LMFDB - Embedded newform 471.2.e.b.301.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(169,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("471.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			301.5
Character	$\chi$	$=$	471.301
Dual form			471.2.e.b.169.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.479742 q^{2} +(0.500000 - 0.866025i) q^{3} -1.76985 q^{4} +(1.73849 - 3.01115i) q^{5} +(-0.239871 + 0.415469i) q^{6} +2.28663 q^{7} +1.80855 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-0.479742 q^{2} +(0.500000 - 0.866025i) q^{3} -1.76985 q^{4} +(1.73849 - 3.01115i) q^{5} +(-0.239871 + 0.415469i) q^{6} +2.28663 q^{7} +1.80855 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.834027 + 1.44458i) q^{10} +(-0.849585 + 1.47152i) q^{11} +(-0.884924 + 1.53273i) q^{12} +(-0.649034 - 1.12416i) q^{13} -1.09699 q^{14} +(-1.73849 - 3.01115i) q^{15} +2.67206 q^{16} +(3.76433 - 6.52001i) q^{17} +(0.239871 + 0.415469i) q^{18} +(-2.59649 + 4.49725i) q^{19} +(-3.07686 + 5.32928i) q^{20} +(1.14332 - 1.98028i) q^{21} +(0.407582 - 0.705952i) q^{22} -7.81322 q^{23} +(0.904277 - 1.56625i) q^{24} +(-3.54469 - 6.13959i) q^{25} +(0.311369 + 0.539306i) q^{26} -1.00000 q^{27} -4.04699 q^{28} +7.07917 q^{29} +(0.834027 + 1.44458i) q^{30} +(-1.57466 - 2.72739i) q^{31} -4.89901 q^{32} +(0.849585 + 1.47152i) q^{33} +(-1.80591 + 3.12792i) q^{34} +(3.97529 - 6.88540i) q^{35} +(0.884924 + 1.53273i) q^{36} +(-4.61969 - 8.00153i) q^{37} +(1.24564 - 2.15752i) q^{38} -1.29807 q^{39} +(3.14415 - 5.44583i) q^{40} +6.25455 q^{41} +(-0.548497 + 0.950024i) q^{42} +(-1.79132 - 3.10266i) q^{43} +(1.50364 - 2.60437i) q^{44} -3.47698 q^{45} +3.74833 q^{46} +(1.42465 + 2.46757i) q^{47} +(1.33603 - 2.31407i) q^{48} -1.77131 q^{49} +(1.70054 + 2.94542i) q^{50} +(-3.76433 - 6.52001i) q^{51} +(1.14869 + 1.98959i) q^{52} +(6.12735 + 10.6129i) q^{53} +0.479742 q^{54} +(2.95399 + 5.11646i) q^{55} +4.13550 q^{56} +(2.59649 + 4.49725i) q^{57} -3.39617 q^{58} +5.58194 q^{59} +(3.07686 + 5.32928i) q^{60} +(-0.121984 + 0.211283i) q^{61} +(0.755430 + 1.30844i) q^{62} +(-1.14332 - 1.98028i) q^{63} -2.99385 q^{64} -4.51335 q^{65} +(-0.407582 - 0.705952i) q^{66} -5.44544 q^{67} +(-6.66229 + 11.5394i) q^{68} +(-3.90661 + 6.76645i) q^{69} +(-1.90711 + 3.30322i) q^{70} +(1.38250 + 2.39455i) q^{71} +(-0.904277 - 1.56625i) q^{72} +(-2.92141 + 5.06002i) q^{73} +(2.21626 + 3.83867i) q^{74} -7.08938 q^{75} +(4.59539 - 7.95945i) q^{76} +(-1.94269 + 3.36484i) q^{77} +0.622737 q^{78} +17.1080 q^{79} +(4.64534 - 8.04597i) q^{80} +(-0.500000 + 0.866025i) q^{81} -3.00057 q^{82} +(1.56363 + 2.70828i) q^{83} +(-2.02350 + 3.50480i) q^{84} +(-13.0885 - 22.6699i) q^{85} +(0.859372 + 1.48848i) q^{86} +(3.53958 - 6.13074i) q^{87} +(-1.53652 + 2.66133i) q^{88} +(1.23924 - 2.14642i) q^{89} +1.66805 q^{90} +(-1.48410 - 2.57054i) q^{91} +13.8282 q^{92} -3.14932 q^{93} +(-0.683465 - 1.18380i) q^{94} +(9.02794 + 15.6368i) q^{95} +(-2.44950 + 4.24266i) q^{96} +(5.54330 + 9.60128i) q^{97} +0.849773 q^{98} +1.69917 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9}+O(q^{10}) $ 22 * q + 2 * q^2 + 11 * q^3 + 30 * q^4 - 4 * q^5 + q^6 + 4 * q^7 - 11 * q^9	\( 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9} - 5 q^{10} + 15 q^{12} + 3 q^{13} - 14 q^{14} + 4 q^{15} + 54 q^{16} - q^{17} - q^{18} - 22 q^{19} - 7 q^{20} + 2 q^{21} - 22 q^{22} - 10 q^{23} - 15 q^{25} - 10 q^{26} - 22 q^{27} - 38 q^{28} + 22 q^{29} + 5 q^{30} - 6 q^{31} + 32 q^{32} + 17 q^{34} - 11 q^{35} - 15 q^{36} + 8 q^{37} + 14 q^{38} + 6 q^{39} + 32 q^{40} - 7 q^{42} + q^{43} - 12 q^{44} + 8 q^{45} + 24 q^{46} + 7 q^{47} + 27 q^{48} + 22 q^{49} + 13 q^{50} + q^{51} + 17 q^{52} + 30 q^{53} - 2 q^{54} + 31 q^{55} - 82 q^{56} + 22 q^{57} - 90 q^{58} - 16 q^{59} + 7 q^{60} + 8 q^{61} - 28 q^{62} - 2 q^{63} - 32 q^{64} - 68 q^{65} + 22 q^{66} - 38 q^{67} - 8 q^{68} - 5 q^{69} + 43 q^{70} + 45 q^{71} - 4 q^{73} + 3 q^{74} - 30 q^{75} - 33 q^{76} + 21 q^{77} - 20 q^{78} + 26 q^{79} - 12 q^{80} - 11 q^{81} + 16 q^{82} + 8 q^{83} - 19 q^{84} - 28 q^{85} - 16 q^{86} + 11 q^{87} - 65 q^{88} + 15 q^{89} + 10 q^{90} - 3 q^{91} - 18 q^{92} - 12 q^{93} - 28 q^{94} - 5 q^{95} + 16 q^{96} - 35 q^{97} + 90 q^{98}+O(q^{100}) \) 22 * q + 2 * q^2 + 11 * q^3 + 30 * q^4 - 4 * q^5 + q^6 + 4 * q^7 - 11 * q^9 - 5 * q^10 + 15 * q^12 + 3 * q^13 - 14 * q^14 + 4 * q^15 + 54 * q^16 - q^17 - q^18 - 22 * q^19 - 7 * q^20 + 2 * q^21 - 22 * q^22 - 10 * q^23 - 15 * q^25 - 10 * q^26 - 22 * q^27 - 38 * q^28 + 22 * q^29 + 5 * q^30 - 6 * q^31 + 32 * q^32 + 17 * q^34 - 11 * q^35 - 15 * q^36 + 8 * q^37 + 14 * q^38 + 6 * q^39 + 32 * q^40 - 7 * q^42 + q^43 - 12 * q^44 + 8 * q^45 + 24 * q^46 + 7 * q^47 + 27 * q^48 + 22 * q^49 + 13 * q^50 + q^51 + 17 * q^52 + 30 * q^53 - 2 * q^54 + 31 * q^55 - 82 * q^56 + 22 * q^57 - 90 * q^58 - 16 * q^59 + 7 * q^60 + 8 * q^61 - 28 * q^62 - 2 * q^63 - 32 * q^64 - 68 * q^65 + 22 * q^66 - 38 * q^67 - 8 * q^68 - 5 * q^69 + 43 * q^70 + 45 * q^71 - 4 * q^73 + 3 * q^74 - 30 * q^75 - 33 * q^76 + 21 * q^77 - 20 * q^78 + 26 * q^79 - 12 * q^80 - 11 * q^81 + 16 * q^82 + 8 * q^83 - 19 * q^84 - 28 * q^85 - 16 * q^86 + 11 * q^87 - 65 * q^88 + 15 * q^89 + 10 * q^90 - 3 * q^91 - 18 * q^92 - 12 * q^93 - 28 * q^94 - 5 * q^95 + 16 * q^96 - 35 * q^97 + 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.479742			−0.339229			−0.169614	−	0.985511i	$-0.554252\pi$
$2$	−0.479742			−0.339229			−0.169614	+	0.985511i	$0.554252\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−1.76985			−0.884924
$5$	1.73849	−	3.01115i	0.777476	−	1.34663i	−0.155916	−	0.987770i	$-0.549833\pi$
$5$	1.73849	−	3.01115i	0.777476	−	1.34663i	0.933392	−	0.358858i	$-0.116834\pi$
$6$	−0.239871	+	0.415469i	−0.0979269	+	0.169614i
$7$	2.28663			0.864266			0.432133	−	0.901810i	$-0.357761\pi$
$7$	2.28663			0.864266			0.432133	+	0.901810i	$0.357761\pi$
$8$	1.80855			0.639421
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.834027	+	1.44458i	−0.263742	+	0.456815i
$11$	−0.849585	+	1.47152i	−0.256160	+	0.443681i	−0.965210	−	0.261477i	$-0.915791\pi$
$11$	−0.849585	+	1.47152i	−0.256160	+	0.443681i	0.709050	+	0.705158i	$0.249124\pi$
$12$	−0.884924	+	1.53273i	−0.255455	+	0.442462i
$13$	−0.649034	−	1.12416i	−0.180010	−	0.311786i	0.761874	−	0.647725i	$-0.224280\pi$
$13$	−0.649034	−	1.12416i	−0.180010	−	0.311786i	−0.941884	+	0.335940i	$0.890946\pi$
$14$	−1.09699			−0.293184
$15$	−1.73849	−	3.01115i	−0.448876	−	0.777476i
$16$	2.67206			0.668014
$17$	3.76433	−	6.52001i	0.912984	−	1.58133i	0.103157	−	0.994665i	$-0.467105\pi$
$17$	3.76433	−	6.52001i	0.912984	−	1.58133i	0.809826	−	0.586670i	$-0.199561\pi$
$18$	0.239871	+	0.415469i	0.0565381	+	0.0979269i
$19$	−2.59649	+	4.49725i	−0.595675	+	1.03174i	0.397776	+	0.917483i	$0.369782\pi$
$19$	−2.59649	+	4.49725i	−0.595675	+	1.03174i	−0.993451	+	0.114257i	$0.963551\pi$
$20$	−3.07686	+	5.32928i	−0.688007	+	1.19166i
$21$	1.14332	−	1.98028i	0.249492	−	0.432133i
$22$	0.407582	−	0.705952i	0.0868967	−	0.150509i
$23$	−7.81322			−1.62917			−0.814585	−	0.580045i	$-0.803035\pi$
$23$	−7.81322			−1.62917			−0.814585	+	0.580045i	$0.803035\pi$
$24$	0.904277	−	1.56625i	0.184585	−	0.319710i
$25$	−3.54469	−	6.13959i	−0.708938	−	1.22792i
$26$	0.311369	+	0.539306i	0.0610644	+	0.105767i
$27$	−1.00000			−0.192450
$28$	−4.04699			−0.764809
$29$	7.07917			1.31457			0.657284	−	0.753643i	$-0.271705\pi$
$29$	7.07917			1.31457			0.657284	+	0.753643i	$0.271705\pi$
$30$	0.834027	+	1.44458i	0.152272	+	0.263742i
$31$	−1.57466	−	2.72739i	−0.282817	−	0.489854i	0.689260	−	0.724514i	$-0.257936\pi$
$31$	−1.57466	−	2.72739i	−0.282817	−	0.489854i	−0.972077	+	0.234660i	$0.924602\pi$
$32$	−4.89901			−0.866030
$33$	0.849585	+	1.47152i	0.147894	+	0.256160i
$34$	−1.80591	+	3.12792i	−0.309710	+	0.536434i
$35$	3.97529	−	6.88540i	0.671946	−	1.16384i
$36$	0.884924	+	1.53273i	0.147487	+	0.255455i
$37$	−4.61969	−	8.00153i	−0.759472	−	1.31544i	−0.943120	−	0.332452i	$-0.892124\pi$
$37$	−4.61969	−	8.00153i	−0.759472	−	1.31544i	0.183648	−	0.982992i	$-0.441209\pi$
$38$	1.24564	−	2.15752i	0.202070	−	0.349996i
$39$	−1.29807			−0.207857
$40$	3.14415	−	5.44583i	0.497134	−	0.861062i
$41$	6.25455			0.976797			0.488398	−	0.872621i	$-0.337581\pi$
$41$	6.25455			0.976797			0.488398	+	0.872621i	$0.337581\pi$
$42$	−0.548497	+	0.950024i	−0.0846349	+	0.146592i
$43$	−1.79132	−	3.10266i	−0.273174	−	0.473151i	0.696499	−	0.717558i	$-0.254740\pi$
$43$	−1.79132	−	3.10266i	−0.273174	−	0.473151i	−0.969673	+	0.244407i	$0.921407\pi$
$44$	1.50364	−	2.60437i	0.226682	−	0.392624i
$45$	−3.47698			−0.518317
$46$	3.74833			0.552661
$47$	1.42465	+	2.46757i	0.207807	+	0.359932i	0.951023	−	0.309119i	$-0.100034\pi$
$47$	1.42465	+	2.46757i	0.207807	+	0.359932i	−0.743217	+	0.669051i	$0.766701\pi$
$48$	1.33603	−	2.31407i	0.192839	−	0.334007i
