LMFDB - Embedded newform 351.2.t.c.64.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,2,Mod(64,351)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			64.7
Root			$-1.65391 - 0.514376i$ of defining polynomial
Character	$\chi$	$=$	351.64
Dual form			351.2.t.c.181.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.929969 - 0.536918i) q^{2} +(-0.423439 + 0.733417i) q^{4} +(1.10543 + 0.638222i) q^{5} +(-0.890926 + 0.514376i) q^{7} +3.05708i q^{8} +1.37069 q^{10} +(4.03796 - 2.33132i) q^{11} +(2.29741 + 2.77883i) q^{13} +(-0.552355 + 0.956708i) q^{14} +(0.794522 + 1.37615i) q^{16} +0.476187 q^{17} +6.69096i q^{19} +(-0.936166 + 0.540496i) q^{20} +(2.50345 - 4.33610i) q^{22} +(0.479867 - 0.831155i) q^{23} +(-1.68535 - 2.91910i) q^{25} +(3.62852 + 1.35071i) q^{26} -0.871227i q^{28} +(-4.68880 - 8.12123i) q^{29} +(1.66927 + 0.963754i) q^{31} +(-3.81725 - 2.20389i) q^{32} +(0.442839 - 0.255673i) q^{34} -1.31314 q^{35} -4.94666i q^{37} +(3.59249 + 6.22238i) q^{38} +(-1.95109 + 3.37939i) q^{40} +(-1.31994 - 0.762068i) q^{41} +(-1.31426 - 2.27637i) q^{43} +3.94868i q^{44} -1.03060i q^{46} +(5.92316 - 3.41974i) q^{47} +(-2.97083 + 5.14564i) q^{49} +(-3.13464 - 1.80978i) q^{50} +(-3.01086 + 0.508296i) q^{52} -0.582145 q^{53} +5.95159 q^{55} +(-1.57249 - 2.72363i) q^{56} +(-8.72087 - 5.03499i) q^{58} +(-3.64799 - 2.10617i) q^{59} +(-4.71645 - 8.16913i) q^{61} +2.06983 q^{62} -7.91132 q^{64} +(0.766122 + 4.53807i) q^{65} +(2.01156 + 1.16138i) q^{67} +(-0.201636 + 0.349243i) q^{68} +(-1.22118 + 0.705051i) q^{70} +1.35071i q^{71} -12.8687i q^{73} +(-2.65595 - 4.60024i) q^{74} +(-4.90726 - 2.83321i) q^{76} +(-2.39835 + 4.15406i) q^{77} +(6.45415 + 11.1789i) q^{79} +2.02833i q^{80} -1.63667 q^{82} +(-8.86189 + 5.11641i) q^{83} +(0.526392 + 0.303913i) q^{85} +(-2.44445 - 1.41130i) q^{86} +(7.12701 + 12.3444i) q^{88} -6.85985i q^{89} +(-3.47619 - 1.29400i) q^{91} +(0.406389 + 0.703886i) q^{92} +(3.67224 - 6.36050i) q^{94} +(-4.27032 + 7.39640i) q^{95} +(14.9635 - 8.63918i) q^{97} +6.38037i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.133770	−	0.991012i	$-0.542708\pi$
$2$	0.929969	−	0.536918i	0.657587	−	0.379658i	0.791357	+	0.611354i	$0.209375\pi$
$3$		0			0
$3$		0			0
$4$	−0.423439	+	0.733417i	−0.211719	+	0.366709i
$5$	1.10543	+	0.638222i	0.494365	+	0.285422i	0.726383	−	0.687290i	$-0.241200\pi$
$5$	1.10543	+	0.638222i	0.494365	+	0.285422i	−0.232019	+	0.972711i	$0.574533\pi$
$6$		0			0
$7$	−0.890926	+	0.514376i	−0.336738	+	0.194416i	−0.658829	−	0.752293i	$-0.728948\pi$
$7$	−0.890926	+	0.514376i	−0.336738	+	0.194416i	0.322090	+	0.946709i	$0.395614\pi$
$8$			3.05708i			1.08084i
$9$		0			0
$10$	1.37069			0.433450
$11$	4.03796	−	2.33132i	1.21749	−	0.702918i	0.253110	−	0.967438i	$-0.418547\pi$
$11$	4.03796	−	2.33132i	1.21749	−	0.702918i	0.964380	+	0.264519i	$0.0852133\pi$
$12$		0			0
$13$	2.29741	+	2.77883i	0.637187	+	0.770709i
$13$	2.29741	+	2.77883i	0.637187	+	0.770709i
$14$	−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	$0.278502\pi$
$19$			6.69096i			1.53501i	−0.641042	+	0.767505i	$0.721498\pi$
$20$	−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	0.642357	−	0.766405i	$-0.277956\pi$
$31$	1.66927	+	0.963754i	0.299810	+	0.173095i	−0.342548	+	0.939500i	$0.611290\pi$
$32$	−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	$-0.866710\pi$
$37$		−	4.94666i		−	0.813226i	0.913601	−	0.406613i	$-0.133290\pi$
