LMFDB - Embedded newform 351.2.h.a.334.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(289,351)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("351.289"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			334.5
Character	$\chi$	$=$	351.334
Dual form			351.2.h.a.289.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.697564 q^{2} -1.51340 q^{4} +(-1.44568 + 2.50399i) q^{5} +(1.58641 - 2.74774i) q^{7} +2.45082 q^{8} +(1.00846 - 1.74670i) q^{10} -2.31294 q^{11} +(-3.15329 + 1.74835i) q^{13} +(-1.10662 + 1.91673i) q^{14} +1.31720 q^{16} +(-2.69365 - 4.66554i) q^{17} +(-2.58760 - 4.48186i) q^{19} +(2.18790 - 3.78956i) q^{20} +1.61342 q^{22} +(-3.27079 - 5.66518i) q^{23} +(-1.67999 - 2.90983i) q^{25} +(2.19962 - 1.21959i) q^{26} +(-2.40088 + 4.15845i) q^{28} -4.02068 q^{29} +(4.23854 - 7.34137i) q^{31} -5.82048 q^{32} +(1.87899 + 3.25451i) q^{34} +(4.58689 + 7.94473i) q^{35} +(-2.42323 + 4.19715i) q^{37} +(1.80502 + 3.12638i) q^{38} +(-3.54311 + 6.13685i) q^{40} +(1.25716 + 2.17746i) q^{41} +(-2.99320 + 5.18437i) q^{43} +3.50041 q^{44} +(2.28159 + 3.95182i) q^{46} +(-0.521283 - 0.902888i) q^{47} +(-1.53340 - 2.65593i) q^{49} +(1.17190 + 2.02979i) q^{50} +(4.77221 - 2.64597i) q^{52} +1.29495 q^{53} +(3.34377 - 5.79158i) q^{55} +(3.88801 - 6.73424i) q^{56} +2.80468 q^{58} +4.70451 q^{59} +(-3.71841 + 6.44047i) q^{61} +(-2.95665 + 5.12107i) q^{62} +1.42575 q^{64} +(0.180794 - 10.4234i) q^{65} +(-4.18368 - 7.24635i) q^{67} +(4.07658 + 7.06085i) q^{68} +(-3.19965 - 5.54196i) q^{70} +(0.680710 + 1.17903i) q^{71} +1.41722 q^{73} +(1.69036 - 2.92778i) q^{74} +(3.91609 + 6.78287i) q^{76} +(-3.66927 + 6.35536i) q^{77} +(-0.0365793 - 0.0633573i) q^{79} +(-1.90426 + 3.29827i) q^{80} +(-0.876947 - 1.51892i) q^{82} +(1.08808 + 1.88462i) q^{83} +15.5766 q^{85} +(2.08795 - 3.61643i) q^{86} -5.66860 q^{88} +(0.0891486 - 0.154410i) q^{89} +(-0.198393 + 11.4381i) q^{91} +(4.95003 + 8.57371i) q^{92} +(0.363628 + 0.629822i) q^{94} +14.9634 q^{95} +(-0.0654501 + 0.113363i) q^{97} +(1.06965 + 1.85268i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} + 18 q^{4} + 2 q^{5} + 3 q^{7} + 18 q^{8} - 6 q^{11} - 2 q^{14} + 6 q^{16} - 6 q^{17} - 3 q^{19} + 11 q^{20} - 18 q^{22} - 17 q^{23} - 6 q^{25} + 12 q^{26} + 24 q^{29} - 6 q^{31} + 38 q^{32}+ \cdots + 61 q^{98}+O(q^{100}) $ 24 * q + 2 * q^2 + 18 * q^4 + 2 * q^5 + 3 * q^7 + 18 * q^8 - 6 * q^11 - 2 * q^14 + 6 * q^16 - 6 * q^17 - 3 * q^19 + 11 * q^20 - 18 * q^22 - 17 * q^23 - 6 * q^25 + 12 * q^26 + 24 * q^29 - 6 * q^31 + 38 * q^32 - 18 * q^35 - 3 * q^37 - 8 * q^38 - 12 * q^40 - 5 * q^41 - 3 * q^43 - 44 * q^44 - 6 * q^46 - 21 * q^47 + 3 * q^49 + 20 * q^50 - 24 * q^52 + 20 * q^53 + 3 * q^55 - 40 * q^56 + 18 * q^58 - 38 * q^59 - 6 * q^61 - 19 * q^62 - 42 * q^64 + 2 * q^65 - 6 * q^67 + 27 * q^70 - 14 * q^71 + 6 * q^73 - 29 * q^74 - 15 * q^76 - 4 * q^77 + 3 * q^79 + 16 * q^80 - 9 * q^82 + 33 * q^83 - 72 * q^86 - 78 * q^88 + q^89 - 6 * q^91 + 10 * q^92 - 9 * q^94 + 100 * q^95 + 24 * q^97 + 61 * q^98

Character values

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

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.697564			−0.493252			−0.246626	−	0.969111i	$-0.579322\pi$
$2$	−0.697564			−0.493252			−0.246626	+	0.969111i	$0.579322\pi$
$3$		0			0
$3$		0			0
$4$	−1.51340			−0.756702
$5$	−1.44568	+	2.50399i	−0.646529	+	1.11982i	0.337417	+	0.941355i	$0.390447\pi$
$5$	−1.44568	+	2.50399i	−0.646529	+	1.11982i	−0.983946	+	0.178465i	$0.942887\pi$
$6$		0			0
$7$	1.58641	−	2.74774i	0.599607	−	1.03855i	−0.393272	−	0.919422i	$-0.628657\pi$
$7$	1.58641	−	2.74774i	0.599607	−	1.03855i	0.992879	−	0.119128i	$-0.0380098\pi$
$8$	2.45082			0.866497
$9$		0			0
$10$	1.00846	−	1.74670i	0.318902	−	0.552354i
$11$	−2.31294			−0.697377			−0.348688	−	0.937239i	$-0.613373\pi$
$11$	−2.31294			−0.697377			−0.348688	+	0.937239i	$0.613373\pi$
$12$		0			0
$13$	−3.15329	+	1.74835i	−0.874566	+	0.484906i
$13$	−3.15329	+	1.74835i	−0.874566	+	0.484906i
$14$	−1.10662	+	1.91673i	−0.295757	+	0.512267i
$15$		0			0
$16$	1.31720			0.329301
$17$	−2.69365	−	4.66554i	−0.653306	−	1.13156i	−0.982316	−	0.187232i	$-0.940048\pi$
$17$	−2.69365	−	4.66554i	−0.653306	−	1.13156i	0.329010	−	0.944326i	$-0.393285\pi$
$18$		0			0
$19$	−2.58760	−	4.48186i	−0.593636	−	1.02821i	−0.993738	−	0.111738i	$-0.964358\pi$
$19$	−2.58760	−	4.48186i	−0.593636	−	1.02821i	0.400101	−	0.916471i	$-0.368975\pi$
$20$	2.18790	−	3.78956i	0.489230	−	0.847371i
$21$		0			0
$22$	1.61342			0.343982
$23$	−3.27079	−	5.66518i	−0.682007	−	1.18127i	−0.974367	−	0.224963i	$-0.927774\pi$
$23$	−3.27079	−	5.66518i	−0.682007	−	1.18127i	0.292360	−	0.956308i	$-0.405559\pi$
$24$		0			0
$25$	−1.67999	−	2.90983i	−0.335999	−	0.581967i
$26$	2.19962	−	1.21959i	0.431382	−	0.239181i
$27$		0			0
$28$	−2.40088	+	4.15845i	−0.453724	+	0.785873i
$29$	−4.02068			−0.746621			−0.373311	−	0.927706i	$-0.621777\pi$
$29$	−4.02068			−0.746621			−0.373311	+	0.927706i	$0.621777\pi$
$30$		0			0
$31$	4.23854	−	7.34137i	0.761264	−	1.31855i	−0.180935	−	0.983495i	$-0.557912\pi$
$31$	4.23854	−	7.34137i	0.761264	−	1.31855i	0.942199	−	0.335053i	$-0.108754\pi$
$32$	−5.82048			−1.02893
$33$		0			0
$34$	1.87899	+	3.25451i	0.322244	+	0.558144i
$35$	4.58689	+	7.94473i	0.775326	+	1.34290i
$36$		0			0
$37$	−2.42323	+	4.19715i	−0.398376	+	0.690008i	−0.993526	−	0.113607i	$-0.963759\pi$
$37$	−2.42323	+	4.19715i	−0.398376	+	0.690008i	0.595150	+	0.803615i	$0.297093\pi$
$38$	1.80502	+	3.12638i	0.292812	+	0.507166i
$39$		0			0
$40$	−3.54311	+	6.13685i	−0.560215	+	0.970321i
$41$	1.25716	+	2.17746i	0.196335	+	0.340062i	0.947337	−	0.320237i	$-0.103763\pi$
$41$	1.25716	+	2.17746i	0.196335	+	0.340062i	−0.751002	+	0.660299i	$0.770429\pi$
$42$		0			0
$43$	−2.99320	+	5.18437i	−0.456458	+	0.790609i	−0.998771	−	0.0495679i	$-0.984216\pi$
$43$	−2.99320	+	5.18437i	−0.456458	+	0.790609i	0.542312	+	0.840177i	$0.317549\pi$
$44$	3.50041			0.527707
$45$		0			0
$46$	2.28159	+	3.95182i	0.336401	+	0.582664i
$47$	−0.521283	−	0.902888i	−0.0760369	−	0.131700i	0.825500	−	0.564402i	$-0.190893\pi$
$47$	−0.521283	−	0.902888i	−0.0760369	−	0.131700i	−0.901537	+	0.432703i	$0.857560\pi$
$48$		0			0
$49$	−1.53340	−	2.65593i	−0.219057	−	0.379418i
$50$	1.17190	+	2.02979i	0.165732	+	0.287056i
$51$		0			0
$52$	4.77221	−	2.64597i	0.661787	−	0.366929i
$53$	1.29495			0.177875			0.0889376	−	0.996037i	$-0.471653\pi$
$53$	1.29495			0.177875			0.0889376	+	0.996037i	$0.471653\pi$
$54$		0			0
$55$	3.34377	−	5.79158i	0.450874	−	0.780937i
$56$	3.88801	−	6.73424i	0.519558	−	0.899900i
$57$		0			0
$58$	2.80468			0.368272
$59$	4.70451			0.612475			0.306238	−	0.951955i	$-0.400930\pi$
$59$	4.70451			0.612475			0.306238	+	0.951955i	$0.400930\pi$
$60$		0			0
$61$	−3.71841	+	6.44047i	−0.476094	+	0.824618i	−0.999625	−	0.0273883i	$-0.991281\pi$
$61$	−3.71841	+	6.44047i	−0.476094	+	0.824618i	0.523531	+	0.852006i	$0.324614\pi$
$62$	−2.95665	+	5.12107i	−0.375495	+	0.650377i
$63$		0			0
$64$	1.42575			0.178218
$65$	0.180794	−	10.4234i	0.0224247	−	1.29286i
$66$		0			0
$67$	−4.18368	−	7.24635i	−0.511118	−	0.885283i	−0.999917	−	0.0128861i	$-0.995898\pi$
$67$	−4.18368	−	7.24635i	−0.511118	−	0.885283i	0.488799	−	0.872397i	$-0.337435\pi$
