LMFDB - Embedded newform 546.2.ch.a.401.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(137,546)]

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, 8, 11]))

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

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

chi := DirichletCharacter("546.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.ch (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:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			401.25
Character	$\chi$	$=$	546.401
Dual form			546.2.ch.a.305.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.24738 + 1.20169i) q^{3} -1.00000i q^{4} +(0.505894 + 1.88802i) q^{5} +(-0.0323060 + 1.73175i) q^{6} +(-2.61407 - 0.408204i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.111892 - 2.99791i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.24738 + 1.20169i) q^{3} -1.00000i q^{4} +(0.505894 + 1.88802i) q^{5} +(-0.0323060 + 1.73175i) q^{6} +(-2.61407 - 0.408204i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.111892 - 2.99791i) q^{9} +(1.69275 + 0.977313i) q^{10} +(-3.42642 + 0.918106i) q^{11} +(1.20169 + 1.24738i) q^{12} +(-1.12860 + 3.42436i) q^{13} +(-2.13707 + 1.55978i) q^{14} +(-2.89985 - 1.74715i) q^{15} -1.00000 q^{16} -2.53611 q^{17} +(-2.04072 - 2.19896i) q^{18} +(1.58408 - 5.91185i) q^{19} +(1.88802 - 0.505894i) q^{20} +(3.75126 - 2.63212i) q^{21} +(-1.77364 + 3.07204i) q^{22} -6.64429 q^{23} +(1.73175 + 0.0323060i) q^{24} +(1.02143 - 0.589721i) q^{25} +(1.62335 + 3.21943i) q^{26} +(3.46298 + 3.87398i) q^{27} +(-0.408204 + 2.61407i) q^{28} +(-7.81199 + 4.51025i) q^{29} +(-3.28593 + 0.815088i) q^{30} +(-0.215339 + 0.803657i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.17075 - 5.26271i) q^{33} +(-1.79330 + 1.79330i) q^{34} +(-0.551746 - 5.14193i) q^{35} +(-2.99791 - 0.111892i) q^{36} +(-3.90449 + 3.90449i) q^{37} +(-3.06020 - 5.30042i) q^{38} +(-2.70722 - 5.62769i) q^{39} +(0.977313 - 1.69275i) q^{40} +(6.19829 + 1.66083i) q^{41} +(0.791357 - 4.51373i) q^{42} +(-4.42594 - 2.55532i) q^{43} +(0.918106 + 3.42642i) q^{44} +(5.71673 - 1.30537i) q^{45} +(-4.69822 + 4.69822i) q^{46} +(-11.1371 + 2.98417i) q^{47} +(1.24738 - 1.20169i) q^{48} +(6.66674 + 2.13415i) q^{49} +(0.305262 - 1.13925i) q^{50} +(3.16348 - 3.04761i) q^{51} +(3.42436 + 1.12860i) q^{52} +(4.87278 - 2.81330i) q^{53} +(5.18802 + 0.290619i) q^{54} +(-3.46681 - 6.00469i) q^{55} +(1.55978 + 2.13707i) q^{56} +(5.12826 + 9.27786i) q^{57} +(-2.33468 + 8.71314i) q^{58} +(7.16184 + 7.16184i) q^{59} +(-1.74715 + 2.89985i) q^{60} +(5.60901 + 9.71509i) q^{61} +(0.416003 + 0.720539i) q^{62} +(-1.51625 + 7.79108i) q^{63} +1.00000i q^{64} +(-7.03623 - 0.398463i) q^{65} +(-1.47924 - 5.96336i) q^{66} +(11.5062 - 3.08307i) q^{67} +2.53611i q^{68} +(8.28793 - 7.98437i) q^{69} +(-4.02604 - 3.24575i) q^{70} +(1.52491 + 5.69106i) q^{71} +(-2.19896 + 2.04072i) q^{72} +(-10.3618 - 2.77643i) q^{73} +5.52178i q^{74} +(-0.565442 + 1.96304i) q^{75} +(-5.91185 - 1.58408i) q^{76} +(9.33168 - 1.00132i) q^{77} +(-5.89368 - 2.06509i) q^{78} +(5.90403 - 10.2261i) q^{79} +(-0.505894 - 1.88802i) q^{80} +(-8.97496 - 0.670883i) q^{81} +(5.55723 - 3.20847i) q^{82} +(0.859699 - 0.859699i) q^{83} +(-2.63212 - 3.75126i) q^{84} +(-1.28300 - 4.78824i) q^{85} +(-4.93650 + 1.32273i) q^{86} +(4.32457 - 15.0136i) q^{87} +(3.07204 + 1.77364i) q^{88} +(1.99327 + 1.99327i) q^{89} +(3.11930 - 4.96538i) q^{90} +(4.34809 - 8.49083i) q^{91} +6.64429i q^{92} +(-0.697136 - 1.26123i) q^{93} +(-5.76497 + 9.98523i) q^{94} +11.9631 q^{95} +(0.0323060 - 1.73175i) q^{96} +(6.95381 - 1.86327i) q^{97} +(6.22317 - 3.20503i) q^{98} +(2.36901 + 10.3748i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 8 q^{7}+O(q^{10}) $ 152 * q + 8 * q^7	$ 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−1.24738	+	1.20169i	−0.720173	+	0.693795i
$3$	−1.24738	+	1.20169i	−0.720173	+	0.693795i
$4$		−	1.00000i		−	0.500000i
$5$	0.505894	+	1.88802i	0.226243	+	0.844349i	0.981903	+	0.189385i	$0.0606496\pi$
$5$	0.505894	+	1.88802i	0.226243	+	0.844349i	−0.755660	+	0.654964i	$0.772684\pi$
$6$	−0.0323060	+	1.73175i	−0.0131889	+	0.706984i
$7$	−2.61407	−	0.408204i	−0.988026	−	0.154286i
$7$	−2.61407	−	0.408204i	−0.988026	−	0.154286i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.111892	−	2.99791i	0.0372973	−	0.999304i
$10$	1.69275	+	0.977313i	0.535296	+	0.309053i
$11$	−3.42642	+	0.918106i	−1.03310	+	0.276819i	−0.735253	−	0.677793i	$-0.762937\pi$
$11$	−3.42642	+	0.918106i	−1.03310	+	0.276819i	−0.297851	+	0.954612i	$0.596270\pi$
$12$	1.20169	+	1.24738i	0.346897	+	0.360086i
$13$	−1.12860	+	3.42436i	−0.313018	+	0.949747i
$13$	−1.12860	+	3.42436i	−0.313018	+	0.949747i
$14$	−2.13707	+	1.55978i	−0.571156	+	0.416870i
$15$	−2.89985	−	1.74715i	−0.748739	−	0.451111i
$16$	−1.00000			−0.250000
$17$	−2.53611			−0.615097			−0.307549	−	0.951532i	$-0.599509\pi$
$17$	−2.53611			−0.615097			−0.307549	+	0.951532i	$0.599509\pi$
$18$	−2.04072	−	2.19896i	−0.481003	−	0.518301i
$19$	1.58408	−	5.91185i	0.363412	−	1.35627i	−0.506149	−	0.862446i	$-0.668932\pi$
$19$	1.58408	−	5.91185i	0.363412	−	1.35627i	0.869561	−	0.493825i	$-0.164402\pi$
$20$	1.88802	−	0.505894i	0.422175	−	0.113121i
$21$	3.75126	−	2.63212i	0.818593	−	0.574375i
$22$	−1.77364	+	3.07204i	−0.378142	+	0.654962i
$23$	−6.64429			−1.38543			−0.692715	−	0.721211i	$-0.743586\pi$
$23$	−6.64429			−1.38543			−0.692715	+	0.721211i	$0.743586\pi$
$24$	1.73175	+	0.0323060i	0.353492	+	0.00659443i
$25$	1.02143	−	0.589721i	0.204285	−	0.117944i
$26$	1.62335	+	3.21943i	0.318364	+	0.631383i
$27$	3.46298	+	3.87398i	0.666452	+	0.745548i
$28$	−0.408204	+	2.61407i	−0.0771432	+	0.494013i
$29$	−7.81199	+	4.51025i	−1.45065	+	0.837533i	−0.998518	−	0.0544178i	$-0.982670\pi$
$29$	−7.81199	+	4.51025i	−1.45065	+	0.837533i	−0.452132	+	0.891951i	$0.649336\pi$
$30$	−3.28593	+	0.815088i	−0.599925	+	0.148814i
$31$	−0.215339	+	0.803657i	−0.0386761	+	0.144341i	−0.982564	−	0.185925i	$-0.940472\pi$
$31$	−0.215339	+	0.803657i	−0.0386761	+	0.144341i	0.943888	+	0.330266i	$0.107138\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	3.17075	−	5.26271i	0.551957	−	0.916120i
$34$	−1.79330	+	1.79330i	−0.307549	+	0.307549i
$35$	−0.551746	−	5.14193i	−0.0932621	−	0.869146i
$36$	−2.99791	−	0.111892i	−0.499652	−	0.0186486i
$37$	−3.90449	+	3.90449i	−0.641894	+	0.641894i	−0.951021	−	0.309127i	$-0.899963\pi$
$37$	−3.90449	+	3.90449i	−0.641894	+	0.641894i	0.309127	+	0.951021i	$0.399963\pi$
$38$	−3.06020	−	5.30042i	−0.496430	−	0.859841i
$39$	−2.70722	−	5.62769i	−0.433503	−	0.901152i
$40$	0.977313	−	1.69275i	0.154527	−	0.267648i
$41$	6.19829	+	1.66083i	0.968010	+	0.259377i	0.707987	−	0.706225i	$-0.249603\pi$
$41$	6.19829	+	1.66083i	0.968010	+	0.259377i	0.260023	+	0.965603i	$0.416270\pi$
$42$	0.791357	−	4.51373i	0.122109	−	0.696484i
$43$	−4.42594	−	2.55532i	−0.674950	−	0.389682i	0.123000	−	0.992407i	$-0.460749\pi$
$43$	−4.42594	−	2.55532i	−0.674950	−	0.389682i	−0.797950	+	0.602724i	$0.794082\pi$
$44$	0.918106	+	3.42642i	0.138410	+	0.516552i
$45$	5.71673	−	1.30537i	0.852200	−	0.194593i
$46$	−4.69822	+	4.69822i	−0.692715	+	0.692715i
$47$	−11.1371	+	2.98417i	−1.62451	+	0.435286i	−0.952322	−	0.305095i	$-0.901312\pi$
$47$	−11.1371	+	2.98417i	−1.62451	+	0.435286i	−0.672187	+	0.740381i	$0.734645\pi$
$48$	1.24738	−	1.20169i	0.180043	−	0.173449i
$49$	6.66674	+	2.13415i	0.952391	+	0.304878i
$50$	0.305262	−	1.13925i	0.0431705	−	0.161115i
$51$	3.16348	−	3.04761i	0.442976	−	0.426751i
$52$	3.42436	+	1.12860i	0.474874	+	0.156509i
$53$	4.87278	−	2.81330i	0.669328	−	0.386437i	−0.126494	−	0.991967i	$-0.540372\pi$
$53$	4.87278	−	2.81330i	0.669328	−	0.386437i	0.795822	+	0.605531i	$0.207039\pi$
$54$	5.18802	+	0.290619i	0.706000	+	0.0395482i
$55$	−3.46681	−	6.00469i	−0.467465	−	0.809672i
$56$	1.55978	+	2.13707i	0.208435	+	0.285578i
$57$	5.12826	+	9.27786i	0.679255	+	1.22888i
$58$	−2.33468	+	8.71314i	−0.306558	+	1.14409i
$59$	7.16184	+	7.16184i	0.932392	+	0.932392i	0.997855	−	0.0654632i	$-0.0208525\pi$
$59$	7.16184	+	7.16184i	0.932392	+	0.932392i	−0.0654632	+	0.997855i	$0.520852\pi$
$60$	−1.74715	+	2.89985i	−0.225556	+	0.374370i
$61$	5.60901	+	9.71509i	0.718160	+	1.24389i	0.961728	+	0.274006i	$0.0883488\pi$
$61$	5.60901	+	9.71509i	0.718160	+	1.24389i	−0.243568	+	0.969884i	$0.578318\pi$
$62$	0.416003	+	0.720539i	0.0528325	+	0.0915085i
$63$	−1.51625	+	7.79108i	−0.191030	+	0.981584i
$64$			1.00000i			0.125000i
$65$	−7.03623	−	0.398463i	−0.872737	−	0.0494233i
$66$	−1.47924	−	5.96336i	−0.182081	−	0.734039i
$67$	11.5062	−	3.08307i	1.40570	−	0.376657i	0.525313	−	0.850909i	$-0.323948\pi$
$67$	11.5062	−	3.08307i	1.40570	−	0.376657i	0.880389	+	0.474252i	$0.157282\pi$
$68$			2.53611i			0.307549i
$69$	8.28793	−	7.98437i	0.997749	−	0.961205i
$70$	−4.02604	−	3.24575i	−0.481204	−	0.387942i
$71$	1.52491	+	5.69106i	0.180974	+	0.675404i	0.995457	+	0.0952161i	$0.0303542\pi$
$71$	1.52491	+	5.69106i	0.180974	+	0.675404i	−0.814483	+	0.580188i	$0.802979\pi$
$72$	−2.19896	+	2.04072i	−0.259150	+	0.240502i
$73$	−10.3618	−	2.77643i	−1.21275	−	0.324957i	−0.404913	−	0.914355i	$-0.632698\pi$
$73$	−10.3618	−	2.77643i	−1.21275	−	0.324957i	−0.807842	+	0.589399i	$0.799365\pi$
