LMFDB - Embedded newform 855.2.bs.c.766.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(226,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("855.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.bs (of order $9$, degree $6$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 15 x^{16} - 14 x^{15} + 72 x^{14} - 51 x^{13} + 231 x^{12} - 93 x^{11} + 438 x^{10} + \cdots + 1 $ x^18 - 3x^17 + 15x^16 - 14x^15 + 72x^14 - 51x^13 + 231x^12 - 93x^11 + 438x^10 - 156x^9 + 582x^8 - 138x^7 + 437x^6 - 132x^5 + 198x^4 - 16x^3 + 15x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			766.3
Root			$0.816390 - 1.41403i$ of defining polynomial
Character	$\chi$	$=$	855.766
Dual form			855.2.bs.c.586.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.484738 - 0.406743i) q^{2} +(-0.277766 + 1.57529i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(-2.04448 + 3.54114i) q^{7} +(1.13887 + 1.97259i) q^{8} +O(q^{10})$	\(q+(0.484738 - 0.406743i) q^{2} +(-0.277766 + 1.57529i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(-2.04448 + 3.54114i) q^{7} +(1.13887 + 1.97259i) q^{8} +(-0.484738 - 0.406743i) q^{10} +(-2.17413 - 3.76571i) q^{11} +(-1.45826 + 0.530764i) q^{13} +(0.449299 + 2.54810i) q^{14} +(-1.65185 - 0.601224i) q^{16} +(-4.87326 + 4.08915i) q^{17} +(0.708014 - 4.30101i) q^{19} +1.59959 q^{20} +(-2.58556 - 0.941068i) q^{22} +(0.583829 - 3.31106i) q^{23} +(-0.939693 + 0.342020i) q^{25} +(-0.490990 + 0.850420i) q^{26} +(-5.01042 - 4.20424i) q^{28} +(-3.99325 - 3.35074i) q^{29} +(-3.28366 + 5.68747i) q^{31} +(-5.32603 + 1.93852i) q^{32} +(-0.699019 + 3.96434i) q^{34} +(3.84236 + 1.39850i) q^{35} +0.180685 q^{37} +(-1.40621 - 2.37284i) q^{38} +(1.74486 - 1.46411i) q^{40} +(0.0242217 + 0.00881597i) q^{41} +(0.793995 + 4.50297i) q^{43} +(6.53598 - 2.37890i) q^{44} +(-1.06375 - 1.84246i) q^{46} +(1.09575 + 0.919441i) q^{47} +(-4.85976 - 8.41736i) q^{49} +(-0.316390 + 0.548004i) q^{50} +(-0.431051 - 2.44461i) q^{52} +(0.278010 - 1.57667i) q^{53} +(-3.33097 + 2.79501i) q^{55} -9.31361 q^{56} -3.29857 q^{58} +(-7.31281 + 6.13617i) q^{59} +(-1.05793 + 5.99980i) q^{61} +(0.721625 + 4.09254i) q^{62} +(-0.0353865 + 0.0612913i) q^{64} +(0.775925 + 1.34394i) q^{65} +(7.87159 + 6.60505i) q^{67} +(-5.08797 - 8.81262i) q^{68} +(2.43137 - 0.884946i) q^{70} +(1.88710 + 10.7023i) q^{71} +(12.7987 + 4.65836i) q^{73} +(0.0875850 - 0.0734926i) q^{74} +(6.57867 + 2.31000i) q^{76} +17.7799 q^{77} +(-16.2283 - 5.90661i) q^{79} +(-0.305250 + 1.73116i) q^{80} +(0.0153270 - 0.00557858i) q^{82} +(-2.57831 + 4.46577i) q^{83} +(4.87326 + 4.08915i) q^{85} +(2.21643 + 1.85981i) q^{86} +(4.95213 - 8.57735i) q^{88} +(-0.477195 + 0.173685i) q^{89} +(1.10187 - 6.24904i) q^{91} +(5.05370 + 1.83940i) q^{92} +0.905127 q^{94} +(-4.35862 + 0.0496059i) q^{95} +(2.51273 - 2.10843i) q^{97} +(-5.77942 - 2.10354i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8}+O(q^{10}) $ 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8	$ 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8} - 3 q^{10} - 3 q^{13} + 12 q^{14} - 3 q^{16} - 24 q^{17} - 12 q^{20} + 9 q^{22} + 9 q^{23} - 3 q^{26} - 12 q^{28} - 15 q^{29} - 18 q^{31} - 15 q^{32} - 12 q^{34} + 36 q^{37} + 33 q^{38} - 6 q^{40} + 30 q^{41} - 36 q^{43} - 42 q^{44} + 9 q^{46} - 21 q^{47} + 9 q^{49} + 6 q^{50} - 39 q^{52} + 12 q^{53} + 3 q^{55} + 12 q^{58} - 18 q^{59} - 30 q^{61} + 24 q^{62} + 36 q^{64} + 9 q^{65} - 51 q^{68} + 33 q^{70} + 12 q^{71} + 24 q^{73} + 15 q^{74} - 33 q^{76} + 60 q^{77} - 51 q^{79} - 15 q^{80} - 15 q^{82} + 24 q^{85} - 63 q^{86} - 27 q^{88} + 54 q^{89} + 30 q^{91} + 42 q^{92} + 30 q^{94} - 15 q^{95} + 27 q^{97} + 3 q^{98}+O(q^{100}) $ 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8 - 3 * q^10 - 3 * q^13 + 12 * q^14 - 3 * q^16 - 24 * q^17 - 12 * q^20 + 9 * q^22 + 9 * q^23 - 3 * q^26 - 12 * q^28 - 15 * q^29 - 18 * q^31 - 15 * q^32 - 12 * q^34 + 36 * q^37 + 33 * q^38 - 6 * q^40 + 30 * q^41 - 36 * q^43 - 42 * q^44 + 9 * q^46 - 21 * q^47 + 9 * q^49 + 6 * q^50 - 39 * q^52 + 12 * q^53 + 3 * q^55 + 12 * q^58 - 18 * q^59 - 30 * q^61 + 24 * q^62 + 36 * q^64 + 9 * q^65 - 51 * q^68 + 33 * q^70 + 12 * q^71 + 24 * q^73 + 15 * q^74 - 33 * q^76 + 60 * q^77 - 51 * q^79 - 15 * q^80 - 15 * q^82 + 24 * q^85 - 63 * q^86 - 27 * q^88 + 54 * q^89 + 30 * q^91 + 42 * q^92 + 30 * q^94 - 15 * q^95 + 27 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	0.484738	−	0.406743i	0.342761	−	0.287611i	−0.455114	−	0.890433i	$-0.650402\pi$
$2$	0.484738	−	0.406743i	0.342761	−	0.287611i	0.797876	+	0.602822i	$0.205957\pi$
$3$		0			0
$3$		0			0
$4$	−0.277766	+	1.57529i	−0.138883	+	0.787644i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$6$		0			0
$7$	−2.04448	+	3.54114i	−0.772739	+	1.33842i	0.163317	+	0.986574i	$0.447781\pi$
$7$	−2.04448	+	3.54114i	−0.772739	+	1.33842i	−0.936056	+	0.351850i	$0.885553\pi$
$8$	1.13887	+	1.97259i	0.402653	+	0.697415i
$9$		0			0
$10$	−0.484738	−	0.406743i	−0.153288	−	0.128624i
$11$	−2.17413	−	3.76571i	−0.655526	−	1.13540i	−0.981762	−	0.190116i	$-0.939114\pi$
$11$	−2.17413	−	3.76571i	−0.655526	−	1.13540i	0.326235	−	0.945289i	$-0.394220\pi$
$12$		0			0
$13$	−1.45826	+	0.530764i	−0.404449	+	0.147207i	−0.536231	−	0.844071i	$-0.680152\pi$
$13$	−1.45826	+	0.530764i	−0.404449	+	0.147207i	0.131782	+	0.991279i	$0.457930\pi$
$14$	0.449299	+	2.54810i	0.120080	+	0.681008i
$15$		0			0
$16$	−1.65185	−	0.601224i	−0.412963	−	0.150306i
$17$	−4.87326	+	4.08915i	−1.18194	+	0.991765i	−0.181976	+	0.983303i	$0.558249\pi$
$17$	−4.87326	+	4.08915i	−1.18194	+	0.991765i	−0.999964	+	0.00846250i	$0.997306\pi$
$18$		0			0
$19$	0.708014	−	4.30101i	0.162429	−	0.986720i
$19$	0.708014	−	4.30101i	0.162429	−	0.986720i
$20$	1.59959			0.357679
$21$		0			0
$22$	−2.58556	−	0.941068i	−0.551244	−	0.200636i
$23$	0.583829	−	3.31106i	0.121737	−	0.690403i	−0.861456	−	0.507832i	$-0.830447\pi$
$23$	0.583829	−	3.31106i	0.121737	−	0.690403i	0.983193	−	0.182571i	$-0.0584419\pi$
$24$		0			0
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	−0.490990	+	0.850420i	−0.0962911	+	0.166781i
$27$		0			0
$28$	−5.01042	−	4.20424i	−0.946881	−	0.794527i
$29$	−3.99325	−	3.35074i	−0.741529	−	0.622216i	0.191719	−	0.981450i	$-0.438594\pi$
$29$	−3.99325	−	3.35074i	−0.741529	−	0.622216i	−0.933248	+	0.359233i	$0.883038\pi$
$30$		0			0
$31$	−3.28366	+	5.68747i	−0.589763	+	1.02150i	0.404500	+	0.914538i	$0.367445\pi$
$31$	−3.28366	+	5.68747i	−0.589763	+	1.02150i	−0.994263	+	0.106961i	$0.965888\pi$
$32$	−5.32603	+	1.93852i	−0.941518	+	0.342684i
$33$		0			0
$34$	−0.699019	+	3.96434i	−0.119881	+	0.679878i
$35$	3.84236	+	1.39850i	0.649477	+	0.236390i
$36$		0			0
$37$	0.180685			0.0297045			0.0148522	−	0.999890i	$-0.495272\pi$
$37$	0.180685			0.0297045			0.0148522	+	0.999890i	$0.495272\pi$
$38$	−1.40621	−	2.37284i	−0.228117	−	0.384926i
$39$		0			0
$40$	1.74486	−	1.46411i	0.275886	−	0.231496i
$41$	0.0242217	+	0.00881597i	0.00378279	+	0.00137682i	0.343911	−	0.939002i	$-0.388248\pi$
$41$	0.0242217	+	0.00881597i	0.00378279	+	0.00137682i	−0.340128	+	0.940379i	$0.610470\pi$
$42$		0			0
$43$	0.793995	+	4.50297i	0.121083	+	0.686696i	0.983557	+	0.180595i	$0.0578025\pi$
$43$	0.793995	+	4.50297i	0.121083	+	0.686696i	−0.862474	+	0.506101i	$0.831086\pi$
$44$	6.53598	−	2.37890i	0.985336	−	0.358633i
$45$		0			0
$46$	−1.06375	−	1.84246i	−0.156841	−	0.271656i
$47$	1.09575	+	0.919441i	0.159831	+	0.134114i	0.719196	−	0.694807i	$-0.244510\pi$
$47$	1.09575	+	0.919441i	0.159831	+	0.134114i	−0.559365	+	0.828922i	$0.688955\pi$
$48$		0			0
$49$	−4.85976	−	8.41736i	−0.694252	−	1.20248i
$50$	−0.316390	+	0.548004i	−0.0447443	+	0.0774995i
$51$		0			0
$52$	−0.431051	−	2.44461i	−0.0597760	−	0.339006i
$53$	0.278010	−	1.57667i	0.0381876	−	0.216573i	−0.959742	−	0.280882i	$-0.909373\pi$
$53$	0.278010	−	1.57667i	0.0381876	−	0.216573i	0.997930	+	0.0643090i	$0.0204843\pi$
$54$		0			0
$55$	−3.33097	+	2.79501i	−0.449148	+	0.376880i
$56$	−9.31361			−1.24458
$57$		0			0
$58$	−3.29857			−0.433124