$68$	4.07658	+	7.06085i	0.494358	+	0.856253i
$69$		0			0
$70$	−3.19965	−	5.54196i	−0.382431	−	0.662390i
$71$	0.680710	+	1.17903i	0.0807855	+	0.139925i	0.903588	−	0.428403i	$-0.140924\pi$
$71$	0.680710	+	1.17903i	0.0807855	+	0.139925i	−0.822802	+	0.568328i	$0.807590\pi$
$72$		0			0
$73$	1.41722			0.165873			0.0829365	−	0.996555i	$-0.473570\pi$
$73$	1.41722			0.165873			0.0829365	+	0.996555i	$0.473570\pi$
$74$	1.69036	−	2.92778i	0.196500	−	0.340348i
$75$		0			0
$76$	3.91609	+	6.78287i	0.449206	+	0.778048i
$77$	−3.66927	+	6.35536i	−0.418152	+	0.724261i
$78$		0			0
$79$	−0.0365793	−	0.0633573i	−0.00411550	−	0.00712825i	0.863960	−	0.503560i	$-0.167977\pi$
$79$	−0.0365793	−	0.0633573i	−0.00411550	−	0.00712825i	−0.868076	+	0.496432i	$0.834643\pi$
$80$	−1.90426	+	3.29827i	−0.212903	+	0.368758i
$81$		0			0
$82$	−0.876947	−	1.51892i	−0.0968426	−	0.167736i
$83$	1.08808	+	1.88462i	0.119433	+	0.206863i	0.919543	−	0.392989i	$-0.128559\pi$
$83$	1.08808	+	1.88462i	0.119433	+	0.206863i	−0.800110	+	0.599853i	$0.795226\pi$
$84$		0			0
$85$	15.5766			1.68952
$86$	2.08795	−	3.61643i	0.225149	−	0.389969i
$87$		0			0
$88$	−5.66860			−0.604275
$89$	0.0891486	−	0.154410i	0.00944973	−	0.0163674i	−0.861262	−	0.508161i	$-0.830325\pi$
$89$	0.0891486	−	0.154410i	0.00944973	−	0.0163674i	0.870712	+	0.491794i	$0.163659\pi$
$90$		0			0
$91$	−0.198393	+	11.4381i	−0.0207973	+	1.19903i
$92$	4.95003	+	8.57371i	0.516077	+	0.893871i
$93$		0			0
$94$	0.363628	+	0.629822i	0.0375053	+	0.0649612i
$95$	14.9634			1.53521
$96$		0			0
$97$	−0.0654501	+	0.113363i	−0.00664545	+	0.0115103i	−0.869329	−	0.494234i	$-0.835449\pi$
$97$	−0.0654501	+	0.113363i	−0.00664545	+	0.0115103i	0.862684	+	0.505744i	$0.168782\pi$
$98$	1.06965	+	1.85268i	0.108050	+	0.187149i
$99$		0			0
$100$	2.54251	+	4.40376i	0.254251	+	0.440376i
$101$	−8.73990			−0.869652			−0.434826	−	0.900514i	$-0.643190\pi$
$101$	−8.73990			−0.869652			−0.434826	+	0.900514i	$0.643190\pi$
$102$		0			0
$103$	−8.78259	+	15.2119i	−0.865375	+	1.49887i	0.00130026	+	0.999999i	$0.499586\pi$
$103$	−8.78259	+	15.2119i	−0.865375	+	1.49887i	−0.866675	+	0.498874i	$0.833747\pi$
$104$	−7.72817	+	4.28490i	−0.757809	+	0.420169i
$105$		0			0
$106$	−0.903310			−0.0877373
$107$	6.23288	−	10.7957i	0.602555	−	1.04366i	−0.389877	−	0.920867i	$-0.627483\pi$
$107$	6.23288	−	10.7957i	0.602555	−	1.04366i	0.992433	−	0.122790i	$-0.0391841\pi$
$108$		0			0
$109$	4.84430			0.463999			0.232000	−	0.972716i	$-0.425473\pi$
$109$	4.84430			0.463999			0.232000	+	0.972716i	$0.425473\pi$
$110$	−2.33249	+	4.04000i	−0.222395	+	0.385199i
$111$		0			0
$112$	2.08963	−	3.61934i	0.197451	−	0.341996i
$113$	−6.14716			−0.578276			−0.289138	−	0.957287i	$-0.593369\pi$
$113$	−6.14716			−0.578276			−0.289138	+	0.957287i	$0.593369\pi$
$114$		0			0
$115$	18.9141			1.76375
$116$	6.08491			0.564970
$117$		0			0
$118$	−3.28170			−0.302105
$119$	−17.0929			−1.56691
$120$		0			0
$121$	−5.65032			−0.513666
$122$	2.59383	−	4.49264i	0.234834	−	0.406745i
$123$		0			0
$124$	−6.41463	+	11.1105i	−0.576051	+	0.997749i
$125$	−4.74187			−0.424126
$126$		0			0
$127$	−2.10206	+	3.64088i	−0.186528	+	0.323076i	−0.944090	−	0.329687i	$-0.893057\pi$
$127$	−2.10206	+	3.64088i	−0.186528	+	0.323076i	0.757562	+	0.652763i	$0.226390\pi$
$128$	10.6464			0.941019
$129$		0			0
$130$	−0.126115	+	7.27098i	−0.0110610	+	0.637707i
$131$	−0.309051	+	0.535292i	−0.0270019	+	0.0467687i	−0.879211	−	0.476433i	$-0.841929\pi$
$131$	−0.309051	+	0.535292i	−0.0270019	+	0.0467687i	0.852209	+	0.523202i	$0.175263\pi$
$132$		0			0
$133$	−16.4200			−1.42379
$134$	2.91838	+	5.05479i	0.252110	+	0.436667i
$135$		0			0
$136$	−6.60166	−	11.4344i	−0.566087	−	0.980492i
$137$	9.47775	−	16.4159i	0.809739	−	1.40251i	−0.103306	−	0.994650i	$-0.532942\pi$
$137$	9.47775	−	16.4159i	0.809739	−	1.40251i	0.913045	−	0.407859i	$-0.133724\pi$
$138$		0			0
$139$	−3.02245			−0.256361			−0.128180	−	0.991751i	$-0.540914\pi$
$139$	−3.02245			−0.256361			−0.128180	+	0.991751i	$0.540914\pi$
$140$	−6.94183	−	12.0236i	−0.586691	−	1.01618i
$141$		0			0
$142$	−0.474839	−	0.822445i	−0.0398476	−	0.0690181i
$143$	7.29337	−	4.04383i	0.609902	−	0.338162i
$144$		0			0
$145$	5.81262	−	10.0678i	0.482712	−	0.836082i
$146$	−0.988601			−0.0818172
$147$		0			0
$148$	3.66732	−	6.35199i	0.301452	−	0.522131i
$149$	5.73426			0.469769			0.234884	−	0.972023i	$-0.424529\pi$
$149$	5.73426			0.469769			0.234884	+	0.972023i	$0.424529\pi$
$150$		0			0
$151$	−1.05976	−	1.83556i	−0.0862420	−	0.149376i	0.819678	−	0.572825i	$-0.194153\pi$
$151$	−1.05976	−	1.83556i	−0.0862420	−	0.149376i	−0.905920	+	0.423449i	$0.860819\pi$
$152$	−6.34175	−	10.9842i	−0.514384	−	0.890940i
$153$		0			0
$154$	2.55955	−	4.43327i	0.206254	−	0.357243i
$155$	12.2552	+	21.2266i	0.984358	+	1.70496i
$156$		0			0
$157$	7.70204	−	13.3403i	0.614690	−	1.06467i	−0.375749	−	0.926721i	$-0.622615\pi$
$157$	7.70204	−	13.3403i	0.614690	−	1.06467i	0.990439	−	0.137952i	$-0.0440520\pi$
$158$	0.0255164	+	0.0441957i	0.00202998	+	0.00351602i
$159$		0			0
$160$	8.41457	−	14.5745i	0.665230	−	1.15221i
$161$	−20.7553			−1.63575
$162$		0			0
$163$	−6.56126	−	11.3644i	−0.513918	−	0.890131i	−0.999870	−	0.0161459i	$-0.994860\pi$
$163$	−6.56126	−	11.3644i	−0.513918	−	0.890131i	0.485952	−	0.873985i	$-0.338473\pi$
$164$	−1.90259	−	3.29538i	−0.148567	−	0.257326i
$165$		0			0
$166$	−0.759007	−	1.31464i	−0.0589104	−	0.102036i
$167$	−2.90872	−	5.03805i	−0.225084	−	0.389856i	0.731261	−	0.682098i	$-0.238932\pi$
$167$	−2.90872	−	5.03805i	−0.225084	−	0.389856i	−0.956345	+	0.292242i	$0.905599\pi$
$168$		0			0
$169$	6.88652	−	11.0261i	0.529733	−	0.848165i
$170$	−10.8657			−0.833361
$171$		0			0
$172$	4.52992	−	7.84605i	0.345403	−	0.598256i
$173$	−9.04187	+	15.6610i	−0.687441	+	1.19068i	0.285222	+	0.958461i	$0.407933\pi$
$173$	−9.04187	+	15.6610i	−0.687441	+	1.19068i	−0.972663	+	0.232221i	$0.925401\pi$
$174$		0			0
$175$	−10.6606			−0.805869
$176$	−3.04661			−0.229647
$177$		0			0
$178$	−0.0621868	+	0.107711i	−0.00466110	+	0.00807326i
$179$	−10.9345	+	18.9391i	−0.817283	+	1.41558i	0.0903935	+	0.995906i	$0.471188\pi$
$179$	−10.9345	+	18.9391i	−0.817283	+	1.41558i	−0.907677	+	0.419670i	$0.862146\pi$
$180$		0			0
$181$	−10.9883			−0.816754			−0.408377	−	0.912813i	$-0.633905\pi$
$181$	−10.9883			−0.816754			−0.408377	+	0.912813i	$0.633905\pi$
$182$	0.138392	−	7.97877i	0.0102583	−	0.591426i
$183$		0			0
$184$	−8.01613	−	13.8843i	−0.590957	−	1.02357i
$185$	−7.00643	−	12.1355i	−0.515123	−	0.892220i
$186$		0			0
$187$	6.23024	+	10.7911i	0.455600	+	0.789123i
$188$	0.788912	+	1.36644i	0.0575373	+	0.0996575i
$189$		0			0
$190$	−10.4379			−0.757246
$191$	−8.99172	+	15.5741i	−0.650618	+	1.12690i	0.332355	+	0.943154i	$0.392157\pi$
$191$	−8.99172	+	15.5741i	−0.650618	+	1.12690i	−0.982973	+	0.183749i	$0.941177\pi$
$192$		0			0
$193$	−1.90083	−	3.29234i	−0.136825	−	0.236988i	0.789468	−	0.613792i	$-0.210356\pi$
$193$	−1.90083	−	3.29234i	−0.136825	−	0.236988i	−0.926293	+	0.376804i	$0.877023\pi$
$194$	0.0456556	−	0.0790778i	0.00327788	−	0.00567745i
$195$		0			0
$196$	2.32066	+	4.01950i	0.165761	+	0.287107i
$197$	12.3633	−	21.4139i	0.880848	−	1.52567i	0.0304487	−	0.999536i	$-0.490306\pi$
