LMFDB - Embedded newform 570.2.x.a.217.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(103,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("570.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.x (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			217.7
Character	$\chi$	$=$	570.217
Dual form			570.2.x.a.373.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.45458 + 1.69830i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.46264 + 2.46264i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.45458 + 1.69830i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.46264 + 2.46264i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-2.01690 - 0.965462i) q^{10} +3.74006 q^{11} +(0.707107 - 0.707107i) q^{12} +(-0.512325 + 1.91202i) q^{13} +(-1.74135 + 3.01611i) q^{14} +(0.965462 - 2.01690i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-4.33706 + 1.16211i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-2.18346 + 3.77260i) q^{19} +(0.410553 - 2.19806i) q^{20} +(-3.01611 - 1.74135i) q^{21} +(0.967999 + 3.61262i) q^{22} +(-7.79176 - 2.08779i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-0.768413 - 4.94060i) q^{25} -1.97947 q^{26} +(-0.707107 + 0.707107i) q^{27} +(-3.36403 - 0.901389i) q^{28} +(-2.22355 - 3.85131i) q^{29} +(2.19806 + 0.410553i) q^{30} +1.07530i q^{31} +(0.965926 + 0.258819i) q^{32} +(-3.61262 + 0.967999i) q^{33} +(-2.24503 - 3.88850i) q^{34} +(-7.76439 + 0.600191i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.80995 - 1.80995i) q^{37} +(-4.20917 - 1.13264i) q^{38} -1.97947i q^{39} +(2.22942 - 0.172335i) q^{40} +(4.07894 + 2.35498i) q^{41} +(0.901389 - 3.36403i) q^{42} +(1.63758 + 6.11154i) q^{43} +(-3.23899 + 1.87003i) q^{44} +(-0.410553 + 2.19806i) q^{45} -8.06662i q^{46} +(-0.263120 + 0.981977i) q^{47} +(-0.258819 + 0.965926i) q^{48} +5.12919i q^{49} +(4.57337 - 2.02095i) q^{50} +(3.88850 - 2.24503i) q^{51} +(-0.512325 - 1.91202i) q^{52} +(-1.81089 + 6.75833i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-5.44021 + 6.35173i) q^{55} -3.48270i q^{56} +(1.13264 - 4.20917i) q^{57} +(3.14458 - 3.14458i) q^{58} +(3.04389 - 5.27217i) q^{59} +(0.172335 + 2.22942i) q^{60} +(6.36253 + 11.0202i) q^{61} +(-1.03866 + 0.278309i) q^{62} +(3.36403 + 0.901389i) q^{63} +1.00000i q^{64} +(-2.50196 - 3.65126i) q^{65} +(-1.87003 - 3.23899i) q^{66} +(1.27797 + 0.342430i) q^{67} +(3.17494 - 3.17494i) q^{68} +8.06662 q^{69} +(-2.58931 - 7.34448i) q^{70} +(-12.6042 - 7.27706i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(2.60924 + 9.73783i) q^{73} +(2.21673 + 1.27983i) q^{74} +(2.02095 + 4.57337i) q^{75} +(0.00463736 - 4.35890i) q^{76} +(9.21043 + 9.21043i) q^{77} +(1.91202 - 0.512325i) q^{78} +(6.64783 - 11.5144i) q^{79} +(0.743478 + 2.10885i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-1.21903 + 4.54947i) q^{82} +(8.69571 - 8.69571i) q^{83} +3.48270 q^{84} +(4.33497 - 9.05598i) q^{85} +(-5.47946 + 3.16357i) q^{86} +(3.14458 + 3.14458i) q^{87} +(-2.64462 - 2.64462i) q^{88} +(3.14122 + 5.44075i) q^{89} +(-2.22942 + 0.172335i) q^{90} +(-5.97030 + 3.44695i) q^{91} +(7.79176 - 2.08779i) q^{92} +(-0.278309 - 1.03866i) q^{93} -1.01662 q^{94} +(-3.23097 - 9.19570i) q^{95} -1.00000 q^{96} +(0.824024 + 3.07530i) q^{97} +(-4.95442 + 1.32753i) q^{98} +(3.23899 - 1.87003i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7}+O(q^{10}) $ 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7	$ 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7} - 12 q^{10} + 8 q^{11} - 24 q^{13} + 20 q^{16} + 8 q^{17} + 12 q^{21} + 24 q^{22} + 16 q^{23} - 16 q^{25} + 32 q^{26} + 4 q^{28} + 16 q^{30} - 24 q^{33} - 4 q^{35} - 20 q^{36} - 8 q^{38} - 36 q^{41} + 4 q^{42} - 4 q^{43} + 8 q^{47} - 24 q^{52} - 16 q^{55} - 8 q^{57} + 16 q^{58} + 12 q^{60} - 8 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{66} - 36 q^{67} - 16 q^{68} + 48 q^{70} + 72 q^{71} - 16 q^{73} - 8 q^{76} + 24 q^{77} + 24 q^{78} + 8 q^{80} + 20 q^{81} - 24 q^{82} - 40 q^{83} - 48 q^{85} + 16 q^{87} - 72 q^{91} - 16 q^{92} + 16 q^{93} - 16 q^{95} - 40 q^{96} + 36 q^{97} - 48 q^{98}+O(q^{100}) $ 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7 - 12 * q^10 + 8 * q^11 - 24 * q^13 + 20 * q^16 + 8 * q^17 + 12 * q^21 + 24 * q^22 + 16 * q^23 - 16 * q^25 + 32 * q^26 + 4 * q^28 + 16 * q^30 - 24 * q^33 - 4 * q^35 - 20 * q^36 - 8 * q^38 - 36 * q^41 + 4 * q^42 - 4 * q^43 + 8 * q^47 - 24 * q^52 - 16 * q^55 - 8 * q^57 + 16 * q^58 + 12 * q^60 - 8 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^66 - 36 * q^67 - 16 * q^68 + 48 * q^70 + 72 * q^71 - 16 * q^73 - 8 * q^76 + 24 * q^77 + 24 * q^78 + 8 * q^80 + 20 * q^81 - 24 * q^82 - 40 * q^83 - 48 * q^85 + 16 * q^87 - 72 * q^91 - 16 * q^92 + 16 * q^93 - 16 * q^95 - 40 * q^96 + 36 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−1.45458	+	1.69830i	−0.650506	+	0.759501i
$5$	−1.45458	+	1.69830i	−0.650506	+	0.759501i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	2.46264	+	2.46264i	0.930791	+	0.930791i	0.997755	−	0.0669648i	$-0.0213315\pi$
$7$	2.46264	+	2.46264i	0.930791	+	0.930791i	−0.0669648	+	0.997755i	$0.521332\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	−2.01690	−	0.965462i	−0.637800	−	0.305306i
$11$	3.74006			1.12767			0.563836	−	0.825887i	$-0.309325\pi$
$11$	3.74006			1.12767			0.563836	+	0.825887i	$0.309325\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−0.512325	+	1.91202i	−0.142093	+	0.530300i	0.857774	+	0.514027i	$0.171847\pi$
$13$	−0.512325	+	1.91202i	−0.142093	+	0.530300i	−0.999868	+	0.0162731i	$0.994820\pi$
$14$	−1.74135	+	3.01611i	−0.465395	+	0.806088i
$15$	0.965462	−	2.01690i	0.249281	−	0.520761i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−4.33706	+	1.16211i	−1.05189	+	0.281853i	−0.743033	−	0.669255i	$-0.766613\pi$
$17$	−4.33706	+	1.16211i	−1.05189	+	0.281853i	−0.308858	+	0.951108i	$0.599947\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	−2.18346	+	3.77260i	−0.500921	+	0.865493i
$19$	−2.18346	+	3.77260i	−0.500921	+	0.865493i
$20$	0.410553	−	2.19806i	0.0918024	−	0.491500i
$21$	−3.01611	−	1.74135i	−0.658168	−	0.379994i
$22$	0.967999	+	3.61262i	0.206378	+	0.770214i
$23$	−7.79176	−	2.08779i	−1.62469	−	0.435335i	−0.672318	−	0.740263i	$-0.734701\pi$
$23$	−7.79176	−	2.08779i	−1.62469	−	0.435335i	−0.952376	+	0.304927i	$0.901368\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−0.768413	−	4.94060i	−0.153683	−	0.988120i
$26$	−1.97947			−0.388206
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−3.36403	−	0.901389i	−0.635742	−	0.170346i
$29$	−2.22355	−	3.85131i	−0.412904	−	0.715170i	0.582302	−	0.812972i	$-0.302152\pi$
$29$	−2.22355	−	3.85131i	−0.412904	−	0.715170i	−0.995206	+	0.0978024i	$0.968819\pi$
$30$	2.19806	+	0.410553i	0.401308	+	0.0749563i
$31$			1.07530i			0.193130i	0.995327	+	0.0965650i	$0.0307856\pi$
$31$			1.07530i			0.193130i	−0.995327	+	0.0965650i	$0.969214\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	−3.61262	+	0.967999i	−0.628877	+	0.168507i
$34$	−2.24503	−	3.88850i	−0.385019	−	0.666872i
$35$	−7.76439	+	0.600191i	−1.31242	+	0.101451i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	1.80995	−	1.80995i	0.297554	−	0.297554i	−0.542501	−	0.840055i	$-0.682522\pi$
$37$	1.80995	−	1.80995i	0.297554	−	0.297554i	0.840055	+	0.542501i	$0.182522\pi$
$38$	−4.20917	−	1.13264i	−0.682818	−	0.183739i
$39$		−	1.97947i		−	0.316969i
$40$	2.22942	−	0.172335i	0.352502	−	0.0272486i
$41$	4.07894	+	2.35498i	0.637024	+	0.367786i	0.783467	−	0.621433i	$-0.213449\pi$
$41$	4.07894	+	2.35498i	0.637024	+	0.367786i	−0.146443	+	0.989219i	$0.546783\pi$
$42$	0.901389	−	3.36403i	0.139087	−	0.519081i
$43$	1.63758	+	6.11154i	0.249729	+	0.932001i	0.970947	+	0.239293i	$0.0769158\pi$
$43$	1.63758	+	6.11154i	0.249729	+	0.932001i	−0.721218	+	0.692708i	$0.756418\pi$
$44$	−3.23899	+	1.87003i	−0.488296	+	0.281918i
$45$	−0.410553	+	2.19806i	−0.0612016	+	0.327667i
$46$		−	8.06662i		−	1.18936i
$47$	−0.263120	+	0.981977i	−0.0383800	+	0.143236i	−0.982457	−	0.186489i	$-0.940289\pi$
$47$	−0.263120	+	0.981977i	−0.0383800	+	0.143236i	0.944077	+	0.329725i	$0.106956\pi$
$48$	−0.258819	+	0.965926i	−0.0373573	+	0.139419i
$49$			5.12919i			0.732742i
$50$	4.57337	−	2.02095i	0.646773	−	0.285806i
$51$	3.88850	−	2.24503i	0.544499	−	0.314366i
$52$	−0.512325	−	1.91202i	−0.0710467	−	0.265150i
$53$	−1.81089	+	6.75833i	−0.248745	+	0.928327i	0.722720	+	0.691141i	$0.242892\pi$
$53$	−1.81089	+	6.75833i	−0.248745	+	0.928327i	−0.971464	+	0.237186i	$0.923775\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	−5.44021	+	6.35173i	−0.733557	+	0.856467i
$56$		−	3.48270i		−	0.465395i
$57$	1.13264	−	4.20917i	0.150022	−	0.557518i
$58$	3.14458	−	3.14458i	0.412904	−	0.412904i
$59$	3.04389	−	5.27217i	0.396280	−	0.686377i	−0.596983	−	0.802254i	$-0.703634\pi$
$59$	3.04389	−	5.27217i	0.396280	−	0.686377i	0.993264	+	0.115876i	$0.0369676\pi$
$60$	0.172335	+	2.22942i	0.0222483	+	0.287817i
$61$	6.36253	+	11.0202i	0.814639	+	1.41100i	0.909587	+	0.415513i	$0.136398\pi$
$61$	6.36253	+	11.0202i	0.814639	+	1.41100i	−0.0949486	+	0.995482i	$0.530269\pi$
$62$	−1.03866	+	0.278309i	−0.131910	+	0.0353453i
$63$	3.36403	+	0.901389i	0.423828	+	0.113564i
$64$			1.00000i			0.125000i
$65$	−2.50196	−	3.65126i	−0.310330	−	0.452883i
$66$	−1.87003	−	3.23899i	−0.230185	−	0.398692i
