LMFDB - Embedded newform 483.2.q.f.64.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			64.8
Character	$\chi$	$=$	483.64
Dual form			483.2.q.f.400.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.67036 + 0.784088i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(4.83351 + 3.10631i) q^{4} +(0.534653 - 3.71859i) q^{5} +(-2.34129 + 1.50465i) q^{6} +(-0.415415 - 0.909632i) q^{7} +(6.82652 + 7.87822i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(2.67036 + 0.784088i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(4.83351 + 3.10631i) q^{4} +(0.534653 - 3.71859i) q^{5} +(-2.34129 + 1.50465i) q^{6} +(-0.415415 - 0.909632i) q^{7} +(6.82652 + 7.87822i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(4.34342 - 9.51076i) q^{10} +(0.114091 - 0.0335001i) q^{11} +(-5.51287 + 1.61873i) q^{12} +(-0.0544331 + 0.119192i) q^{13} +(-0.396076 - 2.75477i) q^{14} +(2.46020 + 2.83922i) q^{15} +(7.27841 + 15.9375i) q^{16} +(-5.87955 + 3.77856i) q^{17} +(0.396076 - 2.75477i) q^{18} +(1.31667 + 0.846171i) q^{19} +(14.1354 - 16.3131i) q^{20} +(0.959493 + 0.281733i) q^{21} +0.330931 q^{22} +(-4.69762 + 0.965614i) q^{23} -10.4244 q^{24} +(-8.74460 - 2.56765i) q^{25} +(-0.238813 + 0.275605i) q^{26} +(0.841254 + 0.540641i) q^{27} +(0.817685 - 5.68713i) q^{28} +(-3.34428 + 2.14924i) q^{29} +(4.34342 + 9.51076i) q^{30} +(-3.47244 - 4.00741i) q^{31} +(3.97248 + 27.6292i) q^{32} +(-0.0493960 + 0.108162i) q^{33} +(-18.6632 + 5.48002i) q^{34} +(-3.60465 + 1.05842i) q^{35} +(2.38681 - 5.22639i) q^{36} +(-0.763352 - 5.30923i) q^{37} +(2.85250 + 3.29196i) q^{38} +(-0.0544331 - 0.119192i) q^{39} +(32.9457 - 21.1729i) q^{40} +(-0.493094 + 3.42954i) q^{41} +(2.34129 + 1.50465i) q^{42} +(6.60874 - 7.62690i) q^{43} +(0.655522 + 0.192479i) q^{44} -3.75683 q^{45} +(-13.3014 - 1.10481i) q^{46} +9.05898 q^{47} +(-16.8111 - 4.93618i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(-21.3380 - 13.7131i) q^{50} +(0.994644 - 6.91790i) q^{51} +(-0.633350 + 0.407029i) q^{52} +(-0.743989 - 1.62911i) q^{53} +(1.82254 + 2.10332i) q^{54} +(-0.0635742 - 0.442168i) q^{55} +(4.33044 - 9.48235i) q^{56} +(-1.50173 + 0.440947i) q^{57} +(-10.6156 + 3.11703i) q^{58} +(-0.586875 + 1.28508i) q^{59} +(3.07191 + 21.3656i) q^{60} +(6.73404 + 7.77150i) q^{61} +(-6.13050 - 13.4239i) q^{62} +(-0.841254 + 0.540641i) q^{63} +(-6.06883 + 42.2096i) q^{64} +(0.414123 + 0.266141i) q^{65} +(-0.216713 + 0.250101i) q^{66} +(11.7724 + 3.45669i) q^{67} -40.1563 q^{68} +(2.34652 - 4.18256i) q^{69} -10.4556 q^{70} +(1.45211 + 0.426377i) q^{71} +(6.82652 - 7.87822i) q^{72} +(-8.29790 - 5.33273i) q^{73} +(2.12448 - 14.7761i) q^{74} +(7.66699 - 4.92728i) q^{75} +(3.73566 + 8.17996i) q^{76} +(-0.0778678 - 0.0898643i) q^{77} +(-0.0518990 - 0.360965i) q^{78} +(0.271570 - 0.594655i) q^{79} +(63.1564 - 18.5444i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-4.00580 + 8.77148i) q^{82} +(-0.0413999 - 0.287943i) q^{83} +(3.76257 + 4.34224i) q^{84} +(10.9074 + 23.8839i) q^{85} +(23.6279 - 15.1847i) q^{86} +(0.565752 - 3.93489i) q^{87} +(1.04276 + 0.670144i) q^{88} +(-3.57384 + 4.12443i) q^{89} +(-10.0321 - 2.94569i) q^{90} +0.131033 q^{91} +(-25.7055 - 9.92495i) q^{92} +5.30257 q^{93} +(24.1907 + 7.10304i) q^{94} +(3.85052 - 4.44374i) q^{95} +(-23.4822 - 15.0911i) q^{96} +(1.17267 - 8.15613i) q^{97} +(-2.34129 + 1.50465i) q^{98} +(-0.0493960 - 0.108162i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9}+O(q^{10}) $ 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9	\( 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9} + 4 q^{10} + q^{11} - 9 q^{12} - 26 q^{13} - q^{14} + 2 q^{15} - 3 q^{16} - 23 q^{17} + q^{18} + 10 q^{19} + 63 q^{20} + 8 q^{21} - 9 q^{23} + 30 q^{24} - 29 q^{25} - 12 q^{26} - 8 q^{27} + 20 q^{28} + 13 q^{29} + 4 q^{30} - 27 q^{31} + 71 q^{32} + q^{33} - 45 q^{34} - 2 q^{35} - 9 q^{36} + 60 q^{37} - 2 q^{38} - 26 q^{39} + 7 q^{40} - 26 q^{41} - q^{42} + 5 q^{43} - 33 q^{44} - 20 q^{45} - 41 q^{46} + 34 q^{47} - 58 q^{48} - 8 q^{49} - 75 q^{50} - q^{51} + 108 q^{52} - 39 q^{53} - 10 q^{54} + 51 q^{55} + 3 q^{56} + 10 q^{57} + 47 q^{58} - 66 q^{59} + 19 q^{60} + 3 q^{61} + 103 q^{62} + 8 q^{63} - 25 q^{64} + 39 q^{65} - 33 q^{66} + 33 q^{67} - 88 q^{68} + 13 q^{69} + 18 q^{70} - 12 q^{71} - 25 q^{72} - 98 q^{73} + 123 q^{74} + 4 q^{75} - 41 q^{76} - 12 q^{77} + 10 q^{78} - 34 q^{79} + 163 q^{80} - 8 q^{81} + 48 q^{82} + 26 q^{83} + 9 q^{84} + 35 q^{85} + 4 q^{86} + 2 q^{87} + 178 q^{88} - 63 q^{89} + 4 q^{90} - 62 q^{91} - 39 q^{92} + 138 q^{93} - 28 q^{94} - 80 q^{95} - 17 q^{96} - 44 q^{97} + q^{98} + q^{99}+O(q^{100}) \) 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9 + 4 * q^10 + q^11 - 9 * q^12 - 26 * q^13 - q^14 + 2 * q^15 - 3 * q^16 - 23 * q^17 + q^18 + 10 * q^19 + 63 * q^20 + 8 * q^21 - 9 * q^23 + 30 * q^24 - 29 * q^25 - 12 * q^26 - 8 * q^27 + 20 * q^28 + 13 * q^29 + 4 * q^30 - 27 * q^31 + 71 * q^32 + q^33 - 45 * q^34 - 2 * q^35 - 9 * q^36 + 60 * q^37 - 2 * q^38 - 26 * q^39 + 7 * q^40 - 26 * q^41 - q^42 + 5 * q^43 - 33 * q^44 - 20 * q^45 - 41 * q^46 + 34 * q^47 - 58 * q^48 - 8 * q^49 - 75 * q^50 - q^51 + 108 * q^52 - 39 * q^53 - 10 * q^54 + 51 * q^55 + 3 * q^56 + 10 * q^57 + 47 * q^58 - 66 * q^59 + 19 * q^60 + 3 * q^61 + 103 * q^62 + 8 * q^63 - 25 * q^64 + 39 * q^65 - 33 * q^66 + 33 * q^67 - 88 * q^68 + 13 * q^69 + 18 * q^70 - 12 * q^71 - 25 * q^72 - 98 * q^73 + 123 * q^74 + 4 * q^75 - 41 * q^76 - 12 * q^77 + 10 * q^78 - 34 * q^79 + 163 * q^80 - 8 * q^81 + 48 * q^82 + 26 * q^83 + 9 * q^84 + 35 * q^85 + 4 * q^86 + 2 * q^87 + 178 * q^88 - 63 * q^89 + 4 * q^90 - 62 * q^91 - 39 * q^92 + 138 * q^93 - 28 * q^94 - 80 * q^95 - 17 * q^96 - 44 * q^97 + q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	2.67036	+	0.784088i	1.88823	+	0.554434i	0.994354	+	0.106118i	$0.0338422\pi$
$2$	2.67036	+	0.784088i	1.88823	+	0.554434i	0.893875	+	0.448316i	$0.147976\pi$
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$4$	4.83351	+	3.10631i	2.41676	+	1.55316i
$5$	0.534653	−	3.71859i	0.239104	−	1.66300i	−0.417431	−	0.908709i	$-0.637069\pi$
$5$	0.534653	−	3.71859i	0.239104	−	1.66300i	0.656535	−	0.754296i	$-0.272021\pi$
$6$	−2.34129	+	1.50465i	−0.955827	+	0.614272i
$7$	−0.415415	−	0.909632i	−0.157012	−	0.343809i
$7$	−0.415415	−	0.909632i	−0.157012	−	0.343809i
$8$	6.82652	+	7.87822i	2.41354	+	2.78537i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	4.34342	−	9.51076i	1.37351	−	3.00757i
$11$	0.114091	−	0.0335001i	0.0343997	−	0.0101007i	−0.264487	−	0.964389i	$-0.585203\pi$
$11$	0.114091	−	0.0335001i	0.0343997	−	0.0101007i	0.298887	+	0.954288i	$0.403385\pi$
$12$	−5.51287	+	1.61873i	−1.59143	+	0.467286i
$13$	−0.0544331	+	0.119192i	−0.0150970	+	0.0330579i	−0.917030	−	0.398817i	$-0.869421\pi$
$13$	−0.0544331	+	0.119192i	−0.0150970	+	0.0330579i	0.901933	+	0.431875i	$0.142148\pi$
$14$	−0.396076	−	2.75477i	−0.105856	−	0.736242i
$15$	2.46020	+	2.83922i	0.635221	+	0.733084i
$16$	7.27841	+	15.9375i	1.81960	+	3.98437i
$17$	−5.87955	+	3.77856i	−1.42600	+	0.916435i	−0.426070	+	0.904690i	$0.640102\pi$
$17$	−5.87955	+	3.77856i	−1.42600	+	0.916435i	−0.999931	+	0.0117447i	$0.996261\pi$
$18$	0.396076	−	2.75477i	0.0933559	−	0.649304i
$19$	1.31667	+	0.846171i	0.302064	+	0.194125i	0.682889	−	0.730522i	$-0.260723\pi$
$19$	1.31667	+	0.846171i	0.302064	+	0.194125i	−0.380824	+	0.924647i	$0.624360\pi$
$20$	14.1354	−	16.3131i	3.16076	−	3.64771i
$21$	0.959493	+	0.281733i	0.209379	+	0.0614791i
$22$	0.330931			0.0705547
$23$	−4.69762	+	0.965614i	−0.979521	+	0.201344i
$23$	−4.69762	+	0.965614i	−0.979521	+	0.201344i
$24$	−10.4244			−2.12787
$25$	−8.74460	−	2.56765i	−1.74892	−	0.513529i
$26$	−0.238813	+	0.275605i	−0.0468350	+	0.0540505i
$27$	0.841254	+	0.540641i	0.161899	+	0.104046i
$28$	0.817685	−	5.68713i	0.154528	−	1.07477i
$29$	−3.34428	+	2.14924i	−0.621017	+	0.399104i	−0.812974	−	0.582300i	$-0.802153\pi$
$29$	−3.34428	+	2.14924i	−0.621017	+	0.399104i	0.191957	+	0.981403i	$0.438517\pi$
$30$	4.34342	+	9.51076i	0.792996	+	1.73642i
$31$	−3.47244	−	4.00741i	−0.623669	−	0.719753i	0.352730	−	0.935725i	$-0.385253\pi$
$31$	−3.47244	−	4.00741i	−0.623669	−	0.719753i	−0.976399	+	0.215972i	$0.930708\pi$
$32$	3.97248	+	27.6292i	0.702241	+	4.88419i
$33$	−0.0493960	+	0.108162i	−0.00859873	+	0.0188286i
$34$	−18.6632	+	5.48002i	−3.20072	+	0.939816i
$35$	−3.60465	+	1.05842i	−0.609297	+	0.178906i
$36$	2.38681	−	5.22639i	0.397802	−	0.871065i
$37$	−0.763352	−	5.30923i	−0.125494	−	0.872832i	−0.951166	−	0.308681i	$-0.900113\pi$
$37$	−0.763352	−	5.30923i	−0.125494	−	0.872832i	0.825671	−	0.564151i	$-0.190797\pi$
$38$	2.85250	+	3.29196i	0.462737	+	0.534027i
$39$	−0.0544331	−	0.119192i	−0.00871627	−	0.0190860i
$40$	32.9457	−	21.1729i	5.20917	−	3.34773i
$41$	−0.493094	+	3.42954i	−0.0770083	+	0.535604i	0.914401	+	0.404809i	$0.132662\pi$
$41$	−0.493094	+	3.42954i	−0.0770083	+	0.535604i	−0.991409	+	0.130795i	$0.958247\pi$
$42$	2.34129	+	1.50465i	0.361268	+	0.232173i
$43$	6.60874	−	7.62690i	1.00782	−	1.16309i	0.0212505	−	0.999774i	$-0.493235\pi$
$43$	6.60874	−	7.62690i	1.00782	−	1.16309i	0.986574	−	0.163317i	$-0.0522193\pi$
$44$	0.655522	+	0.192479i	0.0988236	+	0.0290172i
$45$	−3.75683			−0.560035
$46$	−13.3014	−	1.10481i	−1.96119	−	0.162895i
$47$	9.05898			1.32139			0.660694	−	0.750655i	$-0.270262\pi$
$47$	9.05898			1.32139			0.660694	+	0.750655i	$0.270262\pi$
$48$	−16.8111	−	4.93618i	−2.42647	−	0.712477i
$49$	−0.654861	+	0.755750i	−0.0935515	+	0.107964i
$50$	−21.3380	−	13.7131i	−3.01764	−	1.93932i
$51$	0.994644	−	6.91790i	0.139278	−	0.968699i
$52$	−0.633350	+	0.407029i	−0.0878298	+	0.0564448i
$53$	−0.743989	−	1.62911i	−0.102195	−	0.223775i	0.851627	−	0.524148i	$-0.175616\pi$
