LMFDB - Embedded newform 546.2.bv.a.515.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(317,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("546.317");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bv (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			515.9
Character	$\chi$	$=$	546.515
Dual form			546.2.bv.a.317.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-0.214218 - 1.71875i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.579405 - 0.155251i) q^{5} +(-0.237927 + 1.71563i) q^{6} +(0.0183841 + 2.64569i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.90822 + 0.736375i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.214218 - 1.71875i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.579405 - 0.155251i) q^{5} +(-0.237927 + 1.71563i) q^{6} +(0.0183841 + 2.64569i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.90822 + 0.736375i) q^{9} +(0.519481 + 0.299922i) q^{10} +(3.10273 - 0.831373i) q^{11} +(0.673858 - 1.59559i) q^{12} +(3.60424 + 0.0973883i) q^{13} +(0.666997 - 2.56030i) q^{14} +(-0.142719 + 1.02911i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.59410 - 4.49310i) q^{17} +(2.99971 + 0.0414195i) q^{18} +(2.15080 - 8.02689i) q^{19} +(-0.424154 - 0.424154i) q^{20} +(4.54334 - 0.598351i) q^{21} -3.21218 q^{22} +(-0.637898 - 1.10487i) q^{23} +(-1.06387 + 1.36682i) q^{24} +(-4.01852 - 2.32009i) q^{25} +(-3.45622 - 1.02691i) q^{26} +(1.88864 + 4.84077i) q^{27} +(-1.30692 + 2.30042i) q^{28} +4.10654i q^{29} +(0.404210 - 0.957107i) q^{30} +(-5.29917 + 1.41991i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-2.09358 - 5.15472i) q^{33} +(-3.66860 + 3.66860i) q^{34} +(0.400094 - 1.53578i) q^{35} +(-2.88678 - 0.816391i) q^{36} +(3.77455 + 1.01139i) q^{37} +(-4.15502 + 7.19671i) q^{38} +(-0.604705 - 6.21565i) q^{39} +(0.299922 + 0.519481i) q^{40} +(5.19752 - 5.19752i) q^{41} +(-4.54340 - 0.597941i) q^{42} -9.47120i q^{43} +(3.10273 + 0.831373i) q^{44} +(1.79936 + 0.0248453i) q^{45} +(0.330201 + 1.23233i) q^{46} +(-1.48819 + 5.55402i) q^{47} +(1.38137 - 1.04489i) q^{48} +(-6.99932 + 0.0972771i) q^{49} +(3.28111 + 3.28111i) q^{50} +(-8.27824 - 3.49610i) q^{51} +(3.07267 + 1.88646i) q^{52} +(-1.48181 - 0.855522i) q^{53} +(-0.571402 - 5.16464i) q^{54} -1.92681 q^{55} +(1.85778 - 1.88378i) q^{56} +(-14.2570 - 1.97719i) q^{57} +(1.06285 - 3.96661i) q^{58} +(3.14252 - 0.842037i) q^{59} +(-0.638155 + 0.819878i) q^{60} +(0.398128 + 0.689579i) q^{61} +5.48610 q^{62} +(-2.00168 - 7.68071i) q^{63} +1.00000i q^{64} +(-2.07319 - 0.615989i) q^{65} +(0.688106 + 5.52094i) q^{66} +(6.42620 - 1.72190i) q^{67} +(4.49310 - 2.59410i) q^{68} +(-1.76235 + 1.33307i) q^{69} +(-0.783950 + 1.37990i) q^{70} +(8.81512 - 8.81512i) q^{71} +(2.57712 + 1.53573i) q^{72} +(1.65075 + 6.16069i) q^{73} +(-3.38417 - 1.95385i) q^{74} +(-3.12683 + 7.40385i) q^{75} +(5.87609 - 5.87609i) q^{76} +(2.25659 + 8.19356i) q^{77} +(-1.02463 + 6.16037i) q^{78} +(-2.17550 - 3.76807i) q^{79} +(-0.155251 - 0.579405i) q^{80} +(7.91550 - 4.28308i) q^{81} +(-6.36563 + 3.67520i) q^{82} +(9.60558 - 9.60558i) q^{83} +(4.23383 + 1.75348i) q^{84} +(-2.20059 + 2.20059i) q^{85} +(-2.45133 + 9.14848i) q^{86} +(7.05812 - 0.879694i) q^{87} +(-2.78183 - 1.60609i) q^{88} +(3.10650 - 11.5936i) q^{89} +(-1.73162 - 0.489708i) q^{90} +(-0.191398 + 9.53747i) q^{91} -1.27580i q^{92} +(3.57565 + 8.80379i) q^{93} +(2.87497 - 4.97960i) q^{94} +(-2.49237 + 4.31691i) q^{95} +(-1.60474 + 0.651764i) q^{96} +(9.09518 + 9.09518i) q^{97} +(6.78601 + 1.71760i) q^{98} +(-8.41121 + 4.70259i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 16 q^{7}+O(q^{10}) $ 144 * q - 16 * q^7	$ 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) $ 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	−0.214218	−	1.71875i	−0.123679	−	0.992322i
$3$	−0.214218	−	1.71875i	−0.123679	−	0.992322i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−0.579405	−	0.155251i	−0.259118	−	0.0694304i	0.126921	−	0.991913i	$-0.459490\pi$
$5$	−0.579405	−	0.155251i	−0.259118	−	0.0694304i	−0.386039	+	0.922482i	$0.626157\pi$
$6$	−0.237927	+	1.71563i	−0.0971334	+	0.700404i
$7$	0.0183841	+	2.64569i	0.00694853	+	0.999976i
$7$	0.0183841	+	2.64569i	0.00694853	+	0.999976i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.90822	+	0.736375i	−0.969407	+	0.245458i
$10$	0.519481	+	0.299922i	0.164274	+	0.0948438i
$11$	3.10273	−	0.831373i	0.935507	−	0.250668i	0.241306	−	0.970449i	$-0.422424\pi$
$11$	3.10273	−	0.831373i	0.935507	−	0.250668i	0.694201	+	0.719781i	$0.255758\pi$
$12$	0.673858	−	1.59559i	0.194526	−	0.460608i
$13$	3.60424	+	0.0973883i	0.999635	+	0.0270106i
$13$	3.60424	+	0.0973883i	0.999635	+	0.0270106i
$14$	0.666997	−	2.56030i	0.178262	−	0.684268i
$15$	−0.142719	+	1.02911i	−0.0368500	+	0.265716i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.59410	−	4.49310i	0.629160	−	1.08974i	−0.358560	−	0.933507i	$-0.616732\pi$
$17$	2.59410	−	4.49310i	0.629160	−	1.08974i	0.987721	−	0.156231i	$-0.0499345\pi$
$18$	2.99971	+	0.0414195i	0.707039	+	0.00976267i
$19$	2.15080	−	8.02689i	0.493427	−	1.84149i	−0.0452411	−	0.998976i	$-0.514406\pi$
$19$	2.15080	−	8.02689i	0.493427	−	1.84149i	0.538668	−	0.842518i	$-0.318928\pi$
$20$	−0.424154	−	0.424154i	−0.0948438	−	0.0948438i
$21$	4.54334	−	0.598351i	0.991439	−	0.130571i
$22$	−3.21218			−0.684839
$23$	−0.637898	−	1.10487i	−0.133011	−	0.230382i	0.791825	−	0.610748i	$-0.209131\pi$
$23$	−0.637898	−	1.10487i	−0.133011	−	0.230382i	−0.924836	+	0.380366i	$0.875798\pi$
$24$	−1.06387	+	1.36682i	−0.217161	+	0.279000i
$25$	−4.01852	−	2.32009i	−0.803704	−	0.464019i
$26$	−3.45622	−	1.02691i	−0.677820	−	0.201395i
$27$	1.88864	+	4.84077i	0.363469	+	0.931606i
$28$	−1.30692	+	2.30042i	−0.246985	+	0.434739i
$29$			4.10654i			0.762565i	0.924459	+	0.381283i	$0.124517\pi$
$29$			4.10654i			0.762565i	−0.924459	+	0.381283i	$0.875483\pi$
$30$	0.404210	−	0.957107i	0.0737984	−	0.174743i
$31$	−5.29917	+	1.41991i	−0.951758	+	0.255023i	−0.701108	−	0.713055i	$-0.747311\pi$
$31$	−5.29917	+	1.41991i	−0.951758	+	0.255023i	−0.250650	+	0.968078i	$0.580644\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−2.09358	−	5.15472i	−0.364446	−	0.897322i
$34$	−3.66860	+	3.66860i	−0.629160	+	0.629160i
$35$	0.400094	−	1.53578i	0.0676283	−	0.259594i
$36$	−2.88678	−	0.816391i	−0.481130	−	0.136065i
$37$	3.77455	+	1.01139i	0.620532	+	0.166271i	0.555370	−	0.831604i	$-0.312577\pi$
$37$	3.77455	+	1.01139i	0.620532	+	0.166271i	0.0651624	+	0.997875i	$0.479243\pi$
$38$	−4.15502	+	7.19671i	−0.674034	+	1.16746i
$39$	−0.604705	−	6.21565i	−0.0968303	−	0.995301i
$40$	0.299922	+	0.519481i	0.0474219	+	0.0821371i
$41$	5.19752	−	5.19752i	0.811716	−	0.811716i	−0.173175	−	0.984891i	$-0.555403\pi$
$41$	5.19752	−	5.19752i	0.811716	−	0.811716i	0.984891	+	0.173175i	$0.0554027\pi$
$42$	−4.54340	−	0.597941i	−0.701062	−	0.0922643i
$43$		−	9.47120i		−	1.44434i	−0.691713	−	0.722172i	$-0.743144\pi$
$43$		−	9.47120i		−	1.44434i	0.691713	−	0.722172i	$-0.256856\pi$
$44$	3.10273	+	0.831373i	0.467754	+	0.125334i
$45$	1.79936	+	0.0248453i	0.268233	+	0.00370371i
$46$	0.330201	+	1.23233i	0.0486854	+	0.181696i
$47$	−1.48819	+	5.55402i	−0.217075	+	0.810137i	0.768350	+	0.640030i	$0.221078\pi$
$47$	−1.48819	+	5.55402i	−0.217075	+	0.810137i	−0.985426	+	0.170107i	$0.945589\pi$
$48$	1.38137	−	1.04489i	0.199384	−	0.150818i
$49$	−6.99932	+	0.0972771i	−0.999903	+	0.0138967i
$50$	3.28111	+	3.28111i	0.464019	+	0.464019i
$51$	−8.27824	−	3.49610i	−1.15918	−	0.489553i
$52$	3.07267	+	1.88646i	0.426102	+	0.261605i
$53$	−1.48181	−	0.855522i	−0.203542	−	0.117515i	0.394765	−	0.918782i	$-0.370826\pi$
$53$	−1.48181	−	0.855522i	−0.203542	−	0.117515i	−0.598306	+	0.801267i	$0.704159\pi$
$54$	−0.571402	−	5.16464i	−0.0777580	−	0.702818i
$55$	−1.92681			−0.259811
$56$	1.85778	−	1.88378i	0.248257	−	0.251731i
$57$	−14.2570	−	1.97719i	−1.88838	−	0.261885i
$58$	1.06285	−	3.96661i	0.139559	−	0.520842i
$59$	3.14252	−	0.842037i	0.409122	−	0.109624i	−0.0483876	−	0.998829i	$-0.515408\pi$
$59$	3.14252	−	0.842037i	0.409122	−	0.109624i	0.457509	+	0.889205i	$0.348742\pi$
$60$	−0.638155	+	0.819878i	−0.0823854	+	0.105846i
$61$	0.398128	+	0.689579i	0.0509751	+	0.0882915i	0.890387	−	0.455204i	$-0.150434\pi$
$61$	0.398128	+	0.689579i	0.0509751	+	0.0882915i	−0.839412	+	0.543496i	$0.817100\pi$
$62$	5.48610			0.696736
$63$	−2.00168	−	7.68071i	−0.252188	−	0.967678i
$64$			1.00000i			0.125000i
$65$	−2.07319	−	0.615989i	−0.257148	−	0.0764041i
$66$	0.688106	+	5.52094i	0.0847000	+	0.679581i
$67$	6.42620	−	1.72190i	0.785085	−	0.210363i	0.156060	−	0.987748i	$-0.450121\pi$
$67$	6.42620	−	1.72190i	0.785085	−	0.210363i	0.629026	+	0.777385i	$0.283454\pi$
$68$	4.49310	−	2.59410i	0.544869	−	0.314580i
$69$	−1.76235	+	1.33307i	−0.212162	+	0.160483i
$70$	−0.783950	+	1.37990i	−0.0937000	+	0.164929i
$71$	8.81512	−	8.81512i	1.04616	−	1.04616i	0.0472805	−	0.998882i	$-0.484945\pi$
$71$	8.81512	−	8.81512i	1.04616	−	1.04616i	0.998882	−	0.0472805i	$-0.0150554\pi$
$72$	2.57712	+	1.53573i	0.303716	+	0.180987i
$73$	1.65075	+	6.16069i	0.193206	+	0.721054i	0.992724	+	0.120412i	$0.0384216\pi$
$73$	1.65075	+	6.16069i	0.193206	+	0.721054i	−0.799518	+	0.600642i	$0.794912\pi$
$74$	−3.38417	−	1.95385i	−0.393401	−	0.227130i
