LMFDB - Embedded newform 546.2.bn.e.173.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(101,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 5]))

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

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

chi := DirichletCharacter("546.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bn (of order $6$, degree $2$, 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:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			173.10
Character	$\chi$	$=$	546.173
Dual form			546.2.bn.e.101.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.458130 - 1.67036i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.57344 + 0.908426i) q^{5} +(-1.67564 + 0.438430i) q^{6} +(-0.414054 + 2.61315i) q^{7} +1.00000 q^{8} +(-2.58023 - 1.53049i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.458130 - 1.67036i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.57344 + 0.908426i) q^{5} +(-1.67564 + 0.438430i) q^{6} +(-0.414054 + 2.61315i) q^{7} +1.00000 q^{8} +(-2.58023 - 1.53049i) q^{9} -1.81685i q^{10} +2.05127 q^{11} +(1.21751 + 1.23193i) q^{12} +(3.57560 + 0.463745i) q^{13} +(2.47008 - 0.947995i) q^{14} +(2.23824 - 2.21204i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.84359 - 4.92524i) q^{17} +(-0.0353243 + 2.99979i) q^{18} -1.59352 q^{19} +(-1.57344 + 0.908426i) q^{20} +(4.17522 + 1.88878i) q^{21} +(-1.02563 - 1.77645i) q^{22} +(7.56871 - 4.36980i) q^{23} +(0.458130 - 1.67036i) q^{24} +(-0.849523 - 1.47142i) q^{25} +(-1.38619 - 3.32844i) q^{26} +(-3.73855 + 3.60877i) q^{27} +(-2.05603 - 1.66516i) q^{28} +(0.724381 + 0.418222i) q^{29} +(-3.03481 - 0.832355i) q^{30} +(3.97501 + 6.88493i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.939747 - 3.42636i) q^{33} -5.68717 q^{34} +(-3.02534 + 3.73550i) q^{35} +(2.61556 - 1.46930i) q^{36} +(-3.65306 + 2.10909i) q^{37} +(0.796762 + 1.38003i) q^{38} +(2.41271 - 5.76010i) q^{39} +(1.57344 + 0.908426i) q^{40} +(-0.397180 - 0.229312i) q^{41} +(-0.451878 - 4.56024i) q^{42} +(0.836012 + 1.44802i) q^{43} +(-1.02563 + 1.77645i) q^{44} +(-2.66951 - 4.75208i) q^{45} +(-7.56871 - 4.36980i) q^{46} +(-1.94760 - 1.12445i) q^{47} +(-1.67564 + 0.438430i) q^{48} +(-6.65712 - 2.16397i) q^{49} +(-0.849523 + 1.47142i) q^{50} +(-6.92421 - 7.00622i) q^{51} +(-2.18942 + 2.86469i) q^{52} +(-0.497067 + 0.286982i) q^{53} +(4.99456 + 1.43330i) q^{54} +(3.22755 + 1.86343i) q^{55} +(-0.414054 + 2.61315i) q^{56} +(-0.730041 + 2.66176i) q^{57} -0.836443i q^{58} +(-1.89789 - 1.09575i) q^{59} +(0.796563 + 3.04440i) q^{60} -6.89812i q^{61} +(3.97501 - 6.88493i) q^{62} +(5.06775 - 6.10884i) q^{63} +1.00000 q^{64} +(5.20472 + 3.97785i) q^{65} +(-3.43719 + 0.899337i) q^{66} -5.15514i q^{67} +(2.84359 + 4.92524i) q^{68} +(-3.83170 - 14.6444i) q^{69} +(4.74771 + 0.752275i) q^{70} +(4.24250 + 7.34823i) q^{71} +(-2.58023 - 1.53049i) q^{72} +(-5.11752 - 8.86381i) q^{73} +(3.65306 + 2.10909i) q^{74} +(-2.84699 + 0.744913i) q^{75} +(0.796762 - 1.38003i) q^{76} +(-0.849335 + 5.36027i) q^{77} +(-6.19475 + 0.790580i) q^{78} +(-3.68537 + 6.38325i) q^{79} -1.81685i q^{80} +(4.31521 + 7.89803i) q^{81} +0.458624i q^{82} +15.0678i q^{83} +(-3.72335 + 2.67146i) q^{84} +(8.94843 - 5.16638i) q^{85} +(0.836012 - 1.44802i) q^{86} +(1.03044 - 1.01838i) q^{87} +2.05127 q^{88} +(-3.34558 + 1.93157i) q^{89} +(-2.78067 + 4.68791i) q^{90} +(-2.69233 + 9.15158i) q^{91} +8.73960i q^{92} +(13.3214 - 3.48553i) q^{93} +2.24889i q^{94} +(-2.50731 - 1.44760i) q^{95} +(1.21751 + 1.23193i) q^{96} +(1.72410 + 2.98622i) q^{97} +(1.45451 + 6.84722i) q^{98} +(-5.29275 - 3.13944i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	$ 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * q^21 + 9 * q^22 + 6 * q^23 + 3 * q^24 + 16 * q^25 + 13 * q^26 + 18 * q^27 - q^28 + 27 * q^29 + 13 * q^30 + q^31 - 17 * q^32 + 21 * q^33 - 12 * q^34 - 3 * q^35 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.458130	−	1.67036i	0.264501	−	0.964385i
$3$	0.458130	−	1.67036i	0.264501	−	0.964385i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.57344	+	0.908426i	0.703664	+	0.406261i	0.808711	−	0.588207i	$-0.200166\pi$
$5$	1.57344	+	0.908426i	0.703664	+	0.406261i	−0.105047	+	0.994467i	$0.533499\pi$
$6$	−1.67564	+	0.438430i	−0.684078	+	0.178988i
$7$	−0.414054	+	2.61315i	−0.156498	+	0.987678i
$7$	−0.414054	+	2.61315i	−0.156498	+	0.987678i
$8$	1.00000			0.353553
$9$	−2.58023	−	1.53049i	−0.860078	−	0.510163i
$10$		−	1.81685i		−	0.574539i
$11$	2.05127			0.618480			0.309240	−	0.950984i	$-0.399925\pi$
$11$	2.05127			0.618480			0.309240	+	0.950984i	$0.399925\pi$
$12$	1.21751	+	1.23193i	0.351466	+	0.355629i
$13$	3.57560	+	0.463745i	0.991694	+	0.128620i
$13$	3.57560	+	0.463745i	0.991694	+	0.128620i
$14$	2.47008	−	0.947995i	0.660157	−	0.253362i
$15$	2.23824	−	2.21204i	0.577912	−	0.571147i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.84359	−	4.92524i	0.689671	−	1.19455i	−0.282273	−	0.959334i	$-0.591088\pi$
$17$	2.84359	−	4.92524i	0.689671	−	1.19455i	0.971944	−	0.235211i	$-0.0755782\pi$
$18$	−0.0353243	+	2.99979i	−0.00832601	+	0.707058i
$19$	−1.59352			−0.365579			−0.182790	−	0.983152i	$-0.558513\pi$
$19$	−1.59352			−0.365579			−0.182790	+	0.983152i	$0.558513\pi$
$20$	−1.57344	+	0.908426i	−0.351832	+	0.203130i
$21$	4.17522	+	1.88878i	0.911109	+	0.412166i
$22$	−1.02563	−	1.77645i	−0.218666	−	0.378740i
$23$	7.56871	−	4.36980i	1.57819	−	0.911166i	0.583073	−	0.812420i	$-0.301850\pi$
$23$	7.56871	−	4.36980i	1.57819	−	0.911166i	0.995113	−	0.0987464i	$-0.0314833\pi$
$24$	0.458130	−	1.67036i	0.0935154	−	0.340962i
$25$	−0.849523	−	1.47142i	−0.169905	−	0.294283i
$26$	−1.38619	−	3.32844i	−0.271854	−	0.652760i
$27$	−3.73855	+	3.60877i	−0.719485	+	0.694508i
$28$	−2.05603	−	1.66516i	−0.388553	−	0.314685i
$29$	0.724381	+	0.418222i	0.134514	+	0.0776618i	0.565747	−	0.824579i	$-0.308588\pi$
$29$	0.724381	+	0.418222i	0.134514	+	0.0776618i	−0.431233	+	0.902241i	$0.641921\pi$
$30$	−3.03481	−	0.832355i	−0.554077	−	0.151966i
$31$	3.97501	+	6.88493i	0.713934	+	1.23657i	0.963369	+	0.268178i	$0.0864215\pi$
$31$	3.97501	+	6.88493i	0.713934	+	1.23657i	−0.249436	+	0.968391i	$0.580245\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.939747	−	3.42636i	0.163589	−	0.596453i
$34$	−5.68717			−0.975342
$35$	−3.02534	+	3.73550i	−0.511377	+	0.631415i
$36$	2.61556	−	1.46930i	0.435926	−	0.244884i
$37$	−3.65306	+	2.10909i	−0.600559	+	0.346733i	−0.769262	−	0.638934i	$-0.779376\pi$
$37$	−3.65306	+	2.10909i	−0.600559	+	0.346733i	0.168702	+	0.985667i	$0.446042\pi$
$38$	0.796762	+	1.38003i	0.129252	+	0.223871i
$39$	2.41271	−	5.76010i	0.386344	−	0.922355i
$40$	1.57344	+	0.908426i	0.248783	+	0.143635i
$41$	−0.397180	−	0.229312i	−0.0620290	−	0.0358125i	0.468665	−	0.883376i	$-0.344735\pi$
$41$	−0.397180	−	0.229312i	−0.0620290	−	0.0358125i	−0.530694	+	0.847564i	$0.678069\pi$
$42$	−0.451878	−	4.56024i	−0.0697263	−	0.703661i
$43$	0.836012	+	1.44802i	0.127491	+	0.220820i	0.922704	−	0.385510i	$-0.125974\pi$
$43$	0.836012	+	1.44802i	0.127491	+	0.220820i	−0.795213	+	0.606330i	$0.792641\pi$
$44$	−1.02563	+	1.77645i	−0.154620	+	0.267810i
$45$	−2.66951	−	4.75208i	−0.397947	−	0.708399i
$46$	−7.56871	−	4.36980i	−1.11595	−	0.644292i
$47$	−1.94760	−	1.12445i	−0.284086	−	0.164017i	0.351186	−	0.936306i	$-0.385779\pi$
$47$	−1.94760	−	1.12445i	−0.284086	−	0.164017i	−0.635272	+	0.772289i	$0.719112\pi$
$48$	−1.67564	+	0.438430i	−0.241858	+	0.0632819i
$49$	−6.65712	−	2.16397i	−0.951017	−	0.309139i
$50$	−0.849523	+	1.47142i	−0.120141	+	0.208090i
$51$	−6.92421	−	7.00622i	−0.969583	−	0.981068i
$52$	−2.18942	+	2.86469i	−0.303618	+	0.397261i
$53$	−0.497067	+	0.286982i	−0.0682774	+	0.0394200i	−0.533750	−	0.845642i	$-0.679218\pi$
$53$	−0.497067	+	0.286982i	−0.0682774	+	0.0394200i	0.465473	+	0.885062i	$0.345884\pi$
$54$	4.99456	+	1.43330i	0.679674	+	0.195047i
$55$	3.22755	+	1.86343i	0.435202	+	0.251264i
$56$	−0.414054	+	2.61315i	−0.0553303	+	0.349197i
$57$	−0.730041	+	2.66176i	−0.0966962	+	0.352559i
$58$		−	0.836443i		−	0.109830i
$59$	−1.89789	−	1.09575i	−0.247084	−	0.142654i	0.371344	−	0.928495i	$-0.378897\pi$
$59$	−1.89789	−	1.09575i	−0.247084	−	0.142654i	−0.618428	+	0.785841i	$0.712230\pi$
$60$	0.796563	+	3.04440i	0.102836	+	0.393030i
$61$		−	6.89812i		−	0.883213i	−0.897209	−	0.441607i	$-0.854409\pi$
$61$		−	6.89812i		−	0.883213i	0.897209	−	0.441607i	$-0.145591\pi$
$62$	3.97501	−	6.88493i	0.504827	−	0.874386i
$63$	5.06775	−	6.10884i	0.638477	−	0.769641i
$64$	1.00000			0.125000
$65$	5.20472	+	3.97785i	0.645566	+	0.493391i
$66$	−3.43719	+	0.899337i	−0.423089	+	0.110701i
$67$		−	5.15514i		−	0.629800i	−0.949125	−	0.314900i	$-0.898029\pi$
$67$		−	5.15514i		−	0.629800i	0.949125	−	0.314900i	$-0.101971\pi$
$68$	2.84359	+	4.92524i	0.344836	+	0.597273i
$69$	−3.83170	−	14.6444i	−0.461283	−	1.76298i
$70$	4.74771	+	0.752275i	0.567460	+	0.0899140i
$71$	4.24250	+	7.34823i	0.503493	+	0.872075i	0.999992	+	0.00403764i	$0.00128522\pi$
