LMFDB - Embedded newform 414.2.p.a.5.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(5,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("414.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.p (of order $66$, degree $20$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$24$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			5.7
Character	$\chi$	$=$	414.5
Dual form			414.2.p.a.83.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.971812 + 0.235759i) q^{2} +(-0.201012 - 1.72035i) q^{3} +(0.888835 - 0.458227i) q^{4} +(0.914714 + 0.719339i) q^{5} +(0.600933 + 1.62446i) q^{6} +(3.62325 + 2.58010i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(-2.91919 + 0.691621i) q^{9} +O(q^{10})$	\(q+(-0.971812 + 0.235759i) q^{2} +(-0.201012 - 1.72035i) q^{3} +(0.888835 - 0.458227i) q^{4} +(0.914714 + 0.719339i) q^{5} +(0.600933 + 1.62446i) q^{6} +(3.62325 + 2.58010i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(-2.91919 + 0.691621i) q^{9} +(-1.05852 - 0.483410i) q^{10} +(0.538534 + 0.513491i) q^{11} +(-0.966975 - 1.43700i) q^{12} +(2.72172 + 3.82213i) q^{13} +(-4.12939 - 1.65316i) q^{14} +(1.05364 - 1.71822i) q^{15} +(0.580057 - 0.814576i) q^{16} +(-4.19280 + 2.69455i) q^{17} +(2.67385 - 1.36035i) q^{18} +(-3.19818 + 4.97647i) q^{19} +(1.14265 + 0.220228i) q^{20} +(3.71035 - 6.75187i) q^{21} +(-0.644414 - 0.372052i) q^{22} +(4.66550 - 1.11045i) q^{23} +(1.27850 + 1.16852i) q^{24} +(-0.859542 - 3.54308i) q^{25} +(-3.54610 - 3.07272i) q^{26} +(1.77662 + 4.88299i) q^{27} +(4.40274 + 0.633019i) q^{28} +(3.01532 - 5.84891i) q^{29} +(-0.618858 + 1.91819i) q^{30} +(2.67188 - 0.514964i) q^{31} +(-0.371662 + 0.928368i) q^{32} +(0.775131 - 1.02968i) q^{33} +(3.43935 - 3.60709i) q^{34} +(1.45827 + 4.96640i) q^{35} +(-2.27776 + 1.95239i) q^{36} +(9.49338 - 1.36494i) q^{37} +(1.93478 - 5.59019i) q^{38} +(6.02829 - 5.45060i) q^{39} +(-1.16236 + 0.0553701i) q^{40} +(0.0722997 - 0.0919365i) q^{41} +(-2.01395 + 7.43630i) q^{42} +(1.25283 - 6.50029i) q^{43} +(0.713963 + 0.209639i) q^{44} +(-3.16773 - 1.46725i) q^{45} +(-4.27219 + 2.17908i) q^{46} +(-6.48016 + 3.74132i) q^{47} +(-1.51795 - 0.834160i) q^{48} +(4.18151 + 12.0817i) q^{49} +(1.67062 + 3.24056i) q^{50} +(5.47836 + 6.67144i) q^{51} +(4.17056 + 2.15008i) q^{52} +(-3.78565 - 8.28941i) q^{53} +(-2.87775 - 4.32650i) q^{54} +(0.123230 + 0.857086i) q^{55} +(-4.42787 + 0.422811i) q^{56} +(9.20412 + 4.50165i) q^{57} +(-1.55139 + 6.39492i) q^{58} +(-8.13272 + 5.79128i) q^{59} +(0.149182 - 2.01002i) q^{60} +(1.48561 + 0.514173i) q^{61} +(-2.47516 + 1.13037i) q^{62} +(-12.3614 - 5.02589i) q^{63} +(0.142315 - 0.989821i) q^{64} +(-0.259806 + 5.45400i) q^{65} +(-0.510524 + 1.18340i) q^{66} +(-7.38715 - 7.74742i) q^{67} +(-2.49200 + 4.31626i) q^{68} +(-2.84818 - 7.80307i) q^{69} +(-2.58803 - 4.48260i) q^{70} +(0.330776 - 1.12652i) q^{71} +(1.75326 - 2.43435i) q^{72} +(-3.79485 - 2.43880i) q^{73} +(-8.90398 + 3.56462i) q^{74} +(-5.92255 + 2.19091i) q^{75} +(-0.562307 + 5.88875i) q^{76} +(0.626382 + 3.24998i) q^{77} +(-4.57333 + 6.71818i) q^{78} +(0.0389503 + 0.407906i) q^{79} +(1.11654 - 0.327846i) q^{80} +(8.04332 - 4.03794i) q^{81} +(-0.0485868 + 0.106390i) q^{82} +(3.28319 - 2.58193i) q^{83} +(0.204008 - 7.70149i) q^{84} +(-5.77351 - 0.551303i) q^{85} +(0.314989 + 6.61243i) q^{86} +(-10.6683 - 4.01170i) q^{87} +(-0.743262 - 0.0354059i) q^{88} +(8.76977 - 10.1209i) q^{89} +(3.42436 + 0.679070i) q^{90} +20.8708i q^{91} +(3.63802 - 3.12486i) q^{92} +(-1.42300 - 4.49306i) q^{93} +(5.41544 - 5.16361i) q^{94} +(-6.50519 + 2.25147i) q^{95} +(1.67182 + 0.452775i) q^{96} +(-5.96302 - 14.8949i) q^{97} +(-6.91201 - 10.7553i) q^{98} +(-1.92722 - 1.12652i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{22}\right)$

Coefficient data

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

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

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

$2$	−0.971812	+	0.235759i	−0.687175	+	0.166707i
$2$	−0.971812	+	0.235759i	−0.687175	+	0.166707i
$3$	−0.201012	−	1.72035i	−0.116054	−	0.993243i
$3$	−0.201012	−	1.72035i	−0.116054	−	0.993243i
$4$	0.888835	−	0.458227i	0.444418	−	0.229113i
$5$	0.914714	+	0.719339i	0.409073	+	0.321698i	0.801402	−	0.598127i	$-0.204088\pi$
$5$	0.914714	+	0.719339i	0.409073	+	0.321698i	−0.392329	+	0.919825i	$0.628331\pi$
$6$	0.600933	+	1.62446i	0.245330	+	0.663184i
$7$	3.62325	+	2.58010i	1.36946	+	0.975187i	0.998924	+	0.0463680i	$0.0147647\pi$
$7$	3.62325	+	2.58010i	1.36946	+	0.975187i	0.370534	+	0.928819i	$0.379175\pi$
$8$	−0.755750	+	0.654861i	−0.267198	+	0.231528i
$9$	−2.91919	+	0.691621i	−0.973063	+	0.230540i
$10$	−1.05852	−	0.483410i	−0.334734	−	0.152868i
$11$	0.538534	+	0.513491i	0.162374	+	0.154823i	0.766910	−	0.641754i	$-0.221793\pi$
$11$	0.538534	+	0.513491i	0.162374	+	0.154823i	−0.604536	+	0.796578i	$0.706642\pi$
$12$	−0.966975	−	1.43700i	−0.279142	−	0.414825i
$13$	2.72172	+	3.82213i	0.754870	+	1.06007i	0.995981	+	0.0895695i	$0.0285491\pi$
$13$	2.72172	+	3.82213i	0.754870	+	1.06007i	−0.241110	+	0.970498i	$0.577511\pi$
$14$	−4.12939	−	1.65316i	−1.10363	−	0.441826i
$15$	1.05364	−	1.71822i	0.272050	−	0.443643i
$16$	0.580057	−	0.814576i	0.145014	−	0.203644i
$17$	−4.19280	+	2.69455i	−1.01690	+	0.653524i	−0.939171	−	0.343450i	$-0.888404\pi$
$17$	−4.19280	+	2.69455i	−1.01690	+	0.653524i	−0.0777327	+	0.996974i	$0.524768\pi$
$18$	2.67385	−	1.36035i	0.630231	−	0.320638i
$19$	−3.19818	+	4.97647i	−0.733713	+	1.14168i	0.251083	+	0.967965i	$0.419213\pi$
$19$	−3.19818	+	4.97647i	−0.733713	+	1.14168i	−0.984796	+	0.173714i	$0.944423\pi$
$20$	1.14265	+	0.220228i	0.255504	+	0.0492444i
$21$	3.71035	−	6.75187i	0.809666	−	1.47338i
$22$	−0.644414	−	0.372052i	−0.137389	−	0.0793218i
$23$	4.66550	−	1.11045i	0.972824	−	0.231545i
$23$	4.66550	−	1.11045i	0.972824	−	0.231545i
$24$	1.27850	+	1.16852i	0.260973	+	0.238522i
$25$	−0.859542	−	3.54308i	−0.171908	−	0.708616i
$26$	−3.54610	−	3.07272i	−0.695448	−	0.602609i
$27$	1.77662	+	4.88299i	0.341911	+	0.939732i
$28$	4.40274	+	0.633019i	0.832040	+	0.119629i
$29$	3.01532	−	5.84891i	0.559931	−	1.08611i	−0.423680	−	0.905812i	$-0.639262\pi$
$29$	3.01532	−	5.84891i	0.559931	−	1.08611i	0.983611	−	0.180303i	$-0.0577077\pi$
$30$	−0.618858	+	1.91819i	−0.112987	+	0.350213i
$31$	2.67188	−	0.514964i	0.479885	−	0.0924902i	0.0564282	−	0.998407i	$-0.482029\pi$
$31$	2.67188	−	0.514964i	0.479885	−	0.0924902i	0.423456	+	0.905916i	$0.360817\pi$
$32$	−0.371662	+	0.928368i	−0.0657013	+	0.164114i
$33$	0.775131	−	1.02968i	0.134933	−	0.179245i
$34$	3.43935	−	3.60709i	0.589843	−	0.618610i
$35$	1.45827	+	4.96640i	0.246492	+	0.839475i
$36$	−2.27776	+	1.95239i	−0.379627	+	0.325398i
$37$	9.49338	−	1.36494i	1.56070	−	0.224395i	0.692800	−	0.721130i	$-0.256377\pi$
$37$	9.49338	−	1.36494i	1.56070	−	0.224395i	0.867903	+	0.496734i	$0.165468\pi$
$38$	1.93478	−	5.59019i	0.313863	−	0.906848i
$39$	6.02829	−	5.45060i	0.965298	−	0.872795i
$40$	−1.16236	+	0.0553701i	−0.183786	+	0.00875478i
$41$	0.0722997	−	0.0919365i	0.0112913	−	0.0143581i	−0.780375	−	0.625312i	$-0.784972\pi$
$41$	0.0722997	−	0.0919365i	0.0112913	−	0.0143581i	0.791666	+	0.610954i	$0.209214\pi$
$42$	−2.01395	+	7.43630i	−0.310759	+	1.14745i
$43$	1.25283	−	6.50029i	0.191055	−	0.991286i	−0.752130	−	0.659015i	$-0.770973\pi$
$43$	1.25283	−	6.50029i	0.191055	−	0.991286i	0.943184	−	0.332270i	$-0.107815\pi$
$44$	0.713963	+	0.209639i	0.107634	+	0.0316042i
$45$	−3.16773	−	1.46725i	−0.472218	−	0.218725i
$46$	−4.27219	+	2.17908i	−0.629900	+	0.321288i
$47$	−6.48016	+	3.74132i	−0.945228	+	0.545728i	−0.891595	−	0.452833i	$-0.850413\pi$
$47$	−6.48016	+	3.74132i	−0.945228	+	0.545728i	−0.0536326	+	0.998561i	$0.517080\pi$
$48$	−1.51795	−	0.834160i	−0.219097	−	0.120401i
$49$	4.18151	+	12.0817i	0.597359	+	1.72595i
$50$	1.67062	+	3.24056i	0.236262	+	0.458284i
$51$	5.47836	+	6.67144i	0.767125	+	0.934188i
$52$	4.17056	+	2.15008i	0.578353	+	0.298162i
$53$	−3.78565	−	8.28941i	−0.519999	−	1.13864i	−0.969440	−	0.245329i	$-0.921104\pi$
$53$	−3.78565	−	8.28941i	−0.519999	−	1.13864i	0.449441	−	0.893310i	$-0.351623\pi$
$54$	−2.87775	−	4.32650i	−0.391612	−	0.588761i
$55$	0.123230	+	0.857086i	0.0166164	+	0.115569i
$56$	−4.42787	+	0.422811i	−0.591700	+	0.0565005i
$57$	9.20412	+	4.50165i	1.21912	+	0.596258i
$58$	−1.55139	+	6.39492i	−0.203708	+	0.839694i
$59$	−8.13272	+	5.79128i	−1.05879	+	0.753961i	−0.970248	−	0.242111i	$-0.922160\pi$
$59$	−8.13272	+	5.79128i	−1.05879	+	0.753961i	−0.0885417	+	0.996072i	$0.528221\pi$
$60$	0.149182	−	2.01002i	0.0192593	−	0.259493i
$61$	1.48561	+	0.514173i	0.190212	+	0.0658331i	0.420514	−	0.907286i	$-0.361850\pi$
$61$	1.48561	+	0.514173i	0.190212	+	0.0658331i	−0.230301	+	0.973119i	$0.573971\pi$
$62$	−2.47516	+	1.13037i	−0.314346	+	0.143557i
$63$	−12.3614	−	5.02589i	−1.55739	−	0.633203i
$64$	0.142315	−	0.989821i	0.0177894	−	0.123728i
$65$	−0.259806	+	5.45400i	−0.0322249	+	0.676485i
$66$	−0.510524	+	1.18340i	−0.0628412	+	0.145667i
$67$	−7.38715	−	7.74742i	−0.902484	−	0.946498i	0.0963217	−	0.995350i	$-0.469292\pi$
$67$	−7.38715	−	7.74742i	−0.902484	−	0.946498i	−0.998806	+	0.0488520i	$0.984444\pi$
$68$	−2.49200	+	4.31626i	−0.302199	+	0.523424i
$69$	−2.84818	−	7.80307i	−0.342881	−	0.939379i
$70$	−2.58803	−	4.48260i	−0.309329	−	0.535774i
$71$	0.330776	−	1.12652i	0.0392558	−	0.133693i	−0.937534	−	0.347895i	$-0.886897\pi$
$71$	0.330776	−	1.12652i	0.0392558	−	0.133693i	0.976790	+	0.214201i	$0.0687149\pi$
