LMFDB - Embedded newform 351.2.i.b.161.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(161,351)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("351.161"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.i (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24x^{14} + 184x^{12} + 600x^{10} + 894x^{8} + 600x^{6} + 184x^{4} + 24x^{2} + 1 $ x^16 + 24x^14 + 184x^12 + 600x^10 + 894x^8 + 600x^6 + 184x^4 + 24*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			161.7
Root			$-0.440957i$ of defining polynomial
Character	$\chi$	$=$	351.161
Dual form			351.2.i.b.242.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.35438 + 1.35438i) q^{2} +1.66867i q^{4} +(2.02548 + 2.02548i) q^{5} +(0.0947876 + 0.0947876i) q^{7} +(0.448746 - 0.448746i) q^{8} +5.48652i q^{10} +(1.48275 - 1.48275i) q^{11} +(-3.32235 - 1.40072i) q^{13} +0.256756i q^{14} +4.55288 q^{16} -4.69170 q^{17} +(-4.59030 + 4.59030i) q^{19} +(-3.37986 + 3.37986i) q^{20} +4.01641 q^{22} +3.79420 q^{23} +3.20514i q^{25} +(-2.60260 - 6.39681i) q^{26} +(-0.158169 + 0.158169i) q^{28} -6.75971i q^{29} +(-2.65968 + 2.65968i) q^{31} +(5.26882 + 5.26882i) q^{32} +(-6.35432 - 6.35432i) q^{34} +0.383981i q^{35} +(4.05440 + 4.05440i) q^{37} -12.4340 q^{38} +1.81785 q^{40} +(-1.48275 - 1.48275i) q^{41} -7.45512i q^{43} +(2.47423 + 2.47423i) q^{44} +(5.13878 + 5.13878i) q^{46} +(5.23442 - 5.23442i) q^{47} -6.98203i q^{49} +(-4.34096 + 4.34096i) q^{50} +(2.33734 - 5.54390i) q^{52} -4.43494i q^{53} +6.00658 q^{55} +0.0850712 q^{56} +(9.15519 - 9.15519i) q^{58} +(-0.799482 + 0.799482i) q^{59} -10.9126 q^{61} -7.20443 q^{62} +5.16617i q^{64} +(-3.89221 - 9.56648i) q^{65} +(-4.06338 + 4.06338i) q^{67} -7.82889i q^{68} +(-0.520054 + 0.520054i) q^{70} +(5.81968 + 5.81968i) q^{71} +(-8.62828 - 8.62828i) q^{73} +10.9824i q^{74} +(-7.65968 - 7.65968i) q^{76} +0.281093 q^{77} -4.32835 q^{79} +(9.22177 + 9.22177i) q^{80} -4.01641i q^{82} +(11.0492 + 11.0492i) q^{83} +(-9.50294 - 9.50294i) q^{85} +(10.0970 - 10.0970i) q^{86} -1.33076i q^{88} +(-3.25148 + 3.25148i) q^{89} +(-0.182146 - 0.447688i) q^{91} +6.33127i q^{92} +14.1788 q^{94} -18.5951 q^{95} +(11.1238 - 11.1238i) q^{97} +(9.45630 - 9.45630i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7} + 16 q^{13} - 8 q^{16} - 32 q^{19} + 8 q^{22} + 40 q^{28} + 16 q^{31} + 24 q^{34} - 32 q^{37} - 72 q^{40} + 48 q^{46} + 48 q^{52} + 32 q^{55} + 56 q^{58} - 64 q^{61} - 32 q^{67} - 40 q^{70}+ \cdots + 64 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 + 16 * q^13 - 8 * q^16 - 32 * q^19 + 8 * q^22 + 40 * q^28 + 16 * q^31 + 24 * q^34 - 32 * q^37 - 72 * q^40 + 48 * q^46 + 48 * q^52 + 32 * q^55 + 56 * q^58 - 64 * q^61 - 32 * q^67 - 40 * q^70 - 56 * q^73 - 64 * q^76 - 16 * q^79 - 104 * q^91 - 64 * q^94 + 64 * q^97

Character values

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

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.35438	+	1.35438i	0.957689	+	0.957689i	0.999140	−	0.0414520i	$-0.0131984\pi$
$2$	1.35438	+	1.35438i	0.957689	+	0.957689i	−0.0414520	+	0.999140i	$0.513198\pi$
$3$		0			0
$3$		0			0
$4$			1.66867i			0.834335i
$5$	2.02548	+	2.02548i	0.905822	+	0.905822i	0.995932	−	0.0901097i	$-0.0287218\pi$
$5$	2.02548	+	2.02548i	0.905822	+	0.905822i	−0.0901097	+	0.995932i	$0.528722\pi$
$6$		0			0
$7$	0.0947876	+	0.0947876i	0.0358263	+	0.0358263i	0.724793	−	0.688967i	$-0.241935\pi$
$7$	0.0947876	+	0.0947876i	0.0358263	+	0.0358263i	−0.688967	+	0.724793i	$0.741935\pi$
$8$	0.448746	−	0.448746i	0.158656	−	0.158656i
$9$		0			0
$10$			5.48652i			1.73499i
$11$	1.48275	−	1.48275i	0.447067	−	0.447067i	−0.447311	−	0.894378i	$-0.647618\pi$
$11$	1.48275	−	1.48275i	0.447067	−	0.447067i	0.894378	+	0.447311i	$0.147618\pi$
$12$		0			0
$13$	−3.32235	−	1.40072i	−0.921453	−	0.388490i
$13$	−3.32235	−	1.40072i	−0.921453	−	0.388490i
$14$			0.256756i			0.0686210i
$15$		0			0
$16$	4.55288			1.13822
$17$	−4.69170			−1.13790			−0.568952	−	0.822371i	$-0.692651\pi$
$17$	−4.69170			−1.13790			−0.568952	+	0.822371i	$0.692651\pi$
$18$		0			0
$19$	−4.59030	+	4.59030i	−1.05309	+	1.05309i	−0.0545764	+	0.998510i	$0.517381\pi$
$19$	−4.59030	+	4.59030i	−1.05309	+	1.05309i	−0.998510	+	0.0545764i	$0.982619\pi$
$20$	−3.37986	+	3.37986i	−0.755759	+	0.755759i
$21$		0			0
$22$	4.01641			0.856302
$23$	3.79420			0.791146			0.395573	−	0.918435i	$-0.370546\pi$
$23$	3.79420			0.791146			0.395573	+	0.918435i	$0.370546\pi$
$24$		0			0
$25$			3.20514i			0.641027i
$26$	−2.60260	−	6.39681i	−0.510413	−	1.25452i
$27$		0			0
$28$	−0.158169	+	0.158169i	−0.0298912	+	0.0298912i
$29$		−	6.75971i		−	1.25525i	−0.778517	−	0.627623i	$-0.784028\pi$
$29$		−	6.75971i		−	1.25525i	0.778517	−	0.627623i	$-0.215972\pi$
$30$		0			0
$31$	−2.65968	+	2.65968i	−0.477693	+	0.477693i	−0.904393	−	0.426700i	$-0.859676\pi$
$31$	−2.65968	+	2.65968i	−0.477693	+	0.477693i	0.426700	+	0.904393i	$0.359676\pi$
$32$	5.26882	+	5.26882i	0.931405	+	0.931405i
$33$		0			0
$34$	−6.35432	−	6.35432i	−1.08976	−	1.08976i
$35$			0.383981i			0.0649046i
$36$		0			0
$37$	4.05440	+	4.05440i	0.666539	+	0.666539i	0.956913	−	0.290374i	$-0.0937798\pi$
$37$	4.05440	+	4.05440i	0.666539	+	0.666539i	−0.290374	+	0.956913i	$0.593780\pi$
$38$	−12.4340			−2.01706
$39$		0			0
$40$	1.81785			0.287428
$41$	−1.48275	−	1.48275i	−0.231567	−	0.231567i	0.581779	−	0.813347i	$-0.302357\pi$
$41$	−1.48275	−	1.48275i	−0.231567	−	0.231567i	−0.813347	+	0.581779i	$0.802357\pi$
$42$		0			0
$43$		−	7.45512i		−	1.13689i	−0.822720	−	0.568447i	$-0.807544\pi$
$43$		−	7.45512i		−	1.13689i	0.822720	−	0.568447i	$-0.192456\pi$
$44$	2.47423	+	2.47423i	0.373004	+	0.373004i
$45$		0			0
$46$	5.13878	+	5.13878i	0.757672	+	0.757672i
$47$	5.23442	−	5.23442i	0.763519	−	0.763519i	−0.213438	−	0.976957i	$-0.568466\pi$
$47$	5.23442	−	5.23442i	0.763519	−	0.763519i	0.976957	+	0.213438i	$0.0684660\pi$
$48$		0			0
$49$		−	6.98203i		−	0.997433i
$50$	−4.34096	+	4.34096i	−0.613905	+	0.613905i
$51$		0			0
$52$	2.33734	−	5.54390i	0.324131	−	0.768800i
$53$		−	4.43494i		−	0.609186i	−0.952483	−	0.304593i	$-0.901480\pi$
$53$		−	4.43494i		−	0.609186i	0.952483	−	0.304593i	$-0.0985204\pi$
$54$		0			0
$55$	6.00658			0.809927
$56$	0.0850712			0.0113681
$57$		0			0
$58$	9.15519	−	9.15519i	1.20214	−	1.20214i
$59$	−0.799482	+	0.799482i	−0.104084	+	0.104084i	−0.757231	−	0.653147i	$-0.773448\pi$
$59$	−0.799482	+	0.799482i	−0.104084	+	0.104084i	0.653147	+	0.757231i	$0.273448\pi$
$60$		0			0
$61$	−10.9126			−1.39722			−0.698610	−	0.715502i	$-0.746198\pi$
$61$	−10.9126			−1.39722			−0.698610	+	0.715502i	$0.746198\pi$
$62$	−7.20443			−0.914963
$63$		0			0
$64$			5.16617i			0.645771i
$65$	−3.89221	−	9.56648i	−0.482770	−	1.18658i
$66$		0			0
$67$	−4.06338	+	4.06338i	−0.496421	+	0.496421i	−0.910322	−	0.413901i	$-0.864166\pi$
