LMFDB - Embedded newform 403.2.i.a.216.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(216,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("403.216");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.i (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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			216.5
Character	$\chi$	$=$	403.216
Dual form			403.2.i.a.278.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50749 - 1.50749i) q^{2} -1.65703i q^{3} +2.54505i q^{4} +(2.11743 + 2.11743i) q^{5} +(-2.49795 + 2.49795i) q^{6} +(-2.06359 + 2.06359i) q^{7} +(0.821650 - 0.821650i) q^{8} +0.254264 q^{9} +O(q^{10})$	\(q+(-1.50749 - 1.50749i) q^{2} -1.65703i q^{3} +2.54505i q^{4} +(2.11743 + 2.11743i) q^{5} +(-2.49795 + 2.49795i) q^{6} +(-2.06359 + 2.06359i) q^{7} +(0.821650 - 0.821650i) q^{8} +0.254264 q^{9} -6.38401i q^{10} +(-1.21675 - 1.21675i) q^{11} +4.21721 q^{12} +(3.49118 + 0.900923i) q^{13} +6.22168 q^{14} +(3.50864 - 3.50864i) q^{15} +2.61283 q^{16} +3.51667 q^{17} +(-0.383300 - 0.383300i) q^{18} +(-2.18795 - 2.18795i) q^{19} +(-5.38896 + 5.38896i) q^{20} +(3.41942 + 3.41942i) q^{21} +3.66848i q^{22} +8.25892 q^{23} +(-1.36150 - 1.36150i) q^{24} +3.96704i q^{25} +(-3.90478 - 6.62105i) q^{26} -5.39240i q^{27} +(-5.25193 - 5.25193i) q^{28} +5.44619i q^{29} -10.5785 q^{30} +(4.35438 + 3.46978i) q^{31} +(-5.58212 - 5.58212i) q^{32} +(-2.01619 + 2.01619i) q^{33} +(-5.30134 - 5.30134i) q^{34} -8.73903 q^{35} +0.647114i q^{36} +(-8.01045 - 8.01045i) q^{37} +6.59662i q^{38} +(1.49285 - 5.78498i) q^{39} +3.47958 q^{40} +(4.30972 + 4.30972i) q^{41} -10.3095i q^{42} +1.42480 q^{43} +(3.09669 - 3.09669i) q^{44} +(0.538387 + 0.538387i) q^{45} +(-12.4502 - 12.4502i) q^{46} +(6.04391 - 6.04391i) q^{47} -4.32954i q^{48} -1.51682i q^{49} +(5.98026 - 5.98026i) q^{50} -5.82722i q^{51} +(-2.29289 + 8.88521i) q^{52} +4.78015i q^{53} +(-8.12898 + 8.12898i) q^{54} -5.15279i q^{55} +3.39110i q^{56} +(-3.62549 + 3.62549i) q^{57} +(8.21006 - 8.21006i) q^{58} +(-9.59471 + 9.59471i) q^{59} +(8.92965 + 8.92965i) q^{60} +4.85057i q^{61} +(-1.33351 - 11.7948i) q^{62} +(-0.524697 + 0.524697i) q^{63} +11.6043i q^{64} +(5.48469 + 9.29998i) q^{65} +6.07878 q^{66} +(2.62579 + 2.62579i) q^{67} +8.95009i q^{68} -13.6853i q^{69} +(13.1740 + 13.1740i) q^{70} +(4.73789 + 4.73789i) q^{71} +(0.208916 - 0.208916i) q^{72} +(-7.22387 - 7.22387i) q^{73} +24.1513i q^{74} +6.57348 q^{75} +(5.56843 - 5.56843i) q^{76} +5.02176 q^{77} +(-10.9712 + 6.47033i) q^{78} -14.9861i q^{79} +(5.53250 + 5.53250i) q^{80} -8.17256 q^{81} -12.9937i q^{82} +(1.67927 - 1.67927i) q^{83} +(-8.70259 + 8.70259i) q^{84} +(7.44631 + 7.44631i) q^{85} +(-2.14787 - 2.14787i) q^{86} +9.02447 q^{87} -1.99949 q^{88} +(10.1240 + 10.1240i) q^{89} -1.62323i q^{90} +(-9.06350 + 5.34523i) q^{91} +21.0193i q^{92} +(5.74952 - 7.21532i) q^{93} -18.2223 q^{94} -9.26567i q^{95} +(-9.24972 + 9.24972i) q^{96} +(-4.94417 - 4.94417i) q^{97} +(-2.28658 + 2.28658i) q^{98} +(-0.309377 - 0.309377i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9}+O(q^{10}) $ 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9	$ 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9} - 48 q^{14} - 40 q^{16} + 4 q^{18} - 24 q^{19} - 16 q^{20} + 44 q^{28} + 24 q^{31} + 28 q^{32} - 40 q^{35} - 24 q^{39} + 24 q^{40} + 20 q^{41} - 24 q^{45} - 36 q^{47} + 80 q^{50} + 28 q^{59} - 76 q^{63} + 152 q^{66} - 32 q^{67} - 48 q^{70} + 20 q^{71} - 32 q^{72} + 72 q^{76} + 84 q^{78} - 20 q^{80} + 52 q^{81} - 112 q^{87} - 8 q^{93} - 16 q^{94} - 4 q^{97} - 92 q^{98}+O(q^{100}) $ 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9 - 48 * q^14 - 40 * q^16 + 4 * q^18 - 24 * q^19 - 16 * q^20 + 44 * q^28 + 24 * q^31 + 28 * q^32 - 40 * q^35 - 24 * q^39 + 24 * q^40 + 20 * q^41 - 24 * q^45 - 36 * q^47 + 80 * q^50 + 28 * q^59 - 76 * q^63 + 152 * q^66 - 32 * q^67 - 48 * q^70 + 20 * q^71 - 32 * q^72 + 72 * q^76 + 84 * q^78 - 20 * q^80 + 52 * q^81 - 112 * q^87 - 8 * q^93 - 16 * q^94 - 4 * q^97 - 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.50749	−	1.50749i	−1.06596	−	1.06596i	−0.997666	−	0.0682901i	$-0.978246\pi$
$2$	−1.50749	−	1.50749i	−1.06596	−	1.06596i	−0.0682901	−	0.997666i	$-0.521754\pi$
$3$		−	1.65703i		−	0.956685i	−0.878173	−	0.478342i	$-0.841238\pi$
$3$		−	1.65703i		−	0.956685i	0.878173	−	0.478342i	$-0.158762\pi$
$4$			2.54505i			1.27252i
$5$	2.11743	+	2.11743i	0.946944	+	0.946944i	0.998662	−	0.0517174i	$-0.0164695\pi$
$5$	2.11743	+	2.11743i	0.946944	+	0.946944i	−0.0517174	+	0.998662i	$0.516470\pi$
$6$	−2.49795	+	2.49795i	−1.01978	+	1.01978i
$7$	−2.06359	+	2.06359i	−0.779964	+	0.779964i	−0.979824	−	0.199860i	$-0.935951\pi$
$7$	−2.06359	+	2.06359i	−0.779964	+	0.779964i	0.199860	+	0.979824i	$0.435951\pi$
$8$	0.821650	−	0.821650i	0.290497	−	0.290497i
$9$	0.254264			0.0847547
$10$		−	6.38401i		−	2.01880i
$11$	−1.21675	−	1.21675i	−0.366865	−	0.366865i	0.499468	−	0.866333i	$-0.333529\pi$
$11$	−1.21675	−	1.21675i	−0.366865	−	0.366865i	−0.866333	+	0.499468i	$0.833529\pi$
$12$	4.21721			1.21740
$13$	3.49118	+	0.900923i	0.968279	+	0.249871i
$13$	3.49118	+	0.900923i	0.968279	+	0.249871i
$14$	6.22168			1.66281
$15$	3.50864	−	3.50864i	0.905927	−	0.905927i
$16$	2.61283			0.653209
$17$	3.51667			0.852918			0.426459	−	0.904507i	$-0.359761\pi$
$17$	3.51667			0.852918			0.426459	+	0.904507i	$0.359761\pi$
$18$	−0.383300	−	0.383300i	−0.0903448	−	0.0903448i
$19$	−2.18795	−	2.18795i	−0.501950	−	0.501950i	0.410094	−	0.912043i	$-0.365496\pi$
$19$	−2.18795	−	2.18795i	−0.501950	−	0.501950i	−0.912043	+	0.410094i	$0.865496\pi$
$20$	−5.38896	+	5.38896i	−1.20501	+	1.20501i
$21$	3.41942	+	3.41942i	0.746180	+	0.746180i
$22$			3.66848i			0.782124i
$23$	8.25892			1.72210			0.861052	−	0.508516i	$-0.169806\pi$
$23$	8.25892			1.72210			0.861052	+	0.508516i	$0.169806\pi$
$24$	−1.36150	−	1.36150i	−0.277914	−	0.277914i
$25$			3.96704i			0.793407i
$26$	−3.90478	−	6.62105i	−0.765791	−	1.29849i
$27$		−	5.39240i		−	1.03777i
$28$	−5.25193	−	5.25193i	−0.992522	−	0.992522i
$29$			5.44619i			1.01133i	0.862730	+	0.505666i	$0.168753\pi$
$29$			5.44619i			1.01133i	−0.862730	+	0.505666i	$0.831247\pi$
$30$	−10.5785			−1.93136
$31$	4.35438	+	3.46978i	0.782069	+	0.623192i
$31$	4.35438	+	3.46978i	0.782069	+	0.623192i
$32$	−5.58212	−	5.58212i	−0.986789	−	0.986789i
$33$	−2.01619	+	2.01619i	−0.350974	+	0.350974i
$34$	−5.30134	−	5.30134i	−0.909173	−	0.909173i
$35$	−8.73903			−1.47717
$36$			0.647114i			0.107852i
$37$	−8.01045	−	8.01045i	−1.31691	−	1.31691i	−0.916209	−	0.400701i	$-0.868767\pi$
$37$	−8.01045	−	8.01045i	−1.31691	−	1.31691i	−0.400701	−	0.916209i	$-0.631233\pi$
$38$			6.59662i			1.07011i
$39$	1.49285	−	5.78498i	0.239048	−	0.926338i
$40$	3.47958			0.550169
$41$	4.30972	+	4.30972i	0.673065	+	0.673065i	0.958421	−	0.285357i	$-0.0921120\pi$
$41$	4.30972	+	4.30972i	0.673065	+	0.673065i	−0.285357	+	0.958421i	$0.592112\pi$
$42$		−	10.3095i		−	1.59079i
$43$	1.42480			0.217280			0.108640	−	0.994081i	$-0.465350\pi$
$43$	1.42480			0.217280			0.108640	+	0.994081i	$0.465350\pi$
$44$	3.09669	−	3.09669i	0.466844	−	0.466844i
$45$	0.538387	+	0.538387i	0.0802580	+	0.0802580i
$46$	−12.4502	−	12.4502i	−1.83569	−	1.83569i
$47$	6.04391	−	6.04391i	0.881595	−	0.881595i	−0.112102	−	0.993697i	$-0.535758\pi$
$47$	6.04391	−	6.04391i	0.881595	−	0.881595i	0.993697	+	0.112102i	$0.0357583\pi$
$48$		−	4.32954i		−	0.624915i
$49$		−	1.51682i		−	0.216688i
$50$	5.98026	−	5.98026i	0.845737	−	0.845737i
$51$		−	5.82722i		−	0.815974i
$52$	−2.29289	+	8.88521i	−0.317967	+	1.23216i
$53$			4.78015i			0.656604i	0.944573	+	0.328302i	$0.106476\pi$
$53$			4.78015i			0.656604i	−0.944573	+	0.328302i	$0.893524\pi$
$54$	−8.12898	+	8.12898i	−1.10621	+	1.10621i
$55$		−	5.15279i		−	0.694802i
$56$			3.39110i			0.453155i
$57$	−3.62549	+	3.62549i	−0.480208	+	0.480208i
$58$	8.21006	−	8.21006i	1.07803	−	1.07803i
$59$	−9.59471	+	9.59471i	−1.24912	+	1.24912i	−0.293018	+	0.956107i	$0.594660\pi$
$59$	−9.59471	+	9.59471i	−1.24912	+	1.24912i	−0.956107	+	0.293018i	$0.905340\pi$
$60$	8.92965	+	8.92965i	1.15281	+	1.15281i
$61$			4.85057i			0.621052i	0.950565	+	0.310526i	$0.100505\pi$
$61$			4.85057i			0.621052i	−0.950565	+	0.310526i	$0.899495\pi$
