LMFDB - Embedded newform 750.2.o.b.229.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(19,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

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

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

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

chi := DirichletCharacter("750.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.o (of order $50$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$14$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			229.11
Character	$\chi$	$=$	750.229
Dual form			750.2.o.b.619.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.248690 + 0.968583i) q^{2} +(-0.982287 + 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(0.353264 + 2.20799i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(-0.0177835 + 0.0244769i) q^{7} +(-0.684547 - 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +O(q^{10})$	\(q+(0.248690 + 0.968583i) q^{2} +(-0.982287 + 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(0.353264 + 2.20799i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(-0.0177835 + 0.0244769i) q^{7} +(-0.684547 - 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +(-2.05077 + 0.891269i) q^{10} +(5.22264 - 1.34095i) q^{11} +(0.770513 - 0.637424i) q^{12} +(1.96984 + 4.97524i) q^{13} +(-0.0281305 - 0.0111376i) q^{14} +(-0.760742 - 2.10268i) q^{15} +(0.535827 - 0.844328i) q^{16} +(-1.53446 + 2.79117i) q^{17} +(0.587785 + 0.809017i) q^{18} +(-0.289654 + 1.51842i) q^{19} +(-1.37327 - 1.76469i) q^{20} +(0.0128820 - 0.0273756i) q^{21} +(2.59763 + 4.72508i) q^{22} +(-1.58746 - 0.0998745i) q^{23} +(0.809017 + 0.587785i) q^{24} +(-4.75041 + 1.56000i) q^{25} +(-4.32905 + 3.14524i) q^{26} +(-0.844328 + 0.535827i) q^{27} +(0.00379197 - 0.0300165i) q^{28} +(-9.39932 - 1.18741i) q^{29} +(1.84743 - 1.25976i) q^{30} +(-0.125027 - 0.0687343i) q^{31} +(0.951057 + 0.309017i) q^{32} +(-4.87886 + 2.29582i) q^{33} +(-3.08508 - 0.792114i) q^{34} +(-0.0603269 - 0.0306189i) q^{35} +(-0.637424 + 0.770513i) q^{36} +(2.05007 + 1.30102i) q^{37} +(-1.54275 + 0.0970615i) q^{38} +(-2.86721 - 4.51800i) q^{39} +(1.36773 - 1.76899i) q^{40} +(-0.214331 - 3.40669i) q^{41} +(0.0297192 + 0.00566924i) q^{42} +(3.55595 - 1.15540i) q^{43} +(-3.93063 + 3.69110i) q^{44} +(1.14127 + 1.92289i) q^{45} +(-0.298049 - 1.56243i) q^{46} +(-4.96728 + 5.28961i) q^{47} +(-0.368125 + 0.929776i) q^{48} +(2.16284 + 6.65653i) q^{49} +(-2.69237 - 4.21321i) q^{50} +(0.984265 - 3.02926i) q^{51} +(-4.12302 - 3.41086i) q^{52} +(-6.41210 - 3.01731i) q^{53} +(-0.728969 - 0.684547i) q^{54} +(4.80576 + 11.0578i) q^{55} +(0.0300165 - 0.00379197i) q^{56} -1.54580i q^{57} +(-1.18741 - 9.39932i) q^{58} +(3.48685 + 4.21487i) q^{59} +(1.67962 + 1.47610i) q^{60} +(0.852532 - 13.5506i) q^{61} +(0.0354819 - 0.138193i) q^{62} +(-0.00752413 + 0.0293046i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(-10.2894 + 6.10694i) q^{65} +(-3.43701 - 4.15464i) q^{66} +(-0.166549 - 1.31837i) q^{67} -3.18515i q^{68} +(1.57806 - 0.199355i) q^{69} +(0.0146543 - 0.0660462i) q^{70} +(6.23221 + 5.85244i) q^{71} +(-0.904827 - 0.425779i) q^{72} +(5.79168 + 4.79129i) q^{73} +(-0.750310 + 2.30922i) q^{74} +(4.37395 - 2.42251i) q^{75} +(-0.477678 - 1.47014i) q^{76} +(-0.0600546 + 0.151681i) q^{77} +(3.66302 - 3.90071i) q^{78} +(0.966951 + 5.06893i) q^{79} +(2.05355 + 0.884828i) q^{80} +(0.728969 - 0.684547i) q^{81} +(3.24636 - 1.05481i) q^{82} +(0.435788 + 0.0831310i) q^{83} +(0.00189973 + 0.0301954i) q^{84} +(-6.70493 - 2.40204i) q^{85} +(2.00343 + 3.15690i) q^{86} +(9.45533 - 0.594879i) q^{87} +(-4.55265 - 2.88920i) q^{88} +(-0.538329 + 0.650728i) q^{89} +(-1.57866 + 1.58362i) q^{90} +(-0.156809 - 0.0402617i) q^{91} +(1.43922 - 0.677244i) q^{92} +(0.135692 + 0.0440890i) q^{93} +(-6.35874 - 3.49575i) q^{94} +(-3.45497 - 0.103149i) q^{95} +(-0.992115 - 0.125333i) q^{96} +(-2.05453 + 16.2633i) q^{97} +(-5.90952 + 3.75030i) q^{98} +(4.36225 - 3.16936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q+O(q^{10}) $ 280 * q	$ 280 q - 10 q^{11} - 20 q^{13} + 30 q^{17} + 10 q^{19} + 20 q^{22} + 60 q^{23} + 70 q^{24} + 20 q^{25} + 20 q^{29} + 10 q^{30} + 20 q^{31} + 20 q^{33} - 10 q^{34} + 30 q^{35} - 20 q^{37} + 90 q^{38} - 40 q^{41} - 10 q^{46} - 100 q^{47} + 120 q^{49} - 20 q^{50} - 30 q^{51} + 80 q^{52} - 30 q^{53} - 10 q^{55} + 30 q^{58} + 20 q^{59} + 60 q^{61} - 50 q^{62} - 10 q^{63} + 20 q^{65} + 40 q^{66} + 50 q^{67} + 10 q^{69} + 20 q^{70} + 80 q^{71} - 20 q^{73} + 80 q^{75} - 30 q^{76} - 100 q^{77} - 100 q^{79} + 100 q^{82} + 30 q^{83} - 20 q^{86} - 10 q^{87} - 60 q^{89} - 10 q^{90} + 70 q^{91} - 120 q^{92} + 50 q^{93} + 30 q^{94} - 20 q^{95} + 10 q^{97} + 40 q^{98} + 20 q^{99}+O(q^{100}) $ 280 * q - 10 * q^11 - 20 * q^13 + 30 * q^17 + 10 * q^19 + 20 * q^22 + 60 * q^23 + 70 * q^24 + 20 * q^25 + 20 * q^29 + 10 * q^30 + 20 * q^31 + 20 * q^33 - 10 * q^34 + 30 * q^35 - 20 * q^37 + 90 * q^38 - 40 * q^41 - 10 * q^46 - 100 * q^47 + 120 * q^49 - 20 * q^50 - 30 * q^51 + 80 * q^52 - 30 * q^53 - 10 * q^55 + 30 * q^58 + 20 * q^59 + 60 * q^61 - 50 * q^62 - 10 * q^63 + 20 * q^65 + 40 * q^66 + 50 * q^67 + 10 * q^69 + 20 * q^70 + 80 * q^71 - 20 * q^73 + 80 * q^75 - 30 * q^76 - 100 * q^77 - 100 * q^79 + 100 * q^82 + 30 * q^83 - 20 * q^86 - 10 * q^87 - 60 * q^89 - 10 * q^90 + 70 * q^91 - 120 * q^92 + 50 * q^93 + 30 * q^94 - 20 * q^95 + 10 * q^97 + 40 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{21}{50}\right)$	$1$

Coefficient data

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

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

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

$2$	0.248690	+	0.968583i	0.175850	+	0.684892i
$2$	0.248690	+	0.968583i	0.175850	+	0.684892i
$3$	−0.982287	+	0.187381i	−0.567124	+	0.108185i
$3$	−0.982287	+	0.187381i	−0.567124	+	0.108185i
$4$	−0.876307	+	0.481754i	−0.438153	+	0.240877i
$5$	0.353264	+	2.20799i	0.157984	+	0.987442i
$5$	0.353264	+	2.20799i	0.157984	+	0.987442i
$6$	−0.425779	−	0.904827i	−0.173824	−	0.369394i
$7$	−0.0177835	+	0.0244769i	−0.00672153	+	0.00925139i	−0.812365	−	0.583150i	$-0.801820\pi$
$7$	−0.0177835	+	0.0244769i	−0.00672153	+	0.00925139i	0.805643	+	0.592401i	$0.201820\pi$
$8$	−0.684547	−	0.728969i	−0.242024	−	0.257729i
$9$	0.929776	−	0.368125i	0.309925	−	0.122708i
$10$	−2.05077	+	0.891269i	−0.648509	+	0.281844i
$11$	5.22264	−	1.34095i	1.57468	−	0.404310i	0.642498	−	0.766288i	$-0.277898\pi$
$11$	5.22264	−	1.34095i	1.57468	−	0.404310i	0.932187	+	0.361978i	$0.117898\pi$
$12$	0.770513	−	0.637424i	0.222428	−	0.184008i
$13$	1.96984	+	4.97524i	0.546334	+	1.37988i	0.896437	+	0.443172i	$0.146147\pi$
$13$	1.96984	+	4.97524i	0.546334	+	1.37988i	−0.350103	+	0.936711i	$0.613853\pi$
$14$	−0.0281305	−	0.0111376i	−0.00751818	−	0.00297666i
$15$	−0.760742	−	2.10268i	−0.196423	−	0.542910i
$16$	0.535827	−	0.844328i	0.133957	−	0.211082i
$17$	−1.53446	+	2.79117i	−0.372160	+	0.676957i	−0.994378	−	0.105887i	$-0.966232\pi$
$17$	−1.53446	+	2.79117i	−0.372160	+	0.676957i	0.622218	+	0.782844i	$0.286232\pi$
$18$	0.587785	+	0.809017i	0.138542	+	0.190687i
$19$	−0.289654	+	1.51842i	−0.0664512	+	0.348349i	−0.999948	−	0.0102375i	$-0.996741\pi$
$19$	−0.289654	+	1.51842i	−0.0664512	+	0.348349i	0.933496	+	0.358587i	$0.116741\pi$
$20$	−1.37327	−	1.76469i	−0.307073	−	0.394596i
$21$	0.0128820	−	0.0273756i	0.00281108	−	0.00597385i
$22$	2.59763	+	4.72508i	0.553817	+	1.00739i
$23$	−1.58746	−	0.0998745i	−0.331008	−	0.0208253i	−0.103583	−	0.994621i	$-0.533031\pi$
$23$	−1.58746	−	0.0998745i	−0.331008	−	0.0208253i	−0.227425	+	0.973796i	$0.573031\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	−4.75041	+	1.56000i	−0.950082	+	0.312001i
$26$	−4.32905	+	3.14524i	−0.848997	+	0.616833i
$27$	−0.844328	+	0.535827i	−0.162491	+	0.103120i
$28$	0.00379197	−	0.0300165i	0.000716614	−	0.00567259i
$29$	−9.39932	−	1.18741i	−1.74541	−	0.220497i	−0.813092	−	0.582135i	$-0.802217\pi$
$29$	−9.39932	−	1.18741i	−1.74541	−	0.220497i	−0.932318	+	0.361639i	$0.882217\pi$
$30$	1.84743	−	1.25976i	0.337294	−	0.229999i
$31$	−0.125027	−	0.0687343i	−0.0224555	−	0.0123450i	0.470486	−	0.882407i	$-0.344078\pi$
$31$	−0.125027	−	0.0687343i	−0.0224555	−	0.0123450i	−0.492942	+	0.870062i	$0.664078\pi$
$32$	0.951057	+	0.309017i	0.168125	+	0.0546270i
$33$	−4.87886	+	2.29582i	−0.849301	+	0.399651i
$34$	−3.08508	−	0.792114i	−0.529087	−	0.135846i
$35$	−0.0603269	−	0.0306189i	−0.0101971	−	0.00517554i
$36$	−0.637424	+	0.770513i	−0.106237	+	0.128419i
$37$	2.05007	+	1.30102i	0.337030	+	0.213886i	0.693561	−	0.720398i	$-0.256041\pi$
$37$	2.05007	+	1.30102i	0.337030	+	0.213886i	−0.356531	+	0.934283i	$0.616041\pi$
$38$	−1.54275	+	0.0970615i	−0.250267	+	0.0157455i
$39$	−2.86721	−	4.51800i	−0.459121	−	0.723459i
$40$	1.36773	−	1.76899i	0.216257	−	0.279702i
$41$	−0.214331	−	3.40669i	−0.0334728	−	0.532035i	−0.978657	−	0.205499i	$-0.934118\pi$
$41$	−0.214331	−	3.40669i	−0.0334728	−	0.532035i	0.945185	−	0.326537i	$-0.105882\pi$
$42$	0.0297192	+	0.00566924i	0.00458577	+	0.000874782i
$43$	3.55595	−	1.15540i	0.542278	−	0.176197i	−0.0250539	−	0.999686i	$-0.507976\pi$
$43$	3.55595	−	1.15540i	0.542278	−	0.176197i	0.567332	+	0.823489i	$0.307976\pi$
$44$	−3.93063	+	3.69110i	−0.592564	+	0.556455i
$45$	1.14127	+	1.92289i	0.170131	+	0.286647i
$46$	−0.298049	−	1.56243i	−0.0439449	−	0.230367i
$47$	−4.96728	+	5.28961i	−0.724552	+	0.771570i	−0.980795	−	0.195043i	$-0.937515\pi$
$47$	−4.96728	+	5.28961i	−0.724552	+	0.771570i	0.256243	+	0.966612i	$0.417515\pi$
$48$	−0.368125	+	0.929776i	−0.0531342	+	0.134202i
$49$	2.16284	+	6.65653i	0.308977	+	0.950932i
$50$	−2.69237	−	4.21321i	−0.380759	−	0.595838i
$51$	0.984265	−	3.02926i	0.137825	−	0.424181i
$52$	−4.12302	−	3.41086i	−0.571760	−	0.473001i
$53$	−6.41210	−	3.01731i	−0.880770	−	0.414459i	−0.0684386	−	0.997655i	$-0.521802\pi$
$53$	−6.41210	−	3.01731i	−0.880770	−	0.414459i	−0.812331	+	0.583197i	$0.801802\pi$