$67$	1.27797	+	0.342430i	0.156129	+	0.0418345i	0.336037	−	0.941849i	$-0.390913\pi$
$67$	1.27797	+	0.342430i	0.156129	+	0.0418345i	−0.179908	+	0.983683i	$0.557580\pi$
$68$	3.17494	−	3.17494i	0.385019	−	0.385019i
$69$	8.06662			0.971107
$70$	−2.58931	−	7.34448i	−0.309482	−	0.877834i
$71$	−12.6042	−	7.27706i	−1.49585	−	0.863628i	−0.495859	−	0.868403i	$-0.665147\pi$
$71$	−12.6042	−	7.27706i	−1.49585	−	0.863628i	−0.999989	+	0.00477557i	$0.998480\pi$
$72$	−0.965926	−	0.258819i	−0.113835	−	0.0305021i
$73$	2.60924	+	9.73783i	0.305389	+	1.13973i	0.932610	+	0.360886i	$0.117526\pi$
$73$	2.60924	+	9.73783i	0.305389	+	1.13973i	−0.627221	+	0.778841i	$0.715808\pi$
$74$	2.21673	+	1.27983i	0.257690	+	0.148777i
$75$	2.02095	+	4.57337i	0.233359	+	0.528088i
$76$	0.00463736	−	4.35890i	0.000531942	−	0.500000i
$77$	9.21043	+	9.21043i	1.04963	+	1.04963i
$78$	1.91202	−	0.512325i	0.216494	−	0.0580094i
$79$	6.64783	−	11.5144i	0.747939	−	1.29547i	−0.200870	−	0.979618i	$-0.564377\pi$
$79$	6.64783	−	11.5144i	0.747939	−	1.29547i	0.948809	−	0.315850i	$-0.102290\pi$
$80$	0.743478	+	2.10885i	0.0831234	+	0.235776i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−1.21903	+	4.54947i	−0.134619	+	0.502405i
$83$	8.69571	−	8.69571i	0.954478	−	0.954478i	−0.0445301	−	0.999008i	$-0.514179\pi$
$83$	8.69571	−	8.69571i	0.954478	−	0.954478i	0.999008	+	0.0445301i	$0.0141791\pi$
$84$	3.48270			0.379994
$85$	4.33497	−	9.05598i	0.470194	−	0.982259i
$86$	−5.47946	+	3.16357i	−0.590865	+	0.341136i
$87$	3.14458	+	3.14458i	0.337134	+	0.337134i
$88$	−2.64462	−	2.64462i	−0.281918	−	0.281918i
$89$	3.14122	+	5.44075i	0.332969	+	0.576719i	0.983093	−	0.183110i	$-0.0586163\pi$
$89$	3.14122	+	5.44075i	0.332969	+	0.576719i	−0.650124	+	0.759828i	$0.725283\pi$
$90$	−2.22942	+	0.172335i	−0.235001	+	0.0181657i
$91$	−5.97030	+	3.44695i	−0.625857	+	0.361339i
$92$	7.79176	−	2.08779i	0.812347	−	0.217668i
$93$	−0.278309	−	1.03866i	−0.0288593	−	0.107704i
$94$	−1.01662			−0.104856
$95$	−3.23097	−	9.19570i	−0.331490	−	0.943459i
$96$	−1.00000			−0.102062
$97$	0.824024	+	3.07530i	0.0836670	+	0.312250i	0.995058	−	0.0992911i	$-0.0316575\pi$
$97$	0.824024	+	3.07530i	0.0836670	+	0.312250i	−0.911391	+	0.411541i	$0.864991\pi$
$98$	−4.95442	+	1.32753i	−0.500472	+	0.134101i
$99$	3.23899	−	1.87003i	0.325531	−	0.187945i
$100$	3.13577	+	3.89448i	0.313577	+	0.389448i
$101$	1.56464	+	2.71004i	0.155688	+	0.269659i	0.933309	−	0.359074i	$-0.116907\pi$
$101$	1.56464	+	2.71004i	0.155688	+	0.269659i	−0.777622	+	0.628733i	$0.783574\pi$
$102$	3.17494	+	3.17494i	0.314366	+	0.314366i
$103$	−2.31802	−	2.31802i	−0.228402	−	0.228402i	0.583623	−	0.812025i	$-0.301635\pi$
$103$	−2.31802	−	2.31802i	−0.228402	−	0.228402i	−0.812025	+	0.583623i	$0.801635\pi$
$104$	1.71427	−	0.989736i	0.168098	−	0.0970516i
$105$	7.34448	−	2.58931i	0.716748	−	0.252691i
$106$	−6.99673			−0.679583
$107$	−6.55783	+	6.55783i	−0.633970	+	0.633970i	−0.949061	−	0.315092i	$-0.897965\pi$
$107$	−6.55783	+	6.55783i	−0.633970	+	0.633970i	0.315092	+	0.949061i	$0.397965\pi$
$108$	0.258819	−	0.965926i	0.0249049	−	0.0929463i
$109$	5.77958	−	10.0105i	0.553583	−	0.958834i	−0.444429	−	0.895814i	$-0.646593\pi$
$109$	5.77958	−	10.0105i	0.553583	−	0.958834i	0.998012	−	0.0630201i	$-0.0200732\pi$
$110$	−7.54333	−	3.61089i	−0.719228	−	0.344285i
$111$	−1.27983	+	2.21673i	−0.121476	+	0.210403i
$112$	3.36403	−	0.901389i	0.317871	−	0.0851732i
$113$	10.0852	+	10.0852i	0.948736	+	0.948736i	0.998749	−	0.0500124i	$-0.0159261\pi$
$113$	10.0852	+	10.0852i	0.948736	+	0.948736i	−0.0500124	+	0.998749i	$0.515926\pi$
$114$	4.35890	+	0.00463736i	0.408248	+	0.000434329i
$115$	14.8794	−	10.1958i	1.38751	−	0.950767i
$116$	3.85131	+	2.22355i	0.357585	+	0.206452i
$117$	0.512325	+	1.91202i	0.0473645	+	0.176767i
$118$	5.88034	+	1.57563i	0.541329	+	0.145049i
$119$	−13.5425	−	7.81875i	−1.24144	−	0.716743i
$120$	−2.10885	+	0.743478i	−0.192511	+	0.0678700i
$121$	2.98807			0.271642
$122$	−8.99798	+	8.99798i	−0.814639	+	0.814639i
$123$	−4.54947	−	1.21903i	−0.410212	−	0.109916i
$124$	−0.537651	−	0.931239i	−0.0482825	−	0.0836278i
$125$	9.50832	+	5.88149i	0.850450	+	0.526057i
$126$			3.48270i			0.310264i
$127$	7.83021	+	2.09810i	0.694819	+	0.186176i	0.588909	−	0.808200i	$-0.299558\pi$
$127$	7.83021	+	2.09810i	0.694819	+	0.186176i	0.105910	+	0.994376i	$0.466224\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−3.16357	−	5.47946i	−0.278536	−	0.482439i
$130$	2.87929	−	3.36173i	0.252531	−	0.294843i
$131$	−9.51576	+	16.4818i	−0.831396	+	1.44002i	0.0655353	+	0.997850i	$0.479124\pi$
$131$	−9.51576	+	16.4818i	−0.831396	+	1.44002i	−0.896931	+	0.442170i	$0.854209\pi$
$132$	2.64462	−	2.64462i	0.230185	−	0.230185i
$133$	−14.6676	+	3.91346i	−1.27185	+	0.339340i
$134$			1.32305i			0.114294i
$135$	−0.172335	−	2.22942i	−0.0148322	−	0.191878i
$136$	3.88850	+	2.24503i	0.333436	+	0.192509i
$137$	−4.27001	+	15.9359i	−0.364812	+	1.36150i	0.502865	+	0.864365i	$0.332279\pi$
$137$	−4.27001	+	15.9359i	−0.364812	+	1.36150i	−0.867676	+	0.497130i	$0.834387\pi$
$138$	2.08779	+	7.79176i	0.177725	+	0.663278i
$139$	1.46967	−	0.848514i	0.124656	−	0.0719700i	−0.436376	−	0.899765i	$-0.643738\pi$
$139$	1.46967	−	0.848514i	0.124656	−	0.0719700i	0.561031	+	0.827795i	$0.310405\pi$
$140$	6.42406	−	4.40198i	0.542932	−	0.372035i
$141$		−	1.01662i		−	0.0856147i
$142$	3.76688	−	14.0582i	0.316110	−	1.17974i
$143$	−1.91613	+	7.15109i	−0.160235	+	0.598004i
$144$		−	1.00000i		−	0.0833333i
$145$	9.77499	+	1.82577i	0.811769	+	0.151622i
$146$	−8.73070	+	5.04067i	−0.722558	+	0.417169i
$147$	−1.32753	−	4.95442i	−0.109493	−	0.408634i
$148$	−0.662489	+	2.47244i	−0.0544562	+	0.203233i
$149$	−6.14165	−	3.54589i	−0.503144	−	0.290490i	0.226867	−	0.973926i	$-0.427152\pi$
$149$	−6.14165	−	3.54589i	−0.503144	−	0.290490i	−0.730011	+	0.683435i	$0.760485\pi$
$150$	−3.89448	+	3.13577i	−0.317983	+	0.256034i
$151$		−	8.43777i		−	0.686656i	−0.939216	−	0.343328i	$-0.888446\pi$
$151$		−	8.43777i		−	0.686656i	0.939216	−	0.343328i	$-0.111554\pi$
$152$	4.21157	−	1.12369i	0.341604	−	0.0911430i
$153$	−3.17494	+	3.17494i	−0.256679	+	0.256679i
$154$	−6.51276	+	11.2804i	−0.524813	+	0.909002i
$155$	−1.82618	−	1.56411i	−0.146682	−	0.125632i
$156$	0.989736	+	1.71427i	0.0792423	+	0.137252i
$157$	19.9741	−	5.35204i	1.59411	−	0.427139i	0.650850	−	0.759206i	$-0.274413\pi$
$157$	19.9741	−	5.35204i	1.59411	−	0.427139i	0.943256	+	0.332067i	$0.107746\pi$
$158$	12.8426	+	3.44117i	1.02170	+	0.273765i
$159$		−	6.99673i		−	0.554877i
$160$	−1.84456	+	1.26396i	−0.145826	+	0.0999244i
$161$	−14.0468	−	24.3298i	−1.10704	−	1.91746i
$162$	0.965926	+	0.258819i	0.0758903	+	0.0203347i
$163$	−16.7203	+	16.7203i	−1.30964	+	1.30964i	−0.387964	+	0.921675i	$0.626821\pi$
$163$	−16.7203	+	16.7203i	−1.30964	+	1.30964i	−0.921675	+	0.387964i	$0.873179\pi$
$164$	−4.70996			−0.367786
$165$	3.61089	−	7.54333i	0.281107	−	0.587247i
$166$	10.6500	+	6.14879i	0.826602	+	0.477239i
$167$	−2.67565	−	0.716938i	−0.207048	−	0.0554783i	0.153804	−	0.988101i	$-0.450847\pi$
$167$	−2.67565	−	0.716938i	−0.207048	−	0.0554783i	−0.360852	+	0.932623i	$0.617514\pi$
$168$	0.901389	+	3.36403i	0.0695437	+	0.259540i
$169$	7.86497	+	4.54085i	0.604998	+	0.349296i
$170$	9.86938	+	1.84340i	0.756947	+	0.141383i
$171$	−0.00463736	+	4.35890i	−0.000354628	+	0.333333i
$172$	−4.47396	−	4.47396i	−0.341136	−	0.341136i
$173$	9.30544	−	2.49338i	0.707479	−	0.189568i	0.112901	−	0.993606i	$-0.463986\pi$
$173$	9.30544	−	2.49338i	0.707479	−	0.189568i	0.594578	+	0.804038i	$0.297319\pi$
$174$	−2.22355	+	3.85131i	−0.168567	+	0.291967i
$175$	10.2746	−	14.0592i	0.776687	−	1.06278i
$176$	1.87003	−	3.23899i	0.140959	−	0.244148i
$177$	−1.57563	+	5.88034i	−0.118432	+	0.441993i
$178$	−4.44236	+	4.44236i	−0.332969	+	0.332969i
$179$	23.0895			1.72579			0.862895	−	0.505384i	$-0.168649\pi$
$179$	23.0895			1.72579			0.862895	+	0.505384i	$0.168649\pi$
$180$	−0.743478	−	2.10885i	−0.0554156	−	0.157184i
$181$	16.1244	−	9.30942i	1.19852	−	0.691964i	0.238292	−	0.971194i	$-0.423413\pi$
$181$	16.1244	−	9.30942i	1.19852	−	0.691964i	0.960224	+	0.279230i	$0.0900792\pi$
$182$	−4.87473	−	4.87473i	−0.361339	−	0.361339i
$183$	−8.99798	−	8.99798i	−0.665150	−	0.665150i
$184$	4.03331	+	6.98590i	0.297340	+	0.515007i
$185$	0.441119	+	5.70655i	0.0324317	+	0.419554i
$186$	0.931239	−	0.537651i	0.0682818	−	0.0394225i
$187$	−16.2209	+	4.34637i	−1.18619	+	0.317838i
$188$	−0.263120	−	0.981977i	−0.0191900	−	0.0716181i
$189$	−3.48270			−0.253329
$190$	8.04613	−	5.50090i	0.583727	−	0.399077i
$191$	−10.0980			−0.730664			−0.365332	−	0.930877i	$-0.619045\pi$
$191$	−10.0980			−0.730664			−0.365332	+	0.930877i	$0.619045\pi$
$192$	−0.258819	−	0.965926i	−0.0186787	−	0.0697097i
$193$	−7.05389	+	1.89008i	−0.507750	+	0.136051i	−0.503595	−	0.863940i	$-0.667989\pi$
$193$	−7.05389	+	1.89008i	−0.507750	+	0.136051i	−0.00415568	+	0.999991i	$0.501323\pi$
$194$	−2.75724	+	1.59189i	−0.197958	+	0.114291i
$195$	3.36173	+	2.87929i	0.240738	+	0.206191i
$196$	−2.56460	−	4.44201i	−0.183185	−	0.317287i
$197$	9.18401	+	9.18401i	0.654333	+	0.654333i	0.954033	−	0.299700i	$-0.0968866\pi$
$197$	9.18401	+	9.18401i	0.654333	+	0.654333i	−0.299700	+	0.954033i	$0.596887\pi$
$198$	2.64462	+	2.64462i	0.187945	+	0.187945i
$199$	−4.81844	+	2.78193i	−0.341570	+	0.197206i	−0.660966	−	0.750416i	$-0.729853\pi$
$199$	−4.81844	+	2.78193i	−0.341570	+	0.197206i	0.319396	+	0.947621i	$0.396520\pi$
