LMFDB - Embedded newform 250.2.g.a.231.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,2,Mod(11,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([38]))

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

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

chi := DirichletCharacter("250.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	250.g (of order $25$, degree $20$, 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:	$1.99626005053$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			231.1
Character	$\chi$	$=$	250.231
Dual form			250.2.g.a.171.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.535827 + 0.844328i) q^{2} +(-2.18782 + 2.05450i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(-1.46888 + 1.68594i) q^{5} +(-0.562379 - 2.94809i) q^{6} +(-1.60057 + 1.16288i) q^{7} +(0.992115 + 0.125333i) q^{8} +(0.377216 - 5.99567i) q^{9} +O(q^{10})$	\(q+(-0.535827 + 0.844328i) q^{2} +(-2.18782 + 2.05450i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(-1.46888 + 1.68594i) q^{5} +(-0.562379 - 2.94809i) q^{6} +(-1.60057 + 1.16288i) q^{7} +(0.992115 + 0.125333i) q^{8} +(0.377216 - 5.99567i) q^{9} +(-0.636423 - 2.14359i) q^{10} +(0.783067 - 1.23392i) q^{11} +(2.79050 + 1.10484i) q^{12} +(-0.200535 + 3.18741i) q^{13} +(-0.124225 - 1.97450i) q^{14} +(-0.250126 - 6.70635i) q^{15} +(-0.637424 + 0.770513i) q^{16} +(2.34881 - 4.99147i) q^{17} +(4.86019 + 3.53114i) q^{18} +(2.45104 + 2.30168i) q^{19} +(2.15090 + 0.611241i) q^{20} +(1.11262 - 5.83253i) q^{21} +(0.622242 + 1.32233i) q^{22} +(-7.35617 - 1.88874i) q^{23} +(-2.42807 + 1.76409i) q^{24} +(-0.684797 - 4.95288i) q^{25} +(-2.58377 - 1.87722i) q^{26} +(5.75362 + 6.95493i) q^{27} +(1.73369 + 0.953105i) q^{28} +(-3.66521 - 2.01496i) q^{29} +(5.79638 + 3.38225i) q^{30} +(-3.29000 + 6.99160i) q^{31} +(-0.309017 - 0.951057i) q^{32} +(0.821871 + 4.30840i) q^{33} +(2.95588 + 4.65773i) q^{34} +(0.390489 - 4.40659i) q^{35} +(-5.58566 + 2.21152i) q^{36} +(6.54860 - 7.91590i) q^{37} +(-3.25671 + 0.836180i) q^{38} +(-6.10980 - 7.38548i) q^{39} +(-1.66860 + 1.48855i) q^{40} +(-3.10856 + 0.798142i) q^{41} +(4.32840 + 4.06464i) q^{42} +(-2.07220 + 6.37757i) q^{43} +(-1.44989 - 0.183164i) q^{44} +(9.55427 + 9.44287i) q^{45} +(5.53635 - 5.19898i) q^{46} +(-10.2534 + 1.29530i) q^{47} +(-0.188450 - 2.99533i) q^{48} +(-0.953596 + 2.93487i) q^{49} +(4.54879 + 2.07569i) q^{50} +(5.11621 + 15.7461i) q^{51} +(2.96944 - 1.17568i) q^{52} +(-0.799874 + 4.19308i) q^{53} +(-8.95518 + 1.13130i) q^{54} +(0.930081 + 3.13268i) q^{55} +(-1.73369 + 0.953105i) q^{56} -10.0912 q^{57} +(3.66521 - 2.01496i) q^{58} +(-0.654806 - 0.259256i) q^{59} +(-5.96158 + 3.08174i) q^{60} +(-12.6415 - 3.24580i) q^{61} +(-4.14033 - 6.52412i) q^{62} +(6.36848 + 10.0351i) q^{63} +(0.968583 + 0.248690i) q^{64} +(-5.07922 - 5.02000i) q^{65} +(-4.07808 - 1.61463i) q^{66} +(1.60782 - 0.883909i) q^{67} -5.51649 q^{68} +(19.9744 - 10.9810i) q^{69} +(3.51137 + 2.69087i) q^{70} +(-1.48986 + 0.188213i) q^{71} +(1.12570 - 5.90112i) q^{72} +(-2.98601 + 1.18224i) q^{73} +(3.17470 + 9.77072i) q^{74} +(11.6739 + 9.42910i) q^{75} +(1.03902 - 3.19778i) q^{76} +(0.181545 + 2.88558i) q^{77} +(9.50956 - 1.20134i) q^{78} +(6.64219 - 6.23743i) q^{79} +(-0.362742 - 2.20645i) q^{80} +(-8.99630 - 1.13650i) q^{81} +(0.991755 - 3.05231i) q^{82} +(6.96809 + 6.54347i) q^{83} +(-5.75116 + 1.47665i) q^{84} +(4.96522 + 11.2918i) q^{85} +(-4.27442 - 5.16689i) q^{86} +(12.1586 - 3.12179i) q^{87} +(0.931543 - 1.12604i) q^{88} +(8.47797 - 3.35667i) q^{89} +(-13.0923 + 3.00719i) q^{90} +(-3.38560 - 5.33485i) q^{91} +(1.42312 + 7.46025i) q^{92} +(-7.16631 - 22.0556i) q^{93} +(4.40037 - 9.35126i) q^{94} +(-7.48078 + 0.751424i) q^{95} +(2.63002 + 1.44587i) q^{96} +(5.39580 + 2.96636i) q^{97} +(-1.96703 - 2.37773i) q^{98} +(-7.10277 - 5.16047i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 5 q^{5} + 10 q^{7} + 10 q^{9}+O(q^{10}) $ 120 * q - 5 * q^5 + 10 * q^7 + 10 * q^9	$ 120 q - 5 q^{5} + 10 q^{7} + 10 q^{9} - 20 q^{10} + 20 q^{12} - 20 q^{14} - 10 q^{15} - 5 q^{17} + 25 q^{18} - 60 q^{19} + 5 q^{20} + 5 q^{21} - 10 q^{22} + 10 q^{23} - 5 q^{24} + 55 q^{25} + 5 q^{26} - 90 q^{27} - 5 q^{28} - 10 q^{29} - 10 q^{30} - 45 q^{31} + 30 q^{32} - 15 q^{33} - 10 q^{34} + 15 q^{35} + 10 q^{36} + 10 q^{37} + 10 q^{39} - 55 q^{41} - 5 q^{42} + 5 q^{43} - 40 q^{44} + 85 q^{45} - 20 q^{46} + 90 q^{47} - 5 q^{48} - 20 q^{49} - 30 q^{50} + 60 q^{51} + 5 q^{53} + 5 q^{54} - 15 q^{55} + 5 q^{56} - 120 q^{57} + 10 q^{58} - 75 q^{59} + 15 q^{60} - 85 q^{61} - 15 q^{62} - 45 q^{63} + 5 q^{65} - 15 q^{66} - 25 q^{67} - 70 q^{68} + 5 q^{69} - 65 q^{70} + 55 q^{71} + 5 q^{72} - 30 q^{73} - 70 q^{74} - 20 q^{75} - 5 q^{76} - 130 q^{77} + 60 q^{78} + 10 q^{79} + 5 q^{80} - 65 q^{81} + 80 q^{82} - 135 q^{83} + 20 q^{84} - 30 q^{85} + 10 q^{86} - 200 q^{87} - 80 q^{90} + 175 q^{91} - 5 q^{92} + 50 q^{93} + 35 q^{94} - 20 q^{95} - 15 q^{98} - 120 q^{99}+O(q^{100}) $ 120 * q - 5 * q^5 + 10 * q^7 + 10 * q^9 - 20 * q^10 + 20 * q^12 - 20 * q^14 - 10 * q^15 - 5 * q^17 + 25 * q^18 - 60 * q^19 + 5 * q^20 + 5 * q^21 - 10 * q^22 + 10 * q^23 - 5 * q^24 + 55 * q^25 + 5 * q^26 - 90 * q^27 - 5 * q^28 - 10 * q^29 - 10 * q^30 - 45 * q^31 + 30 * q^32 - 15 * q^33 - 10 * q^34 + 15 * q^35 + 10 * q^36 + 10 * q^37 + 10 * q^39 - 55 * q^41 - 5 * q^42 + 5 * q^43 - 40 * q^44 + 85 * q^45 - 20 * q^46 + 90 * q^47 - 5 * q^48 - 20 * q^49 - 30 * q^50 + 60 * q^51 + 5 * q^53 + 5 * q^54 - 15 * q^55 + 5 * q^56 - 120 * q^57 + 10 * q^58 - 75 * q^59 + 15 * q^60 - 85 * q^61 - 15 * q^62 - 45 * q^63 + 5 * q^65 - 15 * q^66 - 25 * q^67 - 70 * q^68 + 5 * q^69 - 65 * q^70 + 55 * q^71 + 5 * q^72 - 30 * q^73 - 70 * q^74 - 20 * q^75 - 5 * q^76 - 130 * q^77 + 60 * q^78 + 10 * q^79 + 5 * q^80 - 65 * q^81 + 80 * q^82 - 135 * q^83 + 20 * q^84 - 30 * q^85 + 10 * q^86 - 200 * q^87 - 80 * q^90 + 175 * q^91 - 5 * q^92 + 50 * q^93 + 35 * q^94 - 20 * q^95 - 15 * q^98 - 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{17}{25}\right)$

Coefficient data

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

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

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

$2$	−0.535827	+	0.844328i	−0.378887	+	0.597030i
$2$	−0.535827	+	0.844328i	−0.378887	+	0.597030i
$3$	−2.18782	+	2.05450i	−1.26314	+	1.18617i	−0.289725	+	0.957110i	$0.593564\pi$
$3$	−2.18782	+	2.05450i	−1.26314	+	1.18617i	−0.973413	+	0.229056i	$0.926436\pi$
$4$	−0.425779	−	0.904827i	−0.212890	−	0.452414i
$5$	−1.46888	+	1.68594i	−0.656902	+	0.753976i
$5$	−1.46888	+	1.68594i	−0.656902	+	0.753976i
$6$	−0.562379	−	2.94809i	−0.229590	−	1.20355i
$7$	−1.60057	+	1.16288i	−0.604957	+	0.439527i	−0.847635	−	0.530580i	$-0.821974\pi$
$7$	−1.60057	+	1.16288i	−0.604957	+	0.439527i	0.242678	+	0.970107i	$0.421974\pi$
$8$	0.992115	+	0.125333i	0.350766	+	0.0443120i
$9$	0.377216	−	5.99567i	0.125739	−	1.99856i
$10$	−0.636423	−	2.14359i	−0.201255	−	0.677862i
$11$	0.783067	−	1.23392i	0.236104	−	0.372040i	−0.705530	−	0.708681i	$-0.749291\pi$
$11$	0.783067	−	1.23392i	0.236104	−	0.372040i	0.941633	+	0.336641i	$0.109291\pi$
$12$	2.79050	+	1.10484i	0.805547	+	0.318939i
$13$	−0.200535	+	3.18741i	−0.0556183	+	0.884028i	0.866999	+	0.498311i	$0.166046\pi$
$13$	−0.200535	+	3.18741i	−0.0556183	+	0.884028i	−0.922617	+	0.385718i	$0.873954\pi$
$14$	−0.124225	−	1.97450i	−0.0332006	−	0.527708i
$15$	−0.250126	−	6.70635i	−0.0645824	−	1.73157i
$16$	−0.637424	+	0.770513i	−0.159356	+	0.192628i
$17$	2.34881	−	4.99147i	0.569669	−	1.21061i	−0.387711	−	0.921781i	$-0.626734\pi$
$17$	2.34881	−	4.99147i	0.569669	−	1.21061i	0.957381	−	0.288828i	$-0.0932657\pi$
$18$	4.86019	+	3.53114i	1.14556	+	0.832297i
$19$	2.45104	+	2.30168i	0.562307	+	0.528042i	0.912737	−	0.408547i	$-0.133965\pi$
$19$	2.45104	+	2.30168i	0.562307	+	0.528042i	−0.350430	+	0.936589i	$0.613965\pi$
$20$	2.15090	+	0.611241i	0.480957	+	0.136678i
$21$	1.11262	−	5.83253i	0.242793	−	1.27276i
$22$	0.622242	+	1.32233i	0.132662	+	0.281922i
$23$	−7.35617	−	1.88874i	−1.53387	−	0.393830i	−0.615042	−	0.788495i	$-0.710861\pi$
$23$	−7.35617	−	1.88874i	−1.53387	−	0.393830i	−0.918825	+	0.394664i	$0.870861\pi$
$24$	−2.42807	+	1.76409i	−0.495627	+	0.360094i
$25$	−0.684797	−	4.95288i	−0.136959	−	0.990577i
$26$	−2.58377	−	1.87722i	−0.506718	−	0.368152i
$27$	5.75362	+	6.95493i	1.10728	+	1.33848i
$28$	1.73369	+	0.953105i	0.327637	+	0.180120i
$29$	−3.66521	−	2.01496i	−0.680612	−	0.374169i	0.103638	−	0.994615i	$-0.466952\pi$
$29$	−3.66521	−	2.01496i	−0.680612	−	0.374169i	−0.784249	+	0.620446i	$0.786952\pi$
$30$	5.79638	+	3.38225i	1.05827	+	0.617512i
$31$	−3.29000	+	6.99160i	−0.590901	+	1.25573i	0.356086	+	0.934453i	$0.384111\pi$
$31$	−3.29000	+	6.99160i	−0.590901	+	1.25573i	−0.946986	+	0.321274i	$0.895889\pi$
$32$	−0.309017	−	0.951057i	−0.0546270	−	0.168125i
$33$	0.821871	+	4.30840i	0.143069	+	0.749996i
$34$	2.95588	+	4.65773i	0.506930	+	0.798794i
$35$	0.390489	−	4.40659i	0.0660047	−	0.744849i
$36$	−5.58566	+	2.21152i	−0.930943	+	0.368586i
$37$	6.54860	−	7.91590i	1.07658	−	1.30137i	0.125615	−	0.992079i	$-0.459910\pi$
$37$	6.54860	−	7.91590i	1.07658	−	1.30137i	0.950969	−	0.309287i	$-0.100090\pi$
$38$	−3.25671	+	0.836180i	−0.528307	+	0.135646i
$39$	−6.10980	−	7.38548i	−0.978351	−	1.18262i
$40$	−1.66860	+	1.48855i	−0.263829	+	0.235360i
$41$	−3.10856	+	0.798142i	−0.485475	+	0.124649i	−0.483491	−	0.875349i	$-0.660632\pi$
$41$	−3.10856	+	0.798142i	−0.485475	+	0.124649i	−0.00198396	+	0.999998i	$0.500632\pi$
$42$	4.32840	+	4.06464i	0.667887	+	0.627187i
$43$	−2.07220	+	6.37757i	−0.316007	+	0.972570i	0.659331	+	0.751853i	$0.270840\pi$
$43$	−2.07220	+	6.37757i	−0.316007	+	0.972570i	−0.975338	+	0.220717i	$0.929160\pi$
$44$	−1.44989	−	0.183164i	−0.218580	−	0.0276131i
$45$	9.55427	+	9.44287i	1.42427	+	1.40766i
$46$	5.53635	−	5.19898i	0.816290	−	0.766548i
