LMFDB - Embedded newform 546.2.bu.a.197.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(71,546)]

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, 0, 5]))

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

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

chi := DirichletCharacter("546.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bu (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:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.10
Character	$\chi$	$=$	546.197
Dual form			546.2.bu.a.449.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-1.25018 - 1.19877i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.27299 + 2.27299i) q^{5} +(-1.48149 + 0.897320i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.125915 + 2.99736i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-1.25018 - 1.19877i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.27299 + 2.27299i) q^{5} +(-1.48149 + 0.897320i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.125915 + 2.99736i) q^{9} +(2.78383 - 1.60724i) q^{10} +(1.90819 + 0.511298i) q^{11} +(0.483307 + 1.66325i) q^{12} +(1.84108 + 3.10007i) q^{13} +1.00000i q^{14} +(-0.116867 - 5.56643i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.403373 + 0.698663i) q^{17} +(2.92781 + 0.654149i) q^{18} +(1.40284 + 5.23546i) q^{19} +(-0.831970 - 3.10496i) q^{20} +(1.51785 + 0.834349i) q^{21} +(0.987752 - 1.71084i) q^{22} +(-0.417009 - 0.722281i) q^{23} +(1.73167 - 0.0363565i) q^{24} +5.33293i q^{25} +(3.47094 - 0.975992i) q^{26} +(3.43572 - 3.89819i) q^{27} +(0.965926 + 0.258819i) q^{28} +(5.40739 - 3.12196i) q^{29} +(-5.40700 - 1.32781i) q^{30} +(2.93164 - 2.93164i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-1.77266 - 2.92669i) q^{33} +(0.570456 + 0.570456i) q^{34} +(-2.78383 - 1.60724i) q^{35} +(1.38963 - 2.65874i) q^{36} +(-1.64609 + 6.14328i) q^{37} +5.42014 q^{38} +(1.41457 - 6.08268i) q^{39} -3.21449 q^{40} +(0.963357 - 3.59530i) q^{41} +(1.19877 - 1.25018i) q^{42} +(-10.1613 - 5.86664i) q^{43} +(-1.39689 - 1.39689i) q^{44} +(-6.52675 + 7.09915i) q^{45} +(-0.805599 + 0.215860i) q^{46} +(3.93071 - 3.93071i) q^{47} +(0.413071 - 1.68207i) q^{48} +(0.866025 - 0.500000i) q^{49} +(5.15121 + 1.38026i) q^{50} +(1.34182 - 0.389906i) q^{51} +(-0.0443903 - 3.60528i) q^{52} +8.62427i q^{53} +(-2.87613 - 4.32757i) q^{54} +(3.17512 + 5.49946i) q^{55} +(0.500000 - 0.866025i) q^{56} +(4.52229 - 8.22695i) q^{57} +(-1.61604 - 6.03115i) q^{58} +(-0.382012 - 1.42569i) q^{59} +(-2.68200 + 4.87910i) q^{60} +(0.166796 - 0.288899i) q^{61} +(-2.07298 - 3.59051i) q^{62} +(-0.897397 - 2.86263i) q^{63} -1.00000i q^{64} +(-2.86165 + 11.2312i) q^{65} +(-3.28577 + 0.954774i) q^{66} +(-5.60684 - 1.50235i) q^{67} +(0.698663 - 0.403373i) q^{68} +(-0.344509 + 1.40288i) q^{69} +(-2.27299 + 2.27299i) q^{70} +(12.3810 - 3.31747i) q^{71} +(-2.20849 - 2.03042i) q^{72} +(2.04963 + 2.04963i) q^{73} +(5.50791 + 3.18000i) q^{74} +(6.39294 - 6.66713i) q^{75} +(1.40284 - 5.23546i) q^{76} -1.97550 q^{77} +(-5.50930 - 2.94068i) q^{78} -1.02275 q^{79} +(-0.831970 + 3.10496i) q^{80} +(-8.96829 + 0.754823i) q^{81} +(-3.22346 - 1.86106i) q^{82} +(10.6974 + 10.6974i) q^{83} +(-0.897320 - 1.48149i) q^{84} +(-2.50491 + 0.671189i) q^{85} +(-8.29668 + 8.29668i) q^{86} +(-10.5027 - 2.57918i) q^{87} +(-1.71084 + 0.987752i) q^{88} +(2.34981 + 0.629629i) q^{89} +(5.16801 + 8.14175i) q^{90} +(-2.58071 - 2.51793i) q^{91} +0.834018i q^{92} +(-7.17943 + 0.150732i) q^{93} +(-2.77943 - 4.81412i) q^{94} +(-8.71149 + 15.0887i) q^{95} +(-1.51785 - 0.834349i) q^{96} +(3.61919 + 13.5070i) q^{97} +(-0.258819 - 0.965926i) q^{98} +(-1.29227 + 5.78391i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) $ 56 * q - 8 * q^6 + 24 * q^9	$ 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) $ 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	−1.25018	−	1.19877i	−0.721793	−	0.692109i
$3$	−1.25018	−	1.19877i	−0.721793	−	0.692109i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	2.27299	+	2.27299i	1.01651	+	1.01651i	0.999861	+	0.0166486i	$0.00529967\pi$
$5$	2.27299	+	2.27299i	1.01651	+	1.01651i	0.0166486	+	0.999861i	$0.494700\pi$
$6$	−1.48149	+	0.897320i	−0.604816	+	0.366329i
$7$	−0.965926	+	0.258819i	−0.365086	+	0.0978244i
$7$	−0.965926	+	0.258819i	−0.365086	+	0.0978244i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.125915	+	2.99736i	0.0419716	+	0.999119i
$10$	2.78383	−	1.60724i	0.880324	−	0.508255i
$11$	1.90819	+	0.511298i	0.575341	+	0.154162i	0.534745	−	0.845013i	$-0.320408\pi$
$11$	1.90819	+	0.511298i	0.575341	+	0.154162i	0.0405961	+	0.999176i	$0.487074\pi$
$12$	0.483307	+	1.66325i	0.139519	+	0.480140i
$13$	1.84108	+	3.10007i	0.510624	+	0.859804i
$13$	1.84108	+	3.10007i	0.510624	+	0.859804i
$14$			1.00000i			0.267261i
$15$	−0.116867	−	5.56643i	−0.0301750	−	1.43725i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.403373	+	0.698663i	−0.0978323	+	0.169451i	−0.910787	−	0.412876i	$-0.864524\pi$
$17$	−0.403373	+	0.698663i	−0.0978323	+	0.169451i	0.812955	+	0.582327i	$0.197858\pi$
$18$	2.92781	+	0.654149i	0.690092	+	0.154184i
$19$	1.40284	+	5.23546i	0.321833	+	1.20110i	0.917458	+	0.397833i	$0.130238\pi$
$19$	1.40284	+	5.23546i	0.321833	+	1.20110i	−0.595625	+	0.803263i	$0.703096\pi$
$20$	−0.831970	−	3.10496i	−0.186034	−	0.694289i
$21$	1.51785	+	0.834349i	0.331222	+	0.182070i
$22$	0.987752	−	1.71084i	0.210589	−	0.364752i
$23$	−0.417009	−	0.722281i	−0.0869524	−	0.150606i	0.819269	−	0.573409i	$-0.194379\pi$
$23$	−0.417009	−	0.722281i	−0.0869524	−	0.150606i	−0.906221	+	0.422803i	$0.861046\pi$
$24$	1.73167	−	0.0363565i	0.353475	−	0.00742123i
$25$			5.33293i			1.06659i
$26$	3.47094	−	0.975992i	0.680708	−	0.191408i
$27$	3.43572	−	3.89819i	0.661204	−	0.750206i
$28$	0.965926	+	0.258819i	0.182543	+	0.0489122i
$29$	5.40739	−	3.12196i	1.00413	−	0.579733i	0.0946597	−	0.995510i	$-0.469824\pi$
$29$	5.40739	−	3.12196i	1.00413	−	0.579733i	0.909467	+	0.415777i	$0.136490\pi$
$30$	−5.40700	−	1.32781i	−0.987179	−	0.242424i
$31$	2.93164	−	2.93164i	0.526537	−	0.526537i	−0.393001	−	0.919538i	$-0.628563\pi$
$31$	2.93164	−	2.93164i	0.526537	−	0.526537i	0.919538	+	0.393001i	$0.128563\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−1.77266	−	2.92669i	−0.308581	−	0.509472i
$34$	0.570456	+	0.570456i	0.0978323	+	0.0978323i
$35$	−2.78383	−	1.60724i	−0.470553	−	0.271674i
$36$	1.38963	−	2.65874i	0.231605	−	0.443124i
$37$	−1.64609	+	6.14328i	−0.270615	+	1.00995i	0.688108	+	0.725608i	$0.258441\pi$
$37$	−1.64609	+	6.14328i	−0.270615	+	1.00995i	−0.958723	+	0.284341i	$0.908225\pi$
$38$	5.42014			0.879263
$39$	1.41457	−	6.08268i	0.226512	−	0.974008i
$40$	−3.21449			−0.508255
$41$	0.963357	−	3.59530i	0.150451	−	0.561491i	−0.849001	−	0.528391i	$-0.822795\pi$
$41$	0.963357	−	3.59530i	0.150451	−	0.561491i	0.999452	−	0.0330999i	$-0.0105380\pi$
$42$	1.19877	−	1.25018i	0.184974	−	0.192907i
$43$	−10.1613	−	5.86664i	−1.54959	−	0.894655i	−0.998173	−	0.0604229i	$-0.980755\pi$
$43$	−10.1613	−	5.86664i	−1.54959	−	0.894655i	−0.551414	−	0.834232i	$-0.685912\pi$
$44$	−1.39689	−	1.39689i	−0.210589	−	0.210589i
$45$	−6.52675	+	7.09915i	−0.972950	+	1.05828i
$46$	−0.805599	+	0.215860i	−0.118779	+	0.0318268i
$47$	3.93071	−	3.93071i	0.573353	−	0.573353i	−0.359711	−	0.933064i	$-0.617125\pi$
$47$	3.93071	−	3.93071i	0.573353	−	0.573353i	0.933064	+	0.359711i	$0.117125\pi$
$48$	0.413071	−	1.68207i	0.0596217	−	0.242786i
$49$	0.866025	−	0.500000i	0.123718	−	0.0714286i
$50$	5.15121	+	1.38026i	0.728491	+	0.195199i
$51$	1.34182	−	0.389906i	0.187893	−	0.0545977i
$52$	−0.0443903	−	3.60528i	−0.00615582	−	0.499962i
$53$			8.62427i			1.18464i	0.805705	+	0.592318i	$0.201787\pi$
$53$			8.62427i			1.18464i	−0.805705	+	0.592318i	$0.798213\pi$
$54$	−2.87613	−	4.32757i	−0.391392	−	0.588908i
$55$	3.17512	+	5.49946i	0.428133	+	0.741548i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$	4.52229	−	8.22695i	0.598992	−	1.08969i
$58$	−1.61604	−	6.03115i	−0.212197	−	0.791929i
$59$	−0.382012	−	1.42569i	−0.0497337	−	0.185609i	0.936590	−	0.350426i	$-0.113963\pi$
$59$	−0.382012	−	1.42569i	−0.0497337	−	0.185609i	−0.986324	+	0.164817i	$0.947297\pi$
$60$	−2.68200	+	4.87910i	−0.346245	+	0.629889i
$61$	0.166796	−	0.288899i	0.0213560	−	0.0369897i	−0.855150	−	0.518381i	$-0.826535\pi$
$61$	0.166796	−	0.288899i	0.0213560	−	0.0369897i	0.876506	+	0.481391i	$0.159868\pi$
$62$	−2.07298	−	3.59051i	−0.263269	−	0.455995i
$63$	−0.897397	−	2.86263i	−0.113061	−	0.360658i
$64$		−	1.00000i		−	0.125000i
$65$	−2.86165	+	11.2312i	−0.354945	+	1.39305i
$66$	−3.28577	+	0.954774i	−0.404450	+	0.117525i
$67$	−5.60684	−	1.50235i	−0.684984	−	0.183541i	−0.100489	−	0.994938i	$-0.532041\pi$
$67$	−5.60684	−	1.50235i	−0.684984	−	0.183541i	−0.584495	+	0.811397i	$0.698707\pi$
$68$	0.698663	−	0.403373i	0.0847253	−	0.0489162i
$69$	−0.344509	+	1.40288i	−0.0414740	+	0.168887i
$70$	−2.27299	+	2.27299i	−0.271674	+	0.271674i
$71$	12.3810	−	3.31747i	1.46935	−	0.393711i	0.566641	−	0.823965i	$-0.308243\pi$
$71$	12.3810	−	3.31747i	1.46935	−	0.393711i	0.902708	+	0.430254i	$0.141576\pi$
$72$	−2.20849	−	2.03042i	−0.260273	−	0.239287i
$73$	2.04963	+	2.04963i	0.239891	+	0.239891i	0.816805	−	0.576914i	$-0.195743\pi$
