LMFDB - Embedded newform 73.2.k.a.23.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [73,2,Mod(6,73)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(73, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("73.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	73.k (of order $36$, degree $12$, 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:	$0.582907934755$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			23.3
Character	$\chi$	$=$	73.23
Dual form			73.2.k.a.54.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.472051 - 0.171812i) q^{2} +(0.686550 - 0.396380i) q^{3} +(-1.33878 - 1.12337i) q^{4} +(0.980689 - 2.10309i) q^{5} +(-0.392189 + 0.0691536i) q^{6} +(2.33310 + 0.625153i) q^{7} +(0.941308 + 1.63039i) q^{8} +(-1.18577 + 2.05381i) q^{9} +O(q^{10})$	\(q+(-0.472051 - 0.171812i) q^{2} +(0.686550 - 0.396380i) q^{3} +(-1.33878 - 1.12337i) q^{4} +(0.980689 - 2.10309i) q^{5} +(-0.392189 + 0.0691536i) q^{6} +(2.33310 + 0.625153i) q^{7} +(0.941308 + 1.63039i) q^{8} +(-1.18577 + 2.05381i) q^{9} +(-0.824273 + 0.824273i) q^{10} +(-1.24003 - 0.578237i) q^{11} +(-1.36442 - 0.240584i) q^{12} +(-0.369131 + 0.527174i) q^{13} +(-0.993934 - 0.695960i) q^{14} +(-0.160332 - 1.83260i) q^{15} +(0.442729 + 2.51084i) q^{16} +(-0.229595 - 0.856859i) q^{17} +(0.912611 - 0.765772i) q^{18} +(-2.04569 + 5.62050i) q^{19} +(-3.67547 + 1.71390i) q^{20} +(1.84959 - 0.495596i) q^{21} +(0.486010 + 0.486010i) q^{22} +(-0.0467507 - 0.128447i) q^{23} +(1.29251 + 0.746231i) q^{24} +(-0.247315 - 0.294739i) q^{25} +(0.264824 - 0.185432i) q^{26} +4.25833i q^{27} +(-2.42123 - 3.45787i) q^{28} +(-2.96817 - 6.36527i) q^{29} +(-0.239179 + 0.892629i) q^{30} +(10.4687 + 0.915897i) q^{31} +(0.876229 - 4.96934i) q^{32} +(-1.08055 + 0.0945355i) q^{33} +(-0.0388387 + 0.443928i) q^{34} +(3.60281 - 4.29366i) q^{35} +(3.89465 - 1.41754i) q^{36} +(-8.13065 + 2.95932i) q^{37} +(1.93134 - 2.30168i) q^{38} +(-0.0444659 + 0.508247i) q^{39} +(4.35200 - 0.380751i) q^{40} +(1.22086 - 6.92384i) q^{41} +(-0.958250 - 0.0838360i) q^{42} +(1.11159 - 4.14852i) q^{43} +(1.01056 + 2.16714i) q^{44} +(3.15648 + 4.50792i) q^{45} +0.0686656i q^{46} +(0.304101 - 0.212934i) q^{47} +(1.29920 + 1.54833i) q^{48} +(-1.00962 - 0.582904i) q^{49} +(0.0661056 + 0.181624i) q^{50} +(-0.497270 - 0.497270i) q^{51} +(1.08639 - 0.291098i) q^{52} +(-11.9329 + 5.56439i) q^{53} +(0.731635 - 2.01015i) q^{54} +(-2.43217 + 2.04084i) q^{55} +(1.17692 + 4.39234i) q^{56} +(0.823381 + 4.66962i) q^{57} +(0.307496 + 3.51470i) q^{58} +(-5.22225 - 3.65666i) q^{59} +(-1.84404 + 2.63356i) q^{60} +(-0.876156 - 0.154490i) q^{61} +(-4.78442 - 2.23101i) q^{62} +(-4.05046 + 4.05046i) q^{63} +(1.28215 - 2.22076i) q^{64} +(0.746694 + 1.29331i) q^{65} +(0.526315 + 0.141026i) q^{66} +(2.23866 - 0.394736i) q^{67} +(-0.655191 + 1.40506i) q^{68} +(-0.0830103 - 0.0696539i) q^{69} +(-2.43841 + 1.40782i) q^{70} +(14.4771 + 5.26922i) q^{71} -4.46468 q^{72} +(-4.39858 - 7.32479i) q^{73} +4.34653 q^{74} +(-0.286623 - 0.104322i) q^{75} +(9.05261 - 5.22652i) q^{76} +(-2.53164 - 2.12430i) q^{77} +(0.108313 - 0.232279i) q^{78} +(-3.81428 + 0.672560i) q^{79} +(5.71471 + 1.53125i) q^{80} +(-1.86938 - 3.23786i) q^{81} +(-1.76591 + 3.05865i) q^{82} +(-7.48812 + 7.48812i) q^{83} +(-3.03293 - 1.41428i) q^{84} +(-2.02722 - 0.357453i) q^{85} +(-1.23750 + 1.76733i) q^{86} +(-4.56086 - 3.19355i) q^{87} +(-0.224499 - 2.56604i) q^{88} +(1.60279 + 9.08990i) q^{89} +(-0.715502 - 2.67029i) q^{90} +(-1.19079 + 0.999188i) q^{91} +(-0.0817038 + 0.224479i) q^{92} +(7.55036 - 3.52079i) q^{93} +(-0.180136 + 0.0482672i) q^{94} +(9.81424 + 9.81424i) q^{95} +(-1.36817 - 3.75902i) q^{96} +(-10.1182 - 5.84172i) q^{97} +(0.376442 + 0.448626i) q^{98} +(2.65798 - 1.86114i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 12 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) $ 72 * q - 12 * q^2 - 18 * q^3 - 12 * q^4 - 12 * q^5 - 24 * q^6 - 18 * q^7 - 24 * q^8 + 36 * q^9	\( 72 q - 12 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{7} - 24 q^{8} + 36 q^{9} - 6 q^{11} + 6 q^{12} - 12 q^{13} - 12 q^{14} - 30 q^{15} + 30 q^{17} - 12 q^{18} - 6 q^{19} + 60 q^{20} - 30 q^{21} - 12 q^{22} - 12 q^{23} - 18 q^{24} + 36 q^{25} + 12 q^{26} + 120 q^{28} - 6 q^{29} - 72 q^{30} - 18 q^{31} - 18 q^{32} - 60 q^{33} - 60 q^{34} - 36 q^{35} + 60 q^{36} - 6 q^{37} + 48 q^{38} + 78 q^{39} - 18 q^{40} + 54 q^{42} - 24 q^{43} + 48 q^{44} + 36 q^{47} + 30 q^{48} - 18 q^{49} + 132 q^{50} - 18 q^{51} - 24 q^{53} - 6 q^{54} + 72 q^{55} + 24 q^{56} - 6 q^{57} - 18 q^{58} - 66 q^{60} - 36 q^{61} - 36 q^{62} + 12 q^{63} - 84 q^{64} + 24 q^{65} + 156 q^{66} - 54 q^{67} - 84 q^{68} - 6 q^{69} - 162 q^{70} + 48 q^{71} - 72 q^{72} - 36 q^{73} + 144 q^{74} + 6 q^{75} - 180 q^{76} - 24 q^{77} - 198 q^{78} - 36 q^{79} - 126 q^{80} - 48 q^{81} + 30 q^{82} - 48 q^{83} - 126 q^{84} - 6 q^{85} - 120 q^{86} + 6 q^{87} + 6 q^{88} + 6 q^{89} + 210 q^{90} + 48 q^{91} + 96 q^{92} + 144 q^{93} - 6 q^{94} - 12 q^{95} + 162 q^{96} - 18 q^{97} + 186 q^{98} + 78 q^{99}+O(q^{100}) \) 72 * q - 12 * q^2 - 18 * q^3 - 12 * q^4 - 12 * q^5 - 24 * q^6 - 18 * q^7 - 24 * q^8 + 36 * q^9 - 6 * q^11 + 6 * q^12 - 12 * q^13 - 12 * q^14 - 30 * q^15 + 30 * q^17 - 12 * q^18 - 6 * q^19 + 60 * q^20 - 30 * q^21 - 12 * q^22 - 12 * q^23 - 18 * q^24 + 36 * q^25 + 12 * q^26 + 120 * q^28 - 6 * q^29 - 72 * q^30 - 18 * q^31 - 18 * q^32 - 60 * q^33 - 60 * q^34 - 36 * q^35 + 60 * q^36 - 6 * q^37 + 48 * q^38 + 78 * q^39 - 18 * q^40 + 54 * q^42 - 24 * q^43 + 48 * q^44 + 36 * q^47 + 30 * q^48 - 18 * q^49 + 132 * q^50 - 18 * q^51 - 24 * q^53 - 6 * q^54 + 72 * q^55 + 24 * q^56 - 6 * q^57 - 18 * q^58 - 66 * q^60 - 36 * q^61 - 36 * q^62 + 12 * q^63 - 84 * q^64 + 24 * q^65 + 156 * q^66 - 54 * q^67 - 84 * q^68 - 6 * q^69 - 162 * q^70 + 48 * q^71 - 72 * q^72 - 36 * q^73 + 144 * q^74 + 6 * q^75 - 180 * q^76 - 24 * q^77 - 198 * q^78 - 36 * q^79 - 126 * q^80 - 48 * q^81 + 30 * q^82 - 48 * q^83 - 126 * q^84 - 6 * q^85 - 120 * q^86 + 6 * q^87 + 6 * q^88 + 6 * q^89 + 210 * q^90 + 48 * q^91 + 96 * q^92 + 144 * q^93 - 6 * q^94 - 12 * q^95 + 162 * q^96 - 18 * q^97 + 186 * q^98 + 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/73\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{23}{36}\right)$

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 $

$2$	−0.472051	−	0.171812i	−0.333790	−	0.121490i	0.169687	−	0.985498i	$-0.445724\pi$
$2$	−0.472051	−	0.171812i	−0.333790	−	0.121490i	−0.503478	+	0.864008i	$0.667946\pi$
$3$	0.686550	−	0.396380i	0.396380	−	0.228850i	−0.288541	−	0.957468i	$-0.593170\pi$
$3$	0.686550	−	0.396380i	0.396380	−	0.228850i	0.684921	+	0.728618i	$0.259837\pi$
$4$	−1.33878	−	1.12337i	−0.669388	−	0.561683i
$5$	0.980689	−	2.10309i	0.438577	−	0.940532i	−0.555465	−	0.831540i	$-0.687460\pi$
$5$	0.980689	−	2.10309i	0.438577	−	0.940532i	0.994043	−	0.108992i	$-0.0347624\pi$
$6$	−0.392189	+	0.0691536i	−0.160111	+	0.0282318i
$7$	2.33310	+	0.625153i	0.881830	+	0.236286i	0.671197	−	0.741279i	$-0.265781\pi$
$7$	2.33310	+	0.625153i	0.881830	+	0.236286i	0.210634	+	0.977565i	$0.432447\pi$
$8$	0.941308	+	1.63039i	0.332803	+	0.576431i
$9$	−1.18577	+	2.05381i	−0.395255	+	0.684602i
$10$	−0.824273	+	0.824273i	−0.260658	+	0.260658i
$11$	−1.24003	−	0.578237i	−0.373884	−	0.174345i	0.226588	−	0.973991i	$-0.427243\pi$
$11$	−1.24003	−	0.578237i	−0.373884	−	0.174345i	−0.600472	+	0.799646i	$0.705021\pi$
$12$	−1.36442	−	0.240584i	−0.393873	−	0.0694505i
$13$	−0.369131	+	0.527174i	−0.102379	+	0.146212i	−0.867073	−	0.498182i	$-0.834001\pi$
$13$	−0.369131	+	0.527174i	−0.102379	+	0.146212i	0.764694	+	0.644394i	$0.222890\pi$
$14$	−0.993934	−	0.695960i	−0.265640	−	0.186003i
$15$	−0.160332	−	1.83260i	−0.0413976	−	0.473176i
$16$	0.442729	+	2.51084i	0.110682	+	0.627710i
$17$	−0.229595	−	0.856859i	−0.0556849	−	0.207819i	0.932478	−	0.361226i	$-0.117642\pi$
$17$	−0.229595	−	0.856859i	−0.0556849	−	0.207819i	−0.988163	+	0.153408i	$0.950975\pi$
$18$	0.912611	−	0.765772i	0.215105	−	0.180494i
$19$	−2.04569	+	5.62050i	−0.469314	+	1.28943i	0.448984	+	0.893540i	$0.351786\pi$
$19$	−2.04569	+	5.62050i	−0.469314	+	1.28943i	−0.918298	+	0.395890i	$0.870436\pi$
$20$	−3.67547	+	1.71390i	−0.821860	+	0.383240i
$21$	1.84959	−	0.495596i	0.403614	−	0.108148i
$22$	0.486010	+	0.486010i	0.103618	+	0.103618i
$23$	−0.0467507	−	0.128447i	−0.00974820	−	0.0267830i	0.934723	−	0.355377i	$-0.115647\pi$
$23$	−0.0467507	−	0.128447i	−0.00974820	−	0.0267830i	−0.944471	+	0.328594i	$0.893425\pi$
$24$	1.29251	+	0.746231i	0.263833	+	0.152324i
$25$	−0.247315	−	0.294739i	−0.0494631	−	0.0589478i
$26$	0.264824	−	0.185432i	0.0519362	−	0.0363661i
$27$			4.25833i			0.819517i
$28$	−2.42123	−	3.45787i	−0.457569	−	0.653476i
$29$	−2.96817	−	6.36527i	−0.551176	−	1.18200i	−0.962692	−	0.270598i	$-0.912778\pi$
$29$	−2.96817	−	6.36527i	−0.551176	−	1.18200i	0.411516	−	0.911402i	$-0.364999\pi$
$30$	−0.239179	+	0.892629i	−0.0436680	+	0.162971i
$31$	10.4687	+	0.915897i	1.88024	+	0.164500i	0.968949	−	0.247259i	$-0.0795298\pi$
$31$	10.4687	+	0.915897i	1.88024	+	0.164500i	0.911293	+	0.411759i	$0.135085\pi$
$32$	0.876229	−	4.96934i	0.154897	−	0.878463i
$33$	−1.08055	+	0.0945355i	−0.188099	+	0.0164565i
$34$	−0.0388387	+	0.443928i	−0.00666078	+	0.0761330i
$35$	3.60281	−	4.29366i	0.608985	−	0.725760i
$36$	3.89465	−	1.41754i	0.649109	−	0.236256i
$37$	−8.13065	+	2.95932i	−1.33667	+	0.486509i	−0.908763	−	0.417313i	$-0.862972\pi$
$37$	−8.13065	+	2.95932i	−1.33667	+	0.486509i	−0.427909	+	0.903822i	$0.640749\pi$
$38$	1.93134	−	2.30168i	0.313305	−	0.373382i
$39$	−0.0444659	+	0.508247i	−0.00712024	+	0.0813847i
$40$	4.35200	−	0.380751i	0.688112	−	0.0602020i
$41$	1.22086	−	6.92384i	0.190666	−	1.08132i	−0.727790	−	0.685800i	$-0.759452\pi$
$41$	1.22086	−	6.92384i	0.190666	−	1.08132i	0.918456	−	0.395523i	$-0.129437\pi$
$42$	−0.958250	−	0.0838360i	−0.147861	−	0.0129362i
$43$	1.11159	−	4.14852i	0.169516	−	0.632644i	−0.827904	−	0.560869i	$-0.810467\pi$
