LMFDB - Embedded newform 585.2.i.g.391.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			391.5
Character	$\chi$	$=$	585.391
Dual form			585.2.i.g.196.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.643841 - 1.11517i) q^{2} +(-1.73180 + 0.0293427i) q^{3} +(0.170938 - 0.296073i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.14773 + 1.91235i) q^{6} +(0.391685 + 0.678419i) q^{7} -3.01559 q^{8} +(2.99828 - 0.101632i) q^{9} +O(q^{10})$	\(q+(-0.643841 - 1.11517i) q^{2} +(-1.73180 + 0.0293427i) q^{3} +(0.170938 - 0.296073i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.14773 + 1.91235i) q^{6} +(0.391685 + 0.678419i) q^{7} -3.01559 q^{8} +(2.99828 - 0.101632i) q^{9} +1.28768 q^{10} +(0.972557 + 1.68452i) q^{11} +(-0.287343 + 0.517755i) q^{12} +(0.500000 - 0.866025i) q^{13} +(0.504366 - 0.873587i) q^{14} +(0.840490 - 1.51446i) q^{15} +(1.59969 + 2.77074i) q^{16} +0.858016 q^{17} +(-2.04375 - 3.27814i) q^{18} +5.16817 q^{19} +(0.170938 + 0.296073i) q^{20} +(-0.698228 - 1.16339i) q^{21} +(1.25234 - 2.16912i) q^{22} +(1.28804 - 2.23095i) q^{23} +(5.22241 - 0.0884856i) q^{24} +(-0.500000 - 0.866025i) q^{25} -1.28768 q^{26} +(-5.18944 + 0.263983i) q^{27} +0.267815 q^{28} +(-0.344492 - 0.596678i) q^{29} +(-2.23001 + 0.0377841i) q^{30} +(2.29311 - 3.97178i) q^{31} +(-0.955704 + 1.65533i) q^{32} +(-1.73370 - 2.88871i) q^{33} +(-0.552426 - 0.956829i) q^{34} -0.783370 q^{35} +(0.482428 - 0.905081i) q^{36} +8.56300 q^{37} +(-3.32748 - 5.76336i) q^{38} +(-0.840490 + 1.51446i) q^{39} +(1.50780 - 2.61158i) q^{40} +(1.47108 - 2.54798i) q^{41} +(-0.847829 + 1.52768i) q^{42} +(-3.65391 - 6.32875i) q^{43} +0.664986 q^{44} +(-1.41112 + 2.64740i) q^{45} -3.31717 q^{46} +(-2.12366 - 3.67829i) q^{47} +(-2.85164 - 4.75143i) q^{48} +(3.19317 - 5.53072i) q^{49} +(-0.643841 + 1.11517i) q^{50} +(-1.48591 + 0.0251765i) q^{51} +(-0.170938 - 0.296073i) q^{52} +3.78973 q^{53} +(3.63556 + 5.61712i) q^{54} -1.94511 q^{55} +(-1.18116 - 2.04583i) q^{56} +(-8.95025 + 0.151648i) q^{57} +(-0.443597 + 0.768332i) q^{58} +(-2.70371 + 4.68297i) q^{59} +(-0.304718 - 0.507723i) q^{60} +(-4.29427 - 7.43790i) q^{61} -5.90559 q^{62} +(1.24333 + 1.99428i) q^{63} +8.86003 q^{64} +(0.500000 + 0.866025i) q^{65} +(-2.10516 + 3.79324i) q^{66} +(0.687659 - 1.19106i) q^{67} +(0.146667 - 0.254035i) q^{68} +(-2.16517 + 3.90136i) q^{69} +(0.504366 + 0.873587i) q^{70} +1.64996 q^{71} +(-9.04158 + 0.306479i) q^{72} +8.86126 q^{73} +(-5.51321 - 9.54916i) q^{74} +(0.891313 + 1.48511i) q^{75} +(0.883434 - 1.53015i) q^{76} +(-0.761872 + 1.31960i) q^{77} +(2.23001 - 0.0377841i) q^{78} +(2.69235 + 4.66329i) q^{79} -3.19937 q^{80} +(8.97934 - 0.609439i) q^{81} -3.78855 q^{82} +(-2.24085 - 3.88127i) q^{83} +(-0.463802 + 0.00785841i) q^{84} +(-0.429008 + 0.743063i) q^{85} +(-4.70507 + 8.14942i) q^{86} +(0.614101 + 1.02322i) q^{87} +(-2.93283 - 5.07982i) q^{88} +12.3755 q^{89} +(3.86083 - 0.130869i) q^{90} +0.783370 q^{91} +(-0.440349 - 0.762707i) q^{92} +(-3.85467 + 6.94563i) q^{93} +(-2.73460 + 4.73647i) q^{94} +(-2.58408 + 4.47577i) q^{95} +(1.60652 - 2.89474i) q^{96} +(8.35275 + 14.4674i) q^{97} -8.22356 q^{98} +(3.08720 + 4.95181i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9}+O(q^{10}) $ 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9	\( 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9} - 2 q^{10} - 11 q^{11} - 20 q^{12} + 13 q^{13} - 15 q^{14} - 2 q^{15} - 19 q^{16} + 6 q^{17} - 13 q^{18} + 30 q^{19} - 15 q^{20} - q^{21} - 12 q^{22} - 6 q^{23} + 20 q^{24} - 13 q^{25} + 2 q^{26} - 2 q^{27} + 10 q^{28} - 14 q^{29} - 2 q^{30} - 30 q^{31} + 43 q^{32} + 6 q^{33} - 19 q^{34} + 20 q^{35} - 39 q^{36} + 32 q^{37} + 2 q^{38} + 2 q^{39} + 6 q^{40} - 17 q^{41} + 83 q^{42} - 6 q^{43} + 46 q^{44} - 5 q^{45} + 46 q^{46} + 21 q^{47} - 7 q^{48} - 29 q^{49} + q^{50} + 55 q^{51} + 15 q^{52} + 2 q^{53} - 6 q^{54} + 22 q^{55} - 37 q^{56} + 33 q^{57} - 14 q^{58} - 13 q^{59} + 25 q^{60} - 22 q^{61} - 114 q^{62} - 44 q^{63} + 84 q^{64} + 13 q^{65} - 68 q^{66} - 35 q^{67} + 4 q^{68} - 38 q^{69} - 15 q^{70} + 24 q^{71} - 24 q^{72} + 64 q^{73} + 28 q^{74} + q^{75} - 54 q^{76} - 4 q^{77} + 2 q^{78} - 12 q^{79} + 38 q^{80} + 15 q^{81} + 46 q^{82} + 3 q^{83} + 27 q^{84} - 3 q^{85} + 40 q^{86} - 12 q^{87} - 29 q^{88} + 12 q^{89} - 10 q^{90} - 20 q^{91} + 16 q^{92} - 9 q^{93} - 44 q^{94} - 15 q^{95} + 51 q^{96} - 33 q^{97} + 70 q^{98} - 22 q^{99}+O(q^{100}) \) 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9 - 2 * q^10 - 11 * q^11 - 20 * q^12 + 13 * q^13 - 15 * q^14 - 2 * q^15 - 19 * q^16 + 6 * q^17 - 13 * q^18 + 30 * q^19 - 15 * q^20 - q^21 - 12 * q^22 - 6 * q^23 + 20 * q^24 - 13 * q^25 + 2 * q^26 - 2 * q^27 + 10 * q^28 - 14 * q^29 - 2 * q^30 - 30 * q^31 + 43 * q^32 + 6 * q^33 - 19 * q^34 + 20 * q^35 - 39 * q^36 + 32 * q^37 + 2 * q^38 + 2 * q^39 + 6 * q^40 - 17 * q^41 + 83 * q^42 - 6 * q^43 + 46 * q^44 - 5 * q^45 + 46 * q^46 + 21 * q^47 - 7 * q^48 - 29 * q^49 + q^50 + 55 * q^51 + 15 * q^52 + 2 * q^53 - 6 * q^54 + 22 * q^55 - 37 * q^56 + 33 * q^57 - 14 * q^58 - 13 * q^59 + 25 * q^60 - 22 * q^61 - 114 * q^62 - 44 * q^63 + 84 * q^64 + 13 * q^65 - 68 * q^66 - 35 * q^67 + 4 * q^68 - 38 * q^69 - 15 * q^70 + 24 * q^71 - 24 * q^72 + 64 * q^73 + 28 * q^74 + q^75 - 54 * q^76 - 4 * q^77 + 2 * q^78 - 12 * q^79 + 38 * q^80 + 15 * q^81 + 46 * q^82 + 3 * q^83 + 27 * q^84 - 3 * q^85 + 40 * q^86 - 12 * q^87 - 29 * q^88 + 12 * q^89 - 10 * q^90 - 20 * q^91 + 16 * q^92 - 9 * q^93 - 44 * q^94 - 15 * q^95 + 51 * q^96 - 33 * q^97 + 70 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.643841	−	1.11517i	−0.455264	−	0.788541i	0.543439	−	0.839449i	$-0.317122\pi$
$2$	−0.643841	−	1.11517i	−0.455264	−	0.788541i	−0.998703	+	0.0509077i	$0.983789\pi$
$3$	−1.73180	+	0.0293427i	−0.999856	+	0.0169410i
$3$	−1.73180	+	0.0293427i	−0.999856	+	0.0169410i
$4$	0.170938	−	0.296073i	0.0854688	−	0.148036i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	1.14773	+	1.91235i	0.468558	+	0.780715i
$7$	0.391685	+	0.678419i	0.148043	+	0.256418i	0.930504	−	0.366281i	$-0.119369\pi$
$7$	0.391685	+	0.678419i	0.148043	+	0.256418i	−0.782461	+	0.622700i	$0.786036\pi$
$8$	−3.01559			−1.06617
$9$	2.99828	−	0.101632i	0.999426	−	0.0338772i
$10$	1.28768			0.407201
$11$	0.972557	+	1.68452i	0.293237	+	0.507901i	0.974573	−	0.224069i	$-0.0719342\pi$
$11$	0.972557	+	1.68452i	0.293237	+	0.507901i	−0.681336	+	0.731971i	$0.738601\pi$
$12$	−0.287343	+	0.517755i	−0.0829487	+	0.149463i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	0.504366	−	0.873587i	0.134797	−	0.233476i
$15$	0.840490	−	1.51446i	0.217013	−	0.391031i
$16$	1.59969	+	2.77074i	0.399921	+	0.692684i
$17$	0.858016			0.208099			0.104050	−	0.994572i	$-0.466820\pi$
$17$	0.858016			0.208099			0.104050	+	0.994572i	$0.466820\pi$
$18$	−2.04375	−	3.27814i	−0.481717	−	0.772665i
$19$	5.16817			1.18566			0.592830	−	0.805328i	$-0.298011\pi$
$19$	5.16817			1.18566			0.592830	+	0.805328i	$0.298011\pi$
$20$	0.170938	+	0.296073i	0.0382228	+	0.0662039i
$21$	−0.698228	−	1.16339i	−0.152366	−	0.253873i
$22$	1.25234	−	2.16912i	0.267001	−	0.462459i
$23$	1.28804	−	2.23095i	0.268575	−	0.465186i	−0.699919	−	0.714222i	$-0.746781\pi$
$23$	1.28804	−	2.23095i	0.268575	−	0.465186i	0.968494	+	0.249037i	$0.0801139\pi$
$24$	5.22241	−	0.0884856i	1.06602	−	0.0180620i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.28768			−0.252535
$27$	−5.18944	+	0.263983i	−0.998709	+	0.0508036i
$28$	0.267815			0.0506123
$29$	−0.344492	−	0.596678i	−0.0639706	−	0.110800i	0.832266	−	0.554376i	$-0.187043\pi$
$29$	−0.344492	−	0.596678i	−0.0639706	−	0.110800i	−0.896237	+	0.443576i	$0.853710\pi$
$30$	−2.23001	+	0.0377841i	−0.407142	+	0.00689840i
$31$	2.29311	−	3.97178i	0.411855	−	0.713353i	−0.583238	−	0.812301i	$-0.698214\pi$
$31$	2.29311	−	3.97178i	0.411855	−	0.713353i	0.995093	+	0.0989482i	$0.0315478\pi$
$32$	−0.955704	+	1.65533i	−0.168946	+	0.292624i
$33$	−1.73370	−	2.88871i	−0.301799	−	0.502861i
$34$	−0.552426	−	0.956829i	−0.0947402	−	0.164095i
$35$	−0.783370			−0.132414
$36$	0.482428	−	0.905081i	0.0804047	−	0.150847i
$37$	8.56300			1.40775			0.703874	−	0.710325i	$-0.251452\pi$
$37$	8.56300			1.40775			0.703874	+	0.710325i	$0.251452\pi$
$38$	−3.32748	−	5.76336i	−0.539788	−	0.934941i
$39$	−0.840490	+	1.51446i	−0.134586	+	0.242507i
$40$	1.50780	−	2.61158i	0.238403	−	0.412927i
$41$	1.47108	−	2.54798i	0.229743	−	0.397927i	−0.727989	−	0.685589i	$-0.759545\pi$
$41$	1.47108	−	2.54798i	0.229743	−	0.397927i	0.957732	+	0.287662i	$0.0928780\pi$
$42$	−0.847829	+	1.52768i	−0.130823	+	0.235726i
$43$	−3.65391	−	6.32875i	−0.557216	−	0.965126i	−0.997727	−	0.0673792i	$-0.978536\pi$
$43$	−3.65391	−	6.32875i	−0.557216	−	0.965126i	0.440512	−	0.897747i	$-0.354797\pi$
$44$	0.664986			0.100250
$45$	−1.41112	+	2.64740i	−0.210358	+	0.394651i
$46$	−3.31717			−0.489091
$47$	−2.12366	−	3.67829i	−0.309768	−	0.536534i	0.668543	−	0.743673i	$-0.266918\pi$
$47$	−2.12366	−	3.67829i	−0.309768	−	0.536534i	−0.978311	+	0.207139i	$0.933585\pi$
$48$	−2.85164	−	4.75143i	−0.411599	−	0.685810i
$49$	3.19317	−	5.53072i	0.456166	−	0.790104i
$50$	−0.643841	+	1.11517i	−0.0910529	+	0.157708i
$51$	−1.48591	+	0.0251765i	−0.208069	+	0.00352541i
$52$	−0.170938	−	0.296073i	−0.0237048	−	0.0410579i
