LMFDB - Embedded newform 351.2.f.a.172.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(100,351)] 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, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("351.100"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.f (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			172.8
Character	$\chi$	$=$	351.172
Dual form			351.2.f.a.100.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.348782 - 0.604108i) q^{2} +(0.756702 + 1.31065i) q^{4} +(-1.44568 + 2.50399i) q^{5} -3.17282 q^{7} +2.45082 q^{8} +(1.00846 + 1.74670i) q^{10} +(1.15647 - 2.00306i) q^{11} +(0.0625290 + 3.60501i) q^{13} +(-1.10662 + 1.91673i) q^{14} +(-0.658602 + 1.14073i) q^{16} +(-2.69365 + 4.66554i) q^{17} +(-2.58760 + 4.48186i) q^{19} -4.37581 q^{20} +(-0.806710 - 1.39726i) q^{22} +6.54158 q^{23} +(-1.67999 - 2.90983i) q^{25} +(2.19962 + 1.21959i) q^{26} +(-2.40088 - 4.15845i) q^{28} +(2.01034 - 3.48201i) q^{29} +(4.23854 - 7.34137i) q^{31} +(2.91024 + 5.04068i) q^{32} +(1.87899 + 3.25451i) q^{34} +(4.58689 - 7.94473i) q^{35} +(-2.42323 - 4.19715i) q^{37} +(1.80502 + 3.12638i) q^{38} +(-3.54311 + 6.13685i) q^{40} -2.51431 q^{41} +5.98639 q^{43} +3.50041 q^{44} +(2.28159 - 3.95182i) q^{46} +(-0.521283 - 0.902888i) q^{47} +3.06680 q^{49} -2.34381 q^{50} +(-4.67758 + 2.80987i) q^{52} +1.29495 q^{53} +(3.34377 + 5.79158i) q^{55} -7.77603 q^{56} +(-1.40234 - 2.42892i) q^{58} +(-2.35226 - 4.07423i) q^{59} +7.43682 q^{61} +(-2.95665 - 5.12107i) q^{62} +1.42575 q^{64} +(-9.11732 - 5.05513i) q^{65} +8.36736 q^{67} -8.15316 q^{68} +(-3.19965 - 5.54196i) q^{70} +(0.680710 - 1.17903i) q^{71} +1.41722 q^{73} -3.38071 q^{74} -7.83218 q^{76} +(-3.66927 + 6.35536i) q^{77} +(-0.0365793 - 0.0633573i) q^{79} +(-1.90426 - 3.29827i) q^{80} +(-0.876947 + 1.51892i) q^{82} +(1.08808 + 1.88462i) q^{83} +(-7.78832 - 13.4898i) q^{85} +(2.08795 - 3.61643i) q^{86} +(2.83430 - 4.90915i) q^{88} +(0.0891486 + 0.154410i) q^{89} +(-0.198393 - 11.4381i) q^{91} +(4.95003 + 8.57371i) q^{92} -0.727256 q^{94} +(-7.48170 - 12.9587i) q^{95} +0.130900 q^{97} +(1.06965 - 1.85268i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} - 9 q^{4} + 2 q^{5} - 6 q^{7} + 18 q^{8} + 3 q^{11} - 2 q^{14} - 3 q^{16} - 6 q^{17} - 3 q^{19} - 22 q^{20} + 9 q^{22} + 34 q^{23} - 6 q^{25} + 12 q^{26} - 12 q^{29} - 6 q^{31} - 19 q^{32}+ \cdots + 61 q^{98}+O(q^{100}) $ 24 * q - q^2 - 9 * q^4 + 2 * q^5 - 6 * q^7 + 18 * q^8 + 3 * q^11 - 2 * q^14 - 3 * q^16 - 6 * q^17 - 3 * q^19 - 22 * q^20 + 9 * q^22 + 34 * q^23 - 6 * q^25 + 12 * q^26 - 12 * q^29 - 6 * q^31 - 19 * q^32 - 18 * q^35 - 3 * q^37 - 8 * q^38 - 12 * q^40 + 10 * q^41 + 6 * q^43 - 44 * q^44 - 6 * q^46 - 21 * q^47 - 6 * q^49 - 40 * q^50 - 6 * q^52 + 20 * q^53 + 3 * q^55 + 80 * q^56 - 9 * q^58 + 19 * q^59 + 12 * q^61 - 19 * q^62 - 42 * q^64 - 19 * q^65 + 12 * q^67 + 27 * q^70 - 14 * q^71 + 6 * q^73 + 58 * q^74 + 30 * q^76 - 4 * q^77 + 3 * q^79 + 16 * q^80 - 9 * q^82 + 33 * q^83 - 72 * q^86 + 39 * q^88 + q^89 - 6 * q^91 + 10 * q^92 + 18 * q^94 - 50 * q^95 - 48 * q^97 + 61 * q^98

Character values

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

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

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 $

$2$	0.348782	−	0.604108i	0.246626	−	0.427169i	−0.715962	−	0.698140i	$-0.754011\pi$
$2$	0.348782	−	0.604108i	0.246626	−	0.427169i	0.962588	+	0.270971i	$0.0873448\pi$
$3$		0			0
$3$		0			0
$4$	0.756702	+	1.31065i	0.378351	+	0.655324i
$5$	−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
$7$	−3.17282			−1.19921			−0.599607	−	0.800295i	$-0.704676\pi$
$7$	−3.17282			−1.19921			−0.599607	+	0.800295i	$0.704676\pi$
$8$	2.45082			0.866497
$9$		0			0
$10$	1.00846	+	1.74670i	0.318902	+	0.552354i
$11$	1.15647	−	2.00306i	0.348688	−	0.603946i	−0.637328	−	0.770592i	$-0.719961\pi$
$11$	1.15647	−	2.00306i	0.348688	−	0.603946i	0.986017	+	0.166646i	$0.0532938\pi$
$12$		0			0
$13$	0.0625290	+	3.60501i	0.0173424	+	0.999850i
$13$	0.0625290	+	3.60501i	0.0173424	+	0.999850i
$14$	−1.10662	+	1.91673i	−0.295757	+	0.512267i
$15$		0			0
$16$	−0.658602	+	1.14073i	−0.164651	+	0.285183i
$17$	−2.69365	+	4.66554i	−0.653306	+	1.13156i	0.329010	+	0.944326i	$0.393285\pi$
$17$	−2.69365	+	4.66554i	−0.653306	+	1.13156i	−0.982316	+	0.187232i	$0.940048\pi$
$18$		0			0
$19$	−2.58760	+	4.48186i	−0.593636	+	1.02821i	0.400101	+	0.916471i	$0.368975\pi$
$19$	−2.58760	+	4.48186i	−0.593636	+	1.02821i	−0.993738	+	0.111738i	$0.964358\pi$
$20$	−4.37581			−0.978460
$21$		0			0
$22$	−0.806710	−	1.39726i	−0.171991	−	0.297898i
$23$	6.54158			1.36401			0.682007	−	0.731345i	$-0.261107\pi$
$23$	6.54158			1.36401			0.682007	+	0.731345i	$0.261107\pi$
$24$		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
$29$	2.01034	−	3.48201i	0.373311	−	0.646593i	−0.616762	−	0.787150i	$-0.711556\pi$
$29$	2.01034	−	3.48201i	0.373311	−	0.646593i	0.990073	+	0.140557i	$0.0448892\pi$
$30$		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	$-0.108754\pi$
$32$	2.91024	+	5.04068i	0.514463	+	0.891076i
$33$		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	0.595150	−	0.803615i	$-0.297093\pi$
$37$	−2.42323	−	4.19715i	−0.398376	−	0.690008i	−0.993526	+	0.113607i	$0.963759\pi$
$38$	1.80502	+	3.12638i	0.292812	+	0.507166i
$39$		0			0
$40$	−3.54311	+	6.13685i	−0.560215	+	0.970321i
$41$	−2.51431			−0.392670			−0.196335	−	0.980537i	$-0.562904\pi$
$41$	−2.51431			−0.392670			−0.196335	+	0.980537i	$0.562904\pi$
$42$		0			0
$43$	5.98639			0.912917			0.456458	−	0.889745i	$-0.349118\pi$
$43$	5.98639			0.912917			0.456458	+	0.889745i	$0.349118\pi$
$44$	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
$49$	3.06680			0.438115
$50$	−2.34381			−0.331464
$51$		0			0
$52$	−4.67758	+	2.80987i	−0.648664	+	0.389659i
$53$	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
