LMFDB - Embedded newform 126.2.m.a.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(41,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("126.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.m (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.00611506547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.1
Root			$1.62181 - 0.608059i$ of defining polynomial
Character	$\chi$	$=$	126.41
Dual form			126.2.m.a.83.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-1.62181 + 0.608059i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.94556 - 3.36980i) q^{5} +(1.10050 - 1.33750i) q^{6} +(0.343982 + 2.62329i) q^{7} +1.00000i q^{8} +(2.26053 - 1.97231i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.62181 + 0.608059i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.94556 - 3.36980i) q^{5} +(1.10050 - 1.33750i) q^{6} +(0.343982 + 2.62329i) q^{7} +1.00000i q^{8} +(2.26053 - 1.97231i) q^{9} +3.89111i q^{10} +(3.41614 - 1.97231i) q^{11} +(-0.284310 + 1.70856i) q^{12} +(2.46687 + 1.42425i) q^{13} +(-1.60954 - 2.09985i) q^{14} +(-1.10628 + 6.64819i) q^{15} +(-0.500000 - 0.866025i) q^{16} +0.742117 q^{17} +(-0.971521 + 2.83834i) q^{18} -1.78474i q^{19} +(-1.94556 - 3.36980i) q^{20} +(-2.15299 - 4.04532i) q^{21} +(-1.97231 + 3.41614i) q^{22} +(-5.41535 - 3.12656i) q^{23} +(-0.608059 - 1.62181i) q^{24} +(-5.07039 - 8.78217i) q^{25} -2.84849 q^{26} +(-2.46687 + 4.57324i) q^{27} +(2.44383 + 1.01375i) q^{28} +(-2.50079 + 1.44383i) q^{29} +(-2.36603 - 6.31064i) q^{30} +(3.04125 + 1.75587i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.34105 + 5.27592i) q^{33} +(-0.642692 + 0.371058i) q^{34} +(9.50923 + 3.94462i) q^{35} +(-0.577806 - 2.94383i) q^{36} +3.00158 q^{37} +(0.892369 + 1.54563i) q^{38} +(-4.86681 - 0.809856i) q^{39} +(3.36980 + 1.94556i) q^{40} +(-5.24705 + 9.08816i) q^{41} +(3.88721 + 2.42686i) q^{42} +(0.471521 + 0.816699i) q^{43} -3.94462i q^{44} +(-2.24831 - 11.4548i) q^{45} +6.25311 q^{46} +(1.09263 + 1.89248i) q^{47} +(1.33750 + 1.10050i) q^{48} +(-6.76335 + 1.80473i) q^{49} +(8.78217 + 5.07039i) q^{50} +(-1.20357 + 0.451251i) q^{51} +(2.46687 - 1.42425i) q^{52} +(-0.150252 - 5.19398i) q^{54} -15.3490i q^{55} +(-2.62329 + 0.343982i) q^{56} +(1.08523 + 2.89450i) q^{57} +(1.44383 - 2.50079i) q^{58} +(0.0105673 - 0.0183031i) q^{59} +(5.20436 + 4.28217i) q^{60} +(-2.13832 + 1.23456i) q^{61} -3.51174 q^{62} +(5.95153 + 5.25160i) q^{63} -1.00000 q^{64} +(9.59886 - 5.54191i) q^{65} +(1.12150 - 6.73961i) q^{66} +(-6.72463 + 11.6474i) q^{67} +(0.371058 - 0.642692i) q^{68} +(10.6838 + 1.77782i) q^{69} +(-10.2075 + 1.33847i) q^{70} -1.94304i q^{71} +(1.97231 + 2.26053i) q^{72} +4.85486i q^{73} +(-2.59944 + 1.50079i) q^{74} +(13.5633 + 11.1599i) q^{75} +(-1.54563 - 0.892369i) q^{76} +(6.34904 + 8.28311i) q^{77} +(4.61971 - 1.73205i) q^{78} +(-1.81806 - 3.14898i) q^{79} -3.89111 q^{80} +(1.21999 - 8.91693i) q^{81} -10.4941i q^{82} +(-4.02998 - 6.98012i) q^{83} +(-4.57985 - 0.158118i) q^{84} +(1.44383 - 2.50079i) q^{85} +(-0.816699 - 0.471521i) q^{86} +(3.17787 - 3.86224i) q^{87} +(1.97231 + 3.41614i) q^{88} -9.26646 q^{89} +(7.67448 + 8.79598i) q^{90} +(-2.88766 + 6.96124i) q^{91} +(-5.41535 + 3.12656i) q^{92} +(-6.00000 - 0.998423i) q^{93} +(-1.89248 - 1.09263i) q^{94} +(-6.01422 - 3.47231i) q^{95} +(-1.70856 - 0.284310i) q^{96} +(16.2983 - 9.40980i) q^{97} +(4.95487 - 4.94462i) q^{98} +(3.83228 - 11.1962i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 2 q^{7} + 12 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 2 * q^7 + 12 * q^9	$ 16 q + 8 q^{4} + 2 q^{7} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 8 q^{16} - 12 q^{18} + 18 q^{21} - 48 q^{23} - 8 q^{25} + 4 q^{28} - 12 q^{29} - 24 q^{30} + 12 q^{36} - 8 q^{37} - 36 q^{39} - 12 q^{42} + 4 q^{43} + 24 q^{46} - 8 q^{49} + 60 q^{50} + 12 q^{51} - 6 q^{56} + 48 q^{57} - 12 q^{58} + 24 q^{60} + 24 q^{63} - 16 q^{64} + 84 q^{65} - 28 q^{67} + 36 q^{74} + 78 q^{77} - 24 q^{78} - 4 q^{79} + 36 q^{81} + 18 q^{84} - 12 q^{85} - 24 q^{86} + 24 q^{91} - 48 q^{92} - 96 q^{93} + 12 q^{95} - 72 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^7 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 8 * q^16 - 12 * q^18 + 18 * q^21 - 48 * q^23 - 8 * q^25 + 4 * q^28 - 12 * q^29 - 24 * q^30 + 12 * q^36 - 8 * q^37 - 36 * q^39 - 12 * q^42 + 4 * q^43 + 24 * q^46 - 8 * q^49 + 60 * q^50 + 12 * q^51 - 6 * q^56 + 48 * q^57 - 12 * q^58 + 24 * q^60 + 24 * q^63 - 16 * q^64 + 84 * q^65 - 28 * q^67 + 36 * q^74 + 78 * q^77 - 24 * q^78 - 4 * q^79 + 36 * q^81 + 18 * q^84 - 12 * q^85 - 24 * q^86 + 24 * q^91 - 48 * q^92 - 96 * q^93 + 12 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.62181	+	0.608059i	−0.936352	+	0.351063i
$3$	−1.62181	+	0.608059i	−0.936352	+	0.351063i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.94556	−	3.36980i	0.870080	−	1.50702i	0.00816625	−	0.999967i	$-0.497401\pi$
$5$	1.94556	−	3.36980i	0.870080	−	1.50702i	0.861913	−	0.507056i	$-0.169266\pi$
$6$	1.10050	−	1.33750i	0.449277	−	0.546032i
$7$	0.343982	+	2.62329i	0.130013	+	0.991512i
$7$	0.343982	+	2.62329i	0.130013	+	0.991512i
$8$			1.00000i			0.353553i
$9$	2.26053	−	1.97231i	0.753510	−	0.657437i
$10$			3.89111i			1.23048i
$11$	3.41614	−	1.97231i	1.03001	−	0.594674i	0.113019	−	0.993593i	$-0.463948\pi$
$11$	3.41614	−	1.97231i	1.03001	−	0.594674i	0.916986	+	0.398919i	$0.130615\pi$
$12$	−0.284310	+	1.70856i	−0.0820733	+	0.493218i
$13$	2.46687	+	1.42425i	0.684186	+	0.395015i	0.801430	−	0.598088i	$-0.204073\pi$
$13$	2.46687	+	1.42425i	0.684186	+	0.395015i	−0.117244	+	0.993103i	$0.537406\pi$
$14$	−1.60954	−	2.09985i	−0.430169	−	0.561208i
$15$	−1.10628	+	6.64819i	−0.285641	+	1.71656i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.742117			0.179990			0.0899949	−	0.995942i	$-0.471315\pi$
$17$	0.742117			0.179990			0.0899949	+	0.995942i	$0.471315\pi$
$18$	−0.971521	+	2.83834i	−0.228990	+	0.669002i
$19$		−	1.78474i		−	0.409447i	−0.978820	−	0.204723i	$-0.934370\pi$
$19$		−	1.78474i		−	0.409447i	0.978820	−	0.204723i	$-0.0656295\pi$
$20$	−1.94556	−	3.36980i	−0.435040	−	0.753511i
$21$	−2.15299	−	4.04532i	−0.469821	−	0.882762i
$22$	−1.97231	+	3.41614i	−0.420498	+	0.728324i
$23$	−5.41535	−	3.12656i	−1.12918	−	0.651932i	−0.185451	−	0.982654i	$-0.559374\pi$
$23$	−5.41535	−	3.12656i	−1.12918	−	0.651932i	−0.943728	+	0.330722i	$0.892708\pi$
$24$	−0.608059	−	1.62181i	−0.124119	−	0.331050i
$25$	−5.07039	−	8.78217i	−1.01408	−	1.75643i
$26$	−2.84849			−0.558636
$27$	−2.46687	+	4.57324i	−0.474749	+	0.880121i
$28$	2.44383	+	1.01375i	0.461841	+	0.191581i
$29$	−2.50079	+	1.44383i	−0.464385	+	0.268113i	−0.713886	−	0.700262i	$-0.753067\pi$
$29$	−2.50079	+	1.44383i	−0.464385	+	0.268113i	0.249501	+	0.968374i	$0.419733\pi$
$30$	−2.36603	−	6.31064i	−0.431975	−	1.15216i
$31$	3.04125	+	1.75587i	0.546225	+	0.315363i	0.747598	−	0.664152i	$-0.231207\pi$
$31$	3.04125	+	1.75587i	0.546225	+	0.315363i	−0.201373	+	0.979515i	$0.564540\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−4.34105	+	5.27592i	−0.755680	+	0.918420i
$34$	−0.642692	+	0.371058i	−0.110221	+	0.0636360i
$35$	9.50923	+	3.94462i	1.60735	+	0.666762i
$36$	−0.577806	−	2.94383i	−0.0963009	−	0.490638i
$37$	3.00158			0.493456			0.246728	−	0.969085i	$-0.420645\pi$
$37$	3.00158			0.493456			0.246728	+	0.969085i	$0.420645\pi$
$38$	0.892369	+	1.54563i	0.144761	+	0.250734i
$39$	−4.86681	−	0.809856i	−0.779314	−	0.129681i
$40$	3.36980	+	1.94556i	0.532813	+	0.307620i
$41$	−5.24705	+	9.08816i	−0.819452	+	1.41933i	0.0866345	+	0.996240i	$0.472389\pi$
$41$	−5.24705	+	9.08816i	−0.819452	+	1.41933i	−0.906087	+	0.423092i	$0.860945\pi$
$42$	3.88721	+	2.42686i	0.599809	+	0.374472i
$43$	0.471521	+	0.816699i	0.0719063	+	0.124545i	0.899737	−	0.436433i	$-0.143758\pi$
$43$	0.471521	+	0.816699i	0.0719063	+	0.124545i	−0.827830	+	0.560978i	$0.810425\pi$
$44$		−	3.94462i		−	0.594674i
$45$	−2.24831	−	11.4548i	−0.335158	−	1.70758i
$46$	6.25311			0.921971
$47$	1.09263	+	1.89248i	0.159376	+	0.276047i	0.934644	−	0.355585i	$-0.115718\pi$
$47$	1.09263	+	1.89248i	0.159376	+	0.276047i	−0.775268	+	0.631633i	$0.782385\pi$
$48$	1.33750	+	1.10050i	0.193051	+	0.158843i
$49$	−6.76335	+	1.80473i	−0.966193	+	0.257819i
$50$	8.78217	+	5.07039i	1.24199	+	0.717061i
$51$	−1.20357	+	0.451251i	−0.168534	+	0.0631877i
$52$	2.46687	−	1.42425i	0.342093	−	0.197507i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	−0.150252	−	5.19398i	−0.0204467	−	0.706811i
$55$		−	15.3490i		−	2.06965i
$56$	−2.62329	+	0.343982i	−0.350553	+	0.0459665i
$57$	1.08523	+	2.89450i	0.143742	+	0.383386i
$58$	1.44383	−	2.50079i	0.189584	−	0.328370i
$59$	0.0105673	−	0.0183031i	0.00137575	−	0.00238286i	−0.865337	−	0.501191i	$-0.832895\pi$
$59$	0.0105673	−	0.0183031i	0.00137575	−	0.00238286i	0.866712	+	0.498808i	$0.166229\pi$
$60$	5.20436	+	4.28217i	0.671880	+	0.552825i
$61$	−2.13832	+	1.23456i	−0.273783	+	0.158069i	−0.630606	−	0.776103i	$-0.717193\pi$
$61$	−2.13832	+	1.23456i	−0.273783	+	0.158069i	0.356822	+	0.934172i	$0.383860\pi$
$62$	−3.51174			−0.445991
$63$	5.95153	+	5.25160i	0.749822	+	0.661639i
$64$	−1.00000			−0.125000
$65$	9.59886	−	5.54191i	1.19059	−	0.687389i
$66$	1.12150	−	6.73961i	0.138047	−	0.829588i
$67$	−6.72463	+	11.6474i	−0.821544	+	1.42296i	0.0829874	+	0.996551i	$0.473554\pi$
