LMFDB - Embedded newform 546.2.bv.a.317.9

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			317.9
Character	$\chi$	$=$	546.317
Dual form			546.2.bv.a.515.9

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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	−0.386039	−	0.922482i	$-0.626157\pi$
$5$	−0.579405	+	0.155251i	−0.259118	+	0.0694304i	0.126921	+	0.991913i	$0.459490\pi$
$6$	−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	0.694201	−	0.719781i	$-0.255758\pi$
$11$	3.10273	+	0.831373i	0.935507	+	0.250668i	0.241306	+	0.970449i	$0.422424\pi$
$12$	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	0.987721	+	0.156231i	$0.0499345\pi$
$17$	2.59410	+	4.49310i	0.629160	+	1.08974i	−0.358560	+	0.933507i	$0.616732\pi$
$18$	2.99971	−	0.0414195i	0.707039	−	0.00976267i
$19$	2.15080	+	8.02689i	0.493427	+	1.84149i	0.538668	+	0.842518i	$0.318928\pi$
$19$	2.15080	+	8.02689i	0.493427	+	1.84149i	−0.0452411	+	0.998976i	$0.514406\pi$
$20$	−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	−0.924836	−	0.380366i	$-0.875798\pi$
$23$	−0.637898	+	1.10487i	−0.133011	+	0.230382i	0.791825	+	0.610748i	$0.209131\pi$
$24$	−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	$-0.875483\pi$
$29$		−	4.10654i		−	0.762565i	0.924459	−	0.381283i	$-0.124517\pi$
$30$	0.404210	+	0.957107i	0.0737984	+	0.174743i
$31$	−5.29917	−	1.41991i	−0.951758	−	0.255023i	−0.250650	−	0.968078i	$-0.580644\pi$
$31$	−5.29917	−	1.41991i	−0.951758	−	0.255023i	−0.701108	+	0.713055i	$0.747311\pi$
$32$	−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	0.0651624	−	0.997875i	$-0.479243\pi$
$37$	3.77455	−	1.01139i	0.620532	−	0.166271i	0.555370	+	0.831604i	$0.312577\pi$
$38$	−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	0.984891	−	0.173175i	$-0.0554027\pi$
$41$	5.19752	+	5.19752i	0.811716	+	0.811716i	−0.173175	+	0.984891i	$0.555403\pi$
$42$	−4.54340	+	0.597941i	−0.701062	+	0.0922643i
$43$			9.47120i			1.44434i	0.691713	+	0.722172i	$0.256856\pi$
$43$			9.47120i			1.44434i	−0.691713	+	0.722172i	$0.743144\pi$
$44$	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	−0.985426	−	0.170107i	$-0.945589\pi$
$47$	−1.48819	−	5.55402i	−0.217075	−	0.810137i	0.768350	−	0.640030i	$-0.221078\pi$
$48$	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	−0.598306	−	0.801267i	$-0.704159\pi$
$53$	−1.48181	+	0.855522i	−0.203542	+	0.117515i	0.394765	+	0.918782i	$0.370826\pi$
$54$	−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	0.457509	−	0.889205i	$-0.348742\pi$
$59$	3.14252	+	0.842037i	0.409122	+	0.109624i	−0.0483876	+	0.998829i	$0.515408\pi$
$60$	−0.638155	−	0.819878i	−0.0823854	−	0.105846i
$61$	0.398128	−	0.689579i	0.0509751	−	0.0882915i	−0.839412	−	0.543496i	$-0.817100\pi$
$61$	0.398128	−	0.689579i	0.0509751	−	0.0882915i	0.890387	+	0.455204i	$0.150434\pi$
$62$	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	0.629026	−	0.777385i	$-0.283454\pi$
$67$	6.42620	+	1.72190i	0.785085	+	0.210363i	0.156060	+	0.987748i	$0.450121\pi$
$68$	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	0.998882	+	0.0472805i	$0.0150554\pi$
$71$	8.81512	+	8.81512i	1.04616	+	1.04616i	0.0472805	+	0.998882i	$0.484945\pi$
$72$	2.57712	−	1.53573i	0.303716	−	0.180987i
$73$	1.65075	−	6.16069i	0.193206	−	0.721054i	−0.799518	−	0.600642i	$-0.794912\pi$
$73$	1.65075	−	6.16069i	0.193206	−	0.721054i	0.992724	−	0.120412i	$-0.0384216\pi$
$74$	−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	−0.962065	−	0.272821i	$-0.912043\pi$
$79$	−2.17550	+	3.76807i	−0.244763	+	0.423942i	0.717302	+	0.696762i	$0.245377\pi$
$80$	−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	0.998436	+	0.0559134i	$0.0178071\pi$
