LMFDB - Embedded newform 175.2.x.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			3.1
Character	$\chi$	$=$	175.3
Dual form			175.2.x.a.117.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36631 + 2.10393i) q^{2} +(0.553395 - 1.44164i) q^{3} +(-1.74625 - 3.92214i) q^{4} +(0.644473 + 2.14118i) q^{5} +(2.27701 + 3.13403i) q^{6} +(0.377880 - 2.61863i) q^{7} +(5.68228 + 0.899985i) q^{8} +(0.457347 + 0.411797i) q^{9} +O(q^{10})$	\(q+(-1.36631 + 2.10393i) q^{2} +(0.553395 - 1.44164i) q^{3} +(-1.74625 - 3.92214i) q^{4} +(0.644473 + 2.14118i) q^{5} +(2.27701 + 3.13403i) q^{6} +(0.377880 - 2.61863i) q^{7} +(5.68228 + 0.899985i) q^{8} +(0.457347 + 0.411797i) q^{9} +(-5.38544 - 1.56958i) q^{10} +(3.53627 + 3.92742i) q^{11} +(-6.62068 + 0.346975i) q^{12} +(2.31369 + 1.17888i) q^{13} +(4.99310 + 4.37288i) q^{14} +(3.44346 + 0.255818i) q^{15} +(-3.91167 + 4.34435i) q^{16} +(-0.724344 + 0.894491i) q^{17} +(-1.49127 + 0.399585i) q^{18} +(1.19398 + 0.531592i) q^{19} +(7.27259 - 6.26674i) q^{20} +(-3.56601 - 1.99390i) q^{21} +(-13.0946 + 2.07399i) q^{22} +(-7.26201 - 4.71601i) q^{23} +(4.44200 - 7.69377i) q^{24} +(-4.16931 + 2.75987i) q^{25} +(-5.64150 + 3.25712i) q^{26} +(4.97446 - 2.53461i) q^{27} +(-10.9305 + 3.09067i) q^{28} +(1.59083 - 2.18958i) q^{29} +(-5.24305 + 6.89528i) q^{30} +(5.93147 - 0.623423i) q^{31} +(-0.817633 - 3.05145i) q^{32} +(7.61889 - 2.92462i) q^{33} +(-0.892268 - 2.74612i) q^{34} +(5.85049 - 0.878526i) q^{35} +(0.816484 - 2.51288i) q^{36} +(0.168662 + 3.21827i) q^{37} +(-2.74977 + 1.78572i) q^{38} +(2.97991 - 2.68312i) q^{39} +(1.73505 + 12.7468i) q^{40} +(-6.10496 + 1.98362i) q^{41} +(9.06729 - 4.77834i) q^{42} +(-3.37188 - 3.37188i) q^{43} +(9.22869 - 20.7280i) q^{44} +(-0.586984 + 1.24466i) q^{45} +(19.8443 - 8.83524i) q^{46} +(5.54276 - 4.48844i) q^{47} +(4.09831 + 8.04338i) q^{48} +(-6.71441 - 1.97905i) q^{49} +(-0.110010 - 12.5428i) q^{50} +(0.888688 + 1.53925i) q^{51} +(0.583468 - 11.1332i) q^{52} +(-3.18623 - 1.22308i) q^{53} +(-1.46399 + 13.9290i) q^{54} +(-6.13029 + 10.1029i) q^{55} +(4.50395 - 14.5397i) q^{56} +(1.42711 - 1.42711i) q^{57} +(2.43317 + 6.33863i) q^{58} +(1.72149 + 0.365913i) q^{59} +(-5.00979 - 13.9525i) q^{60} +(-0.868947 - 4.08807i) q^{61} +(-6.79258 + 13.3312i) q^{62} +(1.25117 - 1.04201i) q^{63} +(-3.58241 - 1.16399i) q^{64} +(-1.03309 + 5.71379i) q^{65} +(-4.25656 + 20.0255i) q^{66} +(-0.187687 - 0.151986i) q^{67} +(4.77320 + 1.27897i) q^{68} +(-10.8176 + 7.85941i) q^{69} +(-6.14521 + 13.5093i) q^{70} +(-8.50997 - 6.18285i) q^{71} +(2.22817 + 2.75155i) q^{72} +(-12.3451 - 0.646980i) q^{73} +(-7.00145 - 4.04229i) q^{74} +(1.67147 + 7.53795i) q^{75} -5.61123i q^{76} +(11.6207 - 7.77607i) q^{77} +(1.57363 + 9.93549i) q^{78} +(-4.60244 - 0.483736i) q^{79} +(-11.8230 - 5.57578i) q^{80} +(-0.708179 - 6.73788i) q^{81} +(4.16785 - 15.5546i) q^{82} +(-1.46786 + 9.26772i) q^{83} +(-1.59323 + 17.4682i) q^{84} +(-2.38209 - 0.974476i) q^{85} +(11.7012 - 2.48717i) q^{86} +(-2.27624 - 3.50510i) q^{87} +(16.5594 + 25.4993i) q^{88} +(-4.40130 + 0.935526i) q^{89} +(-1.81667 - 2.93556i) q^{90} +(3.96135 - 5.61321i) q^{91} +(-5.81555 + 36.7179i) q^{92} +(2.38369 - 8.89606i) q^{93} +(1.87024 + 17.7942i) q^{94} +(-0.368749 + 2.89912i) q^{95} +(-4.85157 - 0.509920i) q^{96} +(-1.20511 - 7.60880i) q^{97} +(13.3377 - 11.4227i) q^{98} +3.25242i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−1.36631	+	2.10393i	−0.966125	+	1.48770i	−0.0956948	+	0.995411i	$0.530507\pi$
$2$	−1.36631	+	2.10393i	−0.966125	+	1.48770i	−0.870430	+	0.492292i	$0.836159\pi$
$3$	0.553395	−	1.44164i	0.319503	−	0.832333i	−0.675939	−	0.736958i	$-0.736262\pi$
$3$	0.553395	−	1.44164i	0.319503	−	0.832333i	0.995441	−	0.0953749i	$-0.0304050\pi$
$4$	−1.74625	−	3.92214i	−0.873124	−	1.96107i
$5$	0.644473	+	2.14118i	0.288217	+	0.957565i
$5$	0.644473	+	2.14118i	0.288217	+	0.957565i
$6$	2.27701	+	3.13403i	0.929584	+	1.27946i
$7$	0.377880	−	2.61863i	0.142825	−	0.989748i
$7$	0.377880	−	2.61863i	0.142825	−	0.989748i
$8$	5.68228	+	0.899985i	2.00899	+	0.318193i
$9$	0.457347	+	0.411797i	0.152449	+	0.137266i
$10$	−5.38544	−	1.56958i	−1.70303	−	0.496346i
$11$	3.53627	+	3.92742i	1.06622	+	1.18416i	0.982227	+	0.187697i	$0.0601022\pi$
$11$	3.53627	+	3.92742i	1.06622	+	1.18416i	0.0839979	+	0.996466i	$0.473231\pi$
$12$	−6.62068	+	0.346975i	−1.91123	+	0.100163i
$13$	2.31369	+	1.17888i	0.641702	+	0.326963i	0.744385	−	0.667751i	$-0.232743\pi$
$13$	2.31369	+	1.17888i	0.641702	+	0.326963i	−0.102683	+	0.994714i	$0.532743\pi$
$14$	4.99310	+	4.37288i	1.33446	+	1.16870i
$15$	3.44346	+	0.255818i	0.889099	+	0.0660518i
$16$	−3.91167	+	4.34435i	−0.977918	+	1.08609i
$17$	−0.724344	+	0.894491i	−0.175679	+	0.216946i	−0.857378	−	0.514687i	$-0.827908\pi$
$17$	−0.724344	+	0.894491i	−0.175679	+	0.216946i	0.681699	+	0.731633i	$0.261241\pi$
$18$	−1.49127	+	0.399585i	−0.351496	+	0.0941830i
$19$	1.19398	+	0.531592i	0.273917	+	0.121956i	0.539098	−	0.842243i	$-0.318765\pi$
$19$	1.19398	+	0.531592i	0.273917	+	0.121956i	−0.265181	+	0.964199i	$0.585432\pi$
$20$	7.27259	−	6.26674i	1.62620	−	1.40129i
$21$	−3.56601	−	1.99390i	−0.778166	−	0.435105i
$22$	−13.0946	+	2.07399i	−2.79179	+	0.442176i
$23$	−7.26201	−	4.71601i	−1.51423	−	0.983355i	−0.991392	−	0.130925i	$-0.958205\pi$
$23$	−7.26201	−	4.71601i	−1.51423	−	0.983355i	−0.522842	−	0.852430i	$-0.675128\pi$
$24$	4.44200	−	7.69377i	0.906720	−	1.57048i
$25$	−4.16931	+	2.75987i	−0.833862	+	0.551974i
$26$	−5.64150	+	3.25712i	−1.10639	+	0.638774i
$27$	4.97446	−	2.53461i	0.957335	−	0.487786i
$28$	−10.9305	+	3.09067i	−2.06567	+	0.584082i
$29$	1.59083	−	2.18958i	0.295409	−	0.406595i	−0.635353	−	0.772222i	$-0.719145\pi$
$29$	1.59083	−	2.18958i	0.295409	−	0.406595i	0.930762	+	0.365627i	$0.119145\pi$
$30$	−5.24305	+	6.89528i	−0.957246	+	1.25890i
$31$	5.93147	−	0.623423i	1.06532	−	0.111970i	0.444390	−	0.895833i	$-0.353420\pi$
$31$	5.93147	−	0.623423i	1.06532	−	0.111970i	0.620934	+	0.783863i	$0.286754\pi$
$32$	−0.817633	−	3.05145i	−0.144538	−	0.539425i
$33$	7.61889	−	2.92462i	1.32628	−	0.509111i
$34$	−0.892268	−	2.74612i	−0.153023	−	0.470955i
$35$	5.85049	−	0.878526i	0.988913	−	0.148498i
$36$	0.816484	−	2.51288i	0.136081	−	0.418813i
$37$	0.168662	+	3.21827i	0.0277279	+	0.529080i	0.976817	+	0.214074i	$0.0686733\pi$
$37$	0.168662	+	3.21827i	0.0277279	+	0.529080i	−0.949090	+	0.315006i	$0.897993\pi$
$38$	−2.74977	+	1.78572i	−0.446072	+	0.289682i
$39$	2.97991	−	2.68312i	0.477168	−	0.429644i
$40$	1.73505	+	12.7468i	0.274335	+	2.01545i
$41$	−6.10496	+	1.98362i	−0.953434	+	0.309790i	−0.744110	−	0.668057i	$-0.767126\pi$
$41$	−6.10496	+	1.98362i	−0.953434	+	0.309790i	−0.209324	+	0.977846i	$0.567126\pi$
$42$	9.06729	−	4.77834i	1.39911	−	0.737314i
$43$	−3.37188	−	3.37188i	−0.514207	−	0.514207i	0.401605	−	0.915813i	$-0.368452\pi$
$43$	−3.37188	−	3.37188i	−0.514207	−	0.514207i	−0.915813	+	0.401605i	$0.868452\pi$
$44$	9.22869	−	20.7280i	1.39128	−	3.12486i
$45$	−0.586984	+	1.24466i	−0.0875025	+	0.185542i
$46$	19.8443	−	8.83524i	2.92588	−	1.30269i
$47$	5.54276	−	4.48844i	0.808494	−	0.654706i	−0.133232	−	0.991085i	$-0.542536\pi$
$47$	5.54276	−	4.48844i	0.808494	−	0.654706i	0.941727	+	0.336379i	$0.109202\pi$
$48$	4.09831	+	8.04338i	0.591539	+	1.16096i
$49$	−6.71441	−	1.97905i	−0.959202	−	0.282722i
$50$	−0.110010	−	12.5428i	−0.0155578	−	1.77381i
$51$	0.888688	+	1.53925i	0.124441	+	0.215538i