$73$	2.04963	+	2.04963i	0.239891	+	0.239891i	−0.576914	+	0.816805i	$0.695743\pi$
$74$	5.50791	+	3.18000i	0.640282	+	0.369667i
$75$	6.39294	−	6.66713i	0.738193	−	0.769854i
$76$	1.40284	−	5.23546i	0.160916	−	0.600548i
$77$	−1.97550			−0.225130
$78$	−5.50930	−	2.94068i	−0.623805	−	0.332967i
$79$	−1.02275			−0.115069			−0.0575343	−	0.998344i	$-0.518324\pi$
$79$	−1.02275			−0.115069			−0.0575343	+	0.998344i	$0.518324\pi$
$80$	−0.831970	+	3.10496i	−0.0930171	+	0.347145i
$81$	−8.96829	+	0.754823i	−0.996477	+	0.0838692i
$82$	−3.22346	−	1.86106i	−0.355971	−	0.205520i
$83$	10.6974	+	10.6974i	1.17419	+	1.17419i	0.981200	+	0.192993i	$0.0618195\pi$
$83$	10.6974	+	10.6974i	1.17419	+	1.17419i	0.192993	+	0.981200i	$0.438180\pi$
$84$	−0.897320	−	1.48149i	−0.0979057	−	0.161644i
$85$	−2.50491	+	0.671189i	−0.271696	+	0.0728007i
$86$	−8.29668	+	8.29668i	−0.894655	+	0.894655i
$87$	−10.5027	−	2.57918i	−1.12601	−	0.276517i
$88$	−1.71084	+	0.987752i	−0.182376	+	0.105295i
$89$	2.34981	+	0.629629i	0.249079	+	0.0667406i	0.381198	−	0.924493i	$-0.375511\pi$
$89$	2.34981	+	0.629629i	0.249079	+	0.0667406i	−0.132119	+	0.991234i	$0.542178\pi$
$90$	5.16801	+	8.14175i	0.544756	+	0.858216i
$91$	−2.58071	−	2.51793i	−0.270531	−	0.263951i
$92$			0.834018i			0.0869524i
$93$	−7.17943	+	0.150732i	−0.744472	+	0.0156302i
$94$	−2.77943	−	4.81412i	−0.286677	−	0.496539i
$95$	−8.71149	+	15.0887i	−0.893780	+	1.54807i
$96$	−1.51785	−	0.834349i	−0.154915	−	0.0851554i
$97$	3.61919	+	13.5070i	0.367474	+	1.37143i	0.864037	+	0.503429i	$0.167929\pi$
$97$	3.61919	+	13.5070i	0.367474	+	1.37143i	−0.496563	+	0.868001i	$0.665405\pi$
$98$	−0.258819	−	0.965926i	−0.0261447	−	0.0975732i
$99$	−1.29227	+	5.78391i	−0.129878	+	0.581305i
$100$	2.66646	−	4.61845i	0.266646	−	0.461845i
$101$	−0.130884	−	0.226697i	−0.0130234	−	0.0225572i	0.859440	−	0.511236i	$-0.170812\pi$
$101$	−0.130884	−	0.226697i	−0.0130234	−	0.0225572i	−0.872464	+	0.488679i	$0.837479\pi$
$102$	−0.0293304	−	1.39702i	−0.00290415	−	0.138325i
$103$			2.90239i			0.285981i	0.989724	+	0.142991i	$0.0456718\pi$
$103$			2.90239i			0.285981i	−0.989724	+	0.142991i	$0.954328\pi$
$104$	−3.49392	−	0.890237i	−0.342607	−	0.0872949i
$105$	1.55358	+	5.34651i	0.151614	+	0.521766i
$106$	8.33041	+	2.23213i	0.809121	+	0.216803i
$107$	−9.68689	+	5.59273i	−0.936467	+	0.540669i	−0.888851	−	0.458196i	$-0.848496\pi$
$107$	−9.68689	+	5.59273i	−0.936467	+	0.540669i	−0.0476158	+	0.998866i	$0.515162\pi$
$108$	−4.92451	+	1.65807i	−0.473861	+	0.159548i
$109$	−9.64348	+	9.64348i	−0.923678	+	0.923678i	−0.997287	−	0.0736093i	$-0.976548\pi$
$109$	−9.64348	+	9.64348i	−0.923678	+	0.923678i	0.0736093	+	0.997287i	$0.476548\pi$
$110$	6.13385	−	1.64356i	0.584840	−	0.156707i
$111$	9.42227	−	5.70695i	0.894322	−	0.541680i
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	−11.8951	−	6.86764i	−1.11900	−	0.646053i	−0.177852	−	0.984057i	$-0.556915\pi$
$113$	−11.8951	−	6.86764i	−1.11900	−	0.646053i	−0.941145	+	0.338004i	$0.890248\pi$
$114$	−6.77617	−	6.49749i	−0.634647	−	0.608546i
$115$	0.693878	−	2.58959i	0.0647045	−	0.241480i
$116$	−6.24391			−0.579733
$117$	−9.06019	+	5.90872i	−0.837615	+	0.546262i
$118$	−1.47598			−0.135875
$119$	0.208801	−	0.779257i	0.0191408	−	0.0714344i
$120$	4.01870	+	3.85342i	0.366855	+	0.351768i
$121$	−6.14651	−	3.54869i	−0.558774	−	0.322608i
$122$	−0.235885	−	0.235885i	−0.0213560	−	0.0213560i
$123$	−5.51430	+	3.33994i	−0.497208	+	0.301152i
$124$	−4.00469	+	1.07305i	−0.359632	+	0.0963630i
$125$	−0.756738	+	0.756738i	−0.0676847	+	0.0676847i
$126$	−2.99736	+	0.125915i	−0.267026	+	0.0112174i
$127$	−10.2393	+	5.91164i	−0.908587	+	0.524573i	−0.879976	−	0.475018i	$-0.842442\pi$
$127$	−10.2393	+	5.91164i	−0.908587	+	0.524573i	−0.0286108	+	0.999591i	$0.509108\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	5.67077	+	19.5154i	0.499284	+	1.71824i
$130$	10.1078	+	5.67098i	0.886514	+	0.497378i
$131$		−	0.458774i		−	0.0400833i	−0.999799	−	0.0200416i	$-0.993620\pi$
$131$		−	0.458774i		−	0.0400833i	0.999799	−	0.0200416i	$-0.00637988\pi$
$132$	0.0718224	+	3.42092i	0.00625133	+	0.297753i
$133$	−2.71007	−	4.69398i	−0.234993	−	0.407020i
$134$	−2.90231	+	5.02695i	−0.250722	+	0.434263i
$135$	16.6699	−	1.05119i	1.43471	−	0.0904719i
$136$	−0.208801	−	0.779257i	−0.0179046	−	0.0668207i
$137$	−5.42398	−	20.2426i	−0.463402	−	1.72944i	−0.662133	−	0.749387i	$-0.730348\pi$
$137$	−5.42398	−	20.2426i	−0.463402	−	1.72944i	0.198730	−	0.980054i	$-0.436318\pi$
$138$	1.26591	+	0.695862i	0.107762	+	0.0592357i
$139$	9.45727	−	16.3805i	0.802155	−	1.38937i	−0.116040	−	0.993245i	$-0.537020\pi$
$139$	9.45727	−	16.3805i	0.802155	−	1.38937i	0.918195	−	0.396129i	$-0.129647\pi$
$140$	1.60724	+	2.78383i	0.135837	+	0.235276i
$141$	−9.62612	+	0.202101i	−0.810666	+	0.0170200i
$142$		−	12.8177i		−	1.07564i
$143$	1.92808	+	6.85686i	0.161234	+	0.573400i
$144$	−2.53283	+	1.60772i	−0.211069	+	0.133977i
$145$	19.3871	+	5.19475i	1.61001	+	0.431400i
$146$	2.51027	−	1.44931i	0.207752	−	0.119946i
$147$	−1.68207	−	0.413071i	−0.138735	−	0.0340695i
$148$	4.49719	−	4.49719i	0.369667	−	0.369667i
$149$	12.3313	−	3.30416i	1.01022	−	0.270687i	0.284498	−	0.958677i	$-0.408173\pi$
$149$	12.3313	−	3.30416i	1.01022	−	0.270687i	0.725721	+	0.687989i	$0.241506\pi$
$150$	−4.78534	−	7.90068i	−0.390722	−	0.645088i
$151$	−10.6021	−	10.6021i	−0.862785	−	0.862785i	0.128876	−	0.991661i	$-0.458863\pi$
$151$	−10.6021	−	10.6021i	−0.862785	−	0.862785i	−0.991661	+	0.128876i	$0.958863\pi$
$152$	−4.69398	−	2.71007i	−0.380732	−	0.219816i
$153$	−2.14493	−	1.12108i	−0.173407	−	0.0906340i
$154$	−0.511298	+	1.90819i	−0.0412016	+	0.153766i
$155$	13.3271			1.07046
$156$	−4.26639	+	4.56047i	−0.341585	+	0.365130i
$157$	15.6148			1.24620			0.623098	−	0.782143i	$-0.285874\pi$
$157$	15.6148			1.24620			0.623098	+	0.782143i	$0.285874\pi$
$158$	−0.264708	+	0.987903i	−0.0210590	+	0.0785933i
$159$	10.3385	−	10.7819i	0.819896	−	0.855062i
$160$	2.78383	+	1.60724i	0.220081	+	0.127064i
$161$	0.589740	+	0.589740i	0.0464780	+	0.0464780i
$162$	−1.59206	+	8.85807i	−0.125084	+	0.695955i
$163$	8.59318	−	2.30254i	0.673070	−	0.180349i	0.0939327	−	0.995579i	$-0.470056\pi$
$163$	8.59318	−	2.30254i	0.673070	−	0.180349i	0.579137	+	0.815230i	$0.303389\pi$
$164$	−2.63194	+	2.63194i	−0.205520	+	0.205520i
$165$	2.62310	−	10.6816i	0.204208	−	0.831558i
$166$	13.1016	−	7.56421i	1.01688	−	0.587097i
$167$	−17.6556	−	4.73079i	−1.36623	−	0.366080i	−0.500128	−	0.865951i	$-0.666714\pi$
$167$	−17.6556	−	4.73079i	−1.36623	−	0.366080i	−0.866099	+	0.499872i	$0.833381\pi$
$168$	−1.66325	+	0.483307i	−0.128323	+	0.0372879i
$169$	−6.22083	+	11.4150i	−0.478526	+	0.878074i
$170$			2.59328i			0.198895i
$171$	−15.5159	+	4.86402i	−1.18653	+	0.371961i
$172$	5.86664	+	10.1613i	0.447327	+	0.774794i
$173$	9.16378	−	15.8721i	0.696710	−	1.20674i	−0.272891	−	0.962045i	$-0.587980\pi$
$173$	9.16378	−	15.8721i	0.696710	−	1.20674i	0.969601	−	0.244691i	$-0.0786867\pi$
$174$	−5.20960	+	9.47731i	−0.394939	+	0.718473i
$175$	−1.38026	−	5.15121i	−0.104338	−	0.389395i
$176$	0.511298	+	1.90819i	0.0385406	+	0.143835i
$177$	−1.23148	+	2.24031i	−0.0925640	+	0.168392i
$178$	1.21635	−	2.10678i	0.0911693	−	0.157910i
$179$	11.9622	+	20.7192i	0.894100	+	1.54863i	0.834915	+	0.550379i	$0.185517\pi$
$179$	11.9622	+	20.7192i	0.894100	+	1.54863i	0.0591851	+	0.998247i	$0.481150\pi$
$180$	9.20190	−	2.88467i	0.685869	−	0.215011i
$181$		−	24.3916i		−	1.81301i	−0.422194	−	0.906505i	$-0.638740\pi$
$181$		−	24.3916i		−	1.81301i	0.422194	−	0.906505i	$-0.361260\pi$
$182$	−3.10007	+	1.84108i	−0.229792	+	0.136470i
$183$	−0.554848	+	0.161227i	−0.0410155	+	0.0119182i
$184$	0.805599	+	0.215860i	0.0593896	+	0.0159134i
$185$	−17.7051	+	10.2221i	−1.30171	+	0.751540i
$186$	−1.71258	+	6.97381i	−0.125572	+	0.511345i
$187$	−1.12694	+	1.12694i	−0.0824099	+	0.0824099i
$188$	−5.36945	+	1.43874i	−0.391608	+	0.104931i
$189$	−2.30972	+	4.65459i	−0.168008	+	0.338571i
$190$	12.3199	+	12.3199i	0.893780	+	0.893780i
$191$	−20.4753	−	11.8214i	−1.48154	−	0.855369i	−0.481762	−	0.876302i	$-0.660003\pi$
$191$	−20.4753	−	11.8214i	−1.48154	−	0.855369i	−0.999781	+	0.0209324i	$0.993337\pi$
$192$	−1.19877	+	1.25018i	−0.0865136	+	0.0902242i
$193$	0.469522	−	1.75228i	0.0337969	−	0.126132i	−0.946966	−	0.321333i	$-0.895869\pi$
$193$	0.469522	−	1.75228i	0.0337969	−	0.126132i	0.980763	+	0.195201i	$0.0625359\pi$
$194$	13.9835			1.00396
$195$	17.0411	−	10.6105i	1.22034	−	0.759837i
$196$	−1.00000			−0.0714286
$197$	4.83196	−	18.0331i	0.344263	−	1.28481i	−0.549209	−	0.835685i	$-0.685071\pi$
$197$	4.83196	−	18.0331i	0.344263	−	1.28481i	0.893471	−	0.449120i	$-0.148263\pi$
$198$	5.25236	+	2.74523i	0.373269	+	0.195095i
$199$	0.661653	+	0.382006i	0.0469033	+	0.0270797i	0.523268	−	0.852168i	$-0.324713\pi$
$199$	0.661653	+	0.382006i	0.0469033	+	0.0270797i	−0.476365	+	0.879248i	$0.658046\pi$
$200$	−3.77095	−	3.77095i	−0.266646	−	0.266646i
$201$	5.20861	+	8.59950i	0.367387	+	0.606562i
$202$	−0.252848	+	0.0677504i	−0.0177903	+	0.00476690i
$203$	−4.41511	+	4.41511i	−0.309880	+	0.309880i
$204$	−1.35701	−	0.333244i	−0.0950095	−	0.0233317i
$205$	10.3618	−	5.98236i	0.723697	−	0.417826i
