LMFDB - Embedded newform 351.2.t.c.64.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(64,351)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("351.64"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6x^{16} + 9x^{14} + 54x^{12} + 81x^{10} + 486x^{8} + 729x^{6} - 4374x^{4} + 59049 $ x^20 - 6x^16 + 9x^14 + 54x^12 + 81x^10 + 486x^8 + 729x^6 - 4374*x^4 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{9} $
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			64.4
Root			$1.65391 + 0.514376i$ of defining polynomial
Character	$\chi$	$=$	351.64
Dual form			351.2.t.c.181.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.929969 + 0.536918i) q^{2} +(-0.423439 + 0.733417i) q^{4} +(-1.10543 - 0.638222i) q^{5} +(0.890926 - 0.514376i) q^{7} -3.05708i q^{8} +1.37069 q^{10} +(-4.03796 + 2.33132i) q^{11} +(-3.55524 - 0.600200i) q^{13} +(-0.552355 + 0.956708i) q^{14} +(0.794522 + 1.37615i) q^{16} +0.476187 q^{17} -6.69096i q^{19} +(0.936166 - 0.540496i) q^{20} +(2.50345 - 4.33610i) q^{22} +(0.479867 - 0.831155i) q^{23} +(-1.68535 - 2.91910i) q^{25} +(3.62852 - 1.35071i) q^{26} +0.871227i q^{28} +(-4.68880 - 8.12123i) q^{29} +(-1.66927 - 0.963754i) q^{31} +(3.81725 + 2.20389i) q^{32} +(-0.442839 + 0.255673i) q^{34} -1.31314 q^{35} +4.94666i q^{37} +(3.59249 + 6.22238i) q^{38} +(-1.95109 + 3.37939i) q^{40} +(1.31994 + 0.762068i) q^{41} +(-1.31426 - 2.27637i) q^{43} -3.94868i q^{44} +1.03060i q^{46} +(-5.92316 + 3.41974i) q^{47} +(-2.97083 + 5.14564i) q^{49} +(3.13464 + 1.80978i) q^{50} +(1.94563 - 2.35333i) q^{52} -0.582145 q^{53} +5.95159 q^{55} +(-1.57249 - 2.72363i) q^{56} +(8.72087 + 5.03499i) q^{58} +(3.64799 + 2.10617i) q^{59} +(-4.71645 - 8.16913i) q^{61} +2.06983 q^{62} -7.91132 q^{64} +(3.54702 + 2.93252i) q^{65} +(-2.01156 - 1.16138i) q^{67} +(-0.201636 + 0.349243i) q^{68} +(1.22118 - 0.705051i) q^{70} -1.35071i q^{71} +12.8687i q^{73} +(-2.65595 - 4.60024i) q^{74} +(4.90726 + 2.83321i) q^{76} +(-2.39835 + 4.15406i) q^{77} +(6.45415 + 11.1789i) q^{79} -2.02833i q^{80} -1.63667 q^{82} +(8.86189 - 5.11641i) q^{83} +(-0.526392 - 0.303913i) q^{85} +(2.44445 + 1.41130i) q^{86} +(7.12701 + 12.3444i) q^{88} +6.85985i q^{89} +(-3.47619 + 1.29400i) q^{91} +(0.406389 + 0.703886i) q^{92} +(3.67224 - 6.36050i) q^{94} +(-4.27032 + 7.39640i) q^{95} +(-14.9635 + 8.63918i) q^{97} -6.38037i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 12 q^{4} - 16 q^{10} - 4 q^{13} + 18 q^{14} + 4 q^{16} + 12 q^{17} - 10 q^{22} - 24 q^{23} - 12 q^{25} + 12 q^{26} - 12 q^{29} + 12 q^{35} - 12 q^{38} - 8 q^{40} + 4 q^{43} - 10 q^{49} - 108 q^{53}+ \cdots - 24 q^{95}+O(q^{100}) $ 20 * q + 12 * q^4 - 16 * q^10 - 4 * q^13 + 18 * q^14 + 4 * q^16 + 12 * q^17 - 10 * q^22 - 24 * q^23 - 12 * q^25 + 12 * q^26 - 12 * q^29 + 12 * q^35 - 12 * q^38 - 8 * q^40 + 4 * q^43 - 10 * q^49 - 108 * q^53 + 20 * q^55 - 36 * q^56 - 2 * q^61 + 72 * q^62 + 8 * q^64 + 24 * q^65 - 24 * q^68 + 42 * q^74 + 6 * q^77 - 14 * q^79 - 4 * q^82 + 22 * q^88 - 72 * q^91 + 84 * q^92 + 20 * q^94 - 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.929969	+	0.536918i	−0.657587	+	0.379658i	−0.791357	−	0.611354i	$-0.790625\pi$
$2$	−0.929969	+	0.536918i	−0.657587	+	0.379658i	0.133770	+	0.991012i	$0.457292\pi$
$3$		0			0
$3$		0			0
$4$	−0.423439	+	0.733417i	−0.211719	+	0.366709i
$5$	−1.10543	−	0.638222i	−0.494365	−	0.285422i	0.232019	−	0.972711i	$-0.425467\pi$
$5$	−1.10543	−	0.638222i	−0.494365	−	0.285422i	−0.726383	+	0.687290i	$0.758800\pi$
$6$		0			0
$7$	0.890926	−	0.514376i	0.336738	−	0.194416i	−0.322090	−	0.946709i	$-0.604386\pi$
$7$	0.890926	−	0.514376i	0.336738	−	0.194416i	0.658829	+	0.752293i	$0.271052\pi$
$8$		−	3.05708i		−	1.08084i
$9$		0			0
$10$	1.37069			0.433450
$11$	−4.03796	+	2.33132i	−1.21749	+	0.702918i	−0.964380	−	0.264519i	$-0.914787\pi$
$11$	−4.03796	+	2.33132i	−1.21749	+	0.702918i	−0.253110	+	0.967438i	$0.581453\pi$
$12$		0			0
$13$	−3.55524	−	0.600200i	−0.986047	−	0.166466i
$13$	−3.55524	−	0.600200i	−0.986047	−	0.166466i
$14$	−0.552355	+	0.956708i	−0.147623	+	0.255691i
$15$		0			0
$16$	0.794522	+	1.37615i	0.198631	+	0.344038i
$17$	0.476187			0.115492			0.0577461	−	0.998331i	$-0.481609\pi$
$17$	0.476187			0.115492			0.0577461	+	0.998331i	$0.481609\pi$
$18$		0			0
$19$		−	6.69096i		−	1.53501i	−0.641042	−	0.767505i	$-0.721498\pi$
$19$		−	6.69096i		−	1.53501i	0.641042	−	0.767505i	$-0.278502\pi$
$20$	0.936166	−	0.540496i	0.209333	−	0.120859i
$21$		0			0
$22$	2.50345	−	4.33610i	0.533737	−	0.924460i
$23$	0.479867	−	0.831155i	0.100059	−	0.173308i	−0.811650	−	0.584145i	$-0.801430\pi$
$23$	0.479867	−	0.831155i	0.100059	−	0.173308i	0.911709	+	0.410837i	$0.134763\pi$
$24$		0			0
$25$	−1.68535	−	2.91910i	−0.337069	−	0.583821i
$26$	3.62852	−	1.35071i	0.711612	−	0.264895i
$27$		0			0
$28$			0.871227i			0.164646i
$29$	−4.68880	−	8.12123i	−0.870687	−	1.50807i	−0.861287	−	0.508119i	$-0.830341\pi$
$29$	−4.68880	−	8.12123i	−0.870687	−	1.50807i	−0.00940050	−	0.999956i	$-0.502992\pi$
$30$		0			0
$31$	−1.66927	−	0.963754i	−0.299810	−	0.173095i	0.342548	−	0.939500i	$-0.388710\pi$
$31$	−1.66927	−	0.963754i	−0.299810	−	0.173095i	−0.642357	+	0.766405i	$0.722044\pi$
$32$	3.81725	+	2.20389i	0.674801	+	0.389597i
$33$		0			0
$34$	−0.442839	+	0.255673i	−0.0759462	+	0.0438476i
$35$	−1.31314			−0.221962
$36$		0			0
$37$			4.94666i			0.813226i	0.913601	+	0.406613i	$0.133290\pi$
$37$			4.94666i			0.813226i	−0.913601	+	0.406613i	$0.866710\pi$
$38$	3.59249	+	6.22238i	0.582779	+	1.00940i
$39$		0			0
$40$	−1.95109	+	3.37939i	−0.308495	+	0.534329i
$41$	1.31994	+	0.762068i	0.206140	+	0.119015i	0.599516	−	0.800363i	$-0.295360\pi$
$41$	1.31994	+	0.762068i	0.206140	+	0.119015i	−0.393376	+	0.919378i	$0.628693\pi$
$42$		0			0
$43$	−1.31426	−	2.27637i	−0.200423	−	0.347143i	0.748242	−	0.663426i	$-0.230898\pi$
$43$	−1.31426	−	2.27637i	−0.200423	−	0.347143i	−0.948665	+	0.316283i	$0.897565\pi$
$44$		−	3.94868i		−	0.595285i
$45$		0			0
$46$			1.03060i			0.151953i
$47$	−5.92316	+	3.41974i	−0.863982	+	0.498820i	−0.865344	−	0.501179i	$-0.832900\pi$
$47$	−5.92316	+	3.41974i	−0.863982	+	0.498820i	0.00136148	+	0.999999i	$0.499567\pi$
$48$		0			0
$49$	−2.97083	+	5.14564i	−0.424405	+	0.735091i
$50$	3.13464	+	1.80978i	0.443305	+	0.255942i
$51$		0			0
$52$	1.94563	−	2.35333i	0.269810	−	0.326348i
$53$	−0.582145			−0.0799637			−0.0399819	−	0.999200i	$-0.512730\pi$
$53$	−0.582145			−0.0799637			−0.0399819	+	0.999200i	$0.512730\pi$
$54$		0			0
$55$	5.95159			0.802512
$56$	−1.57249	−	2.72363i	−0.210133	−	0.363960i
$57$		0			0
$58$	8.72087	+	5.03499i	1.14511	+	0.661127i
$59$	3.64799	+	2.10617i	0.474927	+	0.274199i	0.718300	−	0.695733i	$-0.244920\pi$
$59$	3.64799	+	2.10617i	0.474927	+	0.274199i	−0.243373	+	0.969933i	$0.578254\pi$
$60$		0			0
$61$	−4.71645	−	8.16913i	−0.603880	−	1.04595i	−0.992227	−	0.124437i	$-0.960287\pi$
$61$	−4.71645	−	8.16913i	−0.603880	−	1.04595i	0.388348	−	0.921513i	$-0.373046\pi$
$62$	2.06983			0.262868
$63$		0			0
$64$	−7.91132			−0.988915
$65$	3.54702	+	2.93252i	0.439954	+	0.363734i
$66$		0			0
$67$	−2.01156	−	1.16138i	−0.245751	−	0.141885i	0.372066	−	0.928206i	$-0.378650\pi$
$67$	−2.01156	−	1.16138i	−0.245751	−	0.141885i	−0.617817	+	0.786322i	$0.711983\pi$
$68$	−0.201636	+	0.349243i	−0.0244519	+	0.0423520i
