LMFDB - Embedded newform 750.2.o.b.589.9

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			589.9
Character	$\chi$	$=$	750.589
Dual form			750.2.o.b.559.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.481754 - 0.876307i) q^{2} +(0.368125 - 0.929776i) q^{3} +(-0.535827 - 0.844328i) q^{4} +(-2.10525 - 0.753615i) q^{5} +(-0.637424 - 0.770513i) q^{6} +(-3.79423 - 1.23282i) q^{7} +(-0.998027 + 0.0627905i) q^{8} +(-0.728969 - 0.684547i) q^{9} +O(q^{10})$	\(q+(0.481754 - 0.876307i) q^{2} +(0.368125 - 0.929776i) q^{3} +(-0.535827 - 0.844328i) q^{4} +(-2.10525 - 0.753615i) q^{5} +(-0.637424 - 0.770513i) q^{6} +(-3.79423 - 1.23282i) q^{7} +(-0.998027 + 0.0627905i) q^{8} +(-0.728969 - 0.684547i) q^{9} +(-1.67461 + 1.48178i) q^{10} +(3.93154 + 2.16138i) q^{11} +(-0.982287 + 0.187381i) q^{12} +(-0.465866 + 0.496097i) q^{13} +(-2.90821 + 2.73099i) q^{14} +(-1.47569 + 1.67998i) q^{15} +(-0.425779 + 0.904827i) q^{16} +(-2.16775 - 1.37569i) q^{17} +(-0.951057 + 0.309017i) q^{18} +(-2.16074 + 0.855499i) q^{19} +(0.491749 + 2.18133i) q^{20} +(-2.54300 + 3.07396i) q^{21} +(3.78807 - 2.40398i) q^{22} +(0.123804 + 0.980010i) q^{23} +(-0.309017 + 0.951057i) q^{24} +(3.86413 + 3.17309i) q^{25} +(0.210301 + 0.647239i) q^{26} +(-0.904827 + 0.425779i) q^{27} +(0.992146 + 3.86415i) q^{28} +(-6.81549 + 1.74992i) q^{29} +(0.761264 + 2.10249i) q^{30} +(-3.47524 + 5.47611i) q^{31} +(0.587785 + 0.809017i) q^{32} +(3.45690 - 2.85980i) q^{33} +(-2.24985 + 1.23686i) q^{34} +(7.05872 + 5.45478i) q^{35} +(-0.187381 + 0.982287i) q^{36} +(2.36686 + 1.11376i) q^{37} +(-0.291267 + 2.30561i) q^{38} +(0.289763 + 0.615777i) q^{39} +(2.14841 + 0.619939i) q^{40} +(-2.76451 - 0.349239i) q^{41} +(1.46863 + 3.70933i) q^{42} +(3.98002 - 5.47802i) q^{43} +(-0.281709 - 4.47764i) q^{44} +(1.01877 + 1.99050i) q^{45} +(0.918432 + 0.363633i) q^{46} +(-13.2798 - 0.835495i) q^{47} +(0.684547 + 0.728969i) q^{48} +(7.21323 + 5.24072i) q^{49} +(4.64216 - 1.85751i) q^{50} +(-2.07709 + 1.50909i) q^{51} +(0.668492 + 0.127522i) q^{52} +(-9.64268 - 7.97712i) q^{53} +(-0.0627905 + 0.998027i) q^{54} +(-6.64801 - 7.51312i) q^{55} +(3.86415 + 0.992146i) q^{56} +2.32394i q^{57} +(-1.74992 + 6.81549i) q^{58} +(-2.18535 - 11.4560i) q^{59} +(2.20917 + 0.345783i) q^{60} +(7.60776 - 0.961083i) q^{61} +(3.12454 + 5.68351i) q^{62} +(1.92195 + 3.49602i) q^{63} +(0.992115 - 0.125333i) q^{64} +(1.35463 - 0.693323i) q^{65} +(-0.840685 - 4.40702i) q^{66} +(2.92532 - 11.3934i) q^{67} +2.56742i q^{68} +(0.956765 + 0.245656i) q^{69} +(8.18063 - 3.55774i) q^{70} +(0.731359 - 11.6246i) q^{71} +(0.770513 + 0.637424i) q^{72} +(-3.85862 - 0.736071i) q^{73} +(2.11624 - 1.53754i) q^{74} +(4.37275 - 2.42468i) q^{75} +(1.88011 + 1.36598i) q^{76} +(-12.2526 - 13.0477i) q^{77} +(0.679204 + 0.0427319i) q^{78} +(1.77483 + 0.702706i) q^{79} +(1.57826 - 1.58401i) q^{80} +(0.0627905 + 0.998027i) q^{81} +(-1.63785 + 2.25431i) q^{82} +(3.92614 + 9.91629i) q^{83} +(3.95803 + 0.500016i) q^{84} +(3.52690 + 4.52982i) q^{85} +(-2.88304 - 6.12677i) q^{86} +(-0.881915 + 6.98107i) q^{87} +(-4.05950 - 1.91025i) q^{88} +(-2.48985 + 13.0523i) q^{89} +(2.23509 + 0.0661736i) q^{90} +(2.37920 - 1.30798i) q^{91} +(0.761112 - 0.629647i) q^{92} +(3.81223 + 5.24709i) q^{93} +(-7.12975 + 11.2347i) q^{94} +(5.19361 - 0.172667i) q^{95} +(0.968583 - 0.248690i) q^{96} +(-2.15398 - 8.38919i) q^{97} +(8.06747 - 3.79626i) q^{98} +(-1.38640 - 4.26691i) 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 $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{33}{50}\right)$	$1$

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 $

$2$	0.481754	−	0.876307i	0.340651	−	0.619642i
$2$	0.481754	−	0.876307i	0.340651	−	0.619642i
$3$	0.368125	−	0.929776i	0.212537	−	0.536807i
$3$	0.368125	−	0.929776i	0.212537	−	0.536807i
$4$	−0.535827	−	0.844328i	−0.267913	−	0.422164i
$5$	−2.10525	−	0.753615i	−0.941495	−	0.337027i
$5$	−2.10525	−	0.753615i	−0.941495	−	0.337027i
$6$	−0.637424	−	0.770513i	−0.260227	−	0.314561i
$7$	−3.79423	−	1.23282i	−1.43408	−	0.465962i	−0.514037	−	0.857768i	$-0.671851\pi$
$7$	−3.79423	−	1.23282i	−1.43408	−	0.465962i	−0.920048	+	0.391806i	$0.871851\pi$
$8$	−0.998027	+	0.0627905i	−0.352856	+	0.0221998i
$9$	−0.728969	−	0.684547i	−0.242990	−	0.228182i
$10$	−1.67461	+	1.48178i	−0.529558	+	0.468582i
$11$	3.93154	+	2.16138i	1.18540	+	0.651682i	0.947546	−	0.319618i	$-0.103555\pi$
$11$	3.93154	+	2.16138i	1.18540	+	0.651682i	0.237858	+	0.971300i	$0.423555\pi$
$12$	−0.982287	+	0.187381i	−0.283562	+	0.0540923i
$13$	−0.465866	+	0.496097i	−0.129208	+	0.137593i	−0.790319	−	0.612695i	$-0.790085\pi$
$13$	−0.465866	+	0.496097i	−0.129208	+	0.137593i	0.661111	+	0.750288i	$0.270085\pi$
$14$	−2.90821	+	2.73099i	−0.777253	+	0.729889i
$15$	−1.47569	+	1.67998i	−0.381021	+	0.433770i
$16$	−0.425779	+	0.904827i	−0.106445	+	0.226207i
$17$	−2.16775	−	1.37569i	−0.525756	−	0.333655i	0.246317	−	0.969189i	$-0.420780\pi$
$17$	−2.16775	−	1.37569i	−0.525756	−	0.333655i	−0.772072	+	0.635535i	$0.780780\pi$
$18$	−0.951057	+	0.309017i	−0.224166	+	0.0728360i
$19$	−2.16074	+	0.855499i	−0.495708	+	0.196265i	−0.602658	−	0.798000i	$-0.705892\pi$
$19$	−2.16074	+	0.855499i	−0.495708	+	0.196265i	0.106950	+	0.994264i	$0.465892\pi$
$20$	0.491749	+	2.18133i	0.109958	+	0.487759i
$21$	−2.54300	+	3.07396i	−0.554928	+	0.670792i
$22$	3.78807	−	2.40398i	0.807619	−	0.512531i
$23$	0.123804	+	0.980010i	0.0258149	+	0.204346i	0.999747	−	0.0224937i	$-0.00716058\pi$
$23$	0.123804	+	0.980010i	0.0258149	+	0.204346i	−0.973932	+	0.226840i	$0.927161\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	3.86413	+	3.17309i	0.772826	+	0.634618i
$26$	0.210301	+	0.647239i	0.0412433	+	0.126934i
$27$	−0.904827	+	0.425779i	−0.174134	+	0.0819413i
$28$	0.992146	+	3.86415i	0.187498	+	0.730256i
$29$	−6.81549	+	1.74992i	−1.26561	+	0.324952i	−0.821079	−	0.570814i	$-0.806628\pi$
$29$	−6.81549	+	1.74992i	−1.26561	+	0.324952i	−0.444526	+	0.895766i	$0.646628\pi$
$30$	0.761264	+	2.10249i	0.138987	+	0.383861i
$31$	−3.47524	+	5.47611i	−0.624172	+	0.983538i	0.374247	+	0.927329i	$0.377901\pi$
$31$	−3.47524	+	5.47611i	−0.624172	+	0.983538i	−0.998419	+	0.0562088i	$0.982099\pi$
$32$	0.587785	+	0.809017i	0.103907	+	0.143015i
$33$	3.45690	−	2.85980i	0.601769	−	0.497827i
$34$	−2.24985	+	1.23686i	−0.385846	+	0.212121i
$35$	7.05872	+	5.45478i	1.19314	+	0.922026i
$36$	−0.187381	+	0.982287i	−0.0312302	+	0.163715i
$37$	2.36686	+	1.11376i	0.389110	+	0.183101i	0.610375	−	0.792112i	$-0.291019\pi$
$37$	2.36686	+	1.11376i	0.389110	+	0.183101i	−0.221265	+	0.975214i	$0.571019\pi$
$38$	−0.291267	+	2.30561i	−0.0472497	+	0.374020i
$39$	0.289763	+	0.615777i	0.0463992	+	0.0986033i
$40$	2.14841	+	0.619939i	0.339694	+	0.0980209i
$41$	−2.76451	−	0.349239i	−0.431744	−	0.0545420i	−0.0935419	−	0.995615i	$-0.529819\pi$
$41$	−2.76451	−	0.349239i	−0.431744	−	0.0545420i	−0.338203	+	0.941073i	$0.609819\pi$
$42$	1.46863	+	3.70933i	0.226614	+	0.572363i
$43$	3.98002	−	5.47802i	0.606947	−	0.835390i	−0.389375	−	0.921079i	$-0.627309\pi$
$43$	3.98002	−	5.47802i	0.606947	−	0.835390i	0.996322	+	0.0856888i	$0.0273091\pi$
$44$	−0.281709	−	4.47764i	−0.0424692	−	0.675029i
$45$	1.01877	+	1.99050i	0.151870	+	0.296727i
$46$	0.918432	+	0.363633i	0.135415	+	0.0536148i
$47$	−13.2798	−	0.835495i	−1.93706	−	0.121870i	−0.953377	−	0.301780i	$-0.902419\pi$
$47$	−13.2798	−	0.835495i	−1.93706	−	0.121870i	−0.983683	+	0.179911i	$0.942419\pi$
$48$	0.684547	+	0.728969i	0.0988059	+	0.105218i
$49$	7.21323	+	5.24072i	1.03046	+	0.748674i
$50$	4.64216	−	1.85751i	0.656501	−	0.262692i
$51$	−2.07709	+	1.50909i	−0.290850	+	0.211315i
$52$	0.668492	+	0.127522i	0.0927032	+	0.0176841i
$53$	−9.64268	−	7.97712i	−1.32452	−	1.09574i	−0.988064	−	0.154043i	$-0.950770\pi$
$53$	−9.64268	−	7.97712i	−1.32452	−	1.09574i	−0.336460	−	0.941698i	$-0.609230\pi$
$54$	−0.0627905	+	0.998027i	−0.00854471	+	0.135814i
$55$	−6.64801	−	7.51312i	−0.896418	−	1.01307i
$56$	3.86415	+	0.992146i	0.516369	+	0.132581i
$57$			2.32394i			0.307813i
$58$	−1.74992	+	6.81549i	−0.229776	+	0.894918i
$59$	−2.18535	−	11.4560i	−0.284508	−	1.49145i	−0.781618	−	0.623758i	$-0.785605\pi$
$59$	−2.18535	−	11.4560i	−0.284508	−	1.49145i	0.497109	−	0.867688i	$-0.334395\pi$
$60$	2.20917	+	0.345783i	0.285203	+	0.0446404i
$61$	7.60776	−	0.961083i	0.974073	−	0.123054i	0.377845	−	0.925869i	$-0.376665\pi$
$61$	7.60776	−	0.961083i	0.974073	−	0.123054i	0.596228	+	0.802815i	$0.296665\pi$
$62$	3.12454	+	5.68351i	0.396817	+	0.721807i
$63$	1.92195	+	3.49602i	0.242143	+	0.440457i
$64$	0.992115	−	0.125333i	0.124014	−	0.0156667i
$65$	1.35463	−	0.693323i	0.168021	−	0.0859962i
$66$	−0.840685	−	4.40702i	−0.103481	−	0.542467i
$67$	2.92532	−	11.3934i	0.357385	−	1.39192i	−0.494947	−	0.868923i	$-0.664813\pi$
$67$	2.92532	−	11.3934i	0.357385	−	1.39192i	0.852333	−	0.523000i	$-0.175187\pi$
$68$			2.56742i			0.311346i
$69$	0.956765	+	0.245656i	0.115181	+	0.0295735i
$70$	8.18063	−	3.55774i	0.977772	−	0.425232i
$71$	0.731359	−	11.6246i	0.0867964	−	1.37959i	−0.677879	−	0.735173i	$-0.737101\pi$
$71$	0.731359	−	11.6246i	0.0867964	−	1.37959i	0.764675	−	0.644416i	$-0.222899\pi$
$72$	0.770513	+	0.637424i	0.0908059	+	0.0751211i
$73$	−3.85862	−	0.736071i	−0.451617	−	0.0861506i	−0.0434457	−	0.999056i	$-0.513834\pi$
$73$	−3.85862	−	0.736071i	−0.451617	−	0.0861506i	−0.408172	+	0.912905i	$0.633834\pi$
$74$	2.11624	−	1.53754i	0.246008	−	0.178735i
