LMFDB - Embedded newform 525.2.bp.a.59.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(59,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 21, 5]))

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

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

chi := DirichletCharacter("525.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bp (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$608$
Relative dimension:	$76$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			59.16
Character	$\chi$	$=$	525.59
Dual form			525.2.bp.a.89.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.182544 + 1.73679i) q^{2} +(1.67865 - 0.426758i) q^{3} +(-1.02683 - 0.218259i) q^{4} +(0.0202789 - 2.23598i) q^{5} +(0.434762 + 2.99337i) q^{6} +(-0.809322 - 2.51893i) q^{7} +(-0.512796 + 1.57822i) q^{8} +(2.63575 - 1.43276i) q^{9} +O(q^{10})$	\(q+(-0.182544 + 1.73679i) q^{2} +(1.67865 - 0.426758i) q^{3} +(-1.02683 - 0.218259i) q^{4} +(0.0202789 - 2.23598i) q^{5} +(0.434762 + 2.99337i) q^{6} +(-0.809322 - 2.51893i) q^{7} +(-0.512796 + 1.57822i) q^{8} +(2.63575 - 1.43276i) q^{9} +(3.87972 + 0.443385i) q^{10} +(-1.69524 - 3.80758i) q^{11} +(-1.81683 + 0.0718262i) q^{12} +(4.34638 - 3.15783i) q^{13} +(4.52259 - 0.945808i) q^{14} +(-0.920180 - 3.76208i) q^{15} +(-4.56546 - 2.03268i) q^{16} +(-0.629655 + 0.566944i) q^{17} +(2.00726 + 4.83930i) q^{18} +(1.38945 + 6.53684i) q^{19} +(-0.508846 + 2.29154i) q^{20} +(-2.43354 - 3.88302i) q^{21} +(6.92243 - 2.24923i) q^{22} +(-0.373486 + 3.55348i) q^{23} +(-0.187287 + 2.86813i) q^{24} +(-4.99918 - 0.0906862i) q^{25} +(4.69108 + 8.12520i) q^{26} +(3.81308 - 3.52994i) q^{27} +(0.281256 + 2.76315i) q^{28} +(1.90285 - 0.618273i) q^{29} +(6.70193 - 0.911415i) q^{30} +(5.08626 - 4.57969i) q^{31} +(2.70429 - 4.68397i) q^{32} +(-4.47064 - 5.66815i) q^{33} +(-0.869724 - 1.19707i) q^{34} +(-5.64867 + 1.75854i) q^{35} +(-3.01918 + 0.895921i) q^{36} +(0.318290 - 0.714891i) q^{37} +(-11.6068 + 1.21992i) q^{38} +(5.94843 - 7.15575i) q^{39} +(3.51847 + 1.17860i) q^{40} +(-5.05593 + 3.67335i) q^{41} +(7.18823 - 3.51774i) q^{42} +7.03026i q^{43} +(0.909686 + 4.27974i) q^{44} +(-3.15016 - 5.92254i) q^{45} +(-6.10348 - 1.29734i) q^{46} +(4.58966 + 4.13255i) q^{47} +(-8.53129 - 1.46381i) q^{48} +(-5.69000 + 4.07725i) q^{49} +(1.07007 - 8.66598i) q^{50} +(-0.815025 + 1.22041i) q^{51} +(-5.15221 + 2.29391i) q^{52} +(7.01936 + 1.49201i) q^{53} +(5.43471 + 7.26689i) q^{54} +(-8.54804 + 3.71331i) q^{55} +(4.39045 + 0.0144049i) q^{56} +(5.12206 + 10.3801i) q^{57} +(0.726458 + 3.41772i) q^{58} +(1.06403 + 10.1235i) q^{59} +(0.123758 + 4.06386i) q^{60} +(-12.7642 - 1.34157i) q^{61} +(7.02550 + 9.66977i) q^{62} +(-5.74219 - 5.47971i) q^{63} +(-0.444734 - 0.323118i) q^{64} +(-6.97269 - 9.78243i) q^{65} +(10.6605 - 6.72989i) q^{66} +(3.61602 - 3.25588i) q^{67} +(0.770290 - 0.444727i) q^{68} +(0.889525 + 6.12445i) q^{69} +(-2.02309 - 10.1316i) q^{70} +(1.62464 - 0.527878i) q^{71} +(0.909610 + 4.89453i) q^{72} +(-7.19602 + 3.20388i) q^{73} +(1.18352 + 0.683303i) q^{74} +(-8.43059 + 1.98121i) q^{75} -7.01549i q^{76} +(-8.21902 + 7.35176i) q^{77} +(11.3422 + 11.6374i) q^{78} +(-7.37971 + 8.19600i) q^{79} +(-4.63760 + 10.1670i) q^{80} +(4.89441 - 7.55280i) q^{81} +(-5.45692 - 9.45165i) q^{82} +(15.3607 + 4.99098i) q^{83} +(1.65133 + 4.51835i) q^{84} +(1.25491 + 1.41939i) q^{85} +(-12.2101 - 1.28333i) q^{86} +(2.93037 - 1.84992i) q^{87} +(6.87853 - 0.722963i) q^{88} +(1.01268 - 9.63503i) q^{89} +(10.8613 - 4.39005i) q^{90} +(-11.4720 - 8.39251i) q^{91} +(1.15909 - 3.56730i) q^{92} +(6.58364 - 9.85831i) q^{93} +(-8.01520 + 7.21692i) q^{94} +(14.6444 - 2.97422i) q^{95} +(2.54064 - 9.01684i) q^{96} +(1.02885 + 3.16648i) q^{97} +(-6.04266 - 10.6266i) q^{98} +(-9.92359 - 7.60697i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9}+O(q^{10}) $ 608 * q - 15 * q^3 + 66 * q^4 - 3 * q^9	$ 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9} - 30 q^{10} - 15 q^{12} - 36 q^{15} + 66 q^{16} - 18 q^{19} + 9 q^{21} - 80 q^{22} - 30 q^{24} + 2 q^{25} - 90 q^{28} - 23 q^{30} - 90 q^{33} + 44 q^{36} - 10 q^{37} - 19 q^{39} + 42 q^{40} - 70 q^{42} - 117 q^{45} - 54 q^{46} - 28 q^{49} - 8 q^{51} - 30 q^{52} - 21 q^{54} + 50 q^{58} - 67 q^{60} - 18 q^{61} - 70 q^{63} - 176 q^{64} + 57 q^{66} - 10 q^{67} + 42 q^{70} - 45 q^{72} - 150 q^{73} + 33 q^{75} + 10 q^{78} - 34 q^{79} + 49 q^{81} - 53 q^{84} - 8 q^{85} - 15 q^{87} + 80 q^{88} - 62 q^{91} + 30 q^{94} - 9 q^{96} + 36 q^{99}+O(q^{100}) $ 608 * q - 15 * q^3 + 66 * q^4 - 3 * q^9 - 30 * q^10 - 15 * q^12 - 36 * q^15 + 66 * q^16 - 18 * q^19 + 9 * q^21 - 80 * q^22 - 30 * q^24 + 2 * q^25 - 90 * q^28 - 23 * q^30 - 90 * q^33 + 44 * q^36 - 10 * q^37 - 19 * q^39 + 42 * q^40 - 70 * q^42 - 117 * q^45 - 54 * q^46 - 28 * q^49 - 8 * q^51 - 30 * q^52 - 21 * q^54 + 50 * q^58 - 67 * q^60 - 18 * q^61 - 70 * q^63 - 176 * q^64 + 57 * q^66 - 10 * q^67 + 42 * q^70 - 45 * q^72 - 150 * q^73 + 33 * q^75 + 10 * q^78 - 34 * q^79 + 49 * q^81 - 53 * q^84 - 8 * q^85 - 15 * q^87 + 80 * q^88 - 62 * q^91 + 30 * q^94 - 9 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.182544	+	1.73679i	−0.129078	+	1.22810i	0.717777	+	0.696273i	$0.245160\pi$
$2$	−0.182544	+	1.73679i	−0.129078	+	1.22810i	−0.846855	+	0.531824i	$0.821507\pi$
$3$	1.67865	−	0.426758i	0.969171	−	0.246389i
$3$	1.67865	−	0.426758i	0.969171	−	0.246389i
$4$	−1.02683	−	0.218259i	−0.513415	−	0.109130i
$5$	0.0202789	−	2.23598i	0.00906900	−	0.999959i
$5$	0.0202789	−	2.23598i	0.00906900	−	0.999959i
$6$	0.434762	+	2.99337i	0.177491	+	1.22204i
$7$	−0.809322	−	2.51893i	−0.305895	−	0.952065i
$7$	−0.809322	−	2.51893i	−0.305895	−	0.952065i
$8$	−0.512796	+	1.57822i	−0.181301	+	0.557987i
$9$	2.63575	−	1.43276i	0.878585	−	0.477586i
$10$	3.87972	+	0.443385i	1.22688	+	0.140211i
$11$	−1.69524	−	3.80758i	−0.511135	−	1.14803i	−0.966252	−	0.257597i	$-0.917069\pi$
$11$	−1.69524	−	3.80758i	−0.511135	−	1.14803i	0.455117	−	0.890432i	$-0.349597\pi$
$12$	−1.81683	+	0.0718262i	−0.524475	+	0.0207344i
$13$	4.34638	−	3.15783i	1.20547	−	0.875824i	0.210656	−	0.977560i	$-0.432440\pi$
$13$	4.34638	−	3.15783i	1.20547	−	0.875824i	0.994811	+	0.101736i	$0.0324399\pi$
$14$	4.52259	−	0.945808i	1.20871	−	0.252778i
$15$	−0.920180	−	3.76208i	−0.237589	−	0.971366i
$16$	−4.56546	−	2.03268i	−1.14137	−	0.508169i
$17$	−0.629655	+	0.566944i	−0.152714	+	0.137504i	−0.741946	−	0.670460i	$-0.766097\pi$
$17$	−0.629655	+	0.566944i	−0.152714	+	0.137504i	0.589232	+	0.807964i	$0.299430\pi$
$18$	2.00726	+	4.83930i	0.473116	+	1.14063i
$19$	1.38945	+	6.53684i	0.318762	+	1.49966i	0.787498	+	0.616317i	$0.211376\pi$
$19$	1.38945	+	6.53684i	0.318762	+	1.49966i	−0.468737	+	0.883338i	$0.655291\pi$
$20$	−0.508846	+	2.29154i	−0.113781	+	0.512404i
$21$	−2.43354	−	3.88302i	−0.531043	−	0.847345i
$22$	6.92243	−	2.24923i	1.47587	−	0.479538i
$23$	−0.373486	+	3.55348i	−0.0778772	+	0.740952i	0.884003	+	0.467481i	$0.154838\pi$
$23$	−0.373486	+	3.55348i	−0.0778772	+	0.740952i	−0.961880	+	0.273471i	$0.911828\pi$
$24$	−0.187287	+	2.86813i	−0.0382297	+	0.585455i
$25$	−4.99918	−	0.0906862i	−0.999836	−	0.0181372i
$26$	4.69108	+	8.12520i	0.919997	+	1.59348i
$27$	3.81308	−	3.52994i	0.733827	−	0.679336i
$28$	0.281256	+	2.76315i	0.0531524	+	0.522187i
$29$	1.90285	−	0.618273i	0.353350	−	0.114810i	−0.126963	−	0.991907i	$-0.540523\pi$
$29$	1.90285	−	0.618273i	0.353350	−	0.114810i	0.480313	+	0.877097i	$0.340523\pi$
$30$	6.70193	−	0.911415i	1.22360	−	0.166401i
$31$	5.08626	−	4.57969i	0.913519	−	0.822536i	−0.0710612	−	0.997472i	$-0.522639\pi$
$31$	5.08626	−	4.57969i	0.913519	−	0.822536i	0.984580	+	0.174936i	$0.0559719\pi$
$32$	2.70429	−	4.68397i	0.478056	−	0.828017i
$33$	−4.47064	−	5.66815i	−0.778239	−	0.986698i
$34$	−0.869724	−	1.19707i	−0.149157	−	0.205296i
$35$	−5.64867	+	1.75854i	−0.954800	+	0.297248i
$36$	−3.01918	+	0.895921i	−0.503197	+	0.149320i
$37$	0.318290	−	0.714891i	0.0523266	−	0.117527i	−0.885490	−	0.464658i	$-0.846177\pi$
$37$	0.318290	−	0.714891i	0.0523266	−	0.117527i	0.937817	+	0.347131i	$0.112844\pi$
$38$	−11.6068	+	1.21992i	−1.88287	+	0.197897i
$39$	5.94843	−	7.15575i	0.952511	−	1.14584i
$40$	3.51847	+	1.17860i	0.556320	+	0.186354i
$41$	−5.05593	+	3.67335i	−0.789604	+	0.573681i	−0.907846	−	0.419304i	$-0.862274\pi$
$41$	−5.05593	+	3.67335i	−0.789604	+	0.573681i	0.118242	+	0.992985i	$0.462274\pi$
$42$	7.18823	−	3.51774i	1.10917	−	0.542799i
$43$			7.03026i			1.07210i	0.844185	+	0.536052i	$0.180085\pi$
$43$			7.03026i			1.07210i	−0.844185	+	0.536052i	$0.819915\pi$
$44$	0.909686	+	4.27974i	0.137140	+	0.645195i
$45$	−3.15016	−	5.92254i	−0.469599	−	0.882880i
$46$	−6.10348	−	1.29734i	−0.899910	−	0.191282i
$47$	4.58966	+	4.13255i	0.669471	+	0.602795i	0.932143	−	0.362091i	$-0.117937\pi$
$47$	4.58966	+	4.13255i	0.669471	+	0.602795i	−0.262672	+	0.964885i	$0.584604\pi$
$48$	−8.53129	−	1.46381i	−1.23139	−	0.211283i
$49$	−5.69000	+	4.07725i	−0.812857	+	0.582464i
$50$	1.07007	−	8.66598i	0.151331	−	1.22555i
$51$	−0.815025	+	1.22041i	−0.114126	+	0.170892i
$52$	−5.15221	+	2.29391i	−0.714483	+	0.318108i
$53$	7.01936	+	1.49201i	0.964183	+	0.204943i	0.662997	−	0.748622i	$-0.269284\pi$
$53$	7.01936	+	1.49201i	0.964183	+	0.204943i	0.301186	+	0.953565i	$0.402617\pi$
$54$	5.43471	+	7.26689i	0.739570	+	0.988899i
$55$	−8.54804	+	3.71331i	−1.15262	+	0.500703i
$56$	4.39045	+	0.0144049i	0.586699	+	0.00192494i
$57$	5.12206	+	10.3801i	0.678433	+	1.37488i
$58$	0.726458	+	3.41772i	0.0953886	+	0.448768i
$59$	1.06403	+	10.1235i	0.138525	+	1.31797i	0.814118	+	0.580699i	$0.197221\pi$
$59$	1.06403	+	10.1235i	0.138525	+	1.31797i	−0.675593	+	0.737274i	$0.736113\pi$
$60$	0.123758	+	4.06386i	0.0159771	+	0.524641i