$43$	1.11159	−	4.14852i	0.169516	−	0.632644i	0.997421	−	0.0717748i	$-0.0228663\pi$
$44$	1.01056	+	2.16714i	0.152347	+	0.326709i
$45$	3.15648	+	4.50792i	0.470541	+	0.672001i
$46$			0.0686656i			0.0101242i
$47$	0.304101	−	0.212934i	0.0443577	−	0.0310596i	−0.551187	−	0.834382i	$-0.685825\pi$
$47$	0.304101	−	0.212934i	0.0443577	−	0.0310596i	0.595545	+	0.803322i	$0.296936\pi$
$48$	1.29920	+	1.54833i	0.187524	+	0.223482i
$49$	−1.00962	−	0.582904i	−0.144231	−	0.0832720i
$50$	0.0661056	+	0.181624i	0.00934874	+	0.0256855i
$51$	−0.497270	−	0.497270i	−0.0696317	−	0.0696317i
$52$	1.08639	−	0.291098i	0.150656	−	0.0403681i
$53$	−11.9329	+	5.56439i	−1.63911	+	0.764327i	−0.999989	−	0.00478237i	$-0.998478\pi$
$53$	−11.9329	+	5.56439i	−1.63911	+	0.764327i	−0.639117	+	0.769110i	$0.720700\pi$
$54$	0.731635	−	2.01015i	0.0995629	−	0.273547i
$55$	−2.43217	+	2.04084i	−0.327954	+	0.275186i
$56$	1.17692	+	4.39234i	0.157273	+	0.586951i
$57$	0.823381	+	4.66962i	0.109059	+	0.618507i
$58$	0.307496	+	3.51470i	0.0403762	+	0.461503i
$59$	−5.22225	−	3.65666i	−0.679879	−	0.476056i	0.181916	−	0.983314i	$-0.441770\pi$
$59$	−5.22225	−	3.65666i	−0.679879	−	0.476056i	−0.861794	+	0.507258i	$0.830659\pi$
$60$	−1.84404	+	2.63356i	−0.238064	+	0.339991i
$61$	−0.876156	−	0.154490i	−0.112180	−	0.0197804i	0.117276	−	0.993099i	$-0.462584\pi$
$61$	−0.876156	−	0.154490i	−0.112180	−	0.0197804i	−0.229456	+	0.973319i	$0.573695\pi$
$62$	−4.78442	−	2.23101i	−0.607622	−	0.283339i
$63$	−4.05046	+	4.05046i	−0.510310	+	0.510310i
$64$	1.28215	−	2.22076i	0.160269	−	0.277594i
$65$	0.746694	+	1.29331i	0.0926159	+	0.160416i
$66$	0.526315	+	0.141026i	0.0647849	+	0.0173591i
$67$	2.23866	−	0.394736i	0.273496	−	0.0482247i	−0.0352181	−	0.999380i	$-0.511213\pi$
$67$	2.23866	−	0.394736i	0.273496	−	0.0482247i	0.308714	+	0.951155i	$0.400101\pi$
$68$	−0.655191	+	1.40506i	−0.0794536	+	0.170389i
$69$	−0.0830103	−	0.0696539i	−0.00999327	−	0.00838535i
$70$	−2.43841	+	1.40782i	−0.291446	+	0.168266i
$71$	14.4771	+	5.26922i	1.71811	+	0.625341i	0.997673	−	0.0681787i	$-0.0217188\pi$
$71$	14.4771	+	5.26922i	1.71811	+	0.625341i	0.720438	+	0.693520i	$0.243941\pi$
$72$	−4.46468			−0.526168
$73$	−4.39858	−	7.32479i	−0.514814	−	0.857302i
$73$	−4.39858	−	7.32479i	−0.514814	−	0.857302i
$74$	4.34653			0.505274
$75$	−0.286623	−	0.104322i	−0.0330964	−	0.0120461i
$76$	9.05261	−	5.22652i	1.03841	−	0.599523i
$77$	−2.53164	−	2.12430i	−0.288507	−	0.242086i
$78$	0.108313	−	0.232279i	0.0122641	−	0.0263004i
$79$	−3.81428	+	0.672560i	−0.429140	+	0.0756689i	−0.384046	−	0.923314i	$-0.625470\pi$
$79$	−3.81428	+	0.672560i	−0.429140	+	0.0756689i	−0.0450934	+	0.998983i	$0.514359\pi$
$80$	5.71471	+	1.53125i	0.638924	+	0.171199i
$81$	−1.86938	−	3.23786i	−0.207709	−	0.359762i
$82$	−1.76591	+	3.05865i	−0.195012	+	0.337771i
$83$	−7.48812	+	7.48812i	−0.821928	+	0.821928i	−0.986384	−	0.164456i	$-0.947413\pi$
$83$	−7.48812	+	7.48812i	−0.821928	+	0.821928i	0.164456	+	0.986384i	$0.447413\pi$
$84$	−3.03293	−	1.41428i	−0.330919	−	0.154310i
$85$	−2.02722	−	0.357453i	−0.219882	−	0.0387712i
$86$	−1.23750	+	1.76733i	−0.133443	+	0.190576i
$87$	−4.56086	−	3.19355i	−0.488976	−	0.342385i
$88$	−0.224499	−	2.56604i	−0.0239317	−	0.273541i
$89$	1.60279	+	9.08990i	0.169896	+	0.963527i	0.943872	+	0.330312i	$0.107154\pi$
$89$	1.60279	+	9.08990i	0.169896	+	0.963527i	−0.773976	+	0.633215i	$0.781735\pi$
$90$	−0.715502	−	2.67029i	−0.0754206	−	0.281473i
$91$	−1.19079	+	0.999188i	−0.124828	+	0.104743i
$92$	−0.0817038	+	0.224479i	−0.00851821	+	0.0234036i
$93$	7.55036	−	3.52079i	0.782936	−	0.365089i
$94$	−0.180136	+	0.0482672i	−0.0185796	+	0.00497838i
$95$	9.81424	+	9.81424i	1.00692	+	1.00692i
$96$	−1.36817	−	3.75902i	−0.139638	−	0.383653i
$97$	−10.1182	−	5.84172i	−1.02734	−	0.593136i	−0.111120	−	0.993807i	$-0.535444\pi$
$97$	−10.1182	−	5.84172i	−1.02734	−	0.593136i	−0.916222	+	0.400670i	$0.868777\pi$
$98$	0.376442	+	0.448626i	0.0380263	+	0.0453180i
$99$	2.65798	−	1.86114i	0.267137	−	0.187051i
$100$			0.672415i			0.0672415i
$101$	−0.441136	−	0.630008i	−0.0438947	−	0.0626881i	0.796605	−	0.604500i	$-0.206627\pi$
$101$	−0.441136	−	0.630008i	−0.0438947	−	0.0626881i	−0.840499	+	0.541812i	$0.817738\pi$
$102$	0.149299	+	0.320174i	0.0147828	+	0.0317019i
$103$	−0.0838109	+	0.312786i	−0.00825813	+	0.0308198i	−0.969932	−	0.243376i	$-0.921745\pi$
$103$	−0.0838109	+	0.312786i	−0.00825813	+	0.0308198i	0.961674	+	0.274196i	$0.0884117\pi$
$104$	−1.20697	−	0.105596i	−0.118353	−	0.0103545i
$105$	0.771587	−	4.37589i	0.0752992	−	0.427043i
$106$	6.58895	−	0.576458i	0.639975	−	0.0559906i
$107$	1.37263	−	15.6892i	0.132697	−	1.51674i	−0.579625	−	0.814883i	$-0.696801\pi$
$107$	1.37263	−	15.6892i	0.132697	−	1.51674i	0.712322	−	0.701852i	$-0.247643\pi$
$108$	4.78367	−	5.70096i	0.460309	−	0.548575i
$109$	13.9065	−	5.06155i	1.33200	−	0.484809i	0.424717	−	0.905326i	$-0.360374\pi$
$109$	13.9065	−	5.06155i	1.33200	−	0.484809i	0.907285	+	0.420517i	$0.138151\pi$
$110$	1.49875	−	0.545500i	0.142900	−	0.0520114i
$111$	−4.40909	+	5.25455i	−0.418492	+	0.498739i
$112$	−0.536727	+	6.13482i	−0.0507160	+	0.579686i
$113$	11.9759	−	1.04776i	1.12660	−	0.0985646i	0.491414	−	0.870926i	$-0.336480\pi$
$113$	11.9759	−	1.04776i	1.12660	−	0.0985646i	0.635183	+	0.772361i	$0.280924\pi$
$114$	0.413622	−	2.34577i	0.0387392	−	0.219701i
$115$	−0.315983	−	0.0276449i	−0.0294656	−	0.00257790i
$116$	−3.17681	+	11.8560i	−0.294959	+	1.10080i
$117$	−0.645010	−	1.38323i	−0.0596312	−	0.127880i
$118$	1.83691	+	2.62337i	0.169101	+	0.241501i
$119$		−	2.14267i		−	0.196418i
$120$	2.83694	−	1.98645i	0.258976	−	0.181337i
$121$	−5.86734	−	6.99242i	−0.533394	−	0.635675i
$122$	0.387047	+	0.223462i	0.0350416	+	0.0202313i
$123$	−1.90629	−	5.23749i	−0.171884	−	0.472249i
$124$	−12.9864	−	12.9864i	−1.16622	−	1.16622i
$125$	10.3448	−	2.77188i	0.925266	−	0.247924i
$126$	2.60794	−	1.21610i	0.232334	−	0.108339i
$127$	−2.82519	+	7.76214i	−0.250695	+	0.688778i	0.748963	+	0.662612i	$0.230552\pi$
$127$	−2.82519	+	7.76214i	−0.250695	+	0.688778i	−0.999658	+	0.0261663i	$0.991670\pi$
$128$	−8.71771	+	7.31503i	−0.770544	+	0.646564i
$129$	−0.881227	−	3.28878i	−0.0775877	−	0.289561i
$130$	−0.130270	−	0.738800i	−0.0114255	−	0.0647970i
$131$	0.640392	+	7.31971i	0.0559513	+	0.639526i	0.971456	+	0.237219i	$0.0762359\pi$
$131$	0.640392	+	7.31971i	0.0559513	+	0.639526i	−0.915505	+	0.402307i	$0.868208\pi$
$132$	1.55281	+	1.08729i	0.135155	+	0.0946363i
$133$	−8.28649	+	11.8343i	−0.718530	+	1.02617i
$134$	−1.12458	−	0.198294i	−0.0971490	−	0.0171300i
$135$	8.95568	+	4.17610i	0.770782	+	0.359421i
$136$	1.18090	−	1.18090i	0.101261	−	0.101261i
$137$	2.53967	−	4.39883i	0.216978	−	0.375818i	−0.736904	−	0.675997i	$-0.763713\pi$
$137$	2.53967	−	4.39883i	0.216978	−	0.375818i	0.953883	+	0.300179i	$0.0970466\pi$
$138$	0.0272177	+	0.0471424i	0.00231692	+	0.00401303i
$139$	13.9355	+	3.73401i	1.18200	+	0.316715i	0.795718	−	0.605667i	$-0.207094\pi$
$139$	13.9355	+	3.73401i	1.18200	+	0.316715i	0.386278	+	0.922382i	$0.373760\pi$
$140$	−9.64670	+	1.70097i	−0.815295	+	0.143759i
$141$	0.124378	−	0.266729i	0.0104745	−	0.0224626i
$142$	−5.92859	−	4.97468i	−0.497516	−	0.417466i
$143$	0.762566	−	0.440268i	0.0637690	−	0.0368171i
$144$	−5.68175	−	2.06799i	−0.473479	−	0.172332i
$145$	−16.2976			−1.35344
$146$	0.817862	+	4.21340i	0.0676867	+	0.348704i
$147$	−0.924206			−0.0762272
$148$	14.2095	+	5.17184i	1.16802	+	0.425123i
$149$	−6.56408	+	3.78977i	−0.537750	+	0.310470i	−0.744167	−	0.667994i	$-0.767153\pi$
$149$	−6.56408	+	3.78977i	−0.537750	+	0.310470i	0.206416	+	0.978464i	$0.433820\pi$
$150$	0.117377	+	0.0984908i	0.00958377	+	0.00804174i
$151$	−3.28631	+	7.04752i	−0.267436	+	0.573519i	−0.993464	−	0.114146i	$-0.963587\pi$
$151$	−3.28631	+	7.04752i	−0.267436	+	0.573519i	0.726028	+	0.687666i	$0.241364\pi$
$152$	−11.0892	+	1.95533i	−0.899457	+	0.158598i
$153$	2.03207	+	0.544491i	0.164283	+	0.0440195i
$154$	0.830082	+	1.43774i	0.0668899	+	0.115857i
$155$	12.1928	−	21.1185i	0.979349	−	1.69628i
$156$	0.630478	−	0.630478i	0.0504787	−	0.0504787i
$157$	15.0549	+	7.02019i	1.20151	+	0.560272i	0.917187	−	0.398457i	$-0.130454\pi$
$157$	15.0549	+	7.02019i	1.20151	+	0.560272i	0.284321	+	0.958729i	$0.408232\pi$
$158$	1.91609	+	0.337858i	0.152436	+	0.0268785i
$159$	−5.98690	+	8.55018i	−0.474792	+	0.678073i
$160$	−9.59168	−	6.71617i	−0.758289	−	0.530960i
$161$	−0.0287755	−	0.328906i	−0.00226783	−	0.0259214i
$162$	0.326138	+	1.84962i	0.0256238	+	0.145320i
$163$	−1.07996	−	4.03048i	−0.0845893	−	0.315692i	0.910647	−	0.413186i	$-0.135584\pi$
$163$	−1.07996	−	4.03048i	−0.0845893	−	0.315692i	−0.995236	+	0.0974940i	$0.968917\pi$
$164$	−9.41248	+	7.89801i	−0.734991	+	0.616731i
$165$	−0.860862	+	2.36520i	−0.0670181	+	0.184131i
$166$	4.82133	−	2.24822i	0.374208	−	0.174496i
$167$	−20.1746	+	5.40576i	−1.56115	+	0.418310i	−0.933029	−	0.359802i	$-0.882844\pi$
$167$	−20.1746	+	5.40576i	−1.56115	+	0.418310i	−0.628126	+	0.778112i	$0.716178\pi$
$168$	2.54905	+	2.54905i	0.196664	+	0.196664i
$169$	4.30461	+	11.8268i	0.331124	+	0.909755i
$170$	0.895534	+	0.517037i	0.0686843	+	0.0396549i
$171$	−9.11770	−	10.8661i	−0.697248	−	0.830948i
$172$	−6.14849	+	4.30522i	−0.468818	+	0.328270i
$173$			6.68712i			0.508412i	0.967150	+	0.254206i	$0.0818141\pi$
$173$			6.68712i			0.508412i	−0.967150	+	0.254206i	$0.918186\pi$
$174$	1.60427	+	2.29113i	0.121619	+	0.173690i
$175$	−0.392755	−	0.842267i	−0.0296895	−	0.0636694i
$176$	0.902862	−	3.36953i	0.0680558	−	0.253988i
$177$	−5.03476	−	0.440484i	−0.378436	−	0.0331088i
$178$	0.805157	−	4.56627i	0.0603491	−	0.342257i
$179$	6.15386	−	0.538393i	0.459961	−	0.0402414i	0.145179	−	0.989405i	$-0.453624\pi$
$179$	6.15386	−	0.538393i	0.459961	−	0.0402414i	0.314782	+	0.949164i	$0.398069\pi$
$180$	0.838228	−	9.58099i	0.0624778	−	0.714125i
$181$	8.48126	−	10.1076i	0.630407	−	0.751290i	−0.352415	−	0.935844i	$-0.614640\pi$
$181$	8.48126	−	10.1076i	0.630407	−	0.751290i	0.982822	+	0.184554i	$0.0590840\pi$