$53$	−0.743989	−	1.62911i	−0.102195	−	0.223775i	−0.953822	+	0.300373i	$0.902889\pi$
$54$	1.82254	+	2.10332i	0.248016	+	0.286226i
$55$	−0.0635742	−	0.442168i	−0.00857234	−	0.0596220i
$56$	4.33044	−	9.48235i	0.578680	−	1.26713i
$57$	−1.50173	+	0.440947i	−0.198909	+	0.0584048i
$58$	−10.6156	+	3.11703i	−1.39390	+	0.409286i
$59$	−0.586875	+	1.28508i	−0.0764046	+	0.167303i	−0.943980	−	0.330003i	$-0.892950\pi$
$59$	−0.586875	+	1.28508i	−0.0764046	+	0.167303i	0.867575	+	0.497306i	$0.165677\pi$
$60$	3.07191	+	21.3656i	0.396581	+	2.75828i
$61$	6.73404	+	7.77150i	0.862206	+	0.995039i	0.999990	+	0.00457629i	$0.00145668\pi$
$61$	6.73404	+	7.77150i	0.862206	+	0.995039i	−0.137784	+	0.990462i	$0.543998\pi$
$62$	−6.13050	−	13.4239i	−0.778575	−	1.70484i
$63$	−0.841254	+	0.540641i	−0.105988	+	0.0681143i
$64$	−6.06883	+	42.2096i	−0.758603	+	5.27620i
$65$	0.414123	+	0.266141i	0.0513656	+	0.0330107i
$66$	−0.216713	+	0.250101i	−0.0266756	+	0.0307853i
$67$	11.7724	+	3.45669i	1.43823	+	0.422302i	0.905631	−	0.424066i	$-0.139398\pi$
$67$	11.7724	+	3.45669i	1.43823	+	0.422302i	0.532598	+	0.846368i	$0.321216\pi$
$68$	−40.1563			−4.86966
$69$	2.34652	−	4.18256i	0.282488	−	0.503521i
$70$	−10.4556			−1.24968
$71$	1.45211	+	0.426377i	0.172333	+	0.0506016i	0.366761	−	0.930315i	$-0.380467\pi$
$71$	1.45211	+	0.426377i	0.172333	+	0.0506016i	−0.194428	+	0.980917i	$0.562285\pi$
$72$	6.82652	−	7.87822i	0.804513	−	0.928457i
$73$	−8.29790	−	5.33273i	−0.971195	−	0.624149i	−0.0441207	−	0.999026i	$-0.514049\pi$
$73$	−8.29790	−	5.33273i	−0.971195	−	0.624149i	−0.927075	+	0.374877i	$0.877685\pi$
$74$	2.12448	−	14.7761i	0.246966	−	1.71768i
$75$	7.66699	−	4.92728i	0.885308	−	0.568953i
$76$	3.73566	+	8.17996i	0.428510	+	0.938305i
$77$	−0.0778678	−	0.0898643i	−0.00887386	−	0.0102410i
$78$	−0.0518990	−	0.360965i	−0.00587640	−	0.0408713i
$79$	0.271570	−	0.594655i	0.0305540	−	0.0669039i	−0.893740	−	0.448586i	$-0.851928\pi$
$79$	0.271570	−	0.594655i	0.0305540	−	0.0669039i	0.924294	+	0.381682i	$0.124655\pi$
$80$	63.1564	−	18.5444i	7.06110	−	2.07333i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	−4.00580	+	8.77148i	−0.442367	+	0.968648i
$83$	−0.0413999	−	0.287943i	−0.00454423	−	0.0316058i	0.987423	−	0.158100i	$-0.0505367\pi$
$83$	−0.0413999	−	0.287943i	−0.00454423	−	0.0316058i	−0.991967	+	0.126494i	$0.959628\pi$
$84$	3.76257	+	4.34224i	0.410530	+	0.473777i
$85$	10.9074	+	23.8839i	1.18307	+	2.59057i
$86$	23.6279	−	15.1847i	2.54786	−	1.63741i
$87$	0.565752	−	3.93489i	0.0606550	−	0.421864i
$88$	1.04276	+	0.670144i	0.111159	+	0.0714376i
$89$	−3.57384	+	4.12443i	−0.378826	+	0.437189i	−0.912859	−	0.408275i	$-0.866131\pi$
$89$	−3.57384	+	4.12443i	−0.378826	+	0.437189i	0.534033	+	0.845464i	$0.320676\pi$
$90$	−10.0321	−	2.94569i	−1.05747	−	0.310502i
$91$	0.131033			0.0137360
$92$	−25.7055	−	9.92495i	−2.67998	−	1.03475i
$93$	5.30257			0.549851
$94$	24.1907	+	7.10304i	2.49508	+	0.732622i
$95$	3.85052	−	4.44374i	0.395055	−	0.455918i
$96$	−23.4822	−	15.0911i	−2.39664	−	1.54023i
$97$	1.17267	−	8.15613i	0.119067	−	0.828130i	−0.839520	−	0.543329i	$-0.817164\pi$
$97$	1.17267	−	8.15613i	0.119067	−	0.828130i	0.958587	−	0.284800i	$-0.0919273\pi$
$98$	−2.34129	+	1.50465i	−0.236506	+	0.151993i
$99$	−0.0493960	−	0.108162i	−0.00496448	−	0.0108707i
$100$	−34.2912	−	39.5742i	−3.42912	−	3.95742i
$101$	−0.0812766	−	0.565291i	−0.00808733	−	0.0562486i	0.985378	−	0.170382i	$-0.0545001\pi$
$101$	−0.0812766	−	0.565291i	−0.00808733	−	0.0562486i	−0.993465	+	0.114133i	$0.963591\pi$
$102$	8.08030	−	17.6934i	0.800069	−	1.75191i
$103$	4.28008	−	1.25675i	0.421729	−	0.123831i	−0.0639805	−	0.997951i	$-0.520380\pi$
$103$	4.28008	−	1.25675i	0.421729	−	0.123831i	0.485709	+	0.874120i	$0.338561\pi$
$104$	−1.31061	+	0.384829i	−0.128516	+	0.0377356i
$105$	1.56064	−	3.41733i	0.152303	−	0.333498i
$106$	−0.709353	−	4.93366i	−0.0688984	−	0.479199i
$107$	−11.7923	−	13.6091i	−1.14001	−	1.31564i	−0.942068	−	0.335422i	$-0.891121\pi$
$107$	−11.7923	−	13.6091i	−1.14001	−	1.31564i	−0.197938	−	0.980215i	$-0.563424\pi$
$108$	2.38681	+	5.22639i	0.229671	+	0.502910i
$109$	−4.24225	+	2.72633i	−0.406333	+	0.261135i	−0.727804	−	0.685785i	$-0.759459\pi$
$109$	−4.24225	+	2.72633i	−0.406333	+	0.261135i	0.321471	+	0.946919i	$0.395823\pi$
$110$	0.176933	−	1.23060i	0.0168699	−	0.117333i
$111$	4.51234	+	2.89990i	0.428292	+	0.275247i
$112$	11.4737	−	13.2413i	1.08416	−	1.25119i
$113$	−5.86869	−	1.72320i	−0.552080	−	0.162105i	−0.00621831	−	0.999981i	$-0.501979\pi$
$113$	−5.86869	−	1.72320i	−0.552080	−	0.162105i	−0.545862	+	0.837875i	$0.683798\pi$
$114$	−4.35589			−0.407967
$115$	1.07913	+	17.9848i	0.100629	+	1.67709i
$116$	−22.8408			−2.12072
$117$	0.125725	+	0.0369163i	0.0116233	+	0.00341291i
$118$	−2.57478	+	2.97145i	−0.237028	+	0.273545i
$119$	5.87955	+	3.77856i	0.538978	+	0.346380i
$120$	−5.57342	+	38.7640i	−0.508782	+	3.53865i
$121$	−9.24189	+	5.93940i	−0.840172	+	0.539946i
$122$	11.8888	+	26.0328i	1.07636	+	2.35690i
$123$	−2.26897	−	2.61853i	−0.204586	−	0.236105i
$124$	−4.33583	−	30.1564i	−0.389369	−	2.70812i
$125$	−6.42013	+	14.0581i	−0.574234	+	1.25740i
$126$	−2.67036	+	0.784088i	−0.237894	+	0.0698521i
$127$	14.7588	−	4.33358i	1.30963	−	0.384543i	0.448892	−	0.893586i	$-0.351819\pi$
$127$	14.7588	−	4.33358i	1.30963	−	0.384543i	0.860741	+	0.509043i	$0.170001\pi$
$128$	−26.1108	+	57.1747i	−2.30789	+	5.05358i
$129$	1.43622	+	9.98911i	0.126452	+	0.879492i
$130$	0.897179	+	1.03540i	0.0786878	+	0.0908106i
$131$	−5.12438	−	11.2208i	−0.447719	−	0.980368i	−0.990117	−	0.140246i	$-0.955211\pi$
$131$	−5.12438	−	11.2208i	−0.447719	−	0.980368i	0.542398	−	0.840122i	$-0.317517\pi$
$132$	−0.574741	+	0.369364i	−0.0500248	+	0.0321490i
$133$	0.222741	−	1.54919i	0.0193141	−	0.134332i
$134$	28.7262	+	18.4612i	2.48157	+	1.59481i
$135$	2.46020	−	2.83922i	0.211740	−	0.244361i
$136$	−69.9052	−	20.5260i	−5.99432	−	1.76009i
$137$	0.251795			0.0215123			0.0107562	−	0.999942i	$-0.496576\pi$
$137$	0.251795			0.0215123			0.0107562	+	0.999942i	$0.496576\pi$
$138$	9.54555	−	9.32906i	0.812571	−	0.794143i
$139$	2.08637			0.176964			0.0884818	−	0.996078i	$-0.471799\pi$
$139$	2.08637			0.176964			0.0884818	+	0.996078i	$0.471799\pi$
$140$	−20.7109	−	6.08128i	−1.75039	−	0.513962i
$141$	−5.93237	+	6.84632i	−0.499596	+	0.576564i
$142$	3.54333	+	2.27716i	0.297349	+	0.191095i
$143$	−0.00221738	+	0.0154222i	−0.000185427	+	0.00128967i
$144$	14.7394	−	9.47246i	1.22829	−	0.789372i
$145$	6.20411	+	13.5851i	0.515223	+	1.12818i
$146$	−17.9770	−	20.7466i	−1.48779	−	1.71700i
$147$	−0.142315	−	0.989821i	−0.0117379	−	0.0816391i
$148$	12.8024	−	28.0334i	1.05235	−	2.30433i
$149$	−1.97488	+	0.579876i	−0.161788	+	0.0475053i	−0.361624	−	0.932324i	$-0.617777\pi$
$149$	−1.97488	+	0.579876i	−0.161788	+	0.0475053i	0.199835	+	0.979829i	$0.435959\pi$
$150$	24.3370	−	7.14600i	1.98711	−	0.583468i
$151$	4.10836	−	8.99606i	0.334334	−	0.732089i	−0.665565	−	0.746340i	$-0.731809\pi$
$151$	4.10836	−	8.99606i	0.334334	−	0.732089i	0.999898	+	0.0142512i	$0.00453646\pi$
$152$	2.32193	+	16.1494i	0.188334	+	1.30989i
$153$	4.57685	+	5.28196i	0.370016	+	0.427021i
$154$	−0.137474	−	0.301025i	−0.0110779	−	0.0242573i
$155$	−16.7585	+	10.7700i	−1.34607	+	0.865069i
$156$	0.107144	−	0.745202i	0.00857837	−	0.0596639i
$157$	−8.42654	−	5.41541i	−0.672511	−	0.432196i	0.159319	−	0.987227i	$-0.449070\pi$
$157$	−8.42654	−	5.41541i	−0.672511	−	0.432196i	−0.831830	+	0.555031i	$0.812706\pi$
$158$	1.19145	−	1.37501i	0.0947867	−	0.109390i
$159$	1.71841	+	0.504570i	0.136279	+	0.0400150i
$160$	104.865			8.29034
$161$	2.82981	+	3.87197i	0.223021	+	0.305154i
$162$	−2.78309			−0.218660
$163$	17.8613	+	5.24455i	1.39901	+	0.410785i	0.892342	−	0.451359i	$-0.149061\pi$
$163$	17.8613	+	5.24455i	1.39901	+	0.410785i	0.506663	+	0.862144i	$0.330879\pi$
$164$	−13.0366	+	15.0450i	−1.01799	+	1.17482i
$165$	0.375801	+	0.241512i	0.0292560	+	0.0188017i
$166$	0.115220	−	0.801371i	0.00894279	−	0.0621984i
$167$	−8.07100	+	5.18691i	−0.624552	+	0.401375i	−0.814289	−	0.580460i	$-0.802873\pi$
$167$	−8.07100	+	5.18691i	−0.624552	+	0.401375i	0.189737	+	0.981835i	$0.439237\pi$
$168$	4.33044	+	9.48235i	0.334101	+	0.731579i
$169$	8.50195	+	9.81177i	0.653996	+	0.754751i
$170$	10.3996	+	72.3308i	0.797613	+	5.54752i
$171$	0.650177	−	1.42369i	0.0497203	−	0.108872i
$172$	55.6350	−	16.3359i	4.24213	−	1.24560i
$173$	22.7248	−	6.67261i	1.72774	−	0.507309i	0.741260	−	0.671218i	$-0.234229\pi$
$173$	22.7248	−	6.67261i	1.72774	−	0.507309i	0.986475	+	0.163909i	$0.0524105\pi$
$174$	4.59606	−	10.0640i	0.348426	−	0.762947i
$175$	1.29702	+	9.02100i	0.0980458	+	0.681924i
$176$	1.36431	+	1.57449i	0.102839	+	0.118682i
$177$	−0.586875	−	1.28508i	−0.0441122	−	0.0965923i
$178$	−12.7774	+	8.21151i	−0.957704	+	0.615479i
$179$	−2.02265	+	14.0679i	−0.151180	+	1.05148i	0.763065	+	0.646322i	$0.223694\pi$
$179$	−2.02265	+	14.0679i	−0.151180	+	1.05148i	−0.914246	+	0.405161i	$0.867216\pi$
$180$	−18.1587	−	11.6699i	−1.35347	−	0.869822i
$181$	−14.1464	+	16.3258i	−1.05149	+	1.21348i	−0.0751663	+	0.997171i	$0.523949\pi$
$181$	−14.1464	+	16.3258i	−1.05149	+	1.21348i	−0.976324	+	0.216313i	$0.930597\pi$
$182$	0.349905	+	0.102741i	0.0259367	+	0.00761570i
$183$	−10.2832			−0.760154
$184$	−39.6757	−	30.4171i	−2.92493	−	2.24238i
$185$	−20.1510			−1.48153
$186$	14.1598	+	4.15768i	1.03824	+	0.304856i
$187$	−0.544221	+	0.628065i	−0.0397974	+	0.0459286i
$188$	43.7867	+	28.1400i	3.19347	+	2.05232i
$189$	0.142315	−	0.989821i	0.0103519	−	0.0719989i
$190$	13.7666	−	8.84723i	0.998731	−	0.641846i
$191$	1.85302	+	4.05756i	0.134080	+	0.293594i	0.964749	−	0.263173i	$-0.0847689\pi$
$191$	1.85302	+	4.05756i	0.134080	+	0.293594i	−0.830669	+	0.556767i	$0.812042\pi$
$192$	−27.9257	−	32.2279i	−2.01536	−	2.32585i