$56$	−7.77603			−1.03912
$57$		0			0
$58$	−1.40234	−	2.42892i	−0.184136	−	0.318933i
$59$	−2.35226	−	4.07423i	−0.306238	−	0.530419i	0.671298	−	0.741187i	$-0.265737\pi$
$59$	−2.35226	−	4.07423i	−0.306238	−	0.530419i	−0.977536	+	0.210768i	$0.932404\pi$
$60$		0			0
$61$	7.43682			0.952187			0.476094	−	0.879395i	$-0.342052\pi$
$61$	7.43682			0.952187			0.476094	+	0.879395i	$0.342052\pi$
$62$	−2.95665	−	5.12107i	−0.375495	−	0.650377i
$63$		0			0
$64$	1.42575			0.178218
$65$	−9.11732	−	5.05513i	−1.13086	−	0.627011i
$66$		0			0
$67$	8.36736			1.02224			0.511118	−	0.859510i	$-0.329231\pi$
$67$	8.36736			1.02224			0.511118	+	0.859510i	$0.329231\pi$
$68$	−8.15316			−0.988716
$69$		0			0
$70$	−3.19965	−	5.54196i	−0.382431	−	0.662390i
$71$	0.680710	−	1.17903i	0.0807855	−	0.139925i	−0.822802	−	0.568328i	$-0.807590\pi$
$71$	0.680710	−	1.17903i	0.0807855	−	0.139925i	0.903588	+	0.428403i	$0.140924\pi$
$72$		0			0
$73$	1.41722			0.165873			0.0829365	−	0.996555i	$-0.473570\pi$
$73$	1.41722			0.165873			0.0829365	+	0.996555i	$0.473570\pi$
$74$	−3.38071			−0.393000
$75$		0			0
$76$	−7.83218			−0.898412
$77$	−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
$85$	−7.78832	−	13.4898i	−0.844762	−	1.46317i
$86$	2.08795	−	3.61643i	0.225149	−	0.389969i
$87$		0			0
$88$	2.83430	−	4.90915i	0.302137	−	0.523317i
$89$	0.0891486	+	0.154410i	0.00944973	+	0.0163674i	0.870712	−	0.491794i	$-0.163659\pi$
$89$	0.0891486	+	0.154410i	0.00944973	+	0.0163674i	−0.861262	+	0.508161i	$0.830325\pi$
$90$		0			0
$91$	−0.198393	−	11.4381i	−0.0207973	−	1.19903i
$92$	4.95003	+	8.57371i	0.516077	+	0.893871i
$93$		0			0
$94$	−0.727256			−0.0750107
$95$	−7.48170	−	12.9587i	−0.767606	−	1.32953i
$96$		0			0
$97$	0.130900			0.0132909			0.00664545	−	0.999978i	$-0.497885\pi$
$97$	0.130900			0.0132909			0.00664545	+	0.999978i	$0.497885\pi$
$98$	1.06965	−	1.85268i	0.108050	−	0.187149i
$99$		0			0
$100$	2.54251	−	4.40376i	0.254251	−	0.440376i
$101$	4.36995	−	7.56897i	0.434826	−	0.753141i	−0.562455	−	0.826828i	$-0.690143\pi$
$101$	4.36995	−	7.56897i	0.434826	−	0.753141i	0.997281	+	0.0736867i	$0.0234765\pi$
$102$		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	$0.833747\pi$
$104$	0.153247	+	8.83524i	0.0150272	+	0.866367i
$105$		0			0
$106$	0.451655	−	0.782290i	0.0438686	−	0.0759827i
$107$	6.23288	+	10.7957i	0.602555	+	1.04366i	0.992433	+	0.122790i	$0.0391841\pi$
$107$	6.23288	+	10.7957i	0.602555	+	1.04366i	−0.389877	+	0.920867i	$0.627483\pi$
$108$		0			0
$109$	4.84430			0.463999			0.232000	−	0.972716i	$-0.425473\pi$
$109$	4.84430			0.463999			0.232000	+	0.972716i	$0.425473\pi$
$110$	4.66499			0.444789
$111$		0			0
$112$	2.08963	−	3.61934i	0.197451	−	0.341996i
$113$	3.07358	+	5.32360i	0.289138	+	0.500802i	0.973604	−	0.228243i	$-0.0732980\pi$
$113$	3.07358	+	5.32360i	0.289138	+	0.500802i	−0.684466	+	0.729045i	$0.739965\pi$
$114$		0			0
$115$	−9.45705	+	16.3801i	−0.881874	+	1.52745i
$116$	6.08491			0.564970
$117$		0			0
$118$	−3.28170			−0.302105
$119$	8.54647	−	14.8029i	0.783454	−	1.35698i
$120$		0			0
$121$	2.82516	+	4.89332i	0.256833	+	0.444848i
$122$	2.59383	−	4.49264i	0.234834	−	0.406745i
$123$		0			0
$124$	12.8293			1.15210
$125$	−4.74187			−0.424126
$126$		0			0
$127$	−2.10206	−	3.64088i	−0.186528	−	0.323076i	0.757562	−	0.652763i	$-0.226390\pi$
$127$	−2.10206	−	3.64088i	−0.186528	−	0.323076i	−0.944090	+	0.329687i	$0.893057\pi$
$128$	−5.32321	+	9.22006i	−0.470509	+	0.814946i
$129$		0			0
$130$	−6.23380	+	3.74471i	−0.546740	+	0.328433i
$131$	−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
$133$	8.21000	−	14.2201i	0.711897	−	1.23304i
$134$	2.91838	−	5.05479i	0.252110	−	0.436667i
$135$		0			0
$136$	−6.60166	+	11.4344i	−0.566087	+	0.980492i
$137$	−18.9555			−1.61948			−0.809739	−	0.586791i	$-0.800391\pi$
$137$	−18.9555			−1.61948			−0.809739	+	0.586791i	$0.800391\pi$
$138$		0			0
$139$	1.51122	+	2.61752i	0.128180	+	0.222015i	0.922972	−	0.384868i	$-0.125753\pi$
$139$	1.51122	+	2.61752i	0.128180	+	0.222015i	−0.794791	+	0.606883i	$0.792420\pi$
$140$	13.8837			1.17338
$141$		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
$146$	0.494301	−	0.856154i	0.0409086	−	0.0708558i
$147$		0			0
$148$	3.66732	−	6.35199i	0.301452	−	0.522131i
$149$	−2.86713	−	4.96601i	−0.234884	−	0.406832i	0.724355	−	0.689428i	$-0.242138\pi$
$149$	−2.86713	−	4.96601i	−0.234884	−	0.406832i	−0.959239	+	0.282596i	$0.908805\pi$
$150$		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	$-0.0440520\pi$
$158$	−0.0510328			−0.00405995
$159$		0			0
$160$	−16.8291			−1.33046
$161$	−20.7553			−1.63575
$162$		0			0
$163$	−6.56126	+	11.3644i	−0.513918	+	0.890131i	0.485952	+	0.873985i	$0.338473\pi$
$163$	−6.56126	+	11.3644i	−0.513918	+	0.890131i	−0.999870	+	0.0161459i	$0.994860\pi$
$164$	−1.90259	−	3.29538i	−0.148567	−	0.257326i
$165$		0			0
$166$	1.51801			0.117821
$167$	5.81744			0.450167			0.225084	−	0.974339i	$-0.427734\pi$
$167$	5.81744			0.450167			0.225084	+	0.974339i	$0.427734\pi$
$168$		0			0
$169$	−12.9922	+	0.450835i	−0.999398	+	0.0346796i
$170$	−10.8657			−0.833361
$171$		0			0
$172$	4.52992	+	7.84605i	0.345403	+	0.598256i
$173$	18.0837			1.37488			0.687441	−	0.726240i	$-0.258734\pi$
$173$	18.0837			1.37488			0.687441	+	0.726240i	$0.258734\pi$
$174$		0			0
$175$	5.33032	+	9.23239i	0.402934	+	0.697903i
$176$	1.52331	+	2.63844i	0.114823	+	0.198880i
$177$		0			0
$178$	0.124374			0.00932220
$179$	−10.9345	−	18.9391i	−0.817283	−	1.41558i	−0.907677	−	0.419670i	$-0.862146\pi$
$179$	−10.9345	−	18.9391i	−0.817283	−	1.41558i	0.0903935	−	0.995906i	$-0.471188\pi$
$180$		0			0
$181$	−10.9883			−0.816754			−0.408377	−	0.912813i	$-0.633905\pi$
$181$	−10.9883			−0.816754			−0.408377	+	0.912813i	$0.633905\pi$
$182$	−6.97901	−	3.86953i	−0.517319	−	0.286829i
$183$		0			0
$184$	16.0323			1.18191
