LMFDB - Embedded newform 351.2.l.b.199.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,2,Mod(127,351)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(351, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("351.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.11
Character	$\chi$	$=$	351.199
Dual form			351.2.l.b.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.59035i q^{2} -4.70993 q^{4} +(-1.18696 - 0.685292i) q^{5} +(-3.20825 - 1.85228i) q^{7} -7.01967i q^{8} +(1.77515 - 3.07465i) q^{10} -0.487471i q^{11} +(3.11904 + 1.80875i) q^{13} +(4.79807 - 8.31050i) q^{14} +8.76356 q^{16} +(-2.88951 - 5.00477i) q^{17} +(-2.80767 + 1.62101i) q^{19} +(5.59049 + 3.22767i) q^{20} +1.26272 q^{22} +(0.175893 + 0.304656i) q^{23} +(-1.56075 - 2.70330i) q^{25} +(-4.68529 + 8.07942i) q^{26} +(15.1106 + 8.72412i) q^{28} -3.00808 q^{29} +(-3.62047 - 2.09028i) q^{31} +8.66137i q^{32} +(12.9641 - 7.48484i) q^{34} +(2.53871 + 4.39718i) q^{35} +(-7.56549 - 4.36794i) q^{37} +(-4.19899 - 7.27286i) q^{38} +(-4.81052 + 8.33206i) q^{40} +(-1.44970 + 0.836982i) q^{41} +(-5.78344 + 10.0172i) q^{43} +2.29595i q^{44} +(-0.789167 + 0.455626i) q^{46} +(-3.26623 + 1.88576i) q^{47} +(3.36191 + 5.82301i) q^{49} +(7.00250 - 4.04289i) q^{50} +(-14.6905 - 8.51907i) q^{52} +12.2232 q^{53} +(-0.334060 + 0.578609i) q^{55} +(-13.0024 + 22.5208i) q^{56} -7.79200i q^{58} +5.70642i q^{59} +(1.17729 - 2.03913i) q^{61} +(5.41456 - 9.37829i) q^{62} -4.90889 q^{64} +(-2.46266 - 4.28437i) q^{65} +(0.0679883 - 0.0392530i) q^{67} +(13.6094 + 23.5721i) q^{68} +(-11.3902 + 6.57615i) q^{70} +(-0.940139 + 0.542789i) q^{71} +2.49602i q^{73} +(11.3145 - 19.5973i) q^{74} +(13.2239 - 7.63484i) q^{76} +(-0.902935 + 1.56393i) q^{77} +(-1.16667 - 2.02073i) q^{79} +(-10.4020 - 6.00559i) q^{80} +(-2.16808 - 3.75522i) q^{82} +(2.19957 - 1.26992i) q^{83} +7.92062i q^{85} +(-25.9481 - 14.9812i) q^{86} -3.42189 q^{88} +(-14.0114 - 8.08948i) q^{89} +(-6.65636 - 11.5803i) q^{91} +(-0.828445 - 1.43491i) q^{92} +(-4.88478 - 8.46068i) q^{94} +4.44346 q^{95} +(-0.732699 - 0.423024i) q^{97} +(-15.0836 + 8.70854i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 20 q^{4} + 3 q^{5} - 6 q^{7} - 7 q^{10} + 9 q^{14} + 24 q^{16} - 9 q^{17} - 6 q^{19} + 24 q^{20} + 26 q^{22} - 6 q^{23} + 4 q^{25} + 12 q^{26} + 3 q^{28} - 48 q^{29} - 27 q^{31} + 15 q^{34} + 27 q^{35}+ \cdots - 117 q^{98}+O(q^{100}) $ 22 * q - 20 * q^4 + 3 * q^5 - 6 * q^7 - 7 * q^10 + 9 * q^14 + 24 * q^16 - 9 * q^17 - 6 * q^19 + 24 * q^20 + 26 * q^22 - 6 * q^23 + 4 * q^25 + 12 * q^26 + 3 * q^28 - 48 * q^29 - 27 * q^31 + 15 * q^34 + 27 * q^35 + 6 * q^37 - 21 * q^38 + 13 * q^40 - 6 * q^41 - 4 * q^43 - 15 * q^46 + 6 * q^47 + 7 * q^49 - 18 * q^50 - 22 * q^52 + 24 * q^53 - 13 * q^55 + 9 * q^56 + 3 * q^61 - 24 * q^64 + 57 * q^65 - 45 * q^67 + 69 * q^68 - 24 * q^70 - 9 * q^71 + 6 * q^74 + 18 * q^76 - 42 * q^77 - 6 * q^79 - 105 * q^80 - 16 * q^82 - 42 * q^83 - 45 * q^86 + 22 * q^88 + 30 * q^89 + 15 * q^91 + 3 * q^92 + 44 * q^94 - 6 * q^95 - 27 * q^97 - 117 * q^98

Character values

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

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$			2.59035i			1.83166i	0.401571	+	0.915828i	$0.368464\pi$
$2$			2.59035i			1.83166i	−0.401571	+	0.915828i	$0.631536\pi$
$3$		0			0
$3$		0			0
$4$	−4.70993			−2.35496
$5$	−1.18696	−	0.685292i	−0.530825	−	0.306472i	0.210528	−	0.977588i	$-0.432482\pi$
$5$	−1.18696	−	0.685292i	−0.530825	−	0.306472i	−0.741352	+	0.671116i	$0.765815\pi$
$6$		0			0
$7$	−3.20825	−	1.85228i	−1.21260	−	0.700098i	−0.249279	−	0.968432i	$-0.580194\pi$
$7$	−3.20825	−	1.85228i	−1.21260	−	0.700098i	−0.963326	+	0.268334i	$0.913527\pi$
$8$		−	7.01967i		−	2.48183i
$9$		0			0
$10$	1.77515	−	3.07465i	0.561351	−	0.972288i
$11$		−	0.487471i		−	0.146978i	−0.997296	−	0.0734891i	$-0.976587\pi$
$11$		−	0.487471i		−	0.146978i	0.997296	−	0.0734891i	$-0.0234134\pi$
$12$		0			0
$13$	3.11904	+	1.80875i	0.865067	+	0.501656i
$13$	3.11904	+	1.80875i	0.865067	+	0.501656i
$14$	4.79807	−	8.31050i	1.28234	−	2.22107i
$15$		0			0
$16$	8.76356			2.19089
$17$	−2.88951	−	5.00477i	−0.700808	−	1.21384i	−0.968183	−	0.250243i	$-0.919490\pi$
$17$	−2.88951	−	5.00477i	−0.700808	−	1.21384i	0.267375	−	0.963593i	$-0.413844\pi$
$18$		0			0
$19$	−2.80767	+	1.62101i	−0.644124	+	0.371885i	−0.786201	−	0.617970i	$-0.787955\pi$
$19$	−2.80767	+	1.62101i	−0.644124	+	0.371885i	0.142077	+	0.989856i	$0.454622\pi$
$20$	5.59049	+	3.22767i	1.25007	+	0.721730i
$21$		0			0
$22$	1.26272			0.269213
$23$	0.175893	+	0.304656i	0.0366763	+	0.0635252i	0.883781	−	0.467901i	$-0.154990\pi$
$23$	0.175893	+	0.304656i	0.0366763	+	0.0635252i	−0.847105	+	0.531426i	$0.821656\pi$
$24$		0			0
$25$	−1.56075	−	2.70330i	−0.312150	−	0.540660i
$26$	−4.68529	+	8.07942i	−0.918861	+	1.58451i
$27$		0			0
$28$	15.1106	+	8.72412i	2.85564	+	1.64870i
$29$	−3.00808			−0.558587			−0.279294	−	0.960206i	$-0.590100\pi$
$29$	−3.00808			−0.558587			−0.279294	+	0.960206i	$0.590100\pi$
$30$		0			0
$31$	−3.62047	−	2.09028i	−0.650255	−	0.375425i	0.138299	−	0.990391i	$-0.455837\pi$
$31$	−3.62047	−	2.09028i	−0.650255	−	0.375425i	−0.788554	+	0.614965i	$0.789170\pi$
$32$			8.66137i			1.53113i
$33$		0			0
$34$	12.9641	−	7.48484i	2.22333	−	1.28364i
$35$	2.53871	+	4.39718i	0.429120	+	0.743258i
$36$		0			0
$37$	−7.56549	−	4.36794i	−1.24376	−	0.718084i	−0.273901	−	0.961758i	$-0.588314\pi$
$37$	−7.56549	−	4.36794i	−1.24376	−	0.718084i	−0.969857	+	0.243673i	$0.921648\pi$
$38$	−4.19899	−	7.27286i	−0.681165	−	1.17981i
$39$		0			0
$40$	−4.81052	+	8.33206i	−0.760610	+	1.31741i
$41$	−1.44970	+	0.836982i	−0.226404	+	0.130715i	−0.608912	−	0.793238i	$-0.708394\pi$
$41$	−1.44970	+	0.836982i	−0.226404	+	0.130715i	0.382508	+	0.923952i	$0.375061\pi$
$42$		0			0
$43$	−5.78344	+	10.0172i	−0.881967	+	1.52761i	−0.0328156	+	0.999461i	$0.510447\pi$
$43$	−5.78344	+	10.0172i	−0.881967	+	1.52761i	−0.849151	+	0.528150i	$0.822886\pi$
$44$			2.29595i			0.346128i
$45$		0			0
$46$	−0.789167	+	0.455626i	−0.116356	+	0.0671784i
$47$	−3.26623	+	1.88576i	−0.476428	+	0.275066i	−0.718927	−	0.695086i	$-0.755366\pi$
$47$	−3.26623	+	1.88576i	−0.476428	+	0.275066i	0.242499	+	0.970152i	$0.422033\pi$
$48$		0			0
$49$	3.36191	+	5.82301i	0.480273	+	0.831858i
$50$	7.00250	−	4.04289i	0.990303	−	0.571752i
$51$		0			0
$52$	−14.6905	−	8.51907i	−2.03720	−	1.18138i
$53$	12.2232			1.67898			0.839492	−	0.543373i	$-0.182853\pi$
$53$	12.2232			1.67898			0.839492	+	0.543373i	$0.182853\pi$
$54$		0			0
$55$	−0.334060	+	0.578609i	−0.0450446	+	0.0780196i
$56$	−13.0024	+	22.5208i	−1.73752	+	3.00947i
$57$		0			0
$58$		−	7.79200i		−	1.02314i
$59$			5.70642i			0.742912i	0.928451	+	0.371456i	$0.121141\pi$
$59$			5.70642i			0.742912i	−0.928451	+	0.371456i	$0.878859\pi$
$60$		0			0
$61$	1.17729	−	2.03913i	0.150737	−	0.261084i	−0.780762	−	0.624829i	$-0.785169\pi$
$61$	1.17729	−	2.03913i	0.150737	−	0.261084i	0.931499	+	0.363745i	$0.118502\pi$
$62$	5.41456	−	9.37829i	0.687650	−	1.19104i
$63$		0			0
$64$	−4.90889			−0.613611
$65$	−2.46266	−	4.28437i	−0.305456	−	0.531410i
$66$		0			0
$67$	0.0679883	−	0.0392530i	0.00830609	−	0.00479552i	−0.495841	−	0.868413i	$-0.665140\pi$
$67$	0.0679883	−	0.0392530i	0.00830609	−	0.00479552i	0.504147	+	0.863618i	$0.331807\pi$
