747i	$-0.695775\pi$
$167$	3.09828	−	3.09828i	0.239752	−	0.239752i	0.816747	+	0.576995i	$0.195775\pi$
$168$	−0.571170	−	11.5108i	−0.0440667	−	0.888080i
$169$		0			0
$170$		−	6.24767i		−	0.479174i
$171$	−6.44765	+	7.87227i	−0.493064	+	0.602008i
$172$	10.7179			0.817230
$173$	4.33355			0.329474			0.164737	−	0.986338i	$-0.447323\pi$
$173$	4.33355			0.329474			0.164737	+	0.986338i	$0.447323\pi$
$174$	−6.45464	−	5.84436i	−0.489325	−	0.443060i
$175$	−5.43539	+	5.43539i	−0.410877	+	0.410877i
$176$	−2.81507	+	2.81507i	−0.212194	+	0.212194i
$177$	6.46546	+	5.85416i	0.485974	+	0.440025i
$178$	−10.4012			−0.779600
$179$	13.9923			1.04583			0.522916	−	0.852384i	$-0.324844\pi$
$179$	13.9923			1.04583			0.522916	+	0.852384i	$0.324844\pi$
$180$	3.79239	−	4.63033i	0.282668	−	0.345124i
$181$			0.976007i			0.0725460i	0.999342	+	0.0362730i	$0.0115486\pi$
$181$			0.976007i			0.0725460i	−0.999342	+	0.0362730i	$0.988451\pi$
$182$		0			0
$183$	0.605020	+	12.1930i	0.0447244	+	0.901334i
$184$	−6.27098	+	6.27098i	−0.462303	+	0.462303i
$185$			11.8288i			0.869667i
$186$	0.0358713	+	0.722918i	0.00263021	+	0.0530069i
$187$	19.4996	−	19.4996i	1.42595	−	1.42595i
$188$	0.344923	+	0.344923i	0.0251561	+	0.0251561i
$189$	−7.87486	+	10.6509i	−0.572812	+	0.774736i
$190$	−2.58168	−	2.58168i	−0.187295	−	0.187295i
$191$			17.1073i			1.23784i	0.785454	+	0.618920i	$0.212429\pi$
$191$			17.1073i			1.23784i	−0.785454	+	0.618920i	$0.787571\pi$
$192$	4.84761	−	0.240539i	0.349846	−	0.0173594i
$193$	1.79543	+	1.79543i	0.129238	+	0.129238i	0.768767	−	0.639529i	$-0.220871\pi$
$193$	1.79543	+	1.79543i	0.129238	+	0.129238i	−0.639529	+	0.768767i	$0.720871\pi$
$194$	−1.45013			−0.104114
$195$		0			0
$196$	−0.710497			−0.0507498
$197$	12.6256	+	12.6256i	0.899536	+	0.899536i	0.995395	−	0.0958594i	$-0.0305599\pi$
$197$	12.6256	+	12.6256i	0.899536	+	0.899536i	−0.0958594	+	0.995395i	$0.530560\pi$
$198$	−10.8373	+	1.07815i	−0.770172	+	0.0766208i
$199$			2.60975i			0.185000i	0.995713	+	0.0925001i	$0.0294859\pi$
$199$			2.60975i			0.185000i	−0.995713	+	0.0925001i	$0.970514\pi$
$200$	−5.56558	−	5.56558i	−0.393546	−	0.393546i
$201$	−8.24437	−	7.46487i	−0.581513	−	0.526532i
$202$	1.11714	+	1.11714i	0.0786018	+	0.0786018i
$203$	11.8597	−	11.8597i	0.832387	−	0.832387i
$204$	14.2196	−	0.705580i	0.995572	−	0.0494005i
$205$		−	1.46335i		−	0.102205i
$206$	7.22998	−	7.22998i	0.503737	−	0.503737i
$207$	10.1427	−	1.00905i	0.704965	−	0.0701337i
$208$		0			0
$209$		−	16.1154i		−	1.11473i
$210$	−3.52305	−	3.18995i	−0.243114	−	0.220128i
$211$	13.5443			0.932426			0.466213	−	0.884673i	$-0.345618\pi$
$211$	13.5443			0.932426			0.466213	+	0.884673i	$0.345618\pi$
$212$	2.93465			0.201552
$213$	−11.1673	+	12.3334i	−0.765171	+	0.845072i
$214$	4.06414	−	4.06414i	0.277819	−	0.277819i
$215$	7.53895	−	7.53895i	0.514152	−	0.514152i
$216$	−10.9060	−	8.06349i	−0.742058	−	0.548651i
$217$	−1.39419			−0.0946439
$218$	−2.27497			−0.154080
$219$	9.94178	−	10.9799i	0.671803	−	0.741954i
$220$			9.47879i			0.639060i
$221$		0			0
$222$	11.0986	−	0.550716i	0.744891	−	0.0369616i
$223$	7.32302	−	7.32302i	0.490386	−	0.490386i	−0.418042	−	0.908428i	$-0.637284\pi$
$223$	7.32302	−	7.32302i	0.490386	−	0.490386i	0.908428	+	0.418042i	$0.137284\pi$
$224$			14.9400i			0.998222i
$225$	0.895545	+	9.00178i	0.0597030	+	0.600119i
$226$	−1.02424	+	1.02424i	−0.0681314	+	0.0681314i
$227$	−0.0467074	−	0.0467074i	−0.00310008	−	0.00310008i	0.705555	−	0.708655i	$-0.250698\pi$
$227$	−0.0467074	−	0.0467074i	−0.00310008	−	0.00310008i	−0.708655	+	0.705555i	$0.750698\pi$
$228$	5.58432	−	6.16744i	0.369831	−	0.408449i
$229$	−19.2246	−	19.2246i	−1.27040	−	1.27040i	−0.945880	−	0.324517i	$-0.894798\pi$
$229$	−19.2246	−	19.2246i	−1.27040	−	1.27040i	−0.324517	−	0.945880i	$-0.605202\pi$
$230$			3.65717i			0.241147i
$231$	−1.03964	−	20.9520i	−0.0684033	−	1.37854i
$232$	12.1438	+	12.1438i	0.797278	+	0.797278i
$233$	16.5148			1.08192			0.540961	−	0.841047i	$-0.318061\pi$
$233$	16.5148			1.08192			0.540961	+	0.841047i	$0.318061\pi$
$234$		0			0
$235$	0.485238			0.0316534
$236$	−5.04265	−	5.04265i	−0.328249	−	0.328249i
$237$	0.753175	+	15.1788i	0.0489240	+	0.985969i
$238$		−	11.3053i		−	0.732813i
$239$	−18.7548	−	18.7548i	−1.21315	−	1.21315i	−0.969985	−	0.243165i	$-0.921814\pi$
$239$	−18.7548	−	18.7548i	−1.21315	−	1.21315i	−0.243165	−	0.969985i	$-0.578186\pi$
$240$	−1.37231	+	1.51561i	−0.0885820	+	0.0978319i
$241$	−3.33327	−	3.33327i	−0.214715	−	0.214715i	0.591552	−	0.806267i	$-0.298515\pi$
$241$	−3.33327	−	3.33327i	−0.214715	−	0.214715i	−0.806267	+	0.591552i	$0.798515\pi$
$242$	6.25295	−	6.25295i	0.401955	−	0.401955i
$243$	3.82488	+	15.1119i	0.245366	+	0.969430i
$244$		−	9.98167i		−	0.639011i
$245$	−0.499763	+	0.499763i	−0.0319287	+	0.0319287i
$246$	−1.37302	+	0.0681296i	−0.0875406	+	0.00434378i
$247$		0			0
$248$		−	1.42759i		−	0.0906519i
$249$	−13.6763	+	15.1044i	−0.866700	+	0.957203i
$250$	−8.62781			−0.545671
$251$	14.0462			0.886586			0.443293	−	0.896377i	$-0.353810\pi$
$251$	14.0462			0.886586			0.443293	+	0.896377i	$0.353810\pi$
$252$	6.86241	−	8.37868i	0.432291	−	0.527807i
$253$	−11.4144	+	11.4144i	−0.717618	+	0.717618i
$254$	−3.84400	+	3.84400i	−0.241194	+	0.241194i
$255$	9.50577	−	10.4984i	0.595275	−	0.657434i
$256$	−12.9246			−0.807785
$257$	−19.5348			−1.21855			−0.609274	−	0.792960i	$-0.708539\pi$
$257$	−19.5348			−1.21855			−0.609274	+	0.792960i	$0.708539\pi$
$258$	−7.42461	−	6.72262i	−0.462236	−	0.418532i
$259$			21.4044i			1.33000i
$260$		0			0
$261$	−1.95403	−	19.6413i	−0.120951	−	1.21577i
$262$	−2.89633	+	2.89633i	−0.178936	+	0.178936i
$263$		−	1.30868i		−	0.0806967i	−0.999186	−	0.0403484i	$-0.987153\pi$
$263$		−	1.30868i		−	0.0806967i	0.999186	−	0.0403484i	$-0.0128468\pi$
$264$	21.4538	−	1.06454i	1.32039	−	0.0655182i
$265$	2.06423	−	2.06423i	0.126805	−	0.126805i
$266$	−4.67162	−	4.67162i	−0.286435	−	0.286435i
$267$	−17.4778	−	15.8253i	−1.06962	−	0.968491i
$268$	6.43009	+	6.43009i	0.392780	+	0.392780i
$269$		−	28.2787i		−	1.72419i	−0.506750	−	0.862093i	$-0.669153\pi$
$269$		−	28.2787i		−	1.72419i	0.506750	−	0.862093i	$-0.330847\pi$
$270$	−5.53140	+	0.828855i	−0.336631	+	0.0504425i
$271$	5.02990	+	5.02990i	0.305545	+	0.305545i	0.843178	−	0.537634i	$-0.180682\pi$
$271$	5.02990	+	5.02990i	0.305545	+	0.305545i	−0.537634	+	0.843178i	$0.680682\pi$
$272$	−4.86350			−0.294893
$273$		0			0
$274$	−3.69843			−0.223431
$275$	−10.1305	−	10.1305i	−0.610889	−	0.610889i
$276$	−8.32368	+	0.413023i	−0.501027	+	0.0248611i
$277$			12.2519i			0.736143i	0.929798	+	0.368071i	$0.119982\pi$