$197$	12.3633	−	21.4139i	0.880848	−	1.52567i	0.850399	−	0.526138i	$-0.176360\pi$
$198$		0			0
$199$	13.8440	+	23.9785i	0.981376	+	1.69979i	0.657047	+	0.753849i	$0.271805\pi$
$199$	13.8440	+	23.9785i	0.981376	+	1.69979i	0.324329	+	0.945944i	$0.394862\pi$
$200$	−4.11737	−	7.13149i	−0.291142	−	0.504273i
$201$		0			0
$202$	6.09664			0.428958
$203$	−6.37845	+	11.0478i	−0.447679	+	0.775403i
$204$		0			0
$205$	−7.26980			−0.507745
$206$	6.12642	−	10.6113i	0.426848	−	0.739322i
$207$		0			0
$208$	−4.15353	+	2.30294i	−0.287996	+	0.159680i
$209$	5.98496	+	10.3663i	0.413988	+	0.717049i
$210$		0			0
$211$	1.89606	+	3.28407i	0.130530	+	0.226085i	0.923881	−	0.382680i	$-0.124999\pi$
$211$	1.89606	+	3.28407i	0.130530	+	0.226085i	−0.793351	+	0.608764i	$0.791665\pi$
$212$	−1.95978			−0.134599
$213$		0			0
$214$	−4.34783	+	7.53066i	−0.297212	+	0.514786i
$215$	−8.65442	−	14.9899i	−0.590227	−	1.02230i
$216$		0			0
$217$	−13.4481	−	23.2929i	−0.912919	−	1.58122i
$218$	−3.37921			−0.228869
$219$		0			0
$220$	−5.06048	+	8.76501i	−0.341178	+	0.590937i
$221$	16.6509	+	10.0024i	1.12006	+	0.672831i
$222$		0			0
$223$	1.11066			0.0743751			0.0371876	−	0.999308i	$-0.488160\pi$
$223$	1.11066			0.0743751			0.0371876	+	0.999308i	$0.488160\pi$
$224$	−9.23368	+	15.9932i	−0.616951	+	1.06859i
$225$		0			0
$226$	4.28803			0.285236
$227$	−4.17223	+	7.22651i	−0.276921	+	0.479641i	−0.970618	−	0.240626i	$-0.922647\pi$
$227$	−4.17223	+	7.22651i	−0.276921	+	0.479641i	0.693697	+	0.720267i	$0.255981\pi$
$228$		0			0
$229$	−3.79878	+	6.57968i	−0.251030	+	0.434797i	−0.963810	−	0.266591i	$-0.914103\pi$
$229$	−3.79878	+	6.57968i	−0.251030	+	0.434797i	0.712779	+	0.701388i	$0.247436\pi$
$230$	−13.1938			−0.869973
$231$		0			0
$232$	−9.85397			−0.646945
$233$	−0.767797			−0.0503001			−0.0251500	−	0.999684i	$-0.508006\pi$
$233$	−0.767797			−0.0503001			−0.0251500	+	0.999684i	$0.508006\pi$
$234$		0			0
$235$	3.01444			0.196640
$236$	−7.11983			−0.463462
$237$		0			0
$238$	11.9234			0.772880
$239$	10.6216	−	18.3972i	0.687055	−	1.19001i	−0.285732	−	0.958310i	$-0.592237\pi$
$239$	10.6216	−	18.3972i	0.687055	−	1.19001i	0.972786	−	0.231704i	$-0.0744300\pi$
$240$		0			0
$241$	11.4305	−	19.7983i	0.736306	−	1.27532i	−0.217842	−	0.975984i	$-0.569902\pi$
$241$	11.4305	−	19.7983i	0.736306	−	1.27532i	0.954148	−	0.299335i	$-0.0967648\pi$
$242$	3.94146			0.253367
$243$		0			0
$244$	5.62746	−	9.74704i	0.360261	−	0.623991i
$245$	8.86725			0.566508
$246$		0			0
$247$	15.9953	+	9.60857i	1.01776	+	0.611379i
$248$	10.3879	−	17.9924i	0.659633	−	1.14252i
$249$		0			0
$250$	3.30776			0.209201
$251$	−8.21662	−	14.2316i	−0.518629	−	0.898291i	−0.999766	−	0.0216457i	$-0.993109\pi$
$251$	−8.21662	−	14.2316i	−0.518629	−	0.898291i	0.481137	−	0.876645i	$-0.340224\pi$
$252$		0			0
$253$	7.56513	+	13.1032i	0.475616	+	0.823791i
$254$	1.46632	−	2.53975i	0.0920053	−	0.159358i
$255$		0			0
$256$	−10.2780			−0.642378
$257$	−1.82657	−	3.16372i	−0.113938	−	0.197347i	0.803416	−	0.595417i	$-0.203013\pi$
$257$	−1.82657	−	3.16372i	−0.113938	−	0.197347i	−0.917355	+	0.398070i	$0.869680\pi$
$258$		0			0
$259$	7.68847	+	13.3168i	0.477738	+	0.827467i
$260$	−0.273615	+	15.7748i	−0.0169689	+	0.978313i
$261$		0			0
$262$	0.215583	−	0.373400i	0.0133187	−	0.0230688i
$263$	24.8898			1.53477			0.767384	−	0.641188i	$-0.221558\pi$
$263$	24.8898			1.53477			0.767384	+	0.641188i	$0.221558\pi$
$264$		0			0
$265$	−1.87209	+	3.24255i	−0.115001	+	0.199188i
$266$	11.4540			0.702290
$267$		0			0
$268$	6.33161	+	10.9667i	0.386764	+	0.669896i
$269$	4.43529	+	7.68215i	0.270424	+	0.468389i	0.968971	−	0.247176i	$-0.0795027\pi$
$269$	4.43529	+	7.68215i	0.270424	+	0.468389i	−0.698546	+	0.715565i	$0.746169\pi$
$270$		0			0
$271$	−5.20415	+	9.01385i	−0.316129	+	0.547552i	−0.979677	−	0.200582i	$-0.935717\pi$
$271$	−5.20415	+	9.01385i	−0.316129	+	0.547552i	0.663548	+	0.748134i	$0.269050\pi$
$272$	−3.54809	−	6.14547i	−0.215134	−	0.372624i
$273$		0			0
$274$	−6.61133	+	11.4512i	−0.399405	+	0.691790i
$275$	3.88572	+	6.73026i	0.234318	+	0.405850i
$276$		0			0
$277$	12.4312	−	21.5315i	0.746918	−	1.29370i	−0.202375	−	0.979308i	$-0.564866\pi$
$277$	12.4312	−	21.5315i	0.746918	−	1.29370i	0.949293	−	0.314392i	$-0.101801\pi$
$278$	2.10835			0.126450
$279$		0			0
$280$	11.2417	+	19.4711i	0.671818	+	1.16362i
$281$	5.46747	+	9.46994i	0.326162	+	0.564929i	0.981747	−	0.190192i	$-0.0609112\pi$
$281$	5.46747	+	9.46994i	0.326162	+	0.564929i	−0.655585	+	0.755122i	$0.727578\pi$
$282$		0			0
$283$	−14.8192	−	25.6676i	−0.880909	−	1.52578i	−0.850331	−	0.526248i	$-0.823599\pi$
$283$	−14.8192	−	25.6676i	−0.880909	−	1.52578i	−0.0305780	−	0.999532i	$-0.509735\pi$
$284$	−1.03019	−	1.78434i	−0.0611306	−	0.105881i
$285$		0			0
$286$	−5.08759	+	2.82083i	−0.300835	+	0.166799i
$287$	7.97747			0.470895
$288$		0			0
$289$	−6.01149	+	10.4122i	−0.353617	+	0.612482i
$290$	−4.05467	+	7.02290i	−0.238099	+	0.412399i
$291$		0			0
$292$	−2.14483			−0.125517
$293$	15.2763			0.892449			0.446225	−	0.894921i	$-0.352768\pi$
$293$	15.2763			0.892449			0.446225	+	0.894921i	$0.352768\pi$
$294$		0			0
$295$	−6.80123	+	11.7801i	−0.395983	+	0.685863i
$296$	−5.93890	+	10.2865i	−0.345192	+	0.597890i
$297$		0			0
$298$	−4.00001			−0.231714
$299$	20.2185	+	12.1455i	1.16927	+	0.702391i
$300$		0			0
$301$	9.49688	+	16.4491i	0.547391	+	0.948110i
$302$	0.739250	+	1.28042i	0.0425391	+	0.0736798i
$303$		0			0
$304$	−3.40840	−	5.90352i	−0.195485	−	0.338590i
$305$	−10.7513	−	18.6218i	−0.615616	−	1.06628i
$306$		0			0
$307$	−2.96530			−0.169238			−0.0846192	−	0.996413i	$-0.526967\pi$
$307$	−2.96530			−0.169238			−0.0846192	+	0.996413i	$0.526967\pi$
$308$	5.55309	−	9.61823i	0.316417	−	0.548050i
$309$		0			0
$310$	−8.54876	−	14.8069i	−0.485537	−	0.840974i
$311$	−0.483334	+	0.837159i	−0.0274073	+	0.0474709i	−0.879404	−	0.476077i	$-0.842058\pi$
$311$	−0.483334	+	0.837159i	−0.0274073	+	0.0474709i	0.851996	+	0.523548i	$0.175392\pi$
$312$		0			0
$313$	−1.56622	−	2.71277i	−0.0885279	−	0.153335i	0.818361	−	0.574704i	$-0.194883\pi$
$313$	−1.56622	−	2.71277i	−0.0885279	−	0.153335i	−0.906889	+	0.421369i	$0.861550\pi$
$314$	−5.37266	+	9.30572i	−0.303197	+	0.525152i
$315$		0			0
$316$	0.0553594	+	0.0958852i	0.00311421	+	0.00539397i
$317$	−14.5827	−	25.2580i	−0.819046	−	1.41863i	−0.906386	−	0.422451i	$-0.861170\pi$
$317$	−14.5827	−	25.2580i	−0.819046	−	1.41863i	0.0873393	−	0.996179i	$-0.472164\pi$
$318$		0			0
$319$	9.29957			0.520676
$320$	−2.06118	+	3.57006i	−0.115223	+	0.199573i
$321$		0			0
$322$	14.4781			0.806835
$323$	−13.9402	+	24.1451i	−0.775652	+	1.34347i
$324$		0			0
$325$	10.3849	+	6.23834i	0.576052	+	0.346041i
$326$	4.57690	+	7.92742i	0.253491	+	0.439059i
$327$		0			0
$328$	3.08107	+	5.33657i	0.170124	+	0.294663i
$329$	−3.30787			−0.182369
$330$		0			0
$331$	−3.57725	+	6.19598i	−0.196624	+	0.340562i	−0.947432	−	0.319959i	$-0.896331\pi$
$331$	−3.57725	+	6.19598i	−0.196624	+	0.340562i	0.750808	+	0.660520i	$0.229664\pi$
$332$	−1.64671	−	2.85219i	−0.0903750	−	0.156534i
$333$		0			0
$334$	2.02902	+	3.51436i	0.111023	+	0.192297i
$335$	24.1931			1.32181
$336$		0			0
$337$	−7.36818	+	12.7621i	−0.401370	+	0.695194i	−0.993892	−	0.110361i	$-0.964799\pi$
$337$	−7.36818	+	12.7621i	−0.401370	+	0.695194i	0.592521	+	0.805555i	$0.298133\pi$