$47$	−10.2534	+	1.29530i	−1.49561	+	0.188939i	−0.830168	−	0.557513i	$-0.811756\pi$
$47$	−10.2534	+	1.29530i	−1.49561	+	0.188939i	−0.665439	+	0.746452i	$0.731756\pi$
$48$	−0.188450	−	2.99533i	−0.0272005	−	0.432339i
$49$	−0.953596	+	2.93487i	−0.136228	+	0.419267i
$50$	4.54879	+	2.07569i	0.643296	+	0.293547i
$51$	5.11621	+	15.7461i	0.716412	+	2.20489i
$52$	2.96944	−	1.17568i	0.411787	−	0.163038i
$53$	−0.799874	+	4.19308i	−0.109871	+	0.575964i	0.884189	+	0.467130i	$0.154712\pi$
$53$	−0.799874	+	4.19308i	−0.109871	+	0.575964i	−0.994060	+	0.108835i	$0.965288\pi$
$54$	−8.95518	+	1.13130i	−1.21865	+	0.153951i
$55$	0.930081	+	3.13268i	0.125412	+	0.422410i
$56$	−1.73369	+	0.953105i	−0.231674	+	0.127364i
$57$	−10.0912			−1.33662
$58$	3.66521	−	2.01496i	0.481265	−	0.264578i
$59$	−0.654806	−	0.259256i	−0.0852485	−	0.0337523i	0.325113	−	0.945675i	$-0.394598\pi$
$59$	−0.654806	−	0.259256i	−0.0852485	−	0.0337523i	−0.410362	+	0.911923i	$0.634598\pi$
$60$	−5.96158	+	3.08174i	−0.769637	+	0.397851i
$61$	−12.6415	−	3.24580i	−1.61858	−	0.415582i	−0.672655	−	0.739956i	$-0.734846\pi$
$61$	−12.6415	−	3.24580i	−1.61858	−	0.415582i	−0.945929	+	0.324375i	$0.894846\pi$
$62$	−4.14033	−	6.52412i	−0.525823	−	0.828564i
$63$	6.36848	+	10.0351i	0.802354	+	1.26431i
$64$	0.968583	+	0.248690i	0.121073	+	0.0310862i
$65$	−5.07922	−	5.02000i	−0.630000	−	0.622655i
$66$	−4.07808	−	1.61463i	−0.501977	−	0.198747i
$67$	1.60782	−	0.883909i	0.196427	−	0.107987i	−0.380505	−	0.924779i	$-0.624250\pi$
$67$	1.60782	−	0.883909i	0.196427	−	0.107987i	0.576932	+	0.816792i	$0.304250\pi$
$68$	−5.51649			−0.668973
$69$	19.9744	−	10.9810i	2.40463	−	1.32196i
$70$	3.51137	+	2.69087i	0.419689	+	0.321620i
$71$	−1.48986	+	0.188213i	−0.176814	+	0.0223368i	−0.213241	−	0.977000i	$-0.568402\pi$
$71$	−1.48986	+	0.188213i	−0.176814	+	0.0223368i	0.0364278	+	0.999336i	$0.488402\pi$
$72$	1.12570	−	5.90112i	0.132665	−	0.695453i
$73$	−2.98601	+	1.18224i	−0.349486	+	0.138371i	−0.536308	−	0.844023i	$-0.680181\pi$
$73$	−2.98601	+	1.18224i	−0.349486	+	0.138371i	0.186822	+	0.982394i	$0.440181\pi$
$74$	3.17470	+	9.77072i	0.369051	+	1.13582i
$75$	11.6739	+	9.42910i	1.34799	+	1.08878i
$76$	1.03902	−	3.19778i	0.119184	−	0.366810i
$77$	0.181545	+	2.88558i	0.0206890	+	0.328842i
$78$	9.50956	−	1.20134i	1.07675	−	0.136025i
$79$	6.64219	−	6.23743i	0.747305	−	0.701766i	−0.214128	−	0.976806i	$-0.568691\pi$
$79$	6.64219	−	6.23743i	0.747305	−	0.701766i	0.961433	+	0.275040i	$0.0886910\pi$
$80$	−0.362742	−	2.20645i	−0.0405558	−	0.246689i
$81$	−8.99630	−	1.13650i	−0.999589	−	0.126278i
$82$	0.991755	−	3.05231i	0.109521	−	0.337071i
$83$	6.96809	+	6.54347i	0.764847	+	0.718239i	0.965208	−	0.261483i	$-0.0842115\pi$
$83$	6.96809	+	6.54347i	0.764847	+	0.718239i	−0.200361	+	0.979722i	$0.564212\pi$
$84$	−5.75116	+	1.47665i	−0.627503	+	0.161115i
$85$	4.96522	+	11.2918i	0.538553	+	1.22477i
$86$	−4.27442	−	5.16689i	−0.460923	−	0.557160i
$87$	12.1586	−	3.12179i	1.30353	−	0.334691i
$88$	0.931543	−	1.12604i	0.0993028	−	0.120037i
$89$	8.47797	−	3.35667i	0.898663	−	0.355806i	0.127049	−	0.991896i	$-0.459450\pi$
$89$	8.47797	−	3.35667i	0.898663	−	0.355806i	0.771614	+	0.636091i	$0.219450\pi$
$90$	−13.0923	+	3.00719i	−1.38005	+	0.316986i
$91$	−3.38560	−	5.33485i	−0.354908	−	0.559245i
$92$	1.42312	+	7.46025i	0.148370	+	0.777785i
$93$	−7.16631	−	22.0556i	−0.743112	−	2.28706i
$94$	4.40037	−	9.35126i	0.453864	−	0.964509i
$95$	−7.48078	+	0.751424i	−0.767511	+	0.0770945i
$96$	2.63002	+	1.44587i	0.268425	+	0.147568i
$97$	5.39580	+	2.96636i	0.547860	+	0.301189i	0.731541	−	0.681797i	$-0.238801\pi$
$97$	5.39580	+	2.96636i	0.547860	+	0.301189i	−0.183681	+	0.982986i	$0.558801\pi$
$98$	−1.96703	−	2.37773i	−0.198700	−	0.240187i
$99$	−7.10277	−	5.16047i	−0.713856	−	0.518646i
$100$	−4.18993	+	2.72846i	−0.418993	+	0.272846i
$101$	2.66503	−	1.93626i	0.265180	−	0.192665i	−0.447247	−	0.894410i	$-0.647596\pi$
$101$	2.66503	−	1.93626i	0.265180	−	0.192665i	0.712428	+	0.701746i	$0.247596\pi$
$102$	−16.0362	−	4.11741i	−1.58782	−	0.407684i
$103$	−8.29923	−	17.6368i	−0.817748	−	1.73780i	−0.661307	−	0.750115i	$-0.729998\pi$
$103$	−8.29923	−	17.6368i	−0.817748	−	1.73780i	−0.156441	−	0.987687i	$-0.550002\pi$
$104$	−0.598442	+	3.13714i	−0.0586820	+	0.307622i
$105$	8.19901	+	10.4431i	0.800142	+	1.01914i
$106$	−3.11174	−	2.92212i	−0.302239	−	0.283822i
$107$	−9.94219	−	7.22343i	−0.961148	−	0.698315i	−0.00773111	−	0.999970i	$-0.502461\pi$
$107$	−9.94219	−	7.22343i	−0.961148	−	0.698315i	−0.953417	+	0.301655i	$0.902461\pi$
$108$	3.84324	−	8.16729i	0.369816	−	0.785898i
$109$	−8.20766	+	9.92136i	−0.786152	+	0.950294i	−0.999645	−	0.0266505i	$-0.991516\pi$
$109$	−8.20766	+	9.92136i	−0.786152	+	0.950294i	0.213493	+	0.976945i	$0.431516\pi$
$110$	−3.14337	−	0.893279i	−0.299709	−	0.0851708i
$111$	1.93605	+	30.7727i	0.183762	+	2.92081i
$112$	0.124225	−	1.97450i	0.0117382	−	0.186573i
$113$	1.56395	+	0.619211i	0.147124	+	0.0582505i	0.440533	−	0.897737i	$-0.354790\pi$
$113$	1.56395	+	0.619211i	0.147124	+	0.0582505i	−0.293409	+	0.955987i	$0.594790\pi$
$114$	5.40715	−	8.52031i	0.506426	−	0.798000i
$115$	13.9896	−	9.62774i	1.30454	−	0.897791i
$116$	−0.262625	+	4.17431i	−0.0243841	+	0.387575i
$117$	19.0350	+	2.40468i	1.75979	+	0.222313i
$118$	0.569760	−	0.413955i	0.0524507	−	0.0381076i
$119$	2.04506	+	10.7206i	0.187470	+	0.982752i
$120$	0.592374	−	6.68481i	0.0540761	−	0.610237i
$121$	3.77422	+	8.02062i	0.343111	+	0.729147i
$122$	9.51419	−	8.93442i	0.861375	−	0.808885i
$123$	5.16118	−	8.13272i	0.465368	−	0.733303i
$124$	7.72700			0.693905
$125$	9.35615	+	6.12065i	0.836840	+	0.547448i
$126$	−11.8853			−1.05883
$127$	−5.65944	+	8.91785i	−0.502194	+	0.791331i	−0.996978	−	0.0776847i	$-0.975247\pi$
$127$	−5.65944	+	8.91785i	−0.502194	+	0.791331i	0.494784	+	0.869016i	$0.335247\pi$
$128$	−0.728969	+	0.684547i	−0.0644323	+	0.0605060i
$129$	−8.56912	−	18.2103i	−0.754469	−	1.60333i
$130$	6.96011	−	1.59868i	0.610442	−	0.140213i
$131$	−2.62654	−	13.7688i	−0.229482	−	1.20299i	−0.891332	−	0.453351i	$-0.850228\pi$
$131$	−2.62654	−	13.7688i	−0.229482	−	1.20299i	0.661850	−	0.749637i	$-0.269772\pi$
$132$	3.54842	−	2.57808i	0.308850	−	0.224393i
$133$	−6.59963	−	0.833727i	−0.572260	−	0.0722933i
$134$	−0.115206	+	1.83115i	−0.00995231	+	0.158187i
$135$	−20.1770	−	0.515677i	−1.73656	−	0.0443824i
$136$	2.95588	−	4.65773i	0.253465	−	0.399397i
$137$	−12.9506	−	5.12752i	−1.10645	−	0.438074i	−0.257355	−	0.966317i	$-0.582851\pi$
$137$	−12.9506	−	5.12752i	−1.10645	−	0.438074i	−0.849093	+	0.528243i	$0.822851\pi$
$138$	−1.43124	+	22.7489i	−0.121835	+	1.93651i
$139$	1.21224	+	19.2680i	0.102821	+	1.63429i	0.624415	+	0.781093i	$0.285337\pi$
$139$	1.21224	+	19.2680i	0.102821	+	1.63429i	−0.521595	+	0.853194i	$0.674663\pi$
$140$	−4.15346	+	1.52291i	−0.351032	+	0.128709i
$141$	19.7713	−	23.8994i	1.66505	−	2.01270i
$142$	0.639393	−	1.35878i	0.0536566	−	0.114026i
$143$	3.77596	+	2.74340i	0.315762	+	0.229414i
$144$	4.37930	+	4.11244i	0.364942	+	0.342703i
$145$	8.78085	−	3.21959i	0.729210	−	0.267372i
$146$	0.601781	−	3.15465i	0.0498038	−	0.261081i
$147$	−3.94339	−	8.38013i	−0.325245	−	0.691181i
$148$	−9.95078	−	2.55493i	−0.817949	−	0.210014i
$149$	−8.57115	+	6.22730i	−0.702176	+	0.510161i	−0.880640	−	0.473786i	$-0.842887\pi$
$149$	−8.57115	+	6.22730i	−0.702176	+	0.510161i	0.178464	+	0.983946i	$0.442887\pi$
$150$	−14.2164	+	4.80424i	−1.16077	+	0.392265i
$151$	5.92190	+	4.30251i	0.481918	+	0.350134i	0.802068	−	0.597233i	$-0.203733\pi$
$151$	5.92190	+	4.30251i	0.481918	+	0.350134i	−0.320150	+	0.947367i	$0.603733\pi$
$152$	2.14324	+	2.59073i	0.173839	+	0.210136i
$153$	−29.0412	−	15.9655i	−2.34784	−	1.29074i
$154$	−2.53365	−	1.39289i	−0.204167	−	0.112242i
$155$	−6.95482	−	15.8165i	−0.558625	−	1.27041i
$156$	−4.08115	+	8.67289i	−0.326754	+	0.694387i
$157$	1.18983	+	3.66193i	0.0949592	+	0.292254i	0.987243	−	0.159221i	$-0.0508981\pi$
$157$	1.18983	+	3.66193i	0.0949592	+	0.292254i	−0.892284	+	0.451475i	$0.850898\pi$
$158$	1.70737	+	8.95037i	0.135831	+	0.712053i
$159$	−6.86471	−	10.8171i	−0.544407	−	0.857848i
$160$	2.05733	+	0.876001i	0.162647	+	0.0692540i
$161$	13.9704	−	5.53128i	1.10102	−	0.435926i
$162$	5.78004	−	6.98687i	0.454123	−	0.548940i
$163$	5.22750	−	1.34219i	0.409449	−	0.105129i	−0.0383466	−	0.999264i	$-0.512209\pi$
$163$	5.22750	−	1.34219i	0.409449	−	0.105129i	0.447796	+	0.894136i	$0.352209\pi$
$164$	2.04574	+	2.47288i	0.159745	+	0.193099i
$165$	−8.47094	−	4.94288i	−0.659461	−	0.384803i
$166$	−9.25852	+	2.37718i	−0.718601	+	0.184505i
$167$	2.70584	+	2.54096i	0.209384	+	0.196625i	0.782143	−	0.623099i	$-0.214127\pi$
$167$	2.70584	+	2.54096i	0.209384	+	0.196625i	−0.572758	+	0.819724i	$0.694127\pi$
$168$	1.83485	−	5.64709i	0.141562	−	0.435683i
$169$	2.77813	+	0.350959i	0.213702	+	0.0269969i
$170$	−12.1945	−	1.85818i	−0.935274	−	0.142516i
$171$	14.7247	−	13.8274i	1.12603	−	1.05741i
$172$	6.65290	−	0.840456i	0.507279	−	0.0640842i
$173$	1.19870	+	19.0527i	0.0911352	+	1.44855i	0.732212	+	0.681077i	$0.238488\pi$
$173$	1.19870	+	19.0527i	0.0911352	+	1.44855i	−0.641077	+	0.767477i	$0.721512\pi$
$174$	−3.87907	+	11.9385i	−0.294071	+	0.905059i
$175$	6.85567	+	7.13108i	0.518240	+	0.539059i
$176$	0.451603	+	1.38989i	0.0340409	+	0.104767i
$177$	1.96524	−	0.778094i	0.147717	−	0.0584851i
$178$	−1.70860	+	8.95678i	−0.128065	+	0.671339i
$179$	−13.0341	+	1.64659i	−0.974216	+	0.123072i	−0.596295	−	0.802766i	$-0.703361\pi$
$179$	−13.0341	+	1.64659i	−0.974216	+	0.123072i	−0.377921	+	0.925838i	$0.623361\pi$
$180$	4.47616	−	12.6655i	0.333633	−	0.944034i
$181$	−6.30787	+	3.46778i	−0.468860	+	0.257758i	−0.698625	−	0.715488i	$-0.746204\pi$
$181$	−6.30787	+	3.46778i	−0.468860	+	0.257758i	0.229765	+	0.973246i	$0.426204\pi$
$182$	6.31846			0.468356
$183$	34.3259	−	18.8708i	2.53744	−	1.39497i
$184$	−7.06144	−	2.79582i	−0.520576	−	0.206111i
$185$	3.72665	+	22.6680i	0.273989	+	1.66659i
$186$	22.4621	+	5.76729i	1.64700	+	0.422878i