$68$	13.6094	+	23.5721i	1.65038	+	2.85854i
$69$		0			0
$70$	−11.3902	+	6.57615i	−1.36139	+	0.786001i
$71$	−0.940139	+	0.542789i	−0.111574	+	0.0644172i	−0.554748	−	0.832018i	$-0.687186\pi$
$71$	−0.940139	+	0.542789i	−0.111574	+	0.0644172i	0.443175	+	0.896435i	$0.353852\pi$
$72$		0			0
$73$			2.49602i			0.292137i	0.989274	+	0.146068i	$0.0466620\pi$
$73$			2.49602i			0.292137i	−0.989274	+	0.146068i	$0.953338\pi$
$74$	11.3145	−	19.5973i	1.31528	−	2.27814i
$75$		0			0
$76$	13.2239	−	7.63484i	1.51689	−	0.875776i
$77$	−0.902935	+	1.56393i	−0.102899	+	0.178226i
$78$		0			0
$79$	−1.16667	−	2.02073i	−0.131260	−	0.227350i	0.792902	−	0.609349i	$-0.208569\pi$
$79$	−1.16667	−	2.02073i	−0.131260	−	0.227350i	−0.924163	+	0.381999i	$0.875236\pi$
$80$	−10.4020	−	6.00559i	−1.16298	−	0.671446i
$81$		0			0
$82$	−2.16808	−	3.75522i	−0.239424	−	0.414695i
$83$	2.19957	−	1.26992i	0.241434	−	0.139392i	−0.374401	−	0.927267i	$-0.622152\pi$
$83$	2.19957	−	1.26992i	0.241434	−	0.139392i	0.615836	+	0.787875i	$0.288818\pi$
$84$		0			0
$85$			7.92062i			0.859112i
$86$	−25.9481	−	14.9812i	−2.79806	−	1.61546i
$87$		0			0
$88$	−3.42189			−0.364774
$89$	−14.0114	−	8.08948i	−1.48520	−	0.857483i	−0.485346	−	0.874322i	$-0.661306\pi$
$89$	−14.0114	−	8.08948i	−1.48520	−	0.857483i	−0.999858	+	0.0168392i	$0.994640\pi$
$90$		0			0
$91$	−6.65636	−	11.5803i	−0.697776	−	1.21394i
$92$	−0.828445	−	1.43491i	−0.0863713	−	0.149600i
$93$		0			0
$94$	−4.88478	−	8.46068i	−0.503826	−	0.872652i
$95$	4.44346			0.455889
$96$		0			0
$97$	−0.732699	−	0.423024i	−0.0743943	−	0.0429516i	0.462341	−	0.886702i	$-0.347009\pi$
$97$	−0.732699	−	0.423024i	−0.0743943	−	0.0429516i	−0.536736	+	0.843750i	$0.680343\pi$
$98$	−15.0836	+	8.70854i	−1.52368	+	0.879696i
$99$		0			0
$100$	7.35102	+	12.7323i	0.735102	+	1.27323i
$101$	3.02905			0.301401			0.150701	−	0.988579i	$-0.451847\pi$
$101$	3.02905			0.301401			0.150701	+	0.988579i	$0.451847\pi$
$102$		0			0
$103$	2.74723	−	4.75835i	0.270693	−	0.468854i	−0.698347	−	0.715760i	$-0.746081\pi$
$103$	2.74723	−	4.75835i	0.270693	−	0.468854i	0.969039	+	0.246906i	$0.0794139\pi$
$104$	12.6968	−	21.8946i	1.24502	−	2.14695i
$105$		0			0
$106$			31.6624i			3.07532i
$107$	2.78934	−	4.83127i	0.269655	−	0.467057i	−0.699118	−	0.715007i	$-0.746424\pi$
$107$	2.78934	−	4.83127i	0.269655	−	0.467057i	0.968773	+	0.247950i	$0.0797569\pi$
$108$		0			0
$109$		−	0.977746i		−	0.0936511i	−0.998903	−	0.0468256i	$-0.985090\pi$
$109$		−	0.977746i		−	0.0936511i	0.998903	−	0.0468256i	$-0.0149105\pi$
$110$	−1.49880	−	0.865333i	−0.142905	−	0.0825063i
$111$		0			0
$112$	−28.1157	−	16.2326i	−2.65668	−	1.53384i
$113$	1.66014			0.156173			0.0780866	−	0.996947i	$-0.475119\pi$
$113$	1.66014			0.156173			0.0780866	+	0.996947i	$0.475119\pi$
$114$		0			0
$115$		−	0.482153i		−	0.0449610i
$116$	14.1679			1.31545
$117$		0			0
$118$	−14.7816			−1.36076
$119$			21.4087i			1.96254i
$120$		0			0
$121$	10.7624			0.978397
$122$	5.28207	+	3.04961i	0.478216	+	0.276098i
$123$		0			0
$124$	17.0521	+	9.84506i	1.53133	+	0.884112i
$125$			11.1312i			0.995604i
$126$		0			0
$127$	8.91305	−	15.4379i	0.790905	−	1.36989i	−0.134502	−	0.990913i	$-0.542943\pi$
$127$	8.91305	−	15.4379i	0.790905	−	1.36989i	0.925407	−	0.378975i	$-0.123723\pi$
$128$			4.60699i			0.407204i
$129$		0			0
$130$	11.0980	−	6.37916i	0.973360	−	0.559489i
$131$	−8.49796	+	14.7189i	−0.742470	+	1.28600i	0.208898	+	0.977937i	$0.433012\pi$
$131$	−8.49796	+	14.7189i	−0.742470	+	1.28600i	−0.951368	+	0.308058i	$0.900321\pi$
$132$		0			0
$133$	12.0103			1.04142
$134$	0.101679	+	0.176114i	0.00878375	+	0.0152139i
$135$		0			0
$136$	−35.1318	+	20.2834i	−3.01253	+	1.73928i
$137$	1.87952	+	1.08514i	0.160579	+	0.0927101i	0.578136	−	0.815941i	$-0.303780\pi$
$137$	1.87952	+	1.08514i	0.160579	+	0.0927101i	−0.417557	+	0.908651i	$0.637114\pi$
$138$		0			0
$139$	−9.19253			−0.779700			−0.389850	−	0.920878i	$-0.627473\pi$
$139$	−9.19253			−0.779700			−0.389850	+	0.920878i	$0.627473\pi$
$140$	−11.9571	−	20.7104i	−1.01056	−	1.75035i
$141$		0			0
$142$	−1.40602	−	2.43529i	−0.117990	−	0.204365i
$143$	0.881712	−	1.52044i	0.0737325	−	0.127146i
$144$		0			0
$145$	3.57048	+	2.06141i	0.296512	+	0.171191i
$146$	−6.46557			−0.535094
$147$		0			0
$148$	35.6329	+	20.5727i	2.92901	+	1.69106i
$149$			5.79717i			0.474923i	0.971397	+	0.237461i	$0.0763153\pi$
$149$			5.79717i			0.474923i	−0.971397	+	0.237461i	$0.923685\pi$
$150$		0			0
$151$	−12.1366	+	7.00709i	−0.987666	+	0.570229i	−0.904576	−	0.426313i	$-0.859812\pi$
$151$	−12.1366	+	7.00709i	−0.987666	+	0.570229i	−0.0830899	+	0.996542i	$0.526479\pi$
$152$	11.3789	+	19.7089i	0.922954	+	1.59860i
$153$		0			0
$154$	−4.05113	−	2.33892i	−0.326449	−	0.188476i
$155$	2.86490	+	4.96215i	0.230114	+	0.398570i
$156$		0			0
$157$	2.77149	−	4.80037i	0.221189	−	0.383111i	−0.733980	−	0.679171i	$-0.762339\pi$
$157$	2.77149	−	4.80037i	0.221189	−	0.383111i	0.955169	+	0.296060i	$0.0956728\pi$
$158$	5.23440	−	3.02208i	0.416426	−	0.240424i
$159$		0			0
$160$	5.93556	−	10.2807i	0.469248	−	0.812761i
$161$		−	1.30322i		−	0.102708i
$162$		0			0
$163$	−0.109427	+	0.0631777i	−0.00857098	+	0.00494846i	−0.504279	−	0.863541i	$-0.668242\pi$
$163$	−0.109427	+	0.0631777i	−0.00857098	+	0.00494846i	0.495708	+	0.868489i	$0.334908\pi$
$164$	6.82796	−	3.94212i	0.533174	−	0.307828i
$165$		0			0
$166$	3.28955	+	5.69767i	0.255319	+	0.442225i
$167$	7.99623	−	4.61663i	0.618767	−	0.357245i	−0.157622	−	0.987500i	$-0.550383\pi$
$167$	7.99623	−	4.61663i	0.618767	−	0.357245i	0.776389	+	0.630254i	$0.217049\pi$
$168$		0			0
$169$	6.45687	+	11.2831i	0.496682	+	0.867932i
$170$	−20.5172			−1.57360
$171$		0			0
$172$	27.2396	−	47.1804i	2.07700	−	3.59747i
$173$	8.08378	−	14.0015i	0.614599	−	1.06452i	−0.375856	−	0.926678i	$-0.622651\pi$
$173$	8.08378	−	14.0015i	0.614599	−	1.06452i	0.990455	−	0.137838i	$-0.0440154\pi$
$174$		0			0
$175$			11.5638i			0.874142i
$176$		−	4.27198i		−	0.322013i
$177$		0			0
$178$	20.9546	−	36.2944i	1.57061	−	2.72038i
$179$	−4.88798	+	8.46622i	−0.365345	+	0.632795i	−0.988831	−	0.149039i	$-0.952382\pi$
$179$	−4.88798	+	8.46622i	−0.365345	+	0.632795i	0.623487	+	0.781834i	$0.285715\pi$
$180$		0			0
$181$	10.9633			0.814896			0.407448	−	0.913229i	$-0.366419\pi$
$181$	10.9633			0.814896			0.407448	+	0.913229i	$0.366419\pi$
$182$	29.9970	−	17.2423i	2.22352	−	1.27809i
$183$		0			0
$184$	2.13858	−	1.23471i	0.157659	−	0.0910242i
$185$	5.98662	+	10.3691i	0.440145	+	0.762354i
$186$		0			0
$187$	−2.43968	+	1.40855i	−0.178407	+	0.103003i
$188$	15.3837	−	8.88178i	1.12197	−	0.647770i
$189$		0			0
$190$			11.5101i			0.835032i
$191$	−1.09288	+	1.89292i	−0.0790778	+	0.136967i	−0.902852	−	0.429951i	$-0.858531\pi$
$191$	−1.09288	+	1.89292i	−0.0790778	+	0.136967i	0.823775	+	0.566918i	$0.191864\pi$
$192$		0			0
$193$	2.64074	−	1.52463i	0.190085	−	0.109746i	−0.401937	−	0.915667i	$-0.631663\pi$
$193$	2.64074	−	1.52463i	0.190085	−	0.109746i	0.592022	+	0.805922i	$0.298330\pi$
$194$	1.09578	−	1.89795i	0.0786725	−	0.136265i
$195$		0			0
$196$	−15.8344	−	27.4259i	−1.13103	−	1.95900i
$197$	−8.84639	−	5.10747i	−0.630279	−	0.363892i	0.150581	−	0.988598i	$-0.451886\pi$
$197$	−8.84639	−	5.10747i	−0.630279	−	0.363892i	−0.780860	+	0.624706i	$0.785219\pi$