$72$	1.75326	−	2.43435i	0.206624	−	0.286891i
$73$	−3.79485	−	2.43880i	−0.444154	−	0.285440i	0.299386	−	0.954132i	$-0.403218\pi$
$73$	−3.79485	−	2.43880i	−0.444154	−	0.285440i	−0.743540	+	0.668692i	$0.766855\pi$
$74$	−8.90398	+	3.56462i	−1.03507	+	0.414378i
$75$	−5.92255	+	2.19091i	−0.683877	+	0.252985i
$76$	−0.562307	+	5.88875i	−0.0645011	+	0.675486i
$77$	0.626382	+	3.24998i	0.0713828	+	0.370369i
$78$	−4.57333	+	6.71818i	−0.517828	+	0.760684i
$79$	0.0389503	+	0.407906i	0.00438225	+	0.0458930i	0.997399	−	0.0720843i	$-0.0229651\pi$
$79$	0.0389503	+	0.407906i	0.00438225	+	0.0458930i	−0.993016	+	0.117977i	$0.962359\pi$
$80$	1.11654	−	0.327846i	0.124833	−	0.0366544i
$81$	8.04332	−	4.03794i	0.893702	−	0.448660i
$82$	−0.0485868	+	0.106390i	−0.00536551	+	0.0117488i
$83$	3.28319	−	2.58193i	0.360377	−	0.283403i	−0.421510	−	0.906824i	$-0.638500\pi$
$83$	3.28319	−	2.58193i	0.360377	−	0.283403i	0.781887	+	0.623420i	$0.214257\pi$
$84$	0.204008	−	7.70149i	0.0222591	−	0.840301i
$85$	−5.77351	−	0.551303i	−0.626225	−	0.0597972i
$86$	0.314989	+	6.61243i	0.0339661	+	0.713036i
$87$	−10.6683	−	4.01170i	−1.14376	−	0.430099i
$88$	−0.743262	−	0.0354059i	−0.0792320	−	0.00377429i
$89$	8.76977	−	10.1209i	0.929594	−	1.07281i	−0.0675829	−	0.997714i	$-0.521529\pi$
$89$	8.76977	−	10.1209i	0.929594	−	1.07281i	0.997176	−	0.0750945i	$-0.0239258\pi$
$90$	3.42436	+	0.679070i	0.360959	+	0.0715803i
$91$			20.8708i			2.18786i
$92$	3.63802	−	3.12486i	0.379290	−	0.325790i
$93$	−1.42300	−	4.49306i	−0.147558	−	0.465908i
$94$	5.41544	−	5.16361i	0.558560	−	0.532586i
$95$	−6.50519	+	2.25147i	−0.667418	+	0.230996i
$96$	1.67182	+	0.452775i	0.170630	+	0.0462112i
$97$	−5.96302	−	14.8949i	−0.605453	−	1.51235i	−0.841306	−	0.540559i	$-0.818213\pi$
$97$	−5.96302	−	14.8949i	−0.605453	−	1.51235i	0.235853	−	0.971789i	$-0.424212\pi$
$98$	−6.91201	−	10.7553i	−0.698218	−	1.08645i
$99$	−1.92722	−	1.12652i	−0.193693	−	0.113219i
$100$	−2.38752	−	2.75535i	−0.238752	−	0.275535i
$101$	6.56690	+	8.35050i	0.653431	+	0.830906i	0.994008	−	0.109311i	$-0.0348645\pi$
$101$	6.56690	+	8.35050i	0.653431	+	0.830906i	−0.340576	+	0.940217i	$0.610622\pi$
$102$	−6.89679	−	5.19181i	−0.682884	−	0.514065i
$103$	1.95957	+	0.475387i	0.193082	+	0.0468412i	0.331134	−	0.943584i	$-0.392569\pi$
$103$	1.95957	+	0.475387i	0.193082	+	0.0468412i	−0.138052	+	0.990425i	$0.544084\pi$
$104$	−4.55990	−	1.10622i	−0.447135	−	0.108474i
$105$	8.25080	−	3.50703i	0.805196	−	0.342251i
$106$	5.63324	+	7.16325i	0.547149	+	0.695756i
$107$	6.64245	+	7.66579i	0.642149	+	0.741080i	0.979753	−	0.200208i	$-0.0641619\pi$
$107$	6.64245	+	7.66579i	0.642149	+	0.741080i	−0.337604	+	0.941288i	$0.609616\pi$
$108$	3.81664	+	3.52608i	0.367256	+	0.339297i
$109$	2.09350	+	3.25754i	0.200521	+	0.312016i	0.926922	−	0.375255i	$-0.122445\pi$
$109$	2.09350	+	3.25754i	0.200521	+	0.312016i	−0.726401	+	0.687271i	$0.758808\pi$
$110$	−0.321822	−	0.803874i	−0.0306846	−	0.0766463i
$111$	−4.25646	−	16.0575i	−0.404005	−	1.52411i
$112$	4.20338	−	1.45480i	0.397182	−	0.137466i
$113$	−6.69520	+	6.38386i	−0.629832	+	0.600543i	−0.936242	−	0.351356i	$-0.885721\pi$
$113$	−6.69520	+	6.38386i	−0.629832	+	0.600543i	0.306410	+	0.951900i	$0.400872\pi$
$114$	−10.0060	−	2.20480i	−0.937145	−	0.206499i
$115$	5.06639	+	2.34033i	0.472443	+	0.218237i
$116$		−	6.58041i		−	0.610976i
$117$	−10.5887	−	9.27511i	−0.978925	−	0.857484i
$118$	6.53813	−	7.54540i	0.601883	−	0.694610i
$119$	−22.1438	−	1.05484i	−2.02992	−	0.0966968i
$120$	0.328904	+	1.98854i	0.0300247	+	0.181528i
$121$	−0.497055	−	10.4345i	−0.0451868	−	0.948589i
$122$	−1.56495	−	0.149435i	−0.141684	−	0.0135292i
$123$	−0.172696	−	0.105900i	−0.0155715	−	0.00954870i
$124$	2.13890	−	1.68205i	0.192079	−	0.151052i
$125$	4.17949	−	9.15181i	0.373825	−	0.818563i
$126$	13.1978	+	1.96991i	1.17576	+	0.175494i
$127$	−9.11518	+	2.67646i	−0.808841	+	0.237497i	−0.659905	−	0.751349i	$-0.729403\pi$
$127$	−9.11518	+	2.67646i	−0.808841	+	0.237497i	−0.148937	+	0.988847i	$0.547585\pi$
$128$	0.0950560	+	0.995472i	0.00840185	+	0.0879881i
$129$	−11.4346	−	0.848663i	−1.00676	−	0.0747206i
$130$	−1.03335	−	5.36151i	−0.0906304	−	0.470235i
$131$	−1.22735	+	12.8533i	−0.107234	+	1.12300i	0.768381	+	0.639992i	$0.221062\pi$
$131$	−1.22735	+	12.8533i	−0.107234	+	1.12300i	−0.875615	+	0.483009i	$0.839544\pi$
$132$	0.217136	−	1.27040i	0.0188993	−	0.110575i
$133$	−24.4276	+	9.77933i	−2.11814	+	0.847975i
$134$	9.00544	+	5.78745i	0.777952	+	0.499959i
$135$	−1.88743	+	5.74453i	−0.162444	+	0.494411i
$136$	1.40415	−	4.78211i	0.120405	−	0.410062i
$137$	−9.00435	−	15.5960i	−0.769293	−	1.33246i	−0.937947	−	0.346780i	$-0.887275\pi$
$137$	−9.00435	−	15.5960i	−0.769293	−	1.33246i	0.168653	−	0.985675i	$-0.446058\pi$
$138$	4.60754	+	6.91163i	0.392220	+	0.588357i
$139$	−9.58994	+	16.6103i	−0.813408	+	1.40886i	0.0970571	+	0.995279i	$0.469057\pi$
$139$	−9.58994	+	16.6103i	−0.813408	+	1.40886i	−0.910465	+	0.413586i	$0.864276\pi$
$140$	3.57189	+	3.74609i	0.301880	+	0.316603i
$141$	7.73896	+	10.3961i	0.651738	+	0.875507i
$142$	−0.0558648	+	1.17275i	−0.00468807	+	0.0984147i
$143$	−0.496887	+	3.45593i	−0.0415518	+	0.288999i
$144$	−1.12992	+	2.77908i	−0.0941598	+	0.231590i
$145$	6.96550	−	3.18104i	0.578453	−	0.264171i
$146$	4.26285	+	1.47539i	0.352796	+	0.122104i
$147$	19.9442	−	9.62222i	1.64497	−	0.793627i
$148$	7.81260	−	5.56333i	0.642192	−	0.457303i
$149$	−0.471811	+	1.94483i	−0.0386523	+	0.159327i	−0.987867	−	0.155302i	$-0.950365\pi$
$149$	−0.471811	+	1.94483i	−0.0386523	+	0.159327i	0.949215	+	0.314629i	$0.101880\pi$
$150$	5.23907	−	3.52545i	0.427768	−	0.287851i
$151$	−6.38632	+	0.609820i	−0.519711	+	0.0496264i	−0.351616	−	0.936144i	$-0.614368\pi$
$151$	−6.38632	+	0.609820i	−0.519711	+	0.0496264i	−0.168095	+	0.985771i	$0.553762\pi$
$152$	−0.841869	−	5.85532i	−0.0682846	−	0.474930i
$153$	10.3760	−	10.7657i	0.838847	−	0.870358i
$154$	−1.37494	−	3.01069i	−0.110796	−	0.242608i
$155$	2.81444	+	1.45095i	0.226062	+	0.116543i
$156$	2.86054	−	7.60701i	0.229027	−	0.609048i
$157$	1.64628	+	3.19334i	0.131387	+	0.254856i	0.945347	−	0.326065i	$-0.105723\pi$
$157$	1.64628	+	3.19334i	0.131387	+	0.254856i	−0.813960	+	0.580921i	$0.802693\pi$
$158$	−0.134020	−	0.387225i	−0.0106621	−	0.0308060i
$159$	−13.4997	+	8.17890i	−1.07060	+	0.648629i
$160$	−1.00778	+	0.581840i	−0.0796717	+	0.0459985i
$161$	19.7693	+	8.01403i	1.55804	+	0.631594i
$162$	−6.86461	+	5.82040i	−0.539335	+	0.457294i
$163$	−16.2683	−	4.77682i	−1.27423	−	0.374149i	−0.426460	−	0.904506i	$-0.640240\pi$
$163$	−16.2683	−	4.77682i	−1.27423	−	0.374149i	−0.847774	+	0.530357i	$0.822058\pi$
$164$	0.0221348	−	0.114846i	0.00172843	−	0.00896797i
$165$	1.44971	−	0.384284i	0.112860	−	0.0299164i
$166$	−2.58193	+	3.28319i	−0.200397	+	0.254825i
$167$	18.2847	−	0.871009i	1.41492	−	0.0674007i	0.673867	−	0.738853i	$-0.264632\pi$
$167$	18.2847	−	0.871009i	1.41492	−	0.0674007i	0.741048	+	0.671452i	$0.234329\pi$
$168$	1.61744	+	7.53249i	0.124788	+	0.581144i
$169$	−2.94899	+	8.52054i	−0.226845	+	0.655426i
$170$	5.74074	−	0.825394i	0.440295	−	0.0633048i
$171$	5.89426	−	16.7392i	0.450746	−	1.28008i
$172$	−1.86505	−	6.35177i	−0.142209	−	0.484318i
$173$	2.03527	−	2.13453i	0.154739	−	0.162285i	−0.641802	−	0.766871i	$-0.721813\pi$
$173$	2.03527	−	2.13453i	0.154739	−	0.162285i	0.796540	+	0.604585i	$0.206661\pi$
$174$	11.3133	+	1.38348i	0.857662	+	0.104881i
$175$	6.02717	−	15.0552i	0.455611	−	1.13806i
$176$	0.730658	−	0.140823i	0.0550754	−	0.0106149i
$177$	11.5978	+	12.8270i	0.871744	+	0.964135i
$178$	−6.13648	+	11.9031i	−0.459949	+	0.892176i
$179$	11.8307	+	1.70099i	0.884265	+	0.127138i	0.569461	−	0.822019i	$-0.307152\pi$
$179$	11.8307	+	1.70099i	0.884265	+	0.127138i	0.314804	+	0.949157i	$0.398061\pi$
$180$	−3.48793	+	0.147394i	−0.259975	+	0.0109861i
$181$	11.3626	+	9.84572i	0.844573	+	0.731827i	0.965379	−	0.260850i	$-0.0840026\pi$
$181$	11.3626	+	9.84572i	0.844573	+	0.731827i	−0.120807	+	0.992676i	$0.538548\pi$
$182$	−4.92049	−	20.2825i	−0.364731	−	1.50344i
$183$	0.585932	−	2.65911i	0.0433133	−	0.196567i
$184$	−2.79876	+	3.89448i	−0.206327	+	0.287105i
$185$	9.66559	+	5.58043i	0.710628	+	0.410281i
$186$	2.44216	+	4.03092i	0.179068	+	0.295561i
$187$	−3.64159	−	0.701860i	−0.266300	−	0.0513251i
$188$	−4.04542	+	6.29480i	−0.295043	+	0.459095i
$189$	−6.16149	+	22.2761i	−0.448182	+	1.62035i
$190$	5.79101	−	3.72166i	0.420124	−	0.269997i
$191$	−0.227811	+	0.319916i	−0.0164838	+	0.0231483i	−0.822736	−	0.568424i	$-0.807553\pi$
$191$	−0.227811	+	0.319916i	−0.0164838	+	0.0231483i	0.806252	+	0.591573i	$0.201493\pi$
$192$	−1.73144	−	0.0458649i	−0.124956	−	0.00331001i
$193$	0.644427	+	0.257990i	0.0463869	+	0.0185705i	0.394740	−	0.918793i	$-0.370835\pi$
$193$	0.644427	+	0.257990i	0.0463869	+	0.0185705i	−0.348353	+	0.937363i	$0.613259\pi$
$194$	9.30654	+	13.0692i	0.668170	+	0.938314i
$195$	9.43499	−	0.649363i	0.675654	−	0.0465018i
$196$	9.25282	+	8.82255i	0.660916	+	0.630182i
$197$	16.4538	+	7.51421i	1.17229	+	0.535365i	0.903815	−	0.427923i	$-0.140754\pi$
$197$	16.4538	+	7.51421i	1.17229	+	0.535365i	0.268471	+	0.963288i	$0.413482\pi$
$198$	2.13848	+	0.640401i	0.151975	+	0.0455113i
$199$	−3.51790	+	3.04828i	−0.249377	+	0.216087i	−0.770575	−	0.637349i	$-0.780031\pi$
$199$	−3.51790	+	3.04828i	−0.249377	+	0.216087i	0.521198	+	0.853436i	$0.325485\pi$
$200$	2.96982	+	2.11480i	0.209998	+	0.149539i
$201$	−11.8433	+	14.2658i	−0.835365	+	1.00623i
$202$	−8.35050	−	6.56690i	−0.587539	−	0.462046i
$203$	26.0160	−	13.4122i	1.82597	−	0.941351i