$38$	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	0.393376	−	0.919378i	$-0.371307\pi$
$41$	−1.31994	−	0.762068i	−0.206140	−	0.119015i	−0.599516	+	0.800363i	$0.704640\pi$
$42$		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	−0.00136148	−	0.999999i	$-0.500433\pi$
$47$	5.92316	−	3.41974i	0.863982	−	0.498820i	0.865344	+	0.501179i	$0.167100\pi$
$48$		0			0
$49$	−2.97083	+	5.14564i	−0.424405	+	0.735091i
$50$	−3.13464	−	1.80978i	−0.443305	−	0.255942i
$51$		0			0
$52$	−3.01086	+	0.508296i	−0.417531	+	0.0704880i
$53$	−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	0.243373	−	0.969933i	$-0.421746\pi$
$59$	−3.64799	−	2.10617i	−0.474927	−	0.274199i	−0.718300	+	0.695733i	$0.755080\pi$
$60$		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
$65$	0.766122	+	4.53807i	0.0950257	+	0.562878i
$66$		0			0
$67$	2.01156	+	1.16138i	0.245751	+	0.141885i	0.617817	−	0.786322i	$-0.288017\pi$
$67$	2.01156	+	1.16138i	0.245751	+	0.141885i	−0.372066	+	0.928206i	$0.621350\pi$
$68$	−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	$0.0255398\pi$
$71$			1.35071i			0.160299i	−0.996783	+	0.0801497i	$0.974460\pi$
$72$		0			0
$73$		−	12.8687i		−	1.50617i	−0.657923	−	0.753085i	$-0.728565\pi$
$73$		−	12.8687i		−	1.50617i	0.657923	−	0.753085i	$-0.271435\pi$
$74$	−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	−0.900064	−	0.435758i	$-0.856480\pi$
$83$	−8.86189	+	5.11641i	−0.972718	+	0.561599i	−0.0726545	+	0.997357i	$0.523147\pi$
$84$		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	$-0.881557\pi$
$89$		−	6.85985i		−	0.727143i	0.931566	−	0.363572i	$-0.118443\pi$
$90$		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	$-0.326092\pi$
$97$	14.9635	−	8.63918i	1.51931	−	0.877175i	0.999741	−	0.0227483i	$-0.00724164\pi$
$98$			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	$0.168309\pi$
$104$	−8.49510	+	7.02336i	−0.833014	+	0.688697i
$105$		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	$0.236304\pi$
$109$			14.1160i			1.35207i	−0.736869	+	0.676036i	$0.763696\pi$
$110$	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
$130$	3.14904	+	3.80892i	0.276189	+	0.334064i
$131$	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	−0.521729	−	0.853111i	$-0.674713\pi$
$137$	−0.512400	+	0.295834i	−0.0437773	+	0.0252748i	0.477952	+	0.878386i	$0.341379\pi$
$138$		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	0.853649	−	0.520848i	$-0.174384\pi$
$149$	10.1242	+	5.84520i	0.829406	+	0.478858i	−0.0242432	+	0.999706i	$0.507718\pi$
$150$		0			0
$151$	−8.83800	+	5.10262i	−0.719226	+	0.415245i	−0.814468	−	0.580209i	$-0.802971\pi$
$151$	−8.83800	+	5.10262i	−0.719226	+	0.415245i	0.0952418	+	0.995454i	$0.469638\pi$
$152$	−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	$0.231285\pi$
$163$			16.9633i			1.32867i	−0.747436	+	0.664334i	$0.768715\pi$
$164$	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	0.943019	−	0.332739i	$-0.107973\pi$
$167$	14.5559	+	8.40384i	1.12637	+	0.650309i	0.183349	+	0.983048i	$0.441306\pi$
$168$		0			0
$169$	−2.44381	+	12.7682i	−0.187985	+	0.982172i
$170$	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	$0.379605\pi$
$182$	−3.92752	+	0.663048i	−0.291127	+	0.0491484i
$183$		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	−0.112577	−	0.993643i	$-0.535910\pi$
$193$	−14.3007	−	8.25650i	−1.02939	−	0.594316i	−0.916809	+	0.399327i	$0.869244\pi$