$74$			5.52178i			0.641894i
$75$	−0.565442	+	1.96304i	−0.0652916	+	0.226672i
$76$	−5.91185	−	1.58408i	−0.678136	−	0.181706i
$77$	9.33168	−	1.00132i	1.06344	−	0.114111i
$78$	−5.89368	−	2.06509i	−0.667327	−	0.233825i
$79$	5.90403	−	10.2261i	0.664255	−	1.15052i	−0.315232	−	0.949015i	$-0.602082\pi$
$79$	5.90403	−	10.2261i	0.664255	−	1.15052i	0.979487	−	0.201509i	$-0.0645845\pi$
$80$	−0.505894	−	1.88802i	−0.0565607	−	0.211087i
$81$	−8.97496	−	0.670883i	−0.997218	−	0.0745426i
$82$	5.55723	−	3.20847i	0.613694	−	0.354316i
$83$	0.859699	−	0.859699i	0.0943642	−	0.0943642i	−0.658349	−	0.752713i	$-0.728745\pi$
$83$	0.859699	−	0.859699i	0.0943642	−	0.0943642i	0.752713	+	0.658349i	$0.228745\pi$
$84$	−2.63212	−	3.75126i	−0.287187	−	0.409296i
$85$	−1.28300	−	4.78824i	−0.139161	−	0.519357i
$86$	−4.93650	+	1.32273i	−0.532316	+	0.142634i
$87$	4.32457	−	15.0136i	0.463642	−	1.60962i
$88$	3.07204	+	1.77364i	0.327481	+	0.189071i
$89$	1.99327	+	1.99327i	0.211286	+	0.211286i	0.804814	−	0.593528i	$-0.202265\pi$
$89$	1.99327	+	1.99327i	0.211286	+	0.211286i	−0.593528	+	0.804814i	$0.702265\pi$
$90$	3.11930	−	4.96538i	0.328803	−	0.523397i
$91$	4.34809	−	8.49083i	0.455803	−	0.890081i
$92$			6.64429i			0.692715i
$93$	−0.697136	−	1.26123i	−0.0722896	−	0.130784i
$94$	−5.76497	+	9.98523i	−0.594612	+	1.02990i
$95$	11.9631			1.22739
$96$	0.0323060	−	1.73175i	0.00329722	−	0.176746i
$97$	6.95381	−	1.86327i	0.706052	−	0.189186i	0.112112	−	0.993696i	$-0.464238\pi$
$97$	6.95381	−	1.86327i	0.706052	−	0.189186i	0.593940	+	0.804509i	$0.297572\pi$
$98$	6.22317	−	3.20503i	0.628635	−	0.323757i
$99$	2.36901	+	10.3748i	0.238095	+	1.04271i
$100$	−0.589721	−	1.02143i	−0.0589721	−	0.102143i
$101$	2.71777	−	4.70732i	0.270429	−	0.468396i	−0.698543	−	0.715568i	$-0.746168\pi$
$101$	2.71777	−	4.70732i	0.270429	−	0.468396i	0.968972	+	0.247172i	$0.0795012\pi$
$102$	0.0819316	−	4.39191i	0.00811244	−	0.434864i
$103$	−10.5376	−	6.08387i	−1.03830	−	0.599461i	−0.118947	−	0.992901i	$-0.537952\pi$
$103$	−10.5376	−	6.08387i	−1.03830	−	0.599461i	−0.919350	+	0.393440i	$0.871285\pi$
$104$	3.21943	−	1.62335i	0.315691	−	0.159182i
$105$	6.86724	+	5.75090i	0.670174	+	0.561230i
$106$	1.45627	−	5.43488i	0.141446	−	0.527882i
$107$			7.08782i			0.685205i	0.939480	+	0.342602i	$0.111308\pi$
$107$			7.08782i			0.685205i	−0.939480	+	0.342602i	$0.888692\pi$
$108$	3.87398	−	3.46298i	0.372774	−	0.333226i
$109$	2.13828	−	7.98018i	0.204810	−	0.764362i	−0.784697	−	0.619879i	$-0.787181\pi$
$109$	2.13828	−	7.98018i	0.204810	−	0.764362i	0.989507	−	0.144483i	$-0.0461519\pi$
$110$	−6.69736	−	1.79455i	−0.638568	−	0.171104i
$111$	0.178387	−	9.56234i	0.0169317	−	0.907617i
$112$	2.61407	+	0.408204i	0.247007	+	0.0385716i
$113$	−9.45842	−	5.46082i	−0.889774	−	0.513711i	−0.0159051	−	0.999874i	$-0.505063\pi$
$113$	−9.45842	−	5.46082i	−0.889774	−	0.513711i	−0.873868	+	0.486163i	$0.838396\pi$
$114$	10.1867	+	2.93421i	0.954069	+	0.274814i
$115$	−3.36131	−	12.5446i	−0.313444	−	1.16979i
$116$	4.51025	+	7.81199i	0.418767	+	0.725325i
$117$	10.1397	+	3.76661i	0.937412	+	0.348223i
$118$	10.1284			0.932392
$119$	6.62958	+	1.03525i	0.607732	+	0.0949012i
$120$	0.815088	+	3.28593i	0.0744070	+	0.299963i
$121$	1.37114	−	0.791629i	0.124649	−	0.0719662i
$122$	10.8358	+	2.90344i	0.981025	+	0.262865i
$123$	−9.72739	+	5.37673i	−0.877089	+	0.484804i
$124$	0.803657	+	0.215339i	0.0721705	+	0.0193380i
$125$	8.54078	+	8.54078i	0.763911	+	0.763911i
$126$	4.43698	+	6.58128i	0.395277	+	0.586307i
$127$	−11.1018	+	6.40962i	−0.985124	+	0.568762i	−0.903813	−	0.427927i	$-0.859244\pi$
$127$	−11.1018	+	6.40962i	−0.985124	+	0.568762i	−0.0813110	+	0.996689i	$0.525911\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	8.59151	−	2.13116i	0.756440	−	0.187638i
$130$	−5.25712	+	4.69361i	−0.461080	+	0.411657i
$131$	−4.78950	−	2.76522i	−0.418461	−	0.241598i	0.275958	−	0.961170i	$-0.411005\pi$
$131$	−4.78950	−	2.76522i	−0.418461	−	0.241598i	−0.694419	+	0.719571i	$0.744338\pi$
$132$	−5.26271	−	3.17075i	−0.458060	−	0.275979i
$133$	−6.55412	+	14.8074i	−0.568315	+	1.28396i
$134$	5.95603	−	10.3161i	0.514523	−	0.891180i
$135$	−5.56226	+	8.49802i	−0.478723	+	0.731393i
$136$	1.79330	+	1.79330i	0.153774	+	0.153774i
$137$	8.89989	+	8.89989i	0.760369	+	0.760369i	0.976389	−	0.216020i	$-0.0693077\pi$
$137$	8.89989	+	8.89989i	0.760369	+	0.760369i	−0.216020	+	0.976389i	$0.569308\pi$
$138$	0.214650	−	11.5062i	0.0182723	−	0.979477i
$139$	−5.11177	+	8.85384i	−0.433574	+	0.750973i	−0.997178	−	0.0750724i	$-0.976081\pi$
$139$	−5.11177	+	8.85384i	−0.433574	+	0.750973i	0.563604	+	0.826045i	$0.309415\pi$
$140$	−5.14193	+	0.551746i	−0.434573	+	0.0466310i
$141$	10.3061	−	17.1057i	0.867928	−	1.44056i
$142$	5.10246	+	2.94591i	0.428189	+	0.247215i
$143$	0.723139	−	12.7695i	0.0604719	−	1.06784i
$144$	−0.111892	+	2.99791i	−0.00932431	+	0.249826i
$145$	−12.4675	−	12.4675i	−1.03537	−	1.03537i
$146$	−9.29012	+	5.36365i	−0.768856	+	0.443899i
$147$	−10.8805	+	5.34926i	−0.897409	+	0.441199i
$148$	3.90449	+	3.90449i	0.320947	+	0.320947i
$149$	−20.4208	−	5.47173i	−1.67294	−	0.448262i	−0.707036	−	0.707177i	$-0.749968\pi$
$149$	−20.4208	−	5.47173i	−1.67294	−	0.448262i	−0.965900	+	0.258915i	$0.916635\pi$
$150$	0.988250	+	1.78791i	0.0806903	+	0.145982i
$151$	2.30442	+	0.617468i	0.187531	+	0.0502488i	0.351362	−	0.936240i	$-0.385719\pi$
$151$	2.30442	+	0.617468i	0.187531	+	0.0502488i	−0.163831	+	0.986488i	$0.552385\pi$
$152$	−5.30042	+	3.06020i	−0.429921	+	0.248215i
$153$	−0.283770	+	7.60304i	−0.0229414	+	0.614669i
$154$	5.89045	−	7.30653i	0.474666	−	0.588777i
$155$	−1.62626			−0.130624
$156$	−5.62769	+	2.70722i	−0.450576	+	0.216751i
$157$	5.47220	+	9.47812i	0.436729	+	0.756437i	0.997435	−	0.0715782i	$-0.0228036\pi$
$157$	5.47220	+	9.47812i	0.436729	+	0.756437i	−0.560706	+	0.828015i	$0.689470\pi$
$158$	−3.05615	−	11.4057i	−0.243134	−	0.907389i
$159$	−2.69748	+	9.36481i	−0.213924	+	0.742678i
$160$	−1.69275	−	0.977313i	−0.133824	−	0.0772633i
$161$	17.3687	+	2.71222i	1.36884	+	0.213753i
$162$	−6.82064	+	5.87187i	−0.535880	+	0.461338i
$163$	19.7291	+	5.28639i	1.54530	+	0.414062i	0.927974	−	0.372645i	$-0.121549\pi$
$163$	19.7291	+	5.28639i	1.54530	+	0.414062i	0.617326	+	0.786707i	$0.288216\pi$
$164$	1.66083	−	6.19829i	0.129689	−	0.484005i
$165$	11.5402	+	3.32408i	0.898402	+	0.258779i
$166$		−	1.21580i		−	0.0943642i
$167$	0.700037	−	2.61257i	0.0541705	−	0.202167i	−0.933537	−	0.358481i	$-0.883295\pi$
$167$	0.700037	−	2.61257i	0.0541705	−	0.202167i	0.987707	+	0.156314i	$0.0499613\pi$
$168$	−4.51373	−	0.791357i	−0.348242	−	0.0610545i
$169$	−10.4525	−	7.72949i	−0.804039	−	0.594576i
$170$	−4.29302	−	2.47857i	−0.329259	−	0.190098i
$171$	−17.5460	−	5.41041i	−1.34177	−	0.413744i
$172$	−2.55532	+	4.42594i	−0.194841	+	0.337475i
$173$	4.29069	+	7.43170i	0.326215	+	0.565022i	0.981758	−	0.190137i	$-0.0608932\pi$
$173$	4.29069	+	7.43170i	0.326215	+	0.565022i	−0.655542	+	0.755159i	$0.727560\pi$
$174$	−7.55826	−	13.6741i	−0.572990	−	1.03663i
$175$	−2.91081	+	1.12462i	−0.220036	+	0.0850134i
$176$	3.42642	−	0.918106i	0.258276	−	0.0692048i
$177$	−17.5398	−	0.327207i	−1.31837	−	0.0245944i
$178$	2.81890			0.211286
$179$	1.02031	−	1.76722i	0.0762612	−	0.132088i	−0.825373	−	0.564588i	$-0.809035\pi$
$179$	1.02031	−	1.76722i	0.0762612	−	0.132088i	0.901634	+	0.432500i	$0.142368\pi$
$180$	−1.30537	−	5.71673i	−0.0972967	−	0.426100i
$181$		−	3.77689i		−	0.280734i	−0.990100	−	0.140367i	$-0.955172\pi$
$181$		−	3.77689i		−	0.280734i	0.990100	−	0.140367i	$-0.0448283\pi$
$182$	−2.92936	−	9.07848i	−0.217139	−	0.672942i
$183$	−18.6710	−	5.37809i	−1.38020	−	0.397560i
$184$	4.69822	+	4.69822i	0.346358	+	0.346358i
$185$	−9.34702	−	5.39651i	−0.687207	−	0.396759i
$186$	−1.38478	−	0.398876i	−0.101537	−	0.0292470i
$187$	8.68978	−	2.32842i	0.635459	−	0.170271i
$188$	2.98417	+	11.1371i	0.217643	+	0.812254i
$189$	−7.47112	−	11.5405i	−0.543444	−	0.839446i
$190$	8.45917	−	8.45917i	0.613693	−	0.613693i
$191$	−8.57497	+	4.95076i	−0.620463	+	0.358224i	−0.777049	−	0.629440i	$-0.783284\pi$
$191$	−8.57497	+	4.95076i	−0.620463	+	0.358224i	0.156586	+	0.987664i	$0.449951\pi$
$192$	−1.20169	−	1.24738i	−0.0867244	−	0.0900216i
$193$	1.01017	+	3.76999i	0.0727134	+	0.271370i	0.992705	−	0.120568i	$-0.0384715\pi$
$193$	1.01017	+	3.76999i	0.0727134	+	0.271370i	−0.919992	+	0.391938i	$0.871805\pi$
$194$	3.59956	−	6.23461i	0.258433	−	0.447619i
$195$	9.25565	−	7.95832i	0.662811	−	0.569907i
$196$	2.13415	−	6.66674i	0.152439	−	0.476196i
$197$	−4.64694	−	1.24514i	−0.331081	−	0.0887129i	0.0894493	−	0.995991i	$-0.471489\pi$
$197$	−4.64694	−	1.24514i	−0.331081	−	0.0887129i	−0.420530	+	0.907279i	$0.638156\pi$
$198$	9.01126	+	5.66097i	0.640402	+	0.402307i
$199$			8.78409i			0.622688i	0.950297	+	0.311344i	$0.100779\pi$
$199$			8.78409i			0.622688i	−0.950297	+	0.311344i	$0.899221\pi$
$200$	−1.13925	−	0.305262i	−0.0805573	−	0.0215853i
$201$	−10.6476	+	17.6726i	−0.751026	+	1.24653i
$202$	−1.40682	−	5.25034i	−0.0989838	−	0.369412i
$203$	22.2622	−	8.60125i	1.56250	−	0.603689i
$204$	−3.04761	−	3.16348i	−0.213376	−	0.221488i
$205$			12.5427i			0.876021i
$206$	−11.7531	+	3.14924i	−0.818879	+	0.219418i
$207$	−0.743442	+	19.9190i	−0.0516728	+	1.38447i