$198$		0			0
$199$	−3.41850	−	5.92102i	−0.242331	−	0.419730i	0.719047	−	0.694962i	$-0.244579\pi$
$199$	−3.41850	−	5.92102i	−0.242331	−	0.419730i	−0.961378	+	0.275232i	$0.911245\pi$
$200$	−18.9763	+	10.9559i	−1.34182	+	0.774702i
$201$		0			0
$202$			7.84630i			0.552064i
$203$	9.65069	+	5.57183i	0.677345	+	0.391066i
$204$		0			0
$205$	2.29431			0.160241
$206$	12.3258	+	7.11630i	0.858779	+	0.495816i
$207$		0			0
$208$	27.3339	+	15.8511i	1.89527	+	1.09907i
$209$	0.790195	+	1.36866i	0.0546590	+	0.0946721i
$210$		0			0
$211$	11.5354	+	19.9799i	0.794128	+	1.37547i	0.923391	+	0.383860i	$0.125405\pi$
$211$	11.5354	+	19.9799i	0.794128	+	1.37547i	−0.129264	+	0.991610i	$0.541261\pi$
$212$	−57.5703			−3.95394
$213$		0			0
$214$	12.5147	+	7.22536i	0.855487	+	0.493916i
$215$	13.7294	−	7.92669i	0.936339	−	0.540596i
$216$		0			0
$217$	7.74358	+	13.4123i	0.525669	+	0.910485i
$218$	2.53271			0.171537
$219$		0			0
$220$	1.57340	−	2.72521i	0.106078	−	0.183733i
$221$	0.0398687	−	20.8365i	0.00268186	−	1.40161i
$222$		0			0
$223$		−	9.67359i		−	0.647791i	−0.946093	−	0.323896i	$-0.895007\pi$
$223$		−	9.67359i		−	0.647791i	0.946093	−	0.323896i	$-0.104993\pi$
$224$	16.0433	−	27.7878i	1.07194	−	1.85665i
$225$		0			0
$226$			4.30036i			0.286055i
$227$	−23.1988	−	13.3938i	−1.53976	−	0.888978i	−0.998852	−	0.0478937i	$-0.984749\pi$
$227$	−23.1988	−	13.3938i	−1.53976	−	0.888978i	−0.540903	−	0.841085i	$-0.681918\pi$
$228$		0			0
$229$	−5.55568	−	3.20757i	−0.367129	−	0.211962i	0.305074	−	0.952329i	$-0.401319\pi$
$229$	−5.55568	−	3.20757i	−0.367129	−	0.211962i	−0.672204	+	0.740366i	$0.734652\pi$
$230$	1.24895			0.0823531
$231$		0			0
$232$			21.1157i			1.38632i
$233$	21.9858			1.44034			0.720170	−	0.693798i	$-0.244064\pi$
$233$	21.9858			1.44034			0.720170	+	0.693798i	$0.244064\pi$
$234$		0			0
$235$	5.16917			0.337200
$236$		−	26.8768i		−	1.74953i
$237$		0			0
$238$	−55.4562			−3.59469
$239$	−9.86048	−	5.69295i	−0.637821	−	0.368246i	0.145954	−	0.989291i	$-0.453375\pi$
$239$	−9.86048	−	5.69295i	−0.637821	−	0.368246i	−0.783775	+	0.621045i	$0.786708\pi$
$240$		0			0
$241$	−17.4620	−	10.0817i	−1.12483	−	0.649419i	−0.182198	−	0.983262i	$-0.558321\pi$
$241$	−17.4620	−	10.0817i	−1.12483	−	0.649419i	−0.942629	+	0.333843i	$0.891655\pi$
$242$			27.8783i			1.79209i
$243$		0			0
$244$	−5.54497	+	9.60416i	−0.354980	+	0.614844i
$245$		−	9.21557i		−	0.588761i
$246$		0			0
$247$	−11.6892	−	0.0223663i	−0.743769	−	0.00142313i
$248$	−14.6731	+	25.4145i	−0.931740	+	1.61382i
$249$		0			0
$250$	−28.8337			−1.82360
$251$	−5.96356	−	10.3292i	−0.376417	−	0.651973i	0.614121	−	0.789212i	$-0.289511\pi$
$251$	−5.96356	−	10.3292i	−0.376417	−	0.651973i	−0.990538	+	0.137239i	$0.956177\pi$
$252$		0			0
$253$	0.148511	−	0.0857430i	0.00933682	−	0.00539061i
$254$	39.9895	+	23.0879i	2.50916	+	1.44867i
$255$		0			0
$256$	−21.7515			−1.35947
$257$	8.18195	+	14.1716i	0.510376	+	0.883997i	0.999928	+	0.0120231i	$0.00382717\pi$
$257$	8.18195	+	14.1716i	0.510376	+	0.883997i	−0.489552	+	0.871974i	$0.662839\pi$
$258$		0			0
$259$	16.1813	+	28.0269i	1.00546	+	1.74151i
$260$	11.5990	+	20.1790i	0.719337	+	1.25145i
$261$		0			0
$262$	−38.1271	−	22.0127i	−2.35550	−	1.35995i
$263$	−14.7168			−0.907476			−0.453738	−	0.891135i	$-0.649910\pi$
$263$	−14.7168			−0.907476			−0.453738	+	0.891135i	$0.649910\pi$
$264$		0			0
$265$	−14.5084	−	8.37645i	−0.891246	−	0.514561i
$266$			31.1109i			1.90753i
$267$		0			0
$268$	−0.320220	+	0.184879i	−0.0195605	+	0.0112933i
$269$	−13.6669	−	23.6718i	−0.833288	−	1.44330i	−0.895416	−	0.445230i	$-0.853122\pi$
$269$	−13.6669	−	23.6718i	−0.833288	−	1.44330i	0.0621279	−	0.998068i	$-0.480211\pi$
$270$		0			0
$271$	10.2655	+	5.92679i	0.623585	+	0.360027i	0.778263	−	0.627938i	$-0.216101\pi$
$271$	10.2655	+	5.92679i	0.623585	+	0.360027i	−0.154678	+	0.987965i	$0.549434\pi$
$272$	−25.3223	−	43.8596i	−1.53539	−	2.65938i
$273$		0			0
$274$	−2.81090	+	4.86863i	−0.169813	+	0.294125i
$275$	−1.31778	+	0.760821i	−0.0794652	+	0.0458792i
$276$		0			0
$277$	7.14586	−	12.3770i	0.429353	−	0.743661i	−0.567463	−	0.823399i	$-0.692075\pi$
$277$	7.14586	−	12.3770i	0.429353	−	0.743661i	0.996816	+	0.0797377i	$0.0254083\pi$
$278$		−	23.8119i		−	1.42814i
$279$		0			0
$280$	30.8667	−	17.8209i	1.84464	−	1.06500i
$281$	−20.3164	+	11.7297i	−1.21198	+	0.699735i	−0.963190	−	0.268823i	$-0.913365\pi$
$281$	−20.3164	+	11.7297i	−1.21198	+	0.699735i	−0.248787	+	0.968558i	$0.580032\pi$
$282$		0			0
$283$	−13.6592	−	23.6584i	−0.811953	−	1.40634i	−0.911496	−	0.411310i	$-0.865071\pi$
$283$	−13.6592	−	23.6584i	−0.811953	−	1.40634i	0.0995428	−	0.995033i	$-0.468262\pi$
$284$	4.42798	−	2.55650i	0.262753	−	0.151700i
$285$		0			0
$286$	3.93849	+	2.28395i	0.232888	+	0.135053i
$287$	6.20132			0.366052
$288$		0			0
$289$	−8.19849	+	14.2002i	−0.482264	+	0.835306i
$290$	−5.33979	+	9.24879i	−0.313563	+	0.543108i
$291$		0			0
$292$		−	11.7561i		−	0.687972i
$293$		−	27.8967i		−	1.62974i	−0.579642	−	0.814871i	$-0.696808\pi$
$293$		−	27.8967i		−	1.62974i	0.579642	−	0.814871i	$-0.303192\pi$
$294$		0			0
$295$	3.91056	−	6.77329i	0.227682	−	0.394356i
$296$	−30.6615	+	53.1072i	−1.78216	+	3.08679i
$297$		0			0
$298$	−15.0167			−0.869895
$299$	−0.00242694	+	1.26838i	−0.000140353	+	0.0733525i
$300$		0			0
$301$	37.1095	−	21.4252i	2.13895	−	1.23493i
$302$	−18.1508	−	31.4382i	−1.04446	−	1.80906i
$303$		0			0
$304$	−24.6052	+	14.2058i	−1.41120	+	0.814759i
$305$	−2.79480	+	1.61358i	−0.160030	+	0.0923933i
$306$		0			0
$307$			28.7426i			1.64043i	0.572059	+	0.820213i	$0.306145\pi$
$307$			28.7426i			1.64043i	−0.572059	+	0.820213i	$0.693855\pi$
$308$	4.25276	−	7.36600i	0.242323	−	0.419717i
$309$		0			0
$310$	−12.8537	+	7.42110i	−0.730043	+	0.421490i
$311$	−6.83305	+	11.8352i	−0.387467	+	0.671112i	−0.992108	−	0.125386i	$-0.959983\pi$
$311$	−6.83305	+	11.8352i	−0.387467	+	0.671112i	0.604641	+	0.796498i	$0.293316\pi$
$312$		0			0
$313$	−5.90331	−	10.2248i	−0.333675	−	0.577942i	0.649554	−	0.760315i	$-0.274955\pi$
$313$	−5.90331	−	10.2248i	−0.333675	−	0.577942i	−0.983229	+	0.182373i	$0.941622\pi$
$314$	12.4346	+	7.17915i	0.701728	+	0.405143i
$315$		0			0
$316$	5.49492	+	9.51748i	0.309113	+	0.535400i
$317$	26.0847	−	15.0600i	1.46506	−	0.845854i	0.465824	−	0.884878i	$-0.345758\pi$
$317$	26.0847	−	15.0600i	1.46506	−	0.845854i	0.999238	+	0.0390236i	$0.0124248\pi$
$318$		0			0
$319$			1.46635i			0.0821001i
$320$	5.82665	+	3.36402i	0.325720	+	0.188054i
$321$		0			0
$322$	3.37579			0.188126
$323$	16.2256	+	9.36783i	0.902814	+	0.521240i
$324$		0			0
$325$	0.0215349	−	11.2547i	0.00119454	−	0.624299i
$326$	−0.163653	−	0.283454i	−0.00906388	−	0.0156991i
$327$		0			0
$328$	5.87533	+	10.1764i	0.324411	+	0.561896i
$329$	13.9718			0.770292
$330$		0			0
$331$	8.20768	+	4.73870i	0.451135	+	0.260463i	0.708309	−	0.705902i	$-0.249458\pi$
$331$	8.20768	+	4.73870i	0.451135	+	0.260463i	−0.257175	+	0.966365i	$0.582792\pi$
$332$	−10.3598	+	5.98125i	−0.568569	+	0.328263i
$333$		0			0
$334$	11.9587	+	20.7131i	0.654350	+	1.13337i
$335$	−0.107599			−0.00587877
$336$		0			0
$337$	8.14215	−	14.1026i	0.443531	−	0.768218i	−0.554417	−	0.832239i	$-0.687059\pi$
$337$	8.14215	−	14.1026i	0.443531	−	0.768218i	0.997949	+	0.0640203i	$0.0203922\pi$
