LMFDB - Embedded newform 546.2.bv.a.473.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.317");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bv (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			473.18
Character	$\chi$	$=$	546.473
Dual form			546.2.bv.a.359.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(1.72288 + 0.178019i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.250746 - 0.935798i) q^{5} +(-0.617867 + 1.61810i) q^{6} +(0.932449 + 2.47599i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.93662 + 0.613411i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(1.72288 + 0.178019i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.250746 - 0.935798i) q^{5} +(-0.617867 + 1.61810i) q^{6} +(0.932449 + 2.47599i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.93662 + 0.613411i) q^{9} +(0.839013 + 0.484404i) q^{10} +(-0.265234 - 0.989868i) q^{11} +(-1.40305 - 1.01561i) q^{12} +(1.28292 + 3.36959i) q^{13} +(-2.63296 + 0.259843i) q^{14} +(0.598595 - 1.56763i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.05787 - 3.56434i) q^{17} +(-1.35256 + 2.67779i) q^{18} +(-2.67167 - 0.715871i) q^{19} +(-0.685051 + 0.685051i) q^{20} +(1.16572 + 4.43183i) q^{21} +1.02479 q^{22} +(-0.318592 - 0.551817i) q^{23} +(1.34414 - 1.09238i) q^{24} +(3.51728 + 2.03070i) q^{25} +(-3.58682 + 0.367090i) q^{26} +(4.95024 + 1.57961i) q^{27} +(0.430471 - 2.61050i) q^{28} +3.48270i q^{29} +(1.35928 + 0.983930i) q^{30} +(0.646325 + 2.41212i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-0.280751 - 1.75264i) q^{33} +(2.91027 + 2.91027i) q^{34} +(2.55084 - 0.251738i) q^{35} +(-2.23648 - 1.99954i) q^{36} +(-0.748834 + 2.79469i) q^{37} +(1.38296 - 2.39535i) q^{38} +(1.61046 + 6.03377i) q^{39} +(-0.484404 - 0.839013i) q^{40} +(-0.0484181 - 0.0484181i) q^{41} +(-4.58253 - 0.0210399i) q^{42} -8.67865i q^{43} +(-0.265234 + 0.989868i) q^{44} +(1.31037 - 2.59427i) q^{45} +(0.615472 - 0.164915i) q^{46} +(3.23906 + 0.867903i) q^{47} +(0.707270 + 1.58107i) q^{48} +(-5.26108 + 4.61748i) q^{49} +(-2.87185 + 2.87185i) q^{50} +(4.17998 - 5.77458i) q^{51} +(0.573754 - 3.55961i) q^{52} +(-6.87259 - 3.96789i) q^{53} +(-2.80700 + 4.37273i) q^{54} -0.992823 q^{55} +(2.41013 + 1.09145i) q^{56} +(-4.47551 - 1.70897i) q^{57} +(-3.36403 - 0.901389i) q^{58} +(-1.50208 - 5.60584i) q^{59} +(-1.30221 + 1.05831i) q^{60} +(0.594016 + 1.02887i) q^{61} -2.49721 q^{62} +(1.21945 + 7.84302i) q^{63} -1.00000i q^{64} +(3.47494 - 0.355640i) q^{65} +(1.76558 + 0.182432i) q^{66} +(-0.436237 - 1.62806i) q^{67} +(-3.56434 + 2.05787i) q^{68} +(-0.450660 - 1.00743i) q^{69} +(-0.417044 + 2.52907i) q^{70} +(-8.55610 - 8.55610i) q^{71} +(2.51025 - 1.64276i) q^{72} +(-12.7721 + 3.42226i) q^{73} +(-2.50565 - 1.44664i) q^{74} +(5.69835 + 4.12480i) q^{75} +(1.95579 + 1.95579i) q^{76} +(2.20359 - 1.57972i) q^{77} +(-6.24500 - 0.00607038i) q^{78} +(-0.0157356 - 0.0272549i) q^{79} +(0.935798 - 0.250746i) q^{80} +(8.24745 + 3.60271i) q^{81} +(0.0592998 - 0.0342367i) q^{82} +(-6.06316 - 6.06316i) q^{83} +(1.20637 - 4.42094i) q^{84} +(-2.81950 - 2.81950i) q^{85} +(8.38293 + 2.24620i) q^{86} +(-0.619988 + 6.00027i) q^{87} +(-0.887491 - 0.512393i) q^{88} +(6.23472 + 1.67059i) q^{89} +(2.16672 + 1.93717i) q^{90} +(-7.14682 + 6.31847i) q^{91} +0.637183i q^{92} +(0.684135 + 4.27084i) q^{93} +(-1.67666 + 2.90406i) q^{94} +(-1.33982 + 2.32064i) q^{95} +(-1.71025 + 0.273960i) q^{96} +(-8.64212 + 8.64212i) q^{97} +(-3.09847 - 6.27690i) q^{98} +(-0.171696 - 3.06956i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 16 q^{7}+O(q^{10}) $ 144 * q - 16 * q^7	$ 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) $ 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	1.72288	+	0.178019i	0.994704	+	0.102779i
$3$	1.72288	+	0.178019i	0.994704	+	0.102779i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.250746	−	0.935798i	0.112137	−	0.418501i	−0.886920	−	0.461924i	$-0.847159\pi$
$5$	0.250746	−	0.935798i	0.112137	−	0.418501i	0.999057	+	0.0434222i	$0.0138261\pi$
$6$	−0.617867	+	1.61810i	−0.252243	+	0.660586i
$7$	0.932449	+	2.47599i	0.352433	+	0.935837i
$7$	0.932449	+	2.47599i	0.352433	+	0.935837i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.93662	+	0.613411i	0.978873	+	0.204470i
$10$	0.839013	+	0.484404i	0.265319	+	0.153182i
$11$	−0.265234	−	0.989868i	−0.0799712	−	0.298456i	0.914343	−	0.404940i	$-0.132708\pi$
$11$	−0.265234	−	0.989868i	−0.0799712	−	0.298456i	−0.994314	+	0.106483i	$0.966041\pi$
$12$	−1.40305	−	1.01561i	−0.405025	−	0.293181i
$13$	1.28292	+	3.36959i	0.355817	+	0.934555i
$13$	1.28292	+	3.36959i	0.355817	+	0.934555i
$14$	−2.63296	+	0.259843i	−0.703688	+	0.0694460i
$15$	0.598595	−	1.56763i	0.154557	−	0.404760i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.05787	−	3.56434i	0.499107	−	0.864479i	−0.500892	−	0.865510i	$-0.666995\pi$
$17$	2.05787	−	3.56434i	0.499107	−	0.864479i	0.999999	+	0.00103068i	$0.000328075\pi$
$18$	−1.35256	+	2.67779i	−0.318802	+	0.631162i
$19$	−2.67167	−	0.715871i	−0.612922	−	0.164232i	−0.0610140	−	0.998137i	$-0.519433\pi$
$19$	−2.67167	−	0.715871i	−0.612922	−	0.164232i	−0.551908	+	0.833905i	$0.686100\pi$
$20$	−0.685051	+	0.685051i	−0.153182	+	0.153182i
$21$	1.16572	+	4.43183i	0.254381	+	0.967104i
$22$	1.02479			0.218485
$23$	−0.318592	−	0.551817i	−0.0664309	−	0.115062i	0.830897	−	0.556426i	$-0.187828\pi$
$23$	−0.318592	−	0.551817i	−0.0664309	−	0.115062i	−0.897328	+	0.441365i	$0.854495\pi$
$24$	1.34414	−	1.09238i	0.274371	−	0.222981i
$25$	3.51728	+	2.03070i	0.703457	+	0.406141i
$26$	−3.58682	+	0.367090i	−0.703432	+	0.0719923i
$27$	4.95024	+	1.57961i	0.952673	+	0.303996i
$28$	0.430471	−	2.61050i	0.0813514	−	0.493338i
$29$			3.48270i			0.646721i	0.946276	+	0.323361i	$0.104813\pi$
$29$			3.48270i			0.646721i	−0.946276	+	0.323361i	$0.895187\pi$
$30$	1.35928	+	0.983930i	0.248170	+	0.179640i
$31$	0.646325	+	2.41212i	0.116083	+	0.433229i	0.999366	−	0.0356126i	$-0.0113382\pi$
$31$	0.646325	+	2.41212i	0.116083	+	0.433229i	−0.883282	+	0.468841i	$0.844672\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−0.280751	−	1.75264i	−0.0488724	−	0.305095i
$34$	2.91027	+	2.91027i	0.499107	+	0.499107i
$35$	2.55084	−	0.251738i	0.431170	−	0.0425515i
$36$	−2.23648	−	1.99954i	−0.372747	−	0.333256i
$37$	−0.748834	+	2.79469i	−0.123107	+	0.459443i	−0.999765	−	0.0216713i	$-0.993101\pi$
$37$	−0.748834	+	2.79469i	−0.123107	+	0.459443i	0.876658	+	0.481115i	$0.159768\pi$
$38$	1.38296	−	2.39535i	0.224345	−	0.388577i
$39$	1.61046	+	6.03377i	0.257880	+	0.966177i
$40$	−0.484404	−	0.839013i	−0.0765911	−	0.132660i
$41$	−0.0484181	−	0.0484181i	−0.00756163	−	0.00756163i	0.703316	−	0.710877i	$-0.251702\pi$
$41$	−0.0484181	−	0.0484181i	−0.00756163	−	0.00756163i	−0.710877	+	0.703316i	$0.751702\pi$
$42$	−4.58253	−	0.0210399i	−0.707099	−	0.00324653i
$43$		−	8.67865i		−	1.32348i	−0.749733	−	0.661741i	$-0.769818\pi$
$43$		−	8.67865i		−	1.32348i	0.749733	−	0.661741i	$-0.230182\pi$
$44$	−0.265234	+	0.989868i	−0.0399856	+	0.149228i
$45$	1.31037	−	2.59427i	0.195339	−	0.386731i
$46$	0.615472	−	0.164915i	0.0907463	−	0.0243154i
$47$	3.23906	+	0.867903i	0.472465	+	0.126597i	0.487192	−	0.873295i	$-0.338021\pi$
$47$	3.23906	+	0.867903i	0.472465	+	0.126597i	−0.0147269	+	0.999892i	$0.504688\pi$
$48$	0.707270	+	1.58107i	0.102086	+	0.228207i
$49$	−5.26108	+	4.61748i	−0.751582	+	0.659639i
$50$	−2.87185	+	2.87185i	−0.406141	+	0.406141i
$51$	4.17998	−	5.77458i	0.585315	−	0.808603i
$52$	0.573754	−	3.55961i	0.0795654	−	0.493629i
$53$	−6.87259	−	3.96789i	−0.944023	−	0.545032i	−0.0528037	−	0.998605i	$-0.516816\pi$
$53$	−6.87259	−	3.96789i	−0.944023	−	0.545032i	−0.891219	+	0.453573i	$0.850149\pi$
$54$	−2.80700	+	4.37273i	−0.381984	+	0.595053i
$55$	−0.992823			−0.133872
$56$	2.41013	+	1.09145i	0.322067	+	0.145851i
$57$	−4.47551	−	1.70897i	−0.592796	−	0.226358i
$58$	−3.36403	−	0.901389i	−0.441719	−	0.118358i
$59$	−1.50208	−	5.60584i	−0.195554	−	0.729818i	−0.992123	−	0.125270i	$-0.960020\pi$
$59$	−1.50208	−	5.60584i	−0.195554	−	0.729818i	0.796568	−	0.604548i	$-0.206646\pi$
$60$	−1.30221	+	1.05831i	−0.168115	+	0.136627i
$61$	0.594016	+	1.02887i	0.0760560	+	0.131733i	0.901545	−	0.432685i	$-0.142434\pi$
$61$	0.594016	+	1.02887i	0.0760560	+	0.131733i	−0.825489	+	0.564418i	$0.809101\pi$
$62$	−2.49721			−0.317146
$63$	1.21945	+	7.84302i	0.153636	+	0.988128i
$64$		−	1.00000i		−	0.125000i
$65$	3.47494	−	0.355640i	0.431013	−	0.0441118i
$66$	1.76558	+	0.182432i	0.217328	+	0.0224558i
$67$	−0.436237	−	1.62806i	−0.0532948	−	0.198899i	0.934145	−	0.356893i	$-0.116164\pi$
$67$	−0.436237	−	1.62806i	−0.0532948	−	0.198899i	−0.987440	+	0.157994i	$0.949497\pi$
$68$	−3.56434	+	2.05787i	−0.432239	+	0.249554i
$69$	−0.450660	−	1.00743i	−0.0542531	−	0.121280i
$70$	−0.417044	+	2.52907i	−0.0498463	+	0.302282i
$71$	−8.55610	−	8.55610i	−1.01542	−	1.01542i	−0.999879	−	0.0155429i	$-0.995052\pi$
$71$	−8.55610	−	8.55610i	−1.01542	−	1.01542i	−0.0155429	−	0.999879i	$-0.504948\pi$
$72$	2.51025	−	1.64276i	0.295836	−	0.193601i
$73$	−12.7721	+	3.42226i	−1.49486	+	0.400545i	−0.911373	−	0.411581i	$-0.864977\pi$
$73$	−12.7721	+	3.42226i	−1.49486	+	0.400545i	−0.583482	+	0.812126i	$0.698310\pi$
$74$	−2.50565	−	1.44664i	−0.291275	−	0.168168i
$75$	5.69835	+	4.12480i	0.657988	+	0.476291i