$54$	−0.728969	−	0.684547i	−0.0992001	−	0.0931551i
$55$	4.80576	+	11.0578i	0.648008	+	1.49103i
$56$	0.0300165	−	0.00379197i	0.00401112	−	0.000506723i
$57$		−	1.54580i		−	0.204746i
$58$	−1.18741	−	9.39932i	−0.155915	−	1.23419i
$59$	3.48685	+	4.21487i	0.453949	+	0.548730i	0.946984	−	0.321279i	$-0.104113\pi$
$59$	3.48685	+	4.21487i	0.453949	+	0.548730i	−0.493036	+	0.870009i	$0.664113\pi$
$60$	1.67962	+	1.47610i	0.216838	+	0.190564i
$61$	0.852532	−	13.5506i	0.109156	−	1.73498i	−0.438901	−	0.898536i	$-0.644632\pi$
$61$	0.852532	−	13.5506i	0.109156	−	1.73498i	0.548056	−	0.836441i	$-0.315368\pi$
$62$	0.0354819	−	0.138193i	0.00450620	−	0.0175505i
$63$	−0.00752413	+	0.0293046i	−0.000947952	+	0.00369203i
$64$	−0.0627905	+	0.998027i	−0.00784881	+	0.124753i
$65$	−10.2894	+	6.10694i	−1.27624	+	0.757473i
$66$	−3.43701	−	4.15464i	−0.423067	−	0.511400i
$67$	−0.166549	−	1.31837i	−0.0203472	−	0.161064i	0.978667	−	0.205452i	$-0.0658664\pi$
$67$	−0.166549	−	1.31837i	−0.0203472	−	0.161064i	−0.999014	+	0.0443874i	$0.985866\pi$
$68$		−	3.18515i		−	0.386256i
$69$	1.57806	−	0.199355i	0.189976	−	0.0239995i
$70$	0.0146543	−	0.0660462i	0.00175152	−	0.00789403i
$71$	6.23221	+	5.85244i	0.739627	+	0.694556i	0.959731	−	0.280920i	$-0.0906396\pi$
$71$	6.23221	+	5.85244i	0.739627	+	0.694556i	−0.220104	+	0.975476i	$0.570640\pi$
$72$	−0.904827	−	0.425779i	−0.106635	−	0.0501786i
$73$	5.79168	+	4.79129i	0.677865	+	0.560778i	0.911376	−	0.411576i	$-0.135021\pi$
$73$	5.79168	+	4.79129i	0.677865	+	0.560778i	−0.233511	+	0.972354i	$0.575021\pi$
$74$	−0.750310	+	2.30922i	−0.0872218	+	0.268441i
$75$	4.37395	−	2.42251i	0.505060	−	0.279727i
$76$	−0.477678	−	1.47014i	−0.0547934	−	0.168637i
$77$	−0.0600546	+	0.151681i	−0.00684385	+	0.0172856i
$78$	3.66302	−	3.90071i	0.414755	−	0.441669i
$79$	0.966951	+	5.06893i	0.108790	+	0.570299i	0.994383	+	0.105837i	$0.0337523\pi$
$79$	0.966951	+	5.06893i	0.108790	+	0.570299i	−0.885593	+	0.464462i	$0.846248\pi$
$80$	2.05355	+	0.884828i	0.229594	+	0.0989268i
$81$	0.728969	−	0.684547i	0.0809965	−	0.0760608i
$82$	3.24636	−	1.05481i	0.358500	−	0.116484i
$83$	0.435788	+	0.0831310i	0.0478340	+	0.00912482i	0.211243	−	0.977434i	$-0.432249\pi$
$83$	0.435788	+	0.0831310i	0.0478340	+	0.00912482i	−0.163409	+	0.986558i	$0.552249\pi$
$84$	0.00189973	+	0.0301954i	0.000207278	+	0.00329459i
$85$	−6.70493	−	2.40204i	−0.727251	−	0.260538i
$86$	2.00343	+	3.15690i	0.216035	+	0.340417i
$87$	9.45533	−	0.594879i	1.01372	−	0.0637777i
$88$	−4.55265	−	2.88920i	−0.485314	−	0.307990i
$89$	−0.538329	+	0.650728i	−0.0570628	+	0.0689770i	−0.798272	−	0.602297i	$-0.794252\pi$
$89$	−0.538329	+	0.650728i	−0.0570628	+	0.0689770i	0.741210	+	0.671274i	$0.234252\pi$
$90$	−1.57866	+	1.58362i	−0.166405	+	0.166928i
$91$	−0.156809	−	0.0402617i	−0.0164380	−	0.00422057i
$92$	1.43922	−	0.677244i	0.150049	−	0.0706076i
$93$	0.135692	+	0.0440890i	0.0140706	+	0.00457182i
$94$	−6.35874	−	3.49575i	−0.655854	−	0.360559i
$95$	−3.45497	−	0.103149i	−0.354473	−	0.0105829i
$96$	−0.992115	−	0.125333i	−0.101257	−	0.0127918i
$97$	−2.05453	+	16.2633i	−0.208606	+	1.65128i	0.445795	+	0.895135i	$0.352921\pi$
$97$	−2.05453	+	16.2633i	−0.208606	+	1.65128i	−0.654400	+	0.756148i	$0.727079\pi$
$98$	−5.90952	+	3.75030i	−0.596952	+	0.378837i
$99$	4.36225	−	3.16936i	0.438423	−	0.318533i
$100$	3.41128	−	3.65557i	0.341128	−	0.365557i
$101$	−4.27474	−	3.10578i	−0.425352	−	0.309037i	0.354435	−	0.935080i	$-0.384673\pi$
$101$	−4.27474	−	3.10578i	−0.425352	−	0.309037i	−0.779788	+	0.626044i	$0.784673\pi$
$102$	3.17886	+	0.199997i	0.314754	+	0.0198027i
$103$	2.17690	+	3.95977i	0.214496	+	0.390168i	0.961564	−	0.274580i	$-0.0885389\pi$
$103$	2.17690	+	3.95977i	0.214496	+	0.390168i	−0.747068	+	0.664748i	$0.768539\pi$
$104$	2.27835	−	4.84173i	0.223410	−	0.474771i
$105$	0.0649957	+	0.0187724i	0.00634293	+	0.00183200i
$106$	1.32789	−	6.96103i	0.128976	−	0.676115i
$107$	5.79054	+	7.97000i	0.559793	+	0.770489i	0.991300	−	0.131621i	$-0.0420181\pi$
$107$	5.79054	+	7.97000i	0.559793	+	0.770489i	−0.431507	+	0.902109i	$0.642018\pi$
$108$	0.481754	−	0.876307i	0.0463568	−	0.0843226i
$109$	4.26881	−	6.72657i	0.408878	−	0.644288i	−0.576018	−	0.817437i	$-0.695394\pi$
$109$	4.26881	−	6.72657i	0.408878	−	0.644288i	0.984896	+	0.173149i	$0.0553942\pi$
$110$	−9.51526	+	7.40474i	−0.907244	+	0.706014i
$111$	−2.25755	−	0.893826i	−0.214277	−	0.0848382i
$112$	0.0111376	+	0.0281305i	0.00105241	+	0.00265808i
$113$	5.51764	−	4.56459i	0.519056	−	0.429400i	−0.340650	−	0.940190i	$-0.610647\pi$
$113$	5.51764	−	4.56459i	0.519056	−	0.429400i	0.859705	+	0.510790i	$0.170647\pi$
$114$	1.49723	−	0.384425i	0.140229	−	0.0360047i
$115$	−0.340271	−	3.54037i	−0.0317304	−	0.330142i
$116$	8.80873	−	3.48762i	0.817870	−	0.323818i
$117$	3.66302	+	3.90071i	0.338646	+	0.360621i
$118$	−3.21531	+	4.42550i	−0.295993	+	0.407400i
$119$	−0.0410310	−	0.0871954i	−0.00376131	−	0.00799319i
$120$	−1.01203	+	1.99394i	−0.0923849	+	0.182021i
$121$	15.8384	−	8.70725i	1.43986	−	0.791568i
$122$	13.3369	−	2.54415i	1.20747	−	0.230337i
$123$	0.848884	+	3.30618i	0.0765413	+	0.298109i
$124$	0.142675			0.0128126
$125$	−5.12262	−	9.93775i	−0.458181	−	0.888859i
$126$	−0.0302551			−0.00269534
$127$	−4.54377	−	17.6968i	−0.403194	−	1.57034i	−0.768751	−	0.639548i	$-0.779121\pi$
$127$	−4.54377	−	17.6968i	−0.403194	−	1.57034i	0.365557	−	0.930789i	$-0.380879\pi$
$128$	−0.982287	+	0.187381i	−0.0868227	+	0.0165623i
$129$	−3.27647	+	1.80125i	−0.288477	+	0.158592i
$130$	−8.47395	−	8.44739i	−0.743215	−	0.740885i
$131$	−1.25012	−	2.65664i	−0.109223	−	0.232112i	0.842742	−	0.538318i	$-0.180940\pi$
$131$	−1.25012	−	2.65664i	−0.109223	−	0.232112i	−0.951965	+	0.306207i	$0.900940\pi$
$132$	3.16936	−	4.36225i	0.275857	−	0.379685i
$133$	−0.0320151	−	0.0340926i	−0.00277606	−	0.00295620i
$134$	1.23553	−	0.489181i	0.106734	−	0.0422588i
$135$	−1.48137	−	1.67498i	−0.127496	−	0.144159i
$136$	3.08508	−	0.792114i	0.264543	−	0.0679232i
$137$	9.64304	−	7.97742i	0.823860	−	0.681557i	−0.126753	−	0.991934i	$-0.540456\pi$
$137$	9.64304	−	7.97742i	0.823860	−	0.681557i	0.950613	+	0.310378i	$0.100456\pi$
$138$	0.585539	+	1.47890i	0.0498444	+	0.125892i
$139$	11.2620	+	4.45894i	0.955229	+	0.378202i	0.793457	−	0.608626i	$-0.208279\pi$
$139$	11.2620	+	4.45894i	0.955229	+	0.378202i	0.161772	+	0.986828i	$0.448279\pi$
$140$	0.0676156	−	0.00223114i	0.00571456	−	0.000188565i
$141$	3.88812	−	6.12670i	0.327439	−	0.515961i
$142$	−4.11868	+	7.49186i	−0.345632	+	0.628703i
$143$	16.9593	+	23.3424i	1.41820	+	1.95199i
$144$	0.187381	−	0.982287i	0.0156151	−	0.0818573i
$145$	−0.698654	−	21.1730i	−0.0580201	−	1.75833i
$146$	−3.20043	+	6.80127i	−0.264870	+	0.562877i
$147$	−3.37183	−	6.13334i	−0.278104	−	0.505870i
$148$	−2.42326	−	0.152459i	−0.199191	−	0.0125320i
$149$	−18.5827	−	13.5011i	−1.52235	−	1.10605i	−0.960307	−	0.278944i	$-0.910016\pi$
$149$	−18.5827	−	13.5011i	−1.52235	−	1.10605i	−0.562043	−	0.827108i	$-0.689984\pi$
$150$	3.43416	+	3.63408i	0.280398	+	0.296722i
$151$	18.9066	−	13.7365i	1.53860	−	1.11786i	0.587394	−	0.809301i	$-0.300154\pi$
$151$	18.9066	−	13.7365i	1.53860	−	1.11786i	0.951206	−	0.308558i	$-0.0998463\pi$
$152$	1.30516	−	0.828281i	0.105863	−	0.0671824i
$153$	−0.399205	+	3.16003i	−0.0322738	+	0.255473i
$154$	−0.161850	−	0.0204464i	−0.0130423	−	0.00164762i
$155$	0.107597	−	0.300340i	0.00864238	−	0.0241239i
$156$	4.68912	+	2.57787i	0.375430	+	0.206394i
$157$	16.3215	+	5.30317i	1.30260	+	0.423239i	0.876484	−	0.481431i	$-0.159883\pi$
$157$	16.3215	+	5.30317i	1.30260	+	0.423239i	0.426113	+	0.904670i	$0.359883\pi$
$158$	−4.66921	+	2.19716i	−0.371463	+	0.174797i
$159$	6.86391	+	1.76235i	0.544344	+	0.139764i
$160$	−0.346331	+	2.20908i	−0.0273799	+	0.174643i
$161$	0.0306752	−	0.0370800i	0.00241754	−	0.00292231i
$162$	0.844328	+	0.535827i	0.0663367	+	0.0420985i
$163$	6.64667	−	0.418173i	0.520607	−	0.0327538i	0.199686	−	0.979860i	$-0.436008\pi$
$163$	6.64667	−	0.418173i	0.520607	−	0.0327538i	0.320921	+	0.947106i	$0.396008\pi$
$164$	1.82900	+	2.88205i	0.142821	+	0.225050i
$165$	−6.79266	−	9.96143i	−0.528808	−	0.775496i
$166$	0.0278568	+	0.442771i	0.00216211	+	0.0343657i
$167$	−4.37932	−	0.835401i	−0.338882	−	0.0646452i	0.0151314	−	0.999886i	$-0.495183\pi$
$167$	−4.37932	−	0.835401i	−0.338882	−	0.0646452i	−0.354014	+	0.935240i	$0.615183\pi$
$168$	−0.0287743	+	0.00934933i	−0.00221998	+	0.000721317i
$169$	−11.3962	+	10.7017i	−0.876627	+	0.823208i
$170$	0.659130	−	7.09164i	0.0505529	−	0.543904i
$171$	0.289654	+	1.51842i	0.0221504	+	0.116116i
$172$	−2.55949	+	2.72558i	−0.195159	+	0.207823i
$173$	−7.45735	+	18.8351i	−0.566971	+	1.43201i	0.309661	+	0.950847i	$0.399784\pi$
$173$	−7.45735	+	18.8351i	−0.566971	+	1.43201i	−0.876633	+	0.481160i	$0.840216\pi$
$174$	2.92764	+	9.01034i	0.221943	+	0.683072i
$175$	0.0462948	−	0.144017i	0.00349956	−	0.0108867i
$176$	1.66623	−	5.12813i	0.125597	−	0.386548i
$177$	−4.21487	−	3.48685i	−0.316809	−	0.262087i
$178$	−0.764161	−	0.359587i	−0.0572763	−	0.0269522i
$179$	1.78951	+	1.68047i	0.133755	+	0.125604i	0.748538	−	0.663092i	$-0.230756\pi$
$179$	1.78951	+	1.68047i	0.133755	+	0.125604i	−0.614783	+	0.788696i	$0.710756\pi$
$180$	−1.92646	−	1.13523i	−0.143590	−	0.0846150i
$181$	3.34858	−	0.423024i	0.248898	−	0.0314431i	0.000105563	−	1.00000i	$-0.499966\pi$
$181$	3.34858	−	0.423024i	0.248898	−	0.0314431i	0.248792	+	0.968557i	$0.419966\pi$
$182$		−	0.161895i		−	0.0120005i
$183$	1.70170	+	13.4703i	0.125793	+	0.995756i
$184$	1.01389	+	1.22558i	0.0747447	+	0.0903508i
$185$	−2.14841	+	4.98614i	−0.157954	+	0.366588i
$186$	−0.00895864	+	0.142394i	−0.000656880	+	0.0104408i
$187$	−4.27111	+	16.6349i	−0.312334	+	1.21646i
$188$	1.80457	−	7.02833i	0.131612	−	0.512594i
$189$	0.00189973	−	0.0301954i	0.000138185	−	0.00219639i
$190$	−0.759308	−	3.37208i	−0.0550860	−	0.244636i
$191$	−13.0670	−	15.7952i	−0.945491	−	1.14290i	−0.989596	−	0.143876i	$-0.954043\pi$
$191$	−13.0670	−	15.7952i	−0.945491	−	1.14290i	0.0441043	−	0.999027i	$-0.485957\pi$