$52$	0.583468	−	11.1332i	0.0809124	−	1.54390i
$53$	−3.18623	−	1.22308i	−0.437663	−	0.168003i	0.129552	−	0.991573i	$-0.458646\pi$
$53$	−3.18623	−	1.22308i	−0.437663	−	0.168003i	−0.567215	+	0.823570i	$0.691979\pi$
$54$	−1.46399	+	13.9290i	−0.199224	+	1.89549i
$55$	−6.13029	+	10.1029i	−0.826608	+	1.36228i
$56$	4.50395	−	14.5397i	0.601865	−	1.94295i
$57$	1.42711	−	1.42711i	0.189025	−	0.189025i
$58$	2.43317	+	6.33863i	0.319491	+	0.832302i
$59$	1.72149	+	0.365913i	0.224118	+	0.0476378i	0.318602	−	0.947889i	$-0.396787\pi$
$59$	1.72149	+	0.365913i	0.224118	+	0.0476378i	−0.0944837	+	0.995526i	$0.530120\pi$
$60$	−5.00979	−	13.9525i	−0.646761	−	1.80125i
$61$	−0.868947	−	4.08807i	−0.111257	−	0.523424i	−0.998114	−	0.0613805i	$-0.980450\pi$
$61$	−0.868947	−	4.08807i	−0.111257	−	0.523424i	0.886857	−	0.462044i	$-0.152884\pi$
$62$	−6.79258	+	13.3312i	−0.862658	+	1.69306i
$63$	1.25117	−	1.04201i	0.157632	−	0.131281i
$64$	−3.58241	−	1.16399i	−0.447801	−	0.145499i
$65$	−1.03309	+	5.71379i	−0.128139	+	0.708708i
$66$	−4.25656	+	20.0255i	−0.523946	+	2.46497i
$67$	−0.187687	−	0.151986i	−0.0229296	−	0.0185680i	0.617787	−	0.786345i	$-0.288029\pi$
$67$	−0.187687	−	0.151986i	−0.0229296	−	0.0185680i	−0.640717	+	0.767777i	$0.721363\pi$
$68$	4.77320	+	1.27897i	0.578835	+	0.155098i
$69$	−10.8176	+	7.85941i	−1.30228	+	0.946162i
$70$	−6.14521	+	13.5093i	−0.734493	+	1.61468i
$71$	−8.50997	−	6.18285i	−1.00995	−	0.733770i	−0.0457493	−	0.998953i	$-0.514568\pi$
$71$	−8.50997	−	6.18285i	−1.00995	−	0.733770i	−0.964198	+	0.265183i	$0.914568\pi$
$72$	2.22817	+	2.75155i	0.262592	+	0.324274i
$73$	−12.3451	−	0.646980i	−1.44489	−	0.0757233i	−0.686311	−	0.727308i	$-0.740771\pi$
$73$	−12.3451	−	0.646980i	−1.44489	−	0.0757233i	−0.758576	+	0.651585i	$0.774104\pi$
$74$	−7.00145	−	4.04229i	−0.813902	−	0.469907i
$75$	1.67147	+	7.53795i	0.193005	+	0.870407i
$76$		−	5.61123i		−	0.643652i
$77$	11.6207	−	7.77607i	1.32431	−	0.886166i
$78$	1.57363	+	9.93549i	0.178178	+	1.12497i
$79$	−4.60244	−	0.483736i	−0.517815	−	0.0544246i	−0.157983	−	0.987442i	$-0.550499\pi$
$79$	−4.60244	−	0.483736i	−0.517815	−	0.0544246i	−0.359832	+	0.933017i	$0.617166\pi$
$80$	−11.8230	−	5.57578i	−1.32185	−	0.623391i
$81$	−0.708179	−	6.73788i	−0.0786866	−	0.748653i
$82$	4.16785	−	15.5546i	0.460262	−	1.71772i
$83$	−1.46786	+	9.26772i	−0.161119	+	1.01726i	0.766094	+	0.642729i	$0.222198\pi$
$83$	−1.46786	+	9.26772i	−0.161119	+	1.01726i	−0.927213	+	0.374536i	$0.877802\pi$
$84$	−1.59323	+	17.4682i	−0.173835	+	1.90594i
$85$	−2.38209	−	0.974476i	−0.258374	−	0.105697i
$86$	11.7012	−	2.48717i	1.26178	−	0.268199i
$87$	−2.27624	−	3.50510i	−0.244039	−	0.375787i
$88$	16.5594	+	25.4993i	1.76524	+	2.71824i
$89$	−4.40130	+	0.935526i	−0.466537	+	0.0991655i	−0.435181	−	0.900343i	$-0.643316\pi$
$89$	−4.40130	+	0.935526i	−0.466537	+	0.0991655i	−0.0313557	+	0.999508i	$0.509982\pi$
$90$	−1.81667	−	2.93556i	−0.191493	−	0.309435i
$91$	3.96135	−	5.61321i	0.415263	−	0.588425i
$92$	−5.81555	+	36.7179i	−0.606313	+	3.82811i
$93$	2.38369	−	8.89606i	0.247177	−	0.922479i
$94$	1.87024	+	17.7942i	0.192901	+	1.83533i
$95$	−0.368749	+	2.89912i	−0.0378329	+	0.297443i
$96$	−4.85157	−	0.509920i	−0.495161	−	0.0520435i
$97$	−1.20511	−	7.60880i	−0.122361	−	0.772556i	−0.970201	−	0.242303i	$-0.922097\pi$
$97$	−1.20511	−	7.60880i	−0.122361	−	0.772556i	0.847840	−	0.530253i	$-0.177903\pi$
$98$	13.3377	−	11.4227i	1.34732	−	1.15386i
$99$			3.25242i			0.326881i
$100$	18.1052	+	11.5332i	1.81052	+	1.15332i
$101$	8.71392	+	5.03098i	0.867067	+	0.500602i	0.866373	−	0.499398i	$-0.166446\pi$
$101$	8.71392	+	5.03098i	0.867067	+	0.500602i	0.000694788		1.00000i	$0.499779\pi$
$102$	−4.45270	−	0.233356i	−0.440883	−	0.0231057i
$103$	8.56910	+	10.5820i	0.844339	+	1.04267i	0.998507	+	0.0546267i	$0.0173969\pi$
$103$	8.56910	+	10.5820i	0.844339	+	1.04267i	−0.154168	+	0.988045i	$0.549270\pi$
$104$	12.0861	+	8.78103i	1.18514	+	0.861051i
$105$	1.97111	−	8.92048i	0.192360	−	0.870550i
$106$	6.92665	−	5.03251i	0.672776	−	0.488800i
$107$	−19.1156	−	5.12202i	−1.84798	−	0.495164i	−0.848555	−	0.529108i	$-0.822527\pi$
$107$	−19.1156	−	5.12202i	−1.84798	−	0.495164i	−0.999424	+	0.0339437i	$0.989193\pi$
$108$	−18.6277	−	15.0844i	−1.79245	−	1.45150i
$109$	1.50561	−	7.08334i	0.144211	−	0.678461i	−0.845334	−	0.534238i	$-0.820598\pi$
$109$	1.50561	−	7.08334i	0.144211	−	0.678461i	0.989545	−	0.144223i	$-0.0460682\pi$
$110$	−12.8799	−	26.7014i	−1.22805	−	2.54588i
$111$	4.73293	+	1.53782i	0.449230	+	0.145964i
$112$	9.89810	+	11.8849i	0.935282	+	1.12301i
$113$	0.227796	−	0.447075i	0.0214293	−	0.0420573i	−0.880044	−	0.474893i	$-0.842487\pi$
$113$	0.227796	−	0.447075i	0.0214293	−	0.0420573i	0.901473	+	0.432835i	$0.142487\pi$
$114$	1.05266	+	4.95239i	0.0985910	+	0.463834i
$115$	5.41765	−	18.5886i	0.505198	−	1.73340i
$116$	−11.3658	−	2.41588i	−1.05529	−	0.224309i
$117$	0.572699	+	1.49193i	0.0529460	+	0.137929i
$118$	−3.12193	+	3.12193i	−0.287397	+	0.287397i
$119$	2.06862	+	2.23480i	0.189630	+	0.204864i
$120$	19.3365	+	4.55269i	1.76517	+	0.415602i
$121$	−1.76965	+	16.8371i	−0.160877	+	1.53065i
$122$	9.78826	+	3.75736i	0.886188	+	0.340176i
$123$	−0.518779	+	9.89889i	−0.0467767	+	0.892553i
$124$	−12.8030	−	22.1754i	−1.14974	−	1.99141i
$125$	−8.59638	−	7.14858i	−0.768884	−	0.639388i
$126$	0.482842	+	4.05607i	0.0430149	+	0.361344i
$127$	0.723490	+	1.41993i	0.0641993	+	0.125998i	0.920876	−	0.389855i	$-0.127475\pi$
$127$	0.723490	+	1.41993i	0.0641993	+	0.125998i	−0.856677	+	0.515853i	$0.827475\pi$
$128$	12.2538	−	9.92291i	1.08309	−	0.877070i
$129$	−6.72703	+	2.99507i	−0.592282	+	0.263701i
$130$	−10.6099	−	9.98034i	−0.930548	−	0.875333i
$131$	−7.41983	+	16.6652i	−0.648273	+	1.45605i	0.227722	+	0.973726i	$0.426872\pi$
$131$	−7.41983	+	16.6652i	−0.648273	+	1.45605i	−0.875995	+	0.482320i	$0.839794\pi$
$132$	−24.7752	−	24.7752i	−2.15641	−	2.15641i
$133$	1.84322	−	2.92570i	0.159828	−	0.253690i
$134$	0.576205	−	0.187220i	0.0497765	−	0.0161734i
$135$	8.63297	+	9.01772i	0.743008	+	0.776122i
$136$	−4.92096	+	4.43085i	−0.421969	+	0.379942i
$137$	7.17553	−	4.65985i	0.613047	−	0.398117i	−0.200435	−	0.979707i	$-0.564236\pi$
$137$	7.17553	−	4.65985i	0.613047	−	0.398117i	0.813482	+	0.581589i	$0.197569\pi$
$138$	−1.75554	−	33.4977i	−0.149442	−	2.85152i
$139$	1.62016	−	4.98635i	0.137420	−	0.422937i	−0.858538	−	0.512750i	$-0.828627\pi$
$139$	1.62016	−	4.98635i	0.137420	−	0.422937i	0.995959	+	0.0898130i	$0.0286269\pi$
$140$	−13.6621	−	21.4123i	−1.15466	−	1.80967i
$141$	−3.40339	−	10.4746i	−0.286617	−	0.882116i
$142$	24.6355	−	9.45669i	2.06737	−	0.793588i
$143$	3.55185	+	13.2557i	0.297021	+	1.10850i
$144$	−3.57799	+	0.376062i	−0.298166	+	0.0313385i
$145$	5.71354	+	1.99512i	0.474483	+	0.165685i
$146$	18.2284	−	25.0893i	1.50859	−	2.07640i
$147$	−6.56881	+	8.58458i	−0.541786	+	0.708045i
$148$	12.3280	−	6.28141i	1.01335	−	0.516329i
$149$	3.28424	−	1.89616i	0.269056	−	0.155339i	−0.359403	−	0.933183i	$-0.617020\pi$
$149$	3.28424	−	1.89616i	0.269056	−	0.155339i	0.628458	+	0.777843i	$0.283686\pi$
$150$	−18.1430	−	6.78250i	−1.48137	−	0.553789i
$151$	−4.87556	+	8.44472i	−0.396768	+	0.687222i	−0.993325	−	0.115349i	$-0.963202\pi$
$151$	−4.87556	+	8.44472i	−0.396768	+	0.687222i	0.596557	+	0.802570i	$0.296535\pi$
$152$	6.30608	+	4.09522i	0.511491	+	0.332166i
$153$	−0.699626	+	0.110810i	−0.0565614	+	0.00895845i
