LMFDB - Embedded newform 927.2.ba.e.244.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [927,2,Mod(19,927)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(927, base_ring=CyclotomicField(102))

chi = DirichletCharacter(H, H._module([0, 80]))

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

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

chi := DirichletCharacter("927.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 927 = 3^{2} \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	927.ba (of order $51$, degree $32$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.40213226737$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$16$ over $\Q(\zeta_{51})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{51}]$

Embedding invariants

Embedding label			244.2
Character	$\chi$	$=$	927.244
Dual form			927.2.ba.e.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0760154 - 2.46726i) q^{2} +(-4.08537 + 0.251977i) q^{4} +(-1.39599 - 1.12335i) q^{5} +(4.25142 - 1.95596i) q^{7} +(0.476728 + 5.14471i) q^{8} +O(q^{10})$	\(q+(-0.0760154 - 2.46726i) q^{2} +(-4.08537 + 0.251977i) q^{4} +(-1.39599 - 1.12335i) q^{5} +(4.25142 - 1.95596i) q^{7} +(0.476728 + 5.14471i) q^{8} +(-2.66547 + 3.52965i) q^{10} +(-0.187871 - 0.100885i) q^{11} +(0.503740 - 5.43622i) q^{13} +(-5.14903 - 10.3407i) q^{14} +(4.53287 - 0.561291i) q^{16} +(-3.57573 - 1.13752i) q^{17} +(3.23995 + 3.34131i) q^{19} +(5.98618 + 4.23753i) q^{20} +(-0.234627 + 0.471195i) q^{22} +(-3.09247 - 1.91478i) q^{23} +(-0.382795 - 1.74789i) q^{25} +(-13.4508 - 0.829619i) q^{26} +(-16.8758 + 9.06209i) q^{28} +(0.799399 - 5.14981i) q^{29} +(1.50349 + 1.99094i) q^{31} +(-0.144342 - 0.929866i) q^{32} +(-2.53475 + 8.90871i) q^{34} +(-8.13213 - 2.04531i) q^{35} +(-3.52794 - 0.659487i) q^{37} +(7.99759 - 8.24778i) q^{38} +(5.11378 - 7.71747i) q^{40} +(-7.51890 + 6.05043i) q^{41} +(-1.05309 + 2.98846i) q^{43} +(0.792945 + 0.364812i) q^{44} +(-4.48918 + 7.77548i) q^{46} +(1.73543 + 3.00586i) q^{47} +(9.69442 - 11.3154i) q^{49} +(-4.28341 + 1.07732i) q^{50} +(-0.688162 + 22.3359i) q^{52} +(12.1347 - 3.05201i) q^{53} +(0.148937 + 0.351878i) q^{55} +(12.0896 + 20.9399i) q^{56} +(-12.7667 - 1.58086i) q^{58} +(7.60879 + 3.50060i) q^{59} +(-6.09150 + 5.55314i) q^{61} +(4.79788 - 3.86084i) q^{62} +(6.69619 - 1.25173i) q^{64} +(-6.80996 + 7.02300i) q^{65} +(-9.84293 + 6.96767i) q^{67} +(14.8948 + 3.74620i) q^{68} +(-4.42815 + 20.2195i) q^{70} +(1.00182 + 6.45385i) q^{71} +(-4.26958 - 1.65404i) q^{73} +(-1.35895 + 8.75447i) q^{74} +(-14.0783 - 12.8341i) q^{76} +(-0.996045 - 0.0614340i) q^{77} +(-6.01983 + 2.33210i) q^{79} +(-6.95834 - 4.30842i) q^{80} +(15.4995 + 18.0911i) q^{82} +(4.65485 + 3.29510i) q^{83} +(3.71384 + 5.60474i) q^{85} +(7.45335 + 2.37108i) q^{86} +(0.429459 - 1.01464i) q^{88} +(-7.17882 - 14.4170i) q^{89} +(-8.49142 - 24.0969i) q^{91} +(13.1164 + 7.04335i) q^{92} +(7.28430 - 4.51025i) q^{94} +(-0.769479 - 8.30401i) q^{95} +(7.52916 - 2.39520i) q^{97} +(-28.6549 - 23.0585i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q + 18 q^{4} - 8 q^{7}+O(q^{10}) $ 512 * q + 18 * q^4 - 8 * q^7	$ 512 q + 18 q^{4} - 8 q^{7} - 36 q^{10} + 4 q^{13} + 18 q^{16} + 30 q^{19} + 40 q^{22} - 42 q^{25} - 110 q^{28} - 32 q^{31} - 110 q^{34} + 48 q^{37} - 22 q^{40} - 2 q^{43} + 152 q^{46} + 76 q^{49} + 68 q^{52} + 32 q^{55} - 44 q^{58} + 20 q^{61} - 170 q^{64} - 8 q^{67} - 38 q^{70} - 4 q^{73} + 188 q^{76} + 20 q^{79} + 212 q^{82} + 60 q^{85} + 164 q^{88} - 310 q^{91} + 228 q^{94} - 100 q^{97}+O(q^{100}) $ 512 * q + 18 * q^4 - 8 * q^7 - 36 * q^10 + 4 * q^13 + 18 * q^16 + 30 * q^19 + 40 * q^22 - 42 * q^25 - 110 * q^28 - 32 * q^31 - 110 * q^34 + 48 * q^37 - 22 * q^40 - 2 * q^43 + 152 * q^46 + 76 * q^49 + 68 * q^52 + 32 * q^55 - 44 * q^58 + 20 * q^61 - 170 * q^64 - 8 * q^67 - 38 * q^70 - 4 * q^73 + 188 * q^76 + 20 * q^79 + 212 * q^82 + 60 * q^85 + 164 * q^88 - 310 * q^91 + 228 * q^94 - 100 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/927\mathbb{Z}\right)^\times$.

$n$	$722$	$829$
$\chi(n)$	$1$	$e\left(\frac{11}{51}\right)$

Coefficient data

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

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

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

$2$	−0.0760154	−	2.46726i	−0.0537510	−	1.74461i	−0.514863	−	0.857272i	$-0.672157\pi$
$2$	−0.0760154	−	2.46726i	−0.0537510	−	1.74461i	0.461112	−	0.887342i	$-0.347451\pi$
$3$		0			0
$3$		0			0
$4$	−4.08537	+	0.251977i	−2.04269	+	0.125989i
$5$	−1.39599	−	1.12335i	−0.624304	−	0.502375i	0.262251	−	0.965000i	$-0.415535\pi$
$5$	−1.39599	−	1.12335i	−0.624304	−	0.502375i	−0.886554	+	0.462625i	$0.846908\pi$
$6$		0			0
$7$	4.25142	−	1.95596i	1.60688	−	0.739284i	0.608363	−	0.793659i	$-0.291826\pi$
$7$	4.25142	−	1.95596i	1.60688	−	0.739284i	0.998521	+	0.0543746i	$0.0173165\pi$
$8$	0.476728	+	5.14471i	0.168549	+	1.81893i
$9$		0			0
$10$	−2.66547	+	3.52965i	−0.842894	+	1.11617i
$11$	−0.187871	−	0.100885i	−0.0566453	−	0.0304179i	0.444526	−	0.895766i	$-0.353372\pi$
$11$	−0.187871	−	0.100885i	−0.0566453	−	0.0304179i	−0.501172	+	0.865348i	$0.667097\pi$
$12$		0			0
$13$	0.503740	−	5.43622i	0.139712	−	1.50774i	−0.580659	−	0.814147i	$-0.697205\pi$
$13$	0.503740	−	5.43622i	0.139712	−	1.50774i	0.720372	−	0.693588i	$-0.243971\pi$
$14$	−5.14903	−	10.3407i	−1.37614	−	2.76366i
$15$		0			0
$16$	4.53287	−	0.561291i	1.13322	−	0.140323i
$17$	−3.57573	−	1.13752i	−0.867242	−	0.275890i	−0.163671	−	0.986515i	$-0.552334\pi$
$17$	−3.57573	−	1.13752i	−0.867242	−	0.275890i	−0.703571	+	0.710625i	$0.748412\pi$
$18$		0			0
$19$	3.23995	+	3.34131i	0.743296	+	0.766549i	0.978688	−	0.205351i	$-0.0658336\pi$
$19$	3.23995	+	3.34131i	0.743296	+	0.766549i	−0.235392	+	0.971900i	$0.575638\pi$
$20$	5.98618	+	4.23753i	1.33855	+	0.947540i
$21$		0			0
$22$	−0.234627	+	0.471195i	−0.0500227	+	0.100459i
$23$	−3.09247	−	1.91478i	−0.644826	−	0.399259i	0.164700	−	0.986344i	$-0.447334\pi$
$23$	−3.09247	−	1.91478i	−0.644826	−	0.399259i	−0.809526	+	0.587085i	$0.800276\pi$
$24$		0			0
$25$	−0.382795	−	1.74789i	−0.0765590	−	0.349579i
$26$	−13.4508	−	0.829619i	−2.63793	−	0.162702i
$27$		0			0
$28$	−16.8758	+	9.06209i	−3.18922	+	1.71257i
$29$	0.799399	−	5.14981i	0.148445	−	0.956296i	−0.790558	−	0.612387i	$-0.790209\pi$
$29$	0.799399	−	5.14981i	0.148445	−	0.956296i	0.939003	−	0.343909i	$-0.111751\pi$
$30$		0			0
$31$	1.50349	+	1.99094i	0.270035	+	0.357584i	0.912748	−	0.408523i	$-0.133956\pi$
$31$	1.50349	+	1.99094i	0.270035	+	0.357584i	−0.642713	+	0.766107i	$0.722191\pi$
$32$	−0.144342	−	0.929866i	−0.0255163	−	0.164379i
$33$		0			0
$34$	−2.53475	+	8.90871i	−0.434706	+	1.52783i
$35$	−8.13213	−	2.04531i	−1.37458	−	0.345721i
$36$		0			0
$37$	−3.52794	−	0.659487i	−0.579990	−	0.108419i	−0.114424	−	0.993432i	$-0.536502\pi$
$37$	−3.52794	−	0.659487i	−0.579990	−	0.108419i	−0.465566	+	0.885013i	$0.654149\pi$
$38$	7.99759	−	8.24778i	1.29738	−	1.33797i
$39$		0			0
$40$	5.11378	−	7.71747i	0.808560	−	1.22024i
$41$	−7.51890	+	6.05043i	−1.17425	+	0.944919i	−0.999214	−	0.0396425i	$-0.987378\pi$
$41$	−7.51890	+	6.05043i	−1.17425	+	0.944919i	−0.175040	+	0.984561i	$0.556006\pi$
$42$		0			0
$43$	−1.05309	+	2.98846i	−0.160595	+	0.455736i	−0.995511	−	0.0946411i	$-0.969830\pi$
$43$	−1.05309	+	2.98846i	−0.160595	+	0.455736i	0.834916	+	0.550377i	$0.185516\pi$
$44$	0.792945	+	0.364812i	0.119541	+	0.0549975i
$45$		0			0
$46$	−4.48918	+	7.77548i	−0.661893	+	1.14643i
$47$	1.73543	+	3.00586i	0.253139	+	0.438449i	0.964388	−	0.264490i	$-0.0852038\pi$
$47$	1.73543	+	3.00586i	0.253139	+	0.438449i	−0.711250	+	0.702940i	$0.751870\pi$
$48$		0			0
$49$	9.69442	−	11.3154i	1.38492	−	1.61648i
$50$	−4.28341	+	1.07732i	−0.605765	+	0.152356i
$51$		0			0
$52$	−0.688162	+	22.3359i	−0.0954308	+	3.09743i
$53$	12.1347	−	3.05201i	1.66683	−	0.419226i	0.708692	−	0.705518i	$-0.249286\pi$
$53$	12.1347	−	3.05201i	1.66683	−	0.419226i	0.958142	+	0.286293i	$0.0924230\pi$
$54$		0			0