$49$	−1.77131			−0.253045
$50$	1.70054	+	2.94542i	0.240492	+	0.416545i
$51$	−3.76433	−	6.52001i	−0.527112	−	0.912984i
$52$	1.14869	+	1.98959i	0.159295	+	0.275907i
$53$	6.12735	+	10.6129i	0.841656	+	1.45779i	0.888494	+	0.458889i	$0.151752\pi$
$53$	6.12735	+	10.6129i	0.841656	+	1.45779i	−0.0468372	+	0.998903i	$0.514914\pi$
$54$	0.479742			0.0652846
$55$	2.95399	+	5.11646i	0.398316	+	0.689903i
$56$	4.13550			0.552629
$57$	2.59649	+	4.49725i	0.343913	+	0.595675i
$58$	−3.39617			−0.445939
$59$	5.58194			0.726706			0.363353	−	0.931652i	$-0.381632\pi$
$59$	5.58194			0.726706			0.363353	+	0.931652i	$0.381632\pi$
$60$	3.07686	+	5.32928i	0.397221	+	0.688007i
$61$	−0.121984	+	0.211283i	−0.0156185	+	0.0270520i	−0.873729	−	0.486413i	$-0.838305\pi$
$61$	−0.121984	+	0.211283i	−0.0156185	+	0.0270520i	0.858111	+	0.513465i	$0.171638\pi$
$62$	0.755430	+	1.30844i	0.0959397	+	0.166172i
$63$	−1.14332	−	1.98028i	−0.144044	−	0.249492i
$64$	−2.99385			−0.374231
$65$	−4.51335			−0.559813
$66$	−0.407582	−	0.705952i	−0.0501698	−	0.0868967i
$67$	−5.44544			−0.665267			−0.332633	−	0.943056i	$-0.607937\pi$
$67$	−5.44544			−0.665267			−0.332633	+	0.943056i	$0.607937\pi$
$68$	−6.66229	+	11.5394i	−0.807921	+	1.39936i
$69$	−3.90661	+	6.76645i	−0.470301	+	0.814585i
$70$	−1.90711	+	3.30322i	−0.227943	+	0.394810i
$71$	1.38250	+	2.39455i	0.164072	+	0.284181i	0.936325	−	0.351134i	$-0.114204\pi$
$71$	1.38250	+	2.39455i	0.164072	+	0.284181i	−0.772253	+	0.635315i	$0.780870\pi$
$72$	−0.904277	−	1.56625i	−0.106570	−	0.184585i
$73$	−2.92141	+	5.06002i	−0.341925	+	0.592231i	−0.984790	−	0.173748i	$-0.944412\pi$
$73$	−2.92141	+	5.06002i	−0.341925	+	0.592231i	0.642865	+	0.765979i	$0.277745\pi$
$74$	2.21626	+	3.83867i	0.257635	+	0.446237i
$75$	−7.08938			−0.818612
$76$	4.59539	−	7.95945i	0.527127	−	0.913011i
$77$	−1.94269	+	3.36484i	−0.221390	+	0.383459i
$78$	0.622737			0.0705111
$79$	17.1080			1.92480			0.962399	−	0.271641i	$-0.0875663\pi$
$79$	17.1080			1.92480			0.962399	+	0.271641i	$0.0875663\pi$
$80$	4.64534	−	8.04597i	0.519365	−	0.899566i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.00057			−0.331358
$83$	1.56363	+	2.70828i	0.171630	+	0.297272i	0.938990	−	0.343944i	$-0.111763\pi$
$83$	1.56363	+	2.70828i	0.171630	+	0.297272i	−0.767360	+	0.641217i	$0.778430\pi$
$84$	−2.02350	+	3.50480i	−0.220781	+	0.382405i
$85$	−13.0885	−	22.6699i	−1.41965	−	2.45890i
$86$	0.859372	+	1.48848i	0.0926684	+	0.160506i
$87$	3.53958	−	6.13074i	0.379483	−	0.657284i
$88$	−1.53652	+	2.66133i	−0.163794	+	0.283699i
$89$	1.23924	−	2.14642i	0.131359	−	0.227520i	−0.792842	−	0.609428i	$-0.791399\pi$
$89$	1.23924	−	2.14642i	0.131359	−	0.227520i	0.924201	+	0.381907i	$0.124733\pi$
$90$	1.66805			0.175828
$91$	−1.48410	−	2.57054i	−0.155576	−	0.269466i
$92$	13.8282			1.44169
$93$	−3.14932			−0.326569
$94$	−0.683465	−	1.18380i	−0.0704941	−	0.122099i
$95$	9.02794	+	15.6368i	0.926247	+	1.60431i
$96$	−2.44950	+	4.24266i	−0.250001	+	0.433015i
$97$	5.54330	+	9.60128i	0.562837	+	0.974862i	0.997247	+	0.0741470i	$0.0236234\pi$
$97$	5.54330	+	9.60128i	0.562837	+	0.974862i	−0.434410	+	0.900715i	$0.643043\pi$
$98$	0.849773			0.0858401
$99$	1.69917			0.170773
$100$	6.27357	+	10.8661i	0.627357	+	1.08661i
$101$	6.26684			0.623574			0.311787	−	0.950152i	$-0.399073\pi$
$101$	6.26684			0.623574			0.311787	+	0.950152i	$0.399073\pi$
$102$	1.80591	+	3.12792i	0.178811	+	0.309710i
$103$	−7.98578			−0.786863			−0.393431	−	0.919354i	$-0.628712\pi$
$103$	−7.98578			−0.786863			−0.393431	+	0.919354i	$0.628712\pi$
$104$	−1.17381	−	2.03310i	−0.115102	−	0.199362i
$105$	−3.97529	−	6.88540i	−0.387948	−	0.671946i
$106$	−2.93955	−	5.09145i	−0.285514	−	0.494525i
$107$	−3.87318	−	6.70855i	−0.374435	−	0.648540i	0.615808	−	0.787897i	$-0.288830\pi$
$107$	−3.87318	−	6.70855i	−0.374435	−	0.648540i	−0.990242	+	0.139357i	$0.955497\pi$
$108$	1.76985			0.170304
$109$	−1.55553	+	2.69426i	−0.148993	+	0.258063i	−0.930855	−	0.365388i	$-0.880936\pi$
$109$	−1.55553	+	2.69426i	−0.148993	+	0.258063i	0.781863	+	0.623451i	$0.214270\pi$
$110$	−1.41715	−	2.45458i	−0.135120	−	0.234035i
$111$	−9.23938			−0.876963
$112$	6.11001			0.577342
$113$	−9.07275	+	15.7145i	−0.853493	+	1.47829i	0.0245435	+	0.999699i	$0.492187\pi$
$113$	−9.07275	+	15.7145i	−0.853493	+	1.47829i	−0.878036	+	0.478594i	$0.841147\pi$
$114$	−1.24564	−	2.15752i	−0.116665	−	0.202070i
$115$	−13.5832	+	23.5268i	−1.26664	+	2.19389i
$116$	−12.5290			−1.16329
$117$	−0.649034	+	1.12416i	−0.0600032	+	0.103929i
$118$	−2.67789			−0.246520
$119$	8.60764	−	14.9089i	0.789061	−	1.36669i
$120$	−3.14415	−	5.44583i	−0.287021	−	0.497134i
$121$	4.05641	+	7.02591i	0.368765	+	0.638719i
$122$	0.0585209	−	0.101361i	0.00529824	−	0.00917682i
$123$	3.12728	−	5.41660i	0.281977	−	0.488398i
$124$	2.78691	+	4.82706i	0.250272	+	0.433483i
$125$	−7.26475			−0.649779
$126$	0.548497	+	0.950024i	0.0488640	+	0.0846349i
$127$	3.11581	+	5.39674i	0.276483	+	0.478883i	0.970508	−	0.241068i	$-0.0774976\pi$
$127$	3.11581	+	5.39674i	0.276483	+	0.478883i	−0.694025	+	0.719951i	$0.744164\pi$
$128$	11.2343			0.992980
$129$	−3.58264			−0.315434
$130$	2.16525			0.189905
$131$	−0.725851	−	1.25721i	−0.0634179	−	0.109843i	0.832573	−	0.553915i	$-0.186867\pi$
$131$	−0.725851	−	1.25721i	−0.0634179	−	0.109843i	−0.895991	+	0.444072i	$0.853533\pi$
$132$	−1.50364	−	2.60437i	−0.130875	−	0.226682i
$133$	−5.93721	+	10.2836i	−0.514822	+	0.891697i
$134$	2.61241			0.225678
$135$	−1.73849	+	3.01115i	−0.149625	+	0.259159i
$136$	6.80799	−	11.7918i	0.583781	−	1.01114i
$137$	8.48983	−	14.7048i	0.725335	−	1.25632i	−0.233500	−	0.972357i	$-0.575018\pi$
$137$	8.48983	−	14.7048i	0.725335	−	1.25632i	0.958836	−	0.283961i	$-0.0916487\pi$
$138$	1.87417	−	3.24615i	0.159540	−	0.276331i
$139$	10.5610	+	18.2923i	0.895776	+	1.55153i	0.832841	+	0.553513i	$0.186713\pi$
$139$	10.5610	+	18.2923i	0.895776	+	1.55153i	0.0629356	+	0.998018i	$0.479954\pi$
$140$	−7.03565	+	12.1861i	−0.594621	+	1.02991i
$141$	2.84930			0.239955
$142$	−0.663241	−	1.14877i	−0.0556580	−	0.0964025i
$143$	2.20564			0.184445
$144$	−1.33603	−	2.31407i	−0.111336	−	0.192839i
$145$	12.3071	−	21.3164i	1.02205	−	1.77023i
$146$	1.40152	−	2.42751i	0.115991	−	0.200902i
$147$	−0.885656	+	1.53400i	−0.0730477	+	0.126522i
$148$	8.17614	+	14.1615i	0.672075	+	1.16407i
$149$	19.8065			1.62261			0.811307	−	0.584621i	$-0.198757\pi$
$149$	19.8065			1.62261			0.811307	+	0.584621i	$0.198757\pi$
$150$	3.40108			0.277697
$151$	−5.83732	+	10.1105i	−0.475034	+	0.822784i	−0.999591	−	0.0285917i	$-0.990898\pi$
$151$	−5.83732	+	10.1105i	−0.475034	+	0.822784i	0.524557	+	0.851376i	$0.324231\pi$
$152$	−4.69589	+	8.13352i	−0.380887	+	0.659716i
$153$	−7.52866			−0.608656
$154$	0.931989	−	1.61425i	0.0751018	−	0.130080i
$155$	−10.9501			−0.879534
$156$	2.29738			0.183938
$157$	9.81073	−	7.79421i	0.782981	−	0.622045i
$157$	9.81073	−	7.79421i	0.782981	−	0.622045i
$158$	−8.20741			−0.652947
$159$	12.2547			0.971861
$160$	−8.51687	+	14.7517i	−0.673318	+	1.16622i
$161$	−17.8660			−1.40804
$162$	0.239871	−	0.415469i	0.0188460	−	0.0326423i
$163$	2.33552	−	4.04524i	0.182932	−	0.316848i	−0.759946	−	0.649987i	$-0.774774\pi$
$163$	2.33552	−	4.04524i	0.182932	−	0.316848i	0.942878	+	0.333139i	$0.108108\pi$
$164$	−11.0696			−0.864391
$165$	5.90798			0.459936
$166$	−0.750138	−	1.29928i	−0.0582220	−	0.100843i
$167$	6.50838	−	11.2729i	0.503634	−	0.872319i	−0.496357	−	0.868118i	$-0.665329\pi$
$167$	6.50838	−	11.2729i	0.503634	−	0.872319i	0.999991	−	0.00420109i	$-0.00133725\pi$
$168$	2.06775	−	3.58145i	0.159530	−	0.276315i
$169$	5.65751	−	9.79910i	0.435193	−	0.753777i
$170$	6.27910	+	10.8757i	0.481585	+	0.834130i
$171$	5.19298			0.397117
$172$	3.17036	+	5.49123i	0.241738	+	0.418702i
$173$	−2.46312			−0.187267			−0.0936337	−	0.995607i	$-0.529848\pi$
$173$	−2.46312			−0.187267			−0.0936337	+	0.995607i	$0.529848\pi$
$174$	−1.69809	+	2.94117i	−0.128732	+	0.222970i
$175$	−8.10541	−	14.0390i	−0.612711	−	1.06125i
$176$	−2.27014	+	3.93199i	−0.171118	+	0.296385i
$177$	2.79097	−	4.83410i	0.209782	−	0.363353i
$178$	−0.594515	+	1.02973i	−0.0445608	+	0.0771815i
$179$	−8.07174	+	13.9807i	−0.603310	+	1.04496i	0.389006	+	0.921235i	$0.372819\pi$
$179$	−8.07174	+	13.9807i	−0.603310	+	1.04496i	−0.992316	+	0.123729i	$0.960515\pi$
$180$	6.15372			0.458671
$181$	−1.27671	+	2.21132i	−0.0948968	+	0.164366i	−0.909566	−	0.415561i	$-0.863585\pi$
$181$	−1.27671	+	2.21132i	−0.0948968	+	0.164366i	0.814669	+	0.579927i	$0.196919\pi$
$182$	0.711986	+	1.23320i	0.0527759	+	0.0914105i
$183$	0.121984	+	0.211283i	0.00901733	+	0.0156185i
$184$	−14.1306			−1.04172
$185$	−32.1251			−2.36189
$186$	1.51086			0.110782
$187$	6.39623	+	11.0786i	0.467739	+	0.810148i
$188$	−2.52142	−	4.36722i	−0.183893	−	0.318512i
$189$	−2.28663			−0.166328
$190$	−4.33108	−	7.50165i	−0.314210	−	0.544227i