$185$	14.0129			1.03025
$186$		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
$191$	17.9834			1.30124			0.650618	−	0.759405i	$-0.274510\pi$
$191$	17.9834			1.30124			0.650618	+	0.759405i	$0.274510\pi$
$192$		0			0
$193$	3.80167			0.273650			0.136825	−	0.990595i	$-0.456310\pi$
$193$	3.80167			0.273650			0.136825	+	0.990595i	$0.456310\pi$
$194$	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	0.850399	+	0.526138i	$0.176360\pi$
$197$	12.3633	+	21.4139i	0.880848	+	1.52567i	0.0304487	+	0.999536i	$0.490306\pi$
$198$		0			0
$199$	13.8440	−	23.9785i	0.981376	−	1.69979i	0.324329	−	0.945944i	$-0.394862\pi$
$199$	13.8440	−	23.9785i	0.981376	−	1.69979i	0.657047	−	0.753849i	$-0.271805\pi$
$200$	−4.11737	−	7.13149i	−0.291142	−	0.504273i
$201$		0			0
$202$	−3.04832	−	5.27984i	−0.214479	−	0.371488i
$203$	−6.37845	+	11.0478i	−0.447679	+	0.775403i
$204$		0			0
$205$	3.63490	−	6.29583i	0.253872	−	0.439720i
$206$	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
$211$	−3.79212			−0.261060			−0.130530	−	0.991444i	$-0.541668\pi$
$211$	−3.79212			−0.261060			−0.130530	+	0.991444i	$0.541668\pi$
$212$	0.979892	+	1.69722i	0.0672993	+	0.116566i
$213$		0			0
$214$	8.69566			0.594423
$215$	−8.65442	+	14.9899i	−0.590227	+	1.02230i
$216$		0			0
$217$	−13.4481	+	23.2929i	−0.912919	+	1.58122i
$218$	1.68960	−	2.92648i	0.114434	−	0.198206i
$219$		0			0
$220$	−5.06048	+	8.76501i	−0.341178	+	0.590937i
$221$	−16.9877	−	9.41890i	−1.14272	−	0.633584i
$222$		0			0
$223$	−0.555329	+	0.961858i	−0.0371876	+	0.0644108i	−0.884020	−	0.467449i	$-0.845173\pi$
$223$	−0.555329	+	0.961858i	−0.0371876	+	0.0644108i	0.846833	+	0.531860i	$0.178507\pi$
$224$	−9.23368	−	15.9932i	−0.616951	−	1.06859i
$225$		0			0
$226$	4.28803			0.285236
$227$	8.34446			0.553841			0.276921	−	0.960893i	$-0.410686\pi$
$227$	8.34446			0.553841			0.276921	+	0.960893i	$0.410686\pi$
$228$		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	$0.247436\pi$
$230$	6.59689	+	11.4262i	0.434986	+	0.753418i
$231$		0			0
$232$	4.92699	−	8.53379i	0.323473	−	0.560271i
$233$	−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
$236$	3.55992	−	6.16596i	0.231731	−	0.401370i
$237$		0			0
$238$	−5.96171	−	10.3260i	−0.386440	−	0.669334i
$239$	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
$241$	−22.8611			−1.47261			−0.736306	−	0.676649i	$-0.763431\pi$
$241$	−22.8611			−1.47261			−0.736306	+	0.676649i	$0.763431\pi$
$242$	3.94146			0.253367
$243$		0			0
$244$	5.62746	+	9.74704i	0.360261	+	0.623991i
$245$	−4.43362	+	7.67926i	−0.283254	+	0.490610i
$246$		0			0
$247$	−16.3189	−	9.04808i	−1.03835	−	0.575716i
$248$	10.3879	−	17.9924i	0.659633	−	1.14252i
$249$		0			0
$250$	−1.65388	+	2.86460i	−0.104601	+	0.181173i
$251$	−8.21662	+	14.2316i	−0.518629	+	0.898291i	0.481137	+	0.876645i	$0.340224\pi$
$251$	−8.21662	+	14.2316i	−0.518629	+	0.898291i	−0.999766	+	0.0216457i	$0.993109\pi$
$252$		0			0
$253$	7.56513	−	13.1032i	0.475616	−	0.823791i
$254$	−2.93265			−0.184011
$255$		0			0
$256$	5.13902	+	8.90105i	0.321189	+	0.556315i
$257$	3.65314			0.227877			0.113938	−	0.993488i	$-0.463653\pi$
$257$	3.65314			0.227877			0.113938	+	0.993488i	$0.463653\pi$
$258$		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
$263$	−12.4449	+	21.5552i	−0.767384	+	1.32915i	0.171593	+	0.985168i	$0.445109\pi$
$263$	−12.4449	+	21.5552i	−0.767384	+	1.32915i	−0.938977	+	0.343980i	$0.888225\pi$
$264$		0			0
$265$	−1.87209	+	3.24255i	−0.115001	+	0.199188i
$266$	−5.72700	−	9.91945i	−0.351145	−	0.608201i
$267$		0			0
$268$	6.33161	+	10.9667i	0.386764	+	0.669896i
$269$	4.43529	−	7.68215i	0.270424	−	0.468389i	−0.698546	−	0.715565i	$-0.746169\pi$
$269$	4.43529	−	7.68215i	0.270424	−	0.468389i	0.968971	+	0.247176i	$0.0795027\pi$
$270$		0			0
$271$	−5.20415	−	9.01385i	−0.316129	−	0.547552i	0.663548	−	0.748134i	$-0.269050\pi$
$271$	−5.20415	−	9.01385i	−0.316129	−	0.547552i	−0.979677	+	0.200582i	$0.935717\pi$
$272$	−3.54809	−	6.14547i	−0.215134	−	0.372624i
$273$		0			0
$274$	−6.61133	+	11.4512i	−0.399405	+	0.691790i
$275$	−7.77144			−0.468635
$276$		0			0
$277$	−24.8624			−1.49384			−0.746918	−	0.664916i	$-0.768467\pi$
$277$	−24.8624			−1.49384			−0.746918	+	0.664916i	$0.768467\pi$
$278$	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
$283$	29.6384			1.76182			0.880909	−	0.473285i	$-0.156932\pi$
$283$	29.6384			1.76182			0.880909	+	0.473285i	$0.156932\pi$
$284$	2.06038			0.122261
$285$		0			0
$286$	4.98670	−	2.99557i	0.294870	−	0.177132i
$287$	7.97747			0.470895
$288$		0			0
$289$	−6.01149	−	10.4122i	−0.353617	−	0.612482i
$290$	8.10935			0.476197
$291$		0			0
$292$	1.07241	+	1.85748i	0.0627583	+	0.108701i
$293$	−7.63814	−	13.2296i	−0.446225	−	0.772884i	0.551912	−	0.833902i	$-0.313898\pi$
$293$	−7.63814	−	13.2296i	−0.446225	−	0.772884i	−0.998137	+	0.0610186i	$0.980565\pi$
$294$		0			0
$295$	13.6025			0.791966
$296$	−5.93890	−	10.2865i	−0.345192	−	0.597890i
$297$		0			0
$298$	−4.00001			−0.231714
$299$	0.409038	+	23.5825i	0.0236553	+	1.36381i
$300$		0			0
$301$	−18.9938			−1.09478
$302$	−1.47850			−0.0850781
$303$		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	$0.526967\pi$
$308$	−11.1062			−0.632833
$309$		0			0
$310$	17.0975			0.971074
$311$	−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
$319$	−4.64979	−	8.05367i	−0.260338	−	0.450919i
$320$	−2.06118	+	3.57006i	−0.115223	+	0.199573i
$321$		0			0
$322$	−7.23907	+	12.5384i	−0.403417	+	0.698739i
$323$	−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
$328$	−6.16214			−0.340247
$329$	1.65394	+	2.86470i	0.0911845	+	0.157936i
$330$		0			0
$331$	7.15450			0.393247			0.196624	−	0.980479i	$-0.437002\pi$
$331$	7.15450			0.393247			0.196624	+	0.980479i	$0.437002\pi$
$332$	−1.64671	+	2.85219i	−0.0903750	+	0.156534i
$333$		0			0
$334$	2.02902	−	3.51436i	0.111023	−	0.192297i
$335$	−12.0966	+	20.9518i	−0.660905	+	1.14472i
