LMFDB - Embedded newform 931.2.o.i.227.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(227,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("931.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.o (of order $6$, degree $2$, not 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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			227.27
Character	$\chi$	$=$	931.227
Dual form			931.2.o.i.607.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.774359 - 0.447076i) q^{2} +(-0.525649 + 0.910452i) q^{3} +(-0.600246 + 1.03966i) q^{4} +(0.249238 - 0.143898i) q^{5} +0.940021i q^{6} +2.86173i q^{8} +(0.947385 + 1.64092i) q^{9} +O(q^{10})$	\(q+(0.774359 - 0.447076i) q^{2} +(-0.525649 + 0.910452i) q^{3} +(-0.600246 + 1.03966i) q^{4} +(0.249238 - 0.143898i) q^{5} +0.940021i q^{6} +2.86173i q^{8} +(0.947385 + 1.64092i) q^{9} +(0.128667 - 0.222857i) q^{10} +(0.238323 - 0.412787i) q^{11} +(-0.631038 - 1.09299i) q^{12} +6.36831 q^{13} +0.302559i q^{15} +(0.0789186 + 0.136691i) q^{16} +(-5.00633 - 2.89040i) q^{17} +(1.46723 + 0.847107i) q^{18} +(-4.33069 - 0.495065i) q^{19} +0.345496i q^{20} -0.426194i q^{22} +(3.26497 + 5.65510i) q^{23} +(-2.60546 - 1.50427i) q^{24} +(-2.45859 + 4.25840i) q^{25} +(4.93136 - 2.84712i) q^{26} -5.14587 q^{27} +5.71402i q^{29} +(0.135267 + 0.234290i) q^{30} +(-2.16608 + 3.75176i) q^{31} +(-4.83443 - 2.79116i) q^{32} +(0.250549 + 0.433963i) q^{33} -5.16892 q^{34} -2.27466 q^{36} +(1.21914 - 0.703868i) q^{37} +(-3.57484 + 1.55279i) q^{38} +(-3.34750 + 5.79804i) q^{39} +(0.411797 + 0.713253i) q^{40} +7.44541 q^{41} -7.20284 q^{43} +(0.286105 + 0.495548i) q^{44} +(0.472250 + 0.272654i) q^{45} +(5.05652 + 2.91938i) q^{46} +(-3.58484 + 2.06971i) q^{47} -0.165934 q^{48} +4.39670i q^{50} +(5.26314 - 3.03868i) q^{51} +(-3.82255 + 6.62086i) q^{52} +(7.21467 + 4.16539i) q^{53} +(-3.98475 + 2.30059i) q^{54} -0.137177i q^{55} +(2.72716 - 3.68266i) q^{57} +(2.55460 + 4.42470i) q^{58} +(0.962041 - 1.66630i) q^{59} +(-0.314558 - 0.181610i) q^{60} +(-2.27164 + 1.31153i) q^{61} +3.87361i q^{62} -5.30712 q^{64} +(1.58723 - 0.916387i) q^{65} +(0.388029 + 0.224029i) q^{66} +(5.71986 + 3.30237i) q^{67} +(6.01005 - 3.46990i) q^{68} -6.86493 q^{69} -12.2159i q^{71} +(-4.69586 + 2.71116i) q^{72} +(-1.13940 - 0.657835i) q^{73} +(0.629365 - 1.09009i) q^{74} +(-2.58471 - 4.47685i) q^{75} +(3.11418 - 4.20527i) q^{76} +5.98635i q^{78} +(10.3899 - 5.99859i) q^{79} +(0.0393391 + 0.0227124i) q^{80} +(-0.137233 + 0.237695i) q^{81} +(5.76541 - 3.32866i) q^{82} -0.627610i q^{83} -1.66369 q^{85} +(-5.57758 + 3.22022i) q^{86} +(-5.20234 - 3.00357i) q^{87} +(1.18128 + 0.682015i) q^{88} +(-0.774284 - 1.34110i) q^{89} +0.487588 q^{90} -7.83915 q^{92} +(-2.27719 - 3.94422i) q^{93} +(-1.85064 + 3.20540i) q^{94} +(-1.15061 + 0.499789i) q^{95} +(5.08244 - 2.93435i) q^{96} +1.36169 q^{97} +0.903134 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 40 q^{4} - 40 q^{9}+O(q^{10}) $ 80 * q + 40 * q^4 - 40 * q^9	$ 80 q + 40 q^{4} - 40 q^{9} - 40 q^{16} - 48 q^{23} + 56 q^{25} + 64 q^{30} - 80 q^{36} - 32 q^{39} - 32 q^{43} - 96 q^{57} + 96 q^{58} + 112 q^{64} - 144 q^{74} + 88 q^{81} - 320 q^{85} - 96 q^{92} - 72 q^{95} - 96 q^{99}+O(q^{100}) $ 80 * q + 40 * q^4 - 40 * q^9 - 40 * q^16 - 48 * q^23 + 56 * q^25 + 64 * q^30 - 80 * q^36 - 32 * q^39 - 32 * q^43 - 96 * q^57 + 96 * q^58 + 112 * q^64 - 144 * q^74 + 88 * q^81 - 320 * q^85 - 96 * q^92 - 72 * q^95 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.774359	−	0.447076i	0.547554	−	0.316131i	−0.200581	−	0.979677i	$-0.564283\pi$
$2$	0.774359	−	0.447076i	0.547554	−	0.316131i	0.748135	+	0.663547i	$0.230950\pi$
$3$	−0.525649	+	0.910452i	−0.303484	+	0.525649i	−0.976923	−	0.213594i	$-0.931483\pi$
$3$	−0.525649	+	0.910452i	−0.303484	+	0.525649i	0.673439	+	0.739243i	$0.264817\pi$
$4$	−0.600246	+	1.03966i	−0.300123	+	0.519828i
$5$	0.249238	−	0.143898i	0.111463	−	0.0643531i	−0.443232	−	0.896407i	$-0.646168\pi$
$5$	0.249238	−	0.143898i	0.111463	−	0.0643531i	0.554695	+	0.832054i	$0.312835\pi$
$6$			0.940021i			0.383762i
$7$		0			0
$7$		0			0
$8$			2.86173i			1.01177i
$9$	0.947385	+	1.64092i	0.315795	+	0.546973i
$10$	0.128667	−	0.222857i	0.0406880	−	0.0704736i
$11$	0.238323	−	0.412787i	0.0718570	−	0.124460i	−0.827858	−	0.560937i	$-0.810441\pi$
$11$	0.238323	−	0.412787i	0.0718570	−	0.124460i	0.899715	+	0.436477i	$0.143774\pi$
$12$	−0.631038	−	1.09299i	−0.182165	−	0.315519i
$13$	6.36831			1.76625			0.883126	−	0.469135i	$-0.155434\pi$
$13$	6.36831			1.76625			0.883126	+	0.469135i	$0.155434\pi$
$14$		0			0
$15$			0.302559i			0.0781205i
$16$	0.0789186	+	0.136691i	0.0197297	+	0.0341728i
$17$	−5.00633	−	2.89040i	−1.21421	−	0.701026i	−0.250538	−	0.968107i	$-0.580608\pi$
$17$	−5.00633	−	2.89040i	−1.21421	−	0.701026i	−0.963674	+	0.267081i	$0.913941\pi$
$18$	1.46723	+	0.847107i	0.345830	+	0.199665i
$19$	−4.33069	−	0.495065i	−0.993529	−	0.113576i
$19$	−4.33069	−	0.495065i	−0.993529	−	0.113576i
$20$			0.345496i			0.0772553i
$21$		0			0
$22$		−	0.426194i		−	0.0908648i
$23$	3.26497	+	5.65510i	0.680794	+	1.17917i	0.974739	+	0.223347i	$0.0716984\pi$
$23$	3.26497	+	5.65510i	0.680794	+	1.17917i	−0.293945	+	0.955822i	$0.594968\pi$
$24$	−2.60546	−	1.50427i	−0.531838	−	0.307057i
$25$	−2.45859	+	4.25840i	−0.491717	+	0.851679i
$26$	4.93136	−	2.84712i	0.967119	−	0.558367i
$27$	−5.14587			−0.990323
$28$		0			0
$29$			5.71402i			1.06107i	0.847664	+	0.530534i	$0.178008\pi$
$29$			5.71402i			1.06107i	−0.847664	+	0.530534i	$0.821992\pi$
$30$	0.135267	+	0.234290i	0.0246963	+	0.0427752i
$31$	−2.16608	+	3.75176i	−0.389039	+	0.673835i	−0.992321	−	0.123693i	$-0.960526\pi$
$31$	−2.16608	+	3.75176i	−0.389039	+	0.673835i	0.603282	+	0.797528i	$0.293859\pi$
$32$	−4.83443	−	2.79116i	−0.854615	−	0.493412i
$33$	0.250549	+	0.433963i	0.0436149	+	0.0755432i
$34$	−5.16892			−0.886463
$35$		0			0
$36$	−2.27466			−0.379109
$37$	1.21914	−	0.703868i	0.200425	−	0.115715i	−0.396429	−	0.918065i	$-0.629751\pi$
$37$	1.21914	−	0.703868i	0.200425	−	0.115715i	0.596854	+	0.802350i	$0.296417\pi$
$38$	−3.57484	+	1.55279i	−0.579916	+	0.251896i
$39$	−3.34750	+	5.79804i	−0.536029	+	0.928430i
$40$	0.411797	+	0.713253i	0.0651108	+	0.112775i
$41$	7.44541			1.16278			0.581389	−	0.813626i	$-0.302510\pi$
$41$	7.44541			1.16278			0.581389	+	0.813626i	$0.302510\pi$
$42$		0			0
$43$	−7.20284			−1.09842			−0.549212	−	0.835683i	$-0.685072\pi$
$43$	−7.20284			−1.09842			−0.549212	+	0.835683i	$0.685072\pi$
$44$	0.286105	+	0.495548i	0.0431319	+	0.0747066i
$45$	0.472250	+	0.272654i	0.0703988	+	0.0406448i
$46$	5.05652	+	2.91938i	0.745543	+	0.430440i
$47$	−3.58484	+	2.06971i	−0.522903	+	0.301898i	−0.738122	−	0.674668i	$-0.764287\pi$
$47$	−3.58484	+	2.06971i	−0.522903	+	0.301898i	0.215218	+	0.976566i	$0.430954\pi$
$48$	−0.165934			−0.0239505
$49$		0			0
$50$			4.39670i			0.621788i
$51$	5.26314	−	3.03868i	0.736988	−	0.425500i
$52$	−3.82255	+	6.62086i	−0.530093	+	0.918148i
$53$	7.21467	+	4.16539i	0.991011	+	0.572161i	0.905576	−	0.424183i	$-0.139439\pi$
$53$	7.21467	+	4.16539i	0.991011	+	0.572161i	0.0854348	+	0.996344i	$0.472772\pi$
$54$	−3.98475	+	2.30059i	−0.542255	+	0.313071i
$55$		−	0.137177i		−	0.0184969i
$56$		0			0
$57$	2.72716	−	3.68266i	0.361221	−	0.487780i
$58$	2.55460	+	4.42470i	0.335436	+	0.580992i
$59$	0.962041	−	1.66630i	0.125247	−	0.216934i	−0.796582	−	0.604530i	$-0.793361\pi$
$59$	0.962041	−	1.66630i	0.125247	−	0.216934i	0.921830	+	0.387596i	$0.126694\pi$
$60$	−0.314558	−	0.181610i	−0.0406092	−	0.0234458i
$61$	−2.27164	+	1.31153i	−0.290853	+	0.167924i	−0.638327	−	0.769766i	$-0.720373\pi$
$61$	−2.27164	+	1.31153i	−0.290853	+	0.167924i	0.347473	+	0.937690i	$0.387040\pi$
$62$			3.87361i			0.491948i
$63$		0			0
$64$	−5.30712			−0.663390
$65$	1.58723	−	0.916387i	0.196872	−	0.113664i
$66$	0.388029	+	0.224029i	0.0477631	+	0.0275760i
$67$	5.71986	+	3.30237i	0.698793	+	0.403448i	0.806898	−	0.590691i	$-0.201145\pi$
$67$	5.71986	+	3.30237i	0.698793	+	0.403448i	−0.108105	+	0.994139i	$0.534478\pi$
$68$	6.01005	−	3.46990i	0.728826	−	0.420788i
$69$	−6.86493			−0.826440
$70$		0			0