$76$	1.95579	+	1.95579i	0.224345	+	0.224345i
$77$	2.20359	−	1.57972i	0.251122	−	0.180026i
$78$	−6.24500	−	0.00607038i	−0.707106	−	0.000687335i
$79$	−0.0157356	−	0.0272549i	−0.00177039	−	0.00306641i	0.865139	−	0.501532i	$-0.167230\pi$
$79$	−0.0157356	−	0.0272549i	−0.00177039	−	0.00306641i	−0.866909	+	0.498466i	$0.833897\pi$
$80$	0.935798	−	0.250746i	0.104625	−	0.0280343i
$81$	8.24745	+	3.60271i	0.916384	+	0.400301i
$82$	0.0592998	−	0.0342367i	0.00654856	−	0.00378082i
$83$	−6.06316	−	6.06316i	−0.665518	−	0.665518i	0.291157	−	0.956675i	$-0.405960\pi$
$83$	−6.06316	−	6.06316i	−0.665518	−	0.665518i	−0.956675	+	0.291157i	$0.905960\pi$
$84$	1.20637	−	4.42094i	0.131626	−	0.482364i
$85$	−2.81950	−	2.81950i	−0.305817	−	0.305817i
$86$	8.38293	+	2.24620i	0.903955	+	0.242214i
$87$	−0.619988	+	6.00027i	−0.0664697	+	0.643296i
$88$	−0.887491	−	0.512393i	−0.0946069	−	0.0546213i
$89$	6.23472	+	1.67059i	0.660879	+	0.177082i	0.573643	−	0.819106i	$-0.305530\pi$
$89$	6.23472	+	1.67059i	0.660879	+	0.177082i	0.0872363	+	0.996188i	$0.472196\pi$
$90$	2.16672	+	1.93717i	0.228393	+	0.204196i
$91$	−7.14682	+	6.31847i	−0.749190	+	0.662355i
$92$			0.637183i			0.0664309i
$93$	0.684135	+	4.27084i	0.0709415	+	0.442866i
$94$	−1.67666	+	2.90406i	−0.172934	+	0.299531i
$95$	−1.33982	+	2.32064i	−0.137463	+	0.238092i
$96$	−1.71025	+	0.273960i	−0.174551	+	0.0279610i
$97$	−8.64212	+	8.64212i	−0.877475	+	0.877475i	−0.993273	−	0.115798i	$-0.963057\pi$
$97$	−8.64212	+	8.64212i	−0.877475	+	0.877475i	0.115798	+	0.993273i	$0.463057\pi$
$98$	−3.09847	−	6.27690i	−0.312993	−	0.634063i
$99$	−0.171696	−	3.06956i	−0.0172561	−	0.308503i
$100$	−2.03070	−	3.51728i	−0.203070	−	0.351728i
$101$	5.68164	−	9.84089i	0.565344	−	0.979205i	−0.431673	−	0.902030i	$-0.642077\pi$
$101$	5.68164	−	9.84089i	0.565344	−	0.979205i	0.997018	−	0.0771748i	$-0.0245900\pi$
$102$	4.49596	+	5.53212i	0.445166	+	0.547762i
$103$	12.5991	−	7.27409i	1.24143	−	0.716738i	0.272042	−	0.962285i	$-0.412301\pi$
$103$	12.5991	−	7.27409i	1.24143	−	0.716738i	0.969385	+	0.245548i	$0.0789678\pi$
$104$	3.28982	+	1.47550i	0.322593	+	0.144685i
$105$	4.43959	+	0.0203837i	0.433260	+	0.00198924i
$106$	5.61145	−	5.61145i	0.545032	−	0.545032i
$107$	−7.41867	+	4.28317i	−0.717189	+	0.414070i	−0.813717	−	0.581261i	$-0.802560\pi$
$107$	−7.41867	+	4.28317i	−0.717189	+	0.414070i	0.0965279	+	0.995330i	$0.469226\pi$
$108$	−3.49723	−	3.84310i	−0.336521	−	0.369802i
$109$	−0.251389	−	0.938198i	−0.0240787	−	0.0898631i	0.952841	−	0.303470i	$-0.0981454\pi$
$109$	−0.251389	−	0.938198i	−0.0240787	−	0.0898631i	−0.976920	+	0.213607i	$0.931479\pi$
$110$	0.256961	−	0.958993i	0.0245003	−	0.0914364i
$111$	−1.78766	+	4.68160i	−0.169677	+	0.444357i
$112$	−1.67805	+	2.04552i	−0.158561	+	0.193284i
$113$		−	8.13853i		−	0.765608i	−0.923829	−	0.382804i	$-0.874958\pi$
$113$		−	8.13853i		−	0.765608i	0.923829	−	0.382804i	$-0.125042\pi$
$114$	2.80908	−	3.88070i	0.263095	−	0.363461i
$115$	−0.596274	+	0.159771i	−0.0556029	+	0.0148987i
$116$	1.74135	−	3.01611i	0.161680	−	0.280039i
$117$	1.70050	+	10.6821i	0.157211	+	0.987565i
$118$	5.80359			0.534264
$119$	10.7441	+	1.77171i	0.984913	+	0.162412i
$120$	−0.685209	−	1.53175i	−0.0625508	−	0.139829i
$121$	8.61679	−	4.97491i	0.783345	−	0.452264i
$122$	−1.14755	+	0.307485i	−0.103894	+	0.0278384i
$123$	−0.0747991	−	0.0920378i	−0.00674440	−	0.00829877i
$124$	0.646325	−	2.41212i	0.0580417	−	0.216614i
$125$	6.20753	−	6.20753i	0.555218	−	0.555218i
$126$	−7.89139	−	0.852027i	−0.703021	−	0.0759046i
$127$		−	20.2101i		−	1.79335i	−0.442687	−	0.896676i	$-0.645975\pi$
$127$		−	20.2101i		−	1.79335i	0.442687	−	0.896676i	$-0.354025\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	1.54497	−	14.9523i	0.136027	−	1.31647i
$130$	−0.555858	+	3.44858i	−0.0487520	+	0.302460i
$131$	−3.53443	+	2.04060i	−0.308805	+	0.178288i	−0.646391	−	0.763006i	$-0.723723\pi$
$131$	−3.53443	+	2.04060i	−0.308805	+	0.178288i	0.337587	+	0.941294i	$0.390389\pi$
$132$	−0.633182	+	1.65820i	−0.0551114	+	0.144328i
$133$	−0.718703	−	7.28254i	−0.0623194	−	0.631476i
$134$	1.68549			0.145604
$135$	2.71945	−	4.23634i	0.234053	−	0.364606i
$136$	−1.06523	−	3.97550i	−0.0913429	−	0.340897i
$137$	−4.66924	−	17.4258i	−0.398920	−	1.48879i	−0.814999	−	0.579462i	$-0.803263\pi$
$137$	−4.66924	−	17.4258i	−0.398920	−	1.48879i	0.416079	−	0.909328i	$-0.363404\pi$
$138$	1.08974	−	0.174563i	0.0927649	−	0.0148598i
$139$	−19.1544			−1.62465			−0.812326	−	0.583204i	$-0.801799\pi$
$139$	−19.1544			−1.62465			−0.812326	+	0.583204i	$0.801799\pi$
$140$	−2.33496	−	1.05741i	−0.197340	−	0.0893671i
$141$	5.42600	+	2.07190i	0.456951	+	0.174486i
$142$	10.4790	−	6.05008i	0.879381	−	0.507711i
$143$	2.99517	−	2.16365i	0.250469	−	0.180933i
$144$	0.937080	+	2.84989i	0.0780900	+	0.237491i
$145$	3.25910	+	0.873274i	0.270654	+	0.0725215i
$146$		−	13.2226i		−	1.09431i
$147$	−9.88619	+	7.01877i	−0.815399	+	0.578899i
$148$	2.04585	−	2.04585i	0.168168	−	0.168168i
$149$	−5.29060	+	19.7448i	−0.433423	+	1.61756i	0.311389	+	0.950282i	$0.399206\pi$
$149$	−5.29060	+	19.7448i	−0.433423	+	1.61756i	−0.744812	+	0.667274i	$0.767461\pi$
$150$	−5.45909	+	4.43660i	−0.445733	+	0.362247i
$151$	−0.159445	+	0.0427232i	−0.0129755	+	0.00347676i	−0.265301	−	0.964166i	$-0.585471\pi$
$151$	−0.159445	+	0.0427232i	−0.0129755	+	0.00347676i	0.252325	+	0.967642i	$0.418805\pi$
$152$	−2.39535	+	1.38296i	−0.194289	+	0.112173i
$153$	8.22959	−	9.20478i	0.665323	−	0.744162i
$154$	0.955562	+	2.53736i	0.0770014	+	0.204467i
$155$	2.41932			0.194324
$156$	1.62219	−	6.03063i	0.129879	−	0.482837i
$157$	2.07855	−	3.60015i	0.165886	−	0.287323i	−0.771083	−	0.636734i	$-0.780285\pi$
$157$	2.07855	−	3.60015i	0.165886	−	0.287323i	0.936970	+	0.349411i	$0.113618\pi$
$158$	0.0303989	−	0.00814535i	0.00241840	−	0.000648009i
$159$	−11.1343	−	8.05965i	−0.883005	−	0.639172i
$160$			0.968809i			0.0765911i
$161$	1.06922	−	1.30337i	0.0842666	−	0.102720i
$162$	−5.61455	+	7.03398i	−0.441120	+	0.552642i
$163$	2.64096	−	9.85619i	0.206856	−	0.771997i	−0.782020	−	0.623253i	$-0.785811\pi$
$163$	2.64096	−	9.85619i	0.206856	−	0.771997i	0.988876	−	0.148743i	$-0.0475228\pi$
$164$	0.0177222	+	0.0661403i	0.00138387	+	0.00516469i
$165$	−1.71051	−	0.176742i	−0.133163	−	0.0137593i
$166$	7.42583	−	4.28730i	0.576356	−	0.332759i
$167$	−18.0695	+	18.0695i	−1.39826	+	1.39826i	−0.593220	+	0.805040i	$0.702144\pi$
$167$	−18.0695	+	18.0695i	−1.39826	+	1.39826i	−0.805040	+	0.593220i	$0.797856\pi$
$168$	3.95807	+	2.30948i	0.305371	+	0.178181i
$169$	−9.70824	+	8.64581i	−0.746788	+	0.665062i
$170$	3.45316	−	1.99368i	0.264845	−	0.152909i
$171$	−7.40654	−	3.74107i	−0.566392	−	0.286087i
$172$	−4.33933	+	7.51593i	−0.330870	+	0.573084i
$173$	2.51736	+	4.36020i	0.191392	+	0.331500i	0.945712	−	0.325007i	$-0.105367\pi$
$173$	2.51736	+	4.36020i	0.191392	+	0.331500i	−0.754320	+	0.656507i	$0.772033\pi$
$174$	−5.63535	−	2.15185i	−0.427215	−	0.163131i
$175$	−1.74832	+	10.6023i	−0.132161	+	0.801458i
$176$	0.724634	−	0.724634i	0.0546213	−	0.0546213i
$177$	−1.58995	−	9.92558i	−0.119508	−	0.746052i
$178$	−3.22733	+	5.58990i	−0.241898	+	0.418980i
$179$	−1.24867	+	2.16277i	−0.0933302	+	0.161653i	−0.908910	−	0.416991i	$-0.863085\pi$
$179$	−1.24867	+	2.16277i	−0.0933302	+	0.161653i	0.815580	+	0.578644i	$0.196418\pi$
$180$	−2.43195	+	1.59152i	−0.181267	+	0.118625i
$181$		−	0.778086i		−	0.0578347i	−0.999582	−	0.0289173i	$-0.990794\pi$
$181$		−	0.778086i		−	0.0578347i	0.999582	−	0.0289173i	$-0.00920596\pi$
$182$	−4.25344	−	8.53863i	−0.315286	−	0.632926i
$183$	0.840259	+	1.87836i	0.0621138	+	0.138852i
$184$	−0.615472	−	0.164915i	−0.0453732	−	0.0121577i
$185$	2.42749	+	1.40151i	0.178473	+	0.103041i
$186$	−4.30238	−	0.444551i	−0.315466	−	0.0325961i
$187$	−4.07404	−	1.09164i	−0.297923	−	0.0798283i
$188$	−2.37115	−	2.37115i	−0.172934	−	0.172934i
$189$	0.704750	+	13.7297i	0.0512630	+	0.998685i
$190$	−1.89479	−	1.89479i	−0.137463	−	0.137463i
$191$	18.0065	−	10.3961i	1.30291	−	0.752234i	0.322006	−	0.946738i	$-0.395643\pi$
$191$	18.0065	−	10.3961i	1.30291	−	0.752234i	0.980902	+	0.194503i	$0.0623095\pi$
$192$	0.178019	−	1.72288i	0.0128474	−	0.124338i
$193$	20.4978	−	5.49236i	1.47546	−	0.395349i	0.570662	−	0.821185i	$-0.306687\pi$
$193$	20.4978	−	5.49236i	1.47546	−	0.395349i	0.904800	+	0.425837i	$0.140020\pi$
$194$	−6.11090	−	10.5844i	−0.438737	−	0.759915i
$195$	6.05021	+	0.00588104i	0.433264	+	0.000421150i
$196$	6.86496	−	1.36831i	0.490355	−	0.0977366i
$197$	2.00709	+	2.00709i	0.142999	+	0.142999i	0.774982	−	0.631983i	$-0.217759\pi$
$197$	2.00709	+	2.00709i	0.142999	+	0.142999i	−0.631983	+	0.774982i	$0.717759\pi$
$198$	3.00941	+	0.628615i	0.213869	+	0.0446738i
$199$	−11.4097	−	6.58738i	−0.808811	−	0.466967i	0.0377317	−	0.999288i	$-0.487987\pi$
$199$	−11.4097	−	6.58738i	−0.808811	−	0.466967i	−0.846543	+	0.532321i	$0.821320\pi$
$200$	3.92302	−	1.05117i	0.277399	−	0.0743289i
$201$	−0.461757	−	2.88260i	−0.0325698	−	0.203323i
$202$	8.03505	+	8.03505i	0.565344	+	0.565344i
$203$	−8.62314	+	3.24744i	−0.605226	+	0.227926i
$204$	−6.50726	+	2.91094i	−0.455599	+	0.203807i
$205$	−0.0574501	+	0.0331689i	−0.00401249	+	0.00231661i
$206$	3.76535	+	14.0525i	0.262344	+	0.979082i
$207$	−0.597091	−	1.81590i	−0.0415007	−	0.126214i
$208$	−2.27669	+	2.79583i	−0.157860	+	0.193856i
$209$			2.83447i			0.196064i