$53$	3.78973			0.520560			0.260280	−	0.965533i	$-0.416185\pi$
$53$	3.78973			0.520560			0.260280	+	0.965533i	$0.416185\pi$
$54$	3.63556	+	5.61712i	0.494737	+	0.764394i
$55$	−1.94511			−0.262279
$56$	−1.18116	−	2.04583i	−0.157839	−	0.273386i
$57$	−8.95025	+	0.151648i	−1.18549	+	0.0200863i
$58$	−0.443597	+	0.768332i	−0.0582471	+	0.100887i
$59$	−2.70371	+	4.68297i	−0.351993	+	0.609670i	−0.986599	−	0.163166i	$-0.947829\pi$
$59$	−2.70371	+	4.68297i	−0.351993	+	0.609670i	0.634605	+	0.772836i	$0.281163\pi$
$60$	−0.304718	−	0.507723i	−0.0393389	−	0.0655468i
$61$	−4.29427	−	7.43790i	−0.549825	−	0.952325i	−0.998286	−	0.0585228i	$-0.981361\pi$
$61$	−4.29427	−	7.43790i	−0.549825	−	0.952325i	0.448461	−	0.893803i	$-0.351972\pi$
$62$	−5.90559			−0.750011
$63$	1.24333	+	1.99428i	0.156645	+	0.251256i
$64$	8.86003			1.10750
$65$	0.500000	+	0.866025i	0.0620174	+	0.107417i
$66$	−2.10516	+	3.79324i	−0.259128	+	0.466915i
$67$	0.687659	−	1.19106i	0.0840109	−	0.145511i	−0.820958	−	0.570988i	$-0.806560\pi$
$67$	0.687659	−	1.19106i	0.0840109	−	0.145511i	0.904969	+	0.425477i	$0.139894\pi$
$68$	0.146667	−	0.254035i	0.0177860	−	0.0308063i
$69$	−2.16517	+	3.90136i	−0.260656	+	0.469669i
$70$	0.504366	+	0.873587i	0.0602833	+	0.104414i
$71$	1.64996			0.195815			0.0979074	−	0.995196i	$-0.468785\pi$
$71$	1.64996			0.195815			0.0979074	+	0.995196i	$0.468785\pi$
$72$	−9.04158	+	0.306479i	−1.06556	+	0.0361189i
$73$	8.86126			1.03713			0.518566	−	0.855038i	$-0.326466\pi$
$73$	8.86126			1.03713			0.518566	+	0.855038i	$0.326466\pi$
$74$	−5.51321	−	9.54916i	−0.640897	−	1.11007i
$75$	0.891313	+	1.48511i	0.102920	+	0.171486i
$76$	0.883434	−	1.53015i	0.101337	−	0.175521i
$77$	−0.761872	+	1.31960i	−0.0868234	+	0.150383i
$78$	2.23001	−	0.0377841i	0.252499	−	0.00427820i
$79$	2.69235	+	4.66329i	0.302913	+	0.524661i	0.976795	−	0.214179i	$-0.0687075\pi$
$79$	2.69235	+	4.66329i	0.302913	+	0.524661i	−0.673881	+	0.738840i	$0.735374\pi$
$80$	−3.19937			−0.357701
$81$	8.97934	−	0.609439i	0.997705	−	0.0677155i
$82$	−3.78855			−0.418376
$83$	−2.24085	−	3.88127i	−0.245966	−	0.426025i	0.716437	−	0.697652i	$-0.245772\pi$
$83$	−2.24085	−	3.88127i	−0.245966	−	0.426025i	−0.962403	+	0.271627i	$0.912438\pi$
$84$	−0.463802	+	0.00785841i	−0.0506050	+	0.000857423i
$85$	−0.429008	+	0.743063i	−0.0465324	+	0.0805965i
$86$	−4.70507	+	8.14942i	−0.507361	+	0.878775i
$87$	0.614101	+	1.02322i	0.0658385	+	0.109701i
$88$	−2.93283	−	5.07982i	−0.312641	−	0.541510i
$89$	12.3755			1.31180			0.655902	−	0.754846i	$-0.272288\pi$
$89$	12.3755			1.31180			0.655902	+	0.754846i	$0.272288\pi$
$90$	3.86083	−	0.130869i	0.406967	−	0.0137948i
$91$	0.783370			0.0821195
$92$	−0.440349	−	0.762707i	−0.0459096	−	0.0795177i
$93$	−3.85467	+	6.94563i	−0.399711	+	0.720228i
$94$	−2.73460	+	4.73647i	−0.282053	+	0.488530i
$95$	−2.58408	+	4.47577i	−0.265121	+	0.459204i
$96$	1.60652	−	2.89474i	0.163965	−	0.295444i
$97$	8.35275	+	14.4674i	0.848093	+	1.46894i	0.882908	+	0.469547i	$0.155583\pi$
$97$	8.35275	+	14.4674i	0.848093	+	1.46894i	−0.0348144	+	0.999394i	$0.511084\pi$
$98$	−8.22356			−0.830705
$99$	3.08720	+	4.95181i	0.310275	+	0.497676i
$100$	−0.341875			−0.0341875
$101$	2.34095	+	4.05464i	0.232933	+	0.403452i	0.958670	−	0.284521i	$-0.0918344\pi$
$101$	2.34095	+	4.05464i	0.232933	+	0.403452i	−0.725737	+	0.687972i	$0.758501\pi$
$102$	0.984768	+	1.64083i	0.0975065	+	0.162466i
$103$	−7.84201	+	13.5828i	−0.772696	+	1.33835i	0.163385	+	0.986562i	$0.447759\pi$
$103$	−7.84201	+	13.5828i	−0.772696	+	1.33835i	−0.936080	+	0.351786i	$0.885574\pi$
$104$	−1.50780	+	2.61158i	−0.147851	+	0.256086i
$105$	1.35664	−	0.0229862i	0.132395	−	0.00224322i
$106$	−2.43999	−	4.22618i	−0.236992	−	0.410483i
$107$	1.86643			0.180435			0.0902174	−	0.995922i	$-0.471244\pi$
$107$	1.86643			0.180435			0.0902174	+	0.995922i	$0.471244\pi$
$108$	−0.808913	+	1.58158i	−0.0778377	+	0.152187i
$109$	6.26091			0.599687			0.299843	−	0.953988i	$-0.403066\pi$
$109$	6.26091			0.599687			0.299843	+	0.953988i	$0.403066\pi$
$110$	1.25234	+	2.16912i	0.119406	+	0.206818i
$111$	−14.8294	+	0.251261i	−1.40755	+	0.0238487i
$112$	−1.25315	+	2.17051i	−0.118411	+	0.205094i
$113$	2.59416	−	4.49322i	0.244038	−	0.422686i	−0.717823	−	0.696226i	$-0.754861\pi$
$113$	2.59416	−	4.49322i	0.244038	−	0.422686i	0.961861	+	0.273540i	$0.0881945\pi$
$114$	5.93165	+	9.88337i	0.555550	+	0.925662i
$115$	1.28804	+	2.23095i	0.120110	+	0.208037i
$116$	−0.235547			−0.0218700
$117$	1.41112	−	2.64740i	0.130458	−	0.244752i
$118$	6.96304			0.641000
$119$	0.336072	+	0.582094i	0.0308077	+	0.0533604i
$120$	−2.53457	+	4.56698i	−0.231374	+	0.416906i
$121$	3.60827	−	6.24970i	0.328024	−	0.568155i
$122$	−5.52966	+	9.57765i	−0.500632	+	0.867119i
$123$	−2.47285	+	4.45576i	−0.222969	+	0.401762i
$124$	−0.783957	−	1.35785i	−0.0704015	−	0.121939i
$125$	1.00000			0.0894427
$126$	1.42345	−	2.67052i	0.126811	−	0.237909i
$127$	10.9548			0.972082			0.486041	−	0.873936i	$-0.338441\pi$
$127$	10.9548			0.972082			0.486041	+	0.873936i	$0.338441\pi$
$128$	−3.79304	−	6.56974i	−0.335261	−	0.580688i
$129$	6.51355	+	10.8529i	0.573486	+	0.955548i
$130$	0.643841	−	1.11517i	0.0564686	−	0.0978065i
$131$	−7.81226	+	13.5312i	−0.682560	+	1.18223i	0.291637	+	0.956529i	$0.405800\pi$
$131$	−7.81226	+	13.5312i	−0.682560	+	1.18223i	−0.974197	+	0.225700i	$0.927533\pi$
$132$	−1.15162	+	0.0195125i	−0.100236	+	0.00169834i
$133$	2.02429	+	3.50618i	0.175529	+	0.304025i
$134$	−1.77097			−0.152989
$135$	2.36610	−	4.62618i	0.203642	−	0.398158i
$136$	−2.58742			−0.221870
$137$	−2.15054	−	3.72484i	−0.183733	−	0.318234i	0.759416	−	0.650605i	$-0.225485\pi$
$137$	−2.15054	−	3.72484i	−0.183733	−	0.318234i	−0.943149	+	0.332371i	$0.892151\pi$
$138$	5.74469	−	0.0973348i	0.489020	−	0.00828569i
$139$	−10.6715	+	18.4835i	−0.905142	+	1.56775i	−0.0844155	+	0.996431i	$0.526902\pi$
$139$	−10.6715	+	18.4835i	−0.905142	+	1.56775i	−0.820727	+	0.571321i	$0.806431\pi$
$140$	−0.133907	+	0.231935i	−0.0113172	+	0.0196020i
$141$	3.78569	+	6.30776i	0.318813	+	0.531209i
$142$	−1.06231	−	1.83998i	−0.0891475	−	0.154408i
$143$	1.94511			0.162659
$144$	5.07790	+	8.14486i	0.423158	+	0.678738i
$145$	0.688985			0.0572171
$146$	−5.70524	−	9.88177i	−0.472169	−	0.817821i
$147$	−5.36764	+	9.67182i	−0.442716	+	0.797718i
$148$	1.46374	−	2.53527i	0.120319	−	0.208398i
$149$	4.34543	−	7.52650i	0.355991	−	0.616595i	−0.631296	−	0.775542i	$-0.717477\pi$
$149$	4.34543	−	7.52650i	0.355991	−	0.616595i	0.987287	+	0.158947i	$0.0508099\pi$
$150$	1.08228	−	1.95014i	0.0883681	−	0.159228i
$151$	−0.930026	−	1.61085i	−0.0756845	−	0.131089i	0.825699	−	0.564111i	$-0.190781\pi$
$151$	−0.930026	−	1.61085i	−0.0756845	−	0.131089i	−0.901384	+	0.433021i	$0.857448\pi$
$152$	−15.5851			−1.26412
$153$	2.57257	−	0.0872014i	0.207980	−	0.00704982i
$154$	1.96210			0.158110
$155$	2.29311	+	3.97178i	0.184187	+	0.319021i
$156$	0.304718	+	0.507723i	0.0243969	+	0.0406504i
$157$	3.68879	−	6.38916i	0.294397	−	0.509911i	−0.680447	−	0.732797i	$-0.738214\pi$
$157$	3.68879	−	6.38916i	0.294397	−	0.509911i	0.974844	+	0.222886i	$0.0715478\pi$
$158$	3.46689	−	6.00483i	0.275811	−	0.477719i
$159$	−6.56307	+	0.111201i	−0.520485	+	0.00881881i
$160$	−0.955704	−	1.65533i	−0.0755551	−	0.130865i
$161$	2.01803			0.159043
$162$	−6.46089	−	9.62107i	−0.507616	−	0.755903i
$163$	−8.71717			−0.682781			−0.341391	−	0.939921i	$-0.610898\pi$
$163$	−8.71717			−0.682781			−0.341391	+	0.939921i	$0.610898\pi$
$164$	−0.502924	−	0.871090i	−0.0392718	−	0.0680207i
$165$	3.36855	−	0.0570749i	0.262241	−	0.00444327i
$166$	−2.88551	+	4.99785i	−0.223959	+	0.387908i
$167$	2.12532	−	3.68116i	0.164462	−	0.284857i	−0.772002	−	0.635620i	$-0.780745\pi$
$167$	2.12532	−	3.68116i	0.164462	−	0.284857i	0.936464	+	0.350763i	$0.114078\pi$
$168$	2.10557	+	3.50832i	0.162448	+	0.270673i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	1.10485			0.0847382
$171$	15.4956	−	0.525249i	1.18498	−	0.0401668i
$172$	−2.49836			−0.190498
$173$	0.787804	+	1.36452i	0.0598956	+	0.103742i	0.894418	−	0.447231i	$-0.147590\pi$
$173$	0.787804	+	1.36452i	0.0598956	+	0.103742i	−0.834523	+	0.550973i	$0.814257\pi$
$174$	0.745677	−	1.34362i	0.0565296	−	0.101859i
$175$	0.391685	−	0.678419i	0.0296086	−	0.0512836i
$176$	−3.11157	+	5.38940i	−0.234543	+	0.406241i
$177$	4.54488	−	8.18931i	0.341614	−	0.615546i
$178$	−7.96788	−	13.8008i	−0.597218	−	1.03441i
$179$	17.5506			1.31180			0.655899	−	0.754849i	$-0.272290\pi$
$179$	17.5506			1.31180			0.655899	+	0.754849i	$0.272290\pi$
$180$	0.542609	+	0.870335i	0.0404437	+	0.0648710i
$181$	−7.18337			−0.533935			−0.266968	−	0.963705i	$-0.586022\pi$
$181$	−7.18337			−0.533935			−0.266968	+	0.963705i	$0.586022\pi$
$182$	−0.504366	−	0.873587i	−0.0373861	−	0.0647546i
$183$	7.65508	+	12.7550i	0.565880	+	0.942874i
$184$	−3.88420	+	6.72764i	−0.286347	+	0.495968i
$185$	−4.28150	+	7.41577i	−0.314782	+	0.545218i
$186$	10.2273	−	0.173286i	0.749903	−	0.0127059i
$187$	0.834469	+	1.44534i	0.0610224	+	0.105694i
$188$	−1.45206			−0.105902
$189$	−2.21172	−	3.41722i	−0.160879	−	0.248566i
$190$	6.65496			0.482801
$191$	−11.2179	−	19.4300i	−0.811701	−	1.40591i	−0.911672	−	0.410918i	$-0.865208\pi$
$191$	−11.2179	−	19.4300i	−0.811701	−	1.40591i	0.0999710	−	0.994990i	$-0.468125\pi$
$192$	−15.3438	+	0.259977i	−1.10734	+	0.0187622i