$336$		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	$0.298133\pi$
$338$	−4.25908	+	8.00592i	−0.231664	+	0.435465i
$339$		0			0
$340$	11.7869	−	20.4155i	0.639233	−	1.10718i
$341$	−9.80348	−	16.9801i	−0.530888	−	0.919525i
$342$		0			0
$343$	12.4793			0.673821
$344$	14.6716			0.791039
$345$		0			0
$346$	6.30728	−	10.9245i	0.339081	−	0.587306i
$347$	−9.95655	−	17.2453i	−0.534496	−	0.925774i	−0.999188	−	0.0403011i	$-0.987168\pi$
$347$	−9.95655	−	17.2453i	−0.534496	−	0.925774i	0.464692	−	0.885472i	$-0.346165\pi$
$348$		0			0
$349$	13.8845	−	24.0487i	0.743221	−	1.28730i	−0.207801	−	0.978171i	$-0.566630\pi$
$349$	13.8845	−	24.0487i	0.743221	−	1.28730i	0.951021	−	0.309125i	$-0.100036\pi$
$350$	7.43648			0.397496
$351$		0			0
$352$	13.4624			0.717549
$353$	14.2852	−	24.7427i	0.760326	−	1.31692i	−0.182357	−	0.983232i	$-0.558373\pi$
$353$	14.2852	−	24.7427i	0.760326	−	1.31692i	0.942683	−	0.333691i	$-0.108294\pi$
$354$		0			0
$355$	1.96818	+	3.40899i	0.104460	+	0.180930i
$356$	−0.134918	+	0.233685i	−0.00715064	+	0.0123853i
$357$		0			0
$358$	−15.2550			−0.806253
$359$	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
$362$	−3.83252	+	6.63812i	−0.201433	+	0.348892i
$363$		0			0
$364$	14.8411	−	8.91523i	0.777886	−	0.467285i
$365$	−2.04885	+	3.54871i	−0.107242	+	0.185748i
$366$		0			0
$367$	−0.235591	+	0.408055i	−0.0122977	+	0.0213003i	−0.872109	−	0.489312i	$-0.837248\pi$
$367$	−0.235591	+	0.408055i	−0.0122977	+	0.0213003i	0.859811	+	0.510612i	$0.170581\pi$
$368$	−4.30830	+	7.46220i	−0.224586	+	0.388994i
$369$		0			0
$370$	4.88743	−	8.46528i	0.254086	−	0.440089i
$371$	−4.10865			−0.213310
$372$		0			0
$373$	−16.1744	−	28.0148i	−0.837478	−	1.45055i	−0.891997	−	0.452041i	$-0.850696\pi$
$373$	−16.1744	−	28.0148i	−0.837478	−	1.45055i	0.0545197	−	0.998513i	$-0.482637\pi$
$374$	8.69198			0.449451
$375$		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	0.883765	−	0.467930i	$-0.155000\pi$
$379$	0.713364	+	1.23558i	0.0366430	+	0.0634676i	−0.847122	+	0.531398i	$0.821667\pi$
$380$	11.3228	−	19.6117i	0.580849	−	1.00606i
$381$		0			0
$382$	6.27229	−	10.8639i	0.320919	−	0.555847i
$383$	−7.97219	−	13.8082i	−0.407360	−	0.705568i	0.587233	−	0.809418i	$-0.300217\pi$
$383$	−7.97219	−	13.8082i	−0.407360	−	0.705568i	−0.994593	+	0.103850i	$0.966884\pi$
$384$		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
$392$	7.51619			0.379625
$393$		0			0
$394$	17.2484			0.868960
$395$	0.211528			0.0106431
$396$		0			0
$397$	1.77422	−	3.07304i	0.0890454	−	0.154231i	−0.818062	−	0.575129i	$-0.804952\pi$
$397$	1.77422	−	3.07304i	0.0890454	−	0.154231i	0.907108	+	0.420898i	$0.138285\pi$
$398$	−9.65708	−	16.7266i	−0.484066	−	0.838427i
$399$		0			0
$400$	4.42579			0.221290
$401$	−26.6424			−1.33046			−0.665229	−	0.746640i	$-0.731666\pi$
$401$	−26.6424			−1.33046			−0.665229	+	0.746640i	$0.731666\pi$
$402$		0			0
$403$	26.7307	+	14.8209i	1.33155	+	0.738283i
$404$	13.2270			0.658068
$405$		0			0
$406$	4.44937	+	7.70654i	0.220819	+	0.382469i
$407$	−11.2095			−0.555636
$408$		0			0
$409$	6.76077	+	11.7100i	0.334299	+	0.579022i	0.983350	−	0.181723i	$-0.0581673\pi$
$409$	6.76077	+	11.7100i	0.334299	+	0.579022i	−0.649051	+	0.760745i	$0.724834\pi$
$410$	−2.53557	−	4.39174i	−0.125223	−	0.216893i
$411$		0			0
$412$	−26.5832			−1.30966
$413$	7.46329	+	12.9268i	0.367245	+	0.636086i
$414$		0			0
$415$	−6.29209			−0.308866
$416$	−17.9897	+	10.8066i	−0.882020	+	0.529839i
$417$		0			0
$418$	8.34978			0.408401
$419$	12.6059			0.615837			0.307918	−	0.951413i	$-0.400368\pi$
$419$	12.6059			0.615837			0.307918	+	0.951413i	$0.400368\pi$
$420$		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
$425$	18.1013			0.878040
$426$		0			0
$427$	−23.5957			−1.14188
$428$	−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	0.992184	−	0.124786i	$-0.0398245\pi$
$431$	8.05558	+	13.9527i	0.388024	+	0.672077i	−0.604160	+	0.796863i	$0.706491\pi$
$432$		0			0
$433$	−13.5252	+	23.4264i	−0.649981	+	1.12580i	0.333146	+	0.942875i	$0.391890\pi$
$433$	−13.5252	+	23.4264i	−0.649981	+	1.12580i	−0.983127	+	0.182924i	$0.941444\pi$
$434$	9.38093	+	16.2482i	0.450299	+	0.779941i
$435$		0			0
$436$	3.66569	+	6.34916i	0.175555	+	0.304070i
$437$	−16.9270	+	29.3184i	−0.809729	+	1.40249i
$438$		0			0
$439$	−1.15165	+	1.99471i	−0.0549651	+	0.0952024i	−0.892199	−	0.451643i	$-0.850838\pi$
$439$	−1.15165	+	1.99471i	−0.0549651	+	0.0952024i	0.837234	+	0.546845i	$0.184171\pi$
$440$	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
$445$	−0.515522			−0.0244381
$446$	0.387377	+	0.670957i	0.0183428	+	0.0317707i
$447$		0			0
$448$	−4.52364			−0.213722
$449$	4.46646	−	7.73613i	0.210785	−	0.365091i	−0.741175	−	0.671311i	$-0.765731\pi$
$449$	4.46646	−	7.73613i	0.210785	−	0.365091i	0.951960	+	0.306221i	$0.0990646\pi$
$450$		0			0
$451$	−2.90772	+	5.03633i	−0.136919	+	0.237151i
$452$	−4.65157	+	8.05676i	−0.218791	+	0.378958i
$453$		0			0
$454$	2.91040	−	5.04095i	0.136592	−	0.236584i
$455$	28.9276	+	16.0390i	1.35615	+	0.751921i
$456$		0			0
$457$	−9.44075	+	16.3519i	−0.441620	+	0.764907i	−0.997810	−	0.0661475i	$-0.978929\pi$
$457$	−9.44075	+	16.3519i	−0.441620	+	0.764907i	0.556190	+	0.831055i	$0.312263\pi$
$458$	2.64989	+	4.58974i	0.123821	+	0.214465i
$459$		0			0
$460$	−28.6247			−1.33463
$461$	23.2255			1.08172			0.540860	−	0.841113i	$-0.318099\pi$
$461$	23.2255			1.08172			0.540860	+	0.841113i	$0.318099\pi$
$462$		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	$0.149646\pi$
$464$	2.64803	+	4.58652i	0.122932	+	0.212924i
$465$		0			0
$466$	−0.267794	+	0.463832i	−0.0124053	+	0.0214866i
$467$	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
$470$	1.05138	−	1.82104i	0.0484966	−	0.0839985i
$471$		0			0
$472$	−5.76497	−	9.98521i	−0.265354	−	0.459607i
$473$	6.92308	−	11.9911i	0.318323	−	0.551352i
$474$		0			0