$67$	−4.06338	+	4.06338i	−0.496421	+	0.496421i	0.413901	+	0.910322i	$0.364166\pi$
$68$		−	7.82889i		−	0.949392i
$69$		0			0
$70$	−0.520054	+	0.520054i	−0.0621584	+	0.0621584i
$71$	5.81968	+	5.81968i	0.690669	+	0.690669i	0.962379	−	0.271710i	$-0.0875891\pi$
$71$	5.81968	+	5.81968i	0.690669	+	0.690669i	−0.271710	+	0.962379i	$0.587589\pi$
$72$		0			0
$73$	−8.62828	−	8.62828i	−1.00986	−	1.00986i	−0.999951	−	0.00991275i	$-0.996845\pi$
$73$	−8.62828	−	8.62828i	−1.00986	−	1.00986i	−0.00991275	−	0.999951i	$-0.503155\pi$
$74$			10.9824i			1.27667i
$75$		0			0
$76$	−7.65968	−	7.65968i	−0.878626	−	0.878626i
$77$	0.281093			0.0320336
$78$		0			0
$79$	−4.32835			−0.486978			−0.243489	−	0.969904i	$-0.578292\pi$
$79$	−4.32835			−0.486978			−0.243489	+	0.969904i	$0.578292\pi$
$80$	9.22177	+	9.22177i	1.03103	+	1.03103i
$81$		0			0
$82$		−	4.01641i		−	0.443539i
$83$	11.0492	+	11.0492i	1.21281	+	1.21281i	0.970098	+	0.242712i	$0.0780370\pi$
$83$	11.0492	+	11.0492i	1.21281	+	1.21281i	0.242712	+	0.970098i	$0.421963\pi$
$84$		0			0
$85$	−9.50294	−	9.50294i	−1.03074	−	1.03074i
$86$	10.0970	−	10.0970i	1.08879	−	1.08879i
$87$		0			0
$88$		−	1.33076i		−	0.141860i
$89$	−3.25148	+	3.25148i	−0.344656	+	0.344656i	−0.858114	−	0.513458i	$-0.828364\pi$
$89$	−3.25148	+	3.25148i	−0.344656	+	0.344656i	0.513458	+	0.858114i	$0.328364\pi$
$90$		0			0
$91$	−0.182146	−	0.447688i	−0.0190941	−	0.0469305i
$92$			6.33127i			0.660081i
$93$		0			0
$94$	14.1788			1.46243
$95$	−18.5951			−1.90782
$96$		0			0
$97$	11.1238	−	11.1238i	1.12945	−	1.12945i	0.139183	−	0.990267i	$-0.455552\pi$
$97$	11.1238	−	11.1238i	1.12945	−	1.12945i	0.990267	−	0.139183i	$-0.0444475\pi$
$98$	9.45630	−	9.45630i	0.955230	−	0.955230i
$99$		0			0
$100$	−5.34831			−0.534831
$101$	17.7421			1.76540			0.882701	−	0.469935i	$-0.155723\pi$
$101$	17.7421			1.76540			0.882701	+	0.469935i	$0.155723\pi$
$102$		0			0
$103$			16.9192i			1.66710i	0.552444	+	0.833550i	$0.313695\pi$
$103$			16.9192i			1.66710i	−0.552444	+	0.833550i	$0.686305\pi$
$104$	−2.11946	+	0.862323i	−0.207830	+	0.0845577i
$105$		0			0
$106$	6.00658	−	6.00658i	0.583410	−	0.583410i
$107$			11.9649i			1.15669i	0.815791	+	0.578346i	$0.196302\pi$
$107$			11.9649i			1.15669i	−0.815791	+	0.578346i	$0.803698\pi$
$108$		0			0
$109$	−3.56787	+	3.56787i	−0.341740	+	0.341740i	−0.857021	−	0.515281i	$-0.827688\pi$
$109$	−3.56787	+	3.56787i	−0.341740	+	0.341740i	0.515281	+	0.857021i	$0.327688\pi$
$110$	8.13516	+	8.13516i	0.775658	+	0.775658i
$111$		0			0
$112$	0.431557	+	0.431557i	0.0407783	+	0.0407783i
$113$			15.8863i			1.49446i	0.664564	+	0.747231i	$0.268617\pi$
$113$			15.8863i			1.49446i	−0.664564	+	0.747231i	$0.731383\pi$
$114$		0			0
$115$	7.68508	+	7.68508i	0.716638	+	0.716638i
$116$	11.2797			1.04730
$117$		0			0
$118$	−2.16560			−0.199359
$119$	−0.444715	−	0.444715i	−0.0407669	−	0.0407669i
$120$		0			0
$121$			6.60288i			0.600262i
$122$	−14.7798	−	14.7798i	−1.33810	−	1.33810i
$123$		0			0
$124$	−4.43813	−	4.43813i	−0.398556	−	0.398556i
$125$	3.63546	−	3.63546i	0.325165	−	0.325165i
$126$		0			0
$127$			2.87981i			0.255542i	0.991804	+	0.127771i	$0.0407823\pi$
$127$			2.87981i			0.255542i	−0.991804	+	0.127771i	$0.959218\pi$
$128$	3.54071	−	3.54071i	0.312957	−	0.312957i
$129$		0			0
$130$	7.68508	−	18.2281i	0.674026	−	1.59871i
$131$		−	18.0232i		−	1.57469i	−0.616512	−	0.787345i	$-0.711455\pi$
$131$		−	18.0232i		−	1.57469i	0.616512	−	0.787345i	$-0.288545\pi$
$132$		0			0
$133$	−0.870206			−0.0754564
$134$	−11.0067			−0.950834
$135$		0			0
$136$	−2.10538	+	2.10538i	−0.180535	+	0.180535i
$137$	−13.6600	+	13.6600i	−1.16705	+	1.16705i	−0.184152	+	0.982898i	$0.558954\pi$
$137$	−13.6600	+	13.6600i	−1.16705	+	1.16705i	−0.982898	+	0.184152i	$0.941046\pi$
$138$		0			0
$139$	−11.7207			−0.994133			−0.497067	−	0.867712i	$-0.665590\pi$
$139$	−11.7207			−0.994133			−0.497067	+	0.867712i	$0.665590\pi$
$140$	−0.640737			−0.0541521
$141$		0			0
$142$			15.7641i			1.32289i
$143$	−7.00315	+	2.84930i	−0.585632	+	0.238270i
$144$		0			0
$145$	13.6917	−	13.6917i	1.13703	−	1.13703i
$146$		−	23.3719i		−	1.93427i
$147$		0			0
$148$	−6.76545	+	6.76545i	−0.556116	+	0.556116i
$149$	−7.55919	−	7.55919i	−0.619273	−	0.619273i	0.326072	−	0.945345i	$-0.394275\pi$
$149$	−7.55919	−	7.55919i	−0.619273	−	0.619273i	−0.945345	+	0.326072i	$0.894275\pi$
$150$		0			0
$151$	1.94702	+	1.94702i	0.158447	+	0.158447i	0.781878	−	0.623431i	$-0.214262\pi$
$151$	1.94702	+	1.94702i	0.158447	+	0.158447i	−0.623431	+	0.781878i	$0.714262\pi$
$152$			4.11976i			0.334156i
$153$		0			0
$154$	0.380706	+	0.380706i	0.0306782	+	0.0306782i
$155$	−10.7743			−0.865411
$156$		0			0
$157$	−4.46410			−0.356274			−0.178137	−	0.984006i	$-0.557007\pi$
$157$	−4.46410			−0.356274			−0.178137	+	0.984006i	$0.557007\pi$
$158$	−5.86222	−	5.86222i	−0.466373	−	0.466373i
$159$		0			0
$160$			21.3438i			1.68737i
$161$	0.359643	+	0.359643i	0.0283439	+	0.0283439i
$162$		0			0
$163$	8.85224	+	8.85224i	0.693361	+	0.693361i	0.962970	−	0.269609i	$-0.0868945\pi$
$163$	8.85224	+	8.85224i	0.693361	+	0.693361i	−0.269609	+	0.962970i	$0.586895\pi$
$164$	2.47423	−	2.47423i	0.193205	−	0.193205i
$165$		0			0
$166$			29.9296i			2.32299i
$167$	−13.3740	+	13.3740i	−1.03491	+	1.03491i	−0.0355431	+	0.999368i	$0.511316\pi$
$167$	−13.3740	+	13.3740i	−1.03491	+	1.03491i	−0.999368	+	0.0355431i	$0.988684\pi$
$168$		0			0
$169$	9.07597	+	9.30735i	0.698151	+	0.715950i
$170$		−	25.7411i		−	1.97425i
$171$		0			0
$172$	12.4401			0.948551
$173$	−15.5024			−1.17862			−0.589312	−	0.807906i	$-0.700601\pi$
$173$	−15.5024			−1.17862			−0.589312	+	0.807906i	$0.700601\pi$
$174$		0			0
$175$	−0.303807	+	0.303807i	−0.0229657	+	0.0229657i
$176$	6.75080	−	6.75080i	0.508861	−	0.508861i
$177$		0			0
$178$	−8.80745			−0.660146
$179$	−2.76949			−0.207001			−0.103501	−	0.994629i	$-0.533004\pi$
$179$	−2.76949			−0.207001			−0.103501	+	0.994629i	$0.533004\pi$
$180$		0			0
$181$		−	11.0448i		−	0.820957i	−0.911870	−	0.410478i	$-0.865362\pi$
$181$		−	11.0448i		−	0.820957i	0.911870	−	0.410478i	$-0.134638\pi$
$182$	0.359643	−	0.853033i	0.0266585	−	0.0632310i
$183$		0			0
$184$	1.70264	−	1.70264i	0.125520	−	0.125520i
$185$			16.4242i			1.20753i
$186$		0			0
$187$	−6.95663	+	6.95663i	−0.508719	+	0.508719i
$188$	8.73452	+	8.73452i	0.637030	+	0.637030i
$189$		0			0
$190$	−25.1848	−	25.1848i	−1.82709	−	1.82709i
$191$		−	21.4577i		−	1.55263i	−0.630347	−	0.776313i	$-0.717088\pi$
$191$		−	21.4577i		−	1.55263i	0.630347	−	0.776313i	$-0.282912\pi$
$192$		0			0
$193$	−7.92460	−	7.92460i	−0.570425	−	0.570425i	0.361822	−	0.932247i	$-0.382155\pi$
$193$	−7.92460	−	7.92460i	−0.570425	−	0.570425i	−0.932247	+	0.361822i	$0.882155\pi$
$194$	30.1316			2.16332
$195$		0			0
$196$	11.6507			0.832193
$197$	−3.76499	−	3.76499i	−0.268244	−	0.268244i	0.560148	−	0.828393i	$-0.310744\pi$
