LMFDB - Embedded newform 61.2.g.a.27.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,2,Mod(3,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("61.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	61.g (of order $10$, 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:	$0.487087452330$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
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} + 17x^{14} + 111x^{12} + 361x^{10} + 624x^{8} + 558x^{6} + 229x^{4} + 34x^{2} + 1 $ x^16 + 17x^14 + 111x^12 + 361x^10 + 624x^8 + 558x^6 + 229x^4 + 34*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			27.2
Root			$1.25523i$ of defining polynomial
Character	$\chi$	$=$	61.27
Dual form			61.2.g.a.52.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.737805 - 1.01550i) q^{2} +(-0.446713 + 0.324556i) q^{3} +(0.131147 - 0.403630i) q^{4} +(0.620635 - 1.91012i) q^{5} +(0.659173 + 0.214178i) q^{6} +(1.40505 - 1.93389i) q^{7} +(-2.89423 + 0.940394i) q^{8} +(-0.832835 + 2.56320i) q^{9} +O(q^{10})$	\(q+(-0.737805 - 1.01550i) q^{2} +(-0.446713 + 0.324556i) q^{3} +(0.131147 - 0.403630i) q^{4} +(0.620635 - 1.91012i) q^{5} +(0.659173 + 0.214178i) q^{6} +(1.40505 - 1.93389i) q^{7} +(-2.89423 + 0.940394i) q^{8} +(-0.832835 + 2.56320i) q^{9} +(-2.39763 + 0.779038i) q^{10} +3.52926i q^{11} +(0.0724152 + 0.222871i) q^{12} +4.88471 q^{13} -3.00052 q^{14} +(0.342694 + 1.05470i) q^{15} +(2.40365 + 1.74636i) q^{16} +(-0.242658 - 0.0788443i) q^{17} +(3.21741 - 1.04540i) q^{18} +(-4.30389 + 3.12696i) q^{19} +(-0.689585 - 0.501013i) q^{20} +1.31991i q^{21} +(3.58396 - 2.60390i) q^{22} +(-1.09816 - 0.356815i) q^{23} +(0.987681 - 1.35943i) q^{24} +(0.781726 + 0.567958i) q^{25} +(-3.60396 - 4.96043i) q^{26} +(-0.971751 - 2.99074i) q^{27} +(-0.596306 - 0.820745i) q^{28} -6.09997i q^{29} +(0.818211 - 1.12617i) q^{30} +(-2.59754 + 3.57520i) q^{31} +2.35697i q^{32} +(-1.14544 - 1.57656i) q^{33} +(0.0989676 + 0.304591i) q^{34} +(-2.82193 - 3.88405i) q^{35} +(0.925361 + 0.672314i) q^{36} +(5.80482 - 7.98965i) q^{37} +(6.35086 + 2.06352i) q^{38} +(-2.18206 + 1.58536i) q^{39} +6.11197i q^{40} +(0.148301 + 0.107747i) q^{41} +(1.34037 - 0.973836i) q^{42} +(-5.29667 + 1.72099i) q^{43} +(1.42451 + 0.462852i) q^{44} +(4.37913 + 3.18163i) q^{45} +(0.447884 + 1.37845i) q^{46} +3.83056 q^{47} -1.64053 q^{48} +(0.397366 + 1.22297i) q^{49} -1.21289i q^{50} +(0.133988 - 0.0435352i) q^{51} +(0.640616 - 1.97161i) q^{52} +(-13.6262 + 4.42743i) q^{53} +(-2.32014 + 3.19340i) q^{54} +(6.74129 + 2.19038i) q^{55} +(-2.24793 + 6.91843i) q^{56} +(0.907729 - 2.79370i) q^{57} +(-6.19452 + 4.50059i) q^{58} +(3.02806 + 4.16777i) q^{59} +0.470653 q^{60} +(-7.52310 - 2.09834i) q^{61} +5.54710 q^{62} +(3.78677 + 5.21204i) q^{63} +(7.20082 - 5.23170i) q^{64} +(3.03162 - 9.33036i) q^{65} +(-0.755890 + 2.32639i) q^{66} +(-11.9252 - 3.87475i) q^{67} +(-0.0636478 + 0.0876037i) q^{68} +(0.606369 - 0.197021i) q^{69} +(-1.86223 + 5.73134i) q^{70} +(1.81332 - 0.589183i) q^{71} -8.20170i q^{72} +(-0.832448 - 2.56201i) q^{73} -12.3963 q^{74} -0.533541 q^{75} +(0.697690 + 2.14727i) q^{76} +(6.82519 + 4.95879i) q^{77} +(3.21987 + 1.04620i) q^{78} +(-7.35678 + 2.39036i) q^{79} +(4.82754 - 3.50741i) q^{80} +(-5.13642 - 3.73183i) q^{81} -0.230096i q^{82} +(12.5362 - 9.10809i) q^{83} +(0.532755 + 0.173103i) q^{84} +(-0.301204 + 0.414571i) q^{85} +(5.65558 + 4.10902i) q^{86} +(1.97978 + 2.72493i) q^{87} +(-3.31889 - 10.2145i) q^{88} +(9.09752 + 12.5217i) q^{89} -6.79443i q^{90} +(6.86327 - 9.44648i) q^{91} +(-0.288042 + 0.396456i) q^{92} -2.44013i q^{93} +(-2.82621 - 3.88994i) q^{94} +(3.30171 + 10.1616i) q^{95} +(-0.764968 - 1.05289i) q^{96} +(3.36013 + 2.44127i) q^{97} +(0.948746 - 1.30584i) q^{98} +(-9.04620 - 2.93929i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9}+O(q^{10}) $ 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9	$ 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9} - 5 q^{10} - 12 q^{13} - 18 q^{14} - 13 q^{15} + 19 q^{16} - 10 q^{18} + 3 q^{19} - 13 q^{20} + 19 q^{22} - 15 q^{23} + 10 q^{24} - 2 q^{25} + 10 q^{26} - 4 q^{27} + 35 q^{28} + 45 q^{30} - 15 q^{31} + 25 q^{33} - 14 q^{34} + 10 q^{35} + 37 q^{36} - 5 q^{37} - 15 q^{38} - 3 q^{39} + 12 q^{41} - 15 q^{42} - 25 q^{43} - 50 q^{44} + 36 q^{45} + 27 q^{46} + 6 q^{47} - 20 q^{48} - 30 q^{49} + 50 q^{51} - 46 q^{52} - 20 q^{53} - 20 q^{54} + 20 q^{55} - 28 q^{56} - 11 q^{57} - 41 q^{58} + 5 q^{59} + 14 q^{60} - 53 q^{61} + 16 q^{62} - 5 q^{63} + 17 q^{64} + 20 q^{65} + 13 q^{66} - 55 q^{67} + 80 q^{68} - 15 q^{69} - 17 q^{70} - 50 q^{71} - 11 q^{73} + 24 q^{74} - 88 q^{75} - 19 q^{76} + 63 q^{77} + 50 q^{78} + 40 q^{79} - 49 q^{80} - 19 q^{81} + 31 q^{83} - 25 q^{84} + 55 q^{85} + 35 q^{86} + 25 q^{87} + 27 q^{88} + 60 q^{89} - 15 q^{91} - 5 q^{92} + 65 q^{94} + 48 q^{95} - 25 q^{96} + 45 q^{97} + 10 q^{98} - 5 q^{99}+O(q^{100}) $ 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9 - 5 * q^10 - 12 * q^13 - 18 * q^14 - 13 * q^15 + 19 * q^16 - 10 * q^18 + 3 * q^19 - 13 * q^20 + 19 * q^22 - 15 * q^23 + 10 * q^24 - 2 * q^25 + 10 * q^26 - 4 * q^27 + 35 * q^28 + 45 * q^30 - 15 * q^31 + 25 * q^33 - 14 * q^34 + 10 * q^35 + 37 * q^36 - 5 * q^37 - 15 * q^38 - 3 * q^39 + 12 * q^41 - 15 * q^42 - 25 * q^43 - 50 * q^44 + 36 * q^45 + 27 * q^46 + 6 * q^47 - 20 * q^48 - 30 * q^49 + 50 * q^51 - 46 * q^52 - 20 * q^53 - 20 * q^54 + 20 * q^55 - 28 * q^56 - 11 * q^57 - 41 * q^58 + 5 * q^59 + 14 * q^60 - 53 * q^61 + 16 * q^62 - 5 * q^63 + 17 * q^64 + 20 * q^65 + 13 * q^66 - 55 * q^67 + 80 * q^68 - 15 * q^69 - 17 * q^70 - 50 * q^71 - 11 * q^73 + 24 * q^74 - 88 * q^75 - 19 * q^76 + 63 * q^77 + 50 * q^78 + 40 * q^79 - 49 * q^80 - 19 * q^81 + 31 * q^83 - 25 * q^84 + 55 * q^85 + 35 * q^86 + 25 * q^87 + 27 * q^88 + 60 * q^89 - 15 * q^91 - 5 * q^92 + 65 * q^94 + 48 * q^95 - 25 * q^96 + 45 * q^97 + 10 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.737805	−	1.01550i	−0.521707	−	0.718068i	0.464132	−	0.885766i	$-0.346366\pi$
$2$	−0.737805	−	1.01550i	−0.521707	−	0.718068i	−0.985838	+	0.167699i	$0.946366\pi$
$3$	−0.446713	+	0.324556i	−0.257910	+	0.187382i	−0.709225	−	0.704982i	$-0.750955\pi$
$3$	−0.446713	+	0.324556i	−0.257910	+	0.187382i	0.451315	+	0.892365i	$0.350955\pi$
$4$	0.131147	−	0.403630i	0.0655736	−	0.201815i
$5$	0.620635	−	1.91012i	0.277556	−	0.854230i	−0.710976	−	0.703217i	$-0.751746\pi$
$5$	0.620635	−	1.91012i	0.277556	−	0.854230i	0.988532	−	0.151013i	$-0.0482537\pi$
$6$	0.659173	+	0.214178i	0.269106	+	0.0874380i
$7$	1.40505	−	1.93389i	0.531060	−	0.730941i	−0.456232	−	0.889861i	$-0.650801\pi$
$7$	1.40505	−	1.93389i	0.531060	−	0.730941i	0.987291	+	0.158920i	$0.0508012\pi$
$8$	−2.89423	+	0.940394i	−1.02327	+	0.332479i
$9$	−0.832835	+	2.56320i	−0.277612	+	0.854401i
$10$	−2.39763	+	0.779038i	−0.758198	+	0.246353i
$11$			3.52926i			1.06411i	0.846710	+	0.532055i	$0.178580\pi$
$11$			3.52926i			1.06411i	−0.846710	+	0.532055i	$0.821420\pi$
$12$	0.0724152	+	0.222871i	0.0209045	+	0.0643373i
$13$	4.88471			1.35477			0.677387	−	0.735627i	$-0.263112\pi$
$13$	4.88471			1.35477			0.677387	+	0.735627i	$0.263112\pi$
$14$	−3.00052			−0.801923
$15$	0.342694	+	1.05470i	0.0884832	+	0.272323i
$16$	2.40365	+	1.74636i	0.600914	+	0.436589i
$17$	−0.242658	−	0.0788443i	−0.0588532	−	0.0191226i	0.279442	−	0.960162i	$-0.409850\pi$
$17$	−0.242658	−	0.0788443i	−0.0588532	−	0.0191226i	−0.338296	+	0.941040i	$0.609850\pi$
$18$	3.21741	−	1.04540i	0.758350	−	0.246403i
$19$	−4.30389	+	3.12696i	−0.987379	+	0.717373i	−0.959346	−	0.282234i	$-0.908925\pi$
$19$	−4.30389	+	3.12696i	−0.987379	+	0.717373i	−0.0280337	+	0.999607i	$0.508925\pi$
$20$	−0.689585	−	0.501013i	−0.154196	−	0.112030i
$21$			1.31991i			0.288028i
$22$	3.58396	−	2.60390i	0.764103	−	0.555154i
$23$	−1.09816	−	0.356815i	−0.228983	−	0.0744010i	0.192278	−	0.981340i	$-0.438412\pi$
$23$	−1.09816	−	0.356815i	−0.228983	−	0.0744010i	−0.421261	+	0.906939i	$0.638412\pi$
$24$	0.987681	−	1.35943i	0.201609	−	0.277492i
$25$	0.781726	+	0.567958i	0.156345	+	0.113592i
$26$	−3.60396	−	4.96043i	−0.706795	−	0.972820i
$27$	−0.971751	−	2.99074i	−0.187014	−	0.575569i
$28$	−0.596306	−	0.820745i	−0.112691	−	0.155106i
$29$		−	6.09997i		−	1.13274i	−0.824153	−	0.566368i	$-0.808348\pi$
$29$		−	6.09997i		−	1.13274i	0.824153	−	0.566368i	$-0.191652\pi$
$30$	0.818211	−	1.12617i	0.149384	−	0.205610i
$31$	−2.59754	+	3.57520i	−0.466531	+	0.642125i	−0.975847	−	0.218454i	$-0.929899\pi$
$31$	−2.59754	+	3.57520i	−0.466531	+	0.642125i	0.509316	+	0.860580i	$0.329899\pi$
$32$			2.35697i			0.416657i
$33$	−1.14544	−	1.57656i	−0.199395	−	0.274444i
$34$	0.0989676	+	0.304591i	0.0169728	+	0.0522369i
$35$	−2.82193	−	3.88405i	−0.476993	−	0.656525i
$36$	0.925361	+	0.672314i	0.154227	+	0.112052i
$37$	5.80482	−	7.98965i	0.954307	−	1.31349i	0.00471946	−	0.999989i	$-0.498498\pi$
$37$	5.80482	−	7.98965i	0.954307	−	1.31349i	0.949588	−	0.313502i	$-0.101502\pi$
$38$	6.35086	+	2.06352i	1.03024	+	0.334747i
$39$	−2.18206	+	1.58536i	−0.349409	+	0.253861i
$40$			6.11197i			0.966387i
$41$	0.148301	+	0.107747i	0.0231607	+	0.0168272i	0.599305	−	0.800520i	$-0.295444\pi$
$41$	0.148301	+	0.107747i	0.0231607	+	0.0168272i	−0.576145	+	0.817348i	$0.695444\pi$
$42$	1.34037	−	0.973836i	0.206824	−	0.150266i
$43$	−5.29667	+	1.72099i	−0.807735	+	0.262449i	−0.683638	−	0.729821i	$-0.739603\pi$
$43$	−5.29667	+	1.72099i	−0.807735	+	0.262449i	−0.124097	+	0.992270i	$0.539603\pi$
$44$	1.42451	+	0.462852i	0.214753	+	0.0697776i
$45$	4.37913	+	3.18163i	0.652802	+	0.474289i