$61$	−12.7642	−	1.34157i	−1.63429	−	0.171771i	−0.757564	−	0.652761i	$-0.773611\pi$
$61$	−12.7642	−	1.34157i	−1.63429	−	0.171771i	−0.876726	+	0.480990i	$0.840277\pi$
$62$	7.02550	+	9.66977i	0.892239	+	1.22806i
$63$	−5.74219	−	5.47971i	−0.723448	−	0.690379i
$64$	−0.444734	−	0.323118i	−0.0555917	−	0.0403898i
$65$	−6.97269	−	9.78243i	−0.864855	−	1.21336i
$66$	10.6605	−	6.72989i	1.31221	−	0.828392i
$67$	3.61602	−	3.25588i	0.441767	−	0.397769i	−0.418007	−	0.908444i	$-0.637271\pi$
$67$	3.61602	−	3.25588i	0.441767	−	0.397769i	0.859774	+	0.510675i	$0.170605\pi$
$68$	0.770290	−	0.444727i	0.0934113	−	0.0539311i
$69$	0.889525	+	6.12445i	0.107086	+	0.737298i
$70$	−2.02309	−	10.1316i	−0.241806	−	1.21096i
$71$	1.62464	−	0.527878i	0.192809	−	0.0626476i	−0.211021	−	0.977482i	$-0.567679\pi$
$71$	1.62464	−	0.527878i	0.192809	−	0.0626476i	0.403830	+	0.914834i	$0.367679\pi$
$72$	0.909610	+	4.89453i	0.107199	+	0.576825i
$73$	−7.19602	+	3.20388i	−0.842231	+	0.374985i	−0.782060	−	0.623203i	$-0.785831\pi$
$73$	−7.19602	+	3.20388i	−0.842231	+	0.374985i	−0.0601704	+	0.998188i	$0.519164\pi$
$74$	1.18352	+	0.683303i	0.137581	+	0.0794323i
$75$	−8.43059	+	1.98121i	−0.973480	+	0.228770i
$76$		−	7.01549i		−	0.804731i
$77$	−8.21902	+	7.35176i	−0.936644	+	0.837810i
$78$	11.3422	+	11.6374i	1.28425	+	1.31768i
$79$	−7.37971	+	8.19600i	−0.830283	+	0.922122i	−0.997968	−	0.0637182i	$-0.979704\pi$
$79$	−7.37971	+	8.19600i	−0.830283	+	0.922122i	0.167685	+	0.985841i	$0.446371\pi$
$80$	−4.63760	+	10.1670i	−0.518499	+	1.13671i
$81$	4.89441	−	7.55280i	0.543823	−	0.839200i
$82$	−5.45692	−	9.45165i	−0.602615	−	1.04376i
$83$	15.3607	+	4.99098i	1.68605	+	0.547832i	0.986070	−	0.166329i	$-0.0531914\pi$
$83$	15.3607	+	4.99098i	1.68605	+	0.547832i	0.699982	+	0.714161i	$0.253191\pi$
$84$	1.65133	+	4.51835i	0.180175	+	0.492992i
$85$	1.25491	+	1.41939i	0.136114	+	0.153955i
$86$	−12.2101	−	1.28333i	−1.31665	−	0.138385i
$87$	2.93037	−	1.84992i	0.314169	−	0.198333i
$88$	6.87853	−	0.722963i	0.733254	−	0.0770681i
$89$	1.01268	−	9.63503i	0.107344	−	1.02131i	−0.799736	−	0.600352i	$-0.795027\pi$
$89$	1.01268	−	9.63503i	0.107344	−	1.02131i	0.907080	−	0.420959i	$-0.138306\pi$
$90$	10.8613	−	4.39005i	1.14488	−	0.462752i
$91$	−11.4720	−	8.39251i	−1.20259	−	0.879774i
$92$	1.15909	−	3.56730i	0.120843	−	0.371917i
$93$	6.58364	−	9.85831i	0.682692	−	1.02226i
$94$	−8.01520	+	7.21692i	−0.826705	+	0.744368i
$95$	14.6444	−	2.97422i	1.50248	−	0.305148i
$96$	2.54064	−	9.01684i	0.259303	−	0.920277i
$97$	1.02885	+	3.16648i	0.104464	+	0.321507i	0.989604	−	0.143817i	$-0.0459377\pi$
$97$	1.02885	+	3.16648i	0.104464	+	0.321507i	−0.885140	+	0.465324i	$0.845938\pi$
$98$	−6.04266	−	10.6266i	−0.610400	−	1.07345i
$99$	−9.92359	−	7.60697i	−0.997358	−	0.764529i
$100$	5.11351	+	1.18424i	0.511351	+	0.118424i
$101$	−4.26100	+	7.38027i	−0.423985	+	0.734364i	−0.996325	−	0.0856524i	$-0.972703\pi$
$101$	−4.26100	+	7.38027i	−0.423985	+	0.734364i	0.572340	+	0.820017i	$0.306036\pi$
$102$	−1.97083	−	1.63831i	−0.195141	−	0.162217i
$103$	2.66361	−	2.95823i	0.262453	−	0.291483i	−0.597487	−	0.801878i	$-0.703834\pi$
$103$	2.66361	−	2.95823i	0.262453	−	0.291483i	0.859940	+	0.510395i	$0.170501\pi$
$104$	2.75496	+	8.47888i	0.270146	+	0.831423i
$105$	−8.73169	+	5.36260i	−0.852126	+	0.523337i
$106$	−3.87266	+	11.9188i	−0.376146	+	1.15766i
$107$	−4.26473	−	7.38674i	−0.412287	−	0.714103i	0.582852	−	0.812578i	$-0.301937\pi$
$107$	−4.26473	−	7.38674i	−0.412287	−	0.714103i	−0.995139	+	0.0984756i	$0.968603\pi$
$108$	−4.68582	+	2.79240i	−0.450893	+	0.268699i
$109$	0.225891	+	2.14921i	0.0216364	+	0.205857i	0.999999	−	0.00103871i	$-0.000330632\pi$
$109$	0.225891	+	2.14921i	0.0216364	+	0.205857i	−0.978363	+	0.206896i	$0.933664\pi$
$110$	−4.88886	−	15.5240i	−0.466134	−	1.48016i
$111$	0.229213	−	1.33589i	0.0217559	−	0.126797i
$112$	−1.42523	+	13.1452i	−0.134672	+	1.24210i
$113$	4.40517	−	3.20054i	0.414403	−	0.301082i	−0.360979	−	0.932574i	$-0.617557\pi$
$113$	4.40517	−	3.20054i	0.414403	−	0.301082i	0.775382	+	0.631492i	$0.217557\pi$
$114$	−18.9631	+	7.00111i	−1.77606	+	0.655714i
$115$	7.93793	+	0.907167i	0.740216	+	0.0845937i
$116$	−2.08885	+	0.219547i	−0.193945	+	0.0203844i
$117$	6.93158	−	14.5506i	0.640825	−	1.34520i
$118$	−17.7767			−1.63648
$119$	1.93769	+	1.12722i	0.177627	+	0.103332i
$120$	6.40928	+	0.476931i	0.585084	+	0.0435377i
$121$	−4.26338	+	4.73496i	−0.387580	+	0.430451i
$122$	4.66007	−	21.9239i	0.421903	−	1.98490i
$123$	−6.91953	+	8.32394i	−0.623913	+	0.750545i
$124$	−6.22228	+	3.59243i	−0.558777	+	0.322610i
$125$	−0.304150	+	11.1762i	−0.0272040	+	0.999630i
$126$	10.5653	−	8.97270i	0.941234	−	0.799352i
$127$	8.14324	−	11.2082i	0.722596	−	0.994568i	−0.276838	−	0.960917i	$-0.589286\pi$
$127$	8.14324	−	11.2082i	0.722596	−	0.994568i	0.999434	−	0.0336511i	$-0.0107135\pi$
$128$	7.88047	−	8.75215i	0.696542	−	0.773588i
$129$	3.00022	+	11.8014i	0.264155	+	1.03905i
$130$	18.2629	−	10.3244i	1.60176	−	0.905508i
$131$	−18.3563	+	3.90175i	−1.60379	+	0.340897i	−0.920954	−	0.389670i	$-0.872589\pi$
$131$	−18.3563	+	3.90175i	−1.60379	+	0.340897i	−0.682840	+	0.730568i	$0.739256\pi$
$132$	3.35346	+	6.79598i	0.291881	+	0.591514i
$133$	15.3413	−	8.79034i	1.33026	−	0.762219i
$134$	4.99470	+	6.87461i	0.431476	+	0.593876i
$135$	−7.81553	−	8.59753i	−0.672653	−	0.739958i
$136$	−0.571880	−	1.28446i	−0.0490383	−	0.110142i
$137$	−0.959911	−	9.13294i	−0.0820107	−	0.780280i	−0.955808	−	0.293990i	$-0.905017\pi$
$137$	−0.959911	−	9.13294i	−0.0820107	−	0.780280i	0.873798	−	0.486290i	$-0.161650\pi$
$138$	−10.7993	+	0.426936i	−0.919296	+	0.0363432i
$139$	7.26368	−	9.99759i	0.616097	−	0.847985i	−0.380965	−	0.924590i	$-0.624408\pi$
$139$	7.26368	−	9.99759i	0.616097	−	0.847985i	0.997062	+	0.0766050i	$0.0244080\pi$
$140$	6.18404	−	0.572848i	0.522647	−	0.0484145i
$141$	9.46806	+	4.97845i	0.797354	+	0.419261i
$142$	0.620245	+	2.91803i	0.0520498	+	0.244875i
$143$	−19.3918	−	11.1959i	−1.62163	−	0.936247i
$144$	−14.9458	+	1.18357i	−1.24548	+	0.0986312i
$145$	−1.34386	−	4.26726i	−0.111601	−	0.354377i
$146$	−4.25087	−	13.0828i	−0.351805	−	1.08274i
$147$	−7.81153	+	9.27254i	−0.644284	+	0.764786i
$148$	−0.482861	+	0.664601i	−0.0396909	+	0.0546299i
$149$	9.68229	−	5.59008i	0.793204	−	0.457957i	−0.0478850	−	0.998853i	$-0.515248\pi$
$149$	9.68229	−	5.59008i	0.793204	−	0.457957i	0.841089	+	0.540896i	$0.181915\pi$
$150$	−1.90199	−	15.0038i	−0.155297	−	1.22506i
$151$	−6.45105	+	11.1736i	−0.524979	+	0.909291i	0.474597	+	0.880203i	$0.342594\pi$
$151$	−6.45105	+	11.1736i	−0.524979	+	0.909291i	−0.999577	+	0.0290880i	$0.990740\pi$
$152$	−11.0291	−	1.15921i	−0.894579	−	0.0940241i
$153$	−0.847323	+	2.39647i	−0.0685020	+	0.193743i
$154$	−11.2681	−	15.6168i	−0.908012	−	1.25843i
$155$	−10.1369	−	11.4656i	−0.814217	−	0.920941i
$156$	−7.66983	+	6.04943i	−0.614078	+	0.484342i
$157$	−3.68665	+	6.38546i	−0.294227	+	0.509615i	−0.974805	−	0.223060i	$-0.928395\pi$
$157$	−3.68665	+	6.38546i	−0.294227	+	0.509615i	0.680578	+	0.732676i	$0.261729\pi$
$158$	−12.8876	−	14.3132i	−1.02528	−	1.13869i
$159$	12.4198	−	0.491001i	0.984954	−	0.0389389i
$160$	−10.4184	−	6.14172i	−0.823647	−	0.485545i
$161$	9.25324	−	1.93513i	0.729257	−	0.152509i
$162$	12.2242	+	9.87929i	0.960424	+	0.776190i
$163$	4.64388	−	10.4303i	0.363737	−	0.816966i	−0.635265	−	0.772294i	$-0.719109\pi$
$163$	4.64388	−	10.4303i	0.363737	−	0.816966i	0.999002	−	0.0446717i	$-0.0142242\pi$
$164$	5.99332	−	2.66840i	0.468000	−	0.208367i
$165$	−12.7645	+	9.88131i	−0.993715	+	0.769259i
$166$	−11.4723	+	25.7672i	−0.890423	+	1.99992i
$167$	6.44296	+	2.09345i	0.498571	+	0.161996i	0.547498	−	0.836807i	$-0.315580\pi$
$167$	6.44296	+	2.09345i	0.498571	+	0.161996i	−0.0489270	+	0.998802i	$0.515580\pi$
$168$	7.37619	−	1.84948i	0.569086	−	0.142691i
$169$	4.90189	−	15.0865i	0.377069	−	1.16050i
$170$	−2.69426	+	1.92041i	−0.206641	+	0.147289i
$171$	13.0280	+	15.2388i	0.996274	+	1.16534i
$172$	1.53442	−	7.21888i	0.116998	−	0.550434i
$173$	−8.56135	−	0.899834i	−0.650907	−	0.0684131i	−0.226681	−	0.973969i	$-0.572787\pi$
$173$	−8.56135	−	0.899834i	−0.650907	−	0.0684131i	−0.424227	+	0.905556i	$0.639454\pi$
$174$	2.67801	+	5.42714i	0.203019	+	0.411430i
$175$	3.81751	+	12.6660i	0.288577	+	0.957457i
$176$			20.8293i			1.57006i
$177$	6.10644	+	16.5398i	0.458988	+	1.24321i
$178$	16.5492	+	3.51764i	1.24041	+	0.263658i
$179$	−2.21774	+	10.4336i	−0.165762	+	0.779847i	0.814188	+	0.580601i	$0.197182\pi$
$179$	−2.21774	+	10.4336i	−0.165762	+	0.779847i	−0.979950	+	0.199246i	$0.936151\pi$
$180$	1.94203	+	6.76899i	0.144750	+	0.504531i
$181$	3.63444	+	1.18090i	0.270146	+	0.0877757i	0.440958	−	0.897528i	$-0.354639\pi$
$181$	3.63444	+	1.18090i	0.270146	+	0.0877757i	−0.170812	+	0.985304i	$0.554639\pi$
$182$	16.6702	−	18.3924i	1.23568	−	1.36334i
$183$	−21.9992	+	3.19520i	−1.62623	+	0.236196i
$184$	−5.41667	−	2.41166i	−0.399322	−	0.177790i
$185$	−1.59202	−	0.726186i	−0.117048	−	0.0533903i
$186$	15.9200	+	13.2340i	1.16731	+	0.970364i
$187$	3.22611	+	1.43635i	0.235916	+	0.105037i
$188$	−3.81083	−	5.24516i	−0.277934	−	0.382543i
$189$	−11.9777	−	6.74801i	−0.871247	−	0.490846i
$190$	2.49234	+	25.9772i	0.180814	+	1.88459i
$191$	0.961636	−	2.15987i	0.0695815	−	0.156283i	−0.875407	−	0.483387i	$-0.839406\pi$
$191$	0.961636	−	2.15987i	0.0695815	−	0.156283i	0.944988	+	0.327105i	$0.106073\pi$
$192$	−0.884447	−	0.352609i	−0.0638295	−	0.0254474i
$193$	−4.18903	−	2.41854i	−0.301533	−	0.174090i	0.341598	−	0.939846i	$-0.389032\pi$
$193$	−4.18903	−	2.41854i	−0.301533	−	0.174090i	−0.643131	+	0.765756i	$0.722365\pi$
$194$	−5.68732	+	1.20888i	−0.408326	+	0.0867924i
$195$	−15.8795	−	13.4457i	−1.13715	−	0.962864i
$196$	6.73255	−	2.94474i	0.480897	−	0.210339i