$71$		−	12.2159i		−	1.44976i	−0.688875	−	0.724880i	$-0.741895\pi$
$71$		−	12.2159i		−	1.44976i	0.688875	−	0.724880i	$-0.258105\pi$
$72$	−4.69586	+	2.71116i	−0.553413	+	0.319513i
$73$	−1.13940	−	0.657835i	−0.133357	−	0.0769937i	0.431837	−	0.901952i	$-0.357865\pi$
$73$	−1.13940	−	0.657835i	−0.133357	−	0.0769937i	−0.565194	+	0.824958i	$0.691199\pi$
$74$	0.629365	−	1.09009i	0.0731622	−	0.126721i
$75$	−2.58471	−	4.47685i	−0.298457	−	0.516942i
$76$	3.11418	−	4.20527i	0.357221	−	0.482378i
$77$		0			0
$78$			5.98635i			0.677821i
$79$	10.3899	−	5.99859i	1.16895	−	0.674895i	0.215519	−	0.976500i	$-0.430856\pi$
$79$	10.3899	−	5.99859i	1.16895	−	0.674895i	0.953433	+	0.301605i	$0.0975224\pi$
$80$	0.0393391	+	0.0227124i	0.00439825	+	0.00253933i
$81$	−0.137233	+	0.237695i	−0.0152481	+	0.0264106i
$82$	5.76541	−	3.32866i	0.636684	−	0.367589i
$83$		−	0.627610i		−	0.0688892i	−0.999407	−	0.0344446i	$-0.989034\pi$
$83$		−	0.627610i		−	0.0688892i	0.999407	−	0.0344446i	$-0.0109662\pi$
$84$		0			0
$85$	−1.66369			−0.180453
$86$	−5.57758	+	3.22022i	−0.601446	+	0.347245i
$87$	−5.20234	−	3.00357i	−0.557750	−	0.322017i
$88$	1.18128	+	0.682015i	0.125925	+	0.0727030i
$89$	−0.774284	−	1.34110i	−0.0820739	−	0.142156i	0.822067	−	0.569391i	$-0.192821\pi$
$89$	−0.774284	−	1.34110i	−0.0820739	−	0.142156i	−0.904141	+	0.427235i	$0.859488\pi$
$90$	0.487588			0.0513962
$91$		0			0
$92$	−7.83915			−0.817287
$93$	−2.27719	−	3.94422i	−0.236134	−	0.408996i
$94$	−1.85064	+	3.20540i	−0.190879	+	0.330611i
$95$	−1.15061	+	0.499789i	−0.118051	+	0.0512772i
$96$	5.08244	−	2.93435i	0.518724	−	0.299485i
$97$	1.36169			0.138258			0.0691291	−	0.997608i	$-0.477978\pi$
$97$	1.36169			0.138258			0.0691291	+	0.997608i	$0.477978\pi$
$98$		0			0
$99$	0.903134			0.0907684
$100$	−2.95151	−	5.11217i	−0.295151	−	0.511217i
$101$	2.89060	+	1.66889i	0.287626	+	0.166061i	0.636871	−	0.770971i	$-0.280229\pi$
$101$	2.89060	+	1.66889i	0.287626	+	0.166061i	−0.349245	+	0.937031i	$0.613562\pi$
$102$	2.71704	−	4.70605i	0.269027	−	0.465969i
$103$	6.85954	+	11.8811i	0.675891	+	1.17068i	0.976208	+	0.216838i	$0.0695743\pi$
$103$	6.85954	+	11.8811i	0.675891	+	1.17068i	−0.300317	+	0.953840i	$0.597092\pi$
$104$			18.2244i			1.78705i
$105$		0			0
$106$	7.44899			0.723510
$107$	−5.34029	+	3.08322i	−0.516266	+	0.298066i	−0.735405	−	0.677627i	$-0.763008\pi$
$107$	−5.34029	+	3.08322i	−0.516266	+	0.298066i	0.219140	+	0.975693i	$0.429675\pi$
$108$	3.08878	−	5.34993i	0.297218	−	0.514797i
$109$	−11.2274	−	6.48217i	−1.07539	−	0.620879i	−0.145744	−	0.989322i	$-0.546558\pi$
$109$	−11.2274	−	6.48217i	−1.07539	−	0.620879i	−0.929650	+	0.368443i	$0.879891\pi$
$110$	−0.0613284	−	0.106224i	−0.00584743	−	0.0101281i
$111$			1.47995i			0.140471i
$112$		0			0
$113$		−	18.6883i		−	1.75804i	−0.476781	−	0.879022i	$-0.658197\pi$
$113$		−	18.6883i		−	1.75804i	0.476781	−	0.879022i	$-0.341803\pi$
$114$	0.465372	−	4.07095i	0.0435861	−	0.381279i
$115$	1.62751	+	0.939646i	0.151766	+	0.0876224i
$116$	−5.94062	−	3.42982i	−0.551573	−	0.318451i
$117$	6.03325	+	10.4499i	0.557774	+	0.966093i
$118$		−	1.72042i		−	0.158378i
$119$		0			0
$120$	−0.865843			−0.0790403
$121$	5.38640	+	9.32953i	0.489673	+	0.848139i
$122$	−1.17271	+	2.03119i	−0.106172	+	0.183895i
$123$	−3.91367	+	6.77868i	−0.352884	+	0.611213i
$124$	−2.60036	−	4.50395i	−0.233519	−	0.404467i
$125$			2.85412i			0.255280i
$126$		0			0
$127$			11.3013i			1.00282i	0.865209	+	0.501412i	$0.167186\pi$
$127$			11.3013i			1.00282i	−0.865209	+	0.501412i	$0.832814\pi$
$128$	5.55925	−	3.20964i	0.491373	−	0.283694i
$129$	3.78617	−	6.55784i	0.333354	−	0.577386i
$130$	0.819390	−	1.41922i	0.0718652	−	0.124474i
$131$	−0.115008	+	0.0663996i	−0.0100483	+	0.00580136i	−0.505016	−	0.863110i	$-0.668513\pi$
$131$	−0.115008	+	0.0663996i	−0.0100483	+	0.00580136i	0.494967	+	0.868912i	$0.335180\pi$
$132$	−0.601563			−0.0523593
$133$		0			0
$134$	5.90564			0.510169
$135$	−1.28255	+	0.740480i	−0.110384	+	0.0637303i
$136$	8.27155	−	14.3267i	0.709279	−	1.22851i
$137$	9.55102	−	16.5429i	0.815999	−	1.41335i	−0.0926095	−	0.995703i	$-0.529521\pi$
$137$	9.55102	−	16.5429i	0.815999	−	1.41335i	0.908608	−	0.417649i	$-0.137146\pi$
$138$	−5.31592	+	3.06915i	−0.452521	+	0.261263i
$139$		−	17.9635i		−	1.52365i	−0.647786	−	0.761823i	$-0.724305\pi$
$139$		−	17.9635i		−	1.52365i	0.647786	−	0.761823i	$-0.275695\pi$
$140$		0			0
$141$		−	4.35177i		−	0.366485i
$142$	−5.46144	−	9.45949i	−0.458314	−	0.793822i
$143$	1.51771	−	2.62876i	0.126918	−	0.219828i
$144$	−0.149533	+	0.258998i	−0.0124611	+	0.0215832i
$145$	0.822236	+	1.42415i	0.0682830	+	0.118270i
$146$	−1.17641			−0.0973603
$147$		0			0
$148$			1.68998i			0.138915i
$149$	2.78010	+	4.81528i	0.227755	+	0.394483i	0.957142	−	0.289618i	$-0.0935282\pi$
$149$	2.78010	+	4.81528i	0.227755	+	0.394483i	−0.729387	+	0.684101i	$0.760195\pi$
$150$	−4.00298	−	2.31112i	−0.326842	−	0.188703i
$151$	8.43878	+	4.87213i	0.686738	+	0.396488i	0.802389	−	0.596801i	$-0.203562\pi$
$151$	8.43878	+	4.87213i	0.686738	+	0.396488i	−0.115651	+	0.993290i	$0.536895\pi$
$152$	1.41674	−	12.3933i	0.114913	−	1.00523i
$153$		−	10.9533i		−	0.885522i
$154$		0			0
$155$			1.24678i			0.100143i
$156$	−4.01865	−	6.96050i	−0.321749	−	0.557286i
$157$	19.8601	+	11.4662i	1.58501	+	0.915106i	0.994112	+	0.108360i	$0.0345598\pi$
$157$	19.8601	+	11.4662i	1.58501	+	0.915106i	0.590898	+	0.806746i	$0.298774\pi$
$158$	5.36366	−	9.29013i	0.426710	−	0.739083i
$159$	−7.58478	+	4.37907i	−0.601512	+	0.347283i
$160$	−1.60657			−0.127010
$161$		0			0
$162$			0.245415i			0.0192816i
$163$	−5.38555	−	9.32805i	−0.421829	−	0.730629i	0.574289	−	0.818652i	$-0.305278\pi$
$163$	−5.38555	−	9.32805i	−0.421829	−	0.730629i	−0.996118	+	0.0880231i	$0.971945\pi$
$164$	−4.46907	+	7.74066i	−0.348976	+	0.604444i
$165$	0.124893	+	0.0721068i	0.00972288	+	0.00561351i
$166$	−0.280590	−	0.485996i	−0.0217780	−	0.0377206i
$167$	11.0372			0.854081			0.427041	−	0.904232i	$-0.359556\pi$
$167$	11.0372			0.854081			0.427041	+	0.904232i	$0.359556\pi$
$168$		0			0
$169$	27.5554			2.11965
$170$	−1.28829	+	0.743797i	−0.0988077	+	0.0570466i
$171$	−3.29047	−	7.57534i	−0.251629	−	0.579300i
$172$	4.32348	−	7.48848i	0.329662	−	0.570991i
$173$	4.07400	+	7.05638i	0.309741	+	0.536487i	0.978306	−	0.207167i	$-0.0664244\pi$
$173$	4.07400	+	7.05638i	0.309741	+	0.536487i	−0.668565	+	0.743654i	$0.733091\pi$
$174$	−5.37131			−0.407198
$175$		0			0
$176$	0.0752324			0.00567086
$177$	1.01139	+	1.75178i	0.0760210	+	0.131672i
$178$	−1.19915	−	0.692328i	−0.0898799	−	0.0518922i
$179$	−8.52516	−	4.92200i	−0.637200	−	0.367888i	0.146335	−	0.989235i	$-0.453252\pi$
$179$	−8.52516	−	4.92200i	−0.637200	−	0.367888i	−0.783535	+	0.621347i	$0.786586\pi$
$180$	−0.566932	+	0.327318i	−0.0422566	+	0.0243969i
$181$	3.29904			0.245216			0.122608	−	0.992455i	$-0.460874\pi$
$181$	3.29904			0.245216			0.122608	+	0.992455i	$0.460874\pi$
$182$		0			0
$183$		−	2.75762i		−	0.203849i
$184$	−16.1834	+	9.34346i	−1.19305	+	0.688809i
$185$	0.202570	−	0.350862i	0.0148933	−	0.0257959i
$186$	−3.52673	−	2.03616i	−0.258592	−	0.149298i
$187$	−2.38624	+	1.37770i	−0.174499	+	0.100747i
$188$		−	4.96934i		−	0.362426i
$189$		0			0
$190$	−0.667545	+	0.901428i	−0.0484288	+	0.0653965i
$191$	−5.65674	−	9.79777i	−0.409308	−	0.708941i	0.585505	−	0.810669i	$-0.300896\pi$
$191$	−5.65674	−	9.79777i	−0.409308	−	0.708941i	−0.994812	+	0.101728i	$0.967563\pi$
$192$	2.78969	−	4.83188i	0.201328	−	0.348711i
$193$	13.1534	+	7.59411i	0.946801	+	0.546636i	0.892086	−	0.451866i	$-0.149241\pi$
$193$	13.1534	+	7.59411i	0.946801	+	0.546636i	0.0547156	+	0.998502i	$0.482575\pi$
$194$	1.05443	−	0.608777i	0.0757039	−	0.0437077i
$195$			1.92679i			0.137981i
$196$		0			0
$197$	10.6450			0.758428			0.379214	−	0.925309i	$-0.376195\pi$
$197$	10.6450			0.758428			0.379214	+	0.925309i	$0.376195\pi$
$198$	0.699350	−	0.403770i	0.0497006	−	0.0286947i
$199$	16.0416	+	9.26165i	1.13716	+	0.656541i	0.945726	−	0.324964i	$-0.105352\pi$
$199$	16.0416	+	9.26165i	1.13716	+	0.656541i	0.191436	+	0.981505i	$0.438686\pi$
$200$	−12.1864	−	7.03580i	−0.861707	−	0.497507i
$201$	−6.01329	+	3.47177i	−0.424145	+	0.244880i
$202$	2.98448			0.209988