$46$	0.447884	+	1.37845i	0.0660369	+	0.203241i
$47$	3.83056			0.558745			0.279372	−	0.960183i	$-0.409874\pi$
$47$	3.83056			0.558745			0.279372	+	0.960183i	$0.409874\pi$
$48$	−1.64053			−0.236791
$49$	0.397366	+	1.22297i	0.0567666	+	0.174710i
$50$		−	1.21289i		−	0.171528i
$51$	0.133988	−	0.0435352i	0.0187620	−	0.00609615i
$52$	0.640616	−	1.97161i	0.0888375	−	0.273414i
$53$	−13.6262	+	4.42743i	−1.87171	+	0.608155i	−0.880823	+	0.473446i	$0.843010\pi$
$53$	−13.6262	+	4.42743i	−1.87171	+	0.608155i	−0.990885	+	0.134709i	$0.956990\pi$
$54$	−2.32014	+	3.19340i	−0.315731	+	0.434567i
$55$	6.74129	+	2.19038i	0.908995	+	0.295350i
$56$	−2.24793	+	6.91843i	−0.300393	+	0.924514i
$57$	0.907729	−	2.79370i	0.120232	−	0.370035i
$58$	−6.19452	+	4.50059i	−0.813381	+	0.590956i
$59$	3.02806	+	4.16777i	0.394220	+	0.542597i	0.959282	−	0.282452i	$-0.0911477\pi$
$59$	3.02806	+	4.16777i	0.394220	+	0.542597i	−0.565062	+	0.825049i	$0.691148\pi$
$60$	0.470653			0.0607611
$61$	−7.52310	−	2.09834i	−0.963234	−	0.268665i
$61$	−7.52310	−	2.09834i	−0.963234	−	0.268665i
$62$	5.54710			0.704482
$63$	3.78677	+	5.21204i	0.477088	+	0.656656i
$64$	7.20082	−	5.23170i	0.900102	−	0.653962i
$65$	3.03162	−	9.33036i	0.376026	−	1.15729i
$66$	−0.755890	+	2.32639i	−0.0930437	+	0.286359i
$67$	−11.9252	−	3.87475i	−1.45690	−	0.473376i	−0.529779	−	0.848136i	$-0.677725\pi$
$67$	−11.9252	−	3.87475i	−1.45690	−	0.473376i	−0.927122	+	0.374760i	$0.877725\pi$
$68$	−0.0636478	+	0.0876037i	−0.00771843	+	0.0106235i
$69$	0.606369	−	0.197021i	0.0729983	−	0.0237186i
$70$	−1.86223	+	5.73134i	−0.222579	+	0.685027i
$71$	1.81332	−	0.589183i	0.215201	−	0.0699231i	−0.199432	−	0.979912i	$-0.563910\pi$
$71$	1.81332	−	0.589183i	0.215201	−	0.0699231i	0.414634	+	0.909988i	$0.363910\pi$
$72$		−	8.20170i		−	0.966580i
$73$	−0.832448	−	2.56201i	−0.0974307	−	0.299861i	0.890449	−	0.455083i	$-0.150391\pi$
$73$	−0.832448	−	2.56201i	−0.0974307	−	0.299861i	−0.987880	+	0.155223i	$0.950391\pi$
$74$	−12.3963			−1.44104
$75$	−0.533541			−0.0616080
$76$	0.697690	+	2.14727i	0.0800305	+	0.246309i
$77$	6.82519	+	4.95879i	0.777802	+	0.565106i
$78$	3.21987	+	1.04620i	0.364578	+	0.118459i
$79$	−7.35678	+	2.39036i	−0.827702	+	0.268937i	−0.692077	−	0.721823i	$-0.743304\pi$
$79$	−7.35678	+	2.39036i	−0.827702	+	0.268937i	−0.135625	+	0.990760i	$0.543304\pi$
$80$	4.82754	−	3.50741i	0.539735	−	0.392140i
$81$	−5.13642	−	3.73183i	−0.570713	−	0.414647i
$82$		−	0.230096i		−	0.0254098i
$83$	12.5362	−	9.10809i	1.37603	−	0.999743i	0.378789	−	0.925483i	$-0.376341\pi$
$83$	12.5362	−	9.10809i	1.37603	−	0.999743i	0.997239	−	0.0742597i	$-0.0236594\pi$
$84$	0.532755	+	0.173103i	0.0581283	+	0.0188870i
$85$	−0.301204	+	0.414571i	−0.0326701	+	0.0449666i
$86$	5.65558	+	4.10902i	0.609857	+	0.443087i
$87$	1.97978	+	2.72493i	0.212255	+	0.292143i
$88$	−3.31889	−	10.2145i	−0.353795	−	1.08887i
$89$	9.09752	+	12.5217i	0.964335	+	1.32729i	0.944857	+	0.327483i	$0.106200\pi$
$89$	9.09752	+	12.5217i	0.964335	+	1.32729i	0.0194775	+	0.999810i	$0.493800\pi$
$90$		−	6.79443i		−	0.716196i
$91$	6.86327	−	9.44648i	0.719466	−	0.990260i
$92$	−0.288042	+	0.396456i	−0.0300305	+	0.0413334i
$93$		−	2.44013i		−	0.253030i
$94$	−2.82621	−	3.88994i	−0.291501	−	0.401217i
$95$	3.30171	+	10.1616i	0.338748	+	1.04256i
$96$	−0.764968	−	1.05289i	−0.0780742	−	0.107460i
$97$	3.36013	+	2.44127i	0.341169	+	0.247874i	0.745155	−	0.666891i	$-0.232376\pi$
$97$	3.36013	+	2.44127i	0.341169	+	0.247874i	−0.403986	+	0.914765i	$0.632376\pi$
$98$	0.948746	−	1.30584i	0.0958379	−	0.131910i
$99$	−9.04620	−	2.93929i	−0.909177	−	0.295410i
$100$	0.331766	−	0.241042i	0.0331766	−	0.0241042i
$101$		−	9.26984i		−	0.922383i	−0.887301	−	0.461192i	$-0.847422\pi$
$101$		−	9.26984i		−	0.922383i	0.887301	−	0.461192i	$-0.152578\pi$
$102$	−0.143067	−	0.103944i	−0.0141657	−	0.0102920i
$103$	−11.6371	+	8.45482i	−1.14663	+	0.833078i	−0.988030	−	0.154264i	$-0.950699\pi$
$103$	−11.6371	+	8.45482i	−1.14663	+	0.833078i	−0.158604	+	0.987342i	$0.550699\pi$
$104$	−14.1375	+	4.59355i	−1.38629	+	0.450434i
$105$	2.52118	+	0.819182i	0.246042	+	0.0799439i
$106$	14.5496	+	10.5709i	1.41318	+	1.02673i
$107$	−4.82546	−	14.8513i	−0.466495	−	1.43572i	−0.857092	−	0.515163i	$-0.827731\pi$
$107$	−4.82546	−	14.8513i	−0.466495	−	1.43572i	0.390597	−	0.920562i	$-0.372269\pi$
$108$	−1.33460			−0.128421
$109$	1.76843			0.169385			0.0846924	−	0.996407i	$-0.473009\pi$
$109$	1.76843			0.169385			0.0846924	+	0.996407i	$0.473009\pi$
$110$	−2.74942	−	8.46186i	−0.262147	−	0.806807i
$111$			5.45307i			0.517582i
$112$	6.75452	−	2.19468i	0.638242	−	0.207377i
$113$	−0.0110103	+	0.0338863i	−0.00103576	+	0.00318776i	−0.951573	−	0.307423i	$-0.900533\pi$
$113$	−0.0110103	+	0.0338863i	−0.00103576	+	0.00318776i	0.950537	+	0.310610i	$0.100533\pi$
$114$	−3.50673	+	1.13941i	−0.328436	+	0.106715i
$115$	−1.36312	+	1.87617i	−0.127111	+	0.174954i
$116$	−2.46213	−	0.799994i	−0.228603	−	0.0742776i
$117$	−4.06816	+	12.5205i	−0.376101	+	1.15752i
$118$	1.99825	−	6.14999i	0.183954	−	0.566153i
$119$	−0.493423	+	0.358493i	−0.0452320	+	0.0328630i
$120$	−1.98367	−	2.73029i	−0.181084	−	0.249240i
$121$	−1.45564			−0.132331
$122$	3.41971	+	9.18788i	0.309606	+	0.831831i
$123$	−0.101218			−0.00912649
$124$	1.10240	+	1.51732i	0.0989983	+	0.136259i
$125$	9.69424	−	7.04328i	0.867079	−	0.629970i
$126$	2.49894	−	7.69094i	0.222623	−	0.685164i
$127$	2.01970	−	6.21599i	0.179219	−	0.551580i	−0.820582	−	0.571529i	$-0.806350\pi$
$127$	2.01970	−	6.21599i	0.179219	−	0.551580i	0.999801	+	0.0199492i	$0.00635045\pi$
$128$	−6.14237	−	1.99578i	−0.542914	−	0.176403i
$129$	1.80753	−	2.48785i	0.159144	−	0.219043i
$130$	−11.7117	+	3.80537i	−1.02719	+	0.333753i
$131$	−0.565003	+	1.73890i	−0.0493646	+	0.151928i	−0.972700	−	0.232065i	$-0.925452\pi$
$131$	−0.565003	+	1.73890i	−0.0493646	+	0.151928i	0.923336	+	0.383994i	$0.125452\pi$
$132$	−0.786569	+	0.255572i	−0.0684620	+	0.0222447i
$133$			12.7168i			1.10268i
$134$	4.86369	+	14.9689i	0.420159	+	1.29312i
$135$	−6.31577			−0.543575
$136$	0.776453			0.0665803
$137$	4.03793	+	12.4275i	0.344984	+	1.06175i	0.961592	+	0.274482i	$0.0885062\pi$
$137$	4.03793	+	12.4275i	0.344984	+	1.06175i	−0.616608	+	0.787270i	$0.711494\pi$
$138$	−0.647458	−	0.470405i	−0.0551152	−	0.0400436i
$139$	11.0028	+	3.57502i	0.933243	+	0.303229i	0.735888	−	0.677103i	$-0.236765\pi$
$139$	11.0028	+	3.57502i	0.933243	+	0.303229i	0.197355	+	0.980332i	$0.436765\pi$
$140$	−1.93781	+	0.629632i	−0.163775	+	0.0532136i
$141$	−1.71116	+	1.24323i	−0.144106	+	0.104699i
$142$	−1.93619	−	1.40672i	−0.162481	−	0.118050i
$143$			17.2394i			1.44163i
$144$	−6.47812	+	4.70663i	−0.539843	+	0.392219i
$145$	−11.6516	−	3.78585i	−0.967617	−	0.314398i
$146$	−1.98754	+	2.73562i	−0.164490	+	0.226401i
$147$	−0.574430	−	0.417348i	−0.0473782	−	0.0344222i
$148$	−2.46358	−	3.39082i	−0.202505	−	0.278724i
$149$	1.54164	+	4.74467i	0.126296	+	0.388698i	0.994135	−	0.108147i	$-0.0344917\pi$
$149$	1.54164	+	4.74467i	0.126296	+	0.388698i	−0.867839	+	0.496845i	$0.834492\pi$
$150$	0.393649	+	0.541811i	0.0321413	+	0.0442387i
$151$		−	19.5832i		−	1.59366i	−0.604203	−	0.796830i	$-0.706508\pi$
$151$		−	19.5832i		−	1.59366i	0.604203	−	0.796830i	$-0.293492\pi$
$152$	9.51589	−	13.0975i	0.771840	−	1.06235i
$153$	0.404188	−	0.556317i	0.0326767	−	0.0449756i
$154$		−	10.5896i		−	0.853334i
$155$	5.21693	+	7.18049i	0.419034	+	0.576751i
$156$	0.353727	+	1.08866i	0.0283208	+	0.0871626i
$157$	1.42877	+	1.96654i	0.114028	+	0.156947i	0.862216	−	0.506540i	$-0.169076\pi$
$157$	1.42877	+	1.96654i	0.114028	+	0.156947i	−0.748188	+	0.663487i	$0.769076\pi$
$158$	7.85528	+	5.70720i	0.624933	+	0.454040i
$159$	4.65006	−	6.40026i	0.368774	−	0.507574i
$160$	4.50209	+	1.46282i	0.355921	+	0.115646i
$161$	−2.23302	+	1.62238i	−0.175986	+	0.127862i
$162$			7.96940i			0.626135i
$163$	11.6916	+	8.49445i	0.915757	+	0.665337i	0.942464	−	0.334307i	$-0.108502\pi$
$163$	11.6916	+	8.49445i	0.915757	+	0.665337i	−0.0267070	+	0.999643i	$0.508502\pi$
$164$	0.0629391	−	0.0457279i	0.00491471	−	0.00357075i
$165$	−3.72232	+	1.20945i	−0.289782	+	0.0941559i
$166$	−18.4986	−	6.01054i	−1.43577	−	0.466509i
$167$	7.43108	+	5.39900i	0.575035	+	0.417787i	0.836931	−	0.547309i	$-0.184348\pi$
$167$	7.43108	+	5.39900i	0.575035	+	0.417787i	−0.261896	+	0.965096i	$0.584348\pi$
$168$	−1.24123	−	3.82013i	−0.0957633	−	0.294729i
$169$	10.8604			0.835413
$170$	0.643227			0.0493333
$171$	−4.43060	−	13.6360i	−0.338816	−	1.04277i
$172$			2.36360i			0.180223i
$173$	−3.83370	+	1.24565i	−0.291471	+	0.0947047i	−0.451103	−	0.892472i	$-0.648969\pi$
$173$	−3.83370	+	1.24565i	−0.291471	+	0.0947047i	0.159632	+	0.987177i	$0.448969\pi$
$174$	1.30648	−	4.02094i	0.0990441	−	0.304826i
$175$	2.19673	−	0.713762i	0.166057	−	0.0539553i
$176$	−6.16334	+	8.48311i	−0.464579	+	0.639439i
$177$	−2.70534	−	0.879019i	−0.203346	−	0.0660711i
$178$	6.00357	−	18.4771i	0.449986	−	1.38492i
$179$	7.04388	−	21.6788i	0.526484	−	1.62035i	−0.234879	−	0.972025i	$-0.575469\pi$
$179$	7.04388	−	21.6788i	0.526484	−	1.62035i	0.761363	−	0.648326i	$-0.224531\pi$
$180$	1.85851	−	1.35029i	0.138525	−	0.100644i
$181$	−6.96035	−	9.58010i	−0.517359	−	0.712084i	0.467780	−	0.883845i	$-0.345054\pi$
$181$	−6.96035	−	9.58010i	−0.517359	−	0.712084i	−0.985139	+	0.171762i	$0.945054\pi$
$182$	−14.6567			−1.08642
$183$	4.04169	−	1.50431i	0.298770	−	0.111202i
$184$	3.51389			0.259047
$185$	−11.6585	−	16.0465i	−0.857150	−	1.17977i
$186$	−2.47796	+	1.80034i	−0.181693	+	0.132007i
$187$	0.278262	−	0.856402i	0.0203485	−	0.0626263i
