LMFDB - Embedded newform 671.2.f.a.538.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(538,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, 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("671.538");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$60$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			538.1
Character	$\chi$	$=$	671.538
Dual form			671.2.f.a.560.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91401 - 1.91401i) q^{2} -0.380921i q^{3} +5.32688i q^{4} +1.26088i q^{5} +(-0.729087 + 0.729087i) q^{6} +(-2.25350 - 2.25350i) q^{7} +(6.36769 - 6.36769i) q^{8} +2.85490 q^{9} +O(q^{10})$	\(q+(-1.91401 - 1.91401i) q^{2} -0.380921i q^{3} +5.32688i q^{4} +1.26088i q^{5} +(-0.729087 + 0.729087i) q^{6} +(-2.25350 - 2.25350i) q^{7} +(6.36769 - 6.36769i) q^{8} +2.85490 q^{9} +(2.41334 - 2.41334i) q^{10} +(-2.27195 - 2.41625i) q^{11} +2.02912 q^{12} +3.94340i q^{13} +8.62644i q^{14} +0.480297 q^{15} -13.7219 q^{16} +(-4.66130 + 4.66130i) q^{17} +(-5.46431 - 5.46431i) q^{18} +6.14588 q^{19} -6.71657 q^{20} +(-0.858405 + 0.858405i) q^{21} +(-0.276183 + 8.97326i) q^{22} +(-2.96299 + 2.96299i) q^{23} +(-2.42559 - 2.42559i) q^{24} +3.41017 q^{25} +(7.54771 - 7.54771i) q^{26} -2.23025i q^{27} +(12.0041 - 12.0041i) q^{28} +(-0.237623 + 0.237623i) q^{29} +(-0.919294 - 0.919294i) q^{30} +(-0.588410 - 0.588410i) q^{31} +(13.5285 + 13.5285i) q^{32} +(-0.920399 + 0.865434i) q^{33} +17.8435 q^{34} +(2.84140 - 2.84140i) q^{35} +15.2077i q^{36} +(6.08084 + 6.08084i) q^{37} +(-11.7633 - 11.7633i) q^{38} +1.50212 q^{39} +(8.02891 + 8.02891i) q^{40} +9.75637 q^{41} +3.28599 q^{42} +(0.399956 - 0.399956i) q^{43} +(12.8711 - 12.1024i) q^{44} +3.59969i q^{45} +11.3424 q^{46} +3.66976 q^{47} +5.22696i q^{48} +3.15651i q^{49} +(-6.52711 - 6.52711i) q^{50} +(1.77559 + 1.77559i) q^{51} -21.0060 q^{52} +(3.94379 - 3.94379i) q^{53} +(-4.26873 + 4.26873i) q^{54} +(3.04660 - 2.86466i) q^{55} -28.6991 q^{56} -2.34110i q^{57} +0.909626 q^{58} +(-4.00485 - 4.00485i) q^{59} +2.55848i q^{60} +(-2.18704 + 7.49779i) q^{61} +2.25245i q^{62} +(-6.43351 - 6.43351i) q^{63} -24.3436i q^{64} -4.97216 q^{65} +(3.41810 + 0.105204i) q^{66} +(3.13556 + 3.13556i) q^{67} +(-24.8302 - 24.8302i) q^{68} +(1.12866 + 1.12866i) q^{69} -10.8769 q^{70} +(5.89382 + 5.89382i) q^{71} +(18.1791 - 18.1791i) q^{72} +1.63275i q^{73} -23.2776i q^{74} -1.29901i q^{75} +32.7384i q^{76} +(-0.325170 + 10.5648i) q^{77} +(-2.87508 - 2.87508i) q^{78} +(9.68253 + 9.68253i) q^{79} -17.3017i q^{80} +7.71515 q^{81} +(-18.6738 - 18.6738i) q^{82} -12.6501i q^{83} +(-4.57262 - 4.57262i) q^{84} +(-5.87735 - 5.87735i) q^{85} -1.53104 q^{86} +(0.0905156 + 0.0905156i) q^{87} +(-29.8530 - 0.918828i) q^{88} +(1.40184 + 1.40184i) q^{89} +(6.88985 - 6.88985i) q^{90} +(8.88644 - 8.88644i) q^{91} +(-15.7835 - 15.7835i) q^{92} +(-0.224138 + 0.224138i) q^{93} +(-7.02396 - 7.02396i) q^{94} +7.74923i q^{95} +(5.15329 - 5.15329i) q^{96} +3.21230i q^{97} +(6.04159 - 6.04159i) q^{98} +(-6.48619 - 6.89814i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 120 q^{9}+O(q^{10}) $ 120 * q - 120 * q^9	$ 120 q - 120 q^{9} - 4 q^{11} + 16 q^{12} + 16 q^{15} - 148 q^{16} + 56 q^{20} - 4 q^{22} - 4 q^{23} - 104 q^{25} + 40 q^{26} - 2 q^{33} - 8 q^{34} - 12 q^{37} + 20 q^{38} + 16 q^{42} - 10 q^{44} - 4 q^{53} + 50 q^{55} - 24 q^{56} + 64 q^{58} - 56 q^{67} + 68 q^{69} + 144 q^{70} - 12 q^{71} - 64 q^{77} + 84 q^{78} + 72 q^{81} + 40 q^{82} - 80 q^{86} + 4 q^{89} - 4 q^{91} + 4 q^{92} + 64 q^{93} + 24 q^{99}+O(q^{100}) $ 120 * q - 120 * q^9 - 4 * q^11 + 16 * q^12 + 16 * q^15 - 148 * q^16 + 56 * q^20 - 4 * q^22 - 4 * q^23 - 104 * q^25 + 40 * q^26 - 2 * q^33 - 8 * q^34 - 12 * q^37 + 20 * q^38 + 16 * q^42 - 10 * q^44 - 4 * q^53 + 50 * q^55 - 24 * q^56 + 64 * q^58 - 56 * q^67 + 68 * q^69 + 144 * q^70 - 12 * q^71 - 64 * q^77 + 84 * q^78 + 72 * q^81 + 40 * q^82 - 80 * q^86 + 4 * q^89 - 4 * q^91 + 4 * q^92 + 64 * q^93 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/671\mathbb{Z}\right)^\times$.

$n$	$123$	$551$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.91401	−	1.91401i	−1.35341	−	1.35341i	−0.881815	−	0.471596i	$-0.843678\pi$
$2$	−1.91401	−	1.91401i	−1.35341	−	1.35341i	−0.471596	−	0.881815i	$-0.656322\pi$
$3$		−	0.380921i		−	0.219925i	−0.993936	−	0.109962i	$-0.964927\pi$
$3$		−	0.380921i		−	0.219925i	0.993936	−	0.109962i	$-0.0350731\pi$
$4$			5.32688i			2.66344i
$5$			1.26088i			0.563884i	0.959431	+	0.281942i	$0.0909786\pi$
$5$			1.26088i			0.563884i	−0.959431	+	0.281942i	$0.909021\pi$
$6$	−0.729087	+	0.729087i	−0.297649	+	0.297649i
$7$	−2.25350	−	2.25350i	−0.851742	−	0.851742i	0.138606	−	0.990348i	$-0.455738\pi$
$7$	−2.25350	−	2.25350i	−0.851742	−	0.851742i	−0.990348	+	0.138606i	$0.955738\pi$
$8$	6.36769	−	6.36769i	2.25132	−	2.25132i
$9$	2.85490			0.951633
$10$	2.41334	−	2.41334i	0.763166	−	0.763166i
$11$	−2.27195	−	2.41625i	−0.685019	−	0.728525i
$11$	−2.27195	−	2.41625i	−0.685019	−	0.728525i
$12$	2.02912			0.585757
$13$			3.94340i			1.09370i	0.837230	+	0.546851i	$0.184173\pi$
$13$			3.94340i			1.09370i	−0.837230	+	0.546851i	$0.815827\pi$
$14$			8.62644i			2.30551i
$15$	0.480297			0.124012
$16$	−13.7219			−3.43047
$17$	−4.66130	+	4.66130i	−1.13053	+	1.13053i	−0.140441	+	0.990089i	$0.544852\pi$
$17$	−4.66130	+	4.66130i	−1.13053	+	1.13053i	−0.990089	+	0.140441i	$0.955148\pi$
$18$	−5.46431	−	5.46431i	−1.28795	−	1.28795i
$19$	6.14588			1.40996			0.704981	−	0.709226i	$-0.250956\pi$
$19$	6.14588			1.40996			0.704981	+	0.709226i	$0.250956\pi$
$20$	−6.71657			−1.50187
$21$	−0.858405	+	0.858405i	−0.187319	+	0.187319i
$22$	−0.276183	+	8.97326i	−0.0588825	+	1.91311i
$23$	−2.96299	+	2.96299i	−0.617826	+	0.617826i	−0.944973	−	0.327148i	$-0.893913\pi$
$23$	−2.96299	+	2.96299i	−0.617826	+	0.617826i	0.327148	+	0.944973i	$0.393913\pi$
$24$	−2.42559	−	2.42559i	−0.495121	−	0.495121i
$25$	3.41017			0.682035
$26$	7.54771	−	7.54771i	1.48023	−	1.48023i
$27$		−	2.23025i		−	0.429213i
$28$	12.0041	−	12.0041i	2.26856	−	2.26856i
$29$	−0.237623	+	0.237623i	−0.0441255	+	0.0441255i	−0.728825	−	0.684700i	$-0.759933\pi$
$29$	−0.237623	+	0.237623i	−0.0441255	+	0.0441255i	0.684700	+	0.728825i	$0.259933\pi$
$30$	−0.919294	−	0.919294i	−0.167839	−	0.167839i
$31$	−0.588410	−	0.588410i	−0.105682	−	0.105682i	0.652289	−	0.757970i	$-0.273809\pi$
$31$	−0.588410	−	0.588410i	−0.105682	−	0.105682i	−0.757970	+	0.652289i	$0.773809\pi$
$32$	13.5285	+	13.5285i	2.39152	+	2.39152i
$33$	−0.920399	+	0.865434i	−0.160221	+	0.150653i
$34$	17.8435			3.06014
$35$	2.84140	−	2.84140i	0.480284	−	0.480284i
$36$			15.2077i			2.53462i
$37$	6.08084	+	6.08084i	0.999684	+	0.999684i	1.00000		0.000316365i	$-0.000100702\pi$
$37$	6.08084	+	6.08084i	0.999684	+	0.999684i	−0.000316365		1.00000i	$0.500101\pi$
$38$	−11.7633	−	11.7633i	−1.90826	−	1.90826i
$39$	1.50212			0.240532
$40$	8.02891	+	8.02891i	1.26948	+	1.26948i
$41$	9.75637			1.52369			0.761845	−	0.647760i	$-0.224294\pi$
$41$	9.75637			1.52369			0.761845	+	0.647760i	$0.224294\pi$
$42$	3.28599			0.507040
$43$	0.399956	−	0.399956i	0.0609927	−	0.0609927i	−0.675953	−	0.736945i	$-0.736268\pi$
$43$	0.399956	−	0.399956i	0.0609927	−	0.0609927i	0.736945	+	0.675953i	$0.236268\pi$
$44$	12.8711	−	12.1024i	1.94038	−	1.82451i
$45$			3.59969i			0.536611i
$46$	11.3424			1.67234
$47$	3.66976			0.535289			0.267645	−	0.963518i	$-0.413755\pi$
$47$	3.66976			0.535289			0.267645	+	0.963518i	$0.413755\pi$
$48$			5.22696i			0.754447i
$49$			3.15651i			0.450929i
$50$	−6.52711	−	6.52711i	−0.923073	−	0.923073i
$51$	1.77559	+	1.77559i	0.248632	+	0.248632i
$52$	−21.0060			−2.91301
$53$	3.94379	−	3.94379i	0.541721	−	0.541721i	−0.382312	−	0.924033i	$-0.624872\pi$
$53$	3.94379	−	3.94379i	0.541721	−	0.541721i	0.924033	+	0.382312i	$0.124872\pi$
$54$	−4.26873	+	4.26873i	−0.580901	+	0.580901i
$55$	3.04660	−	2.86466i	0.410804	−	0.386271i
$56$	−28.6991			−3.83508
$57$		−	2.34110i		−	0.310086i
$58$	0.909626			0.119440
$59$	−4.00485	−	4.00485i	−0.521386	−	0.521386i	0.396604	−	0.917990i	$-0.370189\pi$
$59$	−4.00485	−	4.00485i	−0.521386	−	0.521386i	−0.917990	+	0.396604i	$0.870189\pi$
$60$			2.55848i			0.330299i
$61$	−2.18704	+	7.49779i	−0.280021	+	0.959994i