$182$	0.733784	−	0.267076i	0.0543917	−	0.0197970i
$183$	−0.662762	+	0.241226i	−0.0489928	+	0.0178319i
$184$	0.165412	−	0.197130i	0.0121943	−	0.0145326i
$185$	−1.74992	+	20.0017i	−0.128657	+	1.47055i
$186$	−4.16907	+	0.364746i	−0.305691	+	0.0267445i
$187$	−0.210762	+	1.19529i	−0.0154125	+	0.0874085i
$188$	−0.646326	−	0.0565462i	−0.0471381	−	0.00412405i
$189$	−2.66211	+	9.93514i	−0.193640	+	0.722675i
$190$	−2.94661	−	6.31903i	−0.213770	−	0.458431i
$191$	8.29276	+	11.8433i	0.600043	+	0.856950i	0.998176	−	0.0603779i	$-0.0192306\pi$
$191$	8.29276	+	11.8433i	0.600043	+	0.856950i	−0.398133	+	0.917328i	$0.630342\pi$
$192$		−	2.03288i		−	0.146710i
$193$	20.7778	−	14.5488i	1.49562	−	1.04724i	0.513692	−	0.857974i	$-0.328277\pi$
$193$	20.7778	−	14.5488i	1.49562	−	1.04724i	0.981925	−	0.189268i	$-0.0606116\pi$
$194$	3.77260	+	4.49601i	0.270857	+	0.322795i
$195$	1.02528	+	0.591948i	0.0734222	+	0.0423903i
$196$	0.696840	+	1.91455i	0.0497743	+	0.136754i
$197$	2.71328	+	2.71328i	0.193313	+	0.193313i	0.797126	−	0.603813i	$-0.206353\pi$
$197$	2.71328	+	2.71328i	0.193313	+	0.193313i	−0.603813	+	0.797126i	$0.706353\pi$
$198$	−1.57447	+	0.421877i	−0.111892	+	0.0299815i
$199$	7.56447	−	3.52737i	0.536231	−	0.250049i	−0.135586	−	0.990766i	$-0.543292\pi$
$199$	7.56447	−	3.52737i	0.536231	−	0.250049i	0.671817	+	0.740717i	$0.265514\pi$
$200$	0.247741	−	0.680661i	0.0175179	−	0.0481300i
$201$	1.38049	−	1.15836i	0.0973719	−	0.0817048i
$202$	0.0999955	+	0.373188i	0.00703566	+	0.0262574i
$203$	−2.94579	−	16.7064i	−0.206754	−	1.17256i
$204$	0.107117	+	1.22435i	0.00749967	+	0.0857216i
$205$	−13.3642	−	9.35772i	−0.933397	−	0.653572i
$206$	0.0933036	−	0.133251i	0.00650077	−	0.00928406i
$207$	0.319240	+	0.0562906i	0.0221887	+	0.00391247i
$208$	−1.48707	−	0.693434i	−0.103110	−	0.0480810i
$209$	5.78671	−	5.78671i	0.400275	−	0.400275i
$210$	−1.11606	+	1.93307i	−0.0770155	+	0.133395i
$211$	−7.53614	−	13.0530i	−0.518809	−	0.898604i	−0.999761	−	0.0218568i	$-0.993042\pi$
$211$	−7.53614	−	13.0530i	−0.518809	−	0.898604i	0.480952	−	0.876747i	$-0.340291\pi$
$212$	22.2263	+	5.95552i	1.52651	+	0.409027i
$213$	12.0278	−	2.12083i	0.824134	−	0.145317i
$214$	−3.34356	+	7.17028i	−0.228561	+	0.490150i
$215$	−7.63461	−	6.40620i	−0.520676	−	0.436899i
$216$	−6.94276	+	4.00840i	−0.472395	+	0.272737i
$217$	23.8521	+	8.68145i	1.61919	+	0.589336i
$218$	−7.43421			−0.503509
$219$	−5.92324	−	3.28533i	−0.400256	−	0.222002i
$220$	5.54874			0.374096
$221$	0.536464	+	0.195257i	0.0360865	+	0.0131344i
$222$	2.98411	−	1.72288i	0.200280	−	0.115632i
$223$	−10.8005	−	9.06274i	−0.723258	−	0.606886i	0.205026	−	0.978756i	$-0.434272\pi$
$223$	−10.8005	−	9.06274i	−0.723258	−	0.606886i	−0.928285	+	0.371871i	$0.878716\pi$
$224$	5.15093	−	11.0462i	0.344161	−	0.738056i
$225$	0.898595	−	0.158447i	0.0599063	−	0.0105631i
$226$	−5.83325	−	1.56301i	−0.388022	−	0.103970i
$227$	−12.8944	−	22.3337i	−0.855831	−	1.48234i	−0.875872	−	0.482543i	$-0.839713\pi$
$227$	−12.8944	−	22.3337i	−0.855831	−	1.48234i	0.0200416	−	0.999799i	$-0.493620\pi$
$228$	4.14338	−	7.17654i	0.274402	−	0.475278i
$229$	−9.33924	+	9.33924i	−0.617155	+	0.617155i	−0.944801	−	0.327646i	$-0.893745\pi$
$229$	−9.33924	+	9.33924i	−0.617155	+	0.617155i	0.327646	+	0.944801i	$0.393745\pi$
$230$	0.144410	+	0.0673396i	0.00952213	+	0.00444024i
$231$	−2.58013	−	0.454946i	−0.169760	−	0.0299332i
$232$	7.58393	−	10.8310i	0.497909	−	0.711088i
$233$	−0.934994	−	0.654690i	−0.0612535	−	0.0428902i	0.542549	−	0.840024i	$-0.317459\pi$
$233$	−0.934994	−	0.654690i	−0.0612535	−	0.0428902i	−0.603802	+	0.797134i	$0.706348\pi$
$234$	0.0668217	+	0.763775i	0.00436827	+	0.0499296i
$235$	−0.149591	−	0.848374i	−0.00975826	−	0.0553418i
$236$	2.88365	+	10.7619i	0.187710	+	0.700543i
$237$	−2.35210	+	1.97365i	−0.152785	+	0.128202i
$238$	−0.368138	+	1.01145i	−0.0238628	+	0.0655626i
$239$	25.2722	−	11.7846i	1.63473	−	0.762285i	0.634780	−	0.772693i	$-0.281091\pi$
$239$	25.2722	−	11.7846i	1.63473	−	0.762285i	0.999946	+	0.0104083i	$0.00331311\pi$
$240$	4.53039	−	1.21391i	0.292435	−	0.0783578i
$241$	4.66824	+	4.66824i	0.300708	+	0.300708i	0.841291	−	0.540583i	$-0.181796\pi$
$241$	4.66824	+	4.66824i	0.300708	+	0.300708i	−0.540583	+	0.841291i	$0.681796\pi$
$242$	1.56830	+	4.30886i	0.100814	+	0.276984i
$243$	−13.6303	−	7.86947i	−0.874386	−	0.504827i
$244$	0.999429	+	1.19107i	0.0639819	+	0.0762506i
$245$	−2.21603	+	1.55168i	−0.141577	+	0.0991330i
$246$			2.79989i			0.178514i
$247$	−2.20785	−	3.15314i	−0.140482	−	0.200629i
$248$	8.36104	+	17.9303i	0.530927	+	1.13858i
$249$	−2.17283	+	8.10911i	−0.137697	+	0.513894i
$250$	−5.35951	−	0.468896i	−0.338965	−	0.0296556i
$251$	−0.318452	+	1.80603i	−0.0201005	+	0.113996i	−0.993207	−	0.116359i	$-0.962878\pi$
$251$	−0.318452	+	1.80603i	−0.0201005	+	0.113996i	0.973107	+	0.230355i	$0.0739887\pi$
$252$	9.97281	−	0.872508i	0.628228	−	0.0549628i
$253$	−0.0163001	+	0.186311i	−0.00102478	+	0.0117133i
$254$	2.66726	−	3.17872i	0.167359	−	0.199451i
$255$	−1.53347	+	0.558138i	−0.0960297	+	0.0349520i
$256$	0.552695	−	0.201165i	0.0345435	−	0.0125728i
$257$	−13.5265	+	16.1203i	−0.843761	+	1.00556i	0.156080	+	0.987744i	$0.450114\pi$
$257$	−13.5265	+	16.1203i	−0.843761	+	1.00556i	−0.999841	+	0.0178109i	$0.994330\pi$
$258$	−0.149070	+	1.70388i	−0.00928069	+	0.106079i
$259$	−20.8197	+	1.82149i	−1.29367	+	0.113182i
$260$	0.453207	−	2.57027i	0.0281067	−	0.159401i
$261$	16.5926	+	1.45166i	1.02706	+	0.0898557i
$262$	0.955320	−	3.56530i	0.0590199	−	0.220265i
$263$	8.16438	+	17.5086i	0.503437	+	1.07962i	0.979727	+	0.200336i	$0.0642035\pi$
$263$	8.16438	+	17.5086i	0.503437	+	1.07962i	−0.476290	+	0.879288i	$0.658019\pi$
$264$	−1.17126	−	1.67273i	−0.0720859	−	0.102949i
$265$			30.5529i			1.87685i
$266$	5.94493	−	4.16268i	0.364507	−	0.255231i
$267$	4.70345	+	5.60535i	0.287847	+	0.343042i
$268$	−3.44050	−	1.98637i	−0.210162	−	0.121337i
$269$	−4.71796	−	12.9625i	−0.287659	−	0.790337i	−0.996393	−	0.0848610i	$-0.972955\pi$
$269$	−4.71796	−	12.9625i	−0.287659	−	0.790337i	0.708734	−	0.705476i	$-0.249267\pi$
$270$	−3.51003	−	3.51003i	−0.213613	−	0.213613i
$271$	−16.2240	+	4.34720i	−0.985536	+	0.264074i	−0.715374	−	0.698741i	$-0.753744\pi$
$271$	−16.2240	+	4.34720i	−0.985536	+	0.264074i	−0.270162	+	0.962815i	$0.587077\pi$
$272$	2.04979	−	0.955831i	0.124287	−	0.0579558i
$273$	−0.421476	+	1.15800i	−0.0255089	+	0.0700851i
$274$	−1.95463	+	1.64013i	−0.118083	+	0.0990836i
$275$	0.136250	+	0.508493i	0.00821620	+	0.0306633i
$276$	0.0328853	+	0.186502i	0.00197947	+	0.0112261i
$277$	0.195709	+	2.23696i	0.0117590	+	0.134406i	0.999805	−	0.0197542i	$-0.00628836\pi$
$277$	0.195709	+	2.23696i	0.0117590	+	0.134406i	−0.988046	+	0.154160i	$0.950733\pi$
$278$	−5.93673	−	4.15694i	−0.356061	−	0.249317i
$279$	−14.2946	+	20.4147i	−0.855793	+	1.22220i
$280$	10.3917	+	1.83234i	0.621023	+	0.109503i
$281$	−22.3186	−	10.4073i	−1.33142	−	0.620849i	−0.378928	−	0.925426i	$-0.623707\pi$
$281$	−22.3186	−	10.4073i	−1.33142	−	0.620849i	−0.952488	+	0.304577i	$0.901485\pi$
$282$	−0.104540	+	0.104540i	−0.00622527	+	0.00622527i
$283$	−7.68109	+	13.3040i	−0.456593	+	0.790843i	−0.998778	−	0.0494165i	$-0.984264\pi$
$283$	−7.68109	+	13.3040i	−0.456593	+	0.790843i	0.542185	+	0.840259i	$0.317597\pi$
$284$	−13.4623	−	23.3174i	−0.798839	−	1.38363i
$285$	10.6281	+	2.84780i	0.629556	+	0.168689i
$286$	−0.435614	+	0.0768104i	−0.0257584	+	0.00454190i
$287$	7.17686	−	15.3908i	0.423637	−	0.908492i
$288$	9.16706	+	7.69208i	0.540174	+	0.453260i
$289$	14.0409	−	8.10654i	0.825938	−	0.476855i
$290$	7.69330	+	2.80013i	0.451766	+	0.164429i
$291$	−9.26215			−0.542957
$292$	−2.33971	+	14.7475i	−0.136921	+	0.863030i
$293$	−17.1300			−1.00075			−0.500373	−	0.865810i	$-0.666804\pi$
$293$	−17.1300			−1.00075			−0.500373	+	0.865810i	$0.666804\pi$
$294$	0.436272	+	0.158790i	0.0254439	+	0.00926083i
$295$	−12.8117	+	7.39683i	−0.745926	+	0.430660i
$296$	−12.4783	−	10.4705i	−0.725286	−	0.608588i
$297$	2.46233	−	5.28048i	0.142879	−	0.306404i
$298$	3.74971	−	0.661175i	0.217215	−	0.0383008i
$299$	0.0849708	+	0.0227679i	0.00491399	+	0.00131670i
$300$	0.266532	+	0.461647i	0.0153882	+	0.0266532i
$301$	5.18693	−	8.98402i	0.298970	−	0.517831i
$302$	2.76216	−	2.76216i	0.158944	−	0.158944i
$303$	−0.552584	−	0.257674i	−0.0317451	−	0.0148030i
$304$	−15.0178	−	2.64805i	−0.861333	−	0.151876i
$305$	−1.18414	+	1.69113i	−0.0678039	+	0.0968340i
$306$	−0.865689	−	0.606162i	−0.0494881	−	0.0346520i
$307$	0.215106	+	2.45867i	0.0122767	+	0.140324i	0.999859	−	0.0167774i	$-0.00534066\pi$
$307$	0.215106	+	2.45867i	0.0122767	+	0.140324i	−0.987583	+	0.157101i	$0.949785\pi$
$308$	1.00293	+	5.68792i	0.0571475	+	0.324099i
$309$	0.0664419	+	0.247964i	0.00377975	+	0.0141062i
$310$	−9.38405	+	7.87415i	−0.532978	+	0.447222i
$311$	−5.51072	+	15.1406i	−0.312484	+	0.858544i	0.679669	+	0.733519i	$0.262123\pi$
$311$	−5.51072	+	15.1406i	−0.312484	+	0.858544i	−0.992154	+	0.125025i	$0.960099\pi$
$312$	−0.870499	+	0.405920i	−0.0492823	+	0.0229807i
$313$	18.8826	−	5.05958i	1.06731	−	0.285985i	0.317922	−	0.948117i	$-0.397015\pi$
$313$	18.8826	−	5.05958i	1.06731	−	0.285985i	0.749387	+	0.662132i	$0.230348\pi$
$314$	−5.90050	−	5.90050i	−0.332984	−	0.332984i
$315$	4.54626	+	12.4907i	0.256153	+	0.703773i
$316$	5.86199	+	3.38442i	0.329763	+	0.190389i
$317$	5.17503	+	6.16736i	0.290659	+	0.346394i	0.891538	−	0.452946i	$-0.149627\pi$
$317$	5.17503	+	6.16736i	0.290659	+	0.346394i	−0.600879	+	0.799340i	$0.705183\pi$
$318$	4.29515	−	3.00749i	0.240860	−	0.168652i
$319$			9.60945i			0.538026i
$320$	−3.41306	−	4.87436i	−0.190796	−	0.272485i
$321$	−5.27652	−	11.3155i	−0.294506	−	0.631571i
$322$	−0.0429266	+	0.160204i	−0.00239220	+	0.00892783i
$323$	5.28565	+	0.462435i	0.294102	+	0.0257306i
$324$	−1.13462	+	6.43477i	−0.0630347	+	0.357487i
$325$	0.246671	−	0.0215809i	0.0136828	−	0.00119709i
$326$	−0.182689	+	2.08814i	−0.0101182	+	0.115652i
$327$	7.54121	−	8.98727i	0.417030	−	0.496997i
$328$	12.4378	−	4.52699i	0.686762	−	0.249961i