$208$	1.12860	−	3.42436i	0.0782545	−	0.237437i
$209$			21.7108i			1.50177i
$210$	8.92237	−	0.789370i	0.615702	−	0.0544717i
$211$	−8.63034	−	14.9482i	−0.594137	−	1.02908i	−0.993668	−	0.112356i	$-0.964160\pi$
$211$	−8.63034	−	14.9482i	−0.594137	−	1.02908i	0.399531	−	0.916720i	$-0.369173\pi$
$212$	−2.81330	−	4.87278i	−0.193218	−	0.334664i
$213$	−8.74101	−	5.26641i	−0.598924	−	0.360849i
$214$	5.01184	+	5.01184i	0.342602	+	0.342602i
$215$	2.58544	−	9.64900i	0.176326	−	0.658056i
$216$	0.290619	−	5.18802i	0.0197741	−	0.353000i
$217$	0.890968	−	2.01291i	0.0604828	−	0.136645i
$218$	−4.13084	−	7.15483i	−0.279776	−	0.484586i
$219$	16.2614	−	8.98838i	1.09885	−	0.607378i
$220$	−6.00469	+	3.46681i	−0.404836	+	0.233732i
$221$	2.86226	−	8.68456i	0.192537	−	0.584187i
$222$	−6.63546	−	6.88774i	−0.445343	−	0.462275i
$223$	−4.00258	+	14.9378i	−0.268032	+	1.00031i	0.692336	+	0.721576i	$0.256582\pi$
$223$	−4.00258	+	14.9378i	−0.268032	+	1.00031i	−0.960368	+	0.278735i	$0.910085\pi$
$224$	2.13707	−	1.55978i	0.142789	−	0.104217i
$225$	−1.65364	−	3.12813i	−0.110243	−	0.208542i
$226$	−10.5495	+	2.82673i	−0.701742	+	0.188031i
$227$	−13.7448	+	13.7448i	−0.912278	+	0.912278i	−0.996451	−	0.0841735i	$-0.973175\pi$
$227$	−13.7448	+	13.7448i	−0.912278	+	0.912278i	0.0841735	+	0.996451i	$0.473175\pi$
$228$	9.27786	−	5.12826i	0.614441	−	0.339627i
$229$	−1.38301	−	5.16146i	−0.0913917	−	0.341079i	0.905056	−	0.425292i	$-0.139829\pi$
$229$	−1.38301	−	5.16146i	−0.0913917	−	0.341079i	−0.996448	+	0.0842139i	$0.973162\pi$
$230$	−11.2472	−	6.49355i	−0.741616	−	0.428172i
$231$	−10.4368	+	12.4628i	−0.686693	+	0.819991i
$232$	8.71314	+	2.33468i	0.572046	+	0.153279i
$233$	−2.67277	+	4.62938i	−0.175099	+	0.303281i	−0.940196	−	0.340635i	$-0.889358\pi$
$233$	−2.67277	+	4.62938i	−0.175099	+	0.303281i	0.765096	+	0.643916i	$0.222691\pi$
$234$	9.83322	−	4.50642i	0.642817	−	0.294594i
$235$	−11.2684	−	19.5174i	−0.735067	−	1.27317i
$236$	7.16184	−	7.16184i	0.466196	−	0.466196i
$237$	4.92401	+	19.8506i	0.319849	+	1.28943i
$238$	5.41985	−	3.95579i	0.351317	−	0.256416i
$239$	1.77800	−	1.77800i	0.115009	−	0.115009i	−0.647260	−	0.762269i	$-0.724085\pi$
$239$	1.77800	−	1.77800i	0.115009	−	0.115009i	0.762269	+	0.647260i	$0.224085\pi$
$240$	2.89985	+	1.74715i	0.187185	+	0.112778i
$241$	0.541486	−	0.541486i	0.0348802	−	0.0348802i	−0.689452	−	0.724332i	$-0.742148\pi$
$241$	0.541486	−	0.541486i	0.0348802	−	0.0348802i	0.724332	+	0.689452i	$0.242148\pi$
$242$	0.409777	−	1.52931i	0.0263415	−	0.0983077i
$243$	12.0013	−	9.94826i	0.769886	−	0.638181i
$244$	9.71509	−	5.60901i	0.621945	−	0.359080i
$245$	−0.656653	+	13.6666i	−0.0419520	+	0.873128i
$246$	−3.07638	+	10.6802i	−0.196143	+	0.680946i
$247$	18.4565	+	12.0966i	1.17436	+	0.769687i
$248$	0.720539	−	0.416003i	0.0457543	−	0.0264162i
$249$	−0.0392775	+	2.10546i	−0.00248911	+	0.133428i
$250$	12.0785			0.763911
$251$	−4.20343	+	7.28055i	−0.265318	+	0.459544i	−0.967647	−	0.252308i	$-0.918810\pi$
$251$	−4.20343	+	7.28055i	−0.265318	+	0.459544i	0.702329	+	0.711853i	$0.252144\pi$
$252$	7.79108	+	1.51625i	0.490792	+	0.0955149i
$253$	22.7661	−	6.10016i	1.43129	−	0.383514i
$254$	−3.31786	+	12.3824i	−0.208181	+	0.776943i
$255$	7.35435	+	4.43096i	0.460548	+	0.277477i
$256$	1.00000			0.0625000
$257$	6.24911			0.389808			0.194904	−	0.980822i	$-0.437560\pi$
$257$	6.24911			0.389808			0.194904	+	0.980822i	$0.437560\pi$
$258$	4.56816	−	7.58207i	0.284401	−	0.472039i
$259$	11.8004	−	8.61279i	0.733244	−	0.535173i
$260$	−0.398463	+	7.03623i	−0.0247117	+	0.436368i
$261$	12.6473	+	23.9243i	0.782845	+	1.48088i
$262$	−5.34200	+	1.43138i	−0.330030	+	0.0884312i
$263$	−25.7211	−	14.8501i	−1.58603	−	0.915695i	−0.993952	−	0.109815i	$-0.964974\pi$
$263$	−25.7211	−	14.8501i	−1.58603	−	0.915695i	−0.592078	−	0.805880i	$-0.701692\pi$
$264$	−5.96336	+	1.47924i	−0.367019	+	0.0910407i
$265$	7.77669	+	7.77669i	0.477718	+	0.477718i
$266$	5.83593	+	15.1049i	0.357824	+	0.926138i
$267$	−4.88164	−	0.0910675i	−0.298751	−	0.00557324i
$268$	−3.08307	−	11.5062i	−0.188328	−	0.702851i
$269$		−	24.7830i		−	1.51105i	−0.655121	−	0.755524i	$-0.727382\pi$
$269$		−	24.7830i		−	1.51105i	0.655121	−	0.755524i	$-0.272618\pi$
$270$	2.07589	+	9.94212i	0.126335	+	0.605058i
$271$	−18.8800	+	18.8800i	−1.14688	+	1.14688i	−0.159712	+	0.987164i	$0.551056\pi$
$271$	−18.8800	+	18.8800i	−1.14688	+	1.14688i	−0.987164	+	0.159712i	$0.948944\pi$
$272$	2.53611			0.153774
$273$	4.77963	+	15.8163i	0.289276	+	0.957246i
$274$	12.5863			0.760369
$275$	−2.95841	+	2.95841i	−0.178399	+	0.178399i
$276$	−7.98437	−	8.28793i	−0.480602	−	0.498875i
$277$			12.7942i			0.768728i	0.923182	+	0.384364i	$0.125579\pi$
$277$			12.7942i			0.768728i	−0.923182	+	0.384364i	$0.874421\pi$
$278$	2.64605	+	9.87518i	0.158699	+	0.592274i
$279$	2.38520	+	0.735491i	0.142798	+	0.0440327i
$280$	−3.24575	+	4.02604i	−0.193971	+	0.240602i
$281$	6.25598	+	6.25598i	0.373200	+	0.373200i	0.868641	−	0.495441i	$-0.164994\pi$
$281$	6.25598	+	6.25598i	0.373200	+	0.373200i	−0.495441	+	0.868641i	$0.664994\pi$
$282$	−4.80804	−	19.3830i	−0.286315	−	1.15424i
$283$	−11.8593	−	6.84695i	−0.704961	−	0.407009i	0.104232	−	0.994553i	$-0.466762\pi$
$283$	−11.8593	−	6.84695i	−0.704961	−	0.407009i	−0.809192	+	0.587544i	$0.800095\pi$
$284$	5.69106	−	1.52491i	0.337702	−	0.0904870i
$285$	−14.9225	+	14.3759i	−0.883930	+	0.851554i
$286$	−8.51804	−	9.54072i	−0.503683	−	0.564154i
$287$	−15.5248	−	6.87168i	−0.916401	−	0.405623i
$288$	2.04072	+	2.19896i	0.120251	+	0.129575i
$289$	−10.5681			−0.621655
$290$	−17.6317			−1.03537
$291$	−6.43494	+	10.6805i	−0.377223	+	0.626102i
$292$	−2.77643	+	10.3618i	−0.162478	+	0.606377i
$293$	−4.43762	+	1.18906i	−0.259249	+	0.0694655i	−0.386102	−	0.922456i	$-0.626179\pi$
$293$	−4.43762	+	1.18906i	−0.259249	+	0.0694655i	0.126854	+	0.991921i	$0.459512\pi$
$294$	−3.91118	+	11.4762i	−0.228105	+	0.669304i
$295$	−9.89858	+	17.1448i	−0.576318	+	0.998211i
$296$	5.52178			0.320947
$297$	−15.4224	−	10.0945i	−0.894896	−	0.585742i
$298$	−18.3088	+	10.5706i	−1.06060	+	0.612337i
$299$	7.49877	−	22.7525i	0.433665	−	1.31581i
$300$	1.96304	+	0.565442i	0.113336	+	0.0326458i
$301$	10.5266	+	8.48647i	0.606745	+	0.489152i
$302$	2.06609	−	1.19286i	0.118890	−	0.0686412i
$303$	2.26665	+	9.13772i	0.130216	+	0.524948i
$304$	−1.58408	+	5.91185i	−0.0908529	+	0.339068i
$305$	−15.5047	+	15.5047i	−0.887799	+	0.887799i
$306$	5.17551	+	5.57682i	0.295864	+	0.318805i
$307$	−5.42627	+	5.42627i	−0.309694	+	0.309694i	−0.844791	−	0.535097i	$-0.820275\pi$
$307$	−5.42627	+	5.42627i	−0.309694	+	0.309694i	0.535097	+	0.844791i	$0.320275\pi$
$308$	−1.00132	−	9.33168i	−0.0570554	−	0.531722i
$309$	20.4552	−	5.07400i	1.16366	−	0.288650i
$310$	−1.14994	+	1.14994i	−0.0653122	+	0.0653122i
$311$	−7.38492	−	12.7911i	−0.418760	−	0.725314i	0.577055	−	0.816705i	$-0.304202\pi$
$311$	−7.38492	−	12.7911i	−0.418760	−	0.725314i	−0.995815	+	0.0913914i	$0.970869\pi$
$312$	−2.06509	+	5.89368i	−0.116912	+	0.333664i
$313$	−9.11510	+	15.7878i	−0.515216	+	0.892380i	0.484628	+	0.874720i	$0.338955\pi$
$313$	−9.11510	+	15.7878i	−0.515216	+	0.892380i	−0.999844	+	0.0176598i	$0.994378\pi$
$314$	10.5715	+	2.83262i	0.596583	+	0.159854i
$315$	−15.4768	+	1.07875i	−0.872019	+	0.0607804i
$316$	−10.2261	−	5.90403i	−0.575262	−	0.332128i
$317$	−6.53071	−	24.3729i	−0.366801	−	1.36892i	−0.864963	−	0.501836i	$-0.832658\pi$
$317$	−6.53071	−	24.3729i	−0.366801	−	1.36892i	0.498162	−	0.867084i	$-0.334009\pi$
$318$	4.71451	+	8.52932i	0.264377	+	0.478301i
$319$	22.6263	−	22.6263i	1.26683	−	1.26683i
$320$	−1.88802	+	0.505894i	−0.105544	+	0.0282803i
$321$	−8.51734	−	8.84117i	−0.475392	−	0.493466i
$322$	14.1993	−	10.3637i	0.791297	−	0.577544i
$323$	−4.01739	+	14.9931i	−0.223534	+	0.834239i
$324$	−0.670883	+	8.97496i	−0.0372713	+	0.498609i
$325$	0.866632	+	4.16329i	0.0480721	+	0.230938i
$326$	17.6886	−	10.2125i	0.979681	−	0.565619i
$327$	6.92244	+	12.5238i	0.382812	+	0.692569i
$328$	−3.20847	−	5.55723i	−0.177158	−	0.306847i
$329$	30.3313	−	3.25464i	1.67222	−	0.179434i
$330$	10.5106	−	5.80966i	0.578591	−	0.319811i
$331$	5.03732	−	18.7996i	0.276876	−	1.03332i	−0.677697	−	0.735341i	$-0.737022\pi$
$331$	5.03732	−	18.7996i	0.276876	−	1.03332i	0.954573	−	0.297976i	$-0.0963114\pi$
$332$	−0.859699	−	0.859699i	−0.0471821	−	0.0471821i
$333$	11.2684	+	12.1422i	0.617507	+	0.665388i
$334$	−1.35237	−	2.34237i	−0.0739982	−	0.128169i
$335$	11.6418	+	20.1642i	0.636060	+	1.10169i
$336$	−3.75126	+	2.63212i	−0.204648	+	0.143594i
$337$		−	4.64457i		−	0.253006i	−0.991966	−	0.126503i	$-0.959625\pi$
$337$		−	4.64457i		−	0.253006i	0.991966	−	0.126503i	$-0.0403753\pi$
$338$	−12.8566	+	1.92547i	−0.699308	+	0.104732i
$339$	18.3604	−	4.55438i	0.997201	−	0.247360i
$340$	−4.78824	+	1.28300i	−0.259679	+	0.0695807i
$341$		−	2.95137i		−	0.159826i
$342$	−16.2326	+	8.58113i	−0.877759	+	0.464015i
$343$	−16.5562	−	8.30020i	−0.893949	−	0.448169i
$344$	1.32273	+	4.93650i	0.0713168	+	0.266158i
$345$	19.2675	+	11.6086i	1.03733	+	0.624983i
$346$	8.28899	+	2.22103i	0.445619	+	0.119403i
$347$			16.2364i			0.871618i	0.900039	+	0.435809i	$0.143538\pi$
$347$			16.2364i			0.871618i	−0.900039	+	0.435809i	$0.856462\pi$
$348$	−15.0136	−	4.32457i	−0.804811	−	0.231821i