$61$	−2.18704	+	7.49779i	−0.280021	+	0.959994i
$62$			2.25245i			0.286061i
$63$	−6.43351	−	6.43351i	−0.810546	−	0.810546i
$64$		−	24.3436i		−	3.04295i
$65$	−4.97216			−0.616721
$66$	3.41810	+	0.105204i	0.420740	+	0.0129497i
$67$	3.13556	+	3.13556i	0.383070	+	0.383070i	0.872207	−	0.489137i	$-0.162688\pi$
$67$	3.13556	+	3.13556i	0.383070	+	0.383070i	−0.489137	+	0.872207i	$0.662688\pi$
$68$	−24.8302	−	24.8302i	−3.01110	−	3.01110i
$69$	1.12866	+	1.12866i	0.135875	+	0.135875i
$70$	−10.8769			−1.30004
$71$	5.89382	+	5.89382i	0.699468	+	0.699468i	0.964296	−	0.264828i	$-0.0853152\pi$
$71$	5.89382	+	5.89382i	0.699468	+	0.699468i	−0.264828	+	0.964296i	$0.585315\pi$
$72$	18.1791	−	18.1791i	2.14243	−	2.14243i
$73$			1.63275i			0.191099i	0.995425	+	0.0955494i	$0.0304608\pi$
$73$			1.63275i			0.191099i	−0.995425	+	0.0955494i	$0.969539\pi$
$74$		−	23.2776i		−	2.70596i
$75$		−	1.29901i		−	0.149996i
$76$			32.7384i			3.75535i
$77$	−0.325170	+	10.5648i	−0.0370565	+	1.20398i
$78$	−2.87508	−	2.87508i	−0.325539	−	0.325539i
$79$	9.68253	+	9.68253i	1.08937	+	1.08937i	0.995593	+	0.0937767i	$0.0298940\pi$
$79$	9.68253	+	9.68253i	1.08937	+	1.08937i	0.0937767	+	0.995593i	$0.470106\pi$
$80$		−	17.3017i		−	1.93439i
$81$	7.71515			0.857238
$82$	−18.6738	−	18.6738i	−2.06218	−	2.06218i
$83$		−	12.6501i		−	1.38852i	−0.719723	−	0.694262i	$-0.755731\pi$
$83$		−	12.6501i		−	1.38852i	0.719723	−	0.694262i	$-0.244269\pi$
$84$	−4.57262	−	4.57262i	−0.498914	−	0.498914i
$85$	−5.87735	−	5.87735i	−0.637488	−	0.637488i
$86$	−1.53104			−0.165096
$87$	0.0905156	+	0.0905156i	0.00970429	+	0.00970429i
$88$	−29.8530	−	0.918828i	−3.18234	−	0.0979474i
$89$	1.40184	+	1.40184i	0.148594	+	0.148594i	0.777490	−	0.628895i	$-0.216493\pi$
$89$	1.40184	+	1.40184i	0.148594	+	0.148594i	−0.628895	+	0.777490i	$0.716493\pi$
$90$	6.88985	−	6.88985i	0.726254	−	0.726254i
$91$	8.88644	−	8.88644i	0.931552	−	0.931552i
$92$	−15.7835	−	15.7835i	−1.64554	−	1.64554i
$93$	−0.224138	+	0.224138i	−0.0232420	+	0.0232420i
$94$	−7.02396	−	7.02396i	−0.724466	−	0.724466i
$95$			7.74923i			0.795055i
$96$	5.15329	−	5.15329i	0.525955	−	0.525955i
$97$			3.21230i			0.326160i	0.986613	+	0.163080i	$0.0521428\pi$
$97$			3.21230i			0.326160i	−0.986613	+	0.163080i	$0.947857\pi$
$98$	6.04159	−	6.04159i	0.610292	−	0.610292i
$99$	−6.48619	−	6.89814i	−0.651886	−	0.693289i
$100$			18.1656i			1.81656i
$101$	4.35733	+	4.35733i	0.433570	+	0.433570i	0.889841	−	0.456271i	$-0.150815\pi$
$101$	4.35733	+	4.35733i	0.433570	+	0.433570i	−0.456271	+	0.889841i	$0.650815\pi$
$102$		−	6.79698i		−	0.673002i
$103$	12.9199			1.27303			0.636516	−	0.771264i	$-0.280375\pi$
$103$	12.9199			1.27303			0.636516	+	0.771264i	$0.280375\pi$
$104$	25.1103	+	25.1103i	2.46227	+	2.46227i
$105$	−1.08235	−	1.08235i	−0.105626	−	0.105626i
$106$	−15.0969			−1.46634
$107$	−3.39061			−0.327783			−0.163891	−	0.986478i	$-0.552405\pi$
$107$	−3.39061			−0.327783			−0.163891	+	0.986478i	$0.552405\pi$
$108$	11.8803			1.14318
$109$	5.00477			0.479370			0.239685	−	0.970851i	$-0.422956\pi$
$109$	5.00477			0.479370			0.239685	+	0.970851i	$0.422956\pi$
$110$	−11.3142	−	0.348235i	−1.07877	−	0.0332029i
$111$	2.31632	−	2.31632i	0.219855	−	0.219855i
$112$	30.9223	+	30.9223i	2.92188	+	2.92188i
$113$		−	8.62736i		−	0.811593i	−0.913963	−	0.405797i	$-0.866994\pi$
$113$		−	8.62736i		−	0.811593i	0.913963	−	0.405797i	$-0.133006\pi$
$114$	−4.48088	+	4.48088i	−0.419673	+	0.419673i
$115$	−3.73598	−	3.73598i	−0.348382	−	0.348382i
$116$	−1.26579	−	1.26579i	−0.117526	−	0.117526i
$117$			11.2580i			1.04080i
$118$			15.3306i			1.41130i
$119$	21.0084			1.92584
$120$	3.05838	−	3.05838i	0.279191	−	0.279191i
$121$	−0.676485	+	10.9792i	−0.0614987	+	0.998107i
$122$	18.5369	−	10.1648i	1.67825	−	0.920282i
$123$		−	3.71641i		−	0.335097i
$124$	3.13439	−	3.13439i	0.281477	−	0.281477i
$125$			10.6042i			0.948472i
$126$			24.6276i			2.19400i
$127$	−18.2145			−1.61627			−0.808136	−	0.588996i	$-0.799523\pi$
$127$	−18.2145			−1.61627			−0.808136	+	0.588996i	$0.799523\pi$
$128$	−19.5369	+	19.5369i	−1.72683	+	1.72683i
$129$	−0.152352	−	0.152352i	−0.0134138	−	0.0134138i
$130$	9.51677	+	9.51677i	0.834676	+	0.834676i
$131$			7.19799i			0.628891i	0.949276	+	0.314446i	$0.101819\pi$
$131$			7.19799i			0.628891i	−0.949276	+	0.314446i	$0.898181\pi$
$132$	−4.61006	−	4.90286i	−0.401254	−	0.426739i
$133$	−13.8497	−	13.8497i	−1.20092	−	1.20092i
$134$		−	12.0030i		−	1.03690i
$135$	2.81209			0.242026
$136$			59.3633i			5.09036i
$137$	−17.4256			−1.48877			−0.744385	−	0.667750i	$-0.767257\pi$
$137$	−17.4256			−1.48877			−0.744385	+	0.667750i	$0.767257\pi$
$138$		−	4.32055i		−	0.367790i
$139$	−1.28729	+	1.28729i	−0.109187	+	0.109187i	−0.759589	−	0.650403i	$-0.774600\pi$
$139$	−1.28729	+	1.28729i	−0.109187	+	0.109187i	0.650403	+	0.759589i	$0.274600\pi$
$140$	15.1358	+	15.1358i	1.27921	+	1.27921i
$141$		−	1.39789i		−	0.117723i
$142$		−	22.5617i		−	1.89333i
$143$	9.52822	−	8.95920i	0.796789	−	0.749206i
$144$	−39.1746			−3.26455
$145$	−0.299615	−	0.299615i	−0.0248816	−	0.0248816i
$146$	3.12510	−	3.12510i	0.258635	−	0.258635i
$147$	1.20238			0.0991706
$148$	−32.3919	+	32.3919i	−2.66260	+	2.66260i
$149$	8.72207			0.714540			0.357270	−	0.934001i	$-0.383708\pi$
$149$	8.72207			0.714540			0.357270	+	0.934001i	$0.383708\pi$
$150$	−2.48632	+	2.48632i	−0.203007	+	0.203007i
$151$	7.23342	−	7.23342i	0.588648	−	0.588648i	−0.348617	−	0.937265i	$-0.613349\pi$
$151$	7.23342	−	7.23342i	0.588648	−	0.588648i	0.937265	+	0.348617i	$0.113349\pi$
$152$	39.1350	−	39.1350i	3.17427	−	3.17427i
$153$	−13.3075	+	13.3075i	−1.07585	+	1.07585i
$154$	20.8436	−	19.5988i	1.67963	−	1.57932i
$155$	0.741917	−	0.741917i	0.0595922	−	0.0595922i
$156$			8.00163i			0.640643i
$157$	−17.2687	−	17.2687i	−1.37819	−	1.37819i	−0.847673	−	0.530518i	$-0.821997\pi$
$157$	−17.2687	−	17.2687i	−1.37819	−	1.37819i	−0.530518	−	0.847673i	$-0.678003\pi$
$158$		−	37.0650i		−	2.94873i
$159$	−1.50227	−	1.50227i	−0.119138	−	0.119138i
$160$	−17.0578	+	17.0578i	−1.34854	+	1.34854i
$161$	13.3542			1.05246
$162$	−14.7669	−	14.7669i	−1.16020	−	1.16020i
$163$			21.7396i			1.70278i	0.524535	+	0.851389i	$0.324239\pi$
$163$			21.7396i			1.70278i	−0.524535	+	0.851389i	$0.675761\pi$
$164$			51.9710i			4.05825i
$165$	−1.09121	−	1.16052i	−0.0849506	−	0.0903460i
$166$	−24.2123	+	24.2123i	−1.87924	+	1.87924i
$167$	6.83786			0.529130			0.264565	−	0.964368i	$-0.414772\pi$
$167$	6.83786			0.529130			0.264565	+	0.964368i	$0.414772\pi$
$168$			10.9321i			0.843430i
$169$	−2.55038			−0.196183
$170$			22.4986i			1.72557i
$171$	17.5459			1.34177
$172$	2.13052	+	2.13052i	0.162450	+	0.162450i
$173$	14.2727	+	14.2727i	1.08514	+	1.08514i	0.996021	+	0.0891140i	$0.0284035\pi$
$173$	14.2727	+	14.2727i	1.08514	+	1.08514i	0.0891140	+	0.996021i	$0.471596\pi$
$174$		−	0.346496i		−	0.0262678i
$175$	−7.68482	−	7.68482i	−0.580918	−	0.580918i
$176$	31.1755	+	33.1555i	2.34994	+	2.49919i
$177$	−1.52553	+	1.52553i	−0.114666	+	0.114666i
$178$		−	5.36626i		−	0.402219i
$179$	−24.9859			−1.86753			−0.933765	−	0.357886i	$-0.883498\pi$
$179$	−24.9859			−1.86753			−0.933765	+	0.357886i	$0.883498\pi$
$180$	−19.1751			−1.42923
$181$	13.2763	+	13.2763i	0.986816	+	0.986816i	0.999914	−	0.0130978i	$-0.00416928\pi$
$181$	13.2763	+	13.2763i	0.986816	+	0.986816i	−0.0130978	+	0.999914i	$0.504169\pi$
$182$	−34.0175			−2.52154
$183$	2.85607	+	0.833089i	0.211127	+	0.0615837i
$184$			37.7348i			2.78184i
$185$	−7.66722	+	7.66722i	−0.563705	+	0.563705i
$186$	0.858005			0.0629120
$187$	21.8531	+	0.672604i	1.59805	+	0.0491857i
$188$			19.5484i			1.42571i
$189$	−5.02587	+	5.02587i	−0.365579	+	0.365579i
$190$	14.8321	−	14.8321i	1.07604	−	1.07604i
$191$	−7.12101	−	7.12101i	−0.515258	−	0.515258i	0.400875	−	0.916133i	$-0.368706\pi$
$191$	−7.12101	−	7.12101i	−0.515258	−	0.515258i	−0.916133	+	0.400875i	$0.868706\pi$
$192$	−9.27298			−0.669220
$193$	14.2902	−	14.2902i	1.02863	−	1.02863i	0.0290500	−	0.999578i	$-0.490752\pi$
$193$	14.2902	−	14.2902i	1.02863	−	1.02863i	0.999578	−	0.0290500i	$-0.00924819\pi$
$194$	6.14838	−	6.14838i	0.441428	−	0.441428i
$195$			1.89400i			0.135632i
$196$	−16.8143			−1.20102
$197$	−7.79674			−0.555494			−0.277747	−	0.960654i	$-0.589588\pi$