$192$	−0.125333	−	0.992115i	−0.00904515	−	0.0715997i
$193$			0.577486i			0.0415683i	0.999784	+	0.0207842i	$0.00661628\pi$
$193$			0.577486i			0.0415683i	−0.999784	+	0.0207842i	$0.993384\pi$
$194$	−16.2633	+	2.05453i	−1.16763	+	0.147506i
$195$	8.96281	−	7.92681i	0.641840	−	0.567651i
$196$	−5.10211	−	4.79120i	−0.364437	−	0.342229i
$197$	6.52206	+	3.06905i	0.464677	+	0.218661i	0.643842	−	0.765159i	$-0.277339\pi$
$197$	6.52206	+	3.06905i	0.464677	+	0.218661i	−0.179165	+	0.983819i	$0.557339\pi$
$198$	4.15464	+	3.43701i	0.295257	+	0.244258i
$199$	4.17722	−	12.8561i	0.296115	−	0.911348i	−0.686730	−	0.726913i	$-0.740954\pi$
$199$	4.17722	−	12.8561i	0.296115	−	0.911348i	0.982845	−	0.184435i	$-0.0590456\pi$
$200$	4.38907	+	2.39500i	0.310354	+	0.169352i
$201$	0.410636	+	1.26381i	0.0289641	+	0.0891422i
$202$	1.94512	−	4.91281i	0.136858	−	0.345664i
$203$	0.196217	−	0.208950i	0.0137717	−	0.0146654i
$204$	0.596837	+	3.12873i	0.0417870	+	0.219055i
$205$	7.44620	−	1.67670i	0.520065	−	0.117106i
$206$	−3.29399	+	3.09326i	−0.229503	+	0.215518i
$207$	−1.51275	+	0.491522i	−0.105143	+	0.0341632i
$208$	5.25622	+	1.00268i	0.364454	+	0.0695232i
$209$	0.523359	+	8.31856i	0.0362015	+	0.575407i
$210$	−0.00201889	+	0.0676223i	−0.000139316	+	0.00466638i
$211$	14.0151	+	22.0843i	0.964840	+	1.52034i	0.849882	+	0.526973i	$0.176673\pi$
$211$	14.0151	+	22.0843i	0.964840	+	1.52034i	0.114958	+	0.993370i	$0.463327\pi$
$212$	7.07256	−	0.444968i	0.485746	−	0.0305605i
$213$	−7.21846	−	4.58097i	−0.494601	−	0.313883i
$214$	−6.27955	+	7.59068i	−0.429262	+	0.518888i
$215$	3.80730	+	7.44334i	0.259655	+	0.507631i
$216$	0.968583	+	0.248690i	0.0659037	+	0.0169212i
$217$	0.00390582	−	0.00183794i	0.000265144	−	0.000124767i
$218$	7.57685	+	2.46187i	0.513169	+	0.166739i
$219$	−6.58689	−	3.62117i	−0.445101	−	0.244696i
$220$	−9.53846	−	7.37484i	−0.643083	−	0.497211i
$221$	−16.9093	−	2.13615i	−1.13745	−	0.143693i
$222$	0.304316	−	2.40891i	0.0204243	−	0.161675i
$223$	20.3232	−	12.8975i	1.36094	−	0.863681i	0.363259	−	0.931688i	$-0.381664\pi$
$223$	20.3232	−	12.8975i	1.36094	−	0.863681i	0.997685	+	0.0680070i	$0.0216640\pi$
$224$	−0.0244769	+	0.0177835i	−0.00163543	+	0.00118821i
$225$	−3.84254	+	3.19920i	−0.256170	+	0.213280i
$226$	5.79336	+	4.20912i	0.385369	+	0.279987i
$227$	22.9028	+	1.44092i	1.52011	+	0.0956373i	0.800750	−	0.598998i	$-0.204434\pi$
$227$	22.9028	+	1.44092i	1.52011	+	0.0956373i	0.719362	+	0.694636i	$0.244434\pi$
$228$	0.744694	+	1.35459i	0.0493186	+	0.0897102i
$229$	−1.82967	+	3.88825i	−0.120908	+	0.256943i	−0.956114	−	0.292994i	$-0.905348\pi$
$229$	−1.82967	+	3.88825i	−0.120908	+	0.256943i	0.835206	+	0.549937i	$0.185348\pi$
$230$	3.34452	−	1.21004i	0.220531	−	0.0797874i
$231$	0.0305687	−	0.160247i	0.00201128	−	0.0105435i
$232$	5.56869	+	7.66465i	0.365603	+	0.503209i
$233$	−8.54674	+	15.5465i	−0.559915	+	1.01848i	0.433195	+	0.901300i	$0.357386\pi$
$233$	−8.54674	+	15.5465i	−0.559915	+	1.01848i	−0.993110	+	0.117182i	$0.962614\pi$
$234$	−2.86721	+	4.51800i	−0.187436	+	0.295351i
$235$	−13.4342	−	9.09905i	−0.876348	−	0.593557i
$236$	−5.08608	−	2.01372i	−0.331075	−	0.131082i
$237$	−1.89965	−	4.79796i	−0.123395	−	0.311661i
$238$	0.0742520	−	0.0614266i	0.00481304	−	0.00398169i
$239$	−0.577114	+	0.148178i	−0.0373304	+	0.00958482i	−0.267309	−	0.963611i	$-0.586134\pi$
$239$	−0.577114	+	0.148178i	−0.0373304	+	0.00958482i	0.229978	+	0.973196i	$0.426134\pi$
$240$	−2.18298	−	0.484358i	−0.140911	−	0.0312652i
$241$	2.90658	−	1.15080i	0.187230	−	0.0741294i	−0.272639	−	0.962116i	$-0.587896\pi$
$241$	2.90658	−	1.15080i	0.187230	−	0.0741294i	0.459869	+	0.887987i	$0.347896\pi$
$242$	12.3726	+	13.1754i	0.795338	+	0.846949i
$243$	−0.587785	+	0.809017i	−0.0377064	+	0.0518985i
$244$	5.78097	+	12.2852i	0.370089	+	0.786479i
$245$	−13.9335	+	7.12702i	−0.890176	+	0.455329i
$246$	−2.99121	+	1.64443i	−0.190712	+	0.104845i
$247$	−8.12507	+	1.54994i	−0.516986	+	0.0986203i
$248$	0.0354819	+	0.138193i	0.00225310	+	0.00877524i
$249$	−0.443646			−0.0281149
$250$	8.35159	−	7.43310i	0.528201	−	0.470110i
$251$	−10.5974			−0.668901			−0.334450	−	0.942413i	$-0.608551\pi$
$251$	−10.5974			−0.668901			−0.334450	+	0.942413i	$0.608551\pi$
$252$	−0.00752413	−	0.0293046i	−0.000473976	−	0.00184601i
$253$	−8.42466	+	1.60709i	−0.529654	+	0.101037i
$254$	16.0108	−	8.80203i	1.00461	−	0.552289i
$255$	7.03626	+	1.10312i	0.440628	+	0.0690799i
$256$	−0.425779	−	0.904827i	−0.0266112	−	0.0565517i
$257$	7.72084	−	10.6268i	0.481613	−	0.662883i	−0.497201	−	0.867635i	$-0.665639\pi$
$257$	7.72084	−	10.6268i	0.481613	−	0.662883i	0.978814	+	0.204752i	$0.0656389\pi$
$258$	−2.55949	−	2.72558i	−0.159347	−	0.169687i
$259$	−0.0683023	+	0.0270428i	−0.00424410	+	0.00168036i
$260$	6.07462	−	10.3085i	0.376732	−	0.639306i
$261$	−9.17638	+	2.35609i	−0.568004	+	0.145839i
$262$	2.26228	−	1.87152i	0.139764	−	0.115623i
$263$	−6.52612	−	16.4831i	−0.402418	−	1.01639i	−0.979811	−	0.199925i	$-0.935930\pi$
$263$	−6.52612	−	16.4831i	−0.402418	−	1.01639i	0.577393	−	0.816466i	$-0.304070\pi$
$264$	5.01339	+	1.98494i	0.308553	+	0.122165i
$265$	4.39701	−	15.2237i	0.270106	−	0.935187i
$266$	0.0250597	−	0.0394878i	0.00153651	−	0.00242115i
$267$	0.406860	−	0.740075i	0.0248994	−	0.0452918i
$268$	0.781077	+	1.07506i	0.0477119	+	0.0656697i
$269$	3.62728	−	19.0149i	0.221159	−	1.15936i	−0.682428	−	0.730953i	$-0.739076\pi$
$269$	3.62728	−	19.0149i	0.221159	−	1.15936i	0.903587	−	0.428404i	$-0.140924\pi$
$270$	1.25395	−	1.85138i	0.0763131	−	0.112671i
$271$	4.00855	−	8.51860i	0.243502	−	0.517468i	−0.745295	−	0.666735i	$-0.767691\pi$
$271$	4.00855	−	8.51860i	0.243502	−	0.517468i	0.988797	+	0.149267i	$0.0476913\pi$
$272$	1.53446	+	2.79117i	0.0930401	+	0.169239i
$273$	0.161576	+	0.0101655i	0.00977900	+	0.000615243i
$274$	10.1249	+	7.35618i	0.611669	+	0.444403i
$275$	−22.7178	+	14.5174i	−1.36993	+	0.875430i
$276$	−1.28682	+	0.934931i	−0.0774576	+	0.0562762i
$277$	−27.7515	+	17.6117i	−1.66743	+	1.05818i	−0.749019	+	0.662549i	$0.769475\pi$
$277$	−27.7515	+	17.6117i	−1.66743	+	1.05818i	−0.918409	+	0.395633i	$0.870525\pi$
$278$	−1.51811	+	12.0171i	−0.0910501	+	0.720736i
$279$	−0.141550	−	0.0178819i	−0.00847438	−	0.00107056i
$280$	0.0189764	+	0.0649365i	0.00113405	+	0.00388070i
$281$	17.9534	+	9.86996i	1.07101	+	0.588793i	0.916841	−	0.399252i	$-0.130730\pi$
$281$	17.9534	+	9.86996i	1.07101	+	0.588793i	0.154168	+	0.988045i	$0.450730\pi$
$282$	6.90115	+	2.24232i	0.410958	+	0.133528i
$283$	−24.2989	+	11.4342i	−1.44442	+	0.679692i	−0.978710	−	0.205247i	$-0.934200\pi$
$283$	−24.2989	+	11.4342i	−1.44442	+	0.679692i	−0.465708	+	0.884938i	$0.654200\pi$
$284$	−8.28076	−	2.12614i	−0.491373	−	0.126163i
$285$	3.41310	−	0.546075i	0.202175	−	0.0323467i
$286$	−18.3915	+	22.2315i	−1.08751	+	1.31458i
$287$	0.0871966	+	0.0553366i	0.00514705	+	0.00326642i
$288$	0.998027	−	0.0627905i	0.0588093	−	0.00369997i
$289$	3.67300	+	5.78773i	0.216059	+	0.340455i
$290$	20.3341	−	5.94223i	1.19406	−	0.348940i
$291$	−1.02929	−	16.3602i	−0.0603383	−	0.959050i
$292$	−7.38351	−	1.40848i	−0.432087	−	0.0824250i
$293$	12.4195	−	4.03535i	0.725556	−	0.235748i	0.0771258	−	0.997021i	$-0.475426\pi$
$293$	12.4195	−	4.03535i	0.725556	−	0.235748i	0.648431	+	0.761274i	$0.275426\pi$
$294$	5.10211	−	4.79120i	0.297561	−	0.279429i
$295$	−8.07460	+	9.18787i	−0.470122	+	0.534938i
$296$	−0.454972	−	2.38505i	−0.0264447	−	0.138628i
$297$	−3.69110	+	3.93063i	−0.214180	+	0.228078i
$298$	8.45561	−	21.3564i	0.489820	−	1.23714i
$299$	−2.63014	−	8.09473i	−0.152105	−	0.468130i
$300$	−2.66587	+	4.23003i	−0.153914	+	0.244221i
$301$	−0.0349567	+	0.107586i	−0.00201487	+	0.00620113i
$302$	18.0068	+	14.8965i	1.03618	+	0.857199i
$303$	4.78099	+	2.24976i	0.274660	+	0.129245i
$304$	1.12684	+	1.05817i	0.0646286	+	0.0606903i
$305$	30.2207	−	2.90456i	1.73043	−	0.166315i
$306$	−3.16003	+	0.399205i	−0.180647	+	0.0228210i
$307$		−	11.4676i		−	0.654490i	−0.944940	−	0.327245i	$-0.893880\pi$
$307$		−	11.4676i		−	0.654490i	0.944940	−	0.327245i	$-0.106120\pi$
$308$	−0.0204464	−	0.161850i	−0.00116504	−	0.00922227i
$309$	−2.88033	−	3.48172i	−0.163856	−	0.198068i
$310$	0.317662	+	0.0295250i	0.0180420	+	0.00167691i
$311$	−1.06931	+	16.9962i	−0.0606350	+	0.963766i	0.843665	+	0.536870i	$0.180393\pi$
$311$	−1.06931	+	16.9962i	−0.0606350	+	0.963766i	−0.904300	+	0.426897i	$0.859607\pi$
$312$	−1.33074	+	5.18289i	−0.0753384	+	0.293424i
$313$	2.27314	−	8.85331i	0.128486	−	0.500419i	−0.871465	−	0.490458i	$-0.836829\pi$
$313$	2.27314	−	8.85331i	0.128486	−	0.500419i	0.999950	−	0.00996048i	$-0.00317057\pi$
$314$	−1.07758	+	17.1276i	−0.0608111	+	0.966565i
$315$	−0.0673621	−	0.00626094i	−0.00379542	−	0.000352764i
$316$	−3.28932	−	3.97611i	−0.185039	−	0.223674i
$317$	−3.54822	−	28.0870i	−0.199288	−	1.57752i	−0.701429	−	0.712739i	$-0.747454\pi$
$317$	−3.54822	−	28.0870i	−0.199288	−	1.57752i	0.502142	−	0.864785i	$-0.332546\pi$
$318$			7.08655i			0.397394i
$319$	−50.6815	+	6.40256i	−2.83762	+	0.358475i
$320$	−2.22581	+	0.213926i	−0.124427	+	0.0119588i
$321$	−7.18140	−	6.74379i	−0.400827	−	0.376401i
$322$	0.0435436	+	0.0204901i	0.00242659	+	0.00114187i
$323$	−3.79370	−	3.13842i	−0.211087	−	0.174626i
$324$	−0.309017	+	0.951057i	−0.0171676	+	0.0528365i
$325$	−17.1189	−	20.5615i	−0.949587	−	1.14055i
$326$	2.05799	+	6.33386i	0.113982	+	0.350800i
$327$	−2.93276	+	7.40731i	−0.162182	+	0.409625i
$328$	−2.33665	+	2.48828i	−0.129020	+	0.137392i
$329$	−0.0411377	−	0.215651i	−0.00226799	−	0.0118892i
$330$	7.95921	−	9.05656i	0.438140	−	0.498547i
$331$	7.64387	−	7.17807i	0.420145	−	0.394542i	−0.445434	−	0.895315i	$-0.646951\pi$
$331$	7.64387	−	7.17807i	0.420145	−	0.394542i	0.865579	+	0.500772i	$0.166951\pi$
$332$	−0.421933	+	0.137094i	−0.0231566	+	0.00752402i
$333$	2.38505	+	0.454972i	0.130700	+	0.0249323i
$334$	−0.279938	−	4.44949i	−0.0153176	−	0.243466i
$335$	2.85211	−	0.833470i	0.155827	−	0.0455373i
$336$	−0.0162115	−	0.0255452i	−0.000884409	−	0.00139361i