$277$			12.2519i			0.736143i	−0.929798	+	0.368071i	$0.880018\pi$
$278$	6.36894	+	6.36894i	0.381984	+	0.381984i
$279$	−1.03964	+	1.26935i	−0.0622414	+	0.0759937i
$280$	6.62828	+	6.62828i	0.396116	+	0.396116i
$281$	17.0443	−	17.0443i	1.01678	−	1.01678i	0.0169217	−	0.999857i	$-0.494613\pi$
$281$	17.0443	−	17.0443i	1.01678	−	1.01678i	0.999857	−	0.0169217i	$-0.00538659\pi$
$282$	−0.0225914	−	0.455286i	−0.00134530	−	0.0271119i
$283$			12.3279i			0.732817i	0.930454	+	0.366408i	$0.119413\pi$
$283$			12.3279i			0.732817i	−0.930454	+	0.366408i	$0.880587\pi$
$284$	9.61929	−	9.61929i	0.570800	−	0.570800i
$285$	−0.410170	−	8.26619i	−0.0242964	−	0.489647i
$286$		0			0
$287$		−	2.64796i		−	0.156304i
$288$	13.6022	+	11.1406i	0.801515	+	0.656467i
$289$	16.6888			0.981693
$290$	7.08213			0.415877
$291$	−2.43676	−	2.20637i	−0.142845	−	0.129339i
$292$	−8.56365	+	8.56365i	−0.501150	+	0.501150i
$293$	−11.1173	+	11.1173i	−0.649482	+	0.649482i	−0.952868	−	0.303386i	$-0.901883\pi$
$293$	−11.1173	+	11.1173i	−0.649482	+	0.649482i	0.303386	+	0.952868i	$0.401883\pi$
$294$	0.492183	+	0.445648i	0.0287047	+	0.0259907i
$295$	−7.09400			−0.413029
$296$	−21.9171			−1.27391
$297$	−19.8510	−	14.6771i	−1.15187	−	0.851654i
$298$			5.26290i			0.304872i
$299$		0			0
$300$	−0.366564	−	7.38739i	−0.0211636	−	0.426511i
$301$	13.6419	−	13.6419i	0.786306	−	0.786306i
$302$			13.1887i			0.758924i
$303$	0.177488	+	3.57693i	0.0101964	+	0.205489i
$304$	−2.00971	+	2.00971i	−0.115265	+	0.115265i
$305$	−7.02111	−	7.02111i	−0.402027	−	0.402027i
$306$	−10.2929	−	8.43025i	−0.588408	−	0.481925i
$307$	−1.83038	−	1.83038i	−0.104465	−	0.104465i	0.652942	−	0.757408i	$-0.273534\pi$
$307$	−1.83038	−	1.83038i	−0.104465	−	0.104465i	−0.757408	+	0.652942i	$0.773534\pi$
$308$			17.1521i			0.977330i
$309$	23.1494	−	1.14868i	1.31692	−	0.0653460i
$310$	−0.416278	−	0.416278i	−0.0236430	−	0.0236430i
$311$	15.2844			0.866701			0.433350	−	0.901226i	$-0.357331\pi$
$311$	15.2844			0.866701			0.433350	+	0.901226i	$0.357331\pi$
$312$		0			0
$313$	31.4063			1.77519			0.887593	−	0.460628i	$-0.152376\pi$
$313$	31.4063			1.77519			0.887593	+	0.460628i	$0.152376\pi$
$314$	−7.26200	−	7.26200i	−0.409819	−	0.409819i
$315$	−1.06654	−	10.7206i	−0.0600928	−	0.604037i
$316$		−	12.4259i		−	0.699014i
$317$	−11.8144	−	11.8144i	−0.663565	−	0.663565i	0.292654	−	0.956219i	$-0.405462\pi$
$317$	−11.8144	−	11.8144i	−0.663565	−	0.663565i	−0.956219	+	0.292654i	$0.905462\pi$
$318$	−2.03292	−	1.84071i	−0.114001	−	0.103222i
$319$	22.1041	+	22.1041i	1.23759	+	1.23759i
$320$	−2.79140	+	2.79140i	−0.156044	+	0.156044i
$321$	13.0128	−	0.645698i	0.726304	−	0.0360393i
$322$			6.61774i			0.368792i
$323$	13.9210	−	13.9210i	0.774585	−	0.774585i
$324$	−2.51115	−	12.4958i	−0.139508	−	0.694211i
$325$		0			0
$326$			4.86301i			0.269337i
$327$	−3.82279	−	3.46135i	−0.211401	−	0.191413i
$328$	2.71139			0.149711
$329$	0.878049			0.0484084
$330$	5.94542	−	6.56625i	0.327285	−	0.361460i
$331$	15.8890	−	15.8890i	0.873340	−	0.873340i	−0.119495	−	0.992835i	$-0.538127\pi$
$331$	15.8890	−	15.8890i	0.873340	−	0.873340i	0.992835	+	0.119495i	$0.0381274\pi$
$332$	11.7805	−	11.7805i	0.646538	−	0.646538i
$333$	19.4877	+	15.9611i	1.06792	+	0.874660i
$334$	3.34792			0.183190
$335$	9.04585			0.494228
$336$	−2.48322	+	2.74252i	−0.135471	+	0.149617i
$337$		−	9.19516i		−	0.500892i	−0.968131	−	0.250446i	$-0.919423\pi$
$337$		−	9.19516i		−	0.500892i	0.968131	−	0.250446i	$-0.0805773\pi$
$338$		0			0
$339$	−3.27947	+	0.162728i	−0.178116	+	0.00883817i
$340$	−8.18808	+	8.18808i	−0.444061	+	0.444061i
$341$		−	2.59849i		−	0.140716i
$342$	−7.73686	+	0.769704i	−0.418362	+	0.0416209i
$343$	−13.5221	+	13.5221i	−0.730125	+	0.730125i
$344$	13.9687	+	13.9687i	0.753141	+	0.753141i
$345$	−5.56436	+	6.14540i	−0.299575	+	0.330857i
$346$	2.34136	+	2.34136i	0.125872	+	0.125872i
$347$			11.2350i			0.603128i	0.953446	+	0.301564i	$0.0975087\pi$
$347$			11.2350i			0.603128i	−0.953446	+	0.301564i	$0.902491\pi$
$348$	0.799820	+	16.1188i	0.0428749	+	0.864061i
$349$	24.6546	+	24.6546i	1.31973	+	1.31973i	0.913985	+	0.405748i	$0.132989\pi$
$349$	24.6546	+	24.6546i	1.31973	+	1.31973i	0.405748	+	0.913985i	$0.367011\pi$
$350$	−5.87334			−0.313943
$351$		0			0
$352$	−27.8451			−1.48415
$353$	22.7730	+	22.7730i	1.21209	+	1.21209i	0.970340	+	0.241746i	$0.0777199\pi$
$353$	22.7730	+	22.7730i	1.21209	+	1.21209i	0.241746	+	0.970340i	$0.422280\pi$
$354$	0.330278	+	6.65612i	0.0175541	+	0.353769i
$355$		−	13.5324i		−	0.718226i
$356$	13.6316	+	13.6316i	0.722472	+	0.722472i
$357$	17.2009	−	18.9971i	0.910369	−	1.00543i
$358$	7.55984	+	7.55984i	0.399550	+	0.399550i
$359$	−20.8500	+	20.8500i	−1.10042	+	1.10042i	−0.106064	+	0.994359i	$0.533825\pi$
$359$	−20.8500	+	20.8500i	−1.10042	+	1.10042i	−0.994359	+	0.106064i	$0.966175\pi$
$360$	10.9774	−	1.09209i	0.578559	−	0.0575581i
$361$			7.49502i			0.394475i
$362$	−0.527324	+	0.527324i	−0.0277155	+	0.0277155i
$363$	20.0211	−	0.993449i	1.05083	−	0.0521425i
$364$		0			0
$365$			12.0473i			0.630587i
$366$	−6.26084	+	6.91461i	−0.327260	+	0.361433i
$367$	−21.3180			−1.11279			−0.556395	−	0.830918i	$-0.687816\pi$
$367$	−21.3180			−1.11279			−0.556395	+	0.830918i	$0.687816\pi$
$368$	2.84693			0.148406
$369$	−2.41084	−	1.97456i	−0.125503	−	0.102791i
$370$	−6.39092	+	6.39092i	−0.332248	+	0.332248i
$371$	3.73527	−	3.73527i	0.193926	−	0.193926i
$372$	0.900431	−	0.994455i	0.0466851	−	0.0515601i
$373$	−13.9035			−0.719898			−0.359949	−	0.932972i	$-0.617206\pi$
$373$	−13.9035			−0.719898			−0.359949	+	0.932972i	$0.617206\pi$
$374$	21.0708			1.08954
$375$	−14.4979	−	13.1271i	−0.748669	−	0.677883i
$376$			0.899081i			0.0463666i
$377$		0			0
$378$	−10.0092	+	1.49983i	−0.514818	+	0.0771430i
$379$	24.5826	−	24.5826i	1.26272	−	1.26272i	0.312957	−	0.949767i	$-0.398680\pi$
$379$	24.5826	−	24.5826i	1.26272	−	1.26272i	0.949767	−	0.312957i	$-0.101320\pi$
$380$			6.76702i			0.347141i
$381$	−12.3079	+	0.610722i	−0.630555	+	0.0312883i
$382$	−9.24284	+	9.24284i	−0.472905	+	0.472905i
$383$	−11.9301	−	11.9301i	−0.609600	−	0.609600i	0.333242	−	0.942841i	$-0.391858\pi$
$383$	−11.9301	−	11.9301i	−0.609600	−	0.609600i	−0.942841	+	0.333242i	$0.891858\pi$
$384$	−12.3005	−	11.1375i	−0.627709	−	0.568360i
$385$	12.0648	+	12.0648i	0.614878	+	0.614878i
$386$			1.94009i			0.0987480i
$387$	−2.24767	−	22.5929i	−0.114255	−	1.14846i
$388$	1.90052	+	1.90052i	0.0964842	+	0.0964842i
$389$	−35.0012			−1.77463			−0.887315	−	0.461164i	$-0.847432\pi$
$389$	−35.0012			−1.77463			−0.887315	+	0.461164i	$0.847432\pi$
$390$		0			0
$391$	−19.7203			−0.997297
