LMFDB - Embedded newform 513.2.k.a.8.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [513,2,Mod(8,513)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("513.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(513, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.k (of order $6$, 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:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 171)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			8.16
Character	$\chi$	$=$	513.8
Dual form			513.2.k.a.449.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.07540 + 1.86265i) q^{2} +(-1.31298 + 2.27414i) q^{4} -3.02519i q^{5} +(1.86959 - 3.23822i) q^{7} -1.34630 q^{8} +(5.63486 - 3.25329i) q^{10} +(-4.41421 - 2.54855i) q^{11} +(1.79312 + 1.03526i) q^{13} +8.04222 q^{14} +(1.17814 + 2.04060i) q^{16} +(4.50968 + 2.60366i) q^{17} +(4.31830 - 0.593520i) q^{19} +(6.87970 + 3.97200i) q^{20} -10.9628i q^{22} +(-5.49727 - 3.17385i) q^{23} -4.15176 q^{25} +4.45327i q^{26} +(4.90944 + 8.50340i) q^{28} -1.61159 q^{29} +(-1.31340 + 0.758293i) q^{31} +(-3.88025 + 6.72078i) q^{32} +11.1999i q^{34} +(-9.79622 - 5.65585i) q^{35} +4.54399i q^{37} +(5.74943 + 7.40521i) q^{38} +4.07280i q^{40} -2.02559 q^{41} +(0.973250 + 1.68572i) q^{43} +(11.5915 - 6.69236i) q^{44} -13.6527i q^{46} +3.42876i q^{47} +(-3.49070 - 6.04608i) q^{49} +(-4.46481 - 7.73327i) q^{50} +(-4.70864 + 2.71853i) q^{52} +(4.49378 + 7.78345i) q^{53} +(-7.70983 + 13.3538i) q^{55} +(-2.51702 + 4.35961i) q^{56} +(-1.73310 - 3.00183i) q^{58} +7.20907 q^{59} -7.75044 q^{61} +(-2.82487 - 1.63094i) q^{62} -11.9787 q^{64} +(3.13185 - 5.42452i) q^{65} +(-0.569888 - 0.329025i) q^{67} +(-11.8422 + 6.83709i) q^{68} -24.3292i q^{70} +(2.68449 - 4.64968i) q^{71} +(-1.90331 + 3.29663i) q^{73} +(-8.46387 + 4.88662i) q^{74} +(-4.32008 + 10.5997i) q^{76} +(-16.5055 + 9.52945i) q^{77} +(9.08384 - 5.24456i) q^{79} +(6.17320 - 3.56410i) q^{80} +(-2.17832 - 3.77297i) q^{82} +(4.06246 + 2.34546i) q^{83} +(7.87657 - 13.6426i) q^{85} +(-2.09327 + 3.62565i) q^{86} +(5.94284 + 3.43110i) q^{88} +(-1.49289 - 2.58575i) q^{89} +(6.70478 - 3.87100i) q^{91} +(14.4356 - 8.33438i) q^{92} +(-6.38657 + 3.68729i) q^{94} +(-1.79551 - 13.0637i) q^{95} +(-4.72908 + 2.73034i) q^{97} +(7.50782 - 13.0039i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{2} - 15 q^{4} - q^{7} - 12 q^{8} - 6 q^{10} + 9 q^{11} - 6 q^{13} + 6 q^{14} - 9 q^{16} + 27 q^{17} + q^{19} - 9 q^{20} - 9 q^{23} - 22 q^{25} + 2 q^{28} + 24 q^{29} + 12 q^{31} + 15 q^{32}+ \cdots + 84 q^{98}+O(q^{100}) $ 36 * q + 3 * q^2 - 15 * q^4 - q^7 - 12 * q^8 - 6 * q^10 + 9 * q^11 - 6 * q^13 + 6 * q^14 - 9 * q^16 + 27 * q^17 + q^19 - 9 * q^20 - 9 * q^23 - 22 * q^25 + 2 * q^28 + 24 * q^29 + 12 * q^31 + 15 * q^32 - 15 * q^35 + 18 * q^38 - 36 * q^41 + 3 * q^43 - 66 * q^44 - 9 * q^49 - 3 * q^50 + 15 * q^52 + 12 * q^53 - 7 * q^55 - 6 * q^56 - 6 * q^58 + 18 * q^59 - 16 * q^61 + 12 * q^62 + 12 * q^64 + 18 * q^65 + 27 * q^67 - 60 * q^68 - 9 * q^71 - 18 * q^73 - 90 * q^74 - 23 * q^76 + 6 * q^77 - 6 * q^79 + 12 * q^80 - 9 * q^82 + 9 * q^83 + 11 * q^85 - 51 * q^86 + 3 * q^88 + 18 * q^89 + 27 * q^91 + 93 * q^92 + 12 * q^94 + 24 * q^97 + 84 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.07540	+	1.86265i	0.760424	+	1.31709i	0.942632	+	0.333832i	$0.108342\pi$
$2$	1.07540	+	1.86265i	0.760424	+	1.31709i	−0.182209	+	0.983260i	$0.558325\pi$
$3$		0			0
$3$		0			0
$4$	−1.31298	+	2.27414i	−0.656488	+	1.13707i
$5$		−	3.02519i		−	1.35290i	−0.736486	−	0.676452i	$-0.763516\pi$
$5$		−	3.02519i		−	1.35290i	0.736486	−	0.676452i	$-0.236484\pi$
$6$		0			0
$7$	1.86959	−	3.23822i	0.706637	−	1.22393i	−0.259460	−	0.965754i	$-0.583545\pi$
$7$	1.86959	−	3.23822i	0.706637	−	1.22393i	0.966097	−	0.258178i	$-0.0831220\pi$
$8$	−1.34630			−0.475988
$9$		0			0
$10$	5.63486	−	3.25329i	1.78190	−	1.02878i
$11$	−4.41421	−	2.54855i	−1.33093	−	0.768415i	−0.345492	−	0.938422i	$-0.612288\pi$
$11$	−4.41421	−	2.54855i	−1.33093	−	0.768415i	−0.985443	+	0.170006i	$0.945621\pi$
$12$		0			0
$13$	1.79312	+	1.03526i	0.497321	+	0.287129i	0.727607	−	0.685995i	$-0.240633\pi$
$13$	1.79312	+	1.03526i	0.497321	+	0.287129i	−0.230285	+	0.973123i	$0.573966\pi$
$14$	8.04222			2.14937
$15$		0			0
$16$	1.17814	+	2.04060i	0.294535	+	0.510150i
$17$	4.50968	+	2.60366i	1.09376	+	0.631481i	0.934574	−	0.355768i	$-0.115781\pi$
$17$	4.50968	+	2.60366i	1.09376	+	0.631481i	0.159183	+	0.987249i	$0.449114\pi$
$18$		0			0
$19$	4.31830	−	0.593520i	0.990686	−	0.136163i
$19$	4.31830	−	0.593520i	0.990686	−	0.136163i
$20$	6.87970	+	3.97200i	1.53835	+	0.888166i
$21$		0			0
$22$		−	10.9628i		−	2.33728i
$23$	−5.49727	−	3.17385i	−1.14626	−	0.661794i	−0.198287	−	0.980144i	$-0.563538\pi$
$23$	−5.49727	−	3.17385i	−1.14626	−	0.661794i	−0.947973	+	0.318350i	$0.896871\pi$
$24$		0			0
$25$	−4.15176			−0.830352
$26$			4.45327i			0.873357i
$27$		0			0
$28$	4.90944	+	8.50340i	0.927797	+	1.60699i
$29$	−1.61159			−0.299265			−0.149632	−	0.988742i	$-0.547809\pi$
$29$	−1.61159			−0.299265			−0.149632	+	0.988742i	$0.547809\pi$
$30$		0			0
$31$	−1.31340	+	0.758293i	−0.235894	+	0.136194i	−0.613288	−	0.789859i	$-0.710154\pi$
$31$	−1.31340	+	0.758293i	−0.235894	+	0.136194i	0.377394	+	0.926053i	$0.376820\pi$
$32$	−3.88025	+	6.72078i	−0.685937	+	1.18808i
$33$		0			0
$34$			11.1999i			1.92077i
$35$	−9.79622	−	5.65585i	−1.65586	−	0.956013i
$36$		0			0
$37$			4.54399i			0.747028i	0.927625	+	0.373514i	$0.121847\pi$
$37$			4.54399i			0.747028i	−0.927625	+	0.373514i	$0.878153\pi$
$38$	5.74943	+	7.40521i	0.932680	+	1.20128i
$39$		0			0
$40$			4.07280i			0.643967i
$41$	−2.02559			−0.316344			−0.158172	−	0.987412i	$-0.550560\pi$
$41$	−2.02559			−0.316344			−0.158172	+	0.987412i	$0.550560\pi$
$42$		0			0
$43$	0.973250	+	1.68572i	0.148419	+	0.257070i	0.930643	−	0.365927i	$-0.119248\pi$
$43$	0.973250	+	1.68572i	0.148419	+	0.257070i	−0.782224	+	0.622997i	$0.785915\pi$
$44$	11.5915	−	6.69236i	1.74748	−	1.00891i
$45$		0			0
$46$		−	13.6527i		−	2.01297i
$47$			3.42876i			0.500136i	0.968228	+	0.250068i	$0.0804529\pi$
$47$			3.42876i			0.500136i	−0.968228	+	0.250068i	$0.919547\pi$
$48$		0			0
$49$	−3.49070	−	6.04608i	−0.498672	−	0.863725i
$50$	−4.46481	−	7.73327i	−0.631419	−	1.09365i
$51$		0			0
$52$	−4.70864	+	2.71853i	−0.652971	+	0.376993i
$53$	4.49378	+	7.78345i	0.617268	+	1.06914i	0.989982	+	0.141193i	$0.0450938\pi$
$53$	4.49378	+	7.78345i	0.617268	+	1.06914i	−0.372714	+	0.927946i	$0.621573\pi$
$54$		0			0
$55$	−7.70983	+	13.3538i	−1.03959	+	1.80063i
$56$	−2.51702	+	4.35961i	−0.336351	+	0.582577i
$57$		0			0
$58$	−1.73310	−	3.00183i	−0.227568	−	0.394159i
$59$	7.20907			0.938541			0.469271	−	0.883054i	$-0.344517\pi$
$59$	7.20907			0.938541			0.469271	+	0.883054i	$0.344517\pi$
$60$		0			0
$61$	−7.75044			−0.992342			−0.496171	−	0.868225i	$-0.665261\pi$
$61$	−7.75044			−0.992342			−0.496171	+	0.868225i	$0.665261\pi$
$62$	−2.82487	−	1.63094i	−0.358759	−	0.207129i
$63$		0			0
$64$	−11.9787			−1.49734
$65$	3.13185	−	5.42452i	0.388458	−	0.672829i
$66$		0			0
$67$	−0.569888	−	0.329025i	−0.0696229	−	0.0401968i	0.464784	−	0.885424i	$-0.346132\pi$
$67$	−0.569888	−	0.329025i	−0.0696229	−	0.0401968i	−0.534407	+	0.845227i	$0.679465\pi$