$67$	−6.72463	+	11.6474i	−0.821544	+	1.42296i	−0.904532	+	0.426406i	$0.859779\pi$
$68$	0.371058	−	0.642692i	0.0449974	−	0.0779379i
$69$	10.6838	+	1.77782i	1.28618	+	0.214025i
$70$	−10.2075	+	1.33847i	−1.22003	+	0.159978i
$71$		−	1.94304i		−	0.230597i	−0.993331	−	0.115298i	$-0.963218\pi$
$71$		−	1.94304i		−	0.230597i	0.993331	−	0.115298i	$-0.0367824\pi$
$72$	1.97231	+	2.26053i	0.232439	+	0.266406i
$73$			4.85486i			0.568218i	0.958792	+	0.284109i	$0.0916978\pi$
$73$			4.85486i			0.568218i	−0.958792	+	0.284109i	$0.908302\pi$
$74$	−2.59944	+	1.50079i	−0.302179	+	0.174463i
$75$	13.5633	+	11.1599i	1.56615	+	1.28863i
$76$	−1.54563	−	0.892369i	−0.177296	−	0.102362i
$77$	6.34904	+	8.28311i	0.723540	+	0.943948i
$78$	4.61971	−	1.73205i	0.523079	−	0.196116i
$79$	−1.81806	−	3.14898i	−0.204548	−	0.354288i	0.745440	−	0.666572i	$-0.232239\pi$
$79$	−1.81806	−	3.14898i	−0.204548	−	0.354288i	−0.949989	+	0.312284i	$0.898906\pi$
$80$	−3.89111			−0.435040
$81$	1.21999	−	8.91693i	0.135554	−	0.990770i
$82$		−	10.4941i		−	1.15888i
$83$	−4.02998	−	6.98012i	−0.442347	−	0.766168i	0.555516	−	0.831506i	$-0.312521\pi$
$83$	−4.02998	−	6.98012i	−0.442347	−	0.766168i	−0.997863	+	0.0653378i	$0.979188\pi$
$84$	−4.57985	−	0.158118i	−0.499702	−	0.0172520i
$85$	1.44383	−	2.50079i	0.156605	−	0.271249i
$86$	−0.816699	−	0.471521i	−0.0880669	−	0.0508454i
$87$	3.17787	−	3.86224i	0.340703	−	0.414076i
$88$	1.97231	+	3.41614i	0.210249	+	0.364162i
$89$	−9.26646			−0.982243			−0.491122	−	0.871091i	$-0.663413\pi$
$89$	−9.26646			−0.982243			−0.491122	+	0.871091i	$0.663413\pi$
$90$	7.67448	+	8.79598i	0.808962	+	0.927178i
$91$	−2.88766	+	6.96124i	−0.302709	+	0.729736i
$92$	−5.41535	+	3.12656i	−0.564589	+	0.325966i
$93$	−6.00000	−	0.998423i	−0.622171	−	0.103532i
$94$	−1.89248	−	1.09263i	−0.195195	−	0.112696i
$95$	−6.01422	−	3.47231i	−0.617046	−	0.356251i
$96$	−1.70856	−	0.284310i	−0.174379	−	0.0290173i
$97$	16.2983	−	9.40980i	1.65484	−	0.955421i	0.679794	−	0.733403i	$-0.262069\pi$
$97$	16.2983	−	9.40980i	1.65484	−	0.955421i	0.975043	−	0.222018i	$-0.0712643\pi$
$98$	4.95487	−	4.94462i	0.500517	−	0.499482i
$99$	3.83228	−	11.1962i	0.385159	−	1.12526i
$100$	−10.1408			−1.01408
$101$	4.14079	+	7.17206i	0.412024	+	0.713647i	0.995111	−	0.0987631i	$-0.0314886\pi$
$101$	4.14079	+	7.17206i	0.412024	+	0.713647i	−0.583087	+	0.812410i	$0.698155\pi$
$102$	0.816699	−	0.992580i	0.0808652	−	0.0982801i
$103$	−14.7646	−	8.52435i	−1.45480	−	0.839929i	−0.456051	−	0.889953i	$-0.650737\pi$
$103$	−14.7646	−	8.52435i	−1.45480	−	0.839929i	−0.998748	+	0.0500247i	$0.984070\pi$
$104$	−1.42425	+	2.46687i	−0.139659	+	0.241896i
$105$	−17.8207	−	0.615254i	−1.73912	−	0.0600426i
$106$		0			0
$107$			14.3369i			1.38600i	0.720936	+	0.693001i	$0.243712\pi$
$107$			14.3369i			1.38600i	−0.720936	+	0.693001i	$0.756288\pi$
$108$	2.72711	+	4.42299i	0.262416	+	0.425603i
$109$	11.2800			1.08042			0.540212	−	0.841529i	$-0.318344\pi$
$109$	11.2800			1.08042			0.540212	+	0.841529i	$0.318344\pi$
$110$	7.67448	+	13.2926i	0.731733	+	1.26740i
$111$	−4.86799	+	1.82513i	−0.462049	+	0.173234i
$112$	2.09985	−	1.60954i	0.198417	−	0.152088i
$113$	−8.51501	−	4.91614i	−0.801024	−	0.462472i	0.0428049	−	0.999083i	$-0.486371\pi$
$113$	−8.51501	−	4.91614i	−0.801024	−	0.462472i	−0.843829	+	0.536612i	$0.819704\pi$
$114$	−2.38708	−	1.96410i	−0.223571	−	0.183955i
$115$	−21.0718	+	12.1658i	−1.96495	+	1.13447i
$116$			2.88766i			0.268113i
$117$	8.38548	−	1.64588i	0.775238	−	0.152161i
$118$			0.0211346i			0.00194560i
$119$	0.255275	+	1.94679i	0.0234010	+	0.178462i
$120$	−6.64819	−	1.10628i	−0.606894	−	0.100989i
$121$	2.28001	−	3.94910i	0.207274	−	0.359009i
$122$	1.23456	−	2.13832i	0.111772	−	0.193594i
$123$	2.98358	−	17.9298i	0.269021	−	1.61667i
$124$	3.04125	−	1.75587i	0.273112	−	0.157682i
$125$	−20.0033			−1.78915
$126$	−7.77998	−	1.57225i	−0.693095	−	0.140067i
$127$	2.94462			0.261293			0.130646	−	0.991429i	$-0.458295\pi$
$127$	2.94462			0.261293			0.130646	+	0.991429i	$0.458295\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−1.26132	−	1.03782i	−0.111053	−	0.0913747i
$130$	−5.54191	+	9.59886i	−0.486057	+	0.841876i
$131$	7.53255	−	13.0468i	0.658122	−	1.13990i	−0.322979	−	0.946406i	$-0.604684\pi$
$131$	7.53255	−	13.0468i	0.658122	−	1.13990i	0.981101	−	0.193495i	$-0.0619823\pi$
$132$	2.39856	+	6.39742i	0.208768	+	0.556824i
$133$	4.68189	−	0.613917i	0.405972	−	0.0532334i
$134$		−	13.4493i		−	1.16184i
$135$	10.6115	+	17.2104i	0.913293	+	1.48123i
$136$			0.742117i			0.0636360i
$137$	−13.6139	+	7.85997i	−1.16311	+	0.671523i	−0.952048	−	0.305950i	$-0.901026\pi$
$137$	−13.6139	+	7.85997i	−1.16311	+	0.671523i	−0.211064	+	0.977472i	$0.567693\pi$
$138$	−10.1414	+	3.80226i	−0.863289	+	0.323670i
$139$	2.86373	+	1.65337i	0.242898	+	0.140237i	0.616508	−	0.787349i	$-0.288547\pi$
$139$	2.86373	+	1.65337i	0.242898	+	0.140237i	−0.373610	+	0.927586i	$0.621880\pi$
$140$	8.17075	−	6.26292i	0.690555	−	0.529313i
$141$	−2.92277	−	2.40487i	−0.246142	−	0.202526i
$142$	0.971521	+	1.68272i	0.0815282	+	0.141211i
$143$	11.2362			0.939620
$144$	−2.83834	−	0.971521i	−0.236528	−	0.0809601i
$145$			11.2362i			0.933118i
$146$	−2.42743	−	4.20443i	−0.200896	−	0.347961i
$147$	9.87149	−	7.03944i	0.814186	−	0.580604i
$148$	1.50079	−	2.59944i	0.123364	−	0.213673i
$149$	9.52765	+	5.50079i	0.780535	+	0.450642i	0.836620	−	0.547784i	$-0.184528\pi$
$149$	9.52765	+	5.50079i	0.780535	+	0.450642i	−0.0560848	+	0.998426i	$0.517862\pi$
$150$	−17.3261	−	2.88313i	−1.41467	−	0.235406i
$151$	0.719988	+	1.24706i	0.0585918	+	0.101484i	0.893834	−	0.448399i	$-0.148006\pi$
$151$	0.719988	+	1.24706i	0.0585918	+	0.101484i	−0.835242	+	0.549883i	$0.814672\pi$
$152$	1.78474			0.144761
$153$	1.67758	−	1.46368i	0.135624	−	0.118332i
$154$	−9.63998	−	3.99886i	−0.776812	−	0.322237i
$155$	11.8339	−	6.83228i	0.950518	−	0.548782i
$156$	−3.13476	+	3.80986i	−0.250982	+	0.305033i
$157$	14.3822	+	8.30354i	1.14782	+	0.662695i	0.948355	−	0.317210i	$-0.102746\pi$
$157$	14.3822	+	8.30354i	1.14782	+	0.662695i	0.199465	+	0.979905i	$0.436079\pi$
$158$	3.14898	+	1.81806i	0.250519	+	0.144637i
$159$		0			0
$160$	3.36980	−	1.94556i	0.266406	−	0.153810i
$161$	6.33909	−	15.2815i	0.499591	−	1.20435i
$162$	3.40192	+	8.33228i	0.267280	+	0.654646i
$163$	−12.3955			−0.970887			−0.485444	−	0.874268i	$-0.661342\pi$
$163$	−12.3955			−0.970887			−0.485444	+	0.874268i	$0.661342\pi$
$164$	5.24705	+	9.08816i	0.409726	+	0.709666i
$165$	9.33307	+	24.8931i	0.726579	+	1.93792i
$166$	6.98012	+	4.02998i	0.541763	+	0.312787i
$167$	−5.86087	+	10.1513i	−0.453528	+	0.785534i	−0.998602	−	0.0528541i	$-0.983168\pi$
$167$	−5.86087	+	10.1513i	−0.453528	+	0.785534i	0.545074	+	0.838388i	$0.316502\pi$
$168$	4.04532	−	2.15299i	0.312103	−	0.166107i
$169$	−2.44304	−	4.23147i	−0.187926	−	0.325498i
$170$			2.88766i			0.221474i
$171$	−3.52006	−	4.03445i	−0.269185	−	0.308522i
$172$	0.943042			0.0719063
$173$	−8.38548	−	14.5241i	−0.637536	−	1.10425i	−0.985972	−	0.166913i	$-0.946620\pi$
$173$	−8.38548	−	14.5241i	−0.637536	−	1.10425i	0.348435	−	0.937333i	$-0.386713\pi$
$174$	−0.820992	+	4.93374i	−0.0622393	+	0.374026i
$175$	21.2941	−	16.3220i	1.60968	−	1.23383i
$176$	−3.41614	−	1.97231i	−0.257501	−	0.148668i
$177$	−0.00600879	+	0.0361097i	−0.000451648	+	0.00271417i
$178$	8.02499	−	4.63323i	0.601499	−	0.347275i
$179$		−	5.77532i		−	0.431668i	−0.976430	−	0.215834i	$-0.930753\pi$
$179$		−	5.77532i		−	0.431668i	0.976430	−	0.215834i	$-0.0692470\pi$
$180$	−11.0443	−	3.78030i	−0.823193	−	0.281767i
$181$			5.53310i			0.411272i	0.978629	+	0.205636i	$0.0659263\pi$
$181$			5.53310i			0.411272i	−0.978629	+	0.205636i	$0.934074\pi$
$182$	−0.979830	−	7.47244i	−0.0726298	−	0.553894i
$183$	2.71726	−	3.30244i	0.200865	−	0.244123i
$184$	3.12656	−	5.41535i	0.230493	−	0.399225i
$185$	5.83974	−	10.1147i	0.429346	−	0.743649i
$186$	5.69536	−	2.13534i	0.417604	−	0.156571i
$187$	2.53518	−	1.46368i	0.185390	−	0.107035i
$188$	2.18525			0.159376
$189$	−12.8455	−	4.89821i	−0.934375	−	0.356292i
$190$	6.94462			0.503816
$191$	−5.38124	+	3.10686i	−0.389373	+	0.224805i	−0.681888	−	0.731456i	$-0.738841\pi$
$191$	−5.38124	+	3.10686i	−0.389373	+	0.224805i	0.292515	+	0.956261i	$0.405508\pi$
$192$	1.62181	−	0.608059i	0.117044	−	0.0438828i
$193$	3.90271	−	6.75970i	0.280923	−	0.486574i	−0.690689	−	0.723152i	$-0.742693\pi$
$193$	3.90271	−	6.75970i	0.280923	−	0.486574i	0.971612	+	0.236578i	$0.0760260\pi$
$194$	−9.40980	+	16.2983i	−0.675584	+	1.17015i
$195$	−12.1977	+	14.8246i	−0.873497	+	1.06161i
$196$	−1.81873	+	6.75960i	−0.129910	+	0.482829i
$197$			12.7737i			0.910092i	0.890468	+	0.455046i	$0.150377\pi$
$197$			12.7737i			0.910092i	−0.890468	+	0.455046i	$0.849623\pi$
$198$	2.27922	+	11.6123i	0.161977	+	0.825250i
$199$			1.81201i			0.128450i	0.997935	+	0.0642250i	$0.0204575\pi$
$199$			1.81201i			0.128450i	−0.997935	+	0.0642250i	$0.979542\pi$
$200$	8.78217	−	5.07039i	0.620993	−	0.358530i
$201$	3.82377	−	22.9788i	0.269708	−	1.62080i
$202$	−7.17206	−	4.14079i	−0.504624	−	0.291345i
$203$	−4.64782	−	6.06365i	−0.326213	−	0.425585i
$204$	−0.210992	+	1.26795i	−0.0147724	+	0.0887742i
$205$	20.4169	+	35.3631i	1.42598	+	2.46986i
$206$	17.0487			1.18784
$207$	−18.4081	+	3.61308i	−1.27945	+	0.251127i