$197$	3.11805	+	9.59637i	0.222152	+	0.683713i	0.998568	+	0.0534928i	$0.0170354\pi$
$197$	3.11805	+	9.59637i	0.222152	+	0.683713i	−0.776416	+	0.630220i	$0.782965\pi$
$198$	15.0232	−	15.8466i	1.06765	−	1.12617i
$199$	−14.7937	−	8.54115i	−1.04870	−	0.605466i	−0.126413	−	0.991978i	$-0.540347\pi$
$199$	−14.7937	−	8.54115i	−1.04870	−	0.605466i	−0.922285	+	0.386512i	$0.873680\pi$
$200$	2.70668	−	7.84332i	0.191391	−	0.554607i
$201$	4.68057	−	7.00865i	0.330142	−	0.494352i
$202$	−12.0402	−	8.74770i	−0.847144	−	0.615486i
$203$	−3.09740	−	4.29276i	−0.217395	−	0.301293i
$204$	1.10326	−	1.07527i	0.0772435	−	0.0752839i
$205$	8.11100	+	11.3794i	0.566496	+	0.794774i
$206$	4.65161	+	5.16614i	0.324093	+	0.359942i
$207$	4.10687	+	9.90122i	0.285447	+	0.688183i
$208$	−26.2621	+	5.58217i	−1.82095	+	0.387054i
$209$	22.5341	−	16.3720i	1.55872	−	1.13247i
$210$	−7.71981	−	16.1441i	−0.532717	−	1.11405i
$211$	5.93614	+	4.31286i	0.408661	+	0.296909i	0.773059	−	0.634334i	$-0.218725\pi$
$211$	5.93614	+	4.31286i	0.408661	+	0.296909i	−0.364399	+	0.931243i	$0.618725\pi$
$212$	−6.88204	−	3.06408i	−0.472660	−	0.210442i
$213$	2.50193	−	1.57945i	0.171430	−	0.108222i
$214$	13.6077	−	6.05855i	0.930205	−	0.414154i
$215$	15.7195	+	0.142566i	1.07206	+	0.00972292i
$216$	3.61570	+	7.82803i	0.246017	+	0.532630i
$217$	−15.6523	−	9.10547i	−1.06255	−	0.618120i
$218$	−3.77396			−0.255605
$219$	−10.7123	+	8.44916i	−0.723873	+	0.570941i
$220$	9.58784	−	1.94725i	0.646412	−	0.131283i
$221$	−0.946407	+	4.45250i	−0.0636622	+	0.299507i
$222$	2.27832	+	0.641954i	0.152911	+	0.0430851i
$223$	15.8156	+	11.4907i	1.05909	+	0.769477i	0.973921	−	0.226889i	$-0.0728555\pi$
$223$	15.8156	+	11.4907i	1.05909	+	0.769477i	0.0851736	+	0.996366i	$0.472855\pi$
$224$	−13.9872	−	3.02107i	−0.934561	−	0.201854i
$225$	−13.3065	+	6.92359i	−0.887102	+	0.461573i
$226$	4.75454	+	8.23510i	0.316267	+	0.547791i
$227$	−4.10642	−	9.22317i	−0.272553	−	0.612163i	0.724467	−	0.689309i	$-0.242086\pi$
$227$	−4.10642	−	9.22317i	−0.272553	−	0.612163i	−0.997020	+	0.0771462i	$0.975419\pi$
$228$	−2.99392	−	11.7766i	−0.198277	−	0.779922i
$229$	−10.3809	−	9.34699i	−0.685988	−	0.617666i	0.250603	−	0.968090i	$-0.419371\pi$
$229$	−10.3809	−	9.34699i	−0.685988	−	0.617666i	−0.936591	+	0.350424i	$0.886038\pi$
$230$	−3.02458	+	13.6209i	−0.199435	+	0.898138i
$231$	−10.6595	+	15.8486i	−0.701341	+	1.04276i
$232$			3.32017i			0.217980i
$233$	−3.13244	+	0.665821i	−0.205213	+	0.0436194i	−0.309371	−	0.950941i	$-0.600119\pi$
$233$	−3.13244	+	0.665821i	−0.205213	+	0.0436194i	0.104158	+	0.994561i	$0.466785\pi$
$234$	24.0060	+	14.6948i	1.56932	+	0.960631i
$235$	9.33336	−	10.1786i	0.608841	−	0.663977i
$236$	1.11698	−	10.6274i	0.0727095	−	0.691784i
$237$	−8.89027	+	16.9076i	−0.577485	+	1.09827i
$238$	−2.31145	+	3.15959i	−0.149829	+	0.204806i
$239$	−3.66433	+	5.04351i	−0.237026	+	0.326238i	−0.910915	−	0.412595i	$-0.864623\pi$
$239$	−3.66433	+	5.04351i	−0.237026	+	0.326238i	0.673889	+	0.738832i	$0.264623\pi$
$240$	−3.44605	+	19.0461i	−0.222441	+	1.22942i
$241$	−1.77798	+	0.186873i	−0.114530	+	0.0120375i	−0.161620	−	0.986853i	$-0.551672\pi$
$241$	−1.77798	+	0.186873i	−0.114530	+	0.0120375i	0.0470903	+	0.998891i	$0.485005\pi$
$242$	−7.44539	−	8.26894i	−0.478608	−	0.531548i
$243$	4.99279	−	14.7673i	0.320288	−	0.947320i
$244$	12.8139	+	4.16347i	0.820323	+	0.266539i
$245$	9.00124	+	12.8054i	0.575068	+	0.818105i
$246$	−13.1938	−	13.5373i	−0.841209	−	0.863105i
$247$	26.6813	+	24.0239i	1.69769	+	1.52861i
$248$	4.61956	+	10.3757i	0.293342	+	0.658858i
$249$	27.9152	+	1.82284i	1.76905	+	0.115518i
$250$	−19.3552	−	2.56840i	−1.22413	−	0.162440i
$251$	−22.7429			−1.43552			−0.717759	−	0.696291i	$-0.754832\pi$
$251$	−22.7429			−1.43552			−0.717759	+	0.696291i	$0.754832\pi$
$252$	4.70025	+	6.88002i	0.296088	+	0.433400i
$253$	14.1633	−	4.60194i	0.890440	−	0.289322i
$254$	17.9798	+	16.1891i	1.12815	+	1.01580i
$255$	2.71229	+	1.84713i	0.169850	+	0.115671i
$256$	13.0265	+	14.4673i	0.814153	+	0.904209i
$257$	4.52026	−	2.60977i	0.281966	−	0.162793i	−0.352347	−	0.935869i	$-0.614616\pi$
$257$	4.52026	−	2.60977i	0.281966	−	0.162793i	0.634313	+	0.773076i	$0.281283\pi$
$258$	−21.0442	+	3.05649i	−1.31016	+	0.190289i
$259$	−2.05836	−	0.223173i	−0.127900	−	0.0138673i
$260$	5.02465	+	11.5667i	0.311616	+	0.717339i
$261$	4.12961	−	4.35594i	0.255616	−	0.269626i
$262$	−3.42569	−	32.5933i	−0.211640	−	2.01362i
$263$	1.30582	+	12.4241i	0.0805206	+	0.766102i	0.958054	+	0.286587i	$0.0925207\pi$
$263$	1.30582	+	12.4241i	0.0805206	+	0.766102i	−0.877534	+	0.479515i	$0.840813\pi$
$264$	11.2381	−	4.14907i	0.691660	−	0.255358i
$265$	3.47845	−	15.6649i	0.213679	−	0.962285i
$266$	12.4665	+	28.2493i	0.764371	+	1.73208i
$267$	−2.41189	−	16.6060i	−0.147605	−	1.01627i
$268$	−4.42366	+	2.55400i	−0.270218	+	0.156010i
$269$	7.38170	+	8.19821i	0.450070	+	0.499854i	0.924893	−	0.380228i	$-0.124154\pi$
$269$	7.38170	+	8.19821i	0.450070	+	0.499854i	−0.474823	+	0.880082i	$0.657488\pi$
$270$	16.3588	−	12.0045i	0.995565	−	0.730571i
$271$	19.5880	+	17.6372i	1.18989	+	1.07138i	0.995908	+	0.0903757i	$0.0288068\pi$
$271$	19.5880	+	17.6372i	1.18989	+	1.07138i	0.193981	+	0.981005i	$0.437860\pi$
$272$	4.02708	−	1.30848i	0.244178	−	0.0793382i
$273$	−22.8390	−	9.19236i	−1.38228	−	0.556347i
$274$	16.0372			0.968845
$275$	8.12953	+	19.1885i	0.490229	+	1.15711i
$276$	0.423329	−	6.48292i	0.0254814	−	0.390226i
$277$	5.02315	+	11.2822i	0.301812	+	0.677880i	0.999248	−	0.0387661i	$-0.0123427\pi$
$277$	5.02315	+	11.2822i	0.301812	+	0.677880i	−0.697436	+	0.716647i	$0.745676\pi$
$278$	16.0378	+	14.4405i	0.961883	+	0.866083i
$279$	6.84454	−	19.3583i	0.409772	−	1.15895i
$280$	0.121243	−	9.81665i	0.00724563	−	0.586657i
$281$	−8.66568	−	2.81565i	−0.516951	−	0.167968i	0.0389100	−	0.999243i	$-0.487611\pi$
$281$	−8.66568	−	2.81565i	−0.516951	−	0.167968i	−0.555861	+	0.831275i	$0.687611\pi$
$282$	−10.3749	+	15.5353i	−0.617814	+	0.925111i
$283$	2.58535	+	2.87132i	0.153683	+	0.170682i	0.815070	−	0.579363i	$-0.196698\pi$
$283$	2.58535	+	2.87132i	0.153683	+	0.170682i	−0.661387	+	0.750045i	$0.730032\pi$
$284$	−1.78344	+	0.187447i	−0.105828	+	0.0111230i
$285$	23.3136	−	11.2423i	1.38098	−	0.665936i
$286$	22.9848	−	31.6359i	1.35912	−	1.87067i
$287$	13.3448	+	9.76261i	0.787718	+	0.576269i
$288$	0.416850	−	16.2204i	0.0245631	−	0.955796i
$289$	−1.70194	+	16.1929i	−0.100114	+	0.952524i
$290$	7.65667	−	1.55504i	0.449615	−	0.0913148i
$291$	3.07840	+	4.87635i	0.180459	+	0.285856i
$292$	8.08836	−	1.71923i	0.473336	−	0.100611i
$293$			15.1703i			0.886261i	0.896457	+	0.443131i	$0.146132\pi$
$293$			15.1703i			0.886261i	−0.896457	+	0.443131i	$0.853868\pi$
$294$	−14.6785	−	15.2597i	−0.856069	−	0.889961i
$295$	22.6576	−	2.17385i	1.31918	−	0.126566i
$296$	0.965041	+	0.868927i	0.0560919	+	0.0505053i
$297$	−19.9046	−	8.53449i	−1.15498	−	0.495222i
$298$	7.94135	+	17.8366i	0.460030	+	1.03324i
$299$	9.59797	+	16.6242i	0.555065	+	0.961401i
$300$	9.08919	−	0.194310i	0.524765	−	0.0112185i
$301$	17.7087	−	5.68975i	1.02071	−	0.327951i
$302$	−18.2285	−	13.2438i	−1.04893	−	0.762096i
$303$	−4.00315	+	14.2073i	−0.229975	+	0.816190i
$304$	6.94380	−	32.6680i	0.398255	−	1.87364i
$305$	−3.25857	+	28.5133i	−0.186585	+	1.63266i
$306$	−4.00750	−	1.90909i	−0.229093	−	0.109135i
$307$	29.2914			1.67175			0.835874	−	0.548921i	$-0.184961\pi$
$307$	29.2914			1.67175			0.835874	+	0.548921i	$0.184961\pi$
$308$	10.0441	−	5.75512i	0.572317	−	0.327928i
$309$	3.20882	−	6.10257i	0.182543	−	0.347163i
$310$	21.7638	−	15.5127i	1.23610	−	0.881065i
$311$	−13.0481	+	5.80939i	−0.739890	+	0.329420i	−0.741839	−	0.670578i	$-0.766046\pi$
$311$	−13.0481	+	5.80939i	−0.739890	+	0.329420i	0.00194935	+	0.999998i	$0.499380\pi$
$312$	8.24305	+	13.0574i	0.466671	+	0.739230i
$313$	−31.3844	−	13.9733i	−1.77395	−	0.789815i	−0.984356	−	0.176190i	$-0.943623\pi$
$313$	−31.3844	−	13.9733i	−1.77395	−	0.789815i	−0.789597	−	0.613625i	$-0.789711\pi$
$314$	−10.4172	−	7.56857i	−0.587879	−	0.427119i
$315$	−12.3690	+	12.7283i	−0.696912	+	0.717157i
$316$	9.36656	−	6.80521i	0.526910	−	0.382823i
$317$	−17.0127	+	3.61615i	−0.955526	+	0.203103i	−0.659187	−	0.751979i	$-0.729099\pi$
$317$	−17.0127	+	3.61615i	−0.955526	+	0.203103i	−0.296339	+	0.955083i	$0.595766\pi$
$318$	−1.41440	+	21.6602i	−0.0793154	+	1.21465i
$319$	−5.57992	−	6.19713i	−0.312416	−	0.346973i
$320$	−0.731503	+	0.987862i	−0.0408923	+	0.0552232i
$321$	−10.3114	−	10.5798i	−0.575524	−	0.590505i
$322$	1.67179	+	16.4242i	0.0931652	+	0.915285i
$323$	−4.58090	−	3.32822i	−0.254888	−	0.185187i
$324$	−6.67419	+	6.68719i	−0.370788	+	0.371510i
$325$	−22.0147	+	15.3924i	−1.22115	+	0.853816i
$326$	17.2676	+	9.96945i	0.956363	+	0.552157i
$327$	1.29639	+	3.51138i	0.0716903	+	0.194180i
$328$	−3.20471	−	9.86308i	−0.176950	−	0.544597i
$329$	6.69509	−	14.9056i	0.369112	−	0.821772i
$330$	−14.8317	−	23.9731i	−0.816458	−	1.31967i
$331$	−20.7252	+	4.40528i	−1.13916	+	0.242136i	−0.738606	−	0.674137i	$-0.764516\pi$
$331$	−20.7252	+	4.40528i	−1.13916	+	0.242136i	−0.400554	+	0.916273i	$0.631182\pi$
$332$	−14.6835	−	8.47750i	−0.805859	−	0.465263i
$333$	−0.185332	−	2.34031i	−0.0101561	−	0.128248i
$334$	−4.81201	+	10.8079i	−0.263301	+	0.591384i
$335$	−7.20673	−	8.15135i	−0.393746	−	0.445356i
$336$	3.21734	+	22.6744i	0.175520	+	1.23699i
$337$	−10.7672	−	14.8198i	−0.586527	−	0.807285i	0.407865	−	0.913042i	$-0.366273\pi$
$337$	−10.7672	−	14.8198i	−0.586527	−	0.807285i	−0.994392	+	0.105757i	$0.966273\pi$
$338$	25.3073	+	11.2675i	1.37653	+	0.612872i
$339$	6.02889	−	7.25254i	0.327444	−	0.393904i
$340$	−0.978778	−	1.73137i	−0.0530817	−	0.0938966i
$341$	−26.0600	−	11.6026i	−1.41123	−	0.628318i
$342$	−28.8448	+	19.8451i	−1.55975	+	1.07310i
$343$	14.8753	+	11.0329i	0.803192	+	0.595720i
