LMFDB - Embedded newform 126.2.m.a.83.1

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			83.1
Root			$1.62181 + 0.608059i$ of defining polynomial
Character	$\chi$	$=$	126.83
Dual form			126.2.m.a.41.1

$q$-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 $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

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

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	0.861913	+	0.507056i	$0.169266\pi$
$5$	1.94556	+	3.36980i	0.870080	+	1.50702i	0.00816625	+	0.999967i	$0.497401\pi$
$6$	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	0.916986	−	0.398919i	$-0.130615\pi$
$11$	3.41614	+	1.97231i	1.03001	+	0.594674i	0.113019	+	0.993593i	$0.463948\pi$
$12$	−0.284310	−	1.70856i	−0.0820733	−	0.493218i
$13$	2.46687	−	1.42425i	0.684186	−	0.395015i	−0.117244	−	0.993103i	$-0.537406\pi$
$13$	2.46687	−	1.42425i	0.684186	−	0.395015i	0.801430	+	0.598088i	$0.204073\pi$
$14$	−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	$0.0656295\pi$
$19$			1.78474i			0.409447i	−0.978820	+	0.204723i	$0.934370\pi$
$20$	−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	−0.943728	−	0.330722i	$-0.892708\pi$
$23$	−5.41535	+	3.12656i	−1.12918	+	0.651932i	−0.185451	+	0.982654i	$0.559374\pi$
$24$	−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	0.249501	−	0.968374i	$-0.419733\pi$
$29$	−2.50079	−	1.44383i	−0.464385	−	0.268113i	−0.713886	+	0.700262i	$0.753067\pi$
$30$	−2.36603	+	6.31064i	−0.431975	+	1.15216i
$31$	3.04125	−	1.75587i	0.546225	−	0.315363i	−0.201373	−	0.979515i	$-0.564540\pi$
$31$	3.04125	−	1.75587i	0.546225	−	0.315363i	0.747598	+	0.664152i	$0.231207\pi$
$32$	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	−0.906087	−	0.423092i	$-0.860945\pi$
$41$	−5.24705	−	9.08816i	−0.819452	−	1.41933i	0.0866345	−	0.996240i	$-0.472389\pi$
$42$	3.88721	−	2.42686i	0.599809	−	0.374472i
$43$	0.471521	−	0.816699i	0.0719063	−	0.124545i	−0.827830	−	0.560978i	$-0.810425\pi$
$43$	0.471521	−	0.816699i	0.0719063	−	0.124545i	0.899737	+	0.436433i	$0.143758\pi$
$44$			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	−0.775268	−	0.631633i	$-0.782385\pi$
$47$	1.09263	−	1.89248i	0.159376	−	0.276047i	0.934644	+	0.355585i	$0.115718\pi$
$48$	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	0.866712	−	0.498808i	$-0.166229\pi$
$59$	0.0105673	+	0.0183031i	0.00137575	+	0.00238286i	−0.865337	+	0.501191i	$0.832895\pi$
$60$	5.20436	−	4.28217i	0.671880	−	0.552825i
$61$	−2.13832	−	1.23456i	−0.273783	−	0.158069i	0.356822	−	0.934172i	$-0.383860\pi$
$61$	−2.13832	−	1.23456i	−0.273783	−	0.158069i	−0.630606	+	0.776103i	$0.717193\pi$
$62$	−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	−0.904532	−	0.426406i	$-0.859779\pi$
$67$	−6.72463	−	11.6474i	−0.821544	−	1.42296i	0.0829874	−	0.996551i	$-0.473554\pi$
$68$	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	$0.0367824\pi$
$71$			1.94304i			0.230597i	−0.993331	+	0.115298i	$0.963218\pi$
$72$	1.97231	−	2.26053i	0.232439	−	0.266406i
$73$		−	4.85486i		−	0.568218i	−0.958792	−	0.284109i	$-0.908302\pi$
$73$		−	4.85486i		−	0.568218i	0.958792	−	0.284109i	$-0.0916978\pi$
$74$	−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	−0.949989	−	0.312284i	$-0.898906\pi$
$79$	−1.81806	+	3.14898i	−0.204548	+	0.354288i	0.745440	+	0.666572i	$0.232239\pi$
$80$	−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	−0.997863	−	0.0653378i	$-0.979188\pi$
$83$	−4.02998	+	6.98012i	−0.442347	+	0.766168i	0.555516	+	0.831506i	$0.312521\pi$