$68$	−11.8422	+	6.83709i	−1.43608	+	0.829119i
$69$		0			0
$70$		−	24.3292i		−	2.90790i
$71$	2.68449	−	4.64968i	0.318591	−	0.551815i	−0.661604	−	0.749854i	$-0.730124\pi$
$71$	2.68449	−	4.64968i	0.318591	−	0.551815i	0.980194	+	0.198039i	$0.0634572\pi$
$72$		0			0
$73$	−1.90331	+	3.29663i	−0.222765	+	0.385841i	−0.955647	−	0.294516i	$-0.904842\pi$
$73$	−1.90331	+	3.29663i	−0.222765	+	0.385841i	0.732881	+	0.680357i	$0.238175\pi$
$74$	−8.46387	+	4.88662i	−0.983905	+	0.568058i
$75$		0			0
$76$	−4.32008	+	10.5997i	−0.495547	+	1.21587i
$77$	−16.5055	+	9.52945i	−1.88098	+	1.08598i
$78$		0			0
$79$	9.08384	−	5.24456i	1.02201	−	0.590059i	0.107326	−	0.994224i	$-0.465771\pi$
$79$	9.08384	−	5.24456i	1.02201	−	0.590059i	0.914686	+	0.404165i	$0.132438\pi$
$80$	6.17320	−	3.56410i	0.690185	−	0.398478i
$81$		0			0
$82$	−2.17832	−	3.77297i	−0.240556	−	0.416655i
$83$	4.06246	+	2.34546i	0.445913	+	0.257448i	0.706102	−	0.708110i	$-0.250452\pi$
$83$	4.06246	+	2.34546i	0.445913	+	0.257448i	−0.260190	+	0.965558i	$0.583785\pi$
$84$		0			0
$85$	7.87657	−	13.6426i	0.854334	−	1.47975i
$86$	−2.09327	+	3.62565i	−0.225723	+	0.390963i
$87$		0			0
$88$	5.94284	+	3.43110i	0.633509	+	0.365757i
$89$	−1.49289	−	2.58575i	−0.158246	−	0.274089i	0.775991	−	0.630745i	$-0.217250\pi$
$89$	−1.49289	−	2.58575i	−0.158246	−	0.274089i	−0.934236	+	0.356655i	$0.883917\pi$
$90$		0			0
$91$	6.70478	−	3.87100i	0.702851	−	0.405791i
$92$	14.4356	−	8.33438i	1.50501	−	0.868919i
$93$		0			0
$94$	−6.38657	+	3.68729i	−0.658725	+	0.380315i
$95$	−1.79551	−	13.0637i	−0.184215	−	1.34030i
$96$		0			0
$97$	−4.72908	+	2.73034i	−0.480165	+	0.277224i	−0.720485	−	0.693470i	$-0.756081\pi$
$97$	−4.72908	+	2.73034i	−0.480165	+	0.277224i	0.240320	+	0.970694i	$0.422748\pi$
$98$	7.50782	−	13.0039i	0.758404	−	1.31359i
$99$		0			0
$100$	5.45116	−	9.44168i	0.545116	−	0.944168i
$101$			1.61316i			0.160516i	0.996774	+	0.0802579i	$0.0255744\pi$
$101$			1.61316i			0.160516i	−0.996774	+	0.0802579i	$0.974426\pi$
$102$		0			0
$103$	9.11427	−	5.26213i	0.898056	−	0.518493i	0.0214871	−	0.999769i	$-0.493160\pi$
$103$	9.11427	−	5.26213i	0.898056	−	0.518493i	0.876569	+	0.481276i	$0.159827\pi$
$104$	−2.41407	−	1.39376i	−0.236719	−	0.136670i
$105$		0			0
$106$	−9.66523	+	16.7407i	−0.938770	+	1.62600i
$107$	−10.3237			−0.998028			−0.499014	−	0.866594i	$-0.666304\pi$
$107$	−10.3237			−0.998028			−0.499014	+	0.866594i	$0.666304\pi$
$108$		0			0
$109$	−5.10016	−	2.94458i	−0.488506	−	0.282039i	0.235448	−	0.971887i	$-0.424344\pi$
$109$	−5.10016	−	2.94458i	−0.488506	−	0.282039i	−0.723955	+	0.689848i	$0.757677\pi$
$110$	−33.1646			−3.16212
$111$		0			0
$112$	8.81054			0.832518
$113$	7.68377	+	13.3087i	0.722828	+	1.25197i	0.959862	+	0.280473i	$0.0904915\pi$
$113$	7.68377	+	13.3087i	0.722828	+	1.25197i	−0.237034	+	0.971501i	$0.576175\pi$
$114$		0			0
$115$	−9.60150	+	16.6303i	−0.895344	+	1.55078i
$116$	2.11598	−	3.66498i	0.196464	−	0.340285i
$117$		0			0
$118$	7.75264	+	13.4280i	0.713689	+	1.23615i
$119$	16.8625	−	9.73555i	1.54578	−	0.892456i
$120$		0			0
$121$	7.49017	+	12.9734i	0.680925	+	1.17940i
$122$	−8.33483	−	14.4364i	−0.754600	−	1.30701i
$123$		0			0
$124$		−	3.98248i		−	0.357638i
$125$		−	2.56609i		−	0.229518i
$126$		0			0
$127$	1.69680	−	0.979649i	0.150567	−	0.0869298i	−0.422824	−	0.906212i	$-0.638961\pi$
$127$	1.69680	−	0.979649i	0.150567	−	0.0869298i	0.573391	+	0.819282i	$0.305628\pi$
$128$	−5.12144	−	8.87060i	−0.452676	−	0.784057i
$129$		0			0
$130$	13.4720			1.18157
$131$			13.0386i			1.13919i	0.821926	+	0.569595i	$0.192900\pi$
$131$			13.0386i			1.13919i	−0.821926	+	0.569595i	$0.807100\pi$
$132$		0			0
$133$	6.15149	−	15.0932i	0.533402	−	1.30875i
$134$		−	1.41534i		−	0.122266i
$135$		0			0
$136$	−6.07137	−	3.50531i	−0.520616	−	0.300578i
$137$			11.4560i			0.978752i	0.872073	+	0.489376i	$0.162775\pi$
$137$			11.4560i			0.978752i	−0.872073	+	0.489376i	$0.837225\pi$
$138$		0			0
$139$	−9.26139	+	16.0412i	−0.785541	+	1.36060i	0.143135	+	0.989703i	$0.454282\pi$
$139$	−9.26139	+	16.0412i	−0.785541	+	1.36060i	−0.928676	+	0.370893i	$0.879052\pi$
$140$	25.7244	−	14.8520i	2.17411	−	1.25522i
$141$		0			0
$142$	11.5476			0.969055
$143$	−5.27680	−	9.13968i	−0.441268	−	0.764299i
$144$		0			0
$145$			4.87536i			0.404876i
$146$	−8.18728			−0.677584
$147$		0			0
$148$	−10.3337	−	5.96615i	−0.849423	−	0.490415i
$149$		−	7.28384i		−	0.596716i	−0.954454	−	0.298358i	$-0.903561\pi$
$149$		−	7.28384i		−	0.596716i	0.954454	−	0.298358i	$-0.0964389\pi$
$150$		0			0
$151$	1.90838	+	1.10180i	0.155302	+	0.0896635i	0.575637	−	0.817705i	$-0.304754\pi$
$151$	1.90838	+	1.10180i	0.155302	+	0.0896635i	−0.420335	+	0.907369i	$0.638087\pi$
$152$	−5.81372	+	0.799054i	−0.471555	+	0.0648118i
$153$		0			0
$154$	−35.5001	−	20.4960i	−2.86068	−	1.65161i
$155$	2.29398	+	3.97329i	0.184257	+	0.319142i
$156$		0			0
$157$	−13.5719			−1.08316			−0.541579	−	0.840650i	$-0.682173\pi$
$157$	−13.5719			−1.08316			−0.541579	+	0.840650i	$0.682173\pi$
$158$	19.5375	+	11.2800i	1.55432	+	0.897389i
$159$		0			0
$160$	20.3316	+	11.7385i	1.60736	+	0.928008i
$161$	−20.5552	+	11.8676i	−1.61998	+	0.935296i
$162$		0			0
$163$	3.00114			0.235067			0.117534	−	0.993069i	$-0.462501\pi$
$163$	3.00114			0.235067			0.117534	+	0.993069i	$0.462501\pi$
$164$	2.65955	−	4.60648i	0.207676	−	0.359706i
$165$		0			0
$166$			10.0892i			0.783078i
$167$	2.98146	−	5.16403i	0.230712	−	0.399605i	−0.727306	−	0.686314i	$-0.759228\pi$
$167$	2.98146	−	5.16403i	0.230712	−	0.399605i	0.958018	+	0.286709i	$0.0925611\pi$
$168$		0			0
$169$	−4.35649	−	7.54566i	−0.335114	−	0.580435i
$170$	33.8819			2.59862
$171$		0			0
$172$	−5.11141			−0.389742
$173$	−9.39409	−	16.2710i	−0.714220	−	1.23706i	−0.963260	−	0.268572i	$-0.913448\pi$
$173$	−9.39409	−	16.2710i	−0.714220	−	1.23706i	0.249040	−	0.968493i	$-0.419885\pi$
$174$		0			0
$175$	−7.76207	+	13.4443i	−0.586757	+	1.01629i
$176$		−	12.0102i		−	0.905302i
$177$		0			0
$178$	3.21090	−	5.56144i	0.240667	−	0.416848i
$179$	−14.8755			−1.11184			−0.555922	−	0.831235i	$-0.687635\pi$
$179$	−14.8755			−1.11184			−0.555922	+	0.831235i	$0.687635\pi$
$180$		0			0
$181$	−3.85625	+	2.22640i	−0.286633	+	0.165487i	−0.636422	−	0.771341i	$-0.719586\pi$
$181$	−3.85625	+	2.22640i	−0.286633	+	0.165487i	0.349790	+	0.936828i	$0.386253\pi$
$182$	14.4206	+	8.32577i	1.06893	+	0.617147i
$183$		0			0
$184$	7.40097	+	4.27295i	0.545606	+	0.315006i
$185$	13.7464			1.01066
$186$		0			0
$187$	−13.2711	−	22.9862i	−0.970480	−	1.68092i
$188$	−7.79748	−	4.50187i	−0.568689	−	0.328333i
$189$		0			0
$190$	22.4022	−	17.3931i	1.62522	−	1.26183i
$191$	20.1652	+	11.6424i	1.45910	+	0.842414i	0.998967	−	0.0454345i	$-0.0144672\pi$
$191$	20.1652	+	11.6424i	1.45910	+	0.842414i	0.460136	+	0.887848i	$0.347801\pi$
$192$		0			0
$193$			22.5699i			1.62462i	0.583229	+	0.812308i	$0.301789\pi$
$193$			22.5699i			1.62462i	−0.583229	+	0.812308i	$0.698211\pi$
$194$	−10.1713	−	5.87241i	−0.730258	−	0.421615i
$195$		0			0
$196$	18.3328			1.30949
$197$			2.10025i			0.149637i	0.997197	+	0.0748184i	$0.0238377\pi$
$197$			2.10025i			0.149637i	−0.997197	+	0.0748184i	$0.976162\pi$
$198$		0			0
$199$	−6.81724	−	11.8078i	−0.483261	−	0.837033i	0.516554	−	0.856255i	$-0.327215\pi$