$193$	−4.02595	+	6.97316i	−0.289794	+	0.501939i	−0.973761	−	0.227575i	$-0.926920\pi$
$193$	−4.02595	+	6.97316i	−0.289794	+	0.501939i	0.683966	+	0.729514i	$0.260254\pi$
$194$	10.7557	−	18.6294i	0.772213	−	1.33751i
$195$	−0.891313	−	1.48511i	−0.0638282	−	0.106351i
$196$	−1.09166	−	1.89082i	−0.0779760	−	0.135058i
$197$	18.5112			1.31887			0.659435	−	0.751761i	$-0.270795\pi$
$197$	18.5112			1.31887			0.659435	+	0.751761i	$0.270795\pi$
$198$	3.53442	−	6.63091i	0.251181	−	0.471238i
$199$	−5.58313			−0.395777			−0.197889	−	0.980225i	$-0.563408\pi$
$199$	−5.58313			−0.395777			−0.197889	+	0.980225i	$0.563408\pi$
$200$	1.50780	+	2.61158i	0.106617	+	0.184666i
$201$	−1.15594	+	2.08286i	−0.0815337	+	0.146913i
$202$	3.01439	−	5.22108i	0.212092	−	0.367354i
$203$	0.269865	−	0.467420i	0.0189408	−	0.0328065i
$204$	−0.246544	+	0.444242i	−0.0172616	+	0.0311032i
$205$	1.47108	+	2.54798i	0.102744	+	0.177958i
$206$	20.1960			1.40712
$207$	3.63517	−	6.81992i	0.252662	−	0.474017i
$208$	3.19937			0.221836
$209$	5.02634	+	8.70587i	0.347679	+	0.602198i
$210$	−0.899095	−	1.49808i	−0.0620435	−	0.103377i
$211$	−10.2532	+	17.7591i	−0.705861	+	1.22259i	0.260519	+	0.965469i	$0.416106\pi$
$211$	−10.2532	+	17.7591i	−0.705861	+	1.22259i	−0.966380	+	0.257118i	$0.917227\pi$
$212$	0.647808	−	1.12204i	0.0444916	−	0.0770618i
$213$	−2.85741	+	0.0484144i	−0.195787	+	0.00331730i
$214$	−1.20169	−	2.08138i	−0.0821456	−	0.142280i
$215$	7.30782			0.498389
$216$	15.6492	−	0.796066i	1.06480	−	0.0541654i
$217$	3.59271			0.243889
$218$	−4.03103	−	6.98195i	−0.273016	−	0.472877i
$219$	−15.3459	+	0.260013i	−1.03698	+	0.0175701i
$220$	−0.332493	+	0.575895i	−0.0224167	+	0.0388268i
$221$	0.429008	−	0.743063i	0.0288582	−	0.0499838i
$222$	9.82798	+	16.3755i	0.659611	+	1.09905i
$223$	−2.64078	−	4.57397i	−0.176840	−	0.306296i	0.763957	−	0.645268i	$-0.223254\pi$
$223$	−2.64078	−	4.57397i	−0.176840	−	0.306296i	−0.940796	+	0.338972i	$0.889921\pi$
$224$	−1.49734			−0.100045
$225$	−1.58715	−	2.54577i	−0.105810	−	0.169718i
$226$	−6.68091			−0.444407
$227$	10.3790	+	17.9769i	0.688877	+	1.19317i	0.972202	+	0.234145i	$0.0752291\pi$
$227$	10.3790	+	17.9769i	0.688877	+	1.19317i	−0.283325	+	0.959024i	$0.591438\pi$
$228$	−1.48503	+	2.67585i	−0.0983488	+	0.177212i
$229$	−11.1884	+	19.3788i	−0.739348	+	1.28059i	0.213441	+	0.976956i	$0.431533\pi$
$229$	−11.1884	+	19.3788i	−0.739348	+	1.28059i	−0.952789	+	0.303633i	$0.901800\pi$
$230$	1.65859	−	2.87276i	0.109364	−	0.189424i
$231$	1.28069	−	2.30764i	0.0842633	−	0.151832i
$232$	1.03885	+	1.79934i	0.0682037	+	0.118132i
$233$	−22.6767			−1.48560			−0.742801	−	0.669513i	$-0.766503\pi$
$233$	−22.6767			−1.48560			−0.742801	+	0.669513i	$0.766503\pi$
$234$	−3.86083	+	0.130869i	−0.252390	+	0.00855518i
$235$	4.24733			0.277065
$236$	0.924332	+	1.60099i	0.0601689	+	0.104216i
$237$	−4.79945	−	7.99689i	−0.311758	−	0.519454i
$238$	0.432754	−	0.749552i	0.0280513	−	0.0485862i
$239$	14.8858	−	25.7829i	0.962881	−	1.66776i	0.247679	−	0.968842i	$-0.420332\pi$
$239$	14.8858	−	25.7829i	0.962881	−	1.66776i	0.715202	−	0.698918i	$-0.246335\pi$
$240$	5.54068	−	0.0938782i	0.357649	−	0.00605981i
$241$	−13.5994	−	23.5549i	−0.876015	−	1.51730i	−0.855677	−	0.517510i	$-0.826859\pi$
$241$	−13.5994	−	23.5549i	−0.876015	−	1.51730i	−0.0203382	−	0.999793i	$-0.506474\pi$
$242$	−9.29260			−0.597351
$243$	−15.5326	+	1.31891i	−0.996414	+	0.0846079i
$244$	−2.93621			−0.187972
$245$	3.19317	+	5.53072i	0.204004	+	0.353345i
$246$	6.56103	−	0.111166i	0.418316	−	0.00708771i
$247$	2.58408	−	4.47577i	0.164421	−	0.284786i
$248$	−6.91508	+	11.9773i	−0.439108	+	0.760557i
$249$	3.99460	+	6.65584i	0.253148	+	0.421797i
$250$	−0.643841	−	1.11517i	−0.0407201	−	0.0705292i
$251$	−8.26213			−0.521501			−0.260750	−	0.965406i	$-0.583970\pi$
$251$	−8.26213			−0.521501			−0.260750	+	0.965406i	$0.583970\pi$
$252$	0.802984	−	0.0272184i	0.0505832	−	0.00171460i
$253$	5.01077			0.315024
$254$	−7.05315	−	12.2164i	−0.442554	−	0.766526i
$255$	0.721153	−	1.29943i	0.0451604	−	0.0813733i
$256$	3.97580	−	6.88629i	0.248487	−	0.430393i
$257$	12.3711	−	21.4274i	0.771688	−	1.33660i	−0.164950	−	0.986302i	$-0.552746\pi$
$257$	12.3711	−	21.4274i	0.771688	−	1.33660i	0.936637	−	0.350300i	$-0.113920\pi$
$258$	7.90913	−	14.2512i	0.492401	−	0.887244i
$259$	3.35400	+	5.80930i	0.208407	+	0.360972i
$260$	0.341875			0.0212022
$261$	−1.09353	−	1.75400i	−0.0676875	−	0.108570i
$262$	20.1194			1.24298
$263$	−5.40407	−	9.36013i	−0.333229	−	0.577170i	0.649914	−	0.760008i	$-0.274805\pi$
$263$	−5.40407	−	9.36013i	−0.333229	−	0.577170i	−0.983143	+	0.182838i	$0.941472\pi$
$264$	5.22814	+	8.71118i	0.321770	+	0.536136i
$265$	−1.89487	+	3.28200i	−0.116401	+	0.201612i
$266$	2.60665	−	4.51485i	0.159824	−	0.276823i
$267$	−21.4320	+	0.363132i	−1.31162	+	0.0222233i
$268$	−0.235093	−	0.407194i	−0.0143606	−	0.0248733i
$269$	−11.3283			−0.690701			−0.345351	−	0.938474i	$-0.612240\pi$
$269$	−11.3283			−0.690701			−0.345351	+	0.938474i	$0.612240\pi$
$270$	−6.68235	+	0.339927i	−0.406675	+	0.0206873i
$271$	−31.0340			−1.88518			−0.942591	−	0.333949i	$-0.891619\pi$
$271$	−31.0340			−1.88518			−0.942591	+	0.333949i	$0.891619\pi$
$272$	1.37255	+	2.37733i	0.0832234	+	0.144147i
$273$	−1.35664	+	0.0229862i	−0.0821077	+	0.00139119i
$274$	−2.76921	+	4.79640i	−0.167294	+	0.289761i
$275$	0.972557	−	1.68452i	0.0586474	−	0.101580i
$276$	0.784978	+	1.30794i	0.0472501	+	0.0787286i
$277$	−9.22649	−	15.9807i	−0.554366	−	0.960190i	−0.997953	−	0.0639583i	$-0.979628\pi$
$277$	−9.22649	−	15.9807i	−0.554366	−	0.960190i	0.443587	−	0.896231i	$-0.353706\pi$
$278$	27.4829			1.64832
$279$	6.47172	−	12.1416i	0.387452	−	0.726896i
$280$	2.36232			0.141176
$281$	−1.86860	−	3.23651i	−0.111471	−	0.193074i	0.804892	−	0.593421i	$-0.202223\pi$
$281$	−1.86860	−	3.23651i	−0.111471	−	0.193074i	−0.916364	+	0.400347i	$0.868890\pi$
$282$	4.59681	−	8.28287i	0.273736	−	0.493238i
$283$	−5.69648	+	9.86659i	−0.338620	+	0.586508i	−0.984173	−	0.177208i	$-0.943294\pi$
$283$	−5.69648	+	9.86659i	−0.338620	+	0.586508i	0.645553	+	0.763715i	$0.276627\pi$
$284$	0.282041	−	0.488509i	0.0167361	−	0.0289877i
$285$	4.34379	−	7.82696i	0.257304	−	0.463629i
$286$	−1.25234	−	2.16912i	−0.0740526	−	0.128263i
$287$	2.30479			0.136048
$288$	−2.69723	+	5.06026i	−0.158936	+	0.298179i
$289$	−16.2638			−0.956695
$290$	−0.443597	−	0.768332i	−0.0260489	−	0.0451180i
$291$	−14.8898	−	24.8096i	−0.872857	−	1.45436i
$292$	1.51472	−	2.62358i	0.0886424	−	0.153533i
$293$	−1.69765	+	2.94042i	−0.0991779	+	0.171781i	−0.911345	−	0.411644i	$-0.864955\pi$
$293$	−1.69765	+	2.94042i	−0.0991779	+	0.171781i	0.812167	+	0.583425i	$0.198288\pi$
$294$	14.2416	−	0.241302i	0.830586	−	0.0140730i
$295$	−2.70371	−	4.68297i	−0.157416	−	0.272653i
$296$	−25.8225			−1.50090
$297$	−5.49171	−	8.48497i	−0.318661	−	0.492348i
$298$	−11.1911			−0.648281
$299$	−1.28804	−	2.23095i	−0.0744893	−	0.129019i
$300$	0.592060	−	0.0100315i	0.0341826	−	0.000579171i
$301$	2.86236	−	4.95776i	0.164984	−	0.285760i
$302$	−1.19758	+	2.07427i	−0.0689129	+	0.119361i
$303$	−4.17303	−	6.95314i	−0.239734	−	0.399448i
$304$	8.26744	+	14.3196i	0.474170	+	0.821287i
$305$	8.58855			0.491779
$306$	−1.75357	−	2.81270i	−0.100245	−	0.160791i
$307$	21.0950			1.20395			0.601977	−	0.798514i	$-0.294380\pi$
$307$	21.0950			1.20395			0.601977	+	0.798514i	$0.294380\pi$
$308$	0.260465	+	0.451139i	0.0148414	+	0.0257060i
$309$	13.1822	−	23.7527i	0.749912	−	1.35125i
$310$	2.95280	−	5.11439i	0.167708	−	0.290478i
$311$	−7.63840	+	13.2301i	−0.433134	+	0.750210i	−0.997141	−	0.0755596i	$-0.975926\pi$
$311$	−7.63840	+	13.2301i	−0.433134	+	0.750210i	0.564007	+	0.825770i	$0.309259\pi$
$312$	2.53457	−	4.56698i	0.143492	−	0.258554i
$313$	−4.35979	−	7.55137i	−0.246430	−	0.426829i	0.716103	−	0.697995i	$-0.245924\pi$
$313$	−4.35979	−	7.55137i	−0.246430	−	0.426829i	−0.962533	+	0.271166i	$0.912591\pi$
$314$	−9.49997			−0.536114
$315$	−2.34876	+	0.0796151i	−0.132338	+	0.00448580i
$316$	1.84090			0.103558
$317$	10.7457	+	18.6121i	0.603537	+	1.04536i	0.992281	+	0.124011i	$0.0395758\pi$
$317$	10.7457	+	18.6121i	0.603537	+	1.04536i	−0.388744	+	0.921346i	$0.627091\pi$
$318$	4.34958	+	7.24731i	0.243912	+	0.406409i
$319$	0.670077	−	1.16061i	0.0375171	−	0.0649815i
$320$	−4.43001	+	7.67301i	−0.247645	+	0.428934i
$321$	−3.23229	+	0.0547662i	−0.180409	+	0.00305675i
$322$	−1.29929	−	2.25043i	−0.0724065	−	0.125412i
$323$	4.43437			0.246735
$324$	1.35447	−	2.76271i	0.0752483	−	0.153484i
$325$	−1.00000			−0.0554700
$326$	5.61247	+	9.72108i	0.310846	+	0.538401i
$327$	−10.8427	+	0.183712i	−0.599601	+	0.0101593i
$328$	−4.43616	+	7.68365i	−0.244946	+	0.424259i
$329$	1.66361	−	2.88146i	0.0917180	−	0.158860i
$330$	−2.23246	−	3.71975i	−0.122893	−	0.204765i
$331$	−1.41147	−	2.44474i	−0.0775814	−	0.134375i	0.824625	−	0.565680i	$-0.191386\pi$
$331$	−1.41147	−	2.44474i	−0.0775814	−	0.134375i	−0.902206	+	0.431306i	$0.858053\pi$
$332$	−1.53218			−0.0840896
$333$	25.6742	−	0.870270i	1.40694	−	0.0476905i
$334$	−5.47347			−0.299495
$335$	0.687659	+	1.19106i	0.0375708	+	0.0650745i
$336$	2.10651	−	3.79567i	0.114920	−	0.207071i
$337$	15.4343	−	26.7329i	0.840758	−	1.45624i	−0.0484960	−	0.998823i	$-0.515443\pi$
$337$	15.4343	−	26.7329i	0.840758	−	1.45624i	0.889254	−	0.457413i	$-0.151224\pi$
$338$	−0.643841	+	1.11517i	−0.0350203	+	0.0606570i