$69$		0			0
$70$	1.22118	−	0.705051i	0.145959	−	0.0842697i
$71$		−	1.35071i		−	0.160299i	−0.996783	−	0.0801497i	$-0.974460\pi$
$71$		−	1.35071i		−	0.160299i	0.996783	−	0.0801497i	$-0.0255398\pi$
$72$		0			0
$73$			12.8687i			1.50617i	0.657923	+	0.753085i	$0.271435\pi$
$73$			12.8687i			1.50617i	−0.657923	+	0.753085i	$0.728565\pi$
$74$	−2.65595	−	4.60024i	−0.308748	−	0.534767i
$75$		0			0
$76$	4.90726	+	2.83321i	0.562902	+	0.324991i
$77$	−2.39835	+	4.15406i	−0.273317	+	0.473399i
$78$		0			0
$79$	6.45415	+	11.1789i	0.726149	+	1.25773i	0.958499	+	0.285094i	$0.0920250\pi$
$79$	6.45415	+	11.1789i	0.726149	+	1.25773i	−0.232351	+	0.972632i	$0.574642\pi$
$80$		−	2.02833i		−	0.226774i
$81$		0			0
$82$	−1.63667			−0.180740
$83$	8.86189	−	5.11641i	0.972718	−	0.561599i	0.0726545	−	0.997357i	$-0.476853\pi$
$83$	8.86189	−	5.11641i	0.972718	−	0.561599i	0.900064	+	0.435758i	$0.143520\pi$
$84$		0			0
$85$	−0.526392	−	0.303913i	−0.0570953	−	0.0329640i
$86$	2.44445	+	1.41130i	0.263591	+	0.152185i
$87$		0			0
$88$	7.12701	+	12.3444i	0.759742	+	1.31591i
$89$			6.85985i			0.727143i	0.931566	+	0.363572i	$0.118443\pi$
$89$			6.85985i			0.727143i	−0.931566	+	0.363572i	$0.881557\pi$
$90$		0			0
$91$	−3.47619	+	1.29400i	−0.364403	+	0.135648i
$92$	0.406389	+	0.703886i	0.0423690	+	0.0733852i
$93$		0			0
$94$	3.67224	−	6.36050i	0.378763	−	0.656036i
$95$	−4.27032	+	7.39640i	−0.438125	+	0.758855i
$96$		0			0
$97$	−14.9635	+	8.63918i	−1.51931	+	0.877175i	−0.519571	+	0.854427i	$0.673908\pi$
$97$	−14.9635	+	8.63918i	−1.51931	+	0.877175i	−0.999741	+	0.0227483i	$0.992758\pi$
$98$		−	6.38037i		−	0.644515i
$99$		0			0
$100$	2.85456			0.285456
$101$	6.76434	+	11.7162i	0.673077	+	1.16580i	0.977027	+	0.213116i	$0.0683611\pi$
$101$	6.76434	+	11.7162i	0.673077	+	1.16580i	−0.303950	+	0.952688i	$0.598306\pi$
$102$		0			0
$103$	−0.0523553	+	0.0906821i	−0.00515873	+	0.00893517i	−0.868593	−	0.495526i	$-0.834975\pi$
$103$	−0.0523553	+	0.0906821i	−0.00515873	+	0.00893517i	0.863435	+	0.504461i	$0.168309\pi$
$104$	−1.83486	+	10.8687i	−0.179923	+	1.06576i
$105$		0			0
$106$	0.541376	−	0.312564i	0.0525831	−	0.0303589i
$107$	−12.4240			−1.20107			−0.600535	−	0.799598i	$-0.705046\pi$
$107$	−12.4240			−1.20107			−0.600535	+	0.799598i	$0.705046\pi$
$108$		0			0
$109$		−	14.1160i		−	1.35207i	−0.736869	−	0.676036i	$-0.763696\pi$
$109$		−	14.1160i		−	1.35207i	0.736869	−	0.676036i	$-0.236304\pi$
$110$	−5.53479	+	3.19551i	−0.527722	+	0.304680i
$111$		0			0
$112$	1.41572	+	0.817366i	0.133773	+	0.0772339i
$113$	5.84280	−	10.1200i	0.549645	−	0.952013i	−0.448654	−	0.893706i	$-0.648096\pi$
$113$	5.84280	−	10.1200i	0.549645	−	0.952013i	0.998299	−	0.0583071i	$-0.0185703\pi$
$114$		0			0
$115$	−1.06092	+	0.612524i	−0.0989315	+	0.0571181i
$116$	7.94167			0.737365
$117$		0			0
$118$	−4.52335			−0.416408
$119$	0.424247	−	0.244939i	0.0388906	−	0.0224535i
$120$		0			0
$121$	5.37007	−	9.30123i	0.488188	−	0.845566i
$122$	8.77230	+	5.06469i	0.794207	+	0.458536i
$123$		0			0
$124$	1.41367	−	0.816181i	0.126951	−	0.0732952i
$125$			10.6847i			0.955670i
$126$		0			0
$127$	−8.11161			−0.719789			−0.359894	−	0.932993i	$-0.617187\pi$
$127$	−8.11161			−0.719789			−0.359894	+	0.932993i	$0.617187\pi$
$128$	−0.277222	+	0.160054i	−0.0245032	+	0.0141469i
$129$		0			0
$130$	−4.87314	−	0.822689i	−0.427403	−	0.0721546i
$131$	4.68039	−	8.10667i	0.408927	−	0.708283i	−0.585843	−	0.810425i	$-0.699236\pi$
$131$	4.68039	−	8.10667i	0.408927	−	0.708283i	0.994770	+	0.102142i	$0.0325697\pi$
$132$		0			0
$133$	−3.44167	−	5.96115i	−0.298431	−	0.516897i
$134$	2.49425			0.215471
$135$		0			0
$136$		−	1.45574i		−	0.124829i
$137$	0.512400	−	0.295834i	0.0437773	−	0.0252748i	−0.477952	−	0.878386i	$-0.658621\pi$
$137$	0.512400	−	0.295834i	0.0437773	−	0.0252748i	0.521729	+	0.853111i	$0.325287\pi$
$138$		0			0
$139$	6.33633	−	10.9749i	0.537441	−	0.930875i	−0.461600	−	0.887088i	$-0.652724\pi$
$139$	6.33633	−	10.9749i	0.537441	−	0.930875i	0.999041	−	0.0437867i	$-0.0139422\pi$
$140$	0.556036	−	0.963083i	0.0469936	−	0.0813954i
$141$		0			0
$142$	0.725218	+	1.25611i	0.0608589	+	0.105411i
$143$	15.7552	−	5.86481i	1.31751	−	0.490440i
$144$		0			0
$145$			11.9700i			0.994052i
$146$	−6.90945	−	11.9675i	−0.571830	−	0.990438i
$147$		0			0
$148$	−3.62796	−	2.09461i	−0.298217	−	0.172176i
$149$	−10.1242	−	5.84520i	−0.829406	−	0.478858i	0.0242432	−	0.999706i	$-0.492282\pi$
$149$	−10.1242	−	5.84520i	−0.829406	−	0.478858i	−0.853649	+	0.520848i	$0.825616\pi$
$150$		0			0
$151$	8.83800	−	5.10262i	0.719226	−	0.415245i	−0.0952418	−	0.995454i	$-0.530362\pi$
$151$	8.83800	−	5.10262i	0.719226	−	0.415245i	0.814468	+	0.580209i	$0.197029\pi$
$152$	−20.4548			−1.65910
$153$		0			0
$154$		−	5.15086i		−	0.415068i
$155$	1.23018	+	2.13073i	0.0988102	+	0.171144i
$156$		0			0
$157$	−5.47021	+	9.47468i	−0.436570	+	0.756162i	−0.997422	−	0.0717541i	$-0.977140\pi$
$157$	−5.47021	+	9.47468i	−0.436570	+	0.756162i	0.560852	+	0.827916i	$0.310474\pi$
$158$	−12.0043	−	6.93070i	−0.955012	−	0.551377i
$159$		0			0
$160$	−2.81314	−	4.87251i	−0.222399	−	0.385206i
$161$		−	0.987329i		−	0.0778125i
$162$		0			0
$163$		−	16.9633i		−	1.32867i	−0.747436	−	0.664334i	$-0.768715\pi$
$163$		−	16.9633i		−	1.32867i	0.747436	−	0.664334i	$-0.231285\pi$
$164$	−1.11783	+	0.645378i	−0.0872877	+	0.0503956i
$165$		0			0
$166$	−5.49419	+	9.51621i	−0.426431	+	0.738601i
$167$	−14.5559	−	8.40384i	−1.12637	−	0.650309i	−0.183349	−	0.983048i	$-0.558694\pi$
$167$	−14.5559	−	8.40384i	−1.12637	−	0.650309i	−0.943019	+	0.332739i	$0.892027\pi$
$168$		0			0
$169$	12.2795	+	4.26772i	0.944578	+	0.328286i
$170$	0.652705			0.0500602
$171$		0			0
$172$	2.22604			0.169734
$173$	−9.54320	−	16.5293i	−0.725556	−	1.25670i	−0.958745	−	0.284268i	$-0.908249\pi$
$173$	−9.54320	−	16.5293i	−0.725556	−	1.25670i	0.233189	−	0.972431i	$-0.425084\pi$
$174$		0			0
$175$	−3.00303	−	1.73380i	−0.227008	−	0.131063i
$176$	−6.41649	−	3.70456i	−0.483661	−	0.279242i
$177$		0			0
$178$	−3.68318	−	6.37945i	−0.276066	−	0.478160i
$179$	8.33634			0.623087			0.311544	−	0.950232i	$-0.399154\pi$
$179$	8.33634			0.623087			0.311544	+	0.950232i	$0.399154\pi$
$180$		0			0
$181$	9.93629			0.738558			0.369279	−	0.929318i	$-0.379605\pi$
$181$	9.93629			0.738558			0.369279	+	0.929318i	$0.379605\pi$
$182$	2.53797	−	3.06980i	0.188127	−	0.227549i
$183$		0			0
$184$	−2.54090	−	1.46699i	−0.187318	−	0.108148i
$185$	3.15707	−	5.46820i	0.232112	−	0.402030i
$186$		0			0
$187$	−1.92282	+	1.11014i	−0.140611	+	0.0811816i
$188$		−	5.79220i		−	0.422440i
$189$		0			0
$190$		−	9.17123i		−	0.665351i
$191$	−3.03797	−	5.26192i	−0.219820	−	0.380739i	0.734933	−	0.678140i	$-0.237214\pi$
$191$	−3.03797	−	5.26192i	−0.219820	−	0.380739i	−0.954753	+	0.297401i	$0.903880\pi$
$192$		0			0
$193$	14.3007	+	8.25650i	1.02939	+	0.594316i	0.916809	−	0.399327i	$-0.130756\pi$
$193$	14.3007	+	8.25650i	1.02939	+	0.594316i	0.112577	+	0.993643i	$0.464090\pi$
$194$	9.27705	−	16.0683i	0.666054	−	1.15364i
$195$		0			0
$196$	−2.51593	−	4.35772i	−0.179709	−	0.311266i
$197$			19.1696i			1.36578i	0.730523	+	0.682888i	$0.239276\pi$
$197$			19.1696i			1.36578i	−0.730523	+	0.682888i	$0.760724\pi$
$198$		0			0
$199$	9.06267			0.642436			0.321218	−	0.947005i	$-0.395908\pi$