$197$	−3.76499	−	3.76499i	−0.268244	−	0.268244i	−0.828393	+	0.560148i	$0.810744\pi$
$198$		0			0
$199$			10.3767i			0.735588i	0.929907	+	0.367794i	$0.119887\pi$
$199$			10.3767i			0.735588i	−0.929907	+	0.367794i	$0.880113\pi$
$200$	1.43829	+	1.43829i	0.101703	+	0.101703i
$201$		0			0
$202$	24.0294	+	24.0294i	1.69071	+	1.69071i
$203$	0.640737	−	0.640737i	0.0449709	−	0.0449709i
$204$		0			0
$205$		−	6.00658i		−	0.419518i
$206$	−22.9150	+	22.9150i	−1.59656	+	1.59656i
$207$		0			0
$208$	−15.1262	−	6.37731i	−1.04882	−	0.442187i
$209$			13.6126i			0.941600i
$210$		0			0
$211$	−2.37674			−0.163622			−0.0818109	−	0.996648i	$-0.526070\pi$
$211$	−2.37674			−0.163622			−0.0818109	+	0.996648i	$0.526070\pi$
$212$	7.40045			0.508265
$213$		0			0
$214$	−16.2050	+	16.2050i	−1.10775	+	1.10775i
$215$	15.1002	−	15.1002i	1.02982	−	1.02982i
$216$		0			0
$217$	−0.504210			−0.0342280
$218$	−9.66449			−0.654562
$219$		0			0
$220$			10.0230i			0.675750i
$221$	15.5874	+	6.57175i	1.04852	+	0.442064i
$222$		0			0
$223$	−1.83285	+	1.83285i	−0.122736	+	0.122736i	−0.765807	−	0.643071i	$-0.777660\pi$
$223$	−1.83285	+	1.83285i	−0.122736	+	0.122736i	0.643071	+	0.765807i	$0.277660\pi$
$224$			0.998838i			0.0667376i
$225$		0			0
$226$	−21.5161	+	21.5161i	−1.43123	+	1.43123i
$227$	1.66584	+	1.66584i	0.110565	+	0.110565i	0.760225	−	0.649660i	$-0.225089\pi$
$227$	1.66584	+	1.66584i	0.110565	+	0.110565i	−0.649660	+	0.760225i	$0.725089\pi$
$228$		0			0
$229$	−6.20959	−	6.20959i	−0.410341	−	0.410341i	0.471516	−	0.881857i	$-0.343707\pi$
$229$	−6.20959	−	6.20959i	−0.410341	−	0.410341i	−0.881857	+	0.471516i	$0.843707\pi$
$230$			20.8170i			1.37263i
$231$		0			0
$232$	−3.03340	−	3.03340i	−0.199152	−	0.199152i
$233$	9.34124			0.611965			0.305982	−	0.952037i	$-0.401015\pi$
$233$	9.34124			0.611965			0.305982	+	0.952037i	$0.401015\pi$
$234$		0			0
$235$	21.2044			1.38322
$236$	−1.33407	−	1.33407i	−0.0868406	−	0.0868406i
$237$		0			0
$238$		−	1.20462i		−	0.0780840i
$239$	2.09915	+	2.09915i	0.135783	+	0.135783i	0.771731	−	0.635949i	$-0.219391\pi$
$239$	2.09915	+	2.09915i	0.135783	+	0.135783i	−0.635949	+	0.771731i	$0.719391\pi$
$240$		0			0
$241$	15.1118	+	15.1118i	0.973438	+	0.973438i	0.999656	−	0.0262181i	$-0.00834642\pi$
$241$	15.1118	+	15.1118i	0.973438	+	0.973438i	−0.0262181	+	0.999656i	$0.508346\pi$
$242$	−8.94278	+	8.94278i	−0.574864	+	0.574864i
$243$		0			0
$244$		−	18.2096i		−	1.16575i
$245$	14.1420	−	14.1420i	0.903497	−	0.903497i
$246$		0			0
$247$	21.6803	−	8.82083i	1.37948	−	0.561256i
$248$			2.38705i			0.151578i
$249$		0			0
$250$	9.84756			0.622814
$251$	−8.71832			−0.550295			−0.275148	−	0.961402i	$-0.588727\pi$
$251$	−8.71832			−0.550295			−0.275148	+	0.961402i	$0.588727\pi$
$252$		0			0
$253$	5.62587	−	5.62587i	0.353695	−	0.353695i
$254$	−3.90035	+	3.90035i	−0.244730	+	0.244730i
$255$		0			0
$256$	19.9232			1.24520
$257$	22.0741			1.37695			0.688473	−	0.725262i	$-0.258281\pi$
$257$	22.0741			1.37695			0.688473	+	0.725262i	$0.258281\pi$
$258$		0			0
$259$			0.768613i			0.0477593i
$260$	15.9633	−	6.49482i	0.990001	−	0.402792i
$261$		0			0
$262$	24.4101	−	24.4101i	1.50806	−	1.50806i
$263$			15.2213i			0.938584i	0.883043	+	0.469292i	$0.155491\pi$
$263$			15.2213i			0.938584i	−0.883043	+	0.469292i	$0.844509\pi$
$264$		0			0
$265$	8.98288	−	8.98288i	0.551814	−	0.551814i
$266$	−1.17859	−	1.17859i	−0.0722638	−	0.0722638i
$267$		0			0
$268$	−6.78044	−	6.78044i	−0.414181	−	0.414181i
$269$			4.80110i			0.292729i	0.989231	+	0.146364i	$0.0467572\pi$
$269$			4.80110i			0.292729i	−0.989231	+	0.146364i	$0.953243\pi$
$270$		0			0
$271$	−13.5789	−	13.5789i	−0.824860	−	0.824860i	0.161941	−	0.986800i	$-0.448225\pi$
$271$	−13.5789	−	13.5789i	−0.824860	−	0.824860i	−0.986800	+	0.161941i	$0.948225\pi$
$272$	−21.3607			−1.29518
$273$		0			0
$274$	−37.0015			−2.23534
$275$	4.75243	+	4.75243i	0.286582	+	0.286582i
$276$		0			0
$277$		−	5.59871i		−	0.336394i	−0.985753	−	0.168197i	$-0.946206\pi$
$277$		−	5.59871i		−	0.336394i	0.985753	−	0.168197i	$-0.0537945\pi$
$278$	−15.8742	−	15.8742i	−0.952070	−	0.952070i
$279$		0			0
$280$	0.172310	+	0.172310i	0.0102975	+	0.0102975i
$281$	7.31576	−	7.31576i	0.436422	−	0.436422i	−0.454384	−	0.890806i	$-0.650141\pi$
$281$	7.31576	−	7.31576i	0.436422	−	0.436422i	0.890806	+	0.454384i	$0.150141\pi$
$282$		0			0
$283$			26.6692i			1.58532i	0.609666	+	0.792658i	$0.291304\pi$
$283$			26.6692i			1.58532i	−0.609666	+	0.792658i	$0.708696\pi$
$284$	−9.71113	+	9.71113i	−0.576249	+	0.576249i
$285$		0			0
$286$	−13.3439	−	5.62587i	−0.789042	−	0.332665i
$287$		−	0.281093i		−	0.0165924i
$288$		0			0
$289$	5.01202			0.294824
$290$	37.0873			2.17784
$291$		0			0
$292$	14.3977	−	14.3977i	0.842564	−	0.842564i
$293$	2.50747	−	2.50747i	0.146488	−	0.146488i	−0.630059	−	0.776547i	$-0.716969\pi$
$293$	2.50747	−	2.50747i	0.146488	−	0.146488i	0.776547	+	0.630059i	$0.216969\pi$
$294$		0			0
$295$	−3.23867			−0.188563
$296$	3.63879			0.211501
$297$		0			0
$298$		−	20.4760i		−	1.18614i
$299$	−12.6057	−	5.31462i	−0.729004	−	0.307352i
$300$		0			0
$301$	0.706653	−	0.706653i	0.0407308	−	0.0407308i
$302$			5.27401i			0.303485i
$303$		0			0
$304$	−20.8991	+	20.8991i	−1.19864	+	1.19864i
$305$	−22.1033	−	22.1033i	−1.26563	−	1.26563i
$306$		0			0
$307$	13.4371	+	13.4371i	0.766899	+	0.766899i	0.977559	−	0.210661i	$-0.0675615\pi$
$307$	13.4371	+	13.4371i	0.766899	+	0.766899i	−0.210661	+	0.977559i	$0.567562\pi$
$308$			0.469052i			0.0267267i
$309$		0			0
$310$	−14.5924	−	14.5924i	−0.828794	−	0.828794i
$311$	13.8005			0.782556			0.391278	−	0.920273i	$-0.372033\pi$
$311$	13.8005			0.782556			0.391278	+	0.920273i	$0.372033\pi$
$312$		0			0
$313$	−13.2290			−0.747746			−0.373873	−	0.927480i	$-0.621970\pi$
$313$	−13.2290			−0.747746			−0.373873	+	0.927480i	$0.621970\pi$
$314$	−6.04607	−	6.04607i	−0.341200	−	0.341200i
$315$		0			0
$316$		−	7.22259i		−	0.406302i
$317$	15.6673	+	15.6673i	0.879961	+	0.879961i	0.993530	−	0.113570i	$-0.0362285\pi$
$317$	15.6673	+	15.6673i	0.879961	+	0.879961i	−0.113570	+	0.993530i	$0.536228\pi$
$318$		0			0
$319$	−10.0230	−	10.0230i	−0.561180	−	0.561180i
$320$	−10.4640	+	10.4640i	−0.584954	+	0.584954i
$321$		0			0
$322$			0.974185i			0.0542892i
$323$	21.5363	−	21.5363i	1.19831	−	1.19831i
$324$		0			0
$325$	4.48950	−	10.6486i	0.249033	−	0.590677i
$326$			23.9785i			1.32805i
$327$		0			0
$328$	−1.33076			−0.0734790
$329$	0.992316			0.0547082
$330$		0			0
$331$	22.4676	−	22.4676i	1.23493	−	1.23493i	0.272882	−	0.962048i	$-0.412023\pi$
$331$	22.4676	−	22.4676i	1.23493	−	1.23493i	0.962048	−	0.272882i	$-0.0879767\pi$
$332$	−18.4375	+	18.4375i	−1.01189	+	1.01189i
$333$		0			0
$334$	−36.2269			−1.98225
$335$	−16.4606			−0.899338
$336$		0			0
$337$			2.97375i			0.161990i	0.996714	+	0.0809952i	$0.0258099\pi$
$337$			2.97375i			0.161990i	−0.996714	+	0.0809952i	$0.974190\pi$