$71$	4.24250	+	7.34823i	0.503493	+	0.872075i	−0.496499	+	0.868037i	$0.665381\pi$
$72$	−2.58023	−	1.53049i	−0.304083	−	0.180370i
$73$	−5.11752	−	8.86381i	−0.598961	−	1.03743i	−0.992975	−	0.118326i	$-0.962247\pi$
$73$	−5.11752	−	8.86381i	−0.598961	−	1.03743i	0.394014	−	0.919104i	$-0.371086\pi$
$74$	3.65306	+	2.10909i	0.424659	+	0.245177i
$75$	−2.84699	+	0.744913i	−0.328742	+	0.0860151i
$76$	0.796762	−	1.38003i	0.0913948	−	0.158300i
$77$	−0.849335	+	5.36027i	−0.0967907	+	0.610860i
$78$	−6.19475	+	0.790580i	−0.701418	+	0.0895156i
$79$	−3.68537	+	6.38325i	−0.414637	+	0.718172i	−0.995390	−	0.0959076i	$-0.969425\pi$
$79$	−3.68537	+	6.38325i	−0.414637	+	0.718172i	0.580754	+	0.814079i	$0.302758\pi$
$80$		−	1.81685i		−	0.203130i
$81$	4.31521	+	7.89803i	0.479468	+	0.877559i
$82$			0.458624i			0.0506465i
$83$			15.0678i			1.65391i	0.562269	+	0.826954i	$0.309929\pi$
$83$			15.0678i			1.65391i	−0.562269	+	0.826954i	$0.690071\pi$
$84$	−3.72335	+	2.67146i	−0.406250	+	0.291480i
$85$	8.94843	−	5.16638i	0.970594	−	0.560373i
$86$	0.836012	−	1.44802i	0.0901495	−	0.156143i
$87$	1.03044	−	1.01838i	0.110475	−	0.109182i
$88$	2.05127			0.218666
$89$	−3.34558	+	1.93157i	−0.354630	+	0.204746i	−0.666723	−	0.745306i	$-0.732303\pi$
$89$	−3.34558	+	1.93157i	−0.354630	+	0.204746i	0.312092	+	0.950052i	$0.398970\pi$
$90$	−2.78067	+	4.68791i	−0.293108	+	0.494149i
$91$	−2.69233	+	9.15158i	−0.282233	+	0.959346i
$92$			8.73960i			0.911166i
$93$	13.3214	−	3.48553i	1.38137	−	0.361433i
$94$			2.24889i			0.231955i
$95$	−2.50731	−	1.44760i	−0.257245	−	0.148520i
$96$	1.21751	+	1.23193i	0.124262	+	0.125734i
$97$	1.72410	+	2.98622i	0.175056	+	0.303205i	0.940180	−	0.340677i	$-0.110656\pi$
$97$	1.72410	+	2.98622i	0.175056	+	0.303205i	−0.765125	+	0.643882i	$0.777323\pi$
$98$	1.45451	+	6.84722i	0.146927	+	0.691674i
$99$	−5.29275	−	3.13944i	−0.531941	−	0.315526i
$100$	1.69905			0.169905
$101$	−9.69622			−0.964810			−0.482405	−	0.875948i	$-0.660237\pi$
$101$	−9.69622			−0.964810			−0.482405	+	0.875948i	$0.660237\pi$
$102$	−2.60546	+	9.49965i	−0.257979	+	0.940606i
$103$	8.08628	+	4.66861i	0.796765	+	0.460012i	0.842339	−	0.538949i	$-0.181178\pi$
$103$	8.08628	+	4.66861i	0.796765	+	0.460012i	−0.0455739	+	0.998961i	$0.514512\pi$
$104$	3.57560	+	0.463745i	0.350617	+	0.0454740i
$105$	4.85365	+	6.76477i	0.473667	+	0.660174i
$106$	0.497067	+	0.286982i	0.0482794	+	0.0278742i
$107$	9.27165	−	5.35299i	0.896324	−	0.517493i	0.0203184	−	0.999794i	$-0.493532\pi$
$107$	9.27165	−	5.35299i	0.896324	−	0.517493i	0.876006	+	0.482301i	$0.160199\pi$
$108$	−1.25601	−	5.04207i	−0.120859	−	0.485173i
$109$	4.30381	−	2.48481i	0.412230	−	0.238001i	−0.279517	−	0.960141i	$-0.590174\pi$
$109$	4.30381	−	2.48481i	0.412230	−	0.238001i	0.691748	+	0.722139i	$0.256841\pi$
$110$		−	3.72685i		−	0.355341i
$111$	1.84938	+	7.06818i	0.175535	+	0.670882i
$112$	2.47008	−	0.947995i	0.233401	−	0.0895771i
$113$	−14.4435	+	8.33897i	−1.35873	+	0.784464i	−0.989453	−	0.144855i	$-0.953729\pi$
$113$	−14.4435	+	8.33897i	−1.35873	+	0.784464i	−0.369279	+	0.929319i	$0.620395\pi$
$114$	2.67018	−	0.698648i	0.250085	−	0.0654344i
$115$	15.8786			1.48068
$116$	−0.724381	+	0.418222i	−0.0672571	+	0.0388309i
$117$	−8.51614	−	6.66899i	−0.787317	−	0.616548i
$118$			2.19150i			0.201743i
$119$	11.6930	+	9.47004i	1.07189	+	0.868117i
$120$	2.23824	−	2.21204i	0.204323	−	0.201931i
$121$	−6.79230			−0.617482
$122$	−5.97394	+	3.44906i	−0.540855	+	0.312263i
$123$	−0.564994	+	0.558380i	−0.0509438	+	0.0503474i
$124$	−7.95003			−0.713934
$125$		−	12.1712i		−	1.08862i
$126$	−7.82428	−	1.33438i	−0.697043	−	0.118876i
$127$	−10.6930	+	18.5208i	−0.948852	+	1.64346i	−0.201003	+	0.979591i	$0.564420\pi$
$127$	−10.6930	+	18.5208i	−0.948852	+	1.64346i	−0.747849	+	0.663869i	$0.768913\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	2.80171	−	0.733065i	0.246677	−	0.0645428i
$130$	0.842557	−	6.49635i	0.0738972	−	0.569767i
$131$	7.44741	−	12.8993i	0.650683	−	1.12702i	−0.332274	−	0.943183i	$-0.607816\pi$
$131$	7.44741	−	12.8993i	0.650683	−	1.12702i	0.982957	−	0.183834i	$-0.0588508\pi$
$132$	2.49744	+	2.52703i	0.217375	+	0.219949i
$133$	0.659804	−	4.16412i	0.0572123	−	0.361075i
$134$	−4.46448	+	2.57757i	−0.385672	+	0.222668i
$135$	−9.16069	+	2.28198i	−0.788427	+	0.196402i
$136$	2.84359	−	4.92524i	0.243836	−	0.422336i
$137$	5.80216	−	10.0496i	0.495712	−	0.858598i	−0.504276	−	0.863543i	$-0.668241\pi$
$137$	5.80216	−	10.0496i	0.495712	−	0.858598i	0.999988	+	0.00494447i	$0.00157388\pi$
$138$	−10.7666	+	10.6406i	−0.916515	+	0.905786i
$139$	−13.6556	+	7.88408i	−1.15825	+	0.668719i	−0.950885	−	0.309544i	$-0.899824\pi$
$139$	−13.6556	+	7.88408i	−1.15825	+	0.668719i	−0.207370	+	0.978263i	$0.566490\pi$
$140$	−1.72237	−	4.48778i	−0.145567	−	0.379286i
$141$	−2.77049	+	2.73805i	−0.233317	+	0.230586i
$142$	4.24250	−	7.34823i	0.356023	−	0.616650i
$143$	7.33452	+	0.951266i	0.613343	+	0.0795489i
$144$	−0.0353243	+	2.99979i	−0.00294369	+	0.249983i
$145$	0.759847	+	1.31609i	0.0631019	+	0.109296i
$146$	−5.11752	+	8.86381i	−0.423529	+	0.733574i
$147$	−6.66444	+	10.1284i	−0.549674	+	0.835379i
$148$		−	4.21819i		−	0.346733i
$149$	−4.81481			−0.394444			−0.197222	−	0.980359i	$-0.563192\pi$
$149$	−4.81481			−0.394444			−0.197222	+	0.980359i	$0.563192\pi$
$150$	2.06861	+	2.09311i	0.168901	+	0.170902i
$151$	1.23569	−	0.713427i	0.100559	−	0.0580579i	−0.448877	−	0.893594i	$-0.648176\pi$
$151$	1.23569	−	0.713427i	0.100559	−	0.0580579i	0.549436	+	0.835536i	$0.314843\pi$
$152$	−1.59352			−0.129252
$153$	−14.8751	+	8.35619i	−1.20258	+	0.675558i
$154$	5.06680	−	1.94459i	0.408294	−	0.156700i
$155$			14.4440i			1.16017i
$156$	3.78204	+	4.96952i	0.302806	+	0.397880i
$157$	7.14347	−	4.12428i	0.570111	−	0.329154i	−0.187083	−	0.982344i	$-0.559903\pi$
$157$	7.14347	−	4.12428i	0.570111	−	0.329154i	0.757194	+	0.653191i	$0.226570\pi$
$158$	7.37074			0.586385
$159$	0.251643	+	0.961759i	0.0199566	+	0.0762724i
$160$	−1.57344	+	0.908426i	−0.124391	+	0.0718174i
$161$	8.28509	+	21.5875i	0.652957	+	1.70134i
$162$	4.68229	−	7.68610i	0.367875	−	0.603877i
$163$			23.9508i			1.87597i	0.346676	+	0.937985i	$0.387310\pi$
$163$			23.9508i			1.87597i	−0.346676	+	0.937985i	$0.612690\pi$
$164$	0.397180	−	0.229312i	0.0310145	−	0.0179062i
$165$	4.59124	−	4.53749i	0.357427	−	0.353243i
$166$	13.0491	−	7.53391i	1.01281	−	0.584745i
$167$	−20.2949	−	11.7173i	−1.57047	−	0.906711i	−0.996111	−	0.0881060i	$-0.971919\pi$
$167$	−20.2949	−	11.7173i	−1.57047	−	0.906711i	−0.574358	−	0.818604i	$-0.694748\pi$
$168$	4.17522	+	1.88878i	0.322126	+	0.145723i
$169$	12.5699	+	3.31634i	0.966914	+	0.255103i
$170$	−8.94843	−	5.16638i	−0.686313	−	0.396243i
$171$	4.11166	+	2.43887i	0.314427	+	0.186505i
$172$	−1.67202			−0.127491
$173$	7.60591			0.578267			0.289133	−	0.957289i	$-0.406633\pi$
$173$	7.60591			0.578267			0.289133	+	0.957289i	$0.406633\pi$
$174$	−1.39717	−	0.383200i	−0.105919	−	0.0290503i
$175$	4.19678	−	1.61069i	0.317247	−	0.121756i
$176$	−1.02563	−	1.77645i	−0.0773101	−	0.133905i
$177$	−2.69978	+	2.66817i	−0.202928	+	0.200552i
$178$	3.34558	+	1.93157i	0.250762	+	0.144777i
$179$		−	18.4008i		−	1.37534i	−0.726022	−	0.687671i	$-0.758633\pi$
$179$		−	18.4008i		−	1.37534i	0.726022	−	0.687671i	$-0.241367\pi$
$180$	5.45018	+	0.0641790i	0.406232	+	0.00478362i
$181$		−	0.190838i		−	0.0141849i	−0.999975	−	0.00709245i	$-0.997742\pi$
$181$		−	0.190838i		−	0.0141849i	0.999975	−	0.00709245i	$-0.00225762\pi$
$182$	9.27166	−	2.24416i	0.687261	−	0.166348i
$183$	−11.5224	−	3.16023i	−0.851758	−	0.233611i
$184$	7.56871	−	4.36980i	0.557973	−	0.322146i
$185$	−7.66383			−0.563456
$186$	−9.67926	−	9.79391i	−0.709718	−	0.718124i
$187$	5.83296	−	10.1030i	0.426548	−	0.738803i
$188$	1.94760	−	1.12445i	0.142043	−	0.0820086i
$189$	−7.88230	−	11.2636i	−0.573353	−	0.819309i
$190$			2.89520i			0.210040i
$191$			5.19641i			0.375999i	0.982169	+	0.187999i	$0.0602003\pi$
$191$			5.19641i			0.375999i	−0.982169	+	0.187999i	$0.939800\pi$
$192$	0.458130	−	1.67036i	0.0330627	−	0.120548i
$193$			11.0120i			0.792663i	0.918108	+	0.396331i	$0.129717\pi$
$193$			11.0120i			0.792663i	−0.918108	+	0.396331i	$0.870283\pi$
$194$	1.72410	−	2.98622i	0.123783	−	0.214398i
$195$	9.02890	−	6.87141i	0.646573	−	0.492072i
$196$	5.20261	−	4.68325i	0.371615	−	0.334518i
$197$	−11.1333	+	19.2835i	−0.793218	+	1.37389i	0.130746	+	0.991416i	$0.458263\pi$
$197$	−11.1333	+	19.2835i	−0.793218	+	1.37389i	−0.923964	+	0.382478i	$0.875071\pi$
$198$	−0.0724595	+	6.15338i	−0.00514947	+	0.437301i
$199$	−16.5364	−	9.54728i	−1.17223	−	0.676789i	−0.218027	−	0.975943i	$-0.569962\pi$
$199$	−16.5364	−	9.54728i	−1.17223	−	0.676789i	−0.954205	+	0.299154i	$0.903296\pi$
$200$	−0.849523	−	1.47142i	−0.0600703	−	0.104045i
$201$	−8.61096	−	2.36172i	−0.607370	−	0.166583i
$202$	4.84811	+	8.39717i	0.341112	+	0.590823i
$203$	−1.39281	+	1.71975i	−0.0977560	+	0.120703i
$204$	9.52967	−	2.49343i	0.667211	−	0.174575i
$205$	−0.416626	−	0.721617i	−0.0290984	−	0.0503999i