$193$	−0.716604	−	4.98409i	−0.0515823	−	0.358763i	−0.999223	−	0.0394230i	$-0.987448\pi$
$193$	−0.716604	−	4.98409i	−0.0515823	−	0.358763i	0.947640	−	0.319340i	$-0.103461\pi$
$194$	9.52659	−	20.8603i	0.683969	−	1.49768i
$195$	−0.472328	+	0.138688i	−0.0338241	+	0.00993166i
$196$	−5.51287	+	1.61873i	−0.393777	+	0.115623i
$197$	−0.578719	+	1.26722i	−0.0412320	+	0.0902855i	−0.929127	−	0.369760i	$-0.879440\pi$
$197$	−0.578719	+	1.26722i	−0.0412320	+	0.0902855i	0.887895	+	0.460046i	$0.152167\pi$
$198$	−0.0470963	−	0.327562i	−0.00334699	−	0.0232788i
$199$	15.1809	+	17.5197i	1.07615	+	1.24194i	0.968834	+	0.247712i	$0.0796788\pi$
$199$	15.1809	+	17.5197i	1.07615	+	1.24194i	0.107312	+	0.994225i	$0.465776\pi$
$200$	−39.4667	−	86.4200i	−2.79072	−	6.11081i
$201$	−10.3217	+	6.63335i	−0.728036	+	0.467880i
$202$	0.226200	−	1.57326i	0.0159154	−	0.110694i
$203$	3.34428	+	2.14924i	0.234722	+	0.150847i
$204$	26.2968	−	30.3481i	1.84114	−	2.12479i
$205$	12.4894	+	3.66723i	0.872299	+	0.256130i
$206$	12.4147			0.864977
$207$	1.62433	+	4.51238i	0.112898	+	0.313632i
$208$	−2.29580			−0.159185
$209$	0.178567	+	0.0524319i	0.0123517	+	0.00362679i
$210$	6.84697	−	7.90182i	0.472486	−	0.545277i
$211$	−1.89596	−	1.21846i	−0.130523	−	0.0838823i	0.473750	−	0.880659i	$-0.342900\pi$
$211$	−1.89596	−	1.21846i	−0.130523	−	0.0838823i	−0.604273	+	0.796777i	$0.706536\pi$
$212$	1.46444	−	10.1854i	0.100578	−	0.699535i
$213$	−1.27316	+	0.818211i	−0.0872355	+	0.0560629i
$214$	−20.8190	−	45.5873i	−1.42316	−	3.11628i
$215$	−24.8279	−	28.6530i	−1.69325	−	1.95412i
$216$	1.48354	+	10.3183i	0.100942	+	0.702070i
$217$	−2.20277	+	4.82338i	−0.149533	+	0.327433i
$218$	−13.4660	+	3.95397i	−0.912032	+	0.267797i
$219$	9.46418	−	2.77893i	0.639530	−	0.187783i
$220$	1.06623	−	2.33471i	0.0718849	−	0.157406i
$221$	−0.130331	−	0.906473i	−0.00876702	−	0.0609760i
$222$	9.77578	+	11.2818i	0.656107	+	0.757188i
$223$	8.48159	+	18.5721i	0.567969	+	1.24368i	0.947872	+	0.318652i	$0.103230\pi$
$223$	8.48159	+	18.5721i	0.567969	+	1.24368i	−0.379903	+	0.925026i	$0.624043\pi$
$224$	23.4822	−	15.0911i	1.56897	−	1.00831i
$225$	−1.29702	+	9.02100i	−0.0864683	+	0.601400i
$226$	−14.3204	−	9.20314i	−0.952576	−	0.612184i
$227$	−10.9985	+	12.6929i	−0.729996	+	0.842460i	−0.992471	−	0.122479i	$-0.960916\pi$
$227$	−10.9985	+	12.6929i	−0.729996	+	0.842460i	0.262475	+	0.964939i	$0.415461\pi$
$228$	−8.62834	−	2.53351i	−0.571426	−	0.167786i
$229$	−7.56933			−0.500196			−0.250098	−	0.968221i	$-0.580463\pi$
$229$	−7.56933			−0.500196			−0.250098	+	0.968221i	$0.580463\pi$
$230$	−11.2200	+	48.8719i	−0.739824	+	3.22252i
$231$	0.118907			0.00782354
$232$	−39.7620	−	11.6752i	−2.61050	−	0.766512i
$233$	13.2167	−	15.2528i	0.865853	−	0.999247i	−0.134113	−	0.990966i	$-0.542819\pi$
$233$	13.2167	−	15.2528i	0.865853	−	0.999247i	0.999966	−	0.00828128i	$-0.00263604\pi$
$234$	0.306786	+	0.197159i	0.0200552	+	0.0128887i
$235$	4.84341	−	33.6866i	0.315949	−	2.19747i
$236$	−6.82852	+	4.38842i	−0.444499	+	0.285662i
$237$	0.271570	+	0.594655i	0.0176403	+	0.0386270i
$238$	12.7378	+	14.7002i	0.825668	+	0.952872i
$239$	0.383873	+	2.66989i	0.0248307	+	0.172701i	0.998463	−	0.0554217i	$-0.0176503\pi$
$239$	0.383873	+	2.66989i	0.0248307	+	0.172701i	−0.973632	+	0.228123i	$0.926741\pi$
$240$	−27.3437	+	59.8744i	−1.76503	+	3.86488i
$241$	9.06005	−	2.66027i	0.583609	−	0.171363i	0.0234169	−	0.999726i	$-0.492545\pi$
$241$	9.06005	−	2.66027i	0.583609	−	0.171363i	0.560192	+	0.828363i	$0.310727\pi$
$242$	−29.3362	+	8.61388i	−1.88580	+	0.553721i
$243$	0.415415	−	0.909632i	0.0266489	−	0.0583529i
$244$	8.40840	+	58.4817i	0.538293	+	3.74391i
$245$	2.46020	+	2.83922i	0.157176	+	0.181391i
$246$	−4.00580	−	8.77148i	−0.255400	−	0.559249i
$247$	−0.172527	+	0.110876i	−0.0109776	+	0.00705489i
$248$	7.86659	−	54.7133i	0.499529	−	3.47430i
$249$	0.244724	+	0.157274i	0.0155087	+	0.00996685i
$250$	−28.1668	+	32.5063i	−1.78143	+	2.05588i
$251$	−16.4029	−	4.81633i	−1.03534	−	0.304004i	−0.280461	−	0.959865i	$-0.590487\pi$
$251$	−16.4029	−	4.81633i	−1.03534	−	0.304004i	−0.754881	+	0.655861i	$0.772306\pi$
$252$	−5.74561			−0.361939
$253$	−0.503607	+	0.267538i	−0.0316615	+	0.0168200i
$254$	42.8092			2.68609
$255$	−25.1930	−	7.39734i	−1.57765	−	0.463240i
$256$	−58.7039	+	67.7479i	−3.66899	+	4.23424i
$257$	−1.92682	−	1.23829i	−0.120192	−	0.0772425i	0.479164	−	0.877726i	$-0.340940\pi$
$257$	−1.92682	−	1.23829i	−0.120192	−	0.0772425i	−0.599355	+	0.800483i	$0.704576\pi$
$258$	−3.99713	+	27.8006i	−0.248850	+	1.73079i
$259$	−4.51234	+	2.89990i	−0.280383	+	0.180191i
$260$	1.17495	+	2.57279i	0.0728675	+	0.159558i
$261$	2.60330	+	3.00437i	0.161140	+	0.185966i
$262$	−4.88581	−	33.9816i	−0.301847	−	2.09939i
$263$	−2.84363	+	6.22668i	−0.175346	+	0.383953i	−0.976816	−	0.214081i	$-0.931324\pi$
$263$	−2.84363	+	6.22668i	−0.175346	+	0.383953i	0.801470	+	0.598035i	$0.204052\pi$
$264$	−1.18933	+	0.349218i	−0.0731980	+	0.0214929i
$265$	−6.45576	+	1.89558i	−0.396574	+	0.116445i
$266$	1.80950	−	3.96226i	0.110948	−	0.242942i
$267$	−0.776670	−	5.40186i	−0.0475314	−	0.330588i
$268$	46.1646	+	53.2768i	2.81995	+	3.25440i
$269$	7.58897	+	16.6175i	0.462708	+	1.01319i	0.986862	+	0.161565i	$0.0516542\pi$
$269$	7.58897	+	16.6175i	0.462708	+	1.01319i	−0.524154	+	0.851623i	$0.675618\pi$
$270$	8.79582	−	5.65273i	0.535296	−	0.344014i
$271$	2.76774	−	19.2501i	0.168128	−	1.16936i	−0.714620	−	0.699513i	$-0.753400\pi$
$271$	2.76774	−	19.2501i	0.168128	−	1.16936i	0.882748	−	0.469846i	$-0.155691\pi$
$272$	−103.015	−	66.2034i	−6.24617	−	4.01417i
$273$	−0.0858084	+	0.0990282i	−0.00519336	+	0.00599346i
$274$	0.672383	+	0.197429i	0.0406201	+	0.0119272i
$275$	−1.08370			−0.0653493
$276$	24.3343	−	12.9275i	1.46475	−	0.778141i
$277$	24.4480			1.46894			0.734470	−	0.678641i	$-0.237431\pi$
$277$	24.4480			1.46894			0.734470	+	0.678641i	$0.237431\pi$
$278$	5.57135	+	1.63590i	0.334148	+	0.0981146i
$279$	−3.47244	+	4.00741i	−0.207890	+	0.239918i
$280$	−32.9457	−	21.1729i	−1.96888	−	1.26532i
$281$	3.10646	−	21.6059i	0.185316	−	1.28890i	−0.658629	−	0.752468i	$-0.728863\pi$
$281$	3.10646	−	21.6059i	0.185316	−	1.28890i	0.843944	−	0.536431i	$-0.180228\pi$
$282$	−21.2097	+	13.6306i	−1.26302	+	0.811692i
$283$	−0.0453000	−	0.0991932i	−0.00269281	−	0.00589642i	0.908281	−	0.418361i	$-0.137395\pi$
$283$	−0.0453000	−	0.0991932i	−0.00269281	−	0.00589642i	−0.910974	+	0.412465i	$0.864668\pi$
$284$	5.69431	+	6.57159i	0.337895	+	0.389952i
$285$	0.836798	+	5.82006i	0.0495677	+	0.344751i
$286$	−0.0180136	+	0.0394442i	−0.00106517	+	0.00233239i
$287$	3.32446	−	0.976149i	0.196237	−	0.0576203i
$288$	26.7826	−	7.86408i	1.57818	−	0.463395i
$289$	13.2296	−	28.9687i	0.778210	−	1.70404i
$290$	5.91528	+	41.1417i	0.347357	+	2.41592i
$291$	5.39605	+	6.22738i	0.316322	+	0.365055i
$292$	−23.5429	−	51.5517i	−1.37774	−	3.01683i
$293$	2.12482	−	1.36554i	0.124134	−	0.0797758i	−0.477101	−	0.878849i	$-0.658312\pi$
$293$	2.12482	−	1.36554i	0.124134	−	0.0797758i	0.601234	+	0.799073i	$0.294676\pi$
$294$	0.396076	−	2.75477i	0.0230996	−	0.160661i
$295$	4.46490	+	2.86942i	0.259957	+	0.167064i
$296$	36.6162	−	42.2574i	2.12828	−	2.45616i
$297$	0.114091	+	0.0335001i	0.00662023	+	0.00194387i
$298$	−5.72830			−0.331832
$299$	0.140612	−	0.612479i	0.00813183	−	0.0354206i
$300$	52.3642			3.02325
$301$	−9.68304	−	2.84320i	−0.558121	−	0.163879i
$302$	18.0245	−	20.8014i	1.03719	−	1.19699i
$303$	0.480444	+	0.308762i	0.0276008	+	0.0177379i
$304$	−3.90260	+	27.1431i	−0.223829	+	1.55677i
$305$	32.4994	−	20.8861i	1.86091	−	1.19593i
$306$	8.08030	+	17.6934i	0.461920	+	1.01146i
$307$	−3.87480	−	4.47176i	−0.221146	−	0.255217i	0.634325	−	0.773066i	$-0.281278\pi$
$307$	−3.87480	−	4.47176i	−0.221146	−	0.255217i	−0.855472	+	0.517850i	$0.826733\pi$
$308$	−0.0972289	−	0.676242i	−0.00554013	−	0.0385325i
$309$	−1.85307	+	4.05766i	−0.105418	+	0.230832i
$310$	−53.1958	+	15.6197i	−3.02132	+	0.887139i
$311$	27.5675	−	8.09455i	1.56321	−	0.459000i	0.618195	−	0.786025i	$-0.287864\pi$
$311$	27.5675	−	8.09455i	1.56321	−	0.459000i	0.945016	+	0.327025i	$0.106046\pi$
$312$	0.567431	−	1.24250i	0.0321245	−	0.0703428i
$313$	0.584960	+	4.06849i	0.0330639	+	0.229964i	0.999652	−	0.0263692i	$-0.00839454\pi$
$313$	0.584960	+	4.06849i	0.0330639	+	0.229964i	−0.966588	+	0.256334i	$0.917485\pi$
$314$	−18.2557	−	21.0682i	−1.03023	−	1.18895i
$315$	1.56064	+	3.41733i	0.0879323	+	0.192545i
$316$	3.15982	−	2.03069i	0.177754	−	0.114235i
$317$	−3.26480	+	22.7072i	−0.183370	+	1.27536i	0.665355	+	0.746527i	$0.268280\pi$
$317$	−3.26480	+	22.7072i	−0.183370	+	1.27536i	−0.848724	+	0.528836i	$0.822629\pi$
$318$	4.19314	+	2.69477i	0.235139	+	0.151115i
$319$	−0.309552	+	0.357242i	−0.0173316	+	0.0200017i
$320$	153.716	+	45.1350i	8.59296	+	2.52312i
$321$	18.0074			1.00507
$322$	4.52065	+	12.5584i	0.251926	+	0.699851i
$323$	−10.9387			−0.608647
$324$	−5.51287	−	1.61873i	−0.306271	−	0.0899292i
$325$	0.782038	−	0.902520i	0.0433797	−	0.0500628i
$326$	43.5839	+	28.0097i	2.41389	+	1.55131i
$327$	0.717661	−	4.99144i	0.0396867	−	0.276027i
$328$	−30.3848	+	19.5271i	−1.67772	+	1.07821i
$329$	−3.76324	−	8.24034i	−0.207474	−	0.454304i
$330$	0.814156	+	0.939586i	0.0448178	+	0.0517225i
$331$	−2.80606	−	19.5166i	−0.154235	−	1.07273i	−0.909019	−	0.416756i	$-0.863167\pi$
$331$	−2.80606	−	19.5166i	−0.154235	−	1.07273i	0.754783	−	0.655974i	$-0.227742\pi$
$332$	0.694332	−	1.52038i	0.0381064	−	0.0834414i
$333$	−5.14655	+	1.51116i	−0.282029	+	0.0828113i
$334$	−25.6195	+	7.52255i	−1.40183	+	0.411616i
$335$	19.1482	−	41.9287i	1.04618	−	2.29081i
$336$	2.49347	+	17.3425i	0.136030	+	0.946109i
$337$	−21.1596	−	24.4195i	−1.15264	−	1.33021i	−0.935191	−	0.354143i	$-0.884773\pi$
$337$	−21.1596	−	24.4195i	−1.15264	−	1.33021i	−0.217446	−	0.976072i	$-0.569773\pi$