$338$	−4.80379	+	7.69143i	−0.261292	+	0.418359i
$339$		0			0
$340$	−23.5738			−1.27847
$341$	−9.80348	+	16.9801i	−0.530888	+	0.919525i
$342$		0			0
$343$	12.4793			0.673821
$344$	−7.33580	+	12.7060i	−0.395520	+	0.685060i
$345$		0			0
$346$	6.30728	−	10.9245i	0.339081	−	0.587306i
$347$	19.9131			1.06899			0.534496	−	0.845171i	$-0.320502\pi$
$347$	19.9131			1.06899			0.534496	+	0.845171i	$0.320502\pi$
$348$		0			0
$349$	−27.7690			−1.48644			−0.743221	−	0.669046i	$-0.766703\pi$
$349$	−27.7690			−1.48644			−0.743221	+	0.669046i	$0.766703\pi$
$350$	7.43648			0.397496
$351$		0			0
$352$	13.4624			0.717549
$353$	−28.5705			−1.52065			−0.760326	−	0.649542i	$-0.774961\pi$
$353$	−28.5705			−1.52065			−0.760326	+	0.649542i	$0.774961\pi$
$354$		0			0
$355$	−3.93636			−0.208920
$356$	−0.134918	+	0.233685i	−0.00715064	+	0.0123853i
$357$		0			0
$358$	7.62751	−	13.2112i	0.403127	−	0.698236i
$359$	15.4518			0.815515			0.407757	−	0.913090i	$-0.366311\pi$
$359$	15.4518			0.815515			0.407757	+	0.913090i	$0.366311\pi$
$360$		0			0
$361$	−3.89136	+	6.74004i	−0.204809	+	0.354739i
$362$	7.66504			0.402866
$363$		0			0
$364$	0.300249	−	17.3104i	0.0157373	−	0.907312i
$365$	−2.04885	+	3.54871i	−0.107242	+	0.185748i
$366$		0			0
$367$	0.471182			0.0245955			0.0122977	−	0.999924i	$-0.496085\pi$
$367$	0.471182			0.0245955			0.0122977	+	0.999924i	$0.496085\pi$
$368$	−4.30830	−	7.46220i	−0.224586	−	0.388994i
$369$		0			0
$370$	4.88743	+	8.46528i	0.254086	+	0.440089i
$371$	2.05432	−	3.55819i	0.106655	−	0.184732i
$372$		0			0
$373$	32.3488			1.67496			0.837478	−	0.546472i	$-0.184029\pi$
$373$	32.3488			1.67496			0.837478	+	0.546472i	$0.184029\pi$
$374$	−4.34599	−	7.52747i	−0.224726	−	0.389236i
$375$		0			0
$376$	−1.27757	−	2.21282i	−0.0658857	−	0.114117i
$377$	12.6784	−	7.02956i	0.652970	−	0.362041i
$378$		0			0
$379$	0.713364	−	1.23558i	0.0366430	−	0.0634676i	−0.847122	−	0.531398i	$-0.821667\pi$
$379$	0.713364	−	1.23558i	0.0366430	−	0.0634676i	0.883765	+	0.467930i	$0.155000\pi$
$380$	−22.6457			−1.16170
$381$		0			0
$382$	6.27229	−	10.8639i	0.320919	−	0.555847i
$383$	15.9444			0.814719			0.407360	−	0.913268i	$-0.366450\pi$
$383$	15.9444			0.814719			0.407360	+	0.913268i	$0.366450\pi$
$384$		0			0
$385$	−10.6092	−	18.3757i	−0.540695	−	0.936510i
$386$	1.32595	+	2.29662i	0.0674892	+	0.116895i
$387$		0			0
$388$	0.0990524	−	0.171564i	0.00502863	−	0.00870984i
$389$	−10.0545	−	17.4150i	−0.509785	−	0.882973i	−0.999936	−	0.0113357i	$-0.996392\pi$
$389$	−10.0545	−	17.4150i	−0.509785	−	0.882973i	0.490151	−	0.871638i	$-0.336942\pi$
$390$		0			0
$391$	−17.6207	+	30.5200i	−0.891119	+	1.54346i
$392$	−3.75810	−	6.50921i	−0.189813	−	0.328765i
$393$		0			0
$394$	−8.62418	+	14.9375i	−0.434480	+	0.752542i
$395$	0.211528			0.0106431
$396$		0			0
$397$	1.77422	+	3.07304i	0.0890454	+	0.154231i	0.907108	−	0.420898i	$-0.138285\pi$
$397$	1.77422	+	3.07304i	0.0890454	+	0.154231i	−0.818062	+	0.575129i	$0.804952\pi$
$398$	−9.65708	−	16.7266i	−0.484066	−	0.838427i
$399$		0			0
$400$	−2.21290	−	3.83285i	−0.110645	−	0.191642i
$401$	13.3212	+	23.0730i	0.665229	+	1.15221i	0.979223	+	0.202785i	$0.0649994\pi$
$401$	13.3212	+	23.0730i	0.665229	+	1.15221i	−0.313994	+	0.949425i	$0.601667\pi$
$402$		0			0
$403$	−0.530063	+	30.5600i	−0.0264043	+	1.52230i
$404$	13.2270			0.658068
$405$		0			0
$406$	4.44937	−	7.70654i	0.220819	−	0.382469i
$407$	5.60477	−	9.70775i	0.277818	−	0.481195i
$408$		0			0
$409$	−13.5215			−0.668597			−0.334299	−	0.942467i	$-0.608499\pi$
$409$	−13.5215			−0.668597			−0.334299	+	0.942467i	$0.608499\pi$
$410$	5.07115			0.250446
$411$		0			0
$412$	13.2916	−	23.0218i	0.654831	−	1.13420i
$413$	7.46329	−	12.9268i	0.367245	−	0.636086i
$414$		0			0
$415$	−6.29209			−0.308866
$416$	18.3537	−	10.1763i	0.899864	−	0.498932i
$417$		0			0
$418$	−4.17489	−	7.23112i	−0.204201	−	0.353686i
$419$	−6.30293	−	10.9170i	−0.307918	−	0.533330i	0.669988	−	0.742372i	$-0.266299\pi$
$419$	−6.30293	−	10.9170i	−0.307918	−	0.533330i	−0.977907	+	0.209041i	$0.932966\pi$
$420$		0			0
$421$	4.49703	+	7.78908i	0.219172	+	0.379617i	0.954555	−	0.298035i	$-0.0963312\pi$
$421$	4.49703	+	7.78908i	0.219172	+	0.379617i	−0.735383	+	0.677651i	$0.762998\pi$
$422$	−1.32262	−	2.29085i	−0.0643842	−	0.111517i
$423$		0			0
$424$	3.17370			0.154128
$425$	−9.05063	+	15.6761i	−0.439020	+	0.760405i
$426$		0			0
$427$	11.7979	+	20.4345i	0.570938	+	0.988894i
$428$	−9.43287	+	16.3382i	−0.455955	+	0.789737i
$429$		0			0
$430$	6.03701	+	10.4564i	0.291131	+	0.504253i
$431$	8.05558	−	13.9527i	0.388024	−	0.672077i	−0.604160	−	0.796863i	$-0.706491\pi$
$431$	8.05558	−	13.9527i	0.388024	−	0.672077i	0.992184	+	0.124786i	$0.0398245\pi$
$432$		0			0
$433$	−13.5252	−	23.4264i	−0.649981	−	1.12580i	−0.983127	−	0.182924i	$-0.941444\pi$
$433$	−13.5252	−	23.4264i	−0.649981	−	1.12580i	0.333146	−	0.942875i	$-0.391890\pi$
$434$	9.38093	+	16.2482i	0.450299	+	0.779941i
$435$		0			0
$436$	−7.33138			−0.351110
$437$	−16.9270	+	29.3184i	−0.809729	+	1.40249i
$438$		0			0
$439$	2.30329			0.109930			0.0549651	−	0.998488i	$-0.482495\pi$
$439$	2.30329			0.109930			0.0549651	+	0.998488i	$0.482495\pi$
$440$	8.19499	−	14.1941i	0.390681	−	0.676679i
$441$		0			0
$442$	−11.6150	−	6.97728i	−0.552471	−	0.331875i
$443$	−13.1481	−	22.7731i	−0.624683	−	1.08198i	−0.988602	−	0.150552i	$-0.951895\pi$
$443$	−13.1481	−	22.7731i	−0.624683	−	1.08198i	0.363919	−	0.931431i	$-0.381439\pi$
$444$		0			0
$445$	0.257761	+	0.446455i	0.0122190	+	0.0211640i
$446$	−0.774754			−0.0366857
$447$		0			0
$448$	2.26182	−	3.91759i	0.106861	−	0.185089i
$449$	4.46646	+	7.73613i	0.210785	+	0.365091i	0.951960	−	0.306221i	$-0.0990646\pi$
$449$	4.46646	+	7.73613i	0.210785	+	0.365091i	−0.741175	+	0.671311i	$0.765731\pi$
$450$		0			0
$451$	−2.90772	−	5.03633i	−0.136919	−	0.237151i
$452$	9.30314			0.437583
$453$		0			0
$454$	2.91040	−	5.04095i	0.136592	−	0.236584i
$455$	−28.3540	−	17.0326i	−1.32926	−	0.798499i
$456$		0			0
$457$	18.8815			0.883239			0.441620	−	0.897202i	$-0.354404\pi$
$457$	18.8815			0.883239			0.441620	+	0.897202i	$0.354404\pi$
$458$	2.64989	−	4.58974i	0.123821	−	0.214465i
$459$		0			0
$460$	−28.6247			−1.33463
$461$	−11.6128	+	20.1139i	−0.540860	+	0.936797i	0.457995	+	0.888955i	$0.348568\pi$
$461$	−11.6128	+	20.1139i	−0.540860	+	0.936797i	−0.998855	+	0.0478419i	$0.984766\pi$
$462$		0			0
$463$	1.15005	−	1.99194i	0.0534473	−	0.0925735i	−0.838064	−	0.545572i	$-0.816312\pi$
$463$	1.15005	−	1.99194i	0.0534473	−	0.0925735i	0.891511	+	0.452999i	$0.149646\pi$
$464$	−5.29606			−0.245863
$465$		0			0
$466$	0.535587			0.0248106
$467$	22.4713			1.03985			0.519925	−	0.854212i	$-0.325960\pi$
$467$	22.4713			1.03985			0.519925	+	0.854212i	$0.325960\pi$
$468$		0			0
$469$	−26.5482			−1.22588
$470$	−2.10276			−0.0969931
$471$		0			0
$472$	11.5299			0.530708
$473$	6.92308	−	11.9911i	0.318323	−	0.551352i
$474$		0			0
$475$	−8.69431	+	15.0590i	−0.398922	+	0.690954i
$476$	25.8685			1.18568
$477$		0			0
$478$	−7.40925	+	12.8332i	−0.338891	+	0.586976i
$479$	4.87209			0.222611			0.111306	−	0.993786i	$-0.464497\pi$
$479$	4.87209			0.222611			0.111306	+	0.993786i	$0.464497\pi$
$480$		0			0
$481$	0.303044	−	17.4715i	0.0138176	−	0.796632i