$84$	−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	0.975043	+	0.222018i	$0.0712643\pi$
$97$	16.2983	+	9.40980i	1.65484	+	0.955421i	0.679794	+	0.733403i	$0.262069\pi$
$98$	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	−0.583087	−	0.812410i	$-0.698155\pi$
$101$	4.14079	−	7.17206i	0.412024	−	0.713647i	0.995111	+	0.0987631i	$0.0314886\pi$
$102$	0.816699	+	0.992580i	0.0808652	+	0.0982801i
$103$	−14.7646	+	8.52435i	−1.45480	+	0.839929i	−0.998748	−	0.0500247i	$-0.984070\pi$
$103$	−14.7646	+	8.52435i	−1.45480	+	0.839929i	−0.456051	+	0.889953i	$0.650737\pi$
$104$	−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	$-0.756288\pi$
$107$		−	14.3369i		−	1.38600i	0.720936	−	0.693001i	$-0.243712\pi$
$108$	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	−0.843829	−	0.536612i	$-0.819704\pi$
$113$	−8.51501	+	4.91614i	−0.801024	+	0.462472i	0.0428049	+	0.999083i	$0.486371\pi$
$114$	−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	0.981101	+	0.193495i	$0.0619823\pi$
$131$	7.53255	+	13.0468i	0.658122	+	1.13990i	−0.322979	+	0.946406i	$0.604684\pi$
$132$	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	−0.211064	−	0.977472i	$-0.567693\pi$
$137$	−13.6139	−	7.85997i	−1.16311	−	0.671523i	−0.952048	+	0.305950i	$0.901026\pi$
$138$	−10.1414	−	3.80226i	−0.863289	−	0.323670i
$139$	2.86373	−	1.65337i	0.242898	−	0.140237i	−0.373610	−	0.927586i	$-0.621880\pi$
$139$	2.86373	−	1.65337i	0.242898	−	0.140237i	0.616508	+	0.787349i	$0.288547\pi$
$140$	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	−0.0560848	−	0.998426i	$-0.517862\pi$
$149$	9.52765	−	5.50079i	0.780535	−	0.450642i	0.836620	+	0.547784i	$0.184528\pi$
$150$	−17.3261	+	2.88313i	−1.41467	+	0.235406i
$151$	0.719988	−	1.24706i	0.0585918	−	0.101484i	−0.835242	−	0.549883i	$-0.814672\pi$
$151$	0.719988	−	1.24706i	0.0585918	−	0.101484i	0.893834	+	0.448399i	$0.148006\pi$
$152$	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	0.199465	−	0.979905i	$-0.436079\pi$
$157$	14.3822	−	8.30354i	1.14782	−	0.662695i	0.948355	+	0.317210i	$0.102746\pi$
$158$	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	0.545074	−	0.838388i	$-0.316502\pi$
$167$	−5.86087	−	10.1513i	−0.453528	−	0.785534i	−0.998602	+	0.0528541i	$0.983168\pi$
$168$	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	0.348435	+	0.937333i	$0.386713\pi$
$173$	−8.38548	+	14.5241i	−0.637536	+	1.10425i	−0.985972	+	0.166913i	$0.946620\pi$
$174$	−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	$0.0692470\pi$
$179$			5.77532i			0.431668i	−0.976430	+	0.215834i	$0.930753\pi$
$180$	−11.0443	+	3.78030i	−0.823193	+	0.281767i
$181$		−	5.53310i		−	0.411272i	−0.978629	−	0.205636i	$-0.934074\pi$
$181$		−	5.53310i		−	0.411272i	0.978629	−	0.205636i	$-0.0659263\pi$
$182$	−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	0.292515	−	0.956261i	$-0.405508\pi$
$191$	−5.38124	−	3.10686i	−0.389373	−	0.224805i	−0.681888	+	0.731456i	$0.738841\pi$
$192$	1.62181	+	0.608059i	0.117044	+	0.0438828i
$193$	3.90271	+	6.75970i	0.280923	+	0.486574i	0.971612	−	0.236578i	$-0.0760260\pi$
$193$	3.90271	+	6.75970i	0.280923	+	0.486574i	−0.690689	+	0.723152i	$0.742693\pi$
$194$	−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	$-0.849623\pi$
$197$		−	12.7737i		−	0.910092i	0.890468	−	0.455046i	$-0.150377\pi$
$198$	2.27922	−	11.6123i	0.161977	−	0.825250i
$199$		−	1.81201i		−	0.128450i	−0.997935	−	0.0642250i	$-0.979542\pi$
$199$		−	1.81201i		−	0.128450i	0.997935	−	0.0642250i	$-0.0204575\pi$