$475$	17.3886			0.797845
$476$	25.8685			1.18568
$477$		0			0
$478$	−7.40925	−	12.8332i	−0.338891	−	0.586976i
$479$	−2.43604	+	4.21935i	−0.111306	+	0.192787i	−0.916297	−	0.400500i	$-0.868837\pi$
$479$	−2.43604	+	4.21935i	−0.111306	+	0.192787i	0.804991	+	0.593287i	$0.202170\pi$
$480$		0			0
$481$	14.9793	−	8.99820i	0.682995	−	0.410283i
$482$	−7.97353	+	13.8106i	−0.363184	+	0.629054i
$483$		0			0
$484$	−4.27561	+	7.40558i	−0.194346	+	0.336617i
$485$	−0.189240	+	0.327773i	−0.00859294	+	0.0148834i
$486$		0			0
$487$	−6.17126	+	10.6889i	−0.279647	+	0.484362i	−0.971297	−	0.237870i	$-0.923551\pi$
$487$	−6.17126	+	10.6889i	−0.279647	+	0.484362i	0.691650	+	0.722233i	$0.256884\pi$
$488$	18.2263			0.825067
$489$		0			0
$490$	3.09273	+	5.35677i	0.139715	+	0.241994i
$491$	28.1584			1.27077			0.635386	−	0.772194i	$-0.280841\pi$
$491$	28.1584			1.27077			0.635386	+	0.772194i	$0.280841\pi$
$492$		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
$497$	−2.15977	+	3.74084i	−0.0968791	+	0.167799i
$498$		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	$-0.0145540\pi$
$500$	−3.58819	−	6.21492i	−0.160469	−	0.277940i
$501$		0			0
$502$	5.73162	+	9.92745i	0.255815	+	0.443084i
$503$	1.66703	−	2.88738i	0.0743291	−	0.128742i	−0.826465	−	0.562988i	$-0.809652\pi$
$503$	1.66703	−	2.88738i	0.0743291	−	0.128742i	0.900794	+	0.434246i	$0.142985\pi$
$504$		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
$509$	−34.1316			−1.51286			−0.756429	−	0.654076i	$-0.773058\pi$
$509$	−34.1316			−1.51286			−0.756429	+	0.654076i	$0.773058\pi$
$510$		0			0
$511$	−4.49659			−0.198917
$512$	−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
$517$	−2.41139			−0.106053
$518$	10.7264			0.471291
$519$		0			0
$520$	−22.3449	−	12.3892i	−0.979891	−	0.543303i
$521$	−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	0.832559	−	0.553937i	$-0.186875\pi$
$523$	−1.45092	−	2.51307i	−0.0634443	−	0.109889i	−0.896003	+	0.444048i	$0.853542\pi$
$524$	−0.935439			−0.0408648
$525$		0			0
$526$	8.68109	+	15.0361i	0.378514	+	0.655605i
$527$	22.8343	+	39.5501i	0.994677	+	1.72283i
$528$		0			0
$529$	19.7923			0.860535
$530$	1.30590	+	2.26188i	0.0567247	+	0.0982500i
$531$		0			0
$532$	24.8501			1.07739
$533$	−0.157217	−	9.06412i	−0.00680984	−	0.392611i
$534$		0			0
$535$	−36.0431			−1.55828
$536$	20.5069			0.885765
$537$		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	$0.338482\pi$
$542$	−7.26045			−0.311863
$543$		0			0
$544$	−31.3567			−1.34441
$545$	−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
$553$	0.116060	+	0.201021i	0.00493536	+	0.00854830i
$554$	−8.67155	+	15.0196i	−0.368419	+	0.638120i
$555$		0			0
$556$	−2.28709	+	3.96136i	−0.0969944	+	0.167999i
$557$	−1.08919	−	1.88653i	−0.0461503	−	0.0799347i	0.842027	−	0.539435i	$-0.181362\pi$
$557$	−1.08919	−	1.88653i	−0.0461503	−	0.0799347i	−0.888178	+	0.459500i	$0.848029\pi$
$558$		0			0
$559$	0.374323	+	21.5810i	0.0158322	+	0.912779i
$560$	6.04188	+	10.4648i	0.255316	+	0.442220i
$561$		0			0
$562$	7.62782			0.321760
$563$	3.82852	+	6.63120i	0.161353	+	0.279472i	0.935354	−	0.353713i	$-0.115081\pi$
$563$	3.82852	+	6.63120i	0.161353	+	0.279472i	−0.774001	+	0.633184i	$0.781748\pi$
$564$		0			0
$565$	−17.7737			−0.747744
$566$	10.3373	−	17.9048i	0.434510	−	0.752594i
$567$		0			0
$568$	1.66830	−	2.88958i	0.0700004	−	0.121244i
$569$	−13.2970	+	23.0311i	−0.557440	+	0.965514i	0.440269	+	0.897866i	$0.354883\pi$
$569$	−13.2970	+	23.0311i	−0.557440	+	0.965514i	−0.997709	+	0.0676486i	$0.978450\pi$
$570$		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	$-0.194613\pi$
$572$	0.218877	+	12.6190i	0.00915171	+	0.527627i
$573$		0			0
$574$	2.78240	−	4.81925i	0.116135	−	0.201152i
$575$	−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	$0.670870\pi$
$578$	−8.38679			−0.348844
$579$		0			0
$580$	−8.79685	+	15.2366i	−0.365269	+	0.632665i
$581$	−3.45229	−	5.97955i	−0.143225	−	0.248073i
$582$		0			0
$583$	1.49757	−	2.59387i	0.0620230	−	0.107427i
$584$	3.47336			0.143729
$585$		0			0
$586$	−10.6562			−0.440202
$587$	−6.97935	+	12.0886i	−0.288069	+	0.498950i	−0.973349	−	0.229330i	$-0.926347\pi$
$587$	−6.97935	+	12.0886i	−0.288069	+	0.498950i	0.685280	+	0.728280i	$0.259680\pi$
$588$		0			0
$589$	21.9353	+	37.9931i	0.903829	+	1.56548i
$590$	4.74429	−	8.21735i	0.195319	−	0.338303i
$591$		0			0
$592$	6.38377			0.262371
$593$	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
$596$	4.33913	−	7.51559i	0.177738	−	0.307851i
$597$		0			0
$598$	14.3890	+	7.97803i	0.588411	+	0.326246i
$599$	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
$601$	−8.78997	+	15.2247i	−0.358550	+	0.621028i	−0.987719	−	0.156241i	$-0.950062\pi$
$601$	−8.78997	+	15.2247i	−0.358550	+	0.621028i	0.629168	+	0.777269i	$0.283396\pi$
$602$	−6.62468	+	11.4743i	−0.270002	+	0.467657i
$603$		0			0
$604$	1.60385	−	2.77794i	0.0652596	−	0.113033i
$605$	−16.3371			−0.664199
$606$		0			0
$607$	20.0915	+	34.7995i	0.815489	+	1.41247i	0.908976	+	0.416848i	$0.136865\pi$
$607$	20.0915	+	34.7995i	0.815489	+	1.41247i	−0.0934872	+	0.995620i	$0.529801\pi$
$608$	−30.1222			−1.22162
$609$		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	0.999996	−	0.00278192i	$-0.000885515\pi$
$613$	12.3197	+	21.3384i	0.497589	+	0.861849i	−0.502407	+	0.864631i	$0.667552\pi$
$614$	−1.03424	+	1.79136i	−0.0417386	+	0.0722934i
$615$		0			0
$616$	−8.99273	+	15.5759i	−0.362327	+	0.627570i
$617$	18.0518	+	31.2667i	0.726739	+	1.25875i	0.958254	+	0.285918i	$0.0922986\pi$
$617$	18.0518	+	31.2667i	0.726739	+	1.25875i	−0.231515	+	0.972831i	$0.574368\pi$
$618$		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
$626$	−2.18507			−0.0873331
$627$		0			0
$628$	23.3126			0.930274
$629$	26.1093			1.04105
$630$		0			0
$631$	4.85653	−	8.41176i	0.193335	−	0.334867i	−0.753018	−	0.658000i	$-0.771403\pi$