$329$	0.842615	−	0.306687i	0.0464549	−	0.0169082i
$330$	0.812742	−	0.968588i	0.0447400	−	0.0533190i
$331$	−1.39346	+	15.9274i	−0.0765917	+	0.875447i	0.856580	+	0.516015i	$0.172585\pi$
$331$	−1.39346	+	15.9274i	−0.0765917	+	0.875447i	−0.933171	+	0.359432i	$0.882970\pi$
$332$	18.4368	−	1.61301i	1.01185	−	0.0885256i
$333$	3.56319	−	20.2079i	0.195262	−	1.10738i
$334$	10.4522	+	0.914448i	0.571919	+	0.0500364i
$335$	1.36526	−	5.09522i	0.0745921	−	0.278382i
$336$	2.06323	+	4.42461i	0.112558	+	0.241382i
$337$	7.45358	+	10.6448i	0.406022	+	0.579860i	0.969138	−	0.246518i	$-0.0792865\pi$
$337$	7.45358	+	10.6448i	0.406022	+	0.579860i	−0.563116	+	0.826378i	$0.690398\pi$
$338$		−	6.32244i		−	0.343895i
$339$	7.80675	−	5.46634i	0.424004	−	0.296891i
$340$	2.31244	+	2.75586i	0.125410	+	0.149457i
$341$	−12.4520	−	7.18916i	−0.674313	−	0.389315i
$342$	2.43710	+	6.69586i	0.131783	+	0.362071i
$343$	−13.9468	−	13.9468i	−0.753056	−	0.753056i
$344$	7.81008	−	2.09270i	0.421091	−	0.112831i
$345$	−0.227896	+	0.106270i	−0.0122695	+	0.00572137i
$346$	1.14893	−	3.15666i	0.0617669	−	0.169703i
$347$	17.0197	−	14.2812i	0.913664	−	0.766655i	−0.0591489	−	0.998249i	$-0.518839\pi$
$347$	17.0197	−	14.2812i	0.913664	−	0.766655i	0.972812	+	0.231594i	$0.0743942\pi$
$348$	2.51845	+	9.39897i	0.135003	+	0.503838i
$349$	−3.32372	−	18.8497i	−0.177914	−	1.00900i	−0.934726	−	0.355370i	$-0.884355\pi$
$349$	−3.32372	−	18.8497i	−0.177914	−	1.00900i	0.756811	−	0.653633i	$-0.226756\pi$
$350$	0.0406886	+	0.465073i	0.00217490	+	0.0248592i
$351$	−2.24488	−	1.57188i	−0.119823	−	0.0839010i
$352$	−3.96001	+	5.65548i	−0.211069	+	0.301438i
$353$	−20.7257	−	3.65450i	−1.10312	−	0.194509i	−0.407700	−	0.913116i	$-0.633669\pi$
$353$	−20.7257	−	3.65450i	−1.10312	−	0.194509i	−0.695417	+	0.718607i	$0.744780\pi$
$354$	2.30098	+	1.07297i	0.122296	+	0.0570275i
$355$	25.2791	−	25.2791i	1.34168	−	1.34168i
$356$	8.06551	−	13.9699i	0.427471	−	0.740402i
$357$	−0.849312	−	1.47105i	−0.0449504	−	0.0778563i
$358$	−2.99744	−	0.803161i	−0.158419	−	0.0424484i
$359$	8.47718	−	1.49476i	0.447408	−	0.0788902i	0.0545955	−	0.998509i	$-0.482613\pi$
$359$	8.47718	−	1.49476i	0.447408	−	0.0788902i	0.392813	+	0.919618i	$0.371502\pi$
$360$	−4.37847	+	9.38965i	−0.230765	+	0.494878i
$361$	−12.8503	−	10.7827i	−0.676330	−	0.567509i
$362$	−5.74019	+	3.31410i	−0.301698	+	0.174185i
$363$	−6.79988	−	2.47495i	−0.356901	−	0.129901i
$364$	2.71665			0.142391
$365$	−19.7184	+	2.06728i	−1.03211	+	0.108207i
$366$	0.354303			0.0185197
$367$	15.5573	+	5.66239i	0.812084	+	0.295574i	0.714484	−	0.699652i	$-0.246661\pi$
$367$	15.5573	+	5.66239i	0.812084	+	0.295574i	0.0975993	+	0.995226i	$0.468884\pi$
$368$	0.301811	−	0.174250i	0.0157330	−	0.00908343i
$369$	12.7726	+	10.7175i	0.664914	+	0.557929i
$370$	4.26259	−	9.14116i	0.221602	−	0.475226i
$371$	−31.3192	+	5.52242i	−1.62601	+	0.286710i
$372$	−14.0634	−	3.76827i	−0.729153	−	0.195376i
$373$	8.79402	+	15.2317i	0.455337	+	0.788667i	0.998708	−	0.0508258i	$-0.0161853\pi$
$373$	8.79402	+	15.2317i	0.455337	+	0.788667i	−0.543370	+	0.839493i	$0.682852\pi$
$374$	0.304857	−	0.528028i	0.0157638	−	0.0273037i
$375$	6.00350	−	6.00350i	0.310019	−	0.310019i
$376$	0.633418	+	0.295368i	0.0326660	+	0.0152324i
$377$	4.45125	+	0.784875i	0.229251	+	0.0404231i
$378$	2.96363	−	4.23250i	0.152433	−	0.217697i
$379$	−3.07062	−	2.15007i	−0.157727	−	0.110442i	0.492048	−	0.870568i	$-0.336248\pi$
$379$	−3.07062	−	2.15007i	−0.157727	−	0.110442i	−0.649776	+	0.760126i	$0.725137\pi$
$380$	−2.11408	−	24.1641i	−0.108450	−	1.23959i
$381$	1.13712	+	6.44894i	0.0582566	+	0.330389i
$382$	−1.87978	−	7.01543i	−0.0961778	−	0.358941i
$383$	8.16204	−	6.84876i	0.417061	−	0.349955i	−0.409983	−	0.912093i	$-0.634465\pi$
$383$	8.16204	−	6.84876i	0.417061	−	0.349955i	0.827044	+	0.562138i	$0.190021\pi$
$384$	−3.08562	+	8.47766i	−0.157462	+	0.432624i
$385$	−6.95035	+	3.24100i	−0.354223	+	0.165177i
$386$	−12.3078	+	3.29787i	−0.626452	+	0.167857i
$387$	7.20218	+	7.20218i	0.366107	+	0.366107i
$388$	6.98355	+	19.1871i	0.354536	+	0.974080i
$389$	31.4602	+	18.1635i	1.59509	+	0.920928i	0.992414	+	0.122945i	$0.0392338\pi$
$389$	31.4602	+	18.1635i	1.59509	+	0.920928i	0.602680	+	0.797983i	$0.294100\pi$
$390$	−0.382282	−	0.455586i	−0.0193576	−	0.0230695i
$391$	−0.0993268	+	0.0695494i	−0.00502317	+	0.00351726i
$392$		−	2.19477i		−	0.110853i
$393$	3.34105	+	4.77151i	0.168533	+	0.240691i
$394$	−0.814630	−	1.74698i	−0.0410405	−	0.0880116i
$395$	−2.32616	+	8.68135i	−0.117042	+	0.436806i
$396$	−5.64917	−	0.494239i	−0.283882	−	0.0248364i
$397$	4.93000	−	27.9594i	0.247430	−	1.40324i	−0.567352	−	0.823475i	$-0.692032\pi$
$397$	4.93000	−	27.9594i	0.247430	−	1.40324i	0.814782	−	0.579768i	$-0.196857\pi$
$398$	−4.17686	+	0.365428i	−0.209367	+	0.0183172i
$399$	−0.998198	+	11.4095i	−0.0499724	+	0.571187i
$400$	0.630548	−	0.751458i	0.0315274	−	0.0375729i
$401$	2.80148	−	1.01965i	0.139899	−	0.0509191i	−0.271122	−	0.962545i	$-0.587395\pi$
$401$	2.80148	−	1.01965i	0.139899	−	0.0509191i	0.411021	+	0.911626i	$0.365172\pi$
$402$	−0.850681	+	0.309622i	−0.0424281	+	0.0154426i
$403$	−4.34718	+	5.18076i	−0.216548	+	0.258072i
$404$	−0.117147	+	1.33900i	−0.00582828	+	0.0666176i
$405$	−8.64281	+	0.756148i	−0.429465	+	0.0375733i
$406$	−1.47981	+	8.39239i	−0.0734415	+	0.416507i
$407$	11.7935	+	1.03179i	0.584580	+	0.0511442i
$408$	0.342661	−	1.27883i	0.0169643	−	0.0633115i
$409$	1.66301	+	3.56634i	0.0822305	+	0.176344i	0.943124	−	0.332442i	$-0.107872\pi$
$409$	1.66301	+	3.56634i	0.0822305	+	0.176344i	−0.860893	+	0.508785i	$0.830095\pi$
$410$	4.70081	+	6.71346i	0.232157	+	0.331554i
$411$		−	4.02669i		−	0.198622i
$412$	0.463578	−	0.324601i	0.0228388	−	0.0159919i
$413$	−9.89808	−	11.7961i	−0.487052	−	0.580447i
$414$	−0.141026	−	0.0814214i	−0.00693105	−	0.00400164i
$415$	8.40471	+	23.0917i	0.412571	+	1.13353i
$416$	2.29626	+	2.29626i	0.112584	+	0.112584i
$417$	11.0475	−	2.96018i	0.541000	−	0.144960i
$418$	−3.72585	+	1.73739i	−0.182237	+	0.0849786i
$419$	5.26684	−	14.4705i	0.257302	−	0.706932i	−0.742029	−	0.670368i	$-0.766136\pi$
$419$	5.26684	−	14.4705i	0.257302	−	0.706932i	0.999331	−	0.0365641i	$-0.0116413\pi$
$420$	−5.94871	+	4.99156i	−0.290267	+	0.243563i
$421$	−1.82366	−	6.80599i	−0.0888798	−	0.331704i	0.907141	−	0.420827i	$-0.138260\pi$
$421$	−1.82366	−	6.80599i	−0.0888798	−	0.331704i	−0.996021	+	0.0891234i	$0.971593\pi$
$422$	1.31478	+	7.45647i	0.0640023	+	0.362975i
$423$	0.0767323	+	0.877054i	0.00373085	+	0.0426438i
$424$	−20.3046	−	14.2175i	−0.986081	−	0.690461i
$425$	−0.195767	+	0.279585i	−0.00949611	+	0.0135619i
$426$	−6.04213	−	1.06539i	−0.292742	−	0.0516184i
$427$	−1.94758	−	0.908173i	−0.0942502	−	0.0439496i
$428$	−19.4624	+	19.4624i	−0.940751	+	0.940751i
$429$	0.349027	−	0.604532i	0.0168512	−	0.0291871i
$430$	2.50326	+	4.33577i	0.120718	+	0.209089i
$431$	−0.187828	−	0.0503283i	−0.00904734	−	0.00242423i	0.254293	−	0.967127i	$-0.418157\pi$
$431$	−0.187828	−	0.0503283i	−0.00904734	−	0.00242423i	−0.263340	+	0.964703i	$0.584824\pi$
$432$	−10.6920	+	1.88529i	−0.514419	+	0.0907059i
$433$	−2.54361	+	5.45479i	−0.122238	+	0.262141i	−0.957899	−	0.287105i	$-0.907307\pi$
$433$	−2.54361	+	5.45479i	−0.122238	+	0.262141i	0.835661	+	0.549246i	$0.185085\pi$
$434$	−9.76782	−	8.19617i	−0.468870	−	0.393429i
$435$	−11.1891	+	6.46004i	−0.536478	+	0.309735i
$436$	−24.3037	−	8.84582i	−1.16394	−	0.423638i
$437$	0.817571			0.0391097
$438$	2.23161	+	2.56853i	0.106630	+	0.122729i
$439$	14.9260			0.712377			0.356189	−	0.934414i	$-0.384076\pi$
$439$	14.9260			0.712377			0.356189	+	0.934414i	$0.384076\pi$
$440$	−5.61679	−	2.04434i	−0.267770	−	0.0974603i
$441$	2.39435	−	1.38238i	0.114016	−	0.0658274i
$442$	−0.219691	−	0.184342i	−0.0104496	−	0.00876827i
$443$	6.20529	−	13.3073i	0.294822	−	0.632248i	−0.701977	−	0.712200i	$-0.747699\pi$
$443$	6.20529	−	13.3073i	0.294822	−	0.632248i	0.996799	+	0.0799518i	$0.0254766\pi$
$444$	11.8056	−	2.08164i	0.560267	−	0.0987902i
$445$	20.6888	+	5.54353i	0.980741	+	0.262789i
$446$	3.54132	+	6.13374i	0.167686	+	0.290441i
$447$	−3.00438	+	5.20374i	−0.142102	+	0.246128i
$448$	4.37971	−	4.37971i	0.206922	−	0.206922i
$449$	−8.24066	−	3.84268i	−0.388901	−	0.181347i	0.218326	−	0.975876i	$-0.429940\pi$
$449$	−8.24066	−	3.84268i	−0.388901	−	0.181347i	−0.607227	+	0.794528i	$0.707718\pi$
$450$	−0.451406	−	0.0795950i	−0.0212795	−	0.00375214i
$451$	−5.51753	+	7.87985i	−0.259810	+	0.371048i
$452$	−17.2101	−	12.0506i	−0.809494	−	0.566813i
$453$	0.537277	+	6.14110i	0.0252435	+	0.288534i
$454$	2.24959	+	12.7581i	0.105579	+	0.598766i
$455$	0.933596	+	3.48423i	0.0437677	+	0.163343i
$456$	−6.83827	+	5.73799i	−0.320231	+	0.268706i
$457$	−12.2316	+	33.6060i	−0.572169	+	1.57202i	0.228901	+	0.973450i	$0.426487\pi$
$457$	−12.2316	+	33.6060i	−0.572169	+	1.57202i	−0.801070	+	0.598571i	$0.795735\pi$
$458$	6.01320	−	2.80400i	0.280978	−	0.131022i
$459$	3.64879	−	0.977690i	0.170311	−	0.0456347i
$460$	0.391975	+	0.391975i	0.0182759	+	0.0182759i
$461$	−2.27222	−	6.24287i	−0.105828	−	0.290760i	0.875465	−	0.483282i	$-0.160555\pi$
$461$	−2.27222	−	6.24287i	−0.105828	−	0.290760i	−0.981293	+	0.192522i	$0.938333\pi$
$462$	1.13979	+	0.658055i	0.0530276	+	0.0306155i
$463$	−8.04129	−	9.58324i	−0.373711	−	0.445371i	0.546108	−	0.837715i	$-0.316109\pi$
$463$	−8.04129	−	9.58324i	−0.373711	−	0.445371i	−0.919819	+	0.392344i	$0.871664\pi$
$464$	14.6681	−	10.2707i	0.680948	−	0.476805i
$465$		−	19.3319i		−	0.896496i
$466$	0.328881	+	0.469691i	0.0152351	+	0.0217580i
$467$	10.7789	+	23.1154i	0.498787	+	1.06965i	0.981073	+	0.193638i	$0.0620289\pi$
$467$	10.7789	+	23.1154i	0.498787	+	1.06965i	−0.482286	+	0.876014i	$0.660193\pi$
$468$	−0.690349	+	2.57642i	−0.0319114	+	0.119095i
$469$	5.46979	+	0.478545i	0.252572	+	0.0220971i
$470$	−0.0751466	+	0.426177i	−0.00346625	+	0.0196581i
$471$	13.1186	−	1.14773i	0.604472	−	0.0528844i
$472$	1.04605	−	11.9564i	0.0481482	−	0.550336i
$473$	−3.77724	+	4.50154i	−0.173678	+	0.206981i