$206$	2.80349	+	0.751194i	0.195329	+	0.0523382i
$207$	2.11242	−	1.34087i	0.146824	−	0.0931969i
$208$	−1.76420	+	3.14446i	−0.122325	+	0.218029i
$209$			10.7075i			0.740654i
$210$	5.56643	−	0.116867i	0.384120	−	0.00806462i
$211$	−1.58651	−	2.74791i	−0.109220	−	0.189174i	0.806235	−	0.591596i	$-0.201502\pi$
$211$	−1.58651	−	2.74791i	−0.109220	−	0.189174i	−0.915454	+	0.402422i	$0.868168\pi$
$212$	4.31214	−	7.46884i	0.296159	−	0.512962i
$213$	−19.4553	−	10.6944i	−1.33306	−	0.732771i
$214$	2.89501	+	10.8043i	0.197899	+	0.738568i
$215$	−9.76175	−	36.4313i	−0.665746	−	2.48460i
$216$	0.327016	+	5.18585i	0.0222506	+	0.352853i
$217$	−2.07298	+	3.59051i	−0.140723	+	0.243739i
$218$	6.81897	+	11.8108i	0.461839	+	0.799929i
$219$	−0.105383	−	5.01944i	−0.00712115	−	0.339182i
$220$		−	6.35023i		−	0.428133i
$221$	−2.90854	+	0.0358117i	−0.195650	+	0.00240895i
$222$	−3.07383	−	10.5783i	−0.206302	−	0.709968i
$223$	−18.1578	−	4.86537i	−1.21594	−	0.325810i	−0.406849	−	0.913496i	$-0.633372\pi$
$223$	−18.1578	−	4.86537i	−1.21594	−	0.325810i	−0.809089	+	0.587686i	$0.800039\pi$
$224$	−0.866025	+	0.500000i	−0.0578638	+	0.0334077i
$225$	−15.9847	+	0.671494i	−1.06565	+	0.0447663i
$226$	−9.71230	+	9.71230i	−0.646053	+	0.646053i
$227$	9.86449	−	2.64318i	0.654729	−	0.175434i	0.0838631	−	0.996477i	$-0.473274\pi$
$227$	9.86449	−	2.64318i	0.654729	−	0.175434i	0.570866	+	0.821043i	$0.306607\pi$
$228$	−8.02989	+	4.86360i	−0.531793	+	0.322100i
$229$	−16.7199	−	16.7199i	−1.10488	−	1.10488i	−0.993812	−	0.111073i	$-0.964571\pi$
$229$	−16.7199	−	16.7199i	−1.10488	−	1.10488i	−0.111073	−	0.993812i	$-0.535429\pi$
$230$	−2.32176	−	1.34047i	−0.153092	−	0.0883879i
$231$	2.46974	+	2.36817i	0.162497	+	0.155814i
$232$	−1.61604	+	6.03115i	−0.106098	+	0.395965i
$233$	2.38801			0.156444			0.0782219	−	0.996936i	$-0.475076\pi$
$233$	2.38801			0.156444			0.0782219	+	0.996936i	$0.475076\pi$
$234$	3.36244	+	10.2808i	0.219810	+	0.672074i
$235$	17.8689			1.16564
$236$	−0.382012	+	1.42569i	−0.0248669	+	0.0928044i
$237$	1.27863	+	1.22604i	0.0830558	+	0.0796399i
$238$	−0.698663	−	0.403373i	−0.0452876	−	0.0261468i
$239$	18.0519	+	18.0519i	1.16768	+	1.16768i	0.982752	+	0.184928i	$0.0592053\pi$
$239$	18.0519	+	18.0519i	1.16768	+	1.16768i	0.184928	+	0.982752i	$0.440795\pi$
$240$	4.76223	−	2.88442i	0.307401	−	0.186189i
$241$	0.553255	−	0.148244i	0.0356383	−	0.00954924i	−0.240956	−	0.970536i	$-0.577461\pi$
$241$	0.553255	−	0.148244i	0.0356383	−	0.00954924i	0.276594	+	0.960987i	$0.410794\pi$
$242$	−5.01861	+	5.01861i	−0.322608	+	0.322608i
$243$	12.1169	+	9.80723i	0.777297	+	0.629134i
$244$	−0.288899	+	0.166796i	−0.0184948	+	0.0106780i
$245$	3.10496	+	0.831970i	0.198368	+	0.0531526i
$246$	1.79893	+	6.19084i	0.114696	+	0.394714i
$247$	−13.6475	+	13.9878i	−0.868372	+	0.890022i
$248$			4.14596i			0.263269i
$249$	−0.550016	−	26.1974i	−0.0348558	−	1.66019i
$250$	0.535095	+	0.926811i	0.0338423	+	0.0586167i
$251$	−4.21956	+	7.30848i	−0.266336	+	0.461307i	−0.967913	−	0.251286i	$-0.919146\pi$
$251$	−4.21956	+	7.30848i	−0.266336	+	0.461307i	0.701577	+	0.712594i	$0.252480\pi$
$252$	−0.654149	+	2.92781i	−0.0412075	+	0.184435i
$253$	−0.426432	−	1.59147i	−0.0268095	−	0.100055i
$254$	3.06009	+	11.4204i	0.192007	+	0.716580i
$255$	3.93620	+	2.16370i	0.246494	+	0.135496i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.19640	+	2.07222i	0.0746293	+	0.129262i	0.900925	−	0.433975i	$-0.142889\pi$
$257$	1.19640	+	2.07222i	0.0746293	+	0.129262i	−0.826296	+	0.563237i	$0.809556\pi$
$258$	20.3182	−	0.426581i	1.26495	−	0.0265578i
$259$		−	6.35999i		−	0.395191i
$260$	8.09385	−	8.29564i	0.501959	−	0.514474i
$261$	10.0385	+	15.8148i	0.621366	+	0.978909i
$262$	−0.443142	−	0.118740i	−0.0273774	−	0.00733575i
$263$	3.90412	−	2.25405i	0.240739	−	0.138990i	−0.374778	−	0.927115i	$-0.622281\pi$
$263$	3.90412	−	2.25405i	0.240739	−	0.138990i	0.615516	+	0.788124i	$0.288948\pi$
$264$	3.32294	+	0.816024i	0.204513	+	0.0502228i
$265$	−19.6029	+	19.6029i	−1.20419	+	1.20419i
$266$	−5.23546	+	1.40284i	−0.321006	+	0.0860134i
$267$	−2.18291	−	3.60402i	−0.133592	−	0.220563i
$268$	4.10449	+	4.10449i	0.250722	+	0.250722i
$269$	4.06585	+	2.34742i	0.247899	+	0.143125i	0.618802	−	0.785547i	$-0.287618\pi$
$269$	4.06585	+	2.34742i	0.247899	+	0.143125i	−0.370903	+	0.928672i	$0.620952\pi$
$270$	3.29911	−	16.3739i	0.200777	−	0.996484i
$271$	−3.16884	+	11.8263i	−0.192493	+	0.718394i	0.800409	+	0.599455i	$0.204616\pi$
$271$	−3.16884	+	11.8263i	−0.192493	+	0.718394i	−0.992902	+	0.118939i	$0.962051\pi$
$272$	−0.806746			−0.0489162
$273$	0.207944	+	6.24153i	0.0125854	+	0.377755i
$274$	−20.9567			−1.26604
$275$	−2.72672	+	10.1762i	−0.164427	+	0.613650i
$276$	0.999793	−	1.04267i	0.0601805	−	0.0627616i
$277$	−8.54213	−	4.93180i	−0.513247	−	0.296323i	0.220921	−	0.975292i	$-0.429094\pi$
$277$	−8.54213	−	4.93180i	−0.513247	−	0.296323i	−0.734167	+	0.678969i	$0.762427\pi$
$278$	−13.3746	−	13.3746i	−0.802155	−	0.802155i
$279$	9.15630	+	8.41802i	0.548173	+	0.503974i
$280$	3.10496	−	0.831970i	0.185557	−	0.0497197i
$281$	14.2624	−	14.2624i	0.850826	−	0.850826i	−0.139409	−	0.990235i	$-0.544520\pi$
$281$	14.2624	−	14.2624i	0.850826	−	0.850826i	0.990235	+	0.139409i	$0.0445203\pi$
$282$	−2.29621	+	9.35043i	−0.136737	+	0.556810i
$283$	−2.71968	+	1.57021i	−0.161668	+	0.0933391i	−0.578651	−	0.815575i	$-0.696421\pi$
$283$	−2.71968	+	1.57021i	−0.161668	+	0.0933391i	0.416983	+	0.908914i	$0.363087\pi$
$284$	−12.3810	−	3.31747i	−0.734674	−	0.196855i
$285$	28.9788	−	8.42064i	1.71656	−	0.498796i
$286$	7.12224	−	0.0876932i	0.421147	−	0.00518541i
$287$			3.72213i			0.219710i
$288$	0.897397	+	2.86263i	0.0528796	+	0.168682i
$289$	8.17458	+	14.1588i	0.480858	+	0.832870i
$290$	10.0355	−	17.3820i	0.589304	−	1.02070i
$291$	11.6671	−	21.2248i	0.683938	−	1.24422i
$292$	−0.750217	−	2.79985i	−0.0439031	−	0.163849i
$293$	−2.76614	−	10.3234i	−0.161600	−	0.603098i	−0.998449	−	0.0556657i	$-0.982272\pi$
$293$	−2.76614	−	10.3234i	−0.161600	−	0.603098i	0.836850	−	0.547433i	$-0.184395\pi$
$294$	−0.834349	+	1.51785i	−0.0486602	+	0.0885227i
$295$	2.37226	−	4.10888i	0.138118	−	0.239228i
$296$	−3.18000	−	5.50791i	−0.184833	−	0.320141i
$297$	8.54914	−	5.68181i	0.496071	−	0.329692i
$298$		−	12.7663i		−	0.739532i
$299$	1.47137	−	2.62253i	0.0850916	−	0.151665i
$300$	−8.87001	+	2.57744i	−0.512110	+	0.148808i
$301$	11.3335	+	3.03680i	0.653251	+	0.175038i
$302$	−12.9848	+	7.49680i	−0.747193	+	0.431392i
$303$	−0.108129	+	0.440312i	−0.00621183	+	0.0252953i
$304$	−3.83262	+	3.83262i	−0.219816	+	0.219816i
$305$	1.03579	−	0.277538i	0.0593090	−	0.0158918i
$306$	−1.63803	+	1.78169i	−0.0936400	+	0.101852i
$307$	−23.8752	−	23.8752i	−1.36263	−	1.36263i	−0.870548	−	0.492083i	$-0.836235\pi$
$307$	−23.8752	−	23.8752i	−1.36263	−	1.36263i	−0.492083	−	0.870548i	$-0.663765\pi$
$308$	1.71084	+	0.987752i	0.0974840	+	0.0562824i
$309$	3.47929	−	3.62852i	0.197930	−	0.206419i
$310$	3.44932	−	12.8730i	0.195908	−	0.731139i
$311$	35.0970			1.99017			0.995084	−	0.0990298i	$-0.0315739\pi$
$311$	35.0970			1.99017			0.995084	+	0.0990298i	$0.0315739\pi$
$312$	3.30085	+	5.30136i	0.186874	+	0.300130i
$313$	9.08067			0.513270			0.256635	−	0.966508i	$-0.417386\pi$
$313$	9.08067			0.513270			0.256635	+	0.966508i	$0.417386\pi$
$314$	4.04141	−	15.0827i	0.228070	−	0.851168i
$315$	4.46696	−	8.54650i	0.251685	−	0.481541i
$316$	0.885729	+	0.511376i	0.0498262	+	0.0287671i
$317$	−17.6223	−	17.6223i	−0.989765	−	0.989765i	0.0101830	−	0.999948i	$-0.496759\pi$
$317$	−17.6223	−	17.6223i	−0.989765	−	0.989765i	−0.999948	+	0.0101830i	$0.996759\pi$
$318$	−7.73874	−	12.7768i	−0.433967	−	0.716487i
$319$	11.9146	−	3.19250i	0.667088	−	0.178746i
$320$	2.27299	−	2.27299i	0.127064	−	0.127064i
$321$	18.8148	+	4.62039i	1.05014	+	0.257885i
$322$	0.722281	−	0.417009i	0.0402511	−	0.0232390i
$323$	−4.22368	−	1.13173i	−0.235012	−	0.0629713i
$324$	8.14418	+	3.83045i	0.452454	+	0.212803i
$325$	−16.5324	+	9.81836i	−0.917054	+	0.544624i
$326$		−	8.89632i		−	0.492721i
$327$	23.6164	−	0.495827i	1.30599	−	0.0274193i
$328$	1.86106	+	3.22346i	0.102760	+	0.177986i
$329$	−2.77943	+	4.81412i	−0.153235	+	0.265411i
$330$	−9.63869	−	5.29831i	−0.530592	−	0.291662i
$331$	−6.25531	−	23.3451i	−0.343823	−	1.28316i	−0.893981	−	0.448104i	$-0.852099\pi$
$331$	−6.25531	−	23.3451i	−0.343823	−	1.28316i	0.550159	−	0.835060i	$-0.314567\pi$
$332$	−3.91552	−	14.6129i	−0.214892	−	0.801989i
$333$	−18.6209	−	4.16038i	−1.02042	−	0.227987i
$334$	−9.13919	+	15.8295i	−0.500074	+	0.866154i
$335$	−9.32945	−	16.1591i	−0.509722	−	0.882865i
$336$	0.0363565	+	1.73167i	0.00198341	+	0.0944703i
$337$		−	30.3885i		−	1.65536i	−0.561197	−	0.827682i	$-0.689659\pi$
$337$		−	30.3885i		−	1.65536i	0.561197	−	0.827682i	$-0.310341\pi$
$338$	9.41593	+	8.96327i	0.512159	+	0.487538i
$339$	6.63835	+	22.8452i	0.360546	+	1.24078i
$340$	2.50491	+	0.671189i	0.135848	+	0.0364003i
$341$	7.09306	−	4.09518i	0.384111	−	0.221767i
$342$	0.682476	+	16.2461i	0.0369041	+	0.878489i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	11.3335	−	3.03680i	0.611060	−	0.163733i
$345$	−3.97179	+	2.40566i	−0.213834	+	0.129516i
$346$	−12.9595	−	12.9595i	−0.696710	−	0.696710i
$347$	1.62331	+	0.937218i	0.0871438	+	0.0503125i	0.542939	−	0.839772i	$-0.317312\pi$