$199$	9.06267			0.642436			0.321218	+	0.947005i	$0.395908\pi$
$200$	−8.92393	+	5.15223i	−0.631017	+	0.364318i
$201$		0			0
$202$	−12.5813	−	7.26379i	−0.885214	−	0.511078i
$203$	−8.35474	−	4.82361i	−0.586387	−	0.338551i
$204$		0			0
$205$	−0.972737	−	1.68483i	−0.0679389	−	0.117674i
$206$		−	0.112442i		−	0.00783421i
$207$		0			0
$208$	−1.99875	−	5.36943i	−0.138589	−	0.372303i
$209$	15.5987	+	27.0178i	1.07899	+	1.86886i
$210$		0			0
$211$	7.34882	−	12.7285i	0.505913	−	0.876268i	−0.494063	−	0.869426i	$-0.664489\pi$
$211$	7.34882	−	12.7285i	0.505913	−	0.876268i	0.999977	−	0.00684175i	$-0.00217781\pi$
$212$	0.246503	−	0.426955i	0.0169299	−	0.0293234i
$213$		0			0
$214$	11.5539	−	6.67065i	0.789809	−	0.455996i
$215$			3.35516i			0.228820i
$216$		0			0
$217$	−1.98293			−0.134610
$218$	7.57916	+	13.1275i	0.513325	+	0.889105i
$219$		0			0
$220$	−2.52013	+	4.36500i	−0.169907	+	0.294288i
$221$	−1.69296	−	0.285807i	−0.113881	−	0.0192255i
$222$		0			0
$223$	17.4983	−	10.1026i	1.17177	−	0.676521i	0.217673	−	0.976022i	$-0.430153\pi$
$223$	17.4983	−	10.1026i	1.17177	−	0.676521i	0.954096	+	0.299500i	$0.0968199\pi$
$224$	4.53452			0.302975
$225$		0			0
$226$			12.5484i			0.834709i
$227$	17.8003	−	10.2770i	1.18145	−	0.682109i	0.225098	−	0.974336i	$-0.427730\pi$
$227$	17.8003	−	10.2770i	1.18145	−	0.682109i	0.956349	+	0.292228i	$0.0943965\pi$
$228$		0			0
$229$	−17.2270	−	9.94602i	−1.13839	−	0.657251i	−0.192361	−	0.981324i	$-0.561614\pi$
$229$	−17.2270	−	9.94602i	−1.13839	−	0.657251i	−0.946032	+	0.324073i	$0.894948\pi$
$230$	0.657750	−	1.13926i	0.0433707	−	0.0751203i
$231$		0			0
$232$	−24.8272	+	14.3340i	−1.62999	+	0.941074i
$233$	−28.3932			−1.86010			−0.930049	−	0.367436i	$-0.880236\pi$
$233$	−28.3932			−1.86010			−0.930049	+	0.367436i	$0.880236\pi$
$234$		0			0
$235$	8.73021			0.569496
$236$	−3.08940	+	1.78366i	−0.201103	+	0.116107i
$237$		0			0
$238$	−0.263024	+	0.455571i	−0.0170493	+	0.0295303i
$239$	−12.7434	−	7.35741i	−0.824302	−	0.475911i	0.0275956	−	0.999619i	$-0.491215\pi$
$239$	−12.7434	−	7.35741i	−0.824302	−	0.475911i	−0.851898	+	0.523708i	$0.824548\pi$
$240$		0			0
$241$	−11.4631	+	6.61822i	−0.738403	+	0.426317i	−0.821488	−	0.570225i	$-0.806856\pi$
$241$	−11.4631	+	6.61822i	−0.738403	+	0.426317i	0.0830856	+	0.996542i	$0.473523\pi$
$242$			11.5331i			0.741378i
$243$		0			0
$244$	7.98851			0.511412
$245$	6.56812	−	3.79210i	0.419622	−	0.242269i
$246$		0			0
$247$	−4.01591	+	23.7880i	−0.255526	+	1.51359i
$248$	−2.94627	+	5.10309i	−0.187088	+	0.324047i
$249$		0			0
$250$	−5.73681	−	9.93645i	−0.362828	−	0.628437i
$251$	11.9439			0.753893			0.376946	−	0.926235i	$-0.376974\pi$
$251$	11.9439			0.753893			0.376946	+	0.926235i	$0.376974\pi$
$252$		0			0
$253$			4.47489i			0.281334i
$254$	7.54354	−	4.35527i	0.473324	−	0.273274i
$255$		0			0
$256$	8.08319	−	14.0005i	0.505200	−	0.875032i
$257$	−7.48243	+	12.9600i	−0.466741	+	0.808419i	−0.999278	−	0.0379872i	$-0.987905\pi$
$257$	−7.48243	+	12.9600i	−0.466741	+	0.808419i	0.532537	+	0.846407i	$0.321239\pi$
$258$		0			0
$259$	2.54444	+	4.40710i	0.158104	+	0.273844i
$260$	−3.65270	+	1.35971i	−0.226531	+	0.0843255i
$261$		0			0
$262$			10.0519i			0.621010i
$263$	0.774621	+	1.34168i	0.0477652	+	0.0827317i	0.888919	−	0.458063i	$-0.151457\pi$
$263$	0.774621	+	1.34168i	0.0477652	+	0.0827317i	−0.841154	+	0.540795i	$0.818123\pi$
$264$		0			0
$265$	0.643522	+	0.371538i	0.0395312	+	0.0228234i
$266$	6.40129	+	3.69579i	0.392488	+	0.226603i
$267$		0			0
$268$	1.70355	−	0.983543i	0.104061	−	0.0600794i
$269$	−21.0293			−1.28218			−0.641090	−	0.767466i	$-0.721517\pi$
$269$	−21.0293			−1.28218			−0.641090	+	0.767466i	$0.721517\pi$
$270$		0			0
$271$		−	12.7508i		−	0.774554i	−0.921963	−	0.387277i	$-0.873416\pi$
$271$		−	12.7508i		−	0.774554i	0.921963	−	0.387277i	$-0.126584\pi$
$272$	0.378341	+	0.655305i	0.0229403	+	0.0397337i
$273$		0			0
$274$	−0.317677	+	0.550233i	−0.0191916	+	0.0332408i
$275$	13.6107	+	7.85814i	0.820756	+	0.473864i
$276$		0			0
$277$	5.81364	+	10.0695i	0.349308	+	0.605019i	0.986127	−	0.165995i	$-0.0530835\pi$
$277$	5.81364	+	10.0695i	0.349308	+	0.605019i	−0.636819	+	0.771013i	$0.719750\pi$
$278$			13.6084i			0.816175i
$279$		0			0
$280$			4.01439i			0.239905i
$281$	14.9681	−	8.64183i	0.892921	−	0.515528i	0.0180245	−	0.999838i	$-0.494262\pi$
$281$	14.9681	−	8.64183i	0.892921	−	0.515528i	0.874897	+	0.484309i	$0.160929\pi$
$282$		0			0
$283$	−10.8047	+	18.7143i	−0.642273	+	1.11245i	0.342651	+	0.939463i	$0.388675\pi$
$283$	−10.8047	+	18.7143i	−0.642273	+	1.11245i	−0.984924	+	0.172987i	$0.944658\pi$
$284$	0.990631	+	0.571941i	0.0587831	+	0.0339385i
$285$		0			0
$286$	−11.5029	+	13.9133i	−0.680181	+	0.822712i
$287$	1.56796			0.0925536
$288$		0			0
$289$	−16.7732			−0.986662
$290$	−6.42689	−	11.1317i	−0.377400	−	0.653676i
$291$		0			0
$292$	−9.43814	−	5.44912i	−0.552326	−	0.318885i
$293$	−0.0618730	−	0.0357224i	−0.00361466	−	0.00208692i	0.498192	−	0.867067i	$-0.333998\pi$
$293$	−0.0618730	−	0.0357224i	−0.00361466	−	0.00208692i	−0.501806	+	0.864980i	$0.667331\pi$
$294$		0			0
$295$	−2.68840	−	4.65645i	−0.156525	−	0.271109i
$296$	15.1223			0.878967
$297$		0			0
$298$	12.5536			0.727209
$299$	−2.20491	+	2.66694i	−0.127513	+	0.154233i
$300$		0			0
$301$	−2.34182	−	1.35205i	−0.134980	−	0.0779309i
$302$	−5.47937	+	9.49055i	−0.315303	+	0.546120i
$303$		0			0
$304$	9.20778	−	5.31611i	0.528102	−	0.304900i
$305$			12.0406i			0.689441i
$306$		0			0
$307$			19.9335i			1.13766i	0.822454	+	0.568831i	$0.192604\pi$
$307$			19.9335i			1.13766i	−0.822454	+	0.568831i	$0.807396\pi$
$308$	−2.03111	−	3.51798i	−0.115733	−	0.200455i
$309$		0			0
$310$	−2.28805	−	1.32101i	−0.129953	−	0.0750282i
$311$	3.04014	−	5.26567i	0.172390	−	0.298589i	−0.766865	−	0.641809i	$-0.778184\pi$
$311$	3.04014	−	5.26567i	0.172390	−	0.298589i	0.939255	+	0.343220i	$0.111518\pi$
$312$		0			0
$313$	−3.04622	−	5.27620i	−0.172182	−	0.298228i	0.767000	−	0.641647i	$-0.221748\pi$
$313$	−3.04622	−	5.27620i	−0.172182	−	0.298228i	−0.939183	+	0.343418i	$0.888415\pi$
$314$		−	11.7482i		−	0.662990i
$315$		0			0
$316$	−10.9317			−0.614959
$317$	8.25032	−	4.76332i	0.463384	−	0.267535i	−0.250082	−	0.968225i	$-0.580458\pi$
$317$	8.25032	−	4.76332i	0.463384	−	0.267535i	0.713466	+	0.700690i	$0.247124\pi$
$318$		0			0
$319$	37.8663	+	21.8621i	2.12011	+	1.22404i
$320$	8.74544	+	5.04918i	0.488885	+	0.282258i
$321$		0			0
$322$	0.530115	+	0.918186i	0.0295421	+	0.0511685i
$323$		−	3.18614i		−	0.177282i
$324$		0			0
$325$	4.23977	+	11.3897i	0.235180	+	0.631785i
$326$	9.10790	+	15.7753i	0.504440	+	0.873715i
$327$		0			0
$328$	2.32970	−	4.03516i	0.128636	−	0.222804i
$329$	−3.51807	+	6.09347i	−0.193957	+	0.335944i
$330$		0			0
$331$	15.7143	−	9.07268i	0.863739	−	0.498680i	−0.00152386	−	0.999999i	$-0.500485\pi$
$331$	15.7143	−	9.07268i	0.863739	−	0.498680i	0.865262	+	0.501319i	$0.167152\pi$
$332$			8.66595i			0.475606i
$333$		0			0
$334$	18.0487			0.987580
$335$	1.48243	+	2.56765i	0.0809938	+	0.140285i
$336$		0			0
$337$	4.00930	−	6.94430i	0.218400	−	0.378280i	−0.735919	−	0.677070i	$-0.763250\pi$
$337$	4.00930	−	6.94430i	0.218400	−	0.378280i	0.954319	+	0.298789i	$0.0965828\pi$
$338$	−13.7110	+	2.62425i	−0.745779	+	0.142740i
$339$		0			0
$340$	0.445790	−	0.257377i	0.0241763	−	0.0139582i
$341$	8.98726			0.486687