$474$	1.44941	−	0.527542i	0.0665736	−	0.0242308i
$475$	2.16251	−	0.787090i	0.0992228	−	0.0361141i
$476$	−2.40701	+	2.86856i	−0.110325	+	0.131480i
$477$	2.72141	−	31.1059i	0.124605	−	1.42424i
$478$	−13.9545	+	1.22086i	−0.638265	+	0.0558410i
$479$	1.79200	−	10.1629i	0.0818784	−	0.464355i	−0.916108	−	0.400931i	$-0.868687\pi$
$479$	1.79200	−	10.1629i	0.0818784	−	0.464355i	0.997987	−	0.0634245i	$-0.0202022\pi$
$480$	−9.24732	−	0.809036i	−0.422081	−	0.0369273i
$481$	1.44120	−	5.37864i	0.0657132	−	0.245245i
$482$	−1.40158	−	3.00571i	−0.0638404	−	0.136906i
$483$	−0.150127	−	0.214404i	−0.00683103	−	0.00975572i
$484$			15.9525i			0.725112i
$485$	−22.2084	+	15.5505i	−1.00843	+	0.706112i
$486$	5.08213	+	6.05665i	0.230530	+	0.274735i
$487$	−8.05569	−	4.65095i	−0.365038	−	0.210755i	0.306250	−	0.951951i	$-0.400926\pi$
$487$	−8.05569	−	4.65095i	−0.365038	−	0.210755i	−0.671289	+	0.741196i	$0.734259\pi$
$488$	−0.572854	−	1.57390i	−0.0259319	−	0.0712472i
$489$	−2.33905	−	2.33905i	−0.105776	−	0.105776i
$490$	1.31267	−	0.351730i	0.0593006	−	0.0158895i
$491$	−13.6270	+	6.35436i	−0.614977	+	0.286768i	−0.705040	−	0.709168i	$-0.749071\pi$
$491$	−13.6270	+	6.35436i	−0.614977	+	0.286768i	0.0900631	+	0.995936i	$0.471293\pi$
$492$	−3.33153	+	9.15329i	−0.150197	+	0.412662i
$493$	−4.77266	+	4.00474i	−0.214950	+	0.180364i
$494$	0.500469	+	1.86778i	0.0225172	+	0.0840353i
$495$	−1.30749	−	7.41517i	−0.0587675	−	0.333287i
$496$	2.33515	+	26.6908i	0.104851	+	1.19845i
$497$	30.4824	+	21.3440i	1.36732	+	0.957410i
$498$	2.41893	−	3.45459i	0.108395	−	0.154804i
$499$	15.4423	+	2.72289i	0.691292	+	0.121893i	0.508247	−	0.861211i	$-0.330294\pi$
$499$	15.4423	+	2.72289i	0.691292	+	0.121893i	0.183045	+	0.983105i	$0.441405\pi$
$500$	−16.9632	−	7.91007i	−0.758617	−	0.353749i
$501$	−11.7081	+	11.7081i	−0.523080	+	0.523080i
$502$	0.460624	−	0.797823i	0.0205586	−	0.0356086i
$503$	12.3506	+	21.3919i	0.550688	+	0.953819i	0.998225	+	0.0595538i	$0.0189678\pi$
$503$	12.3506	+	21.3919i	0.550688	+	0.953819i	−0.447537	+	0.894265i	$0.647699\pi$
$504$	−10.4166	−	2.79111i	−0.463991	−	0.124326i
$505$	−1.75758	+	0.309909i	−0.0782114	+	0.0137908i
$506$	0.0397050	−	0.0851477i	0.00176510	−	0.00378528i
$507$	7.64324	+	6.41344i	0.339448	+	0.284831i
$508$	12.5020	−	7.21805i	0.554688	−	0.320249i
$509$	11.6081	+	4.22502i	0.514522	+	0.187271i	0.586214	−	0.810156i	$-0.300618\pi$
$509$	11.6081	+	4.22502i	0.514522	+	0.187271i	−0.0716922	+	0.997427i	$0.522840\pi$
$510$	0.819772			0.0363001
$511$	−5.68322	−	19.8393i	−0.251411	−	0.877638i
$512$	22.4649			0.992817
$513$	−23.9340	−	8.71125i	−1.05671	−	0.384611i
$514$	9.15487	−	5.28557i	0.403804	−	0.233136i
$515$	0.575627	+	0.483008i	0.0253651	+	0.0212839i
$516$	−2.51474	+	5.39289i	−0.110705	+	0.237409i
$517$	−0.500221	+	0.0882025i	−0.0219997	+	0.00387914i
$518$	10.1409	+	2.71725i	0.445566	+	0.119389i
$519$	2.65064	+	4.59104i	0.116350	+	0.201524i
$520$	−1.40574	+	2.43481i	−0.0616457	+	0.106773i
$521$	−6.76052	+	6.76052i	−0.296184	+	0.296184i	−0.839517	−	0.543333i	$-0.817162\pi$
$521$	−6.76052	+	6.76052i	−0.296184	+	0.296184i	0.543333	+	0.839517i	$0.317162\pi$
$522$	−7.58313	−	3.53607i	−0.331905	−	0.154770i
$523$	−23.6375	−	4.16793i	−1.03360	−	0.182251i	−0.368981	−	0.929437i	$-0.620293\pi$
$523$	−23.6375	−	4.16793i	−1.03360	−	0.182251i	−0.664615	+	0.747186i	$0.731404\pi$
$524$	7.36538	−	10.5188i	0.321758	−	0.459518i
$525$	−0.603504	−	0.422578i	−0.0263391	−	0.0184428i
$526$	−0.845812	−	9.66768i	−0.0368792	−	0.421531i
$527$	−1.61877	−	9.18052i	−0.0705149	−	0.399910i
$528$	−0.715752	−	2.67122i	−0.0311491	−	0.116250i
$529$	17.6047	−	14.7721i	0.765422	−	0.642265i
$530$	5.24936	−	14.4225i	0.228018	−	0.626474i
$531$	13.7024	−	6.38955i	0.594635	−	0.277283i
$532$	24.3881	−	6.53476i	1.05736	−	0.283318i
$533$	3.19941	+	3.19941i	0.138582	+	0.138582i
$534$	−1.25720	−	3.45412i	−0.0544043	−	0.149475i
$535$	−31.6498	−	18.2730i	−1.36834	−	0.790012i
$536$	2.75084	+	3.27833i	0.118818	+	0.141602i
$537$	4.01152	−	2.80890i	0.173110	−	0.121213i
$538$			6.92956i			0.298755i
$539$	0.914905	+	1.30662i	0.0394078	+	0.0562801i
$540$	−7.29836	−	15.6514i	−0.314071	−	0.673528i
$541$	4.20536	−	15.6946i	0.180802	−	0.674764i	−0.814688	−	0.579900i	$-0.803092\pi$
$541$	4.20536	−	15.6946i	0.180802	−	0.674764i	0.995490	−	0.0948639i	$-0.0302416\pi$
$542$	8.40544	+	0.735381i	0.361045	+	0.0315873i
$543$	1.81637	−	10.3012i	0.0779480	−	0.442065i
$544$	−4.45920	+	0.390129i	−0.191187	+	0.0167267i
$545$	2.99303	−	34.2105i	0.128207	−	1.46542i
$546$	0.397916	−	0.474218i	0.0170292	−	0.0202947i
$547$	12.1061	−	4.40627i	0.517621	−	0.188399i	−0.0699818	−	0.997548i	$-0.522294\pi$
$547$	12.1061	−	4.40627i	0.517621	−	0.188399i	0.587602	+	0.809150i	$0.300072\pi$
$548$	−8.34155	+	3.03608i	−0.356333	+	0.129695i
$549$	1.35621	−	1.61627i	0.0578816	−	0.0689806i
$550$	0.0230484	−	0.263444i	0.000982786	−	0.0112333i
$551$	41.8479	−	3.66122i	1.78278	−	0.155973i
$552$	0.0354250	−	0.200905i	0.00150779	−	0.00855110i
$553$	−9.31956	−	0.815356i	−0.396308	−	0.0346724i
$554$	0.291953	−	1.08958i	0.0124039	−	0.0462920i
$555$	6.72686	+	14.4258i	0.285539	+	0.612341i
$556$	−14.4619	−	20.6537i	−0.613321	−	0.875913i
$557$			30.3904i			1.28768i	0.765159	+	0.643842i	$0.222661\pi$
$557$			30.3904i			1.28768i	−0.765159	+	0.643842i	$0.777339\pi$
$558$	10.2553	−	7.18081i	0.434140	−	0.303988i
$559$	1.77667	+	2.11735i	0.0751451	+	0.0895545i
$560$	12.3757	+	7.14514i	0.522971	+	0.301937i
$561$	0.329091	+	0.904171i	0.0138942	+	0.0381741i
$562$	8.74740	+	8.74740i	0.368987	+	0.368987i
$563$	1.95339	−	0.523410i	0.0823257	−	0.0220591i	−0.217421	−	0.976078i	$-0.569764\pi$
$563$	1.95339	−	0.523410i	0.0823257	−	0.0220591i	0.299747	+	0.954019i	$0.403098\pi$
$564$	−0.466149	+	0.217369i	−0.0196284	+	0.00915287i
$565$	9.54110	−	26.2140i	0.401397	−	1.10283i
$566$	5.91166	−	4.96047i	0.248486	−	0.208504i
$567$	−2.33730	−	8.72292i	−0.0981573	−	0.366328i
$568$	5.03647	+	28.5633i	0.211326	+	1.19849i
$569$	−0.592379	−	6.77093i	−0.0248338	−	0.283852i	−0.998450	−	0.0556593i	$-0.982274\pi$
$569$	−0.592379	−	6.77093i	−0.0248338	−	0.283852i	0.973616	−	0.228193i	$-0.0732816\pi$
$570$	−4.52773	−	3.17035i	−0.189646	−	0.132791i
$571$	9.45613	−	13.5047i	0.395727	−	0.565156i	−0.571006	−	0.820946i	$-0.693447\pi$
$571$	9.45613	−	13.5047i	0.395727	−	0.565156i	0.966732	+	0.255790i	$0.0823355\pi$
$572$	−1.51549	−	0.267221i	−0.0633658	−	0.0111731i
$573$	10.3878	+	4.84392i	0.433958	+	0.202358i
$574$	−6.03218	+	6.03218i	−0.251778	+	0.251778i
$575$	−0.0262960	+	0.0455461i	−0.00109662	+	0.00189940i
$576$	3.04067	+	5.26659i	0.126695	+	0.219441i
$577$	−34.7305	−	9.30601i	−1.44585	−	0.387414i	−0.551272	−	0.834326i	$-0.685857\pi$
$577$	−34.7305	−	9.30601i	−1.44585	−	0.387414i	−0.894578	+	0.446911i	$0.852524\pi$
$578$	−8.02084	+	1.41429i	−0.333623	+	0.0588267i
$579$	8.49815	−	18.2243i	0.353171	−	0.757378i
$580$	21.8189	+	18.3082i	0.905979	+	0.760207i
$581$	−22.1518	+	12.7893i	−0.919011	+	0.530591i
$582$	4.37221	+	1.59135i	0.181234	+	0.0659637i
$583$	18.0147			0.746092
$584$	7.80187	−	14.0663i	0.322844	−	0.582067i
$585$	−3.54162			−0.146428
$586$	8.08623	+	2.94315i	0.334039	+	0.121580i
$587$	−24.3848	+	14.0786i	−1.00647	+	0.581085i	−0.910156	−	0.414266i	$-0.864038\pi$
$587$	−24.3848	+	14.0786i	−1.00647	+	0.581085i	−0.0963135	+	0.995351i	$0.530705\pi$
$588$	1.23731	+	1.03822i	0.0510256	+	0.0428156i
$589$	−26.5636	+	56.9659i	−1.09454	+	2.34724i
$590$	7.31864	−	1.29047i	0.301304	−	0.0531279i
$591$	2.93829	+	0.787312i	0.120865	+	0.0323857i
$592$	−11.0300	−	19.1046i	−0.453332	−	0.785194i
$593$	−4.43876	+	7.68816i	−0.182278	+	0.315715i	−0.942656	−	0.333766i	$-0.891680\pi$
$593$	−4.43876	+	7.68816i	−0.182278	+	0.315715i	0.760378	+	0.649481i	$0.225014\pi$
$594$	−2.06959	+	2.06959i	−0.0849165	+	0.0849165i
$595$	−4.50624	−	2.10129i	−0.184738	−	0.0861447i
$596$	13.0451	+	2.30021i	0.534350	+	0.0942203i
$597$	3.79521	−	5.42012i	0.155328	−	0.221831i
$598$	−0.0361987	−	0.0253466i	−0.00148028	−	0.00103650i
$599$	2.41674	+	27.6234i	0.0987452	+	1.12866i	0.870307	+	0.492509i	$0.163920\pi$
$599$	2.41674	+	27.6234i	0.0987452	+	1.12866i	−0.771562	+	0.636154i	$0.780524\pi$
$600$	−0.0997142	−	0.565507i	−0.00407082	−	0.0230867i
$601$	−2.91403	−	10.8753i	−0.118866	−	0.443612i	0.880681	−	0.473709i	$-0.157085\pi$
$601$	−2.91403	−	10.8753i	−0.118866	−	0.443612i	−0.999547	+	0.0300966i	$0.990418\pi$
$602$	−3.99206	+	3.34974i	−0.162704	+	0.136525i
$603$	−1.84381	+	5.06584i	−0.0750859	+	0.206297i
$604$	12.3166	−	5.74332i	0.501155	−	0.233692i
$605$	−20.4598	+	5.48217i	−0.831807	+	0.222882i
$606$	0.216576	+	0.216576i	0.00879781	+	0.00879781i
$607$	−6.07526	−	16.6916i	−0.246587	−	0.677493i	−0.999806	−	0.0197221i	$-0.993722\pi$
$607$	−6.07526	−	16.6916i	−0.246587	−	0.677493i	0.753218	−	0.657771i	$-0.228500\pi$
$608$	26.1377	+	15.0906i	1.06002	+	0.612004i
$609$	−8.64451	−	10.3021i	−0.350293	−	0.417463i
$610$	0.849534	−	0.594850i	0.0343966	−	0.0240848i
$611$			0.238914i			0.00966544i
$612$	−2.10882	−	3.01171i	−0.0852441	−	0.121741i
$613$	−6.59175	−	14.1361i	−0.266238	−	0.570950i	0.727054	−	0.686580i	$-0.240889\pi$
$613$	−6.59175	−	14.1361i	−0.266238	−	0.570950i	−0.993292	+	0.115630i	$0.963111\pi$
$614$	0.320889	−	1.19758i	0.0129500	−	0.0483302i
$615$	−12.8844	−	1.12724i	−0.519550	−	0.0454547i
$616$	1.08039	−	6.12719i	0.0435301	−	0.246871i
$617$	−23.5984	+	2.06459i	−0.950034	+	0.0831172i	−0.551626	−	0.834091i	$-0.685993\pi$
$617$	−23.5984	+	2.06459i	−0.950034	+	0.0831172i	−0.398408	+	0.917208i	$0.630437\pi$
$618$	0.0112394	−	0.128467i	0.000452116	−	0.00516771i
$619$	−18.4738	+	22.0163i	−0.742526	+	0.884908i	−0.996610	−	0.0822744i	$-0.973782\pi$
$619$	−18.4738	+	22.0163i	−0.742526	+	0.884908i	0.254084	+	0.967182i	$0.418226\pi$
$620$	−40.0473	+	14.5760i	−1.60834	+	0.585387i
$621$	0.546968	−	0.199080i	0.0219491	−	0.00798881i
$622$	5.20268	−	6.20031i	0.208609	−	0.248610i
$623$	−1.94309	+	22.2097i	−0.0778484	+	0.889812i