$347$	1.62331	+	0.937218i	0.0871438	+	0.0503125i	−0.455795	+	0.890085i	$0.650645\pi$
$348$	7.80603	+	7.48499i	0.418447	+	0.401238i
$349$	−1.40481	+	5.24282i	−0.0751977	+	0.280642i	−0.993278	−	0.115753i	$-0.963072\pi$
$349$	−1.40481	+	5.24282i	−0.0751977	+	0.280642i	0.918080	+	0.396394i	$0.129739\pi$
$350$	−5.33293			−0.285057
$351$	18.4101	+	3.47407i	0.982657	+	0.185432i
$352$	1.97550			0.105295
$353$	−6.21785	+	23.2053i	−0.330943	+	1.23510i	0.577258	+	0.816562i	$0.304123\pi$
$353$	−6.21785	+	23.2053i	−0.330943	+	1.23510i	−0.908201	+	0.418534i	$0.862544\pi$
$354$	1.84525	+	1.76936i	0.0980738	+	0.0940403i
$355$	35.6823	+	20.6012i	1.89382	+	1.09340i
$356$	−1.72018	−	1.72018i	−0.0911693	−	0.0911693i
$357$	−1.19519	+	0.723910i	−0.0632560	+	0.0383134i
$358$	23.1093	−	6.19211i	1.22136	−	0.327263i
$359$	−5.86558	+	5.86558i	−0.309573	+	0.309573i	−0.844744	−	0.535171i	$-0.820247\pi$
$359$	−5.86558	+	5.86558i	−0.309573	+	0.309573i	0.535171	+	0.844744i	$0.320247\pi$
$360$	−0.404751	−	9.63496i	−0.0213323	−	0.507807i
$361$	−8.98757	+	5.18898i	−0.473030	+	0.273104i
$362$	−23.5604	−	6.31300i	−1.23831	−	0.331804i
$363$	3.43021	+	11.8048i	0.180039	+	0.619589i
$364$	0.975992	+	3.47094i	0.0511559	+	0.181927i
$365$			9.31756i			0.487703i
$366$	0.0121282	+	0.577670i	0.000633952	+	0.0301953i
$367$	2.89279	+	5.01046i	0.151002	+	0.261544i	0.931596	−	0.363495i	$-0.118417\pi$
$367$	2.89279	+	5.01046i	0.151002	+	0.261544i	−0.780594	+	0.625039i	$0.785083\pi$
$368$	0.417009	−	0.722281i	0.0217381	−	0.0376515i
$369$	10.8977	+	2.43482i	0.567311	+	0.126752i
$370$	5.29132	+	19.7475i	0.275083	+	1.02662i
$371$	−2.23213	−	8.33041i	−0.115886	−	0.432493i
$372$	6.29294	+	3.45918i	0.326274	+	0.179350i
$373$	−18.8032	+	32.5681i	−0.973594	+	1.68631i	−0.289095	+	0.957301i	$0.593354\pi$
$373$	−18.8032	+	32.5681i	−0.973594	+	1.68631i	−0.684499	+	0.729014i	$0.739979\pi$
$374$	0.796865	+	1.38021i	0.0412049	+	0.0713690i
$375$	1.85321	−	0.0389083i	0.0956995	−	0.00200922i
$376$			5.55887i			0.286677i
$377$	19.6337	+	11.0155i	1.01119	+	0.567326i
$378$	3.89819	+	3.43572i	0.200501	+	0.176714i
$379$	15.8931	+	4.25855i	0.816374	+	0.218747i	0.642761	−	0.766067i	$-0.277789\pi$
$379$	15.8931	+	4.25855i	0.816374	+	0.218747i	0.173614	+	0.984814i	$0.444456\pi$
$380$	15.0887	−	8.71149i	0.774036	−	0.446890i
$381$	19.8876	+	4.88386i	1.01887	+	0.250208i
$382$	−16.7180	+	16.7180i	−0.855369	+	0.855369i
$383$	−32.2825	+	8.65006i	−1.64956	+	0.441997i	−0.959489	−	0.281747i	$-0.909086\pi$
$383$	−32.2825	+	8.65006i	−1.64956	+	0.441997i	−0.690068	+	0.723745i	$0.742419\pi$
$384$	0.897320	+	1.48149i	0.0457912	+	0.0756020i
$385$	−4.49029	−	4.49029i	−0.228847	−	0.228847i
$386$	−1.57105	−	0.907046i	−0.0799644	−	0.0461674i
$387$	16.3050	−	31.1958i	0.828828	−	1.58577i
$388$	3.61919	−	13.5070i	0.183737	−	0.685715i
$389$	9.68139			0.490866			0.245433	−	0.969414i	$-0.421070\pi$
$389$	9.68139			0.490866			0.245433	+	0.969414i	$0.421070\pi$
$390$	−5.83843	−	19.2067i	−0.295640	−	0.972568i
$391$	0.672841			0.0340270
$392$	−0.258819	+	0.965926i	−0.0130723	+	0.0487866i
$393$	−0.549963	+	0.573552i	−0.0277420	+	0.0289319i
$394$	−16.1680	−	9.33462i	−0.814534	−	0.470272i
$395$	−2.32470	−	2.32470i	−0.116968	−	0.116968i
$396$	4.01110	−	4.36287i	0.201565	−	0.219243i
$397$	8.59799	−	2.30383i	0.431521	−	0.115626i	−0.0365191	−	0.999333i	$-0.511627\pi$
$397$	8.59799	−	2.30383i	0.431521	−	0.115626i	0.468040	+	0.883707i	$0.344960\pi$
$398$	0.540237	−	0.540237i	0.0270797	−	0.0270797i
$399$	−2.23891	+	9.11708i	−0.112085	+	0.456425i
$400$	−4.61845	+	2.66646i	−0.230923	+	0.133323i
$401$	−38.5315	−	10.3245i	−1.92417	−	0.515580i	−0.985144	−	0.171733i	$-0.945063\pi$
$401$	−38.5315	−	10.3245i	−1.92417	−	0.515580i	−0.939026	−	0.343847i	$-0.888270\pi$
$402$	9.65457	−	2.80541i	0.481526	−	0.139921i
$403$	14.4857	+	3.69089i	0.721582	+	0.183856i
$404$			0.261768i			0.0130234i
$405$	−22.1005	−	18.6691i	−1.09818	−	0.927675i
$406$	3.12196	+	5.40739i	0.154940	+	0.268364i
$407$	−6.28210	+	10.8809i	−0.311392	+	0.539347i
$408$	−0.673108	+	1.22452i	−0.0333238	+	0.0606227i
$409$	3.78807	+	14.1373i	0.187308	+	0.699043i	0.994125	+	0.108241i	$0.0345219\pi$
$409$	3.78807	+	14.1373i	0.187308	+	0.699043i	−0.806817	+	0.590802i	$0.798811\pi$
$410$	−3.09670	−	11.5570i	−0.152935	−	0.570762i
$411$	−17.4852	+	31.8090i	−0.862480	+	1.56902i
$412$	1.45120	−	2.51354i	0.0714953	−	0.123833i
$413$	0.737991	+	1.27824i	0.0363141	+	0.0628979i
$414$	−0.748445	−	2.38749i	−0.0367841	−	0.117339i
$415$			48.6301i			2.38716i
$416$	2.58071	+	2.51793i	0.126529	+	0.123452i
$417$	−31.4597	+	9.14152i	−1.54059	+	0.447662i
$418$	10.3427	+	2.77131i	0.505876	+	0.135549i
$419$	−6.46800	+	3.73430i	−0.315982	+	0.182433i	−0.649600	−	0.760276i	$-0.725064\pi$
$419$	−6.46800	+	3.73430i	−0.315982	+	0.182433i	0.333618	+	0.942708i	$0.391730\pi$
$420$	1.32781	−	5.40700i	0.0647906	−	0.263835i
$421$	25.9751	−	25.9751i	1.26595	−	1.26595i	0.317789	−	0.948162i	$-0.397060\pi$
$421$	25.9751	−	25.9751i	1.26595	−	1.26595i	0.948162	−	0.317789i	$-0.102940\pi$
$422$	−3.06489	+	0.821236i	−0.149197	+	0.0399771i
$423$	12.2767	+	11.2868i	0.596913	+	0.548784i
$424$	−6.09828	−	6.09828i	−0.296159	−	0.296159i
$425$	−3.72592	−	2.15116i	−0.180734	−	0.104347i
$426$	−15.3654	+	16.0245i	−0.744458	+	0.776389i
$427$	−0.0863399	+	0.322225i	−0.00417828	+	0.0155935i
$428$	11.1855			0.540669
$429$	5.80933	−	10.8836i	0.280477	−	0.525467i
$430$	−37.7165			−1.81885
$431$	5.80211	−	21.6538i	0.279478	−	1.04302i	−0.673303	−	0.739366i	$-0.735125\pi$
$431$	5.80211	−	21.6538i	0.279478	−	1.04302i	0.952781	−	0.303658i	$-0.0982082\pi$
$432$	5.09379	+	1.02632i	0.245075	+	0.0493790i
$433$	27.7210	+	16.0048i	1.33219	+	0.769139i	0.985635	−	0.168891i	$-0.0540186\pi$
$433$	27.7210	+	16.0048i	1.33219	+	0.769139i	0.346554	+	0.938030i	$0.387352\pi$
$434$	2.93164	+	2.93164i	0.140723	+	0.140723i
$435$	−18.0101	−	29.7350i	−0.863518	−	1.42568i
$436$	13.1732	−	3.52976i	0.630884	−	0.169045i
$437$	3.19647	−	3.19647i	0.152908	−	0.152908i
$438$	−4.87568	−	1.19733i	−0.232969	−	0.0572109i
$439$	−12.6436	+	7.29979i	−0.603446	+	0.348400i	−0.770396	−	0.637565i	$-0.779942\pi$
$439$	−12.6436	+	7.29979i	−0.603446	+	0.348400i	0.166950	+	0.985965i	$0.446608\pi$
$440$	−6.13385	−	1.64356i	−0.292420	−	0.0783537i
$441$	1.60772	+	2.53283i	0.0765583	+	0.120611i
$442$	−0.718195	+	2.81871i	−0.0341611	+	0.134072i
$443$		−	32.5416i		−	1.54610i	−0.634347	−	0.773048i	$-0.718731\pi$
$443$		−	32.5416i		−	1.54610i	0.634347	−	0.773048i	$-0.281269\pi$
$444$	−11.0134	+	0.231227i	−0.522673	+	0.0109735i
$445$	3.90994	+	6.77222i	0.185349	+	0.321034i
$446$	−9.39918	+	16.2799i	−0.445064	+	0.770874i
$447$	−19.3773	−	10.6515i	−0.916515	−	0.503801i
$448$	0.258819	+	0.965926i	0.0122281	+	0.0456357i
$449$	3.73921	+	13.9549i	0.176464	+	0.658574i	0.996298	+	0.0859717i	$0.0273995\pi$
$449$	3.73921	+	13.9549i	0.176464	+	0.658574i	−0.819833	+	0.572602i	$0.805934\pi$
$450$	−3.48853	+	15.6138i	−0.164451	+	0.736042i
$451$	3.67654	−	6.36795i	0.173121	−	0.299855i
$452$	6.86764	+	11.8951i	0.323026	+	0.559498i
$453$	0.545114	+	25.9640i	0.0256117	+	1.21989i
$454$		−	10.2125i		−	0.479295i
$455$	−0.142692	−	11.5891i	−0.00668950	−	0.543306i
$456$	2.61959	+	9.01508i	0.122674	+	0.422170i
$457$	20.7063	+	5.54824i	0.968601	+	0.259536i	0.708237	−	0.705975i	$-0.249491\pi$
$457$	20.7063	+	5.54824i	0.968601	+	0.259536i	0.260364	+	0.965511i	$0.416158\pi$
$458$	−20.4777	+	11.8228i	−0.956858	+	0.552442i
$459$	1.33764	+	3.97283i	0.0624358	+	0.185436i
$460$	−1.89571	+	1.89571i	−0.0883879	+	0.0883879i
$461$	9.03646	−	2.42131i	0.420870	−	0.112772i	−0.0421675	−	0.999111i	$-0.513426\pi$
$461$	9.03646	−	2.42131i	0.420870	−	0.112772i	0.463037	+	0.886339i	$0.346760\pi$
$462$	2.92669	−	1.77266i	0.136162	−	0.0824716i
$463$	−2.03534	−	2.03534i	−0.0945902	−	0.0945902i	0.658228	−	0.752818i	$-0.271306\pi$
$463$	−2.03534	−	2.03534i	−0.0945902	−	0.0945902i	−0.752818	+	0.658228i	$0.771306\pi$
$464$	5.40739	+	3.12196i	0.251032	+	0.144933i
$465$	−16.6614	−	15.9761i	−0.772652	−	0.740875i
$466$	0.618063	−	2.30664i	0.0286312	−	0.106853i
$467$	−18.9918			−0.878836			−0.439418	−	0.898283i	$-0.644815\pi$
$467$	−18.9918			−0.878836			−0.439418	+	0.898283i	$0.644815\pi$
$468$	10.8007	−	0.587011i	0.499263	−	0.0271346i
$469$	5.80463			0.268033
$470$	4.62481	−	17.2600i	0.213327	−	0.796146i
$471$	−19.5214	−	18.7185i	−0.899497	−	0.862503i
$472$	1.27824	+	0.737991i	0.0588356	+	0.0339688i
$473$	−16.3901	−	16.3901i	−0.753619	−	0.753619i
$474$	1.51520	−	0.917736i	0.0695954	−	0.0421530i
$475$	−27.9203	+	7.48122i	−1.28107	+	0.343262i
$476$	−0.570456	+	0.570456i	−0.0261468	+	0.0261468i
$477$	−25.8500	+	1.08592i	−1.18359	+	0.0497210i
$478$	22.1090	−	12.7646i	1.01124	−	0.583840i
$479$	−18.5881	−	4.98066i	−0.849311	−	0.227572i	−0.192191	−	0.981358i	$-0.561559\pi$
$479$	−18.5881	−	4.98066i	−0.849311	−	0.227572i	−0.657121	+	0.753785i	$0.728226\pi$
$480$	−1.55358	−	5.34651i	−0.0709110	−	0.244034i
$481$	−22.0752	+	6.20730i	−1.00654	+	0.283029i
$482$		−	0.572771i		−	0.0260890i
$483$	−0.0303219	−	1.44424i	−0.00137970	−	0.0657153i
$484$	3.54869	+	6.14651i	0.161304	+	0.279387i