$154$	0.482795	+	35.0737i	0.0389047	+	2.82632i
$155$	5.15754	+	12.2986i	0.414263	+	0.987845i
$156$	−15.7272	−	7.00222i	−1.25919	−	0.560626i
$157$	15.8553	−	4.24841i	1.26539	−	0.339060i	0.437127	−	0.899400i	$-0.355996\pi$
$157$	15.8553	−	4.24841i	1.26539	−	0.339060i	0.828263	+	0.560340i	$0.189329\pi$
$158$	7.30610	−	9.02228i	0.581242	−	0.717774i
$159$	−3.52649	+	3.91656i	−0.279669	+	0.310604i
$160$	6.00676	−	3.71728i	0.474876	−	0.293876i
$161$	−15.0936	+	17.2344i	−1.18954	+	1.35826i
$162$	15.1436	+	7.71605i	1.18979	+	0.606230i
$163$	6.10618	−	0.320011i	0.478273	−	0.0250652i	0.188323	−	0.982107i	$-0.439695\pi$
$163$	6.10618	−	0.320011i	0.478273	−	0.0250652i	0.289950	+	0.957042i	$0.406361\pi$
$164$	18.4408	+	20.4806i	1.43998	+	1.59926i
$165$	11.1723	+	14.4286i	0.869763	+	1.12326i
$166$	−17.4931	−	15.7508i	−1.35773	−	1.22250i
$167$	19.8065	+	3.13704i	1.53267	+	0.242752i	0.865026	−	0.501726i	$-0.167302\pi$
$167$	19.8065	+	3.13704i	1.53267	+	0.242752i	0.667647	+	0.744478i	$0.267302\pi$
$168$	−18.4686	−	14.5393i	−1.42488	−	1.12173i
$169$	−3.67782	−	5.06208i	−0.282909	−	0.389391i
$170$	5.30489	−	3.68031i	0.406867	−	0.282267i
$171$	0.327153	+	0.734799i	0.0250180	+	0.0561915i
$172$	−7.33684	+	19.1131i	−0.559429	+	1.45736i
$173$	−6.52096	+	10.0414i	−0.495779	+	0.763433i	−0.994657	−	0.103240i	$-0.967079\pi$
$173$	−6.52096	+	10.0414i	−0.495779	+	0.763433i	0.498877	+	0.866673i	$0.333746\pi$
$174$	10.4845			0.794831
$175$	5.65157	+	11.9608i	0.427218	+	0.904149i
$176$	−30.8948			−2.32879
$177$	1.48018	−	2.27927i	0.111257	−	0.171321i
$178$	4.04525	−	10.5382i	0.303205	−	0.789875i
$179$	−9.02204	−	20.2638i	−0.674339	−	1.51459i	−0.848119	−	0.529806i	$-0.822265\pi$
$179$	−9.02204	−	20.2638i	−0.674339	−	1.51459i	0.173780	−	0.984785i	$-0.444402\pi$
$180$	5.90673	+	0.128755i	0.440262	+	0.00959687i
$181$	−1.61496	−	2.22281i	−0.120039	−	0.165220i	0.744769	−	0.667323i	$-0.232560\pi$
$181$	−1.61496	−	2.22281i	−0.120039	−	0.165220i	−0.864808	+	0.502103i	$0.832560\pi$
$182$	6.39737	+	16.0038i	0.474205	+	1.18628i
$183$	−6.37441	−	1.00961i	−0.471210	−	0.0746323i
$184$	−37.0205	−	33.3334i	−2.72918	−	2.45737i
$185$	−6.78220	+	2.43523i	−0.498637	+	0.179041i
$186$	15.4598	+	17.1699i	1.13357	+	1.25896i
$187$	−6.07452	+	0.318352i	−0.444213	+	0.0232802i
$188$	−27.2833	−	13.9015i	−1.98984	−	1.01387i
$189$	−4.75746	−	13.9840i	−0.346054	−	1.01719i
$190$	−5.59571	−	4.73690i	−0.405955	−	0.343651i
$191$	14.4214	−	16.0166i	1.04349	−	1.15892i	0.0564608	−	0.998405i	$-0.482018\pi$
$191$	14.4214	−	16.0166i	1.04349	−	1.15892i	0.987034	−	0.160513i	$-0.0513149\pi$
$192$	−3.66055	+	4.52040i	−0.264177	+	0.326232i
$193$	−6.09432	+	1.63297i	−0.438679	+	0.117544i	−0.471397	−	0.881921i	$-0.656250\pi$
$193$	−6.09432	+	1.63297i	−0.438679	+	0.117544i	0.0327186	+	0.999465i	$0.489584\pi$
$194$	17.6549	+	7.86048i	1.26755	+	0.564349i
$195$	7.66553	+	4.65133i	0.548940	+	0.333088i
$196$	3.96291	+	29.7908i	0.283065	+	2.12791i
$197$	−1.85729	+	0.294166i	−0.132326	+	0.0209584i	−0.222246	−	0.974991i	$-0.571339\pi$
$197$	−1.85729	+	0.294166i	−0.132326	+	0.0209584i	0.0899199	+	0.995949i	$0.471339\pi$
$198$	−6.84287	−	4.44381i	−0.486301	−	0.315808i
$199$	6.41745	−	11.1153i	0.454921	−	0.787946i	−0.543763	−	0.839239i	$-0.683001\pi$
$199$	6.41745	−	11.1153i	0.454921	−	0.787946i	0.998684	+	0.0512931i	$0.0163343\pi$
$200$	−26.1750	+	11.9300i	−1.85085	+	0.843581i
$201$	−0.322974	+	0.186469i	−0.0227808	+	0.0131525i
$202$	−22.4907	+	11.4596i	−1.58244	+	0.806294i
$203$	−5.13256	−	4.99318i	−0.360235	−	0.350452i
$204$	4.48529	−	6.17347i	0.314033	−	0.432229i
$205$	−8.18177	−	11.7934i	−0.571440	−	0.823688i
$206$	−33.9717	+	3.57057i	−2.36692	+	0.248773i
$207$	−1.37922	−	5.14733i	−0.0958626	−	0.357764i
$208$	−14.1719	+	5.44008i	−0.982643	+	0.377201i
$209$	2.13443	+	6.56910i	0.147642	+	0.454394i
$210$	16.0749	+	16.3352i	1.10927	+	1.12724i
$211$	−0.550856	+	1.69536i	−0.0379225	+	0.116713i	−0.968226	−	0.250078i	$-0.919544\pi$
$211$	−0.550856	+	1.69536i	−0.0379225	+	0.116713i	0.930303	+	0.366791i	$0.119544\pi$
$212$	0.766864	+	14.6326i	0.0526685	+	1.00497i
$213$	−13.6228	+	8.84677i	−0.933421	+	0.606171i
$214$	36.8942	−	33.2197i	2.52204	−	2.27085i
$215$	5.04672	−	9.39290i	0.344184	−	0.640591i
$216$	30.5474	−	9.92544i	2.07849	−	0.675341i
$217$	0.608874	−	15.7679i	0.0413330	−	1.07039i
$218$	12.8457	+	12.8457i	0.870022	+	0.870022i
$219$	−7.76444	+	17.4392i	−0.524672	+	1.17843i
$220$	50.3300	+	6.40166i	3.39325	+	0.431600i
$221$	−2.73041	+	1.21566i	−0.183667	+	0.0817739i
$222$	−9.70210	+	7.85661i	−0.651163	+	0.527301i
$223$	−2.23679	−	4.38996i	−0.149787	−	0.293973i	0.803906	−	0.594757i	$-0.202752\pi$
$223$	−2.23679	−	4.38996i	−0.149787	−	0.293973i	−0.953692	+	0.300784i	$0.902752\pi$
$224$	−8.29957	+	0.987994i	−0.554538	+	0.0660131i
$225$	−3.04333	−	0.454692i	−0.202889	−	0.0303128i
$226$	0.629375	+	1.09011i	0.0418654	+	0.0725130i
$227$	−0.720059	+	13.7395i	−0.0477920	+	0.911926i	0.864563	+	0.502525i	$0.167596\pi$
$227$	−0.720059	+	13.7395i	−0.0477920	+	0.911926i	−0.912355	+	0.409401i	$0.865738\pi$
$228$	−8.08938	−	3.10522i	−0.535732	−	0.205648i
$229$	−0.179251	+	1.70546i	−0.0118452	+	0.112700i	−0.998847	−	0.0480106i	$-0.984712\pi$
$229$	−0.179251	+	1.70546i	−0.0118452	+	0.112700i	0.987002	+	0.160710i	$0.0513785\pi$
$230$	31.7070	+	36.7961i	2.09070	+	2.42626i
$231$	−4.77946	−	21.0562i	−0.314465	−	1.38540i
$232$	11.0101	−	11.0101i	0.722849	−	0.722849i
$233$	8.30356	+	21.6315i	0.543984	+	1.41713i	0.879866	+	0.475223i	$0.157632\pi$
$233$	8.30356	+	21.6315i	0.543984	+	1.41713i	−0.335882	+	0.941904i	$0.609034\pi$
$234$	−3.92140	−	0.833519i	−0.256350	−	0.0544888i
$235$	13.1827	+	8.97537i	0.859945	+	0.585488i
$236$	−1.57098	−	7.39087i	−0.102262	−	0.481105i
$237$	−3.24434	+	6.36738i	−0.210743	+	0.413606i
$238$	−7.52823	+	1.29881i	−0.487983	+	0.0841896i
$239$	−0.970343	−	0.315283i	−0.0627662	−	0.0203940i	0.277466	−	0.960736i	$-0.410506\pi$
$239$	−0.970343	−	0.315283i	−0.0627662	−	0.0203940i	−0.340232	+	0.940342i	$0.610506\pi$
$240$	−14.5811	+	13.9590i	−0.941204	+	0.901047i
$241$	1.37375	−	6.46298i	0.0884910	−	0.416317i	−0.911496	−	0.411308i	$-0.865072\pi$
$241$	1.37375	−	6.46298i	0.0884910	−	0.416317i	0.999987	−	0.00500944i	$-0.00159456\pi$
$242$	−33.0062	−	26.7279i	−2.12172	−	1.71813i
$243$	6.07267	+	1.62717i	0.389562	+	0.104383i
$244$	−14.5166	+	10.5469i	−0.929329	+	0.675197i
$245$	−0.0897495	−	15.6522i	−0.00573388	−	0.999984i
$246$	−20.1177	−	14.6164i	−1.28266	−	0.931908i
$247$	2.13580	+	2.63750i	0.135898	+	0.167820i
$248$	34.2654	+	1.79577i	2.17585	+	0.114032i
$249$	12.5484	+	7.24484i	0.795224	+	0.459123i
$250$	26.7854	−	8.31902i	1.69406	−	0.526141i
$251$		−	13.1515i		−	0.830114i	−0.909795	−	0.415057i	$-0.863762\pi$
$251$		−	13.1515i		−	0.830114i	0.909795	−	0.415057i	$-0.136238\pi$
$252$	−6.27176	−	3.08763i	−0.395084	−	0.194503i
$253$	−7.15867	−	45.1981i	−0.450062	−	2.84158i
$254$	−3.97594	−	0.417888i	−0.249473	−	0.0262206i
$255$	−2.72308	+	2.89485i	−0.170526	+	0.181282i
$256$	3.34721	+	31.8466i	0.209201	+	1.99041i
$257$	−4.64973	+	17.3530i	−0.290042	+	1.08245i	0.655033	+	0.755600i	$0.272655\pi$
$257$	−4.64973	+	17.3530i	−0.290042	+	1.08245i	−0.945075	+	0.326852i	$0.894012\pi$
$258$	2.88978	−	18.2454i	0.179910	−	1.13591i
$259$	8.49118	+	0.774456i	0.527616	+	0.0481224i
$260$	24.2143	−	5.92576i	1.50171	−	0.367500i
$261$	1.62922	−	0.346302i	0.100846	−	0.0214356i