$349$	8.30463	+	2.22522i	0.444536	+	0.119113i	0.474142	−	0.880448i	$-0.342758\pi$
$349$	8.30463	+	2.22522i	0.444536	+	0.119113i	−0.0296054	+	0.999562i	$0.509425\pi$
$350$	−1.26302	+	2.85348i	−0.0675114	+	0.152525i
$351$	−17.1743	+	7.48633i	−0.916694	+	0.399590i
$352$	1.77364	−	3.07204i	0.0945356	−	0.163740i
$353$	−7.15637	−	26.7079i	−0.380895	−	1.42152i	−0.844537	−	0.535497i	$-0.820124\pi$
$353$	−7.15637	−	26.7079i	−0.380895	−	1.42152i	0.463642	−	0.886023i	$-0.346542\pi$
$354$	−12.6339	+	12.1711i	−0.671483	+	0.646889i
$355$	−9.97340	+	5.75814i	−0.529333	+	0.305611i
$356$	1.99327	−	1.99327i	0.105643	−	0.105643i
$357$	−9.51362	+	6.67534i	−0.503514	+	0.353296i
$358$	−0.528149	−	1.97108i	−0.0279135	−	0.104175i
$359$	6.30441	−	1.68926i	0.332734	−	0.0891558i	−0.0885842	−	0.996069i	$-0.528234\pi$
$359$	6.30441	−	1.68926i	0.332734	−	0.0891558i	0.421318	+	0.906913i	$0.361568\pi$
$360$	−4.96538	−	3.11930i	−0.261698	−	0.164402i
$361$	−15.9862	−	9.22963i	−0.841378	−	0.485770i
$362$	−2.67067	−	2.67067i	−0.140367	−	0.140367i
$363$	−0.759037	+	2.63514i	−0.0398391	+	0.138309i
$364$	−8.49083	−	4.34809i	−0.445040	−	0.227902i
$365$		−	20.9679i		−	1.09751i
$366$	−17.0053	+	9.39954i	−0.888882	+	0.491322i
$367$	−8.87685	+	15.3751i	−0.463368	+	0.802576i	−0.999126	−	0.0417949i	$-0.986692\pi$
$367$	−8.87685	+	15.3751i	−0.463368	+	0.802576i	0.535759	+	0.844371i	$0.320026\pi$
$368$	6.64429			0.346358
$369$	5.67255	−	18.3961i	0.295301	−	0.957662i
$370$	−10.4252	+	2.79344i	−0.541983	+	0.145224i
$371$	−13.8862	+	5.36508i	−0.720936	+	0.278541i
$372$	−1.26123	+	0.697136i	−0.0653918	+	0.0361448i
$373$	−7.91561	−	13.7102i	−0.409855	−	0.709889i	0.585018	−	0.811020i	$-0.301087\pi$
$373$	−7.91561	−	13.7102i	−0.409855	−	0.709889i	−0.994873	+	0.101131i	$0.967754\pi$
$374$	4.49816	−	7.79104i	0.232594	−	0.402865i
$375$	−20.9169	−	0.390208i	−1.08015	−	0.0201502i
$376$	9.98523	+	5.76497i	0.514949	+	0.297306i
$377$	−6.62811	−	31.8414i	−0.341365	−	1.63991i
$378$	−13.4432	−	2.87747i	−0.691445	−	0.148001i
$379$	−1.80495	+	6.73617i	−0.0927141	+	0.346014i	−0.996663	−	0.0816269i	$-0.973988\pi$
$379$	−1.80495	+	6.73617i	−0.0927141	+	0.346014i	0.903949	+	0.427641i	$0.140655\pi$
$380$		−	11.9631i		−	0.613693i
$381$	6.14574	−	21.3361i	0.314856	−	1.09308i
$382$	−2.56270	+	9.56413i	−0.131119	+	0.489344i
$383$	32.4182	+	8.68644i	1.65649	+	0.443856i	0.961421	−	0.275082i	$-0.0887049\pi$
$383$	32.4182	+	8.68644i	1.65649	+	0.443856i	0.695074	+	0.718938i	$0.255372\pi$
$384$	−1.73175	−	0.0323060i	−0.0883730	−	0.00164861i
$385$	6.61135	+	17.1119i	0.336946	+	0.872101i
$386$	3.38008	+	1.95149i	0.172042	+	0.0993284i
$387$	−8.15585	+	12.9827i	−0.414585	+	0.659946i
$388$	−1.86327	−	6.95381i	−0.0945930	−	0.353026i
$389$	−15.1589	−	26.2560i	−0.768587	−	1.33123i	−0.938329	−	0.345743i	$-0.887627\pi$
$389$	−15.1589	−	26.2560i	−0.768587	−	1.33123i	0.169743	−	0.985488i	$-0.445706\pi$
$390$	0.917351	−	12.1721i	0.0464519	−	0.616359i
$391$	16.8507			0.852175
$392$	−3.20503	−	6.22317i	−0.161878	−	0.314317i
$393$	9.29724	−	2.30622i	0.468984	−	0.116333i
$394$	−4.16633	+	2.40543i	−0.209897	+	0.121184i
$395$	22.2939	+	5.97363i	1.12173	+	0.300566i
$396$	10.3748	−	2.36901i	0.521355	−	0.119047i
$397$	−17.2557	−	4.62365i	−0.866039	−	0.232055i	−0.201665	−	0.979455i	$-0.564635\pi$
$397$	−17.2557	−	4.62365i	−0.866039	−	0.232055i	−0.664374	+	0.747400i	$0.731302\pi$
$398$	6.21129	+	6.21129i	0.311344	+	0.311344i
$399$	−9.61839	−	26.3464i	−0.481522	−	1.31897i
$400$	−1.02143	+	0.589721i	−0.0510713	+	0.0294860i
$401$	0.697848	+	0.697848i	0.0348489	+	0.0348489i	0.724316	−	0.689468i	$-0.242155\pi$
$401$	0.697848	+	0.697848i	0.0348489	+	0.0348489i	−0.689468	+	0.724316i	$0.742155\pi$
$402$	4.96738	+	20.0254i	0.247751	+	0.998776i
$403$	−2.50898	−	1.64441i	−0.124981	−	0.0819138i
$404$	−4.70732	−	2.71777i	−0.234198	−	0.135214i
$405$	−3.27374	−	17.2843i	−0.162673	−	0.858865i
$406$	9.65976	−	21.8238i	0.479406	−	1.08309i
$407$	9.79368	−	16.9631i	0.485455	−	0.840832i
$408$	−4.39191	−	0.0819316i	−0.217432	−	0.00405622i
$409$	−4.54898	−	4.54898i	−0.224932	−	0.224932i	0.585639	−	0.810572i	$-0.300844\pi$
$409$	−4.54898	−	4.54898i	−0.224932	−	0.224932i	−0.810572	+	0.585639i	$0.800844\pi$
$410$	8.86904	+	8.86904i	0.438010	+	0.438010i
$411$	−21.7964	−	0.406614i	−1.07514	−	0.0200568i
$412$	−6.08387	+	10.5376i	−0.299731	+	0.519149i
$413$	−15.7981	−	21.6450i	−0.777372	−	1.06508i
$414$	13.5592	+	14.6106i	0.666397	+	0.718070i
$415$	2.05805	+	1.18821i	0.101026	+	0.0583271i
$416$	−1.62335	−	3.21943i	−0.0795911	−	0.157846i
$417$	−4.26326	−	17.1868i	−0.208773	−	0.841642i
$418$	15.3519	+	15.3519i	0.750884	+	0.750884i
$419$	4.14630	−	2.39387i	0.202560	−	0.116948i	−0.395289	−	0.918557i	$-0.629356\pi$
$419$	4.14630	−	2.39387i	0.202560	−	0.116948i	0.597849	+	0.801609i	$0.296022\pi$
$420$	5.75090	−	6.86724i	0.280615	−	0.335087i
$421$	−0.472730	−	0.472730i	−0.0230395	−	0.0230395i	0.695493	−	0.718533i	$-0.255186\pi$
$421$	−0.472730	−	0.472730i	−0.0230395	−	0.0230395i	−0.718533	+	0.695493i	$0.755186\pi$
$422$	−16.6725	−	4.46739i	−0.811606	−	0.217469i
$423$	7.70013	+	33.7219i	0.374393	+	1.63961i
$424$	−5.43488	−	1.45627i	−0.263941	−	0.0707228i
$425$	−2.59045	+	1.49560i	−0.125655	+	0.0725471i
$426$	−9.90475	+	2.45691i	−0.479887	+	0.119038i
$427$	−10.6966	−	27.6856i	−0.517646	−	1.33980i
$428$	7.08782			0.342602
$429$	14.4429	+	16.7973i	0.697310	+	0.810982i
$430$	−4.99469	−	8.65106i	−0.240865	−	0.417191i
$431$	−1.02355	−	3.81994i	−0.0493027	−	0.184000i	0.936883	−	0.349643i	$-0.113697\pi$
$431$	−1.02355	−	3.81994i	−0.0493027	−	0.184000i	−0.986186	+	0.165642i	$0.947030\pi$
$432$	−3.46298	−	3.87398i	−0.166613	−	0.186387i
$433$	19.3037	+	11.1450i	0.927677	+	0.535595i	0.886076	−	0.463540i	$-0.153421\pi$
$433$	19.3037	+	11.1450i	0.927677	+	0.535595i	0.0416011	+	0.999134i	$0.486754\pi$
$434$	−0.793336	−	2.05335i	−0.0380813	−	0.0985642i
$435$	30.5337	+	0.569610i	1.46398	+	0.0273107i
$436$	−7.98018	−	2.13828i	−0.382181	−	0.102405i
$437$	−10.5251	+	39.2801i	−0.503482	+	1.87902i
$438$	5.14283	−	17.8543i	0.245734	−	0.853112i
$439$			15.3657i			0.733364i	0.930346	+	0.366682i	$0.119506\pi$
$439$			15.3657i			0.733364i	−0.930346	+	0.366682i	$0.880494\pi$
$440$	−1.79455	+	6.69736i	−0.0855519	+	0.319284i
$441$	7.14394	−	19.7475i	0.340188	−	0.940358i
$442$	−4.11699	−	8.16484i	−0.195825	−	0.388362i
$443$	−21.4724	−	12.3971i	−1.02018	−	0.589004i	−0.106027	−	0.994363i	$-0.533813\pi$
$443$	−21.4724	−	12.3971i	−1.02018	−	0.589004i	−0.914157	+	0.405359i	$0.867146\pi$
$444$	−9.56234	−	0.178387i	−0.453809	−	0.00846585i
$445$	−2.75495	+	4.77171i	−0.130597	+	0.226201i
$446$	7.73239	+	13.3929i	0.366139	+	0.634172i
$447$	32.0477	−	17.7141i	1.51580	−	0.837849i
$448$	0.408204	−	2.61407i	0.0192858	−	0.123503i
$449$	25.1155	−	6.72968i	1.18527	−	0.317593i	0.388257	−	0.921551i	$-0.373077\pi$
$449$	25.1155	−	6.72968i	1.18527	−	0.317593i	0.797016	+	0.603958i	$0.206411\pi$
$450$	−3.38122	−	1.04262i	−0.159392	−	0.0491496i
$451$	−22.7627			−1.07186
$452$	−5.46082	+	9.45842i	−0.256855	+	0.444887i
$453$	−3.61648	+	1.99898i	−0.169917	+	0.0939204i
$454$			19.4382i			0.912278i
$455$	18.2305	+	3.91383i	0.854661	+	0.183483i
$456$	2.93421	−	10.1867i	0.137407	−	0.477034i
$457$	−12.5689	−	12.5689i	−0.587946	−	0.587946i	0.349128	−	0.937075i	$-0.386478\pi$
$457$	−12.5689	−	12.5689i	−0.587946	−	0.587946i	−0.937075	+	0.349128i	$0.886478\pi$
$458$	−4.62763	−	2.67177i	−0.216235	−	0.124843i
$459$	−8.78251	−	9.82485i	−0.409933	−	0.458585i
$460$	−12.5446	+	3.36131i	−0.584894	+	0.156722i
$461$	7.94677	+	29.6577i	0.370118	+	1.38130i	0.860349	+	0.509706i	$0.170246\pi$
$461$	7.94677	+	29.6577i	0.370118	+	1.38130i	−0.490231	+	0.871593i	$0.663088\pi$
$462$	1.43256	+	16.1925i	0.0666489	+	0.753342i
$463$	4.70860	−	4.70860i	0.218827	−	0.218827i	−0.589177	−	0.808004i	$-0.700548\pi$
$463$	4.70860	−	4.70860i	0.218827	−	0.218827i	0.808004	+	0.589177i	$0.200548\pi$
$464$	7.81199	−	4.51025i	0.362663	−	0.209383i
$465$	2.02856	−	1.95426i	0.0940721	−	0.0906266i
$466$	1.38353	+	5.16340i	0.0640908	+	0.239190i
$467$	−12.7798	+	22.1352i	−0.591377	+	1.02430i	0.402670	+	0.915345i	$0.368082\pi$
$467$	−12.7798	+	22.1352i	−0.591377	+	1.02430i	−0.994047	+	0.108950i	$0.965251\pi$
$468$	3.76661	−	10.1397i	0.174112	−	0.468706i
$469$	−31.3365	+	3.36250i	−1.44698	+	0.155266i
$470$	−21.7688	−	5.83293i	−1.00412	−	0.269053i
$471$	−18.2156	−	5.24691i	−0.839332	−	0.241765i
$472$		−	10.1284i		−	0.466196i
$473$	17.5112	+	4.69211i	0.805165	+	0.215743i
$474$	17.5183	+	10.5547i	0.804641	+	0.484792i
$475$	−1.86832	−	6.97268i	−0.0857245	−	0.319928i
$476$	1.03525	−	6.62958i	0.0474506	−	0.303866i
$477$	−7.88881	−	14.9230i	−0.361204	−	0.683275i
$478$		−	2.51448i		−	0.115009i
$479$	8.13879	−	2.18078i	0.371871	−	0.0996425i	−0.0680431	−	0.997682i	$-0.521676\pi$
$479$	8.13879	−	2.18078i	0.371871	−	0.0996425i	0.439914	+	0.898040i	$0.355009\pi$
$480$	3.28593	−	0.815088i	0.149981	−	0.0372035i
$481$	−8.96377	−	17.7770i	−0.408713	−	0.810562i
$482$		−	0.765776i		−	0.0348802i
$483$	−24.9245	+	17.4885i	−1.13410	+	0.795756i
$484$	−0.791629	−	1.37114i	−0.0359831	−	0.0623246i
$485$	7.03578	+	12.1863i	0.319478	+	0.553353i
$486$	1.45175	−	15.5207i	0.0658526	−	0.704034i