$631$	4.85653	−	8.41176i	0.193335	−	0.334867i	0.946354	+	0.323133i	$0.104736\pi$
$632$	−0.0896495	−	0.155278i	−0.00356607	−	0.00617661i
$633$		0			0
$634$	−20.3447			−0.807992
$635$	12.1557			0.482383
$636$		0			0
$637$	0.191764	+	11.0559i	0.00759797	+	0.438049i
$638$	−6.48704			−0.256825
$639$		0			0
$640$	−15.3913	−	26.6586i	−0.608396	−	1.05377i
$641$	29.9584			1.18329			0.591643	−	0.806200i	$-0.298479\pi$
$641$	29.9584			1.18329			0.591643	+	0.806200i	$0.298479\pi$
$642$		0			0
$643$	−9.27872	−	16.0712i	−0.365917	−	0.633787i	0.623006	−	0.782217i	$-0.285911\pi$
$643$	−9.27872	−	16.0712i	−0.365917	−	0.633787i	−0.988923	+	0.148430i	$0.952578\pi$
$644$	−15.7056	−	27.2029i	−0.618886	−	1.07194i
$645$		0			0
$646$	−19.4483			−0.765184
$647$	−17.4909	−	30.2951i	−0.687637	−	1.19102i	−0.972600	−	0.232484i	$-0.925315\pi$
$647$	−17.4909	−	30.2951i	−0.687637	−	1.19102i	0.284963	−	0.958538i	$-0.408019\pi$
$648$		0			0
$649$	−10.8812			−0.427126
$650$	−0.146556	−	8.44944i	−0.00574839	−	0.331414i
$651$		0			0
$652$	−19.8597			−0.777765
$653$	15.6864			0.613858			0.306929	−	0.951732i	$-0.400699\pi$
$653$	15.6864			0.613858			0.306929	+	0.951732i	$0.400699\pi$
$654$		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
$659$	−22.3025			−0.868783			−0.434391	−	0.900724i	$-0.643037\pi$
$659$	−22.3025			−0.868783			−0.434391	+	0.900724i	$0.643037\pi$
$660$		0			0
$661$	16.6050			0.645859			0.322930	−	0.946423i	$-0.395332\pi$
$661$	16.6050			0.645859			0.322930	+	0.946423i	$0.395332\pi$
$662$	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
$670$	8.43811	+	14.6152i	0.325993	+	0.564636i
$671$	8.60045	−	14.8964i	0.332017	−	0.575069i
$672$		0			0
$673$	4.31242	−	7.46933i	0.166232	−	0.287922i	−0.770860	−	0.637004i	$-0.780173\pi$
$673$	4.31242	−	7.46933i	0.166232	−	0.287922i	0.937092	+	0.349083i	$0.113507\pi$
$674$	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
$679$	−0.415323			−0.0159386
$680$	−19.0878	−	33.0610i	−0.731984	−	1.26783i
$681$		0			0
$682$	−13.6771			−0.523723
$683$	13.6294	−	23.6068i	0.521514	−	0.903289i	−0.478172	−	0.878266i	$-0.658701\pi$
$683$	13.6294	−	23.6068i	0.521514	−	0.903289i	0.999687	−	0.0250235i	$-0.00796605\pi$
$684$		0			0
$685$	27.4036	−	47.4645i	1.04704	−	1.81352i
$686$	4.35257	−	7.53886i	0.166182	−	0.287835i
$687$		0			0
$688$	−3.94265	+	6.82888i	−0.150312	+	0.260348i
$689$	0.0809719	+	4.66831i	0.00308478	+	0.177848i
$690$		0			0
$691$	10.6237	−	18.4008i	0.404144	−	0.699998i	−0.590077	−	0.807347i	$-0.700903\pi$
$691$	10.6237	−	18.4008i	0.404144	−	0.699998i	0.994221	+	0.107349i	$0.0342361\pi$
$692$	13.6840	+	23.7014i	0.520188	+	0.900992i
$693$		0			0
$694$	−13.8907			−0.527282
$695$	−8.73900			−0.331489
$696$		0			0
$697$	6.77268	−	11.7306i	0.256533	−	0.444329i
$698$	−9.68533	−	16.7755i	−0.366595	−	0.634961i
$699$		0			0
$700$	−8.06694	+	13.9723i	−0.304902	+	0.528105i
$701$	−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
$704$	1.64883	−	2.85586i	0.0621427	−	0.107634i
$705$		0			0
$706$	−9.96486	−	17.2596i	−0.375032	−	0.649575i
$707$	−13.8651	+	24.0150i	−0.521450	+	0.903177i
$708$		0			0
$709$	25.7338			0.966454			0.483227	−	0.875495i	$-0.339465\pi$
$709$	25.7338			0.966454			0.483227	+	0.875495i	$0.339465\pi$
$710$	2.74586			0.103050
$711$		0			0
$712$	0.218487	+	0.378431i	0.00818816	+	0.0141823i
$713$	27.7268	−	48.0242i	1.03838	−	1.79852i
$714$		0			0
$715$	−20.6696	+	12.4165i	−0.773000	+	0.464350i
$716$	16.5483	−	28.6626i	0.618440	−	1.07117i
$717$		0			0
$718$	5.38931	−	9.33455i	0.201127	−	0.348362i
$719$	8.35595	−	14.4729i	0.311624	−	0.539749i	−0.667090	−	0.744977i	$-0.732460\pi$
$719$	8.35595	−	14.4729i	0.311624	−	0.539749i	0.978714	+	0.205228i	$0.0657936\pi$
$720$		0			0
$721$	27.8656	−	48.2646i	1.03777	−	1.79747i
$722$	−5.42895			−0.202044
$723$		0			0
$724$	−8.31488	−	14.4018i	−0.309020	−	0.535238i
$725$	−13.5094			−0.501728
$726$		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
$731$	−16.1252	+	27.9297i	−0.596414	+	1.03302i
$732$		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	$0.924715\pi$
$734$	0.164340	+	0.284644i	0.00606588	+	0.0105064i
$735$		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	−0.980571	−	0.196165i	$-0.937151\pi$
$739$	−17.9464	−	31.0841i	−0.660169	−	1.14345i	0.320401	−	0.947282i	$-0.396182\pi$
$740$	10.6036	+	18.3659i	0.389795	+	0.675145i
$741$		0			0
$742$	−1.43302	+	2.48207i	−0.0526079	+	0.0911195i
$743$	1.50358			0.0551609			0.0275804	−	0.999620i	$-0.491220\pi$
$743$	1.50358			0.0551609			0.0275804	+	0.999620i	$0.491220\pi$
$744$		0			0
$745$	16.5798			0.607438
$746$	−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
$751$	4.21831			0.153928			0.0769642	−	0.997034i	$-0.475477\pi$
$751$	4.21831			0.153928			0.0769642	+	0.997034i	$0.475477\pi$
$752$	1.37327			0.0500781
$753$		0			0
$754$	8.66860	−	5.20732i	0.315692	−	0.189640i
$755$	6.12830			0.223032
$756$		0			0
$757$	−3.70611	−	6.41918i	−0.134701	−	0.233309i	0.790782	−	0.612098i	$-0.209674\pi$
$757$	−3.70611	−	6.41918i	−0.134701	−	0.233309i	−0.925483	+	0.378789i	$0.876341\pi$
$758$	0.995234			0.0361485
$759$		0			0
$760$	−18.3363	−	31.7594i	−0.665128	−	1.15204i
$761$	18.2564	+	31.6210i	0.661795	+	1.14626i	0.980144	+	0.198288i	$0.0635383\pi$
$761$	18.2564	+	31.6210i	0.661795	+	1.14626i	−0.318349	+	0.947974i	$0.603128\pi$
$762$		0			0
$763$	−15.3701			−0.556435
$764$	13.6081	+	23.5699i	0.492324	+	0.852730i
$765$		0			0
$766$	−11.1222			−0.401862
$767$	14.5405	−	8.73466i	0.525029	−	0.315390i
$768$		0			0
$769$	16.0012			0.577018			0.288509	−	0.957477i	$-0.406840\pi$
$769$	16.0012			0.577018			0.288509	+	0.957477i	$0.406840\pi$
$770$	−14.8012			−0.533397
$771$		0			0
$772$	2.87673	+	4.98264i	0.103536	+	0.179329i
$773$	−14.3128	+	24.7905i	−0.514796	+	0.891652i	0.485057	+	0.874483i	$0.338799\pi$