$338$	15.0100	+	32.8672i	0.816434	+	1.78774i
$339$	5.14548	−	3.30680i	0.279464	−	0.179601i
$340$	−21.4697	+	149.325i	−1.16436	+	8.09827i
$341$	−0.530423	−	0.340882i	−0.0287240	−	0.0184598i
$342$	2.85250	−	3.29196i	0.154246	−	0.178009i
$343$	0.959493	+	0.281733i	0.0518078	+	0.0152121i
$344$	105.201			5.67206
$345$	−14.2987	−	10.9620i	−0.769814	−	0.590173i
$346$	65.9153			3.54363
$347$	2.11898	+	0.622189i	0.113753	+	0.0334009i	0.338114	−	0.941105i	$-0.390211\pi$
$347$	2.11898	+	0.622189i	0.113753	+	0.0334009i	−0.224361	+	0.974506i	$0.572029\pi$
$348$	14.9576	−	17.2619i	0.801809	−	0.925337i
$349$	8.12560	+	5.22201i	0.434953	+	0.279528i	0.739740	−	0.672893i	$-0.234949\pi$
$349$	8.12560	+	5.22201i	0.434953	+	0.279528i	−0.304786	+	0.952421i	$0.598585\pi$
$350$	−3.60974	+	25.1063i	−0.192949	+	1.34199i
$351$	−0.110232	+	0.0708418i	−0.00588375	+	0.00378126i
$352$	1.37880	+	3.01916i	0.0734905	+	0.160922i
$353$	2.20157	+	2.54075i	0.117178	+	0.135230i	0.811308	−	0.584619i	$-0.198756\pi$
$353$	2.20157	+	2.54075i	0.117178	+	0.135230i	−0.694130	+	0.719850i	$0.744211\pi$
$354$	−0.559553	−	3.89178i	−0.0297399	−	0.206846i
$355$	2.36189	−	5.17182i	0.125356	−	0.274492i
$356$	−30.0860	+	8.83404i	−1.59455	+	0.468203i
$357$	−6.70593	+	1.96904i	−0.354916	+	0.104213i
$358$	−16.4317	+	35.9803i	−0.868440	+	1.90162i
$359$	1.05241	+	7.31971i	0.0555443	+	0.386319i	0.998564	+	0.0535809i	$0.0170635\pi$
$359$	1.05241	+	7.31971i	0.0555443	+	0.386319i	−0.943019	+	0.332738i	$0.892027\pi$
$360$	−25.6461	−	29.5971i	−1.35167	−	1.55991i
$361$	−6.87528	−	15.0548i	−0.361857	−	0.792356i
$362$	−50.5767	+	32.5037i	−2.65825	+	1.70835i
$363$	1.56345	−	10.8740i	0.0820599	−	0.570739i
$364$	0.633350	+	0.407029i	0.0331966	+	0.0213341i
$365$	−24.2667	+	28.0053i	−1.27018	+	1.46587i
$366$	−27.4597	−	8.06291i	−1.43534	−	0.421455i
$367$	−5.15138			−0.268900			−0.134450	−	0.990920i	$-0.542927\pi$
$367$	−5.15138			−0.268900			−0.134450	+	0.990920i	$0.542927\pi$
$368$	−49.5806	−	67.8401i	−2.58457	−	3.53641i
$369$	3.46481			0.180371
$370$	−53.8103	−	15.8001i	−2.79747	−	0.821410i
$371$	−1.17283	+	1.35351i	−0.0608900	+	0.0702709i
$372$	25.6300	+	16.4714i	1.32886	+	0.854003i
$373$	−0.567314	+	3.94575i	−0.0293744	+	0.204303i	−0.999223	−	0.0394032i	$-0.987454\pi$
$373$	−0.567314	+	3.94575i	−0.0293744	+	0.204303i	0.969849	+	0.243707i	$0.0783634\pi$
$374$	−1.94572	+	1.25044i	−0.100611	+	0.0646588i
$375$	−6.42013	−	14.0581i	−0.331534	−	0.725958i
$376$	61.8413	+	71.3686i	3.18922	+	3.68056i
$377$	−0.0741322	−	0.515601i	−0.00381800	−	0.0265548i
$378$	1.15614	−	2.53159i	0.0594654	−	0.130211i
$379$	−15.0080	+	4.40676i	−0.770911	+	0.226360i	−0.643455	−	0.765484i	$-0.722499\pi$
$379$	−15.0080	+	4.40676i	−0.770911	+	0.226360i	−0.127456	+	0.991844i	$0.540681\pi$
$380$	32.4152	−	9.51796i	1.66286	−	0.488261i
$381$	−6.38987	+	13.9919i	−0.327363	+	0.716825i
$382$	1.76676	+	12.2881i	0.0903951	+	0.628712i
$383$	−11.0160	−	12.7132i	−0.562893	−	0.649613i	0.400945	−	0.916102i	$-0.368682\pi$
$383$	−11.0160	−	12.7132i	−0.562893	−	0.649613i	−0.963838	+	0.266489i	$0.914136\pi$
$384$	−26.1108	−	57.1747i	−1.33246	−	2.91768i
$385$	−0.375801	+	0.241512i	−0.0191526	+	0.0123086i
$386$	1.99438	−	13.8712i	0.101511	−	0.706025i
$387$	−8.48979	−	5.45606i	−0.431560	−	0.277347i
$388$	31.0036	−	35.7801i	1.57397	−	1.81646i
$389$	11.6026	+	3.40683i	0.588275	+	0.172733i	0.562306	−	0.826930i	$-0.309914\pi$
$389$	11.6026	+	3.40683i	0.588275	+	0.172733i	0.0259697	+	0.999663i	$0.491733\pi$
$390$	−1.37003			−0.0693742
$391$	23.9712	−	23.4276i	1.21228	−	1.18478i
$392$	−10.4244			−0.526511
$393$	11.8359	+	3.47533i	0.597041	+	0.175307i
$394$	−2.53900	+	2.93016i	−0.127913	+	0.147619i
$395$	−2.06608	−	1.32779i	−0.103956	−	0.0668084i
$396$	0.0972289	−	0.676242i	0.00488594	−	0.0339824i
$397$	−3.24947	+	2.08831i	−0.163086	+	0.104809i	−0.619638	−	0.784888i	$-0.712721\pi$
$397$	−3.24947	+	2.08831i	−0.163086	+	0.104809i	0.456552	+	0.889697i	$0.349084\pi$
$398$	26.8015	+	58.6870i	1.34344	+	2.94171i
$399$	1.02494	+	1.18284i	0.0513111	+	0.0592162i
$400$	−22.7249	−	158.055i	−1.13625	−	7.90277i
$401$	5.11190	−	11.1935i	0.255276	−	0.558977i	−0.737993	−	0.674809i	$-0.764226\pi$
$401$	5.11190	−	11.1935i	0.255276	−	0.558977i	0.993269	+	0.115832i	$0.0369534\pi$
$402$	−32.7637	+	9.62030i	−1.63411	+	0.479817i
$403$	0.666667	−	0.195751i	0.0332090	−	0.00975105i
$404$	1.36312	−	2.98481i	0.0678177	−	0.148500i
$405$	0.534653	+	3.71859i	0.0265671	+	0.184778i
$406$	7.24524	+	8.36145i	0.359575	+	0.414972i
$407$	−0.264951	−	0.580162i	−0.0131331	−	0.0287576i
$408$	61.2907	−	39.3891i	3.03434	−	1.95005i
$409$	−5.06330	+	35.2160i	−0.250364	+	1.74132i	0.345666	+	0.938358i	$0.387653\pi$
$409$	−5.06330	+	35.2160i	−0.250364	+	1.74132i	−0.596030	+	0.802962i	$0.703256\pi$
$410$	30.4758	+	19.5856i	1.50509	+	0.967265i
$411$	−0.164891	+	0.190294i	−0.00813346	+	0.00938651i
$412$	24.5917	+	7.22077i	1.21154	+	0.355742i
$413$	1.41274			0.0695166
$414$	0.799429	+	13.3233i	0.0392898	+	0.654804i
$415$	−1.09287			−0.0536471
$416$	−3.50941	−	1.03045i	−0.172063	−	0.0505222i
$417$	−1.36628	+	1.57677i	−0.0669071	+	0.0772149i
$418$	0.435726	+	0.280024i	0.0213120	+	0.0136964i
$419$	−1.08076	+	7.51682i	−0.0527984	+	0.367221i	0.946243	+	0.323455i	$0.104845\pi$
$419$	−1.08076	+	7.51682i	−0.0527984	+	0.367221i	−0.999042	+	0.0437656i	$0.986065\pi$
$420$	18.1587	−	11.6699i	0.886053	−	0.569432i
$421$	7.78299	+	17.0424i	0.379320	+	0.830594i	0.998955	+	0.0457046i	$0.0145533\pi$
$421$	7.78299	+	17.0424i	0.379320	+	0.830594i	−0.619635	+	0.784890i	$0.712719\pi$
$422$	−4.10752	−	4.74033i	−0.199951	−	0.230756i
$423$	−1.28923	−	8.96677i	−0.0626844	−	0.435979i
$424$	7.75563	−	16.9825i	0.376646	−	0.824741i
$425$	61.1163	−	17.9454i	2.96458	−	0.870478i
$426$	−4.04135	+	1.18665i	−0.195804	+	0.0574932i
$427$	4.27178	−	9.35390i	0.206726	−	0.452667i
$428$	−14.7244	−	102.410i	−0.711729	−	4.95018i
$429$	−0.0102033	−	0.0117752i	−0.000492618	−	0.000568512i
$430$	−43.8330	−	95.9810i	−2.11382	−	4.62861i
$431$	−18.6664	+	11.9961i	−0.899127	+	0.577834i	−0.906531	−	0.422139i	$-0.861279\pi$
$431$	−18.6664	+	11.9961i	−0.899127	+	0.577834i	0.00740456	+	0.999973i	$0.497643\pi$
$432$	−2.49347	+	17.3425i	−0.119967	+	0.834390i
$433$	−2.28861	−	1.47080i	−0.109983	−	0.0706820i	0.484493	−	0.874795i	$-0.339004\pi$
$433$	−2.28861	−	1.47080i	−0.109983	−	0.0706820i	−0.594476	+	0.804113i	$0.702641\pi$
$434$	−9.66413	+	11.1530i	−0.463893	+	0.535361i
$435$	−14.3298	−	4.20760i	−0.687060	−	0.201739i
$436$	−28.9738			−1.38759
$437$	−7.00227	−	2.70359i	−0.334964	−	0.129330i
$438$	27.4517			1.31169
$439$	−12.1493	−	3.56734i	−0.579852	−	0.170260i	−0.0213632	−	0.999772i	$-0.506801\pi$
$439$	−12.1493	−	3.56734i	−0.579852	−	0.170260i	−0.558489	+	0.829512i	$0.688619\pi$
$440$	3.04951	−	3.51932i	0.145380	−	0.167777i
$441$	0.841254	+	0.540641i	0.0400597	+	0.0257448i
$442$	0.362724	−	2.52280i	0.0172530	−	0.119997i
$443$	−25.6268	+	16.4693i	−1.21756	+	0.782481i	−0.981909	−	0.189356i	$-0.939360\pi$
$443$	−25.6268	+	16.4693i	−1.21756	+	0.782481i	−0.235655	+	0.971837i	$0.575724\pi$
$444$	12.8024	+	28.0334i	0.607577	+	1.33041i
$445$	13.4263	+	15.4948i	0.636468	+	0.734524i
$446$	8.08673	+	56.2444i	0.382918	+	2.66325i
$447$	0.855028	−	1.87225i	0.0404414	−	0.0885544i
$448$	40.9163	−	12.0141i	1.93311	−	0.567613i
$449$	−36.7463	+	10.7897i	−1.73416	+	0.509197i	−0.987718	−	0.156249i	$-0.950060\pi$
$449$	−36.7463	+	10.7897i	−1.73416	+	0.509197i	−0.746447	+	0.665445i	$0.768242\pi$
$450$	−10.5368	+	23.0723i	−0.496709	+	1.08764i
$451$	0.0586325	+	0.407798i	0.00276090	+	0.0192025i
$452$	−23.0136	−	26.5591i	−1.08247	−	1.24923i
$453$	4.10836	+	8.99606i	0.193028	+	0.422672i
$454$	−39.3223	+	25.2709i	−1.84549	+	1.18602i
$455$	0.0700572	−	0.487258i	0.00328433	−	0.0228430i
$456$	−13.7254	−	8.82081i	−0.642753	−	0.413072i
$457$	−1.38071	+	1.59342i	−0.0645869	+	0.0745372i	−0.787124	−	0.616795i	$-0.788431\pi$
$457$	−1.38071	+	1.59342i	−0.0645869	+	0.0745372i	0.722537	+	0.691333i	$0.242976\pi$
$458$	−20.2128	−	5.93502i	−0.944484	−	0.277325i
$459$	−6.98904			−0.326220
$460$	−50.6503	+	90.2818i	−2.36158	+	4.20941i
$461$	−20.8045			−0.968963			−0.484481	−	0.874802i	$-0.660992\pi$
$461$	−20.8045			−0.968963			−0.484481	+	0.874802i	$0.660992\pi$
$462$	0.317526	+	0.0932339i	0.0147726	+	0.00433764i
$463$	−11.5329	+	13.3097i	−0.535979	+	0.618552i	−0.957559	−	0.288239i	$-0.906930\pi$
$463$	−11.5329	+	13.3097i	−0.535979	+	0.618552i	0.421580	+	0.906791i	$0.361476\pi$
$464$	−58.5945	−	37.6564i	−2.72018	−	1.74815i
$465$	2.83503	−	19.7181i	0.131471	−	0.914404i
$466$	47.2528	−	30.3675i	2.18894	−	1.40675i
$467$	−2.50712	−	5.48983i	−0.116016	−	0.254039i	0.842712	−	0.538365i	$-0.180958\pi$
$467$	−2.50712	−	5.48983i	−0.116016	−	0.254039i	−0.958728	+	0.284325i	$0.908230\pi$
$468$	0.493021	+	0.568977i	0.0227899	+	0.0263010i
$469$	−1.74612	−	12.1445i	−0.0806283	−	0.560782i
$470$	39.3469	−	86.1577i	1.81494	−	3.97416i
$471$	9.61090	−	2.82201i	0.442847	−	0.130032i
$472$	−14.1304	+	4.14907i	−0.650406	+	0.190976i
$473$	0.498496	−	1.09155i	0.0229209	−	0.0501897i
$474$	0.258927	+	1.80088i	0.0118929	+	0.0827170i
$475$	−9.34106	−	10.7802i	−0.428597	−	0.494628i
$476$	16.6815	+	36.5274i	0.764596	+	1.67423i
$477$	−1.50665	+	0.968263i	−0.0689846	+	0.0443337i
$478$	−1.06835	+	7.43057i	−0.0488654	+	0.339866i
$479$	3.39233	+	2.18012i	0.154999	+	0.0996121i	0.615841	−	0.787870i	$-0.288816\pi$
$479$	3.39233	+	2.18012i	0.154999	+	0.0996121i	−0.460842	+	0.887482i	$0.652453\pi$
$480$	−68.6723	+	79.2520i	−3.13445	+	3.61734i
$481$	0.674368	+	0.198012i	0.0307486	+	0.00902859i
$482$	26.2795			1.19700
$483$	−4.77937	−	0.396972i	−0.217469	−	0.0180628i
$484$	−63.1205			−2.86911