$204$	7.92639	+	3.41948i	0.554959	+	0.239411i
$205$	0.132267	−	0.0320876i	0.00923793	−	0.00224110i
$206$	−2.01641			−0.140490
$207$	−12.8515	+	6.46837i	−0.893239	+	0.449583i
$208$	4.69217			0.325343
$209$	−4.27770	+	1.03776i	−0.295895	+	0.0717833i
$210$	−7.19141	+	5.35337i	−0.496254	+	0.369418i
$211$	−18.8119	+	9.69818i	−1.29506	+	0.667650i	−0.961429	−	0.275053i	$-0.911305\pi$
$211$	−18.8119	+	9.69818i	−1.29506	+	0.667650i	−0.333632	+	0.942703i	$0.608274\pi$
$212$	−7.16325	−	5.63324i	−0.491974	−	0.386893i
$213$	−2.00449	−	0.342605i	−0.137346	−	0.0234749i
$214$	−8.26248	−	5.88369i	−0.564812	−	0.402201i
$215$	5.82190	−	5.04470i	0.397050	−	0.344046i
$216$	−4.54036	−	2.52688i	−0.308932	−	0.171932i
$217$	11.0096	+	5.02790i	0.747377	+	0.341316i
$218$	−2.80248	−	2.67216i	−0.189808	−	0.180981i
$219$	−3.43278	+	7.01869i	−0.231966	+	0.474279i
$220$	0.502271	+	0.705341i	0.0338631	+	0.0475541i
$221$	−21.7106	−	8.69160i	−1.46041	−	0.584660i
$222$	7.92219	+	14.6014i	0.531702	+	0.979983i
$223$	15.9820	−	22.4436i	1.07024	−	1.50294i	0.220747	−	0.975331i	$-0.429150\pi$
$223$	15.9820	−	22.4436i	1.07024	−	1.50294i	0.849489	−	0.527606i	$-0.176910\pi$
$224$	−3.74191	+	2.40478i	−0.250017	+	0.160676i
$225$	4.95963	+	9.74844i	0.330642	+	0.649896i
$226$	5.00142	−	7.78237i	0.332690	−	0.517675i
$227$	−8.68003	−	1.67294i	−0.576114	−	0.111037i	−0.107132	−	0.994245i	$-0.534167\pi$
$227$	−8.68003	−	1.67294i	−0.576114	−	0.111037i	−0.468981	+	0.883208i	$0.655379\pi$
$228$	10.2437	−	0.216346i	0.678407	−	0.0143278i
$229$	−11.8348	−	6.83280i	−0.782062	−	0.451524i	0.0550983	−	0.998481i	$-0.482453\pi$
$229$	−11.8348	−	6.83280i	−0.782062	−	0.451524i	−0.837161	+	0.546957i	$0.815786\pi$
$230$	−5.47533	−	1.07992i	−0.361033	−	0.0712075i
$231$	5.46518	−	1.73088i	0.359582	−	0.113883i
$232$	1.55139	+	6.39492i	0.101854	+	0.419847i
$233$	−15.5804	−	13.5005i	−1.02071	−	0.884448i	−0.0273629	−	0.999626i	$-0.508711\pi$
$233$	−15.5804	−	13.5005i	−1.02071	−	0.884448i	−0.993345	+	0.115177i	$0.963256\pi$
$234$	12.4769	+	6.51728i	0.815640	+	0.426048i
$235$	−8.61877	−	1.23919i	−0.562226	−	0.0808359i
$236$	−4.57493	+	8.87413i	−0.297803	+	0.577657i
$237$	0.693911	−	0.149002i	0.0450743	−	0.00967873i
$238$	21.7683	−	4.19549i	1.41103	−	0.271953i
$239$	6.45991	−	16.1361i	0.417857	−	1.04376i	−0.558867	−	0.829257i	$-0.688764\pi$
$239$	6.45991	−	16.1361i	0.417857	−	1.04376i	0.976724	−	0.214499i	$-0.0688119\pi$
$240$	−0.788448	−	1.85494i	−0.0508941	−	0.119736i
$241$	17.9727	−	18.8493i	1.15773	−	1.21419i	0.184874	−	0.982762i	$-0.440812\pi$
$241$	17.9727	−	18.8493i	1.15773	−	1.21419i	0.972852	−	0.231426i	$-0.0743391\pi$
$242$	2.94307	+	10.0232i	0.189187	+	0.644313i
$243$	−8.56347	−	13.0256i	−0.549347	−	0.835594i
$244$	1.55607	−	0.223729i	0.0996170	−	0.0143228i
$245$	−4.86594	+	14.0592i	−0.310874	+	0.898210i
$246$	0.192795	+	0.0622004i	0.0122921	+	0.00396576i
$247$	−27.7252	+	1.32072i	−1.76412	+	0.0840352i
$248$	−1.68205	+	2.13890i	−0.106810	+	0.135820i
$249$	−5.10177	−	5.12923i	−0.323312	−	0.325052i
$250$	−1.90406	+	9.87918i	−0.120423	+	0.624814i
$251$	−7.30310	−	2.14439i	−0.460968	−	0.135352i	0.0429994	−	0.999075i	$-0.486309\pi$
$251$	−7.30310	−	2.14439i	−0.460968	−	0.135352i	−0.503967	+	0.863723i	$0.668127\pi$
$252$	−13.2902	+	1.19713i	−0.837206	+	0.0754119i
$253$	3.08274	+	1.79768i	0.193810	+	0.113019i
$254$	8.22724	−	4.75000i	0.516223	−	0.298041i
$255$	0.212112	+	10.0433i	0.0132830	+	0.628933i
$256$	−0.327068	−	0.945001i	−0.0204417	−	0.0590626i
$257$	9.69457	+	18.8049i	0.604731	+	1.17301i	0.970226	+	0.242201i	$0.0778694\pi$
$257$	9.69457	+	18.8049i	0.604731	+	1.17301i	−0.365495	+	0.930813i	$0.619100\pi$
$258$	11.3124	−	1.87107i	0.704276	−	0.116488i
$259$	37.9186	+	19.5484i	2.35614	+	1.21468i
$260$	2.26824	+	4.96675i	0.140670	+	0.308025i
$261$	−4.75706	+	19.1595i	−0.294455	+	1.18594i
$262$	−1.83754	−	12.7804i	−0.113524	−	0.789575i
$263$	4.74398	−	0.452995i	0.292527	−	0.0279329i	0.0522388	−	0.998635i	$-0.483364\pi$
$263$	4.74398	−	0.452995i	0.292527	−	0.0279329i	0.240288	+	0.970702i	$0.422758\pi$
$264$	0.0884941	+	1.28579i	0.00544644	+	0.0791346i
$265$	2.50011	−	10.3056i	0.153581	−	0.633068i
$266$	21.4334	−	15.2627i	1.31417	−	0.935815i
$267$	−19.1742	−	13.0526i	−1.17344	−	0.798808i
$268$	−10.1160	−	3.50119i	−0.617935	−	0.213869i
$269$	−3.81102	+	1.74043i	−0.232362	+	0.106116i	−0.528194	−	0.849124i	$-0.677130\pi$
$269$	−3.81102	+	1.74043i	−0.232362	+	0.106116i	0.295832	+	0.955240i	$0.404403\pi$
$270$	0.479899	−	6.02758i	0.0292057	−	0.366827i
$271$	1.22472	−	8.51815i	0.0743967	−	0.517441i	−0.918213	−	0.396088i	$-0.870368\pi$
$271$	1.22472	−	8.51815i	0.0743967	−	0.517441i	0.992609	−	0.121353i	$-0.0387233\pi$
$272$	−0.237148	+	4.97835i	−0.0143792	+	0.301857i
$273$	35.9051	−	4.19529i	2.17307	−	0.253910i
$274$	12.4274	+	13.0335i	0.750768	+	0.787383i
$275$	1.35645	−	2.34944i	0.0817968	−	0.141676i
$276$	−6.10714	−	5.63053i	−0.367606	−	0.338918i
$277$	7.02151	+	12.1616i	0.421882	+	0.730721i	0.996124	−	0.0879651i	$-0.0280364\pi$
$277$	7.02151	+	12.1616i	0.421882	+	0.730721i	−0.574242	+	0.818686i	$0.694703\pi$
$278$	5.40360	−	18.4030i	0.324086	−	1.10374i
$279$	−7.44357	+	3.35121i	−0.445635	+	0.200632i
$280$	−4.35438	−	2.79839i	−0.260224	−	0.167236i
$281$	−13.2809	+	5.31685i	−0.792269	+	0.317177i	−0.732264	−	0.681021i	$-0.761536\pi$
$281$	−13.2809	+	5.31685i	−0.792269	+	0.317177i	−0.0600056	+	0.998198i	$0.519112\pi$
$282$	−9.97177	−	8.27849i	−0.593811	−	0.492977i
$283$	0.538499	−	5.63941i	0.0320104	−	0.335228i	−0.965254	−	0.261313i	$-0.915844\pi$
$283$	0.538499	−	5.63941i	0.0320104	−	0.335228i	0.997265	−	0.0739153i	$-0.0235494\pi$
$284$	−0.222195	−	1.15286i	−0.0131849	−	0.0684096i
$285$	5.18093	+	10.7386i	0.306892	+	0.636100i
$286$	−0.331885	−	3.47566i	−0.0196248	−	0.205520i
$287$	0.499165	−	0.146568i	0.0294648	−	0.00865164i
$288$	0.442874	−	2.96713i	0.0260966	−	0.174840i
$289$	3.25693	−	7.13168i	0.191584	−	0.419511i
$290$	−6.01920	+	4.73355i	−0.353459	+	0.277964i
$291$	−24.4258	+	13.2525i	−1.43186	+	0.776876i
$292$	−4.49052	−	0.428793i	−0.262788	−	0.0250932i
$293$	−0.434396	−	9.11909i	−0.0253777	−	0.532743i	−0.975384	−	0.220513i	$-0.929227\pi$
$293$	−0.434396	−	9.11909i	−0.0253777	−	0.532743i	0.950006	−	0.312230i	$-0.101076\pi$
$294$	−17.1134	+	14.0530i	−0.998076	+	0.819587i
$295$	−11.6050	−	0.552815i	−0.675670	−	0.0321861i
$296$	−6.28077	+	7.24840i	−0.365063	+	0.421305i
$297$	−1.55060	+	3.54194i	−0.0899751	+	0.205524i
$298$		−	2.00124i		−	0.115929i
$299$	16.9425	+	14.8098i	0.979809	+	0.856473i
$300$	−4.26024	+	4.66123i	−0.245965	+	0.269116i
$301$	21.3107	−	20.3197i	1.22833	−	1.17121i
$302$	6.06253	−	2.09826i	0.348859	−	0.120741i
$303$	13.0457	−	12.9759i	0.749458	−	0.745446i
$304$	2.19858	+	5.49179i	0.126097	+	0.314976i
$305$	0.989040	+	1.53898i	0.0566323	+	0.0881215i
$306$	−7.54537	+	12.9085i	−0.431340	+	0.737929i
$307$	−9.80113	−	11.3111i	−0.559380	−	0.645559i	0.403663	−	0.914908i	$-0.367737\pi$
$307$	−9.80113	−	11.3111i	−0.559380	−	0.645559i	−0.963043	+	0.269349i	$0.913191\pi$
$308$	2.04598	+	2.60167i	0.116580	+	0.148244i
$309$	0.423933	−	3.46670i	0.0241167	−	0.197214i
$310$	−3.07718	−	0.746516i	−0.174772	−	0.0423993i
$311$	22.8524	+	5.54394i	1.29584	+	0.314368i	0.823635	−	0.567120i	$-0.191942\pi$
$311$	22.8524	+	5.54394i	1.29584	+	0.314368i	0.472207	+	0.881488i	$0.343457\pi$
$312$	−0.986488	+	8.06698i	−0.0558489	+	0.456703i
$313$	−20.1808	−	25.6620i	−1.14069	−	1.45050i	−0.873477	−	0.486865i	$-0.838140\pi$
$313$	−20.1808	−	25.6620i	−1.14069	−	1.45050i	−0.267211	−	0.963638i	$-0.586102\pi$
$314$	−2.35273	−	2.71520i	−0.132772	−	0.153227i
$315$	−7.69182	−	13.4893i	−0.433385	−	0.760035i
$316$	0.221534	+	0.344713i	0.0124623	+	0.0193916i
$317$	3.81542	+	9.53047i	0.214296	+	0.535284i	0.996099	−	0.0882403i	$-0.0281243\pi$
$317$	3.81542	+	9.53047i	0.214296	+	0.535284i	−0.781804	+	0.623525i	$0.785700\pi$
$318$	11.1909	−	11.1310i	0.627556	−	0.624197i
$319$	4.62721	−	1.60149i	0.259074	−	0.0896665i
$320$	0.842195	−	0.803031i	0.0470801	−	0.0448908i
$321$	11.8526	−	12.9682i	0.661548	−	0.723816i
$322$	−21.1014	−	3.12733i	−1.17594	−	0.174279i
$323$		−	29.4830i		−	1.64048i
$324$	5.29890	−	7.27473i	0.294383	−	0.404152i
$325$	11.2027	−	12.9286i	0.621412	−	0.717147i
$326$	16.9359	+	0.806758i	0.937995	+	0.0446822i
$327$	5.18329	−	4.25635i	0.286637	−	0.235377i
$328$	0.00556517	+	0.116827i	0.000307285	+	0.00645070i
$329$	−33.1322	−	3.16374i	−1.82664	−	0.174423i
$330$	−1.31825	+	0.715235i	−0.0725673	+	0.0393724i
$331$	−2.59033	+	2.03706i	−0.142377	+	0.111967i	−0.686807	−	0.726840i	$-0.740988\pi$
$331$	−2.59033	+	2.03706i	−0.142377	+	0.111967i	0.544430	+	0.838806i	$0.316746\pi$
$332$	1.73511	−	3.79935i	0.0952264	−	0.208517i
$333$	−26.7690	+	10.5503i	−1.46693	+	0.578155i
$334$	−17.5640	+	5.15725i	−0.961058	+	0.282192i
$335$	−1.18411	−	12.4005i	−0.0646948	−	0.677514i
$336$	−3.34770	−	6.93884i	−0.182632	−	0.378545i
$337$	−3.74996	−	19.4567i	−0.204274	−	1.05987i	−0.928788	−	0.370612i	$-0.879148\pi$
$337$	−3.74996	−	19.4567i	−0.204274	−	1.05987i	0.724514	−	0.689260i	$-0.242064\pi$
$338$	0.857067	−	8.97561i	0.0466183	−	0.488209i
$339$	12.3283	+	10.2348i	0.669580	+	0.555880i
$340$	−5.38432	+	2.15556i	−0.292006	+	0.116902i
$341$	1.70333	+	1.09466i	0.0922405	+	0.0592794i
$342$	−1.78170	+	17.6569i	−0.0963435	+	0.954778i
$343$	−7.24928	+	24.6888i	−0.391424	+	1.33307i
$344$	3.30996	+	5.73302i	0.178461	+	0.309104i
$345$	3.00778	−	9.18638i	0.161933	−	0.494578i