$624$	−1.29581	+	0.113369i	−0.0518741	+	0.00453839i
$625$	4.64956	−	26.3690i	0.185982	−	1.05476i
$626$	−9.78286	−	0.855889i	−0.391002	−	0.0342082i
$627$	1.67913	−	6.26660i	0.0670580	−	0.250264i
$628$	−12.2688	−	26.3106i	−0.489580	−	1.04991i
$629$	4.40247	+	6.28738i	0.175538	+	0.250694i
$630$		−	6.67737i		−	0.266033i
$631$	−16.9767	+	11.8872i	−0.675832	+	0.473222i	−0.860415	−	0.509595i	$-0.829795\pi$
$631$	−16.9767	+	11.8872i	−0.675832	+	0.473222i	0.184583	+	0.982817i	$0.440907\pi$
$632$	−4.68695	−	5.58568i	−0.186437	−	0.222187i
$633$	−10.3479	−	5.97435i	−0.411291	−	0.237459i
$634$	−1.38325	−	3.80044i	−0.0549358	−	0.150935i
$635$	13.5539	+	13.5539i	0.537869	+	0.537869i
$636$	17.6201	−	4.72129i	0.698683	−	0.187211i
$637$	0.679974	−	0.317077i	0.0269416	−	0.0125631i
$638$	1.65102	−	4.53615i	0.0653646	−	0.179588i
$639$	−27.9884	+	23.4850i	−1.10720	+	0.929053i
$640$	6.83483	+	25.5079i	0.270170	+	1.00829i
$641$	3.99894	+	22.6791i	0.157948	+	0.895770i	0.956040	+	0.293235i	$0.0947318\pi$
$641$	3.99894	+	22.6791i	0.157948	+	0.895770i	−0.798092	+	0.602536i	$0.794157\pi$
$642$	0.546636	+	6.24807i	0.0215740	+	0.246592i
$643$	32.1788	+	22.5318i	1.26901	+	0.888568i	0.997273	−	0.0738038i	$-0.0235138\pi$
$643$	32.1788	+	22.5318i	1.26901	+	0.888568i	0.271735	+	0.962372i	$0.412403\pi$
$644$	−0.330958	+	0.472656i	−0.0130416	+	0.0186253i
$645$	−7.78083	−	1.37197i	−0.306370	−	0.0540213i
$646$	−2.41564	−	1.12643i	−0.0950422	−	0.0443189i
$647$	−3.11115	+	3.11115i	−0.122312	+	0.122312i	−0.765613	−	0.643301i	$-0.777564\pi$
$647$	−3.11115	+	3.11115i	−0.122312	+	0.122312i	0.643301	+	0.765613i	$0.277564\pi$
$648$	3.51933	−	6.09565i	0.138252	−	0.239460i
$649$	4.36135	+	7.55407i	0.171198	+	0.296523i
$650$	−0.120149	−	0.0321938i	−0.00471263	−	0.00126274i
$651$	19.8168	−	3.49424i	0.776682	−	0.136950i
$652$	−3.08188	+	6.60911i	−0.120696	+	0.258833i
$653$	−27.5121	−	23.0854i	−1.07663	−	0.903402i	−0.0809957	−	0.996714i	$-0.525810\pi$
$653$	−27.5121	−	23.0854i	−1.07663	−	0.903402i	−0.995637	+	0.0933125i	$0.970254\pi$
$654$	−5.10396	+	2.94677i	−0.199581	+	0.115228i
$655$	16.0221	+	5.83155i	0.626034	+	0.227858i
$656$	17.9252			0.699860
$657$	20.2594	−	0.348343i	0.790394	−	0.0135902i
$658$	−0.450450			−0.0175604
$659$	−7.98683	−	2.90697i	−0.311123	−	0.113239i	0.181740	−	0.983347i	$-0.441827\pi$
$659$	−7.98683	−	2.90697i	−0.311123	−	0.113239i	−0.492862	+	0.870107i	$0.664049\pi$
$660$	3.80949	−	2.19941i	0.148284	−	0.0856119i
$661$	24.7179	+	20.7408i	0.961417	+	0.806724i	0.981183	−	0.193080i	$-0.0618477\pi$
$661$	24.7179	+	20.7408i	0.961417	+	0.806724i	−0.0197662	+	0.999805i	$0.506292\pi$
$662$	3.39431	−	7.27911i	0.131923	−	0.282911i
$663$	0.445705	−	0.0785899i	0.0173098	−	0.00305218i
$664$	−19.2572	−	5.15996i	−0.747325	−	0.200245i
$665$	16.7622	+	29.0331i	0.650012	+	1.12585i
$666$	−5.15397	+	8.92693i	−0.199712	+	0.345912i
$667$	−0.678833	+	0.678833i	−0.0262845	+	0.0262845i
$668$	33.0819	+	15.4263i	1.27998	+	0.596863i
$669$	−11.0074	−	1.94090i	−0.425571	−	0.0750396i
$670$	−1.51989	+	2.17063i	−0.0587187	+	0.0838589i
$671$	0.997131	+	0.698199i	0.0384938	+	0.0269537i
$672$	−0.842122	−	9.62550i	−0.0324856	−	0.371312i
$673$	−4.91608	−	27.8805i	−0.189501	−	1.07471i	−0.920035	−	0.391837i	$-0.871840\pi$
$673$	−4.91608	−	27.8805i	−0.189501	−	1.07471i	0.730534	−	0.682877i	$-0.239271\pi$
$674$	−1.68956	−	6.30551i	−0.0650793	−	0.242879i
$675$	1.25510	−	1.05315i	0.0483087	−	0.0405358i
$676$	7.52294	−	20.6691i	0.289344	−	0.794966i
$677$	−39.3723	+	18.3596i	−1.51320	+	0.705617i	−0.989264	−	0.146140i	$-0.953315\pi$
$677$	−39.3723	+	18.3596i	−1.51320	+	0.705617i	−0.523937	+	0.851757i	$0.675537\pi$
$678$	−4.62437	+	1.23910i	−0.177598	+	0.0475872i
$679$	−19.9547	−	19.9547i	−0.765792	−	0.765792i
$680$	−1.32545	−	3.64163i	−0.0508285	−	0.139650i
$681$	−17.7053	−	10.2222i	−0.678468	−	0.391714i
$682$	4.64278	+	5.53305i	0.177781	+	0.211872i
$683$	−21.4641	+	15.0294i	−0.821302	+	0.575082i	−0.906948	−	0.421244i	$-0.861594\pi$
$683$	−21.4641	+	15.0294i	−0.821302	+	0.575082i	0.0856452	+	0.996326i	$0.472705\pi$
$684$			24.7897i			0.947859i
$685$	−6.76053	−	9.65504i	−0.258307	−	0.368900i
$686$	4.18736	+	8.97983i	0.159874	+	0.342852i
$687$	−2.70997	+	10.1137i	−0.103392	+	0.385863i
$688$	10.9084	+	0.954362i	0.415879	+	0.0363847i
$689$	1.47139	−	8.34469i	0.0560556	−	0.317907i
$690$	0.125837	−	0.0110093i	0.00479053	−	0.000419117i
$691$	−3.78028	+	43.2088i	−0.143809	+	1.64374i	0.491063	+	0.871124i	$0.336608\pi$
$691$	−3.78028	+	43.2088i	−0.143809	+	1.64374i	−0.634872	+	0.772617i	$0.718947\pi$
$692$	7.51209	−	8.95256i	0.285567	−	0.340325i
$693$	7.36483	−	2.68058i	0.279767	−	0.101827i
$694$	−10.4878	+	3.81726i	−0.398113	+	0.144901i
$695$	21.5194	−	25.6458i	0.816277	−	0.972801i
$696$	0.913567	−	10.4421i	0.0346287	−	0.395807i
$697$	−6.21306	+	0.543572i	−0.235336	+	0.0205893i
$698$	−1.66966	+	9.46909i	−0.0631974	+	0.358410i
$699$	−0.901426	−	0.0788646i	−0.0340951	−	0.00298293i
$700$	−0.420363	+	1.56882i	−0.0158882	+	0.0592956i
$701$	−4.55980	−	9.77853i	−0.172221	−	0.369330i	0.801184	−	0.598418i	$-0.204204\pi$
$701$	−4.55980	−	9.77853i	−0.172221	−	0.369330i	−0.973406	+	0.229088i	$0.926426\pi$
$702$	0.789629	+	1.12771i	0.0298026	+	0.0425626i
$703$		−	51.7522i		−	1.95187i
$704$	−2.87404	+	2.01242i	−0.108319	+	0.0758460i
$705$	−0.438980	−	0.523156i	−0.0165330	−	0.0197032i
$706$	9.15569	+	5.28604i	0.344579	+	0.198943i
$707$	−0.635365	−	1.74565i	−0.0238954	−	0.0656520i
$708$	6.24559	+	6.24559i	0.234724	+	0.234724i
$709$	19.5774	−	5.24576i	0.735246	−	0.197009i	0.128282	−	0.991738i	$-0.459054\pi$
$709$	19.5774	−	5.24576i	0.735246	−	0.197009i	0.606964	+	0.794729i	$0.292387\pi$
$710$	−16.2763	+	7.58977i	−0.610839	+	0.284839i
$711$	3.14153	−	8.63129i	0.117817	−	0.323699i
$712$	−13.3114	+	11.1696i	−0.498865	+	0.418598i
$713$	−0.371778	−	1.38749i	−0.0139232	−	0.0519620i
$714$	0.148173	+	0.840333i	0.00554525	+	0.0314487i
$715$	−0.178084	−	2.03551i	−0.00665998	−	0.0761239i
$716$	−8.84345	−	6.19225i	−0.330495	−	0.231415i
$717$	12.6795	−	18.1082i	0.473523	−	0.676261i
$718$	−4.25848	−	0.750884i	−0.158925	−	0.0280228i
$719$	9.72452	+	4.53462i	0.362664	+	0.169113i	0.595405	−	0.803426i	$-0.296992\pi$
$719$	9.72452	+	4.53462i	0.362664	+	0.169113i	−0.232741	+	0.972539i	$0.574770\pi$
$720$	−9.92120	+	9.92120i	−0.369741	+	0.369741i
$721$	−0.391079	+	0.677369i	−0.0145645	+	0.0252265i
$722$	4.21339	+	7.29780i	0.156806	+	0.271596i
$723$	5.05538	+	1.35458i	0.188011	+	0.0503775i
$724$	−22.7090	+	4.00421i	−0.843974	+	0.148815i
$725$	−1.14202	+	2.44907i	−0.0424135	+	0.0909560i
$726$	2.78466	+	2.33661i	0.103348	+	0.0867196i
$727$	18.3491	−	10.5938i	0.680529	−	0.392904i	−0.119525	−	0.992831i	$-0.538137\pi$
$727$	18.3491	−	10.5938i	0.680529	−	0.392904i	0.800054	+	0.599928i	$0.204804\pi$
$728$	−2.74997	−	1.00091i	−0.101921	−	0.0370960i
$729$	−1.26091			−0.0467005
$730$	9.66325	+	2.41200i	0.357653	+	0.0892720i
$731$	−3.80992			−0.140915
$732$	1.15827	+	0.421578i	0.0428111	+	0.0155820i
$733$	29.0328	−	16.7621i	1.07235	−	0.619123i	0.143529	−	0.989646i	$-0.454155\pi$
$733$	29.0328	−	16.7621i	1.07235	−	0.619123i	0.928823	+	0.370524i	$0.120822\pi$
$734$	−6.37096	−	5.34587i	−0.235156	−	0.197320i
$735$	−0.906358	+	1.94369i	−0.0334315	+	0.0716942i
$736$	−0.679259	+	0.119772i	−0.0250378	+	0.00441484i
$737$	−3.00426	−	0.804989i	−0.110663	−	0.0296522i
$738$	−4.18791	−	7.25368i	−0.154159	−	0.267012i
$739$	−9.54425	+	16.5311i	−0.351091	+	0.608107i	−0.986441	−	0.164117i	$-0.947523\pi$
$739$	−9.54425	+	16.5311i	−0.351091	+	0.608107i	0.635350	+	0.772224i	$0.280856\pi$
$740$	24.8120	−	24.8120i	0.912107	−	0.912107i
$741$	−2.76564	−	1.28964i	−0.101598	−	0.0473761i
$742$	15.7331	+	2.77417i	0.577580	+	0.101843i
$743$	−5.19424	+	7.41814i	−0.190558	+	0.272145i	−0.903050	−	0.429535i	$-0.858678\pi$
$743$	−5.19424	+	7.41814i	−0.190558	+	0.272145i	0.712492	+	0.701680i	$0.247566\pi$
$744$	12.8475	+	8.99591i	0.471012	+	0.329806i
$745$	1.53293	+	17.5215i	0.0561622	+	0.641937i
$746$	−1.53423	−	8.70106i	−0.0561722	−	0.318568i
$747$	−6.50000	−	24.2583i	−0.237822	−	0.887566i
$748$	1.62492	−	1.36347i	0.0594128	−	0.0498533i
$749$	13.0107	−	35.7465i	0.475399	−	1.30615i
$750$	−3.86543	+	1.80248i	−0.141146	+	0.0658173i
$751$	−0.0782196	+	0.0209589i	−0.00285427	+	0.000764800i	−0.260246	−	0.965542i	$-0.583804\pi$
$751$	−0.0782196	+	0.0209589i	−0.00285427	+	0.000764800i	0.257392	+	0.966307i	$0.417137\pi$
$752$	0.669276	+	0.669276i	0.0244060	+	0.0244060i
$753$	0.497240	+	1.36616i	0.0181204	+	0.0497855i
$754$	−1.96636	−	1.13528i	−0.0716108	−	0.0413445i
$755$	11.5987	+	13.8228i	0.422122	+	0.503065i
$756$	14.7248	−	10.3104i	0.535535	−	0.374986i
$757$		−	13.5040i		−	0.490810i	−0.969421	−	0.245405i	$-0.921079\pi$
$757$		−	13.5040i		−	0.490810i	0.969421	−	0.245405i	$-0.0789209\pi$
$758$	1.08008	+	1.54251i	0.0392303	+	0.0560266i
$759$	0.0626591	+	0.134373i	0.00227438	+	0.00487742i
$760$	−6.76285	+	25.2393i	−0.245314	+	0.915526i
$761$	2.25760	+	0.197515i	0.0818381	+	0.00715991i	0.128001	−	0.991774i	$-0.459144\pi$
$761$	2.25760	+	0.197515i	0.0818381	+	0.00715991i	−0.0461631	+	0.998934i	$0.514699\pi$
$762$	0.571229	−	3.23960i	0.0206934	−	0.117358i
$763$	35.6096	−	3.11543i	1.28915	−	0.112786i
$764$	2.20220	−	25.1713i	0.0796730	−	0.910666i
$765$	3.13794	−	3.73965i	0.113453	−	0.135207i
$766$	−5.02960	+	1.83062i	−0.181727	+	0.0661431i
$767$	3.85539	−	1.40325i	0.139210	−	0.0506683i
$768$	0.299715	−	0.357187i	0.0108150	−	0.0128889i
$769$	3.73880	−	42.7347i	0.134825	−	1.54105i	−0.564009	−	0.825768i	$-0.690742\pi$
$769$	3.73880	−	42.7347i	0.134825	−	1.54105i	0.698834	−	0.715284i	$-0.253703\pi$
$770$	3.83776	−	0.335761i	0.138303	−	0.0121000i
$771$	−2.89688	+	16.4290i	−0.104329	+	0.591677i
$772$	−44.1604	−	3.86353i	−1.58937	−	0.139052i
$773$	−10.6767	+	39.8460i	−0.384014	+	1.43316i	0.455701	+	0.890133i	$0.349389\pi$
$773$	−10.6767	+	39.8460i	−0.384014	+	1.43316i	−0.839715	+	0.543027i	$0.817278\pi$