$485$	−29.7023	−	8.72139i	−1.34871	−	0.396018i
$486$	1.82254	−	2.10332i	0.0826720	−	0.0954086i
$487$	−0.323082	−	0.207632i	−0.0146403	−	0.00940872i	0.533300	−	0.845926i	$-0.320952\pi$
$487$	−0.323082	−	0.207632i	−0.0146403	−	0.00940872i	−0.547940	+	0.836517i	$0.684588\pi$
$488$	−15.2555	+	106.105i	−0.690586	+	4.80313i
$489$	−15.6602	+	10.0642i	−0.708180	+	0.455120i
$490$	4.34342	+	9.51076i	0.196216	+	0.429652i
$491$	−26.4220	−	30.4926i	−1.19241	−	1.37611i	−0.908833	−	0.417159i	$-0.863026\pi$
$491$	−26.4220	−	30.4926i	−1.19241	−	1.37611i	−0.283573	−	0.958951i	$-0.591520\pi$
$492$	−2.83312	−	19.7048i	−0.127727	−	0.888361i
$493$	11.5418	−	25.2731i	0.519819	−	1.13824i
$494$	−0.547646	+	0.160803i	−0.0246397	+	0.00723488i
$495$	−0.428620	+	0.125854i	−0.0192650	+	0.00565673i
$496$	38.5942	−	84.5096i	1.73293	−	3.79459i
$497$	−0.215381	−	1.49800i	−0.00966114	−	0.0671947i
$498$	0.530183	+	0.611864i	0.0237581	+	0.0274183i
$499$	14.7316	+	32.2578i	0.659479	+	1.44406i	0.883007	+	0.469360i	$0.155515\pi$
$499$	14.7316	+	32.2578i	0.659479	+	1.44406i	−0.223528	+	0.974697i	$0.571758\pi$
$500$	−74.7007	+	48.0072i	−3.34072	+	2.14695i
$501$	1.36537	−	9.49636i	0.0610002	−	0.424266i
$502$	−40.0252	−	25.7226i	−1.78641	−	1.14806i
$503$	17.1186	−	19.7559i	0.763280	−	0.880872i	−0.232505	−	0.972595i	$-0.574692\pi$
$503$	17.1186	−	19.7559i	0.763280	−	0.880872i	0.995785	+	0.0917236i	$0.0292376\pi$
$504$	−10.0021	−	2.93689i	−0.445530	−	0.130819i
$505$	−2.14554			−0.0954754
$506$	−1.55458	+	0.319551i	−0.0691097	+	0.0142058i
$507$	−12.9828			−0.576588
$508$	84.7984	+	24.8991i	3.76232	+	1.10472i
$509$	10.4878	−	12.1036i	0.464865	−	0.536483i	−0.474111	−	0.880465i	$-0.657231\pi$
$509$	10.4878	−	12.1036i	0.464865	−	0.536483i	0.938976	+	0.343982i	$0.111776\pi$
$510$	−61.4743	−	39.5071i	−2.72213	−	1.74940i
$511$	−1.40375	+	9.76333i	−0.0620985	+	0.431904i
$512$	−104.127	+	66.9185i	−4.60181	+	2.95741i
$513$	0.650177	+	1.42369i	0.0287060	+	0.0628574i
$514$	−4.17437	−	4.81748i	−0.184124	−	0.212490i
$515$	−2.38496	−	16.5878i	−0.105094	−	0.730945i
$516$	−24.0873	+	52.7439i	−1.06038	+	2.32192i
$517$	1.03355	−	0.303477i	0.0454553	−	0.0133469i
$518$	−14.3233	+	4.20571i	−0.629331	+	0.184788i
$519$	−9.83877	+	21.5439i	−0.431874	+	0.945672i
$520$	0.730303	+	5.07937i	0.0320259	+	0.222745i
$521$	−3.36710	−	3.88584i	−0.147515	−	0.170242i	0.677183	−	0.735815i	$-0.263201\pi$
$521$	−3.36710	−	3.88584i	−0.147515	−	0.170242i	−0.824698	+	0.565573i	$0.808655\pi$
$522$	4.59606	+	10.0640i	0.201164	+	0.440488i
$523$	21.5062	−	13.8212i	0.940400	−	0.604358i	0.0218917	−	0.999760i	$-0.493031\pi$
$523$	21.5062	−	13.8212i	0.940400	−	0.604358i	0.918508	+	0.395402i	$0.129395\pi$
$524$	10.0866	−	70.1539i	0.440636	−	3.06469i
$525$	−7.66699	−	4.92728i	−0.334615	−	0.215044i
$526$	−12.4758	+	14.3978i	−0.543970	+	0.627774i
$527$	35.5586	+	10.4410i	1.54896	+	0.454815i
$528$	−2.08336			−0.0906664
$529$	21.1352	−	9.07216i	0.918921	−	0.394442i
$530$	−18.7255			−0.813384
$531$	1.35552	+	0.398016i	0.0588245	+	0.0172724i
$532$	5.88890	−	6.79615i	0.255316	−	0.294651i
$533$	−0.381933	−	0.245453i	−0.0165433	−	0.0106318i
$534$	2.16155	−	15.0339i	0.0935392	−	0.650580i
$535$	−56.9113	+	36.5747i	−2.46049	+	1.58126i
$536$	53.1320	+	116.343i	2.29495	+	5.02525i
$537$	−9.30723	−	10.7411i	−0.401637	−	0.463513i
$538$	7.23567	+	50.3252i	0.311952	+	2.16967i
$539$	−0.0493960	+	0.108162i	−0.00212763	+	0.00465887i
$540$	20.7109	−	6.08128i	0.891256	−	0.261696i
$541$	−23.4749	+	6.89285i	−1.00927	+	0.296347i	−0.744253	−	0.667898i	$-0.767194\pi$
$541$	−23.4749	+	6.89285i	−1.00927	+	0.296347i	−0.265012	+	0.964245i	$0.585376\pi$
$542$	22.4846	−	49.2345i	0.965798	−	2.11480i
$543$	−3.07430	−	21.3822i	−0.131931	−	0.917598i
$544$	−127.755	−	147.437i	−5.47744	−	6.32131i
$545$	7.86996	+	17.2328i	0.337112	+	0.738173i
$546$	−0.306786	+	0.197159i	−0.0131292	+	0.00843764i
$547$	2.02915	−	14.1130i	0.0867601	−	0.603430i	−0.899337	−	0.437257i	$-0.855950\pi$
$547$	2.02915	−	14.1130i	0.0867601	−	0.603430i	0.986097	−	0.166173i	$-0.0531409\pi$
$548$	1.21705	+	0.782154i	0.0519900	+	0.0334119i
$549$	6.73404	−	7.77150i	0.287402	−	0.331680i
$550$	−2.89386	−	0.849713i	−0.123394	−	0.0362319i
$551$	−6.22193			−0.265063
$552$	48.9697	−	10.0659i	2.08429	−	0.428434i
$553$	−0.653731			−0.0277995
$554$	65.2851	+	19.1694i	2.77370	+	0.814431i
$555$	13.1961	−	15.2291i	0.560143	−	0.646439i
$556$	10.0845	+	6.48091i	0.427678	+	0.274852i
$557$	1.83236	−	12.7443i	0.0776395	−	0.539995i	−0.913466	−	0.406915i	$-0.866604\pi$
$557$	1.83236	−	12.7443i	0.0776395	−	0.539995i	0.991105	−	0.133079i	$-0.0424865\pi$
$558$	−12.4148	+	7.97853i	−0.525562	+	0.337758i
$559$	0.549330	+	1.20286i	0.0232342	+	0.0508757i
$560$	−43.1047	−	49.7455i	−1.82151	−	2.10213i
$561$	−0.118271	−	0.822590i	−0.00499339	−	0.0347298i
$562$	25.2363	−	55.2597i	1.06453	−	2.33099i
$563$	20.6994	−	6.07789i	0.872375	−	0.256152i	0.185250	−	0.982691i	$-0.440691\pi$
$563$	20.6994	−	6.07789i	0.872375	−	0.256152i	0.687125	+	0.726539i	$0.258872\pi$
$564$	−49.9410	+	14.6640i	−2.10289	+	0.617466i
$565$	−9.54560	+	20.9019i	−0.401586	+	0.879351i
$566$	−0.0431911	−	0.300401i	−0.00181546	−	0.0126268i
$567$	0.654861	+	0.755750i	0.0275016	+	0.0317385i
$568$	6.55373	+	14.3507i	0.274989	+	0.602141i
$569$	5.43719	−	3.49427i	0.227939	−	0.146487i	−0.421687	−	0.906741i	$-0.638562\pi$
$569$	5.43719	−	3.49427i	0.227939	−	0.146487i	0.649626	+	0.760254i	$0.274926\pi$
$570$	−2.32889	+	16.1978i	−0.0975464	+	0.678450i
$571$	−21.2829	−	13.6777i	−0.890663	−	0.572394i	0.0133445	−	0.999911i	$-0.495752\pi$
$571$	−21.2829	−	13.6777i	−0.890663	−	0.572394i	−0.904007	+	0.427517i	$0.859389\pi$
$572$	−0.0586239	+	0.0676556i	−0.00245119	+	0.00282882i
$573$	−4.27997	−	1.25671i	−0.178798	−	0.0524999i
$574$	9.64289			0.402486
$575$	43.5581	+	3.61791i	1.81650	+	0.150877i
$576$	42.6437			1.77682
$577$	−16.5313	−	4.85403i	−0.688207	−	0.202076i	−0.0811118	−	0.996705i	$-0.525847\pi$
$577$	−16.5313	−	4.85403i	−0.688207	−	0.202076i	−0.607095	+	0.794629i	$0.707665\pi$
$578$	58.0417	−	66.9837i	2.41422	−	2.78615i
$579$	4.23600	+	2.72231i	0.176042	+	0.113135i
$580$	−12.2119	+	84.9357i	−0.507072	+	3.52676i
$581$	−0.244724	+	0.157274i	−0.0101528	+	0.00652484i
$582$	9.52659	+	20.8603i	0.394890	+	0.864688i
$583$	−0.139458	−	0.160943i	−0.00577575	−	0.00666557i
$584$	−14.6333	−	101.777i	−0.605529	−	4.21155i
$585$	0.204496	−	0.447783i	0.00845486	−	0.0185136i
$586$	6.74475	−	1.98044i	0.278623	−	0.0818111i
$587$	−13.6696	+	4.01377i	−0.564206	+	0.165666i	−0.551383	−	0.834252i	$-0.685900\pi$
$587$	−13.6696	+	4.01377i	−0.564206	+	0.165666i	−0.0128226	+	0.999918i	$0.504082\pi$
$588$	2.38681	−	5.22639i	0.0984305	−	0.215533i
$589$	−1.18110	−	8.21471i	−0.0486662	−	0.338481i
$590$	9.67301	+	11.1633i	0.398232	+	0.459584i
$591$	−0.578719	−	1.26722i	−0.0238053	−	0.0521264i
$592$	79.0598	−	50.8086i	3.24934	−	2.08822i
$593$	1.00034	−	6.95751i	0.0410790	−	0.285711i	−0.958919	−	0.283680i	$-0.908445\pi$
$593$	1.00034	−	6.95751i	0.0410790	−	0.285711i	0.999998	−	0.00203049i	$-0.000646326\pi$
$594$	0.278397	+	0.178915i	0.0114228	+	0.00734096i
$595$	17.1944	−	19.8434i	0.704903	−	0.813501i
$596$	−11.3469	−	3.33174i	−0.464786	−	0.136473i
$597$	−23.1819			−0.948771
$598$	0.855723	−	1.52529i	0.0349931	−	0.0623736i
$599$	−13.1128			−0.535775			−0.267888	−	0.963450i	$-0.586326\pi$
$599$	−13.1128			−0.535775			−0.267888	+	0.963450i	$0.586326\pi$
$600$	91.1570	+	26.7661i	3.72147	+	1.09272i
$601$	6.39692	−	7.38244i	0.260936	−	0.301136i	−0.610131	−	0.792301i	$-0.708883\pi$
$601$	6.39692	−	7.38244i	0.260936	−	0.301136i	0.871067	+	0.491165i	$0.163429\pi$
$602$	−23.6279	−	15.1847i	−0.963000	−	0.618883i
$603$	1.74612	−	12.1445i	0.0711075	−	0.494563i
$604$	47.8024	−	30.7207i	1.94505	−	1.25001i
$605$	17.1450	+	37.5423i	0.697044	+	1.52631i
$606$	1.04086	+	1.20122i	0.0422820	+	0.0487961i
$607$	1.11043	+	7.72322i	0.0450710	+	0.313476i	0.999868	+	0.0162186i	$0.00516278\pi$
$607$	1.11043	+	7.72322i	0.0450710	+	0.313476i	−0.954797	+	0.297257i	$0.903928\pi$
$608$	−18.1486	+	39.7398i	−0.736022	+	1.61166i
$609$	−3.81432	+	1.11999i	−0.154564	+	0.0453841i
$610$	103.162	−	30.2910i	4.17689	−	1.22645i
$611$	−0.493108	+	1.07976i	−0.0199490	+	0.0436823i
$612$	5.71483	+	39.7475i	0.231008	+	1.60670i
$613$	−26.6886	−	30.8003i	−1.07794	−	1.24401i	−0.968233	−	0.250050i	$-0.919553\pi$
$613$	−26.6886	−	30.8003i	−1.07794	−	1.24401i	−0.109711	−	0.993963i	$-0.534993\pi$
$614$	−6.84085	−	14.9794i	−0.276074	−	0.604518i
$615$	−10.9503	+	7.03736i	−0.441560	+	0.283774i
$616$	0.176405	−	1.22692i	0.00710754	−	0.0494340i
$617$	5.25713	+	3.37855i	0.211644	+	0.136015i	0.642168	−	0.766564i	$-0.278035\pi$
$617$	5.25713	+	3.37855i	0.211644	+	0.136015i	−0.430524	+	0.902579i	$0.641671\pi$
$618$	−8.12993	+	9.38244i	−0.327034	+	0.377417i
$619$	16.7137	+	4.90758i	0.671779	+	0.197252i	0.599795	−	0.800154i	$-0.295249\pi$
$619$	16.7137	+	4.90758i	0.671779	+	0.197252i	0.0719841	+	0.997406i	$0.477067\pi$
$620$	−114.457			−4.59672
$621$	−4.47394	−	1.72740i	−0.179533	−	0.0693180i
$622$	79.9620			3.20618
$623$	5.23634	+	1.53753i	0.209790	+	0.0615998i
$624$	1.50343	−	1.73505i	0.0601855	−	0.0694577i
$625$	10.5089	+	6.75366i	0.420356	+	0.270146i
$626$	−1.62800	+	11.3230i	−0.0650679	+	0.452557i
$627$	−0.156562	+	0.100616i	−0.00625247	+	0.00401822i
$628$	−23.9078	−	52.3509i	−0.954027	−	2.08903i
$629$	24.5494	+	28.3315i	0.978849	+	1.12965i
$630$	1.48799	+	10.3492i	0.0592829	+	0.412321i
$631$	−4.64418	+	10.1693i	−0.184882	+	0.404835i	−0.979265	−	0.202582i	$-0.935067\pi$
$631$	−4.64418	+	10.1693i	−0.184882	+	0.404835i	0.794383	+	0.607417i	$0.207794\pi$
$632$	6.53870	−	1.91993i	0.260095	−	0.0763709i
$633$	2.16244	−	0.634951i	0.0859494	−	0.0252370i