$55$	0.148937	+	0.351878i	0.0200827	+	0.0474472i
$56$	12.0896	+	20.9399i	1.61554	+	2.79821i
$57$		0			0
$58$	−12.7667	−	1.58086i	−1.67635	−	0.207577i
$59$	7.60879	+	3.50060i	0.990580	+	0.455739i	0.845670	−	0.533706i	$-0.179201\pi$
$59$	7.60879	+	3.50060i	0.990580	+	0.455739i	0.144909	+	0.989445i	$0.453711\pi$
$60$		0			0
$61$	−6.09150	+	5.55314i	−0.779937	+	0.711006i	−0.962230	−	0.272238i	$-0.912236\pi$
$61$	−6.09150	+	5.55314i	−0.779937	+	0.711006i	0.182293	+	0.983244i	$0.441648\pi$
$62$	4.79788	−	3.86084i	0.609331	−	0.490327i
$63$		0			0
$64$	6.69619	−	1.25173i	0.837023	−	0.156467i
$65$	−6.80996	+	7.02300i	−0.844672	+	0.871097i
$66$		0			0
$67$	−9.84293	+	6.96767i	−1.20251	+	0.851236i	−0.991985	−	0.126353i	$-0.959673\pi$
$67$	−9.84293	+	6.96767i	−1.20251	+	0.851236i	−0.210521	+	0.977589i	$0.567516\pi$
$68$	14.8948	+	3.74620i	1.80626	+	0.454293i
$69$		0			0
$70$	−4.42815	+	20.2195i	−0.529265	+	2.41670i
$71$	1.00182	+	6.45385i	0.118894	+	0.765931i	0.970386	+	0.241562i	$0.0776596\pi$
$71$	1.00182	+	6.45385i	0.118894	+	0.765931i	−0.851491	+	0.524369i	$0.824301\pi$
$72$		0			0
$73$	−4.26958	−	1.65404i	−0.499716	−	0.193591i	0.0981739	−	0.995169i	$-0.468700\pi$
$73$	−4.26958	−	1.65404i	−0.499716	−	0.193591i	−0.597890	+	0.801578i	$0.703994\pi$
$74$	−1.35895	+	8.75447i	−0.157974	+	1.01769i
$75$		0			0
$76$	−14.0783	−	12.8341i	−1.61490	−	1.47217i
$77$	−0.996045	−	0.0614340i	−0.113510	−	0.00700105i
$78$		0			0
$79$	−6.01983	+	2.33210i	−0.677284	+	0.262381i	−0.675220	−	0.737617i	$-0.735951\pi$
$79$	−6.01983	+	2.33210i	−0.677284	+	0.262381i	−0.00206427	+	0.999998i	$0.500657\pi$
$80$	−6.95834	−	4.30842i	−0.777966	−	0.481696i
$81$		0			0
$82$	15.4995	+	18.0911i	1.71164	+	1.99783i
$83$	4.65485	+	3.29510i	0.510936	+	0.361684i	0.804211	−	0.594344i	$-0.202588\pi$
$83$	4.65485	+	3.29510i	0.510936	+	0.361684i	−0.293275	+	0.956028i	$0.594745\pi$
$84$		0			0
$85$	3.71384	+	5.60474i	0.402822	+	0.607920i
$86$	7.45335	+	2.37108i	0.803715	+	0.255680i
$87$		0			0
$88$	0.429459	−	1.01464i	0.0457805	−	0.108161i
$89$	−7.17882	−	14.4170i	−0.760953	−	1.52820i	−0.846812	−	0.531892i	$-0.821481\pi$
$89$	−7.17882	−	14.4170i	−0.760953	−	1.52820i	0.0858591	−	0.996307i	$-0.472637\pi$
$90$		0			0
$91$	−8.49142	−	24.0969i	−0.890143	−	2.52604i
$92$	13.1164	+	7.04335i	1.36748	+	0.734320i
$93$		0			0
$94$	7.28430	−	4.51025i	0.751318	−	0.465196i
$95$	−0.769479	−	8.30401i	−0.0789469	−	0.851973i
$96$		0			0
$97$	7.52916	−	2.39520i	0.764470	−	0.243196i	0.104538	−	0.994521i	$-0.466664\pi$
$97$	7.52916	−	2.39520i	0.764470	−	0.243196i	0.659932	+	0.751325i	$0.270585\pi$
$98$	−28.6549	−	23.0585i	−2.89458	−	2.32926i
$99$		0			0
$100$	2.00429	+	7.04434i	0.200429	+	0.704434i
$101$	−0.504726	−	16.3820i	−0.0502221	−	1.63007i	−0.603700	−	0.797211i	$-0.706308\pi$
$101$	−0.504726	−	16.3820i	−0.0502221	−	1.63007i	0.553478	−	0.832864i	$-0.313300\pi$
$102$		0			0
$103$	3.14859	−	9.64813i	0.310240	−	0.950658i
$103$	3.14859	−	9.64813i	0.310240	−	0.950658i
$104$	28.2079			2.76601
$105$		0			0
$106$	−8.45251	−	29.7075i	−0.820981	−	2.88545i
$107$	−4.60013	+	0.283726i	−0.444711	+	0.0274288i	−0.282369	−	0.959306i	$-0.591120\pi$
$107$	−4.60013	+	0.283726i	−0.444711	+	0.0274288i	−0.162342	+	0.986735i	$0.551905\pi$
$108$		0			0
$109$	−2.18624	+	0.695493i	−0.209404	+	0.0666162i	−0.406019	−	0.913865i	$-0.633083\pi$
$109$	−2.18624	+	0.695493i	−0.209404	+	0.0666162i	0.196615	+	0.980481i	$0.437005\pi$
$110$	0.856852	−	0.394214i	0.0816976	−	0.0375869i
$111$		0			0
$112$	18.1732	−	11.2524i	1.71721	−	1.06325i
$113$	10.1075	−	13.3844i	0.950830	−	1.25910i	−0.0149894	−	0.999888i	$-0.504771\pi$
$113$	10.1075	−	13.3844i	0.950830	−	1.25910i	0.965820	−	0.259215i	$-0.0834638\pi$
$114$		0			0
$115$	2.16609	+	6.14692i	0.201989	+	0.573203i
$116$	−1.96821	+	21.2403i	−0.182743	+	1.97212i
$117$		0			0
$118$	8.05849	−	19.0389i	0.741844	−	1.75268i
$119$	−17.4269	+	2.15791i	−1.59752	+	0.197816i
$120$		0			0
$121$	−6.05090	−	9.13172i	−0.550082	−	0.830156i
$122$	14.1641	+	14.6072i	1.28235	+	1.32247i
$123$		0			0
$124$	−6.64399	−	7.75490i	−0.596648	−	0.696410i
$125$	−5.42257	+	10.8900i	−0.485009	+	0.974029i
$126$		0			0
$127$	14.4124	−	5.58339i	1.27889	−	0.495446i	0.376523	−	0.926407i	$-0.377120\pi$
$127$	14.4124	−	5.58339i	1.27889	−	0.495446i	0.902370	+	0.430961i	$0.141825\pi$
$128$	−3.99999	−	18.2645i	−0.353552	−	1.61437i
$129$		0			0
$130$	17.8452	+	16.2681i	1.56513	+	1.42680i
$131$	−12.3135	+	6.61218i	−1.07583	+	0.577709i	−0.912590	−	0.408877i	$-0.865921\pi$
$131$	−12.3135	+	6.61218i	−1.07583	+	0.577709i	−0.163242	+	0.986586i	$0.552195\pi$
$132$		0			0
$133$	20.3099	+	7.86808i	1.76109	+	0.682249i
$134$	17.9392	+	23.7554i	1.54971	+	2.05215i
$135$		0			0
$136$	4.14757	−	18.9384i	0.355651	−	1.62395i
$137$	−0.782343	+	2.74965i	−0.0668400	+	0.234918i	−0.988047	−	0.154155i	$-0.950734\pi$
$137$	−0.782343	+	2.74965i	−0.0668400	+	0.234918i	0.921207	+	0.389074i	$0.127205\pi$
$138$		0			0
$139$	−0.502974	+	0.356048i	−0.0426617	+	0.0301996i	−0.598907	−	0.800818i	$-0.704398\pi$
$139$	−0.502974	+	0.356048i	−0.0426617	+	0.0301996i	0.556246	+	0.831018i	$0.312241\pi$
$140$	33.7382	+	6.30676i	2.85140	+	0.533018i
$141$		0			0
$142$	15.8471	−	2.96234i	1.32986	−	0.248594i
$143$	−0.643069	+	0.970489i	−0.0537762	+	0.0811564i
$144$		0			0
$145$	−6.90097	+	6.29106i	−0.573094	+	0.522444i
$146$	−3.75639	+	10.6599i	−0.310881	+	0.882217i
$147$		0			0
$148$	14.5791	+	1.80529i	1.19840	+	0.148394i
$149$	−4.50275	+	7.79900i	−0.368880	+	0.638919i	−0.989391	−	0.145279i	$-0.953592\pi$
$149$	−4.50275	+	7.79900i	−0.368880	+	0.638919i	0.620511	+	0.784198i	$0.286925\pi$
$150$		0			0
$151$	4.51001	+	10.6553i	0.367019	+	0.867117i	0.995971	+	0.0896728i	$0.0285821\pi$
$151$	4.51001	+	10.6553i	0.367019	+	0.867117i	−0.628952	+	0.777444i	$0.716516\pi$
$152$	−15.6455	+	18.2615i	−1.26902	+	1.48120i
$153$		0			0
$154$	−0.0758586	+	2.46217i	−0.00611286	+	0.198407i
$155$	0.137666	−	4.46827i	0.0110576	−	0.358900i
$156$		0			0
$157$	10.8104	−	12.6180i	0.862764	−	1.00702i	−0.137101	−	0.990557i	$-0.543778\pi$
$157$	10.8104	−	12.6180i	0.862764	−	1.00702i	0.999864	−	0.0164650i	$-0.00524121\pi$
$158$	6.21148	+	14.6752i	0.494159	+	1.16750i
$159$		0			0
$160$	−0.843061	+	1.46022i	−0.0666498	+	0.115441i
$161$	−16.8926	−	2.09176i	−1.33133	−	0.164854i
$162$		0			0
$163$	0.624199	−	1.77135i	0.0488910	−	0.138743i	−0.916154	−	0.400826i	$-0.868723\pi$
$163$	0.624199	−	1.77135i	0.0488910	−	0.138743i	0.965045	+	0.262083i	$0.0844095\pi$
$164$	29.1929	−	26.6129i	2.27958	−	2.07811i
$165$		0			0
$166$	7.77601	−	11.7352i	0.603536	−	0.910827i
$167$	16.4297	−	3.07125i	1.27137	−	0.237661i	0.495532	−	0.868590i	$-0.334973\pi$
$167$	16.4297	−	3.07125i	1.27137	−	0.237661i	0.775840	+	0.630929i	$0.217326\pi$
$168$		0			0
$169$	−16.5200	−	3.08813i	−1.27077	−	0.237549i
$170$	13.5460	−	9.58904i	1.03893	−	0.735446i
$171$		0			0
$172$	3.54925	−	12.4743i	0.270628	−	0.951158i
$173$	2.05698	−	9.39247i	0.156389	−	0.714096i	−0.831063	−	0.556179i	$-0.812267\pi$
$173$	2.05698	−	9.39247i	0.156389	−	0.714096i	0.987452	−	0.157918i	$-0.0504780\pi$
$174$		0			0
$175$	−5.04623	−	6.68229i	−0.381459	−	0.505134i
$176$	−0.908221	−	0.351847i	−0.0684597	−	0.0265214i
$177$		0			0
$178$	−35.0248	+	18.8079i	−2.62522	+	1.40971i
$179$	−0.168808	−	0.153889i	−0.0126173	−	0.0115022i	0.667362	−	0.744733i	$-0.267423\pi$
$179$	−0.168808	−	0.153889i	−0.0126173	−	0.0115022i	−0.679980	+	0.733231i	$0.738011\pi$
$180$		0			0
$181$	1.09238	+	4.98798i	0.0811963	+	0.370754i	0.999696	−	0.0246688i	$-0.00785311\pi$
$181$	1.09238	+	4.98798i	0.0811963	+	0.370754i	−0.918499	+	0.395422i	$0.870598\pi$
$182$	−58.8078	+	22.7823i	−4.35912	+	1.68873i
$183$		0			0
$184$	8.37672	−	16.8227i	0.617540	−	1.24019i
$185$	4.18413	+	4.88373i	0.307623	+	0.359059i
$186$		0			0
$187$	0.557018	+	0.574444i	0.0407332	+	0.0420075i
$188$	−7.84729	−	11.8427i	−0.572322	−	0.863721i
$189$		0			0
$190$	−20.4296	+	2.52974i	−1.48212	+	0.183526i
$191$	5.52904	−	13.0629i	0.400067	−	0.945196i	−0.590358	−	0.807142i	$-0.701013\pi$
