LMFDB - Embedded newform 234.2.z.a.137.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(41,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 1]))

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

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

chi := DirichletCharacter("234.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			137.3
Character	$\chi$	$=$	234.137
Dual form			234.2.z.a.41.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.840145 + 1.51465i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.83272 - 0.491075i) q^{5} +(1.20354 - 1.24559i) q^{6} +(-1.44971 + 1.44971i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.58831 - 2.54505i) q^{9} +(1.64317 + 0.948684i) q^{10} +(1.49290 - 5.57157i) q^{11} +(-1.48491 + 0.891650i) q^{12} +(-2.83735 + 2.22474i) q^{13} +(1.77553 - 1.02510i) q^{14} +(2.28355 - 2.36335i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.11311 - 1.92797i) q^{17} +(0.875485 + 2.86941i) q^{18} +(1.13029 - 4.21829i) q^{19} +(-1.34164 - 1.34164i) q^{20} +(-0.977833 - 3.41377i) q^{21} +(-2.88406 + 4.99533i) q^{22} -5.93463 q^{23} +(1.66509 - 0.476945i) q^{24} +(-1.21243 - 0.699997i) q^{25} +(3.31647 - 1.41458i) q^{26} +(5.18926 - 0.267523i) q^{27} +(-1.98034 + 0.530631i) q^{28} +(-5.30738 + 3.06422i) q^{29} +(-2.81742 + 1.69179i) q^{30} +(0.660699 - 2.46576i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(7.18471 + 6.94214i) q^{33} +(0.576189 + 2.15037i) q^{34} +(3.36883 - 1.94499i) q^{35} +(-0.102995 - 2.99823i) q^{36} +(-0.585575 - 2.18540i) q^{37} +(-2.18355 + 3.78201i) q^{38} +(-0.985916 - 6.16668i) q^{39} +(0.948684 + 1.64317i) q^{40} +(-7.91945 + 7.91945i) q^{41} +(0.0609657 + 3.55053i) q^{42} +5.93015i q^{43} +(4.07867 - 4.07867i) q^{44} +(1.66112 + 5.44433i) q^{45} +(5.73241 + 1.53599i) q^{46} +(5.46823 - 1.46521i) q^{47} +(-1.73180 + 0.0297365i) q^{48} +2.79668i q^{49} +(0.989945 + 0.989945i) q^{50} +(3.85537 - 0.0662001i) q^{51} +(-3.56958 + 0.508010i) q^{52} +2.73563i q^{53} +(-5.08168 - 1.08467i) q^{54} +(-5.47212 + 9.47798i) q^{55} +2.05020 q^{56} +(5.43961 + 5.25596i) q^{57} +(5.91962 - 1.58616i) q^{58} +(6.36257 - 1.70485i) q^{59} +(3.15929 - 0.904940i) q^{60} +8.86956 q^{61} +(-1.27637 + 2.21074i) q^{62} +(5.99218 + 1.38699i) q^{63} +1.00000i q^{64} +(6.29257 - 2.68397i) q^{65} +(-5.14314 - 8.56513i) q^{66} +(-9.80081 - 9.80081i) q^{67} -2.22623i q^{68} +(4.98595 - 8.98886i) q^{69} +(-3.75744 + 1.00680i) q^{70} +(-6.43432 - 1.72407i) q^{71} +(-0.676514 + 2.92273i) q^{72} +(6.02332 - 6.02332i) q^{73} +2.26249i q^{74} +(2.07887 - 1.24830i) q^{75} +(3.08800 - 3.08800i) q^{76} +(5.91289 + 10.2414i) q^{77} +(-0.643733 + 6.21173i) q^{78} +(-5.25497 + 9.10187i) q^{79} +(-0.491075 - 1.83272i) q^{80} +(-3.95453 + 8.08466i) q^{81} +(9.69930 - 5.59989i) q^{82} +(0.723746 + 2.70106i) q^{83} +(0.860056 - 3.44533i) q^{84} +(1.09324 + 4.08004i) q^{85} +(1.53483 - 5.72808i) q^{86} +(-0.182238 - 10.6132i) q^{87} +(-4.99533 + 2.88406i) q^{88} +(-12.7827 + 3.42511i) q^{89} +(-0.195419 - 5.68875i) q^{90} +(0.888099 - 7.33856i) q^{91} +(-5.13954 - 2.96731i) q^{92} +(3.17968 + 3.07233i) q^{93} -5.66113 q^{94} +(-4.14299 + 7.17587i) q^{95} +(1.68048 + 0.419498i) q^{96} +(-4.43038 - 4.43038i) q^{97} +(0.723833 - 2.70138i) q^{98} +(-16.5511 + 5.04989i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	−0.840145	+	1.51465i	−0.485058	+	0.874482i
$3$	−0.840145	+	1.51465i	−0.485058	+	0.874482i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−1.83272	−	0.491075i	−0.819616	−	0.219615i	−0.175437	−	0.984491i	$-0.556134\pi$
$5$	−1.83272	−	0.491075i	−0.819616	−	0.219615i	−0.644179	+	0.764875i	$0.722801\pi$
$6$	1.20354	−	1.24559i	0.491342	−	0.508510i
$7$	−1.44971	+	1.44971i	−0.547939	+	0.547939i	−0.925844	−	0.377905i	$-0.876645\pi$
$7$	−1.44971	+	1.44971i	−0.547939	+	0.547939i	0.377905	+	0.925844i	$0.376645\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.58831	−	2.54505i	−0.529437	−	0.848349i
$10$	1.64317	+	0.948684i	0.519616	+	0.300000i
$11$	1.49290	−	5.57157i	0.450125	−	1.67989i	−0.251912	−	0.967750i	$-0.581059\pi$
$11$	1.49290	−	5.57157i	0.450125	−	1.67989i	0.702037	−	0.712141i	$-0.252274\pi$
$12$	−1.48491	+	0.891650i	−0.428657	+	0.257397i
$13$	−2.83735	+	2.22474i	−0.786938	+	0.617032i
$13$	−2.83735	+	2.22474i	−0.786938	+	0.617032i
$14$	1.77553	−	1.02510i	0.474529	−	0.273970i
$15$	2.28355	−	2.36335i	0.589611	−	0.610213i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.11311	−	1.92797i	−0.269969	−	0.467601i	0.698884	−	0.715235i	$-0.253680\pi$
$17$	−1.11311	−	1.92797i	−0.269969	−	0.467601i	−0.968854	+	0.247634i	$0.920347\pi$
$18$	0.875485	+	2.86941i	0.206354	+	0.676327i
$19$	1.13029	−	4.21829i	0.259306	−	0.967742i	−0.706339	−	0.707874i	$-0.749654\pi$
$19$	1.13029	−	4.21829i	0.259306	−	0.967742i	0.965644	−	0.259868i	$-0.0836789\pi$
$20$	−1.34164	−	1.34164i	−0.300000	−	0.300000i
$21$	−0.977833	−	3.41377i	−0.213381	−	0.744945i
$22$	−2.88406	+	4.99533i	−0.614883	+	1.06501i
$23$	−5.93463			−1.23746			−0.618728	−	0.785606i	$-0.712352\pi$
$23$	−5.93463			−1.23746			−0.618728	+	0.785606i	$0.712352\pi$
$24$	1.66509	−	0.476945i	0.339885	−	0.0973560i
$25$	−1.21243	−	0.699997i	−0.242486	−	0.139999i
$26$	3.31647	−	1.41458i	0.650413	−	0.277421i
$27$	5.18926	−	0.267523i	0.998674	−	0.0514848i
$28$	−1.98034	+	0.530631i	−0.374249	+	0.100280i
$29$	−5.30738	+	3.06422i	−0.985556	+	0.569011i	−0.903943	−	0.427653i	$-0.859341\pi$
$29$	−5.30738	+	3.06422i	−0.985556	+	0.569011i	−0.0816131	+	0.996664i	$0.526007\pi$
$30$	−2.81742	+	1.69179i	−0.514389	+	0.308877i
$31$	0.660699	−	2.46576i	0.118665	−	0.442864i	−0.880870	−	0.473359i	$-0.843042\pi$
$31$	0.660699	−	2.46576i	0.118665	−	0.442864i	0.999535	+	0.0304944i	$0.00970818\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	7.18471	+	6.94214i	1.25070	+	1.20847i
$34$	0.576189	+	2.15037i	0.0988157	+	0.368785i
$35$	3.36883	−	1.94499i	0.569436	−	0.328764i
$36$	−0.102995	−	2.99823i	−0.0171658	−	0.499705i
$37$	−0.585575	−	2.18540i	−0.0962680	−	0.359277i	0.900941	−	0.433942i	$-0.142878\pi$
$37$	−0.585575	−	2.18540i	−0.0962680	−	0.359277i	−0.997209	+	0.0746653i	$0.976211\pi$
$38$	−2.18355	+	3.78201i	−0.354218	+	0.613524i
$39$	−0.985916	−	6.16668i	−0.157873	−	0.987459i
$40$	0.948684	+	1.64317i	0.150000	+	0.259808i
$41$	−7.91945	+	7.91945i	−1.23681	+	1.23681i	−0.275512	+	0.961298i	$0.588847\pi$
$41$	−7.91945	+	7.91945i	−1.23681	+	1.23681i	−0.961298	+	0.275512i	$0.911153\pi$
$42$	0.0609657	+	3.55053i	0.00940722	+	0.547858i
$43$			5.93015i			0.904339i	0.891932	+	0.452169i	$0.149350\pi$
$43$			5.93015i			0.904339i	−0.891932	+	0.452169i	$0.850650\pi$
$44$	4.07867	−	4.07867i	0.614883	−	0.614883i
$45$	1.66112	+	5.44433i	0.247625	+	0.811593i
$46$	5.73241	+	1.53599i	0.845198	+	0.226470i
$47$	5.46823	−	1.46521i	0.797623	−	0.213723i	0.163083	−	0.986612i	$-0.447856\pi$
$47$	5.46823	−	1.46521i	0.797623	−	0.213723i	0.634540	+	0.772890i	$0.281189\pi$
$48$	−1.73180	+	0.0297365i	−0.249963	+	0.00429209i
$49$			2.79668i			0.399525i
$50$	0.989945	+	0.989945i	0.139999	+	0.139999i
$51$	3.85537	−	0.0662001i	0.539859	−	0.00926986i
$52$	−3.56958	+	0.508010i	−0.495012	+	0.0704483i
$53$			2.73563i			0.375767i	0.982191	+	0.187884i	$0.0601628\pi$
$53$			2.73563i			0.375767i	−0.982191	+	0.187884i	$0.939837\pi$
$54$	−5.08168	−	1.08467i	−0.691529	−	0.147605i
$55$	−5.47212	+	9.47798i	−0.737860	+	1.27801i
$56$	2.05020			0.273970
$57$	5.43961	+	5.25596i	0.720494	+	0.696169i
$58$	5.91962	−	1.58616i	0.777284	−	0.208273i
$59$	6.36257	−	1.70485i	0.828337	−	0.221952i	0.180349	−	0.983603i	$-0.442277\pi$
$59$	6.36257	−	1.70485i	0.828337	−	0.221952i	0.647988	+	0.761651i	$0.275611\pi$
$60$	3.15929	−	0.904940i	0.407862	−	0.116827i
$61$	8.86956			1.13563			0.567815	−	0.823156i	$-0.307789\pi$
$61$	8.86956			1.13563			0.567815	+	0.823156i	$0.307789\pi$
$62$	−1.27637	+	2.21074i	−0.162100	+	0.280765i
$63$	5.99218	+	1.38699i	0.754943	+	0.174744i
$64$			1.00000i			0.125000i
$65$	6.29257	−	2.68397i	0.780497	−	0.332906i
$66$	−5.14314	−	8.56513i	−0.633077	−	1.05429i
$67$	−9.80081	−	9.80081i	−1.19736	−	1.19736i	−0.974954	−	0.222406i	$-0.928609\pi$
$67$	−9.80081	−	9.80081i	−1.19736	−	1.19736i	−0.222406	−	0.974954i	$-0.571391\pi$
$68$		−	2.22623i		−	0.269969i
$69$	4.98595	−	8.98886i	0.600238	−	1.08213i
$70$	−3.75744	+	1.00680i	−0.449100	+	0.120336i
$71$	−6.43432	−	1.72407i	−0.763613	−	0.204609i	−0.144065	−	0.989568i	$-0.546017\pi$
$71$	−6.43432	−	1.72407i	−0.763613	−	0.204609i	−0.619548	+	0.784959i	$0.712684\pi$
$72$	−0.676514	+	2.92273i	−0.0797279	+	0.344447i
$73$	6.02332	−	6.02332i	0.704976	−	0.704976i	−0.260498	−	0.965474i	$-0.583887\pi$
$73$	6.02332	−	6.02332i	0.704976	−	0.704976i	0.965474	+	0.260498i	$0.0838869\pi$
$74$			2.26249i			0.263009i
$75$	2.07887	−	1.24830i	0.240047	−	0.144142i
$76$	3.08800	−	3.08800i	0.354218	−	0.354218i
$77$	5.91289	+	10.2414i	0.673837	+	1.16712i
$78$	−0.643733	+	6.21173i	−0.0728885	+	0.703340i
$79$	−5.25497	+	9.10187i	−0.591230	+	1.02404i	0.402837	+	0.915272i	$0.368024\pi$