$75$	4.37275	−	2.42468i	0.504921	−	0.279978i
$76$	1.88011	+	1.36598i	0.215663	+	0.156688i
$77$	−12.2526	−	13.0477i	−1.39631	−	1.48692i
$78$	0.679204	+	0.0427319i	0.0769047	+	0.00483843i
$79$	1.77483	+	0.702706i	0.199684	+	0.0790606i	0.465838	−	0.884870i	$-0.345753\pi$
$79$	1.77483	+	0.702706i	0.199684	+	0.0790606i	−0.266154	+	0.963931i	$0.585753\pi$
$80$	1.57826	−	1.58401i	0.176455	−	0.177098i
$81$	0.0627905	+	0.998027i	0.00697672	+	0.110892i
$82$	−1.63785	+	2.25431i	−0.180871	+	0.248947i
$83$	3.92614	+	9.91629i	0.430950	+	1.08845i	0.969332	+	0.245754i	$0.0790356\pi$
$83$	3.92614	+	9.91629i	0.430950	+	1.08845i	−0.538383	+	0.842701i	$0.680964\pi$
$84$	3.95803	+	0.500016i	0.431857	+	0.0545562i
$85$	3.52690	+	4.52982i	0.382546	+	0.491328i
$86$	−2.88304	−	6.12677i	−0.310886	−	0.660667i
$87$	−0.881915	+	6.98107i	−0.0945512	+	0.748450i
$88$	−4.05950	−	1.91025i	−0.432744	−	0.203634i
$89$	−2.48985	+	13.0523i	−0.263924	+	1.38354i	0.565422	+	0.824802i	$0.308713\pi$
$89$	−2.48985	+	13.0523i	−0.263924	+	1.38354i	−0.829346	+	0.558735i	$0.811287\pi$
$90$	2.23509	+	0.0661736i	0.235599	+	0.00697531i
$91$	2.37920	−	1.30798i	0.249408	−	0.137113i
$92$	0.761112	−	0.629647i	0.0793514	−	0.0656452i
$93$	3.81223	+	5.24709i	0.395310	+	0.544098i
$94$	−7.12975	+	11.2347i	−0.735378	+	1.15877i
$95$	5.19361	−	0.172667i	0.532854	−	0.0177153i
$96$	0.968583	−	0.248690i	0.0988556	−	0.0253818i
$97$	−2.15398	−	8.38919i	−0.218703	−	0.851794i	−0.979274	−	0.202539i	$-0.935081\pi$
$97$	−2.15398	−	8.38919i	−0.218703	−	0.851794i	0.760571	−	0.649255i	$-0.224919\pi$
$98$	8.06747	−	3.79626i	0.814938	−	0.383481i
$99$	−1.38640	−	4.26691i	−0.139339	−	0.428840i
$100$	0.608627	−	4.96282i	0.0608627	−	0.496282i
$101$	−3.42489	+	10.5407i	−0.340790	+	1.04884i	0.623010	+	0.782214i	$0.285910\pi$
$101$	−3.42489	+	10.5407i	−0.340790	+	1.04884i	−0.963799	+	0.266629i	$0.914090\pi$
$102$	0.321783	+	2.54718i	0.0318613	+	0.252208i
$103$	−5.57189	+	3.53603i	−0.549015	+	0.348415i	−0.781224	−	0.624250i	$-0.785405\pi$
$103$	−5.57189	+	3.53603i	−0.549015	+	0.348415i	0.232209	+	0.972666i	$0.425405\pi$
$104$	0.433797	−	0.524370i	0.0425373	−	0.0514187i
$105$	7.67022	−	4.55499i	0.748537	−	0.444522i
$106$	−11.6358	+	4.60694i	−1.13017	+	0.447465i
$107$	−12.7823	+	4.15322i	−1.23571	+	0.401507i	−0.852780	−	0.522270i	$-0.825085\pi$
$107$	−12.7823	+	4.15322i	−1.23571	+	0.401507i	−0.382931	+	0.923777i	$0.625085\pi$
$108$	0.844328	+	0.535827i	0.0812455	+	0.0515600i
$109$	1.54033	−	3.27338i	0.147537	−	0.313533i	−0.817375	−	0.576106i	$-0.804571\pi$
$109$	1.54033	−	3.27338i	0.147537	−	0.313533i	0.964912	+	0.262574i	$0.0845714\pi$
$110$	−9.78650	+	2.20623i	−0.933106	+	0.210356i
$111$	1.90685	−	1.79065i	0.180990	−	0.169961i
$112$	2.73099	−	2.90821i	0.258055	−	0.274800i
$113$	9.84732	−	1.87848i	0.926358	−	0.176712i	0.297937	−	0.954586i	$-0.403701\pi$
$113$	9.84732	−	1.87848i	0.926358	−	0.176712i	0.628421	+	0.777873i	$0.283701\pi$
$114$	2.03648	+	1.11957i	0.190734	+	0.104857i
$115$	0.477912	−	2.15646i	0.0445656	−	0.201091i
$116$	5.12943	+	4.81686i	0.476256	+	0.447234i
$117$	0.679204	−	0.0427319i	0.0627924	−	0.00395056i
$118$	−11.0918	−	3.60394i	−1.02108	−	0.331769i
$119$	6.52895	+	7.89214i	0.598508	+	0.723471i
$120$	1.36729	−	1.76933i	0.124816	−	0.161517i
$121$	4.89135	+	7.70753i	0.444668	+	0.700685i
$122$	2.82286	−	7.12973i	0.255570	−	0.645496i
$123$	−1.34240	+	2.44182i	−0.121040	+	0.220171i
$124$	6.48576			0.582438
$125$	−5.74365	−	9.59221i	−0.513728	−	0.857953i
$126$	3.98949			0.355412
$127$	7.28525	−	13.2518i	0.646461	−	1.17591i	−0.326556	−	0.945178i	$-0.605888\pi$
$127$	7.28525	−	13.2518i	0.646461	−	1.17591i	0.973018	−	0.230731i	$-0.0741117\pi$
$128$	0.368125	−	0.929776i	0.0325379	−	0.0821814i
$129$	−3.62819	−	5.71712i	−0.319445	−	0.503364i
$130$	0.0450343	−	1.52108i	0.00394977	−	0.133408i
$131$	−5.91284	−	7.14740i	−0.516607	−	0.624471i	0.446111	−	0.894978i	$-0.352809\pi$
$131$	−5.91284	−	7.14740i	−0.516607	−	0.624471i	−0.962718	+	0.270507i	$0.912809\pi$
$132$	−4.26691	−	1.38640i	−0.371387	−	0.120671i
$133$	9.25304	−	0.582152i	0.802340	−	0.0504790i
$134$	−8.57481	−	8.05228i	−0.740751	−	0.695611i
$135$	2.22576	−	0.214479i	0.191563	−	0.0184594i
$136$	2.24985	+	1.23686i	0.192923	+	0.106060i
$137$	−10.3994	+	1.98379i	−0.888481	+	0.169487i	−0.611364	−	0.791349i	$-0.709379\pi$
$137$	−10.3994	+	1.98379i	−0.888481	+	0.169487i	−0.277117	+	0.960836i	$0.589379\pi$
$138$	0.676195	−	0.720074i	0.0575615	−	0.0612968i
$139$	0.331333	−	0.311142i	0.0281033	−	0.0263907i	−0.670368	−	0.742029i	$-0.733864\pi$
$139$	0.331333	−	0.311142i	0.0281033	−	0.0263907i	0.698472	+	0.715638i	$0.253864\pi$
$140$	0.823373	−	8.88269i	0.0695877	−	0.750725i
$141$	−5.66545	+	12.0397i	−0.477117	+	1.01393i
$142$	−9.83440	−	6.24110i	−0.825285	−	0.523741i
$143$	−2.90383	+	0.943511i	−0.242830	+	0.0789004i
$144$	0.929776	−	0.368125i	0.0774814	−	0.0306770i
$145$	15.6671	+	1.45224i	1.30108	+	0.120602i
$146$	−2.50393	+	3.02673i	−0.207227	+	0.250494i
$147$	7.52806	−	4.77745i	0.620904	−	0.394038i
$148$	−0.327849	−	2.59519i	−0.0269490	−	0.213324i
$149$	1.76409	−	5.42932i	0.144520	−	0.444787i	−0.852429	−	0.522843i	$-0.824871\pi$
$149$	1.76409	−	5.42932i	0.144520	−	0.444787i	0.996949	+	0.0780562i	$0.0248714\pi$
$150$	−0.0181785	−	4.99997i	−0.00148427	−	0.408246i
$151$	−1.18881	−	3.65878i	−0.0967439	−	0.297747i	0.890960	−	0.454081i	$-0.150032\pi$
$151$	−1.18881	−	3.65878i	−0.0967439	−	0.297747i	−0.987704	+	0.156334i	$0.950032\pi$
$152$	2.10276	−	0.989485i	0.170557	−	0.0802578i
$153$	0.638492	+	2.48676i	0.0516190	+	0.201043i
$154$	−17.3365	+	4.45125i	−1.39701	+	0.358692i
$155$	11.4431	−	8.90956i	0.919134	−	0.715633i
$156$	0.364655	−	0.574605i	0.0291958	−	0.0460052i
$157$	4.33021	+	5.96002i	0.345588	+	0.475662i	0.946063	−	0.323982i	$-0.105022\pi$
$157$	4.33021	+	5.96002i	0.345588	+	0.475662i	−0.600475	+	0.799644i	$0.705022\pi$
$158$	1.47082	−	1.21677i	0.117012	−	0.0968008i
$159$	−10.9666	+	6.02896i	−0.869711	+	0.478128i
$160$	−0.627745	−	2.14614i	−0.0496276	−	0.169668i
$161$	0.738435	−	3.87101i	0.0581968	−	0.305079i
$162$	0.904827	+	0.425779i	0.0710899	+	0.0334524i
$163$	−0.883307	+	6.99210i	−0.0691860	+	0.547663i	0.918983	+	0.394296i	$0.129012\pi$
$163$	−0.883307	+	6.99210i	−0.0691860	+	0.547663i	−0.988169	+	0.153367i	$0.950988\pi$
$164$	1.18643	+	2.52129i	0.0926444	+	0.196879i
$165$	−9.43282	+	3.41541i	−0.734344	+	0.265889i
$166$	10.5811	+	1.33671i	0.821256	+	0.103749i
$167$	−6.18248	−	15.6152i	−0.478415	−	1.20834i	−0.945935	−	0.324356i	$-0.894853\pi$
$167$	−6.18248	−	15.6152i	−0.478415	−	1.20834i	0.467520	−	0.883982i	$-0.345147\pi$
$168$	2.34496	−	3.22757i	0.180918	−	0.249012i
$169$	0.787196	+	12.5121i	0.0605535	+	0.962471i
$170$	5.66861	−	0.908385i	0.434762	−	0.0696700i
$171$	2.16074	+	0.855499i	0.165236	+	0.0654216i
$172$	−6.75785	−	0.425168i	−0.515281	−	0.0324187i
$173$	11.6881	+	12.4465i	0.888628	+	0.946293i	0.998866	−	0.0476124i	$-0.0151612\pi$
$173$	11.6881	+	12.4465i	0.888628	+	0.946293i	−0.110238	+	0.993905i	$0.535161\pi$
$174$	5.69270	+	4.13599i	0.431562	+	0.313548i
$175$	−10.7495	−	16.8032i	−0.812589	−	1.27020i
$176$	−3.62965	+	2.63709i	−0.273595	+	0.198778i
$177$	−11.4560	−	2.18535i	−0.861087	−	0.164261i
$178$	10.2383	+	8.46985i	0.767392	+	0.634842i
$179$	1.64898	−	26.2099i	0.123251	−	1.95902i	−0.129739	−	0.991548i	$-0.541414\pi$
$179$	1.64898	−	26.2099i	0.123251	−	1.95902i	0.252990	−	0.967469i	$-0.418586\pi$
$180$	1.13475	−	1.92674i	0.0845793	−	0.143611i
$181$	−5.77289	−	1.48223i	−0.429096	−	0.110173i	0.0279643	−	0.999609i	$-0.491098\pi$
$181$	−5.77289	−	1.48223i	−0.429096	−	0.110173i	−0.457060	+	0.889436i	$0.651098\pi$
$182$		−	2.71504i		−	0.201252i
$183$	1.90701	−	7.42731i	0.140970	−	0.549043i
$184$	−0.185095	−	0.970302i	−0.0136454	−	0.0715316i
$185$	−4.14349	−	4.12845i	−0.304635	−	0.303530i
$186$	6.43462	−	0.812881i	0.471809	−	0.0596033i
$187$	−5.54918	−	10.0939i	−0.405796	−	0.738141i
$188$	6.41025	+	11.6602i	0.467516	+	0.850408i
$189$	3.95803	−	0.500016i	0.287905	−	0.0363708i
$190$	2.35073	−	4.63438i	0.170540	−	0.336213i
$191$	2.25990	+	11.8468i	0.163520	+	0.857204i	0.965609	+	0.259999i	$0.0837222\pi$
$191$	2.25990	+	11.8468i	0.163520	+	0.857204i	−0.802088	+	0.597205i	$0.796278\pi$
$192$	0.248690	−	0.968583i	0.0179476	−	0.0699015i
$193$		−	6.42233i		−	0.462290i	−0.972919	−	0.231145i	$-0.925753\pi$
$193$		−	6.42233i		−	0.462290i	0.972919	−	0.231145i	$-0.0742471\pi$
$194$	−8.38919	−	2.15398i	−0.602309	−	0.154647i
$195$	−0.145963	−	1.51473i	−0.0104526	−	0.108472i
$196$	0.559843	−	8.89845i	0.0399888	−	0.635603i
$197$	0.979832	+	0.810587i	0.0698101	+	0.0577520i	0.671675	−	0.740846i	$-0.265575\pi$
$197$	0.979832	+	0.810587i	0.0698101	+	0.0577520i	−0.601865	+	0.798598i	$0.705575\pi$
$198$	−4.40702	−	0.840685i	−0.313193	−	0.0597448i
$199$	−8.61820	+	6.26149i	−0.610928	+	0.443865i	−0.849741	−	0.527200i	$-0.823242\pi$
$199$	−8.61820	+	6.26149i	−0.610928	+	0.443865i	0.238813	+	0.971066i	$0.423242\pi$
$200$	−4.05574	−	2.92420i	−0.286784	−	0.206772i
$201$	−9.51642	−	6.91408i	−0.671236	−	0.487682i
$202$	7.58696	+	8.07930i	0.533817	+	0.568457i
$203$	28.0169	+	1.76267i	1.96640	+	0.123715i
$204$	2.38713	+	0.945131i	0.167132	+	0.0661724i
$205$	5.55679	+	2.81861i	0.388103	+	0.196861i
$206$	0.414368	+	6.58618i	0.0288704	+	0.458881i
$207$	0.580614	−	0.799146i	0.0403554	−	0.0555445i
$208$	−0.250526	−	0.632756i	−0.0173709	−	0.0438738i