$75$	−3.12683	+	7.40385i	−0.361055	+	0.854923i
$76$	5.87609	−	5.87609i	0.674034	−	0.674034i
$77$	2.25659	+	8.19356i	0.257163	+	0.933743i
$78$	−1.02463	+	6.16037i	−0.116016	+	0.697524i
$79$	−2.17550	−	3.76807i	−0.244763	−	0.423942i	0.717302	−	0.696762i	$-0.245377\pi$
$79$	−2.17550	−	3.76807i	−0.244763	−	0.423942i	−0.962065	+	0.272821i	$0.912043\pi$
$80$	−0.155251	−	0.579405i	−0.0173576	−	0.0647795i
$81$	7.91550	−	4.28308i	0.879500	−	0.475898i
$82$	−6.36563	+	3.67520i	−0.702966	+	0.405858i
$83$	9.60558	−	9.60558i	1.05435	−	1.05435i	0.0559134	−	0.998436i	$-0.482193\pi$
$83$	9.60558	−	9.60558i	1.05435	−	1.05435i	0.998436	−	0.0559134i	$-0.0178071\pi$
$84$	4.23383	+	1.75348i	0.461948	+	0.191321i
$85$	−2.20059	+	2.20059i	−0.238688	+	0.238688i
$86$	−2.45133	+	9.14848i	−0.264333	+	0.986506i
$87$	7.05812	−	0.879694i	0.756710	−	0.0943131i
$88$	−2.78183	−	1.60609i	−0.296544	−	0.171210i
$89$	3.10650	−	11.5936i	0.329288	−	1.22892i	−0.580642	−	0.814159i	$-0.697198\pi$
$89$	3.10650	−	11.5936i	0.329288	−	1.22892i	0.909930	−	0.414762i	$-0.136135\pi$
$90$	−1.73162	−	0.489708i	−0.182529	−	0.0516197i
$91$	−0.191398	+	9.53747i	−0.0200640	+	0.999799i
$92$		−	1.27580i		−	0.133011i
$93$	3.57565	+	8.80379i	0.370777	+	0.912910i
$94$	2.87497	−	4.97960i	0.296531	−	0.513606i
$95$	−2.49237	+	4.31691i	−0.255712	+	0.442905i
$96$	−1.60474	+	0.651764i	−0.163783	+	0.0665204i
$97$	9.09518	+	9.09518i	0.923475	+	0.923475i	0.997273	−	0.0737979i	$-0.0235120\pi$
$97$	9.09518	+	9.09518i	0.923475	+	0.923475i	−0.0737979	+	0.997273i	$0.523512\pi$
$98$	6.78601	+	1.71760i	0.685490	+	0.173503i
$99$	−8.41121	+	4.70259i	−0.845359	+	0.472628i
$100$	−2.32009	−	4.01852i	−0.232009	−	0.401852i
$101$	−5.76486	+	9.98503i	−0.573625	+	0.993548i	0.422564	+	0.906333i	$0.361130\pi$
$101$	−5.76486	+	9.98503i	−0.573625	+	0.993548i	−0.996190	+	0.0872149i	$0.972203\pi$
$102$	7.09130	+	5.51954i	0.702144	+	0.546516i
$103$	0.364990	−	0.210727i	0.0359636	−	0.0207636i	−0.481910	−	0.876220i	$-0.660057\pi$
$103$	0.364990	−	0.210727i	0.0359636	−	0.0207636i	0.517874	+	0.855457i	$0.326724\pi$
$104$	−2.47972	−	2.61744i	−0.243156	−	0.256661i
$105$	−2.72533	−	0.358672i	−0.265965	−	0.0350028i
$106$	1.20989	+	1.20989i	0.117515	+	0.117515i
$107$	−11.0489	+	6.37909i	−1.06814	+	0.616690i	−0.927672	−	0.373396i	$-0.878193\pi$
$107$	−11.0489	+	6.37909i	−1.06814	+	0.616690i	−0.140466	+	0.990086i	$0.544860\pi$
$108$	−0.784775	+	5.13655i	−0.0755150	+	0.494265i
$109$	−6.59696	+	1.76765i	−0.631874	+	0.169310i	−0.560520	−	0.828141i	$-0.689399\pi$
$109$	−6.59696	+	1.76765i	−0.631874	+	0.169310i	−0.0713542	+	0.997451i	$0.522732\pi$
$110$	1.86115	+	0.498695i	0.177454	+	0.0475487i
$111$	0.929749	−	6.70417i	0.0882479	−	0.636332i
$112$	−2.28204	+	1.33876i	−0.215633	+	0.126501i
$113$			16.8438i			1.58453i	0.610175	+	0.792267i	$0.291099\pi$
$113$			16.8438i			1.58453i	−0.610175	+	0.792267i	$0.708901\pi$
$114$	13.2594	+	5.59979i	1.24186	+	0.524469i
$115$	0.198069	+	0.739204i	0.0184700	+	0.0689311i
$116$	−2.05327	+	3.55637i	−0.190641	+	0.330200i
$117$	−10.5536	+	2.37084i	−0.975683	+	0.219184i
$118$	−3.25338			−0.299498
$119$	11.9350	+	6.78056i	1.09408	+	0.621573i
$120$	0.828610	−	0.626774i	0.0756414	−	0.0572164i
$121$	−0.590549	+	0.340954i	−0.0536863	+	0.0309958i
$122$	−0.206086	−	0.769125i	−0.0186582	−	0.0696333i
$123$	−10.0466	−	7.81984i	−0.905876	−	0.705092i
$124$	−5.29917	−	1.41991i	−0.475879	−	0.127511i
$125$	4.08893	+	4.08893i	0.365725	+	0.365725i
$126$	−0.0544360	+	7.93707i	−0.00484955	+	0.707090i
$127$		−	2.45849i		−	0.218155i	−0.994033	−	0.109078i	$-0.965210\pi$
$127$		−	2.45849i		−	0.218155i	0.994033	−	0.109078i	$-0.0347897\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−16.2787	+	2.02890i	−1.43326	+	0.178635i
$130$	1.84312	+	1.13158i	0.161652	+	0.0992463i
$131$	18.1910	−	10.5026i	1.58936	−	0.917616i	0.595944	−	0.803026i	$-0.296778\pi$
$131$	18.1910	−	10.5026i	1.58936	−	0.917616i	0.993413	−	0.114590i	$-0.0365554\pi$
$132$	0.764265	−	5.51091i	0.0665208	−	0.479664i
$133$	21.2762	+	5.54277i	1.84488	+	0.480619i
$134$	−6.65289			−0.574722
$135$	−0.342753	−	3.09798i	−0.0294995	−	0.266632i
$136$	−5.01141	+	1.34280i	−0.429725	+	0.115144i
$137$	−5.66907	+	1.51902i	−0.484342	+	0.129779i	−0.492723	−	0.870186i	$-0.663999\pi$
$137$	−5.66907	+	1.51902i	−0.484342	+	0.129779i	0.00838191	+	0.999965i	$0.497332\pi$
$138$	2.04733	−	0.831519i	0.174280	−	0.0707836i
$139$	3.39367			0.287847			0.143923	−	0.989589i	$-0.454028\pi$
$139$	3.39367			0.287847			0.143923	+	0.989589i	$0.454028\pi$
$140$	1.11438	−	1.12998i	0.0941824	−	0.0955005i
$141$	9.86478	+	1.36807i	0.830764	+	0.115212i
$142$	−10.7963	+	6.23323i	−0.906003	+	0.523081i
$143$	11.2639	−	2.69430i	0.941937	−	0.225308i
$144$	−2.09183	−	2.15041i	−0.174319	−	0.179201i
$145$	0.637545	−	2.37935i	0.0529452	−	0.197594i
$146$		−	6.37801i		−	0.527848i
$147$	1.66658	+	12.0093i	0.137457	+	0.990508i
$148$	2.76316	+	2.76316i	0.227130	+	0.227130i
$149$	−21.0577	−	5.64239i	−1.72511	−	0.462242i	−0.746065	−	0.665873i	$-0.768059\pi$
$149$	−21.0577	−	5.64239i	−1.72511	−	0.462242i	−0.979048	+	0.203631i	$0.934726\pi$
$150$	4.93654	−	6.34228i	0.403067	−	0.517845i
$151$	−2.93466	−	10.9523i	−0.238819	−	0.891286i	−0.976390	−	0.216016i	$-0.930694\pi$
$151$	−2.93466	−	10.9523i	−0.238819	−	0.891286i	0.737571	−	0.675270i	$-0.235973\pi$
$152$	−7.19671	+	4.15502i	−0.583730	+	0.337017i
$153$	−4.23559	+	14.9772i	−0.342427	+	1.21083i
$154$	−0.0590530	−	8.49842i	−0.00475862	−	0.684822i
$155$	3.29081			0.264324
$156$	2.58414	−	5.68527i	0.206896	−	0.455186i
$157$	−11.9352	+	20.6724i	−0.952533	+	1.64984i	−0.212619	+	0.977135i	$0.568199\pi$
$157$	−11.9352	+	20.6724i	−0.952533	+	1.64984i	−0.739915	+	0.672701i	$0.765134\pi$
$158$	1.12612	+	4.20274i	0.0895894	+	0.334352i
$159$	−1.15300	+	2.73013i	−0.0914389	+	0.216513i
$160$			0.599845i			0.0474219i
$161$	2.91142	−	1.70799i	0.229452	−	0.134609i
$162$	−8.75433	+	2.08846i	−0.687805	+	0.164085i
$163$	−1.30429	−	0.349483i	−0.102160	−	0.0273737i	0.207377	−	0.978261i	$-0.433507\pi$
$163$	−1.30429	−	0.349483i	−0.102160	−	0.0273737i	−0.309537	+	0.950887i	$0.600174\pi$
$164$	7.09994	−	1.90242i	0.554412	−	0.148554i
$165$	0.412757	+	3.31171i	0.0321331	+	0.257816i
$166$	−11.7644	+	6.79217i	−0.913093	+	0.527175i
$167$	0.236454	+	0.236454i	0.0182973	+	0.0182973i	0.716196	−	0.697899i	$-0.245882\pi$
$167$	0.236454	+	0.236454i	0.0182973	+	0.0182973i	−0.697899	+	0.716196i	$0.745882\pi$
$168$	−3.63573	−	2.78953i	−0.280502	−	0.215217i
$169$	12.9810	+	0.702021i	0.998541	+	0.0540016i
$170$	2.69516	−	1.55605i	0.206710	−	0.119344i
$171$	−0.344198	+	24.9278i	−0.0263215	+	1.90627i
$172$	4.73560	−	8.20230i	0.361086	−	0.625420i
$173$	12.6750	+	21.9538i	0.963663	+	1.66911i	0.713166	+	0.700996i	$0.247261\pi$
$173$	12.6750	+	21.9538i	0.963663	+	1.66911i	0.250497	+	0.968117i	$0.419406\pi$
$174$	−7.04531	−	0.977058i	−0.534103	−	0.0740706i
$175$	6.06436	−	10.6744i	0.458423	−	0.806909i
$176$	2.27135	+	2.27135i	0.171210	+	0.171210i
$177$	−2.12044	−	5.22084i	−0.159382	−	0.392423i
$178$	−6.00130	+	10.3946i	−0.449816	+	0.779105i
$179$	−1.48007	+	2.56356i	−0.110626	+	0.191609i	−0.916023	−	0.401126i	$-0.868619\pi$
$179$	−1.48007	+	2.56356i	−0.110626	+	0.191609i	0.805397	+	0.592736i	$0.201952\pi$
$180$	1.54587	+	0.921198i	0.115222	+	0.0686620i
$181$			0.717545i			0.0533347i	0.999644	+	0.0266674i	$0.00848949\pi$
$181$			0.717545i			0.0533347i	−0.999644	+	0.0266674i	$0.991511\pi$
$182$	2.65336	−	9.16295i	0.196680	−	0.679203i
$183$	1.09993	−	0.832004i	0.0813091	−	0.0615035i
$184$	−0.330201	+	1.23233i	−0.0243427	+	0.0908482i
$185$	−2.02997	−	1.17201i	−0.149247	−	0.0861676i
$186$	−1.17522	−	9.42925i	−0.0861714	−	0.691386i
$187$	4.31332	−	16.0975i	0.315421	−	1.17717i
$188$	−4.06582	+	4.06582i	−0.296531	+	0.296531i
$189$	−12.7724	+	5.08574i	−0.929058	+	0.369933i
$190$	3.52474	−	3.52474i	0.255712	−	0.255712i
$191$	−12.6313	+	7.29268i	−0.913968	+	0.527680i	−0.881706	−	0.471800i	$-0.843605\pi$
$191$	−12.6313	+	7.29268i	−0.913968	+	0.527680i	−0.0322624	+	0.999479i	$0.510271\pi$
$192$	1.71875	−	0.214218i	0.124040	−	0.0154598i
$193$	5.24169	+	19.5623i	0.377305	+	1.40812i	0.849947	+	0.526868i	$0.176634\pi$
$193$	5.24169	+	19.5623i	0.377305	+	1.40812i	−0.472642	+	0.881255i	$0.656699\pi$
$194$	−6.43126	−	11.1393i	−0.461738	−	0.799753i
$195$	−0.614618	+	3.69526i	−0.0440137	+	0.264623i
$196$	−6.11023	−	3.41542i	−0.436445	−	0.243958i
$197$	−0.904894	+	0.904894i	−0.0644710	+	0.0644710i	−0.738607	−	0.674136i	$-0.764516\pi$
$197$	−0.904894	+	0.904894i	−0.0644710	+	0.0644710i	0.674136	+	0.738607i	$0.264516\pi$
$198$	9.34173	−	2.36537i	0.663888	−	0.168099i
$199$	−2.41271	−	1.39298i	−0.171032	−	0.0987456i	0.412040	−	0.911166i	$-0.364816\pi$
$199$	−2.41271	−	1.39298i	−0.171032	−	0.0987456i	−0.583073	+	0.812420i	$0.698150\pi$
$200$	1.20097	+	4.48208i	0.0849213	+	0.316931i
$201$	−4.33612	−	10.6762i	−0.305846	−	0.753040i
$202$	8.15274	−	8.15274i	0.573625	−	0.573625i
$203$	−10.8646	+	0.0754949i	−0.762547	+	0.00529871i
$204$	−5.42111	−	7.16683i	−0.379554	−	0.501779i
$205$	−3.81839	+	2.20455i	−0.266688	+	0.153972i
$206$	−0.407094	+	0.109080i	−0.0283636	+	0.00760000i
$207$	2.66875	+	2.74348i	0.185491	+	0.190685i
$208$	1.71778	+	3.17005i	0.119106	+	0.219804i
$209$		−	26.6934i		−	1.84642i