$194$	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	$-0.760724\pi$
$197$		−	19.1696i		−	1.36578i	0.730523	−	0.682888i	$-0.239276\pi$
$198$		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
$221$	1.09400	+	1.32324i	0.0735901	+	0.0890109i
$222$		0			0
$223$	−17.4983	+	10.1026i	−1.17177	+	0.676521i	−0.954096	−	0.299500i	$-0.903180\pi$
$223$	−17.4983	+	10.1026i	−1.17177	+	0.676521i	−0.217673	+	0.976022i	$0.569847\pi$
$224$	4.53452			0.302975
$225$		0			0
$226$		−	12.5484i		−	0.834709i
$227$	−17.8003	+	10.2770i	−1.18145	+	0.682109i	−0.956349	−	0.292228i	$-0.905603\pi$
$227$	−17.8003	+	10.2770i	−1.18145	+	0.682109i	−0.225098	+	0.974336i	$0.572270\pi$
$228$		0			0
$229$	17.2270	+	9.94602i	1.13839	+	0.657251i	0.946032	−	0.324073i	$-0.105052\pi$
$229$	17.2270	+	9.94602i	1.13839	+	0.657251i	0.192361	+	0.981324i	$0.438386\pi$
$230$	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	0.851898	−	0.523708i	$-0.175452\pi$
$239$	12.7434	+	7.35741i	0.824302	+	0.475911i	−0.0275956	+	0.999619i	$0.508785\pi$
$240$		0			0
$241$	11.4631	−	6.61822i	0.738403	−	0.426317i	−0.0830856	−	0.996542i	$-0.526477\pi$
$241$	11.4631	−	6.61822i	0.738403	−	0.426317i	0.821488	+	0.570225i	$0.193144\pi$
$242$		−	11.5331i		−	0.741378i
$243$		0			0
$244$	7.98851			0.511412
$245$	−6.56812	+	3.79210i	−0.419622	+	0.242269i
$246$		0			0
$247$	−18.5930	+	15.3719i	−1.18305	+	0.978089i
$248$	−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	$0.126584\pi$
$271$			12.7508i			0.774554i	−0.921963	+	0.387277i	$0.873416\pi$
$272$	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	−0.874897	−	0.484309i	$-0.839071\pi$
$281$	−14.9681	+	8.64183i	−0.892921	+	0.515528i	−0.0180245	+	0.999838i	$0.505738\pi$
$282$		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
$286$	17.8007	−	3.00514i	1.05258	−	0.177698i
$287$	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	0.501806	−	0.864980i	$-0.332669\pi$
$293$	0.0618730	+	0.0357224i	0.00361466	+	0.00208692i	−0.498192	+	0.867067i	$0.666002\pi$
$294$		0			0
$295$	−2.68840	−	4.65645i	−0.156525	−	0.271109i
$296$	15.1223			0.878967
$297$		0			0
$298$	12.5536			0.727209
$299$	3.41209	−	0.576033i	0.197326	−	0.0333129i
$300$		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	$-0.807396\pi$
$307$		−	19.9335i		−	1.13766i	0.822454	−	0.568831i	$-0.192604\pi$
$308$	−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	−0.713466	−	0.700690i	$-0.752876\pi$
$317$	−8.25032	+	4.76332i	−0.463384	+	0.267535i	0.250082	+	0.968225i	$0.419542\pi$
$318$		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	−0.865262	−	0.501319i	$-0.832848\pi$
$331$	−15.7143	+	9.07268i	−0.863739	+	0.498680i	0.00152386	+	0.999999i	$0.499515\pi$
$332$		−	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	$0.0965828\pi$
$338$	4.58283	+	13.1862i	0.249273	+	0.717234i
$339$		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	−0.504143	−	0.863620i	$-0.668192\pi$
$349$	−0.155013	+	0.0894966i	−0.00829764	+	0.00479065i	0.495845	+	0.868411i	$0.334858\pi$
$350$	3.72364			0.199037
$351$		0			0
$352$	−20.5519			−1.09542
$353$	−14.6540	+	8.46052i	−0.779956	+	0.450308i	−0.836415	−	0.548097i	$-0.815352\pi$
$353$	−14.6540	+	8.46052i	−0.779956	+	0.450308i	0.0564585	+	0.998405i	$0.482019\pi$
$354$		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	$0.363049\pi$
$359$			34.4410i			1.81773i	−0.417093	+	0.908864i	$0.636951\pi$
$360$		0			0