$200$	−2.95018	+	4.03688i	−0.208609	+	0.285451i
$201$	−1.32305			−0.0933207
$202$	−2.21274	+	2.21274i	−0.155688	+	0.155688i
$203$	4.00857	−	14.9602i	0.281347	−	1.05000i
$204$	−2.24503	+	3.88850i	−0.157183	+	0.272249i
$205$	−9.93258	+	3.50175i	−0.693722	+	0.244573i
$206$	1.63909	−	2.83899i	0.114201	−	0.197802i
$207$	−7.79176	+	2.08779i	−0.541565	+	0.145112i
$208$	1.39970	+	1.39970i	0.0970516	+	0.0970516i
$209$	−8.16629	+	14.1097i	−0.564874	+	0.975992i
$210$	4.40198	+	6.42406i	0.303765	+	0.443302i
$211$	17.4511	+	10.0754i	1.20138	+	0.693619i	0.960863	−	0.277025i	$-0.0893485\pi$
$211$	17.4511	+	10.0754i	1.20138	+	0.693619i	0.240521	+	0.970644i	$0.422682\pi$
$212$	−1.81089	−	6.75833i	−0.124372	−	0.464164i
$213$	14.0582	+	3.76688i	0.963252	+	0.258102i
$214$	−8.03167	−	4.63709i	−0.549034	−	0.316985i
$215$	−12.7612	−	6.10861i	−0.870306	−	0.416604i
$216$	1.00000			0.0680414
$217$	−2.64808	+	2.64808i	−0.179764	+	0.179764i
$218$	11.1653	+	2.99173i	0.756209	+	0.202625i
$219$	−5.04067	−	8.73070i	−0.340617	−	0.589966i
$220$	1.53549	−	8.22086i	0.103523	−	0.554250i
$221$		−	8.88793i		−	0.597867i
$222$	−2.47244	−	0.662489i	−0.165939	−	0.0444633i
$223$	−17.0400	+	4.56585i	−1.14108	+	0.305752i	−0.779386	−	0.626544i	$-0.784469\pi$
$223$	−17.0400	+	4.56585i	−1.14108	+	0.305752i	−0.361697	+	0.932296i	$0.617802\pi$
$224$	1.74135	+	3.01611i	0.116349	+	0.201522i
$225$	−3.13577	−	3.89448i	−0.209051	−	0.259632i
$226$	−7.13132	+	12.3518i	−0.474368	+	0.821630i
$227$	17.1468	−	17.1468i	1.13807	−	1.13807i	0.149278	−	0.988795i	$-0.452305\pi$
$227$	17.1468	−	17.1468i	1.13807	−	1.13807i	0.988795	−	0.149278i	$-0.0476949\pi$
$228$	1.12369	+	4.21157i	0.0744179	+	0.278918i
$229$		−	4.41482i		−	0.291740i	−0.989304	−	0.145870i	$-0.953402\pi$
$229$		−	4.41482i		−	0.291740i	0.989304	−	0.145870i	$-0.0465981\pi$
$230$	13.6995	+	11.7335i	0.903318	+	0.773685i
$231$	−11.2804	−	6.51276i	−0.742197	−	0.428508i
$232$	−1.15100	+	4.29558i	−0.0755666	+	0.282018i
$233$	−2.68579	−	10.0235i	−0.175952	−	0.656661i	−0.996388	−	0.0849226i	$-0.972936\pi$
$233$	−2.68579	−	10.0235i	−0.175952	−	0.656661i	0.820436	−	0.571739i	$-0.193731\pi$
$234$	−1.71427	+	0.989736i	−0.112066	+	0.0647011i
$235$	−1.28496	−	1.87522i	−0.0838215	−	0.122326i
$236$			6.08777i			0.396280i
$237$	−3.44117	+	12.8426i	−0.223528	+	0.834217i
$238$	4.04728	−	15.1047i	0.262346	−	0.979090i
$239$			7.00921i			0.453388i	0.973966	+	0.226694i	$0.0727918\pi$
$239$			7.00921i			0.453388i	−0.973966	+	0.226694i	$0.927208\pi$
$240$	−1.26396	−	1.84456i	−0.0815879	−	0.119066i
$241$	−13.5253	+	7.80884i	−0.871242	+	0.503012i	−0.867761	−	0.496982i	$-0.834441\pi$
$241$	−13.5253	+	7.80884i	−0.871242	+	0.503012i	−0.00348095	+	0.999994i	$0.501108\pi$
$242$	0.773369	+	2.88625i	0.0497140	+	0.185535i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	−11.0202	−	6.36253i	−0.705498	−	0.407319i
$245$	−8.71088	−	7.46081i	−0.556518	−	0.476653i
$246$		−	4.70996i		−	0.300296i
$247$	−6.09465	−	6.10763i	−0.387793	−	0.388619i
$248$	0.760354	−	0.760354i	0.0482825	−	0.0482825i
$249$	−6.14879	+	10.6500i	−0.389664	+	0.674918i
$250$	−3.22015	+	10.7066i	−0.203660	+	0.677143i
$251$	7.88096	+	13.6502i	0.497442	+	0.861595i	0.999996	−	0.00295141i	$-0.000939464\pi$
$251$	7.88096	+	13.6502i	0.497442	+	0.861595i	−0.502554	+	0.864546i	$0.667606\pi$
$252$	−3.36403	+	0.901389i	−0.211914	+	0.0567822i
$253$	−29.1417	−	7.80848i	−1.83212	−	0.490915i
$254$			8.10643i			0.508643i
$255$	−1.84340	+	9.86938i	−0.115438	+	0.618044i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.146796	−	0.0393339i	−0.00915690	−	0.00245358i	0.254238	−	0.967142i	$-0.418175\pi$
$257$	−0.146796	−	0.0393339i	−0.00915690	−	0.00245358i	−0.263395	+	0.964688i	$0.584842\pi$
$258$	4.47396	−	4.47396i	0.278536	−	0.278536i
$259$	8.91452			0.553922
$260$	3.99240	+	1.91111i	0.247598	+	0.118522i
$261$	−3.85131	−	2.22355i	−0.238390	−	0.137635i
$262$	−18.3830	−	4.92572i	−1.13571	−	0.304312i
$263$	−6.20573	−	23.1601i	−0.382662	−	1.42811i	−0.841820	−	0.539758i	$-0.818516\pi$
$263$	−6.20573	−	23.1601i	−0.382662	−	1.42811i	0.459158	−	0.888355i	$-0.348151\pi$
$264$	3.23899	+	1.87003i	0.199346	+	0.115092i
$265$	−8.84356	−	12.9059i	−0.543255	−	0.792805i
$266$	−7.57638	−	13.1550i	−0.464537	−	0.806583i
$267$	−4.44236	−	4.44236i	−0.271868	−	0.271868i
$268$	−1.27797	+	0.342430i	−0.0780643	+	0.0209173i
$269$	12.7291	−	22.0475i	0.776109	−	1.34426i	−0.158059	−	0.987430i	$-0.550524\pi$
$269$	12.7291	−	22.0475i	0.776109	−	1.34426i	0.934169	−	0.356831i	$-0.116143\pi$
$270$	2.10885	−	0.743478i	0.128340	−	0.0452467i
$271$	9.09668	−	15.7559i	0.552584	−	0.957104i	−0.445503	−	0.895281i	$-0.646975\pi$
$271$	9.09668	−	15.7559i	0.552584	−	0.957104i	0.998087	−	0.0618235i	$-0.0196916\pi$
$272$	−1.16211	+	4.33706i	−0.0704633	+	0.262973i
$273$	4.87473	−	4.87473i	0.295032	−	0.295032i
$274$	−16.4981			−0.996684
$275$	−2.87391	−	18.4782i	−0.173303	−	1.11427i
$276$	−6.98590	+	4.03331i	−0.420502	+	0.242777i
$277$	8.29459	+	8.29459i	0.498373	+	0.498373i	0.910931	−	0.412558i	$-0.135365\pi$
$277$	8.29459	+	8.29459i	0.498373	+	0.498373i	−0.412558	+	0.910931i	$0.635365\pi$
$278$	1.19998	+	1.19998i	0.0719700	+	0.0719700i
$279$	0.537651	+	0.931239i	0.0321883	+	0.0557518i
$280$	5.91465	+	5.06585i	0.353468	+	0.302743i
$281$	10.4255	−	6.01918i	0.621935	−	0.359074i	−0.155687	−	0.987806i	$-0.549759\pi$
$281$	10.4255	−	6.01918i	0.621935	−	0.359074i	0.777622	+	0.628732i	$0.216426\pi$
$282$	0.981977	−	0.263120i	0.0584759	−	0.0156686i
$283$	−4.46814	−	16.6753i	−0.265603	−	0.991245i	−0.961880	−	0.273472i	$-0.911828\pi$
$283$	−4.46814	−	16.6753i	−0.265603	−	0.991245i	0.696277	−	0.717773i	$-0.254839\pi$
$284$	14.5541			0.863628
$285$	5.50090	+	8.04613i	0.325845	+	0.476611i
$286$	−7.40335			−0.437769
$287$	4.24550	+	15.8444i	0.250604	+	0.935267i
$288$	0.965926	−	0.258819i	0.0569177	−	0.0152511i
$289$	2.73712	−	1.58028i	0.161007	−	0.0929574i
$290$	0.766392	+	9.91446i	0.0450041	+	0.582197i
$291$	−1.59189	−	2.75724i	−0.0933184	−	0.161632i
$292$	−7.12859	−	7.12859i	−0.417169	−	0.417169i
$293$	16.7253	+	16.7253i	0.977103	+	0.977103i	0.999744	−	0.0226410i	$-0.00720748\pi$
$293$	16.7253	+	16.7253i	0.977103	+	0.977103i	−0.0226410	+	0.999744i	$0.507207\pi$
$294$	4.44201	−	2.56460i	0.259063	−	0.149570i
$295$	4.52613	+	12.8382i	0.263521	+	0.747468i
$296$	−2.55966			−0.148777
$297$	−2.64462	+	2.64462i	−0.153457	+	0.153457i
$298$	1.83549	−	6.85013i	0.106327	−	0.396817i
$299$	7.98382	−	13.8284i	0.461716	−	0.799716i
$300$	−4.03688	−	2.95018i	−0.233070	−	0.170329i
$301$	−11.0178	+	19.0833i	−0.635053	+	1.09994i
$302$	8.15026	−	2.18386i	0.468995	−	0.125667i
$303$	−2.21274	−	2.21274i	−0.127119	−	0.127119i
$304$	2.17543	+	3.77723i	0.124770	+	0.216639i
$305$	−27.9704	−	5.22431i	−1.60158	−	0.299143i
$306$	−3.88850	−	2.24503i	−0.222291	−	0.128340i
$307$	−1.81966	−	6.79106i	−0.103853	−	0.387586i	0.894359	−	0.447350i	$-0.147632\pi$
$307$	−1.81966	−	6.79106i	−0.103853	−	0.387586i	−0.998213	+	0.0597634i	$0.980965\pi$
$308$	−12.5817	−	3.37125i	−0.716908	−	0.192095i
$309$	2.83899	+	1.63909i	0.161504	+	0.0932446i
$310$	1.03816	−	2.16878i	0.0589637	−	0.123178i
$311$	−5.45137			−0.309119			−0.154559	−	0.987984i	$-0.549396\pi$
$311$	−5.45137			−0.309119			−0.154559	+	0.987984i	$0.549396\pi$
$312$	−1.39970	+	1.39970i	−0.0792423	+	0.0792423i
$313$	4.54437	+	1.21766i	0.256863	+	0.0688262i	0.384952	−	0.922936i	$-0.374218\pi$
$313$	4.54437	+	1.21766i	0.256863	+	0.0688262i	−0.128090	+	0.991763i	$0.540885\pi$
$314$	10.3394	+	17.9083i	0.583483	+	1.01062i
$315$	−6.42406	+	4.40198i	−0.361955	+	0.248023i
$316$			13.2957i			0.747939i
$317$	7.38240	+	1.97811i	0.414637	+	0.111102i	0.460106	−	0.887864i	$-0.347812\pi$
$317$	7.38240	+	1.97811i	0.414637	+	0.111102i	−0.0454689	+	0.998966i	$0.514478\pi$
$318$	6.75833	−	1.81089i	0.378988	−	0.101550i
$319$	−8.31623	−	14.4041i	−0.465619	−	0.806477i
$320$	−1.69830	−	1.45458i	−0.0949376	−	0.0813133i
$321$	4.63709	−	8.03167i	0.258817	−	0.448284i
$322$	19.8652	−	19.8652i	1.10704	−	1.10704i
$323$	5.08563	−	18.8994i	0.282972	−	1.05159i
$324$			1.00000i			0.0555556i
$325$	9.84022	+	1.06197i	0.545837	+	0.0589075i
$326$	−20.4782	−	11.8231i	−1.13418	−	0.654819i
$327$	−2.99173	+	11.1653i	−0.165443	+	0.617442i
$328$	−1.21903	−	4.54947i	−0.0673095	−	0.251202i
$329$	−3.06623	+	1.77029i	−0.169047	+	0.0975991i
$330$	8.22086	+	1.53549i	0.452544	+	0.0845261i
$331$			30.8891i			1.69782i	0.528538	+	0.848910i	$0.322740\pi$
$331$			30.8891i			1.69782i	−0.528538	+	0.848910i	$0.677260\pi$
$332$	−3.18285	+	11.8786i	−0.174682	+	0.651921i
$333$	0.662489	−	2.47244i	0.0363042	−	0.135489i
$334$		−	2.77003i		−	0.151570i
$335$	−2.44045	+	1.67227i	−0.133336	+	0.0913661i
$336$	−3.01611	+	1.74135i	−0.164542	+	0.0949984i
$337$	−4.64493	−	17.3351i	−0.253025	−	0.944303i	−0.969178	−	0.246360i	$-0.920765\pi$
$337$	−4.64493	−	17.3351i	−0.253025	−	0.944303i	0.716153	−	0.697943i	$-0.245901\pi$
$338$	−2.35051	+	8.77224i	−0.127851	+	0.477147i
$339$	−12.3518	−	7.13132i	−0.670858	−	0.387320i
$340$	0.773793	+	10.0102i	0.0419648	+	0.542879i
$341$			4.02170i			0.217787i
$342$	−4.21157	+	1.12369i	−0.227736	+	0.0607620i
$343$	4.60712	−	4.60712i	0.248761	−	0.248761i
$344$	3.16357	−	5.47946i	0.170568	−	0.295433i
$345$	−11.7335	+	13.6995i	−0.631711	+	0.737556i