$191$	2.16087	−	3.74274i	0.156355	−	0.270815i	−0.777196	−	0.629258i	$-0.783359\pi$
$191$	2.16087	−	3.74274i	0.156355	−	0.270815i	0.933552	+	0.358443i	$0.116692\pi$
$192$	−1.49693	+	2.59275i	−0.108031	+	0.187116i
$193$	−5.86464	−	10.1578i	−0.422146	−	0.731178i	0.574003	−	0.818853i	$-0.305390\pi$
$193$	−5.86464	−	10.1578i	−0.422146	−	0.731178i	−0.996149	+	0.0876751i	$0.972056\pi$
$194$	−2.65935	−	4.60614i	−0.190930	−	0.330701i
$195$	−2.25668	+	3.90868i	−0.161604	+	0.279906i
$196$	3.13495			0.223925
$197$	9.14796	−	15.8447i	0.651765	−	1.12889i	−0.330930	−	0.943655i	$-0.607362\pi$
$197$	9.14796	−	15.8447i	0.651765	−	1.12889i	0.982694	−	0.185234i	$-0.0593044\pi$
$198$	−0.815163			−0.0579311
$199$	−2.51030	+	4.34797i	−0.177951	+	0.308220i	−0.941178	−	0.337910i	$-0.890280\pi$
$199$	−2.51030	+	4.34797i	−0.177951	+	0.308220i	0.763228	+	0.646129i	$0.223613\pi$
$200$	−6.41077	−	11.1038i	−0.453310	−	0.785156i
$201$	−2.72272	+	4.71589i	−0.192046	+	0.332633i
$202$	−3.00647			−0.211534
$203$	16.1874			1.13614
$204$	6.66229	+	11.5394i	0.466454	+	0.807921i
$205$	10.8735	−	18.8334i	0.759436	−	1.31538i
$206$	3.83112			0.266927
$207$	3.90661	+	6.76645i	0.271528	+	0.470301i
$208$	−1.73425	−	3.00382i	−0.120249	−	0.208277i
$209$	−4.41187	−	7.64159i	−0.305176	−	0.528580i
$210$	1.90711	+	3.30322i	0.131603	+	0.227943i
$211$	9.18977			0.632650			0.316325	−	0.948651i	$-0.397551\pi$
$211$	9.18977			0.632650			0.316325	+	0.948651i	$0.397551\pi$
$212$	−10.8445	−	18.7832i	−0.744802	−	1.29003i
$213$	2.76499			0.189454
$214$	1.85813	+	3.21837i	0.127019	+	0.220003i
$215$	−12.4568			−0.849544
$216$	−1.80855			−0.123057
$217$	−3.60067	−	6.23654i	−0.244429	−	0.423364i
$218$	0.746253	−	1.29255i	0.0505426	−	0.0875424i
$219$	2.92141	+	5.06002i	0.197410	+	0.341925i
$220$	−5.22811	−	9.05535i	−0.352479	−	0.610512i
$221$	−9.77271			−0.657383
$222$	4.43252			0.297491
$223$	−1.06722	−	1.84848i	−0.0714663	−	0.123783i	0.828078	−	0.560613i	$-0.189435\pi$
$223$	−1.06722	−	1.84848i	−0.0714663	−	0.123783i	−0.899544	+	0.436830i	$0.856101\pi$
$224$	−11.2022			−0.748480
$225$	−3.54469	+	6.13959i	−0.236313	+	0.409306i
$226$	4.35258	−	7.53889i	0.289529	−	0.501480i
$227$	−2.45975	+	4.26041i	−0.163259	+	0.282774i	−0.936036	−	0.351905i	$-0.885534\pi$
$227$	−2.45975	+	4.26041i	−0.163259	+	0.282774i	0.772776	+	0.634678i	$0.218867\pi$
$228$	−4.59539	−	7.95945i	−0.304337	−	0.527127i
$229$	−1.00550	−	1.74157i	−0.0664451	−	0.115086i	0.830889	−	0.556438i	$-0.187832\pi$
$229$	−1.00550	−	1.74157i	−0.0664451	−	0.115086i	−0.897334	+	0.441352i	$0.854499\pi$
$230$	6.51643	−	11.2868i	0.429681	−	0.744229i
$231$	1.94269	+	3.36484i	0.127820	+	0.221390i
$232$	12.8031			0.840562
$233$	12.7614	−	22.1035i	0.836030	−	1.44805i	−0.0571591	−	0.998365i	$-0.518204\pi$
$233$	12.7614	−	22.1035i	0.836030	−	1.44805i	0.893189	−	0.449681i	$-0.148462\pi$
$234$	0.311369	−	0.539306i	0.0203548	−	0.0352556i
$235$	9.90697			0.646259
$236$	−9.87918			−0.643080
$237$	8.55399	−	14.8159i	0.555641	−	0.962399i
$238$	−4.12945	+	7.15241i	−0.267672	+	0.463622i
$239$	−10.2565			−0.663435			−0.331717	−	0.943379i	$-0.607628\pi$
$239$	−10.2565			−0.663435			−0.331717	+	0.943379i	$0.607628\pi$
$240$	−4.64534	−	8.04597i	−0.299855	−	0.519365i
$241$	−15.1290	+	26.2042i	−0.974544	+	1.68796i	−0.293114	+	0.956078i	$0.594692\pi$
$241$	−15.1290	+	26.2042i	−0.974544	+	1.68796i	−0.681430	+	0.731883i	$0.738642\pi$
$242$	−1.94603	−	3.37062i	−0.125096	−	0.216672i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	0.215893	−	0.373938i	0.0138212	−	0.0239389i
$245$	−3.07941	+	5.33369i	−0.196736	+	0.340757i
$246$	−1.50029	+	2.59857i	−0.0956547	+	0.165679i
$247$	6.74083			0.428909
$248$	−2.84786	−	4.93263i	−0.180839	−	0.313222i
$249$	3.12725			0.198182
$250$	3.48520			0.220424
$251$	9.55640	+	16.5522i	0.603195	+	1.04476i	0.992334	+	0.123585i	$0.0394391\pi$
$251$	9.55640	+	16.5522i	0.603195	+	1.04476i	−0.389139	+	0.921179i	$0.627228\pi$
$252$	2.02350	+	3.50480i	0.127468	+	0.220781i
$253$	6.63800	−	11.4973i	0.417327	−	0.722832i
$254$	−1.49478	−	2.58904i	−0.0937911	−	0.162451i
$255$	−26.1770			−1.63927
$256$	0.598143			0.0373839
$257$	−0.341582	−	0.591637i	−0.0213073	−	0.0369053i	0.855175	−	0.518339i	$-0.173450\pi$
$257$	−0.341582	−	0.591637i	−0.0213073	−	0.0369053i	−0.876482	+	0.481434i	$0.840116\pi$
$258$	1.71874			0.107004
$259$	−10.5635	−	18.2966i	−0.656386	−	1.13689i
$260$	7.98795			0.495391
$261$	−3.53958	−	6.13074i	−0.219095	−	0.379483i
$262$	0.348221	+	0.603137i	0.0215132	+	0.0372619i
$263$	−1.90878	−	3.30610i	−0.117700	−	0.203863i	0.801156	−	0.598456i	$-0.204219\pi$
$263$	−1.90878	−	3.30610i	−0.117700	−	0.203863i	−0.918856	+	0.394593i	$0.870886\pi$
$264$	1.53652	+	2.66133i	0.0945663	+	0.163794i
$265$	42.6093			2.61747
$266$	2.84833	−	4.93345i	0.174642	−	0.302489i
$267$	−1.23924	−	2.14642i	−0.0758401	−	0.131359i
$268$	9.63761			0.588711
$269$	−19.0745			−1.16299			−0.581496	−	0.813549i	$-0.697532\pi$
$269$	−19.0745			−1.16299			−0.581496	+	0.813549i	$0.697532\pi$
$270$	0.834027	−	1.44458i	0.0507572	−	0.0879141i
$271$	−1.74172	−	3.01675i	−0.105802	−	0.183255i	0.808263	−	0.588821i	$-0.200408\pi$
$271$	−1.74172	−	3.01675i	−0.105802	−	0.183255i	−0.914066	+	0.405566i	$0.867074\pi$
$272$	10.0585	−	17.4218i	0.609886	−	1.05635i
$273$	−2.96820			−0.179644
$274$	−4.07293	+	7.05452i	−0.246055	+	0.426179i
$275$	12.0461			0.726405
$276$	6.91411	−	11.9756i	0.416180	−	0.720845i
$277$	2.65395	+	4.59678i	0.159461	+	0.276194i	0.934674	−	0.355505i	$-0.115691\pi$
$277$	2.65395	+	4.59678i	0.159461	+	0.276194i	−0.775214	+	0.631699i	$0.782358\pi$
$278$	−5.06658	−	8.77557i	−0.303873	−	0.526324i
$279$	−1.57466	+	2.72739i	−0.0942724	+	0.163285i
$280$	7.18952	−	12.4526i	0.429656	−	0.744186i
$281$	11.9912	+	20.7694i	0.715335	+	1.23900i	0.962830	+	0.270107i	$0.0870592\pi$
$281$	11.9912	+	20.7694i	0.715335	+	1.23900i	−0.247495	+	0.968889i	$0.579607\pi$
$282$	−1.36693			−0.0813995
$283$	−10.1377	−	17.5590i	−0.602622	−	1.04377i	−0.992422	−	0.122872i	$-0.960789\pi$
$283$	−10.1377	−	17.5590i	−0.602622	−	1.04377i	0.389801	−	0.920899i	$-0.372544\pi$
$284$	−2.44681	−	4.23799i	−0.145191	−	0.251479i
$285$	18.0559			1.06954
$286$	−1.05814			−0.0625689
$287$	14.3019			0.844212
$288$	2.44950	+	4.24266i	0.144338	+	0.250001i
$289$	−19.8403	−	34.3645i	−1.16708	−	2.02144i
$290$	−5.90421	+	10.2264i	−0.346707	+	0.600515i
$291$	11.0866			0.649908
$292$	5.17044	−	8.95547i	0.302577	−	0.524079i
$293$	−6.89681	+	11.9456i	−0.402916	+	0.697871i	−0.994076	−	0.108683i	$-0.965337\pi$
$293$	−6.89681	+	11.9456i	−0.402916	+	0.697871i	0.591161	+	0.806554i	$0.298670\pi$
$294$	0.424887	−	0.735925i	0.0247799	−	0.0429200i
$295$	9.70414	−	16.8081i	0.564997	−	0.978603i
$296$	−8.35496	−	14.4712i	−0.485622	−	0.841122i
$297$	0.849585	−	1.47152i	0.0492979	−	0.0853865i
$298$	−9.50202			−0.550437
$299$	5.07104	+	8.78330i	0.293266	+	0.507952i
$300$	12.5471			0.724409
$301$	−4.09609	−	7.09464i	−0.236095	−	0.408928i
$302$	2.80041	−	4.85045i	0.161145	−	0.279112i
$303$	3.13342	−	5.42724i	0.180010	−	0.311787i
$304$	−6.93796	+	12.0169i	−0.397919	+	0.689217i
$305$	0.424136	+	0.734626i	0.0242860	+	0.0420646i
$306$	3.61181			0.206474
$307$	0.831770			0.0474716			0.0237358	−	0.999718i	$-0.492444\pi$
$307$	0.831770			0.0474716			0.0237358	+	0.999718i	$0.492444\pi$
$308$	3.43826	−	5.95525i	0.195913	−	0.339332i
$309$	−3.99289	+	6.91589i	−0.227148	+	0.393431i
$310$	5.25323			0.298363
$311$	13.5394	−	23.4510i	0.767752	−	1.32978i	−0.171028	−	0.985266i	$-0.554709\pi$
$311$	13.5394	−	23.4510i	0.767752	−	1.32978i	0.938780	−	0.344518i	$-0.111958\pi$
$312$	−2.34763			−0.132908
$313$	−29.6698			−1.67704			−0.838518	−	0.544874i	$-0.816577\pi$
$313$	−29.6698			−1.67704			−0.838518	+	0.544874i	$0.816577\pi$
$314$	−4.70662	+	3.73921i	−0.265610	+	0.211016i
$315$	−7.95057			−0.447964
$316$	−30.2785			−1.70330
$317$	−4.96022	+	8.59135i	−0.278594	+	0.482538i	−0.971035	−	0.238935i	$-0.923202\pi$
$317$	−4.96022	+	8.59135i	−0.278594	+	0.482538i	0.692442	+	0.721474i	$0.256535\pi$
$318$	−5.87910			−0.329683
$319$	−6.01435	+	10.4172i	−0.336739	+	0.583249i
$320$	−5.20478	+	9.01494i	−0.290956	+	0.503951i
$321$	−7.74636			−0.432360
$322$	8.57105			0.477646
$323$	19.5481	+	33.8583i	1.08768	+	1.88392i
$324$	0.884924	−	1.53273i	0.0491624	−	0.0851518i
$325$	−4.60125	+	7.96960i	−0.255231	+	0.442074i
$326$	−1.12045	+	1.94067i	−0.0620558	+	0.107484i
$327$	1.55553	+	2.69426i	0.0860210	+	0.148993i
$328$	11.3117			0.624584
$329$	3.25765	+	5.64242i	0.179600	+	0.311077i
$330$	−2.83431			−0.156023
$331$	11.1441	−	19.3021i	0.612533	−	1.06094i	−0.378279	−	0.925692i	$-0.623484\pi$
$331$	11.1441	−	19.3021i	0.612533	−	1.06094i	0.990812	−	0.135246i	$-0.0431826\pi$
$332$	−2.76738	−	4.79324i	−0.151880	−	0.263063i
$333$	−4.61969	+	8.00153i	−0.253157	+	0.438481i
$334$	−3.12235	+	5.40806i	−0.170847	+	0.295916i