$209$	−10.3441	−	1.30677i	−0.715517	−	0.0903909i
$210$	−0.296416	−	8.91585i	−0.0204547	−	0.615252i
$211$	11.0321	+	23.4443i	0.759478	+	1.61397i	0.788987	+	0.614409i	$0.210606\pi$
$211$	11.0321	+	23.4443i	0.759478	+	1.61397i	−0.0295089	+	0.999565i	$0.509394\pi$
$212$	−1.56850	+	12.4159i	−0.107725	+	0.852730i
$213$	−10.5391	−	4.95931i	−0.722125	−	0.339806i
$214$	−2.51842	+	13.2020i	−0.172156	+	0.902473i
$215$	−12.5072	+	8.53319i	−0.852986	+	0.581958i
$216$	0.876307	−	0.481754i	0.0596251	−	0.0327792i
$217$	19.9369	−	16.4933i	1.35341	−	1.11964i
$218$	−2.12642	−	2.92677i	−0.144019	−	0.198226i
$219$	−2.10483	+	3.31669i	−0.142232	+	0.224121i
$220$	−2.78135	+	9.63883i	−0.187518	+	0.649850i
$221$	1.69236	−	0.434524i	0.113840	−	0.0292292i
$222$	−0.650528	−	2.53364i	−0.0436606	−	0.170047i
$223$	−0.868925	+	0.408885i	−0.0581875	+	0.0273810i	−0.454653	−	0.890669i	$-0.650237\pi$
$223$	−0.868925	+	0.408885i	−0.0581875	+	0.0273810i	0.396465	+	0.918050i	$0.370237\pi$
$224$	−1.23282	−	3.79423i	−0.0823713	−	0.253513i
$225$	−0.644697	−	4.95826i	−0.0429798	−	0.330551i
$226$	3.09786	−	9.53424i	0.206067	−	0.634208i
$227$	−1.73906	−	13.7661i	−0.115425	−	0.913685i	−0.938387	−	0.345587i	$-0.887680\pi$
$227$	−1.73906	−	13.7661i	−0.115425	−	0.913685i	0.822961	−	0.568097i	$-0.192320\pi$
$228$	1.96217	−	1.24523i	0.129948	−	0.0824673i
$229$	−16.6661	+	20.1458i	−1.10133	+	1.33127i	−0.162567	+	0.986698i	$0.551977\pi$
$229$	−16.6661	+	20.1458i	−1.10133	+	1.33127i	−0.938758	+	0.344576i	$0.888023\pi$
$230$	−1.65949	−	1.45768i	−0.109423	−	0.0961167i
$231$	−16.6419	+	6.58899i	−1.09496	+	0.433524i
$232$	6.69217	−	2.17442i	0.439362	−	0.142757i
$233$	−15.8958	−	10.0878i	−1.04137	−	0.660873i	−0.0988766	−	0.995100i	$-0.531525\pi$
$233$	−15.8958	−	10.0878i	−1.04137	−	0.660873i	−0.942493	+	0.334227i	$0.891525\pi$
$234$	0.289763	−	0.615777i	0.0189424	−	0.0402546i
$235$	27.3277	+	11.7668i	1.78266	+	0.767581i
$236$	−8.50166	+	7.98359i	−0.553411	+	0.519687i
$237$	1.30672	−	1.39151i	0.0848805	−	0.0903886i
$238$	10.0613	−	1.91929i	0.652176	−	0.124409i
$239$	6.98468	+	3.83986i	0.451801	+	0.248380i	0.691372	−	0.722499i	$-0.257007\pi$
$239$	6.98468	+	3.83986i	0.451801	+	0.248380i	−0.239571	+	0.970879i	$0.577007\pi$
$240$	−0.891779	−	2.05054i	−0.0575641	−	0.132362i
$241$	2.52695	+	2.37296i	0.162775	+	0.152856i	0.761655	−	0.647983i	$-0.224387\pi$
$241$	2.52695	+	2.37296i	0.162775	+	0.152856i	−0.598880	+	0.800839i	$0.704387\pi$
$242$	9.11059	−	0.573189i	0.585651	−	0.0368460i
$243$	0.951057	+	0.309017i	0.0610103	+	0.0198234i
$244$	−4.88791	−	5.90847i	−0.312916	−	0.378251i
$245$	−11.2361	−	16.4690i	−0.717851	−	1.05217i
$246$	1.49307	+	2.35271i	0.0951949	+	0.150003i
$247$	0.582207	−	1.47049i	0.0370449	−	0.0935648i
$248$	3.12454	−	5.68351i	0.198408	−	0.360903i
$249$	10.6652			0.675882
$250$	−11.1727	+	0.412120i	−0.706626	+	0.0260648i
$251$	−16.1454			−1.01909			−0.509544	−	0.860444i	$-0.670186\pi$
$251$	−16.1454			−1.01909			−0.509544	+	0.860444i	$0.670186\pi$
$252$	1.92195	−	3.49602i	0.121072	−	0.220228i
$253$	−1.63144	+	4.12054i	−0.102568	+	0.259056i
$254$	−8.10296	−	12.7682i	−0.508425	−	0.801150i
$255$	5.51006	−	1.61169i	0.345053	−	0.100928i
$256$	−0.637424	−	0.770513i	−0.0398390	−	0.0481571i
$257$	14.9708	+	4.86432i	0.933854	+	0.303428i	0.736138	−	0.676832i	$-0.236647\pi$
$257$	14.9708	+	4.86432i	0.933854	+	0.303428i	0.197717	+	0.980259i	$0.436647\pi$
$258$	−6.75785	+	0.425168i	−0.420725	+	0.0264698i
$259$	−7.60736	−	7.14379i	−0.472698	−	0.443893i
$260$	−1.31124	−	0.772251i	−0.0813196	−	0.0478930i
$261$	6.16618	+	3.38989i	0.381677	+	0.209829i
$262$	−9.11185	+	1.73818i	−0.562932	+	0.107385i
$263$	16.3835	−	17.4467i	1.01025	−	1.07581i	0.0131340	−	0.999914i	$-0.495819\pi$
$263$	16.3835	−	17.4467i	1.01025	−	1.07581i	0.997116	−	0.0758932i	$-0.0241808\pi$
$264$	−3.27051	+	3.07121i	−0.201286	+	0.189020i
$265$	14.2885	+	24.0607i	0.877738	+	1.47804i
$266$	3.94754	−	8.38895i	0.242039	−	0.514360i
$267$	11.2191	+	7.11986i	0.686598	+	0.435729i
$268$	−11.1872	+	3.63495i	−0.683368	+	0.222040i
$269$	10.1318	−	4.01145i	0.617744	−	0.244582i	−0.0383463	−	0.999265i	$-0.512209\pi$
$269$	10.1318	−	4.01145i	0.617744	−	0.244582i	0.656090	+	0.754682i	$0.272209\pi$
$270$	0.884318	−	2.05377i	0.0538179	−	0.124989i
$271$	16.5701	−	20.0298i	1.00656	−	1.21673i	0.0304333	−	0.999537i	$-0.490311\pi$
$271$	16.5701	−	20.0298i	1.00656	−	1.21673i	0.976130	−	0.217189i	$-0.0696887\pi$
$272$	2.16775	−	1.37569i	0.131439	−	0.0834137i
$273$	−0.340284	−	2.69363i	−0.0205949	−	0.163026i
$274$	−3.27154	+	10.0688i	−0.197641	+	0.608277i
$275$	8.33371	+	20.8270i	0.502542	+	1.25592i
$276$	−0.305247	−	0.939453i	−0.0183737	−	0.0565484i
$277$	−6.83614	+	3.21684i	−0.410744	+	0.193281i	−0.620039	−	0.784571i	$-0.712883\pi$
$277$	−6.83614	+	3.21684i	−0.410744	+	0.193281i	0.209295	+	0.977853i	$0.432883\pi$
$278$	−0.113035	−	0.440243i	−0.00677940	−	0.0264040i
$279$	6.28200	−	1.61294i	0.376093	−	0.0965644i
$280$	−7.38730	−	5.00080i	−0.441476	−	0.298855i
$281$	9.57176	−	15.0827i	0.571003	−	0.899757i	−0.428990	−	0.903309i	$-0.641131\pi$
$281$	9.57176	−	15.0827i	0.571003	−	0.899757i	0.999994	+	0.00355182i	$0.00113058\pi$
$282$	7.82111	+	10.7648i	0.465741	+	0.641037i
$283$	11.9298	−	9.86923i	0.709156	−	0.586665i	−0.211342	−	0.977412i	$-0.567783\pi$
$283$	11.9298	−	9.86923i	0.709156	−	0.586665i	0.920498	+	0.390747i	$0.127783\pi$
$284$	−10.2069	+	5.61128i	−0.605667	+	0.332968i
$285$	1.75136	−	4.89246i	0.103741	−	0.289805i
$286$	−0.572125	+	2.99919i	−0.0338305	+	0.177346i
$287$	10.0587	+	4.73324i	0.593744	+	0.279394i
$288$	0.125333	−	0.992115i	0.00738533	−	0.0584609i
$289$	−4.43166	−	9.41775i	−0.260686	−	0.553985i
$290$	8.82028	−	13.0295i	0.517944	−	0.765120i
$291$	−8.59301	−	1.08555i	−0.503731	−	0.0636360i
$292$	1.44607	+	3.65235i	0.0846247	+	0.213738i
$293$	−16.7306	+	23.0277i	−0.977410	+	1.34529i	−0.0391971	+	0.999231i	$0.512480\pi$
$293$	−16.7306	+	23.0277i	−0.977410	+	1.34529i	−0.938213	+	0.346058i	$0.887520\pi$
$294$	−0.559843	−	8.89845i	−0.0326507	−	0.518968i
$295$	−4.03272	+	25.7646i	−0.234794	+	1.50008i
$296$	−2.43213	−	0.962947i	−0.141365	−	0.0559702i
$297$	−4.47764	−	0.281709i	−0.259819	−	0.0163464i
$298$	−3.90789	−	4.16148i	−0.226378	−	0.241068i
$299$	−0.543856	−	0.395135i	−0.0314520	−	0.0228512i
$300$	−4.39026	−	2.39282i	−0.253472	−	0.138150i
$301$	−21.8545	+	15.8782i	−1.25967	+	0.915206i
$302$	−3.77893	−	0.720869i	−0.217453	−	0.0414813i
$303$	8.53974	+	7.06469i	0.490595	+	0.405856i
$304$	0.145921	−	2.31935i	0.00836916	−	0.133024i
$305$	−16.7405	−	3.71000i	−0.958558	−	0.212434i
$306$	2.48676	+	0.638492i	0.142159	+	0.0365001i
$307$		−	21.6310i		−	1.23455i	−0.786748	−	0.617274i	$-0.788237\pi$
$307$		−	21.6310i		−	1.23455i	0.786748	−	0.617274i	$-0.211763\pi$
$308$	−4.45125	+	17.3365i	−0.253634	+	0.987838i
$309$	1.23657	+	6.48231i	0.0703459	+	0.368766i
$310$	−2.29474	−	14.3199i	−0.130333	−	0.813316i
$311$	−0.347138	+	0.0438537i	−0.0196844	+	0.00248672i	−0.135169	−	0.990823i	$-0.543158\pi$
$311$	−0.347138	+	0.0438537i	−0.0196844	+	0.00248672i	0.115485	+	0.993309i	$0.463158\pi$
$312$	−0.327856	−	0.596368i	−0.0185612	−	0.0337627i
$313$	−0.802738	−	1.46018i	−0.0453734	−	0.0825340i	0.852648	−	0.522486i	$-0.174995\pi$
$313$	−0.802738	−	1.46018i	−0.0453734	−	0.0825340i	−0.898021	+	0.439952i	$0.854995\pi$
$314$	7.30890	−	0.923329i	0.412465	−	0.0521065i
$315$	−1.41153	−	8.80839i	−0.0795308	−	0.496297i
$316$	−0.357689	−	1.87507i	−0.0201216	−	0.105481i
$317$	−1.66944	+	6.50204i	−0.0937651	+	0.365191i	−0.998099	−	0.0616353i	$-0.980368\pi$
$317$	−1.66944	+	6.50204i	−0.0937651	+	0.365191i	0.904334	+	0.426826i	$0.140368\pi$
$318$			12.5146i			0.701785i
$319$	−30.5776	−	7.85100i	−1.71202	−	0.439572i
$320$	−2.18310	−	0.483815i	−0.122039	−	0.0270461i
$321$	−0.843911	+	13.4136i	−0.0471025	+	0.748673i
$322$	−3.03645	−	2.51197i	−0.169215	−	0.139987i
$323$	5.86085	+	1.11802i	0.326106	+	0.0622081i
$324$	0.809017	−	0.587785i	0.0449454	−	0.0326547i
$325$	−3.37433	+	0.438747i	−0.187174	+	0.0243373i
$326$	5.70169	+	4.14252i	0.315787	+	0.229433i
$327$	−2.47647	−	2.63718i	−0.136949	−	0.145836i
$328$	2.78099	+	0.174965i	0.153554	+	0.00966082i
$329$	49.3567	+	19.5417i	2.72112	+	1.07737i
$330$	−1.55135	+	9.91142i	−0.0853991	+	0.545606i
$331$	−0.108808	−	1.72945i	−0.00598062	−	0.0950593i	0.993904	−	0.110249i	$-0.0351648\pi$
$331$	−0.108808	−	1.72945i	−0.00598062	−	0.0950593i	−0.999885	+	0.0151896i	$0.995165\pi$
$332$	6.26887	−	8.62836i	0.344049	−	0.473543i
$333$	−0.962947	−	2.43213i	−0.0527692	−	0.133280i
$334$	−16.6621	−	2.10491i	−0.911710	−	0.115176i
$335$	−14.7448	+	21.7813i	−0.805592	+	1.19004i
$336$	−1.69864	−	3.60980i	−0.0926686	−	0.196931i
$337$	−3.62123	+	28.6650i	−0.197261	+	1.56148i	0.513526	+	0.858074i	$0.328339\pi$
$337$	−3.62123	+	28.6650i	−0.197261	+	1.56148i	−0.710787	+	0.703407i	$0.751661\pi$
$338$	11.3437	+	5.33793i	0.617015	+	0.290345i
$339$	1.87848	−	9.84732i	0.102025	−	0.534833i
$340$	1.93485	−	5.40506i	0.104932	−	0.293130i
$341$	−25.4990	+	14.0182i	−1.38085	+	0.759129i
$342$	1.79063	−	1.48133i	0.0968259	−	0.0801014i
$343$	−4.49304	−	6.18414i	−0.242601	−	0.333912i
$344$	−3.62819	+	5.71712i	−0.195619	+	0.308246i
$345$	−1.82910	−	1.23820i	−0.0984753	−	0.0666624i
$346$	16.5378	−	4.24618i	0.889076	−	0.228276i
$347$	3.85897	+	15.0297i	0.207160	+	0.806836i	0.984152	+	0.177326i	$0.0567446\pi$