$487$	13.3275	+	13.3275i	0.603927	+	0.603927i	0.941352	−	0.337425i	$-0.109556\pi$
$487$	13.3275	+	13.3275i	0.603927	+	0.603927i	−0.337425	+	0.941352i	$0.609556\pi$
$488$	2.90344	−	10.8358i	0.131432	−	0.490512i
$489$	−30.9622	+	17.1141i	−1.40016	+	0.773925i
$490$	9.19943	+	10.1281i	0.415588	+	0.457540i
$491$	7.87704	+	13.6434i	0.355486	+	0.615719i	0.987201	−	0.159481i	$-0.0509822\pi$
$491$	7.87704	+	13.6434i	0.355486	+	0.615719i	−0.631715	+	0.775200i	$0.717649\pi$
$492$	5.37673	+	9.72739i	0.242402	+	0.438545i
$493$	19.8121	−	11.4385i	0.892291	−	0.515165i
$494$	21.6043	−	4.49716i	0.972023	−	0.202337i
$495$	−18.3894	+	9.72132i	−0.826544	+	0.436941i
$496$	0.215339	−	0.803657i	0.00966901	−	0.0360853i
$497$	−1.66312	−	15.4993i	−0.0746013	−	0.695239i
$498$	1.46101	+	1.51656i	0.0654694	+	0.0679585i
$499$	12.3274	−	3.30313i	0.551852	−	0.147868i	0.0278916	−	0.999611i	$-0.491121\pi$
$499$	12.3274	−	3.30313i	0.551852	−	0.147868i	0.523960	+	0.851743i	$0.324454\pi$
$500$	8.54078	−	8.54078i	0.381955	−	0.381955i
$501$	2.26629	+	4.10009i	0.101250	+	0.183178i
$502$	2.17585	+	8.12040i	0.0971131	+	0.362431i
$503$	16.2100	+	9.35887i	0.722770	+	0.417291i	0.815771	−	0.578374i	$-0.196313\pi$
$503$	16.2100	+	9.35887i	0.722770	+	0.417291i	−0.0930013	+	0.995666i	$0.529646\pi$
$504$	6.58128	−	4.43698i	0.293154	−	0.197639i
$505$	10.2624	+	2.74981i	0.456673	+	0.122365i
$506$	11.7846	−	20.4115i	0.523890	−	0.907404i
$507$	22.3266	−	2.91908i	0.991561	−	0.129641i
$508$	6.40962	+	11.1018i	0.284381	+	0.492562i
$509$	1.70504	−	1.70504i	0.0755745	−	0.0755745i	−0.668309	−	0.743884i	$-0.732982\pi$
$509$	1.70504	−	1.70504i	0.0755745	−	0.0755745i	0.743884	+	0.668309i	$0.232982\pi$
$510$	8.33347	−	2.06715i	0.369012	−	0.0915351i
$511$	25.9531	+	11.4875i	1.14810	+	0.508177i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	28.3880	−	14.3360i	1.25336	−	0.632948i
$514$	4.41878	−	4.41878i	0.194904	−	0.194904i
$515$	6.15558	−	22.9730i	0.271247	−	1.01231i
$516$	−2.13116	−	8.59151i	−0.0938191	−	0.378220i
$517$	35.4205	−	20.4500i	1.55779	−	0.899391i
$518$	2.25401	−	14.4343i	0.0990356	−	0.634208i
$519$	−14.2827	−	4.11405i	−0.626941	−	0.180587i
$520$	4.69361	+	5.25712i	0.205828	+	0.230540i
$521$	−26.5738	+	15.3424i	−1.16422	+	0.672163i	−0.952312	−	0.305126i	$-0.901301\pi$
$521$	−26.5738	+	15.3424i	−1.16422	+	0.672163i	−0.211909	+	0.977289i	$0.567968\pi$
$522$	25.8600	+	7.97409i	1.13186	+	0.349017i
$523$	17.4701			0.763914			0.381957	−	0.924180i	$-0.375250\pi$
$523$	17.4701			0.763914			0.381957	+	0.924180i	$0.375250\pi$
$524$	−2.76522	+	4.78950i	−0.120799	+	0.209230i
$525$	2.27942	−	4.90071i	0.0994822	−	0.213884i
$526$	−28.6882	+	7.68697i	−1.25086	+	0.335168i
$527$	0.546124	−	2.03816i	0.0237895	−	0.0887838i
$528$	−3.17075	+	5.26271i	−0.137989	+	0.229030i
$529$	21.1466			0.919418
$530$	10.9979			0.477718
$531$	22.2719	−	20.6692i	0.966519	−	0.896967i
$532$	14.8074	+	6.55412i	0.641981	+	0.284157i
$533$	−12.6827	+	19.3508i	−0.549348	+	0.838175i
$534$	−3.51623	+	3.38744i	−0.152162	+	0.146589i
$535$	−13.3820	+	3.58568i	−0.578552	+	0.155023i
$536$	−10.3161	−	5.95603i	−0.445590	−	0.257261i
$537$	0.850944	+	3.43048i	0.0367209	+	0.148036i
$538$	−17.5242	−	17.5242i	−0.755524	−	0.755524i
$539$	−24.8024	−	1.19171i	−1.06832	−	0.0513304i
$540$	8.49802	+	5.56226i	0.365697	+	0.239362i
$541$	3.26775	+	12.1954i	0.140492	+	0.524322i	0.999915	+	0.0130571i	$0.00415634\pi$
$541$	3.26775	+	12.1954i	0.140492	+	0.524322i	−0.859423	+	0.511265i	$0.829177\pi$
$542$			26.7003i			1.14688i
$543$	4.53864	+	4.71120i	0.194772	+	0.202177i
$544$	1.79330	−	1.79330i	0.0768872	−	0.0768872i
$545$	16.1485			0.691726
$546$	14.5635	+	7.80410i	0.623261	+	0.333985i
$547$	3.08215			0.131783			0.0658917	−	0.997827i	$-0.479011\pi$
$547$	3.08215			0.131783			0.0658917	+	0.997827i	$0.479011\pi$
$548$	8.89989	−	8.89989i	0.380184	−	0.380184i
$549$	29.7526	−	15.7283i	1.26981	−	0.671267i
$550$			4.18382i			0.178399i
$551$	14.2892	+	53.3279i	0.608739	+	2.27184i
$552$	−11.5062	−	0.214650i	−0.489739	−	0.00913613i
$553$	−19.6079	+	24.3217i	−0.833812	+	1.03426i
$554$	9.04685	+	9.04685i	0.384364	+	0.384364i
$555$	18.1442	−	4.50074i	0.770177	−	0.191046i
$556$	8.85384	+	5.11177i	0.375486	+	0.216787i
$557$	42.0608	−	11.2702i	1.78217	−	0.477532i	0.791197	−	0.611561i	$-0.209458\pi$
$557$	42.0608	−	11.2702i	1.78217	−	0.477532i	0.990977	+	0.134029i	$0.0427915\pi$
$558$	2.20666	−	1.16652i	0.0934154	−	0.0493827i
$559$	13.7455	−	12.2721i	0.581371	−	0.519054i
$560$	0.551746	+	5.14193i	0.0233155	+	0.217286i
$561$	−8.04138	+	13.3468i	−0.339507	+	0.563503i
$562$	8.84729			0.373200
$563$	4.78291			0.201576			0.100788	−	0.994908i	$-0.467864\pi$
$563$	4.78291			0.201576			0.100788	+	0.994908i	$0.467864\pi$
$564$	−17.1057	−	10.3061i	−0.720278	−	0.433964i
$565$	5.52520	−	20.6203i	0.232447	−	0.867503i
$566$	−13.2273	+	3.54424i	−0.555985	+	0.148976i
$567$	23.1873	+	5.41735i	0.973776	+	0.227507i
$568$	2.94591	−	5.10246i	0.123608	−	0.214094i
$569$	33.1751			1.39077			0.695386	−	0.718637i	$-0.255234\pi$
$569$	33.1751			1.39077			0.695386	+	0.718637i	$0.255234\pi$
$570$	−0.386479	+	20.7171i	−0.0161878	+	0.867742i
$571$	6.52137	−	3.76512i	0.272911	−	0.157565i	−0.357299	−	0.933990i	$-0.616302\pi$
$571$	6.52137	−	3.76512i	0.272911	−	0.157565i	0.630210	+	0.776425i	$0.282969\pi$
$572$	−12.7695	−	0.723139i	−0.533918	−	0.0302359i
$573$	4.74694	−	16.4799i	0.198306	−	0.688457i
$574$	−15.8367	+	6.11869i	−0.661012	+	0.255389i
$575$	−6.78665	+	3.91828i	−0.283023	+	0.163403i
$576$	2.99791	+	0.111892i	0.124913	+	0.00466216i
$577$	3.71436	−	13.8622i	0.154631	−	0.577090i	−0.844506	−	0.535546i	$-0.820106\pi$
$577$	3.71436	−	13.8622i	0.154631	−	0.577090i	0.999137	−	0.0415436i	$-0.0132275\pi$
$578$	−7.47280	+	7.47280i	−0.310828	+	0.310828i
$579$	−5.79042	−	3.48869i	−0.240641	−	0.144985i
$580$	−12.4675	+	12.4675i	−0.517685	+	0.517685i
$581$	−2.59825	+	1.89638i	−0.107793	+	0.0786752i
$582$	3.00206	+	12.1024i	0.124439	+	0.501663i
$583$	−14.1133	+	14.1133i	−0.584512	+	0.584512i
$584$	5.36365	+	9.29012i	0.221950	+	0.384428i
$585$	−1.98185	+	21.0494i	−0.0819396	+	0.870286i
$586$	−2.29708	+	3.97867i	−0.0948916	+	0.164357i
$587$	−34.5575	−	9.25966i	−1.42634	−	0.382187i	−0.538612	−	0.842554i	$-0.681051\pi$
$587$	−34.5575	−	9.25966i	−1.42634	−	0.382187i	−0.887729	+	0.460367i	$0.847718\pi$
$588$	5.34926	+	10.8805i	0.220600	+	0.448705i
$589$	4.40998	+	2.54611i	0.181710	+	0.104910i
$590$	5.12388	+	19.1226i	0.210947	+	0.787264i
$591$	7.29276	−	4.03101i	0.299984	−	0.165814i
$592$	3.90449	−	3.90449i	0.160474	−	0.160474i
$593$	28.8732	−	7.73655i	1.18568	−	0.317702i	0.388503	−	0.921447i	$-0.372992\pi$
$593$	28.8732	−	7.73655i	1.18568	−	0.317702i	0.797177	+	0.603745i	$0.206326\pi$
$594$	−18.0431	+	3.76737i	−0.740319	+	0.154577i
$595$	1.39929	+	13.0405i	0.0573653	+	0.534609i
$596$	−5.47173	+	20.4208i	−0.224131	+	0.836468i
$597$	−10.5557	−	10.9571i	−0.432017	−	0.448443i
$598$	−10.7860	−	21.3909i	−0.441072	−	0.874737i
$599$	28.4385	−	16.4190i	1.16196	−	0.670861i	0.210191	−	0.977660i	$-0.432591\pi$
$599$	28.4385	−	16.4190i	1.16196	−	0.670861i	0.951774	+	0.306800i	$0.0992581\pi$
$600$	1.78791	−	0.988250i	0.0729909	−	0.0403451i
$601$	−10.4847	−	18.1600i	−0.427680	−	0.740764i	0.568986	−	0.822347i	$-0.307336\pi$
$601$	−10.4847	−	18.1600i	−0.427680	−	0.740764i	−0.996667	+	0.0815832i	$0.974002\pi$
$602$	13.4443	−	1.44262i	0.547949	−	0.0587966i
$603$	−7.95533	−	34.8395i	−0.323966	−	1.41877i
$604$	0.617468	−	2.30442i	0.0251244	−	0.0937656i
$605$	2.18827	+	2.18827i	0.0889656	+	0.0889656i
$606$	8.06411	+	4.85858i	0.327582	+	0.197366i
$607$	−4.81188	−	8.33441i	−0.195308	−	0.338283i	0.751693	−	0.659513i	$-0.229237\pi$
$607$	−4.81188	−	8.33441i	−0.195308	−	0.338283i	−0.947001	+	0.321229i	$0.895904\pi$
$608$	3.06020	+	5.30042i	0.124107	+	0.214960i
$609$	−17.4333	+	37.4812i	−0.706434	+	1.51882i
$610$			21.9270i			0.887799i
$611$	2.35046	−	41.5053i	0.0950893	−	1.67913i
$612$	7.60304	+	0.283770i	0.307335	+	0.0114707i
$613$	1.84344	−	0.493947i	0.0744557	−	0.0199503i	−0.221399	−	0.975183i	$-0.571062\pi$
$613$	1.84344	−	0.493947i	0.0744557	−	0.0199503i	0.295855	+	0.955233i	$0.404396\pi$
$614$			7.67391i			0.309694i
$615$	−15.0724	−	15.6455i	−0.607779	−	0.630886i
$616$	−7.30653	−	5.89045i	−0.294388	−	0.237333i
$617$	−2.19996	−	8.21036i	−0.0885670	−	0.330536i	0.907399	−	0.420271i	$-0.138065\pi$
$617$	−2.19996	−	8.21036i	−0.0885670	−	0.330536i	−0.995966	+	0.0897342i	$0.971398\pi$
$618$	10.8762	−	18.0519i	0.437503	−	0.726153i
$619$	21.1857	+	5.67669i	0.851524	+	0.228165i	0.658082	−	0.752946i	$-0.271368\pi$
$619$	21.1857	+	5.67669i	0.851524	+	0.228165i	0.193443	+	0.981112i	$0.438035\pi$
$620$			1.62626i			0.0653122i
$621$	−23.0091	−	25.7399i	−0.923323	−	1.03291i
$622$	−14.2666	−	3.82271i	−0.572037	−	0.153277i
$623$	−4.39688	−	6.02420i	−0.176157	−	0.241354i
$624$	2.70722	+	5.62769i	0.108376	+	0.225288i
$625$	−8.85586	+	15.3388i	−0.354234	+	0.613552i
$626$	4.71832	+	17.6090i	0.188582	+	0.703798i
$627$	−26.0896	−	27.0815i	−1.04192	−	1.08153i
$628$	9.47812	−	5.47220i	0.378218	−	0.218364i
$629$	9.90222	−	9.90222i	0.394827	−	0.394827i
$630$	−10.1810	+	11.7065i	−0.405619	+	0.466400i