$335$	−9.46685	+	16.3971i	−0.517229	+	0.895867i
$336$	3.05500	−	5.29142i	0.166664	−	0.288671i
$337$	−31.1839			−1.69869			−0.849347	−	0.527836i	$-0.823004\pi$
$337$	−31.1839			−1.69869			−0.849347	+	0.527836i	$0.823004\pi$
$338$	−2.71415	+	4.70104i	−0.147630	+	0.255703i
$339$	9.07275	+	15.7145i	0.492764	+	0.853493i
$340$	23.1646	+	40.1223i	1.25628	+	2.17594i
$341$	5.35123			0.289785
$342$	−2.49129			−0.134713
$343$	−20.0568			−1.08296
$344$	−3.23970	−	5.61133i	−0.174673	−	0.302542i
$345$	13.5832	+	23.5268i	0.731295	+	1.26664i
$346$	1.18166			0.0635265
$347$	−0.412520	−	0.714506i	−0.0221453	−	0.0383567i	0.854740	−	0.519056i	$-0.173716\pi$
$347$	−0.412520	−	0.714506i	−0.0221453	−	0.0383567i	−0.876886	+	0.480699i	$0.840383\pi$
$348$	−6.26452	+	10.8505i	−0.335814	+	0.581646i
$349$	−12.1626	+	21.0663i	−0.651050	+	1.12765i	0.331819	+	0.943343i	$0.392338\pi$
$349$	−12.1626	+	21.0663i	−0.651050	+	1.12765i	−0.982869	+	0.184308i	$0.940996\pi$
$350$	3.88851	+	6.73509i	0.207849	+	0.360006i
$351$	0.649034	+	1.12416i	0.0346429	+	0.0600032i
$352$	4.16212	−	7.20901i	0.221842	−	0.384241i
$353$	−20.0034			−1.06467			−0.532336	−	0.846533i	$-0.678686\pi$
$353$	−20.0034			−1.06467			−0.532336	+	0.846533i	$0.678686\pi$
$354$	−1.33894	+	2.31912i	−0.0711641	+	0.123260i
$355$	9.61382			0.510249
$356$	−2.19326	+	3.79884i	−0.116243	+	0.201338i
$357$	−8.60764	−	14.9089i	−0.455564	−	0.789061i
$358$	3.87235	−	6.70711i	0.204660	−	0.354482i
$359$	−20.7519			−1.09524			−0.547621	−	0.836726i	$-0.684466\pi$
$359$	−20.7519			−1.09524			−0.547621	+	0.836726i	$0.684466\pi$
$360$	−6.28831			−0.331423
$361$	−3.98350	−	6.89963i	−0.209658	−	0.363138i
$362$	0.612489	−	1.06086i	0.0321917	−	0.0557577i
$363$	8.11282			0.425813
$364$	2.62663	+	4.54946i	0.137673	+	0.238457i
$365$	10.1577	+	17.5936i	0.531677	+	0.920891i
$366$	−0.0585209	−	0.101361i	−0.00305894	−	0.00529824i
$367$	16.5431	+	28.6535i	0.863544	+	1.49570i	0.868486	+	0.495713i	$0.165093\pi$
$367$	16.5431	+	28.6535i	0.863544	+	1.49570i	−0.00494264	+	0.999988i	$0.501573\pi$
$368$	−20.8774			−1.08831
$369$	−3.12728	−	5.41660i	−0.162799	−	0.281977i
$370$	15.4118			0.801220
$371$	14.0110	+	24.2678i	0.727415	+	1.25992i
$372$	5.57381			0.288989
$373$	25.4504			1.31777			0.658886	−	0.752243i	$-0.271028\pi$
$373$	25.4504			1.31777			0.658886	+	0.752243i	$0.271028\pi$
$374$	−3.06854	−	5.31487i	−0.158671	−	0.274825i
$375$	−3.63237	+	6.29146i	−0.187575	+	0.324889i
$376$	2.57656	+	4.46273i	0.132876	+	0.230148i
$377$	−4.59462	−	7.95811i	−0.236635	−	0.409863i
$378$	1.09699			0.0564233
$379$	6.67731			0.342991			0.171495	−	0.985185i	$-0.445140\pi$
$379$	6.67731			0.342991			0.171495	+	0.985185i	$0.445140\pi$
$380$	−15.9781	−	27.6748i	−0.819658	−	1.41969i
$381$	6.23162			0.319255
$382$	−1.03666	+	1.79555i	−0.0530402	+	0.0918683i
$383$	−15.2526	+	26.4182i	−0.779370	+	1.34991i	0.152935	+	0.988236i	$0.451128\pi$
$383$	−15.2526	+	26.4182i	−0.779370	+	1.34991i	−0.932305	+	0.361673i	$0.882206\pi$
$384$	5.61714	−	9.72918i	0.286649	−	0.496490i
$385$	6.75469	+	11.6995i	0.344251	+	0.596260i
$386$	2.81351	+	4.87315i	0.143204	+	0.248037i
$387$	−1.79132	+	3.10266i	−0.0910579	+	0.157717i
$388$	−9.81080	−	16.9928i	−0.498068	−	0.862679i
$389$	0.494167			0.0250553			0.0125276	−	0.999922i	$-0.496012\pi$
$389$	0.494167			0.0250553			0.0125276	+	0.999922i	$0.496012\pi$
$390$	1.08262	−	1.87516i	0.0548207	−	0.0949523i
$391$	−29.4115	+	50.9423i	−1.48741	+	2.57626i
$392$	−3.20352			−0.161802
$393$	−1.45170			−0.0732287
$394$	−4.38866	+	7.60138i	−0.221097	+	0.382952i
$395$	29.7420	−	51.5147i	1.49648	−	2.59199i
$396$	−3.00727			−0.151121
$397$	3.82206	+	6.62001i	0.191824	+	0.332249i	0.945855	−	0.324590i	$-0.105226\pi$
$397$	3.82206	+	6.62001i	0.191824	+	0.332249i	−0.754031	+	0.656839i	$0.771893\pi$
$398$	1.20430	−	2.08590i	0.0603660	−	0.104557i
$399$	5.93721	+	10.2836i	0.297232	+	0.514822i
$400$	−9.47162	−	16.4053i	−0.473581	−	0.820266i
$401$	1.56438	−	2.70958i	0.0781212	−	0.135310i	−0.824318	−	0.566127i	$-0.808441\pi$
$401$	1.56438	−	2.70958i	0.0781212	−	0.135310i	0.902439	+	0.430817i	$0.141775\pi$
$402$	1.30620	−	2.26241i	0.0651476	−	0.112839i
$403$	−2.04401	+	3.54033i	−0.101820	+	0.176357i
$404$	−11.0913			−0.551815
$405$	1.73849	+	3.01115i	0.0863862	+	0.149625i
$406$	−7.76580			−0.385410
$407$	15.6993			0.778184
$408$	−6.80799	−	11.7918i	−0.337046	−	0.583781i
$409$	8.02145	+	13.8936i	0.396635	+	0.686993i	0.993308	−	0.115492i	$-0.0368444\pi$
$409$	8.02145	+	13.8936i	0.396635	+	0.686993i	−0.596673	+	0.802484i	$0.703511\pi$
$410$	−5.21646	+	9.03518i	−0.257623	+	0.446216i
$411$	−8.48983	−	14.7048i	−0.418773	−	0.725335i
$412$	14.1336			0.696314
$413$	12.7638			0.628067
$414$	−1.87417	−	3.24615i	−0.0921102	−	0.159540i
$415$	10.8734			0.533754
$416$	3.17962	+	5.50726i	0.155894	+	0.270016i
$417$	21.1221			1.03435
$418$	2.11656	+	3.66599i	0.103524	+	0.179310i
$419$	6.89321	+	11.9394i	0.336755	+	0.583277i	0.983820	−	0.179158i	$-0.0573372\pi$
$419$	6.89321	+	11.9394i	0.336755	+	0.583277i	−0.647065	+	0.762435i	$0.724004\pi$
$420$	7.03565	+	12.1861i	0.343305	+	0.594621i
$421$	17.7348	+	30.7176i	0.864341	+	1.49708i	0.867700	+	0.497088i	$0.165597\pi$
$421$	17.7348	+	30.7176i	0.864341	+	1.49708i	−0.00335962	+	0.999994i	$0.501069\pi$
$422$	−4.40872			−0.214613
$423$	1.42465	−	2.46757i	0.0692689	−	0.119977i
$424$	11.0816	+	19.1940i	0.538172	+	0.932142i
$425$	−53.3736			−2.58900
$426$	−1.32648			−0.0642683
$427$	−0.278933	+	0.483126i	−0.0134985	+	0.0233801i
$428$	6.85494	+	11.8731i	0.331346	+	0.573908i
$429$	1.10282	−	1.91014i	0.0532446	−	0.0922223i
$430$	5.97604			0.288190
$431$	8.03486	−	13.9168i	0.387026	−	0.670348i	−0.605022	−	0.796209i	$-0.706836\pi$
$431$	8.03486	−	13.9168i	0.387026	−	0.670348i	0.992048	+	0.125860i	$0.0401691\pi$
$432$	−2.67206			−0.128559
$433$	−8.41650	+	14.5778i	−0.404471	+	0.700564i	−0.994260	−	0.106993i	$-0.965878\pi$
$433$	−8.41650	+	14.5778i	−0.404471	+	0.700564i	0.589789	+	0.807558i	$0.299211\pi$
$434$	1.72739	+	2.99193i	0.0829174	+	0.143617i
$435$	−12.3071	−	21.3164i	−0.590078	−	1.02205i
$436$	2.75305	−	4.76842i	0.131847	−	0.228366i
$437$	20.2869	−	35.1380i	0.970456	−	1.68088i
$438$	−1.40152	−	2.42751i	−0.0669673	−	0.115991i
$439$	−26.3453			−1.25739			−0.628697	−	0.777651i	$-0.716411\pi$
$439$	−26.3453			−1.25739			−0.628697	+	0.777651i	$0.716411\pi$
$440$	5.34245	+	9.25340i	0.254691	+	0.441138i
$441$	0.885656	+	1.53400i	0.0421741	+	0.0730477i
$442$	4.68838			0.223003
$443$	−29.1887			−1.38680			−0.693398	−	0.720555i	$-0.743887\pi$
$443$	−29.1887			−1.38680			−0.693398	+	0.720555i	$0.743887\pi$
$444$	16.3523			0.776045
$445$	−4.30881	−	7.46307i	−0.204257	−	0.353783i
$446$	0.511990	+	0.886793i	0.0242434	+	0.0419908i
$447$	9.90326	−	17.1529i	0.468408	−	0.811307i
$448$	−6.84584			−0.323435
$449$	10.2709	−	17.7897i	0.484713	−	0.839548i	−0.515132	−	0.857111i	$-0.672257\pi$
$449$	10.2709	−	17.7897i	0.484713	−	0.839548i	0.999846	+	0.0175625i	$0.00559062\pi$
$450$	1.70054	−	2.94542i	0.0801641	−	0.138848i
$451$	−5.31377	+	9.20373i	−0.250216	+	0.433387i
$452$	16.0574	−	27.8122i	0.755276	−	1.30818i
$453$	5.83732	+	10.1105i	0.274261	+	0.475034i
$454$	1.18005	−	2.04390i	0.0553823	−	0.0959250i
$455$	−10.3204			−0.483827
$456$	4.69589	+	8.13352i	0.219905	+	0.380887i
$457$	−40.1934			−1.88017			−0.940084	−	0.340944i	$-0.889253\pi$
$457$	−40.1934			−1.88017			−0.940084	+	0.340944i	$0.889253\pi$
$458$	0.482379	+	0.835506i	0.0225401	+	0.0390406i
$459$	−3.76433	+	6.52001i	−0.175704	+	0.304328i
$460$	24.0402	−	41.6388i	1.12088	−	1.94142i
$461$	−11.9930	+	20.7724i	−0.558568	+	0.967468i	0.439048	+	0.898463i	$0.355316\pi$
$461$	−11.9930	+	20.7724i	−0.558568	+	0.967468i	−0.997616	+	0.0690046i	$0.978018\pi$
$462$	−0.931989	−	1.61425i	−0.0433601	−	0.0751018i
$463$	−4.77684			−0.221999			−0.110999	−	0.993820i	$-0.535405\pi$
$463$	−4.77684			−0.221999			−0.110999	+	0.993820i	$0.535405\pi$
$464$	18.9159			0.878150
$465$	−5.47506	+	9.48307i	−0.253900	+	0.439767i
$466$	−6.12220	+	10.6040i	−0.283605	+	0.491219i
$467$	4.42312			0.204678			0.102339	−	0.994750i	$-0.467367\pi$
$467$	4.42312			0.204678			0.102339	+	0.994750i	$0.467367\pi$
$468$	1.14869	−	1.98959i	0.0530982	−	0.0919689i
$469$	−12.4517			−0.574967
$470$	−4.75279			−0.219230
$471$	−1.84462	−	12.3934i	−0.0849956	−	0.571060i
$472$	10.0952			0.464671
$473$	6.08752			0.279904
$474$	−4.10371	+	7.10783i	−0.188490	+	0.326473i
$475$	36.8150			1.68919
$476$	−15.2342	+	26.3864i	−0.698259	+	1.20942i
$477$	6.12735	−	10.6129i	0.280552	−	0.485931i
$478$	4.92045			0.225056
$479$	−4.51964			−0.206508			−0.103254	−	0.994655i	$-0.532925\pi$
$479$	−4.51964			−0.206508			−0.103254	+	0.994655i	$0.532925\pi$
$480$	8.51687	+	14.7517i	0.388740	+	0.673318i
$481$	−5.99667	+	10.3865i	−0.273424	+	0.473585i
$482$	7.25802	−	12.5713i	0.330594	−	0.572605i