$262$	−24.9246	−	38.3806i	−1.53985	−	2.37116i
$263$	1.78960	+	2.75574i	0.110351	+	0.169926i	0.889532	−	0.456874i	$-0.151031\pi$
$263$	1.78960	+	2.75574i	0.110351	+	0.169926i	−0.779180	+	0.626800i	$0.784364\pi$
$264$	45.9248	−	9.76162i	2.82648	−	0.600786i
$265$	0.565393	−	7.61055i	0.0347318	−	0.467512i
$266$	3.63706	+	7.87541i	0.223002	+	0.482872i
$267$	−1.08696	+	6.86282i	−0.0665211	+	0.419998i
$268$	−0.268361	+	1.00154i	−0.0163928	+	0.0611787i
$269$	−0.712511	−	6.77909i	−0.0434426	−	0.413329i	−0.994534	−	0.104418i	$-0.966702\pi$
$269$	−0.712511	−	6.77909i	−0.0434426	−	0.413329i	0.951091	−	0.308911i	$-0.0999645\pi$
$270$	−30.7679	+	5.84217i	−1.87248	+	0.355543i
$271$	12.8849	+	1.35425i	0.782699	+	0.0822650i	0.487445	−	0.873154i	$-0.337929\pi$
$271$	12.8849	+	1.35425i	0.782699	+	0.0822650i	0.295254	+	0.955419i	$0.404596\pi$
$272$	−1.05259	−	6.64576i	−0.0638224	−	0.402959i
$273$	−5.90005	−	8.81718i	−0.357087	−	0.533640i
$274$			21.4636i			1.29666i
$275$	−25.5830	−	6.61500i	−1.54271	−	0.398900i
$276$	49.7158	+	28.7034i	2.99254	+	1.72774i
$277$	−1.47778	−	0.0774472i	−0.0887912	−	0.00465335i	0.00788859	−	0.999969i	$-0.497489\pi$
$277$	−1.47778	−	0.0774472i	−0.0887912	−	0.00465335i	−0.0966798	+	0.995316i	$0.530822\pi$
$278$	8.27728	+	10.2216i	0.496438	+	0.613050i
$279$	2.96947	+	2.15745i	0.177777	+	0.129163i
$280$	34.0348	+	0.273317i	2.03397	+	0.0163338i
$281$	−7.47301	+	5.42946i	−0.445802	+	0.323894i	−0.787936	−	0.615757i	$-0.788850\pi$
$281$	−7.47301	+	5.42946i	−0.445802	+	0.323894i	0.342134	+	0.939651i	$0.388850\pi$
$282$	26.6878	+	7.15097i	1.58923	+	0.425834i
$283$	7.99407	+	6.47347i	0.475198	+	0.384808i	0.836786	−	0.547530i	$-0.184432\pi$
$283$	7.99407	+	6.47347i	0.475198	+	0.384808i	−0.361588	+	0.932338i	$0.617765\pi$
$284$	−9.38948	+	44.1740i	−0.557163	+	2.62125i
$285$	3.97542	+	2.13596i	0.235484	+	0.126523i
$286$	−32.7419	−	10.6385i	−1.93607	−	0.629068i
$287$	2.88742	+	16.7362i	0.170439	+	0.987905i
$288$	0.882636	−	1.73227i	0.0520098	−	0.102075i
$289$	3.25906	+	15.3327i	0.191709	+	0.901922i
$290$	−12.0040	+	9.29493i	−0.704901	+	0.545817i
$291$	−11.6361	−	2.47332i	−0.682118	−	0.144989i
$292$	19.0201	+	49.5490i	1.11307	+	2.89964i
$293$	−3.40255	+	3.40255i	−0.198779	+	0.198779i	−0.799476	−	0.600697i	$-0.794890\pi$
$293$	−3.40255	+	3.40255i	−0.198779	+	0.198779i	0.600697	+	0.799476i	$0.294890\pi$
$294$	−9.08634	−	25.5495i	−0.529926	−	1.49008i
$295$	0.325966	+	3.92183i	0.0189785	+	0.228338i
$296$	−1.93801	+	18.4389i	−0.112644	+	1.07174i
$297$	27.5455	+	10.5737i	1.59835	+	0.613550i
$298$	−0.497903	+	9.50055i	−0.0288427	+	0.550352i
$299$	−11.2424	−	19.4724i	−0.650166	−	1.12612i
$300$	26.6461	−	19.7189i	1.53841	−	1.13847i
$301$	−10.1039	+	7.55554i	−0.582378	+	0.435494i
$302$	−11.1056	−	21.7959i	−0.639054	−	1.25421i
$303$	12.0751	−	9.77824i	0.693697	−	0.561745i
$304$	−6.97987	+	3.10764i	−0.400323	+	0.178235i
$305$	8.19329	−	4.49523i	0.469146	−	0.257396i
$306$	0.722768	−	1.62336i	0.0413179	−	0.0928015i
$307$	−23.4485	−	23.4485i	−1.33828	−	1.33828i	−0.897727	−	0.440551i	$-0.854783\pi$
$307$	−23.4485	−	23.4485i	−1.33828	−	1.33828i	−0.440551	−	0.897727i	$-0.645217\pi$
$308$	−50.7915	−	31.9992i	−2.89411	−	1.82332i
$309$	19.9975	−	6.49758i	1.13762	−	0.369634i
$310$	−32.9221	−	5.95254i	−1.86985	−	0.338082i
$311$	18.6623	−	16.8036i	1.05824	−	0.952847i	0.0592750	−	0.998242i	$-0.481121\pi$
$311$	18.6623	−	16.8036i	1.05824	−	0.952847i	0.998969	+	0.0453944i	$0.0144545\pi$
$312$	19.3475	−	12.5644i	1.09533	−	0.711319i
$313$	0.390025	+	7.44212i	0.0220455	+	0.420653i	0.987252	+	0.159165i	$0.0508801\pi$
$313$	0.390025	+	7.44212i	0.0220455	+	0.420653i	−0.965207	+	0.261489i	$0.915787\pi$
$314$	−12.7248	+	39.1630i	−0.718104	+	2.21010i
$315$	3.03748	+	2.00742i	0.171143	+	0.113106i
$316$	6.13972	+	18.8961i	0.345386	+	1.06299i
$317$	−24.8427	+	9.53621i	−1.39530	+	0.535607i	−0.935788	−	0.352563i	$-0.885310\pi$
$317$	−24.8427	+	9.53621i	−1.39530	+	0.535607i	−0.459516	+	0.888170i	$0.651977\pi$
$318$	−3.42190	−	12.7707i	−0.191891	−	0.716146i
$319$	14.2250	−	1.49511i	0.796447	−	0.0837100i
$320$	0.183556	−	8.42074i	0.0102611	−	0.470734i
$321$	−17.9626	+	24.7234i	−1.00258	+	1.37993i
$322$	−15.6374	−	55.3034i	−0.871441	−	3.08194i
$323$	−1.34035	+	0.682945i	−0.0745793	+	0.0380001i
$324$	−25.1902	+	14.5436i	−1.39946	+	0.807976i
$325$	−12.9000	+	1.47035i	−0.715566	+	0.0815603i
$326$	−7.66963	+	13.2842i	−0.424782	+	0.735743i
$327$	−9.37845	−	6.09044i	−0.518629	−	0.336802i
$328$	−36.4753	+	5.77712i	−2.01401	+	0.318988i
$329$	−9.65904	−	16.2105i	−0.532520	−	0.893714i
$330$	−45.6215	+	3.79187i	−2.51138	+	0.208735i
$331$	−6.18602	−	2.75419i	−0.340015	−	0.151384i	0.229624	−	0.973279i	$-0.426250\pi$
$331$	−6.18602	−	2.75419i	−0.340015	−	0.151384i	−0.569639	+	0.821895i	$0.692917\pi$
$332$	38.9125	−	10.4266i	2.13560	−	0.572233i
$333$	−1.24814	+	1.54132i	−0.0683975	+	0.0844639i
$334$	−33.6619	+	37.3853i	−1.84190	+	2.04563i
$335$	0.204470	−	0.499822i	0.0111714	−	0.0273082i
$336$	22.6113	−	7.69250i	1.23355	−	0.419660i
$337$	18.6572	+	9.50634i	1.01633	+	0.517843i	0.881079	−	0.472969i	$-0.156818\pi$
$337$	18.6572	+	9.50634i	1.01633	+	0.517843i	0.135246	+	0.990812i	$0.456818\pi$
$338$	15.6753	−	0.821507i	0.852623	−	0.0446841i
$339$	−0.518461	−	0.575810i	−0.0281590	−	0.0312737i
$340$	0.337684	+	11.0445i	0.0183135	+	0.598975i
$341$	23.4237	+	21.0908i	1.26847	+	1.14213i
$342$	−1.99296	−	0.315653i	−0.107767	−	0.0170686i
$343$	−7.71965	+	16.8347i	−0.416822	+	0.908988i
$344$	−16.1253	−	22.1946i	−0.869420	−	1.19665i
$345$	−23.8000	−	18.0971i	−1.28135	−	0.974318i
$346$	−12.2167	−	27.4393i	−0.656776	−	1.47514i
$347$	−3.59729	+	9.37125i	−0.193112	+	0.503075i	−0.995612	−	0.0935777i	$-0.970170\pi$
$347$	−3.59729	+	9.37125i	−0.193112	+	0.503075i	0.802500	+	0.596653i	$0.203503\pi$
$348$	−9.77262	+	15.0485i	−0.523867	+	0.806685i
$349$	18.7086			1.00145			0.500725	−	0.865607i	$-0.333067\pi$
$349$	18.7086			1.00145			0.500725	+	0.865607i	$0.333067\pi$
$350$	−32.8864	−	4.45158i	−1.75785	−	0.237947i
$351$	14.4974			0.773812
$352$	9.09296	−	14.0019i	0.484656	−	0.746305i
$353$	3.64433	−	9.49380i	0.193968	−	0.505304i	−0.801759	−	0.597647i	$-0.796102\pi$
$353$	3.64433	−	9.49380i	0.193968	−	0.505304i	0.995727	+	0.0923431i	$0.0294357\pi$
$354$	2.77305	+	6.22837i	0.147386	+	0.331034i
$355$	7.75416	−	22.2061i	0.411548	−	1.17858i
$356$	11.3550	+	15.6288i	0.601815	+	0.828327i
$357$	4.36654	−	1.74549i	0.231102	−	0.0923810i
$358$	54.9606	+	8.70490i	2.90476	+	0.460068i
$359$	2.41843	+	2.17756i	0.127640	+	0.114927i	0.730478	−	0.682936i	$-0.239297\pi$
$359$	2.41843	+	2.17756i	0.127640	+	0.114927i	−0.602839	+	0.797863i	$0.705964\pi$
$360$	−4.45558	+	6.54421i	−0.234830	+	0.344910i
$361$	−11.5705	−	12.8503i	−0.608973	−	0.676333i
$362$	6.88317	−	0.360732i	0.361771	−	0.0189596i
$363$	23.2938	+	11.8688i	1.22261	+	0.622949i
$364$	−28.9333	−	5.73491i	−1.51652	−	0.300591i
$365$	−6.57080	−	26.8501i	−0.343931	−	1.40540i
$366$	10.8335	−	12.0319i	0.566278	−	0.628916i
$367$	−7.81693	+	9.65310i	−0.408040	+	0.503888i	−0.939194	−	0.343388i	$-0.888425\pi$
$367$	−7.81693	+	9.65310i	−0.408040	+	0.503888i	0.531153	+	0.847276i	$0.321759\pi$
$368$	48.8946	−	13.1013i	2.54881	−	0.682951i
$369$	−3.60894	−	1.60680i	−0.187874	−	0.0836468i
$370$	4.14302	−	17.5965i	0.215386	−	0.914800i
$371$	−4.40681	+	7.88138i	−0.228790	+	0.409181i