$346$	4.81685	+	8.34303i	0.258955	+	0.448524i
$347$	16.0250	−	4.29388i	0.860265	−	0.230507i	0.198392	−	0.980123i	$-0.436428\pi$
$347$	16.0250	−	4.29388i	0.860265	−	0.230507i	0.661874	+	0.749615i	$0.269762\pi$
$348$	−4.29558	−	1.15100i	−0.230267	−	0.0616999i
$349$			24.7124i			1.32283i	0.750022	+	0.661413i	$0.230043\pi$
$349$			24.7124i			1.32283i	−0.750022	+	0.661413i	$0.769957\pi$
$350$	16.2395	+	6.28570i	0.868035	+	0.335985i
$351$	−0.989736	−	1.71427i	−0.0528282	−	0.0915011i
$352$	3.61262	+	0.967999i	0.192553	+	0.0515945i
$353$	−4.06778	+	4.06778i	−0.216506	+	0.216506i	−0.807024	−	0.590518i	$-0.798923\pi$
$353$	−4.06778	+	4.06778i	−0.216506	+	0.216506i	0.590518	+	0.807024i	$0.298923\pi$
$354$	−6.08777			−0.323561
$355$	30.6924	−	10.8207i	1.62898	−	0.574301i
$356$	−5.44075	−	3.14122i	−0.288359	−	0.166484i
$357$	15.1047	+	4.04728i	0.799423	+	0.214205i
$358$	5.97600	+	22.3027i	0.315841	+	1.17874i
$359$	−12.2360	−	7.06443i	−0.645789	−	0.372847i	0.141052	−	0.990002i	$-0.454952\pi$
$359$	−12.2360	−	7.06443i	−0.645789	−	0.372847i	−0.786841	+	0.617156i	$0.788285\pi$
$360$	1.84456	−	1.26396i	0.0972171	−	0.0666163i
$361$	−9.46497	−	16.4747i	−0.498156	−	0.867087i
$362$	13.1655	+	13.1655i	0.691964	+	0.691964i
$363$	−2.88625	+	0.773369i	−0.151489	+	0.0405913i
$364$	3.44695	−	5.97030i	0.180669	−	0.312929i
$365$	−20.3331	−	9.73316i	−1.06428	−	0.509457i
$366$	6.36253	−	11.0202i	0.332575	−	0.576036i
$367$	−2.41852	+	9.02604i	−0.126246	+	0.471156i	−0.999881	−	0.0154258i	$-0.995090\pi$
$367$	−2.41852	+	9.02604i	−0.126246	+	0.471156i	0.873635	+	0.486581i	$0.161756\pi$
$368$	−5.70396	+	5.70396i	−0.297340	+	0.297340i
$369$	4.70996			0.245190
$370$	−5.39793	+	1.90305i	−0.280625	+	0.0989349i
$371$	−21.1029	+	12.1838i	−1.09561	+	0.632549i
$372$	0.760354	+	0.760354i	0.0394225	+	0.0394225i
$373$	−4.08162	−	4.08162i	−0.211338	−	0.211338i	0.593497	−	0.804836i	$-0.297747\pi$
$373$	−4.08162	−	4.08162i	−0.211338	−	0.211338i	−0.804836	+	0.593497i	$0.797747\pi$
$374$	−8.39653	−	14.5432i	−0.434174	−	0.752012i
$375$	−10.7066	−	3.22015i	−0.552885	−	0.166288i
$376$	0.880417	−	0.508309i	0.0454040	−	0.0262140i
$377$	8.50297	−	2.27836i	0.437925	−	0.117342i
$378$	−0.901389	−	3.36403i	−0.0463624	−	0.173027i
$379$	−30.2150			−1.55204			−0.776020	−	0.630708i	$-0.782764\pi$
$379$	−30.2150			−1.55204			−0.776020	+	0.630708i	$0.782764\pi$
$380$	7.39595	+	6.34823i	0.379404	+	0.325657i
$381$	−8.10643			−0.415305
$382$	−2.61355	−	9.75390i	−0.133721	−	0.499053i
$383$	−27.3054	+	7.31645i	−1.39524	+	0.373853i	−0.876633	−	0.481160i	$-0.840216\pi$
$383$	−27.3054	+	7.31645i	−1.39524	+	0.373853i	−0.518607	+	0.855013i	$0.673549\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$	−29.0393	+	2.24475i	−1.47998	+	0.114403i
$386$	−3.65136	−	6.32435i	−0.185850	−	0.321901i
$387$	4.47396	+	4.47396i	0.227424	+	0.227424i
$388$	−2.25128	−	2.25128i	−0.114291	−	0.114291i
$389$	−19.9175	+	11.4994i	−1.00986	+	0.583041i	−0.911150	−	0.412075i	$-0.864804\pi$
$389$	−19.9175	+	11.4994i	−1.00986	+	0.583041i	−0.0987073	+	0.995117i	$0.531471\pi$
$390$	−1.91111	+	3.99240i	−0.0967726	+	0.202163i
$391$	36.2195			1.83170
$392$	3.62689	−	3.62689i	0.183185	−	0.183185i
$393$	4.92572	−	18.3830i	0.248470	−	0.927302i
$394$	−6.49407	+	11.2481i	−0.327167	+	0.566669i
$395$	9.88503	+	28.0385i	0.497370	+	1.41077i
$396$	−1.87003	+	3.23899i	−0.0939726	+	0.162765i
$397$	−31.6113	+	8.47022i	−1.58652	+	0.425108i	−0.940938	−	0.338579i	$-0.890054\pi$
$397$	−31.6113	+	8.47022i	−1.58652	+	0.425108i	−0.645587	+	0.763687i	$0.723387\pi$
$398$	−3.93424	−	3.93424i	−0.197206	−	0.197206i
$399$	13.1550	−	7.57638i	0.658572	−	0.379293i
$400$	−4.66289	−	1.80484i	−0.233145	−	0.0902418i
$401$	31.0699	+	17.9382i	1.55156	+	0.895792i	0.998015	+	0.0629707i	$0.0200575\pi$
$401$	31.0699	+	17.9382i	1.55156	+	0.895792i	0.553542	+	0.832821i	$0.313276\pi$
$402$	−0.342430	−	1.27797i	−0.0170789	−	0.0637392i
$403$	−2.05600	−	0.550904i	−0.102417	−	0.0274425i
$404$	−2.71004	−	1.56464i	−0.134830	−	0.0778439i
$405$	0.743478	+	2.10885i	0.0369437	+	0.104789i
$406$	15.4879			0.768653
$407$	6.76934	−	6.76934i	0.335544	−	0.335544i
$408$	−4.33706	−	1.16211i	−0.214716	−	0.0575330i
$409$	−2.29643	−	3.97753i	−0.113551	−	0.196676i	0.803649	−	0.595104i	$-0.202889\pi$
$409$	−2.29643	−	3.97753i	−0.113551	−	0.196676i	−0.917200	+	0.398428i	$0.869556\pi$
$410$	−5.95317	−	8.68782i	−0.294006	−	0.429061i
$411$		−	16.4981i		−	0.813789i
$412$	3.16648	+	0.848455i	0.156001	+	0.0418004i
$413$	20.4794	−	5.48745i	1.00773	−	0.270020i
$414$	−4.03331	−	6.98590i	−0.198226	−	0.343338i
$415$	2.11930	+	27.4165i	0.104033	+	1.34582i
$416$	−0.989736	+	1.71427i	−0.0485258	+	0.0840491i
$417$	−1.19998	+	1.19998i	−0.0587633	+	0.0587633i
$418$	−15.7426	−	4.23616i	−0.769994	−	0.207197i
$419$			11.6070i			0.567039i	0.958967	+	0.283519i	$0.0915020\pi$
$419$			11.6070i			0.567039i	−0.958967	+	0.283519i	$0.908498\pi$
$420$	−5.06585	+	5.91465i	−0.247188	+	0.288605i
$421$	−25.9897	−	15.0051i	−1.26666	−	0.731306i	−0.292305	−	0.956325i	$-0.594422\pi$
$421$	−25.9897	−	15.0051i	−1.26666	−	0.731306i	−0.974354	+	0.225019i	$0.927755\pi$
$422$	−5.21541	+	19.4642i	−0.253882	+	0.947501i
$423$	0.263120	+	0.981977i	0.0127933	+	0.0477454i
$424$	6.05935	−	3.49837i	0.294268	−	0.169896i
$425$	9.07417	+	20.5347i	0.440162	+	0.996078i
$426$			14.5541i			0.705149i
$427$	−11.4702	+	42.8075i	−0.555083	+	2.07160i
$428$	2.40033	−	8.95817i	0.116024	−	0.433009i
$429$		−	7.40335i		−	0.357437i
$430$	2.59762	−	13.9074i	0.125268	−	0.670674i
$431$	−12.4489	+	7.18738i	−0.599643	+	0.346204i	−0.768901	−	0.639368i	$-0.779196\pi$
$431$	−12.4489	+	7.18738i	−0.599643	+	0.346204i	0.169258	+	0.985572i	$0.445863\pi$
$432$	0.258819	+	0.965926i	0.0124524	+	0.0464731i
$433$	3.33854	−	12.4596i	0.160440	−	0.598769i	−0.838138	−	0.545458i	$-0.816356\pi$
$433$	3.33854	−	12.4596i	0.160440	−	0.598769i	0.998578	−	0.0533114i	$-0.0169776\pi$
$434$	−3.24323	−	1.87248i	−0.155680	−	0.0898818i
$435$	−9.91446	+	0.766392i	−0.475362	+	0.0367457i
$436$			11.5592i			0.553583i
$437$	24.8894	−	24.8365i	1.19062	−	1.18809i
$438$	7.12859	−	7.12859i	0.340617	−	0.340617i
$439$	−12.0857	+	20.9330i	−0.576819	+	0.999080i	0.419022	+	0.907976i	$0.362373\pi$
$439$	−12.0857	+	20.9330i	−0.576819	+	0.999080i	−0.995841	+	0.0911040i	$0.970960\pi$
$440$	8.33816	−	0.644544i	0.397506	−	0.0307274i
$441$	2.56460	+	4.44201i	0.122124	+	0.211524i
$442$	8.58508	−	2.30037i	0.408351	−	0.109417i
$443$	40.1662	+	10.7625i	1.90835	+	0.511341i	0.994423	+	0.105467i	$0.0336337\pi$
$443$	40.1662	+	10.7625i	1.90835	+	0.511341i	0.913929	+	0.405874i	$0.133033\pi$
$444$		−	2.55966i		−	0.121476i
$445$	−13.8091	−	2.57927i	−0.654616	−	0.122269i
$446$	−8.82055	−	15.2776i	−0.417665	−	0.723418i
$447$	6.85013	+	1.83549i	0.324000	+	0.0868155i
$448$	−2.46264	+	2.46264i	−0.116349	+	0.116349i
$449$	40.8317			1.92697			0.963484	−	0.267766i	$-0.0862855\pi$
$449$	40.8317			1.92697			0.963484	+	0.267766i	$0.0862855\pi$
$450$	2.95018	−	4.03688i	0.139073	−	0.190300i
$451$	15.2555	+	8.80776i	0.718353	+	0.414741i
$452$	−13.7766	−	3.69144i	−0.647999	−	0.173631i
$453$	2.18386	+	8.15026i	0.102607	+	0.382933i
$454$	21.0005	+	12.1246i	0.985600	+	0.569037i
$455$	2.83031	−	15.1532i	0.132687	−	0.710392i
$456$	−3.77723	+	2.17543i	−0.176885	+	0.101874i
$457$	−8.75083	−	8.75083i	−0.409346	−	0.409346i	0.472164	−	0.881511i	$-0.343473\pi$
$457$	−8.75083	−	8.75083i	−0.409346	−	0.409346i	−0.881511	+	0.472164i	$0.843473\pi$
$458$	4.26439	−	1.14264i	0.199262	−	0.0533920i
$459$	2.24503	−	3.88850i	0.104789	−	0.181500i
$460$	−7.78802	+	16.2696i	−0.363118	+	0.758572i
$461$	10.4858	−	18.1620i	0.488374	−	0.845889i	−0.511536	−	0.859262i	$-0.670923\pi$
$461$	10.4858	−	18.1620i	0.488374	−	0.845889i	0.999911	+	0.0133725i	$0.00425672\pi$
$462$	3.37125	−	12.5817i	0.156845	−	0.585353i
$463$	12.6385	−	12.6385i	0.587360	−	0.587360i	−0.349555	−	0.936916i	$-0.613667\pi$
$463$	12.6385	−	12.6385i	0.587360	−	0.587360i	0.936916	+	0.349555i	$0.113667\pi$
$464$	−4.44711			−0.206452
$465$	2.16878	+	1.03816i	0.100575	+	0.0481437i
$466$	8.98683	−	5.18855i	0.416307	−	0.240355i
$467$	−12.4958	−	12.4958i	−0.578234	−	0.578234i	0.356182	−	0.934417i	$-0.384078\pi$
$467$	−12.4958	−	12.4958i	−0.578234	−	0.578234i	−0.934417	+	0.356182i	$0.884078\pi$
$468$	−1.39970	−	1.39970i	−0.0647011	−	0.0647011i
$469$	2.30389	+	3.99046i	0.106384	+	0.184262i
$470$	1.47875	−	1.72652i	0.0682096	−	0.0796383i
$471$	−17.9083	+	10.3394i	−0.825170	+	0.476412i
$472$	−5.88034	+	1.57563i	−0.270664	+	0.0725243i
$473$	6.12466	+	22.8575i	0.281612	+	1.05099i
$474$	−13.2957			−0.610690
$475$	20.3167	+	7.88871i	0.932194	+	0.361959i
$476$	15.6375			0.716743
$477$	1.81089	+	6.75833i	0.0829149	+	0.309442i
$478$	−6.77038	+	1.81412i	−0.309670	+	0.0829758i
$479$	17.5233	−	10.1171i	0.800658	−	0.462260i	−0.0430433	−	0.999073i	$-0.513705\pi$
$479$	17.5233	−	10.1171i	0.800658	−	0.462260i	0.843701	+	0.536813i	$0.180372\pi$
$480$	1.45458	−	1.69830i	0.0663920	−	0.0775162i
$481$	2.53339	+	4.38796i	0.115513	+	0.200074i
$482$	−11.0434	−	11.0434i	−0.503012	−	0.503012i
$483$	19.8652	+	19.8652i	0.903897	+	0.903897i
$484$	−2.58774	+	1.49403i	−0.117625	+	0.0679106i
$485$	−6.42138	−	3.07382i	−0.291580	−	0.139575i
$486$	−1.00000			−0.0453609
$487$	17.8071	−	17.8071i	0.806919	−	0.806919i	−0.177247	−	0.984166i	$-0.556719\pi$