$337$	−29.8248	+	1.87642i	−1.62466	+	0.102215i	−0.848809	−	0.528699i	$-0.822680\pi$
$337$	−29.8248	+	1.87642i	−1.62466	+	0.102215i	−0.775853	+	0.630914i	$0.782680\pi$
$338$	−13.1996	−	8.37672i	−0.717963	−	0.455633i
$339$	−4.56459	+	5.51764i	−0.247914	+	0.299677i
$340$	7.03276	−	1.12520i	0.381405	−	0.0610224i
$341$	−0.745140	−	0.191319i	−0.0403516	−	0.0103605i
$342$	−1.39868	+	0.658169i	−0.0756320	+	0.0355897i
$343$	−0.402814	−	0.130882i	−0.0217499	−	0.00706697i
$344$	−3.27647	−	1.80125i	−0.176655	−	0.0971171i
$345$	0.997643	+	3.41390i	0.0537113	+	0.183798i
$346$	−20.0979	−	2.53896i	−1.08047	−	0.136495i
$347$	3.25514	−	25.7670i	0.174745	−	1.38325i	−0.623928	−	0.781482i	$-0.714464\pi$
$347$	3.25514	−	25.7670i	0.174745	−	1.38325i	0.798673	−	0.601766i	$-0.205536\pi$
$348$	−7.99919	+	5.07644i	−0.428801	+	0.272126i
$349$	4.63670	−	3.36876i	0.248197	−	0.180326i	−0.456730	−	0.889605i	$-0.650980\pi$
$349$	4.63670	−	3.36876i	0.248197	−	0.180326i	0.704927	+	0.709280i	$0.250980\pi$
$350$	0.151006	+	0.00902471i	0.00807161	+	0.000482391i
$351$	−4.32905	−	3.14524i	−0.231068	−	0.167881i
$352$	5.38140	+	0.338569i	0.286829	+	0.0180458i
$353$	−5.56976	−	10.1314i	−0.296448	−	0.539238i	0.685574	−	0.728003i	$-0.259551\pi$
$353$	−5.56976	−	10.1314i	−0.296448	−	0.539238i	−0.982022	+	0.188765i	$0.939551\pi$
$354$	2.32910	−	4.94960i	0.123790	−	0.263068i
$355$	−10.7205	+	15.8281i	−0.568984	+	0.840068i
$356$	0.158251	−	0.829579i	0.00838727	−	0.0439676i
$357$	0.0566430	+	0.0779625i	0.00299787	+	0.00412621i
$358$	−1.18264	+	2.15121i	−0.0625043	+	0.113695i
$359$	15.2367	−	24.0092i	0.804164	−	1.26716i	−0.156010	−	0.987755i	$-0.549863\pi$
$359$	15.2367	−	24.0092i	0.804164	−	1.26716i	0.960174	−	0.279404i	$-0.0901368\pi$
$360$	0.620472	−	2.14826i	0.0327018	−	0.113223i
$361$	15.4441	+	6.11473i	0.812845	+	0.321828i
$362$	1.24249	+	3.13817i	0.0653038	+	0.164939i
$363$	−13.9263	+	11.5208i	−0.730942	+	0.604688i
$364$	0.156809	−	0.0402617i	0.00821902	−	0.00211028i
$365$	−8.53312	+	14.4805i	−0.446644	+	0.757946i
$366$	−12.6239	+	4.99817i	−0.659864	+	0.261259i
$367$	2.66271	+	2.83550i	0.138992	+	0.148012i	0.794698	−	0.607004i	$-0.207629\pi$
$367$	2.66271	+	2.83550i	0.138992	+	0.148012i	−0.655706	+	0.755016i	$0.727629\pi$
$368$	−0.934931	+	1.28682i	−0.0487366	+	0.0670802i
$369$	−1.45336	−	3.08856i	−0.0756591	−	0.160784i
$370$	−5.36378	−	0.840911i	−0.278849	−	0.0437169i
$371$	0.187884	−	0.103290i	0.00975444	−	0.00536255i
$372$	−0.140148	+	0.0267346i	−0.00726633	+	0.00138613i
$373$	4.84453	+	18.8682i	0.250840	+	0.976959i	0.961806	+	0.273732i	$0.0882581\pi$
$373$	4.84453	+	18.8682i	0.250840	+	0.976959i	−0.710966	+	0.703227i	$0.751742\pi$
$374$	−17.1744			−0.888069
$375$	6.89403	+	8.80184i	0.356006	+	0.454525i
$376$	7.25630			0.374215
$377$	−12.6075	−	49.1029i	−0.649318	−	2.52893i
$378$	0.0297192	−	0.00566924i	0.00152859	−	0.000291594i
$379$	18.0131	−	9.90279i	0.925271	−	0.508672i	0.0534904	−	0.998568i	$-0.482965\pi$
$379$	18.0131	−	9.90279i	0.925271	−	0.508672i	0.871781	+	0.489896i	$0.162965\pi$
$380$	3.07731	−	1.57406i	0.157863	−	0.0807473i
$381$	7.77933	+	16.5319i	0.398547	+	0.846956i
$382$	12.0494	−	16.5845i	0.616500	−	0.848539i
$383$	6.77589	+	7.21559i	0.346232	+	0.368699i	0.878389	−	0.477946i	$-0.158619\pi$
$383$	6.77589	+	7.21559i	0.346232	+	0.368699i	−0.532157	+	0.846645i	$0.678619\pi$
$384$	0.929776	−	0.368125i	0.0474475	−	0.0187858i
$385$	−0.356124	−	0.0790164i	−0.0181497	−	0.00402705i
$386$	−0.559343	+	0.143615i	−0.0284698	+	0.00730981i
$387$	2.88091	−	2.38330i	0.146445	−	0.121150i
$388$	−6.03449	−	15.2414i	−0.306355	−	0.773764i
$389$	−23.3180	−	9.23224i	−1.18227	−	0.468093i	−0.306990	−	0.951713i	$-0.599322\pi$
$389$	−23.3180	−	9.23224i	−1.18227	−	0.468093i	−0.875278	+	0.483620i	$0.839322\pi$
$390$	9.90674	+	6.70991i	0.501647	+	0.339769i
$391$	2.71466	−	4.27761i	0.137286	−	0.216328i
$392$	3.37183	−	6.13334i	0.170303	−	0.309781i
$393$	1.72578	+	2.37533i	0.0870541	+	0.119820i
$394$	−1.35066	+	7.08040i	−0.0680452	+	0.356705i
$395$	−10.8505	+	3.92568i	−0.545950	+	0.197523i
$396$	−2.29582	+	4.87886i	−0.115369	+	0.245172i
$397$	−7.43189	−	13.5186i	−0.372996	−	0.678477i	0.621481	−	0.783429i	$-0.286531\pi$
$397$	−7.43189	−	13.5186i	−0.372996	−	0.678477i	−0.994477	+	0.104952i	$0.966531\pi$
$398$	13.4911	+	0.848787i	0.676247	+	0.0425458i
$399$	0.0378363	+	0.0274897i	0.00189419	+	0.00137621i
$400$	−1.22824	+	4.84680i	−0.0614121	+	0.242340i
$401$	−7.85336	+	5.70580i	−0.392178	+	0.284934i	−0.766347	−	0.642426i	$-0.777928\pi$
$401$	−7.85336	+	5.70580i	−0.392178	+	0.284934i	0.374169	+	0.927360i	$0.377928\pi$
$402$	−1.12198	+	0.712032i	−0.0559594	+	0.0355129i
$403$	0.0956863	−	0.757435i	0.00476647	−	0.0377305i
$404$	5.24220	+	0.662244i	0.260809	+	0.0329479i
$405$	1.76899	+	1.36773i	0.0879018	+	0.0679629i
$406$	0.251182	+	0.138089i	0.0124660	+	0.00685323i
$407$	12.4514	+	4.04570i	0.617192	+	0.200538i
$408$	−2.88201	+	1.35617i	−0.142681	+	0.0671404i
$409$	23.9840	+	6.15804i	1.18593	+	0.304495i	0.789606	−	0.613614i	$-0.210285\pi$
$409$	23.9840	+	6.15804i	1.18593	+	0.304495i	0.396326	+	0.918110i	$0.370285\pi$
$410$	3.47582	+	6.79529i	0.171658	+	0.335595i
$411$	−7.97742	+	9.64304i	−0.393497	+	0.475656i
$412$	−3.81527	−	2.42124i	−0.187965	−	0.119286i
$413$	−0.165175	+	0.0103919i	−0.00812774	+	0.000511354i
$414$	−0.852286	−	1.34299i	−0.0418876	−	0.0660042i
$415$	−0.0296040	+	0.991581i	−0.00145320	+	0.0486748i
$416$	0.335992	+	5.34045i	0.0164734	+	0.261837i
$417$	−11.8980	−	2.26967i	−0.582649	−	0.111146i
$418$	−7.92706	+	2.57566i	−0.387725	+	0.125980i
$419$	−11.7936	+	11.0750i	−0.576157	+	0.541047i	−0.916904	−	0.399108i	$-0.869320\pi$
$419$	−11.7936	+	11.0750i	−0.576157	+	0.541047i	0.340747	+	0.940155i	$0.389320\pi$
$420$	−0.0659999	+	0.0148615i	−0.00322046	+	0.000725168i
$421$	2.02883	+	10.6355i	0.0988792	+	0.518343i	0.996920	+	0.0784300i	$0.0249907\pi$
$421$	2.02883	+	10.6355i	0.0988792	+	0.518343i	−0.898040	+	0.439913i	$0.855009\pi$
$422$	−17.9050	+	19.0669i	−0.871604	+	0.928164i
$423$	−2.67122	+	6.74674i	−0.129879	+	0.328038i
$424$	2.18986	+	6.73971i	0.106349	+	0.327309i
$425$	2.93507	−	15.6529i	0.142372	−	0.759279i
$426$	2.64190	−	8.13092i	0.128000	−	0.393944i
$427$	0.316515	+	0.261844i	0.0153173	+	0.0126715i
$428$	−8.91386	−	4.19455i	−0.430868	−	0.202751i
$429$	−21.0328	−	19.7511i	−1.01547	−	0.953593i
$430$	−6.26266	+	5.53877i	−0.302012	+	0.267103i
$431$	32.4114	−	4.09451i	1.56120	−	0.197226i	0.703244	−	0.710948i	$-0.251734\pi$
$431$	32.4114	−	4.09451i	1.56120	−	0.197226i	0.857956	+	0.513723i	$0.171734\pi$
$432$			1.00000i			0.0481125i
$433$	1.92967	+	15.2749i	0.0927340	+	0.734065i	0.968093	+	0.250591i	$0.0806251\pi$
$433$	1.92967	+	15.2749i	0.0927340	+	0.734065i	−0.875359	+	0.483474i	$0.839375\pi$
$434$	0.00275153	+	0.00332603i	0.000132078	+	0.000159655i
$435$	4.65371	+	20.6671i	0.223128	+	0.990912i
$436$	−0.500238	+	7.95105i	−0.0239570	+	0.380786i
$437$	0.611465	−	2.38150i	0.0292504	−	0.113923i
$438$	1.86931	−	7.28050i	0.0893193	−	0.347876i
$439$	−0.882700	+	14.0301i	−0.0421290	+	0.669621i	0.919127	+	0.393962i	$0.128896\pi$
$439$	−0.882700	+	14.0301i	−0.0421290	+	0.669621i	−0.961256	+	0.275658i	$0.911104\pi$
$440$	4.77103	−	11.0728i	0.227450	−	0.527877i
$441$	4.46138	+	5.39289i	0.212447	+	0.256804i
$442$	−2.13615	−	16.9093i	−0.101606	−	0.804296i
$443$			14.4130i			0.684784i	0.939557	+	0.342392i	$0.111237\pi$
$443$			14.4130i			0.684784i	−0.939557	+	0.342392i	$0.888763\pi$
$444$	2.40891	−	0.304316i	0.114322	−	0.0144422i
$445$	−1.62697	−	0.958745i	−0.0771258	−	0.0454489i
$446$	17.5465	+	16.4773i	0.830850	+	0.780221i
$447$	20.7834	+	9.77990i	0.983019	+	0.462574i
$448$	−0.0233119	−	0.0192853i	−0.00110139	−	0.000911145i
$449$	−5.14384	+	15.8311i	−0.242753	+	0.747117i	0.753245	+	0.657740i	$0.228488\pi$
$449$	−5.14384	+	15.8311i	−0.242753	+	0.747117i	−0.995998	+	0.0893768i	$0.971512\pi$
$450$	−4.05429	−	2.92621i	−0.191121	−	0.137943i
$451$	−5.68755	−	17.5045i	−0.267816	−	0.824254i
$452$	−2.63614	+	6.65812i	−0.123993	+	0.313172i
$453$	−15.9978	+	17.0359i	−0.751642	+	0.800417i
$454$	4.30004	+	22.5416i	0.201811	+	1.05793i
$455$	0.0335023	−	0.360455i	0.00157061	−	0.0168984i
$456$	−1.12684	+	1.05817i	−0.0527691	+	0.0495535i
$457$	−15.6766	+	5.09364i	−0.733320	+	0.238270i	−0.651789	−	0.758401i	$-0.725981\pi$
$457$	−15.6766	+	5.09364i	−0.733320	+	0.238270i	−0.0815316	+	0.996671i	$0.525981\pi$
$458$	−4.22111	−	0.805220i	−0.197240	−	0.0376255i
$459$	−0.199997	−	3.17886i	−0.00933506	−	0.148377i
$460$	2.00377	+	2.93853i	0.0934262	+	0.137009i
$461$	18.5456	+	29.2231i	0.863753	+	1.36106i	0.931647	+	0.363364i	$0.118372\pi$
$461$	18.5456	+	29.2231i	0.863753	+	1.36106i	−0.0678942	+	0.997693i	$0.521628\pi$
$462$	0.162815	−	0.0102434i	0.00757482	−	0.000476567i
$463$	11.7548	+	7.45981i	0.546291	+	0.346687i	0.780159	−	0.625581i	$-0.215138\pi$
$463$	11.7548	+	7.45981i	0.546291	+	0.346687i	−0.233868	+	0.972268i	$0.575138\pi$
$464$	−6.03897	+	7.29986i	−0.280352	+	0.338888i
$465$	−0.0494129	+	0.315181i	−0.00229147	+	0.0146162i
$466$	−17.1835	−	4.41198i	−0.796011	−	0.204381i
$467$	−23.5975	+	11.1041i	−1.09196	+	0.513837i	−0.885510	−	0.464620i	$-0.846191\pi$
$467$	−23.5975	+	11.1041i	−1.09196	+	0.513837i	−0.206450	+	0.978457i	$0.566191\pi$
$468$	−5.08911	−	1.65355i	−0.235244	−	0.0764354i
$469$	0.0352314	+	0.0193686i	0.00162683	+	0.000894359i
$470$	5.47225	−	15.2749i	0.252416	−	0.704581i
$471$	−17.0261	−	2.15090i	−0.784522	−	0.0991081i
$472$	0.685600	−	5.42708i	0.0315573	−	0.249802i
$473$	17.0221	−	10.8026i	0.782678	−	0.496703i
$474$	4.17480	−	3.03317i	0.191755	−	0.139318i
$475$	−0.992764	−	7.66497i	−0.0455512	−	0.351693i
$476$	0.0779625	+	0.0566430i	0.00357340	+	0.00259623i
$477$	−7.07256	−	0.444968i	−0.323830	−	0.0203737i
$478$	−0.287045	−	0.522133i	−0.0131291	−	0.0238818i
$479$	14.4798	−	30.7711i	0.661598	−	1.40597i	−0.238872	−	0.971051i	$-0.576778\pi$
$479$	14.4798	−	30.7711i	0.661598	−	1.40597i	0.900470	−	0.434917i	$-0.143222\pi$