$210$	−1.16874	+	4.28304i	−0.0806508	+	0.295558i
$211$	14.0500			0.967244			0.483622	−	0.875277i	$-0.339321\pi$
$211$	14.0500			0.967244			0.483622	+	0.875277i	$0.339321\pi$
$212$	3.96789	+	6.87259i	0.272516	+	0.472011i
$213$	−13.2180	−	16.2643i	−0.905680	−	1.11441i
$214$	−2.21713	−	8.27445i	−0.151560	−	0.565629i
$215$	−8.12146	−	2.17614i	−0.553879	−	0.148411i
$216$	4.61730	−	2.38340i	0.314167	−	0.162169i
$217$	−5.36972	+	3.84947i	−0.364520	+	0.261319i
$218$	0.971294			0.0657843
$219$	−22.6139	+	3.62247i	−1.52811	+	0.244784i
$220$	0.859810	+	0.496411i	0.0579683	+	0.0334680i
$221$	14.6504	+	2.36142i	0.985495	+	0.158847i
$222$	−4.05939	−	2.93843i	−0.272449	−	0.197215i
$223$	3.20158	−	3.20158i	0.214394	−	0.214394i	−0.591737	−	0.806131i	$-0.701558\pi$
$223$	3.20158	−	3.20158i	0.214394	−	0.214394i	0.806131	+	0.591737i	$0.201558\pi$
$224$	−1.54151	−	2.15029i	−0.102997	−	0.143672i
$225$	9.08326	+	8.12094i	0.605551	+	0.541396i
$226$	7.86122	+	2.10641i	0.522920	+	0.140116i
$227$	−21.4347	+	5.74340i	−1.42267	+	0.381203i	−0.886430	−	0.462863i	$-0.846822\pi$
$227$	−21.4347	+	5.74340i	−1.42267	+	0.381203i	−0.536239	+	0.844066i	$0.680155\pi$
$228$	3.02143	+	3.71777i	0.200099	+	0.246215i
$229$	−0.0552409	+	0.206162i	−0.00365042	+	0.0136236i	−0.967727	−	0.252001i	$-0.918911\pi$
$229$	−0.0552409	+	0.206162i	−0.00365042	+	0.0136236i	0.964077	+	0.265624i	$0.0855781\pi$
$230$		−	0.617309i		−	0.0407041i
$231$	4.07773	−	2.32938i	0.268295	−	0.153262i
$232$	2.46264	+	2.46264i	0.161680	+	0.161680i
$233$	2.96602	+	5.13730i	0.194310	+	0.336556i	0.946674	−	0.322192i	$-0.104420\pi$
$233$	2.96602	+	5.13730i	0.194310	+	0.336556i	−0.752364	+	0.658748i	$0.771086\pi$
$234$	−10.7583	−	1.12219i	−0.703291	−	0.0733597i
$235$	1.62436	−	2.81348i	0.105962	−	0.183531i
$236$	−1.50208	+	5.60584i	−0.0977771	+	0.364909i
$237$	−0.0222586	−	0.0497581i	−0.00144585	−	0.00323213i
$238$	−4.49213	+	9.91948i	−0.291181	+	0.642985i
$239$	16.2577	+	16.2577i	1.05162	+	1.05162i	0.998593	+	0.0530291i	$0.0168876\pi$
$239$	16.2577	+	16.2577i	1.05162	+	1.05162i	0.0530291	+	0.998593i	$0.483112\pi$
$240$	1.65690	−	0.265415i	0.106953	−	0.0171325i
$241$	3.82763	−	1.02561i	0.246559	−	0.0660653i	−0.133423	−	0.991059i	$-0.542597\pi$
$241$	3.82763	−	1.02561i	0.246559	−	0.0660653i	0.379982	+	0.924994i	$0.375930\pi$
$242$	2.57520	+	9.61078i	0.165540	+	0.617804i
$243$	13.5680	+	7.67523i	0.870388	+	0.492366i
$244$		−	1.18803i		−	0.0760560i
$245$	3.00183	+	6.08112i	0.191780	+	0.388508i
$246$	0.108261	−	0.0484292i	0.00690247	−	0.00308773i
$247$	−1.01534	−	9.92081i	−0.0646045	−	0.631246i
$248$	2.16264	+	1.24860i	0.137328	+	0.0792864i
$249$	−9.36673	−	11.5254i	−0.593592	−	0.730395i
$250$	4.38939	+	7.60264i	0.277609	+	0.480833i
$251$	−25.5203			−1.61082			−0.805412	−	0.592715i	$-0.798056\pi$
$251$	−25.5203			−1.61082			−0.805412	+	0.592715i	$0.798056\pi$
$252$	2.86544	−	7.40198i	0.180506	−	0.466281i
$253$	−0.461724	+	0.461724i	−0.0290284	+	0.0290284i
$254$	19.5214	+	5.23075i	1.22488	+	0.328206i
$255$	−4.35572	−	5.35957i	−0.272766	−	0.335629i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.41632	+	9.38134i	0.337861	+	0.585192i	0.984030	−	0.178002i	$-0.0569634\pi$
$257$	5.41632	+	9.38134i	0.337861	+	0.585192i	−0.646169	+	0.763194i	$0.723630\pi$
$258$	14.0429	+	5.36225i	0.874273	+	0.333839i
$259$	−7.61787	+	0.751796i	−0.473351	+	0.0467143i
$260$	−3.18721	−	1.42948i	−0.197662	−	0.0886523i
$261$	−2.13633	+	10.2274i	−0.132235	+	0.633058i
$262$	−1.05629	−	3.94215i	−0.0652581	−	0.243547i
$263$	1.97029	+	1.13755i	0.121493	+	0.0701440i	0.559515	−	0.828820i	$-0.310987\pi$
$263$	1.97029	+	1.13755i	0.121493	+	0.0701440i	−0.438022	+	0.898964i	$0.644321\pi$
$264$	−1.43782	−	1.04078i	−0.0884919	−	0.0640557i
$265$	−5.43642	+	5.43642i	−0.333957	+	0.333957i
$266$	7.22040	+	1.19065i	0.442711	+	0.0730032i
$267$	10.4443	+	3.98812i	0.639179	+	0.244069i
$268$	−0.436237	+	1.62806i	−0.0266474	+	0.0994494i
$269$	14.0370	+	8.10427i	0.855852	+	0.494126i	0.862621	−	0.505851i	$-0.168821\pi$
$269$	14.0370	+	8.10427i	0.855852	+	0.494126i	−0.00676921	+	0.999977i	$0.502155\pi$
$270$	3.38815	+	3.72323i	0.206196	+	0.226588i
$271$	−8.39621	+	31.3351i	−0.510033	+	1.90347i	−0.0900530	+	0.995937i	$0.528704\pi$
$271$	−8.39621	+	31.3351i	−0.510033	+	1.90347i	−0.419980	+	0.907533i	$0.637963\pi$
$272$	4.11574			0.249554
$273$	−13.4379	+	9.61367i	−0.813299	+	0.581846i
$274$	18.0406			1.08987
$275$	1.07723	−	4.02026i	0.0649591	−	0.242431i
$276$	−0.113431	+	1.09779i	−0.00682774	+	0.0660791i
$277$	24.4046	+	14.0900i	1.46633	+	0.846585i	0.999291	−	0.0376525i	$-0.0119880\pi$
$277$	24.4046	+	14.0900i	1.46633	+	0.846585i	0.467037	+	0.884238i	$0.345321\pi$
$278$	4.95751	−	18.5017i	0.297332	−	1.10966i
$279$	0.418390	+	7.47993i	0.0250484	+	0.447812i
$280$	1.62571	−	1.98172i	0.0971546	−	0.118430i
$281$	13.0253	−	13.0253i	0.777021	−	0.777021i	−0.202302	−	0.979323i	$-0.564842\pi$
$281$	13.0253	−	13.0253i	0.777021	−	0.777021i	0.979323	+	0.202302i	$0.0648422\pi$
$282$	−3.40566	+	4.70486i	−0.202804	+	0.280170i
$283$	−17.8732	−	10.3191i	−1.06245	−	0.613408i	−0.136344	−	0.990662i	$-0.543535\pi$
$283$	−17.8732	−	10.3191i	−1.06245	−	0.613408i	−0.926110	+	0.377254i	$0.876868\pi$
$284$	3.13175	+	11.6878i	0.185835	+	0.693546i
$285$	−2.72146	+	3.75966i	−0.161206	+	0.222703i
$286$	1.31472	+	3.45311i	0.0777409	+	0.204187i
$287$	0.0747354	−	0.165030i	0.00441149	−	0.00974142i
$288$	−2.99532	+	0.167543i	−0.176501	+	0.00987258i
$289$	0.0303301	+	0.0525333i	0.00178413	+	0.00309020i
$290$	−1.68704	+	2.92203i	−0.0990662	+	0.171588i
$291$	−16.4278	+	13.3509i	−0.963014	+	0.782641i
$292$	12.7721	+	3.42226i	0.747428	+	0.200273i
$293$	−21.8967	+	21.8967i	−1.27922	+	1.27922i	−0.338117	+	0.941104i	$0.609790\pi$
$293$	−21.8967	+	21.8967i	−1.27922	+	1.27922i	−0.941104	+	0.338117i	$0.890210\pi$
$294$	−4.22088	−	11.3659i	−0.246167	−	0.662874i
$295$	−5.62257			−0.327359
$296$	1.44664	+	2.50565i	0.0840840	+	0.145638i
$297$	0.250630	−	5.31905i	0.0145430	−	0.308642i
$298$	−17.7027	−	10.2207i	−1.02549	−	0.592067i
$299$	1.45067	−	1.78146i	0.0838943	−	0.103024i
$300$	−2.87251	−	6.42136i	−0.165845	−	0.370737i
$301$	21.4883	−	8.09240i	1.23856	−	0.466438i
$302$		−	0.165070i		−	0.00949869i
$303$	11.5406	−	15.9432i	0.662992	−	0.915913i
$304$	−0.715871	−	2.67167i	−0.0410580	−	0.153231i
$305$	1.11176	−	0.297895i	0.0636591	−	0.0170574i
$306$	6.76116	+	10.3315i	0.386510	+	0.590615i
$307$	11.4023	+	11.4023i	0.650764	+	0.650764i	0.953177	−	0.302413i	$-0.0977921\pi$
$307$	11.4023	+	11.4023i	0.650764	+	0.650764i	−0.302413	+	0.953177i	$0.597792\pi$
$308$	−2.69822	+	0.266284i	−0.153746	+	0.0151729i
$309$	23.0016	−	10.2895i	1.30852	−	0.585349i
$310$	−0.626165	+	2.33688i	−0.0355638	+	0.132726i
$311$	−8.76323	+	15.1784i	−0.496917	+	0.860686i	−0.999994	−	0.00355622i	$-0.998868\pi$
$311$	−8.76323	+	15.1784i	−0.496917	+	0.860686i	0.503077	+	0.864242i	$0.332201\pi$
$312$	5.40529	+	3.12775i	0.306014	+	0.177074i
$313$	2.56506	+	4.44282i	0.144986	+	0.251123i	0.929368	−	0.369155i	$-0.120353\pi$
$313$	2.56506	+	4.44282i	0.144986	+	0.251123i	−0.784382	+	0.620278i	$0.787020\pi$
$314$	2.93951	+	2.93951i	0.165886	+	0.165886i
$315$	7.64525	+	0.825452i	0.430761	+	0.0465089i
$316$			0.0314712i			0.00177039i
$317$	−6.96668	+	26.0000i	−0.391288	+	1.46031i	0.436724	+	0.899596i	$0.356139\pi$
$317$	−6.96668	+	26.0000i	−0.391288	+	1.46031i	−0.828012	+	0.560711i	$0.810528\pi$
$318$	10.6668	−	8.66889i	0.598163	−	0.486127i
$319$	3.44741	−	0.923732i	0.193018	−	0.0517191i
$320$	−0.935798	−	0.250746i	−0.0523127	−	0.0140171i
$321$	−13.5439	+	6.05871i	−0.755949	+	0.338164i
$322$	0.982225	+	1.37013i	0.0547372	+	0.0763542i
$323$	−8.04955	+	8.04955i	−0.447889	+	0.447889i
$324$	−5.34115	−	7.24376i	−0.296731	−	0.402431i
$325$	−2.33025	+	14.4570i	−0.129259	+	0.801931i
$326$	8.83682	+	5.10194i	0.489426	+	0.282570i
$327$	−0.266096	−	1.66115i	−0.0147151	−	0.0918620i
$328$	−0.0684735			−0.00378082
$329$	0.871336	+	8.82915i	0.0480383	+	0.486767i
$330$	0.613432	−	1.60648i	0.0337683	−	0.0884340i
$331$	−5.21409	−	1.39711i	−0.286592	−	0.0767922i	0.112659	−	0.993634i	$-0.464063\pi$
$331$	−5.21409	−	1.39711i	−0.286592	−	0.0767922i	−0.399251	+	0.916841i	$0.630730\pi$
$332$	2.21927	+	8.28243i	0.121798	+	0.454557i
$333$	−3.91333	+	7.74758i	−0.214449	+	0.424565i
$334$	−12.7771	−	22.1305i	−0.699130	−	1.21093i
$335$	−1.63292			−0.0892158
$336$	−3.25521	+	3.22546i	−0.177586	+	0.175963i
$337$			24.6635i			1.34350i	0.740776	+	0.671752i	$0.234458\pi$
$337$			24.6635i			1.34350i	−0.740776	+	0.671752i	$0.765542\pi$
$338$	−5.83853	−	11.6151i	−0.317574	−	0.631780i
$339$	1.44881	−	14.0217i	0.0786888	−	0.761554i
$340$	1.03201	+	3.85150i	0.0559684	+	0.208877i
$341$	2.21625	−	1.27955i	0.120017	−	0.0692916i
$342$	5.53055	−	6.18591i	0.299058	−	0.334496i
$343$	−16.3385	−	8.72082i	−0.882197	−	0.470880i
$344$	−6.13673	−	6.13673i	−0.330870	−	0.330870i
$345$	−1.05575	+	0.169118i	−0.0568397	+	0.00910501i
$346$	−4.86317	+	1.30308i	−0.261446	+	0.0700542i
$347$	−22.4958	−	12.9880i	−1.20764	−	0.697230i	−0.245395	−	0.969423i	$-0.578918\pi$
$347$	−22.4958	−	12.9880i	−1.20764	−	0.697230i	−0.962243	+	0.272193i	$0.912251\pi$
$348$	3.53706	−	4.88639i	0.189606	−	0.261938i
$349$	20.0901	+	20.0901i	1.07540	+	1.07540i	0.996916	+	0.0784823i	$0.0250074\pi$