$487$	17.8071	−	17.8071i	0.806919	−	0.806919i	0.984166	+	0.177247i	$0.0567193\pi$
$488$	3.29349	−	12.2915i	0.149089	−	0.556408i
$489$	11.8231	−	20.4782i	0.534658	−	0.926054i
$490$	4.95204	−	10.3451i	0.223710	−	0.467342i
$491$	−3.64033	+	6.30524i	−0.164286	+	0.284551i	−0.936401	−	0.350931i	$-0.885865\pi$
$491$	−3.64033	+	6.30524i	−0.164286	+	0.284551i	0.772116	+	0.635482i	$0.219199\pi$
$492$	4.54947	−	1.21903i	0.205106	−	0.0549579i
$493$	14.1193	+	14.1193i	0.635902	+	0.635902i
$494$	4.32211	−	7.46775i	0.194461	−	0.335990i
$495$	−1.53549	+	8.22086i	−0.0690153	+	0.369500i
$496$	0.931239	+	0.537651i	0.0418139	+	0.0241413i
$497$	−13.1189	−	48.9605i	−0.588464	−	2.19618i
$498$	−11.8786	−	3.18285i	−0.532291	−	0.142627i
$499$	−4.48607	−	2.59003i	−0.200824	−	0.115946i	0.396216	−	0.918157i	$-0.370323\pi$
$499$	−4.48607	−	2.59003i	−0.200824	−	0.115946i	−0.597040	+	0.802212i	$0.703657\pi$
$500$	−11.1752	−	0.339364i	−0.499770	−	0.0151768i
$501$	2.77003			0.123756
$502$	−11.1454	+	11.1454i	−0.497442	+	0.497442i
$503$	2.69563	+	0.722293i	0.120192	+	0.0322054i	0.318414	−	0.947952i	$-0.396850\pi$
$503$	2.69563	+	0.722293i	0.120192	+	0.0322054i	−0.198221	+	0.980157i	$0.563517\pi$
$504$	−1.74135	−	3.01611i	−0.0775659	−	0.134348i
$505$	−6.87834	−	1.28474i	−0.306082	−	0.0571700i
$506$		−	30.1697i		−	1.34121i
$507$	−8.77224	−	2.35051i	−0.389589	−	0.104390i
$508$	−7.83021	+	2.09810i	−0.347409	+	0.0930881i
$509$	−11.4536	−	19.8382i	−0.507671	−	0.879313i	−0.999961	−	0.00888095i	$-0.997173\pi$
$509$	−11.4536	−	19.8382i	−0.507671	−	0.879313i	0.492289	−	0.870432i	$-0.336160\pi$
$510$	−10.0102	+	0.773793i	−0.443259	+	0.0342641i
$511$	−17.5551	+	30.4064i	−0.776594	+	1.34510i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−1.12369	−	4.21157i	−0.0496120	−	0.185945i
$514$		−	0.151975i		−	0.00670332i
$515$	7.30843	−	0.564945i	0.322048	−	0.0248945i
$516$	5.47946	+	3.16357i	0.241220	+	0.139268i
$517$	−0.984085	+	3.67266i	−0.0432800	+	0.161523i
$518$	2.30725	+	8.61077i	0.101375	+	0.378335i
$519$	−8.34303	+	4.81685i	−0.366218	+	0.211436i
$520$	−0.812678	+	4.35099i	−0.0356383	+	0.190803i
$521$		−	17.2224i		−	0.754529i	−0.926106	−	0.377264i	$-0.876865\pi$
$521$		−	17.2224i		−	0.754529i	0.926106	−	0.377264i	$-0.123135\pi$
$522$	1.15100	−	4.29558i	0.0503777	−	0.188012i
$523$	3.83727	−	14.3209i	0.167792	−	0.626209i	−0.829875	−	0.557949i	$-0.811588\pi$
$523$	3.83727	−	14.3209i	0.167792	−	0.626209i	0.997668	−	0.0682603i	$-0.0217448\pi$
$524$		−	19.0315i		−	0.831396i
$525$	−6.28570	+	16.2395i	−0.274330	+	0.708748i
$526$	20.7648	−	11.9886i	0.905387	−	0.522726i
$527$	−1.24962	−	4.66365i	−0.0544343	−	0.203152i
$528$	−0.967999	+	3.61262i	−0.0421268	+	0.157219i
$529$	36.4340	+	21.0352i	1.58409	+	0.914573i
$530$	10.1773	−	11.8825i	0.442073	−	0.516144i
$531$		−	6.08777i		−	0.264187i
$532$	10.7458	−	10.7230i	0.465890	−	0.464900i
$533$	−6.59252	+	6.59252i	−0.285554	+	0.285554i
$534$	3.14122	−	5.44075i	0.135934	−	0.235444i
$535$	−1.59826	−	20.6760i	−0.0690990	−	0.893902i
$536$	−0.661524	−	1.14579i	−0.0285735	−	0.0494908i
$537$	−22.3027	+	5.97600i	−0.962434	+	0.257883i
$538$	24.5908	+	6.58909i	1.06019	+	0.284076i
$539$			19.1835i			0.826292i
$540$	1.26396	+	1.84456i	0.0543920	+	0.0793774i
$541$	15.0054	+	25.9901i	0.645132	+	1.11740i	0.984271	+	0.176666i	$0.0565311\pi$
$541$	15.0054	+	25.9901i	0.645132	+	1.11740i	−0.339139	+	0.940736i	$0.610136\pi$
$542$	17.5734	+	4.70879i	0.754844	+	0.202260i
$543$	−13.1655	+	13.1655i	−0.564986	+	0.564986i
$544$	−4.49005			−0.192509
$545$	8.59398	+	24.3765i	0.368126	+	1.04417i
$546$	5.97030	+	3.44695i	0.255505	+	0.147516i
$547$	5.88786	+	1.57765i	0.251747	+	0.0674553i	0.382485	−	0.923962i	$-0.375068\pi$
$547$	5.88786	+	1.57765i	0.251747	+	0.0674553i	−0.130739	+	0.991417i	$0.541735\pi$
$548$	−4.27001	−	15.9359i	−0.182406	−	0.680748i
$549$	11.0202	+	6.36253i	0.470332	+	0.271546i
$550$	17.1047	−	7.55849i	0.729347	−	0.322295i
$551$	19.3845	+	0.0206229i	0.825807	+	0.000878563i
$552$	−5.70396	−	5.70396i	−0.242777	−	0.242777i
$553$	44.7270	−	11.9846i	1.90198	−	0.509635i
$554$	−5.86516	+	10.1588i	−0.249187	+	0.431604i
$555$	−1.90305	−	5.39793i	−0.0807800	−	0.229129i
$556$	−0.848514	+	1.46967i	−0.0359850	+	0.0623279i
$557$	−0.0184119	+	0.0687143i	−0.000780139	+	0.00291152i	−0.966315	−	0.257363i	$-0.917146\pi$
$557$	−0.0184119	+	0.0687143i	−0.000780139	+	0.00291152i	0.965535	+	0.260275i	$0.0838131\pi$
$558$	−0.760354	+	0.760354i	−0.0321883	+	0.0321883i
$559$	−12.5244			−0.529725
$560$	−3.36241	+	7.02425i	−0.142088	+	0.296829i
$561$	14.5432	−	8.39653i	0.614015	−	0.354502i
$562$	8.51240	+	8.51240i	0.359074	+	0.359074i
$563$	−2.03008	−	2.03008i	−0.0855575	−	0.0855575i	0.663033	−	0.748590i	$-0.269269\pi$
$563$	−2.03008	−	2.03008i	−0.0855575	−	0.0855575i	−0.748590	+	0.663033i	$0.769269\pi$
$564$	0.508309	+	0.880417i	0.0214037	+	0.0370722i
$565$	−31.7974	+	2.45795i	−1.33772	+	0.103407i
$566$	14.9507	−	8.63178i	0.628424	−	0.362821i
$567$	3.36403	−	0.901389i	0.141276	−	0.0378548i
$568$	3.76688	+	14.0582i	0.158055	+	0.589869i
$569$	0.801049			0.0335817			0.0167909	−	0.999859i	$-0.494655\pi$
$569$	0.801049			0.0335817			0.0167909	+	0.999859i	$0.494655\pi$
$570$	−6.34823	+	7.39595i	−0.265898	+	0.309782i
$571$	38.1859			1.59803			0.799016	−	0.601310i	$-0.205354\pi$
$571$	38.1859			1.59803			0.799016	+	0.601310i	$0.205354\pi$
$572$	−1.91613	−	7.15109i	−0.0801173	−	0.299002i
$573$	9.75390	−	2.61355i	0.407475	−	0.109183i
$574$	−14.2057	+	8.20168i	−0.592936	+	0.342331i
$575$	−4.32767	+	40.1003i	−0.180477	+	1.67230i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−23.8361	−	23.8361i	−0.992310	−	0.992310i	0.00766084	−	0.999971i	$-0.497561\pi$
$577$	−23.8361	−	23.8361i	−0.992310	−	0.992310i	−0.999971	+	0.00766084i	$0.997561\pi$
$578$	2.23485	+	2.23485i	0.0929574	+	0.0929574i
$579$	6.32435	−	3.65136i	0.262831	−	0.151745i
$580$	−9.37827	+	3.30633i	−0.389412	+	0.137288i
$581$	42.8288			1.77684
$582$	2.25128	−	2.25128i	0.0933184	−	0.0933184i
$583$	−6.77283	+	25.2766i	−0.280502	+	1.04685i
$584$	5.04067	−	8.73070i	0.208585	−	0.361279i
$585$	−3.99240	−	1.91111i	−0.165065	−	0.0790145i
$586$	−11.8266	+	20.4842i	−0.488551	+	0.846196i
$587$	−27.1179	+	7.26623i	−1.11928	+	0.299909i	−0.770591	−	0.637330i	$-0.780039\pi$
$587$	−27.1179	+	7.26623i	−1.11928	+	0.299909i	−0.348686	+	0.937240i	$0.613372\pi$
$588$	3.62689	+	3.62689i	0.149570	+	0.149570i
$589$	−4.05668	−	2.34788i	−0.167153	−	0.0967429i
$590$	−11.2293	+	7.69467i	−0.462302	+	0.316785i
$591$	−11.2481	−	6.49407i	−0.462684	−	0.267130i
$592$	−0.662489	−	2.47244i	−0.0272281	−	0.101617i
$593$	31.4304	+	8.42176i	1.29069	+	0.345840i	0.837924	−	0.545787i	$-0.183769\pi$
$593$	31.4304	+	8.42176i	1.29069	+	0.345840i	0.452770	+	0.891628i	$0.350436\pi$
$594$	−3.23899	−	1.87003i	−0.132897	−	0.0767283i
$595$	32.9771	−	11.6261i	1.35193	−	0.476625i
$596$	7.09177			0.290490
$597$	3.93424	−	3.93424i	0.161018	−	0.161018i
$598$	15.4236	+	4.13273i	0.630716	+	0.169000i
$599$	16.5727	+	28.7047i	0.677140	+	1.17284i	0.975838	+	0.218494i	$0.0701143\pi$
$599$	16.5727	+	28.7047i	0.677140	+	1.17284i	−0.298698	+	0.954348i	$0.596552\pi$
$600$	1.80484	−	4.66289i	0.0736821	−	0.190362i
$601$			7.24842i			0.295669i	0.989012	+	0.147835i	$0.0472304\pi$
$601$			7.24842i			0.295669i	−0.989012	+	0.147835i	$0.952770\pi$
$602$	−21.2847	−	5.70321i	−0.867498	−	0.232445i
$603$	1.27797	−	0.342430i	0.0520428	−	0.0139448i
$604$	4.21889	+	7.30733i	0.171664	+	0.297331i
$605$	−4.34637	+	5.07462i	−0.176705	+	0.206313i
$606$	1.56464	−	2.71004i	0.0635593	−	0.110088i
$607$	23.0515	−	23.0515i	0.935630	−	0.935630i	−0.0624201	−	0.998050i	$-0.519882\pi$
$607$	23.0515	−	23.0515i	0.935630	−	0.935630i	0.998050	+	0.0624201i	$0.0198819\pi$
$608$	−3.08548	+	3.07893i	−0.125133	+	0.124867i
$609$			15.4879i			0.627603i
$610$	−2.19297	−	28.3695i	−0.0887909	−	1.14865i
$611$	−1.74276	−	1.00618i	−0.0705045	−	0.0407058i
$612$	1.16211	−	4.33706i	0.0469755	−	0.175315i
$613$	3.30352	+	12.3289i	0.133428	+	0.497961i	0.999999	−	0.00109280i	$-0.000347848\pi$
$613$	3.30352	+	12.3289i	0.133428	+	0.497961i	−0.866571	+	0.499053i	$0.833681\pi$
$614$	6.08870	−	3.51531i	0.245720	−	0.141866i
$615$	8.68782	−	5.95317i	0.350327	−	0.240055i
$616$		−	13.0255i		−	0.524813i
$617$	4.50842	−	16.8256i	0.181502	−	0.677375i	−0.813850	−	0.581075i	$-0.802632\pi$
$617$	4.50842	−	16.8256i	0.181502	−	0.677375i	0.995352	−	0.0963003i	$-0.0307009\pi$
$618$	−0.848455	+	3.16648i	−0.0341299	+	0.127374i
$619$		−	1.77041i		−	0.0711587i	−0.999367	−	0.0355794i	$-0.988672\pi$
$619$		−	1.77041i		−	0.0711587i	0.999367	−	0.0355794i	$-0.0113277\pi$
$620$	2.36357	+	0.441469i	0.0949234	+	0.0177298i
$621$	6.98590	−	4.03331i	0.280334	−	0.161851i
$622$	−1.41092	−	5.26561i	−0.0565726	−	0.211132i
$623$	−5.66292	+	21.1343i	−0.226880	+	0.846728i
$624$	−1.71427	−	0.989736i	−0.0686258	−	0.0396211i
$625$	−23.8191	+	7.59285i	−0.952763	+	0.303714i
$626$			4.70467i			0.188037i
$627$	4.23616	−	15.7426i	0.169176	−	0.628697i
$628$	−14.6221	+	14.6221i	−0.583483	+	0.583483i
$629$	−5.74650	+	9.95323i	−0.229128	+	0.396861i
$630$	−5.91465	−	5.06585i	−0.235645	−	0.201828i
$631$	−20.0302	−	34.6933i	−0.797390	−	1.38112i	−0.921310	−	0.388828i	$-0.872880\pi$
$631$	−20.0302	−	34.6933i	−0.797390	−	1.38112i	0.123920	−	0.992292i	$-0.460453\pi$