$187$	−4.31978	−	6.80689i	−0.315894	−	0.497769i
$188$	5.53770	+	8.72601i	0.403878	+	0.636410i
$189$	−17.2968	−	4.44106i	−1.25816	−	0.323039i
$190$	3.37395	−	6.71886i	0.244772	−	0.487437i
$191$	−6.24752	−	2.47357i	−0.452055	−	0.178981i	0.131054	−	0.991375i	$-0.458164\pi$
$191$	−6.24752	−	2.47357i	−0.452055	−	0.178981i	−0.583109	+	0.812394i	$0.698164\pi$
$192$	−2.63002	+	1.44587i	−0.189805	+	0.104346i
$193$	−23.4714			−1.68951			−0.844756	−	0.535152i	$-0.820254\pi$
$193$	−23.4714			−1.68951			−0.844756	+	0.535152i	$0.820254\pi$
$194$	−5.39580	+	2.96636i	−0.387396	+	0.212973i
$195$	21.4260	+	0.547600i	1.53435	+	0.0392145i
$196$	3.06157	−	0.386766i	0.218683	−	0.0276261i
$197$	−1.29639	+	6.79592i	−0.0923641	+	0.484189i	0.905805	+	0.423696i	$0.139267\pi$
$197$	−1.29639	+	6.79592i	−0.0923641	+	0.484189i	−0.998169	+	0.0604936i	$0.980733\pi$
$198$	8.16298	−	3.23195i	0.580118	−	0.229685i
$199$	−1.89349	−	5.82757i	−0.134226	−	0.413106i	0.861243	−	0.508194i	$-0.169687\pi$
$199$	−1.89349	−	5.82757i	−0.134226	−	0.413106i	−0.995469	+	0.0950883i	$0.969687\pi$
$200$	−0.0586364	−	4.99966i	−0.00414622	−	0.353529i
$201$	−1.70164	+	5.23711i	−0.120024	+	0.369397i
$202$	0.206842	+	3.28766i	0.0145533	+	0.231319i
$203$	8.20956	−	1.03711i	0.576198	−	0.0727908i
$204$	12.0691	−	11.3336i	0.845005	−	0.793513i
$205$	3.22047	−	6.41322i	0.224927	−	0.447919i
$206$	19.3382	+	2.44298i	1.34735	+	0.170210i
$207$	−14.0991	+	43.3927i	−0.979959	+	3.01600i
$208$	−2.32812	−	2.18625i	−0.161426	−	0.151589i
$209$	4.75941	−	1.22201i	0.329215	−	0.0845281i
$210$	−13.2106	+	1.32697i	−0.911620	+	0.0915699i
$211$	11.7092	+	14.1540i	0.806095	+	0.974401i	0.999978	−	0.00662333i	$-0.00210829\pi$
$211$	11.7092	+	14.1540i	0.806095	+	0.974401i	−0.193883	+	0.981025i	$0.562108\pi$
$212$	4.13459	−	1.06158i	0.283964	−	0.0729097i
$213$	2.87286	−	3.47269i	0.196845	−	0.237945i
$214$	11.4262	−	4.52397i	0.781081	−	0.309252i
$215$	−7.70840	−	12.8615i	−0.525709	−	0.877145i
$216$	4.83656	+	7.62120i	0.329086	+	0.518557i
$217$	−2.86453	−	15.0164i	−0.194457	−	1.01938i
$218$	−3.97900	−	12.2461i	−0.269492	−	0.829410i
$219$	4.10393	−	8.72129i	0.277318	−	0.589330i
$220$	2.43852	−	2.17539i	0.164405	−	0.146665i
$221$	15.4388	+	8.48757i	1.03853	+	0.570936i
$222$	−27.0196	−	14.8542i	−1.81344	−	0.996946i
$223$	15.1623	+	18.3281i	1.01534	+	1.22734i	0.973612	+	0.228210i	$0.0732872\pi$
$223$	15.1623	+	18.3281i	1.01534	+	1.22734i	0.0417309	+	0.999129i	$0.486713\pi$
$224$	1.60057	+	1.16288i	0.106942	+	0.0776981i
$225$	−29.9542	+	2.23751i	−1.99695	+	0.149168i
$226$	−1.36082	+	0.988696i	−0.0905206	+	0.0657671i
$227$	2.60271	+	0.668263i	0.172748	+	0.0443542i	0.334073	−	0.942547i	$-0.391577\pi$
$227$	2.60271	+	0.668263i	0.172748	+	0.0443542i	−0.161325	+	0.986901i	$0.551577\pi$
$228$	4.29664	+	9.13082i	0.284552	+	0.604704i
$229$	−3.39596	+	17.8023i	−0.224411	+	1.17641i	0.674500	+	0.738275i	$0.264359\pi$
$229$	−3.39596	+	17.8023i	−0.224411	+	1.17641i	−0.898911	+	0.438131i	$0.855641\pi$
$230$	0.632953	+	16.9706i	0.0417357	+	1.11901i
$231$	−6.32560	−	5.94014i	−0.416194	−	0.390832i
$232$	−3.38376	−	2.45845i	−0.222155	−	0.161405i
$233$	−9.14520	+	19.4345i	−0.599122	+	1.27320i	0.343443	+	0.939174i	$0.388407\pi$
$233$	−9.14520	+	19.4345i	−0.599122	+	1.27320i	−0.942564	+	0.334025i	$0.891593\pi$
$234$	−12.2298	+	14.7833i	−0.799488	+	0.966415i
$235$	12.8771	−	19.1892i	0.840012	−	1.25177i
$236$	0.0442210	+	0.702873i	0.00287854	+	0.0457531i
$237$	−1.71712	+	27.2928i	−0.111539	+	1.77286i
$238$	−10.1475	−	4.01766i	−0.657762	−	0.260426i
$239$	−5.47702	+	8.63040i	−0.354279	+	0.558254i	−0.973994	−	0.226572i	$-0.927248\pi$
$239$	−5.47702	+	8.63040i	−0.354279	+	0.558254i	0.619715	+	0.784827i	$0.287248\pi$
$240$	5.32676	+	4.08206i	0.343841	+	0.263496i
$241$	0.956346	−	15.2007i	0.0616036	−	0.979162i	−0.838892	−	0.544297i	$-0.816796\pi$
$241$	0.956346	−	15.2007i	0.0616036	−	0.979162i	0.900496	−	0.434864i	$-0.143204\pi$
$242$	−8.79436	−	1.11099i	−0.565323	−	0.0714169i
$243$	0.109806	−	0.0797789i	0.00704408	−	0.00511782i
$244$	2.44562	+	12.8204i	0.156565	+	0.820742i
$245$	−3.54730	−	5.91867i	−0.226629	−	0.378130i
$246$	4.10119	+	8.71546i	0.261482	+	0.555678i
$247$	−7.82791	+	7.35090i	−0.498078	+	0.467727i
$248$	−4.14033	+	6.52412i	−0.262911	+	0.414282i
$249$	−28.6885			−1.81806
$250$	−10.1811	+	4.62005i	−0.643910	+	0.292198i
$251$	3.43912			0.217075			0.108538	−	0.994092i	$-0.465383\pi$
$251$	3.43912			0.217075			0.108538	+	0.994092i	$0.465383\pi$
$252$	6.36848	−	10.0351i	0.401177	−	0.632153i
$253$	−8.09092	+	7.59788i	−0.508672	+	0.477675i
$254$	−4.49711	−	9.55685i	−0.282174	−	0.599650i
$255$	−34.0620	−	14.5034i	−2.13305	−	0.908239i
$256$	−0.187381	−	0.982287i	−0.0117113	−	0.0613930i
$257$	0.448214	−	0.325647i	0.0279588	−	0.0203133i	−0.573718	−	0.819053i	$-0.694499\pi$
$257$	0.448214	−	0.325647i	0.0279588	−	0.0203133i	0.601677	+	0.798740i	$0.294499\pi$
$258$	19.9670	+	2.52242i	1.24309	+	0.157039i
$259$	−1.27623	+	20.2851i	−0.0793013	+	1.26046i
$260$	−2.37961	+	6.73323i	−0.147577	+	0.417577i
$261$	−13.4636	+	21.2153i	−0.833378	+	1.31319i
$262$	13.0328	+	5.16004i	0.805168	+	0.318788i
$263$	0.641766	−	10.2006i	0.0395730	−	0.628994i	−0.927393	−	0.374089i	$-0.877956\pi$
$263$	0.641766	−	10.2006i	0.0395730	−	0.628994i	0.966966	−	0.254906i	$-0.0820445\pi$
$264$	0.275405	+	4.37743i	0.0169500	+	0.269412i
$265$	−5.89438	−	7.50767i	−0.362089	−	0.461192i
$266$	4.24019	−	5.12552i	0.259983	−	0.314265i
$267$	−11.6520	+	24.7618i	−0.713091	+	1.51540i
$268$	−1.48436	−	1.07845i	−0.0906719	−	0.0658770i
$269$	4.22751	+	3.96990i	0.257756	+	0.242049i	0.802642	−	0.596461i	$-0.203427\pi$
$269$	4.22751	+	3.96990i	0.257756	+	0.242049i	−0.544886	+	0.838510i	$0.683427\pi$
$270$	11.2468	−	16.7597i	0.684456	−	1.01996i
$271$	2.09540	−	10.9845i	0.127286	−	0.667258i	−0.860251	−	0.509871i	$-0.829693\pi$
$271$	2.09540	−	10.9845i	0.127286	−	0.667258i	0.987537	−	0.157387i	$-0.0503070\pi$
$272$	2.34881	+	4.99147i	0.142417	+	0.302652i
$273$	18.3675	+	4.71598i	1.11165	+	0.285424i
$274$	11.2686	−	8.18712i	0.680762	−	0.494602i
$275$	−6.64769	−	3.03346i	−0.400871	−	0.182924i
$276$	−18.4406	−	13.3979i	−1.10999	−	0.806458i
$277$	17.5872	+	21.2592i	1.05671	+	1.27734i	0.959388	+	0.282091i	$0.0910281\pi$
$277$	17.5872	+	21.2592i	1.05671	+	1.27734i	0.0973235	+	0.995253i	$0.468972\pi$
$278$	−16.9180	−	9.30076i	−1.01468	−	0.557822i
$279$	40.6783	+	22.3631i	2.43535	+	1.33884i
$280$	0.939702	−	4.32290i	0.0561579	−	0.258343i
$281$	3.40146	−	7.22848i	0.202914	−	0.431215i	−0.777306	−	0.629122i	$-0.783415\pi$
$281$	3.40146	−	7.22848i	0.202914	−	0.431215i	0.980221	+	0.197907i	$0.0634145\pi$
$282$	9.58495	+	29.4994i	0.570775	+	1.75667i
$283$	−0.806096	−	4.22571i	−0.0479175	−	0.251192i	0.950266	−	0.311439i	$-0.100811\pi$
$283$	−0.806096	−	4.22571i	−0.0479175	−	0.251192i	−0.998183	+	0.0602472i	$0.980811\pi$
$284$	0.804651	+	1.26793i	0.0477472	+	0.0752376i
$285$	14.8228	−	17.0132i	0.878026	−	1.00778i
$286$	−4.33959	+	1.71817i	−0.256605	+	0.101597i
$287$	4.04731	−	4.89236i	0.238905	−	0.288787i
$288$	−5.81879	+	1.49401i	−0.342876	+	0.0880355i
$289$	−8.56167	−	10.3493i	−0.503627	−	0.608781i
$290$	−1.98663	+	9.13906i	−0.116659	+	0.536664i
$291$	−17.8994	+	4.59579i	−1.04928	+	0.269410i
$292$	2.34111	+	2.19845i	0.137003	+	0.128654i
$293$	7.42128	−	22.8404i	0.433556	−	1.33435i	−0.461003	−	0.887399i	$-0.652510\pi$
$293$	7.42128	−	22.8404i	0.433556	−	1.33435i	0.894559	−	0.446950i	$-0.147490\pi$
$294$	9.18855	+	1.16078i	0.535887	+	0.0676983i
$295$	1.39892	−	0.723150i	0.0814484	−	0.0421034i
$296$	7.48909	−	7.03272i	0.435294	−	0.408769i
$297$	13.0873	−	1.65331i	0.759400	−	0.0959346i
$298$	−0.665235	−	10.5736i	−0.0385361	−	0.612513i
$299$	7.49536	−	23.0684i	0.433468	−	1.33408i
$300$	3.56120	−	14.5776i	0.205606	−	0.841637i
$301$	−4.09965	−	12.6174i	−0.236300	−	0.727257i
$302$	−6.80585	+	2.69463i	−0.391632	+	0.155058i
$303$	−1.85256	+	9.71148i	−0.106427	+	0.557910i
$304$	−3.33583	+	0.421413i	−0.191323	+	0.0241697i
$305$	24.0411	−	16.5452i	1.37659	−	0.947377i
$306$	29.0412	−	15.9655i	1.66018	−	0.912689i
$307$	−9.84208			−0.561717			−0.280858	−	0.959749i	$-0.590619\pi$
$307$	−9.84208			−0.561717			−0.280858	+	0.959749i	$0.590619\pi$
$308$	2.53365	−	1.39289i	0.144368	−	0.0793670i
$309$	54.3920	+	21.5353i	3.09425	+	1.22510i
$310$	17.0809	+	2.60278i	0.970131	+	0.147828i
$311$	−31.1387	−	7.99505i	−1.76571	−	0.453358i	−0.780566	−	0.625074i	$-0.785069\pi$
$311$	−31.1387	−	7.99505i	−1.76571	−	0.453358i	−0.985147	+	0.171716i	$0.945069\pi$
$312$	−5.13597	−	8.09300i	−0.290767	−	0.458176i
$313$	−2.58650	−	4.07567i	−0.146198	−	0.230371i	0.763335	−	0.646003i	$-0.223560\pi$
$313$	−2.58650	−	4.07567i	−0.146198	−	0.230371i	−0.909533	+	0.415632i	$0.863560\pi$
$314$	−3.72942	−	0.957552i	−0.210463	−	0.0540378i
$315$	−26.2732	−	4.00348i	−1.48032	−	0.225571i
$316$	−8.47190	−	3.35426i	−0.476582	−	0.188692i
$317$	7.84761	−	4.31426i	0.440766	−	0.242313i	−0.245887	−	0.969298i	$-0.579079\pi$
$317$	7.84761	−	4.31426i	0.440766	−	0.242313i	0.686653	+	0.726985i	$0.259079\pi$
$318$	12.8114			0.718430
$319$	−5.35640	+	2.94470i	−0.299901	+	0.164872i
$320$	−1.84201	+	1.26768i	−0.102971	+	0.0708654i
$321$	36.5923	−	4.62268i	2.04238	−	0.258013i
$322$	−2.81551	+	14.7594i	−0.156902	+	0.822510i
$323$	17.2458	−	6.82809i	0.959581	−	0.379925i
$324$	2.80211	+	8.62400i	0.155673	+	0.479111i
$325$	15.9242	−	1.18950i	0.883315	−	0.0659818i
$326$	−1.66778	+	5.13291i	−0.0923699	+	0.284285i
$327$	−2.42654	−	38.5688i	−0.134188	−	2.13286i
$328$	−3.18408	+	0.402243i	−0.175811	+	0.0222101i
$329$	14.9049	−	13.9966i	0.821734	−	0.771660i
$330$	8.71237	−	4.50372i	0.479600	−	0.247922i
$331$	5.18268	+	0.654725i	0.284866	+	0.0359869i	0.266468	−	0.963844i	$-0.414143\pi$
$331$	5.18268	+	0.654725i	0.284866	+	0.0359869i	0.0183981	+	0.999831i	$0.494143\pi$
$332$	2.95384	−	9.09099i	0.162113	−	0.498933i
$333$	−44.9909	−	42.2493i	−2.46549	−	2.31525i