$338$	−0.313385	+	24.8979i	−0.0170459	+	1.35427i
$339$		0			0
$340$	15.8573	−	15.8573i	0.859981	−	0.859981i
$341$			7.88732i			0.427122i
$342$		0			0
$343$	1.32532	−	1.32532i	0.0715607	−	0.0715607i
$344$	−3.34546	−	3.34546i	−0.180375	−	0.180375i
$345$		0			0
$346$	−20.9960	−	20.9960i	−1.12875	−	1.12875i
$347$		−	24.7141i		−	1.32672i	−0.748300	−	0.663361i	$-0.769130\pi$
$347$		−	24.7141i		−	1.32672i	0.748300	−	0.663361i	$-0.230870\pi$
$348$		0			0
$349$	2.55203	+	2.55203i	0.136607	+	0.136607i	0.772104	−	0.635497i	$-0.219205\pi$
$349$	2.55203	+	2.55203i	0.136607	+	0.136607i	−0.635497	+	0.772104i	$0.719205\pi$
$350$	−0.822938			−0.0439879
$351$		0			0
$352$	15.6247			0.832801
$353$	2.59742	+	2.59742i	0.138247	+	0.138247i	0.772843	−	0.634597i	$-0.218834\pi$
$353$	2.59742	+	2.59742i	0.138247	+	0.138247i	−0.634597	+	0.772843i	$0.718834\pi$
$354$		0			0
$355$			23.5753i			1.25125i
$356$	−5.42564	−	5.42564i	−0.287558	−	0.287558i
$357$		0			0
$358$	−3.75093	−	3.75093i	−0.198243	−	0.198243i
$359$	−4.93025	+	4.93025i	−0.260209	+	0.260209i	−0.825139	−	0.564930i	$-0.808903\pi$
$359$	−4.93025	+	4.93025i	−0.260209	+	0.260209i	0.564930	+	0.825139i	$0.308903\pi$
$360$		0			0
$361$		−	23.1416i		−	1.21798i
$362$	14.9589	−	14.9589i	0.786221	−	0.786221i
$363$		0			0
$364$	0.747043	−	0.303942i	0.0391557	−	0.0159309i
$365$		−	34.9528i		−	1.82951i
$366$		0			0
$367$	14.3492			0.749020			0.374510	−	0.927223i	$-0.377811\pi$
$367$	14.3492			0.749020			0.374510	+	0.927223i	$0.377811\pi$
$368$	17.2746			0.900499
$369$		0			0
$370$	−22.2445	+	22.2445i	−1.15644	+	1.15644i
$371$	0.420377	−	0.420377i	0.0218249	−	0.0218249i
$372$		0			0
$373$	1.81879			0.0941732			0.0470866	−	0.998891i	$-0.485006\pi$
$373$	1.81879			0.0941732			0.0470866	+	0.998891i	$0.485006\pi$
$374$	−18.8438			−0.974389
$375$		0			0
$376$		−	4.69786i		−	0.242273i
$377$	−9.46846	+	22.4581i	−0.487651	+	1.15665i
$378$		0			0
$379$	−3.03283	+	3.03283i	−0.155786	+	0.155786i	−0.780696	−	0.624911i	$-0.785135\pi$
$379$	−3.03283	+	3.03283i	−0.155786	+	0.155786i	0.624911	+	0.780696i	$0.285135\pi$
$380$		−	31.0291i		−	1.59176i
$381$		0			0
$382$	29.0618	−	29.0618i	1.48693	−	1.48693i
$383$	−8.54138	−	8.54138i	−0.436444	−	0.436444i	0.454369	−	0.890813i	$-0.349865\pi$
$383$	−8.54138	−	8.54138i	−0.436444	−	0.436444i	−0.890813	+	0.454369i	$0.849865\pi$
$384$		0			0
$385$	0.569349	+	0.569349i	0.0290167	+	0.0290167i
$386$		−	21.4658i		−	1.09258i
$387$		0			0
$388$	18.5619	+	18.5619i	0.942339	+	0.942339i
$389$	−30.5259			−1.54773			−0.773863	−	0.633353i	$-0.781678\pi$
$389$	−30.5259			−1.54773			−0.773863	+	0.633353i	$0.781678\pi$
$390$		0			0
$391$	−17.8013			−0.900248
$392$	−3.13316	−	3.13316i	−0.158249	−	0.158249i
$393$		0			0
$394$		−	10.1984i		−	0.513789i
$395$	−8.76699	−	8.76699i	−0.441115	−	0.441115i
$396$		0			0
$397$	−20.0700	−	20.0700i	−1.00728	−	1.00728i	−0.999973	−	0.00730907i	$-0.997673\pi$
$397$	−20.0700	−	20.0700i	−1.00728	−	1.00728i	−0.00730907	−	0.999973i	$-0.502327\pi$
$398$	−14.0540	+	14.0540i	−0.704464	+	0.704464i
$399$		0			0
$400$			14.5926i			0.729630i
$401$	14.4906	−	14.4906i	0.723626	−	0.723626i	−0.245716	−	0.969342i	$-0.579023\pi$
$401$	14.4906	−	14.4906i	0.723626	−	0.723626i	0.969342	+	0.245716i	$0.0790231\pi$
$402$		0			0
$403$	12.5619	−	5.11092i	0.625751	−	0.254593i
$404$			29.6056i			1.47294i
$405$		0			0
$406$	1.73560			0.0861362
$407$	12.0233			0.595975
$408$		0			0
$409$	20.7783	−	20.7783i	1.02742	−	1.02742i	0.0278083	−	0.999613i	$-0.491147\pi$
$409$	20.7783	−	20.7783i	1.02742	−	1.02742i	0.999613	−	0.0278083i	$-0.00885278\pi$
$410$	8.13516	−	8.13516i	0.401767	−	0.401767i
$411$		0			0
$412$	−28.2326			−1.39092
$413$	−0.151562			−0.00745787
$414$		0			0
$415$			44.7600i			2.19718i
$416$	−10.1247	−	24.8850i	−0.496404	−	1.22009i
$417$		0			0
$418$	−18.4365	+	18.4365i	−0.901760	+	0.901760i
$419$			17.8086i			0.870005i	0.900429	+	0.435003i	$0.143253\pi$
$419$			17.8086i			0.870005i	−0.900429	+	0.435003i	$0.856747\pi$
$420$		0			0
$421$	3.61130	−	3.61130i	0.176004	−	0.176004i	−0.613607	−	0.789611i	$-0.710282\pi$
$421$	3.61130	−	3.61130i	0.176004	−	0.176004i	0.789611	+	0.613607i	$0.210282\pi$
$422$	−3.21900	−	3.21900i	−0.156699	−	0.156699i
$423$		0			0
$424$	−1.99016	−	1.99016i	−0.0966509	−	0.0966509i
$425$		−	15.0375i		−	0.729427i
$426$		0			0
$427$	−1.03438	−	1.03438i	−0.0500573	−	0.0500573i
$428$	−19.9655			−0.965069
$429$		0			0
$430$	40.9027			1.97250
$431$	0.439838	+	0.439838i	0.0211863	+	0.0211863i	0.717621	−	0.696434i	$-0.245231\pi$
$431$	0.439838	+	0.439838i	0.0211863	+	0.0211863i	−0.696434	+	0.717621i	$0.745231\pi$
$432$		0			0
$433$		−	7.76842i		−	0.373327i	−0.982424	−	0.186663i	$-0.940233\pi$
$433$		−	7.76842i		−	0.373327i	0.982424	−	0.186663i	$-0.0597674\pi$
$434$	−0.682890	−	0.682890i	−0.0327798	−	0.0327798i
$435$		0			0
$436$	−5.95360	−	5.95360i	−0.285126	−	0.285126i
$437$	−17.4165	+	17.4165i	−0.833145	+	0.833145i
$438$		0			0
$439$		−	6.99519i		−	0.333862i	−0.985969	−	0.166931i	$-0.946614\pi$
$439$		−	6.99519i		−	0.333862i	0.985969	−	0.166931i	$-0.0533857\pi$
$440$	2.69543	−	2.69543i	0.128500	−	0.128500i
$441$		0			0
$442$	12.2106	+	30.0119i	0.580800	+	1.42752i
$443$			24.9020i			1.18313i	0.806257	+	0.591566i	$0.201490\pi$
$443$			24.9020i			1.18313i	−0.806257	+	0.591566i	$0.798510\pi$
$444$		0			0
$445$	−13.1716			−0.624394
$446$	−4.96473			−0.235087
$447$		0			0
$448$	−0.489689	+	0.489689i	−0.0231356	+	0.0231356i
$449$	1.53630	−	1.53630i	0.0725027	−	0.0725027i	−0.669926	−	0.742428i	$-0.733674\pi$
$449$	1.53630	−	1.53630i	0.0725027	−	0.0725027i	0.742428	+	0.669926i	$0.233674\pi$
$450$		0			0
$451$	−4.39712			−0.207052
$452$	−26.5091			−1.24688
$453$		0			0
$454$			4.51234i			0.211775i
$455$	0.537849	−	1.27572i	0.0252148	−	0.0598065i
$456$		0			0
$457$	5.13518	−	5.13518i	0.240214	−	0.240214i	−0.576725	−	0.816938i	$-0.695670\pi$
$457$	5.13518	−	5.13518i	0.240214	−	0.240214i	0.816938	+	0.576725i	$0.195670\pi$
$458$		−	16.8202i		−	0.785958i
$459$		0			0
$460$	−12.8239	+	12.8239i	−0.597916	+	0.597916i
$461$	−1.56744	−	1.56744i	−0.0730031	−	0.0730031i	0.669662	−	0.742666i	$-0.266439\pi$
$461$	−1.56744	−	1.56744i	−0.0730031	−	0.0730031i	−0.742666	+	0.669662i	$0.766439\pi$
$462$		0			0
$463$	25.0408	+	25.0408i	1.16375	+	1.16375i	0.983649	+	0.180097i	$0.0576412\pi$
$463$	25.0408	+	25.0408i	1.16375	+	1.16375i	0.180097	+	0.983649i	$0.442359\pi$
$464$		−	30.7762i		−	1.42875i
$465$		0			0
$466$	12.6516	+	12.6516i	0.586072	+	0.586072i
$467$	9.82811			0.454791			0.227395	−	0.973803i	$-0.426979\pi$
$467$	9.82811			0.454791			0.227395	+	0.973803i	$0.426979\pi$
$468$		0			0
$469$	−0.770316			−0.0355699
$470$	28.7188	+	28.7188i	1.32470	+	1.32470i
$471$		0			0
$472$			0.717529i			0.0330270i
$473$	−11.0541	−	11.0541i	−0.508268	−	0.508268i