$361$	−25.7689			−1.35626
$362$	9.24044	−	5.33497i	0.485667	−	0.280400i
$363$		0			0
$364$	2.42099	−	2.00157i	0.126895	−	0.104911i
$365$	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	$0.0920626\pi$
$379$			11.1048i			0.570415i	−0.958466	+	0.285208i	$0.907937\pi$
$380$	−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	0.364256	−	0.931299i	$-0.381323\pi$
$383$	−5.09111	−	2.93935i	−0.260144	−	0.150194i	−0.624400	+	0.781105i	$0.714656\pi$
$384$		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	$0.0107027\pi$
$397$			1.33964i			0.0672345i	−0.999435	+	0.0336172i	$0.989297\pi$
$398$	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	−0.379030	−	0.925384i	$-0.623742\pi$
$401$	−27.4333	−	15.8386i	−1.36995	−	0.790942i	−0.990921	+	0.134442i	$0.957076\pi$
$402$		0			0
$403$	1.15689	+	6.85276i	0.0576288	+	0.341360i
$404$	−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	0.425903	−	0.904769i	$-0.359956\pi$
$409$	−2.92633	−	1.68952i	−0.144698	−	0.0835412i	−0.570601	+	0.821227i	$0.693290\pi$
$410$	−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
$416$	−2.64555	−	15.6707i	−0.129709	−	0.768322i
$417$		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	−0.173240	−	0.984880i	$-0.555424\pi$
$421$	12.1688	−	7.02566i	0.593071	−	0.342409i	0.766311	+	0.642470i	$0.222090\pi$
$422$		−	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	$0.220878\pi$
$431$			26.5547i			1.27909i	−0.768752	+	0.639547i	$0.779122\pi$
$432$		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	$-0.935069\pi$
$449$		−	8.58501i		−	0.405151i	0.979267	−	0.202576i	$-0.0649312\pi$
$450$		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
$455$	−3.01683	−	3.64901i	−0.141431	−	0.171068i
$456$		0			0
$457$	4.76629	−	2.75182i	0.222958	−	0.128725i	−0.384361	−	0.923183i	$-0.625578\pi$
$457$	4.76629	−	2.75182i	0.222958	−	0.128725i	0.607319	+	0.794458i	$0.292245\pi$
$458$	21.3608			0.998123
$459$		0			0
$460$			1.03747i			0.0483721i
$461$	19.9077	−	11.4937i	0.927196	−	0.535317i	0.0412725	−	0.999148i	$-0.486859\pi$
$461$	19.9077	−	11.4937i	0.927196	−	0.535317i	0.885924	+	0.463831i	$0.153525\pi$
$462$		0			0
$463$	21.8412	+	12.6100i	1.01505	+	0.586037i	0.912665	−	0.408708i	$-0.134021\pi$
$463$	21.8412	+	12.6100i	1.01505	+	0.586037i	0.102381	+	0.994745i	$0.467354\pi$
$464$	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	−0.790737	−	0.612157i	$-0.790302\pi$
$479$	−14.3564	+	8.28869i	−0.655962	+	0.378720i	0.134775	+	0.990876i	$0.456969\pi$
$480$		0			0
$481$	13.7459	−	11.3645i	0.626760	−	0.518177i
$482$	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	$0.0418732\pi$
$487$			5.78932i			0.262339i	−0.991360	+	0.131170i	$0.958127\pi$
$488$	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	0.664841	−	0.746985i	$-0.268499\pi$
$499$	7.82629	+	4.51851i	0.350353	+	0.202276i	−0.314488	+	0.949262i	$0.601833\pi$
$500$	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	0.988878	−	0.148727i	$-0.0475175\pi$
$509$	30.5593	+	17.6434i	1.35452	+	0.782030i	0.365638	+	0.930757i	$0.380851\pi$
$510$		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
$520$	−13.8732	+	2.34209i	−0.608381	+	0.102708i
$521$	−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
$533$	−0.914787	−	5.41867i	−0.0396238	−	0.234709i
$534$		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	$0.359041\pi$
$541$			42.0316i			1.80708i	−0.428504	+	0.903540i	$0.640959\pi$