$480$	−0.0737442	−	2.23485i	−0.00336595	−	0.102007i
$481$	−2.43456	+	12.7624i	−0.111006	+	0.581915i
$482$	1.83748	+	2.52908i	0.0836950	+	0.115196i
$483$	−0.0231838	+	0.0421711i	−0.00105490	+	0.00191885i
$484$	−9.68457	+	15.2604i	−0.440208	+	0.693657i
$485$	−36.6348	+	1.20885i	−1.66350	+	0.0548912i
$486$	−0.929776	−	0.368125i	−0.0421755	−	0.0166985i
$487$	5.61823	+	14.1900i	0.254586	+	0.643012i	0.999714	−	0.0239101i	$-0.00761156\pi$
$487$	5.61823	+	14.1900i	0.254586	+	0.643012i	−0.745128	+	0.666922i	$0.767612\pi$
$488$	−10.4616	+	8.65456i	−0.473573	+	0.391773i
$489$	−6.45058	+	1.65623i	−0.291705	+	0.0748972i
$490$	−10.3682	−	11.7233i	−0.468389	−	0.529605i
$491$	−31.0889	+	12.3089i	−1.40302	+	0.555495i	−0.943113	−	0.332472i	$-0.892117\pi$
$491$	−31.0889	+	12.3089i	−1.40302	+	0.555495i	−0.459907	+	0.887967i	$0.652117\pi$
$492$	−2.33665	−	2.48828i	−0.105344	−	0.112180i
$493$	17.7371	−	24.4130i	0.798839	−	1.09951i
$494$	−3.52187	−	7.48435i	−0.158456	−	0.336737i
$495$	8.53893	+	8.51217i	0.383796	+	0.382594i
$496$	−0.125027	+	0.0687343i	−0.00561388	+	0.00308626i
$497$	−0.254080	+	0.0484683i	−0.0113970	+	0.00217410i
$498$	−0.110330	−	0.429708i	−0.00494402	−	0.0192557i
$499$	−19.4856			−0.872294			−0.436147	−	0.899875i	$-0.643657\pi$
$499$	−19.4856			−0.872294			−0.436147	+	0.899875i	$0.643657\pi$
$500$	9.27653	+	6.24068i	0.414859	+	0.279091i
$501$	4.45829			0.199182
$502$	−2.63546	−	10.2644i	−0.117626	−	0.458125i
$503$	24.3818	−	4.65108i	1.08713	−	0.207381i	0.387489	−	0.921874i	$-0.373343\pi$
$503$	24.3818	−	4.65108i	1.08713	−	0.207381i	0.699643	+	0.714493i	$0.253343\pi$
$504$	0.0265127	−	0.0145755i	0.00118097	−	0.000649244i
$505$	5.34741	−	10.5357i	0.237957	−	0.468834i
$506$	−3.65173	−	7.76031i	−0.162339	−	0.344988i
$507$	9.18900	−	12.6476i	0.408098	−	0.561698i
$508$	12.5072	+	13.3189i	0.554919	+	0.590928i
$509$	−13.4739	+	5.33469i	−0.597219	+	0.236456i	−0.647232	−	0.762293i	$-0.724074\pi$
$509$	−13.4739	+	5.33469i	−0.597219	+	0.236456i	0.0500132	+	0.998749i	$0.484074\pi$
$510$	0.681386	+	7.08954i	0.0301723	+	0.313930i
$511$	−0.220272	+	0.0565563i	−0.00974426	+	0.00250190i
$512$	0.770513	−	0.637424i	0.0340522	−	0.0281704i
$513$	−0.569047	−	1.43725i	−0.0251240	−	0.0634560i
$514$	12.2131	+	4.83549i	0.538695	+	0.213284i
$515$	−7.97409	+	6.20541i	−0.351381	+	0.273443i
$516$	2.00343	−	3.15690i	0.0881961	−	0.138975i
$517$	−18.8492	+	34.2866i	−0.828987	+	1.50792i
$518$	−0.0431793	−	0.0594312i	−0.00189719	−	0.00261126i
$519$	3.79591	−	19.8989i	0.166622	−	0.873463i
$520$	11.4953	+	3.32015i	0.504104	+	0.145598i
$521$	13.5864	−	28.8726i	0.595232	−	1.26493i	−0.349453	−	0.936954i	$-0.613632\pi$
$521$	13.5864	−	28.8726i	0.595232	−	1.26493i	0.944685	−	0.327979i	$-0.106368\pi$
$522$	−4.56415	−	8.30215i	−0.199767	−	0.363375i
$523$	−18.5735	−	1.16855i	−0.812163	−	0.0510970i	−0.348724	−	0.937226i	$-0.613385\pi$
$523$	−18.5735	−	1.16855i	−0.812163	−	0.0510970i	−0.463439	+	0.886129i	$0.653385\pi$
$524$	2.37533	+	1.72578i	0.103767	+	0.0753911i
$525$	−0.0184886	+	0.150141i	−0.000806911	+	0.00655270i
$526$	14.3423	−	10.4203i	0.625353	−	0.454345i
$527$	0.383697	−	0.243502i	0.0167141	−	0.0106071i
$528$	−0.675802	+	5.34952i	−0.0294105	+	0.232808i
$529$	−20.3086	−	2.56557i	−0.882982	−	0.111547i
$530$	15.8389	+	0.472877i	0.688000	+	0.0205405i
$531$	4.79358	+	2.63530i	0.208024	+	0.114362i
$532$	0.0444793	+	0.0144522i	0.00192842	+	0.000626582i
$533$	16.5269	−	7.77696i	0.715859	−	0.336858i
$534$	0.818006	+	0.210028i	0.0353986	+	0.00908881i
$535$	−15.5521	+	15.6009i	−0.672374	+	0.674488i
$536$	−0.847039	+	1.02389i	−0.0365865	+	0.0442255i
$537$	−2.07271	−	1.31538i	−0.0894438	−	0.0567628i
$538$	19.3195	−	1.21548i	0.832925	−	0.0524032i
$539$	20.2217	+	31.8644i	0.871012	+	1.37250i
$540$	2.10506	+	0.754138i	0.0905873	+	0.0324529i
$541$	0.338767	+	5.38454i	0.0145647	+	0.231500i	0.998574	+	0.0533830i	$0.0170004\pi$
$541$	0.338767	+	5.38454i	0.0145647	+	0.231500i	−0.984009	+	0.178117i	$0.943000\pi$
$542$	9.24786	+	1.76412i	0.397230	+	0.0757756i
$543$	−3.21000	+	1.04299i	−0.137754	+	0.0447590i
$544$	−2.32187	+	2.18038i	−0.0995495	+	0.0934832i
$545$	16.3602	+	7.04922i	0.700793	+	0.301955i
$546$	0.0303361	+	0.159027i	0.00129827	+	0.00680575i
$547$	18.5789	−	19.7846i	0.794378	−	0.845927i	−0.196526	−	0.980499i	$-0.562966\pi$
$547$	18.5789	−	19.7846i	0.794378	−	0.845927i	0.990904	+	0.134572i	$0.0429659\pi$
$548$	−4.60711	+	11.6362i	−0.196806	+	0.497075i
$549$	−4.19565	−	12.9129i	−0.179066	−	0.551108i
$550$	−19.7110	−	18.3937i	−0.840478	−	0.784312i
$551$	4.52554	−	13.9282i	0.192794	−	0.593360i
$552$	−1.22558	−	1.01389i	−0.0521640	−	0.0431539i
$553$	−0.141267	−	0.0664754i	−0.00600730	−	0.00282682i
$554$	−23.9599	−	22.4998i	−1.01796	−	0.955926i
$555$	1.17605	−	5.30039i	0.0499204	−	0.224989i
$556$	−12.0171	+	1.51811i	−0.509637	+	0.0643821i
$557$			33.1287i			1.40371i	0.712321	+	0.701854i	$0.247644\pi$
$557$			33.1287i			1.40371i	−0.712321	+	0.701854i	$0.752356\pi$
$558$	−0.0178819	−	0.141550i	−0.000757002	−	0.00599229i
$559$	12.7530	+	15.4158i	0.539396	+	0.652018i
$560$	−0.0581772	+	0.0345292i	−0.00245843	+	0.00145913i
$561$	1.07839	−	17.1405i	0.0455297	−	0.723674i
$562$	−5.09505	+	19.8439i	−0.214922	+	0.837065i
$563$	5.33355	−	20.7728i	0.224782	−	0.875470i	−0.751635	−	0.659579i	$-0.770735\pi$
$563$	5.33355	−	20.7728i	0.224782	−	0.875470i	0.976418	−	0.215891i	$-0.0692655\pi$
$564$	−0.455627	+	7.24198i	−0.0191853	+	0.304942i
$565$	12.0277	+	10.5704i	0.506010	+	0.444699i
$566$	−17.1178	−	20.6919i	−0.719517	−	0.869746i
$567$	0.00379197	+	0.0300165i	0.000159248	+	0.00126057i
$568$		−	8.54936i		−	0.358723i
$569$	−11.5911	+	1.46430i	−0.485926	+	0.0613867i	−0.364480	−	0.931211i	$-0.618753\pi$
$569$	−11.5911	+	1.46430i	−0.485926	+	0.0613867i	−0.121446	+	0.992598i	$0.538753\pi$
$570$	1.37772	+	3.17007i	0.0577065	+	0.132780i
$571$	14.6466	+	13.7541i	0.612940	+	0.575589i	0.927581	−	0.373621i	$-0.121884\pi$
$571$	14.6466	+	13.7541i	0.612940	+	0.575589i	−0.314641	+	0.949211i	$0.601884\pi$
$572$	−26.1068	−	12.2849i	−1.09158	−	0.513659i
$573$	15.7952	+	13.0670i	0.659855	+	0.545880i
$574$	−0.0319132	+	0.0982188i	−0.00133203	+	0.00409957i
$575$	7.69689	−	2.00200i	0.320983	−	0.0834891i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	13.3948	−	33.8315i	0.557634	−	1.40842i	−0.328284	−	0.944579i	$-0.606470\pi$
$577$	13.3948	−	33.8315i	0.557634	−	1.40842i	0.885917	−	0.463843i	$-0.153530\pi$
$578$	−4.69246	+	4.99696i	−0.195180	+	0.207846i
$579$	−0.108210	−	0.567257i	−0.00449706	−	0.0235744i
$580$	10.8124	+	18.2175i	0.448962	+	0.756441i
$581$	−0.00978462	+	0.00918837i	−0.000405934	+	0.000381198i
$582$	15.5902	−	5.06557i	0.646235	−	0.209974i
$583$	−37.5341	−	7.16002i	−1.55450	−	0.296538i
$584$	−0.471974	−	7.50182i	−0.0195304	−	0.310427i
$585$	−7.31872	+	9.46587i	−0.302592	+	0.391366i
$586$	6.99718	+	11.0258i	0.289051	+	0.455471i
$587$	27.8841	−	1.75432i	1.15090	−	0.0724085i	0.524148	−	0.851627i	$-0.324384\pi$
$587$	27.8841	−	1.75432i	1.15090	−	0.0724085i	0.626752	+	0.779219i	$0.284384\pi$
$588$	5.90952	+	3.75030i	0.243705	+	0.154660i
$589$	0.140582	−	0.169934i	0.00579258	−	0.00700202i
$590$	−10.9073	−	5.53600i	−0.449046	−	0.227913i
$591$	−6.98162	−	1.79257i	−0.287185	−	0.0737367i
$592$	2.19697	−	1.03382i	0.0902949	−	0.0424895i
$593$	27.5885	+	8.96405i	1.13292	+	0.368110i	0.814687	−	0.579901i	$-0.196909\pi$
$593$	27.5885	+	8.96405i	1.13292	+	0.368110i	0.318238	+	0.948011i	$0.396909\pi$
$594$	−4.72508	−	2.59763i	−0.193872	−	0.106582i
$595$	0.178031	−	0.121399i	0.00729858	−	0.00497687i
$596$	22.7883	+	2.87883i	0.933445	+	0.117922i
$597$	−1.69422	+	13.4112i	−0.0693400	+	0.548882i
$598$	7.18633	−	4.56058i	0.293871	−	0.186496i
$599$	33.9363	−	24.6561i	1.38660	−	1.00742i	0.390369	−	0.920659i	$-0.372348\pi$
$599$	33.9363	−	24.6561i	1.38660	−	1.00742i	0.996229	−	0.0867636i	$-0.0276525\pi$
$600$	−4.76011	−	1.53015i	−0.194331	−	0.0624682i
$601$	13.3449	+	9.69561i	0.544348	+	0.395492i	0.825697	−	0.564113i	$-0.190782\pi$
$601$	13.3449	+	9.69561i	0.544348	+	0.395492i	−0.281349	+	0.959606i	$0.590782\pi$
$602$	−0.112899	−	0.00710301i	−0.00460142	−	0.000289497i
$603$	−0.640177	−	1.16448i	−0.0260700	−	0.0474212i
$604$	−9.95041	+	21.1457i	−0.404877	+	0.860407i
$605$	24.8206	+	31.8951i	1.00910	+	1.29672i
$606$	−0.990098	+	5.19027i	−0.0402200	+	0.210840i
$607$	14.0183	+	19.2946i	0.568986	+	0.783142i	0.992434	−	0.122778i	$-0.0391803\pi$
$607$	14.0183	+	19.2946i	0.568986	+	0.783142i	−0.423448	+	0.905920i	$0.639180\pi$
$608$	−0.744694	+	1.35459i	−0.0302013	+	0.0549360i
$609$	−0.153588	+	0.242016i	−0.00622370	+	0.00980698i
$610$	10.3289	+	28.5489i	0.418205	+	1.15591i
$611$	−36.1018	−	14.2937i	−1.46052	−	0.578262i
$612$	−1.17253	−	2.96148i	−0.0473968	−	0.119711i
$613$	23.6288	−	19.5474i	0.954357	−	0.789512i	−0.0232983	−	0.999729i	$-0.507417\pi$
$613$	23.6288	−	19.5474i	0.954357	−	0.789512i	0.977655	+	0.210216i	$0.0674167\pi$
$614$	11.1073	−	2.85187i	0.448255	−	0.115092i
$615$	−7.00013	+	3.04228i	−0.282272	+	0.122677i
$616$	0.151681	−	0.0600546i	0.00611138	−	0.00241967i
$617$	7.83596	+	8.34445i	0.315464	+	0.335935i	0.867085	−	0.498160i	$-0.165991\pi$
$617$	7.83596	+	8.34445i	0.315464	+	0.335935i	−0.551621	+	0.834095i	$0.685991\pi$
$618$	2.65603	−	3.65571i	0.106841	−	0.147054i
$619$	−4.29127	−	9.11941i	−0.172481	−	0.366540i	0.799832	−	0.600224i	$-0.204922\pi$
$619$	−4.29127	−	9.11941i	−0.172481	−	0.366540i	−0.972313	+	0.233684i	$0.924922\pi$
$620$	0.0504020	+	0.315025i	0.00202419	+	0.0126517i
$621$	1.39385	−	0.766277i	0.0559334	−	0.0307496i
$622$	−16.7282	+	3.19107i	−0.670738	+	0.127950i
$623$	−0.00635442	−	0.0247488i	−0.000254584	−	0.000991541i
$624$	−5.35101			−0.214212
$625$	20.1328	−	14.8213i	0.805311	−	0.592852i
$626$	9.14048			0.365327
$627$	−2.07283	−	8.07315i	−0.0827809	−	0.322410i
$628$	−16.8575	+	3.21573i	−0.672686	+	0.128322i
$629$	−6.77710	+	3.72574i	−0.270221	+	0.148555i