$482$	−7.97353	+	13.8106i	−0.363184	+	0.629054i
$483$		0			0
$484$	8.55123			0.388692
$485$	−0.189240	−	0.327773i	−0.00859294	−	0.0148834i
$486$		0			0
$487$	−6.17126	−	10.6889i	−0.279647	−	0.484362i	0.691650	−	0.722233i	$-0.256884\pi$
$487$	−6.17126	−	10.6889i	−0.279647	−	0.484362i	−0.971297	+	0.237870i	$0.923551\pi$
$488$	−9.11316	+	15.7845i	−0.412534	+	0.714529i
$489$		0			0
$490$	−6.18547			−0.279431
$491$	−14.0792	−	24.3859i	−0.635386	−	1.10052i	−0.986433	−	0.164164i	$-0.947507\pi$
$491$	−14.0792	−	24.3859i	−0.635386	−	1.10052i	0.351047	−	0.936358i	$-0.385826\pi$
$492$		0			0
$493$	10.8303	+	18.7586i	0.487772	+	0.844846i
$494$	−11.1578	−	6.70259i	−0.502012	−	0.301564i
$495$		0			0
$496$	5.58303	−	9.67008i	0.250685	−	0.434200i
$497$	4.31955			0.193758
$498$		0			0
$499$	12.0417	−	20.8568i	0.539061	−	0.933681i	−0.459894	−	0.887974i	$-0.652113\pi$
$499$	12.0417	−	20.8568i	0.539061	−	0.933681i	0.998955	−	0.0457069i	$-0.0145540\pi$
$500$	7.17637			0.320937
$501$		0			0
$502$	5.73162	+	9.92745i	0.255815	+	0.443084i
$503$	1.66703	+	2.88738i	0.0743291	+	0.128742i	0.900794	−	0.434246i	$-0.142985\pi$
$503$	1.66703	+	2.88738i	0.0743291	+	0.128742i	−0.826465	+	0.562988i	$0.809652\pi$
$504$		0			0
$505$	12.6351	−	21.8847i	0.562255	−	0.973855i
$506$	−5.27716	−	9.14031i	−0.234598	−	0.406336i
$507$		0			0
$508$	3.18127	−	5.51013i	0.141146	−	0.244472i
$509$	17.0658	+	29.5589i	0.756429	+	1.31017i	0.944661	+	0.328048i	$0.106391\pi$
$509$	17.0658	+	29.5589i	0.756429	+	1.31017i	−0.188232	+	0.982125i	$0.560276\pi$
$510$		0			0
$511$	2.24829	−	3.89416i	0.0994587	−	0.172267i
$512$	−14.1232			−0.624165
$513$		0			0
$514$	1.27415	+	2.20689i	0.0562004	+	0.0973419i
$515$	−25.3937	−	43.9831i	−1.11898	−	1.93813i
$516$		0			0
$517$	1.20569	+	2.08832i	0.0530264	+	0.0918443i
$518$	−5.36320	−	9.28933i	−0.235645	−	0.408150i
$519$		0			0
$520$	0.443094	−	25.5459i	0.0194310	−	1.12026i
$521$	−42.5774			−1.86535			−0.932675	−	0.360719i	$-0.882531\pi$
$521$	−42.5774			−1.86535			−0.932675	+	0.360719i	$0.882531\pi$
$522$		0			0
$523$	−1.45092	+	2.51307i	−0.0634443	+	0.109889i	−0.896003	−	0.444048i	$-0.853542\pi$
$523$	−1.45092	+	2.51307i	−0.0634443	+	0.109889i	0.832559	+	0.553937i	$0.186875\pi$
$524$	0.467719	−	0.810114i	0.0204324	−	0.0353900i
$525$		0			0
$526$	−17.3622			−0.757027
$527$	−45.6686			−1.98935
$528$		0			0
$529$	−9.89616	+	17.1406i	−0.430268	+	0.745245i
$530$	1.30590	−	2.26188i	0.0567247	−	0.0982500i
$531$		0			0
$532$	24.8501			1.07739
$533$	−7.77115	−	4.66822i	−0.336606	−	0.202203i
$534$		0			0
$535$	18.0215	+	31.2142i	0.779139	+	1.34951i
$536$	−10.2535	−	17.7595i	−0.442882	−	0.767095i
$537$		0			0
$538$	−3.09390	−	5.35879i	−0.133387	−	0.231034i
$539$	3.54666	+	6.14300i	0.152765	+	0.264598i
$540$		0			0
$541$	22.6048			0.971857			0.485929	−	0.873999i	$-0.338482\pi$
$541$	22.6048			0.971857			0.485929	+	0.873999i	$0.338482\pi$
$542$	3.63022	−	6.28773i	0.155931	−	0.270081i
$543$		0			0
$544$	15.6783	+	27.1557i	0.672203	+	1.16429i
$545$	−7.00331	+	12.1301i	−0.299989	+	0.519596i
$546$		0			0
$547$	−18.1136	−	31.3737i	−0.774481	−	1.34144i	−0.935085	−	0.354422i	$-0.884678\pi$
$547$	−18.1136	−	31.3737i	−0.774481	−	1.34144i	0.160604	−	0.987019i	$-0.448656\pi$
$548$	−14.3437	+	24.8440i	−0.612731	+	1.06128i
$549$		0			0
$550$	−2.71054	−	4.69479i	−0.115578	−	0.200186i
$551$	10.4039	+	18.0201i	0.443222	+	0.767682i
$552$		0			0
$553$	−0.232120			−0.00987073
$554$	−8.67155	+	15.0196i	−0.368419	+	0.638120i
$555$		0			0
$556$	4.57419			0.193989
$557$	−1.08919	+	1.88653i	−0.0461503	+	0.0799347i	−0.888178	−	0.459500i	$-0.848029\pi$
$557$	−1.08919	+	1.88653i	−0.0461503	+	0.0799347i	0.842027	+	0.539435i	$0.181362\pi$
$558$		0			0
$559$	0.374323	−	21.5810i	0.0158322	−	0.912779i
$560$	6.04188	+	10.4648i	0.255316	+	0.442220i
$561$		0			0
$562$	−3.81391	−	6.60588i	−0.160880	−	0.278652i
$563$	−7.65705			−0.322706			−0.161353	−	0.986897i	$-0.551586\pi$
$563$	−7.65705			−0.322706			−0.161353	+	0.986897i	$0.551586\pi$
$564$		0			0
$565$	8.88684	−	15.3925i	0.373872	−	0.647565i
$566$	10.3373	+	17.9048i	0.434510	+	0.752594i
$567$		0			0
$568$	1.66830	+	2.88958i	0.0700004	+	0.121244i
$569$	26.5940			1.11488			0.557440	−	0.830217i	$-0.311784\pi$
$569$	26.5940			1.11488			0.557440	+	0.830217i	$0.311784\pi$
$570$		0			0
$571$	21.6621	−	37.5199i	0.906531	−	1.57016i	0.0876825	−	0.996148i	$-0.472054\pi$
$571$	21.6621	−	37.5199i	0.906531	−	1.57016i	0.818849	−	0.574010i	$-0.194613\pi$
$572$	−11.0378	+	6.11995i	−0.461515	+	0.255888i
$573$		0			0
$574$	−5.56479			−0.232270
$575$	−10.9898	+	19.0349i	−0.458307	+	0.793811i
$576$		0			0
$577$	−24.5681			−1.02278			−0.511392	−	0.859348i	$-0.670870\pi$
$577$	−24.5681			−1.02278			−0.511392	+	0.859348i	$0.670870\pi$
$578$	4.19339	−	7.26317i	0.174422	−	0.302108i
$579$		0			0
$580$	−8.79685	+	15.2366i	−0.365269	+	0.632665i
$581$	6.90459			0.286451
$582$		0			0
$583$	−2.99514			−0.124046
$584$	3.47336			0.143729
$585$		0			0
$586$	−10.6562			−0.440202
$587$	13.9587			0.576138			0.288069	−	0.957610i	$-0.406987\pi$
$587$	13.9587			0.576138			0.288069	+	0.957610i	$0.406987\pi$
$588$		0			0
$589$	−43.8706			−1.80766
$590$	4.74429	−	8.21735i	0.195319	−	0.338303i
$591$		0			0
$592$	−3.19189	+	5.52851i	−0.131186	+	0.227220i
$593$	42.3659			1.73976			0.869880	−	0.493263i	$-0.164196\pi$
$593$	42.3659			1.73976			0.869880	+	0.493263i	$0.164196\pi$
$594$		0			0
$595$	24.7110	−	42.8006i	1.01305	−	1.75465i
$596$	−8.67826			−0.355475
$597$		0			0
$598$	−14.1037	−	8.47224i	−0.576743	−	0.346456i
$599$	0.140194	−	0.242822i	0.00572815	−	0.00992145i	−0.863147	−	0.504953i	$-0.831510\pi$
$599$	0.140194	−	0.242822i	0.00572815	−	0.00992145i	0.868875	+	0.495031i	$0.164843\pi$
$600$		0			0
$601$	17.5799			0.717101			0.358550	−	0.933510i	$-0.383271\pi$
$601$	17.5799			0.717101			0.358550	+	0.933510i	$0.383271\pi$
$602$	−6.62468	−	11.4743i	−0.270002	−	0.467657i
$603$		0			0
$604$	1.60385	+	2.77794i	0.0652596	+	0.113033i
$605$	8.16857	−	14.1484i	0.332100	−	0.575214i
$606$		0			0
$607$	−40.1830			−1.63098			−0.815489	−	0.578773i	$-0.803532\pi$
$607$	−40.1830			−1.63098			−0.815489	+	0.578773i	$0.803532\pi$
$608$	15.0611	+	26.0866i	0.610808	+	1.05795i
$609$		0			0
$610$	7.49970	+	12.9899i	0.303654	+	0.525944i
$611$	3.22232	+	1.93569i	0.130361	+	0.0783095i
$612$		0			0
$613$	12.3197	−	21.3384i	0.497589	−	0.861849i	−0.502407	−	0.864631i	$-0.667552\pi$
$613$	12.3197	−	21.3384i	0.497589	−	0.861849i	0.999996	+	0.00278192i	$0.000885515\pi$
$614$	2.06848			0.0834772
$615$		0			0
$616$	−8.99273	+	15.5759i	−0.362327	+	0.627570i
$617$	−36.1037			−1.45348			−0.726739	−	0.686913i	$-0.758965\pi$
$617$	−36.1037			−1.45348			−0.726739	+	0.686913i	$0.758965\pi$
$618$		0			0
$619$	−19.1602	−	33.1865i	−0.770114	−	1.33388i	−0.937500	−	0.347986i	$-0.886866\pi$
$619$	−19.1602	−	33.1865i	−0.770114	−	1.33388i	0.167386	−	0.985892i	$-0.446468\pi$
$620$	−18.5470	−	32.1244i	−0.744867	−	1.29015i
$621$		0			0
$622$	0.337156	−	0.583971i	0.0135187	−	0.0234151i
$623$	−0.282853	−	0.489915i	−0.0113323	−	0.0196280i
$624$		0			0
$625$	15.2552	−	26.4228i	0.610208	−	1.05691i
$626$	1.09254	+	1.89233i	0.0436665	+	0.0756327i
$627$		0			0
$628$	−11.6563	+	20.1893i	−0.465137	+	0.805641i