$59$	−7.31281	+	6.13617i	−0.952046	+	0.798862i	−0.979641	−	0.200758i	$-0.935660\pi$
$59$	−7.31281	+	6.13617i	−0.952046	+	0.798862i	0.0275947	+	0.999619i	$0.491215\pi$
$60$		0			0
$61$	−1.05793	+	5.99980i	−0.135454	+	0.768195i	0.839089	+	0.543994i	$0.183088\pi$
$61$	−1.05793	+	5.99980i	−0.135454	+	0.768195i	−0.974543	+	0.224201i	$0.928023\pi$
$62$	0.721625	+	4.09254i	0.0916464	+	0.519753i
$63$		0			0
$64$	−0.0353865	+	0.0612913i	−0.00442332	+	0.00766141i
$65$	0.775925	+	1.34394i	0.0962416	+	0.166695i
$66$		0			0
$67$	7.87159	+	6.60505i	0.961668	+	0.806935i	0.981224	−	0.192874i	$-0.0617808\pi$
$67$	7.87159	+	6.60505i	0.961668	+	0.806935i	−0.0195559	+	0.999809i	$0.506225\pi$
$68$	−5.08797	−	8.81262i	−0.617007	−	1.06869i
$69$		0			0
$70$	2.43137	−	0.884946i	0.290604	−	0.105771i
$71$	1.88710	+	10.7023i	0.223957	+	1.27012i	0.864669	+	0.502343i	$0.167528\pi$
$71$	1.88710	+	10.7023i	0.223957	+	1.27012i	−0.640711	+	0.767782i	$0.721360\pi$
$72$		0			0
$73$	12.7987	+	4.65836i	1.49798	+	0.545220i	0.955536	−	0.294873i	$-0.0952774\pi$
$73$	12.7987	+	4.65836i	1.49798	+	0.545220i	0.542443	+	0.840093i	$0.317500\pi$
$74$	0.0875850	−	0.0734926i	0.0101816	−	0.00854334i
$75$		0			0
$76$	6.57867	+	2.31000i	0.754625	+	0.264975i
$77$	17.7799			2.02620
$78$		0			0
$79$	−16.2283	−	5.90661i	−1.82582	−	0.664545i	−0.993984	−	0.109529i	$-0.965066\pi$
$79$	−16.2283	−	5.90661i	−1.82582	−	0.664545i	−0.831839	−	0.555016i	$-0.812712\pi$
$80$	−0.305250	+	1.73116i	−0.0341279	+	0.193549i
$81$		0			0
$82$	0.0153270	−	0.00557858i	0.00169259	−	0.000616051i
$83$	−2.57831	+	4.46577i	−0.283007	+	0.490182i	−0.972124	−	0.234468i	$-0.924665\pi$
$83$	−2.57831	+	4.46577i	−0.283007	+	0.490182i	0.689117	+	0.724650i	$0.257999\pi$
$84$		0			0
$85$	4.87326	+	4.08915i	0.528580	+	0.443531i
$86$	2.21643	+	1.85981i	0.239004	+	0.200548i
$87$		0			0
$88$	4.95213	−	8.57735i	0.527899	−	0.914348i
$89$	−0.477195	+	0.173685i	−0.0505826	+	0.0184106i	−0.367188	−	0.930147i	$-0.619679\pi$
$89$	−0.477195	+	0.173685i	−0.0505826	+	0.0184106i	0.316605	+	0.948557i	$0.397457\pi$
$90$		0			0
$91$	1.10187	−	6.24904i	0.115508	−	0.655077i
$92$	5.05370	+	1.83940i	0.526885	+	0.191770i
$93$		0			0
$94$	0.905127			0.0933567
$95$	−4.35862	+	0.0496059i	−0.447185	+	0.00508946i
$96$		0			0
$97$	2.51273	−	2.10843i	0.255129	−	0.214079i	−0.506248	−	0.862388i	$-0.668968\pi$
$97$	2.51273	−	2.10843i	0.255129	−	0.214079i	0.761377	+	0.648309i	$0.224524\pi$
$98$	−5.77942	−	2.10354i	−0.583809	−	0.212489i
$99$		0			0
$100$	−0.277766	−	1.57529i	−0.0277766	−	0.157529i
$101$	−3.27996	+	1.19381i	−0.326369	+	0.118788i	−0.500008	−	0.866021i	$-0.666670\pi$
$101$	−3.27996	+	1.19381i	−0.326369	+	0.118788i	0.173639	+	0.984809i	$0.444447\pi$
$102$		0			0
$103$	−4.31572	−	7.47504i	−0.425240	−	0.736537i	0.571203	−	0.820809i	$-0.306477\pi$
$103$	−4.31572	−	7.47504i	−0.425240	−	0.736537i	−0.996443	+	0.0842716i	$0.973144\pi$
$104$	−2.70776	−	2.27208i	−0.265517	−	0.222796i
$105$		0			0
$106$	−0.506539	−	0.877351i	−0.0491994	−	0.0852159i
$107$	3.13732	−	5.43399i	0.303296	−	0.525324i	−0.673584	−	0.739110i	$-0.735246\pi$
$107$	3.13732	−	5.43399i	0.303296	−	0.525324i	0.976880	+	0.213786i	$0.0685796\pi$
$108$		0			0
$109$	1.71297	+	9.71476i	0.164073	+	0.930506i	0.950015	+	0.312205i	$0.101068\pi$
$109$	1.71297	+	9.71476i	0.164073	+	0.930506i	−0.785942	+	0.618301i	$0.787821\pi$
$110$	−0.477793	+	2.70970i	−0.0455558	+	0.258360i
$111$		0			0
$112$	5.50619	−	4.62024i	0.520286	−	0.436571i
$113$	5.24756			0.493649			0.246825	−	0.969060i	$-0.420613\pi$
$113$	5.24756			0.493649			0.246825	+	0.969060i	$0.420613\pi$
$114$		0			0
$115$	−3.36213			−0.313521
$116$	6.38756	−	5.35980i	0.593071	−	0.497645i
$117$		0			0
$118$	−1.04895	+	5.94887i	−0.0965634	+	0.547638i
$119$	−4.51698	−	25.6171i	−0.414071	−	2.34831i
$120$		0			0
$121$	−3.95372	+	6.84804i	−0.359429	+	0.622550i
$122$	1.92756	+	3.33863i	0.174513	+	0.302266i
$123$		0			0
$124$	−8.04731	−	6.75249i	−0.722669	−	0.606392i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$		0			0
$127$	−5.00719	+	1.82247i	−0.444316	+	0.161718i	−0.554482	−	0.832195i	$-0.687084\pi$
$127$	−5.00719	+	1.82247i	−0.444316	+	0.161718i	0.110167	+	0.993913i	$0.464862\pi$
$128$	−1.96064	−	11.1194i	−0.173298	−	0.982822i
$129$		0			0
$130$	0.922760	+	0.335857i	0.0809314	+	0.0294566i
$131$	1.31194	−	1.10085i	0.114625	−	0.0961816i	−0.583674	−	0.811988i	$-0.698385\pi$
$131$	1.31194	−	1.10085i	0.114625	−	0.0961816i	0.698298	+	0.715807i	$0.253941\pi$
$132$		0			0
$133$	13.7830	+	11.3005i	1.19513	+	0.979877i
$134$	6.50222			0.561706
$135$		0			0
$136$	−13.6163	−	4.95591i	−1.16758	−	0.424966i
$137$	−0.997739	+	5.65846i	−0.0852426	+	0.483435i	0.912061	+	0.410054i	$0.134490\pi$
$137$	−0.997739	+	5.65846i	−0.0852426	+	0.483435i	−0.997304	+	0.0733811i	$0.976621\pi$
$138$		0			0
$139$	16.5249	−	6.01458i	1.40162	−	0.510150i	0.472965	−	0.881081i	$-0.343184\pi$
$139$	16.5249	−	6.01458i	1.40162	−	0.510150i	0.928660	+	0.370932i	$0.120962\pi$
$140$	−3.27032	+	5.66436i	−0.276393	+	0.478726i
$141$		0			0
$142$	5.26782	+	4.42023i	0.442066	+	0.370937i
$143$	5.16916	+	4.33744i	0.432267	+	0.362715i
$144$		0			0
$145$	−2.60641	+	4.51444i	−0.216451	+	0.374904i
$146$	8.09879	−	2.94772i	0.670261	−	0.243955i
$147$		0			0
$148$	−0.0501882	+	0.284631i	−0.00412544	+	0.0233966i
$149$	10.3558	+	3.76921i	0.848381	+	0.308785i	0.729380	−	0.684109i	$-0.239809\pi$
$149$	10.3558	+	3.76921i	0.848381	+	0.308785i	0.119001	+	0.992894i	$0.462031\pi$
$150$		0			0
$151$	−2.37114			−0.192960			−0.0964802	−	0.995335i	$-0.530758\pi$
$151$	−2.37114			−0.192960			−0.0964802	+	0.995335i	$0.530758\pi$
$152$	9.29047	−	3.50170i	0.753557	−	0.284025i
$153$		0			0
$154$	8.61857	−	7.23184i	0.694504	−	0.582758i
$155$	6.17126	+	2.24616i	0.495688	+	0.180416i
$156$		0			0
$157$	−0.561125	−	3.18230i	−0.0447827	−	0.253975i	0.954195	−	0.299186i	$-0.0967151\pi$
$157$	−0.561125	−	3.18230i	−0.0447827	−	0.253975i	−0.998977	+	0.0452110i	$0.985604\pi$
$158$	−10.2689	+	3.73759i	−0.816952	+	0.297346i
$159$		0			0
$160$	2.83392	+	4.90849i	0.224041	+	0.388050i
$161$	10.5313	+	8.83679i	0.829981	+	0.696437i
$162$		0			0
$163$	−3.29087	−	5.69996i	−0.257761	−	0.446455i	0.707881	−	0.706332i	$-0.249651\pi$
$163$	−3.29087	−	5.69996i	−0.257761	−	0.446455i	−0.965642	+	0.259877i	$0.916318\pi$
$164$	−0.0206156	+	0.0357074i	−0.00160981	+	0.00278828i
$165$		0			0
$166$	0.566616	+	3.21344i	0.0439780	+	0.249411i
$167$	−2.75277	+	15.6118i	−0.213016	+	1.20807i	0.671300	+	0.741185i	$0.265736\pi$
$167$	−2.75277	+	15.6118i	−0.213016	+	1.20807i	−0.884316	+	0.466888i	$0.845375\pi$
$168$		0			0
$169$	−8.11376	+	6.80825i	−0.624135	+	0.523712i
$170$	4.02549			0.308741
$171$		0			0
$172$	−7.31401			−0.557688
$173$	1.45639	−	1.22206i	0.110728	−	0.0929114i	−0.585743	−	0.810497i	$-0.699197\pi$
$173$	1.45639	−	1.22206i	0.110728	−	0.0929114i	0.696470	+	0.717585i	$0.254753\pi$
$174$		0			0
$175$	0.710039	−	4.02683i	0.0536739	−	0.304400i
$176$	1.32731	+	7.52753i	0.100050	+	0.567409i
$177$		0			0
$178$	−0.160670	+	0.278288i	−0.0120427	+	0.0208586i
$179$	−7.14016	−	12.3671i	−0.533681	−	0.924362i	−0.999226	−	0.0393383i	$-0.987475\pi$
$179$	−7.14016	−	12.3671i	−0.533681	−	0.924362i	0.465545	−	0.885024i	$-0.345858\pi$
$180$		0			0
$181$	11.0202	+	9.24705i	0.819125	+	0.687328i	0.952767	−	0.303702i	$-0.0982227\pi$
$181$	11.0202	+	9.24705i	0.819125	+	0.687328i	−0.133642	+	0.991030i	$0.542667\pi$
$182$	−2.00763	−	3.47733i	−0.148816	−	0.257756i
$183$		0			0
$184$	7.19626	−	2.61922i	0.530515	−	0.193092i
$185$	−0.0313757	−	0.177940i	−0.00230679	−	0.0130824i
$186$		0			0
$187$	25.9937	+	9.46093i	1.90085	+	0.691852i
$188$	−1.75274	+	1.47073i	−0.127832	+	0.107264i
$189$		0			0
$190$	−2.09261	+	1.79688i	−0.151814	+	0.130360i
$191$	−24.1791			−1.74954			−0.874769	−	0.484540i	$-0.838987\pi$
$191$	−24.1791			−1.74954			−0.874769	+	0.484540i	$0.838987\pi$
$192$		0			0
$193$	4.80540	+	1.74902i	0.345900	+	0.125897i	0.509128	−	0.860691i	$-0.329968\pi$