$339$	−4.36073	+	7.85749i	−0.236842	+	0.426760i
$340$	0.146667	+	0.254035i	0.00795414	+	0.0137770i
$341$	8.92072			0.483084
$342$	−10.5624	−	16.9420i	−0.571152	−	0.916118i
$343$	10.4865			0.566215
$344$	11.0187	+	19.0849i	0.594088	+	1.02899i
$345$	−2.29609	−	3.82577i	−0.123618	−	0.205973i
$346$	1.01444	−	1.75706i	0.0545367	−	0.0944603i
$347$	−1.41472	+	2.45036i	−0.0759459	+	0.131542i	−0.901497	−	0.432785i	$-0.857531\pi$
$347$	−1.41472	+	2.45036i	−0.0759459	+	0.131542i	0.825551	+	0.564327i	$0.190864\pi$
$348$	0.407920	−	0.00691158i	0.0218668	−	0.000370500i
$349$	−8.12743	−	14.0771i	−0.435051	−	0.753531i	0.562249	−	0.826968i	$-0.309936\pi$
$349$	−8.12743	−	14.0771i	−0.435051	−	0.753531i	−0.997300	+	0.0734376i	$0.976603\pi$
$350$	−1.00873			−0.0539190
$351$	−2.36610	+	4.62618i	−0.126293	+	0.246927i
$352$	−3.71791			−0.198165
$353$	14.7198	+	25.4954i	0.783455	+	1.35698i	0.929918	+	0.367767i	$0.119878\pi$
$353$	14.7198	+	25.4954i	0.783455	+	1.35698i	−0.146463	+	0.989216i	$0.546789\pi$
$354$	−12.0586	+	0.204314i	−0.640908	+	0.0108592i
$355$	−0.824982	+	1.42891i	−0.0437855	+	0.0758387i
$356$	2.11544	−	3.66406i	0.112118	−	0.194195i
$357$	−0.599090	−	0.998210i	−0.0317072	−	0.0528309i
$358$	−11.2998	−	19.5719i	−0.597214	−	1.03441i
$359$	−25.1717			−1.32851			−0.664256	−	0.747505i	$-0.731252\pi$
$359$	−25.1717			−1.32851			−0.664256	+	0.747505i	$0.731252\pi$
$360$	4.25537	−	7.98348i	0.224278	−	0.420766i
$361$	7.70997			0.405788
$362$	4.62495	+	8.01064i	0.243082	+	0.421030i
$363$	−6.06542	+	10.9291i	−0.318352	+	0.573630i
$364$	0.133907	−	0.231935i	0.00701866	−	0.0121567i
$365$	−4.43063	+	7.67407i	−0.231910	+	0.401679i
$366$	9.29524	−	16.7488i	0.485870	−	0.875476i
$367$	11.3050	+	19.5808i	0.590114	+	1.02211i	0.994217	+	0.107394i	$0.0342505\pi$
$367$	11.3050	+	19.5808i	0.590114	+	1.02211i	−0.404103	+	0.914714i	$0.632416\pi$
$368$	8.24184			0.429636
$369$	4.15174	−	7.78905i	0.216131	−	0.405482i
$370$	11.0264			0.573236
$371$	1.48438	+	2.57103i	0.0770653	+	0.133481i
$372$	1.39750	+	2.32853i	0.0724571	+	0.120729i
$373$	−17.9568	+	31.1022i	−0.929770	+	1.61041i	−0.146066	+	0.989275i	$0.546661\pi$
$373$	−17.9568	+	31.1022i	−0.929770	+	1.61041i	−0.783704	+	0.621134i	$0.786672\pi$
$374$	1.07453	−	1.86114i	0.0555626	−	0.0962373i
$375$	−1.73180	+	0.0293427i	−0.0894299	+	0.00151525i
$376$	6.40410	+	11.0922i	0.330266	+	0.572038i
$377$	−0.688985			−0.0354845
$378$	−2.38677	+	4.66658i	−0.122762	+	0.240023i
$379$	−12.1182			−0.622471			−0.311235	−	0.950333i	$-0.600743\pi$
$379$	−12.1182			−0.622471			−0.311235	+	0.950333i	$0.600743\pi$
$380$	0.883434	+	1.53015i	0.0453192	+	0.0784952i
$381$	−18.9716	+	0.321444i	−0.971943	+	0.0164681i
$382$	−14.4451	+	25.0197i	−0.739077	+	1.28012i
$383$	7.97518	−	13.8134i	0.407513	−	0.705833i	−0.587097	−	0.809516i	$-0.699729\pi$
$383$	7.97518	−	13.8134i	0.407513	−	0.705833i	0.994610	+	0.103683i	$0.0330628\pi$
$384$	6.76157	+	11.2662i	0.345050	+	0.574925i
$385$	−0.761872	−	1.31960i	−0.0388286	−	0.0672531i
$386$	10.3683			0.527732
$387$	−11.5986	−	18.6040i	−0.589592	−	0.945695i
$388$	5.71120			0.289942
$389$	6.42323	+	11.1254i	0.325671	+	0.564078i	0.981648	−	0.190703i	$-0.0610766\pi$
$389$	6.42323	+	11.1254i	0.325671	+	0.564078i	−0.655977	+	0.754781i	$0.727743\pi$
$390$	−1.08228	+	1.95014i	−0.0548035	+	0.0987491i
$391$	1.10516	−	1.91419i	0.0558903	−	0.0968048i
$392$	−9.62928	+	16.6784i	−0.486352	+	0.842386i
$393$	13.1322	−	23.6626i	0.662434	−	1.19362i
$394$	−11.9183	−	20.6431i	−0.600435	−	1.03998i
$395$	−5.38470			−0.270934
$396$	1.99381	−	0.0675836i	0.100193	−	0.00339620i
$397$	26.1197			1.31091			0.655456	−	0.755234i	$-0.272477\pi$
$397$	26.1197			1.31091			0.655456	+	0.755234i	$0.272477\pi$
$398$	3.59465	+	6.22611i	0.180183	+	0.312087i
$399$	−3.60856	−	6.01262i	−0.180654	−	0.301007i
$400$	1.59969	−	2.77074i	0.0799843	−	0.138537i
$401$	−7.67560	+	13.2945i	−0.383301	+	0.663897i	−0.991532	−	0.129863i	$-0.958546\pi$
$401$	−7.67560	+	13.2945i	−0.383301	+	0.663897i	0.608231	+	0.793760i	$0.291880\pi$
$402$	3.06697	−	0.0519651i	0.152967	−	0.00259178i
$403$	−2.29311	−	3.97178i	−0.114228	−	0.197849i
$404$	1.60062			0.0796340
$405$	−3.96188	+	8.08106i	−0.196867	+	0.401551i
$406$	−0.695001			−0.0344923
$407$	8.32800	+	14.4245i	0.412804	+	0.714997i
$408$	4.48091	−	0.0759220i	0.221838	−	0.00375870i
$409$	−10.2698	+	17.7877i	−0.507807	+	0.879547i	0.492152	+	0.870509i	$0.336210\pi$
$409$	−10.2698	+	17.7877i	−0.507807	+	0.879547i	−0.999959	+	0.00903820i	$0.997123\pi$
$410$	1.89428	−	3.28098i	0.0935517	−	0.162036i
$411$	3.83360	+	6.38758i	0.189097	+	0.315076i
$412$	2.68099	+	4.64361i	0.132083	+	0.228774i
$413$	−4.23602			−0.208441
$414$	−9.94581	+	0.337129i	−0.488810	+	0.0165690i
$415$	4.48171			0.219998
$416$	0.955704	+	1.65533i	0.0468573	+	0.0811592i
$417$	17.9385	−	32.3229i	0.878453	−	1.58286i
$418$	6.47232	−	11.2104i	0.316572	−	0.548318i
$419$	10.7238	−	18.5742i	0.523893	−	0.907409i	−0.475720	−	0.879597i	$-0.657813\pi$
$419$	10.7238	−	18.5742i	0.523893	−	0.907409i	0.999613	−	0.0278124i	$-0.00885410\pi$
$420$	0.225096	−	0.405594i	0.0109835	−	0.0197910i
$421$	0.602017	+	1.04272i	0.0293405	+	0.0508193i	0.880323	−	0.474375i	$-0.157326\pi$
$421$	0.602017	+	1.04272i	0.0293405	+	0.0508193i	−0.850982	+	0.525194i	$0.823993\pi$
$422$	26.4058			1.28541
$423$	−6.74116	−	10.8127i	−0.327766	−	0.525732i
$424$	−11.4283			−0.555006
$425$	−0.429008	−	0.743063i	−0.0208099	−	0.0360439i
$426$	1.89371	+	3.15532i	0.0917505	+	0.152876i
$427$	3.36401	−	5.82663i	0.162796	−	0.281970i
$428$	0.319044	−	0.552600i	0.0154216	−	0.0267109i
$429$	−3.36855	+	0.0570749i	−0.162635	+	0.00275560i
$430$	−4.70507	−	8.14942i	−0.226899	−	0.393000i
$431$	33.6854			1.62257			0.811284	−	0.584653i	$-0.198769\pi$
$431$	33.6854			1.62257			0.811284	+	0.584653i	$0.198769\pi$
$432$	−9.03290	−	13.9563i	−0.434596	−	0.671472i
$433$	4.86475			0.233785			0.116892	−	0.993145i	$-0.462707\pi$
$433$	4.86475			0.233785			0.116892	+	0.993145i	$0.462707\pi$
$434$	−2.31313	−	4.00646i	−0.111034	−	0.192316i
$435$	−1.19319	+	0.0202167i	−0.0572089	+	0.000969315i
$436$	1.07023	−	1.85368i	0.0512545	−	0.0887754i
$437$	6.65681	−	11.5299i	0.318438	−	0.551552i
$438$	10.1703	+	16.9459i	0.485956	+	0.809704i
$439$	−8.81303	−	15.2646i	−0.420623	−	0.728540i	0.575378	−	0.817888i	$-0.304855\pi$
$439$	−8.81303	−	15.2646i	−0.420623	−	0.728540i	−0.996000	+	0.0893478i	$0.971522\pi$
$440$	5.86567			0.279635
$441$	9.01190	−	16.9072i	0.429138	−	0.805104i
$442$	−1.10485			−0.0525524
$443$	−15.8876	−	27.5181i	−0.754842	−	1.30743i	−0.945453	−	0.325759i	$-0.894380\pi$
$443$	−15.8876	−	27.5181i	−0.754842	−	1.30743i	0.190611	−	0.981666i	$-0.438953\pi$
$444$	−2.46051	+	4.43353i	−0.116771	+	0.210406i
$445$	−6.18777	+	10.7175i	−0.293328	+	0.508060i
$446$	−3.40049	+	5.88982i	−0.161018	+	0.278891i
$447$	−7.30458	+	13.1619i	−0.345495	+	0.622538i
$448$	3.47034	+	6.01081i	0.163958	+	0.283984i
$449$	4.77201			0.225205			0.112603	−	0.993640i	$-0.464081\pi$
$449$	4.77201			0.225205			0.112603	+	0.993640i	$0.464081\pi$
$450$	−1.81708	+	3.40901i	−0.0856579	+	0.160702i
$451$	5.72282			0.269477
$452$	−0.886879	−	1.53612i	−0.0417153	−	0.0722530i
$453$	1.65789	+	2.76239i	0.0778944	+	0.129788i
$454$	13.3648	−	23.1485i	0.627242	−	1.08641i
$455$	−0.391685	+	0.678419i	−0.0183625	+	0.0318048i
$456$	26.9903	−	0.457308i	1.26394	−	0.0214154i
$457$	3.94745	+	6.83719i	0.184654	+	0.319830i	0.943460	−	0.331487i	$-0.107550\pi$
$457$	3.94745	+	6.83719i	0.184654	+	0.319830i	−0.758806	+	0.651317i	$0.774217\pi$
$458$	28.8141			1.34640
$459$	−4.45262	+	0.226502i	−0.207831	+	0.0105722i
$460$	0.880698			0.0410628
$461$	18.1729	+	31.4763i	0.846395	+	1.46600i	0.884404	+	0.466722i	$0.154565\pi$
$461$	18.1729	+	31.4763i	0.846395	+	1.46600i	−0.0380089	+	0.999277i	$0.512102\pi$
$462$	−3.39797	+	0.0575733i	−0.158088	+	0.00267855i
$463$	−4.24825	+	7.35818i	−0.197433	+	0.341964i	−0.947695	−	0.319176i	$-0.896594\pi$
$463$	−4.24825	+	7.35818i	−0.197433	+	0.341964i	0.750262	+	0.661140i	$0.229927\pi$
$464$	1.10216	−	1.90899i	0.0511664	−	0.0886229i
$465$	−4.08776	−	6.81106i	−0.189565	−	0.315855i
$466$	14.6002	+	25.2883i	0.676341	+	1.17146i
$467$	−28.3481			−1.31179			−0.655896	−	0.754851i	$-0.727709\pi$
$467$	−28.3481			−1.31179			−0.655896	+	0.754851i	$0.727709\pi$
$468$	−0.542609	−	0.870335i	−0.0250821	−	0.0402313i
$469$	1.07738			0.0497489
$470$	−2.73460	−	4.73647i	−0.126138	−	0.218477i
$471$	−6.20077	+	11.1730i	−0.285717	+	0.514825i
$472$	8.15329	−	14.1219i	0.375285	−	0.650014i
$473$	7.10727	−	12.3101i	0.326792	−	0.566021i
$474$	−5.82777	+	10.5009i	−0.267678	+	0.482323i
$475$	−2.58408	−	4.47577i	−0.118566	−	0.205362i
$476$	0.229789			0.0105324
$477$	11.3627	−	0.385156i	0.520261	−	0.0176351i
$478$	−38.3363			−1.75346
$479$	−5.80748	−	10.0588i	−0.265350	−	0.459601i	0.702305	−	0.711876i	$-0.252154\pi$
$479$	−5.80748	−	10.0588i	−0.265350	−	0.459601i	−0.967655	+	0.252276i	$0.918821\pi$
$480$	1.70366	+	2.83866i	0.0777612	+	0.129566i
$481$	4.28150	−	7.41577i	0.195220	−	0.338130i
$482$	−17.5117	+	30.3312i	−0.797637	+	1.38155i
$483$	−3.49482	+	0.0592143i	−0.159020	+	0.00269435i
$484$	−1.23358	−	2.13662i	−0.0560717	−	0.0971190i
$485$	−16.7055			−0.758558
$486$	11.4713	+	16.4722i	0.520349	+	0.747195i
$487$	15.1592			0.686928			0.343464	−	0.939166i	$-0.388400\pi$