$200$	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	0.793706	−	0.608302i	$-0.208149\pi$
$211$	−1.88766	−	3.26953i	−0.129952	−	0.225083i	−0.923658	+	0.383218i	$0.874816\pi$
$212$		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	0.822451	−	0.568836i	$-0.192606\pi$
$223$	11.0662	+	6.38910i	0.741051	+	0.427846i	−0.0814006	+	0.996681i	$0.525939\pi$
$224$	−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	0.316655	+	0.948541i	$0.397440\pi$
$227$	−9.99110	+	17.3051i	−0.663133	+	1.14858i	−0.979788	+	0.200039i	$0.935893\pi$
$228$	3.04933	−	0.507420i	0.201947	−	0.0336047i
$229$	8.77402	−	5.06568i	0.579804	−	0.334750i	−0.181252	−	0.983437i	$-0.558015\pi$
$229$	8.77402	−	5.06568i	0.579804	−	0.334750i	0.761055	+	0.648687i	$0.224682\pi$
$230$	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	$-0.923033\pi$
$233$		−	7.31007i		−	0.478898i	0.970909	−	0.239449i	$-0.0769669\pi$
$234$	−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	−0.245595	−	0.969373i	$-0.578983\pi$
$239$	7.28317	−	4.20494i	0.471109	−	0.271995i	0.716704	+	0.697378i	$0.245650\pi$
$240$	6.31064	+	2.36603i	0.407350	+	0.152726i
$241$	−7.75277	−	4.47607i	−0.499400	−	0.288329i	0.229066	−	0.973411i	$-0.426433\pi$
$241$	−7.75277	−	4.47607i	−0.499400	−	0.288329i	−0.728466	+	0.685082i	$0.759766\pi$
$242$		−	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	−0.999951	−	0.00994523i	$-0.996834\pi$
$257$	−8.15329	−	14.1219i	−0.508588	−	0.880900i	0.491362	−	0.870955i	$-0.336499\pi$
$258$	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	0.974374	−	0.224934i	$-0.0722166\pi$
$263$	20.5434	+	11.8608i	1.26676	+	0.731366i	0.292389	+	0.956300i	$0.405550\pi$
$264$	−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	$-0.758007\pi$
$271$		−	22.6879i		−	1.37819i	0.724669	−	0.689097i	$-0.241993\pi$
$272$	−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	0.232496	+	0.972597i	$0.425311\pi$
$277$	−12.0838	+	20.9298i	−0.726046	+	1.25755i	−0.958542	+	0.284951i	$0.908023\pi$
$278$	−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	0.372300	−	0.928112i	$-0.378569\pi$
$281$	−4.11229	−	2.37423i	−0.245319	−	0.141635i	−0.617619	+	0.786478i	$0.711903\pi$
$282$	3.73363	−	0.621290i	0.222334	−	0.0369973i
$283$	−25.4484	+	14.6926i	−1.51275	+	0.873387i	−0.512861	+	0.858471i	$0.671415\pi$
$283$	−25.4484	+	14.6926i	−1.51275	+	0.873387i	−0.999889	+	0.0149153i	$0.995252\pi$
$284$	−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	0.946405	−	0.322981i	$-0.104685\pi$
$293$	3.31206	+	5.73666i	0.193493	+	0.335139i	−0.752913	+	0.658121i	$0.771352\pi$
$294$	−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	$0.212840\pi$
$307$			21.7242i			1.23987i	−0.784655	+	0.619933i	$0.787160\pi$
$308$	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	0.941389	−	0.337324i	$-0.109522\pi$
$311$	3.14900	+	5.45422i	0.178563	+	0.309281i	−0.762825	+	0.646605i	$0.776188\pi$
$312$	0.809856	+	4.86681i	0.0458491	+	0.275529i
$313$	−19.2423	−	11.1095i	−1.08764	−	0.627948i	−0.154691	−	0.987963i	$-0.549438\pi$
$313$	−19.2423	−	11.1095i	−1.08764	−	0.627948i	−0.932946	+	0.360015i	$0.882771\pi$
$314$	−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	0.829936	−	0.557859i	$-0.188377\pi$
$317$	13.5632	+	7.83070i	0.761784	+	0.439816i	−0.0681519	+	0.997675i	$0.521710\pi$
$318$		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	−0.882978	−	0.469414i	$-0.844465\pi$
$331$	−0.636129	+	1.10181i	−0.0349648	+	0.0605608i	0.848013	+	0.529975i	$0.177799\pi$