$199$	−6.81724	−	11.8078i	−0.483261	−	0.837033i	−0.999815	+	0.0192216i	$0.993881\pi$
$200$	5.58950			0.395238
$201$		0			0
$202$	−3.00476	+	1.73480i	−0.211414	+	0.122060i
$203$	−3.01300	+	5.21868i	−0.211471	+	0.366279i
$204$		0			0
$205$			6.12780i			0.427984i
$206$	19.6030	+	11.3178i	1.36581	+	0.788548i
$207$		0			0
$208$			4.87871i			0.338278i
$209$	−20.5745	−	8.38547i	−1.42317	−	0.580035i
$210$		0			0
$211$		−	27.3865i		−	1.88537i	−0.333690	−	0.942683i	$-0.608294\pi$
$211$		−	27.3865i		−	1.88537i	0.333690	−	0.942683i	$-0.391706\pi$
$212$	−23.6009			−1.62092
$213$		0			0
$214$	−11.1021	−	19.2294i	−0.758924	−	1.31449i
$215$	5.09961	−	2.94426i	0.347791	−	0.200797i
$216$		0			0
$217$			5.67078i			0.384958i
$218$		−	12.6664i		−	0.857877i
$219$		0			0
$220$	−20.2456	−	35.0665i	−1.36496	−	2.36418i
$221$	5.39092	+	9.33735i	0.362633	+	0.628098i
$222$		0			0
$223$	2.00040	−	1.15493i	0.133956	−	0.0773397i	−0.431524	−	0.902101i	$-0.642024\pi$
$223$	2.00040	−	1.15493i	0.133956	−	0.0773397i	0.565481	+	0.824762i	$0.308691\pi$
$224$	14.5089	+	25.1302i	0.969417	+	1.67908i
$225$		0			0
$226$	−16.5263	+	28.6243i	−1.09931	+	1.90406i
$227$	−5.87376	+	10.1737i	−0.389855	+	0.675249i	−0.992430	−	0.122813i	$-0.960808\pi$
$227$	−5.87376	+	10.1737i	−0.389855	+	0.675249i	0.602574	+	0.798063i	$0.294142\pi$
$228$		0			0
$229$	−3.31652	−	5.74438i	−0.219162	−	0.379599i	0.735390	−	0.677644i	$-0.236999\pi$
$229$	−3.31652	−	5.74438i	−0.219162	−	0.379599i	−0.954552	+	0.298045i	$0.903666\pi$
$230$	−41.3018			−2.72336
$231$		0			0
$232$	2.16968			0.142446
$233$	3.13882	+	1.81220i	0.205631	+	0.118721i	0.599279	−	0.800540i	$-0.295454\pi$
$233$	3.13882	+	1.81220i	0.205631	+	0.118721i	−0.393648	+	0.919261i	$0.628787\pi$
$234$		0			0
$235$	10.3726			0.676636
$236$	−9.46533	+	16.3944i	−0.616141	+	1.06719i
$237$		0			0
$238$	36.2678	+	20.9392i	2.35089	+	1.35729i
$239$	−13.1428	+	7.58803i	−0.850140	+	0.490829i	−0.860698	−	0.509116i	$-0.829973\pi$
$239$	−13.1428	+	7.58803i	−0.850140	+	0.490829i	0.0105580	+	0.999944i	$0.496639\pi$
$240$		0			0
$241$			24.5234i			1.57969i	0.613308	+	0.789844i	$0.289839\pi$
$241$			24.5234i			1.57969i	−0.613308	+	0.789844i	$0.710161\pi$
$242$	−16.1099	+	27.9031i	−1.03558	+	1.79368i
$243$		0			0
$244$	10.1761	−	17.6256i	0.651461	−	1.12836i
$245$	−18.2905	+	10.5600i	−1.16854	+	0.674656i
$246$		0			0
$247$	8.35767	+	3.40630i	0.531786	+	0.216738i
$248$	1.76823	−	1.02089i	0.112283	−	0.0648265i
$249$		0			0
$250$	4.77972	−	2.75957i	0.302296	−	0.174531i
$251$	3.73240	−	2.15490i	0.235587	−	0.136016i	−0.377560	−	0.925985i	$-0.623237\pi$
$251$	3.73240	−	2.15490i	0.235587	−	0.136016i	0.613147	+	0.789969i	$0.289903\pi$
$252$		0			0
$253$	16.1774	+	28.0201i	1.01707	+	1.76161i
$254$	3.64949	+	2.10703i	0.228989	+	0.132207i
$255$		0			0
$256$	−0.963515	+	1.66886i	−0.0602197	+	0.104304i
$257$	12.6266	−	21.8699i	0.787626	−	1.36421i	−0.139792	−	0.990181i	$-0.544643\pi$
$257$	12.6266	−	21.8699i	0.787626	−	1.36421i	0.927418	−	0.374027i	$-0.122023\pi$
$258$		0			0
$259$	14.7144	+	8.49539i	0.914311	+	0.527878i
$260$	8.22408	+	14.2445i	0.510036	+	0.883408i
$261$		0			0
$262$	−24.2864	+	14.0217i	−1.50042	+	0.866266i
$263$	17.4797	−	10.0919i	1.07784	−	0.622293i	0.147530	−	0.989058i	$-0.452868\pi$
$263$	17.4797	−	10.0919i	1.07784	−	0.622293i	0.930314	+	0.366764i	$0.119534\pi$
$264$		0			0
$265$	23.5464	−	13.5945i	1.44644	−	0.835105i
$266$	34.7287	−	4.77322i	2.12936	−	0.292665i
$267$		0			0
$268$	1.49650	−	0.864004i	0.0914132	−	0.0527774i
$269$	2.92165	−	5.06044i	0.178136	−	0.308540i	−0.763106	−	0.646273i	$-0.776327\pi$
$269$	2.92165	−	5.06044i	0.178136	−	0.308540i	0.941242	+	0.337733i	$0.109660\pi$
$270$		0			0
$271$	7.53980	−	13.0593i	0.458010	−	0.793297i	−0.540845	−	0.841122i	$-0.681896\pi$
$271$	7.53980	−	13.0593i	0.458010	−	0.793297i	0.998856	+	0.0478248i	$0.0152289\pi$
$272$			12.2699i			0.743974i
$273$		0			0
$274$	−21.3385	+	12.3198i	−1.28911	+	0.744266i
$275$	18.3267	+	10.5809i	1.10514	+	0.638055i
$276$		0			0
$277$	−8.02211	+	13.8947i	−0.482002	+	0.834852i	−0.999787	−	0.0206591i	$-0.993424\pi$
$277$	−8.02211	+	13.8947i	−0.482002	+	0.834852i	0.517785	+	0.855511i	$0.326757\pi$
$278$	−39.8388			−2.38937
$279$		0			0
$280$	13.1886	+	7.61446i	0.788171	+	0.455051i
$281$	16.9959			1.01389			0.506944	−	0.861979i	$-0.330775\pi$
$281$	16.9959			1.01389			0.506944	+	0.861979i	$0.330775\pi$
$282$		0			0
$283$	−15.5286			−0.923080			−0.461540	−	0.887119i	$-0.652703\pi$
$283$	−15.5286			−0.923080			−0.461540	+	0.887119i	$0.652703\pi$
$284$	7.04935	+	12.2098i	0.418302	+	0.724520i
$285$		0			0
$286$	11.3494	−	19.6577i	0.671101	−	1.16238i
$287$	−3.78702	+	6.55931i	−0.223541	+	0.387184i
$288$		0			0
$289$	5.05813	+	8.76093i	0.297537	+	0.515349i
$290$	−9.08108	+	5.24297i	−0.533260	+	0.307878i
$291$		0			0
$292$	−4.99800	−	8.65678i	−0.292486	−	0.506600i
$293$	15.1343	+	26.2134i	0.884156	+	1.53140i	0.846678	+	0.532105i	$0.178599\pi$
$293$	15.1343	+	26.2134i	0.884156	+	1.53140i	0.0374772	+	0.999297i	$0.488068\pi$
$294$		0			0
$295$		−	21.8088i		−	1.26976i
$296$		−	6.11757i		−	0.355576i
$297$		0			0
$298$	13.5672	−	7.83305i	0.785929	−	0.453757i
$299$	−6.57150	−	11.3822i	−0.380040	−	0.658248i
$300$		0			0
$301$	7.27830			0.419514
$302$			4.73953i			0.272729i
$303$		0			0
$304$	6.29871	+	8.11268i	0.361256	+	0.465294i
$305$			23.4465i			1.34254i
$306$		0			0
$307$	−24.4373	−	14.1089i	−1.39471	−	0.805235i	−0.400876	−	0.916132i	$-0.631294\pi$
$307$	−24.4373	−	14.1089i	−1.39471	−	0.805235i	−0.993832	+	0.110897i	$0.964628\pi$
$308$		−	50.0478i		−	2.85174i
$309$		0			0
$310$	−4.93390	+	8.54576i	−0.280227	+	0.485367i
$311$	−16.5220	+	9.53896i	−0.936875	+	0.540905i	−0.888979	−	0.457947i	$-0.848585\pi$
$311$	−16.5220	+	9.53896i	−0.936875	+	0.540905i	−0.0478956	+	0.998852i	$0.515251\pi$
$312$		0			0
$313$	−11.2368			−0.635141			−0.317571	−	0.948235i	$-0.602867\pi$
$313$	−11.2368			−0.635141			−0.317571	+	0.948235i	$0.602867\pi$
$314$	−14.5953	−	25.2797i	−0.823658	−	1.42662i
$315$		0			0
$316$			27.5439i			1.54947i
$317$	0.376061			0.0211217			0.0105608	−	0.999944i	$-0.496638\pi$
$317$	0.376061			0.0211217			0.0105608	+	0.999944i	$0.496638\pi$
$318$		0			0
$319$	7.11389	+	4.10721i	0.398301	+	0.229959i
$320$			36.2379i			2.02576i
$321$		0			0
$322$	−44.2103	−	25.5248i	−2.46374	−	1.42244i
$323$	21.0195	+	8.56682i	1.16955	+	0.476671i
$324$		0			0
$325$	−7.44459	−	4.29814i	−0.412952	−	0.238418i
$326$	3.22743	+	5.59007i	0.178751	+	0.309605i
$327$		0			0
$328$	2.72705			0.150576
$329$	11.1031	+	6.41036i	0.612132	+	0.353414i
$330$		0			0
$331$	−27.1452	−	15.6723i	−1.49204	−	0.861428i	−0.492078	−	0.870551i	$-0.663763\pi$
$331$	−27.1452	−	15.6723i	−1.49204	−	0.861428i	−0.999958	+	0.00912336i	$0.997096\pi$
$332$	−10.6678	+	6.15907i	−0.585473	+	0.338023i
$333$		0			0
$334$	12.8250			0.701755
$335$	−0.995362	+	1.72402i	−0.0543825	+	0.0941932i
$336$		0			0
$337$		−	1.13840i		−	0.0620123i	−0.999519	−	0.0310062i	$-0.990129\pi$
$337$		−	1.13840i		−	0.0620123i	0.999519	−	0.0310062i	$-0.00987115\pi$
$338$	9.36994	−	16.2292i	0.509658	−	0.882753i
$339$		0			0
$340$	20.6835	+	35.8249i	1.12172	+	1.94288i
$341$	7.73018			0.418613
$342$		0			0