$372$	−39.0541	+	6.18556i	−2.02486	+	0.320706i
$373$	−16.3020	−	10.5867i	−0.844088	−	0.548157i	0.0486074	−	0.998818i	$-0.484522\pi$
$373$	−16.3020	−	10.5867i	−0.844088	−	0.548157i	−0.892695	+	0.450661i	$0.851188\pi$
$374$	7.62987	−	13.2153i	0.394531	−	0.683348i
$375$	−15.0629	+	8.43693i	−0.777844	+	0.435681i
$376$	35.5350	−	20.5162i	1.83258	−	1.05804i
$377$	6.26194	−	3.19062i	0.322506	−	0.164325i
$378$	35.9215	+	9.09713i	1.84760	+	0.467906i
$379$	−13.2455	+	18.2308i	−0.680373	+	0.936453i	−0.999938	−	0.0111109i	$-0.996463\pi$
$379$	−13.2455	+	18.2308i	−0.680373	+	0.936453i	0.319565	+	0.947564i	$0.396463\pi$
$380$	12.0147	−	3.61629i	0.616339	−	0.185512i
$381$	2.44740	−	0.257233i	0.125384	−	0.0131784i
$382$	13.9937	+	52.2251i	0.715979	+	2.67207i
$383$	−17.4937	+	6.71520i	−0.893886	+	0.343131i	−0.761574	−	0.648077i	$-0.775573\pi$
$383$	−17.4937	+	6.71520i	−0.893886	+	0.343131i	−0.132312	+	0.991208i	$0.542240\pi$
$384$	−7.52412	−	23.1569i	−0.383964	−	1.18172i
$385$	24.1392	+	19.8706i	1.23025	+	1.01270i
$386$	4.89106	−	15.0531i	0.248949	−	0.766185i
$387$	−0.153589	−	2.93066i	−0.00780738	−	0.148974i
$388$	−27.7383	+	18.0135i	−1.40820	+	0.914495i
$389$	0.920237	−	0.828585i	0.0466579	−	0.0420109i	−0.645472	−	0.763784i	$-0.723339\pi$
$389$	0.920237	−	0.828585i	0.0466579	−	0.0420109i	0.692130	+	0.721773i	$0.256673\pi$
$390$	−20.2595	+	9.77258i	−1.02588	+	0.494854i
$391$	9.47862	−	3.07979i	0.479354	−	0.155752i
$392$	−36.3721	−	17.2884i	−1.83707	−	0.873197i
$393$	19.9192	+	19.9192i	1.00479	+	1.00479i
$394$	1.91872	−	4.30952i	0.0966639	−	0.217111i
$395$	−1.93039	−	10.1664i	−0.0971282	−	0.511528i
$396$	12.7564	−	5.67954i	0.641036	−	0.285407i
$397$	6.27309	−	5.07984i	0.314837	−	0.254950i	−0.458856	−	0.888511i	$-0.651741\pi$
$397$	6.27309	−	5.07984i	0.314837	−	0.254950i	0.773693	+	0.633561i	$0.218407\pi$
$398$	14.6177	+	28.6888i	0.732718	+	1.43804i
$399$	−3.19778	−	4.27633i	−0.160089	−	0.214084i
$400$	4.31913	−	28.9087i	0.215956	−	1.44543i
$401$	−8.24579	−	14.2821i	−0.411775	−	0.713215i	0.583309	−	0.812250i	$-0.301758\pi$
$401$	−8.24579	−	14.2821i	−0.411775	−	0.713215i	−0.995084	+	0.0990353i	$0.968424\pi$
$402$	0.0489640	−	0.934288i	0.00244210	−	0.0465981i
$403$	14.4585	+	5.55011i	0.720231	+	0.276471i
$404$	4.51554	−	42.9625i	0.224657	−	2.13747i
$405$	13.9706	−	5.85872i	0.694205	−	0.291122i
$406$	17.5179	−	3.97633i	0.869401	−	0.197342i
$407$	−12.0431	+	12.0431i	−0.596953	+	0.596953i
$408$	3.66447	+	9.54627i	0.181418	+	0.472611i
$409$	10.7738	+	2.29004i	0.532730	+	0.113235i	0.466419	−	0.884564i	$-0.345544\pi$
$409$	10.7738	+	2.29004i	0.532730	+	0.113235i	0.0663106	+	0.997799i	$0.478877\pi$
$410$	35.9913	−	1.10043i	1.77749	−	0.0543462i
$411$	−2.74693	−	12.9233i	−0.135496	−	0.637459i
$412$	26.5401	−	52.0879i	1.30754	−	2.56619i
$413$	1.60870	−	4.36966i	0.0791592	−	0.215017i
$414$	12.7141	+	4.13105i	0.624862	+	0.203030i
$415$	−20.7899	+	2.82984i	−1.02053	+	0.138911i
$416$	1.70555	−	8.02399i	0.0836216	−	0.393409i
$417$	−6.29194	−	5.09511i	−0.308118	−	0.249509i
$418$	−16.7372	−	4.48472i	−0.818644	−	0.219355i
$419$	27.4976	−	19.9782i	1.34334	−	0.975997i	0.344031	−	0.938958i	$-0.388208\pi$
$419$	27.4976	−	19.9782i	1.34334	−	0.975997i	0.999314	−	0.0370384i	$-0.0117924\pi$
$420$	−38.4294	+	7.84641i	−1.87516	+	0.382866i
$421$	−1.53583	−	1.11585i	−0.0748519	−	0.0543831i	0.549730	−	0.835342i	$-0.314731\pi$
$421$	−1.53583	−	1.11585i	−0.0748519	−	0.0543831i	−0.624582	+	0.780959i	$0.714731\pi$
$422$	−2.81428	−	3.47535i	−0.136997	−	0.169177i
$423$	4.38329	+	0.229719i	0.213123	+	0.0111693i
$424$	−17.0043	−	9.81745i	−0.825803	−	0.476778i
$425$	0.551338	−	5.72850i	0.0267438	−	0.277873i
$426$		−	40.7489i		−	1.97429i
$427$	−11.0335	+	0.730646i	−0.533948	+	0.0353584i
$428$	13.2914	+	83.9184i	0.642463	+	4.05635i
$429$	21.0755	+	2.21513i	1.01754	+	0.106947i
$430$	12.8666	+	23.4515i	0.620484	+	1.13093i
$431$	−3.39203	−	32.2730i	−0.163388	−	1.55454i	−0.702120	−	0.712058i	$-0.747763\pi$
$431$	−3.39203	−	32.2730i	−0.163388	−	1.55454i	0.538732	−	0.842477i	$-0.318903\pi$
$432$	−8.44720	+	31.5254i	−0.406416	+	1.51677i
$433$	−3.83767	+	24.2301i	−0.184426	+	1.16442i	0.705633	+	0.708578i	$0.250663\pi$
$433$	−3.83767	+	24.2301i	−0.184426	+	1.16442i	−0.890059	+	0.455845i	$0.849337\pi$
$434$	32.3426	+	22.8248i	1.55250	+	1.09563i
$435$	6.03808	−	7.13279i	0.289504	−	0.341991i
$436$	−30.4110	+	6.46406i	−1.45642	+	0.309572i
$437$	−6.16367	−	9.49123i	−0.294849	−	0.454027i
$438$	−26.0822	−	40.1631i	−1.24626	−	1.91907i
$439$	−21.8456	+	4.64342i	−1.04263	+	0.221619i	−0.697239	−	0.716839i	$-0.745588\pi$
$439$	−21.8456	+	4.64342i	−1.04263	+	0.221619i	−0.345394	+	0.938458i	$0.612255\pi$
$440$	−43.9265	+	51.8904i	−2.09411	+	2.47378i
$441$	−2.25585	−	3.67009i	−0.107421	−	0.174766i
$442$	1.17292	−	7.40554i	0.0557903	−	0.352246i
$443$	1.28480	−	4.79492i	0.0610425	−	0.227814i	−0.928665	−	0.370920i	$-0.879042\pi$
$443$	1.28480	−	4.79492i	0.0610425	−	0.227814i	0.989707	+	0.143106i	$0.0457091\pi$
$444$	−2.23332	−	21.2486i	−0.105989	−	1.00841i
$445$	−4.83965	−	8.82106i	−0.229422	−	0.418158i
$446$	12.2923	+	1.29197i	0.582057	+	0.0611767i
$447$	−0.916100	−	5.78403i	−0.0433301	−	0.273575i
$448$	−4.40179	+	8.94113i	−0.207965	+	0.422429i
$449$			2.68091i			0.126520i	0.997997	+	0.0632600i	$0.0201497\pi$
$449$			2.68091i			0.126520i	−0.997997	+	0.0632600i	$0.979850\pi$
$450$	5.11476	−	5.78170i	0.241112	−	0.272552i
$451$	−29.3793	−	16.9621i	−1.38342	−	0.798716i
$452$	−2.15128	−	0.112744i	−0.101188	−	0.00530302i
$453$	9.47616	+	11.7021i	0.445229	+	0.549812i
$454$	−27.9232	−	20.2874i	−1.31050	−	0.952135i
$455$	14.5719	+	4.86441i	0.683141	+	0.228047i
$456$	9.39359	−	6.82484i	0.439895	−	0.319603i
$457$	30.1227	+	8.07135i	1.40908	+	0.377562i	0.881597	−	0.472003i	$-0.156469\pi$
$457$	30.1227	+	8.07135i	1.40908	+	0.377562i	0.527484	+	0.849565i	$0.323136\pi$
$458$	−3.34325	−	2.70731i	−0.156220	−	0.126504i
$459$	−1.33603	+	6.28554i	−0.0623607	+	0.293384i
$460$	−82.3676	+	11.2116i	−3.84041	+	0.522743i
$461$	−13.2462	−	4.30394i	−0.616936	−	0.200455i	−0.0161563	−	0.999869i	$-0.505143\pi$
$461$	−13.2462	−	4.30394i	−0.616936	−	0.200455i	−0.600779	+	0.799415i	$0.705143\pi$
$462$	50.8309	+	18.7136i	2.36487	+	0.870635i
$463$	−4.86495	+	9.54799i	−0.226093	+	0.443733i	−0.975988	−	0.217824i	$-0.930104\pi$
$463$	−4.86495	+	9.54799i	−0.226093	+	0.443733i	0.749895	+	0.661557i	$0.230104\pi$
$464$	3.28953	+	15.4760i	0.152713	+	0.718457i
$465$	20.5843	−	0.629360i	0.954574	−	0.0291859i
$466$	−56.8564	−	12.0852i	−2.63382	−	0.559836i
$467$	−12.9972	−	33.8590i	−0.601441	−	1.56681i	−0.808511	−	0.588481i	$-0.799726\pi$
$467$	−12.9972	−	33.8590i	−0.601441	−	1.56681i	0.207070	−	0.978326i	$-0.433607\pi$
$468$	4.85148	−	4.85148i	0.224260	−	0.224260i
$469$	−0.468917	+	0.434049i	−0.0216526	+	0.0200425i
$470$	−36.8952	+	15.4724i	−1.70185	+	0.713688i
$471$	2.64954	−	25.2087i	0.122084	−	1.16156i
$472$	9.45265	+	3.62853i	0.435093	+	0.167017i
$473$	1.31893	−	25.1667i	0.0606445	−	1.15717i
$474$	−8.96374	−	15.5257i	−0.411718	−	0.713117i
$475$	−6.44518	+	1.07884i	−0.295725	+	0.0495008i
$476$	5.15285	−	12.0159i	0.236181	−	0.550749i
$477$	−0.953555	−	1.87146i	−0.0436603	−	0.0856881i
$478$	1.98912	−	1.61076i	0.0909802	−	0.0736743i
$479$	−15.0028	+	6.67968i	−0.685496	+	0.305202i	−0.719772	−	0.694210i	$-0.755754\pi$