$347$	3.85897	+	15.0297i	0.207160	+	0.806836i	−0.776992	+	0.629511i	$0.783255\pi$
$348$	6.36687	−	2.99602i	0.341300	−	0.160604i
$349$	4.25863	+	13.1067i	0.227959	+	0.701586i	0.997978	+	0.0635648i	$0.0202470\pi$
$349$	4.25863	+	13.1067i	0.227959	+	0.701586i	−0.770018	+	0.638022i	$0.779753\pi$
$350$	−19.9034	+	1.32488i	−1.06388	+	0.0708180i
$351$	0.210301	−	0.647239i	0.0112250	−	0.0345470i
$352$	0.562306	+	4.45111i	0.0299710	+	0.237245i
$353$	4.77572	−	3.03077i	0.254186	−	0.161311i	−0.402629	−	0.915363i	$-0.631903\pi$
$353$	4.77572	−	3.03077i	0.254186	−	0.161311i	0.656815	+	0.754052i	$0.271903\pi$
$354$	−7.43401	+	8.98618i	−0.395113	+	0.477610i
$355$	−10.3002	+	23.9215i	−0.546677	+	1.26962i
$356$	12.3545	−	4.89150i	0.654788	−	0.259249i
$357$	9.74139	−	3.16517i	0.515569	−	0.167519i
$358$	−22.1735	−	14.0717i	−1.17190	−	0.743713i
$359$	14.9677	−	31.8081i	0.789967	−	1.67877i	0.0571255	−	0.998367i	$-0.481806\pi$
$359$	14.9677	−	31.8081i	0.789967	−	1.67877i	0.732842	−	0.680399i	$-0.238194\pi$
$360$	−1.14175	−	1.92261i	−0.0601754	−	0.101330i
$361$	−9.91347	+	9.30937i	−0.521762	+	0.489967i
$362$	−4.08000	+	4.34476i	−0.214440	+	0.228355i
$363$	8.96691	−	1.71053i	0.470641	−	0.0897795i
$364$	−2.37920	−	1.30798i	−0.124704	−	0.0685567i
$365$	7.56864	+	4.45753i	0.396160	+	0.233318i
$366$	−5.58989	−	5.24926i	−0.292188	−	0.274383i
$367$	35.0956	−	2.20803i	1.83197	−	0.115258i	0.891056	−	0.453893i	$-0.149965\pi$
$367$	35.0956	−	2.20803i	1.83197	−	0.115258i	0.940918	+	0.338635i	$0.109965\pi$
$368$	−0.939453	−	0.305247i	−0.0489724	−	0.0159121i
$369$	1.77617	+	2.14702i	0.0924639	+	0.111770i
$370$	−5.61393	+	1.64207i	−0.291854	+	0.0853671i
$371$	26.7522	+	42.1547i	1.38891	+	2.18856i
$372$	2.38757	−	6.03031i	0.123790	−	0.312657i
$373$	13.0970	−	23.8234i	0.678138	−	1.23353i	−0.283438	−	0.958991i	$-0.591475\pi$
$373$	13.0970	−	23.8234i	0.678138	−	1.23353i	0.961576	−	0.274538i	$-0.0885250\pi$
$374$	−11.5187			−0.595619
$375$	−11.0330	+	1.80919i	−0.569741	+	0.0934260i
$376$	13.3061			0.686208
$377$	2.30698	−	4.19638i	0.118815	−	0.216124i
$378$	1.46863	−	3.70933i	0.0755382	−	0.190788i
$379$	−7.55159	−	11.8994i	−0.387899	−	0.611231i	0.593127	−	0.805109i	$-0.297893\pi$
$379$	−7.55159	−	11.8994i	−0.387899	−	0.611231i	−0.981026	+	0.193878i	$0.937893\pi$
$380$	−2.92867	−	4.29259i	−0.150237	−	0.220205i
$381$	−9.63935	−	11.6520i	−0.493839	−	0.596949i
$382$	11.4701	+	3.72687i	0.586863	+	0.190683i
$383$	−13.5685	+	0.853657i	−0.693317	+	0.0436198i	−0.405540	−	0.914077i	$-0.632916\pi$
$383$	−13.5685	+	0.853657i	−0.693317	+	0.0436198i	−0.287778	+	0.957697i	$0.592916\pi$
$384$	−0.728969	−	0.684547i	−0.0372000	−	0.0349331i
$385$	15.9618	+	36.7023i	0.813488	+	1.87052i
$386$	−5.62793	−	3.09398i	−0.286454	−	0.157480i
$387$	−6.65127	+	1.26880i	−0.338103	+	0.0644966i
$388$	−5.92907	+	6.31382i	−0.301003	+	0.320536i
$389$	−16.7125	+	15.6940i	−0.847355	+	0.795719i	−0.980734	−	0.195346i	$-0.937417\pi$
$389$	−16.7125	+	15.6940i	−0.847355	+	0.795719i	0.133379	+	0.991065i	$0.457417\pi$
$390$	−1.39769	−	0.601820i	−0.0707747	−	0.0304743i
$391$	1.07982	−	2.29473i	0.0546087	−	0.116049i
$392$	−7.52806	−	4.77745i	−0.380224	−	0.241298i
$393$	−8.82215	+	2.86649i	−0.445018	+	0.144595i
$394$	1.18236	−	0.468130i	0.0595665	−	0.0235840i
$395$	−3.20689	−	2.81691i	−0.161356	−	0.141734i
$396$	−2.85980	+	3.45690i	−0.143710	+	0.173716i
$397$	−14.1310	+	8.96780i	−0.709214	+	0.450081i	−0.840886	−	0.541212i	$-0.817966\pi$
$397$	−14.1310	+	8.96780i	−0.709214	+	0.450081i	0.131672	+	0.991293i	$0.457966\pi$
$398$	1.33514	+	10.5687i	0.0669243	+	0.529760i
$399$	2.86500	−	8.81756i	0.143429	−	0.441430i
$400$	−4.51637	+	2.14533i	−0.225818	+	0.107267i
$401$	10.4559	+	32.1799i	0.522141	+	1.60699i	0.769901	+	0.638164i	$0.220306\pi$
$401$	10.4559	+	32.1799i	0.522141	+	1.60699i	−0.247759	+	0.968822i	$0.579694\pi$
$402$	−10.6434	+	5.00841i	−0.530846	+	0.249797i
$403$	−1.09768	−	4.27519i	−0.0546795	−	0.212963i
$404$	10.7350	−	2.75628i	0.534086	−	0.137130i
$405$	0.619939	−	2.14841i	0.0308050	−	0.106755i
$406$	15.0419	−	23.7022i	0.746516	−	1.17632i
$407$	6.89816	+	9.49450i	0.341929	+	0.470625i
$408$	1.97823	−	1.63654i	0.0979371	−	0.0810206i
$409$	5.32172	−	2.92564i	0.263142	−	0.144663i	−0.344722	−	0.938705i	$-0.612027\pi$
$409$	5.32172	−	2.92564i	0.263142	−	0.144663i	0.607864	+	0.794041i	$0.292027\pi$
$410$	5.14697	−	3.51157i	0.254191	−	0.173424i
$411$	−1.98379	+	10.3994i	−0.0978533	+	0.512965i
$412$	5.97114	+	2.80980i	0.294177	+	0.138429i
$413$	−5.83148	+	46.1609i	−0.286948	+	2.27143i
$414$	−0.420584	−	0.893787i	−0.0206706	−	0.0439272i
$415$	−0.792420	−	23.8350i	−0.0388984	−	1.17002i
$416$	−0.675181	−	0.0852951i	−0.0331034	−	0.00418194i
$417$	−0.167321	−	0.422604i	−0.00819374	−	0.0206950i
$418$	−6.12844	+	8.43508i	−0.299752	+	0.412573i
$419$	−0.759593	−	12.0734i	−0.0371085	−	0.589823i	−0.972014	−	0.234925i	$-0.924516\pi$
$419$	−0.759593	−	12.0734i	−0.0371085	−	0.589823i	0.934905	−	0.354898i	$-0.115484\pi$
$420$	−7.95582	−	4.03549i	−0.388204	−	0.196912i
$421$	−10.8967	−	4.31432i	−0.531074	−	0.210267i	0.0872558	−	0.996186i	$-0.472190\pi$
$421$	−10.8967	−	4.31432i	−0.531074	−	0.210267i	−0.618329	+	0.785919i	$0.712190\pi$
$422$	25.8592	+	1.62692i	1.25880	+	0.0791972i
$423$	9.10863	+	9.69971i	0.442877	+	0.471616i
$424$	10.1245	+	7.35591i	0.491691	+	0.357234i
$425$	−4.01125	−	12.1943i	−0.194574	−	0.591511i
$426$	−9.42311	+	6.84629i	−0.456551	+	0.331704i
$427$	−30.0504	−	5.73243i	−1.45424	−	0.277412i
$428$	10.3558	+	8.56705i	0.500565	+	0.414104i
$429$	−0.191716	+	3.04724i	−0.00925615	+	0.147122i
$430$	1.45228	+	15.0711i	0.0700353	+	0.726791i
$431$	−16.6276	−	4.26923i	−0.800921	−	0.205642i	−0.174022	−	0.984742i	$-0.555676\pi$
$431$	−16.6276	−	4.26923i	−0.800921	−	0.205642i	−0.626899	+	0.779100i	$0.715676\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	2.20181	−	8.57547i	0.105812	−	0.412111i	−0.893505	−	0.449053i	$-0.851762\pi$
$433$	2.20181	−	8.57547i	0.105812	−	0.412111i	0.999317	+	0.0369416i	$0.0117616\pi$
$434$	−4.84847	−	25.4166i	−0.232734	−	1.22003i
$435$	7.11769	−	14.0323i	0.341267	−	0.672795i
$436$	−3.58916	+	0.453416i	−0.171889	+	0.0217147i
$437$	−1.10591	−	2.01164i	−0.0529027	−	0.0962296i
$438$	1.89242	+	3.44231i	0.0904236	+	0.164480i
$439$	17.0057	−	2.14832i	0.811638	−	0.102534i	0.291450	−	0.956586i	$-0.405862\pi$
$439$	17.0057	−	2.14832i	0.811638	−	0.102534i	0.520187	+	0.854052i	$0.325862\pi$
$440$	7.10665	+	7.08086i	0.338796	+	0.337567i
$441$	−1.67070	−	8.75811i	−0.0795571	−	0.417053i
$442$	0.434524	−	1.69236i	0.0206682	−	0.0804972i
$443$		−	3.41688i		−	0.162341i	−0.996700	−	0.0811704i	$-0.974134\pi$
$443$		−	3.41688i		−	0.162341i	0.996700	−	0.0811704i	$-0.0258658\pi$
$444$	−2.53364	−	0.650528i	−0.120241	−	0.0308727i
$445$	15.0781	−	25.6018i	0.714772	−	1.21364i
$446$	−0.0602991	+	0.958427i	−0.00285525	+	0.0453828i
$447$	−4.39865	−	3.63888i	−0.208049	−	0.172113i
$448$	−3.91883	−	0.747556i	−0.185147	−	0.0353187i
$449$	3.06747	−	2.22865i	0.144763	−	0.105176i	−0.513047	−	0.858361i	$-0.671483\pi$
$449$	3.06747	−	2.22865i	0.144763	−	0.105176i	0.657809	+	0.753184i	$0.271483\pi$
$450$	−4.65554	−	1.82371i	−0.219464	−	0.0859705i
$451$	−10.1140	−	7.34822i	−0.476248	−	0.346014i
$452$	−6.86251	−	7.30783i	−0.322785	−	0.343731i
$453$	−3.83948	−	0.241559i	−0.180394	−	0.0113495i
$454$	−12.9011	−	5.10790i	−0.605478	−	0.239726i
$455$	−5.99452	+	0.960613i	−0.281028	+	0.0450342i
$456$	−0.145921	−	2.31935i	−0.00683339	−	0.108614i
$457$	−8.03518	+	11.0595i	−0.375870	+	0.517341i	−0.954485	−	0.298260i	$-0.903594\pi$
$457$	−8.03518	+	11.0595i	−0.375870	+	0.517341i	0.578614	+	0.815601i	$0.303594\pi$
$458$	9.62498	+	24.3099i	0.449746	+	1.13593i
$459$	2.54718	+	0.321783i	0.118892	+	0.0150196i
$460$	−2.07684	+	0.751976i	−0.0968332	+	0.0350611i
$461$	−4.59403	−	9.76282i	−0.213965	−	0.454700i	0.768816	−	0.639470i	$-0.220846\pi$
$461$	−4.59403	−	9.76282i	−0.213965	−	0.454700i	−0.982782	+	0.184770i	$0.940846\pi$
$462$	−2.24332	+	17.7577i	−0.104369	+	0.826162i
$463$	2.13154	+	1.00303i	0.0990611	+	0.0466146i	0.474671	−	0.880163i	$-0.342567\pi$
$463$	2.13154	+	1.00303i	0.0990611	+	0.0466146i	−0.375610	+	0.926778i	$0.622567\pi$
$464$	1.31852	−	6.91192i	0.0612107	−	0.320878i
$465$	−4.07141	−	13.9194i	−0.188807	−	0.645496i
$466$	−16.4979	+	9.06978i	−0.764249	+	0.420149i
$467$	−26.6459	+	22.0434i	−1.23303	+	1.02005i	−0.234171	+	0.972195i	$0.575238\pi$
$467$	−26.6459	+	22.0434i	−1.23303	+	1.02005i	−0.998854	+	0.0478518i	$0.984762\pi$
$468$	−0.400015	−	0.550574i	−0.0184907	−	0.0254503i
$469$	−25.1454	+	39.6227i	−1.16110	+	1.82961i
$470$	23.4765	−	18.2787i	1.08289	−	0.843134i
$471$	7.13555	−	1.83210i	0.328789	−	0.0844186i
$472$	2.90037	+	11.2962i	0.133500	+	0.519949i
$473$	27.4877	−	12.9347i	1.26389	−	0.594740i
$474$	−0.589877	−	1.81545i	−0.0270939	−	0.0833866i
$475$	−11.0640	−	3.55048i	−0.507650	−	0.162907i
$476$	3.16517	−	9.74139i	0.145075	−	0.446496i
$477$	1.56850	+	12.4159i	0.0718166	+	0.568487i
$478$	6.72979	−	4.27085i	0.307813	−	0.195344i
$479$	−5.37919	+	6.50232i	−0.245781	+	0.297099i	−0.878949	−	0.476916i	$-0.841754\pi$
$479$	−5.37919	+	6.50232i	−0.245781	+	0.297099i	0.633167	+	0.774015i	$0.281754\pi$
$480$	−2.22652	−	0.206385i	−0.101626	−	0.00942016i
$481$	−1.65518	+	0.655331i	−0.0754696	+	0.0298805i
$482$	3.29681	−	1.07120i	0.150166	−	0.0487918i
$483$	−3.32734	−	2.11159i	−0.151399	−	0.0960809i