$343$	0.0695125			0.00375332
$344$	−1.31028	−	2.26948i	−0.0706458	−	0.122362i
$345$		0			0
$346$	20.2048	−	34.9958i	1.08622	−	1.88139i
$347$		−	32.4512i		−	1.74207i	−0.491219	−	0.871036i	$-0.663448\pi$
$347$		−	32.4512i		−	1.74207i	0.491219	−	0.871036i	$-0.336552\pi$
$348$		0			0
$349$	−3.78030	+	6.54768i	−0.202355	+	0.350489i	−0.949287	−	0.314412i	$-0.898193\pi$
$349$	−3.78030	+	6.54768i	−0.202355	+	0.350489i	0.746932	+	0.664901i	$0.231526\pi$
$350$	−33.3894			−1.78474
$351$		0			0
$352$	34.2565	−	19.7780i	1.82587	−	1.05417i
$353$	4.45738	+	2.57347i	0.237242	+	0.136972i	0.613909	−	0.789377i	$-0.289596\pi$
$353$	4.45738	+	2.57347i	0.237242	+	0.136972i	−0.376666	+	0.926349i	$0.622930\pi$
$354$		0			0
$355$	−14.0661	−	8.12109i	−0.746553	−	0.431023i
$356$	7.84049			0.415545
$357$		0			0
$358$	−15.9971	−	27.7078i	−0.845472	−	1.46440i
$359$	−5.46349	−	3.15435i	−0.288352	−	0.166480i	0.348846	−	0.937180i	$-0.386574\pi$
$359$	−5.46349	−	3.15435i	−0.288352	−	0.166480i	−0.637198	+	0.770700i	$0.719907\pi$
$360$		0			0
$361$	18.2955	−	5.12599i	0.962919	−	0.269789i
$362$	−8.29402	−	4.78856i	−0.435924	−	0.251681i
$363$		0			0
$364$			20.3301i			1.06559i
$365$	9.97292	+	5.75787i	0.522006	+	0.301380i
$366$		0			0
$367$	7.42328			0.387492			0.193746	−	0.981052i	$-0.437936\pi$
$367$	7.42328			0.387492			0.193746	+	0.981052i	$0.437936\pi$
$368$		−	14.9570i		−	0.779686i
$369$		0			0
$370$	14.7829	+	25.6048i	0.768528	+	1.33113i
$371$	33.6060			1.74474
$372$		0			0
$373$	21.2019	−	12.2409i	1.09779	−	0.633811i	0.162153	−	0.986766i	$-0.448156\pi$
$373$	21.2019	−	12.2409i	1.09779	−	0.633811i	0.935641	+	0.352954i	$0.114823\pi$
$374$	28.5435	−	49.4389i	1.47595	−	2.55642i
$375$		0			0
$376$		−	4.61613i		−	0.238059i
$377$	−2.88977	−	1.66841i	−0.148831	−	0.0859274i
$378$		0			0
$379$			27.3088i			1.40276i	0.712788	+	0.701380i	$0.247432\pi$
$379$			27.3088i			1.40276i	−0.712788	+	0.701380i	$0.752568\pi$
$380$	32.0661	+	13.0690i	1.64496	+	0.670428i
$381$		0			0
$382$			50.0810i			2.56237i
$383$	1.12796			0.0576362			0.0288181	−	0.999585i	$-0.490826\pi$
$383$	1.12796			0.0576362			0.0288181	+	0.999585i	$0.490826\pi$
$384$		0			0
$385$	28.8284	+	49.9322i	1.46923	+	2.54478i
$386$	−42.0398	+	24.2717i	−2.13977	+	1.23540i
$387$		0			0
$388$		−	14.3395i		−	0.727976i
$389$		−	1.96440i		−	0.0995991i	−0.998759	−	0.0497995i	$-0.984142\pi$
$389$		−	1.96440i		−	0.0995991i	0.998759	−	0.0497995i	$-0.0158582\pi$
$390$		0			0
$391$	−16.5273	−	28.6261i	−0.835821	−	1.44768i
$392$	4.69953	+	8.13982i	0.237362	+	0.411123i
$393$		0			0
$394$	−3.91204	+	2.25862i	−0.197086	+	0.113787i
$395$	−15.8658	−	27.4803i	−0.798293	−	1.38268i
$396$		0			0
$397$	16.7936	−	29.0874i	0.842848	−	1.45985i	−0.0446298	−	0.999004i	$-0.514211\pi$
$397$	16.7936	−	29.0874i	0.842848	−	1.45985i	0.887477	−	0.460851i	$-0.152456\pi$
$398$	14.6625	−	25.3963i	0.734966	−	1.27300i
$399$		0			0
$400$	−4.89136	−	8.47208i	−0.244568	−	0.423604i
$401$	−6.15328			−0.307280			−0.153640	−	0.988127i	$-0.549100\pi$
$401$	−6.15328			−0.307280			−0.153640	+	0.988127i	$0.549100\pi$
$402$		0			0
$403$	−3.14011			−0.156420
$404$	−3.66856	−	2.11805i	−0.182518	−	0.105377i
$405$		0			0
$406$	−12.9608			−0.643231
$407$	11.5806	−	20.0581i	0.574028	−	0.994245i
$408$		0			0
$409$	3.24396	+	1.87290i	0.160404	+	0.0926091i	0.578053	−	0.815999i	$-0.303813\pi$
$409$	3.24396	+	1.87290i	0.160404	+	0.0926091i	−0.417649	+	0.908608i	$0.637146\pi$
$410$	−11.4139	+	6.58984i	−0.563694	+	0.325449i
$411$		0			0
$412$			27.6362i			1.36154i
$413$	13.4780	−	23.3445i	0.663208	−	1.14871i
$414$		0			0
$415$	7.09546	−	12.2897i	0.348302	−	0.603278i
$416$	−13.9155	+	8.03410i	−0.682262	+	0.393904i
$417$		0			0
$418$	−6.50666	−	47.3408i	−0.318251	−	2.31552i
$419$	3.16792	−	1.82900i	0.154763	−	0.0893526i	−0.420618	−	0.907238i	$-0.638187\pi$
$419$	3.16792	−	1.82900i	0.154763	−	0.0893526i	0.575382	+	0.817885i	$0.304854\pi$
$420$		0			0
$421$	−6.40584	+	3.69841i	−0.312202	+	0.180250i	−0.647911	−	0.761716i	$-0.724357\pi$
$421$	−6.40584	+	3.69841i	−0.312202	+	0.180250i	0.335710	+	0.941966i	$0.391024\pi$
$422$	51.0115	−	29.4515i	2.48320	−	1.43368i
$423$		0			0
$424$	−6.04996	−	10.4788i	−0.293812	−	0.508898i
$425$	−18.7231	−	10.8098i	−0.908204	−	0.524352i
$426$		0			0
$427$	−14.4901	+	25.0976i	−0.701226	+	1.21456i
$428$	13.5547	−	23.4775i	0.655193	−	1.13483i
$429$		0			0
$430$	10.9683	+	6.33253i	0.528936	+	0.305382i
$431$	−5.78011	−	10.0114i	−0.278418	−	0.482234i	0.692574	−	0.721347i	$-0.256477\pi$
$431$	−5.78011	−	10.0114i	−0.278418	−	0.482234i	−0.970992	+	0.239113i	$0.923143\pi$
$432$		0			0
$433$	−2.95790	+	1.70774i	−0.142148	+	0.0820689i	−0.569387	−	0.822070i	$-0.692819\pi$
$433$	−2.95790	+	1.70774i	−0.142148	+	0.0820689i	0.427240	+	0.904138i	$0.359486\pi$
$434$	−10.5627	+	6.09836i	−0.507025	+	0.292731i
$435$		0			0
$436$	13.3928	−	7.73231i	0.641397	−	0.370311i
$437$	−25.6226	−	10.4429i	−1.22570	−	0.499552i
$438$		0			0
$439$	21.1340	−	12.2017i	1.00867	−	0.582355i	0.0978674	−	0.995199i	$-0.468798\pi$
$439$	21.1340	−	12.2017i	1.00867	−	0.582355i	0.910802	+	0.412844i	$0.135465\pi$
$440$	10.3797	−	17.9782i	0.494834	−	0.857078i
$441$		0			0
$442$	−11.5948	+	20.0828i	−0.551509	+	0.955241i
$443$		−	38.9864i		−	1.85230i	−0.377157	−	0.926150i	$-0.623098\pi$
$443$		−	38.9864i		−	1.85230i	0.377157	−	0.926150i	$-0.376902\pi$
$444$		0			0
$445$	−7.82239	+	4.51626i	−0.370817	+	0.214091i
$446$	4.30245	+	2.48402i	0.203727	+	0.117622i
$447$		0			0
$448$	−22.3953	+	38.7897i	−1.05808	+	1.83264i
$449$	26.0848			1.23102			0.615509	−	0.788130i	$-0.288950\pi$
$449$	26.0848			1.23102			0.615509	+	0.788130i	$0.288950\pi$
$450$		0			0
$451$	8.94139	+	5.16231i	0.421034	+	0.243084i
$452$	−40.3544			−1.89811
$453$		0			0
$454$	−25.2666			−1.18582
$455$	−11.7105	−	20.2832i	−0.548997	−	0.950891i
$456$		0			0
$457$	8.91236	−	15.4367i	0.416903	−	0.722096i	−0.578724	−	0.815524i	$-0.696449\pi$
$457$	8.91236	−	15.4367i	0.416903	−	0.722096i	0.995626	+	0.0934274i	$0.0297823\pi$
$458$	7.13318	−	12.3550i	0.333312	−	0.577313i
$459$		0			0
$460$	−25.2131	−	43.6703i	−1.17557	−	2.03614i
$461$	−30.8452	+	17.8085i	−1.43660	+	0.829424i	−0.997612	−	0.0690673i	$-0.977998\pi$
$461$	−30.8452	+	17.8085i	−1.43660	+	0.829424i	−0.438992	+	0.898491i	$0.644664\pi$
$462$		0			0
$463$	−5.50447	−	9.53403i	−0.255815	−	0.443084i	0.709302	−	0.704905i	$-0.249010\pi$
$463$	−5.50447	−	9.53403i	−0.255815	−	0.443084i	−0.965116	+	0.261821i	$0.915677\pi$
$464$	−1.89868	−	3.28861i	−0.0881440	−	0.152670i
$465$		0			0
$466$			7.79537i			0.361113i
$467$		−	23.7561i		−	1.09930i	−0.835394	−	0.549651i	$-0.814761\pi$
$467$		−	23.7561i		−	1.09930i	0.835394	−	0.549651i	$-0.185239\pi$
$468$		0			0
$469$	−2.13091	+	1.23028i	−0.0983963	+	0.0568091i
$470$	11.1547	+	19.3206i	0.514530	+	0.891192i
$471$		0			0
$472$	−9.70556			−0.446734
$473$		−	9.92149i		−	0.456190i
$474$		0			0
$475$	−17.9286	+	2.46415i	−0.822618	+	0.113063i
$476$			51.1301i			2.34355i
$477$		0			0
$478$	−28.2677	−	16.3203i	−1.29293	−	0.746475i
$479$			41.4152i			1.89231i	0.323719	+	0.946153i	$0.395067\pi$
$479$			41.4152i			1.89231i	−0.323719	+	0.946153i	$0.604933\pi$
$480$		0			0
$481$	−4.70420	+	8.14792i	−0.214493	+	0.371513i