$197$	−7.79674			−0.555494			−0.277747	+	0.960654i	$0.589588\pi$
$198$	−0.788475	+	25.6178i	−0.0560345	+	1.82057i
$199$	4.93752			0.350011			0.175006	−	0.984567i	$-0.444006\pi$
$199$	4.93752			0.350011			0.175006	+	0.984567i	$0.444006\pi$
$200$	21.7149	−	21.7149i	1.53548	−	1.53548i
$201$	1.19440	−	1.19440i	0.0842465	−	0.0842465i
$202$		−	16.6800i		−	1.17360i
$203$	1.07097			0.0751671
$204$	−9.45833	+	9.45833i	−0.662216	+	0.662216i
$205$			12.3016i			0.859184i
$206$	−24.7288	−	24.7288i	−1.72293	−	1.72293i
$207$	−8.45903	+	8.45903i	−0.587943	+	0.587943i
$208$		−	54.1109i		−	3.75191i
$209$	−13.9631	−	14.8500i	−0.965850	−	1.02719i
$210$			4.14325i			0.285912i
$211$	−5.80747	+	5.80747i	−0.399803	+	0.399803i	−0.878163	−	0.478361i	$-0.841231\pi$
$211$	−5.80747	+	5.80747i	−0.399803	+	0.399803i	0.478361	+	0.878163i	$0.341231\pi$
$212$	21.0081	+	21.0081i	1.44284	+	1.44284i
$213$	2.24508	−	2.24508i	0.153830	−	0.153830i
$214$	6.48967	+	6.48967i	0.443625	+	0.443625i
$215$	0.504297	+	0.504297i	0.0343928	+	0.0343928i
$216$	−14.2016	−	14.2016i	−0.966294	−	0.966294i
$217$			2.65196i			0.180027i
$218$	−9.57920	−	9.57920i	−0.648785	−	0.648785i
$219$	0.621949			0.0420274
$220$	15.2597	+	16.2289i	1.02881	+	1.09415i
$221$	−18.3813	−	18.3813i	−1.23646	−	1.23646i
$222$	−8.86692			−0.595109
$223$	−17.5937	+	17.5937i	−1.17816	+	1.17816i	−0.197948	+	0.980213i	$0.563428\pi$
$223$	−17.5937	+	17.5937i	−1.17816	+	1.17816i	−0.980213	+	0.197948i	$0.936572\pi$
$224$		−	60.9728i		−	4.07392i
$225$	9.73570			0.649047
$226$	−16.5129	+	16.5129i	−1.09842	+	1.09842i
$227$	9.37187	+	9.37187i	0.622033	+	0.622033i	0.946051	−	0.324018i	$-0.105034\pi$
$227$	9.37187	+	9.37187i	0.622033	+	0.622033i	−0.324018	+	0.946051i	$0.605034\pi$
$228$	12.4707			0.825895
$229$		−	1.89185i		−	0.125017i	−0.998044	−	0.0625085i	$-0.980090\pi$
$229$		−	1.89185i		−	0.125017i	0.998044	−	0.0625085i	$-0.0199101\pi$
$230$			14.3014i			0.943008i
$231$	4.02437	+	0.123864i	0.264784	+	0.00814965i
$232$			3.02622i			0.198681i
$233$	−15.6112	−	15.6112i	−1.02272	−	1.02272i	−0.999736	−	0.0229886i	$-0.992682\pi$
$233$	−15.6112	−	15.6112i	−1.02272	−	1.02272i	−0.0229886	−	0.999736i	$-0.507318\pi$
$234$	21.5479	−	21.5479i	1.40863	−	1.40863i
$235$			4.62713i			0.301841i
$236$	21.3333	−	21.3333i	1.38868	−	1.38868i
$237$	3.68828	−	3.68828i	0.239580	−	0.239580i
$238$	−40.2104	−	40.2104i	−2.60645	−	2.60645i
$239$			22.9056i			1.48164i	0.671705	+	0.740819i	$0.265562\pi$
$239$			22.9056i			1.48164i	−0.671705	+	0.740819i	$0.734438\pi$
$240$	−6.59058			−0.425420
$241$		−	14.4788i		−	0.932662i	−0.884610	−	0.466331i	$-0.845576\pi$
$241$		−	14.4788i		−	0.932662i	0.884610	−	0.466331i	$-0.154424\pi$
$242$	22.3091	−	19.7195i	1.43408	−	1.26762i
$243$		−	9.62963i		−	0.617741i
$244$	−39.9398	−	11.6501i	−2.55689	−	0.745820i
$245$	−3.97998			−0.254272
$246$	−7.11325	+	7.11325i	−0.453524	+	0.453524i
$247$			24.2356i			1.54208i
$248$	−7.49363			−0.475846
$249$	−4.81867			−0.305371
$250$	20.2966	−	20.2966i	1.28367	−	1.28367i
$251$	6.97370	−	6.97370i	0.440176	−	0.440176i	−0.451895	−	0.892071i	$-0.649252\pi$
$251$	6.97370	−	6.97370i	0.440176	−	0.440176i	0.892071	+	0.451895i	$0.149252\pi$
$252$	34.2705	−	34.2705i	2.15884	−	2.15884i
$253$	13.8911	+	0.427546i	0.873324	+	0.0268796i
$254$	34.8627	+	34.8627i	2.18748	+	2.18748i
$255$	−2.23881	+	2.23881i	−0.140199	+	0.140199i
$256$	26.1006			1.63129
$257$	23.9078			1.49133			0.745664	−	0.666322i	$-0.232132\pi$
$257$	23.9078			1.49133			0.745664	+	0.666322i	$0.232132\pi$
$258$			0.583205i			0.0363088i
$259$		−	27.4063i		−	1.70295i
$260$		−	26.4861i		−	1.64260i
$261$	−0.678390	+	0.678390i	−0.0419913	+	0.0419913i
$262$	13.7770	−	13.7770i	0.851148	−	0.851148i
$263$	−4.37992			−0.270078			−0.135039	−	0.990840i	$-0.543116\pi$
$263$	−4.37992			−0.270078			−0.135039	+	0.990840i	$0.543116\pi$
$264$	−0.350001	+	11.3716i	−0.0215411	+	0.699875i
$265$	4.97265	+	4.97265i	0.305468	+	0.305468i
$266$			53.0171i			3.25069i
$267$	0.533989	−	0.533989i	0.0326796	−	0.0326796i
$268$	−16.7028	+	16.7028i	−1.02028	+	1.02028i
$269$	−7.94279			−0.484280			−0.242140	−	0.970241i	$-0.577849\pi$
$269$	−7.94279			−0.484280			−0.242140	+	0.970241i	$0.577849\pi$
$270$	−5.38237	−	5.38237i	−0.327561	−	0.327561i
$271$	−20.8836			−1.26859			−0.634294	−	0.773092i	$-0.718709\pi$
$271$	−20.8836			−1.26859			−0.634294	+	0.773092i	$0.718709\pi$
$272$	63.9618	−	63.9618i	3.87825	−	3.87825i
$273$	−3.38503	−	3.38503i	−0.204871	−	0.204871i
$274$	33.3528	+	33.3528i	2.01492	+	2.01492i
$275$	−7.74775	−	8.23982i	−0.467207	−	0.496880i
$276$	−6.01226	+	6.01226i	−0.361896	+	0.361896i
$277$	6.21329	+	6.21329i	0.373321	+	0.373321i	0.868685	−	0.495365i	$-0.164966\pi$
$277$	6.21329	+	6.21329i	0.373321	+	0.373321i	−0.495365	+	0.868685i	$0.664966\pi$
$278$	4.92778			0.295549
$279$	−1.67985	−	1.67985i	−0.100570	−	0.100570i
$280$		−	36.1862i		−	2.16254i
$281$	−12.3000	+	12.3000i	−0.733759	+	0.733759i	−0.971362	−	0.237603i	$-0.923638\pi$
$281$	−12.3000	+	12.3000i	−0.733759	+	0.733759i	0.237603	+	0.971362i	$0.423638\pi$
$282$	−2.67557	+	2.67557i	−0.159328	+	0.159328i
$283$	8.22891			0.489158			0.244579	−	0.969629i	$-0.421350\pi$
$283$	8.22891			0.489158			0.244579	+	0.969629i	$0.421350\pi$
$284$	−31.3957	+	31.3957i	−1.86299	+	1.86299i
$285$	2.95185			0.174852
$286$	−35.3851	−	1.08910i	−2.09237	−	0.0643998i
$287$	−21.9860	−	21.9860i	−1.29779	−	1.29779i
$288$	38.6225	+	38.6225i	2.27585	+	2.27585i
$289$		−	26.4553i		−	1.55620i
$290$			1.14693i			0.0673502i
$291$	1.22363			0.0717306
$292$	−8.69746			−0.508980
$293$	−9.92098			−0.579590			−0.289795	−	0.957089i	$-0.593587\pi$
$293$	−9.92098			−0.579590			−0.289795	+	0.957089i	$0.593587\pi$
$294$	−2.30137	−	2.30137i	−0.134219	−	0.134219i
$295$	5.04964	−	5.04964i	0.294001	−	0.294001i
$296$	77.4417			4.50121
$297$	−5.38884	+	5.06703i	−0.312692	+	0.294019i
$298$	−16.6941	−	16.6941i	−0.967065	−	0.967065i
$299$	−11.6842	−	11.6842i	−0.675717	−	0.675717i
$300$	6.91966			0.399507
$301$	−1.80260			−0.103900
$302$	−27.6897			−1.59336
$303$	1.65980	−	1.65980i	0.0953529	−	0.0953529i
$304$	−84.3331			−4.83683
$305$	−9.45383	−	2.75760i	−0.541325	−	0.157900i
$306$	50.9415			2.91213
$307$	9.86123	+	9.86123i	0.562810	+	0.562810i	0.930105	−	0.367295i	$-0.119716\pi$
$307$	9.86123	+	9.86123i	0.562810	+	0.562810i	−0.367295	+	0.930105i	$0.619716\pi$
$308$	−56.2776	−	1.73214i	−3.20672	−	0.0986978i
$309$		−	4.92145i		−	0.279971i
$310$	−2.84007			−0.161305
$311$	−4.96367	−	4.96367i	−0.281464	−	0.281464i	0.552229	−	0.833693i	$-0.313778\pi$
$311$	−4.96367	−	4.96367i	−0.281464	−	0.281464i	−0.833693	+	0.552229i	$0.813778\pi$
$312$	9.56505	−	9.56505i	0.541514	−	0.541514i
$313$	−12.8414	−	12.8414i	−0.725838	−	0.725838i	0.243950	−	0.969788i	$-0.421557\pi$
$313$	−12.8414	−	12.8414i	−0.725838	−	0.725838i	−0.969788	+	0.243950i	$0.921557\pi$
$314$			66.1050i			3.73052i
$315$	8.11190	−	8.11190i	0.457054	−	0.457054i
$316$	−51.5777	+	51.5777i	−2.90147	+	2.90147i
$317$	−23.1747			−1.30162			−0.650810	−	0.759241i	$-0.725571\pi$
$317$	−23.1747			−1.30162			−0.650810	+	0.759241i	$0.725571\pi$
$318$			5.75073i			0.322485i
$319$	1.11402	+	0.0342879i	0.0623733	+	0.00191976i
$320$	30.6944			1.71587
$321$			1.29156i			0.0720876i
$322$	−25.5600	−	25.5600i	−1.42441	−	1.42441i
$323$	−28.6478	+	28.6478i	−1.59400	+	1.59400i
$324$			41.0977i			2.28320i
$325$			13.4477i			0.745943i
$326$	41.6099	−	41.6099i	2.30456	−	2.30456i
$327$		−	1.90642i		−	0.105425i
$328$	62.1255	−	62.1255i	3.43031	−	3.43031i
$329$	−8.26979	−	8.26979i	−0.455928	−	0.455928i
$330$	−0.132650	+	4.30983i	−0.00730214	+	0.237248i
$331$	−8.03810	+	8.03810i	−0.441814	+	0.441814i	−0.892621	−	0.450807i	$-0.851136\pi$
$331$	−8.03810	+	8.03810i	−0.441814	+	0.441814i	0.450807	+	0.892621i	$0.351136\pi$
$332$	67.3853			3.69825
$333$	17.3602	+	17.3602i	0.951332	+	0.951332i
$334$	−13.0878	−	13.0878i	−0.716130	−	0.716130i
$335$	−3.95357	+	3.95357i	−0.216007	+	0.216007i
$336$	11.7789	−	11.7789i	0.642594	−	0.642594i
$337$	−2.67978	−	2.67978i	−0.145977	−	0.145977i	0.630341	−	0.776318i	$-0.282915\pi$
$337$	−2.67978	−	2.67978i	−0.145977	−	0.145977i	−0.776318	+	0.630341i	$0.782915\pi$