$188$	0.502368	−	1.54613i	0.0366389	−	0.112763i
$189$	−7.14912	−	2.32289i	−0.520022	−	0.168965i
$190$	7.88312	−	10.8502i	0.571902	−	0.787155i
$191$	9.15352	−	2.97416i	0.662326	−	0.215203i	0.0414847	−	0.999139i	$-0.486791\pi$
$191$	9.15352	−	2.97416i	0.662326	−	0.215203i	0.620841	+	0.783936i	$0.286791\pi$
$192$	−1.51872	+	4.67413i	−0.109604	+	0.337326i
$193$	−11.5824	+	3.76334i	−0.833717	+	0.270891i	−0.694610	−	0.719386i	$-0.744423\pi$
$193$	−11.5824	+	3.76334i	−0.833717	+	0.270891i	−0.139107	+	0.990277i	$0.544423\pi$
$194$		−	5.21340i		−	0.374300i
$195$	1.67396	+	5.15192i	0.119875	+	0.368937i
$196$	0.545740			0.0389814
$197$	−8.80635			−0.627427			−0.313713	−	0.949518i	$-0.601573\pi$
$197$	−8.80635			−0.627427			−0.313713	+	0.949518i	$0.601573\pi$
$198$	3.68948	+	11.3550i	0.262200	+	0.806968i
$199$	19.9215	+	14.4738i	1.41220	+	1.02602i	0.992999	+	0.118126i	$0.0376885\pi$
$199$	19.9215	+	14.4738i	1.41220	+	1.02602i	0.419198	+	0.907895i	$0.362311\pi$
$200$	−2.79660	−	0.908671i	−0.197750	−	0.0642528i
$201$	6.58473	−	2.13951i	0.464451	−	0.150909i
$202$	−9.41353	+	6.83933i	−0.662334	+	0.481214i
$203$	−11.7967	−	8.57077i	−0.827963	−	0.601550i
$204$		−	0.0597909i		−	0.00418620i
$205$	0.297850	−	0.216400i	0.0208027	−	0.0151141i
$206$	17.1718	+	5.57944i	1.19641	+	0.388738i
$207$	1.82918	−	2.51765i	0.127137	−	0.174989i
$208$	11.7412	+	8.53045i	0.814102	+	0.591480i
$209$	−11.0358	−	15.1895i	−0.763364	−	1.05068i
$210$	−1.02826	−	3.16466i	−0.0709567	−	0.218382i
$211$	−7.23167	−	9.95355i	−0.497849	−	0.685230i	0.483963	−	0.875089i	$-0.339197\pi$
$211$	−7.23167	−	9.95355i	−0.497849	−	0.685230i	−0.981811	+	0.189858i	$0.939197\pi$
$212$			6.08060i			0.417618i
$213$	−0.618809	+	0.851718i	−0.0424001	+	0.0583588i
$214$	−11.5212	+	15.8576i	−0.787574	+	1.08400i
$215$			11.1854i			0.762836i
$216$	5.62495	+	7.74208i	0.382729	+	0.526782i
$217$	3.26437	+	10.0467i	0.221600	+	0.682014i
$218$	−1.30476	−	1.79584i	−0.0883692	−	0.121630i
$219$	1.20338	+	0.874307i	0.0813169	+	0.0590802i
$220$	1.76820	−	2.43372i	0.119212	−	0.164082i
$221$	−1.18531	−	0.385131i	−0.0797328	−	0.0259067i
$222$	5.53760	−	4.02330i	0.371659	−	0.270026i
$223$			2.62388i			0.175708i	0.996133	+	0.0878541i	$0.0280009\pi$
$223$			2.62388i			0.175708i	−0.996133	+	0.0878541i	$0.971999\pi$
$224$	4.55812	+	3.31167i	0.304552	+	0.221270i
$225$	−2.10684	+	1.53071i	−0.140456	+	0.102047i
$226$	0.0425351	−	0.0138205i	0.00282939	−	0.000919325i
$227$	−10.4947	−	3.40994i	−0.696559	−	0.226326i	−0.0607285	−	0.998154i	$-0.519342\pi$
$227$	−10.4947	−	3.40994i	−0.696559	−	0.226326i	−0.635831	+	0.771828i	$0.719342\pi$
$228$	−1.00858	−	0.732773i	−0.0667945	−	0.0485291i
$229$	8.75958	+	26.9592i	0.578849	+	1.78152i	0.622680	+	0.782477i	$0.286044\pi$
$229$	8.75958	+	26.9592i	0.578849	+	1.78152i	−0.0438306	+	0.999039i	$0.513956\pi$
$230$	2.91096			0.191943
$231$	−4.65830			−0.306494
$232$	5.73637	+	17.6547i	0.376611	+	1.15909i
$233$		−	4.83039i		−	0.316449i	−0.987403	−	0.158225i	$-0.949423\pi$
$233$		−	4.83039i		−	0.316449i	0.987403	−	0.158225i	$-0.0505770\pi$
$234$	15.7161	−	5.10647i	1.02739	−	0.333820i
$235$	2.37738	−	7.31682i	0.155083	−	0.477297i
$236$	2.07936	−	0.675624i	0.135355	−	0.0439794i
$237$	2.51056	−	3.45549i	0.163078	−	0.224458i
$238$	0.728100	+	0.236574i	0.0471957	+	0.0153348i
$239$	0.405160	−	1.24695i	0.0262076	−	0.0806588i	−0.937097	−	0.349068i	$-0.886498\pi$
$239$	0.405160	−	1.24695i	0.0262076	−	0.0806588i	0.963305	+	0.268410i	$0.0864981\pi$
$240$	−1.01817	+	3.13361i	−0.0657227	+	0.202274i
$241$	−18.5731	+	13.4942i	−1.19640	+	0.869236i	−0.993926	−	0.110052i	$-0.964898\pi$
$241$	−18.5731	+	13.4942i	−1.19640	+	0.869236i	−0.202474	+	0.979288i	$0.564898\pi$
$242$	1.07398	+	1.47821i	0.0690381	+	0.0950228i
$243$	12.9396			0.830079
$244$	−1.83359	+	2.76135i	−0.117383	+	0.176778i
$245$	2.58263			0.164998
$246$	0.0746789	+	0.102787i	0.00476135	+	0.00655344i
$247$	−21.0232	+	15.2743i	−1.33768	+	0.971879i
$248$	4.15578	−	12.7902i	0.263892	−	0.812177i
$249$	−2.64400	+	8.13740i	−0.167557	+	0.515687i
$250$	−14.3049	−	4.64795i	−0.904722	−	0.293962i
$251$	−9.34235	+	12.8586i	−0.589684	+	0.811630i	−0.994715	−	0.102673i	$-0.967261\pi$
$251$	−9.34235	+	12.8586i	−0.589684	+	0.811630i	0.405031	+	0.914303i	$0.367261\pi$
$252$	2.60036	−	0.844909i	0.163807	−	0.0532242i
$253$	1.25929	−	3.87570i	0.0791709	−	0.243663i
$254$	−7.80249	+	2.53518i	−0.489572	+	0.159071i
$255$		−	0.282952i		−	0.0177191i
$256$	−2.99578	−	9.22006i	−0.187236	−	0.576254i
$257$	2.44266			0.152369			0.0761843	−	0.997094i	$-0.475726\pi$
$257$	2.44266			0.152369			0.0761843	+	0.997094i	$0.475726\pi$
$258$	−3.86002			−0.240315
$259$	−7.29502	−	22.4518i	−0.453290	−	1.39508i
$260$	−3.36842	−	2.44730i	−0.208901	−	0.151775i
$261$	15.6355	+	5.08027i	0.967811	+	0.314461i
$262$	2.18272	−	0.709208i	0.134849	−	0.0438150i
$263$	5.65529	−	4.10881i	0.348720	−	0.253360i	−0.399612	−	0.916684i	$-0.630855\pi$
$263$	5.65529	−	4.10881i	0.348720	−	0.253360i	0.748332	+	0.663324i	$0.230855\pi$
$264$	4.79776	+	3.48578i	0.295282	+	0.214535i
$265$			28.7755i			1.76767i
$266$	12.9139	−	9.38250i	0.791802	−	0.575278i
$267$	−8.12795	−	2.64093i	−0.497422	−	0.161622i
$268$	−3.12793	+	4.30522i	−0.191069	+	0.262983i
$269$	−13.9956	−	10.1684i	−0.853326	−	0.619978i	0.0727351	−	0.997351i	$-0.476827\pi$
$269$	−13.9956	−	10.1684i	−0.853326	−	0.619978i	−0.926061	+	0.377374i	$0.876827\pi$
$270$	4.65981	+	6.41367i	0.283587	+	0.390324i
$271$	−4.58539	−	14.1124i	−0.278543	−	0.857266i	−0.988260	−	0.152780i	$-0.951178\pi$
$271$	−4.58539	−	14.1124i	−0.278543	−	0.857266i	0.709718	−	0.704486i	$-0.248822\pi$
$272$	−0.445575	−	0.613282i	−0.0270170	−	0.0371857i
$273$			6.44737i			0.390213i
$274$	9.64092	−	13.2696i	0.582429	−	0.801645i
$275$	−2.00447	+	2.75891i	−0.120874	+	0.166369i
$276$		−	0.270588i		−	0.0162875i
$277$	−2.67671	−	3.68417i	−0.160828	−	0.221361i	0.720996	−	0.692939i	$-0.243684\pi$
$277$	−2.67671	−	3.68417i	−0.160828	−	0.221361i	−0.881824	+	0.471578i	$0.843684\pi$
$278$	−4.48747	−	13.8110i	−0.269140	−	0.828329i
$279$	−7.00065	−	9.63557i	−0.419118	−	0.576866i
$280$	11.8199	+	8.58763i	0.706372	+	0.513209i
$281$	9.25243	−	12.7349i	0.551954	−	0.759699i	−0.438322	−	0.898818i	$-0.644427\pi$
$281$	9.25243	−	12.7349i	0.551954	−	0.759699i	0.990276	+	0.139119i	$0.0444270\pi$
$282$	2.52500	+	0.820423i	0.150362	+	0.0488555i
$283$	11.7365	−	8.52706i	0.697662	−	0.506881i	−0.181508	−	0.983389i	$-0.558098\pi$
$283$	11.7365	−	8.52706i	0.697662	−	0.506881i	0.879170	+	0.476508i	$0.158098\pi$
$284$		−	0.809179i		−	0.0480159i
$285$	−4.77293	−	3.46774i	−0.282724	−	0.205411i
$286$	17.5066	−	12.7193i	1.03519	−	0.752108i
$287$	0.416741	−	0.135407i	0.0245994	−	0.00799283i
$288$	−6.04140	−	1.96297i	−0.355993	−	0.115669i
$289$	−13.7006	−	9.95408i	−0.805919	−	0.585534i
$290$	4.75211	+	14.6255i	0.279053	+	0.858838i
$291$	−2.29334			−0.134438
$292$	−1.14328			−0.0669053
$293$	−5.41202	−	16.6565i	−0.316173	−	0.973082i	−0.975269	−	0.221022i	$-0.929061\pi$
$293$	−5.41202	−	16.6565i	−0.316173	−	0.973082i	0.659095	−	0.752059i	$-0.270939\pi$
$294$			0.891255i			0.0519790i
$295$	9.84024	−	3.19729i	0.572921	−	0.186153i
$296$	−9.28710	+	28.5827i	−0.539802	+	1.66134i
$297$	10.5551	−	3.42956i	0.612469	−	0.199003i
$298$	3.68079	−	5.06617i	0.213222	−	0.293475i
$299$	−5.36420	−	1.74294i	−0.310220	−	0.100797i
$300$	−0.0699724	+	0.215353i	−0.00403986	+	0.0124334i
$301$	−4.11389	+	12.6613i	−0.237121	+	0.729783i
$302$	−19.8868	+	14.4486i	−1.14436	+	0.831423i
$303$	3.00858	+	4.14095i	0.172838	+	0.237892i
$304$	−15.8058			−0.906527
$305$	−8.67717	+	13.0677i	−0.496853	+	0.748254i
$306$	−0.863153			−0.0493431
$307$	−11.4833	−	15.8053i	−0.655384	−	0.902058i	0.343934	−	0.938994i	$-0.388240\pi$
$307$	−11.4833	−	15.8053i	−0.655384	−	0.902058i	−0.999318	+	0.0369354i	$0.988240\pi$
$308$	2.89662	−	2.10452i	0.165050	−	0.119916i
$309$	2.45436	−	7.55375i	0.139624	−	0.429718i
$310$	3.44272	−	10.5956i	0.195533	−	0.601790i
$311$	21.3585	+	6.93979i	1.21113	+	0.393519i	0.843843	−	0.536590i	$-0.180288\pi$
$311$	21.3585	+	6.93979i	1.21113	+	0.393519i	0.367284	+	0.930109i	$0.380288\pi$
$312$	4.82453	−	6.64040i	0.273135	−	0.375938i
$313$	12.2136	−	3.96845i	0.690355	−	0.224310i	0.0572318	−	0.998361i	$-0.481773\pi$
$313$	12.2136	−	3.96845i	0.690355	−	0.224310i	0.633123	+	0.774051i	$0.281773\pi$
$314$	0.942865	−	2.90184i	0.0532089	−	0.163760i
$315$	12.3058	−	3.99840i	0.693354	−	0.225284i
$316$			3.28290i			0.184678i
$317$	−0.930921	−	2.86508i	−0.0522857	−	0.160919i	0.921504	−	0.388369i	$-0.126961\pi$
$317$	−0.930921	−	2.86508i	−0.0522857	−	0.160919i	−0.973790	+	0.227450i	$0.926961\pi$
$318$	−9.93032			−0.556864
$319$	21.5283			1.20536
$320$	−5.52408	−	17.0014i	−0.308805	−	0.950406i
$321$	6.97565	+	5.06811i	0.389343	+	0.282874i
$322$	3.29506	+	1.07063i	0.183626	+	0.0596639i
$323$	1.29091	−	0.419444i	0.0718284	−	0.0233385i
$324$	−2.17990	+	1.58379i	−0.121106	+	0.0879885i
$325$	3.81851	+	2.77431i	0.211813	+	0.153891i
$326$		−	18.1401i		−	1.00469i
$327$	−0.789980	+	0.573954i	−0.0436860	+	0.0317397i
$328$	−0.530541	−	0.172383i	−0.0292943	−	0.00951828i
$329$	5.38214	−	7.40788i	0.296727	−	0.408409i
$330$	3.97455	+	2.88768i	0.218792	+	0.158961i
$331$	11.0764	+	15.2454i	0.608815	+	0.837962i	0.996479	−	0.0838389i	$-0.0267181\pi$
$331$	11.0764	+	15.2454i	0.608815	+	0.837962i	−0.387665	+	0.921801i	$0.626718\pi$
$332$	−2.03221	−	6.25449i	−0.111532	−	0.343260i
$333$	15.6446	+	21.5330i	0.857321	+	1.18000i
$334$		−	11.5297i		−	0.630876i