$210$	2.53964	+	1.05182i	0.175252	+	0.0725824i
$211$	2.68634			0.184935			0.0924677	−	0.995716i	$-0.470524\pi$
$211$	2.68634			0.184935			0.0924677	+	0.995716i	$0.470524\pi$
$212$	−0.855522	−	1.48181i	−0.0587575	−	0.101771i
$213$	−17.0394	−	13.2627i	−1.16752	−	0.908742i
$214$	12.3235	−	3.30206i	0.842414	−	0.225724i
$215$	−1.47042	+	5.48766i	−0.100281	+	0.374256i
$216$	2.08747	−	4.75841i	0.142034	−	0.323769i
$217$	−3.85405	−	13.9938i	−0.261630	−	0.949963i
$218$	6.82968			0.462564
$219$	10.2351	−	4.15696i	0.691622	−	0.280901i
$220$	−1.66866	−	0.963404i	−0.112501	−	0.0649527i
$221$	9.78731	−	15.9416i	0.658365	−	1.07235i
$222$	−2.63324	+	6.23510i	−0.176731	+	0.418472i
$223$	2.18383	+	2.18383i	0.146240	+	0.146240i	0.776436	−	0.630196i	$-0.217025\pi$
$223$	2.18383	+	2.18383i	0.146240	+	0.146240i	−0.630196	+	0.776436i	$0.717025\pi$
$224$	2.55078	−	0.702512i	0.170431	−	0.0469386i
$225$	13.3952	+	3.78821i	0.893014	+	0.252547i
$226$	4.35950	−	16.2699i	0.289990	−	1.08226i
$227$	5.50302	+	20.5375i	0.365248	+	1.36312i	0.867084	+	0.498162i	$0.165991\pi$
$227$	5.50302	+	20.5375i	0.365248	+	1.36312i	−0.501836	+	0.864963i	$0.667342\pi$
$228$	−11.3583	−	8.84078i	−0.752222	−	0.585495i
$229$	4.13582	+	1.10819i	0.273303	+	0.0732312i	0.392867	−	0.919595i	$-0.371483\pi$
$229$	4.13582	+	1.10819i	0.273303	+	0.0732312i	−0.119565	+	0.992826i	$0.538150\pi$
$230$		−	0.765280i		−	0.0504611i
$231$	13.5993	−	5.63373i	0.894768	−	0.370672i
$232$	2.90376	−	2.90376i	0.190641	−	0.190641i
$233$	−7.18694	−	12.4481i	−0.470832	−	0.815505i	0.528612	−	0.848864i	$-0.322713\pi$
$233$	−7.18694	−	12.4481i	−0.470832	−	0.815505i	−0.999443	+	0.0333591i	$0.989379\pi$
$234$	10.8076	+	0.441423i	0.706518	+	0.0288567i
$235$	1.72454	−	2.98698i	0.112496	−	0.194849i
$236$	3.14252	+	0.842037i	0.204561	+	0.0548119i
$237$	−6.01036	+	4.54633i	−0.390415	+	0.295316i
$238$	−9.77342	−	9.63854i	−0.633517	−	0.624774i
$239$	−7.07117	+	7.07117i	−0.457396	+	0.457396i	−0.897800	−	0.440404i	$-0.854835\pi$
$239$	−7.07117	+	7.07117i	−0.457396	+	0.457396i	0.440404	+	0.897800i	$0.354835\pi$
$240$	−0.962597	+	0.390957i	−0.0621354	+	0.0252362i
$241$	2.14060	+	7.98882i	0.137888	+	0.514605i	0.999969	+	0.00783522i	$0.00249405\pi$
$241$	2.14060	+	7.98882i	0.137888	+	0.514605i	−0.862081	+	0.506770i	$0.830839\pi$
$242$	0.658672	−	0.176491i	0.0423411	−	0.0113453i
$243$	−9.05720	−	12.6873i	−0.581020	−	0.813889i
$244$			0.796257i			0.0509751i
$245$	4.07055	+	1.03029i	0.260058	+	0.0658229i
$246$	7.68039	+	10.1537i	0.489684	+	0.647373i
$247$	8.53371	−	28.7213i	0.542987	−	1.82749i
$248$	4.75110	+	2.74305i	0.301695	+	0.174184i
$249$	−18.5673	−	14.4519i	−1.17665	−	0.915854i
$250$	−2.89131	−	5.00789i	−0.182862	−	0.316727i
$251$	−25.4886			−1.60882			−0.804412	−	0.594071i	$-0.797520\pi$
$251$	−25.4886			−1.60882			−0.804412	+	0.594071i	$0.797520\pi$
$252$	2.10685	−	7.65253i	0.132719	−	0.482064i
$253$	−2.89779	−	2.89779i	−0.182182	−	0.182182i
$254$	−0.636303	+	2.37472i	−0.0399252	+	0.149003i
$255$	4.25368	+	3.31087i	0.266376	+	0.207335i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.50252	−	11.2627i	−0.405616	−	0.702548i	0.588777	−	0.808296i	$-0.299610\pi$
$257$	−6.50252	−	11.2627i	−0.405616	−	0.702548i	−0.994393	+	0.105748i	$0.966276\pi$
$258$	16.2491	+	2.25346i	1.01162	+	0.140294i
$259$	−2.60642	+	10.0049i	−0.161955	+	0.621672i
$260$	−1.48744	−	1.57006i	−0.0922474	−	0.0973709i
$261$	−3.02395	−	11.9427i	−0.187178	−	0.739236i
$262$	−20.2894	+	5.43654i	−1.25349	+	0.335871i
$263$	7.46602	+	4.31051i	0.460375	+	0.265797i	0.712202	−	0.701975i	$-0.247698\pi$
$263$	7.46602	+	4.31051i	0.460375	+	0.265797i	−0.251827	+	0.967772i	$0.581031\pi$
$264$	−2.16455	+	5.12533i	−0.133219	+	0.315442i
$265$	0.725746	+	0.725746i	0.0445822	+	0.0445822i
$266$	−19.1166	−	10.8606i	−1.17212	−	0.665905i
$267$	−20.5920	−	2.85575i	−1.26021	−	0.174769i
$268$	6.42620	+	1.72190i	0.392543	+	0.105181i
$269$	−19.8943	−	11.4860i	−1.21298	−	0.700313i	−0.249571	−	0.968357i	$-0.580290\pi$
$269$	−19.8943	−	11.4860i	−1.21298	−	0.700313i	−0.963407	+	0.268044i	$0.913623\pi$
$270$	−0.470743	+	3.08113i	−0.0286485	+	0.187512i
$271$	19.2021	+	5.14519i	1.16645	+	0.312548i	0.789538	−	0.613702i	$-0.210320\pi$
$271$	19.2021	+	5.14519i	1.16645	+	0.312548i	0.376909	+	0.926250i	$0.376987\pi$
$272$	5.18819			0.314580
$273$	16.4336	−	1.71413i	0.994604	−	0.103744i
$274$	5.86906			0.354563
$275$	−14.3972	−	3.85773i	−0.868186	−	0.232630i
$276$	−2.19278	+	0.273298i	−0.131990	+	0.0164506i
$277$	12.9397	+	7.47073i	0.777470	+	0.448872i	0.835533	−	0.549440i	$-0.185159\pi$
$277$	12.9397	+	7.47073i	0.777470	+	0.448872i	−0.0580630	+	0.998313i	$0.518492\pi$
$278$	−3.27803	−	0.878345i	−0.196603	−	0.0526796i
$279$	14.3656	−	8.03158i	0.860044	−	0.480838i
$280$	−1.36887	+	0.803051i	−0.0818056	+	0.0479915i
$281$	−0.842761	−	0.842761i	−0.0502749	−	0.0502749i	0.681522	−	0.731797i	$-0.261318\pi$
$281$	−0.842761	−	0.842761i	−0.0502749	−	0.0502749i	−0.731797	+	0.681522i	$0.761318\pi$
$282$	−9.17456	−	3.87465i	−0.546337	−	0.230732i
$283$	4.36513	+	2.52021i	0.259480	+	0.149811i	0.624097	−	0.781346i	$-0.285467\pi$
$283$	4.36513	+	2.52021i	0.259480	+	0.149811i	−0.364617	+	0.931158i	$0.618800\pi$
$284$	12.0417	−	3.22656i	0.714542	−	0.191461i
$285$	7.95361	+	3.35901i	0.471131	+	0.198970i
$286$	−11.5774	−	0.312829i	−0.684589	−	0.0184979i
$287$	13.8466	+	13.6555i	0.817336	+	0.806056i
$288$	1.46399	+	2.61854i	0.0862662	+	0.154299i
$289$	−4.95866	−	8.58865i	−0.291686	−	0.505215i
$290$	−1.23164	+	2.13327i	−0.0723245	+	0.125270i
$291$	13.6840	−	17.5807i	0.802171	−	1.03060i
$292$	−1.65075	+	6.16069i	−0.0966029	+	0.360527i
$293$	−4.76090	−	4.76090i	−0.278135	−	0.278135i	0.554229	−	0.832364i	$-0.313013\pi$
$293$	−4.76090	−	4.76090i	−0.278135	−	0.278135i	−0.832364	+	0.554229i	$0.813013\pi$
$294$	1.49844	−	12.0314i	0.0873907	−	0.701686i
$295$	−1.95152			−0.113622
$296$	−1.95385	−	3.38417i	−0.113565	−	0.196701i
$297$	9.88442	+	13.4494i	0.573552	+	0.780414i
$298$	18.8798	+	10.9003i	1.09368	+	0.631435i
$299$	−2.19153	−	4.04434i	−0.126740	−	0.233891i
$300$	−6.40984	+	4.84850i	−0.370072	+	0.279929i
$301$	25.0578	−	0.174119i	1.44431	−	0.0100361i
$302$			11.3387i			0.652466i
$303$	18.3967	+	7.76940i	1.05686	+	0.446340i
$304$	8.02689	−	2.15080i	0.460374	−	0.123357i
$305$	−0.123620	−	0.461355i	−0.00707845	−	0.0264171i
$306$	7.96765	−	13.3706i	0.455480	−	0.764345i
$307$	−17.3519	+	17.3519i	−0.990324	+	0.990324i	−0.999954	−	0.00962922i	$-0.996935\pi$
$307$	−17.3519	+	17.3519i	−0.990324	+	0.990324i	0.00962922	+	0.999954i	$0.496935\pi$
$308$	−2.14251	+	8.22413i	−0.122081	+	0.468613i
$309$	−0.440376	−	0.582187i	−0.0250521	−	0.0331194i
$310$	−3.17868	−	0.851724i	−0.180537	−	0.0483747i
$311$	12.1990	−	21.1294i	0.691744	−	1.19814i	−0.279521	−	0.960139i	$-0.590176\pi$
$311$	12.1990	−	21.1294i	0.691744	−	1.19814i	0.971266	−	0.237997i	$-0.0764909\pi$
$312$	−3.96754	+	4.82272i	−0.224618	+	0.273033i
$313$	12.9180	+	22.3747i	0.730171	+	1.26469i	0.956810	+	0.290714i	$0.0938930\pi$
$313$	12.9180	+	22.3747i	0.730171	+	1.26469i	−0.226639	+	0.973979i	$0.572774\pi$
$314$	16.8789	−	16.8789i	0.952533	−	0.952533i
$315$	−0.0326531	+	4.76101i	−0.00183980	+	0.268252i
$316$		−	4.35100i		−	0.244763i
$317$	−14.2207	−	3.81041i	−0.798712	−	0.214014i	−0.163693	−	0.986511i	$-0.552341\pi$
$317$	−14.2207	−	3.81041i	−0.798712	−	0.214014i	−0.635018	+	0.772497i	$0.719007\pi$
$318$	1.82032	−	2.33868i	0.102079	−	0.131147i
$319$	3.41407	+	12.7415i	0.191151	+	0.713385i
$320$	0.155251	−	0.579405i	0.00867881	−	0.0323897i
$321$	13.3310	+	17.6238i	0.744061	+	0.983666i
$322$	−3.25428	+	0.896263i	−0.181354	+	0.0499468i
$323$	−30.4863	−	30.4863i	−1.69630	−	1.69630i
$324$	8.99657	+	0.248493i	0.499809	+	0.0138052i
$325$	−14.2577	−	8.75352i	−0.790877	−	0.485558i
$326$	1.16939	+	0.675150i	0.0647668	+	0.0373931i
$327$	4.45134	+	10.9599i	0.246160	+	0.606083i
$328$	−7.35040			−0.405858
$329$	−14.7216	−	3.83519i	−0.811626	−	0.211441i
$330$	0.458440	−	3.30569i	0.0252363	−	0.181972i
$331$	0.769457	−	2.87165i	0.0422932	−	0.157840i	−0.941550	−	0.336874i	$-0.890630\pi$
$331$	0.769457	−	2.87165i	0.0422932	−	0.157840i	0.983843	+	0.179034i	$0.0572971\pi$
$332$	13.1215	−	3.51589i	0.720134	−	0.192959i
$333$	−11.7220	−	0.161855i	−0.642361	−	0.00886959i
$334$	−0.167198	−	0.289596i	−0.00914867	−	0.0158460i
$335$	−3.99070			−0.218035
$336$	2.78986	+	3.63548i	0.152199	+	0.198331i
$337$			13.9931i			0.762255i	0.924523	+	0.381127i	$0.124464\pi$
$337$			13.9931i			0.762255i	−0.924523	+	0.381127i	$0.875536\pi$
$338$	−12.3570	−	4.03784i	−0.672133	−	0.219629i
$339$	28.9504	−	3.60825i	1.57237	−	0.195973i
$340$	−3.00607	+	0.805473i	−0.163027	+	0.0436829i
$341$	−15.2614	+	8.81117i	−0.826451	+	0.477152i
$342$	6.78425	−	23.9893i	0.366850	−	1.29719i
$343$	−0.386041	−	18.5162i	−0.0208442	−	0.999783i
$344$	−6.69715	+	6.69715i	−0.361086	+	0.361086i
$345$	1.22808	−	0.498782i	0.0661175	−	0.0268535i
$346$	−6.56107	−	24.4862i	−0.352725	−	1.31639i
$347$	8.62184	+	4.97782i	0.462845	+	0.267224i	0.713240	−	0.700920i	$-0.247227\pi$
$347$	8.62184	+	4.97782i	0.462845	+	0.267224i	−0.250395	+	0.968144i	$0.580560\pi$
$348$	6.55236	+	2.76723i	0.351243	+	0.148339i
$349$	13.9690	−	13.9690i	0.747742	−	0.747742i	−0.226313	−	0.974055i	$-0.572667\pi$