$206$		−	9.33723i		−	0.650556i
$207$	−26.2170	−	0.308720i	−1.82221	−	0.0214575i
$208$	−1.38619	−	3.32844i	−0.0961147	−	0.230786i
$209$	−3.26874			−0.226104
$210$	3.43164	−	7.58577i	0.236806	−	0.523468i
$211$	−7.80557	+	13.5196i	−0.537358	+	0.930731i	0.461688	+	0.887043i	$0.347244\pi$
$211$	−7.80557	+	13.5196i	−0.537358	+	0.930731i	−0.999045	+	0.0436882i	$0.986089\pi$
$212$		−	0.573964i		−	0.0394200i
$213$	14.2178	−	3.72008i	0.974191	−	0.254896i
$214$	−9.27165	−	5.35299i	−0.633797	−	0.365923i
$215$			3.03782i			0.207178i
$216$	−3.73855	+	3.60877i	−0.254376	+	0.245546i
$217$	−19.6372	+	7.53658i	−1.33306	+	0.511617i
$218$	−4.30381	−	2.48481i	−0.291491	−	0.168292i
$219$	−17.1503	+	4.48735i	−1.15891	+	0.303227i
$220$	−3.22755	+	1.86343i	−0.217601	+	0.125632i
$221$	12.4516	−	16.2920i	0.837585	−	1.09592i
$222$	5.19653	−	5.13570i	0.348768	−	0.344686i
$223$	4.91509	−	8.51319i	0.329139	−	0.570085i	−0.653202	−	0.757183i	$-0.726575\pi$
$223$	4.91509	−	8.51319i	0.329139	−	0.570085i	0.982341	+	0.187098i	$0.0599082\pi$
$224$	−2.05603	−	1.66516i	−0.137374	−	0.111258i
$225$	−0.0600175	+	5.09678i	−0.00400117	+	0.339786i
$226$	14.4435	+	8.33897i	0.960768	+	0.554700i
$227$	−9.84889	−	5.68626i	−0.653694	−	0.377410i	0.136176	−	0.990685i	$-0.456519\pi$
$227$	−9.84889	−	5.68626i	−0.653694	−	0.377410i	−0.789870	+	0.613274i	$0.789852\pi$
$228$	−1.94014	−	1.96312i	−0.128489	−	0.130011i
$229$	9.48968	−	16.4366i	0.627096	−	1.08616i	−0.361036	−	0.932552i	$-0.617577\pi$
$229$	9.48968	−	16.4366i	0.627096	−	1.08616i	0.988132	−	0.153610i	$-0.0490898\pi$
$230$	−7.93928	−	13.7512i	−0.523501	−	0.906730i
$231$	8.56450	+	3.87440i	0.563503	+	0.254917i
$232$	0.724381	+	0.418222i	0.0475580	+	0.0274576i
$233$	−18.2307	−	10.5255i	−1.19433	−	0.689550i	−0.235048	−	0.971984i	$-0.575525\pi$
$233$	−18.2307	−	10.5255i	−1.19433	−	0.689550i	−0.959287	+	0.282434i	$0.908858\pi$
$234$	−1.51745	+	10.7097i	−0.0991985	+	0.700114i
$235$	−2.04295	−	3.53850i	−0.133267	−	0.230826i
$236$	1.89789	−	1.09575i	0.123542	−	0.0713271i
$237$	8.97398	+	9.08027i	0.582922	+	0.589827i
$238$	2.35480	−	14.8614i	0.152639	−	0.963324i
$239$	16.6885			1.07949			0.539746	−	0.841828i	$-0.318520\pi$
$239$	16.6885			1.07949			0.539746	+	0.841828i	$0.318520\pi$
$240$	−3.03481	−	0.832355i	−0.195896	−	0.0537283i
$241$	7.63733	−	13.2282i	0.491963	−	0.852106i	−0.507994	−	0.861361i	$-0.669613\pi$
$241$	7.63733	−	13.2282i	0.491963	−	0.852106i	0.999957	+	0.00925504i	$0.00294601\pi$
$242$	3.39615	+	5.88231i	0.218313	+	0.378129i
$243$	15.1695	−	3.58966i	0.973125	−	0.230277i
$244$	5.97394	+	3.44906i	0.382443	+	0.220803i
$245$	−8.50877	−	9.45238i	−0.543606	−	0.603891i
$246$	0.766068	+	0.210109i	0.0488427	+	0.0133961i
$247$	−5.69781	−	0.738989i	−0.362543	−	0.0470208i
$248$	3.97501	+	6.88493i	0.252414	+	0.437193i
$249$	25.1688	+	6.90302i	1.59501	+	0.437461i
$250$	−10.5406	+	6.08559i	−0.666643	+	0.384887i
$251$	−4.91975	−	8.52125i	−0.310532	−	0.537857i	0.667946	−	0.744210i	$-0.267174\pi$
$251$	−4.91975	−	8.52125i	−0.310532	−	0.537857i	−0.978478	+	0.206353i	$0.933840\pi$
$252$	2.75653	+	7.44322i	0.173645	+	0.468879i
$253$	15.5255	−	8.96363i	0.976077	−	0.563538i
$254$	21.3860			1.34188
$255$	−4.53019	−	17.3140i	−0.283692	−	1.08425i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.766166	+	1.32704i	0.0477921	+	0.0827784i	0.888932	−	0.458039i	$-0.151448\pi$
$257$	0.766166	+	1.32704i	0.0477921	+	0.0827784i	−0.841140	+	0.540818i	$0.818115\pi$
$258$	−2.03571	−	2.05982i	−0.126738	−	0.128239i
$259$	−3.99882	−	10.4193i	−0.248475	−	0.647422i
$260$	−6.04728	+	2.51850i	−0.375036	+	0.156191i
$261$	−1.22899	−	2.18777i	−0.0760726	−	0.135419i
$262$	−14.8948			−0.920205
$263$			19.5745i			1.20701i	0.797358	+	0.603507i	$0.206230\pi$
$263$			19.5745i			1.20701i	−0.797358	+	0.603507i	$0.793770\pi$
$264$	0.939747	−	3.42636i	0.0578374	−	0.210878i
$265$	−1.04281			−0.0640592
$266$	−3.93613	+	1.51065i	−0.241340	+	0.0926240i
$267$	1.69372	+	6.47324i	0.103654	+	0.396156i
$268$	4.46448	+	2.57757i	0.272712	+	0.157450i
$269$	6.77900	−	11.7416i	0.413323	−	0.715897i	−0.581928	−	0.813241i	$-0.697701\pi$
$269$	6.77900	−	11.7416i	0.413323	−	0.715897i	0.995251	+	0.0973438i	$0.0310346\pi$
$270$	6.55660	+	6.79240i	0.399022	+	0.413373i
$271$	−14.0278	−	24.2968i	−0.852127	−	1.47593i	−0.879285	−	0.476296i	$-0.841979\pi$
$271$	−14.0278	−	24.2968i	−0.852127	−	1.47593i	0.0271578	−	0.999631i	$-0.491354\pi$
$272$	−5.68717			−0.344836
$273$	14.0530	+	8.68978i	0.850528	+	0.525929i
$274$	−11.6043			−0.701042
$275$	−1.74260	−	3.01827i	−0.105083	−	0.182008i
$276$	14.5983	+	4.00387i	0.878715	+	0.241005i
$277$	−11.6642	+	20.2030i	−0.700836	+	1.21388i	0.267338	+	0.963603i	$0.413856\pi$
$277$	−11.6642	+	20.2030i	−0.700836	+	1.21388i	−0.968173	+	0.250280i	$0.919477\pi$
$278$	13.6556	+	7.88408i	0.819010	+	0.472856i
$279$	0.280829	−	23.8484i	0.0168128	−	1.42777i
$280$	−3.02534	+	3.73550i	−0.180799	+	0.223239i
$281$	26.6302			1.58862			0.794311	−	0.607512i	$-0.207832\pi$
$281$	26.6302			1.58862			0.794311	+	0.607512i	$0.207832\pi$
$282$	3.75647	+	1.03028i	0.223694	+	0.0613525i
$283$			26.9193i			1.60019i	0.599875	+	0.800093i	$0.295217\pi$
$283$			26.9193i			1.60019i	−0.599875	+	0.800093i	$0.704783\pi$
$284$	−8.48501			−0.503493
$285$	−3.56669	+	3.52494i	−0.211273	+	0.208799i
$286$	−2.84344	−	6.82751i	−0.168136	−	0.403719i
$287$	0.763680	−	0.942943i	0.0450786	−	0.0556602i
$288$	2.61556	−	1.46930i	0.154123	−	0.0865796i
$289$	−7.67197	−	13.2882i	−0.451293	−	0.781662i
$290$	0.759847	−	1.31609i	0.0446198	−	0.0772837i
$291$	5.77794	−	1.51179i	0.338709	−	0.0886228i
$292$	10.2350			0.598961
$293$	−6.97220	+	4.02540i	−0.407320	+	0.235167i	−0.689638	−	0.724154i	$-0.742230\pi$
$293$	−6.97220	+	4.02540i	−0.407320	+	0.235167i	0.282317	+	0.959321i	$0.408897\pi$
$294$	12.1037	+	0.707360i	0.705902	+	0.0412541i
$295$	−1.99081	−	3.44819i	−0.115910	−	0.200761i
$296$	−3.65306	+	2.10909i	−0.212330	+	0.122589i
$297$	−7.66878	+	7.40255i	−0.444987	+	0.429539i
$298$	2.40740	+	4.16974i	0.139457	+	0.241547i
$299$	29.0892	−	12.1147i	1.68227	−	0.700612i
$300$	0.778384	−	2.83803i	0.0449400	−	0.163853i
$301$	−4.13004	+	1.58507i	−0.238051	+	0.0913619i
$302$	−1.23569	−	0.713427i	−0.0711061	−	0.0410531i
$303$	−4.44213	+	16.1962i	−0.255194	+	0.930449i
$304$	0.796762	+	1.38003i	0.0456974	+	0.0791502i
$305$	6.26643	−	10.8538i	0.358815	−	0.621486i
$306$	14.6742	+	8.70415i	0.838870	+	0.497583i
$307$	−13.6194			−0.777300			−0.388650	−	0.921385i	$-0.627058\pi$
$307$	−13.6194			−0.777300			−0.388650	+	0.921385i	$0.627058\pi$
$308$	−4.21746	−	3.41568i	−0.240312	−	0.194627i
$309$	11.5029	−	11.3682i	0.654374	−	0.646714i
$310$	12.5089	−	7.22202i	0.710458	−	0.410183i
$311$	−12.6742	−	21.9523i	−0.718685	−	1.24480i	−0.961521	−	0.274732i	$-0.911411\pi$
$311$	−12.6742	−	21.9523i	−0.718685	−	1.24480i	0.242835	−	0.970068i	$-0.421923\pi$
$312$	2.41271	−	5.76010i	0.136593	−	0.326102i
$313$	−7.41295	−	4.27987i	−0.419005	−	0.241913i	0.275647	−	0.961259i	$-0.411108\pi$
$313$	−7.41295	−	4.27987i	−0.419005	−	0.241913i	−0.694651	+	0.719347i	$0.744441\pi$
$314$	−7.14347	−	4.12428i	−0.403129	−	0.232747i
$315$	13.5232	−	5.00821i	0.761948	−	0.282181i
$316$	−3.68537	−	6.38325i	−0.207318	−	0.359086i
$317$	−11.7752	+	20.3952i	−0.661360	+	1.14551i	0.318898	+	0.947789i	$0.396687\pi$
$317$	−11.7752	+	20.3952i	−0.661360	+	1.14551i	−0.980258	+	0.197721i	$0.936646\pi$
$318$	0.707086	−	0.698809i	0.0396514	−	0.0391872i
$319$	1.48590	+	0.857885i	0.0831944	+	0.0480323i
$320$	1.57344	+	0.908426i	0.0879580	+	0.0507826i
$321$	−4.69382	−	17.9394i	−0.261984	−	1.00128i
$322$	14.5528	−	17.9689i	0.810996	−	1.00137i
$323$	−4.53132	+	7.84848i	−0.252129	+	0.436701i
$324$	−8.99750	−	0.211931i	−0.499861	−	0.0117739i
$325$	−2.35519	−	5.65516i	−0.130643	−	0.313692i
$326$	20.7420	−	11.9754i	1.14879	−	0.663256i
$327$	−2.17883	−	8.32730i	−0.120489	−	0.460501i
$328$	−0.397180	−	0.229312i	−0.0219306	−	0.0126616i
$329$	3.74476	−	4.62378i	0.206455	−	0.254917i
$330$	−6.22520	−	1.70738i	−0.342686	−	0.0939883i
$331$		−	7.11121i		−	0.390868i	−0.980717	−	0.195434i	$-0.937389\pi$
$331$		−	7.11121i		−	0.390868i	0.980717	−	0.195434i	$-0.0626115\pi$
$332$	−13.0491	−	7.53391i	−0.716163	−	0.413477i
$333$	12.6537	+	0.149004i	0.693418	+	0.00816539i
$334$			23.4346i			1.28228i
$335$	4.68306	−	8.11130i	0.255863	−	0.443168i
$336$	−0.451878	−	4.56024i	−0.0246520	−	0.248782i
$337$	19.1187			1.04146			0.520730	−	0.853722i	$-0.325660\pi$
$337$	19.1187			1.04146			0.520730	+	0.853722i	$0.325660\pi$
$338$	−3.41291	−	12.5440i	−0.185638	−	0.682304i
$339$	7.31211	+	27.9463i	0.397139	+	1.51783i
$340$			10.3328i			0.560373i
$341$	8.15382	+	14.1228i	0.441554	+	0.764794i
$342$	0.0562900	−	4.78024i	0.00304382	−	0.258486i
$343$	8.41119	−	16.5001i	0.454161	−	0.890919i
$344$	0.836012	+	1.44802i	0.0450747	+	0.0780717i
$345$	7.27444	−	26.5230i	0.391643	−	1.42795i
$346$	−3.80295	−	6.58691i	−0.204448	−	0.354114i