$332$	−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	0.744512	−	0.667609i	$-0.232682\pi$
$337$	−3.78001	−	6.54717i	−0.205910	−	0.356647i	−0.950422	+	0.310962i	$0.899349\pi$
$338$	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	0.111494	−	0.993765i	$-0.464436\pi$
$347$	19.1470	−	11.0545i	1.02787	−	0.593439i	0.916373	+	0.400326i	$0.131103\pi$
$348$	−1.75587	+	4.68324i	−0.0941244	+	0.251048i
$349$	−12.7682	−	7.37173i	−0.683467	−	0.394600i	0.117693	−	0.993050i	$-0.462450\pi$
$349$	−12.7682	−	7.37173i	−0.683467	−	0.394600i	−0.801160	+	0.598450i	$0.795783\pi$
$350$	−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	−0.539152	−	0.842208i	$-0.681255\pi$
$353$	8.63881	−	14.9629i	0.459798	−	0.796393i	0.998950	+	0.0458154i	$0.0145886\pi$
$354$	−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	$-0.907016\pi$
$359$		−	10.9129i		−	0.575963i	0.957636	−	0.287982i	$-0.0929842\pi$
$360$	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	0.988166	+	0.153391i	$0.0490194\pi$
$367$	30.9407	+	17.8636i	1.61509	+	0.932472i	0.626923	+	0.779081i	$0.284314\pi$
$368$		−	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	0.898035	+	0.439923i	$0.144994\pi$
$373$	16.0300	+	27.7648i	0.830003	+	1.43761i	−0.0680328	+	0.997683i	$0.521672\pi$
$374$	−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	0.550276	−	0.834983i	$-0.314523\pi$
$383$	−8.76711	−	15.1851i	−0.447978	−	0.775921i	−0.998254	+	0.0590616i	$0.981189\pi$
$384$	−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	0.323246	−	0.946315i	$-0.395226\pi$
$389$	−6.60060	−	3.81086i	−0.334664	−	0.193218i	−0.657910	+	0.753097i	$0.728559\pi$
$390$	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	$0.393668\pi$
$397$			37.6469i			1.88944i	−0.327873	+	0.944722i	$0.606332\pi$
$398$	−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	0.0413326	−	0.999145i	$-0.486840\pi$
$401$	18.5689	−	10.7207i	0.927284	−	0.535368i	0.885952	+	0.463778i	$0.153506\pi$
$402$	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	−0.974279	−	0.225344i	$-0.927649\pi$
$409$	−25.6086	+	14.7851i	−1.26627	+	0.731079i	−0.291986	+	0.956423i	$0.594316\pi$
$410$	−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	0.939868	−	0.341539i	$-0.110948\pi$
$419$	3.56481	+	6.17443i	0.174152	+	0.301641i	−0.765715	+	0.643180i	$0.777615\pi$
$420$	−9.44318	−	15.1256i	−0.460780	−	0.738052i
$421$	−2.31007	+	4.00115i	−0.112586	+	0.195004i	−0.916812	−	0.399319i	$-0.869247\pi$
$421$	−2.31007	+	4.00115i	−0.112586	+	0.195004i	0.804226	+	0.594323i	$0.202580\pi$
$422$			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	$0.0307719\pi$
$431$			4.00771i			0.193045i	−0.995331	+	0.0965223i	$0.969228\pi$
$432$	5.19398	+	0.150252i	0.249895	+	0.00722900i
$433$		−	29.4125i		−	1.41348i	−0.707475	−	0.706738i	$-0.750166\pi$
$433$		−	29.4125i		−	1.41348i	0.707475	−	0.706738i	$-0.249834\pi$
$434$	−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	0.871836	−	0.489799i	$-0.162930\pi$
$439$	18.5130	+	10.6885i	0.883575	+	0.510133i	0.0117398	+	0.999931i	$0.496263\pi$
$440$	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	0.615195	−	0.788375i	$-0.289077\pi$
$443$	5.05227	+	2.91693i	0.240041	+	0.138587i	−0.375155	+	0.926962i	$0.622410\pi$
$444$	−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	$0.178884\pi$
$449$			22.5823i			1.06573i	−0.846202	+	0.532863i	$0.821116\pi$
$450$	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	−0.153029	+	0.988222i	$0.548903\pi$