$392$	−0.925995	−	0.925995i	−0.0467698	−	0.0467698i
$393$	−9.27363	+	0.460160i	−0.467793	+	0.0232120i
$394$			13.6429i			0.687318i
$395$	−8.74040	−	8.74040i	−0.439777	−	0.439777i
$396$	15.6162	+	12.7901i	0.784741	+	0.642729i
$397$	−0.937607	−	0.937607i	−0.0470571	−	0.0470571i	0.683187	−	0.730244i	$-0.260594\pi$
$397$	−0.937607	−	0.937607i	−0.0470571	−	0.0470571i	−0.730244	+	0.683187i	$0.760594\pi$
$398$	−1.41001	+	1.41001i	−0.0706776	+	0.0706776i
$399$	−0.742212	−	14.9579i	−0.0371571	−	0.748830i
$400$			2.52669i			0.126335i
$401$	−18.7960	+	18.7960i	−0.938629	+	0.938629i	−0.998223	−	0.0595935i	$-0.981020\pi$
$401$	−18.7960	+	18.7960i	−0.938629	+	0.938629i	0.0595935	+	0.998223i	$0.481020\pi$
$402$	−0.421151	−	8.48750i	−0.0210051	−	0.423318i
$403$		0			0
$404$		−	2.92821i		−	0.145684i
$405$	−10.5559	−	7.02320i	−0.524526	−	0.348986i
$406$	12.8153			0.636011
$407$	−39.8934			−1.97744
$408$	19.4521	+	17.6129i	0.963023	+	0.871970i
$409$	6.64641	−	6.64641i	0.328644	−	0.328644i	−0.523427	−	0.852071i	$-0.675347\pi$
$409$	6.64641	−	6.64641i	0.328644	−	0.328644i	0.852071	+	0.523427i	$0.175347\pi$
$410$	0.790627	−	0.790627i	0.0390463	−	0.0390463i
$411$	−6.21473	−	5.62713i	−0.306550	−	0.277566i
$412$	−18.9510			−0.933648
$413$	−12.8368			−0.631656
$414$	6.02514	+	4.93478i	0.296119	+	0.242531i
$415$		−	16.5728i		−	0.813526i
$416$		0			0
$417$	1.01188	+	20.3925i	0.0495519	+	0.998623i
$418$	8.70694	−	8.70694i	0.425870	−	0.425870i
$419$		−	31.8789i		−	1.55738i	−0.627406	−	0.778692i	$-0.715883\pi$
$419$		−	31.8789i		−	1.55738i	0.627406	−	0.778692i	$-0.284117\pi$
$420$	0.436556	+	8.79794i	0.0213017	+	0.429296i
$421$	19.6414	−	19.6414i	0.957263	−	0.957263i	−0.0418609	−	0.999123i	$-0.513329\pi$
$421$	19.6414	−	19.6414i	0.957263	−	0.957263i	0.999123	+	0.0418609i	$0.0133286\pi$
$422$	7.31779	+	7.31779i	0.356224	+	0.356224i
$423$	0.654752	−	0.799421i	0.0318351	−	0.0388692i
$424$	3.82475	+	3.82475i	0.185746	+	0.185746i
$425$		−	17.5020i		−	0.848973i
$426$	−12.6971	+	0.630034i	−0.615178	+	0.0305252i
$427$	−12.7049	−	12.7049i	−0.614831	−	0.614831i
$428$	−10.6528			−0.514921
$429$		0			0
$430$	8.14640			0.392854
$431$	3.36047	+	3.36047i	0.161868	+	0.161868i	0.783394	−	0.621526i	$-0.213487\pi$
$431$	3.36047	+	3.36047i	0.161868	+	0.161868i	−0.621526	+	0.783394i	$0.713487\pi$
$432$	0.645222	+	4.30593i	0.0310433	+	0.207169i
$433$		−	2.05935i		−	0.0989662i	−0.998775	−	0.0494831i	$-0.984243\pi$
$433$		−	2.05935i		−	0.0989662i	0.998775	−	0.0494831i	$-0.0157574\pi$
$434$	−0.753264	−	0.753264i	−0.0361578	−	0.0361578i
$435$	11.9006	+	10.7754i	0.570590	+	0.516641i
$436$	2.98153	+	2.98153i	0.142790	+	0.142790i
$437$	−8.14889	+	8.14889i	−0.389814	+	0.389814i
$438$	11.3037	−	0.560893i	0.540113	−	0.0268005i
$439$			12.8652i			0.614023i	0.951706	+	0.307011i	$0.0993290\pi$
$439$			12.8652i			0.614023i	−0.951706	+	0.307011i	$0.900671\pi$
$440$	−12.3538	+	12.3538i	−0.588943	+	0.588943i
$441$	0.149000	+	1.49770i	0.00709522	+	0.0713193i
$442$		0			0
$443$			14.4060i			0.684449i	0.939618	+	0.342224i	$0.111180\pi$
$443$			14.4060i			0.684449i	−0.939618	+	0.342224i	$0.888820\pi$
$444$	−15.2674	−	13.8239i	−0.724559	−	0.656053i
$445$	19.1769			0.909072
$446$	7.91306			0.374694
$447$	−8.00746	+	8.84361i	−0.378740	+	0.418288i
$448$	−5.05110	+	5.05110i	−0.238642	+	0.238642i
$449$	−11.6046	+	11.6046i	−0.547657	+	0.547657i	−0.925763	−	0.378105i	$-0.876576\pi$
$449$	−11.6046	+	11.6046i	−0.547657	+	0.547657i	0.378105	+	0.925763i	$0.376576\pi$
$450$	−4.37969	+	5.34739i	−0.206461	+	0.252079i
$451$	4.93525			0.232392
$452$	2.68470			0.126278
$453$	−20.0665	+	22.1619i	−0.942806	+	1.04126i
$454$		−	0.0504707i		−	0.00236871i
$455$		0			0
$456$	15.3162	−	0.759991i	0.717245	−	0.0355898i
$457$	−16.1290	+	16.1290i	−0.754481	+	0.754481i	−0.975312	−	0.220831i	$-0.929123\pi$
$457$	−16.1290	+	16.1290i	−0.754481	+	0.754481i	0.220831	+	0.975312i	$0.429123\pi$
$458$		−	20.7736i		−	0.970686i
$459$	−4.46936	−	29.8265i	−0.208612	−	1.39218i
$460$	4.79303	−	4.79303i	0.223476	−	0.223476i
$461$	−20.8758	−	20.8758i	−0.972282	−	0.972282i	0.0273439	−	0.999626i	$-0.491295\pi$
$461$	−20.8758	−	20.8758i	−0.972282	−	0.972282i	−0.999626	+	0.0273439i	$0.991295\pi$
$462$	10.7584	−	11.8818i	0.500525	−	0.552790i
$463$	−25.6118	−	25.6118i	−1.19028	−	1.19028i	−0.976988	−	0.213295i	$-0.931580\pi$
$463$	−25.6118	−	25.6118i	−1.19028	−	1.19028i	−0.213295	−	0.976988i	$-0.568420\pi$
$464$		−	5.51309i		−	0.255939i
$465$	−0.0661369	−	1.33286i	−0.00306703	−	0.0618100i
$466$	8.92275	+	8.92275i	0.413338	+	0.413338i
$467$	14.0544			0.650361			0.325180	−	0.945652i	$-0.394575\pi$
$467$	14.0544			0.650361			0.325180	+	0.945652i	$0.394575\pi$
$468$		0			0
$469$	16.3687			0.755835
$470$	0.262168	+	0.262168i	0.0120929	+	0.0120929i
$471$	−1.15376	−	23.2519i	−0.0531627	−	1.07139i
$472$		−	13.1442i		−	0.605013i
$473$	25.4257	+	25.4257i	1.16908	+	1.16908i
$474$	−7.79397	+	8.60783i	−0.357989	+	0.395371i
$475$	−7.23225	−	7.23225i	−0.331838	−	0.331838i
$476$	−14.8165	+	14.8165i	−0.679114	+	0.679114i
$477$	−0.615431	−	6.18614i	−0.0281786	−	0.283244i
$478$		−	20.2660i		−	0.926945i
$479$	9.09054	−	9.09054i	0.415357	−	0.415357i	−0.468243	−	0.883600i	$-0.655113\pi$
$479$	9.09054	−	9.09054i	0.415357	−	0.415357i	0.883600	+	0.468243i	$0.155113\pi$
$480$	−14.2828	+	0.708716i	−0.651918	+	0.0323483i
$481$		0			0
$482$		−	3.60185i		−	0.164060i
$483$	−10.0688	+	11.1202i	−0.458148	+	0.505988i
$484$	−16.3900			−0.745000
$485$	2.67365			0.121404
$486$	−6.09824	+	10.2313i	−0.276622	+	0.464102i
$487$	−19.1664	+	19.1664i	−0.868515	+	0.868515i	−0.992308	−	0.123793i	$-0.960494\pi$
$487$	−19.1664	+	19.1664i	−0.868515	+	0.868515i	0.123793	+	0.992308i	$0.460494\pi$
$488$	13.0092	−	13.0092i	0.588898	−	0.588898i
$489$	−7.39903	+	8.17165i	−0.334596	+	0.369535i
$490$	−0.540031			−0.0243961
$491$	12.5414			0.565983			0.282992	−	0.959122i	$-0.408673\pi$
$491$	12.5414			0.565983			0.282992	+	0.959122i	$0.408673\pi$
$492$	1.88875	+	1.71017i	0.0851512	+	0.0771003i
$493$			38.1884i			1.71992i
$494$		0			0
$495$	19.9810	−	1.98782i	0.898079	−	0.0893457i
$496$	−0.324052	+	0.324052i	−0.0145503	+	0.0145503i
$497$		−	24.4872i		−	1.09840i
$498$	−15.5498	+	0.771586i	−0.696805	+	0.0345756i
$499$	−5.98039	+	5.98039i	−0.267719	+	0.267719i	−0.828180	−	0.560461i	$-0.810624\pi$
$499$	−5.98039	+	5.98039i	−0.267719	+	0.267719i	0.560461	+	0.828180i	$0.310624\pi$
$500$	11.3075	+	11.3075i	0.505685	+	0.505685i
$501$	5.62573	+	5.09383i	0.251339	+	0.227575i
$502$	7.58896	+	7.58896i	0.338712	+	0.338712i