$346$	−1.47467	+	2.55420i	−0.0792785	+	0.137314i
$347$	−4.20052	−	4.40538i	−0.225496	−	0.236493i	0.601261	−	0.799053i	$-0.294665\pi$
$347$	−4.20052	−	4.40538i	−0.225496	−	0.236493i	−0.826757	+	0.562560i	$0.809817\pi$
$348$	−11.3206	+	1.32274i	−0.606848	+	0.0709064i
$349$	−0.406429	+	8.53200i	−0.0217557	+	0.456707i	0.961537	+	0.274676i	$0.0885704\pi$
$349$	−0.406429	+	8.53200i	−0.0217557	+	0.456707i	−0.983293	+	0.182032i	$0.941733\pi$
$350$	−2.30789	+	16.0517i	−0.123362	+	0.858001i
$351$	−13.8279	+	20.0806i	−0.738081	+	1.07182i
$352$	−0.676862	+	0.309112i	−0.0360768	+	0.0164757i
$353$	−18.7048	−	6.47380i	−0.995557	−	0.344566i	−0.219764	−	0.975553i	$-0.570529\pi$
$353$	−18.7048	−	6.47380i	−0.995557	−	0.344566i	−0.775793	+	0.630987i	$0.782650\pi$
$354$	−14.2949	−	9.73113i	−0.759768	−	0.517204i
$355$	1.11291	−	0.792502i	0.0590673	−	0.0420617i
$356$	3.15724	−	13.0143i	0.167333	−	0.689757i
$357$	2.63648	+	38.3070i	0.139537	+	2.02742i
$358$	−11.8982	+	1.13614i	−0.628839	+	0.0600469i
$359$	2.02098	+	14.0562i	0.106663	+	0.741859i	0.971023	+	0.238985i	$0.0768148\pi$
$359$	2.02098	+	14.0562i	0.106663	+	0.741859i	−0.864360	+	0.502874i	$0.832276\pi$
$360$	3.35486	−	0.965549i	0.176817	−	0.0508889i
$361$	−6.64397	−	14.5483i	−0.349682	−	0.765698i
$362$	−13.3635	−	6.88936i	−0.702369	−	0.362097i
$363$	−17.8510	+	2.95256i	−0.936935	+	0.154969i
$364$	9.56357	+	18.5507i	0.501267	+	0.972323i
$365$	−1.71688	−	4.96059i	−0.0898655	−	0.259649i
$366$	0.0574944	+	2.72230i	0.00300528	+	0.142297i
$367$	−13.2356	+	7.64161i	−0.690895	+	0.398889i	−0.803947	−	0.594701i	$-0.797271\pi$
$367$	−13.2356	+	7.64161i	−0.690895	+	0.398889i	0.113052	+	0.993589i	$0.463937\pi$
$368$	1.80171	−	4.44453i	0.0939206	−	0.231687i
$369$	−0.147471	+	0.318384i	−0.00767704	+	0.0165744i
$370$	−10.7088	−	3.14438i	−0.556722	−	0.163468i
$371$	7.67120	−	39.8019i	0.398269	−	2.06641i
$372$	−3.32365	−	3.34153i	−0.172323	−	0.173250i
$373$	3.21008	−	4.08195i	0.166212	−	0.211355i	−0.695811	−	0.718225i	$-0.744955\pi$
$373$	3.21008	−	4.08195i	0.166212	−	0.211355i	0.862023	+	0.506869i	$0.169197\pi$
$374$	3.70441	−	0.176463i	0.191551	−	0.00912468i
$375$	−16.5844	−	5.35055i	−0.856415	−	0.276301i
$376$	2.44733	−	7.07110i	0.126211	−	0.364664i
$377$	30.5621	−	4.39417i	1.57403	−	0.226311i
$378$	0.736005	−	23.1008i	0.0378560	−	1.18818i
$379$	8.63982	+	29.4245i	0.443798	+	1.51144i	0.813098	+	0.582127i	$0.197779\pi$
$379$	8.63982	+	29.4245i	0.443798	+	1.51144i	−0.369300	+	0.929310i	$0.620403\pi$
$380$	−4.75036	+	4.98203i	−0.243688	+	0.255573i
$381$	6.43670	+	15.1433i	0.329762	+	0.775813i
$382$	0.145966	−	0.364607i	0.00746830	−	0.0186549i
$383$	1.32008	−	0.254425i	0.0674532	−	0.0130005i	−0.155413	−	0.987850i	$-0.549671\pi$
$383$	1.32008	−	0.254425i	0.0674532	−	0.0130005i	0.222866	+	0.974849i	$0.428459\pi$
$384$	1.69345	−	0.363631i	0.0864185	−	0.0185565i
$385$	−1.76488	+	3.42338i	−0.0899464	+	0.174472i
$386$	−0.687085	−	0.0987879i	−0.0349717	−	0.00502817i
$387$	0.838496	+	19.8421i	0.0426231	+	1.00863i
$388$	−12.1254	−	10.5067i	−0.615573	−	0.533397i
$389$	−7.34590	−	30.2802i	−0.372452	−	1.53527i	−0.782176	−	0.623058i	$-0.785890\pi$
$389$	−7.34590	−	30.2802i	−0.372452	−	1.53527i	0.409724	−	0.912210i	$-0.365625\pi$
$390$	−9.01594	+	2.85544i	−0.456540	+	0.144591i
$391$	−16.5694	+	17.2273i	−0.837948	+	0.871223i
$392$	−11.0720	−	6.39242i	−0.559220	−	0.322866i
$393$	22.3589	−	0.472216i	1.12786	−	0.0238202i
$394$	−17.7616	−	3.42326i	−0.894814	−	0.172461i
$395$	−0.257794	+	0.401136i	−0.0129710	+	0.0201833i
$396$	−2.22918	−	0.118182i	−0.112021	−	0.00593889i
$397$	−6.59050	+	4.23546i	−0.330768	+	0.212571i	−0.695474	−	0.718551i	$-0.744806\pi$
$397$	−6.59050	+	4.23546i	−0.330768	+	0.212571i	0.364707	+	0.931123i	$0.381169\pi$
$398$	2.70008	−	3.79173i	0.135343	−	0.190062i
$399$	21.7341	+	40.0582i	1.08806	+	2.00542i
$400$	−3.38469	−	1.35503i	−0.169234	−	0.0677513i
$401$	−4.97883	−	6.99179i	−0.248631	−	0.349153i	0.671333	−	0.741156i	$-0.265722\pi$
$401$	−4.97883	−	6.99179i	−0.248631	−	0.349153i	−0.919964	+	0.392002i	$0.871783\pi$
$402$	8.14622	−	16.6558i	0.406296	−	0.830718i
$403$	9.24039	+	8.81069i	0.460297	+	0.438892i
$404$	9.66332	+	4.41309i	0.480768	+	0.219559i
$405$	10.2620	+	2.09231i	0.509922	+	0.103968i
$406$	−22.1206	+	19.1676i	−1.09783	+	0.951274i
$407$	5.81340	+	4.13970i	0.288159	+	0.205197i
$408$	−8.50913	−	1.45437i	−0.421265	−	0.0720020i
$409$	−20.1094	−	15.8142i	−0.994346	−	0.781963i	−0.0183682	−	0.999831i	$-0.505847\pi$
$409$	−20.1094	−	15.8142i	−0.994346	−	0.781963i	−0.975978	+	0.217869i	$0.930090\pi$
$410$	−0.120974	+	0.0623663i	−0.00597447	+	0.00308005i
$411$	−25.0205	+	18.6256i	−1.23417	+	0.918732i
$412$	1.95957	−	0.475387i	0.0965411	−	0.0234206i
$413$	−44.4090			−2.18522
$414$	10.9642	−	9.31589i	0.538862	−	0.457851i
$415$	4.86046			0.238591
$416$	−4.55990	+	1.10622i	−0.223568	+	0.0542369i
$417$	30.5031	+	13.1592i	1.49374	+	0.644407i
$418$	3.91246	−	2.01701i	0.191365	−	0.0986553i
$419$	9.62587	+	7.56987i	0.470254	+	0.369812i	0.824983	−	0.565157i	$-0.191184\pi$
$419$	9.62587	+	7.56987i	0.470254	+	0.369812i	−0.354729	+	0.934969i	$0.615427\pi$
$420$	5.72659	−	6.89791i	0.279429	−	0.336583i
$421$	1.62010	+	1.15367i	0.0789589	+	0.0562264i	0.618855	−	0.785505i	$-0.287597\pi$
$421$	1.62010	+	1.15367i	0.0789589	+	0.0562264i	−0.539896	+	0.841732i	$0.681536\pi$
$422$	15.9951	−	13.8599i	0.778631	−	0.674688i
$423$	16.3292	−	15.4034i	0.793954	−	0.748940i
$424$	8.28941	+	3.78565i	0.402570	+	0.183847i
$425$	13.1509	+	12.5393i	0.637912	+	0.608248i
$426$	2.02876	−	0.139629i	0.0982938	−	0.00676506i
$427$	4.05610	+	5.69599i	0.196288	+	0.275648i
$428$	9.41671	+	3.76988i	0.455174	+	0.182224i
$429$	6.04527	+	0.160136i	0.291869	+	0.00773142i
$430$	−4.46845	+	6.27506i	−0.215488	+	0.302610i
$431$	−8.94337	+	5.74755i	−0.430787	+	0.276850i	−0.738013	−	0.674787i	$-0.764236\pi$
$431$	−8.94337	+	5.74755i	−0.430787	+	0.276850i	0.307226	+	0.951637i	$0.400599\pi$
$432$	5.00811	+	1.38522i	0.240953	+	0.0666465i
$433$	9.48076	−	14.7524i	0.455616	−	0.708953i	−0.535116	−	0.844778i	$-0.679732\pi$
$433$	9.48076	−	14.7524i	0.455616	−	0.708953i	0.990733	+	0.135825i	$0.0433686\pi$
$434$	−11.8846	−	2.29057i	−0.570478	−	0.109951i
$435$	−6.87264	−	11.3437i	−0.329518	−	0.543887i
$436$	3.35347	+	1.93613i	0.160602	+	0.0927236i
$437$	−9.39500	+	26.7691i	−0.449424	+	1.28054i
$438$	1.68129	−	7.63015i	0.0803353	−	0.364583i
$439$	−2.22744	−	9.18164i	−0.106310	−	0.438216i	0.893634	−	0.448796i	$-0.148147\pi$
$439$	−2.22744	−	9.18164i	−0.106310	−	0.438216i	−0.999944	+	0.0105806i	$0.996632\pi$
$440$	−0.654403	−	0.567044i	−0.0311975	−	0.0270327i
$441$	−20.5626	−	32.3767i	−0.979170	−	1.54175i
$442$	23.1477	+	3.32814i	1.10102	+	0.158303i
$443$	4.06116	−	7.87756i	0.192952	−	0.374274i	−0.772436	−	0.635092i	$-0.780962\pi$
$443$	4.06116	−	7.87756i	0.192952	−	0.374274i	0.965388	+	0.260818i	$0.0839923\pi$
$444$	−11.1413	−	12.3221i	−0.528742	−	0.584781i
$445$	15.3022	−	2.94925i	0.725392	−	0.139808i
$446$	−10.2402	+	25.5789i	−0.484890	+	1.21120i
$447$	3.44062	+	0.420744i	0.162736	+	0.0199005i
$448$	3.06948	−	3.21918i	0.145019	−	0.152092i
$449$	7.46039	+	25.4077i	0.352077	+	1.19907i	0.925163	+	0.379570i	$0.123928\pi$
$449$	7.46039	+	25.4077i	0.352077	+	1.19907i	−0.573085	+	0.819496i	$0.694254\pi$
$450$	−7.11811	−	8.30437i	−0.335551	−	0.391472i
$451$	0.0861444	−	0.0123857i	0.00405638	−	0.000583220i
$452$	−3.02568	+	8.74212i	−0.142316	+	0.411195i
$453$	2.33283	+	10.8641i	0.109606	+	0.510440i
$454$	8.82976	−	0.420613i	0.414401	−	0.0197404i
$455$	−15.0132	+	19.0908i	−0.703830	+	0.894993i
$456$	−9.90396	+	2.62530i	−0.463796	+	0.122941i
$457$	2.94626	−	15.2866i	0.137820	−	0.715078i	−0.845612	−	0.533799i	$-0.820764\pi$
$457$	2.94626	−	15.2866i	0.137820	−	0.715078i	0.983432	−	0.181280i	$-0.0580239\pi$
$458$	13.1120	+	3.85004i	0.612685	+	0.179901i
$459$	−20.6065	−	15.6862i	−0.961828	−	0.732170i
$460$	5.57559	−	0.241383i	0.259963	−	0.0112546i
$461$	−22.9216	+	13.2338i	−1.06756	+	0.616359i	−0.927515	−	0.373786i	$-0.878060\pi$
$461$	−22.9216	+	13.2338i	−1.06756	+	0.616359i	−0.140050	+	0.990144i	$0.544726\pi$
$462$	−4.90305	+	2.97055i	−0.228111	+	0.138203i
$463$	1.40698	+	4.06521i	0.0653880	+	0.188926i	0.972962	−	0.230967i	$-0.0741888\pi$
$463$	1.40698	+	4.06521i	0.0653880	+	0.188926i	−0.907574	+	0.419893i	$0.862068\pi$
$464$	−3.01532	−	5.84891i	−0.139983	−	0.271529i
$465$	1.93039	−	5.13348i	0.0895199	−	0.238059i
$466$	18.3241	+	9.44673i	0.848848	+	0.437612i
$467$	1.82204	+	3.98972i	0.0843141	+	0.184622i	0.947093	−	0.320959i	$-0.104005\pi$
$467$	1.82204	+	3.98972i	0.0843141	+	0.184622i	−0.862779	+	0.505581i	$0.831278\pi$
$468$	−13.6617	−	3.39203i	−0.631512	−	0.156796i
$469$	−6.77633	−	47.1304i	−0.312902	−	2.17628i
$470$	8.66797	−	0.827691i	0.399824	−	0.0381785i
$471$	5.16272	−	3.47407i	0.237886	−	0.160077i
$472$	2.35382	−	9.70256i	0.108343	−	0.446597i
$473$	4.01253	−	2.85731i	0.184497	−	0.131379i
$474$	−0.639222	+	0.308398i	−0.0293604	+	0.0141652i
$475$	20.3810	+	7.05392i	0.935143	+	0.323656i
$476$	−20.1655	+	9.20928i	−0.924285	+	0.422107i
$477$	16.7842	+	21.5801i	0.768494	+	0.988086i
$478$	−2.47359	+	17.2042i	−0.113139	+	0.786902i
$479$	0.971475	−	20.3938i	0.0443878	−	0.931815i	−0.861359	−	0.507996i	$-0.830386\pi$
$479$	0.971475	−	20.3938i	0.0443878	−	0.931815i	0.905747	−	0.423819i	$-0.139311\pi$
$480$	1.20354	+	1.61677i	0.0549339	+	0.0737950i
$481$	31.0554	+	32.5699i	1.41600	+	1.48506i