$191$	5.52904	−	13.0629i	0.400067	−	0.945196i	0.990425	−	0.138054i	$-0.0440847\pi$
$192$		0			0
$193$	−1.47181	+	15.8833i	−0.105943	+	1.14331i	0.762320	+	0.647201i	$0.224060\pi$
$193$	−1.47181	+	15.8833i	−0.105943	+	1.14331i	−0.868263	+	0.496105i	$0.834763\pi$
$194$	−6.48190	−	18.3943i	−0.465373	−	1.32063i
$195$		0			0
$196$	−36.7541	+	48.6703i	−2.62529	+	3.47645i
$197$	22.0525	−	13.6544i	1.57118	−	0.972832i	0.584268	−	0.811561i	$-0.301382\pi$
$197$	22.0525	−	13.6544i	1.57118	−	0.972832i	0.986910	−	0.161271i	$-0.0515594\pi$
$198$		0			0
$199$	17.6345	−	8.11316i	1.25008	−	0.575127i	0.321726	−	0.946833i	$-0.395737\pi$
$199$	17.6345	−	8.11316i	1.25008	−	0.575127i	0.928350	+	0.371706i	$0.121227\pi$
$200$	8.80993	−	2.80264i	0.622956	−	0.198177i
$201$		0			0
$202$	−40.3804	+	2.49058i	−2.84115	+	0.175236i
$203$	−6.67426	−	23.4576i	−0.468441	−	1.64640i
$204$		0			0
$205$	17.2930			1.20780
$206$	−24.0438	−	7.03498i	−1.67521	−	0.490150i
$207$		0			0
$208$	−0.767912	−	24.9244i	−0.0532451	−	1.72820i
$209$	−0.271607	−	0.954598i	−0.0187874	−	0.0660309i
$210$		0			0
$211$	−12.8116	−	10.3094i	−0.881984	−	0.709730i	0.0758297	−	0.997121i	$-0.475839\pi$
$211$	−12.8116	−	10.3094i	−0.881984	−	0.709730i	−0.957813	+	0.287391i	$0.907212\pi$
$212$	−48.8059	+	15.5263i	−3.35200	+	1.06635i
$213$		0			0
$214$	1.04971	+	11.3281i	0.0717564	+	0.774375i
$215$	4.82717	−	2.98886i	0.329210	−	0.203838i
$216$		0			0
$217$	10.2862	+	5.52356i	0.698271	+	0.374963i
$218$	1.88215	+	5.34115i	0.127475	+	0.361748i
$219$		0			0
$220$	−0.697129	−	1.40002i	−0.0470004	−	0.0943895i
$221$	−7.98505	+	18.8654i	−0.537133	+	1.26903i
$222$		0			0
$223$	−20.0337	−	6.37318i	−1.34156	−	0.426780i	−0.455450	−	0.890261i	$-0.650522\pi$
$223$	−20.0337	−	6.37318i	−1.34156	−	0.426780i	−0.886107	+	0.463482i	$0.846600\pi$
$224$	−2.43244	−	3.67092i	−0.162524	−	0.245274i
$225$		0			0
$226$	−33.7912	−	23.9203i	−2.24776	−	1.59115i
$227$	15.4243	+	18.0033i	1.02375	+	1.19492i	0.980633	+	0.195852i	$0.0627472\pi$
$227$	15.4243	+	18.0033i	1.02375	+	1.19492i	0.0431131	+	0.999070i	$0.486272\pi$
$228$		0			0
$229$	12.0714	+	7.47428i	0.797699	+	0.493914i	0.863761	−	0.503901i	$-0.168102\pi$
$229$	12.0714	+	7.47428i	0.797699	+	0.493914i	−0.0660624	+	0.997815i	$0.521044\pi$
$230$	15.0014	−	5.81156i	0.989162	−	0.383203i
$231$		0			0
$232$	26.8754	+	1.65762i	1.76446	+	0.108828i
$233$	7.24253	+	6.60243i	0.474474	+	0.432540i	0.875275	−	0.483625i	$-0.160680\pi$
$233$	7.24253	+	6.60243i	0.474474	+	0.432540i	−0.400802	+	0.916165i	$0.631268\pi$
$234$		0			0
$235$	0.953976	−	6.14562i	0.0622306	−	0.400896i
$236$	−31.9668	−	12.3840i	−2.08086	−	0.806130i
$237$		0			0
$238$	6.64884	+	42.8325i	0.430980	+	2.77642i
$239$	0.216920	−	0.990485i	0.0140314	−	0.0640692i	−0.969307	−	0.245853i	$-0.920932\pi$
$239$	0.216920	−	0.990485i	0.0140314	−	0.0640692i	0.983339	+	0.181783i	$0.0581870\pi$
$240$		0			0
$241$	4.00242	+	1.00665i	0.257818	+	0.0648439i	0.370659	−	0.928769i	$-0.379132\pi$
$241$	4.00242	+	1.00665i	0.257818	+	0.0648439i	−0.112840	+	0.993613i	$0.535995\pi$
$242$	−22.0703	+	15.6233i	−1.41874	+	1.00430i
$243$		0			0
$244$	23.4868	−	24.2216i	1.50359	−	1.55063i
$245$	−26.2443	+	4.90592i	−1.67669	+	0.313428i
$246$		0			0
$247$	19.7962	−	15.9299i	1.25960	−	1.01360i
$248$	−9.52607	+	8.68416i	−0.604906	+	0.551445i
$249$		0			0
$250$	27.2806	+	12.5511i	1.72538	+	0.793798i
$251$	7.84538	+	0.971469i	0.495196	+	0.0613186i	0.366600	−	0.930379i	$-0.380522\pi$
$251$	7.84538	+	0.971469i	0.495196	+	0.0613186i	0.128596	+	0.991697i	$0.458953\pi$
$252$		0			0
$253$	0.387815	+	0.671715i	0.0243817	+	0.0422304i
$254$	−14.8712	−	35.1347i	−0.933104	−	2.20455i
$255$		0			0
$256$	−31.5463	+	7.93421i	−1.97164	+	0.495888i
$257$	0.648610	−	21.0521i	0.0404592	−	1.31320i	−0.733382	−	0.679817i	$-0.762059\pi$
$257$	0.648610	−	21.0521i	0.0404592	−	1.31320i	0.773841	−	0.633380i	$-0.218333\pi$
$258$		0			0
$259$	−16.2887	+	4.09677i	−1.01213	+	0.254561i
$260$	26.0516	−	30.4075i	1.61565	−	1.88580i
$261$		0			0
$262$	17.2500	+	29.8778i	1.06571	+	1.84586i
$263$	−1.94758	+	3.37331i	−0.120093	+	0.208007i	−0.919804	−	0.392378i	$-0.871653\pi$
$263$	−1.94758	+	3.37331i	−0.120093	+	0.208007i	0.799711	+	0.600385i	$0.204986\pi$
$264$		0			0
$265$	−20.3684	−	9.37094i	−1.25122	−	0.575652i
$266$	17.8687	−	50.7077i	1.09560	−	3.10909i
$267$		0			0
$268$	38.4564	−	30.9457i	2.34910	−	1.89031i
$269$	−8.01078	+	12.0895i	−0.488426	+	0.737109i	−0.991917	−	0.126892i	$-0.959500\pi$
$269$	−8.01078	+	12.0895i	−0.488426	+	0.737109i	0.503491	+	0.864001i	$0.332049\pi$
$270$		0			0
$271$	5.84750	−	6.03043i	0.355210	−	0.366323i	−0.516549	−	0.856258i	$-0.672783\pi$
$271$	5.84750	−	6.03043i	0.355210	−	0.366323i	0.871759	+	0.489935i	$0.162980\pi$
$272$	−16.8468	−	3.14921i	−1.02149	−	0.190949i
$273$		0			0
$274$	6.84356	+	1.72122i	0.413435	+	0.103983i
$275$	−0.104420	+	0.366997i	−0.00629675	+	0.0221308i
$276$		0			0
$277$	−0.388633	−	2.50362i	−0.0233507	−	0.150428i	0.973624	−	0.228161i	$-0.0732711\pi$
$277$	−0.388633	−	2.50362i	−0.0233507	−	0.150428i	−0.996974	+	0.0777328i	$0.975232\pi$
$278$	0.916696	+	1.21390i	0.0549798	+	0.0728050i
$279$		0			0
$280$	6.64574	−	42.8126i	0.397159	−	2.55854i
$281$	26.6360	−	14.3033i	1.58897	−	0.853260i	0.590026	−	0.807384i	$-0.299118\pi$
$281$	26.6360	−	14.3033i	1.58897	−	0.853260i	0.998947	−	0.0458761i	$-0.0146079\pi$
$282$		0			0
$283$	12.2136	+	0.753311i	0.726025	+	0.0447797i	0.420357	−	0.907359i	$-0.361905\pi$
$283$	12.2136	+	0.753311i	0.726025	+	0.0447797i	0.305668	+	0.952138i	$0.401120\pi$
$284$	−5.71904	−	26.1139i	−0.339362	−	1.54958i
$285$		0			0
$286$	2.44333	+	1.51285i	0.144477	+	0.0894564i
$287$	−20.1315	+	40.4296i	−1.18833	+	2.38648i
$288$		0			0
$289$	−2.38346	−	1.68721i	−0.140203	−	0.0992478i
$290$	16.0462	+	16.5482i	0.942268	+	0.971746i
$291$		0			0
$292$	17.8596	+	5.68154i	1.04515	+	0.332487i
$293$	−20.8965	+	2.58754i	−1.22078	+	0.151166i	−0.707288	−	0.706926i	$-0.750081\pi$
$293$	−20.8965	+	2.58754i	−1.22078	+	0.151166i	−0.513496	+	0.858092i	$0.671650\pi$
$294$		0			0
$295$	−6.68938	−	13.4341i	−0.389470	−	0.782162i
$296$	1.71100	−	18.4646i	0.0994500	−	1.07324i
$297$		0			0
$298$	19.5844	+	10.5166i	1.13449	+	0.609211i
$299$	−11.9670	+	15.8468i	−0.692067	+	0.916445i
$300$		0			0
$301$	1.36818	+	14.7650i	0.0788604	+	0.851040i
$302$	25.9466	−	11.9373i	1.49306	−	0.686915i
$303$		0			0
$304$	16.5617	+	13.3272i	0.949880	+	0.764365i
$305$	14.7417	−	0.909239i	0.844110	−	0.0520629i
$306$		0			0
$307$	−0.0305718	−	0.992281i	−0.00174483	−	0.0566324i	0.998252	−	0.0590989i	$-0.0188227\pi$
$307$	−0.0305718	−	0.992281i	−0.00174483	−	0.0566324i	−0.999997	+	0.00246648i	$0.999215\pi$
$308$	4.08470			0.232747
$309$		0			0
$310$	−11.0348			−0.626736
$311$	0.123950	+	4.02310i	0.00702858	+	0.228129i	0.996510	+	0.0834706i	$0.0266005\pi$
$311$	0.123950	+	4.02310i	0.00702858	+	0.228129i	−0.989482	+	0.144658i	$0.953792\pi$
$312$		0			0
$313$	−4.91661	+	0.303246i	−0.277903	+	0.0171405i	−0.199913	−	0.979814i	$-0.564066\pi$
$313$	−4.91661	+	0.303246i	−0.277903	+	0.0171405i	−0.0779902	+	0.996954i	$0.524850\pi$
$314$	−31.9535	−	25.7129i	−1.80324	−	1.45106i
$315$		0			0
$316$	24.0056	−	11.0443i	1.35042	−	0.621292i
$317$	2.93074	+	31.6278i	0.164607	+	1.77639i	0.532408	+	0.846488i	$0.321287\pi$
$317$	2.93074	+	31.6278i	0.164607	+	1.77639i	−0.367801	+	0.929904i	$0.619889\pi$
$318$		0			0
$319$	−0.669721	+	0.886855i	−0.0374972	+	0.0496543i
$320$	−10.7539	−	5.77473i	−0.601162	−	0.322817i
$321$		0			0
$322$	−3.87681	+	41.8375i	−0.216046	+	2.33151i
$323$	−7.78438	−	15.6331i	−0.433135	−	0.869851i
$324$		0			0
$325$	−9.69476	+	1.20047i	−0.537769	+	0.0665902i
$326$	−4.41782	−	1.40541i	−0.244680	−	0.0778384i
$327$		0			0
$328$	−34.7122	−	35.7981i	−1.91666	−	1.97662i
$329$	13.2574	+	9.38470i	0.730903	+	0.517395i
$330$		0			0
$331$	7.24072	−	14.5413i	0.397986	−	0.799263i	−0.602014	−	0.798486i	$-0.705635\pi$
$331$	7.24072	−	14.5413i	0.397986	−	0.799263i	1.00000		0.000777786i	$-0.000247577\pi$