$474$		0			0
$475$	−14.7125	−	14.7125i	−0.675057	−	0.675057i
$476$	0.742082	−	0.742082i	0.0340133	−	0.0340133i
$477$		0			0
$478$			5.68609i			0.260076i
$479$	24.6241	−	24.6241i	1.12511	−	1.12511i	0.134143	−	0.990962i	$-0.457172\pi$
$479$	24.6241	−	24.6241i	1.12511	−	1.12511i	0.990962	−	0.134143i	$-0.0428282\pi$
$480$		0			0
$481$	−7.79103	−	19.1492i	−0.355241	−	0.873128i
$482$			40.9342i			1.86450i
$483$		0			0
$484$	−11.0180			−0.500819
$485$	45.0620			2.04616
$486$		0			0
$487$	11.7321	−	11.7321i	0.531630	−	0.531630i	−0.389427	−	0.921057i	$-0.627327\pi$
$487$	11.7321	−	11.7321i	0.531630	−	0.531630i	0.921057	+	0.389427i	$0.127327\pi$
$488$	−4.89701	+	4.89701i	−0.221677	+	0.221677i
$489$		0			0
$490$	38.3071			1.73054
$491$	1.02472			0.0462449			0.0231224	−	0.999733i	$-0.492639\pi$
$491$	1.02472			0.0462449			0.0231224	+	0.999733i	$0.492639\pi$
$492$		0			0
$493$			31.7145i			1.42835i
$494$	41.3100	+	17.4165i	1.85862	+	0.783606i
$495$		0			0
$496$	−12.1092	+	12.1092i	−0.543720	+	0.543720i
$497$			1.10327i			0.0494883i
$498$		0			0
$499$	−4.95006	+	4.95006i	−0.221595	+	0.221595i	−0.809170	−	0.587575i	$-0.800083\pi$
$499$	−4.95006	+	4.95006i	−0.221595	+	0.221595i	0.587575	+	0.809170i	$0.300083\pi$
$500$	6.06638	+	6.06638i	0.271297	+	0.271297i
$501$		0			0
$502$	−11.8079	−	11.8079i	−0.527012	−	0.527012i
$503$			29.3272i			1.30764i	0.756652	+	0.653818i	$0.226834\pi$
$503$			29.3272i			1.30764i	−0.756652	+	0.653818i	$0.773166\pi$
$504$		0			0
$505$	35.9362	+	35.9362i	1.59914	+	1.59914i
$506$	15.2391			0.677460
$507$		0			0
$508$	−4.80546			−0.213208
$509$	−9.77877	−	9.77877i	−0.433436	−	0.433436i	0.456359	−	0.889796i	$-0.349153\pi$
$509$	−9.77877	−	9.77877i	−0.433436	−	0.433436i	−0.889796	+	0.456359i	$0.849153\pi$
$510$		0			0
$511$		−	1.63571i		−	0.0723594i
$512$	19.9021	+	19.9021i	0.879559	+	0.879559i
$513$		0			0
$514$	29.8967	+	29.8967i	1.31869	+	1.31869i
$515$	−34.2695	+	34.2695i	−1.51010	+	1.51010i
$516$		0			0
$517$		−	15.5227i		−	0.682689i
$518$	−1.04099	+	1.04099i	−0.0457385	+	0.0457385i
$519$		0			0
$520$	−6.03954	−	2.54630i	−0.264851	−	0.111663i
$521$			31.4316i			1.37704i	0.725215	+	0.688522i	$0.241740\pi$
$521$			31.4316i			1.37704i	−0.725215	+	0.688522i	$0.758260\pi$
$522$		0			0
$523$	−10.7925			−0.471921			−0.235961	−	0.971763i	$-0.575824\pi$
$523$	−10.7925			−0.471921			−0.235961	+	0.971763i	$0.575824\pi$
$524$	30.0747			1.31382
$525$		0			0
$526$	−20.6153	+	20.6153i	−0.898871	+	0.898871i
$527$	12.4784	−	12.4784i	0.543569	−	0.543569i
$528$		0			0
$529$	−8.60402			−0.374088
$530$	24.3324			1.05693
$531$		0			0
$532$		−	1.45209i		−	0.0629559i
$533$	2.84930	+	7.00315i	0.123417	+	0.303340i
$534$		0			0
$535$	−24.2347	+	24.2347i	−1.04776	+	1.04776i
$536$			3.64686i			0.157520i
$537$		0			0
$538$	−6.50250	+	6.50250i	−0.280343	+	0.280343i
$539$	−10.3526	−	10.3526i	−0.445920	−	0.445920i
$540$		0			0
$541$	8.05355	+	8.05355i	0.346249	+	0.346249i	0.858710	−	0.512461i	$-0.171266\pi$
$541$	8.05355	+	8.05355i	0.346249	+	0.346249i	−0.512461	+	0.858710i	$0.671266\pi$
$542$		−	36.7819i		−	1.57992i
$543$		0			0
$544$	−24.7197	−	24.7197i	−1.05985	−	1.05985i
$545$	−14.4533			−0.619112
$546$		0			0
$547$	−29.1250			−1.24529			−0.622647	−	0.782503i	$-0.713943\pi$
$547$	−29.1250			−1.24529			−0.622647	+	0.782503i	$0.713943\pi$
$548$	−22.7940	−	22.7940i	−0.973710	−	0.973710i
$549$		0			0
$550$			12.8732i			0.548913i
$551$	31.0291	+	31.0291i	1.32188	+	1.32188i
$552$		0			0
$553$	−0.410274	−	0.410274i	−0.0174466	−	0.0174466i
$554$	7.58276	−	7.58276i	0.322161	−	0.322161i
$555$		0			0
$556$		−	19.5579i		−	0.829440i
$557$	2.05469	−	2.05469i	0.0870602	−	0.0870602i	−0.662236	−	0.749296i	$-0.730392\pi$
$557$	2.05469	−	2.05469i	0.0870602	−	0.0870602i	0.749296	+	0.662236i	$0.230392\pi$
$558$		0			0
$559$	−10.4425	+	24.7685i	−0.441672	+	1.04760i
$560$			1.74822i			0.0738757i
$561$		0			0
$562$	19.8166			0.835912
$563$	37.2590			1.57028			0.785140	−	0.619319i	$-0.212591\pi$
$563$	37.2590			1.57028			0.785140	+	0.619319i	$0.212591\pi$
$564$		0			0
$565$	−32.1775	+	32.1775i	−1.35372	+	1.35372i
$566$	−36.1201	+	36.1201i	−1.51824	+	1.51824i
$567$		0			0
$568$	5.22312			0.219157
$569$	5.88656			0.246777			0.123389	−	0.992358i	$-0.460624\pi$
$569$	5.88656			0.246777			0.123389	+	0.992358i	$0.460624\pi$
$570$		0			0
$571$			6.89581i			0.288581i	0.989535	+	0.144290i	$0.0460899\pi$
$571$			6.89581i			0.288581i	−0.989535	+	0.144290i	$0.953910\pi$
$572$	−4.75454	−	11.6859i	−0.198797	−	0.488613i
$573$		0			0
$574$	0.380706	−	0.380706i	0.0158904	−	0.0158904i
$575$			12.1609i			0.507146i
$576$		0			0
$577$	0.568497	−	0.568497i	0.0236669	−	0.0236669i	−0.695174	−	0.718841i	$-0.744673\pi$
$577$	0.568497	−	0.568497i	0.0236669	−	0.0236669i	0.718841	+	0.695174i	$0.244673\pi$
$578$	6.78815	+	6.78815i	0.282350	+	0.282350i
$579$		0			0
$580$	22.8469	+	22.8469i	0.948664	+	0.948664i
$581$			2.09466i			0.0869011i
$582$		0			0
$583$	−6.57593	−	6.57593i	−0.272347	−	0.272347i
$584$	−7.74382			−0.320441
$585$		0			0
$586$	6.79212			0.280580
$587$	−9.19839	−	9.19839i	−0.379658	−	0.379658i	0.491321	−	0.870979i	$-0.336514\pi$
$587$	−9.19839	−	9.19839i	−0.379658	−	0.379658i	−0.870979	+	0.491321i	$0.836514\pi$
$588$		0			0
$589$		−	24.4175i		−	1.00610i
$590$	−4.38638	−	4.38638i	−0.180584	−	0.180584i
$591$		0			0
$592$	18.4592	+	18.4592i	0.758668	+	0.758668i
$593$	28.1213	−	28.1213i	1.15481	−	1.15481i	0.169228	−	0.985577i	$-0.445872\pi$
$593$	28.1213	−	28.1213i	1.15481	−	1.15481i	0.985577	−	0.169228i	$-0.0541276\pi$
$594$		0			0
$595$		−	1.80152i		−	0.0738552i
$596$	12.6138	−	12.6138i	0.516681	−	0.516681i
$597$		0			0
$598$	−9.87481	−	24.2708i	−0.403811	−	0.992506i
$599$		−	5.76908i		−	0.235718i	−0.993030	−	0.117859i	$-0.962397\pi$
$599$		−	5.76908i		−	0.235718i	0.993030	−	0.117859i	$-0.0376031\pi$
$600$		0			0
$601$	14.3439			0.585101			0.292550	−	0.956250i	$-0.405496\pi$
$601$	14.3439			0.585101			0.292550	+	0.956250i	$0.405496\pi$
$602$	1.91415			0.0780148
$603$		0			0
$604$	−3.24894	+	3.24894i	−0.132197	+	0.132197i
$605$	−13.3740	+	13.3740i	−0.543730	+	0.543730i
$606$		0			0
$607$	42.3384			1.71846			0.859231	−	0.511587i	$-0.170942\pi$
$607$	42.3384			1.71846			0.859231	+	0.511587i	$0.170942\pi$
$608$	−48.3709			−1.96170
$609$		0			0
$610$		−	59.8725i		−	2.42416i
$611$	−24.7225	+	10.0586i	−1.00017	+	0.406927i
$612$		0			0
$613$	−25.9886	+	25.9886i	−1.04967	+	1.04967i	−0.0509698	+	0.998700i	$0.516231\pi$
$613$	−25.9886	+	25.9886i	−1.04967	+	1.04967i	−0.998700	+	0.0509698i	$0.983769\pi$
$614$			36.3979i			1.46890i
$615$		0			0
$616$	0.126140	−	0.126140i	0.00508231	−	0.00508231i
$617$	−31.8840	−	31.8840i	−1.28360	−	1.28360i	−0.938603	−	0.345000i	$-0.887879\pi$
$617$	−31.8840	−	31.8840i	−1.28360	−	1.28360i	−0.345000	−	0.938603i	$-0.612121\pi$