$344$	−11.0953	−	3.60509i	−0.598220	−	0.194374i
$345$	13.7122	−	1.86476i	0.738239	−	0.100395i
$346$	3.12565	−	14.7050i	0.168036	−	0.790547i
$347$	6.09182	+	1.29486i	0.327026	+	0.0695115i	0.368499	−	0.929628i	$-0.379872\pi$
$347$	6.09182	+	1.29486i	0.327026	+	0.0695115i	−0.0414732	+	0.999140i	$0.513205\pi$
$348$	−3.41276	+	1.25998i	−0.182943	+	0.0675418i
$349$			19.1419i			1.02464i	0.858794	+	0.512321i	$0.171214\pi$
$349$			19.1419i			1.02464i	−0.858794	+	0.512321i	$0.828786\pi$
$350$	−22.6950	+	4.31813i	−1.21310	+	0.230814i
$351$	5.42614	−	27.3835i	0.289626	−	1.46162i
$352$	−22.4190	−	2.35633i	−1.19494	−	0.125593i
$353$	−2.05212	+	9.65447i	−0.109223	+	0.513856i	0.889190	+	0.457539i	$0.151269\pi$
$353$	−2.05212	+	9.65447i	−0.109223	+	0.513856i	−0.998413	+	0.0563167i	$0.982064\pi$
$354$	−29.8410	+	7.58637i	−1.58603	+	0.403211i
$355$	−1.14738	−	3.64336i	−0.0608964	−	0.193370i
$356$	−3.14279	+	9.67251i	−0.166567	+	0.512642i
$357$	3.73375	+	1.06528i	0.197611	+	0.0563807i
$358$	−17.7162	−	5.75635i	−0.936332	−	0.304233i
$359$	−0.152674	+	0.342911i	−0.00805781	+	0.0180981i	−0.917530	−	0.397668i	$-0.869820\pi$
$359$	−0.152674	+	0.342911i	−0.00805781	+	0.0180981i	0.909472	+	0.415766i	$0.136486\pi$
$360$	10.9625	−	1.93461i	0.577774	−	0.101963i
$361$	−23.4424	+	10.4372i	−1.23381	+	0.549328i
$362$	−2.71443	+	6.09670i	−0.142667	+	0.320436i
$363$	−5.13605	+	9.76779i	−0.269573	+	0.512676i
$364$	9.94800	+	11.1215i	0.521417	+	0.582927i
$365$	7.01786	+	16.1551i	0.367332	+	0.845597i
$366$	−1.53356	−	38.7913i	−0.0801607	−	2.02766i
$367$	6.12483	+	6.80231i	0.319714	+	0.355078i	0.881483	−	0.472216i	$-0.156546\pi$
$367$	6.12483	+	6.80231i	0.319714	+	0.355078i	−0.561769	+	0.827294i	$0.689879\pi$
$368$	8.92822	−	15.4641i	0.465415	−	0.806123i
$369$	−8.06318	+	16.9260i	−0.419752	+	0.881131i
$370$	1.55185	−	2.63246i	0.0806768	−	0.136855i
$371$	−1.92265	−	18.8888i	−0.0998192	−	0.980657i
$372$	−8.91195	+	8.68586i	−0.462063	+	0.450341i
$373$	−12.1493	−	1.27694i	−0.629068	−	0.0661177i	−0.215371	−	0.976532i	$-0.569096\pi$
$373$	−12.1493	−	1.27694i	−0.629068	−	0.0661177i	−0.413697	+	0.910415i	$0.635763\pi$
$374$	−3.08356	+	5.34088i	−0.159447	+	0.276170i
$375$	4.25897	+	18.8908i	0.219932	+	0.975515i
$376$	−8.87566	+	5.12436i	−0.457727	+	0.264269i
$377$	6.31810	−	8.69612i	0.325399	−	0.447873i
$378$	13.9063	−	19.5709i	0.715265	−	1.00662i
$379$	−4.89046	−	15.0513i	−0.251206	−	0.773133i	−0.994553	−	0.104228i	$-0.966763\pi$
$379$	−4.89046	−	15.0513i	−0.251206	−	0.773133i	0.743347	−	0.668906i	$-0.233237\pi$
$380$	−15.6865	−	0.142266i	−0.804698	−	0.00729811i
$381$	8.88648	−	22.2899i	0.455268	−	1.14195i
$382$	3.57570	+	2.06443i	0.182949	+	0.105626i
$383$	−6.42304	−	30.2180i	−0.328202	−	1.54407i	−0.764713	−	0.644371i	$-0.777119\pi$
$383$	−6.42304	−	30.2180i	−0.328202	−	1.54407i	0.436511	−	0.899699i	$-0.356214\pi$
$384$	9.49352	−	18.0549i	0.484464	−	0.921359i
$385$	16.2717	+	18.5266i	0.829281	+	0.944204i
$386$	4.96519	−	6.83399i	0.252721	−	0.347841i
$387$	10.0727	+	18.5300i	0.512023	+	0.941935i
$388$	−0.365341	−	3.47599i	−0.0185474	−	0.176467i
$389$	−12.7285	−	28.5887i	−0.645361	−	1.44951i	−0.878827	−	0.477140i	$-0.841673\pi$
$389$	−12.7285	−	28.5887i	−0.645361	−	1.44951i	0.233466	−	0.972365i	$-0.424993\pi$
$390$	26.2510	−	25.1249i	1.32927	−	1.27225i
$391$	−1.77946	−	2.44922i	−0.0899911	−	0.123862i
$392$	−3.51700	−	11.0709i	−0.177636	−	0.559164i
$393$	−29.1487	+	14.3834i	−1.47036	+	0.725545i
$394$	−17.2361	+	3.66364i	−0.868341	+	0.184572i
$395$	18.1764	+	16.6671i	0.914555	+	0.838611i
$396$	8.52954	+	9.97698i	0.428626	+	0.501362i
$397$	2.61538	−	2.90467i	0.131262	−	0.145781i	−0.673930	−	0.738795i	$-0.735395\pi$
$397$	2.61538	−	2.90467i	0.131262	−	0.145781i	0.805193	+	0.593013i	$0.202062\pi$
$398$	17.5347	−	24.1345i	0.878936	−	1.20975i
$399$	22.0014	−	21.3030i	1.10145	−	1.06648i
$400$	22.6392	+	10.5757i	1.13196	+	0.528787i
$401$	3.48849	−	2.01408i	0.174207	−	0.100579i	−0.410361	−	0.911923i	$-0.634597\pi$
$401$	3.48849	−	2.01408i	0.174207	−	0.100579i	0.584568	+	0.811345i	$0.301264\pi$
$402$	11.3182	+	9.40856i	0.564499	+	0.469256i
$403$	7.64493	−	35.9666i	0.380821	−	1.79162i
$404$	5.98613	−	6.64827i	0.297821	−	0.330764i
$405$	−16.7886	−	11.0969i	−0.834234	−	0.551411i
$406$	8.02104	−	4.59593i	0.398078	−	0.228092i
$407$	−3.26158			−0.161671
$408$	−1.50815	−	1.91212i	−0.0746643	−	0.0946639i
$409$	−0.418086	+	0.0439426i	−0.0206730	+	0.00217282i	−0.114859	−	0.993382i	$-0.536642\pi$
$409$	−0.418086	+	0.0439426i	−0.0206730	+	0.00217282i	0.0941863	+	0.995555i	$0.469975\pi$
$410$	−21.2443	+	12.0099i	−1.04918	+	0.593125i
$411$	−5.50892	−	14.9214i	−0.271735	−	0.736018i
$412$	−3.38073	+	2.45624i	−0.166557	+	0.121010i
$413$	24.6393	−	10.8734i	1.21242	−	0.535046i
$414$	−17.9461	+	5.32536i	−0.882000	+	0.261727i
$415$	11.4712	−	34.2449i	0.563100	−	1.68101i
$416$	−3.03730	−	28.8980i	−0.148916	−	1.41684i
$417$	7.92664	−	19.8823i	0.388169	−	0.973642i
$418$	24.3213	+	42.1257i	1.18959	+	2.06043i
$419$	−5.96899	+	18.3707i	−0.291604	+	0.897466i	0.692737	+	0.721191i	$0.256405\pi$
$419$	−5.96899	+	18.3707i	−0.291604	+	0.897466i	−0.984341	+	0.176275i	$0.943595\pi$
$420$	10.1364	−	3.60071i	0.494606	−	0.175696i
$421$	−6.87153	−	21.1484i	−0.334898	−	1.03071i	−0.966772	−	0.255639i	$-0.917714\pi$
$421$	−6.87153	−	21.1484i	−0.334898	−	1.03071i	0.631875	−	0.775071i	$-0.282286\pi$
$422$	−8.57415	+	9.52255i	−0.417383	+	0.463551i
$423$	18.0182	+	4.31651i	0.876074	+	0.209876i
$424$	−5.95423	+	10.3130i	−0.289163	+	0.500845i
$425$	3.19917	−	2.77715i	0.155183	−	0.134712i
$426$	2.28647	+	4.63366i	0.110780	+	0.224501i
$427$	6.95103	+	33.2379i	0.336384	+	1.60849i
$428$	2.76693	+	8.51574i	0.133745	+	0.411624i
$429$	−37.3301	−	10.5184i	−1.80232	−	0.507832i
$430$	−3.11711	+	27.2755i	−0.150320	+	1.31534i
$431$	23.9054	−	21.5245i	1.15148	−	1.03680i	0.152662	−	0.988278i	$-0.451215\pi$
$431$	23.9054	−	21.5245i	1.15148	−	1.03680i	0.998822	−	0.0485223i	$-0.0154512\pi$
$432$	−24.5837	+	8.36505i	−1.18278	+	0.402463i
$433$	−2.73976	+	8.43211i	−0.131664	+	0.405221i	−0.995056	−	0.0993126i	$-0.968336\pi$
$433$	−2.73976	+	8.43211i	−0.131664	+	0.405221i	0.863392	+	0.504534i	$0.168336\pi$
$434$	18.6716	−	25.5227i	0.896263	−	1.22513i
$435$	−4.07696	−	6.58976i	−0.195475	−	0.315955i
$436$	0.237133	−	2.25617i	0.0113566	−	0.108051i
$437$	−23.7475	+	2.49596i	−1.13600	+	0.119398i
$438$	−12.7190	−	20.1475i	−0.607735	−	0.962683i
$439$	22.7431	+	2.39040i	1.08547	+	0.114087i	0.630326	−	0.776331i	$-0.282921\pi$
$439$	22.7431	+	2.39040i	1.08547	+	0.114087i	0.455144	+	0.890418i	$0.349588\pi$
$440$	−1.47704	−	15.3949i	−0.0704150	−	0.733923i
$441$	−9.15572	+	18.8990i	−0.435987	+	0.899953i
$442$	−7.56030	−	2.45649i	−0.359607	−	0.116843i
$443$	0.761183	+	1.31841i	0.0361649	+	0.0626394i	0.883541	−	0.468353i	$-0.155153\pi$
$443$	0.761183	+	1.31841i	0.0361649	+	0.0626394i	−0.847376	+	0.530993i	$0.821819\pi$
$444$	−0.526932	+	1.32170i	−0.0250071	+	0.0627251i
$445$	−21.5232	−	2.45972i	−1.02030	−	0.116602i
$446$	−22.8441	+	25.3709i	−1.08170	+	1.20135i
$447$	13.8676	−	13.5158i	0.655915	−	0.639275i
$448$	−0.453978	+	1.38176i	−0.0214485	+	0.0652820i
$449$		−	32.0007i		−	1.51021i	−0.655605	−	0.755104i	$-0.727586\pi$
$449$		−	32.0007i		−	1.51021i	0.655605	−	0.755104i	$-0.272414\pi$
$450$	−9.59580	−	24.3746i	−0.452350	−	1.14903i
$451$	22.5576	+	13.0236i	1.06220	+	0.613260i
$452$	−5.22190	+	2.32494i	−0.245618	+	0.109356i
$453$	−6.06068	+	21.5096i	−0.284755	+	1.01061i
$454$	16.7683	−	5.44836i	0.786977	−	0.255704i
$455$	−18.9981	+	25.4808i	−0.890644	+	1.19456i
$456$	−19.0088	+	2.76086i	−0.890167	+	0.129289i
$457$	−11.8447	+	6.83852i	−0.554070	+	0.319893i	−0.750762	−	0.660573i	$-0.770314\pi$
$457$	−11.8447	+	6.83852i	−0.554070	+	0.319893i	0.196692	+	0.980465i	$0.436980\pi$
$458$	18.1287	−	16.3232i	0.847101	−	0.762733i
$459$	−0.399648	+	4.38444i	−0.0186540	+	0.204648i
$460$	−7.95290	−	2.66403i	−0.370806	−	0.124211i
$461$	−20.4249	−	14.8395i	−0.951281	−	0.691146i	−0.000171319	−	1.00000i	$-0.500055\pi$
$461$	−20.4249	−	14.8395i	−0.951281	−	0.691146i	−0.951109	+	0.308854i	$0.900055\pi$
$462$	−25.5799	−	21.4063i	−1.19008	−	0.995913i
$463$	14.2929	+	19.6725i	0.664246	+	0.914256i	0.999613	−	0.0278314i	$-0.00886016\pi$
$463$	14.2929	+	19.6725i	0.664246	+	0.914256i	−0.335367	+	0.942088i	$0.608860\pi$
$464$	−9.94414	−	1.04517i	−0.461645	−	0.0485209i
$465$	−21.9094	−	14.9208i	−1.01603	−	0.691935i
$466$	−0.584584	−	5.56194i	−0.0270803	−	0.257652i
$467$	6.53247	+	30.7329i	0.302287	+	1.42215i	0.822818	+	0.568305i	$0.192401\pi$
$467$	6.53247	+	30.7329i	0.302287	+	1.42215i	−0.520531	+	0.853842i	$0.674266\pi$
$468$	−10.2933	+	13.4281i	−0.475810	+	0.620713i
$469$	−11.1278	−	6.47343i	−0.513836	−	0.298915i
$470$	15.9743	+	18.0682i	0.736840	+	0.833422i
$471$	−3.46356	+	12.2923i	−0.159592	+	0.566399i
$472$	−16.5229	−	3.51204i	−0.760526	−	0.161655i
$473$	26.7683	−	11.9180i	1.23081	−	0.547991i
$474$	−27.7421	−	18.5269i	−1.27424	−	0.850970i
$475$	−6.35330	−	32.8049i	−0.291509	−	1.50519i
$476$	−1.74365	−	1.58038i	−0.0799199	−	0.0724364i
$477$	20.6390	−	6.12447i	0.944995	−	0.280420i
$478$	−8.09063	−	7.28484i	−0.370057	−	0.333201i
$479$	22.6983	+	4.82468i	1.03711	+	0.220445i	0.694847	−	0.719158i	$-0.255472\pi$
$479$	22.6983	+	4.82468i	1.03711	+	0.220445i	0.342266	+	0.939603i	$0.388806\pi$
$480$	−20.1099	−	5.86367i	−0.917888	−	0.267639i
$481$	−0.874094	−	4.11229i	−0.0398553	−	0.187504i
$482$		−	3.12209i		−	0.142207i
$483$	14.7071	−	7.19730i	0.669198	−	0.327489i
$484$	5.41121	−	3.93147i	0.245964	−	0.178703i
$485$	7.10103	−	2.23627i	0.322441	−	0.101544i
$486$	24.7363	+	11.3671i	1.12206	+	0.515623i