$349$	13.9690	−	13.9690i	0.747742	−	0.747742i	0.974055	+	0.226313i	$0.0726672\pi$
$350$	−8.62046	+	8.74110i	−0.460783	+	0.467232i
$351$	6.33567	+	17.6312i	0.338173	+	0.941084i
$352$	−1.60609	−	2.78183i	−0.0856049	−	0.148272i
$353$	3.84065	+	14.3335i	0.204417	+	0.762896i	0.989626	+	0.143665i	$0.0458889\pi$
$353$	3.84065	+	14.3335i	0.204417	+	0.762896i	−0.785209	+	0.619231i	$0.787444\pi$
$354$	0.696932	+	5.59176i	0.0370415	+	0.297199i
$355$	−6.47608	+	3.73897i	−0.343715	+	0.198444i
$356$	8.48711	−	8.48711i	0.449816	−	0.449816i
$357$	9.09741	−	21.9659i	0.481486	−	1.16256i
$358$	2.09314	−	2.09314i	0.110626	−	0.110626i
$359$	−3.87962	+	14.4789i	−0.204759	+	0.764169i	0.784764	+	0.619794i	$0.212784\pi$
$359$	−3.87962	+	14.4789i	−0.204759	+	0.764169i	−0.989523	+	0.144375i	$0.953883\pi$
$360$	−1.25477	−	1.28991i	−0.0661323	−	0.0679842i
$361$	−43.3505	−	25.0284i	−2.28161	−	1.31729i
$362$	0.185714	−	0.693096i	0.00976093	−	0.0364283i
$363$	0.712522	+	0.941970i	0.0373977	+	0.0494406i
$364$	−4.93449	+	8.16399i	−0.258638	+	0.427910i
$365$		−	3.82582i		−	0.200252i
$366$	−1.27779	+	0.518972i	−0.0667911	+	0.0271271i
$367$	−6.15961	+	10.6688i	−0.321529	+	0.556905i	−0.980804	−	0.194998i	$-0.937530\pi$
$367$	−6.15961	+	10.6688i	−0.321529	+	0.556905i	0.659275	+	0.751902i	$0.270863\pi$
$368$	0.637898	−	1.10487i	0.0332528	−	0.0575955i
$369$	−11.2882	+	18.9429i	−0.587641	+	0.986125i
$370$	1.65747	+	1.65747i	0.0861676	+	0.0861676i
$371$	2.23620	−	3.93613i	0.116098	−	0.204354i
$372$	−1.30529	+	9.41213i	−0.0676763	+	0.487996i
$373$	−2.52756	−	4.37786i	−0.130872	−	0.226677i	0.793141	−	0.609038i	$-0.208444\pi$
$373$	−2.52756	−	4.37786i	−0.130872	−	0.226677i	−0.924013	+	0.382361i	$0.875111\pi$
$374$	−8.33270	+	14.4327i	−0.430874	+	0.746295i
$375$	6.15193	−	7.90377i	0.317684	−	0.408149i
$376$	4.97960	−	2.87497i	0.256803	−	0.148265i
$377$	−0.399929	+	14.8009i	−0.0205974	+	0.762287i
$378$	13.6535	−	1.60670i	0.702261	−	0.0826397i
$379$	−1.20575	−	1.20575i	−0.0619353	−	0.0619353i	0.675461	−	0.737396i	$-0.263945\pi$
$379$	−1.20575	−	1.20575i	−0.0619353	−	0.0619353i	−0.737396	+	0.675461i	$0.763945\pi$
$380$	−4.31691	+	2.49237i	−0.221453	+	0.127856i
$381$	−4.22553	+	0.526652i	−0.216481	+	0.0269812i
$382$	14.0884	−	3.77497i	0.720824	−	0.193144i
$383$	−17.5705	−	4.70799i	−0.897808	−	0.240567i	−0.219734	−	0.975560i	$-0.570519\pi$
$383$	−17.5705	−	4.70799i	−0.897808	−	0.240567i	−0.678075	+	0.734993i	$0.737185\pi$
$384$	−1.71563	−	0.237927i	−0.0875504	−	0.0121417i
$385$	−0.0354226	−	5.09773i	−0.00180530	−	0.259804i
$386$		−	20.2524i		−	1.03082i
$387$	6.97435	+	27.5443i	0.354526	+	1.40016i
$388$	3.32907	+	12.4242i	0.169008	+	0.630745i
$389$	−15.4549	+	26.7687i	−0.783595	+	1.35723i	0.146240	+	0.989249i	$0.453283\pi$
$389$	−15.4549	+	26.7687i	−0.783595	+	1.35723i	−0.929835	+	0.367977i	$0.880051\pi$
$390$	1.55008	−	3.41028i	0.0784913	−	0.172686i
$391$	−6.61908			−0.334741
$392$	5.01805	+	4.88048i	0.253450	+	0.246502i
$393$	−21.9482	−	29.0160i	−1.10714	−	1.46366i
$394$	1.10826	−	0.639857i	0.0558336	−	0.0322355i
$395$	0.675498	+	2.52099i	0.0339880	+	0.126845i
$396$	−9.63562	−	0.133047i	−0.484208	−	0.00668585i
$397$	6.56445	+	1.75894i	0.329461	+	0.0882787i	0.419758	−	0.907636i	$-0.362115\pi$
$397$	6.56445	+	1.75894i	0.329461	+	0.0882787i	−0.0902972	+	0.995915i	$0.528782\pi$
$398$	1.96997	+	1.96997i	0.0987456	+	0.0987456i
$399$	4.96892	−	37.7558i	0.248757	−	1.89016i
$400$		−	4.64019i		−	0.232009i
$401$	6.13006	−	22.8777i	0.306121	−	1.14246i	−0.625856	−	0.779939i	$-0.715250\pi$
$401$	6.13006	−	22.8777i	0.306121	−	1.14246i	0.931976	−	0.362519i	$-0.118083\pi$
$402$	1.42517	+	11.4347i	0.0710809	+	0.570310i
$403$	−19.2377	+	4.60160i	−0.958299	+	0.229222i
$404$	−9.98503	+	5.76486i	−0.496774	+	0.286813i
$405$	−5.25124	+	1.25275i	−0.260936	+	0.0622496i
$406$	10.5140	+	2.73905i	0.521799	+	0.135937i
$407$	12.5522			0.622191
$408$	3.38148	+	8.32572i	0.167408	+	0.412184i
$409$	−2.45363	+	0.657447i	−0.121324	+	0.0325087i	−0.318970	−	0.947765i	$-0.603337\pi$
$409$	−2.45363	+	0.657447i	−0.121324	+	0.0325087i	0.197646	+	0.980273i	$0.436670\pi$
$410$	4.25886	−	1.14116i	0.210330	−	0.0563578i
$411$	3.82524	+	9.41833i	0.188685	+	0.464572i
$412$	0.421455			0.0207636
$413$	2.28554	+	8.29866i	0.112464	+	0.408350i
$414$	−1.86775	−	3.34072i	−0.0917949	−	0.164188i
$415$	−7.05680	+	4.07425i	−0.346405	+	0.199997i
$416$	−0.838775	−	3.50663i	−0.0411243	−	0.171927i
$417$	−0.726984	−	5.83287i	−0.0356005	−	0.285637i
$418$	−6.90875	+	25.7838i	−0.337918	+	1.26113i
$419$			3.88080i			0.189590i	0.995497	+	0.0947948i	$0.0302195\pi$
$419$			3.88080i			0.189590i	−0.995497	+	0.0947948i	$0.969781\pi$
$420$	−2.18087	−	1.67329i	−0.106416	−	0.0816480i
$421$	0.262070	+	0.262070i	0.0127725	+	0.0127725i	0.713464	−	0.700692i	$-0.247125\pi$
$421$	0.262070	+	0.262070i	0.0127725	+	0.0127725i	−0.700692	+	0.713464i	$0.747125\pi$
$422$	−2.59481	−	0.695277i	−0.126313	−	0.0338455i
$423$	0.238160	−	17.2482i	0.0115797	−	0.838635i
$424$	0.442851	+	1.65274i	0.0215067	+	0.0802642i
$425$	−20.8488	+	12.0371i	−1.01132	+	0.583884i
$426$	13.0261	+	17.2209i	0.631118	+	0.834353i
$427$	−1.81709	+	1.06600i	−0.0879352	+	0.0515874i
$428$	−12.7582			−0.616690
$429$	−7.04376	−	18.7827i	−0.340076	−	0.906839i
$430$	2.84062	−	4.92011i	0.136987	−	0.237269i
$431$	3.75773	+	14.0240i	0.181004	+	0.675514i	0.995451	+	0.0952769i	$0.0303736\pi$
$431$	3.75773	+	14.0240i	0.181004	+	0.675514i	−0.814447	+	0.580238i	$0.802960\pi$
$432$	−3.24791	+	4.05599i	−0.156265	+	0.195144i
$433$		−	9.24282i		−	0.444182i	−0.975026	−	0.222091i	$-0.928712\pi$
$433$		−	9.24282i		−	0.444182i	0.975026	−	0.222091i	$-0.0712881\pi$
$434$	0.100857	+	14.5145i	0.00484129	+	0.696719i
$435$	−4.22609	−	0.586083i	−0.202625	−	0.0281005i
$436$	−6.59696	−	1.76765i	−0.315937	−	0.0846551i
$437$	−10.2407	+	2.74398i	−0.489878	+	0.131262i
$438$	−10.9622	+	1.36628i	−0.523795	+	0.0652836i
$439$	5.46918	−	3.15763i	0.261030	−	0.150705i	−0.363775	−	0.931487i	$-0.618512\pi$
$439$	5.46918	−	3.15763i	0.261030	−	0.150705i	0.624804	+	0.780782i	$0.285179\pi$
$440$	1.36246	+	1.36246i	0.0649527	+	0.0649527i
$441$	20.2840	−	5.43703i	0.965902	−	0.258906i
$442$	−13.5798	+	12.8652i	−0.645925	+	0.611937i
$443$	13.0061	−	7.50906i	0.617937	−	0.356766i	−0.158128	−	0.987419i	$-0.550546\pi$
$443$	13.0061	−	7.50906i	0.617937	−	0.356766i	0.776065	+	0.630652i	$0.217213\pi$
$444$	4.15727	−	5.34111i	0.197295	−	0.253478i
$445$	−3.59985	+	6.23511i	−0.170649	+	0.295573i
$446$	−1.54420	−	2.67463i	−0.0731200	−	0.126648i
$447$	−5.18694	+	37.4016i	−0.245334	+	1.76904i
$448$	−2.64569	+	0.0183841i	−0.124997	+	0.000868566i
$449$	11.2960	+	11.2960i	0.533091	+	0.533091i	0.921491	−	0.388400i	$-0.126972\pi$
$449$	11.2960	+	11.2960i	0.533091	+	0.533091i	−0.388400	+	0.921491i	$0.626972\pi$
$450$	−11.9583	−	7.12606i	−0.563720	−	0.335926i
$451$	11.8054	−	20.4475i	0.555894	−	0.962837i
$452$	−8.42191	+	14.5872i	−0.396133	+	0.686123i
$453$	−18.1956	+	7.39013i	−0.854906	+	0.347219i
$454$		−	21.2620i		−	0.997877i
$455$	1.59160	−	5.49635i	0.0746154	−	0.257673i
$456$	8.68312	+	11.4793i	0.406624	+	0.537567i
$457$	−4.29015	+	16.0111i	−0.200685	+	0.748966i	0.790037	+	0.613059i	$0.210061\pi$
$457$	−4.29015	+	16.0111i	−0.200685	+	0.748966i	−0.990722	+	0.135907i	$0.956605\pi$
$458$	−3.70807	−	2.14086i	−0.173267	−	0.100036i
$459$	26.6494	+	4.07156i	1.24389	+	0.190044i
$460$	−0.198069	+	0.739204i	−0.00923501	+	0.0344655i
$461$	−12.3842	+	12.3842i	−0.576788	+	0.576788i	−0.934017	−	0.357229i	$-0.883722\pi$
$461$	−12.3842	+	12.3842i	−0.576788	+	0.576788i	0.357229	+	0.934017i	$0.383722\pi$
$462$	−14.5940	+	1.92201i	−0.678976	+	0.0894200i
$463$	15.3743	−	15.3743i	0.714503	−	0.714503i	−0.252971	−	0.967474i	$-0.581408\pi$
$463$	15.3743	−	15.3743i	0.714503	−	0.714503i	0.967474	+	0.252971i	$0.0814076\pi$
$464$	−3.55637	+	2.05327i	−0.165100	+	0.0953206i
$465$	−0.704950	−	5.65608i	−0.0326913	−	0.262295i
$466$	3.72023	+	13.8841i	0.172336	+	0.643168i
$467$	2.94747	+	5.10517i	0.136393	+	0.236239i	0.926129	−	0.377208i	$-0.123116\pi$
$467$	2.94747	+	5.10517i	0.136393	+	0.236239i	−0.789736	+	0.613447i	$0.789782\pi$
$468$	−10.3251	−	3.22361i	−0.477279	−	0.149011i
$469$	4.67374	+	16.9701i	0.215813	+	0.783605i
$470$	−2.43886	+	2.43886i	−0.112496	+	0.112496i
$471$	38.0875	+	16.0853i	1.75498	+	0.741170i
$472$	−2.81751	−	1.62669i	−0.129686	−	0.0748745i
$473$	−7.87410	−	29.3865i	−0.362052	−	1.35119i
$474$	6.98224	−	2.83583i	0.320705	−	0.130254i
$475$	−27.2662	+	27.2662i	−1.25106	+	1.25106i
$476$	6.94577	+	11.8397i	0.318359	+	0.542670i
$477$	4.93941	+	1.39688i	0.226160	+	0.0639588i
$478$	8.66038	−	5.00007i	0.396117	−	0.228698i
$479$	17.4615	−	4.67881i	0.797838	−	0.213780i	0.163204	−	0.986592i	$-0.447817\pi$
$479$	17.4615	−	4.67881i	0.797838	−	0.213780i	0.634635	+	0.772812i	$0.281151\pi$
$480$	1.03098	−	0.128497i	0.0470578	−	0.00586508i
$481$	13.5059	+	4.01287i	0.615814	+	0.182971i
$482$		−	8.27064i		−	0.376717i
$483$	−3.55929	−	4.63813i	−0.161953	−	0.211042i
$484$	−0.681908			−0.0309958
$485$	−3.85776	−	6.68183i	−0.175172	−	0.303406i
$486$	5.46488	+	14.5991i	0.247892	+	0.662231i
$487$	−37.4584	+	10.0369i	−1.69740	+	0.454817i	−0.972283	−	0.233807i	$-0.924882\pi$