$483$	−8.93298	+	15.4724i	−0.406465	+	0.704018i
$484$	−7.17923	−	12.4348i	−0.326329	−	0.565218i
$485$	38.5479			1.75037
$486$	−0.239871	−	0.415469i	−0.0108808	−	0.0188460i
$487$	42.7234			1.93598			0.967990	−	0.250988i	$-0.0807553\pi$
$487$	42.7234			1.93598			0.967990	+	0.250988i	$0.0807553\pi$
$488$	−0.220615	+	0.382116i	−0.00998677	+	0.0172976i
$489$	−2.33552	−	4.04524i	−0.105616	−	0.182932i
$490$	1.47732	−	2.55880i	0.0667386	−	0.115595i
$491$	10.4087	−	18.0284i	0.469739	−	0.813612i	−0.529662	−	0.848209i	$-0.677681\pi$
$491$	10.4087	−	18.0284i	0.469739	−	0.813612i	0.999401	+	0.0345967i	$0.0110147\pi$
$492$	−5.53480	+	9.58656i	−0.249528	+	0.432195i
$493$	26.6483	−	46.1562i	1.20018	−	2.07877i
$494$	−3.23386			−0.145498
$495$	2.95399	−	5.11646i	0.132772	−	0.229968i
$496$	−4.20758	−	7.28773i	−0.188926	−	0.327229i
$497$	3.16126	+	5.47546i	0.141802	+	0.245608i
$498$	−1.50028			−0.0672289
$499$	3.24351			0.145199			0.0725997	−	0.997361i	$-0.476870\pi$
$499$	3.24351			0.145199			0.0725997	+	0.997361i	$0.476870\pi$
$500$	12.8575			0.575005
$501$	−6.50838	−	11.2729i	−0.290773	−	0.503634i
$502$	−4.58461	−	7.94077i	−0.204621	−	0.354414i
$503$	3.07205			0.136976			0.0684879	−	0.997652i	$-0.478183\pi$
$503$	3.07205			0.136976			0.0684879	+	0.997652i	$0.478183\pi$
$504$	−2.06775	−	3.58145i	−0.0921049	−	0.159530i
$505$	10.8948	−	18.8704i	0.484814	−	0.839722i
$506$	−3.18453	+	5.51576i	−0.141569	+	0.245205i
$507$	−5.65751	−	9.79910i	−0.251259	−	0.435193i
$508$	−5.51450	−	9.55140i	−0.244667	−	0.423775i
$509$	10.4573	−	18.1126i	0.463512	−	0.802827i	−0.535621	−	0.844459i	$-0.679922\pi$
$509$	10.4573	−	18.1126i	0.463512	−	0.802827i	0.999133	+	0.0416318i	$0.0132556\pi$
$510$	12.5582			0.556087
$511$	−6.68018	+	11.5704i	−0.295514	+	0.511845i
$512$	−22.7555			−1.00566
$513$	2.59649	−	4.49725i	0.114638	−	0.198558i
$514$	0.163871	+	0.283833i	0.00722805	+	0.0125193i
$515$	−13.8832	+	24.0464i	−0.611767	+	1.05961i
$516$	6.34073			0.279135
$517$	−4.84145			−0.212927
$518$	5.06777	+	8.77763i	0.222665	+	0.385667i
$519$	−1.23156	+	2.13312i	−0.0540594	+	0.0936337i
$520$	−8.16264			−0.357956
$521$	−15.2905	−	26.4839i	−0.669887	−	1.16028i	−0.977935	−	0.208908i	$-0.933009\pi$
$521$	−15.2905	−	26.4839i	−0.669887	−	1.16028i	0.308048	−	0.951371i	$-0.400324\pi$
$522$	1.69809	+	2.94117i	0.0743232	+	0.128732i
$523$	2.39512	+	4.14846i	0.104731	+	0.181400i	0.913628	−	0.406550i	$-0.133268\pi$
$523$	2.39512	+	4.14846i	0.104731	+	0.181400i	−0.808897	+	0.587950i	$0.799935\pi$
$524$	1.28465	+	2.22507i	0.0561200	+	0.0972027i
$525$	−16.2108			−0.707498
$526$	0.915722	+	1.58608i	0.0399274	+	0.0691562i
$527$	−23.7101			−1.03283
$528$	2.27014	+	3.93199i	0.0987951	+	0.171118i
$529$	38.0464			1.65419
$530$	−20.4415			−0.887922
$531$	−2.79097	−	4.83410i	−0.121118	−	0.209782i
$532$	10.5080	−	18.2003i	0.455578	−	0.789084i
$533$	−4.05941	−	7.03111i	−0.175833	−	0.304551i
$534$	0.594515	+	1.02973i	0.0257272	+	0.0445608i
$535$	−26.9339			−1.16446
$536$	−9.84838			−0.425385
$537$	8.07174	+	13.9807i	0.348321	+	0.603310i
$538$	9.15084			0.394521
$539$	1.50488	−	2.60653i	0.0648198	−	0.112271i
$540$	3.07686	−	5.32928i	0.132407	−	0.229336i
$541$	−12.8298	+	22.2218i	−0.551596	+	0.955392i	0.446564	+	0.894752i	$0.352647\pi$
$541$	−12.8298	+	22.2218i	−0.551596	+	0.955392i	−0.998160	+	0.0606399i	$0.980686\pi$
$542$	0.835578	+	1.44726i	0.0358912	+	0.0621653i
$543$	1.27671	+	2.21132i	0.0547887	+	0.0948968i
$544$	−18.4415	+	31.9416i	−0.790672	+	1.36948i
$545$	5.40854	+	9.36787i	0.231677	+	0.401276i
$546$	1.42397			0.0609404
$547$	−17.1847	+	29.7647i	−0.734764	+	1.27265i	0.220063	+	0.975486i	$0.429374\pi$
$547$	−17.1847	+	29.7647i	−0.734764	+	1.27265i	−0.954827	+	0.297162i	$0.903960\pi$
$548$	−15.0257	+	26.0253i	−0.641867	+	1.11175i
$549$	0.243968			0.0104123
$550$	−5.77901			−0.246418
$551$	−18.3810	+	31.8368i	−0.783056	+	1.35629i
$552$	−7.06532	+	12.2375i	−0.300720	+	0.520862i
$553$	39.1196			1.66354
$554$	−1.27321	−	2.20527i	−0.0540936	−	0.0936929i
$555$	−16.0626	+	27.8212i	−0.681818	+	1.18094i
$556$	−18.6914	−	32.3745i	−0.792694	−	1.37299i
$557$	−4.92335	−	8.52749i	−0.208609	−	0.361321i	0.742668	−	0.669660i	$-0.233560\pi$
$557$	−4.92335	−	8.52749i	−0.208609	−	0.361321i	−0.951277	+	0.308339i	$0.900227\pi$
$558$	0.755430	−	1.30844i	0.0319799	−	0.0553908i
$559$	−2.32525	+	4.02746i	−0.0983478	+	0.170343i
$560$	10.6222	−	18.3982i	0.448869	−	0.777464i
$561$	12.7925			0.540099
$562$	−5.75268	−	9.96394i	−0.242662	−	0.420303i
$563$	18.8006			0.792349			0.396175	−	0.918175i	$-0.370337\pi$
$563$	18.8006			0.792349			0.396175	+	0.918175i	$0.370337\pi$
$564$	−5.04283			−0.212342
$565$	31.5458	+	54.6389i	1.32714	+	2.29867i
$566$	4.86347	+	8.42377i	0.204427	+	0.354078i
$567$	−1.14332	+	1.98028i	−0.0480148	+	0.0831640i
$568$	2.50032	+	4.33068i	0.104911	+	0.181711i
$569$	−39.1430			−1.64096			−0.820481	−	0.571674i	$-0.806294\pi$
$569$	−39.1430			−1.64096			−0.820481	+	0.571674i	$0.806294\pi$
$570$	−8.66216			−0.362818
$571$	0.119894	+	0.207663i	0.00501742	+	0.00869043i	0.868523	−	0.495648i	$-0.165070\pi$
$571$	0.119894	+	0.207663i	0.00501742	+	0.00869043i	−0.863506	+	0.504339i	$0.831736\pi$
$572$	−3.90364			−0.163219
$573$	−2.16087	−	3.74274i	−0.0902717	−	0.156355i
$574$	−6.86120			−0.286381
$575$	27.6955	+	47.9700i	1.15498	+	2.00049i
$576$	1.49693	+	2.59275i	0.0623719	+	0.108031i
$577$	−0.938473	−	1.62548i	−0.0390692	−	0.0676698i	0.845830	−	0.533453i	$-0.179106\pi$
$577$	−0.938473	−	1.62548i	−0.0390692	−	0.0676698i	−0.884899	+	0.465783i	$0.845773\pi$
$578$	9.51825	+	16.4861i	0.395907	+	0.685731i
$579$	−11.7293			−0.487452
$580$	−21.7816	+	37.7269i	−0.904432	+	1.56652i
$581$	3.57544	+	6.19284i	0.148334	+	0.256922i
$582$	−5.31871			−0.220468
$583$	−20.8228			−0.862393
$584$	−5.28352	+	9.15133i	−0.218634	+	0.378685i
$585$	2.25668	+	3.90868i	0.0933021	+	0.161604i
$586$	3.30869	−	5.73082i	0.136681	−	0.236738i
$587$	45.9134			1.89505			0.947524	−	0.319685i	$-0.103577\pi$
$587$	45.9134			1.89505			0.947524	+	0.319685i	$0.103577\pi$
$588$	1.56748	−	2.71495i	0.0646417	−	0.111963i
$589$	16.3543			0.673868
$590$	−4.65548	+	8.06353i	−0.191663	+	0.331970i
$591$	−9.14796	−	15.8447i	−0.376297	−	0.651765i
$592$	−12.3441	−	21.3805i	−0.507338	−	0.878735i
$593$	12.5101	−	21.6681i	0.513728	−	0.889802i	−0.486146	−	0.873878i	$-0.661598\pi$
$593$	12.5101	−	21.6681i	0.513728	−	0.889802i	0.999873	−	0.0159244i	$-0.00506911\pi$
$594$	−0.407582	+	0.705952i	−0.0167233	+	0.0289656i
$595$	−29.9286	−	51.8378i	−1.22695	−	2.12514i
$596$	−35.0545			−1.43589
$597$	2.51030	+	4.34797i	0.102740	+	0.177951i
$598$	−2.43279	−	4.21372i	−0.0994843	−	0.172312i
$599$	1.67363			0.0683826			0.0341913	−	0.999415i	$-0.489114\pi$
$599$	1.67363			0.0683826			0.0341913	+	0.999415i	$0.489114\pi$
$600$	−12.8215			−0.523437
$601$	−23.6040			−0.962827			−0.481414	−	0.876494i	$-0.659877\pi$
$601$	−23.6040			−0.962827			−0.481414	+	0.876494i	$0.659877\pi$
$602$	1.96507	+	3.40360i	0.0800902	+	0.138720i
$603$	2.72272	+	4.71589i	0.110878	+	0.192046i
$604$	10.3312	−	17.8941i	0.420369	−	0.728101i
$605$	28.2081			1.14682
$606$	−1.50323	+	2.60368i	−0.0610647	+	0.105767i
$607$	6.87704	−	11.9114i	0.279130	−	0.483468i	−0.692038	−	0.721861i	$-0.743287\pi$
$607$	6.87704	−	11.9114i	0.279130	−	0.483468i	0.971169	+	0.238393i	$0.0766205\pi$
$608$	12.7202	−	22.0321i	0.515873	−	0.893518i
$609$	8.09372	−	14.0187i	0.327974	−	0.568068i
$610$	−0.203476	−	0.352431i	−0.00823851	−	0.0142695i
$611$	1.84929	−	3.20307i	0.0748144	−	0.129582i
$612$	13.3246			0.538614
$613$	−0.204597	−	0.354372i	−0.00826358	−	0.0143129i	0.861864	−	0.507139i	$-0.169297\pi$
$613$	−0.204597	−	0.354372i	−0.00826358	−	0.0143129i	−0.870128	+	0.492826i	$0.835964\pi$
$614$	−0.399035			−0.0161037
$615$	−10.8735	−	18.8334i	−0.438461	−	0.759436i
$616$	−3.51346	+	6.08549i	−0.141561	+	0.245191i
$617$	−3.44630	+	5.96917i	−0.138743	+	0.240310i	−0.927021	−	0.375009i	$-0.877640\pi$
$617$	−3.44630	+	5.96917i	−0.138743	+	0.240310i	0.788278	+	0.615319i	$0.210973\pi$
$618$	1.91556	−	3.31784i	0.0770551	−	0.133463i
$619$	−3.00238	−	5.20028i	−0.120676	−	0.209017i	0.799359	−	0.600854i	$-0.205173\pi$
$619$	−3.00238	−	5.20028i	−0.120676	−	0.209017i	−0.920034	+	0.391838i	$0.871839\pi$
$620$	19.3800			0.778321
$621$	7.81322			0.313534
$622$	−6.49544	+	11.2504i	−0.260443	+	0.451101i
$623$	2.83368	−	4.90808i	0.113529	−	0.196638i
$624$	−3.46851			−0.138851
$625$	5.09377	−	8.82267i	0.203751	−	0.352907i
$626$	14.2338			0.568899
$627$	−8.82375			−0.352387
$628$	−17.3635	+	13.7946i	−0.692879	+	0.550463i
$629$	−69.5601			−2.77354
$630$	3.81422			0.151962
$631$	2.68665	−	4.65341i	0.106954	−	0.185250i	−0.807581	−	0.589757i	$-0.799224\pi$
$631$	2.68665	−	4.65341i	0.106954	−	0.185250i	0.914535	+	0.404507i	$0.132557\pi$
$632$	30.9407			1.23075
$633$	4.59488	−	7.95857i	0.182630	−	0.316325i