$482$	−45.6784	+	26.3724i	−2.08059	+	1.20123i
$483$		0			0
$484$	−39.3376			−1.78807
$485$	8.25978	+	14.3064i	0.375057	+	0.649618i
$486$		0			0
$487$		−	15.0755i		−	0.683134i	−0.939857	−	0.341567i	$-0.889042\pi$
$487$		−	15.0755i		−	0.683134i	0.939857	−	0.341567i	$-0.110958\pi$
$488$	10.4344			0.472343
$489$		0			0
$490$	−39.3393	−	22.7126i	−1.77717	−	1.02605i
$491$			42.3091i			1.90938i	0.297597	+	0.954691i	$0.403815\pi$
$491$			42.3091i			1.90938i	−0.297597	+	0.954691i	$0.596185\pi$
$492$		0			0
$493$	−7.26775	−	4.19603i	−0.327323	−	0.188980i
$494$	2.64310	+	19.2306i	0.118919	+	0.865223i
$495$		0			0
$496$	−3.09475	−	1.78675i	−0.138958	−	0.0802276i
$497$	−10.0378	−	17.3859i	−0.450256	−	0.779866i
$498$		0			0
$499$	43.2590			1.93654			0.968268	−	0.249912i	$-0.0804018\pi$
$499$	43.2590			1.93654			0.968268	+	0.249912i	$0.0804018\pi$
$500$	5.83564	+	3.36921i	0.260978	+	0.150676i
$501$		0			0
$502$	8.02766	+	4.63477i	0.358292	+	0.206860i
$503$	−5.29464	+	3.05686i	−0.236077	+	0.136299i	−0.613372	−	0.789794i	$-0.710187\pi$
$503$	−5.29464	+	3.05686i	−0.236077	+	0.136299i	0.377296	+	0.926093i	$0.376854\pi$
$504$		0			0
$505$	4.88012			0.217163
$506$	−34.7944	+	60.2657i	−1.54680	+	2.67914i
$507$		0			0
$508$			5.14502i			0.228273i
$509$	−13.8830	+	24.0460i	−0.615353	+	1.06582i	0.374970	+	0.927037i	$0.377653\pi$
$509$	−13.8830	+	24.0460i	−0.615353	+	1.06582i	−0.990322	+	0.138785i	$0.955680\pi$
$510$		0			0
$511$	7.11680	+	12.3267i	0.314829	+	0.545299i
$512$	−24.6304			−1.08852
$513$		0			0
$514$	54.3147			2.39572
$515$	−15.9189	−	27.5724i	−0.701472	−	1.21498i
$516$		0			0
$517$	8.73834	−	15.1353i	0.384312	−	0.665648i
$518$			36.5438i			1.60564i
$519$		0			0
$520$	−4.21640	+	7.30302i	−0.184901	+	0.320258i
$521$	3.72919			0.163379			0.0816894	−	0.996658i	$-0.473968\pi$
$521$	3.72919			0.163379			0.0816894	+	0.996658i	$0.473968\pi$
$522$		0			0
$523$	−38.8829	+	22.4491i	−1.70023	+	0.981629i	−0.754715	+	0.656053i	$0.772225\pi$
$523$	−38.8829	+	22.4491i	−1.70023	+	0.981629i	−0.945516	+	0.325575i	$0.894442\pi$
$524$	−29.6516	−	17.1194i	−1.29534	−	0.747864i
$525$		0			0
$526$	37.5953	+	21.7057i	1.63924	+	0.946413i
$527$	−7.89736			−0.344015
$528$		0			0
$529$	8.64667	+	14.9765i	0.375942	+	0.651151i
$530$	50.6437	+	29.2391i	2.19982	+	1.27007i
$531$		0			0
$532$	26.2474	+	33.8064i	1.13797	+	1.46569i
$533$	−3.63213	−	2.09701i	−0.157325	−	0.0908315i
$534$		0			0
$535$			31.2311i			1.35024i
$536$	0.767239	+	0.442966i	0.0331397	+	0.0191332i
$537$		0			0
$538$	12.5678			0.541835
$539$			35.5849i			1.53275i
$540$		0			0
$541$	−16.3200	−	28.2670i	−0.701651	−	1.21530i	−0.967887	−	0.251387i	$-0.919113\pi$
$541$	−16.3200	−	28.2670i	−0.701651	−	1.21530i	0.266236	−	0.963908i	$-0.414220\pi$
$542$	32.4333			1.39313
$543$		0			0
$544$	−34.9973	+	20.2057i	−1.50050	+	0.866313i
$545$	−8.90789	+	15.4289i	−0.381572	+	0.660903i
$546$		0			0
$547$			10.2878i			0.439874i	0.975514	+	0.219937i	$0.0705851\pi$
$547$			10.2878i			0.439874i	−0.975514	+	0.219937i	$0.929415\pi$
$548$	−26.0525	−	15.0414i	−1.11291	−	0.642539i
$549$		0			0
$550$			45.5151i			1.94077i
$551$	−6.95933	+	0.956509i	−0.296477	+	0.0407487i
$552$		0			0
$553$		−	39.2206i		−	1.66783i
$554$	−34.5080			−1.46610
$555$		0			0
$556$	−24.3199	−	42.1234i	−1.03140	−	1.78643i
$557$	−1.55437	+	0.897418i	−0.0658609	+	0.0380248i	−0.532569	−	0.846387i	$-0.678773\pi$
$557$	−1.55437	+	0.897418i	−0.0658609	+	0.0380248i	0.466708	+	0.884411i	$0.345440\pi$
$558$		0			0
$559$			4.03025i			0.170462i
$560$		−	26.6535i		−	1.12632i
$561$		0			0
$562$	18.2774	+	31.6573i	0.770984	+	1.33538i
$563$	−2.51042	−	4.34817i	−0.105801	−	0.183254i	0.808264	−	0.588820i	$-0.200407\pi$
$563$	−2.51042	−	4.34817i	−0.105801	−	0.183254i	−0.914065	+	0.405567i	$0.867074\pi$
$564$		0			0
$565$	40.2612	−	23.2448i	1.69380	−	0.977918i
$566$	−16.6995	−	28.9244i	−0.701932	−	1.21578i
$567$		0			0
$568$	−3.61413	+	6.25985i	−0.151645	+	0.262657i
$569$	10.4266	−	18.0595i	0.437107	−	0.757092i	−0.560358	−	0.828251i	$-0.689336\pi$
$569$	10.4266	−	18.0595i	0.437107	−	0.757092i	0.997465	+	0.0711585i	$0.0226696\pi$
$570$		0			0
$571$	−18.2645	−	31.6350i	−0.764345	−	1.32388i	−0.940592	−	0.339538i	$-0.889729\pi$
$571$	−18.2645	−	31.6350i	−0.764345	−	1.32388i	0.176248	−	0.984346i	$-0.443604\pi$
$572$	27.7132			1.15875
$573$		0			0
$574$	−16.2903			−0.679942
$575$	22.8234	+	13.1771i	0.951800	+	0.549522i
$576$		0			0
$577$	−13.8317			−0.575822			−0.287911	−	0.957657i	$-0.592961\pi$
$577$	−13.8317			−0.575822			−0.287911	+	0.957657i	$0.592961\pi$
$578$	−10.8790	+	18.8430i	−0.452508	+	0.783767i
$579$		0			0
$580$	−11.0872	−	6.40123i	−0.460373	−	0.265796i
$581$	15.1902	−	8.77008i	0.630197	−	0.363844i
$582$		0			0
$583$		−	45.8104i		−	1.89727i
$584$	2.56242	−	4.43824i	0.106034	−	0.183656i
$585$		0			0
$586$	−32.5509	+	56.3798i	−1.34467	+	2.32903i
$587$	3.05306	−	1.76269i	0.126013	−	0.0727539i	−0.435668	−	0.900107i	$-0.643488\pi$
$587$	3.05306	−	1.76269i	0.126013	−	0.0727539i	0.561682	+	0.827353i	$0.310155\pi$
$588$		0			0
$589$	−5.22161	+	4.05407i	−0.215153	+	0.167045i
$590$	40.6221	−	23.4532i	1.67239	−	0.965553i
$591$		0			0
$592$	−9.27247	+	5.35347i	−0.381096	+	0.220026i
$593$	−3.25664	+	1.88022i	−0.133734	+	0.0772113i	−0.565374	−	0.824834i	$-0.691268\pi$
$593$	−3.25664	+	1.88022i	−0.133734	+	0.0772113i	0.431640	+	0.902046i	$0.357935\pi$
$594$		0			0
$595$	−29.4519	−	51.0121i	−1.20741	−	2.09129i
$596$	16.5645	+	9.56351i	0.678508	+	0.391737i
$597$		0			0
$598$	14.1340	−	24.4808i	0.577983	−	1.00110i
$599$	1.34996	−	2.33820i	0.0551580	−	0.0955365i	−0.837128	−	0.547007i	$-0.815767\pi$
$599$	1.34996	−	2.33820i	0.0551580	−	0.0955365i	0.892286	+	0.451471i	$0.149100\pi$
$600$		0			0
$601$	3.51336	+	2.02844i	0.143313	+	0.0827417i	0.569942	−	0.821685i	$-0.306966\pi$
$601$	3.51336	+	2.02844i	0.143313	+	0.0827417i	−0.426629	+	0.904427i	$0.640299\pi$
$602$	7.82709	+	13.5569i	0.319008	+	0.552539i
$603$		0			0
$604$	−5.01131	+	2.89328i	−0.203907	+	0.117726i
$605$	39.2468	−	22.6592i	1.59561	−	0.921226i
$606$		0			0
$607$	4.17611	−	2.41108i	0.169503	−	0.0978627i	−0.412848	−	0.910800i	$-0.635466\pi$
$607$	4.17611	−	2.41108i	0.169503	−	0.0978627i	0.582352	+	0.812937i	$0.302133\pi$
$608$	−12.7672	+	31.3254i	−0.517777	+	1.27041i
$609$		0			0
$610$	−43.6727	+	25.2144i	−1.76826	+	1.02090i
$611$	−3.54964	+	6.14817i	−0.143603	+	0.248728i
$612$		0			0
$613$	4.89396	−	8.47658i	0.197665	−	0.342366i	−0.750106	−	0.661318i	$-0.769997\pi$
$613$	4.89396	−	8.47658i	0.197665	−	0.342366i	0.947771	+	0.318952i	$0.103331\pi$
$614$		−	60.6907i		−	2.44928i
$615$		0			0
$616$	22.2213	−	12.8295i	0.895322	−	0.516914i
$617$	−3.36966	−	1.94547i	−0.135657	−	0.0783219i	0.430635	−	0.902526i	$-0.358290\pi$
$617$	−3.36966	−	1.94547i	−0.135657	−	0.0783219i	−0.566293	+	0.824204i	$0.691623\pi$
$618$		0			0
$619$	−9.13436	+	15.8212i	−0.367141	+	0.635907i	−0.989117	−	0.147129i	$-0.952997\pi$
$619$	−9.13436	+	15.8212i	−0.367141	+	0.635907i	0.621976	+	0.783036i	$0.286330\pi$
$620$	−12.0478			−0.483850
$621$		0			0
$622$	−35.5355	−	20.5164i	−1.42484	−	0.822634i
$623$	−11.1643			−0.447289
$624$		0			0
$625$	−28.5217			−1.14087
$626$	−12.0841	−	20.9302i	−0.482976	−	0.836540i