$338$	−29.2273	+	16.7256i	−1.58975	+	0.909751i
$339$		0			0
$340$		−	37.3055i		−	2.02318i
$341$	−1.01895	+	1.76487i	−0.0551793	+	0.0955733i
$342$		0			0
$343$			1.02310i			0.0552420i
$344$	70.3175	+	40.5978i	3.79127	+	2.18889i
$345$		0			0
$346$	36.2689	+	20.9399i	1.94983	+	1.12573i
$347$	−3.27692			−0.175914			−0.0879571	−	0.996124i	$-0.528034\pi$
$347$	−3.27692			−0.175914			−0.0879571	+	0.996124i	$0.528034\pi$
$348$		0			0
$349$		−	23.3467i		−	1.24972i	−0.780736	−	0.624861i	$-0.785156\pi$
$349$		−	23.3467i		−	1.24972i	0.780736	−	0.624861i	$-0.214844\pi$
$350$	−29.9544			−1.60113
$351$		0			0
$352$	4.22217			0.225042
$353$		−	1.48233i		−	0.0788963i	−0.999222	−	0.0394482i	$-0.987440\pi$
$353$		−	1.48233i		−	0.0788963i	0.999222	−	0.0394482i	$-0.0125600\pi$
$354$		0			0
$355$	1.48788			0.0789683
$356$	65.9926	+	38.1009i	3.49760	+	2.01934i
$357$		0			0
$358$	−21.9305	−	12.6616i	−1.15906	−	0.669185i
$359$			5.04499i			0.266264i	0.991098	+	0.133132i	$0.0425035\pi$
$359$			5.04499i			0.266264i	−0.991098	+	0.133132i	$0.957497\pi$
$360$		0			0
$361$	−4.24466	+	7.35196i	−0.223403	+	0.386945i
$362$			28.3988i			1.49261i
$363$		0			0
$364$	31.3510	+	54.5422i	1.64324	+	2.85879i
$365$	1.71050	−	2.96267i	0.0895317	−	0.155073i
$366$		0			0
$367$	−4.19706			−0.219085			−0.109542	−	0.993982i	$-0.534939\pi$
$367$	−4.19706			−0.219085			−0.109542	+	0.993982i	$0.534939\pi$
$368$	1.54145	+	2.66987i	0.0803537	+	0.139177i
$369$		0			0
$370$	−26.8597	+	15.5075i	−1.39637	+	0.806195i
$371$	−39.2150	−	22.6408i	−2.03594	−	1.17545i
$372$		0			0
$373$	−27.2515			−1.41103			−0.705515	−	0.708695i	$-0.749284\pi$
$373$	−27.2515			−1.41103			−0.705515	+	0.708695i	$0.749284\pi$
$374$	−3.64864	−	6.31964i	−0.188667	−	0.326781i
$375$		0			0
$376$	13.2374	+	22.9278i	0.682666	+	1.18241i
$377$	−9.38235	−	5.44086i	−0.483215	−	0.280219i
$378$		0			0
$379$	−3.91133	−	2.25821i	−0.200912	−	0.115996i	0.396169	−	0.918178i	$-0.370339\pi$
$379$	−3.91133	−	2.25821i	−0.200912	−	0.115996i	−0.597081	+	0.802181i	$0.703673\pi$
$380$	−20.9284			−1.07360
$381$		0			0
$382$	−4.90332	−	2.83093i	−0.250876	−	0.144843i
$383$		−	19.2761i		−	0.984961i	−0.870324	−	0.492480i	$-0.836090\pi$
$383$		−	19.2761i		−	0.984961i	0.870324	−	0.492480i	$-0.163910\pi$
$384$		0			0
$385$	2.14350	−	1.23755i	0.109243	−	0.0630713i
$386$	3.94934	+	6.84045i	0.201016	+	0.348170i
$387$		0			0
$388$	3.45096	+	1.99241i	0.175196	+	0.101149i
$389$	2.21704	+	3.84003i	0.112409	+	0.194697i	0.916741	−	0.399482i	$-0.130810\pi$
$389$	2.21704	+	3.84003i	0.112409	+	0.194697i	−0.804332	+	0.594180i	$0.797477\pi$
$390$		0			0
$391$	1.01649	−	1.76061i	0.0514061	−	0.0890380i
$392$	40.8756	−	23.5995i	2.06453	−	1.19196i
$393$		0			0
$394$	13.2301	−	22.9153i	0.666525	−	1.15445i
$395$			3.19803i			0.160910i
$396$		0			0
$397$	5.79822	−	3.34760i	0.291004	−	0.168011i	−0.347390	−	0.937721i	$-0.612932\pi$
$397$	5.79822	−	3.34760i	0.291004	−	0.168011i	0.638395	+	0.769709i	$0.279599\pi$
$398$	15.3375	−	8.85513i	0.768801	−	0.443867i
$399$		0			0
$400$	−13.6777	−	23.6905i	−0.683886	−	1.18453i
$401$	12.6939	−	7.32884i	0.633905	−	0.365985i	−0.148358	−	0.988934i	$-0.547399\pi$
$401$	12.6939	−	7.32884i	0.633905	−	0.365985i	0.782263	+	0.622949i	$0.214065\pi$
$402$		0			0
$403$	−7.51162	−	13.0682i	−0.374180	−	0.650973i
$404$	−14.2666			−0.709789
$405$		0			0
$406$	−14.4330	+	24.9987i	−0.716298	+	1.24066i
$407$	−2.12924	+	3.68796i	−0.105543	+	0.182805i
$408$		0			0
$409$			14.9121i			0.737358i	0.929557	+	0.368679i	$0.120190\pi$
$409$			14.9121i			0.737358i	−0.929557	+	0.368679i	$0.879810\pi$
$410$			5.94307i			0.293507i
$411$		0			0
$412$	−12.9393	+	22.4115i	−0.637472	+	1.10413i
$413$	10.5699	−	18.3076i	0.520111	−	0.900859i
$414$		0			0
$415$	−3.48107			−0.170879
$416$	−15.6662	+	27.0152i	−0.768100	+	1.32453i
$417$		0			0
$418$	−3.54531	+	2.04688i	−0.173407	+	0.100116i
$419$	−6.36693	−	11.0278i	−0.311045	−	0.538745i	0.667544	−	0.744570i	$-0.267346\pi$
$419$	−6.36693	−	11.0278i	−0.311045	−	0.538745i	−0.978589	+	0.205825i	$0.934012\pi$
$420$		0			0
$421$	11.8508	−	6.84207i	0.577573	−	0.333462i	−0.182595	−	0.983188i	$-0.558450\pi$
$421$	11.8508	−	6.84207i	0.577573	−	0.333462i	0.760168	+	0.649726i	$0.225116\pi$
$422$	−51.7549	+	29.8807i	−2.51939	+	1.45457i
$423$		0			0
$424$		−	85.8027i		−	4.16695i
$425$	−9.01960	+	15.6224i	−0.437515	+	0.757798i
$426$		0			0
$427$	−7.55411	+	4.36136i	−0.365569	+	0.211061i
$428$	−13.1376	+	22.7549i	−0.635028	+	1.09990i
$429$		0			0
$430$	20.5329	+	35.5641i	0.990186	+	1.71505i
$431$	19.8288	+	11.4482i	0.955120	+	0.551439i	0.894668	−	0.446732i	$-0.147412\pi$
$431$	19.8288	+	11.4482i	0.955120	+	0.551439i	0.0604526	+	0.998171i	$0.480746\pi$
$432$		0			0
$433$	−7.61501	−	13.1896i	−0.365954	−	0.633851i	0.622975	−	0.782242i	$-0.285924\pi$
$433$	−7.61501	−	13.1896i	−0.365954	−	0.633851i	−0.988929	+	0.148391i	$0.952591\pi$
$434$	−34.7425	+	20.0586i	−1.66769	+	0.962844i
$435$		0			0
$436$			4.60511i			0.220545i
$437$	−0.987701	−	0.570250i	−0.0472482	−	0.0272787i
$438$		0			0
$439$	−27.3214			−1.30398			−0.651991	−	0.758227i	$-0.726066\pi$
$439$	−27.3214			−1.30398			−0.651991	+	0.758227i	$0.726066\pi$
$440$	4.06164	+	2.34499i	0.193631	+	0.111793i
$441$		0			0
$442$	53.9738	+	0.103274i	2.56727	+	0.00491225i
$443$	0.234040	+	0.405370i	0.0111196	+	0.0192597i	0.871532	−	0.490339i	$-0.163127\pi$
$443$	0.234040	+	0.405370i	0.0111196	+	0.0192597i	−0.860412	+	0.509599i	$0.829794\pi$
$444$		0			0
$445$	11.0873	+	19.2038i	0.525589	+	0.910346i
$446$	25.0580			1.18653
$447$		0			0
$448$	15.7489	+	9.09266i	0.744068	+	0.429588i
$449$	−32.6429	+	18.8464i	−1.54051	+	0.889416i	−0.541708	+	0.840567i	$0.682222\pi$
$449$	−32.6429	+	18.8464i	−1.54051	+	0.889416i	−0.998806	+	0.0488494i	$0.984445\pi$
$450$		0			0
$451$	0.408005	+	0.706685i	0.0192122	+	0.0332765i
$452$	−7.81915			−0.367782
$453$		0			0
$454$	34.6947	−	60.0930i	1.62830	−	2.82030i
$455$	−0.0350285	+	18.3069i	−0.00164216	+	0.858239i
$456$		0			0
$457$			30.8944i			1.44518i	0.691277	+	0.722590i	$0.257049\pi$
$457$			30.8944i			1.44518i	−0.691277	+	0.722590i	$0.742951\pi$
$458$	8.30874	−	14.3912i	0.388242	−	0.672455i
$459$		0			0
$460$			2.27091i			0.105882i
$461$	34.6487	+	20.0045i	1.61375	+	0.931700i	0.988490	+	0.151285i	$0.0483412\pi$
$461$	34.6487	+	20.0045i	1.61375	+	0.931700i	0.625262	+	0.780415i	$0.284992\pi$
$462$		0			0
$463$	−12.0417	−	6.95225i	−0.559623	−	0.323099i	0.193371	−	0.981126i	$-0.438058\pi$
$463$	−12.0417	−	6.95225i	−0.559623	−	0.323099i	−0.752994	+	0.658027i	$0.771391\pi$
$464$	−26.3615			−1.22380
$465$		0			0
$466$			56.9511i			2.63821i
$467$	36.5921			1.69328			0.846640	−	0.532166i	$-0.178622\pi$
$467$	36.5921			1.69328			0.846640	+	0.532166i	$0.178622\pi$
$468$		0			0
$469$	−0.290831			−0.0134293
$470$			13.3900i			0.617634i
$471$		0			0
$472$	40.0571			1.84378
$473$	4.88311	+	2.81926i	0.224525	+	0.129630i
$474$		0			0
$475$	8.76415	+	5.05998i	0.402127	+	0.232168i
$476$		−	100.834i		−	4.62170i
$477$		0			0
$478$	14.7467	−	25.5421i	0.674500	−	1.16827i
$479$		−	31.7921i		−	1.45262i	−0.687368	−	0.726309i	$-0.741234\pi$
$479$		−	31.7921i		−	1.45262i	0.687368	−	0.726309i	$-0.258766\pi$
$480$		0			0
$481$	−15.6966	−	27.3078i	−0.715703	−	1.24513i