$487$	15.1592			0.686928			0.343464	+	0.939166i	$0.388400\pi$
$488$	12.9498	+	22.4297i	0.586208	+	1.01534i
$489$	15.0964	−	0.255785i	0.682683	−	0.0115670i
$490$	4.11178	−	7.12181i	0.185751	−	0.321731i
$491$	−7.13316	+	12.3550i	−0.321915	+	0.557573i	−0.980883	−	0.194598i	$-0.937660\pi$
$491$	−7.13316	+	12.3550i	−0.321915	+	0.557573i	0.658968	+	0.752171i	$0.270993\pi$
$492$	0.896525	+	1.49380i	0.0404185	+	0.0673456i
$493$	−0.295580	−	0.511959i	−0.0133122	−	0.0230575i
$494$	−6.65496			−0.299421
$495$	−5.83199	+	0.197685i	−0.262129	+	0.00888527i
$496$	14.6730			0.658838
$497$	0.646267	+	1.11937i	0.0289890	+	0.0502104i
$498$	4.85048	−	8.73995i	0.217355	−	0.391646i
$499$	−12.5140	+	21.6748i	−0.560202	+	0.970298i	0.437277	+	0.899327i	$0.355943\pi$
$499$	−12.5140	+	21.6748i	−0.560202	+	0.970298i	−0.997478	+	0.0709706i	$0.977390\pi$
$500$	0.170938	−	0.296073i	0.00764456	−	0.0132408i
$501$	−3.57262	+	6.43740i	−0.159613	+	0.287602i
$502$	5.31950	+	9.21364i	0.237421	+	0.411225i
$503$	−11.2079			−0.499734			−0.249867	−	0.968280i	$-0.580387\pi$
$503$	−11.2079			−0.499734			−0.249867	+	0.968280i	$0.580387\pi$
$504$	−3.74937	−	6.01393i	−0.167010	−	0.267882i
$505$	−4.68189			−0.208341
$506$	−3.22614	−	5.58784i	−0.143419	−	0.248410i
$507$	0.891313	+	1.48511i	0.0395846	+	0.0659562i
$508$	1.87259	−	3.24342i	0.0830827	−	0.143903i
$509$	−13.6107	+	23.5745i	−0.603286	+	1.04492i	0.389034	+	0.921223i	$0.372809\pi$
$509$	−13.6107	+	23.5745i	−0.603286	+	1.04492i	−0.992320	+	0.123698i	$0.960525\pi$
$510$	−1.91338	+	0.0324193i	−0.0847261	+	0.00143555i
$511$	3.47082	+	6.01164i	0.153540	+	0.265939i
$512$	−25.4113			−1.12303
$513$	−26.8199	+	1.36431i	−1.18413	+	0.0602358i
$514$	−31.8601			−1.40529
$515$	−7.84201	−	13.5828i	−0.345560	−	0.598528i
$516$	4.32667	−	0.0733087i	0.190471	−	0.00322724i
$517$	4.13076	−	7.15469i	0.181671	−	0.314663i
$518$	4.31888	−	7.48053i	0.189761	−	0.328675i
$519$	−1.40436	−	2.33996i	−0.0616445	−	0.102713i
$520$	−1.50780	−	2.61158i	−0.0661212	−	0.114525i
$521$	18.6746			0.818148			0.409074	−	0.912501i	$-0.365852\pi$
$521$	18.6746			0.818148			0.409074	+	0.912501i	$0.365852\pi$
$522$	−1.25194	+	2.34876i	−0.0547959	+	0.102802i
$523$	−6.24551			−0.273097			−0.136549	−	0.990633i	$-0.543601\pi$
$523$	−6.24551			−0.273097			−0.136549	+	0.990633i	$0.543601\pi$
$524$	2.67082	+	4.62599i	0.116675	+	0.202087i
$525$	−0.658415	+	1.18638i	−0.0287356	+	0.0517779i
$526$	−6.95873	+	12.0529i	−0.303415	+	0.525530i
$527$	1.96752	−	3.40785i	0.0857067	−	0.148448i
$528$	5.23048	−	9.42467i	0.227628	−	0.410156i
$529$	8.18190	+	14.1715i	0.355735	+	0.616151i
$530$	4.87997			0.211972
$531$	−7.63054	+	14.3156i	−0.331137	+	0.621245i
$532$	1.38411			0.0600089
$533$	−1.47108	−	2.54798i	−0.0637193	−	0.110365i
$534$	14.2037	+	23.6664i	0.614656	+	1.02415i
$535$	−0.933216	+	1.61638i	−0.0403465	+	0.0698821i
$536$	−2.07370	+	3.59175i	−0.0895701	+	0.155140i
$537$	−30.3943	+	0.514984i	−1.31161	+	0.0222232i
$538$	7.29365	+	12.6330i	0.314452	+	0.544646i
$539$	12.4221			0.535059
$540$	−0.965229	−	1.49133i	−0.0415368	−	0.0641765i
$541$	−15.8889			−0.683118			−0.341559	−	0.939860i	$-0.610955\pi$
$541$	−15.8889			−0.683118			−0.341559	+	0.939860i	$0.610955\pi$
$542$	19.9810	+	34.6081i	0.858256	+	1.48654i
$543$	12.4402	−	0.210779i	0.533859	−	0.00904541i
$544$	−0.820009	+	1.42030i	−0.0351576	+	0.0608948i
$545$	−3.13046	+	5.42211i	−0.134094	+	0.232258i
$546$	0.899095	+	1.49808i	0.0384777	+	0.0641120i
$547$	−1.13527	−	1.96634i	−0.0485405	−	0.0840747i	0.840734	−	0.541448i	$-0.182124\pi$
$547$	−1.13527	−	1.96634i	−0.0485405	−	0.0840747i	−0.889275	+	0.457373i	$0.848790\pi$
$548$	−1.47043			−0.0628136
$549$	−13.6313	−	21.8645i	−0.581772	−	0.933152i
$550$	−2.50469			−0.106800
$551$	−1.78039	−	3.08373i	−0.0758474	−	0.131371i
$552$	6.52926	−	11.7649i	0.277904	−	0.500748i
$553$	−2.10911	+	3.65308i	−0.0896884	+	0.155345i
$554$	−11.8808	+	20.5781i	−0.504766	+	0.874280i
$555$	7.19711	−	12.9683i	0.305500	−	0.550473i
$556$	3.64831	+	6.31906i	0.154723	+	0.267988i
$557$	14.6196			0.619454			0.309727	−	0.950826i	$-0.399762\pi$
$557$	14.6196			0.619454			0.309727	+	0.950826i	$0.399762\pi$
$558$	−17.7066	+	0.600194i	−0.749580	+	0.0254083i
$559$	−7.30782			−0.309088
$560$	−1.25315	−	2.17051i	−0.0529551	−	0.0917209i
$561$	−1.48755	−	2.47856i	−0.0628042	−	0.104645i
$562$	−2.40616	+	4.16760i	−0.101498	+	0.175800i
$563$	−6.40536	+	11.0944i	−0.269954	+	0.467573i	−0.968850	−	0.247650i	$-0.920342\pi$
$563$	−6.40536	+	11.0944i	−0.269954	+	0.467573i	0.698896	+	0.715223i	$0.253675\pi$
$564$	2.51467	−	0.0426072i	0.105887	−	0.00179409i
$565$	2.59416	+	4.49322i	0.109137	+	0.189031i
$566$	14.6705			0.616647
$567$	3.93053	+	5.85304i	0.165067	+	0.245805i
$568$	−4.97562			−0.208772
$569$	−4.24785	−	7.35748i	−0.178079	−	0.308442i	0.763144	−	0.646229i	$-0.223655\pi$
$569$	−4.24785	−	7.35748i	−0.178079	−	0.308442i	−0.941223	+	0.337787i	$0.890322\pi$
$570$	−11.5251	+	0.195274i	−0.482732	+	0.00817915i
$571$	−14.7178	+	25.4920i	−0.615920	+	1.06681i	0.374302	+	0.927307i	$0.377882\pi$
$571$	−14.7178	+	25.4920i	−0.615920	+	1.06681i	−0.990222	+	0.139499i	$0.955451\pi$
$572$	0.332493	−	0.575895i	0.0139022	−	0.0240794i
$573$	19.9974	+	33.3198i	0.835402	+	1.39196i
$574$	−1.48392	−	2.57023i	−0.0619376	−	0.107279i
$575$	−2.57608			−0.107430
$576$	26.5648	−	0.900458i	1.10687	−	0.0375191i
$577$	−42.3637			−1.76362			−0.881812	−	0.471602i	$-0.843676\pi$
$577$	−42.3637			−1.76362			−0.881812	+	0.471602i	$0.843676\pi$
$578$	10.4713	+	18.1368i	0.435549	+	0.754393i
$579$	6.76754	−	12.1943i	0.281250	−	0.506776i
$580$	0.117773	−	0.203990i	0.00489027	−	0.00847020i
$581$	1.75542	−	3.04047i	0.0728270	−	0.126140i
$582$	−18.0801	+	32.5780i	−0.749444	+	1.35040i
$583$	3.68573	+	6.38387i	0.152647	+	0.264393i
$584$	−26.7219			−1.10576
$585$	1.58715	+	2.54577i	0.0656208	+	0.105255i
$586$	4.37207			0.180609
$587$	19.3986	+	33.5994i	0.800667	+	1.38680i	0.919177	+	0.393844i	$0.128855\pi$
$587$	19.3986	+	33.5994i	0.800667	+	1.38680i	−0.118510	+	0.992953i	$0.537812\pi$
$588$	1.94603	+	3.24249i	0.0802529	+	0.133718i
$589$	11.8512	−	20.5268i	0.488319	−	0.845794i
$590$	−3.48152	+	6.03017i	−0.143332	+	0.248258i
$591$	−32.0578	+	0.543170i	−1.31868	+	0.0223430i
$592$	13.6981	+	23.7258i	0.562988	+	0.975125i
$593$	−30.3554			−1.24655			−0.623273	−	0.782005i	$-0.714197\pi$
$593$	−30.3554			−1.24655			−0.623273	+	0.782005i	$0.714197\pi$
$594$	−5.92635	+	11.5871i	−0.243161	+	0.475426i
$595$	−0.672144			−0.0275552
$596$	−1.48559	−	2.57313i	−0.0608523	−	0.105399i
$597$	9.66887	−	0.163824i	0.395721	−	0.00670487i
$598$	−1.65859	+	2.87276i	−0.0678247	+	0.117476i
$599$	12.0756	−	20.9155i	0.493394	−	0.854583i	−0.506577	−	0.862195i	$-0.669089\pi$
$599$	12.0756	−	20.9155i	0.493394	−	0.854583i	0.999971	+	0.00761137i	$0.00242280\pi$
$600$	−2.68783	−	4.47849i	−0.109730	−	0.182834i
$601$	19.2549	+	33.3504i	0.785423	+	1.36039i	0.928746	+	0.370716i	$0.120888\pi$
$601$	19.2549	+	33.3504i	0.785423	+	1.36039i	−0.143324	+	0.989676i	$0.545779\pi$
$602$	−7.37163			−0.300445
$603$	1.94074	−	3.64102i	0.0790331	−	0.148274i
$604$	−0.635906			−0.0258746
$605$	3.60827	+	6.24970i	0.146697	+	0.254086i
$606$	−5.06713	+	9.13034i	−0.205838	+	0.370895i
$607$	−5.24754	+	9.08900i	−0.212991	+	0.368911i	−0.952649	−	0.304072i	$-0.901654\pi$
$607$	−5.24754	+	9.08900i	−0.212991	+	0.368911i	0.739658	+	0.672983i	$0.234987\pi$
$608$	−4.93924	+	8.55502i	−0.200313	+	0.346952i
$609$	−0.453638	+	0.817398i	−0.0183823	+	0.0331226i
$610$	−5.52966	−	9.57765i	−0.223889	−	0.387788i
$611$	−4.24733			−0.171828
$612$	0.413931	−	0.776573i	0.0167322	−	0.0313911i
$613$	48.4392			1.95644			0.978219	−	0.207573i	$-0.0665565\pi$
$613$	48.4392			1.95644			0.978219	+	0.207573i	$0.0665565\pi$
$614$	−13.5818	−	23.5244i	−0.548117	−	0.949367i
$615$	−2.62238	−	4.36943i	−0.105744	−	0.176192i
$616$	2.29749	−	3.97938i	0.0925687	−	0.160334i
$617$	4.47464	−	7.75031i	0.180142	−	0.312016i	−0.761786	−	0.647828i	$-0.775677\pi$
$617$	4.47464	−	7.75031i	0.180142	−	0.312016i	0.941929	+	0.335812i	$0.109011\pi$
$618$	−34.9755	+	0.592606i	−1.40692	+	0.0238381i
$619$	−7.22060	−	12.5065i	−0.290221	−	0.502677i	0.683641	−	0.729818i	$-0.260395\pi$
$619$	−7.22060	−	12.5065i	−0.290221	−	0.502677i	−0.973862	+	0.227142i	$0.927062\pi$
$620$	1.56791			0.0629690
$621$	−6.09528	+	11.9174i	−0.244595	+	0.478229i
$622$	19.6717			0.788762
$623$	4.84731	+	8.39579i	0.194204	+	0.336370i
$624$	−5.54068	+	0.0938782i	−0.221805	+	0.00375814i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−5.61402	+	9.72377i	−0.224381	+	0.388640i
$627$	−8.96008	−	14.9294i	−0.357831	−	0.596221i
$628$	−1.26110	−	2.18430i	−0.0503236	−	0.0871629i
$629$	7.34718			0.292951
$630$	1.60101	+	2.56800i	0.0637859	+	0.102312i
$631$	21.5165			0.856559			0.428280	−	0.903646i	$-0.359120\pi$
$631$	21.5165			0.856559			0.428280	+	0.903646i	$0.359120\pi$
$632$	−8.11903	−	14.0626i	−0.322958	−	0.559379i
$633$	17.2355	−	31.0561i	0.685048	−	1.23437i
$634$	13.8370	−	23.9664i	0.549538	−	0.951828i
$635$	−5.47740	+	9.48714i	−0.217364	+	0.376486i
$636$	−1.08895	+	1.96215i	−0.0431797	+	0.0778044i
$637$	−3.19317	−	5.53072i	−0.126518	−	0.219135i
$638$	−1.72569			−0.0683208
$639$	4.94705	−	0.167688i	0.195702	−	0.00663365i
$640$	7.58608			0.299866