$62$	−1.33351	−	11.7948i	−0.169356	−	1.49795i
$63$	−0.524697	+	0.524697i	−0.0661057	+	0.0661057i
$64$			11.6043i			1.45054i
$65$	5.48469	+	9.29998i	0.680293	+	1.15352i
$66$	6.07878			0.748246
$67$	2.62579	+	2.62579i	0.320792	+	0.320792i	0.849071	−	0.528279i	$-0.177162\pi$
$67$	2.62579	+	2.62579i	0.320792	+	0.320792i	−0.528279	+	0.849071i	$0.677162\pi$
$68$			8.95009i			1.08536i
$69$		−	13.6853i		−	1.64751i
$70$	13.1740	+	13.1740i	1.57459	+	1.57459i
$71$	4.73789	+	4.73789i	0.562284	+	0.562284i	0.929956	−	0.367672i	$-0.119845\pi$
$71$	4.73789	+	4.73789i	0.562284	+	0.562284i	−0.367672	+	0.929956i	$0.619845\pi$
$72$	0.208916	−	0.208916i	0.0246210	−	0.0246210i
$73$	−7.22387	−	7.22387i	−0.845490	−	0.845490i	0.144077	−	0.989567i	$-0.453979\pi$
$73$	−7.22387	−	7.22387i	−0.845490	−	0.845490i	−0.989567	+	0.144077i	$0.953979\pi$
$74$			24.1513i			2.80753i
$75$	6.57348			0.759040
$76$	5.56843	−	5.56843i	0.638743	−	0.638743i
$77$	5.02176			0.572283
$78$	−10.9712	+	6.47033i	−1.24225	+	0.732621i
$79$		−	14.9861i		−	1.68606i	−0.537864	−	0.843031i	$-0.680769\pi$
$79$		−	14.9861i		−	1.68606i	0.537864	−	0.843031i	$-0.319231\pi$
$80$	5.53250	+	5.53250i	0.618552	+	0.618552i
$81$	−8.17256			−0.908062
$82$		−	12.9937i		−	1.43491i
$83$	1.67927	−	1.67927i	0.184324	−	0.184324i	−0.608913	−	0.793237i	$-0.708394\pi$
$83$	1.67927	−	1.67927i	0.184324	−	0.184324i	0.793237	+	0.608913i	$0.208394\pi$
$84$	−8.70259	+	8.70259i	−0.949530	+	0.949530i
$85$	7.44631	+	7.44631i	0.807666	+	0.807666i
$86$	−2.14787	−	2.14787i	−0.231611	−	0.231611i
$87$	9.02447			0.967525
$88$	−1.99949			−0.213146
$89$	10.1240	+	10.1240i	1.07315	+	1.07315i	0.997105	+	0.0760403i	$0.0242278\pi$
$89$	10.1240	+	10.1240i	1.07315	+	1.07315i	0.0760403	+	0.997105i	$0.475772\pi$
$90$		−	1.62323i		−	0.171103i
$91$	−9.06350	+	5.34523i	−0.950113	+	0.560333i
$92$			21.0193i			2.19142i
$93$	5.74952	−	7.21532i	0.596198	−	0.748193i
$94$	−18.2223			−1.87948
$95$		−	9.26567i		−	0.950637i
$96$	−9.24972	+	9.24972i	−0.944045	+	0.944045i
$97$	−4.94417	−	4.94417i	−0.502004	−	0.502004i	0.410056	−	0.912060i	$-0.365509\pi$
$97$	−4.94417	−	4.94417i	−0.502004	−	0.502004i	−0.912060	+	0.410056i	$0.865509\pi$
$98$	−2.28658	+	2.28658i	−0.230980	+	0.230980i
$99$	−0.309377	−	0.309377i	−0.0310935	−	0.0310935i
$100$	−10.0963			−1.00963
$101$			5.17436i			0.514868i	0.966296	+	0.257434i	$0.0828770\pi$
$101$			5.17436i			0.514868i	−0.966296	+	0.257434i	$0.917123\pi$
$102$	−8.78446	+	8.78446i	−0.869792	+	0.869792i
$103$		−	3.68175i		−	0.362773i	−0.983412	−	0.181387i	$-0.941941\pi$
$103$		−	3.68175i		−	0.362773i	0.983412	−	0.181387i	$-0.0580585\pi$
$104$	3.60877	−	2.12828i	0.353869	−	0.208695i
$105$			14.4808i			1.41318i
$106$	7.20602	−	7.20602i	0.699910	−	0.699910i
$107$	−1.69973			−0.164319			−0.0821594	−	0.996619i	$-0.526182\pi$
$107$	−1.69973			−0.164319			−0.0821594	+	0.996619i	$0.526182\pi$
$108$	13.7239			1.32058
$109$	5.21508	+	5.21508i	0.499514	+	0.499514i	0.911287	−	0.411772i	$-0.135090\pi$
$109$	5.21508	+	5.21508i	0.499514	+	0.499514i	−0.411772	+	0.911287i	$0.635090\pi$
$110$	−7.76777	+	7.76777i	−0.740628	+	0.740628i
$111$	−13.2735	+	13.2735i	−1.25987	+	1.25987i
$112$	−5.39182	+	5.39182i	−0.509479	+	0.509479i
$113$	5.29510			0.498121			0.249060	−	0.968488i	$-0.419878\pi$
$113$	5.29510			0.498121			0.249060	+	0.968488i	$0.419878\pi$
$114$	10.9308			1.02376
$115$	17.4877	+	17.4877i	1.63074	+	1.63074i
$116$	−13.8608			−1.28694
$117$	0.887682	+	0.229072i	0.0820662	+	0.0211778i
$118$	28.9278			2.66302
$119$	−7.25697	+	7.25697i	−0.665245	+	0.665245i
$120$		−	5.76575i		−	0.526338i
$121$		−	8.03902i		−	0.730820i
$122$	7.31218	−	7.31218i	0.662014	−	0.662014i
$123$	7.14132	−	7.14132i	0.643911	−	0.643911i
$124$	−8.83076	+	11.0821i	−0.793026	+	0.995201i
$125$	2.18723	−	2.18723i	0.195632	−	0.195632i
$126$	1.58195			0.140931
$127$	−18.5731			−1.64810			−0.824050	−	0.566517i	$-0.808290\pi$
$127$	−18.5731			−1.64810			−0.824050	+	0.566517i	$0.808290\pi$
$128$	6.32911	−	6.32911i	0.559419	−	0.559419i
$129$		−	2.36093i		−	0.207868i
$130$	5.75150	−	22.2877i	0.504440	−	1.95476i
$131$	−9.27337			−0.810218			−0.405109	−	0.914268i	$-0.632767\pi$
$131$	−9.27337			−0.810218			−0.405109	+	0.914268i	$0.632767\pi$
$132$	−5.13130	−	5.13130i	−0.446622	−	0.446622i
$133$	9.03006			0.783006
$134$		−	7.91671i		−	0.683900i
$135$	11.4180	−	11.4180i	0.982709	−	0.982709i
$136$	2.88947	−	2.88947i	0.247770	−	0.247770i
$137$	−6.98388	−	6.98388i	−0.596673	−	0.596673i	0.342753	−	0.939426i	$-0.388641\pi$
$137$	−6.98388	−	6.98388i	−0.596673	−	0.596673i	−0.939426	+	0.342753i	$0.888641\pi$
$138$	−20.6304	+	20.6304i	−1.75617	+	1.75617i
$139$			1.45412i			0.123337i	0.998097	+	0.0616684i	$0.0196421\pi$
$139$			1.45412i			0.123337i	−0.998097	+	0.0616684i	$0.980358\pi$
$140$		−	22.2412i		−	1.87973i
$141$	−10.0149	−	10.0149i	−0.843408	−	0.843408i
$142$		−	14.2846i		−	1.19874i
$143$	−3.15170	−	5.34411i	−0.263559	−	0.446897i
$144$	0.664350			0.0553625
$145$	−11.5319	+	11.5319i	−0.957674	+	0.957674i
$146$			21.7798i			1.80251i
$147$	−2.51340			−0.207302
$148$	20.3870	−	20.3870i	1.67580	−	1.67580i
$149$	2.68035	+	2.68035i	0.219583	+	0.219583i	0.808323	−	0.588740i	$-0.200376\pi$
$149$	2.68035	+	2.68035i	0.219583	+	0.219583i	−0.588740	+	0.808323i	$0.700376\pi$
$150$	−9.90945	−	9.90945i	−0.809103	−	0.809103i
$151$	−9.59165	−	9.59165i	−0.780558	−	0.780558i	0.199367	−	0.979925i	$-0.436111\pi$
$151$	−9.59165	−	9.59165i	−0.780558	−	0.780558i	−0.979925	+	0.199367i	$0.936111\pi$
$152$	−3.59546			−0.291630
$153$	0.894164			0.0722889
$154$	−7.57025	−	7.57025i	−0.610028	−	0.610028i
$155$	1.87306	+	16.5671i	0.150448	+	1.33070i
$156$	14.7230	+	3.79938i	1.17879	+	0.304194i
$157$	16.7516			1.33692			0.668460	−	0.743748i	$-0.266954\pi$
$157$	16.7516			1.33692			0.668460	+	0.743748i	$0.266954\pi$
$158$	−22.5913	+	22.5913i	−1.79727	+	1.79727i
$159$	7.92083			0.628163
$160$		−	23.6395i		−	1.86887i
$161$	−17.0430	+	17.0430i	−1.34318	+	1.34318i
$162$	12.3200	+	12.3200i	0.967954	+	0.967954i
$163$	6.79908	−	6.79908i	0.532545	−	0.532545i	−0.388784	−	0.921329i	$-0.627105\pi$
$163$	6.79908	−	6.79908i	0.532545	−	0.532545i	0.921329	+	0.388784i	$0.127105\pi$
$164$	−10.9684	+	10.9684i	−0.856490	+	0.856490i
$165$	−8.53830			−0.664706
$166$	−5.06296			−0.392962
$167$	−3.80114	−	3.80114i	−0.294141	−	0.294141i	0.544572	−	0.838714i	$-0.316692\pi$
$167$	−3.80114	−	3.80114i	−0.294141	−	0.294141i	−0.838714	+	0.544572i	$0.816692\pi$
$168$	5.61914			0.433526
$169$	11.3767	+	6.29057i	0.875129	+	0.483890i
$170$		−	22.4505i		−	1.72187i
$171$	−0.556317	−	0.556317i	−0.0425426	−	0.0425426i
$172$			3.62618i			0.276494i
$173$		−	7.36092i		−	0.559640i	−0.960052	−	0.279820i	$-0.909725\pi$
$173$		−	7.36092i		−	0.559640i	0.960052	−	0.279820i	$-0.0902749\pi$
$174$	−13.6043	−	13.6043i	−1.03134	−	1.03134i
$175$	−8.18634	−	8.18634i	−0.618829	−	0.618829i
$176$	−3.17918	−	3.17918i	−0.239639	−	0.239639i
$177$	15.8987	+	15.8987i	1.19502	+	1.19502i
$178$		−	30.5237i		−	2.28785i
$179$	−4.84115			−0.361845			−0.180922	−	0.983497i	$-0.557908\pi$
$179$	−4.84115			−0.361845			−0.180922	+	0.983497i	$0.557908\pi$
$180$	−1.37022	+	1.37022i	−0.102130	+	0.102130i
$181$	−8.59778			−0.639068			−0.319534	−	0.947575i	$-0.603526\pi$
$181$	−8.59778			−0.639068			−0.319534	+	0.947575i	$0.603526\pi$
$182$	21.7210	+	5.60525i	1.61007	+	0.415489i
$183$	8.03752			0.594151
$184$	6.78594	−	6.78594i	0.500266	−	0.500266i
$185$		−	33.9232i		−	2.49408i
$186$	−19.5444	+	2.20967i	−1.43306	+	0.162021i
$187$	−4.27892	−	4.27892i	−0.312906	−	0.312906i
$188$	15.3820	+	15.3820i	1.12185	+	1.12185i
$189$	11.1277	+	11.1277i	0.809422	+	0.809422i
$190$	−13.9679	+	13.9679i	−1.01334	+	1.01334i
$191$	−10.0958			−0.730504			−0.365252	−	0.930909i	$-0.619017\pi$
$191$	−10.0958			−0.730504			−0.365252	+	0.930909i	$0.619017\pi$
$192$	19.2286			1.38771
$193$	−7.73860	+	7.73860i	−0.557037	+	0.557037i	−0.928463	−	0.371426i	$-0.878869\pi$
$193$	−7.73860	+	7.73860i	−0.557037	+	0.557037i	0.371426	+	0.928463i	$0.378869\pi$
$194$			14.9065i			1.07023i
$195$	15.4103	−	9.08828i	1.10356	−	0.650825i
$196$	3.86036			0.275740
$197$	1.30937	−	1.30937i	0.0932884	−	0.0932884i	−0.658922	−	0.752211i	$-0.728987\pi$