$484$	3.88677	−	8.25980i	0.176671	−	0.375446i
$485$	−1.78757	+	19.2846i	−0.0811692	+	0.875668i
$486$	0.728969	−	0.684547i	0.0330667	−	0.0310517i
$487$	6.02801	−	6.41918i	0.273155	−	0.290881i	−0.577735	−	0.816224i	$-0.696063\pi$
$487$	6.02801	−	6.41918i	0.273155	−	0.290881i	0.850890	+	0.525344i	$0.176063\pi$
$488$	−7.53240	+	1.43688i	−0.340976	+	0.0650446i
$489$	6.17592	+	3.39524i	0.279285	+	0.153538i
$490$	−19.8449	+	1.91230i	−0.896503	+	0.0863891i
$491$	−1.33492	−	1.25358i	−0.0602443	−	0.0565731i	0.653840	−	0.756633i	$-0.273157\pi$
$491$	−1.33492	−	1.25358i	−0.0602443	−	0.0565731i	−0.714085	+	0.700059i	$0.753157\pi$
$492$	2.78099	−	0.174965i	0.125377	−	0.00788803i
$493$	17.1816	+	5.58264i	0.773821	+	0.251430i
$494$	−1.00812	−	1.21860i	−0.0453573	−	0.0548276i
$495$	−0.296887	+	10.0277i	−0.0133441	+	0.450712i
$496$	−3.47524	−	5.47611i	−0.156043	−	0.245884i
$497$	−17.1060	+	43.2049i	−0.767310	+	1.93800i
$498$	5.13802	−	9.34602i	0.230240	−	0.418805i
$499$	−6.09162			−0.272698			−0.136349	−	0.990661i	$-0.543537\pi$
$499$	−6.09162			−0.272698			−0.136349	+	0.990661i	$0.543537\pi$
$500$	−5.02137	+	9.98929i	−0.224562	+	0.446735i
$501$	−16.7945			−0.750325
$502$	−7.77811	+	14.1483i	−0.347154	+	0.631471i
$503$	7.09428	−	17.9181i	0.316318	−	0.798928i	−0.681432	−	0.731882i	$-0.738642\pi$
$503$	7.09428	−	17.9181i	0.316318	−	0.798928i	0.997750	−	0.0670467i	$-0.0213576\pi$
$504$	−2.13768	−	3.36844i	−0.0952197	−	0.150042i
$505$	15.1539	−	19.6098i	0.674340	−	0.872625i
$506$	2.82490	+	3.41472i	0.125582	+	0.151803i
$507$	11.9233	+	3.87410i	0.529531	+	0.172055i
$508$	−15.0925	+	0.949540i	−0.669622	+	0.0421290i
$509$	14.8769	+	13.9704i	0.659408	+	0.619225i	0.940232	−	0.340534i	$-0.110608\pi$
$509$	14.8769	+	13.9704i	0.659408	+	0.619225i	−0.280825	+	0.959759i	$0.590608\pi$
$510$	1.24216	−	5.60494i	0.0550037	−	0.248191i
$511$	13.7331	+	7.54981i	0.607515	+	0.333984i
$512$	−0.982287	+	0.187381i	−0.0434114	+	0.00828116i
$513$	1.59085	−	1.69408i	0.0702375	−	0.0747954i
$514$	11.4749	−	10.7756i	0.506135	−	0.475293i
$515$	14.3950	−	3.24515i	0.634320	−	0.142999i
$516$	−2.88304	+	6.12677i	−0.126919	+	0.269716i
$517$	−50.4043	−	31.9876i	−2.21678	−	1.40681i
$518$	−9.92502	+	3.22484i	−0.436080	+	0.141691i
$519$	15.8752	−	6.28542i	0.696843	−	0.275899i
$520$	−1.30842	+	0.777013i	−0.0573781	+	0.0340743i
$521$	18.0051	−	21.7645i	0.788820	−	0.953519i	−0.210893	−	0.977509i	$-0.567637\pi$
$521$	18.0051	−	21.7645i	0.788820	−	0.953519i	0.999712	+	0.0239902i	$0.00763704\pi$
$522$	5.94116	−	3.77038i	0.260038	−	0.165025i
$523$	0.806837	+	6.38677i	0.0352805	+	0.279274i	0.999879	+	0.0155514i	$0.00495036\pi$
$523$	0.806837	+	6.38677i	0.0352805	+	0.279274i	−0.964599	+	0.263723i	$0.915050\pi$
$524$	−2.86649	+	8.82215i	−0.125223	+	0.385397i
$525$	−19.5804	+	3.80899i	−0.854559	+	0.166238i
$526$	−7.39581	−	22.7620i	−0.322473	−	0.992469i
$527$	15.0669	−	7.08994i	0.656324	−	0.308843i
$528$	1.11574	+	4.34554i	0.0485566	+	0.189115i
$529$	21.3323	−	5.47721i	0.927492	−	0.238140i
$530$	27.9681	−	0.929827i	1.21486	−	0.0403891i
$531$	−6.24913	+	9.84705i	−0.271189	+	0.427326i
$532$	−5.44955	−	7.50066i	−0.236268	−	0.325195i
$533$	1.46115	−	1.20877i	0.0632894	−	0.0523576i
$534$	11.6440	−	6.40136i	0.503887	−	0.277014i
$535$	30.0398	+	0.889381i	1.29873	+	0.0384513i
$536$	−2.20415	+	11.5546i	−0.0952050	+	0.499082i
$537$	−23.7623	−	11.1817i	−1.02542	−	0.482525i
$538$	1.36575	−	10.8111i	0.0588818	−	0.466098i
$539$	17.0319	+	36.1946i	0.733616	+	1.55901i
$540$	−1.37371	−	1.76435i	−0.0591151	−	0.0759254i
$541$	5.14257	+	0.649658i	0.221096	+	0.0279310i	0.235101	−	0.971971i	$-0.424458\pi$
$541$	5.14257	+	0.649658i	0.221096	+	0.0279310i	−0.0140045	+	0.999902i	$0.504458\pi$
$542$	−9.56956	−	24.1699i	−0.411048	−	1.03819i
$543$	−3.50328	+	4.82186i	−0.150340	+	0.206926i
$544$	−0.161210	−	2.56236i	−0.00691181	−	0.109860i
$545$	−5.70965	+	5.73045i	−0.244575	+	0.245465i
$546$	−2.52438	−	0.999471i	−0.108033	−	0.0427734i
$547$	26.2631	+	1.65233i	1.12293	+	0.0706487i	0.613376	−	0.789791i	$-0.289811\pi$
$547$	26.2631	+	1.65233i	1.12293	+	0.0706487i	0.509552	+	0.860440i	$0.329811\pi$
$548$	7.24725	+	7.71754i	0.309587	+	0.329677i
$549$	−6.20372	−	4.50727i	−0.264768	−	0.192366i
$550$	22.2656	+	2.73060i	0.949410	+	0.116433i
$551$	13.2295	−	9.61178i	0.563595	−	0.409475i
$552$	−0.970302	−	0.185095i	−0.0412988	−	0.00787817i
$553$	−5.86782	−	4.85428i	−0.249525	−	0.206425i
$554$	−0.474394	+	7.54028i	−0.0201551	+	0.320356i
$555$	−5.36385	+	2.33273i	−0.227683	+	0.0990190i
$556$	−0.440243	−	0.113035i	−0.0186705	−	0.00479376i
$557$			27.6725i			1.17252i	0.810122	+	0.586262i	$0.199401\pi$
$557$			27.6725i			1.17252i	−0.810122	+	0.586262i	$0.800599\pi$
$558$	1.61294	−	6.28200i	0.0682813	−	0.265938i
$559$	0.863476	+	4.52650i	0.0365212	+	0.191451i
$560$	−7.94109	+	4.06439i	−0.335572	+	0.171752i
$561$	−11.4279	+	1.44368i	−0.482486	+	0.0609521i
$562$	−8.60582	−	15.6539i	−0.363015	−	0.660321i
$563$	−16.6112	−	30.2157i	−0.700080	−	1.27344i	−0.952120	−	0.305724i	$-0.901101\pi$
$563$	−16.6112	−	30.2157i	−0.700080	−	1.27344i	0.252040	−	0.967717i	$-0.418899\pi$
$564$	13.2012	−	1.66769i	0.555869	−	0.0702226i
$565$	−22.1467	−	3.46643i	−0.931718	−	0.145834i
$566$	−2.90122	−	15.2087i	−0.121947	−	0.639271i
$567$	0.992146	−	3.86415i	0.0416662	−	0.162279i
$568$			11.6476i			0.488723i
$569$	0.0866472	+	0.0222472i	0.00363244	+	0.000932652i	0.250506	−	0.968115i	$-0.419403\pi$
$569$	0.0866472	+	0.0222472i	0.00363244	+	0.000932652i	−0.246873	+	0.969048i	$0.579403\pi$
$570$	−3.44358	−	3.89169i	−0.144236	−	0.163005i
$571$	−1.71319	+	27.2303i	−0.0716946	+	1.13955i	0.783550	+	0.621328i	$0.213407\pi$
$571$	−1.71319	+	27.2303i	−0.0716946	+	1.13955i	−0.855245	+	0.518224i	$0.826593\pi$
$572$	2.35258	+	1.94623i	0.0983664	+	0.0813758i
$573$	11.8468	+	2.25990i	0.494907	+	0.0944086i
$574$	8.99357	−	6.53421i	0.375384	−	0.272733i
$575$	−2.63127	+	4.17973i	−0.109731	+	0.174307i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	−15.0791	−	16.0576i	−0.627752	−	0.668488i	0.333948	−	0.942591i	$-0.391619\pi$
$577$	−15.0791	−	16.0576i	−0.627752	−	0.668488i	−0.961700	+	0.274104i	$0.911619\pi$
$578$	−10.3878	−	0.653545i	−0.432076	−	0.0271839i
$579$	−5.97134	−	2.36422i	−0.248160	−	0.0982536i
$580$	−7.16866	−	14.0063i	−0.297662	−	0.581579i
$581$	−2.67167	−	42.4649i	−0.110839	−	1.76174i
$582$	−5.09099	+	7.00714i	−0.211028	+	0.290455i
$583$	−20.6690	−	52.2039i	−0.856022	−	2.16206i
$584$	3.89723	+	0.492334i	0.161268	+	0.0203729i
$585$	−1.46210	−	0.421897i	−0.0604502	−	0.0174433i
$586$	12.1193	+	25.7548i	0.500642	+	1.06392i
$587$	−4.65404	+	36.8405i	−0.192093	+	1.52057i	0.541336	+	0.840806i	$0.317919\pi$
$587$	−4.65404	+	36.8405i	−0.192093	+	1.52057i	−0.733429	+	0.679766i	$0.762081\pi$
$588$	−8.06747	−	3.79626i	−0.332697	−	0.156555i
$589$	2.82431	−	14.8055i	0.116373	−	0.610051i
$590$	20.6350	+	15.9461i	0.849528	+	0.656491i
$591$	1.11437	−	0.612627i	0.0458389	−	0.0252001i
$592$	−2.01552	+	1.66739i	−0.0828375	+	0.0685291i
$593$	10.3815	+	14.2890i	0.426319	+	0.586778i	0.967103	−	0.254383i	$-0.0818725\pi$
$593$	10.3815	+	14.2890i	0.426319	+	0.586778i	−0.540784	+	0.841161i	$0.681873\pi$
$594$	−2.40398	+	3.78807i	−0.0986366	+	0.155426i
$595$	−7.79741	−	21.5352i	−0.319663	−	0.882858i
$596$	−5.52937	+	1.41970i	−0.226492	+	0.0581532i
$597$	2.64922	+	10.3180i	0.108425	+	0.422288i
$598$	−0.608264	+	0.286227i	−0.0248738	+	0.0117047i
$599$	−2.81270	−	8.65659i	−0.114924	−	0.353699i	0.877007	−	0.480477i	$-0.159536\pi$
$599$	−2.81270	−	8.65659i	−0.114924	−	0.353699i	−0.991931	+	0.126778i	$0.959536\pi$
$600$	−4.21187	+	2.69446i	−0.171949	+	0.110001i
$601$	−2.45028	+	7.54117i	−0.0999488	+	0.307611i	−0.988512	−	0.151144i	$-0.951704\pi$
$601$	−2.45028	+	7.54117i	−0.0999488	+	0.307611i	0.888563	+	0.458755i	$0.151704\pi$
$602$	3.38571	+	26.8007i	0.137991	+	1.09231i
$603$	−9.93178	+	6.30290i	−0.404453	+	0.256674i
$604$	−2.45221	+	2.96422i	−0.0997791	+	0.120612i
$605$	−4.48898	−	19.9124i	−0.182503	−	0.809556i
$606$	10.3049	−	4.07999i	0.418607	−	0.165738i
$607$	39.1674	−	12.7263i	1.58976	−	0.516543i	0.625209	−	0.780457i	$-0.285014\pi$
$607$	39.1674	−	12.7263i	1.58976	−	0.516543i	0.964546	+	0.263914i	$0.0850136\pi$
$608$	−1.96217	−	1.24523i	−0.0795763	−	0.0505007i
$609$	11.9526	−	25.4006i	0.484344	−	1.02928i
$610$	−11.3159	+	12.8825i	−0.458167	+	0.521597i
$611$	6.60111	−	6.19885i	0.267052	−	0.250779i
$612$	1.75752	−	1.87157i	0.0710436	−	0.0756537i
$613$	−21.6508	+	4.13011i	−0.874467	+	0.166813i	−0.605028	−	0.796204i	$-0.706838\pi$
$613$	−21.6508	+	4.13011i	−0.874467	+	0.166813i	−0.269439	+	0.963018i	$0.586838\pi$
$614$	−18.9554	−	10.4208i	−0.764978	−	0.420550i
$615$	4.66627	−	4.12897i	0.188162	−	0.166496i
$616$	13.0477	+	12.2526i	0.525706	+	0.493671i
$617$	−10.1015	+	0.635531i	−0.406670	+	0.0255855i	−0.264808	−	0.964301i	$-0.585309\pi$
$617$	−10.1015	+	0.635531i	−0.406670	+	0.0255855i	−0.141861	+	0.989887i	$0.545309\pi$
$618$	6.27622	+	2.03927i	0.252466	+	0.0820313i
$619$	−20.0675	−	24.2575i	−0.806582	−	0.974990i	0.193399	−	0.981120i	$-0.438049\pi$
$619$	−20.0675	−	24.2575i	−0.806582	−	0.974990i	−0.999981	+	0.00612978i	$0.998049\pi$
$620$	−13.6541	−	4.88777i	−0.548363	−	0.196297i
$621$	−0.529289	−	0.834026i	−0.0212396	−	0.0334683i
$622$	−0.128806	+	0.325326i	−0.00516464	+	0.0130444i
$623$	25.5382	−	46.4538i	1.02317	−	1.86113i
$624$	−0.680547			−0.0272437