$83$	9.60558	+	9.60558i	1.05435	+	1.05435i	0.0559134	+	0.998436i	$0.482193\pi$
$84$	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	0.909930	+	0.414762i	$0.136135\pi$
$89$	3.10650	+	11.5936i	0.329288	+	1.22892i	−0.580642	+	0.814159i	$0.697198\pi$
$90$	−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	−0.0737979	−	0.997273i	$-0.523512\pi$
$97$	9.09518	−	9.09518i	0.923475	−	0.923475i	0.997273	+	0.0737979i	$0.0235120\pi$
$98$	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	−0.996190	−	0.0872149i	$-0.972203\pi$
$101$	−5.76486	−	9.98503i	−0.573625	−	0.993548i	0.422564	−	0.906333i	$-0.361130\pi$
$102$	7.09130	−	5.51954i	0.702144	−	0.546516i
$103$	0.364990	+	0.210727i	0.0359636	+	0.0207636i	0.517874	−	0.855457i	$-0.326724\pi$
$103$	0.364990	+	0.210727i	0.0359636	+	0.0207636i	−0.481910	+	0.876220i	$0.660057\pi$
$104$	−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	−0.140466	−	0.990086i	$-0.544860\pi$
$107$	−11.0489	−	6.37909i	−1.06814	−	0.616690i	−0.927672	+	0.373396i	$0.878193\pi$
$108$	−0.784775	−	5.13655i	−0.0755150	−	0.494265i
$109$	−6.59696	−	1.76765i	−0.631874	−	0.169310i	−0.0713542	−	0.997451i	$-0.522732\pi$
$109$	−6.59696	−	1.76765i	−0.631874	−	0.169310i	−0.560520	+	0.828141i	$0.689399\pi$
$110$	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	$-0.708901\pi$
$113$		−	16.8438i		−	1.58453i	0.610175	−	0.792267i	$-0.291099\pi$
$114$	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	$0.0347897\pi$
$127$			2.45849i			0.218155i	−0.994033	+	0.109078i	$0.965210\pi$
$128$	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	0.993413	+	0.114590i	$0.0365554\pi$
$131$	18.1910	+	10.5026i	1.58936	+	0.917616i	0.595944	+	0.803026i	$0.296778\pi$
$132$	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	0.00838191	−	0.999965i	$-0.497332\pi$
$137$	−5.66907	−	1.51902i	−0.484342	−	0.129779i	−0.492723	+	0.870186i	$0.663999\pi$
$138$	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	−0.979048	−	0.203631i	$-0.934726\pi$
$149$	−21.0577	+	5.64239i	−1.72511	+	0.462242i	−0.746065	+	0.665873i	$0.768059\pi$
$150$	4.93654	+	6.34228i	0.403067	+	0.517845i
$151$	−2.93466	+	10.9523i	−0.238819	+	0.891286i	0.737571	+	0.675270i	$0.235973\pi$
$151$	−2.93466	+	10.9523i	−0.238819	+	0.891286i	−0.976390	+	0.216016i	$0.930694\pi$
$152$	−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	−0.739915	−	0.672701i	$-0.765134\pi$
$157$	−11.9352	−	20.6724i	−0.952533	−	1.64984i	−0.212619	−	0.977135i	$-0.568199\pi$
$158$	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	−0.309537	−	0.950887i	$-0.600174\pi$
$163$	−1.30429	+	0.349483i	−0.102160	+	0.0273737i	0.207377	+	0.978261i	$0.433507\pi$
$164$	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	−0.697899	−	0.716196i	$-0.745882\pi$
$167$	0.236454	−	0.236454i	0.0182973	−	0.0182973i	0.716196	+	0.697899i	$0.245882\pi$
$168$	−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	0.250497	−	0.968117i	$-0.419406\pi$
$173$	12.6750	−	21.9538i	0.963663	−	1.66911i	0.713166	−	0.700996i	$-0.247261\pi$
$174$	−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	0.805397	−	0.592736i	$-0.201952\pi$
$179$	−1.48007	−	2.56356i	−0.110626	−	0.191609i	−0.916023	+	0.401126i	$0.868619\pi$
$180$	1.54587	−	0.921198i	0.115222	−	0.0686620i
$181$		−	0.717545i		−	0.0533347i	−0.999644	−	0.0266674i	$-0.991511\pi$
$181$		−	0.717545i		−	0.0533347i	0.999644	−	0.0266674i	$-0.00848949\pi$
$182$	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	−0.0322624	−	0.999479i	$-0.510271\pi$
$191$	−12.6313	−	7.29268i	−0.913968	−	0.527680i	−0.881706	+	0.471800i	$0.843605\pi$
$192$	1.71875	+	0.214218i	0.124040	+	0.0154598i