$332$	−19.8471	−	12.2888i	−1.08925	−	0.674435i
$333$		0			0
$334$	−8.82648	−	40.3029i	−0.482963	−	2.20528i
$335$	21.5677	+	1.33025i	1.17837	+	0.0726793i
$336$		0			0
$337$	2.20312	−	1.18305i	0.120011	−	0.0644448i	−0.411989	−	0.911189i	$-0.635166\pi$
$337$	2.20312	−	1.18305i	0.120011	−	0.0644448i	0.532001	+	0.846744i	$0.321440\pi$
$338$	−6.36344	+	40.9939i	−0.346125	+	2.22978i
$339$		0			0
$340$	−16.5847	−	21.9617i	−0.899430	−	1.19104i
$341$	−0.0816069	−	0.525720i	−0.00441926	−	0.0284693i
$342$		0			0
$343$	10.1178	−	35.5604i	0.546310	−	1.92008i
$344$	−15.8768	−	3.99318i	−0.856020	−	0.215298i
$345$		0			0
$346$	−23.3300	−	4.36113i	−1.25423	−	0.234456i
$347$	−0.495515	+	0.511017i	−0.0266007	+	0.0274328i	−0.731081	−	0.682290i	$-0.760984\pi$
$347$	−0.495515	+	0.511017i	−0.0266007	+	0.0274328i	0.704481	+	0.709723i	$0.251180\pi$
$348$		0			0
$349$	10.5969	−	15.9923i	0.567238	−	0.856048i	−0.431705	−	0.902015i	$-0.642088\pi$
$349$	10.5969	−	15.9923i	0.567238	−	0.856048i	0.998943	+	0.0459668i	$0.0146368\pi$
$350$	−16.1033	+	12.9583i	−0.860760	+	0.692651i
$351$		0			0
$352$	−0.0666916	+	0.189257i	−0.00355467	+	0.0100874i
$353$	30.2495	+	13.9170i	1.61002	+	0.740726i	0.998715	−	0.0506703i	$-0.0161358\pi$
$353$	30.2495	+	13.9170i	1.61002	+	0.740726i	0.611303	+	0.791396i	$0.290646\pi$
$354$		0			0
$355$	5.85137	−	10.1349i	0.310558	−	0.537903i
$356$	32.9609	+	57.0899i	1.74692	+	3.02576i
$357$		0			0
$358$	−0.366852	+	0.428191i	−0.0193887	+	0.0226306i
$359$	24.5435	−	6.17295i	1.29536	−	0.325796i	0.466135	−	0.884713i	$-0.345646\pi$
$359$	24.5435	−	6.17295i	1.29536	−	0.325796i	0.829223	+	0.558918i	$0.188783\pi$
$360$		0			0
$361$	−0.0819656	+	2.66039i	−0.00431398	+	0.140020i
$362$	12.2236	−	3.07436i	0.642458	−	0.161585i
$363$		0			0
$364$	40.7625	+	96.3052i	2.13654	+	5.04776i
$365$	4.10220	+	7.10523i	0.214719	+	0.371905i
$366$		0			0
$367$	31.7713	+	3.93414i	1.65845	+	0.205360i	0.896739	−	0.442560i	$-0.145930\pi$
$367$	31.7713	+	3.93414i	1.65845	+	0.205360i	0.761708	+	0.647920i	$0.224361\pi$
$368$	−15.0925	−	6.94366i	−0.786752	−	0.361963i
$369$		0			0
$370$	11.7314	−	10.6946i	0.609885	−	0.555983i
$371$	45.6202	−	36.7104i	2.36848	−	1.90591i
$372$		0			0
$373$	−27.4852	+	5.13788i	−1.42313	+	0.266029i	−0.838337	−	0.545152i	$-0.816472\pi$
$373$	−27.4852	+	5.13788i	−1.42313	+	0.266029i	−0.584795	+	0.811181i	$0.698825\pi$
$374$	1.37496	−	1.41797i	0.0710975	−	0.0733217i
$375$		0			0
$376$	−14.6369	+	10.3613i	−0.754842	+	0.534342i
$377$	−27.5928	−	6.93987i	−1.42110	−	0.357421i
$378$		0			0
$379$	−4.54246	+	20.7415i	−0.233331	+	1.06542i	0.702146	+	0.712033i	$0.252225\pi$
$379$	−4.54246	+	20.7415i	−0.233331	+	1.06542i	−0.935477	+	0.353388i	$0.885030\pi$
$380$	5.23603	+	33.7311i	0.268603	+	1.73037i
$381$		0			0
$382$	−32.6497	−	12.6486i	−1.67051	−	0.647157i
$383$	−1.16475	+	7.50344i	−0.0595159	+	0.383408i	0.939634	+	0.342181i	$0.111166\pi$
$383$	−1.16475	+	7.50344i	−0.0595159	+	0.383408i	−0.999150	+	0.0412266i	$0.986873\pi$
$384$		0			0
$385$	1.32145	+	1.20466i	0.0673475	+	0.0613953i
$386$	39.3001	+	2.42395i	2.00032	+	0.123376i
$387$		0			0
$388$	−30.1559	+	11.6825i	−1.53093	+	0.593087i
$389$	2.18249	+	1.35134i	0.110657	+	0.0685158i	0.580645	−	0.814157i	$-0.302801\pi$
$389$	2.18249	+	1.35134i	0.110657	+	0.0685158i	−0.469988	+	0.882673i	$0.655742\pi$
$390$		0			0
$391$	8.87975	+	10.3645i	0.449068	+	0.524155i
$392$	62.8360	+	44.4807i	3.17370	+	2.24661i
$393$		0			0
$394$	−35.3651	−	53.3713i	−1.78167	−	2.68881i
$395$	11.0233	+	3.50678i	0.554645	+	0.176445i
$396$		0			0
$397$	−6.54233	+	15.4569i	−0.328350	+	0.775758i	0.671060	+	0.741403i	$0.265839\pi$
$397$	−6.54233	+	15.4569i	−0.328350	+	0.775758i	−0.999410	+	0.0343542i	$0.989063\pi$
$398$	−21.3577	−	42.8921i	−1.07057	−	2.14999i
$399$		0			0
$400$	−2.71623	−	7.70811i	−0.135812	−	0.385406i
$401$	−17.6105	−	9.45661i	−0.879424	−	0.472241i	−0.0297551	−	0.999557i	$-0.509473\pi$
$401$	−17.6105	−	9.45661i	−0.879424	−	0.472241i	−0.849669	+	0.527316i	$0.823198\pi$
$402$		0			0
$403$	11.5806	−	7.17038i	0.576869	−	0.357182i
$404$	6.18989	+	66.7996i	0.307959	+	3.32340i
$405$		0			0
$406$	−57.3686	+	18.2503i	−2.84715	+	0.905745i
$407$	0.596267	+	0.479814i	0.0295559	+	0.0237835i
$408$		0			0
$409$	4.51054	+	15.8529i	0.223032	+	0.783876i	0.989863	+	0.142027i	$0.0453618\pi$
$409$	4.51054	+	15.8529i	0.223032	+	0.783876i	−0.766831	+	0.641849i	$0.778168\pi$
$410$	−1.31453	−	42.6663i	−0.0649202	−	2.10714i
$411$		0			0
$412$	−10.4321	+	40.2096i	−0.513950	+	1.98098i
$413$	39.1951			1.92867
$414$		0			0
$415$	−2.79657	−	9.82891i	−0.137278	−	0.482482i
$416$	−5.12766	+	0.316263i	−0.251404	+	0.0155061i
$417$		0			0
$418$	−2.33459	+	0.742687i	−0.114189	+	0.0363260i
$419$	−27.1047	+	12.4702i	−1.32415	+	0.609207i	−0.948272	−	0.317460i	$-0.897170\pi$
$419$	−27.1047	+	12.4702i	−1.32415	+	0.609207i	−0.375882	+	0.926668i	$0.622660\pi$
$420$		0			0
$421$	−12.2559	+	7.58852i	−0.597315	+	0.369842i	−0.791542	−	0.611115i	$-0.790721\pi$
$421$	−12.2559	+	7.58852i	−0.597315	+	0.369842i	0.194227	+	0.980957i	$0.437780\pi$
$422$	−24.4621	+	32.3931i	−1.19080	+	1.57687i
$423$		0			0
$424$	21.4867	+	60.9747i	1.04348	+	2.96120i
$425$	−0.619497	+	6.68544i	−0.0300500	+	0.324291i
$426$		0			0
$427$	−15.0358	+	35.5234i	−0.727633	+	1.71910i
$428$	18.7217	−	2.31825i	0.904949	−	0.112057i
$429$		0			0
$430$	−7.74122	−	11.6827i	−0.373315	−	0.563389i
$431$	−16.4617	−	16.9767i	−0.792931	−	0.817737i	0.193639	−	0.981073i	$-0.437971\pi$
$431$	−16.4617	−	16.9767i	−0.792931	−	0.817737i	−0.986571	+	0.163335i	$0.947775\pi$
$432$		0			0
$433$	−18.3690	−	21.4404i	−0.882759	−	1.03036i	−0.999309	−	0.0371756i	$-0.988164\pi$
$433$	−18.3690	−	21.4404i	−0.882759	−	1.03036i	0.116550	−	0.993185i	$-0.462816\pi$
$434$	12.8461	−	25.7985i	0.616634	−	1.23837i
$435$		0			0
$436$	8.75636	−	3.39223i	0.419354	−	0.162458i
$437$	−3.62160	−	16.5367i	−0.173244	−	0.791058i
$438$		0			0
$439$	5.01593	+	4.57262i	0.239397	+	0.218239i	0.784498	−	0.620131i	$-0.212921\pi$
$439$	5.01593	+	4.57262i	0.239397	+	0.218239i	−0.545101	+	0.838370i	$0.683509\pi$
$440$	−1.73931	+	0.933989i	−0.0829183	+	0.0445262i
$441$		0			0
$442$	47.1528	+	18.2671i	2.24283	+	0.868878i
$443$	18.7292	+	24.8015i	0.889851	+	1.17835i	0.983166	+	0.182717i	$0.0584891\pi$
$443$	18.7292	+	24.8015i	0.889851	+	1.17835i	−0.0933145	+	0.995637i	$0.529746\pi$
$444$		0			0
$445$	−6.17375	+	28.1902i	−0.292664	+	1.33634i
$446$	−14.2014	+	49.9128i	−0.672456	+	2.36344i
$447$		0			0
$448$	26.0199	−	18.4191i	1.22933	−	0.870222i
$449$	−10.8517	−	2.02853i	−0.512121	−	0.0957321i	−0.0786551	−	0.996902i	$-0.525063\pi$
$449$	−10.8517	−	2.02853i	−0.512121	−	0.0957321i	−0.433466	+	0.901170i	$0.642710\pi$
$450$		0			0
$451$	2.02298	−	0.378161i	0.0952584	−	0.0178069i
$452$	−37.9202	+	57.2273i	−1.78362	+	2.69175i
$453$		0			0
$454$	43.2463	−	39.4242i	2.02965	−	1.85027i
$455$	−15.2152	+	43.1777i	−0.713302	+	2.02420i
$456$		0			0
$457$	−13.0268	−	1.61307i	−0.609370	−	0.0754563i	−0.187731	−	0.982220i	$-0.560113\pi$
$457$	−13.0268	−	1.61307i	−0.609370	−	0.0754563i	−0.421638	+	0.906764i	$0.638545\pi$
$458$	17.5234	−	30.3513i	0.818813	−	1.41823i
$459$		0			0
$460$	−10.3982	−	24.5667i	−0.484817	−	1.14543i
$461$	15.4351	−	18.0159i	0.718883	−	0.839084i	−0.273552	−	0.961857i	$-0.588198\pi$
$461$	15.4351	−	18.0159i	0.718883	−	0.839084i	0.992435	+	0.122773i	$0.0391788\pi$
$462$		0			0
$463$	0.968128	−	31.4229i	0.0449927	−	1.46034i	−0.660072	−	0.751202i	$-0.729474\pi$
$463$	0.968128	−	31.4229i	0.0449927	−	1.46034i	0.705065	−	0.709143i	$-0.250918\pi$
$464$	0.733027	−	23.7921i	0.0340299	−	1.10452i
$465$		0			0
$466$	15.7394	−	18.3711i	0.729112	−	0.851023i
$467$	−4.82878	−	11.4084i	−0.223449	−	0.527920i	0.770541	−	0.637391i	$-0.219986\pi$
$467$	−4.82878	−	11.4084i	−0.223449	−	0.527920i	−0.993990	+	0.109471i	$0.965084\pi$
$468$		0			0
$469$	−28.2179	+	48.8749i	−1.30298	+	2.25683i
$470$	−15.2353	−	1.88654i	−0.702754	−	0.0870198i
$471$		0			0