$503$			18.5579i			0.827458i	0.910400	+	0.413729i	$0.135774\pi$
$503$			18.5579i			0.827458i	−0.910400	+	0.413729i	$0.864226\pi$
$504$	19.8638	−	1.97616i	0.884805	−	0.0880251i
$505$	−2.05970	−	2.05970i	−0.0916556	−	0.0916556i
$506$	−12.3341			−0.548318
$507$		0			0
$508$	10.0757			0.447039
$509$	−25.8788	−	25.8788i	−1.14706	−	1.14706i	−0.987129	−	0.159928i	$-0.948874\pi$
$509$	−25.8788	−	25.8788i	−1.14706	−	1.14706i	−0.159928	−	0.987129i	$-0.551126\pi$
$510$	10.8080	−	0.536294i	0.478585	−	0.0237475i
$511$			21.7999i			0.964372i
$512$	6.56566	+	6.56566i	0.290164	+	0.290164i
$513$	−14.1719	−	10.4782i	−0.625704	−	0.462623i
$514$	−10.5544	−	10.5544i	−0.465534	−	0.465534i
$515$	−13.3301	+	13.3301i	−0.587395	+	0.587395i
$516$	0.920013	+	18.5411i	0.0405013	+	0.816226i
$517$			1.63650i			0.0719733i
$518$	−11.5645	+	11.5645i	−0.508116	+	0.508116i
$519$	0.371988	+	7.49670i	0.0163285	+	0.329069i
$520$		0			0
$521$			32.0270i			1.40313i	0.712605	+	0.701565i	$0.247515\pi$
$521$			32.0270i			1.40313i	−0.712605	+	0.701565i	$0.752485\pi$
$522$	9.55623	−	11.6677i	0.418265	−	0.510681i
$523$	16.4059			0.717380			0.358690	−	0.933457i	$-0.383224\pi$
$523$	16.4059			0.717380			0.358690	+	0.933457i	$0.383224\pi$
$524$	7.59175			0.331647
$525$	−9.86937	−	8.93623i	−0.430735	−	0.390009i
$526$	0.707063	−	0.707063i	0.0308294	−	0.0308294i
$527$	2.24466	−	2.24466i	0.0977789	−	0.0977789i
$528$	−5.11150	−	4.62822i	−0.222450	−	0.201417i
$529$	−11.4564			−0.498105
$530$	2.23055			0.0968891
$531$	−9.57225	+	11.6873i	−0.415400	+	0.507184i
$532$			12.2451i			0.530891i
$533$		0			0
$534$	−0.892826	−	17.9932i	−0.0386364	−	0.778642i
$535$	−7.49316	+	7.49316i	−0.323958	+	0.323958i
$536$			16.7608i			0.723955i
$537$	1.20108	+	24.2055i	0.0518306	+	1.04455i
$538$	15.2786	−	15.2786i	0.658709	−	0.658709i
$539$	−1.68549	−	1.68549i	−0.0725993	−	0.0725993i
$540$	8.33564	+	6.16308i	0.358709	+	0.265217i
$541$	−10.4088	−	10.4088i	−0.447508	−	0.447508i	0.447017	−	0.894525i	$-0.352486\pi$
$541$	−10.4088	−	10.4088i	−0.447508	−	0.447508i	−0.894525	+	0.447017i	$0.852486\pi$
$542$			5.43518i			0.233461i
$543$	−1.68842	+	0.0837796i	−0.0724569	+	0.00359532i
$544$	−24.0535	−	24.0535i	−1.03129	−	1.03129i
$545$	4.19442			0.179669
$546$		0			0
$547$	−18.0787			−0.772988			−0.386494	−	0.922292i	$-0.626314\pi$
$547$	−18.0787			−0.772988			−0.386494	+	0.922292i	$0.626314\pi$
$548$	4.84710	+	4.84710i	0.207058	+	0.207058i
$549$	−21.0410	+	2.09328i	−0.898010	+	0.0893388i
$550$		−	10.9467i		−	0.466769i
$551$	15.7803	+	15.7803i	0.672265	+	0.672265i
$552$	−11.3866	−	10.3100i	−0.484646	−	0.438823i
$553$	−15.8160	−	15.8160i	−0.672563	−	0.672563i
$554$	−6.61952	+	6.61952i	−0.281236	+	0.281236i
$555$	−20.4628	+	1.01537i	−0.868599	+	0.0431000i
$556$		−	16.6940i		−	0.707985i
$557$	−9.10043	+	9.10043i	−0.385597	+	0.385597i	−0.873114	−	0.487516i	$-0.837903\pi$
$557$	−9.10043	+	9.10043i	−0.385597	+	0.385597i	0.487516	+	0.873114i	$0.337903\pi$
$558$	−1.24751	+	0.124109i	−0.0528114	+	0.00525396i
$559$		0			0
$560$		−	3.00914i		−	0.127159i
$561$	35.4066	+	32.0590i	1.49487	+	1.35353i
$562$	18.4176			0.776901
$563$	−27.8875			−1.17532			−0.587659	−	0.809109i	$-0.699950\pi$
$563$	−27.8875			−1.17532			−0.587659	+	0.809109i	$0.699950\pi$
$564$	−0.567082	+	0.626298i	−0.0238785	+	0.0263719i
$565$	1.88842	−	1.88842i	0.0794463	−	0.0794463i
$566$	−6.66059	+	6.66059i	−0.279966	+	0.279966i
$567$	−19.1011	−	12.7086i	−0.802172	−	0.533713i
$568$	25.0738			1.05207
$569$	1.75416			0.0735383			0.0367692	−	0.999324i	$-0.488293\pi$
$569$	1.75416			0.0735383			0.0367692	+	0.999324i	$0.488293\pi$
$570$	4.24450	−	4.68772i	0.177783	−	0.196347i
$571$		−	13.1497i		−	0.550300i	−0.961401	−	0.275150i	$-0.911273\pi$
$571$		−	13.1497i		−	0.550300i	0.961401	−	0.275150i	$-0.0887275\pi$
$572$		0			0
$573$	−29.5943	+	1.46847i	−1.23632	+	0.0613464i
$574$	1.43066	−	1.43066i	0.0597145	−	0.0597145i
$575$			10.2451i			0.427250i
$576$	0.832228	+	8.36533i	0.0346762	+	0.348556i
$577$	2.17547	−	2.17547i	0.0905662	−	0.0905662i	−0.660372	−	0.750938i	$-0.729601\pi$
$577$	2.17547	−	2.17547i	0.0905662	−	0.0905662i	0.750938	+	0.660372i	$0.229601\pi$
$578$	9.01673	+	9.01673i	0.375046	+	0.375046i
$579$	−2.95183	+	3.26007i	−0.122674	+	0.135484i
$580$	−9.28171	−	9.28171i	−0.385402	−	0.385402i
$581$		−	29.9888i		−	1.24415i
$582$	−0.124478	−	2.50862i	−0.00515979	−	0.103986i
$583$	6.96179	+	6.96179i	0.288328	+	0.288328i
$584$	−22.3221			−0.923696
$585$		0			0
$586$	−12.0131			−0.496257
$587$	−10.6501	−	10.6501i	−0.439576	−	0.439576i	0.452294	−	0.891869i	$-0.350606\pi$
$587$	−10.6501	−	10.6501i	−0.439576	−	0.439576i	−0.891869	+	0.452294i	$0.850606\pi$
$588$	−0.0609884	−	1.22910i	−0.00251512	−	0.0506874i
$589$		−	1.85509i		−	0.0764378i
$590$	−3.83280	−	3.83280i	−0.157794	−	0.157794i
$591$	−20.7575	+	22.9250i	−0.853850	+	0.943010i
$592$	4.97502	+	4.97502i	0.204472	+	0.204472i
$593$	18.1461	−	18.1461i	0.745171	−	0.745171i	−0.228397	−	0.973568i	$-0.573348\pi$
$593$	18.1461	−	18.1461i	0.745171	−	0.745171i	0.973568	+	0.228397i	$0.0733483\pi$
$594$	−2.79538	−	18.6551i	−0.114696	−	0.765428i
$595$			20.8439i			0.854516i
$596$	6.89746	−	6.89746i	0.282531	−	0.282531i
$597$	−4.51467	+	0.224019i	−0.184773	+	0.00916847i
$598$		0			0
$599$		−	19.9578i		−	0.815455i	−0.913104	−	0.407728i	$-0.866321\pi$
$599$		−	19.9578i		−	0.815455i	0.913104	−	0.407728i	$-0.133679\pi$
$600$	9.15029	−	10.1058i	0.373559	−	0.412567i
$601$	−46.9281			−1.91424			−0.957118	−	0.289697i	$-0.906445\pi$
$601$	−46.9281			−1.91424			−0.957118	+	0.289697i	$0.906445\pi$
$602$	14.7411			0.600802
$603$	12.2060	−	14.9029i	0.497065	−	0.606893i
$604$	17.2849	−	17.2849i	0.703311	−	0.703311i
$605$	−11.5287	+	11.5287i	−0.468709	+	0.468709i
$606$	−1.83667	+	2.02846i	−0.0746097	+	0.0824006i
$607$	33.5601			1.36216			0.681081	−	0.732208i	$-0.261510\pi$
$607$	33.5601			1.36216			0.681081	+	0.732208i	$0.261510\pi$
$608$	−19.8790			−0.806199
$609$	21.5344	+	19.4983i	0.872617	+	0.790112i
$610$		−	7.58682i		−	0.307182i
$611$		0			0
$612$	2.44120	+	24.5383i	0.0986796	+	0.991901i
$613$	−21.7869	+	21.7869i	−0.879966	+	0.879966i	−0.993531	−	0.113565i	$-0.963773\pi$
$613$	−21.7869	+	21.7869i	−0.879966	+	0.879966i	0.113565	+	0.993531i	$0.463773\pi$
$614$		−	1.97786i		−	0.0798199i
$615$	2.53148	−	0.125612i	0.102079	−	0.00506518i
$616$	−22.3544	+	22.3544i	−0.900685	+	0.900685i
$617$	20.5242	+	20.5242i	0.826274	+	0.826274i	0.986999	−	0.160725i	$-0.0513832\pi$
$617$	20.5242	+	20.5242i	0.826274	+	0.826274i	−0.160725	+	0.986999i	$0.551383\pi$