$631$	1.95596	+	7.29974i	0.0778655	+	0.290598i	0.993868	−	0.110575i	$-0.0352692\pi$
$631$	1.95596	+	7.29974i	0.0778655	+	0.290598i	−0.916002	+	0.401173i	$0.868603\pi$
$632$	−11.4057	+	3.05615i	−0.453695	+	0.121567i
$633$	28.7283	+	8.27502i	1.14185	+	0.328903i
$634$	−21.8522	−	12.6164i	−0.867861	−	0.501060i
$635$	−17.7178	−	17.7178i	−0.703111	−	0.703111i
$636$	9.36481	+	2.69748i	0.371339	+	0.106962i
$637$	−14.8322	+	20.4207i	−0.587673	+	0.809099i
$638$		−	31.9984i		−	1.26683i
$639$	17.2319	−	3.93478i	0.681684	−	0.155657i
$640$	−0.977313	+	1.69275i	−0.0386317	+	0.0669120i
$641$	−7.94978			−0.313997			−0.156999	−	0.987599i	$-0.550182\pi$
$641$	−7.94978			−0.313997			−0.156999	+	0.987599i	$0.550182\pi$
$642$	−12.2743	−	0.228979i	−0.484429	−	0.00903708i
$643$	24.7126	−	6.62172i	0.974570	−	0.261135i	0.263814	−	0.964574i	$-0.415020\pi$
$643$	24.7126	−	6.62172i	0.974570	−	0.261135i	0.710756	+	0.703438i	$0.248353\pi$
$644$	2.71222	−	17.3687i	0.106877	−	0.684421i
$645$	8.37007	+	15.1428i	0.329571	+	0.596248i
$646$	7.76100	+	13.4425i	0.305353	+	0.528886i
$647$	−8.25581	+	14.2995i	−0.324569	+	0.562170i	−0.981425	−	0.191846i	$-0.938553\pi$
$647$	−8.25581	+	14.2995i	−0.324569	+	0.562170i	0.656856	+	0.754016i	$0.271886\pi$
$648$	5.87187	+	6.82064i	0.230669	+	0.267940i
$649$	−31.1148	−	17.9641i	−1.22136	−	0.705153i
$650$	3.55669	+	2.33109i	0.139505	+	0.0914329i
$651$	1.30752	+	3.58152i	0.0512459	+	0.140371i
$652$	5.28639	−	19.7291i	0.207031	−	0.772650i
$653$		−	14.5471i		−	0.569271i	−0.958636	−	0.284635i	$-0.908128\pi$
$653$		−	14.5471i		−	0.569271i	0.958636	−	0.284635i	$-0.0918725\pi$
$654$	13.7506	+	3.96078i	0.537691	+	0.154879i
$655$	2.79782	−	10.4416i	0.109320	−	0.407987i
$656$	−6.19829	−	1.66083i	−0.242002	−	0.0648444i
$657$	−9.48290	+	30.7531i	−0.369963	+	1.19979i
$658$	19.1461	−	23.7488i	0.746391	−	0.925825i
$659$	−22.4966	−	12.9884i	−0.876342	−	0.505956i	−0.00689143	−	0.999976i	$-0.502194\pi$
$659$	−22.4966	−	12.9884i	−0.876342	−	0.505956i	−0.869451	+	0.494020i	$0.835527\pi$
$660$	3.32408	−	11.5402i	0.129390	−	0.449201i
$661$	5.38872	+	20.1110i	0.209597	+	0.782226i	0.987999	+	0.154460i	$0.0493639\pi$
$661$	5.38872	+	20.1110i	0.209597	+	0.782226i	−0.778402	+	0.627766i	$0.783969\pi$
$662$	−9.73136	−	16.8552i	−0.378220	−	0.655097i
$663$	6.86582	+	14.2725i	0.266646	+	0.554296i
$664$	−1.21580			−0.0471821
$665$	−31.2723	−	4.88337i	−1.21269	−	0.189369i
$666$	16.5538	+	0.617842i	0.641447	+	0.0239409i
$667$	51.9051	−	29.9675i	2.00978	−	1.16034i
$668$	−2.61257	−	0.700037i	−0.101083	−	0.0270852i
$669$	−12.9579	−	23.4429i	−0.500981	−	0.906356i
$670$	22.4902	+	6.02624i	0.868874	+	0.232814i
$671$	−28.1383	−	28.1383i	−1.08627	−	1.08627i
$672$	−0.791357	+	4.51373i	−0.0305272	+	0.174121i
$673$	−42.3938	+	24.4761i	−1.63416	+	0.943484i	−0.651372	+	0.758758i	$0.725806\pi$
$673$	−42.3938	+	24.4761i	−1.63416	+	0.943484i	−0.982790	+	0.184726i	$0.940860\pi$
$674$	−3.28421	−	3.28421i	−0.126503	−	0.126503i
$675$	5.82175	+	1.91479i	0.224079	+	0.0737004i
$676$	−7.72949	+	10.4525i	−0.297288	+	0.402020i
$677$	−25.5319	−	14.7409i	−0.981273	−	0.566538i	−0.0786184	−	0.996905i	$-0.525051\pi$
$677$	−25.5319	−	14.7409i	−0.981273	−	0.566538i	−0.902654	+	0.430367i	$0.858384\pi$
$678$	9.76234	−	16.2032i	0.374920	−	0.622280i
$679$	−18.9383	+	2.03214i	−0.726787	+	0.0779865i
$680$	−2.47857	+	4.29302i	−0.0950490	+	0.164630i
$681$	0.627969	−	33.6620i	0.0240638	−	1.28993i
$682$	−2.08693	−	2.08693i	−0.0799128	−	0.0799128i
$683$	28.0663	+	28.0663i	1.07393	+	1.07393i	0.997040	+	0.0768873i	$0.0244982\pi$
$683$	28.0663	+	28.0663i	1.07393	+	1.07393i	0.0768873	+	0.997040i	$0.475502\pi$
$684$	−5.41041	+	17.5460i	−0.206872	+	0.670887i
$685$	−12.3008	+	21.3056i	−0.469989	+	0.814045i
$686$	−17.5761	+	5.83785i	−0.671059	+	0.222890i
$687$	7.92759	+	4.77633i	0.302456	+	0.182228i
$688$	4.42594	+	2.55532i	0.168737	+	0.0974206i
$689$	4.13433	+	19.8613i	0.157505	+	0.756654i
$690$	21.8327	−	5.41568i	0.831155	−	0.206171i
$691$	16.5377	+	16.5377i	0.629122	+	0.629122i	0.947847	−	0.318725i	$-0.103255\pi$
$691$	16.5377	+	16.5377i	0.629122	+	0.629122i	−0.318725	+	0.947847i	$0.603255\pi$
$692$	7.43170	−	4.29069i	0.282511	−	0.163108i
$693$	−1.95773	−	28.0876i	−0.0743679	−	1.06696i
$694$	11.4809	+	11.4809i	0.435809	+	0.435809i
$695$	−19.3023	−	5.17203i	−0.732177	−	0.196186i
$696$	−13.6741	+	7.55826i	−0.518316	+	0.286495i
$697$	−15.7195	−	4.21204i	−0.595420	−	0.159542i
$698$	7.44572	−	4.29879i	0.281825	−	0.162712i
$699$	−2.22912	−	8.98642i	−0.0843130	−	0.339897i
$700$	1.12462	+	2.91081i	0.0425067	+	0.110018i
$701$	−14.3867			−0.543379			−0.271689	−	0.962385i	$-0.587582\pi$
$701$	−14.3867			−0.543379			−0.271689	+	0.962385i	$0.587582\pi$
$702$	−6.85040	+	17.4377i	−0.258552	+	0.658142i
$703$	16.8977	+	29.2678i	0.637311	+	1.10385i
$704$	−0.918106	−	3.42642i	−0.0346024	−	0.129138i
$705$	37.5097	+	10.8044i	1.41270	+	0.406919i
$706$	−23.9457	−	13.8250i	−0.901207	−	0.520312i
$707$	−9.02600	+	11.1959i	−0.339458	+	0.421064i
$708$	−0.327207	+	17.5398i	−0.0122972	+	0.659186i
$709$	−35.3193	−	9.46378i	−1.32644	−	0.355420i	−0.475056	−	0.879955i	$-0.657572\pi$
$709$	−35.3193	−	9.46378i	−1.32644	−	0.355420i	−0.851388	+	0.524536i	$0.824239\pi$
$710$	−2.98063	+	11.1239i	−0.111861	+	0.417472i
$711$	−29.9963	−	18.8440i	−1.12495	−	0.706704i
$712$		−	2.81890i		−	0.105643i
$713$	1.43078	−	5.33973i	0.0535830	−	0.199974i
$714$	−2.00697	+	11.4473i	−0.0751089	+	0.428405i
$715$	24.4749	−	5.09470i	0.915309	−	0.190531i
$716$	−1.76722	−	1.02031i	−0.0660441	−	0.0381306i
$717$	−0.0812326	+	4.35444i	−0.00303369	+	0.162620i
$718$	3.26340	−	5.65238i	0.121789	−	0.210945i
$719$	−9.58652	−	16.6043i	−0.357517	−	0.619238i	0.630028	−	0.776572i	$-0.283043\pi$
$719$	−9.58652	−	16.6043i	−0.357517	−	0.619238i	−0.987545	+	0.157334i	$0.949710\pi$
$720$	−5.71673	+	1.30537i	−0.213050	+	0.0486484i
$721$	25.0625	+	20.2051i	0.933376	+	0.752478i
$722$	−17.8303	+	4.77761i	−0.663574	+	0.177804i
$723$	−0.0247392	+	1.32613i	−0.000920059	+	0.0493194i
$724$	−3.77689			−0.140367
$725$	−5.31958	+	9.21378i	−0.197564	+	0.342191i
$726$	1.32661	+	2.40005i	0.0492350	+	0.0890741i
$727$		−	50.2236i		−	1.86269i	−0.364138	−	0.931345i	$-0.618636\pi$
$727$		−	50.2236i		−	1.86269i	0.364138	−	0.931345i	$-0.381364\pi$
$728$	−9.07848	+	2.92936i	−0.336471	+	0.108569i
$729$	−3.01547	+	26.8311i	−0.111684	+	0.993744i
$730$	−14.8265	−	14.8265i	−0.548754	−	0.548754i
$731$	11.2247	+	6.48057i	0.415160	+	0.239693i
$732$	−5.37809	+	18.6710i	−0.198780	+	0.690102i
$733$	28.7300	−	7.69817i	1.06117	−	0.284338i	0.314307	−	0.949321i	$-0.398228\pi$
$733$	28.7300	−	7.69817i	1.06117	−	0.284338i	0.746858	+	0.664983i	$0.231561\pi$
$734$	4.59499	+	17.1488i	0.169604	+	0.632972i
$735$	−15.6039	−	17.8365i	−0.575559	−	0.657909i
$736$	4.69822	−	4.69822i	0.173179	−	0.173179i
$737$	−36.5944	+	21.1278i	−1.34797	+	0.778251i
$738$	−8.99690	−	17.0191i	−0.331181	−	0.626482i
$739$	5.59057	+	20.8643i	0.205653	+	0.767506i	0.989250	+	0.146236i	$0.0467160\pi$
$739$	5.59057	+	20.8643i	0.205653	+	0.767506i	−0.783597	+	0.621269i	$0.786617\pi$
$740$	−5.39651	+	9.34702i	−0.198380	+	0.343603i
$741$	−37.5585	+	7.09000i	−1.37975	+	0.260458i
$742$	−6.02534	+	13.6127i	−0.221197	+	0.499738i
$743$	35.6490	+	9.55213i	1.30784	+	0.350434i	0.844408	−	0.535701i	$-0.179952\pi$
$743$	35.6490	+	9.55213i	1.30784	+	0.350434i	0.463428	+	0.886134i	$0.346619\pi$
$744$	−0.398876	+	1.38478i	−0.0146235	+	0.0507683i
$745$		−	41.3230i		−	1.51396i
$746$	−15.2918	−	4.09742i	−0.559872	−	0.150017i
$747$	−2.48111	−	2.67349i	−0.0907790	−	0.0978180i
$748$	−2.32842	−	8.68978i	−0.0851354	−	0.317730i
$749$	2.89327	−	18.5281i	0.105718	−	0.677000i
$750$	−15.0664	+	14.5146i	−0.550148	+	0.529997i
$751$		−	14.7783i		−	0.539267i	−0.962963	−	0.269633i	$-0.913097\pi$
$751$		−	14.7783i		−	0.539267i	0.962963	−	0.269633i	$-0.0869025\pi$
$752$	11.1371	−	2.98417i	0.406127	−	0.108821i
$753$	−3.50570	−	14.1328i	−0.127755	−	0.515027i
$754$	−27.2020	−	17.8285i	−0.990639	−	0.649275i
$755$			4.66318i			0.169710i
$756$	−11.5405	+	7.47112i	−0.419723	+	0.271722i
$757$	10.7098	+	18.5499i	0.389255	+	0.674209i	0.992349	−	0.123461i	$-0.0393993\pi$
$757$	10.7098	+	18.5499i	0.389255	+	0.674209i	−0.603095	+	0.797669i	$0.706066\pi$
$758$	3.48690	+	6.03948i	0.126650	+	0.219364i
$759$	−21.0674	+	34.9670i	−0.764699	+	1.26922i
$760$	−8.45917	−	8.45917i	−0.306847	−	0.306847i
$761$	−7.86963	+	29.3698i	−0.285274	+	1.06466i	0.663365	+	0.748296i	$0.269128\pi$
$761$	−7.86963	+	29.3698i	−0.285274	+	1.06466i	−0.948639	+	0.316360i	$0.897539\pi$
$762$	−10.7412	−	19.4326i	−0.389113	−	0.703968i
$763$	−8.84716	+	19.9879i	−0.320289	+	0.723611i
$764$	4.95076	+	8.57497i	0.179112	+	0.310231i
$765$	−14.4983	+	3.31057i	−0.524186	+	0.119694i
$766$	29.0654	−	16.7809i	1.05018	−	0.606319i
$767$	−32.6076	+	16.4419i	−1.17739	+	0.593681i
$768$	−1.24738	+	1.20169i	−0.0450108	+	0.0433622i
$769$	−4.68811	+	17.4963i	−0.169058	+	0.630931i	0.828430	+	0.560092i	$0.189234\pi$
$769$	−4.68811	+	17.4963i	−0.169058	+	0.630931i	−0.997488	+	0.0708390i	$0.977432\pi$
$770$	16.7748	+	7.42498i	0.604523	+	0.267578i
$771$	−7.79498	+	7.50947i	−0.280729	+	0.270447i
$772$	3.76999	−	1.01017i	0.135685	−	0.0363567i