$193$	4.80540	+	1.74902i	0.345900	+	0.125897i	−0.163227	+	0.986588i	$0.552190\pi$
$194$	0.360425	−	2.04407i	0.0258770	−	0.146756i
$195$		0			0
$196$	14.6096	−	5.31747i	1.04355	−	0.379819i
$197$	0.0321431	−	0.0556735i	0.00229010	−	0.00396658i	−0.864878	−	0.501982i	$-0.832604\pi$
$197$	0.0321431	−	0.0556735i	0.00229010	−	0.00396658i	0.867168	+	0.498015i	$0.165938\pi$
$198$		0			0
$199$	−4.88735	−	4.10098i	−0.346455	−	0.290711i	0.452910	−	0.891556i	$-0.350386\pi$
$199$	−4.88735	−	4.10098i	−0.346455	−	0.290711i	−0.799365	+	0.600846i	$0.794831\pi$
$200$	−1.74486	−	1.46411i	−0.123380	−	0.103528i
$201$		0			0
$202$	−1.10435	+	1.91279i	−0.0777017	+	0.134583i
$203$	20.0295	−	7.29015i	1.40580	−	0.511668i
$204$		0			0
$205$	0.00447599	−	0.0253846i	0.000312617	−	0.00177294i
$206$	−5.13241	−	1.86805i	−0.357592	−	0.130153i
$207$		0			0
$208$	2.72794			0.189149
$209$	−17.7357	+	6.68481i	−1.22680	+	0.462398i
$210$		0			0
$211$	−4.52874	+	3.80006i	−0.311771	+	0.261607i	−0.785224	−	0.619212i	$-0.787452\pi$
$211$	−4.52874	+	3.80006i	−0.311771	+	0.261607i	0.473453	+	0.880819i	$0.343008\pi$
$212$	2.40649	+	0.875891i	0.165278	+	0.0601564i
$213$		0			0
$214$	−0.689464	−	3.91015i	−0.0471308	−	0.267292i
$215$	4.29668	−	1.56386i	0.293031	−	0.106655i
$216$		0			0
$217$	−13.4267	−	23.2558i	−0.911466	−	1.57870i
$218$	4.78176	+	4.01237i	0.323862	+	0.271752i
$219$		0			0
$220$	−3.47772	−	6.02359i	−0.234468	−	0.406110i
$221$	4.93612	−	8.54961i	0.332039	−	0.575109i
$222$		0			0
$223$	−5.09043	−	28.8693i	−0.340881	−	1.93323i	−0.358859	−	0.933392i	$-0.616834\pi$
$223$	−5.09043	−	28.8693i	−0.340881	−	1.93323i	0.0179785	−	0.999838i	$-0.494277\pi$
$224$	4.02439	−	22.8234i	0.268891	−	1.52495i
$225$		0			0
$226$	2.54369	−	2.13441i	0.169204	−	0.141979i
$227$	−8.00202			−0.531113			−0.265557	−	0.964095i	$-0.585556\pi$
$227$	−8.00202			−0.531113			−0.265557	+	0.964095i	$0.585556\pi$
$228$		0			0
$229$	28.2694			1.86809			0.934047	−	0.357150i	$-0.116251\pi$
$229$	28.2694			1.86809			0.934047	+	0.357150i	$0.116251\pi$
$230$	−1.62975	+	1.36753i	−0.107463	+	0.0901720i
$231$		0			0
$232$	2.06181	−	11.6931i	0.135365	−	0.767691i
$233$	1.18970	+	6.74715i	0.0779401	+	0.442020i	0.998658	+	0.0517912i	$0.0164930\pi$
$233$	1.18970	+	6.74715i	0.0779401	+	0.442020i	−0.920718	+	0.390229i	$0.872396\pi$
$234$		0			0
$235$	0.715198	−	1.23876i	0.0466544	−	0.0808078i
$236$	−7.63499	−	13.2242i	−0.496996	−	0.860821i
$237$		0			0
$238$	−12.6091	−	10.5803i	−0.817328	−	0.685820i
$239$	−6.69674	−	11.5991i	−0.433176	−	0.750283i	0.563969	−	0.825796i	$-0.309274\pi$
$239$	−6.69674	−	11.5991i	−0.433176	−	0.750283i	−0.997145	+	0.0755132i	$0.975941\pi$
$240$		0			0
$241$	24.1069	−	8.77421i	1.55286	−	0.565196i	0.583777	−	0.811914i	$-0.301574\pi$
$241$	24.1069	−	8.77421i	1.55286	−	0.565196i	0.969087	+	0.246717i	$0.0793520\pi$
$242$	0.868879	+	4.92766i	0.0558536	+	0.316762i
$243$		0			0
$244$	−9.15755	−	3.33308i	−0.586252	−	0.213378i
$245$	−7.44559	+	6.24759i	−0.475681	+	0.399144i
$246$		0			0
$247$	1.25035	+	6.64779i	0.0795581	+	0.422989i
$248$	−14.9587			−0.949879
$249$		0			0
$250$	0.594619	+	0.216424i	0.0376070	+	0.0136878i
$251$	1.58376	−	8.98194i	0.0999660	−	0.566935i	−0.893146	−	0.449767i	$-0.851507\pi$
$251$	1.58376	−	8.98194i	0.0999660	−	0.566935i	0.993112	−	0.117168i	$-0.0373817\pi$
$252$		0			0
$253$	−13.7378	+	5.00015i	−0.863688	+	0.314357i
$254$	−1.68590	+	2.92006i	−0.105783	+	0.183221i
$255$		0			0
$256$	−5.58156	−	4.68348i	−0.348847	−	0.292718i
$257$	18.9570	+	15.9068i	1.18250	+	0.992237i	0.999959	+	0.00903962i	$0.00287744\pi$
$257$	18.9570	+	15.9068i	1.18250	+	0.992237i	0.182543	+	0.983198i	$0.441567\pi$
$258$		0			0
$259$	−0.369407	+	0.639831i	−0.0229538	+	0.0397572i
$260$	−2.33262	+	0.849004i	−0.144663	+	0.0526530i
$261$		0			0
$262$	0.188184	−	1.06725i	0.0116261	−	0.0659347i
$263$	−13.7492	−	5.00428i	−0.847809	−	0.308577i	−0.118662	−	0.992935i	$-0.537861\pi$
$263$	−13.7492	−	5.00428i	−0.847809	−	0.308577i	−0.729147	+	0.684357i	$0.760083\pi$
$264$		0			0
$265$	−1.60099			−0.0983483
$266$	11.2775	−	0.128351i	0.691469	−	0.00786969i
$267$		0			0
$268$	−12.5913	+	10.5654i	−0.769136	+	0.645382i
$269$	16.1661	+	5.88396i	0.985662	+	0.358752i	0.784039	−	0.620712i	$-0.213156\pi$
$269$	16.1661	+	5.88396i	0.985662	+	0.358752i	0.201623	+	0.979463i	$0.435378\pi$
$270$		0			0
$271$	2.37389	+	13.4630i	0.144203	+	0.817819i	0.968003	+	0.250938i	$0.0807389\pi$
$271$	2.37389	+	13.4630i	0.144203	+	0.817819i	−0.823800	+	0.566881i	$0.808150\pi$
$272$	10.5084	−	3.82475i	0.637165	−	0.231909i
$273$		0			0
$274$	1.81790	+	3.14869i	0.109823	+	0.190220i
$275$	3.33097	+	2.79501i	0.200865	+	0.168546i
$276$		0			0
$277$	6.72984	+	11.6564i	0.404357	+	0.700367i	0.994246	−	0.107117i	$-0.0341620\pi$
$277$	6.72984	+	11.6564i	0.404357	+	0.700367i	−0.589889	+	0.807484i	$0.700829\pi$
$278$	5.56386	−	9.63689i	0.333698	−	0.577982i
$279$		0			0
$280$	1.61729	+	9.17211i	0.0966516	+	0.548139i
$281$	3.03476	−	17.2110i	0.181039	−	1.02672i	−0.749901	−	0.661550i	$-0.769899\pi$
$281$	3.03476	−	17.2110i	0.181039	−	1.02672i	0.930940	−	0.365172i	$-0.118990\pi$
$282$		0			0
$283$	−16.1126	+	13.5201i	−0.957794	+	0.803684i	−0.980593	−	0.196056i	$-0.937187\pi$
$283$	−16.1126	+	13.5201i	−0.957794	+	0.803684i	0.0227990	+	0.999740i	$0.492742\pi$
$284$	−17.3833			−1.03151
$285$		0			0
$286$	4.26991			0.252485
$287$	−0.0807392	+	0.0677483i	−0.00476589	+	0.00399905i
$288$		0			0
$289$	4.07550	−	23.1133i	0.239735	−	1.35961i
$290$	0.572791	+	3.24846i	0.0336354	+	0.190756i
$291$		0			0
$292$	−10.8933	+	18.8678i	−0.637483	+	1.10415i
$293$	−5.36574	−	9.29373i	−0.313470	−	0.542945i	0.665641	−	0.746272i	$-0.268158\pi$
$293$	−5.36574	−	9.29373i	−0.313470	−	0.542945i	−0.979111	+	0.203326i	$0.934825\pi$
$294$		0			0
$295$	7.31281	+	6.13617i	0.425768	+	0.357262i
$296$	0.205778	+	0.356418i	0.0119606	+	0.0207164i
$297$		0			0
$298$	6.55295	−	2.38508i	0.379602	−	0.138164i
$299$	0.906014	+	5.13826i	0.0523962	+	0.297153i
$300$		0			0
$301$	−17.5689	−	6.39457i	−1.01266	−	0.368577i
$302$	−1.14938	+	0.964444i	−0.0661394	+	0.0554975i
$303$		0			0
$304$	−3.75541	+	6.67896i	−0.215387	+	0.383064i
$305$	6.09235			0.348847
$306$		0			0
$307$	2.54584	+	0.926610i	0.145299	+	0.0528845i	0.413646	−	0.910438i	$-0.364255\pi$
$307$	2.54584	+	0.926610i	0.145299	+	0.0528845i	−0.268347	+	0.963322i	$0.586477\pi$
$308$	−4.93864	+	28.0084i	−0.281405	+	1.59593i
$309$		0			0
$310$	3.90505	−	1.42132i	0.221792	−	0.0807257i
$311$	−3.62852	+	6.28478i	−0.205755	+	0.356377i	−0.950373	−	0.311113i	$-0.899298\pi$
$311$	−3.62852	+	6.28478i	−0.205755	+	0.356377i	0.744618	+	0.667491i	$0.232632\pi$
$312$		0			0
$313$	−6.64853	−	5.57878i	−0.375797	−	0.315331i	0.435253	−	0.900308i	$-0.356659\pi$
$313$	−6.64853	−	5.57878i	−0.375797	−	0.315331i	−0.811050	+	0.584977i	$0.801103\pi$
$314$	−1.56638	−	1.31435i	−0.0883958	−	0.0741729i
$315$		0			0
$316$	13.8123	−	23.9235i	0.777000	−	1.34580i
$317$	−30.0020	+	10.9198i	−1.68508	+	0.613319i	−0.993992	−	0.109451i	$-0.965091\pi$
$317$	−30.0020	+	10.9198i	−1.68508	+	0.613319i	−0.691089	+	0.722770i	$0.742869\pi$
$318$		0			0
$319$	−3.93604	+	22.3224i	−0.220376	+	1.24981i
$320$	0.0665049	+	0.0242058i	0.00371774	+	0.00135315i
$321$		0			0
$322$	8.69922			0.484788
$323$	14.1372	+	23.8551i	0.786613	+	1.32734i
$324$		0			0
$325$	1.18879	−	0.997510i	0.0659420	−	0.0553319i
$326$	−3.91363	−	1.42445i	−0.216756	−	0.0788928i
$327$		0			0
$328$	0.0101952	+	0.0578197i	0.000562935	+	0.00319256i
$329$	−5.49609	+	2.00041i	−0.303009	+	0.110286i
$330$		0			0
$331$	−12.1500	−	21.0443i	−0.667822	−	1.15670i	−0.978512	−	0.206190i	$-0.933893\pi$
$331$	−12.1500	−	21.0443i	−0.667822	−	1.15670i	0.310690	−	0.950511i	$-0.399440\pi$
$332$	−6.31871	−	5.30202i	−0.346784	−	0.290986i
$333$		0			0
$334$	5.01560	+	8.68728i	0.274442	+	0.475347i
$335$	5.13781	−	8.89896i	0.280709	−	0.486202i
$336$		0			0
$337$	4.92922	+	27.9550i	0.268512	+	1.52280i	0.758846	+	0.651270i	$0.225764\pi$
$337$	4.92922	+	27.9550i	0.268512	+	1.52280i	−0.490334	+	0.871534i	$0.663125\pi$