$630$	−0.0106880	−	0.0668028i	−0.000425821	−	0.00266149i
$631$	12.2919	+	26.1215i	0.489331	+	1.03988i	0.985188	+	0.171477i	$0.0548539\pi$
$631$	12.2919	+	26.1215i	0.489331	+	1.03988i	−0.495857	+	0.868404i	$0.665146\pi$
$632$	3.03317	−	4.17480i	0.120653	−	0.166065i
$633$	−17.9050	−	19.0669i	−0.711661	−	0.757842i
$634$	26.3222	−	10.4217i	1.04539	−	0.413899i
$635$	37.4692	−	16.2842i	1.48692	−	0.646219i
$636$	−6.86391	+	1.76235i	−0.272172	+	0.0698818i
$637$	−28.8574	+	23.8729i	−1.14337	+	0.945878i
$638$	−18.8054	−	47.4970i	−0.744513	−	1.88042i
$639$	7.94899	+	3.14723i	0.314457	+	0.124502i
$640$	−0.760742	−	2.10268i	−0.0300710	−	0.0831158i
$641$	−22.7654	+	35.8726i	−0.899180	+	1.41688i	0.00975886	+	0.999952i	$0.496894\pi$
$641$	−22.7654	+	35.8726i	−0.899180	+	1.41688i	−0.908939	+	0.416929i	$0.863106\pi$
$642$	4.74598	−	8.63290i	0.187309	−	0.340713i
$643$	−15.0568	−	20.7238i	−0.593780	−	0.817269i	0.401341	−	0.915929i	$-0.368544\pi$
$643$	−15.0568	−	20.7238i	−0.593780	−	0.817269i	−0.995121	+	0.0986603i	$0.968544\pi$
$644$	−0.00901748	+	0.0472713i	−0.000355339	+	0.00186275i
$645$	−5.13460	−	6.59808i	−0.202175	−	0.259799i
$646$	2.09637	−	4.45500i	0.0824804	−	0.175280i
$647$	−11.4785	−	20.8793i	−0.451266	−	0.820849i	0.548619	−	0.836073i	$-0.315154\pi$
$647$	−11.4785	−	20.8793i	−0.451266	−	0.820849i	−0.999884	+	0.0152237i	$0.995154\pi$
$648$	−0.998027	−	0.0627905i	−0.0392062	−	0.00246664i
$649$	23.8624	+	17.3371i	0.936683	+	0.680540i
$650$	15.6582	−	21.6945i	0.614165	−	0.850929i
$651$	−0.00349224	+	0.00253726i	−0.000136872	+	9.94431e-5i
$652$	−5.62306	+	3.56850i	−0.220216	+	0.139753i
$653$	1.35053	−	10.6905i	0.0528503	−	0.418353i	−0.943388	−	0.331692i	$-0.892380\pi$
$653$	1.35053	−	10.6905i	0.0528503	−	0.418353i	0.996238	−	0.0866607i	$-0.0276196\pi$
$654$	−7.90395	−	0.998501i	−0.309069	−	0.0390445i
$655$	5.42420	−	3.69874i	0.211941	−	0.144522i
$656$	−2.99121	−	1.64443i	−0.116787	−	0.0642042i
$657$	7.14876	+	2.32277i	0.278900	+	0.0906200i
$658$	0.198646	−	0.0934755i	0.00774401	−	0.00364406i
$659$	12.6589	+	3.25026i	0.493121	+	0.126612i	0.487058	−	0.873370i	$-0.338070\pi$
$659$	12.6589	+	3.25026i	0.493121	+	0.126612i	0.00606330	+	0.999982i	$0.498070\pi$
$660$	10.7514	+	5.45688i	0.418498	+	0.212409i
$661$	−19.2220	+	23.2354i	−0.747648	+	0.903751i	−0.997923	−	0.0644241i	$-0.979479\pi$
$661$	−19.2220	+	23.2354i	−0.747648	+	0.903751i	0.250275	+	0.968175i	$0.419479\pi$
$662$	8.85351	+	5.61861i	0.344101	+	0.218373i
$663$	17.0101	−	1.07019i	0.660618	−	0.0415626i
$664$	−0.237718	−	0.374583i	−0.00922523	−	0.0145366i
$665$	0.0639662	−	0.0827326i	0.00248050	−	0.00320823i
$666$	0.152459	+	2.42326i	0.00590766	+	0.0938995i
$667$	14.8025	+	2.82372i	0.573154	+	0.109335i
$668$	4.24009	−	1.37769i	0.164054	−	0.0533043i
$669$	−17.5465	+	16.4773i	−0.678387	+	0.637047i
$670$	1.51657	+	2.55523i	0.0585904	+	0.0987170i
$671$	−13.7182	−	71.9131i	−0.529583	−	2.77617i
$672$	0.0207110	−	0.0220550i	0.000798945	−	0.000850790i
$673$	−13.1527	+	33.2198i	−0.506998	+	1.28053i	0.420700	+	0.907200i	$0.361784\pi$
$673$	−13.1527	+	33.2198i	−0.506998	+	1.28053i	−0.927698	+	0.373331i	$0.878216\pi$
$674$	−9.23460	−	28.4212i	−0.355704	−	1.09474i
$675$	3.17501	−	3.86255i	0.122206	−	0.148670i
$676$	4.83094	−	14.8681i	0.185805	−	0.571850i
$677$	−36.6719	−	30.3376i	−1.40942	−	1.16597i	−0.962463	−	0.271412i	$-0.912509\pi$
$677$	−36.6719	−	30.3376i	−1.40942	−	1.16597i	−0.446952	−	0.894558i	$-0.647491\pi$
$678$	−6.47946	−	3.04900i	−0.248842	−	0.117096i
$679$	−0.361537	−	0.339506i	−0.0138745	−	0.0130290i
$680$	2.83882	+	6.53199i	0.108864	+	0.250490i
$681$	−22.7671	+	2.87616i	−0.872438	+	0.110215i
$682$		−	0.769310i		−	0.0294584i
$683$	−4.99280	−	39.5221i	−0.191044	−	1.51227i	−0.737824	−	0.674993i	$-0.764146\pi$
$683$	−4.99280	−	39.5221i	−0.191044	−	1.51227i	0.546780	−	0.837277i	$-0.315854\pi$
$684$	−0.985329	−	1.19106i	−0.0376750	−	0.0455413i
$685$	21.0206	+	18.4736i	0.803154	+	0.705839i
$686$	0.0265945	−	0.422708i	0.00101538	−	0.0161391i
$687$	1.06868	−	4.16222i	0.0407726	−	0.158799i
$688$	0.929839	−	3.62149i	0.0354498	−	0.138068i
$689$	2.38103	−	37.8453i	0.0907099	−	1.44179i
$690$	−3.05855	+	1.81530i	−0.116437	+	0.0691074i
$691$	−3.40788	−	4.11942i	−0.129642	−	0.156710i	0.701698	−	0.712475i	$-0.252426\pi$
$691$	−3.40788	−	4.11942i	−0.129642	−	0.156710i	−0.831340	+	0.555764i	$0.812426\pi$
$692$	−2.53896	−	20.0979i	−0.0965167	−	0.764009i
$693$			0.163137i			0.00619704i
$694$	25.7670	−	3.25514i	0.978104	−	0.123563i
$695$	−5.86682	+	26.4415i	−0.222541	+	1.00298i
$696$	−6.90627	−	6.48542i	−0.261781	−	0.245829i
$697$	9.83751	+	4.62918i	0.372622	+	0.175343i
$698$	4.41602	+	3.65325i	0.167149	+	0.138278i
$699$	5.48223	−	16.8726i	0.207357	−	0.638180i
$700$	0.0288125	+	0.148506i	0.00108901	+	0.00561301i
$701$	4.69772	+	14.4581i	0.177430	+	0.546075i	0.999736	−	0.0229713i	$-0.00731262\pi$
$701$	4.69772	+	14.4581i	0.177430	+	0.546075i	−0.822306	+	0.569046i	$0.807313\pi$
$702$	1.96984	−	4.97524i	0.0743467	−	0.187778i
$703$	−2.56930	+	2.73603i	−0.0969030	+	0.103191i
$704$	1.01037	+	5.29653i	0.0380796	+	0.199620i
$705$	14.9012	+	6.42058i	0.561211	+	0.241813i
$706$	8.42792	−	7.91434i	0.317189	−	0.297860i
$707$	0.152040	−	0.0494006i	0.00571803	−	0.00185790i
$708$	5.37332	+	1.02502i	0.201942	+	0.0385225i
$709$	0.772288	+	12.2752i	0.0290039	+	0.461003i	0.985546	+	0.169409i	$0.0541858\pi$
$709$	0.772288	+	12.2752i	0.0290039	+	0.461003i	−0.956542	+	0.291595i	$0.905814\pi$
$710$	−17.9969	−	6.44740i	−0.675412	−	0.241966i
$711$	2.76505	+	4.35702i	0.103697	+	0.163401i
$712$	0.842872	−	0.0530290i	0.0315880	−	0.00198735i
$713$	0.191611	+	0.121600i	0.00717588	+	0.00455395i
$714$	−0.0614266	+	0.0742520i	−0.00229883	+	0.00277881i
$715$	−45.5487	+	45.6919i	−1.70342	+	1.70878i
$716$	−2.37773	−	0.610498i	−0.0888601	−	0.0228154i
$717$	0.539126	−	0.253694i	0.0201340	−	0.00947436i
$718$	27.0442	+	8.78718i	1.00928	+	0.327935i
$719$	39.0791	+	21.4839i	1.45741	+	0.801215i	0.996285	−	0.0861219i	$-0.0274474\pi$
$719$	39.0791	+	21.4839i	1.45741	+	0.801215i	0.461121	+	0.887337i	$0.347447\pi$
$720$	2.23507	+	0.0667288i	0.0832962	+	0.00248684i
$721$	−0.135636	−	0.0171348i	−0.00505133	−	0.000638132i
$722$	−2.08185	+	16.4795i	−0.0774784	+	0.613304i
$723$	−2.63946	+	1.67505i	−0.0981627	+	0.0622959i
$724$	−2.73059	+	1.98389i	−0.101481	+	0.0737306i
$725$	46.5030	−	9.02229i	1.72708	−	0.335079i
$726$	−14.6222	−	10.6237i	−0.542682	−	0.394282i
$727$	−36.3121	−	2.28456i	−1.34674	−	0.0847298i	−0.627026	−	0.778999i	$-0.715728\pi$
$727$	−36.3121	−	2.28456i	−1.34674	−	0.0847298i	−0.719716	+	0.694269i	$0.755728\pi$
$728$	0.0779936	+	0.141870i	0.00289063	+	0.00525804i
$729$	0.425779	−	0.904827i	0.0157696	−	0.0335121i
$730$	−16.1477	−	4.66387i	−0.597653	−	0.172618i
$731$	−2.23154	+	11.6982i	−0.0825367	+	0.432672i
$732$	−7.98059	−	10.9843i	−0.294971	−	0.405993i
$733$	24.5382	−	44.6348i	0.906339	−	1.64862i	0.155809	−	0.987787i	$-0.450202\pi$
$733$	24.5382	−	44.6348i	0.906339	−	1.64862i	0.750530	−	0.660836i	$-0.229798\pi$
$734$	−2.08423	+	3.28422i	−0.0769302	+	0.121223i
$735$	12.3512	−	9.61165i	0.455581	−	0.354531i
$736$	−1.47890	−	0.585539i	−0.0545130	−	0.0215832i
$737$	−2.63768	−	6.66203i	−0.0971604	−	0.245399i
$738$	2.63009	−	2.17580i	0.0968149	−	0.0800922i
$739$	20.8842	−	5.36214i	0.768236	−	0.197249i	0.155820	−	0.987785i	$-0.450198\pi$
$739$	20.8842	−	5.36214i	0.768236	−	0.197249i	0.612416	+	0.790536i	$0.290198\pi$
$740$	−0.519424	−	5.40439i	−0.0190944	−	0.198669i
$741$	7.69072	−	3.04497i	0.282526	−	0.111860i
$742$	0.146770	+	0.156294i	0.00538808	+	0.00573773i
$743$	5.86750	−	8.07591i	0.215258	−	0.296277i	−0.687710	−	0.725986i	$-0.741384\pi$
$743$	5.86750	−	8.07591i	0.215258	−	0.296277i	0.902967	+	0.429709i	$0.141384\pi$
$744$	−0.0607481	−	0.129096i	−0.00222713	−	0.00473290i
$745$	23.2456	−	45.7997i	0.851654	−	1.67797i
$746$	−17.0706	+	9.38466i	−0.625001	+	0.343597i
$747$	0.435788	−	0.0831310i	0.0159447	−	0.00304161i
$748$	−4.27111	−	16.6349i	−0.156167	−	0.608231i
$749$	−0.298057			−0.0108908
$750$	−6.81084	+	8.86637i	−0.248697	+	0.323754i
$751$	−37.4421			−1.36628			−0.683141	−	0.730287i	$-0.739387\pi$
$751$	−37.4421			−1.36628			−0.683141	+	0.730287i	$0.739387\pi$
$752$	1.80457	+	7.02833i	0.0658058	+	0.256297i
$753$	10.4097	−	1.98575i	0.379350	−	0.0723648i
$754$	44.4249	−	24.4228i	1.61786	−	0.889425i
$755$	37.0090	+	36.8930i	1.34689	+	1.34267i
$756$	0.0128820	+	0.0273756i	0.000468513	+	0.000995641i
$757$	−2.64434	+	3.63963i	−0.0961103	+	0.132284i	−0.854364	−	0.519675i	$-0.826053\pi$
$757$	−2.64434	+	3.63963i	−0.0961103	+	0.132284i	0.758254	+	0.651960i	$0.226053\pi$
$758$	14.0714	+	14.9845i	0.511095	+	0.544260i
$759$	7.97429	−	3.15725i	0.289449	−	0.114601i
$760$	2.28990	+	2.58918i	0.0830634	+	0.0939193i
$761$	−10.4574	+	2.68500i	−0.379080	+	0.0973313i	−0.433422	−	0.901191i	$-0.642694\pi$
$761$	−10.4574	+	2.68500i	−0.379080	+	0.0973313i	0.0543416	+	0.998522i	$0.482694\pi$
$762$	−14.0779	+	11.6463i	−0.509989	+	0.421899i
$763$	0.0887310	+	0.224109i	0.00321228	+	0.00811329i
$764$	19.0601	+	7.54641i	0.689569	+	0.273020i
$765$	−7.11833	+	0.234886i	−0.257364	+	0.00849232i
$766$	−5.30380	+	8.35746i	−0.191634	+	0.301967i
$767$	−14.1015	+	25.6505i	−0.509175	+	0.926186i
$768$	0.587785	+	0.809017i	0.0212099	+	0.0291929i
$769$	−0.398054	+	2.08667i	−0.0143542	+	0.0752474i	−0.988744	−	0.149620i	$-0.952195\pi$
$769$	−0.398054	+	2.08667i	−0.0143542	+	0.0752474i	0.974389	+	0.224867i	$0.0721949\pi$
$770$	−0.0120304	−	0.364586i	−0.000433544	−	0.0131388i
$771$	−5.59281	+	11.8853i	−0.201420	+	0.428040i
$772$	−0.278206	−	0.506055i	−0.0100129	−	0.0182133i
$773$	−21.3660	−	1.34423i	−0.768482	−	0.0483488i	−0.326290	−	0.945270i	$-0.605799\pi$
$773$	−21.3660	−	1.34423i	−0.768482	−	0.0483488i	−0.442191	+	0.896921i	$0.645799\pi$
$774$	3.02487	+	2.19770i	0.108727	+	0.0789947i
$775$	0.701156	+	0.131473i	0.0251863	+	0.00472265i
$776$	13.2618	−	9.63528i	0.476072	−	0.345886i