$618$	13.1279	+	11.8867i	0.528083	+	0.478153i
$619$	28.5202	+	28.5202i	1.14633	+	1.14633i	0.987270	+	0.159056i	$0.0508449\pi$
$619$	28.5202	+	28.5202i	1.14633	+	1.14633i	0.159056	+	0.987270i	$0.449155\pi$
$620$			1.09113i			0.0438209i
$621$	2.61622	+	17.4594i	0.104985	+	0.700623i
$622$	8.25798	+	8.25798i	0.331115	+	0.331115i
$623$	34.7010			1.39027
$624$		0			0
$625$	0.830307			0.0332123
$626$	16.9684	+	16.9684i	0.678193	+	0.678193i
$627$	27.8784	−	1.38333i	1.11336	−	0.0552449i
$628$			19.0349i			0.759575i
$629$	−34.4612	−	34.4612i	−1.37406	−	1.37406i
$630$	5.21595	−	6.36843i	0.207809	−	0.253724i
$631$	17.1705	+	17.1705i	0.683545	+	0.683545i	0.960797	−	0.277252i	$-0.0894238\pi$
$631$	17.1705	+	17.1705i	0.683545	+	0.683545i	−0.277252	+	0.960797i	$0.589424\pi$
$632$	16.1948	−	16.1948i	0.644195	−	0.644195i
$633$	1.16263	+	23.4305i	0.0462103	+	0.931280i
$634$		−	12.7664i		−	0.507017i
$635$	7.08728	−	7.08728i	0.281250	−	0.281250i
$636$	0.251907	+	5.07671i	0.00998878	+	0.201305i
$637$		0			0
$638$			23.8851i			0.945619i
$639$	−22.2944	−	18.2599i	−0.881955	−	0.722350i
$640$	13.4963			0.533490
$641$	−9.40735			−0.371568			−0.185784	−	0.982591i	$-0.559482\pi$
$641$	−9.40735			−0.371568			−0.185784	+	0.982591i	$0.559482\pi$
$642$	7.37951	+	6.68178i	0.291246	+	0.263709i
$643$	32.3448	−	32.3448i	1.27555	−	1.27555i	0.332424	−	0.943130i	$-0.392134\pi$
$643$	32.3448	−	32.3448i	1.27555	−	1.27555i	0.943130	−	0.332424i	$-0.107866\pi$
$644$	8.67309	−	8.67309i	0.341768	−	0.341768i
$645$	13.6889	+	12.3947i	0.539002	+	0.488040i
$646$	15.0427			0.591846
$647$	8.80759			0.346262			0.173131	−	0.984899i	$-0.444612\pi$
$647$	8.80759			0.346262			0.173131	+	0.984899i	$0.444612\pi$
$648$	13.0131	−	19.5587i	0.511201	−	0.768337i
$649$		−	23.9251i		−	0.939142i
$650$		0			0
$651$	−0.119676	−	2.41184i	−0.00469048	−	0.0945276i
$652$	6.37337	−	6.37337i	0.249601	−	0.249601i
$653$			16.2320i			0.635207i	0.948224	+	0.317603i	$0.102878\pi$
$653$			16.2320i			0.635207i	−0.948224	+	0.317603i	$0.897122\pi$
$654$	−0.195281	−	3.93552i	−0.00763610	−	0.153891i
$655$	5.34004	−	5.34004i	0.208653	−	0.208653i
$656$	−0.615464	−	0.615464i	−0.0240298	−	0.0240298i
$657$	19.8478	+	16.2560i	0.774336	+	0.634207i
$658$	0.474398	+	0.474398i	0.0184940	+	0.0184940i
$659$		−	18.6480i		−	0.726422i	−0.931707	−	0.363211i	$-0.881680\pi$
$659$		−	18.6480i		−	0.726422i	0.931707	−	0.363211i	$-0.118320\pi$
$660$	−16.3976	+	0.813651i	−0.638274	+	0.0316713i
$661$	−19.9989	−	19.9989i	−0.777867	−	0.777867i	0.201601	−	0.979468i	$-0.435386\pi$
$661$	−19.9989	−	19.9989i	−0.777867	−	0.777867i	−0.979468	+	0.201601i	$0.935386\pi$
$662$	17.1693			0.667303
$663$		0			0
$664$	30.7072			1.19167
$665$	8.61318	+	8.61318i	0.334005	+	0.334005i
$666$	1.90539	+	19.1525i	0.0738324	+	0.742144i
$667$		−	22.3542i		−	0.865558i
$668$	−4.38772	−	4.38772i	−0.169766	−	0.169766i
$669$	13.2969	+	12.0397i	0.514086	+	0.465480i
$670$	4.88736	+	4.88736i	0.188815	+	0.188815i
$671$	23.6793	−	23.6793i	0.914128	−	0.914128i
$672$	−25.8451	+	1.28244i	−0.996995	+	0.0494711i
$673$		−	24.6690i		−	0.950918i	−0.879738	−	0.475459i	$-0.842282\pi$
$673$		−	24.6690i		−	0.950918i	0.879738	−	0.475459i	$-0.157718\pi$
$674$	4.96802	−	4.96802i	0.191361	−	0.191361i
$675$	−15.4955	+	2.32193i	−0.596422	+	0.0893710i
$676$		0			0
$677$		−	48.4537i		−	1.86223i	−0.364727	−	0.931114i	$-0.618838\pi$
$677$		−	48.4537i		−	1.86223i	0.364727	−	0.931114i	$-0.381162\pi$
$678$	−1.85977	−	1.68393i	−0.0714242	−	0.0646711i
$679$	4.83803			0.185667
$680$	−21.3432			−0.818473
$681$	0.0767908	−	0.0848094i	0.00294263	−	0.00324990i
$682$	1.40393	−	1.40393i	0.0537593	−	0.0537593i
$683$	12.9552	−	12.9552i	0.495716	−	0.495716i	−0.414385	−	0.910101i	$-0.636003\pi$
$683$	12.9552	−	12.9552i	0.495716	−	0.495716i	0.910101	+	0.414385i	$0.136003\pi$
$684$	11.1486	+	9.13103i	0.426276	+	0.349134i
$685$	6.81890			0.260537
$686$	−14.6116			−0.557875
$687$	31.6068	−	34.9073i	1.20588	−	1.33180i
$688$		−	6.34157i		−	0.241770i
$689$		0			0
$690$	−6.32663	+	0.313929i	−0.240851	+	0.0119511i
$691$	−7.31417	+	7.31417i	−0.278244	+	0.278244i	−0.832408	−	0.554164i	$-0.813038\pi$
$691$	−7.31417	+	7.31417i	−0.278244	+	0.278244i	0.554164	+	0.832408i	$0.313038\pi$
$692$		−	6.13708i		−	0.233297i
$693$	36.1560	−	3.59700i	1.37345	−	0.136639i
$694$	−6.07014	+	6.07014i	−0.230419	+	0.230419i
$695$	−11.7426	−	11.7426i	−0.445422	−	0.445422i
$696$	−19.9654	+	22.0502i	−0.756786	+	0.835811i
$697$	4.26323	+	4.26323i	0.161481	+	0.161481i
$698$			26.6412i			1.00838i
$699$	1.41762	+	28.5694i	0.0536193	+	1.08059i
$700$	7.69749	+	7.69749i	0.290938	+	0.290938i
$701$	1.23945			0.0468132			0.0234066	−	0.999726i	$-0.492549\pi$
$701$	1.23945			0.0468132			0.0234066	+	0.999726i	$0.492549\pi$
$702$		0			0
$703$	−28.4804			−1.07416
$704$	−9.41421	−	9.41421i	−0.354811	−	0.354811i
$705$	0.0416524	+	0.839424i	0.00156872	+	0.0316145i
$706$			24.6079i			0.926131i
$707$	−3.72708	−	3.72708i	−0.140171	−	0.140171i
$708$	8.29054	−	9.15625i	0.311578	−	0.344113i
$709$	−19.1156	−	19.1156i	−0.717900	−	0.717900i	0.250275	−	0.968175i	$-0.419479\pi$
$709$	−19.1156	−	19.1156i	−0.717900	−	0.717900i	−0.968175	+	0.250275i	$0.919479\pi$
$710$	7.31139	−	7.31139i	0.274392	−	0.274392i
$711$	−26.1935	+	2.60587i	−0.982332	+	0.0977277i
$712$			35.5322i			1.33163i
$713$	−1.31395	+	1.31395i	−0.0492077	+	0.0492077i
$714$	19.5573	−	0.970436i	0.731913	−	0.0363177i
$715$		0			0
$716$		−	19.8156i		−	0.740543i
$717$	30.8345	−	34.0543i	1.15154	−	1.27178i
$718$	−22.5300			−0.840812
$719$	38.1356			1.42222			0.711109	−	0.703082i	$-0.248193\pi$
$719$	38.1356			1.42222			0.711109	+	0.703082i	$0.248193\pi$
$720$	−2.73968	−	2.24389i	−0.102102	−	0.0836247i
$721$	−24.1211	+	24.1211i	−0.898318	+	0.898318i
$722$	−4.04946	+	4.04946i	−0.150705	+	0.150705i
$723$	5.48018	−	6.05243i	0.203810	−	0.225092i
$724$	1.38220			0.0513691
$725$	19.8397			0.736827
$726$	11.3539	+	10.2804i	0.421381	+	0.381540i
$727$		−	15.5870i		−	0.578091i	−0.957315	−	0.289046i	$-0.906662\pi$
$727$		−	15.5870i		−	0.578091i	0.957315	−	0.289046i	$-0.0933379\pi$
$728$		0			0
$729$	−25.8141	+	7.91395i	−0.956079	+	0.293109i
$730$	−6.50902	+	6.50902i	−0.240910	+	0.240910i
$731$			43.9271i			1.62470i
$732$	17.2675	−	0.856818i	0.638226	−	0.0316689i
$733$	0.240557	−	0.240557i	0.00888518	−	0.00888518i	−0.702650	−	0.711535i	$-0.748000\pi$
$733$	0.240557	−	0.240557i	0.00888518	−	0.00888518i	0.711535	+	0.702650i	$0.248000\pi$
$734$	−11.5178	−	11.5178i	−0.425131	−	0.425131i
$735$	−0.907451	−	0.821653i	−0.0334718	−	0.0303071i
$736$	14.0801	+	14.0801i	0.519000	+	0.519000i