$618$		0			0
$619$	−26.7918	−	26.7918i	−1.07685	−	1.07685i	−0.996790	−	0.0800615i	$-0.974488\pi$
$619$	−26.7918	−	26.7918i	−1.07685	−	1.07685i	−0.0800615	−	0.996790i	$-0.525512\pi$
$620$		−	17.9787i		−	0.722042i
$621$		0			0
$622$	18.6911	+	18.6911i	0.749444	+	0.749444i
$623$	−0.616399			−0.0246955
$624$		0			0
$625$	30.7528			1.23011
$626$	−17.9170	−	17.9170i	−0.716108	−	0.716108i
$627$		0			0
$628$		−	7.44911i		−	0.297252i
$629$	−19.0220	−	19.0220i	−0.758457	−	0.758457i
$630$		0			0
$631$	−6.22813	−	6.22813i	−0.247938	−	0.247938i	0.572186	−	0.820124i	$-0.306096\pi$
$631$	−6.22813	−	6.22813i	−0.247938	−	0.247938i	−0.820124	+	0.572186i	$0.806096\pi$
$632$	−1.94233	+	1.94233i	−0.0772619	+	0.0772619i
$633$		0			0
$634$			42.4387i			1.68546i
$635$	−5.83301	+	5.83301i	−0.231476	+	0.231476i
$636$		0			0
$637$	−9.77987	+	23.1967i	−0.387493	+	0.919088i
$638$		−	27.1498i		−	1.07487i
$639$		0			0
$640$	14.3433			0.566967
$641$	−19.2034			−0.758490			−0.379245	−	0.925296i	$-0.623816\pi$
$641$	−19.2034			−0.758490			−0.379245	+	0.925296i	$0.623816\pi$
$642$		0			0
$643$	19.7368	−	19.7368i	0.778343	−	0.778343i	−0.201206	−	0.979549i	$-0.564486\pi$
$643$	19.7368	−	19.7368i	0.778343	−	0.778343i	0.979549	+	0.201206i	$0.0644860\pi$
$644$	−0.600126	+	0.600126i	−0.0236483	+	0.0236483i
$645$		0			0
$646$	58.3364			2.29522
$647$	−4.50220			−0.177000			−0.0884998	−	0.996076i	$-0.528207\pi$
$647$	−4.50220			−0.177000			−0.0884998	+	0.996076i	$0.528207\pi$
$648$		0			0
$649$			2.37087i			0.0930648i
$650$	20.5026	−	8.34170i	0.804180	−	0.327189i
$651$		0			0
$652$	−14.7715	+	14.7715i	−0.578495	+	0.578495i
$653$			10.0849i			0.394651i	0.980338	+	0.197326i	$0.0632256\pi$
$653$			10.0849i			0.394651i	−0.980338	+	0.197326i	$0.936774\pi$
$654$		0			0
$655$	36.5056	−	36.5056i	1.42639	−	1.42639i
$656$	−6.75080	−	6.75080i	−0.263575	−	0.263575i
$657$		0			0
$658$	1.34397	+	1.34397i	0.0523934	+	0.0523934i
$659$		−	17.4772i		−	0.680817i	−0.940278	−	0.340408i	$-0.889435\pi$
$659$		−	17.4772i		−	0.680817i	0.940278	−	0.340408i	$-0.110565\pi$
$660$		0			0
$661$	−24.6426	−	24.6426i	−0.958485	−	0.958485i	0.0406872	−	0.999172i	$-0.487045\pi$
$661$	−24.6426	−	24.6426i	−0.958485	−	0.958485i	−0.999172	+	0.0406872i	$0.987045\pi$
$662$	60.8591			2.36536
$663$		0			0
$664$	9.91660			0.384839
$665$	−1.76258	−	1.76258i	−0.0683501	−	0.0683501i
$666$		0			0
$667$		−	25.6477i		−	0.993084i
$668$	−22.3168	−	22.3168i	−0.863462	−	0.863462i
$669$		0			0
$670$	−22.2938	−	22.2938i	−0.861286	−	0.861286i
$671$	−16.1808	+	16.1808i	−0.624651	+	0.624651i
$672$		0			0
$673$			23.6387i			0.911206i	0.890183	+	0.455603i	$0.150576\pi$
$673$			23.6387i			0.911206i	−0.890183	+	0.455603i	$0.849424\pi$
$674$	−4.02758	+	4.02758i	−0.155136	+	0.155136i
$675$		0			0
$676$	−15.5309	+	15.1448i	−0.597342	+	0.582492i
$677$		−	4.39279i		−	0.168829i	−0.996431	−	0.0844143i	$-0.973098\pi$
$677$		−	4.39279i		−	0.168829i	0.996431	−	0.0844143i	$-0.0269019\pi$
$678$		0			0
$679$	2.10879			0.0809281
$680$	−8.52882			−0.327065
$681$		0			0
$682$	−10.6824	+	10.6824i	−0.409050	+	0.409050i
$683$	31.9691	−	31.9691i	1.22326	−	1.22326i	0.256799	−	0.966465i	$-0.417332\pi$
$683$	31.9691	−	31.9691i	1.22326	−	1.22326i	0.966465	−	0.256799i	$-0.0826678\pi$
$684$		0			0
$685$	−55.3360			−2.11428
$686$	3.58997			0.137066
$687$		0			0
$688$		−	33.9423i		−	1.29404i
$689$	−6.21211	+	14.7344i	−0.236663	+	0.561336i
$690$		0			0
$691$	−6.85195	+	6.85195i	−0.260661	+	0.260661i	−0.825322	−	0.564662i	$-0.809007\pi$
$691$	−6.85195	+	6.85195i	−0.260661	+	0.260661i	0.564662	+	0.825322i	$0.309007\pi$
$692$		−	25.8683i		−	0.983366i
$693$		0			0
$694$	33.4722	−	33.4722i	1.27059	−	1.27059i
$695$	−23.7400	−	23.7400i	−0.900508	−	0.900508i
$696$		0			0
$697$	6.95663	+	6.95663i	0.263501	+	0.263501i
$698$			6.91282i			0.261654i
$699$		0			0
$700$	−0.506954	−	0.506954i	−0.0191611	−	0.0191611i
$701$	−41.0030			−1.54866			−0.774331	−	0.632781i	$-0.781913\pi$
$701$	−41.0030			−1.54866			−0.774331	+	0.632781i	$0.781913\pi$
$702$		0			0
$703$	−37.2218			−1.40385
$704$	7.66016	+	7.66016i	0.288703	+	0.288703i
$705$		0			0
$706$			7.03576i			0.264794i
$707$	1.68173	+	1.68173i	0.0632479	+	0.0632479i
$708$		0			0
$709$	−3.13935	−	3.13935i	−0.117901	−	0.117901i	0.645695	−	0.763596i	$-0.276568\pi$
$709$	−3.13935	−	3.13935i	−0.117901	−	0.117901i	−0.763596	+	0.645695i	$0.776568\pi$
$710$	−31.9298	+	31.9298i	−1.19831	+	1.19831i
$711$		0			0
$712$			2.91818i			0.109363i
$713$	−10.0914	+	10.0914i	−0.377925	+	0.377925i
$714$		0			0
$715$	−19.9559	−	8.41353i	−0.746309	−	0.314648i
$716$		−	4.62136i		−	0.172708i
$717$		0			0
$718$	−13.3548			−0.498398
$719$	−28.1080			−1.04825			−0.524126	−	0.851641i	$-0.675608\pi$
$719$	−28.1080			−1.04825			−0.524126	+	0.851641i	$0.675608\pi$
$720$		0			0
$721$	−1.60373	+	1.60373i	−0.0597261	+	0.0597261i
$722$	31.3425	−	31.3425i	1.16645	−	1.16645i
$723$		0			0
$724$	18.4302			0.684953
$725$	21.6658			0.804648
$726$		0			0
$727$		−	40.5328i		−	1.50328i	−0.659575	−	0.751639i	$-0.729264\pi$
$727$		−	40.5328i		−	1.50328i	0.659575	−	0.751639i	$-0.270736\pi$
$728$	−0.282636	−	0.119161i	−0.0104752	−	0.00441640i
$729$		0			0
$730$	47.3392	−	47.3392i	1.75210	−	1.75210i
$731$			34.9771i			1.29368i
$732$		0			0
$733$	−21.5128	+	21.5128i	−0.794592	+	0.794592i	−0.982237	−	0.187645i	$-0.939915\pi$
$733$	−21.5128	+	21.5128i	−0.794592	+	0.794592i	0.187645	+	0.982237i	$0.439915\pi$
$734$	19.4342	+	19.4342i	0.717328	+	0.717328i
$735$		0			0
$736$	19.9910	+	19.9910i	0.736877	+	0.736877i
$737$			12.0500i			0.443867i
$738$		0			0
$739$	19.0690	+	19.0690i	0.701463	+	0.701463i	0.964725	−	0.263261i	$-0.0847981\pi$
$739$	19.0690	+	19.0690i	0.701463	+	0.701463i	−0.263261	+	0.964725i	$0.584798\pi$
$740$	−27.4066			−1.00748
$741$		0			0
$742$	1.13870			0.0418029
$743$	36.3797	+	36.3797i	1.33464	+	1.33464i	0.901164	+	0.433478i	$0.142714\pi$
$743$	36.3797	+	36.3797i	1.33464	+	1.33464i	0.433478	+	0.901164i	$0.357286\pi$
$744$		0			0
$745$		−	30.6220i		−	1.12190i
$746$	2.46332	+	2.46332i	0.0901886	+	0.0901886i
$747$		0			0
$748$	−11.6083	−	11.6083i	−0.424442	−	0.424442i
$749$	−1.13413	+	1.13413i	−0.0414401	+	0.0414401i
$750$		0			0
$751$		−	15.6238i		−	0.570121i	−0.958510	−	0.285060i	$-0.907986\pi$
$751$		−	15.6238i		−	0.570121i	0.958510	−	0.285060i	$-0.0920136\pi$
$752$	23.8317	−	23.8317i	0.869053	−	0.869053i
$753$		0			0
$754$	−43.2406	+	17.5929i	−1.57473	+	0.640694i
$755$			7.88732i			0.287049i
$756$		0			0
$757$	−26.7775			−0.973245			−0.486623	−	0.873612i	$-0.661771\pi$
$757$	−26.7775			−0.973245			−0.486623	+	0.873612i	$0.661771\pi$
$758$	−8.21518			−0.298389
$759$		0			0
$760$	−8.34449	+	8.34449i	−0.302686	+	0.302686i
$761$	−8.72446	+	8.72446i	−0.316261	+	0.316261i	−0.847329	−	0.531068i	$-0.821791\pi$