$629$	26.1093			1.04105
$630$		0			0
$631$	4.85653	+	8.41176i	0.193335	+	0.334867i	0.946354	−	0.323133i	$-0.104736\pi$
$631$	4.85653	+	8.41176i	0.193335	+	0.334867i	−0.753018	+	0.658000i	$0.771403\pi$
$632$	−0.0896495	−	0.155278i	−0.00356607	−	0.00617661i
$633$		0			0
$634$	10.1724	+	17.6191i	0.403996	+	0.699742i
$635$	−6.07783	−	10.5271i	−0.241191	−	0.417756i
$636$		0			0
$637$	9.47877	+	5.69400i	0.375562	+	0.225604i
$638$	−6.48704			−0.256825
$639$		0			0
$640$	−15.3913	+	26.6586i	−0.608396	+	1.05377i
$641$	−14.9792	+	25.9448i	−0.591643	+	1.02476i	0.402368	+	0.915478i	$0.368187\pi$
$641$	−14.9792	+	25.9448i	−0.591643	+	1.02476i	−0.994011	+	0.109278i	$0.965146\pi$
$642$		0			0
$643$	18.5574			0.731834			0.365917	−	0.930647i	$-0.380755\pi$
$643$	18.5574			0.731834			0.365917	+	0.930647i	$0.380755\pi$
$644$	31.4111			1.23777
$645$		0			0
$646$	9.72416	−	16.8427i	0.382592	−	0.662669i
$647$	−17.4909	+	30.2951i	−0.687637	+	1.19102i	0.284963	+	0.958538i	$0.408019\pi$
$647$	−17.4909	+	30.2951i	−0.687637	+	1.19102i	−0.972600	+	0.232484i	$0.925315\pi$
$648$		0			0
$649$	−10.8812			−0.427126
$650$	−7.24415	−	4.35164i	−0.284139	−	0.170685i
$651$		0			0
$652$	9.92984	+	17.1990i	0.388883	+	0.673565i
$653$	−7.84322	−	13.5849i	−0.306929	−	0.531616i	0.670760	−	0.741674i	$-0.265968\pi$
$653$	−7.84322	−	13.5849i	−0.306929	−	0.531616i	−0.977689	+	0.210058i	$0.932635\pi$
$654$		0			0
$655$	−0.893579	−	1.54772i	−0.0349150	−	0.0604746i
$656$	1.65593	+	2.86816i	0.0646533	+	0.111983i
$657$		0			0
$658$	2.30745			0.0899539
$659$	11.1513	−	19.3146i	0.434391	−	0.752388i	−0.562854	−	0.826556i	$-0.690297\pi$
$659$	11.1513	−	19.3146i	0.434391	−	0.752388i	0.997246	+	0.0741680i	$0.0236301\pi$
$660$		0			0
$661$	−8.30249	−	14.3803i	−0.322930	−	0.559330i	0.658162	−	0.752877i	$-0.271334\pi$
$661$	−8.30249	−	14.3803i	−0.322930	−	0.559330i	−0.981091	+	0.193546i	$0.938001\pi$
$662$	2.49536	−	4.32209i	0.0969849	−	0.167983i
$663$		0			0
$664$	2.66670	+	4.61886i	0.103488	+	0.179246i
$665$	23.7381	−	41.1156i	0.920524	−	1.59439i
$666$		0			0
$667$	13.1508	+	22.7779i	0.509201	+	0.881962i
$668$	4.40207	+	7.62462i	0.170321	+	0.295005i
$669$		0			0
$670$	−16.8762			−0.651986
$671$	8.60045	−	14.8964i	0.332017	−	0.575069i
$672$		0			0
$673$	−8.62484			−0.332463			−0.166232	−	0.986087i	$-0.553160\pi$
$673$	−8.62484			−0.332463			−0.166232	+	0.986087i	$0.553160\pi$
$674$	5.13978	−	8.90235i	0.197977	−	0.342906i
$675$		0			0
$676$	−10.4221	+	16.6870i	−0.400850	+	0.641808i
$677$	−11.5236	−	19.9595i	−0.442888	−	0.767105i	0.555014	−	0.831841i	$-0.312713\pi$
$677$	−11.5236	−	19.9595i	−0.442888	−	0.767105i	−0.997902	+	0.0647358i	$0.979380\pi$
$678$		0			0
$679$	0.207661	+	0.359680i	0.00796931	+	0.0138033i
$680$	38.1756			1.46397
$681$		0			0
$682$	6.83855	−	11.8447i	0.261862	−	0.453557i
$683$	13.6294	+	23.6068i	0.521514	+	0.903289i	0.999687	+	0.0250235i	$0.00796605\pi$
$683$	13.6294	+	23.6068i	0.521514	+	0.903289i	−0.478172	+	0.878266i	$0.658701\pi$
$684$		0			0
$685$	27.4036	+	47.4645i	1.04704	+	1.81352i
$686$	−8.70513			−0.332363
$687$		0			0
$688$	−3.94265	+	6.82888i	−0.150312	+	0.260348i
$689$	−4.08336	+	2.26403i	−0.155564	+	0.0862527i
$690$		0			0
$691$	−21.2474			−0.808288			−0.404144	−	0.914695i	$-0.632431\pi$
$691$	−21.2474			−0.808288			−0.404144	+	0.914695i	$0.632431\pi$
$692$	13.6840	−	23.7014i	0.520188	−	0.900992i
$693$		0			0
$694$	−13.8907			−0.527282
$695$	4.36950	−	7.56820i	0.165745	−	0.287078i
$696$		0			0
$697$	6.77268	−	11.7306i	0.256533	−	0.444329i
$698$	19.3707			0.733190
$699$		0			0
$700$	16.1339			0.609803
$701$	−10.1915			−0.384928			−0.192464	−	0.981304i	$-0.561648\pi$
$701$	−10.1915			−0.384928			−0.192464	+	0.981304i	$0.561648\pi$
$702$		0			0
$703$	25.0814			0.945962
$704$	−3.29766			−0.124285
$705$		0			0
$706$	19.9297			0.750065
$707$	−13.8651	+	24.0150i	−0.521450	+	0.903177i
$708$		0			0
$709$	−12.8669	+	22.2861i	−0.483227	+	0.836973i	−0.999814	−	0.0192609i	$-0.993869\pi$
$709$	−12.8669	+	22.2861i	−0.483227	+	0.836973i	0.516588	+	0.856234i	$0.327202\pi$
$710$	2.74586			0.103050
$711$		0			0
$712$	0.218487	−	0.378431i	0.00818816	−	0.0141823i
$713$	−55.4535			−2.07675
$714$		0			0
$715$	−0.418165	+	24.1087i	−0.0156385	+	0.901612i
$716$	16.5483	−	28.6626i	0.618440	−	1.07117i
$717$		0			0
$718$	−10.7786			−0.402254
$719$	8.35595	+	14.4729i	0.311624	+	0.539749i	0.978714	−	0.205228i	$-0.0657936\pi$
$719$	8.35595	+	14.4729i	0.311624	+	0.539749i	−0.667090	+	0.744977i	$0.732460\pi$
$720$		0			0
$721$	27.8656	+	48.2646i	1.03777	+	1.79747i
$722$	2.71447	−	4.70161i	0.101022	−	0.174976i
$723$		0			0
$724$	16.6298			0.618040
$725$	6.75471	+	11.6995i	0.250864	+	0.434509i
$726$		0			0
$727$	−20.7535	−	35.9461i	−0.769705	−	1.33317i	−0.937723	−	0.347384i	$-0.887070\pi$
$727$	−20.7535	−	35.9461i	−0.769705	−	1.33317i	0.168018	−	0.985784i	$-0.446263\pi$
$728$	−0.486227	+	28.0327i	−0.0180208	+	1.03896i
$729$		0			0
$730$	1.42920	−	2.47545i	0.0528972	−	0.0916206i
$731$	32.2505			1.19283
$732$		0			0
$733$	−18.6541	+	32.3098i	−0.689003	+	1.19339i	0.283157	+	0.959073i	$0.408618\pi$
$733$	−18.6541	+	32.3098i	−0.689003	+	1.19339i	−0.972161	+	0.234315i	$0.924715\pi$
$734$	−0.328679			−0.0121318
$735$		0			0
$736$	19.0376	+	32.9741i	0.701735	+	1.21544i
$737$	9.67659	+	16.7604i	0.356442	+	0.617375i
$738$		0			0
$739$	−17.9464	+	31.0841i	−0.660169	+	1.14345i	0.320401	+	0.947282i	$0.396182\pi$
$739$	−17.9464	+	31.0841i	−0.660169	+	1.14345i	−0.980571	+	0.196165i	$0.937151\pi$
$740$	10.6036	+	18.3659i	0.389795	+	0.675145i
$741$		0			0
$742$	−1.43302	+	2.48207i	−0.0526079	+	0.0911195i
$743$	−0.751788	−	1.30214i	−0.0275804	−	0.0477707i	0.851906	−	0.523695i	$-0.175447\pi$
$743$	−0.751788	−	1.30214i	−0.0275804	−	0.0477707i	−0.879486	+	0.475924i	$0.842114\pi$
$744$		0			0
$745$	−8.28992	+	14.3586i	−0.303719	+	0.526057i
$746$	−22.5653			−0.826175
$747$		0			0
$748$	−9.42888	−	16.3313i	−0.344754	−	0.597131i
$749$	−19.7758	−	34.2527i	−0.722593	−	1.25157i
$750$		0			0
$751$	−2.10916	−	3.65317i	−0.0769642	−	0.133306i	0.824975	−	0.565170i	$-0.191189\pi$
$751$	−2.10916	−	3.65317i	−0.0769642	−	0.133306i	−0.901939	+	0.431864i	$0.857856\pi$
$752$	−0.686636	−	1.18929i	−0.0250390	−	0.0433689i
$753$		0			0
$754$	−8.84398	+	4.90357i	−0.322079	+	0.178577i
$755$	6.12830			0.223032
$756$		0			0
$757$	−3.70611	+	6.41918i	−0.134701	+	0.233309i	−0.925483	−	0.378789i	$-0.876341\pi$
$757$	−3.70611	+	6.41918i	−0.134701	+	0.233309i	0.790782	+	0.612098i	$0.209674\pi$
$758$	−0.497617	+	0.861898i	−0.0180743	+	0.0313055i
$759$		0			0
$760$	36.6726			1.33026
$761$	−36.5128			−1.32359			−0.661795	−	0.749685i	$-0.730205\pi$
$761$	−36.5128			−1.32359			−0.661795	+	0.749685i	$0.730205\pi$
$762$		0			0
$763$	7.68505	−	13.3109i	0.278217	−	0.481887i
$764$	13.6081	−	23.5699i	0.492324	−	0.852730i
$765$		0			0
$766$	−11.1222			−0.401862
$767$	−14.8347	+	8.22515i	−0.535650	+	0.296993i
$768$		0			0
$769$	−8.00060	−	13.8575i	−0.288509	−	0.499712i	0.684945	−	0.728595i	$-0.259826\pi$
$769$	−8.00060	−	13.8575i	−0.288509	−	0.499712i	−0.973454	+	0.228882i	$0.926493\pi$
$770$	7.40059	+	12.8182i	0.266699	+	0.461936i
$771$		0			0
$772$	2.87673	+	4.98264i	0.103536	+	0.179329i