$737$			30.5079i			1.12377i
$738$	−0.235718	−	2.36937i	−0.00867689	−	0.0872178i
$739$	−23.9551	−	23.9551i	−0.881204	−	0.881204i	0.112453	−	0.993657i	$-0.464129\pi$
$739$	−23.9551	−	23.9551i	−0.881204	−	0.881204i	−0.993657	+	0.112453i	$0.964129\pi$
$740$	16.7517			0.615803
$741$		0			0
$742$	4.03624			0.148175
$743$	23.3974	+	23.3974i	0.858367	+	0.858367i	0.991146	−	0.132779i	$-0.0423900\pi$
$743$	23.3974	+	23.3974i	0.858367	+	0.858367i	−0.132779	+	0.991146i	$0.542390\pi$
$744$	2.46962	−	0.122543i	0.0905405	−	0.00449264i
$745$		−	9.70335i		−	0.355503i
$746$	−7.51190	−	7.51190i	−0.275030	−	0.275030i
$747$	−27.3034	−	22.3624i	−0.998979	−	0.818197i
$748$	−27.6150	−	27.6150i	−1.00970	−	1.00970i
$749$	−13.5590	+	13.5590i	−0.495437	+	0.495437i
$750$	−0.740604	−	14.9254i	−0.0270430	−	0.545000i
$751$		−	5.37402i		−	0.196101i	−0.995181	−	0.0980503i	$-0.968739\pi$
$751$		−	5.37402i		−	0.196101i	0.995181	−	0.0980503i	$-0.0312606\pi$
$752$	0.204085	−	0.204085i	0.00744220	−	0.00744220i
$753$	1.20571	+	24.2988i	0.0439385	+	0.885497i
$754$		0			0
$755$		−	24.3164i		−	0.884963i
$756$	15.0835	+	11.1522i	0.548583	+	0.405603i
$757$	−41.6670			−1.51441			−0.757207	−	0.653175i	$-0.773437\pi$
$757$	−41.6670			−1.51441			−0.757207	+	0.653175i	$0.773437\pi$
$758$	26.5633			0.964824
$759$	−20.7259	−	18.7663i	−0.752301	−	0.681172i
$760$	−8.81950	+	8.81950i	−0.319917	+	0.319917i
$761$	−4.81729	+	4.81729i	−0.174626	+	0.174626i	−0.789009	−	0.614382i	$-0.789405\pi$
$761$	−4.81729	+	4.81729i	−0.174626	+	0.174626i	0.614382	+	0.789009i	$0.289405\pi$
$762$	−6.97978	−	6.31985i	−0.252851	−	0.228944i
$763$	7.58990			0.274773
$764$	24.2270			0.876502
$765$	18.9774	+	15.5431i	0.686128	+	0.561961i
$766$		−	12.8914i		−	0.465784i
$767$		0			0
$768$	−1.10943	−	22.3585i	−0.0400332	−	0.806793i
$769$	15.2356	−	15.2356i	0.549410	−	0.549410i	−0.376860	−	0.926270i	$-0.622996\pi$
$769$	15.2356	−	15.2356i	0.549410	−	0.549410i	0.926270	+	0.376860i	$0.122996\pi$
$770$			13.0369i			0.469816i
$771$	−1.67685	−	33.7937i	−0.0603903	−	1.21705i
$772$	2.54265	−	2.54265i	0.0915119	−	0.0915119i
$773$	1.99339	+	1.99339i	0.0716973	+	0.0716973i	0.742046	−	0.670349i	$-0.233856\pi$
$773$	1.99339	+	1.99339i	0.0716973	+	0.0716973i	−0.670349	+	0.742046i	$0.733856\pi$
$774$	10.9923	−	13.4211i	0.395110	−	0.482410i
$775$	−1.16615	−	1.16615i	−0.0418893	−	0.0418893i
$776$			4.95392i			0.177835i
$777$	−37.0280	+	1.83733i	−1.32837	+	0.0659140i
$778$	−18.9107	−	18.9107i	−0.677980	−	0.677980i
$779$	3.52334			0.126237
$780$		0			0
$781$	45.6392			1.63310
$782$	−10.6546	−	10.6546i	−0.381008	−	0.381008i
$783$	33.8103	−	5.06631i	1.20828	−	0.181055i
$784$			0.420388i			0.0150138i
$785$	13.3892	+	13.3892i	0.477879	+	0.477879i
$786$	−5.25904	−	4.76180i	−0.187584	−	0.169848i
$787$	−15.2212	−	15.2212i	−0.542576	−	0.542576i	0.381707	−	0.924283i	$-0.375336\pi$
$787$	−15.2212	−	15.2212i	−0.542576	−	0.542576i	−0.924283	+	0.381707i	$0.875336\pi$
$788$	17.8801	−	17.8801i	0.636952	−	0.636952i
$789$	2.26392	−	0.112336i	0.0805976	−	0.00399927i
$790$		−	9.44465i		−	0.336026i
$791$	3.41713	−	3.41713i	0.121499	−	0.121499i
$792$	3.68316	+	37.0221i	0.130875	+	1.31552i
$793$		0			0
$794$		−	1.01315i		−	0.0359555i
$795$	3.74815	+	3.39377i	0.132933	+	0.120365i
$796$	3.69588			0.130997
$797$	37.5528			1.33019			0.665095	−	0.746759i	$-0.268391\pi$
$797$	37.5528			1.33019			0.665095	+	0.746759i	$0.268391\pi$
$798$	7.68053	−	8.48254i	0.271888	−	0.300279i
$799$	−1.41366	+	1.41366i	−0.0500118	+	0.0500118i
$800$	−12.4963	+	12.4963i	−0.441811	+	0.441811i
$801$	25.8762	−	31.5936i	0.914292	−	1.11631i
$802$	−20.3105			−0.717189
$803$	−40.6306			−1.43382
$804$	−10.5716	+	11.6755i	−0.372832	+	0.411764i
$805$		−	12.2013i		−	0.430039i
$806$		0			0
$807$	48.9200	−	2.42742i	1.72207	−	0.0854493i
$808$	3.81636	−	3.81636i	0.134259	−	0.134259i
$809$			32.4453i			1.14072i	0.821396	+	0.570358i	$0.193196\pi$
$809$			32.4453i			1.14072i	−0.821396	+	0.570358i	$0.806804\pi$
$810$	−1.90866	−	9.49775i	−0.0670636	−	0.333717i
$811$	−26.3972	+	26.3972i	−0.926930	+	0.926930i	−0.997506	−	0.0705768i	$-0.977516\pi$
$811$	−26.3972	+	26.3972i	−0.926930	+	0.926930i	0.0705768	+	0.997506i	$0.477516\pi$
$812$	−16.7955	−	16.7955i	−0.589405	−	0.589405i
$813$	−8.26957	+	9.13310i	−0.290027	+	0.320312i
$814$	−21.5539	−	21.5539i	−0.755464	−	0.755464i
$815$		−	8.96606i		−	0.314067i
$816$	−0.417479	−	8.41348i	−0.0146147	−	0.294531i
$817$	18.1517	+	18.1517i	0.635049	+	0.635049i
$818$	7.18193			0.251110
$819$		0			0
$820$	−2.07236			−0.0723700
$821$	−13.9802	−	13.9802i	−0.487911	−	0.487911i	0.419736	−	0.907646i	$-0.362123\pi$
$821$	−13.9802	−	13.9802i	−0.487911	−	0.487911i	−0.907646	+	0.419736i	$0.862123\pi$
$822$	−0.317470	−	6.39800i	−0.0110730	−	0.223156i
$823$			2.45399i			0.0855409i	0.999085	+	0.0427704i	$0.0136184\pi$
$823$			2.45399i			0.0855409i	−0.999085	+	0.0427704i	$0.986382\pi$
$824$	−24.6989	−	24.6989i	−0.860428	−	0.860428i
$825$	16.6553	−	18.3945i	0.579864	−	0.640414i
$826$	−6.93553	−	6.93553i	−0.241318	−	0.241318i
$827$	12.7904	−	12.7904i	0.444765	−	0.444765i	−0.448845	−	0.893610i	$-0.648164\pi$
$827$	12.7904	−	12.7904i	0.444765	−	0.444765i	0.893610	+	0.448845i	$0.148164\pi$
$828$	−1.42899	−	14.3639i	−0.0496610	−	0.499179i
$829$		−	47.1067i		−	1.63608i	−0.575159	−	0.818042i	$-0.695060\pi$
$829$		−	47.1067i		−	1.63608i	0.575159	−	0.818042i	$-0.304940\pi$
$830$	8.95406	−	8.95406i	0.310800	−	0.310800i
$831$	−21.1948	+	1.05169i	−0.735238	+	0.0364827i
$832$		0			0
$833$		−	2.91196i		−	0.100894i
$834$	−10.4711	+	11.5645i	−0.362583	+	0.400445i
$835$	−6.17264			−0.213613
$836$	−22.8223			−0.789326
$837$	−2.28511	−	1.68953i	−0.0789850	−	0.0583987i
$838$	17.2237	−	17.2237i	0.594984	−	0.594984i
$839$	4.27577	−	4.27577i	0.147616	−	0.147616i	−0.629436	−	0.777052i	$-0.716714\pi$
$839$	4.27577	−	4.27577i	0.147616	−	0.147616i	0.777052	+	0.629436i	$0.216714\pi$
$840$	−10.8974	+	12.0354i	−0.375998	+	0.415260i
$841$	−14.2890			−0.492723
$842$	21.2240			0.731426
$843$	30.9484	+	28.0223i	1.06592	+	0.965138i
$844$		−	19.1811i		−	0.660242i
$845$		0			0
$846$	0.785671	−	0.0781627i	0.0270119	−	0.00268729i
$847$	−20.8615	+	20.8615i	−0.716809	+	0.716809i
$848$		−	1.73638i		−	0.0596274i
$849$	−21.3263	+	1.05821i	−0.731916	+	0.0363178i
$850$	9.45611	−	9.45611i	0.324342	−	0.324342i
$851$	20.1724	+	20.1724i	0.691503	+	0.691503i
$852$	17.4663	+	15.8149i	0.598387	+	0.541810i
$853$	13.7031	+	13.7031i	0.469185	+	0.469185i	0.901650	−	0.432466i	$-0.142356\pi$
$853$	13.7031	+	13.7031i	0.469185	+	0.469185i	−0.432466	+	0.901650i	$0.642356\pi$