$632$	−12.8426	+	3.44117i	−0.510852	+	0.136882i
$633$	−19.4642	−	5.21541i	−0.773631	−	0.207294i
$634$			7.64282i			0.303535i
$635$	−14.9528	+	10.2462i	−0.593385	+	0.406607i
$636$	3.49837	+	6.05935i	0.138719	+	0.240269i
$637$	−9.80714	−	2.62781i	−0.388573	−	0.104118i
$638$	11.7609	−	11.7609i	0.465619	−	0.465619i
$639$	−14.5541			−0.575752
$640$	0.965462	−	2.01690i	0.0381632	−	0.0797249i
$641$	19.4503	+	11.2297i	0.768242	+	0.443545i	0.832247	−	0.554405i	$-0.187054\pi$
$641$	19.4503	+	11.2297i	0.768242	+	0.443545i	−0.0640053	+	0.997950i	$0.520387\pi$
$642$	8.95817	+	2.40033i	0.353551	+	0.0947336i
$643$	−7.86796	−	29.3636i	−0.310282	−	1.15799i	−0.928302	−	0.371826i	$-0.878732\pi$
$643$	−7.86796	−	29.3636i	−0.310282	−	1.15799i	0.618020	−	0.786162i	$-0.287935\pi$
$644$	24.3298	+	14.0468i	0.958728	+	0.553522i
$645$	13.9074	+	2.59762i	0.547603	+	0.102281i
$646$	19.5717	+	0.0208220i	0.770037	+	0.000819230i
$647$	−34.2299	−	34.2299i	−1.34572	−	1.34572i	−0.890255	−	0.455463i	$-0.849474\pi$
$647$	−34.2299	−	34.2299i	−1.34572	−	1.34572i	−0.455463	−	0.890255i	$-0.650526\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	11.3843	−	19.7182i	0.446874	−	0.774008i
$650$	1.52105	+	9.77978i	0.0596606	+	0.383595i
$651$	1.87248	−	3.24323i	0.0733882	−	0.127112i
$652$	6.12007	−	22.8404i	0.239680	−	0.894500i
$653$	−2.83976	+	2.83976i	−0.111129	+	0.111129i	−0.760485	−	0.649356i	$-0.775039\pi$
$653$	−2.83976	+	2.83976i	−0.111129	+	0.111129i	0.649356	+	0.760485i	$0.275039\pi$
$654$	−11.5592			−0.451999
$655$	−14.1495	−	40.1346i	−0.552868	−	1.56819i
$656$	4.07894	−	2.35498i	0.159256	−	0.0919464i
$657$	7.12859	+	7.12859i	0.278113	+	0.278113i
$658$	−2.50356	−	2.50356i	−0.0975991	−	0.0975991i
$659$	−15.9164	−	27.5680i	−0.620015	−	1.07390i	−0.989482	−	0.144653i	$-0.953793\pi$
$659$	−15.9164	−	27.5680i	−0.620015	−	1.07390i	0.369468	−	0.929244i	$-0.379540\pi$
$660$	0.644544	+	8.33816i	0.0250888	+	0.324562i
$661$	29.9775	−	17.3075i	1.16599	−	0.673183i	0.213256	−	0.976996i	$-0.431593\pi$
$661$	29.9775	−	17.3075i	1.16599	−	0.673183i	0.952732	+	0.303813i	$0.0982598\pi$
$662$	−29.8366	+	7.99469i	−1.15963	+	0.310723i
$663$	2.30037	+	8.58508i	0.0893388	+	0.333417i
$664$	−12.2976			−0.477239
$665$	14.6890	−	30.6024i	0.569615	−	1.18671i
$666$	2.55966			0.0991848
$667$	9.28465	+	34.6508i	0.359503	+	1.34168i
$668$	2.67565	−	0.716938i	0.103524	−	0.0277392i
$669$	15.2776	−	8.82055i	0.590668	−	0.341022i
$670$	−2.24693	−	1.92448i	−0.0868064	−	0.0743490i
$671$	23.7963	+	41.2163i	0.918644	+	1.59114i
$672$	−2.46264	−	2.46264i	−0.0949984	−	0.0949984i
$673$	−22.9217	−	22.9217i	−0.883567	−	0.883567i	0.110328	−	0.993895i	$-0.464810\pi$
$673$	−22.9217	−	22.9217i	−0.883567	−	0.883567i	−0.993895	+	0.110328i	$0.964810\pi$
$674$	15.5422	−	8.97331i	0.598664	−	0.345639i
$675$	4.03688	+	2.95018i	0.155380	+	0.113553i
$676$	−9.08169			−0.349296
$677$	−10.0010	+	10.0010i	−0.384368	+	0.384368i	−0.872673	−	0.488305i	$-0.837615\pi$
$677$	−10.0010	+	10.0010i	−0.384368	+	0.384368i	0.488305	+	0.872673i	$0.337615\pi$
$678$	3.69144	−	13.7766i	0.141769	−	0.529089i
$679$	−5.54408	+	9.60264i	−0.212762	+	0.368515i
$680$	−9.46883	+	3.33826i	−0.363113	+	0.128016i
$681$	−12.1246	+	21.0005i	−0.464616	+	0.804739i
$682$	−3.88466	+	1.04089i	−0.148751	+	0.0398578i
$683$	−35.4015	−	35.4015i	−1.35460	−	1.35460i	−0.880437	−	0.474164i	$-0.842750\pi$
$683$	−35.4015	−	35.4015i	−1.35460	−	1.35460i	−0.474164	−	0.880437i	$-0.657250\pi$
$684$	−2.17543	−	3.77723i	−0.0831797	−	0.144426i
$685$	−20.8528	−	30.4317i	−0.796744	−	1.16274i
$686$	5.64255	+	3.25773i	0.215434	+	0.124381i
$687$	1.14264	+	4.26439i	0.0435944	+	0.162697i
$688$	6.11154	+	1.63758i	0.233000	+	0.0624322i
$689$	−11.9943	−	6.92492i	−0.456947	−	0.263818i
$690$	−16.2696	−	7.78802i	−0.619372	−	0.296485i
$691$	47.5837			1.81017			0.905084	−	0.425233i	$-0.139808\pi$
$691$	47.5837			1.81017			0.905084	+	0.425233i	$0.139808\pi$
$692$	−6.81205	+	6.81205i	−0.258955	+	0.258955i
$693$	12.5817	+	3.37125i	0.477938	+	0.128063i
$694$	8.29513	+	14.3676i	0.314879	+	0.545386i
$695$	−0.696720	+	3.73016i	−0.0264281	+	0.141493i
$696$		−	4.44711i		−	0.168567i
$697$	−20.4273	−	5.47349i	−0.773741	−	0.207323i
$698$	−23.8704	+	6.39605i	−0.903507	+	0.242094i
$699$	5.18855	+	8.98683i	0.196249	+	0.339913i
$700$	−1.86844	+	17.3130i	−0.0706204	+	0.654369i
$701$	−9.88044	+	17.1134i	−0.373179	+	0.646365i	−0.990053	−	0.140697i	$-0.955066\pi$
$701$	−9.88044	+	17.1134i	−0.373179	+	0.646365i	0.616874	+	0.787062i	$0.288399\pi$
$702$	1.39970	−	1.39970i	0.0528282	−	0.0528282i
$703$	2.87625	+	10.7802i	0.108480	+	0.406582i
$704$			3.74006i			0.140959i
$705$	1.72652	+	1.47875i	0.0650244	+	0.0556929i
$706$	−4.98200	−	2.87636i	−0.187500	−	0.108253i
$707$	−2.82070	+	10.5270i	−0.106083	+	0.395909i
$708$	−1.57563	−	5.88034i	−0.0592159	−	0.220997i
$709$	−21.0925	+	12.1778i	−0.792147	+	0.457346i	−0.840718	−	0.541474i	$-0.817867\pi$
$709$	−21.0925	+	12.1778i	−0.792147	+	0.457346i	0.0485710	+	0.998820i	$0.484533\pi$
$710$	18.3957	+	26.8460i	0.690380	+	1.00751i
$711$		−	13.2957i		−	0.498626i
$712$	1.62602	−	6.06837i	0.0609375	−	0.227422i
$713$	2.24501	−	8.37850i	0.0840763	−	0.313777i
$714$			15.6375i			0.585218i
$715$	−9.35750	−	13.6560i	−0.349951	−	0.510704i
$716$	−19.9961	+	11.5447i	−0.747289	+	0.431447i
$717$	−1.81412	−	6.77038i	−0.0677495	−	0.252844i
$718$	3.65682	−	13.6474i	0.136471	−	0.509318i
$719$	16.0327	+	9.25647i	0.597918	+	0.345208i	0.768222	−	0.640183i	$-0.221142\pi$
$719$	16.0327	+	9.25647i	0.597918	+	0.345208i	−0.170304	+	0.985392i	$0.554475\pi$
$720$	1.69830	+	1.45458i	0.0632917	+	0.0542089i
$721$		−	11.4169i		−	0.425188i
$722$	13.4636	−	13.4064i	0.501063	−	0.498935i
$723$	11.0434	−	11.0434i	0.410707	−	0.410707i
$724$	−9.30942	+	16.1244i	−0.345982	+	0.599258i
$725$	−17.3192	+	13.9451i	−0.643218	+	0.517908i
$726$	−1.49403	−	2.58774i	−0.0554488	−	0.0960401i
$727$	−33.7149	+	9.03387i	−1.25041	+	0.335048i	−0.822497	−	0.568770i	$-0.807420\pi$
$727$	−33.7149	+	9.03387i	−1.25041	+	0.335048i	−0.427918	+	0.903817i	$0.640753\pi$
$728$	6.65900	+	1.78427i	0.246799	+	0.0661296i
$729$		−	1.00000i		−	0.0370370i
$730$	4.13892	−	22.1594i	0.153188	−	0.820154i
$731$	−14.2046	−	24.6030i	−0.525375	−	0.909976i
$732$	12.2915	+	3.29349i	0.454306	+	0.121731i
$733$	−31.2908	+	31.2908i	−1.15575	+	1.15575i	−0.170371	+	0.985380i	$0.554496\pi$
$733$	−31.2908	+	31.2908i	−1.15575	+	1.15575i	−0.985380	+	0.170371i	$0.945504\pi$
$734$	−9.34445			−0.344910
$735$	10.3451	+	4.95204i	0.381584	+	0.182659i
$736$	−6.98590	−	4.03331i	−0.257504	−	0.148670i
$737$	4.77968	+	1.28071i	0.176062	+	0.0471756i
$738$	1.21903	+	4.54947i	0.0448730	+	0.167468i
$739$	3.05929	+	1.76628i	0.112538	+	0.0649738i	0.555212	−	0.831709i	$-0.312637\pi$
$739$	3.05929	+	1.76628i	0.112538	+	0.0649738i	−0.442675	+	0.896682i	$0.645970\pi$
$740$	−3.23529	−	4.72146i	−0.118932	−	0.173564i
$741$	7.46775	+	4.32211i	0.274335	+	0.158777i
$742$	−17.2304	−	17.2304i	−0.632549	−	0.632549i
$743$	7.04033	−	1.88645i	0.258285	−	0.0692071i	−0.127353	−	0.991857i	$-0.540648\pi$
$743$	7.04033	−	1.88645i	0.258285	−	0.0692071i	0.385638	+	0.922650i	$0.373981\pi$
$744$	−0.537651	+	0.931239i	−0.0197113	+	0.0341409i
$745$	14.9555	−	5.27258i	0.547926	−	0.193172i
$746$	2.88614	−	4.99894i	0.105669	−	0.183024i
$747$	3.18285	−	11.8786i	0.116454	−	0.434614i
$748$	11.8745	−	11.8745i	0.434174	−	0.434174i
$749$	−32.2992			−1.18019
$750$	0.339364	−	11.1752i	0.0123918	−	0.408060i
$751$	13.0032	−	7.50738i	0.474492	−	0.273948i	−0.243626	−	0.969869i	$-0.578337\pi$
$751$	13.0032	−	7.50738i	0.474492	−	0.273948i	0.718118	+	0.695921i	$0.245004\pi$
$752$	0.718857	+	0.718857i	0.0262140	+	0.0262140i
$753$	−11.1454	−	11.1454i	−0.406160	−	0.406160i
$754$	4.40146	+	7.62356i	0.160292	+	0.277634i
$755$	14.3298	+	12.2734i	0.521516	+	0.446674i
$756$	3.01611	−	1.74135i	0.109695	−	0.0633323i
$757$	17.7688	−	4.76115i	0.645820	−	0.173047i	0.0789815	−	0.996876i	$-0.474833\pi$
$757$	17.7688	−	4.76115i	0.645820	−	0.173047i	0.566838	+	0.823829i	$0.308167\pi$
$758$	−7.82021	−	29.1854i	−0.284043	−	1.06006i
$759$	30.1697			1.09509
$760$	−4.21770	+	8.78698i	−0.152992	+	0.318737i
$761$	−14.1228			−0.511950			−0.255975	−	0.966683i	$-0.582396\pi$
$761$	−14.1228			−0.511950			−0.255975	+	0.966683i	$0.582396\pi$
$762$	−2.09810	−	7.83021i	−0.0760061	−	0.283659i
$763$	38.8853	−	10.4193i	1.40774	−	0.377204i
$764$	8.74510	−	5.04899i	0.316387	−	0.182666i
$765$	−0.773793	−	10.0102i	−0.0279765	−	0.361919i
$766$	−14.1343	−	24.4813i	−0.510693	−	0.884547i
$767$	8.52104	+	8.52104i	0.307677	+	0.307677i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	27.0177	−	15.5987i	0.974284	−	0.562503i	0.0737444	−	0.997277i	$-0.476505\pi$
$769$	27.0177	−	15.5987i	0.974284	−	0.562503i	0.900540	+	0.434774i	$0.143172\pi$
$770$	−9.68419	−	27.4688i	−0.348994	−	0.989908i
$771$	0.151975			0.00547323
$772$	5.16381	−	5.16381i	0.185850	−	0.185850i
$773$	−11.6436	+	43.4544i	−0.418790	+	1.56294i	0.358332	+	0.933594i	$0.383346\pi$
$773$	−11.6436	+	43.4544i	−0.418790	+	1.56294i	−0.777122	+	0.629350i	$0.783321\pi$
$774$	−3.16357	+	5.47946i	−0.113712	+	0.196955i
$775$	5.31264	−	0.826277i	0.190836	−	0.0296807i
$776$	1.59189	−	2.75724i	0.0571456	−	0.0989791i
$777$	−8.61077	+	2.30725i	−0.308910	+	0.0827721i
$778$	−16.2626	−	16.2626i	−0.583041	−	0.583041i