$634$	2.37962	−	4.12163i	0.0945070	−	0.163691i
$635$	21.6672			0.859836
$636$	−21.6890			−0.860023
$637$	1.14964	+	1.99124i	0.0455505	+	0.0788957i
$638$	2.88534	−	4.99755i	0.114232	−	0.197855i
$639$	1.38250	−	2.39455i	0.0546907	−	0.0947271i
$640$	19.5307	−	33.8282i	0.772019	−	1.33718i
$641$	−13.5656	−	23.4964i	−0.535810	−	0.928050i	−0.999124	−	0.0418559i	$-0.986673\pi$
$641$	−13.5656	−	23.4964i	−0.535810	−	0.928050i	0.463314	−	0.886194i	$-0.346660\pi$
$642$	3.71626			0.146669
$643$	−2.33212	−	4.03935i	−0.0919698	−	0.159296i	0.816370	−	0.577529i	$-0.195983\pi$
$643$	−2.33212	−	4.03935i	−0.0919698	−	0.159296i	−0.908340	+	0.418233i	$0.862650\pi$
$644$	31.6200			1.24600
$645$	−6.22838	+	10.7879i	−0.245242	+	0.424772i
$646$	−9.37803	−	16.2432i	−0.368974	−	0.639081i
$647$	−20.5133	+	35.5301i	−0.806461	+	1.39683i	0.108840	+	0.994059i	$0.465286\pi$
$647$	−20.5133	+	35.5301i	−0.806461	+	1.39683i	−0.915301	+	0.402772i	$0.868047\pi$
$648$	−0.904277	+	1.56625i	−0.0355234	+	0.0615283i
$649$	−4.74233	+	8.21395i	−0.186153	+	0.322426i
$650$	2.20741	−	3.82335i	0.0865818	−	0.149964i
$651$	−7.20133			−0.282242
$652$	−4.13352	+	7.15946i	−0.161881	+	0.280386i
$653$	6.94180	+	12.0236i	0.271654	+	0.470518i	0.969285	−	0.245939i	$-0.0790962\pi$
$653$	6.94180	+	12.0236i	0.271654	+	0.470518i	−0.697632	+	0.716457i	$0.745763\pi$
$654$	−0.746253	−	1.29255i	−0.0291808	−	0.0505426i
$655$	−5.04754			−0.197224
$656$	16.7125			0.652514
$657$	5.84281			0.227950
$658$	−1.56283	−	2.70691i	−0.0609256	−	0.105526i
$659$	−1.60515	−	2.78020i	−0.0625278	−	0.108301i	0.833067	−	0.553172i	$-0.186583\pi$
$659$	−1.60515	−	2.78020i	−0.0625278	−	0.108301i	−0.895595	+	0.444871i	$0.853250\pi$
$660$	−10.4562			−0.407008
$661$	−15.3069	−	26.5124i	−0.595370	−	1.03121i	−0.993494	−	0.113880i	$-0.963672\pi$
$661$	−15.3069	−	26.5124i	−0.595370	−	1.03121i	0.398124	−	0.917332i	$-0.369661\pi$
$662$	−5.34627	+	9.26002i	−0.207789	+	0.359901i
$663$	−4.88635	+	8.46341i	−0.189770	+	0.328692i
$664$	2.82790	+	4.89807i	0.109744	+	0.190082i
$665$	20.6436	+	35.7557i	0.800523	+	1.38655i
$666$	2.21626	−	3.83867i	0.0858783	−	0.148746i
$667$	−55.3111			−2.14165
$668$	−11.5188	+	19.9512i	−0.445678	+	0.771936i
$669$	−2.13444			−0.0825222
$670$	4.54165	−	7.86636i	0.175459	−	0.303904i
$671$	−0.207272	−	0.359005i	−0.00800164	−	0.0138592i
$672$	−5.60111	+	9.70141i	−0.216068	+	0.374240i
$673$	28.5468			1.10040			0.550199	−	0.835034i	$-0.314552\pi$
$673$	28.5468			1.10040			0.550199	+	0.835034i	$0.314552\pi$
$674$	14.9602			0.576246
$675$	3.54469	+	6.13959i	0.136435	+	0.236313i
$676$	−10.0129	+	17.3429i	−0.385113	+	0.667035i
$677$	9.21308			0.354087			0.177044	−	0.984203i	$-0.443347\pi$
$677$	9.21308			0.354087			0.177044	+	0.984203i	$0.443347\pi$
$678$	−4.35258	−	7.53889i	−0.167160	−	0.289529i
$679$	12.6755	+	21.9546i	0.486441	+	0.842540i
$680$	−23.6713	−	40.9998i	−0.907751	−	1.57227i
$681$	2.45975	+	4.26041i	0.0942579	+	0.163259i
$682$	−2.56721			−0.0983035
$683$	−17.4324	−	30.1937i	−0.667030	−	1.15533i	−0.978731	−	0.205150i	$-0.934232\pi$
$683$	−17.4324	−	30.1937i	−0.667030	−	1.15533i	0.311700	−	0.950181i	$-0.399102\pi$
$684$	−9.19078			−0.351418
$685$	−29.5190	−	51.1284i	−1.12786	−	1.95351i
$686$	9.62207			0.367373
$687$	−2.01100			−0.0767242
$688$	−4.78651	−	8.29047i	−0.182484	−	0.316071i
$689$	7.95371	−	13.7762i	0.303012	−	0.524833i
$690$	−6.51643	−	11.2868i	−0.248076	−	0.429681i
$691$	−16.0739	−	27.8408i	−0.611479	−	1.05911i	−0.990991	−	0.133926i	$-0.957242\pi$
$691$	−16.0739	−	27.8408i	−0.611479	−	1.05911i	0.379513	−	0.925187i	$-0.376092\pi$
$692$	4.35934			0.165717
$693$	3.88538			0.147593
$694$	0.197903	+	0.342779i	0.00751231	+	0.0130117i
$695$	73.4411			2.78578
$696$	6.40153	−	11.0878i	0.242649	−	0.420281i
$697$	23.5442	−	40.7797i	0.891800	−	1.54464i
$698$	5.83492	−	10.1064i	0.220855	−	0.382532i
$699$	−12.7614	−	22.1035i	−0.482682	−	0.836030i
$700$	14.3453	+	24.8469i	0.542203	+	0.939123i
$701$	1.98848	−	3.44414i	0.0751037	−	0.130083i	−0.826028	−	0.563630i	$-0.809405\pi$
$701$	1.98848	−	3.44414i	0.0751037	−	0.130083i	0.901131	+	0.433546i	$0.142738\pi$
$702$	−0.311369	−	0.539306i	−0.0117519	−	0.0203548i
$703$	47.9799			1.80959
$704$	2.54353	−	4.40553i	0.0958630	−	0.166040i
$705$	4.95348	−	8.57969i	0.186559	−	0.323130i
$706$	9.59647			0.361168
$707$	14.3300			0.538933
$708$	−4.93959	+	8.55562i	−0.185641	+	0.321540i
$709$	−15.6382	+	27.0861i	−0.587304	+	1.01724i	0.407279	+	0.913304i	$0.366477\pi$
$709$	−15.6382	+	27.0861i	−0.587304	+	1.01724i	−0.994584	+	0.103937i	$0.966856\pi$
$710$	−4.61215			−0.173091
$711$	−8.55399	−	14.8159i	−0.320800	−	0.555641i
$712$	2.24123	−	3.88192i	0.0839936	−	0.145481i
$713$	12.3032	+	21.3097i	0.460757	+	0.798054i
$714$	4.12945	+	7.15241i	0.154541	+	0.267672i
$715$	3.83448	−	6.64151i	0.143401	−	0.248378i
$716$	14.2857	−	24.7436i	0.533883	−	0.924713i
$717$	−5.12823	+	8.88235i	−0.191517	+	0.331717i
$718$	9.95555			0.371538
$719$	−7.59725	−	13.1588i	−0.283329	−	0.490741i	0.688873	−	0.724882i	$-0.258106\pi$
$719$	−7.59725	−	13.1588i	−0.283329	−	0.490741i	−0.972203	+	0.234141i	$0.924772\pi$
$720$	−9.29068			−0.346243
$721$	−18.2606			−0.680059
$722$	1.91105	+	3.31004i	0.0711221	+	0.123187i
$723$	15.1290	+	26.2042i	0.562653	+	0.974544i
$724$	2.25957	−	3.91370i	0.0839764	−	0.145451i
$725$	−25.0935	−	43.4632i	−0.931948	−	1.61418i
$726$	−3.89206			−0.144448
$727$	−20.9038			−0.775277			−0.387639	−	0.921811i	$-0.626709\pi$
$727$	−20.9038			−0.775277			−0.387639	+	0.921811i	$0.626709\pi$
$728$	−2.68408	−	4.64896i	−0.0994785	−	0.172302i
$729$	1.00000			0.0370370
$730$	−4.87306	−	8.44039i	−0.180360	−	0.312393i
$731$	−26.9725			−0.997613
$732$	−0.215893	−	0.373938i	−0.00797965	−	0.0138212i
$733$	−10.6503	−	18.4469i	−0.393379	−	0.681352i	0.599514	−	0.800364i	$-0.295361\pi$
$733$	−10.6503	−	18.4469i	−0.393379	−	0.681352i	−0.992893	+	0.119012i	$0.962027\pi$
$734$	−7.93643	−	13.7463i	−0.292939	−	0.507385i
$735$	3.07941	+	5.33369i	0.113586	+	0.196736i
$736$	38.2770			1.41091
$737$	4.62637	−	8.01310i	0.170414	−	0.295166i
$738$	1.50029	+	2.59857i	0.0552263	+	0.0956547i
$739$	−2.39323			−0.0880364			−0.0440182	−	0.999031i	$-0.514016\pi$
$739$	−2.39323			−0.0880364			−0.0440182	+	0.999031i	$0.514016\pi$
$740$	56.8566			2.09009
$741$	3.37042	−	5.83773i	0.123815	−	0.214454i
$742$	−6.72166	−	11.6423i	−0.246760	−	0.427401i
$743$	17.1281	−	29.6668i	0.628371	−	1.08837i	−0.359508	−	0.933142i	$-0.617055\pi$
$743$	17.1281	−	29.6668i	0.628371	−	1.08837i	0.987879	−	0.155228i	$-0.0496112\pi$
$744$	−5.69571			−0.208815
$745$	34.4334	−	59.6404i	1.26154	−	2.18506i
$746$	−12.2096			−0.447026
$747$	1.56363	−	2.70828i	0.0572101	−	0.0990908i
$748$	−11.3204	−	19.6074i	−0.413913	−	0.716919i
$749$	−8.85654	−	15.3400i	−0.323611	−	0.560511i
$750$	1.74260	−	3.01828i	0.0636308	−	0.110212i
$751$	0.317169	−	0.549352i	0.0115737	−	0.0200462i	−0.860181	−	0.509990i	$-0.829649\pi$
$751$	0.317169	−	0.549352i	0.0115737	−	0.0200462i	0.871754	+	0.489943i	$0.162983\pi$
$752$	3.80675	+	6.59348i	0.138818	+	0.240440i
$753$	19.1128			0.696509
$754$	2.20423	+	3.81784i	0.0802733	+	0.139038i
$755$	20.2962	+	35.1541i	0.738656	+	1.27939i
$756$	4.04699			0.147188
$757$	10.7503			0.390727			0.195363	−	0.980731i	$-0.437411\pi$
$757$	10.7503			0.390727			0.195363	+	0.980731i	$0.437411\pi$
$758$	−3.20339			−0.116352
$759$	−6.63800	−	11.4973i	−0.240944	−	0.417327i
$760$	16.3275	+	28.2801i	0.592261	+	1.02583i
$761$	−8.97898	+	15.5521i	−0.325488	+	0.563762i	−0.981611	−	0.190892i	$-0.938862\pi$
$761$	−8.97898	+	15.5521i	−0.325488	+	0.563762i	0.656123	+	0.754654i	$0.272195\pi$
$762$	−2.98957			−0.108301
$763$	−3.55692	+	6.16077i	−0.128769	+	0.223035i
$764$	−3.82441	+	6.62408i	−0.138362	+	0.239651i
$765$	−13.0885	+	22.6699i	−0.473216	+	0.819633i
$766$	7.31730	−	12.6739i	0.264385	−	0.457928i
$767$	−3.62286	−	6.27498i	−0.130814	−	0.226577i
$768$	0.299072	−	0.518007i	0.0107918	−	0.0186920i
$769$	−42.2387			−1.52317			−0.761583	−	0.648067i	$-0.775578\pi$
$769$	−42.2387			−1.52317			−0.761583	+	0.648067i	$0.775578\pi$
$770$	−3.24051	−	5.61272i	−0.116780	−	0.202269i
$771$	−0.683164			−0.0246035
$772$	10.3795	+	17.9778i	0.373567	+	0.647037i
$773$	6.42611	−	11.1304i	0.231131	−	0.400331i	−0.727010	−	0.686627i	$-0.759091\pi$
$773$	6.42611	−	11.1304i	0.231131	−	0.400331i	0.958141	+	0.286296i	$0.0924240\pi$
$774$	0.859372	−	1.48848i	0.0308895	−	0.0535021i
$775$	−11.1634	+	19.3355i	−0.401000	+	0.694552i
$776$	10.0254	+	17.3644i	0.359889	+	0.623347i
$777$	−21.1271			−0.757929
$778$	−0.237073			−0.00849947
$779$	−16.2399	+	28.1283i	−0.581854	+	1.00780i
$780$	3.99397	−	6.91776i	0.143007	−	0.247696i
$781$	−4.69819			−0.168114
$782$	14.1100	−	24.4392i	0.504571	−	0.873942i
$783$	−7.07917			−0.252989
$784$	−4.73305			−0.169037
$785$	−6.41370	−	43.0917i	−0.228915	−	1.53801i