$208$		−	2.84849i		−	0.197507i
$209$	−3.52006	−	6.09692i	−0.243487	−	0.421732i
$210$	15.7408	−	8.37753i	1.08622	−	0.578104i
$211$	−1.88766	+	3.26953i	−0.129952	+	0.225083i	−0.923658	−	0.383218i	$-0.874816\pi$
$211$	−1.88766	+	3.26953i	−0.129952	+	0.225083i	0.793706	+	0.608302i	$0.208149\pi$
$212$		0			0
$213$	1.18148	+	3.15124i	0.0809539	+	0.215920i
$214$	−7.16846	−	12.4161i	−0.490026	−	0.848750i
$215$	3.66949			0.250257
$216$	−4.57324	−	2.46687i	−0.311170	−	0.167849i
$217$	−3.56002	+	8.58209i	−0.241670	+	0.582590i
$218$	−9.76874	+	5.63998i	−0.661622	+	0.381988i
$219$	−2.95204	−	7.87366i	−0.199480	−	0.532052i
$220$	−13.2926	−	7.67448i	−0.896187	−	0.517414i
$221$	1.83070	+	1.05696i	0.123146	+	0.0710987i
$222$	3.30323	−	4.01461i	0.221698	−	0.269443i
$223$	11.0662	−	6.38910i	0.741051	−	0.427846i	−0.0814006	−	0.996681i	$-0.525939\pi$
$223$	11.0662	−	6.38910i	0.741051	−	0.427846i	0.822451	+	0.568836i	$0.192606\pi$
$224$	−1.01375	+	2.44383i	−0.0677341	+	0.163285i
$225$	−28.7829	−	9.85197i	−1.91886	−	0.656798i
$226$	9.83228			0.654034
$227$	−9.99110	−	17.3051i	−0.663133	−	1.14858i	−0.979788	−	0.200039i	$-0.935893\pi$
$227$	−9.99110	−	17.3051i	−0.663133	−	1.14858i	0.316655	−	0.948541i	$-0.397440\pi$
$228$	3.04933	+	0.507420i	0.201947	+	0.0336047i
$229$	8.77402	+	5.06568i	0.579804	+	0.334750i	0.761055	−	0.648687i	$-0.224682\pi$
$229$	8.77402	+	5.06568i	0.579804	+	0.334750i	−0.181252	+	0.983437i	$0.558015\pi$
$230$	12.1658	−	21.0718i	0.802188	−	1.38943i
$231$	−15.3335	−	9.57303i	−1.00887	−	0.629859i
$232$	−1.44383	−	2.50079i	−0.0947921	−	0.164185i
$233$			7.31007i			0.478898i	0.970909	+	0.239449i	$0.0769669\pi$
$233$			7.31007i			0.478898i	−0.970909	+	0.239449i	$0.923033\pi$
$234$	−6.43910	+	5.61811i	−0.420937	+	0.367267i
$235$	8.50307			0.554679
$236$	−0.0105673	−	0.0183031i	−0.000687873	−	0.00119143i
$237$	4.86332	+	4.00156i	0.315906	+	0.259929i
$238$	−1.19447	−	1.55833i	−0.0774260	−	0.101012i
$239$	7.28317	+	4.20494i	0.471109	+	0.271995i	0.716704	−	0.697378i	$-0.245650\pi$
$239$	7.28317	+	4.20494i	0.471109	+	0.271995i	−0.245595	+	0.969373i	$0.578983\pi$
$240$	6.31064	−	2.36603i	0.407350	−	0.152726i
$241$	−7.75277	+	4.47607i	−0.499400	+	0.288329i	−0.728466	−	0.685082i	$-0.759766\pi$
$241$	−7.75277	+	4.47607i	−0.499400	+	0.288329i	0.229066	+	0.973411i	$0.426433\pi$
$242$			4.56002i			0.293129i
$243$	3.44343	+	15.2034i	0.220896	+	0.975297i
$244$			2.46911i			0.158069i
$245$	−7.07690	+	26.3024i	−0.452127	+	1.68040i
$246$	6.38103	+	17.0194i	0.406840	+	1.08512i
$247$	2.54191	−	4.40271i	0.161738	−	0.280138i
$248$	−1.75587	+	3.04125i	−0.111498	+	0.193120i
$249$	10.7802	+	8.86997i	0.683166	+	0.562111i
$250$	17.3234	−	10.0017i	1.09563	−	0.632561i
$251$	12.6432			0.798033			0.399017	−	0.916944i	$-0.369352\pi$
$251$	12.6432			0.798033			0.399017	+	0.916944i	$0.369352\pi$
$252$	7.52378	−	2.52838i	0.473954	−	0.159273i
$253$	−24.6661			−1.55075
$254$	−2.55012	+	1.47231i	−0.160008	+	0.0923809i
$255$	−0.820992	+	4.93374i	−0.0514125	+	0.308962i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.15329	+	14.1219i	−0.508588	+	0.880900i	0.491362	+	0.870955i	$0.336499\pi$
$257$	−8.15329	+	14.1219i	−0.508588	+	0.880900i	−0.999951	+	0.00994523i	$0.996834\pi$
$258$	1.61124	+	0.268117i	0.100312	+	0.0166922i
$259$	1.03249	+	7.87402i	0.0641557	+	0.489268i
$260$		−	11.0838i		−	0.687389i
$261$	−2.80542	+	8.19615i	−0.173651	+	0.507329i
$262$			15.0651i			0.930725i
$263$	20.5434	−	11.8608i	1.26676	−	0.731366i	0.292389	−	0.956300i	$-0.405550\pi$
$263$	20.5434	−	11.8608i	1.26676	−	0.731366i	0.974374	+	0.224934i	$0.0722166\pi$
$264$	−5.27592	−	4.34105i	−0.324711	−	0.267173i
$265$		0			0
$266$	−3.74768	+	2.87261i	−0.229785	+	0.176131i
$267$	15.0284	−	5.63455i	0.919725	−	0.344829i
$268$	6.72463	+	11.6474i	0.410772	+	0.711478i
$269$	7.28288			0.444045			0.222022	−	0.975042i	$-0.428734\pi$
$269$	7.28288			0.444045			0.222022	+	0.975042i	$0.428734\pi$
$270$	−17.7950	−	9.59886i	−1.08297	−	0.584168i
$271$			22.6879i			1.37819i	0.724669	+	0.689097i	$0.241993\pi$
$271$			22.6879i			1.37819i	−0.724669	+	0.689097i	$0.758007\pi$
$272$	−0.371058	−	0.642692i	−0.0224987	−	0.0389689i
$273$	0.450397	−	13.0457i	0.0272593	−	0.789560i
$274$	7.85997	−	13.6139i	0.474838	−	0.822444i
$275$	−34.6423	−	20.0007i	−2.08901	−	1.20609i
$276$	6.88154	−	8.36353i	0.414220	−	0.503425i
$277$	−12.0838	−	20.9298i	−0.726046	−	1.25755i	−0.958542	−	0.284951i	$-0.908023\pi$
$277$	−12.0838	−	20.9298i	−0.726046	−	1.25755i	0.232496	−	0.972597i	$-0.425311\pi$
$278$	−3.30675			−0.198326
$279$	10.3380	−	2.02910i	0.618917	−	0.121479i
$280$	−3.94462	+	9.50923i	−0.235736	+	0.568285i
$281$	−4.11229	+	2.37423i	−0.245319	+	0.141635i	−0.617619	−	0.786478i	$-0.711903\pi$
$281$	−4.11229	+	2.37423i	−0.245319	+	0.141635i	0.372300	+	0.928112i	$0.378569\pi$
$282$	3.73363	+	0.621290i	0.222334	+	0.0369973i
$283$	−25.4484	−	14.6926i	−1.51275	−	0.873387i	−0.999889	−	0.0149153i	$-0.995252\pi$
$283$	−25.4484	−	14.6926i	−1.51275	−	0.873387i	−0.512861	−	0.858471i	$-0.671415\pi$
$284$	−1.68272	−	0.971521i	−0.0998513	−	0.0576492i
$285$	11.8653	+	1.97443i	0.702838	+	0.116955i
$286$	−9.73085	+	5.61811i	−0.575398	+	0.332206i
$287$	−25.6458	−	10.6384i	−1.51382	−	0.627965i
$288$	2.94383	−	0.577806i	0.173467	−	0.0340475i
$289$	−16.4493			−0.967604
$290$	−5.61811	−	9.73085i	−0.329907	−	0.571415i
$291$	−20.7109	+	25.1712i	−1.21410	+	1.47556i
$292$	4.20443	+	2.42743i	0.246046	+	0.142055i
$293$	3.31206	−	5.73666i	0.193493	−	0.335139i	−0.752913	−	0.658121i	$-0.771352\pi$
$293$	3.31206	−	5.73666i	0.193493	−	0.335139i	0.946405	+	0.322981i	$0.104685\pi$
$294$	−5.02924	+	11.0321i	−0.293311	+	0.643404i
$295$	−0.0411186	−	0.0712195i	−0.00239402	−	0.00414656i
$296$			3.00158i			0.174463i
$297$	0.592687	+	20.4883i	0.0343912	+	1.18885i
$298$	−11.0016			−0.637304
$299$	−8.90597	−	15.4256i	−0.515046	−	0.892085i
$300$	16.4464	−	6.16618i	0.949533	−	0.356005i
$301$	−1.98025	+	1.51787i	−0.114140	+	0.0874885i
$302$	−1.24706	−	0.719988i	−0.0717600	−	0.0414307i
$303$	−11.0766	−	9.11387i	−0.636334	−	0.523578i
$304$	−1.54563	+	0.892369i	−0.0886479	+	0.0511809i
$305$			9.60761i			0.550130i
$306$	−0.720982	+	2.10638i	−0.0412158	+	0.120414i
$307$		−	21.7242i		−	1.23987i	−0.784655	−	0.619933i	$-0.787160\pi$
$307$		−	21.7242i		−	1.23987i	0.784655	−	0.619933i	$-0.212840\pi$
$308$	10.3479	−	1.35688i	0.589626	−	0.0773152i
$309$	29.1287	+	4.84712i	1.65707	+	0.275743i
$310$	−6.83228	+	11.8339i	−0.388048	+	0.672118i
$311$	3.14900	−	5.45422i	0.178563	−	0.309281i	−0.762825	−	0.646605i	$-0.776188\pi$
$311$	3.14900	−	5.45422i	0.178563	−	0.309281i	0.941389	+	0.337324i	$0.109522\pi$
$312$	0.809856	−	4.86681i	0.0458491	−	0.275529i
$313$	−19.2423	+	11.1095i	−1.08764	+	0.627948i	−0.932946	−	0.360015i	$-0.882771\pi$
$313$	−19.2423	+	11.1095i	−1.08764	+	0.627948i	−0.154691	+	0.987963i	$0.549438\pi$
$314$	−16.6071			−0.937192
$315$	29.2759	−	9.83821i	1.64951	−	0.554320i
$316$	−3.63613			−0.204548
$317$	13.5632	−	7.83070i	0.761784	−	0.439816i	−0.0681519	−	0.997675i	$-0.521710\pi$
$317$	13.5632	−	7.83070i	0.761784	−	0.439816i	0.829936	+	0.557859i	$0.188377\pi$
$318$		0			0
$319$	−5.69536	+	9.86466i	−0.318879	+	0.552315i
$320$	−1.94556	+	3.36980i	−0.108760	+	0.188378i
$321$	−8.71769	−	23.2518i	−0.486574	−	1.29779i
$322$	2.15096	+	16.4038i	0.119868	+	0.914145i
$323$		−	1.32448i		−	0.0736963i
$324$	−7.11229	−	5.51501i	−0.395127	−	0.306389i
$325$		−	28.8859i		−	1.60230i
$326$	10.7348	−	6.19773i	0.594545	−	0.343260i
$327$	−18.2940	+	6.85888i	−1.01166	+	0.379297i
$328$	−9.08816	−	5.24705i	−0.501810	−	0.289720i
$329$	−4.58870	+	3.51726i	−0.252983	+	0.193913i
$330$	−20.5292	−	16.8915i	−1.13010	−	0.929847i
$331$	−0.636129	−	1.10181i	−0.0349648	−	0.0605608i	0.848013	−	0.529975i	$-0.177799\pi$
$331$	−0.636129	−	1.10181i	−0.0349648	−	0.0605608i	−0.882978	+	0.469414i	$0.844465\pi$
$332$	−8.05995			−0.442347
$333$	6.78515	−	5.92004i	0.371824	−	0.324416i
$334$		−	11.7217i		−	0.641386i
$335$	26.1663	+	45.3214i	1.42962	+	2.47617i
$336$	−2.42686	+	3.88721i	−0.132396	+	0.212064i
$337$	−3.78001	+	6.54717i	−0.205910	+	0.356647i	−0.950422	−	0.310962i	$-0.899349\pi$
$337$	−3.78001	+	6.54717i	−0.205910	+	0.356647i	0.744512	+	0.667609i	$0.232682\pi$
$338$	4.23147	+	2.44304i	0.230162	+	0.132884i
$339$	16.7990	+	2.79542i	0.912397	+	0.151826i
$340$	−1.44383	−	2.50079i	−0.0783027	−	0.135624i
$341$	13.8525			0.750153
$342$	5.06568	+	1.73391i	0.273921	+	0.0937592i
$343$	−7.06081	−	17.1215i	−0.381248	−	0.924473i
$344$	−0.816699	+	0.471521i	−0.0440334	+	0.0254227i
$345$	26.7769	−	32.5434i	1.44162	−	1.75208i
$346$	14.5241	+	8.38548i	0.780820	+	0.450806i
$347$	19.1470	+	11.0545i	1.02787	+	0.593439i	0.916373	−	0.400326i	$-0.131103\pi$
$347$	19.1470	+	11.0545i	1.02787	+	0.593439i	0.111494	+	0.993765i	$0.464436\pi$
$348$	−1.75587	−	4.68324i	−0.0941244	−	0.251048i
$349$	−12.7682	+	7.37173i	−0.683467	+	0.394600i	−0.801160	−	0.598450i	$-0.795783\pi$
$349$	−12.7682	+	7.37173i	−0.683467	+	0.394600i	0.117693	+	0.993050i	$0.462450\pi$
$350$	−10.2802	+	24.7823i	−0.549501	+	1.32467i
$351$	−12.5989	+	7.76816i	−0.672478	+	0.414634i
$352$	3.94462			0.210249
$353$	8.63881	+	14.9629i	0.459798	+	0.796393i	0.998950	−	0.0458154i	$-0.0145886\pi$