$338$	4.88146	+	4.88146i	0.265516	+	0.265516i
$339$	−3.28634			−0.178490
$340$	31.3079	−	31.3079i	1.69791	−	1.69791i
$341$	−0.0849050	+	2.75858i	−0.00459786	+	0.149386i
$342$	−33.5830	−	33.5830i	−1.81596	−	1.81596i
$343$	−8.66131	+	8.66131i	−0.467667	+	0.467667i
$344$		−	5.09359i		−	0.274628i
$345$	−1.42311	+	1.42311i	−0.0766179	+	0.0766179i
$346$		−	54.6363i		−	2.93727i
$347$			31.2364i			1.67686i	0.545009	+	0.838430i	$0.316526\pi$
$347$			31.2364i			1.67686i	−0.545009	+	0.838430i	$0.683474\pi$
$348$	−0.482166	+	0.482166i	−0.0258468	+	0.0258468i
$349$	−4.50565	−	4.50565i	−0.241182	−	0.241182i	0.576157	−	0.817339i	$-0.304552\pi$
$349$	−4.50565	−	4.50565i	−0.241182	−	0.241182i	−0.817339	+	0.576157i	$0.804552\pi$
$350$			29.4177i			1.57244i
$351$	8.79478			0.469431
$352$	1.95210	−	63.4242i	0.104047	−	3.38052i
$353$		−	16.7963i		−	0.893976i	−0.894540	−	0.446988i	$-0.852497\pi$
$353$		−	16.7963i		−	0.893976i	0.894540	−	0.446988i	$-0.147503\pi$
$354$	5.83976			0.310380
$355$	−7.43142	+	7.43142i	−0.394419	+	0.394419i
$356$	−7.46742	+	7.46742i	−0.395772	+	0.395772i
$357$		−	8.00256i		−	0.423540i
$358$	47.8232	+	47.8232i	2.52754	+	2.52754i
$359$	24.0582	−	24.0582i	1.26974	−	1.26974i	0.323522	−	0.946221i	$-0.395133\pi$
$359$	24.0582	−	24.0582i	1.26974	−	1.26974i	0.946221	−	0.323522i	$-0.104867\pi$
$360$	22.9217	+	22.9217i	1.20808	+	1.20808i
$361$	18.7718			0.987991
$362$		−	50.8218i		−	2.67114i
$363$	4.18220	+	0.257688i	0.219509	+	0.0135251i
$364$	47.3370	+	47.3370i	2.48113	+	2.48113i
$365$	−2.05871			−0.107758
$366$	−3.87200	−	7.06109i	−0.202393	−	0.369089i
$367$	18.4602			0.963615			0.481808	−	0.876277i	$-0.339980\pi$
$367$	18.4602			0.963615			0.481808	+	0.876277i	$0.339980\pi$
$368$	40.6578	−	40.6578i	2.11943	−	2.11943i
$369$	27.8535			1.44999
$370$	29.3503			1.52585
$371$	−17.7746			−0.922813
$372$	−1.19396	−	1.19396i	−0.0619037	−	0.0619037i
$373$	−8.80013	−	8.80013i	−0.455653	−	0.455653i	0.441572	−	0.897226i	$-0.354421\pi$
$373$	−8.80013	−	8.80013i	−0.455653	−	0.455653i	−0.897226	+	0.441572i	$0.854421\pi$
$374$	−40.5396	−	43.1144i	−2.09626	−	2.22939i
$375$	4.03938			0.208593
$376$	23.3679	−	23.3679i	1.20511	−	1.20511i
$377$	−0.937042	−	0.937042i	−0.0482601	−	0.0482601i
$378$	19.2392			0.989556
$379$	−20.6864			−1.06259			−0.531294	−	0.847188i	$-0.678294\pi$
$379$	−20.6864			−1.06259			−0.531294	+	0.847188i	$0.678294\pi$
$380$	−41.2792			−2.11758
$381$			6.93827i			0.355459i
$382$			27.2594i			1.39471i
$383$	7.99381	+	7.99381i	0.408464	+	0.408464i	0.881203	−	0.472738i	$-0.156734\pi$
$383$	7.99381	+	7.99381i	0.408464	+	0.408464i	−0.472738	+	0.881203i	$0.656734\pi$
$384$	7.44202	+	7.44202i	0.379774	+	0.379774i
$385$	−13.3210	−	0.410001i	−0.678902	−	0.0208956i
$386$	−54.7030			−2.78431
$387$	1.14183	−	1.14183i	0.0580426	−	0.0580426i
$388$	−17.1115			−0.868707
$389$	0.349832	−	0.349832i	0.0177372	−	0.0177372i	−0.698183	−	0.715920i	$-0.746008\pi$
$389$	0.349832	−	0.349832i	0.0177372	−	0.0177372i	0.715920	+	0.698183i	$0.246008\pi$
$390$	3.62514	−	3.62514i	0.183566	−	0.183566i
$391$		−	27.6227i		−	1.39694i
$392$	20.0996	+	20.0996i	1.01519	+	1.01519i
$393$	2.74187			0.138309
$394$	14.9230	+	14.9230i	0.751812	+	0.751812i
$395$	−12.2085	+	12.2085i	−0.614278	+	0.614278i
$396$	36.7456	−	34.5511i	1.84653	−	1.73626i
$397$	13.9263	+	13.9263i	0.698940	+	0.698940i	0.964182	−	0.265242i	$-0.0854518\pi$
$397$	13.9263	+	13.9263i	0.698940	+	0.698940i	−0.265242	+	0.964182i	$0.585452\pi$
$398$	−9.45047	−	9.45047i	−0.473709	−	0.473709i
$399$	−5.27565	+	5.27565i	−0.264113	+	0.264113i
$400$	−46.7941			−2.33970
$401$	−3.64347	−	3.64347i	−0.181946	−	0.181946i	0.610257	−	0.792203i	$-0.291066\pi$
$401$	−3.64347	−	3.64347i	−0.181946	−	0.181946i	−0.792203	+	0.610257i	$0.791066\pi$
$402$	−4.57219			−0.228040
$403$	2.32034	−	2.32034i	0.115584	−	0.115584i
$404$	−23.2110	+	23.2110i	−1.15479	+	1.15479i
$405$			9.72789i			0.483383i
$406$	−2.04984	−	2.04984i	−0.101732	−	0.101732i
$407$	0.877437	−	28.5082i	0.0434930	−	1.41310i
$408$	22.6127			1.11950
$409$	2.91653	−	2.91653i	0.144213	−	0.144213i	−0.631314	−	0.775527i	$-0.717484\pi$
$409$	2.91653	−	2.91653i	0.144213	−	0.144213i	0.775527	+	0.631314i	$0.217484\pi$
$410$	23.5455	−	23.5455i	1.16283	−	1.16283i
$411$			6.63778i			0.327418i
$412$			68.8226i			3.39064i
$413$			18.0498i			0.888174i
$414$	32.3814			1.59146
$415$	15.9502			0.782966
$416$	−53.3482	+	53.3482i	−2.61561	+	2.61561i
$417$	0.490357	+	0.490357i	0.0240129	+	0.0240129i
$418$	−1.69739	+	55.1486i	−0.0830220	+	2.69741i
$419$	5.84048	−	5.84048i	0.285326	−	0.285326i	−0.549903	−	0.835229i	$-0.685335\pi$
$419$	5.84048	−	5.84048i	0.285326	−	0.285326i	0.835229	+	0.549903i	$0.185335\pi$
$420$	5.76554	−	5.76554i	0.281329	−	0.281329i
$421$	12.3239	−	12.3239i	0.600630	−	0.600630i	−0.339850	−	0.940480i	$-0.610376\pi$
$421$	12.3239	−	12.3239i	0.600630	−	0.600630i	0.940480	+	0.339850i	$0.110376\pi$
$422$	22.2311			1.08219
$423$	10.4768			0.509399
$424$		−	50.2256i		−	2.43917i
$425$	−15.8958	+	15.8958i	−0.771061	+	0.771061i
$426$	−8.59422			−0.416391
$427$	21.8247	−	11.9678i	1.05617	−	0.579161i
$428$		−	18.0614i		−	0.873030i
$429$	−3.41275	−	3.62950i	−0.164769	−	0.175234i
$430$		−	1.93046i		−	0.0930951i
$431$	−3.66683			−0.176625			−0.0883126	−	0.996093i	$-0.528147\pi$
$431$	−3.66683			−0.176625			−0.0883126	+	0.996093i	$0.528147\pi$
$432$			30.6033i			1.47240i
$433$	10.8431	+	10.8431i	0.521088	+	0.521088i	0.917900	−	0.396812i	$-0.129883\pi$
$433$	10.8431	+	10.8431i	0.521088	+	0.521088i	−0.396812	+	0.917900i	$0.629883\pi$
$434$	5.07589	−	5.07589i	0.243650	−	0.243650i
$435$	−0.114130	+	0.114130i	−0.00547209	+	0.00547209i
$436$			26.6598i			1.27677i
$437$	−18.2102	+	18.2102i	−0.871110	+	0.871110i
$438$	−1.19042	−	1.19042i	−0.0568803	−	0.0568803i
$439$		−	22.5639i		−	1.07691i	−0.842653	−	0.538457i	$-0.819007\pi$
$439$		−	22.5639i		−	1.07691i	0.842653	−	0.538457i	$-0.180993\pi$
$440$	1.15853	−	37.6411i	0.0552310	−	1.79447i
$441$			9.01150i			0.429119i
$442$			70.3642i			3.34688i
$443$	−35.3910			−1.68148			−0.840738	−	0.541443i	$-0.817878\pi$
$443$	−35.3910			−1.68148			−0.840738	+	0.541443i	$0.817878\pi$
$444$	12.3388	+	12.3388i	0.585572	+	0.585572i
$445$	−1.76755	+	1.76755i	−0.0837900	+	0.0837900i
$446$	67.3490			3.18907
$447$		−	3.32242i		−	0.157145i
$448$	−54.8582	+	54.8582i	−2.59181	+	2.59181i
$449$	−20.7741			−0.980391			−0.490196	−	0.871612i	$-0.663075\pi$
$449$	−20.7741			−0.980391			−0.490196	+	0.871612i	$0.663075\pi$
$450$	−18.6343	−	18.6343i	−0.878427	−	0.878427i
$451$	−22.1660	−	23.5738i	−1.04376	−	1.11005i
$452$	45.9569			2.16163
$453$	−2.75536	−	2.75536i	−0.129458	−	0.129458i
$454$		−	35.8757i		−	1.68373i
$455$	11.2048	+	11.2048i	0.525287	+	0.525287i
$456$	−14.9074	−	14.9074i	−0.698101	−	0.698101i
$457$	−1.21578	−	1.21578i	−0.0568717	−	0.0568717i	0.678099	−	0.734971i	$-0.262804\pi$
$457$	−1.21578	−	1.21578i	−0.0568717	−	0.0568717i	−0.734971	+	0.678099i	$0.762804\pi$
$458$	−3.62103	+	3.62103i	−0.169199	+	0.169199i
$459$	10.3959	+	10.3959i	0.485238	+	0.485238i
$460$	19.9011	−	19.9011i	0.927894	−	0.927894i
$461$		−	10.0307i		−	0.467176i	−0.972336	−	0.233588i	$-0.924953\pi$
$461$		−	10.0307i		−	0.467176i	0.972336	−	0.233588i	$-0.0750467\pi$
$462$	−7.46561	−	7.93977i	−0.347332	−	0.369391i
$463$		−	37.2220i		−	1.72985i	−0.501899	−	0.864926i	$-0.667365\pi$
$463$		−	37.2220i		−	1.72985i	0.501899	−	0.864926i	$-0.332635\pi$
$464$	3.26064	−	3.26064i	0.151371	−	0.151371i
$465$	−0.282612	−	0.282612i	−0.0131058	−	0.0131058i
$466$			59.7601i			2.76833i
$467$	14.5597	−	14.5597i	0.673743	−	0.673743i	−0.284834	−	0.958577i	$-0.591938\pi$
$467$	14.5597	−	14.5597i	0.673743	−	0.673743i	0.958577	+	0.284834i	$0.0919384\pi$
$468$	−59.9700			−2.77212
$469$		−	14.1320i		−	0.652553i
$470$	8.85639	−	8.85639i	0.408515	−	0.408515i
$471$	−6.57801	+	6.57801i	−0.303099	+	0.303099i
$472$	−51.0032			−2.34761
$473$	−1.87507	−	0.0577118i	−0.0862158	−	0.00265359i
$474$	−14.1188			−0.648499
$475$	20.9585			0.961643
$476$			111.909i			5.12936i
$477$	11.2591	−	11.2591i	0.515520	−	0.515520i
$478$	43.8415	−	43.8415i	2.00526	−	2.00526i
$479$	2.20778			0.100876			0.0504380	−	0.998727i	$-0.483938\pi$
$479$	2.20778			0.100876			0.0504380	+	0.998727i	$0.483938\pi$