$457$	−19.9311	+	34.5218i	−0.932340	+	1.61486i	−0.779310	+	0.626638i	$0.784430\pi$
$458$	−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	−0.767436	−	0.641125i	$-0.778468\pi$
$461$	3.68254	−	6.37834i	0.171513	−	0.297069i	0.938949	+	0.344056i	$0.111801\pi$
$462$	18.0658	−	0.623714i	0.840495	−	0.0290178i
$463$	−14.3457	−	24.8475i	−0.666702	−	1.15476i	−0.978821	−	0.204718i	$-0.934372\pi$
$463$	−14.3457	−	24.8475i	−0.666702	−	1.15476i	0.312119	−	0.950043i	$-0.398961\pi$
$464$	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	−0.960094	−	0.279677i	$-0.909773\pi$
$479$	−5.20537	+	9.01596i	−0.237839	+	0.411950i	0.722255	+	0.691627i	$0.243106\pi$
$480$	−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	−0.984413	−	0.175871i	$-0.943726\pi$
$491$	−29.3448	+	16.9422i	−1.32431	+	0.764591i	−0.339898	+	0.940462i	$0.610392\pi$
$492$	−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	0.989821	−	0.142319i	$-0.0454558\pi$
$499$	8.30223	+	14.3799i	0.371659	+	0.643732i	−0.618162	+	0.786051i	$0.712123\pi$
$500$	−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	0.904724	+	0.425998i	$0.140077\pi$
$509$	18.5291	+	32.0933i	0.821287	+	1.42251i	−0.0834371	+	0.996513i	$0.526590\pi$
$510$	−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	$-0.823728\pi$
$523$		−	24.0538i		−	1.05180i	0.850546	−	0.525901i	$-0.176272\pi$
$524$	−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	−0.999010	−	0.0444765i	$-0.985838\pi$
$547$	−10.7816	+	18.6743i	−0.460987	+	0.798454i	0.538023	+	0.842930i	$0.319171\pi$
$548$		−	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	$0.286190\pi$
$557$			36.9477i			1.56552i	−0.622321	+	0.782762i	$0.713810\pi$
$558$	−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	0.660776	−	0.750584i	$-0.270228\pi$
$563$	−7.58422	−	13.1363i	−0.319637	−	0.553627i	−0.980412	+	0.196957i	$0.936894\pi$
$564$	−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	−0.347648	−	0.937625i	$-0.613020\pi$
$569$	−31.8084	−	18.3646i	−1.33348	−	0.769885i	−0.985831	+	0.167740i	$0.946353\pi$
$570$	−11.2628	−	4.22274i	−0.471749	−	0.176871i
$571$	−5.61387	−	9.72351i	−0.234933	−	0.406916i	0.724320	−	0.689464i	$-0.242154\pi$
$571$	−5.61387	−	9.72351i	−0.234933	−	0.406916i	−0.959253	+	0.282548i	$0.908820\pi$
$572$	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	$0.275208\pi$
$577$			36.5515i			1.52166i	−0.648952	+	0.760829i	$0.724792\pi$
$578$	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	−0.950535	−	0.310619i	$-0.899464\pi$
$587$	−4.99738	+	8.65571i	−0.206264	+	0.357259i	0.744271	+	0.667878i	$0.232797\pi$
$588$	−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	0.0127373	−	0.999919i	$-0.495945\pi$
$599$	21.6614	−	12.5062i	0.885061	−	0.510990i	0.872324	+	0.488929i	$0.162612\pi$
$600$	−11.1599	−	13.5633i	−0.455601	−	0.553718i
$601$	−25.9925	−	15.0068i	−1.06026	−	0.612139i	−0.134753	−	0.990879i	$-0.543024\pi$
$601$	−25.9925	−	15.0068i	−1.06026	−	0.612139i	−0.925503	+	0.378740i	$0.876357\pi$
$602$	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	−0.578378	−	0.815769i	$-0.696314\pi$
$607$	−3.96882	+	2.29140i	−0.161089	+	0.0930050i	0.417288	+	0.908774i	$0.362981\pi$
$608$	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	−0.945745	−	0.324909i	$-0.894666\pi$
$617$	−28.2484	+	16.3092i	−1.13724	+	0.656585i	−0.191493	+	0.981494i	$0.561333\pi$
$618$	−27.6497	−	10.3666i	−1.11224	−	0.417006i
$619$	17.3244	+	10.0023i	0.696327	+	0.402024i	0.805978	−	0.591946i	$-0.201640\pi$