$335$	−14.8024	+	20.3738i	−0.808744	+	1.11314i
$336$	−2.30503	+	3.17261i	−0.125750	+	0.173080i
$337$			12.5489i			0.683580i	0.939776	+	0.341790i	$0.111033\pi$
$337$			12.5489i			0.683580i	−0.939776	+	0.341790i	$0.888967\pi$
$338$	−8.01284	−	11.0287i	−0.435841	−	0.599883i
$339$	−0.00607954	−	0.0187109i	−0.000330195	−	0.00101624i
$340$	0.127831	+	0.175945i	0.00693262	+	0.00954194i
$341$	−12.6178	−	9.16737i	−0.683292	−	0.496441i
$342$	−10.5784	+	14.5600i	−0.572016	+	0.787313i
$343$	18.8374	+	6.12063i	1.01712	+	0.330483i
$344$	13.7114	−	9.96191i	0.739269	−	0.537110i
$345$		−	1.28051i		−	0.0689406i
$346$	4.09348	+	2.97409i	0.220067	+	0.159888i
$347$	−11.5376	+	8.38259i	−0.619373	+	0.450001i	−0.852703	−	0.522397i	$-0.825038\pi$
$347$	−11.5376	+	8.38259i	−0.619373	+	0.450001i	0.233329	+	0.972398i	$0.425038\pi$
$348$	1.35951	−	0.441730i	0.0728772	−	0.0236792i
$349$	13.1239	+	4.26420i	0.702504	+	0.228257i	0.638421	−	0.769687i	$-0.279588\pi$
$349$	13.1239	+	4.26420i	0.702504	+	0.228257i	0.0640828	+	0.997945i	$0.479588\pi$
$350$	−2.34559	−	1.70417i	−0.125377	−	0.0910916i
$351$	−4.74672	−	14.6089i	−0.253361	−	0.779766i
$352$	−8.31835			−0.443370
$353$	−0.783067			−0.0416785			−0.0208392	−	0.999783i	$-0.506634\pi$
$353$	−0.783067			−0.0416785			−0.0208392	+	0.999783i	$0.506634\pi$
$354$	1.10337	+	3.39582i	0.0586435	+	0.180486i
$355$		−	3.82932i		−	0.203239i
$356$	6.24723	−	2.02985i	0.331102	−	0.107582i
$357$	0.104067	−	0.320286i	0.00550783	−	0.0169514i
$358$	−27.2119	+	8.84167i	−1.43819	+	0.467297i
$359$	−7.44237	+	10.2435i	−0.392793	+	0.540633i	−0.958917	−	0.283687i	$-0.908442\pi$
$359$	−7.44237	+	10.2435i	−0.392793	+	0.540633i	0.566124	+	0.824320i	$0.308442\pi$
$360$	−15.6662	−	5.09026i	−0.825682	−	0.268280i
$361$	2.87426	−	8.84606i	0.151277	−	0.465582i
$362$	−4.59323	+	14.1365i	−0.241415	+	0.742998i
$363$	0.650254	−	0.472437i	0.0341295	−	0.0247965i
$364$	−2.91278	−	4.00910i	−0.152671	−	0.210134i
$365$	−5.41039			−0.283193
$366$	−4.50960	−	2.99445i	−0.235721	−	0.156523i
$367$	−19.0239			−0.993040			−0.496520	−	0.868025i	$-0.665389\pi$
$367$	−19.0239			−0.993040			−0.496520	+	0.868025i	$0.665389\pi$
$368$	−2.01648	−	2.77544i	−0.105116	−	0.144680i
$369$	−0.399687	+	0.290390i	−0.0208069	+	0.0151171i
$370$	−7.69359	+	23.6784i	−0.399971	+	1.23098i
$371$	−10.5834	+	32.5724i	−0.549464	+	1.69107i
$372$	−0.984910	−	0.320017i	−0.0510652	−	0.0165921i
$373$	−5.41223	+	7.44929i	−0.280235	+	0.385710i	−0.925812	−	0.377985i	$-0.876617\pi$
$373$	−5.41223	+	7.44929i	−0.280235	+	0.385710i	0.645577	+	0.763695i	$0.276617\pi$
$374$	−1.07498	+	0.349282i	−0.0555859	+	0.0180609i
$375$	−2.04460	+	6.29264i	−0.105583	+	0.324951i
$376$	−11.0865	+	3.60224i	−0.571745	+	0.185771i
$377$		−	29.7966i		−	1.53460i
$378$	2.91576	+	8.97378i	0.149970	+	0.461562i
$379$	25.8699			1.32885			0.664424	−	0.747356i	$-0.268677\pi$
$379$	25.8699			1.32885			0.664424	+	0.747356i	$0.268677\pi$
$380$	4.53454			0.232617
$381$	1.11521	+	3.43226i	0.0571340	+	0.175840i
$382$	−9.77378	−	7.10106i	−0.500070	−	0.363322i
$383$	6.65914	+	2.16369i	0.340266	+	0.110559i	0.474165	−	0.880436i	$-0.342750\pi$
$383$	6.65914	+	2.16369i	0.340266	+	0.110559i	−0.133899	+	0.990995i	$0.542750\pi$
$384$	3.39161	−	1.10200i	0.173078	−	0.0562363i
$385$	13.7078	−	9.95931i	0.698615	−	0.507573i
$386$	12.3672	+	8.98530i	0.629474	+	0.457340i
$387$		−	15.0098i		−	0.762989i
$388$	1.42604	−	1.03608i	0.0723963	−	0.0525990i
$389$	−3.42124	−	1.11163i	−0.173464	−	0.0563618i	0.220998	−	0.975274i	$-0.429069\pi$
$389$	−3.42124	−	1.11163i	−0.173464	−	0.0563618i	−0.394461	+	0.918913i	$0.629069\pi$
$390$	3.99672	−	5.50102i	0.202382	−	0.278555i
$391$	0.238345	+	0.173168i	0.0120536	+	0.00875747i
$392$	−2.30014	−	3.16587i	−0.116175	−	0.159901i
$393$	−0.311976	−	0.960164i	−0.0157371	−	0.0484339i
$394$	6.49737	+	8.94286i	0.327333	+	0.450535i
$395$			15.5358i			0.781693i
$396$	−2.37277	+	3.26584i	−0.119236	+	0.164114i
$397$	10.1841	−	14.0172i	0.511126	−	0.703504i	−0.472983	−	0.881072i	$-0.656823\pi$
$397$	10.1841	−	14.0172i	0.511126	−	0.703504i	0.984109	+	0.177567i	$0.0568227\pi$
$398$		−	30.9091i		−	1.54933i
$399$	−4.12730	−	5.68074i	−0.206623	−	0.284393i
$400$	0.887144	+	2.73035i	0.0443572	+	0.136517i
$401$	12.0486	+	16.5835i	0.601678	+	0.828138i	0.995861	−	0.0908937i	$-0.0289723\pi$
$401$	12.0486	+	16.5835i	0.601678	+	0.828138i	−0.394183	+	0.919032i	$0.628972\pi$
$402$	−7.03092	−	5.10826i	−0.350670	−	0.254777i
$403$	−12.6882	+	17.4638i	−0.632045	+	0.869935i
$404$	−3.74158	−	1.21571i	−0.186151	−	0.0604840i
$405$	−10.3161	+	7.49506i	−0.512609	+	0.372432i
$406$			18.3031i			0.908366i
$407$	28.1975	+	20.4867i	1.39770	+	1.01549i
$408$	−0.346851	+	0.252002i	−0.0171717	+	0.0124760i
$409$	21.8989	−	7.11537i	1.08283	−	0.351833i	0.287358	−	0.957823i	$-0.407223\pi$
$409$	21.8989	−	7.11537i	1.08283	−	0.351833i	0.795472	+	0.605991i	$0.207223\pi$
$410$	−0.439510	−	0.142805i	−0.0217058	−	0.00705265i
$411$	−5.83721	−	4.24098i	−0.287928	−	0.209192i
$412$	1.88645	+	5.80589i	0.0929386	+	0.286036i
$413$	12.3146			0.605961
$414$	−3.90625			−0.191982
$415$	−9.61711	−	29.5984i	−0.472085	−	1.45293i
$416$			11.5131i			0.564477i
$417$	−6.07537	+	1.97401i	−0.297512	+	0.0966676i
$418$	−7.28268	+	22.4138i	−0.356208	+	1.09629i
$419$	19.1455	−	6.22074i	0.935317	−	0.303903i	0.198582	−	0.980084i	$-0.436366\pi$
$419$	19.1455	−	6.22074i	0.935317	−	0.303903i	0.736735	+	0.676181i	$0.236366\pi$
$420$	0.661292	−	0.910191i	0.0322678	−	0.0444128i
$421$	−28.5022	−	9.26093i	−1.38911	−	0.451350i	−0.483459	−	0.875367i	$-0.660620\pi$
$421$	−28.5022	−	9.26093i	−1.38911	−	0.451350i	−0.905654	+	0.424017i	$0.860620\pi$
$422$	−4.77227	+	14.6875i	−0.232311	+	0.714979i
$423$	−3.19023	+	9.81851i	−0.155114	+	0.477392i
$424$	35.2740	−	25.6281i	1.71306	−	1.24461i
$425$	−0.144912	−	0.199454i	−0.00702926	−	0.00967494i
$426$	1.32148			0.0640260
$427$	−14.6283	+	11.6005i	−0.707913	+	0.561390i
$428$	−6.62725			−0.320340
$429$	−5.59514	−	7.70105i	−0.270136	−	0.371810i
$430$	11.3588	−	8.25262i	0.547768	−	0.397977i
$431$	4.35017	−	13.3885i	0.209540	−	0.644899i	−0.789956	−	0.613164i	$-0.789897\pi$
$431$	4.35017	−	13.3885i	0.209540	−	0.644899i	0.999496	−	0.0317355i	$-0.0101034\pi$
$432$	2.88715	−	8.88574i	0.138908	−	0.427515i
$433$	4.00362	+	1.30085i	0.192401	+	0.0625150i	0.403633	−	0.914921i	$-0.367747\pi$
$433$	4.00362	+	1.30085i	0.192401	+	0.0625150i	−0.211231	+	0.977436i	$0.567747\pi$
$434$	7.79396	−	10.7275i	0.374122	−	0.514935i
$435$	6.43366	−	2.09042i	0.308470	−	0.100228i
$436$	0.231925	−	0.713791i	0.0111072	−	0.0341844i
$437$	5.84211	−	1.89822i	0.279466	−	0.0908041i
$438$		−	1.86710i		−	0.0892136i
$439$	−1.02979	−	3.16938i	−0.0491494	−	0.151266i	0.923470	−	0.383671i	$-0.125340\pi$
$439$	−1.02979	−	3.16938i	−0.0491494	−	0.151266i	−0.972619	+	0.232405i	$0.925340\pi$
$440$	−21.5707			−1.02834
$441$	−3.46566			−0.165031
$442$	0.483428	+	1.48784i	0.0229943	+	0.0707693i
$443$	−7.22885	−	5.25207i	−0.343453	−	0.249533i	0.402664	−	0.915348i	$-0.368084\pi$
$443$	−7.22885	−	5.25207i	−0.343453	−	0.249533i	−0.746117	+	0.665815i	$0.768084\pi$
$444$	2.20102	+	0.715155i	0.104456	+	0.0339397i
$445$	29.5641	−	9.60594i	1.40147	−	0.455365i
$446$	2.66455	−	1.93591i	0.126170	−	0.0916681i
$447$	−2.22858	−	1.61916i	−0.105408	−	0.0765835i
$448$		−	21.2764i		−	1.00521i
$449$	−29.4981	+	21.4317i	−1.39210	+	1.01142i	−0.396473	+	0.918046i	$0.629766\pi$
$449$	−29.4981	+	21.4317i	−1.39210	+	1.01142i	−0.995631	+	0.0933760i	$0.970234\pi$
$450$	3.10887	+	1.01013i	0.146554	+	0.0476182i
$451$	−0.380266	+	0.523391i	−0.0179060	+	0.0246455i
$452$	0.0122336	+	0.00888820i	0.000575418	+	0.000418066i
$453$	6.35585	+	8.74807i	0.298624	+	0.411020i
$454$	4.28026	+	13.1733i	0.200882	+	0.618253i
$455$	−13.7843	−	18.9725i	−0.646218	−	0.889443i
$456$			8.93925i			0.418619i
$457$	4.53332	−	6.23958i	0.212060	−	0.291875i	−0.689715	−	0.724081i	$-0.742264\pi$
$457$	4.53332	−	6.23958i	0.212060	−	0.291875i	0.901775	+	0.432205i	$0.142264\pi$
$458$	20.9143	−	28.7860i	0.977259	−	1.34508i
$459$			0.802344i			0.0374502i
$460$	0.578508	+	0.796248i	0.0269731	+	0.0371253i
$461$	7.48218	+	23.0278i	0.348480	+	1.07251i	0.959694	+	0.281045i	$0.0906812\pi$
$461$	7.48218	+	23.0278i	0.348480	+	1.07251i	−0.611215	+	0.791465i	$0.709319\pi$
$462$	3.43692	+	4.73051i	0.159900	+	0.220083i
$463$	−20.6003	−	14.9670i	−0.957375	−	0.695574i	−0.00483540	−	0.999988i	$-0.501539\pi$
$463$	−20.6003	−	14.9670i	−0.957375	−	0.695574i	−0.952540	+	0.304415i	$0.901539\pi$
$464$	10.6527	−	14.6622i	0.494540	−	0.680676i
$465$	−4.66094	−	1.51443i	−0.216146	−	0.0702300i
$466$	−4.90526	+	3.56388i	−0.227232	+	0.165094i
$467$			4.87498i			0.225587i	0.993618	+	0.112794i	$0.0359799\pi$
$467$			4.87498i			0.225587i	−0.993618	+	0.112794i	$0.964020\pi$
$468$	4.52012	+	3.28406i	0.208943	+	0.151806i
$469$	−24.2489	+	17.6179i	−1.11971	+	0.813518i
$470$	−9.18428	+	2.98415i	−0.423639	+	0.137649i
$471$	−1.27650	−	0.414760i	−0.0588181	−	0.0191111i
$472$	−12.6833	−	9.21492i	−0.583794	−	0.424151i
$473$	−6.07382	−	18.6933i	−0.279275	−	0.859519i
$474$	−5.36136			−0.246255
$475$	−5.14044			−0.235860
$476$	0.0799873	+	0.246176i	0.00366621	+	0.0112834i
$477$		−	38.6142i		−	1.76802i
$478$	−1.56521	+	0.508568i	−0.0715911	+	0.0232614i
$479$	−2.21313	+	6.81133i	−0.101121	+	0.311217i	−0.988800	−	0.149244i	$-0.952316\pi$
$479$	−2.21313	+	6.81133i	−0.101121	+	0.311217i	0.887680	+	0.460461i	$0.152316\pi$
$480$	−2.48591	+	0.807720i	−0.113466	+	0.0368672i
$481$	28.3549	−	39.0271i	1.29287	−	1.77948i