$487$	−37.4584	+	10.0369i	−1.69740	+	0.454817i	−0.725118	+	0.688624i	$0.758215\pi$
$488$	0.206086	−	0.769125i	0.00932909	−	0.0348167i
$489$	−0.321273	+	2.31662i	−0.0145285	+	0.104761i
$490$	−3.66519	−	2.04872i	−0.165576	−	0.0925517i
$491$	9.27442			0.418549			0.209274	−	0.977857i	$-0.432890\pi$
$491$	9.27442			0.418549			0.209274	+	0.977857i	$0.432890\pi$
$492$	−4.79073	−	11.7955i	−0.215983	−	0.531783i
$493$	18.4511	+	10.6528i	0.830996	+	0.479776i
$494$	−15.6766	+	25.5340i	−0.705322	+	1.14883i
$495$	5.60358	−	1.41885i	0.251862	−	0.0637727i
$496$	−3.87926	−	3.87926i	−0.174184	−	0.174184i
$497$	23.4841	+	23.1600i	1.05341	+	1.03887i
$498$	14.1942	+	18.7651i	0.636057	+	0.840882i
$499$	−9.84950	+	36.7588i	−0.440924	+	1.64555i	0.285555	+	0.958362i	$0.407822\pi$
$499$	−9.84950	+	36.7588i	−0.440924	+	1.64555i	−0.726479	+	0.687189i	$0.758845\pi$
$500$	1.49665	+	5.58558i	0.0669322	+	0.249795i
$501$	0.355753	−	0.457058i	0.0158939	−	0.0204199i
$502$	24.6201	+	6.59693i	1.09885	+	0.294435i
$503$		−	13.4961i		−	0.601763i	−0.953662	−	0.300882i	$-0.902719\pi$
$503$		−	13.4961i		−	0.601763i	0.953662	−	0.300882i	$-0.0972809\pi$
$504$	−4.01568	+	6.84648i	−0.178872	+	0.304967i
$505$	4.89038	−	4.89038i	0.217619	−	0.217619i
$506$	2.04904	+	3.54905i	0.0910911	+	0.157774i
$507$	−1.57417	−	22.4616i	−0.0699113	−	0.997553i
$508$	1.22924	−	2.12911i	0.0545389	−	0.0944641i
$509$	40.8332	+	10.9412i	1.80990	+	0.484961i	0.995451	−	0.0952733i	$-0.0303725\pi$
$509$	40.8332	+	10.9412i	1.80990	+	0.484961i	0.814449	+	0.580235i	$0.197039\pi$
$510$	−3.25182	−	4.29899i	−0.143993	−	0.190362i
$511$	−16.2689	+	4.48063i	−0.719694	+	0.198211i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	42.9184	−	4.74838i	1.89489	−	0.209646i
$514$	3.36595	+	12.5619i	0.148466	+	0.554082i
$515$	−0.244193	+	0.0654313i	−0.0107604	+	0.00288325i
$516$	−15.1122	−	6.38225i	−0.665276	−	0.280963i
$517$			18.4698i			0.812303i
$518$	5.10706	−	8.98937i	0.224391	−	0.394970i
$519$	35.0179	−	26.4881i	1.53711	−	1.16270i
$520$	1.03040	+	1.90154i	0.0451860	+	0.0833880i
$521$	−23.0923	−	13.3323i	−1.01169	−	0.584099i	−0.100004	−	0.994987i	$-0.531886\pi$
$521$	−23.0923	−	13.3323i	−1.01169	−	0.584099i	−0.911686	+	0.410888i	$0.865219\pi$
$522$	−0.170091	+	12.3184i	−0.00744467	+	0.539164i
$523$	−9.51589	−	16.4820i	−0.416101	−	0.720708i	0.579443	−	0.815013i	$-0.303270\pi$
$523$	−9.51589	−	16.4820i	−0.416101	−	0.720708i	−0.995543	+	0.0943055i	$0.969937\pi$
$524$	21.0052			0.917616
$525$	−19.6457	−	8.13650i	−0.857411	−	0.355106i
$526$	−6.09598	−	6.09598i	−0.265797	−	0.265797i
$527$	−7.36675	+	27.4931i	−0.320901	+	1.19762i
$528$	3.41733	−	4.39046i	0.148720	−	0.191070i
$529$	10.6862	−	18.5090i	0.464616	−	0.804739i
$530$	−0.513180	−	0.888854i	−0.0222911	−	0.0386094i
$531$	−8.51910	+	4.76291i	−0.369698	+	0.206693i
$532$	15.6543	+	15.4383i	0.678701	+	0.669334i
$533$	19.2393	−	18.2269i	0.833345	−	0.789495i
$534$	19.1512	+	8.08805i	0.828755	+	0.350004i
$535$	7.39216	−	1.98072i	0.319591	−	0.0856341i
$536$	−5.76157	−	3.32645i	−0.248862	−	0.143681i
$537$	4.72318	+	1.99472i	0.203820	+	0.0860784i
$538$	16.2436	+	16.2436i	0.700313	+	0.700313i
$539$	−21.6361	+	6.12087i	−0.931933	+	0.263645i
$540$	1.25216	−	2.85431i	0.0538843	−	0.122830i
$541$	−43.3634	−	11.6192i	−1.86434	−	0.499547i	−0.864342	−	0.502905i	$-0.832265\pi$
$541$	−43.3634	−	11.6192i	−1.86434	−	0.499547i	−0.999994	+	0.00335721i	$0.998931\pi$
$542$	−17.2162	−	9.93975i	−0.739497	−	0.426949i
$543$	1.23328	−	0.153711i	0.0529252	−	0.00659637i
$544$	−5.01141	−	1.34280i	−0.214862	−	0.0575722i
$545$	4.09674			0.175485
$546$	−16.3172	−	2.59759i	−0.698314	−	0.111167i
$547$	−10.8785			−0.465131			−0.232566	−	0.972581i	$-0.574712\pi$
$547$	−10.8785			−0.465131			−0.232566	+	0.972581i	$0.574712\pi$
$548$	−5.66907	−	1.51902i	−0.242171	−	0.0648895i
$549$	−1.66563	−	1.71228i	−0.0710875	−	0.0730781i
$550$	12.9082	+	7.45255i	0.550408	+	0.317778i
$551$	32.9627	+	8.83234i	1.40426	+	0.376270i
$552$	2.18880	+	0.303547i	0.0931614	+	0.0129198i
$553$	9.92915	−	5.82496i	0.422231	−	0.247703i
$554$	−10.5652	−	10.5652i	−0.448872	−	0.448872i
$555$	−1.57953	+	3.74009i	−0.0670474	+	0.158758i
$556$	2.93900	+	1.69683i	0.124641	+	0.0719617i
$557$	36.3533	−	9.74083i	1.54034	−	0.412732i	0.613963	−	0.789335i	$-0.289574\pi$
$557$	36.3533	−	9.74083i	1.54034	−	0.412732i	0.926375	+	0.376603i	$0.122908\pi$
$558$	−15.9548	+	4.03983i	−0.675420	+	0.171020i
$559$	0.922384	−	34.1364i	0.0390127	−	1.44382i
$560$	1.53007	−	0.421398i	0.0646573	−	0.0178073i
$561$	−28.5917	−	3.96515i	−1.20714	−	0.167409i
$562$	0.595922	+	1.03217i	0.0251375	+	0.0435393i
$563$	−6.20164	+	10.7416i	−0.261368	+	0.452703i	−0.966606	−	0.256268i	$-0.917507\pi$
$563$	−6.20164	+	10.7416i	−0.261368	+	0.452703i	0.705238	+	0.708971i	$0.250840\pi$
$564$	7.85912	+	6.11717i	0.330929	+	0.257579i
$565$	2.61502	−	9.75940i	0.110015	−	0.410581i
$566$	−3.56412	−	3.56412i	−0.149811	−	0.149811i
$567$	11.4772	+	20.8632i	0.481998	+	0.876172i
$568$	−12.4665			−0.523081
$569$	13.3186	+	23.0685i	0.558344	+	0.967081i	0.997635	+	0.0687356i	$0.0218965\pi$
$569$	13.3186	+	23.0685i	0.558344	+	0.967081i	−0.439291	+	0.898345i	$0.644770\pi$
$570$	−6.81322	−	5.30309i	−0.285374	−	0.222122i
$571$	−38.6796	−	22.3317i	−1.61869	−	0.934552i	−0.987259	−	0.159121i	$-0.949134\pi$
$571$	−38.6796	−	22.3317i	−1.61869	−	0.934552i	−0.631432	−	0.775431i	$-0.717533\pi$
$572$	11.1020	+	3.29863i	0.464198	+	0.137923i
$573$	15.2402	+	20.1478i	0.636667	+	0.841688i
$574$	−9.84045	−	16.7739i	−0.410733	−	0.700129i
$575$			5.91994i			0.246878i
$576$	−0.736375	−	2.90822i	−0.0306823	−	0.121176i
$577$	10.4543	−	2.80122i	0.435218	−	0.116616i	−0.0345564	−	0.999403i	$-0.511002\pi$
$577$	10.4543	−	2.80122i	0.435218	−	0.116616i	0.469775	+	0.882786i	$0.344335\pi$
$578$	2.56679	+	9.57939i	0.106764	+	0.398450i
$579$	32.4998	−	13.1998i	1.35065	−	0.548563i
$580$	1.74181	−	1.74181i	0.0723245	−	0.0723245i
$581$	25.5899	+	25.2368i	1.06165	+	1.04700i
$582$	−17.7680	+	13.4400i	−0.736506	+	0.557105i
$583$	−5.30890	−	1.42252i	−0.219872	−	0.0589146i
$584$	3.18901	−	5.52352i	0.131962	−	0.228565i
$585$	6.48291	+	0.264785i	0.268035	+	0.0109475i
$586$	3.36646	+	5.83089i	0.139067	+	0.240872i
$587$	9.59239	−	9.59239i	0.395920	−	0.395920i	−0.480871	−	0.876791i	$-0.659679\pi$
$587$	9.59239	−	9.59239i	0.395920	−	0.395920i	0.876791	+	0.480871i	$0.159679\pi$
$588$	−4.56134	+	11.2336i	−0.188106	+	0.463267i
$589$			45.5897i			1.87849i
$590$	1.88503	+	0.505091i	0.0776053	+	0.0207943i
$591$	1.74913	+	1.36144i	0.0719498	+	0.0560024i
$592$	1.01139	+	3.77455i	0.0415678	+	0.155133i
$593$	5.39354	−	20.1290i	0.221486	−	0.826598i	−0.762295	−	0.647229i	$-0.775928\pi$
$593$	5.39354	−	20.1290i	0.221486	−	0.826598i	0.983782	−	0.179369i	$-0.0574056\pi$
$594$	−6.06665	−	15.5494i	−0.248918	−	0.638000i
$595$	−5.86254	−	5.78162i	−0.240341	−	0.237023i
$596$	−15.4153	−	15.4153i	−0.631435	−	0.631435i
$597$	−1.87734	+	4.44525i	−0.0768344	+	0.181932i
$598$	1.07011	+	4.47375i	0.0437599	+	0.182945i
$599$	−20.0588	−	11.5809i	−0.819579	−	0.473184i	0.0306925	−	0.999529i	$-0.490229\pi$
$599$	−20.0588	−	11.5809i	−0.819579	−	0.473184i	−0.850271	+	0.526345i	$0.823562\pi$
$600$	7.44631	−	3.02431i	0.303994	−	0.123467i
$601$	−4.85103			−0.197877			−0.0989387	−	0.995094i	$-0.531545\pi$
$601$	−4.85103			−0.197877			−0.0989387	+	0.995094i	$0.531545\pi$
$602$	−24.2491	−	6.31726i	−0.988319	−	0.257472i
$603$	−17.4209	+	9.73975i	−0.709432	+	0.396633i
$604$	2.93466	−	10.9523i	0.119410	−	0.445643i
$605$	0.395101	−	0.105867i	0.0160631	−	0.00430411i
$606$	−15.7590	−	12.2661i	−0.640166	−	0.498276i
$607$	−17.4499	−	30.2241i	−0.708268	−	1.22676i	−0.965499	−	0.260407i	$-0.916143\pi$
$607$	−17.4499	−	30.2241i	−0.708268	−	1.22676i	0.257231	−	0.966350i	$-0.417190\pi$
$608$	−8.31005			−0.337017
$609$	2.45715	+	18.6574i	0.0995688	+	0.756037i
$610$			0.477630i			0.0193387i
$611$	−5.90470	+	19.8731i	−0.238879	+	0.803978i
$612$	−11.1567	+	10.8528i	−0.450984	+	0.438699i
$613$	18.8091	−	5.03987i	0.759691	−	0.203559i	0.141879	−	0.989884i	$-0.454686\pi$
$613$	18.8091	−	5.03987i	0.759691	−	0.203559i	0.617812	+	0.786325i	$0.288019\pi$
$614$	21.2516	−	12.2696i	0.857646	−	0.495162i
$615$	4.60704	+	6.09061i	0.185774	+	0.245597i
$616$	4.19807	−	7.38937i	0.169145	−	0.297726i
$617$	−7.75021	+	7.75021i	−0.312012	+	0.312012i	−0.845688	−	0.533677i	$-0.820810\pi$
$617$	−7.75021	+	7.75021i	−0.312012	+	0.312012i	0.533677	+	0.845688i	$0.320810\pi$
$618$	0.274689	+	0.676327i	0.0110496	+	0.0272059i
$619$	−10.8113	−	40.3484i	−0.434544	−	1.62174i	−0.742156	−	0.670228i	$-0.766196\pi$
$619$	−10.8113	−	40.3484i	−0.434544	−	1.62174i	0.307612	−	0.951512i	$-0.400470\pi$
$620$	2.84992	+	1.64540i	0.114456	+	0.0660810i
$621$	4.14367	−	5.17462i	0.166280	−	0.207651i
$622$	−17.2521	+	17.2521i	−0.691744	+	0.691744i
$623$	30.7302	+	8.00569i	1.23118	+	0.320741i
$624$	5.08056	−	3.63152i	0.203385	−	0.145377i
$625$	9.86613	+	17.0886i	0.394645	+	0.683546i
$626$	−6.68687	−	24.9557i	−0.267261	−	0.997432i
$627$	−45.8793	+	5.71819i	−1.83224	+	0.228363i
$628$	−20.6724	+	11.9352i	−0.824918	+	0.476267i
$629$	14.3358	−	14.3358i	0.571606	−	0.571606i
$630$	1.26378	−	4.59033i	0.0503502	−	0.182883i
$631$	−2.77766	+	2.77766i	−0.110577	+	0.110577i	−0.760230	−	0.649653i	$-0.774914\pi$