$485$	−22.4749	+	38.9276i	−1.02053	+	1.76761i
$486$	12.6091	−	9.16569i	0.571962	−	0.415764i
$487$	−6.93975	−	25.8995i	−0.314470	−	1.17362i	−0.924482	−	0.381226i	$-0.875502\pi$
$487$	−6.93975	−	25.8995i	−0.314470	−	1.17362i	0.610012	−	0.792392i	$-0.291165\pi$
$488$	0.0863399	+	0.322225i	0.00390842	+	0.0145864i
$489$	−13.5033	−	7.42263i	−0.610638	−	0.335663i
$490$	1.60724	−	2.78383i	0.0726079	−	0.125761i
$491$	7.40878	+	12.8324i	0.334353	+	0.579117i	0.983360	−	0.181665i	$-0.0581488\pi$
$491$	7.40878	+	12.8324i	0.334353	+	0.579117i	−0.649007	+	0.760782i	$0.724815\pi$
$492$	6.44549	−	0.135323i	0.290585	−	0.00610085i
$493$			5.03725i			0.226866i
$494$	9.97893	+	16.8028i	0.448973	+	0.755994i
$495$	−16.0841	+	10.2094i	−0.722925	+	0.458879i
$496$	4.00469	+	1.07305i	0.179816	+	0.0481815i
$497$	−11.1005	+	6.40885i	−0.497924	+	0.287476i
$498$	−25.4471	−	6.24912i	−1.14031	−	0.280030i
$499$	2.18202	−	2.18202i	0.0976806	−	0.0976806i	−0.656578	−	0.754258i	$-0.727997\pi$
$499$	2.18202	−	2.18202i	0.0976806	−	0.0976806i	0.754258	+	0.656578i	$0.227997\pi$
$500$	1.03372	−	0.276985i	0.0462295	−	0.0123872i
$501$	16.4016	+	27.0793i	0.732767	+	1.20981i
$502$	5.96735	+	5.96735i	0.266336	+	0.266336i
$503$	−11.1019	−	6.40966i	−0.495007	−	0.285792i	0.231642	−	0.972801i	$-0.425590\pi$
$503$	−11.1019	−	6.40966i	−0.495007	−	0.285792i	−0.726649	+	0.687009i	$0.758923\pi$
$504$	2.65874	+	1.38963i	0.118430	+	0.0618992i
$505$	0.217783	−	0.812777i	0.00969121	−	0.0361681i
$506$	−1.64761			−0.0732450
$507$	21.4611	−	6.81345i	0.953119	−	0.302596i
$508$	11.8233			0.524573
$509$	−3.11993	+	11.6437i	−0.138288	+	0.516100i	0.861674	+	0.507462i	$0.169416\pi$
$509$	−3.11993	+	11.6437i	−0.138288	+	0.516100i	−0.999963	+	0.00863772i	$0.997250\pi$
$510$	3.10873	−	3.24207i	0.137657	−	0.143561i
$511$	−2.51027	−	1.44931i	−0.111048	−	0.0641136i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	25.2285	+	12.5190i	1.11387	+	0.552728i
$514$	2.31126	−	0.619302i	0.101946	−	0.0273162i
$515$	−6.59709	+	6.59709i	−0.290703	+	0.290703i
$516$	4.84668	−	19.7362i	0.213363	−	0.868840i
$517$	9.51032	−	5.49078i	0.418263	−	0.241484i
$518$	−6.14328	−	1.64609i	−0.269920	−	0.0723249i
$519$	−30.4834	+	8.85783i	−1.33807	+	0.388816i
$520$	−5.91813	−	9.96513i	−0.259527	−	0.437000i
$521$			29.2174i			1.28004i	0.768359	+	0.640019i	$0.221074\pi$
$521$			29.2174i			1.28004i	−0.768359	+	0.640019i	$0.778926\pi$
$522$	17.8740	−	5.60327i	0.782325	−	0.245248i
$523$	−8.57887	−	14.8590i	−0.375128	−	0.649741i	0.615218	−	0.788357i	$-0.289068\pi$
$523$	−8.57887	−	14.8590i	−0.375128	−	0.649741i	−0.990346	+	0.138616i	$0.955735\pi$
$524$	−0.229387	+	0.397310i	−0.0100208	+	0.0173566i
$525$	−4.44952	+	8.09457i	−0.194193	+	0.353276i
$526$	−1.16678	−	4.35448i	−0.0508740	−	0.189864i
$527$	0.865682	+	3.23077i	0.0377097	+	0.140734i
$528$	1.64826	−	2.99852i	0.0717313	−	0.130494i
$529$	11.1522	−	19.3162i	0.484879	−	0.839834i
$530$	13.8613	+	24.0085i	0.602097	+	1.04286i
$531$	4.22520	−	1.32454i	0.183358	−	0.0574802i
$532$			5.42014i			0.234993i
$533$	12.9193	−	3.63277i	0.559596	−	0.157353i
$534$	−4.04620	+	1.17574i	−0.175096	+	0.0508793i
$535$	−34.7303	−	9.30597i	−1.50152	−	0.402332i
$536$	5.02695	−	2.90231i	0.217131	−	0.125361i
$537$	9.88252	−	40.2427i	0.426462	−	1.73660i
$538$	3.31976	−	3.31976i	0.143125	−	0.143125i
$539$	1.90819	−	0.511298i	0.0821916	−	0.0220232i
$540$	−14.9621	−	7.42457i	−0.643867	−	0.319503i
$541$	−6.80439	−	6.80439i	−0.292544	−	0.292544i	0.545541	−	0.838084i	$-0.316324\pi$
$541$	−6.80439	−	6.80439i	−0.292544	−	0.292544i	−0.838084	+	0.545541i	$0.816324\pi$
$542$	10.6031	+	6.12172i	0.455443	+	0.262950i
$543$	−29.2398	+	30.4939i	−1.25480	+	1.30862i
$544$	−0.208801	+	0.779257i	−0.00895228	+	0.0334104i
$545$	−43.8390			−1.87786
$546$	6.08268	+	1.41457i	0.260315	+	0.0605380i
$547$	6.48386			0.277230			0.138615	−	0.990346i	$-0.455735\pi$
$547$	6.48386			0.277230			0.138615	+	0.990346i	$0.455735\pi$
$548$	−5.42398	+	20.2426i	−0.231701	+	0.864720i
$549$	0.886935	+	0.463570i	0.0378534	+	0.0197847i
$550$	9.12377	+	5.26761i	0.389039	+	0.224612i
$551$	23.9305	+	23.9305i	1.01948	+	1.01948i
$552$	−0.748381	−	1.23559i	−0.0318532	−	0.0525902i
$553$	0.987903	−	0.264708i	0.0420099	−	0.0112565i
$554$	−6.97462	+	6.97462i	−0.296323	+	0.296323i
$555$	34.3885	+	8.44487i	1.45971	+	0.358465i
$556$	−16.3805	+	9.45727i	−0.694687	+	0.401077i
$557$	15.6091	+	4.18244i	0.661378	+	0.177216i	0.573868	−	0.818948i	$-0.305442\pi$
$557$	15.6091	+	4.18244i	0.661378	+	0.177216i	0.0875103	+	0.996164i	$0.472109\pi$
$558$	10.5010	−	6.66556i	0.444543	−	0.282176i
$559$	−0.520844	−	42.3018i	−0.0220293	−	1.78917i
$560$		−	3.21449i		−	0.135837i
$561$	2.75981	−	0.0579424i	0.116519	−	0.00244633i
$562$	−10.0851	−	17.4679i	−0.425413	−	0.736837i
$563$	9.19607	−	15.9281i	0.387568	−	0.671288i	−0.604554	−	0.796564i	$-0.706648\pi$
$563$	9.19607	−	15.9281i	0.387568	−	0.671288i	0.992122	+	0.125277i	$0.0399818\pi$
$564$	8.43752	+	4.63804i	0.355283	+	0.195297i
$565$	−11.4273	−	42.6474i	−0.480752	−	1.79419i
$566$	0.812799	+	3.03341i	0.0341645	+	0.127504i
$567$	8.46734	−	3.05027i	0.355595	−	0.128099i
$568$	−6.40885	+	11.1005i	−0.268910	+	0.465765i
$569$	10.0485	+	17.4045i	0.421254	+	0.729633i	0.996062	−	0.0886546i	$-0.0282567\pi$
$569$	10.0485	+	17.4045i	0.421254	+	0.729633i	−0.574808	+	0.818288i	$0.694923\pi$
$570$	−0.633438	−	30.1708i	−0.0265318	−	1.26372i
$571$			34.0518i			1.42502i	0.701661	+	0.712511i	$0.252442\pi$
$571$			34.0518i			1.42502i	−0.701661	+	0.712511i	$0.747558\pi$
$572$	1.75867	−	6.90226i	0.0735336	−	0.288598i
$573$	11.4268	+	39.3241i	0.477360	+	1.64279i
$574$	3.59530	+	0.963357i	0.150065	+	0.0402098i
$575$	3.85187	−	2.22388i	0.160634	−	0.0927421i
$576$	2.99736	−	0.125915i	0.124890	−	0.00524645i
$577$	22.9358	−	22.9358i	0.954829	−	0.954829i	−0.0441943	−	0.999023i	$-0.514072\pi$
$577$	22.9358	−	22.9358i	0.954829	−	0.954829i	0.999023	+	0.0441943i	$0.0140721\pi$
$578$	15.7921	−	4.23147i	0.656864	−	0.176006i
$579$	−2.68756	+	1.62782i	−0.111691	+	0.0676500i
$580$	−14.1923	−	14.1923i	−0.589304	−	0.589304i
$581$	−13.1016	−	7.56421i	−0.543546	−	0.313816i
$582$	−17.4819	−	16.7630i	−0.724649	−	0.694847i
$583$	−4.40958	+	16.4568i	−0.182626	+	0.681569i
$584$	−2.89861			−0.119946
$585$	−34.0241	−	7.16323i	−1.40672	−	0.296163i
$586$	−10.6876			−0.441499
$587$	7.31735	−	27.3087i	0.302019	−	1.12715i	−0.633462	−	0.773774i	$-0.718367\pi$
$587$	7.31735	−	27.3087i	0.302019	−	1.12715i	0.935481	−	0.353377i	$-0.114967\pi$
$588$	1.25018	+	1.19877i	0.0515567	+	0.0494363i
$589$	19.4611	+	11.2358i	0.801879	+	0.462965i
$590$	−3.35488	−	3.35488i	−0.138118	−	0.138118i
$591$	−27.6583	+	16.7523i	−1.13771	+	0.689097i
$592$	−6.14328	+	1.64609i	−0.252487	+	0.0676538i
$593$	−20.4507	+	20.4507i	−0.839809	+	0.839809i	−0.988834	−	0.149024i	$-0.952387\pi$
$593$	−20.4507	+	20.4507i	−0.839809	+	0.839809i	0.149024	+	0.988834i	$0.452387\pi$
$594$	−3.27553	−	9.72839i	−0.134396	−	0.399161i
$595$	2.24584	−	1.29664i	0.0920705	−	0.0531570i
$596$	−12.3313	−	3.30416i	−0.505110	−	0.135344i
$597$	−0.369252	−	1.27074i	−0.0151125	−	0.0520081i
$598$	−2.15235	−	2.10000i	−0.0880163	−	0.0858752i
$599$			4.44002i			0.181414i	0.995878	+	0.0907071i	$0.0289127\pi$
$599$			4.44002i			0.181414i	−0.995878	+	0.0907071i	$0.971087\pi$
$600$	0.193886	+	9.23487i	0.00791538	+	0.377012i
$601$	−3.92618	−	6.80034i	−0.160152	−	0.277392i	0.774771	−	0.632242i	$-0.217865\pi$
$601$	−3.92618	−	6.80034i	−0.160152	−	0.277392i	−0.934923	+	0.354850i	$0.884532\pi$
$602$	5.86664	−	10.1613i	0.239106	−	0.414145i
$603$	3.79709	−	16.9949i	0.154629	−	0.692084i
$604$	3.88063	+	14.4827i	0.157901	+	0.589293i
$605$	−5.90481	−	22.0371i	−0.240065	−	0.895934i
$606$	0.397323	+	0.218405i	0.0161402	+	0.00887212i
$607$	−15.8724	+	27.4918i	−0.644240	+	1.11586i	0.340236	+	0.940340i	$0.389493\pi$
$607$	−15.8724	+	27.4918i	−0.644240	+	1.11586i	−0.984476	+	0.175517i	$0.943840\pi$
$608$	2.71007	+	4.69398i	0.109908	+	0.190366i
$609$	10.8124	−	0.227006i	0.438140	−	0.00919877i
$610$		−	1.07233i		−	0.0434172i
$611$	19.4222	+	4.94871i	0.785740	+	0.200203i
$612$	1.29702	+	2.04335i	0.0524291	+	0.0825975i
$613$	−29.5200	−	7.90985i	−1.19230	−	0.319476i	−0.392506	−	0.919750i	$-0.628392\pi$
$613$	−29.5200	−	7.90985i	−1.19230	−	0.319476i	−0.799795	+	0.600274i	$0.795058\pi$
$614$	−29.2411	+	16.8823i	−1.18007	+	0.681316i
$615$	−20.1256	−	4.94229i	−0.811541	−	0.199292i
$616$	1.39689	−	1.39689i	0.0562824	−	0.0562824i
$617$	5.52873	−	1.48142i	0.222578	−	0.0596397i	−0.145806	−	0.989313i	$-0.546578\pi$
$617$	5.52873	−	1.48142i	0.222578	−	0.0596397i	0.368385	+	0.929673i	$0.379911\pi$
$618$	−2.60437	−	4.29987i	−0.104763	−	0.172966i
$619$	31.3461	+	31.3461i	1.25991	+	1.25991i	0.951136	+	0.308772i	$0.0999179\pi$
$619$	31.3461	+	31.3461i	1.25991	+	1.25991i	0.308772	+	0.951136i	$0.400082\pi$
$620$	−11.5416	−	6.66357i	−0.463523	−	0.267615i
$621$	−4.24831	−	0.855973i	−0.170479	−	0.0343490i
$622$	9.08377	−	33.9011i	0.364226	−	1.35931i
$623$	−2.43270			−0.0974641
$624$	5.97504	−	1.81629i	0.239193	−	0.0727097i
$625$	23.2245			0.928981
$626$	2.35025	−	8.77125i	0.0939349	−	0.350570i
$627$	12.8358	−	13.3864i	0.512613	−	0.534600i