$482$	−13.0222	+	22.5552i	−0.593147	+	1.02736i
$483$	9.81305	−	35.6210i	0.446509	−	1.62081i
$484$	−5.22315	−	9.04677i	−0.237416	−	0.411217i
$485$	5.26003	−	17.9140i	0.238846	−	0.813433i
$486$	11.3930	+	10.6395i	0.516796	+	0.482619i
$487$	17.9118	+	11.5112i	0.811663	+	0.521624i	0.879403	−	0.476079i	$-0.157942\pi$
$487$	17.9118	+	11.5112i	0.811663	+	0.521624i	−0.0677395	+	0.997703i	$0.521579\pi$
$488$	−1.45946	+	0.584279i	−0.0660666	+	0.0264491i
$489$	−4.94765	+	28.9474i	−0.223740	+	1.30905i
$490$	1.41419	−	14.8101i	0.0638867	−	0.669052i
$491$	−3.61314	−	18.7468i	−0.163059	−	0.846030i	−0.967668	−	0.252225i	$-0.918838\pi$
$491$	−3.61314	−	18.7468i	−0.163059	−	0.846030i	0.804610	−	0.593804i	$-0.202375\pi$
$492$	−0.202024	−	0.0149940i	−0.00910797	−	0.000675983i
$493$	3.11753	+	32.6482i	0.140406	+	1.47040i
$494$	26.6323	−	7.81996i	1.19825	−	0.351837i
$495$	−0.952511	−	2.41677i	−0.0428122	−	0.108626i
$496$	1.13037	−	2.47516i	0.0507550	−	0.111138i
$497$	4.10501	−	3.22822i	0.184135	−	0.144805i
$498$	6.16722	+	3.78185i	0.276360	+	0.169469i
$499$	−7.90678	−	0.755006i	−0.353956	−	0.0337987i	−0.0834362	−	0.996513i	$-0.526589\pi$
$499$	−7.90678	−	0.755006i	−0.353956	−	0.0337987i	−0.270520	+	0.962714i	$0.587196\pi$
$500$	−0.478722	−	10.0496i	−0.0214091	−	0.449432i
$501$	−5.17389	−	31.2810i	−0.231152	−	1.39753i
$502$	7.60280	+	0.362166i	0.339330	+	0.0161643i
$503$	−19.2634	+	22.2311i	−0.858911	+	0.991236i	0.141088	+	0.989997i	$0.454940\pi$
$503$	−19.2634	+	22.2311i	−0.858911	+	0.991236i	−0.999999	+	0.00123920i	$0.999606\pi$
$504$	12.6334	−	4.29667i	0.562735	−	0.191389i
$505$			12.3621i			0.550108i
$506$	−3.41966	−	1.02022i	−0.152022	−	0.0453544i
$507$	15.2511	+	3.36055i	0.677324	+	0.149247i
$508$	−6.87547	+	6.55575i	−0.305050	+	0.290864i
$509$	0.632892	−	0.219046i	0.0280525	−	0.00970905i	−0.313006	−	0.949751i	$-0.601336\pi$
$509$	0.632892	−	0.219046i	0.0280525	−	0.00970905i	0.341058	+	0.940042i	$0.389215\pi$
$510$	−2.57392	−	9.71015i	−0.113975	−	0.429973i
$511$	−7.45732	−	18.6275i	−0.329892	−	0.824031i
$512$	0.540641	+	0.841254i	0.0238932	+	0.0371785i
$513$	−29.9820	−	6.77540i	−1.32374	−	0.299141i
$514$	−13.8547	−	15.9892i	−0.611105	−	0.705253i
$515$	1.45048	+	1.84444i	0.0639159	+	0.0812757i
$516$	−10.5524	+	4.48531i	−0.464542	+	0.197455i
$517$	−5.41092	−	1.31267i	−0.237972	−	0.0577314i
$518$	−41.4584	−	10.0577i	−1.82158	−	0.441910i
$519$	−4.08125	−	3.07231i	−0.179147	−	0.134859i
$520$	−3.37526	−	4.29199i	−0.148015	−	0.188216i
$521$	0.319847	+	0.369123i	0.0140128	+	0.0161716i	0.762713	−	0.646737i	$-0.223867\pi$
$521$	0.319847	+	0.369123i	0.0140128	+	0.0161716i	−0.748700	+	0.662909i	$0.769322\pi$
$522$	0.105941	−	19.7410i	0.00463693	−	0.864038i
$523$	18.9138	+	29.4304i	0.827041	+	1.28690i	0.955442	+	0.295179i	$0.0953791\pi$
$523$	18.9138	+	29.4304i	0.827041	+	1.28690i	−0.128401	+	0.991722i	$0.540985\pi$
$524$	4.79883	+	11.9869i	0.209638	+	0.523650i
$525$	−27.1116	−	7.34256i	−1.18325	−	0.320456i
$526$	−4.50346	+	1.55866i	−0.196360	+	0.0679609i
$527$	−9.81509	+	9.35867i	−0.427552	+	0.407670i
$528$	−0.389135	−	1.22868i	−0.0169349	−	0.0534714i
$529$	20.5338	−	10.3616i	0.892774	−	0.450505i
$530$			10.6045i			0.460631i
$531$	19.7356	−	22.5306i	0.856451	−	0.977745i
$532$	−17.2310	+	19.8856i	−0.747057	+	0.862149i
$533$	0.548173	+	0.0261127i	0.0237440	+	0.00113107i
$534$	21.7110	+	8.16421i	0.939526	+	0.353300i
$535$	0.561635	+	11.7902i	0.0242816	+	0.509734i
$536$	10.6563	+	1.01756i	0.460283	+	0.0439517i
$537$	0.548192	−	20.6948i	0.0236562	−	0.893045i
$538$	3.29327	−	2.58986i	0.141983	−	0.111657i
$539$	−3.95195	+	8.65357i	−0.170223	+	0.372736i
$540$	0.954685	+	5.97082i	0.0410831	+	0.256943i
$541$	−5.32193	+	1.56266i	−0.228808	+	0.0671840i	−0.394127	−	0.919056i	$-0.628953\pi$
$541$	−5.32193	+	1.56266i	−0.228808	+	0.0671840i	0.165319	+	0.986240i	$0.447135\pi$
$542$	0.818028	+	8.56678i	0.0351373	+	0.367975i
$543$	14.6540	−	21.5267i	0.628865	−	0.923798i
$544$	−0.943227	−	4.89393i	−0.0404405	−	0.209825i
$545$	−0.428328	+	4.48566i	−0.0183476	+	0.192144i
$546$	−33.9039	+	12.5420i	−1.45095	+	0.536747i
$547$	11.1479	−	4.46294i	0.476649	−	0.190822i	−0.120882	−	0.992667i	$-0.538572\pi$
$547$	11.1479	−	4.46294i	0.476649	−	0.190822i	0.597532	+	0.801845i	$0.296148\pi$
$548$	−15.1499	−	9.73624i	−0.647171	−	0.415911i
$549$	−4.69238	−	0.473492i	−0.200266	−	0.0202082i
$550$	−0.764311	+	2.60300i	−0.0325903	+	0.110992i
$551$	19.4633	+	33.7115i	0.829166	+	1.43616i
$552$	7.26243	+	4.03200i	0.309110	+	0.171613i
$553$	−0.911313	+	1.57844i	−0.0387530	+	0.0671221i
$554$	−9.69080	−	10.1634i	−0.411722	−	0.431802i
$555$	7.65738	−	17.7499i	0.325038	−	0.753441i
$556$	−0.912616	+	19.1582i	−0.0387035	+	0.812487i
$557$	4.11680	−	28.6330i	0.174435	−	1.21322i	−0.694941	−	0.719067i	$-0.744570\pi$
$557$	4.11680	−	28.6330i	0.174435	−	1.21322i	0.869376	−	0.494152i	$-0.164521\pi$
$558$	6.44368	−	5.01163i	0.272783	−	0.212159i
$559$	28.2548	−	12.9035i	1.19505	−	0.545761i
$560$	4.89139	+	1.69293i	0.206699	+	0.0715391i
$561$	−0.475438	+	6.40589i	−0.0200730	+	0.270457i
$562$	11.6530	−	8.29806i	0.491552	−	0.350032i
$563$	2.17396	−	8.96117i	0.0916213	−	0.377668i	−0.907478	−	0.420099i	$-0.861995\pi$
$563$	2.17396	−	8.96117i	0.0916213	−	0.377668i	0.999099	+	0.0424313i	$0.0135103\pi$
$564$	11.6424	+	5.69420i	0.490234	+	0.239769i
$565$	−10.7164	+	1.02329i	−0.450841	+	0.0430501i
$566$	0.806223	+	5.60740i	0.0338881	+	0.235697i
$567$	39.5612	+	6.12212i	1.66142	+	0.257105i
$568$	0.487729	+	1.06798i	0.0204647	+	0.0448113i
$569$	32.1476	+	16.5732i	1.34770	+	0.694786i	0.972662	−	0.232225i	$-0.0746006\pi$
$569$	32.1476	+	16.5732i	1.34770	+	0.694786i	0.375034	+	0.927011i	$0.377631\pi$
$570$	−7.56661	−	9.21445i	−0.316930	−	0.385951i
$571$	11.7722	+	22.8348i	0.492650	+	0.955607i	0.995813	+	0.0914154i	$0.0291391\pi$
$571$	11.7722	+	22.8348i	0.492650	+	0.955607i	−0.503163	+	0.864191i	$0.667831\pi$
$572$	1.14195	+	3.29944i	0.0477472	+	0.137956i
$573$	0.596160	+	0.327607i	0.0249049	+	0.0136860i
$574$	−0.450540	+	0.260119i	−0.0188052	+	0.0108572i
$575$	−7.94460	−	15.5758i	−0.331313	−	0.649554i
$576$	0.269137	+	2.98790i	0.0112141	+	0.124496i
$577$	−12.6514	−	3.71479i	−0.526686	−	0.154649i	0.00757062	−	0.999971i	$-0.497590\pi$
$577$	−12.6514	−	3.71479i	−0.526686	−	0.154649i	−0.534257	+	0.845322i	$0.679408\pi$
$578$	−1.48376	+	7.69850i	−0.0617165	+	0.320215i
$579$	0.314294	−	1.16050i	0.0130616	−	0.0482286i
$580$	4.73355	−	6.01920i	0.196550	−	0.249934i
$581$	18.5574	−	0.884000i	0.769892	−	0.0366745i
$582$	20.6128	−	18.6375i	0.854430	−	0.772551i
$583$	2.21784	−	6.40803i	0.0918535	−	0.265393i
$584$	4.46503	−	0.641975i	0.184764	−	0.0265651i
$585$	−3.01368	−	16.1009i	−0.124600	−	0.665691i
$586$	2.57206	+	8.75962i	0.106251	+	0.361857i
$587$	3.32799	−	3.49029i	0.137361	−	0.144060i	−0.651460	−	0.758683i	$-0.725843\pi$
$587$	3.32799	−	3.49029i	0.137361	−	0.144060i	0.788821	+	0.614623i	$0.210692\pi$
$588$	13.3179	−	17.6915i	0.549222	−	0.729585i
$589$	−5.98247	+	14.9435i	−0.246503	+	0.615736i
$590$	11.4082	−	2.19875i	0.469669	−	0.0905212i
$591$	9.61963	−	29.8167i	0.395699	−	1.22650i
$592$	4.39485	−	8.52483i	0.180627	−	0.350368i
$593$	−19.1081	−	2.74732i	−0.784674	−	0.112819i	−0.261679	−	0.965155i	$-0.584276\pi$
$593$	−19.1081	−	2.74732i	−0.784674	−	0.112819i	−0.522995	+	0.852336i	$0.675185\pi$
$594$	0.671851	−	3.80766i	0.0275664	−	0.156230i
$595$	−19.4964	−	16.8938i	−0.799276	−	0.692576i
$596$	0.471811	+	1.94483i	0.0193261	+	0.0796634i
$597$	5.95124	+	5.43927i	0.243568	+	0.222615i
$598$	−19.9564	−	10.3980i	−0.816080	−	0.425205i
$599$	−2.49827	−	1.44237i	−0.102076	−	0.0589338i	0.448093	−	0.893987i	$-0.352103\pi$
$599$	−2.49827	−	1.44237i	−0.102076	−	0.0589338i	−0.550169	+	0.835053i	$0.685437\pi$
$600$	3.04122	−	5.53422i	0.124157	−	0.225934i
$601$	7.25241	+	1.39779i	0.295832	+	0.0570169i	0.335008	−	0.942215i	$-0.391261\pi$
$601$	7.25241	+	1.39779i	0.295832	+	0.0570169i	−0.0391758	+	0.999232i	$0.512473\pi$
$602$	−15.9195	+	24.7712i	−0.648828	+	1.00960i
$603$	26.9228	+	17.5071i	1.09638	+	0.712943i
$604$	−5.39695	+	3.46841i	−0.219599	+	0.141128i
$605$	7.05126	−	9.90211i	0.286675	−	0.402578i
$606$	−9.61880	+	15.6858i	−0.390737	+	0.637191i
$607$	31.5013	+	12.6112i	1.27860	+	0.511874i	0.908798	−	0.417237i	$-0.137002\pi$
$607$	31.5013	+	12.6112i	1.27860	+	0.511874i	0.369801	+	0.929111i	$0.379426\pi$
$608$	−3.43135	−	4.81865i	−0.139160	−	0.195422i
$609$	−28.3032	−	42.0606i	−1.14690	−	1.70438i
$610$	−1.32399	−	1.26242i	−0.0536067	−	0.0511139i
$611$	−31.9370	−	14.5851i	−1.29203	−	0.590051i
$612$	4.28939	−	14.3235i	0.173388	−	0.578993i
$613$	16.8092	−	14.5652i	0.678916	−	0.588284i	−0.245626	−	0.969365i	$-0.578993\pi$
$613$	16.8092	−	14.5652i	0.678916	−	0.588284i	0.924542	+	0.381081i	$0.124448\pi$
$614$	12.1915	+	8.68156i	0.492011	+	0.350359i
$615$	−0.0817892	−	0.221095i	−0.00329806	−	0.00891542i
$616$	−2.60167	−	2.04598i	−0.104824	−	0.0824347i
$617$	−26.8233	+	13.8284i	−1.07986	+	0.556708i	−0.903924	−	0.427693i	$-0.859327\pi$
$617$	−26.8233	+	13.8284i	−1.07986	+	0.556708i	−0.175939	+	0.984401i	$0.556296\pi$
$618$	0.405323	+	3.46892i	0.0163045	+	0.139541i
$619$	17.0405	−	4.13399i	0.684917	−	0.166159i	0.121823	−	0.992552i	$-0.461126\pi$
$619$	17.0405	−	4.13399i	0.684917	−	0.166159i	0.563094	+	0.826393i	$0.309611\pi$
$620$	3.16644			0.127167
$621$	13.7111	+	20.8088i	0.550209	+	0.835027i
$622$	−23.5153			−0.942877
$623$	57.8879	−	14.0434i	2.31923	−	0.562639i
$624$	−0.943182	−	8.07216i	−0.0377575	−	0.323145i
