LMFDB - Embedded newform 425.2.m.e.376.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(26,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("425.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.m (of order $8$, degree $4$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			376.1
Character	$\chi$	$=$	425.376
Dual form			425.2.m.e.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.48843 - 1.48843i) q^{2} +(-1.66813 + 0.690961i) q^{3} +2.43082i q^{4} +(3.51133 + 1.45444i) q^{6} +(-1.02689 + 2.47912i) q^{7} +(0.641241 - 0.641241i) q^{8} +(0.183901 - 0.183901i) q^{9} +(-0.901470 - 0.373401i) q^{11} +(-1.67960 - 4.05491i) q^{12} -2.65240i q^{13} +(5.21843 - 2.16155i) q^{14} +2.95276 q^{16} +(2.53030 - 3.25539i) q^{17} -0.547447 q^{18} +(0.478059 + 0.478059i) q^{19} -4.84503i q^{21} +(0.785991 + 1.89755i) q^{22} +(3.72748 + 1.54397i) q^{23} +(-0.626599 + 1.51274i) q^{24} +(-3.94790 + 3.94790i) q^{26} +(1.89318 - 4.57054i) q^{27} +(-6.02630 - 2.49617i) q^{28} +(-3.83958 - 9.26957i) q^{29} +(-9.10497 + 3.77140i) q^{31} +(-5.67744 - 5.67744i) q^{32} +1.76177 q^{33} +(-8.61157 + 1.07924i) q^{34} +(0.447031 + 0.447031i) q^{36} +(-6.31669 + 2.61646i) q^{37} -1.42311i q^{38} +(1.83270 + 4.42454i) q^{39} +(2.80190 - 6.76439i) q^{41} +(-7.21147 + 7.21147i) q^{42} +(6.29628 - 6.29628i) q^{43} +(0.907670 - 2.19131i) q^{44} +(-3.24999 - 7.84616i) q^{46} -0.874497i q^{47} +(-4.92558 + 2.04024i) q^{48} +(-0.141809 - 0.141809i) q^{49} +(-1.97152 + 7.17875i) q^{51} +6.44750 q^{52} +(-2.00842 - 2.00842i) q^{53} +(-9.62077 + 3.98505i) q^{54} +(0.931234 + 2.24820i) q^{56} +(-1.12778 - 0.467144i) q^{57} +(-8.08213 + 19.5120i) q^{58} +(7.59005 - 7.59005i) q^{59} +(0.793008 - 1.91449i) q^{61} +(19.1655 + 7.93862i) q^{62} +(0.267068 + 0.644760i) q^{63} +10.9954i q^{64} +(-2.62227 - 2.62227i) q^{66} +5.73990 q^{67} +(7.91327 + 6.15070i) q^{68} -7.28473 q^{69} +(1.03955 - 0.430595i) q^{71} -0.235850i q^{72} +(1.14748 + 2.77027i) q^{73} +(13.2963 + 5.50752i) q^{74} +(-1.16208 + 1.16208i) q^{76} +(1.85141 - 1.85141i) q^{77} +(3.85775 - 9.31343i) q^{78} +(0.377872 + 0.156520i) q^{79} +9.71259i q^{81} +(-14.2387 + 5.89786i) q^{82} +(-4.64846 - 4.64846i) q^{83} +11.7774 q^{84} -18.7431 q^{86} +(12.8098 + 12.8098i) q^{87} +(-0.817499 + 0.338619i) q^{88} -5.62649i q^{89} +(6.57562 + 2.72371i) q^{91} +(-3.75312 + 9.06082i) q^{92} +(12.5824 - 12.5824i) q^{93} +(-1.30162 + 1.30162i) q^{94} +(13.3936 + 5.54781i) q^{96} +(-5.89862 - 14.2405i) q^{97} +0.422145i q^{98} +(-0.234451 + 0.0971126i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{9} + 24 q^{14} + 8 q^{16} + 24 q^{19} - 32 q^{24} - 16 q^{26} - 24 q^{29} - 24 q^{31} - 8 q^{34} + 8 q^{36} + 24 q^{39} - 48 q^{41} - 72 q^{44} - 16 q^{46} - 48 q^{49} - 32 q^{54} + 24 q^{56}+ \cdots + 80 q^{99}+O(q^{100}) $ 24 * q + 8 * q^9 + 24 * q^14 + 8 * q^16 + 24 * q^19 - 32 * q^24 - 16 * q^26 - 24 * q^29 - 24 * q^31 - 8 * q^34 + 8 * q^36 + 24 * q^39 - 48 * q^41 - 72 * q^44 - 16 * q^46 - 48 * q^49 - 32 * q^54 + 24 * q^56 + 48 * q^59 + 16 * q^61 - 96 * q^66 - 32 * q^69 + 16 * q^71 + 64 * q^74 - 24 * q^76 + 72 * q^79 + 96 * q^84 - 8 * q^91 + 40 * q^94 + 96 * q^96 + 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−1.48843	−	1.48843i	−1.05248	−	1.05248i	−0.998545	−	0.0539308i	$-0.982825\pi$
$2$	−1.48843	−	1.48843i	−1.05248	−	1.05248i	−0.0539308	−	0.998545i	$-0.517175\pi$
$3$	−1.66813	+	0.690961i	−0.963094	+	0.398926i	−0.808137	−	0.588995i	$-0.799524\pi$
$3$	−1.66813	+	0.690961i	−0.963094	+	0.398926i	−0.154957	+	0.987921i	$0.549524\pi$
$4$			2.43082i			1.21541i
$5$		0			0
$5$		0			0
$6$	3.51133	+	1.45444i	1.43349	+	0.593772i
$7$	−1.02689	+	2.47912i	−0.388127	+	0.937021i	0.602210	+	0.798338i	$0.294287\pi$
$7$	−1.02689	+	2.47912i	−0.388127	+	0.937021i	−0.990337	+	0.138683i	$0.955713\pi$
$8$	0.641241	−	0.641241i	0.226713	−	0.226713i
$9$	0.183901	−	0.183901i	0.0613005	−	0.0613005i
$10$		0			0
$11$	−0.901470	−	0.373401i	−0.271803	−	0.112585i	0.242619	−	0.970122i	$-0.421994\pi$
$11$	−0.901470	−	0.373401i	−0.271803	−	0.112585i	−0.514422	+	0.857537i	$0.671994\pi$
$12$	−1.67960	−	4.05491i	−0.484859	−	1.17055i
$13$		−	2.65240i		−	0.735643i	−0.929896	−	0.367821i	$-0.880104\pi$
$13$		−	2.65240i		−	0.735643i	0.929896	−	0.367821i	$-0.119896\pi$
$14$	5.21843	−	2.16155i	1.39468	−	0.577697i
$15$		0			0
$16$	2.95276			0.738190
$17$	2.53030	−	3.25539i	0.613688	−	0.789548i
$17$	2.53030	−	3.25539i	0.613688	−	0.789548i
$18$	−0.547447			−0.129034
$19$	0.478059	+	0.478059i	0.109674	+	0.109674i	0.759814	−	0.650140i	$-0.225290\pi$
$19$	0.478059	+	0.478059i	0.109674	+	0.109674i	−0.650140	+	0.759814i	$0.725290\pi$
$20$		0			0
$21$		−	4.84503i		−	1.05727i
$22$	0.785991	+	1.89755i	0.167574	+	0.404559i
$23$	3.72748	+	1.54397i	0.777233	+	0.321940i	0.735798	−	0.677201i	$-0.236807\pi$
$23$	3.72748	+	1.54397i	0.777233	+	0.321940i	0.0414347	+	0.999141i	$0.486807\pi$
$24$	−0.626599	+	1.51274i	−0.127904	+	0.308788i
$25$		0			0
$26$	−3.94790	+	3.94790i	−0.774246	+	0.774246i
$27$	1.89318	−	4.57054i	0.364343	−	0.879601i
$28$	−6.02630	−	2.49617i	−1.13886	−	0.471733i
$29$	−3.83958	−	9.26957i	−0.712992	−	1.72132i	−0.692385	−	0.721528i	$-0.743440\pi$
$29$	−3.83958	−	9.26957i	−0.712992	−	1.72132i	−0.0206072	−	0.999788i	$-0.506560\pi$
$30$		0			0
$31$	−9.10497	+	3.77140i	−1.63530	+	0.677364i	−0.995811	−	0.0914357i	$-0.970854\pi$
$31$	−9.10497	+	3.77140i	−1.63530	+	0.677364i	−0.639490	+	0.768800i	$0.720854\pi$
$32$	−5.67744	−	5.67744i	−1.00364	−	1.00364i
$33$	1.76177			0.306685
$34$	−8.61157	+	1.07924i	−1.47687	+	0.185089i
$35$		0			0
$36$	0.447031	+	0.447031i	0.0745052	+	0.0745052i
$37$	−6.31669	+	2.61646i	−1.03846	+	0.430143i	−0.835758	−	0.549098i	$-0.814971\pi$
$37$	−6.31669	+	2.61646i	−1.03846	+	0.430143i	−0.202699	+	0.979241i	$0.564971\pi$
$38$		−	1.42311i		−	0.230859i
$39$	1.83270	+	4.42454i	0.293467	+	0.708493i
$40$		0			0
$41$	2.80190	−	6.76439i	0.437583	−	1.05642i	−0.539198	−	0.842179i	$-0.681272\pi$
$41$	2.80190	−	6.76439i	0.437583	−	1.05642i	0.976781	−	0.214240i	$-0.0687276\pi$
$42$	−7.21147	+	7.21147i	−1.11275	+	1.11275i
$43$	6.29628	−	6.29628i	0.960173	−	0.960173i	−0.0390633	−	0.999237i	$-0.512437\pi$
$43$	6.29628	−	6.29628i	0.960173	−	0.960173i	0.999237	+	0.0390633i	$0.0124374\pi$
$44$	0.907670	−	2.19131i	0.136836	−	0.330352i
$45$		0			0
$46$	−3.24999	−	7.84616i	−0.479184	−	1.15685i
$47$		−	0.874497i		−	0.127558i	−0.997964	−	0.0637792i	$-0.979685\pi$
$47$		−	0.874497i		−	0.127558i	0.997964	−	0.0637792i	$-0.0203154\pi$
$48$	−4.92558	+	2.04024i	−0.710946	+	0.294483i
$49$	−0.141809	−	0.141809i	−0.0202585	−	0.0202585i
$50$		0			0
$51$	−1.97152	+	7.17875i	−0.276067	+	1.00523i
$52$	6.44750			0.894107
$53$	−2.00842	−	2.00842i	−0.275878	−	0.275878i	0.555583	−	0.831461i	$-0.312495\pi$
$53$	−2.00842	−	2.00842i	−0.275878	−	0.275878i	−0.831461	+	0.555583i	$0.812495\pi$
$54$	−9.62077	+	3.98505i	−1.30922	+	0.542297i
$55$		0			0
$56$	0.931234	+	2.24820i	0.124441	+	0.300428i
$57$	−1.12778	−	0.467144i	−0.149379	−	0.0618747i
$58$	−8.08213	+	19.5120i	−1.06124	+	2.56205i
$59$	7.59005	−	7.59005i	0.988140	−	0.988140i	−0.0117908	−	0.999930i	$-0.503753\pi$
$59$	7.59005	−	7.59005i	0.988140	−	0.988140i	0.999930	+	0.0117908i	$0.00375321\pi$
$60$		0			0
$61$	0.793008	−	1.91449i	0.101534	−	0.245125i	−0.864947	−	0.501864i	$-0.832648\pi$
$61$	0.793008	−	1.91449i	0.101534	−	0.245125i	0.966481	+	0.256738i	$0.0826479\pi$
$62$	19.1655	+	7.93862i	2.43402	+	1.00821i
$63$	0.267068	+	0.644760i	0.0336475	+	0.0812321i
$64$			10.9954i			1.37442i
$65$		0			0
$66$	−2.62227	−	2.62227i	−0.322779	−	0.322779i
$67$	5.73990			0.701240			0.350620	−	0.936518i	$-0.385971\pi$
$67$	5.73990			0.701240			0.350620	+	0.936518i	$0.385971\pi$
$68$	7.91327	+	6.15070i	0.959624	+	0.745882i
$69$	−7.28473			−0.876979
$70$		0			0
$71$	1.03955	−	0.430595i	0.123372	−	0.0511022i	−0.320144	−	0.947369i	$-0.603731\pi$
$71$	1.03955	−	0.430595i	0.123372	−	0.0511022i	0.443515	+	0.896267i	$0.353731\pi$
$72$		−	0.235850i		−	0.0277952i