$627$		0			0
$628$	17.8196	−	30.8645i	0.711079	−	1.23163i
$629$	−11.8310	+	20.4919i	−0.471734	+	0.817067i
$630$		0			0
$631$	−7.88091	−	13.6501i	−0.313734	−	0.543404i	0.665433	−	0.746457i	$-0.268247\pi$
$631$	−7.88091	−	13.6501i	−0.313734	−	0.543404i	−0.979168	+	0.203054i	$0.934913\pi$
$632$	−12.2296	+	7.06073i	−0.486465	+	0.280861i
$633$		0			0
$634$	0.404417	+	0.700470i	0.0160614	+	0.0278192i
$635$	−2.96362	−	5.13314i	−0.117608	−	0.203703i
$636$		0			0
$637$		−	14.4551i		−	0.572732i
$638$			17.6676i			0.699466i
$639$		0			0
$640$	−26.8352	+	15.4933i	−1.06076	+	0.612427i
$641$	3.93679	+	6.81871i	0.155494	+	0.269323i	0.933239	−	0.359257i	$-0.116970\pi$
$641$	3.93679	+	6.81871i	0.155494	+	0.269323i	−0.777745	+	0.628580i	$0.783637\pi$
$642$		0			0
$643$	28.1800			1.11131			0.555656	−	0.831413i	$-0.312467\pi$
$643$	28.1800			1.11131			0.555656	+	0.831413i	$0.312467\pi$
$644$		−	62.3274i		−	2.45604i
$645$		0			0
$646$	6.64738	+	48.3647i	0.261538	+	1.90288i
$647$		−	41.2832i		−	1.62301i	−0.584346	−	0.811504i	$-0.698649\pi$
$647$		−	41.2832i		−	1.62301i	0.584346	−	0.811504i	$-0.301351\pi$
$648$		0			0
$649$	−31.8224	−	18.3726i	−1.24914	−	0.721189i
$650$		−	18.4889i		−	0.725194i
$651$		0			0
$652$	−3.94042	+	6.82501i	−0.154319	+	0.267288i
$653$	30.9349	−	17.8602i	1.21057	−	0.698925i	0.247690	−	0.968839i	$-0.420329\pi$
$653$	30.9349	−	17.8602i	1.21057	−	0.698925i	0.962884	+	0.269914i	$0.0869953\pi$
$654$		0			0
$655$	39.4443			1.54121
$656$	−2.38643	−	4.13342i	−0.0931746	−	0.161383i
$657$		0			0
$658$			27.5748i			1.07498i
$659$	−33.0448			−1.28724			−0.643621	−	0.765344i	$-0.722569\pi$
$659$	−33.0448			−1.28724			−0.643621	+	0.765344i	$0.722569\pi$
$660$		0			0
$661$	38.6931	+	22.3395i	1.50499	+	0.868905i	0.999983	+	0.00578816i	$0.00184244\pi$
$661$	38.6931	+	22.3395i	1.50499	+	0.868905i	0.505004	+	0.863117i	$0.331491\pi$
$662$		−	67.4161i		−	2.62020i
$663$		0			0
$664$	−5.46928	−	3.15769i	−0.212249	−	0.122542i
$665$	−45.6599	−	18.6094i	−1.77061	−	0.721642i
$666$		0			0
$667$	8.85934	+	5.11494i	0.343035	+	0.198051i
$668$	7.82916	+	13.5605i	0.302919	+	0.524672i
$669$		0			0
$670$	−4.28166			−0.165415
$671$	34.2121	+	19.7524i	1.32074	+	0.762531i
$672$		0			0
$673$	15.8318	+	9.14047i	0.610269	+	0.352339i	0.773071	−	0.634320i	$-0.218720\pi$
$673$	15.8318	+	9.14047i	0.610269	+	0.352339i	−0.162802	+	0.986659i	$0.552053\pi$
$674$	2.12043	−	1.22423i	0.0816760	−	0.0471556i
$675$		0			0
$676$	22.8798			0.879994
$677$	−12.5993	+	21.8227i	−0.484232	+	0.838715i	−0.999836	−	0.0181123i	$-0.994234\pi$
$677$	−12.5993	+	21.8227i	−0.484232	+	0.838715i	0.515604	+	0.856827i	$0.327568\pi$
$678$		0			0
$679$			20.4184i			0.783586i
$680$	−10.6042	+	18.3670i	−0.406653	+	0.704343i
$681$		0			0
$682$	8.31305	+	14.3986i	0.318323	+	0.551352i
$683$	13.1758			0.504159			0.252080	−	0.967706i	$-0.418886\pi$
$683$	13.1758			0.504159			0.252080	+	0.967706i	$0.418886\pi$
$684$		0			0
$685$	34.6565			1.32416
$686$	0.0747538	+	0.129477i	0.00285412	+	0.00494347i
$687$		0			0
$688$	−2.29325	+	3.97203i	−0.0874294	+	0.151432i
$689$			18.6089i			0.708941i
$690$		0			0
$691$	25.6729	−	44.4667i	0.976641	−	1.69159i	0.302233	−	0.953234i	$-0.402268\pi$
$691$	25.6729	−	44.4667i	0.976641	−	1.69159i	0.674409	−	0.738358i	$-0.264399\pi$
$692$	49.3369			1.87551
$693$		0			0
$694$	60.4452	−	34.8981i	2.29447	−	1.32471i
$695$	48.5276	+	28.0174i	1.84076	+	1.06276i
$696$		0			0
$697$	−9.13477	−	5.27396i	−0.346004	−	0.199766i
$698$	−16.2614			−0.615502
$699$		0			0
$700$	−20.3828	−	35.3041i	−0.770398	−	1.33437i
$701$	−25.4463	−	14.6914i	−0.961092	−	0.554887i	−0.0645833	−	0.997912i	$-0.520572\pi$
$701$	−25.4463	−	14.6914i	−0.961092	−	0.554887i	−0.896509	+	0.443025i	$0.853905\pi$
$702$		0			0
$703$	2.69695	+	19.6223i	0.101717	+	0.740071i
$704$	52.8766	+	30.5283i	1.99286	+	1.15058i
$705$		0			0
$706$			11.0700i			0.416626i
$707$	5.22378	+	3.01595i	0.196460	+	0.113426i
$708$		0			0
$709$	46.1959			1.73492			0.867462	−	0.497504i	$-0.165750\pi$
$709$	46.1959			1.73492			0.867462	+	0.497504i	$0.165750\pi$
$710$		−	34.9337i		−	1.31104i
$711$		0			0
$712$	2.00987	+	3.48119i	0.0753230	+	0.130463i
$713$	9.62684			0.360528
$714$		0			0
$715$	−27.6493	+	15.9633i	−1.03402	+	0.596994i
$716$	19.5311	−	33.8289i	0.729912	−	1.26424i
$717$		0			0
$718$		−	13.5688i		−	0.506382i
$719$	5.87831	+	3.39385i	0.219224	+	0.126569i	0.605591	−	0.795776i	$-0.292937\pi$
$719$	5.87831	+	3.39385i	0.219224	+	0.126569i	−0.386367	+	0.922345i	$0.626270\pi$
$720$		0			0
$721$		−	39.3520i		−	1.46555i
$722$	29.2229	+	28.5655i	1.08756	+	1.06310i
$723$		0			0
$724$		−	11.6929i		−	0.434562i
$725$	6.69093			0.248495
$726$		0			0
$727$	−1.33747	−	2.31657i	−0.0496040	−	0.0859167i	0.840157	−	0.542343i	$-0.182463\pi$
$727$	−1.33747	−	2.31657i	−0.0496040	−	0.0859167i	−0.889761	+	0.456426i	$0.849129\pi$
$728$	−9.02663	+	5.21152i	−0.334549	+	0.193152i
$729$		0			0
$730$			24.7681i			0.916707i
$731$			10.1361i			0.374896i
$732$		0			0
$733$	11.4965	+	19.9126i	0.424634	+	0.735488i	0.996386	−	0.0849388i	$-0.0270695\pi$
$733$	11.4965	+	19.9126i	0.424634	+	0.735488i	−0.571752	+	0.820426i	$0.693736\pi$
$734$	7.98301	+	13.8270i	0.294658	+	0.510363i
$735$		0			0
$736$	42.6615	−	24.6307i	1.57253	−	0.907898i
$737$	1.67707	+	2.90477i	0.0617757	+	0.106999i
$738$		0			0
$739$	−14.6521	+	25.3781i	−0.538985	+	0.933550i	0.459974	+	0.887933i	$0.347859\pi$
$739$	−14.6521	+	25.3781i	−0.538985	+	0.933550i	−0.998959	+	0.0456175i	$0.985474\pi$
$740$	−18.0487	+	31.2613i	−0.663485	+	1.14919i
$741$		0			0
$742$	36.1400	+	62.5962i	1.32674	+	2.29798i
$743$	−13.5165			−0.495872			−0.247936	−	0.968776i	$-0.579752\pi$
$743$	−13.5165			−0.495872			−0.247936	+	0.968776i	$0.579752\pi$
$744$		0			0
$745$	−22.0350			−0.807300
$746$	45.6011	+	26.3278i	1.66958	+	0.963930i
$747$		0			0
$748$	69.6986			2.54843
$749$	−19.3010	+	33.4303i	−0.705243	+	1.22152i
$750$		0			0
$751$	−27.4491	−	15.8478i	−1.00163	−	0.578293i	−0.0929020	−	0.995675i	$-0.529614\pi$
$751$	−27.4491	−	15.8478i	−1.00163	−	0.578293i	−0.908731	+	0.417382i	$0.862948\pi$
$752$	−6.99672	+	4.03956i	−0.255144	+	0.147308i
$753$		0			0
$754$		−	7.17683i		−	0.261365i
$755$	3.33316	−	5.77321i	0.121306	−	0.210109i
$756$		0			0
$757$	−2.36484	+	4.09603i	−0.0859517	+	0.148873i	−0.905796	−	0.423713i	$-0.860726\pi$
$757$	−2.36484	+	4.09603i	−0.0859517	+	0.148873i	0.819845	+	0.572586i	$0.194060\pi$
$758$	−50.8668	+	29.3679i	−1.84756	+	1.06669i
$759$		0			0
$760$	2.41729	+	17.5876i	0.0876843	+	0.637969i
$761$	−0.577494	+	0.333416i	−0.0209342	+	0.0120863i	−0.510431	−	0.859919i	$-0.670514\pi$
$761$	−0.577494	+	0.333416i	−0.0209342	+	0.0120863i	0.489496	+	0.872005i	$0.337181\pi$
$762$		0			0
$763$	−19.0704	+	11.0103i	−0.690393	+	0.398599i
$764$	−52.9529	+	30.5724i	−1.91577	+	1.10607i
$765$		0			0
$766$	1.21301	+	2.10100i	0.0438279	+	0.0759122i
$767$	12.9267	+	7.46324i	0.466757	+	0.269482i
$768$		0			0
$769$	−11.9041	+	20.6185i	−0.429273	+	0.743523i	−0.996809	−	0.0798259i	$-0.974564\pi$
$769$	−11.9041	+	20.6185i	−0.429273	+	0.743523i	0.567536	+	0.823349i	$0.307897\pi$
$770$	−62.0041	+	107.394i	−2.23447	+	3.87022i
$771$		0			0
$772$	−51.3271	−	29.6337i	−1.84730	−	1.06654i