$197$	1.30937	−	1.30937i	0.0932884	−	0.0932884i	0.752211	+	0.658922i	$0.228987\pi$
$198$			0.932764i			0.0662887i
$199$	−8.02951			−0.569197			−0.284599	−	0.958647i	$-0.591860\pi$
$199$	−8.02951			−0.569197			−0.284599	+	0.958647i	$0.591860\pi$
$200$	3.25951	+	3.25951i	0.230482	+	0.230482i
$201$	4.35101	−	4.35101i	0.306897	−	0.306897i
$202$	7.80029	−	7.80029i	0.548826	−	0.548826i
$203$	−11.2387	−	11.2387i	−0.788802	−	0.788802i
$204$	14.8305			1.03834
$205$			18.2511i			1.27471i
$206$	−5.55019	+	5.55019i	−0.386700	+	0.386700i
$207$	2.09995			0.145957
$208$	9.12188	+	2.35396i	0.632488	+	0.163218i
$209$			5.32439i			0.368296i
$210$	21.8296	−	21.8296i	1.50639	−	1.50639i
$211$	−21.7480			−1.49720			−0.748598	−	0.663024i	$-0.769273\pi$
$211$	−21.7480			−1.49720			−0.748598	+	0.663024i	$0.769273\pi$
$212$	−12.1657			−0.835543
$213$	7.85080	−	7.85080i	0.537928	−	0.537928i
$214$	2.56232	+	2.56232i	0.175156	+	0.175156i
$215$	3.01692	+	3.01692i	0.205752	+	0.205752i
$216$	−4.43067	−	4.43067i	−0.301469	−	0.301469i
$217$	−16.1459	+	1.82544i	−1.09605	+	0.123919i
$218$		−	15.7234i		−	1.06492i
$219$	−11.9701	+	11.9701i	−0.808867	+	0.808867i
$220$	13.1141			0.884151
$221$	12.2773	+	3.16825i	0.825863	+	0.213120i
$222$	40.0194			2.68592
$223$	3.58291	−	3.58291i	0.239930	−	0.239930i	−0.576891	−	0.816821i	$-0.695734\pi$
$223$	3.58291	−	3.58291i	0.239930	−	0.239930i	0.816821	+	0.576891i	$0.195734\pi$
$224$	23.0384			1.53932
$225$			1.00868i			0.0672450i
$226$	−7.98230	−	7.98230i	−0.530975	−	0.530975i
$227$	2.61765	+	2.61765i	0.173740	+	0.173740i	0.788620	−	0.614881i	$-0.210796\pi$
$227$	2.61765	+	2.61765i	0.173740	+	0.173740i	−0.614881	+	0.788620i	$0.710796\pi$
$228$	−9.22703	−	9.22703i	−0.611075	−	0.611075i
$229$	−5.57111	−	5.57111i	−0.368150	−	0.368150i	0.498652	−	0.866802i	$-0.333828\pi$
$229$	−5.57111	−	5.57111i	−0.368150	−	0.368150i	−0.866802	+	0.498652i	$0.833828\pi$
$230$		−	52.7251i		−	3.47659i
$231$		−	8.32119i		−	0.547494i
$232$	4.47486	+	4.47486i	0.293789	+	0.293789i
$233$			6.72600i			0.440635i	0.975428	+	0.220318i	$0.0707094\pi$
$233$			6.72600i			0.440635i	−0.975428	+	0.220318i	$0.929291\pi$
$234$	−0.992847	−	1.68350i	−0.0649044	−	0.110054i
$235$	25.5951			1.66964
$236$	−24.4190	−	24.4190i	−1.58954	−	1.58954i
$237$	−24.8323			−1.61303
$238$	21.8796			1.41824
$239$	−12.3057	+	12.3057i	−0.795990	+	0.795990i	−0.982461	−	0.186471i	$-0.940295\pi$
$239$	−12.3057	+	12.3057i	−0.795990	+	0.795990i	0.186471	+	0.982461i	$0.440295\pi$
$240$	9.16750	−	9.16750i	0.591759	−	0.591759i
$241$	2.45355	+	2.45355i	0.158047	+	0.158047i	0.781701	−	0.623654i	$-0.214352\pi$
$241$	2.45355	+	2.45355i	0.158047	+	0.158047i	−0.623654	+	0.781701i	$0.714352\pi$
$242$	−12.1187	+	12.1187i	−0.779022	+	0.779022i
$243$		−	2.63506i		−	0.169039i
$244$	−12.3449			−0.790303
$245$	3.21175	−	3.21175i	0.205191	−	0.205191i
$246$	−21.5309			−1.37276
$247$	−5.66735	−	9.60970i	−0.360605	−	0.611450i
$248$	6.42872	−	0.726825i	0.408224	−	0.0461535i
$249$	−2.78260	−	2.78260i	−0.176340	−	0.176340i
$250$	−6.59445			−0.417070
$251$	−6.44780			−0.406981			−0.203491	−	0.979077i	$-0.565229\pi$
$251$	−6.44780			−0.406981			−0.203491	+	0.979077i	$0.565229\pi$
$252$	−1.33538	−	1.33538i	−0.0841209	−	0.0841209i
$253$	−10.0491	−	10.0491i	−0.631780	−	0.631780i
$254$	27.9988	+	27.9988i	1.75680	+	1.75680i
$255$	12.3387	−	12.3387i	0.772682	−	0.772682i
$256$	4.12647			0.257904
$257$		−	30.5869i		−	1.90796i	−0.299874	−	0.953979i	$-0.596945\pi$
$257$		−	30.5869i		−	1.90796i	0.299874	−	0.953979i	$-0.403055\pi$
$258$	−3.55908	+	3.55908i	−0.221578	+	0.221578i
$259$	33.0606			2.05428
$260$	−23.6689	+	13.9588i	−1.46788	+	0.865688i
$261$			1.38477i			0.0857151i
$262$	13.9795	+	13.9795i	0.863657	+	0.863657i
$263$		−	1.20149i		−	0.0740869i	−0.999314	−	0.0370434i	$-0.988206\pi$
$263$		−	1.20149i		−	0.0740869i	0.999314	−	0.0370434i	$-0.0117940\pi$
$264$			3.31321i			0.203914i
$265$	−10.1216	+	10.1216i	−0.621767	+	0.621767i
$266$	−13.6127	−	13.6127i	−0.834649	−	0.834649i
$267$	16.7758	−	16.7758i	1.02666	−	1.02666i
$268$	−6.68277	+	6.68277i	−0.408215	+	0.408215i
$269$		−	15.3629i		−	0.936693i	−0.883545	−	0.468347i	$-0.844850\pi$
$269$		−	15.3629i		−	0.936693i	0.883545	−	0.468347i	$-0.155150\pi$
$270$	−34.4251			−2.09505
$271$	11.6569	+	11.6569i	0.708105	+	0.708105i	0.966137	−	0.258031i	$-0.0830738\pi$
$271$	11.6569	+	11.6569i	0.708105	+	0.708105i	−0.258031	+	0.966137i	$0.583074\pi$
$272$	9.18848			0.557133
$273$	8.85719	+	15.0185i	0.536061	+	0.908959i
$274$			21.0562i			1.27205i
$275$	4.82691	−	4.82691i	0.291073	−	0.291073i
$276$	34.8296			2.09650
$277$	−26.2008			−1.57425			−0.787126	−	0.616793i	$-0.788432\pi$
$277$	−26.2008			−1.57425			−0.787126	+	0.616793i	$0.788432\pi$
$278$	2.19207	−	2.19207i	0.131471	−	0.131471i
$279$	1.10716	+	0.882242i	0.0662841	+	0.0528184i
$280$	−7.18042	+	7.18042i	−0.429112	+	0.429112i
$281$	14.7633	−	14.7633i	0.880703	−	0.880703i	−0.112903	−	0.993606i	$-0.536015\pi$
$281$	14.7633	−	14.7633i	0.880703	−	0.880703i	0.993606	+	0.112903i	$0.0360150\pi$
$282$			30.1948i			1.79807i
$283$			31.0134i			1.84356i	0.387719	+	0.921778i	$0.373263\pi$
$283$			31.0134i			1.84356i	−0.387719	+	0.921778i	$0.626737\pi$
$284$	−12.0581	+	12.0581i	−0.715519	+	0.715519i
$285$	−15.3535			−0.909460
$286$	−3.30502	+	12.8073i	−0.195430	+	0.757314i
$287$	−17.7870			−1.04993
$288$	−1.41933	−	1.41933i	−0.0836350	−	0.0836350i
$289$	−4.63302			−0.272531
$290$	34.7685			2.04168
$291$	−8.19261	+	8.19261i	−0.480259	+	0.480259i
$292$	18.3851	−	18.3851i	1.07590	−	1.07590i
$293$	−18.1666	+	18.1666i	−1.06131	+	1.06131i	−0.0633128	+	0.997994i	$0.520167\pi$
$293$	−18.1666	+	18.1666i	−1.06131	+	1.06131i	−0.997994	+	0.0633128i	$0.979833\pi$
$294$	3.78893	+	3.78893i	0.220975	+	0.220975i
$295$	−40.6323			−2.36570
$296$	−13.1636			−0.765117
$297$	−6.56122	+	6.56122i	−0.380721	+	0.380721i
$298$		−	8.08121i		−	0.468132i
$299$	28.8334	+	7.44065i	1.66748	+	0.430304i
$300$			16.7298i			0.965896i
$301$	−2.94020	+	2.94020i	−0.169470	+	0.169470i
$302$			28.9186i			1.66408i
$303$	8.57405			0.492566
$304$	−5.71675	−	5.71675i	−0.327878	−	0.327878i
$305$	−10.2708	+	10.2708i	−0.588102	+	0.588102i
$306$	−1.34794	−	1.34794i	−0.0770567	−	0.0770567i
$307$	−12.6893	+	12.6893i	−0.724217	+	0.724217i	−0.969461	−	0.245244i	$-0.921132\pi$
$307$	−12.6893	+	12.6893i	−0.724217	+	0.724217i	0.245244	+	0.969461i	$0.421132\pi$
$308$			12.7806i			0.728243i
$309$	−6.10075			−0.347059
$310$	22.1511	−	27.7984i	1.25810	−	1.57884i
$311$		−	7.71365i		−	0.437401i	−0.975792	−	0.218701i	$-0.929818\pi$
$311$		−	7.71365i		−	0.437401i	0.975792	−	0.218701i	$-0.0701818\pi$
$312$	−3.52662	−	5.97983i	−0.199656	−	0.338541i
$313$			21.4944i			1.21494i	0.794344	+	0.607469i	$0.207815\pi$
$313$			21.4944i			1.21494i	−0.794344	+	0.607469i	$0.792185\pi$
$314$	−25.2528	−	25.2528i	−1.42510	−	1.42510i
$315$	−2.22202			−0.125197
$316$	38.1402			2.14555
$317$	−3.62279	−	3.62279i	−0.203476	−	0.203476i	0.598011	−	0.801488i	$-0.295958\pi$
$317$	−3.62279	−	3.62279i	−0.203476	−	0.203476i	−0.801488	+	0.598011i	$0.795958\pi$
$318$	−11.9406	−	11.9406i	−0.669593	−	0.669593i
$319$	6.62667	−	6.62667i	0.371022	−	0.371022i
$320$	−24.5713	+	24.5713i	−1.37358	+	1.37358i
$321$			2.81649i			0.157201i
$322$	51.3844			2.86354
$323$	−7.69430	−	7.69430i	−0.428122	−	0.428122i
$324$		−	20.7995i		−	1.15553i
$325$	−3.57399	+	13.8496i	−0.198249	+	0.768240i
$326$	−20.4991			−1.13534
$327$	8.64153	−	8.64153i	0.477878	−	0.477878i
$328$	7.08216			0.391047
$329$			24.9443i			1.37522i
$330$	12.8714	+	12.8714i	0.708547	+	0.708547i
$331$	−15.6782	+	15.6782i	−0.861751	+	0.861751i	−0.991541	−	0.129790i	$-0.958570\pi$
$331$	−15.6782	+	15.6782i	−0.861751	+	0.861751i	0.129790	+	0.991541i	$0.458570\pi$
$332$	4.27382	+	4.27382i	0.234556	+	0.234556i
$333$	−2.03677	−	2.03677i	−0.111614	−	0.111614i
$334$			11.4604i			0.627083i
$335$			11.1199i			0.607544i
$336$	8.93439	+	8.93439i	0.487411	+	0.487411i
$337$	−30.4349			−1.65790			−0.828948	−	0.559325i	$-0.811060\pi$
$337$	−30.4349			−1.65790			−0.828948	+	0.559325i	$0.811060\pi$
$338$	−7.66725	−	26.6332i	−0.417044	−	1.44865i
$339$		−	8.77411i		−	0.476544i