$73$	1.14748	+	2.77027i	0.134303	+	0.324236i	0.976696	−	0.214628i	$-0.0688538\pi$
$73$	1.14748	+	2.77027i	0.134303	+	0.324236i	−0.842393	+	0.538864i	$0.818854\pi$
$74$	13.2963	+	5.50752i	1.54567	+	0.640236i
$75$		0			0
$76$	−1.16208	+	1.16208i	−0.133299	+	0.133299i
$77$	1.85141	−	1.85141i	0.210988	−	0.210988i
$78$	3.85775	−	9.31343i	0.436804	−	1.05454i
$79$	0.377872	+	0.156520i	0.0425139	+	0.0176099i	0.403839	−	0.914830i	$-0.367676\pi$
$79$	0.377872	+	0.156520i	0.0425139	+	0.0176099i	−0.361325	+	0.932440i	$0.617676\pi$
$80$		0			0
$81$			9.71259i			1.07918i
$82$	−14.2387	+	5.89786i	−1.57240	+	0.651310i
$83$	−4.64846	−	4.64846i	−0.510235	−	0.510235i	0.404363	−	0.914598i	$-0.367493\pi$
$83$	−4.64846	−	4.64846i	−0.510235	−	0.510235i	−0.914598	+	0.404363i	$0.867493\pi$
$84$	11.7774			1.28502
$85$		0			0
$86$	−18.7431			−2.02112
$87$	12.8098	+	12.8098i	1.37336	+	1.37336i
$88$	−0.817499	+	0.338619i	−0.0871457	+	0.0360969i
$89$		−	5.62649i		−	0.596407i	−0.954502	−	0.298204i	$-0.903613\pi$
$89$		−	5.62649i		−	0.596407i	0.954502	−	0.298204i	$-0.0963874\pi$
$90$		0			0
$91$	6.57562	+	2.72371i	0.689312	+	0.285523i
$92$	−3.75312	+	9.06082i	−0.391289	+	0.944656i
$93$	12.5824	−	12.5824i	1.30473	−	1.30473i
$94$	−1.30162	+	1.30162i	−0.134252	+	0.134252i
$95$		0			0
$96$	13.3936	+	5.54781i	1.36698	+	0.566221i
$97$	−5.89862	−	14.2405i	−0.598915	−	1.44591i	−0.874689	−	0.484685i	$-0.838934\pi$
$97$	−5.89862	−	14.2405i	−0.598915	−	1.44591i	0.275774	−	0.961222i	$-0.411066\pi$
$98$			0.422145i			0.0426430i
$99$	−0.234451	+	0.0971126i	−0.0235632	+	0.00976018i
$100$		0			0
$101$	14.6242			1.45516			0.727582	−	0.686021i	$-0.240644\pi$
$101$	14.6242			1.45516			0.727582	+	0.686021i	$0.240644\pi$
$102$	13.6195	−	7.75057i	1.34853	−	0.767421i
$103$	−1.63280			−0.160884			−0.0804421	−	0.996759i	$-0.525633\pi$
$103$	−1.63280			−0.160884			−0.0804421	+	0.996759i	$0.525633\pi$
$104$	−1.70083	−	1.70083i	−0.166780	−	0.166780i
$105$		0			0
$106$			5.97877i			0.580710i
$107$	2.13151	+	5.14591i	0.206060	+	0.497474i	0.992796	−	0.119816i	$-0.0382305\pi$
$107$	2.13151	+	5.14591i	0.206060	+	0.497474i	−0.786736	+	0.617290i	$0.788231\pi$
$108$	11.1102	+	4.60198i	1.06908	+	0.442826i
$109$	1.00965	−	2.43750i	0.0967066	−	0.233470i	−0.868122	−	0.496351i	$-0.834673\pi$
$109$	1.00965	−	2.43750i	0.0967066	−	0.233470i	0.964828	+	0.262881i	$0.0846727\pi$
$110$		0			0
$111$	8.72917	−	8.72917i	0.828536	−	0.828536i
$112$	−3.03215	+	7.32025i	−0.286511	+	0.691699i
$113$	5.36662	+	2.22293i	0.504849	+	0.209115i	0.620547	−	0.784169i	$-0.286910\pi$
$113$	5.36662	+	2.22293i	0.504849	+	0.209115i	−0.115698	+	0.993284i	$0.536910\pi$
$114$	0.983314	+	2.37393i	0.0920958	+	0.222339i
$115$		0			0
$116$	22.5326	−	9.33332i	2.09210	−	0.866577i
$117$	−0.487780	−	0.487780i	−0.0450952	−	0.0450952i
$118$	−22.5944			−2.07999
$119$	5.47219	+	9.61585i	0.501634	+	0.881483i
$120$		0			0
$121$	−7.10496	−	7.10496i	−0.645905	−	0.645905i
$122$	−4.02991	+	1.66924i	−0.364851	+	0.151126i
$123$			13.2199i			1.19199i
$124$	−9.16759	−	22.1325i	−0.823274	−	1.98756i
$125$		0			0
$126$	0.562166	−	1.35719i	0.0500817	−	0.120908i
$127$	7.53018	−	7.53018i	0.668195	−	0.668195i	−0.289103	−	0.957298i	$-0.593357\pi$
$127$	7.53018	−	7.53018i	0.668195	−	0.668195i	0.957298	+	0.289103i	$0.0933569\pi$
$128$	5.01091	−	5.01091i	0.442906	−	0.442906i
$129$	−6.15251	+	14.8535i	−0.541698	+	1.30778i
$130$		0			0
$131$	−0.619360	−	1.49527i	−0.0541137	−	0.130642i	0.894511	−	0.447047i	$-0.147524\pi$
$131$	−0.619360	−	1.49527i	−0.0541137	−	0.130642i	−0.948624	+	0.316405i	$0.897524\pi$
$132$			4.28255i			0.372748i
$133$	−1.67608	+	0.694256i	−0.145335	+	0.0601996i
$134$	−8.54341	−	8.54341i	−0.738038	−	0.738038i
$135$		0			0
$136$	−0.464958	−	3.71002i	−0.0398698	−	0.318132i
$137$	−4.70326			−0.401826			−0.200913	−	0.979609i	$-0.564391\pi$
$137$	−4.70326			−0.401826			−0.200913	+	0.979609i	$0.564391\pi$
$138$	10.8428	+	10.8428i	0.922999	+	0.922999i
$139$	−0.761078	+	0.315249i	−0.0645538	+	0.0267391i	−0.414727	−	0.909946i	$-0.636123\pi$
$139$	−0.761078	+	0.315249i	−0.0645538	+	0.0267391i	0.350173	+	0.936685i	$0.386123\pi$
$140$		0			0
$141$	0.604243	+	1.45877i	0.0508865	+	0.122851i
$142$	−2.18820	−	0.906381i	−0.183629	−	0.0760618i
$143$	−0.990408	+	2.39106i	−0.0828221	+	0.199950i
$144$	0.543017	−	0.543017i	0.0452514	−	0.0452514i
$145$		0			0
$146$	2.41540	−	5.83129i	0.199900	−	0.482601i
$147$	0.334540	+	0.138571i	0.0275924	+	0.0114292i
$148$	−6.36014	−	15.3547i	−0.522800	−	1.26215i
$149$		−	9.60320i		−	0.786725i	−0.919383	−	0.393362i	$-0.871312\pi$
$149$		−	9.60320i		−	0.786725i	0.919383	−	0.393362i	$-0.128688\pi$
$150$		0			0
$151$	−1.00179	−	1.00179i	−0.0815244	−	0.0815244i	0.665169	−	0.746693i	$-0.268360\pi$
$151$	−1.00179	−	1.00179i	−0.0815244	−	0.0815244i	−0.746693	+	0.665169i	$0.768360\pi$
$152$	0.613103			0.0497292
$153$	−0.133345	−	1.06400i	−0.0107803	−	0.0860191i
$154$	−5.51138			−0.444120
$155$		0			0
$156$	−10.7552	+	4.45497i	−0.861109	+	0.356683i
$157$			4.81882i			0.384584i	0.981338	+	0.192292i	$0.0615920\pi$
$157$			4.81882i			0.384584i	−0.981338	+	0.192292i	$0.938408\pi$
$158$	−0.329467	−	0.795403i	−0.0262109	−	0.0632788i
$159$	4.73804	+	1.96256i	0.375751	+	0.155641i
$160$		0			0
$161$	−7.65539	+	7.65539i	−0.603330	+	0.603330i
$162$	14.4565	−	14.4565i	1.13581	−	1.13581i
$163$	0.619572	−	1.49578i	0.0485286	−	0.117158i	−0.897756	−	0.440493i	$-0.854804\pi$
$163$	0.619572	−	1.49578i	0.0485286	−	0.117158i	0.946285	+	0.323334i	$0.104804\pi$
$164$	16.4430	+	6.81091i	1.28398	+	0.531843i
$165$		0			0
$166$			13.8378i			1.07402i
$167$	−20.4490	+	8.47025i	−1.58239	+	0.655447i	−0.988790	−	0.149313i	$-0.952294\pi$
$167$	−20.4490	+	8.47025i	−1.58239	+	0.655447i	−0.593600	+	0.804760i	$0.702294\pi$
$168$	−3.10683	−	3.10683i	−0.239697	−	0.239697i
$169$	5.96479			0.458830
$170$		0			0
$171$	0.175832			0.0134462
$172$	15.3051	+	15.3051i	1.16700	+	1.16700i
$173$	−9.58685	+	3.97100i	−0.728875	+	0.301910i	−0.716089	−	0.698008i	$-0.754070\pi$
$173$	−9.58685	+	3.97100i	−0.728875	+	0.301910i	−0.0127852	+	0.999918i	$0.504070\pi$
$174$		−	38.1329i		−	2.89085i
$175$		0			0
$176$	−2.66182	−	1.10256i	−0.200642	−	0.0831088i
$177$	−7.41674	+	17.9056i	−0.557476	+	1.34587i
$178$	−8.37461	+	8.37461i	−0.627704	+	0.627704i
$179$	−13.2428	+	13.2428i	−0.989813	+	0.989813i	−0.999949	−	0.0101361i	$-0.996774\pi$
$179$	−13.2428	+	13.2428i	−0.989813	+	0.989813i	0.0101361	+	0.999949i	$0.496774\pi$
$180$		0			0
$181$	−2.26809	−	0.939472i	−0.168585	−	0.0698304i	0.296795	−	0.954941i	$-0.404082\pi$
$181$	−2.26809	−	0.939472i	−0.168585	−	0.0698304i	−0.465380	+	0.885111i	$0.654082\pi$
$182$	−5.73328	−	13.8414i	−0.424979	−	1.02599i
$183$			3.74155i			0.276584i
$184$	3.38027	−	1.40015i	0.249197	−	0.103221i
$185$		0			0
$186$	−37.4558			−2.74639
$187$	−3.49656	+	1.98982i	−0.255694	+	0.145510i
$188$	2.12574			0.155036
$189$	9.38686	+	9.38686i	0.682793	+	0.682793i
$190$		0			0
$191$		−	10.9126i		−	0.789607i	−0.918766	−	0.394803i	$-0.870813\pi$
$191$		−	10.9126i		−	0.789607i	0.918766	−	0.394803i	$-0.129187\pi$
$192$	−7.59738	−	18.3417i	−0.548293	−	1.32370i
$193$	−16.9768	−	7.03202i	−1.22202	−	0.506176i	−0.323966	−	0.946069i	$-0.605016\pi$
$193$	−16.9768	−	7.03202i	−1.22202	−	0.506176i	−0.898050	+	0.439893i	$0.855016\pi$
$194$	−12.4163	+	29.9756i	−0.891439	+	2.15213i
$195$		0			0
$196$	0.344712	−	0.344712i	0.0246223	−	0.0246223i
$197$	7.45879	−	18.0071i	0.531417	−	1.28295i	−0.399168	−	0.916878i	$-0.630701\pi$
$197$	7.45879	−	18.0071i	0.531417	−	1.28295i	0.930585	−	0.366076i	$-0.119299\pi$
$198$	0.493507	+	0.204417i	0.0350720	+	0.0145273i
$199$	8.92336	+	21.5429i	0.632560	+	1.52713i	0.836394	+	0.548129i	$0.184660\pi$
$199$	8.92336	+	21.5429i	0.632560	+	1.52713i	−0.203834	+	0.979005i	$0.565340\pi$
$200$		0			0
$201$	−9.57488	+	3.96605i	−0.675360	+	0.279743i
$202$	−21.7670	−	21.7670i	−1.53152	−	1.53152i
$203$	26.9232			1.88964
$204$	−17.4502	−	4.79240i	−1.22176	−	0.335535i
$205$		0			0
$206$	2.43029	+	2.43029i	0.169327	+	0.169327i
$207$	0.969427	−	0.401550i	0.0673798	−	0.0279096i