$193$	5.24169	−	19.5623i	0.377305	−	1.40812i	−0.472642	−	0.881255i	$-0.656699\pi$
$193$	5.24169	−	19.5623i	0.377305	−	1.40812i	0.849947	−	0.526868i	$-0.176634\pi$
$194$	−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	0.674136	−	0.738607i	$-0.264516\pi$
$197$	−0.904894	−	0.904894i	−0.0644710	−	0.0644710i	−0.738607	+	0.674136i	$0.764516\pi$
$198$	9.34173	+	2.36537i	0.663888	+	0.168099i
$199$	−2.41271	+	1.39298i	−0.171032	+	0.0987456i	−0.583073	−	0.812420i	$-0.698150\pi$
$199$	−2.41271	+	1.39298i	−0.171032	+	0.0987456i	0.412040	+	0.911166i	$0.364816\pi$
$200$	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	−0.630196	−	0.776436i	$-0.717025\pi$
$223$	2.18383	−	2.18383i	0.146240	−	0.146240i	0.776436	+	0.630196i	$0.217025\pi$
$224$	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	−0.501836	−	0.864963i	$-0.667342\pi$
$227$	5.50302	−	20.5375i	0.365248	−	1.36312i	0.867084	−	0.498162i	$-0.165991\pi$
$228$	−11.3583	+	8.84078i	−0.752222	+	0.585495i
$229$	4.13582	−	1.10819i	0.273303	−	0.0732312i	−0.119565	−	0.992826i	$-0.538150\pi$
$229$	4.13582	−	1.10819i	0.273303	−	0.0732312i	0.392867	+	0.919595i	$0.371483\pi$
$230$			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	−0.999443	−	0.0333591i	$-0.989379\pi$
$233$	−7.18694	+	12.4481i	−0.470832	+	0.815505i	0.528612	+	0.848864i	$0.322713\pi$
$234$	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	0.440404	−	0.897800i	$-0.354835\pi$
$239$	−7.07117	−	7.07117i	−0.457396	−	0.457396i	−0.897800	+	0.440404i	$0.854835\pi$
$240$	−0.962597	−	0.390957i	−0.0621354	−	0.0252362i
$241$	2.14060	−	7.98882i	0.137888	−	0.514605i	−0.862081	−	0.506770i	$-0.830839\pi$
$241$	2.14060	−	7.98882i	0.137888	−	0.514605i	0.999969	−	0.00783522i	$-0.00249405\pi$
$242$	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	−0.994393	−	0.105748i	$-0.966276\pi$
$257$	−6.50252	+	11.2627i	−0.405616	+	0.702548i	0.588777	+	0.808296i	$0.299610\pi$
$258$	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	−0.251827	−	0.967772i	$-0.581031\pi$
$263$	7.46602	−	4.31051i	0.460375	−	0.265797i	0.712202	+	0.701975i	$0.247698\pi$
$264$	−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	−0.963407	−	0.268044i	$-0.913623\pi$
$269$	−19.8943	+	11.4860i	−1.21298	+	0.700313i	−0.249571	+	0.968357i	$0.580290\pi$
$270$	−0.470743	−	3.08113i	−0.0286485	−	0.187512i
$271$	19.2021	−	5.14519i	1.16645	−	0.312548i	0.376909	−	0.926250i	$-0.376987\pi$
$271$	19.2021	−	5.14519i	1.16645	−	0.312548i	0.789538	+	0.613702i	$0.210320\pi$
$272$	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	−0.0580630	−	0.998313i	$-0.518492\pi$
$277$	12.9397	−	7.47073i	0.777470	−	0.448872i	0.835533	+	0.549440i	$0.185159\pi$
$278$	−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	−0.731797	−	0.681522i	$-0.761318\pi$
$281$	−0.842761	+	0.842761i	−0.0502749	+	0.0502749i	0.681522	+	0.731797i	$0.261318\pi$
$282$	−9.17456	+	3.87465i	−0.546337	+	0.230732i
$283$	4.36513	−	2.52021i	0.259480	−	0.149811i	−0.364617	−	0.931158i	$-0.618800\pi$
$283$	4.36513	−	2.52021i	0.259480	−	0.149811i	0.624097	+	0.781346i	$0.285467\pi$
$284$	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	−0.832364	−	0.554229i	$-0.813013\pi$
$293$	−4.76090	+	4.76090i	−0.278135	+	0.278135i	0.554229	+	0.832364i	$0.313013\pi$
$294$	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	0.00962922	−	0.999954i	$-0.496935\pi$
$307$	−17.3519	−	17.3519i	−0.990324	−	0.990324i	−0.999954	+	0.00962922i	$0.996935\pi$
$308$	−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	0.971266	+	0.237997i	$0.0764909\pi$
$311$	12.1990	+	21.1294i	0.691744	+	1.19814i	−0.279521	+	0.960139i	$0.590176\pi$
$312$	−3.96754	−	4.82272i	−0.224618	−	0.273033i