$777$	0.0620251	−	0.0393624i	0.00222514	−	0.00141212i
$778$	3.14325	−	24.8814i	0.112691	−	0.892040i
$779$	5.23486	+	0.661316i	0.187558	+	0.0236941i
$780$	−4.03540	+	11.2642i	−0.144490	+	0.403322i
$781$	40.3964	+	22.2081i	1.44550	+	0.794668i
$782$	4.81833	+	1.56557i	0.172303	+	0.0559847i
$783$	8.57236	−	4.03384i	0.306351	−	0.144158i
$784$	6.77920	+	1.74060i	0.242114	+	0.0621643i
$785$	−5.94354	+	37.9111i	−0.212134	+	1.35310i
$786$	−1.87152	+	2.26228i	−0.0667550	+	0.0806930i
$787$	9.73417	+	6.17749i	0.346986	+	0.220204i	0.697886	−	0.716209i	$-0.254124\pi$
$787$	9.73417	+	6.17749i	0.346986	+	0.220204i	−0.350900	+	0.936413i	$0.614124\pi$
$788$	−7.19385	+	0.452599i	−0.256270	+	0.0161232i
$789$	9.49915	+	14.9683i	0.338179	+	0.532884i
$790$	−6.50077	−	9.53338i	−0.231287	−	0.339182i
$791$	0.0136040	+	0.216229i	0.000483701	+	0.00768821i
$792$	−5.29653	−	1.01037i	−0.188204	−	0.0359018i
$793$	69.0968	−	22.4509i	2.45370	−	0.797256i
$794$	11.2456	−	10.5603i	0.399092	−	0.374772i
$795$	−1.46648	+	15.7780i	−0.0520107	+	0.559588i
$796$	2.53297	+	13.2783i	0.0897789	+	0.470637i
$797$	−27.5045	+	29.2893i	−0.974260	+	1.03748i	0.0250251	+	0.999687i	$0.492033\pi$
$797$	−27.5045	+	29.2893i	−0.974260	+	1.03748i	−0.999286	+	0.0377952i	$0.987967\pi$
$798$	−0.0172165	+	0.0434840i	−0.000609459	+	0.00153932i
$799$	−7.14212	−	21.9812i	−0.252670	−	0.777638i
$800$	−4.99998	+	0.0156945i	−0.176776	+	0.000554883i
$801$	−0.260977	+	0.803204i	−0.00922116	+	0.0283798i
$802$	−7.47959	−	6.18766i	−0.264114	−	0.218494i
$803$	36.6727	+	17.2569i	1.29415	+	0.608981i
$804$	−0.968688	−	0.909659i	−0.0341630	−	0.0320812i
$805$	0.0927085	+	0.0546314i	0.00326754	+	0.00192550i
$806$	0.757435	−	0.0956863i	0.0266795	−	0.00337041i
$807$			19.3577i			0.681425i
$808$	0.662244	+	5.24220i	0.0232977	+	0.184420i
$809$	0.359097	+	0.434073i	0.0126252	+	0.0152612i	0.776788	−	0.629762i	$-0.216848\pi$
$809$	0.359097	+	0.434073i	0.0126252	+	0.0152612i	−0.764163	+	0.645023i	$0.776848\pi$
$810$	−0.884828	+	2.05355i	−0.0310897	+	0.0721545i
$811$	0.770421	−	12.2455i	0.0270531	−	0.429997i	−0.961067	−	0.276315i	$-0.910887\pi$
$811$	0.770421	−	12.2455i	0.0270531	−	0.429997i	0.988120	−	0.153682i	$-0.0491133\pi$
$812$	−0.0712838	+	0.277632i	−0.00250157	+	0.00974298i
$813$	−2.34132	+	9.11884i	−0.0821137	+	0.319812i
$814$	−0.822063	+	13.0663i	−0.0288133	+	0.457974i
$815$	3.27135	+	14.5280i	0.114590	+	0.508895i
$816$	−2.03029	−	2.45420i	−0.0710744	−	0.0859141i
$817$	0.724384	+	5.73409i	0.0253430	+	0.200610i
$818$			24.7619i			0.865780i
$819$	−0.160618	+	0.0202908i	−0.00561246	+	0.000709019i
$820$	−5.71740	+	5.05654i	−0.199660	+	0.176582i
$821$	5.34363	+	5.01801i	0.186494	+	0.175130i	0.772171	−	0.635415i	$-0.219171\pi$
$821$	5.34363	+	5.01801i	0.186494	+	0.175130i	−0.585676	+	0.810545i	$0.699171\pi$
$822$	−11.3240	−	5.32866i	−0.394969	−	0.185858i
$823$	−26.5059	−	21.9276i	−0.923939	−	0.764349i	0.0481796	−	0.998839i	$-0.484658\pi$
$823$	−26.5059	−	21.9276i	−0.923939	−	0.764349i	−0.972119	+	0.234490i	$0.924658\pi$
$824$	1.39636	−	4.29754i	0.0486443	−	0.149712i
$825$	19.5951	−	18.5171i	0.682214	−	0.644683i
$826$	−0.0511429	−	0.157402i	−0.00177949	−	0.00547670i
$827$	11.4559	−	28.9343i	0.398360	−	1.00614i	−0.582742	−	0.812657i	$-0.698020\pi$
$827$	11.4559	−	28.9343i	0.398360	−	1.00614i	0.981103	−	0.193487i	$-0.0619797\pi$
$828$	1.08884	−	1.15950i	0.0378398	−	0.0402953i
$829$	−6.85913	−	35.9568i	−0.238227	−	1.24883i	−0.877397	−	0.479766i	$-0.840722\pi$
$829$	−6.85913	−	35.9568i	−0.238227	−	1.24883i	0.639169	−	0.769066i	$-0.279278\pi$
$830$	−0.967791	+	0.217922i	−0.0335925	+	0.00756420i
$831$	23.9599	−	22.4998i	0.831159	−	0.780510i
$832$	−5.08911	+	1.65355i	−0.176433	+	0.0573266i
$833$	−21.8982	−	4.17731i	−0.758729	−	0.144735i
$834$	−0.760555	−	12.0887i	−0.0263359	−	0.418597i
$835$	0.297497	−	9.96460i	0.0102953	−	0.344839i
$836$	−4.46612	−	7.03748i	−0.154464	−	0.243396i
$837$	0.142394	−	0.00895864i	0.00492184	−	0.000309656i
$838$	−13.6600	−	8.66888i	−0.471876	−	0.299462i
$839$	26.5019	−	32.0353i	0.914946	−	1.10598i	−0.0790831	−	0.996868i	$-0.525199\pi$
$839$	26.5019	−	32.0353i	0.914946	−	1.10598i	0.994029	−	0.109112i	$-0.0348008\pi$
$840$	−0.0308081	−	0.0602305i	−0.00106298	−	0.00207815i
$841$	58.8484	+	15.1097i	2.02926	+	0.521024i
$842$	−9.79683	+	4.61004i	−0.337621	+	0.158872i
$843$	−19.4848	−	6.33101i	−0.671093	−	0.218051i
$844$	−22.9207	−	12.6008i	−0.788963	−	0.433736i
$845$	−27.6551	−	21.3820i	−0.951363	−	0.735564i
$846$	−7.19908	−	0.909455i	−0.247509	−	0.0312677i
$847$	−0.0685363	+	0.542521i	−0.00235493	+	0.0186412i
$848$	−5.98337	+	3.79716i	−0.205470	+	0.130395i
$849$	21.7259	−	15.7848i	0.745632	−	0.541733i
$850$	15.8911	−	1.04987i	0.545060	−	0.0360103i
$851$	−3.12447	−	2.27006i	−0.107106	−	0.0778167i
$852$	8.53249	+	0.536818i	0.292318	+	0.0183911i
$853$	−13.9253	−	25.3300i	−0.476792	−	0.867282i	−0.999887	−	0.0150077i	$-0.995223\pi$
$853$	−13.9253	−	25.3300i	−0.476792	−	0.867282i	0.523095	−	0.852274i	$-0.324777\pi$
$854$	−0.174904	+	0.371690i	−0.00598509	+	0.0127190i
$855$	−3.25032	+	1.17595i	−0.111159	+	0.0402168i
$856$	1.84598	−	9.67696i	0.0630943	−	0.330752i
$857$	−18.4261	−	25.3613i	−0.629422	−	0.866326i	0.368574	−	0.929598i	$-0.379846\pi$
$857$	−18.4261	−	25.3613i	−0.629422	−	0.866326i	−0.997996	+	0.0632729i	$0.979846\pi$
$858$	13.9000	−	25.2839i	0.474537	−	0.863179i
$859$	28.5973	−	45.0622i	0.975728	−	1.53750i	0.138706	−	0.990334i	$-0.455706\pi$
$859$	28.5973	−	45.0622i	0.975728	−	1.53750i	0.837023	−	0.547168i	$-0.184294\pi$
$860$	−6.92221	−	4.68847i	−0.236046	−	0.159875i
$861$	−0.0960212	−	0.0380175i	−0.00327239	−	0.00129563i
$862$	12.0263	+	30.3748i	0.409616	+	1.03457i
$863$	9.38038	−	7.76012i	0.319312	−	0.264158i	−0.463934	−	0.885870i	$-0.653563\pi$
$863$	9.38038	−	7.76012i	0.319312	−	0.264158i	0.783246	+	0.621712i	$0.213563\pi$
$864$	−0.968583	+	0.248690i	−0.0329519	+	0.00846060i
$865$	−44.2221	−	9.81196i	−1.50360	−	0.333617i
$866$	−14.3151	+	5.66776i	−0.486448	+	0.192598i
$867$	−4.69246	−	4.99696i	−0.159364	−	0.169706i
$868$	−0.00253726	+	0.00349224i	−8.61203e−5	+	0.000118534i
$869$	11.8472	+	25.1766i	0.401888	+	0.854057i
$870$	−18.8605	+	9.64721i	−0.639430	+	0.327071i
$871$	6.23113	−	3.42559i	0.211134	−	0.116072i
$872$	−7.82566	+	1.49282i	−0.265010	+	0.0505534i
$873$	4.07665	+	15.8775i	0.137974	+	0.537373i
$874$	2.45875			0.0831683
$875$	0.334343	+	0.0513422i	0.0113029	+	0.00173568i
$876$	7.51665			0.253964
$877$	−11.3182	−	44.0816i	−0.382190	−	1.48853i	−0.810952	−	0.585113i	$-0.801050\pi$
$877$	−11.3182	−	44.0816i	−0.382190	−	1.48853i	0.428762	−	0.903417i	$-0.358950\pi$
$878$	−13.8088	+	2.63418i	−0.466026	+	0.0888992i
$879$	−11.4434	+	6.29106i	−0.385976	+	0.212192i
$880$	11.9115	+	1.86743i	0.401535	+	0.0629511i
$881$	13.8007	+	29.3281i	0.464959	+	0.988087i	0.990525	+	0.137334i	$0.0438535\pi$
$881$	13.8007	+	29.3281i	0.464959	+	0.988087i	−0.525566	+	0.850753i	$0.676146\pi$
$882$	−4.11396	+	5.66238i	−0.138524	+	0.190662i
$883$	−37.4023	−	39.8294i	−1.25869	−	1.34037i	−0.916136	−	0.400868i	$-0.868708\pi$
$883$	−37.4023	−	39.8294i	−1.25869	−	1.34037i	−0.342553	−	0.939499i	$-0.611292\pi$
$884$	15.8469	−	6.27422i	0.532988	−	0.211025i
$885$	6.20995	−	10.5382i	0.208745	−	0.354236i
$886$	−13.9602	+	3.58438i	−0.469003	+	0.120419i
$887$	5.73748	−	4.74646i	0.192646	−	0.159370i	−0.536101	−	0.844154i	$-0.680103\pi$
$887$	5.73748	−	4.74646i	0.192646	−	0.159370i	0.728746	+	0.684784i	$0.240103\pi$
$888$	0.893826	+	2.25755i	0.0299948	+	0.0757583i
$889$	0.513966	+	0.203494i	0.0172379	+	0.00682496i
$890$	0.524013	−	1.81429i	0.0175649	−	0.0608150i
$891$	2.88920	−	4.55265i	0.0967918	−	0.152519i
$892$	−11.5960	+	21.0930i	−0.388261	+	0.706245i
$893$	−6.59306	−	9.07457i	−0.220628	−	0.303669i
$894$	−4.30404	+	22.5626i	−0.143949	+	0.754605i
$895$	−3.07828	+	4.54487i	−0.102895	+	0.151918i
$896$	0.0128820	−	0.0273756i	0.000430357	−	0.000914555i
$897$	4.10035	+	7.45851i	0.136907	+	0.249032i
$898$	−16.6130	−	1.04520i	−0.554382	−	0.0348788i
$899$	1.09355	+	0.794514i	0.0364721	+	0.0264985i
$900$	1.82602	−	4.65464i	0.0608674	−	0.155155i
$901$	18.2609	−	13.2673i	0.608358	−	0.441998i
$902$	15.5401	−	9.86206i	0.517429	−	0.328371i
$903$	0.0141780	−	0.112230i	0.000471814	−	0.00373479i
$904$	−7.10452	−	0.897510i	−0.236293	−	0.0298507i
$905$	2.11696	+	7.24417i	0.0703702	+	0.240804i
$906$	−20.4792	−	11.2585i	−0.680375	−	0.374040i
$907$	−3.75163	−	1.21898i	−0.124571	−	0.0404756i	0.246068	−	0.969253i	$-0.420861\pi$
$907$	−3.75163	−	1.21898i	−0.124571	−	0.0404756i	−0.370639	+	0.928777i	$0.620861\pi$
$908$	−20.7640	+	9.77082i	−0.689079	+	0.324256i
$909$	−5.11786	−	1.31404i	−0.169749	−	0.0435841i
$910$	0.357462	−	0.0571917i	0.0118498	−	0.00189589i
$911$	−11.2071	+	13.5470i	−0.371306	+	0.448832i	−0.922761	−	0.385372i	$-0.874073\pi$
$911$	−11.2071	+	13.5470i	−0.371306	+	0.448832i	0.551455	+	0.834205i	$0.314073\pi$
$912$	−1.30516	−	0.828281i	−0.0432182	−	0.0274271i
$913$	2.38744	−	0.150205i	0.0790126	−	0.00497105i
$914$	−8.83222	−	13.9174i	−0.292144	−	0.460345i
$915$	−29.1412	+	8.51591i	−0.963377	+	0.281527i
$916$	−0.269825	−	4.28875i	−0.00891527	−	0.141704i
$917$	0.0872577	+	0.0166453i	0.00288150	+	0.000549676i
$918$	3.02926	−	0.984265i	0.0999803	−	0.0324856i
$919$	−35.5873	+	33.4187i	−1.17392	+	1.10238i	−0.181011	+	0.983481i	$0.557937\pi$
$919$	−35.5873	+	33.4187i	−1.17392	+	1.10238i	−0.992906	+	0.118901i	$0.962063\pi$
$920$	−2.34789	+	2.67160i	−0.0774076	+	0.0880800i
$921$	2.14881	+	11.2645i	0.0708058	+	0.371177i
$922$	−23.6929	+	25.2304i	−0.780285	+	0.830919i
$923$	−16.8408	+	42.5351i	−0.554323	+	1.40006i
$924$	0.0504120	+	0.155152i	0.00165843	+	0.00510413i
$925$	−11.7683	−	2.98224i	−0.386939	−	0.0980554i
$926$	−4.30215	+	13.2407i	−0.141378	+	0.435115i
$927$	3.48172	+	2.88033i	0.114355	+	0.0946024i
$928$	−8.57236	−	4.03384i	−0.281401	−	0.132417i
$929$	31.4188	+	29.5042i	1.03082	+	0.968002i	0.999504	−	0.0315078i	$-0.0100309\pi$