$338$	−1.16384	+	6.60044i	−0.0633043	+	0.359016i
$339$		0			0
$340$	−7.79522	+	6.54097i	−0.422755	+	0.354734i
$341$	28.5565			1.54642
$342$		0			0
$343$	11.1200			0.600424
$344$	−7.97824	+	6.69454i	−0.430158	+	0.360945i
$345$		0			0
$346$	0.208905	−	1.18476i	0.0112308	−	0.0636929i
$347$	5.40071	+	30.6289i	0.289925	+	1.64425i	0.687142	+	0.726523i	$0.258865\pi$
$347$	5.40071	+	30.6289i	0.289925	+	1.64425i	−0.397217	+	0.917725i	$0.630024\pi$
$348$		0			0
$349$	−8.73989	+	15.1379i	−0.467836	+	0.810315i	−0.999324	−	0.0367503i	$-0.988299\pi$
$349$	−8.73989	+	15.1379i	−0.467836	+	0.810315i	0.531489	+	0.847065i	$0.321633\pi$
$350$	−1.29370	−	2.24076i	−0.0691514	−	0.119774i
$351$		0			0
$352$	18.8794	+	15.8417i	1.00627	+	0.844365i
$353$	−4.41270	−	7.64303i	−0.234865	−	0.406797i	0.724369	−	0.689413i	$-0.242131\pi$
$353$	−4.41270	−	7.64303i	−0.234865	−	0.406797i	−0.959233	+	0.282615i	$0.908798\pi$
$354$		0			0
$355$	10.2120	−	3.71686i	0.541996	−	0.197270i
$356$	−0.141055	−	0.799964i	−0.00747591	−	0.0423980i
$357$		0			0
$358$	−8.49136	−	3.09060i	−0.448782	−	0.163343i
$359$	−15.2610	+	12.8055i	−0.805443	+	0.675847i	−0.949515	−	0.313720i	$-0.898425\pi$
$359$	−15.2610	+	12.8055i	−0.805443	+	0.675847i	0.144073	+	0.989567i	$0.453980\pi$
$360$		0			0
$361$	−17.9974	−	6.09035i	−0.947233	−	0.320545i
$362$	9.10309			0.478448
$363$		0			0
$364$	9.53797	+	3.47154i	0.499925	+	0.181958i
$365$	2.36511	−	13.4132i	0.123796	−	0.702080i
$366$		0			0
$367$	−7.94641	+	2.89226i	−0.414799	+	0.150975i	−0.540985	−	0.841032i	$-0.681949\pi$
$367$	−7.94641	+	2.89226i	−0.414799	+	0.150975i	0.126186	+	0.992007i	$0.459726\pi$
$368$	−2.95509	+	5.11836i	−0.154044	+	0.266813i
$369$		0			0
$370$	−0.0875850	−	0.0734926i	−0.00455333	−	0.00382070i
$371$	5.01483	+	4.20794i	0.260357	+	0.218465i
$372$		0			0
$373$	3.56895	−	6.18160i	0.184793	−	0.320071i	−0.758714	−	0.651424i	$-0.774172\pi$
$373$	3.56895	−	6.18160i	0.184793	−	0.320071i	0.943507	+	0.331353i	$0.107505\pi$
$374$	16.4483	−	5.98669i	0.850522	−	0.309565i
$375$		0			0
$376$	−0.565760	+	3.20859i	−0.0291769	+	0.165470i
$377$	7.60166	+	2.76678i	0.391505	+	0.142496i
$378$		0			0
$379$	6.11358			0.314033			0.157017	−	0.987596i	$-0.449812\pi$
$379$	6.11358			0.314033			0.157017	+	0.987596i	$0.449812\pi$
$380$	1.13253	−	6.87985i	0.0580976	−	0.352929i
$381$		0			0
$382$	−11.7205	+	9.83469i	−0.599674	+	0.503186i
$383$	0.492206	+	0.179148i	0.0251505	+	0.00915404i	0.354565	−	0.935031i	$-0.384629\pi$
$383$	0.492206	+	0.179148i	0.0251505	+	0.00915404i	−0.329414	+	0.944185i	$0.606851\pi$
$384$		0			0
$385$	−3.08744	−	17.5097i	−0.157351	−	0.892379i
$386$	3.04076	−	1.10675i	0.154771	−	0.0563319i
$387$		0			0
$388$	2.62343	+	4.54392i	0.133185	+	0.230683i
$389$	1.91233	+	1.60464i	0.0969590	+	0.0813583i	0.689979	−	0.723830i	$-0.257620\pi$
$389$	1.91233	+	1.60464i	0.0969590	+	0.0813583i	−0.593020	+	0.805188i	$0.702064\pi$
$390$		0			0
$391$	10.6943	+	18.5230i	0.540832	+	0.936749i
$392$	11.0693	−	19.1726i	0.559085	−	0.968364i
$393$		0			0
$394$	−0.00706385	−	0.0400611i	−0.000355872	−	0.00201825i
$395$	−2.99886	+	17.0074i	−0.150889	+	0.855735i
$396$		0			0
$397$	−2.21214	+	1.85621i	−0.111024	+	0.0931604i	−0.696610	−	0.717450i	$-0.745309\pi$
$397$	−2.21214	+	1.85621i	−0.111024	+	0.0931604i	0.585586	+	0.810611i	$0.300865\pi$
$398$	−4.03713			−0.202363
$399$		0			0
$400$	1.75786			0.0878931
$401$	13.2096	−	11.0842i	0.659658	−	0.553519i	−0.250326	−	0.968162i	$-0.580538\pi$
$401$	13.2096	−	11.0842i	0.659658	−	0.553519i	0.909984	+	0.414643i	$0.136093\pi$
$402$		0			0
$403$	1.76973	−	10.0367i	0.0881567	−	0.499962i
$404$	−0.969531	−	5.49848i	−0.0482360	−	0.273560i
$405$		0			0
$406$	6.74385	−	11.6807i	0.334692	−	0.579703i
$407$	−0.392834	−	0.680409i	−0.0194721	−	0.0337266i
$408$		0			0
$409$	−20.0017	−	16.7834i	−0.989019	−	0.829886i	−0.00359375	−	0.999994i	$-0.501144\pi$
$409$	−20.0017	−	16.7834i	−0.989019	−	0.829886i	−0.985425	+	0.170108i	$0.945588\pi$
$410$	−0.00815533	−	0.0141255i	−0.000402763	−	0.000697606i
$411$		0			0
$412$	12.9741	−	4.72218i	0.639188	−	0.232645i
$413$	−6.77817	−	38.4409i	−0.333532	−	1.89155i
$414$		0			0
$415$	4.84565	+	1.76367i	0.237863	+	0.0865752i
$416$	6.73785	−	5.65373i	0.330350	−	0.277197i
$417$		0			0
$418$	−5.87816	+	10.4543i	−0.287510	+	0.511334i
$419$	0.112702			0.00550586			0.00275293	−	0.999996i	$-0.499124\pi$
$419$	0.112702			0.00550586			0.00275293	+	0.999996i	$0.499124\pi$
$420$		0			0
$421$	−18.9996	−	6.91529i	−0.925985	−	0.337031i	−0.165368	−	0.986232i	$-0.552881\pi$
$421$	−18.9996	−	6.91529i	−0.925985	−	0.337031i	−0.760617	+	0.649201i	$0.775103\pi$
$422$	−0.649600	+	3.68407i	−0.0316221	+	0.179338i
$423$		0			0
$424$	3.42674	−	1.24723i	0.166417	−	0.0605710i
$425$	3.18080	−	5.50930i	0.154291	−	0.267240i
$426$		0			0
$427$	−19.0832	−	16.0127i	−0.923500	−	0.774909i
$428$	7.68866	+	6.45156i	0.371646	+	0.311848i
$429$		0			0
$430$	1.44667	−	2.50571i	0.0697648	−	0.120836i
$431$	−38.1011	+	13.8677i	−1.83526	+	0.667982i	−0.843958	+	0.536409i	$0.819781\pi$
$431$	−38.1011	+	13.8677i	−1.83526	+	0.667982i	−0.991306	+	0.131573i	$0.957997\pi$
$432$		0			0
$433$	−3.95457	+	22.4275i	−0.190044	+	1.07779i	0.729257	+	0.684240i	$0.239866\pi$
$433$	−3.95457	+	22.4275i	−0.190044	+	1.07779i	−0.919301	+	0.393555i	$0.871245\pi$
$434$	−15.9676	−	5.81172i	−0.766468	−	0.278972i
$435$		0			0
$436$	−15.7794			−0.755694
$437$	−13.8275	−	4.85533i	−0.661461	−	0.232262i
$438$		0			0
$439$	−25.0285	+	21.0014i	−1.19455	+	1.00234i	−0.194777	+	0.980848i	$0.562398\pi$
$439$	−25.0285	+	21.0014i	−1.19455	+	1.00234i	−0.999769	+	0.0214950i	$0.993157\pi$
$440$	−9.30697	−	3.38746i	−0.443692	−	0.161491i
$441$		0			0
$442$	−1.08477	−	6.15205i	−0.0515974	−	0.292623i
$443$	−13.0384	+	4.74560i	−0.619475	+	0.225470i	−0.632644	−	0.774443i	$-0.718030\pi$
$443$	−13.0384	+	4.74560i	−0.619475	+	0.225470i	0.0131689	+	0.999913i	$0.495808\pi$
$444$		0			0
$445$	0.253910	+	0.439786i	0.0120365	+	0.0208478i
$446$	−14.2099	−	11.9235i	−0.672859	−	0.564596i
$447$		0			0
$448$	−0.144694	−	0.250617i	−0.00683614	−	0.0118405i
$449$	−3.00375	+	5.20265i	−0.141756	+	0.245528i	−0.928158	−	0.372187i	$-0.878608\pi$
$449$	−3.00375	+	5.20265i	−0.141756	+	0.245528i	0.786402	+	0.617715i	$0.211941\pi$
$450$		0			0
$451$	−0.0194628	−	0.110379i	−0.000916467	−	0.00519754i
$452$	−1.45759	+	8.26642i	−0.0685594	+	0.388820i
$453$		0			0
$454$	−3.87889	+	3.25477i	−0.182045	+	0.152754i
$455$	−6.34544			−0.297479
$456$		0			0
$457$	−23.9751			−1.12151			−0.560754	−	0.827982i	$-0.689489\pi$
$457$	−23.9751			−1.12151			−0.560754	+	0.827982i	$0.689489\pi$
$458$	13.7032	−	11.4984i	0.640311	−	0.537285i
$459$		0			0
$460$	0.933886	−	5.29633i	0.0435426	−	0.246943i
$461$	6.26625	+	35.5376i	0.291848	+	1.65515i	0.679744	+	0.733450i	$0.262091\pi$
$461$	6.26625	+	35.5376i	0.291848	+	1.65515i	−0.387896	+	0.921703i	$0.626798\pi$
$462$		0			0
$463$	−3.52141	+	6.09926i	−0.163654	+	0.283457i	−0.936176	−	0.351531i	$-0.885661\pi$
$463$	−3.52141	+	6.09926i	−0.163654	+	0.283457i	0.772523	+	0.634987i	$0.218995\pi$
$464$	4.58171	+	7.93576i	0.212701	+	0.368408i
$465$		0			0
$466$	3.32105	+	2.78669i	0.153845	+	0.129091i
$467$	19.8650	+	34.4072i	0.919244	+	1.59218i	0.800566	+	0.599245i	$0.204532\pi$
$467$	19.8650	+	34.4072i	0.919244	+	1.59218i	0.118678	+	0.992933i	$0.462134\pi$
$468$		0			0
$469$	−39.4826	+	14.3705i	−1.82314	+	0.663568i
$470$	−0.157174	−	0.891376i	−0.00724988	−	0.0411161i
$471$		0			0
$472$	−20.4325	−	7.43683i	−0.940483	−	0.342308i
$473$	15.2306	−	12.7800i	0.700305	−	0.587626i
$474$		0			0
$475$	0.805718	+	4.28379i	0.0369689	+	0.196554i
$476$	41.6089			1.90714
$477$		0			0
$478$	−7.96402	−	2.89867i	−0.364266	−	0.132582i
$479$	6.30401	−	35.7518i	0.288038	−	1.63354i	−0.406192	−	0.913788i	$-0.633143\pi$
$479$	6.30401	−	35.7518i	0.288038	−	1.63354i	0.694229	−	0.719754i	$-0.255745\pi$
$480$		0			0
$481$	−0.263486	+	0.0959012i	−0.0120139	+	0.00437272i
$482$	8.11670	−	14.0585i	0.369705	−	0.640349i
$483$		0			0