$342$		0			0
$343$			13.3138i			0.718876i
$344$	−6.95904	+	4.01780i	−0.375206	+	0.216625i
$345$		0			0
$346$	17.7497	+	10.2478i	0.954232	+	0.550926i
$347$	8.31364	−	14.3996i	0.446299	−	0.773013i	−0.551842	−	0.833949i	$-0.686075\pi$
$347$	8.31364	−	14.3996i	0.446299	−	0.773013i	0.998142	+	0.0609351i	$0.0194083\pi$
$348$		0			0
$349$	0.155013	−	0.0894966i	0.00829764	−	0.00479065i	−0.495845	−	0.868411i	$-0.665142\pi$
$349$	0.155013	−	0.0894966i	0.00829764	−	0.00479065i	0.504143	+	0.863620i	$0.331808\pi$
$350$	3.72364			0.199037
$351$		0			0
$352$	−20.5519			−1.09542
$353$	14.6540	−	8.46052i	0.779956	−	0.450308i	−0.0564585	−	0.998405i	$-0.517981\pi$
$353$	14.6540	−	8.46052i	0.779956	−	0.450308i	0.836415	+	0.548097i	$0.184648\pi$
$354$		0			0
$355$	−0.862050	+	1.49311i	−0.0457529	+	0.0792463i
$356$	−5.03114	−	2.90473i	−0.266650	−	0.153950i
$357$		0			0
$358$	−7.75253	+	4.47593i	−0.409734	+	0.236560i
$359$		−	34.4410i		−	1.81773i	−0.417093	−	0.908864i	$-0.636951\pi$
$359$		−	34.4410i		−	1.81773i	0.417093	−	0.908864i	$-0.363049\pi$
$360$		0			0
$361$	−25.7689			−1.35626
$362$	−9.24044	+	5.33497i	−0.485667	+	0.280400i
$363$		0			0
$364$	0.522911	−	3.09742i	0.0274080	−	0.162349i
$365$	8.21310	−	14.2255i	0.429893	−	0.744597i
$366$		0			0
$367$	−12.5426	−	21.7244i	−0.654717	−	1.13400i	−0.981965	−	0.189064i	$-0.939455\pi$
$367$	−12.5426	−	21.7244i	−0.654717	−	1.13400i	0.327248	−	0.944939i	$-0.393879\pi$
$368$	1.52506			0.0794993
$369$		0			0
$370$			6.78034i			0.352493i
$371$	−0.518648	+	0.299441i	−0.0269268	+	0.0155462i
$372$		0			0
$373$	−5.47530	+	9.48350i	−0.283500	+	0.491037i	−0.972244	−	0.233968i	$-0.924829\pi$
$373$	−5.47530	+	9.48350i	−0.283500	+	0.491037i	0.688744	+	0.725005i	$0.258162\pi$
$374$	1.19211	−	2.06479i	0.0616425	−	0.106768i
$375$		0			0
$376$	10.4544	+	18.1076i	0.539145	+	0.933827i
$377$	11.7954	+	31.6872i	0.607496	+	1.63197i
$378$		0			0
$379$		−	11.1048i		−	0.570415i	−0.958466	−	0.285208i	$-0.907937\pi$
$379$		−	11.1048i		−	0.570415i	0.958466	−	0.285208i	$-0.0920626\pi$
$380$	−3.61643	−	6.26385i	−0.185519	−	0.321329i
$381$		0			0
$382$	5.65043	+	3.26228i	0.289101	+	0.166913i
$383$	5.09111	+	2.93935i	0.260144	+	0.150194i	0.624400	−	0.781105i	$-0.285344\pi$
$383$	5.09111	+	2.93935i	0.260144	+	0.150194i	−0.364256	+	0.931299i	$0.618677\pi$
$384$		0			0
$385$	5.30242	−	3.06135i	0.270236	−	0.156021i
$386$	−17.7322			−0.902548
$387$		0			0
$388$		−	14.6326i		−	0.742860i
$389$	−0.0401383	−	0.0695217i	−0.00203510	−	0.00352489i	0.865006	−	0.501761i	$-0.167314\pi$
$389$	−0.0401383	−	0.0695217i	−0.00203510	−	0.00352489i	−0.867041	+	0.498237i	$0.833981\pi$
$390$		0			0
$391$	0.228506	−	0.395785i	0.0115561	−	0.0200157i
$392$	15.7306	+	9.08207i	0.794516	+	0.458714i
$393$		0			0
$394$	−10.2925	−	17.8271i	−0.518528	−	0.898117i
$395$		−	16.4767i		−	0.829034i
$396$		0			0
$397$		−	1.33964i		−	0.0672345i	−0.999435	−	0.0336172i	$-0.989297\pi$
$397$		−	1.33964i		−	0.0672345i	0.999435	−	0.0336172i	$-0.0107027\pi$
$398$	−8.42800	+	4.86591i	−0.422458	+	0.243906i
$399$		0			0
$400$	2.67809	−	4.63858i	0.133904	−	0.231929i
$401$	27.4333	+	15.8386i	1.36995	+	0.790942i	0.990921	−	0.134442i	$-0.0429243\pi$
$401$	27.4333	+	15.8386i	1.36995	+	0.790942i	0.379030	+	0.925384i	$0.376258\pi$
$402$		0			0
$403$	5.35622	+	4.42828i	0.266812	+	0.220588i
$404$	−11.4571			−0.570014
$405$		0			0
$406$	10.3595			0.514135
$407$	−11.5322	−	19.9744i	−0.571631	−	0.990094i
$408$		0			0
$409$	2.92633	+	1.68952i	0.144698	+	0.0835412i	0.570601	−	0.821227i	$-0.306710\pi$
$409$	2.92633	+	1.68952i	0.144698	+	0.0835412i	−0.425903	+	0.904769i	$0.640044\pi$
$410$	1.80923	+	1.04456i	0.0893515	+	0.0515871i
$411$		0			0
$412$	−0.0443386	−	0.0767966i	−0.00218440	−	0.00378350i
$413$	4.33345			0.213235
$414$		0			0
$415$	−13.0616			−0.641170
$416$	−12.2485	−	10.1265i	−0.600532	−	0.496492i
$417$		0			0
$418$	−29.0127	−	16.7505i	−1.41906	−	0.819293i
$419$	−10.8330	+	18.7633i	−0.529228	+	0.916649i	0.470191	+	0.882565i	$0.344185\pi$
$419$	−10.8330	+	18.7633i	−0.529228	+	0.916649i	−0.999419	+	0.0340847i	$0.989148\pi$
$420$		0			0
$421$	−12.1688	+	7.02566i	−0.593071	+	0.342409i	−0.766311	−	0.642470i	$-0.777910\pi$
$421$	−12.1688	+	7.02566i	−0.593071	+	0.342409i	0.173240	+	0.984880i	$0.444576\pi$
$422$			15.7828i			0.768297i
$423$		0			0
$424$			1.77966i			0.0864280i
$425$	−0.802539	−	1.39004i	−0.0389288	−	0.0674267i
$426$		0			0
$427$	−8.40401	−	4.85206i	−0.406699	−	0.234808i
$428$	5.26079	−	9.11195i	0.254290	−	0.440443i
$429$		0			0
$430$	−1.80145	−	3.12020i	−0.0868735	−	0.150469i
$431$		−	26.5547i		−	1.27909i	−0.768752	−	0.639547i	$-0.779122\pi$
$431$		−	26.5547i		−	1.27909i	0.768752	−	0.639547i	$-0.220878\pi$
$432$		0			0
$433$	21.7861			1.04697			0.523485	−	0.852035i	$-0.324631\pi$
$433$	21.7861			1.04697			0.523485	+	0.852035i	$0.324631\pi$
$434$	1.84406	−	1.06467i	0.0885178	−	0.0511058i
$435$		0			0
$436$	10.3530	+	5.97728i	0.495817	+	0.286260i
$437$	−5.56122	−	3.21077i	−0.266029	−	0.153592i
$438$		0			0
$439$	3.89690	+	6.74963i	0.185989	+	0.322142i	0.943909	−	0.330205i	$-0.107118\pi$
$439$	3.89690	+	6.74963i	0.185989	+	0.322142i	−0.757920	+	0.652347i	$0.773784\pi$
$440$		−	18.1945i		−	0.867387i
$441$		0			0
$442$	1.72785	−	0.643188i	0.0821857	−	0.0305933i
$443$	8.00154	+	13.8591i	0.380165	+	0.658465i	0.991086	−	0.133227i	$-0.0425339\pi$
$443$	8.00154	+	13.8591i	0.380165	+	0.658465i	−0.610921	+	0.791692i	$0.709201\pi$
$444$		0			0
$445$	4.37811	−	7.58311i	0.207542	−	0.359474i
$446$	−10.8486	+	18.7902i	−0.513694	+	0.889744i
$447$		0			0
$448$	−7.04840	+	4.06940i	−0.333006	+	0.192261i
$449$			8.58501i			0.405151i	0.979267	+	0.202576i	$0.0649312\pi$
$449$			8.58501i			0.405151i	−0.979267	+	0.202576i	$0.935069\pi$
$450$		0			0
$451$	−7.10648			−0.334631
$452$	4.94814	+	8.57043i	0.232741	+	0.403119i
$453$		0			0
$454$	−11.0358	+	19.1146i	−0.517936	+	0.897092i
$455$	4.66855	+	0.788150i	0.218865	+	0.0369490i
$456$		0			0
$457$	−4.76629	+	2.75182i	−0.222958	+	0.128725i	−0.607319	−	0.794458i	$-0.707755\pi$
$457$	−4.76629	+	2.75182i	−0.222958	+	0.128725i	0.384361	+	0.923183i	$0.374422\pi$
$458$	21.3608			0.998123
$459$		0			0
$460$		−	1.03747i		−	0.0483721i
$461$	−19.9077	+	11.4937i	−0.927196	+	0.535317i	−0.885924	−	0.463831i	$-0.846475\pi$
$461$	−19.9077	+	11.4937i	−0.927196	+	0.535317i	−0.0412725	+	0.999148i	$0.513141\pi$
$462$		0			0
$463$	−21.8412	−	12.6100i	−1.01505	−	0.586037i	−0.102381	−	0.994745i	$-0.532646\pi$
$463$	−21.8412	−	12.6100i	−1.01505	−	0.586037i	−0.912665	+	0.408708i	$0.865979\pi$
$464$	7.45070	−	12.9050i	0.345890	−	0.599099i
$465$		0			0
$466$	26.4048	−	15.2448i	1.22318	−	0.706201i
$467$	−18.1098			−0.838023			−0.419012	−	0.907981i	$-0.637623\pi$
$467$	−18.1098			−0.838023			−0.419012	+	0.907981i	$0.637623\pi$
$468$		0			0
$469$	−2.38954			−0.110338
$470$	−8.11883	+	4.68741i	−0.374494	+	0.216214i
$471$		0			0
$472$	6.43871	−	11.1522i	0.296366	−	0.513321i
$473$	10.6139	+	6.12792i	0.488026	+	0.281762i
$474$		0			0
$475$	−19.5316	+	11.2766i	−0.896171	+	0.517405i
$476$			0.414867i			0.0190154i
$477$		0			0
$478$	15.8013			0.722734
$479$	14.3564	−	8.28869i	0.655962	−	0.378720i	−0.134775	−	0.990876i	$-0.543031\pi$
$479$	14.3564	−	8.28869i	0.655962	−	0.378720i	0.790737	+	0.612157i	$0.209698\pi$