$349$	20.0901	+	20.0901i	1.07540	+	1.07540i	0.0784823	+	0.996916i	$0.474993\pi$
$350$	−9.78853	−	4.43282i	−0.523219	−	0.236944i
$351$	1.02812	+	18.7068i	0.0548772	+	0.998493i
$352$	0.512393	+	0.887491i	0.0273107	+	0.0473034i
$353$	−12.7338	+	3.41201i	−0.677752	+	0.181603i	−0.581244	−	0.813729i	$-0.697434\pi$
$353$	−12.7338	+	3.41201i	−0.677752	+	0.181603i	−0.0965075	+	0.995332i	$0.530767\pi$
$354$	9.99889	+	1.03315i	0.531435	+	0.0549114i
$355$	−10.1522	+	5.86137i	−0.538822	+	0.311089i
$356$	−4.56413	−	4.56413i	−0.241898	−	0.241898i
$357$	18.1954	+	4.96510i	0.963005	+	0.262781i
$358$	−1.76589	−	1.76589i	−0.0933302	−	0.0933302i
$359$	−8.86671	−	2.37583i	−0.467967	−	0.125391i	0.0171272	−	0.999853i	$-0.494548\pi$
$359$	−8.86671	−	2.37583i	−0.467967	−	0.125391i	−0.485094	+	0.874462i	$0.661215\pi$
$360$	−0.907851	−	2.76100i	−0.0478480	−	0.145518i
$361$	−9.82916	−	5.67487i	−0.517324	−	0.298677i
$362$	0.751574	+	0.201384i	0.0395018	+	0.0105845i
$363$	15.7313	−	7.03720i	0.825680	−	0.369357i
$364$	9.34856	−	1.89854i	0.489998	−	0.0995107i
$365$			12.8102i			0.670515i
$366$	−2.03183	+	0.325474i	−0.106205	+	0.0170128i
$367$	−7.46508	+	12.9299i	−0.389674	+	0.674935i	−0.992406	−	0.123009i	$-0.960746\pi$
$367$	−7.46508	+	12.9299i	−0.389674	+	0.674935i	0.602732	+	0.797944i	$0.294079\pi$
$368$	0.318592	−	0.551817i	0.0166077	−	0.0287654i
$369$	−0.112485	−	0.171886i	−0.00585574	−	0.00894800i
$370$	−1.98204	+	1.98204i	−0.103041	+	0.103041i
$371$	3.41613	−	20.7163i	0.177356	−	1.07554i
$372$	1.54294	−	4.04072i	0.0799978	−	0.209502i
$373$	−10.8093	−	18.7223i	−0.559686	−	0.969404i	−0.997522	−	0.0703493i	$-0.977589\pi$
$373$	−10.8093	−	18.7223i	−0.559686	−	0.969404i	0.437837	−	0.899054i	$-0.355745\pi$
$374$	2.10888	−	3.65269i	0.109048	−	0.188876i
$375$	11.7999	−	9.58976i	0.609343	−	0.495213i
$376$	2.90406	−	1.67666i	0.149765	−	0.0864671i
$377$	−11.7353	+	4.46802i	−0.604397	+	0.230115i
$378$	−13.4442	−	2.87276i	−0.691496	−	0.147759i
$379$	14.4640	−	14.4640i	0.742967	−	0.742967i	−0.230181	−	0.973148i	$-0.573932\pi$
$379$	14.4640	−	14.4640i	0.742967	−	0.742967i	0.973148	+	0.230181i	$0.0739318\pi$
$380$	2.32064	−	1.33982i	0.119046	−	0.0687313i
$381$	3.59778	−	34.8195i	0.184320	−	1.78386i
$382$	5.38141	+	20.0837i	0.275337	+	1.02757i
$383$	7.44941	−	27.8016i	0.380647	−	1.42059i	−0.464268	−	0.885695i	$-0.653683\pi$
$383$	7.44941	−	27.8016i	0.380647	−	1.42059i	0.844915	−	0.534900i	$-0.179651\pi$
$384$	1.61810	+	0.617867i	0.0825732	+	0.0315304i
$385$	−0.925757	−	2.45822i	−0.0471809	−	0.125283i
$386$			21.2209i			1.08011i
$387$	5.32358	−	25.4859i	0.270613	−	1.29552i
$388$	11.8054	−	3.16324i	0.599326	−	0.160589i
$389$	2.90415	−	5.03013i	0.147246	−	0.255038i	−0.782963	−	0.622069i	$-0.786292\pi$
$389$	2.90415	−	5.03013i	0.147246	−	0.255038i	0.930209	+	0.367031i	$0.119626\pi$
$390$	−1.57159	+	5.84253i	−0.0795805	+	0.295848i
$391$	−2.62248			−0.132625
$392$	−0.455095	+	6.98519i	−0.0229858	+	0.352805i
$393$	−6.45266	+	2.88652i	−0.325494	+	0.145605i
$394$	−2.45817	+	1.41923i	−0.123841	+	0.0714997i
$395$	−0.0294507	+	0.00789129i	−0.00148183	+	0.000397054i
$396$	−1.38609	+	2.74417i	−0.0696535	+	0.137900i
$397$	5.51587	−	20.5855i	0.276834	−	1.03316i	−0.677769	−	0.735275i	$-0.737053\pi$
$397$	5.51587	−	20.5855i	0.276834	−	1.03316i	0.954603	−	0.297882i	$-0.0962803\pi$
$398$	9.31597	−	9.31597i	0.466967	−	0.466967i
$399$	0.0581946	−	12.6749i	0.00291337	−	0.634537i
$400$			4.06141i			0.203070i
$401$	−5.68116	−	1.52226i	−0.283703	−	0.0760181i	0.114161	−	0.993462i	$-0.463582\pi$
$401$	−5.68116	−	1.52226i	−0.283703	−	0.0760181i	−0.397865	+	0.917444i	$0.630249\pi$
$402$	2.90389	+	0.300049i	0.144833	+	0.0149651i
$403$	−7.29866	+	5.27240i	−0.363572	+	0.262637i
$404$	−9.84089	+	5.68164i	−0.489602	+	0.282672i
$405$	5.43942	−	6.81458i	0.270287	−	0.338619i
$406$	−0.904955	−	9.16981i	−0.0449122	−	0.455090i
$407$	2.96499			0.146969
$408$	−1.12755	−	7.03894i	−0.0558220	−	0.348479i
$409$	−0.0937626	−	0.349927i	−0.00463626	−	0.0173028i	0.963569	−	0.267460i	$-0.0861843\pi$
$409$	−0.0937626	−	0.349927i	−0.00463626	−	0.0173028i	−0.968205	+	0.250157i	$0.919518\pi$
$410$	−0.0171695	−	0.0640773i	−0.000847939	−	0.00316455i
$411$	−4.94240	−	30.8538i	−0.243790	−	1.52191i
$412$	−14.5482			−0.716738
$413$	12.4794	−	8.94630i	0.614071	−	0.440219i
$414$	1.90857	−	0.106756i	0.0938009	−	0.00524676i
$415$	−7.19421	+	4.15358i	−0.353150	+	0.203891i
$416$	−2.11132	−	2.92273i	−0.103516	−	0.143299i
$417$	−33.0006	−	3.40985i	−1.61605	−	0.166981i
$418$	−2.73789	−	0.733615i	−0.133914	−	0.0358823i
$419$			4.19355i			0.204869i	0.994740	+	0.102434i	$0.0326631\pi$
$419$			4.19355i			0.204869i	−0.994740	+	0.102434i	$0.967337\pi$
$420$	−3.83461	−	2.23745i	−0.187110	−	0.109176i
$421$	−1.34291	+	1.34291i	−0.0654495	+	0.0654495i	−0.739074	−	0.673624i	$-0.764737\pi$
$421$	−1.34291	+	1.34291i	−0.0654495	+	0.0654495i	0.673624	+	0.739074i	$0.264737\pi$
$422$	−3.63642	+	13.5713i	−0.177018	+	0.660640i
$423$	8.97949	+	4.53557i	0.436598	+	0.220527i
$424$	−7.66538	+	2.05393i	−0.372264	+	0.0997477i
$425$	14.4762	−	8.35786i	0.702201	−	0.405416i
$426$	19.1311	−	8.55807i	0.926907	−	0.414640i
$427$	−1.99357	+	2.43015i	−0.0964758	+	0.117603i
$428$	8.56634			0.414070
$429$	5.54549	−	3.19451i	0.267739	−	0.154232i
$430$	4.20398	−	7.28150i	0.202734	−	0.351145i
$431$	31.4848	−	8.43634i	1.51657	−	0.406364i	0.597960	−	0.801526i	$-0.295978\pi$
$431$	31.4848	−	8.43634i	1.51657	−	0.406364i	0.918611	+	0.395162i	$0.129312\pi$
$432$	1.10714	+	5.07683i	0.0532672	+	0.244259i
$433$		−	21.9098i		−	1.05292i	−0.850201	−	0.526458i	$-0.823520\pi$
$433$		−	21.9098i		−	1.05292i	0.850201	−	0.526458i	$-0.176480\pi$
$434$	−2.32852	−	6.18306i	−0.111772	−	0.296797i
$435$	5.45958	+	2.08473i	0.261767	+	0.0999551i
$436$	−0.251389	+	0.938198i	−0.0120394	+	0.0449315i
$437$	0.456141	+	1.70234i	0.0218202	+	0.0814340i
$438$	2.35388	−	22.7809i	0.112473	−	1.08852i
$439$	5.86906	−	3.38851i	0.280115	−	0.161725i	−0.353360	−	0.935487i	$-0.614961\pi$
$439$	5.86906	−	3.38851i	0.280115	−	0.161725i	0.633476	+	0.773763i	$0.281628\pi$
$440$	−0.702032	+	0.702032i	−0.0334680	+	0.0334680i
$441$	−18.2822	+	10.3326i	−0.870580	+	0.492027i
$442$	−6.07277	+	13.5400i	−0.288852	+	0.644034i
$443$	30.3397	−	17.5166i	1.44148	−	0.832240i	0.443533	−	0.896258i	$-0.353725\pi$
$443$	30.3397	−	17.5166i	1.44148	−	0.832240i	0.997949	+	0.0640182i	$0.0203916\pi$
$444$	3.88895	−	3.16055i	0.184562	−	0.149993i
$445$	3.12666	−	5.41554i	0.148218	−	0.256721i
$446$	2.26386	+	3.92112i	0.107197	+	0.185671i
$447$	−12.6300	+	33.0760i	−0.597379	+	1.56444i
$448$	2.47599	−	0.932449i	0.116980	−	0.0440541i
$449$	−2.14151	+	2.14151i	−0.101064	+	0.101064i	−0.755831	−	0.654767i	$-0.772767\pi$
$449$	−2.14151	+	2.14151i	−0.101064	+	0.101064i	0.654767	+	0.755831i	$0.272767\pi$
$450$	−10.1952	+	6.67190i	−0.480604	+	0.314517i
$451$	−0.0350854	+	0.0607696i	−0.00165210	+	0.00286153i
$452$	−4.06926	+	7.04817i	−0.191402	+	0.331518i
$453$	−0.282310	+	0.0452225i	−0.0132641	+	0.00212474i
$454$		−	22.1908i		−	1.04147i
$455$	4.12077	+	8.27231i	0.193185	+	0.387812i
$456$	−4.37309	+	1.95625i	−0.204789	+	0.0916096i
$457$	30.6514	+	8.21302i	1.43381	+	0.384189i	0.890363	−	0.455252i	$-0.150451\pi$
$457$	30.6514	+	8.21302i	1.43381	+	0.384189i	0.543451	+	0.839441i	$0.317118\pi$
$458$	−0.184840	−	0.106717i	−0.00863698	−	0.00498657i
$459$	15.8172	−	14.3937i	0.738284	−	0.671840i
$460$	0.596274	+	0.159771i	0.0278014	+	0.00744937i
$461$	−11.2027	−	11.2027i	−0.521764	−	0.521764i	0.396340	−	0.918104i	$-0.370280\pi$
$461$	−11.2027	−	11.2027i	−0.521764	−	0.521764i	−0.918104	+	0.396340i	$0.870280\pi$
$462$	1.19462	+	4.54168i	0.0555786	+	0.211298i
$463$	−17.5213	−	17.5213i	−0.814284	−	0.814284i	0.170989	−	0.985273i	$-0.445304\pi$
$463$	−17.5213	−	17.5213i	−0.814284	−	0.814284i	−0.985273	+	0.170989i	$0.945304\pi$
$464$	−3.01611	+	1.74135i	−0.140019	+	0.0808402i
$465$	4.16819	+	0.430685i	0.193295	+	0.0199725i
$466$	−5.72991	+	1.53533i	−0.265433	+	0.0711226i
$467$	17.3288	+	30.0144i	0.801882	+	1.38890i	0.918376	+	0.395708i	$0.129501\pi$
$467$	17.3288	+	30.0144i	0.801882	+	1.38890i	−0.116495	+	0.993191i	$0.537166\pi$
$468$	3.86840	−	10.1013i	0.178817	−	0.466931i
$469$	3.62429	−	2.59820i	0.167354	−	0.119974i
$470$	2.29720	+	2.29720i	0.105962	+	0.105962i
$471$	4.22198	−	5.83260i	0.194539	−	0.268752i
$472$	−5.02606	−	2.90180i	−0.231343	−	0.133566i
$473$	−8.59072	+	2.30188i	−0.395002	+	0.105840i
$474$	0.0538236	−	0.00862186i	0.00247220	−	0.000396015i
$475$	−7.94328	−	7.94328i	−0.364463	−	0.364463i
$476$	−8.41884	−	6.90641i	−0.385877	−	0.316555i
$477$	−17.7482	−	15.8679i	−0.812635	−	0.726541i
$478$	−19.9115	+	11.4959i	−0.910731	+	0.525811i
$479$	−1.42097	−	5.30314i	−0.0649259	−	0.242307i	0.925835	−	0.377929i	$-0.123363\pi$
$479$	−1.42097	−	5.30314i	−0.0649259	−	0.242307i	−0.990761	+	0.135622i	$0.956697\pi$
$480$	−0.172467	+	1.66914i	−0.00787199	+	0.0761855i
$481$	−10.3776	+	1.06209i	−0.473179	+	0.0484272i
$482$			3.96265i			0.180494i
$483$	2.07417	−	2.05521i	0.0943779	−	0.0935152i
$484$	−9.94981			−0.452264
$485$	5.92030	+	10.2543i	0.268827	+	0.465622i
$486$	−10.9254	+	11.1192i	−0.495585	+	0.504377i
$487$	6.42991	+	23.9967i	0.291367	+	1.08740i	0.944060	+	0.329774i	$0.106972\pi$
$487$	6.42991	+	23.9967i	0.291367	+	1.08740i	−0.652693	+	0.757622i	$0.726361\pi$