$484$	−9.68943	−	8.13040i	−0.440429	−	0.369564i
$485$	−2.51273	−	2.10843i	−0.114097	−	0.0957389i
$486$		0			0
$487$	1.26752	−	2.19541i	0.0574368	−	0.0994835i	−0.835877	−	0.548916i	$-0.815041\pi$
$487$	1.26752	−	2.19541i	0.0574368	−	0.0994835i	0.893314	+	0.449433i	$0.148374\pi$
$488$	−13.0400	+	4.74616i	−0.590292	+	0.214849i
$489$		0			0
$490$	−1.06799	+	6.05689i	−0.0482470	+	0.273622i
$491$	−34.1243	−	12.4202i	−1.54001	−	0.560516i	−0.573959	−	0.818884i	$-0.694593\pi$
$491$	−34.1243	−	12.4202i	−1.54001	−	0.560516i	−0.966047	+	0.258367i	$0.916815\pi$
$492$		0			0
$493$	33.1619			1.49354
$494$	3.31004	+	2.71386i	0.148926	+	0.122102i
$495$		0			0
$496$	8.84356	−	7.42063i	0.397088	−	0.333196i
$497$	−41.7563	−	15.1980i	−1.87303	−	0.681725i
$498$		0			0
$499$	−3.11167	−	17.6471i	−0.139297	−	0.789994i	−0.971770	−	0.235929i	$-0.924187\pi$
$499$	−3.11167	−	17.6471i	−0.139297	−	0.789994i	0.832473	−	0.554066i	$-0.186924\pi$
$500$	−1.50312	+	0.547092i	−0.0672217	+	0.0244667i
$501$		0			0
$502$	−2.88564	−	4.99807i	−0.128792	−	0.223075i
$503$	15.7096	+	13.1819i	0.700457	+	0.587753i	0.921904	−	0.387419i	$-0.126633\pi$
$503$	15.7096	+	13.1819i	0.700457	+	0.587753i	−0.221447	+	0.975173i	$0.571078\pi$
$504$		0			0
$505$	1.74523	+	3.02283i	0.0776618	+	0.134514i
$506$	−4.62546	+	8.01153i	−0.205627	+	0.356156i
$507$		0			0
$508$	−1.48008	−	8.39397i	−0.0656681	−	0.372422i
$509$	2.67442	−	15.1674i	0.118542	−	0.672283i	−0.866394	−	0.499361i	$-0.833568\pi$
$509$	2.67442	−	15.1674i	0.118542	−	0.672283i	0.984936	−	0.172922i	$-0.0553207\pi$
$510$		0			0
$511$	−42.6626	+	35.7982i	−1.88728	+	1.58362i
$512$	17.9712			0.794223
$513$		0			0
$514$	15.6591			0.690695
$515$	−6.61206	+	5.54818i	−0.291362	+	0.244482i
$516$		0			0
$517$	1.08005	−	6.12526i	0.0475004	−	0.269388i
$518$	0.0811817	+	0.460404i	0.00356692	+	0.0202290i
$519$		0			0
$520$	−1.76736	+	3.06116i	−0.0775040	+	0.134241i
$521$	−1.17999	−	2.04381i	−0.0516965	−	0.0895409i	0.839019	−	0.544102i	$-0.183130\pi$
$521$	−1.17999	−	2.04381i	−0.0516965	−	0.0895409i	−0.890716	+	0.454561i	$0.849796\pi$
$522$		0			0
$523$	14.5909	+	12.2432i	0.638014	+	0.535358i	0.903408	−	0.428783i	$-0.141057\pi$
$523$	14.5909	+	12.2432i	0.638014	+	0.535358i	−0.265393	+	0.964140i	$0.585502\pi$
$524$	1.36974	+	2.37246i	0.0598374	+	0.103641i
$525$		0			0
$526$	−8.70019	+	3.16661i	−0.379346	+	0.138071i
$527$	−7.25478	−	41.1439i	−0.316023	−	1.79226i
$528$		0			0
$529$	10.9907	+	4.00028i	0.477856	+	0.173925i
$530$	−0.776063	+	0.651194i	−0.0337100	+	0.0282861i
$531$		0			0
$532$	−21.6300	+	18.5732i	−0.937777	+	0.805252i
$533$	−0.0400008			−0.00173263
$534$		0			0
$535$	−5.89623	−	2.14605i	−0.254916	−	0.0927819i
$536$	−4.06429	+	23.0497i	−0.175551	+	0.995597i
$537$		0			0
$538$	10.2296	−	3.72326i	0.441028	−	0.160521i
$539$	−21.1316	+	36.6009i	−0.910200	+	1.57651i
$540$		0			0
$541$	−3.83099	−	3.21458i	−0.164707	−	0.138206i	0.556709	−	0.830708i	$-0.312064\pi$
$541$	−3.83099	−	3.21458i	−0.164707	−	0.138206i	−0.721416	+	0.692502i	$0.756508\pi$
$542$	6.62670	+	5.56046i	0.284641	+	0.238842i
$543$		0			0
$544$	18.0282	−	31.2258i	0.772955	−	1.33880i
$545$	9.26972	−	3.37390i	0.397071	−	0.144522i
$546$		0			0
$547$	−0.426450	+	2.41852i	−0.0182337	+	0.103408i	−0.992566	−	0.121705i	$-0.961164\pi$
$547$	−0.426450	+	2.41852i	−0.0182337	+	0.103408i	0.974333	+	0.225113i	$0.0722751\pi$
$548$	−8.63656	−	3.14345i	−0.368936	−	0.134282i
$549$		0			0
$550$	2.75150			0.117324
$551$	−17.2388	+	14.8027i	−0.734400	+	0.630615i
$552$		0			0
$553$	54.0944	−	45.3906i	2.30033	−	1.93020i
$554$	8.00339	+	2.91299i	0.340031	+	0.123761i
$555$		0			0
$556$	4.88463	+	27.7021i	0.207155	+	1.17483i
$557$	−4.38265	+	1.59515i	−0.185699	+	0.0675889i	−0.433196	−	0.901300i	$-0.642614\pi$
$557$	−4.38265	+	1.59515i	−0.185699	+	0.0675889i	0.247497	+	0.968889i	$0.420392\pi$
$558$		0			0
$559$	−3.54786	−	6.14508i	−0.150059	−	0.259909i
$560$	−5.50619	−	4.62024i	−0.232679	−	0.195241i
$561$		0			0
$562$	−5.52939	−	9.57719i	−0.233243	−	0.403989i
$563$	17.3165	−	29.9930i	0.729803	−	1.26406i	−0.227163	−	0.973857i	$-0.572945\pi$
$563$	17.3165	−	29.9930i	0.729803	−	1.26406i	0.956966	−	0.290199i	$-0.0937215\pi$
$564$		0			0
$565$	−0.911229	−	5.16784i	−0.0383357	−	0.217413i
$566$	−2.31118	+	13.1074i	−0.0971463	+	0.550944i
$567$		0			0
$568$	−18.9620	+	15.9110i	−0.795628	+	0.667611i
$569$	20.6116			0.864081			0.432041	−	0.901854i	$-0.357794\pi$
$569$	20.6116			0.864081			0.432041	+	0.901854i	$0.357794\pi$
$570$		0			0
$571$	11.1132			0.465071			0.232536	−	0.972588i	$-0.425298\pi$
$571$	11.1132			0.465071			0.232536	+	0.972588i	$0.425298\pi$
$572$	−8.26853	+	6.93812i	−0.345725	+	0.290097i
$573$		0			0
$574$	−0.0115812	+	0.0656803i	−0.000483390	+	0.00274144i
$575$	0.583829	+	3.31106i	0.0243473	+	0.138081i
$576$		0			0
$577$	14.3527	−	24.8596i	0.597510	−	1.03492i	−0.395677	−	0.918390i	$-0.629490\pi$
$577$	14.3527	−	24.8596i	0.597510	−	1.03492i	0.993187	−	0.116528i	$-0.0371765\pi$
$578$	−7.42564	−	12.8616i	−0.308866	−	0.534971i
$579$		0			0
$580$	−6.38756	−	5.35980i	−0.265229	−	0.222554i
$581$	−10.5426	−	18.2603i	−0.437381	−	0.757566i
$582$		0			0
$583$	−6.54172	+	2.38099i	−0.270930	+	0.0986106i
$584$	5.38713	+	30.5519i	0.222921	+	1.26425i
$585$		0			0
$586$	−6.38114	−	2.32254i	−0.263602	−	0.0959434i
$587$	−1.37306	+	1.15213i	−0.0566723	+	0.0475537i	−0.670684	−	0.741743i	$-0.733999\pi$
$587$	−1.37306	+	1.15213i	−0.0566723	+	0.0475537i	0.614012	+	0.789297i	$0.289555\pi$
$588$		0			0
$589$	22.1370	+	18.1499i	0.912139	+	0.747852i
$590$	6.04064			0.248689
$591$		0			0
$592$	−0.298465	−	0.108632i	−0.0122668	−	0.00446476i
$593$	−0.291962	+	1.65580i	−0.0119894	+	0.0679955i	−0.990215	−	0.139547i	$-0.955435\pi$
$593$	−0.291962	+	1.65580i	−0.0119894	+	0.0679955i	0.978226	+	0.207542i	$0.0665465\pi$
$594$		0			0
$595$	−24.4435	+	8.89671i	−1.00209	+	0.364730i
$596$	−8.81407	+	15.2664i	−0.361039	+	0.625337i
$597$		0			0
$598$	2.52913	+	2.12220i	0.103424	+	0.0867830i
$599$	1.65586	+	1.38943i	0.0676568	+	0.0567708i	0.675989	−	0.736912i	$-0.263717\pi$
$599$	1.65586	+	1.38943i	0.0676568	+	0.0567708i	−0.608332	+	0.793683i	$0.708161\pi$
$600$		0			0
$601$	−2.21602	+	3.83826i	−0.0903934	+	0.156566i	−0.907677	−	0.419670i	$-0.862146\pi$
$601$	−2.21602	+	3.83826i	−0.0903934	+	0.156566i	0.817283	+	0.576236i	$0.195479\pi$
$602$	−11.1173	+	4.04636i	−0.453106	+	0.164917i
$603$		0			0
$604$	0.658620	−	3.73522i	0.0267989	−	0.151984i
$605$	7.43056	+	2.70450i	0.302095	+	0.109954i
$606$		0			0
$607$	29.9817			1.21692			0.608460	−	0.793585i	$-0.291788\pi$
$607$	29.9817			1.21692			0.608460	+	0.793585i	$0.291788\pi$
$608$	4.56668	+	24.2798i	0.185203	+	0.984676i
$609$		0			0
$610$	2.95319	−	2.47802i	0.119571	−	0.100332i
$611$	−2.08589	−	0.759203i	−0.0843862	−	0.0307141i
$612$		0			0
$613$	3.44456	+	19.5351i	0.139124	+	0.789013i	0.971898	+	0.235400i	$0.0756402\pi$
$613$	3.44456	+	19.5351i	0.139124	+	0.789013i	−0.832774	+	0.553613i	$0.813249\pi$
$614$	1.61096	−	0.586341i	0.0650130	−	0.0236628i
$615$		0			0
$616$	20.2490	+	35.0724i	0.815857	+	1.41311i
$617$	−16.1011	−	13.5104i	−0.648206	−	0.543909i	0.258320	−	0.966059i	$-0.416831\pi$
$617$	−16.1011	−	13.5104i	−0.648206	−	0.543909i	−0.906526	+	0.422150i	$0.861275\pi$
$618$		0			0
$619$	−10.1316	−	17.5484i	−0.407223	−	0.705331i	0.587354	−	0.809330i	$-0.300169\pi$
$619$	−10.1316	−	17.5484i	−0.407223	−	0.705331i	−0.994577	+	0.103999i	$0.966836\pi$
$620$	−5.25251	+	9.09761i	−0.210946	+	0.365369i
$621$		0			0
$622$	0.797413	+	4.52235i	0.0319733	+	0.181330i
$623$	0.360573	−	2.04491i	0.0144460	−	0.0819275i
$624$		0			0
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$	−5.49193			−0.219501
$627$		0			0
$628$	5.16890			0.206261
$629$	−0.880527	+	0.738850i	−0.0351089	+	0.0294599i
$630$		0			0
$631$	6.98027	−	39.5871i	0.277880	−	1.57594i	−0.451781	−	0.892129i	$-0.649211\pi$
$631$	6.98027	−	39.5871i	0.277880	−	1.57594i	0.729661	−	0.683809i	$-0.239678\pi$
$632$	−6.83066	−	38.7386i	−0.271709	−	1.54094i
$633$		0			0