$482$	27.4067	+	8.90497i	1.24834	+	0.405610i
$483$	0.470963	−	1.44948i	0.0214296	−	0.0659534i
$484$	−0.190904	+	0.587541i	−0.00867744	+	0.0267064i
$485$	6.74853	−	4.90309i	0.306435	−	0.222638i
$486$	−9.54693	−	13.1402i	−0.433058	−	0.596053i
$487$	2.83599			0.128511			0.0642555	−	0.997933i	$-0.479533\pi$
$487$	2.83599			0.128511			0.0642555	+	0.997933i	$0.479533\pi$
$488$	23.7469	−	1.00158i	1.07497	−	0.0453396i
$489$	−7.97971			−0.360855
$490$	−1.90548	−	2.62266i	−0.0860807	−	0.118480i
$491$	−18.9613	+	13.7762i	−0.855710	+	0.621710i	−0.926714	−	0.375766i	$-0.877380\pi$
$491$	−18.9613	+	13.7762i	−0.855710	+	0.621710i	0.0710045	+	0.997476i	$0.477380\pi$
$492$	−0.0132744	+	0.0408544i	−0.000598457	+	0.00184186i
$493$	−0.480948	+	1.48021i	−0.0216608	+	0.0666651i
$494$	31.0221	+	10.0797i	1.39575	+	0.453506i
$495$	−11.2288	+	15.4551i	−0.504696	+	0.694654i
$496$	−12.4872	+	4.05732i	−0.560690	+	0.182179i
$497$	1.40839	−	4.33459i	0.0631750	−	0.194433i
$498$	10.2143	−	3.31882i	0.457713	−	0.148720i
$499$			4.02101i			0.180005i	0.995942	+	0.0900026i	$0.0286875\pi$
$499$			4.02101i			0.180005i	−0.995942	+	0.0900026i	$0.971312\pi$
$500$	−1.57150	−	4.83659i	−0.0702798	−	0.216299i
$501$	−5.07183			−0.226593
$502$	19.9508			0.890448
$503$	−0.844107	−	2.59790i	−0.0376369	−	0.115834i	0.930473	−	0.366361i	$-0.119396\pi$
$503$	−0.844107	−	2.59790i	−0.0376369	−	0.115834i	−0.968110	+	0.250526i	$0.919396\pi$
$504$	−15.8612	−	11.5238i	−0.706513	−	0.513312i
$505$	−17.7065	−	5.75318i	−0.787928	−	0.256013i
$506$	−4.86489	+	1.58070i	−0.216271	+	0.0702706i
$507$	−4.85146	+	3.52480i	−0.215461	+	0.156542i
$508$	−2.24408	−	1.63042i	−0.0995650	−	0.0723382i
$509$			21.9223i			0.971688i	0.874045	+	0.485844i	$0.161488\pi$
$509$			21.9223i			0.971688i	−0.874045	+	0.485844i	$0.838512\pi$
$510$	−0.287338	+	0.208763i	−0.0127235	+	0.00924418i
$511$	−6.12428	−	1.98990i	−0.270922	−	0.0880279i
$512$	−14.7451	+	20.2948i	−0.651646	+	0.896914i
$513$	13.5342	+	9.83319i	0.597551	+	0.434146i
$514$	−1.80220	−	2.48052i	−0.0794918	−	0.109411i
$515$	8.92733	+	27.4755i	0.393385	+	1.21072i
$516$	−0.767119	−	1.05585i	−0.0337705	−	0.0464812i
$517$			13.5190i			0.594566i
$518$	−17.4175	+	23.9731i	−0.765280	+	1.05332i
$519$	1.30828	−	1.80070i	0.0574272	−	0.0790418i
$520$			29.8552i			1.30924i
$521$	−0.644761	−	0.887437i	−0.0282475	−	0.0388793i	0.794660	−	0.607055i	$-0.207649\pi$
$521$	−0.644761	−	0.887437i	−0.0282475	−	0.0388793i	−0.822907	+	0.568176i	$0.807649\pi$
$522$	−6.37690	−	19.6261i	−0.279109	−	0.859010i
$523$	−0.440254	−	0.605958i	−0.0192510	−	0.0264967i	0.799283	−	0.600955i	$-0.205213\pi$
$523$	−0.440254	−	0.605958i	−0.0192510	−	0.0264967i	−0.818534	+	0.574458i	$0.805213\pi$
$524$	0.627774	+	0.456104i	0.0274244	+	0.0199250i
$525$	−0.749653	+	1.03181i	−0.0327175	+	0.0450318i
$526$	−8.34500	−	2.71146i	−0.363859	−	0.118225i
$527$	0.912197	−	0.662750i	0.0397359	−	0.0288698i
$528$		−	5.78986i		−	0.251971i
$529$	−17.5287	−	12.7354i	−0.762119	−	0.553712i
$530$	29.2216	−	21.2307i	1.26930	−	0.922204i
$531$	−13.2047	+	4.29047i	−0.573035	+	0.186190i
$532$	5.13287	+	1.66777i	0.222538	+	0.0723070i
$533$	0.724406	+	0.526312i	0.0313775	+	0.0227971i
$534$	3.31497	+	10.2024i	0.143453	+	0.441502i
$535$	−31.3625			−1.35592
$536$	38.1582			1.64818
$537$	3.88940	+	11.9703i	0.167840	+	0.516558i
$538$			21.7148i			0.936192i
$539$	−4.31617	+	1.40241i	−0.185910	+	0.0604060i
$540$	−0.828296	+	2.54923i	−0.0356442	+	0.109702i
$541$	29.4720	−	9.57603i	1.26710	−	0.411706i	0.403081	−	0.915165i	$-0.367939\pi$
$541$	29.4720	−	9.57603i	1.26710	−	0.411706i	0.864019	+	0.503459i	$0.167939\pi$
$542$	−10.9480	+	15.0686i	−0.470257	+	0.647254i
$543$	6.21855	+	2.02053i	0.266864	+	0.0867093i
$544$	0.185834	−	0.571937i	0.00796756	−	0.0245216i
$545$	1.09755	−	3.37791i	0.0470138	−	0.144694i
$546$	6.54732	−	4.75690i	0.280199	−	0.203577i
$547$	14.5034	+	19.9623i	0.620122	+	0.853525i	0.997362	−	0.0725904i	$-0.0231266\pi$
$547$	14.5034	+	19.9623i	0.620122	+	0.853525i	−0.377239	+	0.926116i	$0.623127\pi$
$548$	5.54567			0.236899
$549$	11.6440	−	17.5357i	0.496953	−	0.748403i
$550$	4.28058			0.182525
$551$	19.0743	+	26.2536i	0.812594	+	1.11844i
$552$	−1.56970	+	1.14045i	−0.0668107	+	0.0485408i
$553$	−5.71396	+	17.5858i	−0.242982	+	0.747823i
$554$	−1.76639	+	5.43640i	−0.0750469	+	0.230971i
$555$	10.4160	+	3.38436i	0.442134	+	0.143658i
$556$	2.88597	−	3.97220i	0.122392	−	0.168459i
$557$	31.9393	−	10.3777i	1.35331	−	0.439717i	0.459507	−	0.888174i	$-0.348026\pi$
$557$	31.9393	−	10.3777i	1.35331	−	0.439717i	0.893804	+	0.448457i	$0.148026\pi$
$558$	−4.61982	+	14.2183i	−0.195572	+	0.601910i
$559$	−25.8727	+	8.40655i	−1.09430	+	0.355559i
$560$		−	14.2640i		−	0.602765i
$561$	0.153647	+	0.472877i	0.00648698	+	0.0199649i
$562$	−19.7588			−0.833474
$563$	−33.6701			−1.41903			−0.709513	−	0.704692i	$-0.751085\pi$
$563$	−33.6701			−1.41903			−0.709513	+	0.704692i	$0.751085\pi$
$564$	0.277391	+	0.853721i	0.0116803	+	0.0359481i
$565$	0.0578934	+	0.0420620i	0.00243559	+	0.00176956i
$566$	−17.3185	−	5.62712i	−0.727950	−	0.236525i
$567$	−14.4339	+	4.68985i	−0.606165	+	0.196955i
$568$	−4.69410	+	3.41047i	−0.196960	+	0.143100i
$569$	8.09730	+	5.88303i	0.339456	+	0.246630i	0.744432	−	0.667698i	$-0.232720\pi$
$569$	8.09730	+	5.88303i	0.339456	+	0.246630i	−0.404976	+	0.914327i	$0.632720\pi$
$570$			7.40543i			0.310179i
$571$	−10.8513	+	7.88391i	−0.454112	+	0.329931i	−0.791217	−	0.611535i	$-0.790552\pi$
$571$	−10.8513	+	7.88391i	−0.454112	+	0.329931i	0.337105	+	0.941467i	$0.390552\pi$
$572$	6.95833	+	2.26090i	0.290942	+	0.0945329i
$573$	−3.12371	+	4.29942i	−0.130495	+	0.179611i
$574$	−0.444979	−	0.323296i	−0.0185731	−	0.0134941i
$575$	−0.655807	−	0.902641i	−0.0273491	−	0.0376427i
$576$	7.41281	+	22.8143i	0.308867	+	0.950596i
$577$	5.97826	+	8.22837i	0.248878	+	0.342552i	0.915118	−	0.403186i	$-0.132097\pi$
$577$	5.97826	+	8.22837i	0.248878	+	0.342552i	−0.666240	+	0.745738i	$0.732097\pi$
$578$			21.2572i			0.884182i
$579$	3.95257	−	5.44025i	0.164263	−	0.226089i
$580$	−3.05616	+	4.20645i	−0.126900	+	0.174663i
$581$		−	37.0410i		−	1.53672i
$582$	1.69204	+	2.32889i	0.0701372	+	0.0965356i
$583$	−15.6255	−	48.0905i	−0.647144	−	1.99170i
$584$	4.81860	+	6.63223i	0.199395	+	0.274444i
$585$	21.3908	+	15.5413i	0.884400	+	0.642554i
$586$	−12.9217	+	17.7851i	−0.533789	+	0.734697i
$587$	−24.6772	−	8.01811i	−1.01854	−	0.330943i	−0.248289	−	0.968686i	$-0.579868\pi$
$587$	−24.6772	−	8.01811i	−1.01854	−	0.330943i	−0.770249	+	0.637743i	$0.779868\pi$
$588$	−0.243789	+	0.177123i	−0.0100537	+	0.00730443i
$589$		−	23.5097i		−	0.968698i
$590$	−10.5070	−	7.63380i	−0.432567	−	0.314278i
$591$	3.93391	−	2.85815i	0.161819	−	0.117569i
$592$	27.9056	−	9.06707i	1.14691	−	0.372654i
$593$	−6.35039	−	2.06337i	−0.260779	−	0.0847323i	0.175709	−	0.984442i	$-0.443778\pi$
$593$	−6.35039	−	2.06337i	−0.260779	−	0.0847323i	−0.436489	+	0.899710i	$0.643778\pi$
$594$	−11.2703	−	8.18837i	−0.462427	−	0.335973i
$595$	0.378528	+	1.16499i	0.0155181	+	0.0477599i
$596$	2.11727			0.0867268
$597$	−13.5967			−0.556477
$598$	2.18778	+	6.73330i	0.0894651	+	0.275345i
$599$		−	19.6048i		−	0.801032i	−0.916290	−	0.400516i	$-0.868831\pi$
$599$		−	19.6048i		−	0.801032i	0.916290	−	0.400516i	$-0.131169\pi$
$600$	1.54419	−	0.501738i	0.0630414	−	0.0204834i
$601$	11.2805	−	34.7179i	0.460142	−	1.41617i	−0.404848	−	0.914384i	$-0.632676\pi$
$601$	11.2805	−	34.7179i	0.460142	−	1.41617i	0.864990	−	0.501788i	$-0.167324\pi$
$602$	15.8928	−	5.16387i	0.647741	−	0.210464i
$603$	19.8635	−	27.3398i	0.808906	−	1.11336i
$604$	−7.90437	−	2.56829i	−0.321624	−	0.104502i
$605$	−0.903423	+	2.78045i	−0.0367294	+	0.113041i
$606$	1.98540	−	6.11043i	0.0806513	−	0.248219i
$607$	−2.93759	+	2.13429i	−0.119233	+	0.0866280i	−0.645804	−	0.763503i	$-0.723478\pi$
$607$	−2.93759	+	2.13429i	−0.119233	+	0.0866280i	0.526571	+	0.850131i	$0.323478\pi$
$608$	−7.37015	−	10.1441i	−0.298899	−	0.411399i
$609$	8.05141			0.326259
$610$	19.6723	−	0.829729i	0.796508	−	0.0335947i
$611$	18.7112			0.756973
$612$	−0.171538	−	0.236102i	−0.00693401	−	0.00954385i
$613$	−17.5058	+	12.7187i	−0.707055	+	0.513705i	−0.882222	−	0.470833i	$-0.843953\pi$
$613$	−17.5058	+	12.7187i	−0.707055	+	0.513705i	0.175168	+	0.984539i	$0.443953\pi$
$614$	−7.57794	+	23.3225i	−0.305821	+	0.941220i
$615$	−0.0628192	+	0.193337i	−0.00253311	+	0.00779612i
$616$	−24.4169	−	7.93353i	−0.983785	−	0.319651i
$617$	−2.05889	+	2.83382i	−0.0828879	+	0.114085i	−0.848447	−	0.529280i	$-0.822462\pi$
$617$	−2.05889	+	2.83382i	−0.0828879	+	0.114085i	0.765560	+	0.643365i	$0.222462\pi$
$618$	−9.48168	+	3.08078i	−0.381409	+	0.123927i
$619$	8.73648	−	26.8881i	0.351149	−	1.08073i	−0.607060	−	0.794656i	$-0.707651\pi$
$619$	8.73648	−	26.8881i	0.351149	−	1.08073i	0.958209	−	0.286069i	$-0.0923487\pi$
$620$	3.58245	−	1.16401i	0.143875	−	0.0467477i
$621$			3.63106i			0.145709i
$622$	−8.71102	−	26.8098i	−0.349280	−	1.07497i
$623$	36.9980			1.48229
$624$	−8.01352			−0.320798
$625$	−5.94394	−	18.2936i	−0.237758	−	0.731743i
$626$	−13.0412	−	9.47501i	−0.521233	−	0.378698i
$627$	9.85969	+	3.20361i	0.393758	+	0.127940i
$628$	0.981132	−	0.318789i	0.0391514	−	0.0127211i
$629$	−2.03852	+	1.48107i	−0.0812813	+	0.0590543i
$630$	−13.1397	−	9.54653i	−0.523497	−	0.380343i
$631$		−	1.49128i		−	0.0593671i	−0.999559	−	0.0296836i	$-0.990550\pi$
$631$		−	1.49128i		−	0.0593671i	0.999559	−	0.0296836i	$-0.00944996\pi$
$632$	19.0444	−	13.8365i	0.757544	−	0.550388i
$633$	6.46096	+	2.09929i	0.256800	+	0.0834394i