$773$	5.80883	+	10.0612i	0.208929	+	0.361876i	0.951377	−	0.308027i	$-0.0996689\pi$
$773$	5.80883	+	10.0612i	0.208929	+	0.361876i	−0.742448	+	0.669903i	$0.766336\pi$
$774$		0			0
$775$	5.45293	−	3.14825i	0.195875	−	0.113089i
$776$	6.36675	−	3.67585i	0.228553	−	0.131955i
$777$		0			0
$778$	3.65899	−	2.11252i	0.131181	−	0.0757375i
$779$	−8.74712	+	1.20223i	−0.313398	+	0.0430743i
$780$		0			0
$781$	−23.6998	+	13.6831i	−0.848046	+	0.489620i
$782$	35.5469	−	61.5691i	1.27116	−	2.20171i
$783$		0			0
$784$	8.22509	−	14.2463i	0.293753	−	0.508795i
$785$			41.0576i			1.46541i
$786$		0			0
$787$	8.15629	−	4.70904i	0.290740	−	0.167859i	−0.347535	−	0.937667i	$-0.612981\pi$
$787$	8.15629	−	4.70904i	0.290740	−	0.167859i	0.638276	+	0.769808i	$0.279648\pi$
$788$	−4.77627	−	2.75758i	−0.170148	−	0.0982348i
$789$		0			0
$790$	34.1241	−	59.1047i	1.21408	−	2.10285i
$791$	57.4619			2.04311
$792$		0			0
$793$	−13.8975	−	8.02370i	−0.493513	−	0.284930i
$794$	72.2395			2.56368
$795$		0			0
$796$	35.8035			1.26902
$797$	−22.1959	−	38.4444i	−0.786218	−	1.36177i	−0.928269	−	0.371910i	$-0.878703\pi$
$797$	−22.1959	−	38.4444i	−0.786218	−	1.36177i	0.142051	−	0.989859i	$-0.454630\pi$
$798$		0			0
$799$	−8.92733	+	15.4626i	−0.315826	+	0.547027i
$800$	16.1099	−	27.9031i	0.569569	−	0.986523i
$801$		0			0
$802$	−6.61724	−	11.4614i	−0.233663	−	0.404716i
$803$	16.8032	−	9.70134i	0.592972	−	0.342353i
$804$		0			0
$805$	35.9016	+	62.1835i	1.26537	+	2.19168i
$806$	−3.37688	−	5.84893i	−0.118946	−	0.206020i
$807$		0			0
$808$		−	2.17180i		−	0.0764036i
$809$			4.81244i			0.169196i	0.996415	+	0.0845982i	$0.0269607\pi$
$809$			4.81244i			0.169196i	−0.996415	+	0.0845982i	$0.973039\pi$
$810$		0			0
$811$	−17.1253	+	9.88731i	−0.601351	+	0.347190i	−0.769573	−	0.638559i	$-0.779531\pi$
$811$	−17.1253	+	9.88731i	−0.601351	+	0.347190i	0.168222	+	0.985749i	$0.446198\pi$
$812$	−7.91200	−	13.7040i	−0.277657	−	0.480916i
$813$		0			0
$814$	49.8151			1.74602
$815$		−	9.07901i		−	0.318024i
$816$		0			0
$817$	5.20329	+	6.70180i	0.182040	+	0.234466i
$818$			8.05649i			0.281689i
$819$		0			0
$820$	−13.9355	−	8.04565i	−0.486648	−	0.280966i
$821$		−	6.25639i		−	0.218350i	−0.994023	−	0.109175i	$-0.965179\pi$
$821$		−	6.25639i		−	0.218350i	0.994023	−	0.109175i	$-0.0348208\pi$
$822$		0			0
$823$	−7.11827	+	12.3292i	−0.248127	+	0.429769i	−0.963006	−	0.269479i	$-0.913148\pi$
$823$	−7.11827	+	12.3292i	−0.248127	+	0.429769i	0.714879	+	0.699248i	$0.246482\pi$
$824$	−12.2705	+	7.08439i	−0.427464	+	0.246796i
$825$		0			0
$826$	57.9769			2.01728
$827$	−6.98747	−	12.1027i	−0.242978	−	0.420851i	0.718583	−	0.695441i	$-0.244791\pi$
$827$	−6.98747	−	12.1027i	−0.242978	−	0.420851i	−0.961561	+	0.274590i	$0.911458\pi$
$828$		0			0
$829$			6.20264i			0.215427i	0.994182	+	0.107713i	$0.0343529\pi$
$829$			6.20264i			0.215427i	−0.994182	+	0.107713i	$0.965647\pi$
$830$	30.5219			1.05943
$831$		0			0
$832$	−21.4793	−	12.4011i	−0.744659	−	0.429929i
$833$		−	36.3545i		−	1.25961i
$834$		0			0
$835$	−15.6222	−	9.01946i	−0.540628	−	0.312131i
$836$	46.0836	−	35.7794i	1.59383	−	1.23746i
$837$		0			0
$838$	6.81358	+	3.93382i	0.235371	+	0.135892i
$839$	11.2033	+	19.4047i	0.386781	+	0.669925i	0.992015	−	0.126123i	$-0.0402535\pi$
$839$	11.2033	+	19.4047i	0.386781	+	0.669925i	−0.605233	+	0.796048i	$0.706920\pi$
$840$		0			0
$841$	−26.4028			−0.910441
$842$	−13.7777	−	7.95456i	−0.474811	−	0.274132i
$843$		0			0
$844$	62.2808	+	35.9578i	2.14379	+	1.23772i
$845$	−22.8270	+	13.1792i	−0.785273	+	0.453378i
$846$		0			0
$847$	56.0141			1.92467
$848$	−10.5886	+	18.3400i	−0.363614	+	0.629798i
$849$		0			0
$850$		−	46.4994i		−	1.59492i
$851$	14.4220	−	24.9796i	0.494379	−	0.856289i
$852$		0			0
$853$	−6.00853	−	10.4071i	−0.205728	−	0.356332i	0.744636	−	0.667471i	$-0.232623\pi$
$853$	−6.00853	−	10.4071i	−0.205728	−	0.356332i	−0.950365	+	0.311139i	$0.899290\pi$
$854$	−62.3308			−2.13291
$855$		0			0
$856$	13.8987			0.475049
$857$	−18.0738	−	31.3047i	−0.617389	−	1.06935i	−0.989960	−	0.141346i	$-0.954857\pi$
$857$	−18.0738	−	31.3047i	−0.617389	−	1.06935i	0.372571	−	0.928004i	$-0.378476\pi$
$858$		0			0
$859$	−17.8252	+	30.8741i	−0.608187	+	1.05341i	0.383352	+	0.923602i	$0.374770\pi$
$859$	−17.8252	+	30.8741i	−0.608187	+	1.05341i	−0.991539	+	0.129809i	$0.958564\pi$
$860$			15.4630i			0.527283i
$861$		0			0
$862$	12.4319	−	21.5326i	0.423431	−	0.733404i
$863$	−21.0718			−0.717294			−0.358647	−	0.933473i	$-0.616762\pi$
$863$	−21.0718			−0.717294			−0.358647	+	0.933473i	$0.616762\pi$
$864$		0			0
$865$	−49.2230	+	28.4189i	−1.67363	+	0.966271i
$866$	−6.36186	−	3.67302i	−0.216185	−	0.124814i
$867$		0			0
$868$	−12.8961	−	7.44560i	−0.437724	−	0.252720i
$869$	−53.4640			−1.81364
$870$		0			0
$871$	−0.681251	−	1.17996i	−0.0230833	−	0.0399815i
$872$	6.86633	+	3.96428i	0.232523	+	0.134247i
$873$		0			0
$874$	−8.10312	−	58.9563i	−0.274092	−	1.99423i
$875$	−8.30955	−	4.79752i	−0.280914	−	0.162186i
$876$		0			0
$877$		−	51.2369i		−	1.73015i	−0.501645	−	0.865073i	$-0.667272\pi$
$877$		−	51.2369i		−	1.73015i	0.501645	−	0.865073i	$-0.332728\pi$
$878$	45.4550	+	26.2434i	1.53403	+	0.885673i
$879$		0			0
$880$	−36.3331			−1.22479
$881$		−	11.1100i		−	0.374304i	−0.982331	−	0.187152i	$-0.940074\pi$
$881$		−	11.1100i		−	0.374304i	0.982331	−	0.187152i	$-0.0599257\pi$
$882$		0			0
$883$	15.1216	+	26.1914i	0.508883	+	0.881411i	0.999947	+	0.0102875i	$0.00327469\pi$
$883$	15.1216	+	26.1914i	0.508883	+	0.881411i	−0.491064	+	0.871123i	$0.663392\pi$
$884$	−28.3126			−0.952256
$885$		0			0
$886$	72.6180	−	41.9260i	2.43965	−	1.40853i
$887$	−0.648824	+	1.12380i	−0.0217854	+	0.0377334i	−0.876713	−	0.481015i	$-0.840268\pi$
$887$	−0.648824	+	1.12380i	−0.0217854	+	0.0377334i	0.854927	+	0.518748i	$0.173602\pi$
$888$		0			0
$889$		−	7.32615i		−	0.245711i
$890$	−16.8244	−	9.71358i	−0.563956	−	0.325600i
$891$		0			0
$892$			6.06557i			0.203090i
$893$	2.03503	+	14.8064i	0.0680998	+	0.495478i
$894$		0			0
$895$			45.0010i			1.50422i
$896$	−38.2999			−1.27951
$897$		0			0
$898$	28.0516	+	48.5869i	0.936096	+	1.62137i
$899$	2.11666	−	1.22206i	0.0705947	−	0.0407579i
$900$		0			0
$901$			46.8011i			1.55917i
$902$			22.2062i			0.739387i
$903$		0			0
$904$	−10.3446	−	17.9174i	−0.344058	−	0.595925i
$905$	6.73529	+	11.6659i	0.223889	+	0.387787i
$906$		0			0
$907$	−31.1588	+	17.9895i	−1.03461	+	0.597333i	−0.918302	−	0.395880i	$-0.870440\pi$
$907$	−31.1588	+	17.9895i	−1.03461	+	0.597333i	−0.116309	+	0.993213i	$0.537106\pi$
$908$	−15.4242	−	26.7155i	−0.511871	−	0.886586i
$909$		0			0
$910$	25.1870	−	43.6252i	0.834941	−	1.44616i
$911$	6.18966	−	10.7208i	0.205073	−	0.355196i	−0.745083	−	0.666972i	$-0.767590\pi$
$911$	6.18966	−	10.7208i	0.205073	−	0.355196i	0.950156	+	0.311775i	$0.100924\pi$
$912$		0			0
$913$	−11.9550	−	20.7067i	−0.395654	−	0.685292i
$914$	38.3374			1.26809
$915$		0			0
$916$	17.4180			0.575508
$917$	42.2219	+	24.3768i	1.39429	+	0.804993i
$918$		0			0
$919$	−10.1943			−0.336279			−0.168139	−	0.985763i	$-0.553776\pi$
$919$	−10.1943			−0.336279			−0.168139	+	0.985763i	$0.553776\pi$
$920$	12.9265	−	22.3893i	0.426173	−	0.738154i
$921$		0			0
$922$	−66.3419	−	38.3025i	−2.18485	−	1.26143i
$923$	9.62722	−	5.55828i	0.316884	−	0.182953i
$924$		0			0