$628$	−13.5228	−	7.80740i	−0.539619	−	0.311549i
$629$	−3.62809	−	3.62809i	−0.144662	−	0.144662i
$630$	−7.09915	−	6.52675i	−0.282837	−	0.260032i
$631$	−9.16796	+	2.45655i	−0.364971	+	0.0977936i	−0.436644	−	0.899635i	$-0.643833\pi$
$631$	−9.16796	+	2.45655i	−0.364971	+	0.0977936i	0.0716729	+	0.997428i	$0.477166\pi$
$632$	0.723195	−	0.723195i	0.0287671	−	0.0287671i
$633$	−1.31068	+	5.33724i	−0.0520948	+	0.212136i
$634$	−21.5828	+	12.4608i	−0.857162	+	0.494883i
$635$	−36.7107	−	9.83662i	−1.45682	−	0.390354i
$636$	−14.3444	+	4.16817i	−0.568791	+	0.165279i
$637$	3.14446	+	1.76420i	0.124588	+	0.0699000i
$638$		−	12.3349i		−	0.488342i
$639$	11.5026	+	36.6924i	0.455035	+	1.45153i
$640$	−1.60724	−	2.78383i	−0.0635319	−	0.110040i
$641$	20.1937	−	34.9766i	0.797604	−	1.38149i	−0.123568	−	0.992336i	$-0.539434\pi$
$641$	20.1937	−	34.9766i	0.797604	−	1.38149i	0.921172	−	0.389155i	$-0.127233\pi$
$642$	9.33257	−	16.9778i	0.368327	−	0.670061i
$643$	8.16642	+	30.4775i	0.322052	+	1.20192i	0.917242	+	0.398330i	$0.130410\pi$
$643$	8.16642	+	30.4775i	0.322052	+	1.20192i	−0.595190	+	0.803585i	$0.702923\pi$
$644$	−0.215860	−	0.805599i	−0.00850606	−	0.0317451i
$645$	−31.4687	+	57.2479i	−1.23908	+	2.25413i
$646$	−2.18634	+	3.78685i	−0.0860204	+	0.148992i
$647$	−13.8364	−	23.9654i	−0.543967	−	0.942178i	−0.998671	−	0.0515355i	$-0.983588\pi$
$647$	−13.8364	−	23.9654i	−0.543967	−	0.942178i	0.454705	−	0.890642i	$-0.349745\pi$
$648$	5.80780	−	6.87528i	0.228152	−	0.270086i
$649$		−	2.91581i		−	0.114455i
$650$	5.20490	+	18.5103i	0.204153	+	0.726033i
$651$	6.89579	−	2.00377i	0.270267	−	0.0785339i
$652$	−8.59318	−	2.30254i	−0.336535	−	0.0901743i
$653$	43.1637	−	24.9206i	1.68913	−	0.975218i	0.733941	−	0.679213i	$-0.237679\pi$
$653$	43.1637	−	24.9206i	1.68913	−	0.975218i	0.955186	−	0.296006i	$-0.0956547\pi$
$654$	5.63344	−	22.9400i	0.220285	−	0.897026i
$655$	1.04279	−	1.04279i	0.0407451	−	0.0407451i
$656$	3.59530	−	0.963357i	0.140373	−	0.0376128i
$657$	−5.88539	+	6.40155i	−0.229611	+	0.249748i
$658$	3.93071	+	3.93071i	0.153235	+	0.153235i
$659$	10.8662	+	6.27359i	0.423286	+	0.244384i	0.696482	−	0.717574i	$-0.254748\pi$
$659$	10.8662	+	6.27359i	0.423286	+	0.244384i	−0.273196	+	0.961958i	$0.588081\pi$
$660$	−7.61245	+	7.93895i	−0.296314	+	0.309023i
$661$	−2.82265	+	10.5343i	−0.109788	+	0.409736i	−0.998844	−	0.0480627i	$-0.984695\pi$
$661$	−2.82265	+	10.5343i	−0.109788	+	0.409736i	0.889056	+	0.457799i	$0.151362\pi$
$662$	−24.1687			−0.939341
$663$	3.67914	+	3.44190i	0.142886	+	0.133672i
$664$	−15.1284			−0.587097
$665$	4.50940	−	16.8293i	0.174867	−	0.652613i
$666$	−8.83805	+	16.9096i	−0.342468	+	0.655233i
$667$	−4.50986	−	2.60377i	−0.174622	−	0.100818i
$668$	12.9248	+	12.9248i	0.500074	+	0.500074i
$669$	16.8682	+	27.8496i	0.652160	+	1.07673i
$670$	−18.0231	+	4.82928i	−0.696293	+	0.186571i
$671$	0.465992	−	0.465992i	0.0179894	−	0.0179894i
$672$	1.68207	+	0.413071i	0.0648874	+	0.0159346i
$673$	−3.52986	+	2.03796i	−0.136066	+	0.0785577i	−0.566488	−	0.824070i	$-0.691698\pi$
$673$	−3.52986	+	2.03796i	−0.136066	+	0.0785577i	0.430422	+	0.902628i	$0.358365\pi$
$674$	−29.3530	−	7.86511i	−1.13064	−	0.302953i
$675$	20.7887	+	18.3224i	0.800159	+	0.705230i
$676$	11.0949	−	6.77523i	0.426726	−	0.260586i
$677$			21.6400i			0.831694i	0.909435	+	0.415847i	$0.136515\pi$
$677$			21.6400i			0.831694i	−0.909435	+	0.415847i	$0.863485\pi$
$678$	23.7849	−	0.499366i	0.913455	−	0.0191780i
$679$	−6.99175	−	12.1101i	−0.268319	−	0.464741i
$680$	1.29664	−	2.24584i	0.0497238	−	0.0861241i
$681$	−15.5010	−	8.52077i	−0.593999	−	0.326517i
$682$	−2.11982	−	7.91128i	−0.0811722	−	0.302939i
$683$	2.22255	+	8.29468i	0.0850436	+	0.317387i	0.995322	−	0.0966086i	$-0.0307995\pi$
$683$	2.22255	+	8.29468i	0.0850436	+	0.317387i	−0.910279	+	0.413996i	$0.864133\pi$
$684$	15.8692	+	3.54558i	0.606773	+	0.135569i
$685$	33.6825	−	58.3397i	1.28694	−	2.22905i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$	0.859669	+	40.9463i	0.0327984	+	1.56220i
$688$		−	11.7333i		−	0.447327i
$689$	−26.7358	+	15.8780i	−1.01855	+	0.604904i
$690$	1.29572	+	4.45908i	0.0493271	+	0.169754i
$691$	−9.52639	−	2.55259i	−0.362401	−	0.0971051i	0.0730237	−	0.997330i	$-0.476735\pi$
$691$	−9.52639	−	2.55259i	−0.362401	−	0.0971051i	−0.435425	+	0.900225i	$0.643402\pi$
$692$	−15.8721	+	9.16378i	−0.603368	+	0.348355i
$693$	−0.248745	−	5.92129i	−0.00944905	−	0.224931i
$694$	1.32543	−	1.32543i	0.0503125	−	0.0503125i
$695$	58.7288	−	15.7363i	2.22771	−	0.596913i
$696$	9.25030	−	5.60279i	0.350632	−	0.212373i
$697$	2.12331	+	2.12331i	0.0804260	+	0.0804260i
$698$	4.70058	+	2.71388i	0.177920	+	0.102722i
$699$	−2.98545	−	2.86267i	−0.112920	−	0.108276i
$700$	−1.38026	+	5.15121i	−0.0521690	+	0.194698i
$701$	10.0189			0.378410			0.189205	−	0.981938i	$-0.439409\pi$
$701$	10.0189			0.378410			0.189205	+	0.981938i	$0.439409\pi$
$702$	8.12057	−	16.8836i	0.306491	−	0.637231i
$703$	−34.4721			−1.30014
$704$	0.511298	−	1.90819i	0.0192703	−	0.0719176i
$705$	−22.3394	−	21.4207i	−0.841351	−	0.806749i
$706$	20.8053	+	12.0120i	0.783020	+	0.452077i
$707$	0.185098	+	0.185098i	0.00696131	+	0.00696131i
$708$	2.18665	−	1.32443i	0.0821795	−	0.0497750i
$709$	−31.5448	+	8.45239i	−1.18469	+	0.317436i	−0.796784	−	0.604264i	$-0.793467\pi$
$709$	−31.5448	+	8.45239i	−1.18469	+	0.317436i	−0.387904	+	0.921700i	$0.626801\pi$
$710$	29.1345	−	29.1345i	1.09340	−	1.09340i
$711$	−0.128780	−	3.06555i	−0.00482961	−	0.114967i
$712$	−2.10678	+	1.21635i	−0.0789549	+	0.0455847i
$713$	−3.33998	−	0.894946i	−0.125083	−	0.0335160i
$714$	0.389906	+	1.34182i	0.0145919	+	0.0502165i
$715$	−11.2031	+	19.9680i	−0.418971	+	0.746762i
$716$		−	23.9245i		−	0.894100i
$717$	−0.928153	−	44.2082i	−0.0346625	−	1.65099i
$718$	4.14759	+	7.18384i	0.154787	+	0.268098i
$719$	−11.8380	+	20.5041i	−0.441484	+	0.764672i	−0.997800	−	0.0662986i	$-0.978881\pi$
$719$	−11.8380	+	20.5041i	−0.441484	+	0.764672i	0.556316	+	0.830971i	$0.312214\pi$
$720$	−9.41142	−	2.10275i	−0.350743	−	0.0783650i
$721$	−0.751194	−	2.80349i	−0.0279759	−	0.104408i
$722$	2.68601	+	10.0243i	0.0999630	+	0.373067i
$723$	−0.869380	−	0.477891i	−0.0323326	−	0.0177730i
$724$	−12.1958	+	21.1237i	−0.453253	+	0.785057i
$725$	16.6492	+	28.8372i	0.618334	+	1.07099i
$726$	12.2903	−	0.258036i	0.456136	−	0.00957660i
$727$			34.8435i			1.29227i	0.763222	+	0.646136i	$0.223616\pi$
$727$			34.8435i			1.29227i	−0.763222	+	0.646136i	$0.776384\pi$
$728$	3.60528	−	0.0443903i	0.133620	−	0.00164521i
$729$	−3.39171	−	26.7861i	−0.125619	−	0.992079i
$730$	9.00007	+	2.41156i	0.333108	+	0.0892559i
$731$	8.19761	−	4.73289i	0.303199	−	0.175052i
$732$	0.561126	+	0.137797i	0.0207398	+	0.00509313i
$733$	4.06240	−	4.06240i	0.150048	−	0.150048i	−0.628091	−	0.778140i	$-0.716164\pi$
$733$	4.06240	−	4.06240i	0.150048	−	0.150048i	0.778140	+	0.628091i	$0.216164\pi$
$734$	5.58844	−	1.49742i	0.206273	−	0.0552707i
$735$	−2.88442	−	4.76223i	−0.106394	−	0.175658i
$736$	−0.589740	−	0.589740i	−0.0217381	−	0.0217381i
$737$	−9.93077	−	5.73353i	−0.365805	−	0.211197i
$738$	5.17239	−	9.89618i	0.190398	−	0.364284i
$739$	5.85651	−	21.8568i	0.215435	−	0.804015i	−0.770578	−	0.637346i	$-0.780032\pi$
$739$	5.85651	−	21.8568i	0.215435	−	0.804015i	0.986013	−	0.166669i	$-0.0533012\pi$
$740$	20.4441			0.751540
$741$	33.8300	−	1.12709i	1.24278	−	0.0414046i
$742$	−8.62427			−0.316607
$743$	−3.24612	+	12.1147i	−0.119089	+	0.444444i	−0.999560	−	0.0296543i	$-0.990559\pi$
$743$	−3.24612	+	12.1147i	−0.119089	+	0.444444i	0.880472	+	0.474099i	$0.157226\pi$
$744$	4.97004	−	5.18321i	0.182211	−	0.190026i
$745$	35.5392	+	20.5185i	1.30205	+	0.751741i
$746$	26.5918	+	26.5918i	0.973594	+	0.973594i
$747$	−30.7170	+	33.4109i	−1.12388	+	1.22244i
$748$	1.53943	−	0.412488i	0.0562870	−	0.0150820i
$749$	7.90931	−	7.90931i	0.289000	−	0.289000i
$750$	0.442064	−	1.80014i	0.0161419	−	0.0657317i
$751$	13.9581	−	8.05870i	0.509337	−	0.294066i	−0.223224	−	0.974767i	$-0.571658\pi$
$751$	13.9581	−	8.05870i	0.509337	−	0.294066i	0.732561	+	0.680701i	$0.238325\pi$
$752$	5.36945	+	1.43874i	0.195804	+	0.0524655i
$753$	14.0364	−	4.07868i	0.511514	−	0.148635i
$754$	15.7217	−	16.1137i	0.572551	−	0.586826i
$755$		−	48.1967i		−	1.75406i
$756$	4.32757	−	2.87613i	0.157392	−	0.104604i
$757$	11.7925	+	20.4253i	0.428607	+	0.742369i	0.996750	−	0.0805613i	$-0.0256713\pi$
$757$	11.7925	+	20.4253i	0.428607	+	0.742369i	−0.568143	+	0.822930i	$0.692338\pi$
$758$	8.22688	−	14.2494i	0.298814	−	0.517560i
$759$	−1.37468	+	2.50081i	−0.0498977	+	0.0907738i
$760$	−4.50940	−	16.8293i	−0.163573	−	0.610463i
$761$	−3.36919	−	12.5740i	−0.122133	−	0.455807i	0.877588	−	0.479415i	$-0.159151\pi$
$761$	−3.36919	−	12.5740i	−0.122133	−	0.455807i	−0.999721	+	0.0236084i	$0.992485\pi$
$762$	9.86474	−	17.9459i	0.357362	−	0.650112i
$763$	6.81897	−	11.8108i	0.246863	−	0.427580i
$764$	11.8214	+	20.4753i	0.427685	+	0.740772i
$765$	−2.32720	−	7.42360i	−0.0841400	−	0.268401i
$766$			33.4213i			1.20756i
$767$	3.71641	−	3.80907i	0.134192	−	0.137538i
$768$	1.66325	−	0.483307i	0.0600175	−	0.0174398i
$769$	3.86673	+	1.03609i	0.139438	+	0.0373623i	0.327863	−	0.944725i	$-0.393672\pi$
$769$	3.86673	+	1.03609i	0.139438	+	0.0373623i	−0.188425	+	0.982088i	$0.560338\pi$