$634$	−10.1015	+	17.4964i	−0.401183	+	0.694870i
$635$	2.66427	+	4.61465i	0.105728	+	0.183127i
$636$		0			0
$637$	11.5544	+	9.69532i	0.457803	+	0.384143i
$638$	7.17154	+	12.4215i	0.283924	+	0.491771i
$639$		0			0
$640$	−10.6100	+	3.86171i	−0.419396	+	0.152648i
$641$	−0.606201	−	3.43794i	−0.0239435	−	0.135790i	0.970493	−	0.241130i	$-0.0775181\pi$
$641$	−0.606201	−	3.43794i	−0.0239435	−	0.135790i	−0.994436	+	0.105340i	$0.966407\pi$
$642$		0			0
$643$	−34.0072	−	12.3776i	−1.34111	−	0.488125i	−0.430949	−	0.902376i	$-0.641821\pi$
$643$	−34.0072	−	12.3776i	−1.34111	−	0.488125i	−0.910162	+	0.414252i	$0.864043\pi$
$644$	−16.8457	+	14.1352i	−0.663814	+	0.557006i
$645$		0			0
$646$	16.5557	+	5.81330i	0.651377	+	0.228721i
$647$	21.1005			0.829545			0.414772	−	0.909925i	$-0.363861\pi$
$647$	21.1005			0.829545			0.414772	+	0.909925i	$0.363861\pi$
$648$		0			0
$649$	39.0061	+	14.1971i	1.53112	+	0.557283i
$650$	0.170519	−	0.967062i	0.00668831	−	0.0379313i
$651$		0			0
$652$	9.89317	−	3.60082i	0.387446	−	0.141019i
$653$	−8.38024	+	14.5150i	−0.327944	+	0.568016i	−0.982104	−	0.188341i	$-0.939689\pi$
$653$	−8.38024	+	14.5150i	−0.327944	+	0.568016i	0.654160	+	0.756356i	$0.273022\pi$
$654$		0			0
$655$	−1.31194	−	1.10085i	−0.0512617	−	0.0430137i
$656$	−0.0347102	−	0.0291253i	−0.00135521	−	0.00113715i
$657$		0			0
$658$	−1.85051	+	3.20518i	−0.0721404	+	0.124951i
$659$	34.8179	−	12.6727i	1.35631	−	0.493658i	0.441401	−	0.897310i	$-0.354482\pi$
$659$	34.8179	−	12.6727i	1.35631	−	0.493658i	0.914913	+	0.403652i	$0.132259\pi$
$660$		0			0
$661$	3.76649	−	21.3608i	0.146500	−	0.830841i	−0.819651	−	0.572863i	$-0.805833\pi$
$661$	3.76649	−	21.3608i	0.146500	−	0.830841i	0.966151	−	0.257978i	$-0.0830561\pi$
$662$	−14.4492	−	5.25908i	−0.561584	−	0.204400i
$663$		0			0
$664$	−11.7455			−0.455814
$665$	8.73543	−	15.5359i	0.338745	−	0.602455i
$666$		0			0
$667$	−13.4259	+	11.2656i	−0.519851	+	0.436207i
$668$	−23.8284	−	8.67282i	−0.921948	−	0.335561i
$669$		0			0
$670$	−1.12910	−	6.40343i	−0.0436209	−	0.247386i
$671$	24.8936	−	9.06052i	0.961006	−	0.349777i
$672$		0			0
$673$	2.69790	+	4.67290i	0.103996	+	0.180127i	0.913328	−	0.407225i	$-0.133504\pi$
$673$	2.69790	+	4.67290i	0.103996	+	0.180127i	−0.809331	+	0.587352i	$0.800170\pi$
$674$	13.7599	+	11.5459i	0.530011	+	0.444732i
$675$		0			0
$676$	−8.47123	−	14.6726i	−0.325817	−	0.564331i
$677$	−15.4611	+	26.7794i	−0.594217	+	1.02921i	0.399440	+	0.916759i	$0.369205\pi$
$677$	−15.4611	+	26.7794i	−0.594217	+	1.02921i	−0.993657	+	0.112455i	$0.964129\pi$
$678$		0			0
$679$	2.32902	+	13.2086i	0.0893798	+	0.506898i
$680$	−2.51618	+	14.2700i	−0.0964912	+	0.547229i
$681$		0			0
$682$	13.8424	−	11.6152i	0.530053	−	0.444767i
$683$	21.3136			0.815542			0.407771	−	0.913084i	$-0.366306\pi$
$683$	21.3136			0.815542			0.407771	+	0.913084i	$0.366306\pi$
$684$		0			0
$685$	5.74575			0.219534
$686$	5.39029	−	4.52299i	0.205802	−	0.172689i
$687$		0			0
$688$	1.39573	−	7.91560i	0.0532118	−	0.301779i
$689$	0.431429	+	2.44676i	0.0164362	+	0.0932141i
$690$		0			0
$691$	3.81597	−	6.60946i	0.145166	−	0.251436i	−0.784269	−	0.620421i	$-0.786962\pi$
$691$	3.81597	−	6.60946i	0.145166	−	0.251436i	0.929435	+	0.368986i	$0.120295\pi$
$692$	1.52056	+	2.63368i	0.0578029	+	0.100118i
$693$		0			0
$694$	15.0760	+	12.6503i	0.572279	+	0.480199i
$695$	−8.79272	−	15.2294i	−0.333527	−	0.577686i
$696$		0			0
$697$	−0.154089	+	0.0560837i	−0.00583652	+	0.00212432i
$698$	1.92070	+	10.8928i	0.0726995	+	0.412299i
$699$		0			0
$700$	6.14619	+	2.23703i	0.232304	+	0.0845518i
$701$	−12.1942	+	10.2321i	−0.460568	+	0.386463i	−0.843340	−	0.537380i	$-0.819414\pi$
$701$	−12.1942	+	10.2321i	−0.460568	+	0.386463i	0.382772	+	0.923843i	$0.374970\pi$
$702$		0			0
$703$	0.127928	−	0.777130i	0.00482488	−	0.0293100i
$704$	0.307740			0.0115984
$705$		0			0
$706$	−5.24776	−	1.91003i	−0.197502	−	0.0718848i
$707$	2.47837	−	14.0555i	0.0932085	−	0.528612i
$708$		0			0
$709$	37.3356	−	13.5890i	1.40217	−	0.510347i	0.473346	−	0.880877i	$-0.343046\pi$
$709$	37.3356	−	13.5890i	1.40217	−	0.510347i	0.928821	+	0.370530i	$0.120824\pi$
$710$	3.43833	−	5.95536i	0.129038	−	0.223501i
$711$		0			0
$712$	−0.886075	−	0.743505i	−0.0332071	−	0.0278640i
$713$	16.9144	+	14.1929i	0.633450	+	0.531528i
$714$		0			0
$715$	3.37393	−	5.84382i	0.126178	−	0.218546i
$716$	21.4651	−	7.81265i	0.802187	−	0.291972i
$717$		0			0
$718$	−2.18903	+	12.4146i	−0.0816938	+	0.463308i
$719$	−7.66940	−	2.79143i	−0.286020	−	0.104103i	0.195026	−	0.980798i	$-0.437521\pi$
$719$	−7.66940	−	2.79143i	−0.286020	−	0.104103i	−0.481046	+	0.876695i	$0.659743\pi$
$720$		0			0
$721$	35.2935			1.31440
$722$	−11.2012	+	4.36811i	−0.416867	+	0.162564i
$723$		0			0
$724$	−17.6278	+	14.7915i	−0.655132	+	0.549721i
$725$	4.89845	+	1.78289i	0.181924	+	0.0662149i
$726$		0			0
$727$	−0.272620	−	1.54611i	−0.0101109	−	0.0573419i	0.979335	−	0.202246i	$-0.0648239\pi$
$727$	−0.272620	−	1.54611i	−0.0101109	−	0.0573419i	−0.989446	+	0.144904i	$0.953713\pi$
$728$	13.5817	−	4.94333i	0.503370	−	0.183212i
$729$		0			0
$730$	−4.30928	−	7.46389i	−0.159493	−	0.276251i
$731$	−22.2827	−	18.6974i	−0.824154	−	0.691548i
$732$		0			0
$733$	−2.20731	−	3.82317i	−0.0815288	−	0.141212i	0.822378	−	0.568941i	$-0.192647\pi$
$733$	−2.20731	−	3.82317i	−0.0815288	−	0.141212i	−0.903907	+	0.427729i	$0.859314\pi$
$734$	−2.67552	+	4.63414i	−0.0987553	+	0.171049i
$735$		0			0
$736$	3.30905	+	18.7665i	0.121973	+	0.691744i
$737$	7.75881	−	44.0024i	0.285799	−	1.62085i
$738$		0			0
$739$	−7.78848	+	6.53531i	−0.286504	+	0.240405i	−0.774700	−	0.632328i	$-0.782099\pi$
$739$	−7.78848	+	6.53531i	−0.286504	+	0.240405i	0.488197	+	0.872734i	$0.337655\pi$
$740$	0.289022			0.0106247
$741$		0			0
$742$	4.14243			0.152073
$743$	−5.39641	+	4.52813i	−0.197975	+	0.166121i	−0.736386	−	0.676562i	$-0.763469\pi$
$743$	−5.39641	+	4.52813i	−0.197975	+	0.166121i	0.538411	+	0.842682i	$0.319025\pi$
$744$		0			0
$745$	1.91368	−	10.8530i	0.0701117	−	0.397623i
$746$	−0.784320	−	4.44810i	−0.0287160	−	0.162857i
$747$		0			0
$748$	−22.1239	+	38.3196i	−0.808928	+	1.40110i
$749$	12.8283	+	22.2193i	0.468737	+	0.811877i
$750$		0			0
$751$	19.7520	+	16.5739i	0.720760	+	0.604789i	0.927595	−	0.373586i	$-0.121872\pi$
$751$	19.7520	+	16.5739i	0.720760	+	0.604789i	−0.206835	+	0.978376i	$0.566316\pi$
$752$	−1.25722	−	2.17757i	−0.0458461	−	0.0794078i
$753$		0			0
$754$	4.81018	−	1.75076i	0.175176	−	0.0637590i
$755$	0.411744	+	2.33511i	0.0149849	+	0.0849835i
$756$		0			0
$757$	−18.0947	−	6.58595i	−0.657665	−	0.239370i	−0.00843696	−	0.999964i	$-0.502686\pi$
$757$	−18.0947	−	6.58595i	−0.657665	−	0.239370i	−0.649228	+	0.760594i	$0.724908\pi$
$758$	2.96348	−	2.48666i	0.107639	−	0.0903195i
$759$		0			0
$760$	−5.06177	−	8.54126i	−0.183610	−	0.309824i
$761$	−30.9500			−1.12194			−0.560969	−	0.827837i	$-0.689571\pi$
$761$	−30.9500			−1.12194			−0.560969	+	0.827837i	$0.689571\pi$
$762$		0			0
$763$	−37.9034	−	13.7957i	−1.37220	−	0.499439i
$764$	6.71612	−	38.0890i	0.242981	−	1.37801i
$765$		0			0
$766$	0.311458	−	0.113361i	0.0112534	−	0.00409592i
$767$	7.40713	−	12.8295i	0.267456	−	0.463247i
$768$		0			0
$769$	−22.7690	−	19.1055i	−0.821071	−	0.688960i	0.132152	−	0.991230i	$-0.457811\pi$
$769$	−22.7690	−	19.1055i	−0.821071	−	0.688960i	−0.953223	+	0.302269i	$0.902256\pi$
$770$	−8.61857	−	7.23184i	−0.310592	−	0.260617i
$771$		0			0
$772$	−4.08999	+	7.08407i	−0.147202	+	0.254961i
$773$	−11.6190	+	4.22899i	−0.417908	+	0.152106i	−0.542411	−	0.840113i	$-0.682488\pi$
$773$	−11.6190	+	4.22899i	−0.417908	+	0.152106i	0.124503	+	0.992219i	$0.460266\pi$
$774$		0			0
$775$	1.14040	−	6.46755i	0.0409645	−	0.232321i
$776$	7.02075	+	2.55534i	0.252030	+	0.0917315i
$777$		0			0
$778$	1.57965			0.0566333
$779$	0.0550669	−	0.0979360i	0.00197298	−	0.00350892i
$780$		0			0
$781$	36.1988	−	30.3744i	1.29530	−	1.08688i
$782$	12.7180	+	4.62899i	0.454796	+	0.165532i
$783$		0			0
$784$	2.96688	+	16.8260i	0.105960	+	0.600929i
$785$	−3.03651	+	1.10520i	−0.108378	+	0.0394463i
$786$		0			0