$480$		0			0
$481$	2.96899	−	17.5866i	0.135374	−	0.801879i
$482$	7.10688	−	12.3095i	0.323709	−	0.560681i
$483$		0			0
$484$	4.54779	+	7.87700i	0.206718	+	0.358045i
$485$	22.0548			1.00146
$486$		0			0
$487$		−	5.78932i		−	0.262339i	−0.991360	−	0.131170i	$-0.958127\pi$
$487$		−	5.78932i		−	0.262339i	0.991360	−	0.131170i	$-0.0418732\pi$
$488$	−24.9737	+	14.4186i	−1.13051	+	0.652697i
$489$		0			0
$490$	−4.07210	+	7.05308i	−0.183959	+	0.318626i
$491$	−5.23530	+	9.06781i	−0.236266	+	0.409224i	−0.959640	−	0.281232i	$-0.909257\pi$
$491$	−5.23530	+	9.06781i	−0.236266	+	0.409224i	0.723374	+	0.690456i	$0.242590\pi$
$492$		0			0
$493$	−2.23274	−	3.86722i	−0.100558	−	0.174171i
$494$	−9.03752	−	24.2783i	−0.406617	−	1.09233i
$495$		0			0
$496$		−	3.06289i		−	0.137528i
$497$	−0.694771	−	1.20338i	−0.0311647	−	0.0539789i
$498$		0			0
$499$	−7.82629	−	4.51851i	−0.350353	−	0.202276i	0.314488	−	0.949262i	$-0.398167\pi$
$499$	−7.82629	−	4.51851i	−0.350353	−	0.202276i	−0.664841	+	0.746985i	$0.731501\pi$
$500$	−7.83636	−	4.52432i	−0.350453	−	0.202334i
$501$		0			0
$502$	−11.1075	+	6.41289i	−0.495750	+	0.286221i
$503$	9.96486			0.444311			0.222155	−	0.975011i	$-0.428691\pi$
$503$	9.96486			0.444311			0.222155	+	0.975011i	$0.428691\pi$
$504$		0			0
$505$		−	17.2686i		−	0.768443i
$506$	−2.40265	−	4.16151i	−0.106811	−	0.185002i
$507$		0			0
$508$	3.43477	−	5.94920i	0.152393	−	0.263953i
$509$	−30.5593	−	17.6434i	−1.35452	−	0.782030i	−0.365638	−	0.930757i	$-0.619149\pi$
$509$	−30.5593	−	17.6434i	−1.35452	−	0.782030i	−0.988878	+	0.148727i	$0.952482\pi$
$510$		0			0
$511$	6.61936	+	11.4651i	0.292823	+	0.507185i
$512$			16.7198i			0.738919i
$513$		0			0
$514$		−	16.0698i		−	0.708808i
$515$	0.115751	−	0.0668287i	0.00510058	−	0.00294482i
$516$		0			0
$517$	15.9450	−	27.6175i	0.701260	−	1.21462i
$518$	−4.73251	−	2.73231i	−0.207934	−	0.120051i
$519$		0			0
$520$	8.96493	−	10.8435i	0.393138	−	0.475520i
$521$	−12.9544			−0.567541			−0.283770	−	0.958892i	$-0.591585\pi$
$521$	−12.9544			−0.567541			−0.283770	+	0.958892i	$0.591585\pi$
$522$		0			0
$523$	−0.367139			−0.0160539			−0.00802694	−	0.999968i	$-0.502555\pi$
$523$	−0.367139			−0.0160539			−0.00802694	+	0.999968i	$0.502555\pi$
$524$	3.96371	+	6.86535i	0.173156	+	0.299914i
$525$		0			0
$526$	−1.44075	−	0.831815i	−0.0628195	−	0.0362689i
$527$	−0.794884	−	0.458927i	−0.0346257	−	0.0199912i
$528$		0			0
$529$	11.0395	+	19.1209i	0.479976	+	0.831343i
$530$	−0.797940			−0.0346603
$531$		0			0
$532$	5.82934			0.252734
$533$	−4.23532	−	3.50157i	−0.183452	−	0.151670i
$534$		0			0
$535$	13.7339	+	7.92925i	0.593767	+	0.342811i
$536$	−3.55042	+	6.14950i	−0.153355	+	0.265618i
$537$		0			0
$538$	19.5566	−	11.2910i	0.843145	−	0.486790i
$539$		−	27.7038i		−	1.19329i
$540$		0			0
$541$		−	42.0316i		−	1.80708i	−0.428504	−	0.903540i	$-0.640959\pi$
$541$		−	42.0316i		−	1.80708i	0.428504	−	0.903540i	$-0.359041\pi$
$542$	6.84612	+	11.8578i	0.294066	+	0.509337i
$543$		0			0
$544$	1.81772	+	1.04946i	0.0779343	+	0.0449954i
$545$	−9.00917	+	15.6043i	−0.385911	+	0.668417i
$546$		0			0
$547$	14.2892	+	24.7496i	0.610962	+	1.05822i	0.991079	+	0.133279i	$0.0425506\pi$
$547$	14.2892	+	24.7496i	0.610962	+	1.05822i	−0.380116	+	0.924939i	$0.624116\pi$
$548$			0.501071i			0.0214047i
$549$		0			0
$550$	−16.8767			−0.719625
$551$	−54.3388	+	31.3725i	−2.31491	+	1.33651i
$552$		0			0
$553$	11.5003	+	6.63972i	0.489044	+	0.282350i
$554$	−10.8130	−	6.24289i	−0.459401	−	0.265235i
$555$		0			0
$556$	5.36610	+	9.29435i	0.227573	+	0.394168i
$557$		−	3.59187i		−	0.152192i	−0.997100	−	0.0760961i	$-0.975754\pi$
$557$		−	3.59187i		−	0.152192i	0.997100	−	0.0760961i	$-0.0242456\pi$
$558$		0			0
$559$	3.30625	+	8.88187i	0.139839	+	0.375663i
$560$	−1.04332	−	1.80709i	−0.0440884	−	0.0763634i
$561$		0			0
$562$	−9.27991	+	16.0733i	−0.391449	+	0.678010i
$563$	−15.3227	+	26.5396i	−0.645774	+	1.11851i	0.338349	+	0.941021i	$0.390132\pi$
$563$	−15.3227	+	26.5396i	−0.645774	+	1.11851i	−0.984122	+	0.177492i	$0.943202\pi$
$564$		0			0
$565$	−12.9177	+	7.45801i	−0.543450	+	0.313761i
$566$		−	23.2050i		−	0.975377i
$567$		0			0
$568$	−4.12921			−0.173258
$569$	−17.3324	−	30.0206i	−0.726612	−	1.25853i	−0.958307	−	0.285740i	$-0.907761\pi$
$569$	−17.3324	−	30.0206i	−0.726612	−	1.25853i	0.231695	−	0.972788i	$-0.425573\pi$
$570$		0			0
$571$	7.76050	−	13.4416i	0.324767	−	0.562512i	−0.656698	−	0.754153i	$-0.728048\pi$
$571$	7.76050	−	13.4416i	0.324767	−	0.562512i	0.981465	+	0.191641i	$0.0613809\pi$
$572$	−2.37000	+	14.0385i	−0.0990946	+	0.586980i
$573$		0			0
$574$	−1.45815	+	0.841864i	−0.0608621	+	0.0351387i
$575$	−3.23497			−0.134908
$576$		0			0
$577$			18.6264i			0.775426i	0.921780	+	0.387713i	$0.126735\pi$
$577$			18.6264i			0.775426i	−0.921780	+	0.387713i	$0.873265\pi$
$578$	15.5986	−	9.00585i	0.648816	−	0.374594i
$579$		0			0
$580$	−8.77898	−	5.06855i	−0.364527	−	0.210460i
$581$	5.26352	−	9.11669i	0.218368	−	0.378224i
$582$		0			0
$583$	2.35068	−	1.35716i	0.0973550	−	0.0562080i
$584$	39.3407			1.62793
$585$		0			0
$586$	0.0767199			0.00316927
$587$	−30.6515	+	17.6966i	−1.26512	+	0.730418i	−0.974061	−	0.226287i	$-0.927341\pi$
$587$	−30.6515	+	17.6966i	−1.26512	+	0.730418i	−0.291060	+	0.956705i	$0.594008\pi$
$588$		0			0
$589$	−6.44844	+	11.1690i	−0.265703	+	0.460211i
$590$	5.00026	+	2.88690i	0.205857	+	0.118852i
$591$		0			0
$592$	−6.80736	+	3.93023i	−0.279781	+	0.161531i
$593$		−	2.41535i		−	0.0991864i	−0.998770	−	0.0495932i	$-0.984208\pi$
$593$		−	2.41535i		−	0.0991864i	0.998770	−	0.0495932i	$-0.0157925\pi$
$594$		0			0
$595$	−0.625302			−0.0256349
$596$	8.57395	−	4.95017i	0.351203	−	0.202767i
$597$		0			0
$598$	0.618565	−	3.66402i	0.0252950	−	0.149833i
$599$	20.4683	−	35.4522i	0.836314	−	1.44854i	−0.0566424	−	0.998395i	$-0.518040\pi$
$599$	20.4683	−	35.4522i	0.836314	−	1.44854i	0.892956	−	0.450143i	$-0.148627\pi$
$600$		0			0
$601$	8.82077	+	15.2780i	0.359807	+	0.623203i	0.987928	−	0.154912i	$-0.0495093\pi$
$601$	8.82077	+	15.2780i	0.359807	+	0.623203i	−0.628122	+	0.778115i	$0.716176\pi$
$602$	2.90376			0.118348
$603$		0			0
$604$			8.64259i			0.351662i
$605$	−11.8725	+	6.85459i	−0.482686	+	0.278679i
$606$		0			0
$607$	9.22956	−	15.9861i	0.374616	−	0.648854i	−0.615653	−	0.788017i	$-0.711108\pi$
$607$	9.22956	−	15.9861i	0.374616	−	0.648854i	0.990270	+	0.139163i	$0.0444412\pi$
$608$	14.7461	−	25.5411i	0.598035	−	1.03583i
$609$		0			0
$610$	−6.46480	−	11.1974i	−0.261752	−	0.453368i
$611$	23.1108	−	8.60293i	0.934964	−	0.348037i
$612$		0			0
$613$		−	7.01548i		−	0.283352i	−0.989913	−	0.141676i	$-0.954751\pi$
$613$		−	7.01548i		−	0.283352i	0.989913	−	0.141676i	$-0.0452492\pi$
$614$	−10.7026	−	18.5375i	−0.431923	−	0.748112i
$615$		0			0
$616$	12.6993	+	7.33193i	0.511669	+	0.295412i
$617$	−8.78344	−	5.07112i	−0.353608	−	0.204156i	0.312665	−	0.949863i	$-0.398778\pi$
$617$	−8.78344	−	5.07112i	−0.353608	−	0.204156i	−0.666273	+	0.745708i	$0.732112\pi$
$618$		0			0
$619$	8.11092	−	4.68284i	0.326005	−	0.188219i	−0.328061	−	0.944657i	$-0.606395\pi$
$619$	8.11092	−	4.68284i	0.326005	−	0.188219i	0.654066	+	0.756437i	$0.273062\pi$
$620$	−2.08362			−0.0836802
$621$		0			0
$622$			6.52922i			0.261798i
$623$	3.52855	+	6.11162i	0.141368	+	0.244857i
$624$		0			0