$334$	−3.59526	+	0.923106i	−0.196724	+	0.0505101i
$335$	−0.871478	+	4.00905i	−0.0476139	+	0.219038i
$336$	3.78484	+	4.57508i	0.206480	+	0.249591i
$337$	−19.4103	+	4.98371i	−1.05735	+	0.271480i	−0.737051	−	0.675838i	$-0.763782\pi$
$337$	−19.4103	+	4.98371i	−1.05735	+	0.271480i	−0.320295	+	0.947318i	$0.603782\pi$
$338$	−1.78492	+	2.15760i	−0.0970869	+	0.117358i
$339$	−4.69381	+	1.85841i	−0.254933	+	0.100935i
$340$	8.10305	−	9.30048i	0.439450	−	0.504389i
$341$	6.05076	+	9.53447i	0.327667	+	0.516320i
$342$	3.78498	+	19.8416i	0.204668	+	1.07291i
$343$	−6.16613	−	18.9774i	−0.332940	−	1.02468i
$344$	−2.85518	+	6.06757i	−0.153941	+	0.327141i
$345$	−10.8266	+	49.8054i	−0.582884	+	2.68143i
$346$	−16.7291	−	9.19688i	−0.899360	−	0.494427i
$347$	−16.7954	−	9.23337i	−0.901626	−	0.495673i	−0.0376984	−	0.999289i	$-0.512003\pi$
$347$	−16.7954	−	9.23337i	−0.901626	−	0.495673i	−0.863928	+	0.503616i	$0.832003\pi$
$348$	−8.00154	−	9.67220i	−0.428927	−	0.518484i
$349$	−2.56293	−	1.86208i	−0.137190	−	0.0996747i	0.517073	−	0.855941i	$-0.327021\pi$
$349$	−2.56293	−	1.86208i	−0.137190	−	0.0996747i	−0.654264	+	0.756266i	$0.727021\pi$
$350$	−9.69442	+	1.96741i	−0.518188	+	0.105162i
$351$	−23.3220	+	16.9444i	−1.24484	+	0.904426i
$352$	−1.41551	−	0.363440i	−0.0754467	−	0.0193714i
$353$	14.9471	+	31.7643i	0.795556	+	1.69064i	0.720491	+	0.693465i	$0.243917\pi$
$353$	14.9471	+	31.7643i	0.795556	+	1.69064i	0.0750658	+	0.997179i	$0.476083\pi$
$354$	−0.396062	+	2.07623i	−0.0210505	+	0.110350i
$355$	1.87110	−	2.78828i	0.0993079	−	0.147986i
$356$	−6.64695	−	6.24190i	−0.352288	−	0.330820i
$357$	−26.4996	−	19.2531i	−1.40251	−	1.01898i
$358$	5.59377	−	11.8874i	0.295640	−	0.628266i
$359$	1.74653	−	2.11119i	0.0921782	−	0.111424i	−0.722407	−	0.691468i	$-0.756964\pi$
$359$	1.74653	−	2.11119i	0.0921782	−	0.111424i	0.814586	+	0.580043i	$0.196964\pi$
$360$	8.29543	+	10.5659i	0.437207	+	0.556871i
$361$	−0.483152	−	7.67949i	−0.0254291	−	0.404184i
$362$	0.451982	−	7.18404i	0.0237556	−	0.377585i
$363$	−24.7357	−	9.79354i	−1.29829	−	0.514028i
$364$	−3.38560	+	5.33485i	−0.177454	+	0.279622i
$365$	2.39289	−	6.77081i	0.125249	−	0.354400i
$366$	−2.45957	+	39.0938i	−0.128564	+	2.04347i
$367$	−9.10967	−	1.15082i	−0.475521	−	0.0600723i	−0.116080	−	0.993240i	$-0.537033\pi$
$367$	−9.10967	−	1.15082i	−0.475521	−	0.0600723i	−0.359441	+	0.933168i	$0.617033\pi$
$368$	6.14430	−	4.46409i	0.320294	−	0.232707i
$369$	3.61280	+	18.9390i	0.188075	+	0.985924i
$370$	−21.1361	−	8.99963i	−1.09881	−	0.467869i
$371$	−3.59580	−	7.64146i	−0.186685	−	0.396725i
$372$	−16.9053	+	15.8751i	−0.876498	+	0.823086i
$373$	14.2856	−	22.5105i	0.739679	−	1.16555i	−0.241114	−	0.970497i	$-0.577513\pi$
$373$	14.2856	−	22.5105i	0.739679	−	1.16555i	0.980793	−	0.195051i	$-0.0624874\pi$
$374$	8.06190			0.416871
$375$	−33.0445	+	5.83133i	−1.70641	+	0.301129i
$376$	−10.3349			−0.532980
$377$	7.15751	−	11.2784i	0.368631	−	0.580869i
$378$	13.0178	−	12.2245i	0.669563	−	0.628761i
$379$	−7.94153	−	16.8766i	−0.407929	−	0.866894i	−0.998216	−	0.0597003i	$-0.980986\pi$
$379$	−7.94153	−	16.8766i	−0.407929	−	0.866894i	0.590287	−	0.807193i	$-0.299014\pi$
$380$	3.86507	+	6.44887i	0.198274	+	0.330820i
$381$	−5.93989	−	31.1380i	−0.304310	−	1.59525i
$382$	5.43609	−	3.94955i	0.278135	−	0.202077i
$383$	11.8256	+	1.49393i	0.604262	+	0.0763361i	0.421511	−	0.906823i	$-0.361500\pi$
$383$	11.8256	+	1.49393i	0.604262	+	0.0763361i	0.182751	+	0.983159i	$0.441500\pi$
$384$	0.188450	−	2.99533i	0.00961682	−	0.152855i
$385$	−5.13158	−	3.93248i	−0.261530	−	0.200418i
$386$	12.5766	−	19.8176i	0.640134	−	1.00869i
$387$	37.4562	+	14.8299i	1.90400	+	0.753848i
$388$	0.386628	−	6.14528i	0.0196281	−	0.311979i
$389$	0.798193	+	12.6869i	0.0404700	+	0.643252i	0.965018	+	0.262185i	$0.0844432\pi$
$389$	0.798193	+	12.6869i	0.0404700	+	0.643252i	−0.924548	+	0.381067i	$0.875557\pi$
$390$	−11.9430	+	17.7972i	−0.604757	+	0.901195i
$391$	−26.7058	+	32.2818i	−1.35057	+	1.63256i
$392$	−1.31391	+	2.79221i	−0.0663626	+	0.141028i
$393$	34.0345	+	24.7275i	1.71681	+	1.24734i
$394$	−5.04335	−	4.73602i	−0.254080	−	0.238597i
$395$	0.759380	+	20.3604i	0.0382086	+	1.02444i
$396$	−1.64512	+	8.62400i	−0.0826702	+	0.433372i
$397$	−6.15580	−	13.0817i	−0.308951	−	0.656553i	0.688701	−	0.725045i	$-0.258181\pi$
$397$	−6.15580	−	13.0817i	−0.308951	−	0.656553i	−0.997652	+	0.0684921i	$0.978181\pi$
$398$	5.93497	+	1.52384i	0.297493	+	0.0763832i
$399$	16.1517	−	11.7349i	0.808596	−	0.587479i
$400$	4.25277	+	2.62944i	0.212638	+	0.131472i
$401$	3.28681	+	2.38801i	0.164135	+	0.119251i	0.666821	−	0.745218i	$-0.267655\pi$
$401$	3.28681	+	2.38801i	0.164135	+	0.119251i	−0.502685	+	0.864469i	$0.667655\pi$
$402$	−3.51005	−	4.24292i	−0.175065	−	0.211618i
$403$	−21.6253	−	11.8886i	−1.07723	−	0.592214i
$404$	−2.88669	−	1.58697i	−0.143618	−	0.0789548i
$405$	15.1305	−	13.4979i	0.751843	−	0.670714i
$406$	−3.52324	+	7.48727i	−0.174856	+	0.371587i
$407$	−4.63956	−	14.2791i	−0.229975	−	0.707789i
$408$	3.10236	+	16.2631i	0.153590	+	0.805145i
$409$	8.26207	+	13.0189i	0.408533	+	0.643745i	0.984835	−	0.173491i	$-0.0555049\pi$
$409$	8.26207	+	13.0189i	0.408533	+	0.643745i	−0.576302	+	0.817237i	$0.695505\pi$
$410$	3.68925	+	6.15551i	0.182199	+	0.303999i
$411$	38.8682	−	15.3890i	1.91723	−	0.759083i
$412$	−12.4246	+	15.0187i	−0.612115	+	0.739920i
$413$	1.34954	−	0.346504i	0.0664067	−	0.0170504i
$414$	−29.0830	−	35.1553i	−1.42935	−	1.72779i
$415$	−21.2672	+	2.13623i	−1.04396	+	0.104863i
$416$	3.09337	−	0.794244i	0.151665	−	0.0389410i
$417$	−42.2382	−	39.6643i	−2.06841	−	1.94237i
$418$	−1.51844	+	4.67329i	−0.0742695	+	0.228578i
$419$	−7.05265	−	0.890957i	−0.344545	−	0.0435261i	−0.0488430	−	0.998806i	$-0.515553\pi$
$419$	−7.05265	−	0.890957i	−0.344545	−	0.0435261i	−0.295702	+	0.955280i	$0.595553\pi$
$420$	5.95821	−	11.8651i	0.290731	−	0.578959i
$421$	−26.5102	+	24.8947i	−1.29203	+	1.21330i	−0.328865	+	0.944377i	$0.606666\pi$
$421$	−26.5102	+	24.8947i	−1.29203	+	1.21330i	−0.963163	+	0.268918i	$0.913334\pi$
$422$	−18.2247	+	2.30232i	−0.887165	+	0.112075i
$423$	3.89847	+	61.9645i	0.189550	+	3.01281i
$424$	−1.31910	+	4.05977i	−0.0640611	+	0.197160i
$425$	−26.3306	−	8.21522i	−1.27722	−	0.398497i
$426$	1.39273	+	4.28640i	0.0674782	+	0.207677i
$427$	24.0081	−	9.50547i	1.16183	−	0.460002i
$428$	−2.30277	+	12.0716i	−0.111309	+	0.583501i
$429$	−13.8974	+	1.75566i	−0.670975	+	0.0847638i
$430$	14.9897	+	0.383102i	0.722866	+	0.0184748i
$431$	16.2108	−	8.91194i	0.780845	−	0.429273i	−0.0408752	−	0.999164i	$-0.513015\pi$
$431$	16.2108	−	8.91194i	0.780845	−	0.429273i	0.821720	+	0.569891i	$0.193015\pi$
$432$	−9.02636			−0.434281
$433$	22.7103	−	12.4851i	1.09139	−	0.599994i	0.168747	−	0.985659i	$-0.446028\pi$
$433$	22.7103	−	12.4851i	1.09139	−	0.599994i	0.922639	+	0.385665i	$0.126028\pi$
$434$	14.2136	+	5.62758i	0.682276	+	0.270132i
$435$	−12.5963	+	25.0841i	−0.603945	+	1.20269i
$436$	12.4718	+	3.20221i	0.597289	+	0.153358i
$437$	−13.6830	−	21.5609i	−0.654546	−	1.03140i
$438$	5.16464	+	8.13816i	0.246776	+	0.388857i
$439$	−8.82816	−	2.26669i	−0.421345	−	0.108183i	0.0320634	−	0.999486i	$-0.489792\pi$
$439$	−8.82816	−	2.26669i	−0.421345	−	0.108183i	−0.453409	+	0.891303i	$0.649792\pi$
$440$	0.530118	+	3.22455i	0.0252724	+	0.153724i
$441$	17.2368	+	6.82453i	0.820800	+	0.324978i
$442$	−15.4388	+	8.48757i	−0.734351	+	0.403713i
$443$	39.0895			1.85720			0.928599	−	0.371085i	$-0.121014\pi$
$443$	39.0895			1.85720			0.928599	+	0.371085i	$0.121014\pi$
$444$	27.0196	−	14.8542i	1.28229	−	0.704947i
$445$	−6.79396	+	19.2239i	−0.322065	+	0.911300i
$446$	−23.5993	+	2.98128i	−1.11746	+	0.141168i
$447$	5.95814	−	31.2336i	0.281810	−	1.47730i
$448$	−1.83948	+	0.728301i	−0.0869071	+	0.0344090i
$449$	−2.00177	−	6.16081i	−0.0944693	−	0.290747i	0.892646	−	0.450759i	$-0.148847\pi$
$449$	−2.00177	−	6.16081i	−0.0944693	−	0.290747i	−0.987115	+	0.160012i	$0.948847\pi$
$450$	14.1611	−	26.4901i	0.667559	−	1.24875i
$451$	−1.44937	+	4.46070i	−0.0682481	+	0.210046i
$452$	−0.105618	−	1.67875i	−0.00496786	−	0.0789618i
$453$	−21.7956	+	2.75342i	−1.02405	+	0.129367i
$454$	−1.95884	+	1.83947i	−0.0919327	+	0.0863306i
$455$	13.9673	+	2.12832i	0.654797	+	0.0997773i
$456$	−10.0117	−	1.26477i	−0.468839	−	0.0592282i
$457$	2.88925	−	8.89220i	0.135153	−	0.415960i	−0.860460	−	0.509517i	$-0.829824\pi$
$457$	2.88925	−	8.89220i	0.135153	−	0.415960i	0.995614	+	0.0935577i	$0.0298240\pi$
$458$	−13.2113	−	12.4062i	−0.617323	−	0.579705i
$459$	48.2294	−	12.3832i	2.25116	−	0.577999i
$460$	−14.6679	−	8.55890i	−0.683896	−	0.399061i
$461$	7.56574	+	9.14541i	0.352372	+	0.425944i	0.916681	−	0.399619i	$-0.130858\pi$
$461$	7.56574	+	9.14541i	0.352372	+	0.425944i	−0.564310	+	0.825563i	$0.690858\pi$
$462$	8.40485	−	2.15800i	0.391029	−	0.100399i
$463$	24.2565	−	29.3211i	1.12730	−	1.36267i	0.203821	−	0.979008i	$-0.434664\pi$
$463$	24.2565	−	29.3211i	1.12730	−	1.36267i	0.923475	−	0.383658i	$-0.125336\pi$
$464$	3.88885	−	1.53970i	0.180535	−	0.0714789i
$465$	47.7110	+	20.3151i	2.21254	+	0.942088i
$466$	−11.5089	−	18.1351i	−0.533138	−	0.840092i
$467$	6.40312	+	33.5663i	0.296301	+	1.55326i	0.749591	+	0.661901i	$0.230250\pi$
$467$	6.40312	+	33.5663i	0.296301	+	1.55326i	−0.453290	+	0.891363i	$0.649750\pi$
$468$	−5.92890	−	18.2473i	−0.274063	−	0.843480i
$469$	−1.54555	+	3.28446i	−0.0713668	+	0.151662i
$470$	9.30208	+	21.1546i	0.429073	+	0.975790i
$471$	−10.1266	−	5.56714i	−0.466609	−	0.256520i
$472$	−0.617150	−	0.339281i	−0.0284066	−	0.0156167i
$473$	6.24672	+	7.55098i	0.287224	+	0.347195i
$474$	−22.1240	−	16.0740i	−1.01619	−	0.738303i
$475$	9.72149	−	13.7159i	0.446052	−	0.629329i
$476$	8.82951	−	6.41501i	0.404700	−	0.294032i
$477$	24.8386	+	6.37748i	1.13728	+	0.292005i
$478$	−4.35215	−	9.24880i	−0.199063	−	0.423030i
$479$	0.648456	−	3.39933i	0.0296287	−	0.155319i	−0.964398	−	0.264454i	$-0.914808\pi$
$479$	0.648456	−	3.39933i	0.0296287	−	0.155319i	0.994027	+	0.109135i	$0.0348081\pi$