$488$	1.14755	+	0.307485i	0.0519472	+	0.0139192i
$489$	6.30464	−	16.5109i	0.285106	−	0.746648i
$490$	−6.65084	+	1.32563i	−0.300454	+	0.0598860i
$491$	−13.7326			−0.619744			−0.309872	−	0.950778i	$-0.600286\pi$
$491$	−13.7326			−0.619744			−0.309872	+	0.950778i	$0.600286\pi$
$492$	0.0187590	+	0.117107i	0.000845722	+	0.00527957i
$493$	12.4135	+	7.16695i	0.559077	+	0.322783i
$494$	9.84556	+	1.58695i	0.442973	+	0.0714004i
$495$	−2.91554	−	0.609008i	−0.131044	−	0.0273729i
$496$	−1.76579	+	1.76579i	−0.0792864	+	0.0792864i
$497$	13.2067	−	29.1630i	0.592402	−	1.30814i
$498$	13.5570	−	6.06456i	0.607504	−	0.271759i
$499$	−24.9838	−	6.69439i	−1.11843	−	0.299682i	−0.348181	−	0.937427i	$-0.613201\pi$
$499$	−24.9838	−	6.69439i	−1.11843	−	0.299682i	−0.770247	+	0.637745i	$0.779867\pi$
$500$	−8.47965	+	2.27211i	−0.379221	+	0.101612i
$501$	−34.3483	+	27.9148i	−1.53457	+	1.24714i
$502$	6.60513	−	24.6507i	0.294801	−	1.10021i
$503$			23.5158i			1.04852i	0.851559	+	0.524260i	$0.175658\pi$
$503$			23.5158i			1.04852i	−0.851559	+	0.524260i	$0.824342\pi$
$504$	6.40813	+	4.68357i	0.285441	+	0.208623i
$505$	−7.78443	−	7.78443i	−0.346403	−	0.346403i
$506$	−0.326488	−	0.565494i	−0.0145142	−	0.0251393i
$507$	−18.2652	+	13.1674i	−0.811188	+	0.584786i
$508$	−10.1050	+	17.5024i	−0.448338	+	0.776544i
$509$	9.72802	−	36.3055i	0.431187	−	1.60921i	−0.318843	−	0.947808i	$-0.603294\pi$
$509$	9.72802	−	36.3055i	0.431187	−	1.60921i	0.750030	−	0.661404i	$-0.230039\pi$
$510$	6.30429	−	2.82015i	0.279159	−	0.124878i
$511$	−20.3828	−	28.4324i	−0.901681	−	1.25778i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−12.0946	−	7.76391i	−0.533989	−	0.342785i
$514$	−10.4635	+	2.80369i	−0.461526	+	0.123666i
$515$	−3.64790	−	13.6142i	−0.160746	−	0.599912i
$516$	−8.81411	+	12.1766i	−0.388020	+	0.536043i
$517$		−	3.43644i		−	0.151134i
$518$	1.24547	−	7.55288i	0.0547228	−	0.331854i
$519$	3.56091	+	7.96024i	0.156307	+	0.349416i
$520$	2.20568	−	2.70863i	0.0967253	−	0.118781i
$521$	35.6395	+	20.5765i	1.56139	+	0.901472i	0.997116	+	0.0758870i	$0.0241788\pi$
$521$	35.6395	+	20.5765i	1.56139	+	0.901472i	0.564278	+	0.825585i	$0.309155\pi$
$522$	−9.32595	−	4.71057i	−0.408186	−	0.206176i
$523$	14.4894	+	25.0964i	0.633578	+	1.09739i	0.986814	+	0.161855i	$0.0517478\pi$
$523$	14.4894	+	25.0964i	0.633578	+	1.09739i	−0.353236	+	0.935534i	$0.614919\pi$
$524$	4.08121			0.178288
$525$	−4.89956	+	17.9552i	−0.213834	+	0.783630i
$526$	−1.60873	+	1.60873i	−0.0701440	+	0.0701440i
$527$	9.92765	+	2.66011i	0.432455	+	0.115876i
$528$	1.37745	−	1.11946i	0.0599460	−	0.0487181i
$529$	11.2970	−	19.5670i	0.491174	−	0.850738i
$530$	−3.84413	−	6.65823i	−0.166978	−	0.289215i
$531$	−0.972353	−	17.3836i	−0.0421965	−	0.754384i
$532$	−3.01885	+	6.66621i	−0.130884	+	0.289017i
$533$	0.101032	−	0.225265i	0.00437620	−	0.00975732i
$534$	−6.55540	+	9.05618i	−0.283680	+	0.391899i
$535$	2.14798	+	8.01636i	0.0928651	+	0.346577i
$536$	−1.45968	−	0.842744i	−0.0630484	−	0.0364010i
$537$	−2.53633	+	3.50389i	−0.109451	+	0.151204i
$538$	−11.4612	+	11.4612i	−0.494126	+	0.494126i
$539$	5.96611	+	3.98306i	0.256978	+	0.171562i
$540$	−4.47328	+	2.30905i	−0.192499	+	0.0993659i
$541$	−1.85695	+	6.93022i	−0.0798364	+	0.297953i	−0.994286	−	0.106745i	$-0.965957\pi$
$541$	−1.85695	+	6.93022i	−0.0798364	+	0.297953i	0.914450	+	0.404699i	$0.132624\pi$
$542$	−28.0943	−	16.2202i	−1.20675	−	0.696718i
$543$	0.138514	−	1.34055i	0.00594422	−	0.0575284i
$544$	−1.06523	+	3.97550i	−0.0456715	+	0.170448i
$545$	−0.940998			−0.0403079
$546$	−5.80811	−	15.4682i	−0.248564	−	0.661979i
$547$	3.41524			0.146025			0.0730126	−	0.997331i	$-0.476739\pi$
$547$	3.41524			0.146025			0.0730126	+	0.997331i	$0.476739\pi$
$548$	−4.66924	+	17.4258i	−0.199460	+	0.744395i
$549$	1.11328	+	3.38576i	0.0475137	+	0.144501i
$550$	3.60447	+	2.08104i	0.153695	+	0.0887358i
$551$	2.49316	−	9.30461i	0.106212	−	0.396390i
$552$	−1.03102	−	0.393694i	−0.0438833	−	0.0167567i
$553$	0.0528102	−	0.0643750i	0.00224572	−	0.00273751i
$554$	−19.9262	+	19.9262i	−0.846585	+	0.846585i
$555$	3.93278	+	2.84678i	0.166937	+	0.120839i
$556$	16.5882	+	9.57718i	0.703495	+	0.406163i
$557$	−1.14902	−	4.28820i	−0.0486855	−	0.181697i	0.937301	−	0.348520i	$-0.113316\pi$
$557$	−1.14902	−	4.28820i	−0.0486855	−	0.181697i	−0.985987	+	0.166823i	$0.946649\pi$
$558$	−7.33334	−	1.53181i	−0.310445	−	0.0648469i
$559$	29.2435	−	11.1340i	1.23687	−	0.470918i
$560$	1.49343	+	2.08322i	0.0631089	+	0.0880321i
$561$	−6.82475	−	2.60601i	−0.288141	−	0.110026i
$562$	9.21024	+	15.9526i	0.388511	+	0.672920i
$563$	−11.0361	+	19.1151i	−0.465116	+	0.805605i	−0.999207	−	0.0398220i	$-0.987321\pi$
$563$	−11.0361	+	19.1151i	−0.465116	+	0.805605i	0.534090	+	0.845427i	$0.320654\pi$
$564$	−3.66310	−	4.50732i	−0.154244	−	0.189792i
$565$	−7.61602	−	2.04071i	−0.320408	−	0.0858531i
$566$	14.5934	−	14.5934i	0.613408	−	0.613408i
$567$	−1.22994	+	23.7800i	−0.0516528	+	0.998665i
$568$	−12.1002			−0.507711
$569$	21.7766	+	37.7183i	0.912925	+	1.58123i	0.809912	+	0.586552i	$0.199515\pi$
$569$	21.7766	+	37.7183i	0.912925	+	1.58123i	0.103013	+	0.994680i	$0.467152\pi$
$570$	−2.92719	−	3.60180i	−0.122606	−	0.150863i
$571$	−29.0000	−	16.7431i	−1.21361	−	0.700678i	−0.250067	−	0.968229i	$-0.580452\pi$
$571$	−29.0000	−	16.7431i	−1.21361	−	0.700678i	−0.963544	+	0.267550i	$0.913786\pi$
$572$	−3.67572	+	0.376189i	−0.153690	+	0.0157293i
$573$	32.8738	−	14.7057i	1.37332	−	0.614338i
$574$	0.140064	+	0.114902i	0.00584616	+	0.00479591i
$575$		−	2.58786i		−	0.107921i
$576$	0.613411	−	2.93662i	0.0255588	−	0.122359i
$577$	3.61803	+	13.5027i	0.150621	+	0.562124i	0.999441	+	0.0334420i	$0.0106469\pi$
$577$	3.61803	+	13.5027i	0.150621	+	0.562124i	−0.848820	+	0.528682i	$0.822686\pi$
$578$	−0.0585933	+	0.0157000i	−0.00243716	+	0.000653035i
$579$	36.2929	−	5.81367i	1.50828	−	0.241608i
$580$	−2.38583	−	2.38583i	−0.0990662	−	0.0990662i
$581$	9.35875	−	20.6659i	0.388266	−	0.857367i
$582$	−8.64412	−	19.3235i	−0.358310	−	0.800984i
$583$	−2.10484	+	7.85538i	−0.0871736	+	0.325336i
$584$	−6.61130	+	11.4511i	−0.273578	+	0.473850i
$585$	10.4227	+	1.08719i	0.430927	+	0.0449496i
$586$	−15.4833	−	26.8179i	−0.639610	−	1.10784i
$587$	16.7060	+	16.7060i	0.689531	+	0.689531i	0.962128	−	0.272597i	$-0.0878826\pi$
$587$	16.7060	+	16.7060i	0.689531	+	0.689531i	−0.272597	+	0.962128i	$0.587883\pi$
$588$	12.0711	−	1.13534i	0.497803	−	0.0468206i
$589$		−	6.90705i		−	0.284600i
$590$	1.45523	−	5.43099i	0.0599108	−	0.223590i
$591$	3.10067	+	3.81527i	0.127545	+	0.156939i
$592$	−2.79469	+	0.748834i	−0.114861	+	0.0307769i
$593$	−25.6377	−	6.86959i	−1.05281	−	0.282100i	−0.309399	−	0.950932i	$-0.600128\pi$
$593$	−25.6377	−	6.86959i	−1.05281	−	0.282100i	−0.743413	+	0.668832i	$0.766795\pi$
$594$	5.07294	+	1.61876i	0.208145	+	0.0664185i
$595$	4.35201	−	9.61009i	0.178415	−	0.393975i
$596$	14.4542	−	14.4542i	0.592067	−	0.592067i
$597$	−18.4848	−	13.3804i	−0.756533	−	0.547623i
$598$	1.34530	+	1.86231i	0.0550132	+	0.0761556i
$599$	32.0100	+	18.4810i	1.30789	+	0.755112i	0.981744	−	0.190206i	$-0.0609157\pi$
$599$	32.0100	+	18.4810i	1.30789	+	0.755112i	0.326148	+	0.945319i	$0.394249\pi$
$600$	6.94601	−	1.11266i	0.283570	−	0.0454244i
$601$	10.4935			0.428041			0.214020	−	0.976829i	$-0.431344\pi$
$601$	10.4935			0.428041			0.214020	+	0.976829i	$0.431344\pi$
$602$	2.25509	+	22.8505i	0.0919105	+	0.931319i
$603$	−0.282392	−	5.04857i	−0.0114999	−	0.205594i
$604$	0.159445	+	0.0427232i	0.00648773	+	0.00173838i
$605$	−2.49488	−	9.31101i	−0.101431	−	0.378546i
$606$	12.4130	+	15.2738i	0.504244	+	0.620456i
$607$	13.3739	+	23.1642i	0.542829	+	0.940207i	0.998740	+	0.0501821i	$0.0159802\pi$
$607$	13.3739	+	23.1642i	0.542829	+	0.940207i	−0.455911	+	0.890025i	$0.650686\pi$
$608$	2.76591			0.112173
$609$	−15.4347	+	4.05986i	−0.625447	+	0.164514i
$610$			1.15098i			0.0466017i
$611$	1.23097	+	12.0277i	0.0497997	+	0.486590i
$612$	−11.7294	+	3.85678i	−0.474134	+	0.155901i
$613$	−1.55387	−	5.79912i	−0.0627602	−	0.234224i	0.927420	−	0.374022i	$-0.122021\pi$
$613$	−1.55387	−	5.79912i	−0.0627602	−	0.234224i	−0.990180	+	0.139798i	$0.955355\pi$
$614$	−13.9649	+	8.06265i	−0.563578	+	0.325382i
$615$	−0.104884	+	0.0469187i	−0.00422934	+	0.00189194i
$616$	0.441141	−	2.67520i	0.0177741	−	0.107787i
$617$	−18.6670	−	18.6670i	−0.751503	−	0.751503i	0.223257	−	0.974760i	$-0.428331\pi$
$617$	−18.6670	−	18.6670i	−0.751503	−	0.751503i	−0.974760	+	0.223257i	$0.928331\pi$
$618$	3.98563	+	24.8810i	0.160325	+	1.00086i
$619$	22.2321	−	5.95707i	0.893583	−	0.239435i	0.217324	−	0.976099i	$-0.430267\pi$
$619$	22.2321	−	5.95707i	0.893583	−	0.239435i	0.676258	+	0.736665i	$0.263600\pi$
$620$	−2.09519	−	1.20966i	−0.0841448	−	0.0485810i
$621$	−0.705450	−	3.23487i	−0.0283087	−	0.129811i
$622$	−12.3931	−	12.3931i	−0.496917	−	0.496917i
$623$	1.67720	+	16.9949i	0.0671955	+	0.680885i
$624$	−4.42017	+	4.41159i	−0.176948	+	0.176605i
$625$	5.90105	+	10.2209i	0.236042	+	0.408836i
$626$	−4.95532	+	1.32777i	−0.198055	+	0.0530686i
$627$	−0.504590	+	4.88344i	−0.0201514	+	0.195026i
$628$	−3.60015	+	2.07855i	−0.143662	+	0.0829431i
$629$	8.42020	+	8.42020i	0.335735	+	0.335735i
$630$	−2.77606	+	7.17110i	−0.110601	+	0.285704i
$631$	1.85070	+	1.85070i	0.0736750	+	0.0736750i	0.742984	−	0.669309i	$-0.233410\pi$