$625$	4.86297	+	24.5225i	0.194519	+	0.980899i
$626$	−1.66628			−0.0665981
$627$	−5.02292	+	9.13666i	−0.200596	+	0.364883i
$628$	2.71197	−	6.84966i	0.108219	−	0.273331i
$629$	−3.59857	−	5.67043i	−0.143484	−	0.226095i
$630$	−8.39886	−	3.00654i	−0.334619	−	0.119783i
$631$	−15.8695	−	19.1830i	−0.631756	−	0.763661i	0.353372	−	0.935483i	$-0.385035\pi$
$631$	−15.8695	−	19.1830i	−0.631756	−	0.763661i	−0.985128	+	0.171821i	$0.945035\pi$
$632$	−1.81545	−	0.589877i	−0.0722149	−	0.0234640i
$633$	25.8592	−	1.62692i	1.02781	−	0.0646643i
$634$	4.89352	+	4.59532i	0.194347	+	0.182504i
$635$	−25.3240	+	22.4081i	−1.00495	+	0.889237i
$636$	10.9666	+	6.02896i	0.434856	+	0.239064i
$637$	−5.96030	+	1.13699i	−0.236156	+	0.0450491i
$638$	−21.6108	+	23.0131i	−0.855579	+	0.911099i
$639$	−8.49074	+	7.97334i	−0.335888	+	0.315420i
$640$	−1.47569	+	1.67998i	−0.0583316	+	0.0664072i
$641$	−1.02165	+	2.17112i	−0.0403528	+	0.0857541i	−0.923987	−	0.382424i	$-0.875089\pi$
$641$	−1.02165	+	2.17112i	−0.0403528	+	0.0857541i	0.883634	+	0.468178i	$0.155089\pi$
$642$	11.3479	+	7.20157i	0.447864	+	0.284223i
$643$	−33.7223	+	10.9570i	−1.32988	+	0.432103i	−0.885876	−	0.463923i	$-0.846441\pi$
$643$	−33.7223	+	10.9570i	−1.32988	+	0.432103i	−0.444001	+	0.896026i	$0.646441\pi$
$644$	−3.66408	+	1.45071i	−0.144385	+	0.0571660i
$645$	3.32974	+	14.7702i	0.131108	+	0.581576i
$646$	3.80321	−	4.59729i	0.149635	−	0.180878i
$647$	−20.0345	+	12.7143i	−0.787639	+	0.499851i	−0.867789	−	0.496932i	$-0.834460\pi$
$647$	−20.0345	+	12.7143i	−0.787639	+	0.499851i	0.0801508	+	0.996783i	$0.474460\pi$
$648$	−0.125333	−	0.992115i	−0.00492355	−	0.0389739i
$649$	16.1690	−	49.7632i	0.634690	−	1.95338i
$650$	−1.24112	+	3.16832i	−0.0486807	+	0.124272i
$651$	−7.99578	−	24.6085i	−0.313379	−	0.964482i
$652$	6.37692	−	3.00075i	0.249740	−	0.117519i
$653$	2.96790	+	11.5592i	0.116143	+	0.452347i	0.999878	−	0.0156411i	$-0.00497892\pi$
$653$	2.96790	+	11.5592i	0.116143	+	0.452347i	−0.883735	+	0.467988i	$0.844979\pi$
$654$	−3.50403	+	0.899681i	−0.137018	+	0.0351803i
$655$	7.06160	+	19.5030i	0.275920	+	0.762047i
$656$	1.49307	−	2.35271i	0.0582947	−	0.0918578i
$657$	2.30894	+	3.17798i	0.0900803	+	0.123985i
$658$	40.9023	−	33.8373i	1.59454	−	1.31912i
$659$	−26.6438	+	14.6475i	−1.03789	+	0.570587i	−0.907141	−	0.420828i	$-0.861740\pi$
$659$	−26.6438	+	14.6475i	−1.03789	+	0.570587i	−0.130754	+	0.991415i	$0.541740\pi$
$660$	7.93808	+	6.13432i	0.308989	+	0.238778i
$661$	8.05700	−	42.2363i	0.313381	−	1.64280i	−0.382002	−	0.924162i	$-0.624765\pi$
$661$	8.05700	−	42.2363i	0.313381	−	1.64280i	0.695383	−	0.718640i	$-0.255235\pi$
$662$	−1.56795	−	0.737821i	−0.0609401	−	0.0286762i
$663$	0.218989	−	1.73347i	0.00850481	−	0.0673225i
$664$	−4.54104	−	9.65020i	−0.176227	−	0.374500i
$665$	−19.9186	−	5.74766i	−0.772412	−	0.222885i
$666$	−2.59519	−	0.327849i	−0.100562	−	0.0127039i
$667$	−2.55873	−	6.46260i	−0.0990743	−	0.250233i
$668$	−9.87158	+	13.5871i	−0.381943	+	0.525699i
$669$	0.0602991	+	0.958427i	0.00233130	+	0.0370549i
$670$	11.9838	+	23.4142i	0.462973	+	0.904568i
$671$	31.9875	+	12.6647i	1.23486	+	0.488917i
$672$	−3.98162	−	0.250502i	−0.153594	−	0.00966333i
$673$	−1.40348	−	1.49456i	−0.0541003	−	0.0576109i	0.701349	−	0.712818i	$-0.252581\pi$
$673$	−1.40348	−	1.49456i	−0.0541003	−	0.0576109i	−0.755449	+	0.655207i	$0.772581\pi$
$674$	23.3748	+	16.9828i	0.900363	+	0.654152i
$675$	−4.84740	−	1.22583i	−0.186577	−	0.0471824i
$676$	10.1425	−	7.36898i	0.390097	−	0.283422i
$677$	−10.4944	−	2.00192i	−0.403334	−	0.0769400i	−0.0182770	−	0.999833i	$-0.505818\pi$
$677$	−10.4944	−	2.00192i	−0.403334	−	0.0769400i	−0.385057	+	0.922893i	$0.625818\pi$
$678$	−7.72431	−	6.39010i	−0.296650	−	0.245410i
$679$	−2.16968	+	34.4860i	−0.0832645	+	1.32345i
$680$	−3.80437	−	4.29943i	−0.145891	−	0.164875i
$681$	−13.4395	−	3.45069i	−0.515004	−	0.132231i
$682$			29.0983i			1.11423i
$683$	6.31428	−	24.5925i	0.241609	−	0.941006i	−0.725824	−	0.687880i	$-0.758541\pi$
$683$	6.31428	−	24.5925i	0.241609	−	0.941006i	0.967433	−	0.253125i	$-0.0814585\pi$
$684$	−0.435463	−	2.28278i	−0.0166503	−	0.0872841i
$685$	23.3883	+	3.66078i	0.893622	+	0.139871i
$686$	−7.58374	+	0.958050i	−0.289549	+	0.0365785i
$687$	12.5959	+	22.9119i	0.480564	+	0.874143i
$688$	3.26205	+	5.93365i	0.124365	+	0.226218i
$689$	8.44963	−	1.06744i	0.321905	−	0.0406661i
$690$	−1.96622	+	1.00634i	−0.0748526	+	0.0383108i
$691$	4.53127	+	23.7537i	0.172378	+	0.903635i	0.958398	+	0.285435i	$0.0921380\pi$
$691$	4.53127	+	23.7537i	0.172378	+	0.903635i	−0.786021	+	0.618200i	$0.787862\pi$
$692$	4.24618	−	16.5378i	0.161415	−	0.628671i
$693$			17.8988i			0.679920i
$694$	15.0297	+	3.85897i	0.570519	+	0.146484i
$695$	−0.932018	+	0.405334i	−0.0353535	+	0.0153752i
$696$	0.441829	−	7.02267i	0.0167475	−	0.266194i
$697$	5.51232	+	4.56018i	0.208794	+	0.172729i
$698$	13.5371	+	2.58234i	0.512387	+	0.0977431i
$699$	−15.2310	+	11.0660i	−0.576090	+	0.418554i
$700$	−8.42754	+	18.0798i	−0.318531	+	0.683351i
$701$	7.27768	+	5.28754i	0.274874	+	0.199708i	0.716679	−	0.697404i	$-0.245662\pi$
$701$	7.27768	+	5.28754i	0.274874	+	0.199708i	−0.441804	+	0.897111i	$0.645662\pi$
$702$	−0.465866	−	0.496097i	−0.0175830	−	0.0187240i
$703$	−6.06701	−	0.381704i	−0.228822	−	0.0143962i
$704$	4.17143	+	1.65159i	0.157217	+	0.0622465i
$705$	21.0005	−	21.0770i	0.790923	−	0.793804i
$706$	−0.355158	−	5.64508i	−0.0133666	−	0.212455i
$707$	25.9897	−	35.7717i	0.977442	−	1.34533i
$708$	4.29328	+	10.8436i	0.161352	+	0.407527i
$709$	39.0320	+	4.93089i	1.46588	+	0.185184i	0.817410	−	0.576057i	$-0.195409\pi$
$709$	39.0320	+	4.93089i	1.46588	+	0.185184i	0.648470	+	0.761241i	$0.275409\pi$
$710$	16.0005	+	20.5504i	0.600486	+	0.771243i
$711$	−0.812762	−	1.72721i	−0.0304810	−	0.0647754i
$712$	1.66538	−	13.1828i	0.0624128	−	0.494048i
$713$	−5.79689	−	2.72781i	−0.217095	−	0.102157i
$714$	1.91929	−	10.0613i	0.0718277	−	0.376534i
$715$	6.82432	+	0.202046i	0.255215	+	0.00755608i
$716$	−23.0133	+	12.6517i	−0.860047	+	0.472815i
$717$	6.14144	−	5.08064i	0.229356	−	0.189740i
$718$	−20.6629	−	28.4400i	−0.771131	−	1.06137i
$719$	9.31852	−	14.6836i	0.347522	−	0.547607i	−0.624939	−	0.780674i	$-0.714876\pi$
$719$	9.31852	−	14.6836i	0.347522	−	0.547607i	0.972461	+	0.233066i	$0.0748760\pi$
$720$	−2.23483	+	0.0742993i	−0.0832873	+	0.00276897i
$721$	25.5003	−	6.54738i	0.949682	−	0.243837i
$722$	3.38201	+	13.1721i	0.125865	+	0.490213i
$723$	3.13656	−	1.47595i	0.116650	−	0.0548913i
$724$	1.84178	+	5.66843i	0.0684494	+	0.210666i
$725$	−31.8886	−	14.8643i	−1.18431	−	0.552045i
$726$	2.82089	−	8.68181i	0.104693	−	0.322212i
$727$	−4.59315	−	36.3585i	−0.170351	−	1.34846i	−0.812982	−	0.582289i	$-0.802157\pi$
$727$	−4.59315	−	36.3585i	−0.170351	−	1.34846i	0.642632	−	0.766175i	$-0.277843\pi$
$728$	−2.29238	+	1.45479i	−0.0849613	+	0.0539181i
$729$	0.637424	−	0.770513i	0.0236083	−	0.0285375i
$730$	7.55238	−	4.48502i	0.279526	−	0.165998i
$731$	−16.1637	+	6.39968i	−0.597837	+	0.236701i
$732$	−7.29291	+	2.36961i	−0.269554	+	0.0875834i
$733$	−40.0627	−	25.4245i	−1.47975	−	0.939077i	−0.998029	−	0.0627513i	$-0.980013\pi$
$733$	−40.0627	−	25.4245i	−1.47975	−	0.939077i	−0.481719	−	0.876326i	$-0.659987\pi$
$734$	14.9725	−	31.8182i	0.552645	−	1.17443i
$735$	−19.4488	+	4.38446i	−0.717379	+	0.161723i
$736$	−0.720074	+	0.676195i	−0.0265423	+	0.0249249i
$737$	36.1265	−	38.4708i	1.33074	−	1.41709i
$738$	2.73713	−	0.522135i	0.100755	−	0.0192201i
$739$	−1.86227	−	1.02379i	−0.0685047	−	0.0376608i	0.447133	−	0.894467i	$-0.352445\pi$
$739$	−1.86227	−	1.02379i	−0.0685047	−	0.0376608i	−0.515638	+	0.856807i	$0.672445\pi$
$740$	−1.26557	+	5.71059i	−0.0465234	+	0.209926i
$741$	−1.15290	−	1.08264i	−0.0423528	−	0.0397719i
$742$	49.8284	−	3.13494i	1.82926	−	0.115087i
$743$	−32.6002	−	10.5924i	−1.19598	−	0.388599i	−0.357702	−	0.933836i	$-0.616440\pi$
$743$	−32.6002	−	10.5924i	−1.19598	−	0.388599i	−0.838282	+	0.545237i	$0.816440\pi$
$744$	−4.13418	−	4.99736i	−0.151566	−	0.183212i
$745$	−7.80546	+	10.1006i	−0.285970	+	0.370058i
$746$	−14.5671	−	22.9540i	−0.533338	−	0.840406i
$747$	3.92614	−	9.91629i	0.143650	−	0.362818i
$748$	−5.54918	+	10.0939i	−0.202898	+	0.369070i
$749$	53.6192			1.95920
$750$	−3.72978	+	10.5399i	−0.136192	+	0.384861i
$751$	8.28892			0.302467			0.151233	−	0.988498i	$-0.451675\pi$
$751$	8.28892			0.302467			0.151233	+	0.988498i	$0.451675\pi$
$752$	6.41025	−	11.6602i	0.233758	−	0.425204i
$753$	−5.94352	+	15.0116i	−0.216594	+	0.547054i
$754$	−2.56592	−	4.04324i	−0.0934452	−	0.147246i
$755$	−0.254574	+	8.59854i	−0.00926491	+	0.312933i
$756$	−2.54300	−	3.07396i	−0.0924879	−	0.111799i
$757$	−8.26716	−	2.68616i	−0.300475	−	0.0976303i	0.154899	−	0.987930i	$-0.450495\pi$
$757$	−8.26716	−	2.68616i	−0.300475	−	0.0976303i	−0.455375	+	0.890300i	$0.650495\pi$
$758$	−14.0655	+	0.884928i	−0.510883	+	0.0321420i
$759$	3.23061	+	3.03374i	0.117264	+	0.110118i
$760$	−5.17252	+	0.498436i	−0.187627	+	0.0180802i
$761$	−15.4822	−	8.51143i	−0.561230	−	0.308539i	0.175770	−	0.984431i	$-0.443758\pi$
$761$	−15.4822	−	8.51143i	−0.561230	−	0.308539i	−0.737000	+	0.675892i	$0.763758\pi$
$762$	−14.8545	+	2.83365i	−0.538121	+	0.102652i
$763$	−9.87987	+	10.5210i	−0.357675	+	0.380885i
$764$	8.79167	−	8.25593i	0.318071	−	0.298689i
$765$	0.529878	−	5.71642i	0.0191578	−	0.206678i
$766$	−5.78860	+	12.3014i	−0.209151	+	0.444468i
$767$	6.70138	+	4.25282i	0.241973	+	0.153561i