$480$	−6.30082	+	2.31026i	−0.287592	+	0.105448i
$481$	23.9180	+	22.4605i	1.09057	+	1.02411i
$482$	12.3219	+	8.95240i	0.561248	+	0.407771i
$483$	−19.2007	+	40.8036i	−0.873664	+	1.85663i
$484$	5.65029	−	6.83003i	0.256831	−	0.310456i
$485$	−12.9269	+	4.73977i	−0.586979	+	0.215222i
$486$	0.00852244	+	0.135460i	0.000386586	+	0.00614460i
$487$	−0.219762	+	3.49302i	−0.00995838	+	0.158284i	0.989905	+	0.141735i	$0.0452680\pi$
$487$	−0.219762	+	3.49302i	−0.00995838	+	0.158284i	−0.999863	+	0.0165492i	$0.994732\pi$
$488$	−12.1351	−	4.80461i	−0.549328	−	0.217494i
$489$	−8.67929	+	13.6764i	−0.392491	+	0.618467i
$490$	6.89803	+	0.176298i	0.311621	+	0.00796433i
$491$	0.174673	−	2.77635i	0.00788289	−	0.125295i	−0.992117	−	0.125314i	$-0.960006\pi$
$491$	0.174673	−	2.77635i	0.00788289	−	0.125295i	1.00000		1.92258e-5i	$6.11978e-6\pi$
$492$	−9.55623	−	1.20723i	−0.430828	−	0.0544263i
$493$	−18.6665	+	13.5620i	−0.840697	+	0.610802i
$494$	−2.01216	−	10.5481i	−0.0905316	−	0.474583i
$495$	19.1334	−	4.39477i	0.859980	−	0.197530i
$496$	−3.29000	−	6.99160i	−0.147725	−	0.313932i
$497$	2.16575	−	2.03377i	0.0971470	−	0.0912271i
$498$	15.3721	−	24.2225i	0.688838	−	1.08544i
$499$	2.67078			0.119561			0.0597803	−	0.998212i	$-0.480960\pi$
$499$	2.67078			0.119561			0.0597803	+	0.998212i	$0.480960\pi$
$500$	1.55447	−	11.0717i	0.0695182	−	0.495144i
$501$	−11.1403			−0.497711
$502$	−1.84277	+	2.90375i	−0.0822470	+	0.129601i
$503$	0.838172	−	0.787095i	0.0373722	−	0.0350949i	−0.665636	−	0.746277i	$-0.731840\pi$
$503$	0.838172	−	0.787095i	0.0373722	−	0.0350949i	0.703008	+	0.711182i	$0.251840\pi$
$504$	5.06053	+	10.7542i	0.225414	+	0.479029i
$505$	−0.650185	+	7.33720i	−0.0289329	+	0.326501i
$506$	−2.07977	−	10.9025i	−0.0924571	−	0.484677i
$507$	−6.79909	+	4.93983i	−0.301958	+	0.219386i
$508$	10.4788	+	1.32378i	0.464921	+	0.0587332i
$509$	−1.78963	+	28.4454i	−0.0793241	+	1.26082i	0.734057	+	0.679088i	$0.237625\pi$
$509$	−1.78963	+	28.4454i	−0.0793241	+	1.26082i	−0.813381	+	0.581732i	$0.802375\pi$
$510$	30.4970	−	20.9882i	1.35043	−	0.929373i
$511$	3.40450	−	5.36463i	0.150606	−	0.237317i
$512$	0.929776	+	0.368125i	0.0410907	+	0.0162690i
$513$	−1.90567	+	30.2898i	−0.0841375	+	1.33733i
$514$	0.0347874	+	0.552930i	0.00153441	+	0.0243887i
$515$	41.9251	+	11.9142i	1.84744	+	0.525004i
$516$	−12.8286	+	15.5071i	−0.564749	+	0.682664i
$517$	−6.43078	+	13.6661i	−0.282825	+	0.601035i
$518$	−16.4435	−	11.9469i	−0.722485	−	0.524916i
$519$	−41.7664	−	39.2213i	−1.83334	−	1.72162i
$520$	−4.41000	−	5.61701i	−0.193391	−	0.246322i
$521$	−5.43617	+	28.4974i	−0.238163	+	1.24849i	0.639341	+	0.768924i	$0.279207\pi$
$521$	−5.43617	+	28.4974i	−0.238163	+	1.24849i	−0.877504	+	0.479570i	$0.840793\pi$
$522$	−10.6985	−	22.7355i	−0.468260	−	0.995104i
$523$	−38.3107	−	9.83653i	−1.67521	−	0.430121i	−0.712724	−	0.701445i	$-0.752539\pi$
$523$	−38.3107	−	9.83653i	−1.67521	−	0.430121i	−0.962488	+	0.271323i	$0.912539\pi$
$524$	−11.3401	+	8.23905i	−0.495394	+	0.359925i
$525$	−29.6498	−	1.51655i	−1.29402	−	0.0661877i
$526$	8.26876	+	6.00760i	0.360535	+	0.261944i
$527$	27.1708	+	32.8438i	1.18358	+	1.43070i
$528$	−3.84356	−	2.11301i	−0.167269	−	0.0919571i
$529$	30.3908	+	16.7075i	1.32134	+	0.726412i
$530$	9.49730	−	0.953978i	0.412536	−	0.0414382i
$531$	−1.80142	+	3.82821i	−0.0781749	+	0.166130i
$532$	2.05561	+	6.32650i	0.0891218	+	0.274289i
$533$	−1.92063	−	10.0683i	−0.0831918	−	0.436107i
$534$	−14.6636	−	23.1061i	−0.634556	−	0.999900i
$535$	26.7821	−	6.15163i	1.15789	−	0.265958i
$536$	1.70593	−	0.675425i	0.0736849	−	0.0291739i
$537$	25.1334	−	30.3810i	1.08459	−	1.31104i
$538$	−5.61711	+	1.44223i	−0.242171	+	0.0621789i
$539$	2.87465	+	3.47486i	0.123820	+	0.149673i
$540$	8.12433	+	18.4762i	0.349616	+	0.795090i
$541$	−17.1280	+	4.39773i	−0.736391	+	0.189073i	−0.598216	−	0.801335i	$-0.704124\pi$
$541$	−17.1280	+	4.39773i	−0.736391	+	0.189073i	−0.138175	+	0.990408i	$0.544124\pi$
$542$	8.15171	+	7.65497i	0.350146	+	0.328809i
$543$	6.67593	−	20.5464i	0.286492	−	0.881731i
$544$	−5.47299	−	0.691400i	−0.234653	−	0.0296435i
$545$	−4.67078	−	28.4109i	−0.200074	−	1.21699i
$546$	−13.8237	+	12.9813i	−0.591598	+	0.555548i
$547$	21.5576	−	2.72336i	0.921737	−	0.116442i	0.349879	−	0.936795i	$-0.386223\pi$
$547$	21.5576	−	2.72336i	0.921737	−	0.116442i	0.571858	+	0.820353i	$0.306223\pi$
$548$	0.874595	+	13.9013i	0.0373608	+	0.593833i
$549$	−24.2293	+	74.5702i	−1.03408	+	3.18258i
$550$	6.12324	−	3.98742i	0.261096	−	0.170024i
$551$	−4.34576	−	13.3749i	−0.185136	−	0.569789i
$552$	21.1932	−	8.39097i	0.902042	−	0.357144i
$553$	−3.37788	+	17.7075i	−0.143642	+	0.752999i
$554$	−27.3735	+	3.45807i	−1.16299	+	0.146919i
$555$	−54.7247	−	41.9372i	−2.32294	−	1.78014i
$556$	16.9180	−	9.30076i	0.717484	−	0.394440i
$557$	31.2038			1.32215			0.661074	−	0.750321i	$-0.270101\pi$
$557$	31.2038			1.32215			0.661074	+	0.750321i	$0.270101\pi$
$558$	−40.6783	+	22.3631i	−1.72205	+	0.946705i
$559$	−19.9124	−	7.88387i	−0.842204	−	0.333452i
$560$	3.14643	+	3.10974i	0.132961	+	0.131411i
$561$	23.4357	+	6.01725i	0.989454	+	0.254049i
$562$	4.28061	+	6.74516i	0.180567	+	0.284527i
$563$	8.03823	+	12.6662i	0.338771	+	0.533818i	0.970416	−	0.241440i	$-0.0776198\pi$
$563$	8.03823	+	12.6662i	0.338771	+	0.533818i	−0.631645	+	0.775258i	$0.717620\pi$
$564$	−30.0431	−	7.71375i	−1.26504	−	0.324807i
$565$	−3.34120	+	1.72718i	−0.140566	+	0.0726631i
$566$	3.99981	+	1.58364i	0.168125	+	0.0665652i
$567$	15.7208	−	8.64257i	0.660211	−	0.362954i
$568$	−1.50170			−0.0630099
$569$	26.1456	−	14.3737i	1.09608	−	0.602576i	0.172126	−	0.985075i	$-0.444936\pi$
$569$	26.1456	−	14.3737i	1.09608	−	0.602576i	0.923956	+	0.382499i	$0.124936\pi$
$570$	6.42230	+	21.6314i	0.269001	+	0.906041i
$571$	−1.65784	+	0.209434i	−0.0693785	+	0.00876455i	−0.159946	−	0.987126i	$-0.551132\pi$
$571$	−1.65784	+	0.209434i	−0.0693785	+	0.00876455i	0.0905673	+	0.995890i	$0.471132\pi$
$572$	0.874574	−	4.58468i	0.0365678	−	0.191695i
$573$	18.7504	−	7.42381i	0.783309	−	0.310134i
$574$	1.96210	+	6.03871i	0.0818963	+	0.252051i
$575$	−4.31724	+	37.7276i	−0.180041	+	1.57335i
$576$	1.85643	−	5.71350i	0.0773512	−	0.238062i
$577$	−0.582003	−	9.25068i	−0.0242291	−	0.385111i	−0.991390	−	0.130945i	$-0.958199\pi$
$577$	−0.582003	−	9.25068i	−0.0242291	−	0.385111i	0.967161	−	0.254166i	$-0.0818010\pi$
$578$	13.3258	−	1.68343i	0.554278	−	0.0700216i
$579$	51.3513	−	48.2221i	2.13409	−	2.00404i
$580$	−6.65187	−	6.57432i	−0.276204	−	0.272984i
$581$	−18.7621	−	2.37021i	−0.778385	−	0.0983329i
$582$	5.71064	−	17.5755i	0.236714	−	0.728529i
$583$	4.54756	+	4.27044i	0.188341	+	0.176864i
$584$	−3.11064	+	0.798676i	−0.128719	+	0.0330494i
$585$	−32.0143	+	28.5597i	−1.32363	+	1.18080i
$586$	15.3082	+	18.5045i	0.632377	+	0.764413i
$587$	−9.68255	+	2.48606i	−0.399642	+	0.102611i	−0.443161	−	0.896442i	$-0.646143\pi$
$587$	−9.68255	+	2.48606i	−0.399642	+	0.102611i	0.0435193	+	0.999053i	$0.486143\pi$
$588$	−5.90355	+	7.13617i	−0.243458	+	0.294291i
$589$	−24.1563	+	9.56417i	−0.995344	+	0.394085i
$590$	−0.139004	+	1.56863i	−0.00572271	+	0.0645795i
$591$	−11.1260	−	17.5317i	−0.457660	−	0.721158i
$592$	1.92507	+	10.0916i	0.0791199	+	0.414761i
$593$	10.6688	+	32.8353i	0.438116	+	1.34838i	0.889860	+	0.456235i	$0.150802\pi$
$593$	10.6688	+	32.8353i	0.438116	+	1.34838i	−0.451744	+	0.892148i	$0.649198\pi$
$594$	−5.61658	+	11.9358i	−0.230451	+	0.489733i
$595$	−21.0782	−	12.2993i	−0.864120	−	0.504224i
$596$	9.28405	+	5.10395i	0.380289	+	0.209066i
$597$	16.1154	+	8.85950i	0.659558	+	0.362595i
$598$	15.4610	+	18.6892i	0.632249	+	0.764258i
$599$	−0.00901338	−	0.00654860i	−0.000368277	−	0.000267569i	0.587601	−	0.809151i	$-0.300072\pi$
$599$	−0.00901338	−	0.00654860i	−0.000368277	−	0.000267569i	−0.587969	+	0.808883i	$0.700072\pi$
$600$	10.4001	+	10.8179i	0.424581	+	0.441638i
$601$	−5.63317	+	4.09274i	−0.229782	+	0.166946i	−0.696719	−	0.717344i	$-0.745357\pi$
$601$	−5.63317	+	4.09274i	−0.229782	+	0.166946i	0.466937	+	0.884291i	$0.345357\pi$
$602$	12.8500	+	3.29931i	0.523725	+	0.134470i
$603$	−4.69313	−	9.97341i	−0.191119	−	0.406149i
$604$	1.37161	−	7.19022i	0.0558099	−	0.292566i
$605$	−19.0662	−	5.41820i	−0.775149	−	0.220281i
$606$	−7.20702	−	6.76784i	−0.292765	−	0.274925i
$607$	39.4821	+	28.6854i	1.60253	+	1.16431i	0.882440	+	0.470425i	$0.155899\pi$
$607$	39.4821	+	28.6854i	1.60253	+	1.16431i	0.720090	+	0.693881i	$0.244101\pi$
$608$	1.43161	−	3.04234i	0.0580596	−	0.123383i
$609$	−15.8303	+	19.1355i	−0.641476	+	0.775412i
$610$	1.08773	+	29.1639i	0.0440408	+	1.18081i
$611$	−2.07250	−	32.9414i	−0.0838443	−	1.33267i
$612$	−2.08091	+	33.0751i	−0.0841157	+	1.33698i
$613$	−0.369586	−	0.146329i	−0.0149274	−	0.00591018i	0.360649	−	0.932702i	$-0.382555\pi$
$613$	−0.369586	−	0.146329i	−0.0149274	−	0.00591018i	−0.375576	+	0.926791i	$0.622555\pi$
$614$	5.27365	−	8.30994i	0.212827	−	0.335362i
$615$	6.13015	+	20.6474i	0.247192	+	0.832585i
$616$	−0.181545	+	2.88558i	−0.00731466	+	0.116263i
$617$	−6.53005	−	0.824937i	−0.262890	−	0.0332107i	−0.00721665	−	0.999974i	$-0.502297\pi$
$617$	−6.53005	−	0.824937i	−0.262890	−	0.0332107i	−0.255673	+	0.966763i	$0.582297\pi$
$618$	−47.3275	+	34.3855i	−1.90379	+	1.38319i
$619$	3.10718	+	16.2884i	0.124888	+	0.654685i	0.988584	+	0.150672i	$0.0481438\pi$
$619$	3.10718	+	16.2884i	0.124888	+	0.654685i	−0.863696	+	0.504013i	$0.831856\pi$
$620$	−11.3500	+	13.0273i	−0.455827	+	0.523188i
$621$	−29.1885	−	62.0287i	−1.17129	−	2.48913i
$622$	23.4354	−	22.0073i	0.939673	−	0.882412i
$623$	−9.66615	+	15.2314i	−0.387266	+	0.610234i
$624$	9.58514			0.383713
$625$	−24.0621	+	6.78344i	−0.962484	+	0.271338i
$626$	4.82712			0.192931
$627$	−7.90212	+	12.4517i	−0.315580	+	0.497275i
$628$	2.80681	−	2.63577i	0.112004	−	0.105179i
$629$	−24.1306	−	51.2801i	−0.962149	−	2.04467i
$630$	17.4581	−	20.0380i	0.695548	−	0.798333i
$631$	−2.59297	−	13.5928i	−0.103225	−	0.541122i	−0.995903	−	0.0904281i	$-0.971176\pi$