$203$		0			0
$204$			7.29581i			0.510809i
$205$	1.85568	−	1.07138i	0.129606	−	0.0748283i
$206$	10.6235	+	6.13348i	0.740174	+	0.427340i
$207$	−6.18637	+	10.7151i	−0.429983	+	0.744752i
$208$	0.502579	+	0.870492i	0.0348476	+	0.0603577i
$209$	−1.23646	+	1.66967i	−0.0855277	+	0.115494i
$210$		0			0
$211$			6.64234i			0.457277i	0.973511	+	0.228639i	$0.0734274\pi$
$211$			6.64234i			0.457277i	−0.973511	+	0.228639i	$0.926573\pi$
$212$	−8.66115	+	5.00052i	−0.594850	+	0.343437i
$213$	11.1220	+	6.42128i	0.762066	+	0.439979i
$214$	−2.75687	+	4.77504i	−0.188456	+	0.326415i
$215$	−1.79523	+	1.03647i	−0.122433	+	0.0706869i
$216$		−	14.7261i		−	1.00198i
$217$		0			0
$218$	−11.5921			−0.785115
$219$	1.19785	−	0.691581i	0.0809434	−	0.0467327i
$220$	0.142617	+	0.0823397i	0.00961520	+	0.00555134i
$221$	−31.8819	−	18.4070i	−2.14461	−	1.23819i
$222$	0.661651	+	1.14601i	0.0444071	+	0.0769154i
$223$	−26.9969			−1.80785			−0.903924	−	0.427692i	$-0.859327\pi$
$223$	−26.9969			−1.80785			−0.903924	+	0.427692i	$0.859327\pi$
$224$		0			0
$225$	−9.31692			−0.621128
$226$	−8.35508	−	14.4714i	−0.555772	−	0.962625i
$227$	10.9921	−	19.0388i	0.729570	−	1.26365i	−0.227496	−	0.973779i	$-0.573054\pi$
$227$	10.9921	−	19.0388i	0.729570	−	1.26365i	0.957065	−	0.289873i	$-0.0936129\pi$
$228$	2.19173	+	5.04581i	0.145151	+	0.334167i
$229$	8.35773	−	4.82534i	0.552294	−	0.318867i	−0.197753	−	0.980252i	$-0.563364\pi$
$229$	8.35773	−	4.82534i	0.552294	−	0.318867i	0.750047	+	0.661385i	$0.230031\pi$
$230$	1.68037			0.110801
$231$		0			0
$232$	−16.3520			−1.07356
$233$	5.06082	+	8.76559i	0.331545	+	0.574253i	0.982815	−	0.184593i	$-0.0590967\pi$
$233$	5.06082	+	8.76559i	0.331545	+	0.574253i	−0.651270	+	0.758846i	$0.725763\pi$
$234$	9.34380	+	5.39464i	0.610823	+	0.352659i
$235$	−0.595654	+	1.03170i	−0.0388562	+	0.0673009i
$236$	1.15492	+	2.00038i	0.0751790	+	0.130214i
$237$			12.6126i			0.819279i
$238$		0			0
$239$	26.4382			1.71014			0.855072	−	0.518509i	$-0.173513\pi$
$239$	26.4382			1.71014			0.855072	+	0.518509i	$0.173513\pi$
$240$	−0.0413572	+	0.0238776i	−0.00266959	+	0.00154129i
$241$	−2.87291	+	4.97603i	−0.185060	+	0.320534i	−0.943597	−	0.331097i	$-0.892581\pi$
$241$	−2.87291	+	4.97603i	−0.185060	+	0.320534i	0.758536	+	0.651631i	$0.225915\pi$
$242$	8.34202	+	4.81627i	0.536245	+	0.309601i
$243$	−7.86307	−	13.6192i	−0.504416	−	0.873675i
$244$		−	3.14896i		−	0.201592i
$245$		0			0
$246$			6.99884i			0.446230i
$247$	−27.5792	−	3.15273i	−1.75482	−	0.200603i
$248$	−10.7365	−	6.19872i	−0.681768	−	0.393619i
$249$	0.571409	+	0.329903i	0.0362116	+	0.0209068i
$250$	1.27601	+	2.21011i	0.0807019	+	0.139780i
$251$			5.77064i			0.364240i	0.983276	+	0.182120i	$0.0582959\pi$
$251$			5.77064i			0.364240i	−0.983276	+	0.182120i	$0.941704\pi$
$252$		0			0
$253$	3.11247			0.195679
$254$	5.05252	+	8.75123i	0.317023	+	0.549101i
$255$	0.874519	−	1.51471i	0.0547645	−	0.0948549i
$256$	8.17703	−	14.1630i	0.511064	−	0.885189i
$257$	−11.4760	−	19.8769i	−0.715851	−	1.23989i	−0.962631	−	0.270818i	$-0.912706\pi$
$257$	−11.4760	−	19.8769i	−0.715851	−	1.23989i	0.246780	−	0.969072i	$-0.420627\pi$
$258$		−	6.77083i		−	0.421533i
$259$		0			0
$260$			2.20023i			0.136452i
$261$	−9.37625	+	5.41338i	−0.580375	+	0.335080i
$262$	−0.0593714	+	0.102834i	−0.00366798	+	0.00635312i
$263$	2.17844	−	3.77317i	0.134328	−	0.232663i	−0.791012	−	0.611800i	$-0.790446\pi$
$263$	2.17844	−	3.77317i	0.134328	−	0.232663i	0.925341	+	0.379137i	$0.123779\pi$
$264$	−1.24188	+	0.717002i	−0.0764326	+	0.0441284i
$265$	2.39756			0.147281
$266$		0			0
$267$	1.62801			0.0996325
$268$	−6.86665	+	3.96446i	−0.419447	+	0.242168i
$269$	−2.08605	+	3.61315i	−0.127189	+	0.220298i	−0.922586	−	0.385790i	$-0.873929\pi$
$269$	−2.08605	+	3.61315i	−0.127189	+	0.220298i	0.795397	+	0.606088i	$0.207262\pi$
$270$	−0.662102	+	1.14679i	−0.0402942	+	0.0697916i
$271$	−23.7473	+	13.7105i	−1.44254	+	0.832853i	−0.998019	−	0.0629130i	$-0.979961\pi$
$271$	−23.7473	+	13.7105i	−1.44254	+	0.832853i	−0.444525	+	0.895766i	$0.646628\pi$
$272$		−	0.912427i		−	0.0553240i
$273$		0			0
$274$		−	17.0801i		−	1.03185i
$275$	1.17187	+	2.02975i	0.0706667	+	0.122398i
$276$	4.12064	−	7.13716i	0.248034	−	0.429607i
$277$	−0.795257	+	1.37742i	−0.0477823	+	0.0827614i	−0.888927	−	0.458048i	$-0.848549\pi$
$277$	−0.795257	+	1.37742i	−0.0477823	+	0.0827614i	0.841145	+	0.540810i	$0.181882\pi$
$278$	−8.03106	−	13.9102i	−0.481671	−	0.834278i
$279$	−8.20844			−0.491426
$280$		0			0
$281$		−	29.2240i		−	1.74336i	−0.490079	−	0.871678i	$-0.663032\pi$
$281$		−	29.2240i		−	1.74336i	0.490079	−	0.871678i	$-0.336968\pi$
$282$	−1.94557	−	3.36983i	−0.115857	−	0.200670i
$283$	−12.2556	−	7.07578i	−0.728521	−	0.420612i	0.0893599	−	0.995999i	$-0.471518\pi$
$283$	−12.2556	−	7.07578i	−0.728521	−	0.420612i	−0.817881	+	0.575388i	$0.804851\pi$
$284$	12.7003	+	7.33254i	0.753626	+	0.435106i
$285$	0.149787	−	1.31029i	0.00887259	−	0.0776150i
$286$		−	2.71414i		−	0.160490i
$287$		0			0
$288$		−	10.5772i		−	0.623269i
$289$	8.20886	+	14.2182i	0.482874	+	0.836363i
$290$	1.27341	+	0.735204i	0.0747773	+	0.0431727i
$291$	−0.715770	+	1.23975i	−0.0419592	+	0.0726754i
$292$	1.36784	−	0.789725i	0.0800470	−	0.0462152i
$293$	8.00946			0.467918			0.233959	−	0.972246i	$-0.424832\pi$
$293$	8.00946			0.467918			0.233959	+	0.972246i	$0.424832\pi$
$294$		0			0
$295$		−	0.553743i		−	0.0322402i
$296$	2.01428	+	3.48883i	0.117078	+	0.202784i
$297$	−1.22638	+	2.12415i	−0.0711617	+	0.123256i
$298$	4.30559	+	2.48584i	0.249416	+	0.144001i
$299$	20.7924	+	36.0135i	1.20245	+	2.08271i
$300$	6.20584			0.358295
$301$		0			0
$302$	8.71286			0.501369
$303$	−3.03889	+	1.75450i	−0.174580	+	0.100794i
$304$	−0.274101	−	0.631037i	−0.0157208	−	0.0361925i
$305$	−0.377453	+	0.653767i	−0.0216129	+	0.0374346i
$306$	−4.89696	−	8.48178i	−0.279941	−	0.484871i
$307$	−13.3461			−0.761701			−0.380850	−	0.924637i	$-0.624369\pi$
$307$	−13.3461			−0.761701			−0.380850	+	0.924637i	$0.624369\pi$
$308$		0			0
$309$	−14.4229			−0.820488
$310$	0.557404	+	0.965452i	0.0316584	+	0.0548340i
$311$	20.2373	+	11.6840i	1.14755	+	0.662538i	0.948289	−	0.317408i	$-0.102812\pi$
$311$	20.2373	+	11.6840i	1.14755	+	0.662538i	0.199261	+	0.979946i	$0.436146\pi$
$312$	−16.5924	−	9.57964i	−0.939361	−	0.542340i
$313$	−19.3478	+	11.1704i	−1.09360	+	0.631391i	−0.934533	−	0.355877i	$-0.884182\pi$
$313$	−19.3478	+	11.1704i	−1.09360	+	0.631391i	−0.159068	+	0.987268i	$0.550849\pi$
$314$	20.5051			1.15717
$315$		0			0
$316$			14.4025i			0.810205i
$317$	4.89845	−	2.82812i	0.275124	−	0.158843i	−0.356090	−	0.934452i	$-0.615890\pi$
$317$	4.89845	−	2.82812i	0.275124	−	0.158843i	0.631214	+	0.775609i	$0.282557\pi$
$318$	−3.91556	+	6.78195i	−0.219574	+	0.380313i
$319$	2.35868	+	1.36178i	0.132061	+	0.0762452i
$320$	−1.32274	+	0.763684i	−0.0739434	+	0.0426912i
$321$		−	6.48277i		−	0.361833i
$322$		0			0
$323$	20.2499	+	14.9959i	1.12674	+	0.834395i
$324$	−0.164747	−	0.285351i	−0.00915263	−	0.0158528i
$325$	−15.6571	+	27.1188i	−0.868497	+	1.50428i
$326$	−8.34070	−	4.81550i	−0.461949	−	0.266706i
$327$	11.8034	−	6.81470i	0.652729	−	0.376854i
$328$			21.3067i			1.17647i
$329$		0			0
$330$	0.128949			0.00709841
$331$	22.7878	−	13.1565i	1.25253	−	0.723148i	0.280918	−	0.959732i	$-0.409361\pi$
$331$	22.7878	−	13.1565i	1.25253	−	0.723148i	0.971611	+	0.236584i	$0.0760279\pi$
$332$	0.652499	+	0.376721i	0.0358105	+	0.0206752i
$333$	2.30998	+	1.33367i	0.126586	+	0.0730846i
$334$	8.54672	−	4.93445i	0.467656	−	0.270001i
$335$	1.90081			0.103853
$336$		0			0
$337$			23.8906i			1.30141i	0.759333	+	0.650703i	$0.225526\pi$
$337$			23.8906i			1.30141i	−0.759333	+	0.650703i	$0.774474\pi$
$338$	21.3378	−	12.3194i	1.16062	−	0.670086i
$339$	17.0148	+	9.82348i	0.924115	+	0.533538i
$340$	0.998624	−	1.72967i	0.0541580	−	0.0938044i
$341$	1.03245	+	1.78826i	0.0559104	+	0.0968396i
$342$	−5.93476	−	4.39494i	−0.320915	−	0.237651i
$343$		0			0
$344$		−	20.6126i		−	1.11136i
$345$	−1.71100	+	0.987848i	−0.0921173	+	0.0531840i
$346$	6.30948	+	3.64278i	0.339200	+	0.195837i
$347$	3.45781	−	5.98911i	0.185625	−	0.321512i	−0.758162	−	0.652066i	$-0.773902\pi$