$347$	−19.9793	−	11.5350i	−1.07254	−	0.619233i	−0.143668	−	0.989626i	$-0.545890\pi$
$347$	−19.9793	−	11.5350i	−1.07254	−	0.619233i	−0.928875	+	0.370393i	$0.879223\pi$
$348$	0.366722	+	1.40158i	0.0196584	+	0.0751326i
$349$	−2.11359	+	3.66085i	−0.113138	+	0.195961i	−0.917034	−	0.398809i	$-0.869424\pi$
$349$	−2.11359	+	3.66085i	−0.113138	+	0.195961i	0.803896	+	0.594770i	$0.202757\pi$
$350$	−3.49329	−	2.82918i	−0.186724	−	0.151226i
$351$	−15.0411	+	11.1698i	−0.802837	+	0.596199i
$352$	−1.02563	+	1.77645i	−0.0546665	+	0.0946851i
$353$		−	31.9394i		−	1.69996i	−0.526813	−	0.849981i	$-0.676613\pi$
$353$		−	31.9394i		−	1.69996i	0.526813	−	0.849981i	$-0.323387\pi$
$354$	3.66060	+	1.00399i	0.194558	+	0.0533614i
$355$			15.4160i			0.818197i
$356$		−	3.86314i		−	0.204746i
$357$	21.1753	−	15.1931i	1.12072	−	0.804101i
$358$	−15.9356	+	9.20041i	−0.842222	+	0.486257i
$359$	−12.2496	+	21.2169i	−0.646509	+	1.11979i	0.337442	+	0.941346i	$0.390438\pi$
$359$	−12.2496	+	21.2169i	−0.646509	+	1.11979i	−0.983951	+	0.178440i	$0.942895\pi$
$360$	−2.66951	−	4.75208i	−0.140696	−	0.250457i
$361$	−16.4607			−0.866352
$362$	−0.165271	+	0.0954192i	−0.00868645	+	0.00501512i
$363$	−3.11176	+	11.3456i	−0.163325	+	0.595491i
$364$	−6.57933	−	6.90741i	−0.344851	−	0.362047i
$365$		−	18.5956i		−	0.973337i
$366$	3.02434	+	11.5588i	0.158085	+	0.604187i
$367$			33.2113i			1.73361i	0.498643	+	0.866807i	$0.333832\pi$
$367$			33.2113i			1.73361i	−0.498643	+	0.866807i	$0.666168\pi$
$368$	−7.56871	−	4.36980i	−0.394546	−	0.227792i
$369$	0.673858	+	1.19956i	0.0350796	+	0.0624464i
$370$	3.83191	+	6.63707i	0.199212	+	0.345045i
$371$	−0.544115	−	1.41774i	−0.0282490	−	0.0736053i
$372$	−3.64215	+	13.2794i	−0.188836	+	0.688507i
$373$	−4.12006			−0.213328			−0.106664	−	0.994295i	$-0.534017\pi$
$373$	−4.12006			−0.213328			−0.106664	+	0.994295i	$0.534017\pi$
$374$	−11.6659			−0.603230
$375$	−20.3303	−	5.57598i	−1.04985	−	0.287942i
$376$	−1.94760	−	1.12445i	−0.100440	−	0.0579888i
$377$	2.39615	+	1.83132i	0.123408	+	0.0943179i
$378$	−5.81344	+	12.4581i	−0.299011	+	0.640775i
$379$	−2.80001	−	1.61659i	−0.143827	−	0.0830385i	0.426360	−	0.904554i	$-0.359796\pi$
$379$	−2.80001	−	1.61659i	−0.143827	−	0.0830385i	−0.570187	+	0.821515i	$0.693129\pi$
$380$	2.50731	−	1.44760i	0.128623	−	0.0742602i
$381$	26.0378	+	26.3462i	1.33396	+	1.34976i
$382$	4.50022	−	2.59820i	0.230251	−	0.132936i
$383$		−	4.17622i		−	0.213395i	−0.994292	−	0.106698i	$-0.965972\pi$
$383$		−	4.17622i		−	0.213395i	0.994292	−	0.106698i	$-0.0340276\pi$
$384$	−1.67564	+	0.438430i	−0.0855098	+	0.0223735i
$385$	−6.20579	+	7.66251i	−0.316276	+	0.390518i
$386$	9.53669	−	5.50601i	0.485405	−	0.280249i
$387$	0.0590630	−	5.01572i	0.00300234	−	0.254964i
$388$	−3.44819			−0.175056
$389$	3.57665	−	2.06498i	0.181343	−	0.104699i	−0.406580	−	0.913615i	$-0.633279\pi$
$389$	3.57665	−	2.06498i	0.181343	−	0.104699i	0.587924	+	0.808916i	$0.299946\pi$
$390$	−10.4653	−	4.38355i	−0.529929	−	0.221970i
$391$		−	49.7036i		−	2.51362i
$392$	−6.65712	−	2.16397i	−0.336235	−	0.109297i
$393$	−18.1346	−	18.3494i	−0.914772	−	0.925607i
$394$	22.2667			1.12178
$395$	−11.5974	+	6.69578i	−0.583530	+	0.336901i
$396$	5.36521	−	3.01394i	0.269612	−	0.151456i
$397$	4.76265			0.239031			0.119515	−	0.992832i	$-0.461866\pi$
$397$	4.76265			0.239031			0.119515	+	0.992832i	$0.461866\pi$
$398$			19.0946i			0.957124i
$399$	−6.65332	−	3.00982i	−0.333082	−	0.150679i
$400$	−0.849523	+	1.47142i	−0.0424761	+	0.0735708i
$401$	−7.74045	−	13.4069i	−0.386540	−	0.669507i	0.605442	−	0.795890i	$-0.292996\pi$
$401$	−7.74045	−	13.4069i	−0.386540	−	0.669507i	−0.991982	+	0.126383i	$0.959663\pi$
$402$	2.26017	+	8.63817i	0.112727	+	0.430833i
$403$	11.0202	+	26.4612i	0.548956	+	1.31812i
$404$	4.84811	−	8.39717i	0.241202	−	0.417775i
$405$	−0.385047	+	16.3471i	−0.0191331	+	0.812296i
$406$	2.18575	+	0.346332i	0.108477	+	0.0171882i
$407$	−7.49340	+	4.32632i	−0.371434	+	0.214448i
$408$	−6.92421	−	7.00622i	−0.342799	−	0.346860i
$409$	−19.8942	+	34.4578i	−0.983706	+	1.70383i	−0.336155	+	0.941807i	$0.609127\pi$
$409$	−19.8942	+	34.4578i	−0.983706	+	1.70383i	−0.647551	+	0.762022i	$0.724207\pi$
$410$	−0.416626	+	0.721617i	−0.0205757	+	0.0356381i
$411$	−14.1284	−	14.2958i	−0.696903	−	0.705158i
$412$	−8.08628	+	4.66861i	−0.398382	+	0.230006i
$413$	3.64918	−	4.50578i	0.179565	−	0.221715i
$414$	12.8411	+	22.8589i	0.631107	+	1.12345i
$415$	−13.6880	+	23.7083i	−0.671918	+	1.16380i
$416$	−2.18942	+	2.86469i	−0.107345	+	0.140453i
$417$	6.91323	+	26.4218i	0.338542	+	1.29388i
$418$	1.63437	+	2.83081i	0.0799397	+	0.138460i
$419$	−13.1146	+	22.7152i	−0.640690	+	1.10971i	0.344589	+	0.938754i	$0.388018\pi$
$419$	−13.1146	+	22.7152i	−0.640690	+	1.10971i	−0.985279	+	0.170954i	$0.945315\pi$
$420$	−8.28529	+	0.820996i	−0.404281	+	0.0400605i
$421$		−	14.0343i		−	0.683989i	−0.939702	−	0.341994i	$-0.888898\pi$
$421$		−	14.0343i		−	0.683989i	0.939702	−	0.341994i	$-0.111102\pi$
$422$	15.6111			0.759939
$423$	3.30430	+	5.88210i	0.160661	+	0.285998i
$424$	−0.497067	+	0.286982i	−0.0241397	+	0.0139371i
$425$	−9.66277			−0.468713
$426$	−10.3306	−	10.4530i	−0.500520	−	0.506448i
$427$	18.0258	+	2.85619i	0.872331	+	0.138221i
$428$			10.7060i			0.517493i
$429$	4.94912	−	11.8155i	0.238946	−	0.570458i
$430$	2.63083	−	1.51891i	0.126870	−	0.0732484i
$431$	−16.1254			−0.776735			−0.388368	−	0.921504i	$-0.626961\pi$
$431$	−16.1254			−0.776735			−0.388368	+	0.921504i	$0.626961\pi$
$432$	4.99456	+	1.43330i	0.240301	+	0.0689596i
$433$	13.9038	−	8.02734i	0.668172	−	0.385769i	−0.127211	−	0.991876i	$-0.540603\pi$
$433$	13.9038	−	8.02734i	0.668172	−	0.385769i	0.795384	+	0.606106i	$0.207269\pi$
$434$	16.3455	+	13.2380i	0.784608	+	0.635446i
$435$	2.54647	−	0.666280i	0.122094	−	0.0319457i
$436$			4.96961i			0.238001i
$437$	−12.0609	+	6.96338i	−0.576952	+	0.333103i
$438$	12.4613	+	12.6089i	0.595424	+	0.602477i
$439$	14.0100	−	8.08869i	0.668662	−	0.386052i	−0.126907	−	0.991915i	$-0.540505\pi$
$439$	14.0100	−	8.08869i	0.668662	−	0.386052i	0.795570	+	0.605862i	$0.207172\pi$
$440$	3.22755	+	1.86343i	0.153867	+	0.0888353i
$441$	13.8650	+	15.7722i	0.660238	+	0.751057i
$442$	−20.3351	−	2.63740i	−0.967241	−	0.125448i
$443$	10.8594	+	6.26970i	0.515948	+	0.297883i	0.735275	−	0.677769i	$-0.237053\pi$
$443$	10.8594	+	6.26970i	0.515948	+	0.297883i	−0.219327	+	0.975651i	$0.570386\pi$
$444$	−7.04591	−	1.93248i	−0.334384	−	0.0917114i
$445$	−7.01875			−0.332721
$446$	−9.83018			−0.465473
$447$	−2.20581	+	8.04248i	−0.104331	+	0.380396i
$448$	−0.414054	+	2.61315i	−0.0195622	+	0.123460i
$449$	−8.48307	−	14.6931i	−0.400341	−	0.693411i	0.593426	−	0.804888i	$-0.297775\pi$
$449$	−8.48307	−	14.6931i	−0.400341	−	0.693411i	−0.993767	+	0.111478i	$0.964442\pi$
$450$	4.44395	−	2.49641i	0.209490	−	0.117682i
$451$	−0.814722	−	0.470380i	−0.0383637	−	0.0221493i
$452$		−	16.6779i		−	0.784464i
$453$	−0.625576	−	2.39090i	−0.0293921	−	0.112334i
$454$			11.3725i			0.533739i
$455$	−12.5498	+	11.9537i	−0.588342	+	0.560397i
$456$	−0.730041	+	2.66176i	−0.0341873	+	0.124649i
$457$	−8.20508	+	4.73720i	−0.383817	+	0.221597i	−0.679478	−	0.733696i	$-0.737794\pi$
$457$	−8.20508	+	4.73720i	−0.383817	+	0.221597i	0.295660	+	0.955293i	$0.404460\pi$
$458$	−18.9794			−0.886847
$459$	7.14314	+	28.6751i	0.333413	+	1.33844i
$460$	−7.93928	+	13.7512i	−0.370171	+	0.641155i
$461$	31.5250	−	18.2010i	1.46827	−	0.847703i	0.468898	−	0.883253i	$-0.344651\pi$
$461$	31.5250	−	18.2010i	1.46827	−	0.847703i	0.999368	+	0.0355490i	$0.0113180\pi$
$462$	−0.926922	−	9.35428i	−0.0431243	−	0.435200i
$463$			17.8517i			0.829638i	0.909904	+	0.414819i	$0.136155\pi$
$463$			17.8517i			0.829638i	−0.909904	+	0.414819i	$0.863845\pi$
$464$		−	0.836443i		−	0.0388309i
$465$	24.1268	+	6.61724i	1.11885	+	0.306867i
$466$			21.0510i			0.975170i
$467$	−15.1928	+	26.3147i	−0.703039	+	1.21770i	0.264355	+	0.964425i	$0.414841\pi$
$467$	−15.1928	+	26.3147i	−0.703039	+	1.21770i	−0.967394	+	0.253274i	$0.918492\pi$
$468$	10.0336	−	4.04070i	0.463803	−	0.186781i
$469$	13.4712	+	2.13450i	0.622040	+	0.0985622i
$470$	−2.04295	+	3.53850i	−0.0942343	+	0.163219i
$471$	−3.61642	−	13.8217i	−0.166636	−	0.636868i
$472$	−1.89789	−	1.09575i	−0.0873575	−	0.0504359i
$473$	1.71488	+	2.97027i	0.0788505	+	0.136573i
$474$	3.37676	−	12.3118i	0.155100	−	0.565501i
$475$	1.35373	+	2.34474i	0.0621136	+	0.107584i
$476$	−14.0478	+	5.39141i	−0.643879	+	0.247115i
$477$	1.72177	+	0.0202748i	0.0788345	+	0.000928322i
$478$	−8.34427	−	14.4527i	−0.381658	−	0.661051i
$479$			23.0354i			1.05251i	0.850326	+	0.526257i	$0.176405\pi$
$479$			23.0354i			1.05251i	−0.850326	+	0.526257i	$0.823595\pi$
$480$	0.796563	+	3.04440i	0.0363580	+	0.138957i
$481$	−14.0400	+	5.84720i	−0.640168	+	0.266609i
$482$	−15.2747			−0.695741
$483$	39.8547	−	3.94923i	1.81345	−	0.179696i
$484$	3.39615	−	5.88231i	0.154370	−	0.267378i
$485$			6.26486i			0.284473i
$486$	−10.6935	−	11.3424i	−0.485067	−	0.514500i