$79$	−5.25497	+	9.10187i	−0.591230	+	1.02404i	−0.994067	+	0.108769i	$0.965309\pi$
$80$	−0.491075	−	1.83272i	−0.0549039	−	0.204904i
$81$	−3.95453	+	8.08466i	−0.439392	+	0.898295i
$82$	9.69930	−	5.59989i	1.07111	−	0.618405i
$83$	0.723746	+	2.70106i	0.0794414	+	0.296479i	0.994204	−	0.107513i	$-0.0342888\pi$
$83$	0.723746	+	2.70106i	0.0794414	+	0.296479i	−0.914762	+	0.403993i	$0.867622\pi$
$84$	0.860056	−	3.44533i	0.0938398	−	0.375916i
$85$	1.09324	+	4.08004i	0.118579	+	0.442543i
$86$	1.53483	−	5.72808i	0.165505	−	0.617675i
$87$	−0.182238	−	10.6132i	−0.0195380	−	1.13785i
$88$	−4.99533	+	2.88406i	−0.532504	+	0.307441i
$89$	−12.7827	+	3.42511i	−1.35496	+	0.363061i	−0.861965	−	0.506969i	$-0.830766\pi$
$89$	−12.7827	+	3.42511i	−1.35496	+	0.363061i	−0.492999	+	0.870030i	$0.664099\pi$
$90$	−0.195419	−	5.68875i	−0.0205990	−	0.599647i
$91$	0.888099	−	7.33856i	0.0930981	−	0.769290i
$92$	−5.13954	−	2.96731i	−0.535834	−	0.309364i
$93$	3.17968	+	3.07233i	0.329717	+	0.318585i
$94$	−5.66113			−0.583901
$95$	−4.14299	+	7.17587i	−0.425062	+	0.736229i
$96$	1.68048	+	0.419498i	0.171514	+	0.0428149i
$97$	−4.43038	−	4.43038i	−0.449837	−	0.449837i	0.445463	−	0.895300i	$-0.353039\pi$
$97$	−4.43038	−	4.43038i	−0.449837	−	0.449837i	−0.895300	+	0.445463i	$0.853039\pi$
$98$	0.723833	−	2.70138i	0.0731182	−	0.272881i
$99$	−16.5511	+	5.04989i	−1.66345	+	0.507533i
$100$	−0.699997	−	1.21243i	−0.0699997	−	0.121243i
$101$	1.76416	+	3.05561i	0.175540	+	0.304045i	0.940348	−	0.340214i	$-0.110499\pi$
$101$	1.76416	+	3.05561i	0.175540	+	0.304045i	−0.764808	+	0.644258i	$0.777166\pi$
$102$	−3.74113	−	0.933898i	−0.370427	−	0.0924697i
$103$	−2.08972	+	1.20650i	−0.205906	+	0.118880i	−0.599407	−	0.800444i	$-0.704597\pi$
$103$	−2.08972	+	1.20650i	−0.205906	+	0.118880i	0.393501	+	0.919324i	$0.371264\pi$
$104$	3.57944	+	0.433177i	0.350993	+	0.0424765i
$105$	0.115674	+	6.73666i	0.0112887	+	0.657431i
$106$	0.708032	−	2.64241i	0.0687702	−	0.256654i
$107$	−11.9580	−	6.90393i	−1.15602	−	0.667428i	−0.205673	−	0.978621i	$-0.565938\pi$
$107$	−11.9580	−	6.90393i	−1.15602	−	0.667428i	−0.950347	+	0.311193i	$0.899272\pi$
$108$	4.62779	+	2.36295i	0.445310	+	0.227375i
$109$	−8.53541	−	8.53541i	−0.817544	−	0.817544i	0.168207	−	0.985752i	$-0.446202\pi$
$109$	−8.53541	−	8.53541i	−0.817544	−	0.817544i	−0.985752	+	0.168207i	$0.946202\pi$
$110$	7.73874	−	7.73874i	0.737860	−	0.737860i
$111$	3.80207	+	0.949111i	0.360877	+	0.0900856i
$112$	−1.98034	−	0.530631i	−0.187125	−	0.0501399i
$113$	−7.95194	−	4.59106i	−0.748056	−	0.431890i	0.0769351	−	0.997036i	$-0.475487\pi$
$113$	−7.95194	−	4.59106i	−0.748056	−	0.431890i	−0.824991	+	0.565146i	$0.808820\pi$
$114$	−3.89392	−	6.48474i	−0.364699	−	0.607352i
$115$	10.8765	+	2.91435i	1.01424	+	0.271764i
$116$	−6.12844			−0.569011
$117$	10.1687	+	3.68759i	0.940093	+	0.340918i
$118$	−6.58702			−0.606384
$119$	4.40869	+	1.18130i	0.404144	+	0.108290i
$120$	−3.28585	+	0.0564210i	−0.299956	+	0.00515051i
$121$	−19.2873	−	11.1356i	−1.75339	−	1.01232i
$122$	−8.56734	−	2.29561i	−0.775650	−	0.207835i
$123$	−5.34168	−	18.6487i	−0.481643	−	1.68149i
$124$	1.80506	−	1.80506i	0.162100	−	0.162100i
$125$	8.58650	+	8.58650i	0.768000	+	0.768000i
$126$	−5.42902	−	2.89062i	−0.483655	−	0.257517i
$127$	7.73808	+	4.46758i	0.686643	+	0.396434i	0.802353	−	0.596849i	$-0.203581\pi$
$127$	7.73808	+	4.46758i	0.686643	+	0.396434i	−0.115710	+	0.993283i	$0.536914\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−8.98208	−	4.98218i	−0.790828	−	0.438657i
$130$	−6.77281	+	0.963881i	−0.594015	+	0.0845380i
$131$	16.1712	−	9.33646i	1.41289	−	0.815731i	0.417227	−	0.908802i	$-0.363002\pi$
$131$	16.1712	−	9.33646i	1.41289	−	0.815731i	0.995659	+	0.0930716i	$0.0296686\pi$
$132$	2.75107	+	9.60442i	0.239450	+	0.835958i
$133$	4.47671	+	7.75389i	0.388180	+	0.672347i
$134$	6.93022	+	12.0035i	0.598680	+	1.03694i
$135$	−9.64182	−	2.05802i	−0.829836	−	0.177126i
$136$	−0.576189	+	2.15037i	−0.0494078	+	0.184393i
$137$	7.30587	+	7.30587i	0.624183	+	0.624183i	0.946598	−	0.322416i	$-0.104495\pi$
$137$	7.30587	+	7.30587i	0.624183	+	0.624183i	−0.322416	+	0.946598i	$0.604495\pi$
$138$	−7.14255	+	7.39212i	−0.608014	+	0.629259i
$139$	9.34661	−	16.1888i	0.792769	−	1.37312i	−0.131478	−	0.991319i	$-0.541972\pi$
$139$	9.34661	−	16.1888i	0.792769	−	1.37312i	0.924246	−	0.381797i	$-0.124695\pi$
$140$	3.88999			0.328764
$141$	−2.37483	+	9.51343i	−0.199997	+	0.801175i
$142$	5.76885	+	3.33065i	0.484111	+	0.279502i
$143$	8.15943	+	19.1298i	0.682326	+	1.59971i
$144$	1.40992	−	2.64804i	0.117493	−	0.220670i
$145$	11.2317	−	3.00952i	0.932741	−	0.249927i
$146$	−7.37702	+	4.25913i	−0.610527	+	0.352488i
$147$	−4.23598	−	2.34961i	−0.349378	−	0.193793i
$148$	0.585575	−	2.18540i	0.0481340	−	0.179639i
$149$	1.41941	+	5.29732i	0.116283	+	0.433973i	0.999380	−	0.0352173i	$-0.0112123\pi$
$149$	1.41941	+	5.29732i	0.116283	+	0.433973i	−0.883097	+	0.469191i	$0.844546\pi$
$150$	−2.33112	+	0.667720i	−0.190335	+	0.0545191i
$151$	−1.68500	−	6.28851i	−0.137124	−	0.511752i	−0.999980	−	0.00630324i	$-0.997994\pi$
$151$	−1.68500	−	6.28851i	−0.137124	−	0.511752i	0.862857	−	0.505449i	$-0.168673\pi$
$152$	−3.78201	+	2.18355i	−0.306762	+	0.177109i
$153$	−3.13880	+	5.89514i	−0.253757	+	0.476594i
$154$	−3.06074	−	11.4228i	−0.246641	−	0.920478i
$155$	−2.42175	+	4.19459i	−0.194520	+	0.336918i
$156$	2.22951	−	5.83346i	0.178504	−	0.467051i
$157$	−5.12269	−	8.87276i	−0.408835	−	0.708123i	0.585924	−	0.810366i	$-0.300732\pi$
$157$	−5.12269	−	8.87276i	−0.408835	−	0.708123i	−0.994759	+	0.102243i	$0.967398\pi$
$158$	7.43165	−	7.43165i	0.591230	−	0.591230i
$159$	−4.14351	−	2.29832i	−0.328602	−	0.182269i
$160$			1.89737i			0.150000i
$161$	8.60349	−	8.60349i	0.678050	−	0.678050i
$162$	5.91225	−	6.78567i	0.464510	−	0.533133i
$163$	15.5355	+	4.16272i	1.21683	+	0.326049i	0.809439	−	0.587203i	$-0.199771\pi$
$163$	15.5355	+	4.16272i	1.21683	+	0.326049i	0.407393	+	0.913253i	$0.366438\pi$
$164$	−10.8182	+	2.89872i	−0.844757	+	0.226352i
$165$	−9.75843	−	16.2512i	−0.759692	−	1.26515i
$166$		−	2.79634i		−	0.217038i
$167$	−4.00324	−	4.00324i	−0.309780	−	0.309780i	0.535044	−	0.844824i	$-0.320295\pi$
$167$	−4.00324	−	4.00324i	−0.309780	−	0.309780i	−0.844824	+	0.535044i	$0.820295\pi$
$168$	−1.72247	+	3.10533i	−0.132891	+	0.239581i
$169$	3.10105	−	12.6247i	0.238543	−	0.971132i
$170$		−	4.22397i		−	0.323964i
$171$	−12.5310	+	3.82332i	−0.958269	+	0.292377i
$172$	−2.96507	+	5.13566i	−0.226085	+	0.391590i
$173$	11.2165			0.852772			0.426386	−	0.904541i	$-0.359787\pi$
$173$	11.2165			0.852772			0.426386	+	0.904541i	$0.359787\pi$
$174$	−2.57087	+	10.2987i	−0.194897	+	0.780745i
$175$	2.77247	−	0.742880i	0.209579	−	0.0561565i
$176$	5.57157	−	1.49290i	0.419973	−	0.112531i
$177$	−2.76325	+	11.0694i	−0.207698	+	0.832025i
$178$	13.2336			0.991902
$179$	5.57461	−	9.65551i	0.416666	−	0.721687i	−0.578936	−	0.815373i	$-0.696532\pi$
$179$	5.57461	−	9.65551i	0.416666	−	0.721687i	0.995602	+	0.0936864i	$0.0298651\pi$
$180$	−1.28360	+	5.54549i	−0.0956736	+	0.413336i
$181$			2.01561i			0.149819i	0.997190	+	0.0749094i	$0.0238668\pi$
$181$			2.01561i			0.149819i	−0.997190	+	0.0749094i	$0.976133\pi$
$182$	−2.75720	+	6.85865i	−0.204377	+	0.508397i
$183$	−7.45172	+	13.4343i	−0.550847	+	0.993089i
$184$	4.19641	+	4.19641i	0.309364	+	0.309364i
$185$			4.29278i			0.315611i
$186$	−2.27616	−	3.79060i	−0.166896	−	0.277940i
$187$	−12.4036	+	3.32352i	−0.907038	+	0.243040i
$188$	5.46823	+	1.46521i	0.398812	+	0.106861i
$189$	−7.13510	+	7.91076i	−0.519002	+	0.575423i
$190$	5.85908	−	5.85908i	0.425062	−	0.425062i
$191$			0.561217i			0.0406082i	0.999794	+	0.0203041i	$0.00646344\pi$
$191$			0.561217i			0.0406082i	−0.999794	+	0.0203041i	$0.993537\pi$
$192$	−1.51465	−	0.840145i	−0.109310	−	0.0606323i
$193$	−6.30863	+	6.30863i	−0.454105	+	0.454105i	−0.896714	−	0.442610i	$-0.854053\pi$
$193$	−6.30863	+	6.30863i	−0.454105	+	0.454105i	0.442610	+	0.896714i	$0.354053\pi$
$194$	3.13275	+	5.42608i	0.224918	+	0.389570i
$195$	−1.22140	+	11.7859i	−0.0874662	+	0.844009i
$196$	−1.39834	+	2.42199i	−0.0998813	+	0.173000i
$197$	−2.52062	−	9.40707i	−0.179586	−	0.670226i	−0.995725	−	0.0923693i	$-0.970556\pi$
$197$	−2.52062	−	9.40707i	−0.179586	−	0.670226i	0.816138	−	0.577857i	$-0.196111\pi$
$198$	17.2941	−	0.594086i	1.22904	−	0.0422199i
$199$	−7.42000	+	4.28394i	−0.525990	+	0.303680i	−0.739382	−	0.673286i	$-0.764882\pi$
$199$	−7.42000	+	4.28394i	−0.525990	+	0.303680i	0.213392	+	0.976967i	$0.431549\pi$
$200$	0.362345	+	1.35229i	0.0256217	+	0.0956214i
$201$	23.0789	−	6.61067i	1.62786	−	0.466281i
$202$	−0.913195	−	3.40809i	−0.0642522	−	0.239792i
$203$	3.25194	−	12.1364i	0.228241	−	0.851808i
$204$	3.37195	+	1.87035i	0.236083	+	0.130951i
$205$	18.4031	−	10.6251i	1.28533	−	0.742087i
$206$	2.33078	−	0.624531i	0.162393	−	0.0435131i
$207$	9.42604	+	15.1039i	0.655155	+	1.04979i
$208$	−3.34535	−	1.34484i	−0.231959	−	0.0932480i
$209$	−21.8151	−	12.5949i	−1.50898	−	0.871210i
$210$	1.63184	−	6.53705i	0.112608	−	0.451099i
$211$	12.8435			0.884180			0.442090	−	0.896971i	$-0.354237\pi$