$347$	3.45781	−	5.98911i	0.185625	−	0.321512i	0.943787	+	0.330554i	$0.107236\pi$
$348$	6.24537	−	3.60576i	0.334787	−	0.193289i
$349$			13.1300i			0.702831i	0.936220	+	0.351416i	$0.114300\pi$
$349$			13.1300i			0.702831i	−0.936220	+	0.351416i	$0.885700\pi$
$350$		0			0
$351$	−32.7705			−1.74916
$352$	−2.30431	+	1.33040i	−0.122820	+	0.0709103i
$353$	−18.5310	−	10.6989i	−0.986307	−	0.569445i	−0.0821389	−	0.996621i	$-0.526175\pi$
$353$	−18.5310	−	10.6989i	−0.986307	−	0.569445i	−0.904168	+	0.427176i	$0.859508\pi$
$354$	1.56636	+	0.904340i	0.0832512	+	0.0480651i
$355$	−1.75784	−	3.04467i	−0.0932966	−	0.161594i
$356$	1.85904			0.0985291
$357$		0			0
$358$	−8.80204			−0.465202
$359$	5.50977	+	9.54320i	0.290795	+	0.503671i	0.973998	−	0.226557i	$-0.0727471\pi$
$359$	5.50977	+	9.54320i	0.290795	+	0.503671i	−0.683203	+	0.730228i	$0.739414\pi$
$360$	−0.780260	+	1.35145i	−0.0411233	+	0.0712277i
$361$	18.5098	+	4.28795i	0.974201	+	0.225682i
$362$	2.55464	−	1.47492i	0.134269	−	0.0775203i
$363$	−11.3254			−0.594432
$364$		0			0
$365$	−0.378644			−0.0198191
$366$	−1.23287	−	2.13539i	−0.0644430	−	0.111618i
$367$	−21.5490	−	12.4413i	−1.12485	−	0.649432i	−0.182215	−	0.983259i	$-0.558327\pi$
$367$	−21.5490	−	12.4413i	−1.12485	−	0.649432i	−0.942634	+	0.333827i	$0.891660\pi$
$368$	−0.515334	+	0.892585i	−0.0268637	+	0.0465292i
$369$	7.05367	+	12.2173i	0.367199	+	0.636008i
$370$		−	0.362257i		−	0.0188329i
$371$		0			0
$372$	5.46750			0.283477
$373$	−5.17977	+	2.99054i	−0.268198	+	0.154844i	−0.628069	−	0.778158i	$-0.716154\pi$
$373$	−5.17977	+	2.99054i	−0.268198	+	0.154844i	0.359870	+	0.933002i	$0.382821\pi$
$374$	−1.23187	+	2.13367i	−0.0636986	+	0.110329i
$375$	−2.59854	−	1.50027i	−0.134188	−	0.0774735i
$376$	−5.92295	−	10.2588i	−0.305453	−	0.529060i
$377$			36.3887i			1.87411i
$378$		0			0
$379$			3.98456i			0.204673i	0.994750	+	0.102336i	$0.0326318\pi$
$379$			3.98456i			0.204673i	−0.994750	+	0.102336i	$0.967368\pi$
$380$	0.171043	−	1.49624i	0.00877433	−	0.0767555i
$381$	−10.2892	−	5.94050i	−0.527134	−	0.304341i
$382$	−8.76070	−	5.05799i	−0.448236	−	0.258789i
$383$	−5.09215	−	8.81987i	−0.260197	−	0.450674i	0.706097	−	0.708115i	$-0.250454\pi$
$383$	−5.09215	−	8.81987i	−0.260197	−	0.450674i	−0.966294	+	0.257441i	$0.917121\pi$
$384$			6.74857i			0.344387i
$385$		0			0
$386$	13.5806			0.691234
$387$	−6.82387	−	11.8193i	−0.346877	−	0.600808i
$388$	−0.817346	+	1.41569i	−0.0414945	+	0.0718705i
$389$	5.55875	−	9.62803i	0.281840	−	0.488161i	−0.689998	−	0.723811i	$-0.742389\pi$
$389$	5.55875	−	9.62803i	0.281840	−	0.488161i	0.971838	+	0.235651i	$0.0757221\pi$
$390$	0.861424	+	1.49203i	0.0436199	+	0.0755518i
$391$		−	37.7484i		−	1.90902i
$392$		0			0
$393$		−	0.139612i		−	0.00704248i
$394$	8.24308	−	4.75914i	0.415280	−	0.239762i
$395$	1.72637	−	2.99016i	0.0868631	−	0.150451i
$396$	−0.542102	+	0.938949i	−0.0272417	+	0.0471840i
$397$	27.3946	−	15.8163i	1.37490	−	0.793797i	0.383358	−	0.923600i	$-0.374768\pi$
$397$	27.3946	−	15.8163i	1.37490	−	0.793797i	0.991540	+	0.129803i	$0.0414344\pi$
$398$	16.5627			0.830211
$399$		0			0
$400$	−0.776113			−0.0388057
$401$	15.7772	−	9.10899i	0.787878	−	0.454881i	−0.0513372	−	0.998681i	$-0.516348\pi$
$401$	15.7772	−	9.10899i	0.787878	−	0.454881i	0.839215	+	0.543800i	$0.183015\pi$
$402$	−3.10429	+	5.37680i	−0.154828	+	0.268170i
$403$	−13.7943	+	23.8924i	−0.687141	+	1.19016i
$404$	−3.47014	+	2.00349i	−0.172646	+	0.0996773i
$405$			0.0789903i			0.00392506i
$406$		0			0
$407$		−	0.670991i		−	0.0332598i
$408$	8.69587	+	15.0617i	0.430510	+	0.745664i
$409$	−2.66242	+	4.61145i	−0.131648	+	0.228021i	−0.924312	−	0.381638i	$-0.875360\pi$
$409$	−2.66242	+	4.61145i	−0.131648	+	0.228021i	0.792664	+	0.609659i	$0.208694\pi$
$410$	0.957975	−	1.65926i	0.0473110	−	0.0819451i
$411$	10.0410	+	17.3915i	0.495285	+	0.857859i
$412$	−16.4696			−0.811401
$413$		0			0
$414$			11.0631i			0.543723i
$415$	−0.0903118	−	0.156425i	−0.00443323	−	0.00767859i
$416$	−30.7872	−	17.7750i	−1.50947	−	0.871491i
$417$	16.3549	+	9.44251i	0.800903	+	0.462402i
$418$	−0.210994	+	1.84572i	−0.0103200	+	0.0902769i
$419$		−	8.09389i		−	0.395412i	−0.980261	−	0.197706i	$-0.936651\pi$
$419$		−	8.09389i		−	0.395412i	0.980261	−	0.197706i	$-0.0633492\pi$
$420$		0			0
$421$		−	25.4935i		−	1.24248i	−0.783621	−	0.621239i	$-0.786629\pi$
$421$		−	25.4935i		−	1.24248i	0.783621	−	0.621239i	$-0.213371\pi$
$422$	2.96963	+	5.14355i	0.144559	+	0.250384i
$423$	−6.79246	−	3.92163i	−0.330261	−	0.190676i
$424$	−11.9202	+	20.6464i	−0.578897	+	1.00268i
$425$	24.6170	−	14.2126i	1.19410	−	0.689413i
$426$	11.4832			0.556363
$427$		0			0
$428$		−	7.40276i		−	0.357826i
$429$	1.59557	+	2.76361i	0.0770349	+	0.133428i
$430$	−0.926766	+	1.60521i	−0.0446926	+	0.0774099i
$431$	5.56360	+	3.21215i	0.267989	+	0.154724i	0.627973	−	0.778235i	$-0.283885\pi$
$431$	5.56360	+	3.21215i	0.267989	+	0.154724i	−0.359984	+	0.932958i	$0.617218\pi$
$432$	−0.406105	−	0.703394i	−0.0195387	−	0.0338421i
$433$	24.2261			1.16423			0.582115	−	0.813106i	$-0.302225\pi$
$433$	24.2261			1.16423			0.582115	+	0.813106i	$0.302225\pi$
$434$		0			0
$435$	−1.72883			−0.0828911
$436$	13.4785	−	7.78179i	0.645501	−	0.372680i
$437$	−11.3400	−	26.1069i	−0.542464	−	1.24886i
$438$	0.618379	−	1.07106i	0.0295473	−	0.0511774i
$439$	−0.916950	−	1.58820i	−0.0437636	−	0.0758008i	0.843314	−	0.537421i	$-0.180602\pi$
$439$	−0.916950	−	1.58820i	−0.0437636	−	0.0758008i	−0.887077	+	0.461621i	$0.847268\pi$
$440$	0.392562			0.0187147
$441$		0			0
$442$	−32.9173			−1.56572
$443$	5.35119	+	9.26854i	0.254243	+	0.440361i	0.964690	−	0.263389i	$-0.0848404\pi$
$443$	5.35119	+	9.26854i	0.254243	+	0.440361i	−0.710447	+	0.703751i	$0.751507\pi$
$444$	−1.53864	−	0.888335i	−0.0730207	−	0.0421585i
$445$	−0.385963	−	0.222836i	−0.0182964	−	0.0105634i
$446$	−20.9053	+	12.0697i	−0.989895	+	0.571516i
$447$	−5.84544			−0.276480
$448$		0			0
$449$			19.6699i			0.928278i	0.885762	+	0.464139i	$0.153636\pi$
$449$			19.6699i			0.928278i	−0.885762	+	0.464139i	$0.846364\pi$
$450$	−7.21463	+	4.16537i	−0.340101	+	0.196357i
$451$	1.77441	−	3.07337i	0.0835537	−	0.144719i
$452$	19.4294	+	11.2176i	0.913881	+	0.527629i
$453$	−8.87168	+	5.12207i	−0.416828	+	0.240656i
$454$		−	19.6572i		−	0.922557i
$455$		0			0
$456$	10.5388	+	7.80439i	0.493523	+	0.365474i
$457$	4.70869	+	8.15569i	0.220263	+	0.381507i	0.954888	−	0.296967i	$-0.0959751\pi$
$457$	4.70869	+	8.15569i	0.220263	+	0.381507i	−0.734625	+	0.678474i	$0.762642\pi$
$458$	4.31459	−	7.47308i	0.201607	−	0.349194i
$459$	25.7619	+	14.8736i	1.20246	+	0.694242i
$460$	−1.95382	+	1.12804i	−0.0910972	+	0.0525950i
$461$			28.3908i			1.32229i	0.750258	+	0.661145i	$0.229929\pi$
$461$			28.3908i			1.32229i	−0.750258	+	0.661145i	$0.770071\pi$
$462$		0			0
$463$	−25.1625			−1.16940			−0.584700	−	0.811250i	$-0.698788\pi$
$463$	−25.1625			−1.16940			−0.584700	+	0.811250i	$0.698788\pi$
$464$	−0.781056	+	0.450943i	−0.0362596	+	0.0209345i
$465$	−1.13513	−	0.655367i	−0.0526403	−	0.0303919i
$466$	7.83778	+	4.52514i	0.363078	+	0.209623i
$467$	14.3282	−	8.27241i	0.663031	−	0.382801i	−0.130400	−	0.991462i	$-0.541626\pi$
$467$	14.3282	−	8.27241i	0.663031	−	0.382801i	0.793431	+	0.608660i	$0.208293\pi$
$468$	−14.4857			−0.669603
$469$		0			0
$470$			1.06521i			0.0491345i
$471$	−20.8789	+	12.0545i	−0.962050	+	0.555440i
$472$	4.76851	+	2.75310i	0.219488	+	0.126722i
$473$	−1.71660	+	2.97324i	−0.0789294	+	0.136710i
$474$	5.63881	+	9.76670i	0.258999	+	0.448599i
$475$	12.7556	−	17.2247i	0.585266	−	0.790321i
$476$		0			0
$477$			15.7849i			0.722742i
$478$	20.4726	−	11.8199i	0.936397	−	0.540629i
$479$	5.63404	+	3.25282i	0.257426	+	0.148625i	0.623160	−	0.782095i	$-0.285849\pi$
$479$	5.63404	+	3.25282i	0.257426	+	0.148625i	−0.365734	+	0.930719i	$0.619182\pi$
$480$	0.844492	−	1.46270i	0.0385456	−	0.0667630i
$481$	7.76384	−	4.48245i	0.354001	−	0.204382i
$482$			5.13764i			0.234013i
$483$		0			0
$484$	−12.9327			−0.587848
$485$	0.339385	−	0.195944i	0.0154107	−	0.00889735i
$486$	−12.1777	−	7.03079i	−0.552391	−	0.318923i
$487$	−4.90255	−	2.83049i	−0.222156	−	0.128262i	0.384792	−	0.923003i	$-0.374273\pi$