$542$	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	$0.0242456\pi$
$557$			3.59187i			0.152192i	−0.997100	+	0.0760961i	$0.975754\pi$
$558$		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	$0.0613809\pi$
$572$	−10.9727	+	9.07173i	−0.458792	+	0.379308i
$573$		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	$-0.873265\pi$
$577$		−	18.6264i		−	0.775426i	0.921780	−	0.387713i	$-0.126735\pi$
$578$	−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	0.291060	−	0.956705i	$-0.405992\pi$
$587$	30.6515	−	17.6966i	1.26512	−	0.730418i	0.974061	+	0.226287i	$0.0726587\pi$
$588$		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	$0.0157925\pi$
$593$			2.41535i			0.0991864i	−0.998770	+	0.0495932i	$0.984208\pi$
$594$		0			0
$595$	−0.625302			−0.0256349
$596$	−8.57395	+	4.95017i	−0.351203	+	0.202767i
$597$		0			0
$598$	2.86386	−	2.36771i	0.117112	−	0.0968227i
$599$	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	$0.0452492\pi$
$613$			7.01548i			0.283352i	−0.989913	+	0.141676i	$0.954751\pi$
$614$	−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	0.666273	−	0.745708i	$-0.267888\pi$
$617$	8.78344	+	5.07112i	0.353608	+	0.204156i	−0.312665	+	0.949863i	$0.601222\pi$
$618$		0			0
$619$	−8.11092	+	4.68284i	−0.326005	+	0.188219i	−0.654066	−	0.756437i	$-0.726938\pi$
$619$	−8.11092	+	4.68284i	−0.326005	+	0.188219i	0.328061	+	0.944657i	$0.393605\pi$
$620$	−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	$-0.993668\pi$
$631$		−	0.999379i		−	0.0397846i	0.999802	−	0.0198923i	$-0.00633234\pi$
$632$	−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
$637$	−21.1241	+	3.56619i	−0.836967	+	0.141298i
$638$	−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	0.484479	−	0.874803i	$-0.339009\pi$
$643$	−0.783139	−	0.452145i	−0.0308840	−	0.0178309i	−0.515362	+	0.856972i	$0.672343\pi$
$644$	−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
$650$	−2.17247	−	12.8684i	−0.0852111	−	0.504742i
$651$		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	0.838671	−	0.544638i	$-0.183333\pi$
$661$	20.2167	+	11.6721i	0.786337	+	0.453992i	−0.0523346	+	0.998630i	$0.516666\pi$
$662$	−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	$-0.847740\pi$
$683$		−	24.0595i		−	0.920610i	0.887761	−	0.460305i	$-0.152260\pi$
$684$		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
$689$	−1.33743	−	1.61768i	−0.0509518	−	0.0616288i
$690$		0			0
$691$	25.4878	−	14.7154i	0.969600	−	0.559799i	0.0704856	−	0.997513i	$-0.477545\pi$
$691$	25.4878	−	14.7154i	0.969600	−	0.559799i	0.899114	+	0.437714i	$0.144212\pi$
$692$	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	−0.933059	−	0.359724i	$-0.882871\pi$
$709$	−28.9718	+	16.7269i	−1.08806	+	0.628191i	−0.155000	+	0.987915i	$0.549538\pi$
$710$			1.85140i			0.0694818i
$711$		0			0
$712$	20.9711			0.785925
$713$	1.60206	−	0.924948i	0.0599975	−	0.0346396i
$714$		0			0
$715$	13.6732	+	16.5385i	0.511350	+	0.618503i
$716$	−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	0.393975	−	0.919121i	$-0.371100\pi$
$733$	−5.55072	−	3.20471i	−0.205021	−	0.118369i	−0.598995	+	0.800753i	$0.704433\pi$
$734$	−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	$-0.839755\pi$
$739$		−	26.2292i		−	0.964856i	0.875936	−	0.482428i	$-0.160245\pi$
$740$	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	−0.00362278	−	0.999993i	$-0.501153\pi$