$472$	−14.3822	+	40.8138i	−0.661997	+	1.87861i
$473$	0.499336	−	0.455204i	0.0229595	−	0.0209303i
$474$		0			0
$475$	4.60002	−	6.94213i	0.211064	−	0.318527i
$476$	70.6515	−	13.2071i	3.23831	−	0.605344i
$477$		0			0
$478$	−2.46027	−	0.459904i	−0.112530	−	0.0210355i
$479$	14.5483	−	10.2985i	0.664727	−	0.470551i	−0.195337	−	0.980736i	$-0.562580\pi$
$479$	14.5483	−	10.2985i	0.664727	−	0.470551i	0.860064	+	0.510186i	$0.170423\pi$
$480$		0			0
$481$	−5.36228	+	18.8465i	−0.244499	+	0.859324i
$482$	2.17942	−	9.95152i	0.0992697	−	0.453279i
$483$		0			0
$484$	27.0211	+	35.7818i	1.22823	+	1.62644i
$485$	−13.2012	−	5.11418i	−0.599437	−	0.232223i
$486$		0			0
$487$	37.4266	−	20.0976i	1.69596	−	0.910711i	0.719649	−	0.694338i	$-0.244303\pi$
$487$	37.4266	−	20.0976i	1.69596	−	0.910711i	0.976311	−	0.216373i	$-0.0694229\pi$
$488$	−31.4733	−	28.6917i	−1.42473	−	1.29881i
$489$		0			0
$490$	14.0991	+	64.3786i	0.636934	+	2.90833i
$491$	−3.60619	+	1.39704i	−0.162745	+	0.0630477i	−0.441236	−	0.897391i	$-0.645460\pi$
$491$	−3.60619	+	1.39704i	−0.162745	+	0.0630477i	0.278491	+	0.960439i	$0.410166\pi$
$492$		0			0
$493$	−8.71646	+	17.5050i	−0.392570	+	0.788386i
$494$	−40.8080	−	47.6313i	−1.83604	−	2.14304i
$495$		0			0
$496$	7.93262	+	8.18078i	0.356185	+	0.367328i
$497$	16.8826	+	25.4785i	0.757290	+	1.14286i
$498$		0			0
$499$	18.3169	−	2.26812i	0.819976	−	0.101535i	0.298077	−	0.954542i	$-0.403655\pi$
$499$	18.3169	−	2.26812i	0.819976	−	0.101535i	0.521900	+	0.853007i	$0.325224\pi$
$500$	19.4092	−	45.8560i	0.868005	−	2.05074i
$501$		0			0
$502$	1.80049	−	19.4304i	0.0803600	−	0.867222i
$503$	−1.32323	−	3.75505i	−0.0589998	−	0.167429i	0.909932	−	0.414758i	$-0.136134\pi$
$503$	−1.32323	−	3.75505i	−0.0589998	−	0.167429i	−0.968932	+	0.247328i	$0.920447\pi$
$504$		0			0
$505$	−17.6981	+	23.4361i	−0.787555	+	1.04289i
$506$	1.62781	−	1.00790i	0.0723652	−	0.0448066i
$507$		0			0
$508$	−57.4731	+	26.4418i	−2.54996	+	1.17317i
$509$	34.5873	−	11.0030i	1.53306	−	0.487700i	0.586420	−	0.810007i	$-0.300537\pi$
$509$	34.5873	−	11.0030i	1.53306	−	0.487700i	0.946635	+	0.322307i	$0.104458\pi$
$510$		0			0
$511$	−21.3870	+	1.31910i	−0.946104	+	0.0583537i
$512$	11.7402	+	41.2624i	0.518847	+	1.82356i
$513$		0			0
$514$	−51.9904			−2.29320
$515$	−15.2336	+	9.93169i	−0.671271	+	0.437643i
$516$		0			0
$517$	−0.0227928	−	0.739792i	−0.00100242	−	0.0325360i
$518$	11.3460	+	39.8770i	0.498513	+	1.75209i
$519$		0			0
$520$	−39.3778	−	31.6872i	−1.72683	−	1.38958i
$521$	−11.8085	+	3.75654i	−0.517338	+	0.164577i	−0.550440	−	0.834875i	$-0.685540\pi$
$521$	−11.8085	+	3.75654i	−0.517338	+	0.164577i	0.0331015	+	0.999452i	$0.489462\pi$
$522$		0			0
$523$	−2.00830	−	21.6730i	−0.0878168	−	0.947694i	−0.919668	−	0.392696i	$-0.871542\pi$
$523$	−2.00830	−	21.6730i	−0.0878168	−	0.947694i	0.831852	−	0.554998i	$-0.187281\pi$
$524$	48.6389	−	30.1159i	2.12480	−	1.31562i
$525$		0			0
$526$	8.47087	+	4.54876i	0.369348	+	0.198335i
$527$	−3.11134	−	8.82933i	−0.135532	−	0.384612i
$528$		0			0
$529$	−4.35496	−	8.74594i	−0.189346	−	0.380258i
$530$	−21.5722	+	50.9663i	−0.937037	+	2.21384i
$531$		0			0
$532$	−84.9559	−	27.0264i	−3.68331	−	1.17174i
$533$	29.1039	+	43.9222i	1.26063	+	1.90248i
$534$		0			0
$535$	6.74043	+	4.77145i	0.291414	+	0.206288i
$536$	−40.5391	−	47.3174i	−1.75102	−	2.04380i
$537$		0			0
$538$	30.4368	+	18.8457i	1.31222	+	0.812494i
$539$	−2.96285	+	1.14781i	−0.127619	+	0.0494399i
$540$		0			0
$541$	16.9835	+	1.04750i	0.730176	+	0.0450357i	0.422383	−	0.906418i	$-0.361194\pi$
$541$	16.9835	+	1.04750i	0.730176	+	0.0450357i	0.307793	+	0.951453i	$0.400410\pi$
$542$	−15.3231	−	13.9689i	−0.658185	−	0.600015i
$543$		0			0
$544$	−0.541615	+	3.48914i	−0.0232215	+	0.149596i
$545$	3.83324	+	1.48500i	0.164198	+	0.0636106i
$546$		0			0
$547$	3.43966	+	22.1587i	0.147069	+	0.947437i	0.940750	+	0.339102i	$0.110123\pi$
$547$	3.43966	+	22.1587i	0.147069	+	0.947437i	−0.793680	+	0.608335i	$0.791838\pi$
$548$	2.50331	−	11.4305i	0.106936	−	0.488286i
$549$		0			0
$550$	0.913414	+	0.229733i	0.0389481	+	0.00979584i
$551$	19.7971	−	14.0141i	0.843387	−	0.597021i
$552$		0			0
$553$	−21.0313	+	21.6893i	−0.894343	+	0.922321i
$554$	−6.14752	+	1.14917i	−0.261183	+	0.0488236i
$555$		0			0
$556$	1.96512	−	1.58133i	0.0833397	−	0.0670632i
$557$	−18.3890	+	16.7638i	−0.779166	+	0.710304i	−0.962063	−	0.272828i	$-0.912041\pi$
$557$	−18.3890	+	16.7638i	−0.779166	+	0.710304i	0.182896	+	0.983132i	$0.441453\pi$
$558$		0			0
$559$	15.7154	+	7.23024i	0.664692	+	0.305807i
$560$	−38.0099	−	4.70664i	−1.60621	−	0.198892i
$561$		0			0
$562$	−37.3145	−	64.6307i	−1.57402	−	2.72628i
$563$	14.3064	+	33.8001i	0.602941	+	1.42451i	0.885220	+	0.465173i	$0.154008\pi$
$563$	14.3064	+	33.8001i	0.602941	+	1.42451i	−0.282278	+	0.959333i	$0.591090\pi$
$564$		0			0
$565$	−29.1452	+	7.33032i	−1.22615	+	0.308389i
$566$	0.930188	−	30.1914i	0.0390987	−	1.26904i
$567$		0			0
$568$	−32.7256	+	8.23082i	−1.37314	+	0.345357i
$569$	3.32718	−	3.88350i	0.139483	−	0.162805i	−0.685288	−	0.728272i	$-0.740324\pi$
$569$	3.32718	−	3.88350i	0.139483	−	0.162805i	0.824771	+	0.565467i	$0.191304\pi$
$570$		0			0
$571$	−8.31999	−	14.4106i	−0.348181	−	0.603067i	0.637746	−	0.770247i	$-0.279867\pi$
$571$	−8.31999	−	14.4106i	−0.348181	−	0.603067i	−0.985926	+	0.167180i	$0.946534\pi$
$572$	2.38264	−	4.12685i	0.0996230	−	0.172552i
$573$		0			0
$574$	101.280	+	46.5964i	4.22736	+	1.94490i
$575$	−2.16305	+	6.13829i	−0.0902054	+	0.255984i
$576$		0			0
$577$	16.8603	−	13.5675i	0.701905	−	0.564821i	−0.208760	−	0.977967i	$-0.566943\pi$
$577$	16.8603	−	13.5675i	0.701905	−	0.564821i	0.910665	+	0.413146i	$0.135570\pi$
$578$	−3.98161	+	6.00885i	−0.165613	+	0.249935i
$579$		0			0
$580$	26.6078	−	27.4402i	1.10483	−	1.13939i
$581$	26.2348	+	4.90413i	1.08840	+	0.203458i
$582$		0			0
$583$	−2.58767	−	0.650825i	−0.107170	−	0.0269544i
$584$	6.47415	−	22.7543i	0.267902	−	0.941578i
$585$		0			0
$586$	7.97258	+	51.3602i	0.329344	+	2.12167i
$587$	16.0865	+	21.3020i	0.663961	+	0.879227i	0.997992	−	0.0633351i	$-0.0201737\pi$
$587$	16.0865	+	21.3020i	0.663961	+	0.879227i	−0.334031	+	0.942562i	$0.608409\pi$
$588$		0			0
$589$	−1.78112	+	11.4742i	−0.0733899	+	0.472786i
$590$	−32.6368	+	17.5256i	−1.34364	+	0.721518i
$591$		0			0
$592$	−16.3619	−	1.00916i	−0.672468	−	0.0414764i
$593$	0.899235	+	4.10603i	0.0369272	+	0.168615i	0.991667	−	0.128828i	$-0.0411214\pi$
$593$	0.899235	+	4.10603i	0.0369272	+	0.168615i	−0.954740	+	0.297442i	$0.903866\pi$
$594$		0			0
$595$	26.7517	+	16.5640i	1.09671	+	0.679057i
$596$	16.4303	−	32.9964i	0.673010	−	1.35159i
$597$		0			0
$598$	40.0078	+	28.3210i	1.63604	+	1.15813i
$599$	9.46814	+	9.76434i	0.386858	+	0.398960i	0.883070	−	0.469241i	$-0.155472\pi$
$599$	9.46814	+	9.76434i	0.386858	+	0.398960i	−0.496212	+	0.868201i	$0.665276\pi$
$600$		0			0
$601$	7.85089	+	2.49755i	0.320244	+	0.101877i	0.458965	−	0.888455i	$-0.348220\pi$
$601$	7.85089	+	2.49755i	0.320244	+	0.101877i	−0.138720	+	0.990332i	$0.544299\pi$
$602$	36.3250	−	4.49801i	1.48050	−	0.183325i
$603$		0			0
$604$	−21.1099	−	42.3945i	−0.858951	−	1.72501i
$605$	−1.81111	+	19.5450i	−0.0736321	+	0.794617i
$606$		0			0
$607$	5.73817	+	3.08133i	0.232905	+	0.125068i	0.585395	−	0.810748i	$-0.300939\pi$
$607$	5.73817	+	3.08133i	0.232905	+	0.125068i	−0.352490	+	0.935816i	$0.614665\pi$
$608$	2.63931	−	3.49501i	0.107038	−	0.141741i
$609$		0			0
$610$	−3.36393	−	36.3025i	−0.136201	−	1.46985i
$611$	17.2147	−	7.92001i	0.696432	−	0.320409i
$612$		0			0
$613$	−23.4990	−	18.9096i	−0.949117	−	0.763752i	0.0226377	−	0.999744i	$-0.492794\pi$
$613$	−23.4990	−	18.9096i	−0.949117	−	0.763752i	−0.971755	+	0.235992i	$0.924166\pi$
$614$	−2.44589	+	0.150857i	−0.0987080	+	0.00608810i
$615$		0			0
$616$	−0.158782	−	5.15365i	−0.00639752	−	0.207647i
$617$	−17.2285			−0.693595			−0.346797	−	0.937940i	$-0.612731\pi$
$617$	−17.2285			−0.693595			−0.346797	+	0.937940i	$0.612731\pi$
$618$		0			0
$619$	−38.0694			−1.53014			−0.765070	−	0.643948i	$-0.777295\pi$
$619$	−38.0694			−1.53014			−0.765070	+	0.643948i	$0.777295\pi$