$487$	−12.3041	−	7.10375i	−0.557550	−	0.321902i	0.194611	−	0.980880i	$-0.437655\pi$
$487$	−12.3041	−	7.10375i	−0.557550	−	0.321902i	−0.752162	+	0.658979i	$0.770989\pi$
$488$		−	6.89812i		−	0.312263i
$489$	40.0065	+	10.9726i	1.80916	+	0.496197i
$490$	−3.93162	+	12.0950i	−0.177612	+	0.546397i
$491$	2.47085	+	1.42654i	0.111508	+	0.0643790i	0.554717	−	0.832039i	$-0.312827\pi$
$491$	2.47085	+	1.42654i	0.111508	+	0.0643790i	−0.443209	+	0.896418i	$0.646160\pi$
$492$	−0.201074	−	0.768489i	−0.00906513	−	0.0346462i
$493$	4.11968	−	2.37850i	0.185541	−	0.107122i
$494$	2.20892	+	5.30394i	0.0993840	+	0.238636i
$495$	−5.47588	−	9.74780i	−0.246122	−	0.438131i
$496$	3.97501	−	6.88493i	0.178483	−	0.309142i
$497$	−20.9587	+	8.04374i	−0.940125	+	0.360811i
$498$	−6.60619	−	25.2483i	−0.296030	−	1.13140i
$499$	15.9720	+	9.22146i	0.715007	+	0.412809i	0.812912	−	0.582386i	$-0.197881\pi$
$499$	15.9720	+	9.22146i	0.715007	+	0.412809i	−0.0979055	+	0.995196i	$0.531214\pi$
$500$	10.5406	+	6.08559i	0.471388	+	0.272156i
$501$	−28.8698	+	28.5319i	−1.28981	+	1.27471i
$502$	−4.91975	+	8.52125i	−0.219579	+	0.380322i
$503$	−6.05432	−	10.4864i	−0.269949	−	0.467565i	0.698900	−	0.715220i	$-0.253673\pi$
$503$	−6.05432	−	10.4864i	−0.269949	−	0.467565i	−0.968848	+	0.247655i	$0.920340\pi$
$504$	5.06775	−	6.10884i	0.225736	−	0.272109i
$505$	−15.2564	−	8.80830i	−0.678902	−	0.391964i
$506$	−15.5255	−	8.96363i	−0.690191	−	0.398482i
$507$	11.2981	−	19.4770i	0.501768	−	0.865002i
$508$	−10.6930	−	18.5208i	−0.474426	−	0.821730i
$509$	−31.9977	+	18.4739i	−1.41827	+	0.818839i	−0.996147	−	0.0876987i	$-0.972049\pi$
$509$	−31.9977	+	18.4739i	−1.41827	+	0.818839i	−0.422124	+	0.906538i	$0.638715\pi$
$510$	−12.7293	+	12.5803i	−0.563662	+	0.557064i
$511$	25.2814	−	9.70277i	1.11838	−	0.429225i
$512$	1.00000			0.0441942
$513$	5.95747	−	5.75066i	0.263029	−	0.253898i
$514$	0.766166	−	1.32704i	0.0337941	−	0.0585332i
$515$	8.48219	+	14.6916i	0.373770	+	0.647388i
$516$	−0.766004	+	2.79289i	−0.0337215	+	0.122950i
$517$	−3.99504	−	2.30654i	−0.175702	−	0.101441i
$518$	−7.02394	+	8.67272i	−0.308614	+	0.381057i
$519$	3.48449	−	12.7046i	0.152952	−	0.557672i
$520$	5.20472	+	3.97785i	0.228242	+	0.174440i
$521$	9.03063	+	15.6415i	0.395639	+	0.685267i	0.993183	−	0.116569i	$-0.0371898\pi$
$521$	9.03063	+	15.6415i	0.395639	+	0.685267i	−0.597543	+	0.801837i	$0.703856\pi$
$522$	−1.28017	+	2.15822i	−0.0560314	+	0.0944627i
$523$	34.2864	−	19.7952i	1.49924	−	0.865585i	0.499238	−	0.866465i	$-0.333613\pi$
$523$	34.2864	−	19.7952i	1.49924	−	0.865585i	1.00000		0.000879658i	$0.000280004\pi$
$524$	7.44741	+	12.8993i	0.325342	+	0.563508i
$525$	−0.767761	−	7.74806i	−0.0335078	−	0.338153i
$526$	16.9520	−	9.78724i	0.739142	−	0.426744i
$527$	45.2132			1.96952
$528$	−3.43719	+	0.899337i	−0.149585	+	0.0391386i
$529$	26.6903	−	46.2289i	1.16045	−	2.00995i
$530$	0.521404	+	0.903098i	0.0226483	+	0.0392281i
$531$	3.21997	+	5.73198i	0.139735	+	0.248747i
$532$	3.27633	+	2.65347i	0.142047	+	0.115042i
$533$	−1.31381	−	1.00412i	−0.0569076	−	0.0434932i
$534$	4.75913	−	4.70342i	0.205948	−	0.203537i
$535$	19.4512			0.840948
$536$		−	5.15514i		−	0.222668i
$537$	−30.7361	−	8.42997i	−1.32636	−	0.363780i
$538$	−13.5580			−0.584527
$539$	−13.6555	−	4.43888i	−0.588185	−	0.191196i
$540$	2.60409	−	9.07439i	0.112062	−	0.390499i
$541$	21.7849	+	12.5775i	0.936606	+	0.540750i	0.888895	−	0.458111i	$-0.151474\pi$
$541$	21.7849	+	12.5775i	0.936606	+	0.540750i	0.0477116	+	0.998861i	$0.484807\pi$
$542$	−14.0278	+	24.2968i	−0.602545	+	1.04364i
$543$	−0.318770	−	0.0874288i	−0.0136797	−	0.00375193i
$544$	2.84359	+	4.92524i	0.121918	+	0.211168i
$545$	9.02906			0.386762
$546$	0.499056	−	16.5152i	0.0213576	−	0.706784i
$547$	9.83208			0.420389			0.210195	−	0.977660i	$-0.432590\pi$
$547$	9.83208			0.420389			0.210195	+	0.977660i	$0.432590\pi$
$548$	5.80216	+	10.0496i	0.247856	+	0.429299i
$549$	−10.5575	+	17.7988i	−0.450582	+	0.759632i
$550$	−1.74260	+	3.01827i	−0.0743046	+	0.128699i
$551$	−1.15432	−	0.666446i	−0.0491756	−	0.0283916i
$552$	−3.83170	−	14.6444i	−0.163088	−	0.623309i
$553$	−15.1545	−	12.2734i	−0.644433	−	0.521920i
$554$	23.3285			0.991131
$555$	−3.51103	+	12.8014i	−0.149035	+	0.543389i
$556$		−	15.7682i		−	0.668719i
$557$	−5.46504			−0.231561			−0.115781	−	0.993275i	$-0.536937\pi$
$557$	−5.46504			−0.231561			−0.115781	+	0.993275i	$0.536937\pi$
$558$	−20.7938	+	11.6810i	−0.880270	+	0.494497i
$559$	2.31774	+	5.56522i	0.0980298	+	0.235384i
$560$	4.74771	+	0.752275i	0.200627	+	0.0317894i
$561$	−14.2034	−	14.3716i	−0.599668	−	0.606771i
$562$	−13.3151	−	23.0624i	−0.561663	−	0.972828i
$563$	12.7679	−	22.1146i	0.538101	−	0.932018i	−0.460906	−	0.887449i	$-0.652475\pi$
$563$	12.7679	−	22.1146i	0.538101	−	0.932018i	0.999006	−	0.0445687i	$-0.0141914\pi$
$564$	−0.985981	−	3.76834i	−0.0415173	−	0.158676i
$565$	−30.3014			−1.27479
$566$	23.3128	−	13.4597i	0.979910	−	0.565752i
$567$	−22.4255	+	8.00610i	−0.941782	+	0.336225i
$568$	4.24250	+	7.34823i	0.178012	+	0.308325i
$569$	14.3032	−	8.25797i	0.599622	−	0.346192i	−0.169271	−	0.985570i	$-0.554141\pi$
$569$	14.3032	−	8.25797i	0.599622	−	0.346192i	0.768893	+	0.639378i	$0.220808\pi$
$570$	4.83603	+	1.32638i	0.202559	+	0.0555558i
$571$	−1.84946	−	3.20337i	−0.0773977	−	0.134057i	0.824729	−	0.565529i	$-0.191328\pi$
$571$	−1.84946	−	3.20337i	−0.0773977	−	0.134057i	−0.902126	+	0.431472i	$0.857994\pi$
$572$	−4.49108	+	5.87625i	−0.187781	+	0.245698i
$573$	8.67989	+	2.38063i	0.362608	+	0.0994522i
$574$	−1.19845	−	0.189895i	−0.0500225	−	0.00792606i
$575$	−12.8596	−	7.42449i	−0.536282	−	0.309623i
$576$	−2.58023	−	1.53049i	−0.107510	−	0.0637703i
$577$	4.25571	+	7.37111i	0.177168	+	0.306863i	0.940909	−	0.338659i	$-0.109973\pi$
$577$	4.25571	+	7.37111i	0.177168	+	0.306863i	−0.763742	+	0.645522i	$0.776640\pi$
$578$	−7.67197	+	13.2882i	−0.319112	+	0.552718i
$579$	18.3941	+	5.04494i	0.764432	+	0.209660i
$580$	−1.51969			−0.0631019
$581$	−39.3745	−	6.23889i	−1.63353	−	0.258833i
$582$	−4.19822	−	4.24795i	−0.174022	−	0.176083i
$583$	−1.01962	+	0.588677i	−0.0422283	+	0.0243805i
$584$	−5.11752	−	8.86381i	−0.211765	−	0.366787i
$585$	−7.34135	−	18.2295i	−0.303528	−	0.753699i
$586$	6.97220	+	4.02540i	0.288019	+	0.166288i
$587$	5.89064	+	3.40096i	0.243133	+	0.140373i	0.616616	−	0.787264i	$-0.288503\pi$
$587$	5.89064	+	3.40096i	0.243133	+	0.140373i	−0.373483	+	0.927637i	$0.621837\pi$
$588$	−5.43926	−	10.8358i	−0.224311	−	0.446861i
$589$	−6.33428	−	10.9713i	−0.260999	−	0.452064i
$590$	−1.99081	+	3.44819i	−0.0819604	+	0.141960i
$591$	27.1100	+	27.4311i	1.11516	+	1.12837i
$592$	3.65306	+	2.10909i	0.150140	+	0.0866832i
$593$	−6.06317	−	3.50057i	−0.248984	−	0.143751i	0.370315	−	0.928906i	$-0.379250\pi$
$593$	−6.06317	−	3.50057i	−0.248984	−	0.143751i	−0.619299	+	0.785155i	$0.712583\pi$
$594$	10.2452	+	2.94008i	0.420365	+	0.120633i
$595$	9.79540	+	25.5228i	0.401572	+	1.04633i
$596$	2.40740	−	4.16974i	0.0986111	−	0.170799i
$597$	−23.5232	+	23.2479i	−0.962742	+	0.951472i
$598$	−25.0362	−	19.1346i	−1.02381	−	0.782473i
$599$	36.0831	−	20.8326i	1.47432	−	0.851197i	0.474735	−	0.880129i	$-0.342544\pi$
$599$	36.0831	−	20.8326i	1.47432	−	0.851197i	0.999581	+	0.0289321i	$0.00921067\pi$
$600$	−2.84699	+	0.744913i	−0.116228	+	0.0304109i
$601$	−1.93484	−	1.11708i	−0.0789239	−	0.0455668i	0.460019	−	0.887909i	$-0.347843\pi$
$601$	−1.93484	−	1.11708i	−0.0789239	−	0.0455668i	−0.538943	+	0.842342i	$0.681176\pi$
$602$	3.43773	+	2.78418i	0.140111	+	0.113475i
$603$	−7.88987	+	13.3015i	−0.321301	+	0.541677i
$604$			1.42685i			0.0580579i
$605$	−10.6873	−	6.17031i	−0.434500	−	0.250859i
$606$	16.2474	−	4.25111i	0.660006	−	0.172690i
$607$		−	0.676987i		−	0.0274781i	−0.999906	−	0.0137390i	$-0.995627\pi$
$607$		−	0.676987i		−	0.0274781i	0.999906	−	0.0137390i	$-0.00437341\pi$
$608$	0.796762	−	1.38003i	0.0323129	−	0.0559677i
$609$	2.23452	+	3.11437i	0.0905475	+	0.126201i
$610$	−12.5329			−0.507441
$611$	−6.44238	−	4.92376i	−0.260631	−	0.199194i
$612$	0.200895	−	17.0603i	0.00812071	−	0.689623i
$613$			7.33142i			0.296113i	0.988979	+	0.148057i	$0.0473018\pi$
$613$			7.33142i			0.296113i	−0.988979	+	0.148057i	$0.952698\pi$
$614$	6.80970	+	11.7947i	0.274817	+	0.475997i
$615$	−1.39623	+	0.365323i	−0.0563015	+	0.0147312i
$616$	−0.849335	+	5.36027i	−0.0342207	+	0.215972i
$617$	22.6183	+	39.1761i	0.910579	+	1.57717i	0.813248	+	0.581917i	$0.197697\pi$
$617$	22.6183	+	39.1761i	0.910579	+	1.57717i	0.0973311	+	0.995252i	$0.468969\pi$
$618$	−15.5966	−	4.27766i	−0.627386	−	0.172073i
$619$	−5.37271	−	9.30581i	−0.215948	−	0.374032i	0.737618	−	0.675219i	$-0.235951\pi$
$619$	−5.37271	−	9.30581i	−0.215948	−	0.374032i	−0.953565	+	0.301186i	$0.902617\pi$
$620$	−12.5089	−	7.22202i	−0.502369	−	0.290043i
$621$	−12.5265	+	43.6505i	−0.502669	+	1.75163i
$622$	−12.6742	+	21.9523i	−0.508187	+	0.880206i
$623$	−3.66223	−	9.54227i	−0.146724	−	0.382303i
$624$	−6.19475	+	0.790580i	−0.247989	+	0.0316485i
$625$	6.80901	−	11.7935i	0.272360	−	0.471742i