$313$	12.9180	−	22.3747i	0.730171	−	1.26469i	−0.226639	−	0.973979i	$-0.572774\pi$
$313$	12.9180	−	22.3747i	0.730171	−	1.26469i	0.956810	−	0.290714i	$-0.0938930\pi$
$314$	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	−0.635018	−	0.772497i	$-0.719007\pi$
$317$	−14.2207	+	3.81041i	−0.798712	+	0.214014i	−0.163693	+	0.986511i	$0.552341\pi$
$318$	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	0.983843	−	0.179034i	$-0.0572971\pi$
$331$	0.769457	+	2.87165i	0.0422932	+	0.157840i	−0.941550	+	0.336874i	$0.890630\pi$
$332$	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	$-0.875536\pi$
$337$		−	13.9931i		−	0.762255i	0.924523	−	0.381127i	$-0.124464\pi$
$338$	−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	−0.250395	−	0.968144i	$-0.580560\pi$
$347$	8.62184	−	4.97782i	0.462845	−	0.267224i	0.713240	+	0.700920i	$0.247227\pi$
$348$	6.55236	−	2.76723i	0.351243	−	0.148339i
$349$	13.9690	+	13.9690i	0.747742	+	0.747742i	0.974055	−	0.226313i	$-0.0726672\pi$
$349$	13.9690	+	13.9690i	0.747742	+	0.747742i	−0.226313	+	0.974055i	$0.572667\pi$
$350$	−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	−0.785209	−	0.619231i	$-0.787444\pi$
$353$	3.84065	−	14.3335i	0.204417	−	0.762896i	0.989626	−	0.143665i	$-0.0458889\pi$
$354$	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	−0.989523	−	0.144375i	$-0.953883\pi$
$359$	−3.87962	−	14.4789i	−0.204759	−	0.764169i	0.784764	−	0.619794i	$-0.212784\pi$
$360$	−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	0.659275	−	0.751902i	$-0.270863\pi$
$367$	−6.15961	−	10.6688i	−0.321529	−	0.556905i	−0.980804	+	0.194998i	$0.937530\pi$
$368$	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	−0.924013	−	0.382361i	$-0.875111\pi$
$373$	−2.52756	+	4.37786i	−0.130872	+	0.226677i	0.793141	+	0.609038i	$0.208444\pi$
$374$	−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	−0.737396	−	0.675461i	$-0.763945\pi$
$379$	−1.20575	+	1.20575i	−0.0619353	+	0.0619353i	0.675461	+	0.737396i	$0.263945\pi$
$380$	−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	−0.678075	−	0.734993i	$-0.737185\pi$
$383$	−17.5705	+	4.70799i	−0.897808	+	0.240567i	−0.219734	+	0.975560i	$0.570519\pi$
$384$	−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	−0.929835	−	0.367977i	$-0.880051\pi$
$389$	−15.4549	−	26.7687i	−0.783595	−	1.35723i	0.146240	−	0.989249i	$-0.453283\pi$
$390$	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	−0.0902972	−	0.995915i	$-0.528782\pi$
$397$	6.56445	−	1.75894i	0.329461	−	0.0882787i	0.419758	+	0.907636i	$0.362115\pi$
$398$	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	0.931976	+	0.362519i	$0.118083\pi$
$401$	6.13006	+	22.8777i	0.306121	+	1.14246i	−0.625856	+	0.779939i	$0.715250\pi$
$402$	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	0.197646	−	0.980273i	$-0.436670\pi$
$409$	−2.45363	−	0.657447i	−0.121324	−	0.0325087i	−0.318970	+	0.947765i	$0.603337\pi$
$410$	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	$-0.969781\pi$
$419$		−	3.88080i		−	0.189590i	0.995497	−	0.0947948i	$-0.0302195\pi$
$420$	−2.18087	+	1.67329i	−0.106416	+	0.0816480i
$421$	0.262070	−	0.262070i	0.0127725	−	0.0127725i	−0.700692	−	0.713464i	$-0.747125\pi$
$421$	0.262070	−	0.262070i	0.0127725	−	0.0127725i	0.713464	+	0.700692i	$0.247125\pi$
$422$	−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	−0.814447	−	0.580238i	$-0.802960\pi$
$431$	3.75773	−	14.0240i	0.181004	−	0.675514i	0.995451	−	0.0952769i	$-0.0303736\pi$
$432$	−3.24791	−	4.05599i	−0.156265	−	0.195144i
$433$			9.24282i			0.444182i	0.975026	+	0.222091i	$0.0712881\pi$
$433$			9.24282i			0.444182i	−0.975026	+	0.222091i	$0.928712\pi$