$774$	−2.16237	−	4.63722i	−0.0777248	−	0.166681i
$775$	−2.31913	−	3.31206i	−0.0833057	−	0.118973i
$776$		−	21.9954i		−	0.789590i
$777$	−13.5718	+	9.50305i	−0.486884	+	0.340920i
$778$	−11.7301	−	13.9794i	−0.420544	−	0.501184i
$779$	36.4179	+	21.0259i	1.30481	+	0.753331i
$780$	−0.707652	−	1.94426i	−0.0253380	−	0.0696156i
$781$	−14.9052	−	14.9052i	−0.533349	−	0.533349i
$782$	0.0588368	−	0.0157653i	0.00210400	−	0.000563765i
$783$	27.1054	−	12.6395i	0.968669	−	0.451698i
$784$	1.01659	−	2.79306i	0.0363068	−	0.0997522i
$785$	29.5282	−	24.7771i	1.05391	−	0.884334i
$786$	−0.757339	−	2.82643i	−0.0270134	−	0.100815i
$787$	−6.01916	−	34.1364i	−0.214560	−	1.21683i	−0.881668	−	0.471869i	$-0.843579\pi$
$787$	−6.01916	−	34.1364i	−0.214560	−	1.21683i	0.667108	−	0.744961i	$-0.267532\pi$
$788$	−0.584466	−	6.68048i	−0.0208207	−	0.237982i
$789$	12.5453	+	8.78431i	0.446624	+	0.312730i
$790$	2.58963	−	3.69838i	0.0921349	−	0.131582i
$791$	28.5960	+	5.04225i	1.01676	+	0.179282i
$792$	5.53636	+	2.58165i	0.196726	+	0.0917348i
$793$	0.404860	−	0.404860i	0.0143770	−	0.0143770i
$794$	−7.13098	+	12.3512i	−0.253069	+	0.438329i
$795$	12.1105	+	20.9761i	0.429517	+	0.743945i
$796$	−14.0897	−	3.77531i	−0.499395	−	0.133812i
$797$	7.05050	−	1.24319i	0.249741	−	0.0440361i	−0.0473759	−	0.998877i	$-0.515086\pi$
$797$	7.05050	−	1.24319i	0.249741	−	0.0440361i	0.297117	+	0.954841i	$0.403975\pi$
$798$	2.43149	−	5.21434i	0.0860737	−	0.184586i
$799$	−0.252274	−	0.211683i	−0.00892481	−	0.00748881i
$800$	−1.68136	+	0.970735i	−0.0594452	+	0.0343207i
$801$	−20.5694	−	7.48666i	−0.726785	−	0.264528i
$802$	−1.49763			−0.0528831
$803$	1.21892	+	11.6264i	0.0430147	+	0.410287i
$804$	−3.14943			−0.111072
$805$	−0.719939	−	0.262036i	−0.0253745	−	0.00923557i
$806$	2.94221	−	1.69868i	0.103635	−	0.0598336i
$807$	−8.37719	−	7.02929i	−0.294891	−	0.247443i
$808$	0.611915	−	1.31226i	0.0215271	−	0.0461650i
$809$	2.25060	−	0.396842i	0.0791269	−	0.0139522i	−0.133945	−	0.990989i	$-0.542764\pi$
$809$	2.25060	−	0.396842i	0.0791269	−	0.0139522i	0.213071	+	0.977037i	$0.431653\pi$
$810$	4.20976	+	1.12800i	0.147916	+	0.0396339i
$811$	10.4439	+	18.0893i	0.366734	+	0.635202i	0.989053	−	0.147562i	$-0.0471426\pi$
$811$	10.4439	+	18.0893i	0.366734	+	0.635202i	−0.622319	+	0.782764i	$0.713809\pi$
$812$	−14.8237	+	25.6753i	−0.520209	+	0.901028i
$813$	−9.41542	+	9.41542i	−0.330213	+	0.330213i
$814$	−5.38984	−	2.51332i	−0.188914	−	0.0880919i
$815$	−9.53559	−	1.68138i	−0.334017	−	0.0588962i
$816$	1.02841	−	1.46872i	0.0360015	−	0.0514155i
$817$	21.0428	+	14.7343i	0.736194	+	0.515489i
$818$	−0.172284	−	1.96922i	−0.00602377	−	0.0688521i
$819$	−0.640146	−	3.63045i	−0.0223685	−	0.126858i
$820$	7.37954	+	27.5408i	0.257705	+	0.961767i
$821$	40.7529	−	34.1957i	1.42228	−	1.19344i	0.472182	−	0.881501i	$-0.343467\pi$
$821$	40.7529	−	34.1957i	1.42228	−	1.19344i	0.950103	−	0.311937i	$-0.100978\pi$
$822$	−0.691835	+	1.90080i	−0.0241305	+	0.0662981i
$823$	−21.6408	+	10.0913i	−0.754351	+	0.351760i	−0.761457	−	0.648215i	$-0.775516\pi$
$823$	−21.6408	+	10.0913i	−0.754351	+	0.351760i	0.00710630	+	0.999975i	$0.497738\pi$
$824$	−0.588857	+	0.157784i	−0.0205138	+	0.00549665i
$825$	0.295099	+	0.295099i	0.0102740	+	0.0102740i
$826$	2.64568	+	7.26896i	0.0920551	+	0.252919i
$827$	−25.4800	−	14.7109i	−0.886028	−	0.511549i	−0.0133868	−	0.999910i	$-0.504261\pi$
$827$	−25.4800	−	14.7109i	−0.886028	−	0.511549i	−0.872641	+	0.488362i	$0.837595\pi$
$828$	−0.364156	−	0.433984i	−0.0126553	−	0.0150820i
$829$	−29.1166	+	20.3877i	−1.01126	+	0.708092i	−0.956897	−	0.290429i	$-0.906202\pi$
$829$	−29.1166	+	20.3877i	−1.01126	+	0.708092i	−0.0543641	+	0.998521i	$0.517313\pi$
$830$		−	12.3445i		−	0.428484i
$831$	1.02105	+	1.45821i	0.0354198	+	0.0505848i
$832$	0.697442	+	1.49567i	0.0241794	+	0.0518530i
$833$	−0.267663	+	0.998933i	−0.00927399	+	0.0346110i
$834$	−5.72359	−	0.500749i	−0.198192	−	0.0173395i
$835$	−8.41615	+	47.7304i	−0.291253	+	1.65178i
$836$	−14.2477	+	1.24651i	−0.492767	+	0.0431115i
$837$	−3.90019	+	44.5794i	−0.134810	+	1.54089i
$838$	−4.97243	+	5.92592i	−0.171770	+	0.204707i
$839$	−43.2743	+	15.7505i	−1.49399	+	0.543769i	−0.954497	−	0.298219i	$-0.903607\pi$
$839$	−43.2743	+	15.7505i	−1.49399	+	0.543769i	−0.539496	+	0.841988i	$0.681385\pi$
$840$	7.86072	−	2.86107i	0.271221	−	0.0987162i
$841$	−13.0658	+	15.5712i	−0.450543	+	0.536936i
$842$	−0.308494	+	3.52610i	−0.0106314	+	0.121517i
$843$	−19.4481	+	1.70149i	−0.669827	+	0.0586023i
$844$	−4.57407	+	25.9409i	−0.157446	+	0.892921i
$845$	29.0944	+	2.54543i	1.00088	+	0.0875654i
$846$	0.114467	−	0.427198i	0.00393546	−	0.0146874i
$847$	−9.31778	−	19.9820i	−0.320163	−	0.686591i
$848$	−19.2543	−	27.4980i	−0.661195	−	0.944285i
$849$			12.1785i			0.417965i
$850$	0.140448	−	0.0983430i	0.00481734	−	0.00337314i
$851$	0.760228	+	0.906004i	0.0260603	+	0.0310574i
$852$	−18.4851	−	10.6724i	−0.633288	−	0.365629i
$853$	−0.365121	−	1.00316i	−0.0125015	−	0.0343476i	0.933285	−	0.359137i	$-0.116929\pi$
$853$	−0.365121	−	1.00316i	−0.0125015	−	0.0343476i	−0.945786	+	0.324789i	$0.894707\pi$
$854$	0.763323	+	0.763323i	0.0261204	+	0.0261204i
$855$	−31.7940	+	8.51917i	−1.08733	+	0.291349i
$856$	26.8717	−	12.5305i	0.918456	−	0.428283i
$857$	−15.2204	+	41.8178i	−0.519920	+	1.42847i	0.350689	+	0.936492i	$0.385947\pi$
$857$	−15.2204	+	41.8178i	−0.519920	+	1.42847i	−0.870609	+	0.491976i	$0.836275\pi$
$858$	−0.268624	+	0.225403i	−0.00917069	+	0.00769512i
$859$	−4.17262	−	15.5724i	−0.142368	−	0.531325i	−0.999858	−	0.0168248i	$-0.994644\pi$
$859$	−4.17262	−	15.5724i	−0.142368	−	0.531325i	0.857490	−	0.514500i	$-0.172022\pi$
$860$	3.02453	+	17.1529i	0.103135	+	0.584910i
$861$	−1.17334	−	13.4113i	−0.0399873	−	0.457057i
$862$	0.0800172	+	0.0560286i	0.00272540	+	0.00190834i
$863$	26.3375	−	37.6138i	0.896538	−	1.28039i	−0.0627706	−	0.998028i	$-0.519994\pi$
$863$	26.3375	−	37.6138i	0.896538	−	1.28039i	0.959308	−	0.282361i	$-0.0911175\pi$
$864$	21.1611	+	3.73127i	0.719915	+	0.126941i
$865$	14.0636	+	6.55798i	0.478178	+	0.222978i
$866$	2.13791	−	2.13791i	0.0726493	−	0.0726493i
$867$	6.42654	−	11.1311i	0.218257	−	0.378032i
$868$	−22.1802	−	38.4172i	−0.752844	−	1.30396i
$869$	5.11873	+	1.37156i	0.173641	+	0.0465270i
$870$	6.39175	−	1.12704i	0.216701	−	0.0382102i
$871$	−0.618264	+	1.32587i	−0.0209491	+	0.0449254i
$872$	21.3426	+	17.9086i	0.722753	+	0.606461i
$873$	23.9955	−	13.8538i	0.812125	−	0.468881i
$874$	−0.385935	−	0.140469i	−0.0130544	−	0.00475143i
$875$	25.8683			0.874509
$876$	4.23927	+	11.0523i	0.143232	+	0.373422i
$877$	−18.2280			−0.615516			−0.307758	−	0.951465i	$-0.599579\pi$
$877$	−18.2280			−0.615516			−0.307758	+	0.951465i	$0.599579\pi$
$878$	−7.04581	−	2.56447i	−0.237785	−	0.0865465i
$879$	−11.7606	+	6.78999i	−0.396675	+	0.229021i
$880$	−6.20100	−	5.20326i	−0.209036	−	0.175402i
$881$	8.14069	−	17.4578i	0.274267	−	0.588167i	−0.720135	−	0.693834i	$-0.755920\pi$
$881$	8.14069	−	17.4578i	0.274267	−	0.588167i	0.994402	+	0.105667i	$0.0336978\pi$
$882$	−1.36776	+	0.241173i	−0.0460550	+	0.00812073i
$883$	21.3078	+	5.70940i	0.717064	+	0.192137i	0.598861	−	0.800853i	$-0.295620\pi$
$883$	21.3078	+	5.70940i	0.717064	+	0.192137i	0.118203	+	0.992989i	$0.462287\pi$
$884$	−0.498860	−	0.864051i	−0.0167785	−	0.0290612i
$885$	−5.86391	+	10.1566i	−0.197113	+	0.341410i
$886$	−5.21557	+	5.21557i	−0.175220	+	0.175220i
$887$	−5.38267	−	2.50998i	−0.180732	−	0.0842768i	0.330146	−	0.943930i	$-0.392902\pi$
$887$	−5.38267	−	2.50998i	−0.180732	−	0.0842768i	−0.510878	+	0.859653i	$0.670680\pi$
$888$	−12.7173	−	2.24240i	−0.426764	−	0.0752500i
$889$	−11.4440	+	16.3437i	−0.383819	+	0.548150i
$890$	−8.81369	−	6.17141i	−0.295436	−	0.206866i
$891$	0.445842	+	5.09600i	0.0149363	+	0.170722i
$892$	4.27874	+	24.2660i	0.143263	+	0.812484i
$893$	0.574696	+	2.14479i	0.0192315	+	0.0717728i
$894$	2.31229	−	1.94024i	0.0773344	−	0.0648913i
$895$	4.90273	−	13.4701i	0.163880	−	0.450257i
$896$	−24.9124	+	11.6168i	−0.832263	+	0.388091i
$897$	0.0673614	−	0.0180494i	0.00224913	−	0.000602653i
$898$	3.22979	+	3.22979i	0.107779	+	0.107779i
$899$	−25.2431	−	69.3549i	−0.841906	−	2.31312i
$900$	−1.38101	−	0.797327i	−0.0460337	−	0.0265776i
$901$	7.50762	+	8.94723i	0.250115	+	0.298075i
$902$	3.95841	−	2.77171i	0.131801	−	0.0922878i
$903$		−	8.22397i		−	0.273677i
$904$	12.9813	+	18.5392i	0.431750	+	0.616604i
$905$	−12.9397	−	27.7493i	−0.430130	−	0.922417i
$906$	0.801496	−	2.99122i	0.0266279	−	0.0993767i
$907$	−3.35078	−	0.293155i	−0.111261	−	0.00973406i	0.0313894	−	0.999507i	$-0.490007\pi$
$907$	−3.35078	−	0.293155i	−0.111261	−	0.00973406i	−0.142650	+	0.989773i	$0.545562\pi$
$908$	−7.82627	+	44.3850i	−0.259724	+	1.47297i
$909$	1.81700	−	0.158967i	0.0602660	−	0.00527259i
$910$	0.157929	−	1.80514i	0.00523529	−	0.0598397i
$911$	−27.5251	+	32.8031i	−0.911946	+	1.08682i	0.0839641	+	0.996469i	$0.473242\pi$
$911$	−27.5251	+	32.8031i	−0.911946	+	1.08682i	−0.995910	+	0.0903465i	$0.971203\pi$
$912$	−11.3601	+	4.13475i	−0.376172	+	0.136915i
$913$	13.6154	−	4.95561i	0.450605	−	0.164007i
$914$	11.5478	−	13.7622i	0.381969	−	0.455213i
$915$	−0.142643	+	1.63042i	−0.00471563	+	0.0539000i
$916$	22.9946	−	2.01176i	0.759761	−	0.0664705i
$917$	−3.08184	+	17.4780i	−0.101771	+	0.577174i
$918$	−1.89039	−	0.165388i	−0.0623923	−	0.00545862i
$919$	0.725286	−	2.70681i	0.0239250	−	0.0892893i	−0.952931	−	0.303187i	$-0.901949\pi$
$919$	0.725286	−	2.70681i	0.0239250	−	0.0892893i	0.976856	+	0.213898i	$0.0686160\pi$
$920$	−0.252365	−	0.541199i	−0.00832024	−	0.0178428i
$921$	1.12225	+	1.60274i	0.0369794	+	0.0528120i
$922$			3.33735i			0.109910i
$923$	−8.12173	+	5.68690i	−0.267330	+	0.187186i
$924$	2.94314	+	3.50750i	0.0968222	+	0.115388i
$925$	2.88306	+	1.66454i	0.0947945	+	0.0547296i
$926$	2.14938	+	5.90537i	0.0706330	+	0.194062i
$927$	−0.543023	−	0.543023i	−0.0178352	−	0.0178352i
$928$	−34.2320	+	9.17243i	−1.12372	+	0.301100i
$929$	−1.49000	+	0.694799i	−0.0488853	+	0.0227956i	−0.446907	−	0.894580i	$-0.647475\pi$