$773$	−19.1477	+	19.1477i	−0.688694	+	0.688694i	−0.961943	−	0.273249i	$-0.911902\pi$
$773$	−19.1477	+	19.1477i	−0.688694	+	0.688694i	0.273249	+	0.961943i	$0.411902\pi$
$774$	3.41308	+	14.9472i	0.122681	+	0.537266i
$775$	0.253980	+	0.947866i	0.00912323	+	0.0340483i
$776$	−6.23461	−	3.59956i	−0.223810	−	0.129217i
$777$	−4.36970	+	24.9238i	−0.156762	+	0.894137i
$778$	−29.2847	−	7.84682i	−1.04991	−	0.281322i
$779$	19.6371	−	34.0125i	0.703572	−	1.21862i
$780$	−7.95832	−	9.25565i	−0.284953	−	0.331405i
$781$	−10.4500	−	18.0999i	−0.373930	−	0.647665i
$782$	11.9152	−	11.9152i	0.426087	−	0.426087i
$783$	−44.5254	−	14.6446i	−1.59121	−	0.523354i
$784$	−6.66674	−	2.13415i	−0.238098	−	0.0762195i
$785$	−15.1266	+	15.1266i	−0.539890	+	0.539890i
$786$	4.94340	−	8.20488i	0.176325	−	0.292659i
$787$	21.7489	−	21.7489i	0.775264	−	0.775264i	−0.203758	−	0.979021i	$-0.565315\pi$
$787$	21.7489	−	21.7489i	0.775264	−	0.775264i	0.979021	+	0.203758i	$0.0653155\pi$
$788$	−1.24514	+	4.64694i	−0.0443564	+	0.165540i
$789$	49.9290	−	12.3851i	1.77752	−	0.440921i
$790$	19.9881	−	11.5402i	0.711146	−	0.410581i
$791$	22.4959	+	18.1359i	0.799861	+	0.644840i
$792$	5.66097	−	9.01126i	0.201154	−	0.320201i
$793$	−39.5983	+	8.24280i	−1.40618	+	0.292710i
$794$	−15.4711	+	8.93222i	−0.549047	+	0.316992i
$795$	−19.0456	−	0.355298i	−0.675478	−	0.0126011i
$796$	8.78409			0.311344
$797$	−10.7972	+	18.7014i	−0.382458	+	0.662436i	−0.991413	−	0.130768i	$-0.958256\pi$
$797$	−10.7972	+	18.7014i	−0.382458	+	0.662436i	0.608955	+	0.793205i	$0.291589\pi$
$798$	−25.4309	−	11.8285i	−0.900245	−	0.418723i
$799$	28.2449	−	7.56819i	0.999231	−	0.267743i
$800$	−0.305262	+	1.13925i	−0.0107926	+	0.0402787i
$801$	6.19867	−	5.75261i	0.219019	−	0.203258i
$802$	0.986906			0.0348489
$803$	38.0528			1.34286
$804$	17.6726	+	10.6476i	0.623263	+	0.375513i
$805$	3.66596	+	34.1645i	0.129208	+	1.20414i
$806$	−2.93689	+	0.611344i	−0.103447	+	0.0215337i
$807$	29.7815	+	30.9137i	1.04836	+	1.08822i
$808$	−5.25034	+	1.40682i	−0.184706	+	0.0494919i
$809$	−38.2652	−	22.0924i	−1.34533	−	0.776729i	−0.357750	−	0.933818i	$-0.616456\pi$
$809$	−38.2652	−	22.0924i	−1.34533	−	0.776729i	−0.987585	+	0.157089i	$0.949789\pi$
$810$	−14.5367	−	9.90698i	−0.510769	−	0.348096i
$811$	13.8741	+	13.8741i	0.487184	+	0.487184i	0.907416	−	0.420233i	$-0.138051\pi$
$811$	13.8741	+	13.8741i	0.487184	+	0.487184i	−0.420233	+	0.907416i	$0.638051\pi$
$812$	−8.60125	−	22.2622i	−0.301845	−	0.781250i
$813$	0.862579	−	46.2382i	0.0302520	−	1.62164i
$814$	−5.06958	−	18.9199i	−0.177689	−	0.663143i
$815$			39.9233i			1.39845i
$816$	−3.16348	+	3.04761i	−0.110744	+	0.106688i
$817$	−22.1177	+	22.1177i	−0.773800	+	0.773800i
$818$	−6.43323			−0.224932
$819$	−24.9682	−	13.9852i	−0.872461	−	0.488684i
$820$	12.5427			0.438010
$821$	−5.67358	+	5.67358i	−0.198009	+	0.198009i	−0.799146	−	0.601137i	$-0.794715\pi$
$821$	−5.67358	+	5.67358i	−0.198009	+	0.198009i	0.601137	+	0.799146i	$0.294715\pi$
$822$	−15.6999	+	15.1249i	−0.547597	+	0.527540i
$823$			32.3014i			1.12596i	0.826472	+	0.562978i	$0.190345\pi$
$823$			32.3014i			1.12596i	−0.826472	+	0.562978i	$0.809655\pi$
$824$	3.14924	+	11.7531i	0.109709	+	0.409440i
$825$	0.135162	−	7.24532i	0.00470575	−	0.252250i
$826$	−26.4763	−	4.13444i	−0.921227	−	0.143855i
$827$	10.5632	+	10.5632i	0.367318	+	0.367318i	0.866498	−	0.499180i	$-0.166365\pi$
$827$	10.5632	+	10.5632i	0.367318	+	0.367318i	−0.499180	+	0.866498i	$0.666365\pi$
$828$	19.9190	+	0.743442i	0.692233	+	0.0258364i
$829$	−6.25655	−	3.61222i	−0.217299	−	0.125458i	0.387400	−	0.921912i	$-0.373373\pi$
$829$	−6.25655	−	3.61222i	−0.217299	−	0.125458i	−0.604699	+	0.796454i	$0.706707\pi$
$830$	2.29545	−	0.615065i	0.0796763	−	0.0213492i
$831$	−15.3746	−	15.9592i	−0.533340	−	0.553617i
$832$	−3.42436	−	1.12860i	−0.118718	−	0.0391273i
$833$	−16.9076	−	5.41243i	−0.585813	−	0.187530i
$834$	−15.1675	−	9.13833i	−0.525207	−	0.316435i
$835$	5.28674			0.182955
$836$	21.7108			0.750884
$837$	−3.85907	+	1.94883i	−0.133389	+	0.0673614i
$838$	1.23916	−	4.62460i	0.0428060	−	0.159754i
$839$	−43.2150	+	11.5794i	−1.49195	+	0.399766i	−0.910395	−	0.413741i	$-0.864222\pi$
$839$	−43.2150	+	11.5794i	−1.49195	+	0.399766i	−0.581554	+	0.813508i	$0.697555\pi$
$840$	−0.789370	−	8.92237i	−0.0272359	−	0.307851i
$841$	26.1848	−	45.3534i	0.902924	−	1.56391i
$842$	−0.668542			−0.0230395
$843$	−15.3213	−	0.285820i	−0.527693	−	0.00984418i
$844$	−14.9482	+	8.63034i	−0.514538	+	0.297068i
$845$	9.30559	−	23.6449i	0.320122	−	0.813409i
$846$	29.2898	+	18.4001i	1.00700	+	0.632610i
$847$	−3.90741	+	1.50967i	−0.134260	+	0.0518729i
$848$	−4.87278	+	2.81330i	−0.167332	+	0.0966092i
$849$	23.0209	−	5.71042i	0.790074	−	0.195981i
$850$	−0.774178	+	2.88927i	−0.0265541	+	0.0991012i
$851$	25.9426	−	25.9426i	0.889300	−	0.889300i
$852$	−5.26641	+	8.74101i	−0.180424	+	0.299462i
$853$	−28.3574	+	28.3574i	−0.970940	+	0.970940i	−0.999590	−	0.0286493i	$-0.990879\pi$
$853$	−28.3574	+	28.3574i	−0.970940	+	0.970940i	0.0286493	+	0.999590i	$0.490879\pi$
$854$	−27.1403	−	12.0130i	−0.928722	−	0.411076i
$855$	1.33857	−	35.8643i	0.0457781	−	1.22653i
$856$	5.01184	−	5.01184i	0.171301	−	0.171301i
$857$	2.28469	+	3.95720i	0.0780435	+	0.135175i	0.902406	−	0.430887i	$-0.141799\pi$
$857$	2.28469	+	3.95720i	0.0780435	+	0.135175i	−0.824362	+	0.566063i	$0.808466\pi$
$858$	22.0902	+	1.66483i	0.754146	+	0.0568362i
$859$	22.8984	−	39.6613i	0.781285	−	1.35322i	−0.149909	−	0.988700i	$-0.547898\pi$
$859$	22.8984	−	39.6613i	0.781285	−	1.35322i	0.931194	−	0.364525i	$-0.118769\pi$
$860$	−9.64900	−	2.58544i	−0.329028	−	0.0881628i
$861$	27.6229	−	10.0844i	0.941386	−	0.343676i
$862$	−3.42487	−	1.97735i	−0.116651	−	0.0673488i
$863$	6.68238	+	24.9390i	0.227471	+	0.848933i	0.981400	+	0.191976i	$0.0614897\pi$
$863$	6.68238	+	24.9390i	0.227471	+	0.848933i	−0.753929	+	0.656956i	$0.771844\pi$
$864$	−5.18802	−	0.290619i	−0.176500	−	0.00988706i
$865$	−11.8606	+	11.8606i	−0.403272	+	0.403272i
$866$	21.5305	−	5.76908i	0.731636	−	0.196041i
$867$	13.1824	−	12.6996i	0.447699	−	0.431301i
$868$	−2.01291	−	0.890968i	−0.0683227	−	0.0302414i
$869$	−10.8410	+	40.4593i	−0.367757	+	1.37249i
$870$	21.9934	−	21.1878i	0.745645	−	0.718334i
$871$	−2.42835	+	42.8808i	−0.0822816	+	1.45296i
$872$	−7.15483	+	4.13084i	−0.242293	+	0.139888i
$873$	−4.80784	−	21.0554i	−0.162721	−	0.712617i
$874$	20.3329	+	35.2175i	0.687769	+	1.19125i
$875$	−18.8398	−	25.8126i	−0.636903	−	0.872625i
$876$	−8.98838	−	16.2614i	−0.303689	−	0.549423i
$877$	−2.36625	+	8.83096i	−0.0799025	+	0.298200i	−0.994300	−	0.106617i	$-0.965998\pi$
$877$	−2.36625	+	8.83096i	−0.0799025	+	0.298200i	0.914398	+	0.404817i	$0.132665\pi$
$878$	10.8652	+	10.8652i	0.366682	+	0.366682i
$879$	4.10651	−	6.81584i	0.138509	−	0.229893i
$880$	3.46681	+	6.00469i	0.116866	+	0.202418i
$881$	9.57090	+	16.5773i	0.322452	+	0.558503i	0.980993	−	0.194042i	$-0.0621597\pi$
$881$	9.57090	+	16.5773i	0.322452	+	0.558503i	−0.658542	+	0.752544i	$0.728826\pi$
$882$	−8.91207	−	19.0151i	−0.300085	−	0.640273i
$883$			40.2359i			1.35405i	0.735962	+	0.677023i	$0.236730\pi$
$883$			40.2359i			1.35405i	−0.735962	+	0.677023i	$0.763270\pi$
$884$	−8.68456	−	2.86226i	−0.292093	−	0.0962683i
$885$	−8.25551	−	33.2811i	−0.277506	−	1.11873i
$886$	−23.9493	+	6.41721i	−0.804594	+	0.215590i
$887$			17.1535i			0.575957i	0.957637	+	0.287979i	$0.0929832\pi$
$887$			17.1535i			0.575957i	−0.957637	+	0.287979i	$0.907017\pi$
$888$	−6.88774	+	6.63546i	−0.231137	+	0.222671i
$889$	31.6373	−	12.2234i	1.06108	−	0.409960i
$890$	1.42607	+	5.32216i	0.0478019	+	0.178399i
$891$	31.3679	−	5.94124i	1.05086	−	0.199039i
$892$	14.9378	+	4.00258i	0.500155	+	0.134016i
$893$			70.5678i			2.36146i
$894$	10.1354	−	35.1869i	0.338978	−	1.17683i
$895$	3.85272	+	1.03233i	0.128782	+	0.0345071i
$896$	−1.55978	−	2.13707i	−0.0521087	−	0.0713945i
$897$	17.9876	+	37.3920i	0.600588	+	1.24848i
$898$	13.0007	−	22.5179i	0.433840	−	0.751433i
$899$	−1.94247	−	7.24939i	−0.0647850	−	0.241781i
$900$	−3.12813	+	1.65364i	−0.104271	+	0.0551214i
$901$	−12.3579	+	7.13485i	−0.411702	+	0.237696i
$902$	−16.0957	+	16.0957i	−0.535928	+	0.535928i
$903$	−23.3288	+	2.06392i	−0.776333	+	0.0686829i
$904$	2.82673	+	10.5495i	0.0940156	+	0.350871i
$905$	7.13086	−	1.91071i	0.237038	−	0.0635141i
$906$	−1.14375	+	3.97073i	−0.0379984	+	0.131919i
$907$	6.63919	+	3.83314i	0.220451	+	0.127277i	0.606159	−	0.795344i	$-0.292710\pi$
$907$	6.63919	+	3.83314i	0.220451	+	0.127277i	−0.385708	+	0.922621i	$0.626043\pi$
$908$	13.7448	+	13.7448i	0.456139	+	0.456139i
$909$	−13.8080	−	8.67436i	−0.457984	−	0.287710i
$910$	15.6584	−	10.1235i	0.519072	−	0.335589i
$911$			57.7098i			1.91201i	0.293347	+	0.956006i	$0.405231\pi$
$911$			57.7098i			1.91201i	−0.293347	+	0.956006i	$0.594769\pi$
$912$	−5.12826	−	9.27786i	−0.169814	−	0.307221i
$913$	−2.15639	+	3.73498i	−0.0713662	+	0.123610i
$914$	−17.7750			−0.587946
$915$	0.708374	−	37.9721i	0.0234181	−	1.25532i
$916$	−5.16146	+	1.38301i	−0.170539	+	0.0456959i
$917$	11.3913	+	9.18358i	0.376175	+	0.303268i
$918$	−13.1574	−	0.737042i	−0.434259	−	0.0243260i
$919$	4.20166	+	7.27749i	0.138600	+	0.240062i	0.926967	−	0.375143i	$-0.122406\pi$
$919$	4.20166	+	7.27749i	0.138600	+	0.240062i	−0.788367	+	0.615205i	$0.789073\pi$