$786$	0.696442			0.0248413
$787$	2.55869			0.0912074			0.0456037	−	0.998960i	$-0.485479\pi$
$787$	2.55869			0.0912074			0.0456037	+	0.998960i	$0.485479\pi$
$788$	−16.1905	+	28.0427i	−0.576762	+	0.998981i
$789$	−3.81756			−0.135909
$790$	−14.2685	+	24.7138i	−0.507651	+	0.879277i
$791$	−20.7460	+	35.9332i	−0.737645	+	1.27764i
$792$	3.07304			0.109196
$793$	0.316687			0.0112459
$794$	−1.83360	−	3.17590i	−0.0650722	−	0.112708i
$795$	21.3047	−	36.9008i	0.755599	−	1.30874i
$796$	4.44285	−	7.69525i	0.157473	−	0.272751i
$797$	−0.533600	+	0.924222i	−0.0189011	+	0.0327376i	−0.875321	−	0.483542i	$-0.839350\pi$
$797$	−0.533600	+	0.924222i	−0.0189011	+	0.0327376i	0.856420	+	0.516279i	$0.172683\pi$
$798$	−2.84833	−	4.93345i	−0.100830	−	0.174642i
$799$	21.4514			0.758897
$800$	17.3655	+	30.0779i	0.613962	+	1.06341i
$801$	−2.47848			−0.0875726
$802$	−0.750497	+	1.29990i	−0.0265010	+	0.0459010i
$803$	−4.96396	−	8.59784i	−0.175174	−	0.303411i
$804$	4.81880	−	8.34641i	0.169946	−	0.294355i
$805$	−31.0598	+	53.7971i	−1.09471	+	1.89610i
$806$	0.980599	−	1.69845i	0.0345401	−	0.0598253i
$807$	−9.53725	+	16.5190i	−0.335727	+	0.581496i
$808$	11.3339			0.398726
$809$	8.78711	−	15.2197i	0.308938	−	0.535097i	−0.669192	−	0.743090i	$-0.733360\pi$
$809$	8.78711	−	15.2197i	0.308938	−	0.535097i	0.978130	+	0.207992i	$0.0666929\pi$
$810$	−0.834027	−	1.44458i	−0.0293047	−	0.0507572i
$811$	−11.7216	−	20.3024i	−0.411600	−	0.712913i	0.583465	−	0.812139i	$-0.301697\pi$
$811$	−11.7216	−	20.3024i	−0.411600	−	0.712913i	−0.995065	+	0.0992258i	$0.968363\pi$
$812$	−28.6493			−1.00539
$813$	−3.48345			−0.122170
$814$	−7.53160			−0.263982
$815$	−8.12056	−	14.0652i	−0.284451	−	0.492683i
$816$	−10.0585	−	17.4218i	−0.352118	−	0.609886i
$817$	18.6046			0.650891
$818$	−3.84823	−	6.66533i	−0.134550	−	0.233048i
$819$	−1.48410	+	2.57054i	−0.0518587	+	0.0898219i
$820$	−19.2444	+	33.3323i	−0.672043	+	1.16401i
$821$	13.3203	+	23.0714i	0.464881	+	0.805198i	0.999196	−	0.0400878i	$-0.0127638\pi$
$821$	13.3203	+	23.0714i	0.464881	+	0.805198i	−0.534315	+	0.845285i	$0.679430\pi$
$822$	4.07293	+	7.05452i	0.142060	+	0.246055i
$823$	−14.1996	+	24.5944i	−0.494966	+	0.857306i	−0.999983	−	0.00580296i	$-0.998153\pi$
$823$	−14.1996	+	24.5944i	−0.494966	+	0.857306i	0.505017	+	0.863109i	$0.331486\pi$
$824$	−14.4427			−0.503136
$825$	6.02303	−	10.4322i	0.209695	−	0.363203i
$826$	−6.12335			−0.213059
$827$	13.9731	−	24.2021i	0.485892	−	0.841590i	−0.513976	−	0.857804i	$-0.671828\pi$
$827$	13.9731	−	24.2021i	0.485892	−	0.841590i	0.999869	+	0.0162145i	$0.00516146\pi$
$828$	−6.91411	−	11.9756i	−0.240282	−	0.416180i
$829$	−20.8167	+	36.0557i	−0.722995	+	1.25226i	0.236798	+	0.971559i	$0.423902\pi$
$829$	−20.8167	+	36.0557i	−0.722995	+	1.25226i	−0.959794	+	0.280706i	$0.909431\pi$
$830$	−5.21643			−0.181065
$831$	5.30791			0.184129
$832$	1.94311	+	3.36557i	0.0673652	+	0.116680i
$833$	−6.66780	+	11.5490i	−0.231026	+	0.400148i
$834$	−10.1332			−0.350883
$835$	−22.6295	−	39.1955i	−0.783127	−	1.35642i
$836$	7.80835	+	13.5245i	0.270057	+	0.467753i
$837$	1.57466	+	2.72739i	0.0544282	+	0.0942724i
$838$	−3.30696	−	5.72782i	−0.114237	−	0.197864i
$839$	10.0899			0.348340			0.174170	−	0.984716i	$-0.444276\pi$
$839$	10.0899			0.348340			0.174170	+	0.984716i	$0.444276\pi$
$840$	−7.18952	−	12.4526i	−0.248062	−	0.429656i
$841$	21.1146			0.728089
$842$	−8.50812	−	14.7365i	−0.293209	−	0.507853i
$843$	23.9824			0.825998
$844$	−16.2645			−0.559847
$845$	−19.6710	−	34.0713i	−0.676705	−	1.17209i
$846$	−0.683465	+	1.18380i	−0.0234980	+	0.0406998i
$847$	9.27552	+	16.0657i	0.318711	+	0.552023i
$848$	16.3726	+	28.3582i	0.562238	+	0.973825i
$849$	−20.2753			−0.695848
$850$	25.6055			0.878263
$851$	36.0946	+	62.5178i	1.23731	+	2.14308i
$852$	−4.89361			−0.167652
$853$	−7.13370	+	12.3559i	−0.244253	+	0.423059i	−0.961921	−	0.273326i	$-0.911876\pi$
$853$	−7.13370	+	12.3559i	−0.244253	+	0.423059i	0.717668	+	0.696385i	$0.245209\pi$
$854$	0.133816	−	0.231776i	0.00457908	−	0.00793121i
$855$	9.02794	−	15.6368i	0.308749	−	0.534769i
$856$	−7.00486	−	12.1328i	−0.239421	−	0.414690i
$857$	2.60814	+	4.51743i	0.0890924	+	0.154313i	0.907128	−	0.420855i	$-0.138270\pi$
$857$	2.60814	+	4.51743i	0.0890924	+	0.154313i	−0.818035	+	0.575168i	$0.804937\pi$
$858$	−0.529068	+	0.916373i	−0.0180621	+	0.0312845i
$859$	4.42884	+	7.67098i	0.151110	+	0.261730i	0.931636	−	0.363393i	$-0.118382\pi$
$859$	4.42884	+	7.67098i	0.151110	+	0.261730i	−0.780526	+	0.625124i	$0.785049\pi$
$860$	22.0466			0.751782
$861$	7.15093	−	12.3858i	0.243703	−	0.422106i
$862$	−3.85466	+	6.67647i	−0.131290	+	0.227402i
$863$	−21.9599			−0.747524			−0.373762	−	0.927525i	$-0.621932\pi$
$863$	−21.9599			−0.747524			−0.373762	+	0.927525i	$0.621932\pi$
$864$	4.89901			0.166668
$865$	−4.28210	+	7.41682i	−0.145596	+	0.252180i
$866$	4.03775	−	6.99358i	0.137208	−	0.237652i
$867$	−39.6807			−1.34763
$868$	6.37263	+	11.0377i	0.216301	+	0.374645i
$869$	−14.5347	+	25.1748i	−0.493055	+	0.853997i
$870$	5.90421	+	10.2264i	0.200172	+	0.346707i
$871$	3.53428	+	6.12155i	0.119754	+	0.207421i
$872$	−2.81326	+	4.87271i	−0.0952690	+	0.165011i
$873$	5.54330	−	9.60128i	0.187612	−	0.324954i
$874$	−9.73250	+	16.8572i	−0.329207	+	0.570203i
$875$	−16.6118			−0.561582
$876$	−5.17044	−	8.95547i	−0.174693	−	0.302577i
$877$	48.0952			1.62406			0.812030	−	0.583615i	$-0.198362\pi$
$877$	48.0952			1.62406			0.812030	+	0.583615i	$0.198362\pi$
$878$	12.6390			0.426544
$879$	6.89681	+	11.9456i	0.232624	+	0.402916i
$880$	7.89322	+	13.6715i	0.266081	+	0.460865i
$881$	12.0182	−	20.8162i	0.404904	−	0.701314i	−0.589406	−	0.807837i	$-0.700638\pi$
$881$	12.0182	−	20.8162i	0.404904	−	0.701314i	0.994310	+	0.106523i	$0.0339716\pi$
$882$	−0.424887	−	0.735925i	−0.0143067	−	0.0247799i
$883$	−46.4095			−1.56180			−0.780902	−	0.624653i	$-0.785240\pi$
$883$	−46.4095			−1.56180			−0.780902	+	0.624653i	$0.785240\pi$
$884$	17.2962			0.581734
$885$	−9.70414	−	16.8081i	−0.326201	−	0.564997i
$886$	14.0030			0.470441
$887$	−22.9290	−	39.7142i	−0.769881	−	1.33347i	−0.937627	−	0.347643i	$-0.886982\pi$
$887$	−22.9290	−	39.7142i	−0.769881	−	1.33347i	0.167746	−	0.985830i	$-0.446351\pi$
$888$	−16.7099			−0.560748
$889$	7.12471	+	12.3404i	0.238955	+	0.413882i
$890$	2.06711	+	3.58035i	0.0692899	+	0.120014i
$891$	−0.849585	−	1.47152i	−0.0284622	−	0.0492979i
$892$	1.88882	+	3.27152i	0.0632422	+	0.109539i
$893$	−14.7964			−0.495142
$894$	−4.75101	+	8.22899i	−0.158898	+	0.275219i
$895$	28.0653	+	48.6105i	0.938118	+	1.62487i
$896$	25.6887			0.858199
$897$	10.1421			0.338634
$898$	−4.92738	+	8.53447i	−0.164429	+	0.284799i
$899$	−11.1473	−	19.3076i	−0.371782	−	0.643946i
$900$	6.27357	−	10.8661i	0.209119	−	0.362204i
$901$	92.2615			3.07367
$902$	2.54924	−	4.41541i	0.0848804	−	0.147017i
$903$	−8.19218			−0.272619
$904$	−16.4086	+	28.4205i	−0.545741	+	0.945251i
$905$	4.43908	+	7.68871i	0.147560	+	0.255581i
$906$	−2.80041	−	4.85045i	−0.0930373	−	0.161145i
$907$	16.0749	−	27.8425i	0.533757	−	0.924494i	−0.465465	−	0.885066i	$-0.654113\pi$
$907$	16.0749	−	27.8425i	0.533757	−	0.924494i	0.999222	−	0.0394281i	$-0.0125536\pi$
$908$	4.35338	−	7.54028i	0.144472	−	0.250233i
$909$	−3.13342	−	5.42724i	−0.103929	−	0.180010i
$910$	4.95112			0.164128
$911$	2.21658	+	3.83923i	0.0734385	+	0.127199i	0.900406	−	0.435050i	$-0.143269\pi$
$911$	2.21658	+	3.83923i	0.0734385	+	0.127199i	−0.826968	+	0.562250i	$0.809936\pi$
$912$	6.93796	+	12.0169i	0.229739	+	0.397919i
$913$	−5.31374			−0.175859
$914$	19.2825			0.637807
$915$	0.848273			0.0280430
$916$	1.77958	+	3.08232i	0.0587989	+	0.101843i
$917$	−1.65975	−	2.87478i	−0.0548099	−	0.0949335i
$918$	1.80591	−	3.12792i	0.0596038	−	0.103237i
$919$	−40.6569			−1.34115			−0.670573	−	0.741844i	$-0.733952\pi$
$919$	−40.6569			−1.34115			−0.670573	+	0.741844i	$0.733952\pi$
$920$	−24.5660	+	42.5495i	−0.809916	+	1.40282i
$921$	0.415885	−	0.720334i	0.0137039	−	0.0237358i
$922$	5.75353	−	9.96540i	0.189482	−	0.328193i
$923$	1.79457	−	3.10829i	0.0590691	−	0.102311i
$924$	−3.43826	−	5.95525i	−0.113111	−	0.195913i
$925$	−32.7507	+	56.7260i	−1.07684	+	1.86514i
$926$	2.29165			0.0753084
$927$	3.99289	+	6.91589i	0.131144	+	0.227148i
$928$	−34.6809			−1.13846
$929$	−9.83049	−	17.0269i	−0.322528	−	0.558635i	0.658481	−	0.752597i	$-0.271199\pi$
$929$	−9.83049	−	17.0269i	−0.322528	−	0.558635i	−0.981009	+	0.193962i	$0.937866\pi$
$930$	2.62661	−	4.54943i	0.0861301	−	0.149182i
$931$	4.59919	−	7.96604i	0.150732	−	0.261076i
$932$	−22.5858	+	39.1198i	−0.739823	+	1.28141i
$933$	−13.5394	−	23.4510i	−0.443262	−	0.767752i
$934$	−2.12196			−0.0694325
$935$	44.4792			1.45462
$936$	−1.17381	+	2.03310i	−0.0383673	+	0.0664541i
$937$	23.4091	−	40.5458i	0.764743	−	1.32457i	−0.175640	−	0.984455i	$-0.556199\pi$
$937$	23.4091	−	40.5458i	0.764743	−	1.32457i	0.940382	−	0.340119i	$-0.110467\pi$
$938$	5.97362			0.195046