$625$	−5.79651	+	2.98831i	−0.231860	+	0.119532i
$626$	25.6620	+	20.1808i	1.02566	+	0.806588i
$627$	2.64517	+	7.15053i	0.105638	+	0.285565i
$628$	2.92654	+	2.08398i	0.116782	+	0.0831599i
$629$	−36.1260	+	31.3033i	−1.44044	+	1.24815i
$630$	10.6552	+	11.2956i	0.424514	+	0.450029i
$631$	−18.2298	−	8.32526i	−0.725716	−	0.331424i	0.0180739	−	0.999837i	$-0.494247\pi$
$631$	−18.2298	−	8.32526i	−0.725716	−	0.331424i	−0.743790	+	0.668413i	$0.766974\pi$
$632$	−0.296558	−	0.282768i	−0.0117965	−	0.0112479i
$633$	20.4657	+	30.4135i	0.813437	+	1.20883i
$634$	−5.95477	−	8.36230i	−0.236494	−	0.332109i
$635$	−10.2631	−	4.10871i	−0.407277	−	0.163049i
$636$	−8.25123	+	13.4556i	−0.327183	+	0.533550i
$637$	−34.7968	+	48.8653i	−1.37870	+	1.93611i
$638$	−4.11921	+	2.64726i	−0.163081	+	0.104806i
$639$	−0.186473	+	3.51729i	−0.00737675	+	0.139142i
$640$	−0.629133	+	0.978950i	−0.0248687	+	0.0386964i
$641$	−21.5457	−	4.15259i	−0.851003	−	0.164017i	−0.254942	−	0.966956i	$-0.582056\pi$
$641$	−21.5457	−	4.15259i	−0.851003	−	0.164017i	−0.596061	+	0.802939i	$0.703268\pi$
$642$	−8.46113	+	15.3970i	−0.333934	+	0.607672i
$643$	17.0521	+	9.84503i	0.672469	+	0.388250i	0.797012	−	0.603964i	$-0.206413\pi$
$643$	17.0521	+	9.84503i	0.672469	+	0.388250i	−0.124542	+	0.992214i	$0.539746\pi$
$644$	21.2439	−	1.93568i	0.837128	−	0.0762763i
$645$	−9.84891	−	9.00164i	−0.387800	−	0.354439i
$646$	6.95088	+	28.6519i	0.273479	+	1.12729i
$647$	−1.22177	−	1.05867i	−0.0480328	−	0.0416207i	0.630514	−	0.776178i	$-0.282844\pi$
$647$	−1.22177	−	1.05867i	−0.0480328	−	0.0416207i	−0.678546	+	0.734558i	$0.737390\pi$
$648$	−3.43445	+	8.31893i	−0.134918	+	0.326798i
$649$	−7.35352	−	1.05728i	−0.288651	−	0.0415017i
$650$	−7.83885	+	15.2053i	−0.307465	+	0.596399i
$651$	6.43667	−	19.9509i	0.252273	−	0.781938i
$652$	−16.6487	+	3.20878i	−0.652015	+	0.125666i
$653$	1.40914	−	3.51986i	0.0551440	−	0.137743i	−0.898238	−	0.439510i	$-0.855152\pi$
$653$	1.40914	−	3.51986i	0.0551440	−	0.137743i	0.953382	+	0.301767i	$0.0975764\pi$
$654$	−4.03371	+	5.35837i	−0.157731	+	0.209529i
$655$	−10.3686	+	10.8743i	−0.405134	+	0.424892i
$656$	−0.0329513	−	0.112222i	−0.00128653	−	0.00438153i
$657$	12.7646	+	4.49473i	0.497995	+	0.175356i
$658$	32.9441	−	4.73665i	1.28430	−	0.184654i
$659$	−2.09752	+	6.06040i	−0.0817080	+	0.236080i	−0.978454	−	0.206467i	$-0.933804\pi$
$659$	−2.09752	+	6.06040i	−0.0817080	+	0.236080i	0.896746	+	0.442546i	$0.145925\pi$
$660$	1.11247	−	1.00586i	0.0433028	−	0.0391532i
$661$	−35.5712	+	1.69447i	−1.38356	+	0.0659071i	−0.726103	−	0.687586i	$-0.758671\pi$
$661$	−35.5712	+	1.69447i	−1.38356	+	0.0659071i	−0.657456	+	0.753493i	$0.728368\pi$
$662$	2.03706	−	2.59033i	0.0791724	−	0.100676i
$663$	−10.5885	+	39.0968i	−0.411223	+	1.51839i
$664$	−0.790465	+	4.10132i	−0.0306760	+	0.159162i
$665$	−29.3789	−	8.62643i	−1.13927	−	0.334518i
$666$	23.5270	−	16.5640i	0.911654	−	0.641841i
$667$	7.57306	−	30.6364i	0.293230	−	1.18625i
$668$	15.8530	−	9.15273i	0.613371	−	0.354130i
$669$	−41.8234	−	22.9832i	−1.61699	−	0.888582i
$670$	4.07427	+	11.7718i	0.157403	+	0.454785i
$671$	0.536026	+	1.03975i	0.0206931	+	0.0401389i
$672$	4.88922	+	5.95399i	0.188606	+	0.229680i
$673$	31.7056	+	16.3453i	1.22216	+	0.630067i	0.943834	−	0.330420i	$-0.107190\pi$
$673$	31.7056	+	16.3453i	1.22216	+	0.630067i	0.278325	+	0.960487i	$0.410221\pi$
$674$	8.23134	+	18.0241i	0.317059	+	0.694263i
$675$	15.7737	−	10.4918i	0.607132	−	0.403831i
$676$	1.28317	+	8.92466i	0.0493528	+	0.343256i
$677$	−22.7473	+	2.17210i	−0.874249	+	0.0834807i	−0.522526	−	0.852623i	$-0.675010\pi$
$677$	−22.7473	+	2.17210i	−0.874249	+	0.0834807i	−0.351723	+	0.936104i	$0.614404\pi$
$678$	−14.3937	−	7.03983i	−0.552787	−	0.270363i
$679$	16.8249	−	69.3531i	0.645680	−	2.66153i
$680$	4.72435	−	3.36420i	0.181171	−	0.129011i
$681$	−1.13324	+	15.2689i	−0.0434260	+	0.585107i
$682$	−1.91339	−	0.662232i	−0.0732676	−	0.0253582i
$683$	43.5538	−	19.8903i	1.66654	−	0.761083i	0.666662	−	0.745360i	$-0.267722\pi$
$683$	43.5538	−	19.8903i	1.66654	−	0.761083i	0.999876	−	0.0157227i	$-0.00500491\pi$
$684$	−2.43130	−	17.5793i	−0.0929631	−	0.672160i
$685$	2.98240	−	20.7431i	0.113952	−	0.792551i
$686$	1.22433	−	25.7019i	0.0467452	−	0.981304i
$687$	−9.37586	+	21.7334i	−0.357711	+	0.829179i
$688$	−4.56827	−	4.79106i	−0.174164	−	0.182658i
$689$	21.3797	−	37.0307i	0.814502	−	1.41076i
$690$	−0.757223	+	9.63655i	−0.0288270	+	0.366857i
$691$	−24.9523	−	43.2186i	−0.949230	−	1.64411i	−0.747052	−	0.664765i	$-0.768531\pi$
$691$	−24.9523	−	43.2186i	−0.949230	−	1.64411i	−0.202178	−	0.979349i	$-0.564802\pi$
$692$	0.830922	−	2.82986i	0.0315869	−	0.107575i
$693$	−4.07628	−	9.05408i	−0.154845	−	0.343936i
$694$	5.12072	+	3.29089i	0.194380	+	0.124920i
$695$	−20.7205	+	8.29522i	−0.785972	+	0.314656i
$696$	10.6896	−	3.95439i	0.405190	−	0.149891i
$697$	−0.0554107	+	0.580287i	−0.00209883	+	0.0219799i
$698$	−1.61652	−	8.38731i	−0.0611863	−	0.317464i
$699$	−20.0937	+	29.5175i	−0.760014	+	1.11645i
$700$	−1.54150	−	16.1434i	−0.0582634	−	0.610162i
$701$	−25.4971	+	7.48663i	−0.963013	+	0.282766i	−0.725195	−	0.688544i	$-0.758250\pi$
$701$	−25.4971	+	7.48663i	−0.963013	+	0.282766i	−0.237818	+	0.971310i	$0.576432\pi$
$702$	8.70397	−	22.7746i	0.328510	−	0.859574i
$703$	−23.5690	+	51.6088i	−0.888920	+	1.94646i
$704$	0.584906	−	0.459975i	0.0220445	−	0.0173360i
$705$	−0.399364	+	15.0764i	−0.0150409	+	0.567809i
$706$	19.7038	+	1.88149i	0.741563	+	0.0708107i
$707$	2.24837	+	47.1992i	0.0845588	+	1.77511i
$708$	16.1862	+	6.08666i	0.608314	+	0.228751i
$709$	37.2652	+	1.77516i	1.39952	+	0.0666675i	0.733716	−	0.679457i	$-0.237784\pi$
$709$	37.2652	+	1.77516i	1.39952	+	0.0666675i	0.665807	+	0.746124i	$0.268087\pi$
$710$	−0.894703	+	1.03254i	−0.0335776	+	0.0387506i
$711$	−0.395820	−	1.16382i	−0.0148444	−	0.0436465i
$712$			13.3918i			0.501879i
$713$	11.8938	−	5.36956i	0.445428	−	0.201092i
$714$	−11.5934	−	36.6056i	−0.433871	−	1.36993i
$715$	−2.94049	+	2.80375i	−0.109968	+	0.104854i
$716$	11.2949	−	3.90922i	0.422112	−	0.146094i
$717$	−29.0582	−	7.86975i	−1.08520	−	0.293901i
$718$	−5.27789	−	13.1835i	−0.196969	−	0.492005i
$719$	27.2535	+	42.4072i	1.01638	+	1.58152i	0.795252	+	0.606279i	$0.207339\pi$
$719$	27.2535	+	42.4072i	1.01638	+	1.58152i	0.221131	+	0.975244i	$0.429025\pi$
$720$	−3.03265	+	1.72927i	−0.113020	+	0.0644461i
$721$	5.87346	+	6.77833i	0.218739	+	0.252438i
$722$	9.88657	+	12.5718i	0.367940	+	0.467874i
$723$	−36.0400	−	27.1304i	−1.34034	−	1.00899i
$724$	14.6110	+	3.54460i	0.543014	+	0.131734i
$725$	−23.3149	−	5.65614i	−0.865895	−	0.210064i
$726$	16.6517	−	7.07787i	0.618003	−	0.262684i
$727$	−16.3312	−	20.7668i	−0.605690	−	0.770197i	0.382413	−	0.923991i	$-0.375093\pi$
$727$	−16.3312	−	20.7668i	−0.605690	−	0.770197i	−0.988103	+	0.153794i	$0.950851\pi$
$728$	−13.6675	−	15.7731i	−0.506551	−	0.584591i
$729$	−20.6872	+	17.3504i	−0.766194	+	0.642609i
$730$	2.83799	+	4.41599i	0.105039	+	0.163443i
$731$	12.2625	+	30.6303i	0.453545	+	1.13290i
$732$	−0.697679	−	2.63200i	−0.0257870	−	0.0972816i
$733$	10.3697	−	3.58898i	0.383012	−	0.132562i	−0.128775	−	0.991674i	$-0.541105\pi$
$733$	10.3697	−	3.58898i	0.383012	−	0.132562i	0.511788	+	0.859112i	$0.328983\pi$
$734$	11.0610	−	10.5466i	0.408268	−	0.389283i
$735$	25.1648	+	5.54504i	0.928219	+	0.204532i
$736$	−0.703085	+	4.74401i	−0.0259161	+	0.174867i
$737$		−	7.96549i		−	0.293413i
$738$	0.0682523	−	0.344177i	0.00251240	−	0.0126693i
$739$	−6.52655	+	7.53203i	−0.240083	+	0.277070i	−0.862985	−	0.505229i	$-0.831408\pi$
$739$	−6.52655	+	7.53203i	−0.240083	+	0.277070i	0.622902	+	0.782300i	$0.285953\pi$
$740$	11.1482	+	0.531055i	0.409817	+	0.0195220i
$741$	7.84520	+	47.4316i	0.288201	+	1.74244i
$742$	1.92871	+	40.4885i	0.0708051	+	1.48638i
$743$	−0.317924	−	0.0303580i	−0.0116635	−	0.00111373i	0.0892227	−	0.996012i	$-0.471562\pi$
$743$	−0.317924	−	0.0303580i	−0.0116635	−	0.00111373i	−0.100886	+	0.994898i	$0.532168\pi$
$744$	4.01775	+	2.46376i	0.147298	+	0.0903258i
$745$	−1.83057	+	1.43957i	−0.0670667	+	0.0527419i
$746$	−2.15724	+	4.72369i	−0.0789821	+	0.172947i
$747$	−7.79853	+	9.80786i	−0.285333	+	0.358851i
$748$	−3.55839	+	1.04484i	−0.130108	+	0.0382030i
$749$	4.28869	+	44.9132i	0.156705	+	1.64109i
$750$	17.3784	+	1.28980i	0.634568	+	0.0470970i
$751$	5.33777	+	27.6950i	0.194778	+	1.01060i	0.939323	+	0.343033i	$0.111454\pi$
$751$	5.33777	+	27.6950i	0.194778	+	1.01060i	−0.744545	+	0.667572i	$0.767334\pi$
$752$	−0.711270	+	7.44876i	−0.0259374	+	0.271628i
$753$	−2.22107	+	12.9949i	−0.0809405	+	0.473561i
$754$	−28.6647	+	11.4756i	−1.04391	+	0.417917i
$755$	−6.28032	−	4.03612i	−0.228564	−	0.146889i
$756$	4.73097	+	22.6232i	0.172064	+	0.822797i
$757$	−5.98934	+	20.3978i	−0.217686	+	0.741371i	0.776154	+	0.630544i	$0.217168\pi$
$757$	−5.98934	+	20.3978i	−0.217686	+	0.741371i	−0.993840	+	0.110827i	$0.964650\pi$
$758$	−15.3334	−	26.5582i	−0.556933	−	0.964637i
$759$	2.47296	−	5.66473i	0.0897629	−	0.205617i
$760$	3.44189	−	5.96154i	0.124851	−	0.216248i
$761$	−22.5625	−	23.6629i	−0.817891	−	0.857780i	0.174016	−	0.984743i	$-0.444325\pi$
$761$	−22.5625	−	23.6629i	−0.817891	−	0.857780i	−0.991907	+	0.126963i	$0.959477\pi$
$762$	−9.82542	−	13.1989i	−0.355937	−	0.478146i
$763$	−0.819543	+	17.2043i	−0.0296694	+	0.622838i
$764$	−0.0558926	+	0.388742i	−0.00202213	+	0.0140642i
$765$	17.2353	−	2.38372i	0.623142	−	0.0861836i
$766$	−1.22289	+	0.558475i	−0.0441848	+	0.0201785i
$767$	−44.2700	−	15.3220i	−1.59850	−	0.553246i