$487$	−9.35126	+	0.982857i	−0.423746	+	0.0445375i	−0.314002	−	0.949422i	$-0.601670\pi$
$487$	−9.35126	+	0.982857i	−0.423746	+	0.0445375i	−0.109744	+	0.993960i	$0.535003\pi$
$488$	8.66274	−	19.4568i	0.392144	−	0.880770i
$489$	3.34424	−	19.4907i	0.151232	−	0.881400i
$490$	−23.8834	+	13.2957i	−1.07894	+	0.600640i
$491$	3.45347	+	4.75330i	0.155853	+	0.214513i	0.879802	−	0.475340i	$-0.157675\pi$
$491$	3.45347	+	4.75330i	0.155853	+	0.214513i	−0.723949	+	0.689853i	$0.757675\pi$
$492$	8.92195	−	7.03702i	0.402233	−	0.317253i
$493$	−0.847613	+	1.46811i	−0.0381746	+	0.0661203i
$494$	−46.5951	+	41.9544i	−2.09641	+	1.88762i
$495$	−17.2102	+	22.0346i	−0.773543	+	0.990384i
$496$	−32.5301	+	10.5697i	−1.46065	+	0.474593i
$497$	−2.64454	−	3.66513i	−0.118624	−	0.164404i
$498$	−8.26165	+	48.1501i	−0.370213	+	2.15766i
$499$	−11.7279	−	20.3132i	−0.525011	−	0.909345i	−0.999576	−	0.0291248i	$-0.990728\pi$
$499$	−11.7279	−	20.3132i	−0.525011	−	0.909345i	0.474565	−	0.880220i	$-0.342605\pi$
$500$	2.75162	−	11.4097i	0.123056	−	0.510256i
$501$	11.7089	+	0.764582i	0.523115	+	0.0341590i
$502$	4.15158	−	39.4997i	0.185294	−	1.76296i
$503$	−12.9604	+	4.21109i	−0.577875	+	0.187763i	−0.583349	−	0.812222i	$-0.698258\pi$
$503$	−12.9604	+	4.21109i	−0.577875	+	0.187763i	0.00547316	+	0.999985i	$0.498258\pi$
$504$	11.5928	−	6.25249i	0.516384	−	0.278508i
$505$	16.4157	+	9.67716i	0.730489	+	0.430628i
$506$	5.40718	+	25.4388i	0.240379	+	1.13089i
$507$	1.79030	−	27.4169i	0.0795100	−	1.21763i
$508$	−10.8080	+	9.73158i	−0.479528	+	0.431769i
$509$	23.0889	+	10.2799i	1.02340	+	0.455647i	0.848644	−	0.528965i	$-0.177420\pi$
$509$	23.0889	+	10.2799i	1.02340	+	0.455647i	0.174756	+	0.984612i	$0.444086\pi$
$510$	−3.70318	+	4.37350i	−0.163980	+	0.193662i
$511$	13.8942	+	15.5333i	0.614645	+	0.687152i
$512$	−8.44880	+	6.13842i	−0.373388	+	0.271282i
$513$	28.3727	+	20.0208i	1.25269	+	0.883941i
$514$	3.70749	+	8.32716i	0.163530	+	0.367295i
$515$	−6.56052	−	6.01575i	−0.289091	−	0.265086i
$516$	−0.504957	−	12.7728i	−0.0222295	−	0.562292i
$517$	7.95442	−	24.4812i	0.349835	−	1.07668i
$518$	0.763346	−	3.53420i	0.0335395	−	0.155284i
$519$	−14.7555	+	2.14312i	−0.647697	+	0.0940724i
$520$	19.0144	−	5.98807i	0.833838	−	0.262594i
$521$	−3.34435	−	0.710863i	−0.146519	−	0.0311435i	0.134068	−	0.990972i	$-0.457196\pi$
$521$	−3.34435	−	0.710863i	−0.146519	−	0.0311435i	−0.280587	+	0.959829i	$0.590529\pi$
$522$	6.81153	+	7.96743i	0.298133	+	0.348725i
$523$	1.17600	−	11.1889i	0.0514231	−	0.489258i	−0.938254	−	0.345946i	$-0.887558\pi$
$523$	1.17600	−	11.1889i	0.0514231	−	0.489258i	0.989678	−	0.143312i	$-0.0457753\pi$
$524$	19.7004			0.860614
$525$	11.8136	+	19.6326i	0.515587	+	0.856837i
$526$	−21.8164			−0.951241
$527$	−0.606162	+	5.76725i	−0.0264048	+	0.251225i
$528$	8.88906	+	34.9651i	0.386847	+	1.52166i
$529$	10.0096	+	2.12762i	0.435202	+	0.0925050i
$530$	26.5716	+	8.90087i	1.15420	+	0.386629i
$531$	17.3091	+	25.1587i	0.751152	+	1.09179i
$532$	−17.6715	+	5.67779i	−0.766157	+	0.246163i
$533$	−10.3752	+	31.9315i	−0.449399	+	1.38311i
$534$	29.2815	−	1.15761i	1.26714	−	0.0500946i
$535$	−16.6030	+	9.38605i	−0.717812	+	0.405794i
$536$	3.28422	+	7.37649i	0.141857	+	0.318616i
$537$	0.729828	+	18.4609i	0.0314944	+	0.796647i
$538$	−15.5861	+	11.3239i	−0.671963	+	0.488210i
$539$	25.1704	+	14.7532i	1.08416	+	0.635465i
$540$	6.14872	+	10.5340i	0.264599	+	0.453312i
$541$	19.4967	+	8.68048i	0.838227	+	0.373203i	0.780520	−	0.625131i	$-0.214954\pi$
$541$	19.4967	+	8.68048i	0.838227	+	0.373203i	0.0577073	+	0.998334i	$0.481621\pi$
$542$	−34.2078	+	30.8008i	−1.46935	+	1.32301i
$543$	6.60493	+	0.431297i	0.283445	+	0.0185087i
$544$	0.952778	+	4.48247i	0.0408500	+	0.192184i
$545$	4.81016	−	0.461503i	0.206045	−	0.0197686i
$546$	20.1344	−	37.9886i	0.861671	−	1.62576i
$547$	−13.7293	+	4.46092i	−0.587023	+	0.190735i	−0.587444	−	0.809265i	$-0.699866\pi$
$547$	−13.7293	+	4.46092i	−0.587023	+	0.190735i	0.000421475		1.00000i	$0.499866\pi$
$548$	−1.00768	+	9.58748i	−0.0430462	+	0.409557i
$549$	−35.5655	+	14.7520i	−1.51790	+	0.629599i
$550$	−34.8104	+	10.6166i	−1.48432	+	0.452691i
$551$	6.68547	+	11.5796i	0.284811	+	0.493307i
$552$	−10.1219	−	1.73673i	−0.430817	−	0.0739200i
$553$	26.6177	+	11.9558i	1.13190	+	0.508411i
$554$	−20.5117	+	6.66467i	−0.871461	+	0.283155i
$555$	−2.98236	−	0.539605i	−0.126594	−	0.0229050i
$556$	−9.64062	+	8.68046i	−0.408854	+	0.368133i
$557$	18.7524	−	32.4802i	0.794566	−	1.37623i	−0.128548	−	0.991703i	$-0.541032\pi$
$557$	18.7524	−	32.4802i	0.794566	−	1.37623i	0.923114	−	0.384526i	$-0.125635\pi$
$558$	32.3719	+	15.4213i	1.37041	+	0.652835i
$559$	22.2004	+	30.5562i	0.938975	+	1.29239i
$560$	29.3634	+	3.45336i	1.24083	+	0.145931i
$561$	6.02849	+	1.03437i	0.254523	+	0.0436713i
$562$	6.47207	−	14.5365i	0.273008	−	0.613186i
$563$	−34.4877	+	3.62481i	−1.45349	+	0.152767i	−0.798099	−	0.602526i	$-0.794161\pi$
$563$	−34.4877	+	3.62481i	−1.45349	+	0.152767i	−0.655386	+	0.755294i	$0.727494\pi$
$564$	−8.63549	−	7.17851i	−0.363620	−	0.302270i
$565$	−7.06700	−	9.91475i	−0.297311	−	0.417117i
$566$	−5.45883	+	3.96607i	−0.229452	+	0.166706i
$567$	−22.9861	−	6.21601i	−0.965326	−	0.261048i
$568$			2.83474i			0.118943i
$569$	−6.19761	−	29.1575i	−0.259817	−	1.22234i	−0.893611	−	0.448843i	$-0.851836\pi$
$569$	−6.19761	−	29.1575i	−0.259817	−	1.22234i	0.633793	−	0.773502i	$-0.281497\pi$
$570$	15.2698	+	42.5431i	0.639580	+	1.78193i
$571$	18.0540	+	3.83749i	0.755535	+	0.160594i	0.569548	−	0.821958i	$-0.307118\pi$
$571$	18.0540	+	3.83749i	0.755535	+	0.160594i	0.185987	+	0.982552i	$0.440452\pi$
$572$	17.4685	+	15.7287i	0.730395	+	0.657651i
$573$	0.692511	−	4.03606i	0.0289301	−	0.168609i
$574$	−19.3916	+	21.3950i	−0.809391	+	0.893010i
$575$	2.18938	−	17.7306i	0.0913033	−	0.739418i
$576$	−1.63516	−	0.214464i	−0.0681316	−	0.00893599i
$577$	−4.94862	+	2.20327i	−0.206014	+	0.0917232i	−0.507150	−	0.861858i	$-0.669301\pi$
$577$	−4.94862	+	2.20327i	−0.206014	+	0.0917232i	0.301136	+	0.953581i	$0.402634\pi$
$578$	−27.8130	−	5.91185i	−1.15687	−	0.245900i
$579$	−8.06407	−	2.27219i	−0.335131	−	0.0944288i
$580$	0.448541	+	4.67506i	0.0186247	+	0.194121i
$581$	0.140201	−	42.7317i	0.00581654	−	1.77281i
$582$	−9.03114	+	4.45640i	−0.374353	+	0.184724i
$583$	−6.21858	−	29.2561i	−0.257547	−	1.21166i
$584$	−1.36634	−	12.9999i	−0.0565396	−	0.537939i
$585$	−32.3942	−	15.7939i	−1.33933	−	0.652998i
$586$	−26.3477	−	2.76926i	−1.08842	−	0.114397i
$587$	−5.84433	−	8.04403i	−0.241221	−	0.332013i	0.671191	−	0.741284i	$-0.265783\pi$
$587$	−5.84433	−	8.04403i	−0.241221	−	0.332013i	−0.912413	+	0.409271i	$0.865783\pi$
$588$	10.0449	−	7.81638i	0.414246	−	0.322342i
$589$	37.0038	+	26.8848i	1.52471	+	1.10777i
$590$	−0.360492	+	39.7483i	−0.0148412	+	1.63641i
$591$	9.32946	+	14.7783i	0.383763	+	0.607899i
$592$	−2.90628	+	2.61683i	−0.119448	+	0.107551i
$593$	−12.0053	+	6.93126i	−0.492998	+	0.284633i	−0.725818	−	0.687887i	$-0.758538\pi$
$593$	−12.0053	+	6.93126i	−0.492998	+	0.284633i	0.232819	+	0.972520i	$0.425205\pi$
$594$	18.4561	−	33.0122i	0.757264	−	1.35451i
$595$	2.55972	−	4.30976i	0.104938	−	0.176683i
$596$	−11.1622	+	3.62680i	−0.457220	+	0.148560i
$597$	−28.4785	−	8.02429i	−1.16555	−	0.328413i
$598$	−30.6248	+	13.6350i	−1.25234	+	0.557578i
$599$	−19.7513	−	11.4034i	−0.807015	−	0.465930i	0.0389035	−	0.999243i	$-0.487614\pi$
$599$	−19.7513	−	11.4034i	−0.807015	−	0.465930i	−0.845918	+	0.533313i	$0.820947\pi$
$600$	1.19638	−	14.3213i	0.0488420	−	0.584665i
$601$		−	39.1555i		−	1.59719i	−0.601870	−	0.798594i	$-0.705578\pi$
$601$		−	39.1555i		−	1.59719i	0.601870	−	0.798594i	$-0.294422\pi$
$602$	6.64928	+	31.7950i	0.271004	+	1.29587i
$603$	4.86605	−	13.7626i	0.198161	−	0.560455i
$604$	9.06287	−	10.0653i	0.368763	−	0.409553i
$605$	10.5008	+	9.62883i	0.426918	+	0.391468i
$606$	−23.9444	−	9.54611i	−0.972676	−	0.387784i
$607$	14.9017	+	25.8105i	0.604840	+	1.04761i	0.992077	+	0.125634i	$0.0400964\pi$
$607$	14.9017	+	25.8105i	0.604840	+	1.04761i	−0.387236	+	0.921980i	$0.626570\pi$
$608$	34.3759	+	11.1694i	1.39413	+	0.452979i
$609$	−7.03144	−	5.88421i	−0.284928	−	0.238440i
$610$	−48.9268	−	10.8644i	−1.98099	−	0.439886i
$611$	32.9983	+	3.46826i	1.33497	+	0.140311i
$612$	1.39311	−	2.27583i	0.0563131	−	0.0919950i
$613$	−35.7221	+	3.75454i	−1.44280	+	0.151645i	−0.793354	−	0.608761i	$-0.791667\pi$
$613$	−35.7221	+	3.75454i	−1.44280	+	0.151645i	−0.649448	+	0.760406i	$0.725000\pi$
$614$	−5.34697	+	50.8731i	−0.215786	+	2.05307i
$615$	18.4718	+	15.6407i	0.744856	+	0.630694i
$616$	−7.38804	−	16.7414i	−0.297673	−	0.674531i
$617$	−7.37777	+	22.7065i	−0.297018	+	0.914127i	0.685518	+	0.728055i	$0.259576\pi$
$617$	−7.37777	+	22.7065i	−0.297018	+	0.914127i	−0.982536	+	0.186072i	$0.940424\pi$
$618$	10.0131	+	6.68704i	0.402787	+	0.268992i
$619$	−18.7364	+	16.8703i	−0.753079	+	0.678075i	−0.953418	−	0.301651i	$-0.902462\pi$
$619$	−18.7364	+	16.8703i	−0.753079	+	0.678075i	0.200339	+	0.979727i	$0.435796\pi$
$620$	7.90641	+	13.9857i	0.317529	+	0.561680i
$621$	11.1194	+	14.8681i	0.446208	+	0.596636i
$622$	−7.70784	−	23.7223i	−0.309056	−	0.951178i
$623$	−25.0895	+	5.24697i	−1.00519	+	0.210215i
$624$	−41.7027	+	20.5781i	−1.66944	+	0.823783i
$625$	24.9836	+	0.906713i	0.999342	+	0.0362685i
$626$	29.9977	−	51.9575i	1.19895	−	2.07664i
$627$	30.8401	−	37.0995i	1.23163	−	1.48161i
$628$	5.17925	−	5.75214i	0.206674	−	0.229535i
$629$	0.204890	+	0.630588i	0.00816951	+	0.0251432i
$630$	−19.8485	−	23.8058i	−0.790783	−	0.948445i
$631$	12.6825	−	39.0326i	0.504881	−	1.55386i	−0.296089	−	0.955160i	$-0.595683\pi$
$631$	12.6825	−	39.0326i	0.504881	−	1.55386i	0.800970	−	0.598704i	$-0.204317\pi$
$632$	−9.15084	−	15.8497i	−0.364001	−	0.630468i
$633$	11.8053	+	4.70650i	0.469217	+	0.187066i