$743$	−23.7541	−	13.7144i	−0.871454	−	0.503134i	−0.867831	+	0.496859i	$0.834487\pi$
$744$		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
$754$	−6.04401	−	35.8013i	−0.220110	−	1.30381i
$755$	−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	0.164728	−	0.986339i	$-0.447325\pi$
$761$	−16.7477	−	9.66927i	−0.607103	−	0.350511i	−0.771831	+	0.635828i	$0.780659\pi$
$762$		0			0
$763$	−7.26096	−	12.5763i	−0.262864	−	0.455294i
$764$	5.14558			0.186160
$765$		0			0
$766$	−6.31277			−0.228089
$767$	−2.52824	−	14.9759i	−0.0912895	−	0.540747i
$768$		0			0
$769$	−8.74040	−	5.04627i	−0.315187	−	0.181973i	0.334058	−	0.942552i	$-0.391582\pi$
$769$	−8.74040	−	5.04627i	−0.315187	−	0.181973i	−0.649245	+	0.760579i	$0.724915\pi$
$770$	−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	$0.0484708\pi$
$773$			8.43470i			0.303375i	−0.988428	+	0.151688i	$0.951529\pi$
$774$		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	0.684579	−	0.728939i	$-0.259986\pi$
$787$	11.0977	+	6.40724i	0.395589	+	0.228393i	−0.288990	+	0.957332i	$0.593319\pi$
$788$	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
$806$	4.75524	+	5.75170i	0.167496	+	0.202595i
$807$		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	$0.156463\pi$
$811$			26.8826i			0.943974i	−0.881605	+	0.471987i	$0.843537\pi$
$812$	−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	−0.727898	−	0.685685i	$-0.759503\pi$
$821$	−14.2700	+	8.23880i	−0.498027	+	0.287536i	0.229871	+	0.973221i	$0.426169\pi$
$822$		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	$-0.725664\pi$
$827$		−	43.6569i		−	1.51810i	0.651033	−	0.759049i	$-0.274336\pi$
$828$		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
$832$	−18.1756	−	21.9842i	−0.630124	−	0.762166i
$833$	−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	−0.280638	−	0.959814i	$-0.590546\pi$
$839$	11.8836	−	6.86099i	0.410267	−	0.236868i	0.690904	+	0.722946i	$0.257213\pi$
$840$		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	−0.255175	−	0.966895i	$-0.582133\pi$
$853$	13.2769	−	7.66545i	0.454594	−	0.262460i	0.709768	+	0.704435i	$0.248800\pi$
$854$	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	$-0.956335\pi$
$863$		−	8.03444i		−	0.273495i	0.990606	−	0.136748i	$-0.0436650\pi$
$864$		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
$871$	1.39412	+	8.25795i	0.0472378	+	0.279810i
$872$	−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	0.394561	−	0.918870i	$-0.370897\pi$
$877$	−6.03899	−	3.48661i	−0.203922	−	0.117735i	−0.598484	+	0.801135i	$0.704230\pi$
$878$	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	$0.508104\pi$
$884$	−1.43373	+	0.242044i	−0.0482215	+	0.00814081i
$885$		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
$923$	−3.75338	+	3.10313i	−0.123544	+	0.102141i
$924$		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	−0.863483	−	0.504378i	$-0.831722\pi$
$929$	−26.1642	+	15.1059i	−0.858421	+	0.495610i	0.00506213	+	0.999987i	$0.498389\pi$
$930$		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	0.958596	−	0.284769i	$-0.0919168\pi$
$941$	36.5433	+	21.0983i	1.19128	+	0.687784i	0.232681	+	0.972553i	$0.425250\pi$
$942$		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	−0.295910	−	0.955216i	$-0.595623\pi$
$947$	11.7977	−	6.81143i	0.383375	−	0.221342i	0.679286	+	0.733874i	$0.262290\pi$
$948$		0			0
$949$	35.7600	−	29.5647i	1.16082	−	0.959712i