$479$	−15.0028	+	6.67968i	−0.685496	+	0.305202i	0.0342768	+	0.999412i	$0.489087\pi$
$480$	−2.03488	−	10.7167i	−0.0928790	−	0.489149i
$481$	−3.40373	+	7.64491i	−0.155197	+	0.348578i
$482$	11.7207	+	11.7207i	0.533863	+	0.533863i
$483$	16.4931	+	31.2970i	0.750463	+	1.42406i
$484$	69.1277	−	22.4609i	3.14217	−	1.02095i
$485$	15.5151	−	7.48404i	0.704506	−	0.339833i
$486$	−11.7206	+	10.5533i	−0.531656	+	0.478706i
$487$	27.1004	−	17.5992i	1.22804	−	0.797496i	0.243030	−	0.970019i	$-0.421859\pi$
$487$	27.1004	−	17.5992i	1.22804	−	0.797496i	0.985006	+	0.172523i	$0.0551919\pi$
$488$	−1.25840	−	24.0116i	−0.0569649	−	1.08695i
$489$	2.91778	−	8.98001i	0.131947	−	0.406090i
$490$	33.0538	+	21.1969i	1.49322	+	0.957579i
$491$	7.15620	+	22.0245i	0.322955	+	0.993953i	0.972355	+	0.233506i	$0.0750199\pi$
$491$	7.15620	+	22.0245i	0.322955	+	0.993953i	−0.649401	+	0.760447i	$0.724980\pi$
$492$	39.7307	−	15.2512i	1.79120	−	0.687577i
$493$	0.806257	+	3.00899i	0.0363120	+	0.135518i
$494$	−8.46727	+	0.889946i	−0.380961	+	0.0400406i
$495$	−6.96403	+	2.09610i	−0.313010	+	0.0942127i
$496$	−20.4936	+	28.2070i	−0.920191	+	1.26653i
$497$	−19.4063	+	19.9481i	−0.870493	+	0.894792i
$498$	−32.3876	+	16.5023i	−1.45132	+	0.739487i
$499$	15.3858	−	8.88299i	0.688763	−	0.397657i	−0.114386	−	0.993436i	$-0.536490\pi$
$499$	15.3858	−	8.88299i	0.688763	−	0.397657i	0.803148	+	0.595779i	$0.203157\pi$
$500$	−13.0263	+	46.1994i	−0.582553	+	2.06610i
$501$	15.4833	−	26.8179i	0.691743	−	1.19813i
$502$	27.6698	+	17.9690i	1.23496	+	0.801994i
$503$	−10.3863	+	1.64503i	−0.463104	+	0.0733484i	−0.383627	−	0.923488i	$-0.625325\pi$
$503$	−10.3863	+	1.64503i	−0.463104	+	0.0733484i	−0.0794771	+	0.996837i	$0.525325\pi$
$504$	8.04728	−	4.79498i	0.358454	−	0.213585i
$505$	−5.15635	+	21.9004i	−0.229455	+	0.974555i
$506$	104.874	+	46.6931i	4.66224	+	2.07576i
$507$	−9.33299	+	2.50077i	−0.414493	+	0.111063i
$508$	4.30576	−	5.31717i	0.191037	−	0.235911i
$509$	−10.4505	+	11.6065i	−0.463212	+	0.514449i	−0.928814	−	0.370545i	$-0.879171\pi$
$509$	−10.4505	+	11.6065i	−0.463212	+	0.514449i	0.465603	+	0.884994i	$0.345838\pi$
$510$	−2.36999	−	9.68442i	−0.104945	−	0.428833i
$511$	−6.35917	+	32.0828i	−0.281313	+	1.41926i
$512$	−43.4780	−	22.1532i	−1.92148	−	0.979041i
$513$	7.28676	−	0.381883i	0.321718	−	0.0168605i
$514$	−30.1566	−	33.4923i	−1.33015	−	1.47728i
$515$	−17.1353	+	25.1678i	−0.755073	+	1.10902i
$516$	23.4941	+	21.1542i	1.03427	+	0.931262i
$517$	37.2287	+	5.89644i	1.63731	+	0.259325i
$518$	−13.2310	+	16.8067i	−0.581335	+	0.738444i
$519$	10.8674	+	14.9577i	0.477027	+	0.656572i
$520$	−11.0126	+	31.5376i	−0.482936	+	1.38301i
$521$	12.0877	+	27.1495i	0.529572	+	1.18944i	0.958237	+	0.285975i	$0.0923176\pi$
$521$	12.0877	+	27.1495i	0.529572	+	1.18944i	−0.428665	+	0.903464i	$0.641016\pi$
$522$	−1.49743	+	3.90093i	−0.0655406	+	0.170739i
$523$	18.7760	−	28.9125i	0.821017	−	1.26426i	−0.140656	−	0.990058i	$-0.544921\pi$
$523$	18.7760	−	28.9125i	0.821017	−	1.26426i	0.961673	−	0.274197i	$-0.0884121\pi$
$524$	78.3201			3.42143
$525$	20.3707	−	1.52852i	0.889050	−	0.0667099i
$526$	−8.24303			−0.359413
$527$	−3.73878	+	5.75722i	−0.162864	+	0.250789i
$528$	−17.0970	+	44.5393i	−0.744053	+	1.93832i
$529$	21.1412	+	47.4838i	0.919181	+	2.06451i
$530$	15.2395	+	11.5879i	0.661964	+	0.503346i
$531$	0.636635	+	0.876253i	0.0276276	+	0.0380261i
$532$	−14.6937	−	2.12037i	−0.637053	−	0.0919297i
$533$	−16.4634	−	2.60755i	−0.713110	−	0.112946i
$534$	−12.9538	−	11.6636i	−0.560564	−	0.504734i
$535$	−1.35235	−	44.2310i	−0.0584673	−	1.91227i
$536$	−0.929704	−	1.03254i	−0.0401571	−	0.0445990i
$537$	−34.2060	+	1.79266i	−1.47610	+	0.0773589i
$538$	15.2362	+	7.76325i	0.656881	+	0.334697i
$539$	−15.9714	−	33.3688i	−0.687936	−	1.43730i
$540$	20.2934	−	49.6068i	0.873290	−	2.13474i
$541$	−23.8775	+	26.5186i	−1.02657	+	1.14012i	−0.0365333	+	0.999332i	$0.511631\pi$
$541$	−23.8775	+	26.5186i	−1.02657	+	1.14012i	−0.990039	+	0.140792i	$0.955035\pi$
$542$	−20.4539	+	25.2585i	−0.878571	+	1.08495i
$543$	−4.09821	+	1.09811i	−0.175871	+	0.0471245i
$544$	3.32174	+	1.47893i	0.142418	+	0.0634088i
$545$	16.1370	−	1.34124i	0.691235	−	0.0574525i
$546$	26.6120	−	0.366318i	1.13889	−	0.0156770i
$547$	9.01623	−	1.42803i	0.385506	−	0.0610582i	0.0393265	−	0.999226i	$-0.487479\pi$
$547$	9.01623	−	1.42803i	0.385506	−	0.0610582i	0.346180	+	0.938168i	$0.387479\pi$
$548$	−30.8068	−	20.0062i	−1.31600	−	0.854621i
$549$	1.28605	−	2.22750i	0.0548872	−	0.0950674i
$550$	48.8717	−	44.7866i	2.08390	−	1.90971i
$551$	3.06337	−	1.76864i	0.130504	−	0.0753466i
$552$	−68.5417	+	34.9238i	−2.91733	+	1.48645i
$553$	−3.00590	+	11.8693i	−0.127824	+	0.504733i
$554$	2.18205	−	3.00333i	0.0927063	−	0.127599i
$555$	−0.242507	+	11.1251i	−0.0102938	+	0.472236i
$556$	−22.3863	+	2.35290i	−0.949393	+	0.0997852i
$557$	10.1973	+	38.0569i	0.432074	+	1.61252i	0.747972	+	0.663730i	$0.231028\pi$
$557$	10.1973	+	38.0569i	0.432074	+	1.61252i	−0.315898	+	0.948793i	$0.602306\pi$
$558$	−8.59632	+	3.29982i	−0.363911	+	0.139692i
$559$	−3.82643	−	11.7765i	−0.161841	−	0.498095i
$560$	−19.0686	+	28.8531i	−0.805794	+	1.21927i
$561$	−2.90266	+	8.93346i	−0.122550	+	0.377171i
$562$	−1.21277	−	23.1410i	−0.0511575	−	0.976143i
$563$	30.3162	−	19.6876i	1.27767	−	0.829732i	0.285966	−	0.958240i	$-0.407685\pi$
$563$	30.3162	−	19.6876i	1.27767	−	0.829732i	0.991708	+	0.128508i	$0.0410188\pi$
$564$	−35.1395	+	31.6397i	−1.47964	+	1.33227i
$565$	1.10408	+	0.199625i	0.0464489	+	0.00839827i
$566$	−24.5421	+	7.97420i	−1.03158	+	0.335181i
$567$	−17.9116	−	0.691652i	−0.752216	−	0.0290467i
$568$	−42.7916	−	42.7916i	−1.79549	−	1.79549i
$569$	−6.97573	+	15.6677i	−0.292438	+	0.656826i	−0.998692	−	0.0511326i	$-0.983717\pi$
$569$	−6.97573	+	15.6677i	−0.292438	+	0.656826i	0.706254	+	0.707958i	$0.250384\pi$
$570$	−9.92556	+	5.44563i	−0.415736	+	0.228092i
$571$	−33.6853	+	14.9977i	−1.40969	+	0.627632i	−0.963598	−	0.267357i	$-0.913850\pi$
$571$	−33.6853	+	14.9977i	−1.40969	+	0.627632i	−0.446088	+	0.894989i	$0.647183\pi$
$572$	45.7882	−	37.0785i	1.91450	−	1.55033i
$573$	−15.1094	−	29.6540i	−0.631206	−	1.23881i
$574$	−39.1568	−	16.7918i	−1.63437	−	0.700878i
$575$	43.2931	−	0.379716i	1.80545	−	0.0158352i
$576$	−1.15907	−	2.00758i	−0.0482948	−	0.0836490i
$577$	−0.112060	+	2.13823i	−0.00466511	+	0.0890156i	−0.999970	−	0.00777616i	$-0.997525\pi$
$577$	−0.112060	+	2.13823i	−0.00466511	+	0.0890156i	0.995305	+	0.0967917i	$0.0308581\pi$
$578$	−36.7117	−	14.0923i	−1.52701	−	0.586163i
$579$	−1.01841	+	9.68950i	−0.0423236	+	0.402682i
$580$	−2.15213	−	25.8932i	−0.0893625	−	1.07516i
$581$	23.7140	+	7.34587i	0.983823	+	0.304758i
$582$	21.1021	−	21.1021i	0.874712	−	0.874712i
$583$	−6.46382	−	16.8388i	−0.267704	−	0.697393i
$584$	−69.5661	−	14.7867i	−2.87867	−	0.611880i
$585$	−2.82540	+	2.18776i	−0.116816	+	0.0904528i
$586$	−2.50979	−	11.8076i	−0.103679	−	0.487769i
$587$	−8.93180	+	17.5297i	−0.368655	+	0.723526i	−0.998588	−	0.0531234i	$-0.983082\pi$
$587$	−8.93180	+	17.5297i	−0.368655	+	0.723526i	0.629933	+	0.776649i	$0.283082\pi$
$588$	45.1407	+	10.7730i	1.86157	+	0.444269i
$589$	7.41344	+	2.40877i	0.305466	+	0.0992518i
$590$	−8.69662	−	4.67262i	−0.358034	−	0.192369i
$591$	−0.603732	+	2.84034i	−0.0248342	+	0.116836i
$592$	−14.6410	−	11.8561i	−0.601743	−	0.487282i
$593$	22.6753	+	6.07582i	0.931161	+	0.249504i	0.692350	−	0.721562i	$-0.256576\pi$
$593$	22.6753	+	6.07582i	0.931161	+	0.249504i	0.238811	+	0.971066i	$0.423242\pi$