$208$		−	7.83189i		−	0.543044i
$209$	−0.252448	−	0.609464i	−0.0174622	−	0.0421575i
$210$		0			0
$211$	−8.77140	+	21.1760i	−0.603848	+	1.45782i	0.265742	+	0.964044i	$0.414383\pi$
$211$	−8.77140	+	21.1760i	−0.603848	+	1.45782i	−0.869590	+	0.493774i	$0.835617\pi$
$212$	4.88211	−	4.88211i	0.335305	−	0.335305i
$213$	−1.43657	+	1.43657i	−0.0984324	+	0.0984324i
$214$	4.48671	−	10.8319i	0.306706	−	0.740453i
$215$		0			0
$216$	−1.71683	−	4.14480i	−0.116816	−	0.282018i
$217$		−	26.4451i		−	1.79521i
$218$	−5.13082	+	2.12526i	−0.347503	+	0.143940i
$219$	−3.82830	−	3.82830i	−0.258692	−	0.258692i
$220$		0			0
$221$	−8.63459	−	6.71137i	−0.580826	−	0.451455i
$222$	−25.9854			−1.74403
$223$	−9.23194	−	9.23194i	−0.618217	−	0.618217i	0.326857	−	0.945074i	$-0.394010\pi$
$223$	−9.23194	−	9.23194i	−0.618217	−	0.618217i	−0.945074	+	0.326857i	$0.894010\pi$
$224$	19.9052	−	8.24499i	1.32997	−	0.550892i
$225$		0			0
$226$	−4.67915	−	11.2965i	−0.311253	−	0.751430i
$227$	9.88506	+	4.09453i	0.656095	+	0.271763i	0.685794	−	0.727796i	$-0.259455\pi$
$227$	9.88506	+	4.09453i	0.656095	+	0.271763i	−0.0296996	+	0.999559i	$0.509455\pi$
$228$	1.13554	−	2.74144i	0.0752031	−	0.181556i
$229$	−13.3171	+	13.3171i	−0.880020	+	0.880020i	−0.993536	−	0.113516i	$-0.963789\pi$
$229$	−13.3171	+	13.3171i	−0.880020	+	0.880020i	0.113516	+	0.993536i	$0.463789\pi$
$230$		0			0
$231$	−1.80914	+	4.36765i	−0.119033	+	0.287370i
$232$	−8.40612	−	3.48193i	−0.551889	−	0.228600i
$233$	−0.859469	−	2.07494i	−0.0563057	−	0.135934i	0.893223	−	0.449613i	$-0.148438\pi$
$233$	−0.859469	−	2.07494i	−0.0563057	−	0.135934i	−0.949529	+	0.313679i	$0.898438\pi$
$234$			1.45205i			0.0949233i
$235$		0			0
$236$	18.4500	+	18.4500i	1.20099	+	1.20099i
$237$	−0.738488			−0.0479700
$238$	6.16753	−	22.4574i	0.399782	−	1.45570i
$239$	−16.7293			−1.08213			−0.541063	−	0.840982i	$-0.681978\pi$
$239$	−16.7293			−1.08213			−0.541063	+	0.840982i	$0.681978\pi$
$240$		0			0
$241$	10.8767	−	4.50526i	0.700627	−	0.290209i	−0.00379273	−	0.999993i	$-0.501207\pi$
$241$	10.8767	−	4.50526i	0.700627	−	0.290209i	0.704420	+	0.709784i	$0.251207\pi$
$242$			21.1504i			1.35960i
$243$	−1.03148	−	2.49021i	−0.0661693	−	0.159747i
$244$	4.65378	+	1.92766i	0.297928	+	0.123406i
$245$		0			0
$246$	19.6768	−	19.6768i	1.25455	−	1.25455i
$247$	1.26800	−	1.26800i	0.0806812	−	0.0806812i
$248$	−3.42010	+	8.25686i	−0.217177	+	0.524311i
$249$	10.9661	+	4.54232i	0.694950	+	0.287858i
$250$		0			0
$251$		−	17.7019i		−	1.11733i	−0.829392	−	0.558666i	$-0.811313\pi$
$251$		−	17.7019i		−	1.11733i	0.829392	−	0.558666i	$-0.188687\pi$
$252$	−1.56729	+	0.649195i	−0.0987303	+	0.0408954i
$253$	−2.78369	−	2.78369i	−0.175009	−	0.175009i
$254$	−22.4162			−1.40652
$255$		0			0
$256$	7.07403			0.442127
$257$	5.44763	+	5.44763i	0.339814	+	0.339814i	0.856297	−	0.516483i	$-0.172759\pi$
$257$	5.44763	+	5.44763i	0.339814	+	0.339814i	−0.516483	+	0.856297i	$0.672759\pi$
$258$	31.2658	−	12.9507i	1.94653	−	0.806278i
$259$		−	18.3467i		−	1.14001i
$260$		0			0
$261$	−2.41079	−	0.998582i	−0.149224	−	0.0618107i
$262$	−1.30372	+	3.14746i	−0.0805442	+	0.194451i
$263$	4.45259	−	4.45259i	0.274558	−	0.274558i	−0.556374	−	0.830932i	$-0.687808\pi$
$263$	4.45259	−	4.45259i	0.274558	−	0.274558i	0.830932	+	0.556374i	$0.187808\pi$
$264$	1.12972	−	1.12972i	0.0695295	−	0.0695295i
$265$		0			0
$266$	3.52807	+	1.46137i	0.216320	+	0.0896026i
$267$	3.88769	+	9.38571i	0.237923	+	0.574396i
$268$			13.9527i			0.852294i
$269$	8.55428	−	3.54330i	0.521563	−	0.216039i	−0.106340	−	0.994330i	$-0.533913\pi$
$269$	8.55428	−	3.54330i	0.521563	−	0.216039i	0.627904	+	0.778291i	$0.283913\pi$
$270$		0			0
$271$	16.7791			1.01926			0.509628	−	0.860395i	$-0.329783\pi$
$271$	16.7791			1.01926			0.509628	+	0.860395i	$0.329783\pi$
$272$	7.47137	−	9.61239i	0.453018	−	0.582837i
$273$	−12.8510			−0.777775
$274$	7.00044	+	7.00044i	0.422912	+	0.422912i
$275$		0			0
$276$		−	17.7079i		−	1.06589i
$277$	−4.59456	−	11.0923i	−0.276061	−	0.666469i	0.723659	−	0.690158i	$-0.242459\pi$
$277$	−4.59456	−	11.0923i	−0.276061	−	0.666469i	−0.999719	+	0.0236887i	$0.992459\pi$
$278$	1.60203	+	0.663584i	0.0960835	+	0.0397991i
$279$	−0.980851	+	2.36798i	−0.0587220	+	0.141767i
$280$		0			0
$281$	−19.9411	+	19.9411i	−1.18959	+	1.18959i	−0.212403	+	0.977182i	$0.568129\pi$
$281$	−19.9411	+	19.9411i	−1.18959	+	1.18959i	−0.977182	+	0.212403i	$0.931871\pi$
$282$	1.27190	−	3.07064i	0.0757407	−	0.182854i
$283$	15.7782	+	6.53556i	0.937919	+	0.388499i	0.798677	−	0.601760i	$-0.205534\pi$
$283$	15.7782	+	6.53556i	0.937919	+	0.388499i	0.139242	+	0.990258i	$0.455534\pi$
$284$	1.04670	+	2.52695i	0.0621101	+	0.149947i
$285$		0			0
$286$	5.03306	−	2.08476i	0.297611	−	0.123274i
$287$	13.8925	+	13.8925i	0.820049	+	0.820049i
$288$	−2.08818			−0.123047
$289$	−4.19515	−	16.4742i	−0.246774	−	0.969073i
$290$		0			0
$291$	19.6793	+	19.6793i	1.15362	+	1.15362i
$292$	−6.73403	+	2.78933i	−0.394079	+	0.163233i
$293$			6.82563i			0.398758i	0.979922	+	0.199379i	$0.0638924\pi$
$293$			6.82563i			0.398758i	−0.979922	+	0.199379i	$0.936108\pi$
$294$	−0.291685	−	0.704191i	−0.0170114	−	0.0410693i
$295$		0			0
$296$	−2.37274	+	5.72830i	−0.137913	+	0.332951i
$297$	−3.41329	+	3.41329i	−0.198059	+	0.198059i
$298$	−14.2936	+	14.2936i	−0.828009	+	0.828009i
$299$	4.09523	−	9.88676i	0.236833	−	0.571766i
$300$		0			0
$301$	9.14369	+	22.0748i	0.527033	+	1.27237i
$302$			2.98218i			0.171605i
$303$	−24.3950	+	10.1048i	−1.40146	+	0.580503i
$304$	1.41159	+	1.41159i	0.0809605	+	0.0809605i
$305$		0			0
$306$	−1.38521	+	1.78215i	−0.0791869	+	0.101879i
$307$	−0.746287			−0.0425929			−0.0212964	−	0.999773i	$-0.506779\pi$
$307$	−0.746287			−0.0425929			−0.0212964	+	0.999773i	$0.506779\pi$
$308$	4.50045	+	4.50045i	0.256437	+	0.256437i
$309$	2.72371	−	1.12820i	0.154947	−	0.0641810i
$310$		0			0
$311$	−6.96494	−	16.8149i	−0.394946	−	0.953483i	−0.988846	−	0.148944i	$-0.952413\pi$
$311$	−6.96494	−	16.8149i	−0.394946	−	0.953483i	0.593900	−	0.804539i	$-0.297587\pi$
$312$	4.01240	+	1.66199i	0.227157	+	0.0940916i
$313$	−3.79773	+	9.16854i	−0.214661	+	0.518236i	−0.994129	−	0.108206i	$-0.965490\pi$
$313$	−3.79773	+	9.16854i	−0.214661	+	0.518236i	0.779468	+	0.626442i	$0.215490\pi$
$314$	7.17245	−	7.17245i	0.404765	−	0.404765i
$315$		0			0
$316$	−0.380471	+	0.918539i	−0.0214032	+	0.0516718i
$317$	−22.4610	−	9.30367i	−1.26154	−	0.522546i	−0.351157	−	0.936317i	$-0.614212\pi$
$317$	−22.4610	−	9.30367i	−1.26154	−	0.522546i	−0.910381	+	0.413770i	$0.864212\pi$
$318$	−4.13110	−	9.97335i	−0.231660	−	0.559278i
$319$			9.78994i			0.548131i
$320$		0			0
$321$	−7.11125	−	7.11125i	−0.396911	−	0.396911i
$322$	22.7890			1.26998
$323$	2.76591	−	0.346636i	0.153899	−	0.0192874i
$324$	−23.6095			−1.31164
$325$		0			0
$326$	−3.14854	+	1.30417i	−0.174381	+	0.0722312i
$327$			4.76369i			0.263433i
$328$	−2.54091	−	6.13429i	−0.140298	−	0.338710i
$329$	2.16799	+	0.898009i	0.119525	+	0.0495088i
$330$		0			0
$331$	−0.346315	+	0.346315i	−0.0190352	+	0.0190352i	−0.716560	−	0.697525i	$-0.754285\pi$
$331$	−0.346315	+	0.346315i	−0.0190352	+	0.0190352i	0.697525	+	0.716560i	$0.254285\pi$
$332$	11.2996	−	11.2996i	0.620144	−	0.620144i
$333$	−0.680478	+	1.64282i	−0.0372899	+	0.0900259i
$334$	43.0441	+	17.8295i	2.35527	+	0.975584i
$335$		0			0
$336$		−	14.3062i		−	0.780468i
$337$	5.55719	−	2.30186i	0.302719	−	0.125390i	−0.226153	−	0.974092i	$-0.572615\pi$
$337$	5.55719	−	2.30186i	0.302719	−	0.125390i	0.528872	+	0.848701i	$0.322615\pi$
$338$	−8.87814	−	8.87814i	−0.482907	−	0.482907i
$339$	−10.4882			−0.569639
$340$		0			0
$341$	9.61610			0.520741
$342$	−0.261712	−	0.261712i	−0.0141518	−	0.0141518i
$343$	−16.8567	+	6.98227i	−0.910175	+	0.377007i
$344$		−	8.07486i		−	0.435367i
$345$		0			0
$346$	20.1798	+	8.35877i	1.08488	+	0.449370i
$347$	−3.02306	+	7.29831i	−0.162286	+	0.391794i	−0.984015	−	0.178085i	$-0.943010\pi$
$347$	−3.02306	+	7.29831i	−0.162286	+	0.391794i	0.821729	+	0.569879i	$0.193010\pi$
$348$	−31.1383	+	31.1383i	−1.66919	+	1.66919i
$349$	13.5417	−	13.5417i	0.724868	−	0.724868i	−0.244725	−	0.969593i	$-0.578698\pi$