$631$	−2.59297	−	13.5928i	−0.103225	−	0.541122i	0.892678	−	0.450694i	$-0.148824\pi$
$632$	7.37157	−	5.35576i	0.293225	−	0.213041i
$633$	−54.6970	−	6.90984i	−2.17401	−	0.274642i
$634$	−0.562310	+	8.93766i	−0.0223322	+	0.354960i
$635$	−6.72195	−	22.6407i	−0.266752	−	0.898470i
$636$	−6.86471	+	10.8171i	−0.272204	+	0.428924i
$637$	−9.16339	−	3.62804i	−0.363067	−	0.143748i
$638$	0.383805	−	6.10041i	0.0151950	−	0.241517i
$639$	0.566465	+	9.00370i	0.0224090	+	0.356181i
$640$	−0.0833406	−	2.23451i	−0.00329433	−	0.0883269i
$641$	12.4257	−	15.0201i	0.490786	−	0.593259i	−0.465734	−	0.884925i	$-0.654210\pi$
$641$	12.4257	−	15.0201i	0.490786	−	0.593259i	0.956520	+	0.291666i	$0.0942096\pi$
$642$	−15.7041	+	33.3728i	−0.619790	+	1.31712i
$643$	4.39375	+	3.19224i	0.173272	+	0.125890i	0.671041	−	0.741420i	$-0.265847\pi$
$643$	4.39375	+	3.19224i	0.173272	+	0.125890i	−0.497769	+	0.867310i	$0.665847\pi$
$644$	−10.9532	−	10.2857i	−0.431615	−	0.405313i
$645$	43.2885	+	12.3017i	1.70448	+	0.484378i
$646$	−3.47561	+	18.2198i	−0.136746	+	0.716847i
$647$	−6.28799	−	13.3627i	−0.247206	−	0.525340i	0.742258	−	0.670114i	$-0.233755\pi$
$647$	−6.28799	−	13.3627i	−0.247206	−	0.525340i	−0.989465	+	0.144773i	$0.953755\pi$
$648$	−8.78293	−	2.25507i	−0.345026	−	0.0885876i
$649$	−0.832658	+	0.604961i	−0.0326847	+	0.0237468i
$650$	−7.52828	+	14.0826i	−0.295283	+	0.552365i
$651$	37.1182	+	26.9680i	1.45478	+	1.05696i
$652$	−3.44021	−	4.15850i	−0.134729	−	0.162860i
$653$	16.7388	+	9.20222i	0.655039	+	0.360111i	0.774360	−	0.632745i	$-0.218072\pi$
$653$	16.7388	+	9.20222i	0.655039	+	0.360111i	−0.119321	+	0.992856i	$0.538072\pi$
$654$	33.8649	+	18.6174i	1.32422	+	0.727998i
$655$	27.0715	+	15.7965i	1.05777	+	0.617221i
$656$	1.36649	−	2.90394i	0.0533525	−	0.113380i
$657$	5.96198	+	18.3491i	0.232599	+	0.715866i
$658$	3.83131	+	20.0844i	0.149360	+	0.782972i
$659$	−9.41597	−	14.8372i	−0.366794	−	0.577975i	0.609935	−	0.792451i	$-0.291195\pi$
$659$	−9.41597	−	14.8372i	−0.366794	−	0.577975i	−0.976729	+	0.214476i	$0.931195\pi$
$660$	−0.865706	+	9.76931i	−0.0336976	+	0.380270i
$661$	−14.0533	+	5.56409i	−0.546610	+	0.216418i	−0.625166	−	0.780492i	$-0.714969\pi$
$661$	−14.0533	+	5.56409i	−0.546610	+	0.216418i	0.0785567	+	0.996910i	$0.474969\pi$
$662$	−3.32982	+	4.02506i	−0.129417	+	0.156439i
$663$	−51.2151	+	13.1498i	−1.98903	+	0.510696i
$664$	6.09303	+	7.36521i	0.236455	+	0.285825i
$665$	11.0997	−	9.90194i	0.430426	−	0.383981i
$666$	59.7796	−	15.3488i	2.31641	−	0.594753i
$667$	23.1561	+	21.7450i	0.896608	+	0.841971i
$668$	1.14703	−	3.53021i	0.0443801	−	0.136588i
$669$	−70.8274	−	8.94758i	−2.73835	−	0.345934i
$670$	−2.91799	−	2.88397i	−0.112732	−	0.111417i
$671$	−13.9042	+	13.0569i	−0.536766	+	0.504057i
$672$	−5.89088	+	0.744192i	−0.227246	+	0.0287078i
$673$	−0.478910	−	7.61205i	−0.0184606	−	0.293423i	−0.996415	−	0.0846032i	$-0.973038\pi$
$673$	−0.478910	−	7.61205i	−0.0184606	−	0.293423i	0.977954	−	0.208820i	$-0.0669623\pi$
$674$	6.19266	−	19.0591i	0.238532	−	0.734127i
$675$	30.5069	−	33.2597i	1.17421	−	1.28017i
$676$	−0.865312	−	2.66316i	−0.0332812	−	0.102429i
$677$	−22.6062	+	8.95042i	−0.868826	+	0.343993i	−0.759886	−	0.650056i	$-0.774745\pi$
$677$	−22.6062	+	8.95042i	−0.868826	+	0.343993i	−0.108940	+	0.994048i	$0.534745\pi$
$678$	0.945961	−	4.95890i	0.0363294	−	0.190445i
$679$	−12.0859	+	1.52680i	−0.463812	+	0.0585931i
$680$	3.51082	+	11.8251i	0.134634	+	0.453471i
$681$	−7.06721	+	3.88523i	−0.270816	+	0.148882i
$682$	−11.2924			−0.432407
$683$	−2.72904	+	1.50030i	−0.104424	+	0.0574076i	−0.533110	−	0.846046i	$-0.678977\pi$
$683$	−2.72904	+	1.50030i	−0.104424	+	0.0574076i	0.428686	+	0.903454i	$0.358977\pi$
$684$	−18.7809	−	7.43588i	−0.718105	−	0.284318i
$685$	27.6676	−	14.3023i	1.05712	−	0.546464i
$686$	19.3271	+	4.96237i	0.737913	+	0.189464i
$687$	−29.1450	−	45.9251i	−1.11195	−	1.75215i
$688$	−3.59313	−	5.66187i	−0.136987	−	0.215857i
$689$	−13.2047	−	3.39038i	−0.503058	−	0.129163i
$690$	−36.2509	−	35.8283i	−1.38005	−	1.36396i
$691$	−40.6767	−	16.1050i	−1.54741	−	0.612665i	−0.569560	−	0.821950i	$-0.692886\pi$
$691$	−40.6767	−	16.1050i	−1.54741	−	0.612665i	−0.977855	+	0.209285i	$0.932886\pi$
$692$	16.7291	−	9.19688i	0.635943	−	0.349613i
$693$	17.3695			0.659811
$694$	16.7954	−	9.23337i	0.637546	−	0.350494i
$695$	−34.2653	−	26.2585i	−1.29976	−	0.996042i
$696$	12.4539	−	1.57330i	0.472066	−	0.0596357i
$697$	−3.31750	+	17.3910i	−0.125659	+	0.658729i
$698$	2.94549	−	1.16620i	0.111488	−	0.0441414i
$699$	−19.9202	−	61.3081i	−0.753451	−	2.31888i
$700$	3.53339	−	9.23946i	0.133550	−	0.349219i
$701$	0.0559849	−	0.172304i	0.00211452	−	0.00650783i	−0.949994	−	0.312269i	$-0.898911\pi$
$701$	0.0559849	−	0.172304i	0.00211452	−	0.00650783i	0.952108	+	0.305761i	$0.0989109\pi$
$702$	−1.81010	−	28.7707i	−0.0683178	−	1.08588i
$703$	34.2708	−	4.32940i	1.29255	−	0.163287i
$704$	1.06533	−	1.00041i	0.0401511	−	0.0377044i
$705$	11.2514	+	68.4386i	0.423751	+	2.57755i
$706$	−34.8286	−	4.39987i	−1.31079	−	0.165591i
$707$	−2.01392	+	6.19821i	−0.0757413	+	0.233108i
$708$	−1.54080	−	1.44691i	−0.0579068	−	0.0543781i
$709$	−29.9502	+	7.68990i	−1.12480	+	0.288800i	−0.764874	−	0.644179i	$-0.777199\pi$
$709$	−29.9502	+	7.68990i	−1.12480	+	0.288800i	−0.359929	+	0.932980i	$0.617199\pi$
$710$	1.35163	+	3.07386i	0.0507258	+	0.115360i
$711$	−34.8921	−	42.1773i	−1.30855	−	1.58177i
$712$	8.83182	−	2.26763i	0.330987	−	0.0849829i
$713$	37.4071	−	45.2174i	1.40091	−	1.69340i
$714$	30.4551	−	12.0580i	1.13975	−	0.451260i
$715$	−10.1716	+	2.33634i	−0.380398	+	0.0873741i
$716$	7.03954	+	11.0925i	0.263080	+	0.414548i
$717$	−5.74843	−	30.1343i	−0.214679	−	1.12539i
$718$	0.846699	+	2.60587i	0.0315985	+	0.0972503i
$719$	−7.46884	+	15.8721i	−0.278541	+	0.591929i	−0.994324	−	0.106393i	$-0.966070\pi$
$719$	−7.46884	+	15.8721i	−0.278541	+	0.591929i	0.715783	+	0.698322i	$0.246070\pi$
$720$	−13.3660	+	1.34258i	−0.498121	+	0.0500349i
$721$	33.7929	+	18.5778i	1.25851	+	0.691873i
$722$	6.74289	+	3.70694i	0.250944	+	0.137958i
$723$	29.1375	+	35.2212i	1.08363	+	1.30989i
$724$	5.82350	+	4.23102i	0.216429	+	0.157245i
$725$	−7.46996	+	19.5332i	−0.277427	+	0.725444i
$726$	21.5230	−	15.6374i	0.798793	−	0.580357i
$727$	34.6745	+	8.90289i	1.28601	+	0.330190i	0.828987	−	0.559268i	$-0.188918\pi$
$727$	34.6745	+	8.90289i	1.28601	+	0.330190i	0.457018	+	0.889458i	$0.348918\pi$
$728$	−2.69027	−	5.71712i	−0.0997081	−	0.211890i
$729$	5.02108	−	26.3214i	0.185966	−	0.974868i
$730$	4.43461	+	5.64836i	0.164132	+	0.209055i
$731$	26.9663	+	25.3230i	0.997383	+	0.936605i
$732$	−31.6901	−	23.0242i	−1.17130	−	0.850999i
$733$	1.29387	−	2.74961i	0.0477901	−	0.101559i	−0.879506	−	0.475888i	$-0.842127\pi$
$733$	1.29387	−	2.74961i	0.0477901	−	0.101559i	0.927296	+	0.374329i	$0.122127\pi$
$734$	5.85287	−	7.07491i	0.216034	−	0.261140i
$735$	19.9208	+	5.66106i	0.734788	+	0.208811i
$736$	0.476880	+	7.57979i	0.0175780	+	0.279395i
$737$	0.168365	−	2.67608i	0.00620179	−	0.0985747i
$738$	−17.9265	−	7.09762i	−0.659885	−	0.261267i
$739$	6.66262	−	10.4986i	0.245088	−	0.386198i	−0.699406	−	0.714724i	$-0.746552\pi$
$739$	6.66262	−	10.4986i	0.245088	−	0.386198i	0.944495	+	0.328527i	$0.106552\pi$
$740$	18.9239	−	13.0236i	0.695658	−	0.478755i
$741$	2.02364	−	32.1649i	0.0743404	−	1.18161i
$742$	8.37863	+	1.05847i	0.307589	+	0.0388575i
$743$	−23.3331	+	16.9525i	−0.856008	+	0.621926i	−0.926796	−	0.375565i	$-0.877449\pi$
$743$	−23.3331	+	16.9525i	−0.856008	+	0.621926i	0.0707879	+	0.997491i	$0.477449\pi$
$744$	−4.34550	−	22.7799i	−0.159314	−	0.835152i
$745$	2.09110	−	23.5976i	0.0766119	−	0.864549i
$746$	11.3516	+	24.1234i	0.415613	+	0.883222i
$747$	41.8610	−	39.3101i	1.53161	−	1.43828i
$748$	−4.31978	+	6.80689i	−0.157947	+	0.248884i
$749$	24.3131			0.888382
$750$	12.7826	−	31.0249i	0.466753	−	1.13287i
$751$	27.9722			1.02072			0.510360	−	0.859961i	$-0.329512\pi$
$751$	27.9722			1.02072			0.510360	+	0.859961i	$0.329512\pi$
$752$	5.53770	−	8.72601i	0.201939	−	0.318205i
$753$	−7.52418	+	7.06567i	−0.274196	+	0.257487i
$754$	5.68751	+	12.0866i	0.207127	+	0.440167i
$755$	−15.9523	+	3.66411i	−0.580565	+	0.133351i
$756$	3.34622	+	17.5415i	0.121701	+	0.637978i
$757$	32.2980	−	23.4659i	1.17389	−	0.852881i	0.182421	−	0.983220i	$-0.441607\pi$
$757$	32.2980	−	23.4659i	1.17389	−	0.852881i	0.991469	+	0.130339i	$0.0416066\pi$
$758$	18.5047	+	2.33769i	0.672120	+	0.0849086i
$759$	2.09164	−	33.2456i	0.0759216	−	1.20674i
$760$	−7.51597	−	0.192091i	−0.272633	−	0.00696787i
$761$	0.545164	−	0.859041i	0.0197622	−	0.0311402i	−0.834303	−	0.551306i	$-0.814130\pi$
$761$	0.545164	−	0.859041i	0.0197622	−	0.0311402i	0.854065	+	0.520166i	$0.174130\pi$
$762$	29.4734	+	11.6694i	1.06771	+	0.422736i
$763$	1.59956	−	25.4243i	0.0579080	−	0.920422i
$764$	0.421913	+	6.70612i	0.0152643	+	0.242619i
$765$	69.5750	−	25.5104i	2.51549	−	0.922329i
$766$	−7.59786	+	9.18424i	−0.274522	+	0.331840i
$767$	0.957667	−	2.03515i	0.0345794	−	0.0734849i
$768$	2.42807	+	1.76409i	0.0876153	+	0.0636562i
$769$	−5.65817	−	5.31337i	−0.204039	−	0.191605i	0.575791	−	0.817597i	$-0.304694\pi$
$769$	−5.65817	−	5.31337i	−0.204039	−	0.191605i	−0.779830	+	0.625992i	$0.784694\pi$
$770$	6.06994	−	2.22561i	0.218746	−	0.0802053i
$771$	−0.311571	+	1.63331i	−0.0112210	+	0.0588223i
$772$	9.99365	+	21.2376i	0.359680	+	0.764358i
$773$	−28.0641	−	7.20565i	−1.00940	−	0.259169i	−0.292438	−	0.956284i	$-0.594467\pi$
$773$	−28.0641	−	7.20565i	−1.00940	−	0.259169i	−0.716959	+	0.697115i	$0.754467\pi$
$774$	−32.5914	+	23.6790i	−1.17147	+	0.851124i
$775$	36.8815	+	11.5071i	1.32482	+	0.413349i
$776$	4.98147	+	3.61925i	0.178824	+	0.129923i
$777$	−38.8837	−	47.0023i	−1.39494	−	1.68620i
$778$	−11.1396	−	6.12405i	−0.399374	−	0.219558i
$779$	−9.45627	−	5.19863i	−0.338806	−	0.186260i
$780$	−8.62727	−	19.6200i	−0.308906	−	0.702509i
$781$	−0.934420	+	1.98574i	−0.0334362	+	0.0710555i
$782$	−12.9467	−	39.8459i	−0.462974	−	1.42489i