$761$	−8.72446	+	8.72446i	−0.316261	+	0.316261i	0.531068	+	0.847329i	$0.321791\pi$
$762$		0			0
$763$	−0.676380			−0.0244866
$764$	35.8058			1.29541
$765$		0			0
$766$		−	23.1365i		−	0.835955i
$767$	3.77601	−	1.53630i	0.136344	−	0.0554728i
$768$		0			0
$769$	2.91922	−	2.91922i	0.105270	−	0.105270i	−0.652510	−	0.757780i	$-0.726284\pi$
$769$	2.91922	−	2.91922i	0.105270	−	0.105270i	0.757780	+	0.652510i	$0.226284\pi$
$770$			1.54223i			0.0555779i
$771$		0			0
$772$	13.2235	−	13.2235i	0.475926	−	0.475926i
$773$	14.8123	+	14.8123i	0.532761	+	0.532761i	0.921393	−	0.388632i	$-0.127052\pi$
$773$	14.8123	+	14.8123i	0.532761	+	0.532761i	−0.388632	+	0.921393i	$0.627052\pi$
$774$		0			0
$775$	−8.52465	−	8.52465i	−0.306215	−	0.306215i
$776$		−	9.98352i		−	0.358387i
$777$		0			0
$778$	−41.3436	−	41.3436i	−1.48224	−	1.48224i
$779$	13.6126			0.487721
$780$		0			0
$781$	17.2583			0.617551
$782$	−24.1096	−	24.1096i	−0.862157	−	0.862157i
$783$		0			0
$784$		−	31.7884i		−	1.13530i
$785$	−9.04195	−	9.04195i	−0.322721	−	0.322721i
$786$		0			0
$787$	−1.79401	−	1.79401i	−0.0639496	−	0.0639496i	0.674409	−	0.738358i	$-0.264399\pi$
$787$	−1.79401	−	1.79401i	−0.0639496	−	0.0639496i	−0.738358	+	0.674409i	$0.764399\pi$
$788$	6.28252	−	6.28252i	0.223806	−	0.223806i
$789$		0			0
$790$		−	23.7476i		−	0.844902i
$791$	−1.50583	+	1.50583i	−0.0535411	+	0.0535411i
$792$		0			0
$793$	36.2556	+	15.2856i	1.28747	+	0.542806i
$794$		−	54.3645i		−	1.92933i
$795$		0			0
$796$	−17.3154			−0.613726
$797$	−7.36405			−0.260848			−0.130424	−	0.991458i	$-0.541634\pi$
$797$	−7.36405			−0.260848			−0.130424	+	0.991458i	$0.541634\pi$
$798$		0			0
$799$	−24.5583	+	24.5583i	−0.868811	+	0.868811i
$800$	−16.8873	+	16.8873i	−0.597056	+	0.597056i
$801$		0			0
$802$	39.2514			1.38602
$803$	−25.5872			−0.902954
$804$		0			0
$805$			1.45690i			0.0513490i
$806$	23.9356	+	10.0914i	0.843095	+	0.355454i
$807$		0			0
$808$	7.96169	−	7.96169i	0.280091	−	0.280091i
$809$		−	41.0718i		−	1.44401i	−0.691889	−	0.722004i	$-0.743221\pi$
$809$		−	41.0718i		−	1.44401i	0.691889	−	0.722004i	$-0.256779\pi$
$810$		0			0
$811$	−3.35971	+	3.35971i	−0.117975	+	0.117975i	−0.763630	−	0.645654i	$-0.776585\pi$
$811$	−3.35971	+	3.35971i	−0.117975	+	0.117975i	0.645654	+	0.763630i	$0.276585\pi$
$812$	1.06918	+	1.06918i	0.0375208	+	0.0375208i
$813$		0			0
$814$	16.2841	+	16.2841i	0.570759	+	0.570759i
$815$			35.8601i			1.25612i
$816$		0			0
$817$	34.2212	+	34.2212i	1.19725	+	1.19725i
$818$	56.2833			1.96790
$819$		0			0
$820$	10.0230			0.350018
$821$	−11.0784	−	11.0784i	−0.386640	−	0.386640i	0.486847	−	0.873487i	$-0.338147\pi$
$821$	−11.0784	−	11.0784i	−0.386640	−	0.386640i	−0.873487	+	0.486847i	$0.838147\pi$
$822$		0			0
$823$			31.0471i			1.08223i	0.840947	+	0.541117i	$0.181999\pi$
$823$			31.0471i			1.08223i	−0.840947	+	0.541117i	$0.818001\pi$
$824$	7.59244	+	7.59244i	0.264495	+	0.264495i
$825$		0			0
$826$	−0.205272	−	0.205272i	−0.00714232	−	0.00714232i
$827$	20.9575	−	20.9575i	0.728765	−	0.728765i	−0.241609	−	0.970374i	$-0.577675\pi$
$827$	20.9575	−	20.9575i	0.728765	−	0.728765i	0.970374	+	0.241609i	$0.0776751\pi$
$828$		0			0
$829$		−	53.7940i		−	1.86834i	−0.356823	−	0.934172i	$-0.616140\pi$
$829$		−	53.7940i		−	1.86834i	0.356823	−	0.934172i	$-0.383860\pi$
$830$	−60.6219	+	60.6219i	−2.10422	+	2.10422i
$831$		0			0
$832$	7.23635	−	17.1638i	0.250875	−	0.595048i
$833$			32.7576i			1.13498i
$834$		0			0
$835$	−54.1775			−1.87489
$836$	−22.7149			−0.785610
$837$		0			0
$838$	−24.1195	+	24.1195i	−0.833194	+	0.833194i
$839$	10.4530	−	10.4530i	0.360876	−	0.360876i	−0.503259	−	0.864135i	$-0.667866\pi$
$839$	10.4530	−	10.4530i	0.360876	−	0.360876i	0.864135	+	0.503259i	$0.167866\pi$
$840$		0			0
$841$	−16.6937			−0.575645
$842$	9.78210			0.337114
$843$		0			0
$844$		−	3.96600i		−	0.136515i
$845$	−0.468670	+	37.2350i	−0.0161227	+	1.28092i
$846$		0			0
$847$	−0.625871	+	0.625871i	−0.0215052	+	0.0215052i
$848$		−	20.1918i		−	0.693388i
$849$		0			0
$850$	20.3665	−	20.3665i	0.698564	−	0.698564i
$851$	15.3832	+	15.3832i	0.527330	+	0.527330i
$852$		0			0
$853$	14.9996	+	14.9996i	0.513576	+	0.513576i	0.915620	−	0.402044i	$-0.131700\pi$
$853$	14.9996	+	14.9996i	0.513576	+	0.513576i	−0.402044	+	0.915620i	$0.631700\pi$
$854$		−	2.80189i		−	0.0958786i
$855$		0			0
$856$	5.36922	+	5.36922i	0.183516	+	0.183516i
$857$	45.9861			1.57086			0.785428	−	0.618953i	$-0.212443\pi$
$857$	45.9861			1.57086			0.785428	+	0.618953i	$0.212443\pi$
$858$		0			0
$859$	6.37149			0.217393			0.108696	−	0.994075i	$-0.465332\pi$
$859$	6.37149			0.217393			0.108696	+	0.994075i	$0.465332\pi$
$860$	25.1972	+	25.1972i	0.859218	+	0.859218i
$861$		0			0
$862$			1.19141i			0.0405797i
$863$	−31.1988	−	31.1988i	−1.06202	−	1.06202i	−0.997945	−	0.0640756i	$-0.979590\pi$
$863$	−31.1988	−	31.1988i	−1.06202	−	1.06202i	−0.0640756	−	0.997945i	$-0.520410\pi$
$864$		0			0
$865$	−31.3997	−	31.3997i	−1.06762	−	1.06762i
$866$	10.5214	−	10.5214i	0.357531	−	0.357531i
$867$		0			0
$868$		−	0.841360i		−	0.0285576i
$869$	−6.41788	+	6.41788i	−0.217712	+	0.217712i
$870$		0			0
$871$	19.1916	−	7.80830i	0.650283	−	0.264574i
$872$			3.20214i			0.108438i
$873$		0			0
$874$	−47.1770			−1.59579
$875$	0.689193			0.0232990
$876$		0			0
$877$	4.71190	−	4.71190i	0.159110	−	0.159110i	−0.623062	−	0.782172i	$-0.714112\pi$
$877$	4.71190	−	4.71190i	0.159110	−	0.159110i	0.782172	+	0.623062i	$0.214112\pi$
$878$	9.47411	−	9.47411i	0.319736	−	0.319736i
$879$		0			0
$880$	27.3472			0.921875
$881$	−1.54054			−0.0519020			−0.0259510	−	0.999663i	$-0.508261\pi$
$881$	−1.54054			−0.0519020			−0.0259510	+	0.999663i	$0.508261\pi$
$882$		0			0
$883$		−	5.61774i		−	0.189052i	−0.995522	−	0.0945260i	$-0.969866\pi$
$883$		−	5.61774i		−	0.189052i	0.995522	−	0.0945260i	$-0.0301335\pi$
$884$	−10.9661	+	26.0103i	−0.368829	+	0.874820i
$885$		0			0
$886$	−33.7267	+	33.7267i	−1.13307	+	1.13307i
$887$		−	10.3838i		−	0.348653i	−0.984688	−	0.174326i	$-0.944225\pi$
$887$		−	10.3838i		−	0.348653i	0.984688	−	0.174326i	$-0.0557748\pi$
$888$		0			0
$889$	−0.272971	+	0.272971i	−0.00915514	+	0.00915514i
$890$	−17.8393	−	17.8393i	−0.597975	−	0.597975i
$891$		0			0
$892$	−3.05841	−	3.05841i	−0.102403	−	0.102403i
$893$			48.0551i			1.60810i
$894$		0			0
$895$	−5.60954	−	5.60954i	−0.187506	−	0.187506i
$896$	0.671230			0.0224242
$897$		0			0
$898$	4.16147			0.138870
$899$	17.9787	+	17.9787i	0.599623	+	0.599623i
$900$		0			0
$901$			20.8074i			0.693195i
$902$	−5.95535	−	5.95535i	−0.198292	−	0.198292i
$903$		0			0
$904$	7.12894	+	7.12894i	0.237105	+	0.237105i
$905$	22.3711	−	22.3711i	0.743641	−	0.743641i
$906$		0			0
$907$			4.54380i			0.150875i	0.997151	+	0.0754373i	$0.0240353\pi$
$907$			4.54380i			0.150875i	−0.997151	+	0.0754373i	$0.975965\pi$
$908$	−2.77973	+	2.77973i	−0.0922486	+	0.0922486i