$770$	−5.49946	+	3.17512i	−0.198187	+	0.114423i
$771$	0.988396	−	4.02486i	0.0355962	−	0.144952i
$772$	−1.28276	+	1.28276i	−0.0461674	+	0.0461674i
$773$	−1.12750	+	0.302113i	−0.0405534	+	0.0108662i	−0.279039	−	0.960280i	$-0.590016\pi$
$773$	−1.12750	+	0.302113i	−0.0405534	+	0.0108662i	0.238485	+	0.971146i	$0.423349\pi$
$774$	−25.9128	−	23.8234i	−0.931416	−	0.856316i
$775$	15.6342	+	15.6342i	0.561597	+	0.561597i
$776$	−12.1101	−	6.99175i	−0.434726	−	0.250989i
$777$	−7.62415	+	7.95115i	−0.273515	+	0.285246i
$778$	2.50573	−	9.35150i	0.0898347	−	0.335268i
$779$	20.1745			0.722825
$780$	−20.0633	+	0.668435i	−0.718383	+	0.0239338i
$781$	25.3214			0.906072
$782$	0.174144	−	0.649914i	0.00622738	−	0.0232409i
$783$	6.40828	−	31.8051i	0.229013	−	1.13662i
$784$	0.866025	+	0.500000i	0.0309295	+	0.0178571i
$785$	35.4922	+	35.4922i	1.26677	+	1.26677i
$786$	0.411667	+	0.679670i	0.0146837	+	0.0242430i
$787$	29.0401	−	7.78127i	1.03517	−	0.277372i	0.299058	−	0.954235i	$-0.403327\pi$
$787$	29.0401	−	7.78127i	1.03517	−	0.277372i	0.736110	+	0.676862i	$0.236661\pi$
$788$	−13.2012	+	13.2012i	−0.470272	+	0.470272i
$789$	−7.58294	−	1.86216i	−0.269960	−	0.0662948i
$790$	−2.84716	+	1.64381i	−0.101298	+	0.0584842i
$791$	13.2673	+	3.55495i	0.471729	+	0.126399i
$792$	−3.17607	−	5.00362i	−0.112857	−	0.177796i
$793$	1.20269	−	0.0148082i	0.0427088	−	0.000525855i
$794$		−	8.90130i		−	0.315895i
$795$	48.0064	−	1.00790i	1.70261	−	0.0357464i
$796$	−0.382006	−	0.661653i	−0.0135398	−	0.0234517i
$797$	4.73370	−	8.19901i	0.167676	−	0.290424i	−0.769926	−	0.638133i	$-0.779707\pi$
$797$	4.73370	−	8.19901i	0.167676	−	0.290424i	0.937602	+	0.347709i	$0.113040\pi$
$798$	8.22695	+	4.52229i	0.291231	+	0.160087i
$799$	1.16070	+	4.33179i	0.0410626	+	0.153248i
$800$	1.38026	+	5.15121i	0.0487997	+	0.182123i
$801$	−1.59135	+	7.12249i	−0.0562275	+	0.251661i
$802$	−19.9454	+	34.5464i	−0.704295	+	1.21987i
$803$	2.86311	+	4.95906i	0.101037	+	0.175001i
$804$	−0.211036	−	10.0517i	−0.00744265	−	0.354496i
$805$			2.68094i			0.0944907i
$806$	7.31429	−	13.0368i	0.257635	−	0.459202i
$807$	−2.26905	−	7.80872i	−0.0798743	−	0.274880i
$808$	0.252848	+	0.0677504i	0.00889516	+	0.00238345i
$809$	−22.6228	+	13.0613i	−0.795375	+	0.459210i	−0.841851	−	0.539709i	$-0.818534\pi$
$809$	−22.6228	+	13.0613i	−0.795375	+	0.459210i	0.0464763	+	0.998919i	$0.485201\pi$
$810$	−23.7530	+	16.5155i	−0.834595	+	0.580296i
$811$	−5.68327	+	5.68327i	−0.199567	+	0.199567i	−0.799814	−	0.600248i	$-0.795069\pi$
$811$	−5.68327	+	5.68327i	−0.199567	+	0.199567i	0.600248	+	0.799814i	$0.295069\pi$
$812$	6.03115	−	1.61604i	0.211652	−	0.0567120i
$813$	18.1386	−	10.9863i	0.636147	−	0.385306i
$814$	8.88422	+	8.88422i	0.311392	+	0.311392i
$815$	24.7658	+	14.2985i	0.867509	+	0.500856i
$816$	1.00858	+	0.967101i	0.0353074	+	0.0338553i
$817$	16.4599	−	61.4291i	0.575858	−	2.14913i
$818$	14.6360			0.511735
$819$	7.22218	−	8.05234i	0.252363	−	0.281371i
$820$	−11.9647			−0.417826
$821$	−1.88673	+	7.04136i	−0.0658472	+	0.245745i	−0.991002	−	0.133844i	$-0.957268\pi$
$821$	−1.88673	+	7.04136i	−0.0658472	+	0.245745i	0.925155	+	0.379589i	$0.123935\pi$
$822$	26.1997	+	25.1222i	0.913818	+	0.876236i
$823$	−8.15877	−	4.71047i	−0.284397	−	0.164196i	0.351015	−	0.936370i	$-0.385836\pi$
$823$	−8.15877	−	4.71047i	−0.284397	−	0.164196i	−0.635412	+	0.772173i	$0.719170\pi$
$824$	−2.05230	−	2.05230i	−0.0714953	−	0.0714953i
$825$	15.6078	−	9.45347i	0.543395	−	0.329127i
$826$	1.42569	−	0.382012i	0.0496060	−	0.0132919i
$827$	−9.04435	+	9.04435i	−0.314503	+	0.314503i	−0.846651	−	0.532148i	$-0.821385\pi$
$827$	−9.04435	+	9.04435i	−0.314503	+	0.314503i	0.532148	+	0.846651i	$0.321385\pi$
$828$	−2.49985	+	0.105015i	−0.0868757	+	0.00364953i
$829$	25.4467	−	14.6917i	0.883802	−	0.510263i	0.0118920	−	0.999929i	$-0.496215\pi$
$829$	25.4467	−	14.6917i	0.883802	−	0.510263i	0.871910	+	0.489666i	$0.162881\pi$
$830$	46.9731	+	12.5864i	1.63046	+	0.436880i
$831$	4.76714	+	16.4057i	0.165370	+	0.569106i
$832$	3.10007	−	1.84108i	0.107475	−	0.0638280i
$833$			0.806746i			0.0279521i
$834$	0.687666	+	32.7537i	0.0238119	+	1.13417i
$835$	−29.3778	−	50.8838i	−1.01666	−	1.76091i
$836$	5.35376	−	9.27298i	0.185164	−	0.320713i
$837$	−1.35580	−	21.5003i	−0.0468631	−	0.743160i
$838$	1.93302	+	7.21412i	0.0667750	+	0.249208i
$839$	10.7154	+	39.9905i	0.369937	+	1.38062i	0.860603	+	0.509277i	$0.170087\pi$
$839$	10.7154	+	39.9905i	0.369937	+	1.38062i	−0.490666	+	0.871348i	$0.663246\pi$
$840$	−4.87910	−	2.68200i	−0.168345	−	0.0925379i
$841$	4.99321	−	8.64849i	0.172180	−	0.298224i
$842$	−18.3672	−	31.8129i	−0.632975	−	1.09635i
$843$	−34.9280	+	0.733315i	−1.20298	+	0.0252567i
$844$			3.17301i			0.109220i
$845$	−40.0859	+	11.8062i	−1.37900	+	0.406144i
$846$	14.0797	−	8.93712i	0.484069	−	0.307265i
$847$	6.85554	+	1.83694i	0.235559	+	0.0631179i
$848$	−7.46884	+	4.31214i	−0.256481	+	0.148079i
$849$	5.28241	+	1.29722i	0.181292	+	0.0445203i
$850$	−3.04220	+	3.04220i	−0.104347	+	0.104347i
$851$	5.12360	−	1.37287i	0.175635	−	0.0470612i
$852$	11.5016	+	18.9893i	0.394038	+	0.650563i
$853$	14.8807	+	14.8807i	0.509507	+	0.509507i	0.914375	−	0.404868i	$-0.132683\pi$
$853$	14.8807	+	14.8807i	0.509507	+	0.509507i	−0.404868	+	0.914375i	$0.632683\pi$
$854$	0.288899	+	0.166796i	0.00988591	+	0.00570763i
$855$	−46.3232	−	24.2115i	−1.58422	−	0.828017i
$856$	2.89501	−	10.8043i	0.0989494	−	0.369284i
$857$	45.4500			1.55254			0.776272	−	0.630398i	$-0.217108\pi$
$857$	45.4500			1.55254			0.776272	+	0.630398i	$0.217108\pi$
$858$	−9.00923	−	8.42828i	−0.307570	−	0.287737i
$859$	−6.85337			−0.233834			−0.116917	−	0.993142i	$-0.537301\pi$
$859$	−6.85337			−0.233834			−0.116917	+	0.993142i	$0.537301\pi$
$860$	−9.76175	+	36.4313i	−0.332873	+	1.24230i
$861$	4.46196	−	4.65334i	0.152063	−	0.158585i
$862$	−19.4142	−	11.2088i	−0.661251	−	0.381774i
$863$	0.114990	+	0.114990i	0.00391429	+	0.00391429i	0.709061	−	0.705147i	$-0.249119\pi$
$863$	0.114990	+	0.114990i	0.00391429	+	0.00391429i	−0.705147	+	0.709061i	$0.749119\pi$
$864$	2.30972	−	4.65459i	0.0785783	−	0.158352i
$865$	56.9063	−	15.2480i	1.93487	−	0.518447i
$866$	22.6341	−	22.6341i	0.769139	−	0.769139i
$867$	6.75337	−	27.5005i	0.229356	−	0.933966i
$868$	3.59051	−	2.07298i	0.121870	−	0.0703615i
$869$	−1.95161	−	0.522931i	−0.0662037	−	0.0177392i
$870$	−33.3831	+	9.70043i	−1.13179	+	0.328875i
$871$	−5.66527	−	20.1475i	−0.191960	−	0.682673i
$872$		−	13.6379i		−	0.461839i
$873$	−40.0296	+	12.5487i	−1.35480	+	0.424711i
$874$	−2.26025	−	3.91486i	−0.0764540	−	0.132422i
$875$	0.535095	−	0.926811i	0.0180895	−	0.0313319i
$876$	−2.41846	+	4.39966i	−0.0817121	+	0.148651i
$877$	0.917472	+	3.42405i	0.0309808	+	0.115622i	0.979685	−	0.200544i	$-0.0642710\pi$
$877$	0.917472	+	3.42405i	0.0309808	+	0.115622i	−0.948704	+	0.316166i	$0.897604\pi$
$878$	3.77865	+	14.1021i	0.127523	+	0.475923i
$879$	−8.91715	+	16.2221i	−0.300768	+	0.547157i
$880$	−3.17512	+	5.49946i	−0.107033	+	0.185387i
$881$	10.4170	+	18.0428i	0.350958	+	0.607877i	0.986418	−	0.164257i	$-0.0525226\pi$
$881$	10.4170	+	18.0428i	0.350958	+	0.607877i	−0.635460	+	0.772134i	$0.719189\pi$
$882$	2.86263	−	0.897397i	0.0963899	−	0.0302169i
$883$		−	16.3110i		−	0.548909i	−0.961600	−	0.274455i	$-0.911503\pi$
$883$		−	16.3110i		−	0.548909i	0.961600	−	0.274455i	$-0.0884973\pi$
$884$	2.53678	+	1.42326i	0.0853211	+	0.0478694i
$885$	−7.89135	+	2.29306i	−0.265265	+	0.0770803i
$886$	−31.4327	−	8.42238i	−1.05600	−	0.282955i
$887$	−18.5286	+	10.6975i	−0.622130	+	0.359187i	−0.777698	−	0.628638i	$-0.783613\pi$
$887$	−18.5286	+	10.6975i	−0.622130	+	0.359187i	0.155568	+	0.987825i	$0.450279\pi$
$888$	−2.62713	+	10.6980i	−0.0881607	+	0.359000i
$889$	8.36032	−	8.36032i	0.280396	−	0.280396i
$890$	7.55343	−	2.02393i	0.253191	−	0.0678424i
$891$	−17.4992	−	3.14513i	−0.586244	−	0.105366i
$892$	13.2925	+	13.2925i	0.445064	+	0.445064i
$893$	26.0932	+	15.0649i	0.873176	+	0.504129i
$894$	−15.3038	+	15.9602i	−0.511836	+	0.533789i
$895$	−19.9045	+	74.2845i	−0.665333	+	2.48306i
$896$	1.00000			0.0334077
$897$	−4.98329	+	1.51482i	−0.166387	+	0.0505782i
$898$	14.4472			0.482110
$899$	6.70005	−	25.0049i	0.223459	−	0.833961i
$900$	14.1789	+	7.41081i	0.472630	+	0.247027i
$901$	−6.02546	−	3.47880i	−0.200737	−	0.115896i
$902$	−5.19941	−	5.19941i	−0.173121	−	0.173121i
$903$	−10.5285	−	17.3828i	−0.350367	−	0.578462i
$904$	13.2673	−	3.55495i	0.441262	−	0.118236i
$905$	55.4417	−	55.4417i	1.84294	−	1.84294i
$906$	25.2203	+	6.19343i	0.837890	+	0.205763i
$907$	−20.3038	+	11.7224i	−0.674178	+	0.389237i	−0.797658	−	0.603110i	$-0.793928\pi$
$907$	−20.3038	+	11.7224i	−0.674178	+	0.389237i	0.123480	+	0.992347i	$0.460595\pi$
$908$	−9.86449	−	2.64318i	−0.327365	−	0.0877171i
$909$	0.663013	−	0.420850i	0.0219907	−	0.0139587i
$910$	−11.2312	−	2.86165i	−0.372309	−	0.0948629i
$911$		−	26.8792i		−	0.890549i	−0.895394	−	0.445274i	$-0.853106\pi$
$911$		−	26.8792i		−	0.890549i	0.895394	−	0.445274i	$-0.146894\pi$
$912$	9.38589	−	0.197057i	0.310798	−	0.00652522i
$913$	14.9431	+	25.8823i	0.494546	+	0.856578i
$914$	10.7184	−	18.5648i	0.354532	−	0.614068i
$915$	−1.62763	−	0.894694i	−0.0538077	−	0.0295777i
$916$	6.11992	+	22.8399i	0.202208	+	0.754650i