$594$	−59.8820	+	43.5068i	−2.45699	+	1.78511i
$595$	−3.45193	+	5.86956i	−0.141515	+	0.240629i
$596$	−13.1721	−	9.57009i	−0.539550	−	0.392006i
$597$	−12.4730	−	15.4028i	−0.510485	−	0.630396i
$598$	56.3292	+	2.95209i	2.30347	+	0.120720i
$599$	−20.7625	−	11.9873i	−0.848334	−	0.489786i	0.0117543	−	0.999931i	$-0.496258\pi$
$599$	−20.7625	−	11.9873i	−0.848334	−	0.489786i	−0.860088	+	0.510145i	$0.829592\pi$
$600$	2.71372	+	44.3370i	0.110787	+	1.81005i
$601$			18.5996i			0.758692i	0.925255	+	0.379346i	$0.123851\pi$
$601$			18.5996i			0.758692i	−0.925255	+	0.379346i	$0.876149\pi$
$602$	−2.09132	−	31.5810i	−0.0852357	−	1.28715i
$603$	−0.0232507	−	0.146799i	−0.000946843	−	0.00597813i
$604$	41.6353	+	4.37605i	1.69412	+	0.178059i
$605$	−37.1918	+	7.06192i	−1.51206	+	0.287108i
$606$	4.07439	+	38.7653i	0.165511	+	1.57473i
$607$	1.85270	−	6.91436i	0.0751987	−	0.280645i	−0.918080	−	0.396396i	$-0.870261\pi$
$607$	1.85270	−	6.91436i	0.0751987	−	0.280645i	0.993278	+	0.115751i	$0.0369274\pi$
$608$	0.645892	−	4.07800i	0.0261944	−	0.165385i
$609$	−10.0387	+	4.63612i	−0.406789	+	0.187865i
$610$	−1.73691	+	23.3800i	−0.0703256	+	0.946627i
$611$	18.1156	−	3.85058i	0.732877	−	0.155778i
$612$	1.65633	+	2.55053i	0.0669532	+	0.103099i
$613$	2.20647	+	3.39767i	0.0891186	+	0.137231i	0.880418	−	0.474198i	$-0.157262\pi$
$613$	2.20647	+	3.39767i	0.0891186	+	0.137231i	−0.791300	+	0.611428i	$0.790595\pi$
$614$	81.3720	−	17.2961i	3.28391	−	0.698016i
$615$	−21.5296	+	5.26877i	−0.868159	+	0.212457i
$616$	73.0307	−	33.7273i	2.94249	−	1.35891i
$617$	−1.01342	+	6.39846i	−0.0407986	+	0.257592i	−0.999654	−	0.0263025i	$-0.991627\pi$
$617$	−1.01342	+	6.39846i	−0.0407986	+	0.257592i	0.958855	+	0.283895i	$0.0916267\pi$
$618$	−13.6523	+	50.9510i	−0.549175	+	2.04955i
$619$	3.77294	+	35.8971i	0.151647	+	1.44283i	0.760393	+	0.649463i	$0.225006\pi$
$619$	3.77294	+	35.8971i	0.151647	+	1.44283i	−0.608746	+	0.793365i	$0.708327\pi$
$620$	39.2303	−	41.7049i	1.57553	−	1.67491i
$621$	−48.0778	−	5.05318i	−1.92930	−	0.202777i
$622$	9.85518	+	62.2232i	0.395157	+	2.49492i
$623$	0.786628	+	11.8789i	0.0315156	+	0.475918i
$624$			23.4413i			0.938403i
$625$	9.76626	−	23.0135i	0.390650	−	0.920539i
$626$	−16.1906	−	9.34763i	−0.647106	−	0.373607i
$627$	10.6515	+	0.558220i	0.425379	+	0.0222932i
$628$	−44.3501	−	54.7678i	−1.76976	−	2.18547i
$629$	−3.00088	−	2.18027i	−0.119653	−	0.0869330i
$630$	−8.37361	+	3.64788i	−0.333613	+	0.145335i
$631$	4.47810	−	3.25353i	0.178270	−	0.129521i	−0.495072	−	0.868852i	$-0.664858\pi$
$631$	4.47810	−	3.25353i	0.178270	−	0.129521i	0.673342	+	0.739331i	$0.264858\pi$
$632$	−25.7170	−	6.89085i	−1.02297	−	0.274103i
$633$	2.13926	+	1.73234i	0.0850281	+	0.0688544i
$634$	13.8792	−	65.2966i	0.551214	−	2.59326i
$635$	−2.57405	+	2.46423i	−0.102148	+	0.0977899i
$636$	21.5194	+	6.99208i	0.853301	+	0.277254i
$637$	−13.2020	−	12.4944i	−0.523082	−	0.495047i
$638$	−16.2901	+	31.9712i	−0.644932	+	1.26575i
$639$	−1.34593	−	6.33210i	−0.0532441	−	0.250494i
$640$	29.1440	+	19.8425i	1.15202	+	0.784343i
$641$	21.0666	+	4.47784i	0.832079	+	0.176864i	0.604207	−	0.796827i	$-0.293490\pi$
$641$	21.0666	+	4.47784i	0.832079	+	0.176864i	0.227872	+	0.973691i	$0.426823\pi$
$642$	−27.4739	−	71.5718i	−1.08431	−	2.82471i
$643$	18.0306	−	18.0306i	0.711059	−	0.711059i	−0.255698	−	0.966757i	$-0.582305\pi$
$643$	18.0306	−	18.0306i	0.711059	−	0.711059i	0.966757	+	0.255698i	$0.0823052\pi$
$644$	93.9529	+	29.1037i	3.70226	+	1.14685i
$645$	−10.7484	−	12.4735i	−0.423217	−	0.491146i
$646$	0.394469	−	3.75312i	0.0155202	−	0.147665i
$647$	−25.1556	−	9.65632i	−0.988968	−	0.379629i	−0.190514	−	0.981685i	$-0.561015\pi$
$647$	−25.1556	−	9.65632i	−0.988968	−	0.379629i	−0.798454	+	0.602055i	$0.794349\pi$
$648$	2.03991	−	38.9239i	0.0801354	−	1.52907i
$649$	4.65054	+	8.05497i	0.182550	+	0.316185i
$650$	14.5319	−	29.1497i	0.569989	−	1.14335i
$651$	−22.3947	−	9.60365i	−0.877718	−	0.376397i
$652$	−11.9180	−	23.3904i	−0.466746	−	0.916040i
$653$	24.3265	−	19.6992i	0.951970	−	0.770890i	−0.0214848	−	0.999769i	$-0.506839\pi$
$653$	24.3265	−	19.6992i	0.951970	−	0.770890i	0.973455	+	0.228879i	$0.0735060\pi$
$654$	25.6277	−	11.4102i	1.00212	−	0.446173i
$655$	−40.4651	−	5.14691i	−1.58110	−	0.201106i
$656$	15.2630	−	34.2814i	0.595922	−	1.33846i
$657$	−5.37958	−	5.37958i	−0.209878	−	0.209878i
$658$	47.3030	+	1.82659i	1.84406	+	0.0712080i
$659$	39.1971	−	12.7359i	1.52690	−	0.496121i	0.579175	−	0.815203i	$-0.303375\pi$
$659$	39.1971	−	12.7359i	1.52690	−	0.496121i	0.947727	+	0.319082i	$0.103375\pi$
$660$	37.0812	−	69.0152i	1.44339	−	2.68641i
$661$	20.3801	−	18.3503i	0.792695	−	0.713746i	−0.169672	−	0.985501i	$-0.554271\pi$
$661$	20.3801	−	18.3503i	0.792695	−	0.713746i	0.962366	+	0.271755i	$0.0876041\pi$
$662$	14.2466	−	9.25187i	0.553711	−	0.359584i
$663$	0.241548	+	4.60901i	0.00938095	+	0.178999i
$664$	−16.6816	+	51.3407i	−0.647372	+	1.99241i
$665$	7.45236	+	2.06113i	0.288990	+	0.0799274i
$666$	−1.53749	−	4.73191i	−0.0595766	−	0.183358i
$667$	−21.8787	+	8.39844i	−0.847146	+	0.325189i
$668$	−22.2832	−	83.1619i	−0.862161	−	3.21763i
$669$	−7.56658	+	0.795279i	−0.292541	+	0.0307473i
$670$	0.772222	+	1.11310i	0.0298335	+	0.0430028i
$671$	12.9828	−	17.8692i	0.501194	−	0.689834i
$672$	−3.16860	+	12.5118i	−0.122232	+	0.482652i
$673$	−21.6856	+	11.0493i	−0.835917	+	0.425921i	−0.818901	−	0.573934i	$-0.805416\pi$
$673$	−21.6856	+	11.0493i	−0.835917	+	0.425921i	−0.0170154	+	0.999855i	$0.505416\pi$
$674$	−45.4922	+	26.2649i	−1.75229	+	1.01169i
$675$	−13.7448	+	24.2964i	−0.529039	+	0.935170i
$676$	−13.4318	+	23.2645i	−0.516607	+	0.894790i
$677$	−10.7360	−	6.97204i	−0.412618	−	0.267957i	0.321594	−	0.946878i	$-0.395781\pi$
$677$	−10.7360	−	6.97204i	−0.412618	−	0.267957i	−0.734212	+	0.678920i	$0.762448\pi$
$678$	1.91984	−	0.304073i	0.0737310	−	0.0116778i
$679$	−20.3800	+	0.280534i	−0.782112	+	0.0107659i
$680$	−12.6587	−	7.68109i	−0.485438	−	0.294556i
$681$	19.4090	+	8.64146i	0.743756	+	0.331142i
$682$	−76.3776	+	20.4653i	−2.92465	+	0.783657i
$683$	−9.08452	+	11.2184i	−0.347609	+	0.429262i	−0.920725	−	0.390213i	$-0.872401\pi$
$683$	−9.08452	+	11.2184i	−0.347609	+	0.429262i	0.573115	+	0.819475i	$0.305735\pi$
$684$	2.31069	−	2.56628i	0.0883514	−	0.0981242i
$685$	14.6020	+	12.3610i	0.557914	+	0.472288i
$686$	−24.8716	−	39.2430i	−0.949602	−	1.49830i
$687$	2.35946	+	1.20221i	0.0900192	+	0.0458671i
$688$	27.8384	−	1.45895i	1.06133	−	0.0556218i
$689$	−5.93009	−	6.58603i	−0.225918	−	0.250908i
$690$	70.5933	−	25.3473i	2.68744	−	0.964956i
$691$	26.9032	+	24.2238i	1.02345	+	0.921516i	0.996943	−	0.0781324i	$-0.0248957\pi$
$691$	26.9032	+	24.2238i	1.02345	+	0.921516i	0.0265046	+	0.999649i	$0.491562\pi$
$692$	50.7709	+	8.04132i	1.93002	+	0.305685i
$693$	8.51688	+	1.22903i	0.323530	+	0.0466868i
$694$	−14.8014	−	20.3724i	−0.561855	−	0.773327i
$695$	11.7208	+	0.255492i	0.444596	+	0.00969135i
$696$	−9.77970	−	21.9656i	−0.370699	−	0.832603i
$697$	2.64776	−	6.89765i	0.100291	−	0.261267i
$698$	−25.5617	+	39.3616i	−0.967525	+	1.48986i
$699$	35.7800			1.35333
$700$	37.0427	−	43.0527i	1.40008	−	1.62724i
$701$	−21.7031			−0.819713			−0.409856	−	0.912150i	$-0.634421\pi$
$701$	−21.7031			−0.819713			−0.409856	+	0.912150i	$0.634421\pi$
$702$	−19.8078	+	30.5014i	−0.747599	+	1.15120i
$703$	−1.50943	+	3.93219i	−0.0569292	+	0.148306i