$634$	−26.5226	+	58.0765i	−1.05335	+	2.30651i
$635$	−8.22397	−	57.1990i	−0.326358	−	2.26987i
$636$	6.73860	+	7.77675i	0.267203	+	0.308368i
$637$	−0.0544331	−	0.119192i	−0.00215672	−	0.00472255i
$638$	−1.10672	+	0.711249i	−0.0438157	+	0.0281586i
$639$	0.215381	−	1.49800i	0.00852032	−	0.0592602i
$640$	198.649	+	127.664i	7.85229	+	5.04636i
$641$	−24.3046	+	28.0490i	−0.959972	+	1.10787i	0.0341296	+	0.999417i	$0.489134\pi$
$641$	−24.3046	+	28.0490i	−0.959972	+	1.10787i	−0.994102	+	0.108450i	$0.965411\pi$
$642$	48.0861	+	14.1194i	1.89781	+	0.557246i
$643$	−41.6240			−1.64149			−0.820746	−	0.571294i	$-0.806442\pi$
$643$	−41.6240			−1.64149			−0.820746	+	0.571294i	$0.806442\pi$
$644$	1.65040	+	27.5055i	0.0650347	+	1.08387i
$645$	37.9133			1.49283
$646$	−29.2103	−	8.57692i	−1.14926	−	0.337454i
$647$	20.5685	−	23.7373i	0.808631	−	0.933210i	−0.190190	−	0.981747i	$-0.560910\pi$
$647$	20.5685	−	23.7373i	0.808631	−	0.933210i	0.998821	+	0.0485371i	$0.0154559\pi$
$648$	−8.76955	−	5.63585i	−0.344500	−	0.221397i
$649$	−0.0239069	+	0.166276i	−0.000938427	+	0.00652690i
$650$	2.79598	−	1.79687i	0.109667	−	0.0704788i
$651$	−2.20277	−	4.82338i	−0.0863332	−	0.189043i
$652$	70.0417	+	80.8324i	2.74304	+	3.16564i
$653$	2.05012	+	14.2589i	0.0802276	+	0.557995i	0.989802	+	0.142453i	$0.0454990\pi$
$653$	2.05012	+	14.2589i	0.0802276	+	0.557995i	−0.909574	+	0.415542i	$0.863592\pi$
$654$	5.83014	−	12.7662i	0.227976	−	0.499199i
$655$	−44.4654	+	13.0562i	−1.73741	+	0.510149i
$656$	−58.2472	+	17.1029i	−2.27417	+	0.667757i
$657$	−4.09754	+	8.97236i	−0.159860	+	0.350045i
$658$	−3.58804	−	24.9554i	−0.139876	−	0.972861i
$659$	4.12796	+	4.76392i	0.160802	+	0.185576i	0.830433	−	0.557118i	$-0.188093\pi$
$659$	4.12796	+	4.76392i	0.160802	+	0.185576i	−0.669631	+	0.742694i	$0.733548\pi$
$660$	1.06623	+	2.33471i	0.0415028	+	0.0908784i
$661$	12.0119	−	7.71957i	0.467208	−	0.300257i	−0.285774	−	0.958297i	$-0.592251\pi$
$661$	12.0119	−	7.71957i	0.467208	−	0.300257i	0.752983	+	0.658040i	$0.228614\pi$
$662$	7.80954	−	54.3165i	0.303526	−	2.11107i
$663$	0.770415	+	0.495116i	0.0299205	+	0.0192287i
$664$	1.98586	−	2.29180i	0.0770662	−	0.0889392i
$665$	−5.64173	−	1.65656i	−0.218777	−	0.0642387i
$666$	−14.9280			−0.578449
$667$	13.6348	−	13.3256i	0.527942	−	0.515968i
$668$	−55.1234			−2.13279
$669$	−19.5901	−	5.75217i	−0.757397	−	0.222392i
$670$	84.0083	−	96.9507i	3.24552	−	3.74553i
$671$	1.02864	+	0.661066i	0.0397102	+	0.0255202i
$672$	−3.97248	+	27.6292i	−0.153242	+	1.06582i
$673$	−8.31665	+	5.34479i	−0.320583	+	0.206026i	−0.691028	−	0.722828i	$-0.742842\pi$
$673$	−8.31665	+	5.34479i	−0.320583	+	0.206026i	0.370444	+	0.928855i	$0.379205\pi$
$674$	−37.3567	−	81.7998i	−1.43893	−	3.15081i
$675$	−5.96825	−	6.88773i	−0.229718	−	0.265109i
$676$	10.6159	+	73.8350i	0.408303	+	2.83981i
$677$	−4.44727	+	9.73817i	−0.170923	+	0.374268i	−0.975636	−	0.219395i	$-0.929592\pi$
$677$	−4.44727	+	9.73817i	−0.170923	+	0.374268i	0.804713	+	0.593663i	$0.202319\pi$
$678$	16.3331	−	4.79583i	0.627269	−	0.184183i
$679$	−7.90622	+	2.32148i	−0.303413	+	0.0890901i
$680$	−113.703	+	248.974i	−4.36030	+	9.54774i
$681$	−2.39020	−	16.6242i	−0.0915927	−	0.637041i
$682$	−1.14914	−	1.32618i	−0.0440028	−	0.0507819i
$683$	8.33834	+	18.2584i	0.319058	+	0.698639i	0.999414	−	0.0342431i	$-0.0109021\pi$
$683$	8.33834	+	18.2584i	0.319058	+	0.698639i	−0.680356	+	0.732882i	$0.738175\pi$
$684$	7.56506	−	4.86177i	0.289257	−	0.185894i
$685$	0.134623	−	0.936323i	0.00514368	−	0.0357750i
$686$	2.34129	+	1.50465i	0.0893908	+	0.0574480i
$687$	4.95686	−	5.72052i	0.189116	−	0.218251i
$688$	169.655	+	49.8151i	6.46803	+	1.89918i
$689$	0.234674			0.00894037
$690$	−29.5874	−	40.4838i	−1.12637	−	1.54119i
$691$	42.5485			1.61862			0.809310	−	0.587382i	$-0.199841\pi$
$691$	42.5485			1.61862			0.809310	+	0.587382i	$0.199841\pi$
$692$	130.568	+	38.3382i	4.96345	+	1.45740i
$693$	−0.0778678	+	0.0898643i	−0.00295795	+	0.00341366i
$694$	5.17059	+	3.32294i	0.196273	+	0.126137i
$695$	1.11548	−	7.75835i	0.0423127	−	0.294291i
$696$	34.8621	−	22.4045i	1.32144	−	0.849240i
$697$	−10.0596	−	22.0273i	−0.381033	−	0.834345i
$698$	17.6038	+	20.3158i	0.666312	+	0.768965i
$699$	2.87226	+	19.9770i	0.108639	+	0.755599i
$700$	−21.7529	+	47.6321i	−0.822181	+	1.80032i
$701$	−14.1526	+	4.15559i	−0.534538	+	0.156954i	−0.537851	−	0.843040i	$-0.680764\pi$
$701$	−14.1526	+	4.15559i	−0.534538	+	0.156954i	0.00331308	+	0.999995i	$0.498945\pi$
$702$	−0.349905	+	0.102741i	−0.0132063	+	0.00387773i
$703$	3.48743	−	7.63641i	0.131531	−	0.288013i
$704$	0.721629	+	5.01904i	0.0271974	+	0.189162i
$705$	22.2869	+	25.7205i	0.839373	+	0.968688i
$706$	3.88681	+	8.51093i	0.146282	+	0.320313i
$707$	−0.480444	+	0.308762i	−0.0180689	+	0.0116122i
$708$	1.15518	−	8.03445i	0.0434143	−	0.301953i
$709$	−34.4619	−	22.1473i	−1.29424	−	0.831759i	−0.301670	−	0.953412i	$-0.597544\pi$
$709$	−34.4619	−	22.1473i	−1.29424	−	0.831759i	−0.992573	+	0.121653i	$0.961181\pi$
$710$	10.3623	−	11.9587i	0.388889	−	0.448802i
$711$	−0.627250	−	0.184177i	−0.0235237	−	0.00690719i
$712$	−56.8901			−2.13205
$713$	20.1818	+	15.4722i	0.755815	+	0.579440i
$714$	−19.4511			−0.727941
$715$	0.0561634	+	0.0164911i	0.00210039	+	0.000616731i
$716$	−53.4757	+	61.7143i	−1.99848	+	2.30637i
$717$	−2.26915	−	1.45830i	−0.0847431	−	0.0544611i
$718$	−2.92897	+	20.3714i	−0.109308	+	0.760255i
$719$	4.01398	−	2.57963i	0.149696	−	0.0962038i	−0.463649	−	0.886019i	$-0.653460\pi$
$719$	4.01398	−	2.57963i	0.149696	−	0.0962038i	0.613345	+	0.789815i	$0.289824\pi$
$720$	−27.3437	−	59.8744i	−1.01904	−	2.23139i
$721$	−2.92119	−	3.37123i	−0.108791	−	0.125551i
$722$	−6.55520	−	45.5924i	−0.243959	−	1.69677i
$723$	−3.92257	+	8.58923i	−0.145882	+	0.319437i
$724$	−119.090	+	34.9678i	−4.42593	+	1.29957i
$725$	34.7629	−	10.2073i	1.29106	−	0.379090i
$726$	12.7012	−	27.8117i	0.471385	−	1.03219i
$727$	−6.11862	−	42.5559i	−0.226927	−	1.57831i	−0.710941	−	0.703251i	$-0.751731\pi$
$727$	−6.11862	−	42.5559i	−0.226927	−	1.57831i	0.484014	−	0.875060i	$-0.339178\pi$
$728$	0.894499	+	1.03231i	0.0331524	+	0.0382599i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	−86.7596	+	55.7570i	−3.21112	+	2.06366i
$731$	−10.0378	+	69.8143i	−0.371261	+	2.58217i
$732$	−49.7038	−	31.9427i	−1.83711	−	1.18064i
$733$	−12.2141	+	14.0958i	−0.451139	+	0.520642i	−0.935069	−	0.354465i	$-0.884663\pi$
$733$	−12.2141	+	14.0958i	−0.451139	+	0.520642i	0.483931	+	0.875106i	$0.339209\pi$
$734$	−13.7560	−	4.03913i	−0.507744	−	0.149087i
$735$	−3.75683			−0.138573
$736$	−45.3403	−	125.955i	−1.67126	−	4.64278i
$737$	1.45893			0.0537402
$738$	9.25228	+	2.71671i	0.340581	+	0.100004i
$739$	−8.24508	+	9.51533i	−0.303300	+	0.350027i	−0.886856	−	0.462046i	$-0.847116\pi$
$739$	−8.24508	+	9.51533i	−0.303300	+	0.350027i	0.583556	+	0.812073i	$0.301661\pi$
$740$	−97.4000	−	62.5952i	−3.58050	−	2.30105i
$741$	0.0291864	−	0.202996i	0.00107219	−	0.00745723i
$742$	−4.19314	+	2.69477i	−0.153935	+	0.0989279i
$743$	14.6855	+	32.1568i	0.538759	+	1.17972i	0.961837	+	0.273624i	$0.0882225\pi$
$743$	14.6855	+	32.1568i	0.538759	+	1.17972i	−0.423078	+	0.906093i	$0.639050\pi$
$744$	36.1981	+	41.7748i	1.32709	+	1.53154i
$745$	1.10045	+	7.65379i	0.0403173	+	0.280413i
$746$	−4.60875	+	10.0918i	−0.168738	+	0.369485i
$747$	−0.279120	+	0.0819570i	−0.0102125	+	0.00299865i
$748$	−4.58147	+	1.34524i	−0.167515	+	0.0491868i
$749$	−7.48053	+	16.3801i	−0.273333	+	0.598515i
$750$	−6.12124	−	42.5742i	−0.223516	−	1.55459i
$751$	32.0337	+	36.9688i	1.16893	+	1.34901i	0.925343	+	0.379132i	$0.123777\pi$
$751$	32.0337	+	36.9688i	1.16893	+	1.34901i	0.243583	+	0.969880i	$0.421677\pi$
$752$	65.9349	+	144.377i	2.40440	+	5.26490i
$753$	14.3816	−	9.24247i	0.524093	−	0.336814i
$754$	0.206317	−	1.43496i	0.00751361	−	0.0522583i
$755$	−31.2561	−	20.0871i	−1.13753	−	0.731044i
$756$	3.76257	−	4.34224i	0.136843	−	0.157926i
$757$	−47.2481	−	13.8733i	−1.71726	−	0.504233i	−0.732891	−	0.680346i	$-0.761830\pi$
$757$	−47.2481	−	13.8733i	−1.71726	−	0.504233i	−0.984370	+	0.176112i	$0.943648\pi$
$758$	−43.5321			−1.58116
$759$	0.127600	−	0.555801i	0.00463160	−	0.0201743i
$760$	61.2944			2.22338
$761$	−37.4381	−	10.9928i	−1.35713	−	0.398489i	−0.479379	−	0.877608i	$-0.659138\pi$
$761$	−37.4381	−	10.9928i	−1.35713	−	0.398489i	−0.877750	+	0.479119i	$0.840956\pi$
$762$	−28.0341	+	32.3531i	−1.01557	+	1.17203i
$763$	4.24225	+	2.72633i	0.153580	+	0.0986996i
$764$	−3.64741	+	25.3683i	−0.131959	+	0.917794i
$765$	22.0885	−	14.1954i	0.798610	−	0.513236i
$766$	−19.4485	−	42.5863i	−0.702703	−	1.53870i
$767$	−0.121225	−	0.139901i	−0.00437719	−	0.00505155i
$768$	−12.7576	−	88.7309i	−0.460349	−	3.20180i
$769$	8.64043	−	18.9199i	0.311582	−	0.682270i	−0.687451	−	0.726231i	$-0.741270\pi$
$769$	8.64043	−	18.9199i	0.311582	−	0.682270i	0.999033	+	0.0439611i	$0.0139978\pi$
$770$	−1.19289	+	0.350264i	−0.0429888	+	0.0126226i
$771$	2.19764	−	0.645284i	0.0791459	−	0.0232393i
$772$	12.0184	−	26.3167i	0.432552	−	0.947157i
$773$	0.726976	+	5.05623i	0.0261475	+	0.181860i	0.998710	−	0.0507831i	$-0.0161717\pi$
$773$	0.726976	+	5.05623i	0.0261475	+	0.181860i	−0.972562	+	0.232643i	$0.925263\pi$
$774$	−18.3928	−	21.2264i	−0.661114	−	0.762966i
$775$	20.0755	+	43.9592i	0.721133	+	1.57906i
$776$	72.2611	−	46.4394i	2.59402	−	1.66708i
$777$	0.763352	−	5.30923i	0.0273851	−	0.190468i
$778$	28.3119	+	18.1949i	1.01503	+	0.652320i
$779$	−3.55122	+	4.09832i	−0.127236	+	0.146838i
$780$	−2.71381	−	0.796848i	−0.0971702	−	0.0285317i
$781$	0.179956			0.00643932
$782$	82.3811	−	43.7645i	2.94594	−	1.56502i
$783$	−3.97535			−0.142068
$784$	−16.8111	−	4.93618i	−0.600396	−	0.176292i
$785$	−24.6429	+	28.4395i	−0.879544	+	1.01505i
$786$	28.8811	+	18.5607i	1.03015	+	0.662040i