$779$	−17.7906	+	10.2462i	−0.637415	+	0.367108i
$780$	−4.35099	−	0.812678i	−0.155790	−	0.0290985i
$781$	−47.1406	−	27.2166i	−1.68682	−	0.973888i
$782$	9.37430	+	34.9854i	0.335224	+	1.25107i
$783$	4.29558	+	1.15100i	0.153511	+	0.0411332i
$784$	4.44201	+	2.56460i	0.158643	+	0.0915927i
$785$	−19.9645	+	41.7069i	−0.712564	+	1.48858i
$786$	19.0315			0.678832
$787$	11.8493	−	11.8493i	0.422381	−	0.422381i	−0.463642	−	0.886023i	$-0.653458\pi$
$787$	11.8493	−	11.8493i	0.422381	−	0.422381i	0.886023	+	0.463642i	$0.153458\pi$
$788$	−12.5456	−	3.36158i	−0.446918	−	0.119751i
$789$	11.9886	+	20.7648i	0.426804	+	0.739246i
$790$	−24.5247	+	16.8051i	−0.872549	+	0.597899i
$791$			49.6725i			1.76615i
$792$	−3.61262	−	0.967999i	−0.128369	−	0.0343964i
$793$	−24.3306	+	6.51937i	−0.864005	+	0.231510i
$794$	−16.3632	−	28.3419i	−0.580708	−	1.00582i
$795$	11.8825	+	10.1773i	0.421430	+	0.360951i
$796$	2.78193	−	4.81844i	0.0986028	−	0.170785i
$797$	−17.0570	+	17.0570i	−0.604191	+	0.604191i	−0.941422	−	0.337231i	$-0.890510\pi$
$797$	−17.0570	+	17.0570i	−0.604191	+	0.604191i	0.337231	+	0.941422i	$0.390510\pi$
$798$	10.7230	+	10.7458i	0.379589	+	0.380398i
$799$		−	4.56466i		−	0.161486i
$800$	0.536492	−	4.97113i	0.0189678	−	0.175756i
$801$	5.44075	+	3.14122i	0.192240	+	0.110990i
$802$	−9.28551	+	34.6540i	−0.327883	+	1.22367i
$803$	9.75874	+	36.4201i	0.344378	+	1.28524i
$804$	1.14579	−	0.661524i	0.0404090	−	0.0233302i
$805$	61.7513	+	11.5339i	2.17645	+	0.406517i
$806$		−	2.12853i		−	0.0749743i
$807$	−6.58909	+	24.5908i	−0.231947	+	0.865638i
$808$	0.809918	−	3.02266i	0.0284928	−	0.106337i
$809$			36.9827i			1.30024i	0.759831	+	0.650120i	$0.225282\pi$
$809$			36.9827i			1.30024i	−0.759831	+	0.650120i	$0.774718\pi$
$810$	−1.84456	+	1.26396i	−0.0648114	+	0.0444109i
$811$	−24.5436	+	14.1703i	−0.861844	+	0.497586i	−0.864629	−	0.502410i	$-0.832447\pi$
$811$	−24.5436	+	14.1703i	−0.861844	+	0.497586i	0.00278563	+	0.999996i	$0.499113\pi$
$812$	4.00857	+	14.9602i	0.140673	+	0.525000i
$813$	−4.70879	+	17.5734i	−0.165144	+	0.616328i
$814$	8.29071	+	4.78664i	0.290589	+	0.167772i
$815$	−4.07506	−	52.7171i	−0.142743	−	1.84660i
$816$		−	4.49005i		−	0.157183i
$817$	−26.6320	−	7.16639i	−0.931735	−	0.250720i
$818$	3.24764	−	3.24764i	0.113551	−	0.113551i
$819$	−3.44695	+	5.97030i	−0.120446	+	0.208619i
$820$	6.85099	−	7.99889i	0.239247	−	0.279334i
$821$	−15.1171	−	26.1836i	−0.527590	−	0.913813i	−0.999483	−	0.0321570i	$-0.989762\pi$
$821$	−15.1171	−	26.1836i	−0.527590	−	0.913813i	0.471893	−	0.881656i	$-0.343571\pi$
$822$	15.9359	−	4.27001i	0.555828	−	0.148934i
$823$	−10.5991	−	2.84002i	−0.369462	−	0.0989969i	0.0693110	−	0.997595i	$-0.477920\pi$
$823$	−10.5991	−	2.84002i	−0.369462	−	0.0989969i	−0.438773	+	0.898598i	$0.644587\pi$
$824$			3.27818i			0.114201i
$825$	7.55849	+	17.1047i	0.263153	+	0.595509i
$826$	10.6009	+	18.3614i	0.368854	+	0.638874i
$827$	−13.2504	−	3.55045i	−0.460763	−	0.123461i	0.0209681	−	0.999780i	$-0.493325\pi$
$827$	−13.2504	−	3.55045i	−0.460763	−	0.123461i	−0.481731	+	0.876319i	$0.659992\pi$
$828$	5.70396	−	5.70396i	0.198226	−	0.198226i
$829$	−10.3770			−0.360407			−0.180203	−	0.983629i	$-0.557676\pi$
$829$	−10.3770			−0.360407			−0.180203	+	0.983629i	$0.557676\pi$
$830$	−25.9337	+	9.14299i	−0.900173	+	0.317358i
$831$	−10.1588	−	5.86516i	−0.352403	−	0.203460i
$832$	−1.91202	−	0.512325i	−0.0662875	−	0.0177617i
$833$	−5.96069	−	22.2456i	−0.206526	−	0.770764i
$834$	−1.46967	−	0.848514i	−0.0508905	−	0.0293816i
$835$	5.10951	−	3.50120i	0.176822	−	0.121164i
$836$	0.0173440	−	16.3025i	0.000599856	−	0.563835i
$837$	−0.760354	−	0.760354i	−0.0262817	−	0.0262817i
$838$	−11.2115	+	3.00411i	−0.387295	+	0.103775i
$839$	−10.6616	+	18.4664i	−0.368080	+	0.637533i	−0.989265	−	0.146131i	$-0.953318\pi$
$839$	−10.6616	+	18.4664i	−0.368080	+	0.637533i	0.621186	+	0.783663i	$0.286651\pi$
$840$	−7.02425	−	3.36241i	−0.242360	−	0.116014i
$841$	4.61162	−	7.98756i	0.159021	−	0.275433i
$842$	7.76723	−	28.9877i	0.267677	−	0.998982i
$843$	−8.51240	+	8.51240i	−0.293183	+	0.293183i
$844$	−20.1508			−0.693619
$845$	−19.1519	+	6.75204i	−0.658846	+	0.232277i
$846$	−0.880417	+	0.508309i	−0.0302694	+	0.0174760i
$847$	7.35853	+	7.35853i	0.252842	+	0.252842i
$848$	4.94744	+	4.94744i	0.169896	+	0.169896i
$849$	8.63178	+	14.9507i	0.296242	+	0.513106i
$850$	−17.4864	+	14.0797i	−0.599779	+	0.482931i
$851$	−17.8815	+	10.3239i	−0.612971	+	0.353899i
$852$	−14.0582	+	3.76688i	−0.481626	+	0.129051i
$853$	1.60657	+	5.99581i	0.0550079	+	0.205292i	0.987960	−	0.154707i	$-0.0494434\pi$
$853$	1.60657	+	5.99581i	0.0550079	+	0.205292i	−0.932952	+	0.360000i	$0.882777\pi$
$854$	−44.3176			−1.51652
$855$	−7.39595	−	6.34823i	−0.252936	−	0.217105i
$856$	9.27418			0.316985
$857$	9.35278	+	34.9050i	0.319485	+	1.19233i	0.919741	+	0.392526i	$0.128399\pi$
$857$	9.35278	+	34.9050i	0.319485	+	1.19233i	−0.600256	+	0.799808i	$0.704935\pi$
$858$	7.15109	−	1.91613i	0.244134	−	0.0654155i
$859$	−44.3854	+	25.6259i	−1.51441	+	0.874344i	−0.514552	+	0.857459i	$0.672042\pi$
$859$	−44.3854	+	25.6259i	−1.51441	+	0.874344i	−0.999857	+	0.0168850i	$0.994625\pi$
$860$	14.1058	−	1.09039i	0.481004	−	0.0371819i
$861$	−8.20168	−	14.2057i	−0.279512	−	0.484130i
$862$	−10.1645	−	10.1645i	−0.346204	−	0.346204i
$863$	−6.15504	−	6.15504i	−0.209520	−	0.209520i	0.594543	−	0.804063i	$-0.297333\pi$
$863$	−6.15504	−	6.15504i	−0.209520	−	0.209520i	−0.804063	+	0.594543i	$0.797333\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	−9.30097	+	19.4302i	−0.316242	+	0.660646i
$866$	12.8991			0.438330
$867$	−2.23485	+	2.23485i	−0.0758994	+	0.0758994i
$868$	0.969266	−	3.61735i	0.0328990	−	0.122781i
$869$	24.8633	−	43.0645i	0.843429	−	1.46086i
$870$	−3.30633	−	9.37827i	−0.112095	−	0.317953i
$871$	−1.30947	+	2.26807i	−0.0443697	+	0.0768505i
$872$	−11.1653	+	2.99173i	−0.378104	+	0.101313i
$873$	2.25128	+	2.25128i	0.0761942	+	0.0761942i
$874$	30.4321	+	17.6132i	1.02938	+	0.595775i
$875$	8.93156	+	37.8996i	0.301942	+	1.28124i
$876$	8.73070	+	5.04067i	0.294983	+	0.170309i
$877$	−1.75453	−	6.54799i	−0.0592462	−	0.221110i	0.929955	−	0.367673i	$-0.119845\pi$
$877$	−1.75453	−	6.54799i	−0.0592462	−	0.221110i	−0.989201	+	0.146563i	$0.953179\pi$
$878$	−23.3478	−	6.25602i	−0.787949	−	0.211130i
$879$	−20.4842	−	11.8266i	−0.690916	−	0.398900i
$880$	2.78066	+	7.88722i	0.0937359	+	0.265878i
$881$	−28.6226			−0.964320			−0.482160	−	0.876083i	$-0.660148\pi$
$881$	−28.6226			−0.964320			−0.482160	+	0.876083i	$0.660148\pi$
$882$	−3.62689	+	3.62689i	−0.122124	+	0.122124i
$883$	−7.52975	−	2.01759i	−0.253396	−	0.0678973i	0.129885	−	0.991529i	$-0.458539\pi$
$883$	−7.52975	−	2.01759i	−0.253396	−	0.0678973i	−0.383281	+	0.923632i	$0.625206\pi$
$884$	4.44396	+	7.69717i	0.149467	+	0.258884i
$885$	−7.69467	−	11.2293i	−0.258653	−	0.377468i
$886$			41.5831i			1.39701i
$887$	16.9519	+	4.54224i	0.569188	+	0.152513i	0.531924	−	0.846792i	$-0.321469\pi$
$887$	16.9519	+	4.54224i	0.569188	+	0.152513i	0.0372638	+	0.999305i	$0.488136\pi$
$888$	2.47244	−	0.662489i	0.0829697	−	0.0222317i
$889$	14.1161	+	24.4499i	0.473440	+	0.820022i
$890$	−1.08268	−	14.0062i	−0.0362917	−	0.469488i
$891$	1.87003	−	3.23899i	0.0626484	−	0.108510i
$892$	12.4741	−	12.4741i	0.417665	−	0.417665i
$893$	−3.13009	−	3.13676i	−0.104744	−	0.104968i
$894$			7.09177i			0.237184i
$895$	−33.5854	+	39.2128i	−1.12264	+	1.31074i
$896$	−3.01611	−	1.74135i	−0.100761	−	0.0581744i
$897$	−4.13273	+	15.4236i	−0.137988	+	0.514978i
$898$	10.5680	+	39.4404i	0.352660	+	1.31614i
$899$	4.14132	−	2.39099i	0.138121	−	0.0797441i
$900$	4.66289	+	1.80484i	0.155430	+	0.0601612i
$901$		−	31.4157i		−	1.04661i
$902$	−4.55923	+	17.0153i	−0.151806	+	0.566547i
$903$	5.70321	−	21.2847i	0.189791	−	0.708309i
$904$		−	14.2626i		−	0.474368i
$905$	−7.64402	+	40.9252i	−0.254096	+	1.36040i
$906$	−7.30733	+	4.21889i	−0.242770	+	0.140163i
$907$	−12.6098	−	47.0604i	−0.418701	−	1.56261i	−0.777305	−	0.629124i	$-0.783414\pi$
$907$	−12.6098	−	47.0604i	−0.418701	−	1.56261i	0.358603	−	0.933490i	$-0.383253\pi$
$908$	−6.27616	+	23.4230i	−0.208282	+	0.777318i
$909$	2.71004	+	1.56464i	0.0898864	+	0.0518959i
$910$	15.3694	−	1.18806i	0.509490	−	0.0393838i
$911$		−	57.4887i		−	1.90469i	−0.305028	−	0.952343i	$-0.598666\pi$
$911$		−	57.4887i		−	1.90469i	0.305028	−	0.952343i	$-0.401334\pi$
$912$	−3.07893	−	3.08548i	−0.101953	−	0.102171i
$913$	32.5225	−	32.5225i	1.07634	−	1.07634i
$914$	6.18777	−	10.7175i	0.204673	−	0.354504i
$915$	28.3695	−	2.19297i	0.937866	−	0.0724974i
$916$	2.20741	+	3.82335i	0.0729349	+	0.126327i
$917$	−64.0226	+	17.1548i	−2.11421	+	0.566502i
$918$	4.33706	+	1.16211i	0.143144	+	0.0383554i
$919$			7.42815i			0.245032i	0.992467	+	0.122516i	$0.0390963\pi$
$919$			7.42815i			0.245032i	−0.992467	+	0.122516i	$0.960904\pi$
$920$	−17.7309	−	3.31177i	−0.584570	−	0.109186i
$921$	3.51531	+	6.08870i	0.115833	+	0.200629i
$922$	20.2571	+	5.42787i	0.667132	+	0.178757i
$923$	20.3714	−	20.3714i	0.670532	−	0.670532i
$924$	13.0255			0.428508
$925$	−10.3330	−	7.55146i	−0.339748	−	0.248291i
$926$	15.4789	+	8.93676i	0.508669	+	0.293680i
$927$	−3.16648	−	0.848455i	−0.104001	−	0.0278669i
$928$	−1.15100	−	4.29558i	−0.0377833	−	0.141009i
$929$	−26.7892	−	15.4667i	−0.878924	−	0.507447i	−0.00862036	−	0.999963i	$-0.502744\pi$
$929$	−26.7892	−	15.4667i	−0.878924	−	0.507447i	−0.870303	+	0.492516i	$0.836077\pi$