$211$	12.8435			0.884180			0.442090	+	0.896971i	$0.354237\pi$
$212$	−1.36781	+	2.36912i	−0.0939418	+	0.162712i
$213$	8.01712	−	8.29725i	0.549324	−	0.568518i
$214$	9.76363	+	9.76363i	0.667428	+	0.667428i
$215$	2.91215	−	10.8683i	0.198607	−	0.741211i
$216$	−3.85853	−	3.48019i	−0.262540	−	0.236797i
$217$	2.61682	+	4.53247i	0.177641	+	0.307684i
$218$	6.03545	+	10.4537i	0.408772	+	0.708014i
$219$	4.06274	+	14.1837i	0.274534	+	0.958443i
$220$	−9.47798	+	5.47212i	−0.639005	+	0.368930i
$221$	7.44751	+	2.99392i	0.500974	+	0.201393i
$222$	−3.42687	−	1.90082i	−0.229997	−	0.127575i
$223$	−3.12393	+	11.6587i	−0.209194	+	0.780721i	0.778937	+	0.627103i	$0.215759\pi$
$223$	−3.12393	+	11.6587i	−0.209194	+	0.780721i	−0.988130	+	0.153619i	$0.950907\pi$
$224$	1.77553	+	1.02510i	0.118632	+	0.0684924i
$225$	0.144192	+	4.19751i	0.00961282	+	0.279834i
$226$	6.49274	+	6.49274i	0.431890	+	0.431890i
$227$	−9.08871	+	9.08871i	−0.603239	+	0.603239i	−0.941171	−	0.337932i	$-0.890273\pi$
$227$	−9.08871	+	9.08871i	−0.603239	+	0.603239i	0.337932	+	0.941171i	$0.390273\pi$
$228$	2.08286	+	7.27160i	0.137941	+	0.481574i
$229$	18.7930	+	5.03556i	1.24187	+	0.332759i	0.819192	−	0.573519i	$-0.194422\pi$
$229$	18.7930	+	5.03556i	1.24187	+	0.332759i	0.422682	+	0.906278i	$0.361089\pi$
$230$	−9.75159	−	5.63009i	−0.643001	−	0.371237i
$231$	−20.4798	+	0.351657i	−1.34747	+	0.0231373i
$232$	5.91962	+	1.58616i	0.388642	+	0.104136i
$233$	−4.00407			−0.262316			−0.131158	−	0.991361i	$-0.541869\pi$
$233$	−4.00407			−0.262316			−0.131158	+	0.991361i	$0.541869\pi$
$234$	−8.86775	−	6.19379i	−0.579703	−	0.404900i
$235$	−10.7412			−0.700682
$236$	6.36257	+	1.70485i	0.414168	+	0.110976i
$237$	−9.37119	−	15.6063i	−0.608724	−	1.01374i
$238$	−3.95272	−	2.28210i	−0.256217	−	0.147927i
$239$	8.86245	+	2.37469i	0.573264	+	0.153606i	0.533793	−	0.845615i	$-0.320766\pi$
$239$	8.86245	+	2.37469i	0.573264	+	0.153606i	0.0394708	+	0.999221i	$0.487433\pi$
$240$	3.18849	+	0.795943i	0.205816	+	0.0513779i
$241$	−13.6909	+	13.6909i	−0.881911	+	0.881911i	−0.993729	−	0.111818i	$-0.964333\pi$
$241$	−13.6909	+	13.6909i	−0.881911	+	0.881911i	0.111818	+	0.993729i	$0.464333\pi$
$242$	15.7480	+	15.7480i	1.01232	+	1.01232i
$243$	−8.92302	−	12.7820i	−0.572412	−	0.819966i
$244$	7.68127	+	4.43478i	0.491743	+	0.283908i
$245$	1.37338	−	5.12552i	0.0877419	−	0.327457i
$246$	0.333042	+	19.3957i	0.0212340	+	1.23663i
$247$	6.17758	+	14.4833i	0.393070	+	0.921553i
$248$	−2.21074	+	1.27637i	−0.140382	+	0.0810498i
$249$	−4.69920	−	1.17306i	−0.297800	−	0.0743396i
$250$	−6.07157	−	10.5163i	−0.384000	−	0.665107i
$251$	7.58584	+	13.1391i	0.478814	+	0.829331i	0.999705	−	0.0242928i	$-0.00773340\pi$
$251$	7.58584	+	13.1391i	0.478814	+	0.829331i	−0.520891	+	0.853623i	$0.674400\pi$
$252$	4.49588	+	4.19726i	0.283214	+	0.264402i
$253$	−8.85979	+	33.0652i	−0.557010	+	2.07879i
$254$	−6.31811	−	6.31811i	−0.396434	−	0.396434i
$255$	−7.09831	−	1.77195i	−0.444513	−	0.110964i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.12985			−0.444748			−0.222374	−	0.974961i	$-0.571381\pi$
$257$	−7.12985			−0.444748			−0.222374	+	0.974961i	$0.571381\pi$
$258$	7.38654	+	7.13715i	0.459866	+	0.444340i
$259$	4.01711	+	2.31928i	0.249611	+	0.144113i
$260$	6.79151	+	0.821895i	0.421191	+	0.0509718i
$261$	16.2284	+	8.64060i	1.00451	+	0.534840i
$262$	−18.0367	+	4.83291i	−1.11431	+	0.298578i
$263$	8.95993	−	5.17302i	0.552493	−	0.318982i	−0.197634	−	0.980276i	$-0.563326\pi$
$263$	8.95993	−	5.17302i	0.552493	−	0.318982i	0.750127	+	0.661294i	$0.229992\pi$
$264$	−0.171523	−	9.98919i	−0.0105565	−	0.614792i
$265$	1.34340	−	5.01363i	0.0825243	−	0.307985i
$266$	−2.31731	−	8.64834i	−0.142084	−	0.530264i
$267$	5.55148	−	22.2389i	0.339745	−	1.36100i
$268$	−3.58735	−	13.3882i	−0.219132	−	0.817812i
$269$	−16.9068	+	9.76113i	−1.03082	+	0.595146i	−0.917221	−	0.398380i	$-0.869573\pi$
$269$	−16.9068	+	9.76113i	−1.03082	+	0.595146i	−0.113603	+	0.993526i	$0.536239\pi$
$270$	8.78063	+	4.48338i	0.534372	+	0.272850i
$271$	−4.18848	−	15.6316i	−0.254432	−	0.949553i	−0.968406	−	0.249380i	$-0.919773\pi$
$271$	−4.18848	−	15.6316i	−0.254432	−	0.949553i	0.713974	−	0.700172i	$-0.246894\pi$
$272$	1.11311	−	1.92797i	0.0674924	−	0.116900i
$273$	10.3692	+	7.51061i	0.627572	+	0.454563i
$274$	−5.16603	−	8.94783i	−0.312091	−	0.540558i
$275$	−5.71011	+	5.71011i	−0.344333	+	0.344333i
$276$	8.81239	−	5.29161i	0.530444	−	0.318518i
$277$		−	30.8376i		−	1.85285i	−0.376475	−	0.926427i	$-0.622864\pi$
$277$		−	30.8376i		−	1.85285i	0.376475	−	0.926427i	$-0.377136\pi$
$278$	−13.2181	+	13.2181i	−0.792769	+	0.792769i
$279$	−7.32488	+	2.23489i	−0.438529	+	0.133799i
$280$	−3.75744	−	1.00680i	−0.224550	−	0.0601679i
$281$	−8.78669	+	2.35439i	−0.524170	+	0.140451i	−0.511195	−	0.859465i	$-0.670797\pi$
$281$	−8.78669	+	2.35439i	−0.524170	+	0.140451i	−0.0129751	+	0.999916i	$0.504130\pi$
$282$	4.75617	−	8.57461i	0.283226	−	0.510611i
$283$			17.1581i			1.01994i	0.860192	+	0.509970i	$0.170344\pi$
$283$			17.1581i			1.01994i	−0.860192	+	0.509970i	$0.829656\pi$
$284$	−4.71025	−	4.71025i	−0.279502	−	0.279502i
$285$	−7.38820	−	12.3039i	−0.437639	−	0.728823i
$286$	−2.93026	−	20.5898i	−0.173270	−	1.21750i
$287$		−	22.9618i		−	1.35539i
$288$	−2.04724	+	2.19290i	−0.120635	+	0.129218i
$289$	6.02196	−	10.4303i	0.354233	−	0.613550i
$290$	−11.6279			−0.682814
$291$	10.4326	−	2.98830i	0.611571	−	0.175177i
$292$	8.22800	−	2.20469i	0.481507	−	0.129020i
$293$	10.1264	−	2.71337i	0.591592	−	0.158517i	0.0494113	−	0.998779i	$-0.484265\pi$
$293$	10.1264	−	2.71337i	0.591592	−	0.158517i	0.542181	+	0.840262i	$0.317599\pi$
$294$	3.48352	+	3.36591i	0.203163	+	0.196304i
$295$	−12.4980			−0.727662
$296$	−1.13124	+	1.95937i	−0.0657523	+	0.113886i
$297$	6.25651	−	29.3117i	0.363040	−	1.70084i
$298$		−	5.48419i		−	0.317691i
$299$	16.8386	−	13.2030i	0.973800	−	0.763550i
$300$	2.42450	−	0.0416309i	0.139979	−	0.00240356i
$301$	−8.59700	−	8.59700i	−0.495523	−	0.495523i
$302$			6.51035i			0.374629i
$303$	−6.11032	+	0.104920i	−0.351029	+	0.00602748i
$304$	4.21829	−	1.13029i	0.241935	−	0.0648264i
$305$	−16.2554	−	4.35562i	−0.930781	−	0.249402i
$306$	4.55762	−	4.88189i	0.260542	−	0.279079i
$307$	6.92368	−	6.92368i	0.395155	−	0.395155i	−0.481365	−	0.876520i	$-0.659859\pi$
$307$	6.92368	−	6.92368i	0.395155	−	0.395155i	0.876520	+	0.481365i	$0.159859\pi$
$308$			11.8258i			0.673837i
$309$	−0.0717542	−	4.17883i	−0.00408195	−	0.237725i
$310$	3.42487	−	3.42487i	0.194520	−	0.194520i
$311$	−7.54546	−	13.0691i	−0.427864	−	0.741082i	0.568819	−	0.822462i	$-0.307400\pi$
$311$	−7.54546	−	13.0691i	−0.427864	−	0.741082i	−0.996683	+	0.0813809i	$0.974067\pi$
$312$	−3.66336	+	5.05765i	−0.207397	+	0.286333i
$313$	−13.2146	+	22.8883i	−0.746933	+	1.29373i	0.202353	+	0.979313i	$0.435141\pi$
$313$	−13.2146	+	22.8883i	−0.746933	+	1.29373i	−0.949286	+	0.314413i	$0.898192\pi$
$314$	2.65170	+	9.89627i	0.149644	+	0.558479i
$315$	−10.3008	−	5.48457i	−0.580387	−	0.309020i
$316$	−9.10187	+	5.25497i	−0.512020	+	0.295615i
$317$	−7.90095	−	29.4867i	−0.443761	−	1.65614i	−0.719186	−	0.694817i	$-0.755485\pi$
$317$	−7.90095	−	29.4867i	−0.443761	−	1.65614i	0.275425	−	0.961323i	$-0.411182\pi$
$318$	3.40747	+	3.29243i	0.191082	+	0.184630i
$319$	9.14912	+	34.1450i	0.512253	+	1.91175i
$320$	0.491075	−	1.83272i	0.0274519	−	0.102452i
$321$	20.5034	−	12.3118i	1.14439	−	0.687177i
$322$	−10.5371	+	6.08359i	−0.587209	+	0.339025i
$323$	−9.39086	+	2.51627i	−0.522521	+	0.140009i
$324$	−7.46705	+	5.02425i	−0.414836	+	0.279125i
$325$	4.99739	−	0.711210i	0.277206	−	0.0394509i
$326$	−13.9287	−	8.04176i	−0.771441	−	0.445392i
$327$	20.0991	−	5.75715i	1.11148	−	0.318371i
$328$	11.1998			0.618405
$329$	−5.80323	+	10.0515i	−0.319942	+	0.554156i
$330$	5.21979	+	18.2231i	0.287340	+	1.00315i
$331$	−7.44027	−	7.44027i	−0.408954	−	0.408954i	0.472420	−	0.881374i	$-0.343381\pi$
$331$	−7.44027	−	7.44027i	−0.408954	−	0.408954i	−0.881374	+	0.472420i	$0.843381\pi$
$332$	−0.723746	+	2.70106i	−0.0397207	+	0.148240i
$333$	−4.63186	+	4.96141i	−0.253824	+	0.271884i
$334$	2.83072	+	4.90295i	0.154890	+	0.268277i
$335$	13.1492	+	22.7751i	0.718417	+	1.24433i
$336$	2.46749	−	2.55371i	0.134613	−	0.139316i
$337$	0.605437	−	0.349549i	0.0329803	−	0.0190412i	−0.483419	−	0.875389i	$-0.660605\pi$
$337$	0.605437	−	0.349549i	0.0329803	−	0.0190412i	0.516399	+	0.856348i	$0.327272\pi$
$338$	−6.26291	+	11.3919i	−0.340657	+	0.619639i
$339$	13.6346	−	8.18723i	0.740531	−	0.444670i
$340$	−1.09324	+	4.08004i	−0.0592895	+	0.221271i
$341$	−12.7518	−	7.36226i	−0.690549	−	0.398689i
$342$	13.0936	−	0.449789i	0.708018	−	0.0243218i
$343$	−14.2023	−	14.2023i	−0.766855	−	0.766855i
$344$	4.19325	−	4.19325i	0.226085	−	0.226085i
$345$	−13.5520	+	14.0256i	−0.729617	+	0.755111i
$346$	−10.8343	−	2.90303i	−0.582454	−	0.156068i
$347$	20.0278	+	11.5630i	1.07515	+	0.620737i	0.929583	−	0.368612i	$-0.120167\pi$
$347$	20.0278	+	11.5630i	1.07515	+	0.620737i	0.145564	+	0.989349i	$0.453500\pi$
$348$	5.14878	−	9.28242i	0.276003	−	0.497590i
$349$	3.12934	+	0.838505i	0.167510	+	0.0448842i	0.341599	−	0.939846i	$-0.389031\pi$