$634$	−3.17494	−	30.2076i	−0.126093	−	1.19970i
$635$	−24.8962	−	18.4354i	−0.987974	−	0.731586i
$636$	−12.8602	−	2.20656i	−0.509939	−	0.0874959i
$637$	−11.8556	+	35.6893i	−0.469737	+	1.41406i
$638$	11.7817	−	8.55991i	0.466442	−	0.338890i
$639$	3.52583	−	3.71908i	0.139480	−	0.147124i
$640$	−19.4098	−	17.7980i	−0.767239	−	0.703529i
$641$	−17.2428	+	1.81229i	−0.681050	+	0.0715812i	−0.438735	−	0.898617i	$-0.644573\pi$
$641$	−17.2428	+	1.81229i	−0.681050	+	0.0715812i	−0.242315	+	0.970198i	$0.577907\pi$
$642$	20.2571	−	15.9774i	0.799485	−	0.630578i
$643$	41.9290			1.65352			0.826760	−	0.562555i	$-0.190182\pi$
$643$	41.9290			1.65352			0.826760	+	0.562555i	$0.190182\pi$
$644$	−9.92386	−	0.0325599i	−0.391055	−	0.00128304i
$645$	26.4484	−	6.46911i	1.04141	−	0.254721i
$646$	6.61664	−	7.34853i	0.260328	−	0.289124i
$647$	−1.15735	+	5.44489i	−0.0455000	+	0.214061i	−0.995024	−	0.0996328i	$-0.968233\pi$
$647$	−1.15735	+	5.44489i	−0.0455000	+	0.214061i	0.949524	+	0.313694i	$0.101567\pi$
$648$	9.41018	+	11.5975i	0.369667	+	0.455594i
$649$	36.7424	−	21.2133i	1.44227	−	0.832693i
$650$	−22.7147	−	41.0447i	−0.890944	−	1.60991i
$651$	−30.1607	−	8.60518i	−1.18209	−	0.337263i
$652$	−7.04499	+	9.69659i	−0.275903	+	0.379748i
$653$	26.8942	−	29.8690i	1.05245	−	1.16886i	0.0672015	−	0.997739i	$-0.478593\pi$
$653$	26.8942	−	29.8690i	1.05245	−	1.16886i	0.985249	−	0.171126i	$-0.0547404\pi$
$654$	−6.33518	+	1.61057i	−0.247725	+	0.0629783i
$655$	8.35196	+	41.1233i	0.326338	+	1.60682i
$656$	30.5494	−	6.49348i	1.19275	−	0.253528i
$657$	−14.3766	+	18.7548i	−0.560883	+	0.731694i
$658$	24.6658	+	14.3489i	0.961572	+	0.559379i
$659$	4.67172	+	6.43008i	0.181985	+	0.250480i	0.890257	−	0.455459i	$-0.150525\pi$
$659$	4.67172	+	6.43008i	0.181985	+	0.250480i	−0.708272	+	0.705940i	$0.750525\pi$
$660$	15.2637	−	7.36045i	0.594137	−	0.286505i
$661$	8.86903	+	19.9202i	0.344965	+	0.774804i	0.999819	+	0.0190485i	$0.00606369\pi$
$661$	8.86903	+	19.9202i	0.344965	+	0.774804i	−0.654853	+	0.755756i	$0.727270\pi$
$662$	−3.86779	−	36.7995i	−0.150326	−	1.43025i
$663$	0.311450	+	7.87808i	0.0120957	+	0.305959i
$664$	−15.7538	+	21.6832i	−0.611365	+	0.841472i
$665$	−19.3439	−	34.4811i	−0.750123	−	1.33712i
$666$	4.09846	+	0.105327i	0.158812	+	0.00408134i
$667$	1.48634	+	6.99266i	0.0575512	+	0.270757i
$668$	−6.15891	−	3.55585i	−0.238295	−	0.137580i
$669$	31.4528	+	12.5395i	1.21603	+	0.484806i
$670$	15.4727	−	11.0286i	0.597764	−	0.426072i
$671$	16.5303	+	50.8750i	0.638145	+	1.96401i
$672$	−24.7690	+	0.897826i	−0.955484	+	0.0346344i
$673$	6.38832	−	8.79277i	0.246252	−	0.338936i	−0.667942	−	0.744213i	$-0.732825\pi$
$673$	6.38832	−	8.79277i	0.246252	−	0.338936i	0.914194	+	0.405277i	$0.132825\pi$
$674$	27.7044	−	15.9951i	1.06713	−	0.616109i
$675$	−19.3824	+	17.3010i	−0.746028	+	0.665915i
$676$	−8.32617	+	14.4214i	−0.320237	+	0.554667i
$677$	−20.6698	−	2.17248i	−0.794405	−	0.0834953i	−0.301373	−	0.953506i	$-0.597445\pi$
$677$	−20.6698	−	2.17248i	−0.794405	−	0.0834953i	−0.493032	+	0.870011i	$0.664111\pi$
$678$	11.4956	+	11.7948i	0.441487	+	0.452978i
$679$	7.14345	−	5.15430i	0.274141	−	0.197804i
$680$	−2.88363	+	1.25266i	−0.110582	+	0.0480375i
$681$	−10.8293	−	13.7301i	−0.414980	−	0.526137i
$682$	24.9085	−	43.1427i	0.953795	−	1.65202i
$683$	−14.8951	−	16.5427i	−0.569945	−	0.632988i	0.387408	−	0.921908i	$-0.373370\pi$
$683$	−14.8951	−	16.5427i	−0.569945	−	0.632988i	−0.957353	+	0.288920i	$0.906704\pi$
$684$	−10.0515	−	18.4911i	−0.384329	−	0.707025i
$685$	−20.4405	+	1.96113i	−0.780991	+	0.0749310i
$686$	−21.8772	+	23.8214i	−0.835277	+	0.909504i
$687$	−21.4148	−	11.2602i	−0.817026	−	0.429604i
$688$	14.2902	−	32.0964i	0.544810	−	1.22366i
$689$	35.2203	−	15.6811i	1.34179	−	0.597402i
$690$	0.735620	+	24.1556i	0.0280046	+	0.919588i
$691$	15.1949	−	34.1284i	0.578042	−	1.29830i	−0.353759	−	0.935336i	$-0.615097\pi$
$691$	15.1949	−	34.1284i	0.578042	−	1.29830i	0.931802	−	0.362968i	$-0.118236\pi$
$692$	8.59465	+	2.79257i	0.326719	+	0.106158i
$693$	−11.1300	+	31.1533i	−0.422795	+	1.18342i
$694$	−3.36092	+	10.3438i	−0.127579	+	0.392647i
$695$	−22.2071	−	16.4441i	−0.842362	−	0.623762i
$696$	1.41691	+	5.57342i	0.0537079	+	0.211260i
$697$	1.10091	−	5.17938i	0.0417000	−	0.196183i
$698$	−33.2455	−	3.49424i	−1.25836	−	0.132259i
$699$	−4.97414	+	2.45448i	−0.188139	+	0.0928369i
$700$	−1.15547	−	13.8390i	−0.0436726	−	0.523065i
$701$		−	30.6397i		−	1.15725i	−0.815595	−	0.578624i	$-0.803590\pi$
$701$		−	30.6397i		−	1.15725i	0.815595	−	0.578624i	$-0.196410\pi$
$702$	46.5689	+	14.4228i	1.75763	+	0.544353i
$703$	5.11538	+	1.08731i	0.192930	+	0.0410086i
$704$	−0.476366	+	2.24112i	−0.0179537	+	0.0844655i
$705$	11.3237	−	21.0694i	0.426475	−	0.793519i
$706$	−16.3932	−	5.32648i	−0.616966	−	0.200465i
$707$	22.0389	+	4.76014i	0.828858	+	0.179023i
$708$	−2.66030	−	18.3164i	−0.0999802	−	0.688372i
$709$	−13.4156	−	5.97302i	−0.503834	−	0.224321i	0.139049	−	0.990285i	$-0.455595\pi$
$709$	−13.4156	−	5.97302i	−0.503834	−	0.224321i	−0.642883	+	0.765964i	$0.722262\pi$
$710$	6.53721	−	1.32768i	0.245337	−	0.0498269i
$711$	−7.70822	+	32.1760i	−0.289081	+	1.20669i
$712$	14.6869	+	6.53905i	0.550416	+	0.245061i
$713$	14.3742	+	19.7844i	0.538318	+	0.740931i
$714$	−2.53175	+	6.29029i	−0.0947483	+	0.235408i
$715$	−25.4270	+	43.1327i	−0.950915	+	1.61307i
$716$	4.55448	−	10.2295i	0.170209	−	0.382295i
$717$	−3.99877	+	10.0301i	−0.149337	+	0.374581i
$718$	−0.567695	−	0.327759i	−0.0211862	−	0.0122319i
$719$	−24.5587	+	5.22010i	−0.915883	+	0.194677i	−0.641660	−	0.766989i	$-0.721754\pi$
$719$	−24.5587	+	5.22010i	−0.915883	+	0.194677i	−0.274223	+	0.961666i	$0.588421\pi$
$720$	2.34336	+	33.4424i	0.0873318	+	1.24632i
$721$	−9.60729	−	4.31527i	−0.357794	−	0.160709i
$722$	−13.8480	−	42.6198i	−0.515370	−	1.58615i
$723$	−2.90486	+	1.07246i	−0.108033	+	0.0398853i
$724$	−3.47421	−	2.00584i	−0.129118	−	0.0745463i
$725$	−9.56875	+	2.91830i	−0.355375	+	0.108383i
$726$	−16.0271	−	10.7033i	−0.594820	−	0.397237i
$727$	−19.3891	−	14.0870i	−0.719102	−	0.522458i	0.166995	−	0.985958i	$-0.446594\pi$
$727$	−19.3891	−	14.0870i	−0.719102	−	0.522458i	−0.886097	+	0.463500i	$0.846594\pi$
$728$	19.1280	−	13.8017i	0.708932	−	0.511524i
$729$	2.07911	−	26.9198i	0.0770042	−	0.997031i
$730$	−29.3391	+	9.23955i	−1.08589	+	0.341971i
$731$	−3.98577	−	4.42664i	−0.147419	−	0.163725i
$732$	23.2868	+	1.52061i	0.860706	+	0.0562034i
$733$	−1.83430	+	0.389892i	−0.0677514	+	0.0144010i	−0.241663	−	0.970360i	$-0.577693\pi$
$733$	−1.83430	+	0.389892i	−0.0677514	+	0.0144010i	0.173911	+	0.984761i	$0.444359\pi$
$734$	−12.9323	+	9.39584i	−0.477338	+	0.346807i
$735$	20.5748	+	17.6544i	0.758912	+	0.651194i
$736$	15.6344	+	11.3590i	0.576291	+	0.418700i
$737$	−18.5270	−	8.24877i	−0.682452	−	0.303847i
$738$	−27.9250	−	17.0938i	−1.02793	−	0.629231i
$739$	−5.37319	+	2.39230i	−0.197656	+	0.0880022i	−0.503178	−	0.864183i	$-0.667836\pi$
$739$	−5.37319	+	2.39230i	−0.197656	+	0.0880022i	0.305522	+	0.952185i	$0.401169\pi$
$740$	1.47624	+	1.09314i	0.0542677	+	0.0401848i
$741$	55.0411	+	28.9414i	2.02198	+	1.06319i
$742$	33.1569	+	0.108787i	1.21723	+	0.00399368i
$743$	29.3237			1.07578			0.537892	−	0.843014i	$-0.319221\pi$
$743$	29.3237			1.07578			0.537892	+	0.843014i	$0.319221\pi$
$744$	12.1826	+	15.4458i	0.446634	+	0.566269i
$745$	−12.3029	−	21.7627i	−0.450744	−	0.797325i
$746$	4.43557	−	20.8677i	0.162398	−	0.764022i
$747$	47.6378	−	8.85312i	1.74298	−	0.323919i
$748$	−2.99916	−	2.17902i	−0.109660	−	0.0796728i
$749$	−15.1551	+	16.7208i	−0.553756	+	0.610965i
$750$	−33.5868	+	3.94855i	−1.22642	+	0.144181i
$751$	−4.87750	−	8.44809i	−0.177983	−	0.308275i	0.763207	−	0.646154i	$-0.223624\pi$
$751$	−4.87750	−	8.44809i	−0.177983	−	0.308275i	−0.941189	+	0.337879i	$0.890290\pi$
$752$	−12.5538	−	28.1963i	−0.457790	−	1.02821i
$753$	−38.1774	+	9.70572i	−1.39126	+	0.353696i
$754$	13.9500	+	12.5607i	0.508030	+	0.457432i
$755$	24.8530	+	14.6510i	0.904492	+	0.533204i
$756$	10.8262	+	9.54329i	0.393745	+	0.347086i
$757$		−	49.6640i		−	1.80507i	−0.430617	−	0.902535i	$-0.641704\pi$
$757$		−	49.6640i		−	1.80507i	0.430617	−	0.902535i	$-0.358296\pi$
$758$	27.0337	−	5.74619i	0.981908	−	0.208711i
$759$	21.8114	−	13.7694i	0.791703	−	0.499797i
$760$	−2.81562	+	24.6373i	−0.102133	+	0.893690i
$761$	4.73283	−	45.0299i	0.171565	−	1.63233i	−0.482501	−	0.875895i	$-0.660272\pi$
$761$	4.73283	−	45.0299i	0.171565	−	1.63233i	0.654066	−	0.756437i	$-0.273062\pi$
$762$	37.0907	+	19.5029i	1.34366	+	0.706514i
$763$	5.23088	−	2.30840i	0.189371	−	0.0835699i
$764$	−1.45885	+	2.00793i	−0.0527792	+	0.0726444i
$765$	5.34127	+	1.94319i	0.193114	+	0.0702562i
$766$	53.6549	−	5.63936i	1.93863	−	0.203758i
$767$	36.5931	+	40.6407i	1.32130	+	1.46745i
$768$	28.0410	+	18.7265i	1.01184	+	0.675735i
$769$	−1.75154	−	0.569110i	−0.0631622	−	0.0205226i	0.277265	−	0.960793i	$-0.410572\pi$
$769$	−1.75154	−	0.569110i	−0.0631622	−	0.0205226i	−0.340428	+	0.940271i	$0.610572\pi$
$770$	−35.1472	+	24.8786i	−1.26662	+	0.896562i
$771$	6.47421	−	6.30997i	0.233163	−	0.227248i
$772$	3.77355	+	3.39772i	0.135813	+	0.122287i
$773$	14.2315	+	31.9644i	0.511871	+	1.14968i	0.965952	+	0.258721i	$0.0833009\pi$
$773$	14.2315	+	31.9644i	0.511871	+	1.14968i	−0.454081	+	0.890960i	$0.650032\pi$
$774$	−34.0215	+	14.1116i	−1.22288	+	0.507230i
$775$	−25.8424	+	22.4334i	−0.928287	+	0.805832i
$776$	−5.52500			−0.198336
$777$	−3.55051	+	0.503792i	−0.127374	+	0.0180734i
$778$	51.9762	−	16.8881i	1.86344	−	0.605467i
$779$	−31.0371	−	27.9459i	−1.11202	−	1.00127i
$780$	13.3709	+	17.2722i	0.478753	+	0.618445i
$781$	−4.76410	−	5.29107i	−0.170473	−	0.189329i
$782$	4.57861	−	2.64346i	0.163731	−	0.0945300i
$783$	5.07325	−	9.07446i	0.181303	−	0.324295i
$784$	34.2652	−	7.04861i	1.22376	−	0.251736i