$787$	−2.19808	+	15.2880i	−0.0783529	+	0.544957i	0.912402	+	0.409295i	$0.134225\pi$
$787$	−2.19808	+	15.2880i	−0.0783529	+	0.544957i	−0.990755	+	0.135662i	$0.956684\pi$
$788$	−6.73362	+	4.32743i	−0.239875	+	0.154158i
$789$	−2.84363	−	6.22668i	−0.101236	−	0.221676i
$790$	−4.47607	−	5.16567i	−0.159252	−	0.183786i
$791$	0.870461	+	6.05419i	0.0309500	+	0.215262i
$792$	0.514922	−	1.12752i	0.0182970	−	0.0400648i
$793$	−1.29285	+	0.379616i	−0.0459106	+	0.0134806i
$794$	−10.3147	+	3.02866i	−0.366054	+	0.107483i
$795$	2.79504	−	6.12028i	0.0991299	−	0.217064i
$796$	18.9555	+	131.838i	0.671859	+	4.67288i
$797$	23.8012	+	27.4680i	0.843081	+	0.972967i	0.999893	−	0.0146613i	$-0.00466701\pi$
$797$	23.8012	+	27.4680i	0.843081	+	0.972967i	−0.156812	+	0.987629i	$0.550122\pi$
$798$	1.80950	+	3.96226i	0.0640557	+	0.140262i
$799$	−53.2627	+	34.2299i	−1.88430	+	1.21097i
$800$	36.2042	−	251.806i	1.28001	−	8.90268i
$801$	4.59106	+	2.95050i	0.162217	+	0.104251i
$802$	22.4273	−	25.8825i	0.791935	−	0.913942i
$803$	−1.12536	−	0.330436i	−0.0397132	−	0.0116608i
$804$	−70.4953			−2.48618
$805$	15.9112	−	8.45276i	0.560798	−	0.297921i
$806$	1.93373			0.0681126
$807$	−17.5284	−	5.14681i	−0.617029	−	0.181176i
$808$	3.89866	−	4.49929i	0.137154	−	0.158284i
$809$	42.4264	+	27.2658i	1.49163	+	0.958613i	0.995931	+	0.0901199i	$0.0287250\pi$
$809$	42.4264	+	27.2658i	1.49163	+	0.958613i	0.495701	+	0.868493i	$0.334911\pi$
$810$	−1.48799	+	10.3492i	−0.0522826	+	0.363633i
$811$	12.4294	−	7.98792i	0.436457	−	0.280494i	−0.303905	−	0.952702i	$-0.598291\pi$
$811$	12.4294	−	7.98792i	0.436457	−	0.280494i	0.740362	+	0.672208i	$0.234654\pi$
$812$	9.48842	+	20.7767i	0.332978	+	0.729121i
$813$	12.7358	+	14.6978i	0.446662	+	0.515476i
$814$	−0.252617	−	1.75699i	−0.00885421	−	0.0615823i
$815$	29.0519	−	63.6149i	1.01765	−	2.22833i
$816$	117.493	−	34.4992i	4.11309	−	1.20771i
$817$	15.1552	−	4.44996i	0.530213	−	0.155684i
$818$	−41.1333	+	90.0693i	−1.43819	+	3.14920i
$819$	−0.0186479	−	0.129699i	−0.000651612	−	0.00453206i
$820$	48.9763	+	56.5216i	1.71033	+	1.97382i
$821$	−22.6540	−	49.6052i	−0.790628	−	1.73123i	−0.674844	−	0.737960i	$-0.735789\pi$
$821$	−22.6540	−	49.6052i	−0.790628	−	1.73123i	−0.115784	−	0.993274i	$-0.536938\pi$
$822$	−0.589524	+	0.378864i	−0.0205620	+	0.0132144i
$823$	−1.35941	+	9.45489i	−0.0473860	+	0.329577i	0.952315	+	0.305117i	$0.0986956\pi$
$823$	−1.35941	+	9.45489i	−0.0473860	+	0.329577i	−0.999701	+	0.0244596i	$0.992214\pi$
$824$	39.1190	+	25.1402i	1.36277	+	0.875802i
$825$	0.709670	−	0.819002i	0.0247075	−	0.0285140i
$826$	3.77253	+	1.10772i	0.131263	+	0.0385424i
$827$	33.7427			1.17335			0.586675	−	0.809823i	$-0.300437\pi$
$827$	33.7427			1.17335			0.586675	+	0.809823i	$0.300437\pi$
$828$	−6.16565	+	26.8563i	−0.214271	+	0.933321i
$829$	−22.0405			−0.765497			−0.382748	−	0.923853i	$-0.625022\pi$
$829$	−22.0405			−0.765497			−0.382748	+	0.923853i	$0.625022\pi$
$830$	−2.91837	−	0.856910i	−0.101298	−	0.0297438i
$831$	−16.0101	+	18.4766i	−0.555383	+	0.640946i
$832$	−4.70070	−	3.02095i	−0.162967	−	0.104733i
$833$	0.994644	−	6.91790i	0.0344624	−	0.239691i
$834$	−4.88479	+	3.13926i	−0.169146	+	0.108704i
$835$	14.9728	+	32.7859i	0.518156	+	1.13460i
$836$	0.700234	+	0.808114i	0.0242181	+	0.0279492i
$837$	−0.754634	−	5.24859i	−0.0260840	−	0.181418i
$838$	−8.77986	+	19.2252i	−0.303295	+	0.664124i
$839$	51.4437	−	15.1052i	1.77603	−	0.521490i	0.781315	−	0.624137i	$-0.214549\pi$
$839$	51.4437	−	15.1052i	1.77603	−	0.521490i	0.994718	+	0.102646i	$0.0327310\pi$
$840$	37.5763	−	11.0334i	1.29650	−	0.380688i
$841$	−5.48205	+	12.0040i	−0.189036	+	0.413932i
$842$	7.42066	+	51.6118i	0.255733	+	1.77866i
$843$	14.2943	+	16.4965i	0.492323	+	0.568171i
$844$	−5.37924	−	11.7789i	−0.185161	−	0.405446i
$845$	41.0315	−	26.3694i	1.41153	−	0.907134i
$846$	3.58804	−	24.9554i	0.123359	−	0.857983i
$847$	9.24189	+	5.93940i	0.317555	+	0.204080i
$848$	20.5488	−	23.7146i	0.705650	−	0.814364i
$849$	0.104630	+	0.0307223i	0.00359091	+	0.00105439i
$850$	177.273			6.08042
$851$	8.71260	+	24.2036i	0.298664	+	0.829689i
$852$	−8.69546			−0.297901
$853$	−14.9772	−	4.39771i	−0.512810	−	0.150575i	0.0150817	−	0.999886i	$-0.495199\pi$
$853$	−14.9772	−	4.39771i	−0.512810	−	0.150575i	−0.527892	+	0.849312i	$0.677017\pi$
$854$	18.7415	−	21.6288i	0.641320	−	0.740123i
$855$	−4.94650	−	3.17892i	−0.169167	−	0.108717i
$856$	26.7147	−	185.805i	0.913090	−	6.35068i
$857$	−18.7000	+	12.0178i	−0.638779	+	0.410519i	−0.819551	−	0.573007i	$-0.805777\pi$
$857$	−18.7000	+	12.0178i	−0.638779	+	0.410519i	0.180771	+	0.983525i	$0.442141\pi$
$858$	−0.0180136	−	0.0394442i	−0.000614973	−	0.00134660i
$859$	−2.51591	−	2.90351i	−0.0858416	−	0.0990665i	0.711204	−	0.702986i	$-0.248150\pi$
$859$	−2.51591	−	2.90351i	−0.0858416	−	0.0990665i	−0.797045	+	0.603919i	$0.793605\pi$
$860$	−31.0012	−	215.618i	−1.05713	−	7.35250i
$861$	−1.43933	+	3.15170i	−0.0490523	+	0.107410i
$862$	−59.2519	+	17.3979i	−2.01813	+	0.592576i
$863$	−24.7345	+	7.26271i	−0.841973	+	0.247226i	−0.674153	−	0.738592i	$-0.735491\pi$
$863$	−24.7345	+	7.26271i	−0.841973	+	0.247226i	−0.167820	+	0.985818i	$0.553673\pi$
$864$	−11.5956	+	25.3908i	−0.394490	+	0.863813i
$865$	−12.6628	−	88.0718i	−0.430549	−	2.99453i
$866$	−4.95816	−	5.72203i	−0.168485	−	0.194442i
$867$	13.2296	+	28.9687i	0.449300	+	0.983829i
$868$	−25.6300	+	16.4714i	−0.869940	+	0.559076i
$869$	0.0110626	−	0.0769423i	0.000375274	−	0.00261009i
$870$	−34.9665	−	22.4716i	−1.18547	−	0.761858i
$871$	−1.05282	+	1.21502i	−0.0356734	+	0.0411693i
$872$	−50.4384	−	14.8100i	−1.70806	−	0.501531i
$873$	−8.24000			−0.278882
$874$	−16.5787	−	12.7100i	−0.560784	−	0.429921i
$875$	15.4547			0.522465
$876$	54.3775	+	15.9667i	1.83724	+	0.539464i
$877$	28.1392	−	32.4743i	0.950192	−	1.09658i	−0.0450343	−	0.998985i	$-0.514340\pi$
$877$	28.1392	−	32.4743i	0.950192	−	1.09658i	0.995226	−	0.0975945i	$-0.0311148\pi$
$878$	−29.6458	−	19.0522i	−1.00050	−	0.642980i
$879$	−0.359456	+	2.50007i	−0.0121242	+	0.0843254i
$880$	6.58433	−	4.23149i	0.221958	−	0.142644i
$881$	−3.65949	−	8.01317i	−0.123291	−	0.269970i	0.837915	−	0.545801i	$-0.183774\pi$
$881$	−3.65949	−	8.01317i	−0.123291	−	0.269970i	−0.961206	+	0.275830i	$0.911047\pi$
$882$	1.82254	+	2.10332i	0.0613681	+	0.0708225i
$883$	−2.33463	−	16.2377i	−0.0785664	−	0.546441i	−0.990649	−	0.136435i	$-0.956436\pi$
$883$	−2.33463	−	16.2377i	−0.0785664	−	0.546441i	0.912083	−	0.410006i	$-0.134474\pi$
$884$	2.18583	−	4.78630i	0.0735174	−	0.160981i
$885$	−5.09245	+	1.49528i	−0.171181	+	0.0502632i
$886$	−81.3460	+	23.8853i	−2.73287	+	0.802444i
$887$	5.59105	−	12.2427i	0.187729	−	0.411069i	−0.792243	−	0.610206i	$-0.791087\pi$
$887$	5.59105	−	12.2427i	0.187729	−	0.411069i	0.979972	+	0.199137i	$0.0638138\pi$
$888$	7.95747	+	55.3454i	0.267035	+	1.85727i
$889$	−10.0730	−	11.6249i	−0.337837	−	0.389885i
$890$	23.7038	+	51.9041i	0.794553	+	1.73983i
$891$	−0.100031	+	0.0642862i	−0.00335118	+	0.00215367i
$892$	−16.6948	+	116.115i	−0.558983	+	3.88781i
$893$	11.9277	+	7.66544i	0.399144	+	0.256514i
$894$	3.75124	−	4.32916i	0.125460	−	0.144789i
$895$	51.2312	+	15.0429i	1.71247	+	0.502827i
$896$	62.8548			2.09983
$897$	0.370799	+	0.507356i	0.0123806	+	0.0169401i
$898$	−106.586			−3.55682
$899$	20.2257	+	5.93880i	0.674565	+	0.198070i
$900$	−34.2912	+	39.5742i	−1.14304	+	1.31914i
$901$	10.5300	+	6.76722i	0.350805	+	0.225449i
$902$	−0.163180	+	1.13494i	−0.00543329	+	0.0377894i
$903$	8.48979	−	5.45606i	0.282523	−	0.181566i
$904$	−26.4869	−	57.9983i	−0.880943	−	1.92900i
$905$	53.1454	+	61.3331i	1.76661	+	2.03878i
$906$	3.91710	+	27.2440i	0.130137	+	0.905122i
$907$	−14.3689	+	31.4634i	−0.477111	+	1.04473i	0.506137	+	0.862453i	$0.331073\pi$
$907$	−14.3689	+	31.4634i	−0.477111	+	1.04473i	−0.983248	+	0.182274i	$0.941654\pi$
$908$	−92.5896	+	27.1868i	−3.07269	+	0.902224i
$909$	−0.547971	+	0.160899i	−0.0181750	+	0.00533667i
$910$	0.569131	−	1.24622i	0.0188665	−	0.0413119i
$911$	−2.69678	−	18.7565i	−0.0893484	−	0.621432i	−0.984463	−	0.175595i	$-0.943815\pi$
$911$	−2.69678	−	18.7565i	−0.0893484	−	0.621432i	0.895114	−	0.445837i	$-0.147094\pi$
$912$	−17.9578	−	20.7244i	−0.594641	−	0.686252i
$913$	−0.0143695	−	0.0314647i	−0.000475560	−	0.00104133i
$914$	−4.93637	+	3.17241i	−0.163281	+	0.104934i
$915$	−5.49792	+	38.2389i	−0.181756	+	1.26414i
$916$	−36.5865	−	23.5127i	−1.20885	−	0.776882i
$917$	−8.07807	+	9.32259i	−0.266762	+	0.307859i
$918$	−18.6632	−	5.48002i	−0.615979	−	0.180868i
$919$	11.9841			0.395320			0.197660	−	0.980271i	$-0.436666\pi$
$919$	11.9841			0.395320			0.197660	+	0.980271i	$0.436666\pi$
$920$	−134.321	+	131.275i	−4.42844	+	4.32801i
$921$	5.91698			0.194971
$922$	−55.5555	−	16.3126i	−1.82962	−	0.537226i
$923$	−0.129863	+	0.149870i	−0.00427450	+	0.00493304i
$924$	0.574741	+	0.369364i	0.0189076	+	0.0121512i
$925$	−6.95701	+	48.3871i	−0.228745	+	1.59096i
$926$	−41.2329	+	26.4988i	−1.35500	+	0.870804i
$927$	−1.85307	−	4.05766i	−0.0608629	−	0.133271i
$928$	−72.6667	−	83.8619i	−2.38540	−	2.75290i
$929$	5.84054	+	40.6219i	0.191622	+	1.33276i	0.827715	+	0.561148i	$0.189640\pi$
$929$	5.84054	+	40.6219i	0.191622	+	1.33276i	−0.636093	+	0.771612i	$0.719451\pi$
$930$	23.0313	−	50.4314i	0.755225	−	1.65371i
$931$	−1.50173	+	0.440947i	−0.0492171	+	0.0144514i
$932$	111.263	−	32.6698i	3.64454	−	1.07013i
$933$	−11.9354	+	26.1349i	−0.390748	+	0.855620i
$934$	−2.39040	−	16.6256i	−0.0782164	−	0.544007i
$935$	2.04455	+	2.35953i	0.0668638	+	0.0771650i
$936$	0.567431	+	1.24250i	0.0185471	+	0.0406124i
$937$	13.4532	−	8.64582i	0.439495	−	0.282447i	−0.302123	−	0.953269i	$-0.597695\pi$
$937$	13.4532	−	8.64582i	0.439495	−	0.282447i	0.741618	+	0.670823i	$0.234059\pi$
$938$	4.85961	−	33.7994i	0.158672	−	1.10359i
$939$	−3.45782	−	2.22221i	−0.112842	−	0.0725190i