$768$	−0.951057	+	0.309017i	−0.0343183	+	0.0111507i
$769$	9.34014	−	3.69802i	0.336814	−	0.133354i	−0.193629	−	0.981075i	$-0.562026\pi$
$769$	9.34014	−	3.69802i	0.336814	−	0.133354i	0.530443	+	0.847721i	$0.322026\pi$
$770$	39.8521	+	3.69405i	1.43617	+	0.133124i
$771$	10.0339	−	12.1288i	0.361360	−	0.436810i
$772$	−5.42256	+	3.44126i	−0.195162	+	0.123854i
$773$	−4.66462	−	36.9243i	−0.167775	−	1.32807i	−0.821008	−	0.570917i	$-0.806588\pi$
$773$	−4.66462	−	36.9243i	−0.167775	−	1.32807i	0.653233	−	0.757157i	$-0.273412\pi$
$774$	−2.09242	+	6.43980i	−0.0752104	+	0.231474i
$775$	−30.8050	+	10.1331i	−1.10655	+	0.363992i
$776$	2.67649	+	8.23739i	0.0960804	+	0.295705i
$777$	−9.44258	+	4.44334i	−0.338751	+	0.159404i
$778$	5.70150	+	22.2059i	0.204409	+	0.796120i
$779$	6.27218	−	1.61042i	0.224724	−	0.0576993i
$780$	−1.20072	+	0.934875i	−0.0429927	+	0.0334739i
$781$	28.0006	−	44.1219i	1.00194	−	1.57881i
$782$	−1.49068	−	2.05175i	−0.0533066	−	0.0733703i
$783$	5.42176	−	4.48527i	0.193758	−	0.160291i
$784$	−7.81318	+	4.29533i	−0.279042	+	0.153405i
$785$	−4.62460	−	15.8106i	−0.165059	−	0.564306i
$786$	−1.73818	+	9.11185i	−0.0619987	+	0.325009i
$787$	42.2792	+	19.8951i	1.50709	+	0.709183i	0.989242	−	0.146290i	$-0.0467331\pi$
$787$	42.2792	+	19.8951i	1.50709	+	0.709183i	0.517848	+	0.855472i	$0.326733\pi$
$788$	0.159381	−	1.26163i	0.00567773	−	0.0449438i
$789$	−10.1903	−	21.6555i	−0.362785	−	0.770958i
$790$	−4.01341	+	1.45316i	−0.142791	+	0.0517012i
$791$	−39.6788	−	5.01260i	−1.41082	−	0.178228i
$792$	1.65159	+	4.17143i	0.0586866	+	0.148225i
$793$	−3.06741	+	4.22192i	−0.108927	+	0.149925i
$794$	1.05089	+	16.7034i	0.0372946	+	0.592780i
$795$	27.6310	−	4.42783i	0.979971	−	0.157039i
$796$	9.90462	+	3.92152i	0.351060	+	0.138994i
$797$	1.18007	+	0.0742437i	0.0418002	+	0.00262985i	0.0836769	−	0.996493i	$-0.473334\pi$
$797$	1.18007	+	0.0742437i	0.0418002	+	0.00262985i	−0.0418766	+	0.999123i	$0.513334\pi$
$798$	−6.34666	−	6.75851i	−0.224669	−	0.239249i
$799$	27.6379	+	20.0801i	0.977758	+	0.710383i
$800$	−0.295808	+	4.99124i	−0.0104584	+	0.176467i
$801$	10.7499	−	7.81027i	0.379829	−	0.275962i
$802$	33.2366	+	6.34022i	1.17362	+	0.223881i
$803$	−13.5794	−	11.2339i	−0.479207	−	0.396434i
$804$	−0.738601	+	11.7397i	−0.0260484	+	0.414028i
$805$	−4.47184	+	7.59294i	−0.157612	+	0.267616i
$806$	−4.27519	−	1.09768i	−0.150587	−	0.0386642i
$807$		−	10.8970i		−	0.383592i
$808$	2.75628	−	10.7350i	0.0969655	−	0.377656i
$809$	−5.46753	−	28.6618i	−0.192228	−	1.00769i	−0.939338	−	0.342994i	$-0.888559\pi$
$809$	−5.46753	−	28.6618i	−0.192228	−	1.00769i	0.747110	−	0.664701i	$-0.231441\pi$
$810$	−1.58401	−	1.57826i	−0.0556565	−	0.0554545i
$811$	14.7875	−	1.86810i	0.519261	−	0.0655979i	0.138665	−	0.990339i	$-0.455719\pi$
$811$	14.7875	−	1.86810i	0.519261	−	0.0655979i	0.380596	+	0.924741i	$0.375719\pi$
$812$	−13.5239	−	24.5999i	−0.474597	−	0.863288i
$813$	−12.5234	−	22.7800i	−0.439215	−	0.798929i
$814$	11.6433	−	1.47089i	0.408098	−	0.0515547i
$815$	7.12893	−	14.0544i	0.249716	−	0.492305i
$816$	−0.481087	−	2.52195i	−0.0168414	−	0.0882858i
$817$	−3.91335	+	15.2415i	−0.136911	+	0.533232i
$818$		−	6.07289i		−	0.212334i
$819$	−2.62974	−	0.675202i	−0.0918905	−	0.0235935i
$820$	−0.597643	−	6.20204i	−0.0208706	−	0.216585i
$821$	2.86494	−	45.5369i	0.0999871	−	1.58925i	−0.553852	−	0.832615i	$-0.686843\pi$
$821$	2.86494	−	45.5369i	0.0999871	−	1.58925i	0.653839	−	0.756634i	$-0.273157\pi$
$822$	8.15737	+	6.74836i	0.284521	+	0.235376i
$823$	−33.7198	−	6.43239i	−1.17540	−	0.224219i	−0.437555	−	0.899192i	$-0.644155\pi$
$823$	−33.7198	−	6.43239i	−1.17540	−	0.224219i	−0.737843	+	0.674973i	$0.764155\pi$
$824$	5.33887	−	3.87892i	0.185988	−	0.135128i
$825$	22.4323	−	0.0815577i	0.780993	−	0.00283947i
$826$	37.6418	+	27.3483i	1.30972	+	0.951571i
$827$	28.7021	+	30.5646i	0.998068	+	1.06283i	0.998024	+	0.0628349i	$0.0200141\pi$
$827$	28.7021	+	30.5646i	0.998068	+	1.06283i	4.44497e−5		1.00000i	$0.499986\pi$
$828$	−0.985850	−	0.0620244i	−0.0342606	−	0.00215550i
$829$	1.57055	+	0.621825i	0.0545475	+	0.0215969i	0.395240	−	0.918578i	$-0.370661\pi$
$829$	1.57055	+	0.621825i	0.0545475	+	0.0215969i	−0.340692	+	0.940175i	$0.610661\pi$
$830$	−21.2686	−	10.7882i	−0.738242	−	0.374464i
$831$	0.474394	+	7.54028i	0.0164566	+	0.261569i
$832$	−0.400015	+	0.550574i	−0.0138680	+	0.0190877i
$833$	−8.42682	−	21.2837i	−0.291972	−	0.737438i
$834$	−0.450938	−	0.0569668i	−0.0156147	−	0.00197260i
$835$	1.24782	+	37.5330i	0.0431827	+	1.29888i
$836$	4.43931	+	9.43402i	0.153537	+	0.326283i
$837$	0.812881	−	6.43462i	0.0280973	−	0.222413i
$838$	−10.9459	−	5.15076i	−0.378120	−	0.177930i
$839$	−10.2386	+	53.6727i	−0.353476	+	1.85299i	0.149603	+	0.988746i	$0.452201\pi$
$839$	−10.2386	+	53.6727i	−0.353476	+	1.85299i	−0.503079	+	0.864241i	$0.667799\pi$
$840$	−7.36907	+	5.02762i	−0.254257	+	0.173469i
$841$	17.9758	−	9.88229i	0.619856	−	0.340769i
$842$	−9.03020	+	7.47043i	−0.311201	+	0.257448i
$843$	−10.4999	−	14.4519i	−0.361636	−	0.497750i
$844$	13.8834	−	21.8768i	0.477887	−	0.753030i
$845$	7.77208	−	26.9343i	0.267368	−	0.926569i
$846$	12.8880	−	3.30909i	0.443100	−	0.113769i
$847$	−9.05690	−	35.2743i	−0.311199	−	1.21204i
$848$	11.3236	−	5.32846i	0.388853	−	0.182980i
$849$	−4.78451	−	14.7252i	−0.164204	−	0.505367i
$850$	−12.6184	−	2.35957i	−0.432807	−	0.0809327i
$851$	−0.798470	+	2.45744i	−0.0273712	+	0.0842399i
$852$	1.45983	+	11.5558i	0.0500130	+	0.395894i
$853$	−20.0955	+	12.7530i	−0.688058	+	0.436655i	−0.833359	−	0.552733i	$-0.813585\pi$
$853$	−20.0955	+	12.7530i	−0.688058	+	0.436655i	0.145301	+	0.989388i	$0.453585\pi$
$854$	−19.5003	+	23.5718i	−0.667286	+	0.806610i
$855$	−3.90418	−	3.42941i	−0.133520	−	0.117283i
$856$	12.4963	−	4.94763i	0.427115	−	0.169107i
$857$	17.1658	−	5.57750i	0.586372	−	0.190524i	−0.000781020	−	1.00000i	$-0.500249\pi$
$857$	17.1658	−	5.57750i	0.586372	−	0.190524i	0.587153	+	0.809476i	$0.300249\pi$
$858$	2.57796	+	1.63602i	0.0880101	+	0.0558529i
$859$	11.7959	−	25.0676i	0.402472	−	0.855296i	−0.596153	−	0.802871i	$-0.703305\pi$
$859$	11.7959	−	25.0676i	0.402472	−	0.855296i	0.998625	−	0.0524253i	$-0.0166952\pi$
$860$	13.9065	+	5.98790i	0.474208	+	0.204186i
$861$	8.10370	−	7.60988i	0.276173	−	0.259344i
$862$	−11.7515	+	12.5141i	−0.400259	+	0.426233i
$863$	51.6740	−	9.85734i	1.75900	−	0.335548i	0.796052	−	0.605228i	$-0.206918\pi$
$863$	51.6740	−	9.85734i	1.75900	−	0.335548i	0.962950	+	0.269680i	$0.0869180\pi$
$864$	−0.876307	−	0.481754i	−0.0298126	−	0.0163896i
$865$	−15.2264	−	35.0114i	−0.517713	−	1.19042i
$866$	−6.45402	−	6.06073i	−0.219316	−	0.205952i
$867$	−10.3878	+	0.653545i	−0.352788	+	0.0221956i
$868$	−24.6085	−	7.99578i	−0.835266	−	0.271394i
$869$	5.45901	+	6.59881i	0.185184	+	0.223849i
$870$	−8.86759	−	12.9974i	−0.300639	−	0.440652i
$871$	4.28942	+	6.75904i	0.145341	+	0.229021i
$872$	−1.33176	+	3.36364i	−0.0450990	+	0.113907i
$873$	−4.17262	+	7.58996i	−0.141222	+	0.256881i
$874$	−2.29558			−0.0776493
$875$	9.96728	+	43.4760i	0.336955	+	1.46976i
$876$	3.92820			0.132722
$877$	4.18067	−	7.60460i	0.141171	−	0.256789i	−0.796264	−	0.604949i	$-0.793193\pi$
$877$	4.18067	−	7.60460i	0.141171	−	0.256789i	0.937435	+	0.348160i	$0.113193\pi$
$878$	6.30997	−	15.9372i	0.212951	−	0.537853i
$879$	15.2516	+	24.0327i	0.514425	+	0.810604i
$880$	9.62866	−	2.81637i	0.324582	−	0.0949400i
$881$	3.96938	+	4.79815i	0.133732	+	0.161654i	0.833128	−	0.553080i	$-0.186548\pi$
$881$	3.96938	+	4.79815i	0.133732	+	0.161654i	−0.699396	+	0.714734i	$0.746548\pi$
$882$	−8.47966	−	2.75521i	−0.285525	−	0.0927727i
$883$	−55.4917	+	3.49124i	−1.86745	+	0.117490i	−0.955897	−	0.293703i	$-0.905112\pi$
$883$	−55.4917	+	3.49124i	−1.86745	+	0.117490i	−0.911549	+	0.411192i	$0.865112\pi$
$884$	−1.27369	−	1.19608i	−0.0428389	−	0.0402284i
$885$	22.4708	+	13.2341i	0.755348	+	0.444860i
$886$	−2.99423	−	1.64609i	−0.100593	−	0.0553016i
$887$	−26.4526	+	5.04610i	−0.888191	+	0.169431i	−0.611233	−	0.791451i	$-0.709326\pi$
$887$	−26.4526	+	5.04610i	−0.888191	+	0.169431i	−0.276958	+	0.960882i	$0.589326\pi$
$888$	−1.79065	+	1.90685i	−0.0600903	+	0.0639897i
$889$	−43.9790	+	41.2991i	−1.47501	+	1.38513i
$890$	−15.1711	−	25.5469i	−0.508537	−	0.856333i
$891$	−1.91025	+	4.05950i	−0.0639959	+	0.135998i
$892$	0.810827	+	0.514566i	0.0271485	+	0.0172290i
$893$	29.4090	−	9.55558i	0.984136	−	0.319765i
$894$	−5.30783	+	2.10152i	−0.177521	+	0.0702854i
$895$	−23.2237	+	53.9355i	−0.776282	+	1.80287i
$896$	−2.54300	+	3.07396i	−0.0849556	+	0.102694i
$897$	−0.567594	+	0.360206i	−0.0189514	+	0.0120269i
$898$	−0.475213	−	3.76170i	−0.0158581	−	0.125530i
$899$	14.1027	−	43.4038i	0.470353	−	1.44760i
$900$	−3.84095	+	3.20111i	−0.128032	+	0.106704i
$901$	9.92881	+	30.5577i	0.330777	+	1.01803i
$902$	−11.3117	+	5.32290i	−0.376639	+	0.177233i
$903$	6.71803	+	26.1650i	0.223562	+	0.870716i
$904$	−9.70994	+	2.49309i	−0.322948	+	0.0829189i
$905$	11.0363	+	7.47099i	0.366860	+	0.248344i
$906$	−2.06136	+	3.24819i	−0.0684842	+	0.107914i
$907$	−21.5209	−	29.6210i	−0.714591	−	0.983550i	−0.999686	−	0.0250511i	$-0.992025\pi$
$907$	−21.5209	−	29.6210i	−0.714591	−	0.983550i	0.285095	−	0.958499i	$-0.407975\pi$
$908$	−10.6912	+	8.84455i	−0.354801	+	0.293517i
$909$	9.71227	−	5.33937i	0.322136	−	0.177096i
$910$	−2.04609	+	5.71582i	−0.0678273	+	0.189478i
$911$	−4.88994	+	25.6340i	−0.162011	+	0.849292i	0.804751	+	0.593613i	$0.202299\pi$
$911$	−4.88994	+	25.6340i	−0.162011	+	0.849292i	−0.966762	+	0.255679i	$0.917701\pi$