$768$	−1.55998	+	0.752627i	−0.0562911	+	0.0271581i
$769$	11.3061	−	8.05102i	0.407708	−	0.290327i	−0.357745	−	0.933819i	$-0.616454\pi$
$769$	11.3061	−	8.05102i	0.407708	−	0.290327i	0.765453	+	0.643492i	$0.222515\pi$
$770$	0.908034	−	3.74297i	0.0327233	−	0.134887i
$771$	30.4021	−	20.4580i	1.09491	−	0.736778i
$772$	0.691008	−	0.0659832i	0.0248699	−	0.00237479i
$773$	4.70260	+	32.7073i	0.169141	+	1.17640i	0.880665	+	0.473739i	$0.157096\pi$
$773$	4.70260	+	32.7073i	0.169141	+	1.17640i	−0.711524	+	0.702661i	$0.751995\pi$
$774$	−5.49280	−	19.0851i	−0.197435	−	0.685999i
$775$	−4.12115	−	9.02406i	−0.148036	−	0.324154i
$776$	14.2606	+	7.35187i	0.511927	+	0.263917i
$777$	26.0079	−	69.1625i	0.933028	−	2.48119i
$778$	14.2777	+	27.6948i	0.511879	+	0.992906i
$779$	0.226292	+	0.653826i	0.00810773	+	0.0234258i
$780$	8.08860	−	4.90054i	0.289618	−	0.175467i
$781$	0.756591	−	0.436818i	0.0270730	−	0.0156306i
$782$	12.0408	−	20.6481i	0.430578	−	0.738374i
$783$	33.9172	+	4.33251i	1.21210	+	0.154831i
$784$	12.2670	+	3.60191i	0.438106	+	0.128639i
$785$	−0.791217	+	4.10522i	−0.0282397	+	0.146522i
$786$	−21.6173	+	5.73022i	−0.771064	+	0.204390i
$787$	5.20664	−	6.62079i	0.185597	−	0.236006i	−0.684347	−	0.729157i	$-0.739913\pi$
$787$	5.20664	−	6.62079i	0.185597	−	0.236006i	0.869944	+	0.493151i	$0.164155\pi$
$788$	18.0679	−	0.860682i	0.643644	−	0.0306605i
$789$	−1.73291	−	8.07024i	−0.0616931	−	0.287308i
$790$	0.155956	−	0.450606i	0.00554867	−	0.0160318i
$791$	−40.7294	+	5.85600i	−1.44817	+	0.208215i
$792$	2.19421	−	0.410699i	0.0779678	−	0.0145936i
$793$	2.07817	+	7.07761i	0.0737981	+	0.251333i
$794$	5.40618	−	5.66984i	0.191858	−	0.201215i
$795$	−18.2318	−	2.22951i	−0.646614	−	0.0790726i
$796$	−1.73003	+	4.32142i	−0.0613194	+	0.153169i
$797$	−16.0503	+	3.09343i	−0.568529	+	0.109575i	−0.465412	−	0.885094i	$-0.654094\pi$
$797$	−16.0503	+	3.09343i	−0.568529	+	0.109575i	−0.103117	+	0.994669i	$0.532882\pi$
$798$	−30.5655	−	33.8050i	−1.08201	−	1.19668i
$799$	17.0888	−	33.1477i	0.604559	−	1.17268i
$800$	3.60874	+	0.518858i	0.127588	+	0.0183444i
$801$	−18.6008	+	35.6100i	−0.657227	+	1.25822i
$802$	6.48686	+	5.62090i	0.229059	+	0.198481i
$803$	−0.791353	−	3.26200i	−0.0279262	−	0.115114i
$804$	−3.98982	+	18.1069i	−0.140710	+	0.638580i
$805$	12.3185	+	21.5514i	0.434169	+	0.759587i
$806$	−11.0571	−	6.38383i	−0.389470	−	0.224861i
$807$	3.76021	+	6.20643i	0.132366	+	0.218477i
$808$	−10.4313	−	2.01048i	−0.366974	−	0.0707284i
$809$	24.4392	−	38.0281i	0.859235	−	1.33700i	−0.0810860	−	0.996707i	$-0.525839\pi$
$809$	24.4392	−	38.0281i	0.859235	−	1.33700i	0.940321	−	0.340289i	$-0.110525\pi$
$810$	−10.4660	+	0.386023i	−0.367738	+	0.0135635i
$811$	−37.7915	+	24.2871i	−1.32704	+	0.852837i	−0.995875	−	0.0907361i	$-0.971078\pi$
$811$	−37.7915	+	24.2871i	−1.32704	+	0.852837i	−0.331165	+	0.943573i	$0.607442\pi$
$812$	16.9781	−	23.8425i	0.595816	−	0.836706i
$813$	−14.9004	−	0.394702i	−0.522578	−	0.0138428i
$814$	−6.62550	−	2.65245i	−0.232224	−	0.0929683i
$815$	−11.4447	−	16.0719i	−0.400891	−	0.562973i
$816$	8.61216	−	0.592731i	0.301486	−	0.0207497i
$817$	28.3417	+	27.0238i	0.991551	+	0.945442i
$818$	23.2709	+	10.6275i	0.813648	+	0.371581i
$819$	−14.4347	−	60.9259i	−0.504389	−	2.12892i
$820$	0.102860	−	0.0891289i	0.00359204	−	0.00311252i
$821$	37.2920	+	26.5555i	1.30150	+	0.926795i	0.999647	−	0.0265595i	$-0.00845514\pi$
$821$	37.2920	+	26.5555i	1.30150	+	0.926795i	0.301854	+	0.953354i	$0.402395\pi$
$822$	19.9241	−	23.9994i	0.694933	−	0.837074i
$823$	−26.3688	−	20.7366i	−0.919158	−	0.722834i	0.0419173	−	0.999121i	$-0.486653\pi$
$823$	−26.3688	−	20.7366i	−0.919158	−	0.722834i	−0.961075	+	0.276287i	$0.910896\pi$
$824$	−1.79226	+	0.923972i	−0.0624362	+	0.0321881i
$825$	−4.31451	−	1.86130i	−0.150212	−	0.0648020i
$826$	43.1571	−	10.4698i	1.50163	−	0.364291i
$827$	−44.5912			−1.55059			−0.775294	−	0.631600i	$-0.782399\pi$
$827$	−44.5912			−1.55059			−0.775294	+	0.631600i	$0.782399\pi$
$828$	−8.45886	+	11.6382i	−0.293966	+	0.404455i
$829$	24.4653			0.849714			0.424857	−	0.905260i	$-0.360324\pi$
$829$	24.4653			0.849714			0.424857	+	0.905260i	$0.360324\pi$
$830$	−4.72345	+	1.14590i	−0.163953	+	0.0397747i
$831$	19.5108	−	14.5241i	0.676822	−	0.503834i
$832$	4.17056	−	2.15008i	0.144588	−	0.0745405i
$833$	−50.0869	−	39.3888i	−1.73541	−	1.36474i
$834$	−32.7457	−	5.59685i	−1.13389	−	0.193803i
$835$	17.3519	+	12.3562i	0.600486	+	0.427604i
$836$	−3.32664	+	2.88255i	−0.115054	+	0.0996952i
$837$	7.26149	+	12.1319i	0.250994	+	0.419340i
$838$	−11.1392	−	5.08710i	−0.384797	−	0.175731i
$839$	15.8548	+	15.1175i	0.547369	+	0.521915i	0.912519	−	0.409033i	$-0.134134\pi$
$839$	15.8548	+	15.1175i	0.547369	+	0.521915i	−0.365151	+	0.930948i	$0.618982\pi$
$840$	−3.93892	+	8.05356i	−0.135906	+	0.277874i
$841$	−8.29589	−	11.6499i	−0.286065	−	0.401722i
$842$	−1.84642	−	0.739195i	−0.0636319	−	0.0254744i
$843$	11.8164	+	21.7789i	0.406980	+	0.750106i
$844$	−12.2767	+	17.2402i	−0.422581	+	0.593431i
$845$	−8.82664	+	5.67254i	−0.303646	+	0.195141i
$846$	−12.2374	+	18.8190i	−0.420731	+	0.647010i
$847$	25.1211	−	39.0891i	0.863170	−	1.34312i
$848$	−8.94825	−	1.72463i	−0.307284	−	0.0592242i
$849$	−9.80999	+	0.207185i	−0.336678	+	0.00711058i
$850$	−15.7364	−	9.08544i	−0.539756	−	0.311628i
$851$	42.7757	−	16.9101i	1.46633	−	0.579670i
$852$	−1.93865	+	0.613992i	−0.0664172	+	0.0210350i
$853$	−8.09419	−	33.3647i	−0.277140	−	1.14239i	−0.924799	−	0.380456i	$-0.875767\pi$
$853$	−8.09419	−	33.3647i	−0.277140	−	1.14239i	0.647659	−	0.761930i	$-0.275748\pi$
$854$	−5.28464	−	4.57917i	−0.180837	−	0.156696i
$855$	17.4327	−	11.0716i	0.596186	−	0.378640i
$856$	−10.0401	−	1.44354i	−0.343162	−	0.0493392i
$857$	10.4241	−	20.2198i	0.356079	−	0.690697i	−0.640962	−	0.767573i	$-0.721464\pi$
$857$	10.4241	−	20.2198i	0.356079	−	0.690697i	0.997041	+	0.0768760i	$0.0244946\pi$
$858$	−5.91262	+	1.26961i	−0.201854	+	0.0433436i
$859$	4.63899	−	0.894093i	0.158280	−	0.0305061i	−0.109495	−	0.993987i	$-0.534923\pi$
$859$	4.63899	−	0.894093i	0.158280	−	0.0305061i	0.267776	+	0.963481i	$0.413711\pi$
$860$	2.86309	−	7.15166i	0.0976306	−	0.243869i
$861$	−0.352486	−	0.829275i	−0.0120127	−	0.0282616i
$862$	7.33623	−	7.69402i	0.249873	−	0.262059i
$863$	2.93303	+	9.98898i	0.0998414	+	0.340029i	0.994231	−	0.107260i	$-0.0342078\pi$
$863$	2.93303	+	9.98898i	0.0998414	+	0.340029i	−0.894390	+	0.447289i	$0.852390\pi$
$864$	−5.19352	−	0.165468i	−0.176687	−	0.00562934i
$865$	3.39714	−	0.488435i	0.115506	−	0.0166073i
$866$	−5.73552	+	16.5717i	−0.194901	+	0.563129i
$867$	−12.9237	−	4.16950i	−0.438910	−	0.141604i
$868$	12.0896	−	0.575899i	0.410348	−	0.0195473i
$869$	−0.188480	+	0.239672i	−0.00639375	+	0.00813032i
$870$	9.35328	+	9.40361i	0.317106	+	0.318812i
$871$	9.50584	−	49.3210i	0.322093	−	1.67118i
$872$	−3.71540	−	1.09094i	−0.125819	−	0.0369439i
$873$	27.7088	+	39.3569i	0.937801	+	1.33203i
$874$	2.81910	−	28.2295i	0.0953576	−	0.954877i
$875$	38.7559	−	22.3757i	1.31019	−	0.756438i
$876$	0.164976	+	7.81145i	0.00557404	+	0.263924i
$877$	18.6232	+	53.8083i	0.628861	+	1.81698i	0.574578	+	0.818450i	$0.305166\pi$
$877$	18.6232	+	53.8083i	0.628861	+	1.81698i	0.0542836	+	0.998526i	$0.482713\pi$
$878$	4.32931	+	8.39769i	0.146107	+	0.283408i
$879$	−15.6007	+	2.58036i	−0.526198	+	0.0870333i
$880$	0.769642	+	0.396778i	0.0259446	+	0.0133754i
$881$	−16.8543	−	36.9057i	−0.567834	−	1.24338i	−0.947943	−	0.318441i	$-0.896841\pi$
$881$	−16.8543	−	36.9057i	−0.567834	−	1.24338i	0.380108	−	0.924942i	$-0.375887\pi$
$882$	27.6160	+	26.6162i	0.929880	+	0.896215i
$883$	4.29382	+	29.8642i	0.144499	+	1.00501i	0.925030	+	0.379894i	$0.124039\pi$
$883$	4.29382	+	29.8642i	0.144499	+	1.00501i	−0.780531	+	0.625116i	$0.785051\pi$
$884$	−23.2798	+	2.22295i	−0.782986	+	0.0747661i
$885$	1.38171	+	20.0758i	0.0464458	+	0.674840i
$886$	−2.08948	+	8.61296i	−0.0701975	+	0.289358i
$887$	−39.0145	+	27.7821i	−1.30998	+	0.932832i	−0.999841	−	0.0178589i	$-0.994315\pi$
$887$	−39.0145	+	27.7821i	−1.30998	+	0.932832i	−0.310139	+	0.950691i	$0.600376\pi$
$888$	13.7323	+	9.34810i	0.460825	+	0.313702i
$889$	−39.9321	−	13.8206i	−1.33928	−	0.463529i
$890$	−14.1755	+	6.47373i	−0.475164	+	0.217000i
$891$	6.40505	+	1.95560i	0.214577	+	0.0655152i
$892$	3.92113	−	27.2721i	0.131289	−	0.913137i
$893$	2.10616	−	44.2137i	0.0704799	−	1.47955i
$894$	−3.44283	+	0.402274i	−0.115146	+	0.0134541i
$895$	9.59808	+	10.0662i	0.320828	+	0.336475i
$896$	−2.22401	+	3.85209i	−0.0742989	+	0.128689i
$897$	22.0723	−	32.1239i	0.736974	−	1.07259i
$898$	−13.2402	−	22.9327i	−0.441831	−	0.765274i
$899$	5.04462	−	17.1804i	0.168247	−	0.572998i
$900$	8.87529	+	6.39212i	0.295843	+	0.213071i
$901$	38.2087	+	24.5552i	1.27292	+	0.818054i
$902$	−0.0807961	+	0.0323459i	−0.00269022	+	0.00107700i
$903$	−39.2407	−	32.5773i	−1.30585	−	1.08411i
$904$	0.879356	−	9.20903i	0.0292469	−	0.306288i
$905$	3.31109	+	17.1796i	0.110064	+	0.571068i
$906$	−4.82838	−	10.0079i	−0.160412	−	0.332489i
$907$	4.38555	+	45.9276i	0.145620	+	1.52500i	0.712777	+	0.701391i	$0.247437\pi$
$907$	4.38555	+	45.9276i	0.145620	+	1.52500i	−0.567157	+	0.823610i	$0.691957\pi$
$908$	−8.48170	+	2.49045i	−0.281475	+	0.0826485i
$909$	−24.9454	−	19.8349i	−0.827387	−	0.657881i
$910$	10.0892	−	22.0922i	0.334453	−	0.732349i
$911$	−38.0340	+	29.9103i	−1.26012	+	0.990971i	−0.260447	+	0.965488i	$0.583870\pi$
$911$	−38.0340	+	29.9103i	−1.26012	+	0.990971i	−0.999675	+	0.0254830i	$0.991888\pi$
$912$	9.00585	−	4.88624i	0.298213	−	0.161800i
$913$	3.09391	+	0.295432i	0.102393	+	0.00977738i