$434$	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	0.624804	−	0.780782i	$-0.285179\pi$
$439$	5.46918	+	3.15763i	0.261030	+	0.150705i	−0.363775	+	0.931487i	$0.618512\pi$
$440$	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	0.776065	−	0.630652i	$-0.217213\pi$
$443$	13.0061	+	7.50906i	0.617937	+	0.356766i	−0.158128	+	0.987419i	$0.550546\pi$
$444$	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	−0.388400	−	0.921491i	$-0.626972\pi$
$449$	11.2960	−	11.2960i	0.533091	−	0.533091i	0.921491	+	0.388400i	$0.126972\pi$
$450$	−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	−0.990722	−	0.135907i	$-0.956605\pi$
$457$	−4.29015	−	16.0111i	−0.200685	−	0.748966i	0.790037	−	0.613059i	$-0.210061\pi$
$458$	−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	0.357229	−	0.934017i	$-0.383722\pi$
$461$	−12.3842	−	12.3842i	−0.576788	−	0.576788i	−0.934017	+	0.357229i	$0.883722\pi$
$462$	−14.5940	−	1.92201i	−0.678976	−	0.0894200i
$463$	15.3743	+	15.3743i	0.714503	+	0.714503i	0.967474	−	0.252971i	$-0.0814076\pi$
$463$	15.3743	+	15.3743i	0.714503	+	0.714503i	−0.252971	+	0.967474i	$0.581408\pi$
$464$	−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	−0.789736	−	0.613447i	$-0.789782\pi$
$467$	2.94747	−	5.10517i	0.136393	−	0.236239i	0.926129	+	0.377208i	$0.123116\pi$
$468$	−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	0.634635	−	0.772812i	$-0.281151\pi$
$479$	17.4615	+	4.67881i	0.797838	+	0.213780i	0.163204	+	0.986592i	$0.447817\pi$
$480$	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	−0.725118	−	0.688624i	$-0.758215\pi$
$487$	−37.4584	−	10.0369i	−1.69740	−	0.454817i	−0.972283	+	0.233807i	$0.924882\pi$
$488$	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	−0.726479	−	0.687189i	$-0.758845\pi$
$499$	−9.84950	−	36.7588i	−0.440924	−	1.64555i	0.285555	−	0.958362i	$-0.407822\pi$
$500$	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	$0.0972809\pi$
$503$			13.4961i			0.601763i	−0.953662	+	0.300882i	$0.902719\pi$
$504$	−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	0.814449	−	0.580235i	$-0.197039\pi$
$509$	40.8332	−	10.9412i	1.80990	−	0.484961i	0.995451	+	0.0952733i	$0.0303725\pi$
$510$	−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	−0.911686	−	0.410888i	$-0.865219\pi$
$521$	−23.0923	+	13.3323i	−1.01169	+	0.584099i	−0.100004	+	0.994987i	$0.531886\pi$
$522$	−0.170091	−	12.3184i	−0.00744467	−	0.539164i
$523$	−9.51589	+	16.4820i	−0.416101	+	0.720708i	−0.995543	−	0.0943055i	$-0.969937\pi$
$523$	−9.51589	+	16.4820i	−0.416101	+	0.720708i	0.579443	+	0.815013i	$0.303270\pi$
$524$	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	−0.999994	−	0.00335721i	$-0.998931\pi$
$541$	−43.3634	+	11.6192i	−1.86434	+	0.499547i	−0.864342	+	0.502905i	$0.832265\pi$
$542$	−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	0.926375	−	0.376603i	$-0.122908\pi$
$557$	36.3533	+	9.74083i	1.54034	+	0.412732i	0.613963	+	0.789335i	$0.289574\pi$
$558$	−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	0.705238	−	0.708971i	$-0.250840\pi$
$563$	−6.20164	−	10.7416i	−0.261368	−	0.452703i	−0.966606	+	0.256268i	$0.917507\pi$
$564$	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	−0.439291	−	0.898345i	$-0.644770\pi$
$569$	13.3186	−	23.0685i	0.558344	−	0.967081i	0.997635	−	0.0687356i	$-0.0218965\pi$
$570$	−6.81322	+	5.30309i	−0.285374	+	0.222122i
$571$	−38.6796	+	22.3317i	−1.61869	+	0.934552i	−0.631432	+	0.775431i	$0.717533\pi$
$571$	−38.6796	+	22.3317i	−1.61869	+	0.934552i	−0.987259	+	0.159121i	$0.949134\pi$
$572$	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	0.469775	−	0.882786i	$-0.344335\pi$
$577$	10.4543	+	2.80122i	0.435218	+	0.116616i	−0.0345564	+	0.999403i	$0.511002\pi$