$480$	6.49769	+	6.49769i	0.296578	+	0.296578i
$481$	−23.9792	+	23.9792i	−1.09336	+	1.09336i
$482$	−27.7126	+	27.7126i	−1.26227	+	1.26227i
$483$		−	5.08689i		−	0.231461i
$484$	−58.4848	−	3.60356i	−2.65840	−	0.163798i
$485$	−4.05033			−0.183916
$486$	−18.4312	+	18.4312i	−0.836057	+	0.836057i
$487$			9.33595i			0.423052i	0.977372	+	0.211526i	$0.0678434\pi$
$487$			9.33595i			0.423052i	−0.977372	+	0.211526i	$0.932157\pi$
$488$	33.8172	+	61.6700i	1.53083	+	2.79167i
$489$	8.28108			0.374483
$490$	7.61773	+	7.61773i	0.344134	+	0.344134i
$491$	16.5444			0.746640			0.373320	−	0.927703i	$-0.378219\pi$
$491$	16.5444			0.746640			0.373320	+	0.927703i	$0.378219\pi$
$492$	19.7969			0.892511
$493$		−	2.21526i		−	0.0997704i
$494$	46.3873	−	46.3873i	2.08706	−	2.08706i
$495$	8.69774	−	8.17832i	0.390934	−	0.367588i
$496$	8.07410	+	8.07410i	0.362538	+	0.362538i
$497$		−	26.5634i		−	1.19153i
$498$	9.22299	+	9.22299i	0.413292	+	0.413292i
$499$	8.01325	+	8.01325i	0.358723	+	0.358723i	0.863342	−	0.504619i	$-0.168367\pi$
$499$	8.01325	+	8.01325i	0.358723	+	0.358723i	−0.504619	+	0.863342i	$0.668367\pi$
$500$	−56.4875			−2.52620
$501$		−	2.60469i		−	0.116369i
$502$	−26.6955			−1.19148
$503$			13.6465i			0.608469i	0.952597	+	0.304235i	$0.0984007\pi$
$503$			13.6465i			0.608469i	−0.952597	+	0.304235i	$0.901599\pi$
$504$	−81.9331			−3.64959
$505$	−5.49408	+	5.49408i	−0.244483	+	0.244483i
$506$	−25.7693	−	27.4060i	−1.14559	−	1.21834i
$507$			0.971494i			0.0431455i
$508$		−	97.0263i		−	4.30484i
$509$	8.43966	+	8.43966i	0.374081	+	0.374081i	0.868961	−	0.494880i	$-0.164788\pi$
$509$	8.43966	+	8.43966i	0.374081	+	0.374081i	−0.494880	+	0.868961i	$0.664788\pi$
$510$	8.57020			0.379495
$511$	3.67940	−	3.67940i	0.162767	−	0.162767i
$512$	−10.8830	−	10.8830i	−0.480965	−	0.480965i
$513$		−	13.7069i		−	0.605173i
$514$	−45.7598	−	45.7598i	−2.01838	−	2.01838i
$515$			16.2904i			0.717842i
$516$	0.811559	−	0.811559i	0.0357269	−	0.0357269i
$517$	−8.33751	−	8.86703i	−0.366683	−	0.389972i
$518$	−52.4560	+	52.4560i	−2.30478	+	2.30478i
$519$	5.43678	−	5.43678i	0.238648	−	0.238648i
$520$	−31.6612	+	31.6612i	−1.38843	+	1.38843i
$521$	−26.4754	+	26.4754i	−1.15991	+	1.15991i	−0.175411	+	0.984495i	$0.556125\pi$
$521$	−26.4754	+	26.4754i	−1.15991	+	1.15991i	−0.984495	+	0.175411i	$0.943875\pi$
$522$	2.59689			0.113663
$523$	3.02357	−	3.02357i	0.132212	−	0.132212i	−0.637904	−	0.770116i	$-0.720198\pi$
$523$	3.02357	−	3.02357i	0.132212	−	0.132212i	0.770116	+	0.637904i	$0.220198\pi$
$524$	−38.3428			−1.67501
$525$	−2.92731	+	2.92731i	−0.127758	+	0.127758i
$526$	8.38322	+	8.38322i	0.365526	+	0.365526i
$527$	5.48551			0.238953
$528$	12.6296	−	11.8754i	0.549633	−	0.516810i
$529$			5.44141i			0.236583i
$530$		−	19.0354i		−	0.826846i
$531$	−11.4334	−	11.4334i	−0.496169	−	0.496169i
$532$	73.7758	−	73.7758i	3.19859	−	3.19859i
$533$			38.4732i			1.66646i
$534$	−2.04412			−0.0884579
$535$		−	4.27516i		−	0.184831i
$536$	39.9325			1.72482
$537$			9.51764i			0.410717i
$538$	15.2026	+	15.2026i	0.655430	+	0.655430i
$539$	7.62689	−	7.17142i	0.328513	−	0.308895i
$540$			14.9797i			0.644622i
$541$	4.89932	+	4.89932i	0.210638	+	0.210638i	0.804539	−	0.593900i	$-0.202413\pi$
$541$	4.89932	+	4.89932i	0.210638	+	0.210638i	−0.593900	+	0.804539i	$0.702413\pi$
$542$	39.9714	+	39.9714i	1.71692	+	1.71692i
$543$	5.05721	−	5.05721i	0.217026	−	0.217026i
$544$	−126.121			−5.40737
$545$			6.31043i			0.270309i
$546$			12.9580i			0.554550i
$547$	6.59530	−	6.59530i	0.281995	−	0.281995i	−0.551909	−	0.833904i	$-0.686101\pi$
$547$	6.59530	−	6.59530i	0.281995	−	0.281995i	0.833904	+	0.551909i	$0.186101\pi$
$548$		−	92.8242i		−	3.96525i
$549$	−6.24377	+	21.4054i	−0.266478	+	0.913562i
$550$	−0.941833	+	30.6004i	−0.0401599	+	1.30480i
$551$	−1.46040	+	1.46040i	−0.0622152	+	0.0622152i
$552$	14.3740			0.611797
$553$		−	43.6391i		−	1.85572i
$554$		−	23.7846i		−	1.01051i
$555$	2.92061	+	2.92061i	0.123973	+	0.123973i
$556$	−6.85725	−	6.85725i	−0.290812	−	0.290812i
$557$	−30.7676	+	30.7676i	−1.30366	+	1.30366i	−0.377760	+	0.925904i	$0.623305\pi$
$557$	−30.7676	+	30.7676i	−1.30366	+	1.30366i	−0.925904	+	0.377760i	$0.876695\pi$
$558$			6.43051i			0.272225i
$559$	1.57718	+	1.57718i	0.0667078	+	0.0667078i
$560$	−38.9893	+	38.9893i	−1.64760	+	1.64760i
$561$	0.256209	−	8.32429i	0.0108172	−	0.351452i
$562$	47.0848			1.98615
$563$	18.5720			0.782717			0.391359	−	0.920238i	$-0.372005\pi$
$563$	18.5720			0.782717			0.391359	+	0.920238i	$0.372005\pi$
$564$	7.44638			0.313549
$565$	10.8781			0.457644
$566$	−15.7502	−	15.7502i	−0.662032	−	0.662032i
$567$	−17.3861	−	17.3861i	−0.730146	−	0.730146i
$568$	75.0600			3.14945
$569$		−	10.3873i		−	0.435460i	−0.976009	−	0.217730i	$-0.930135\pi$
$569$		−	10.3873i		−	0.435460i	0.976009	−	0.217730i	$-0.0698653\pi$
$570$	−5.64987	−	5.64987i	−0.236647	−	0.236647i
$571$		−	40.0088i		−	1.67432i	−0.546961	−	0.837158i	$-0.684216\pi$
$571$		−	40.0088i		−	1.67432i	0.546961	−	0.837158i	$-0.315784\pi$
$572$	47.7246	+	50.7557i	1.99547	+	2.12220i
$573$	−2.71254	+	2.71254i	−0.113318	+	0.113318i
$574$			84.1628i			3.51289i
$575$	−10.1043	+	10.1043i	−0.421379	+	0.421379i
$576$		−	69.4984i		−	2.89577i
$577$	−28.7729	−	28.7729i	−1.19783	−	1.19783i	−0.974814	−	0.223019i	$-0.928409\pi$
$577$	−28.7729	−	28.7729i	−1.19783	−	1.19783i	−0.223019	−	0.974814i	$-0.571591\pi$
$578$	−50.6358	+	50.6358i	−2.10617	+	2.10617i
$579$	−5.44342	−	5.44342i	−0.226221	−	0.226221i
$580$	1.59601	−	1.59601i	0.0662708	−	0.0662708i
$581$	−28.5069	+	28.5069i	−1.18266	+	1.18266i
$582$	−2.34205	−	2.34205i	−0.0970810	−	0.0970810i
$583$	−18.4892	−	0.569071i	−0.765746	−	0.0235685i
$584$	10.3968	+	10.3968i	0.430224	+	0.430224i
$585$	−14.1950			−0.586892
$586$	18.9889	+	18.9889i	0.784423	+	0.784423i
$587$	12.2834	+	12.2834i	0.506990	+	0.506990i	0.913601	−	0.406612i	$-0.133290\pi$
$587$	12.2834	+	12.2834i	0.506990	+	0.506990i	−0.406612	+	0.913601i	$0.633290\pi$
$588$			6.40493i			0.264135i
$589$	−3.61630	−	3.61630i	−0.149007	−	0.149007i
$590$	−19.3301			−0.795809
$591$			2.96994i			0.122167i
$592$	−83.4406	−	83.4406i	−3.42939	−	3.42939i
$593$	12.8148	+	12.8148i	0.526242	+	0.526242i	0.919450	−	0.393207i	$-0.128635\pi$
$593$	12.8148	+	12.8148i	0.526242	+	0.526242i	−0.393207	+	0.919450i	$0.628635\pi$
$594$	20.0127	+	0.615959i	0.821129	+	0.0252731i
$595$			26.4892i			1.08595i
$596$			46.4614i			1.90313i
$597$		−	1.88081i		−	0.0769762i
$598$			44.7275i			1.82904i
$599$	13.2996	−	13.2996i	0.543406	−	0.543406i	−0.381120	−	0.924526i	$-0.624462\pi$
$599$	13.2996	−	13.2996i	0.543406	−	0.543406i	0.924526	+	0.381120i	$0.124462\pi$
$600$	−8.27167	−	8.27167i	−0.337690	−	0.337690i
$601$	−13.5399			−0.552304			−0.276152	−	0.961114i	$-0.589059\pi$
$601$	−13.5399			−0.552304			−0.276152	+	0.961114i	$0.589059\pi$
$602$	3.45019	+	3.45019i	0.140619	+	0.140619i
$603$	8.95171	+	8.95171i	0.364542	+	0.364542i
$604$	38.5316	+	38.5316i	1.56783	+	1.56783i
$605$	−13.8435	−	0.852969i	−0.562817	−	0.0346781i
$606$	−6.35375			−0.258103
$607$		−	17.7925i		−	0.722176i	−0.932532	−	0.361088i	$-0.882405\pi$
$607$		−	17.7925i		−	0.722176i	0.932532	−	0.361088i	$-0.117595\pi$
$608$	83.1444	+	83.1444i	3.37195	+	3.37195i
$609$		−	0.407954i		−	0.0165311i
$610$	12.8167	+	23.3728i	0.518932	+	0.946338i
$611$			14.4713i			0.585447i
$612$	−70.8876	−	70.8876i	−2.86546	−	2.86546i
$613$	2.90057			0.117153			0.0585765	−	0.998283i	$-0.481344\pi$
$613$	2.90057			0.117153			0.0585765	+	0.998283i	$0.481344\pi$
$614$		−	37.7490i		−	1.52343i
$615$	4.68595			0.188956
$616$	65.2030	+	69.3442i	2.62710	+	2.79396i
$617$	7.94533	−	7.94533i	0.319867	−	0.319867i	−0.528849	−	0.848716i	$-0.677376\pi$
$617$	7.94533	−	7.94533i	0.319867	−	0.319867i	0.848716	+	0.528849i	$0.177376\pi$
$618$	−9.41971	+	9.41971i	−0.378916	+	0.378916i
$619$	17.1646			0.689904			0.344952	−	0.938620i	$-0.387895\pi$
$619$	17.1646			0.689904			0.344952	+	0.938620i	$0.387895\pi$
$620$	3.95210	+	3.95210i	0.158720	+	0.158720i
$621$	6.60822	+	6.60822i	0.265179	+	0.265179i
$622$			19.0011i			0.761873i
$623$		−	6.31807i		−	0.253128i
$624$	−20.6120			−0.825139
$625$	3.68017			0.147207
$626$			49.1571i			1.96471i
$627$	−5.65666	+	5.31885i	−0.225905	+	0.212414i