$625$	−1.60751	+	2.78428i	−0.0643002	+	0.111371i
$626$	5.66577	+	3.27113i	0.226450	+	0.130741i
$627$		0			0
$628$	−4.63260	−	8.02389i	−0.184861	−	0.320188i
$629$			2.35553i			0.0939212i
$630$		0			0
$631$			0.999379i			0.0397846i	0.999802	+	0.0198923i	$0.00633234\pi$
$631$			0.999379i			0.0397846i	−0.999802	+	0.0198923i	$0.993668\pi$
$632$	34.1748	−	19.7308i	1.35940	−	0.784851i
$633$		0			0
$634$	−5.11503	+	8.85948i	−0.203144	+	0.351855i
$635$	8.96684	+	5.17701i	0.355838	+	0.205443i
$636$		0			0
$637$	13.6505	−	16.5109i	0.540851	−	0.654186i
$638$	−46.9526			−1.85887
$639$		0			0
$640$	0.408601			0.0161514
$641$	−4.27107	−	7.39770i	−0.168697	−	0.292192i	0.769265	−	0.638930i	$-0.220623\pi$
$641$	−4.27107	−	7.39770i	−0.168697	−	0.292192i	−0.937962	+	0.346738i	$0.887289\pi$
$642$		0			0
$643$	0.783139	+	0.452145i	0.0308840	+	0.0178309i	0.515362	−	0.856972i	$-0.327657\pi$
$643$	0.783139	+	0.452145i	0.0308840	+	0.0178309i	−0.484479	+	0.874803i	$0.660991\pi$
$644$	0.724124	+	0.418073i	0.0285345	+	0.0164744i
$645$		0			0
$646$	1.71070	+	2.96301i	0.0673065	+	0.116578i
$647$	−20.5148			−0.806518			−0.403259	−	0.915086i	$-0.632123\pi$
$647$	−20.5148			−0.806518			−0.403259	+	0.915086i	$0.632123\pi$
$648$		0			0
$649$	−19.6406			−0.770959
$650$	−10.0582	−	8.31563i	−0.394514	−	0.326166i
$651$		0			0
$652$	12.4412	+	7.18292i	0.487234	+	0.281305i
$653$	4.68449	−	8.11378i	0.183318	−	0.317517i	−0.759690	−	0.650285i	$-0.774649\pi$
$653$	4.68449	−	8.11378i	0.183318	−	0.317517i	0.943009	+	0.332768i	$0.107983\pi$
$654$		0			0
$655$	−10.3477	+	5.97425i	−0.404318	+	0.233433i
$656$			2.42192i			0.0945600i
$657$		0			0
$658$		−	7.55565i		−	0.294550i
$659$	17.6521	+	30.5743i	0.687627	+	1.19101i	0.972603	+	0.232471i	$0.0746811\pi$
$659$	17.6521	+	30.5743i	0.687627	+	1.19101i	−0.284976	+	0.958535i	$0.591986\pi$
$660$		0			0
$661$	−20.2167	−	11.6721i	−0.786337	−	0.453992i	0.0523346	−	0.998630i	$-0.483334\pi$
$661$	−20.2167	−	11.6721i	−0.786337	−	0.453992i	−0.838671	+	0.544638i	$0.816667\pi$
$662$	−9.74257	+	16.8746i	−0.378656	+	0.655851i
$663$		0			0
$664$	−15.6413	−	27.0915i	−0.606999	−	1.05135i
$665$			8.78619i			0.340714i
$666$		0			0
$667$	−9.00000			−0.348481
$668$	12.3270	−	7.11702i	0.476948	−	0.275366i
$669$		0			0
$670$	−2.75723	−	1.59189i	−0.106521	−	0.0615000i
$671$	38.0897	+	21.9911i	1.47043	+	0.848956i
$672$		0			0
$673$	−24.9264	−	43.1738i	−0.960842	−	1.66423i	−0.720393	−	0.693566i	$-0.756039\pi$
$673$	−24.9264	−	43.1738i	−0.960842	−	1.66423i	−0.240449	−	0.970662i	$-0.577295\pi$
$674$			8.61065i			0.331670i
$675$		0			0
$676$	−8.32964	+	7.19890i	−0.320371	+	0.276881i
$677$	5.45592	+	9.44994i	0.209688	+	0.363191i	0.951616	−	0.307289i	$-0.0994218\pi$
$677$	5.45592	+	9.44994i	0.209688	+	0.363191i	−0.741928	+	0.670479i	$0.766088\pi$
$678$		0			0
$679$	−8.88757	+	15.3937i	−0.341074	+	0.590757i
$680$	−0.929085	+	1.60922i	−0.0356288	+	0.0617109i
$681$		0			0
$682$	−8.35787	+	4.82542i	−0.320039	+	0.184775i
$683$			24.0595i			0.920610i	0.887761	+	0.460305i	$0.152260\pi$
$683$			24.0595i			0.920610i	−0.887761	+	0.460305i	$0.847740\pi$
$684$		0			0
$685$	−0.755232			−0.0288559
$686$	−7.14840	−	12.3814i	−0.272927	−	0.472724i
$687$		0			0
$688$	2.08842	−	3.61725i	0.0796203	−	0.137906i
$689$	2.06967	+	0.349403i	0.0788480	+	0.0133112i
$690$		0			0
$691$	−25.4878	+	14.7154i	−0.969600	+	0.559799i	−0.899114	−	0.437714i	$-0.855788\pi$
$691$	−25.4878	+	14.7154i	−0.969600	+	0.559799i	−0.0704856	+	0.997513i	$0.522455\pi$
$692$	16.1638			0.614457
$693$		0			0
$694$			17.8550i			0.677765i
$695$	−14.0088	+	8.08798i	−0.531383	+	0.306794i
$696$		0			0
$697$	0.628538	+	0.362886i	0.0238076	+	0.0137453i
$698$	−0.0961047	+	0.166458i	−0.00363762	+	0.00630053i
$699$		0			0
$700$	2.54320	−	1.46832i	0.0961240	−	0.0554972i
$701$	−16.6961			−0.630604			−0.315302	−	0.948991i	$-0.602106\pi$
$701$	−16.6961			−0.630604			−0.315302	+	0.948991i	$0.602106\pi$
$702$		0			0
$703$	33.0979			1.24831
$704$	31.9456	−	18.4438i	1.20399	−	0.695127i
$705$		0			0
$706$	−9.08520	+	15.7360i	−0.341926	+	0.592234i
$707$	12.0530	+	6.95883i	0.453302	+	0.261714i
$708$		0			0
$709$	28.9718	−	16.7269i	1.08806	−	0.628191i	0.155000	−	0.987915i	$-0.450462\pi$
$709$	28.9718	−	16.7269i	1.08806	−	0.628191i	0.933059	+	0.359724i	$0.117129\pi$
$710$		−	1.85140i		−	0.0694818i
$711$		0			0
$712$	20.9711			0.785925
$713$	−1.60206	+	0.924948i	−0.0599975	+	0.0346396i
$714$		0			0
$715$	−21.1593	−	3.57214i	−0.791315	−	0.133591i
$716$	−3.52993	+	6.11401i	−0.131920	+	0.228491i
$717$		0			0
$718$	18.4920	+	32.0291i	0.690115	+	1.19531i
$719$	31.3183			1.16797			0.583987	−	0.811763i	$-0.301492\pi$
$719$	31.3183			1.16797			0.583987	+	0.811763i	$0.301492\pi$
$720$		0			0
$721$			0.107721i			0.00401175i
$722$	23.9643	−	13.8358i	0.891858	−	0.514915i
$723$		0			0
$724$	−4.20741	+	7.28745i	−0.156367	+	0.270836i
$725$	−15.8045	+	27.3742i	−0.586964	+	1.01665i
$726$		0			0
$727$	−18.8915	−	32.7210i	−0.700646	−	1.21356i	−0.968240	−	0.250023i	$-0.919562\pi$
$727$	−18.8915	−	32.7210i	−0.700646	−	1.21356i	0.267593	−	0.963532i	$-0.413772\pi$
$728$	3.95586	+	10.6270i	0.146614	+	0.393862i
$729$		0			0
$730$			17.6390i			0.652850i
$731$	−0.625834	−	1.08398i	−0.0231473	−	0.0400923i
$732$		0			0
$733$	5.55072	+	3.20471i	0.205021	+	0.118369i	0.598995	−	0.800753i	$-0.295567\pi$
$733$	5.55072	+	3.20471i	0.205021	+	0.118369i	−0.393975	+	0.919121i	$0.628900\pi$
$734$	23.3284	+	13.4687i	0.861067	+	0.497137i
$735$		0			0
$736$	3.66355	−	2.11515i	0.135040	−	0.0779655i
$737$	10.8301			0.398933
$738$		0			0
$739$			26.2292i			0.964856i	0.875936	+	0.482428i	$0.160245\pi$
$739$			26.2292i			0.964856i	−0.875936	+	0.482428i	$0.839755\pi$
$740$	2.67365	+	4.63089i	0.0982852	+	0.170235i
$741$		0			0
$742$	0.321551	−	0.556942i	0.0118045	−	0.0204460i
$743$	23.7541	+	13.7144i	0.871454	+	0.503134i	0.867831	−	0.496859i	$-0.165513\pi$
$743$	23.7541	+	13.7144i	0.871454	+	0.503134i	0.00362278	+	0.999993i	$0.498847\pi$
$744$		0			0
$745$	7.46108	+	12.9230i	0.273353	+	0.473461i
$746$		−	11.7591i		−	0.430533i
$747$		0			0
$748$		−	1.88031i		−	0.0687508i
$749$	−11.0688	+	6.39059i	−0.404446	+	0.233507i
$750$		0			0
$751$	7.31837	−	12.6758i	0.267051	−	0.462546i	−0.701048	−	0.713114i	$-0.747284\pi$
$751$	7.31837	−	12.6758i	0.267051	−	0.462546i	0.968099	+	0.250568i	$0.0806174\pi$
$752$	−9.41217	−	5.43412i	−0.343227	−	0.198162i
$753$		0			0
$754$	−27.9828	−	23.1349i	−1.01907	−	0.842523i
$755$	−13.0264			−0.474080
$756$		0			0
$757$	4.79203			0.174169			0.0870846	−	0.996201i	$-0.472245\pi$
$757$	4.79203			0.174169			0.0870846	+	0.996201i	$0.472245\pi$
$758$	5.96236	+	10.3271i	0.216563	+	0.375098i
$759$		0			0
$760$	22.6114	+	13.0547i	0.820201	+	0.473543i
$761$	16.7477	+	9.66927i	0.607103	+	0.350511i	0.771831	−	0.635828i	$-0.219341\pi$
$761$	16.7477	+	9.66927i	0.607103	+	0.350511i	−0.164728	+	0.986339i	$0.552675\pi$
$762$		0			0
$763$	−7.26096	−	12.5763i	−0.262864	−	0.455294i
$764$	5.14558			0.186160
$765$		0			0
$766$	−6.31277			−0.228089
$767$	−11.7054	−	9.67746i	−0.422656	−	0.349433i
$768$		0			0
$769$	8.74040	+	5.04627i	0.315187	+	0.181973i	0.649245	−	0.760579i	$-0.275085\pi$
$769$	8.74040	+	5.04627i	0.315187	+	0.181973i	−0.334058	+	0.942552i	$0.608418\pi$