$340$	−18.9512	+	18.9512i	−1.02777	+	1.02777i
$341$	−1.07633	−	9.52008i	−0.0582866	−	0.515541i
$342$			1.67728i			0.0906971i
$343$	−11.3151	−	11.3151i	−0.610955	−	0.610955i
$344$	1.17069	−	1.17069i	0.0631192	−	0.0631192i
$345$	28.9776	−	28.9776i	1.56010	−	1.56010i
$346$	−11.0965	+	11.0965i	−0.596552	+	0.596552i
$347$			11.1222i			0.597074i	0.954398	+	0.298537i	$0.0964986\pi$
$347$			11.1222i			0.597074i	−0.954398	+	0.298537i	$0.903501\pi$
$348$			22.9677i			1.23120i
$349$	−8.01166	+	8.01166i	−0.428854	+	0.428854i	−0.888238	−	0.459384i	$-0.848070\pi$
$349$	−8.01166	+	8.01166i	−0.428854	+	0.428854i	0.459384	+	0.888238i	$0.348070\pi$
$350$			24.6816i			1.31929i
$351$	4.85814	−	18.8258i	0.259308	−	1.00485i
$352$			13.5841i			0.724036i
$353$	9.63347	−	9.63347i	0.512738	−	0.512738i	−0.402627	−	0.915364i	$-0.631903\pi$
$353$	9.63347	−	9.63347i	0.512738	−	0.512738i	0.915364	+	0.402627i	$0.131903\pi$
$354$		−	47.9342i		−	2.54767i
$355$			20.0643i			1.06490i
$356$	−25.7661	+	25.7661i	−1.36560	+	1.36560i
$357$	12.0250	+	12.0250i	0.636430	+	0.636430i
$358$	7.29798	+	7.29798i	0.385710	+	0.385710i
$359$	17.3436	−	17.3436i	0.915360	−	0.915360i	−0.0813275	−	0.996687i	$-0.525916\pi$
$359$	17.3436	−	17.3436i	0.915360	−	0.915360i	0.996687	+	0.0813275i	$0.0259160\pi$
$360$	0.884732			0.0466294
$361$		−	9.42576i		−	0.496093i
$362$	12.9611	+	12.9611i	0.681218	+	0.681218i
$363$	−13.3209			−0.699164
$364$	−13.6039	−	23.0670i	−0.713036	−	1.20904i
$365$		−	30.5921i		−	1.60126i
$366$	−12.1165	−	12.1165i	−0.633338	−	0.633338i
$367$			25.1106i			1.31076i	0.755299	+	0.655381i	$0.227492\pi$
$367$			25.1106i			1.31076i	−0.755299	+	0.655381i	$0.772508\pi$
$368$	21.5792			1.12489
$369$	1.09581	+	1.09581i	0.0570454	+	0.0570454i
$370$	−51.1388	+	51.1388i	−2.65858	+	2.65858i
$371$	−9.86427	−	9.86427i	−0.512127	−	0.512127i
$372$	18.3633	+	14.6328i	0.952093	+	0.758675i
$373$	13.4876			0.698361			0.349181	−	0.937055i	$-0.386460\pi$
$373$	13.4876			0.698361			0.349181	+	0.937055i	$0.386460\pi$
$374$			12.9009i			0.667087i
$375$	−3.62430	−	3.62430i	−0.187158	−	0.187158i
$376$		−	9.93196i		−	0.512201i
$377$	−4.90659	+	19.0136i	−0.252702	+	0.979251i
$378$		−	33.5498i		−	1.72562i
$379$	−0.981863	−	0.981863i	−0.0504349	−	0.0504349i	0.681440	−	0.731874i	$-0.261354\pi$
$379$	−0.981863	−	0.981863i	−0.0504349	−	0.0504349i	−0.731874	+	0.681440i	$0.761354\pi$
$380$	23.5815			1.20971
$381$			30.7762i			1.57671i
$382$	15.2193	+	15.2193i	0.778685	+	0.778685i
$383$	13.9142	−	13.9142i	0.710983	−	0.710983i	−0.255758	−	0.966741i	$-0.582325\pi$
$383$	13.9142	−	13.9142i	0.710983	−	0.710983i	0.966741	+	0.255758i	$0.0823250\pi$
$384$	−10.4875	−	10.4875i	−0.535188	−	0.535188i
$385$	10.6332	+	10.6332i	0.541920	+	0.541920i
$386$	23.3317			1.18755
$387$	0.362275			0.0184155
$388$	12.5831	−	12.5831i	0.638811	−	0.638811i
$389$	21.2617			1.07801			0.539005	−	0.842303i	$-0.318801\pi$
$389$	21.2617			1.07801			0.539005	+	0.842303i	$0.318801\pi$
$390$	−36.9314	−	9.53039i	−1.87009	−	0.482590i
$391$	29.0439			1.46881
$392$	−1.24629	−	1.24629i	−0.0629472	−	0.0629472i
$393$			15.3662i			0.775123i
$394$	−3.94771			−0.198883
$395$	31.7320	−	31.7320i	1.59661	−	1.59661i
$396$	0.787378	−	0.787378i	0.0395672	−	0.0395672i
$397$	7.39713	−	7.39713i	0.371251	−	0.371251i	−0.496681	−	0.867933i	$-0.665448\pi$
$397$	7.39713	−	7.39713i	0.371251	−	0.371251i	0.867933	+	0.496681i	$0.165448\pi$
$398$	12.1044	+	12.1044i	0.606739	+	0.606739i
$399$		−	14.9631i		−	0.749089i
$400$			10.3652i			0.518260i
$401$	−3.14225	−	3.14225i	−0.156916	−	0.156916i	0.624282	−	0.781199i	$-0.285391\pi$
$401$	−3.14225	−	3.14225i	−0.156916	−	0.156916i	−0.781199	+	0.624282i	$0.785391\pi$
$402$	−13.1182			−0.654276
$403$	12.0759	+	16.0366i	0.601544	+	0.798840i
$404$	−13.1690			−0.655181
$405$	−17.3048	−	17.3048i	−0.859884	−	0.859884i
$406$			33.8844i			1.68166i
$407$			19.4935i			0.966256i
$408$	−4.78793	−	4.78793i	−0.237038	−	0.237038i
$409$	17.5273	−	17.5273i	0.866670	−	0.866670i	−0.125432	−	0.992102i	$-0.540032\pi$
$409$	17.5273	−	17.5273i	0.866670	−	0.866670i	0.992102	+	0.125432i	$0.0400316\pi$
$410$	27.5133	−	27.5133i	1.35878	−	1.35878i
$411$	−11.5725	+	11.5725i	−0.570828	+	0.570828i
$412$	9.37021			0.461637
$413$		−	39.5991i		−	1.94854i
$414$	−3.16565	−	3.16565i	−0.155583	−	0.155583i
$415$	7.11148			0.349089
$416$	−14.4591	−	24.5172i	−0.708917	−	1.20206i
$417$	2.40951			0.117994
$418$	8.02646	−	8.02646i	0.392587	−	0.392587i
$419$	11.4521			0.559472			0.279736	−	0.960077i	$-0.409753\pi$
$419$	11.4521			0.559472			0.279736	+	0.960077i	$0.409753\pi$
$420$	−36.8543			−1.79830
$421$	−22.1995	−	22.1995i	−1.08194	−	1.08194i	−0.996329	−	0.0856066i	$-0.972717\pi$
$421$	−22.1995	−	22.1995i	−1.08194	−	1.08194i	−0.0856066	−	0.996329i	$-0.527283\pi$
$422$	32.7849	+	32.7849i	1.59594	+	1.59594i
$423$	1.53675	−	1.53675i	0.0747193	−	0.0747193i
$424$	3.92761	+	3.92761i	0.190741	+	0.190741i
$425$			13.9508i			0.676711i
$426$	−23.6700			−1.14681
$427$	−10.0096	−	10.0096i	−0.484398	−	0.484398i
$428$		−	4.32588i		−	0.209099i
$429$	−8.85532	+	5.22246i	−0.427539	+	0.252143i
$430$		−	9.09593i		−	0.438645i
$431$	12.2376	+	12.2376i	0.589465	+	0.589465i	0.937487	−	0.348022i	$-0.113146\pi$
$431$	12.2376	+	12.2376i	0.589465	+	0.589465i	−0.348022	+	0.937487i	$0.613146\pi$
$432$		−	14.0895i		−	0.677879i
$433$	0.954373			0.0458643			0.0229321	−	0.999737i	$-0.492700\pi$
$433$	0.954373			0.0458643			0.0229321	+	0.999737i	$0.492700\pi$
$434$	27.0915	+	21.5879i	1.30044	+	1.03625i
$435$	19.1087	+	19.1087i	0.916192	+	0.916192i
$436$	−13.2726	+	13.2726i	−0.635643	+	0.635643i
$437$	−18.0701	−	18.0701i	−0.864410	−	0.864410i
$438$	36.0897			1.72443
$439$		−	0.294063i		−	0.0140348i	−0.999975	−	0.00701742i	$-0.997766\pi$
$439$		−	0.294063i		−	0.0140348i	0.999975	−	0.00701742i	$-0.00223373\pi$
$440$	−4.23379	−	4.23379i	−0.201838	−	0.201838i
$441$		−	0.385672i		−	0.0183653i
$442$	−13.7318	−	23.2840i	−0.653157	−	1.10751i
$443$	−32.7234			−1.55474			−0.777368	−	0.629047i	$-0.783445\pi$
$443$	−32.7234			−1.55474			−0.777368	+	0.629047i	$0.783445\pi$
$444$	−33.7817	−	33.7817i	−1.60321	−	1.60321i
$445$			42.8739i			2.03242i
$446$	−10.8024			−0.511509
$447$	4.44142	−	4.44142i	0.210072	−	0.210072i
$448$	−23.9465	−	23.9465i	−1.13137	−	1.13137i
$449$	−10.8768	−	10.8768i	−0.513308	−	0.513308i	0.402231	−	0.915538i	$-0.368235\pi$
$449$	−10.8768	−	10.8768i	−0.513308	−	0.513308i	−0.915538	+	0.402231i	$0.868235\pi$
$450$	1.52057	−	1.52057i	0.0716802	−	0.0716802i
$451$		−	10.4877i		−	0.493848i
$452$			13.4763i			0.633870i
$453$	−15.8936	+	15.8936i	−0.746747	+	0.746747i
$454$		−	7.89216i		−	0.370398i
$455$	−30.5095	−	7.87319i	−1.43031	−	0.369101i
$456$			5.95776i			0.278998i
$457$	20.6990	−	20.6990i	0.968258	−	0.968258i	−0.0312535	−	0.999511i	$-0.509950\pi$
$457$	20.6990	−	20.6990i	0.968258	−	0.968258i	0.999511	+	0.0312535i	$0.00994992\pi$
$458$			16.7968i			0.784862i
$459$		−	18.9633i		−	0.885131i
$460$	−44.5070	+	44.5070i	−2.07515	+	2.07515i
$461$	−9.10310	+	9.10310i	−0.423974	+	0.423974i	−0.886569	−	0.462596i	$-0.846918\pi$
$461$	−9.10310	+	9.10310i	−0.423974	+	0.423974i	0.462596	+	0.886569i	$0.346918\pi$
$462$	−12.5441	+	12.5441i	−0.583605	+	0.583605i
$463$	6.96711	+	6.96711i	0.323789	+	0.323789i	0.850219	−	0.526430i	$-0.176470\pi$
$463$	6.96711	+	6.96711i	0.323789	+	0.323789i	−0.526430	+	0.850219i	$0.676470\pi$
$464$			14.2300i			0.660610i
$465$	27.4522	−	3.10372i	1.27306	−	0.143931i
$466$	10.1394	−	10.1394i	0.469698	−	0.469698i
$467$			17.4208i			0.806137i	0.915170	+	0.403068i	$0.132056\pi$
$467$			17.4208i			0.806137i	−0.915170	+	0.403068i	$0.867944\pi$
$468$	−0.583000	+	2.25919i	−0.0269492	+	0.104431i
$469$	−10.8371			−0.500412
$470$	−38.5844	−	38.5844i	−1.77976	−	1.77976i
$471$		−	27.7578i		−	1.27901i
$472$			15.7670i			0.725734i
$473$	−1.73363	−	1.73363i	−0.0797124	−	0.0797124i
$474$	37.4344	+	37.4344i	1.71942	+	1.71942i
$475$	8.67967	−	8.67967i	0.398251	−	0.398251i
$476$	−18.4693	−	18.4693i	−0.846540	−	0.846540i
$477$			1.21542i			0.0556503i
$478$	37.1014			1.69698
$479$	23.2726	−	23.2726i	1.06335	−	1.06335i	0.0655003	−	0.997853i	$-0.479136\pi$
$479$	23.2726	−	23.2726i	1.06335	−	1.06335i	0.997853	−	0.0655003i	$-0.0208643\pi$