$854$		−	13.7285i		−	0.469781i
$855$	14.2647	−	1.41912i	0.487841	−	0.0485330i
$856$	−13.8838	−	13.8838i	−0.474539	−	0.474539i
$857$	15.1228			0.516585			0.258292	−	0.966067i	$-0.416840\pi$
$857$	15.1228			0.516585			0.258292	+	0.966067i	$0.416840\pi$
$858$		0			0
$859$	−5.35366			−0.182665			−0.0913323	−	0.995820i	$-0.529113\pi$
$859$	−5.35366			−0.182665			−0.0913323	+	0.995820i	$0.529113\pi$
$860$	−10.6765	−	10.6765i	−0.364066	−	0.364066i
$861$	4.58076	−	0.227298i	0.156112	−	0.00774631i
$862$			3.63124i			0.123680i
$863$	18.3335	+	18.3335i	0.624080	+	0.624080i	0.946572	−	0.322492i	$-0.104521\pi$
$863$	18.3335	+	18.3335i	0.624080	+	0.624080i	−0.322492	+	0.946572i	$0.604521\pi$
$864$	−18.1048	+	24.4870i	−0.615938	+	0.833065i
$865$	−4.31683	−	4.31683i	−0.146776	−	0.146776i
$866$	1.11264	−	1.11264i	0.0378091	−	0.0378091i
$867$	1.43255	+	28.8703i	0.0486519	+	0.980487i
$868$			1.97443i			0.0670164i
$869$	29.4777	−	29.4777i	0.999963	−	0.999963i
$870$	0.607924	+	12.2515i	0.0206105	+	0.415366i
$871$		0			0
$872$			7.77170i			0.263183i
$873$	3.60767	−	4.40480i	0.122101	−	0.149080i
$874$	−8.80547			−0.297850
$875$	28.7847			0.973100
$876$	−15.5495	−	14.0794i	−0.525370	−	0.475697i
$877$	−19.7646	+	19.7646i	−0.667402	+	0.667402i	−0.957114	−	0.289712i	$-0.906440\pi$
$877$	−19.7646	+	19.7646i	−0.667402	+	0.667402i	0.289712	+	0.957114i	$0.406440\pi$
$878$	−6.95090	+	6.95090i	−0.234582	+	0.234582i
$879$	−20.1865	−	18.2778i	−0.680872	−	0.616496i
$880$	5.60842			0.189060
$881$	−21.9951			−0.741035			−0.370517	−	0.928826i	$-0.620820\pi$
$881$	−21.9951			−0.741035			−0.370517	+	0.928826i	$0.620820\pi$
$882$	−0.728687	+	0.889693i	−0.0245362	+	0.0299575i
$883$		−	11.7640i		−	0.395889i	−0.980213	−	0.197945i	$-0.936573\pi$
$883$		−	11.7640i		−	0.395889i	0.980213	−	0.197945i	$-0.0634266\pi$
$884$		0			0
$885$	−0.608943	−	12.2721i	−0.0204694	−	0.412521i
$886$	−7.78336	+	7.78336i	−0.261487	+	0.261487i
$887$		−	30.5005i		−	1.02411i	−0.858953	−	0.512054i	$-0.828885\pi$
$887$		−	30.5005i		−	1.02411i	0.858953	−	0.512054i	$-0.171115\pi$
$888$	−1.88134	−	37.9149i	−0.0631338	−	1.27234i
$889$	12.8246	−	12.8246i	0.430123	−	0.430123i
$890$	10.3610	+	10.3610i	0.347302	+	0.347302i
$891$	23.6863	−	35.6006i	0.793521	−	1.19266i
$892$	−10.3707	−	10.3707i	−0.347237	−	0.347237i
$893$			1.16832i			0.0390963i
$894$	−9.10441	+	0.451763i	−0.304497	+	0.0151092i
$895$	−13.9383	−	13.9383i	−0.465905	−	0.465905i
$896$	24.4219			0.815880
$897$		0			0
$898$	−12.5397			−0.418454
$899$	2.54446	+	2.54446i	0.0848627	+	0.0848627i
$900$	12.7481	−	1.26825i	0.424938	−	0.0422751i
$901$			12.0276i			0.400698i
$902$	2.66645	+	2.66645i	0.0887832	+	0.0887832i
$903$	24.7705	+	22.4284i	0.824309	+	0.746372i
$904$	3.49898	+	3.49898i	0.116375	+	0.116375i
$905$	0.972241	−	0.972241i	0.0323184	−	0.0323184i
$906$	−22.8154	+	1.13211i	−0.757992	+	0.0376117i
$907$		−	18.8219i		−	0.624971i	−0.949923	−	0.312485i	$-0.898838\pi$
$907$		−	18.8219i		−	0.624971i	0.949923	−	0.312485i	$-0.101162\pi$
$908$	−0.0661461	+	0.0661461i	−0.00219513	+	0.00219513i
$909$	−6.17257	+	0.614081i	−0.204731	+	0.0203678i
$910$		0			0
$911$			52.2340i			1.73059i	0.501262	+	0.865296i	$0.332869\pi$
$911$			52.2340i			1.73059i	−0.501262	+	0.865296i	$0.667131\pi$
$912$	−3.64916	−	3.30414i	−0.120836	−	0.109411i
$913$	55.8931			1.84979
$914$	−17.4285			−0.576485
$915$	11.5433	−	12.7487i	0.381609	−	0.421458i
$916$	−27.2255	+	27.2255i	−0.899556	+	0.899556i
$917$	9.66292	−	9.66292i	0.319098	−	0.319098i
$918$	13.7001	−	18.5296i	0.452172	−	0.611569i
$919$	2.88054			0.0950204			0.0475102	−	0.998871i	$-0.484871\pi$
$919$	2.88054			0.0950204			0.0475102	+	0.998871i	$0.484871\pi$
$920$	12.4936			0.411901
$921$	3.00930	−	3.32353i	0.0991596	−	0.109514i
$922$		−	22.5578i		−	0.742902i
$923$		0			0
$924$	−29.6718	+	1.47232i	−0.976129	+	0.0484357i
$925$	−17.9033	+	17.9033i	−0.588658	+	0.588658i
$926$		−	27.6755i		−	0.909473i
$927$	3.97425	+	39.9481i	0.130531	+	1.31207i
$928$	27.2662	−	27.2662i	0.895057	−	0.895057i
$929$	5.13978	+	5.13978i	0.168631	+	0.168631i	0.786377	−	0.617747i	$-0.211954\pi$
$929$	5.13978	+	5.13978i	0.168631	+	0.168631i	−0.617747	+	0.786377i	$0.711954\pi$
$930$	0.684395	−	0.755861i	0.0224422	−	0.0247857i
$931$	−1.20329	−	1.20329i	−0.0394363	−	0.0394363i
$932$		−	23.3880i		−	0.766099i
$933$	1.31200	+	26.4409i	0.0429530	+	0.865636i
$934$	7.59341	+	7.59341i	0.248464	+	0.248464i
$935$	−38.8487			−1.27049
$936$		0			0
$937$	3.76482			0.122991			0.0614957	−	0.998107i	$-0.480413\pi$
$937$	3.76482			0.122991			0.0614957	+	0.998107i	$0.480413\pi$
$938$	8.84378	+	8.84378i	0.288760	+	0.288760i
$939$	2.69588	+	54.3304i	0.0879769	+	1.77300i
$940$		−	0.687184i		−	0.0224135i
$941$	10.0291	+	10.0291i	0.326941	+	0.326941i	0.851422	−	0.524481i	$-0.175741\pi$
$941$	10.0291	+	10.0291i	0.326941	+	0.326941i	−0.524481	+	0.851422i	$0.675741\pi$
$942$	11.9393	−	13.1861i	0.389005	−	0.429625i
$943$	−2.49555	−	2.49555i	−0.0812663	−	0.0812663i
$944$	−2.98364	+	2.98364i	−0.0971093	+	0.0971093i
$945$	18.4542	−	2.76528i	0.600316	−	0.0899545i
$946$			27.4744i			0.893269i
$947$	−12.7618	+	12.7618i	−0.414703	+	0.414703i	−0.883373	−	0.468671i	$-0.844733\pi$
$947$	−12.7618	+	12.7618i	−0.414703	+	0.414703i	0.468671	+	0.883373i	$0.344733\pi$
$948$	21.4959	−	1.06663i	0.698155	−	0.0346426i
$949$		0			0
$950$		−	7.81498i		−	0.253551i
$951$	19.4239	−	21.4522i	0.629864	−	0.695635i
$952$	−38.6209			−1.25171
$953$	−56.2122			−1.82089			−0.910445	−	0.413630i	$-0.864261\pi$
$953$	−56.2122			−1.82089			−0.910445	+	0.413630i	$0.864261\pi$
$954$	3.00978	−	3.67480i	0.0974453	−	0.118976i
$955$	17.0413	−	17.0413i	0.551443	−	0.551443i
$956$	−26.5602	+	26.5602i	−0.859019	+	0.859019i
$957$	−36.3409	+	40.1357i	−1.17473	+	1.29740i
$958$	9.82300			0.317367
$959$	12.3390			0.398446
$960$	−5.06851	−	4.58929i	−0.163586	−	0.148119i
$961$			30.7009i			0.990351i
$962$		0			0
$963$	2.23401	+	22.4557i	0.0719901	+	0.723625i
$964$	−4.72051	+	4.72051i	−0.152038	+	0.152038i
$965$		−	3.57700i		−	0.115148i
$966$	−11.4482	+	0.568061i	−0.368339	+	0.0182771i
$967$	−29.9079	+	29.9079i	−0.961772	+	0.961772i	−0.999296	−	0.0375237i	$-0.988053\pi$
$967$	−29.9079	+	29.9079i	−0.961772	+	0.961772i	0.0375237	+	0.999296i	$0.488053\pi$
$968$	−21.3612	−	21.3612i	−0.686575	−	0.686575i
$969$	25.2772	+	22.8873i	0.812021	+	0.735246i
$970$	1.44454	+	1.44454i	0.0463813	+	0.0463813i
$971$		−	3.11267i		−	0.0998905i	−0.998752	−	0.0499452i	$-0.984095\pi$
$971$		−	3.11267i		−	0.0998905i	0.998752	−	0.0499452i	$-0.0159047\pi$