$641$	−9.59686	−	16.6222i	−0.379053	−	0.656539i	0.611872	−	0.790957i	$-0.290417\pi$
$641$	−9.59686	−	16.6222i	−0.379053	−	0.656539i	−0.990925	+	0.134418i	$0.957084\pi$
$642$	2.14216	+	3.56928i	0.0845441	+	0.140868i
$643$	−11.1032	+	19.2313i	−0.437866	+	0.758407i	−0.997525	−	0.0703165i	$-0.977599\pi$
$643$	−11.1032	+	19.2313i	−0.437866	+	0.758407i	0.559658	+	0.828724i	$0.310932\pi$
$644$	0.344956	−	0.597482i	0.0135932	−	0.0235441i
$645$	−12.6557	+	0.214431i	−0.498317	+	0.00844322i
$646$	−2.85503	−	4.94505i	−0.112330	−	0.194561i
$647$	−43.3065			−1.70255			−0.851277	−	0.524717i	$-0.824171\pi$
$647$	−43.3065			−1.70255			−0.851277	+	0.524717i	$0.824171\pi$
$648$	−27.0780	+	1.83782i	−1.06373	+	0.0721963i
$649$	−10.5181			−0.412870
$650$	0.643841	+	1.11517i	0.0252535	+	0.0437404i
$651$	−6.22186	+	0.105420i	−0.243854	+	0.00413173i
$652$	−1.49009	+	2.58092i	−0.0583565	+	0.101076i
$653$	20.9352	−	36.2609i	0.819259	−	1.41900i	−0.0869695	−	0.996211i	$-0.527718\pi$
$653$	20.9352	−	36.2609i	0.819259	−	1.41900i	0.906229	−	0.422788i	$-0.138948\pi$
$654$	7.18582	+	11.9731i	0.280988	+	0.468184i
$655$	−7.81226	−	13.5312i	−0.305250	−	0.528709i
$656$	9.41303			0.367517
$657$	26.5685	−	0.900583i	1.03654	−	0.0351351i
$658$	−4.28441			−0.167024
$659$	−12.3732	−	21.4310i	−0.481992	−	0.834834i	0.517794	−	0.855505i	$-0.326753\pi$
$659$	−12.3732	−	21.4310i	−0.481992	−	0.834834i	−0.999786	+	0.0206706i	$0.993420\pi$
$660$	0.558914	−	1.00709i	0.0217557	−	0.0392010i
$661$	1.35767	−	2.35155i	0.0528071	−	0.0914645i	−0.838414	−	0.545035i	$-0.816516\pi$
$661$	1.35767	−	2.35155i	0.0528071	−	0.0914645i	0.891221	+	0.453570i	$0.149850\pi$
$662$	−1.81752	+	3.14804i	−0.0706400	+	0.122352i
$663$	−0.721153	+	1.29943i	−0.0280073	+	0.0504656i
$664$	6.75750	+	11.7043i	0.262242	+	0.454216i
$665$	−4.04859			−0.156998
$666$	−17.5006	−	28.0707i	−0.678135	−	1.08772i
$667$	−1.77488			−0.0687236
$668$	−0.726594	−	1.25850i	−0.0281128	−	0.0486927i
$669$	4.70753	+	7.84373i	0.182004	+	0.303256i
$670$	0.885486	−	1.53371i	0.0342093	−	0.0592522i
$671$	8.35285	−	14.4676i	0.322458	−	0.558514i
$672$	2.59310	−	0.0439360i	0.100031	−	0.00169487i
$673$	−4.45422	−	7.71494i	−0.171698	−	0.297389i	0.767316	−	0.641269i	$-0.221592\pi$
$673$	−4.45422	−	7.71494i	−0.171698	−	0.297389i	−0.939014	+	0.343880i	$0.888259\pi$
$674$	−39.7489			−1.53107
$675$	2.82334	+	4.36220i	0.108670	+	0.167901i
$676$	−0.341875			−0.0131490
$677$	2.36444	+	4.09533i	0.0908727	+	0.157396i	0.907879	−	0.419233i	$-0.137701\pi$
$677$	2.36444	+	4.09533i	0.0908727	+	0.157396i	−0.817006	+	0.576629i	$0.804368\pi$
$678$	11.5700	−	0.196036i	0.444344	−	0.00752871i
$679$	−6.54330	+	11.3333i	−0.251109	+	0.434933i
$680$	1.29371	−	2.24077i	0.0496116	−	0.0859298i
$681$	−18.5018	−	30.8279i	−0.708991	−	1.18133i
$682$	−5.74352	−	9.94807i	−0.219931	−	0.380931i
$683$	39.6701			1.51794			0.758968	−	0.651128i	$-0.225704\pi$
$683$	39.6701			1.51794			0.758968	+	0.651128i	$0.225704\pi$
$684$	2.49327	−	4.67761i	0.0953326	−	0.178853i
$685$	4.30107			0.164335
$686$	−6.75161	−	11.6941i	−0.257778	−	0.446484i
$687$	18.8074	−	33.8886i	0.717548	−	1.29293i
$688$	11.6902	−	20.2480i	0.445685	−	0.771949i
$689$	1.89487	−	3.28200i	0.0721887	−	0.125034i
$690$	−2.78805	+	5.02371i	−0.106139	+	0.191249i
$691$	−1.62519	−	2.81490i	−0.0618250	−	0.107084i	0.833456	−	0.552586i	$-0.186359\pi$
$691$	−1.62519	−	2.81490i	−0.0618250	−	0.107084i	−0.895281	+	0.445501i	$0.853025\pi$
$692$	0.538661			0.0204768
$693$	−2.15019	+	4.03396i	−0.0816790	+	0.153238i
$694$	3.64341			0.138302
$695$	−10.6715	−	18.4835i	−0.404792	−	0.701120i
$696$	−1.85188	−	3.08561i	−0.0701952	−	0.116960i
$697$	1.26221	−	2.18620i	0.0478094	−	0.0828084i
$698$	−10.4655	+	18.1268i	−0.396126	+	0.686111i
$699$	39.2716	−	0.665396i	1.48539	−	0.0251676i
$700$	−0.133907	−	0.231935i	−0.00506123	−	0.00876630i
$701$	−40.4835			−1.52904			−0.764521	−	0.644598i	$-0.777025\pi$
$701$	−40.4835			−1.52904			−0.764521	+	0.644598i	$0.777025\pi$
$702$	6.68235	−	0.339927i	0.252209	−	0.0128297i
$703$	44.2550			1.66911
$704$	8.61688	+	14.9249i	0.324761	+	0.562502i
$705$	−7.35553	+	0.124628i	−0.277025	+	0.00469376i
$706$	18.9544	−	32.8300i	0.713358	−	1.23557i
$707$	−1.83383	+	3.17628i	−0.0689682	+	0.119456i
$708$	−1.64774	−	2.74548i	−0.0619258	−	0.103181i
$709$	−14.8958	−	25.8003i	−0.559424	−	0.968950i	−0.997545	−	0.0700343i	$-0.977689\pi$
$709$	−14.8958	−	25.8003i	−0.559424	−	0.968950i	0.438121	−	0.898916i	$-0.355644\pi$
$710$	2.12463			0.0797359
$711$	8.54635	+	13.7082i	0.320513	+	0.514098i
$712$	−37.3195			−1.39861
$713$	−5.90724	−	10.2316i	−0.221228	−	0.383178i
$714$	−0.727450	+	1.31077i	−0.0272241	+	0.0490545i
$715$	−0.972557	+	1.68452i	−0.0363716	+	0.0629974i
$716$	3.00007	−	5.19627i	0.112118	−	0.194194i
$717$	−25.0227	+	45.0877i	−0.934490	+	1.68383i
$718$	16.2066	+	28.0706i	0.604824	+	1.04759i
$719$	23.3505			0.870828			0.435414	−	0.900230i	$-0.356602\pi$
$719$	23.3505			0.870828			0.435414	+	0.900230i	$0.356602\pi$
$720$	−9.59260	+	0.325157i	−0.357495	+	0.0121179i
$721$	−12.2864			−0.457569
$722$	−4.96399	−	8.59789i	−0.184741	−	0.319980i
$723$	24.2427	+	40.3933i	0.901594	+	1.50224i
$724$	−1.22791	+	2.12680i	−0.0456348	+	0.0790418i
$725$	−0.344492	+	0.596678i	−0.0127941	+	0.0221601i
$726$	16.0929	−	0.272670i	0.597265	−	0.0101197i
$727$	−10.8320	−	18.7616i	−0.401737	−	0.695829i	0.592199	−	0.805792i	$-0.298260\pi$
$727$	−10.8320	−	18.7616i	−0.401737	−	0.695829i	−0.993936	+	0.109963i	$0.964927\pi$
$728$	−2.36232			−0.0875536
$729$	26.8606	−	2.73985i	0.994838	−	0.101476i
$730$	11.4105			0.422321
$731$	−3.13511	−	5.43017i	−0.115956	−	0.200842i
$732$	5.08494	−	0.0861564i	0.187945	−	0.00318443i
$733$	−15.0190	+	26.0137i	−0.554739	+	0.960836i	0.443185	+	0.896430i	$0.353849\pi$
$733$	−15.0190	+	26.0137i	−0.554739	+	0.960836i	−0.997924	+	0.0644059i	$0.979485\pi$
$734$	14.5572	−	25.2138i	0.537316	−	0.930658i
$735$	−5.69222	−	9.48443i	−0.209961	−	0.349838i
$736$	2.46197	+	4.26426i	0.0907495	+	0.157183i
$737$	2.67515			0.0985403
$738$	−11.3591	+	0.385037i	−0.418136	+	0.0141734i
$739$	−26.6863			−0.981673			−0.490836	−	0.871252i	$-0.663309\pi$
$739$	−26.6863			−0.981673			−0.490836	+	0.871252i	$0.663309\pi$
$740$	1.46374	+	2.53527i	0.0538081	+	0.0931983i
$741$	−4.34379	+	7.82696i	−0.159573	+	0.287531i
$742$	1.91141	−	3.31066i	0.0701701	−	0.121538i
$743$	18.2185	−	31.5554i	0.668374	−	1.15766i	−0.309985	−	0.950741i	$-0.600324\pi$
$743$	18.2185	−	31.5554i	0.668374	−	1.15766i	0.978359	−	0.206916i	$-0.0663425\pi$
$744$	11.6241	−	20.9452i	0.426160	−	0.767887i
$745$	4.34543	+	7.52650i	0.159204	+	0.275750i
$746$	46.2454			1.69316
$747$	−7.11316	−	11.4094i	−0.260257	−	0.417448i
$748$	0.570568			0.0208620
$749$	0.731054	+	1.26622i	0.0267121	+	0.0462668i
$750$	1.14773	+	1.91235i	0.0419091	+	0.0698293i
$751$	1.33250	−	2.30796i	0.0486238	−	0.0842188i	−0.840689	−	0.541518i	$-0.817850\pi$
$751$	1.33250	−	2.30796i	0.0486238	−	0.0842188i	0.889313	+	0.457299i	$0.151183\pi$
$752$	6.79438	−	11.7682i	0.247766	−	0.429143i
$753$	14.3084	−	0.242433i	0.521426	−	0.00883476i
$754$	0.443597	+	0.768332i	0.0161548	+	0.0279810i
$755$	1.86005			0.0676943
$756$	−1.38981	+	0.0706987i	−0.0505469	+	0.00257129i
$757$	−11.7937			−0.428651			−0.214325	−	0.976762i	$-0.568755\pi$
$757$	−11.7937			−0.428651			−0.214325	+	0.976762i	$0.568755\pi$
$758$	7.80220	+	13.5138i	0.283389	+	0.490844i
$759$	−8.67766	+	0.147030i	−0.314979	+	0.00533684i
$760$	7.79254	−	13.4971i	0.282665	−	0.489590i
$761$	11.4484	−	19.8291i	0.415003	−	0.718806i	−0.580426	−	0.814313i	$-0.697114\pi$
$761$	11.4484	−	19.8291i	0.415003	−	0.718806i	0.995429	+	0.0955072i	$0.0304473\pi$
$762$	12.5731	+	20.9495i	0.455476	+	0.758919i
$763$	2.45231	+	4.24752i	0.0887794	+	0.153771i
$764$	−7.67027			−0.277501
$765$	−1.21077	+	2.27151i	−0.0437753	+	0.0821267i
$766$	−20.5390			−0.742104
$767$	2.70371	+	4.68297i	0.0976254	+	0.169092i
$768$	−6.68323	+	12.0423i	−0.241160	+	0.434541i
$769$	2.42351	−	4.19763i	0.0873938	−	0.151371i	−0.819015	−	0.573772i	$-0.805479\pi$
$769$	2.42351	−	4.19763i	0.0873938	−	0.151371i	0.906409	+	0.422402i	$0.138813\pi$
$770$	−0.981049	+	1.69923i	−0.0353546	+	0.0612359i
$771$	−20.7956	+	37.4710i	−0.748934	+	1.34948i
$772$	1.37637	+	2.38395i	0.0495368	+	0.0858002i
$773$	−50.8230			−1.82798			−0.913988	−	0.405742i	$-0.867013\pi$
$773$	−50.8230			−1.82798			−0.913988	+	0.405742i	$0.867013\pi$
$774$	−13.2789	+	24.9124i	−0.477299	+	0.895458i
$775$	−4.58622			−0.164742
$776$	−25.1885	−	43.6277i	−0.904213	−	1.56614i
$777$	−5.97892	−	9.96214i	−0.214493	−	0.357390i
$778$	8.27108	−	14.3259i	0.296532	−	0.513609i
$779$	7.60276	−	13.1684i	0.272397	−	0.471806i
$780$	−0.592060	+	0.0100315i	−0.0211992	+	0.000359187i
$781$	1.60468	+	2.77939i	0.0574201	+	0.0994545i
$782$	−2.84619			−0.101779
$783$	1.94524	+	3.00549i	0.0695171	+	0.107407i
$784$	20.4322			0.729723
$785$	3.68879	+	6.38916i	0.131658	+	0.228039i
$786$	−34.8428	+	0.590358i	−1.24280	+	0.0210574i
$787$	6.32482	−	10.9549i	0.225455	−	0.390500i	−0.731001	−	0.682377i	$-0.760946\pi$
$787$	6.32482	−	10.9549i	0.225455	−	0.390500i	0.956456	+	0.291877i	$0.0942797\pi$
$788$	3.16427	−	5.48067i	0.112722	−	0.195241i
$789$	9.63344	+	16.0513i	0.342959	+	0.571442i
$790$	3.46689	+	6.00483i	0.123346	+	0.213642i
$791$	4.06438			0.144513