$480$	−39.1713			−1.78792
$481$	−20.7491	−	35.1827i	−0.946079	−	1.60419i
$482$		−	7.39741i		−	0.336943i
$483$	28.2408	+	28.2408i	1.28500	+	1.28500i
$484$	20.4597			0.929985
$485$		−	20.9379i		−	0.950740i
$486$	−3.97233	+	3.97233i	−0.180188	+	0.180188i
$487$	26.8058	−	26.8058i	1.21469	−	1.21469i	0.245220	−	0.969468i	$-0.421140\pi$
$487$	26.8058	−	26.8058i	1.21469	−	1.21469i	0.969468	−	0.245220i	$-0.0788601\pi$
$488$	3.98547	+	3.98547i	0.180414	+	0.180414i
$489$	−11.2662	−	11.2662i	−0.509477	−	0.509477i
$490$	−9.68337			−0.437450
$491$	−31.5481			−1.42374			−0.711872	−	0.702309i	$-0.752152\pi$
$491$	−31.5481			−1.42374			−0.711872	+	0.702309i	$0.752152\pi$
$492$	18.1750	+	18.1750i	0.819391	+	0.819391i
$493$			19.1524i			0.862583i
$494$	−5.94304	+	23.0300i	−0.267390	+	1.03617i
$495$		−	1.31017i		−	0.0588877i
$496$	11.3773	+	9.06597i	0.510854	+	0.407074i
$497$	−19.5541			−0.877122
$498$			8.38946i			0.375941i
$499$	12.7782	−	12.7782i	0.572031	−	0.572031i	−0.360665	−	0.932696i	$-0.617450\pi$
$499$	12.7782	−	12.7782i	0.572031	−	0.572031i	0.932696	+	0.360665i	$0.117450\pi$
$500$	5.56660	+	5.56660i	0.248946	+	0.248946i
$501$	−6.29859	+	6.29859i	−0.281400	+	0.281400i
$502$	9.71999	+	9.71999i	0.433824	+	0.433824i
$503$	9.57192			0.426791			0.213395	−	0.976966i	$-0.431548\pi$
$503$	9.57192			0.426791			0.213395	+	0.976966i	$0.431548\pi$
$504$			0.862235i			0.0384070i
$505$	−10.9564	+	10.9564i	−0.487551	+	0.487551i
$506$			30.2977i			1.34690i
$507$	10.4236	−	18.8515i	0.462930	−	0.837222i
$508$		−	47.2695i		−	2.09724i
$509$	18.5296	−	18.5296i	0.821312	−	0.821312i	−0.164984	−	0.986296i	$-0.552757\pi$
$509$	18.5296	−	18.5296i	0.821312	−	0.821312i	0.986296	+	0.164984i	$0.0527573\pi$
$510$	−37.2010			−1.64729
$511$	29.8142			1.31890
$512$	−18.8788	−	18.8788i	−0.834334	−	0.834334i
$513$	−11.7983	+	11.7983i	−0.520908	+	0.520908i
$514$	−46.1094	+	46.1094i	−2.03380	+	2.03380i
$515$	7.79585	−	7.79585i	0.343526	−	0.343526i
$516$	6.00867			0.264517
$517$	−14.7079			−0.646853
$518$	−49.8385	−	49.8385i	−2.18978	−	2.18978i
$519$	−12.1972			−0.535399
$520$	12.1478	+	3.13483i	0.532717	+	0.137471i
$521$	−39.4675			−1.72910			−0.864551	−	0.502545i	$-0.832397\pi$
$521$	−39.4675			−1.72910			−0.864551	+	0.502545i	$0.832397\pi$
$522$	2.08753	−	2.08753i	0.0913685	−	0.0913685i
$523$		−	33.4176i		−	1.46125i	−0.682779	−	0.730625i	$-0.739229\pi$
$523$		−	33.4176i		−	1.46125i	0.682779	−	0.730625i	$-0.260771\pi$
$524$		−	23.6012i		−	1.03102i
$525$	−13.5650	+	13.5650i	−0.592024	+	0.592024i
$526$	−1.81123	+	1.81123i	−0.0789733	+	0.0789733i
$527$	15.3129	+	12.2021i	0.667041	+	0.531531i
$528$	−5.26798	+	5.26798i	−0.229259	+	0.229259i
$529$	45.2098			1.96565
$530$	30.5165			1.32555
$531$	−2.43959	+	2.43959i	−0.105869	+	0.105869i
$532$			22.9819i			0.996393i
$533$	11.1633	+	18.9287i	0.483535	+	0.819894i
$534$	−50.5786			−2.18875
$535$	−3.59905	−	3.59905i	−0.155601	−	0.155601i
$536$	4.31497			0.186378
$537$			8.02192i			0.346171i
$538$	−23.1594	+	23.1594i	−0.998474	+	0.998474i
$539$	−1.84559	+	1.84559i	−0.0794952	+	0.0794952i
$540$	29.0594	+	29.0594i	1.25052	+	1.25052i
$541$	19.8645	−	19.8645i	0.854042	−	0.854042i	−0.136586	−	0.990628i	$-0.543613\pi$
$541$	19.8645	−	19.8645i	0.854042	−	0.854042i	0.990628	+	0.136586i	$0.0436131\pi$
$542$		−	35.1452i		−	1.50962i
$543$			14.2468i			0.611387i
$544$	−19.6305	−	19.6305i	−0.841650	−	0.841650i
$545$			22.0852i			0.946025i
$546$	9.28805	−	35.9923i	0.397492	−	1.54033i
$547$	33.5511			1.43454			0.717270	−	0.696795i	$-0.245391\pi$
$547$	33.5511			1.43454			0.717270	+	0.696795i	$0.245391\pi$
$548$	17.7743	−	17.7743i	0.759280	−	0.759280i
$549$			1.23333i			0.0526371i
$550$	−14.5530			−0.620543
$551$	11.9160	−	11.9160i	0.507638	−	0.507638i
$552$	−11.2445	−	11.2445i	−0.478597	−	0.478597i
$553$	30.9251	+	30.9251i	1.31507	+	1.31507i
$554$	39.4974	+	39.4974i	1.67808	+	1.67808i
$555$	−56.2116			−2.38605
$556$	−3.70080			−0.156949
$557$	1.43217	+	1.43217i	0.0606831	+	0.0606831i	0.736797	−	0.676114i	$-0.236337\pi$
$557$	1.43217	+	1.43217i	0.0606831	+	0.0606831i	−0.676114	+	0.736797i	$0.736337\pi$
$558$	−0.339065	−	2.99900i	−0.0143538	−	0.126958i
$559$	4.97423	+	1.28363i	0.210388	+	0.0542919i
$560$	−22.8336			−0.964897
$561$	−7.09029	+	7.09029i	−0.299352	+	0.299352i
$562$	−44.5109			−1.87758
$563$		−	29.6794i		−	1.25084i	−0.780290	−	0.625418i	$-0.784928\pi$
$563$		−	29.6794i		−	1.25084i	0.780290	−	0.625418i	$-0.215072\pi$
$564$	25.4884	−	25.4884i	1.07326	−	1.07326i
$565$	11.2120	+	11.2120i	0.471693	+	0.471693i
$566$	46.7523	−	46.7523i	1.96515	−	1.96515i
$567$	16.8648	−	16.8648i	0.708256	−	0.708256i
$568$	7.78577			0.326684
$569$	2.63218			0.110347			0.0551735	−	0.998477i	$-0.482429\pi$
$569$	2.63218			0.110347			0.0551735	+	0.998477i	$0.482429\pi$
$570$	23.1452	+	23.1452i	0.969444	+	0.969444i
$571$	21.6661			0.906698			0.453349	−	0.891333i	$-0.350229\pi$
$571$	21.6661			0.906698			0.453349	+	0.891333i	$0.350229\pi$
$572$	13.6010	−	8.02123i	0.568686	−	0.335385i
$573$			16.7289i			0.698862i
$574$	26.8137	+	26.8137i	1.11918	+	1.11918i
$575$			32.7635i			1.36633i
$576$			2.95056i			0.122940i
$577$	−20.8861	−	20.8861i	−0.869498	−	0.869498i	0.122918	−	0.992417i	$-0.460775\pi$
$577$	−20.8861	−	20.8861i	−0.869498	−	0.869498i	−0.992417	+	0.122918i	$0.960775\pi$
$578$	6.98423	+	6.98423i	0.290506	+	0.290506i
$579$	12.8231	+	12.8231i	0.532908	+	0.532908i
$580$	−29.3493	−	29.3493i	−1.21866	−	1.21866i
$581$			6.93066i			0.287532i
$582$	24.7005			1.02387
$583$	5.81626	−	5.81626i	0.240885	−	0.240885i
$584$	−11.8710			−0.491225
$585$	1.39456	+	2.36465i	0.0576580	+	0.0977663i
$586$	54.7720			2.26261
$587$	−19.6901	+	19.6901i	−0.812696	+	0.812696i	−0.985037	−	0.172341i	$-0.944867\pi$
$587$	−19.6901	+	19.6901i	−0.812696	+	0.812696i	0.172341	+	0.985037i	$0.444867\pi$
$588$		−	6.39672i		−	0.263796i
$589$	−1.93544	−	17.1189i	−0.0797485	−	0.705371i
$590$	61.2527	+	61.2527i	2.52173	+	2.52173i
$591$	−2.16965	−	2.16965i	−0.0892476	−	0.0892476i
$592$	−20.9300	−	20.9300i	−0.860217	−	0.860217i
$593$	−8.48280	+	8.48280i	−0.348347	+	0.348347i	−0.859493	−	0.511147i	$-0.829221\pi$
$593$	−8.48280	+	8.48280i	−0.348347	+	0.348347i	0.511147	+	0.859493i	$0.329221\pi$
$594$	19.7819			0.811663
$595$	−30.7323			−1.25990
$596$	−6.82162	+	6.82162i	−0.279424	+	0.279424i
$597$			13.3051i			0.544542i
$598$	−32.2493	−	54.6827i	−1.31877	−	2.23614i
$599$	−10.2006			−0.416787			−0.208393	−	0.978045i	$-0.566823\pi$
$599$	−10.2006			−0.416787			−0.208393	+	0.978045i	$0.566823\pi$
$600$	5.40110	−	5.40110i	0.220499	−	0.220499i
$601$		−	28.6933i		−	1.17042i	−0.810880	−	0.585212i	$-0.801011\pi$
$601$		−	28.6933i		−	1.17042i	0.810880	−	0.585212i	$-0.198989\pi$
$602$	8.86465			0.361296
$603$	0.667646	+	0.667646i	0.0271886	+	0.0271886i
$604$	24.4112	−	24.4112i	0.993277	−	0.993277i
$605$	17.0221	−	17.0221i	0.692046	−	0.692046i
$606$	−12.9253	−	12.9253i	−0.525054	−	0.525054i
$607$	−13.9213			−0.565049			−0.282525	−	0.959260i	$-0.591172\pi$
$607$	−13.9213			−0.565049			−0.282525	+	0.959260i	$0.591172\pi$
$608$			24.4268i			0.990637i
$609$	−18.6228	+	18.6228i	−0.754635	+	0.754635i
$610$	30.9661			1.25378
$611$	26.5455	−	15.6553i	1.07391	−	0.633345i
$612$			2.27569i			0.0919892i
$613$	−28.0860	+	28.0860i	−1.13438	+	1.13438i	−0.144943	+	0.989440i	$0.546300\pi$
$613$	−28.0860	+	28.0860i	−1.13438	+	1.13438i	−0.989440	+	0.144943i	$0.953700\pi$
$614$	38.2580			1.54397
$615$	30.2425			1.21950
$616$	4.12613	−	4.12613i	0.166247	−	0.166247i
$617$	3.49162	+	3.49162i	0.140568	+	0.140568i	0.773889	−	0.633321i	$-0.218309\pi$
$617$	3.49162	+	3.49162i	0.140568	+	0.140568i	−0.633321	+	0.773889i	$0.718309\pi$
$618$	9.19681	+	9.19681i	0.369950	+	0.369950i
$619$	30.8537	+	30.8537i	1.24011	+	1.24011i	0.959953	+	0.280160i	$0.0903876\pi$
$619$	30.8537	+	30.8537i	1.24011	+	1.24011i	0.280160	+	0.959953i	$0.409612\pi$
$620$	−42.1641	+	4.76703i	−1.69335	+	0.191449i
$621$		−	44.5354i		−	1.78715i
$622$	−11.6282	+	11.6282i	−0.466250	+	0.466250i
$623$	−41.7837			−1.67403
$624$	3.90058	−	15.1152i	0.156148	−	0.605092i
$625$	29.0978			1.16391
$626$	32.4026	−	32.4026i	1.29507	−	1.29507i
$627$	8.82265			0.352343
$628$			42.6335i			1.70126i