$631$	−2.77766	+	2.77766i	−0.110577	+	0.110577i	0.649653	+	0.760230i	$0.274914\pi$
$632$	−1.12612	+	4.20274i	−0.0447947	+	0.167176i
$633$	−0.575463	−	4.61716i	−0.0228726	−	0.183516i
$634$	12.7499	+	7.36115i	0.506363	+	0.292349i
$635$	−0.381683	+	1.42446i	−0.0151466	+	0.0565280i
$636$	−2.36359	+	1.78786i	−0.0937225	+	0.0708933i
$637$	−25.2367	−	0.331043i	−0.999914	−	0.0131164i
$638$		−	13.1909i		−	0.522234i
$639$	−19.1451	+	32.1275i	−0.757368	+	1.27095i
$640$	−0.299922	+	0.519481i	−0.0118555	+	0.0205343i
$641$	−8.54841	+	14.8063i	−0.337642	+	0.584813i	−0.983989	−	0.178231i	$-0.942963\pi$
$641$	−8.54841	+	14.8063i	−0.337642	+	0.584813i	0.646347	+	0.763044i	$0.276296\pi$
$642$	−8.31533	−	20.4736i	−0.328180	−	0.808029i
$643$	15.2523	+	15.2523i	0.601493	+	0.601493i	0.940709	−	0.339215i	$-0.110162\pi$
$643$	15.2523	+	15.2523i	0.601493	+	0.601493i	−0.339215	+	0.940709i	$0.610162\pi$
$644$	3.37536	−	0.0234544i	0.133008	−	0.000924231i
$645$	9.74693	+	1.35172i	0.383785	+	0.0532241i
$646$	21.5570	+	37.3379i	0.848151	+	1.46904i
$647$	6.39763	−	11.0810i	0.251517	−	0.435640i	−0.712427	−	0.701746i	$-0.752404\pi$
$647$	6.39763	−	11.0810i	0.251517	−	0.435640i	0.963944	+	0.266106i	$0.0857373\pi$
$648$	−8.62570	−	2.56851i	−0.338850	−	0.100901i
$649$	9.05035	−	5.22522i	0.355257	−	0.205108i
$650$	11.5063	+	12.1454i	0.451316	+	0.476383i
$651$	−23.2263	+	9.62189i	−0.910312	+	0.377112i
$652$	−0.954807	−	0.954807i	−0.0373931	−	0.0373931i
$653$	9.47898	−	5.47269i	0.370941	−	0.214163i	−0.302928	−	0.953013i	$-0.597964\pi$
$653$	9.47898	−	5.47269i	0.370941	−	0.214163i	0.673870	+	0.738850i	$0.264631\pi$
$654$	−1.46304	−	11.7385i	−0.0572093	−	0.459013i
$655$	−12.1705	+	3.26108i	−0.475541	+	0.127421i
$656$	7.09994	+	1.90242i	0.277206	+	0.0742771i
$657$	−9.33733	−	16.7011i	−0.364284	−	0.651571i
$658$	13.2273	+	7.51473i	0.515654	+	0.292955i
$659$		−	19.1808i		−	0.747177i	−0.927595	−	0.373588i	$-0.878127\pi$
$659$		−	19.1808i		−	0.747177i	0.927595	−	0.373588i	$-0.121873\pi$
$660$	−1.29840	+	3.07440i	−0.0505400	+	0.119671i
$661$	−0.274549	−	1.02463i	−0.0106787	−	0.0398535i	0.960381	−	0.278691i	$-0.0899004\pi$
$661$	−0.274549	−	1.02463i	−0.0106787	−	0.0398535i	−0.971060	+	0.238837i	$0.923234\pi$
$662$	−1.48648	+	2.57465i	−0.0577735	+	0.100067i
$663$	−29.4962	−	13.4070i	−1.14554	−	0.520684i
$664$	−13.5843			−0.527175
$665$	−11.4670	−	6.51466i	−0.444672	−	0.252628i
$666$	11.2807	+	3.19021i	0.437117	+	0.123618i
$667$	4.53720	−	2.61955i	0.175681	−	0.101430i
$668$	0.0865481	+	0.323002i	0.00334865	+	0.0124973i
$669$	3.28565	−	4.22128i	0.127031	−	0.163204i
$670$	3.85472	+	1.03287i	0.148921	+	0.0399032i
$671$	1.80858	+	1.80858i	0.0698195	+	0.0698195i
$672$	−1.75387	−	4.23367i	−0.0676569	−	0.163317i
$673$		−	20.6567i		−	0.796258i	−0.917329	−	0.398129i	$-0.869660\pi$
$673$		−	20.6567i		−	0.796258i	0.917329	−	0.398129i	$-0.130340\pi$
$674$	3.62169	−	13.5163i	0.139502	−	0.520630i
$675$	3.64150	−	23.8345i	0.140161	−	0.917392i
$676$	10.8909	+	7.09848i	0.418880	+	0.273019i
$677$	16.6890	−	9.63538i	0.641409	−	0.370318i	−0.143748	−	0.989614i	$-0.545916\pi$
$677$	16.6890	−	9.63538i	0.641409	−	0.370318i	0.785157	+	0.619297i	$0.212582\pi$
$678$	−28.8978	−	4.00761i	−1.10981	−	0.153911i
$679$	−23.8958	+	24.2302i	−0.917036	+	0.929870i
$680$	3.11211			0.119344
$681$	34.1201	−	13.8578i	1.30749	−	0.531033i
$682$	17.0219	−	4.56100i	0.651801	−	0.174650i
$683$	23.0006	−	6.16299i	0.880093	−	0.235820i	0.209646	−	0.977777i	$-0.432769\pi$
$683$	23.0006	−	6.16299i	0.880093	−	0.235820i	0.670447	+	0.741957i	$0.266102\pi$
$684$	−12.7620	+	21.4160i	−0.487966	+	0.818860i
$685$	3.52052			0.134512
$686$	−4.41947	+	17.9852i	−0.168736	+	0.686679i
$687$	1.01874	−	7.34585i	0.0388673	−	0.280261i
$688$	8.20230	−	4.73560i	0.312710	−	0.180543i
$689$	−5.25746	−	3.22781i	−0.200293	−	0.122970i
$690$	−1.31533	+	0.163937i	−0.0500736	+	0.00624096i
$691$	1.29565	−	4.83543i	0.0492888	−	0.183948i	−0.936893	−	0.349617i	$-0.886312\pi$
$691$	1.29565	−	4.83543i	0.0492888	−	0.183948i	0.986181	+	0.165669i	$0.0529783\pi$
$692$			25.3500i			0.963663i
$693$	−12.5962	−	22.1670i	−0.478490	−	0.842054i
$694$	−7.03971	−	7.03971i	−0.267224	−	0.267224i
$695$	−1.96631	−	0.526871i	−0.0745863	−	0.0199853i
$696$	−5.61289	−	4.36881i	−0.212756	−	0.165599i
$697$	−9.87013	−	36.8358i	−0.373858	−	1.39526i
$698$	−17.1084	+	9.87755i	−0.647563	+	0.373871i
$699$	−19.8557	+	15.0192i	−0.751012	+	0.568078i
$700$	10.5891	−	6.21212i	0.400230	−	0.234796i
$701$	−12.9949			−0.490810			−0.245405	−	0.969421i	$-0.578921\pi$
$701$	−12.9949			−0.490810			−0.245405	+	0.969421i	$0.578921\pi$
$702$	−1.55649	−	18.6702i	−0.0587461	−	0.704662i
$703$	16.2366	−	28.1226i	0.612374	−	1.06066i
$704$	0.831373	+	3.10273i	0.0313336	+	0.116938i
$705$	−5.50331	−	2.32419i	−0.207267	−	0.0875339i
$706$		−	14.8391i		−	0.558479i
$707$	−26.5233	−	15.0685i	−0.997510	−	0.566708i
$708$	0.774068	−	5.58160i	0.0290913	−	0.209769i
$709$	42.1942	+	11.3059i	1.58464	+	0.424602i	0.940358	−	0.340187i	$-0.110490\pi$
$709$	42.1942	+	11.3059i	1.58464	+	0.424602i	0.644280	+	0.764789i	$0.277157\pi$
$710$	7.22313	−	1.93543i	0.271079	−	0.0726355i
$711$	9.10155	+	9.35641i	0.341335	+	0.350893i
$712$	−10.3946	+	6.00130i	−0.389552	+	0.224908i
$713$	4.94915	+	4.94915i	0.185347	+	0.185347i
$714$	−14.4726	+	18.8628i	−0.541624	+	0.705924i
$715$	−6.94467	−	0.187648i	−0.259716	−	0.00701766i
$716$	−2.56356	+	1.48007i	−0.0958047	+	0.0553129i
$717$	13.6684	+	10.6388i	0.510454	+	0.397314i
$718$	7.49485	−	12.9815i	0.279705	−	0.484464i
$719$	−15.7316	−	27.2479i	−0.586690	−	1.01618i	−0.994662	−	0.103182i	$-0.967098\pi$
$719$	−15.7316	−	27.2479i	−0.586690	−	1.01618i	0.407973	−	0.912994i	$-0.366236\pi$
$720$	0.878164	+	1.57072i	0.0327273	+	0.0585371i
$721$	0.564229	+	0.961777i	0.0210130	+	0.0358184i
$722$	35.3955	+	35.3955i	1.31729	+	1.31729i
$723$	13.2723	−	5.39051i	0.493601	−	0.200475i
$724$	−0.358773	+	0.621412i	−0.0133337	+	0.0230946i
$725$	9.52755	−	16.5022i	0.353844	−	0.612877i
$726$	−0.444443	−	1.09429i	−0.0164948	−	0.0406128i
$727$		−	42.0789i		−	1.56062i	−0.625393	−	0.780310i	$-0.715061\pi$
$727$		−	42.0789i		−	1.56062i	0.625393	−	0.780310i	$-0.284939\pi$
$728$	6.87935	−	6.60867i	0.254966	−	0.244934i
$729$	−19.8661	+	18.2849i	−0.735781	+	0.677220i
$730$	−0.990194	+	3.69545i	−0.0366487	+	0.136775i
$731$	−42.5551	−	24.5692i	−1.57396	−	0.908724i
$732$	1.36857	−	0.170572i	0.0505837	−	0.00630454i
$733$	5.35665	−	19.9913i	0.197852	−	0.738395i	−0.793658	−	0.608365i	$-0.791826\pi$
$733$	5.35665	−	19.9913i	0.197852	−	0.738395i	0.991510	−	0.130030i	$-0.0415075\pi$
$734$	8.71100	−	8.71100i	0.321529	−	0.321529i
$735$	0.898831	−	7.21697i	0.0331539	−	0.266202i
$736$	−0.902125	+	0.902125i	−0.0332528	+	0.0332528i
$737$	18.5072	−	10.6851i	0.681722	−	0.393592i
$738$	15.8063	−	15.3758i	0.581839	−	0.565990i
$739$	9.97235	+	37.2173i	0.366839	+	1.36906i	0.864911	+	0.501925i	$0.167375\pi$
$739$	9.97235	+	37.2173i	0.366839	+	1.36906i	−0.498072	+	0.867136i	$0.665959\pi$
$740$	−1.17201	−	2.02997i	−0.0430838	−	0.0746233i
$741$	−51.1929	−	8.51471i	−1.88062	−	0.312796i
$742$	−3.17875	+	3.22323i	−0.116696	+	0.118329i
$743$	−1.60617	+	1.60617i	−0.0589248	+	0.0589248i	−0.735955	−	0.677030i	$-0.763267\pi$
$743$	−1.60617	+	1.60617i	−0.0589248	+	0.0589248i	0.677030	+	0.735955i	$0.263267\pi$
$744$	3.69685	−	8.75358i	0.135533	−	0.320922i
$745$	11.3249	+	6.53846i	0.414914	+	0.239551i
$746$	1.30836	+	4.88287i	0.0479025	+	0.178775i
$747$	−20.8618	+	35.0085i	−0.763295	+	1.28089i
$748$	11.7842	−	11.7842i	0.430874	−	0.430874i
$749$	−17.0802	−	29.1147i	−0.624097	−	1.06383i
$750$	−7.98796	+	6.04222i	−0.291679	+	0.220631i
$751$	1.80427	−	1.04170i	0.0658387	−	0.0380120i	−0.466719	−	0.884406i	$-0.654564\pi$
$751$	1.80427	−	1.04170i	0.0658387	−	0.0380120i	0.532558	+	0.846394i	$0.321231\pi$
$752$	−5.55402	+	1.48819i	−0.202534	+	0.0542689i
$753$	5.46011	+	43.8086i	0.198977	+	1.59647i
$754$	4.21707	−	14.1931i	0.153576	−	0.516882i
$755$			6.80143i			0.247529i
$756$	−13.6041	−	1.98184i	−0.494777	−	0.0720787i
$757$	−10.9645			−0.398510			−0.199255	−	0.979948i	$-0.563852\pi$
$757$	−10.9645			−0.398510			−0.199255	+	0.979948i	$0.563852\pi$
$758$	0.852595	+	1.47674i	0.0309676	+	0.0536375i
$759$	−4.35982	+	5.60133i	−0.158251	+	0.203316i
$760$	4.81488	−	1.29014i	0.174654	−	0.0467985i
$761$	−5.57308	+	20.7990i	−0.202024	+	0.753964i	0.788312	+	0.615276i	$0.210955\pi$
$761$	−5.57308	+	20.7990i	−0.202024	+	0.753964i	−0.990336	+	0.138688i	$0.955711\pi$
$762$	4.21786	+	0.584941i	0.152797	+	0.0211902i
$763$	−4.79793	−	17.4210i	−0.173697	−	0.630683i
$764$	−14.5854			−0.527680
$765$	4.77935	−	8.02027i	0.172798	−	0.289974i
$766$	15.7532	+	9.09514i	0.569188	+	0.328621i
$767$	11.4084	−	2.72885i	0.411934	−	0.0985332i
$768$	1.59559	+	0.673858i	0.0575760	+	0.0243158i
$769$	15.9582	+	15.9582i	0.575466	+	0.575466i	0.933651	−	0.358185i	$-0.116604\pi$
$769$	15.9582	+	15.9582i	0.575466	+	0.575466i	−0.358185	+	0.933651i	$0.616604\pi$
$770$	−1.28517	+	4.93320i	−0.0463145	+	0.177780i
$771$	−17.9648	+	13.5889i	−0.646988	+	0.489392i
$772$	−5.24169	+	19.5623i	−0.188653	+	0.704061i
$773$	−7.23162	−	26.9888i	−0.260103	−	0.970719i	−0.965180	−	0.261588i	$-0.915754\pi$
$773$	−7.23162	−	26.9888i	−0.260103	−	0.970719i	0.705076	−	0.709131i	$-0.250913\pi$