$787$	−21.9353	−	37.9930i	−0.781909	−	1.35431i	−0.930829	−	0.365456i	$-0.880913\pi$
$787$	−21.9353	−	37.9930i	−0.781909	−	1.35431i	0.148920	−	0.988849i	$-0.452420\pi$
$788$	0.0787736	+	0.0660989i	0.00280619	+	0.00235468i
$789$		0			0
$790$	5.46398	+	9.46390i	0.194400	+	0.336710i
$791$	−10.7285	+	18.5823i	−0.381462	+	0.660712i
$792$		0			0
$793$	−1.64174	−	9.31078i	−0.0583000	−	0.330636i
$794$	−0.317309	+	1.79955i	−0.0112609	+	0.0638636i
$795$		0			0
$796$	7.81776	−	6.55988i	0.277093	−	0.232509i
$797$	5.08657			0.180176			0.0900879	−	0.995934i	$-0.471285\pi$
$797$	5.08657			0.180176			0.0900879	+	0.995934i	$0.471285\pi$
$798$		0			0
$799$	−9.09960			−0.321921
$800$	4.34182	−	3.64322i	0.153506	−	0.128807i
$801$		0			0
$802$	1.89479	−	10.7459i	0.0669073	−	0.379450i
$803$	−10.2841	−	58.3242i	−0.362919	−	2.05822i
$804$		0			0
$805$	6.87380	−	11.9058i	0.242270	−	0.419624i
$806$	−3.22449	−	5.58498i	−0.113578	−	0.196722i
$807$		0			0
$808$	−6.09036	−	5.11042i	−0.214258	−	0.179784i
$809$	15.1064	+	26.1650i	0.531112	+	0.919914i	0.999341	+	0.0363062i	$0.0115591\pi$
$809$	15.1064	+	26.1650i	0.531112	+	0.919914i	−0.468228	+	0.883608i	$0.655108\pi$
$810$		0			0
$811$	−3.43739	+	1.25111i	−0.120703	+	0.0439323i	−0.401666	−	0.915786i	$-0.631569\pi$
$811$	−3.43739	+	1.25111i	−0.120703	+	0.0439323i	0.280963	+	0.959719i	$0.409346\pi$
$812$	5.92057	+	33.5772i	0.207771	+	1.17833i
$813$		0			0
$814$	−0.467173	−	0.170037i	−0.0163744	−	0.00595980i
$815$	−5.04191	+	4.23067i	−0.176610	+	0.148194i
$816$		0			0
$817$	19.9295	−	0.226820i	0.697244	−	0.00793541i
$818$	−16.5221			−0.577682
$819$		0			0
$820$	0.0387447	+	0.0141019i	0.00135303	+	0.000492461i
$821$	3.37413	−	19.1357i	0.117758	−	0.667839i	−0.867589	−	0.497281i	$-0.834332\pi$
$821$	3.37413	−	19.1357i	0.117758	−	0.667839i	0.985348	−	0.170558i	$-0.0545571\pi$
$822$		0			0
$823$	4.92429	−	1.79230i	0.171650	−	0.0624755i	−0.254766	−	0.967003i	$-0.581998\pi$
$823$	4.92429	−	1.79230i	0.171650	−	0.0624755i	0.426416	+	0.904527i	$0.359776\pi$
$824$	9.83012	−	17.0263i	0.342448	−	0.593138i
$825$		0			0
$826$	−18.9212	−	15.8768i	−0.658353	−	0.552424i
$827$	−43.8018	−	36.7541i	−1.52314	−	1.27806i	−0.830950	−	0.556346i	$-0.812203\pi$
$827$	−43.8018	−	36.7541i	−1.52314	−	1.27806i	−0.692187	−	0.721718i	$-0.743353\pi$
$828$		0			0
$829$	7.34286	−	12.7182i	0.255028	−	0.441722i	−0.709875	−	0.704328i	$-0.751249\pi$
$829$	7.34286	−	12.7182i	0.255028	−	0.441722i	0.964903	+	0.262606i	$0.0845819\pi$
$830$	3.06623	−	1.11602i	0.106430	−	0.0387375i
$831$		0			0
$832$	0.0190716	−	0.108161i	0.000661190	−	0.00374979i
$833$	58.1028	+	21.1477i	2.01314	+	0.732724i
$834$		0			0
$835$	15.8526			0.548602
$836$	−5.60413	−	29.7956i	−0.193823	−	1.03050i
$837$		0			0
$838$	0.0546310	−	0.0458408i	0.00188720	−	0.00158354i
$839$	19.6431	+	7.14950i	0.678155	+	0.246828i	0.658055	−	0.752970i	$-0.271379\pi$
$839$	19.6431	+	7.14950i	0.678155	+	0.246828i	0.0200999	+	0.999798i	$0.493602\pi$
$840$		0			0
$841$	−0.317165	−	1.79873i	−0.0109367	−	0.0620252i
$842$	−12.0226	+	4.37586i	−0.414326	+	0.150802i
$843$		0			0
$844$	−4.72826	−	8.18959i	−0.162753	−	0.281897i
$845$	8.11376	+	6.80825i	0.279122	+	0.234211i
$846$		0			0
$847$	−16.1666	−	28.0013i	−0.555490	−	0.962137i
$848$	−1.40716	+	2.43728i	−0.0483222	+	0.0836965i
$849$		0			0
$850$	−0.699019	−	3.96434i	−0.0239762	−	0.135976i
$851$	0.105489	−	0.598259i	0.00361612	−	0.0205081i
$852$		0			0
$853$	16.4723	−	13.8219i	0.564000	−	0.473253i	−0.315648	−	0.948876i	$-0.602222\pi$
$853$	16.4723	−	13.8219i	0.564000	−	0.473253i	0.879649	+	0.475624i	$0.157778\pi$
$854$	−15.7634			−0.539413
$855$		0			0
$856$	14.2920			0.488492
$857$	38.9182	−	32.6562i	1.32942	−	1.11552i	0.345208	−	0.938526i	$-0.387808\pi$
$857$	38.9182	−	32.6562i	1.32942	−	1.11552i	0.984213	−	0.176990i	$-0.0566359\pi$
$858$		0			0
$859$	−1.25062	+	7.09262i	−0.0426706	+	0.241997i	−0.998682	−	0.0513340i	$-0.983653\pi$
$859$	−1.25062	+	7.09262i	−0.0426706	+	0.241997i	0.956011	+	0.293331i	$0.0947638\pi$
$860$	1.27007	+	7.20290i	0.0433089	+	0.245617i
$861$		0			0
$862$	−12.8285	+	22.2195i	−0.436939	+	0.756801i
$863$	9.02344	+	15.6291i	0.307161	+	0.532019i	0.977740	−	0.209819i	$-0.0672875\pi$
$863$	9.02344	+	15.6291i	0.307161	+	0.532019i	−0.670579	+	0.741838i	$0.733954\pi$
$864$		0			0
$865$	−1.45639	−	1.22206i	−0.0495189	−	0.0415512i
$866$	7.20529	+	12.4799i	0.244846	+	0.424085i
$867$		0			0
$868$	40.3640	−	14.6913i	1.37004	−	0.498655i
$869$	13.0399	+	73.9527i	0.442347	+	2.50867i
$870$		0			0
$871$	−14.9846	−	5.45393i	−0.507732	−	0.184799i
$872$	−17.2124	+	14.4429i	−0.582884	+	0.489098i
$873$		0			0
$874$	−8.67761	+	3.27070i	−0.293524	+	0.110633i
$875$	−4.08895			−0.138232
$876$		0			0
$877$	22.3078	+	8.11936i	0.753280	+	0.274171i	0.689985	−	0.723824i	$-0.257617\pi$
$877$	22.3078	+	8.11936i	0.753280	+	0.274171i	0.0632945	+	0.997995i	$0.479839\pi$
$878$	−3.59008	+	20.3604i	−0.121159	+	0.687129i
$879$		0			0
$880$	7.18269	−	2.61429i	0.242128	−	0.0881275i
$881$	16.7038	−	28.9318i	0.562765	−	0.974737i	−0.434489	−	0.900677i	$-0.643071\pi$
$881$	16.7038	−	28.9318i	0.562765	−	0.974737i	0.997254	−	0.0740599i	$-0.0235956\pi$
$882$		0			0
$883$	32.5424	+	27.3063i	1.09514	+	0.918931i	0.997089	−	0.0762507i	$-0.0242949\pi$
$883$	32.5424	+	27.3063i	1.09514	+	0.918931i	0.0980503	+	0.995181i	$0.468739\pi$
$884$	12.0970	+	10.1506i	0.406866	+	0.341401i
$885$		0			0
$886$	−4.38998	+	7.60367i	−0.147484	+	0.255450i
$887$	−8.82015	+	3.21027i	−0.296152	+	0.107790i	−0.485823	−	0.874057i	$-0.661480\pi$
$887$	−8.82015	+	3.21027i	−0.296152	+	0.107790i	0.189671	+	0.981848i	$0.439258\pi$
$888$		0			0
$889$	3.78347	−	21.4571i	0.126893	−	0.719648i
$890$	0.301960	+	0.109904i	0.0101217	+	0.00368401i
$891$		0			0
$892$	46.8914			1.57004
$893$	4.73033	−	4.06185i	0.158295	−	0.135924i
$894$		0			0
$895$	−10.9394	+	9.17922i	−0.365663	+	0.306827i
$896$	43.3837	+	15.7904i	1.44935	+	0.527519i
$897$		0			0
$898$	0.660111	+	3.74368i	0.0220282	+	0.124928i
$899$	32.1697	−	11.7088i	1.07292	−	0.390511i
$900$		0			0
$901$	5.09244	+	8.82036i	0.169654	+	0.293849i
$902$	−0.0543303	−	0.0455885i	−0.00180900	−	0.00151793i
$903$		0			0
$904$	5.97631	+	10.3513i	0.198769	+	0.344278i
$905$	7.19293	−	12.4585i	0.239101	−	0.414135i
$906$		0			0
$907$	−1.34450	−	7.62501i	−0.0446432	−	0.253184i	0.954316	−	0.298800i	$-0.0965863\pi$
$907$	−1.34450	−	7.62501i	−0.0446432	−	0.253184i	−0.998959	+	0.0456153i	$0.985475\pi$
$908$	2.22269	−	12.6055i	0.0737625	−	0.418328i
$909$		0			0
$910$	−3.07587	+	2.58097i	−0.101964	+	0.0855582i
$911$	31.8865			1.05645			0.528223	−	0.849106i	$-0.322858\pi$
$911$	31.8865			1.05645			0.528223	+	0.849106i	$0.322858\pi$
$912$		0			0
$913$	22.4224			0.742073
$914$	−11.6216	+	9.75172i	−0.384410	+	0.322558i
$915$		0			0
$916$	−7.85227	+	44.5324i	−0.259446	+	1.47139i
$917$	1.21602	+	6.89642i	0.0401567	+	0.227740i
$918$		0			0
$919$	9.68427	−	16.7736i	0.319455	−	0.553311i	−0.660920	−	0.750457i	$-0.729834\pi$
$919$	9.68427	−	16.7736i	0.319455	−	0.553311i	0.980374	+	0.197145i	$0.0631670\pi$
$920$	−3.82905	−	6.63211i	−0.126240	−	0.218654i
$921$		0			0
$922$	17.4922	+	14.6777i	0.576075	+	0.483384i
$923$	−8.43225	−	14.6051i	−0.277551	−	0.480733i
$924$		0			0
$925$	−0.169789	+	0.0617980i	−0.00558262	+	0.00203191i
$926$	0.773873	+	4.38885i	0.0254311	+	0.144227i
$927$		0			0
$928$	27.7636	+	10.1051i	0.911386	+	0.331717i
$929$	−18.6717	+	15.6674i	−0.612600	+	0.514032i	−0.895468	−	0.445127i	$-0.853159\pi$
$929$	−18.6717	+	15.6674i	−0.612600	+	0.514032i	0.282868	+	0.959159i	$0.408714\pi$
$930$		0			0
$931$	−39.6439	+	14.9423i	−1.29928	+	0.489714i
$932$	−10.9592			−0.358979
$933$		0			0
$934$	23.6243	+	8.59853i	0.773009	+	0.281352i
$935$	4.80344	−	27.2417i	0.157089	−	0.890898i
$936$		0			0
$937$	−17.5551	+	6.38953i	−0.573499	+	0.208737i	−0.612457	−	0.790504i	$-0.709819\pi$
$937$	−17.5551	+	6.38953i	−0.573499	+	0.208737i	0.0389573	+	0.999241i	$0.487596\pi$
$938$	−13.2936	+	23.0252i	−0.434052	+	0.751801i
$939$		0			0