$487$	−4.90255	−	2.83049i	−0.222156	−	0.128262i	−0.606948	+	0.794741i	$0.707606\pi$
$488$	−3.75324	−	6.50080i	−0.169901	−	0.294278i
$489$	11.3237			0.512073
$490$		0			0
$491$	−19.0570			−0.860031			−0.430015	−	0.902822i	$-0.641492\pi$
$491$	−19.0570			−0.860031			−0.430015	+	0.902822i	$0.641492\pi$
$492$	−4.69833	−	8.13775i	−0.211817	−	0.366878i
$493$	16.5158	−	28.6063i	0.743836	−	1.28836i
$494$	−22.7657	+	9.88867i	−1.02428	+	0.444912i
$495$	0.225096	−	0.129959i	0.0101173	−	0.00584123i
$496$	−0.683775			−0.0307024
$497$		0			0
$498$	0.589967			0.0264371
$499$	−0.520471	−	0.901483i	−0.0232995	−	0.0403559i	0.854141	−	0.520042i	$-0.174084\pi$
$499$	−0.520471	−	0.901483i	−0.0232995	−	0.0403559i	−0.877440	+	0.479686i	$0.840750\pi$
$500$	−2.96730	−	1.71317i	−0.132702	−	0.0766155i
$501$	−5.80168	+	10.0488i	−0.259200	+	0.448947i
$502$	2.57992	+	4.46855i	0.115147	+	0.199441i
$503$			23.5048i			1.04803i	0.851710	+	0.524013i	$0.175566\pi$
$503$			23.5048i			1.04803i	−0.851710	+	0.524013i	$0.824434\pi$
$504$		0			0
$505$	0.960599			0.0427461
$506$	2.41017	−	1.39151i	0.107145	−	0.0618602i
$507$	−14.4845	+	25.0879i	−0.643279	+	1.11419i
$508$	−11.7494	−	6.78353i	−0.521296	−	0.300971i
$509$	9.42499	+	16.3246i	0.417755	+	0.723574i	0.995713	−	0.0924929i	$-0.0294835\pi$
$509$	9.42499	+	16.3246i	0.417755	+	0.723574i	−0.577958	+	0.816067i	$0.696150\pi$
$510$		−	1.56391i		−	0.0692509i
$511$		0			0
$512$		−	1.78447i		−	0.0788633i
$513$	22.2852	+	2.54754i	0.983915	+	0.112477i
$514$	−17.7730	−	10.2613i	−0.783934	−	0.452605i
$515$	3.41932	+	1.97415i	0.150673	+	0.0869913i
$516$	4.54527	+	7.87263i	0.200094	+	0.346573i
$517$			1.97304i			0.0867741i
$518$		0			0
$519$	−8.56599			−0.376005
$520$	2.62245	+	4.54222i	0.115002	+	0.199189i
$521$	−14.4853	+	25.0893i	−0.634614	+	1.09918i	0.351983	+	0.936006i	$0.385508\pi$
$521$	−14.4853	+	25.0893i	−0.634614	+	1.09918i	−0.986597	+	0.163177i	$0.947826\pi$
$522$	−4.84039	+	8.38380i	−0.211858	+	0.366949i
$523$	−4.98226	−	8.62952i	−0.217859	−	0.377343i	0.736294	−	0.676661i	$-0.236574\pi$
$523$	−4.98226	−	8.62952i	−0.217859	−	0.377343i	−0.954153	+	0.299319i	$0.903241\pi$
$524$		−	0.159424i		−	0.00696449i
$525$		0			0
$526$		−	3.89571i		−	0.169861i
$527$	21.6882	−	12.5217i	0.944752	−	0.545453i
$528$	−0.0395459	+	0.0684955i	−0.00172101	+	0.00298088i
$529$	−9.82010	+	17.0089i	−0.426961	+	0.739518i
$530$	1.85658	−	1.07189i	0.0806445	−	0.0465601i
$531$	3.64570			0.158210
$532$		0			0
$533$	47.4147			2.05376
$534$	1.26066	−	0.727844i	0.0545542	−	0.0314969i
$535$	−0.887338	+	1.53691i	−0.0383630	+	0.0664466i
$536$	−9.45047	+	16.3687i	−0.408198	+	0.707020i
$537$	8.96249	−	5.17450i	0.386760	−	0.223296i
$538$			3.73050i			0.160833i
$539$		0			0
$540$		−	1.77788i		−	0.0765077i
$541$	4.62179	+	8.00517i	0.198706	+	0.344169i	0.948109	−	0.317945i	$-0.102993\pi$
$541$	4.62179	+	8.00517i	0.198706	+	0.344169i	−0.749403	+	0.662114i	$0.769659\pi$
$542$	−12.2593	+	21.2337i	−0.526581	+	0.912065i
$543$	−1.73414	+	3.00362i	−0.0744191	+	0.128898i
$544$	16.1352	+	27.9469i	0.691790	+	1.19821i
$545$	−3.73108			−0.159822
$546$		0			0
$547$			34.8556i			1.49032i	0.666887	+	0.745158i	$0.267626\pi$
$547$			34.8556i			1.49032i	−0.666887	+	0.745158i	$0.732374\pi$
$548$	11.4659	+	19.8596i	0.489800	+	0.848358i
$549$	−4.30423	−	2.48505i	−0.183700	−	0.106059i
$550$	1.81490	+	1.04783i	0.0773877	+	0.0446798i
$551$	2.82881	−	24.7457i	0.120511	−	1.05420i
$552$		−	19.6455i		−	0.836170i
$553$		0			0
$554$			1.42216i			0.0604218i
$555$	0.212962	+	0.368861i	0.00903973	+	0.0156573i
$556$	18.6759	+	10.7825i	0.792034	+	0.457281i
$557$	18.5283	−	32.0919i	0.785068	−	1.35978i	−0.143890	−	0.989594i	$-0.545961\pi$
$557$	18.5283	−	32.0919i	0.785068	−	1.35978i	0.928958	−	0.370184i	$-0.120705\pi$
$558$	−6.35627	+	3.66980i	−0.269083	+	0.155355i
$559$	−45.8700			−1.94009
$560$		0			0
$561$		−	2.89675i		−	0.122301i
$562$	−13.0653	−	22.6298i	−0.551128	−	0.954582i
$563$	−7.30046	+	12.6448i	−0.307678	+	0.532913i	−0.977854	−	0.209289i	$-0.932885\pi$
$563$	−7.30046	+	12.6448i	−0.307678	+	0.532913i	0.670176	+	0.742202i	$0.266218\pi$
$564$	4.52434	+	2.61213i	0.190509	+	0.109991i
$565$	−2.68920	−	4.65784i	−0.113136	−	0.195957i
$566$	−12.6537			−0.531873
$567$		0			0
$568$	34.9586			1.46683
$569$	14.1095	−	8.14614i	0.591502	−	0.341504i	−0.174189	−	0.984712i	$-0.555730\pi$
$569$	14.1095	−	8.14614i	0.591502	−	0.341504i	0.765691	+	0.643208i	$0.222397\pi$
$570$	−0.469812	−	1.08160i	−0.0196783	−	0.0453033i
$571$	−6.77687	+	11.7379i	−0.283603	+	0.491215i	−0.972270	−	0.233863i	$-0.924863\pi$
$571$	−6.77687	+	11.7379i	−0.283603	+	0.491215i	0.688666	+	0.725079i	$0.258197\pi$
$572$	1.82200	+	3.15580i	0.0761818	+	0.131951i
$573$	11.8939			0.496873
$574$		0			0
$575$	−32.1089			−1.33903
$576$	−5.02789	−	8.70856i	−0.209495	−	0.362857i
$577$	−29.0158	−	16.7523i	−1.20794	−	0.697407i	−0.245635	−	0.969362i	$-0.578996\pi$
$577$	−29.0158	−	16.7523i	−1.20794	−	0.697407i	−0.962310	+	0.271955i	$0.912330\pi$
$578$	12.7132	+	7.33997i	0.528800	+	0.305303i
$579$	−13.8281	+	7.98368i	−0.574678	+	0.331790i
$580$	−1.97417			−0.0819731
$581$		0			0
$582$			1.28001i			0.0530583i
$583$	3.43884	−	1.98542i	0.142422	−	0.0822275i
$584$	1.88254	−	3.26066i	0.0779002	−	0.134927i
$585$	3.00743	+	1.73634i	0.124342	+	0.0717890i
$586$	6.20220	−	3.58084i	0.256210	−	0.147923i
$587$		−	23.4332i		−	0.967190i	−0.875292	−	0.483595i	$-0.839331\pi$
$587$		−	23.4332i		−	0.967190i	0.875292	−	0.483595i	$-0.160669\pi$
$588$		0			0
$589$	11.2380	−	15.1754i	0.463053	−	0.625290i
$590$	−0.247565	−	0.428796i	−0.0101921	−	0.0176532i
$591$	−5.59556	+	9.69179i	−0.230171	+	0.398667i
$592$	0.192425	+	0.111097i	0.00790862	+	0.00456604i
$593$	−35.6805	+	20.6002i	−1.46522	+	0.845947i	−0.999245	−	0.0388484i	$-0.987631\pi$
$593$	−35.6805	+	20.6002i	−1.46522	+	0.845947i	−0.465979	+	0.884796i	$0.654298\pi$
$594$			2.19314i			0.0899855i
$595$		0			0
$596$	−6.67498			−0.273418
$597$	−16.8646	+	9.73676i	−0.690221	+	0.398499i
$598$	32.2015	+	18.5916i	1.31682	+	0.760265i
$599$	21.1840	+	12.2306i	0.865556	+	0.499729i	0.865869	−	0.500271i	$-0.166766\pi$
$599$	21.1840	+	12.2306i	0.865556	+	0.499729i	−0.000312831		1.00000i	$0.500100\pi$
$600$	12.8115	−	7.39673i	0.523028	−	0.301970i
$601$	24.4746			0.998340			0.499170	−	0.866504i	$-0.333638\pi$
$601$	24.4746			0.998340			0.499170	+	0.866504i	$0.333638\pi$
$602$		0			0
$603$			12.5144i			0.509628i
$604$	−10.1307	+	5.84895i	−0.412212	+	0.237990i
$605$	2.68500	+	1.55018i	0.109161	+	0.0630240i
$606$	−1.56879	+	2.71723i	−0.0637278	+	0.110380i
$607$	−18.2596	−	31.6265i	−0.741132	−	1.28368i	−0.951980	−	0.306160i	$-0.900956\pi$
$607$	−18.2596	−	31.6265i	−0.741132	−	1.28368i	0.210848	−	0.977519i	$-0.432378\pi$
$608$	19.5546	+	14.4810i	0.793046	+	0.587283i
$609$		0			0
$610$			0.675001i			0.0273300i
$611$	−22.8294	+	13.1806i	−0.923579	+	0.533229i
$612$	11.3877	+	6.57467i	0.460319	+	0.265765i
$613$	16.1048	−	27.8944i	0.650468	−	1.12664i	−0.332542	−	0.943089i	$-0.607906\pi$
$613$	16.1048	−	27.8944i	0.650468	−	1.12664i	0.983009	−	0.183555i	$-0.0587605\pi$
$614$	−10.3346	+	5.96671i	−0.417072	+	0.240797i
$615$			2.25268i			0.0908367i
$616$		0			0
$617$	−34.7646			−1.39957			−0.699785	−	0.714354i	$-0.746721\pi$
$617$	−34.7646			−1.39957			−0.699785	+	0.714354i	$0.746721\pi$
$618$	−11.1685	+	6.44812i	−0.449262	+	0.259381i
$619$	−33.8046	−	19.5171i	−1.35872	−	0.784458i	−0.369269	−	0.929323i	$-0.620392\pi$
$619$	−33.8046	−	19.5171i	−1.35872	−	0.784458i	−0.989451	+	0.144865i	$0.953725\pi$
$620$	−1.29622	−	0.748372i	−0.0520574	−	0.0300553i
$621$	−16.8011	−	29.1004i	−0.674206	−	1.16776i
$622$	20.8945			0.837795
$623$		0			0
$624$	−1.05672			−0.0423027
$625$	−11.8822	−	20.5806i	−0.475289	−	0.823225i
$626$	−9.98808	+	17.2999i	−0.399204	+	0.691442i
$627$	−0.870209	−	2.00340i	−0.0347528	−	0.0800080i
$628$	−23.8419	+	13.7651i	−0.951395	+	0.549288i
$629$	−8.13785			−0.324477
$630$		0			0
$631$	−28.8349			−1.14790			−0.573950	−	0.818890i	$-0.694590\pi$
$631$	−28.8349			−1.14790			−0.573950	+	0.818890i	$0.694590\pi$
$632$	17.1663	+	29.7330i	0.682840	+	1.18271i