$349$	3.12934	+	0.838505i	0.167510	+	0.0448842i	−0.174089	+	0.984730i	$0.555698\pi$
$350$	−2.87027			−0.153422
$351$	−14.1286	+	12.3038i	−0.754127	+	0.656729i
$352$	−5.76811			−0.307441
$353$	−11.0229	−	2.95358i	−0.586690	−	0.157203i	−0.0467497	−	0.998907i	$-0.514886\pi$
$353$	−11.0229	−	2.95358i	−0.586690	−	0.157203i	−0.539940	+	0.841704i	$0.681553\pi$
$354$	5.53405	−	9.97701i	0.294132	−	0.530272i
$355$	10.9456	+	6.31946i	0.580934	+	0.335402i
$356$	−12.7827	−	3.42511i	−0.677482	−	0.181531i
$357$	−5.49320	+	5.68514i	−0.290731	+	0.300889i
$358$	−7.88369	+	7.88369i	−0.416666	+	0.416666i
$359$	20.7218	+	20.7218i	1.09366	+	1.09366i	0.995135	+	0.0985204i	$0.0314110\pi$
$359$	20.7218	+	20.7218i	1.09366	+	1.09366i	0.0985204	+	0.995135i	$0.468589\pi$
$360$	2.67514	−	5.02431i	0.140992	−	0.264804i
$361$	−0.0619225	−	0.0357510i	−0.00325908	−	0.00188163i
$362$	0.521677	−	1.94693i	0.0274187	−	0.102328i
$363$	33.0706	−	19.8580i	1.73576	−	1.04228i
$364$	4.43840	−	5.91133i	0.232635	−	0.309838i
$365$	−13.9969	+	8.08113i	−0.732633	+	0.422986i
$366$	10.6748	−	11.0478i	0.557983	−	0.577480i
$367$	6.15156	+	10.6548i	0.321109	+	0.556177i	0.980717	−	0.195433i	$-0.0626111\pi$
$367$	6.15156	+	10.6548i	0.321109	+	0.556177i	−0.659608	+	0.751610i	$0.729278\pi$
$368$	−2.96731	−	5.13954i	−0.154682	−	0.267917i
$369$	32.7339	+	7.57681i	1.70406	+	0.394433i
$370$	1.11105	−	4.14650i	0.0577608	−	0.215566i
$371$	−3.96587	−	3.96587i	−0.205898	−	0.205898i
$372$	1.21752	+	4.25055i	0.0631254	+	0.220381i
$373$	−14.1688	+	24.5411i	−0.733633	+	1.27069i	0.221688	+	0.975118i	$0.428843\pi$
$373$	−14.1688	+	24.5411i	−0.733633	+	1.27069i	−0.955321	+	0.295572i	$0.904490\pi$
$374$	12.8411			0.663998
$375$	−20.2194	+	5.79161i	−1.04413	+	0.299077i
$376$	−4.90268	−	2.83056i	−0.252836	−	0.145975i
$377$	8.24178	−	20.5018i	0.424473	−	1.05590i
$378$	8.93943	−	5.79451i	0.459795	−	0.298037i
$379$	−17.5171	+	4.69369i	−0.899793	+	0.241099i	−0.678927	−	0.734206i	$-0.737555\pi$
$379$	−17.5171	+	4.69369i	−0.899793	+	0.241099i	−0.220866	+	0.975304i	$0.570888\pi$
$380$	−7.17587	+	4.14299i	−0.368114	+	0.212531i
$381$	−13.2679	+	7.96704i	−0.679736	+	0.408164i
$382$	0.145254	−	0.542094i	0.00743182	−	0.0277359i
$383$	−5.23117	−	19.5230i	−0.267301	−	0.997579i	−0.960827	−	0.277148i	$-0.910611\pi$
$383$	−5.23117	−	19.5230i	−0.267301	−	0.997579i	0.693527	−	0.720431i	$-0.256056\pi$
$384$	1.24559	+	1.20354i	0.0635638	+	0.0614178i
$385$	−5.80735	−	21.6733i	−0.295970	−	1.10457i
$386$	7.72646	−	4.46087i	0.393266	−	0.227052i
$387$	15.0925	−	9.41892i	0.767195	−	0.478791i
$388$	−1.62163	−	6.05201i	−0.0823259	−	0.307244i
$389$	13.1281	−	22.7385i	0.665620	−	1.15289i	−0.313497	−	0.949589i	$-0.601501\pi$
$389$	13.1281	−	22.7385i	0.665620	−	1.15289i	0.979117	−	0.203298i	$-0.0651660\pi$
$390$	4.23021	−	11.0682i	0.214205	−	0.560461i
$391$	6.60591	+	11.4418i	0.334075	+	0.578635i
$392$	1.97755	−	1.97755i	0.0998813	−	0.0998813i
$393$	0.555267	+	32.3377i	0.0280095	+	1.63122i
$394$			9.73891i			0.490639i
$395$	14.1006	−	14.1006i	0.709477	−	0.709477i
$396$	−16.8586	−	3.90221i	−0.847177	−	0.196093i
$397$	−29.4918	−	7.90232i	−1.48015	−	0.396606i	−0.573754	−	0.819028i	$-0.694513\pi$
$397$	−29.4918	−	7.90232i	−1.48015	−	0.396606i	−0.906399	+	0.422422i	$0.861180\pi$
$398$	8.27594	−	2.21753i	0.414835	−	0.111155i
$399$	−15.5055	+	0.266243i	−0.776245	+	0.0133288i
$400$		−	1.39999i		−	0.0699997i
$401$	2.17000	+	2.17000i	0.108364	+	0.108364i	0.759210	−	0.650846i	$-0.225586\pi$
$401$	2.17000	+	2.17000i	0.108364	+	0.108364i	−0.650846	+	0.759210i	$0.725586\pi$
$402$	−24.0035	+	0.412161i	−1.19718	+	0.0205567i
$403$	3.61105	+	8.46610i	0.179879	+	0.421727i
$404$			3.52832i			0.175540i
$405$	11.2177	−	12.8749i	0.557412	−	0.639760i
$406$	−6.28226	+	10.8812i	−0.311783	+	0.540025i
$407$	−13.0503			−0.646879
$408$	−2.77297	−	2.67935i	−0.137282	−	0.132647i
$409$	17.7258	−	4.74963i	0.876487	−	0.234854i	0.207596	−	0.978215i	$-0.433436\pi$
$409$	17.7258	−	4.74963i	0.876487	−	0.234854i	0.668891	+	0.743361i	$0.266769\pi$
$410$	−20.5260	+	5.49994i	−1.01371	+	0.271623i
$411$	−17.2038	+	4.92782i	−0.848601	+	0.243072i
$412$	−2.41300			−0.118880
$413$	−6.75236	+	11.6954i	−0.332262	+	0.575494i
$414$	−5.19568	−	17.0289i	−0.255354	−	0.836924i
$415$		−	5.30568i		−	0.260446i
$416$	2.88329	+	2.16486i	0.141365	+	0.106141i
$417$	16.6678	+	27.7577i	0.816226	+	1.35930i
$418$	17.8119	+	17.8119i	0.871210	+	0.871210i
$419$		−	19.0261i		−	0.929486i	−0.885446	−	0.464743i	$-0.846147\pi$
$419$		−	19.0261i		−	0.929486i	0.885446	−	0.464743i	$-0.153853\pi$
$420$	−3.26815	+	5.89196i	−0.159470	+	0.287498i
$421$	−30.5835	+	8.19483i	−1.49055	+	0.399392i	−0.909923	−	0.414777i	$-0.863859\pi$
$421$	−30.5835	+	8.19483i	−1.49055	+	0.399392i	−0.580628	+	0.814169i	$0.697193\pi$
$422$	−12.4058	−	3.32413i	−0.603906	−	0.161816i
$423$	−12.4143	−	11.5897i	−0.603603	−	0.563510i
$424$	1.93438	−	1.93438i	0.0939418	−	0.0939418i
$425$			3.11670i			0.151182i
$426$	−9.89143	+	5.93954i	−0.479241	+	0.287772i
$427$	−12.8583	+	12.8583i	−0.622257	+	0.622257i
$428$	−6.90393	−	11.9580i	−0.333714	−	0.578010i
$429$	−35.8300	−	3.71313i	−1.72989	−	0.179271i
$430$	−5.62584	+	9.74423i	−0.271302	+	0.469909i
$431$	−2.93713	−	10.9615i	−0.141477	−	0.527999i	−0.999887	−	0.0150347i	$-0.995214\pi$
$431$	−2.93713	−	10.9615i	−0.141477	−	0.527999i	0.858410	−	0.512964i	$-0.171453\pi$
$432$	2.82631	+	4.36027i	0.135981	+	0.209784i
$433$	19.3513	−	11.1725i	0.929963	−	0.536915i	0.0431634	−	0.999068i	$-0.486256\pi$
$433$	19.3513	−	11.1725i	0.929963	−	0.536915i	0.886800	+	0.462153i	$0.152923\pi$
$434$	−1.35457	−	5.05531i	−0.0650212	−	0.242663i
$435$	−4.87789	+	19.5405i	−0.233877	+	0.936894i
$436$	−3.12418	−	11.6596i	−0.149621	−	0.558393i
$437$	−6.70783	+	25.0340i	−0.320879	+	1.19754i
$438$	−0.253303	−	14.7519i	−0.0121033	−	0.704872i
$439$	27.3401	−	15.7848i	1.30487	−	0.753368i	0.323636	−	0.946182i	$-0.395095\pi$
$439$	27.3401	−	15.7848i	1.30487	−	0.753368i	0.981235	+	0.192814i	$0.0617613\pi$
$440$	10.5713	−	2.83258i	0.503968	−	0.135038i
$441$	7.11768	−	4.44200i	0.338937	−	0.211524i
$442$	−6.41886	−	4.81946i	−0.305314	−	0.229239i
$443$	4.41781	+	2.55062i	0.209897	+	0.121184i	0.601263	−	0.799051i	$-0.294664\pi$
$443$	4.41781	+	2.55062i	0.209897	+	0.121184i	−0.391367	+	0.920235i	$0.627998\pi$
$444$	2.81814	+	2.72299i	0.133743	+	0.129227i
$445$	25.1091			1.19028
$446$	6.03496	−	10.4529i	0.285764	−	0.494958i
$447$	−9.21609	−	2.30061i	−0.435906	−	0.108815i
$448$	−1.44971	−	1.44971i	−0.0684924	−	0.0684924i
$449$	7.26523	−	27.1142i	0.342867	−	1.27960i	−0.552216	−	0.833701i	$-0.686218\pi$
$449$	7.26523	−	27.1142i	0.342867	−	1.27960i	0.895084	−	0.445898i	$-0.147116\pi$
$450$	0.947115	−	4.09180i	0.0446474	−	0.192889i
$451$	32.3008	+	55.9466i	1.52099	+	2.63442i
$452$	−4.59106	−	7.95194i	−0.215945	−	0.374028i
$453$	10.9405	+	2.73108i	0.514031	+	0.128317i
$454$	11.1313	−	6.42669i	0.522420	−	0.301619i
$455$	−5.23142	+	13.0134i	−0.245253	+	0.610077i
$456$	−0.129862	−	7.56291i	−0.00608134	−	0.354166i
$457$	9.22222	−	34.4178i	0.431397	−	1.61000i	−0.318147	−	0.948041i	$-0.603060\pi$
$457$	9.22222	−	34.4178i	0.431397	−	1.61000i	0.749544	−	0.661955i	$-0.230273\pi$
$458$	−16.8493	−	9.72795i	−0.787316	−	0.454557i
$459$	−6.29201	−	9.70694i	−0.293686	−	0.453081i
$460$	7.96214	+	7.96214i	0.371237	+	0.371237i
$461$	−12.5859	+	12.5859i	−0.586185	+	0.586185i	−0.936596	−	0.350411i	$-0.886042\pi$
$461$	−12.5859	+	12.5859i	−0.586185	+	0.586185i	0.350411	+	0.936596i	$0.386042\pi$
$462$	19.8730	+	4.96090i	0.924577	+	0.230802i
$463$	−26.6170	−	7.13200i	−1.23700	−	0.331452i	−0.419696	−	0.907665i	$-0.637863\pi$
$463$	−26.6170	−	7.13200i	−1.23700	−	0.331452i	−0.817300	+	0.576212i	$0.804530\pi$
$464$	−5.30738	−	3.06422i	−0.246389	−	0.142253i
$465$	−4.31871	−	7.19216i	−0.200275	−	0.333529i
$466$	3.86764	+	1.03633i	0.179165	+	0.0480071i
$467$	−16.8628			−0.780315			−0.390158	−	0.920748i	$-0.627580\pi$
$467$	−16.8628			−0.780315			−0.390158	+	0.920748i	$0.627580\pi$
$468$	6.96252	+	8.27788i	0.321843	+	0.382645i
$469$	28.4167			1.31216
$470$	10.3752	+	2.78004i	0.478574	+	0.128234i
$471$	17.7429	−	0.304661i	0.817550	−	0.0140381i
$472$	−5.70453	−	3.29351i	−0.262572	−	0.151596i
$473$	33.0402	+	8.85310i	1.51919	+	0.407066i
$474$	5.01266	+	17.5000i	0.230239	+	0.803801i
$475$	−4.32318	+	4.32318i	−0.198361	+	0.198361i
$476$	3.22738	+	3.22738i	0.147927	+	0.147927i
$477$	6.96230	−	4.34503i	0.318782	−	0.198945i
$478$	−7.94585	−	4.58754i	−0.363435	−	0.209829i
$479$	−9.87124	+	36.8400i	−0.451028	+	1.68326i	0.248480	+	0.968637i	$0.420069\pi$
$479$	−9.87124	+	36.8400i	−0.451028	+	1.68326i	−0.699509	+	0.714624i	$0.746598\pi$
$480$	−2.87384	−	1.59406i	−0.131172	−	0.0727588i
$481$	6.52342	+	4.89797i	0.297442	+	0.223328i
$482$	16.7679	−	9.68096i	0.763757	−	0.440956i
$483$	5.80307	+	20.2594i	0.264049	+	0.921836i
$484$	−11.1356	−	19.2873i	−0.506161	−	0.876697i
$485$	5.94398	+	10.2953i	0.269902	+	0.467485i
$486$	5.31075	+	14.6559i	0.240901	+	0.664806i