$785$	14.2030	+	8.37275i	0.506926	+	0.298836i
$786$	−19.6600	−	53.2509i	−0.701249	−	1.89940i
$787$	4.28532	+	40.7721i	0.152755	+	1.45337i	0.755351	+	0.655321i	$0.227467\pi$
$787$	4.28532	+	40.7721i	0.152755	+	1.45337i	−0.602595	+	0.798047i	$0.705867\pi$
$788$	−1.10721	−	10.5344i	−0.0394426	−	0.375272i
$789$	7.49411	+	20.2985i	0.266797	+	0.722644i
$790$	−32.2652	+	28.5262i	−1.14795	+	1.01492i
$791$	−11.6271	−	8.50603i	−0.413413	−	0.302440i
$792$	17.0943	−	11.7608i	0.607419	−	0.417903i
$793$	−59.7145	+	34.4762i	−2.12052	+	1.22429i
$794$	4.56739	+	5.07260i	0.162091	+	0.180020i
$795$	−0.846006	−	27.7803i	−0.0300047	−	0.985267i
$796$	13.3264	+	11.9992i	0.472343	+	0.425299i
$797$	−14.3523	+	4.66334i	−0.508383	+	0.165184i	−0.551967	−	0.833866i	$-0.686123\pi$
$797$	−14.3523	+	4.66334i	−0.508383	+	0.165184i	0.0435835	+	0.999050i	$0.486123\pi$
$798$	32.9826	+	42.1006i	1.16757	+	1.49035i
$799$	−5.23283			−0.185124
$800$	−13.9440	+	23.1708i	−0.492995	+	0.819210i
$801$	−11.1355	−	26.8465i	−0.393453	−	0.948575i
$802$	2.86124	+	6.42645i	0.101034	+	0.226926i
$803$	24.3980	+	21.9681i	0.860988	+	0.775237i
$804$	−6.33585	+	6.17511i	−0.223448	+	0.217779i
$805$	−4.13925	−	20.7293i	−0.145889	−	0.730610i
$806$	61.0709	+	19.8431i	2.15113	+	0.698945i
$807$	15.8900	+	10.6118i	0.559354	+	0.373551i
$808$	−9.46270	−	10.5094i	−0.332897	−	0.369719i
$809$	−48.5755	+	5.10549i	−1.70782	+	0.179499i	−0.907495	−	0.420063i	$-0.862008\pi$
$809$	−48.5755	+	5.10549i	−1.70782	+	0.179499i	−0.800328	+	0.599562i	$0.795341\pi$
$810$	22.3377	−	27.1327i	0.784868	−	0.953345i
$811$	−8.29445	+	11.4163i	−0.291258	+	0.400882i	−0.929422	−	0.369018i	$-0.879694\pi$
$811$	−8.29445	+	11.4163i	−0.291258	+	0.400882i	0.638165	+	0.769900i	$0.279694\pi$
$812$	2.24357	+	5.08397i	0.0787339	+	0.178412i
$813$	40.4083	+	21.2473i	1.41718	+	0.745176i
$814$	0.595383	−	5.66469i	0.0208682	−	0.198547i
$815$	−23.2278	−	10.5951i	−0.813633	−	0.371131i
$816$	6.20167	−	3.91507i	0.217102	−	0.137055i
$817$	−45.9557	+	9.76819i	−1.60779	+	0.341746i
$818$		−	0.734149i		−	0.0256689i
$819$	−42.2617	−	5.68405i	−1.47674	−	0.198617i
$820$	−5.84494	−	13.4550i	−0.204114	−	0.469870i
$821$	20.8018	+	18.7300i	0.725987	+	0.653681i	0.946869	−	0.321619i	$-0.104227\pi$
$821$	20.8018	+	18.7300i	0.725987	+	0.653681i	−0.220883	+	0.975300i	$0.570894\pi$
$822$	26.9210	−	6.84403i	0.938977	−	0.238713i
$823$	−6.44266	−	14.4705i	−0.224577	−	0.504408i	0.765754	−	0.643134i	$-0.222366\pi$
$823$	−6.44266	−	14.4705i	−0.224577	−	0.504408i	−0.990331	+	0.138726i	$0.955699\pi$
$824$	3.30287	+	5.72074i	0.115061	+	0.199291i
$825$	21.8355	+	28.7415i	0.760215	+	1.00065i
$826$	14.3871	+	44.7783i	0.500591	+	1.55804i
$827$	−34.9918	−	25.4230i	−1.21678	−	0.884046i	−0.220955	−	0.975284i	$-0.570918\pi$
$827$	−34.9918	−	25.4230i	−1.21678	−	0.884046i	−0.995829	+	0.0912382i	$0.970918\pi$
$828$	−2.05602	−	11.0632i	−0.0714515	−	0.384474i
$829$	7.65493	−	36.0136i	0.265867	−	1.25080i	−0.619160	−	0.785265i	$-0.712527\pi$
$829$	7.65493	−	36.0136i	0.265867	−	1.25080i	0.885027	−	0.465540i	$-0.154140\pi$
$830$	57.3822	+	26.1743i	1.99177	+	0.908524i
$831$	13.2469	+	16.7952i	0.459530	+	0.582619i
$832$	−2.95333			−0.102388
$833$	1.27116	−	5.79317i	0.0440432	−	0.200721i
$834$	33.0845	+	17.3963i	1.14562	+	0.602386i
$835$	4.81155	−	14.3639i	0.166511	−	0.497082i
$836$	−26.7120	+	11.8930i	−0.923855	+	0.411327i
$837$	3.22829	−	35.4169i	0.111586	−	1.22419i
$838$	−30.8164	−	13.7204i	−1.06454	−	0.473962i
$839$	−25.4604	−	18.4981i	−0.878990	−	0.638624i	0.0539939	−	0.998541i	$-0.482805\pi$
$839$	−25.4604	−	18.4981i	−0.878990	−	0.638624i	−0.932984	+	0.359917i	$0.882805\pi$
$840$	−3.98581	−	16.5305i	−0.137524	−	0.570356i
$841$	−20.2229	+	14.6928i	−0.697342	+	0.506649i
$842$	37.9847	−	8.07390i	1.30904	−	0.278245i
$843$	−15.7483	−	1.02835i	−0.542400	−	0.0354183i
$844$	−5.15408	−	5.72419i	−0.177411	−	0.197035i
$845$	−33.6336	−	11.2665i	−1.15703	−	0.387578i
$846$	−10.7860	+	30.5059i	−0.370830	+	1.04881i
$847$	15.3775	+	6.90703i	0.528376	+	0.237328i
$848$	−29.0139	−	21.0798i	−0.996340	−	0.723883i
$849$	5.56527	+	3.71663i	0.190999	+	0.127555i
$850$	4.23935	+	6.06325i	0.145408	+	0.207968i
$851$	2.42148	+	1.39804i	0.0830071	+	0.0479242i
$852$	−2.91379	+	1.07576i	−0.0998248	+	0.0368549i
$853$	−3.25517	−	10.0184i	−0.111455	−	0.343023i	0.879736	−	0.475462i	$-0.157719\pi$
$853$	−3.25517	−	10.0184i	−0.111455	−	0.343023i	−0.991191	+	0.132439i	$0.957719\pi$
$854$	−58.9962	+	6.00511i	−2.01881	+	0.205491i
$855$	34.3377	−	28.8212i	1.17433	−	0.985664i
$856$	13.8449	−	2.94282i	0.473208	−	0.100583i
$857$	27.6315	+	15.9531i	0.943874	+	0.544946i	0.891173	−	0.453664i	$-0.149884\pi$
$857$	27.6315	+	15.9531i	0.943874	+	0.544946i	0.0527013	+	0.998610i	$0.483217\pi$
$858$	25.0826	−	62.9146i	0.856307	−	2.14787i
$859$	−16.6974	+	37.5029i	−0.569706	+	1.27958i	0.367246	+	0.930124i	$0.380301\pi$
$859$	−16.6974	+	37.5029i	−0.569706	+	1.27958i	−0.936952	+	0.349458i	$0.886366\pi$
$860$	−16.1101	−	3.57732i	−0.549351	−	0.121986i
$861$	26.5675	+	10.6930i	0.905419	+	0.364418i
$862$	33.0199	+	45.4479i	1.12466	+	1.54796i
$863$	−1.98307	−	0.882921i	−0.0675046	−	0.0300550i	0.372707	−	0.927949i	$-0.378430\pi$
$863$	−1.98307	−	0.882921i	−0.0675046	−	0.0300550i	−0.440211	+	0.897894i	$0.645096\pi$
$864$	−6.22244	−	27.4063i	−0.211692	−	0.932381i
$865$	−2.18562	+	19.1247i	−0.0743134	+	0.650260i
$866$	−14.1447	−	6.29762i	−0.480656	−	0.214002i
$867$	4.05349	+	27.9086i	0.137664	+	0.947826i
$868$	14.0849	+	12.7660i	0.478073	+	0.433307i
$869$	43.7174	+	14.2046i	1.48301	+	0.481859i
$870$	12.1893	−	5.87791i	0.413255	−	0.199280i
$871$	5.43507	−	25.5700i	0.184160	−	0.866407i
$872$	−3.50777	−	0.745600i	−0.118788	−	0.0252492i
$873$	7.24859	+	6.87196i	0.245328	+	0.232581i
$874$		−	41.7001i		−	1.41053i
$875$	28.3982	−	8.27901i	0.960034	−	0.279882i
$876$	12.8439	−	6.33778i	0.433954	−	0.214134i
$877$	−11.8511	−	1.24560i	−0.400182	−	0.0420609i	−0.0977001	−	0.995216i	$-0.531149\pi$
$877$	−11.8511	−	1.24560i	−0.400182	−	0.0420609i	−0.302482	+	0.953155i	$0.597815\pi$
$878$	−8.30325	+	39.0637i	−0.280221	+	1.31834i
$879$	6.47407	+	25.4658i	0.218365	+	0.858939i
$880$	46.5737	+	0.422394i	1.57000	+	0.0142389i
$881$	7.20340	−	22.1698i	0.242689	−	0.746920i	−0.753319	−	0.657655i	$-0.771548\pi$
$881$	7.20340	−	22.1698i	0.242689	−	0.746920i	0.996008	−	0.0892644i	$-0.0284516\pi$
$882$	−31.1523	−	19.3515i	−1.04895	−	0.651599i
$883$	9.05989	+	2.94374i	0.304890	+	0.0990646i	0.457466	−	0.889227i	$-0.348757\pi$
$883$	9.05989	+	2.94374i	0.304890	+	0.0990646i	−0.152577	+	0.988292i	$0.548757\pi$
$884$	1.94360	−	4.36539i	0.0653703	−	0.146824i
$885$	37.1065	−	13.3184i	1.24732	−	0.447695i
$886$	−2.42875	+	1.08135i	−0.0815954	+	0.0363286i
$887$	13.0297	−	29.2653i	0.437496	−	0.982632i	−0.551430	−	0.834221i	$-0.685917\pi$
$887$	13.0297	−	29.2653i	0.437496	−	0.982632i	0.988926	−	0.148411i	$-0.0474158\pi$
$888$	1.99079	+	1.04679i	0.0668066	+	0.0351279i
$889$	−34.8232	−	11.4412i	−1.16793	−	0.383725i
$890$	8.20095	−	36.9323i	0.274897	−	1.23797i
$891$	−37.0551	−	5.83200i	−1.24139	−	0.195379i
$892$	−13.7320	−	15.2509i	−0.459782	−	0.510639i
$893$	−20.6368	+	35.7439i	−0.690583	+	1.19612i
$894$	20.9427	+	26.5524i	0.700428	+	0.888044i
$895$	23.2844	+	5.17039i	0.778312	+	0.172827i
$896$	−28.4239	−	12.7670i	−0.949575	−	0.426516i
$897$	23.2062	+	23.8102i	0.774832	+	0.795000i
$898$	55.5786	+	5.84155i	1.85468	+	0.194935i
$899$	6.84689	−	11.8592i	0.228356	−	0.395525i
$900$	15.1747	−	4.20507i	0.505823	−	0.140169i
$901$	−5.26566	+	3.04013i	−0.175425	+	0.101282i
$902$	−26.7371	+	36.8005i	−0.890249	+	1.22532i
$903$	27.2987	−	17.1085i	0.908443	−	0.569334i
$904$	2.79222	+	8.59357i	0.0928679	+	0.285818i
$905$	2.71417	−	8.10258i	0.0902221	−	0.269339i
$906$	−36.2513	−	14.4526i	−1.20437	−	0.480155i
$907$	6.38278	+	3.68510i	0.211937	+	0.122362i	0.602211	−	0.798337i	$-0.294287\pi$
$907$	6.38278	+	3.68510i	0.211937	+	0.122362i	−0.390274	+	0.920699i	$0.627620\pi$
$908$	2.20355	+	10.3669i	0.0731273	+	0.344037i
$909$	−0.656808	+	25.5576i	−0.0217849	+	0.847691i
$910$	−40.7869	−	37.6471i	−1.35207	−	1.24799i
$911$	21.2048	−	29.1859i	0.702546	−	0.966971i	−0.297380	−	0.954759i	$-0.596113\pi$
$911$	21.2048	−	29.1859i	0.702546	−	0.966971i	0.999925	−	0.0122120i	$-0.00388729\pi$
$912$	−2.28511	−	57.8016i	−0.0756676	−	1.91400i
$913$	−7.03651	−	66.9479i	−0.232874	−	2.21565i
$914$	−9.71492	−	21.8201i	−0.321341	−	0.721744i
$915$	6.69827	+	49.2545i	0.221438	+	1.62830i
$916$	8.61933	+	11.8635i	0.284791	+	0.391981i
$917$	24.6843	+	43.0804i	0.815149	+	1.42264i
$918$	−7.54192	−	1.49446i	−0.248920	−	0.0493245i
$919$	52.1400	−	11.0827i	1.71994	−	0.365584i	0.760903	−	0.648866i	$-0.224756\pi$
$919$	52.1400	−	11.0827i	1.71994	−	0.365584i	0.959037	+	0.283282i	$0.0914231\pi$
$920$	−5.50225	+	12.0626i	−0.181404	+	0.397694i
$921$	49.1701	−	12.5003i	1.62021	−	0.411900i
$922$	29.5016	−	32.7649i	0.971584	−	1.07905i
$923$	5.39435	−	7.42469i	0.177557	−	0.244387i
$924$	14.4046	−	13.9473i	0.473875	−	0.458831i
$925$	−1.65602	+	3.54500i	−0.0544496	+	0.116559i
$926$	−36.7760	+	21.2327i	−1.20854	+	0.697748i
$927$	2.78218	−	11.6135i	0.0913787	−	0.381437i
$928$	2.24989	−	10.5849i	0.0738561	−	0.347466i
$929$	4.05214	−	4.50036i	0.132946	−	0.147652i	−0.672995	−	0.739647i	$-0.734993\pi$
$929$	4.05214	−	4.50036i	0.132946	−	0.147652i	0.805942	+	0.591995i	$0.201659\pi$
$930$	29.9137	−	35.3284i	0.980910	−	1.15846i
$931$	−34.5583	−	31.5295i	−1.13260	−	1.03334i
$932$	3.36181			0.110120
$933$	−19.4240	+	15.3203i	−0.635914	+	0.501565i
$934$	−54.5691	+	5.73544i	−1.78555	+	0.187669i
$935$	3.27708	−	7.18437i	0.107172	−	0.234954i
$936$	19.4096	+	18.4011i	0.634422	+	0.601458i