$626$			8.55974i			0.342116i
$627$	−1.49751	+	5.45999i	−0.0598047	+	0.218051i
$628$			8.24857i			0.329154i
$629$			23.9896i			0.956527i
$630$	−11.0989	−	9.20736i	−0.442189	−	0.366830i
$631$	15.7277	−	9.08038i	0.626109	−	0.361484i	−0.153135	−	0.988205i	$-0.548937\pi$
$631$	15.7277	−	9.08038i	0.626109	−	0.361484i	0.779244	+	0.626721i	$0.215603\pi$
$632$	−3.68537	+	6.38325i	−0.146596	+	0.253912i
$633$	19.0068	+	19.2319i	0.755451	+	0.764399i
$634$	23.5504			0.935305
$635$	−33.6497	+	19.4276i	−1.33535	+	0.770962i
$636$	−0.958729	−	0.262950i	−0.0380161	−	0.0104266i
$637$	−22.7997	−	10.8247i	−0.903356	−	0.428891i
$638$		−	1.71577i		−	0.0679279i
$639$	0.299727	−	25.4533i	0.0118570	−	1.00692i
$640$		−	1.81685i		−	0.0718174i
$641$	12.5354	+	7.23732i	0.495119	+	0.285857i	0.726696	−	0.686960i	$-0.241055\pi$
$641$	12.5354	+	7.23732i	0.495119	+	0.285857i	−0.231577	+	0.972817i	$0.574388\pi$
$642$	−13.1891	+	13.0347i	−0.520531	+	0.514437i
$643$	−6.24408	−	10.8151i	−0.246243	−	0.426505i	0.716238	−	0.697856i	$-0.245863\pi$
$643$	−6.24408	−	10.8151i	−0.246243	−	0.426505i	−0.962480	+	0.271352i	$0.912529\pi$
$644$	−22.8379	−	3.61866i	−0.899939	−	0.142595i
$645$	5.07427	+	1.39172i	0.199799	+	0.0547988i
$646$	9.06264			0.356565
$647$	−32.2302			−1.26710			−0.633550	−	0.773702i	$-0.718403\pi$
$647$	−32.2302			−1.26710			−0.633550	+	0.773702i	$0.718403\pi$
$648$	4.31521	+	7.89803i	0.169518	+	0.310264i
$649$	−3.89308	−	2.24767i	−0.152817	−	0.0882288i
$650$	−3.71992	+	4.86724i	−0.145907	+	0.190909i
$651$	3.59244	+	36.2540i	0.140799	+	1.42091i
$652$	−20.7420	−	11.9754i	−0.812319	−	0.468992i
$653$	31.8138	−	18.3677i	1.24497	−	0.718783i	0.274868	−	0.961482i	$-0.411366\pi$
$653$	31.8138	−	18.3677i	1.24497	−	0.718783i	0.970102	+	0.242699i	$0.0780327\pi$
$654$	−6.12224	+	6.05057i	−0.239398	+	0.236596i
$655$	23.4361	−	13.5309i	0.915725	−	0.528694i
$656$			0.458624i			0.0179062i
$657$	−0.361545	+	30.7030i	−0.0141052	+	1.19784i
$658$	−5.87669	−	0.931162i	−0.229097	−	0.0363005i
$659$	39.7060	−	22.9243i	1.54673	−	0.893003i	0.548338	−	0.836257i	$-0.315261\pi$
$659$	39.7060	−	22.9243i	1.54673	−	0.893003i	0.998389	−	0.0567462i	$-0.0180726\pi$
$660$	1.63396	+	6.24487i	0.0636019	+	0.243081i
$661$	−15.0273			−0.584496			−0.292248	−	0.956343i	$-0.594403\pi$
$661$	−15.0273			−0.584496			−0.292248	+	0.956343i	$0.594403\pi$
$662$	−6.15849	+	3.55561i	−0.239356	+	0.138193i
$663$	−21.5091	−	28.2626i	−0.835345	−	1.09763i
$664$			15.0678i			0.584745i
$665$	4.82096	−	5.95261i	0.186949	−	0.230832i
$666$	−6.19780	−	11.0329i	−0.240160	−	0.427517i
$667$	7.31018			0.283051
$668$	20.2949	−	11.7173i	0.785234	−	0.453355i
$669$	−11.9684	−	12.1101i	−0.462724	−	0.468205i
$670$	−9.36613			−0.361845
$671$		−	14.1499i		−	0.546250i
$672$	−3.72335	+	2.67146i	−0.143631	+	0.103054i
$673$	−13.8713	+	24.0258i	−0.534700	+	0.926127i	0.464478	+	0.885585i	$0.346242\pi$
$673$	−13.8713	+	24.0258i	−0.534700	+	0.926127i	−0.999178	+	0.0405428i	$0.987091\pi$
$674$	−9.55933	−	16.5572i	−0.368211	−	0.637761i
$675$	8.48599	+	2.43524i	0.326626	+	0.0937324i
$676$	−9.15697	+	9.22767i	−0.352191	+	0.354910i
$677$	0.275329	−	0.476883i	0.0105817	−	0.0183281i	−0.860686	−	0.509136i	$-0.829965\pi$
$677$	0.275329	−	0.476883i	0.0105817	−	0.0183281i	0.871268	+	0.490808i	$0.163298\pi$
$678$	20.5461	−	20.3056i	0.789069	−	0.779832i
$679$	−8.51732	+	3.26887i	−0.326865	+	0.125448i
$680$	8.94843	−	5.16638i	0.343157	−	0.198122i
$681$	−14.0102	+	13.8462i	−0.536872	+	0.530587i
$682$	8.15382	−	14.1228i	0.312226	−	0.540791i
$683$	18.1878	−	31.5022i	0.695938	−	1.20540i	−0.273926	−	0.961751i	$-0.588322\pi$
$683$	18.1878	−	31.5022i	0.695938	−	1.20540i	0.969864	−	0.243648i	$-0.0783443\pi$
$684$	−4.16795	+	2.34137i	−0.159366	+	0.0895245i
$685$	18.2587	−	10.5417i	0.697629	−	0.402776i
$686$	−18.4951	+	0.965729i	−0.706145	+	0.0368717i
$687$	−23.1076	−	23.3813i	−0.881610	−	0.892053i
$688$	0.836012	−	1.44802i	0.0318727	−	0.0552051i
$689$	−1.91040	+	0.795621i	−0.0727805	+	0.0303107i
$690$	−26.6068	+	6.96164i	−1.01290	+	0.265025i
$691$	16.1760	+	28.0176i	0.615363	+	1.06584i	0.990321	+	0.138797i	$0.0443237\pi$
$691$	16.1760	+	28.0176i	0.615363	+	1.06584i	−0.374958	+	0.927042i	$0.622343\pi$
$692$	−3.80295	+	6.58691i	−0.144567	+	0.250397i
$693$	10.3953	−	12.5309i	0.394885	−	0.476008i
$694$			23.0701i			0.875728i
$695$	−28.6484			−1.08670
$696$	1.03044	−	1.01838i	0.0390588	−	0.0386016i
$697$	−2.25883	+	1.30414i	−0.0855593	+	0.0493977i
$698$	4.22719			0.160001
$699$	−25.9335	+	25.6299i	−0.980895	+	0.969412i
$700$	−0.703496	+	4.43986i	−0.0265897	+	0.167811i
$701$		−	13.2279i		−	0.499612i	−0.968296	−	0.249806i	$-0.919633\pi$
$701$		−	13.2279i		−	0.499612i	0.968296	−	0.249806i	$-0.0803669\pi$
$702$	17.1939	+	7.44111i	0.648942	+	0.280847i
$703$	5.82123	−	3.36089i	0.219552	−	0.126758i
$704$	2.05127			0.0773101
$705$	−6.84652	+	1.79138i	−0.257855	+	0.0674674i
$706$	−27.6603	+	15.9697i	−1.04101	+	0.601028i
$707$	4.01476	−	25.3377i	0.150990	−	0.952922i
$708$	−0.960817	−	3.67216i	−0.0361097	−	0.138008i
$709$		−	27.2697i		−	1.02413i	−0.858946	−	0.512067i	$-0.828880\pi$
$709$		−	27.2697i		−	1.02413i	0.858946	−	0.512067i	$-0.171120\pi$
$710$	13.3507	−	7.70801i	0.501041	−	0.289276i
$711$	19.2786	−	10.8299i	0.723004	−	0.406152i
$712$	−3.34558	+	1.93157i	−0.125381	+	0.0723886i
$713$	60.1715	+	34.7400i	2.25344	+	1.30102i
$714$	−23.7452	−	10.7418i	−0.888643	−	0.402003i
$715$	10.6763	+	8.15963i	0.399270	+	0.305153i
$716$	15.9356	+	9.20041i	0.595541	+	0.343836i
$717$	7.64552	−	27.8760i	0.285527	−	1.04105i
$718$	24.4992			0.914301
$719$	−15.3808			−0.573608			−0.286804	−	0.957989i	$-0.592593\pi$
$719$	−15.3808			−0.573608			−0.286804	+	0.957989i	$0.592593\pi$
$720$	−2.78067	+	4.68791i	−0.103629	+	0.174708i
$721$	−15.5480	+	19.1976i	−0.579036	+	0.714956i
$722$	8.23034	+	14.2554i	0.306302	+	0.530530i
$723$	−18.5971	−	18.8174i	−0.691633	−	0.699826i
$724$	0.165271	+	0.0954192i	0.00614225	+	0.00354623i
$725$		−	1.42116i		−	0.0527804i
$726$	11.3815	−	2.97795i	0.422406	−	0.110522i
$727$		−	34.8309i		−	1.29181i	−0.763420	−	0.645903i	$-0.776481\pi$
$727$		−	34.8309i		−	1.29181i	0.763420	−	0.645903i	$-0.223519\pi$
$728$	−2.69233	+	9.15158i	−0.0997843	+	0.339180i
$729$	0.953579	−	26.9832i	0.0353177	−	0.999376i
$730$	−16.1042	+	9.29779i	−0.596045	+	0.344127i
$731$	9.50909			0.351706
$732$	8.49803	−	8.39855i	0.314096	−	0.310419i
$733$	−9.43951	+	16.3497i	−0.348656	+	0.603890i	−0.986011	−	0.166680i	$-0.946695\pi$
$733$	−9.43951	+	16.3497i	−0.348656	+	0.603890i	0.637355	+	0.770570i	$0.280029\pi$
$734$	28.7618	−	16.6056i	1.06162	−	0.612925i
$735$	−19.6870	+	9.88234i	−0.726168	+	0.364515i
$736$			8.73960i			0.322146i
$737$		−	10.5746i		−	0.389519i
$738$	0.701918	−	1.18336i	0.0258379	−	0.0435599i
$739$			7.95816i			0.292746i	0.989229	+	0.146373i	$0.0467599\pi$
$739$			7.95816i			0.292746i	−0.989229	+	0.146373i	$0.953240\pi$
$740$	3.83191	−	6.63707i	0.140864	−	0.243984i
$741$	−3.84472	+	9.17886i	−0.141239	+	0.337194i
$742$	−0.955740	+	1.18009i	−0.0350863	+	0.0433223i
$743$	9.17025	−	15.8833i	0.336424	−	0.582703i	−0.647334	−	0.762207i	$-0.724116\pi$
$743$	9.17025	−	15.8833i	0.336424	−	0.582703i	0.983757	+	0.179504i	$0.0574492\pi$
$744$	13.3214	−	3.48553i	0.488386	−	0.127786i
$745$	−7.57581	−	4.37390i	−0.277556	−	0.160247i
$746$	2.06003	+	3.56807i	0.0754230	+	0.130636i
$747$	23.0611	−	38.8785i	0.843762	−	1.42249i
$748$	5.83296	+	10.1030i	0.213274	+	0.369401i
$749$	10.1492	+	26.4446i	0.370844	+	0.966266i
$750$	5.33621	+	20.3946i	0.194851	+	0.744704i
$751$	6.89641	+	11.9449i	0.251654	+	0.435877i	0.963981	−	0.265970i	$-0.0856923\pi$
$751$	6.89641	+	11.9449i	0.251654	+	0.435877i	−0.712328	+	0.701847i	$0.752359\pi$
$752$			2.24889i			0.0820086i
$753$	−16.4875	+	4.31393i	−0.600837	+	0.157208i
$754$	0.387897	−	2.99079i	0.0141264	−	0.108918i
$755$	2.59238			0.0943465
$756$	13.6957	−	1.19445i	0.498109	−	0.0434418i
$757$	21.2683	−	36.8378i	0.773010	−	1.33889i	−0.162896	−	0.986643i	$-0.552084\pi$
$757$	21.2683	−	36.8378i	0.773010	−	1.33889i	0.935906	−	0.352249i	$-0.114583\pi$
$758$			3.23318i			0.117434i
$759$	−7.85985	−	30.0397i	−0.285294	−	1.09037i
$760$	−2.50731	−	1.44760i	−0.0909498	−	0.0525099i
$761$		−	32.3111i		−	1.17128i	−0.810573	−	0.585638i	$-0.800844\pi$
$761$		−	32.3111i		−	1.17128i	0.810573	−	0.585638i	$-0.199156\pi$
$762$	9.79758	−	35.7225i	0.354929	−	1.29409i
$763$	4.71117	+	12.2754i	0.170556	+	0.444398i
$764$	−4.50022	−	2.59820i	−0.162812	−	0.0939997i
$765$	−30.9961	−	0.364997i	−1.12067	−	0.0131965i
$766$	−3.61672	+	2.08811i	−0.130677	+	0.0754465i
$767$	−6.27796	−	4.79810i	−0.226684	−	0.173249i
$768$	1.21751	+	1.23193i	0.0439332	+	0.0444536i
$769$	−6.20736	+	10.7515i	−0.223843	+	0.387707i	−0.955972	−	0.293459i	$-0.905194\pi$
$769$	−6.20736	+	10.7515i	−0.223843	+	0.387707i	0.732129	+	0.681166i	$0.238527\pi$
$770$	9.73883	+	1.54312i	0.350963	+	0.0556101i
$771$	2.56764	−	0.671821i	0.0924714	−	0.0241950i