$487$	−3.49748	+	13.0528i	−0.158486	+	0.591478i	0.840296	+	0.542128i	$0.182381\pi$
$487$	−3.49748	+	13.0528i	−0.158486	+	0.591478i	−0.998782	+	0.0493492i	$0.984285\pi$
$488$	−6.27173	−	6.27173i	−0.283908	−	0.283908i
$489$	−19.3571	+	20.0335i	−0.875359	+	0.905945i
$490$	−2.65316	+	4.59541i	−0.119858	+	0.207600i
$491$	−30.4970			−1.37631			−0.688155	−	0.725564i	$-0.741579\pi$
$491$	−30.4970			−1.37631			−0.688155	+	0.725564i	$0.741579\pi$
$492$	4.69829	−	18.8210i	0.211815	−	0.848518i
$493$	11.8154	+	6.82164i	0.532140	+	0.307231i
$494$	−2.21853	−	15.5887i	−0.0998162	−	0.701369i
$495$	32.8133	−	1.12720i	1.47485	−	0.0506639i
$496$	2.46576	−	0.660699i	0.110716	−	0.0296663i
$497$	11.8273	−	6.82849i	0.530527	−	0.306300i
$498$	4.23547	+	2.34933i	0.189796	+	0.105276i
$499$	−0.215030	+	0.802501i	−0.00962605	+	0.0359249i	−0.970572	−	0.240812i	$-0.922586\pi$
$499$	−0.215030	+	0.802501i	−0.00962605	+	0.0359249i	0.960946	+	0.276737i	$0.0892530\pi$
$500$	3.14288	+	11.7294i	0.140554	+	0.524554i
$501$	9.42680	−	2.70019i	0.421158	−	0.120636i
$502$	−3.92672	−	14.6547i	−0.175258	−	0.654072i
$503$	−1.71989	+	0.992977i	−0.0766860	+	0.0442747i	−0.537853	−	0.843039i	$-0.680764\pi$
$503$	−1.71989	+	0.992977i	−0.0766860	+	0.0442747i	0.461167	+	0.887314i	$0.347431\pi$
$504$	−3.25636	−	5.21786i	−0.145050	−	0.232422i
$505$	−1.73267	−	6.46640i	−0.0771027	−	0.287751i
$506$	17.1158	−	29.6454i	0.760890	−	1.31790i
$507$	16.5167	+	15.3036i	0.733530	+	0.679657i
$508$	4.46758	+	7.73808i	0.198217	+	0.343322i
$509$	−12.0729	+	12.0729i	−0.535122	+	0.535122i	−0.922092	−	0.386970i	$-0.873522\pi$
$509$	−12.0729	+	12.0729i	−0.535122	+	0.535122i	0.386970	+	0.922092i	$0.373522\pi$
$510$	6.39782	+	3.54875i	0.283300	+	0.157141i
$511$			17.4641i			0.772568i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	4.73686	−	22.1922i	0.209138	−	0.979808i
$514$	6.88691	+	1.84534i	0.303768	+	0.0813945i
$515$	4.42235	−	1.18497i	0.194872	−	0.0522158i
$516$	−5.28762	−	8.80574i	−0.232774	−	0.387651i
$517$		−	32.6540i		−	1.43612i
$518$	−3.27996	−	3.27996i	−0.144113	−	0.144113i
$519$	−9.42346	+	16.9890i	−0.413644	+	0.745734i
$520$	−6.34737	−	2.55166i	−0.278351	−	0.111898i
$521$			14.9970i			0.657030i	0.944499	+	0.328515i	$0.106548\pi$
$521$			14.9970i			0.657030i	−0.944499	+	0.328515i	$0.893452\pi$
$522$	−13.4390	−	12.5464i	−0.588211	−	0.549141i
$523$	−18.1632	+	31.4596i	−0.794221	+	1.37563i	0.129112	+	0.991630i	$0.458787\pi$
$523$	−18.1632	+	31.4596i	−0.794221	+	1.37563i	−0.923333	+	0.384001i	$0.874546\pi$
$524$	18.6729			0.815731
$525$	−1.20407	+	4.82344i	−0.0525501	+	0.210512i
$526$	−9.99351	+	2.67775i	−0.435738	+	0.116756i
$527$	−5.48934	+	1.47087i	−0.239120	+	0.0640719i
$528$	−2.41971	+	9.69321i	−0.105305	+	0.421843i
$529$	12.2198			0.531295
$530$	−2.59524	+	4.49510i	−0.112730	+	0.195254i
$531$	−14.4447	−	13.4852i	−0.626845	−	0.585209i
$532$			8.95342i			0.388180i
$533$	4.85149	−	40.0889i	0.210141	−	1.73644i
$534$	−11.1182	+	20.0443i	−0.481130	+	0.867400i
$535$	18.5252	+	18.5252i	0.800915	+	0.800915i
$536$			13.8604i			0.598680i
$537$	9.94121	+	16.5556i	0.428995	+	0.714427i
$538$	18.8570	−	5.05273i	0.812985	−	0.217839i
$539$	15.5819	+	4.17515i	0.671159	+	0.179836i
$540$	−7.32105	−	6.60321i	−0.315048	−	0.284157i
$541$	−12.6107	+	12.6107i	−0.542176	+	0.542176i	−0.924166	−	0.381990i	$-0.875239\pi$
$541$	−12.6107	+	12.6107i	−0.542176	+	0.542176i	0.381990	+	0.924166i	$0.375239\pi$
$542$			16.1830i			0.695121i
$543$	−3.05293	−	1.69340i	−0.131014	−	0.0726708i
$544$	−1.57418	+	1.57418i	−0.0674924	+	0.0674924i
$545$	11.4515	+	19.8345i	0.490527	+	0.849618i
$546$	−8.07199	−	9.93844i	−0.345449	−	0.425326i
$547$	3.89564	−	6.74745i	0.166566	−	0.288500i	−0.770644	−	0.637265i	$-0.780066\pi$
$547$	3.89564	−	6.74745i	0.166566	−	0.288500i	0.937210	+	0.348765i	$0.113399\pi$
$548$	2.67413	+	9.98001i	0.114233	+	0.426325i
$549$	−14.0876	−	22.5735i	−0.601245	−	0.963411i
$550$	6.99343	−	4.03766i	0.298201	−	0.172166i
$551$	6.92689	+	25.8515i	0.295095	+	1.10131i
$552$	−9.88168	+	2.83049i	−0.420592	+	0.120474i
$553$	−5.57690	−	20.8133i	−0.237154	−	0.885070i
$554$	−7.98136	+	29.7869i	−0.339096	+	1.26552i
$555$	−6.50204	−	3.60656i	−0.275996	−	0.153090i
$556$	16.1888	−	9.34661i	0.686558	−	0.396384i
$557$	18.3374	−	4.91350i	0.776982	−	0.208192i	0.151528	−	0.988453i	$-0.451581\pi$
$557$	18.3374	−	4.91350i	0.776982	−	0.208192i	0.625454	+	0.780261i	$0.284914\pi$
$558$	7.65372	−	0.262920i	0.324008	−	0.0111303i
$559$	−13.1930	−	16.8259i	−0.558006	−	0.711659i
$560$	3.36883	+	1.94499i	0.142359	+	0.0821909i
$561$	5.38683	−	21.5793i	0.227432	−	0.911077i
$562$	9.09665			0.383719
$563$	14.6652	−	25.4009i	0.618066	−	1.07052i	−0.371772	−	0.928324i	$-0.621250\pi$
$563$	14.6652	−	25.4009i	0.618066	−	1.07052i	0.989838	−	0.142198i	$-0.0454169\pi$
$564$	−6.81338	+	7.05145i	−0.286895	+	0.296920i
$565$	12.3191	+	12.3191i	0.518269	+	0.518269i
$566$	4.44083	−	16.5734i	0.186662	−	0.696632i
$567$	−5.98749	−	17.4533i	−0.251451	−	0.732971i
$568$	3.33065	+	5.76885i	0.139751	+	0.242056i
$569$	−2.33915	−	4.05152i	−0.0980622	−	0.169849i	0.812820	−	0.582515i	$-0.197931\pi$
$569$	−2.33915	−	4.05152i	−0.0980622	−	0.169849i	−0.910883	+	0.412666i	$0.864598\pi$
$570$	3.95196	+	13.7969i	0.165529	+	0.577889i
$571$	−1.98594	+	1.14658i	−0.0831088	+	0.0479829i	−0.540978	−	0.841036i	$-0.681946\pi$
$571$	−1.98594	+	1.14658i	−0.0831088	+	0.0479829i	0.457870	+	0.889019i	$0.348613\pi$
$572$	−2.49861	+	20.6466i	−0.104472	+	0.863277i
$573$	−0.850045	−	0.471503i	−0.0355111	−	0.0196973i
$574$	−5.94296	+	22.1794i	−0.248054	+	0.925751i
$575$	7.19532	+	4.15422i	0.300066	+	0.173243i
$576$	2.54505	−	1.58831i	0.106044	−	0.0661797i
$577$	13.7676	+	13.7676i	0.573154	+	0.573154i	0.933008	−	0.359854i	$-0.117174\pi$
$577$	13.7676	+	13.7676i	0.573154	+	0.573154i	−0.359854	+	0.933008i	$0.617174\pi$
$578$	−8.51634	+	8.51634i	−0.354233	+	0.354233i
$579$	−4.25518	−	14.8555i	−0.176839	−	0.617374i
$580$	11.2317	+	3.00952i	0.466371	+	0.124964i
$581$	−4.96497	−	2.86653i	−0.205982	−	0.118924i
$582$	−10.8506	+	0.186314i	−0.449771	+	0.00772296i
$583$	15.2417	+	4.08401i	0.631248	+	0.169142i
$584$	−8.51825			−0.352488
$585$	−16.8254	−	11.7519i	−0.695644	−	0.485881i
$586$	−10.4836			−0.433075
$587$	−17.2487	−	4.62178i	−0.711931	−	0.190761i	−0.115363	−	0.993323i	$-0.536803\pi$
$587$	−17.2487	−	4.62178i	−0.711931	−	0.190761i	−0.596569	+	0.802562i	$0.703470\pi$
$588$	−2.49366	−	4.15282i	−0.102837	−	0.171259i
$589$	−9.65452	−	5.57404i	−0.397807	−	0.229674i
$590$	12.0721	+	3.23472i	0.497002	+	0.133171i
$591$	16.3661	+	4.08546i	0.673210	+	0.168053i
$592$	1.59982	−	1.59982i	0.0657523	−	0.0657523i
$593$	1.54480	+	1.54480i	0.0634372	+	0.0634372i	0.738114	−	0.674676i	$-0.235717\pi$
$593$	1.54480	+	1.54480i	0.0634372	+	0.0634372i	−0.674676	+	0.738114i	$0.735717\pi$
$594$	−13.6298	+	26.6936i	−0.559235	+	1.09525i
$595$	−7.49977	−	4.32999i	−0.307460	−	0.177512i
$596$	−1.41941	+	5.29732i	−0.0581414	+	0.216987i
$597$	−0.254778	−	14.8378i	−0.0104274	−	0.607271i
$598$	−19.6820	+	8.39498i	−0.804857	+	0.343296i
$599$	6.23611	−	3.60042i	0.254801	−	0.147109i	−0.367160	−	0.930158i	$-0.619670\pi$
$599$	6.23611	−	3.60042i	0.254801	−	0.147109i	0.621960	+	0.783049i	$0.286336\pi$
$600$	−2.35266	−	0.587295i	−0.0960471	−	0.0239762i
$601$	−3.81318	−	6.60462i	−0.155543	−	0.269408i	0.777714	−	0.628619i	$-0.216379\pi$
$601$	−3.81318	−	6.60462i	−0.155543	−	0.269408i	−0.933257	+	0.359211i	$0.883046\pi$
$602$	6.07899	+	10.5291i	0.247761	+	0.429135i
$603$	−9.37678	+	40.5103i	−0.381852	+	1.64971i
$604$	1.68500	−	6.28851i	0.0685618	−	0.255876i
$605$	29.8798	+	29.8798i	1.21479	+	1.21479i
$606$	5.92927	+	1.48012i	0.240860	+	0.0601259i
$607$	20.9414	−	36.2716i	0.849987	−	1.47222i	−0.0312320	−	0.999512i	$-0.509943\pi$
$607$	20.9414	−	36.2716i	0.849987	−	1.47222i	0.881219	−	0.472708i	$-0.156724\pi$
$608$	−4.36709			−0.177109
$609$	15.6503	+	15.1219i	0.634181	+	0.612769i
$610$	14.5742	+	8.41441i	0.590092	+	0.340690i
$611$	−12.2555	+	16.3227i	−0.495806	+	0.660346i
$612$	−5.66585	+	3.53594i	−0.229028	+	0.142932i
$613$	−27.6735	+	7.41508i	−1.11772	+	0.299492i	−0.769961	−	0.638091i	$-0.779724\pi$
$613$	−27.6735	+	7.41508i	−1.11772	+	0.299492i	−0.347760	+	0.937584i	$0.613058\pi$
$614$	−8.47974	+	4.89578i	−0.342215	+	0.197578i
$615$	0.631904	+	36.8009i	0.0254808	+	1.48395i
$616$	3.06074	−	11.4228i	0.123321	−	0.460239i
$617$	2.55572	+	9.53809i	0.102890	+	0.383989i	0.998097	−	0.0616601i	$-0.0196395\pi$
$617$	2.55572	+	9.53809i	0.102890	+	0.383989i	−0.895208	+	0.445649i	$0.852973\pi$
$618$	−1.01225	+	4.05501i	−0.0407187	+	0.163116i
$619$	−10.1033	−	37.7062i	−0.406088	−	1.51554i	−0.802041	−	0.597269i	$-0.796252\pi$
$619$	−10.1033	−	37.7062i	−0.406088	−	1.51554i	0.395953	−	0.918271i	$-0.370414\pi$
$620$	−4.19459	+	2.42175i	−0.168459	+	0.0972598i
$621$	−30.7963	+	1.58765i	−1.23581	+	0.0637102i
$622$	3.90582	+	14.5767i	0.156609	+	0.584473i
$623$	13.5658	−	23.4966i	0.543502	−	0.941373i
$624$	4.84755	−	3.93717i	0.194057	−	0.157613i
$625$	−8.02002	−	13.8911i	−0.320801	−	0.555644i
$626$	18.6883	−	18.6883i	0.746933	−	0.746933i