$628$	91.9883	−	91.9883i	3.67073	−	3.67073i
$629$	−56.6892			−2.26034
$630$	−31.0525			−1.23716
$631$	−7.96552	−	7.96552i	−0.317102	−	0.317102i	0.530551	−	0.847653i	$-0.321985\pi$
$631$	−7.96552	−	7.96552i	−0.317102	−	0.317102i	−0.847653	+	0.530551i	$0.821985\pi$
$632$	123.311			4.90504
$633$	2.21219	+	2.21219i	0.0879266	+	0.0879266i
$634$	44.3566	+	44.3566i	1.76163	+	1.76163i
$635$		−	22.9663i		−	0.911390i
$636$	8.00242	−	8.00242i	0.317317	−	0.317317i
$637$	−12.4474			−0.493182
$638$	−2.06663	−	2.19788i	−0.0818185	−	0.0870149i
$639$	16.8263	+	16.8263i	0.665637	+	0.665637i
$640$	−24.6337	−	24.6337i	−0.973734	−	0.973734i
$641$	3.98210	+	3.98210i	0.157284	+	0.157284i	0.781362	−	0.624078i	$-0.214525\pi$
$641$	3.98210	+	3.98210i	0.157284	+	0.157284i	−0.624078	+	0.781362i	$0.714525\pi$
$642$	2.47205	−	2.47205i	0.0975641	−	0.0975641i
$643$	23.8665	−	23.8665i	0.941203	−	0.941203i	−0.0571621	−	0.998365i	$-0.518205\pi$
$643$	23.8665	−	23.8665i	0.941203	−	0.941203i	0.998365	+	0.0571621i	$0.0182052\pi$
$644$			71.1361i			2.80315i
$645$	0.192097	−	0.192097i	0.00756383	−	0.00756383i
$646$	109.664			4.31468
$647$	21.3715	+	21.3715i	0.840200	+	0.840200i	0.988885	−	0.148685i	$-0.0475041\pi$
$647$	21.3715	+	21.3715i	0.840200	+	0.840200i	−0.148685	+	0.988885i	$0.547504\pi$
$648$	49.1276	−	49.1276i	1.92992	−	1.92992i
$649$	−0.577881	+	18.7755i	−0.0226838	+	0.737003i
$650$	25.7390	−	25.7390i	1.00957	−	1.00957i
$651$	1.01019			0.0395924
$652$	−115.804			−4.53525
$653$	14.7164	+	14.7164i	0.575896	+	0.575896i	0.933770	−	0.357874i	$-0.116498\pi$
$653$	14.7164	+	14.7164i	0.575896	+	0.575896i	−0.357874	+	0.933770i	$0.616498\pi$
$654$	−3.64892	+	3.64892i	−0.142684	+	0.142684i
$655$	−9.07582			−0.354622
$656$	−133.876			−5.22697
$657$			4.66134i			0.181856i
$658$			31.6569i			1.23412i
$659$	16.7769			0.653535			0.326767	−	0.945105i	$-0.394041\pi$
$659$	16.7769			0.653535			0.326767	+	0.945105i	$0.394041\pi$
$660$	6.18193	−	5.81275i	0.240631	−	0.226261i
$661$	19.9025	−	19.9025i	0.774116	−	0.774116i	−0.204707	−	0.978823i	$-0.565624\pi$
$661$	19.9025	−	19.9025i	0.774116	−	0.774116i	0.978823	+	0.204707i	$0.0656242\pi$
$662$	30.7700			1.19591
$663$	−7.00184	+	7.00184i	−0.271929	+	0.271929i
$664$	−80.5516	−	80.5516i	−3.12601	−	3.12601i
$665$	17.4629	−	17.4629i	0.677181	−	0.677181i
$666$		−	66.4552i		−	2.57509i
$667$		−	1.40815i		−	0.0545237i
$668$			36.4245i			1.40931i
$669$	6.70181	+	6.70181i	0.259107	+	0.259107i
$670$	15.1344			0.584692
$671$	23.0853	−	11.7502i	0.891200	−	0.453611i
$672$	−23.2258			−0.895956
$673$	−27.5392	−	27.5392i	−1.06156	−	1.06156i	−0.997977	−	0.0635821i	$-0.979748\pi$
$673$	−27.5392	−	27.5392i	−1.06156	−	1.06156i	−0.0635821	−	0.997977i	$-0.520252\pi$
$674$			10.2583i			0.395134i
$675$		−	7.60556i		−	0.292738i
$676$		−	13.5856i		−	0.522522i
$677$	29.6117	−	29.6117i	1.13807	−	1.13807i	0.149272	−	0.988796i	$-0.452307\pi$
$677$	29.6117	−	29.6117i	1.13807	−	1.13807i	0.988796	−	0.149272i	$-0.0476930\pi$
$678$	6.29010	+	6.29010i	0.241570	+	0.241570i
$679$	7.23891	−	7.23891i	0.277804	−	0.277804i
$680$	−74.8502			−2.87037
$681$	3.56994	−	3.56994i	0.136801	−	0.136801i
$682$	5.44247	−	5.11745i	0.208403	−	0.195957i
$683$	6.50541			0.248923			0.124461	−	0.992224i	$-0.460280\pi$
$683$	6.50541			0.248923			0.124461	+	0.992224i	$0.460280\pi$
$684$			93.4647i			3.57371i
$685$		−	21.9717i		−	0.839494i
$686$	33.1557			1.26589
$687$	−0.720646			−0.0274944
$688$	−5.48815	+	5.48815i	−0.209234	+	0.209234i
$689$	15.5519	+	15.5519i	0.592481	+	0.592481i
$690$	5.44771			0.207391
$691$	40.1986			1.52923			0.764613	−	0.644489i	$-0.222930\pi$
$691$	40.1986			1.52923			0.764613	+	0.644489i	$0.222930\pi$
$692$	−76.0291	+	76.0291i	−2.89019	+	2.89019i
$693$	−0.928326	+	30.1615i	−0.0352642	+	1.14574i
$694$	59.7869	−	59.7869i	2.26948	−	2.26948i
$695$	−1.62312	−	1.62312i	−0.0615686	−	0.0615686i
$696$	1.15275			0.0436949
$697$	−45.4773	+	45.4773i	−1.72258	+	1.72258i
$698$			17.2477i			0.652836i
$699$	−5.94664	+	5.94664i	−0.224923	+	0.224923i
$700$	40.9361	−	40.9361i	1.54724	−	1.54724i
$701$	−8.69195	−	8.69195i	−0.328291	−	0.328291i	0.523646	−	0.851936i	$-0.324572\pi$
$701$	−8.69195	−	8.69195i	−0.328291	−	0.328291i	−0.851936	+	0.523646i	$0.824572\pi$
$702$	−16.8333	−	16.8333i	−0.635332	−	0.635332i
$703$	37.3721	+	37.3721i	1.40952	+	1.40952i
$704$	−58.8201	+	55.3074i	−2.21686	+	2.08448i
$705$	1.76257			0.0663823
$706$	−32.1483	+	32.1483i	−1.20992	+	1.20992i
$707$		−	19.6385i		−	0.738580i
$708$	−8.12632	−	8.12632i	−0.305406	−	0.305406i
$709$	23.7377	+	23.7377i	0.891489	+	0.891489i	0.994663	−	0.103174i	$-0.0328999\pi$
$709$	23.7377	+	23.7377i	0.891489	+	0.891489i	−0.103174	+	0.994663i	$0.532900\pi$
$710$	28.4476			1.06762
$711$	27.6427	+	27.6427i	1.03668	+	1.03668i
$712$	17.8529			0.669066
$713$	3.48691			0.130586
$714$	−15.3170	+	15.3170i	−0.573224	+	0.573224i
$715$	11.2965	+	12.0140i	0.422465	+	0.449297i
$716$		−	133.097i		−	4.97406i
$717$	8.72521			0.325849
$718$	−92.0953			−3.43697
$719$			1.35624i			0.0505794i	0.999680	+	0.0252897i	$0.00805082\pi$
$719$			1.35624i			0.0505794i	−0.999680	+	0.0252897i	$0.991949\pi$
$720$		−	49.3946i		−	1.84083i
$721$	−29.1149	−	29.1149i	−1.08429	−	1.08429i
$722$	−35.9295	−	35.9295i	−1.33716	−	1.33716i
$723$	−5.51528			−0.205116
$724$	−70.7210	+	70.7210i	−2.62833	+	2.62833i
$725$	−0.810336	+	0.810336i	−0.0300951	+	0.0300951i
$726$	−7.51156	−	8.49800i	−0.278780	−	0.315390i
$727$	0.137140			0.00508624			0.00254312	−	0.999997i	$-0.499190\pi$
$727$	0.137140			0.00508624			0.00254312	+	0.999997i	$0.499190\pi$
$728$		−	113.172i		−	4.19444i
$729$	19.4773			0.721382
$730$	3.94039	+	3.94039i	0.145840	+	0.145840i
$731$			3.72862i			0.137908i
$732$	−4.43776	+	15.2139i	−0.164024	+	0.562323i
$733$			11.8218i			0.436648i	0.975876	+	0.218324i	$0.0700590\pi$
$733$			11.8218i			0.436648i	−0.975876	+	0.218324i	$0.929941\pi$
$734$	−35.3331	−	35.3331i	−1.30417	−	1.30417i
$735$			1.51606i			0.0559207i
$736$	−80.1695			−2.95509
$737$	0.452447	−	14.7001i	0.0166661	−	0.541486i
$738$	−53.3118	−	53.3118i	−1.96244	−	1.96244i
$739$	−12.0867	−	12.0867i	−0.444615	−	0.444615i	0.448944	−	0.893560i	$-0.351800\pi$
$739$	−12.0867	−	12.0867i	−0.444615	−	0.444615i	−0.893560	+	0.448944i	$0.851800\pi$
$740$	−40.8424	−	40.8424i	−1.50140	−	1.50140i
$741$	9.23187			0.339141
$742$	34.0209	+	34.0209i	1.24894	+	1.24894i
$743$	14.1785	−	14.1785i	0.520159	−	0.520159i	−0.397460	−	0.917619i	$-0.630108\pi$
$743$	14.1785	−	14.1785i	0.520159	−	0.520159i	0.917619	+	0.397460i	$0.130108\pi$
$744$			2.85448i			0.104650i
$745$			10.9975i			0.402917i
$746$			33.6871i			1.23337i
$747$		−	36.1146i		−	1.32136i
$748$	−3.58288	+	116.409i	−0.131003	+	4.25632i
$749$	7.64073	+	7.64073i	0.279186	+	0.279186i
$750$	−7.73142	−	7.73142i	−0.282312	−	0.282312i
$751$		−	22.9992i		−	0.839254i	−0.907697	−	0.419627i	$-0.862161\pi$
$751$		−	22.9992i		−	0.839254i	0.907697	−	0.419627i	$-0.137839\pi$
$752$	−50.3560			−1.83629
$753$	−2.65643	−	2.65643i	−0.0968057	−	0.0968057i
$754$			3.58702i			0.130631i
$755$	9.12050	+	9.12050i	0.331929	+	0.331929i
$756$	−26.7722	−	26.7722i	−0.973697	−	0.973697i
$757$	24.2905			0.882852			0.441426	−	0.897298i	$-0.354473\pi$
$757$	24.2905			0.882852			0.441426	+	0.897298i	$0.354473\pi$
$758$	39.5940	+	39.5940i	1.43812	+	1.43812i
$759$	0.162861	−	5.29140i	0.00591149	−	0.192066i
$760$	49.3447	+	49.3447i	1.78992	+	1.78992i
$761$	31.6167	−	31.6167i	1.14610	−	1.14610i	0.158791	−	0.987312i	$-0.449240\pi$
$761$	31.6167	−	31.6167i	1.14610	−	1.14610i	0.987312	−	0.158791i	$-0.0507597\pi$
$762$	13.2799	−	13.2799i	0.481081	−	0.481081i
$763$	−11.2782	−	11.2782i	−0.408300	−	0.408300i
$764$	37.9328	−	37.9328i	1.37236	−	1.37236i
$765$	−16.7792	−	16.7792i	−0.606654	−	0.606654i
$766$		−	30.6005i		−	1.10564i
$767$	15.7927	−	15.7927i	0.570241	−	0.570241i
$768$		−	9.94226i		−	0.358761i
$769$	10.9102	−	10.9102i	0.393434	−	0.393434i	−0.482476	−	0.875909i	$-0.660262\pi$
$769$	10.9102	−	10.9102i	0.393434	−	0.393434i	0.875909	+	0.482476i	$0.160262\pi$
$770$	24.7118	+	26.2813i	0.890553	+	0.947114i
$771$		−	9.10699i		−	0.327980i
$772$	76.1219	+	76.1219i	2.73969	+	2.73969i