$909$		0			0
$910$	2.45625	−	0.999350i	0.0814239	−	0.0331281i
$911$		−	41.6008i		−	1.37830i	−0.724621	−	0.689148i	$-0.757985\pi$
$911$		−	41.6008i		−	1.37830i	0.724621	−	0.689148i	$-0.242015\pi$
$912$		0			0
$913$	32.7666			1.08442
$914$	13.9099			0.460099
$915$		0			0
$916$	10.3618	−	10.3618i	0.342362	−	0.342362i
$917$	1.70837	−	1.70837i	0.0564154	−	0.0564154i
$918$		0			0
$919$	−45.8945			−1.51392			−0.756960	−	0.653462i	$-0.773316\pi$
$919$	−45.8945			−1.51392			−0.756960	+	0.653462i	$0.773316\pi$
$920$	6.89731			0.227397
$921$		0			0
$922$		−	4.24582i		−	0.139828i
$923$	−11.1833	−	27.4867i	−0.368101	−	0.904737i
$924$		0			0
$925$	−12.9949	+	12.9949i	−0.427270	+	0.427270i
$926$			67.8294i			2.22901i
$927$		0			0
$928$	35.6157	−	35.6157i	1.16914	−	1.16914i
$929$	35.3235	+	35.3235i	1.15893	+	1.15893i	0.984707	+	0.174218i	$0.0557398\pi$
$929$	35.3235	+	35.3235i	1.15893	+	1.15893i	0.174218	+	0.984707i	$0.444260\pi$
$930$		0			0
$931$	32.0496	+	32.0496i	1.05038	+	1.05038i
$932$			15.5874i			0.510584i
$933$		0			0
$934$	13.3110	+	13.3110i	0.435548	+	0.435548i
$935$	−28.1810			−0.921618
$936$		0			0
$937$	13.8756			0.453298			0.226649	−	0.973977i	$-0.427223\pi$
$937$	13.8756			0.453298			0.226649	+	0.973977i	$0.427223\pi$
$938$	−1.04330	−	1.04330i	−0.0340649	−	0.0340649i
$939$		0			0
$940$			35.3832i			1.15407i
$941$	15.7013	+	15.7013i	0.511849	+	0.511849i	0.915093	−	0.403244i	$-0.132117\pi$
$941$	15.7013	+	15.7013i	0.511849	+	0.511849i	−0.403244	+	0.915093i	$0.632117\pi$
$942$		0			0
$943$	−5.62587	−	5.62587i	−0.183204	−	0.183204i
$944$	−3.63995	+	3.63995i	−0.118470	+	0.118470i
$945$		0			0
$946$		−	29.9428i		−	0.973525i
$947$	2.20242	−	2.20242i	0.0715691	−	0.0715691i	−0.670416	−	0.741985i	$-0.733884\pi$
$947$	2.20242	−	2.20242i	0.0715691	−	0.0715691i	0.741985	+	0.670416i	$0.233884\pi$
$948$		0			0
$949$	16.5803	+	40.7519i	0.538220	+	1.32286i
$950$		−	39.8526i		−	1.29299i
$951$		0			0
$952$	−0.399128			−0.0129358
$953$	39.5636			1.28159			0.640796	−	0.767711i	$-0.278604\pi$
$953$	39.5636			1.28159			0.640796	+	0.767711i	$0.278604\pi$
$954$		0			0
$955$	43.4622	−	43.4622i	1.40640	−	1.40640i
$956$	−3.50279	+	3.50279i	−0.113288	+	0.113288i
$957$		0			0
$958$	66.7007			2.15500
$959$	−2.58959			−0.0836223
$960$		0			0
$961$			16.8522i			0.543618i
$962$	15.3832	−	36.4872i	0.495975	−	1.17639i
$963$		0			0
$964$	−25.2166	+	25.2166i	−0.812173	+	0.812173i
$965$		−	32.1022i		−	1.03341i
$966$		0			0
$967$	12.3885	−	12.3885i	0.398387	−	0.398387i	−0.479277	−	0.877664i	$-0.659101\pi$
$967$	12.3885	−	12.3885i	0.398387	−	0.398387i	0.877664	+	0.479277i	$0.159101\pi$
$968$	2.96302	+	2.96302i	0.0952350	+	0.0952350i
$969$		0			0
$970$	61.0309	+	61.0309i	1.95958	+	1.95958i
$971$			22.7133i			0.728905i	0.931222	+	0.364452i	$0.118744\pi$
$971$			22.7133i			0.728905i	−0.931222	+	0.364452i	$0.881256\pi$
$972$		0			0
$973$	−1.11097	−	1.11097i	−0.0356162	−	0.0356162i
$974$	31.7792			1.01827
$975$		0			0
$976$	−49.6840			−1.59034
$977$	−15.5894	−	15.5894i	−0.498748	−	0.498748i	0.412300	−	0.911048i	$-0.364726\pi$
$977$	−15.5894	−	15.5894i	−0.498748	−	0.498748i	−0.911048	+	0.412300i	$0.864726\pi$
$978$		0			0
$979$			9.64228i			0.308169i
$980$	23.5983	+	23.5983i	0.753819	+	0.753819i
$981$		0			0
$982$	1.38785	+	1.38785i	0.0442882	+	0.0442882i
$983$	31.8104	−	31.8104i	1.01459	−	1.01459i	0.0147009	−	0.999892i	$-0.495320\pi$
$983$	31.8104	−	31.8104i	1.01459	−	1.01459i	0.999892	−	0.0147009i	$-0.00467960\pi$
$984$		0			0
$985$		−	15.2518i		−	0.485963i
$986$	−42.9534	+	42.9534i	−1.36791	+	1.36791i
$987$		0			0
$988$	14.7190	+	36.1772i	0.468275	+	1.15095i
$989$		−	28.2862i		−	0.899450i
$990$		0			0
$991$	−22.7905			−0.723964			−0.361982	−	0.932185i	$-0.617900\pi$
$991$	−22.7905			−0.723964			−0.361982	+	0.932185i	$0.617900\pi$
$992$	−28.0268			−0.889852
$993$		0			0
$994$	−1.49424	+	1.49424i	−0.0473944	+	0.0473944i
$995$	−21.0179	+	21.0179i	−0.666312	+	0.666312i
$996$		0			0
$997$	−58.2891			−1.84603			−0.923017	−	0.384758i	$-0.874285\pi$
$997$	−58.2891			−1.84603			−0.923017	+	0.384758i	$0.874285\pi$
$998$	−13.4085			−0.424438
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.i.b.161.7	yes	16
3.2	odd	2	inner	351.2.i.b.161.2	✓	16
13.8	odd	4	inner	351.2.i.b.242.2	yes	16
39.8	even	4	inner	351.2.i.b.242.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
351.2.i.b.161.2	✓	16	3.2	odd	2	inner
351.2.i.b.161.7	yes	16	1.1	even	1	trivial
351.2.i.b.242.2	yes	16	13.8	odd	4	inner
351.2.i.b.242.7	yes	16	39.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35438 + 1.35438i) q^{2} +1.66867i q^{4} +(2.02548 + 2.02548i) q^{5} +(0.0947876 + 0.0947876i) q^{7} +(0.448746 - 0.448746i) q^{8} +5.48652i q^{10} +(1.48275 - 1.48275i) q^{11} +(-3.32235 - 1.40072i) q^{13} +0.256756i q^{14} +4.55288 q^{16} -4.69170 q^{17} +(-4.59030 + 4.59030i) q^{19} +(-3.37986 + 3.37986i) q^{20} +4.01641 q^{22} +3.79420 q^{23} +3.20514i q^{25} +(-2.60260 - 6.39681i) q^{26} +(-0.158169 + 0.158169i) q^{28} -6.75971i q^{29} +(-2.65968 + 2.65968i) q^{31} +(5.26882 + 5.26882i) q^{32} +(-6.35432 - 6.35432i) q^{34} +0.383981i q^{35} +(4.05440 + 4.05440i) q^{37} -12.4340 q^{38} +1.81785 q^{40} +(-1.48275 - 1.48275i) q^{41} -7.45512i q^{43} +(2.47423 + 2.47423i) q^{44} +(5.13878 + 5.13878i) q^{46} +(5.23442 - 5.23442i) q^{47} -6.98203i q^{49} +(-4.34096 + 4.34096i) q^{50} +(2.33734 - 5.54390i) q^{52} -4.43494i q^{53} +6.00658 q^{55} +0.0850712 q^{56} +(9.15519 - 9.15519i) q^{58} +(-0.799482 + 0.799482i) q^{59} -10.9126 q^{61} -7.20443 q^{62} +5.16617i q^{64} +(-3.89221 - 9.56648i) q^{65} +(-4.06338 + 4.06338i) q^{67} -7.82889i q^{68} +(-0.520054 + 0.520054i) q^{70} +(5.81968 + 5.81968i) q^{71} +(-8.62828 - 8.62828i) q^{73} +10.9824i q^{74} +(-7.65968 - 7.65968i) q^{76} +0.281093 q^{77} -4.32835 q^{79} +(9.22177 + 9.22177i) q^{80} -4.01641i q^{82} +(11.0492 + 11.0492i) q^{83} +(-9.50294 - 9.50294i) q^{85} +(10.0970 - 10.0970i) q^{86} -1.33076i q^{88} +(-3.25148 + 3.25148i) q^{89} +(-0.182146 - 0.447688i) q^{91} +6.33127i q^{92} +14.1788 q^{94} -18.5951 q^{95} +(11.1238 - 11.1238i) q^{97} +(9.45630 - 9.45630i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} + 16 q^{13} - 8 q^{16} - 32 q^{19} + 8 q^{22} + 40 q^{28} + 16 q^{31} + 24 q^{34} - 32 q^{37} - 72 q^{40} + 48 q^{46} + 48 q^{52} + 32 q^{55} + 56 q^{58} - 64 q^{61} - 32 q^{67} - 40 q^{70}+ \cdots + 64 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 + 16 * q^13 - 8 * q^16 - 32 * q^19 + 8 * q^22 + 40 * q^28 + 16 * q^31 + 24 * q^34 - 32 * q^37 - 72 * q^40 + 48 * q^46 + 48 * q^52 + 32 * q^55 + 56 * q^58 - 64 * q^61 - 32 * q^67 - 40 * q^70 - 56 * q^73 - 64 * q^76 - 16 * q^79 - 104 * q^91 - 64 * q^94 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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