$482$	26.1151	−	45.2328i	1.18951	−	2.06030i
$483$		0			0
$484$	−50.6900			−2.30409
$485$	0.579790	+	1.00423i	0.0263269	+	0.0455995i
$486$		0			0
$487$	−1.10889	+	0.640220i	−0.0502488	+	0.0290111i	−0.524914	−	0.851155i	$-0.675902\pi$
$487$	−1.10889	+	0.640220i	−0.0502488	+	0.0290111i	0.474665	+	0.880166i	$0.342569\pi$
$488$	−14.3140	−	8.26421i	−0.647966	−	0.374103i
$489$		0			0
$490$	23.8716			1.07841
$491$	−10.8321	−	18.7618i	−0.488846	−	0.846706i	0.511072	−	0.859538i	$-0.329249\pi$
$491$	−10.8321	−	18.7618i	−0.488846	−	0.846706i	−0.999918	+	0.0128321i	$0.995915\pi$
$492$		0			0
$493$	8.69188	+	15.0548i	0.391462	+	0.678033i
$494$	0.0579366	−	30.2793i	0.00260669	−	1.36233i
$495$		0			0
$496$	−31.7282	−	18.3183i	−1.42464	−	0.822515i
$497$	4.02160			0.180393
$498$		0			0
$499$	−8.28148	−	4.78131i	−0.370730	−	0.214041i	0.303047	−	0.952975i	$-0.401996\pi$
$499$	−8.28148	−	4.78131i	−0.370730	−	0.214041i	−0.673777	+	0.738935i	$0.735329\pi$
$500$		−	52.4271i		−	2.34461i
$501$		0			0
$502$	26.7563	−	15.4477i	1.19419	−	0.689466i
$503$	12.2128	+	21.1531i	0.544540	+	0.943171i	0.998636	+	0.0522178i	$0.0166290\pi$
$503$	12.2128	+	21.1531i	0.544540	+	0.943171i	−0.454096	+	0.890953i	$0.650038\pi$
$504$		0			0
$505$	−3.59536	−	2.07578i	−0.159991	−	0.0923710i
$506$	0.222104	+	0.384696i	0.00987375	+	0.0171018i
$507$		0			0
$508$	−41.9798	+	72.7112i	−1.86255	+	3.22604i
$509$	12.9810	−	7.49461i	0.575375	−	0.332193i	−0.183919	−	0.982941i	$-0.558878\pi$
$509$	12.9810	−	7.49461i	0.575375	−	0.332193i	0.759293	+	0.650749i	$0.225545\pi$
$510$		0			0
$511$	4.62334	−	8.00785i	0.204524	−	0.354246i
$512$		−	47.1301i		−	2.08287i
$513$		0			0
$514$	−36.7093	+	21.1941i	−1.61918	+	0.934834i
$515$	−6.52171	+	3.76531i	−0.287381	+	0.165919i
$516$		0			0
$517$	0.919252	+	1.59219i	0.0404287	+	0.0700245i
$518$	−72.5995	+	41.9153i	−3.18984	+	1.84165i
$519$		0			0
$520$	−30.0748	+	17.2871i	−1.31887	+	0.758088i
$521$	−13.1757			−0.577239			−0.288619	−	0.957444i	$-0.593196\pi$
$521$	−13.1757			−0.577239			−0.288619	+	0.957444i	$0.593196\pi$
$522$		0			0
$523$	−4.56640	+	7.90924i	−0.199675	+	0.345847i	−0.948423	−	0.317008i	$-0.897322\pi$
$523$	−4.56640	+	7.90924i	−0.199675	+	0.345847i	0.748748	+	0.662854i	$0.230655\pi$
$524$	40.0247	−	69.3249i	1.74849	−	3.02847i
$525$		0			0
$526$		−	38.1217i		−	1.66218i
$527$			24.1595i			1.05240i
$528$		0			0
$529$	11.4381	−	19.8114i	0.497310	−	0.861366i
$530$	21.6979	−	37.5820i	0.942499	−	1.63246i
$531$		0			0
$532$	−56.5675			−2.45251
$533$	−6.03555	−	0.0115485i	−0.261429	−	0.000500220i
$534$		0			0
$535$	−6.62166	+	3.82302i	−0.286279	+	0.165283i
$536$	−0.275543	−	0.477255i	−0.0119017	−	0.0206143i
$537$		0			0
$538$	61.3184	−	35.4022i	2.64363	−	1.52630i
$539$	2.83855	−	1.63884i	0.122265	−	0.0705897i
$540$		0			0
$541$		−	1.26741i		−	0.0544903i	−0.999629	−	0.0272451i	$-0.991327\pi$
$541$		−	1.26741i		−	0.0544903i	0.999629	−	0.0272451i	$-0.00867347\pi$
$542$	−15.3525	+	26.5913i	−0.659445	+	1.14219i
$543$		0			0
$544$	43.3482	−	25.0271i	1.85854	−	1.07303i
$545$	−0.670041	+	1.16055i	−0.0287014	+	0.0497123i
$546$		0			0
$547$	16.8274	+	29.1459i	0.719487	+	1.24619i	0.961203	+	0.275840i	$0.0889561\pi$
$547$	16.8274	+	29.1459i	0.719487	+	1.24619i	−0.241717	+	0.970347i	$0.577711\pi$
$548$	−8.85242	−	5.11095i	−0.378157	−	0.218329i
$549$		0			0
$550$	−1.97079	−	3.41352i	−0.0840350	−	0.145553i
$551$	8.44571	−	4.87613i	0.359799	−	0.207730i
$552$		0			0
$553$			8.64400i			0.367580i
$554$	32.0608	+	18.5103i	1.36213	+	0.786427i
$555$		0			0
$556$	43.2961			1.83617
$557$	−36.9465	−	21.3311i	−1.56547	−	0.903826i	−0.996686	−	0.0813415i	$-0.974080\pi$
$557$	−36.9465	−	21.3311i	−1.56547	−	0.903826i	−0.568787	−	0.822485i	$-0.692587\pi$
$558$		0			0
$559$	−36.1574	+	20.7834i	−1.52930	+	0.879042i
$560$	22.2481	+	38.5349i	0.940155	+	1.62840i
$561$		0			0
$562$	−30.3841	−	52.6267i	−1.28167	−	2.21993i
$563$	−4.71871			−0.198870			−0.0994349	−	0.995044i	$-0.531703\pi$
$563$	−4.71871			−0.198870			−0.0994349	+	0.995044i	$0.531703\pi$
$564$		0			0
$565$	−1.97052	−	1.13768i	−0.0829006	−	0.0478627i
$566$	61.2835	−	35.3820i	2.57594	−	1.48722i
$567$		0			0
$568$	3.81020	+	6.59946i	0.159872	+	0.276907i
$569$	24.0375			1.00770			0.503851	−	0.863790i	$-0.331916\pi$
$569$	24.0375			1.00770			0.503851	+	0.863790i	$0.331916\pi$
$570$		0			0
$571$	5.86175	−	10.1528i	0.245306	−	0.424883i	−0.716911	−	0.697164i	$-0.754445\pi$
$571$	5.86175	−	10.1528i	0.245306	−	0.424883i	0.962218	+	0.272281i	$0.0877781\pi$
$572$	−4.15280	+	7.16118i	−0.173637	+	0.299424i
$573$		0			0
$574$			16.0636i			0.670481i
$575$	0.549051	−	0.950985i	0.0228970	−	0.0396588i
$576$		0			0
$577$		−	6.65490i		−	0.277047i	−0.990359	−	0.138523i	$-0.955764\pi$
$577$		−	6.65490i		−	0.277047i	0.990359	−	0.138523i	$-0.0442356\pi$
$578$	−36.7835	−	21.2370i	−1.52999	−	0.883342i
$579$		0			0
$580$	−16.8167	−	9.70911i	−0.698275	−	0.403149i
$581$	−9.40904			−0.390353
$582$		0			0
$583$		−	5.95845i		−	0.246774i
$584$	17.5212			0.725033
$585$		0			0
$586$	72.2623			2.98513
$587$		−	21.5477i		−	0.889367i	−0.895688	−	0.444684i	$-0.853316\pi$
$587$		−	21.5477i		−	0.889367i	0.895688	−	0.444684i	$-0.146684\pi$
$588$		0			0
$589$	13.5534			0.558460
$590$	17.5452	+	10.1297i	0.722325	+	0.417034i
$591$		0			0
$592$	−66.3006	−	38.2787i	−2.72494	−	1.57324i
$593$		−	0.0314626i		−	0.00129201i	−1.00000		0.000646006i	$-0.999794\pi$
$593$		−	0.0314626i		−	0.00129201i	1.00000		0.000646006i	$-0.000205630\pi$
$594$		0			0
$595$	14.6712	−	25.4113i	0.601462	−	1.04176i
$596$		−	27.3042i		−	1.11843i
$597$		0			0
$598$	−3.28556	−	0.00628662i	−0.134356	−	0.000257079i
$599$	−14.1320	+	24.4773i	−0.577416	+	1.00011i	0.418358	+	0.908282i	$0.362606\pi$
$599$	−14.1320	+	24.4773i	−0.577416	+	1.00011i	−0.995774	+	0.0918325i	$0.970728\pi$
$600$		0			0
$601$	−26.3337			−1.07417			−0.537087	−	0.843527i	$-0.680475\pi$
$601$	−26.3337			−1.07417			−0.537087	+	0.843527i	$0.680475\pi$
$602$	55.4987	+	96.1266i	2.26196	+	3.91783i
$603$		0			0
$604$	57.1627	−	33.0029i	2.32592	−	1.34287i
$605$	−12.7745	−	7.37536i	−0.519358	−	0.299851i
$606$		0			0
$607$	8.05575			0.326973			0.163486	−	0.986546i	$-0.447726\pi$
$607$	8.05575			0.326973			0.163486	+	0.986546i	$0.447726\pi$
$608$	−14.0402	−	24.3183i	−0.569404	−	0.986236i
$609$		0			0
$610$	−4.17974	−	7.23952i	−0.169233	−	0.293120i
$611$	−13.5984	−	0.0260192i	−0.550131	−	0.00105263i
$612$		0			0
$613$	31.5638	+	18.2234i	1.27485	+	0.736036i	0.975897	−	0.218232i	$-0.0700289\pi$
$613$	31.5638	+	18.2234i	1.27485	+	0.736036i	0.298954	+	0.954267i	$0.403362\pi$
$614$	−74.4534			−3.00469
$615$		0			0
$616$	10.9783	+	6.33830i	0.442327	+	0.255378i
$617$			11.4369i			0.460432i	0.973140	+	0.230216i	$0.0739433\pi$
$617$			11.4369i			0.460432i	−0.973140	+	0.230216i	$0.926057\pi$
$618$		0			0
$619$	32.5739	−	18.8065i	1.30925	−	0.755899i	0.327283	−	0.944926i	$-0.393867\pi$
$619$	32.5739	−	18.8065i	1.30925	−	0.755899i	0.981972	+	0.189028i	$0.0605336\pi$
$620$	−13.4935	−	23.3714i	−0.541911	−	0.938617i
$621$		0			0
$622$	−30.6573	−	17.7000i	−1.22925	−	0.709705i
$623$	29.9680	+	51.9061i	1.20064	+	2.07958i
$624$		0			0
$625$	−0.175637	+	0.304212i	−0.00702548	+	0.0121685i
$626$	26.4859	−	15.2917i	1.05859	−	0.611178i
$627$		0			0