$774$	0.392292	−	28.4109i	0.0141007	−	1.02121i
$775$	24.5891	+	6.58864i	0.883267	+	0.236671i
$776$		−	12.8625i		−	0.461738i
$777$	17.7542	+	2.33657i	0.636930	+	0.0838242i
$778$	21.8565	−	21.8565i	0.783595	−	0.783595i
$779$	−30.5411	−	52.8987i	−1.09425	−	1.89529i
$780$	−2.37991	+	2.89288i	−0.0852143	+	0.103582i
$781$	20.0222	−	34.6796i	0.716452	−	1.24093i
$782$	6.39354	+	1.71314i	0.228632	+	0.0612619i
$783$	−19.8788	+	7.75577i	−0.710411	+	0.277169i
$784$	−3.58391	−	6.01295i	−0.127997	−	0.214748i
$785$	10.1247	−	10.1247i	0.361367	−	0.361367i
$786$	13.6904	+	33.7079i	0.488322	+	1.20232i
$787$	4.16696	+	15.5513i	0.148536	+	0.554344i	0.999572	+	0.0292373i	$0.00930784\pi$
$787$	4.16696	+	15.5513i	0.148536	+	0.554344i	−0.851037	+	0.525106i	$0.824025\pi$
$788$	−1.23611	+	0.331214i	−0.0440345	+	0.0117990i
$789$	5.80935	−	13.7556i	0.206818	−	0.489714i
$790$		−	2.60992i		−	0.0928569i
$791$	−44.5635	+	0.309658i	−1.58450	+	0.0110102i
$792$	9.27286	+	2.62239i	0.329497	+	0.0931827i
$793$	1.36779	+	2.52418i	0.0485717	+	0.0896362i
$794$	−5.88553	−	3.39801i	−0.208870	−	0.120591i
$795$	1.09191	−	1.40285i	0.0387261	−	0.0497538i
$796$	−1.39298	−	2.41271i	−0.0493728	−	0.0855162i
$797$	−36.5440			−1.29446			−0.647228	−	0.762297i	$-0.724072\pi$
$797$	−36.5440			−1.29446			−0.647228	+	0.762297i	$0.724072\pi$
$798$	−14.5715	+	35.1833i	−0.515827	+	1.24548i
$799$	21.0943	+	21.0943i	0.746261	+	0.746261i
$800$	−1.20097	+	4.48208i	−0.0424607	+	0.158465i
$801$	−0.497141	+	36.0043i	−0.0175656	+	1.27215i
$802$	−11.8424	+	20.5116i	−0.418169	+	0.724289i
$803$	10.2437	+	17.7425i	0.361491	+	0.626120i
$804$	1.58291	−	11.4139i	0.0558248	−	0.402538i
$805$	−1.95206	+	0.537618i	−0.0688011	+	0.0189486i
$806$	19.7732	+	0.534282i	0.696481	+	0.0188193i
$807$	−15.4799	+	36.6539i	−0.544917	+	1.29028i
$808$	11.1369	−	2.98411i	0.391793	−	0.104981i
$809$	34.2469	+	19.7725i	1.20406	+	0.695163i	0.961455	−	0.274963i	$-0.0886655\pi$
$809$	34.2469	+	19.7725i	1.20406	+	0.695163i	0.242603	+	0.970126i	$0.421999\pi$
$810$	5.39654	+	0.149057i	0.189615	+	0.00523734i
$811$	12.9524	+	12.9524i	0.454821	+	0.454821i	0.896951	−	0.442130i	$-0.145777\pi$
$811$	12.9524	+	12.9524i	0.454821	+	0.454821i	−0.442130	+	0.896951i	$0.645777\pi$
$812$	−9.44678	−	5.36693i	−0.331517	−	0.188342i
$813$	4.72988	−	34.1059i	0.165884	−	1.19615i
$814$	−12.1245	−	3.24876i	−0.424964	−	0.113869i
$815$	0.701455	+	0.404985i	0.0245709	+	0.0141860i
$816$	−1.11140	−	8.91722i	−0.0389069	−	0.312165i
$817$	−76.0243	−	20.3706i	−2.65975	−	0.712678i
$818$	2.54018			0.0888153
$819$	−6.46653	−	27.8780i	−0.225959	−	0.974137i
$820$	−4.40910			−0.153972
$821$	49.2090	+	13.1855i	1.71741	+	0.460178i	0.977221	−	0.212224i	$-0.0680706\pi$
$821$	49.2090	+	13.1855i	1.71741	+	0.460178i	0.740186	+	0.672402i	$0.234737\pi$
$822$	−1.25726	−	10.0875i	−0.0438519	−	0.351840i
$823$	24.0663	+	13.8947i	0.838897	+	0.484337i	0.856889	−	0.515501i	$-0.172394\pi$
$823$	24.0663	+	13.8947i	0.838897	+	0.484337i	−0.0179923	+	0.999838i	$0.505727\pi$
$824$	−0.407094	−	0.109080i	−0.0141818	−	0.00380000i
$825$	−3.54633	+	25.5717i	−0.123467	+	0.890291i
$826$	−0.0598104	−	8.60743i	−0.00208107	−	0.299491i
$827$	28.9331	+	28.9331i	1.00610	+	1.00610i	0.999981	+	0.00612059i	$0.00194825\pi$
$827$	28.9331	+	28.9331i	1.00610	+	1.00610i	0.00612059	+	0.999981i	$0.498052\pi$
$828$	0.939465	+	3.71030i	0.0326487	+	0.128942i
$829$	11.7669	+	6.79364i	0.408682	+	0.235953i	0.690223	−	0.723596i	$-0.257512\pi$
$829$	11.7669	+	6.79364i	0.408682	+	0.235953i	−0.281541	+	0.959549i	$0.590846\pi$
$830$	7.87084	−	2.10898i	0.273201	−	0.0732039i
$831$	10.0684	−	23.8405i	0.349270	−	0.827017i
$832$	−0.0973883	+	3.60424i	−0.00337633	+	0.124954i
$833$	−17.7198	+	31.7010i	−0.613956	+	1.09838i
$834$	−0.807446	+	5.82228i	−0.0279596	+	0.201609i
$835$	−0.100293	−	0.173712i	−0.00347078	−	0.00601157i
$836$	13.3467	−	23.1171i	0.461604	−	0.799522i
$837$	−16.8817	−	22.9703i	−0.583515	−	0.793971i
$838$	1.00443	−	3.74857i	0.0346973	−	0.129492i
$839$	10.8590	+	10.8590i	0.374896	+	0.374896i	0.869257	−	0.494361i	$-0.164598\pi$
$839$	10.8590	+	10.8590i	0.374896	+	0.374896i	−0.494361	+	0.869257i	$0.664598\pi$
$840$	1.67348	+	2.18072i	0.0577406	+	0.0752420i
$841$	12.1363			0.418494
$842$	−0.185312	−	0.320969i	−0.00638627	−	0.0110613i
$843$	−1.26796	+	1.62903i	−0.0436710	+	0.0561068i
$844$	2.32644	+	1.34317i	0.0800794	+	0.0462339i
$845$	−7.41229	−	2.42208i	−0.254991	−	0.0833219i
$846$	−4.69420	+	16.5988i	−0.161390	+	0.570679i
$847$	−0.912914	−	1.55614i	−0.0313681	−	0.0534696i
$848$		−	1.71104i		−	0.0587575i
$849$	3.39653	−	8.04246i	0.116569	−	0.276017i
$850$	23.2539	−	6.23085i	0.797601	−	0.213717i
$851$	−1.29032	−	4.81556i	−0.0442318	−	0.165075i
$852$	−8.12520	−	20.0055i	−0.278365	−	0.685376i
$853$	−17.7621	+	17.7621i	−0.608162	+	0.608162i	−0.942465	−	0.334304i	$-0.891499\pi$
$853$	−17.7621	+	17.7621i	−0.608162	+	0.608162i	0.334304	+	0.942465i	$0.391499\pi$
$854$	2.03108	−	0.559380i	0.0695020	−	0.0191416i
$855$	4.06949	−	14.3898i	0.139174	−	0.492122i
$856$	12.3235	+	3.30206i	0.421207	+	0.112862i
$857$	2.75343	−	4.76907i	0.0940553	−	0.162908i	−0.815159	−	0.579238i	$-0.803350\pi$
$857$	2.75343	−	4.76907i	0.0940553	−	0.162908i	0.909214	+	0.416329i	$0.136684\pi$
$858$	1.94242	+	19.9658i	0.0663132	+	0.681621i
$859$	20.8680	+	36.1445i	0.712008	+	1.23323i	0.964102	+	0.265531i	$0.0855472\pi$
$859$	20.8680	+	36.1445i	0.712008	+	1.23323i	−0.252095	+	0.967703i	$0.581119\pi$
$860$	−4.01725	+	4.01725i	−0.136987	+	0.136987i
$861$	20.5042	−	26.7240i	0.698780	−	0.910753i
$862$		−	14.5188i		−	0.494511i
$863$	0.943703	+	0.252864i	0.0321240	+	0.00860761i	0.274845	−	0.961488i	$-0.411373\pi$
$863$	0.943703	+	0.252864i	0.0321240	+	0.00860761i	−0.242721	+	0.970096i	$0.578040\pi$
$864$	4.18701	−	3.07717i	0.142445	−	0.104687i
$865$	−3.93562	−	14.6879i	−0.133815	−	0.499405i
$866$	−2.39222	+	8.92788i	−0.0812909	+	0.303382i
$867$	−13.6995	+	10.3625i	−0.465260	+	0.351931i
$868$	3.65921	−	14.0460i	0.124202	−	0.476754i
$869$	−9.88265	−	9.88265i	−0.335246	−	0.335246i
$870$	3.93040	+	1.65990i	0.133253	+	0.0562760i
$871$	23.3292	−	5.58028i	0.790481	−	0.189081i
$872$	5.91467	+	3.41484i	0.200296	+	0.115641i
$873$	−33.1482	−	19.7533i	−1.12190	−	0.668549i
$874$	10.6019			0.358616
$875$	−10.7428	+	10.8932i	−0.363175	+	0.368257i
$876$	10.9423	+	1.51750i	0.369707	+	0.0512717i
$877$	5.91791	−	22.0859i	0.199833	−	0.745789i	−0.791129	−	0.611649i	$-0.790506\pi$
$877$	5.91791	−	22.0859i	0.199833	−	0.745789i	0.990962	−	0.134139i	$-0.0428270\pi$
$878$	−6.10007	+	1.63451i	−0.205867	+	0.0551620i
$879$	−7.16294	+	9.20268i	−0.241600	+	0.310399i
$880$	−0.963404	−	1.66866i	−0.0324763	−	0.0562507i
$881$	8.65737			0.291674			0.145837	−	0.989309i	$-0.453412\pi$
$881$	8.65737			0.291674			0.145837	+	0.989309i	$0.453412\pi$
$882$	−21.0000	+	0.00189502i	−0.707107	+	6.38087e-5i
$883$			32.3230i			1.08776i	0.839164	+	0.543878i	$0.183045\pi$
$883$			32.3230i			1.08776i	−0.839164	+	0.543878i	$0.816955\pi$
$884$	16.4468	−	8.91215i	0.553167	−	0.299748i
$885$	0.418051	+	3.35419i	0.0140526	+	0.112750i
$886$	−14.5064	+	3.88698i	−0.487352	+	0.130586i
$887$	−31.4819	+	18.1761i	−1.05706	+	0.610292i	−0.924617	−	0.380899i	$-0.875615\pi$
$887$	−31.4819	+	18.1761i	−1.05706	+	0.610292i	−0.132440	+	0.991191i	$0.542281\pi$
$888$	−5.39800	+	4.08313i	−0.181145	+	0.137021i
$889$	6.50439	−	0.0451970i	0.218150	−	0.00151586i
$890$	5.09095	−	5.09095i	0.170649	−	0.170649i
$891$	20.9988	−	19.8700i	0.703486	−	0.665669i
$892$	0.799337	+	2.98317i	0.0267638	+	0.0998838i
$893$	41.3807	+	23.8911i	1.38475	+	0.799487i
$894$	14.6905	−	34.7847i	0.491322	−	1.16338i
$895$	1.25556	−	1.25556i	0.0419686	−	0.0419686i
$896$	2.56030	+	0.666997i	0.0855335	+	0.0222828i
$897$	−6.48176	+	4.63308i	−0.216420	+	0.154694i
$898$	−7.98748	−	13.8347i	−0.266546	−	0.461671i
$899$	−5.83090	−	21.7612i	−0.194472	−	0.725778i
$900$	9.70648	+	9.97829i	0.323549	+	0.332610i
$901$	−7.68790	+	4.43861i	−0.256121	+	0.147872i
$902$	−16.6954	+	16.6954i	−0.555894	+	0.555894i
$903$	−5.66710	−	43.0309i	−0.188589	−	1.43198i
$904$	11.9104	−	11.9104i	0.396133	−	0.396133i
$905$	0.111400	−	0.415750i	0.00370305	−	0.0138200i
$906$	19.4883	−	2.42894i	0.647457	−	0.0806962i
$907$	−0.583687	−	0.336992i	−0.0193810	−	0.0111896i	0.490278	−	0.871566i	$-0.336895\pi$
$907$	−0.583687	−	0.336992i	−0.0193810	−	0.0111896i	−0.509659	+	0.860376i	$0.670229\pi$
$908$	−5.50302	+	20.5375i	−0.182624	+	0.681562i
$909$	9.41276	−	33.2838i	0.312202	−	1.10395i
$910$	−2.95993	+	4.89713i	−0.0981207	+	0.162338i
$911$		−	12.7937i		−	0.423875i	−0.977283	−	0.211937i	$-0.932023\pi$
$911$		−	12.7937i		−	0.423875i	0.977283	−	0.211937i	$-0.0679772\pi$
$912$	−5.41619	−	13.3355i	−0.179348	−	0.441582i
$913$	21.8177	−	37.7893i	0.722059	−	1.25064i
$914$	8.28794	−	14.3551i	0.274141	−	0.474825i
$915$	−0.766474	+	0.311302i	−0.0253389	+	0.0102913i
$916$	3.02763	+	3.02763i	0.100036	+	0.100036i
$917$	28.1210	+	47.9347i	0.928637	+	1.58294i
$918$	−24.6875	−	10.8302i	−0.814810	−	0.357450i
$919$	18.3696	+	31.8172i	0.605959	+	1.04955i	0.991899	+	0.127027i	$0.0405436\pi$
$919$	18.3696	+	31.8172i	0.605959	+	1.04955i	−0.385941	+	0.922524i	$0.626123\pi$
$920$	0.382640	−	0.662752i	0.0126153	−	0.0218503i