$634$	−2.22266	+	3.05922i	−0.0882729	+	0.121497i
$635$	−10.6198	−	7.71571i	−0.421433	−	0.306189i
$636$	−1.97349	−	2.71628i	−0.0782541	−	0.107708i
$637$	1.94102	+	5.97384i	0.0769060	+	0.236692i
$638$	−15.8837	−	21.8621i	−0.628842	−	0.865527i
$639$			5.13860i			0.203280i
$640$	−7.62433	+	10.4940i	−0.301378	+	0.414811i
$641$	−10.4584	+	14.3948i	−0.413082	+	0.568559i	−0.963967	−	0.266022i	$-0.914291\pi$
$641$	−10.4584	+	14.3948i	−0.413082	+	0.568559i	0.550884	+	0.834582i	$0.314291\pi$
$642$		−	10.8231i		−	0.427152i
$643$	8.72980	+	12.0155i	0.344270	+	0.473846i	0.945682	−	0.325092i	$-0.105395\pi$
$643$	8.72980	+	12.0155i	0.344270	+	0.473846i	−0.601413	+	0.798938i	$0.705395\pi$
$644$	0.361987	+	1.11408i	0.0142643	+	0.0439010i
$645$	−3.63028	−	4.99664i	−0.142942	−	0.196743i
$646$	−1.37839	−	1.00146i	−0.0542320	−	0.0394018i
$647$	−10.5750	+	14.5552i	−0.415745	+	0.572224i	−0.964608	−	0.263689i	$-0.915061\pi$
$647$	−10.5750	+	14.5552i	−0.415745	+	0.572224i	0.548863	+	0.835912i	$0.315061\pi$
$648$	18.3754	+	5.97052i	0.721853	+	0.234544i
$649$	−14.7091	+	10.6868i	−0.577383	+	0.419493i
$650$		−	5.92459i		−	0.232382i
$651$	−4.71894	−	3.42851i	−0.184950	−	0.134374i
$652$	4.96194	−	3.60506i	0.194324	−	0.141185i
$653$	32.7027	−	10.6258i	1.27976	−	0.415818i	0.411261	−	0.911517i	$-0.365088\pi$
$653$	32.7027	−	10.6258i	1.27976	−	0.415818i	0.868494	+	0.495700i	$0.165088\pi$
$654$	1.16570	+	0.378759i	0.0455825	+	0.0148107i
$655$	2.97084	+	2.15844i	0.116080	+	0.0843374i
$656$	0.168299	+	0.517972i	0.00657099	+	0.0202234i
$657$	7.26025			0.283249
$658$	−11.4937			−0.448070
$659$	9.94999	+	30.6229i	0.387596	+	1.19290i	0.934579	+	0.355755i	$0.115776\pi$
$659$	9.94999	+	30.6229i	0.387596	+	1.19290i	−0.546983	+	0.837144i	$0.684224\pi$
$660$			1.66106i			0.0646565i
$661$	−22.8551	+	7.42607i	−0.888960	+	0.288840i	−0.717673	−	0.696381i	$-0.754793\pi$
$661$	−22.8551	+	7.42607i	−0.888960	+	0.288840i	−0.171287	+	0.985221i	$0.554793\pi$
$662$	7.30947	−	22.4962i	0.284090	−	0.874340i
$663$	0.654491	−	0.212657i	0.0254183	−	0.00825891i
$664$	−27.7175	+	38.1499i	−1.07565	+	1.48050i
$665$	24.2905	+	7.89247i	0.941946	+	0.306057i
$666$	10.3241	−	31.7743i	0.400051	−	1.23123i
$667$	−2.17656	+	6.69876i	−0.0842767	+	0.259377i
$668$	3.15376	−	2.29134i	0.122023	−	0.0886547i
$669$	−0.851596	−	1.17212i	−0.0329246	−	0.0453168i
$670$	31.6109			1.22124
$671$	7.40558	−	26.5509i	0.285889	−	1.02499i
$672$	−3.11099			−0.120009
$673$	10.0946	+	13.8940i	0.389117	+	0.535573i	0.957971	−	0.286865i	$-0.0926132\pi$
$673$	10.0946	+	13.8940i	0.389117	+	0.535573i	−0.568854	+	0.822438i	$0.692613\pi$
$674$	12.7434	−	9.25861i	0.490857	−	0.356628i
$675$	0.938971	−	2.88986i	0.0361410	−	0.111231i
$676$	1.42431	−	4.38357i	0.0547811	−	0.168599i
$677$	10.1805	+	3.30785i	0.391269	+	0.127131i	0.498043	−	0.867152i	$-0.334052\pi$
$677$	10.1805	+	3.30785i	0.391269	+	0.127131i	−0.106774	+	0.994283i	$0.534052\pi$
$678$	−0.0145154	+	0.0199788i	−0.000557462	+	0.000767280i
$679$	9.44230	−	3.06799i	0.362362	−	0.117739i
$680$	0.481894	−	1.48312i	0.0184798	−	0.0568749i
$681$	5.79484	−	1.88286i	0.222059	−	0.0721513i
$682$			19.5771i			0.749647i
$683$	1.46127	+	4.49733i	0.0559140	+	0.172086i	0.975113	−	0.221707i	$-0.0711628\pi$
$683$	1.46127	+	4.49733i	0.0559140	+	0.172086i	−0.919199	+	0.393793i	$0.871163\pi$
$684$	−6.08495			−0.232664
$685$	26.2440			1.00273
$686$	−7.68279	−	23.6452i	−0.293330	−	0.902777i
$687$	−12.6628	−	9.20005i	−0.483115	−	0.351004i
$688$	−15.7368	−	5.11321i	−0.599961	−	0.194939i
$689$	−66.5602	+	21.6267i	−2.53574	+	0.823913i
$690$	−1.30036	+	0.944770i	−0.0495040	+	0.0359668i
$691$	23.9273	+	17.3842i	0.910239	+	0.661327i	0.941075	−	0.338197i	$-0.109817\pi$
$691$	23.9273	+	17.3842i	0.910239	+	0.661327i	−0.0308365	+	0.999524i	$0.509817\pi$
$692$			1.71076i			0.0650333i
$693$	−18.3946	+	13.3645i	−0.698754	+	0.507675i
$694$	17.0251	+	5.53178i	0.646263	+	0.209983i
$695$	13.6574	−	18.7978i	0.518055	−	0.713042i
$696$	−8.29245	−	6.02482i	−0.314325	−	0.228370i
$697$	−0.0274911	−	0.0378383i	−0.00104130	−	0.00143323i
$698$	−5.35254	−	16.4734i	−0.202597	−	0.623529i
$699$	1.56773	+	2.15779i	0.0592970	+	0.0816153i
$700$		−	0.980275i		−	0.0370509i
$701$	−28.1898	+	38.7999i	−1.06471	+	1.46545i	−0.189397	+	0.981901i	$0.560653\pi$
$701$	−28.1898	+	38.7999i	−1.06471	+	1.46545i	−0.875316	+	0.483551i	$0.839347\pi$
$702$	−11.3332	+	15.5988i	−0.427744	+	0.588740i
$703$			52.5380i			1.98151i
$704$	18.4640	+	25.4135i	0.695888	+	0.957808i
$705$	1.31271	+	4.04011i	0.0494395	+	0.152159i
$706$	0.577751	+	0.795206i	0.0217439	+	0.0299280i
$707$	−17.9268	−	13.0246i	−0.674208	−	0.489841i
$708$	−0.709597	+	0.976676i	−0.0266683	+	0.0367057i
$709$	13.2695	+	4.31152i	0.498347	+	0.161923i	0.547396	−	0.836874i	$-0.315619\pi$
$709$	13.2695	+	4.31152i	0.498347	+	0.161923i	−0.0490494	+	0.998796i	$0.515619\pi$
$710$	−3.88868	+	2.82529i	−0.145939	+	0.106031i
$711$		−	20.8477i		−	0.781850i
$712$	−38.1056	−	27.6854i	−1.42807	−	1.03755i
$713$	4.12820	−	2.99931i	0.154602	−	0.112325i
$714$	−0.402033	+	0.130628i	−0.0150457	+	0.00488864i
$715$	32.9292	+	10.6994i	1.23148	+	0.400133i
$716$	−7.82643	−	5.68624i	−0.292487	−	0.212505i
$717$	0.223716	+	0.688527i	0.00835483	+	0.0257135i
$718$	15.8933			0.593134
$719$	−19.0866			−0.711811			−0.355906	−	0.934522i	$-0.615828\pi$
$719$	−19.0866			−0.711811			−0.355906	+	0.934522i	$0.615828\pi$
$720$	4.96966	+	15.2951i	0.185208	+	0.570013i
$721$			34.3842i			1.28054i
$722$	−11.1038	+	3.60785i	−0.413242	+	0.134270i
$723$	3.91724	−	12.0560i	0.145684	−	0.448368i
$724$	−4.77965	+	1.55300i	−0.177634	+	0.0577168i
$725$	3.46452	−	4.76851i	0.128669	−	0.177098i
$726$	−0.959522	−	0.311767i	−0.0356112	−	0.0115708i
$727$	9.57763	−	29.4769i	0.355215	−	1.09324i	−0.600670	−	0.799497i	$-0.705100\pi$
$727$	9.57763	−	29.4769i	0.355215	−	1.09324i	0.955885	−	0.293741i	$-0.0949004\pi$
$728$	−10.9805	+	33.7945i	−0.406964	+	1.25251i
$729$	9.62895	−	6.99584i	0.356628	−	0.259105i
$730$	3.99181	+	5.49426i	0.147744	+	0.203352i
$731$	1.42097			0.0525565
$732$	−0.0771271	−	1.82863i	−0.00285070	−	0.0675882i
$733$	17.5817			0.649393			0.324697	−	0.945818i	$-0.394738\pi$
$733$	17.5817			0.649393			0.324697	+	0.945818i	$0.394738\pi$
$734$	14.0359	+	19.3188i	0.518076	+	0.713070i
$735$	−1.15369	+	0.838207i	−0.0425546	+	0.0309177i
$736$	0.841002	−	2.58834i	0.0309997	−	0.0954074i
$737$	13.6750	−	42.0872i	0.503724	−	1.55030i
$738$	0.589782	+	0.191632i	0.0217102	+	0.00705406i
$739$	−11.1192	+	15.3043i	−0.409027	+	0.562978i	−0.962981	−	0.269570i	$-0.913118\pi$
$739$	−11.1192	+	15.3043i	−0.409027	+	0.562978i	0.553954	+	0.832548i	$0.313118\pi$
$740$	−8.00584	+	2.60126i	−0.294301	+	0.0956241i
$741$	4.43399	−	13.6464i	0.162887	−	0.501314i
$742$	40.8858	−	13.2846i	1.50097	−	0.487693i
$743$			32.3581i			1.18711i	0.804795	+	0.593553i	$0.202275\pi$
$743$			32.3581i			1.18711i	−0.804795	+	0.593553i	$0.797725\pi$
$744$	2.29469	+	7.06232i	0.0841272	+	0.258917i
$745$	10.0197			0.367092
$746$	11.5579			0.423166
$747$	12.9053	+	39.7184i	0.472180	+	1.45322i
$748$	−0.309176	−	0.224629i	−0.0113046	−	0.00821327i
$749$	−35.5007	−	11.5349i	−1.29717	−	0.421475i
$750$	7.89870	−	2.56644i	0.288420	−	0.0937133i
$751$	12.7216	−	9.24278i	0.464218	−	0.337274i	−0.330966	−	0.943643i	$-0.607375\pi$
$751$	12.7216	−	9.24278i	0.464218	−	0.337274i	0.795183	+	0.606369i	$0.207375\pi$
$752$	9.20735	+	6.68953i	0.335757	+	0.243942i
$753$		−	8.77623i		−	0.319824i
$754$	−30.2584	+	21.9840i	−1.10195	+	0.800612i
$755$	−37.4063	−	12.1540i	−1.36135	−	0.442330i
$756$	−1.87518	+	2.58096i	−0.0681995	+	0.0938686i
$757$	−38.1540	−	27.7205i	−1.38673	−	1.00752i	−0.996215	−	0.0869206i	$-0.972297\pi$
$757$	−38.1540	−	27.7205i	−1.38673	−	1.00752i	−0.390514	−	0.920597i	$-0.627703\pi$
$758$	−19.0870	−	26.2709i	−0.693269	−	0.954203i
$759$	0.695339	+	2.14003i	0.0252392	+	0.0776782i
$760$	−19.1119	−	26.3052i	−0.693260	−	0.954190i
$761$			8.31072i			0.301263i	0.988590	+	0.150632i	$0.0481308\pi$
$761$			8.31072i			0.301263i	−0.988590	+	0.150632i	$0.951869\pi$
$762$	2.66266	−	3.66484i	0.0964580	−	0.132763i
$763$	2.48474	−	3.41994i	0.0899535	−	0.123810i
$764$		−	4.08469i		−	0.147779i
$765$	−0.811778	−	1.11732i	−0.0293499	−	0.0403966i
$766$	−2.71592	−	8.35875i	−0.0981302	−	0.302014i
$767$	14.7912	+	20.3583i	0.534079	+	0.735096i
$768$	4.33067	+	3.14642i	0.156270	+	0.113537i
$769$	−8.97573	+	12.3540i	−0.323673	+	0.445498i	−0.939584	−	0.342318i	$-0.888788\pi$
$769$	−8.97573	+	12.3540i	−0.323673	+	0.445498i	0.615911	+	0.787816i	$0.288788\pi$
$770$	−20.2274	−	6.57227i	−0.728944	−	0.236848i
$771$	−1.09116	+	0.792778i	−0.0392973	+	0.0285512i
$772$			5.16854i			0.186020i
$773$	−23.2033	−	16.8582i	−0.834564	−	0.606346i	0.0862829	−	0.996271i	$-0.472501\pi$
$773$	−23.2033	−	16.8582i	−0.834564	−	0.606346i	−0.920847	+	0.389924i	$0.872501\pi$
$774$	−15.2424	+	11.0743i	−0.547877	+	0.398056i
$775$	−4.06113	+	1.31954i	−0.145880	+	0.0473993i
$776$	−12.0207	−	3.90578i	−0.431520	−	0.140209i
$777$	10.5456	+	7.66184i	0.378322	+	0.274867i
$778$	1.39535	+	4.29444i	0.0500256	+	0.153963i
$779$	−0.975189			−0.0349398
$780$	2.29900			0.0823175
$781$	2.07938	+	6.39966i	0.0744059	+	0.228998i
$782$		−	0.369804i		−	0.0132242i
$783$	−18.2434	+	5.92765i	−0.651967	+	0.211837i
$784$	−1.18061	+	3.63354i	−0.0421645	+	0.129769i
$785$	4.64306	−	1.50862i	0.165718	−	0.0538450i
$786$	−0.744870	+	1.02523i	−0.0265686	+	0.0365686i
$787$	47.0311	+	15.2813i	1.67648	+	0.544721i	0.984223	−	0.176931i	$-0.0566169\pi$