$578$	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	0.876791	−	0.480871i	$-0.159679\pi$
$587$	9.59239	+	9.59239i	0.395920	+	0.395920i	−0.480871	+	0.876791i	$0.659679\pi$
$588$	−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	0.983782	+	0.179369i	$0.0574056\pi$
$593$	5.39354	+	20.1290i	0.221486	+	0.826598i	−0.762295	+	0.647229i	$0.775928\pi$
$594$	−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	−0.850271	−	0.526345i	$-0.823562\pi$
$599$	−20.0588	+	11.5809i	−0.819579	+	0.473184i	0.0306925	+	0.999529i	$0.490229\pi$
$600$	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	0.257231	+	0.966350i	$0.417190\pi$
$607$	−17.4499	+	30.2241i	−0.708268	+	1.22676i	−0.965499	+	0.260407i	$0.916143\pi$
$608$	−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	0.617812	−	0.786325i	$-0.288019\pi$
$613$	18.8091	+	5.03987i	0.759691	+	0.203559i	0.141879	+	0.989884i	$0.454686\pi$
$614$	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	0.533677	−	0.845688i	$-0.320810\pi$
$617$	−7.75021	−	7.75021i	−0.312012	−	0.312012i	−0.845688	+	0.533677i	$0.820810\pi$
$618$	0.274689	−	0.676327i	0.0110496	−	0.0272059i
$619$	−10.8113	+	40.3484i	−0.434544	+	1.62174i	0.307612	+	0.951512i	$0.400470\pi$
$619$	−10.8113	+	40.3484i	−0.434544	+	1.62174i	−0.742156	+	0.670228i	$0.766196\pi$
$620$	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	0.649653	−	0.760230i	$-0.274914\pi$
$631$	−2.77766	−	2.77766i	−0.110577	−	0.110577i	−0.760230	+	0.649653i	$0.774914\pi$
$632$	−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	0.646347	−	0.763044i	$-0.276296\pi$
$641$	−8.54841	−	14.8063i	−0.337642	−	0.584813i	−0.983989	+	0.178231i	$0.942963\pi$
$642$	−8.31533	+	20.4736i	−0.328180	+	0.808029i
$643$	15.2523	−	15.2523i	0.601493	−	0.601493i	−0.339215	−	0.940709i	$-0.610162\pi$
$643$	15.2523	−	15.2523i	0.601493	−	0.601493i	0.940709	+	0.339215i	$0.110162\pi$
$644$	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	0.963944	−	0.266106i	$-0.0857373\pi$
$647$	6.39763	+	11.0810i	0.251517	+	0.435640i	−0.712427	+	0.701746i	$0.752404\pi$
$648$	−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	0.673870	−	0.738850i	$-0.264631\pi$
$653$	9.47898	+	5.47269i	0.370941	+	0.214163i	−0.302928	+	0.953013i	$0.597964\pi$
$654$	−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	$0.121873\pi$
$659$			19.1808i			0.747177i	−0.927595	+	0.373588i	$0.878127\pi$
$660$	−1.29840	−	3.07440i	−0.0505400	−	0.119671i
$661$	−0.274549	+	1.02463i	−0.0106787	+	0.0398535i	−0.971060	−	0.238837i	$-0.923234\pi$
$661$	−0.274549	+	1.02463i	−0.0106787	+	0.0398535i	0.960381	+	0.278691i	$0.0899004\pi$
$662$	−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	$0.130340\pi$
$673$			20.6567i			0.796258i	−0.917329	+	0.398129i	$0.869660\pi$
$674$	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	0.785157	−	0.619297i	$-0.212582\pi$
$677$	16.6890	+	9.63538i	0.641409	+	0.370318i	−0.143748	+	0.989614i	$0.545916\pi$
$678$	−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	0.670447	−	0.741957i	$-0.266102\pi$
$683$	23.0006	+	6.16299i	0.880093	+	0.235820i	0.209646	+	0.977777i	$0.432769\pi$
$684$	−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	0.986181	−	0.165669i	$-0.0529783\pi$
$691$	1.29565	+	4.83543i	0.0492888	+	0.183948i	−0.936893	+	0.349617i	$0.886312\pi$
$692$		−	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	0.644280	−	0.764789i	$-0.277157\pi$
$709$	42.1942	−	11.3059i	1.58464	−	0.424602i	0.940358	+	0.340187i	$0.110490\pi$
$710$	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	0.407973	+	0.912994i	$0.366236\pi$
$719$	−15.7316	+	27.2479i	−0.586690	+	1.01618i	−0.994662	+	0.103182i	$0.967098\pi$