$631$	1.85070	+	1.85070i	0.0736750	+	0.0736750i	−0.669309	+	0.742984i	$0.733410\pi$
$632$	−0.0303989	−	0.00814535i	−0.00120920	−	0.000324005i
$633$	24.2065	+	2.50118i	0.962122	+	0.0994128i
$634$	−23.3110	−	13.4586i	−0.925797	−	0.534509i
$635$	−18.9125	−	5.06760i	−0.750521	−	0.201101i
$636$	5.61274	+	12.5470i	0.222560	+	0.497521i
$637$	−22.3085	−	11.8038i	−0.883896	−	0.467684i
$638$			3.56903i			0.141299i
$639$	−19.8776	−	30.3744i	−0.786345	−	1.20159i
$640$	0.484404	−	0.839013i	0.0191478	−	0.0331649i
$641$	16.8365	−	29.1616i	0.665001	−	1.15181i	−0.314285	−	0.949329i	$-0.601765\pi$
$641$	16.8365	−	29.1616i	0.665001	−	1.15181i	0.979285	−	0.202486i	$-0.0649021\pi$
$642$	−2.34684	−	14.6506i	−0.0926222	−	0.578211i
$643$	−2.15687	+	2.15687i	−0.0850587	+	0.0850587i	−0.748356	−	0.663297i	$-0.769157\pi$
$643$	−2.15687	+	2.15687i	−0.0850587	+	0.0850587i	0.663297	+	0.748356i	$0.269157\pi$
$644$	−1.57766	+	0.594141i	−0.0621685	+	0.0234124i
$645$	−13.6049	−	5.19500i	−0.535692	−	0.204553i
$646$	−5.69189	−	9.85864i	−0.223944	−	0.387883i
$647$	−20.9209	+	36.2361i	−0.822487	+	1.42459i	0.0813383	+	0.996687i	$0.474081\pi$
$647$	−20.9209	+	36.2361i	−0.822487	+	1.42459i	−0.903825	+	0.427902i	$0.859253\pi$
$648$	8.37933	−	3.28433i	0.329171	−	0.129021i
$649$	−5.15064	+	2.97372i	−0.202180	+	0.116729i
$650$	−13.3613	−	5.99260i	−0.524073	−	0.235049i
$651$	−9.93665	+	5.67626i	−0.389448	+	0.222470i
$652$	−7.21523	+	7.21523i	−0.282570	+	0.282570i
$653$	−11.1683	+	6.44801i	−0.437049	+	0.252330i	−0.702345	−	0.711837i	$-0.747864\pi$
$653$	−11.1683	+	6.44801i	−0.437049	+	0.252330i	0.265296	+	0.964167i	$0.414530\pi$
$654$	1.67342	+	0.172909i	0.0654359	+	0.00676128i
$655$	1.02335	+	3.81919i	0.0399855	+	0.149228i
$656$	0.0177222	−	0.0661403i	0.000691937	−	0.00258234i
$657$	−39.6059	+	2.21536i	−1.54517	+	0.0864293i
$658$	−8.75383	−	1.44351i	−0.341260	−	0.0562738i
$659$		−	39.5546i		−	1.54083i	−0.637543	−	0.770415i	$-0.720049\pi$
$659$		−	39.5546i		−	1.54083i	0.637543	−	0.770415i	$-0.279951\pi$
$660$	1.39298	+	1.00832i	0.0542215	+	0.0392488i
$661$	41.4429	−	11.1046i	1.61194	−	0.431919i	0.663323	−	0.748333i	$-0.269146\pi$
$661$	41.4429	−	11.1046i	1.61194	−	0.431919i	0.948621	+	0.316414i	$0.102479\pi$
$662$	2.69901	−	4.67483i	0.104900	−	0.181692i
$663$	24.8205	+	6.67651i	0.963949	+	0.259294i
$664$	−8.57460			−0.332759
$665$	−6.99519	−	1.15351i	−0.271262	−	0.0447311i
$666$	−6.47074	−	5.78521i	−0.250736	−	0.224172i
$667$	1.92181	−	1.10956i	0.0744129	−	0.0429623i
$668$	24.6834	−	6.61390i	0.955030	−	0.255899i
$669$	6.08588	−	4.94599i	0.235294	−	0.191223i
$670$	0.422630	−	1.57728i	0.0163276	−	0.0609355i
$671$	0.860888	−	0.860888i	0.0332342	−	0.0332342i
$672$	−2.27304	−	3.97911i	−0.0876845	−	0.153497i
$673$			17.9661i			0.692541i	0.938135	+	0.346271i	$0.112552\pi$
$673$			17.9661i			0.692541i	−0.938135	+	0.346271i	$0.887448\pi$
$674$	−23.8231	−	6.38338i	−0.917631	−	0.245878i
$675$	14.2037	+	15.6084i	0.546700	+	0.600767i
$676$	12.7305	−	2.63337i	0.489634	−	0.101283i
$677$	−4.04856	+	2.33744i	−0.155599	+	0.0898350i	−0.575778	−	0.817606i	$-0.695301\pi$
$677$	−4.04856	+	2.33744i	−0.155599	+	0.0898350i	0.420179	+	0.907441i	$0.361967\pi$
$678$	13.1689	+	5.02853i	0.505750	+	0.193119i
$679$	−29.4562	−	13.3395i	−1.13042	−	0.511923i
$680$	−3.98737			−0.152909
$681$	−37.9518	+	6.07940i	−1.45431	+	0.232963i
$682$	0.662345	+	2.47190i	0.0253625	+	0.0946541i
$683$	−13.2214	−	49.3429i	−0.505902	−	1.88805i	−0.457466	−	0.889227i	$-0.651243\pi$
$683$	−13.2214	−	49.3429i	−0.505902	−	1.88805i	−0.0484369	−	0.998826i	$-0.515424\pi$
$684$	4.54372	+	6.94313i	0.173733	+	0.265477i
$685$	−17.4779			−0.667795
$686$	12.6524	−	13.5247i	0.483070	−	0.516375i
$687$	−0.131874	+	0.345358i	−0.00503131	+	0.0131762i
$688$	7.51593	−	4.33933i	0.286542	−	0.165435i
$689$	4.55319	−	28.2483i	0.173463	−	1.07617i
$690$	0.109893	−	1.06355i	0.00418355	−	0.0404886i
$691$	12.5372	+	3.35934i	0.476938	+	0.127795i	0.489277	−	0.872129i	$-0.337261\pi$
$691$	12.5372	+	3.35934i	0.476938	+	0.127795i	−0.0123385	+	0.999924i	$0.503928\pi$
$692$		−	5.03473i		−	0.191392i
$693$	7.44011	−	3.28733i	0.282627	−	0.124875i
$694$	18.3677	−	18.3677i	0.697230	−	0.697230i
$695$	−4.80288	+	17.9246i	−0.182184	+	0.679919i
$696$	3.80443	+	4.68123i	0.144207	+	0.177442i
$697$	−0.272216	+	0.0729402i	−0.0103109	+	0.00276281i
$698$	−24.6052	+	14.2058i	−0.931322	+	0.537699i
$699$	4.19555	+	9.37895i	0.158690	+	0.354744i
$700$	6.81524	−	8.30770i	0.257592	−	0.314001i
$701$	−34.1302			−1.28908			−0.644541	−	0.764570i	$-0.722951\pi$
$701$	−34.1302			−1.28908			−0.644541	+	0.764570i	$0.722951\pi$
$702$	−18.3354	−	3.84857i	−0.692027	−	0.145255i
$703$	4.00127	−	6.93040i	0.150911	−	0.261385i
$704$	−0.989868	+	0.265234i	−0.0373071	+	0.00999639i
$705$	3.29943	−	4.55811i	0.124264	−	0.171668i
$706$		−	13.1830i		−	0.496149i
$707$	29.6638	+	4.89156i	1.11562	+	0.183966i
$708$	−3.58585	+	9.39078i	−0.134764	+	0.352927i
$709$	−6.98166	+	26.0559i	−0.262202	+	0.978550i	0.701739	+	0.712434i	$0.252407\pi$
$709$	−6.98166	+	26.0559i	−0.262202	+	0.978550i	−0.963941	+	0.266116i	$0.914259\pi$
$710$	−3.03407	−	11.3233i	−0.113867	−	0.424956i
$711$	−0.0294910	−	0.0896896i	−0.00110600	−	0.00336362i
$712$	5.58990	−	3.22733i	0.209490	−	0.120949i
$713$	1.12513	−	1.12513i	0.0421365	−	0.0421365i
$714$	−9.50525	+	16.2904i	−0.355725	+	0.609652i
$715$	−1.27371	−	3.34540i	−0.0476341	−	0.125111i
$716$	2.16277	−	1.24867i	0.0808263	−	0.0466651i
$717$	25.1158	+	30.9042i	0.937968	+	1.15414i
$718$	4.58974	−	7.94967i	0.171288	−	0.296679i
$719$	0.115201	+	0.199534i	0.00429627	+	0.00744135i	0.868166	−	0.496275i	$-0.165299\pi$
$719$	0.115201	+	0.199534i	0.00429627	+	0.00744135i	−0.863869	+	0.503716i	$0.831966\pi$
$720$	2.90189	−	0.162317i	0.108147	−	0.00604921i
$721$	29.7586	+	24.4126i	1.10827	+	0.909171i
$722$	8.02547	−	8.02547i	0.298677	−	0.298677i
$723$	6.77712	−	1.08561i	0.252044	−	0.0403743i
$724$	−0.389043	+	0.673842i	−0.0144587	+	0.0250432i
$725$	−7.07234	+	12.2496i	−0.262660	+	0.454940i
$726$	2.72585	+	17.0166i	0.101166	+	0.631547i
$727$		−	19.6490i		−	0.728740i	−0.931254	−	0.364370i	$-0.881284\pi$
$727$		−	19.6490i		−	0.728740i	0.931254	−	0.364370i	$-0.118716\pi$
$728$	−0.585733	+	9.52139i	−0.0217087	+	0.352886i
$729$	22.0097	+	15.6389i	0.815173	+	0.579217i
$730$	−12.3737	−	3.31552i	−0.457970	−	0.122713i
$731$	−30.9336	−	17.8595i	−1.14412	−	0.660559i
$732$	0.211493	−	2.04683i	0.00781699	−	0.0756532i
$733$	9.84548	+	2.63809i	0.363651	+	0.0974401i	0.436018	−	0.899938i	$-0.356388\pi$
$733$	9.84548	+	2.63809i	0.363651	+	0.0974401i	−0.0723665	+	0.997378i	$0.523055\pi$
$734$	−10.5572	−	10.5572i	−0.389674	−	0.389674i
$735$	4.08923	+	11.0114i	0.150833	+	0.406162i
$736$	0.450556	+	0.450556i	0.0166077	+	0.0166077i
$737$	−1.49586	+	0.863633i	−0.0551006	+	0.0318123i
$738$	0.195142	−	0.0641651i	0.00718328	−	0.00236195i
$739$	26.1139	−	6.99720i	0.960616	−	0.257396i	0.255755	−	0.966742i	$-0.417676\pi$
$739$	26.1139	−	6.99720i	0.960616	−	0.257396i	0.704861	+	0.709345i	$0.251009\pi$
$740$	−1.40151	−	2.42749i	−0.0515207	−	0.0892364i
$741$	0.0167901	−	17.2731i	0.000616801	−	0.634543i
$742$	19.1263	+	8.66151i	0.702148	+	0.317974i
$743$	19.6477	+	19.6477i	0.720804	+	0.720804i	0.968769	−	0.247965i	$-0.0797618\pi$
$743$	19.6477	+	19.6477i	0.720804	+	0.720804i	−0.247965	+	0.968769i	$0.579762\pi$
$744$	3.50370	+	2.53618i	0.128452	+	0.0929810i
$745$	17.1505	+	9.90187i	0.628347	+	0.362776i
$746$	20.8820	−	5.59532i	0.764545	−	0.204859i
$747$	−14.0860	−	21.5244i	−0.515379	−	0.787537i
$748$	2.98241	+	2.98241i	0.109048	+	0.109048i
$749$	−17.5226	−	14.3747i	−0.640263	−	0.525241i
$750$	6.20896	+	13.8798i	0.226719	+	0.506819i
$751$	−29.8497	+	17.2337i	−1.08923	+	0.628867i	−0.933371	−	0.358912i	$-0.883148\pi$
$751$	−29.8497	+	17.2337i	−1.08923	+	0.628867i	−0.155859	+	0.987779i	$0.549815\pi$
$752$	0.867903	+	3.23906i	0.0316492	+	0.118116i
$753$	−43.9683	−	4.54310i	−1.60229	−	0.165560i
$754$	−1.27847	−	12.4918i	−0.0465590	−	0.454925i
$755$			0.159921i			0.00582012i
$756$	6.25449	−	12.2426i	0.227474	−	0.445259i
$757$	17.4476			0.634144			0.317072	−	0.948401i	$-0.397300\pi$
$757$	17.4476			0.634144			0.317072	+	0.948401i	$0.397300\pi$
$758$	10.2276	+	17.7147i	0.371483	+	0.643428i
$759$	−0.877690	+	0.713299i	−0.0318581	+	0.0258911i
$760$	0.693542	+	2.58833i	0.0251574	+	0.0938887i
$761$	−47.8027	−	12.8087i	−1.73284	−	0.464314i	−0.752009	−	0.659152i	$-0.770915\pi$
$761$	−47.8027	−	12.8087i	−1.73284	−	0.464314i	−0.980835	+	0.194838i	$0.937582\pi$
$762$	32.7018	+	12.4871i	1.18466	+	0.452361i
$763$	2.08856	−	1.49726i	0.0756111	−	0.0542045i
$764$	−20.7922			−0.752234
$765$	−6.55027	−	10.0093i	−0.236826	−	0.361887i
$766$	24.9262	+	14.3912i	0.900621	+	0.519974i
$767$	16.9623	−	12.2532i	0.612474	−	0.442438i
$768$	−1.01561	+	1.40305i	−0.0366476	+	0.0506281i
$769$	16.7245	−	16.7245i	0.603100	−	0.603100i	−0.338034	−	0.941134i	$-0.609762\pi$
$769$	16.7245	−	16.7245i	0.603100	−	0.603100i	0.941134	+	0.338034i	$0.109762\pi$
$770$	2.61406	−	0.257978i	0.0942043	−	0.00929688i
$771$	7.66160	+	17.1271i	0.275926	+	0.616818i
$772$	−20.4978	−	5.49236i	−0.737731	−	0.197674i
$773$	9.89355	−	2.65097i	0.355846	−	0.0953487i	−0.0764673	−	0.997072i	$-0.524364\pi$
$773$	9.89355	−	2.65097i	0.355846	−	0.0953487i	0.432313	+	0.901723i	$0.357697\pi$