$353$	8.63881	+	14.9629i	0.459798	+	0.796393i	−0.539152	+	0.842208i	$0.681255\pi$
$354$	−0.0128511	−	0.0342763i	−0.000683027	−	0.00182176i
$355$	−6.54767	−	3.78030i	−0.347514	−	0.200638i
$356$	−4.63323	+	8.02499i	−0.245561	+	0.425324i
$357$	−1.59777	−	3.00210i	−0.0845630	−	0.158888i
$358$	2.88766	+	5.00158i	0.152618	+	0.264342i
$359$			10.9129i			0.575963i	0.957636	+	0.287982i	$0.0929842\pi$
$359$			10.9129i			0.575963i	−0.957636	+	0.287982i	$0.907016\pi$
$360$	11.4548	−	2.24831i	0.603720	−	0.118496i
$361$	15.8147			0.832353
$362$	−2.76655	−	4.79180i	−0.145407	−	0.251852i
$363$	−1.29646	+	7.79106i	−0.0680466	+	0.408925i
$364$	4.58478	+	5.98141i	0.240308	+	0.313511i
$365$	16.3599	+	9.44541i	0.856318	+	0.494395i
$366$	−0.701995	+	4.21862i	−0.0366939	+	0.220511i
$367$	30.9407	−	17.8636i	1.61509	−	0.932472i	0.626923	−	0.779081i	$-0.284314\pi$
$367$	30.9407	−	17.8636i	1.61509	−	0.932472i	0.988166	−	0.153391i	$-0.0490194\pi$
$368$			6.25311i			0.325966i
$369$	6.06355	+	30.8929i	0.315656	+	1.60822i
$370$			11.6795i			0.607187i
$371$		0			0
$372$	−3.86466	+	4.69694i	−0.200373	+	0.243525i
$373$	16.0300	−	27.7648i	0.830003	−	1.43761i	−0.0680328	−	0.997683i	$-0.521672\pi$
$373$	16.0300	−	27.7648i	0.830003	−	1.43761i	0.898035	−	0.439923i	$-0.144994\pi$
$374$	−1.46368	+	2.53518i	−0.0756853	+	0.131091i
$375$	32.4416	−	12.1632i	1.67528	−	0.628105i
$376$	−1.89248	+	1.09263i	−0.0975974	+	0.0563479i
$377$	−8.22549			−0.423634
$378$	13.5737	−	2.18079i	0.698154	−	0.112168i
$379$	34.8891			1.79214			0.896068	−	0.443918i	$-0.146412\pi$
$379$	34.8891			1.79214			0.896068	+	0.443918i	$0.146412\pi$
$380$	−6.01422	+	3.47231i	−0.308523	+	0.178126i
$381$	−4.77561	+	1.79050i	−0.244662	+	0.0917301i
$382$	3.10686	−	5.38124i	0.158961	−	0.275328i
$383$	−8.76711	+	15.1851i	−0.447978	+	0.775921i	−0.998254	−	0.0590616i	$-0.981189\pi$
$383$	−8.76711	+	15.1851i	−0.447978	+	0.775921i	0.550276	+	0.834983i	$0.314523\pi$
$384$	−1.10050	+	1.33750i	−0.0561596	+	0.0682539i
$385$	40.2649	−	5.27976i	2.05209	−	0.269082i
$386$			7.80542i			0.397286i
$387$	2.67667	+	0.916186i	0.136063	+	0.0465723i
$388$		−	18.8196i		−	0.955421i
$389$	−6.60060	+	3.81086i	−0.334664	+	0.193218i	−0.657910	−	0.753097i	$-0.728559\pi$
$389$	−6.60060	+	3.81086i	−0.334664	+	0.193218i	0.323246	+	0.946315i	$0.395226\pi$
$390$	3.15124	−	18.9373i	0.159569	−	0.958929i
$391$	−4.01882	−	2.32027i	−0.203241	−	0.117341i
$392$	−1.80473	−	6.76335i	−0.0911527	−	0.341601i
$393$	−4.28317	+	25.7396i	−0.216057	+	1.29839i
$394$	−6.38687	−	11.0624i	−0.321766	−	0.557315i
$395$	−14.1486			−0.711893
$396$	−7.78001	−	8.91693i	−0.390960	−	0.448093i
$397$		−	37.6469i		−	1.88944i	−0.327873	−	0.944722i	$-0.606332\pi$
$397$		−	37.6469i		−	1.88944i	0.327873	−	0.944722i	$-0.393668\pi$
$398$	−0.906005	−	1.56925i	−0.0454139	−	0.0786592i
$399$	−7.21984	+	3.84252i	−0.361444	+	0.192367i
$400$	−5.07039	+	8.78217i	−0.253519	+	0.439108i
$401$	18.5689	+	10.7207i	0.927284	+	0.535368i	0.885952	−	0.463778i	$-0.153506\pi$
$401$	18.5689	+	10.7207i	0.927284	+	0.535368i	0.0413326	+	0.999145i	$0.486840\pi$
$402$	8.17794	+	21.8121i	0.407879	+	1.08789i
$403$	5.00158	+	8.66299i	0.249146	+	0.431534i
$404$	8.28158			0.412024
$405$	−27.6747	−	21.4595i	−1.37517	−	1.06633i
$406$	7.05696	+	2.92737i	0.350231	+	0.145283i
$407$	10.2538	−	5.92004i	0.508262	−	0.293445i
$408$	−0.451251	−	1.20357i	−0.0223402	−	0.0595857i
$409$	−25.6086	−	14.7851i	−1.26627	−	0.731079i	−0.291986	−	0.956423i	$-0.594316\pi$
$409$	−25.6086	−	14.7851i	−1.26627	−	0.731079i	−0.974279	+	0.225344i	$0.927649\pi$
$410$	−35.3631	−	20.4169i	−1.74646	−	1.00832i
$411$	17.2998	−	21.0254i	0.853335	−	1.03711i
$412$	−14.7646	+	8.52435i	−0.727400	+	0.419964i
$413$	0.0516494	+	0.0214252i	0.00254150	+	0.00105427i
$414$	14.1353	−	12.3331i	0.694714	−	0.606137i
$415$	−31.3622			−1.53951
$416$	1.42425	+	2.46687i	0.0698294	+	0.120948i
$417$	−5.64977	−	0.940143i	−0.276670	−	0.0460390i
$418$	6.09692	+	3.52006i	0.298210	+	0.172172i
$419$	3.56481	−	6.17443i	0.174152	−	0.301641i	−0.765715	−	0.643180i	$-0.777615\pi$
$419$	3.56481	−	6.17443i	0.174152	−	0.301641i	0.939868	+	0.341539i	$0.110948\pi$
$420$	−9.44318	+	15.1256i	−0.460780	+	0.738052i
$421$	−2.31007	−	4.00115i	−0.112586	−	0.195004i	0.804226	−	0.594323i	$-0.202580\pi$
$421$	−2.31007	−	4.00115i	−0.112586	−	0.195004i	−0.916812	+	0.399319i	$0.869247\pi$
$422$		−	3.77532i		−	0.183780i
$423$	6.20248	+	2.12302i	0.301575	+	0.103225i
$424$		0			0
$425$	−3.76282	−	6.51739i	−0.182524	−	0.316140i
$426$	−2.59882	−	2.13832i	−0.125913	−	0.103602i
$427$	−3.97415	−	5.18477i	−0.192323	−	0.250908i
$428$	12.4161	+	7.16846i	0.600157	+	0.346501i
$429$	−18.2230	+	6.83228i	−0.879815	+	0.329866i
$430$	−3.17787	+	1.83474i	−0.153250	+	0.0884792i
$431$		−	4.00771i		−	0.193045i	−0.995331	−	0.0965223i	$-0.969228\pi$
$431$		−	4.00771i		−	0.193045i	0.995331	−	0.0965223i	$-0.0307719\pi$
$432$	5.19398	−	0.150252i	0.249895	−	0.00722900i
$433$			29.4125i			1.41348i	0.707475	+	0.706738i	$0.249834\pi$
$433$			29.4125i			1.41348i	−0.707475	+	0.706738i	$0.750166\pi$
$434$	−1.20797	−	9.21232i	−0.0579845	−	0.442205i
$435$	−6.83228	−	18.2230i	−0.327583	−	0.873726i
$436$	5.63998	−	9.76874i	0.270106	−	0.467838i
$437$	−5.58008	+	9.66498i	−0.266931	+	0.462339i
$438$	6.49337	+	5.34277i	0.310265	+	0.255287i
$439$	18.5130	−	10.6885i	0.883575	−	0.510133i	0.0117398	−	0.999931i	$-0.496263\pi$
$439$	18.5130	−	10.6885i	0.883575	−	0.510133i	0.871836	+	0.489799i	$0.162930\pi$
$440$	15.3490			0.731733
$441$	−11.7293	+	17.4191i	−0.558537	+	0.829480i
$442$	−2.11392			−0.100549
$443$	5.05227	−	2.91693i	0.240041	−	0.138587i	−0.375155	−	0.926962i	$-0.622410\pi$
$443$	5.05227	−	2.91693i	0.240041	−	0.138587i	0.615195	+	0.788375i	$0.289077\pi$
$444$	−0.853380	+	5.12837i	−0.0404996	+	0.243381i
$445$	−18.0284	+	31.2262i	−0.854630	+	1.48026i
$446$	−6.38910	+	11.0662i	−0.302533	+	0.524002i
$447$	−18.7968	−	3.12786i	−0.889059	−	0.147943i
$448$	−0.343982	−	2.62329i	−0.0162516	−	0.123939i
$449$		−	22.5823i		−	1.06573i	−0.846202	−	0.532863i	$-0.821116\pi$
$449$		−	22.5823i		−	1.06573i	0.846202	−	0.532863i	$-0.178884\pi$
$450$	29.8527	−	5.85939i	1.40727	−	0.276215i
$451$			41.3953i			1.94923i
$452$	−8.51501	+	4.91614i	−0.400512	+	0.231236i
$453$	−1.92597	−	1.58469i	−0.0904898	−	0.0744553i
$454$	17.3051	+	9.99110i	0.812168	+	0.468906i
$455$	17.8399	+	23.2743i	0.836347	+	1.09112i
$456$	−2.89450	+	1.08523i	−0.135548	+	0.0508203i
$457$	−19.9311	−	34.5218i	−0.932340	−	1.61486i	−0.779310	−	0.626638i	$-0.784430\pi$
$457$	−19.9311	−	34.5218i	−0.932340	−	1.61486i	−0.153029	−	0.988222i	$-0.548903\pi$
$458$	−10.1314			−0.473408
$459$	−1.83070	+	3.39388i	−0.0854500	+	0.158413i
$460$			24.3316i			1.13447i
$461$	3.68254	+	6.37834i	0.171513	+	0.297069i	0.938949	−	0.344056i	$-0.111801\pi$
$461$	3.68254	+	6.37834i	0.171513	+	0.297069i	−0.767436	+	0.641125i	$0.778468\pi$
$462$	18.0658	+	0.623714i	0.840495	+	0.0290178i
$463$	−14.3457	+	24.8475i	−0.666702	+	1.15476i	0.312119	+	0.950043i	$0.398961\pi$
$463$	−14.3457	+	24.8475i	−0.666702	+	1.15476i	−0.978821	+	0.204718i	$0.934372\pi$
$464$	2.50079	+	1.44383i	0.116096	+	0.0670282i
$465$	−15.0378	+	18.2763i	−0.697363	+	0.847545i
$466$	−3.65503	−	6.33070i	−0.169316	−	0.293264i
$467$	13.6704			0.632590			0.316295	−	0.948661i	$-0.397561\pi$
$467$	13.6704			0.632590			0.316295	+	0.948661i	$0.397561\pi$
$468$	2.76737	−	8.08498i	0.127922	−	0.373728i
$469$	−32.8677	−	13.6342i	−1.51769	−	0.629569i
$470$	−7.36387	+	4.25153i	−0.339670	+	0.196109i
$471$	−28.3741	−	4.72157i	−1.30741	−	0.217558i
$472$	0.0183031	+	0.0105673i	0.000842469	+	0.000486400i
$473$	3.22157	+	1.85997i	0.148128	+	0.0855216i
$474$	−6.21253	−	1.03379i	−0.285351	−	0.0474835i
$475$	−15.6739	+	9.04931i	−0.719166	+	0.415211i
$476$	1.81361	+	0.752321i	0.0831266	+	0.0344826i
$477$		0			0
$478$	−8.40988			−0.384659
$479$	−5.20537	−	9.01596i	−0.237839	−	0.411950i	0.722255	−	0.691627i	$-0.243106\pi$
$479$	−5.20537	−	9.01596i	−0.237839	−	0.411950i	−0.960094	+	0.279677i	$0.909773\pi$
$480$	−4.28217	+	5.20436i	−0.195453	+	0.237545i
$481$	7.40449	+	4.27499i	0.337616	+	0.194923i
$482$	4.47607	−	7.75277i	0.203879	−	0.353129i
$483$	−0.988727	+	28.6383i	−0.0449886	+	1.30309i
$484$	−2.28001	−	3.94910i	−0.103637	−	0.179504i
$485$		−	73.2292i		−	3.32517i
$486$	−10.5838	−	11.4448i	−0.480090	−	0.519147i
$487$	2.33850			0.105968			0.0529838	−	0.998595i	$-0.483127\pi$
$487$	2.33850			0.105968			0.0529838	+	0.998595i	$0.483127\pi$
$488$	−1.23456	−	2.13832i	−0.0558858	−	0.0967970i
$489$	20.1031	−	7.53716i	0.909092	−	0.340842i
$490$	−7.02242	−	26.3170i	−0.317240	−	1.18888i
$491$	−29.3448	−	16.9422i	−1.32431	−	0.764591i	−0.339898	−	0.940462i	$-0.610392\pi$
$491$	−29.3448	−	16.9422i	−1.32431	−	0.764591i	−0.984413	+	0.175871i	$0.943726\pi$
$492$	−14.0359	−	11.5487i	−0.632785	−	0.520658i
$493$	−1.85588	+	1.07149i	−0.0835845	+	0.0482575i
$494$			5.08381i			0.228732i
$495$	−30.2729	−	34.6968i	−1.36067	−	1.55950i
$496$		−	3.51174i		−	0.157682i
$497$	5.09717	−	0.668371i	0.228639	−	0.0299805i
$498$	−13.7709	−	2.29153i	−0.617088	−	0.102686i
$499$	8.30223	−	14.3799i	0.371659	−	0.643732i	−0.618162	−	0.786051i	$-0.712123\pi$
$499$	8.30223	−	14.3799i	0.371659	−	0.643732i	0.989821	+	0.142319i	$0.0454558\pi$
$500$	−10.0017	+	17.3234i	−0.447288	+	0.774726i