$627$	37.4047	−	22.4606i	1.49380	−	0.896988i
$628$		−	10.2454i		−	0.408835i
$629$	−3.56156	+	3.56156i	−0.142009	+	0.142009i
$630$	8.53034	+	7.96374i	0.339857	+	0.317283i
$631$	−28.3493	−	7.59618i	−1.12857	−	0.302399i	−0.354223	−	0.935161i	$-0.615254\pi$
$631$	−28.3493	−	7.59618i	−1.12857	−	0.302399i	−0.774346	+	0.632762i	$0.781921\pi$
$632$	10.1518	−	2.72017i	0.403818	−	0.108203i
$633$	−10.7904	+	19.4533i	−0.428879	+	0.773200i
$634$			30.5269i			1.21238i
$635$	−11.9878	−	11.9878i	−0.475721	−	0.475721i
$636$	−2.43922	−	4.06216i	−0.0967214	−	0.161075i
$637$	−6.22188	−	7.93514i	−0.246520	−	0.314402i
$638$		−	35.3495i		−	1.39950i
$639$	5.83186	+	19.1140i	0.230705	+	0.756138i
$640$	−0.948684	+	1.64317i	−0.0375000	+	0.0649520i
$641$	−13.5860			−0.536616			−0.268308	−	0.963333i	$-0.586465\pi$
$641$	−13.5860			−0.536616			−0.268308	+	0.963333i	$0.586465\pi$
$642$	−22.9913	+	6.58559i	−0.907395	+	0.259912i
$643$	−18.1514	+	4.86366i	−0.715822	+	0.191804i	−0.598307	−	0.801267i	$-0.704160\pi$
$643$	−18.1514	+	4.86366i	−0.715822	+	0.191804i	−0.117515	+	0.993071i	$0.537493\pi$
$644$	11.7526	−	3.14910i	0.463117	−	0.124092i
$645$	14.0150	+	13.5418i	0.551839	+	0.533208i
$646$	9.72213			0.382512
$647$	−11.7916	+	20.4237i	−0.463576	+	0.802937i	−0.999136	−	0.0415601i	$-0.986767\pi$
$647$	−11.7916	+	20.4237i	−0.463576	+	0.802937i	0.535560	+	0.844497i	$0.320101\pi$
$648$	8.51299	−	2.92044i	0.334422	−	0.114726i
$649$		−	37.9947i		−	1.49142i
$650$	−5.01119	−	0.606444i	−0.196555	−	0.0237867i
$651$	−9.06360	+	0.155630i	−0.355230	+	0.00609962i
$652$	11.3728	+	11.3728i	0.445392	+	0.445392i
$653$		−	38.2655i		−	1.49744i	−0.662884	−	0.748722i	$-0.730668\pi$
$653$		−	38.2655i		−	1.49744i	0.662884	−	0.748722i	$-0.269332\pi$
$654$	−20.9043	+	0.358946i	−0.817424	+	0.0140359i
$655$	−34.2222	+	9.16981i	−1.33717	+	0.358294i
$656$	−10.8182	−	2.89872i	−0.422378	−	0.113176i
$657$	−24.8965	−	5.76272i	−0.971306	−	0.224825i
$658$	8.20700	−	8.20700i	0.319942	−	0.319942i
$659$			36.7491i			1.43154i	0.698335	+	0.715771i	$0.253925\pi$
$659$			36.7491i			1.43154i	−0.698335	+	0.715771i	$0.746075\pi$
$660$	−0.325443	−	18.9532i	−0.0126678	−	0.737751i
$661$	−4.17485	+	4.17485i	−0.162383	+	0.162383i	−0.783621	−	0.621239i	$-0.786630\pi$
$661$	−4.17485	+	4.17485i	−0.162383	+	0.162383i	0.621239	+	0.783621i	$0.286630\pi$
$662$	5.26107	+	9.11243i	0.204477	+	0.354165i
$663$	−10.7917	+	8.76503i	−0.419116	+	0.340405i
$664$	1.39817	−	2.42170i	0.0542595	−	0.0939802i
$665$	−4.39680	−	16.4091i	−0.170501	−	0.636317i
$666$	5.75814	−	3.59354i	0.223123	−	0.139247i
$667$	31.4973	−	18.1850i	1.21958	−	0.704126i
$668$	−1.46529	−	5.46853i	−0.0566937	−	0.211584i
$669$	−15.0342	−	14.5266i	−0.581256	−	0.561631i
$670$	−6.80652	−	25.4023i	−0.262959	−	0.981375i
$671$	13.2413	−	49.4174i	0.511176	−	1.90774i
$672$	−3.04436	+	1.82806i	−0.117439	+	0.0705190i
$673$	18.5818	−	10.7282i	0.716277	−	0.413543i	−0.0971040	−	0.995274i	$-0.530958\pi$
$673$	18.5818	−	10.7282i	0.716277	−	0.413543i	0.813381	+	0.581732i	$0.197625\pi$
$674$	−0.675277	+	0.180940i	−0.0260107	+	0.00696955i
$675$	−6.47888	−	3.30811i	−0.249372	−	0.127329i
$676$	8.99795	−	9.38280i	0.346075	−	0.360877i
$677$	12.9054	+	7.45094i	0.495995	+	0.286363i	0.727058	−	0.686576i	$-0.240887\pi$
$677$	12.9054	+	7.45094i	0.495995	+	0.286363i	−0.231063	+	0.972939i	$0.574220\pi$
$678$	−15.2890	+	4.37936i	−0.587172	+	0.168188i
$679$	12.8455			0.492967
$680$	2.11198	−	3.65806i	0.0809909	−	0.140280i
$681$	−6.13035	−	21.4020i	−0.234915	−	0.820127i
$682$	10.4118	+	10.4118i	0.398689	+	0.398689i
$683$	6.54752	−	24.4357i	0.250534	−	0.935005i	−0.719987	−	0.693988i	$-0.755852\pi$
$683$	6.54752	−	24.4357i	0.250534	−	0.935005i	0.970521	−	0.241018i	$-0.0774811\pi$
$684$	−12.7638	−	2.95440i	−0.488037	−	0.112964i
$685$	−9.80186	−	16.9773i	−0.374510	−	0.648670i
$686$	10.0426	+	17.3943i	0.383427	+	0.664116i
$687$	−23.4159	+	24.2341i	−0.893373	+	0.924589i
$688$	−5.13566	+	2.96507i	−0.195795	+	0.113042i
$689$	−6.08606	−	7.76192i	−0.231860	−	0.295705i
$690$	16.7203	−	10.0401i	0.636533	−	0.382221i
$691$	9.88451	−	36.8895i	0.376025	−	1.40334i	−0.475817	−	0.879544i	$-0.657848\pi$
$691$	9.88451	−	36.8895i	0.376025	−	1.40334i	0.851842	−	0.523799i	$-0.175486\pi$
$692$	9.71374	+	5.60823i	0.369261	+	0.213193i
$693$	16.6734	−	31.3152i	0.633370	−	1.18957i
$694$	−16.3526	−	16.3526i	−0.620737	−	0.620737i
$695$	−25.0796	+	25.0796i	−0.951323	+	0.951323i
$696$	−7.37580	+	7.63353i	−0.279579	+	0.289348i
$697$	24.0837	+	6.45320i	0.912234	+	0.244432i
$698$	−2.80569	−	1.61987i	−0.106197	−	0.0613129i
$699$	3.36400	−	6.06476i	0.127238	−	0.229390i
$700$	2.77247	+	0.742880i	0.104789	+	0.0280782i
$701$	5.62024			0.212274			0.106137	−	0.994352i	$-0.466152\pi$
$701$	5.62024			0.212274			0.106137	+	0.994352i	$0.466152\pi$
$702$	16.8316	−	8.22784i	0.635268	−	0.310540i
$703$	−9.88050			−0.372650
$704$	5.57157	+	1.49290i	0.209986	+	0.0562657i
$705$	9.02421	−	16.2692i	0.339871	−	0.612733i
$706$	9.88286	+	5.70587i	0.371946	+	0.214743i
$707$	−6.98727	−	1.87223i	−0.262783	−	0.0704126i
$708$	−7.92773	+	8.20474i	−0.297942	+	0.308353i
$709$	−6.16652	+	6.16652i	−0.231588	+	0.231588i	−0.813355	−	0.581767i	$-0.802362\pi$
$709$	−6.16652	+	6.16652i	−0.231588	+	0.231588i	0.581767	+	0.813355i	$0.302362\pi$
$710$	−8.93707	−	8.93707i	−0.335402	−	0.335402i
$711$	31.5112	−	1.08247i	1.18176	−	0.0405958i
$712$	11.4607	+	6.61681i	0.429506	+	0.247976i
$713$	−3.92100	+	14.6334i	−0.146843	+	0.548024i
$714$	6.77744	−	4.06968i	0.253639	−	0.152304i
$715$	−5.55977	−	39.0663i	−0.207924	−	1.46100i
$716$	9.65551	−	5.57461i	0.360843	−	0.208333i
$717$	−11.0426	+	11.4284i	−0.412392	+	0.426801i
$718$	−14.6525	−	25.3789i	−0.546828	−	0.947133i
$719$	17.1214	+	29.6552i	0.638522	+	1.10595i	0.985757	+	0.168175i	$0.0537873\pi$
$719$	17.1214	+	29.6552i	0.638522	+	1.10595i	−0.347235	+	0.937778i	$0.612879\pi$
$720$	−3.88437	+	4.16074i	−0.144762	+	0.155061i
$721$	1.28041	−	4.77857i	0.0476851	−	0.177963i
$722$	0.0505595	+	0.0505595i	0.00188163	+	0.00188163i
$723$	−9.23457	−	32.2393i	−0.343437	−	1.19899i
$724$	−1.00780	+	1.74557i	−0.0374547	+	0.0648734i
$725$	8.57977			0.318645
$726$	−37.0834	+	10.6221i	−1.37629	+	0.394223i
$727$	−27.5561	−	15.9095i	−1.02200	−	0.590052i	−0.107318	−	0.994225i	$-0.534226\pi$
$727$	−27.5561	−	15.9095i	−1.02200	−	0.590052i	−0.914683	+	0.404172i	$0.867560\pi$
$728$	−5.81713	+	4.56117i	−0.215597	+	0.169048i
$729$	26.8569	−	2.77649i	0.994699	−	0.102833i
$730$	15.6115	−	4.18310i	0.577809	−	0.154824i
$731$	11.4331	−	6.60092i	0.422870	−	0.244144i
$732$	−13.1705	+	7.90855i	−0.486796	+	0.292308i
$733$	3.28845	−	12.2727i	0.121462	−	0.453301i	−0.878227	−	0.478244i	$-0.841274\pi$
$733$	3.28845	−	12.2727i	0.121462	−	0.453301i	0.999689	+	0.0249426i	$0.00794030\pi$
$734$	−3.18428	−	11.8839i	−0.117534	−	0.438643i
$735$	6.60951	+	6.38636i	0.243796	+	0.235565i
$736$	1.53599	+	5.73241i	0.0566175	+	0.211299i
$737$	−69.2375	+	39.9743i	−2.55040	+	1.47247i
$738$	−29.6575	−	15.7908i	−1.09171	−	0.581267i
$739$	−7.36509	−	27.4869i	−0.270929	−	1.01112i	−0.958521	−	0.285024i	$-0.907999\pi$
$739$	−7.36509	−	27.4869i	−0.270929	−	1.01112i	0.687591	−	0.726098i	$-0.258668\pi$
$740$	−2.14639	+	3.71765i	−0.0789028	+	0.136664i
$741$	−27.1272	−	2.81124i	−0.996543	−	0.103274i
$742$	2.80429	+	4.85717i	0.102949	+	0.178312i
$743$	−18.4334	+	18.4334i	−0.676254	+	0.676254i	−0.959151	−	0.282896i	$-0.908705\pi$
$743$	−18.4334	+	18.4334i	−0.676254	+	0.676254i	0.282896	+	0.959151i	$0.408705\pi$
$744$	−0.0759096	−	4.42083i	−0.00278298	−	0.162076i
$745$		−	10.4055i		−	0.381229i
$746$	20.0377	−	20.0377i	0.733633	−	0.733633i
$747$	5.72478	−	6.13209i	0.209459	−	0.224361i
$748$	−12.4036	−	3.32352i	−0.453519	−	0.121520i
$749$	27.3443	−	7.32688i	0.999138	−	0.267718i
$750$	21.0294	−	0.361094i	0.767887	−	0.0131853i
$751$		−	27.1909i		−	0.992210i	−0.868263	−	0.496105i	$-0.834763\pi$
$751$		−	27.1909i		−	0.992210i	0.868263	−	0.496105i	$-0.165237\pi$
$752$	4.00302	+	4.00302i	0.145975	+	0.145975i
$753$	−26.2743	+	0.451152i	−0.957487	+	0.0164409i
$754$	−13.2672	+	17.6701i	−0.483163	+	0.643506i
$755$			12.3525i			0.449555i
$756$	−10.1346	+	3.28337i	−0.368590	+	0.119415i
$757$	−22.3587	+	38.7264i	−0.812640	+	1.40753i	0.0983707	+	0.995150i	$0.468637\pi$
$757$	−22.3587	+	38.7264i	−0.812640	+	1.40753i	−0.911010	+	0.412383i	$0.864696\pi$
$758$	18.1350			0.658694
$759$	−42.6386	−	41.1990i	−1.54768	−	1.49543i
$760$	8.00365	−	2.14457i	0.290323	−	0.0777917i
$761$	−48.5771	+	13.0162i	−1.76092	+	0.471837i	−0.986901	−	0.161327i	$-0.948423\pi$
$761$	−48.5771	+	13.0162i	−1.76092	+	0.471837i	−0.774018	+	0.633164i	$0.781756\pi$
$762$	14.8778	−	4.26158i	0.538968	−	0.154381i
$763$	24.7478			0.895929
$764$	−0.280608	+	0.486028i	−0.0101521	+	0.0175839i
$765$	8.64748	−	9.26273i	0.312650	−	0.334895i
$766$			20.2117i			0.730279i
$767$	−14.2600	+	18.9923i	−0.514898	+	0.685773i
$768$	−0.891650	−	1.48491i	−0.0321747	−	0.0535821i
$769$	29.1868	+	29.1868i	1.05250	+	1.05250i	0.998543	+	0.0539592i	$0.0171841\pi$