$619$	17.3244	+	10.0023i	0.696327	+	0.402024i	−0.109651	+	0.993970i	$0.534973\pi$
$620$			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	0.947393	−	0.320074i	$-0.103708\pi$
$641$	28.9612	+	16.7207i	1.14390	+	0.660429i	0.196504	+	0.980503i	$0.437041\pi$
$642$	19.1756	−	15.7778i	0.756801	−	0.622699i
$643$	16.6022	−	9.58527i	0.654726	−	0.378006i	−0.135539	−	0.990772i	$-0.543276\pi$
$643$	16.6022	−	9.58527i	0.654726	−	0.378006i	0.790264	+	0.612766i	$0.209943\pi$
$644$	−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	−0.511010	−	0.859575i	$-0.670728\pi$
$653$	−0.564755	+	0.326061i	−0.0221006	+	0.0127598i	0.488909	+	0.872335i	$0.337395\pi$
$654$	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	0.915111	−	0.403202i	$-0.132103\pi$
$659$	26.2738	+	15.1692i	1.02348	+	0.590908i	0.108372	+	0.994110i	$0.465436\pi$
$660$	26.2246	−	4.36387i	1.02079	−	0.169863i
$661$	−11.1004	+	6.40881i	−0.431755	+	0.249274i	−0.700094	−	0.714051i	$-0.746859\pi$
$661$	−11.1004	+	6.40881i	−0.431755	+	0.249274i	0.268339	+	0.963325i	$0.413525\pi$
$662$	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	−0.564425	−	0.825484i	$-0.690902\pi$
$673$	11.2246	−	19.4416i	0.432678	−	0.749420i	0.997103	+	0.0760644i	$0.0242355\pi$
$674$			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	0.335163	−	0.942160i	$-0.391209\pi$
$677$	25.5903	−	44.3237i	0.983516	−	1.70350i	0.648353	−	0.761340i	$-0.275458\pi$
$678$	−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	$0.0898677\pi$
$683$			14.5616i			0.557184i	−0.960410	+	0.278592i	$0.910132\pi$
$684$	−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	0.0398517	−	0.999206i	$-0.487311\pi$
$691$	−21.1757	−	12.2258i	−0.805560	−	0.465090i	−0.845412	+	0.534115i	$0.820645\pi$
$692$	−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	$0.0133305\pi$
$701$			2.21697i			0.0837337i	−0.999123	+	0.0418669i	$0.986669\pi$
$702$	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	−0.540821	−	0.841138i	$-0.681886\pi$
$709$	12.1962	−	21.1244i	0.458036	−	0.793342i	0.998857	+	0.0477959i	$0.0152197\pi$
$710$	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	0.681717	−	0.731616i	$-0.261234\pi$
$727$	10.4880	+	6.05523i	0.388977	+	0.224576i	−0.292740	+	0.956192i	$0.594567\pi$
$728$	−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	−0.228057	−	0.973648i	$-0.573237\pi$
$733$	13.5673	−	7.83306i	0.501118	−	0.289321i	0.729175	+	0.684327i	$0.239904\pi$
$734$	−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	−0.680765	−	0.732502i	$-0.738353\pi$
$743$	−10.5429	+	6.08697i	−0.386783	+	0.223309i	0.293982	+	0.955811i	$0.405019\pi$
$744$	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	−0.987243	−	0.159221i	$-0.949102\pi$
$751$	−17.3062	−	29.9752i	−0.631511	−	1.09381i	0.355732	−	0.934588i	$-0.384232\pi$
$752$	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	0.943688	−	0.330835i	$-0.107330\pi$
$761$	5.11262	+	8.85532i	0.185332	+	0.321005i	−0.758356	+	0.651840i	$0.773997\pi$
$762$	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	−0.896760	−	0.442517i	$-0.854086\pi$
$769$	−26.6746	+	15.4006i	−0.961910	+	0.555359i	−0.0651494	+	0.997876i	$0.520752\pi$
$770$	−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	−0.244150	−	0.969737i	$-0.578509\pi$
$787$	13.2859	−	7.67064i	0.473592	−	0.273429i	0.717742	+	0.696309i	$0.245176\pi$
$788$	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	−0.989376	−	0.145379i	$-0.953560\pi$
$797$	−17.5200	−	30.3455i	−0.620590	−	1.07489i	0.368786	−	0.929514i	$-0.379774\pi$