$770$	−3.28739	+	5.69393i	−0.118469	+	0.205195i
$771$		0			0
$772$	−12.1109	+	6.99224i	−0.435882	+	0.251656i
$773$		−	8.43470i		−	0.303375i	−0.988428	−	0.151688i	$-0.951529\pi$
$773$		−	8.43470i		−	0.303375i	0.988428	−	0.151688i	$-0.0484708\pi$
$774$		0			0
$775$			6.49703i			0.233380i
$776$	26.4106	+	45.7446i	0.948087	+	1.64213i
$777$		0			0
$778$	0.0746548	+	0.0431020i	0.00267651	+	0.00154528i
$779$	5.09896	−	8.83166i	0.182689	−	0.316427i
$780$		0			0
$781$	3.14892	+	5.45409i	0.112677	+	0.195163i
$782$			0.490757i			0.0175494i
$783$		0			0
$784$	−9.44157			−0.337199
$785$	12.0939	−	6.98242i	0.431650	−	0.249213i
$786$		0			0
$787$	−11.0977	−	6.40724i	−0.395589	−	0.228393i	0.288990	−	0.957332i	$-0.406681\pi$
$787$	−11.0977	−	6.40724i	−0.395589	−	0.228393i	−0.684579	+	0.728939i	$0.740014\pi$
$788$	−14.0593	−	8.11714i	−0.500842	−	0.289161i
$789$		0			0
$790$	8.84665	+	15.3228i	0.314750	+	0.545162i
$791$		−	12.0216i		−	0.427439i
$792$		0			0
$793$	11.8650	+	31.8741i	0.421339	+	1.13188i
$794$	0.719275	+	1.24582i	0.0255261	+	0.0442125i
$795$		0			0
$796$	−3.83749	+	6.64672i	−0.136016	+	0.235587i
$797$	14.6074	−	25.3008i	0.517421	−	0.896200i	−0.482374	−	0.875965i	$-0.660225\pi$
$797$	14.6074	−	25.3008i	0.517421	−	0.896200i	0.999795	−	0.0202344i	$-0.00644124\pi$
$798$		0			0
$799$	−2.82053	+	1.62843i	−0.0997832	+	0.0576099i
$800$		−	14.8573i		−	0.525284i
$801$		0			0
$802$	−34.0161			−1.20115
$803$	−30.0011	−	51.9634i	−1.05871	−	1.83375i
$804$		0			0
$805$	−0.630135	+	1.09143i	−0.0222094	+	0.0384677i
$806$	−7.35874	−	1.24231i	−0.259200	−	0.0437585i
$807$		0			0
$808$	35.8173	−	20.6791i	1.26005	−	0.727489i
$809$	11.3570			0.399292			0.199646	−	0.979868i	$-0.436021\pi$
$809$	11.3570			0.399292			0.199646	+	0.979868i	$0.436021\pi$
$810$		0			0
$811$		−	26.8826i		−	0.943974i	−0.881605	−	0.471987i	$-0.843537\pi$
$811$		−	26.8826i		−	0.943974i	0.881605	−	0.471987i	$-0.156463\pi$
$812$	7.07544	−	4.08500i	0.248299	−	0.143356i
$813$		0			0
$814$	21.4492	+	12.3837i	0.751795	+	0.434049i
$815$	−10.8264	+	18.7518i	−0.379231	+	0.656847i
$816$		0			0
$817$	−15.2311	+	8.79367i	−0.532868	+	0.307652i
$818$	−3.62852			−0.126868
$819$		0			0
$820$	1.64758			0.0575359
$821$	14.2700	−	8.23880i	0.498027	−	0.287536i	−0.229871	−	0.973221i	$-0.573831\pi$
$821$	14.2700	−	8.23880i	0.498027	−	0.287536i	0.727898	+	0.685685i	$0.240497\pi$
$822$		0			0
$823$	−4.10205	+	7.10496i	−0.142988	+	0.247663i	−0.928621	−	0.371031i	$-0.879005\pi$
$823$	−4.10205	+	7.10496i	−0.142988	+	0.247663i	0.785632	+	0.618694i	$0.212338\pi$
$824$	0.277222	+	0.160054i	0.00965750	+	0.00557576i
$825$		0			0
$826$	−4.02997	+	2.32670i	−0.140221	+	0.0809564i
$827$			43.6569i			1.51810i	0.651033	+	0.759049i	$0.274336\pi$
$827$			43.6569i			1.51810i	−0.651033	+	0.759049i	$0.725664\pi$
$828$		0			0
$829$	23.3338			0.810415			0.405208	−	0.914225i	$-0.367199\pi$
$829$	23.3338			0.810415			0.405208	+	0.914225i	$0.367199\pi$
$830$	12.1469	−	7.01302i	0.421625	−	0.243425i
$831$		0			0
$832$	28.1267	+	4.74838i	0.975117	+	0.164620i
$833$	−1.41467	+	2.45028i	−0.0490155	+	0.0848973i
$834$		0			0
$835$	10.7270	+	18.5798i	0.371224	+	0.642979i
$836$	−26.4204			−0.913770
$837$		0			0
$838$		−	23.2658i		−	0.803702i
$839$	−11.8836	+	6.86099i	−0.410267	+	0.236868i	−0.690904	−	0.722946i	$-0.742787\pi$
$839$	−11.8836	+	6.86099i	−0.410267	+	0.236868i	0.280638	+	0.959814i	$0.409454\pi$
$840$		0			0
$841$	−29.4696	+	51.0428i	−1.01619	+	1.76010i
$842$	7.54440	−	13.0673i	0.259997	−	0.450328i
$843$		0			0
$844$	6.22355	+	10.7795i	0.214223	+	0.371046i
$845$	−10.8504	−	12.5547i	−0.373266	−	0.431896i
$846$		0			0
$847$		−	11.0489i		−	0.379646i
$848$	−0.462527	−	0.801120i	−0.0158832	−	0.0275106i
$849$		0			0
$850$	1.49267	+	0.861795i	0.0511982	+	0.0295593i
$851$	4.11144	+	2.37374i	0.140938	+	0.0813708i
$852$		0			0
$853$	−13.2769	+	7.66545i	−0.454594	+	0.262460i	−0.709768	−	0.704435i	$-0.751200\pi$
$853$	−13.2769	+	7.66545i	−0.454594	+	0.262460i	0.255175	+	0.966895i	$0.417867\pi$
$854$	10.4206			0.356587
$855$		0			0
$856$			37.9810i			1.29817i
$857$	21.3961	+	37.0590i	0.730875	+	1.26591i	0.956510	+	0.291701i	$0.0942212\pi$
$857$	21.3961	+	37.0590i	0.730875	+	1.26591i	−0.225634	+	0.974212i	$0.572445\pi$
$858$		0			0
$859$	13.1536	−	22.7826i	0.448793	−	0.777333i	−0.549514	−	0.835484i	$-0.685187\pi$
$859$	13.1536	−	22.7826i	0.448793	−	0.777333i	0.998308	+	0.0581513i	$0.0185206\pi$
$860$	−2.46074	−	1.42071i	−0.0839104	−	0.0484457i
$861$		0			0
$862$	14.2577	+	24.6950i	0.485618	+	0.841116i
$863$			8.03444i			0.273495i	0.990606	+	0.136748i	$0.0436650\pi$
$863$			8.03444i			0.273495i	−0.990606	+	0.136748i	$0.956335\pi$
$864$		0			0
$865$			24.3627i			0.828357i
$866$	−20.2603	+	11.6973i	−0.688475	+	0.397491i
$867$		0			0
$868$	0.839648	−	1.45431i	0.0284995	−	0.0493626i
$869$	−52.1232	−	30.0933i	−1.76816	−	1.02085i
$870$		0			0
$871$	6.45453	+	5.33631i	0.218704	+	0.180814i
$872$	−43.1539			−1.46137
$873$		0			0
$874$	6.89568			0.233250
$875$	5.49596	+	9.51929i	0.185797	+	0.321811i
$876$		0			0
$877$	6.03899	+	3.48661i	0.203922	+	0.117735i	0.598484	−	0.801135i	$-0.295770\pi$
$877$	6.03899	+	3.48661i	0.203922	+	0.117735i	−0.394561	+	0.918870i	$0.629103\pi$
$878$	−7.24799	−	4.18463i	−0.244608	−	0.141224i
$879$		0			0
$880$	4.72867	+	8.19029i	0.159403	+	0.276095i
$881$	−30.4317			−1.02527			−0.512635	−	0.858606i	$-0.671331\pi$
$881$	−30.4317			−1.02527			−0.512635	+	0.858606i	$0.671331\pi$
$882$		0			0
$883$	−1.51291			−0.0509134			−0.0254567	−	0.999676i	$-0.508104\pi$
$883$	−1.51291			−0.0509134			−0.0254567	+	0.999676i	$0.508104\pi$
$884$	0.926480	−	1.12062i	0.0311609	−	0.0376907i
$885$		0			0
$886$	−14.8824	−	8.59234i	−0.499983	−	0.288665i
$887$	−18.4472	+	31.9514i	−0.619395	+	1.07282i	0.370201	+	0.928952i	$0.379289\pi$
$887$	−18.4472	+	31.9514i	−0.619395	+	1.07282i	−0.989596	+	0.143872i	$0.954045\pi$
$888$		0			0
$889$	−7.22684	+	4.17242i	−0.242380	+	0.139938i
$890$			9.40274i			0.315181i
$891$		0			0
$892$			17.1114i			0.572931i
$893$	22.8813	+	39.6316i	0.765695	+	1.32622i
$894$		0			0
$895$	−9.21526	−	5.32043i	−0.308032	−	0.177842i
$896$	−0.164656	+	0.285193i	−0.00550078	+	0.00952763i
$897$		0			0
$898$	−4.60944	−	7.98379i	−0.153819	−	0.266422i
$899$			18.0754i			0.602848i
$900$		0			0
$901$	−0.277209			−0.00923519
$902$	6.60881	−	3.81560i	0.220049	−	0.127045i
$903$		0			0
$904$	−30.9377	−	17.8619i	−1.02897	−	0.594078i
$905$	−10.9839	−	6.34156i	−0.365117	−	0.210801i
$906$		0			0
$907$	−14.3940	−	24.9312i	−0.477946	−	0.827827i	0.521734	−	0.853108i	$-0.325285\pi$
$907$	−14.3940	−	24.9312i	−0.477946	−	0.827827i	−0.999680	+	0.0252808i	$0.991952\pi$
$908$			17.4067i			0.577662i
$909$		0			0
$910$	−4.76478	+	1.77367i	−0.157951	+	0.0587967i
$911$	−19.8931	−	34.4559i	−0.659089	−	1.14158i	−0.980852	−	0.194755i	$-0.937609\pi$
$911$	−19.8931	−	34.4559i	−0.659089	−	1.14158i	0.321763	−	0.946820i	$-0.395725\pi$
$912$		0			0
$913$	−23.8559	+	41.3197i	−0.789517	+	1.36748i
$914$	2.95500	−	5.11822i	0.0977428	−	0.169296i
$915$		0			0
$916$	14.5892	−	8.42306i	0.482039	−	0.278306i
$917$		−	9.62991i		−	0.318008i
$918$		0			0
$919$	28.4990			0.940095			0.470047	−	0.882641i	$-0.344237\pi$
$919$	28.4990			0.940095			0.470047	+	0.882641i	$0.344237\pi$