$628$	−13.0535	+	22.6094i	−0.520893	+	0.902213i
$629$			50.4847i			2.01296i
$630$		0			0
$631$	−22.9975	+	13.2776i	−0.915516	+	0.528573i	−0.882202	−	0.470872i	$-0.843939\pi$
$631$	−22.9975	+	13.2776i	−0.915516	+	0.528573i	−0.0333140	+	0.999445i	$0.510606\pi$
$632$	−14.1848	+	8.18962i	−0.564242	+	0.325765i
$633$		0			0
$634$	39.0107	+	67.5685i	1.54931	+	2.68349i
$635$	−21.1589	+	12.2161i	−0.839664	+	0.484780i
$636$		0			0
$637$	−0.0463869	+	24.2431i	−0.00183792	+	0.960545i
$638$	−3.79838			−0.150379
$639$		0			0
$640$	3.15713	−	5.46831i	0.124797	−	0.216154i
$641$	−8.30243	+	14.3802i	−0.327926	+	0.567985i	−0.982100	−	0.188359i	$-0.939683\pi$
$641$	−8.30243	+	14.3802i	−0.327926	+	0.567985i	0.654174	+	0.756344i	$0.273016\pi$
$642$		0			0
$643$		−	3.67108i		−	0.144773i	−0.997377	−	0.0723866i	$-0.976938\pi$
$643$		−	3.67108i		−	0.144773i	0.997377	−	0.0723866i	$-0.0230615\pi$
$644$			6.13806i			0.241873i
$645$		0			0
$646$	−24.2660	+	42.0299i	−0.954733	+	1.65365i
$647$	3.97129	−	6.87848i	0.156128	−	0.270421i	−0.777341	−	0.629079i	$-0.783432\pi$
$647$	3.97129	−	6.87848i	0.156128	−	0.270421i	0.933469	+	0.358658i	$0.116766\pi$
$648$		0			0
$649$	2.78171			0.109192
$650$	29.1537	+	0.0557829i	1.14350	+	0.00218799i
$651$		0			0
$652$	0.515393	−	0.297562i	0.0201844	−	0.0116534i
$653$	−17.9235	−	31.0443i	−0.701399	−	1.21486i	−0.967975	−	0.251045i	$-0.919226\pi$
$653$	−17.9235	−	31.0443i	−0.701399	−	1.21486i	0.266576	−	0.963814i	$-0.414108\pi$
$654$		0			0
$655$	20.1735	−	11.6472i	0.788243	−	0.455092i
$656$	−12.7045	+	7.33494i	−0.496027	+	0.286381i
$657$		0			0
$658$			36.1920i			1.41091i
$659$	9.36059	−	16.2130i	0.364637	−	0.631570i	−0.624081	−	0.781360i	$-0.714526\pi$
$659$	9.36059	−	16.2130i	0.364637	−	0.631570i	0.988718	+	0.149790i	$0.0478598\pi$
$660$		0			0
$661$	−25.3674	+	14.6459i	−0.986679	+	0.569659i	−0.904280	−	0.426940i	$-0.859591\pi$
$661$	−25.3674	+	14.6459i	−0.986679	+	0.569659i	−0.0823989	+	0.996599i	$0.526258\pi$
$662$	−12.2749	+	21.2608i	−0.477078	+	0.826323i
$663$		0			0
$664$	−8.91444	−	15.4403i	−0.345947	−	0.599198i
$665$	−14.2557	−	8.23055i	−0.552813	−	0.319167i
$666$		0			0
$667$	−0.529102	−	0.916431i	−0.0204869	−	0.0354844i
$668$	−37.6617	+	21.7440i	−1.45717	+	0.841300i
$669$		0			0
$670$		−	0.278720i		−	0.0107679i
$671$	−0.994018	−	0.573897i	−0.0383737	−	0.0221550i
$672$		0			0
$673$	−9.27930			−0.357691			−0.178845	−	0.983877i	$-0.557236\pi$
$673$	−9.27930			−0.357691			−0.178845	+	0.983877i	$0.557236\pi$
$674$	36.5307	+	21.0910i	1.40711	+	0.812396i
$675$		0			0
$676$	−30.4114	−	53.1427i	−1.16967	−	2.04395i
$677$	21.0550	+	36.4684i	0.809210	+	1.40159i	0.913412	+	0.407037i	$0.133438\pi$
$677$	21.0550	+	36.4684i	0.809210	+	1.40159i	−0.104202	+	0.994556i	$0.533229\pi$
$678$		0			0
$679$	1.56712	+	2.71433i	0.0601406	+	0.104167i
$680$	55.6001			2.13217
$681$		0			0
$682$	−4.57165	−	2.63944i	−0.175057	−	0.101069i
$683$	−28.6729	+	16.5543i	−1.09714	+	0.633434i	−0.935468	−	0.353411i	$-0.885022\pi$
$683$	−28.6729	+	16.5543i	−1.09714	+	0.633434i	−0.161671	+	0.986845i	$0.551688\pi$
$684$		0			0
$685$	−1.48728	−	2.57604i	−0.0568260	−	0.0984256i
$686$	−2.65018			−0.101184
$687$		0			0
$688$	−50.6835	+	87.7864i	−1.93229	+	3.34683i
$689$	38.1246	+	22.1086i	1.45243	+	0.842272i
$690$		0			0
$691$		−	24.4135i		−	0.928733i	−0.885643	−	0.464366i	$-0.846282\pi$
$691$		−	24.4135i		−	0.928733i	0.885643	−	0.464366i	$-0.153718\pi$
$692$	−38.0740	+	65.9462i	−1.44736	+	2.50690i
$693$		0			0
$694$		−	8.48837i		−	0.322214i
$695$	10.9112	+	6.29957i	0.413884	+	0.238956i
$696$		0			0
$697$	8.37781	+	4.83693i	0.317332	+	0.183212i
$698$	60.4763			2.28906
$699$		0			0
$700$		−	54.4647i		−	2.05857i
$701$	−14.3928			−0.543607			−0.271803	−	0.962353i	$-0.587620\pi$
$701$	−14.3928			−0.543607			−0.271803	+	0.962353i	$0.587620\pi$
$702$		0			0
$703$	28.3219			1.06818
$704$			2.39294i			0.0901874i
$705$		0			0
$706$	3.83975			0.144511
$707$	−9.71794	−	5.61065i	−0.365481	−	0.211010i
$708$		0			0
$709$	29.2083	+	16.8634i	1.09694	+	0.633320i	0.935416	−	0.353548i	$-0.115025\pi$
$709$	29.2083	+	16.8634i	1.09694	+	0.633320i	0.161526	+	0.986868i	$0.448358\pi$
$710$			3.85412i			0.144643i
$711$		0			0
$712$	−56.7854	+	98.3553i	−2.12812	+	3.68602i
$713$		−	1.47066i		−	0.0550768i
$714$		0			0
$715$	−2.08850	+	1.20048i	−0.0781057	+	0.0448953i
$716$	23.0220	−	39.8753i	0.860373	−	1.49021i
$717$		0			0
$718$	−13.0683			−0.487704
$719$	−17.3402	−	30.0341i	−0.646679	−	1.12008i	−0.983911	−	0.178659i	$-0.942824\pi$
$719$	−17.3402	−	30.0341i	−0.646679	−	1.12008i	0.337232	−	0.941422i	$-0.390509\pi$
$720$		0			0
$721$	−17.6276	+	10.1773i	−0.656487	+	0.379023i
$722$	−19.0442	−	10.9952i	−0.708751	−	0.409197i
$723$		0			0
$724$	−51.6363			−1.91905
$725$	4.69487	+	8.13175i	0.174363	+	0.302006i
$726$		0			0
$727$	−2.57894	−	4.46685i	−0.0956474	−	0.165666i	0.814231	−	0.580541i	$-0.197159\pi$
$727$	−2.57894	−	4.46685i	−0.0956474	−	0.165666i	−0.909879	+	0.414875i	$0.863825\pi$
$728$	−81.2896	+	46.7254i	−3.01279	+	1.73176i
$729$		0			0
$730$	7.67437	+	4.43080i	0.284041	+	0.163991i
$731$	66.8452			2.47236
$732$		0			0
$733$	15.9989	+	9.23695i	0.590931	+	0.341174i	0.765466	−	0.643477i	$-0.222509\pi$
$733$	15.9989	+	9.23695i	0.590931	+	0.341174i	−0.174534	+	0.984651i	$0.555842\pi$
$734$		−	10.8719i		−	0.401288i
$735$		0			0
$736$	−2.63874	+	1.52348i	−0.0972653	+	0.0561561i
$737$	−0.0191347	−	0.0331423i	−0.000704837	−	0.00122081i
$738$		0			0
$739$	40.0149	+	23.1026i	1.47197	+	0.849844i	0.999504	−	0.0315024i	$-0.0100292\pi$
$739$	40.0149	+	23.1026i	1.47197	+	0.849844i	0.472470	+	0.881347i	$0.343363\pi$
$740$	−28.1966	−	48.8379i	−1.03653	−	1.79532i
$741$		0			0
$742$	58.6477	−	101.581i	2.15302	−	3.72915i
$743$	−21.0503	+	12.1534i	−0.772260	+	0.445865i	−0.833680	−	0.552247i	$-0.813770\pi$
$743$	−21.0503	+	12.1534i	−0.772260	+	0.445865i	0.0614202	+	0.998112i	$0.480437\pi$
$744$		0			0
$745$	3.97275	−	6.88101i	0.145550	−	0.252101i
$746$		−	70.5910i		−	2.58452i
$747$		0			0
$748$	11.4907	−	6.63417i	0.420142	−	0.242569i
$749$	−17.8978	+	10.3333i	−0.653971	+	0.377570i
$750$		0			0
$751$	15.8328	+	27.4232i	0.577746	+	1.00069i	0.995737	+	0.0922350i	$0.0294011\pi$
$751$	15.8328	+	27.4232i	0.577746	+	1.00069i	−0.417991	+	0.908451i	$0.637266\pi$
$752$	−28.6238	+	16.5259i	−1.04380	+	0.602639i
$753$		0			0
$754$	14.0938	−	24.3036i	0.513264	−	0.885084i
$755$	19.2076			0.699036
$756$		0			0
$757$	−10.5340	+	18.2454i	−0.382863	+	0.663139i	−0.991470	−	0.130333i	$-0.958395\pi$
$757$	−10.5340	+	18.2454i	−0.382863	+	0.663139i	0.608607	+	0.793472i	$0.291729\pi$
$758$	5.84955	−	10.1317i	0.212465	−	0.368001i
$759$		0			0
$760$		−	31.1916i		−	1.13144i
$761$			11.8420i			0.429272i	0.976694	+	0.214636i	$0.0688566\pi$
$761$			11.8420i			0.429272i	−0.976694	+	0.214636i	$0.931143\pi$
$762$		0			0
$763$	−1.81106	+	3.13686i	−0.0655649	+	0.113562i
$764$	5.14737	−	8.91550i	0.186225	−	0.322552i
$765$		0			0
$766$	49.9318			1.80411
$767$	−10.3215	+	17.7986i	−0.372686	+	0.642669i
$768$		0			0
$769$	−23.3468	+	13.4793i	−0.841906	+	0.486075i	−0.857912	−	0.513797i	$-0.828238\pi$
$769$	−23.3468	+	13.4793i	−0.841906	+	0.486075i	0.0160056	+	0.999872i	$0.494905\pi$
$770$	3.20569	+	5.55241i	0.115525	+	0.200095i