$769$	29.1868	+	29.1868i	1.05250	+	1.05250i	0.0539592	+	0.998543i	$0.482816\pi$
$770$			22.4379i			0.808605i
$771$	5.99011	−	10.7992i	0.215729	−	0.388924i
$772$	−8.61775	+	2.30912i	−0.310159	+	0.0831070i
$773$	13.9509	+	3.73812i	0.501778	+	0.134451i	0.500825	−	0.865549i	$-0.333030\pi$
$773$	13.9509	+	3.73812i	0.501778	+	0.134451i	0.000952768		1.00000i	$0.499697\pi$
$774$	−17.0160	+	5.19175i	−0.611629	+	0.186614i
$775$	−2.52708	+	2.52708i	−0.0907753	+	0.0907753i
$776$			6.26550i			0.224918i
$777$	−6.88784	+	4.13597i	−0.247100	+	0.148377i
$778$	−18.5659	+	18.5659i	−0.665620	+	0.665620i
$779$	24.4553	+	42.3578i	0.876201	+	1.51762i
$780$	−6.95073	+	9.59623i	−0.248876	+	0.343600i
$781$	−19.2115	+	33.2754i	−0.687443	+	1.19069i
$782$	−3.41947	−	12.7616i	−0.122280	−	0.456355i
$783$	−26.7216	+	17.3209i	−0.954954	+	0.618998i
$784$	−2.42199	+	1.39834i	−0.0864998	+	0.0499407i
$785$	5.03125	+	18.7769i	0.179573	+	0.670175i
$786$	7.83326	−	31.3795i	0.279403	−	1.11927i
$787$	−6.96484	−	25.9931i	−0.248270	−	0.926555i	−0.971712	−	0.236170i	$-0.924108\pi$
$787$	−6.96484	−	25.9931i	−0.248270	−	0.926555i	0.723442	−	0.690385i	$-0.242559\pi$
$788$	2.52062	−	9.40707i	0.0897932	−	0.335113i
$789$	0.307655	+	17.9172i	0.0109528	+	0.637870i
$790$	−17.2696	+	9.97061i	−0.614425	+	0.354738i
$791$	18.1837	−	4.87231i	0.646539	−	0.173240i
$792$	15.2742	+	8.13257i	0.542745	+	0.288978i
$793$	−25.1660	+	19.7325i	−0.893671	+	0.700721i
$794$	26.4417	+	15.2661i	0.938380	+	0.541774i
$795$	6.46523	+	6.24695i	0.229298	+	0.221556i
$796$	−8.56788			−0.303680
$797$	10.3405	−	17.9102i	0.366278	−	0.634412i	−0.622703	−	0.782459i	$-0.713965\pi$
$797$	10.3405	−	17.9102i	0.366278	−	0.634412i	0.988980	+	0.148047i	$0.0472987\pi$
$798$	15.0461	+	3.75594i	0.532625	+	0.132959i
$799$	−8.91163	−	8.91163i	−0.315271	−	0.315271i
$800$	−0.362345	+	1.35229i	−0.0128108	+	0.0478107i
$801$	29.0200	+	27.0924i	1.02537	+	0.957264i
$802$	−1.53442	−	2.65769i	−0.0541822	−	0.0938463i
$803$	−24.5671	−	42.5515i	−0.866955	−	1.50161i
$804$	23.2922	+	5.81443i	0.821454	+	0.205059i
$805$	−19.9927	+	11.5428i	−0.704651	+	0.406830i
$806$	−1.29682	−	9.11224i	−0.0456785	−	0.320965i
$807$	−0.580523	−	33.8085i	−0.0204354	−	1.19012i
$808$	0.913195	−	3.40809i	0.0321261	−	0.119896i
$809$	10.9263	+	6.30829i	0.384147	+	0.221788i	0.679621	−	0.733563i	$-0.262144\pi$
$809$	10.9263	+	6.30829i	0.384147	+	0.221788i	−0.295474	+	0.955351i	$0.595478\pi$
$810$	−14.1677	+	9.53286i	−0.497804	+	0.334951i
$811$	−0.473478	−	0.473478i	−0.0166261	−	0.0166261i	0.698745	−	0.715371i	$-0.253742\pi$
$811$	−0.473478	−	0.473478i	−0.0166261	−	0.0166261i	−0.715371	+	0.698745i	$0.753742\pi$
$812$	8.88446	−	8.88446i	0.311783	−	0.311783i
$813$	27.1953	+	6.78876i	0.953781	+	0.238092i
$814$	12.6056	+	3.37766i	0.441827	+	0.118387i
$815$	−26.4279	−	15.2582i	−0.925730	−	0.534471i
$816$	1.98501	+	3.30575i	0.0694894	+	0.115724i
$817$	25.0151	+	6.70277i	0.875166	+	0.234500i
$818$	−18.3511			−0.641633
$819$	−20.0876	+	9.39567i	−0.701916	+	0.328311i
$820$	21.2501			0.742087
$821$	48.3995	+	12.9686i	1.68916	+	0.452608i	0.970172	−	0.242419i	$-0.0779408\pi$
$821$	48.3995	+	12.9686i	1.68916	+	0.452608i	0.718984	+	0.695027i	$0.244607\pi$
$822$	17.8930	−	0.307239i	0.624091	−	0.0107162i
$823$	−27.4222	−	15.8322i	−0.955878	−	0.551877i	−0.0609763	−	0.998139i	$-0.519421\pi$
$823$	−27.4222	−	15.8322i	−0.955878	−	0.551877i	−0.894902	+	0.446263i	$0.852755\pi$
$824$	2.33078	+	0.624531i	0.0811966	+	0.0217566i
$825$	−3.85148	−	13.4461i	−0.134091	−	0.468134i
$826$	9.54928	−	9.54928i	0.332262	−	0.332262i
$827$	20.7929	+	20.7929i	0.723039	+	0.723039i	0.969223	−	0.246184i	$-0.0791769\pi$
$827$	20.7929	+	20.7929i	0.723039	+	0.723039i	−0.246184	+	0.969223i	$0.579177\pi$
$828$	0.611237	+	17.7934i	0.0212419	+	0.618363i
$829$	1.10256	+	0.636564i	0.0382935	+	0.0221088i	0.519025	−	0.854759i	$-0.326295\pi$
$829$	1.10256	+	0.636564i	0.0382935	+	0.0221088i	−0.480731	+	0.876868i	$0.659629\pi$
$830$	−1.37321	+	5.12490i	−0.0476649	+	0.177888i
$831$	46.7081	+	25.9081i	1.62029	+	0.898741i
$832$	−2.22474	−	2.83735i	−0.0771290	−	0.0983672i
$833$	5.39190	−	3.11302i	0.186818	−	0.107860i
$834$	−8.91563	−	31.1259i	−0.308723	−	1.07780i
$835$	5.37091	+	9.30269i	0.185868	+	0.321933i
$836$	−12.5949	−	21.8151i	−0.435605	−	0.754490i
$837$	2.76889	−	12.9722i	0.0957069	−	0.448386i
$838$	−4.92432	+	18.3778i	−0.170108	+	0.634851i
$839$	−32.2567	−	32.2567i	−1.11363	−	1.11363i	−0.992656	−	0.120970i	$-0.961399\pi$
$839$	−32.2567	−	32.2567i	−1.11363	−	1.11363i	−0.120970	−	0.992656i	$-0.538601\pi$
$840$	4.68174	−	4.84533i	0.161536	−	0.167180i
$841$	4.27887	−	7.41122i	0.147547	−	0.255559i
$842$	31.6624			1.09116
$843$	3.81603	−	15.2868i	0.131431	−	0.526504i
$844$	11.1228	+	6.42173i	0.382861	+	0.221045i
$845$	−11.8830	+	21.6147i	−0.408789	+	0.743568i
$846$	8.99164	+	14.4078i	0.309139	+	0.495352i
$847$	44.1044	−	11.8177i	1.51545	−	0.406062i
$848$	−2.36912	+	1.36781i	−0.0813560	+	0.0469709i
$849$	−25.9884	−	14.4153i	−0.891920	−	0.494730i
$850$	0.806662	−	3.01050i	0.0276683	−	0.103259i
$851$	3.47517	+	12.9695i	0.119127	+	0.444589i
$852$	11.0917	−	3.17707i	0.379994	−	0.108845i
$853$	3.05217	+	11.3909i	0.104504	+	0.390016i	0.998288	−	0.0584818i	$-0.0186260\pi$
$853$	3.05217	+	11.3909i	0.104504	+	0.390016i	−0.893784	+	0.448498i	$0.851959\pi$
$854$	15.7481	−	9.09219i	0.538890	−	0.311128i
$855$	24.8433	−	0.853415i	0.849623	−	0.0291862i
$856$	3.57374	+	13.3374i	0.122148	+	0.455862i
$857$	−21.4436	+	37.1414i	−0.732499	+	1.26872i	0.223314	+	0.974747i	$0.428313\pi$
$857$	−21.4436	+	37.1414i	−0.732499	+	1.26872i	−0.955812	+	0.293978i	$0.905021\pi$
$858$	33.6481	+	12.8601i	1.14873	+	0.439036i
$859$	−9.82545	−	17.0182i	−0.335240	−	0.580653i	0.648291	−	0.761393i	$-0.275484\pi$
$859$	−9.82545	−	17.0182i	−0.335240	−	0.580653i	−0.983531	+	0.180740i	$0.942151\pi$
$860$	7.95613	−	7.95613i	0.271302	−	0.271302i
$861$	34.7790	+	19.2913i	1.18527	+	0.657444i
$862$			11.3482i			0.386522i
$863$	13.1900	−	13.1900i	0.448992	−	0.448992i	−0.446027	−	0.895019i	$-0.647162\pi$
$863$	13.1900	−	13.1900i	0.448992	−	0.448992i	0.895019	+	0.446027i	$0.147162\pi$
$864$	−1.60149	−	4.94320i	−0.0544837	−	0.168171i
$865$	−20.5566	−	5.50812i	−0.698945	−	0.187282i
$866$	−21.5836	+	5.78330i	−0.733439	+	0.196524i
$867$	10.7390	+	17.8841i	0.364714	+	0.607377i
$868$			5.23364i			0.177641i
$869$	42.8666	+	42.8666i	1.45415	+	1.45415i
$870$	9.76913	−	17.6122i	0.331204	−	0.597108i
$871$	49.6126	+	6.00402i	1.68106	+	0.203438i
$872$			12.0709i			0.408772i
$873$	−4.23870	+	18.3123i	−0.143458	+	0.619779i
$874$	12.9585	−	22.4448i	0.438329	−	0.759208i
$875$	−24.8959			−0.841634
$876$	−3.57339	+	14.3148i	−0.120734	+	0.483651i
$877$	−43.4457	+	11.6413i	−1.46706	+	0.393097i	−0.901922	−	0.431900i	$-0.857843\pi$
$877$	−43.4457	+	11.6413i	−1.46706	+	0.393097i	−0.565137	+	0.824997i	$0.691177\pi$
$878$	−30.4939	+	8.17082i	−1.02912	+	0.275752i
$879$	−4.39787	+	17.6176i	−0.148337	+	0.594226i
$880$	−10.9442			−0.368930
$881$	−6.29938	+	10.9108i	−0.212232	+	0.367596i	−0.952413	−	0.304812i	$-0.901406\pi$
$881$	−6.29938	+	10.9108i	−0.212232	+	0.367596i	0.740181	+	0.672408i	$0.234740\pi$
$882$	−8.02482	+	2.44845i	−0.270210	+	0.0824436i
$883$		−	36.0877i		−	1.21445i	−0.794531	−	0.607224i	$-0.792283\pi$
$883$		−	36.0877i		−	1.21445i	0.794531	−	0.607224i	$-0.207717\pi$
$884$	4.95277	+	6.31657i	0.166580	+	0.212449i
$885$	10.5001	−	18.9301i	0.352958	−	0.636327i
$886$	−3.60713	−	3.60713i	−0.121184	−	0.121184i
$887$		−	17.3236i		−	0.581670i	−0.956773	−	0.290835i	$-0.906067\pi$
$887$		−	17.3236i		−	0.581670i	0.956773	−	0.290835i	$-0.0939331\pi$
$888$	−2.01735	−	3.35959i	−0.0676978	−	0.112741i
$889$	−17.6947	+	4.74127i	−0.593460	+	0.159017i
$890$	−24.2535	−	6.49870i	−0.812979	−	0.217837i
$891$	39.1405	+	34.1025i	1.31126	+	1.14248i
$892$	−8.53473	+	8.53473i	−0.285764	+	0.285764i
$893$		−	24.7227i		−	0.827313i
$894$	8.30661	+	4.60752i	0.277815	+	0.154098i
$895$	−14.9583	+	14.9583i	−0.500000	+	0.500000i
$896$	1.02510	+	1.77553i	0.0342462	+	0.0593162i
$897$	5.85104	+	36.5970i	0.195361	+	1.22194i
$898$	−14.0353	+	24.3099i	−0.468366	+	0.811233i
$899$	4.04905	+	15.1113i	0.135043	+	0.503989i
$900$	−1.97388	+	3.70724i	−0.0657960	+	0.123575i
$901$	5.27420	−	3.04506i	0.175709	−	0.101446i
$902$	−16.7201	−	62.4004i	−0.556719	−	2.07771i
$903$	20.2441	−	5.79869i	0.673683	−	0.192968i
$904$	2.37651	+	8.86924i	0.0790414	+	0.294987i
$905$	0.989813	−	3.69403i	0.0329025	−	0.122794i
$906$	−9.86088	−	5.46964i	−0.327606	−	0.181717i
$907$	−35.3599	+	20.4151i	−1.17411	+	0.677871i	−0.954644	−	0.297750i	$-0.903764\pi$
$907$	−35.3599	+	20.4151i	−1.17411	+	0.677871i	−0.219463	+	0.975621i	$0.570431\pi$
$908$	−12.4154	+	3.32670i	−0.412020	+	0.110400i
$909$	4.97464	−	9.34313i	0.164998	−	0.309892i
$910$	8.42127	−	11.2160i	0.279162	−	0.371806i
$911$	−33.7655	−	19.4945i	−1.11870	−	0.645883i	−0.177632	−	0.984097i	$-0.556844\pi$
$911$	−33.7655	−	19.4945i	−1.11870	−	0.645883i	−0.941069	+	0.338214i	$0.890177\pi$
$912$	−1.83199	+	7.33882i	−0.0606632	+	0.243013i