$774$	23.2396	+	11.7384i	0.835331	+	0.421929i
$775$	−2.62499	+	9.79659i	−0.0942924	+	0.351904i
$776$			12.2218i			0.438737i
$777$	−13.2585	−	0.0608742i	−0.475646	−	0.00218385i
$778$	4.10709	+	4.10709i	0.147246	+	0.147246i
$779$	0.0946958	+	0.164018i	0.00339283	+	0.00587655i
$780$	−5.23669	−	3.03020i	−0.187504	−	0.108498i
$781$	−6.20004	+	10.7388i	−0.221855	+	0.384264i
$782$	0.678748	−	2.53312i	0.0242720	−	0.0905843i
$783$	−5.50130	+	17.2402i	−0.196600	+	0.616114i
$784$	−6.62939	−	2.24749i	−0.236764	−	0.0802674i
$785$	−2.84783	−	2.84783i	−0.101643	−	0.101643i
$786$	−1.11809	−	6.97988i	−0.0398809	−	0.248964i
$787$	30.7983	−	8.25238i	1.09784	−	0.294166i	0.335956	−	0.941878i	$-0.390941\pi$
$787$	30.7983	−	8.25238i	1.09784	−	0.294166i	0.761885	+	0.647712i	$0.224274\pi$
$788$	−0.734646	−	2.74174i	−0.0261707	−	0.0976704i
$789$	3.19206	+	2.31060i	0.113640	+	0.0822596i
$790$		−	0.0304896i		−	0.00108477i
$791$	20.1509	−	7.58877i	0.716485	−	0.269825i
$792$	−2.29192	−	2.04910i	−0.0814397	−	0.0728116i
$793$	−2.70478	+	3.32154i	−0.0960496	+	0.117951i
$794$	18.4565	+	10.6558i	0.654995	+	0.378162i
$795$	−10.3341	+	8.39850i	−0.366512	+	0.297864i
$796$	6.58738	+	11.4097i	0.233484	+	0.404406i
$797$	−49.1361			−1.74049			−0.870245	−	0.492620i	$-0.836039\pi$
$797$	−49.1361			−1.74049			−0.870245	+	0.492620i	$0.836039\pi$
$798$	12.2279	+	3.33671i	0.432864	+	0.118118i
$799$	9.75906	−	9.75906i	0.345251	−	0.345251i
$800$	−3.92302	−	1.05117i	−0.138700	−	0.0371645i
$801$	17.2842	+	8.73033i	0.610708	+	0.308471i
$802$	2.94078	−	5.09359i	0.103843	−	0.179861i
$803$	6.77517	+	11.7349i	0.239091	+	0.414117i
$804$	−1.04141	+	2.72729i	−0.0367276	+	0.0961839i
$805$	−0.951588	−	1.32739i	−0.0335391	−	0.0467844i
$806$	−3.20371	−	8.41456i	−0.112846	−	0.296390i
$807$	22.7413	+	16.4615i	0.800533	+	0.579473i
$808$	−2.94103	−	10.9761i	−0.103465	−	0.386137i
$809$	−18.2677	−	10.5468i	−0.642257	−	0.370807i	0.143226	−	0.989690i	$-0.454252\pi$
$809$	−18.2677	−	10.5468i	−0.642257	−	0.370807i	−0.785483	+	0.618883i	$0.787586\pi$
$810$	5.17455	+	7.01782i	0.181815	+	0.246581i
$811$	1.50378	−	1.50378i	0.0528049	−	0.0528049i	−0.680211	−	0.733016i	$-0.738112\pi$
$811$	1.50378	−	1.50378i	0.0528049	−	0.0528049i	0.733016	+	0.680211i	$0.238112\pi$
$812$	9.09158	+	1.49920i	0.319052	+	0.0526117i
$813$	−20.0439	+	52.4918i	−0.702970	+	1.84097i
$814$	−0.767395	+	2.86396i	−0.0268972	+	0.100382i
$815$	−8.56119	−	4.94281i	−0.299885	−	0.173139i
$816$	7.09092	+	0.732681i	0.248232	+	0.0256490i
$817$	−6.21279	+	23.1865i	−0.217358	+	0.811191i
$818$	0.362271			0.0126665
$819$	−24.8633	+	14.1710i	−0.868794	+	0.495174i
$820$	0.0663377			0.00231661
$821$	9.50486	−	35.4726i	0.331722	−	1.23800i	−0.575658	−	0.817691i	$-0.695254\pi$
$821$	9.50486	−	35.4726i	0.331722	−	1.23800i	0.907380	−	0.420312i	$-0.138079\pi$
$822$	31.0817	+	3.21157i	1.08410	+	0.112016i
$823$	35.4546	+	20.4697i	1.23587	+	0.713530i	0.968248	−	0.249993i	$-0.0804284\pi$
$823$	35.4546	+	20.4697i	1.23587	+	0.713530i	0.267623	+	0.963524i	$0.413762\pi$
$824$	3.76535	−	14.0525i	0.131172	−	0.489541i
$825$	2.57161	−	6.73465i	0.0895320	−	0.234470i
$826$	5.41156	+	14.3697i	0.188292	+	0.499984i
$827$	−4.37880	+	4.37880i	−0.152266	+	0.152266i	−0.779129	−	0.626863i	$-0.784338\pi$
$827$	−4.37880	+	4.37880i	−0.152266	+	0.152266i	0.626863	+	0.779129i	$0.284338\pi$
$828$	−0.390855	+	1.87116i	−0.0135832	+	0.0650274i
$829$	1.09178	+	0.630338i	0.0379190	+	0.0218925i	0.518840	−	0.854872i	$-0.326364\pi$
$829$	1.09178	+	0.630338i	0.0379190	+	0.0218925i	−0.480921	+	0.876764i	$0.659697\pi$
$830$	−2.15005	−	8.02409i	−0.0746293	−	0.278520i
$831$	39.5378	+	28.6198i	1.37155	+	0.992810i
$832$	3.36959	−	1.28292i	0.116819	−	0.0444772i
$833$	5.63162	+	28.2544i	0.195124	+	0.978958i
$834$	11.8349	−	30.9936i	0.409807	−	1.07322i
$835$	12.3785	+	21.4403i	0.428377	+	0.741971i
$836$	1.41723	−	2.45472i	0.0490161	−	0.0848983i
$837$	−0.610736	+	12.9615i	−0.0211101	+	0.448015i
$838$	−4.05066	−	1.08537i	−0.139928	−	0.0374935i
$839$	30.2143	−	30.2143i	1.04311	−	1.04311i	0.0440850	−	0.999028i	$-0.485963\pi$
$839$	30.2143	−	30.2143i	1.04311	−	1.04311i	0.999028	−	0.0440850i	$-0.0140372\pi$
$840$	3.15368	−	3.12485i	0.108812	−	0.107818i
$841$	16.8708			0.581751
$842$	−0.949582	−	1.64472i	−0.0327248	−	0.0566810i
$843$	24.7597	−	20.1222i	0.852768	−	0.693045i
$844$	−12.1677	−	7.02502i	−0.418829	−	0.241811i
$845$	5.65642	+	11.2529i	0.194587	+	0.387110i
$846$	−6.70509	+	7.49963i	−0.230526	+	0.257843i
$847$	20.3526	+	16.6963i	0.699322	+	0.573690i
$848$		−	7.93578i		−	0.272516i
$849$	−28.9564	−	20.9604i	−0.993781	−	0.719358i
$850$	4.32635	+	16.1461i	0.148392	+	0.553808i
$851$	1.78073	−	0.477144i	0.0610425	−	0.0163563i
$852$	3.31496	+	20.6943i	0.113569	+	0.708973i
$853$	12.0364	+	12.0364i	0.412120	+	0.412120i	0.882476	−	0.470356i	$-0.155875\pi$
$853$	12.0364	+	12.0364i	0.412120	+	0.412120i	−0.470356	+	0.882476i	$0.655875\pi$
$854$	−1.83136	−	2.55461i	−0.0626680	−	0.0874171i
$855$	−5.35804	+	5.99296i	−0.183241	+	0.204955i
$856$	−2.21713	+	8.27445i	−0.0757800	+	0.282815i
$857$	3.54715	−	6.14385i	0.121168	−	0.209870i	−0.799060	−	0.601251i	$-0.794669\pi$
$857$	3.54715	−	6.14385i	0.121168	−	0.209870i	0.920229	+	0.391381i	$0.128003\pi$
$858$	1.65038	+	6.18333i	0.0563430	+	0.211095i
$859$	−19.5791	−	33.9120i	−0.668030	−	1.15706i	−0.978454	−	0.206464i	$-0.933804\pi$
$859$	−19.5791	−	33.9120i	−0.668030	−	1.15706i	0.310424	−	0.950598i	$-0.399529\pi$
$860$	5.94532	+	5.94532i	0.202734	+	0.202734i
$861$	0.158138	−	0.271022i	0.00538934	−	0.00923642i
$862$			32.5955i			1.11021i
$863$	3.31443	−	12.3696i	0.112824	−	0.421067i	−0.886290	−	0.463130i	$-0.846726\pi$
$863$	3.31443	−	12.3696i	0.112824	−	0.421067i	0.999115	+	0.0420631i	$0.0133931\pi$
$864$	−5.19039	−	0.244568i	−0.176581	−	0.00832036i
$865$	4.71149	−	1.26244i	0.160195	−	0.0429242i
$866$	21.1632	+	5.67067i	0.719155	+	0.192697i
$867$	0.0429032	+	0.0959079i	0.00145707	+	0.00325720i
$868$	6.57505	−	0.648882i	0.223172	−	0.0220245i
$869$	−0.0228051	+	0.0228051i	−0.000773610	+	0.000773610i
$870$	−3.42674	+	4.73398i	−0.116177	+	0.160497i
$871$	4.92623	−	3.55860i	0.166919	−	0.120579i
$872$	−0.841165	−	0.485647i	−0.0284855	−	0.0164461i
$873$	−30.6798	+	20.0774i	−1.03835	+	0.679519i
$874$	−1.76239			−0.0596138
$875$	21.1580	+	9.58159i	0.715271	+	0.323917i
$876$	21.3955	+	8.16981i	0.722886	+	0.276032i
$877$	−16.4221	−	4.40030i	−0.554536	−	0.148588i	−0.0293413	−	0.999569i	$-0.509341\pi$
$877$	−16.4221	−	4.40030i	−0.554536	−	0.148588i	−0.525195	+	0.850982i	$0.676008\pi$
$878$	1.75402	+	6.54609i	0.0591953	+	0.220920i
$879$	−41.6234	+	33.8274i	−1.40392	+	1.14097i
$880$	−0.496411	−	0.859810i	−0.0167340	−	0.0289842i
$881$	−31.1168			−1.04835			−0.524175	−	0.851610i	$-0.675626\pi$
$881$	−31.1168			−1.04835			−0.524175	+	0.851610i	$0.675626\pi$
$882$	−5.24871	−	20.3335i	−0.176733	−	0.684664i
$883$			36.5043i			1.22847i	0.789124	+	0.614234i	$0.210535\pi$
$883$			36.5043i			1.22847i	−0.789124	+	0.614234i	$0.789465\pi$
$884$	−11.5069	−	9.37027i	−0.387020	−	0.315156i
$885$	−9.68701	−	1.00093i	−0.325625	−	0.0336458i
$886$	9.06727	+	33.8395i	0.304621	+	1.13686i
$887$	−29.2300	+	16.8760i	−0.981449	+	0.566640i	−0.902707	−	0.430255i	$-0.858424\pi$
$887$	−29.2300	+	16.8760i	−0.981449	+	0.566640i	−0.0787416	+	0.996895i	$0.525090\pi$
$888$	2.04632	+	4.57445i	0.0686701	+	0.153509i
$889$	50.0400	−	18.8449i	1.67829	−	0.632036i
$890$	4.42177	+	4.42177i	0.148218	+	0.148218i
$891$	1.37870	−	9.11945i	0.0461881	−	0.305513i
$892$	−4.37344	+	1.17186i	−0.146434	+	0.0392368i
$893$	−8.03237	−	4.63749i	−0.268793	−	0.155188i
$894$	−28.6801	−	20.7604i	−0.959207	−	0.694331i
$895$	1.71081	+	1.71081i	0.0571861	+	0.0571861i
$896$	0.259843	+	2.63296i	0.00868074	+	0.0879610i
$897$	2.81646	−	2.81099i	0.0940388	−	0.0938562i
$898$	−1.51427	−	2.62280i	−0.0505320	−	0.0875240i
$899$	−8.40068	+	2.25096i	−0.280178	+	0.0750736i
$900$	−3.80586	−	11.5746i	−0.126862	−	0.385819i
$901$	−28.2858	+	16.3308i	−0.942337	+	0.544059i
$902$	−0.0496182	−	0.0496182i	−0.00165210	−	0.00165210i
$903$	38.4623	−	10.1169i	1.27994	−	0.336669i
$904$	−5.75481	−	5.75481i	−0.191402	−	0.191402i
$905$	−0.728131	−	0.195102i	−0.0242039	−	0.00648542i
$906$	0.0293856	−	0.284395i	0.000976270	−	0.00944839i
$907$	−7.54896	−	4.35840i	−0.250659	−	0.144718i	0.369407	−	0.929268i	$-0.379561\pi$
$907$	−7.54896	−	4.35840i	−0.250659	−	0.144718i	−0.620066	+	0.784550i	$0.712894\pi$
$908$	21.4347	+	5.74340i	0.711334	+	0.190601i
$909$	22.7213	−	25.4137i	0.753618	−	0.842921i
$910$	−9.05697	+	1.83933i	−0.300236	+	0.0609730i
$911$			1.75437i			0.0581250i	0.999578	+	0.0290625i	$0.00925219\pi$
$911$			1.75437i			0.0581250i	−0.999578	+	0.0290625i	$0.990748\pi$
$912$	−0.757750	−	4.73039i	−0.0250916	−	0.156639i
$913$	−4.39357	+	7.60989i	−0.145406	+	0.251850i
$914$	−15.8663	+	27.4813i	−0.524812	+	0.909001i
$915$	1.96845	−	0.315322i	0.0650751	−	0.0104242i
$916$	0.150921	−	0.150921i	0.00498657	−	0.00498657i
$917$	−8.34820	−	6.84846i	−0.275682	−	0.226156i
$918$	9.80944	+	19.0036i	0.323760	+	0.627212i
$919$	18.9448	+	32.8134i	0.624932	+	1.08241i	0.988554	+	0.150868i	$0.0482068\pi$
$919$	18.9448	+	32.8134i	0.624932	+	1.08241i	−0.363621	+	0.931547i	$0.618460\pi$
$920$	−0.308654	+	0.534605i	−0.0101760	+	0.0176254i