$772$	−9.53669	−	5.50601i	−0.343233	−	0.198166i
$773$	10.8428	+	6.26007i	0.389987	+	0.225159i	0.682154	−	0.731208i	$-0.261043\pi$
$773$	10.8428	+	6.26007i	0.389987	+	0.225159i	−0.292168	+	0.956367i	$0.594377\pi$
$774$	−4.37328	+	2.45671i	−0.157194	+	0.0883047i
$775$	6.75373	−	11.6978i	0.242601	−	0.420197i
$776$	1.72410	+	2.98622i	0.0618915	+	0.107199i
$777$	−19.2360	+	1.90611i	−0.690086	+	0.0683812i
$778$	−3.57665	−	2.06498i	−0.128229	−	0.0740331i
$779$	0.632915	+	0.365414i	0.0226765	+	0.0130923i
$780$	1.43637	+	11.2550i	0.0514302	+	0.402992i
$781$	8.70251	+	15.0732i	0.311400	+	0.539361i
$782$	−43.0446	+	24.8518i	−1.53927	+	0.888699i
$783$	−4.21740	+	1.05058i	−0.150718	+	0.0375447i
$784$	1.45451	+	6.84722i	0.0519467	+	0.244544i
$785$	14.9864			0.534889
$786$	−6.82376	+	24.8798i	−0.243396	+	0.887433i
$787$	19.6903	−	34.1045i	0.701882	−	1.21569i	−0.265924	−	0.963994i	$-0.585677\pi$
$787$	19.6903	−	34.1045i	0.701882	−	1.21569i	0.967805	−	0.251701i	$-0.0809898\pi$
$788$	−11.1333	−	19.2835i	−0.396609	−	0.686947i
$789$	32.6965	+	8.96765i	1.16403	+	0.319257i
$790$	11.5974	+	6.69578i	0.412618	+	0.238225i
$791$	−15.8106	−	41.1959i	−0.562160	−	1.46476i
$792$	−5.29275	−	3.13944i	−0.188070	−	0.111555i
$793$	3.19897	−	24.6649i	0.113599	−	0.875877i
$794$	−2.38133	−	4.12458i	−0.0845101	−	0.146376i
$795$	−0.477742	+	1.74187i	−0.0169437	+	0.0617777i
$796$	16.5364	−	9.54728i	0.586116	−	0.338394i
$797$	−15.1983	−	26.3242i	−0.538350	−	0.932449i	−0.998993	−	0.0448640i	$-0.985715\pi$
$797$	−15.1983	−	26.3242i	−0.538350	−	0.932449i	0.460643	−	0.887585i	$-0.347619\pi$
$798$	0.720078	+	7.26685i	0.0254905	+	0.257244i
$799$	−11.0763	+	6.39492i	−0.391852	+	0.226236i
$800$	1.69905			0.0600703
$801$	11.5886	+	0.136462i	0.409463	+	0.00482166i
$802$	−7.74045	+	13.4069i	−0.273325	+	0.473413i
$803$	−10.4974	−	18.1820i	−0.370446	−	0.641631i
$804$	6.35079	−	6.27645i	0.223975	−	0.221353i
$805$	−6.57458	+	41.4931i	−0.231723	+	1.46244i
$806$	17.4059	−	22.7744i	0.613098	−	0.802193i
$807$	−16.5071	−	16.7026i	−0.581076	−	0.587959i
$808$	−9.69622			−0.341112
$809$			16.3178i			0.573702i	0.957975	+	0.286851i	$0.0926085\pi$
$809$			16.3178i			0.573702i	−0.957975	+	0.286851i	$0.907391\pi$
$810$	14.3496	−	7.84011i	0.504192	−	0.275473i
$811$	5.92788			0.208156			0.104078	−	0.994569i	$-0.466811\pi$
$811$	5.92788			0.208156			0.104078	+	0.994569i	$0.466811\pi$
$812$	−0.792944	−	2.06608i	−0.0278269	−	0.0725053i
$813$	−47.0111	+	12.3004i	−1.64875	+	0.431394i
$814$	7.49340	+	4.32632i	0.262644	+	0.151637i
$815$	−21.7575	+	37.6851i	−0.762133	+	1.32005i
$816$	−2.60546	+	9.49965i	−0.0912095	+	0.332554i
$817$	−1.33220	−	2.30745i	−0.0466079	−	0.0807273i
$818$	39.7884			1.39117
$819$	20.9532	−	19.4926i	0.732165	−	0.681128i
$820$	0.833252			0.0290984
$821$	16.6292	+	28.8027i	0.580364	+	1.00522i	0.995436	+	0.0954314i	$0.0304231\pi$
$821$	16.6292	+	28.8027i	0.580364	+	1.00522i	−0.415072	+	0.909789i	$0.636244\pi$
$822$	−5.31628	+	19.3834i	−0.185427	+	0.676075i
$823$	−1.58413	+	2.74379i	−0.0552193	+	0.0956427i	−0.892314	−	0.451416i	$-0.850919\pi$
$823$	−1.58413	+	2.74379i	−0.0552193	+	0.0956427i	0.837094	+	0.547058i	$0.184252\pi$
$824$	8.08628	+	4.66861i	0.281699	+	0.162639i
$825$	−5.83995	+	1.52801i	−0.203321	+	0.0531987i
$826$	−5.72671	−	0.907397i	−0.199258	−	0.0315724i
$827$	24.0773			0.837250			0.418625	−	0.908159i	$-0.362512\pi$
$827$	24.0773			0.837250			0.418625	+	0.908159i	$0.362512\pi$
$828$	13.3758	−	22.5502i	0.464843	−	0.783674i
$829$		−	34.9812i		−	1.21495i	−0.794340	−	0.607474i	$-0.792183\pi$
$829$		−	34.9812i		−	1.21495i	0.794340	−	0.607474i	$-0.207817\pi$
$830$	27.3760			0.950236
$831$	28.4027	+	28.7391i	0.985279	+	0.996949i
$832$	3.57560	+	0.463745i	0.123962	+	0.0160775i
$833$	−29.5882	+	26.6345i	−1.02517	+	0.922829i
$834$	19.4253	−	19.1979i	0.672644	−	0.664770i
$835$	−21.2886	−	36.8729i	−0.736722	−	1.27604i
$836$	1.63437	−	2.83081i	0.0565259	−	0.0979057i
$837$	−39.7069	−	11.3948i	−1.37247	−	0.393861i
$838$	26.2292			0.906073
$839$	−1.10165	+	0.636039i	−0.0380332	+	0.0219585i	−0.518896	−	0.854837i	$-0.673657\pi$
$839$	−1.10165	+	0.636039i	−0.0380332	+	0.0219585i	0.480863	+	0.876796i	$0.340324\pi$
$840$	4.85365	+	6.76477i	0.167467	+	0.233407i
$841$	−14.1502	−	24.5088i	−0.487937	−	0.845132i
$842$	−12.1540	+	7.01714i	−0.418856	+	0.241827i
$843$	12.2001	−	44.4821i	0.420193	−	1.53204i
$844$	−7.80557	−	13.5196i	−0.268679	−	0.465365i
$845$	16.7653	+	16.6369i	0.576744	+	0.572326i
$846$	3.44190	−	5.80266i	0.118335	−	0.199500i
$847$	2.81238	−	17.7493i	0.0966344	−	0.609874i
$848$	0.497067	+	0.286982i	0.0170694	+	0.00985500i
$849$	44.9651	+	12.3325i	1.54320	+	0.423252i
$850$	4.83138	+	8.36820i	0.165715	+	0.287027i
$851$	−18.4326	+	31.9263i	−0.631863	+	1.09442i
$852$	−3.88724	+	14.1731i	−0.133175	+	0.485561i
$853$	8.88125			0.304088			0.152044	−	0.988374i	$-0.451414\pi$
$853$	8.88125			0.304088			0.152044	+	0.988374i	$0.451414\pi$
$854$	−6.53938	−	17.0389i	−0.223773	−	0.583060i
$855$	4.25393	+	7.57256i	0.145481	+	0.258976i
$856$	9.27165	−	5.35299i	0.316898	−	0.182961i
$857$	14.1680	+	24.5397i	0.483969	+	0.838259i	0.999830	−	0.0184131i	$-0.00586142\pi$
$857$	14.1680	+	24.5397i	0.483969	+	0.838259i	−0.515861	+	0.856672i	$0.672528\pi$
$858$	−12.7071	+	1.62169i	−0.433813	+	0.0553636i
$859$	15.6163	+	9.01607i	0.532821	+	0.307624i	0.742164	−	0.670218i	$-0.233799\pi$
$859$	15.6163	+	9.01607i	0.532821	+	0.307624i	−0.209343	+	0.977842i	$0.567133\pi$
$860$	−2.63083	−	1.51891i	−0.0897106	−	0.0517944i
$861$	−1.22519	−	1.70761i	−0.0417545	−	0.0581953i
$862$	8.06272	+	13.9650i	0.274617	+	0.475651i
$863$	20.8330	−	36.0838i	0.709163	−	1.22831i	−0.256005	−	0.966675i	$-0.582406\pi$
$863$	20.8330	−	36.0838i	0.709163	−	1.22831i	0.965168	−	0.261631i	$-0.0842603\pi$
$864$	−1.25601	−	5.04207i	−0.0427303	−	0.171535i
$865$	11.9674	+	6.90941i	0.406905	+	0.234927i
$866$	−13.9038	−	8.02734i	−0.472469	−	0.272780i
$867$	−25.7110	+	6.72725i	−0.873191	+	0.228469i
$868$	3.29174	−	20.7746i	0.111729	−	0.705137i
$869$	−7.55968	+	13.0938i	−0.256445	+	0.444175i
$870$	−1.85025	−	1.87216i	−0.0627293	−	0.0634723i
$871$	2.39067	−	18.4327i	0.0810048	−	0.624569i
$872$	4.30381	−	2.48481i	0.145745	−	0.0841462i
$873$	0.121805	−	10.3439i	0.00412247	−	0.350087i
$874$	12.0609	+	6.96338i	0.407967	+	0.235540i
$875$	31.8051	+	5.03952i	1.07521	+	0.170367i
$876$	4.68898	−	17.0963i	0.158426	−	0.577629i
$877$			37.0013i			1.24944i	0.780847	+	0.624722i	$0.214788\pi$
$877$			37.0013i			1.24944i	−0.780847	+	0.624722i	$0.785212\pi$
$878$	−14.0100	−	8.08869i	−0.472816	−	0.272980i
$879$	3.52972	+	13.4903i	0.119054	+	0.455016i
$880$		−	3.72685i		−	0.125632i
$881$	12.5417	−	21.7228i	0.422540	−	0.731861i	−0.573647	−	0.819103i	$-0.694472\pi$
$881$	12.5417	−	21.7228i	0.422540	−	0.731861i	0.996187	+	0.0872416i	$0.0278052\pi$
$882$	6.72662	−	19.8935i	0.226497	−	0.669850i
$883$	23.5431			0.792287			0.396144	−	0.918189i	$-0.370348\pi$
$883$	23.5431			0.792287			0.396144	+	0.918189i	$0.370348\pi$
$884$	7.88348	+	18.9294i	0.265150	+	0.636664i
$885$	−6.67178	+	1.74566i	−0.224269	+	0.0586798i
$886$		−	12.5394i		−	0.421270i
$887$	14.7227	+	25.5005i	0.494341	+	0.856224i	0.999979	−	0.00652219i	$-0.00207609\pi$
$887$	14.7227	+	25.5005i	0.494341	+	0.856224i	−0.505638	+	0.862746i	$0.668743\pi$
$888$	1.84938	+	7.06818i	0.0620611	+	0.237193i
$889$	−43.9703	−	35.6111i	−1.47472	−	1.19436i
$890$	3.50938	+	6.07842i	0.117635	+	0.203749i
$891$	8.85166	+	16.2010i	0.296542	+	0.542753i
$892$	4.91509	+	8.51319i	0.164569	+	0.285043i
$893$	3.10354	+	1.79183i	0.103856	+	0.0599613i
$894$	8.06790	−	2.11096i	0.269831	−	0.0706009i
$895$	16.7158	−	28.9526i	0.558748	−	0.967779i
$896$	2.47008	−	0.947995i	0.0825197	−	0.0316703i
$897$	−6.90935	−	54.1397i	−0.230697	−	1.80767i
$898$	−8.48307	+	14.6931i	−0.283084	+	0.490315i
$899$			6.64975i			0.221781i
$900$	−4.38393	−	2.60037i	−0.146131	−	0.0866789i
$901$			3.26423i			0.108747i
$902$			0.940760i			0.0313239i
$903$	0.755550	+	7.62483i	0.0251431	+	0.253739i
$904$	−14.4435	+	8.33897i	−0.480384	+	0.277350i
$905$	0.173363	−	0.300273i	0.00576277	−	0.00998141i
$906$	−1.75779	+	1.73721i	−0.0583987	+	0.0577151i
$907$	13.8539			0.460013			0.230006	−	0.973189i	$-0.426125\pi$
$907$	13.8539			0.460013			0.230006	+	0.973189i	$0.426125\pi$
$908$	9.84889	−	5.68626i	0.326847	−	0.188705i
$909$	25.0185	+	14.8399i	0.829812	+	0.492210i
$910$	16.6271	+	4.89157i	0.551182	+	0.162154i
$911$		−	27.4426i		−	0.909213i	−0.890692	−	0.454607i	$-0.849780\pi$
$911$		−	27.4426i		−	0.909213i	0.890692	−	0.454607i	$-0.150220\pi$
$912$	2.67018	−	0.698648i	0.0884184	−	0.0231346i
$913$			30.9081i			1.02291i
$914$	8.20508	+	4.73720i	0.271400	+	0.156693i
$915$	−15.2589	−	15.4397i	−0.504444	−	0.510420i
$916$	9.48968	+	16.4366i	0.313548	+	0.543081i
$917$	30.6242	+	24.8022i	1.01130	+	0.819041i
$918$	21.2618	−	20.5237i	0.701744	−	0.677383i
$919$	−44.0687			−1.45369			−0.726845	−	0.686801i	$-0.759014\pi$