$629$	−28.1701	−	28.1701i	−1.12322	−	1.12322i
$630$	3.34967	+	3.34967i	0.133454	+	0.133454i
$631$	−7.48000	−	7.48000i	−0.297774	−	0.297774i	0.542367	−	0.840142i	$-0.317528\pi$
$631$	−7.48000	−	7.48000i	−0.297774	−	0.297774i	−0.840142	+	0.542367i	$0.817528\pi$
$632$	−12.3133	−	12.3133i	−0.489796	−	0.489796i
$633$			36.0371i			1.43234i
$634$			10.9226i			0.433793i
$635$	−39.3274	−	39.3274i	−1.56066	−	1.56066i
$636$			20.1589i			0.799351i
$637$	1.36653	−	5.29548i	0.0541440	−	0.209814i
$638$	−19.9793			−0.790986
$639$	1.20467	+	1.20467i	0.0476562	+	0.0476562i
$640$	26.8029			1.05948
$641$	−2.37255			−0.0937102			−0.0468551	−	0.998902i	$-0.514920\pi$
$641$	−2.37255			−0.0937102			−0.0468551	+	0.998902i	$0.514920\pi$
$642$	4.24583	−	4.24583i	0.167569	−	0.167569i
$643$	−32.2921	+	32.2921i	−1.27348	+	1.27348i	−0.329223	+	0.944252i	$0.606787\pi$
$643$	−32.2921	+	32.2921i	−1.27348	+	1.27348i	−0.944252	+	0.329223i	$0.893213\pi$
$644$	−43.3753	−	43.3753i	−1.70923	−	1.70923i
$645$	4.99911	−	4.99911i	0.196840	−	0.196840i
$646$			23.1981i			0.912718i
$647$	−19.0151			−0.747562			−0.373781	−	0.927517i	$-0.621939\pi$
$647$	−19.0151			−0.747562			−0.373781	+	0.927517i	$0.621939\pi$
$648$	−6.71498	+	6.71498i	−0.263789	+	0.263789i
$649$	23.3488			0.916520
$650$	26.2659	−	15.4904i	1.03023	−	0.607584i
$651$	3.02480	+	26.7541i	0.118551	+	1.04858i
$652$	17.3040	+	17.3040i	0.677675	+	0.677675i
$653$	34.0922			1.33413			0.667066	−	0.744999i	$-0.267550\pi$
$653$	34.0922			1.33413			0.667066	+	0.744999i	$0.267550\pi$
$654$	−26.0540			−1.01879
$655$	−19.6357	−	19.6357i	−0.767232	−	0.767232i
$656$	11.2606	+	11.2606i	0.439652	+	0.439652i
$657$	−1.83677	−	1.83677i	−0.0716593	−	0.0716593i
$658$	37.6033	−	37.6033i	1.46593	−	1.46593i
$659$	−37.0556			−1.44348			−0.721740	−	0.692164i	$-0.756657\pi$
$659$	−37.0556			−1.44348			−0.721740	+	0.692164i	$0.756657\pi$
$660$		−	21.7304i		−	0.845853i
$661$	−22.8755	+	22.8755i	−0.889752	+	0.889752i	−0.994499	−	0.104747i	$-0.966597\pi$
$661$	−22.8755	+	22.8755i	−0.889752	+	0.889752i	0.104747	+	0.994499i	$0.466597\pi$
$662$	47.2694			1.83718
$663$	5.24987	−	20.3439i	0.203888	−	0.790090i
$664$		−	2.75955i		−	0.107091i
$665$	19.1205	+	19.1205i	0.741463	+	0.741463i
$666$			6.14082i			0.237952i
$667$			44.9796i			1.74162i
$668$	9.67408	−	9.67408i	0.374301	−	0.374301i
$669$	−5.93698	−	5.93698i	−0.229537	−	0.229537i
$670$	16.7631	−	16.7631i	0.647615	−	0.647615i
$671$	5.90195	−	5.90195i	0.227842	−	0.227842i
$672$		−	38.1753i		−	1.47264i
$673$	13.3157			0.513281			0.256640	−	0.966507i	$-0.417384\pi$
$673$	13.3157			0.513281			0.256640	+	0.966507i	$0.417384\pi$
$674$	45.8803	+	45.8803i	1.76724	+	1.76724i
$675$	21.3918			0.823373
$676$	−16.0098	+	28.9542i	−0.615761	+	1.11362i
$677$			4.46150i			0.171469i	0.996318	+	0.0857347i	$0.0273238\pi$
$677$			4.46150i			0.171469i	−0.996318	+	0.0857347i	$0.972676\pi$
$678$	−13.2269	+	13.2269i	−0.507975	+	0.507975i
$679$	20.4055			0.783090
$680$	12.2365			0.469249
$681$	4.33752	−	4.33752i	0.166214	−	0.166214i
$682$	−12.7289	+	15.9740i	−0.487413	+	0.611675i
$683$	6.46323	−	6.46323i	0.247309	−	0.247309i	−0.572557	−	0.819865i	$-0.694048\pi$
$683$	6.46323	−	6.46323i	0.247309	−	0.247309i	0.819865	+	0.572557i	$0.194048\pi$
$684$	1.41585	−	1.41585i	0.0541365	−	0.0541365i
$685$		−	29.5758i		−	1.13003i
$686$			34.1146i			1.30250i
$687$	−9.23148	+	9.23148i	−0.352203	+	0.352203i
$688$	3.72276			0.141929
$689$	−4.30654	+	16.6884i	−0.164066	+	0.635776i
$690$	−87.3668			−3.32600
$691$	−6.61617	−	6.61617i	−0.251691	−	0.251691i	0.569973	−	0.821664i	$-0.306954\pi$
$691$	−6.61617	−	6.61617i	−0.251691	−	0.251691i	−0.821664	+	0.569973i	$0.806954\pi$
$692$	18.7339			0.712155
$693$	1.27685			0.0485037
$694$	16.7667	−	16.7667i	0.636454	−	0.636454i
$695$	−3.07900	+	3.07900i	−0.116793	+	0.116793i
$696$	7.41496	−	7.41496i	0.281063	−	0.281063i
$697$	15.1559	+	15.1559i	0.574069	+	0.574069i
$698$	24.1550			0.914279
$699$	11.1452			0.421549
$700$	20.8346	−	20.8346i	0.787474	−	0.787474i
$701$			36.8544i			1.39197i	0.718055	+	0.695986i	$0.245033\pi$
$701$			36.8544i			1.39197i	−0.718055	+	0.695986i	$0.754967\pi$
$702$	−35.7033	+	21.0562i	−1.34754	+	0.794714i
$703$			35.0529i			1.32205i
$704$	14.1196	−	14.1196i	0.532151	−	0.532151i
$705$		−	42.4118i		−	1.59732i
$706$	−29.0447			−1.09311
$707$	−10.6778	−	10.6778i	−0.401578	−	0.401578i
$708$	−40.4629	+	40.4629i	−1.52069	+	1.52069i
$709$	−32.0322	−	32.0322i	−1.20299	−	1.20299i	−0.973252	−	0.229742i	$-0.926212\pi$
$709$	−32.0322	−	32.0322i	−1.20299	−	1.20299i	−0.229742	−	0.973252i	$-0.573788\pi$
$710$	30.2467	−	30.2467i	1.13514	−	1.13514i
$711$		−	3.81042i		−	0.142902i
$712$	16.6368			0.623491
$713$	35.9625	+	28.6567i	1.34681	+	1.07320i
$714$		−	36.2551i		−	1.35681i
$715$	4.64226	−	17.9893i	0.173611	−	0.672762i
$716$		−	12.3210i		−	0.460456i
$717$	20.3909	+	20.3909i	0.761511	+	0.761511i
$718$	−52.2906			−1.95147
$719$	−2.23887			−0.0834957			−0.0417478	−	0.999128i	$-0.513293\pi$
$719$	−2.23887			−0.0834957			−0.0417478	+	0.999128i	$0.513293\pi$
$720$	1.40672	+	1.40672i	0.0524252	+	0.0524252i
$721$	7.59762	+	7.59762i	0.282950	+	0.282950i
$722$	−14.2092	+	14.2092i	−0.528813	+	0.528813i
$723$	4.06560	−	4.06560i	0.151201	−	0.151201i
$724$		−	21.8817i		−	0.813229i
$725$	−21.6052			−0.802398
$726$	20.0811	+	20.0811i	0.745278	+	0.745278i
$727$		−	4.64456i		−	0.172257i	−0.996284	−	0.0861286i	$-0.972550\pi$
$727$		−	4.64456i		−	0.172257i	0.996284	−	0.0861286i	$-0.0274496\pi$
$728$	−3.05512	+	11.8389i	−0.113230	+	0.438780i
$729$	−28.8840			−1.06978
$730$	−46.1172	+	46.1172i	−1.70688	+	1.70688i
$731$	5.01055			0.185322
$732$			20.4559i			0.756070i
$733$	5.46257	+	5.46257i	0.201765	+	0.201765i	0.800756	−	0.598991i	$-0.204432\pi$
$733$	5.46257	+	5.46257i	0.201765	+	0.201765i	−0.598991	+	0.800756i	$0.704432\pi$
$734$	37.8539	−	37.8539i	1.39721	−	1.39721i
$735$	−5.32196	−	5.32196i	−0.196303	−	0.196303i
$736$	−46.1023	−	46.1023i	−1.69935	−	1.69935i
$737$		−	6.38989i		−	0.235375i
$738$		−	3.30383i		−	0.121616i
$739$	7.31568	+	7.31568i	0.269112	+	0.269112i	0.828742	−	0.559631i	$-0.189057\pi$
$739$	7.31568	+	7.31568i	0.269112	+	0.269112i	−0.559631	+	0.828742i	$0.689057\pi$
$740$	86.3360			3.17377
$741$	−15.9235	+	9.39095i	−0.584965	+	0.344985i
$742$			29.7405i			1.09181i
$743$	−9.10936	+	9.10936i	−0.334190	+	0.334190i	−0.854175	−	0.519985i	$-0.825937\pi$
$743$	−9.10936	+	9.10936i	−0.334190	+	0.334190i	0.519985	+	0.854175i	$0.325937\pi$
$744$	−1.20437	−	10.6526i	−0.0441543	−	0.390542i
$745$			11.3509i			0.415866i
$746$	−20.3324	−	20.3324i	−0.744422	−	0.744422i
$747$	0.426978	−	0.426978i	0.0156223	−	0.0156223i
$748$	10.8901	−	10.8901i	0.398180	−	0.398180i
$749$	3.50754	−	3.50754i	0.128163	−	0.128163i
$750$			10.9272i			0.399004i
$751$			18.4941i			0.674858i	0.941351	+	0.337429i	$0.109557\pi$
$751$			18.4941i			0.674858i	−0.941351	+	0.337429i	$0.890443\pi$
$752$	15.7917	−	15.7917i	0.575865	−	0.575865i
$753$			10.6842i			0.389353i
$754$	36.0594	−	21.2662i	1.31321	−	0.774469i
$755$		−	40.6193i		−	1.47829i
$756$	−28.3205	+	28.3205i	−1.03001	+	1.03001i
$757$		−	4.34477i		−	0.157913i	−0.996878	−	0.0789567i	$-0.974841\pi$
$757$		−	4.34477i		−	0.157913i	0.996878	−	0.0789567i	$-0.0251589\pi$
$758$			2.96029i			0.107523i
$759$	−16.6516	+	16.6516i	−0.604414	+	0.604414i
$760$	−7.61313	−	7.61313i	−0.276157	−	0.276157i
$761$	14.2124	+	14.2124i	0.515199	+	0.515199i	0.916115	−	0.400916i	$-0.131308\pi$
$761$	14.2124	+	14.2124i	0.515199	+	0.515199i	−0.400916	+	0.916115i	$0.631308\pi$
$762$	46.3948	−	46.3948i	1.68070	−	1.68070i
$763$	−21.5236			−0.779207
$764$		−	25.6942i		−	0.929583i
$765$	1.89333	+	1.89333i	0.0684535	+	0.0684535i
$766$	−41.9510			−1.51575
$767$	−42.1410	+	24.8528i	−1.52162	+	0.897381i
$768$		−	6.83767i		−	0.246733i
$769$	−1.33137	−	1.33137i	−0.0480106	−	0.0480106i	0.682694	−	0.730704i	$-0.260808\pi$
$769$	−1.33137	−	1.33137i	−0.0480106	−	0.0480106i	−0.730704	+	0.682694i	$0.760808\pi$
$770$		−	32.0590i		−	1.15533i
$771$	−50.6833			−1.82531
$772$	−19.6951	−	19.6951i	−0.708842	−	0.708842i
$773$	−5.95385	+	5.95385i	−0.214145	+	0.214145i	−0.806026	−	0.591881i	$-0.798386\pi$