$940$	1.75274	+	1.47073i	0.0571682	+	0.0479698i
$941$	17.9348	+	15.0491i	0.584659	+	0.490587i	0.886473	−	0.462779i	$-0.153148\pi$
$941$	17.9348	+	15.0491i	0.584659	+	0.490587i	−0.301814	+	0.953367i	$0.597592\pi$
$942$		0			0
$943$	0.0433315	−	0.0750524i	0.00141107	−	0.00244404i
$944$	15.7689	−	5.73940i	0.513233	−	0.186802i
$945$		0			0
$946$	2.18468	−	12.3899i	0.0710299	−	0.402831i
$947$	37.3038	+	13.5775i	1.21221	+	0.441208i	0.867470	−	0.497490i	$-0.165745\pi$
$947$	37.3038	+	13.5775i	1.21221	+	0.441208i	0.344740	+	0.938698i	$0.387967\pi$
$948$		0			0
$949$	−21.1364			−0.686117
$950$	2.13296	+	1.74879i	0.0692025	+	0.0567383i
$951$		0			0
$952$	45.3877	−	38.0848i	1.47102	−	1.23433i
$953$	−46.8875	−	17.0657i	−1.51884	−	0.552811i	−0.557978	−	0.829856i	$-0.688423\pi$
$953$	−46.8875	−	17.0657i	−1.51884	−	0.552811i	−0.960857	+	0.277045i	$0.910645\pi$
$954$		0			0
$955$	4.19866	+	23.8118i	0.135865	+	0.770531i
$956$	20.1320	−	7.32746i	0.651116	−	0.236987i
$957$		0			0
$958$	−11.4860	−	19.8944i	−0.371097	−	0.642758i
$959$	−17.9975	−	15.1017i	−0.581170	−	0.487660i
$960$		0			0
$961$	−6.06485	−	10.5046i	−0.195640	−	0.338859i
$962$	−0.0887147	+	0.153658i	−0.00286028	+	0.00495414i
$963$		0			0
$964$	7.12582	+	40.4125i	0.229507	+	1.30160i
$965$	0.888002	−	5.03611i	0.0285858	−	0.162118i
$966$		0			0
$967$	−41.2501	+	34.6130i	−1.32651	+	1.11308i	−0.341636	+	0.939832i	$0.610981\pi$
$967$	−41.2501	+	34.6130i	−1.32651	+	1.11308i	−0.984879	+	0.173246i	$0.944575\pi$
$968$	−18.0112			−0.578901
$969$		0			0
$970$	−2.07561			−0.0666437
$971$	18.3652	−	15.4102i	0.589367	−	0.494537i	−0.298641	−	0.954365i	$-0.596533\pi$
$971$	18.3652	−	15.4102i	0.589367	−	0.494537i	0.888008	+	0.459828i	$0.152089\pi$
$972$		0			0
$973$	−12.4864	+	70.8136i	−0.400294	+	2.27018i
$974$	−0.278553	−	1.57975i	−0.00892542	−	0.0506186i
$975$		0			0
$976$	5.35476	−	9.27472i	0.171402	−	0.296876i
$977$	−26.3233	−	45.5933i	−0.842157	−	1.45866i	−0.888067	−	0.459713i	$-0.847952\pi$
$977$	−26.3233	−	45.5933i	−0.842157	−	1.45866i	0.0459104	−	0.998946i	$-0.485381\pi$
$978$		0			0
$979$	1.69153	+	1.41937i	0.0540617	+	0.0453631i
$980$	−7.77362	−	13.4643i	−0.248319	−	0.430102i
$981$		0			0
$982$	−21.5932	+	7.85927i	−0.689065	+	0.250799i
$983$	7.12467	+	40.4060i	0.227242	+	1.28875i	0.858353	+	0.513059i	$0.171488\pi$
$983$	7.12467	+	40.4060i	0.227242	+	1.28875i	−0.631112	+	0.775692i	$0.717401\pi$
$984$		0			0
$985$	−0.0604093	−	0.0219872i	−0.00192480	−	0.000700570i
$986$	16.0748	−	13.4884i	0.511926	−	0.429557i
$987$		0			0
$988$	−10.8195	+	0.123138i	−0.344214	+	0.00391753i
$989$	15.3731			0.488837
$990$		0			0
$991$	−26.7308	−	9.72922i	−0.849133	−	0.309059i	−0.119446	−	0.992841i	$-0.538112\pi$
$991$	−26.7308	−	9.72922i	−0.849133	−	0.309059i	−0.729687	+	0.683782i	$0.760334\pi$
$992$	6.46362	−	36.6570i	0.205220	−	1.16386i
$993$		0			0
$994$	−26.4226	+	9.61703i	−0.838073	+	0.305034i
$995$	−3.18999	+	5.52523i	−0.101130	+	0.175162i
$996$		0			0
$997$	−26.9547	−	22.6177i	−0.853664	−	0.716309i	0.106929	−	0.994267i	$-0.465898\pi$
$997$	−26.9547	−	22.6177i	−0.853664	−	0.716309i	−0.960593	+	0.277957i	$0.910343\pi$
$998$	−8.68620	−	7.28859i	−0.274957	−	0.230716i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.bs.c.766.3		18
3.2	odd	2		95.2.k.a.6.1	✓	18
15.2	even	4		475.2.u.b.424.3		36
15.8	even	4		475.2.u.b.424.4		36
15.14	odd	2		475.2.l.c.101.3		18
19.16	even	9	inner	855.2.bs.c.586.3		18
57.23	odd	18		1805.2.a.v.1.2		9
57.35	odd	18		95.2.k.a.16.1	yes	18
57.53	even	18		1805.2.a.s.1.8		9
285.92	even	36		475.2.u.b.149.4		36
285.149	odd	18		475.2.l.c.301.3		18
285.194	odd	18		9025.2.a.cc.1.8		9
285.224	even	18		9025.2.a.cf.1.2		9
285.263	even	36		475.2.u.b.149.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.6.1	✓	18	3.2	odd	2
95.2.k.a.16.1	yes	18	57.35	odd	18
475.2.l.c.101.3		18	15.14	odd	2
475.2.l.c.301.3		18	285.149	odd	18
475.2.u.b.149.3		36	285.263	even	36
475.2.u.b.149.4		36	285.92	even	36
475.2.u.b.424.3		36	15.2	even	4
475.2.u.b.424.4		36	15.8	even	4
855.2.bs.c.586.3		18	19.16	even	9	inner
855.2.bs.c.766.3		18	1.1	even	1	trivial
1805.2.a.s.1.8		9	57.53	even	18
1805.2.a.v.1.2		9	57.23	odd	18
9025.2.a.cc.1.8		9	285.194	odd	18
9025.2.a.cf.1.2		9	285.224	even	18

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.bs (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.484738 - 0.406743i) q^{2} +(-0.277766 + 1.57529i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(-2.04448 + 3.54114i) q^{7} +(1.13887 + 1.97259i) q^{8} +O(q^{10})\)	\(q+(0.484738 - 0.406743i) q^{2} +(-0.277766 + 1.57529i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(-2.04448 + 3.54114i) q^{7} +(1.13887 + 1.97259i) q^{8} +(-0.484738 - 0.406743i) q^{10} +(-2.17413 - 3.76571i) q^{11} +(-1.45826 + 0.530764i) q^{13} +(0.449299 + 2.54810i) q^{14} +(-1.65185 - 0.601224i) q^{16} +(-4.87326 + 4.08915i) q^{17} +(0.708014 - 4.30101i) q^{19} +1.59959 q^{20} +(-2.58556 - 0.941068i) q^{22} +(0.583829 - 3.31106i) q^{23} +(-0.939693 + 0.342020i) q^{25} +(-0.490990 + 0.850420i) q^{26} +(-5.01042 - 4.20424i) q^{28} +(-3.99325 - 3.35074i) q^{29} +(-3.28366 + 5.68747i) q^{31} +(-5.32603 + 1.93852i) q^{32} +(-0.699019 + 3.96434i) q^{34} +(3.84236 + 1.39850i) q^{35} +0.180685 q^{37} +(-1.40621 - 2.37284i) q^{38} +(1.74486 - 1.46411i) q^{40} +(0.0242217 + 0.00881597i) q^{41} +(0.793995 + 4.50297i) q^{43} +(6.53598 - 2.37890i) q^{44} +(-1.06375 - 1.84246i) q^{46} +(1.09575 + 0.919441i) q^{47} +(-4.85976 - 8.41736i) q^{49} +(-0.316390 + 0.548004i) q^{50} +(-0.431051 - 2.44461i) q^{52} +(0.278010 - 1.57667i) q^{53} +(-3.33097 + 2.79501i) q^{55} -9.31361 q^{56} -3.29857 q^{58} +(-7.31281 + 6.13617i) q^{59} +(-1.05793 + 5.99980i) q^{61} +(0.721625 + 4.09254i) q^{62} +(-0.0353865 + 0.0612913i) q^{64} +(0.775925 + 1.34394i) q^{65} +(7.87159 + 6.60505i) q^{67} +(-5.08797 - 8.81262i) q^{68} +(2.43137 - 0.884946i) q^{70} +(1.88710 + 10.7023i) q^{71} +(12.7987 + 4.65836i) q^{73} +(0.0875850 - 0.0734926i) q^{74} +(6.57867 + 2.31000i) q^{76} +17.7799 q^{77} +(-16.2283 - 5.90661i) q^{79} +(-0.305250 + 1.73116i) q^{80} +(0.0153270 - 0.00557858i) q^{82} +(-2.57831 + 4.46577i) q^{83} +(4.87326 + 4.08915i) q^{85} +(2.21643 + 1.85981i) q^{86} +(4.95213 - 8.57735i) q^{88} +(-0.477195 + 0.173685i) q^{89} +(1.10187 - 6.24904i) q^{91} +(5.05370 + 1.83940i) q^{92} +0.905127 q^{94} +(-4.35862 + 0.0496059i) q^{95} +(2.51273 - 2.10843i) q^{97} +(-5.77942 - 2.10354i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8}+O(q^{10}) \) 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8	\( 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8} - 3 q^{10} - 3 q^{13} + 12 q^{14} - 3 q^{16} - 24 q^{17} - 12 q^{20} + 9 q^{22} + 9 q^{23} - 3 q^{26} - 12 q^{28} - 15 q^{29} - 18 q^{31} - 15 q^{32} - 12 q^{34} + 36 q^{37} + 33 q^{38} - 6 q^{40} + 30 q^{41} - 36 q^{43} - 42 q^{44} + 9 q^{46} - 21 q^{47} + 9 q^{49} + 6 q^{50} - 39 q^{52} + 12 q^{53} + 3 q^{55} + 12 q^{58} - 18 q^{59} - 30 q^{61} + 24 q^{62} + 36 q^{64} + 9 q^{65} - 51 q^{68} + 33 q^{70} + 12 q^{71} + 24 q^{73} + 15 q^{74} - 33 q^{76} + 60 q^{77} - 51 q^{79} - 15 q^{80} - 15 q^{82} + 24 q^{85} - 63 q^{86} - 27 q^{88} + 54 q^{89} + 30 q^{91} + 42 q^{92} + 30 q^{94} - 15 q^{95} + 27 q^{97} + 3 q^{98}+O(q^{100}) \) 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8 - 3 * q^10 - 3 * q^13 + 12 * q^14 - 3 * q^16 - 24 * q^17 - 12 * q^20 + 9 * q^22 + 9 * q^23 - 3 * q^26 - 12 * q^28 - 15 * q^29 - 18 * q^31 - 15 * q^32 - 12 * q^34 + 36 * q^37 + 33 * q^38 - 6 * q^40 + 30 * q^41 - 36 * q^43 - 42 * q^44 + 9 * q^46 - 21 * q^47 + 9 * q^49 + 6 * q^50 - 39 * q^52 + 12 * q^53 + 3 * q^55 + 12 * q^58 - 18 * q^59 - 30 * q^61 + 24 * q^62 + 36 * q^64 + 9 * q^65 - 51 * q^68 + 33 * q^70 + 12 * q^71 + 24 * q^73 + 15 * q^74 - 33 * q^76 + 60 * q^77 - 51 * q^79 - 15 * q^80 - 15 * q^82 + 24 * q^85 - 63 * q^86 - 27 * q^88 + 54 * q^89 + 30 * q^91 + 42 * q^92 + 30 * q^94 - 15 * q^95 + 27 * q^97 + 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more