$914$	0.740753	+	15.5503i	0.0245019	+	0.514359i
$915$	2.44876	−	2.01084i	0.0809536	−	0.0664765i
$916$	−13.6501	−	0.650235i	−0.451013	−	0.0214844i
$917$	−37.6099	+	43.4041i	−1.24199	+	1.43333i
$918$	23.7238	+	10.3859i	0.783002	+	0.342786i
$919$		−	4.74918i		−	0.156661i	−0.996927	−	0.0783304i	$-0.975041\pi$
$919$		−	4.74918i		−	0.156661i	0.996927	−	0.0783304i	$-0.0249589\pi$
$920$	−5.36151	+	1.54907i	−0.176764	+	0.0510715i
$921$	−17.4889	+	19.1350i	−0.576278	+	0.630520i
$922$	19.1555	−	18.2647i	0.630852	−	0.601516i
$923$	5.20598	−	1.80181i	0.171357	−	0.0593072i
$924$	4.06451	−	4.04276i	0.133713	−	0.132997i
$925$	−12.9961	−	32.4626i	−0.427308	−	1.06736i
$926$	−2.32573	−	3.61891i	−0.0764283	−	0.118925i
$927$	−6.04914	−	0.0324632i	−0.198680	−	0.00106623i
$928$	4.30925	+	4.97315i	0.141458	+	0.163251i
$929$	22.8539	+	29.0612i	0.749814	+	0.953465i	0.999891	−	0.0147603i	$-0.00469853\pi$
$929$	22.8539	+	29.0612i	0.749814	+	0.953465i	−0.250078	+	0.968226i	$0.580456\pi$
$930$	−0.665717	+	5.44388i	−0.0218297	+	0.178512i
$931$	−73.4973	−	17.8303i	−2.40878	−	0.584363i
$932$	−20.0347	−	4.86037i	−0.656259	−	0.159207i
$933$	4.94389	−	40.4285i	0.161856	−	1.32357i
$934$	−2.71129	−	3.44769i	−0.0887162	−	0.112812i
$935$	−2.82614	−	3.26154i	−0.0924247	−	0.106664i
$936$	14.0763	+	0.0755416i	0.460098	+	0.00246915i
$937$	−14.8881	−	23.1664i	−0.486374	−	0.756813i	0.508156	−	0.861265i	$-0.330327\pi$
$937$	−14.8881	−	23.1664i	−0.486374	−	0.756813i	−0.994530	+	0.104452i	$0.966691\pi$
$938$	17.6967	+	44.2043i	0.577819	+	1.44332i
$939$	−40.0910	+	39.8764i	−1.30832	+	1.30132i
$940$	−8.22850	+	2.84791i	−0.268384	+	0.0928886i
$941$	19.0725	−	18.1856i	0.621746	−	0.592834i	−0.312301	−	0.949983i	$-0.601100\pi$
$941$	19.0725	−	18.1856i	0.621746	−	0.592834i	0.934047	+	0.357149i	$0.116251\pi$
$942$	−4.19815	+	4.59330i	−0.136783	+	0.149658i
$943$	0.235223	−	0.509215i	0.00765992	−	0.0165823i
$944$			9.98399i			0.324951i
$945$	−21.6601	+	15.9441i	−0.704603	+	0.518662i
$946$	−3.22579	+	3.72276i	−0.104879	+	0.121037i
$947$	−12.8995	−	0.614477i	−0.419176	−	0.0199678i	−0.163065	−	0.986615i	$-0.552138\pi$
$947$	−12.8995	−	0.614477i	−0.419176	−	0.0199678i	−0.256111	+	0.966647i	$0.582441\pi$
$948$	0.548496	−	0.450407i	0.0178143	−	0.0146285i
$949$	−1.00712	−	21.1422i	−0.0326927	−	0.686303i
$950$	−21.4695	−	2.05009i	−0.696562	−	0.0665136i
$951$	15.6288	−	8.47959i	0.506797	−	0.274970i
$952$	17.4259	−	13.7039i	0.564777	−	0.444146i
$953$	−16.7657	+	36.7118i	−0.543095	+	1.18921i	0.416837	+	0.908981i	$0.363139\pi$
$953$	−16.7657	+	36.7118i	−0.543095	+	1.18921i	−0.959932	+	0.280232i	$0.909589\pi$
$954$	−21.3987	−	17.0148i	−0.692810	−	0.550875i
$955$	−0.438510	+	0.128758i	−0.0141899	+	0.00416652i
$956$	−1.65218	−	17.3024i	−0.0534354	−	0.559600i
$957$	−3.68525	−	7.63849i	−0.119127	−	0.246917i
$958$	3.86392	+	20.0479i	0.124838	+	0.647719i
$959$	7.61427	−	79.7403i	0.245878	−	2.57495i
$960$	−1.55078	−	1.28745i	−0.0500513	−	0.0415522i
$961$	−21.9056	+	8.76969i	−0.706633	+	0.282893i
$962$	−37.8586	−	24.3302i	−1.22061	−	0.784439i
$963$	−24.6924	−	17.7838i	−0.795701	−	0.573076i
$964$	7.33758	−	24.9895i	0.236327	−	0.804857i
$965$	0.403885	+	0.699549i	0.0130015	+	0.0225193i
$966$	−1.13845	+	36.9304i	−0.0366292	+	1.18822i
$967$	−10.6845	+	18.5060i	−0.343589	+	0.595114i	−0.985096	−	0.172003i	$-0.944976\pi$
$967$	−10.6845	+	18.5060i	−0.343589	+	0.595114i	0.641507	+	0.767117i	$0.278309\pi$
$968$	7.20878	+	7.56035i	0.231699	+	0.242999i
$969$	−50.7210	+	5.92644i	−1.62939	+	0.190385i
$970$	−0.888368	+	18.6491i	−0.0285238	+	0.598788i
$971$	−0.736041	+	5.11928i	−0.0236207	+	0.164286i	−0.998217	−	0.0596812i	$-0.980992\pi$
$971$	−0.736041	+	5.11928i	−0.0236207	+	0.164286i	0.974597	+	0.223967i	$0.0719007\pi$
$972$	−13.5802	−	7.65363i	−0.435585	−	0.245490i
$973$	−77.6029	+	35.4401i	−2.48783	+	1.13616i
$974$	−20.1208	−	6.96388i	−0.644713	−	0.223137i
$975$	−24.4935	−	16.6737i	−0.784419	−	0.533985i
$976$	1.28057	−	0.911889i	0.0409900	−	0.0291889i
$977$	0.495920	−	2.04421i	0.0158659	−	0.0654001i	−0.963328	−	0.268325i	$-0.913530\pi$
$977$	0.495920	−	2.04421i	0.0158659	−	0.0654001i	0.979194	+	0.202925i	$0.0650449\pi$
$978$	−2.01642	−	29.2979i	−0.0644781	−	0.936842i
$979$	9.91979	−	0.947225i	0.317038	−	0.0302734i
$980$	2.11728	+	14.7260i	0.0676341	+	0.470406i
$981$	−8.36430	−	8.06148i	−0.267051	−	0.257383i
$982$	7.93101	+	17.3665i	0.253089	+	0.554187i
$983$	−34.5695	−	17.8218i	−1.10260	−	0.568428i	−0.191863	−	0.981422i	$-0.561453\pi$
$983$	−34.5695	−	17.8218i	−1.10260	−	0.568428i	−0.910734	+	0.412994i	$0.864483\pi$
$984$	0.199865	−	0.0330577i	0.00637145	−	0.00105384i
$985$	9.64528	+	18.7092i	0.307324	+	0.596125i
$986$	−10.7268	−	30.9929i	−0.341610	−	0.987016i
$987$	1.21724	+	57.6348i	0.0387451	+	1.83454i
$988$	−24.0380	+	13.8783i	−0.764751	+	0.441529i
$989$	−1.37318	−	31.7183i	−0.0436645	−	1.00858i
$990$	1.49544	+	2.12408i	0.0475281	+	0.0675077i
$991$	21.2591	+	6.24223i	0.675317	+	0.198291i	0.601369	−	0.798971i	$-0.294622\pi$
$991$	21.2591	+	6.24223i	0.675317	+	0.198291i	0.0739476	+	0.997262i	$0.476440\pi$
$992$	−0.514964	+	2.67188i	−0.0163501	+	0.0848324i
$993$	4.02513	+	4.04679i	0.127734	+	0.128421i
$994$	−3.22822	+	4.10501i	−0.102393	+	0.130203i
$995$	−5.41062	+	0.257740i	−0.171528	+	0.00817090i
$996$	−6.88499	−	2.22127i	−0.218159	−	0.0703836i
$997$	17.9534	−	51.8729i	0.568589	−	1.64283i	−0.182934	−	0.983125i	$-0.558560\pi$
$997$	17.9534	−	51.8729i	0.568589	−	1.64283i	0.751524	−	0.659706i	$-0.229319\pi$
$998$	7.86190	−	1.13037i	0.248864	−	0.0357812i
$999$	23.5311	+	43.9311i	0.744492	+	1.38992i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.p.a.5.7	✓	480
9.2	odd	6	inner	414.2.p.a.281.12	yes	480
23.14	odd	22	inner	414.2.p.a.221.12	yes	480
207.83	even	66	inner	414.2.p.a.83.7	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.p.a.5.7	✓	480	1.1	even	1	trivial
414.2.p.a.83.7	yes	480	207.83	even	66	inner
414.2.p.a.221.12	yes	480	23.14	odd	22	inner
414.2.p.a.281.12	yes	480	9.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.p (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.971812 + 0.235759i) q^{2} +(-0.201012 - 1.72035i) q^{3} +(0.888835 - 0.458227i) q^{4} +(0.914714 + 0.719339i) q^{5} +(0.600933 + 1.62446i) q^{6} +(3.62325 + 2.58010i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(-2.91919 + 0.691621i) q^{9} +O(q^{10})\)	\(q+(-0.971812 + 0.235759i) q^{2} +(-0.201012 - 1.72035i) q^{3} +(0.888835 - 0.458227i) q^{4} +(0.914714 + 0.719339i) q^{5} +(0.600933 + 1.62446i) q^{6} +(3.62325 + 2.58010i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(-2.91919 + 0.691621i) q^{9} +(-1.05852 - 0.483410i) q^{10} +(0.538534 + 0.513491i) q^{11} +(-0.966975 - 1.43700i) q^{12} +(2.72172 + 3.82213i) q^{13} +(-4.12939 - 1.65316i) q^{14} +(1.05364 - 1.71822i) q^{15} +(0.580057 - 0.814576i) q^{16} +(-4.19280 + 2.69455i) q^{17} +(2.67385 - 1.36035i) q^{18} +(-3.19818 + 4.97647i) q^{19} +(1.14265 + 0.220228i) q^{20} +(3.71035 - 6.75187i) q^{21} +(-0.644414 - 0.372052i) q^{22} +(4.66550 - 1.11045i) q^{23} +(1.27850 + 1.16852i) q^{24} +(-0.859542 - 3.54308i) q^{25} +(-3.54610 - 3.07272i) q^{26} +(1.77662 + 4.88299i) q^{27} +(4.40274 + 0.633019i) q^{28} +(3.01532 - 5.84891i) q^{29} +(-0.618858 + 1.91819i) q^{30} +(2.67188 - 0.514964i) q^{31} +(-0.371662 + 0.928368i) q^{32} +(0.775131 - 1.02968i) q^{33} +(3.43935 - 3.60709i) q^{34} +(1.45827 + 4.96640i) q^{35} +(-2.27776 + 1.95239i) q^{36} +(9.49338 - 1.36494i) q^{37} +(1.93478 - 5.59019i) q^{38} +(6.02829 - 5.45060i) q^{39} +(-1.16236 + 0.0553701i) q^{40} +(0.0722997 - 0.0919365i) q^{41} +(-2.01395 + 7.43630i) q^{42} +(1.25283 - 6.50029i) q^{43} +(0.713963 + 0.209639i) q^{44} +(-3.16773 - 1.46725i) q^{45} +(-4.27219 + 2.17908i) q^{46} +(-6.48016 + 3.74132i) q^{47} +(-1.51795 - 0.834160i) q^{48} +(4.18151 + 12.0817i) q^{49} +(1.67062 + 3.24056i) q^{50} +(5.47836 + 6.67144i) q^{51} +(4.17056 + 2.15008i) q^{52} +(-3.78565 - 8.28941i) q^{53} +(-2.87775 - 4.32650i) q^{54} +(0.123230 + 0.857086i) q^{55} +(-4.42787 + 0.422811i) q^{56} +(9.20412 + 4.50165i) q^{57} +(-1.55139 + 6.39492i) q^{58} +(-8.13272 + 5.79128i) q^{59} +(0.149182 - 2.01002i) q^{60} +(1.48561 + 0.514173i) q^{61} +(-2.47516 + 1.13037i) q^{62} +(-12.3614 - 5.02589i) q^{63} +(0.142315 - 0.989821i) q^{64} +(-0.259806 + 5.45400i) q^{65} +(-0.510524 + 1.18340i) q^{66} +(-7.38715 - 7.74742i) q^{67} +(-2.49200 + 4.31626i) q^{68} +(-2.84818 - 7.80307i) q^{69} +(-2.58803 - 4.48260i) q^{70} +(0.330776 - 1.12652i) q^{71} +(1.75326 - 2.43435i) q^{72} +(-3.79485 - 2.43880i) q^{73} +(-8.90398 + 3.56462i) q^{74} +(-5.92255 + 2.19091i) q^{75} +(-0.562307 + 5.88875i) q^{76} +(0.626382 + 3.24998i) q^{77} +(-4.57333 + 6.71818i) q^{78} +(0.0389503 + 0.407906i) q^{79} +(1.11654 - 0.327846i) q^{80} +(8.04332 - 4.03794i) q^{81} +(-0.0485868 + 0.106390i) q^{82} +(3.28319 - 2.58193i) q^{83} +(0.204008 - 7.70149i) q^{84} +(-5.77351 - 0.551303i) q^{85} +(0.314989 + 6.61243i) q^{86} +(-10.6683 - 4.01170i) q^{87} +(-0.743262 - 0.0354059i) q^{88} +(8.76977 - 10.1209i) q^{89} +(3.42436 + 0.679070i) q^{90} +20.8708i q^{91} +(3.63802 - 3.12486i) q^{92} +(-1.42300 - 4.49306i) q^{93} +(5.41544 - 5.16361i) q^{94} +(-6.50519 + 2.25147i) q^{95} +(1.67182 + 0.452775i) q^{96} +(-5.96302 - 14.8949i) q^{97} +(-6.91201 - 10.7553i) q^{98} +(-1.92722 - 1.12652i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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