$349$	13.5417	−	13.5417i	0.724868	−	0.724868i	0.969593	+	0.244725i	$0.0786976\pi$
$350$		0			0
$351$	−12.1229	−	5.02147i	−0.647072	−	0.268026i
$352$	2.99808	+	7.23801i	0.159798	+	0.385787i
$353$		−	13.7165i		−	0.730055i	−0.930997	−	0.365027i	$-0.881060\pi$
$353$		−	13.7165i		−	0.730055i	0.930997	−	0.365027i	$-0.118940\pi$
$354$	37.6904	−	15.6119i	2.00322	−	0.829761i
$355$		0			0
$356$	13.6770			0.724879
$357$	−15.7725	−	12.2594i	−0.834768	−	0.648836i
$358$	39.4218			2.08351
$359$	−17.6460	−	17.6460i	−0.931322	−	0.931322i	0.0664662	−	0.997789i	$-0.478828\pi$
$359$	−17.6460	−	17.6460i	−0.931322	−	0.931322i	−0.997789	+	0.0664662i	$0.978828\pi$
$360$		0			0
$361$		−	18.5429i		−	0.975943i
$362$	1.97754	+	4.77421i	0.103937	+	0.250927i
$363$	16.7612	+	6.94272i	0.879736	+	0.364398i
$364$	−6.62085	+	15.9841i	−0.347027	+	0.837797i
$365$		0			0
$366$	5.56902	−	5.56902i	0.291097	−	0.291097i
$367$	−3.26363	+	7.87910i	−0.170360	+	0.411286i	−0.985882	−	0.167440i	$-0.946450\pi$
$367$	−3.26363	+	7.87910i	−0.170360	+	0.411286i	0.815522	+	0.578726i	$0.196450\pi$
$368$	11.0063	+	4.55898i	0.573745	+	0.237653i
$369$	−0.728707	−	1.75925i	−0.0379350	−	0.0915831i
$370$		0			0
$371$	7.04155	−	2.91670i	0.365579	−	0.151428i
$372$	30.5854	+	30.5854i	1.58578	+	1.58578i
$373$	−11.5593			−0.598519			−0.299260	−	0.954172i	$-0.596740\pi$
$373$	−11.5593			−0.598519			−0.299260	+	0.954172i	$0.596740\pi$
$374$	8.16606	+	2.24266i	0.422257	+	0.115965i
$375$		0			0
$376$	−0.560763	−	0.560763i	−0.0289192	−	0.0289192i
$377$	−24.5866	+	10.1841i	−1.26627	+	0.524508i
$378$		−	27.9433i		−	1.43725i
$379$	−4.70807	−	11.3663i	−0.241837	−	0.583847i	0.755628	−	0.655001i	$-0.227332\pi$
$379$	−4.70807	−	11.3663i	−0.241837	−	0.583847i	−0.997465	+	0.0711543i	$0.977332\pi$
$380$		0			0
$381$	−7.35824	+	17.7644i	−0.376974	+	0.910096i
$382$	−16.2426	+	16.2426i	−0.831042	+	0.831042i
$383$	−4.00295	+	4.00295i	−0.204541	+	0.204541i	−0.801942	−	0.597401i	$-0.796200\pi$
$383$	−4.00295	+	4.00295i	−0.204541	+	0.204541i	0.597401	+	0.801942i	$0.296200\pi$
$384$	−4.89649	+	11.8212i	−0.249873	+	0.603247i
$385$		0			0
$386$	14.8020	+	35.7353i	0.753404	+	1.81888i
$387$		−	2.31579i		−	0.117718i
$388$	34.6162	−	14.3385i	1.75737	−	0.727926i
$389$	−1.15168	−	1.15168i	−0.0583927	−	0.0583927i	0.677307	−	0.735700i	$-0.263147\pi$
$389$	−1.15168	−	1.15168i	−0.0583927	−	0.0583927i	−0.735700	+	0.677307i	$0.763147\pi$
$390$		0			0
$391$	14.4579	−	8.22769i	0.731166	−	0.416092i
$392$	−0.181868			−0.00918570
$393$	2.06634	+	2.06634i	0.104233	+	0.104233i
$394$	−37.9041	+	15.7004i	−1.90958	+	0.790975i
$395$		0			0
$396$	−0.236063	−	0.569907i	−0.0118626	−	0.0286389i
$397$	11.8736	+	4.91819i	0.595917	+	0.246837i	0.660194	−	0.751095i	$-0.270474\pi$
$397$	11.8736	+	4.91819i	0.595917	+	0.246837i	−0.0642772	+	0.997932i	$0.520474\pi$
$398$	18.7832	−	45.3467i	0.941518	−	2.27303i
$399$	2.31621	−	2.31621i	0.115956	−	0.115956i
$400$		0			0
$401$	−11.0222	+	26.6099i	−0.550422	+	1.32884i	0.366741	+	0.930323i	$0.380473\pi$
$401$	−11.0222	+	26.6099i	−0.550422	+	1.32884i	−0.917163	+	0.398512i	$0.869527\pi$
$402$	20.1547	+	8.34833i	1.00522	+	0.416377i
$403$	10.0033	+	24.1500i	0.498298	+	1.20300i
$404$			35.5488i			1.76862i
$405$		0			0
$406$	−40.0732	−	40.0732i	−1.98880	−	1.98880i
$407$	6.67129			0.330684
$408$	3.33909	+	5.86752i	0.165310	+	0.290486i
$409$	13.6197			0.673451			0.336725	−	0.941603i	$-0.390681\pi$
$409$	13.6197			0.673451			0.336725	+	0.941603i	$0.390681\pi$
$410$		0			0
$411$	7.84563	−	3.24977i	0.386996	−	0.160299i
$412$		−	3.96903i		−	0.195540i
$413$	11.0225	+	26.6108i	0.542384	+	1.30943i
$414$	−2.04060	−	0.845243i	−0.100290	−	0.0415414i
$415$		0			0
$416$	−15.0588	+	15.0588i	−0.738320	+	0.738320i
$417$	1.05175	−	1.05175i	0.0515045	−	0.0515045i
$418$	−0.531391	+	1.28289i	−0.0259912	+	0.0627483i
$419$	−13.1802	−	5.45940i	−0.643893	−	0.266709i	0.0367500	−	0.999324i	$-0.488299\pi$
$419$	−13.1802	−	5.45940i	−0.643893	−	0.266709i	−0.680643	+	0.732615i	$0.738299\pi$
$420$		0			0
$421$		−	28.9349i		−	1.41020i	−0.709107	−	0.705101i	$-0.750902\pi$
$421$		−	28.9349i		−	1.41020i	0.709107	−	0.705101i	$-0.249098\pi$
$422$	44.5745	−	18.4634i	2.16985	−	0.898783i
$423$	−0.160821	−	0.160821i	−0.00781940	−	0.00781940i
$424$	−2.57576			−0.125090
$425$		0			0
$426$	4.27646			0.207195
$427$	3.93193	+	3.93193i	0.190279	+	0.190279i
$428$	−12.5088	+	5.18130i	−0.604634	+	0.250448i
$429$		−	4.67292i		−	0.225611i
$430$		0			0
$431$	−18.9908	−	7.86623i	−0.914753	−	0.378903i	−0.124879	−	0.992172i	$-0.539854\pi$
$431$	−18.9908	−	7.86623i	−0.914753	−	0.378903i	−0.789874	+	0.613269i	$0.789854\pi$
$432$	5.59011	−	13.4957i	0.268954	−	0.649313i
$433$	17.0995	−	17.0995i	0.821748	−	0.821748i	−0.164611	−	0.986359i	$-0.552637\pi$
$433$	17.0995	−	17.0995i	0.821748	−	0.821748i	0.986359	+	0.164611i	$0.0526368\pi$
$434$	−39.3616	+	39.3616i	−1.88942	+	1.88942i
$435$		0			0
$436$	5.92512	+	2.45427i	0.283762	+	0.117538i
$437$	1.04385	+	2.52007i	0.0499339	+	0.120551i
$438$			11.3963i			0.544535i
$439$	20.3668	−	8.43621i	0.972055	−	0.402638i	0.160578	−	0.987023i	$-0.448664\pi$
$439$	20.3668	−	8.43621i	0.972055	−	0.402638i	0.811477	+	0.584385i	$0.198664\pi$
$440$		0			0
$441$	−0.0521578			−0.00248371
$442$	2.86258	+	22.8413i	0.136159	+	1.08645i
$443$	−32.3324			−1.53616			−0.768079	−	0.640356i	$-0.778787\pi$
$443$	−32.3324			−1.53616			−0.768079	+	0.640356i	$0.778787\pi$
$444$	21.2190	+	21.2190i	1.00701	+	1.00701i
$445$		0			0
$446$			27.4821i			1.30132i
$447$	6.63544	+	16.0194i	0.313845	+	0.757690i
$448$	−27.2589	−	11.2910i	−1.28786	−	0.533450i
$449$	−12.0051	+	28.9829i	−0.566556	+	1.36779i	0.337885	+	0.941187i	$0.390288\pi$
$449$	−12.0051	+	28.9829i	−0.566556	+	1.36779i	−0.904441	+	0.426599i	$0.859712\pi$
$450$		0			0
$451$	−5.05166	+	5.05166i	−0.237873	+	0.237873i
$452$	−5.40353	+	13.0453i	−0.254161	+	0.613598i
$453$	2.36331	+	0.978914i	0.111038	+	0.0459934i
$454$	−8.61878	−	20.8076i	−0.404499	−	0.976548i
$455$		0			0
$456$	−1.02273	+	0.423630i	−0.0478939	+	0.0198383i
$457$	9.01432	+	9.01432i	0.421672	+	0.421672i	0.885779	−	0.464107i	$-0.153625\pi$
$457$	9.01432	+	9.01432i	0.421672	+	0.421672i	−0.464107	+	0.885779i	$0.653625\pi$
$458$	39.6431			1.85240
$459$	−10.0886	−	17.7279i	−0.470895	−	0.827467i
$460$		0			0
$461$	−12.3023	−	12.3023i	−0.572974	−	0.572974i	0.359984	−	0.932958i	$-0.382782\pi$
$461$	−12.3023	−	12.3023i	−0.572974	−	0.572974i	−0.932958	+	0.359984i	$0.882782\pi$
$462$	9.19369	−	3.80815i	0.427729	−	0.177171i
$463$			29.5747i			1.37445i	0.726443	+	0.687227i	$0.241172\pi$
$463$			29.5747i			1.37445i	−0.726443	+	0.687227i	$0.758828\pi$
$464$	−11.3374	−	27.3708i	−0.526324	−	1.27066i
$465$		0			0
$466$	−1.80914	+	4.36765i	−0.0838068	+	0.202327i
$467$	23.2530	−	23.2530i	1.07602	−	1.07602i	0.0791599	−	0.996862i	$-0.474776\pi$
$467$	23.2530	−	23.2530i	1.07602	−	1.07602i	0.996862	−	0.0791599i	$-0.0252238\pi$
$468$	1.18570	−	1.18570i	0.0548092	−	0.0548092i
$469$	−5.89422	+	14.2299i	−0.272170	+	0.657076i
$470$		0			0
$471$	−3.32962	−	8.03840i	−0.153421	−	0.370390i
$472$		−	9.73409i		−	0.448048i
$473$	−8.02694	+	3.32487i	−0.369079	+	0.152878i
$474$	1.09918	+	1.09918i	0.0504872	+	0.0504872i
$475$		0			0
$476$	−23.3744	+	13.3019i	−1.07136	+	0.609691i
$477$	−0.738703			−0.0338229
$478$	24.9003	+	24.9003i	1.13891	+	1.13891i
$479$	−0.548605	+	0.227240i	−0.0250664	+	0.0103828i	−0.395181	−	0.918603i	$-0.629318\pi$
$479$	−0.548605	+	0.227240i	−0.0250664	+	0.0103828i	0.370115	+	0.928986i	$0.379318\pi$
$480$		0			0
$481$	6.93989	+	16.7544i	0.316432	+	0.763934i
$482$	−22.8948	−	9.48335i	−1.04283	−	0.431955i
$483$	7.48059	−	18.0598i	0.340379	−	0.821747i
$484$	17.2709	−	17.2709i	0.785039	−	0.785039i
$485$		0			0
$486$	−2.17121	+	5.24176i	−0.0984881	+	0.237771i
$487$	−2.08130	−	0.862103i	−0.0943127	−	0.0390656i	0.335028	−	0.942208i	$-0.391254\pi$
$487$	−2.08130	−	0.862103i	−0.0943127	−	0.0390656i	−0.429341	+	0.903142i	$0.641254\pi$
$488$	−0.719141	−	1.73616i	−0.0325540	−	0.0785922i
$489$			2.92325i			0.132194i