$921$	17.6150	+	21.6746i	0.580433	+	0.714203i
$922$	13.7205	−	7.92154i	0.451861	−	0.260882i
$923$	17.8538	−	39.8073i	0.587663	−	1.31027i
$924$	−4.69611	−	0.0215614i	−0.154491	−	0.000709319i
$925$	−8.30904	+	8.30904i	−0.273200	+	0.273200i
$926$	21.4591	−	12.3894i	0.705191	−	0.407142i
$927$	41.4608	−	13.6328i	1.36175	−	0.447760i
$928$	−0.901389	−	3.36403i	−0.0295896	−	0.110430i
$929$	−2.90941	+	10.8581i	−0.0954547	+	0.356242i	−0.997088	−	0.0762595i	$-0.975702\pi$
$929$	−2.90941	+	10.8581i	−0.0954547	+	0.356242i	0.901633	+	0.432501i	$0.142369\pi$
$930$	−1.49482	+	3.91469i	−0.0490169	+	0.128368i
$931$	17.3613	−	8.57010i	0.568995	−	0.280874i
$932$		−	5.93204i		−	0.194310i
$933$	−17.8000	+	24.5904i	−0.582746	+	0.805055i
$934$	−33.4767	+	8.97005i	−1.09539	+	0.293509i
$935$	−2.04310	+	3.53875i	−0.0668166	+	0.115730i
$936$	8.75585	+	6.35099i	0.286194	+	0.207588i
$937$	−12.1574			−0.397164			−0.198582	−	0.980084i	$-0.563634\pi$
$937$	−12.1574			−0.397164			−0.198582	+	0.980084i	$0.563634\pi$
$938$	1.57163	+	4.17326i	0.0513156	+	0.136262i
$939$	3.62839	+	8.11107i	0.118408	+	0.264695i
$940$	−2.81348	+	1.62436i	−0.0917655	+	0.0529809i
$941$	17.4796	−	4.68365i	0.569819	−	0.152683i	0.0376056	−	0.999293i	$-0.488027\pi$
$941$	17.4796	−	4.68365i	0.569819	−	0.152683i	0.532214	+	0.846610i	$0.321360\pi$
$942$	4.54113	+	5.58771i	0.147958	+	0.182057i
$943$	−0.0112923	+	0.0421435i	−0.000367728	+	0.00137238i
$944$	4.10376	−	4.10376i	0.133566	−	0.133566i
$945$	13.0249	+	2.78315i	0.423700	+	0.0905360i
$946$		−	8.89377i		−	0.289161i
$947$	−10.3457	−	2.77214i	−0.336192	−	0.0900823i	0.0867739	−	0.996228i	$-0.472344\pi$
$947$	−10.3457	−	2.77214i	−0.336192	−	0.0900823i	−0.422966	+	0.906146i	$0.639011\pi$
$948$	−0.00560248	+	0.0542211i	−0.000181960	+	0.00176102i
$949$	−27.9171	−	38.6461i	−0.906228	−	1.25450i
$950$	9.72849	−	5.61675i	0.315634	−	0.182231i
$951$	−16.6313	+	43.5547i	−0.539305	+	1.41236i
$952$	8.85004	−	6.34446i	0.286831	−	0.205625i
$953$	−4.17491			−0.135238			−0.0676192	−	0.997711i	$-0.521540\pi$
$953$	−4.17491			−0.135238			−0.0676192	+	0.997711i	$0.521540\pi$
$954$	19.9208	−	13.0366i	0.644960	−	0.422074i
$955$	−5.21356	−	19.4573i	−0.168707	−	0.629622i
$956$	−5.95072	−	22.2084i	−0.192460	−	0.718271i
$957$	6.10392	−	0.977771i	0.197312	−	0.0316069i
$958$	5.49022			0.177381
$959$	38.7924	−	27.8097i	1.25267	−	0.898023i
$960$	−1.56763	−	0.598595i	−0.0505950	−	0.0193196i
$961$	21.4462	−	12.3820i	0.691813	−	0.399419i
$962$	1.66003	−	10.2989i	0.0535214	−	0.332050i
$963$	−24.4131	+	8.02734i	−0.786702	+	0.258677i
$964$	−3.82763	−	1.02561i	−0.123280	−	0.0330327i
$965$		−	20.5590i		−	0.661816i
$966$	1.44834	+	2.53542i	0.0465997	+	0.0815758i
$967$	1.37016	−	1.37016i	0.0440615	−	0.0440615i	−0.684733	−	0.728794i	$-0.740081\pi$
$967$	1.37016	−	1.37016i	0.0440615	−	0.0440615i	0.728794	+	0.684733i	$0.240081\pi$
$968$	2.57520	−	9.61078i	0.0827701	−	0.308902i
$969$	−15.3014	+	12.4354i	−0.491551	+	0.399483i
$970$	−11.4371	+	3.06457i	−0.367224	+	0.0983975i
$971$	−17.8130	+	10.2843i	−0.571645	+	0.330039i	−0.757806	−	0.652480i	$-0.773729\pi$
$971$	−17.8130	+	10.2843i	−0.571645	+	0.330039i	0.186161	+	0.982519i	$0.440395\pi$
$972$	−7.91262	−	13.4309i	−0.253797	−	0.430798i
$973$	−17.8605	−	47.4261i	−0.572581	−	1.52041i
$974$	−24.8432			−0.796029
$975$	−6.58837	+	24.4929i	−0.210997	+	0.784399i
$976$	−0.594016	+	1.02887i	−0.0190140	+	0.0329332i
$977$	−33.7718	+	9.04912i	−1.08045	+	0.289507i	−0.754782	−	0.655976i	$-0.772257\pi$
$977$	−33.7718	+	9.04912i	−1.08045	+	0.289507i	−0.325673	+	0.945483i	$0.605591\pi$
$978$	14.3165	+	10.3631i	0.457792	+	0.331377i
$979$		−	6.61465i		−	0.211405i
$980$	0.440900	−	6.76732i	0.0140840	−	0.216174i
$981$	−0.162734	−	2.90933i	−0.00519569	−	0.0928879i
$982$	3.55426	−	13.2647i	0.113421	−	0.423293i
$983$	4.81096	+	17.9548i	0.153446	+	0.572668i	0.999233	+	0.0391479i	$0.0124644\pi$
$983$	4.81096	+	17.9548i	0.153446	+	0.572668i	−0.845788	+	0.533520i	$0.820869\pi$
$984$	−0.117971	−	0.0121896i	−0.00376079	−	0.000388590i
$985$	2.38150	−	1.37496i	0.0758809	−	0.0438099i
$986$	−10.1356	+	10.1356i	−0.322783	+	0.322783i
$987$	−0.0705535	+	15.3667i	−0.00224574	+	0.489127i
$988$	−4.08110	+	9.09935i	−0.129837	+	0.289489i
$989$	−4.78903	+	2.76494i	−0.152282	+	0.0879201i
$990$	1.34285	−	2.65857i	0.0426787	−	0.0844950i
$991$	12.7044	−	22.0047i	0.403569	−	0.699001i	−0.590585	−	0.806975i	$-0.701103\pi$
$991$	12.7044	−	22.0047i	0.403569	−	0.699001i	0.994154	+	0.107974i	$0.0344364\pi$
$992$	−1.24860	−	2.16264i	−0.0396432	−	0.0686640i
$993$	−8.73453	−	3.33526i	−0.277182	−	0.105841i
$994$	24.7511	+	20.3046i	0.785058	+	0.644024i
$995$	−9.02539	+	9.02539i	−0.286124	+	0.286124i
$996$	2.34910	+	14.6647i	0.0744341	+	0.464669i
$997$	−13.2786	+	22.9991i	−0.420536	+	0.728390i	−0.995992	−	0.0894429i	$-0.971491\pi$
$997$	−13.2786	+	22.9991i	−0.420536	+	0.728390i	0.575456	+	0.817833i	$0.304825\pi$
$998$	12.9326	−	22.3999i	0.409373	−	0.709055i
$999$	−8.12141	+	12.6515i	−0.256950	+	0.400275i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bv.a.473.18	yes	144
3.2	odd	2	inner	546.2.bv.a.473.25	yes	144
7.2	even	3	inner	546.2.bv.a.317.25	yes	144
13.8	odd	4	inner	546.2.bv.a.515.18	yes	144
21.2	odd	6	inner	546.2.bv.a.317.18	✓	144
39.8	even	4	inner	546.2.bv.a.515.25	yes	144
91.86	odd	12	inner	546.2.bv.a.359.25	yes	144
273.86	even	12	inner	546.2.bv.a.359.18	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.18	✓	144	21.2	odd	6	inner
546.2.bv.a.317.25	yes	144	7.2	even	3	inner
546.2.bv.a.359.18	yes	144	273.86	even	12	inner
546.2.bv.a.359.25	yes	144	91.86	odd	12	inner
546.2.bv.a.473.18	yes	144	1.1	even	1	trivial
546.2.bv.a.473.25	yes	144	3.2	odd	2	inner
546.2.bv.a.515.18	yes	144	13.8	odd	4	inner
546.2.bv.a.515.25	yes	144	39.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(1.72288 + 0.178019i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.250746 - 0.935798i) q^{5} +(-0.617867 + 1.61810i) q^{6} +(0.932449 + 2.47599i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.93662 + 0.613411i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(1.72288 + 0.178019i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.250746 - 0.935798i) q^{5} +(-0.617867 + 1.61810i) q^{6} +(0.932449 + 2.47599i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.93662 + 0.613411i) q^{9} +(0.839013 + 0.484404i) q^{10} +(-0.265234 - 0.989868i) q^{11} +(-1.40305 - 1.01561i) q^{12} +(1.28292 + 3.36959i) q^{13} +(-2.63296 + 0.259843i) q^{14} +(0.598595 - 1.56763i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.05787 - 3.56434i) q^{17} +(-1.35256 + 2.67779i) q^{18} +(-2.67167 - 0.715871i) q^{19} +(-0.685051 + 0.685051i) q^{20} +(1.16572 + 4.43183i) q^{21} +1.02479 q^{22} +(-0.318592 - 0.551817i) q^{23} +(1.34414 - 1.09238i) q^{24} +(3.51728 + 2.03070i) q^{25} +(-3.58682 + 0.367090i) q^{26} +(4.95024 + 1.57961i) q^{27} +(0.430471 - 2.61050i) q^{28} +3.48270i q^{29} +(1.35928 + 0.983930i) q^{30} +(0.646325 + 2.41212i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-0.280751 - 1.75264i) q^{33} +(2.91027 + 2.91027i) q^{34} +(2.55084 - 0.251738i) q^{35} +(-2.23648 - 1.99954i) q^{36} +(-0.748834 + 2.79469i) q^{37} +(1.38296 - 2.39535i) q^{38} +(1.61046 + 6.03377i) q^{39} +(-0.484404 - 0.839013i) q^{40} +(-0.0484181 - 0.0484181i) q^{41} +(-4.58253 - 0.0210399i) q^{42} -8.67865i q^{43} +(-0.265234 + 0.989868i) q^{44} +(1.31037 - 2.59427i) q^{45} +(0.615472 - 0.164915i) q^{46} +(3.23906 + 0.867903i) q^{47} +(0.707270 + 1.58107i) q^{48} +(-5.26108 + 4.61748i) q^{49} +(-2.87185 + 2.87185i) q^{50} +(4.17998 - 5.77458i) q^{51} +(0.573754 - 3.55961i) q^{52} +(-6.87259 - 3.96789i) q^{53} +(-2.80700 + 4.37273i) q^{54} -0.992823 q^{55} +(2.41013 + 1.09145i) q^{56} +(-4.47551 - 1.70897i) q^{57} +(-3.36403 - 0.901389i) q^{58} +(-1.50208 - 5.60584i) q^{59} +(-1.30221 + 1.05831i) q^{60} +(0.594016 + 1.02887i) q^{61} -2.49721 q^{62} +(1.21945 + 7.84302i) q^{63} -1.00000i q^{64} +(3.47494 - 0.355640i) q^{65} +(1.76558 + 0.182432i) q^{66} +(-0.436237 - 1.62806i) q^{67} +(-3.56434 + 2.05787i) q^{68} +(-0.450660 - 1.00743i) q^{69} +(-0.417044 + 2.52907i) q^{70} +(-8.55610 - 8.55610i) q^{71} +(2.51025 - 1.64276i) q^{72} +(-12.7721 + 3.42226i) q^{73} +(-2.50565 - 1.44664i) q^{74} +(5.69835 + 4.12480i) q^{75} +(1.95579 + 1.95579i) q^{76} +(2.20359 - 1.57972i) q^{77} +(-6.24500 - 0.00607038i) q^{78} +(-0.0157356 - 0.0272549i) q^{79} +(0.935798 - 0.250746i) q^{80} +(8.24745 + 3.60271i) q^{81} +(0.0592998 - 0.0342367i) q^{82} +(-6.06316 - 6.06316i) q^{83} +(1.20637 - 4.42094i) q^{84} +(-2.81950 - 2.81950i) q^{85} +(8.38293 + 2.24620i) q^{86} +(-0.619988 + 6.00027i) q^{87} +(-0.887491 - 0.512393i) q^{88} +(6.23472 + 1.67059i) q^{89} +(2.16672 + 1.93717i) q^{90} +(-7.14682 + 6.31847i) q^{91} +0.637183i q^{92} +(0.684135 + 4.27084i) q^{93} +(-1.67666 + 2.90406i) q^{94} +(-1.33982 + 2.32064i) q^{95} +(-1.71025 + 0.273960i) q^{96} +(-8.64212 + 8.64212i) q^{97} +(-3.09847 - 6.27690i) q^{98} +(-0.171696 - 3.06956i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 16 q^{7}+O(q^{10}) \) 144 * q - 16 * q^7	\( 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) \) 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Introduction

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