$773$	−5.95385	+	5.95385i	−0.214145	+	0.214145i	0.591881	+	0.806026i	$0.298386\pi$
$774$	−0.546126	−	0.546126i	−0.0196301	−	0.0196301i
$775$	−13.7648	+	17.2740i	−0.494445	+	0.620499i
$776$	−8.12475			−0.291661
$777$		−	54.7823i		−	1.96530i
$778$	−32.0517	−	32.0517i	−1.14911	−	1.14911i
$779$		−	18.8589i		−	0.675690i
$780$	23.1301	+	39.2199i	0.828190	+	1.40430i
$781$		−	11.5297i		−	0.412564i
$782$	−43.7834	−	43.7834i	−1.56569	−	1.56569i
$783$	29.3680			1.04953
$784$		−	3.96319i		−	0.141542i
$785$	35.4703	+	35.4703i	1.26599	+	1.26599i
$786$	23.1644	−	23.1644i	0.826247	−	0.826247i
$787$	−16.4104	−	16.4104i	−0.584967	−	0.584967i	0.351297	−	0.936264i	$-0.385741\pi$
$787$	−16.4104	−	16.4104i	−0.584967	−	0.584967i	−0.936264	+	0.351297i	$0.885741\pi$
$788$	3.33239	+	3.33239i	0.118712	+	0.118712i
$789$	−1.99090			−0.0708778
$790$	−95.6711			−3.40383
$791$	−10.9269	+	10.9269i	−0.388516	+	0.388516i
$792$	−0.508399			−0.0180652
$793$	−4.36999	+	16.9342i	−0.155183	+	0.601352i
$794$	−22.3022			−0.791475
$795$	16.7718	+	16.7718i	0.594835	+	0.594835i
$796$		−	20.4355i		−	0.724316i
$797$	−10.3701			−0.367327			−0.183664	−	0.982989i	$-0.558796\pi$
$797$	−10.3701			−0.367327			−0.183664	+	0.982989i	$0.558796\pi$
$798$	−22.5566	+	22.5566i	−0.798496	+	0.798496i
$799$	21.2544	−	21.2544i	0.751928	−	0.751928i
$800$	22.1445	−	22.1445i	0.782925	−	0.782925i
$801$	2.57418	+	2.57418i	0.0909541	+	0.0909541i
$802$			9.47380i			0.334531i
$803$			17.5793i			0.620361i
$804$	11.0735	+	11.0735i	0.390533	+	0.390533i
$805$	−72.1750			−2.54383
$806$	5.97070	−	42.3793i	0.210309	−	1.49275i
$807$	−25.4567			−0.896120
$808$	4.25151	+	4.25151i	0.149568	+	0.149568i
$809$			42.8130i			1.50523i	0.658464	+	0.752613i	$0.271207\pi$
$809$			42.8130i			1.50523i	−0.658464	+	0.752613i	$0.728793\pi$
$810$			52.1737i			1.83320i
$811$	6.70682	+	6.70682i	0.235508	+	0.235508i	0.814987	−	0.579479i	$-0.196744\pi$
$811$	6.70682	+	6.70682i	0.235508	+	0.235508i	−0.579479	+	0.814987i	$0.696744\pi$
$812$	28.6030	−	28.6030i	1.00377	−	1.00377i
$813$	19.3158	−	19.3158i	0.677433	−	0.677433i
$814$	29.3862	−	29.3862i	1.02999	−	1.02999i
$815$	28.7932			1.00858
$816$		−	15.2256i		−	0.533001i
$817$	−3.11739	−	3.11739i	−0.109064	−	0.109064i
$818$	−52.8445			−1.84766
$819$	−2.30452	+	1.35910i	−0.0805266	+	0.0474908i
$820$	−46.4498			−1.62210
$821$	2.65512	−	2.65512i	0.0926642	−	0.0926642i	−0.659255	−	0.751919i	$-0.729128\pi$
$821$	2.65512	−	2.65512i	0.0926642	−	0.0926642i	0.751919	+	0.659255i	$0.229128\pi$
$822$	34.8907			1.21695
$823$	−3.06556			−0.106859			−0.0534293	−	0.998572i	$-0.517015\pi$
$823$	−3.06556			−0.106859			−0.0534293	+	0.998572i	$0.517015\pi$
$824$	−3.02511	−	3.02511i	−0.105385	−	0.105385i
$825$	−7.99831	−	7.99831i	−0.278465	−	0.278465i
$826$	−59.6952	+	59.6952i	−2.07706	+	2.07706i
$827$	−10.8929	−	10.8929i	−0.378784	−	0.378784i	0.491879	−	0.870664i	$-0.336310\pi$
$827$	−10.8929	−	10.8929i	−0.378784	−	0.378784i	−0.870664	+	0.491879i	$0.836310\pi$
$828$			5.34447i			0.185733i
$829$	21.0765			0.732016			0.366008	−	0.930612i	$-0.380724\pi$
$829$	21.0765			0.732016			0.366008	+	0.930612i	$0.380724\pi$
$830$	−10.7205	−	10.7205i	−0.372113	−	0.372113i
$831$			43.4153i			1.50606i
$832$	−10.4546	+	40.5127i	−0.362447	+	1.40452i
$833$		−	5.33414i		−	0.184817i
$834$	−3.63231	−	3.63231i	−0.125777	−	0.125777i
$835$		−	16.0973i		−	0.557071i
$836$	−13.5508			−0.468665
$837$	18.7105	−	23.4805i	0.646728	−	0.811606i
$838$	−17.2639	−	17.2639i	−0.596373	−	0.596373i
$839$	−13.5288	+	13.5288i	−0.467067	+	0.467067i	−0.900963	−	0.433896i	$-0.857139\pi$
$839$	−13.5288	+	13.5288i	−0.467067	+	0.467067i	0.433896	+	0.900963i	$0.357139\pi$
$840$	11.8981	+	11.8981i	0.410525	+	0.410525i
$841$	−0.660940			−0.0227910
$842$			66.9309i			2.30659i
$843$	−24.4631	−	24.4631i	−0.842555	−	0.842555i
$844$		−	55.3497i		−	1.90522i
$845$	10.7695	+	37.4092i	0.370482	+	1.28692i
$846$	−4.63327			−0.159295
$847$	16.5893	+	16.5893i	0.570013	+	0.570013i
$848$			12.4897i			0.428899i
$849$	51.3900			1.76370
$850$	21.0306	−	21.0306i	0.721344	−	0.721344i
$851$	−66.1577	−	66.1577i	−2.26786	−	2.26786i
$852$	19.9806	+	19.9806i	0.684526	+	0.684526i
$853$	9.14864	−	9.14864i	0.313244	−	0.313244i	−0.532921	−	0.846165i	$-0.678906\pi$
$853$	9.14864	−	9.14864i	0.313244	−	0.313244i	0.846165	+	0.532921i	$0.178906\pi$
$854$			30.1787i			1.03269i
$855$		−	2.35593i		−	0.0805710i
$856$	−1.39658	+	1.39658i	−0.0477341	+	0.0477341i
$857$		−	55.6921i		−	1.90241i	−0.308565	−	0.951203i	$-0.599849\pi$
$857$		−	55.6921i		−	1.90241i	0.308565	−	0.951203i	$-0.400151\pi$
$858$	21.2221	+	5.47651i	0.724511	+	0.186965i
$859$		−	30.5332i		−	1.04178i	−0.853624	−	0.520890i	$-0.825600\pi$
$859$		−	30.5332i		−	1.04178i	0.853624	−	0.520890i	$-0.174400\pi$
$860$	−7.67819	+	7.67819i	−0.261824	+	0.261824i
$861$			29.4735i			1.00445i
$862$		−	36.8961i		−	1.25669i
$863$	−8.86753	+	8.86753i	−0.301854	+	0.301854i	−0.841739	−	0.539885i	$-0.818468\pi$
$863$	−8.86753	+	8.86753i	−0.301854	+	0.301854i	0.539885	+	0.841739i	$0.318468\pi$
$864$	−30.1010	+	30.1010i	−1.02406	+	1.02406i
$865$	15.5862	−	15.5862i	0.529948	−	0.529948i
$866$	−1.43871	−	1.43871i	−0.0488893	−	0.0488893i
$867$			7.67704i			0.260726i
$868$	−4.64582	−	41.0920i	−0.157689	−	1.39475i
$869$	−18.2343	+	18.2343i	−0.618558	+	0.618558i
$870$		−	57.6123i		−	1.95324i
$871$	6.80148	+	11.5328i	0.230459	+	0.390773i
$872$	8.56995			0.290215
$873$	−1.25712	−	1.25712i	−0.0425472	−	0.0425472i
$874$			54.4810i			1.84285i
$875$			9.02710i			0.305172i
$876$	−30.4645	−	30.4645i	−1.02930	−	1.02930i
$877$	16.9305	+	16.9305i	0.571703	+	0.571703i	0.932604	−	0.360901i	$-0.117531\pi$
$877$	16.9305	+	16.9305i	0.571703	+	0.571703i	−0.360901	+	0.932604i	$0.617531\pi$
$878$	−0.443296	+	0.443296i	−0.0149605	+	0.0149605i
$879$	30.1026	+	30.1026i	1.01534	+	1.01534i
$880$		−	13.4634i		−	0.453850i
$881$	37.9068			1.27711			0.638556	−	0.769575i	$-0.279532\pi$
$881$	37.9068			1.27711			0.638556	+	0.769575i	$0.279532\pi$
$882$	−0.581396	+	0.581396i	−0.0195766	+	0.0195766i
$883$	36.5697			1.23067			0.615334	−	0.788267i	$-0.289021\pi$
$883$	36.5697			1.23067			0.615334	+	0.788267i	$0.289021\pi$
$884$	−8.06334	+	31.2464i	−0.271199	+	1.05093i
$885$			67.3288i			2.26323i
$886$	49.3301	+	49.3301i	1.65728	+	1.65728i
$887$	−3.07706			−0.103317			−0.0516587	−	0.998665i	$-0.516451\pi$
$887$	−3.07706			−0.103317			−0.0516587	+	0.998665i	$0.516451\pi$
$888$			21.8124i			0.731976i
$889$	38.3274	−	38.3274i	1.28546	−	1.28546i
$890$	64.6319	−	64.6319i	2.16647	−	2.16647i
$891$	9.94399	+	9.94399i	0.333136	+	0.333136i
$892$	9.11868	+	9.11868i	0.305316	+	0.305316i
$893$	−26.4475			−0.885033
$894$	−13.3908			−0.447854
$895$	−10.2508	−	10.2508i	−0.342647	−	0.342647i
$896$			26.1214i			0.872654i
$897$	12.3294	−	47.7777i	0.411665	−	1.59525i
$898$			32.7933i			1.09433i
$899$	−18.8971	+	23.7147i	−0.630253	+	0.790931i
$900$	−2.56712			−0.0855708
$901$			16.8102i			0.560029i
$902$	−15.8101	+	15.8101i	−0.526420	+	0.526420i
$903$	4.87199	+	4.87199i	0.162130	+	0.162130i
$904$	4.35071	−	4.35071i	0.144703	−	0.144703i
$905$	−18.2052	−	18.2052i	−0.605162	−	0.605162i
$906$	47.9189			1.59200
$907$		−	10.9732i		−	0.364359i	−0.983265	−	0.182179i	$-0.941685\pi$
$907$		−	10.9732i		−	0.364359i	0.983265	−	0.182179i	$-0.0583152\pi$
$908$	−6.66205	+	6.66205i	−0.221088	+	0.221088i
$909$			1.31565i			0.0436375i
$910$	34.1240	+	57.8615i	1.13120	+	1.91809i
$911$			44.4665i			1.47324i	0.676306	+	0.736621i	$0.263580\pi$
$911$			44.4665i			1.47324i	−0.676306	+	0.736621i	$0.736420\pi$
$912$	−9.47280	+	9.47280i	−0.313676	+	0.313676i
$913$	−4.08652			−0.135244
$914$	−62.4070			−2.06424
$915$	17.0189	+	17.0189i	0.562628	+	0.562628i
$916$	14.1787	−	14.1787i	0.468479	−	0.468479i
$917$	19.1365	−	19.1365i	0.631941	−	0.631941i
$918$	−28.5870	+	28.5870i	−0.943511	+	0.943511i
$919$	−3.39920			−0.112129			−0.0560646	−	0.998427i	$-0.517855\pi$
$919$	−3.39920			−0.112129			−0.0560646	+	0.998427i	$0.517855\pi$
$920$	28.7376			0.947449
$921$	21.0265	+	21.0265i	0.692847	+	0.692847i
$922$	27.4456			0.903874
$923$	12.2723	+	20.8093i	0.403949	+	0.684946i
$924$	21.1778			0.696699
$925$	31.7777	−	31.7777i	1.04485	−	1.04485i
$926$		−	21.0057i		−	0.690290i
$927$		−	0.936136i		−	0.0307467i