$633$	−6.04753	−	3.49154i	−0.240368	−	0.138776i
$634$	2.52877	−	4.37996i	0.100430	−	0.173950i
$635$	1.62623	+	2.81671i	0.0645349	+	0.111778i
$636$		−	10.5141i		−	0.416910i
$637$		0			0
$638$	2.43528			0.0964137
$639$	20.0453	−	11.5732i	0.792980	−	0.457827i
$640$	0.923720	−	1.59993i	0.0365132	−	0.0632428i
$641$	−34.5535	−	19.9495i	−1.36478	−	0.787957i	−0.374526	−	0.927216i	$-0.622195\pi$
$641$	−34.5535	−	19.9495i	−1.36478	−	0.787957i	−0.990256	+	0.139259i	$0.955528\pi$
$642$	−2.89829	−	5.01999i	−0.114386	−	0.198123i
$643$			20.5969i			0.812263i	0.913815	+	0.406132i	$0.133123\pi$
$643$			20.5969i			0.812263i	−0.913815	+	0.406132i	$0.866877\pi$
$644$		0			0
$645$		−	2.17929i		−	0.0858094i
$646$	22.3850	+	2.55895i	0.880727	+	0.100681i
$647$	−1.85762	−	1.07250i	−0.0730306	−	0.0421642i	0.463040	−	0.886337i	$-0.346759\pi$
$647$	−1.85762	−	1.07250i	−0.0730306	−	0.0421642i	−0.536071	+	0.844173i	$0.680092\pi$
$648$	−0.680218	−	0.392724i	−0.0267215	−	0.0154277i
$649$	−0.458553	−	0.794237i	−0.0179998	−	0.0311765i
$650$			27.9996i			1.09823i
$651$		0			0
$652$	12.9306			0.506402
$653$	−8.38182	−	14.5177i	−0.328006	−	0.568123i	0.654110	−	0.756399i	$-0.273043\pi$
$653$	−8.38182	−	14.5177i	−0.328006	−	0.568123i	−0.982116	+	0.188276i	$0.939710\pi$
$654$	6.09338	−	10.5540i	0.238270	−	0.412696i
$655$	−0.0191095	+	0.0330987i	−0.000746671	+	0.00129327i
$656$	0.587581	+	1.01772i	0.0229412	+	0.0397353i
$657$		−	2.49289i		−	0.0972570i
$658$		0			0
$659$		−	41.1006i		−	1.60105i	−0.599297	−	0.800527i	$-0.704553\pi$
$659$		−	41.1006i		−	1.60105i	0.599297	−	0.800527i	$-0.295447\pi$
$660$	−0.149933	+	0.0865636i	−0.00583612	+	0.00336948i
$661$	9.10759	−	15.7748i	0.354244	−	0.613569i	−0.632744	−	0.774361i	$-0.718072\pi$
$661$	9.10759	−	15.7748i	0.354244	−	0.613569i	0.986988	+	0.160792i	$0.0514049\pi$
$662$	11.7639	−	20.3757i	0.457218	−	0.791925i
$663$	33.5174	−	19.3513i	1.30171	−	0.751541i
$664$	1.79605			0.0697003
$665$		0			0
$666$	2.38501			0.0924171
$667$	−32.3134	+	18.6561i	−1.25118	+	0.722368i
$668$	−6.62501	+	11.4749i	−0.256329	+	0.443975i
$669$	14.1909	−	24.5794i	0.548653	−	0.950295i
$670$	1.47191	−	0.849809i	0.0568649	−	0.0328310i
$671$			1.25027i			0.0482661i
$672$		0			0
$673$			35.7582i			1.37838i	0.724581	+	0.689189i	$0.242033\pi$
$673$			35.7582i			1.37838i	−0.724581	+	0.689189i	$0.757967\pi$
$674$	10.6809	+	18.4999i	0.411414	+	0.712590i
$675$	12.6516	−	21.9131i	0.486959	−	0.843437i
$676$	−16.5400	+	28.6482i	−0.636155	+	1.10185i
$677$	−16.2540	−	28.1527i	−0.624691	−	1.08200i	−0.988600	−	0.150563i	$-0.951891\pi$
$677$	−16.2540	−	28.1527i	−0.624691	−	1.08200i	0.363909	−	0.931434i	$-0.381442\pi$
$678$	17.5674			0.674671
$679$		0			0
$680$		−	4.76103i		−	0.182577i
$681$	11.5560	+	20.0155i	0.442825	+	0.766996i
$682$	1.59898	+	0.923169i	0.0612279	+	0.0353500i
$683$	−14.7801	−	8.53331i	−0.565546	−	0.326518i	0.189823	−	0.981818i	$-0.439209\pi$
$683$	−14.7801	−	8.53331i	−0.565546	−	0.326518i	−0.755368	+	0.655300i	$0.772542\pi$
$684$	9.85084	+	1.12610i	0.376656	+	0.0430576i
$685$		−	5.49749i		−	0.210048i
$686$		0			0
$687$			10.1457i			0.387084i
$688$	−0.568438	−	0.984564i	−0.0216715	−	0.0375362i
$689$	45.9453	+	26.5265i	1.75038	+	1.01058i
$690$	−0.883287	+	1.52990i	−0.0336262	+	0.0582422i
$691$	−18.4114	+	10.6298i	−0.700402	+	0.404378i	−0.807497	−	0.589871i	$-0.799178\pi$
$691$	−18.4114	+	10.6298i	−0.700402	+	0.404378i	0.107095	+	0.994249i	$0.465845\pi$
$692$	−9.78161			−0.371841
$693$		0			0
$694$		−	6.18362i		−	0.234727i
$695$	−2.58491	−	4.47720i	−0.0980513	−	0.169830i
$696$	8.59541	−	14.8877i	0.325808	−	0.564316i
$697$	−37.2741	−	21.5202i	−1.41186	−	0.815137i
$698$	5.87010	+	10.1673i	0.222186	+	0.384838i
$699$	−10.6409			−0.402474
$700$		0			0
$701$	47.7171			1.80225			0.901126	−	0.433558i	$-0.142742\pi$
$701$	47.7171			1.80225			0.901126	+	0.433558i	$0.142742\pi$
$702$	−25.3761	+	14.6509i	−0.957760	+	0.552963i
$703$	−5.62816	+	2.44469i	−0.212270	+	0.0922031i
$704$	−1.26481	+	2.19071i	−0.0476693	+	0.0825656i
$705$	−0.626210	−	1.08463i	−0.0235845	−	0.0408495i
$706$	−19.1329			−0.720076
$707$		0			0
$708$	−2.42834			−0.0912625
$709$	2.40313	+	4.16234i	0.0902514	+	0.156320i	0.907617	−	0.419800i	$-0.137900\pi$
$709$	2.40313	+	4.16234i	0.0902514	+	0.156320i	−0.817365	+	0.576120i	$0.804566\pi$
$710$	−2.72240	−	1.57178i	−0.102170	−	0.0589878i
$711$	19.6864	+	11.3660i	0.738298	+	0.426257i
$712$	3.83786	−	2.21579i	0.143830	−	0.0830402i
$713$	−28.2887			−1.05942
$714$		0			0
$715$		−	0.873584i		−	0.0326702i
$716$	10.2344	−	5.90882i	0.382477	−	0.220823i
$717$	−13.8972	+	24.0707i	−0.519001	+	0.898937i
$718$	8.53308	+	4.92657i	0.318452	+	0.183858i
$719$	−24.3098	+	14.0353i	−0.906604	+	0.523428i	−0.879337	−	0.476200i	$-0.842014\pi$
$719$	−24.3098	+	14.0353i	−0.906604	+	0.523428i	−0.0272673	+	0.999628i	$0.508681\pi$
$720$			0.0860697i			0.00320763i
$721$		0			0
$722$	16.2503	−	4.95489i	0.604773	−	0.184402i
$723$	−3.02029	−	5.23129i	−0.112326	−	0.194554i
$724$	−1.98024	+	3.42987i	−0.0735949	+	0.127470i
$725$	−24.3326	−	14.0484i	−0.903689	−	0.521745i
$726$	−8.76996	+	5.06334i	−0.325484	+	0.187918i
$727$			11.6510i			0.432111i	0.976381	+	0.216055i	$0.0693192\pi$
$727$			11.6510i			0.432111i	−0.976381	+	0.216055i	$0.930681\pi$
$728$		0			0
$729$	15.7095			0.581833
$730$	−0.293206	+	0.169283i	−0.0108521	+	0.00626544i
$731$	36.0598	+	20.8191i	1.33372	+	0.770023i
$732$	2.86698	+	1.65525i	0.105967	+	0.0611798i
$733$	0.738349	−	0.426286i	0.0272715	−	0.0157452i	−0.486302	−	0.873791i	$-0.661655\pi$
$733$	0.738349	−	0.426286i	0.0272715	−	0.0157452i	0.513574	+	0.858045i	$0.328321\pi$
$734$	−22.2489			−0.821221
$735$		0			0
$736$		−	36.4523i		−	1.34365i
$737$	2.72635	−	1.57406i	0.100426	−	0.0579812i
$738$	10.9241	+	6.30705i	0.402123	+	0.232166i
$739$	−12.4593	+	21.5802i	−0.458324	+	0.793841i	−0.998873	−	0.0474723i	$-0.984883\pi$
$739$	−12.4593	+	21.5802i	−0.458324	+	0.793841i	0.540548	+	0.841313i	$0.318217\pi$
$740$	0.243184	+	0.421207i	0.00893962	+	0.0154839i
$741$	17.3674	−	23.4523i	0.638008	−	0.861542i
$742$		0			0
$743$		−	13.5921i		−	0.498646i	−0.968420	−	0.249323i	$-0.919792\pi$
$743$		−	13.5921i		−	0.498646i	0.968420	−	0.249323i	$-0.0802080\pi$
$744$	11.2873	−	6.51671i	0.413811	−	0.238914i
$745$	1.38582	+	0.800102i	0.0507724	+	0.0293135i
$746$	−2.67400	+	4.63150i	−0.0979020	+	0.169571i
$747$	1.02986	−	0.594589i	0.0376805	−	0.0217549i
$748$		−	3.30783i		−	0.120946i
$749$		0			0
$750$	−2.68294			−0.0979669
$751$	−26.5760	+	15.3437i	−0.969772	+	0.559898i	−0.899167	−	0.437606i	$-0.855826\pi$
$751$	−26.5760	+	15.3437i	−0.969772	+	0.559898i	−0.0706054	+	0.997504i	$0.522493\pi$
$752$	−0.565822	−	0.326677i	−0.0206334	−	0.0119127i
$753$	−5.25389	−	3.03333i	−0.191462	−	0.110541i
$754$	16.2685	+	28.1779i	0.592465	+	1.02618i
$755$	2.80436			0.102061
$756$		0			0
$757$	−33.7950			−1.22830			−0.614150	−	0.789189i	$-0.710501\pi$
$757$	−33.7950			−1.22830			−0.614150	+	0.789189i	$0.710501\pi$
$758$	1.78140	+	3.08548i	0.0647034	+	0.112070i
$759$	−1.63607	+	2.83375i	−0.0593855	+	0.102859i
$760$	−1.43026	−	3.29274i	−0.0518809	−	0.119440i
$761$	28.5566	−	16.4871i	1.03517	−	0.597658i	0.116712	−	0.993166i	$-0.462765\pi$
$761$	28.5566	−	16.4871i	1.03517	−	0.597658i	0.918463	+	0.395507i	$0.129431\pi$
$762$	−10.6234			−0.384846
$763$		0			0
$764$	13.5817			0.491370
$765$	−1.57616	−	2.72998i	−0.0569861	−	0.0987028i
$766$	−7.88631	−	4.55316i	−0.284944	−	0.164512i
$767$	6.12658	−	10.6116i	0.221218	−	0.383161i
$768$	8.59650	+	14.8896i	0.310199	+	0.537281i
$769$			39.5435i			1.42598i	0.701176	+	0.712988i	$0.252659\pi$
$769$			39.5435i			1.42598i	−0.701176	+	0.712988i	$0.747341\pi$
$770$		0			0
$771$	24.1293			0.868996
$772$	−15.7905	+	9.11667i	−0.568314	+	0.328116i
$773$	9.89411	−	17.1371i	0.355866	−	0.616379i	−0.631400	−	0.775458i	$-0.717519\pi$
$773$	9.89411	−	17.1371i	0.355866	−	0.616379i	0.987266	+	0.159079i	$0.0508525\pi$
$774$	−10.5682	−	6.10158i	−0.379868	−	0.219317i
$775$	−10.6510	−	18.4480i	−0.382594	−	0.662673i
$776$			3.89677i			0.139886i
$777$		0			0
$778$		−	9.94073i		−	0.356393i
$779$	−32.2438	−	3.68596i	−1.15525	−	0.132063i