$771$		0			0
$772$	−12.4377	+	7.18091i	−0.447643	+	0.258447i
$773$	30.2027	−	17.4375i	1.08631	−	0.627184i	0.153722	−	0.988114i	$-0.450874\pi$
$773$	30.2027	−	17.4375i	1.08631	−	0.627184i	0.932593	+	0.360930i	$0.117541\pi$
$774$		0			0
$775$			13.0496i			0.468756i
$776$	−2.96949	+	5.14330i	−0.106598	+	0.184634i
$777$		0			0
$778$	−9.94703	+	5.74292i	−0.356618	+	0.205894i
$779$	2.71351	−	4.69994i	0.0972216	−	0.168393i
$780$		0			0
$781$	0.264594	+	0.458291i	0.00946792	+	0.0163989i
$782$	4.56061	+	2.63307i	0.163087	+	0.0941583i
$783$		0			0
$784$	29.4623	+	51.0302i	1.05223	+	1.82251i
$785$	−6.57931	+	3.79856i	−0.234825	+	0.135577i
$786$		0			0
$787$		−	33.3246i		−	1.18789i	−0.804504	−	0.593947i	$-0.797569\pi$
$787$		−	33.3246i		−	1.18789i	0.804504	−	0.593947i	$-0.202431\pi$
$788$	41.6658	+	24.0558i	1.48428	+	0.856952i
$789$		0			0
$790$	−8.28403			−0.294732
$791$	−5.32616	−	3.07506i	−0.189376	−	0.109336i
$792$		0			0
$793$	7.36030	−	4.23072i	0.261372	−	0.150237i
$794$	8.67147	+	15.0194i	0.307739	+	0.533019i
$795$		0			0
$796$	16.1009	+	27.8876i	0.570681	+	0.988449i
$797$	−38.5783			−1.36651			−0.683257	−	0.730178i	$-0.739437\pi$
$797$	−38.5783			−1.36651			−0.683257	+	0.730178i	$0.739437\pi$
$798$		0			0
$799$	18.8756	+	10.8978i	0.667769	+	0.385537i
$800$	23.4143	−	13.5182i	0.827820	−	0.477942i
$801$		0			0
$802$	18.9843	+	32.8818i	0.670359	+	1.16110i
$803$	1.21674			0.0429377
$804$		0			0
$805$	−0.893085	+	1.54687i	−0.0314771	+	0.0545199i
$806$	33.8512	−	19.4577i	1.19236	−	0.685369i
$807$		0			0
$808$		−	21.2629i		−	0.748026i
$809$	−17.9720	+	31.1284i	−0.631862	+	1.09442i	0.355309	+	0.934749i	$0.384376\pi$
$809$	−17.9720	+	31.1284i	−0.631862	+	1.09442i	−0.987171	+	0.159668i	$0.948958\pi$
$810$		0			0
$811$		−	27.4003i		−	0.962156i	−0.876678	−	0.481078i	$-0.840245\pi$
$811$		−	27.4003i		−	0.962156i	0.876678	−	0.481078i	$-0.159755\pi$
$812$	−45.4540	−	26.2429i	−1.59512	−	0.920945i
$813$		0			0
$814$	−9.55311	−	5.51549i	−0.334836	−	0.193318i
$815$	0.173181			0.00606625
$816$		0			0
$817$		−	37.5001i		−	1.31196i
$818$	−38.6277			−1.35059
$819$		0			0
$820$	−10.8060			−0.377363
$821$			37.1277i			1.29576i	0.761741	+	0.647882i	$0.224345\pi$
$821$			37.1277i			1.29576i	−0.761741	+	0.647882i	$0.775655\pi$
$822$		0			0
$823$	−14.0029			−0.488111			−0.244056	−	0.969761i	$-0.578478\pi$
$823$	−14.0029			−0.488111			−0.244056	+	0.969761i	$0.578478\pi$
$824$	−33.4020	−	19.2847i	−1.16361	−	0.671813i
$825$		0			0
$826$	47.4232	+	27.3798i	1.65006	+	0.952664i
$827$			16.4147i			0.570796i	0.958409	+	0.285398i	$0.0921258\pi$
$827$			16.4147i			0.570796i	−0.958409	+	0.285398i	$0.907874\pi$
$828$		0			0
$829$	18.1805	−	31.4895i	0.631435	−	1.09368i	−0.355824	−	0.934553i	$-0.615800\pi$
$829$	18.1805	−	31.4895i	0.631435	−	1.09368i	0.987259	−	0.159124i	$-0.0508669\pi$
$830$		−	9.01720i		−	0.312992i
$831$		0			0
$832$	−15.3110	−	8.87894i	−0.530815	−	0.307822i
$833$	19.4285	−	33.6512i	0.673159	−	1.16595i
$834$		0			0
$835$	−12.6549			−0.437942
$836$	−3.72176	−	6.44628i	−0.128720	−	0.222949i
$837$		0			0
$838$	28.5660	−	16.4926i	0.986796	−	0.569727i
$839$	−26.3679	−	15.2235i	−0.910321	−	0.525574i	−0.0297863	−	0.999556i	$-0.509483\pi$
$839$	−26.3679	−	15.2235i	−0.910321	−	0.525574i	−0.880534	+	0.473982i	$0.842816\pi$
$840$		0			0
$841$	−19.9514			−0.687980
$842$	17.7234	+	30.6978i	0.610788	+	1.05792i
$843$		0			0
$844$	−54.3308	−	94.1037i	−1.87014	−	3.23918i
$845$	0.0681844	−	17.8175i	0.00234561	−	0.612939i
$846$		0			0
$847$	−34.5284	−	19.9350i	−1.18641	−	0.684974i
$848$	107.119			3.67847
$849$		0			0
$850$	−40.4675	−	23.3639i	−1.38802	−	0.801376i
$851$		−	3.07316i		−	0.105347i
$852$		0			0
$853$	−9.06197	+	5.23193i	−0.310276	+	0.179138i	−0.647050	−	0.762448i	$-0.723998\pi$
$853$	−9.06197	+	5.23193i	−0.310276	+	0.179138i	0.336774	+	0.941586i	$0.390664\pi$
$854$	−11.2975	−	19.5678i	−0.386592	−	0.669596i
$855$		0			0
$856$	−33.9139	−	19.5802i	−1.15915	−	0.669238i
$857$	−3.72589	−	6.45343i	−0.127274	−	0.220445i	0.795346	−	0.606156i	$-0.207289\pi$
$857$	−3.72589	−	6.45343i	−0.127274	−	0.220445i	−0.922620	+	0.385711i	$0.873956\pi$
$858$		0			0
$859$	−19.7941	+	34.2843i	−0.675365	+	1.16977i	0.300997	+	0.953625i	$0.402681\pi$
$859$	−19.7941	+	34.2843i	−0.675365	+	1.16977i	−0.976362	+	0.216141i	$0.930653\pi$
$860$	−64.6646	+	37.3341i	−2.20505	+	1.27308i
$861$		0			0
$862$	−29.6548	+	51.3636i	−1.01005	+	1.74945i
$863$		−	39.0451i		−	1.32911i	−0.747240	−	0.664555i	$-0.768621\pi$
$863$		−	39.0451i		−	1.32911i	0.747240	−	0.664555i	$-0.231379\pi$
$864$		0			0
$865$	−19.1903	+	11.0795i	−0.652488	+	0.376714i
$866$	34.1657	−	19.7256i	1.16100	−	0.670302i
$867$		0			0
$868$	−36.4717	−	63.1708i	−1.23793	−	2.14416i
$869$	−0.985047	+	0.568717i	−0.0334154	+	0.0192924i
$870$		0			0
$871$	0.283057		0.000541604i	0.00959103		1.83516e-5i
$872$	−6.86345			−0.232426
$873$		0			0
$874$	1.47715	−	2.55849i	0.0499653	−	0.0865424i
$875$	20.6181	−	35.7117i	0.697020	−	1.20727i
$876$		0			0
$877$			25.3962i			0.857567i	0.903407	+	0.428784i	$0.141058\pi$
$877$			25.3962i			0.857567i	−0.903407	+	0.428784i	$0.858942\pi$
$878$		−	70.7722i		−	2.38844i
$879$		0			0
$880$	−2.92755	+	5.07067i	−0.0986878	+	0.170932i
$881$	−20.1610	+	34.9200i	−0.679243	+	1.17648i	0.295966	+	0.955198i	$0.404358\pi$
$881$	−20.1610	+	34.9200i	−0.679243	+	1.17648i	−0.975209	+	0.221285i	$0.928975\pi$
$882$		0			0
$883$	2.60260			0.0875845			0.0437923	−	0.999041i	$-0.486056\pi$
$883$	2.60260			0.0875845			0.0437923	+	0.999041i	$0.486056\pi$
$884$	−0.187779	+	98.1383i	−0.00631568	+	3.30075i
$885$		0			0
$886$	−1.05005	+	0.606247i	−0.0352772	+	0.0203673i
$887$	13.8663	+	24.0172i	0.465585	+	0.806418i	0.999228	−	0.0392926i	$-0.0125105\pi$
$887$	13.8663	+	24.0172i	0.465585	+	0.806418i	−0.533642	+	0.845710i	$0.679177\pi$
$888$		0			0
$889$	−57.1906	+	33.0190i	−1.91811	+	1.10742i
$890$	−49.7446	+	28.7200i	−1.66744	+	0.962698i
$891$		0			0
$892$			45.5619i			1.52552i
$893$	6.11366	−	10.5892i	0.204586	−	0.354353i
$894$		0			0
$895$	11.6037	−	6.69938i	0.387868	−	0.223936i
$896$	8.53345	−	14.7804i	0.285083	−	0.493777i
$897$		0			0
$898$	−48.8188	−	84.5566i	−1.62910	−	2.82169i
$899$	10.8907	+	6.28773i	0.363224	+	0.209708i
$900$		0			0
$901$	−35.3190	−	61.1742i	−1.17665	−	2.03801i
$902$	−1.83056	+	1.05688i	−0.0609511	+	0.0351901i
$903$		0			0
$904$		−	11.6537i		−	0.387595i
$905$	−13.0130	−	7.51306i	−0.432567	−	0.249742i
$906$		0			0
$907$	−57.1851			−1.89880			−0.949400	−	0.314068i	$-0.898308\pi$
$907$	−57.1851			−1.89880			−0.949400	+	0.314068i	$0.898308\pi$
$908$	109.264	+	63.0839i	3.62607	+	2.09351i
$909$		0			0
$910$	−47.4212	−	0.0907362i	−1.57200	−	0.00300788i
$911$	−19.8268	−	34.3411i	−0.656893	−	1.13777i	−0.981416	−	0.191894i	$-0.938537\pi$
$911$	−19.8268	−	34.3411i	−0.656893	−	1.13777i	0.324523	−	0.945878i	$-0.394796\pi$
$912$		0			0
$913$	−0.619051	−	1.07223i	−0.0204876	−	0.0354856i
$914$	−80.0275			−2.64707
$915$		0			0
$916$	26.1668	+	15.1074i	0.864576	+	0.499163i
$917$	54.5271	−	31.4813i	1.80064	−	1.03960i
$918$		0			0
$919$	−2.93836	−	5.08939i	−0.0969276	−	0.167884i	0.813484	−	0.581587i	$-0.197568\pi$
$919$	−2.93836	−	5.08939i	−0.0969276	−	0.167884i	−0.910411	+	0.413704i	$0.864235\pi$