$501$	3.33262	−	20.0273i	0.148890	−	0.894753i
$502$	−10.9494	+	6.32161i	−0.488694	+	0.282147i
$503$	35.3661			1.57690			0.788449	−	0.615100i	$-0.210885\pi$
$503$	35.3661			1.57690			0.788449	+	0.615100i	$0.210885\pi$
$504$	−5.25160	+	5.95153i	−0.233925	+	0.265102i
$505$	32.2246			1.43398
$506$	21.3615	−	12.3331i	0.949635	−	0.548272i
$507$	6.53513	+	5.37713i	0.290235	+	0.238807i
$508$	1.47231	−	2.55012i	0.0653232	−	0.113143i
$509$	18.5291	−	32.0933i	0.821287	−	1.42251i	−0.0834371	−	0.996513i	$-0.526590\pi$
$509$	18.5291	−	32.0933i	0.821287	−	1.42251i	0.904724	−	0.425998i	$-0.140077\pi$
$510$	−1.75587	−	4.68324i	−0.0777511	−	0.207377i
$511$	−12.7357	+	1.66998i	−0.563396	+	0.0738757i
$512$		−	1.00000i		−	0.0441942i
$513$	8.16204	+	4.40271i	0.360363	+	0.194384i
$514$		−	16.3066i		−	0.719252i
$515$	−57.4507	+	33.1692i	−2.53158	+	1.46161i
$516$	−1.52943	+	0.573425i	−0.0673296	+	0.0252436i
$517$	7.46513	+	4.30999i	0.328316	+	0.189553i
$518$	−4.83117	−	6.30286i	−0.212270	−	0.276932i
$519$	22.4311	+	18.4564i	0.984618	+	0.810147i
$520$	5.54191	+	9.59886i	0.243029	+	0.420938i
$521$	−1.78309			−0.0781187			−0.0390594	−	0.999237i	$-0.512436\pi$
$521$	−1.78309			−0.0781187			−0.0390594	+	0.999237i	$0.512436\pi$
$522$	−1.66851	−	8.50079i	−0.0730286	−	0.372069i
$523$			24.0538i			1.05180i	0.850546	+	0.525901i	$0.176272\pi$
$523$			24.0538i			1.05180i	−0.850546	+	0.525901i	$0.823728\pi$
$524$	−7.53255	−	13.0468i	−0.329061	−	0.569950i
$525$	−24.6102	+	39.4193i	−1.07408	+	1.72040i
$526$	−11.8608	+	20.5434i	−0.517154	+	0.895737i
$527$	2.25696	+	1.30306i	0.0983149	+	0.0567621i
$528$	6.73961	+	1.12150i	0.293304	+	0.0488069i
$529$	8.05069	+	13.9442i	0.350030	+	0.606270i
$530$		0			0
$531$	−0.0122117	−	0.0622167i	−0.000529942	−	0.00269998i
$532$	1.80928	−	4.36160i	0.0784422	−	0.189099i
$533$	−25.8876	+	14.9462i	−1.12132	+	0.647392i
$534$	−10.1977	+	12.3939i	−0.441299	+	0.536336i
$535$	48.3126	+	27.8933i	2.08874	+	1.20593i
$536$	−11.6474	−	6.72463i	−0.503091	−	0.290460i
$537$	3.51174	+	9.36647i	0.151543	+	0.404193i
$538$	−6.30716	+	3.64144i	−0.271921	+	0.156994i
$539$	−19.5451	+	19.5046i	−0.841866	+	0.840124i
$540$	20.2104	−	0.584648i	0.869716	−	0.0251592i
$541$	30.0032			1.28994			0.644968	−	0.764209i	$-0.276871\pi$
$541$	30.0032			1.28994			0.644968	+	0.764209i	$0.276871\pi$
$542$	−11.3440	−	19.6483i	−0.487265	−	0.843968i
$543$	−3.36445	−	8.97363i	−0.144382	−	0.385095i
$544$	0.642692	+	0.371058i	0.0275552	+	0.0159090i
$545$	21.9458	−	38.0113i	0.940056	−	1.62822i
$546$	6.13278	+	11.5231i	0.262459	+	0.493142i
$547$	−10.7816	−	18.6743i	−0.460987	−	0.798454i	0.538023	−	0.842930i	$-0.319171\pi$
$547$	−10.7816	−	18.6743i	−0.460987	−	0.798454i	−0.999010	+	0.0444765i	$0.985838\pi$
$548$			15.7199i			0.671523i
$549$	−2.39880	+	7.00817i	−0.102378	+	0.299102i
$550$	40.0015			1.70567
$551$	2.57686	+	4.46325i	0.109778	+	0.190141i
$552$	−1.77782	+	10.6838i	−0.0756692	+	0.454733i
$553$	7.63532	−	5.85251i	0.324687	−	0.248874i
$554$	20.9298	+	12.0838i	0.889221	+	0.513392i
$555$	−3.32060	+	19.9551i	−0.140952	+	0.847045i
$556$	2.86373	−	1.65337i	0.121449	−	0.0701187i
$557$		−	36.9477i		−	1.56552i	−0.622321	−	0.782762i	$-0.713810\pi$
$557$		−	36.9477i		−	1.56552i	0.622321	−	0.782762i	$-0.286190\pi$
$558$	−7.93838	+	6.92623i	−0.336058	+	0.293211i
$559$			2.68625i			0.113616i
$560$	−1.33847	−	10.2075i	−0.0565608	−	0.431347i
$561$	−3.22157	+	3.91535i	−0.136015	+	0.165306i
$562$	2.37423	−	4.11229i	0.100151	−	0.173467i
$563$	−7.58422	+	13.1363i	−0.319637	+	0.553627i	−0.980412	−	0.196957i	$-0.936894\pi$
$563$	−7.58422	+	13.1363i	−0.319637	+	0.553627i	0.660776	+	0.750584i	$0.270228\pi$
$564$	−3.54406	+	1.32876i	−0.149232	+	0.0559509i
$565$	−33.1329	+	19.1293i	−1.39391	+	0.804774i
$566$	29.3853			1.23516
$567$	23.8114	+	0.133128i	0.999984	+	0.00559087i
$568$	1.94304			0.0815282
$569$	−31.8084	+	18.3646i	−1.33348	+	0.769885i	−0.985831	−	0.167740i	$-0.946353\pi$
$569$	−31.8084	+	18.3646i	−1.33348	+	0.769885i	−0.347648	+	0.937625i	$0.613020\pi$
$570$	−11.2628	+	4.22274i	−0.471749	+	0.176871i
$571$	−5.61387	+	9.72351i	−0.234933	+	0.406916i	−0.959253	−	0.282548i	$-0.908820\pi$
$571$	−5.61387	+	9.72351i	−0.234933	+	0.406916i	0.724320	+	0.689464i	$0.242154\pi$
$572$	5.61811	−	9.73085i	0.234905	−	0.406867i
$573$	6.83819	−	8.31085i	0.285670	−	0.347191i
$574$	27.5291	−	3.60978i	1.14904	−	0.150669i
$575$			63.4114i			2.64444i
$576$	−2.26053	+	1.97231i	−0.0941887	+	0.0821796i
$577$		−	36.5515i		−	1.52166i	−0.648952	−	0.760829i	$-0.724792\pi$
$577$		−	36.5515i		−	1.52166i	0.648952	−	0.760829i	$-0.275208\pi$
$578$	14.2455	−	8.22463i	0.592534	−	0.342100i
$579$	−2.21916	+	13.3360i	−0.0922253	+	0.554226i
$580$	9.73085	+	5.61811i	0.404052	+	0.233279i
$581$	16.9247	−	12.9729i	0.702154	−	0.538205i
$582$	5.35061	−	32.1544i	0.221790	−	1.33284i
$583$		0			0
$584$	−4.85486			−0.200896
$585$	10.7682	−	31.4596i	0.445209	−	1.30069i
$586$			6.62413i			0.273640i
$587$	−4.99738	−	8.65571i	−0.206264	−	0.357259i	0.744271	−	0.667878i	$-0.232797\pi$
$587$	−4.99738	−	8.65571i	−0.206264	−	0.357259i	−0.950535	+	0.310619i	$0.899464\pi$
$588$	−1.16059	−	12.0687i	−0.0478621	−	0.497704i
$589$	3.13376	−	5.42784i	0.129124	−	0.223650i
$590$	0.0712195	+	0.0411186i	0.00293206	+	0.00169283i
$591$	−7.76719	−	20.7166i	−0.319499	−	0.852166i
$592$	−1.50079	−	2.59944i	−0.0616820	−	0.106836i
$593$	−7.78223			−0.319578			−0.159789	−	0.987151i	$-0.551081\pi$
$593$	−7.78223			−0.319578			−0.159789	+	0.987151i	$0.551081\pi$
$594$	−10.7574	−	17.4470i	−0.441382	−	0.715860i
$595$	7.05696	+	2.92737i	0.289307	+	0.120010i
$596$	9.52765	−	5.50079i	0.390268	−	0.225321i
$597$	−1.10181	−	2.93873i	−0.0450940	−	0.120274i
$598$	15.4256	+	8.90597i	0.630800	+	0.364192i
$599$	21.6614	+	12.5062i	0.885061	+	0.510990i	0.872324	−	0.488929i	$-0.162612\pi$
$599$	21.6614	+	12.5062i	0.885061	+	0.510990i	0.0127373	+	0.999919i	$0.495945\pi$
$600$	−11.1599	+	13.5633i	−0.455601	+	0.553718i
$601$	−25.9925	+	15.0068i	−1.06026	+	0.612139i	−0.925503	−	0.378740i	$-0.876357\pi$
$601$	−25.9925	+	15.0068i	−1.06026	+	0.612139i	−0.134753	+	0.990879i	$0.543024\pi$
$602$	0.956010	−	2.30464i	0.0389640	−	0.0939300i
$603$	7.77106	+	39.5924i	0.316462	+	1.61233i
$604$	1.43998			0.0585918
$605$	−8.87179	−	15.3664i	−0.360689	−	0.624732i
$606$	14.1496	+	2.35454i	0.574786	+	0.0956467i
$607$	−3.96882	−	2.29140i	−0.161089	−	0.0930050i	0.417288	−	0.908774i	$-0.362981\pi$
$607$	−3.96882	−	2.29140i	−0.161089	−	0.0930050i	−0.578378	+	0.815769i	$0.696314\pi$
$608$	0.892369	−	1.54563i	0.0361903	−	0.0626835i
$609$	11.2249	+	7.00794i	0.454857	+	0.283976i
$610$	−4.80380	−	8.32043i	−0.194500	−	0.336884i
$611$			6.22468i			0.251823i
$612$	−0.428799	−	2.18467i	−0.0173332	−	0.0883099i
$613$	30.5522			1.23399			0.616996	−	0.786966i	$-0.288349\pi$
$613$	30.5522			1.23399			0.616996	+	0.786966i	$0.288349\pi$
$614$	10.8621	+	18.8137i	0.438359	+	0.759259i
$615$	−54.6151	−	44.9375i	−2.20229	−	1.81206i
$616$	−8.28311	+	6.34904i	−0.333736	+	0.255810i
$617$	−28.2484	−	16.3092i	−1.13724	−	0.656585i	−0.191493	−	0.981494i	$-0.561333\pi$
$617$	−28.2484	−	16.3092i	−1.13724	−	0.656585i	−0.945745	+	0.324909i	$0.894666\pi$
$618$	−27.6497	+	10.3666i	−1.11224	+	0.417006i
$619$	17.3244	−	10.0023i	0.696327	−	0.402024i	−0.109651	−	0.993970i	$-0.534973\pi$
$619$	17.3244	−	10.0023i	0.696327	−	0.402024i	0.805978	+	0.591946i	$0.201640\pi$
$620$		−	13.6646i		−	0.548782i
$621$	27.6575	−	17.0529i	1.10986	−	0.684311i
$622$			6.29800i			0.252527i
$623$	−3.18749	−	24.3087i	−0.127704	−	0.973906i
$624$	1.73205	+	4.61971i	0.0693375	+	0.184937i
$625$	−13.5657	+	23.4965i	−0.542628	+	0.939859i
$626$	11.1095	−	19.2423i	0.444026	−	0.769076i
$627$	9.41614	+	7.74763i	0.376044	+	0.309411i
$628$	14.3822	−	8.30354i	0.573910	−	0.331347i
$629$	2.22752			0.0888171
$630$	−20.4346	+	23.1581i	−0.814133	+	0.922640i
$631$	6.09634			0.242692			0.121346	−	0.992610i	$-0.461279\pi$
$631$	6.09634			0.242692			0.121346	+	0.992610i	$0.461279\pi$
$632$	3.14898	−	1.81806i	0.125260	−	0.0723187i
$633$	1.07336	−	6.45036i	0.0426624	−	0.256379i
$634$	−7.83070	+	13.5632i	−0.310997	+	0.538663i
$635$	5.72893	−	9.92279i	0.227345	−	0.393774i
$636$		0			0
$637$	−19.2547	−	5.18065i	−0.762898	−	0.205265i
$638$		−	11.3907i		−	0.450963i
$639$	−3.83228	−	4.39230i	−0.151603	−	0.173757i
$640$		−	3.89111i		−	0.153810i
$641$	28.9612	−	16.7207i	1.14390	−	0.660429i	0.196504	−	0.980503i	$-0.437041\pi$
$641$	28.9612	−	16.7207i	1.14390	−	0.660429i	0.947393	+	0.320074i	$0.103708\pi$
$642$	19.1756	+	15.7778i	0.756801	+	0.622699i
$643$	16.6022	+	9.58527i	0.654726	+	0.378006i	0.790264	−	0.612766i	$-0.209943\pi$
$643$	16.6022	+	9.58527i	0.654726	+	0.378006i	−0.135539	+	0.990772i	$0.543276\pi$
$644$	−10.0647	−	13.1306i	−0.396603	−	0.517418i
$645$	−5.95121	+	2.23126i	−0.234328	+	0.0878559i
$646$	0.662242	+	1.14704i	0.0260556	+	0.0451296i
$647$	−44.6049			−1.75360			−0.876800	−	0.480854i	$-0.840327\pi$
$647$	−44.6049			−1.75360			−0.876800	+	0.480854i	$0.840327\pi$
$648$	8.91693	+	1.21999i	0.350290	+	0.0479257i
$649$		−	0.0833680i		−	0.00327248i
$650$	14.4430	+	25.0159i	0.566500	+	0.981206i
$651$	0.555267	−	16.0832i	0.0217626	−	0.630351i
$652$	−6.19773	+	10.7348i	−0.242722	+	0.420407i