$787$	47.0311	+	15.2813i	1.67648	+	0.544721i	0.692256	+	0.721652i	$0.256617\pi$
$788$	−1.15493	+	3.55451i	−0.0411426	+	0.126624i
$789$	−1.19275	+	3.67091i	−0.0424631	+	0.130688i
$790$	15.7767	−	11.4624i	0.561309	−	0.407815i
$791$	0.0500623	+	0.0689048i	0.00178001	+	0.00244997i
$792$	28.9459			1.02855
$793$	−36.7481	−	10.2498i	−1.30496	−	0.363980i
$794$	−21.7484			−0.771822
$795$	−9.33926	−	12.8544i	−0.331229	−	0.455898i
$796$	8.45471	−	6.14270i	0.299669	−	0.217722i
$797$	−15.9355	+	49.0444i	−0.564464	+	1.73724i	0.105075	+	0.994464i	$0.466492\pi$
$797$	−15.9355	+	49.0444i	−0.564464	+	1.73724i	−0.669539	+	0.742777i	$0.733508\pi$
$798$	−2.72366	+	8.38256i	−0.0964165	+	0.296739i
$799$	−0.929516	−	0.302018i	−0.0328839	−	0.0106846i
$800$	−1.33866	+	1.84251i	−0.0473288	+	0.0651424i
$801$	−39.6723	+	12.8903i	−1.40175	+	0.455457i
$802$	7.95102	−	24.4707i	0.280760	−	0.864091i
$803$	9.04200	−	2.93792i	0.319085	−	0.103677i
$804$		−	2.93838i		−	0.103629i
$805$	1.71305	+	5.27223i	0.0603771	+	0.185822i
$806$	27.0959			0.954414
$807$	9.55221			0.336254
$808$	8.71730	+	26.8291i	0.306673	+	0.943844i
$809$	10.2459	+	7.44408i	0.360227	+	0.261720i	0.753147	−	0.657853i	$-0.228535\pi$
$809$	10.2459	+	7.44408i	0.360227	+	0.261720i	−0.392920	+	0.919573i	$0.628535\pi$
$810$	15.2225	+	4.94608i	0.534863	+	0.173788i
$811$	46.1020	−	14.9794i	1.61886	−	0.525999i	0.647187	−	0.762331i	$-0.275945\pi$
$811$	46.1020	−	14.9794i	1.61886	−	0.525999i	0.971672	+	0.236332i	$0.0759452\pi$
$812$	−5.00652	+	3.63745i	−0.175694	+	0.127649i
$813$	6.62860	+	4.81596i	0.232475	+	0.168903i
$814$		−	43.7498i		−	1.53343i
$815$	23.4816	−	17.0604i	0.822525	−	0.597599i
$816$	0.398088	+	0.129347i	0.0139359	+	0.00452804i
$817$	17.4148	−	23.9694i	0.609267	−	0.838584i
$818$	−23.3828	−	16.9886i	−0.817559	−	0.593991i
$819$	18.4973	+	25.4593i	0.646347	+	0.889621i
$820$	−0.0482835	−	0.148601i	−0.00168613	−	0.00518938i
$821$	−19.7460	−	27.1780i	−0.689140	−	0.948520i	0.310858	−	0.950456i	$-0.399384\pi$
$821$	−19.7460	−	27.1780i	−0.689140	−	0.948520i	−0.999998	+	0.00193620i	$0.999384\pi$
$822$			9.05670i			0.315889i
$823$	15.3973	−	21.1926i	0.536716	−	0.738726i	−0.451419	−	0.892312i	$-0.649082\pi$
$823$	15.3973	−	21.1926i	0.536716	−	0.738726i	0.988135	+	0.153586i	$0.0490822\pi$
$824$	25.7295	−	35.4136i	0.896330	−	1.23369i
$825$		−	1.88300i		−	0.0655577i
$826$	−9.08575	−	12.5055i	−0.316134	−	0.435121i
$827$	9.76503	+	30.0537i	0.339563	+	1.04507i	0.964430	+	0.264338i	$0.0851533\pi$
$827$	9.76503	+	30.0537i	0.339563	+	1.04507i	−0.624867	+	0.780731i	$0.714847\pi$
$828$	−0.776306	−	1.06849i	−0.0269785	−	0.0371327i
$829$	19.6250	+	14.2584i	0.681606	+	0.495216i	0.873890	−	0.486123i	$-0.161589\pi$
$829$	19.6250	+	14.2584i	0.681606	+	0.495216i	−0.192284	+	0.981339i	$0.561589\pi$
$830$	−22.9617	+	31.6040i	−0.797012	+	1.09699i
$831$	2.39144	+	0.777026i	0.0829581	+	0.0269547i
$832$	35.1739	−	25.5553i	1.21943	−	0.885971i
$833$		−	0.328093i		−	0.0113677i
$834$	6.48705	+	4.71311i	0.224628	+	0.163202i
$835$	14.9247	−	10.8434i	0.516491	−	0.375252i
$836$	−7.57826	+	2.46233i	−0.262100	+	0.0851613i
$837$	13.2167	+	4.29436i	0.456835	+	0.148435i
$838$	−20.4428	−	14.8526i	−0.706184	−	0.513073i
$839$	−14.6860	−	45.1990i	−0.507018	−	1.56044i	−0.797351	−	0.603516i	$-0.793766\pi$
$839$	−14.6860	−	45.1990i	−0.507018	−	1.56044i	0.290333	−	0.956926i	$-0.406234\pi$
$840$	−8.06724			−0.278346
$841$	−8.20960			−0.283090
$842$	11.6246	+	35.7768i	0.400610	+	1.23295i
$843$			8.69176i			0.299360i
$844$	−4.96596	+	1.61354i	−0.170935	+	0.0555403i
$845$	6.74032	−	20.7446i	0.231874	−	0.713635i
$846$	12.3245	−	4.00446i	0.423724	−	0.137676i
$847$	−2.04526	+	2.81505i	−0.0702758	+	0.0967264i
$848$	−40.4847	−	13.1543i	−1.39025	−	0.451719i
$849$	−2.47533	+	7.61829i	−0.0849532	+	0.261459i
$850$	−0.0956292	+	0.294316i	−0.00328005	+	0.0100950i
$851$	−9.22547	+	6.70269i	−0.316245	+	0.229765i
$852$	0.262624	+	0.361470i	0.00899734	+	0.0123838i
$853$	−22.7667			−0.779516			−0.389758	−	0.920917i	$-0.627441\pi$
$853$	−22.7667			−0.779516			−0.389758	+	0.920917i	$0.627441\pi$
$854$	22.5732	+	6.29611i	0.772439	+	0.215449i
$855$	−28.7961			−0.984805
$856$	27.9320	+	38.4452i	0.954698	+	1.31403i
$857$	42.9379	−	31.1962i	1.46673	−	1.06564i	0.485184	−	0.874412i	$-0.338753\pi$
$857$	42.9379	−	31.1962i	1.46673	−	1.06564i	0.981545	−	0.191229i	$-0.0612474\pi$
$858$	−3.69230	+	11.3637i	−0.126053	+	0.387952i
$859$	1.44916	−	4.46005i	0.0494446	−	0.152175i	−0.923286	−	0.384114i	$-0.874507\pi$
$859$	1.44916	−	4.46005i	0.0494446	−	0.152175i	0.972730	+	0.231939i	$0.0745070\pi$
$860$	4.51475	+	1.46693i	0.153952	+	0.0500219i
$861$	−0.142216	+	0.195744i	−0.00484671	+	0.00667092i
$862$	−16.8056	+	5.46046i	−0.572400	+	0.185984i
$863$	3.42592	−	10.5439i	0.116620	−	0.358918i	−0.875662	−	0.482925i	$-0.839574\pi$
$863$	3.42592	−	10.5439i	0.116620	−	0.358918i	0.992281	+	0.124007i	$0.0395744\pi$
$864$	7.04909	−	2.29039i	0.239815	−	0.0779206i
$865$			8.09591i			0.275269i
$866$	−1.63287	−	5.02545i	−0.0554871	−	0.170772i
$867$	9.35089			0.317573
$868$	4.48326			0.152172
$869$	−8.43620	−	25.9640i	−0.286178	−	0.880767i
$870$	−6.86961	−	4.99106i	−0.232902	−	0.169213i
$871$	−58.2513	−	18.9270i	−1.97377	−	0.641317i
$872$	−5.11825	+	1.66302i	−0.173326	+	0.0563170i
$873$	−9.05591	+	6.57951i	−0.306496	+	0.222683i
$874$	−6.23798	−	4.53216i	−0.211003	−	0.153303i
$875$		−	28.6438i		−	0.968336i
$876$	0.510716	−	0.371057i	0.0172555	−	0.0125369i
$877$	36.8856	+	11.9849i	1.24554	+	0.404700i	0.856320	−	0.516445i	$-0.172745\pi$
$877$	36.8856	+	11.9849i	1.24554	+	0.404700i	0.389219	+	0.921145i	$0.372745\pi$
$878$	−2.45872	+	3.38414i	−0.0829779	+	0.114209i
$879$	7.82357	+	5.68416i	0.263882	+	0.191722i
$880$	12.3785	+	17.0376i	0.417281	+	0.574338i
$881$	5.65144	+	17.3933i	0.190402	+	0.585996i	1.00000		0.000988752i	$-0.000314730\pi$
$881$	5.65144	+	17.3933i	0.190402	+	0.585996i	−0.809598	+	0.586985i	$0.800315\pi$
$882$	2.55698	+	3.51938i	0.0860979	+	0.118504i
$883$		−	11.4786i		−	0.386287i	−0.981171	−	0.193143i	$-0.938132\pi$
$883$		−	11.4786i		−	0.386287i	0.981171	−	0.193143i	$-0.0618683\pi$
$884$	−0.310901	+	0.427919i	−0.0104567	+	0.0143925i
$885$	−3.35806	+	4.62197i	−0.112880	+	0.155366i
$886$			11.2159i			0.376806i
$887$	−21.9563	−	30.2203i	−0.737221	−	1.01470i	−0.998774	−	0.0495088i	$-0.984234\pi$
$887$	−21.9563	−	30.2203i	−0.737221	−	1.01470i	0.261552	−	0.965189i	$-0.415766\pi$
$888$	−5.12803	−	15.7825i	−0.172085	−	0.529624i
$889$	−9.18325	−	12.6397i	−0.307996	−	0.423920i
$890$	−31.5673	−	22.9350i	−1.05814	−	0.768784i
$891$	13.1706	−	18.1277i	0.441231	−	0.607302i
$892$	1.05908	+	0.344115i	0.0354605	+	0.0115218i
$893$	−16.4863	+	11.9780i	−0.551693	+	0.400828i
$894$			3.45774i			0.115644i
$895$	−37.0374	−	26.9092i	−1.23802	−	0.899477i
$896$	−12.4900	+	9.07448i	−0.417260	+	0.303157i
$897$	2.96194	−	0.962392i	0.0988962	−	0.0321333i
$898$	43.5277	+	14.1430i	1.45254	+	0.471959i
$899$	21.8086	+	15.8449i	0.727358	+	0.528457i
$900$	0.341533	+	1.05113i	0.0113844	+	0.0350377i
$901$	3.65559			0.121785
$902$	0.812066			0.0270389
$903$	−2.27156	−	6.99113i	−0.0755926	−	0.232650i
$904$		−	0.108429i		−	0.00360629i
$905$	−22.6190	+	7.34934i	−0.751879	+	0.244300i
$906$	4.19430	−	12.9087i	0.139346	−	0.428864i
$907$	−28.7648	+	9.34625i	−0.955119	+	0.310337i	−0.744794	−	0.667294i	$-0.767452\pi$
$907$	−28.7648	+	9.34625i	−0.955119	+	0.310337i	−0.210325	+	0.977631i	$0.567452\pi$
$908$	−2.75271	+	3.78878i	−0.0913519	+	0.125735i
$909$	23.7605	+	7.72025i	0.788085	+	0.256064i
$910$	−9.09643	+	27.9959i	−0.301544	+	0.928056i
$911$	7.37466	−	22.6969i	0.244333	−	0.751981i	−0.751412	−	0.659833i	$-0.770627\pi$
$911$	7.37466	−	22.6969i	0.244333	−	0.751981i	0.995745	−	0.0921477i	$-0.0293732\pi$
$912$	7.06067	−	5.12988i	0.233802	−	0.169867i
$913$	32.1448	+	44.2435i	1.06384	+	1.46425i
$914$	−9.68101			−0.320219
$915$	−0.364992	−	8.65372i	−0.0120663	−	0.286083i
$916$	12.0303			0.397494
$917$	2.56898	+	3.53590i	0.0848352	+	0.116766i
$918$	0.814782	−	0.591973i	0.0268918	−	0.0195380i
$919$	−7.70856	+	23.7245i	−0.254282	+	0.782599i	0.739688	+	0.672949i	$0.234973\pi$
$919$	−7.70856	+	23.7245i	−0.254282	+	0.782599i	−0.993970	+	0.109650i	$0.965027\pi$
$920$	2.18084	−	6.71193i	0.0719001	−	0.221286i
$921$	10.2594	+	3.33349i	0.338060	+	0.109842i
$922$	17.8643	−	24.5882i	0.588331	−	0.809768i
$923$	8.85753	−	2.87799i	0.291549	−	0.0947301i
$924$	−0.610923	+	1.88023i	−0.0200979	+	0.0618550i
$925$	9.07557	−	2.94883i	0.298403	−	0.0969570i
$926$			31.9623i			1.05035i
$927$	−11.9797	−	36.8696i	−0.393464	−	1.21096i
$928$	14.3774			0.471963
$929$	−52.0441			−1.70751			−0.853756	−	0.520674i	$-0.825681\pi$
$929$	−52.0441			−1.70751			−0.853756	+	0.520674i	$0.825681\pi$
$930$	1.90096	+	5.85054i	0.0623348	+	0.191847i
$931$	−5.53439	−	4.02097i	−0.181382	−	0.131782i
$932$	−1.94969	−	0.633492i	−0.0638641	−	0.0207507i
$933$	−11.7934	+	3.83192i	−0.386100	+	0.125451i
$934$	4.95055	−	3.59679i	0.161987	−	0.117690i
$935$	−1.46313	−	1.06302i	−0.0478494	−	0.0347646i
$936$		−	40.0629i		−	1.30950i
$937$	−23.7282	+	17.2395i	−0.775166	+	0.563191i	−0.903524	−	0.428537i	$-0.859029\pi$
$937$	−23.7282	+	17.2395i	−0.775166	+	0.563191i	0.128358	+	0.991728i	$0.459029\pi$
$938$	35.7819	+	11.6263i	1.16832	+	0.379611i
$939$	−4.16800	+	5.73676i	−0.136018	+	0.187212i
$940$	−2.64150	−	1.91916i	−0.0861562	−	0.0625961i
$941$	18.9947	+	26.1439i	0.619208	+	0.852267i	0.997295	−	0.0735029i	$-0.0234178\pi$
$941$	18.9947	+	26.1439i	0.619208	+	0.852267i	−0.378087	+	0.925770i	$0.623418\pi$