$912$	−2.10276	−	0.989485i	−0.0696294	−	0.0327651i
$913$	−5.99713	+	47.4722i	−0.198476	+	1.57110i
$914$	5.82052	+	12.3692i	0.192526	+	0.409138i
$915$	−9.61206	+	14.1992i	−0.317765	+	0.469410i
$916$	25.9398	+	3.27696i	0.857076	+	0.108274i
$917$	13.6232	+	34.4084i	0.449879	+	1.13626i
$918$	1.50909	−	2.07709i	0.0498075	−	0.0685541i
$919$	−1.98135	−	31.4927i	−0.0653588	−	1.03885i	−0.884886	−	0.465808i	$-0.845764\pi$
$919$	−1.98135	−	31.4927i	−0.0653588	−	1.03885i	0.819527	−	0.573041i	$-0.194236\pi$
$920$	−0.341564	+	2.18222i	−0.0112610	+	0.0719455i
$921$	−20.1120	−	7.96291i	−0.662713	−	0.262387i
$922$	−10.7684	−	0.677491i	−0.354639	−	0.0223120i
$923$	5.42623	+	5.77835i	0.178606	+	0.190197i
$924$	14.4804	+	10.5207i	0.476372	+	0.346104i
$925$	5.61180	+	11.8140i	0.184515	+	0.388442i
$926$	1.90584	−	1.38467i	0.0626297	−	0.0455031i
$927$	6.48231	+	1.23657i	0.212907	+	0.0406142i
$928$	−5.42176	−	4.48527i	−0.177978	−	0.147236i
$929$	2.29689	−	36.5080i	0.0753585	−	1.19779i	−0.760683	−	0.649123i	$-0.775136\pi$
$929$	2.29689	−	36.5080i	0.0753585	−	1.19779i	0.836042	−	0.548666i	$-0.184864\pi$
$930$	−14.1591	−	3.13791i	−0.464294	−	0.102896i
$931$	−20.0694	−	5.15294i	−0.657747	−	0.168881i
$932$			18.8266i			0.616685i
$933$	−0.0870159	+	0.338904i	−0.00284877	+	0.0110952i
$934$	6.48002	+	33.9695i	0.212033	+	1.11152i
$935$	4.07546	+	25.4322i	0.133282	+	0.831720i
$936$	−0.675181	+	0.0852951i	−0.0220690	+	0.00278796i
$937$	15.0792	+	27.4290i	0.492616	+	0.896065i	0.999422	+	0.0340048i	$0.0108262\pi$
$937$	15.0792	+	27.4290i	0.492616	+	0.896065i	−0.506806	+	0.862060i	$0.669174\pi$
$938$	22.6078	+	41.1234i	0.738171	+	1.34273i
$939$	−1.65314	+	0.208841i	−0.0539483	+	0.00681526i
$940$	−4.70785	−	29.3785i	−0.153553	−	0.958220i
$941$	−5.94896	−	31.1855i	−0.193930	−	1.01662i	−0.937506	−	0.347968i	$-0.886872\pi$
$941$	−5.94896	−	31.1855i	−0.193930	−	1.01662i	0.743576	−	0.668651i	$-0.233128\pi$
$942$	1.83210	−	7.13555i	0.0596929	−	0.232489i
$943$		−	2.75249i		−	0.0896333i
$944$	11.2962	+	2.90037i	0.367660	+	0.0943989i
$945$	−8.70946	−	1.93018i	−0.283319	−	0.0627887i
$946$	1.90751	−	30.3190i	0.0620185	−	0.985756i
$947$	13.2042	+	10.9235i	0.429079	+	0.354965i	0.826756	−	0.562560i	$-0.190184\pi$
$947$	13.2042	+	10.9235i	0.429079	+	0.354965i	−0.397677	+	0.917525i	$0.630184\pi$
$948$	−1.87507	−	0.357689i	−0.0608994	−	0.0116172i
$949$	2.16276	−	1.57134i	0.0702063	−	0.0510079i
$950$	−8.44142	+	7.98497i	−0.273876	+	0.259067i
$951$	5.43088	+	3.94577i	0.176108	+	0.127950i
$952$	−7.01161	−	7.46661i	−0.227248	−	0.241994i
$953$	−36.5440	−	2.29915i	−1.18378	−	0.0744768i	−0.541331	−	0.840809i	$-0.682080\pi$
$953$	−36.5440	−	2.29915i	−1.18378	−	0.0744768i	−0.642444	+	0.766333i	$0.722080\pi$
$954$	11.6358	+	4.60694i	0.376723	+	0.149155i
$955$	4.17028	−	26.6435i	0.134947	−	0.862164i
$956$	−0.500477	−	7.95486i	−0.0161866	−	0.257279i
$957$	−18.5561	+	25.5402i	−0.599832	+	0.825598i
$958$	3.10658	+	7.84633i	0.100369	+	0.253504i
$959$	41.9034	+	5.29363i	1.35313	+	0.170940i
$960$	−1.25349	+	1.85169i	−0.0404563	+	0.0597630i
$961$	−4.71128	−	10.0120i	−0.151977	−	0.322967i
$962$	−0.223117	+	1.76615i	−0.00719357	+	0.0569430i
$963$	12.1610	+	5.72252i	0.391882	+	0.184406i
$964$	0.649552	−	3.40507i	0.0209207	−	0.109670i
$965$	−4.83997	+	13.5206i	−0.155804	+	0.435243i
$966$	−3.45336	+	1.89850i	−0.111110	+	0.0610833i
$967$	1.66357	−	1.37622i	0.0534967	−	0.0442563i	−0.610291	−	0.792177i	$-0.708948\pi$
$967$	1.66357	−	1.37622i	0.0534967	−	0.0442563i	0.663788	+	0.747921i	$0.268948\pi$
$968$	−5.36566	−	7.38519i	−0.172459	−	0.237369i
$969$	3.19703	−	5.03771i	0.102703	−	0.161834i
$970$	16.0381	+	10.8569i	0.514951	+	0.348593i
$971$	−13.0051	+	3.33915i	−0.417354	+	0.107158i	−0.451527	−	0.892258i	$-0.649120\pi$
$971$	−13.0051	+	3.33915i	−0.417354	+	0.107158i	0.0341725	+	0.999416i	$0.489120\pi$
$972$	−0.248690	−	0.968583i	−0.00797673	−	0.0310673i
$973$	−1.64074	+	0.772071i	−0.0525996	+	0.0247515i
$974$	−2.72115	−	8.37484i	−0.0871913	−	0.268347i
$975$	−0.834237	+	3.29889i	−0.0267170	+	0.105649i
$976$	−2.36961	+	7.29291i	−0.0758494	+	0.233440i
$977$	1.93391	+	15.3084i	0.0618711	+	0.489760i	0.992354	+	0.123425i	$0.0393878\pi$
$977$	1.93391	+	15.3084i	0.0618711	+	0.489760i	−0.930483	+	0.366336i	$0.880612\pi$
$978$	5.95055	−	3.77633i	0.190277	−	0.120754i
$979$	−37.9999	+	45.9340i	−1.21448	+	1.46806i
$980$	−7.88461	+	18.3115i	−0.251865	+	0.584940i
$981$	−3.36364	+	1.33176i	−0.107393	+	0.0425197i
$982$	−1.74162	+	0.565887i	−0.0555774	+	0.0180582i
$983$	−11.4652	−	7.27607i	−0.365685	−	0.232070i	0.340270	−	0.940328i	$-0.389482\pi$
$983$	−11.4652	−	7.27607i	−0.365685	−	0.232070i	−0.705954	+	0.708257i	$0.749482\pi$
$984$	1.18643	−	2.52129i	0.0378219	−	0.0803757i
$985$	−1.45192	−	2.44490i	−0.0462619	−	0.0779011i
$986$	13.1694	−	12.3669i	0.419400	−	0.393842i
$987$	36.3388	−	38.6969i	1.15668	−	1.23174i
$988$	−1.55354	+	0.296353i	−0.0494245	+	0.00942824i
$989$	5.86126	+	3.22225i	0.186377	+	0.102462i
$990$	8.64432	+	5.09105i	0.274734	+	0.161804i
$991$	−20.9276	−	19.6523i	−0.664786	−	0.624275i	0.276848	−	0.960914i	$-0.410710\pi$
$991$	−20.9276	−	19.6523i	−0.664786	−	0.624275i	−0.941634	+	0.336638i	$0.890710\pi$
$992$	−6.47296	+	0.407244i	−0.205517	+	0.0129300i
$993$	−1.64806	−	0.535487i	−0.0522996	−	0.0169932i
$994$	29.6198	+	35.8042i	0.939484	+	1.13564i
$995$	22.8622	−	6.68718i	0.724781	−	0.211998i
$996$	−5.71472	−	9.00496i	−0.181078	−	0.285333i
$997$	6.84166	−	17.2801i	0.216677	−	0.547265i	−0.780261	−	0.625454i	$-0.784914\pi$
$997$	6.84166	−	17.2801i	0.216677	−	0.547265i	0.996939	+	0.0781891i	$0.0249138\pi$
$998$	−2.93466	+	5.33812i	−0.0928950	+	0.168975i
$999$	−2.61582			−0.0827609

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.b.589.9	yes	280
125.59	even	50	inner	750.2.o.b.559.9	✓	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.b.559.9	✓	280	125.59	even	50	inner
750.2.o.b.589.9	yes	280	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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.481754 - 0.876307i) q^{2} +(0.368125 - 0.929776i) q^{3} +(-0.535827 - 0.844328i) q^{4} +(-2.10525 - 0.753615i) q^{5} +(-0.637424 - 0.770513i) q^{6} +(-3.79423 - 1.23282i) q^{7} +(-0.998027 + 0.0627905i) q^{8} +(-0.728969 - 0.684547i) q^{9} +O(q^{10})\)	\(q+(0.481754 - 0.876307i) q^{2} +(0.368125 - 0.929776i) q^{3} +(-0.535827 - 0.844328i) q^{4} +(-2.10525 - 0.753615i) q^{5} +(-0.637424 - 0.770513i) q^{6} +(-3.79423 - 1.23282i) q^{7} +(-0.998027 + 0.0627905i) q^{8} +(-0.728969 - 0.684547i) q^{9} +(-1.67461 + 1.48178i) q^{10} +(3.93154 + 2.16138i) q^{11} +(-0.982287 + 0.187381i) q^{12} +(-0.465866 + 0.496097i) q^{13} +(-2.90821 + 2.73099i) q^{14} +(-1.47569 + 1.67998i) q^{15} +(-0.425779 + 0.904827i) q^{16} +(-2.16775 - 1.37569i) q^{17} +(-0.951057 + 0.309017i) q^{18} +(-2.16074 + 0.855499i) q^{19} +(0.491749 + 2.18133i) q^{20} +(-2.54300 + 3.07396i) q^{21} +(3.78807 - 2.40398i) q^{22} +(0.123804 + 0.980010i) q^{23} +(-0.309017 + 0.951057i) q^{24} +(3.86413 + 3.17309i) q^{25} +(0.210301 + 0.647239i) q^{26} +(-0.904827 + 0.425779i) q^{27} +(0.992146 + 3.86415i) q^{28} +(-6.81549 + 1.74992i) q^{29} +(0.761264 + 2.10249i) q^{30} +(-3.47524 + 5.47611i) q^{31} +(0.587785 + 0.809017i) q^{32} +(3.45690 - 2.85980i) q^{33} +(-2.24985 + 1.23686i) q^{34} +(7.05872 + 5.45478i) q^{35} +(-0.187381 + 0.982287i) q^{36} +(2.36686 + 1.11376i) q^{37} +(-0.291267 + 2.30561i) q^{38} +(0.289763 + 0.615777i) q^{39} +(2.14841 + 0.619939i) q^{40} +(-2.76451 - 0.349239i) q^{41} +(1.46863 + 3.70933i) q^{42} +(3.98002 - 5.47802i) q^{43} +(-0.281709 - 4.47764i) q^{44} +(1.01877 + 1.99050i) q^{45} +(0.918432 + 0.363633i) q^{46} +(-13.2798 - 0.835495i) q^{47} +(0.684547 + 0.728969i) q^{48} +(7.21323 + 5.24072i) q^{49} +(4.64216 - 1.85751i) q^{50} +(-2.07709 + 1.50909i) q^{51} +(0.668492 + 0.127522i) q^{52} +(-9.64268 - 7.97712i) q^{53} +(-0.0627905 + 0.998027i) q^{54} +(-6.64801 - 7.51312i) q^{55} +(3.86415 + 0.992146i) q^{56} +2.32394i q^{57} +(-1.74992 + 6.81549i) q^{58} +(-2.18535 - 11.4560i) q^{59} +(2.20917 + 0.345783i) q^{60} +(7.60776 - 0.961083i) q^{61} +(3.12454 + 5.68351i) q^{62} +(1.92195 + 3.49602i) q^{63} +(0.992115 - 0.125333i) q^{64} +(1.35463 - 0.693323i) q^{65} +(-0.840685 - 4.40702i) q^{66} +(2.92532 - 11.3934i) q^{67} +2.56742i q^{68} +(0.956765 + 0.245656i) q^{69} +(8.18063 - 3.55774i) q^{70} +(0.731359 - 11.6246i) q^{71} +(0.770513 + 0.637424i) q^{72} +(-3.85862 - 0.736071i) q^{73} +(2.11624 - 1.53754i) q^{74} +(4.37275 - 2.42468i) q^{75} +(1.88011 + 1.36598i) q^{76} +(-12.2526 - 13.0477i) q^{77} +(0.679204 + 0.0427319i) q^{78} +(1.77483 + 0.702706i) q^{79} +(1.57826 - 1.58401i) q^{80} +(0.0627905 + 0.998027i) q^{81} +(-1.63785 + 2.25431i) q^{82} +(3.92614 + 9.91629i) q^{83} +(3.95803 + 0.500016i) q^{84} +(3.52690 + 4.52982i) q^{85} +(-2.88304 - 6.12677i) q^{86} +(-0.881915 + 6.98107i) q^{87} +(-4.05950 - 1.91025i) q^{88} +(-2.48985 + 13.0523i) q^{89} +(2.23509 + 0.0661736i) q^{90} +(2.37920 - 1.30798i) q^{91} +(0.761112 - 0.629647i) q^{92} +(3.81223 + 5.24709i) q^{93} +(-7.12975 + 11.2347i) q^{94} +(5.19361 - 0.172667i) q^{95} +(0.968583 - 0.248690i) q^{96} +(-2.15398 - 8.38919i) q^{97} +(8.06747 - 3.79626i) q^{98} +(-1.38640 - 4.26691i) 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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