$792$	−9.30972	−	14.9326i	−0.330806	−	0.530608i
$793$	−8.58855			−0.304988
$794$	−16.8169	−	29.1278i	−0.596811	−	1.03371i
$795$	3.18523	−	5.73938i	0.112968	−	0.203555i
$796$	−0.954366	+	1.65301i	−0.0338266	+	0.0585894i
$797$	−24.5669	+	42.5511i	−0.870203	+	1.50724i	−0.00841680	+	0.999965i	$0.502679\pi$
$797$	−24.5669	+	42.5511i	−0.870203	+	1.50724i	−0.861786	+	0.507271i	$0.830654\pi$
$798$	−4.38172	+	7.89531i	−0.155111	+	0.279491i
$799$	−1.82214	−	3.15603i	−0.0644625	−	0.111652i
$800$	1.91141			0.0675785
$801$	37.1053	−	1.25774i	1.31105	−	0.0444402i
$802$	19.7675			0.698014
$803$	8.61808	+	14.9269i	0.304125	+	0.526760i
$804$	0.419084	+	0.698281i	0.0147799	+	0.0246265i
$805$	−1.00901	+	1.74766i	−0.0355630	+	0.0615970i
$806$	−2.95280	+	5.11439i	−0.104008	+	0.180147i
$807$	19.6185	−	0.332404i	0.690602	−	0.0117012i
$808$	−7.05934	−	12.2271i	−0.248347	−	0.430149i
$809$	31.6357			1.11225			0.556127	−	0.831098i	$-0.312287\pi$
$809$	31.6357			1.11225			0.556127	+	0.831098i	$0.312287\pi$
$810$	11.5625	−	0.784764i	0.406266	−	0.0275738i
$811$	20.3533			0.714700			0.357350	−	0.933971i	$-0.383680\pi$
$811$	20.3533			0.714700			0.357350	+	0.933971i	$0.383680\pi$
$812$	−0.0922602	−	0.159799i	−0.00323770	−	0.00560786i
$813$	53.7448	−	0.910622i	1.88491	−	0.0319369i
$814$	10.7238	−	18.5742i	0.375870	−	0.651025i
$815$	4.35858	−	7.54929i	0.152675	−	0.264440i
$816$	−2.44675	−	4.07680i	−0.0856534	−	0.142717i
$817$	−18.8840	−	32.7081i	−0.660668	−	1.14431i
$818$	26.4484			0.924745
$819$	2.34876	−	0.0796151i	0.0820724	−	0.00278198i
$820$	1.00585			0.0351257
$821$	−23.6545	−	40.9708i	−0.825548	−	1.42989i	−0.901500	−	0.432779i	$-0.857533\pi$
$821$	−23.6545	−	40.9708i	−0.825548	−	1.42989i	0.0759523	−	0.997111i	$-0.475800\pi$
$822$	4.65498	−	8.38768i	0.162361	−	0.292554i
$823$	0.537438	−	0.930869i	0.0187339	−	0.0324481i	−0.856506	−	0.516136i	$-0.827370\pi$
$823$	0.537438	−	0.930869i	0.0187339	−	0.0324481i	0.875240	+	0.483688i	$0.160703\pi$
$824$	23.6483	−	40.9600i	0.823827	−	1.42691i
$825$	−1.63485	+	2.94579i	−0.0569181	+	0.102559i
$826$	2.72732	+	4.72386i	0.0948956	+	0.164364i
$827$	−35.1881			−1.22361			−0.611806	−	0.791008i	$-0.709557\pi$
$827$	−35.1881			−1.22361			−0.611806	+	0.791008i	$0.709557\pi$
$828$	−1.39780	−	2.24205i	−0.0485771	−	0.0779168i
$829$	15.4729			0.537395			0.268698	−	0.963225i	$-0.413407\pi$
$829$	15.4729			0.537395			0.268698	+	0.963225i	$0.413407\pi$
$830$	−2.88551	−	4.99785i	−0.100157	−	0.173478i
$831$	16.4474	+	27.4048i	0.570553	+	0.950660i
$832$	4.43001	−	7.67301i	0.153583	−	0.266014i
$833$	2.73979	−	4.74545i	0.0949279	−	0.164420i
$834$	−47.5950	+	0.806423i	−1.64808	+	0.0279241i
$835$	2.12532	+	3.68116i	0.0735497	+	0.127392i
$836$	3.43676			0.118863
$837$	−10.8515	+	21.2167i	−0.375082	+	0.733356i
$838$	−27.6177			−0.954039
$839$	0.145648	+	0.252269i	0.00502831	+	0.00870930i	0.868529	−	0.495639i	$-0.165066\pi$
$839$	0.145648	+	0.252269i	0.00502831	+	0.00870930i	−0.863500	+	0.504348i	$0.831733\pi$
$840$	−4.09108	+	0.0693170i	−0.141156	+	0.00239166i
$841$	14.2627	−	24.7036i	0.491816	−	0.851849i
$842$	0.775206	−	1.34270i	0.0267154	−	0.0462724i
$843$	3.33102	+	5.55017i	0.114726	+	0.191158i
$844$	3.50532	+	6.07140i	0.120658	+	0.208986i
$845$	1.00000			0.0344010
$846$	−7.71772	+	14.4792i	−0.265341	+	0.497804i
$847$	5.65322			0.194247
$848$	6.06238	+	10.5003i	0.208183	+	0.360583i
$849$	9.57566	−	17.2541i	0.328636	−	0.592160i
$850$	−0.552426	+	0.956829i	−0.0189480	+	0.0328190i
$851$	11.0295	−	19.1036i	0.378086	−	0.654864i
$852$	−0.474105	+	0.854277i	−0.0162426	+	0.0292671i
$853$	3.71548	+	6.43540i	0.127216	+	0.220344i	0.922597	−	0.385766i	$-0.126063\pi$
$853$	3.71548	+	6.43540i	0.127216	+	0.220344i	−0.795381	+	0.606110i	$0.792729\pi$
$854$	−8.66354			−0.296460
$855$	−7.29292	+	13.6822i	−0.249413	+	0.467922i
$856$	−5.62840			−0.192375
$857$	18.1178	+	31.3810i	0.618893	+	1.07195i	0.989688	+	0.143239i	$0.0457518\pi$
$857$	18.1178	+	31.3810i	0.618893	+	1.07195i	−0.370795	+	0.928715i	$0.620915\pi$
$858$	2.23246	+	3.71975i	0.0762149	+	0.126990i
$859$	23.5673	−	40.8198i	0.804106	−	1.39275i	−0.112787	−	0.993619i	$-0.535978\pi$
$859$	23.5673	−	40.8198i	0.804106	−	1.39275i	0.916893	−	0.399133i	$-0.130689\pi$
$860$	1.24918	−	2.16364i	0.0425967	−	0.0737797i
$861$	−3.99145	+	0.0676289i	−0.136028	+	0.00230479i
$862$	−21.6880	−	37.5648i	−0.738697	−	1.27946i
$863$	−8.17961			−0.278437			−0.139219	−	0.990262i	$-0.544459\pi$
$863$	−8.17961			−0.278437			−0.139219	+	0.990262i	$0.544459\pi$
$864$	4.52259	−	8.84252i	0.153862	−	0.300829i
$865$	−1.57561			−0.0535723
$866$	−3.13212	−	5.42500i	−0.106434	−	0.184349i
$867$	28.1657	−	0.477224i	0.956557	−	0.0162074i
$868$	0.614129	−	1.06370i	0.0208449	−	0.0361044i
$869$	−5.23693	+	9.07063i	−0.177651	+	0.307700i
$870$	0.790766	+	1.31758i	0.0268095	+	0.0446702i
$871$	−0.687659	−	1.19106i	−0.0233004	−	0.0403575i
$872$	−18.8803			−0.639369
$873$	26.5142	+	42.5283i	0.897370	+	1.43937i
$874$	−17.1437			−0.579895
$875$	0.391685	+	0.678419i	0.0132414	+	0.0229347i
$876$	−2.54622	+	4.58796i	−0.0860287	+	0.155013i
$877$	−4.08791	+	7.08047i	−0.138039	+	0.239090i	−0.926754	−	0.375668i	$-0.877413\pi$
$877$	−4.08791	+	7.08047i	−0.138039	+	0.239090i	0.788715	+	0.614759i	$0.210747\pi$
$878$	−11.3484	+	19.6560i	−0.382989	+	0.663356i
$879$	2.85372	−	5.14204i	0.0962535	−	0.173437i
$880$	−3.11157	−	5.38940i	−0.104891	−	0.181677i
$881$	7.14317			0.240660			0.120330	−	0.992734i	$-0.461605\pi$
$881$	7.14317			0.240660			0.120330	+	0.992734i	$0.461605\pi$
$882$	−24.6565	+	0.835773i	−0.830228	+	0.0281420i
$883$	34.1110			1.14793			0.573964	−	0.818881i	$-0.305405\pi$
$883$	34.1110			1.14793			0.573964	+	0.818881i	$0.305405\pi$
$884$	−0.146667	−	0.254035i	−0.00493295	−	0.00854412i
$885$	4.81971	+	8.03064i	0.162013	+	0.269947i
$886$	−20.4582	+	35.4346i	−0.687305	+	1.19045i
$887$	25.4311	−	44.0479i	0.853892	−	1.47898i	−0.0237768	−	0.999717i	$-0.507569\pi$
$887$	25.4311	−	44.0479i	0.853892	−	1.47898i	0.877669	−	0.479267i	$-0.159098\pi$
$888$	44.7194	−	0.757702i	1.50069	−	0.0254268i
$889$	4.29084	+	7.43195i	0.143910	+	0.249259i
$890$	15.9358			0.534168
$891$	9.75953	+	14.5331i	0.326957	+	0.486879i
$892$	−1.80564			−0.0604572
$893$	−10.9754	−	19.0100i	−0.367279	−	0.636146i
$894$	19.3807	−	0.328376i	0.648188	−	0.0109825i
$895$	−8.77532	+	15.1993i	−0.293327	+	0.508057i
$896$	2.97136	−	5.14654i	0.0992660	−	0.171934i
$897$	2.29609	+	3.82577i	0.0766643	+	0.127739i
$898$	−3.07242	−	5.32158i	−0.102528	−	0.177583i
$899$	−3.15983			−0.105386
$900$	−1.02504	+	0.0347453i	−0.0341679	+	0.00115818i
$901$	3.25165			0.108328
$902$	−3.68458	−	6.38189i	−0.122683	−	0.212494i
$903$	−4.81157	+	8.66985i	−0.160119	+	0.288514i
$904$	−7.82293	+	13.5497i	−0.260187	+	0.450657i
$905$	3.59168	−	6.22098i	0.119392	−	0.206792i
$906$	2.01310	−	3.62736i	0.0668809	−	0.120511i
$907$	24.0726	+	41.6949i	0.799316	+	1.38446i	0.920062	+	0.391773i	$0.128138\pi$
$907$	24.0726	+	41.6949i	0.799316	+	1.38446i	−0.120745	+	0.992684i	$0.538528\pi$
$908$	7.09663			0.235510
$909$	7.43089	+	11.9190i	0.246467	+	0.395329i
$910$	1.00873			0.0334391
$911$	11.5535	+	20.0113i	0.382785	+	0.663003i	0.991459	−	0.130417i	$-0.0416318\pi$
$911$	11.5535	+	20.0113i	0.382785	+	0.663003i	−0.608674	+	0.793420i	$0.708298\pi$
$912$	−14.7378	−	24.5562i	−0.488016	−	0.813137i
$913$	4.35872	−	7.54952i	0.144252	−	0.249853i
$914$	5.08306	−	8.80412i	0.168133	−	0.291214i
$915$	−14.8737	+	0.252011i	−0.491708	+	0.00833123i
$916$	3.82503	+	6.62514i	0.126382	+	0.218901i
$917$	−12.2398			−0.404193
$918$	3.11937	+	4.81958i	0.102954	+	0.159070i
$919$	8.44313			0.278513			0.139257	−	0.990256i	$-0.455529\pi$
$919$	8.44313			0.278513			0.139257	+	0.990256i	$0.455529\pi$
$920$	−3.88420	−	6.72764i	−0.128058	−	0.221804i
$921$	−36.5323	+	0.618983i	−1.20378	+	0.0203962i
$922$	23.4009	−	40.5315i	0.770667	−	1.33483i
$923$	0.824982	−	1.42891i	0.0271546	−	0.0470332i
$924$	−0.464312	−	0.773641i	−0.0152747	−	0.0254509i
$925$	−4.28150	−	7.41577i	−0.140775	−	0.243829i
$926$	10.9408			0.359537
$927$	−22.1321	+	41.5219i	−0.726913	+	1.36376i
$928$	1.31693			0.0432304
$929$	−0.0338547	−	0.0586381i	−0.00111074	−	0.00192385i	0.865470	−	0.500962i	$-0.167020\pi$
$929$	−0.0338547	−	0.0586381i	−0.00111074	−	0.00192385i	−0.866580	+	0.499038i	$0.833687\pi$
$930$	−4.96359	+	8.94376i	−0.162762	+	0.293277i
$931$	16.5028	−	28.5837i	0.540858	−	0.936794i
$932$	−3.87630	+	6.71396i	−0.126973	+	0.219923i
$933$	12.8400	−	23.1361i	0.420363	−	0.757440i
$934$	18.2517	+	31.6128i	0.597212	+	1.03440i
$935$	−1.66894			−0.0545801
$936$	−4.25537	+	7.98348i	−0.139091	+	0.260948i
$937$	−35.3939			−1.15627			−0.578134	−	0.815942i	$-0.696219\pi$
$937$	−35.3939			−1.15627			−0.578134	+	0.815942i	$0.696219\pi$
$938$	−0.693663	−	1.20146i	−0.0226489	−	0.0392291i
$939$	7.77187	+	12.9496i	0.253625	+	0.422593i
$940$	0.726028	−	1.25752i	0.0236804	−	0.0410157i
$941$	16.9912	−	29.4295i	0.553896	−	0.959376i	−0.444093	−	0.895981i	$-0.646474\pi$
$941$	16.9912	−	29.4295i	0.553896	−	0.959376i	0.997989	−	0.0633949i	$-0.0201927\pi$
$942$	16.4521	−	0.278755i	0.536037	−	0.00908232i
$943$	−3.78961	−	6.56380i	−0.123407	−	0.213747i
$944$	−17.3004			−0.563079
$945$	4.06526	−	0.206797i	0.132243	−	0.00672710i
$946$	−18.3038			−0.595108