$783$	−7.07426	−	37.0846i	−0.252813	−	1.32529i
$784$	−1.65351	−	2.60551i	−0.0590539	−	0.0930540i
$785$	−7.92153	−	3.37294i	−0.282732	−	0.120385i
$786$	−39.1147	+	15.4866i	−1.39517	+	0.552389i
$787$	11.8825	−	14.3634i	0.423564	−	0.512001i	−0.514960	−	0.857214i	$-0.672193\pi$
$787$	11.8825	−	14.3634i	0.423564	−	0.512001i	0.938524	+	0.345213i	$0.112193\pi$
$788$	6.70111	−	1.72055i	0.238717	−	0.0612922i
$789$	19.5530	+	23.6355i	0.696106	+	0.841447i
$790$	−17.5977	−	10.2685i	−0.626099	−	0.365336i
$791$	−3.22327	+	0.827595i	−0.114606	+	0.0294259i
$792$	−6.39999	−	6.00999i	−0.227414	−	0.213556i
$793$	12.8807	−	39.6429i	0.457409	−	1.40776i
$794$	14.3437	+	1.81203i	0.509039	+	0.0643066i
$795$	28.3203	+	4.31543i	1.00442	+	0.153052i
$796$	−4.46673	+	4.19454i	−0.158319	+	0.148672i
$797$	−0.804600	+	0.101645i	−0.0285004	+	0.00360044i	−0.139571	−	0.990212i	$-0.544572\pi$
$797$	−0.804600	+	0.101645i	−0.0285004	+	0.00360044i	0.111070	+	0.993813i	$0.464572\pi$
$798$	1.25359	+	19.9252i	0.0443765	+	0.705344i
$799$	−17.6177	+	54.2218i	−0.623270	+	1.91823i
$800$	−4.49886	+	2.18181i	−0.159059	+	0.0771385i
$801$	−16.9275	−	52.0973i	−0.598102	−	1.84077i
$802$	−3.77742	+	1.49559i	−0.133385	+	0.0528110i
$803$	−0.879454	+	4.61026i	−0.0310353	+	0.162693i
$804$	5.46320	−	0.690162i	0.192672	−	0.0243402i
$805$	−11.1954	+	31.6781i	−0.394586	+	1.11650i
$806$	21.6253	−	11.8886i	0.761719	−	0.418759i
$807$	−17.4052			−0.612692
$808$	2.88669	−	1.58697i	0.101553	−	0.0558295i
$809$	27.3076	+	10.8118i	0.960083	+	0.380124i	0.795307	−	0.606207i	$-0.207310\pi$
$809$	27.3076	+	10.8118i	0.960083	+	0.380124i	0.164776	+	0.986331i	$0.447310\pi$
$810$	3.28928	+	20.0077i	0.115573	+	0.702997i
$811$	−10.1231	−	2.59916i	−0.355469	−	0.0912689i	0.0667327	−	0.997771i	$-0.478743\pi$
$811$	−10.1231	−	2.59916i	−0.355469	−	0.0912689i	−0.422201	+	0.906502i	$0.638743\pi$
$812$	−4.43386	−	6.98665i	−0.155598	−	0.245183i
$813$	17.9832	+	28.3370i	0.630699	+	0.993822i
$814$	14.5423	+	3.73382i	0.509706	+	0.130870i
$815$	−5.41570	+	10.7848i	−0.189704	+	0.377774i
$816$	−15.3937	−	6.09481i	−0.538889	−	0.213361i
$817$	−19.7582	+	10.8621i	−0.691251	+	0.380018i
$818$	−15.4193			−0.539123
$819$	−33.2632	+	18.2866i	−1.16231	+	0.638985i
$820$	−7.17407	−	0.183353i	−0.250529	−	0.00640295i
$821$	−7.23880	+	0.914473i	−0.252636	+	0.0319153i	−0.250631	−	0.968083i	$-0.580638\pi$
$821$	−7.23880	+	0.914473i	−0.252636	+	0.0319153i	−0.00200466	+	0.999998i	$0.500638\pi$
$822$	−7.83325	+	41.0633i	−0.273216	+	1.43225i
$823$	−27.4783	+	10.8794i	−0.957832	+	0.379233i	−0.794450	−	0.607330i	$-0.792241\pi$
$823$	−27.4783	+	10.8794i	−0.957832	+	0.379233i	−0.163383	+	0.986563i	$0.552241\pi$
$824$	−6.02332	−	18.5379i	−0.209832	−	0.645797i
$825$	20.7762	−	7.02101i	0.723334	−	0.244440i
$826$	−0.430559	+	1.32512i	−0.0149811	+	0.0461070i
$827$	2.76819	+	43.9991i	0.0962594	+	1.53000i	0.689092	+	0.724674i	$0.258009\pi$
$827$	2.76819	+	43.9991i	0.0962594	+	1.53000i	−0.592833	+	0.805325i	$0.701991\pi$
$828$	45.2660	−	5.71843i	1.57310	−	0.198729i
$829$	−12.3020	+	11.5524i	−0.427267	+	0.401230i	−0.868124	−	0.496347i	$-0.834674\pi$
$829$	−12.3020	+	11.5524i	−0.427267	+	0.401230i	0.440858	+	0.897577i	$0.354674\pi$
$830$	9.59184	−	19.1011i	0.332938	−	0.663010i
$831$	−82.1547	−	10.3786i	−2.84991	−	0.360028i
$832$	−0.986911	+	3.03740i	−0.0342150	+	0.105303i
$833$	12.4095	+	11.6533i	0.429963	+	0.403762i
$834$	56.1220	−	14.4097i	1.94335	−	0.498966i
$835$	−8.25845	+	0.829540i	−0.285796	+	0.0287074i
$836$	−3.13216	−	3.78614i	−0.108328	−	0.130946i
$837$	−67.5554	+	17.3453i	−2.33506	+	0.599541i
$838$	4.53126	−	5.47735i	0.156530	−	0.189212i
$839$	37.8300	−	14.9780i	1.30604	−	0.517097i	0.390973	−	0.920402i	$-0.372139\pi$
$839$	37.8300	−	14.9780i	1.30604	−	0.517097i	0.915066	+	0.403305i	$0.132139\pi$
$840$	6.82550	+	11.3883i	0.235502	+	0.392935i
$841$	−6.16533	−	9.71500i	−0.212597	−	0.335000i
$842$	−6.81444	−	35.7226i	−0.234841	−	1.23108i
$843$	7.40912	+	22.8029i	0.255184	+	0.785374i
$844$	7.82138	−	16.6213i	0.269223	−	0.572128i
$845$	−4.67243	+	4.16825i	−0.160736	+	0.143392i
$846$	−54.4072	−	29.9106i	−1.87056	−	1.02835i
$847$	−15.3679	−	8.44857i	−0.528047	−	0.290296i
$848$	−2.72097	−	3.28909i	−0.0934384	−	0.112948i
$849$	10.4453	+	7.58896i	0.358482	+	0.260452i
$850$	21.0450	−	17.8297i	0.721837	−	0.611555i
$851$	−63.1237	+	45.8621i	−2.16385	+	1.57213i
$852$	−4.36539	−	1.12084i	−0.149556	−	0.0383994i
$853$	3.22531	+	6.85414i	0.110433	+	0.234681i	0.952403	−	0.304843i	$-0.0986040\pi$
$853$	3.22531	+	6.85414i	0.110433	+	0.234681i	−0.841970	+	0.539524i	$0.818604\pi$
$854$	−4.83844	+	25.3640i	−0.165568	+	0.867938i
$855$	1.68343	+	45.1357i	0.0575720	+	1.54361i
$856$	−8.95846	−	8.41256i	−0.306194	−	0.287535i
$857$	−3.59755	−	2.61378i	−0.122890	−	0.0892849i	0.524642	−	0.851323i	$-0.324199\pi$
$857$	−3.59755	−	2.61378i	−0.122890	−	0.0892849i	−0.647533	+	0.762038i	$0.724199\pi$
$858$	5.96427	−	12.6747i	0.203617	−	0.432708i
$859$	−11.7529	+	14.2068i	−0.401003	+	0.484729i	−0.931904	−	0.362704i	$-0.881853\pi$
$859$	−11.7529	+	14.2068i	−0.401003	+	0.484729i	0.530901	+	0.847434i	$0.321853\pi$
$860$	−8.35533	+	12.4509i	−0.284914	+	0.424573i
$861$	1.19656	+	19.0188i	0.0407787	+	0.648159i
$862$	−1.16156	+	18.4625i	−0.0395629	+	0.628834i
$863$	−26.7006	−	10.5715i	−0.908898	−	0.359858i	−0.133293	−	0.991077i	$-0.542555\pi$
$863$	−26.7006	−	10.5715i	−0.908898	−	0.359858i	−0.775605	+	0.631219i	$0.782555\pi$
$864$	4.83656	−	7.62120i	0.164543	−	0.259279i
$865$	−33.8825	−	25.9652i	−1.15204	−	0.882844i
$866$	−1.62727	+	25.8647i	−0.0552969	+	0.878920i
$867$	39.9940	+	5.05241i	1.35827	+	0.171589i
$868$	−12.3676	+	8.98556i	−0.419783	+	0.304990i
$869$	−2.49519	−	13.0802i	−0.0846435	−	0.443717i
$870$	−14.4298	−	24.0761i	−0.489216	−	0.816258i
$871$	2.49495	+	5.30205i	0.0845383	+	0.179653i
$872$	−9.38642	+	8.81443i	−0.317864	+	0.298494i
$873$	19.8207	−	31.2325i	0.670830	−	1.05706i
$874$	25.5362			0.863775
$875$	−22.0927	+	1.08357i	−0.746870	+	0.0366314i
$876$	−9.63863			−0.325659
$877$	14.4721	−	22.8043i	0.488687	−	0.770048i	−0.507086	−	0.861896i	$-0.669277\pi$
$877$	14.4721	−	22.8043i	0.488687	−	0.770048i	0.995773	+	0.0918475i	$0.0292772\pi$
$878$	6.64419	−	6.23931i	0.224231	−	0.210567i
$879$	30.6891	+	65.2176i	1.03512	+	2.19974i
$880$	−3.00663	−	1.28020i	−0.101353	−	0.0431557i
$881$	8.93117	+	46.8188i	0.300899	+	1.57737i	0.735998	+	0.676984i	$0.236713\pi$
$881$	8.93117	+	46.8188i	0.300899	+	1.57737i	−0.435099	+	0.900383i	$0.643287\pi$
$882$	−14.9981	+	10.8967i	−0.505012	+	0.366912i
$883$	15.4059	+	1.94621i	0.518448	+	0.0654953i	0.380204	−	0.924903i	$-0.375854\pi$
$883$	15.4059	+	1.94621i	0.518448	+	0.0654953i	0.138245	+	0.990398i	$0.455854\pi$
$884$	1.10625	−	17.5833i	0.0372072	−	0.591391i
$885$	−1.57488	+	4.45621i	−0.0529389	+	0.149794i
$886$	−20.9452	+	33.0044i	−0.703668	+	1.10880i
$887$	2.22322	+	0.880234i	0.0746483	+	0.0295554i	0.405152	−	0.914249i	$-0.367219\pi$
$887$	2.22322	+	0.880234i	0.0746483	+	0.0295554i	−0.330504	+	0.943805i	$0.607219\pi$
$888$	−1.93605	+	30.7727i	−0.0649697	+	1.03266i
$889$	−1.31208	−	20.8549i	−0.0440056	−	0.699449i
$890$	−12.5909	−	16.0370i	−0.422047	−	0.537562i
$891$	−8.44705	+	10.2107i	−0.282987	+	0.342072i
$892$	10.1279	−	21.5230i	0.339109	−	0.720643i
$893$	−28.1128	−	20.4251i	−0.940759	−	0.683501i
$894$	23.1789	+	21.7664i	0.775219	+	0.727979i
$895$	16.3695	−	24.3934i	0.547171	−	0.815382i
$896$	0.370717	−	1.94336i	0.0123848	−	0.0649233i
$897$	30.9954	+	65.8686i	1.03491	+	2.19929i
$898$	6.27434	+	1.61098i	0.209378	+	0.0537590i
$899$	26.1463	−	18.9964i	0.872029	−	0.633566i
$900$	14.7784	+	26.1507i	0.492615	+	0.871689i
$901$	19.0509	+	13.8413i	0.634678	+	0.461120i
$902$	−2.98968	−	3.61391i	−0.0995455	−	0.120330i
$903$	34.8918	+	19.1819i	1.16113	+	0.638335i
$904$	1.47401	+	0.810343i	0.0490248	+	0.0269516i
$905$	3.41901	−	15.7284i	0.113652	−	0.522831i
$906$	9.35386	−	19.8780i	0.310761	−	0.660401i
$907$	−3.43833	−	10.5821i	−0.114168	−	0.351373i	0.877605	−	0.479385i	$-0.159140\pi$
$907$	−3.43833	−	10.5821i	−0.114168	−	0.351373i	−0.991773	+	0.128012i	$0.959140\pi$
$908$	−0.503519	−	2.63954i	−0.0167099	−	0.0875961i
$909$	−10.6039	−	16.7090i	−0.351708	−	0.554203i
$910$	−9.28105	+	10.6526i	−0.307664	+	0.353129i
$911$	−24.4677	+	9.68743i	−0.810649	+	0.320959i	−0.736628	−	0.676298i	$-0.763583\pi$
$911$	−24.4677	+	9.68743i	−0.810649	+	0.320959i	−0.0740212	+	0.997257i	$0.523583\pi$
$912$	6.43240	−	7.77543i	0.212998	−	0.257470i
$913$	13.5306	−	3.47406i	0.447797	−	0.114975i
$914$	5.95980	+	7.20416i	0.197133	+	0.238292i
$915$	−18.6054	+	85.5904i	−0.615077	+	2.82953i
$916$	17.5539	−	4.50707i	0.579997	−	0.148918i
$917$	20.2154	+	18.9836i	0.667572	+	0.626892i
$918$	−15.3871	+	47.3567i	−0.507851	+	1.56300i
$919$	44.5256	+	5.62489i	1.46876	+	0.185548i	0.818652	−	0.574290i	$-0.194722\pi$
$919$	44.5256	+	5.62489i	1.46876	+	0.185548i	0.650112	+	0.759838i	$0.274722\pi$
$920$	15.0860	−	7.79845i	0.497370	−	0.257107i
$921$	21.5327	−	20.2205i	0.709526	−	0.666290i
$922$	−11.7756	+	1.48761i	−0.387810	+	0.0489918i
$923$	−0.301143	−	4.78653i	−0.00991224	−	0.157551i
$924$	−2.68149	+	8.25277i	−0.0882144	+	0.271496i
$925$	−43.6910	−	27.0137i	−1.43655	−	0.888204i
$926$	11.7593	+	36.1915i	0.386435	+	1.18933i
$927$	−108.875	+	43.1066i	−3.57592	+	1.41581i
$928$	−0.783734	+	4.10848i	−0.0257273	+	0.134867i
$929$	−53.0095	+	6.69666i	−1.73919	+	0.219710i	−0.929928	−	0.367743i	$-0.880131\pi$
$929$	−53.0095	+	6.69666i	−1.73919	+	0.219710i	−0.809258	+	0.587453i	$0.800131\pi$
$930$	−42.7174	+	29.3984i	−1.40076	+	0.964010i
$931$	−9.09243	+	4.99860i	−0.297992	+	0.163823i
$932$	21.4787			0.703559
$933$	84.5517	−	46.4827i	2.76810	−	1.52177i
$934$	−31.7719	−	12.5794i	−1.03961	−	0.411611i
$935$	17.8212	+	2.71559i	0.582817	+	0.0888091i
$936$	18.5835	+	4.77144i	0.607422	+	0.155959i
$937$	−31.8161	−	50.1342i	−1.03939	−	1.63781i	−0.725321	−	0.688410i	$-0.758309\pi$