$920$	−3.38455			−0.111585
$921$		0			0
$922$	−51.8186	+	89.7524i	−1.70655	+	2.95584i
$923$	−3.91410	−	0.00748928i	−0.128834	−	0.000246513i
$924$		0			0
$925$			27.2690i			0.896601i
$926$	18.0088	−	31.1921i	0.591805	−	1.02504i
$927$		0			0
$928$		−	26.0541i		−	0.855269i
$929$	5.62125	+	3.24543i	0.184427	+	0.106479i	0.589371	−	0.807862i	$-0.299376\pi$
$929$	5.62125	+	3.24543i	0.184427	+	0.106479i	−0.404944	+	0.914342i	$0.632709\pi$
$930$		0			0
$931$	−18.8783	−	10.8994i	−0.618711	−	0.357213i
$932$	−103.552			−3.39195
$933$		0			0
$934$			94.7864i			3.10151i
$935$	3.86107			0.126271
$936$		0			0
$937$	−34.5116			−1.12744			−0.563722	−	0.825964i	$-0.690631\pi$
$937$	−34.5116			−1.12744			−0.563722	+	0.825964i	$0.690631\pi$
$938$		−	0.753355i		−	0.0245979i
$939$		0			0
$940$	−24.3464			−0.794093
$941$	−16.5489	−	9.55449i	−0.539477	−	0.311467i	0.205390	−	0.978680i	$-0.434154\pi$
$941$	−16.5489	−	9.55449i	−0.539477	−	0.311467i	−0.744867	+	0.667213i	$0.767487\pi$
$942$		0			0
$943$	−0.509984	−	0.294439i	−0.0166074	−	0.00958826i
$944$			50.0085i			1.62764i
$945$		0			0
$946$	−7.30288	+	12.6490i	−0.237437	+	0.411253i
$947$		−	48.1442i		−	1.56448i	−0.622980	−	0.782238i	$-0.714078\pi$
$947$		−	48.1442i		−	1.56448i	0.622980	−	0.782238i	$-0.285922\pi$
$948$		0			0
$949$	−4.51467	+	7.78519i	−0.146552	+	0.252718i
$950$	−13.1071	+	22.7022i	−0.425252	+	0.736558i
$951$		0			0
$952$	150.282			4.87068
$953$	14.5624	+	25.2228i	0.471721	+	0.817045i	0.999477	−	0.0323512i	$-0.0102995\pi$
$953$	14.5624	+	25.2228i	0.471721	+	0.817045i	−0.527755	+	0.849396i	$0.676966\pi$
$954$		0			0
$955$	2.59440	−	1.49788i	0.0839528	−	0.0484702i
$956$	46.4421	+	26.8134i	1.50205	+	0.867206i
$957$		0			0
$958$	82.3527			2.66070
$959$	−4.01999	−	6.96282i	−0.129812	−	0.224841i
$960$		0			0
$961$	−6.76147	−	11.7112i	−0.218112	−	0.377781i
$962$	70.7369	−	40.6597i	2.28065	−	1.31092i
$963$		0			0
$964$	82.2448	+	47.4841i	2.64893	+	1.52936i
$965$	−4.17927			−0.134536
$966$		0			0
$967$	36.5969	+	21.1292i	1.17688	+	0.679469i	0.955290	−	0.295671i	$-0.0955433\pi$
$967$	36.5969	+	21.1292i	1.17688	+	0.679469i	0.221586	+	0.975141i	$0.428877\pi$
$968$		−	75.5483i		−	2.42821i
$969$		0			0
$970$	−2.60130	+	1.50186i	−0.0835226	+	0.0482218i
$971$	13.7985	+	23.8997i	0.442816	+	0.766979i	0.997897	−	0.0648168i	$-0.0206463\pi$
$971$	13.7985	+	23.8997i	0.442816	+	0.766979i	−0.555082	+	0.831796i	$0.687313\pi$
$972$		0			0
$973$	29.4919	+	17.0272i	0.945468	+	0.545866i
$974$	−1.65840	−	2.87243i	−0.0531384	−	0.0920385i
$975$		0			0
$976$	10.3173	−	17.8701i	0.330248	−	0.572006i
$977$	34.5310	−	19.9365i	1.10475	−	0.637825i	0.167282	−	0.985909i	$-0.446501\pi$
$977$	34.5310	−	19.9365i	1.10475	−	0.637825i	0.937463	+	0.348084i	$0.113168\pi$
$978$		0			0
$979$	−3.94339	+	6.83015i	−0.126031	+	0.218293i
$980$			43.4046i			1.38651i
$981$		0			0
$982$	48.5996	−	28.0590i	1.55087	−	0.895398i
$983$	7.38449	−	4.26344i	0.235529	−	0.135983i	−0.377591	−	0.925972i	$-0.623248\pi$
$983$	7.38449	−	4.26344i	0.235529	−	0.135983i	0.613120	+	0.789990i	$0.289914\pi$
$984$		0			0
$985$	7.00021	+	12.1247i	0.223045	+	0.386326i
$986$	−38.9972	+	22.5150i	−1.24192	+	0.717024i
$987$		0			0
$988$	55.0555	+	0.105344i	1.75155	+	0.00335143i
$989$	−4.06908			−0.129389
$990$		0			0
$991$	26.2767	−	45.5127i	0.834708	−	1.44576i	−0.0595594	−	0.998225i	$-0.518970\pi$
$991$	26.2767	−	45.5127i	0.834708	−	1.44576i	0.894268	−	0.447532i	$-0.147697\pi$
$992$	18.1047	−	31.3582i	0.574824	−	0.995624i
$993$		0			0
$994$			10.4174i			0.330419i
$995$			9.37068i			0.297071i
$996$		0			0
$997$	2.25570	−	3.90698i	0.0714387	−	0.123735i	−0.828093	−	0.560590i	$-0.810574\pi$
$997$	2.25570	−	3.90698i	0.0714387	−	0.123735i	0.899532	+	0.436855i	$0.143908\pi$
$998$	12.3853	−	21.4519i	0.392049	−	0.679049i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.l.b.199.11		22
3.2	odd	2		117.2.l.b.4.1	✓	22
9.2	odd	6		117.2.r.b.43.1	yes	22
9.7	even	3		351.2.r.b.316.11		22
13.10	even	6		351.2.r.b.10.11		22
39.23	odd	6		117.2.r.b.49.1	yes	22
117.88	even	6	inner	351.2.l.b.127.1		22
117.101	odd	6		117.2.l.b.88.11	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.1	✓	22	3.2	odd	2
117.2.l.b.88.11	yes	22	117.101	odd	6
117.2.r.b.43.1	yes	22	9.2	odd	6
117.2.r.b.49.1	yes	22	39.23	odd	6
351.2.l.b.127.1		22	117.88	even	6	inner
351.2.l.b.199.11		22	1.1	even	1	trivial
351.2.r.b.10.11		22	13.10	even	6
351.2.r.b.316.11		22	9.7	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+2.59035i q^{2} -4.70993 q^{4} +(-1.18696 - 0.685292i) q^{5} +(-3.20825 - 1.85228i) q^{7} -7.01967i q^{8} +(1.77515 - 3.07465i) q^{10} -0.487471i q^{11} +(3.11904 + 1.80875i) q^{13} +(4.79807 - 8.31050i) q^{14} +8.76356 q^{16} +(-2.88951 - 5.00477i) q^{17} +(-2.80767 + 1.62101i) q^{19} +(5.59049 + 3.22767i) q^{20} +1.26272 q^{22} +(0.175893 + 0.304656i) q^{23} +(-1.56075 - 2.70330i) q^{25} +(-4.68529 + 8.07942i) q^{26} +(15.1106 + 8.72412i) q^{28} -3.00808 q^{29} +(-3.62047 - 2.09028i) q^{31} +8.66137i q^{32} +(12.9641 - 7.48484i) q^{34} +(2.53871 + 4.39718i) q^{35} +(-7.56549 - 4.36794i) q^{37} +(-4.19899 - 7.27286i) q^{38} +(-4.81052 + 8.33206i) q^{40} +(-1.44970 + 0.836982i) q^{41} +(-5.78344 + 10.0172i) q^{43} +2.29595i q^{44} +(-0.789167 + 0.455626i) q^{46} +(-3.26623 + 1.88576i) q^{47} +(3.36191 + 5.82301i) q^{49} +(7.00250 - 4.04289i) q^{50} +(-14.6905 - 8.51907i) q^{52} +12.2232 q^{53} +(-0.334060 + 0.578609i) q^{55} +(-13.0024 + 22.5208i) q^{56} -7.79200i q^{58} +5.70642i q^{59} +(1.17729 - 2.03913i) q^{61} +(5.41456 - 9.37829i) q^{62} -4.90889 q^{64} +(-2.46266 - 4.28437i) q^{65} +(0.0679883 - 0.0392530i) q^{67} +(13.6094 + 23.5721i) q^{68} +(-11.3902 + 6.57615i) q^{70} +(-0.940139 + 0.542789i) q^{71} +2.49602i q^{73} +(11.3145 - 19.5973i) q^{74} +(13.2239 - 7.63484i) q^{76} +(-0.902935 + 1.56393i) q^{77} +(-1.16667 - 2.02073i) q^{79} +(-10.4020 - 6.00559i) q^{80} +(-2.16808 - 3.75522i) q^{82} +(2.19957 - 1.26992i) q^{83} +7.92062i q^{85} +(-25.9481 - 14.9812i) q^{86} -3.42189 q^{88} +(-14.0114 - 8.08948i) q^{89} +(-6.65636 - 11.5803i) q^{91} +(-0.828445 - 1.43491i) q^{92} +(-4.88478 - 8.46068i) q^{94} +4.44346 q^{95} +(-0.732699 - 0.423024i) q^{97} +(-15.0836 + 8.70854i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 20 q^{4} + 3 q^{5} - 6 q^{7} - 7 q^{10} + 9 q^{14} + 24 q^{16} - 9 q^{17} - 6 q^{19} + 24 q^{20} + 26 q^{22} - 6 q^{23} + 4 q^{25} + 12 q^{26} + 3 q^{28} - 48 q^{29} - 27 q^{31} + 15 q^{34} + 27 q^{35}+ \cdots - 117 q^{98}+O(q^{100}) \) 22 * q - 20 * q^4 + 3 * q^5 - 6 * q^7 - 7 * q^10 + 9 * q^14 + 24 * q^16 - 9 * q^17 - 6 * q^19 + 24 * q^20 + 26 * q^22 - 6 * q^23 + 4 * q^25 + 12 * q^26 + 3 * q^28 - 48 * q^29 - 27 * q^31 + 15 * q^34 + 27 * q^35 + 6 * q^37 - 21 * q^38 + 13 * q^40 - 6 * q^41 - 4 * q^43 - 15 * q^46 + 6 * q^47 + 7 * q^49 - 18 * q^50 - 22 * q^52 + 24 * q^53 - 13 * q^55 + 9 * q^56 + 3 * q^61 - 24 * q^64 + 57 * q^65 - 45 * q^67 + 69 * q^68 - 24 * q^70 - 9 * q^71 + 6 * q^74 + 18 * q^76 - 42 * q^77 - 6 * q^79 - 105 * q^80 - 16 * q^82 - 42 * q^83 - 45 * q^86 + 22 * q^88 + 30 * q^89 + 15 * q^91 + 3 * q^92 + 44 * q^94 - 6 * q^95 - 27 * q^97 - 117 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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