$773$	−14.3128	−	24.7905i	−0.514796	−	0.891652i	−0.999853	−	0.0171698i	$-0.994534\pi$
$773$	−14.3128	−	24.7905i	−0.514796	−	0.891652i	0.485057	−	0.874483i	$-0.338799\pi$
$774$		0			0
$775$	−28.4829			−1.02314
$776$	−0.160407	+	0.277832i	−0.00575826	+	0.00997360i
$777$		0			0
$778$	7.01367	+	12.1480i	0.251452	+	0.435528i
$779$	6.50604	−	11.2688i	0.233103	−	0.403746i
$780$		0			0
$781$	−1.57444	−	2.72701i	−0.0563379	−	0.0975801i
$782$	12.2916	−	21.2896i	0.439546	−	0.761316i
$783$		0			0
$784$	−2.01980	−	3.49840i	−0.0721358	−	0.124943i
$785$	22.2694	+	38.5717i	0.794829	+	1.37668i
$786$		0			0
$787$	−5.75106			−0.205003			−0.102502	−	0.994733i	$-0.532685\pi$
$787$	−5.75106			−0.205003			−0.102502	+	0.994733i	$0.532685\pi$
$788$	−18.7107	+	32.4078i	−0.666540	+	1.15448i
$789$		0			0
$790$	−0.147555			−0.00524975
$791$	−9.75192	+	16.8908i	−0.346738	+	0.600569i
$792$		0			0
$793$	0.465017	−	26.8098i	0.0165132	−	0.952044i
$794$	−1.23763	−	2.14364i	−0.0439218	−	0.0760748i
$795$		0			0
$796$	−20.9516	−	36.2892i	−0.742610	−	1.28624i
$797$	53.9162			1.90981			0.954905	−	0.296911i	$-0.0959565\pi$
$797$	53.9162			1.90981			0.954905	+	0.296911i	$0.0959565\pi$
$798$		0			0
$799$	−2.80830	+	4.86413i	−0.0993507	+	0.172080i
$800$	9.77837	+	16.9366i	0.345718	+	0.598801i
$801$		0			0
$802$	−9.29238	−	16.0949i	−0.328125	−	0.568330i
$803$	−3.27794			−0.115676
$804$		0			0
$805$	30.0055	−	51.9711i	1.05756	−	1.83174i
$806$	0.369753	−	21.3175i	0.0130240	−	0.750877i
$807$		0			0
$808$	−21.4199			−0.753551
$809$	−2.00874	+	3.47924i	−0.0706235	+	0.122324i	−0.899175	−	0.437590i	$-0.855832\pi$
$809$	−2.00874	+	3.47924i	−0.0706235	+	0.122324i	0.828551	+	0.559913i	$0.189166\pi$
$810$		0			0
$811$	14.2338			0.499815			0.249908	−	0.968270i	$-0.419600\pi$
$811$	14.2338			0.499815			0.249908	+	0.968270i	$0.419600\pi$
$812$	9.65318	−	16.7198i	0.338760	−	0.586750i
$813$		0			0
$814$	−3.90969	+	6.77177i	−0.137034	+	0.237351i
$815$	37.9420			1.32905
$816$		0			0
$817$	30.9808			1.08388
$818$	9.43213			0.329787
$819$		0			0
$820$	11.0021			0.384212
$821$	49.6673			1.73340			0.866701	−	0.498828i	$-0.166236\pi$
$821$	49.6673			1.73340			0.866701	+	0.498828i	$0.166236\pi$
$822$		0			0
$823$	11.9719			0.417313			0.208656	−	0.977989i	$-0.433091\pi$
$823$	11.9719			0.417313			0.208656	+	0.977989i	$0.433091\pi$
$824$	−21.5246	+	37.2817i	−0.749844	+	1.29877i
$825$		0			0
$826$	−5.20612	+	9.01727i	−0.181144	+	0.313751i
$827$	−35.1205			−1.22126			−0.610630	−	0.791916i	$-0.709084\pi$
$827$	−35.1205			−1.22126			−0.610630	+	0.791916i	$0.709084\pi$
$828$		0			0
$829$	−25.4527	+	44.0853i	−0.884008	+	1.53115i	−0.0371606	+	0.999309i	$0.511831\pi$
$829$	−25.4527	+	44.0853i	−0.884008	+	1.53115i	−0.846847	+	0.531837i	$0.821502\pi$
$830$	4.38913			0.152349
$831$		0			0
$832$	−4.49580	+	2.49271i	−0.155864	+	0.0864191i
$833$	−8.26089	+	14.3083i	−0.286223	+	0.495753i
$834$		0			0
$835$	16.8204			0.582092
$836$	−9.05767	−	15.6883i	−0.313266	−	0.542593i
$837$		0			0
$838$	4.39670	+	7.61530i	0.151881	+	0.263066i
$839$	−4.21345	+	7.29790i	−0.145464	+	0.251952i	−0.929546	−	0.368706i	$-0.879801\pi$
$839$	−4.21345	+	7.29790i	−0.145464	+	0.251952i	0.784082	+	0.620658i	$0.213134\pi$
$840$		0			0
$841$	−12.8341			−0.442557
$842$	−3.13696	−	5.43338i	−0.108107	−	0.187247i
$843$		0			0
$844$	−2.86950	−	4.97013i	−0.0987724	−	0.171079i
$845$	17.6537	+	33.1841i	0.607305	+	1.14157i
$846$		0			0
$847$	−8.96374	+	15.5256i	−0.307998	+	0.533468i
$848$	1.70571			0.0585745
$849$		0			0
$850$	6.31339	−	10.9351i	0.216547	−	0.375071i
$851$	31.7035			1.08678
$852$		0			0
$853$	16.9960	+	29.4380i	0.581932	+	1.00794i	0.995250	+	0.0973495i	$0.0310365\pi$
$853$	16.9960	+	29.4380i	0.581932	+	1.00794i	−0.413318	+	0.910587i	$0.635630\pi$
$854$	−8.22975	−	14.2543i	−0.281616	−	0.487774i
$855$		0			0
$856$	15.2757	−	26.4583i	0.522112	−	0.904325i
$857$	−26.4677	−	45.8435i	−0.904121	−	1.56598i	−0.822093	−	0.569353i	$-0.807194\pi$
$857$	−26.4677	−	45.8435i	−0.904121	−	1.56598i	−0.0820272	−	0.996630i	$-0.526139\pi$
$858$		0			0
$859$	2.49176	−	4.31585i	0.0850177	−	0.147255i	−0.820381	−	0.571817i	$-0.806239\pi$
$859$	2.49176	−	4.31585i	0.0850177	−	0.147255i	0.905399	+	0.424562i	$0.139572\pi$
$860$	13.0976	+	22.6858i	0.446626	+	0.773579i
$861$		0			0
$862$	−5.61928	+	9.73288i	−0.191393	+	0.331503i
$863$	−40.1602			−1.36707			−0.683535	−	0.729918i	$-0.739558\pi$
$863$	−40.1602			−1.36707			−0.683535	+	0.729918i	$0.739558\pi$
$864$		0			0
$865$	−26.1433	−	45.2816i	−0.888900	−	1.53962i
$866$	9.43470	+	16.3414i	0.320604	+	0.555303i
$867$		0			0
$868$	20.3525	+	35.2515i	0.690808	+	1.19651i
$869$	0.0846057	+	0.146541i	0.00287005	+	0.00497108i
$870$		0			0
$871$	25.8616	+	15.5353i	0.876285	+	0.526394i
$872$	11.8725			0.402054
$873$		0			0
$874$	11.8077	−	20.4515i	0.399400	−	0.691782i
$875$	−7.52256	+	13.0295i	−0.254309	+	0.440476i
$876$		0			0
$877$	8.10431			0.273663			0.136832	−	0.990594i	$-0.456308\pi$
$877$	8.10431			0.273663			0.136832	+	0.990594i	$0.456308\pi$
$878$	−1.60669			−0.0542233
$879$		0			0
$880$	4.40443	−	7.62870i	0.148473	−	0.257163i
$881$	−8.71424	+	15.0935i	−0.293590	+	0.508513i	−0.974656	−	0.223709i	$-0.928183\pi$
$881$	−8.71424	+	15.0935i	−0.293590	+	0.508513i	0.681066	+	0.732222i	$0.261517\pi$
$882$		0			0
$883$	7.78098			0.261851			0.130925	−	0.991392i	$-0.458205\pi$
$883$	7.78098			0.261851			0.130925	+	0.991392i	$0.458205\pi$
$884$	−25.1995	−	15.1376i	−0.847551	−	0.509133i
$885$		0			0
$886$	9.17161	+	15.8857i	0.308126	+	0.533690i
$887$	15.9757	+	27.6708i	0.536413	+	0.929094i	0.999094	+	0.0425694i	$0.0135544\pi$
$887$	15.9757	+	27.6708i	0.536413	+	0.929094i	−0.462681	+	0.886525i	$0.653112\pi$
$888$		0			0
$889$	6.66948	+	11.5519i	0.223687	+	0.387437i
$890$	−0.179805	−	0.311431i	−0.00602707	−	0.0104392i
$891$		0			0
$892$	−1.68087			−0.0562799
$893$	−2.69774	+	4.67263i	−0.0902765	+	0.156364i
$894$		0			0
$895$	−31.6156	−	54.7599i	−1.05679	−	1.83042i
$896$	16.8896	−	29.2536i	0.564242	−	0.977295i
$897$		0			0
$898$	−3.11564	−	5.39644i	−0.103970	−	0.180082i
$899$	−17.0418	+	29.5173i	−0.568376	+	0.984456i
$900$		0			0
$901$	−3.48814	−	6.04164i	−0.116207	−	0.201276i
$902$	2.02832	+	3.51316i	0.0675358	+	0.116975i
$903$		0			0
$904$	−15.0656			−0.501074
$905$	15.8856	−	27.5147i	0.528055	−	0.914618i
$906$		0			0
$907$	20.5686			0.682969			0.341484	−	0.939887i	$-0.389070\pi$
$907$	20.5686			0.682969			0.341484	+	0.939887i	$0.389070\pi$
$908$	6.31427	−	10.9366i	0.209547	−	0.362945i
$909$		0			0
$910$	19.7787	+	11.8813i	0.655659	+	0.393861i
$911$	18.5114	+	32.0627i	0.613311	+	1.06229i	0.990678	+	0.136222i	$0.0434960\pi$
$911$	18.5114	+	32.0627i	0.613311	+	1.06229i	−0.377368	+	0.926064i	$0.623171\pi$
$912$		0			0
$913$	−2.51667	−	4.35900i	−0.0832895	−	0.144262i
$914$	−13.1710			−0.435659
$915$		0			0
$916$	5.74909	−	9.95772i	0.189955	−	0.329012i
$917$	0.980564	+	1.69839i	0.0323811	+	0.0560857i
$918$		0			0
$919$	9.27825	+	16.0704i	0.306061	+	0.530114i	0.977497	−	0.210949i	$-0.0676554\pi$
$919$	9.27825	+	16.0704i	0.306061	+	0.530114i	−0.671436	+	0.741063i	$0.734322\pi$
$920$	46.3551			1.52828
$921$		0			0
$922$	8.10063	−	14.0307i	0.266780	−	0.462077i