$653$	−0.564755	−	0.326061i	−0.0221006	−	0.0127598i	0.488909	−	0.872335i	$-0.337395\pi$
$653$	−0.564755	−	0.326061i	−0.0221006	−	0.0127598i	−0.511010	+	0.859575i	$0.670728\pi$
$654$	12.4136	−	15.0869i	0.485410	−	0.589946i
$655$	−29.3100	−	50.7664i	−1.14524	−	1.98361i
$656$	10.4941			0.409726
$657$	9.57529	+	10.9746i	0.373568	+	0.428158i
$658$	2.21530	−	5.34039i	0.0863614	−	0.208190i
$659$	26.2738	−	15.1692i	1.02348	−	0.590908i	0.108372	−	0.994110i	$-0.465436\pi$
$659$	26.2738	−	15.1692i	1.02348	−	0.590908i	0.915111	+	0.403202i	$0.132103\pi$
$660$	26.2246	+	4.36387i	1.02079	+	0.169863i
$661$	−11.1004	−	6.40881i	−0.431755	−	0.249274i	0.268339	−	0.963325i	$-0.413525\pi$
$661$	−11.1004	−	6.40881i	−0.431755	−	0.249274i	−0.700094	+	0.714051i	$0.746859\pi$
$662$	1.10181	+	0.636129i	0.0428230	+	0.0247239i
$663$	−3.61175	−	0.601008i	−0.140269	−	0.0233412i
$664$	6.98012	−	4.02998i	0.270881	−	0.156393i
$665$	7.04011	−	16.9715i	0.273004	−	0.658126i
$666$	−2.91610	+	8.51948i	−0.112996	+	0.330123i
$667$	18.0569			0.699165
$668$	5.86087	+	10.1513i	0.226764	+	0.392767i
$669$	−14.0624	+	17.0908i	−0.543683	+	0.660769i
$670$	−45.3214	−	26.1663i	−1.75092	−	1.01089i
$671$	−4.86986	+	8.43484i	−0.187999	+	0.325623i
$672$	0.158118	−	4.57985i	0.00609952	−	0.176671i
$673$	11.2246	+	19.4416i	0.432678	+	0.749420i	0.997103	−	0.0760644i	$-0.0242355\pi$
$673$	11.2246	+	19.4416i	0.432678	+	0.749420i	−0.564425	+	0.825484i	$0.690902\pi$
$674$		−	7.56002i		−	0.291201i
$675$	52.6710	−	1.52367i	2.02731	−	0.0586461i
$676$	−4.88608			−0.187926
$677$	25.5903	+	44.3237i	0.983516	+	1.70350i	0.648353	+	0.761340i	$0.275458\pi$
$677$	25.5903	+	44.3237i	0.983516	+	1.70350i	0.335163	+	0.942160i	$0.391209\pi$
$678$	−15.9461	+	5.97860i	−0.612406	+	0.229607i
$679$	30.2910	+	39.5183i	1.16246	+	1.51657i
$680$	2.50079	+	1.44383i	0.0959009	+	0.0553684i
$681$	26.7262	+	21.9904i	1.02415	+	0.842673i
$682$	−11.9966	+	6.92623i	−0.459373	+	0.265219i
$683$		−	14.5616i		−	0.557184i	−0.960410	−	0.278592i	$-0.910132\pi$
$683$		−	14.5616i		−	0.557184i	0.960410	−	0.278592i	$-0.0898677\pi$
$684$	−5.25397	+	1.03123i	−0.200890	+	0.0394301i
$685$			61.1681i			2.33711i
$686$	14.6756	+	11.2972i	0.560316	+	0.431330i
$687$	−17.3100	−	2.88045i	−0.660419	−	0.109896i
$688$	0.471521	−	0.816699i	0.0179766	−	0.0311363i
$689$		0			0
$690$	−6.91772	+	41.5719i	−0.263353	+	1.58261i
$691$	−21.1757	+	12.2258i	−0.805560	+	0.465090i	−0.845412	−	0.534115i	$-0.820645\pi$
$691$	−21.1757	+	12.2258i	−0.805560	+	0.465090i	0.0398517	+	0.999206i	$0.487311\pi$
$692$	−16.7710			−0.637536
$693$	30.6890	+	6.20193i	1.16578	+	0.235592i
$694$	−22.1091			−0.839250
$695$	11.1431	−	6.43347i	0.422682	−	0.244035i
$696$	3.86224	+	3.17787i	0.146398	+	0.120457i
$697$	−3.89393	+	6.74448i	−0.147493	+	0.255465i
$698$	7.37173	−	12.7682i	0.279024	−	0.483284i
$699$	−4.44495	−	11.8555i	−0.168123	−	0.448417i
$700$	−3.48824	−	26.6022i	−0.131843	−	1.00547i
$701$		−	2.21697i		−	0.0837337i	−0.999123	−	0.0418669i	$-0.986669\pi$
$701$		−	2.21697i		−	0.0837337i	0.999123	−	0.0418669i	$-0.0133305\pi$
$702$	7.02686	−	13.0269i	0.265212	−	0.491667i
$703$		−	5.35703i		−	0.202044i
$704$	−3.41614	+	1.97231i	−0.128751	+	0.0743342i
$705$	−13.7903	+	5.17036i	−0.519375	+	0.194727i
$706$	−14.9629	−	8.63881i	−0.563135	−	0.325126i
$707$	−17.3901	+	13.3296i	−0.654021	+	0.501310i
$708$	0.0282675	+	0.0232586i	0.00106236	+	0.000874112i
$709$	12.1962	+	21.1244i	0.458036	+	0.793342i	0.998857	−	0.0477959i	$-0.0152197\pi$
$709$	12.1962	+	21.1244i	0.458036	+	0.793342i	−0.540821	+	0.841138i	$0.681886\pi$
$710$	7.56060			0.283744
$711$	−10.3206	−	3.53258i	−0.387051	−	0.132482i
$712$		−	9.26646i		−	0.347275i
$713$	−10.9796	−	19.0173i	−0.411190	−	0.712203i
$714$	2.88476	+	1.80101i	0.107959	+	0.0674012i
$715$	21.8607	−	37.8639i	0.817544	−	1.41603i
$716$	−5.00158	−	2.88766i	−0.186918	−	0.107917i
$717$	−14.3688	−	2.39102i	−0.536611	−	0.0892941i
$718$	−5.45647	−	9.45088i	−0.203634	−	0.352704i
$719$	−2.22752			−0.0830725			−0.0415363	−	0.999137i	$-0.513225\pi$
$719$	−2.22752			−0.0830725			−0.0415363	+	0.999137i	$0.513225\pi$
$720$	−8.79598	+	7.67448i	−0.327807	+	0.286011i
$721$	17.2831	−	41.6641i	0.643657	−	1.55165i
$722$	−13.6959	+	7.90736i	−0.509710	+	0.294281i
$723$	9.85181	−	11.9735i	0.366393	−	0.445298i
$724$	4.79180	+	2.76655i	0.178086	+	0.102818i
$725$	25.3599	+	14.6416i	0.941844	+	0.543774i
$726$	−2.77276	−	7.39549i	−0.102907	−	0.274472i
$727$	10.4880	−	6.05523i	0.388977	−	0.224576i	−0.292740	−	0.956192i	$-0.594567\pi$
$727$	10.4880	−	6.05523i	0.388977	−	0.224576i	0.681717	+	0.731616i	$0.261234\pi$
$728$	−6.96124	−	2.88766i	−0.258001	−	0.107024i
$729$	−14.8291	−	22.5632i	−0.549227	−	0.835673i
$730$	−18.8908			−0.699180
$731$	0.349924	+	0.606086i	0.0129424	+	0.0224169i
$732$	−1.50137	−	4.00443i	−0.0554921	−	0.148008i
$733$	13.5673	+	7.83306i	0.501118	+	0.289321i	0.729175	−	0.684327i	$-0.239904\pi$
$733$	13.5673	+	7.83306i	0.501118	+	0.289321i	−0.228057	+	0.973648i	$0.573237\pi$
$734$	−17.8636	+	30.9407i	−0.659357	+	1.14204i
$735$	−4.51601	−	46.9606i	−0.166575	−	1.73217i
$736$	−3.12656	−	5.41535i	−0.115246	−	0.199613i
$737$			53.0522i			1.95420i
$738$	−20.6976	−	23.7222i	−0.761890	−	0.873228i
$739$	−8.10454			−0.298130			−0.149065	−	0.988827i	$-0.547626\pi$
$739$	−8.10454			−0.298130			−0.149065	+	0.988827i	$0.547626\pi$
$740$	−5.83974	−	10.1147i	−0.214673	−	0.371825i
$741$	−1.44538	+	8.68599i	−0.0530974	+	0.319088i
$742$		0			0
$743$	−10.5429	−	6.08697i	−0.386783	−	0.223309i	0.293982	−	0.955811i	$-0.405019\pi$
$743$	−10.5429	−	6.08697i	−0.386783	−	0.223309i	−0.680765	+	0.732502i	$0.738353\pi$
$744$	0.998423	−	6.00000i	0.0366040	−	0.219971i
$745$	37.0732	−	21.4042i	1.35826	−	0.784189i
$746$			32.0600i			1.17380i
$747$	−22.8769	−	7.83042i	−0.837020	−	0.286500i
$748$		−	2.92737i		−	0.107035i
$749$	−37.6100	+	4.93164i	−1.37424	+	0.180198i
$750$	−22.0136	+	26.7544i	−0.803824	+	0.976934i
$751$	−17.3062	+	29.9752i	−0.631511	+	1.09381i	0.355732	+	0.934588i	$0.384232\pi$
$751$	−17.3062	+	29.9752i	−0.631511	+	1.09381i	−0.987243	+	0.159221i	$0.949102\pi$
$752$	1.09263	−	1.89248i	0.0398440	−	0.0690118i
$753$	−20.5049	+	7.68782i	−0.747240	+	0.280160i
$754$	7.12348	−	4.11274i	0.259422	−	0.149777i
$755$	5.60311			0.203918
$756$	−10.6647	+	8.67545i	−0.387873	+	0.315523i
$757$	−39.0553			−1.41949			−0.709744	−	0.704459i	$-0.751190\pi$
$757$	−39.0553			−1.41949			−0.709744	+	0.704459i	$0.751190\pi$
$758$	−30.2149	+	17.4446i	−1.09745	+	0.633615i
$759$	40.0038	−	14.9985i	1.45204	−	0.544410i
$760$	3.47231	−	6.01422i	0.125954	−	0.218159i
$761$	5.11262	−	8.85532i	0.185332	−	0.321005i	−0.758356	−	0.651840i	$-0.773997\pi$
$761$	5.11262	−	8.85532i	0.185332	−	0.321005i	0.943688	+	0.330835i	$0.107330\pi$
$762$	3.24055	−	3.93842i	0.117393	−	0.142674i
$763$	3.88010	+	29.5907i	0.140469	+	1.07125i
$764$			6.21372i			0.224805i
$765$	−1.66851	−	8.50079i	−0.0603250	−	0.307347i
$766$		−	17.5342i		−	0.633537i
$767$	0.0521363	−	0.0301009i	0.00188253	−	0.00108688i
$768$	0.284310	−	1.70856i	0.0102592	−	0.0616522i
$769$	−26.6746	−	15.4006i	−0.961910	−	0.555359i	−0.0651494	−	0.997876i	$-0.520752\pi$
$769$	−26.6746	−	15.4006i	−0.961910	−	0.555359i	−0.896760	+	0.442517i	$0.854086\pi$
$770$	−32.2305	+	24.7048i	−1.16151	+	0.890301i
$771$	4.63613	−	27.8607i	0.166966	−	1.00338i
$772$	−3.90271	−	6.75970i	−0.140462	−	0.243287i
$773$	−35.7833			−1.28704			−0.643518	−	0.765431i	$-0.722526\pi$
$773$	−35.7833			−1.28704			−0.643518	+	0.765431i	$0.722526\pi$
$774$	−2.77616	+	0.544895i	−0.0997869	+	0.0195859i
$775$		−	35.6117i		−	1.27921i
$776$	9.40980	+	16.2983i	0.337792	+	0.585073i
$777$	−6.46236	−	12.1423i	−0.231836	−	0.435604i
$778$	3.81086	−	6.60060i	0.136626	−	0.236643i
$779$	16.2200	+	9.36461i	0.581141	+	0.335522i
$780$	6.73961	+	17.9758i	0.241317	+	0.643638i
$781$	−3.83228	−	6.63771i	−0.137130	−	0.237516i
$782$	4.64054			0.165945
$783$	−0.433877	−	14.9985i	−0.0155055	−	0.536001i
$784$	4.94462	+	4.95487i	0.176594	+	0.176960i
$785$	55.9626	−	32.3100i	1.99739	−	1.15319i
$786$	−9.16047	−	24.4327i	−0.326743	−	0.871486i
$787$	13.2859	+	7.67064i	0.473592	+	0.273429i	0.717742	−	0.696309i	$-0.245176\pi$
$787$	13.2859	+	7.67064i	0.473592	+	0.273429i	−0.244150	+	0.969737i	$0.578509\pi$
$788$	11.0624	+	6.38687i	0.394081	+	0.227523i
$789$	−26.1055	+	31.7275i	−0.929380	+	1.12953i
$790$	12.2530	−	7.07430i	0.435944	−	0.251692i
$791$	9.96748	−	24.0284i	0.354403	−	0.854353i
$792$	11.1962	+	3.83228i	0.397838	+	0.136174i
$793$	−7.03326			−0.249758
$794$	18.8234	+	32.6032i	0.668019	+	1.15704i
$795$		0			0
$796$	1.56925	+	0.906005i	0.0556205	+	0.0321125i
$797$	−17.5200	+	30.3455i	−0.620590	+	1.07489i	0.368786	+	0.929514i	$0.379774\pi$
$797$	−17.5200	+	30.3455i	−0.620590	+	1.07489i	−0.989376	+	0.145379i	$0.953560\pi$
$798$	4.33130	−	6.93764i	0.153327	−	0.245590i
$799$	0.810856	+	1.40444i	0.0286860	+	0.0496857i
$800$		−	10.1408i		−	0.358530i
$801$	−20.9471	+	18.2763i	−0.740130	+	0.645763i
$802$	−21.4415			−0.757124
$803$	9.57529	+	16.5849i	0.337905	+	0.585268i
$804$	−17.9884	−	14.8009i	−0.634401	−	0.521987i
$805$	−39.1627	−	51.0926i	−1.38031	−	1.80078i
$806$	−8.66299	−	5.00158i	−0.305141	−	0.176173i
$807$	−11.8114	+	4.42841i	−0.415782	+	0.155888i
$808$	−7.17206	+	4.14079i	−0.252312	+	0.145673i