$780$	−2.00320	−	1.15655i	−0.0717262	−	0.0414111i
$781$	−5.04257	−	2.91133i	−0.180437	−	0.104175i
$782$	−16.8764	−	29.2308i	−0.603499	−	1.04529i
$783$		−	29.4036i		−	1.05080i
$784$		0			0
$785$	6.59987			0.235560
$786$	−0.0624171	−	0.108110i	−0.00222634	−	0.00385614i
$787$	8.72110	−	15.1054i	0.310874	−	0.538449i	−0.667678	−	0.744450i	$-0.732712\pi$
$787$	8.72110	−	15.1054i	0.310874	−	0.538449i	0.978552	+	0.206001i	$0.0660450\pi$
$788$	−6.38964	+	11.0672i	−0.227621	+	0.394252i
$789$	2.29019	+	3.96673i	0.0815329	+	0.141219i
$790$		−	3.08728i		−	0.109840i
$791$		0			0
$792$			2.58452i			0.0918371i
$793$	−14.4665	+	8.35224i	−0.513720	+	0.296597i
$794$	14.1422	−	24.4950i	0.501887	−	0.869294i
$795$	−1.26028	+	2.18287i	−0.0446975	+	0.0774183i
$796$	−19.2579	+	11.1185i	−0.682577	+	0.394086i
$797$	23.8795			0.845854			0.422927	−	0.906164i	$-0.361003\pi$
$797$	23.8795			0.845854			0.422927	+	0.906164i	$0.361003\pi$
$798$		0			0
$799$	23.9292			0.846554
$800$	23.7718	−	13.7246i	0.840458	−	0.485239i
$801$	1.46709	−	2.54108i	0.0518371	−	0.0897845i
$802$	8.14483	−	14.1073i	0.287604	−	0.498144i
$803$	−0.543092	+	0.313554i	−0.0191653	+	0.0110651i
$804$		−	8.33567i		−	0.293976i
$805$		0			0
$806$			24.6683i			0.868905i
$807$	−2.19307	−	3.79850i	−0.0771996	−	0.133714i
$808$	−4.77591	+	8.27212i	−0.168016	+	0.291012i
$809$	8.26901	−	14.3223i	0.290723	−	0.503547i	−0.683258	−	0.730177i	$-0.739438\pi$
$809$	8.26901	−	14.3223i	0.290723	−	0.503547i	0.973981	+	0.226630i	$0.0727709\pi$
$810$	0.0353147	+	0.0611668i	0.00124083	+	0.00214918i
$811$	35.1379			1.23386			0.616930	−	0.787018i	$-0.288376\pi$
$811$	35.1379			1.23386			0.616930	+	0.787018i	$0.288376\pi$
$812$		0			0
$813$		−	28.8277i		−	1.01103i
$814$	−0.299984	−	0.519588i	−0.0105144	−	0.0182116i
$815$	−2.68457	−	1.54994i	−0.0940365	−	0.0542920i
$816$	0.830720	+	0.479617i	0.0290810	+	0.0167899i
$817$	31.1933	+	3.56588i	1.09132	+	0.124754i
$818$			4.76122i			0.166472i
$819$		0			0
$820$			2.57236i			0.0898307i
$821$	−25.0660	−	43.4156i	−0.874809	−	1.51521i	−0.856966	−	0.515373i	$-0.827654\pi$
$821$	−25.0660	−	43.4156i	−0.874809	−	1.51521i	−0.0178426	−	0.999841i	$-0.505680\pi$
$822$	15.5506	+	8.97817i	0.542391	+	0.313150i
$823$	3.09005	−	5.35212i	0.107712	−	0.186563i	−0.807131	−	0.590373i	$-0.798981\pi$
$823$	3.09005	−	5.35212i	0.107712	−	0.186563i	0.914843	+	0.403810i	$0.132314\pi$
$824$	−34.0004	+	19.6301i	−1.18446	+	0.683848i
$825$	−2.46398			−0.0857848
$826$		0			0
$827$			39.4829i			1.37296i	0.727151	+	0.686478i	$0.240844\pi$
$827$			39.4829i			1.37296i	−0.727151	+	0.686478i	$0.759156\pi$
$828$	−7.42669	−	12.8634i	−0.258095	−	0.447034i
$829$	−7.17020	+	12.4192i	−0.249031	+	0.431335i	−0.963257	−	0.268580i	$-0.913446\pi$
$829$	−7.17020	+	12.4192i	−0.249031	+	0.431335i	0.714226	+	0.699915i	$0.246779\pi$
$830$	−0.139868	−	0.0807525i	−0.00485487	−	0.00280296i
$831$	−0.836052	−	1.44809i	−0.0290023	−	0.0502335i
$832$	−33.7974			−1.17171
$833$		0			0
$834$	16.8861			0.584717
$835$	2.75089	−	1.58822i	0.0951983	−	0.0549628i
$836$	−0.993703	−	2.28771i	−0.0343679	−	0.0791219i
$837$	11.1463	−	19.3060i	0.385274	−	0.667314i
$838$	−3.61859	−	6.26757i	−0.125002	−	0.216510i
$839$	38.1902			1.31847			0.659237	−	0.751935i	$-0.270879\pi$
$839$	38.1902			1.31847			0.659237	+	0.751935i	$0.270879\pi$
$840$		0			0
$841$	−3.65007			−0.125864
$842$	−11.3976	−	19.7411i	−0.392786	−	0.680325i
$843$	26.6070	+	15.3616i	0.916394	+	0.529080i
$844$	−6.90575	−	3.98704i	−0.237706	−	0.137239i
$845$	6.86787	−	3.96517i	0.236262	−	0.136406i
$846$	−7.01306			−0.241114
$847$		0			0
$848$			1.31491i			0.0451541i
$849$	12.8843	−	7.43876i	0.442189	−	0.255298i
$850$	12.7082	−	22.0113i	0.435889	−	0.754982i
$851$	7.96089	+	4.59622i	0.272896	+	0.157556i
$852$	−13.3518	+	7.70869i	−0.457427	+	0.264095i
$853$		−	42.6408i		−	1.45999i	−0.683450	−	0.729997i	$-0.739521\pi$
$853$		−	42.6408i		−	1.45999i	0.683450	−	0.729997i	$-0.260479\pi$
$854$		0			0
$855$	−1.91019	−	1.41457i	−0.0653270	−	0.0483774i
$856$	−8.82333	−	15.2825i	−0.301575	−	0.522344i
$857$	15.7382	−	27.2594i	0.537607	−	0.931162i	−0.461426	−	0.887179i	$-0.652662\pi$
$857$	15.7382	−	27.2594i	0.537607	−	0.931162i	0.999032	−	0.0439830i	$-0.0140048\pi$
$858$	2.47109	+	1.42668i	0.0843616	+	0.0487062i
$859$	−9.72197	+	5.61298i	−0.331709	+	0.191512i	−0.656600	−	0.754239i	$-0.728006\pi$
$859$	−9.72197	+	5.61298i	−0.331709	+	0.191512i	0.324890	+	0.945752i	$0.394673\pi$
$860$		−	2.48856i		−	0.0848591i
$861$		0			0
$862$	5.74430			0.195652
$863$	−20.2175	+	11.6726i	−0.688210	+	0.397338i	−0.802941	−	0.596058i	$-0.796733\pi$
$863$	−20.2175	+	11.6726i	−0.688210	+	0.397338i	0.114731	+	0.993397i	$0.463399\pi$
$864$	24.8774	+	14.3629i	0.846345	+	0.488637i
$865$	2.03080	+	1.17248i	0.0690492	+	0.0398656i
$866$	18.7597	−	10.8309i	0.637479	−	0.368049i
$867$	−17.2599			−0.586178
$868$		0			0
$869$		−	5.71841i		−	0.193984i
$870$	−1.33874	+	0.772920i	−0.0453874	+	0.0262044i
$871$	36.4259	+	21.0305i	1.23424	+	0.712591i
$872$	18.5502	−	32.1299i	0.628189	−	1.08806i
$873$	1.29004	+	2.23442i	0.0436613	+	0.0756236i
$874$	−20.4530	−	15.1463i	−0.691832	−	0.512330i
$875$		0			0
$876$			1.66047i			0.0561022i
$877$	0.0709141	−	0.0409423i	0.00239460	−	0.00138252i	−0.498802	−	0.866716i	$-0.666227\pi$
$877$	0.0709141	−	0.0409423i	0.00239460	−	0.00138252i	0.501197	+	0.865333i	$0.332893\pi$
$878$	−1.42010	−	0.819893i	−0.0479259	−	0.0276700i
$879$	−4.21017	+	7.29223i	−0.142005	+	0.245961i
$880$	0.0187508	−	0.0108258i	0.000632090	−	0.000364937i
$881$		−	4.56861i		−	0.153920i	−0.997034	−	0.0769602i	$-0.975479\pi$
$881$		−	4.56861i		−	0.153920i	0.997034	−	0.0769602i	$-0.0245215\pi$
$882$		0			0
$883$	−38.5387			−1.29693			−0.648466	−	0.761244i	$-0.724589\pi$
$883$	−38.5387			−1.29693			−0.648466	+	0.761244i	$0.724589\pi$
$884$	38.2739	−	22.0974i	1.28729	−	0.743217i
$885$	0.504156	+	0.291075i	0.0169470	+	0.00978437i
$886$	8.28748	+	4.78478i	0.278423	+	0.160748i
$887$	9.31331	+	16.1311i	0.312710	+	0.541630i	0.978948	−	0.204109i	$-0.0654298\pi$
$887$	9.31331	+	16.1311i	0.312710	+	0.541630i	−0.666238	+	0.745739i	$0.732096\pi$
$888$	−4.23522			−0.142125
$889$		0			0
$890$	−0.398498			−0.0133577
$891$	0.0654117	+	0.113296i	0.00219137	+	0.00379557i
$892$	16.2048	−	28.0675i	0.542577	−	0.939770i
$893$	16.5495	−	7.18855i	0.553808	−	0.240556i
$894$	−4.52647	+	2.61336i	−0.151388	+	0.0874037i
$895$	−2.83306			−0.0946989
$896$		0			0
$897$	−43.7180			−1.45970
$898$	8.79392	+	15.2315i	0.293457	+	0.508282i
$899$	−21.4376	−	12.3770i	−0.714985	−	0.412797i
$900$	5.59244	−	9.68639i	0.186415	−	0.322880i
$901$	−24.0793	−	41.7066i	−0.802199	−	1.38945i
$902$		−	3.17319i		−	0.105656i
$903$		0			0
$904$	53.4807			1.77874
$905$	0.822249	−	0.474726i	0.0273325	−	0.0157804i
$906$	−4.57991	+	7.93263i	−0.152157	+	0.263544i
$907$	22.0220	+	12.7144i	0.731227	+	0.422174i	0.818871	−	0.573978i	$-0.194600\pi$
$907$	22.0220	+	12.7144i	0.731227	+	0.422174i	−0.0876439	+	0.996152i	$0.527934\pi$
$908$	13.1959	+	22.8560i	0.437921	+	0.758502i
$909$			6.32433i			0.209765i
$910$		0			0
$911$			20.7634i			0.687921i	0.938984	+	0.343961i	$0.111769\pi$
$911$			20.7634i			0.687921i	−0.938984	+	0.343961i	$0.888231\pi$
$912$	0.718610	+	0.0821482i	0.0237956	+	0.00272020i
$913$	−0.259070	−	0.149574i	−0.00857395	−	0.00495017i
$914$	7.29243	+	4.21028i	0.241212	+	0.139264i
$915$	−0.396816	−	0.687305i	−0.0131183	−	0.0227216i
$916$			11.5855i			0.382797i
$917$		0			0
$918$	26.5986			0.877884
$919$	−11.4561	−	19.8425i	−0.377901	−	0.654544i	0.612856	−	0.790195i	$-0.290021\pi$
$919$	−11.4561	−	19.8425i	−0.377901	−	0.654544i	−0.990757	+	0.135651i	$0.956687\pi$
$920$	−2.68901	+	4.65750i	−0.0886540	+	0.153553i
$921$	7.01536	−	12.1510i	0.231164	−	0.400388i
$922$	12.6928	+	21.9846i	0.418017	+	0.724026i
$923$		−	77.7947i		−	2.56064i
$924$		0			0
$925$			6.92208i			0.227597i
$926$	−19.4848	+	11.2496i	−0.640310	+	0.369683i
$927$	−12.9973	+	22.5119i	−0.426886	+	0.739388i
$928$	15.9488	−	27.6241i	0.523544	−	0.906805i
$929$	29.7938	−	17.2015i	0.977504	−	0.564362i	0.0759886	−	0.997109i	$-0.475789\pi$