$928$	30.4013	−	30.4013i	0.997970	−	0.997970i
$929$	−20.0016	+	20.0016i	−0.656230	+	0.656230i	−0.954486	−	0.298256i	$-0.903595\pi$
$929$	−20.0016	+	20.0016i	−0.656230	+	0.656230i	0.298256	+	0.954486i	$0.403595\pi$
$930$	−46.0627	−	36.7050i	−1.51045	−	1.20360i
$931$	−3.31871	+	3.31871i	−0.108766	+	0.108766i
$932$	−17.1180			−0.560718
$933$	−12.7817			−0.418455
$934$	26.2616	−	26.2616i	0.859306	−	0.859306i
$935$		−	18.1207i		−	0.592609i
$936$	0.917581	−	0.541147i	0.0299921	−	0.0176879i
$937$	−47.9555			−1.56664			−0.783319	−	0.621620i	$-0.786475\pi$
$937$	−47.9555			−1.56664			−0.783319	+	0.621620i	$0.786475\pi$
$938$	16.3369	+	16.3369i	0.533417	+	0.533417i
$939$	35.6169			1.16231
$940$			65.1408i			2.12466i
$941$	33.4816	−	33.4816i	1.09147	−	1.09147i	0.0960956	−	0.995372i	$-0.469365\pi$
$941$	33.4816	−	33.4816i	1.09147	−	1.09147i	0.995372	−	0.0960956i	$-0.0306354\pi$
$942$	−41.8445	+	41.8445i	−1.36337	+	1.36337i
$943$	35.5936	+	35.5936i	1.15909	+	1.15909i
$944$	−25.0694	+	25.0694i	−0.815939	+	0.815939i
$945$			47.1243i			1.53295i
$946$			5.22685i			0.169940i
$947$	39.4820	+	39.4820i	1.28299	+	1.28299i	0.938956	+	0.344038i	$0.111795\pi$
$947$	39.4820	+	39.4820i	1.28299	+	1.28299i	0.344038	+	0.938956i	$0.388205\pi$
$948$		−	63.1993i		−	2.05262i
$949$	−18.7117	−	31.7280i	−0.607407	−	1.02993i
$950$	−26.1690			−0.849035
$951$	−6.00305	+	6.00305i	−0.194662	+	0.194662i
$952$			11.9254i			0.386504i
$953$	10.8661			0.351989			0.175994	−	0.984391i	$-0.443686\pi$
$953$	10.8661			0.351989			0.175994	+	0.984391i	$0.443686\pi$
$954$	1.83223	−	1.83223i	0.0593207	−	0.0593207i
$955$	−21.3771	−	21.3771i	−0.691746	−	0.691746i
$956$	−31.3186	−	31.3186i	−1.01292	−	1.01292i
$957$	−10.9806	−	10.9806i	−0.354951	−	0.354951i
$958$	−70.1664			−2.26697
$959$	28.8237			0.930767
$960$	40.7153	+	40.7153i	1.31408	+	1.31408i
$961$	6.92119	+	30.2175i	0.223264	+	0.974758i
$962$	−21.7585	+	84.3166i	−0.701522	+	2.71848i
$963$	−0.432180			−0.0139268
$964$	−6.24440	+	6.24440i	−0.201119	+	0.201119i
$965$	−32.7719			−1.05497
$966$		−	85.1453i		−	2.73950i
$967$	−7.18480	+	7.18480i	−0.231048	+	0.231048i	−0.813130	−	0.582082i	$-0.802238\pi$
$967$	−7.18480	+	7.18480i	−0.231048	+	0.231048i	0.582082	+	0.813130i	$0.302238\pi$
$968$	−6.60526	−	6.60526i	−0.212301	−	0.212301i
$969$	−12.7497	+	12.7497i	−0.409578	+	0.409578i
$970$	−31.5636	+	31.5636i	−1.01345	+	1.01345i
$971$	33.0128			1.05943			0.529716	−	0.848175i	$-0.322299\pi$
$971$	33.0128			1.05943			0.529716	+	0.848175i	$0.322299\pi$
$972$	6.70635			0.215106
$973$	−3.00071	−	3.00071i	−0.0961982	−	0.0961982i
$974$	−80.8189			−2.58961
$975$	22.9492	+	5.92220i	0.734963	+	0.189662i
$976$			12.6737i			0.405677i
$977$	30.9086	+	30.9086i	0.988854	+	0.988854i	0.999939	−	0.0110843i	$-0.00352832\pi$
$977$	30.9086	+	30.9086i	0.988854	+	0.988854i	−0.0110843	+	0.999939i	$0.503528\pi$
$978$			33.9675i			1.08616i
$979$		−	24.6369i		−	0.787399i
$980$	8.17406	+	8.17406i	0.261111	+	0.261111i
$981$	1.32601	+	1.32601i	0.0423362	+	0.0423362i
$982$	47.5584	+	47.5584i	1.51765	+	1.51765i
$983$	18.1326	+	18.1326i	0.578340	+	0.578340i	0.934446	−	0.356106i	$-0.115896\pi$
$983$	18.1326	+	18.1326i	0.578340	+	0.578340i	−0.356106	+	0.934446i	$0.615896\pi$
$984$		−	11.7353i		−	0.374108i
$985$	5.54498			0.176678
$986$	28.8721	−	28.8721i	0.919475	−	0.919475i
$987$	41.3334			1.31566
$988$	24.4571	−	14.4237i	0.778084	−	0.458878i
$989$	11.7673			0.374179
$990$	−1.97507	+	1.97507i	−0.0627717	+	0.0627717i
$991$			34.3568i			1.09138i	0.837987	+	0.545690i	$0.183732\pi$
$991$			34.3568i			1.09138i	−0.837987	+	0.545690i	$0.816268\pi$
$992$	−4.93790	−	43.6754i	−0.156778	−	1.38670i
$993$	25.9792	+	25.9792i	0.824424	+	0.824424i
$994$	29.4776	+	29.4776i	0.934973	+	0.934973i
$995$	−17.0020	−	17.0020i	−0.538998	−	0.538998i
$996$	7.08183	−	7.08183i	0.224396	−	0.224396i
$997$	11.6282			0.368270			0.184135	−	0.982901i	$-0.441052\pi$
$997$	11.6282			0.368270			0.184135	+	0.982901i	$0.441052\pi$
$998$	−38.5260			−1.21952
$999$	−43.1956	+	43.1956i	−1.36665	+	1.36665i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.i.a.216.5	✓	68
13.5	odd	4	inner	403.2.i.a.278.5	yes	68
31.30	odd	2	inner	403.2.i.a.216.6	yes	68
403.278	even	4	inner	403.2.i.a.278.6	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.i.a.216.5	✓	68	1.1	even	1	trivial
403.2.i.a.216.6	yes	68	31.30	odd	2	inner
403.2.i.a.278.5	yes	68	13.5	odd	4	inner
403.2.i.a.278.6	yes	68	403.278	even	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50749 - 1.50749i) q^{2} -1.65703i q^{3} +2.54505i q^{4} +(2.11743 + 2.11743i) q^{5} +(-2.49795 + 2.49795i) q^{6} +(-2.06359 + 2.06359i) q^{7} +(0.821650 - 0.821650i) q^{8} +0.254264 q^{9} +O(q^{10})\)	\(q+(-1.50749 - 1.50749i) q^{2} -1.65703i q^{3} +2.54505i q^{4} +(2.11743 + 2.11743i) q^{5} +(-2.49795 + 2.49795i) q^{6} +(-2.06359 + 2.06359i) q^{7} +(0.821650 - 0.821650i) q^{8} +0.254264 q^{9} -6.38401i q^{10} +(-1.21675 - 1.21675i) q^{11} +4.21721 q^{12} +(3.49118 + 0.900923i) q^{13} +6.22168 q^{14} +(3.50864 - 3.50864i) q^{15} +2.61283 q^{16} +3.51667 q^{17} +(-0.383300 - 0.383300i) q^{18} +(-2.18795 - 2.18795i) q^{19} +(-5.38896 + 5.38896i) q^{20} +(3.41942 + 3.41942i) q^{21} +3.66848i q^{22} +8.25892 q^{23} +(-1.36150 - 1.36150i) q^{24} +3.96704i q^{25} +(-3.90478 - 6.62105i) q^{26} -5.39240i q^{27} +(-5.25193 - 5.25193i) q^{28} +5.44619i q^{29} -10.5785 q^{30} +(4.35438 + 3.46978i) q^{31} +(-5.58212 - 5.58212i) q^{32} +(-2.01619 + 2.01619i) q^{33} +(-5.30134 - 5.30134i) q^{34} -8.73903 q^{35} +0.647114i q^{36} +(-8.01045 - 8.01045i) q^{37} +6.59662i q^{38} +(1.49285 - 5.78498i) q^{39} +3.47958 q^{40} +(4.30972 + 4.30972i) q^{41} -10.3095i q^{42} +1.42480 q^{43} +(3.09669 - 3.09669i) q^{44} +(0.538387 + 0.538387i) q^{45} +(-12.4502 - 12.4502i) q^{46} +(6.04391 - 6.04391i) q^{47} -4.32954i q^{48} -1.51682i q^{49} +(5.98026 - 5.98026i) q^{50} -5.82722i q^{51} +(-2.29289 + 8.88521i) q^{52} +4.78015i q^{53} +(-8.12898 + 8.12898i) q^{54} -5.15279i q^{55} +3.39110i q^{56} +(-3.62549 + 3.62549i) q^{57} +(8.21006 - 8.21006i) q^{58} +(-9.59471 + 9.59471i) q^{59} +(8.92965 + 8.92965i) q^{60} +4.85057i q^{61} +(-1.33351 - 11.7948i) q^{62} +(-0.524697 + 0.524697i) q^{63} +11.6043i q^{64} +(5.48469 + 9.29998i) q^{65} +6.07878 q^{66} +(2.62579 + 2.62579i) q^{67} +8.95009i q^{68} -13.6853i q^{69} +(13.1740 + 13.1740i) q^{70} +(4.73789 + 4.73789i) q^{71} +(0.208916 - 0.208916i) q^{72} +(-7.22387 - 7.22387i) q^{73} +24.1513i q^{74} +6.57348 q^{75} +(5.56843 - 5.56843i) q^{76} +5.02176 q^{77} +(-10.9712 + 6.47033i) q^{78} -14.9861i q^{79} +(5.53250 + 5.53250i) q^{80} -8.17256 q^{81} -12.9937i q^{82} +(1.67927 - 1.67927i) q^{83} +(-8.70259 + 8.70259i) q^{84} +(7.44631 + 7.44631i) q^{85} +(-2.14787 - 2.14787i) q^{86} +9.02447 q^{87} -1.99949 q^{88} +(10.1240 + 10.1240i) q^{89} -1.62323i q^{90} +(-9.06350 + 5.34523i) q^{91} +21.0193i q^{92} +(5.74952 - 7.21532i) q^{93} -18.2223 q^{94} -9.26567i q^{95} +(-9.24972 + 9.24972i) q^{96} +(-4.94417 - 4.94417i) q^{97} +(-2.28658 + 2.28658i) q^{98} +(-0.309377 - 0.309377i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9}+O(q^{10}) \) 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9	\( 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9} - 48 q^{14} - 40 q^{16} + 4 q^{18} - 24 q^{19} - 16 q^{20} + 44 q^{28} + 24 q^{31} + 28 q^{32} - 40 q^{35} - 24 q^{39} + 24 q^{40} + 20 q^{41} - 24 q^{45} - 36 q^{47} + 80 q^{50} + 28 q^{59} - 76 q^{63} + 152 q^{66} - 32 q^{67} - 48 q^{70} + 20 q^{71} - 32 q^{72} + 72 q^{76} + 84 q^{78} - 20 q^{80} + 52 q^{81} - 112 q^{87} - 8 q^{93} - 16 q^{94} - 4 q^{97} - 92 q^{98}+O(q^{100}) \) 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9 - 48 * q^14 - 40 * q^16 + 4 * q^18 - 24 * q^19 - 16 * q^20 + 44 * q^28 + 24 * q^31 + 28 * q^32 - 40 * q^35 - 24 * q^39 + 24 * q^40 + 20 * q^41 - 24 * q^45 - 36 * q^47 + 80 * q^50 + 28 * q^59 - 76 * q^63 + 152 * q^66 - 32 * q^67 - 48 * q^70 + 20 * q^71 - 32 * q^72 + 72 * q^76 + 84 * q^78 - 20 * q^80 + 52 * q^81 - 112 * q^87 - 8 * q^93 - 16 * q^94 - 4 * q^97 - 92 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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