$809$			27.2925i			0.959553i	0.877391	+	0.479777i	$0.159282\pi$
$809$			27.2925i			0.959553i	−0.877391	+	0.479777i	$0.840718\pi$
$810$	34.6968	+	4.74711i	1.21912	+	0.166797i
$811$		−	27.7628i		−	0.974883i	−0.873156	−	0.487442i	$-0.837930\pi$
$811$		−	27.7628i		−	0.974883i	0.873156	−	0.487442i	$-0.162070\pi$
$812$	−7.57519	+	0.993303i	−0.265837	+	0.0348581i
$813$	−13.7956	−	36.7955i	−0.483833	−	1.29047i
$814$	−5.92004	+	10.2538i	−0.207497	+	0.359396i
$815$	−24.1161	+	41.7703i	−0.844749	+	1.46315i
$816$	0.992580	+	0.816699i	0.0347473	+	0.0285902i
$817$	1.45759	−	0.841542i	0.0509947	−	0.0294418i
$818$	29.5703			1.03390
$819$	7.20207	+	21.4314i	0.251661	+	0.748875i
$820$	40.8338			1.42598
$821$	−38.4968	+	22.2262i	−1.34355	+	0.775698i	−0.987326	−	0.158703i	$-0.949269\pi$
$821$	−38.4968	+	22.2262i	−1.34355	+	0.775698i	−0.356223	+	0.934401i	$0.615936\pi$
$822$	−4.46934	+	26.8584i	−0.155886	+	0.936795i
$823$	25.5577	−	44.2672i	0.890884	−	1.54306i	0.0520663	−	0.998644i	$-0.483419\pi$
$823$	25.5577	−	44.2672i	0.890884	−	1.54306i	0.838818	−	0.544413i	$-0.183247\pi$
$824$	8.52435	−	14.7646i	0.296960	−	0.514349i
$825$	68.3448	+	11.3728i	2.37946	+	0.395951i
$826$	−0.0554423	+	0.00726992i	−0.00192908	+	0.000252953i
$827$		−	14.5414i		−	0.505653i	−0.967512	−	0.252826i	$-0.918640\pi$
$827$		−	14.5414i		−	0.505653i	0.967512	−	0.252826i	$-0.0813601\pi$
$828$	−6.07503	+	17.7484i	−0.211122	+	0.616800i
$829$			27.9681i			0.971373i	0.874133	+	0.485686i	$0.161430\pi$
$829$			27.9681i			0.971373i	−0.874133	+	0.485686i	$0.838570\pi$
$830$	27.1605	−	15.6811i	0.942754	−	0.544299i
$831$	32.3242	+	26.5964i	1.12131	+	0.922620i
$832$	−2.46687	−	1.42425i	−0.0855233	−	0.0493769i
$833$	−5.01920	+	1.33932i	−0.173905	+	0.0464047i
$834$	5.36291	−	2.01070i	0.185703	−	0.0696247i
$835$	22.8053	+	39.5000i	0.789211	+	1.36695i
$836$	−7.04011			−0.243487
$837$	−15.5324	+	9.57689i	−0.536877	+	0.331026i
$838$			7.12962i			0.246289i
$839$	−0.499354	−	0.864906i	−0.0172396	−	0.0298599i	0.857277	−	0.514856i	$-0.172154\pi$
$839$	−0.499354	−	0.864906i	−0.0172396	−	0.0298599i	−0.874517	+	0.484996i	$0.838821\pi$
$840$	0.615254	−	17.8207i	0.0212283	−	0.614873i
$841$	−10.3307	+	17.8933i	−0.356231	+	0.617011i
$842$	4.00115	+	2.31007i	0.137889	+	0.0796102i
$843$	5.22568	−	6.35107i	0.179982	−	0.218742i
$844$	1.88766	+	3.26953i	0.0649760	+	0.112542i
$845$	−19.0123			−0.654044
$846$	−6.43301	+	1.26265i	−0.221172	+	0.0434108i
$847$	11.1439	+	4.62273i	0.382910	+	0.158839i
$848$		0			0
$849$	50.2064	+	8.35454i	1.72308	+	0.286727i
$850$	6.51739	+	3.76282i	0.223545	+	0.129064i
$851$	−16.2546	−	9.38460i	−0.557200	−	0.321700i
$852$	3.31980	+	0.552427i	0.113734	+	0.0189258i
$853$	8.48739	−	4.90020i	0.290603	−	0.167780i	−0.347611	−	0.937639i	$-0.613007\pi$
$853$	8.48739	−	4.90020i	0.290603	−	0.167780i	0.638214	+	0.769859i	$0.279674\pi$
$854$	6.03410	+	2.50307i	0.206483	+	0.0856531i
$855$	−20.4438	+	4.01264i	−0.699163	+	0.137229i
$856$	−14.3369			−0.490026
$857$	3.85002	+	6.66842i	0.131514	+	0.227789i	0.924260	−	0.381763i	$-0.124683\pi$
$857$	3.85002	+	6.66842i	0.131514	+	0.227789i	−0.792746	+	0.609552i	$0.791349\pi$
$858$	12.3654	−	15.0284i	0.422149	−	0.513062i
$859$	−16.4022	−	9.46979i	−0.559634	−	0.323105i	0.193364	−	0.981127i	$-0.438060\pi$
$859$	−16.4022	−	9.46979i	−0.559634	−	0.323105i	−0.752999	+	0.658022i	$0.771393\pi$
$860$	1.83474	−	3.17787i	0.0625642	−	0.108364i
$861$	48.0614	+	1.65930i	1.63793	+	0.0565489i
$862$	2.00385	+	3.47078i	0.0682515	+	0.118215i
$863$			17.4540i			0.594141i	0.954856	+	0.297070i	$0.0960096\pi$
$863$			17.4540i			0.594141i	−0.954856	+	0.297070i	$0.903990\pi$
$864$	−4.42299	+	2.72711i	−0.150473	+	0.0927782i
$865$	−65.2578			−2.21883
$866$	−14.7063	−	25.4720i	−0.499740	−	0.865574i
$867$	26.6776	−	10.0021i	0.906018	−	0.339690i
$868$	5.65229	+	7.37411i	0.191851	+	0.250294i
$869$	−12.4215	−	7.17157i	−0.421371	−	0.243279i
$870$	15.0284	+	12.3654i	0.509512	+	0.419228i
$871$	−33.1776	+	19.1551i	−1.12418	+	0.649045i
$872$			11.2800i			0.381988i
$873$	18.2836	−	53.4163i	0.618808	−	1.80787i
$874$		−	11.1602i		−	0.377498i
$875$	−6.88078	−	52.4746i	−0.232613	−	1.77397i
$876$	−8.29481	−	1.38029i	−0.280256	−	0.0466356i
$877$	−0.196152	+	0.339746i	−0.00662360	+	0.0114724i	−0.869318	−	0.494253i	$-0.835442\pi$
$877$	−0.196152	+	0.339746i	−0.00662360	+	0.0114724i	0.862695	+	0.505725i	$0.168775\pi$
$878$	−10.6885	+	18.5130i	−0.360718	+	0.624782i
$879$	−1.88331	+	11.3177i	−0.0635224	+	0.381736i
$880$	−13.2926	+	7.67448i	−0.448093	+	0.258707i
$881$	37.0259			1.24744			0.623718	−	0.781650i	$-0.285622\pi$
$881$	37.0259			1.24744			0.623718	+	0.781650i	$0.285622\pi$
$882$	1.44831	−	20.9500i	0.0487671	−	0.705423i
$883$	−29.9586			−1.00819			−0.504094	−	0.863649i	$-0.668174\pi$
$883$	−29.9586			−1.00819			−0.504094	+	0.863649i	$0.668174\pi$
$884$	1.83070	−	1.05696i	0.0615732	−	0.0355493i
$885$	0.109992	+	0.0905019i	0.00369734	+	0.00304219i
$886$	−2.91693	+	5.05227i	−0.0979962	+	0.169734i
$887$	−14.4930	+	25.1026i	−0.486626	+	0.842861i	−0.999882	−	0.0153745i	$-0.995106\pi$
$887$	−14.4930	+	25.1026i	−0.486626	+	0.842861i	0.513256	+	0.858236i	$0.328439\pi$
$888$	−1.82513	−	4.86799i	−0.0612475	−	0.163359i
$889$	1.01290	+	7.72461i	0.0339714	+	0.259075i
$890$		−	36.0569i		−	1.20863i
$891$	−13.4193	−	32.8677i	−0.449563	−	1.10111i
$892$		−	12.7782i		−	0.427846i
$893$	3.37759	−	1.95005i	0.113027	−	0.0652560i
$894$	17.8425	−	6.68960i	0.596741	−	0.223734i
$895$	−19.4617	−	11.2362i	−0.650533	−	0.375586i
$896$	1.60954	+	2.09985i	0.0537711	+	0.0701510i
$897$	23.8235	+	19.6020i	0.795442	+	0.654492i
$898$	11.2912	+	19.5569i	0.376791	+	0.652621i
$899$	−10.1407			−0.338211
$900$	−22.9235	+	20.0007i	−0.764117	+	0.666691i
$901$		0			0
$902$	−20.6976	−	35.8493i	−0.689156	−	1.19365i
$903$	2.28863	−	3.66580i	0.0761608	−	0.121990i
$904$	4.91614	−	8.51501i	0.163508	−	0.283205i
$905$	18.6455	+	10.7650i	0.619796	+	0.357839i
$906$	2.46028	+	0.409400i	0.0817374	+	0.0136014i
$907$	1.94773	+	3.37357i	0.0646733	+	0.112017i	0.896549	−	0.442945i	$-0.146066\pi$
$907$	1.94773	+	3.37357i	0.0646733	+	0.112017i	−0.831876	+	0.554962i	$0.812733\pi$
$908$	−19.9822			−0.663133
$909$	23.5059	+	8.04573i	0.779642	+	0.266860i
$910$	−27.0870	−	11.2362i	−0.897924	−	0.372477i
$911$	1.32768	−	0.766538i	0.0439881	−	0.0253966i	−0.477845	−	0.878444i	$-0.658582\pi$
$911$	1.32768	−	0.766538i	0.0439881	−	0.0253966i	0.521833	+	0.853048i	$0.325248\pi$
$912$	1.96410	−	2.38708i	0.0650379	−	0.0790443i
$913$	−27.5339	−	15.8967i	−0.911240	−	0.526105i
$914$	34.5218	+	19.9311i	1.14188	+	0.659264i
$915$	−5.84199	−	15.5817i	−0.193130	−	0.515115i
$916$	8.77402	−	5.06568i	0.289902	−	0.167375i
$917$	36.8166	+	15.2723i	1.21579	+	0.504334i
$918$	−0.111505	−	3.85454i	−0.00368020	−	0.127219i
$919$	28.2531			0.931984			0.465992	−	0.884789i	$-0.345698\pi$
$919$	28.2531			0.931984			0.465992	+	0.884789i	$0.345698\pi$
$920$	−12.1658	−	21.0718i	−0.401094	−	0.694715i
$921$	13.2096	+	35.2325i	0.435270	+	1.16095i
$922$	−6.37834	−	3.68254i	−0.210059	−	0.121278i
$923$	2.76737	−	4.79323i	0.0910892	−	0.157771i
$924$	−15.9573	+	8.49272i	−0.524955	+	0.279390i
$925$	−15.2192	−	26.3603i	−0.500403	−	0.866723i
$926$		−	28.6914i		−	0.942859i
$927$	−50.1885	+	9.85083i	−1.64841	+	0.323544i
$928$	−2.88766			−0.0947921
$929$	1.64363	+	2.84685i	0.0539257	+	0.0934021i	0.891728	−	0.452571i	$-0.149493\pi$
$929$	1.64363	+	2.84685i	0.0539257	+	0.0934021i	−0.837802	+	0.545974i	$0.816160\pi$
$930$	3.88498	−	23.3467i	0.127393	−	0.765568i
$931$	3.22097	+	12.0708i	0.105563	+	0.395605i
$932$	6.33070	+	3.65503i	0.207369	+	0.119725i
$933$	−1.79059	+	10.7605i	−0.0586211	+	0.352282i
$934$	−11.8389	+	6.83519i	−0.387380	+	0.223654i
$935$		−	11.3907i		−	0.372517i
$936$	1.64588	+	8.38548i	0.0537971	+	0.274088i
$937$			35.5084i			1.16001i	0.814613	+	0.580005i	$0.196949\pi$
$937$			35.5084i			1.16001i	−0.814613	+	0.580005i	$0.803051\pi$
$938$	35.2814	−	4.62630i	1.15198	−	0.151054i
$939$	24.4520	−	29.7180i	0.797962	−	0.969809i
$940$	4.25153	−	7.36387i	0.138670	−	0.240183i
$941$	6.24941	−	10.8243i	0.203725	−	0.352862i	−0.746001	−	0.665945i	$-0.768028\pi$
$941$	6.24941	−	10.8243i	0.203725	−	0.352862i	0.949726	+	0.313083i	$0.101362\pi$
$942$	26.9335	−	10.0981i	0.877541	−	0.329013i
$943$	56.8293	−	32.8104i	1.85062	−	1.06845i
$944$	−0.0211346			−0.000687873
$945$	−41.4977	+	33.7572i	−1.34992	+	1.09812i
$946$	−3.71994			−0.120946
$947$	31.2769	−	18.0577i	1.01636	−	0.586796i	0.103313	−	0.994649i	$-0.467056\pi$
$947$	31.2769	−	18.0577i	1.01636	−	0.586796i	0.913048	+	0.407852i	$0.133722\pi$
$948$	5.89711	−	2.21098i	0.191529	−	0.0718093i
$949$	−6.91452	+	11.9763i	−0.224455	+	0.388767i
$950$	9.04931	−	15.6739i	0.293598	−	0.508527i
$951$	−17.2354	+	20.9471i	−0.558895	+	0.679257i
$952$	−1.94679	+	0.255275i	−0.0630959	+	0.00827350i
$953$			45.2925i			1.46717i	0.679599	+	0.733584i	$0.262154\pi$
$953$			45.2925i			1.46717i	−0.679599	+	0.733584i	$0.737846\pi$
$954$		0			0
$955$			24.1783i			0.782392i
$956$	7.28317	−	4.20494i	0.235554	−	0.135997i
$957$	3.23850	−	19.4617i	0.104686	−	0.629108i
$958$	9.01596	+	5.20537i	0.291293	+	0.168178i
$959$	−25.3019	−	33.0095i	−0.817042	−	1.06593i
$960$	1.10628	−	6.64819i	0.0357052	−	0.214569i