$940$	128.052	−	147.780i	4.17659	−	4.82004i
$941$	−38.8701	−	11.4133i	−1.26713	−	0.372062i	−0.421985	−	0.906603i	$-0.638667\pi$
$941$	−38.8701	−	11.4133i	−1.26713	−	0.372062i	−0.845143	+	0.534540i	$0.820485\pi$
$942$	27.8773			0.908290
$943$	−0.995248	−	16.5868i	−0.0324097	−	0.540141i
$944$	−24.7524			−0.805623
$945$	−3.60465	−	1.05842i	−0.117259	−	0.0344304i
$946$	2.18704	−	2.52397i	0.0711067	−	0.0820615i
$947$	−16.2392	−	10.4363i	−0.527702	−	0.339134i	0.249510	−	0.968372i	$-0.419731\pi$
$947$	−16.2392	−	10.4363i	−0.527702	−	0.339134i	−0.777212	+	0.629238i	$0.783367\pi$
$948$	−0.534546	+	3.71785i	−0.0173613	+	0.120750i
$949$	1.08730	−	0.698764i	0.0352952	−	0.0226829i
$950$	−16.4914	−	36.1111i	−0.535051	−	1.17160i
$951$	−15.0230	−	17.3374i	−0.487153	−	0.562204i
$952$	10.3685	+	72.1148i	0.336046	+	2.33725i
$953$	8.04135	−	17.6081i	0.260485	−	0.570382i	−0.733526	−	0.679661i	$-0.762127\pi$
$953$	8.04135	−	17.6081i	0.260485	−	0.570382i	0.994011	+	0.109279i	$0.0348541\pi$
$954$	−4.78249	+	1.40427i	−0.154839	+	0.0454648i
$955$	16.0791	−	4.72125i	0.520308	−	0.152776i
$956$	−6.43807	+	14.0974i	−0.208222	+	0.455943i
$957$	−0.0672721	−	0.467888i	−0.00217460	−	0.0151247i
$958$	7.34933	+	8.48158i	0.237446	+	0.274027i
$959$	−0.104599	−	0.229041i	−0.00337769	−	0.00739611i
$960$	−134.773	+	86.6134i	−4.34978	+	2.79543i
$961$	0.410263	−	2.85344i	0.0132343	−	0.0920466i
$962$	1.64555	+	1.05753i	0.0530545	+	0.0340961i
$963$	−11.7923	+	13.6091i	−0.380002	+	0.438546i
$964$	52.0555	+	15.2849i	1.67659	+	0.492293i
$965$	−18.9169			−0.608957
$966$	−12.4514	−	4.80751i	−0.400617	−	0.154679i
$967$	23.5163			0.756234			0.378117	−	0.925758i	$-0.376572\pi$
$967$	23.5163			0.756234			0.378117	+	0.925758i	$0.376572\pi$
$968$	−109.882	−	32.2642i	−3.53174	−	1.03701i
$969$	7.16334	−	8.26693i	0.230120	−	0.265572i
$970$	−72.4776	−	46.5785i	−2.32711	−	1.49555i
$971$	−0.714078	+	4.96652i	−0.0229159	+	0.159383i	−0.998066	−	0.0621612i	$-0.980201\pi$
$971$	−0.714078	+	4.96652i	−0.0229159	+	0.159383i	0.975150	+	0.221544i	$0.0711098\pi$
$972$	4.83351	−	3.10631i	0.155035	−	0.0996350i
$973$	−0.866709	−	1.89783i	−0.0277854	−	0.0608416i
$974$	−0.699944	−	0.807778i	−0.0224276	−	0.0258829i
$975$	0.169953	+	1.18205i	0.00544285	+	0.0378559i
$976$	−74.8451	+	163.888i	−2.39573	+	5.24592i
$977$	2.60963	−	0.766255i	0.0834893	−	0.0245147i	−0.239721	−	0.970842i	$-0.577056\pi$
$977$	2.60963	−	0.766255i	0.0834893	−	0.0245147i	0.323210	+	0.946327i	$0.395238\pi$
$978$	−49.7097	+	14.5961i	−1.58954	+	0.466731i
$979$	−0.269574	+	0.590284i	−0.00861562	+	0.0188656i
$980$	3.07191	+	21.3656i	0.0981284	+	0.682498i
$981$	3.30231	+	3.81107i	0.105435	+	0.121678i
$982$	−46.6472	−	102.143i	−1.48857	−	3.25952i
$983$	4.75349	−	3.05488i	0.151613	−	0.0974356i	−0.462635	−	0.886549i	$-0.653096\pi$
$983$	4.75349	−	3.05488i	0.151613	−	0.0974356i	0.614248	+	0.789113i	$0.289460\pi$
$984$	5.14020	−	35.7508i	0.163863	−	1.13970i
$985$	4.40285	+	2.82954i	0.140286	+	0.0901566i
$986$	50.6372	−	58.4385i	1.61262	−	1.86106i
$987$	8.69203	+	2.55221i	0.276670	+	0.0812377i
$988$	−1.17833			−0.0374876
$989$	−23.6807	+	42.2097i	−0.753003	+	1.34219i
$990$	−1.24325			−0.0395131
$991$	30.6763	+	9.00737i	0.974464	+	0.286128i	0.729937	−	0.683514i	$-0.239549\pi$
$991$	30.6763	+	9.00737i	0.974464	+	0.286128i	0.244527	+	0.969643i	$0.421367\pi$
$992$	96.9273	−	111.860i	3.07744	−	3.55156i
$993$	16.5872	+	10.6600i	0.526380	+	0.338284i
$994$	0.599424	−	4.16909i	0.0190126	−	0.132235i
$995$	73.2651	−	47.0846i	2.32266	−	1.49268i
$996$	0.694332	+	1.52038i	0.0220008	+	0.0481749i
$997$	36.5920	+	42.2294i	1.15888	+	1.33742i	0.931555	+	0.363601i	$0.118453\pi$
$997$	36.5920	+	42.2294i	1.15888	+	1.33742i	0.227326	+	0.973819i	$0.427002\pi$
$998$	14.0458	+	97.6908i	0.444612	+	3.09235i
$999$	2.22821	−	4.87911i	0.0704976	−	0.154368i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.f.64.8	✓	80
23.9	even	11	inner	483.2.q.f.400.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.f.64.8	✓	80	1.1	even	1	trivial
483.2.q.f.400.8	yes	80	23.9	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(2.67036 + 0.784088i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(4.83351 + 3.10631i) q^{4} +(0.534653 - 3.71859i) q^{5} +(-2.34129 + 1.50465i) q^{6} +(-0.415415 - 0.909632i) q^{7} +(6.82652 + 7.87822i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(2.67036 + 0.784088i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(4.83351 + 3.10631i) q^{4} +(0.534653 - 3.71859i) q^{5} +(-2.34129 + 1.50465i) q^{6} +(-0.415415 - 0.909632i) q^{7} +(6.82652 + 7.87822i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(4.34342 - 9.51076i) q^{10} +(0.114091 - 0.0335001i) q^{11} +(-5.51287 + 1.61873i) q^{12} +(-0.0544331 + 0.119192i) q^{13} +(-0.396076 - 2.75477i) q^{14} +(2.46020 + 2.83922i) q^{15} +(7.27841 + 15.9375i) q^{16} +(-5.87955 + 3.77856i) q^{17} +(0.396076 - 2.75477i) q^{18} +(1.31667 + 0.846171i) q^{19} +(14.1354 - 16.3131i) q^{20} +(0.959493 + 0.281733i) q^{21} +0.330931 q^{22} +(-4.69762 + 0.965614i) q^{23} -10.4244 q^{24} +(-8.74460 - 2.56765i) q^{25} +(-0.238813 + 0.275605i) q^{26} +(0.841254 + 0.540641i) q^{27} +(0.817685 - 5.68713i) q^{28} +(-3.34428 + 2.14924i) q^{29} +(4.34342 + 9.51076i) q^{30} +(-3.47244 - 4.00741i) q^{31} +(3.97248 + 27.6292i) q^{32} +(-0.0493960 + 0.108162i) q^{33} +(-18.6632 + 5.48002i) q^{34} +(-3.60465 + 1.05842i) q^{35} +(2.38681 - 5.22639i) q^{36} +(-0.763352 - 5.30923i) q^{37} +(2.85250 + 3.29196i) q^{38} +(-0.0544331 - 0.119192i) q^{39} +(32.9457 - 21.1729i) q^{40} +(-0.493094 + 3.42954i) q^{41} +(2.34129 + 1.50465i) q^{42} +(6.60874 - 7.62690i) q^{43} +(0.655522 + 0.192479i) q^{44} -3.75683 q^{45} +(-13.3014 - 1.10481i) q^{46} +9.05898 q^{47} +(-16.8111 - 4.93618i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(-21.3380 - 13.7131i) q^{50} +(0.994644 - 6.91790i) q^{51} +(-0.633350 + 0.407029i) q^{52} +(-0.743989 - 1.62911i) q^{53} +(1.82254 + 2.10332i) q^{54} +(-0.0635742 - 0.442168i) q^{55} +(4.33044 - 9.48235i) q^{56} +(-1.50173 + 0.440947i) q^{57} +(-10.6156 + 3.11703i) q^{58} +(-0.586875 + 1.28508i) q^{59} +(3.07191 + 21.3656i) q^{60} +(6.73404 + 7.77150i) q^{61} +(-6.13050 - 13.4239i) q^{62} +(-0.841254 + 0.540641i) q^{63} +(-6.06883 + 42.2096i) q^{64} +(0.414123 + 0.266141i) q^{65} +(-0.216713 + 0.250101i) q^{66} +(11.7724 + 3.45669i) q^{67} -40.1563 q^{68} +(2.34652 - 4.18256i) q^{69} -10.4556 q^{70} +(1.45211 + 0.426377i) q^{71} +(6.82652 - 7.87822i) q^{72} +(-8.29790 - 5.33273i) q^{73} +(2.12448 - 14.7761i) q^{74} +(7.66699 - 4.92728i) q^{75} +(3.73566 + 8.17996i) q^{76} +(-0.0778678 - 0.0898643i) q^{77} +(-0.0518990 - 0.360965i) q^{78} +(0.271570 - 0.594655i) q^{79} +(63.1564 - 18.5444i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-4.00580 + 8.77148i) q^{82} +(-0.0413999 - 0.287943i) q^{83} +(3.76257 + 4.34224i) q^{84} +(10.9074 + 23.8839i) q^{85} +(23.6279 - 15.1847i) q^{86} +(0.565752 - 3.93489i) q^{87} +(1.04276 + 0.670144i) q^{88} +(-3.57384 + 4.12443i) q^{89} +(-10.0321 - 2.94569i) q^{90} +0.131033 q^{91} +(-25.7055 - 9.92495i) q^{92} +5.30257 q^{93} +(24.1907 + 7.10304i) q^{94} +(3.85052 - 4.44374i) q^{95} +(-23.4822 - 15.0911i) q^{96} +(1.17267 - 8.15613i) q^{97} +(-2.34129 + 1.50465i) q^{98} +(-0.0493960 - 0.108162i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9}+O(q^{10}) \) 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9	\( 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9} + 4 q^{10} + q^{11} - 9 q^{12} - 26 q^{13} - q^{14} + 2 q^{15} - 3 q^{16} - 23 q^{17} + q^{18} + 10 q^{19} + 63 q^{20} + 8 q^{21} - 9 q^{23} + 30 q^{24} - 29 q^{25} - 12 q^{26} - 8 q^{27} + 20 q^{28} + 13 q^{29} + 4 q^{30} - 27 q^{31} + 71 q^{32} + q^{33} - 45 q^{34} - 2 q^{35} - 9 q^{36} + 60 q^{37} - 2 q^{38} - 26 q^{39} + 7 q^{40} - 26 q^{41} - q^{42} + 5 q^{43} - 33 q^{44} - 20 q^{45} - 41 q^{46} + 34 q^{47} - 58 q^{48} - 8 q^{49} - 75 q^{50} - q^{51} + 108 q^{52} - 39 q^{53} - 10 q^{54} + 51 q^{55} + 3 q^{56} + 10 q^{57} + 47 q^{58} - 66 q^{59} + 19 q^{60} + 3 q^{61} + 103 q^{62} + 8 q^{63} - 25 q^{64} + 39 q^{65} - 33 q^{66} + 33 q^{67} - 88 q^{68} + 13 q^{69} + 18 q^{70} - 12 q^{71} - 25 q^{72} - 98 q^{73} + 123 q^{74} + 4 q^{75} - 41 q^{76} - 12 q^{77} + 10 q^{78} - 34 q^{79} + 163 q^{80} - 8 q^{81} + 48 q^{82} + 26 q^{83} + 9 q^{84} + 35 q^{85} + 4 q^{86} + 2 q^{87} + 178 q^{88} - 63 q^{89} + 4 q^{90} - 62 q^{91} - 39 q^{92} + 138 q^{93} - 28 q^{94} - 80 q^{95} - 17 q^{96} - 44 q^{97} + q^{98} + q^{99}+O(q^{100}) \) 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9 + 4 * q^10 + q^11 - 9 * q^12 - 26 * q^13 - q^14 + 2 * q^15 - 3 * q^16 - 23 * q^17 + q^18 + 10 * q^19 + 63 * q^20 + 8 * q^21 - 9 * q^23 + 30 * q^24 - 29 * q^25 - 12 * q^26 - 8 * q^27 + 20 * q^28 + 13 * q^29 + 4 * q^30 - 27 * q^31 + 71 * q^32 + q^33 - 45 * q^34 - 2 * q^35 - 9 * q^36 + 60 * q^37 - 2 * q^38 - 26 * q^39 + 7 * q^40 - 26 * q^41 - q^42 + 5 * q^43 - 33 * q^44 - 20 * q^45 - 41 * q^46 + 34 * q^47 - 58 * q^48 - 8 * q^49 - 75 * q^50 - q^51 + 108 * q^52 - 39 * q^53 - 10 * q^54 + 51 * q^55 + 3 * q^56 + 10 * q^57 + 47 * q^58 - 66 * q^59 + 19 * q^60 + 3 * q^61 + 103 * q^62 + 8 * q^63 - 25 * q^64 + 39 * q^65 - 33 * q^66 + 33 * q^67 - 88 * q^68 + 13 * q^69 + 18 * q^70 - 12 * q^71 - 25 * q^72 - 98 * q^73 + 123 * q^74 + 4 * q^75 - 41 * q^76 - 12 * q^77 + 10 * q^78 - 34 * q^79 + 163 * q^80 - 8 * q^81 + 48 * q^82 + 26 * q^83 + 9 * q^84 + 35 * q^85 + 4 * q^86 + 2 * q^87 + 178 * q^88 - 63 * q^89 + 4 * q^90 - 62 * q^91 - 39 * q^92 + 138 * q^93 - 28 * q^94 - 80 * q^95 - 17 * q^96 - 44 * q^97 + q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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