$950$	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	0.707665	−	0.706549i	$-0.249749\pi$
$967$	13.9813	+	8.07210i	0.449608	+	0.259581i	−0.258057	+	0.966130i	$0.583082\pi$
$968$	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	0.606530	−	0.795061i	$-0.292561\pi$
$977$	6.91568	+	3.99277i	0.221252	+	0.127740i	−0.385278	+	0.922801i	$0.625894\pi$
$978$		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	−0.0626793	−	0.998034i	$-0.519965\pi$
$983$	24.1512	−	13.9437i	0.770304	−	0.444735i	0.832983	+	0.553299i	$0.186631\pi$
$984$		0			0
$985$	12.2344	−	21.1907i	0.389822	−	0.675191i
$986$	−4.15276	−	2.39760i	−0.132251	−	0.0763550i
$987$		0			0
$988$	−3.40099	−	20.1455i	−0.108200	−	0.640914i
$989$	−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.64.7		20
3.2	odd	2		117.2.t.c.103.4	yes	20
9.2	odd	6		117.2.t.c.25.7	yes	20
9.4	even	3		1053.2.b.i.649.7		10
9.5	odd	6		1053.2.b.j.649.4		10
9.7	even	3	inner	351.2.t.c.181.4		20
13.12	even	2	inner	351.2.t.c.64.4		20
39.38	odd	2		117.2.t.c.103.7	yes	20
117.25	even	6	inner	351.2.t.c.181.7		20
117.38	odd	6		117.2.t.c.25.4	✓	20
117.77	odd	6		1053.2.b.j.649.7		10
117.103	even	6		1053.2.b.i.649.4		10

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

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

\(f(q)\)	\(=\)	\(q+(0.929969 - 0.536918i) q^{2} +(-0.423439 + 0.733417i) q^{4} +(1.10543 + 0.638222i) q^{5} +(-0.890926 + 0.514376i) q^{7} +3.05708i q^{8} +1.37069 q^{10} +(4.03796 - 2.33132i) q^{11} +(2.29741 + 2.77883i) q^{13} +(-0.552355 + 0.956708i) q^{14} +(0.794522 + 1.37615i) q^{16} +0.476187 q^{17} +6.69096i q^{19} +(-0.936166 + 0.540496i) q^{20} +(2.50345 - 4.33610i) q^{22} +(0.479867 - 0.831155i) q^{23} +(-1.68535 - 2.91910i) q^{25} +(3.62852 + 1.35071i) q^{26} -0.871227i q^{28} +(-4.68880 - 8.12123i) q^{29} +(1.66927 + 0.963754i) q^{31} +(-3.81725 - 2.20389i) q^{32} +(0.442839 - 0.255673i) q^{34} -1.31314 q^{35} -4.94666i q^{37} +(3.59249 + 6.22238i) q^{38} +(-1.95109 + 3.37939i) q^{40} +(-1.31994 - 0.762068i) q^{41} +(-1.31426 - 2.27637i) q^{43} +3.94868i q^{44} -1.03060i q^{46} +(5.92316 - 3.41974i) q^{47} +(-2.97083 + 5.14564i) q^{49} +(-3.13464 - 1.80978i) q^{50} +(-3.01086 + 0.508296i) q^{52} -0.582145 q^{53} +5.95159 q^{55} +(-1.57249 - 2.72363i) q^{56} +(-8.72087 - 5.03499i) q^{58} +(-3.64799 - 2.10617i) q^{59} +(-4.71645 - 8.16913i) q^{61} +2.06983 q^{62} -7.91132 q^{64} +(0.766122 + 4.53807i) q^{65} +(2.01156 + 1.16138i) q^{67} +(-0.201636 + 0.349243i) q^{68} +(-1.22118 + 0.705051i) q^{70} +1.35071i q^{71} -12.8687i q^{73} +(-2.65595 - 4.60024i) q^{74} +(-4.90726 - 2.83321i) q^{76} +(-2.39835 + 4.15406i) q^{77} +(6.45415 + 11.1789i) q^{79} +2.02833i q^{80} -1.63667 q^{82} +(-8.86189 + 5.11641i) q^{83} +(0.526392 + 0.303913i) q^{85} +(-2.44445 - 1.41130i) q^{86} +(7.12701 + 12.3444i) q^{88} -6.85985i q^{89} +(-3.47619 - 1.29400i) q^{91} +(0.406389 + 0.703886i) q^{92} +(3.67224 - 6.36050i) q^{94} +(-4.27032 + 7.39640i) q^{95} +(14.9635 - 8.63918i) q^{97} +6.38037i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 12 q^{4} - 16 q^{10} - 4 q^{13} + 18 q^{14} + 4 q^{16} + 12 q^{17} - 10 q^{22} - 24 q^{23} - 12 q^{25} + 12 q^{26} - 12 q^{29} + 12 q^{35} - 12 q^{38} - 8 q^{40} + 4 q^{43} - 10 q^{49} - 108 q^{53}+ \cdots - 24 q^{95}+O(q^{100}) \) 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

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