$939$	−14.8349	+	25.6948i	−0.484118	+	0.838518i
$940$	−17.5338			−0.571890
$941$	5.58154			0.181953			0.0909766	−	0.995853i	$-0.471001\pi$
$941$	5.58154			0.181953			0.0909766	+	0.995853i	$0.471001\pi$
$942$	0.884941	+	5.94565i	0.0288330	+	0.193720i
$943$	−48.8682			−1.59137
$944$	14.9152			0.485450
$945$	−3.97529	+	6.88540i	−0.129316	+	0.223982i
$946$	−2.92044			−0.0949516
$947$	−12.2517	+	21.2205i	−0.398126	+	0.689574i	−0.993495	−	0.113878i	$-0.963673\pi$
$947$	−12.2517	+	21.2205i	−0.398126	+	0.689574i	0.595369	+	0.803452i	$0.297006\pi$
$948$	−15.1393	+	26.2220i	−0.491700	+	0.851649i
$949$	7.58436			0.246199
$950$	−17.6617			−0.573021
$951$	4.96022	+	8.59135i	0.160846	+	0.278594i
$952$	15.5674	−	26.9635i	0.504542	−	0.873892i
$953$	−0.0147005	+	0.0254620i	−0.000476195	+	0.000824794i	−0.866263	−	0.499588i	$-0.833485\pi$
$953$	−0.0147005	+	0.0254620i	−0.000476195	+	0.000824794i	0.865787	+	0.500412i	$0.166818\pi$
$954$	−2.93955	+	5.09145i	−0.0951714	+	0.164842i
$955$	−7.51330	−	13.0134i	−0.243125	−	0.421105i
$956$	18.1524			0.587089
$957$	6.01435	+	10.4172i	0.194416	+	0.336739i
$958$	2.16826			0.0700534
$959$	19.4131	−	33.6245i	0.626883	−	1.08579i
$960$	5.20478	+	9.01494i	0.167984	+	0.290956i
$961$	10.5409	−	18.2574i	0.340029	−	0.588948i
$962$	2.87685	−	4.98285i	0.0927534	−	0.160654i
$963$	−3.87318	+	6.70855i	−0.124812	+	0.216180i
$964$	26.7760	−	46.3774i	0.862398	−	1.49372i
$965$	−40.7824			−1.31283
$966$	4.28553	−	7.42275i	0.137885	−	0.238823i
$967$	−26.0099	−	45.0505i	−0.836422	−	1.44872i	−0.892868	−	0.450319i	$-0.851310\pi$
$967$	−26.0099	−	45.0505i	−0.836422	−	1.44872i	0.0564459	−	0.998406i	$-0.482023\pi$
$968$	7.33624	+	12.7067i	0.235796	+	0.408410i
$969$	39.0961			1.25595
$970$	−18.4930			−0.593776
$971$	51.2646			1.64516			0.822579	−	0.568651i	$-0.192534\pi$
$971$	51.2646			1.64516			0.822579	+	0.568651i	$0.192534\pi$
$972$	−0.884924	−	1.53273i	−0.0283839	−	0.0491624i
$973$	24.1492	+	41.8277i	0.774189	+	1.34093i
$974$	−20.4962			−0.656740
$975$	4.60125	+	7.96960i	0.147358	+	0.255231i
$976$	−0.325948	+	0.564559i	−0.0104334	+	0.0180711i
$977$	1.88525	−	3.26536i	0.0603146	−	0.104468i	−0.834291	−	0.551324i	$-0.814123\pi$
$977$	1.88525	−	3.26536i	0.0603146	−	0.104468i	0.894606	+	0.446856i	$0.147456\pi$
$978$	1.12045	+	1.94067i	0.0358280	+	0.0620558i
$979$	2.10568	+	3.64714i	0.0672977	+	0.116563i
$980$	5.45008	−	9.43982i	0.174097	−	0.301544i
$981$	3.11106			0.0993285
$982$	−4.99350	+	8.64900i	−0.159349	+	0.276001i
$983$	37.5823			1.19869			0.599344	−	0.800492i	$-0.295428\pi$
$983$	37.5823			1.19869			0.599344	+	0.800492i	$0.295428\pi$
$984$	5.65585	−	9.79622i	0.180302	−	0.312292i
$985$	−31.8073	−	55.0918i	−1.01346	−	1.75537i
$986$	−12.7843	+	22.1431i	−0.407135	+	0.705179i
$987$	6.51531			0.207385
$988$	−11.9302			−0.379552
$989$	13.9960	+	24.2418i	0.445046	+	0.770843i
$990$	−1.41715	+	2.45458i	−0.0450401	+	0.0780117i
$991$	14.9588			0.475182			0.237591	−	0.971365i	$-0.423642\pi$
$991$	14.9588			0.475182			0.237591	+	0.971365i	$0.423642\pi$
$992$	7.71426	+	13.3615i	0.244928	+	0.424228i
$993$	−11.1441	−	19.3021i	−0.353646	−	0.612533i
$994$	−1.51659	−	2.62681i	−0.0481033	−	0.0833173i
$995$	8.72827	+	15.1178i	0.276705	+	0.479267i
$996$	−5.53476			−0.175376
$997$	6.21198	+	10.7595i	0.196735	+	0.340756i	0.947468	−	0.319851i	$-0.103633\pi$
$997$	6.21198	+	10.7595i	0.196735	+	0.340756i	−0.750733	+	0.660606i	$0.770299\pi$
$998$	−1.55605			−0.0492558
$999$	4.61969	+	8.00153i	0.146160	+	0.253157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.e.b.301.5	yes	22
157.12	even	3	inner	471.2.e.b.169.5	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.e.b.169.5	✓	22	157.12	even	3	inner
471.2.e.b.301.5	yes	22	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.479742 q^{2} +(0.500000 - 0.866025i) q^{3} -1.76985 q^{4} +(1.73849 - 3.01115i) q^{5} +(-0.239871 + 0.415469i) q^{6} +2.28663 q^{7} +1.80855 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-0.479742 q^{2} +(0.500000 - 0.866025i) q^{3} -1.76985 q^{4} +(1.73849 - 3.01115i) q^{5} +(-0.239871 + 0.415469i) q^{6} +2.28663 q^{7} +1.80855 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.834027 + 1.44458i) q^{10} +(-0.849585 + 1.47152i) q^{11} +(-0.884924 + 1.53273i) q^{12} +(-0.649034 - 1.12416i) q^{13} -1.09699 q^{14} +(-1.73849 - 3.01115i) q^{15} +2.67206 q^{16} +(3.76433 - 6.52001i) q^{17} +(0.239871 + 0.415469i) q^{18} +(-2.59649 + 4.49725i) q^{19} +(-3.07686 + 5.32928i) q^{20} +(1.14332 - 1.98028i) q^{21} +(0.407582 - 0.705952i) q^{22} -7.81322 q^{23} +(0.904277 - 1.56625i) q^{24} +(-3.54469 - 6.13959i) q^{25} +(0.311369 + 0.539306i) q^{26} -1.00000 q^{27} -4.04699 q^{28} +7.07917 q^{29} +(0.834027 + 1.44458i) q^{30} +(-1.57466 - 2.72739i) q^{31} -4.89901 q^{32} +(0.849585 + 1.47152i) q^{33} +(-1.80591 + 3.12792i) q^{34} +(3.97529 - 6.88540i) q^{35} +(0.884924 + 1.53273i) q^{36} +(-4.61969 - 8.00153i) q^{37} +(1.24564 - 2.15752i) q^{38} -1.29807 q^{39} +(3.14415 - 5.44583i) q^{40} +6.25455 q^{41} +(-0.548497 + 0.950024i) q^{42} +(-1.79132 - 3.10266i) q^{43} +(1.50364 - 2.60437i) q^{44} -3.47698 q^{45} +3.74833 q^{46} +(1.42465 + 2.46757i) q^{47} +(1.33603 - 2.31407i) q^{48} -1.77131 q^{49} +(1.70054 + 2.94542i) q^{50} +(-3.76433 - 6.52001i) q^{51} +(1.14869 + 1.98959i) q^{52} +(6.12735 + 10.6129i) q^{53} +0.479742 q^{54} +(2.95399 + 5.11646i) q^{55} +4.13550 q^{56} +(2.59649 + 4.49725i) q^{57} -3.39617 q^{58} +5.58194 q^{59} +(3.07686 + 5.32928i) q^{60} +(-0.121984 + 0.211283i) q^{61} +(0.755430 + 1.30844i) q^{62} +(-1.14332 - 1.98028i) q^{63} -2.99385 q^{64} -4.51335 q^{65} +(-0.407582 - 0.705952i) q^{66} -5.44544 q^{67} +(-6.66229 + 11.5394i) q^{68} +(-3.90661 + 6.76645i) q^{69} +(-1.90711 + 3.30322i) q^{70} +(1.38250 + 2.39455i) q^{71} +(-0.904277 - 1.56625i) q^{72} +(-2.92141 + 5.06002i) q^{73} +(2.21626 + 3.83867i) q^{74} -7.08938 q^{75} +(4.59539 - 7.95945i) q^{76} +(-1.94269 + 3.36484i) q^{77} +0.622737 q^{78} +17.1080 q^{79} +(4.64534 - 8.04597i) q^{80} +(-0.500000 + 0.866025i) q^{81} -3.00057 q^{82} +(1.56363 + 2.70828i) q^{83} +(-2.02350 + 3.50480i) q^{84} +(-13.0885 - 22.6699i) q^{85} +(0.859372 + 1.48848i) q^{86} +(3.53958 - 6.13074i) q^{87} +(-1.53652 + 2.66133i) q^{88} +(1.23924 - 2.14642i) q^{89} +1.66805 q^{90} +(-1.48410 - 2.57054i) q^{91} +13.8282 q^{92} -3.14932 q^{93} +(-0.683465 - 1.18380i) q^{94} +(9.02794 + 15.6368i) q^{95} +(-2.44950 + 4.24266i) q^{96} +(5.54330 + 9.60128i) q^{97} +0.849773 q^{98} +1.69917 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9}+O(q^{10}) \) 22 * q + 2 * q^2 + 11 * q^3 + 30 * q^4 - 4 * q^5 + q^6 + 4 * q^7 - 11 * q^9	\( 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9} - 5 q^{10} + 15 q^{12} + 3 q^{13} - 14 q^{14} + 4 q^{15} + 54 q^{16} - q^{17} - q^{18} - 22 q^{19} - 7 q^{20} + 2 q^{21} - 22 q^{22} - 10 q^{23} - 15 q^{25} - 10 q^{26} - 22 q^{27} - 38 q^{28} + 22 q^{29} + 5 q^{30} - 6 q^{31} + 32 q^{32} + 17 q^{34} - 11 q^{35} - 15 q^{36} + 8 q^{37} + 14 q^{38} + 6 q^{39} + 32 q^{40} - 7 q^{42} + q^{43} - 12 q^{44} + 8 q^{45} + 24 q^{46} + 7 q^{47} + 27 q^{48} + 22 q^{49} + 13 q^{50} + q^{51} + 17 q^{52} + 30 q^{53} - 2 q^{54} + 31 q^{55} - 82 q^{56} + 22 q^{57} - 90 q^{58} - 16 q^{59} + 7 q^{60} + 8 q^{61} - 28 q^{62} - 2 q^{63} - 32 q^{64} - 68 q^{65} + 22 q^{66} - 38 q^{67} - 8 q^{68} - 5 q^{69} + 43 q^{70} + 45 q^{71} - 4 q^{73} + 3 q^{74} - 30 q^{75} - 33 q^{76} + 21 q^{77} - 20 q^{78} + 26 q^{79} - 12 q^{80} - 11 q^{81} + 16 q^{82} + 8 q^{83} - 19 q^{84} - 28 q^{85} - 16 q^{86} + 11 q^{87} - 65 q^{88} + 15 q^{89} + 10 q^{90} - 3 q^{91} - 18 q^{92} - 12 q^{93} - 28 q^{94} - 5 q^{95} + 16 q^{96} - 35 q^{97} + 90 q^{98}+O(q^{100}) \) 22 * q + 2 * q^2 + 11 * q^3 + 30 * q^4 - 4 * q^5 + q^6 + 4 * q^7 - 11 * q^9 - 5 * q^10 + 15 * q^12 + 3 * q^13 - 14 * q^14 + 4 * q^15 + 54 * q^16 - q^17 - q^18 - 22 * q^19 - 7 * q^20 + 2 * q^21 - 22 * q^22 - 10 * q^23 - 15 * q^25 - 10 * q^26 - 22 * q^27 - 38 * q^28 + 22 * q^29 + 5 * q^30 - 6 * q^31 + 32 * q^32 + 17 * q^34 - 11 * q^35 - 15 * q^36 + 8 * q^37 + 14 * q^38 + 6 * q^39 + 32 * q^40 - 7 * q^42 + q^43 - 12 * q^44 + 8 * q^45 + 24 * q^46 + 7 * q^47 + 27 * q^48 + 22 * q^49 + 13 * q^50 + q^51 + 17 * q^52 + 30 * q^53 - 2 * q^54 + 31 * q^55 - 82 * q^56 + 22 * q^57 - 90 * q^58 - 16 * q^59 + 7 * q^60 + 8 * q^61 - 28 * q^62 - 2 * q^63 - 32 * q^64 - 68 * q^65 + 22 * q^66 - 38 * q^67 - 8 * q^68 - 5 * q^69 + 43 * q^70 + 45 * q^71 - 4 * q^73 + 3 * q^74 - 30 * q^75 - 33 * q^76 + 21 * q^77 - 20 * q^78 + 26 * q^79 - 12 * q^80 - 11 * q^81 + 16 * q^82 + 8 * q^83 - 19 * q^84 - 28 * q^85 - 16 * q^86 + 11 * q^87 - 65 * q^88 + 15 * q^89 + 10 * q^90 - 3 * q^91 - 18 * q^92 - 12 * q^93 - 28 * q^94 - 5 * q^95 + 16 * q^96 - 35 * q^97 + 90 * q^98

Introduction

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