$942$	0.520619	+	1.60230i	0.0169627	+	0.0522058i
$943$	−0.124413	−	0.171239i	−0.00405144	−	0.00557632i
$944$			15.3059i			0.498166i
$945$	−8.87399	+	12.2140i	−0.288671	+	0.397321i
$946$	−14.5018	+	19.9600i	−0.471494	+	0.648955i
$947$		−	14.8438i		−	0.482358i	−0.970481	−	0.241179i	$-0.922466\pi$
$947$		−	14.8438i		−	0.482358i	0.970481	−	0.241179i	$-0.0775341\pi$
$948$	−1.06549	−	1.46651i	−0.0346054	−	0.0476302i
$949$	−4.06627	−	12.5147i	−0.131997	−	0.406244i
$950$	3.79264	+	5.22012i	0.123050	+	0.169363i
$951$	1.34573	+	0.977732i	0.0436384	+	0.0317051i
$952$	1.09096	−	1.50157i	0.0353581	−	0.0486663i
$953$	−26.0333	−	8.45873i	−0.843301	−	0.274005i	−0.144664	−	0.989481i	$-0.546210\pi$
$953$	−26.0333	−	8.45873i	−0.843301	−	0.274005i	−0.698638	+	0.715476i	$0.746210\pi$
$954$	−39.2127	+	28.4897i	−1.26956	+	0.922388i
$955$		−	19.3302i		−	0.625509i
$956$	−0.450172	−	0.327069i	−0.0145596	−	0.0105782i
$957$	−9.61698	+	6.98715i	−0.310873	+	0.225862i
$958$	8.54977	−	2.77799i	0.276231	−	0.0897527i
$959$	29.7069	+	9.65235i	0.959285	+	0.311691i
$960$	7.98557	+	5.80185i	0.257733	+	0.187254i
$961$	3.54465	+	10.9093i	0.114344	+	0.351913i
$962$	−60.5524			−1.95229
$963$	42.0856			1.35619
$964$	3.01083	+	9.26639i	0.0969724	+	0.298450i
$965$			24.4593i			0.787374i
$966$	−1.81942	+	0.591166i	−0.0585390	+	0.0190205i
$967$	−5.05294	+	15.5514i	−0.162492	+	0.500098i	−0.998843	−	0.0480963i	$-0.984685\pi$
$967$	−5.05294	+	15.5514i	−0.162492	+	0.500098i	0.836351	+	0.548194i	$0.184685\pi$
$968$	4.21297	−	1.36888i	0.135410	−	0.0439974i
$969$	−0.440535	+	0.606344i	−0.0141520	+	0.0194786i
$970$	−9.95819	−	3.23561i	−0.319738	−	0.103889i
$971$	−14.8704	+	45.7663i	−0.477213	+	1.46871i	0.365738	+	0.930718i	$0.380817\pi$
$971$	−14.8704	+	45.7663i	−0.477213	+	1.46871i	−0.842950	+	0.537991i	$0.819183\pi$
$972$	1.69700	−	5.22283i	0.0544313	−	0.167522i
$973$	22.3732	−	16.2551i	0.717251	−	0.521113i
$974$	−2.09241	−	2.87995i	−0.0670451	−	0.0922796i
$975$	−2.60619			−0.0834649
$976$	−14.4185	−	18.1817i	−0.461524	−	0.581982i
$977$	14.2862			0.457058			0.228529	−	0.973537i	$-0.426608\pi$
$977$	14.2862			0.457058			0.228529	+	0.973537i	$0.426608\pi$
$978$	5.88747	+	8.10340i	0.188260	+	0.259118i
$979$	−44.1921	+	32.1075i	−1.41239	+	1.02616i
$980$	0.338705	−	1.04243i	0.0108195	−	0.0332991i
$981$	−1.47281	+	4.53284i	−0.0470232	+	0.144723i
$982$	27.9794	+	9.09107i	0.892859	+	0.290108i
$983$	−0.478789	+	0.658996i	−0.0152710	+	0.0210187i	−0.816584	−	0.577226i	$-0.804135\pi$
$983$	−0.478789	+	0.658996i	−0.0152710	+	0.0210187i	0.801313	+	0.598245i	$0.204135\pi$
$984$	0.292948	−	0.0951844i	0.00933883	−	0.00303437i
$985$	−5.46553	+	16.8212i	−0.174146	+	0.535967i
$986$	1.85800	−	0.603699i	0.0591706	−	0.0192257i
$987$			5.05599i			0.160934i
$988$	3.40801	+	10.4888i	0.108423	+	0.333693i
$989$	6.43068			0.204484
$990$	23.9793			0.762112
$991$	5.32256	+	16.3812i	0.169077	+	0.520365i	0.999314	−	0.0370460i	$-0.0117948\pi$
$991$	5.32256	+	16.3812i	0.169077	+	0.520365i	−0.830237	+	0.557411i	$0.811795\pi$
$992$	−8.42665	−	6.12232i	−0.267546	−	0.194384i
$993$	−9.89595	−	3.21539i	−0.314038	−	0.102037i
$994$	−5.44090	+	1.76785i	−0.172575	+	0.0560729i
$995$	40.0106	−	29.0694i	1.26842	−	0.921562i
$996$	2.93774	+	2.13439i	0.0930859	+	0.0676309i
$997$		−	9.58063i		−	0.303422i	−0.988425	−	0.151711i	$-0.951522\pi$
$997$		−	9.58063i		−	0.303422i	0.988425	−	0.151711i	$-0.0484782\pi$
$998$	4.08334	−	2.96672i	0.129256	−	0.0939100i
$999$	−29.5358	−	9.59678i	−0.934473	−	0.303629i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.2.g.a.27.2	✓	16
3.2	odd	2		549.2.y.b.271.3		16
4.3	odd	2		976.2.bd.b.881.3		16
61.28	odd	20		3721.2.a.k.1.5		16
61.33	odd	20		3721.2.a.k.1.12		16
61.52	even	10	inner	61.2.g.a.52.2	yes	16
183.113	odd	10		549.2.y.b.235.3		16
244.235	odd	10		976.2.bd.b.113.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.g.a.27.2	✓	16	1.1	even	1	trivial
61.2.g.a.52.2	yes	16	61.52	even	10	inner
549.2.y.b.235.3		16	183.113	odd	10
549.2.y.b.271.3		16	3.2	odd	2
976.2.bd.b.113.3		16	244.235	odd	10
976.2.bd.b.881.3		16	4.3	odd	2
3721.2.a.k.1.5		16	61.28	odd	20
3721.2.a.k.1.12		16	61.33	odd	20

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:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	61.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.737805 - 1.01550i) q^{2} +(-0.446713 + 0.324556i) q^{3} +(0.131147 - 0.403630i) q^{4} +(0.620635 - 1.91012i) q^{5} +(0.659173 + 0.214178i) q^{6} +(1.40505 - 1.93389i) q^{7} +(-2.89423 + 0.940394i) q^{8} +(-0.832835 + 2.56320i) q^{9} +O(q^{10})\)	\(q+(-0.737805 - 1.01550i) q^{2} +(-0.446713 + 0.324556i) q^{3} +(0.131147 - 0.403630i) q^{4} +(0.620635 - 1.91012i) q^{5} +(0.659173 + 0.214178i) q^{6} +(1.40505 - 1.93389i) q^{7} +(-2.89423 + 0.940394i) q^{8} +(-0.832835 + 2.56320i) q^{9} +(-2.39763 + 0.779038i) q^{10} +3.52926i q^{11} +(0.0724152 + 0.222871i) q^{12} +4.88471 q^{13} -3.00052 q^{14} +(0.342694 + 1.05470i) q^{15} +(2.40365 + 1.74636i) q^{16} +(-0.242658 - 0.0788443i) q^{17} +(3.21741 - 1.04540i) q^{18} +(-4.30389 + 3.12696i) q^{19} +(-0.689585 - 0.501013i) q^{20} +1.31991i q^{21} +(3.58396 - 2.60390i) q^{22} +(-1.09816 - 0.356815i) q^{23} +(0.987681 - 1.35943i) q^{24} +(0.781726 + 0.567958i) q^{25} +(-3.60396 - 4.96043i) q^{26} +(-0.971751 - 2.99074i) q^{27} +(-0.596306 - 0.820745i) q^{28} -6.09997i q^{29} +(0.818211 - 1.12617i) q^{30} +(-2.59754 + 3.57520i) q^{31} +2.35697i q^{32} +(-1.14544 - 1.57656i) q^{33} +(0.0989676 + 0.304591i) q^{34} +(-2.82193 - 3.88405i) q^{35} +(0.925361 + 0.672314i) q^{36} +(5.80482 - 7.98965i) q^{37} +(6.35086 + 2.06352i) q^{38} +(-2.18206 + 1.58536i) q^{39} +6.11197i q^{40} +(0.148301 + 0.107747i) q^{41} +(1.34037 - 0.973836i) q^{42} +(-5.29667 + 1.72099i) q^{43} +(1.42451 + 0.462852i) q^{44} +(4.37913 + 3.18163i) q^{45} +(0.447884 + 1.37845i) q^{46} +3.83056 q^{47} -1.64053 q^{48} +(0.397366 + 1.22297i) q^{49} -1.21289i q^{50} +(0.133988 - 0.0435352i) q^{51} +(0.640616 - 1.97161i) q^{52} +(-13.6262 + 4.42743i) q^{53} +(-2.32014 + 3.19340i) q^{54} +(6.74129 + 2.19038i) q^{55} +(-2.24793 + 6.91843i) q^{56} +(0.907729 - 2.79370i) q^{57} +(-6.19452 + 4.50059i) q^{58} +(3.02806 + 4.16777i) q^{59} +0.470653 q^{60} +(-7.52310 - 2.09834i) q^{61} +5.54710 q^{62} +(3.78677 + 5.21204i) q^{63} +(7.20082 - 5.23170i) q^{64} +(3.03162 - 9.33036i) q^{65} +(-0.755890 + 2.32639i) q^{66} +(-11.9252 - 3.87475i) q^{67} +(-0.0636478 + 0.0876037i) q^{68} +(0.606369 - 0.197021i) q^{69} +(-1.86223 + 5.73134i) q^{70} +(1.81332 - 0.589183i) q^{71} -8.20170i q^{72} +(-0.832448 - 2.56201i) q^{73} -12.3963 q^{74} -0.533541 q^{75} +(0.697690 + 2.14727i) q^{76} +(6.82519 + 4.95879i) q^{77} +(3.21987 + 1.04620i) q^{78} +(-7.35678 + 2.39036i) q^{79} +(4.82754 - 3.50741i) q^{80} +(-5.13642 - 3.73183i) q^{81} -0.230096i q^{82} +(12.5362 - 9.10809i) q^{83} +(0.532755 + 0.173103i) q^{84} +(-0.301204 + 0.414571i) q^{85} +(5.65558 + 4.10902i) q^{86} +(1.97978 + 2.72493i) q^{87} +(-3.31889 - 10.2145i) q^{88} +(9.09752 + 12.5217i) q^{89} -6.79443i q^{90} +(6.86327 - 9.44648i) q^{91} +(-0.288042 + 0.396456i) q^{92} -2.44013i q^{93} +(-2.82621 - 3.88994i) q^{94} +(3.30171 + 10.1616i) q^{95} +(-0.764968 - 1.05289i) q^{96} +(3.36013 + 2.44127i) q^{97} +(0.948746 - 1.30584i) q^{98} +(-9.04620 - 2.93929i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9}+O(q^{10}) \) 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9	\( 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9} - 5 q^{10} - 12 q^{13} - 18 q^{14} - 13 q^{15} + 19 q^{16} - 10 q^{18} + 3 q^{19} - 13 q^{20} + 19 q^{22} - 15 q^{23} + 10 q^{24} - 2 q^{25} + 10 q^{26} - 4 q^{27} + 35 q^{28} + 45 q^{30} - 15 q^{31} + 25 q^{33} - 14 q^{34} + 10 q^{35} + 37 q^{36} - 5 q^{37} - 15 q^{38} - 3 q^{39} + 12 q^{41} - 15 q^{42} - 25 q^{43} - 50 q^{44} + 36 q^{45} + 27 q^{46} + 6 q^{47} - 20 q^{48} - 30 q^{49} + 50 q^{51} - 46 q^{52} - 20 q^{53} - 20 q^{54} + 20 q^{55} - 28 q^{56} - 11 q^{57} - 41 q^{58} + 5 q^{59} + 14 q^{60} - 53 q^{61} + 16 q^{62} - 5 q^{63} + 17 q^{64} + 20 q^{65} + 13 q^{66} - 55 q^{67} + 80 q^{68} - 15 q^{69} - 17 q^{70} - 50 q^{71} - 11 q^{73} + 24 q^{74} - 88 q^{75} - 19 q^{76} + 63 q^{77} + 50 q^{78} + 40 q^{79} - 49 q^{80} - 19 q^{81} + 31 q^{83} - 25 q^{84} + 55 q^{85} + 35 q^{86} + 25 q^{87} + 27 q^{88} + 60 q^{89} - 15 q^{91} - 5 q^{92} + 65 q^{94} + 48 q^{95} - 25 q^{96} + 45 q^{97} + 10 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9 - 5 * q^10 - 12 * q^13 - 18 * q^14 - 13 * q^15 + 19 * q^16 - 10 * q^18 + 3 * q^19 - 13 * q^20 + 19 * q^22 - 15 * q^23 + 10 * q^24 - 2 * q^25 + 10 * q^26 - 4 * q^27 + 35 * q^28 + 45 * q^30 - 15 * q^31 + 25 * q^33 - 14 * q^34 + 10 * q^35 + 37 * q^36 - 5 * q^37 - 15 * q^38 - 3 * q^39 + 12 * q^41 - 15 * q^42 - 25 * q^43 - 50 * q^44 + 36 * q^45 + 27 * q^46 + 6 * q^47 - 20 * q^48 - 30 * q^49 + 50 * q^51 - 46 * q^52 - 20 * q^53 - 20 * q^54 + 20 * q^55 - 28 * q^56 - 11 * q^57 - 41 * q^58 + 5 * q^59 + 14 * q^60 - 53 * q^61 + 16 * q^62 - 5 * q^63 + 17 * q^64 + 20 * q^65 + 13 * q^66 - 55 * q^67 + 80 * q^68 - 15 * q^69 - 17 * q^70 - 50 * q^71 - 11 * q^73 + 24 * q^74 - 88 * q^75 - 19 * q^76 + 63 * q^77 + 50 * q^78 + 40 * q^79 - 49 * q^80 - 19 * q^81 + 31 * q^83 - 25 * q^84 + 55 * q^85 + 35 * q^86 + 25 * q^87 + 27 * q^88 + 60 * q^89 - 15 * q^91 - 5 * q^92 + 65 * q^94 + 48 * q^95 - 25 * q^96 + 45 * q^97 + 10 * q^98 - 5 * q^99

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