$925$		−	18.8656i		−	0.620296i
$926$	11.8390	−	20.5058i	0.389055	−	0.673863i
$927$		0			0
$928$	6.25336	−	10.8311i	0.205277	−	0.355550i
$929$	−0.786138	+	0.453877i	−0.0257924	+	0.0148912i	−0.512841	−	0.858484i	$-0.671407\pi$
$929$	−0.786138	+	0.453877i	−0.0257924	+	0.0148912i	0.487048	+	0.873375i	$0.338074\pi$
$930$		0			0
$931$	−18.6624	−	24.0370i	−0.611635	−	0.787781i
$932$	−8.24239	+	4.75875i	−0.269989	+	0.155878i
$933$		0			0
$934$	44.2493	−	25.5474i	1.44788	−	0.835935i
$935$	−69.5377	+	40.1476i	−2.27413	+	1.31297i
$936$		0			0
$937$	−23.0292	−	39.8878i	−0.752332	−	1.30308i	−0.946690	−	0.322146i	$-0.895596\pi$
$937$	−23.0292	−	39.8878i	−0.752332	−	1.30308i	0.194358	−	0.980931i	$-0.437738\pi$
$938$	−4.58317	−	2.64609i	−0.149646	−	0.0863980i
$939$		0			0
$940$	−13.6190	+	23.5888i	−0.444203	+	0.769383i
$941$	−26.4298	+	45.7778i	−0.861587	+	1.49231i	0.00880912	+	0.999961i	$0.497196\pi$
$941$	−26.4298	+	45.7778i	−0.861587	+	1.49231i	−0.870396	+	0.492352i	$0.836137\pi$
$942$		0			0
$943$	11.1352	+	6.42893i	0.362613	+	0.209355i
$944$	8.49330	+	14.7108i	0.276433	+	0.478797i
$945$		0			0
$946$	18.4803	−	10.6696i	0.600845	−	0.346898i
$947$	−5.73555	+	3.31142i	−0.186380	+	0.107607i	−0.590287	−	0.807193i	$-0.700985\pi$
$947$	−5.73555	+	3.31142i	−0.186380	+	0.107607i	0.403907	+	0.914800i	$0.367652\pi$
$948$		0			0
$949$	−6.82571	+	3.94083i	−0.221572	+	0.127925i
$950$	−23.8702	−	30.7447i	−0.774453	−	0.997488i
$951$		0			0
$952$	−22.7019	+	13.1069i	−0.735773	+	0.424799i
$953$	7.59011	−	13.1465i	0.245868	−	0.425855i	−0.716508	−	0.697579i	$-0.754260\pi$
$953$	7.59011	−	13.1465i	0.245868	−	0.425855i	0.962375	+	0.271724i	$0.0875938\pi$
$954$		0			0
$955$	35.2204	−	61.0035i	1.13971	−	1.97403i
$956$		−	39.8516i		−	1.28889i
$957$		0			0
$958$	−77.1419	+	44.5379i	−2.49234	+	1.43895i
$959$	37.0970	+	21.4180i	1.19793	+	0.691622i
$960$		0			0
$961$	−14.3500	+	24.8549i	−0.462903	+	0.801771i
$962$	−20.2356			−0.652422
$963$		0			0
$964$	−55.7696	−	32.1986i	−1.79622	−	1.03705i
$965$	68.2781			2.19795
$966$		0			0
$967$	29.5659			0.950775			0.475387	−	0.879777i	$-0.342308\pi$
$967$	29.5659			0.950775			0.475387	+	0.879777i	$0.342308\pi$
$968$	−10.0840	−	17.4660i	−0.324112	−	0.561378i
$969$		0			0
$970$	−17.7652	+	30.7702i	−0.570405	+	0.987970i
$971$	17.8609	−	30.9360i	0.573184	−	0.992784i	−0.423052	−	0.906105i	$-0.639041\pi$
$971$	17.8609	−	30.9360i	0.573184	−	0.992784i	0.996236	−	0.0866789i	$-0.0276254\pi$
$972$		0			0
$973$	34.6299	+	59.9808i	1.11018	+	1.92290i
$974$	28.0803	−	16.2122i	0.899750	−	0.519471i
$975$		0			0
$976$	−9.13111	−	15.8155i	−0.292280	−	0.506243i
$977$	−0.303010	−	0.524829i	−0.00969416	−	0.0167908i	0.861138	−	0.508372i	$-0.169752\pi$
$977$	−0.303010	−	0.524829i	−0.00969416	−	0.0167908i	−0.870832	+	0.491581i	$0.836419\pi$
$978$		0			0
$979$			15.2187i			0.486393i
$980$		−	55.4603i		−	1.77161i
$981$		0			0
$982$	−78.8070	+	45.4993i	−2.51483	+	1.45194i
$983$	14.1525	+	24.5129i	0.451395	+	0.781839i	0.998473	−	0.0552427i	$-0.0175933\pi$
$983$	14.1525	+	24.5129i	0.451395	+	0.781839i	−0.547078	+	0.837082i	$0.684260\pi$
$984$		0			0
$985$	6.35366			0.202444
$986$		−	18.0497i		−	0.574819i
$987$		0			0
$988$	−18.7198	+	14.5341i	−0.595557	+	0.462392i
$989$		−	12.3558i		−	0.392892i
$990$		0			0
$991$	49.4706	+	28.5619i	1.57149	+	0.907298i	0.995987	+	0.0894946i	$0.0285252\pi$
$991$	49.4706	+	28.5619i	1.57149	+	0.907298i	0.575498	+	0.817803i	$0.304808\pi$
$992$		−	11.7695i		−	0.373681i
$993$		0			0
$994$	21.5893	−	37.3937i	0.684770	−	1.18606i
$995$	−35.7208	+	20.6234i	−1.13243	+	0.653806i
$996$		0			0
$997$	−36.7425			−1.16365			−0.581823	−	0.813316i	$-0.697660\pi$
$997$	−36.7425			−1.16365			−0.581823	+	0.813316i	$0.697660\pi$
$998$	46.5207	+	80.5763i	1.47259	+	2.55060i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.k.a.8.16		36
3.2	odd	2		171.2.k.a.65.3	yes	36
9.4	even	3		171.2.t.a.122.3	yes	36
9.5	odd	6		513.2.t.a.179.16		36
19.12	odd	6		513.2.t.a.278.16		36
57.50	even	6		171.2.t.a.164.3	yes	36
171.31	odd	6		171.2.k.a.50.3	✓	36
171.50	even	6	inner	513.2.k.a.449.16		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.k.a.50.3	✓	36	171.31	odd	6
171.2.k.a.65.3	yes	36	3.2	odd	2
171.2.t.a.122.3	yes	36	9.4	even	3
171.2.t.a.164.3	yes	36	57.50	even	6
513.2.k.a.8.16		36	1.1	even	1	trivial
513.2.k.a.449.16		36	171.50	even	6	inner
513.2.t.a.179.16		36	9.5	odd	6
513.2.t.a.278.16		36	19.12	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.07540 + 1.86265i) q^{2} +(-1.31298 + 2.27414i) q^{4} -3.02519i q^{5} +(1.86959 - 3.23822i) q^{7} -1.34630 q^{8} +(5.63486 - 3.25329i) q^{10} +(-4.41421 - 2.54855i) q^{11} +(1.79312 + 1.03526i) q^{13} +8.04222 q^{14} +(1.17814 + 2.04060i) q^{16} +(4.50968 + 2.60366i) q^{17} +(4.31830 - 0.593520i) q^{19} +(6.87970 + 3.97200i) q^{20} -10.9628i q^{22} +(-5.49727 - 3.17385i) q^{23} -4.15176 q^{25} +4.45327i q^{26} +(4.90944 + 8.50340i) q^{28} -1.61159 q^{29} +(-1.31340 + 0.758293i) q^{31} +(-3.88025 + 6.72078i) q^{32} +11.1999i q^{34} +(-9.79622 - 5.65585i) q^{35} +4.54399i q^{37} +(5.74943 + 7.40521i) q^{38} +4.07280i q^{40} -2.02559 q^{41} +(0.973250 + 1.68572i) q^{43} +(11.5915 - 6.69236i) q^{44} -13.6527i q^{46} +3.42876i q^{47} +(-3.49070 - 6.04608i) q^{49} +(-4.46481 - 7.73327i) q^{50} +(-4.70864 + 2.71853i) q^{52} +(4.49378 + 7.78345i) q^{53} +(-7.70983 + 13.3538i) q^{55} +(-2.51702 + 4.35961i) q^{56} +(-1.73310 - 3.00183i) q^{58} +7.20907 q^{59} -7.75044 q^{61} +(-2.82487 - 1.63094i) q^{62} -11.9787 q^{64} +(3.13185 - 5.42452i) q^{65} +(-0.569888 - 0.329025i) q^{67} +(-11.8422 + 6.83709i) q^{68} -24.3292i q^{70} +(2.68449 - 4.64968i) q^{71} +(-1.90331 + 3.29663i) q^{73} +(-8.46387 + 4.88662i) q^{74} +(-4.32008 + 10.5997i) q^{76} +(-16.5055 + 9.52945i) q^{77} +(9.08384 - 5.24456i) q^{79} +(6.17320 - 3.56410i) q^{80} +(-2.17832 - 3.77297i) q^{82} +(4.06246 + 2.34546i) q^{83} +(7.87657 - 13.6426i) q^{85} +(-2.09327 + 3.62565i) q^{86} +(5.94284 + 3.43110i) q^{88} +(-1.49289 - 2.58575i) q^{89} +(6.70478 - 3.87100i) q^{91} +(14.4356 - 8.33438i) q^{92} +(-6.38657 + 3.68729i) q^{94} +(-1.79551 - 13.0637i) q^{95} +(-4.72908 + 2.73034i) q^{97} +(7.50782 - 13.0039i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{2} - 15 q^{4} - q^{7} - 12 q^{8} - 6 q^{10} + 9 q^{11} - 6 q^{13} + 6 q^{14} - 9 q^{16} + 27 q^{17} + q^{19} - 9 q^{20} - 9 q^{23} - 22 q^{25} + 2 q^{28} + 24 q^{29} + 12 q^{31} + 15 q^{32}+ \cdots + 84 q^{98}+O(q^{100}) \) 36 * q + 3 * q^2 - 15 * q^4 - q^7 - 12 * q^8 - 6 * q^10 + 9 * q^11 - 6 * q^13 + 6 * q^14 - 9 * q^16 + 27 * q^17 + q^19 - 9 * q^20 - 9 * q^23 - 22 * q^25 + 2 * q^28 + 24 * q^29 + 12 * q^31 + 15 * q^32 - 15 * q^35 + 18 * q^38 - 36 * q^41 + 3 * q^43 - 66 * q^44 - 9 * q^49 - 3 * q^50 + 15 * q^52 + 12 * q^53 - 7 * q^55 - 6 * q^56 - 6 * q^58 + 18 * q^59 - 16 * q^61 + 12 * q^62 + 12 * q^64 + 18 * q^65 + 27 * q^67 - 60 * q^68 - 9 * q^71 - 18 * q^73 - 90 * q^74 - 23 * q^76 + 6 * q^77 - 6 * q^79 + 12 * q^80 - 9 * q^82 + 9 * q^83 + 11 * q^85 - 51 * q^86 + 3 * q^88 + 18 * q^89 + 27 * q^91 + 93 * q^92 + 12 * q^94 + 24 * q^97 + 84 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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