$972$	21.4012	−	5.41673i	0.686444	−	0.173742i
$973$	−21.2485	−	21.2485i	−0.681195	−	0.681195i
$974$	−20.7108			−0.663616
$975$		0			0
$976$	−5.90597			−0.189045
$977$	22.3521	+	22.3521i	0.715108	+	0.715108i	0.967599	−	0.252491i	$-0.0812498\pi$
$977$	22.3521	+	22.3521i	0.715108	+	0.715108i	−0.252491	+	0.967599i	$0.581250\pi$
$978$	−8.41263	+	0.417436i	−0.269006	+	0.0133481i
$979$			64.6757i			2.06704i
$980$	0.707755	+	0.707755i	0.0226084	+	0.0226084i
$981$	5.65971	−	6.91024i	0.180701	−	0.220627i
$982$	6.77593	+	6.77593i	0.216229	+	0.216229i
$983$	−19.2933	+	19.2933i	−0.615360	+	0.615360i	−0.944338	−	0.328978i	$-0.893296\pi$
$983$	−19.2933	+	19.2933i	−0.615360	+	0.615360i	0.328978	+	0.944338i	$0.393296\pi$
$984$	0.232743	+	4.69049i	0.00741957	+	0.149527i
$985$		−	25.1537i		−	0.801464i
$986$	−20.6327	+	20.6327i	−0.657078	+	0.657078i
$987$	0.0753709	+	1.51896i	0.00239908	+	0.0483489i
$988$		0			0
$989$		−	25.7135i		−	0.817641i
$990$	11.8695	+	9.72147i	0.377236	+	0.308969i
$991$	−30.3951			−0.965533			−0.482767	−	0.875749i	$-0.660368\pi$
$991$	−30.3951			−0.965533			−0.482767	+	0.875749i	$0.660368\pi$
$992$	−3.20534			−0.101770
$993$	28.8507	+	26.1229i	0.915549	+	0.828985i
$994$	13.2301	−	13.2301i	0.419634	−	0.419634i
$995$	2.59968	−	2.59968i	0.0824154	−	0.0824154i
$996$	21.3906	+	19.3681i	0.677786	+	0.613702i
$997$	39.2462			1.24294			0.621470	−	0.783438i	$-0.286536\pi$
$997$	39.2462			1.24294			0.621470	+	0.783438i	$0.286536\pi$
$998$	−6.46225			−0.204559
$999$	−25.9386	+	35.0823i	−0.820660	+	1.10995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.f.g.239.16	yes	48
3.2	odd	2	inner	507.2.f.g.239.9	✓	48
13.2	odd	12		507.2.k.k.488.15		96
13.3	even	3		507.2.k.k.188.9		96
13.4	even	6		507.2.k.k.80.10		96
13.5	odd	4	inner	507.2.f.g.437.16	yes	48
13.6	odd	12		507.2.k.k.89.10		96
13.7	odd	12		507.2.k.k.89.16		96
13.8	odd	4	inner	507.2.f.g.437.10	yes	48
13.9	even	3		507.2.k.k.80.16		96
13.10	even	6		507.2.k.k.188.15		96
13.11	odd	12		507.2.k.k.488.9		96
13.12	even	2	inner	507.2.f.g.239.10	yes	48
39.2	even	12		507.2.k.k.488.10		96
39.5	even	4	inner	507.2.f.g.437.9	yes	48
39.8	even	4	inner	507.2.f.g.437.15	yes	48
39.11	even	12		507.2.k.k.488.16		96
39.17	odd	6		507.2.k.k.80.15		96
39.20	even	12		507.2.k.k.89.9		96
39.23	odd	6		507.2.k.k.188.10		96
39.29	odd	6		507.2.k.k.188.16		96
39.32	even	12		507.2.k.k.89.15		96
39.35	odd	6		507.2.k.k.80.9		96
39.38	odd	2	inner	507.2.f.g.239.15	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.f.g.239.9	✓	48	3.2	odd	2	inner
507.2.f.g.239.10	yes	48	13.12	even	2	inner
507.2.f.g.239.15	yes	48	39.38	odd	2	inner
507.2.f.g.239.16	yes	48	1.1	even	1	trivial
507.2.f.g.437.9	yes	48	39.5	even	4	inner
507.2.f.g.437.10	yes	48	13.8	odd	4	inner
507.2.f.g.437.15	yes	48	39.8	even	4	inner
507.2.f.g.437.16	yes	48	13.5	odd	4	inner
507.2.k.k.80.9		96	39.35	odd	6
507.2.k.k.80.10		96	13.4	even	6
507.2.k.k.80.15		96	39.17	odd	6
507.2.k.k.80.16		96	13.9	even	3
507.2.k.k.89.9		96	39.20	even	12
507.2.k.k.89.10		96	13.6	odd	12
507.2.k.k.89.15		96	39.32	even	12
507.2.k.k.89.16		96	13.7	odd	12
507.2.k.k.188.9		96	13.3	even	3
507.2.k.k.188.10		96	39.23	odd	6
507.2.k.k.188.15		96	13.10	even	6
507.2.k.k.188.16		96	39.29	odd	6
507.2.k.k.488.9		96	13.11	odd	12
507.2.k.k.488.10		96	39.2	even	12
507.2.k.k.488.15		96	13.2	odd	12
507.2.k.k.488.16		96	39.11	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540287 + 0.540287i) q^{2} +(0.0858391 + 1.72992i) q^{3} -1.41618i q^{4} +(-0.996141 - 0.996141i) q^{5} +(-0.888277 + 0.981032i) q^{6} +(-1.80254 - 1.80254i) q^{7} +(1.84572 - 1.84572i) q^{8} +(-2.98526 + 0.296990i) q^{9} +O(q^{10})\)	\(q+(0.540287 + 0.540287i) q^{2} +(0.0858391 + 1.72992i) q^{3} -1.41618i q^{4} +(-0.996141 - 0.996141i) q^{5} +(-0.888277 + 0.981032i) q^{6} +(-1.80254 - 1.80254i) q^{7} +(1.84572 - 1.84572i) q^{8} +(-2.98526 + 0.296990i) q^{9} -1.07640i q^{10} +(3.35957 - 3.35957i) q^{11} +(2.44988 - 0.121564i) q^{12} -1.94778i q^{14} +(1.63774 - 1.80876i) q^{15} -0.837927 q^{16} +5.80420 q^{17} +(-1.77336 - 1.45244i) q^{18} +(2.39843 - 2.39843i) q^{19} +(-1.41072 + 1.41072i) q^{20} +(2.96353 - 3.27298i) q^{21} +3.63026 q^{22} -3.39759 q^{23} +(3.35138 + 3.03451i) q^{24} -3.01541i q^{25} +(-0.770022 - 5.13878i) q^{27} +(-2.55272 + 2.55272i) q^{28} +6.57944i q^{29} +(1.86210 - 0.0923975i) q^{30} +(0.386730 - 0.386730i) q^{31} +(-4.14416 - 4.14416i) q^{32} +(6.10017 + 5.52341i) q^{33} +(3.13593 + 3.13593i) q^{34} +3.59117i q^{35} +(0.420591 + 4.22767i) q^{36} +(-5.93729 - 5.93729i) q^{37} +2.59169 q^{38} -3.67719 q^{40} +(0.734507 + 0.734507i) q^{41} +(3.36950 - 0.167195i) q^{42} +7.56816i q^{43} +(-4.75775 - 4.75775i) q^{44} +(3.26959 + 2.67790i) q^{45} +(-1.83567 - 1.83567i) q^{46} +(-0.243559 + 0.243559i) q^{47} +(-0.0719269 - 1.44955i) q^{48} -0.501699i q^{49} +(1.62918 - 1.62918i) q^{50} +(0.498228 + 10.0408i) q^{51} +2.07223i q^{53} +(2.36038 - 3.19245i) q^{54} -6.69321 q^{55} -6.65396 q^{56} +(4.35499 + 3.94323i) q^{57} +(-3.55478 + 3.55478i) q^{58} +(3.56074 - 3.56074i) q^{59} +(-2.56152 - 2.31933i) q^{60} +7.04831 q^{61} +0.417890 q^{62} +(5.91639 + 4.84572i) q^{63} -2.80221i q^{64} +(0.311618 + 6.28007i) q^{66} +(-4.54045 + 4.54045i) q^{67} -8.21980i q^{68} +(-0.291646 - 5.87756i) q^{69} +(-1.94026 + 1.94026i) q^{70} +(6.79242 + 6.79242i) q^{71} +(-4.96179 + 6.05811i) q^{72} +(-6.04700 - 6.04700i) q^{73} -6.41568i q^{74} +(5.21642 - 0.258840i) q^{75} +(-3.39662 - 3.39662i) q^{76} -12.1115 q^{77} +8.77426 q^{79} +(0.834694 + 0.834694i) q^{80} +(8.82359 - 1.77319i) q^{81} +0.793689i q^{82} +(8.31849 + 8.31849i) q^{83} +(-4.63513 - 4.19689i) q^{84} +(-5.78181 - 5.78181i) q^{85} +(-4.08898 + 4.08898i) q^{86} +(-11.3819 + 0.564773i) q^{87} -12.4016i q^{88} +(-9.62559 + 9.62559i) q^{89} +(0.319681 + 3.21335i) q^{90} +4.81159i q^{92} +(0.702209 + 0.635816i) q^{93} -0.263183 q^{94} -4.77836 q^{95} +(6.81334 - 7.52480i) q^{96} +(-1.34200 + 1.34200i) q^{97} +(0.271062 - 0.271062i) q^{98} +(-9.03143 + 11.0270i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{9}+O(q^{10}) \) 48 * q - 24 * q^9	\( 48 q - 24 q^{9} - 8 q^{16} + 112 q^{22} - 84 q^{27} + 128 q^{40} - 56 q^{42} - 188 q^{48} + 8 q^{55} + 56 q^{61} - 92 q^{66} - 72 q^{81} - 112 q^{87} + 296 q^{94}+O(q^{100}) \) 48 * q - 24 * q^9 - 8 * q^16 + 112 * q^22 - 84 * q^27 + 128 * q^40 - 56 * q^42 - 188 * q^48 + 8 * q^55 + 56 * q^61 - 92 * q^66 - 72 * q^81 - 112 * q^87 + 296 * q^94

Introduction

L-functions

Modular forms

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