$773$			3.19881i			0.115053i	0.998344	+	0.0575266i	$0.0183214\pi$
$773$			3.19881i			0.115053i	−0.998344	+	0.0575266i	$0.981679\pi$
$774$	−4.37096			−0.157111
$775$	−2.00658	−	2.00658i	−0.0720786	−	0.0720786i
$776$	20.4549	+	20.4549i	0.734289	+	0.734289i
$777$	−10.4396			−0.374520
$778$	−1.33917			−0.0480115
$779$	59.9615			2.14834
$780$	−10.0891			−0.361248
$781$	0.850452	−	27.6314i	0.0304315	−	0.988729i
$782$	−52.8702	+	52.8702i	−1.89063	+	1.89063i
$783$	0.529960	+	0.529960i	0.0189392	+	0.0189392i
$784$		−	43.3132i		−	1.54690i
$785$	21.7738	−	21.7738i	0.777140	−	0.777140i
$786$	−5.24796	−	5.24796i	−0.187189	−	0.187189i
$787$	−16.9189	−	16.9189i	−0.603095	−	0.603095i	0.338038	−	0.941133i	$-0.390237\pi$
$787$	−16.9189	−	16.9189i	−0.603095	−	0.603095i	−0.941133	+	0.338038i	$0.890237\pi$
$788$		−	41.5323i		−	1.47953i
$789$			1.66840i			0.0593968i
$790$	46.7346			1.66274
$791$	−19.4417	+	19.4417i	−0.691268	+	0.691268i
$792$	−85.2272	−	2.62316i	−3.02842	−	0.0932100i
$793$	−29.5668	−	8.62436i	−1.04995	−	0.306260i
$794$		−	53.3101i		−	1.89191i
$795$	1.89419	−	1.89419i	0.0671800	−	0.0671800i
$796$			26.3016i			0.932234i
$797$			14.5423i			0.515115i	0.966263	+	0.257558i	$0.0829177\pi$
$797$			14.5423i			0.515115i	−0.966263	+	0.257558i	$0.917082\pi$
$798$	20.1953			0.714907
$799$	−17.1058	+	17.1058i	−0.605160	+	0.605160i
$800$	46.1345	+	46.1345i	1.63110	+	1.63110i
$801$	4.00210	+	4.00210i	0.141407	+	0.141407i
$802$			13.9473i			0.492496i
$803$	3.94512	−	3.70953i	0.139220	−	0.130906i
$804$	6.36243	+	6.36243i	0.224386	+	0.224386i
$805$			16.8380i			0.593463i
$806$	−8.88230			−0.312866
$807$			3.02558i			0.106505i
$808$	55.4922			1.95221
$809$		−	23.9583i		−	0.842327i	−0.906985	−	0.421164i	$-0.861622\pi$
$809$		−	23.9583i		−	0.842327i	0.906985	−	0.421164i	$-0.138378\pi$
$810$	18.6193	−	18.6193i	0.654216	−	0.654216i
$811$	−30.3237	−	30.3237i	−1.06481	−	1.06481i	−0.997749	−	0.0670596i	$-0.978638\pi$
$811$	−30.3237	−	30.3237i	−1.06481	−	1.06481i	−0.0670596	−	0.997749i	$-0.521362\pi$
$812$			5.70491i			0.200203i
$813$			7.95500i			0.278994i
$814$	−56.2444	+	52.8855i	−1.97136	+	1.85364i
$815$	−27.4111			−0.960169
$816$	−24.3644	−	24.3644i	−0.852925	−	0.852925i
$817$	2.45808	−	2.45808i	0.0859973	−	0.0859973i
$818$	−11.1645			−0.390359
$819$	25.3699	−	25.3699i	0.886495	−	0.886495i
$820$	−65.5294			−2.28838
$821$	0.138072	−	0.138072i	0.00481875	−	0.00481875i	−0.704693	−	0.709512i	$-0.748915\pi$
$821$	0.138072	−	0.138072i	0.00481875	−	0.00481875i	0.709512	+	0.704693i	$0.248915\pi$
$822$	12.7048	−	12.7048i	0.443131	−	0.443131i
$823$	−23.7026	+	23.7026i	−0.826220	+	0.826220i	−0.986992	−	0.160772i	$-0.948602\pi$
$823$	−23.7026	+	23.7026i	−0.826220	+	0.826220i	0.160772	+	0.986992i	$0.448602\pi$
$824$	82.2696	−	82.2696i	2.86600	−	2.86600i
$825$	−3.13872	+	2.95128i	−0.109276	+	0.102750i
$826$	34.5476	−	34.5476i	1.20206	−	1.20206i
$827$		−	34.1896i		−	1.18889i	−0.804137	−	0.594444i	$-0.797372\pi$
$827$		−	34.1896i		−	1.18889i	0.804137	−	0.594444i	$-0.202628\pi$
$828$	−45.0602	−	45.0602i	−1.56595	−	1.56595i
$829$		−	54.2986i		−	1.88587i	−0.332978	−	0.942934i	$-0.608054\pi$
$829$		−	54.2986i		−	1.88587i	0.332978	−	0.942934i	$-0.391946\pi$
$830$	−30.5289	−	30.5289i	−1.05967	−	1.05967i
$831$	2.36677	−	2.36677i	0.0821025	−	0.0821025i
$832$	95.9964			3.32808
$833$	−14.7134	−	14.7134i	−0.509789	−	0.509789i
$834$		−	1.87710i		−	0.0649986i
$835$			8.62174i			0.298368i
$836$	79.1039	−	74.3799i	2.73587	−	2.57248i
$837$	−1.31231	+	1.31231i	−0.0453599	+	0.0453599i
$838$	−22.3575			−0.772327
$839$		−	25.0741i		−	0.865655i	−0.901477	−	0.432827i	$-0.857516\pi$
$839$		−	25.0741i		−	0.865655i	0.901477	−	0.432827i	$-0.142484\pi$
$840$	−13.7841			−0.475597
$841$			28.8871i			0.996106i
$842$	−47.1761			−1.62580
$843$	4.68535	+	4.68535i	0.161372	+	0.161372i
$844$	−30.9357	−	30.9357i	−1.06485	−	1.06485i
$845$		−	3.21573i		−	0.110624i
$846$	−20.0527	−	20.0527i	−0.689426	−	0.689426i
$847$	26.2660	−	23.2171i	0.902511	−	0.797749i
$848$	−54.1162	+	54.1162i	−1.85836	+	1.85836i
$849$		−	3.13457i		−	0.107578i
$850$	60.8496			2.08712
$851$	−36.0349			−1.23526
$852$	11.9593	+	11.9593i	0.409718	+	0.409718i
$853$	31.7232			1.08618			0.543091	−	0.839674i	$-0.317254\pi$
$853$	31.7232			1.08618			0.543091	+	0.839674i	$0.317254\pi$
$854$	−64.6793	−	18.8663i	−2.21328	−	0.645593i
$855$			22.1233i			0.756600i
$856$	−21.5903	+	21.5903i	−0.737943	+	0.737943i
$857$	−30.3974			−1.03835			−0.519177	−	0.854667i	$-0.673762\pi$
$857$	−30.3974			−1.03835			−0.519177	+	0.854667i	$0.673762\pi$
$858$	−0.414861	+	13.4789i	−0.0141631	+	0.460164i
$859$			53.2790i			1.81785i	0.416955	+	0.908927i	$0.363097\pi$
$859$			53.2790i			1.81785i	−0.416955	+	0.908927i	$0.636903\pi$
$860$	−2.68633	+	2.68633i	−0.0916031	+	0.0916031i
$861$	−8.37492	+	8.37492i	−0.285416	+	0.285416i
$862$	7.01836	+	7.01836i	0.239046	+	0.239046i
$863$	17.8486			0.607575			0.303787	−	0.952740i	$-0.401749\pi$
$863$	17.8486			0.607575			0.303787	+	0.952740i	$0.401749\pi$
$864$	30.1720	−	30.1720i	1.02647	−	1.02647i
$865$	−17.9962	+	17.9962i	−0.611890	+	0.611890i
$866$		−	41.5078i		−	1.41049i
$867$	−10.0774			−0.342246
$868$	−14.1267			−0.479491
$869$	1.39715	−	45.3936i	0.0473949	−	1.53987i
$870$	0.436891			0.0148120
$871$	−12.3648	+	12.3648i	−0.418964	+	0.418964i
$872$	31.8688	−	31.8688i	1.07921	−	1.07921i
$873$			9.17079i			0.310384i
$874$	69.7089			2.35794
$875$	23.8966	−	23.8966i	0.807854	−	0.807854i
$876$			3.31305i			0.111937i
$877$	19.4515	+	19.4515i	0.656831	+	0.656831i	0.954629	−	0.297798i	$-0.0962523\pi$
$877$	19.4515	+	19.4515i	0.656831	+	0.656831i	−0.297798	+	0.954629i	$0.596252\pi$
$878$	−43.1875	+	43.1875i	−1.45751	+	1.45751i
$879$			3.77911i			0.127466i
$880$	−41.8051	+	39.3086i	−1.40925	+	1.32509i
$881$			23.1588i			0.780240i	0.920764	+	0.390120i	$0.127567\pi$
$881$			23.1588i			0.780240i	−0.920764	+	0.390120i	$0.872433\pi$
$882$	17.2481	−	17.2481i	0.580774	−	0.580774i
$883$	15.5402	+	15.5402i	0.522970	+	0.522970i	0.918467	−	0.395497i	$-0.129428\pi$
$883$	15.5402	+	15.5402i	0.522970	+	0.522970i	−0.395497	+	0.918467i	$0.629428\pi$
$884$	97.9152	−	97.9152i	3.29324	−	3.29324i
$885$	−1.92351	−	1.92351i	−0.0646582	−	0.0646582i
$886$	67.7387	+	67.7387i	2.27573	+	2.27573i
$887$	5.06045	+	5.06045i	0.169913	+	0.169913i	0.786941	−	0.617028i	$-0.211663\pi$
$887$	5.06045	+	5.06045i	0.169913	+	0.169913i	−0.617028	+	0.786941i	$0.711663\pi$
$888$		−	29.4992i		−	0.989928i
$889$	41.0463	+	41.0463i	1.37665	+	1.37665i
$890$	6.76623			0.226805
$891$	−17.5284	−	18.6417i	−0.587224	−	0.624520i
$892$	−93.7195	−	93.7195i	−3.13796	−	3.13796i
$893$	22.5539			0.754737
$894$	−6.35915	+	6.35915i	−0.212682	+	0.212682i
$895$		−	31.5042i		−	1.05307i
$896$	88.0528			2.94164
$897$	−4.45077	+	4.45077i	−0.148607	+	0.148607i
$898$	39.7619	+	39.7619i	1.32687	+	1.32687i
$899$	0.279640			0.00932651
$900$			51.8609i			1.72870i
$901$			36.7663i			1.22486i
$902$	−2.69455	+	87.5465i	−0.0897186	+	2.91498i
$903$			0.686648i			0.0228502i
$904$	−54.9363	−	54.9363i	−1.82715	−	1.82715i
$905$	−16.7398	+	16.7398i	−0.556450	+	0.556450i
$906$			10.5476i			0.350420i
$907$	0.144548	−	0.144548i	0.00479965	−	0.00479965i	−0.704703	−	0.709503i	$-0.748920\pi$
$907$	0.144548	−	0.144548i	0.00479965	−	0.00479965i	0.709503	+	0.704703i	$0.248920\pi$
$908$	−49.9228	+	49.9228i	−1.65675	+	1.65675i
$909$	12.4397	+	12.4397i	0.412600	+	0.412600i
$910$		−	42.8921i		−	1.42186i
$911$	−42.9793			−1.42397			−0.711984	−	0.702195i	$-0.752203\pi$
$911$	−42.9793			−1.42397			−0.711984	+	0.702195i	$0.752203\pi$
$912$			32.1243i			1.06374i
$913$	−30.5656	+	28.7403i	−1.01157	+	0.951165i
$914$			4.65403i			0.153942i
$915$	−1.05043	+	3.60117i	−0.0347260	+	0.119051i
$916$	10.0777			0.332975
$917$	16.2207	−	16.2207i	0.535653	−	0.535653i
$918$		−	39.7957i		−	1.31345i
$919$	−42.7042			−1.40868			−0.704341	−	0.709862i	$-0.748757\pi$
$919$	−42.7042			−1.40868			−0.704341	+	0.709862i	$0.748757\pi$
$920$	−47.5791			−1.56864
$921$	3.75635	−	3.75635i	0.123776	−	0.123776i
$922$	−19.1989	+	19.1989i	−0.632281	+	0.632281i
$923$	−23.2417	+	23.2417i	−0.765009	+	0.765009i
$924$	−0.659808	+	21.4373i	−0.0217061	+	0.705237i
$925$	20.7367	+	20.7367i	0.681819	+	0.681819i