$920$	−6.49355	+	11.2472i	−0.214086	+	0.370808i
$921$	0.247913	−	13.2893i	0.00816902	−	0.437897i
$922$	26.5904	+	15.3520i	0.875708	+	0.505590i
$923$	−21.2093	−	1.20109i	−0.698111	−	0.0395342i
$924$	12.4628	+	10.4368i	0.409995	+	0.343347i
$925$	−1.68559	+	6.29070i	−0.0554218	+	0.206837i
$926$		−	6.65897i		−	0.218827i
$927$	−19.4180	+	30.9100i	−0.637770	+	1.01522i
$928$	2.33468	−	8.71314i	0.0766396	−	0.286023i
$929$	−35.3366	−	9.46841i	−1.15936	−	0.310649i	−0.372648	−	0.927973i	$-0.621550\pi$
$929$	−35.3366	−	9.46841i	−1.15936	−	0.310649i	−0.786709	+	0.617324i	$0.788217\pi$
$930$	0.0525380	−	2.81628i	0.00172279	−	0.0923493i
$931$	23.1774	−	36.0321i	0.759608	−	1.18090i
$932$	4.62938	+	2.67277i	0.151640	+	0.0875496i
$933$	24.5826	+	7.08088i	0.804799	+	0.231818i
$934$	6.61530	+	24.6886i	0.216459	+	0.807836i
$935$	8.79222	+	15.2286i	0.287536	+	0.498027i
$936$	−4.50642	−	9.83322i	−0.147297	−	0.321409i
$937$	−28.6653			−0.936453			−0.468227	−	0.883608i	$-0.655107\pi$
$937$	−28.6653			−0.936453			−0.468227	+	0.883608i	$0.655107\pi$
$938$	−19.7806	+	24.5359i	−0.645859	+	0.801125i
$939$	−7.60208	−	30.6468i	−0.248084	−	1.00012i
$940$	−19.5174	+	11.2684i	−0.636586	+	0.367533i
$941$	35.6733	+	9.55863i	1.16292	+	0.311602i	0.788130	−	0.615509i	$-0.211050\pi$
$941$	35.6733	+	9.55863i	1.16292	+	0.311602i	0.374786	+	0.927111i	$0.377716\pi$
$942$	−16.5905	+	9.17028i	−0.540548	+	0.298784i
$943$	−41.1832	−	11.0350i	−1.34111	−	0.359350i
$944$	−7.16184	−	7.16184i	−0.233098	−	0.233098i
$945$	18.0091	−	19.9439i	0.585835	−	0.648775i
$946$	15.7001	−	9.06445i	0.510454	−	0.294711i
$947$	2.28585	+	2.28585i	0.0742802	+	0.0742802i	0.743271	−	0.668991i	$-0.233273\pi$
$947$	2.28585	+	2.28585i	0.0742802	+	0.0742802i	−0.668991	+	0.743271i	$0.733273\pi$
$948$	19.8506	−	4.92401i	0.644716	−	0.159925i
$949$	21.2018	−	32.3490i	0.688241	−	1.05009i
$950$	−6.25153	−	3.60932i	−0.202826	−	0.117102i
$951$	37.4349	+	22.5543i	1.21391	+	0.731374i
$952$	−3.95579	−	5.41985i	−0.128208	−	0.175658i
$953$	22.8899	−	39.6465i	0.741477	−	1.28428i	−0.210346	−	0.977627i	$-0.567459\pi$
$953$	22.8899	−	39.6465i	0.741477	−	1.28428i	0.951823	−	0.306649i	$-0.0992077\pi$
$954$	−16.1304	−	4.97390i	−0.522240	−	0.161036i
$955$	−13.6852	−	13.6852i	−0.442842	−	0.442842i
$956$	−1.77800	−	1.77800i	−0.0575047	−	0.0575047i
$957$	−1.03374	+	55.4131i	−0.0334160	+	1.79125i
$958$	4.21295	−	7.29704i	0.136114	−	0.235757i
$959$	−19.6320	−	26.8979i	−0.633950	−	0.868579i
$960$	1.74715	−	2.89985i	0.0563889	−	0.0935924i
$961$	26.2473	+	15.1539i	0.846687	+	0.488835i
$962$	−18.9086	−	6.23190i	−0.609637	−	0.200925i
$963$	21.2487	+	0.793068i	0.684728	+	0.0255563i
$964$	−0.541486	−	0.541486i	−0.0174401	−	0.0174401i
$965$	−6.60680	+	3.81444i	−0.212680	+	0.122791i
$966$	−5.25800	+	29.9905i	−0.169174	+	0.964930i
$967$	11.8127	+	11.8127i	0.379871	+	0.379871i	0.871055	−	0.491185i	$-0.163436\pi$
$967$	11.8127	+	11.8127i	0.379871	+	0.379871i	−0.491185	+	0.871055i	$0.663436\pi$
$968$	−1.52931	−	0.409777i	−0.0491539	−	0.0131707i
$969$	−13.0058	−	23.5297i	−0.417808	−	0.755882i
$970$	13.5921	+	3.64199i	0.436416	+	0.116937i
$971$	5.39932	−	3.11730i	0.173272	−	0.100039i	−0.410856	−	0.911700i	$-0.634770\pi$
$971$	5.39932	−	3.11730i	0.173272	−	0.100039i	0.584128	+	0.811662i	$0.301437\pi$
$972$	−9.94826	−	12.0013i	−0.319091	−	0.384943i
$973$	16.9767	−	21.0579i	0.544248	−	0.675086i
$974$	18.8480			0.603927
$975$	−6.08399	−	4.15177i	−0.194844	−	0.132963i
$976$	−5.60901	−	9.71509i	−0.179540	−	0.310972i
$977$	1.35365	+	5.05189i	0.0433071	+	0.161624i	0.984193	−	0.177100i	$-0.0566715\pi$
$977$	1.35365	+	5.05189i	0.0433071	+	0.161624i	−0.940886	+	0.338724i	$0.890005\pi$
$978$	−9.79207	+	33.9950i	−0.313116	+	1.08704i
$979$	−8.65979	−	4.99973i	−0.276768	−	0.159792i
$980$	13.6666	+	0.656653i	0.436564	+	0.0209760i
$981$	−23.6846	−	7.30330i	−0.756192	−	0.233176i
$982$	15.2173	+	4.07745i	0.485602	+	0.130117i
$983$	−1.47355	+	5.49935i	−0.0469988	+	0.175402i	−0.985436	−	0.170049i	$-0.945607\pi$
$983$	−1.47355	+	5.49935i	−0.0469988	+	0.175402i	0.938437	+	0.345451i	$0.112274\pi$
$984$	10.6802	+	3.07638i	0.340473	+	0.0980713i
$985$		−	9.40344i		−	0.299619i
$986$	5.92101	−	22.0975i	0.188563	−	0.703728i
$987$	−33.9234	+	40.5085i	−1.07979	+	1.28940i
$988$	12.0966	−	18.4565i	0.384843	−	0.587180i
$989$	29.4073	+	16.9783i	0.935096	+	0.539878i
$990$	−6.12929	+	19.8773i	−0.194802	+	0.631742i
$991$	20.1364	−	34.8772i	0.639653	−	1.10791i	−0.345855	−	0.938288i	$-0.612411\pi$
$991$	20.1364	−	34.8772i	0.639653	−	1.10791i	0.985509	−	0.169624i	$-0.0542554\pi$
$992$	−0.416003	−	0.720539i	−0.0132081	−	0.0228771i
$993$	16.3078	+	29.5034i	0.517511	+	0.936262i
$994$	−12.1357	−	9.78365i	−0.384920	−	0.310319i
$995$	−16.5846	+	4.44382i	−0.525766	+	0.140879i
$996$	2.10546	+	0.0392775i	0.0667139	+	0.00124456i
$997$	1.35153			0.0428034			0.0214017	−	0.999771i	$-0.493187\pi$
$997$	1.35153			0.0428034			0.0214017	+	0.999771i	$0.493187\pi$
$998$	6.38115	−	11.0525i	0.201992	−	0.349860i
$999$	−28.6471	−	1.60473i	−0.906354	−	0.0507716i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.ch.a.401.25	yes	152
3.2	odd	2	inner	546.2.ch.a.401.8	yes	152
7.4	even	3		546.2.bw.a.11.37	yes	152
13.6	odd	12		546.2.bw.a.149.18	yes	152
21.11	odd	6		546.2.bw.a.11.18	✓	152
39.32	even	12		546.2.bw.a.149.37	yes	152
91.32	odd	12	inner	546.2.ch.a.305.8	yes	152
273.32	even	12	inner	546.2.ch.a.305.25	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.11.18	✓	152	21.11	odd	6
546.2.bw.a.11.37	yes	152	7.4	even	3
546.2.bw.a.149.18	yes	152	13.6	odd	12
546.2.bw.a.149.37	yes	152	39.32	even	12
546.2.ch.a.305.8	yes	152	91.32	odd	12	inner
546.2.ch.a.305.25	yes	152	273.32	even	12	inner
546.2.ch.a.401.8	yes	152	3.2	odd	2	inner
546.2.ch.a.401.25	yes	152	1.1	even	1	trivial

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.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.24738 + 1.20169i) q^{3} -1.00000i q^{4} +(0.505894 + 1.88802i) q^{5} +(-0.0323060 + 1.73175i) q^{6} +(-2.61407 - 0.408204i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.111892 - 2.99791i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.24738 + 1.20169i) q^{3} -1.00000i q^{4} +(0.505894 + 1.88802i) q^{5} +(-0.0323060 + 1.73175i) q^{6} +(-2.61407 - 0.408204i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.111892 - 2.99791i) q^{9} +(1.69275 + 0.977313i) q^{10} +(-3.42642 + 0.918106i) q^{11} +(1.20169 + 1.24738i) q^{12} +(-1.12860 + 3.42436i) q^{13} +(-2.13707 + 1.55978i) q^{14} +(-2.89985 - 1.74715i) q^{15} -1.00000 q^{16} -2.53611 q^{17} +(-2.04072 - 2.19896i) q^{18} +(1.58408 - 5.91185i) q^{19} +(1.88802 - 0.505894i) q^{20} +(3.75126 - 2.63212i) q^{21} +(-1.77364 + 3.07204i) q^{22} -6.64429 q^{23} +(1.73175 + 0.0323060i) q^{24} +(1.02143 - 0.589721i) q^{25} +(1.62335 + 3.21943i) q^{26} +(3.46298 + 3.87398i) q^{27} +(-0.408204 + 2.61407i) q^{28} +(-7.81199 + 4.51025i) q^{29} +(-3.28593 + 0.815088i) q^{30} +(-0.215339 + 0.803657i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.17075 - 5.26271i) q^{33} +(-1.79330 + 1.79330i) q^{34} +(-0.551746 - 5.14193i) q^{35} +(-2.99791 - 0.111892i) q^{36} +(-3.90449 + 3.90449i) q^{37} +(-3.06020 - 5.30042i) q^{38} +(-2.70722 - 5.62769i) q^{39} +(0.977313 - 1.69275i) q^{40} +(6.19829 + 1.66083i) q^{41} +(0.791357 - 4.51373i) q^{42} +(-4.42594 - 2.55532i) q^{43} +(0.918106 + 3.42642i) q^{44} +(5.71673 - 1.30537i) q^{45} +(-4.69822 + 4.69822i) q^{46} +(-11.1371 + 2.98417i) q^{47} +(1.24738 - 1.20169i) q^{48} +(6.66674 + 2.13415i) q^{49} +(0.305262 - 1.13925i) q^{50} +(3.16348 - 3.04761i) q^{51} +(3.42436 + 1.12860i) q^{52} +(4.87278 - 2.81330i) q^{53} +(5.18802 + 0.290619i) q^{54} +(-3.46681 - 6.00469i) q^{55} +(1.55978 + 2.13707i) q^{56} +(5.12826 + 9.27786i) q^{57} +(-2.33468 + 8.71314i) q^{58} +(7.16184 + 7.16184i) q^{59} +(-1.74715 + 2.89985i) q^{60} +(5.60901 + 9.71509i) q^{61} +(0.416003 + 0.720539i) q^{62} +(-1.51625 + 7.79108i) q^{63} +1.00000i q^{64} +(-7.03623 - 0.398463i) q^{65} +(-1.47924 - 5.96336i) q^{66} +(11.5062 - 3.08307i) q^{67} +2.53611i q^{68} +(8.28793 - 7.98437i) q^{69} +(-4.02604 - 3.24575i) q^{70} +(1.52491 + 5.69106i) q^{71} +(-2.19896 + 2.04072i) q^{72} +(-10.3618 - 2.77643i) q^{73} +5.52178i q^{74} +(-0.565442 + 1.96304i) q^{75} +(-5.91185 - 1.58408i) q^{76} +(9.33168 - 1.00132i) q^{77} +(-5.89368 - 2.06509i) q^{78} +(5.90403 - 10.2261i) q^{79} +(-0.505894 - 1.88802i) q^{80} +(-8.97496 - 0.670883i) q^{81} +(5.55723 - 3.20847i) q^{82} +(0.859699 - 0.859699i) q^{83} +(-2.63212 - 3.75126i) q^{84} +(-1.28300 - 4.78824i) q^{85} +(-4.93650 + 1.32273i) q^{86} +(4.32457 - 15.0136i) q^{87} +(3.07204 + 1.77364i) q^{88} +(1.99327 + 1.99327i) q^{89} +(3.11930 - 4.96538i) q^{90} +(4.34809 - 8.49083i) q^{91} +6.64429i q^{92} +(-0.697136 - 1.26123i) q^{93} +(-5.76497 + 9.98523i) q^{94} +11.9631 q^{95} +(0.0323060 - 1.73175i) q^{96} +(6.95381 - 1.86327i) q^{97} +(6.22317 - 3.20503i) q^{98} +(2.36901 + 10.3748i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 8 q^{7}+O(q^{10}) \) 152 * q + 8 * q^7	\( 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

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