$773$	−14.3128	+	24.7905i	−0.514796	+	0.891652i	−0.999853	+	0.0171698i	$0.994534\pi$
$774$		0			0
$775$	−28.4829			−1.02314
$776$	0.320813			0.0115165
$777$		0			0
$778$	−14.0273			−0.502905
$779$	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
$787$	2.87553	+	4.98057i	0.102502	+	0.177538i	0.912715	−	0.408597i	$-0.133982\pi$
$787$	2.87553	+	4.98057i	0.102502	+	0.177538i	−0.810213	+	0.586135i	$0.800649\pi$
$788$	−18.7107	+	32.4078i	−0.666540	+	1.15448i
$789$		0			0
$790$	0.0737773	−	0.127786i	0.00262488	−	0.00454642i
$791$	−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
$796$	41.9032			1.48522
$797$	−26.9581	−	46.6928i	−0.954905	−	1.65394i	−0.734585	−	0.678517i	$-0.762623\pi$
$797$	−26.9581	−	46.6928i	−0.954905	−	1.65394i	−0.220320	−	0.975428i	$-0.570710\pi$
$798$		0			0
$799$	5.61661			0.198701
$800$	9.77837	−	16.9366i	0.345718	−	0.598801i
$801$		0			0
$802$	−9.29238	+	16.0949i	−0.328125	+	0.568330i
$803$	1.63897	−	2.83878i	0.0578380	−	0.100178i
$804$		0			0
$805$	30.0055	−	51.9711i	1.05756	−	1.83174i
$806$	18.2766	−	10.9790i	0.643767	−	0.386718i
$807$		0			0
$808$	10.7100	−	18.5502i	0.376776	−	0.652594i
$809$	−2.00874	−	3.47924i	−0.0706235	−	0.122324i	0.828551	−	0.559913i	$-0.189166\pi$
$809$	−2.00874	−	3.47924i	−0.0706235	−	0.122324i	−0.899175	+	0.437590i	$0.855832\pi$
$810$		0			0
$811$	14.2338			0.499815			0.249908	−	0.968270i	$-0.419600\pi$
$811$	14.2338			0.499815			0.249908	+	0.968270i	$0.419600\pi$
$812$	−19.3064			−0.677520
$813$		0			0
$814$	−3.90969	+	6.77177i	−0.137034	+	0.237351i
$815$	−18.9710	−	32.8587i	−0.664525	−	1.15099i
$816$		0			0
$817$	−15.4904	+	26.8302i	−0.541941	+	0.938669i
$818$	9.43213			0.329787
$819$		0			0
$820$	11.0021			0.384212
$821$	−24.8337	+	43.0132i	−0.866701	+	1.50117i	−0.00135317	+	0.999999i	$0.500431\pi$
$821$	−24.8337	+	43.0132i	−0.866701	+	1.50117i	−0.865348	+	0.501171i	$0.832903\pi$
$822$		0			0
$823$	−5.98593	−	10.3679i	−0.208656	−	0.361403i	0.742635	−	0.669696i	$-0.233576\pi$
$823$	−5.98593	−	10.3679i	−0.208656	−	0.361403i	−0.951292	+	0.308293i	$0.900242\pi$
$824$	−21.5246	+	37.2817i	−0.749844	+	1.29877i
$825$		0			0
$826$	10.4122			0.362288
$827$	−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	−0.846847	−	0.531837i	$-0.821502\pi$
$829$	−25.4527	−	44.0853i	−0.884008	−	1.53115i	−0.0371606	−	0.999309i	$-0.511831\pi$
$830$	−2.19457	+	3.80110i	−0.0761745	+	0.131938i
$831$		0			0
$832$	0.0891505	+	5.13983i	0.00309074	+	0.178192i
$833$	−8.26089	+	14.3083i	−0.286223	+	0.495753i
$834$		0			0
$835$	−8.41018	+	14.5669i	−0.291046	+	0.504107i
$836$	−9.05767	+	15.6883i	−0.313266	+	0.542593i
$837$		0			0
$838$	4.39670	−	7.61530i	0.151881	−	0.263066i
$839$	8.42689			0.290929			0.145464	−	0.989364i	$-0.453532\pi$
$839$	8.42689			0.290929			0.145464	+	0.989364i	$0.453532\pi$
$840$		0			0
$841$	6.41707	+	11.1147i	0.221278	+	0.383265i
$842$	6.27393			0.216214
$843$		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
$848$	−0.852857	+	1.47719i	−0.0292872	+	0.0507270i
$849$		0			0
$850$	6.31339	−	10.9351i	0.216547	−	0.375071i
$851$	−15.8517	−	27.4560i	−0.543391	−	0.941180i
$852$		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	$0.139572\pi$
$860$	−26.1953			−0.893252
$861$		0			0
$862$	11.2386			0.382787
$863$	−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
$868$	−40.7050			−1.38162
$869$	−0.169211			−0.00574010
$870$		0			0
$871$	0.523203	+	30.1644i	0.0177280	+	1.02208i
$872$	11.8725			0.402054
$873$		0			0
$874$	11.8077	+	20.4515i	0.399400	+	0.691782i
$875$	15.0451			0.508618
$876$		0			0
$877$	−4.05215	−	7.01854i	−0.136832	−	0.236999i	0.789464	−	0.613797i	$-0.210359\pi$
$877$	−4.05215	−	7.01854i	−0.136832	−	0.236999i	−0.926296	+	0.376798i	$0.877025\pi$
$878$	0.803347	+	1.39144i	0.0271117	+	0.0469588i
$879$		0			0
$880$	−8.80886			−0.296947
$881$	−8.71424	−	15.0935i	−0.293590	−	0.508513i	0.681066	−	0.732222i	$-0.261517\pi$
$881$	−8.71424	−	15.0935i	−0.293590	−	0.508513i	−0.974656	+	0.223709i	$0.928183\pi$
$882$		0			0
$883$	7.78098			0.261851			0.130925	−	0.991392i	$-0.458205\pi$
$883$	7.78098			0.261851			0.130925	+	0.991392i	$0.458205\pi$
$884$	−0.509809	−	29.3922i	−0.0171467	−	0.988568i
$885$		0			0
$886$	−18.3432			−0.616253
$887$	−31.9515			−1.07283			−0.536413	−	0.843956i	$-0.680221\pi$
$887$	−31.9515			−1.07283			−0.536413	+	0.843956i	$0.680221\pi$
$888$		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
$893$	5.39549			0.180553
$894$		0			0
$895$	63.2313			2.11359
$896$	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
$904$	7.53280	+	13.0472i	0.250537	+	0.433943i
$905$	15.8856	−	27.5147i	0.528055	−	0.914618i
$906$		0			0
$907$	−10.2843	+	17.8129i	−0.341484	+	0.591468i	−0.984709	−	0.174210i	$-0.944263\pi$
$907$	−10.2843	+	17.8129i	−0.341484	+	0.591468i	0.643224	+	0.765678i	$0.277596\pi$
$908$	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
$913$	5.03333			0.166579
$914$	6.58552	+	11.4065i	0.217830	+	0.377292i
$915$		0			0
$916$	−11.4982			−0.379911
$917$	0.980564	−	1.69839i	0.0323811	−	0.0560857i
$918$		0			0
$919$	9.27825	−	16.0704i	0.306061	−	0.530114i	−0.671436	−	0.741063i	$-0.734322\pi$
$919$	9.27825	−	16.0704i	0.306061	−	0.530114i	0.977497	+	0.210949i	$0.0676554\pi$
$920$	−23.1776	+	40.1447i	−0.764142	+	1.32353i
$921$		0			0
$922$	8.10063	−	14.0307i	0.266780	−	0.462077i
$923$	4.29296	+	2.38024i	0.141305	+	0.0783467i
$924$		0			0
$925$	−8.14201	+	14.1024i	−0.267708	+	0.463683i
$926$	−0.802232	−	1.38951i	−0.0263630	−	0.0456620i
$927$		0			0
$928$	23.4023			0.768218
$929$	48.2623			1.58344			0.791718	−	0.610887i	$-0.209187\pi$
$929$	48.2623			1.58344			0.791718	+	0.610887i	$0.209187\pi$
$930$		0			0
$931$	−7.93566	+	13.7450i	−0.260081	+	0.450473i
$932$	−0.580994	−	1.00631i	−0.0190311	−	0.0329628i
$933$		0			0
$934$	7.83760	−	13.5751i	0.256454	−	0.444191i