$926$	−71.2433	+	71.2433i	−2.34120	+	2.34120i
$927$	36.8849			1.21146
$928$	−6.42936			−0.211054
$929$		−	11.2437i		−	0.368893i	−0.982843	−	0.184446i	$-0.940951\pi$
$929$		−	11.2437i		−	0.368893i	0.982843	−	0.184446i	$-0.0590492\pi$
$930$			1.08184i			0.0354751i
$931$			19.3995i			0.635793i
$932$	83.1590	−	83.1590i	2.72397	−	2.72397i
$933$	−1.89077	+	1.89077i	−0.0619010	+	0.0619010i
$934$	−55.7349			−1.82370
$935$	−0.848074	+	27.5541i	−0.0277350	+	0.901117i
$936$	71.6874	+	71.6874i	2.34318	+	2.34318i
$937$		−	8.56698i		−	0.279871i	−0.990161	−	0.139936i	$-0.955310\pi$
$937$		−	8.56698i		−	0.279871i	0.990161	−	0.139936i	$-0.0446896\pi$
$938$	−27.0487	+	27.0487i	−0.883172	+	0.883172i
$939$	−4.89156	+	4.89156i	−0.159630	+	0.159630i
$940$	−24.6482			−0.803935
$941$	11.5678	+	11.5678i	0.377101	+	0.377101i	0.870055	−	0.492954i	$-0.164083\pi$
$941$	11.5678	+	11.5678i	0.377101	+	0.377101i	−0.492954	+	0.870055i	$0.664083\pi$
$942$	25.1808			0.820434
$943$	−28.9080	+	28.9080i	−0.941374	+	0.941374i
$944$	54.9541	+	54.9541i	1.78860	+	1.78860i
$945$	−6.33704	−	6.33704i	−0.206144	−	0.206144i
$946$	3.47845	+	3.69937i	0.113094	+	0.120277i
$947$	−4.69606	+	4.69606i	−0.152602	+	0.152602i	−0.779279	−	0.626677i	$-0.784414\pi$
$947$	−4.69606	+	4.69606i	−0.152602	+	0.152602i	0.626677	+	0.779279i	$0.284414\pi$
$948$	19.6470	+	19.6470i	0.638106	+	0.638106i
$949$	−6.43858			−0.209005
$950$	−40.1149	−	40.1149i	−1.30150	−	1.30150i
$951$			8.82773i			0.286259i
$952$	133.775	−	133.775i	4.33568	−	4.33568i
$953$	0.408271	−	0.408271i	0.0132252	−	0.0132252i	−0.700463	−	0.713688i	$-0.747023\pi$
$953$	0.408271	−	0.408271i	0.0132252	−	0.0132252i	0.713688	+	0.700463i	$0.247023\pi$
$954$	−43.1002			−1.39542
$955$	8.97876	−	8.97876i	0.290546	−	0.290546i
$956$	−122.015			−3.94625
$957$	0.0130610	−	0.424355i	0.000422202	−	0.0137174i
$958$	−4.22572	−	4.22572i	−0.136527	−	0.136527i
$959$	39.2686	+	39.2686i	1.26805	+	1.26805i
$960$		−	11.6921i		−	0.377362i
$961$		−	30.3075i		−	0.977663i
$962$	91.7928			2.95952
$963$	−9.67985			−0.311929
$964$	77.1268			2.48409
$965$	18.0182	+	18.0182i	0.580027	+	0.580027i
$966$	−9.73636	+	9.73636i	−0.313262	+	0.313262i
$967$	4.70326			0.151247			0.0756233	−	0.997136i	$-0.475905\pi$
$967$	4.70326			0.151247			0.0756233	+	0.997136i	$0.475905\pi$
$968$	65.6043	+	74.2196i	2.10860	+	2.38551i
$969$	10.9125	+	10.9125i	0.350561	+	0.350561i
$970$	7.75239	+	7.75239i	0.248914	+	0.248914i
$971$	−48.1723			−1.54592			−0.772961	−	0.634453i	$-0.781225\pi$
$971$	−48.1723			−1.54592			−0.772961	+	0.634453i	$0.781225\pi$
$972$	51.2959			1.64532
$973$	5.80182			0.185998
$974$	17.8691	−	17.8691i	0.572564	−	0.572564i
$975$	5.12250			0.164051
$976$	30.0103	−	102.884i	0.960606	−	3.29323i
$977$	55.8038			1.78532			0.892661	−	0.450730i	$-0.148836\pi$
$977$	55.8038			1.78532			0.892661	+	0.450730i	$0.148836\pi$
$978$	−15.8501	−	15.8501i	−0.506830	−	0.506830i
$979$	0.202279	−	6.57209i	0.00646486	−	0.210045i
$980$		−	21.2009i		−	0.677238i
$981$	14.2881			0.456185
$982$	−31.6663	−	31.6663i	−1.01051	−	1.01051i
$983$	−23.4550	+	23.4550i	−0.748098	+	0.748098i	−0.974122	−	0.226024i	$-0.927427\pi$
$983$	−23.4550	+	23.4550i	−0.748098	+	0.748098i	0.226024	+	0.974122i	$0.427427\pi$
$984$	−23.6649	−	23.6649i	−0.754410	−	0.754410i
$985$		−	9.83077i		−	0.313234i
$986$	−4.24004	+	4.24004i	−0.135030	+	0.135030i
$987$	−3.15014	+	3.15014i	−0.100270	+	0.100270i
$988$	−129.100			−4.10723
$989$			2.37013i			0.0753657i
$990$	−32.3010	−	0.994175i	−1.02659	−	0.0315969i
$991$	−26.5823			−0.844416			−0.422208	−	0.906499i	$-0.638745\pi$
$991$	−26.5823			−0.844416			−0.422208	+	0.906499i	$0.638745\pi$
$992$		−	15.9206i		−	0.505480i
$993$	3.06188	+	3.06188i	0.0971659	+	0.0971659i
$994$	−50.8427	+	50.8427i	−1.61263	+	1.61263i
$995$			6.22563i			0.197366i
$996$		−	25.6685i		−	0.813337i
$997$	−3.40232	+	3.40232i	−0.107753	+	0.107753i	−0.758928	−	0.651175i	$-0.774276\pi$
$997$	−3.40232	+	3.40232i	−0.107753	+	0.107753i	0.651175	+	0.758928i	$0.274276\pi$
$998$		−	30.6749i		−	0.970998i
$999$	13.5618	−	13.5618i	0.429077	−	0.429077i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.f.a.538.1	✓	120
11.10	odd	2	inner	671.2.f.a.538.60	yes	120
61.11	odd	4	inner	671.2.f.a.560.60	yes	120
671.560	even	4	inner	671.2.f.a.560.1	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.f.a.538.1	✓	120	1.1	even	1	trivial
671.2.f.a.538.60	yes	120	11.10	odd	2	inner
671.2.f.a.560.1	yes	120	671.560	even	4	inner
671.2.f.a.560.60	yes	120	61.11	odd	4	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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.91401 - 1.91401i) q^{2} -0.380921i q^{3} +5.32688i q^{4} +1.26088i q^{5} +(-0.729087 + 0.729087i) q^{6} +(-2.25350 - 2.25350i) q^{7} +(6.36769 - 6.36769i) q^{8} +2.85490 q^{9} +O(q^{10})\)	\(q+(-1.91401 - 1.91401i) q^{2} -0.380921i q^{3} +5.32688i q^{4} +1.26088i q^{5} +(-0.729087 + 0.729087i) q^{6} +(-2.25350 - 2.25350i) q^{7} +(6.36769 - 6.36769i) q^{8} +2.85490 q^{9} +(2.41334 - 2.41334i) q^{10} +(-2.27195 - 2.41625i) q^{11} +2.02912 q^{12} +3.94340i q^{13} +8.62644i q^{14} +0.480297 q^{15} -13.7219 q^{16} +(-4.66130 + 4.66130i) q^{17} +(-5.46431 - 5.46431i) q^{18} +6.14588 q^{19} -6.71657 q^{20} +(-0.858405 + 0.858405i) q^{21} +(-0.276183 + 8.97326i) q^{22} +(-2.96299 + 2.96299i) q^{23} +(-2.42559 - 2.42559i) q^{24} +3.41017 q^{25} +(7.54771 - 7.54771i) q^{26} -2.23025i q^{27} +(12.0041 - 12.0041i) q^{28} +(-0.237623 + 0.237623i) q^{29} +(-0.919294 - 0.919294i) q^{30} +(-0.588410 - 0.588410i) q^{31} +(13.5285 + 13.5285i) q^{32} +(-0.920399 + 0.865434i) q^{33} +17.8435 q^{34} +(2.84140 - 2.84140i) q^{35} +15.2077i q^{36} +(6.08084 + 6.08084i) q^{37} +(-11.7633 - 11.7633i) q^{38} +1.50212 q^{39} +(8.02891 + 8.02891i) q^{40} +9.75637 q^{41} +3.28599 q^{42} +(0.399956 - 0.399956i) q^{43} +(12.8711 - 12.1024i) q^{44} +3.59969i q^{45} +11.3424 q^{46} +3.66976 q^{47} +5.22696i q^{48} +3.15651i q^{49} +(-6.52711 - 6.52711i) q^{50} +(1.77559 + 1.77559i) q^{51} -21.0060 q^{52} +(3.94379 - 3.94379i) q^{53} +(-4.26873 + 4.26873i) q^{54} +(3.04660 - 2.86466i) q^{55} -28.6991 q^{56} -2.34110i q^{57} +0.909626 q^{58} +(-4.00485 - 4.00485i) q^{59} +2.55848i q^{60} +(-2.18704 + 7.49779i) q^{61} +2.25245i q^{62} +(-6.43351 - 6.43351i) q^{63} -24.3436i q^{64} -4.97216 q^{65} +(3.41810 + 0.105204i) q^{66} +(3.13556 + 3.13556i) q^{67} +(-24.8302 - 24.8302i) q^{68} +(1.12866 + 1.12866i) q^{69} -10.8769 q^{70} +(5.89382 + 5.89382i) q^{71} +(18.1791 - 18.1791i) q^{72} +1.63275i q^{73} -23.2776i q^{74} -1.29901i q^{75} +32.7384i q^{76} +(-0.325170 + 10.5648i) q^{77} +(-2.87508 - 2.87508i) q^{78} +(9.68253 + 9.68253i) q^{79} -17.3017i q^{80} +7.71515 q^{81} +(-18.6738 - 18.6738i) q^{82} -12.6501i q^{83} +(-4.57262 - 4.57262i) q^{84} +(-5.87735 - 5.87735i) q^{85} -1.53104 q^{86} +(0.0905156 + 0.0905156i) q^{87} +(-29.8530 - 0.918828i) q^{88} +(1.40184 + 1.40184i) q^{89} +(6.88985 - 6.88985i) q^{90} +(8.88644 - 8.88644i) q^{91} +(-15.7835 - 15.7835i) q^{92} +(-0.224138 + 0.224138i) q^{93} +(-7.02396 - 7.02396i) q^{94} +7.74923i q^{95} +(5.15329 - 5.15329i) q^{96} +3.21230i q^{97} +(6.04159 - 6.04159i) q^{98} +(-6.48619 - 6.89814i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 120 q^{9}+O(q^{10}) \) 120 * q - 120 * q^9	\( 120 q - 120 q^{9} - 4 q^{11} + 16 q^{12} + 16 q^{15} - 148 q^{16} + 56 q^{20} - 4 q^{22} - 4 q^{23} - 104 q^{25} + 40 q^{26} - 2 q^{33} - 8 q^{34} - 12 q^{37} + 20 q^{38} + 16 q^{42} - 10 q^{44} - 4 q^{53} + 50 q^{55} - 24 q^{56} + 64 q^{58} - 56 q^{67} + 68 q^{69} + 144 q^{70} - 12 q^{71} - 64 q^{77} + 84 q^{78} + 72 q^{81} + 40 q^{82} - 80 q^{86} + 4 q^{89} - 4 q^{91} + 4 q^{92} + 64 q^{93} + 24 q^{99}+O(q^{100}) \) 120 * q - 120 * q^9 - 4 * q^11 + 16 * q^12 + 16 * q^15 - 148 * q^16 + 56 * q^20 - 4 * q^22 - 4 * q^23 - 104 * q^25 + 40 * q^26 - 2 * q^33 - 8 * q^34 - 12 * q^37 + 20 * q^38 + 16 * q^42 - 10 * q^44 - 4 * q^53 + 50 * q^55 - 24 * q^56 + 64 * q^58 - 56 * q^67 + 68 * q^69 + 144 * q^70 - 12 * q^71 - 64 * q^77 + 84 * q^78 + 72 * q^81 + 40 * q^82 - 80 * q^86 + 4 * q^89 - 4 * q^91 + 4 * q^92 + 64 * q^93 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more