$704$	−8.09685	−	18.1858i	−0.305161	−	0.685404i
$705$	20.2345	−	14.0378i	0.762076	−	0.528696i
$706$	14.9950	+	20.6389i	0.564345	+	0.776754i
$707$	16.4671	−	20.9174i	0.619308	−	0.786680i
$708$	−11.5244	−	1.82528i	−0.433112	−	0.0685982i
$709$	28.1100	+	25.3104i	1.05569	+	0.950550i	0.998855	−	0.0478330i	$-0.0152315\pi$
$709$	28.1100	+	25.3104i	1.05569	+	0.950550i	0.0568378	+	0.998383i	$0.481898\pi$
$710$	36.1254	+	46.6545i	1.35576	+	1.75091i
$711$	−1.90571	−	2.11651i	−0.0714699	−	0.0793753i
$712$	−25.8514	+	1.35481i	−0.968822	+	0.0507738i
$713$	−46.0145	−	23.4456i	−1.72326	−	0.878043i
$714$	−2.29366	+	11.5718i	−0.0858380	+	0.433063i
$715$	−26.0937	+	16.1481i	−0.975851	+	0.603904i
$716$	−63.7228	+	70.7713i	−2.38143	+	2.64485i
$717$	−0.991508	+	1.22441i	−0.0370286	+	0.0457265i
$718$	−7.88575	+	2.11298i	−0.294294	+	0.0788557i
$719$	−23.5643	−	10.4915i	−0.878799	−	0.391267i	−0.0828015	−	0.996566i	$-0.526387\pi$
$719$	−23.5643	−	10.4915i	−0.878799	−	0.391267i	−0.795998	+	0.605299i	$0.793053\pi$
$720$	−3.11113	−	7.41876i	−0.115945	−	0.276481i
$721$	30.9483	−	18.4406i	1.15257	−	0.686763i
$722$	42.8450	−	6.78599i	1.59453	−	0.252548i
$723$	−8.55708	−	5.55704i	−0.318241	−	0.206668i
$724$	−5.89803	+	10.2157i	−0.219198	+	0.379663i
$725$	−0.589679	+	13.5195i	−0.0219001	+	0.502102i
$726$	−56.7975	+	32.7920i	−2.10795	+	1.21703i
$727$	−16.7072	+	8.51272i	−0.619634	+	0.315719i	−0.735478	−	0.677548i	$-0.763043\pi$
$727$	−16.7072	+	8.51272i	−0.619634	+	0.315719i	0.115845	+	0.993267i	$0.463043\pi$
$728$	27.5613	−	28.3307i	1.02149	−	1.05001i
$729$	17.6531	−	24.2974i	0.653818	−	0.899904i
$730$	65.4684	+	22.8610i	2.42309	+	0.846123i
$731$	5.45852	−	0.573714i	0.201891	−	0.0212196i
$732$	7.17148	+	26.7643i	0.265065	+	0.989238i
$733$	32.4005	−	12.4374i	1.19674	−	0.459385i	0.323290	−	0.946300i	$-0.395211\pi$
$733$	32.4005	−	12.4374i	1.19674	−	0.459385i	0.873449	+	0.486915i	$0.161878\pi$
$734$	−9.62911	−	29.6354i	−0.355417	−	1.09386i
$735$	−22.6146	−	8.53247i	−0.834151	−	0.314725i
$736$	−8.45298	+	26.0156i	−0.311581	+	0.958948i
$737$	−0.0667983	−	1.27459i	−0.00246055	−	0.0469501i
$738$	8.31151	−	5.39756i	0.305951	−	0.198687i
$739$	12.7524	−	11.4824i	0.469106	−	0.422385i	−0.400375	−	0.916351i	$-0.631120\pi$
$739$	12.7524	−	11.4824i	0.469106	−	0.422385i	0.869481	+	0.493966i	$0.164453\pi$
$740$	21.3947	+	22.3482i	0.786484	+	0.821536i
$741$	4.98427	−	1.61949i	0.183102	−	0.0594934i
$742$	−10.5608	−	20.0400i	−0.387700	−	0.735691i
$743$	−27.5202	−	27.5202i	−1.00962	−	1.00962i	−0.999953	−	0.00966488i	$-0.996924\pi$
$743$	−27.5202	−	27.5202i	−1.00962	−	1.00962i	−0.00966488	−	0.999953i	$-0.503076\pi$
$744$	21.5511	−	48.4046i	0.790103	−	1.77460i
$745$	6.17663	+	5.81013i	0.226294	+	0.212867i
$746$	44.5472	−	19.8337i	1.63099	−	0.726163i
$747$	−4.48775	+	3.63411i	−0.164198	+	0.132965i
$748$	11.8562	+	23.2692i	0.433507	+	0.850805i
$749$	−20.6361	+	48.1212i	−0.754026	+	1.75831i
$750$	2.82984	−	43.2187i	0.103331	−	1.57812i
$751$	19.5835	+	33.9196i	0.714612	+	1.23774i	0.963109	+	0.269112i	$0.0867301\pi$
$751$	19.5835	+	33.9196i	0.714612	+	1.23774i	−0.248497	+	0.968633i	$0.579937\pi$
$752$	−2.18210	+	41.6370i	−0.0795731	+	1.51835i
$753$	−18.9597	−	7.27796i	−0.690931	−	0.265223i
$754$	−1.84290	+	17.5340i	−0.0671145	+	0.638552i
$755$	−21.2239	−	4.99706i	−0.772415	−	0.181862i
$756$	−46.5396	+	43.0790i	−1.69263	+	1.56677i
$757$	−5.61158	+	5.61158i	−0.203956	+	0.203956i	−0.801693	−	0.597736i	$-0.796067\pi$
$757$	−5.61158	+	5.61158i	−0.203956	+	0.203956i	0.597736	+	0.801693i	$0.296067\pi$
$758$	−20.2590	−	52.7764i	−0.735838	−	1.91692i
$759$	−69.1210	−	14.6921i	−2.50893	−	0.533290i
$760$	−4.70450	+	16.1417i	−0.170650	+	0.585522i
$761$	5.54682	+	26.0957i	0.201072	+	0.945970i	0.956724	+	0.290997i	$0.0939868\pi$
$761$	5.54682	+	26.0957i	0.201072	+	0.945970i	−0.755652	+	0.654973i	$0.772680\pi$
$762$	−2.80271	+	5.50062i	−0.101531	+	0.199267i
$763$	−17.9797	−	6.61929i	−0.650909	−	0.239634i
$764$	−88.0024	−	28.5937i	−3.18382	−	1.03448i
$765$	−0.688155	−	1.42661i	−0.0248803	−	0.0515793i
$766$	9.77346	−	45.9805i	0.353130	−	1.66134i

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36631 + 2.10393i) q^{2} +(0.553395 - 1.44164i) q^{3} +(-1.74625 - 3.92214i) q^{4} +(0.644473 + 2.14118i) q^{5} +(2.27701 + 3.13403i) q^{6} +(0.377880 - 2.61863i) q^{7} +(5.68228 + 0.899985i) q^{8} +(0.457347 + 0.411797i) q^{9} +O(q^{10})\)	\(q+(-1.36631 + 2.10393i) q^{2} +(0.553395 - 1.44164i) q^{3} +(-1.74625 - 3.92214i) q^{4} +(0.644473 + 2.14118i) q^{5} +(2.27701 + 3.13403i) q^{6} +(0.377880 - 2.61863i) q^{7} +(5.68228 + 0.899985i) q^{8} +(0.457347 + 0.411797i) q^{9} +(-5.38544 - 1.56958i) q^{10} +(3.53627 + 3.92742i) q^{11} +(-6.62068 + 0.346975i) q^{12} +(2.31369 + 1.17888i) q^{13} +(4.99310 + 4.37288i) q^{14} +(3.44346 + 0.255818i) q^{15} +(-3.91167 + 4.34435i) q^{16} +(-0.724344 + 0.894491i) q^{17} +(-1.49127 + 0.399585i) q^{18} +(1.19398 + 0.531592i) q^{19} +(7.27259 - 6.26674i) q^{20} +(-3.56601 - 1.99390i) q^{21} +(-13.0946 + 2.07399i) q^{22} +(-7.26201 - 4.71601i) q^{23} +(4.44200 - 7.69377i) q^{24} +(-4.16931 + 2.75987i) q^{25} +(-5.64150 + 3.25712i) q^{26} +(4.97446 - 2.53461i) q^{27} +(-10.9305 + 3.09067i) q^{28} +(1.59083 - 2.18958i) q^{29} +(-5.24305 + 6.89528i) q^{30} +(5.93147 - 0.623423i) q^{31} +(-0.817633 - 3.05145i) q^{32} +(7.61889 - 2.92462i) q^{33} +(-0.892268 - 2.74612i) q^{34} +(5.85049 - 0.878526i) q^{35} +(0.816484 - 2.51288i) q^{36} +(0.168662 + 3.21827i) q^{37} +(-2.74977 + 1.78572i) q^{38} +(2.97991 - 2.68312i) q^{39} +(1.73505 + 12.7468i) q^{40} +(-6.10496 + 1.98362i) q^{41} +(9.06729 - 4.77834i) q^{42} +(-3.37188 - 3.37188i) q^{43} +(9.22869 - 20.7280i) q^{44} +(-0.586984 + 1.24466i) q^{45} +(19.8443 - 8.83524i) q^{46} +(5.54276 - 4.48844i) q^{47} +(4.09831 + 8.04338i) q^{48} +(-6.71441 - 1.97905i) q^{49} +(-0.110010 - 12.5428i) q^{50} +(0.888688 + 1.53925i) q^{51} +(0.583468 - 11.1332i) q^{52} +(-3.18623 - 1.22308i) q^{53} +(-1.46399 + 13.9290i) q^{54} +(-6.13029 + 10.1029i) q^{55} +(4.50395 - 14.5397i) q^{56} +(1.42711 - 1.42711i) q^{57} +(2.43317 + 6.33863i) q^{58} +(1.72149 + 0.365913i) q^{59} +(-5.00979 - 13.9525i) q^{60} +(-0.868947 - 4.08807i) q^{61} +(-6.79258 + 13.3312i) q^{62} +(1.25117 - 1.04201i) q^{63} +(-3.58241 - 1.16399i) q^{64} +(-1.03309 + 5.71379i) q^{65} +(-4.25656 + 20.0255i) q^{66} +(-0.187687 - 0.151986i) q^{67} +(4.77320 + 1.27897i) q^{68} +(-10.8176 + 7.85941i) q^{69} +(-6.14521 + 13.5093i) q^{70} +(-8.50997 - 6.18285i) q^{71} +(2.22817 + 2.75155i) q^{72} +(-12.3451 - 0.646980i) q^{73} +(-7.00145 - 4.04229i) q^{74} +(1.67147 + 7.53795i) q^{75} -5.61123i q^{76} +(11.6207 - 7.77607i) q^{77} +(1.57363 + 9.93549i) q^{78} +(-4.60244 - 0.483736i) q^{79} +(-11.8230 - 5.57578i) q^{80} +(-0.708179 - 6.73788i) q^{81} +(4.16785 - 15.5546i) q^{82} +(-1.46786 + 9.26772i) q^{83} +(-1.59323 + 17.4682i) q^{84} +(-2.38209 - 0.974476i) q^{85} +(11.7012 - 2.48717i) q^{86} +(-2.27624 - 3.50510i) q^{87} +(16.5594 + 25.4993i) q^{88} +(-4.40130 + 0.935526i) q^{89} +(-1.81667 - 2.93556i) q^{90} +(3.96135 - 5.61321i) q^{91} +(-5.81555 + 36.7179i) q^{92} +(2.38369 - 8.89606i) q^{93} +(1.87024 + 17.7942i) q^{94} +(-0.368749 + 2.89912i) q^{95} +(-4.85157 - 0.509920i) q^{96} +(-1.20511 - 7.60880i) q^{97} +(13.3377 - 11.4227i) q^{98} +3.25242i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more