$935$	−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	$0.288465\pi$
$938$	−9.25952	+	16.0380i	−0.302334	+	0.523658i
$939$		0			0
$940$	2.28103	+	3.95086i	0.0743990	+	0.128863i
$941$	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
$943$	−16.4476			−0.535607
$944$	6.19681			0.201689
$945$		0			0
$946$	−4.82929	−	8.36457i	−0.157014	−	0.271956i
$947$	−0.883784	+	1.53076i	−0.0287191	+	0.0497430i	−0.880028	−	0.474922i	$-0.842476\pi$
$947$	−0.883784	+	1.53076i	−0.0287191	+	0.0497430i	0.851309	+	0.524665i	$0.175810\pi$
$948$		0			0
$949$	0.0886173	+	5.10909i	0.00287664	+	0.165848i
$950$	6.06483	−	10.5046i	0.196769	−	0.340814i
$951$		0			0
$952$	20.9459	−	36.2793i	0.678860	−	1.17582i
$953$	−17.6033	+	30.4898i	−0.570228	+	0.987663i	0.426315	+	0.904575i	$0.359812\pi$
$953$	−17.6033	+	30.4898i	−0.570228	+	0.987663i	−0.996542	+	0.0830881i	$0.973522\pi$
$954$		0			0
$955$	−25.9983	+	45.0304i	−0.841286	+	1.45715i
$956$	32.1496			1.03979
$957$		0			0
$958$	1.69930	+	2.94327i	0.0549018	+	0.0950926i
$959$	60.1424			1.94210
$960$		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
$965$	−5.49600	+	9.51935i	−0.176923	+	0.306439i
$966$		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	$0.839133\pi$
$968$	6.92397	+	11.9927i	0.222545	+	0.385459i
$969$		0			0
$970$	0.132007	+	0.228643i	0.00423849	+	0.00734127i
$971$	−24.0513	+	41.6582i	−0.771844	+	1.33687i	0.164707	+	0.986343i	$0.447332\pi$
$971$	−24.0513	+	41.6582i	−0.771844	+	1.33687i	−0.936551	+	0.350531i	$0.886001\pi$
$972$		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
$977$	55.7438			1.78340			0.891700	−	0.452626i	$-0.149513\pi$
$977$	55.7438			1.78340			0.891700	+	0.452626i	$0.149513\pi$
$978$		0			0
$979$	0.412390			0.0131800
$980$	−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
$985$	−71.4936			−2.27797
$986$	15.1096			0.481189
$987$		0			0
$988$	−0.489738	−	28.2351i	−0.0155806	−	0.898277i
$989$	39.1605			1.24523
$990$		0			0
$991$	15.5487	+	26.9312i	0.493922	+	0.855498i	0.999975	−	0.00700424i	$-0.00222954\pi$
$991$	15.5487	+	26.9312i	0.493922	+	0.855498i	−0.506054	+	0.862502i	$0.668896\pi$
$992$	49.3407			1.56657
$993$		0			0
$994$	1.50658	+	2.60947i	0.0477858	+	0.0827674i
$995$	40.0281	+	69.3307i	1.26898	+	2.19793i
$996$		0			0
$997$	21.0784			0.667561			0.333781	−	0.942651i	$-0.391676\pi$
$997$	21.0784			0.667561			0.333781	+	0.942651i	$0.391676\pi$
$998$	−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.f.a.172.8		24
3.2	odd	2		117.2.f.a.94.5	yes	24
9.2	odd	6		117.2.h.a.16.8	yes	24
9.7	even	3		351.2.h.a.289.5		24
13.9	even	3		351.2.h.a.334.5		24
39.35	odd	6		117.2.h.a.22.8	yes	24
117.61	even	3	inner	351.2.f.a.100.8		24
117.74	odd	6		117.2.f.a.61.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.f.a.61.5	✓	24	117.74	odd	6
117.2.f.a.94.5	yes	24	3.2	odd	2
117.2.h.a.16.8	yes	24	9.2	odd	6
117.2.h.a.22.8	yes	24	39.35	odd	6
351.2.f.a.100.8		24	117.61	even	3	inner
351.2.f.a.172.8		24	1.1	even	1	trivial
351.2.h.a.289.5		24	9.7	even	3
351.2.h.a.334.5		24	13.9	even	3

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

\(f(q)\)	\(=\)	\(q+(0.348782 - 0.604108i) q^{2} +(0.756702 + 1.31065i) q^{4} +(-1.44568 + 2.50399i) q^{5} -3.17282 q^{7} +2.45082 q^{8} +(1.00846 + 1.74670i) q^{10} +(1.15647 - 2.00306i) q^{11} +(0.0625290 + 3.60501i) q^{13} +(-1.10662 + 1.91673i) q^{14} +(-0.658602 + 1.14073i) q^{16} +(-2.69365 + 4.66554i) q^{17} +(-2.58760 + 4.48186i) q^{19} -4.37581 q^{20} +(-0.806710 - 1.39726i) q^{22} +6.54158 q^{23} +(-1.67999 - 2.90983i) q^{25} +(2.19962 + 1.21959i) q^{26} +(-2.40088 - 4.15845i) q^{28} +(2.01034 - 3.48201i) q^{29} +(4.23854 - 7.34137i) q^{31} +(2.91024 + 5.04068i) q^{32} +(1.87899 + 3.25451i) q^{34} +(4.58689 - 7.94473i) q^{35} +(-2.42323 - 4.19715i) q^{37} +(1.80502 + 3.12638i) q^{38} +(-3.54311 + 6.13685i) q^{40} -2.51431 q^{41} +5.98639 q^{43} +3.50041 q^{44} +(2.28159 - 3.95182i) q^{46} +(-0.521283 - 0.902888i) q^{47} +3.06680 q^{49} -2.34381 q^{50} +(-4.67758 + 2.80987i) q^{52} +1.29495 q^{53} +(3.34377 + 5.79158i) q^{55} -7.77603 q^{56} +(-1.40234 - 2.42892i) q^{58} +(-2.35226 - 4.07423i) q^{59} +7.43682 q^{61} +(-2.95665 - 5.12107i) q^{62} +1.42575 q^{64} +(-9.11732 - 5.05513i) q^{65} +8.36736 q^{67} -8.15316 q^{68} +(-3.19965 - 5.54196i) q^{70} +(0.680710 - 1.17903i) q^{71} +1.41722 q^{73} -3.38071 q^{74} -7.83218 q^{76} +(-3.66927 + 6.35536i) q^{77} +(-0.0365793 - 0.0633573i) q^{79} +(-1.90426 - 3.29827i) q^{80} +(-0.876947 + 1.51892i) q^{82} +(1.08808 + 1.88462i) q^{83} +(-7.78832 - 13.4898i) q^{85} +(2.08795 - 3.61643i) q^{86} +(2.83430 - 4.90915i) q^{88} +(0.0891486 + 0.154410i) q^{89} +(-0.198393 - 11.4381i) q^{91} +(4.95003 + 8.57371i) q^{92} -0.727256 q^{94} +(-7.48170 - 12.9587i) q^{95} +0.130900 q^{97} +(1.06965 - 1.85268i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} - 9 q^{4} + 2 q^{5} - 6 q^{7} + 18 q^{8} + 3 q^{11} - 2 q^{14} - 3 q^{16} - 6 q^{17} - 3 q^{19} - 22 q^{20} + 9 q^{22} + 34 q^{23} - 6 q^{25} + 12 q^{26} - 12 q^{29} - 6 q^{31} - 19 q^{32}+ \cdots + 61 q^{98}+O(q^{100}) \) 24 * q - q^2 - 9 * q^4 + 2 * q^5 - 6 * q^7 + 18 * q^8 + 3 * q^11 - 2 * q^14 - 3 * q^16 - 6 * q^17 - 3 * q^19 - 22 * q^20 + 9 * q^22 + 34 * q^23 - 6 * q^25 + 12 * q^26 - 12 * q^29 - 6 * q^31 - 19 * q^32 - 18 * q^35 - 3 * q^37 - 8 * q^38 - 12 * q^40 + 10 * q^41 + 6 * q^43 - 44 * q^44 - 6 * q^46 - 21 * q^47 - 6 * q^49 - 40 * q^50 - 6 * q^52 + 20 * q^53 + 3 * q^55 + 80 * q^56 - 9 * q^58 + 19 * q^59 + 12 * q^61 - 19 * q^62 - 42 * q^64 - 19 * q^65 + 12 * q^67 + 27 * q^70 - 14 * q^71 + 6 * q^73 + 58 * q^74 + 30 * q^76 - 4 * q^77 + 3 * q^79 + 16 * q^80 - 9 * q^82 + 33 * q^83 - 72 * q^86 + 39 * q^88 + q^89 - 6 * q^91 + 10 * q^92 + 18 * q^94 - 50 * q^95 - 48 * q^97 + 61 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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