$913$	16.1296			0.533811
$914$	−17.8160	+	30.8581i	−0.589299	+	1.02070i
$915$	20.2541	−	20.9618i	0.669581	−	0.692977i
$916$	13.7574	+	13.7574i	0.454557	+	0.454557i
$917$	−9.90843	+	36.9788i	−0.327205	+	1.22115i
$918$	3.56527	+	11.0047i	0.117671	+	0.363209i
$919$	18.8145	+	32.5876i	0.620632	+	1.07497i	0.989368	+	0.145432i	$0.0464573\pi$
$919$	18.8145	+	32.5876i	0.620632	+	1.07497i	−0.368736	+	0.929534i	$0.620209\pi$
$920$	−5.63009	−	9.75159i	−0.185618	−	0.321501i
$921$	4.67004	+	16.3038i	0.153883	+	0.537230i
$922$	15.4145	−	8.89959i	0.507651	−	0.293092i
$923$	22.0920	−	9.42290i	0.727166	−	0.310159i
$924$	−17.9119	−	9.93538i	−0.589258	−	0.326850i
$925$	−0.819802	+	3.05954i	−0.0269549	+	0.100597i
$926$	23.8641	+	13.7780i	0.784224	+	0.452772i
$927$	6.38973	+	3.40214i	0.209866	+	0.111741i
$928$	4.33346	+	4.33346i	0.142253	+	0.142253i
$929$	5.88700	−	5.88700i	0.193146	−	0.193146i	−0.603908	−	0.797054i	$-0.706391\pi$
$929$	5.88700	−	5.88700i	0.193146	−	0.193146i	0.797054	+	0.603908i	$0.206391\pi$
$930$	2.31008	+	8.06486i	0.0757506	+	0.264457i
$931$	11.7972	+	3.16105i	0.386637	+	0.103599i
$932$	−3.46763	−	2.00204i	−0.113586	−	0.0655789i
$933$	26.1344	−	0.448751i	0.855601	−	0.0146914i
$934$	16.2882	+	4.36440i	0.532965	+	0.142808i
$935$	24.3643			0.796799
$936$	−4.58281	−	9.79785i	−0.149794	−	0.320253i
$937$	37.9409			1.23948			0.619738	−	0.784809i	$-0.287239\pi$
$937$	37.9409			1.23948			0.619738	+	0.784809i	$0.287239\pi$
$938$	−27.4484	−	7.35478i	−0.896222	−	0.240142i
$939$	−23.5656	−	39.2450i	−0.769034	−	1.28071i
$940$	−9.30219	−	5.37062i	−0.303404	−	0.175170i
$941$	−1.05869	−	0.283676i	−0.0345124	−	0.00924757i	0.241522	−	0.970395i	$-0.422354\pi$
$941$	−1.05869	−	0.283676i	−0.0345124	−	0.00924757i	−0.276034	+	0.961148i	$0.589020\pi$
$942$	−17.2172	−	4.29792i	−0.560966	−	0.140034i
$943$	46.9990	−	46.9990i	1.53050	−	1.53050i
$944$	4.65773	+	4.65773i	0.151596	+	0.151596i
$945$	16.9614	−	10.9943i	0.551754	−	0.357645i
$946$	−29.6230	−	17.1029i	−0.963128	−	0.556062i
$947$	5.94762	−	22.1968i	0.193272	−	0.721299i	−0.799436	−	0.600751i	$-0.794868\pi$
$947$	5.94762	−	22.1968i	0.193272	−	0.721299i	0.992708	−	0.120548i	$-0.0384651\pi$
$948$	−0.312528	−	18.2011i	−0.0101504	−	0.591143i
$949$	−3.68991	+	30.4905i	−0.119779	+	0.989765i
$950$	5.29480	−	3.05695i	0.171786	−	0.0991806i
$951$	51.2999	+	12.8060i	1.66351	+	0.415263i
$952$	−2.28210	−	3.95272i	−0.0739634	−	0.128108i
$953$	−23.9953	−	41.5611i	−0.777285	−	1.34630i	−0.933501	−	0.358575i	$-0.883263\pi$
$953$	−23.9953	−	41.5611i	−0.777285	−	1.34630i	0.156216	−	0.987723i	$-0.450070\pi$
$954$	−7.84964	+	2.39500i	−0.254141	+	0.0775410i
$955$	0.275599	−	1.02855i	0.00891819	−	0.0332831i
$956$	6.48776	+	6.48776i	0.209829	+	0.209829i
$957$	−59.4042	−	14.8291i	−1.92027	−	0.479355i
$958$	19.0698	−	33.0298i	0.616116	−	1.06714i
$959$	−21.1828			−0.684028
$960$	2.36335	+	2.28355i	0.0762766	+	0.0737014i
$961$	21.2033	+	12.2417i	0.683978	+	0.394895i
$962$	−5.03345	−	6.41946i	−0.162285	−	0.206972i
$963$	1.42214	+	41.3992i	0.0458278	+	1.33407i
$964$	−18.7022	+	5.01123i	−0.602357	+	0.161401i
$965$	14.6599	−	8.46392i	0.471920	−	0.272463i
$966$	−0.361809	−	21.0711i	−0.0116410	−	0.677950i
$967$	−9.57153	+	35.7214i	−0.307800	+	1.14872i	0.622709	+	0.782454i	$0.286032\pi$
$967$	−9.57153	+	35.7214i	−0.307800	+	1.14872i	−0.930509	+	0.366270i	$0.880635\pi$
$968$	5.76419	+	21.5122i	0.185268	+	0.691429i
$969$	4.07842	−	16.3379i	0.131018	−	0.524848i
$970$	−3.07683	−	11.4829i	−0.0987911	−	0.368693i
$971$	17.1597	−	9.90717i	0.550682	−	0.317936i	−0.198715	−	0.980057i	$-0.563677\pi$
$971$	17.1597	−	9.90717i	0.550682	−	0.317936i	0.749397	+	0.662121i	$0.230344\pi$
$972$	−1.33656	−	15.5311i	−0.0428703	−	0.498159i
$973$	9.91920	+	37.0189i	0.317995	+	1.18677i
$974$	6.75661	−	11.7028i	0.216496	−	0.374982i
$975$	−3.12130	+	8.16681i	−0.0999617	+	0.261547i
$976$	4.43478	+	7.68127i	0.141954	+	0.245871i
$977$	22.9537	−	22.9537i	0.734354	−	0.734354i	−0.237125	−	0.971479i	$-0.576205\pi$
$977$	22.9537	−	22.9537i	0.734354	−	0.734354i	0.971479	+	0.237125i	$0.0762050\pi$
$978$	23.8826	−	14.3409i	0.763681	−	0.458570i
$979$			76.3330i			2.43961i
$980$	3.75214	−	3.75214i	0.119858	−	0.119858i
$981$	−8.16613	+	35.2799i	−0.260724	+	1.12640i
$982$	29.4578	+	7.89320i	0.940037	+	0.251882i
$983$	20.8049	−	5.57467i	0.663575	−	0.177804i	0.0887159	−	0.996057i	$-0.471724\pi$
$983$	20.8049	−	5.57467i	0.663575	−	0.177804i	0.574859	+	0.818253i	$0.305057\pi$
$984$	−9.40945	+	16.9637i	−0.299962	+	0.540784i
$985$			18.4783i			0.588768i
$986$	−9.64726	−	9.64726i	−0.307231	−	0.307231i
$987$	−10.3489	−	17.2345i	−0.329409	−	0.548582i
$988$	−1.89172	+	15.6317i	−0.0601837	+	0.497312i
$989$		−	35.1932i		−	1.11908i
$990$	−31.9870	−	7.40392i	−1.01661	−	0.235312i
$991$	5.50674	−	9.53796i	0.174927	−	0.302983i	−0.765209	−	0.643782i	$-0.777364\pi$
$991$	5.50674	−	9.53796i	0.174927	−	0.302983i	0.940136	+	0.340799i	$0.110698\pi$
$992$	−2.55275			−0.0810498
$993$	17.5203	−	5.01848i	0.555990	−	0.159257i
$994$	−13.1916	+	3.53469i	−0.418413	+	0.112114i
$995$	15.7025	−	4.20747i	0.497803	−	0.133386i
$996$	−3.48309	−	3.36550i	−0.110366	−	0.106640i
$997$	−42.3228			−1.34038			−0.670188	−	0.742191i	$-0.733787\pi$
$997$	−42.3228			−1.34038			−0.670188	+	0.742191i	$0.733787\pi$
$998$	0.415405	−	0.719503i	0.0131494	−	0.0227755i
$999$	−3.62335	−	11.1839i	−0.114638	−	0.353844i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.z.a.137.3	yes	56
3.2	odd	2		702.2.bc.a.683.12		56
9.4	even	3		702.2.bb.a.449.12		56
9.5	odd	6		234.2.y.a.59.2	✓	56
13.2	odd	12		234.2.y.a.119.2	yes	56
39.2	even	12		702.2.bb.a.197.12		56
117.41	even	12	inner	234.2.z.a.41.3	yes	56
117.67	odd	12		702.2.bc.a.665.12		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.2	✓	56	9.5	odd	6
234.2.y.a.119.2	yes	56	13.2	odd	12
234.2.z.a.41.3	yes	56	117.41	even	12	inner
234.2.z.a.137.3	yes	56	1.1	even	1	trivial
702.2.bb.a.197.12		56	39.2	even	12
702.2.bb.a.449.12		56	9.4	even	3
702.2.bc.a.665.12		56	117.67	odd	12
702.2.bc.a.683.12		56	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.840145 + 1.51465i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.83272 - 0.491075i) q^{5} +(1.20354 - 1.24559i) q^{6} +(-1.44971 + 1.44971i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.58831 - 2.54505i) q^{9} +(1.64317 + 0.948684i) q^{10} +(1.49290 - 5.57157i) q^{11} +(-1.48491 + 0.891650i) q^{12} +(-2.83735 + 2.22474i) q^{13} +(1.77553 - 1.02510i) q^{14} +(2.28355 - 2.36335i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.11311 - 1.92797i) q^{17} +(0.875485 + 2.86941i) q^{18} +(1.13029 - 4.21829i) q^{19} +(-1.34164 - 1.34164i) q^{20} +(-0.977833 - 3.41377i) q^{21} +(-2.88406 + 4.99533i) q^{22} -5.93463 q^{23} +(1.66509 - 0.476945i) q^{24} +(-1.21243 - 0.699997i) q^{25} +(3.31647 - 1.41458i) q^{26} +(5.18926 - 0.267523i) q^{27} +(-1.98034 + 0.530631i) q^{28} +(-5.30738 + 3.06422i) q^{29} +(-2.81742 + 1.69179i) q^{30} +(0.660699 - 2.46576i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(7.18471 + 6.94214i) q^{33} +(0.576189 + 2.15037i) q^{34} +(3.36883 - 1.94499i) q^{35} +(-0.102995 - 2.99823i) q^{36} +(-0.585575 - 2.18540i) q^{37} +(-2.18355 + 3.78201i) q^{38} +(-0.985916 - 6.16668i) q^{39} +(0.948684 + 1.64317i) q^{40} +(-7.91945 + 7.91945i) q^{41} +(0.0609657 + 3.55053i) q^{42} +5.93015i q^{43} +(4.07867 - 4.07867i) q^{44} +(1.66112 + 5.44433i) q^{45} +(5.73241 + 1.53599i) q^{46} +(5.46823 - 1.46521i) q^{47} +(-1.73180 + 0.0297365i) q^{48} +2.79668i q^{49} +(0.989945 + 0.989945i) q^{50} +(3.85537 - 0.0662001i) q^{51} +(-3.56958 + 0.508010i) q^{52} +2.73563i q^{53} +(-5.08168 - 1.08467i) q^{54} +(-5.47212 + 9.47798i) q^{55} +2.05020 q^{56} +(5.43961 + 5.25596i) q^{57} +(5.91962 - 1.58616i) q^{58} +(6.36257 - 1.70485i) q^{59} +(3.15929 - 0.904940i) q^{60} +8.86956 q^{61} +(-1.27637 + 2.21074i) q^{62} +(5.99218 + 1.38699i) q^{63} +1.00000i q^{64} +(6.29257 - 2.68397i) q^{65} +(-5.14314 - 8.56513i) q^{66} +(-9.80081 - 9.80081i) q^{67} -2.22623i q^{68} +(4.98595 - 8.98886i) q^{69} +(-3.75744 + 1.00680i) q^{70} +(-6.43432 - 1.72407i) q^{71} +(-0.676514 + 2.92273i) q^{72} +(6.02332 - 6.02332i) q^{73} +2.26249i q^{74} +(2.07887 - 1.24830i) q^{75} +(3.08800 - 3.08800i) q^{76} +(5.91289 + 10.2414i) q^{77} +(-0.643733 + 6.21173i) q^{78} +(-5.25497 + 9.10187i) q^{79} +(-0.491075 - 1.83272i) q^{80} +(-3.95453 + 8.08466i) q^{81} +(9.69930 - 5.59989i) q^{82} +(0.723746 + 2.70106i) q^{83} +(0.860056 - 3.44533i) q^{84} +(1.09324 + 4.08004i) q^{85} +(1.53483 - 5.72808i) q^{86} +(-0.182238 - 10.6132i) q^{87} +(-4.99533 + 2.88406i) q^{88} +(-12.7827 + 3.42511i) q^{89} +(-0.195419 - 5.68875i) q^{90} +(0.888099 - 7.33856i) q^{91} +(-5.13954 - 2.96731i) q^{92} +(3.17968 + 3.07233i) q^{93} -5.66113 q^{94} +(-4.14299 + 7.17587i) q^{95} +(1.68048 + 0.419498i) q^{96} +(-4.43038 - 4.43038i) q^{97} +(0.723833 - 2.70138i) q^{98} +(-16.5511 + 5.04989i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

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