$798$	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	$-0.840718\pi$
$809$		−	27.2925i		−	0.959553i	0.877391	−	0.479777i	$-0.159282\pi$
$810$	34.6968	−	4.74711i	1.21912	−	0.166797i
$811$			27.7628i			0.974883i	0.873156	+	0.487442i	$0.162070\pi$
$811$			27.7628i			0.974883i	−0.873156	+	0.487442i	$0.837930\pi$
$812$	−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	−0.356223	−	0.934401i	$-0.615936\pi$
$821$	−38.4968	−	22.2262i	−1.34355	−	0.775698i	−0.987326	+	0.158703i	$0.949269\pi$
$822$	−4.46934	−	26.8584i	−0.155886	−	0.936795i
$823$	25.5577	+	44.2672i	0.890884	+	1.54306i	0.838818	+	0.544413i	$0.183247\pi$
$823$	25.5577	+	44.2672i	0.890884	+	1.54306i	0.0520663	+	0.998644i	$0.483419\pi$
$824$	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	$0.0813601\pi$
$827$			14.5414i			0.505653i	−0.967512	+	0.252826i	$0.918640\pi$
$828$	−6.07503	−	17.7484i	−0.211122	−	0.616800i
$829$		−	27.9681i		−	0.971373i	−0.874133	−	0.485686i	$-0.838570\pi$
$829$		−	27.9681i		−	0.971373i	0.874133	−	0.485686i	$-0.161430\pi$
$830$	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	−0.874517	−	0.484996i	$-0.838821\pi$
$839$	−0.499354	+	0.864906i	−0.0172396	+	0.0298599i	0.857277	+	0.514856i	$0.172154\pi$
$840$	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	0.638214	−	0.769859i	$-0.279674\pi$
$853$	8.48739	+	4.90020i	0.290603	+	0.167780i	−0.347611	+	0.937639i	$0.613007\pi$
$854$	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	−0.792746	−	0.609552i	$-0.791349\pi$
$857$	3.85002	−	6.66842i	0.131514	−	0.227789i	0.924260	+	0.381763i	$0.124683\pi$
$858$	12.3654	+	15.0284i	0.422149	+	0.513062i
$859$	−16.4022	+	9.46979i	−0.559634	+	0.323105i	−0.752999	−	0.658022i	$-0.771393\pi$
$859$	−16.4022	+	9.46979i	−0.559634	+	0.323105i	0.193364	+	0.981127i	$0.438060\pi$
$860$	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	$-0.903990\pi$
$863$		−	17.4540i		−	0.594141i	0.954856	−	0.297070i	$-0.0960096\pi$
$864$	−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	0.862695	−	0.505725i	$-0.168775\pi$
$877$	−0.196152	−	0.339746i	−0.00662360	−	0.0114724i	−0.869318	+	0.494253i	$0.835442\pi$
$878$	−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	0.513256	−	0.858236i	$-0.328439\pi$
$887$	−14.4930	−	25.1026i	−0.486626	−	0.842861i	−0.999882	+	0.0153745i	$0.995106\pi$
$888$	−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	−0.831876	−	0.554962i	$-0.812733\pi$
$907$	1.94773	−	3.37357i	0.0646733	−	0.112017i	0.896549	+	0.442945i	$0.146066\pi$
$908$	−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	0.521833	−	0.853048i	$-0.325248\pi$
$911$	1.32768	+	0.766538i	0.0439881	+	0.0253966i	−0.477845	+	0.878444i	$0.658582\pi$
$912$	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	−0.837802	−	0.545974i	$-0.816160\pi$
$929$	1.64363	−	2.84685i	0.0539257	−	0.0934021i	0.891728	+	0.452571i	$0.149493\pi$
$930$	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	$-0.803051\pi$
$937$		−	35.5084i		−	1.16001i	0.814613	−	0.580005i	$-0.196949\pi$
$938$	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	0.949726	−	0.313083i	$-0.101362\pi$
$941$	6.24941	+	10.8243i	0.203725	+	0.352862i	−0.746001	+	0.665945i	$0.768028\pi$
$942$	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	0.913048	−	0.407852i	$-0.133722\pi$
$947$	31.2769	+	18.0577i	1.01636	+	0.586796i	0.103313	+	0.994649i	$0.467056\pi$
$948$	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	$-0.737846\pi$
$953$		−	45.2925i		−	1.46717i	0.679599	−	0.733584i	$-0.262154\pi$