$720$	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	$0.284939\pi$
$727$			42.0789i			1.56062i	−0.625393	+	0.780310i	$0.715061\pi$
$728$	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	0.991510	+	0.130030i	$0.0415075\pi$
$733$	5.35665	+	19.9913i	0.197852	+	0.738395i	−0.793658	+	0.608365i	$0.791826\pi$
$734$	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	−0.498072	−	0.867136i	$-0.665959\pi$
$739$	9.97235	−	37.2173i	0.366839	−	1.36906i	0.864911	−	0.501925i	$-0.167375\pi$
$740$	−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	0.677030	−	0.735955i	$-0.263267\pi$
$743$	−1.60617	−	1.60617i	−0.0589248	−	0.0589248i	−0.735955	+	0.677030i	$0.763267\pi$
$744$	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	0.532558	−	0.846394i	$-0.321231\pi$
$751$	1.80427	+	1.04170i	0.0658387	+	0.0380120i	−0.466719	+	0.884406i	$0.654564\pi$
$752$	−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	−0.990336	−	0.138688i	$-0.955711\pi$
$761$	−5.57308	−	20.7990i	−0.202024	−	0.753964i	0.788312	−	0.615276i	$-0.210955\pi$
$762$	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	−0.358185	−	0.933651i	$-0.616604\pi$
$769$	15.9582	−	15.9582i	0.575466	−	0.575466i	0.933651	+	0.358185i	$0.116604\pi$
$770$	−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	0.705076	+	0.709131i	$0.250913\pi$
$773$	−7.23162	+	26.9888i	−0.260103	+	0.970719i	−0.965180	+	0.261588i	$0.915754\pi$
$774$	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	−0.851037	−	0.525106i	$-0.824025\pi$
$787$	4.16696	−	15.5513i	0.148536	−	0.554344i	0.999572	−	0.0292373i	$-0.00930784\pi$
$788$	−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	0.242603	−	0.970126i	$-0.421999\pi$
$809$	34.2469	−	19.7725i	1.20406	−	0.695163i	0.961455	+	0.274963i	$0.0886655\pi$
$810$	5.39654	−	0.149057i	0.189615	−	0.00523734i
$811$	12.9524	−	12.9524i	0.454821	−	0.454821i	−0.442130	−	0.896951i	$-0.645777\pi$
$811$	12.9524	−	12.9524i	0.454821	−	0.454821i	0.896951	+	0.442130i	$0.145777\pi$
$812$	−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	0.740186	−	0.672402i	$-0.234737\pi$
$821$	49.2090	−	13.1855i	1.71741	−	0.460178i	0.977221	+	0.212224i	$0.0680706\pi$
$822$	−1.25726	+	10.0875i	−0.0438519	+	0.351840i
$823$	24.0663	−	13.8947i	0.838897	−	0.484337i	−0.0179923	−	0.999838i	$-0.505727\pi$
$823$	24.0663	−	13.8947i	0.838897	−	0.484337i	0.856889	+	0.515501i	$0.172394\pi$
$824$	−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	0.00612059	−	0.999981i	$-0.498052\pi$
$827$	28.9331	−	28.9331i	1.00610	−	1.00610i	0.999981	−	0.00612059i	$-0.00194825\pi$
$828$	0.939465	−	3.71030i	0.0326487	−	0.128942i
$829$	11.7669	−	6.79364i	0.408682	−	0.235953i	−0.281541	−	0.959549i	$-0.590846\pi$
$829$	11.7669	−	6.79364i	0.408682	−	0.235953i	0.690223	+	0.723596i	$0.257512\pi$
$830$	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	−0.494361	−	0.869257i	$-0.664598\pi$
$839$	10.8590	−	10.8590i	0.374896	−	0.374896i	0.869257	+	0.494361i	$0.164598\pi$
$840$	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	0.334304	−	0.942465i	$-0.391499\pi$
$853$	−17.7621	−	17.7621i	−0.608162	−	0.608162i	−0.942465	+	0.334304i	$0.891499\pi$
$854$	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	0.909214	−	0.416329i	$-0.136684\pi$
$857$	2.75343	+	4.76907i	0.0940553	+	0.162908i	−0.815159	+	0.579238i	$0.803350\pi$
$858$	1.94242	−	19.9658i	0.0663132	−	0.681621i
$859$	20.8680	−	36.1445i	0.712008	−	1.23323i	−0.252095	−	0.967703i	$-0.581119\pi$
$859$	20.8680	−	36.1445i	0.712008	−	1.23323i	0.964102	−	0.265531i	$-0.0855472\pi$
$860$	−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	−0.242721	−	0.970096i	$-0.578040\pi$