$490$		0			0
$491$	−5.16155	−	5.16155i	−0.232937	−	0.232937i	0.580980	−	0.813918i	$-0.302669\pi$
$491$	−5.16155	−	5.16155i	−0.232937	−	0.232937i	−0.813918	+	0.580980i	$0.802669\pi$
$492$	−32.1351			−1.44876
$493$	−39.8914	−	10.9555i	−1.79662	−	0.493409i
$494$	−3.77466			−0.169830
$495$		0			0
$496$	−26.8848	+	11.1360i	−1.20716	+	0.500023i
$497$			3.01934i			0.135436i
$498$	−9.56136	−	23.0832i	−0.428455	−	1.03438i
$499$	7.02196	+	2.90859i	0.314346	+	0.130206i	0.534278	−	0.845309i	$-0.320584\pi$
$499$	7.02196	+	2.90859i	0.314346	+	0.130206i	−0.219932	+	0.975515i	$0.570584\pi$
$500$		0			0
$501$	28.2589	−	28.2589i	1.26251	−	1.26251i
$502$	−26.3479	+	26.3479i	−1.17597	+	1.17597i
$503$	−5.93402	+	14.3260i	−0.264585	+	0.638764i	−0.999211	−	0.0397075i	$-0.987357\pi$
$503$	−5.93402	+	14.3260i	−0.264585	+	0.638764i	0.734627	+	0.678472i	$0.237357\pi$
$504$	0.584702	+	0.242191i	0.0260447	+	0.0107881i
$505$		0			0
$506$			8.28662i			0.368385i
$507$	−9.95002	+	4.12143i	−0.441896	+	0.183039i
$508$	18.3045	+	18.3045i	0.812131	+	0.812131i
$509$	29.3375			1.30036			0.650182	−	0.759779i	$-0.274693\pi$
$509$	29.3375			1.30036			0.650182	+	0.759779i	$0.274693\pi$
$510$		0			0
$511$	−8.04618			−0.355942
$512$	−20.5510	−	20.5510i	−0.908233	−	0.908233i
$513$	3.09004	−	1.27994i	0.136429	−	0.0565107i
$514$		−	16.2168i		−	0.715292i
$515$		0			0
$516$	−36.1061	−	14.9556i	−1.58948	−	0.658385i
$517$	−0.326538	+	0.788333i	−0.0143611	+	0.0346708i
$518$	−27.3076	+	27.3076i	−1.19983	+	1.19983i
$519$	13.2483	−	13.2483i	0.581535	−	0.581535i
$520$		0			0
$521$	−14.0288	−	5.81093i	−0.614614	−	0.254581i	0.0535860	−	0.998563i	$-0.482935\pi$
$521$	−14.0288	−	5.81093i	−0.614614	−	0.254581i	−0.668200	+	0.743982i	$0.732935\pi$
$522$	2.10197	+	5.07460i	0.0920006	+	0.222109i
$523$		−	35.8569i		−	1.56791i	−0.620815	−	0.783957i	$-0.713198\pi$
$523$		−	35.8569i		−	1.56791i	0.620815	−	0.783957i	$-0.286802\pi$
$524$	3.63472	−	1.50555i	0.158784	−	0.0657703i
$525$		0			0
$526$	−13.2547			−0.577932
$527$	−10.7609	+	39.1830i	−0.468753	+	1.70684i
$528$	5.20209			0.226392
$529$	−4.75321	−	4.75321i	−0.206661	−	0.206661i
$530$		0			0
$531$		−	2.79164i		−	0.121147i
$532$	−1.68761	−	4.07425i	−0.0731671	−	0.176641i
$533$	−17.9418	−	7.43175i	−0.777148	−	0.321905i
$534$	8.18339	−	19.7565i	0.354130	−	0.854945i
$535$		0			0
$536$	3.68066	−	3.68066i	0.158980	−	0.158980i
$537$	12.9404	−	31.2409i	0.558420	−	1.34814i
$538$	−18.0063	−	7.45847i	−0.776308	−	0.321557i
$539$	0.0748850	+	0.180788i	0.00322553	+	0.00778711i
$540$		0			0
$541$	24.6831	−	10.2241i	1.06121	−	0.439568i	0.217329	−	0.976098i	$-0.430266\pi$
$541$	24.6831	−	10.2241i	1.06121	−	0.439568i	0.843881	+	0.536531i	$0.180266\pi$
$542$	−24.9744	−	24.9744i	−1.07274	−	1.07274i
$543$	4.43259			0.190221
$544$	−32.8479	+	4.11666i	−1.40834	+	0.176500i
$545$		0			0
$546$	19.1277	+	19.1277i	0.818589	+	0.818589i
$547$	12.4802	−	5.16946i	0.533614	−	0.221030i	−0.0995712	−	0.995030i	$-0.531747\pi$
$547$	12.4802	−	5.16946i	0.533614	−	0.221030i	0.633185	+	0.774000i	$0.281747\pi$
$548$		−	11.4328i		−	0.488383i
$549$	−0.206242	−	0.497913i	−0.00880221	−	0.0212504i
$550$		0			0
$551$	2.59586	−	6.26695i	0.110587	−	0.266981i
$552$	−4.67127	+	4.67127i	−0.198822	+	0.198822i
$553$	−0.776064	+	0.776064i	−0.0330016	+	0.0330016i
$554$	−9.67133	+	23.3487i	−0.410895	+	0.991989i
$555$		0			0
$556$	−0.766313	−	1.85004i	−0.0324989	−	0.0784593i
$557$			16.9198i			0.716915i	0.933546	+	0.358458i	$0.116697\pi$
$557$			16.9198i			0.716915i	−0.933546	+	0.358458i	$0.883303\pi$
$558$	4.98449	−	2.06464i	0.211010	−	0.0874033i
$559$	−16.7002	−	16.7002i	−0.706345	−	0.706345i
$560$		0			0
$561$	4.45781	−	5.73526i	0.188209	−	0.242143i
$562$	59.3616			2.50402
$563$	−26.6224	−	26.6224i	−1.12200	−	1.12200i	−0.991441	−	0.130558i	$-0.958323\pi$
$563$	−26.6224	−	26.6224i	−1.12200	−	1.12200i	−0.130558	−	0.991441i	$-0.541677\pi$
$564$	−3.54601	+	1.46881i	−0.149314	+	0.0618479i
$565$		0			0
$566$	−13.7570	−	33.2124i	−0.578251	−	1.39602i
$567$	−24.0787	−	9.97373i	−1.01121	−	0.418857i
$568$	0.390485	−	0.942715i	0.0163844	−	0.0395555i
$569$	21.0557	−	21.0557i	0.882701	−	0.882701i	−0.111108	−	0.993808i	$-0.535440\pi$
$569$	21.0557	−	21.0557i	0.882701	−	0.882701i	0.993808	+	0.111108i	$0.0354398\pi$
$570$		0			0
$571$	−3.82363	+	9.23107i	−0.160014	+	0.386308i	−0.983470	−	0.181072i	$-0.942043\pi$
$571$	−3.82363	+	9.23107i	−0.160014	+	0.386308i	0.823456	+	0.567381i	$0.192043\pi$
$572$	−5.81222	−	2.40750i	−0.243021	−	0.100663i
$573$	7.54017	+	18.2036i	0.314995	+	0.760465i
$574$		−	41.3559i		−	1.72616i
$575$		0			0
$576$	2.02207	+	2.02207i	0.0842527	+	0.0842527i
$577$	−17.5104			−0.728968			−0.364484	−	0.931210i	$-0.618755\pi$
$577$	−17.5104			−0.728968			−0.364484	+	0.931210i	$0.618755\pi$
$578$	−18.2765	+	30.7648i	−0.760203	+	1.27965i
$579$	33.1783			1.37884
$580$		0			0
$581$	16.2976	−	6.75067i	0.676137	−	0.280065i
$582$		−	58.5824i		−	2.42832i
$583$	1.06058	+	2.56048i	0.0439249	+	0.106044i
$584$	2.51222	+	1.04060i	0.103957	+	0.0430602i
$585$		0			0
$586$	10.1594	−	10.1594i	0.419683	−	0.419683i
$587$	11.3396	−	11.3396i	0.468036	−	0.468036i	−0.433242	−	0.901278i	$-0.642630\pi$
$587$	11.3396	−	11.3396i	0.468036	−	0.468036i	0.901278	+	0.433242i	$0.142630\pi$
$588$	−0.336841	+	0.813207i	−0.0138911	+	0.0335361i
$589$	−6.15567	−	2.54976i	−0.253640	−	0.105061i
$590$		0			0
$591$			35.1919i			1.44760i
$592$	−18.6517	+	7.72577i	−0.766579	+	0.317527i
$593$	27.1563	+	27.1563i	1.11517	+	1.11517i	0.992439	+	0.122735i	$0.0391667\pi$
$593$	27.1563	+	27.1563i	1.11517	+	1.11517i	0.122735	+	0.992439i	$0.460833\pi$
$594$	10.1609			0.416905
$595$		0			0
$596$	23.3436			0.956193
$597$	−29.7706	−	29.7706i	−1.21843	−	1.21843i
$598$	−20.8111	+	8.62025i	−0.851031	+	0.352508i
$599$			23.5261i			0.961251i	0.876926	+	0.480625i	$0.159590\pi$
$599$			23.5261i			0.961251i	−0.876926	+	0.480625i	$0.840410\pi$
$600$		0			0
$601$	23.1362	+	9.58331i	0.943744	+	0.390911i	0.800876	−	0.598830i	$-0.204368\pi$
$601$	23.1362	+	9.58331i	0.943744	+	0.390911i	0.142868	+	0.989742i	$0.454368\pi$
$602$	19.2470	−	46.4664i	0.784450	−	1.89383i
$603$	1.05558	−	1.05558i	0.0429864	−	0.0429864i
$604$	2.43517	−	2.43517i	0.0990855	−	0.0990855i
$605$		0			0
$606$	51.3504	+	21.2700i	2.08597	+	0.864036i
$607$	12.3827	+	29.8946i	0.502600	+	1.21338i	0.948063	+	0.318083i	$0.103039\pi$
$607$	12.3827	+	29.8946i	0.502600	+	1.21338i	−0.445463	+	0.895300i	$0.646961\pi$
$608$		−	5.42831i		−	0.220147i
$609$	−44.9114	+	18.6029i	−1.81990	+	0.753827i
$610$		0			0
$611$	−2.31951			−0.0938375
$612$	2.58638	−	0.324138i	0.104548	−	0.0131025i
$613$	25.0386			1.01130			0.505650	−	0.862739i	$-0.331253\pi$
$613$	25.0386			1.01130			0.505650	+	0.862739i	$0.331253\pi$
$614$	1.11079	+	1.11079i	0.0448280	+	0.0448280i
$615$		0			0
$616$		−	2.37441i		−	0.0956675i
$617$	3.72834	+	9.00101i	0.150097	+	0.362367i	0.980988	−	0.194069i	$-0.0621685\pi$
$617$	3.72834	+	9.00101i	0.150097	+	0.362367i	−0.830891	+	0.556436i	$0.812169\pi$
$618$	−5.73328	−	2.37480i	−0.230626	−	0.0955285i
$619$	2.82897	−	6.82973i	0.113706	−	0.274510i	−0.856774	−	0.515692i	$-0.827535\pi$
$619$	2.82897	−	6.82973i	0.113706	−	0.274510i	0.970480	+	0.241182i	$0.0775350\pi$
$620$		0			0
$621$	14.1136	−	14.1136i	0.566358	−	0.566358i
$622$	−14.6609	+	35.3944i	−0.587847	+	1.41919i
$623$	13.9488	+	5.77777i	0.558846	+	0.231481i
$624$	5.41153	+	13.0646i	0.216635	+	0.523002i
$625$		0			0
$626$	19.2993	−	7.99404i	0.771356	−	0.319506i
$627$	0.842232	+	0.842232i	0.0336355	+	0.0336355i
$628$	−11.7137			−0.467426
$629$	−7.46553	+	27.1837i	−0.297670	+	1.08389i
$630$		0			0
$631$	−6.09529	−	6.09529i	−0.242650	−	0.242650i	0.575296	−	0.817945i	$-0.304887\pi$
$631$	−6.09529	−	6.09529i	−0.242650	−	0.242650i	−0.817945	+	0.575296i	$0.804887\pi$
$632$	0.342674	−	0.141940i	0.0136308	−	0.00564608i
$633$		−	41.3850i		−	1.64491i
$634$	19.5838	+	47.2794i	0.777771	+	1.87770i
$635$		0			0
$636$	−4.77063	+	11.5173i	−0.189168	+	0.456692i
$637$	−0.376134	+	0.376134i	−0.0149030	+	0.0149030i