$937$	7.53360	−	5.47348i	0.246112	−	0.178811i	−0.457890	−	0.889009i	$-0.651395\pi$
$937$	7.53360	−	5.47348i	0.246112	−	0.178811i	0.704002	+	0.710198i	$0.251395\pi$
$938$	13.2743	−	18.1451i	0.433422	−	0.592457i
$939$	−58.6468	−	10.0627i	−1.91387	−	0.328383i
$940$	−11.8053	+	8.41457i	−0.385048	+	0.274453i
$941$	−1.32777	−	12.6329i	−0.0432842	−	0.411822i	−0.994614	−	0.103647i	$-0.966949\pi$
$941$	−1.32777	−	12.6329i	−0.0432842	−	0.411822i	0.951330	−	0.308174i	$-0.0997180\pi$
$942$	−20.7169	−	8.25936i	−0.674993	−	0.269105i
$943$	−11.1649	−	19.3381i	−0.363578	−	0.629736i
$944$	15.7201	−	48.3815i	0.511646	−	1.57468i
$945$	−15.3313	+	26.6449i	−0.498727	+	0.866759i
$946$	15.8127	+	48.6665i	0.514116	+	1.58228i
$947$	8.67218	−	9.63144i	0.281808	−	0.312980i	−0.585577	−	0.810617i	$-0.699132\pi$
$947$	8.67218	−	9.63144i	0.281808	−	0.312980i	0.867385	+	0.497637i	$0.165799\pi$
$948$	12.8190	−	15.4208i	0.416343	−	0.500846i
$949$	−21.1593	+	36.6490i	−0.686861	+	1.18968i
$950$	58.1350	−	5.04603i	1.88615	−	0.163715i
$951$	−27.0151	+	13.3306i	−0.876026	+	0.432273i
$952$	−2.77264	+	2.48007i	−0.0898617	+	0.0803796i
$953$	4.95321	+	15.2444i	0.160450	+	0.493815i	0.998672	−	0.0515139i	$-0.0164047\pi$
$953$	4.95321	+	15.2444i	0.160450	+	0.493815i	−0.838222	+	0.545329i	$0.816405\pi$
$954$	6.86941	+	36.9636i	0.222405	+	1.19674i
$955$	−4.80991	−	2.19399i	−0.155645	−	0.0709960i
$956$	4.86343	−	4.37905i	0.157295	−	0.141629i
$957$	−12.0114	−	8.02156i	−0.388274	−	0.259300i
$958$	−12.5229	+	38.5415i	−0.404597	+	1.24522i
$959$	−22.2283	+	9.80944i	−0.717791	+	0.316763i
$960$	−0.806362	+	1.97045i	−0.0260252	+	0.0635961i
$961$	1.65610	−	15.7567i	0.0534226	−	0.508282i
$962$	7.30176	−	0.767445i	0.235418	−	0.0247434i
$963$	−21.8242	−	13.3593i	−0.703275	−	0.430497i
$964$	1.86647	+	0.196173i	0.0601148	+	0.00631832i
$965$	−5.49275	+	9.31753i	−0.176818	+	0.299942i
$966$	9.81552	+	26.8571i	0.315809	+	0.864113i
$967$	−14.6793	−	4.76960i	−0.472055	−	0.153380i	0.0633222	−	0.997993i	$-0.479830\pi$
$967$	−14.6793	−	4.76960i	−0.472055	−	0.153380i	−0.535377	+	0.844613i	$0.679830\pi$
$968$	−5.28659	−	9.15664i	−0.169917	−	0.294305i
$969$	−9.11009	−	3.63199i	−0.292658	−	0.116676i
$970$	2.58769	+	12.7412i	0.0830857	+	0.409096i
$971$	−0.493345	+	0.547915i	−0.0158322	+	0.0175834i	−0.751009	−	0.660292i	$-0.770432\pi$
$971$	−0.493345	+	0.547915i	−0.0158322	+	0.0175834i	0.735177	+	0.677875i	$0.237099\pi$
$972$	−8.34984	+	14.0737i	−0.267821	+	0.451415i
$973$	−31.0619	−	10.2054i	−0.995798	−	0.327170i
$974$		−	16.4206i		−	0.526150i
$975$	−30.3862	+	35.2334i	−0.973137	+	1.12837i
$976$	55.5476	+	32.0704i	1.77803	+	1.02655i
$977$	6.24648	−	2.78111i	0.199842	−	0.0889756i	−0.304375	−	0.952552i	$-0.598448\pi$
$977$	6.24648	−	2.78111i	0.199842	−	0.0889756i	0.504218	+	0.863577i	$0.331781\pi$
$978$	33.2408	+	9.36616i	1.06292	+	0.299497i
$979$	−38.4029	+	12.4779i	−1.22736	+	0.398794i
$980$	−6.44785	−	15.1135i	−0.205969	−	0.482784i
$981$	3.67469	+	5.34114i	0.117324	+	0.170529i
$982$	−8.88590	+	5.13028i	−0.283560	+	0.163714i
$983$	−21.1325	+	19.0278i	−0.674023	+	0.606893i	−0.933380	−	0.358889i	$-0.883156\pi$
$983$	−21.1325	+	19.0278i	−0.674023	+	0.606893i	0.259358	+	0.965781i	$0.416489\pi$
$984$	−9.58875	−	15.1891i	−0.305678	−	0.484209i
$985$	21.5205	−	6.77728i	0.685700	−	0.215942i
$986$	−2.39507	−	1.74012i	−0.0762747	−	0.0554168i
$987$	4.87764	−	27.8785i	0.155257	−	0.887383i
$988$	−22.1537	−	30.4919i	−0.704803	−	0.970078i
$989$	−24.9819	−	2.62571i	−0.794379	−	0.0834926i
$990$	−35.1280	−	33.9129i	−1.11644	−	1.07782i
$991$	0.512569	+	4.87677i	0.0162823	+	0.154916i	0.999642	−	0.0267531i	$-0.00851680\pi$
$991$	0.512569	+	4.87677i	0.0162823	+	0.154916i	−0.983360	+	0.181669i	$0.941850\pi$
$992$	−7.69639	−	36.2087i	−0.244361	−	1.14963i
$993$	−32.9105	+	16.2396i	−1.04438	+	0.515348i
$994$	6.84832	−	3.92398i	0.217215	−	0.124461i
$995$	−19.3978	+	32.9052i	−0.614952	+	1.04316i
$996$	−28.2663	−	7.96449i	−0.895651	−	0.252365i
$997$	−14.7865	−	3.14297i	−0.468294	−	0.0995389i	−0.0322800	−	0.999479i	$-0.510277\pi$
$997$	−14.7865	−	3.14297i	−0.468294	−	0.0995389i	−0.436014	+	0.899940i	$0.643610\pi$
$998$	37.4207	−	16.6608i	1.18453	−	0.527388i
$999$	−1.30985	−	3.84948i	−0.0414420	−	0.121792i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bp.a.59.16	✓	608
3.2	odd	2	inner	525.2.bp.a.59.61	yes	608
7.5	odd	6	inner	525.2.bp.a.509.61	yes	608
21.5	even	6	inner	525.2.bp.a.509.16	yes	608
25.14	even	10	inner	525.2.bp.a.164.16	yes	608
75.14	odd	10	inner	525.2.bp.a.164.61	yes	608
175.89	odd	30	inner	525.2.bp.a.89.61	yes	608
525.89	even	30	inner	525.2.bp.a.89.16	yes	608

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bp.a.59.16	✓	608	1.1	even	1	trivial
525.2.bp.a.59.61	yes	608	3.2	odd	2	inner
525.2.bp.a.89.16	yes	608	525.89	even	30	inner
525.2.bp.a.89.61	yes	608	175.89	odd	30	inner
525.2.bp.a.164.16	yes	608	25.14	even	10	inner
525.2.bp.a.164.61	yes	608	75.14	odd	10	inner
525.2.bp.a.509.16	yes	608	21.5	even	6	inner
525.2.bp.a.509.61	yes	608	7.5	odd	6	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bp (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.182544 + 1.73679i) q^{2} +(1.67865 - 0.426758i) q^{3} +(-1.02683 - 0.218259i) q^{4} +(0.0202789 - 2.23598i) q^{5} +(0.434762 + 2.99337i) q^{6} +(-0.809322 - 2.51893i) q^{7} +(-0.512796 + 1.57822i) q^{8} +(2.63575 - 1.43276i) q^{9} +O(q^{10})\)	\(q+(-0.182544 + 1.73679i) q^{2} +(1.67865 - 0.426758i) q^{3} +(-1.02683 - 0.218259i) q^{4} +(0.0202789 - 2.23598i) q^{5} +(0.434762 + 2.99337i) q^{6} +(-0.809322 - 2.51893i) q^{7} +(-0.512796 + 1.57822i) q^{8} +(2.63575 - 1.43276i) q^{9} +(3.87972 + 0.443385i) q^{10} +(-1.69524 - 3.80758i) q^{11} +(-1.81683 + 0.0718262i) q^{12} +(4.34638 - 3.15783i) q^{13} +(4.52259 - 0.945808i) q^{14} +(-0.920180 - 3.76208i) q^{15} +(-4.56546 - 2.03268i) q^{16} +(-0.629655 + 0.566944i) q^{17} +(2.00726 + 4.83930i) q^{18} +(1.38945 + 6.53684i) q^{19} +(-0.508846 + 2.29154i) q^{20} +(-2.43354 - 3.88302i) q^{21} +(6.92243 - 2.24923i) q^{22} +(-0.373486 + 3.55348i) q^{23} +(-0.187287 + 2.86813i) q^{24} +(-4.99918 - 0.0906862i) q^{25} +(4.69108 + 8.12520i) q^{26} +(3.81308 - 3.52994i) q^{27} +(0.281256 + 2.76315i) q^{28} +(1.90285 - 0.618273i) q^{29} +(6.70193 - 0.911415i) q^{30} +(5.08626 - 4.57969i) q^{31} +(2.70429 - 4.68397i) q^{32} +(-4.47064 - 5.66815i) q^{33} +(-0.869724 - 1.19707i) q^{34} +(-5.64867 + 1.75854i) q^{35} +(-3.01918 + 0.895921i) q^{36} +(0.318290 - 0.714891i) q^{37} +(-11.6068 + 1.21992i) q^{38} +(5.94843 - 7.15575i) q^{39} +(3.51847 + 1.17860i) q^{40} +(-5.05593 + 3.67335i) q^{41} +(7.18823 - 3.51774i) q^{42} +7.03026i q^{43} +(0.909686 + 4.27974i) q^{44} +(-3.15016 - 5.92254i) q^{45} +(-6.10348 - 1.29734i) q^{46} +(4.58966 + 4.13255i) q^{47} +(-8.53129 - 1.46381i) q^{48} +(-5.69000 + 4.07725i) q^{49} +(1.07007 - 8.66598i) q^{50} +(-0.815025 + 1.22041i) q^{51} +(-5.15221 + 2.29391i) q^{52} +(7.01936 + 1.49201i) q^{53} +(5.43471 + 7.26689i) q^{54} +(-8.54804 + 3.71331i) q^{55} +(4.39045 + 0.0144049i) q^{56} +(5.12206 + 10.3801i) q^{57} +(0.726458 + 3.41772i) q^{58} +(1.06403 + 10.1235i) q^{59} +(0.123758 + 4.06386i) q^{60} +(-12.7642 - 1.34157i) q^{61} +(7.02550 + 9.66977i) q^{62} +(-5.74219 - 5.47971i) q^{63} +(-0.444734 - 0.323118i) q^{64} +(-6.97269 - 9.78243i) q^{65} +(10.6605 - 6.72989i) q^{66} +(3.61602 - 3.25588i) q^{67} +(0.770290 - 0.444727i) q^{68} +(0.889525 + 6.12445i) q^{69} +(-2.02309 - 10.1316i) q^{70} +(1.62464 - 0.527878i) q^{71} +(0.909610 + 4.89453i) q^{72} +(-7.19602 + 3.20388i) q^{73} +(1.18352 + 0.683303i) q^{74} +(-8.43059 + 1.98121i) q^{75} -7.01549i q^{76} +(-8.21902 + 7.35176i) q^{77} +(11.3422 + 11.6374i) q^{78} +(-7.37971 + 8.19600i) q^{79} +(-4.63760 + 10.1670i) q^{80} +(4.89441 - 7.55280i) q^{81} +(-5.45692 - 9.45165i) q^{82} +(15.3607 + 4.99098i) q^{83} +(1.65133 + 4.51835i) q^{84} +(1.25491 + 1.41939i) q^{85} +(-12.2101 - 1.28333i) q^{86} +(2.93037 - 1.84992i) q^{87} +(6.87853 - 0.722963i) q^{88} +(1.01268 - 9.63503i) q^{89} +(10.8613 - 4.39005i) q^{90} +(-11.4720 - 8.39251i) q^{91} +(1.15909 - 3.56730i) q^{92} +(6.58364 - 9.85831i) q^{93} +(-8.01520 + 7.21692i) q^{94} +(14.6444 - 2.97422i) q^{95} +(2.54064 - 9.01684i) q^{96} +(1.02885 + 3.16648i) q^{97} +(-6.04266 - 10.6266i) q^{98} +(-9.92359 - 7.60697i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9}+O(q^{10}) \) 608 * q - 15 * q^3 + 66 * q^4 - 3 * q^9	\( 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9} - 30 q^{10} - 15 q^{12} - 36 q^{15} + 66 q^{16} - 18 q^{19} + 9 q^{21} - 80 q^{22} - 30 q^{24} + 2 q^{25} - 90 q^{28} - 23 q^{30} - 90 q^{33} + 44 q^{36} - 10 q^{37} - 19 q^{39} + 42 q^{40} - 70 q^{42} - 117 q^{45} - 54 q^{46} - 28 q^{49} - 8 q^{51} - 30 q^{52} - 21 q^{54} + 50 q^{58} - 67 q^{60} - 18 q^{61} - 70 q^{63} - 176 q^{64} + 57 q^{66} - 10 q^{67} + 42 q^{70} - 45 q^{72} - 150 q^{73} + 33 q^{75} + 10 q^{78} - 34 q^{79} + 49 q^{81} - 53 q^{84} - 8 q^{85} - 15 q^{87} + 80 q^{88} - 62 q^{91} + 30 q^{94} - 9 q^{96} + 36 q^{99}+O(q^{100}) \) 608 * q - 15 * q^3 + 66 * q^4 - 3 * q^9 - 30 * q^10 - 15 * q^12 - 36 * q^15 + 66 * q^16 - 18 * q^19 + 9 * q^21 - 80 * q^22 - 30 * q^24 + 2 * q^25 - 90 * q^28 - 23 * q^30 - 90 * q^33 + 44 * q^36 - 10 * q^37 - 19 * q^39 + 42 * q^40 - 70 * q^42 - 117 * q^45 - 54 * q^46 - 28 * q^49 - 8 * q^51 - 30 * q^52 - 21 * q^54 + 50 * q^58 - 67 * q^60 - 18 * q^61 - 70 * q^63 - 176 * q^64 + 57 * q^66 - 10 * q^67 + 42 * q^70 - 45 * q^72 - 150 * q^73 + 33 * q^75 + 10 * q^78 - 34 * q^79 + 49 * q^81 - 53 * q^84 - 8 * q^85 - 15 * q^87 + 80 * q^88 - 62 * q^91 + 30 * q^94 - 9 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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