$863$	0.943703	−	0.252864i	0.0321240	−	0.00860761i	0.274845	+	0.961488i	$0.411373\pi$
$864$	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	0.990962	+	0.134139i	$0.0428270\pi$
$877$	5.91791	+	22.0859i	0.199833	+	0.745789i	−0.791129	+	0.611649i	$0.790506\pi$
$878$	−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	$-0.816955\pi$
$883$		−	32.3230i		−	1.08776i	0.839164	−	0.543878i	$-0.183045\pi$
$884$	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	−0.132440	−	0.991191i	$-0.542281\pi$
$887$	−31.4819	−	18.1761i	−1.05706	−	0.610292i	−0.924617	+	0.380899i	$0.875615\pi$
$888$	−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	−0.509659	−	0.860376i	$-0.670229\pi$
$907$	−0.583687	+	0.336992i	−0.0193810	+	0.0111896i	0.490278	+	0.871566i	$0.336895\pi$
$908$	−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	$0.0679772\pi$
$911$			12.7937i			0.423875i	−0.977283	+	0.211937i	$0.932023\pi$
$912$	−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	−0.385941	−	0.922524i	$-0.626123\pi$
$919$	18.3696	−	31.8172i	0.605959	−	1.04955i	0.991899	−	0.127027i	$-0.0405436\pi$
$920$	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	−0.0891581	−	0.996017i	$-0.528418\pi$
$929$	10.1081	−	2.70847i	0.331638	−	0.0888620i	0.420796	+	0.907155i	$0.361751\pi$
$930$	−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	0.402090	+	0.915600i	$0.368284\pi$
$941$	−12.3909	+	46.2433i	−0.403930	+	1.50749i	−0.806020	+	0.591888i	$0.798383\pi$
$942$	−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	−0.910977	−	0.412457i	$-0.864671\pi$
$947$	−10.1022	−	37.7018i	−0.328276	−	1.22514i	0.582701	−	0.812687i	$-0.301996\pi$
$948$	−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	−0.843160	−	0.537664i	$-0.819307\pi$
$967$	−9.49989	+	9.49989i	−0.305496	+	0.305496i	0.537664	+	0.843160i	$0.319307\pi$
$968$	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	0.751183	−	0.660094i	$-0.229484\pi$
$971$	17.2979	+	9.98695i	0.555116	+	0.320496i	−0.196067	+	0.980591i	$0.562817\pi$
$972$	−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	−0.962330	−	0.271884i	$-0.912353\pi$
$977$	0.219237	−	0.818205i	0.00701403	−	0.0261767i	0.969344	+	0.245707i	$0.0790201\pi$
$978$	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	0.103571	−	0.994622i	$-0.466973\pi$
$983$	−9.53265	−	2.55427i	−0.304044	−	0.0814685i	−0.407616	+	0.913154i	$0.633640\pi$
$984$	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	0.900328	−	0.435211i	$-0.143326\pi$
$991$	2.30625	+	3.99454i	0.0732605	+	0.126891i	−0.827068	+	0.562102i	$0.809993\pi$
$992$	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	−0.945839	−	0.324635i	$-0.894758\pi$
$997$	−23.8097	−	41.2397i	−0.754062	−	1.30607i	0.191777	−	0.981439i	$-0.438575\pi$
$998$	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.317.9	✓	144
3.2	odd	2	inner	546.2.bv.a.317.33	yes	144
7.4	even	3	inner	546.2.bv.a.473.33	yes	144
13.8	odd	4	inner	546.2.bv.a.359.9	yes	144
21.11	odd	6	inner	546.2.bv.a.473.9	yes	144
39.8	even	4	inner	546.2.bv.a.359.33	yes	144
91.60	odd	12	inner	546.2.bv.a.515.33	yes	144
273.242	even	12	inner	546.2.bv.a.515.9	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.9	✓	144	1.1	even	1	trivial
546.2.bv.a.317.33	yes	144	3.2	odd	2	inner
546.2.bv.a.359.9	yes	144	13.8	odd	4	inner
546.2.bv.a.359.33	yes	144	39.8	even	4	inner
546.2.bv.a.473.9	yes	144	21.11	odd	6	inner
546.2.bv.a.473.33	yes	144	7.4	even	3	inner
546.2.bv.a.515.9	yes	144	273.242	even	12	inner
546.2.bv.a.515.33	yes	144	91.60	odd	12	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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more