$620$	0.563485	+	18.2892i	0.0226301	+	0.734513i
$621$		0			0
$622$	9.91659	−	0.611634i	0.397619	−	0.0245243i
$623$	−58.7192	−	47.2512i	−2.35254	−	1.89308i
$624$		0			0
$625$	11.6754	−	5.37151i	0.467014	−	0.214861i
$626$	1.12192	+	12.1075i	0.0448411	+	0.483913i
$627$		0			0
$628$	−40.9851	+	54.2730i	−1.63548	+	2.16573i
$629$	11.8648	+	6.37126i	0.473080	+	0.254039i
$630$		0			0
$631$	1.50536	−	16.2455i	0.0599276	−	0.646722i	−0.911803	−	0.410629i	$-0.865309\pi$
$631$	1.50536	−	16.2455i	0.0599276	−	0.646722i	0.971730	−	0.236094i	$-0.0758672\pi$
$632$	−14.8678	−	29.8585i	−0.591409	−	1.18771i
$633$		0			0
$634$	77.8110	−	9.63510i	3.09027	−	0.382659i
$635$	−26.3916	−	8.39576i	−1.04732	−	0.333176i
$636$		0			0
$637$	−56.6294	−	58.4010i	−2.24374	−	2.31393i
$638$	2.23901	+	1.58496i	0.0886431	+	0.0627492i
$639$		0			0
$640$	−14.9334	+	29.9903i	−0.590295	+	1.18547i
$641$	37.6971	+	23.3410i	1.48894	+	0.921915i	0.998734	+	0.0503113i	$0.0160213\pi$
$641$	37.6971	+	23.3410i	1.48894	+	0.921915i	0.490211	+	0.871604i	$0.336920\pi$
$642$		0			0
$643$	−2.79674	−	12.7703i	−0.110293	−	0.503612i	−0.998982	−	0.0451027i	$-0.985639\pi$
$643$	−2.79674	−	12.7703i	−0.110293	−	0.503612i	0.888690	−	0.458509i	$-0.151616\pi$
$644$	69.5398	+	4.28907i	2.74025	+	0.169013i
$645$		0			0
$646$	−37.9792	+	20.3944i	−1.49427	+	0.802408i
$647$	2.65005	−	17.0719i	0.104184	−	0.671167i	−0.877346	−	0.479859i	$-0.840688\pi$
$647$	2.65005	−	17.0719i	0.104184	−	0.671167i	0.981530	−	0.191308i	$-0.0612729\pi$
$648$		0			0
$649$	−1.07632	−	1.42527i	−0.0422491	−	0.0559468i
$650$	3.69882	+	23.8282i	0.145080	+	0.934619i
$651$		0			0
$652$	−2.10375	+	7.39390i	−0.0823891	+	0.289567i
$653$	−46.6770	−	11.7397i	−1.82661	−	0.459411i	−0.831274	−	0.555863i	$-0.812388\pi$
$653$	−46.6770	−	11.7397i	−1.82661	−	0.459411i	−0.995338	+	0.0964520i	$0.969251\pi$
$654$		0			0
$655$	24.6172	+	4.60175i	0.961872	+	0.179805i
$656$	−30.6861	+	31.6461i	−1.19809	+	1.23557i
$657$		0			0
$658$	22.1467	−	33.4227i	0.863369	−	1.30295i
$659$	14.4449	−	11.6238i	0.562695	−	0.452799i	−0.303269	−	0.952905i	$-0.598078\pi$
$659$	14.4449	−	11.6238i	0.562695	−	0.452799i	0.865964	+	0.500106i	$0.166706\pi$
$660$		0			0
$661$	−14.4682	+	41.0578i	−0.562749	+	1.59696i	0.220588	+	0.975367i	$0.429202\pi$
$661$	−14.4682	+	41.0578i	−0.562749	+	1.59696i	−0.783337	+	0.621597i	$0.786484\pi$
$662$	−36.4276	−	16.7594i	−1.41580	−	0.651371i
$663$		0			0
$664$	−14.7332	+	25.5187i	−0.571761	+	0.990318i
$665$	−19.5137	−	33.7987i	−0.756709	−	1.31066i
$666$		0			0
$667$	−12.3329	+	14.3950i	−0.477531	+	0.557376i
$668$	−66.3477	+	16.6871i	−2.56707	+	0.645644i
$669$		0			0
$670$	1.64259	−	53.3142i	0.0634589	−	2.05971i
$671$	1.70464	−	0.428735i	0.0658071	−	0.0165511i
$672$		0			0
$673$	8.21152	+	19.4005i	0.316531	+	0.747834i	0.999843	+	0.0177077i	$0.00563683\pi$
$673$	8.21152	+	19.4005i	0.316531	+	0.747834i	−0.683312	+	0.730126i	$0.739461\pi$
$674$	−3.08636	−	5.34572i	−0.118882	−	0.205910i
$675$		0			0
$676$	68.2687	+	8.45349i	2.62572	+	0.325134i
$677$	−6.05799	−	2.78712i	−0.232828	−	0.107118i	0.298101	−	0.954534i	$-0.403647\pi$
$677$	−6.05799	−	2.78712i	−0.232828	−	0.107118i	−0.530928	+	0.847417i	$0.678157\pi$
$678$		0			0
$679$	27.3247	−	24.9097i	1.04862	−	0.955948i
$680$	−27.0643	+	21.7786i	−1.03787	+	0.835170i
$681$		0			0
$682$	−1.29088	+	0.241308i	−0.0494305	+	0.00924016i
$683$	−1.55666	+	1.60536i	−0.0595638	+	0.0614272i	−0.747037	−	0.664783i	$-0.768524\pi$
$683$	−1.55666	+	1.60536i	−0.0595638	+	0.0614272i	0.687473	+	0.726210i	$0.258720\pi$
$684$		0			0
$685$	4.18094	−	2.95963i	0.159746	−	0.113082i
$686$	−88.5057	−	22.2601i	−3.37916	−	0.849894i
$687$		0			0
$688$	−3.09613	+	14.1374i	−0.118039	+	0.538982i
$689$	−10.4786	−	67.5045i	−0.399204	−	2.57171i
$690$		0			0
$691$	−3.71961	−	1.44099i	−0.141501	−	0.0548177i	0.289450	−	0.957193i	$-0.406528\pi$
$691$	−3.71961	−	1.44099i	−0.141501	−	0.0548177i	−0.430951	+	0.902375i	$0.641822\pi$
$692$	−6.03685	+	38.8900i	−0.229487	+	1.47838i
$693$		0			0
$694$	1.29848	+	1.18372i	0.0492895	+	0.0449333i
$695$	1.10211	+	0.0679758i	0.0418054	+	0.00257847i
$696$		0			0
$697$	33.7680	−	13.0818i	1.27906	−	0.495509i
$698$	−40.2626	−	24.9296i	−1.52396	−	0.943598i
$699$		0			0
$700$	22.2995	+	26.0281i	0.842843	+	0.983770i
$701$	−18.3596	−	12.9965i	−0.693431	−	0.490869i	0.176338	−	0.984330i	$-0.443575\pi$
$701$	−18.3596	−	12.9965i	−0.693431	−	0.490869i	−0.869768	+	0.493460i	$0.835732\pi$
$702$		0			0
$703$	−9.22682	−	13.9247i	−0.347996	−	0.525179i
$704$	−1.38430	−	0.440378i	−0.0521728	−	0.0165974i
$705$		0			0
$706$	32.0373	−	75.6912i	1.20574	−	2.84868i
$707$	−34.1885	−	68.6597i	−1.28579	−	2.58221i
$708$		0			0
$709$	15.9764	+	45.3377i	0.600006	+	1.70269i	0.705895	+	0.708317i	$0.250545\pi$
$709$	15.9764	+	45.3377i	0.600006	+	1.70269i	−0.105889	+	0.994378i	$0.533769\pi$
$710$	−25.4501	−	13.6664i	−0.955126	−	0.512892i
$711$		0			0
$712$	70.7490	−	43.8059i	2.65143	−	1.64170i
$713$	−0.837290	−	9.03579i	−0.0313567	−	0.338393i
$714$		0			0
$715$	1.98791	−	0.632400i	0.0743436	−	0.0236504i
$716$	0.728421	+	0.586158i	0.0272224	+	0.0219057i
$717$		0			0
$718$	−17.0959	−	60.0860i	−0.638015	−	2.24239i
$719$	0.456815	+	14.8270i	0.0170363	+	0.552954i	0.969045	+	0.246883i	$0.0794064\pi$
$719$	0.456815	+	14.8270i	0.0170363	+	0.552954i	−0.952009	+	0.306070i	$0.900986\pi$
$720$		0			0
$721$	−5.48540	−	47.1767i	−0.204287	−	1.75695i
$722$	6.57009			0.244513
$723$		0			0
$724$	−5.71965	−	20.1025i	−0.212569	−	0.747103i
$725$	−9.30734	+	0.574057i	−0.345666	+	0.0213199i
$726$		0			0
$727$	10.3015	−	3.27713i	0.382060	−	0.121542i	−0.105969	−	0.994369i	$-0.533794\pi$
$727$	10.3015	−	3.27713i	0.382060	−	0.121542i	0.488029	+	0.872827i	$0.337716\pi$
$728$	119.924	−	55.1736i	4.44466	−	2.04487i
$729$		0			0
$730$	17.2186	−	10.6613i	0.637289	−	0.394592i
$731$	7.16501	−	9.48801i	0.265007	−	0.350927i
$732$		0			0
$733$	8.00921	+	22.7285i	0.295827	+	0.839496i	0.992515	+	0.122122i	$0.0389699\pi$
$733$	8.00921	+	22.7285i	0.295827	+	0.839496i	−0.696688	+	0.717374i	$0.745344\pi$
$734$	7.29142	−	78.6870i	0.269131	−	2.90439i
$735$		0			0
$736$	−1.33411	+	3.15197i	−0.0491761	+	0.116183i
$737$	2.55214	−	0.316023i	0.0940091	−	0.0116409i
$738$		0			0
$739$	−1.93894	−	2.92615i	−0.0713250	−	0.107640i	0.796201	−	0.605033i	$-0.206840\pi$
$739$	−1.93894	−	2.92615i	−0.0713250	−	0.107640i	−0.867526	+	0.497392i	$0.834291\pi$
$740$	−18.3243	−	18.8976i	−0.673615	−	0.694688i
$741$		0			0
$742$	−94.0419	−	109.766i	−3.45239	−	4.02964i
$743$	−19.0818	+	38.3214i	−0.700043	+	1.40588i	0.204230	+	0.978923i	$0.434531\pi$
$743$	−19.0818	+	38.3214i	−0.700043	+	1.40588i	−0.904274	+	0.426953i	$0.859587\pi$
$744$		0			0
$745$	15.0467	−	5.82914i	0.551270	−	0.213563i
$746$	14.7658	+	67.4226i	0.540614	+	2.46852i
$747$		0			0
$748$	−2.42037	−	2.20646i	−0.0884976	−	0.0806763i
$749$	−19.0021	+	10.2039i	−0.694321	+	0.372843i
$750$		0			0
$751$	−3.30601	−	1.28076i	−0.120638	−	0.0467355i	0.300166	−	0.953887i	$-0.402958\pi$
$751$	−3.30601	−	1.28076i	−0.120638	−	0.0467355i	−0.420804	+	0.907152i	$0.638252\pi$
$752$	9.55364	+	12.6511i	0.348385	+	0.461337i
$753$		0			0
$754$	−15.0250	+	68.6061i	−0.547177	+	2.49849i
$755$	5.67369	−	19.9410i	0.206487	−	0.725725i
$756$		0			0
$757$	−35.7974	+	25.3404i	−1.30108	+	0.921014i	−0.999474	−	0.0324190i	$-0.989679\pi$
$757$	−35.7974	+	25.3404i	−1.30108	+	0.921014i	−0.301604	+	0.953433i	$0.597522\pi$
$758$	51.5199	+	9.63075i	1.87129	+	0.349804i
$759$		0			0
$760$	42.3549	−	7.91750i	1.53637	−	0.287198i
$761$	−20.2007	+	30.4860i	−0.732276	+	1.10512i	0.258019	+	0.966140i	$0.416930\pi$
$761$	−20.2007	+	30.4860i	−0.732276	+	1.10512i	−0.990296	+	0.138976i	$0.955619\pi$
$762$		0			0
$763$	−7.93426	+	7.23303i	−0.287240	+	0.261853i
$764$	−19.2966	+	54.7598i	−0.698127	+	1.98114i
$765$		0			0
$766$	18.6015	+	2.30336i	0.672098	+	0.0832238i
$767$	22.8628	−	39.5996i	0.825530	−	1.42986i
$768$		0			0
$769$	9.80901	+	23.1747i	0.353722	+	0.835701i	0.997512	+	0.0704988i	$0.0224591\pi$