$921$	33.5407	+	26.1065i	1.10520	+	0.860239i
$922$	15.1674	−	8.75692i	0.499513	−	0.288394i
$923$	32.6303	−	30.9133i	1.07404	−	1.01752i
$924$	14.5942	+	1.92069i	0.480114	+	0.0631862i
$925$	−12.8216	−	12.8216i	−0.421571	−	0.421571i
$926$	−18.8296	+	10.8713i	−0.618778	+	0.357252i
$927$	−0.906299	+	0.881612i	−0.0297668	+	0.0289559i
$928$	3.96661	−	1.06285i	0.130210	−	0.0348898i
$929$	10.1081	+	2.70847i	0.331638	+	0.0888620i	0.420796	−	0.907155i	$-0.361751\pi$
$929$	10.1081	+	2.70847i	0.331638	+	0.0888620i	−0.0891581	+	0.996017i	$0.528418\pi$
$930$	−0.782973	+	5.64581i	−0.0256747	+	0.185133i
$931$	−14.2733	+	56.3920i	−0.467789	+	1.84817i
$932$		−	14.3739i		−	0.470832i
$933$	−38.9294	−	16.4409i	−1.27449	−	0.538249i
$934$	−1.52572	−	5.69408i	−0.0499232	−	0.186316i
$935$	−4.99832	+	8.65735i	−0.163463	+	0.283126i
$936$	9.13898	+	5.78610i	0.298717	+	0.189125i
$937$	−22.8370			−0.746052			−0.373026	−	0.927821i	$-0.621680\pi$
$937$	−22.8370			−0.746052			−0.373026	+	0.927821i	$0.621680\pi$
$938$	−0.122307	−	17.6015i	−0.00399348	−	0.574708i
$939$	35.6893	−	26.9960i	1.16468	−	0.880981i
$940$	2.98698	−	1.72454i	0.0974247	−	0.0562482i
$941$	−12.3909	−	46.2433i	−0.403930	−	1.50749i	−0.806020	−	0.591888i	$-0.798383\pi$
$941$	−12.3909	−	46.2433i	−0.403930	−	1.50749i	0.402090	−	0.915600i	$-0.368284\pi$
$942$	−32.6265	−	25.3949i	−1.06303	−	0.827412i
$943$	−9.05808	−	2.42711i	−0.294972	−	0.0790374i
$944$	2.30049	+	2.30049i	0.0748745	+	0.0748745i
$945$	8.18999	−	0.963770i	0.266420	−	0.0313514i
$946$			30.4232i			0.989143i
$947$	−10.1022	+	37.7018i	−0.328276	+	1.22514i	0.582701	+	0.812687i	$0.301996\pi$
$947$	−10.1022	+	37.7018i	−0.328276	+	1.22514i	−0.910977	+	0.412457i	$0.864671\pi$
$948$	−7.47829	+	0.932061i	−0.242884	+	0.0302719i
$949$	5.34972	+	22.3653i	0.173659	+	0.726009i
$950$	33.3941	−	19.2801i	1.08345	−	0.625528i
$951$	−3.50284	+	25.2580i	−0.113587	+	0.819048i
$952$	−3.64477	−	13.2339i	−0.118128	−	0.428914i
$953$	−16.5271			−0.535364			−0.267682	−	0.963507i	$-0.586258\pi$
$953$	−16.5271			−0.535364			−0.267682	+	0.963507i	$0.586258\pi$
$954$	−4.40956	−	2.62770i	−0.142765	−	0.0850748i
$955$	8.45084	−	2.26439i	0.273463	−	0.0732741i
$956$	−9.65940	+	2.58823i	−0.312407	+	0.0837093i
$957$	21.1681	−	8.59738i	0.684267	−	0.277914i
$958$	−18.0775			−0.584058
$959$	−4.12308	−	14.9707i	−0.133141	−	0.483428i
$960$	−1.02911	−	0.142719i	−0.0332145	−	0.00460625i
$961$	−0.781758	+	0.451348i	−0.0252180	+	0.0145596i
$962$	−12.0071	−	7.37171i	−0.387123	−	0.237674i
$963$	27.4353	−	26.6879i	0.884089	−	0.860007i
$964$	−2.14060	+	7.98882i	−0.0689440	+	0.257303i
$965$		−	12.1483i		−	0.391066i
$966$	2.23758	+	5.40130i	0.0719929	+	0.173784i
$967$	−9.49989	−	9.49989i	−0.305496	−	0.305496i	0.537664	−	0.843160i	$-0.319307\pi$
$967$	−9.49989	−	9.49989i	−0.305496	−	0.305496i	−0.843160	+	0.537664i	$0.819307\pi$
$968$	0.658672	+	0.176491i	0.0211705	+	0.00567263i
$969$	−45.8677	+	58.9291i	−1.47348	+	1.89307i
$970$	1.99692	+	7.45261i	0.0641173	+	0.239289i
$971$	17.2979	−	9.98695i	0.555116	−	0.320496i	−0.196067	−	0.980591i	$-0.562817\pi$
$971$	17.2979	−	9.98695i	0.555116	−	0.320496i	0.751183	+	0.660094i	$0.229484\pi$
$972$	−1.50013	−	15.5161i	−0.0481166	−	0.497679i
$973$	0.0623894	+	8.97858i	0.00200011	+	0.287840i
$974$	38.7798			1.24258
$975$	−11.9909	+	26.3807i	−0.384015	+	0.844858i
$976$	−0.398128	+	0.689579i	−0.0127438	+	0.0220729i
$977$	0.219237	+	0.818205i	0.00701403	+	0.0261767i	0.969344	−	0.245707i	$-0.0790201\pi$
$977$	0.219237	+	0.818205i	0.00701403	+	0.0261767i	−0.962330	+	0.271884i	$0.912353\pi$
$978$	0.909911	−	2.15453i	0.0290957	−	0.0688942i
$979$		−	38.5545i		−	1.23221i
$980$	3.01005	+	2.92753i	0.0961526	+	0.0935166i
$981$	17.8838	−	9.99856i	0.570985	−	0.319229i
$982$	−8.95841	−	2.40040i	−0.285874	−	0.0765998i
$983$	−9.53265	+	2.55427i	−0.304044	+	0.0814685i	−0.407616	−	0.913154i	$-0.633640\pi$
$983$	−9.53265	+	2.55427i	−0.304044	+	0.0814685i	0.103571	+	0.994622i	$0.466973\pi$
$984$	1.57459	+	12.6335i	0.0501960	+	0.402742i
$985$	0.664787	−	0.383815i	0.0211819	−	0.0122294i
$986$	−15.0653	−	15.0653i	−0.479776	−	0.479776i
$987$	−3.43813	+	26.1243i	−0.109437	+	0.831545i
$988$	21.7511	−	20.6065i	0.691994	−	0.655582i
$989$	−10.4645	+	6.04166i	−0.332751	+	0.192114i
$990$	−5.77987	−	0.0798074i	−0.183696	−	0.00253645i
$991$	2.30625	−	3.99454i	0.0732605	−	0.126891i	−0.827068	−	0.562102i	$-0.809993\pi$
$991$	2.30625	−	3.99454i	0.0732605	−	0.126891i	0.900328	+	0.435211i	$0.143326\pi$
$992$	2.74305	+	4.75110i	0.0870919	+	0.150848i
$993$	−5.10049	−	0.707347i	−0.161859	−	0.0224470i
$994$	−16.6897	−	28.4490i	−0.529364	−	0.902346i
$995$	1.18168	+	1.18168i	0.0374616	+	0.0374616i
$996$	−8.85379	−	21.7994i	−0.280543	−	0.690740i
$997$	−23.8097	+	41.2397i	−0.754062	+	1.30607i	0.191777	+	0.981439i	$0.438575\pi$
$997$	−23.8097	+	41.2397i	−0.754062	+	1.30607i	−0.945839	+	0.324635i	$0.894758\pi$
$998$	19.0278	−	32.9571i	0.602313	−	1.04324i
$999$	2.23287	+	20.1819i	0.0706449	+	0.638526i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bv.a.515.9	yes	144
3.2	odd	2	inner	546.2.bv.a.515.33	yes	144
7.2	even	3	inner	546.2.bv.a.359.33	yes	144
13.5	odd	4	inner	546.2.bv.a.473.9	yes	144
21.2	odd	6	inner	546.2.bv.a.359.9	yes	144
39.5	even	4	inner	546.2.bv.a.473.33	yes	144
91.44	odd	12	inner	546.2.bv.a.317.33	yes	144
273.44	even	12	inner	546.2.bv.a.317.9	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.9	✓	144	273.44	even	12	inner
546.2.bv.a.317.33	yes	144	91.44	odd	12	inner
546.2.bv.a.359.9	yes	144	21.2	odd	6	inner
546.2.bv.a.359.33	yes	144	7.2	even	3	inner
546.2.bv.a.473.9	yes	144	13.5	odd	4	inner
546.2.bv.a.473.33	yes	144	39.5	even	4	inner
546.2.bv.a.515.9	yes	144	1.1	even	1	trivial
546.2.bv.a.515.33	yes	144	3.2	odd	2	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.214218 - 1.71875i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.579405 - 0.155251i) q^{5} +(-0.237927 + 1.71563i) q^{6} +(0.0183841 + 2.64569i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.90822 + 0.736375i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.214218 - 1.71875i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.579405 - 0.155251i) q^{5} +(-0.237927 + 1.71563i) q^{6} +(0.0183841 + 2.64569i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.90822 + 0.736375i) q^{9} +(0.519481 + 0.299922i) q^{10} +(3.10273 - 0.831373i) q^{11} +(0.673858 - 1.59559i) q^{12} +(3.60424 + 0.0973883i) q^{13} +(0.666997 - 2.56030i) q^{14} +(-0.142719 + 1.02911i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.59410 - 4.49310i) q^{17} +(2.99971 + 0.0414195i) q^{18} +(2.15080 - 8.02689i) q^{19} +(-0.424154 - 0.424154i) q^{20} +(4.54334 - 0.598351i) q^{21} -3.21218 q^{22} +(-0.637898 - 1.10487i) q^{23} +(-1.06387 + 1.36682i) q^{24} +(-4.01852 - 2.32009i) q^{25} +(-3.45622 - 1.02691i) q^{26} +(1.88864 + 4.84077i) q^{27} +(-1.30692 + 2.30042i) q^{28} +4.10654i q^{29} +(0.404210 - 0.957107i) q^{30} +(-5.29917 + 1.41991i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-2.09358 - 5.15472i) q^{33} +(-3.66860 + 3.66860i) q^{34} +(0.400094 - 1.53578i) q^{35} +(-2.88678 - 0.816391i) q^{36} +(3.77455 + 1.01139i) q^{37} +(-4.15502 + 7.19671i) q^{38} +(-0.604705 - 6.21565i) q^{39} +(0.299922 + 0.519481i) q^{40} +(5.19752 - 5.19752i) q^{41} +(-4.54340 - 0.597941i) q^{42} -9.47120i q^{43} +(3.10273 + 0.831373i) q^{44} +(1.79936 + 0.0248453i) q^{45} +(0.330201 + 1.23233i) q^{46} +(-1.48819 + 5.55402i) q^{47} +(1.38137 - 1.04489i) q^{48} +(-6.99932 + 0.0972771i) q^{49} +(3.28111 + 3.28111i) q^{50} +(-8.27824 - 3.49610i) q^{51} +(3.07267 + 1.88646i) q^{52} +(-1.48181 - 0.855522i) q^{53} +(-0.571402 - 5.16464i) q^{54} -1.92681 q^{55} +(1.85778 - 1.88378i) q^{56} +(-14.2570 - 1.97719i) q^{57} +(1.06285 - 3.96661i) q^{58} +(3.14252 - 0.842037i) q^{59} +(-0.638155 + 0.819878i) q^{60} +(0.398128 + 0.689579i) q^{61} +5.48610 q^{62} +(-2.00168 - 7.68071i) q^{63} +1.00000i q^{64} +(-2.07319 - 0.615989i) q^{65} +(0.688106 + 5.52094i) q^{66} +(6.42620 - 1.72190i) q^{67} +(4.49310 - 2.59410i) q^{68} +(-1.76235 + 1.33307i) q^{69} +(-0.783950 + 1.37990i) q^{70} +(8.81512 - 8.81512i) q^{71} +(2.57712 + 1.53573i) q^{72} +(1.65075 + 6.16069i) q^{73} +(-3.38417 - 1.95385i) q^{74} +(-3.12683 + 7.40385i) q^{75} +(5.87609 - 5.87609i) q^{76} +(2.25659 + 8.19356i) q^{77} +(-1.02463 + 6.16037i) q^{78} +(-2.17550 - 3.76807i) q^{79} +(-0.155251 - 0.579405i) q^{80} +(7.91550 - 4.28308i) q^{81} +(-6.36563 + 3.67520i) q^{82} +(9.60558 - 9.60558i) q^{83} +(4.23383 + 1.75348i) q^{84} +(-2.20059 + 2.20059i) q^{85} +(-2.45133 + 9.14848i) q^{86} +(7.05812 - 0.879694i) q^{87} +(-2.78183 - 1.60609i) q^{88} +(3.10650 - 11.5936i) q^{89} +(-1.73162 - 0.489708i) q^{90} +(-0.191398 + 9.53747i) q^{91} -1.27580i q^{92} +(3.57565 + 8.80379i) q^{93} +(2.87497 - 4.97960i) q^{94} +(-2.49237 + 4.31691i) q^{95} +(-1.60474 + 0.651764i) q^{96} +(9.09518 + 9.09518i) q^{97} +(6.78601 + 1.71760i) q^{98} +(-8.41121 + 4.70259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 16 q^{7}+O(q^{10}) \) 144 * q - 16 * q^7	\( 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) \) 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Introduction

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