$919$	−44.0687			−1.45369			−0.726845	+	0.686801i	$0.759014\pi$
$920$	15.8786			0.523501
$921$	−6.23945	+	22.7494i	−0.205597	+	0.749617i
$922$	−31.5250	−	18.2010i	−1.03822	−	0.599417i
$923$	11.7618	+	28.2418i	0.387144	+	0.929590i
$924$	−7.63758	+	5.47988i	−0.251258	+	0.180275i
$925$	6.20671	+	3.58345i	0.204075	+	0.117823i
$926$	15.4600	−	8.92584i	0.508047	−	0.293321i
$927$	−13.7192	−	24.4221i	−0.450599	−	0.802126i
$928$	−0.724381	+	0.418222i	−0.0237790	+	0.0137288i
$929$			41.9005i			1.37471i	0.726321	+	0.687356i	$0.241229\pi$
$929$			41.9005i			1.37471i	−0.726321	+	0.687356i	$0.758771\pi$
$930$	−6.33270	−	24.2030i	−0.207657	−	0.793649i
$931$	10.6083	+	3.44834i	0.347672	+	0.113015i
$932$	18.2307	−	10.5255i	0.597167	−	0.344775i
$933$	−42.4747	+	11.1135i	−1.39056	+	0.363838i
$934$	30.3856			0.994248
$935$	18.3556	−	10.5976i	0.600293	−	0.346579i
$936$	−8.51614	−	6.66899i	−0.278359	−	0.217983i
$937$			1.71598i			0.0560586i	0.999607	+	0.0280293i	$0.00892317\pi$
$937$			1.71598i			0.0560586i	−0.999607	+	0.0280293i	$0.991077\pi$
$938$	−4.88704	−	12.7336i	−0.159568	−	0.415767i
$939$	−10.5450	+	10.4216i	−0.344124	+	0.340096i
$940$	4.08590			0.133267
$941$	−1.26611	+	0.730989i	−0.0412740	+	0.0238296i	−0.520495	−	0.853865i	$-0.674253\pi$
$941$	−1.26611	+	0.730989i	−0.0412740	+	0.0238296i	0.479221	+	0.877694i	$0.340919\pi$
$942$	−10.1617	+	10.0427i	−0.331086	+	0.327210i
$943$	−4.00819			−0.130524
$944$			2.19150i			0.0713271i
$945$	−2.17014	−	24.8831i	−0.0705948	−	0.809449i
$946$	1.71488	−	2.97027i	0.0557557	−	0.0965717i
$947$	7.63402	+	13.2225i	0.248072	+	0.429674i	0.962991	−	0.269534i	$-0.0868696\pi$
$947$	7.63402	+	13.2225i	0.248072	+	0.429674i	−0.714919	+	0.699208i	$0.753536\pi$
$948$	−12.3507	+	3.23156i	−0.401133	+	0.104956i
$949$	−14.1877	−	34.0667i	−0.460552	−	1.10585i
$950$	1.35373	−	2.34474i	0.0439209	−	0.0760733i
$951$	28.6729	+	29.0125i	0.929782	+	0.940795i
$952$	11.6930	+	9.47004i	0.378972	+	0.306926i
$953$	20.0074	−	11.5513i	0.648104	−	0.374183i	−0.139625	−	0.990204i	$-0.544590\pi$
$953$	20.0074	−	11.5513i	0.648104	−	0.374183i	0.787729	+	0.616021i	$0.211257\pi$
$954$	−0.843328	−	1.50124i	−0.0273037	−	0.0486043i
$955$	−4.72055	+	8.17624i	−0.152754	+	0.264577i
$956$	−8.34427	+	14.4527i	−0.269873	+	0.467434i
$957$	2.11371	−	2.08897i	0.0683267	−	0.0675268i
$958$	19.9492	−	11.5177i	0.644530	−	0.372120i
$959$	23.8588	+	19.3230i	0.770441	+	0.623972i
$960$	2.23824	−	2.21204i	0.0722390	−	0.0713933i
$961$	−16.1015	+	27.8886i	−0.519402	+	0.899631i
$962$	12.0838	+	9.23537i	0.389598	+	0.297760i
$963$	−32.1157	−	0.378181i	−1.03491	−	0.0121867i
$964$	7.63733	+	13.2282i	0.245982	+	0.426053i
$965$	−10.0036	+	17.3268i	−0.322028	+	0.557768i
$966$	−23.3475	−	32.5405i	−0.751193	−	1.04697i
$967$			14.3674i			0.462026i	0.972951	+	0.231013i	$0.0742040\pi$
$967$			14.3674i			0.462026i	−0.972951	+	0.231013i	$0.925796\pi$
$968$	−6.79230			−0.218313
$969$	11.0339	+	11.1646i	0.354459	+	0.358658i
$970$	5.42553	−	3.13243i	0.174203	−	0.100576i
$971$	31.3969			1.00758			0.503788	−	0.863827i	$-0.331939\pi$
$971$	31.3969			1.00758			0.503788	+	0.863827i	$0.331939\pi$
$972$	−4.47603	+	14.9320i	−0.143569	+	0.478945i
$973$	−14.9481	−	38.9486i	−0.479215	−	1.24864i
$974$			14.2075i			0.455238i
$975$	−10.5252	+	1.34323i	−0.337075	+	0.0430178i
$976$	−5.97394	+	3.44906i	−0.191221	+	0.110402i
$977$	−43.7552			−1.39985			−0.699926	−	0.714215i	$-0.746784\pi$
$977$	−43.7552			−1.39985			−0.699926	+	0.714215i	$0.746784\pi$
$978$	−10.5007	−	40.1330i	−0.335777	−	1.28331i
$979$	−6.86267	+	3.96217i	−0.219332	+	0.126631i
$980$	12.4404	−	2.64262i	0.397394	−	0.0844155i
$981$	−14.9078	−	0.175548i	−0.475970	−	0.00560481i
$982$		−	2.85309i		−	0.0910457i
$983$	−3.21594	+	1.85672i	−0.102572	+	0.0592202i	−0.550409	−	0.834895i	$-0.685528\pi$
$983$	−3.21594	+	1.85672i	−0.102572	+	0.0592202i	0.447836	+	0.894116i	$0.352195\pi$
$984$	−0.564994	+	0.558380i	−0.0180114	+	0.0178005i
$985$	−35.0353	+	20.2277i	−1.11632	+	0.644507i
$986$	−4.11968	−	2.37850i	−0.131197	−	0.0757469i
$987$	−6.00782	−	8.37340i	−0.191231	−	0.266528i
$988$	3.48889	−	4.56495i	0.110996	−	0.145230i
$989$	12.6551	+	7.30641i	0.402408	+	0.232330i
$990$	−5.70390	+	9.61615i	−0.181282	+	0.305621i
$991$	−42.0533			−1.33587			−0.667934	−	0.744221i	$-0.732821\pi$
$991$	−42.0533			−1.33587			−0.667934	+	0.744221i	$0.732821\pi$
$992$	−7.95003			−0.252414
$993$	−11.8783	−	3.25786i	−0.376947	−	0.103385i
$994$	17.4454	+	14.1289i	0.553335	+	0.448140i
$995$	−17.3460	−	30.0442i	−0.549905	−	0.952464i
$996$	−18.5626	+	18.3453i	−0.588178	+	0.581292i
$997$	39.1056	+	22.5776i	1.23849	+	0.715041i	0.968785	−	0.247903i	$-0.0797414\pi$
$997$	39.1056	+	22.5776i	1.23849	+	0.715041i	0.269702	+	0.962944i	$0.413075\pi$
$998$		−	18.4429i		−	0.583800i
$999$	6.04592	−	21.0680i	0.191285	−	0.666562i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bn.e.173.10	yes	34
3.2	odd	2		546.2.bn.f.173.8	yes	34
7.3	odd	6		546.2.bi.f.17.15	yes	34
13.10	even	6		546.2.bi.e.257.14	yes	34
21.17	even	6		546.2.bi.e.17.14	✓	34
39.23	odd	6		546.2.bi.f.257.15	yes	34
91.10	odd	6		546.2.bn.f.101.8	yes	34
273.101	even	6	inner	546.2.bn.e.101.10	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.14	✓	34	21.17	even	6
546.2.bi.e.257.14	yes	34	13.10	even	6
546.2.bi.f.17.15	yes	34	7.3	odd	6
546.2.bi.f.257.15	yes	34	39.23	odd	6
546.2.bn.e.101.10	yes	34	273.101	even	6	inner
546.2.bn.e.173.10	yes	34	1.1	even	1	trivial
546.2.bn.f.101.8	yes	34	91.10	odd	6
546.2.bn.f.173.8	yes	34	3.2	odd	2

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.bn (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.458130 - 1.67036i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.57344 + 0.908426i) q^{5} +(-1.67564 + 0.438430i) q^{6} +(-0.414054 + 2.61315i) q^{7} +1.00000 q^{8} +(-2.58023 - 1.53049i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.458130 - 1.67036i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.57344 + 0.908426i) q^{5} +(-1.67564 + 0.438430i) q^{6} +(-0.414054 + 2.61315i) q^{7} +1.00000 q^{8} +(-2.58023 - 1.53049i) q^{9} -1.81685i q^{10} +2.05127 q^{11} +(1.21751 + 1.23193i) q^{12} +(3.57560 + 0.463745i) q^{13} +(2.47008 - 0.947995i) q^{14} +(2.23824 - 2.21204i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.84359 - 4.92524i) q^{17} +(-0.0353243 + 2.99979i) q^{18} -1.59352 q^{19} +(-1.57344 + 0.908426i) q^{20} +(4.17522 + 1.88878i) q^{21} +(-1.02563 - 1.77645i) q^{22} +(7.56871 - 4.36980i) q^{23} +(0.458130 - 1.67036i) q^{24} +(-0.849523 - 1.47142i) q^{25} +(-1.38619 - 3.32844i) q^{26} +(-3.73855 + 3.60877i) q^{27} +(-2.05603 - 1.66516i) q^{28} +(0.724381 + 0.418222i) q^{29} +(-3.03481 - 0.832355i) q^{30} +(3.97501 + 6.88493i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.939747 - 3.42636i) q^{33} -5.68717 q^{34} +(-3.02534 + 3.73550i) q^{35} +(2.61556 - 1.46930i) q^{36} +(-3.65306 + 2.10909i) q^{37} +(0.796762 + 1.38003i) q^{38} +(2.41271 - 5.76010i) q^{39} +(1.57344 + 0.908426i) q^{40} +(-0.397180 - 0.229312i) q^{41} +(-0.451878 - 4.56024i) q^{42} +(0.836012 + 1.44802i) q^{43} +(-1.02563 + 1.77645i) q^{44} +(-2.66951 - 4.75208i) q^{45} +(-7.56871 - 4.36980i) q^{46} +(-1.94760 - 1.12445i) q^{47} +(-1.67564 + 0.438430i) q^{48} +(-6.65712 - 2.16397i) q^{49} +(-0.849523 + 1.47142i) q^{50} +(-6.92421 - 7.00622i) q^{51} +(-2.18942 + 2.86469i) q^{52} +(-0.497067 + 0.286982i) q^{53} +(4.99456 + 1.43330i) q^{54} +(3.22755 + 1.86343i) q^{55} +(-0.414054 + 2.61315i) q^{56} +(-0.730041 + 2.66176i) q^{57} -0.836443i q^{58} +(-1.89789 - 1.09575i) q^{59} +(0.796563 + 3.04440i) q^{60} -6.89812i q^{61} +(3.97501 - 6.88493i) q^{62} +(5.06775 - 6.10884i) q^{63} +1.00000 q^{64} +(5.20472 + 3.97785i) q^{65} +(-3.43719 + 0.899337i) q^{66} -5.15514i q^{67} +(2.84359 + 4.92524i) q^{68} +(-3.83170 - 14.6444i) q^{69} +(4.74771 + 0.752275i) q^{70} +(4.24250 + 7.34823i) q^{71} +(-2.58023 - 1.53049i) q^{72} +(-5.11752 - 8.86381i) q^{73} +(3.65306 + 2.10909i) q^{74} +(-2.84699 + 0.744913i) q^{75} +(0.796762 - 1.38003i) q^{76} +(-0.849335 + 5.36027i) q^{77} +(-6.19475 + 0.790580i) q^{78} +(-3.68537 + 6.38325i) q^{79} -1.81685i q^{80} +(4.31521 + 7.89803i) q^{81} +0.458624i q^{82} +15.0678i q^{83} +(-3.72335 + 2.67146i) q^{84} +(8.94843 - 5.16638i) q^{85} +(0.836012 - 1.44802i) q^{86} +(1.03044 - 1.01838i) q^{87} +2.05127 q^{88} +(-3.34558 + 1.93157i) q^{89} +(-2.78067 + 4.68791i) q^{90} +(-2.69233 + 9.15158i) q^{91} +8.73960i q^{92} +(13.3214 - 3.48553i) q^{93} +2.24889i q^{94} +(-2.50731 - 1.44760i) q^{95} +(1.21751 + 1.23193i) q^{96} +(1.72410 + 2.98622i) q^{97} +(1.45451 + 6.84722i) q^{98} +(-5.29275 - 3.13944i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * q^21 + 9 * q^22 + 6 * q^23 + 3 * q^24 + 16 * q^25 + 13 * q^26 + 18 * q^27 - q^28 + 27 * q^29 + 13 * q^30 + q^31 - 17 * q^32 + 21 * q^33 - 12 * q^34 - 3 * q^35 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

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