$930$	−0.441469	+	2.36357i	−0.0144763	+	0.0775047i
$931$	−19.3504	−	11.1994i	−0.634183	−	0.367046i
$932$	7.33771	+	7.33771i	0.240355	+	0.240355i
$933$	5.26561	−	1.41092i	0.172388	−	0.0461914i
$934$	8.83583	−	15.3041i	0.289117	−	0.500766i
$935$	16.2131	−	33.8699i	0.530224	−	1.10767i
$936$	0.989736	−	1.71427i	0.0323505	−	0.0560328i
$937$	−10.3566	+	38.6513i	−0.338335	+	1.26268i	0.561874	+	0.827223i	$0.310081\pi$
$937$	−10.3566	+	38.6513i	−0.338335	+	1.26268i	−0.900209	+	0.435459i	$0.856586\pi$
$938$	−3.25819	+	3.25819i	−0.106384	+	0.106384i
$939$	−4.70467			−0.153531
$940$	2.05042	+	0.981506i	0.0668772	+	0.0320132i
$941$	16.0738	−	9.28024i	0.523992	−	0.302527i	−0.214574	−	0.976708i	$-0.568836\pi$
$941$	16.0738	−	9.28024i	0.523992	−	0.302527i	0.738567	+	0.674181i	$0.235503\pi$
$942$	−14.6221	−	14.6221i	−0.476412	−	0.476412i
$943$	−26.8654	−	26.8654i	−0.874858	−	0.874858i
$944$	−3.04389	−	5.27217i	−0.0990700	−	0.171594i
$945$	5.06585	−	5.91465i	0.164792	−	0.192404i
$946$	−20.4935	+	11.8319i	−0.666302	+	0.384689i
$947$	40.4136	−	10.8288i	1.31326	−	0.351888i	0.466814	−	0.884356i	$-0.345402\pi$
$947$	40.4136	−	10.8288i	1.31326	−	0.351888i	0.846450	+	0.532468i	$0.178735\pi$
$948$	−3.44117	−	12.8426i	−0.111764	−	0.417109i
$949$	−19.9557			−0.647791
$950$	−2.36156	+	21.6662i	−0.0766193	+	0.702943i
$951$	−7.64282			−0.247835
$952$	4.04728	+	15.1047i	0.131173	+	0.489545i
$953$	−30.5331	+	8.18131i	−0.989064	+	0.265019i	−0.716857	−	0.697220i	$-0.754420\pi$
$953$	−30.5331	+	8.18131i	−0.989064	+	0.265019i	−0.272206	+	0.962239i	$0.587753\pi$
$954$	−6.05935	+	3.49837i	−0.196179	+	0.113264i
$955$	14.6883	−	17.1493i	0.475302	−	0.554940i
$956$	−3.50461	−	6.07016i	−0.113347	−	0.196323i
$957$	11.7609	+	11.7609i	0.380177	+	0.380177i
$958$	14.3077	+	14.3077i	0.462260	+	0.462260i
$959$	−49.7599	+	28.7289i	−1.60683	+	0.927704i
$960$	2.01690	+	0.965462i	0.0650951	+	0.0311602i
$961$	29.8437			0.962701
$962$	−3.58275	+	3.58275i	−0.115513	+	0.115513i
$963$	−2.40033	+	8.95817i	−0.0773497	+	0.288673i
$964$	7.80884	−	13.5253i	0.251506	−	0.435621i
$965$	7.05051	−	14.7289i	0.226964	−	0.474139i
$966$	−14.0468	+	24.3298i	−0.451949	+	0.782798i
$967$	30.4029	−	8.14643i	0.977692	−	0.261972i	0.265619	−	0.964078i	$-0.414424\pi$
$967$	30.4029	−	8.14643i	0.977692	−	0.261972i	0.712072	+	0.702106i	$0.247757\pi$
$968$	−2.11288	−	2.11288i	−0.0679106	−	0.0679106i
$969$	−0.0208220	+	19.5717i	−0.000668899	+	0.628732i
$970$	1.30711	−	6.99814i	0.0419688	−	0.224697i
$971$	37.3466	+	21.5621i	1.19851	+	0.691960i	0.960223	−	0.279235i	$-0.0900808\pi$
$971$	37.3466	+	21.5621i	1.19851	+	0.691960i	0.238287	+	0.971195i	$0.423414\pi$
$972$	−0.258819	−	0.965926i	−0.00830162	−	0.0309821i
$973$	5.70885	+	1.52968i	0.183017	+	0.0490394i
$974$	21.8092	+	12.5916i	0.698812	+	0.403459i
$975$	−9.77978	+	1.52105i	−0.313204	+	0.0487127i
$976$	12.7251			0.407319
$977$	30.0523	−	30.0523i	0.961457	−	0.961457i	−0.0378273	−	0.999284i	$-0.512044\pi$
$977$	30.0523	−	30.0523i	0.961457	−	0.961457i	0.999284	+	0.0378273i	$0.0120437\pi$
$978$	22.8404	+	6.12007i	0.730356	+	0.195698i
$979$	11.7484	+	20.3488i	0.375479	+	0.650349i
$980$	11.2743	+	2.10580i	0.360143	+	0.0672675i
$981$		−	11.5592i		−	0.369055i
$982$	−7.03258	−	1.88437i	−0.224419	−	0.0601328i
$983$	−12.2775	+	3.28976i	−0.391593	+	0.104927i	−0.449242	−	0.893410i	$-0.648306\pi$
$983$	−12.2775	+	3.28976i	−0.391593	+	0.104927i	0.0576497	+	0.998337i	$0.481639\pi$
$984$	2.35498	+	4.07894i	0.0750740	+	0.130032i
$985$	−28.9560	+	2.23831i	−0.922615	+	0.0713185i
$986$	−9.98387	+	17.2926i	−0.317951	+	0.550707i
$987$	2.50356	−	2.50356i	0.0796893	−	0.0796893i
$988$	8.33193	+	2.24204i	0.265074	+	0.0713287i
$989$		−	51.0386i		−	1.62293i
$990$	−8.33816	+	0.644544i	−0.265004	+	0.0204849i
$991$	29.0509	+	16.7726i	0.922833	+	0.532798i	0.884538	−	0.466468i	$-0.154474\pi$
$991$	29.0509	+	16.7726i	0.922833	+	0.532798i	0.0382955	+	0.999266i	$0.487807\pi$
$992$	−0.278309	+	1.03866i	−0.00883631	+	0.0329776i
$993$	−7.99469	−	29.8366i	−0.253704	−	0.946836i
$994$	43.8967	−	25.3438i	1.39232	−	0.803857i
$995$	2.28426	−	12.2297i	0.0724158	−	0.387706i
$996$		−	12.2976i		−	0.389664i
$997$	7.75441	−	28.9399i	0.245585	−	0.916534i	−0.727504	−	0.686103i	$-0.759320\pi$
$997$	7.75441	−	28.9399i	0.245585	−	0.916534i	0.973089	−	0.230431i	$-0.0740136\pi$
$998$	1.34070	−	5.00356i	0.0424391	−	0.158385i
$999$			2.55966i			0.0809840i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.x.a.217.7	yes	40
5.3	odd	4	inner	570.2.x.a.103.8	✓	40
19.12	odd	6	inner	570.2.x.a.487.8	yes	40
95.88	even	12	inner	570.2.x.a.373.7	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.x.a.103.8	✓	40	5.3	odd	4	inner
570.2.x.a.217.7	yes	40	1.1	even	1	trivial
570.2.x.a.373.7	yes	40	95.88	even	12	inner
570.2.x.a.487.8	yes	40	19.12	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.45458 + 1.69830i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.46264 + 2.46264i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.45458 + 1.69830i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.46264 + 2.46264i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-2.01690 - 0.965462i) q^{10} +3.74006 q^{11} +(0.707107 - 0.707107i) q^{12} +(-0.512325 + 1.91202i) q^{13} +(-1.74135 + 3.01611i) q^{14} +(0.965462 - 2.01690i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-4.33706 + 1.16211i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-2.18346 + 3.77260i) q^{19} +(0.410553 - 2.19806i) q^{20} +(-3.01611 - 1.74135i) q^{21} +(0.967999 + 3.61262i) q^{22} +(-7.79176 - 2.08779i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-0.768413 - 4.94060i) q^{25} -1.97947 q^{26} +(-0.707107 + 0.707107i) q^{27} +(-3.36403 - 0.901389i) q^{28} +(-2.22355 - 3.85131i) q^{29} +(2.19806 + 0.410553i) q^{30} +1.07530i q^{31} +(0.965926 + 0.258819i) q^{32} +(-3.61262 + 0.967999i) q^{33} +(-2.24503 - 3.88850i) q^{34} +(-7.76439 + 0.600191i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.80995 - 1.80995i) q^{37} +(-4.20917 - 1.13264i) q^{38} -1.97947i q^{39} +(2.22942 - 0.172335i) q^{40} +(4.07894 + 2.35498i) q^{41} +(0.901389 - 3.36403i) q^{42} +(1.63758 + 6.11154i) q^{43} +(-3.23899 + 1.87003i) q^{44} +(-0.410553 + 2.19806i) q^{45} -8.06662i q^{46} +(-0.263120 + 0.981977i) q^{47} +(-0.258819 + 0.965926i) q^{48} +5.12919i q^{49} +(4.57337 - 2.02095i) q^{50} +(3.88850 - 2.24503i) q^{51} +(-0.512325 - 1.91202i) q^{52} +(-1.81089 + 6.75833i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-5.44021 + 6.35173i) q^{55} -3.48270i q^{56} +(1.13264 - 4.20917i) q^{57} +(3.14458 - 3.14458i) q^{58} +(3.04389 - 5.27217i) q^{59} +(0.172335 + 2.22942i) q^{60} +(6.36253 + 11.0202i) q^{61} +(-1.03866 + 0.278309i) q^{62} +(3.36403 + 0.901389i) q^{63} +1.00000i q^{64} +(-2.50196 - 3.65126i) q^{65} +(-1.87003 - 3.23899i) q^{66} +(1.27797 + 0.342430i) q^{67} +(3.17494 - 3.17494i) q^{68} +8.06662 q^{69} +(-2.58931 - 7.34448i) q^{70} +(-12.6042 - 7.27706i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(2.60924 + 9.73783i) q^{73} +(2.21673 + 1.27983i) q^{74} +(2.02095 + 4.57337i) q^{75} +(0.00463736 - 4.35890i) q^{76} +(9.21043 + 9.21043i) q^{77} +(1.91202 - 0.512325i) q^{78} +(6.64783 - 11.5144i) q^{79} +(0.743478 + 2.10885i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-1.21903 + 4.54947i) q^{82} +(8.69571 - 8.69571i) q^{83} +3.48270 q^{84} +(4.33497 - 9.05598i) q^{85} +(-5.47946 + 3.16357i) q^{86} +(3.14458 + 3.14458i) q^{87} +(-2.64462 - 2.64462i) q^{88} +(3.14122 + 5.44075i) q^{89} +(-2.22942 + 0.172335i) q^{90} +(-5.97030 + 3.44695i) q^{91} +(7.79176 - 2.08779i) q^{92} +(-0.278309 - 1.03866i) q^{93} -1.01662 q^{94} +(-3.23097 - 9.19570i) q^{95} -1.00000 q^{96} +(0.824024 + 3.07530i) q^{97} +(-4.95442 + 1.32753i) q^{98} +(3.23899 - 1.87003i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7}+O(q^{10}) \) 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7	\( 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7} - 12 q^{10} + 8 q^{11} - 24 q^{13} + 20 q^{16} + 8 q^{17} + 12 q^{21} + 24 q^{22} + 16 q^{23} - 16 q^{25} + 32 q^{26} + 4 q^{28} + 16 q^{30} - 24 q^{33} - 4 q^{35} - 20 q^{36} - 8 q^{38} - 36 q^{41} + 4 q^{42} - 4 q^{43} + 8 q^{47} - 24 q^{52} - 16 q^{55} - 8 q^{57} + 16 q^{58} + 12 q^{60} - 8 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{66} - 36 q^{67} - 16 q^{68} + 48 q^{70} + 72 q^{71} - 16 q^{73} - 8 q^{76} + 24 q^{77} + 24 q^{78} + 8 q^{80} + 20 q^{81} - 24 q^{82} - 40 q^{83} - 48 q^{85} + 16 q^{87} - 72 q^{91} - 16 q^{92} + 16 q^{93} - 16 q^{95} - 40 q^{96} + 36 q^{97} - 48 q^{98}+O(q^{100}) \) 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7 - 12 * q^10 + 8 * q^11 - 24 * q^13 + 20 * q^16 + 8 * q^17 + 12 * q^21 + 24 * q^22 + 16 * q^23 - 16 * q^25 + 32 * q^26 + 4 * q^28 + 16 * q^30 - 24 * q^33 - 4 * q^35 - 20 * q^36 - 8 * q^38 - 36 * q^41 + 4 * q^42 - 4 * q^43 + 8 * q^47 - 24 * q^52 - 16 * q^55 - 8 * q^57 + 16 * q^58 + 12 * q^60 - 8 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^66 - 36 * q^67 - 16 * q^68 + 48 * q^70 + 72 * q^71 - 16 * q^73 - 8 * q^76 + 24 * q^77 + 24 * q^78 + 8 * q^80 + 20 * q^81 - 24 * q^82 - 40 * q^83 - 48 * q^85 + 16 * q^87 - 72 * q^91 - 16 * q^92 + 16 * q^93 - 16 * q^95 - 40 * q^96 + 36 * q^97 - 48 * q^98

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