$638$	14.5716	−	14.5716i	0.576895	−	0.576895i
$639$	0.111987	−	0.270361i	0.00443015	−	0.0106953i
$640$		0			0
$641$	−14.9873	−	36.1825i	−0.591963	−	1.42912i	−0.881604	−	0.471989i	$-0.843536\pi$
$641$	−14.9873	−	36.1825i	−0.591963	−	1.42912i	0.289641	−	0.957135i	$-0.406464\pi$
$642$			21.1691i			0.835478i
$643$	42.2011	−	17.4803i	1.66425	−	0.689355i	0.665861	−	0.746076i	$-0.268065\pi$
$643$	42.2011	−	17.4803i	1.66425	−	0.689355i	0.998390	+	0.0567210i	$0.0180645\pi$
$644$	−18.6089	−	18.6089i	−0.733292	−	0.733292i
$645$		0			0
$646$	−4.63279	−	3.60090i	−0.182275	−	0.141676i
$647$	−9.17577			−0.360737			−0.180368	−	0.983599i	$-0.557729\pi$
$647$	−9.17577			−0.360737			−0.180368	+	0.983599i	$0.557729\pi$
$648$	6.22811	+	6.22811i	0.244663	+	0.244663i
$649$	−9.67633	+	4.00807i	−0.379829	+	0.157330i
$650$		0			0
$651$	18.2726	+	44.1139i	0.716158	+	1.72896i
$652$	3.63596	+	1.50607i	0.142395	+	0.0589821i
$653$	6.36250	−	15.3604i	0.248984	−	0.601100i	−0.749134	−	0.662418i	$-0.769530\pi$
$653$	6.36250	−	15.3604i	0.248984	−	0.601100i	0.998118	+	0.0613178i	$0.0195303\pi$
$654$	7.09039	−	7.09039i	0.277256	−	0.277256i
$655$		0			0
$656$	8.27334	−	19.9736i	0.323020	−	0.779838i
$657$	0.720481	+	0.298433i	0.0281086	+	0.0116430i
$658$	−1.89027	−	4.56350i	−0.0736902	−	0.177904i
$659$			5.95839i			0.232106i	0.993243	+	0.116053i	$0.0370242\pi$
$659$			5.95839i			0.232106i	−0.993243	+	0.116053i	$0.962976\pi$
$660$		0			0
$661$	30.3724	+	30.3724i	1.18135	+	1.18135i	0.979395	+	0.201955i	$0.0647296\pi$
$661$	30.3724	+	30.3724i	1.18135	+	1.18135i	0.201955	+	0.979395i	$0.435270\pi$
$662$	1.03093			0.0400681
$663$	19.0409	+	5.22924i	0.739487	+	0.203087i
$664$	−5.96157			−0.231354
$665$		0			0
$666$	3.45805	−	1.43237i	0.133997	−	0.0555033i
$667$		−	40.4803i		−	1.56740i
$668$	−20.5896	−	49.7078i	−0.796637	−	1.92325i
$669$	21.7790	+	9.02114i	0.842024	+	0.348778i
$670$		0			0
$671$	−1.42975	+	1.42975i	−0.0551947	+	0.0551947i
$672$	−27.5074	+	27.5074i	−1.06112	+	1.06112i
$673$	6.63803	−	16.0256i	0.255877	−	0.617743i	−0.742781	−	0.669535i	$-0.766493\pi$
$673$	6.63803	−	16.0256i	0.255877	−	0.617743i	0.998658	+	0.0517924i	$0.0164934\pi$
$674$	−11.6976	−	4.84531i	−0.450575	−	0.186634i
$675$		0			0
$676$			14.4993i			0.557666i
$677$	23.6441	−	9.79369i	0.908715	−	0.376402i	0.121150	−	0.992634i	$-0.461342\pi$
$677$	23.6441	−	9.79369i	0.908715	−	0.376402i	0.787565	+	0.616232i	$0.211342\pi$
$678$	15.6108	+	15.6108i	0.599531	+	0.599531i
$679$	41.3613			1.58730
$680$		0			0
$681$	−19.3187			−0.740294
$682$	−14.3128	−	14.3128i	−0.548067	−	0.548067i
$683$	5.66085	−	2.34480i	0.216606	−	0.0897213i	−0.271742	−	0.962370i	$-0.587600\pi$
$683$	5.66085	−	2.34480i	0.216606	−	0.0897213i	0.488348	+	0.872649i	$0.337600\pi$
$684$			0.427415i			0.0163426i
$685$		0			0
$686$	35.4825	+	14.6973i	1.35473	+	0.561146i
$687$	13.0130	−	31.4163i	0.496479	−	1.19861i
$688$	18.5914	−	18.5914i	0.708790	−	0.708790i
$689$	−5.32713	+	5.32713i	−0.202948	+	0.202948i
$690$		0			0
$691$	−6.87633	−	2.84827i	−0.261588	−	0.108353i	0.248035	−	0.968751i	$-0.420215\pi$
$691$	−6.87633	−	2.84827i	−0.261588	−	0.108353i	−0.509623	+	0.860398i	$0.670215\pi$
$692$	−9.65279	−	23.3039i	−0.366944	−	0.885881i
$693$		−	0.680955i		−	0.0258674i
$694$	15.3626	−	6.36339i	0.583156	−	0.241551i
$695$		0			0
$696$	16.4284			0.622715
$697$	−14.9311	−	26.2372i	−0.565555	−	0.993806i
$698$	−40.3115			−1.52581
$699$	2.86741	+	2.86741i	0.108455	+	0.108455i
$700$		0			0
$701$			25.3350i			0.956891i	0.878117	+	0.478445i	$0.158800\pi$
$701$			25.3350i			0.956891i	−0.878117	+	0.478445i	$0.841200\pi$
$702$	10.5699	+	25.5181i	0.398937	+	0.963119i
$703$	−4.27058	−	1.76893i	−0.161068	−	0.0667165i
$704$	4.10568	−	9.91200i	0.154739	−	0.373573i
$705$		0			0
$706$	−20.4160	+	20.4160i	−0.768365	+	0.768365i
$707$	−15.0174	+	36.2552i	−0.564788	+	1.36352i
$708$	−43.5252	−	18.0287i	−1.63578	−	0.677562i
$709$	−6.10174	−	14.7309i	−0.229156	−	0.553231i	0.766919	−	0.641744i	$-0.221789\pi$
$709$	−6.10174	−	14.7309i	−0.229156	−	0.553231i	−0.996075	+	0.0885126i	$0.971789\pi$
$710$		0			0
$711$	0.0982755	−	0.0407070i	0.00368562	−	0.00152663i
$712$	−3.60794	−	3.60794i	−0.135213	−	0.135213i
$713$	−39.7615			−1.48908
$714$	5.22897	+	41.7233i	0.195689	+	1.56146i
$715$		0			0
$716$	−32.1908	−	32.1908i	−1.20303	−	1.20303i
$717$	27.9066	−	11.5593i	1.04219	−	0.431689i
$718$			52.5296i			1.96039i
$719$	−7.42813	−	17.9331i	−0.277022	−	0.668791i	0.722728	−	0.691132i	$-0.242888\pi$
$719$	−7.42813	−	17.9331i	−0.277022	−	0.668791i	−0.999750	+	0.0223415i	$0.992888\pi$
$720$		0			0
$721$	1.67670	−	4.04790i	0.0624434	−	0.150752i
$722$	−27.5997	+	27.5997i	−1.02716	+	1.02716i
$723$	−15.0307	+	15.0307i	−0.558997	+	0.558997i
$724$	2.28369	−	5.51330i	0.0848725	−	0.204900i
$725$		0			0
$726$	−14.6141	−	35.2815i	−0.542380	−	1.30942i
$727$		−	26.1442i		−	0.969633i	−0.874616	−	0.484817i	$-0.838886\pi$
$727$		−	26.1442i		−	0.969633i	0.874616	−	0.484817i	$-0.161114\pi$
$728$	5.96311	−	2.47000i	0.221008	−	0.0915444i
$729$	−17.1622	−	17.1622i	−0.635639	−	0.635639i
$730$		0			0
$731$	−4.56537	−	36.4283i	−0.168856	−	1.34735i
$732$	−9.09503			−0.336162
$733$	3.23474	+	3.23474i	0.119478	+	0.119478i	0.764318	−	0.644840i	$-0.223076\pi$
$733$	3.23474	+	3.23474i	0.119478	+	0.119478i	−0.644840	+	0.764318i	$0.723076\pi$
$734$	16.5851	−	6.86978i	0.612168	−	0.253568i
$735$		0			0
$736$	−12.3967	−	29.9284i	−0.456950	−	1.10317i
$737$	−5.17435	−	2.14328i	−0.190599	−	0.0789489i
$738$	−1.53389	+	3.70314i	−0.0564633	+	0.136315i
$739$	−28.5736	+	28.5736i	−1.05110	+	1.05110i	−0.0524727	+	0.998622i	$0.516710\pi$
$739$	−28.5736	+	28.5736i	−1.05110	+	1.05110i	−0.998622	+	0.0524727i	$0.983290\pi$
$740$		0			0
$741$	−1.23905	+	2.99133i	−0.0455177	+	0.109889i
$742$	−14.8221	−	6.13952i	−0.544137	−	0.225389i
$743$	8.97795	+	21.6747i	0.329369	+	0.795168i	0.998639	+	0.0521484i	$0.0166069\pi$
$743$	8.97795	+	21.6747i	0.329369	+	0.795168i	−0.669270	+	0.743019i	$0.733393\pi$
$744$		−	16.1366i		−	0.591598i
$745$		0			0
$746$	17.2052	+	17.2052i	0.629927	+	0.629927i
$747$	−1.70972			−0.0625553
$748$	−4.83689	−	8.49949i	−0.176854	−	0.310772i
$749$	−14.9462			−0.546121
$750$		0			0
$751$	−29.7279	+	12.3137i	−1.08479	+	0.449333i	−0.852186	−	0.523239i	$-0.824723\pi$
$751$	−29.7279	+	12.3137i	−1.08479	+	0.449333i	−0.232600	+	0.972572i	$0.574723\pi$
$752$		−	2.58218i		−	0.0941624i
$753$	12.2313	+	29.5290i	0.445734	+	1.07610i
$754$	51.7536	+	21.4370i	1.88475	+	0.780690i
$755$		0			0
$756$	−22.8177	+	22.8177i	−0.829873	+	0.829873i
$757$	−25.3721	+	25.3721i	−0.922165	+	0.922165i	−0.997182	−	0.0750172i	$-0.976099\pi$
$757$	−25.3721	+	25.3721i	−0.922165	+	0.922165i	0.0750172	+	0.997182i	$0.476099\pi$
$758$	−9.91025	+	23.9255i	−0.359957	+	0.869012i
$759$	6.56697	+	2.72013i	0.238366	+	0.0987343i
$760$		0			0
$761$			26.9643i			0.977453i	0.872437	+	0.488727i	$0.162538\pi$
$761$			26.9643i			0.977453i	−0.872437	+	0.488727i	$0.837462\pi$
$762$	37.3931	−	15.4887i	1.35461	−	0.561098i
$763$	5.00607	+	5.00607i	0.181232	+	0.181232i
$764$	26.5265			0.959695
$765$		0			0
$766$	11.9162			0.430549
$767$	−20.1318	−	20.1318i	−0.726918	−	0.726918i
$768$	−11.8004	+	4.88788i	−0.425809	+	0.176376i
$769$			13.1666i			0.474800i	0.971412	+	0.237400i	$0.0762952\pi$
$769$			13.1666i			0.474800i	−0.971412	+	0.237400i	$0.923705\pi$
$770$		0			0
$771$	−12.8514	−	5.32324i	−0.462834	−	0.191712i
$772$	17.0936	−	41.2675i	0.615210	−	1.48525i
$773$	22.4347	−	22.4347i	0.806920	−	0.806920i	−0.177247	−	0.984166i	$-0.556719\pi$
$773$	22.4347	−	22.4347i	0.806920	−	0.806920i	0.984166	+	0.177247i	$0.0567191\pi$
$774$	−3.44688	+	3.44688i	−0.123895	+	0.123895i
$775$		0			0
$776$	−12.9141	−	5.34918i	−0.463587	−	0.192024i
$777$	12.6768	+	30.6046i	0.454779	+	1.09793i
$778$			3.42839i			0.122914i
$779$	4.57325	−	1.89430i	0.163854	−	0.0678705i
$780$		0			0
$781$	−1.09791			−0.0392861
$782$	−33.7658	−	9.27317i	−1.20746	−	0.331608i
$783$	−49.6360			−1.77385
$784$	−0.418728	−	0.418728i	−0.0149546	−	0.0149546i
$785$		0			0
$786$		−	6.15119i		−	0.219406i