$929$	31.4188	+	29.5042i	1.03082	+	0.968002i	0.0313137	+	0.999510i	$0.490031\pi$
$930$	−0.317568	+	0.0305219i	−0.0104135	+	0.00100085i
$931$	−10.7339	+	1.35600i	−0.351788	+	0.0444412i
$932$		−	17.7409i		−	0.581122i
$933$	−2.13440	−	16.8955i	−0.0698772	−	0.553135i
$934$	−16.6237	−	20.0946i	−0.543944	−	0.657516i
$935$	−38.2384	−	3.55405i	−1.25053	−	0.116230i
$936$	0.335992	−	5.34045i	0.0109823	−	0.174558i
$937$	1.00223	−	3.90343i	0.0327414	−	0.127519i	−0.950112	−	0.311910i	$-0.899031\pi$
$937$	1.00223	−	3.90343i	0.0327414	−	0.127519i	0.982853	+	0.184391i	$0.0590312\pi$
$938$	−0.00999842	+	0.0389413i	−0.000326460	+	0.00127148i
$939$	−0.573935	+	9.12244i	−0.0187297	+	0.297700i
$940$	16.1559	+	1.50161i	0.526949	+	0.0489770i
$941$	−29.5862	−	35.7635i	−0.964481	−	1.16586i	−0.986110	−	0.166091i	$-0.946885\pi$
$941$	−29.5862	−	35.7635i	−0.964481	−	1.16586i	0.0216291	−	0.999766i	$-0.493115\pi$
$942$	−2.15090	−	17.0261i	−0.0700800	−	0.554741i
$943$			5.42939i			0.176805i
$944$	5.42708	−	0.685600i	0.176636	−	0.0223144i
$945$	0.0673421	−	0.00647235i	0.00219064	−	0.000210546i
$946$	14.6964	+	13.8009i	0.477822	+	0.448705i
$947$	−21.9795	−	10.3428i	−0.714239	−	0.336095i	0.0340942	−	0.999419i	$-0.489145\pi$
$947$	−21.9795	−	10.3428i	−0.714239	−	0.336095i	−0.748333	+	0.663323i	$0.769145\pi$
$948$	3.97611	+	3.28932i	0.129138	+	0.106832i
$949$	−12.4292	+	38.2530i	−0.403468	+	1.24175i
$950$	7.17727	−	2.86778i	0.232861	−	0.0930429i
$951$	8.74835	+	26.9247i	0.283685	+	0.873092i
$952$	−0.0354750	+	0.0895997i	−0.00114975	+	0.00290394i
$953$	−0.336487	+	0.358322i	−0.0108999	+	0.0116072i	−0.734395	−	0.678722i	$-0.762534\pi$
$953$	−0.336487	+	0.358322i	−0.0108999	+	0.0116072i	0.723496	+	0.690329i	$0.242534\pi$
$954$	−1.32789	−	6.96103i	−0.0429919	−	0.225372i
$955$	30.2596	−	34.4315i	0.979177	−	1.11418i
$956$	0.434344	−	0.407876i	0.0140477	−	0.0131917i
$957$	48.5841	−	15.7859i	1.57050	−	0.510286i
$958$	33.4054	+	6.37241i	1.07928	+	0.205883i
$959$	0.0237753	+	0.377898i	0.000767745	+	0.0122030i
$960$	2.14630	−	0.627212i	0.0692715	−	0.0202432i
$961$	−16.5997	−	26.1570i	−0.535475	−	0.843773i
$962$	−12.9669	+	0.815808i	−0.418069	+	0.0263027i
$963$	8.31786	+	5.27867i	0.268039	+	0.170103i
$964$	−1.99266	+	2.40871i	−0.0641792	+	0.0775793i
$965$	−1.27508	+	0.204005i	−0.0410463	+	0.00656715i
$966$	−0.0466118	−	0.0119679i	−0.00149971	−	0.000385060i
$967$	−50.7949	+	23.9023i	−1.63345	+	0.768645i	−0.999987	−	0.00512353i	$-0.998369\pi$
$967$	−50.7949	+	23.9023i	−1.63345	+	0.768645i	−0.633468	+	0.773769i	$0.718369\pi$
$968$	−17.1895	−	5.58520i	−0.552490	−	0.179515i
$969$	4.31458	+	2.37196i	0.138604	+	0.0761984i
$970$	−10.2816	−	35.1833i	−0.330122	−	1.12967i
$971$	35.4034	+	4.47249i	1.13615	+	0.143529i	0.670828	−	0.741613i	$-0.265939\pi$
$971$	35.4034	+	4.47249i	1.13615	+	0.143529i	0.465321	+	0.885142i	$0.345939\pi$
$972$	0.125333	−	0.992115i	0.00402007	−	0.0318221i
$973$	−0.309418	+	0.196363i	−0.00991949	+	0.00629510i
$974$	−12.3470	+	8.97064i	−0.395624	+	0.287438i
$975$	20.6685	+	16.9895i	0.661923	+	0.544100i
$976$	−10.9843	−	7.98059i	−0.351600	−	0.255453i
$977$	7.74356	+	0.487183i	0.247738	+	0.0155864i	0.186174	−	0.982517i	$-0.440391\pi$
$977$	7.74356	+	0.487183i	0.247738	+	0.0155864i	0.0615642	+	0.998103i	$0.480391\pi$
$978$	−3.20839	−	5.83604i	−0.102593	−	0.186616i
$979$	−1.93891	+	4.12039i	−0.0619677	+	0.131688i
$980$	8.77652	−	12.9580i	0.280356	−	0.413927i
$981$	1.49282	−	7.82566i	0.0476622	−	0.249854i
$982$	−19.6537	−	27.0510i	−0.627176	−	0.863233i
$983$	−25.6528	+	46.6623i	−0.818198	+	1.48830i	0.0536725	+	0.998559i	$0.482907\pi$
$983$	−25.6528	+	46.6623i	−0.818198	+	1.48830i	−0.871870	+	0.489737i	$0.837093\pi$
$984$	1.82900	−	2.88205i	0.0583065	−	0.0918763i
$985$	−4.47241	+	15.4848i	−0.142503	+	0.493387i
$986$	28.0571	+	11.1086i	0.893520	+	0.353770i
$987$	0.0808180	+	0.204123i	0.00257247	+	0.00649731i
$988$	6.37336	−	5.27250i	0.202764	−	0.167741i
$989$	−5.76033	+	1.47900i	−0.183168	+	0.0470295i
$990$	−6.12120	+	10.3876i	−0.194544	+	0.330138i
$991$	−13.6971	+	5.42305i	−0.435102	+	0.172269i	−0.575457	−	0.817832i	$-0.695176\pi$
$991$	−13.6971	+	5.42305i	−0.435102	+	0.172269i	0.140355	+	0.990101i	$0.455176\pi$
$992$	−0.0976678	−	0.104006i	−0.00310096	−	0.00330218i
$993$	−6.16344	+	8.48324i	−0.195591	+	0.269208i
$994$	−0.110133	−	0.234044i	−0.00349320	−	0.00742342i
$995$	29.8619	+	4.68162i	0.946685	+	0.148417i
$996$	0.388770	−	0.213728i	0.0123187	−	0.00677224i
$997$	−7.16247	+	1.36631i	−0.226838	+	0.0432716i	−0.299547	−	0.954082i	$-0.596835\pi$
$997$	−7.16247	+	1.36631i	−0.226838	+	0.0432716i	0.0727092	+	0.997353i	$0.476835\pi$
$998$	−4.84586	−	18.8734i	−0.153393	−	0.597427i
$999$	−2.42805			−0.0768202

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.b.229.11	✓	280
125.119	even	50	inner	750.2.o.b.619.11	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.b.229.11	✓	280	1.1	even	1	trivial
750.2.o.b.619.11	yes	280	125.119	even	50	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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.248690 + 0.968583i) q^{2} +(-0.982287 + 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(0.353264 + 2.20799i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(-0.0177835 + 0.0244769i) q^{7} +(-0.684547 - 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +O(q^{10})\)	\(q+(0.248690 + 0.968583i) q^{2} +(-0.982287 + 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(0.353264 + 2.20799i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(-0.0177835 + 0.0244769i) q^{7} +(-0.684547 - 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +(-2.05077 + 0.891269i) q^{10} +(5.22264 - 1.34095i) q^{11} +(0.770513 - 0.637424i) q^{12} +(1.96984 + 4.97524i) q^{13} +(-0.0281305 - 0.0111376i) q^{14} +(-0.760742 - 2.10268i) q^{15} +(0.535827 - 0.844328i) q^{16} +(-1.53446 + 2.79117i) q^{17} +(0.587785 + 0.809017i) q^{18} +(-0.289654 + 1.51842i) q^{19} +(-1.37327 - 1.76469i) q^{20} +(0.0128820 - 0.0273756i) q^{21} +(2.59763 + 4.72508i) q^{22} +(-1.58746 - 0.0998745i) q^{23} +(0.809017 + 0.587785i) q^{24} +(-4.75041 + 1.56000i) q^{25} +(-4.32905 + 3.14524i) q^{26} +(-0.844328 + 0.535827i) q^{27} +(0.00379197 - 0.0300165i) q^{28} +(-9.39932 - 1.18741i) q^{29} +(1.84743 - 1.25976i) q^{30} +(-0.125027 - 0.0687343i) q^{31} +(0.951057 + 0.309017i) q^{32} +(-4.87886 + 2.29582i) q^{33} +(-3.08508 - 0.792114i) q^{34} +(-0.0603269 - 0.0306189i) q^{35} +(-0.637424 + 0.770513i) q^{36} +(2.05007 + 1.30102i) q^{37} +(-1.54275 + 0.0970615i) q^{38} +(-2.86721 - 4.51800i) q^{39} +(1.36773 - 1.76899i) q^{40} +(-0.214331 - 3.40669i) q^{41} +(0.0297192 + 0.00566924i) q^{42} +(3.55595 - 1.15540i) q^{43} +(-3.93063 + 3.69110i) q^{44} +(1.14127 + 1.92289i) q^{45} +(-0.298049 - 1.56243i) q^{46} +(-4.96728 + 5.28961i) q^{47} +(-0.368125 + 0.929776i) q^{48} +(2.16284 + 6.65653i) q^{49} +(-2.69237 - 4.21321i) q^{50} +(0.984265 - 3.02926i) q^{51} +(-4.12302 - 3.41086i) q^{52} +(-6.41210 - 3.01731i) q^{53} +(-0.728969 - 0.684547i) q^{54} +(4.80576 + 11.0578i) q^{55} +(0.0300165 - 0.00379197i) q^{56} -1.54580i q^{57} +(-1.18741 - 9.39932i) q^{58} +(3.48685 + 4.21487i) q^{59} +(1.67962 + 1.47610i) q^{60} +(0.852532 - 13.5506i) q^{61} +(0.0354819 - 0.138193i) q^{62} +(-0.00752413 + 0.0293046i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(-10.2894 + 6.10694i) q^{65} +(-3.43701 - 4.15464i) q^{66} +(-0.166549 - 1.31837i) q^{67} -3.18515i q^{68} +(1.57806 - 0.199355i) q^{69} +(0.0146543 - 0.0660462i) q^{70} +(6.23221 + 5.85244i) q^{71} +(-0.904827 - 0.425779i) q^{72} +(5.79168 + 4.79129i) q^{73} +(-0.750310 + 2.30922i) q^{74} +(4.37395 - 2.42251i) q^{75} +(-0.477678 - 1.47014i) q^{76} +(-0.0600546 + 0.151681i) q^{77} +(3.66302 - 3.90071i) q^{78} +(0.966951 + 5.06893i) q^{79} +(2.05355 + 0.884828i) q^{80} +(0.728969 - 0.684547i) q^{81} +(3.24636 - 1.05481i) q^{82} +(0.435788 + 0.0831310i) q^{83} +(0.00189973 + 0.0301954i) q^{84} +(-6.70493 - 2.40204i) q^{85} +(2.00343 + 3.15690i) q^{86} +(9.45533 - 0.594879i) q^{87} +(-4.55265 - 2.88920i) q^{88} +(-0.538329 + 0.650728i) q^{89} +(-1.57866 + 1.58362i) q^{90} +(-0.156809 - 0.0402617i) q^{91} +(1.43922 - 0.677244i) q^{92} +(0.135692 + 0.0440890i) q^{93} +(-6.35874 - 3.49575i) q^{94} +(-3.45497 - 0.103149i) q^{95} +(-0.992115 - 0.125333i) q^{96} +(-2.05453 + 16.2633i) q^{97} +(-5.90952 + 3.75030i) q^{98} +(4.36225 - 3.16936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q+O(q^{10}) \) 280 * q	\( 280 q - 10 q^{11} - 20 q^{13} + 30 q^{17} + 10 q^{19} + 20 q^{22} + 60 q^{23} + 70 q^{24} + 20 q^{25} + 20 q^{29} + 10 q^{30} + 20 q^{31} + 20 q^{33} - 10 q^{34} + 30 q^{35} - 20 q^{37} + 90 q^{38} - 40 q^{41} - 10 q^{46} - 100 q^{47} + 120 q^{49} - 20 q^{50} - 30 q^{51} + 80 q^{52} - 30 q^{53} - 10 q^{55} + 30 q^{58} + 20 q^{59} + 60 q^{61} - 50 q^{62} - 10 q^{63} + 20 q^{65} + 40 q^{66} + 50 q^{67} + 10 q^{69} + 20 q^{70} + 80 q^{71} - 20 q^{73} + 80 q^{75} - 30 q^{76} - 100 q^{77} - 100 q^{79} + 100 q^{82} + 30 q^{83} - 20 q^{86} - 10 q^{87} - 60 q^{89} - 10 q^{90} + 70 q^{91} - 120 q^{92} + 50 q^{93} + 30 q^{94} - 20 q^{95} + 10 q^{97} + 40 q^{98} + 20 q^{99}+O(q^{100}) \) 280 * q - 10 * q^11 - 20 * q^13 + 30 * q^17 + 10 * q^19 + 20 * q^22 + 60 * q^23 + 70 * q^24 + 20 * q^25 + 20 * q^29 + 10 * q^30 + 20 * q^31 + 20 * q^33 - 10 * q^34 + 30 * q^35 - 20 * q^37 + 90 * q^38 - 40 * q^41 - 10 * q^46 - 100 * q^47 + 120 * q^49 - 20 * q^50 - 30 * q^51 + 80 * q^52 - 30 * q^53 - 10 * q^55 + 30 * q^58 + 20 * q^59 + 60 * q^61 - 50 * q^62 - 10 * q^63 + 20 * q^65 + 40 * q^66 + 50 * q^67 + 10 * q^69 + 20 * q^70 + 80 * q^71 - 20 * q^73 + 80 * q^75 - 30 * q^76 - 100 * q^77 - 100 * q^79 + 100 * q^82 + 30 * q^83 - 20 * q^86 - 10 * q^87 - 60 * q^89 - 10 * q^90 + 70 * q^91 - 120 * q^92 + 50 * q^93 + 30 * q^94 - 20 * q^95 + 10 * q^97 + 40 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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