$769$	9.80901	+	23.1747i	0.353722	+	0.835701i	−0.643790	+	0.765202i	$0.722639\pi$
$770$	2.87176	−	3.35194i	0.103491	−	0.120795i
$771$		0			0
$772$	2.01064	−	65.2601i	0.0723646	−	2.34876i
$773$	−0.00739243	+	0.239939i	−0.000265887	+	0.00862999i	−0.999649	−	0.0264798i	$-0.991570\pi$
$773$	−0.00739243	+	0.239939i	−0.000265887	+	0.00862999i	0.999383	+	0.0351098i	$0.0111781\pi$
$774$		0			0
$775$	2.90443	−	3.39007i	0.104330	−	0.121775i
$776$	15.9120	+	37.5935i	0.571206	+	1.34953i
$777$		0			0
$778$	3.16821	−	5.48750i	0.113586	−	0.196736i
$779$	−44.5772	−	5.51986i	−1.59715	−	0.197769i
$780$		0			0
$781$	0.462881	−	1.31356i	0.0165632	−	0.0470029i
$782$	24.8969	−	22.6965i	0.890310	−	0.811625i
$783$		0			0
$784$	37.5923	−	56.7325i	1.34258	−	2.02616i
$785$	−29.2655	+	5.47067i	−1.04453	+	0.195256i
$786$		0			0
$787$	35.7014	+	6.67375i	1.27262	+	0.237893i	0.776364	−	0.630285i	$-0.217062\pi$
$787$	35.7014	+	6.67375i	1.27262	+	0.237893i	0.496253	+	0.868178i	$0.334709\pi$
$788$	−86.6522	+	61.3398i	−3.08686	+	2.18514i
$789$		0			0
$790$	7.81418	−	27.4640i	0.278016	−	0.977125i
$791$	16.7916	−	76.6727i	0.597039	−	2.72617i
$792$		0			0
$793$	27.1195	+	35.9121i	0.963043	+	1.27527i
$794$	38.6334	+	14.9666i	1.37105	+	0.531146i
$795$		0			0
$796$	−69.9992	+	37.5888i	−2.48105	+	1.33230i
$797$	10.3724	+	9.45570i	0.367410	+	0.334938i	0.836254	−	0.548343i	$-0.184741\pi$
$797$	10.3724	+	9.45570i	0.367410	+	0.334938i	−0.468844	+	0.883281i	$0.655329\pi$
$798$		0			0
$799$	−2.78621	−	12.7222i	−0.0985690	−	0.450080i
$800$	−1.57005	+	0.608242i	−0.0555098	+	0.0215046i
$801$		0			0
$802$	−21.9932	+	44.1684i	−0.776608	+	1.55964i
$803$	0.635263	+	0.741482i	0.0224179	+	0.0261663i
$804$		0			0
$805$	21.2321	+	21.8963i	0.748333	+	0.771744i
$806$	−18.5715	−	28.0272i	−0.654152	−	0.987215i
$807$		0			0
$808$	84.0403	−	10.4064i	2.95653	−	0.366098i
$809$	−1.86134	+	4.39758i	−0.0654411	+	0.154611i	−0.950376	−	0.311105i	$-0.899301\pi$
$809$	−1.86134	+	4.39758i	−0.0654411	+	0.154611i	0.884935	+	0.465715i	$0.154203\pi$
$810$		0			0
$811$	−0.877987	+	9.47499i	−0.0308303	+	0.332712i	0.966324	+	0.257327i	$0.0828419\pi$
$811$	−0.877987	+	9.47499i	−0.0308303	+	0.332712i	−0.997155	+	0.0753843i	$0.975982\pi$
$812$	33.1776	+	94.1512i	1.16431	+	3.30406i
$813$		0			0
$814$	1.13850	−	1.50762i	0.0399044	−	0.0528419i
$815$	−2.86121	+	1.77159i	−0.100224	+	0.0620559i
$816$		0			0
$817$	−13.3973	+	6.16375i	−0.468713	+	0.215642i
$818$	38.7703	−	12.3337i	1.35557	−	0.431239i
$819$		0			0
$820$	−70.6483	+	4.35744i	−2.46715	+	0.152168i
$821$	−4.99316	−	17.5492i	−0.174263	−	0.612470i	−0.998904	−	0.0468132i	$-0.985093\pi$
$821$	−4.99316	−	17.5492i	−0.174263	−	0.612470i	0.824641	−	0.565656i	$-0.191377\pi$
$822$		0			0
$823$	−47.5367			−1.65702			−0.828512	−	0.559972i	$-0.810812\pi$
$823$	−47.5367			−1.65702			−0.828512	+	0.559972i	$0.810812\pi$
$824$	51.1379	+	11.5991i	1.78147	+	0.404072i
$825$		0			0
$826$	−2.97943	−	96.7045i	−0.103668	−	3.36478i
$827$	8.02131	+	28.1920i	0.278928	+	0.980331i	0.967019	+	0.254706i	$0.0819787\pi$
$827$	8.02131	+	28.1920i	0.278928	+	0.980331i	−0.688090	+	0.725625i	$0.741551\pi$
$828$		0			0
$829$	14.5548	+	11.7122i	0.505508	+	0.406781i	0.845768	−	0.533551i	$-0.179143\pi$
$829$	14.5548	+	11.7122i	0.505508	+	0.406781i	−0.340260	+	0.940331i	$0.610515\pi$
$830$	−24.0379	+	7.64700i	−0.834366	+	0.265431i
$831$		0			0
$832$	−3.43156	−	37.0325i	−0.118968	−	1.28387i
$833$	−47.5361	+	29.4331i	−1.64703	+	1.01980i
$834$		0			0
$835$	−26.3858	−	14.1689i	−0.913117	−	0.490333i
$836$	1.35015	+	3.83145i	0.0466959	+	0.132513i
$837$		0			0
$838$	32.8275	+	65.9264i	1.13401	+	2.27739i
$839$	−4.07810	+	9.63489i	−0.140792	+	0.332633i	−0.976158	−	0.217060i	$-0.930353\pi$
$839$	−4.07810	+	9.63489i	−0.140792	+	0.332633i	0.835367	+	0.549693i	$0.185255\pi$
$840$		0			0
$841$	1.75378	+	0.557919i	0.0604753	+	0.0192386i
$842$	19.6545	+	29.6616i	0.677338	+	1.02221i
$843$		0			0
$844$	54.9377	+	38.8896i	1.89103	+	1.33863i
$845$	19.5927	+	22.8687i	0.674009	+	0.786707i
$846$		0			0
$847$	−43.5862	−	26.9874i	−1.49764	−	0.927299i
$848$	53.2921	−	20.6455i	1.83006	−	0.708968i
$849$		0			0
$850$	16.5418	+	1.02026i	0.567378	+	0.0349947i
$851$	9.64730	+	8.79468i	0.330705	+	0.301478i
$852$		0			0
$853$	−3.61453	+	23.2852i	−0.123759	+	0.797270i	0.842311	+	0.538992i	$0.181195\pi$
$853$	−3.61453	+	23.2852i	−0.123759	+	0.797270i	−0.966070	+	0.258279i	$0.916845\pi$
$854$	88.7884	+	34.3968i	3.03828	+	1.17703i
$855$		0			0
$856$	−3.65270	−	23.5311i	−0.124847	−	0.804275i
$857$	11.5947	−	52.9429i	0.396066	−	1.80849i	−0.171520	−	0.985181i	$-0.554868\pi$
$857$	11.5947	−	52.9429i	0.396066	−	1.80849i	0.567587	−	0.823314i	$-0.307877\pi$
$858$		0			0
$859$	−35.7945	−	9.00267i	−1.22129	−	0.307167i	−0.421157	−	0.906988i	$-0.638376\pi$
$859$	−35.7945	−	9.00267i	−1.22129	−	0.307167i	−0.800134	+	0.599821i	$0.795238\pi$
$860$	−18.9677	+	13.4269i	−0.646792	+	0.457855i
$861$		0			0
$862$	−40.6345	+	41.9057i	−1.38402	+	1.42731i
$863$	−17.0382	+	3.18499i	−0.579987	+	0.108418i	−0.465565	−	0.885014i	$-0.654149\pi$
$863$	−17.0382	+	3.18499i	−0.579987	+	0.108418i	−0.114422	+	0.993432i	$0.536502\pi$
$864$		0			0
$865$	−13.4225	+	10.8010i	−0.456379	+	0.367247i
$866$	−51.5027	+	46.9509i	−1.75013	+	1.59546i
$867$		0			0
$868$	−43.4146	−	19.9739i	−1.47359	−	0.677959i
$869$	1.36623	+	0.169175i	0.0463460	+	0.00573888i
$870$		0			0
$871$	32.9195	+	57.0182i	1.11543	+	1.93199i
$872$	−4.62036	−	10.9160i	−0.156465	−	0.369663i
$873$		0			0
$874$	−40.5250	+	10.1925i	−1.37078	+	0.344765i
$875$	−1.75320	+	56.9042i	−0.0592689	+	1.92371i
$876$		0			0
$877$	−20.7715	+	5.22425i	−0.701405	+	0.176410i	−0.578109	−	0.815959i	$-0.696209\pi$
$877$	−20.7715	+	5.22425i	−0.701405	+	0.176410i	−0.123296	+	0.992370i	$0.539346\pi$
$878$	10.9005	−	12.7232i	0.367876	−	0.429386i
$879$		0			0
$880$	0.872618	+	1.51142i	0.0294159	+	0.0509499i
$881$	15.1743	−	26.2827i	0.511236	−	0.885486i	−0.488680	−	0.872463i	$-0.662521\pi$
$881$	15.1743	−	26.2827i	0.511236	−	0.885486i	0.999915	−	0.0130227i	$-0.00414536\pi$
$882$		0			0
$883$	32.3454	+	14.8812i	1.08851	+	0.500794i	0.878907	−	0.476993i	$-0.158273\pi$
$883$	32.3454	+	14.8812i	1.08851	+	0.500794i	0.209602	+	0.977787i	$0.432783\pi$
$884$	27.8682	−	79.0843i	0.937311	−	2.65989i
$885$		0			0
$886$	59.7679	−	48.0950i	2.00794	−	1.61578i
$887$	30.6388	−	46.2387i	1.02875	−	1.55254i	0.210573	−	0.977578i	$-0.432467\pi$
$887$	30.6388	−	46.2387i	1.02875	−	1.55254i	0.818179	−	0.574964i	$-0.194984\pi$
$888$		0			0
$889$	50.3522	−	51.9274i	1.68876	−	1.74159i
$890$	70.0218	+	13.0893i	2.34714	+	0.438756i
$891$		0			0
$892$	83.4510	+	20.9888i	2.79415	+	0.702756i
$893$	−4.42078	+	15.5374i	−0.147936	+	0.519941i
$894$		0			0
$895$	0.0627833	+	0.404457i	0.00209861	+	0.0135195i
$896$	−52.7302	−	69.8261i	−1.76159	−	2.33273i
$897$		0			0
$898$	−4.18000	+	26.9280i	−0.139489	+	0.898600i
$899$	11.4549	−	6.15114i	0.382041	−	0.205152i
$900$		0			0
$901$	−46.8623	−	2.89037i	−1.56121	−	0.0962920i
$902$	−1.08680	−	4.96247i	−0.0361864	−	0.165232i
$903$		0			0
$904$	73.6776	+	45.6193i	2.45048	+	1.51727i
$905$	4.07827	−	8.19027i	0.135566	−	0.272254i
$906$		0			0
$907$	−0.931615	−	0.659477i	−0.0309338	−	0.0218976i	0.562203	−	0.826999i	$-0.309954\pi$
$907$	−0.931615	−	0.659477i	−0.0309338	−	0.0218976i	−0.593137	+	0.805102i	$0.702111\pi$
$908$	−67.5504	−	69.6637i	−2.24174	−	2.31187i
$909$		0			0
$910$	107.687	+	34.2578i	3.56979	+	1.13563i
$911$	−16.1051	+	1.99424i	−0.533585	+	0.0660722i	−0.385157	−	0.922851i	$-0.625853\pi$
$911$	−16.1051	+	1.99424i	−0.533585	+	0.0660722i	−0.148428	+	0.988923i	$0.547421\pi$
$912$		0			0
$913$	−0.542087	−	1.08866i	−0.0179405	−	0.0360293i
$914$	−2.98962	+	32.2632i	−0.0988879	+	1.06717i
$915$		0			0
$916$	−51.1994	−	27.4935i	−1.69168	−	0.908411i
$917$	−39.4164	+	52.1958i	−1.30165	+	1.72366i
$918$		0			0
$919$	−5.20345	−	56.1542i	−0.171646	−	1.85236i	−0.451447	−	0.892298i	$-0.649092\pi$