$787$	−4.29554	−	10.3704i	−0.153120	−	0.369663i	0.828642	−	0.559779i	$-0.189114\pi$
$787$	−4.29554	−	10.3704i	−0.153120	−	0.369663i	−0.981762	+	0.190115i	$0.939114\pi$
$788$	43.7720	+	18.1310i	1.55931	+	0.645889i
$789$	−4.35092	+	10.5041i	−0.154897	+	0.373954i
$790$		0			0
$791$	−11.0218	+	11.0218i	−0.391891	+	0.391891i
$792$	−0.0880667	+	0.212612i	−0.00312931	+	0.00755483i
$793$	−5.07799	−	2.10337i	−0.180325	−	0.0746930i
$794$	−10.3525	−	24.9932i	−0.367398	−	0.886977i
$795$		0			0
$796$	−52.3668	+	21.6911i	−1.85609	+	0.768819i
$797$	23.8591	+	23.8591i	0.845134	+	0.845134i	0.989521	−	0.144388i	$-0.0461212\pi$
$797$	23.8591	+	23.8591i	0.845134	+	0.845134i	−0.144388	+	0.989521i	$0.546121\pi$
$798$	−6.89502			−0.244081
$799$	−2.84683	−	2.21274i	−0.100714	−	0.0782811i
$800$		0			0
$801$	−1.03472	−	1.03472i	−0.0365600	−	0.0365600i
$802$	56.0125	−	23.2012i	1.97787	−	0.819261i
$803$		−	2.92579i		−	0.103249i
$804$	−9.64074	−	23.2748i	−0.340003	−	0.820839i
$805$		0			0
$806$	21.0564	−	50.8346i	0.741679	−	1.79057i
$807$	−11.8213	+	11.8213i	−0.416131	+	0.416131i
$808$	9.37764	−	9.37764i	0.329904	−	0.329904i
$809$	5.44317	−	13.1410i	0.191372	−	0.462012i	−0.798847	−	0.601534i	$-0.794557\pi$
$809$	5.44317	−	13.1410i	0.191372	−	0.462012i	0.990219	+	0.139522i	$0.0445566\pi$
$810$		0			0
$811$	−9.42238	−	22.7476i	−0.330865	−	0.798778i	−0.998524	−	0.0543111i	$-0.982704\pi$
$811$	−9.42238	−	22.7476i	−0.330865	−	0.798778i	0.667659	−	0.744467i	$-0.267296\pi$
$812$			65.4455i			2.29669i
$813$	−27.9896	+	11.5937i	−0.981639	+	0.406608i
$814$	−9.92972	−	9.92972i	−0.348037	−	0.348037i
$815$		0			0
$816$	−5.82141	+	21.1971i	−0.203790	+	0.742047i
$817$	6.01999			0.210613
$818$	−20.2719	−	20.2719i	−0.708790	−	0.708790i
$819$	1.71016	−	0.708372i	0.0597578	−	0.0247525i
$820$		0			0
$821$	9.55514	+	23.0681i	0.333477	+	0.805084i	0.998311	+	0.0580931i	$0.0185020\pi$
$821$	9.55514	+	23.0681i	0.333477	+	0.805084i	−0.664835	+	0.746991i	$0.731498\pi$
$822$	−16.5147	−	6.84060i	−0.576015	−	0.238593i
$823$	−11.0503	+	26.6778i	−0.385190	+	0.929931i	0.605753	+	0.795652i	$0.292872\pi$
$823$	−11.0503	+	26.6778i	−0.385190	+	0.929931i	−0.990944	+	0.134279i	$0.957128\pi$
$824$	−1.04702	+	1.04702i	−0.0364745	+	0.0364745i
$825$		0			0
$826$	23.2019	−	56.0144i	0.807298	−	1.94899i
$827$	14.9690	+	6.20037i	0.520524	+	0.215608i	0.627447	−	0.778659i	$-0.284100\pi$
$827$	14.9690	+	6.20037i	0.520524	+	0.215608i	−0.106923	+	0.994267i	$0.534100\pi$
$828$	0.976095	+	2.35650i	0.0339216	+	0.0818941i
$829$			22.2311i			0.772117i	0.922474	+	0.386058i	$0.126164\pi$
$829$			22.2311i			0.772117i	−0.922474	+	0.386058i	$0.873836\pi$
$830$		0			0
$831$	15.3286	+	15.3286i	0.531744	+	0.531744i
$832$	29.1641			1.01108
$833$	−0.820464	+	0.102824i	−0.0284274	+	0.00356266i
$834$	−3.13090			−0.108414
$835$		0			0
$836$	1.48150	−	0.613656i	0.0512386	−	0.0212237i
$837$			48.7546i			1.68521i
$838$	11.4918	+	27.7436i	0.396977	+	0.958386i
$839$	−43.2196	−	17.9021i	−1.49211	−	0.618051i	−0.520332	−	0.853964i	$-0.674192\pi$
$839$	−43.2196	−	17.9021i	−1.49211	−	0.618051i	−0.971774	+	0.235914i	$0.924192\pi$
$840$		0			0
$841$	−50.6764	+	50.6764i	−1.74746	+	1.74746i
$842$	−43.0675	+	43.0675i	−1.48420	+	1.48420i
$843$	19.4858	−	47.0428i	0.671125	−	1.62024i
$844$	−51.4751	−	21.3217i	−1.77185	−	0.733923i
$845$		0			0
$846$			0.478741i			0.0164594i
$847$	24.9100	−	10.3181i	0.855919	−	0.354533i
$848$	−5.93039	−	5.93039i	−0.203650	−	0.203650i
$849$	−30.8359			−1.05829
$850$		0			0
$851$	−27.5851			−0.945604
$852$	−3.49205	−	3.49205i	−0.119636	−	0.119636i
$853$	35.4475	−	14.6828i	1.21370	−	0.502731i	0.318299	−	0.947990i	$-0.396889\pi$
$853$	35.4475	−	14.6828i	1.21370	−	0.502731i	0.895402	+	0.445259i	$0.146889\pi$
$854$		−	11.7048i		−	0.400529i
$855$		0			0
$856$	4.66658	+	1.93296i	0.159500	+	0.0660672i
$857$	2.11426	−	5.10428i	0.0722218	−	0.174359i	−0.883646	−	0.468155i	$-0.844919\pi$
$857$	2.11426	−	5.10428i	0.0722218	−	0.174359i	0.955868	+	0.293796i	$0.0949188\pi$
$858$	−6.95529	+	6.95529i	−0.237450	+	0.237450i
$859$	−10.1314	+	10.1314i	−0.345680	+	0.345680i	−0.858498	−	0.512817i	$-0.828602\pi$
$859$	−10.1314	+	10.1314i	−0.345680	+	0.345680i	0.512817	+	0.858498i	$0.328602\pi$
$860$		0			0
$861$	−32.7737	−	13.5753i	−1.11692	−	0.462645i
$862$	16.5580	+	39.9746i	0.563969	+	1.36154i
$863$			9.68459i			0.329667i	0.986321	+	0.164834i	$0.0527087\pi$
$863$			9.68459i			0.329667i	−0.986321	+	0.164834i	$0.947291\pi$
$864$	−36.6974	+	15.2006i	−1.24847	+	0.517134i
$865$		0			0
$866$	−50.9025			−1.72974
$867$	18.3811	+	24.5825i	0.624255	+	0.834864i
$868$	64.2833			2.18192
$869$	−0.282196	−	0.282196i	−0.00957284	−	0.00957284i
$870$		0			0
$871$		−	15.2245i		−	0.515862i
$872$	−0.915599	−	2.21045i	−0.0310061	−	0.0748553i
$873$	−3.70362	−	1.53409i	−0.125349	−	0.0519211i
$874$	2.19724	−	5.30462i	0.0743229	−	0.179431i
$875$		0			0
$876$	9.30590	−	9.30590i	0.314417	−	0.314417i
$877$	5.72500	−	13.8214i	0.193319	−	0.466714i	−0.797263	−	0.603632i	$-0.793720\pi$
$877$	5.72500	−	13.8214i	0.193319	−	0.466714i	0.990582	+	0.136918i	$0.0437196\pi$
$878$	−42.8711	−	17.7578i	−1.44683	−	0.599297i
$879$	−4.71625	−	11.3860i	−0.159075	−	0.384041i
$880$		0			0
$881$	9.80896	−	4.06301i	0.330472	−	0.136886i	−0.211277	−	0.977426i	$-0.567762\pi$
$881$	9.80896	−	4.06301i	0.330472	−	0.136886i	0.541749	+	0.840540i	$0.317762\pi$
$882$	0.0776330	+	0.0776330i	0.00261404	+	0.00261404i
$883$	52.5251			1.76761			0.883805	−	0.467855i	$-0.154973\pi$
$883$	52.5251			1.76761			0.883805	+	0.467855i	$0.154973\pi$
$884$	16.3141	−	20.9891i	0.548703	−	0.705941i
$885$		0			0
$886$	48.1243	+	48.1243i	1.61677	+	1.61677i
$887$	15.8819	−	6.57850i	0.533262	−	0.220884i	−0.0997691	−	0.995011i	$-0.531810\pi$
$887$	15.8819	−	6.57850i	0.533262	−	0.220884i	0.633031	+	0.774126i	$0.281810\pi$
$888$		−	11.1950i		−	0.375680i
$889$	10.9356	+	26.4009i	0.366768	+	0.885457i
$890$		0			0
$891$	3.62669	−	8.75561i	0.121499	−	0.293324i
$892$	22.4412	−	22.4412i	0.751386	−	0.751386i
$893$	0.418062	−	0.418062i	0.0139899	−	0.0139899i
$894$	13.9673	−	33.7200i	0.467135	−	1.12776i
$895$		0			0
$896$	7.27703	+	17.5683i	0.243108	+	0.586916i
$897$			19.3220i			0.645143i
$898$	61.0075	−	25.2701i	2.03585	−	0.843276i
$899$	69.9185	+	69.9185i	2.33191	+	2.33191i
$900$		0			0
$901$	−11.6201	+	1.45629i	−0.387122	+	0.0485160i
$902$	15.0380			0.500712
$903$	−30.5057	−	30.5057i	−1.01517	−	1.01517i
$904$	4.86673	−	2.01586i	0.161865	−	0.0670467i
$905$		0			0
$906$	−2.06057	−	4.97465i	−0.0684577	−	0.165272i
$907$	10.3374	+	4.28190i	0.343248	+	0.142178i	0.547647	−	0.836710i	$-0.315524\pi$
$907$	10.3374	+	4.28190i	0.343248	+	0.142178i	−0.204398	+	0.978888i	$0.565524\pi$
$908$	−9.95305	+	24.0288i	−0.330304	+	0.797423i
$909$	2.68941	−	2.68941i	0.0892022	−	0.0892022i
$910$		0			0
$911$	1.24981	−	3.01730i	0.0414080	−	0.0999677i	−0.901822	−	0.432107i	$-0.857770\pi$
$911$	1.24981	−	3.01730i	0.0414080	−	0.0999677i	0.943230	+	0.332139i	$0.107770\pi$
$912$	−3.33008	−	1.37936i	−0.110270	−	0.0456753i
$913$	2.45471	+	5.92619i	0.0812390	+	0.196128i
$914$		−	26.8343i		−	0.887599i
$915$		0			0
$916$	−32.3715	−	32.3715i	−1.06958	−	1.06958i
$917$	4.34296			0.143417
$918$	−11.3705	+	41.4027i	−0.375284	+	1.36649i
$919$	−32.6905			−1.07836			−0.539179	−	0.842191i	$-0.681265\pi$
$919$	−32.6905			−1.07836			−0.539179	+	0.842191i	$0.681265\pi$
$920$		0			0
$921$	1.24490	−	0.515655i	0.0410209	−	0.0169914i
$922$			36.6220i			1.20608i
$923$	−1.14211	−	2.75729i	−0.0375930	−	0.0907574i
$924$	−10.6170	−	4.39769i	−0.349272	−	0.144673i
$925$		0			0
$926$	44.0198	−	44.0198i	1.44658	−	1.44658i
$927$	−0.300273	+	0.300273i	−0.00986227	+	0.00986227i
$928$	−30.8284	+	74.4264i	−1.01199	+	2.44317i
$929$	7.83598	+	3.24577i	0.257090	+	0.106490i	0.507506	−	0.861648i	$-0.330567\pi$
$929$	7.83598	+	3.24577i	0.257090	+	0.106490i	−0.250416	+	0.968138i	$0.580567\pi$
$930$		0			0
$931$		−	0.135586i		−	0.00444367i
$932$	5.04381	−	2.08921i	0.165215	−	0.0684344i
$933$	23.2368	+	23.2368i	0.760739	+	0.760739i
$934$	−69.2208			−2.26497