$937$	−31.8161	−	50.1342i	−1.03939	−	1.63781i	−0.314066	−	0.949401i	$-0.601691\pi$
$938$	−1.94501	−	3.06485i	−0.0635069	−	0.100071i
$939$	14.0323	+	3.60287i	0.457926	+	0.117575i
$940$	−22.8457	−	3.48121i	−0.745146	−	0.113545i
$941$	25.7168	+	10.1820i	0.838345	+	0.331924i	0.747764	−	0.663965i	$-0.231128\pi$
$941$	25.7168	+	10.1820i	0.838345	+	0.331924i	0.0905809	+	0.995889i	$0.471128\pi$
$942$	10.1266	−	5.56714i	0.329942	−	0.181387i
$943$	24.3746			0.793745
$944$	0.617150	−	0.339281i	0.0200865	−	0.0110427i
$945$	32.8942	−	22.6380i	1.07005	−	0.736414i
$946$	−9.72267	+	1.22826i	−0.316111	+	0.0399341i
$947$	−5.30991	+	27.8355i	−0.172549	+	0.904534i	0.785702	+	0.618605i	$0.212302\pi$
$947$	−5.30991	+	27.8355i	−0.172549	+	0.904534i	−0.958251	+	0.285928i	$0.907698\pi$
$948$	25.4263	−	10.0670i	0.825809	−	0.326961i
$949$	−3.16950	−	9.75471i	−0.102886	−	0.316651i
$950$	6.37168	+	15.5575i	0.206725	+	0.504751i
$951$	−8.30552	+	25.5618i	−0.269325	+	0.828897i
$952$	0.685287	+	10.8923i	0.0222103	+	0.353023i
$953$	2.27647	−	0.287586i	0.0737423	−	0.00931581i	−0.0883755	−	0.996087i	$-0.528168\pi$
$953$	2.27647	−	0.287586i	0.0737423	−	0.00931581i	0.162118	+	0.986771i	$0.448168\pi$
$954$	−18.6939	+	17.5547i	−0.605237	+	0.568355i
$955$	13.3471	−	6.89958i	0.431903	−	0.223265i
$956$	10.1410	+	1.28111i	0.327984	+	0.0414340i
$957$	5.66894	−	17.4472i	0.183251	−	0.563988i
$958$	2.52269	+	2.36896i	0.0815043	+	0.0765376i
$959$	26.6910	−	6.85309i	0.861899	−	0.221298i
$960$	1.42553	−	6.55786i	0.0460089	−	0.211654i
$961$	−18.2982	−	22.1187i	−0.590264	−	0.713507i
$962$	−31.7799	+	8.15969i	−1.02463	+	0.263079i
$963$	−47.0597	+	56.8854i	−1.51648	+	1.83311i
$964$	−14.1612	+	5.60681i	−0.456101	+	0.180583i
$965$	34.4767	−	39.5715i	1.10984	−	1.27385i
$966$	−24.1634	−	38.0754i	−0.777444	−	1.22506i
$967$	−8.13480	−	42.6441i	−0.261597	−	1.37134i	−0.834179	−	0.551494i	$-0.814058\pi$
$967$	−8.13480	−	42.6441i	−0.261597	−	1.37134i	0.572581	−	0.819848i	$-0.305942\pi$
$968$	2.73921	+	8.43041i	0.0880414	+	0.270964i
$969$	−23.7024	+	50.3701i	−0.761430	+	1.61812i
$970$	2.92465	−	13.4542i	0.0939048	−	0.431989i
$971$	−10.8012	−	5.93801i	−0.346627	−	0.190560i	0.298924	−	0.954277i	$-0.403372\pi$
$971$	−10.8012	−	5.93801i	−0.346627	−	0.190560i	−0.645551	+	0.763717i	$0.723372\pi$
$972$	−0.118939	−	0.0653875i	−0.00381498	−	0.00209730i
$973$	−24.3466	−	29.4299i	−0.780515	−	0.943480i
$974$	−2.83150	−	2.05721i	−0.0907271	−	0.0659171i
$975$	−32.3954	+	35.3187i	−1.03748	+	1.13110i
$976$	10.5590	−	7.67153i	0.337984	−	0.245560i
$977$	−21.3917	−	5.49247i	−0.684383	−	0.175720i	−0.109539	−	0.993983i	$-0.534937\pi$
$977$	−21.3917	−	5.49247i	−0.684383	−	0.175720i	−0.574844	+	0.818263i	$0.694937\pi$
$978$	−6.89675	−	14.6563i	−0.220534	−	0.468658i
$979$	2.49698	−	13.0896i	0.0798037	−	0.418346i
$980$	−3.84501	+	5.72974i	−0.122824	+	0.183030i
$981$	56.3892	+	52.9530i	1.80037	+	1.69066i
$982$	2.25056	+	1.63512i	0.0718181	+	0.0521789i
$983$	16.0303	−	34.0662i	0.511288	−	1.08654i	−0.467937	−	0.883762i	$-0.655002\pi$
$983$	16.0303	−	34.0662i	0.511288	−	1.08654i	0.979224	−	0.202780i	$-0.0649976\pi$
$984$	6.13979	−	7.42173i	0.195729	−	0.236596i
$985$	−9.55329	−	12.1680i	−0.304393	−	0.387705i
$986$	−1.44877	−	23.0275i	−0.0461382	−	0.733346i
$987$	−3.85316	+	61.2443i	−0.122648	+	1.94943i
$988$	9.98426	+	3.95305i	0.317642	+	0.125763i
$989$	27.2890	−	43.0006i	0.867741	−	1.36734i
$990$	−6.54154	+	18.5097i	−0.207904	+	0.588276i
$991$	1.36698	−	21.7276i	0.0434236	−	0.690199i	−0.914752	−	0.404017i	$-0.867614\pi$
$991$	1.36698	−	21.7276i	0.0434236	−	0.690199i	0.958175	−	0.286182i	$-0.0923862\pi$
$992$	7.66607	+	0.968449i	0.243398	+	0.0307483i
$993$	−12.6839	+	9.21540i	−0.402512	+	0.292442i
$994$	0.556705	+	2.91835i	0.0176576	+	0.0925644i
$995$	12.6063	+	5.36767i	0.399645	+	0.170167i
$996$	12.2150	+	25.9581i	0.387046	+	0.822514i
$997$	2.73336	−	2.56680i	0.0865665	−	0.0812914i	−0.640056	−	0.768328i	$-0.721089\pi$
$997$	2.73336	−	2.56680i	0.0865665	−	0.0812914i	0.726623	+	0.687037i	$0.241089\pi$
$998$	−1.43108	+	2.25502i	−0.0452999	+	0.0713813i
$999$	92.7326			2.93393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.g.a.231.1	yes	120
125.46	even	25	inner	250.2.g.a.171.1	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
250.2.g.a.171.1	✓	120	125.46	even	25	inner
250.2.g.a.231.1	yes	120	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.g (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.535827 + 0.844328i) q^{2} +(-2.18782 + 2.05450i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(-1.46888 + 1.68594i) q^{5} +(-0.562379 - 2.94809i) q^{6} +(-1.60057 + 1.16288i) q^{7} +(0.992115 + 0.125333i) q^{8} +(0.377216 - 5.99567i) q^{9} +O(q^{10})\)	\(q+(-0.535827 + 0.844328i) q^{2} +(-2.18782 + 2.05450i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(-1.46888 + 1.68594i) q^{5} +(-0.562379 - 2.94809i) q^{6} +(-1.60057 + 1.16288i) q^{7} +(0.992115 + 0.125333i) q^{8} +(0.377216 - 5.99567i) q^{9} +(-0.636423 - 2.14359i) q^{10} +(0.783067 - 1.23392i) q^{11} +(2.79050 + 1.10484i) q^{12} +(-0.200535 + 3.18741i) q^{13} +(-0.124225 - 1.97450i) q^{14} +(-0.250126 - 6.70635i) q^{15} +(-0.637424 + 0.770513i) q^{16} +(2.34881 - 4.99147i) q^{17} +(4.86019 + 3.53114i) q^{18} +(2.45104 + 2.30168i) q^{19} +(2.15090 + 0.611241i) q^{20} +(1.11262 - 5.83253i) q^{21} +(0.622242 + 1.32233i) q^{22} +(-7.35617 - 1.88874i) q^{23} +(-2.42807 + 1.76409i) q^{24} +(-0.684797 - 4.95288i) q^{25} +(-2.58377 - 1.87722i) q^{26} +(5.75362 + 6.95493i) q^{27} +(1.73369 + 0.953105i) q^{28} +(-3.66521 - 2.01496i) q^{29} +(5.79638 + 3.38225i) q^{30} +(-3.29000 + 6.99160i) q^{31} +(-0.309017 - 0.951057i) q^{32} +(0.821871 + 4.30840i) q^{33} +(2.95588 + 4.65773i) q^{34} +(0.390489 - 4.40659i) q^{35} +(-5.58566 + 2.21152i) q^{36} +(6.54860 - 7.91590i) q^{37} +(-3.25671 + 0.836180i) q^{38} +(-6.10980 - 7.38548i) q^{39} +(-1.66860 + 1.48855i) q^{40} +(-3.10856 + 0.798142i) q^{41} +(4.32840 + 4.06464i) q^{42} +(-2.07220 + 6.37757i) q^{43} +(-1.44989 - 0.183164i) q^{44} +(9.55427 + 9.44287i) q^{45} +(5.53635 - 5.19898i) q^{46} +(-10.2534 + 1.29530i) q^{47} +(-0.188450 - 2.99533i) q^{48} +(-0.953596 + 2.93487i) q^{49} +(4.54879 + 2.07569i) q^{50} +(5.11621 + 15.7461i) q^{51} +(2.96944 - 1.17568i) q^{52} +(-0.799874 + 4.19308i) q^{53} +(-8.95518 + 1.13130i) q^{54} +(0.930081 + 3.13268i) q^{55} +(-1.73369 + 0.953105i) q^{56} -10.0912 q^{57} +(3.66521 - 2.01496i) q^{58} +(-0.654806 - 0.259256i) q^{59} +(-5.96158 + 3.08174i) q^{60} +(-12.6415 - 3.24580i) q^{61} +(-4.14033 - 6.52412i) q^{62} +(6.36848 + 10.0351i) q^{63} +(0.968583 + 0.248690i) q^{64} +(-5.07922 - 5.02000i) q^{65} +(-4.07808 - 1.61463i) q^{66} +(1.60782 - 0.883909i) q^{67} -5.51649 q^{68} +(19.9744 - 10.9810i) q^{69} +(3.51137 + 2.69087i) q^{70} +(-1.48986 + 0.188213i) q^{71} +(1.12570 - 5.90112i) q^{72} +(-2.98601 + 1.18224i) q^{73} +(3.17470 + 9.77072i) q^{74} +(11.6739 + 9.42910i) q^{75} +(1.03902 - 3.19778i) q^{76} +(0.181545 + 2.88558i) q^{77} +(9.50956 - 1.20134i) q^{78} +(6.64219 - 6.23743i) q^{79} +(-0.362742 - 2.20645i) q^{80} +(-8.99630 - 1.13650i) q^{81} +(0.991755 - 3.05231i) q^{82} +(6.96809 + 6.54347i) q^{83} +(-5.75116 + 1.47665i) q^{84} +(4.96522 + 11.2918i) q^{85} +(-4.27442 - 5.16689i) q^{86} +(12.1586 - 3.12179i) q^{87} +(0.931543 - 1.12604i) q^{88} +(8.47797 - 3.35667i) q^{89} +(-13.0923 + 3.00719i) q^{90} +(-3.38560 - 5.33485i) q^{91} +(1.42312 + 7.46025i) q^{92} +(-7.16631 - 22.0556i) q^{93} +(4.40037 - 9.35126i) q^{94} +(-7.48078 + 0.751424i) q^{95} +(2.63002 + 1.44587i) q^{96} +(5.39580 + 2.96636i) q^{97} +(-1.96703 - 2.37773i) q^{98} +(-7.10277 - 5.16047i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 5 q^{5} + 10 q^{7} + 10 q^{9}+O(q^{10}) \) 120 * q - 5 * q^5 + 10 * q^7 + 10 * q^9	\( 120 q - 5 q^{5} + 10 q^{7} + 10 q^{9} - 20 q^{10} + 20 q^{12} - 20 q^{14} - 10 q^{15} - 5 q^{17} + 25 q^{18} - 60 q^{19} + 5 q^{20} + 5 q^{21} - 10 q^{22} + 10 q^{23} - 5 q^{24} + 55 q^{25} + 5 q^{26} - 90 q^{27} - 5 q^{28} - 10 q^{29} - 10 q^{30} - 45 q^{31} + 30 q^{32} - 15 q^{33} - 10 q^{34} + 15 q^{35} + 10 q^{36} + 10 q^{37} + 10 q^{39} - 55 q^{41} - 5 q^{42} + 5 q^{43} - 40 q^{44} + 85 q^{45} - 20 q^{46} + 90 q^{47} - 5 q^{48} - 20 q^{49} - 30 q^{50} + 60 q^{51} + 5 q^{53} + 5 q^{54} - 15 q^{55} + 5 q^{56} - 120 q^{57} + 10 q^{58} - 75 q^{59} + 15 q^{60} - 85 q^{61} - 15 q^{62} - 45 q^{63} + 5 q^{65} - 15 q^{66} - 25 q^{67} - 70 q^{68} + 5 q^{69} - 65 q^{70} + 55 q^{71} + 5 q^{72} - 30 q^{73} - 70 q^{74} - 20 q^{75} - 5 q^{76} - 130 q^{77} + 60 q^{78} + 10 q^{79} + 5 q^{80} - 65 q^{81} + 80 q^{82} - 135 q^{83} + 20 q^{84} - 30 q^{85} + 10 q^{86} - 200 q^{87} - 80 q^{90} + 175 q^{91} - 5 q^{92} + 50 q^{93} + 35 q^{94} - 20 q^{95} - 15 q^{98} - 120 q^{99}+O(q^{100}) \) 120 * q - 5 * q^5 + 10 * q^7 + 10 * q^9 - 20 * q^10 + 20 * q^12 - 20 * q^14 - 10 * q^15 - 5 * q^17 + 25 * q^18 - 60 * q^19 + 5 * q^20 + 5 * q^21 - 10 * q^22 + 10 * q^23 - 5 * q^24 + 55 * q^25 + 5 * q^26 - 90 * q^27 - 5 * q^28 - 10 * q^29 - 10 * q^30 - 45 * q^31 + 30 * q^32 - 15 * q^33 - 10 * q^34 + 15 * q^35 + 10 * q^36 + 10 * q^37 + 10 * q^39 - 55 * q^41 - 5 * q^42 + 5 * q^43 - 40 * q^44 + 85 * q^45 - 20 * q^46 + 90 * q^47 - 5 * q^48 - 20 * q^49 - 30 * q^50 + 60 * q^51 + 5 * q^53 + 5 * q^54 - 15 * q^55 + 5 * q^56 - 120 * q^57 + 10 * q^58 - 75 * q^59 + 15 * q^60 - 85 * q^61 - 15 * q^62 - 45 * q^63 + 5 * q^65 - 15 * q^66 - 25 * q^67 - 70 * q^68 + 5 * q^69 - 65 * q^70 + 55 * q^71 + 5 * q^72 - 30 * q^73 - 70 * q^74 - 20 * q^75 - 5 * q^76 - 130 * q^77 + 60 * q^78 + 10 * q^79 + 5 * q^80 - 65 * q^81 + 80 * q^82 - 135 * q^83 + 20 * q^84 - 30 * q^85 + 10 * q^86 - 200 * q^87 - 80 * q^90 + 175 * q^91 - 5 * q^92 + 50 * q^93 + 35 * q^94 - 20 * q^95 - 15 * q^98 - 120 * q^99

Introduction

L-functions

Modular forms

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