$919$	−5.20345	−	56.1542i	−0.171646	−	1.85236i	0.279801	−	0.960058i	$-0.409731\pi$
$920$	−30.5915	+	14.0743i	−1.00857	+	0.464017i
$921$		0			0
$922$	−45.6232	−	36.7128i	−1.50252	−	1.20907i
$923$	35.5892	−	2.19506i	1.17143	−	0.0722514i
$924$		0			0
$925$	0.197765	+	6.41892i	0.00650247	+	0.211053i
$926$	−77.6019			−2.55016
$927$		0			0
$928$	−4.90402			−0.160982
$929$	−0.416880	−	13.5308i	−0.0136774	−	0.443932i	−0.981407	−	0.191940i	$-0.938522\pi$
$929$	−0.416880	−	13.5308i	−0.0136774	−	0.443932i	0.967729	−	0.251992i	$-0.0810856\pi$
$930$		0			0
$931$	69.2177	−	4.26920i	2.26852	−	0.139917i
$932$	−31.2521	−	25.1485i	−1.02370	−	0.823765i
$933$		0			0
$934$	−27.7805	+	12.7811i	−0.909006	+	0.418209i
$935$	−0.132290	−	1.42764i	−0.00432636	−	0.0466888i
$936$		0			0
$937$	−16.1853	+	21.4328i	−0.528751	+	0.700179i	−0.981501	−	0.191458i	$-0.938678\pi$
$937$	−16.1853	+	21.4328i	−0.528751	+	0.700179i	0.452750	+	0.891638i	$0.350443\pi$
$938$	122.732	+	65.9056i	4.00734	+	2.15189i
$939$		0			0
$940$	−2.34879	+	25.3475i	−0.0766092	+	0.826745i
$941$	5.39150	+	10.8276i	0.175758	+	0.352970i	0.965473	−	0.260505i	$-0.0838890\pi$
$941$	5.39150	+	10.8276i	0.175758	+	0.352970i	−0.789715	+	0.613474i	$0.789771\pi$
$942$		0			0
$943$	34.8372	−	4.31378i	1.13446	−	0.140476i
$944$	36.4545	+	11.5970i	1.18649	+	0.377450i
$945$		0			0
$946$	−1.16106	−	1.19739i	−0.0377494	−	0.0389304i
$947$	−37.9956	−	26.8965i	−1.23469	−	0.874019i	−0.239396	−	0.970922i	$-0.576949\pi$
$947$	−37.9956	−	26.8965i	−1.23469	−	0.874019i	−0.995294	+	0.0969035i	$0.969106\pi$
$948$		0			0
$949$	−11.1425	+	22.3771i	−0.361700	+	0.726392i
$950$	−17.4777	−	10.8217i	−0.567051	−	0.351103i
$951$		0			0
$952$	−19.4097	−	88.6275i	−0.629073	−	2.87243i
$953$	10.9843	+	0.677486i	0.355815	+	0.0219459i	0.238483	−	0.971147i	$-0.423350\pi$
$953$	10.9843	+	0.677486i	0.355815	+	0.0219459i	0.117332	+	0.993093i	$0.462566\pi$
$954$		0			0
$955$	−22.3926	+	12.0245i	−0.724606	+	0.389105i
$956$	−0.636618	+	4.10116i	−0.0205897	+	0.132641i
$957$		0			0
$958$	−26.5149	−	35.1115i	−0.856659	−	1.13440i
$959$	2.05214	+	13.2201i	0.0662672	+	0.426900i
$960$		0			0
$961$	6.78018	−	23.8299i	0.218716	−	0.768705i
$962$	46.9067	+	11.7975i	1.51233	+	0.380367i
$963$		0			0
$964$	−16.6050	−	3.10402i	−0.534812	−	0.0999736i
$965$	19.8971	−	20.5195i	0.640509	−	0.660547i
$966$		0			0
$967$	−30.5574	+	46.1158i	−0.982660	+	1.48298i	−0.110432	+	0.993884i	$0.535224\pi$
$967$	−30.5574	+	46.1158i	−0.982660	+	1.48298i	−0.872228	+	0.489100i	$0.837325\pi$
$968$	44.0954	−	35.4835i	1.41728	−	1.14048i
$969$		0			0
$970$	−11.6145	+	32.9596i	−0.372919	+	1.05827i
$971$	5.61816	+	2.58476i	0.180295	+	0.0829489i	0.506045	−	0.862507i	$-0.331107\pi$
$971$	5.61816	+	2.58476i	0.180295	+	0.0829489i	−0.325750	+	0.945456i	$0.605617\pi$
$972$		0			0
$973$	−1.44194	+	2.49751i	−0.0462264	+	0.0800664i
$974$	−52.4310	−	90.8132i	−1.68000	−	2.90984i
$975$		0			0
$976$	−24.4950	+	28.5907i	−0.784067	+	0.915167i
$977$	−48.6064	+	12.2250i	−1.55506	+	0.391112i	−0.923308	−	0.384061i	$-0.874525\pi$
$977$	−48.6064	+	12.2250i	−1.55506	+	0.391112i	−0.631749	+	0.775173i	$0.717663\pi$
$978$		0			0
$979$	−0.105763	+	3.43277i	−0.00338019	+	0.109712i
$980$	105.982	−	26.6555i	3.38546	−	0.851478i
$981$		0			0
$982$	3.72099	+	8.79119i	0.118742	+	0.280538i
$983$	−6.66925	−	11.5515i	−0.212716	−	0.368435i	0.739848	−	0.672774i	$-0.234898\pi$
$983$	−6.66925	−	11.5515i	−0.212716	−	0.368435i	−0.952564	+	0.304340i	$0.901564\pi$
$984$		0			0
$985$	−46.1236	−	5.71133i	−1.46962	−	0.181978i
$986$	43.8519	+	20.1751i	1.39653	+	0.642506i
$987$		0			0
$988$	−76.8608	+	70.0679i	−2.44527	+	2.22916i
$989$	8.97890	−	7.22529i	0.285512	−	0.229751i
$990$		0			0
$991$	−43.8980	+	8.20596i	−1.39447	+	0.260671i	−0.826758	−	0.562558i	$-0.809817\pi$
$991$	−43.8980	+	8.20596i	−1.39447	+	0.260671i	−0.567709	+	0.823229i	$0.692170\pi$
$992$	1.63429	−	1.68542i	0.0518889	−	0.0535122i
$993$		0			0
$994$	61.5786	−	43.5906i	1.95315	−	1.38261i
$995$	−33.7314	−	8.48378i	−1.06936	−	0.268954i
$996$		0			0
$997$	5.64433	−	25.7728i	0.178758	−	0.816233i	−0.798131	−	0.602484i	$-0.794178\pi$
$997$	5.64433	−	25.7728i	0.178758	−	0.816233i	0.976889	−	0.213749i	$-0.0685674\pi$
$998$	−6.98840	−	45.0200i	−0.221214	−	1.42508i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	927.2.ba.e.244.2	yes	512
3.2	odd	2	inner	927.2.ba.e.244.15	yes	512
103.19	even	51	inner	927.2.ba.e.19.2	✓	512
309.122	odd	102	inner	927.2.ba.e.19.15	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
927.2.ba.e.19.2	✓	512	103.19	even	51	inner
927.2.ba.e.19.15	yes	512	309.122	odd	102	inner
927.2.ba.e.244.2	yes	512	1.1	even	1	trivial
927.2.ba.e.244.15	yes	512	3.2	odd	2	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:	\( N \)	\(=\)	\( 927 = 3^{2} \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	927.ba (of order \(51\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0760154 - 2.46726i) q^{2} +(-4.08537 + 0.251977i) q^{4} +(-1.39599 - 1.12335i) q^{5} +(4.25142 - 1.95596i) q^{7} +(0.476728 + 5.14471i) q^{8} +O(q^{10})\)	\(q+(-0.0760154 - 2.46726i) q^{2} +(-4.08537 + 0.251977i) q^{4} +(-1.39599 - 1.12335i) q^{5} +(4.25142 - 1.95596i) q^{7} +(0.476728 + 5.14471i) q^{8} +(-2.66547 + 3.52965i) q^{10} +(-0.187871 - 0.100885i) q^{11} +(0.503740 - 5.43622i) q^{13} +(-5.14903 - 10.3407i) q^{14} +(4.53287 - 0.561291i) q^{16} +(-3.57573 - 1.13752i) q^{17} +(3.23995 + 3.34131i) q^{19} +(5.98618 + 4.23753i) q^{20} +(-0.234627 + 0.471195i) q^{22} +(-3.09247 - 1.91478i) q^{23} +(-0.382795 - 1.74789i) q^{25} +(-13.4508 - 0.829619i) q^{26} +(-16.8758 + 9.06209i) q^{28} +(0.799399 - 5.14981i) q^{29} +(1.50349 + 1.99094i) q^{31} +(-0.144342 - 0.929866i) q^{32} +(-2.53475 + 8.90871i) q^{34} +(-8.13213 - 2.04531i) q^{35} +(-3.52794 - 0.659487i) q^{37} +(7.99759 - 8.24778i) q^{38} +(5.11378 - 7.71747i) q^{40} +(-7.51890 + 6.05043i) q^{41} +(-1.05309 + 2.98846i) q^{43} +(0.792945 + 0.364812i) q^{44} +(-4.48918 + 7.77548i) q^{46} +(1.73543 + 3.00586i) q^{47} +(9.69442 - 11.3154i) q^{49} +(-4.28341 + 1.07732i) q^{50} +(-0.688162 + 22.3359i) q^{52} +(12.1347 - 3.05201i) q^{53} +(0.148937 + 0.351878i) q^{55} +(12.0896 + 20.9399i) q^{56} +(-12.7667 - 1.58086i) q^{58} +(7.60879 + 3.50060i) q^{59} +(-6.09150 + 5.55314i) q^{61} +(4.79788 - 3.86084i) q^{62} +(6.69619 - 1.25173i) q^{64} +(-6.80996 + 7.02300i) q^{65} +(-9.84293 + 6.96767i) q^{67} +(14.8948 + 3.74620i) q^{68} +(-4.42815 + 20.2195i) q^{70} +(1.00182 + 6.45385i) q^{71} +(-4.26958 - 1.65404i) q^{73} +(-1.35895 + 8.75447i) q^{74} +(-14.0783 - 12.8341i) q^{76} +(-0.996045 - 0.0614340i) q^{77} +(-6.01983 + 2.33210i) q^{79} +(-6.95834 - 4.30842i) q^{80} +(15.4995 + 18.0911i) q^{82} +(4.65485 + 3.29510i) q^{83} +(3.71384 + 5.60474i) q^{85} +(7.45335 + 2.37108i) q^{86} +(0.429459 - 1.01464i) q^{88} +(-7.17882 - 14.4170i) q^{89} +(-8.49142 - 24.0969i) q^{91} +(13.1164 + 7.04335i) q^{92} +(7.28430 - 4.51025i) q^{94} +(-0.769479 - 8.30401i) q^{95} +(7.52916 - 2.39520i) q^{97} +(-28.6549 - 23.0585i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q + 18 q^{4} - 8 q^{7}+O(q^{10}) \) 512 * q + 18 * q^4 - 8 * q^7	\( 512 q + 18 q^{4} - 8 q^{7} - 36 q^{10} + 4 q^{13} + 18 q^{16} + 30 q^{19} + 40 q^{22} - 42 q^{25} - 110 q^{28} - 32 q^{31} - 110 q^{34} + 48 q^{37} - 22 q^{40} - 2 q^{43} + 152 q^{46} + 76 q^{49} + 68 q^{52} + 32 q^{55} - 44 q^{58} + 20 q^{61} - 170 q^{64} - 8 q^{67} - 38 q^{70} - 4 q^{73} + 188 q^{76} + 20 q^{79} + 212 q^{82} + 60 q^{85} + 164 q^{88} - 310 q^{91} + 228 q^{94} - 100 q^{97}+O(q^{100}) \) 512 * q + 18 * q^4 - 8 * q^7 - 36 * q^10 + 4 * q^13 + 18 * q^16 + 30 * q^19 + 40 * q^22 - 42 * q^25 - 110 * q^28 - 32 * q^31 - 110 * q^34 + 48 * q^37 - 22 * q^40 - 2 * q^43 + 152 * q^46 + 76 * q^49 + 68 * q^52 + 32 * q^55 - 44 * q^58 + 20 * q^61 - 170 * q^64 - 8 * q^67 - 38 * q^70 - 4 * q^73 + 188 * q^76 + 20 * q^79 + 212 * q^82 + 60 * q^85 + 164 * q^88 - 310 * q^91 + 228 * q^94 - 100 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more