$923$	−4.20783	−	2.52769i	−0.138502	−	0.0831999i
$924$		0			0
$925$	16.2840			0.535416
$926$	−0.802232	+	1.38951i	−0.0263630	+	0.0456620i
$927$		0			0
$928$	23.4023			0.768218
$929$	−24.1312	+	41.7964i	−0.791718	+	1.37130i	0.133185	+	0.991091i	$0.457480\pi$
$929$	−24.1312	+	41.7964i	−0.791718	+	1.37130i	−0.924903	+	0.380204i	$0.875854\pi$
$930$		0			0
$931$	−7.93566	+	13.7450i	−0.260081	+	0.450473i
$932$	1.16199			0.0380622
$933$		0			0
$934$	−15.6752			−0.512908
$935$	−36.0278			−1.17823
$936$		0			0
$937$	37.7556			1.23342			0.616711	−	0.787190i	$-0.288465\pi$
$937$	37.7556			1.23342			0.616711	+	0.787190i	$0.288465\pi$
$938$	18.5190			0.604668
$939$		0			0
$940$	−4.56206			−0.148798
$941$	20.6525	−	35.7713i	0.673254	−	1.16611i	−0.303722	−	0.952761i	$-0.598230\pi$
$941$	20.6525	−	35.7713i	0.673254	−	1.16611i	0.976976	−	0.213349i	$-0.0684371\pi$
$942$		0			0
$943$	8.22380	−	14.2440i	0.267804	−	0.463850i
$944$	6.19681			0.201689
$945$		0			0
$946$	−4.82929	+	8.36457i	−0.157014	+	0.271956i
$947$	1.76757			0.0574382			0.0287191	−	0.999588i	$-0.490857\pi$
$947$	1.76757			0.0574382			0.0287191	+	0.999588i	$0.490857\pi$
$948$		0			0
$949$	−4.46891	+	2.47780i	−0.145067	+	0.0804328i
$950$	6.06483	−	10.5046i	0.196769	−	0.340814i
$951$		0			0
$952$	−41.8918			−1.35772
$953$	−17.6033	−	30.4898i	−0.570228	−	0.987663i	−0.996542	−	0.0830881i	$-0.973522\pi$
$953$	−17.6033	−	30.4898i	−0.570228	−	0.987663i	0.426315	−	0.904575i	$-0.359812\pi$
$954$		0			0
$955$	−25.9983	−	45.0304i	−0.841286	−	1.45715i
$956$	−16.0748	+	27.8424i	−0.519896	+	0.900486i
$957$		0			0
$958$	−3.39859			−0.109804
$959$	−30.0712	−	52.0849i	−0.971050	−	1.68191i
$960$		0			0
$961$	−20.4304	−	35.3866i	−0.659047	−	1.14150i
$962$	−0.211392	+	12.1875i	−0.00681556	+	0.392941i
$963$		0			0
$964$	−17.2990	+	29.9628i	−0.557164	+	0.965037i
$965$	10.9920			0.353845
$966$		0			0
$967$	−26.6427	+	46.1466i	−0.856773	+	1.48397i	0.0182182	+	0.999834i	$0.494201\pi$
$967$	−26.6427	+	46.1466i	−0.856773	+	1.48397i	−0.874991	+	0.484140i	$0.839133\pi$
$968$	−13.8479			−0.445090
$969$		0			0
$970$	0.132007	+	0.228643i	0.00423849	+	0.00734127i
$971$	−24.0513	−	41.6582i	−0.771844	−	1.33687i	−0.936551	−	0.350531i	$-0.886001\pi$
$971$	−24.0513	−	41.6582i	−0.771844	−	1.33687i	0.164707	−	0.986343i	$-0.447332\pi$
$972$		0			0
$973$	−4.79485	+	8.30492i	−0.153716	+	0.266243i
$974$	4.30485	+	7.45622i	0.137936	+	0.238913i
$975$		0			0
$976$	−4.89791	+	8.48342i	−0.156778	+	0.271548i
$977$	−27.8719	−	48.2755i	−0.891700	−	1.54447i	−0.837836	−	0.545922i	$-0.816179\pi$
$977$	−27.8719	−	48.2755i	−0.891700	−	1.54447i	−0.0538646	−	0.998548i	$-0.517154\pi$
$978$		0			0
$979$	−0.206195	+	0.357140i	−0.00659002	+	0.0114143i
$980$	−13.4197			−0.428678
$981$		0			0
$982$	9.82115	+	17.0107i	0.313406	+	0.542834i
$983$	11.9465	+	20.6920i	0.381035	+	0.659973i	0.991211	−	0.132294i	$-0.0422343\pi$
$983$	11.9465	+	20.6920i	0.381035	+	0.659973i	−0.610175	+	0.792267i	$0.708901\pi$
$984$		0			0
$985$	35.7468	+	61.9153i	1.13899	+	1.97278i
$986$	−7.55482	−	13.0853i	−0.240594	−	0.416722i
$987$		0			0
$988$	−24.2074	−	14.5417i	−0.770141	−	0.462632i
$989$	39.1605			1.24523
$990$		0			0
$991$	15.5487	−	26.9312i	0.493922	−	0.855498i	−0.506054	−	0.862502i	$-0.668896\pi$
$991$	15.5487	−	26.9312i	0.493922	−	0.855498i	0.999975	+	0.00700424i	$0.00222954\pi$
$992$	−24.6703	+	42.7303i	−0.783284	+	1.35669i
$993$		0			0
$994$	−3.01316			−0.0955716
$995$	−80.0562			−2.53795
$996$		0			0
$997$	−10.5392	+	18.2545i	−0.333781	+	0.578125i	−0.983250	−	0.182263i	$-0.941658\pi$
$997$	−10.5392	+	18.2545i	−0.333781	+	0.578125i	0.649469	+	0.760388i	$0.274991\pi$
$998$	−8.39986	+	14.5490i	−0.265893	+	0.460540i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.h.a.334.5		24
3.2	odd	2		117.2.h.a.22.8	yes	24
9.2	odd	6		117.2.f.a.61.5	✓	24
9.7	even	3		351.2.f.a.100.8		24
13.3	even	3		351.2.f.a.172.8		24
39.29	odd	6		117.2.f.a.94.5	yes	24
117.16	even	3	inner	351.2.h.a.289.5		24
117.29	odd	6		117.2.h.a.16.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.f.a.61.5	✓	24	9.2	odd	6
117.2.f.a.94.5	yes	24	39.29	odd	6
117.2.h.a.16.8	yes	24	117.29	odd	6
117.2.h.a.22.8	yes	24	3.2	odd	2
351.2.f.a.100.8		24	9.7	even	3
351.2.f.a.172.8		24	13.3	even	3
351.2.h.a.289.5		24	117.16	even	3	inner
351.2.h.a.334.5		24	1.1	even	1	trivial

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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.697564 q^{2} -1.51340 q^{4} +(-1.44568 + 2.50399i) q^{5} +(1.58641 - 2.74774i) q^{7} +2.45082 q^{8} +(1.00846 - 1.74670i) q^{10} -2.31294 q^{11} +(-3.15329 + 1.74835i) q^{13} +(-1.10662 + 1.91673i) q^{14} +1.31720 q^{16} +(-2.69365 - 4.66554i) q^{17} +(-2.58760 - 4.48186i) q^{19} +(2.18790 - 3.78956i) q^{20} +1.61342 q^{22} +(-3.27079 - 5.66518i) q^{23} +(-1.67999 - 2.90983i) q^{25} +(2.19962 - 1.21959i) q^{26} +(-2.40088 + 4.15845i) q^{28} -4.02068 q^{29} +(4.23854 - 7.34137i) q^{31} -5.82048 q^{32} +(1.87899 + 3.25451i) q^{34} +(4.58689 + 7.94473i) q^{35} +(-2.42323 + 4.19715i) q^{37} +(1.80502 + 3.12638i) q^{38} +(-3.54311 + 6.13685i) q^{40} +(1.25716 + 2.17746i) q^{41} +(-2.99320 + 5.18437i) q^{43} +3.50041 q^{44} +(2.28159 + 3.95182i) q^{46} +(-0.521283 - 0.902888i) q^{47} +(-1.53340 - 2.65593i) q^{49} +(1.17190 + 2.02979i) q^{50} +(4.77221 - 2.64597i) q^{52} +1.29495 q^{53} +(3.34377 - 5.79158i) q^{55} +(3.88801 - 6.73424i) q^{56} +2.80468 q^{58} +4.70451 q^{59} +(-3.71841 + 6.44047i) q^{61} +(-2.95665 + 5.12107i) q^{62} +1.42575 q^{64} +(0.180794 - 10.4234i) q^{65} +(-4.18368 - 7.24635i) q^{67} +(4.07658 + 7.06085i) q^{68} +(-3.19965 - 5.54196i) q^{70} +(0.680710 + 1.17903i) q^{71} +1.41722 q^{73} +(1.69036 - 2.92778i) q^{74} +(3.91609 + 6.78287i) q^{76} +(-3.66927 + 6.35536i) q^{77} +(-0.0365793 - 0.0633573i) q^{79} +(-1.90426 + 3.29827i) q^{80} +(-0.876947 - 1.51892i) q^{82} +(1.08808 + 1.88462i) q^{83} +15.5766 q^{85} +(2.08795 - 3.61643i) q^{86} -5.66860 q^{88} +(0.0891486 - 0.154410i) q^{89} +(-0.198393 + 11.4381i) q^{91} +(4.95003 + 8.57371i) q^{92} +(0.363628 + 0.629822i) q^{94} +14.9634 q^{95} +(-0.0654501 + 0.113363i) q^{97} +(1.06965 + 1.85268i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 18 q^{4} + 2 q^{5} + 3 q^{7} + 18 q^{8} - 6 q^{11} - 2 q^{14} + 6 q^{16} - 6 q^{17} - 3 q^{19} + 11 q^{20} - 18 q^{22} - 17 q^{23} - 6 q^{25} + 12 q^{26} + 24 q^{29} - 6 q^{31} + 38 q^{32}+ \cdots + 61 q^{98}+O(q^{100}) \) 24 * q + 2 * q^2 + 18 * q^4 + 2 * q^5 + 3 * q^7 + 18 * q^8 - 6 * q^11 - 2 * q^14 + 6 * q^16 - 6 * q^17 - 3 * q^19 + 11 * q^20 - 18 * q^22 - 17 * q^23 - 6 * q^25 + 12 * q^26 + 24 * q^29 - 6 * q^31 + 38 * q^32 - 18 * q^35 - 3 * q^37 - 8 * q^38 - 12 * q^40 - 5 * q^41 - 3 * q^43 - 44 * q^44 - 6 * q^46 - 21 * q^47 + 3 * q^49 + 20 * q^50 - 24 * q^52 + 20 * q^53 + 3 * q^55 - 40 * q^56 + 18 * q^58 - 38 * q^59 - 6 * q^61 - 19 * q^62 - 42 * q^64 + 2 * q^65 - 6 * q^67 + 27 * q^70 - 14 * q^71 + 6 * q^73 - 29 * q^74 - 15 * q^76 - 4 * q^77 + 3 * q^79 + 16 * q^80 - 9 * q^82 + 33 * q^83 - 72 * q^86 - 78 * q^88 + q^89 - 6 * q^91 + 10 * q^92 - 9 * q^94 + 100 * q^95 + 24 * q^97 + 61 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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