$935$		0			0
$936$	−0.625569			−0.0204473
$937$	−22.0610	−	22.0610i	−0.720703	−	0.720703i	0.248045	−	0.968748i	$-0.420212\pi$
$937$	−22.0610	−	22.0610i	−0.720703	−	0.720703i	−0.968748	+	0.248045i	$0.920212\pi$
$938$	29.9533	−	12.4071i	0.978009	−	0.405105i
$939$		−	17.9184i		−	0.584744i
$940$		0			0
$941$	19.9946	+	8.28202i	0.651804	+	0.269986i	0.683985	−	0.729496i	$-0.260245\pi$
$941$	19.9946	+	8.28202i	0.651804	+	0.269986i	−0.0321810	+	0.999482i	$0.510245\pi$
$942$	−7.00868	+	16.9204i	−0.228355	+	0.551298i
$943$	20.8880	−	20.8880i	0.680208	−	0.680208i
$944$	22.4116	−	22.4116i	0.729435	−	0.729435i
$945$		0			0
$946$	16.8963	+	6.99868i	0.549347	+	0.227547i
$947$	−1.50513	−	3.63370i	−0.0489101	−	0.118079i	0.897536	−	0.440941i	$-0.145355\pi$
$947$	−1.50513	−	3.63370i	−0.0489101	−	0.118079i	−0.946446	+	0.322862i	$0.895355\pi$
$948$		−	1.79513i		−	0.0583031i
$949$	7.34786	−	3.04358i	0.238522	−	0.0987989i
$950$		0			0
$951$	43.8964			1.42344
$952$	9.67506	+	2.65708i	0.313571	+	0.0861166i
$953$	4.24356			0.137462			0.0687312	−	0.997635i	$-0.478105\pi$
$953$	4.24356			0.137462			0.0687312	+	0.997635i	$0.478105\pi$
$954$	1.09950	+	1.09950i	0.0355978	+	0.0355978i
$955$		0			0
$956$		−	40.6658i		−	1.31523i
$957$	−6.76447	−	16.3309i	−0.218664	−	0.527902i
$958$	1.15479	+	0.478328i	0.0373095	+	0.0154541i
$959$	4.82971	−	11.6600i	0.155959	−	0.376519i
$960$		0			0
$961$	46.7567	−	46.7567i	1.50828	−	1.50828i
$962$	14.6081	−	35.2671i	0.470985	−	1.13706i
$963$	1.33833	+	0.554353i	0.0431270	+	0.0178638i
$964$	10.9515	+	26.4392i	0.352723	+	0.851549i
$965$		0			0
$966$	−38.0149	+	15.7463i	−1.22311	+	0.506628i
$967$	−25.3036	−	25.3036i	−0.813708	−	0.813708i	0.171480	−	0.985188i	$-0.445145\pi$
$967$	−25.3036	−	25.3036i	−0.813708	−	0.813708i	−0.985188	+	0.171480i	$0.945145\pi$
$968$	−9.11197			−0.292870
$969$	−4.37437	+	2.48937i	−0.140525	+	0.0799700i
$970$		0			0
$971$	−26.0013	−	26.0013i	−0.834423	−	0.834423i	0.153695	−	0.988118i	$-0.450883\pi$
$971$	−26.0013	−	26.0013i	−0.834423	−	0.834423i	−0.988118	+	0.153695i	$0.950883\pi$
$972$	6.05324	−	2.50733i	0.194158	−	0.0804228i
$973$		−	2.21053i		−	0.0708664i
$974$	1.81468	+	4.38103i	0.0581462	+	0.140377i
$975$		0			0
$976$	2.34156	−	5.65303i	0.0749516	−	0.180949i
$977$	18.3472	−	18.3472i	0.586977	−	0.586977i	−0.349834	−	0.936812i	$-0.613762\pi$
$977$	18.3472	−	18.3472i	0.586977	−	0.586977i	0.936812	+	0.349834i	$0.113762\pi$
$978$	4.35104	−	4.35104i	0.139131	−	0.139131i
$979$	−2.10094	+	5.07211i	−0.0671463	+	0.162105i
$980$		0			0
$981$	−0.262585	−	0.633935i	−0.00838368	−	0.0202400i
$982$			15.3652i			0.490322i
$983$	−30.5712	+	12.6630i	−0.975071	+	0.403888i	−0.812598	−	0.582825i	$-0.801947\pi$
$983$	−30.5712	+	12.6630i	−0.975071	+	0.403888i	−0.162474	+	0.986713i	$0.551947\pi$
$984$	8.47711	+	8.47711i	0.270241	+	0.270241i
$985$		0			0
$986$	43.0689	+	75.6817i	1.37159	+	2.41020i
$987$	−4.23697			−0.134864
$988$	3.08229	+	3.08229i	0.0980606	+	0.0980606i
$989$	33.1905	−	13.7480i	1.05540	−	0.437160i
$990$		0			0
$991$	13.3710	+	32.2804i	0.424744	+	1.02542i	0.980930	+	0.194364i	$0.0622643\pi$
$991$	13.3710	+	32.2804i	0.424744	+	1.02542i	−0.556186	+	0.831058i	$0.687736\pi$
$992$	73.1049	+	30.2810i	2.32108	+	0.961423i
$993$	0.338407	−	0.816987i	0.0107390	−	0.0259263i
$994$	4.49406	−	4.49406i	0.142543	−	0.142543i
$995$		0			0
$996$	−11.0416	+	26.6567i	−0.349865	+	0.844649i
$997$	−15.1950	−	6.29396i	−0.481229	−	0.199332i	0.128862	−	0.991662i	$-0.458867\pi$
$997$	−15.1950	−	6.29396i	−0.481229	−	0.199332i	−0.610092	+	0.792331i	$0.708867\pi$
$998$	−6.12244	−	14.7809i	−0.193802	−	0.467881i
$999$			33.8241i			1.07015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.m.e.376.1		24
5.2	odd	4		85.2.m.a.19.6	yes	24
5.3	odd	4		85.2.m.a.19.1	yes	24
5.4	even	2	inner	425.2.m.e.376.6		24
15.2	even	4		765.2.bh.b.19.1		24
15.8	even	4		765.2.bh.b.19.6		24
17.3	odd	16		7225.2.a.by.1.3		24
17.9	even	8	inner	425.2.m.e.26.1		24
17.14	odd	16		7225.2.a.by.1.4		24
85.3	even	16		1445.2.b.i.579.21		24
85.9	even	8	inner	425.2.m.e.26.6		24
85.14	odd	16		7225.2.a.by.1.21		24
85.37	even	16		1445.2.b.i.579.4		24
85.43	odd	8		85.2.m.a.9.6	yes	24
85.48	even	16		1445.2.b.i.579.22		24
85.54	odd	16		7225.2.a.by.1.22		24
85.77	odd	8		85.2.m.a.9.1	✓	24
85.82	even	16		1445.2.b.i.579.3		24
255.77	even	8		765.2.bh.b.604.6		24
255.128	even	8		765.2.bh.b.604.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.m.a.9.1	✓	24	85.77	odd	8
85.2.m.a.9.6	yes	24	85.43	odd	8
85.2.m.a.19.1	yes	24	5.3	odd	4
85.2.m.a.19.6	yes	24	5.2	odd	4
425.2.m.e.26.1		24	17.9	even	8	inner
425.2.m.e.26.6		24	85.9	even	8	inner
425.2.m.e.376.1		24	1.1	even	1	trivial
425.2.m.e.376.6		24	5.4	even	2	inner
765.2.bh.b.19.1		24	15.2	even	4
765.2.bh.b.19.6		24	15.8	even	4
765.2.bh.b.604.1		24	255.128	even	8
765.2.bh.b.604.6		24	255.77	even	8
1445.2.b.i.579.3		24	85.82	even	16
1445.2.b.i.579.4		24	85.37	even	16
1445.2.b.i.579.21		24	85.3	even	16
1445.2.b.i.579.22		24	85.48	even	16
7225.2.a.by.1.3		24	17.3	odd	16
7225.2.a.by.1.4		24	17.14	odd	16
7225.2.a.by.1.21		24	85.14	odd	16
7225.2.a.by.1.22		24	85.54	odd	16

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.48843 - 1.48843i) q^{2} +(-1.66813 + 0.690961i) q^{3} +2.43082i q^{4} +(3.51133 + 1.45444i) q^{6} +(-1.02689 + 2.47912i) q^{7} +(0.641241 - 0.641241i) q^{8} +(0.183901 - 0.183901i) q^{9} +(-0.901470 - 0.373401i) q^{11} +(-1.67960 - 4.05491i) q^{12} -2.65240i q^{13} +(5.21843 - 2.16155i) q^{14} +2.95276 q^{16} +(2.53030 - 3.25539i) q^{17} -0.547447 q^{18} +(0.478059 + 0.478059i) q^{19} -4.84503i q^{21} +(0.785991 + 1.89755i) q^{22} +(3.72748 + 1.54397i) q^{23} +(-0.626599 + 1.51274i) q^{24} +(-3.94790 + 3.94790i) q^{26} +(1.89318 - 4.57054i) q^{27} +(-6.02630 - 2.49617i) q^{28} +(-3.83958 - 9.26957i) q^{29} +(-9.10497 + 3.77140i) q^{31} +(-5.67744 - 5.67744i) q^{32} +1.76177 q^{33} +(-8.61157 + 1.07924i) q^{34} +(0.447031 + 0.447031i) q^{36} +(-6.31669 + 2.61646i) q^{37} -1.42311i q^{38} +(1.83270 + 4.42454i) q^{39} +(2.80190 - 6.76439i) q^{41} +(-7.21147 + 7.21147i) q^{42} +(6.29628 - 6.29628i) q^{43} +(0.907670 - 2.19131i) q^{44} +(-3.24999 - 7.84616i) q^{46} -0.874497i q^{47} +(-4.92558 + 2.04024i) q^{48} +(-0.141809 - 0.141809i) q^{49} +(-1.97152 + 7.17875i) q^{51} +6.44750 q^{52} +(-2.00842 - 2.00842i) q^{53} +(-9.62077 + 3.98505i) q^{54} +(0.931234 + 2.24820i) q^{56} +(-1.12778 - 0.467144i) q^{57} +(-8.08213 + 19.5120i) q^{58} +(7.59005 - 7.59005i) q^{59} +(0.793008 - 1.91449i) q^{61} +(19.1655 + 7.93862i) q^{62} +(0.267068 + 0.644760i) q^{63} +10.9954i q^{64} +(-2.62227 - 2.62227i) q^{66} +5.73990 q^{67} +(7.91327 + 6.15070i) q^{68} -7.28473 q^{69} +(1.03955 - 0.430595i) q^{71} -0.235850i q^{72} +(1.14748 + 2.77027i) q^{73} +(13.2963 + 5.50752i) q^{74} +(-1.16208 + 1.16208i) q^{76} +(1.85141 - 1.85141i) q^{77} +(3.85775 - 9.31343i) q^{78} +(0.377872 + 0.156520i) q^{79} +9.71259i q^{81} +(-14.2387 + 5.89786i) q^{82} +(-4.64846 - 4.64846i) q^{83} +11.7774 q^{84} -18.7431 q^{86} +(12.8098 + 12.8098i) q^{87} +(-0.817499 + 0.338619i) q^{88} -5.62649i q^{89} +(6.57562 + 2.72371i) q^{91} +(-3.75312 + 9.06082i) q^{92} +(12.5824 - 12.5824i) q^{93} +(-1.30162 + 1.30162i) q^{94} +(13.3936 + 5.54781i) q^{96} +(-5.89862 - 14.2405i) q^{97} +0.422145i q^{98} +(-0.234451 + 0.0971126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{9} + 24 q^{14} + 8 q^{16} + 24 q^{19} - 32 q^{24} - 16 q^{26} - 24 q^{29} - 24 q^{31} - 8 q^{34} + 8 q^{36} + 24 q^{39} - 48 q^{41} - 72 q^{44} - 16 q^{46} - 48 q^{49} - 32 q^{54} + 24 q^{56}+ \cdots + 80 q^{99}+O(q^{100}) \) 24 * q + 8 * q^9 + 24 * q^14 + 8 * q^16 + 24 * q^19 - 32 * q^24 - 16 * q^26 - 24 * q^29 - 24 * q^31 - 8 * q^34 + 8 * q^36 + 24 * q^39 - 48 * q^41 - 72 * q^44 - 16 * q^46 - 48 * q^49 - 32 * q^54 + 24 * q^56 + 48 * q^59 + 16 * q^61 - 96 * q^66 - 32 * q^69 + 16 * q^71 + 64 * q^74 - 24 * q^76 + 72 * q^79 + 96 * q^84 - 8 * q^91 + 40 * q^94 + 96 * q^96 + 80 * q^99

Introduction

L-functions

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