$954$		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	0.991893	−	0.127079i	$-0.0405602\pi$
$967$	12.0000	+	20.7845i	0.385893	+	0.668385i	−0.606000	+	0.795465i	$0.707227\pi$
$968$	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	−0.894968	−	0.446131i	$-0.852802\pi$
$977$	−29.8846	+	17.2539i	−0.956091	+	0.552000i	−0.0611236	+	0.998130i	$0.519468\pi$
$978$	−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	−0.884625	−	0.466304i	$-0.845585\pi$
$983$	−1.20651	+	2.08973i	−0.0384817	+	0.0666522i	0.846143	+	0.532956i	$0.178919\pi$
$984$	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	0.967078	−	0.254481i	$-0.0819045\pi$
$997$	38.8449	+	22.4271i	1.23023	+	0.710274i	0.263152	+	0.964754i	$0.415238\pi$
$998$		−	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.83.1	yes	16
3.2	odd	2		378.2.m.a.251.5		16
4.3	odd	2		1008.2.cc.b.209.7		16
7.2	even	3		882.2.l.a.227.8		16
7.3	odd	6		882.2.t.b.803.6		16
7.4	even	3		882.2.t.b.803.7		16
7.5	odd	6		882.2.l.a.227.5		16
7.6	odd	2	inner	126.2.m.a.83.4	yes	16
9.2	odd	6		1134.2.d.a.1133.8		16
9.4	even	3		378.2.m.a.125.8		16
9.5	odd	6	inner	126.2.m.a.41.4	yes	16
9.7	even	3		1134.2.d.a.1133.9		16
12.11	even	2		3024.2.cc.b.2897.1		16
21.2	odd	6		2646.2.l.b.521.1		16
21.5	even	6		2646.2.l.b.521.4		16
21.11	odd	6		2646.2.t.a.1979.4		16
21.17	even	6		2646.2.t.a.1979.1		16
21.20	even	2		378.2.m.a.251.8		16
28.27	even	2		1008.2.cc.b.209.2		16
36.23	even	6		1008.2.cc.b.545.2		16
36.31	odd	6		3024.2.cc.b.881.8		16
63.4	even	3		2646.2.l.b.1097.8		16
63.5	even	6		882.2.t.b.815.7		16
63.13	odd	6		378.2.m.a.125.5		16
63.20	even	6		1134.2.d.a.1133.1		16
63.23	odd	6		882.2.t.b.815.6		16
63.31	odd	6		2646.2.l.b.1097.5		16
63.32	odd	6		882.2.l.a.509.1		16
63.34	odd	6		1134.2.d.a.1133.16		16
63.40	odd	6		2646.2.t.a.2285.4		16
63.41	even	6	inner	126.2.m.a.41.1	✓	16
63.58	even	3		2646.2.t.a.2285.1		16
63.59	even	6		882.2.l.a.509.4		16
84.83	odd	2		3024.2.cc.b.2897.8		16
252.139	even	6		3024.2.cc.b.881.1		16
252.167	odd	6		1008.2.cc.b.545.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.1	✓	16	63.41	even	6	inner
126.2.m.a.41.4	yes	16	9.5	odd	6	inner
126.2.m.a.83.1	yes	16	1.1	even	1	trivial
126.2.m.a.83.4	yes	16	7.6	odd	2	inner
378.2.m.a.125.5		16	63.13	odd	6
378.2.m.a.125.8		16	9.4	even	3
378.2.m.a.251.5		16	3.2	odd	2
378.2.m.a.251.8		16	21.20	even	2
882.2.l.a.227.5		16	7.5	odd	6
882.2.l.a.227.8		16	7.2	even	3
882.2.l.a.509.1		16	63.32	odd	6
882.2.l.a.509.4		16	63.59	even	6
882.2.t.b.803.6		16	7.3	odd	6
882.2.t.b.803.7		16	7.4	even	3
882.2.t.b.815.6		16	63.23	odd	6
882.2.t.b.815.7		16	63.5	even	6
1008.2.cc.b.209.2		16	28.27	even	2
1008.2.cc.b.209.7		16	4.3	odd	2
1008.2.cc.b.545.2		16	36.23	even	6
1008.2.cc.b.545.7		16	252.167	odd	6
1134.2.d.a.1133.1		16	63.20	even	6
1134.2.d.a.1133.8		16	9.2	odd	6
1134.2.d.a.1133.9		16	9.7	even	3
1134.2.d.a.1133.16		16	63.34	odd	6
2646.2.l.b.521.1		16	21.2	odd	6
2646.2.l.b.521.4		16	21.5	even	6
2646.2.l.b.1097.5		16	63.31	odd	6
2646.2.l.b.1097.8		16	63.4	even	3
2646.2.t.a.1979.1		16	21.17	even	6
2646.2.t.a.1979.4		16	21.11	odd	6
2646.2.t.a.2285.1		16	63.58	even	3
2646.2.t.a.2285.4		16	63.40	odd	6
3024.2.cc.b.881.1		16	252.139	even	6
3024.2.cc.b.881.8		16	36.31	odd	6
3024.2.cc.b.2897.1		16	12.11	even	2
3024.2.cc.b.2897.8		16	84.83	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
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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