$929$	29.7938	−	17.2015i	0.977504	−	0.564362i	0.901516	+	0.432746i	$0.142455\pi$
$930$	−1.17200			−0.0384313
$931$		0			0
$932$	−12.1509			−0.398017
$933$	−21.2754	+	12.2834i	−0.696526	+	0.402139i
$934$	7.39679	−	12.8116i	0.242030	−	0.419209i
$935$	−0.396496	+	0.686751i	−0.0129668	+	0.0224592i
$936$	−29.9047	+	17.2655i	−0.977467	+	0.564341i
$937$			27.7349i			0.906058i	0.891496	+	0.453029i	$0.149657\pi$
$937$			27.7349i			0.906058i	−0.891496	+	0.453029i	$0.850343\pi$
$938$		0			0
$939$		−	23.4870i		−	0.766468i
$940$	−0.715078	−	1.23855i	−0.0233233	−	0.0403971i
$941$	27.5423	−	47.7046i	0.897853	−	1.55513i	0.0676192	−	0.997711i	$-0.478460\pi$
$941$	27.5423	−	47.7046i	0.897853	−	1.55513i	0.830234	−	0.557416i	$-0.188207\pi$
$942$	−10.7785	+	18.6689i	−0.351183	+	0.608267i
$943$	24.3091	+	42.1045i	0.791612	+	1.37111i
$944$	0.303692			0.00988433
$945$		0			0
$946$			3.06981i			0.0998081i
$947$	−29.4083	−	50.9367i	−0.955641	−	1.65522i	−0.732894	−	0.680343i	$-0.761831\pi$
$947$	−29.4083	−	50.9367i	−0.955641	−	1.65522i	−0.222747	−	0.974876i	$-0.571502\pi$
$948$	−13.1128	−	7.57068i	−0.425884	−	0.245884i
$949$	−7.25608	−	4.18930i	−0.235542	−	0.135990i
$950$	2.17665	−	19.0408i	0.0706200	−	0.617764i
$951$			5.94640i			0.192825i
$952$		0			0
$953$			3.64330i			0.118018i	0.998257	+	0.0590090i	$0.0187941\pi$
$953$			3.64330i			0.118018i	−0.998257	+	0.0590090i	$0.981206\pi$
$954$	7.05706	+	12.2232i	0.228481	+	0.395740i
$955$	−2.81976	−	1.62799i	−0.0912452	−	0.0526804i
$956$	−15.8694	+	27.4866i	−0.513254	+	0.888981i
$957$	−2.47967	+	1.43164i	−0.0801565	+	0.0462784i
$958$	5.81702			0.187940
$959$		0			0
$960$		−	1.60572i		−	0.0518244i
$961$	6.11622	+	10.5936i	0.197298	+	0.341729i
$962$	4.00800	−	6.94205i	0.129223	−	0.223821i
$963$	−10.1186	−	5.84199i	−0.326068	−	0.188256i
$964$	−3.44890	−	5.97368i	−0.111082	−	0.192399i
$965$	4.37111			0.140711
$966$		0			0
$967$	0.538006			0.0173011			0.00865055	−	0.999963i	$-0.497246\pi$
$967$	0.538006			0.0173011			0.00865055	+	0.999963i	$0.497246\pi$
$968$	−26.6986	+	15.4144i	−0.858124	+	0.495438i
$969$	−24.2974	+	10.5540i	−0.780545	+	0.339043i
$970$	0.175204	−	0.303462i	0.00562545	−	0.00974356i
$971$	27.0391	+	46.8330i	0.867725	+	1.50294i	0.864316	+	0.502949i	$0.167752\pi$
$971$	27.0391	+	46.8330i	0.867725	+	1.50294i	0.00340911	+	0.999994i	$0.498915\pi$
$972$	18.8791			0.605548
$973$		0			0
$974$	−5.06178			−0.162190
$975$	−16.4602	−	28.5100i	−0.527150	−	0.913050i
$976$	−0.358549	−	0.207008i	−0.0114769	−	0.00662617i
$977$	−39.8029	−	22.9802i	−1.27341	−	0.735202i	−0.297780	−	0.954634i	$-0.596246\pi$
$977$	−39.8029	−	22.9802i	−1.27341	−	0.735202i	−0.975628	+	0.219432i	$0.929580\pi$
$978$	8.76857	−	5.06253i	0.280388	−	0.161882i
$979$	−0.738118			−0.0235904
$980$		0			0
$981$		−	24.5644i		−	0.784282i
$982$	−14.7570	+	8.51994i	−0.470914	+	0.271882i
$983$	−4.26160	+	7.38130i	−0.135924	+	0.235427i	−0.925950	−	0.377646i	$-0.876734\pi$
$983$	−4.26160	+	7.38130i	−0.135924	+	0.235427i	0.790026	+	0.613073i	$0.210067\pi$
$984$	−19.3987	−	11.1999i	−0.618409	−	0.357039i
$985$	2.65315	−	1.53180i	0.0845365	−	0.0488072i
$986$		−	29.5353i		−	0.940597i
$987$		0			0
$988$	19.8321	−	26.7805i	0.630942	−	0.852001i
$989$	−23.5171	−	40.7328i	−0.747800	−	1.29523i
$990$	0.116203	−	0.201270i	0.00369318	−	0.00639678i
$991$	−40.0810	−	23.1408i	−1.27321	−	0.735091i	−0.297623	−	0.954683i	$-0.596194\pi$
$991$	−40.0810	−	23.1408i	−1.27321	−	0.735091i	−0.975592	+	0.219593i	$0.929527\pi$
$992$	20.9435	−	12.0917i	0.664957	−	0.383913i
$993$			27.6629i			0.877855i
$994$		0			0
$995$	5.33093			0.169002
$996$	−0.685972	+	0.396046i	−0.0217358	+	0.0125492i
$997$	23.0463	+	13.3058i	0.729883	+	0.421398i	0.818379	−	0.574678i	$-0.194873\pi$
$997$	23.0463	+	13.3058i	0.729883	+	0.421398i	−0.0884962	+	0.996077i	$0.528206\pi$
$998$	−0.806063	−	0.465381i	−0.0255155	−	0.0147314i
$999$	−6.27351	+	3.62201i	−0.198485	+	0.114595i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.o.i.227.27		80
7.2	even	3	inner	931.2.o.i.607.13		80
7.3	odd	6		931.2.c.f.930.27	yes	40
7.4	even	3		931.2.c.f.930.28	yes	40
7.5	odd	6	inner	931.2.o.i.607.14		80
7.6	odd	2	inner	931.2.o.i.227.28		80
19.18	odd	2	inner	931.2.o.i.227.14		80
133.18	odd	6		931.2.c.f.930.13	✓	40
133.37	odd	6	inner	931.2.o.i.607.28		80
133.75	even	6	inner	931.2.o.i.607.27		80
133.94	even	6		931.2.c.f.930.14	yes	40
133.132	even	2	inner	931.2.o.i.227.13		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
931.2.c.f.930.13	✓	40	133.18	odd	6
931.2.c.f.930.14	yes	40	133.94	even	6
931.2.c.f.930.27	yes	40	7.3	odd	6
931.2.c.f.930.28	yes	40	7.4	even	3
931.2.o.i.227.13		80	133.132	even	2	inner
931.2.o.i.227.14		80	19.18	odd	2	inner
931.2.o.i.227.27		80	1.1	even	1	trivial
931.2.o.i.227.28		80	7.6	odd	2	inner
931.2.o.i.607.13		80	7.2	even	3	inner
931.2.o.i.607.14		80	7.5	odd	6	inner
931.2.o.i.607.27		80	133.75	even	6	inner
931.2.o.i.607.28		80	133.37	odd	6	inner

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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.774359 - 0.447076i) q^{2} +(-0.525649 + 0.910452i) q^{3} +(-0.600246 + 1.03966i) q^{4} +(0.249238 - 0.143898i) q^{5} +0.940021i q^{6} +2.86173i q^{8} +(0.947385 + 1.64092i) q^{9} +O(q^{10})\)	\(q+(0.774359 - 0.447076i) q^{2} +(-0.525649 + 0.910452i) q^{3} +(-0.600246 + 1.03966i) q^{4} +(0.249238 - 0.143898i) q^{5} +0.940021i q^{6} +2.86173i q^{8} +(0.947385 + 1.64092i) q^{9} +(0.128667 - 0.222857i) q^{10} +(0.238323 - 0.412787i) q^{11} +(-0.631038 - 1.09299i) q^{12} +6.36831 q^{13} +0.302559i q^{15} +(0.0789186 + 0.136691i) q^{16} +(-5.00633 - 2.89040i) q^{17} +(1.46723 + 0.847107i) q^{18} +(-4.33069 - 0.495065i) q^{19} +0.345496i q^{20} -0.426194i q^{22} +(3.26497 + 5.65510i) q^{23} +(-2.60546 - 1.50427i) q^{24} +(-2.45859 + 4.25840i) q^{25} +(4.93136 - 2.84712i) q^{26} -5.14587 q^{27} +5.71402i q^{29} +(0.135267 + 0.234290i) q^{30} +(-2.16608 + 3.75176i) q^{31} +(-4.83443 - 2.79116i) q^{32} +(0.250549 + 0.433963i) q^{33} -5.16892 q^{34} -2.27466 q^{36} +(1.21914 - 0.703868i) q^{37} +(-3.57484 + 1.55279i) q^{38} +(-3.34750 + 5.79804i) q^{39} +(0.411797 + 0.713253i) q^{40} +7.44541 q^{41} -7.20284 q^{43} +(0.286105 + 0.495548i) q^{44} +(0.472250 + 0.272654i) q^{45} +(5.05652 + 2.91938i) q^{46} +(-3.58484 + 2.06971i) q^{47} -0.165934 q^{48} +4.39670i q^{50} +(5.26314 - 3.03868i) q^{51} +(-3.82255 + 6.62086i) q^{52} +(7.21467 + 4.16539i) q^{53} +(-3.98475 + 2.30059i) q^{54} -0.137177i q^{55} +(2.72716 - 3.68266i) q^{57} +(2.55460 + 4.42470i) q^{58} +(0.962041 - 1.66630i) q^{59} +(-0.314558 - 0.181610i) q^{60} +(-2.27164 + 1.31153i) q^{61} +3.87361i q^{62} -5.30712 q^{64} +(1.58723 - 0.916387i) q^{65} +(0.388029 + 0.224029i) q^{66} +(5.71986 + 3.30237i) q^{67} +(6.01005 - 3.46990i) q^{68} -6.86493 q^{69} -12.2159i q^{71} +(-4.69586 + 2.71116i) q^{72} +(-1.13940 - 0.657835i) q^{73} +(0.629365 - 1.09009i) q^{74} +(-2.58471 - 4.47685i) q^{75} +(3.11418 - 4.20527i) q^{76} +5.98635i q^{78} +(10.3899 - 5.99859i) q^{79} +(0.0393391 + 0.0227124i) q^{80} +(-0.137233 + 0.237695i) q^{81} +(5.76541 - 3.32866i) q^{82} -0.627610i q^{83} -1.66369 q^{85} +(-5.57758 + 3.22022i) q^{86} +(-5.20234 - 3.00357i) q^{87} +(1.18128 + 0.682015i) q^{88} +(-0.774284 - 1.34110i) q^{89} +0.487588 q^{90} -7.83915 q^{92} +(-2.27719 - 3.94422i) q^{93} +(-1.85064 + 3.20540i) q^{94} +(-1.15061 + 0.499789i) q^{95} +(5.08244 - 2.93435i) q^{96} +1.36169 q^{97} +0.903134 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 40 q^{4} - 40 q^{9}+O(q^{10}) \) 80 * q + 40 * q^4 - 40 * q^9	\( 80 q + 40 q^{4} - 40 q^{9} - 40 q^{16} - 48 q^{23} + 56 q^{25} + 64 q^{30} - 80 q^{36} - 32 q^{39} - 32 q^{43} - 96 q^{57} + 96 q^{58} + 112 q^{64} - 144 q^{74} + 88 q^{81} - 320 q^{85} - 96 q^{92} - 72 q^{95} - 96 q^{99}+O(q^{100}) \) 80 * q + 40 * q^4 - 40 * q^9 - 40 * q^16 - 48 * q^23 + 56 * q^25 + 64 * q^30 - 80 * q^36 - 32 * q^39 - 32 * q^43 - 96 * q^57 + 96 * q^58 + 112 * q^64 - 144 * q^74 + 88 * q^81 - 320 * q^85 - 96 * q^92 - 72 * q^95 - 96 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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