$947$	−15.6487	−	27.1043i	−0.508513	−	0.880771i	−0.999951	−	0.00985829i	$-0.996862\pi$
$947$	−15.6487	−	27.1043i	−0.508513	−	0.880771i	0.491438	−	0.870912i	$-0.336471\pi$
$948$	−3.18807	+	0.0540169i	−0.103544	+	0.00175439i
$949$	4.43063	−	7.67407i	0.143824	−	0.249111i
$950$	−3.32748	+	5.76336i	−0.107958	+	0.186988i
$951$	−19.1555	−	31.9171i	−0.621160	−	1.03498i
$952$	−1.01346	−	1.75536i	−0.0328463	−	0.0568914i
$953$	2.39773			0.0776702			0.0388351	−	0.999246i	$-0.487635\pi$
$953$	2.39773			0.0776702			0.0388351	+	0.999246i	$0.487635\pi$
$954$	−7.74527	−	12.4233i	−0.250762	−	0.402218i
$955$	22.4359			0.726008
$956$	−5.08908	−	8.81455i	−0.164593	−	0.285083i
$957$	−1.12639	+	2.02960i	−0.0364109	+	0.0656078i
$958$	−7.47819	+	12.9526i	−0.241609	+	0.418479i
$959$	1.68467	−	2.91793i	0.0544007	−	0.0942248i
$960$	7.44676	−	13.4181i	0.240343	−	0.433068i
$961$	4.98330	+	8.63132i	0.160751	+	0.278430i
$962$	−11.0264			−0.355506
$963$	5.59608	−	0.189688i	0.180331	−	0.00611262i
$964$	−9.29861			−0.299488
$965$	−4.02595	−	6.97316i	−0.129600	−	0.224474i
$966$	2.31614	+	3.85918i	0.0745207	+	0.124167i
$967$	−16.9715	+	29.3955i	−0.545766	+	0.945295i	0.452792	+	0.891616i	$0.350428\pi$
$967$	−16.9715	+	29.3955i	−0.545766	+	0.945295i	−0.998558	+	0.0536785i	$0.982905\pi$
$968$	−10.8811	+	18.8465i	−0.349730	+	0.605751i
$969$	−7.67945	+	0.130116i	−0.246699	+	0.00417994i
$970$	10.7557	+	18.6294i	0.345344	+	0.598154i
$971$	−35.6928			−1.14544			−0.572719	−	0.819752i	$-0.694111\pi$
$971$	−35.6928			−1.14544			−0.572719	+	0.819752i	$0.694111\pi$
$972$	−2.26461	+	4.82422i	−0.0726373	+	0.154737i
$973$	−16.7194			−0.536000
$974$	−9.76010	−	16.9050i	−0.312734	−	0.541671i
$975$	1.73180	−	0.0293427i	0.0554621	−	0.000939719i
$976$	13.7390	−	23.7966i	0.439774	−	0.761710i
$977$	−9.10320	+	15.7672i	−0.291237	+	0.504437i	−0.974103	−	0.226107i	$-0.927400\pi$
$977$	−9.10320	+	15.7672i	−0.291237	+	0.504437i	0.682865	+	0.730544i	$0.260734\pi$
$978$	−10.0049	−	16.6703i	−0.319922	−	0.533058i
$979$	12.0359	+	20.8468i	0.384669	+	0.666267i
$980$	2.18333			0.0697439
$981$	18.7720	−	0.636306i	0.599342	−	0.0203157i
$982$	18.3705			0.586226
$983$	−12.5721	−	21.7755i	−0.400988	−	0.694531i	0.592858	−	0.805307i	$-0.298000\pi$
$983$	−12.5721	−	21.7755i	−0.400988	−	0.694531i	−0.993845	+	0.110776i	$0.964666\pi$
$984$	7.45709	−	13.4367i	0.237723	−	0.428348i
$985$	−9.25561	+	16.0312i	−0.294908	+	0.510796i
$986$	−0.380613	+	0.659241i	−0.0121212	+	0.0209945i
$987$	−2.79650	+	5.03894i	−0.0890136	+	0.160391i
$988$	−0.883434	−	1.53015i	−0.0281058	−	0.0486807i
$989$	−18.8255			−0.598617
$990$	3.97533	+	6.37636i	0.126344	+	0.202654i
$991$	22.6943			0.720910			0.360455	−	0.932777i	$-0.382622\pi$
$991$	22.6943			0.720910			0.360455	+	0.932777i	$0.382622\pi$
$992$	4.38307	+	7.59170i	0.139163	+	0.241037i
$993$	2.51612	+	4.19238i	0.0798467	+	0.133041i
$994$	0.832186	−	1.44139i	0.0263953	−	0.0457181i
$995$	2.79156	−	4.83513i	0.0884985	−	0.153284i
$996$	2.65344	−	0.0449585i	0.0840775	−	0.00142456i
$997$	−6.86502	−	11.8906i	−0.217417	−	0.376578i	0.736600	−	0.676328i	$-0.236430\pi$
$997$	−6.86502	−	11.8906i	−0.217417	−	0.376578i	−0.954018	+	0.299750i	$0.903097\pi$
$998$	32.2280			1.02016
$999$	−44.4372	+	2.26049i	−1.40593	+	0.0715187i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.g.391.5	yes	26
3.2	odd	2		1755.2.i.g.1171.9		26
9.2	odd	6		1755.2.i.g.586.9		26
9.4	even	3		5265.2.a.bg.1.9		13
9.5	odd	6		5265.2.a.bh.1.5		13
9.7	even	3	inner	585.2.i.g.196.5	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.g.196.5	✓	26	9.7	even	3	inner
585.2.i.g.391.5	yes	26	1.1	even	1	trivial
1755.2.i.g.586.9		26	9.2	odd	6
1755.2.i.g.1171.9		26	3.2	odd	2
5265.2.a.bg.1.9		13	9.4	even	3
5265.2.a.bh.1.5		13	9.5	odd	6

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.643841 - 1.11517i) q^{2} +(-1.73180 + 0.0293427i) q^{3} +(0.170938 - 0.296073i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.14773 + 1.91235i) q^{6} +(0.391685 + 0.678419i) q^{7} -3.01559 q^{8} +(2.99828 - 0.101632i) q^{9} +O(q^{10})\)	\(q+(-0.643841 - 1.11517i) q^{2} +(-1.73180 + 0.0293427i) q^{3} +(0.170938 - 0.296073i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.14773 + 1.91235i) q^{6} +(0.391685 + 0.678419i) q^{7} -3.01559 q^{8} +(2.99828 - 0.101632i) q^{9} +1.28768 q^{10} +(0.972557 + 1.68452i) q^{11} +(-0.287343 + 0.517755i) q^{12} +(0.500000 - 0.866025i) q^{13} +(0.504366 - 0.873587i) q^{14} +(0.840490 - 1.51446i) q^{15} +(1.59969 + 2.77074i) q^{16} +0.858016 q^{17} +(-2.04375 - 3.27814i) q^{18} +5.16817 q^{19} +(0.170938 + 0.296073i) q^{20} +(-0.698228 - 1.16339i) q^{21} +(1.25234 - 2.16912i) q^{22} +(1.28804 - 2.23095i) q^{23} +(5.22241 - 0.0884856i) q^{24} +(-0.500000 - 0.866025i) q^{25} -1.28768 q^{26} +(-5.18944 + 0.263983i) q^{27} +0.267815 q^{28} +(-0.344492 - 0.596678i) q^{29} +(-2.23001 + 0.0377841i) q^{30} +(2.29311 - 3.97178i) q^{31} +(-0.955704 + 1.65533i) q^{32} +(-1.73370 - 2.88871i) q^{33} +(-0.552426 - 0.956829i) q^{34} -0.783370 q^{35} +(0.482428 - 0.905081i) q^{36} +8.56300 q^{37} +(-3.32748 - 5.76336i) q^{38} +(-0.840490 + 1.51446i) q^{39} +(1.50780 - 2.61158i) q^{40} +(1.47108 - 2.54798i) q^{41} +(-0.847829 + 1.52768i) q^{42} +(-3.65391 - 6.32875i) q^{43} +0.664986 q^{44} +(-1.41112 + 2.64740i) q^{45} -3.31717 q^{46} +(-2.12366 - 3.67829i) q^{47} +(-2.85164 - 4.75143i) q^{48} +(3.19317 - 5.53072i) q^{49} +(-0.643841 + 1.11517i) q^{50} +(-1.48591 + 0.0251765i) q^{51} +(-0.170938 - 0.296073i) q^{52} +3.78973 q^{53} +(3.63556 + 5.61712i) q^{54} -1.94511 q^{55} +(-1.18116 - 2.04583i) q^{56} +(-8.95025 + 0.151648i) q^{57} +(-0.443597 + 0.768332i) q^{58} +(-2.70371 + 4.68297i) q^{59} +(-0.304718 - 0.507723i) q^{60} +(-4.29427 - 7.43790i) q^{61} -5.90559 q^{62} +(1.24333 + 1.99428i) q^{63} +8.86003 q^{64} +(0.500000 + 0.866025i) q^{65} +(-2.10516 + 3.79324i) q^{66} +(0.687659 - 1.19106i) q^{67} +(0.146667 - 0.254035i) q^{68} +(-2.16517 + 3.90136i) q^{69} +(0.504366 + 0.873587i) q^{70} +1.64996 q^{71} +(-9.04158 + 0.306479i) q^{72} +8.86126 q^{73} +(-5.51321 - 9.54916i) q^{74} +(0.891313 + 1.48511i) q^{75} +(0.883434 - 1.53015i) q^{76} +(-0.761872 + 1.31960i) q^{77} +(2.23001 - 0.0377841i) q^{78} +(2.69235 + 4.66329i) q^{79} -3.19937 q^{80} +(8.97934 - 0.609439i) q^{81} -3.78855 q^{82} +(-2.24085 - 3.88127i) q^{83} +(-0.463802 + 0.00785841i) q^{84} +(-0.429008 + 0.743063i) q^{85} +(-4.70507 + 8.14942i) q^{86} +(0.614101 + 1.02322i) q^{87} +(-2.93283 - 5.07982i) q^{88} +12.3755 q^{89} +(3.86083 - 0.130869i) q^{90} +0.783370 q^{91} +(-0.440349 - 0.762707i) q^{92} +(-3.85467 + 6.94563i) q^{93} +(-2.73460 + 4.73647i) q^{94} +(-2.58408 + 4.47577i) q^{95} +(1.60652 - 2.89474i) q^{96} +(8.35275 + 14.4674i) q^{97} -8.22356 q^{98} +(3.08720 + 4.95181i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9}+O(q^{10}) \) 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9	\( 26 q + q^{2} + q^{3} - 15 q^{4} - 13 q^{5} + 7 q^{6} - 10 q^{7} - 12 q^{8} + 7 q^{9} - 2 q^{10} - 11 q^{11} - 20 q^{12} + 13 q^{13} - 15 q^{14} - 2 q^{15} - 19 q^{16} + 6 q^{17} - 13 q^{18} + 30 q^{19} - 15 q^{20} - q^{21} - 12 q^{22} - 6 q^{23} + 20 q^{24} - 13 q^{25} + 2 q^{26} - 2 q^{27} + 10 q^{28} - 14 q^{29} - 2 q^{30} - 30 q^{31} + 43 q^{32} + 6 q^{33} - 19 q^{34} + 20 q^{35} - 39 q^{36} + 32 q^{37} + 2 q^{38} + 2 q^{39} + 6 q^{40} - 17 q^{41} + 83 q^{42} - 6 q^{43} + 46 q^{44} - 5 q^{45} + 46 q^{46} + 21 q^{47} - 7 q^{48} - 29 q^{49} + q^{50} + 55 q^{51} + 15 q^{52} + 2 q^{53} - 6 q^{54} + 22 q^{55} - 37 q^{56} + 33 q^{57} - 14 q^{58} - 13 q^{59} + 25 q^{60} - 22 q^{61} - 114 q^{62} - 44 q^{63} + 84 q^{64} + 13 q^{65} - 68 q^{66} - 35 q^{67} + 4 q^{68} - 38 q^{69} - 15 q^{70} + 24 q^{71} - 24 q^{72} + 64 q^{73} + 28 q^{74} + q^{75} - 54 q^{76} - 4 q^{77} + 2 q^{78} - 12 q^{79} + 38 q^{80} + 15 q^{81} + 46 q^{82} + 3 q^{83} + 27 q^{84} - 3 q^{85} + 40 q^{86} - 12 q^{87} - 29 q^{88} + 12 q^{89} - 10 q^{90} - 20 q^{91} + 16 q^{92} - 9 q^{93} - 44 q^{94} - 15 q^{95} + 51 q^{96} - 33 q^{97} + 70 q^{98} - 22 q^{99}+O(q^{100}) \) 26 * q + q^2 + q^3 - 15 * q^4 - 13 * q^5 + 7 * q^6 - 10 * q^7 - 12 * q^8 + 7 * q^9 - 2 * q^10 - 11 * q^11 - 20 * q^12 + 13 * q^13 - 15 * q^14 - 2 * q^15 - 19 * q^16 + 6 * q^17 - 13 * q^18 + 30 * q^19 - 15 * q^20 - q^21 - 12 * q^22 - 6 * q^23 + 20 * q^24 - 13 * q^25 + 2 * q^26 - 2 * q^27 + 10 * q^28 - 14 * q^29 - 2 * q^30 - 30 * q^31 + 43 * q^32 + 6 * q^33 - 19 * q^34 + 20 * q^35 - 39 * q^36 + 32 * q^37 + 2 * q^38 + 2 * q^39 + 6 * q^40 - 17 * q^41 + 83 * q^42 - 6 * q^43 + 46 * q^44 - 5 * q^45 + 46 * q^46 + 21 * q^47 - 7 * q^48 - 29 * q^49 + q^50 + 55 * q^51 + 15 * q^52 + 2 * q^53 - 6 * q^54 + 22 * q^55 - 37 * q^56 + 33 * q^57 - 14 * q^58 - 13 * q^59 + 25 * q^60 - 22 * q^61 - 114 * q^62 - 44 * q^63 + 84 * q^64 + 13 * q^65 - 68 * q^66 - 35 * q^67 + 4 * q^68 - 38 * q^69 - 15 * q^70 + 24 * q^71 - 24 * q^72 + 64 * q^73 + 28 * q^74 + q^75 - 54 * q^76 - 4 * q^77 + 2 * q^78 - 12 * q^79 + 38 * q^80 + 15 * q^81 + 46 * q^82 + 3 * q^83 + 27 * q^84 - 3 * q^85 + 40 * q^86 - 12 * q^87 - 29 * q^88 + 12 * q^89 - 10 * q^90 - 20 * q^91 + 16 * q^92 - 9 * q^93 - 44 * q^94 - 15 * q^95 + 51 * q^96 - 33 * q^97 + 70 * q^98 - 22 * q^99

Introduction

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