$920$	1.87253	+	3.24332i	0.0617356	+	0.106929i
$921$		0			0
$922$	12.3424	−	21.3776i	0.406475	−	0.704035i
$923$	−0.810694	+	4.80209i	−0.0266843	+	0.158063i
$924$		0			0
$925$	14.4398	−	8.33683i	0.474778	−	0.274113i
$926$	27.0822			0.889975
$927$		0			0
$928$		−	41.3344i		−	1.35687i
$929$	26.1642	−	15.1059i	0.858421	−	0.495610i	−0.00506213	−	0.999987i	$-0.501611\pi$
$929$	26.1642	−	15.1059i	0.858421	−	0.495610i	0.863483	+	0.504378i	$0.168278\pi$
$930$		0			0
$931$	34.4292	+	19.8777i	1.12837	+	0.651466i
$932$	12.0228	−	20.8240i	0.393819	−	0.682114i
$933$		0			0
$934$	16.8416	−	9.72349i	0.551073	−	0.318162i
$935$	2.83407			0.0926839
$936$		0			0
$937$	6.31683			0.206362			0.103181	−	0.994663i	$-0.467098\pi$
$937$	6.31683			0.206362			0.103181	+	0.994663i	$0.467098\pi$
$938$	2.22219	−	1.28298i	0.0725572	−	0.0418909i
$939$		0			0
$940$	−3.69671	+	6.40289i	−0.120573	+	0.208839i
$941$	−36.5433	−	21.0983i	−1.19128	−	0.687784i	−0.232681	−	0.972553i	$-0.574750\pi$
$941$	−36.5433	−	21.0983i	−1.19128	−	0.687784i	−0.958596	+	0.284769i	$0.908083\pi$
$942$		0			0
$943$	1.26679	−	0.731383i	0.0412524	−	0.0238171i
$944$			6.69358i			0.217857i
$945$		0			0
$946$	−13.1608			−0.427893
$947$	−11.7977	+	6.81143i	−0.383375	+	0.221342i	−0.679286	−	0.733874i	$-0.737710\pi$
$947$	−11.7977	+	6.81143i	−0.383375	+	0.221342i	0.295910	+	0.955216i	$0.404377\pi$
$948$		0			0
$949$	7.72381	−	45.7515i	0.250726	−	1.48515i
$950$	12.1092	−	20.9737i	0.392874	−	0.680477i
$951$		0			0
$952$	−0.748798	−	1.29696i	−0.0242687	−	0.0420346i
$953$	43.5443			1.41054			0.705268	−	0.708940i	$-0.250826\pi$
$953$	43.5443			1.41054			0.705268	+	0.708940i	$0.250826\pi$
$954$		0			0
$955$			7.75560i			0.250965i
$956$	10.7921	−	6.23082i	0.349041	−	0.201519i
$957$		0			0
$958$	−8.90068	+	15.4164i	−0.287568	+	0.498082i
$959$	0.304340	−	0.527132i	0.00982765	−	0.0170220i
$960$		0			0
$961$	−13.6424	−	23.6293i	−0.440076	−	0.762234i
$962$	6.68148	+	17.9491i	0.215420	+	0.578701i
$963$		0			0
$964$		−	11.2096i		−	0.361038i
$965$	−10.5390	−	18.2540i	−0.339261	−	0.587618i
$966$		0			0
$967$	−13.9813	−	8.07210i	−0.449608	−	0.259581i	0.258057	−	0.966130i	$-0.416918\pi$
$967$	−13.9813	−	8.07210i	−0.449608	−	0.259581i	−0.707665	+	0.706549i	$0.750251\pi$
$968$	−28.4346	−	16.4167i	−0.913922	−	0.527653i
$969$		0			0
$970$	−20.5103	+	11.8416i	−0.658547	+	0.380212i
$971$	0.206193			0.00661704			0.00330852	−	0.999995i	$-0.498947\pi$
$971$	0.206193			0.00661704			0.00330852	+	0.999995i	$0.498947\pi$
$972$		0			0
$973$		−	13.0370i		−	0.417948i
$974$	3.10839	+	5.38389i	0.0995992	+	0.172511i
$975$		0			0
$976$	7.49465	−	12.9811i	0.239898	−	0.415515i
$977$	−6.91568	−	3.99277i	−0.221252	−	0.127740i	0.385278	−	0.922801i	$-0.374106\pi$
$977$	−6.91568	−	3.99277i	−0.221252	−	0.127740i	−0.606530	+	0.795061i	$0.707439\pi$
$978$		0			0
$979$	−15.9925	−	27.6998i	−0.511122	−	0.885289i
$980$			6.42289i			0.205172i
$981$		0			0
$982$		−	11.2437i		−	0.358801i
$983$	−24.1512	+	13.9437i	−0.770304	+	0.444735i	−0.832983	−	0.553299i	$-0.813369\pi$
$983$	−24.1512	+	13.9437i	−0.770304	+	0.444735i	0.0626793	+	0.998034i	$0.480035\pi$
$984$		0			0
$985$	12.2344	−	21.1907i	0.389822	−	0.675191i
$986$	4.15276	+	2.39760i	0.132251	+	0.0763550i
$987$		0			0
$988$	−15.7460	−	13.0181i	−0.500948	−	0.414161i
$989$	−2.52269			−0.0802168
$990$		0			0
$991$	−8.84780			−0.281059			−0.140530	−	0.990076i	$-0.544881\pi$
$991$	−8.84780			−0.281059			−0.140530	+	0.990076i	$0.544881\pi$
$992$	−4.24802	−	7.35778i	−0.134875	−	0.233610i
$993$		0			0
$994$	1.29223	+	0.746070i	0.0409871	+	0.0236639i
$995$	−10.0182	−	5.78400i	−0.317598	−	0.183365i
$996$		0			0
$997$	12.7226	+	22.0362i	0.402929	+	0.697893i	0.994078	−	0.108669i	$-0.0346590\pi$
$997$	12.7226	+	22.0362i	0.402929	+	0.697893i	−0.591149	+	0.806562i	$0.701326\pi$
$998$	9.70427			0.307183
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.t.c.64.4		20
3.2	odd	2		117.2.t.c.103.7	yes	20
9.2	odd	6		117.2.t.c.25.4	✓	20
9.4	even	3		1053.2.b.i.649.4		10
9.5	odd	6		1053.2.b.j.649.7		10
9.7	even	3	inner	351.2.t.c.181.7		20
13.12	even	2	inner	351.2.t.c.64.7		20
39.38	odd	2		117.2.t.c.103.4	yes	20
117.25	even	6	inner	351.2.t.c.181.4		20
117.38	odd	6		117.2.t.c.25.7	yes	20
117.77	odd	6		1053.2.b.j.649.4		10
117.103	even	6		1053.2.b.i.649.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.t.c.25.4	✓	20	9.2	odd	6
117.2.t.c.25.7	yes	20	117.38	odd	6
117.2.t.c.103.4	yes	20	39.38	odd	2
117.2.t.c.103.7	yes	20	3.2	odd	2
351.2.t.c.64.4		20	1.1	even	1	trivial
351.2.t.c.64.7		20	13.12	even	2	inner
351.2.t.c.181.4		20	117.25	even	6	inner
351.2.t.c.181.7		20	9.7	even	3	inner
1053.2.b.i.649.4		10	9.4	even	3
1053.2.b.i.649.7		10	117.103	even	6
1053.2.b.j.649.4		10	117.77	odd	6
1053.2.b.j.649.7		10	9.5	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.929969 + 0.536918i) q^{2} +(-0.423439 + 0.733417i) q^{4} +(-1.10543 - 0.638222i) q^{5} +(0.890926 - 0.514376i) q^{7} -3.05708i q^{8} +1.37069 q^{10} +(-4.03796 + 2.33132i) q^{11} +(-3.55524 - 0.600200i) q^{13} +(-0.552355 + 0.956708i) q^{14} +(0.794522 + 1.37615i) q^{16} +0.476187 q^{17} -6.69096i q^{19} +(0.936166 - 0.540496i) q^{20} +(2.50345 - 4.33610i) q^{22} +(0.479867 - 0.831155i) q^{23} +(-1.68535 - 2.91910i) q^{25} +(3.62852 - 1.35071i) q^{26} +0.871227i q^{28} +(-4.68880 - 8.12123i) q^{29} +(-1.66927 - 0.963754i) q^{31} +(3.81725 + 2.20389i) q^{32} +(-0.442839 + 0.255673i) q^{34} -1.31314 q^{35} +4.94666i q^{37} +(3.59249 + 6.22238i) q^{38} +(-1.95109 + 3.37939i) q^{40} +(1.31994 + 0.762068i) q^{41} +(-1.31426 - 2.27637i) q^{43} -3.94868i q^{44} +1.03060i q^{46} +(-5.92316 + 3.41974i) q^{47} +(-2.97083 + 5.14564i) q^{49} +(3.13464 + 1.80978i) q^{50} +(1.94563 - 2.35333i) q^{52} -0.582145 q^{53} +5.95159 q^{55} +(-1.57249 - 2.72363i) q^{56} +(8.72087 + 5.03499i) q^{58} +(3.64799 + 2.10617i) q^{59} +(-4.71645 - 8.16913i) q^{61} +2.06983 q^{62} -7.91132 q^{64} +(3.54702 + 2.93252i) q^{65} +(-2.01156 - 1.16138i) q^{67} +(-0.201636 + 0.349243i) q^{68} +(1.22118 - 0.705051i) q^{70} -1.35071i q^{71} +12.8687i q^{73} +(-2.65595 - 4.60024i) q^{74} +(4.90726 + 2.83321i) q^{76} +(-2.39835 + 4.15406i) q^{77} +(6.45415 + 11.1789i) q^{79} -2.02833i q^{80} -1.63667 q^{82} +(8.86189 - 5.11641i) q^{83} +(-0.526392 - 0.303913i) q^{85} +(2.44445 + 1.41130i) q^{86} +(7.12701 + 12.3444i) q^{88} +6.85985i q^{89} +(-3.47619 + 1.29400i) q^{91} +(0.406389 + 0.703886i) q^{92} +(3.67224 - 6.36050i) q^{94} +(-4.27032 + 7.39640i) q^{95} +(-14.9635 + 8.63918i) q^{97} -6.38037i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 12 q^{4} - 16 q^{10} - 4 q^{13} + 18 q^{14} + 4 q^{16} + 12 q^{17} - 10 q^{22} - 24 q^{23} - 12 q^{25} + 12 q^{26} - 12 q^{29} + 12 q^{35} - 12 q^{38} - 8 q^{40} + 4 q^{43} - 10 q^{49} - 108 q^{53}+ \cdots - 24 q^{95}+O(q^{100}) \) 20 * q + 12 * q^4 - 16 * q^10 - 4 * q^13 + 18 * q^14 + 4 * q^16 + 12 * q^17 - 10 * q^22 - 24 * q^23 - 12 * q^25 + 12 * q^26 - 12 * q^29 + 12 * q^35 - 12 * q^38 - 8 * q^40 + 4 * q^43 - 10 * q^49 - 108 * q^53 + 20 * q^55 - 36 * q^56 - 2 * q^61 + 72 * q^62 + 8 * q^64 + 24 * q^65 - 24 * q^68 + 42 * q^74 + 6 * q^77 - 14 * q^79 - 4 * q^82 + 22 * q^88 - 72 * q^91 + 84 * q^92 + 20 * q^94 - 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more