$917$	0.118740	+	0.443142i	0.00392112	+	0.0146338i
$918$	4.18367	−	0.263819i	0.138082	−	0.00870732i
$919$	−10.0878	+	17.4725i	−0.332764	+	0.576365i	−0.983053	−	0.183323i	$-0.941315\pi$
$919$	−10.0878	+	17.4725i	−0.332764	+	0.576365i	0.650288	+	0.759687i	$0.274648\pi$
$920$	1.34047	+	2.32176i	0.0441940	+	0.0765462i
$921$	1.22756	+	58.4693i	0.0404496	+	1.92663i
$922$		−	9.35523i		−	0.308098i
$923$	33.0787	+	32.2741i	1.08880	+	1.06231i
$924$	−0.954774	−	3.28577i	−0.0314098	−	0.108094i
$925$	−32.7617	−	8.77846i	−1.07720	−	0.288634i
$926$	−2.49277	+	1.43920i	−0.0819175	+	0.0472951i
$927$	−8.69950	+	0.365454i	−0.285729	+	0.0120031i
$928$	4.41511	−	4.41511i	0.144933	−	0.144933i
$929$	13.8049	−	3.69900i	0.452923	−	0.121360i	−0.0251438	−	0.999684i	$-0.508004\pi$
$929$	13.8049	−	3.69900i	0.452923	−	0.121360i	0.478067	+	0.878323i	$0.341338\pi$
$930$	−19.7440	+	11.9587i	−0.647432	+	0.392141i
$931$	3.83262	+	3.83262i	0.125609	+	0.125609i
$932$	−2.06808	−	1.19401i	−0.0677422	−	0.0391110i
$933$	−43.8777	−	42.0731i	−1.43649	−	1.37741i
$934$	−4.91544	+	18.3447i	−0.160838	+	0.600256i
$935$	−5.12303			−0.167541
$936$	2.22842	−	10.5846i	0.0728382	−	0.345969i
$937$	−0.682171			−0.0222856			−0.0111428	−	0.999938i	$-0.503547\pi$
$937$	−0.682171			−0.0222856			−0.0111428	+	0.999938i	$0.503547\pi$
$938$	1.50235	−	5.60684i	0.0490534	−	0.183070i
$939$	−11.3525	−	10.8856i	−0.370475	−	0.355238i
$940$	−15.4749	−	8.93445i	−0.504737	−	0.291410i
$941$	−2.86903	−	2.86903i	−0.0935276	−	0.0935276i	0.658795	−	0.752323i	$-0.271066\pi$
$941$	−2.86903	−	2.86903i	−0.0935276	−	0.0935276i	−0.752323	+	0.658795i	$0.771066\pi$
$942$	−23.1332	+	14.0115i	−0.753720	+	0.456519i
$943$	−2.99854	+	0.803457i	−0.0976460	+	0.0261642i
$944$	1.04368	−	1.04368i	0.0339688	−	0.0339688i
$945$	−15.8298	+	5.32985i	−0.514943	+	0.173380i
$946$	−20.0737	+	11.5896i	−0.652653	+	0.376810i
$947$	−3.50952	−	0.940372i	−0.114044	−	0.0305580i	0.201346	−	0.979520i	$-0.435469\pi$
$947$	−3.50952	−	0.940372i	−0.114044	−	0.0305580i	−0.315390	+	0.948962i	$0.602135\pi$
$948$	−0.494303	−	1.70110i	−0.0160542	−	0.0552490i
$949$	−2.58045	+	10.1275i	−0.0837651	+	0.328753i
$950$			28.9052i			0.937809i
$951$	0.906063	+	43.1561i	0.0293811	+	1.39943i
$952$	0.403373	+	0.698663i	0.0130734	+	0.0226438i
$953$	−7.14367	+	12.3732i	−0.231406	+	0.400807i	−0.958222	−	0.286025i	$-0.907666\pi$
$953$	−7.14367	+	12.3732i	−0.231406	+	0.400807i	0.726816	+	0.686832i	$0.240999\pi$
$954$	−5.64156	+	25.2503i	−0.182652	+	0.817507i
$955$	−19.6702	−	73.4101i	−0.636512	−	2.37550i
$956$	−6.60745	−	24.6594i	−0.213700	−	0.797541i
$957$	−18.7225	−	10.2916i	−0.605211	−	0.332680i
$958$	−9.62190	+	16.6656i	−0.310869	+	0.538442i
$959$	10.4783	+	18.1490i	0.338363	+	0.586062i
$960$	−5.56643	+	0.116867i	−0.179656	+	0.00377188i
$961$			13.8110i			0.445517i
$962$	0.282322	+	22.9295i	0.00910242	+	0.739278i
$963$	−17.9831	−	28.3308i	−0.579498	−	0.912949i
$964$	−0.553255	−	0.148244i	−0.0178191	−	0.00477462i
$965$	5.05012	−	2.91569i	0.162569	−	0.0938593i
$966$	−1.40288	−	0.344509i	−0.0451369	−	0.0110844i
$967$	−2.75883	+	2.75883i	−0.0887179	+	0.0887179i	−0.750073	−	0.661355i	$-0.769982\pi$
$967$	−2.75883	+	2.75883i	−0.0887179	+	0.0887179i	0.661355	+	0.750073i	$0.269982\pi$
$968$	6.85554	−	1.83694i	0.220346	−	0.0590414i
$969$	3.92369	+	6.47809i	0.126047	+	0.208106i
$970$	31.7843	+	31.7843i	1.02053	+	1.02053i
$971$	37.9420	+	21.9058i	1.21762	+	0.702992i	0.964408	−	0.264419i	$-0.0851803\pi$
$971$	37.9420	+	21.9058i	1.21762	+	0.702992i	0.253210	+	0.967411i	$0.418514\pi$
$972$	−5.58990	−	14.5517i	−0.179296	−	0.466747i
$973$	−4.89544	+	18.2700i	−0.156941	+	0.585710i
$974$	−26.8131			−0.859149
$975$	32.4385	+	7.54379i	1.03886	+	0.241595i
$976$	0.333592			0.0106780
$977$	2.29792	−	8.57596i	0.0735170	−	0.274369i	−0.919376	−	0.393380i	$-0.871306\pi$
$977$	2.29792	−	8.57596i	0.0735170	−	0.274369i	0.992893	+	0.119011i	$0.0379723\pi$
$978$	−10.6646	+	11.1220i	−0.341017	+	0.355643i
$979$	4.16195	+	2.40291i	0.133017	+	0.0767972i
$980$	−2.27299	−	2.27299i	−0.0726079	−	0.0726079i
$981$	−30.1192	−	27.6907i	−0.961632	−	0.884096i
$982$	14.3127	−	3.83506i	0.456735	−	0.122382i
$983$	34.3047	−	34.3047i	1.09415	−	1.09415i	0.0990706	−	0.995080i	$-0.468413\pi$
$983$	34.3047	−	34.3047i	1.09415	−	1.09415i	0.995080	−	0.0990706i	$-0.0315870\pi$
$984$	1.53750	−	6.26089i	0.0490138	−	0.199590i
$985$	51.9720	−	30.0060i	1.65596	−	0.956072i
$986$	4.86561	+	1.30374i	0.154953	+	0.0415194i
$987$	9.24581	−	2.68664i	0.294297	−	0.0855166i
$988$	18.8130	−	5.29002i	0.598521	−	0.168298i
$989$			9.78577i			0.311169i
$990$	5.69868	+	18.1784i	0.181116	+	0.577747i
$991$	−6.25293	−	10.8304i	−0.198631	−	0.344039i	0.749454	−	0.662057i	$-0.230316\pi$
$991$	−6.25293	−	10.8304i	−0.198631	−	0.344039i	−0.948085	+	0.318018i	$0.896983\pi$
$992$	2.07298	−	3.59051i	0.0658172	−	0.113999i
$993$	−20.1651	+	36.6843i	−0.639920	+	1.16414i
$994$	3.31747	+	12.3810i	0.105224	+	0.392700i
$995$	0.635635	+	2.37222i	0.0201510	+	0.0752045i
$996$	−12.6224	+	22.9626i	−0.399956	+	0.727599i
$997$	1.43810	−	2.49086i	0.0455451	−	0.0788865i	−0.842354	−	0.538924i	$-0.818831\pi$
$997$	1.43810	−	2.49086i	0.0455451	−	0.0788865i	0.887899	+	0.460038i	$0.152164\pi$
$998$	−1.54292	−	2.67242i	−0.0488403	−	0.0845938i
$999$	18.2922	+	27.5233i	0.578738	+	0.870799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.a.197.10	✓	56
3.2	odd	2		546.2.bu.b.197.4	yes	56
13.7	odd	12		546.2.bu.b.449.4	yes	56
39.20	even	12	inner	546.2.bu.a.449.10	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.197.10	✓	56	1.1	even	1	trivial
546.2.bu.a.449.10	yes	56	39.20	even	12	inner
546.2.bu.b.197.4	yes	56	3.2	odd	2
546.2.bu.b.449.4	yes	56	13.7	odd	12

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

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.25018 - 1.19877i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.27299 + 2.27299i) q^{5} +(-1.48149 + 0.897320i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.125915 + 2.99736i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.25018 - 1.19877i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.27299 + 2.27299i) q^{5} +(-1.48149 + 0.897320i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.125915 + 2.99736i) q^{9} +(2.78383 - 1.60724i) q^{10} +(1.90819 + 0.511298i) q^{11} +(0.483307 + 1.66325i) q^{12} +(1.84108 + 3.10007i) q^{13} +1.00000i q^{14} +(-0.116867 - 5.56643i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.403373 + 0.698663i) q^{17} +(2.92781 + 0.654149i) q^{18} +(1.40284 + 5.23546i) q^{19} +(-0.831970 - 3.10496i) q^{20} +(1.51785 + 0.834349i) q^{21} +(0.987752 - 1.71084i) q^{22} +(-0.417009 - 0.722281i) q^{23} +(1.73167 - 0.0363565i) q^{24} +5.33293i q^{25} +(3.47094 - 0.975992i) q^{26} +(3.43572 - 3.89819i) q^{27} +(0.965926 + 0.258819i) q^{28} +(5.40739 - 3.12196i) q^{29} +(-5.40700 - 1.32781i) q^{30} +(2.93164 - 2.93164i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-1.77266 - 2.92669i) q^{33} +(0.570456 + 0.570456i) q^{34} +(-2.78383 - 1.60724i) q^{35} +(1.38963 - 2.65874i) q^{36} +(-1.64609 + 6.14328i) q^{37} +5.42014 q^{38} +(1.41457 - 6.08268i) q^{39} -3.21449 q^{40} +(0.963357 - 3.59530i) q^{41} +(1.19877 - 1.25018i) q^{42} +(-10.1613 - 5.86664i) q^{43} +(-1.39689 - 1.39689i) q^{44} +(-6.52675 + 7.09915i) q^{45} +(-0.805599 + 0.215860i) q^{46} +(3.93071 - 3.93071i) q^{47} +(0.413071 - 1.68207i) q^{48} +(0.866025 - 0.500000i) q^{49} +(5.15121 + 1.38026i) q^{50} +(1.34182 - 0.389906i) q^{51} +(-0.0443903 - 3.60528i) q^{52} +8.62427i q^{53} +(-2.87613 - 4.32757i) q^{54} +(3.17512 + 5.49946i) q^{55} +(0.500000 - 0.866025i) q^{56} +(4.52229 - 8.22695i) q^{57} +(-1.61604 - 6.03115i) q^{58} +(-0.382012 - 1.42569i) q^{59} +(-2.68200 + 4.87910i) q^{60} +(0.166796 - 0.288899i) q^{61} +(-2.07298 - 3.59051i) q^{62} +(-0.897397 - 2.86263i) q^{63} -1.00000i q^{64} +(-2.86165 + 11.2312i) q^{65} +(-3.28577 + 0.954774i) q^{66} +(-5.60684 - 1.50235i) q^{67} +(0.698663 - 0.403373i) q^{68} +(-0.344509 + 1.40288i) q^{69} +(-2.27299 + 2.27299i) q^{70} +(12.3810 - 3.31747i) q^{71} +(-2.20849 - 2.03042i) q^{72} +(2.04963 + 2.04963i) q^{73} +(5.50791 + 3.18000i) q^{74} +(6.39294 - 6.66713i) q^{75} +(1.40284 - 5.23546i) q^{76} -1.97550 q^{77} +(-5.50930 - 2.94068i) q^{78} -1.02275 q^{79} +(-0.831970 + 3.10496i) q^{80} +(-8.96829 + 0.754823i) q^{81} +(-3.22346 - 1.86106i) q^{82} +(10.6974 + 10.6974i) q^{83} +(-0.897320 - 1.48149i) q^{84} +(-2.50491 + 0.671189i) q^{85} +(-8.29668 + 8.29668i) q^{86} +(-10.5027 - 2.57918i) q^{87} +(-1.71084 + 0.987752i) q^{88} +(2.34981 + 0.629629i) q^{89} +(5.16801 + 8.14175i) q^{90} +(-2.58071 - 2.51793i) q^{91} +0.834018i q^{92} +(-7.17943 + 0.150732i) q^{93} +(-2.77943 - 4.81412i) q^{94} +(-8.71149 + 15.0887i) q^{95} +(-1.51785 - 0.834349i) q^{96} +(3.61919 + 13.5070i) q^{97} +(-0.258819 - 0.965926i) q^{98} +(-1.29227 + 5.78391i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) \) 56 * q - 8 * q^6 + 24 * q^9	\( 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) \) 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Introduction

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