$961$	−9.33386	−	16.1667i	−0.301092	−	0.521507i
$962$	−8.54997			−0.275662
$963$	28.2769	+	32.4090i	0.911209	+	1.04437i
$964$			8.95213i			0.288329i
$965$	−15.1859	−	26.3028i	−0.488851	−	0.846716i
$966$	−13.4629	−	25.2958i	−0.433161	−	0.813881i
$967$	12.0000	−	20.7845i	0.385893	−	0.668385i	−0.606000	−	0.795465i	$-0.707227\pi$
$967$	12.0000	−	20.7845i	0.385893	−	0.668385i	0.991893	+	0.127079i	$0.0405602\pi$
$968$	3.94910	+	2.28001i	0.126929	+	0.0732824i
$969$	0.805364	+	2.14806i	0.0258720	+	0.0690056i
$970$	36.6146	+	63.4184i	1.17562	+	2.03624i
$971$	−33.3626			−1.07066			−0.535328	−	0.844644i	$-0.679812\pi$
$971$	−33.3626			−1.07066			−0.535328	+	0.844644i	$0.679812\pi$
$972$	14.8882	+	4.61960i	0.477540	+	0.148174i
$973$	−3.35222	+	8.08113i	−0.107467	+	0.259069i
$974$	−2.02520	+	1.16925i	−0.0648917	+	0.0374652i
$975$	17.5643	+	46.8475i	0.562509	+	1.50032i
$976$	2.13832	+	1.23456i	0.0684458	+	0.0395172i
$977$	−29.8846	−	17.2539i	−0.956091	−	0.552000i	−0.0611236	−	0.998130i	$-0.519468\pi$
$977$	−29.8846	−	17.2539i	−0.956091	−	0.552000i	−0.894968	+	0.446131i	$0.852802\pi$
$978$	−13.6412	+	16.5789i	−0.436197	+	0.530135i
$979$	−31.6555	+	18.2763i	−1.01172	+	0.584114i
$980$	19.2401	+	19.2800i	0.614602	+	0.615876i
$981$	25.4987	−	22.2476i	0.814111	−	0.710311i
$982$	33.8844			1.08130
$983$	−1.20651	−	2.08973i	−0.0384817	−	0.0666522i	0.846143	−	0.532956i	$-0.178919\pi$
$983$	−1.20651	−	2.08973i	−0.0384817	−	0.0666522i	−0.884625	+	0.466304i	$0.845585\pi$
$984$	17.9298	+	2.98358i	0.571581	+	0.0951132i
$985$	43.0450	+	24.8521i	1.37153	+	0.791852i
$986$	1.07149	−	1.85588i	0.0341232	−	0.0591032i
$987$	5.30330	−	8.49452i	0.168806	−	0.270384i
$988$	−2.54191	−	4.40271i	−0.0808688	−	0.140069i
$989$		−	5.89695i		−	0.187512i
$990$	43.5655	+	14.9118i	1.38460	+	0.473930i
$991$	48.5982			1.54377			0.771887	−	0.635760i	$-0.219313\pi$
$991$	48.5982			1.54377			0.771887	+	0.635760i	$0.219313\pi$
$992$	1.75587	+	3.04125i	0.0557488	+	0.0965598i
$993$	1.70164	+	1.40012i	0.0540000	+	0.0444314i
$994$	−4.08010	+	3.12741i	−0.129413	+	0.0991955i
$995$	6.10612	+	3.52537i	0.193577	+	0.111762i
$996$	13.0717	−	4.90092i	0.414193	−	0.155292i
$997$	38.8449	−	22.4271i	1.23023	−	0.710274i	0.263152	−	0.964754i	$-0.415238\pi$
$997$	38.8449	−	22.4271i	1.23023	−	0.710274i	0.967078	+	0.254481i	$0.0819045\pi$
$998$			16.6045i			0.525605i
$999$	−7.40449	+	13.7269i	−0.234268	+	0.434301i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.m.a.41.1	✓	16
3.2	odd	2		378.2.m.a.125.5		16
4.3	odd	2		1008.2.cc.b.545.7		16
7.2	even	3		882.2.t.b.815.7		16
7.3	odd	6		882.2.l.a.509.1		16
7.4	even	3		882.2.l.a.509.4		16
7.5	odd	6		882.2.t.b.815.6		16
7.6	odd	2	inner	126.2.m.a.41.4	yes	16
9.2	odd	6	inner	126.2.m.a.83.4	yes	16
9.4	even	3		1134.2.d.a.1133.1		16
9.5	odd	6		1134.2.d.a.1133.16		16
9.7	even	3		378.2.m.a.251.8		16
12.11	even	2		3024.2.cc.b.881.1		16
21.2	odd	6		2646.2.t.a.2285.4		16
21.5	even	6		2646.2.t.a.2285.1		16
21.11	odd	6		2646.2.l.b.1097.5		16
21.17	even	6		2646.2.l.b.1097.8		16
21.20	even	2		378.2.m.a.125.8		16
28.27	even	2		1008.2.cc.b.545.2		16
36.7	odd	6		3024.2.cc.b.2897.8		16
36.11	even	6		1008.2.cc.b.209.2		16
63.2	odd	6		882.2.l.a.227.5		16
63.11	odd	6		882.2.t.b.803.6		16
63.13	odd	6		1134.2.d.a.1133.8		16
63.16	even	3		2646.2.l.b.521.4		16
63.20	even	6	inner	126.2.m.a.83.1	yes	16
63.25	even	3		2646.2.t.a.1979.1		16
63.34	odd	6		378.2.m.a.251.5		16
63.38	even	6		882.2.t.b.803.7		16
63.41	even	6		1134.2.d.a.1133.9		16
63.47	even	6		882.2.l.a.227.8		16
63.52	odd	6		2646.2.t.a.1979.4		16
63.61	odd	6		2646.2.l.b.521.1		16
84.83	odd	2		3024.2.cc.b.881.8		16
252.83	odd	6		1008.2.cc.b.209.7		16
252.223	even	6		3024.2.cc.b.2897.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.1	✓	16	1.1	even	1	trivial
126.2.m.a.41.4	yes	16	7.6	odd	2	inner
126.2.m.a.83.1	yes	16	63.20	even	6	inner
126.2.m.a.83.4	yes	16	9.2	odd	6	inner
378.2.m.a.125.5		16	3.2	odd	2
378.2.m.a.125.8		16	21.20	even	2
378.2.m.a.251.5		16	63.34	odd	6
378.2.m.a.251.8		16	9.7	even	3
882.2.l.a.227.5		16	63.2	odd	6
882.2.l.a.227.8		16	63.47	even	6
882.2.l.a.509.1		16	7.3	odd	6
882.2.l.a.509.4		16	7.4	even	3
882.2.t.b.803.6		16	63.11	odd	6
882.2.t.b.803.7		16	63.38	even	6
882.2.t.b.815.6		16	7.5	odd	6
882.2.t.b.815.7		16	7.2	even	3
1008.2.cc.b.209.2		16	36.11	even	6
1008.2.cc.b.209.7		16	252.83	odd	6
1008.2.cc.b.545.2		16	28.27	even	2
1008.2.cc.b.545.7		16	4.3	odd	2
1134.2.d.a.1133.1		16	9.4	even	3
1134.2.d.a.1133.8		16	63.13	odd	6
1134.2.d.a.1133.9		16	63.41	even	6
1134.2.d.a.1133.16		16	9.5	odd	6
2646.2.l.b.521.1		16	63.61	odd	6
2646.2.l.b.521.4		16	63.16	even	3
2646.2.l.b.1097.5		16	21.11	odd	6
2646.2.l.b.1097.8		16	21.17	even	6
2646.2.t.a.1979.1		16	63.25	even	3
2646.2.t.a.1979.4		16	63.52	odd	6
2646.2.t.a.2285.1		16	21.5	even	6
2646.2.t.a.2285.4		16	21.2	odd	6
3024.2.cc.b.881.1		16	12.11	even	2
3024.2.cc.b.881.8		16	84.83	odd	2
3024.2.cc.b.2897.1		16	252.223	even	6
3024.2.cc.b.2897.8		16	36.7	odd	6

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.62181 + 0.608059i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.94556 - 3.36980i) q^{5} +(1.10050 - 1.33750i) q^{6} +(0.343982 + 2.62329i) q^{7} +1.00000i q^{8} +(2.26053 - 1.97231i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.62181 + 0.608059i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.94556 - 3.36980i) q^{5} +(1.10050 - 1.33750i) q^{6} +(0.343982 + 2.62329i) q^{7} +1.00000i q^{8} +(2.26053 - 1.97231i) q^{9} +3.89111i q^{10} +(3.41614 - 1.97231i) q^{11} +(-0.284310 + 1.70856i) q^{12} +(2.46687 + 1.42425i) q^{13} +(-1.60954 - 2.09985i) q^{14} +(-1.10628 + 6.64819i) q^{15} +(-0.500000 - 0.866025i) q^{16} +0.742117 q^{17} +(-0.971521 + 2.83834i) q^{18} -1.78474i q^{19} +(-1.94556 - 3.36980i) q^{20} +(-2.15299 - 4.04532i) q^{21} +(-1.97231 + 3.41614i) q^{22} +(-5.41535 - 3.12656i) q^{23} +(-0.608059 - 1.62181i) q^{24} +(-5.07039 - 8.78217i) q^{25} -2.84849 q^{26} +(-2.46687 + 4.57324i) q^{27} +(2.44383 + 1.01375i) q^{28} +(-2.50079 + 1.44383i) q^{29} +(-2.36603 - 6.31064i) q^{30} +(3.04125 + 1.75587i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.34105 + 5.27592i) q^{33} +(-0.642692 + 0.371058i) q^{34} +(9.50923 + 3.94462i) q^{35} +(-0.577806 - 2.94383i) q^{36} +3.00158 q^{37} +(0.892369 + 1.54563i) q^{38} +(-4.86681 - 0.809856i) q^{39} +(3.36980 + 1.94556i) q^{40} +(-5.24705 + 9.08816i) q^{41} +(3.88721 + 2.42686i) q^{42} +(0.471521 + 0.816699i) q^{43} -3.94462i q^{44} +(-2.24831 - 11.4548i) q^{45} +6.25311 q^{46} +(1.09263 + 1.89248i) q^{47} +(1.33750 + 1.10050i) q^{48} +(-6.76335 + 1.80473i) q^{49} +(8.78217 + 5.07039i) q^{50} +(-1.20357 + 0.451251i) q^{51} +(2.46687 - 1.42425i) q^{52} +(-0.150252 - 5.19398i) q^{54} -15.3490i q^{55} +(-2.62329 + 0.343982i) q^{56} +(1.08523 + 2.89450i) q^{57} +(1.44383 - 2.50079i) q^{58} +(0.0105673 - 0.0183031i) q^{59} +(5.20436 + 4.28217i) q^{60} +(-2.13832 + 1.23456i) q^{61} -3.51174 q^{62} +(5.95153 + 5.25160i) q^{63} -1.00000 q^{64} +(9.59886 - 5.54191i) q^{65} +(1.12150 - 6.73961i) q^{66} +(-6.72463 + 11.6474i) q^{67} +(0.371058 - 0.642692i) q^{68} +(10.6838 + 1.77782i) q^{69} +(-10.2075 + 1.33847i) q^{70} -1.94304i q^{71} +(1.97231 + 2.26053i) q^{72} +4.85486i q^{73} +(-2.59944 + 1.50079i) q^{74} +(13.5633 + 11.1599i) q^{75} +(-1.54563 - 0.892369i) q^{76} +(6.34904 + 8.28311i) q^{77} +(4.61971 - 1.73205i) q^{78} +(-1.81806 - 3.14898i) q^{79} -3.89111 q^{80} +(1.21999 - 8.91693i) q^{81} -10.4941i q^{82} +(-4.02998 - 6.98012i) q^{83} +(-4.57985 - 0.158118i) q^{84} +(1.44383 - 2.50079i) q^{85} +(-0.816699 - 0.471521i) q^{86} +(3.17787 - 3.86224i) q^{87} +(1.97231 + 3.41614i) q^{88} -9.26646 q^{89} +(7.67448 + 8.79598i) q^{90} +(-2.88766 + 6.96124i) q^{91} +(-5.41535 + 3.12656i) q^{92} +(-6.00000 - 0.998423i) q^{93} +(-1.89248 - 1.09263i) q^{94} +(-6.01422 - 3.47231i) q^{95} +(-1.70856 - 0.284310i) q^{96} +(16.2983 - 9.40980i) q^{97} +(4.95487 - 4.94462i) q^{98} +(3.83228 - 11.1962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{7} + 12 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 2 * q^7 + 12 * q^9	\( 16 q + 8 q^{4} + 2 q^{7} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 8 q^{16} - 12 q^{18} + 18 q^{21} - 48 q^{23} - 8 q^{25} + 4 q^{28} - 12 q^{29} - 24 q^{30} + 12 q^{36} - 8 q^{37} - 36 q^{39} - 12 q^{42} + 4 q^{43} + 24 q^{46} - 8 q^{49} + 60 q^{50} + 12 q^{51} - 6 q^{56} + 48 q^{57} - 12 q^{58} + 24 q^{60} + 24 q^{63} - 16 q^{64} + 84 q^{65} - 28 q^{67} + 36 q^{74} + 78 q^{77} - 24 q^{78} - 4 q^{79} + 36 q^{81} + 18 q^{84} - 12 q^{85} - 24 q^{86} + 24 q^{91} - 48 q^{92} - 96 q^{93} + 12 q^{95} - 72 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^7 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 8 * q^16 - 12 * q^18 + 18 * q^21 - 48 * q^23 - 8 * q^25 + 4 * q^28 - 12 * q^29 - 24 * q^30 + 12 * q^36 - 8 * q^37 - 36 * q^39 - 12 * q^42 + 4 * q^43 + 24 * q^46 - 8 * q^49 + 60 * q^50 + 12 * q^51 - 6 * q^56 + 48 * q^57 - 12 * q^58 + 24 * q^60 + 24 * q^63 - 16 * q^64 + 84 * q^65 - 28 * q^67 + 36 * q^74 + 78 * q^77 - 24 * q^78 - 4 * q^79 + 36 * q^81 + 18 * q^84 - 12 * q^85 - 24 * q^86 + 24 * q^91 - 48 * q^92 - 96 * q^93 + 12 * q^95 - 72 * q^99

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