$929$	−1.49000	+	0.694799i	−0.0488853	+	0.0227956i	0.398022	+	0.917376i	$0.369697\pi$
$930$	−3.32146	+	9.12565i	−0.108915	+	0.299242i
$931$	5.34158	−	4.48212i	0.175063	−	0.146896i
$932$	0.516291	+	1.92683i	0.0169117	+	0.0631153i
$933$	2.21804	+	12.5791i	0.0726152	+	0.411822i
$934$	−1.11667	−	12.7636i	−0.0365385	−	0.417637i
$935$	2.30712	+	1.61546i	0.0754510	+	0.0528313i
$936$	1.64805	−	2.35367i	0.0538683	−	0.0769320i
$937$	−26.3916	−	4.65355i	−0.862176	−	0.152025i	−0.274961	−	0.961455i	$-0.588665\pi$
$937$	−26.3916	−	4.65355i	−0.862176	−	0.152025i	−0.587216	+	0.809430i	$0.699776\pi$
$938$	−2.49980	−	1.16568i	−0.0816214	−	0.0380607i
$939$	10.9584	−	10.9584i	0.357612	−	0.357612i
$940$	−0.752766	+	1.30383i	−0.0245525	+	0.0425262i
$941$	0.661949	+	1.14653i	0.0215789	+	0.0373758i	0.876613	−	0.481196i	$-0.159797\pi$
$941$	0.661949	+	1.14653i	0.0215789	+	0.0373758i	−0.855034	+	0.518571i	$0.826464\pi$
$942$	−6.38983	−	1.71215i	−0.208192	−	0.0557848i
$943$	−0.946420	+	0.166879i	−0.0308197	+	0.00543434i
$944$	6.86924	−	14.7311i	0.223575	−	0.479457i
$945$	18.2838	+	15.3419i	0.594773	+	0.499074i
$946$	2.55647	−	1.47598i	0.0831181	−	0.0479882i
$947$	−35.9831	−	13.0968i	−1.16929	−	0.425588i	−0.316885	−	0.948464i	$-0.602637\pi$
$947$	−35.9831	−	13.0968i	−1.16929	−	0.425588i	−0.852409	+	0.522876i	$0.824859\pi$
$948$	5.36607			0.174282
$949$	5.48509	+	0.384992i	0.178054	+	0.0124974i
$950$	−1.15605			−0.0375071
$951$	5.99753	+	2.18292i	0.194483	+	0.0707862i
$952$	3.49340	−	2.01691i	0.113222	−	0.0653686i
$953$	−34.7112	−	29.1261i	−1.12440	−	0.943488i	−0.125586	−	0.992083i	$-0.540081\pi$
$953$	−34.7112	−	29.1261i	−1.12440	−	0.943488i	−0.998819	+	0.0485949i	$0.984526\pi$
$954$	−6.62902	+	14.2160i	−0.214622	+	0.460259i
$955$	33.0401	−	5.82587i	1.06915	−	0.188521i
$956$	−47.0724	−	12.6130i	−1.52243	−	0.407934i
$957$	3.80899	+	6.59737i	0.123127	+	0.213263i
$958$	−2.59203	+	4.48953i	−0.0837446	+	0.145050i
$959$	8.67525	−	8.67525i	0.280138	−	0.280138i
$960$	−4.27534	−	1.99362i	−0.137986	−	0.0643439i
$961$	78.2268	+	13.7935i	2.52344	+	0.444951i
$962$	−1.60444	+	2.29138i	−0.0517292	+	0.0738770i
$963$	30.5950	+	21.4229i	0.985912	+	0.690343i
$964$	−1.00558	−	11.4939i	−0.0323877	−	0.370193i
$965$	−10.2209	−	57.9654i	−0.329021	−	1.86597i
$966$	0.0340304	+	0.127003i	0.00109491	+	0.00408627i
$967$	−10.8678	+	9.11919i	−0.349486	+	0.293253i	−0.800584	−	0.599221i	$-0.795477\pi$
$967$	−10.8678	+	9.11919i	−0.349486	+	0.293253i	0.451098	+	0.892475i	$0.351033\pi$
$968$	5.87743	−	16.1481i	0.188908	−	0.519019i
$969$	3.81216	−	1.77764i	0.122464	−	0.0571061i
$970$	13.1553	−	3.52495i	0.422391	−	0.113179i
$971$	18.1235	+	18.1235i	0.581612	+	0.581612i	0.935346	−	0.353734i	$-0.115088\pi$
$971$	18.1235	+	18.1235i	0.581612	+	0.581612i	−0.353734	+	0.935346i	$0.615088\pi$
$972$	9.40765	+	25.8473i	0.301751	+	0.829053i
$973$	30.1787	+	17.4237i	0.967485	+	0.558578i
$974$	3.00360	+	3.57955i	0.0962416	+	0.114696i
$975$	0.160797	−	0.112592i	0.00514964	−	0.00360582i
$976$		−	2.26828i		−	0.0726060i
$977$	−5.71571	−	8.16288i	−0.182862	−	0.261154i	0.717247	−	0.696819i	$-0.245402\pi$
$977$	−5.71571	−	8.16288i	−0.182862	−	0.261154i	−0.900109	+	0.435665i	$0.856513\pi$
$978$	0.702273	+	1.50603i	0.0224562	+	0.0481575i
$979$	3.26860	−	12.1986i	0.104465	−	0.389868i
$980$	4.70987	+	0.412060i	0.150451	+	0.0131628i
$981$	−6.09441	+	34.5631i	−0.194579	+	1.10351i
$982$	7.52438	−	0.658298i	0.240113	−	0.0210071i
$983$	−2.92762	+	33.4628i	−0.0933765	+	1.06730i	0.794515	+	0.607245i	$0.207725\pi$
$983$	−2.92762	+	33.4628i	−0.0933765	+	1.06730i	−0.887891	+	0.460054i	$0.847830\pi$
$984$	6.74476	−	8.03809i	0.215015	−	0.256245i
$985$	8.36716	−	3.04540i	0.266600	−	0.0970344i
$986$	2.94100	−	1.07044i	0.0936606	−	0.0340897i
$987$	0.456933	−	0.544551i	0.0145443	−	0.0173333i
$988$	−0.586312	+	6.70157i	−0.0186531	+	0.213205i
$989$	−0.584831	+	0.0511661i	−0.0185966	+	0.00162699i
$990$	−0.656814	+	3.72498i	−0.0208749	+	0.118388i
$991$	10.2780	+	0.899212i	0.326493	+	0.0285644i	0.249224	−	0.968446i	$-0.419824\pi$
$991$	10.2780	+	0.899212i	0.326493	+	0.0285644i	0.0772688	+	0.997010i	$0.475380\pi$
$992$	13.7244	−	51.2202i	0.435751	−	1.62624i
$993$	5.35660	+	11.4873i	0.169987	+	0.364538i
$994$	−10.7221	−	15.3127i	−0.340084	−	0.485690i
$995$		−	19.3680i		−	0.614008i
$996$	12.0184	−	8.41540i	0.380819	−	0.266652i
$997$	30.7509	+	36.6475i	0.973891	+	1.16064i	0.986999	+	0.160724i	$0.0513827\pi$
$997$	30.7509	+	36.6475i	0.973891	+	1.16064i	−0.0131089	+	0.999914i	$0.504173\pi$
$998$	−6.82172	−	3.93852i	−0.215938	−	0.124672i
$999$	−12.6018	−	34.6230i	−0.398702	−	1.09542i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	73.2.k.a.23.3	✓	72
3.2	odd	2		657.2.cc.d.388.4		72
73.28	odd	72		5329.2.a.o.1.39		72
73.45	odd	72		5329.2.a.o.1.40		72
73.54	even	36	inner	73.2.k.a.54.3	yes	72
219.200	odd	36		657.2.cc.d.127.4		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
73.2.k.a.23.3	✓	72	1.1	even	1	trivial
73.2.k.a.54.3	yes	72	73.54	even	36	inner
657.2.cc.d.127.4		72	219.200	odd	36
657.2.cc.d.388.4		72	3.2	odd	2
5329.2.a.o.1.39		72	73.28	odd	72
5329.2.a.o.1.40		72	73.45	odd	72

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:	\( N \)	\(=\)	\( 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	73.k (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.472051 - 0.171812i) q^{2} +(0.686550 - 0.396380i) q^{3} +(-1.33878 - 1.12337i) q^{4} +(0.980689 - 2.10309i) q^{5} +(-0.392189 + 0.0691536i) q^{6} +(2.33310 + 0.625153i) q^{7} +(0.941308 + 1.63039i) q^{8} +(-1.18577 + 2.05381i) q^{9} +O(q^{10})\)	\(q+(-0.472051 - 0.171812i) q^{2} +(0.686550 - 0.396380i) q^{3} +(-1.33878 - 1.12337i) q^{4} +(0.980689 - 2.10309i) q^{5} +(-0.392189 + 0.0691536i) q^{6} +(2.33310 + 0.625153i) q^{7} +(0.941308 + 1.63039i) q^{8} +(-1.18577 + 2.05381i) q^{9} +(-0.824273 + 0.824273i) q^{10} +(-1.24003 - 0.578237i) q^{11} +(-1.36442 - 0.240584i) q^{12} +(-0.369131 + 0.527174i) q^{13} +(-0.993934 - 0.695960i) q^{14} +(-0.160332 - 1.83260i) q^{15} +(0.442729 + 2.51084i) q^{16} +(-0.229595 - 0.856859i) q^{17} +(0.912611 - 0.765772i) q^{18} +(-2.04569 + 5.62050i) q^{19} +(-3.67547 + 1.71390i) q^{20} +(1.84959 - 0.495596i) q^{21} +(0.486010 + 0.486010i) q^{22} +(-0.0467507 - 0.128447i) q^{23} +(1.29251 + 0.746231i) q^{24} +(-0.247315 - 0.294739i) q^{25} +(0.264824 - 0.185432i) q^{26} +4.25833i q^{27} +(-2.42123 - 3.45787i) q^{28} +(-2.96817 - 6.36527i) q^{29} +(-0.239179 + 0.892629i) q^{30} +(10.4687 + 0.915897i) q^{31} +(0.876229 - 4.96934i) q^{32} +(-1.08055 + 0.0945355i) q^{33} +(-0.0388387 + 0.443928i) q^{34} +(3.60281 - 4.29366i) q^{35} +(3.89465 - 1.41754i) q^{36} +(-8.13065 + 2.95932i) q^{37} +(1.93134 - 2.30168i) q^{38} +(-0.0444659 + 0.508247i) q^{39} +(4.35200 - 0.380751i) q^{40} +(1.22086 - 6.92384i) q^{41} +(-0.958250 - 0.0838360i) q^{42} +(1.11159 - 4.14852i) q^{43} +(1.01056 + 2.16714i) q^{44} +(3.15648 + 4.50792i) q^{45} +0.0686656i q^{46} +(0.304101 - 0.212934i) q^{47} +(1.29920 + 1.54833i) q^{48} +(-1.00962 - 0.582904i) q^{49} +(0.0661056 + 0.181624i) q^{50} +(-0.497270 - 0.497270i) q^{51} +(1.08639 - 0.291098i) q^{52} +(-11.9329 + 5.56439i) q^{53} +(0.731635 - 2.01015i) q^{54} +(-2.43217 + 2.04084i) q^{55} +(1.17692 + 4.39234i) q^{56} +(0.823381 + 4.66962i) q^{57} +(0.307496 + 3.51470i) q^{58} +(-5.22225 - 3.65666i) q^{59} +(-1.84404 + 2.63356i) q^{60} +(-0.876156 - 0.154490i) q^{61} +(-4.78442 - 2.23101i) q^{62} +(-4.05046 + 4.05046i) q^{63} +(1.28215 - 2.22076i) q^{64} +(0.746694 + 1.29331i) q^{65} +(0.526315 + 0.141026i) q^{66} +(2.23866 - 0.394736i) q^{67} +(-0.655191 + 1.40506i) q^{68} +(-0.0830103 - 0.0696539i) q^{69} +(-2.43841 + 1.40782i) q^{70} +(14.4771 + 5.26922i) q^{71} -4.46468 q^{72} +(-4.39858 - 7.32479i) q^{73} +4.34653 q^{74} +(-0.286623 - 0.104322i) q^{75} +(9.05261 - 5.22652i) q^{76} +(-2.53164 - 2.12430i) q^{77} +(0.108313 - 0.232279i) q^{78} +(-3.81428 + 0.672560i) q^{79} +(5.71471 + 1.53125i) q^{80} +(-1.86938 - 3.23786i) q^{81} +(-1.76591 + 3.05865i) q^{82} +(-7.48812 + 7.48812i) q^{83} +(-3.03293 - 1.41428i) q^{84} +(-2.02722 - 0.357453i) q^{85} +(-1.23750 + 1.76733i) q^{86} +(-4.56086 - 3.19355i) q^{87} +(-0.224499 - 2.56604i) q^{88} +(1.60279 + 9.08990i) q^{89} +(-0.715502 - 2.67029i) q^{90} +(-1.19079 + 0.999188i) q^{91} +(-0.0817038 + 0.224479i) q^{92} +(7.55036 - 3.52079i) q^{93} +(-0.180136 + 0.0482672i) q^{94} +(9.81424 + 9.81424i) q^{95} +(-1.36817 - 3.75902i) q^{96} +(-10.1182 - 5.84172i) q^{97} +(0.376442 + 0.448626i) q^{98} +(2.65798 - 1.86114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 12 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) \) 72 * q - 12 * q^2 - 18 * q^3 - 12 * q^4 - 12 * q^5 - 24 * q^6 - 18 * q^7 - 24 * q^8 + 36 * q^9	\( 72 q - 12 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{7} - 24 q^{8} + 36 q^{9} - 6 q^{11} + 6 q^{12} - 12 q^{13} - 12 q^{14} - 30 q^{15} + 30 q^{17} - 12 q^{18} - 6 q^{19} + 60 q^{20} - 30 q^{21} - 12 q^{22} - 12 q^{23} - 18 q^{24} + 36 q^{25} + 12 q^{26} + 120 q^{28} - 6 q^{29} - 72 q^{30} - 18 q^{31} - 18 q^{32} - 60 q^{33} - 60 q^{34} - 36 q^{35} + 60 q^{36} - 6 q^{37} + 48 q^{38} + 78 q^{39} - 18 q^{40} + 54 q^{42} - 24 q^{43} + 48 q^{44} + 36 q^{47} + 30 q^{48} - 18 q^{49} + 132 q^{50} - 18 q^{51} - 24 q^{53} - 6 q^{54} + 72 q^{55} + 24 q^{56} - 6 q^{57} - 18 q^{58} - 66 q^{60} - 36 q^{61} - 36 q^{62} + 12 q^{63} - 84 q^{64} + 24 q^{65} + 156 q^{66} - 54 q^{67} - 84 q^{68} - 6 q^{69} - 162 q^{70} + 48 q^{71} - 72 q^{72} - 36 q^{73} + 144 q^{74} + 6 q^{75} - 180 q^{76} - 24 q^{77} - 198 q^{78} - 36 q^{79} - 126 q^{80} - 48 q^{81} + 30 q^{82} - 48 q^{83} - 126 q^{84} - 6 q^{85} - 120 q^{86} + 6 q^{87} + 6 q^{88} + 6 q^{89} + 210 q^{90} + 48 q^{91} + 96 q^{92} + 144 q^{93} - 6 q^{94} - 12 q^{95} + 162 q^{96} - 18 q^{97} + 186 q^{98} + 78 q^{99}+O(q^{100}) \) 72 * q - 12 * q^2 - 18 * q^3 - 12 * q^4 - 12 * q^5 - 24 * q^6 - 18 * q^7 - 24 * q^8 + 36 * q^9 - 6 * q^11 + 6 * q^12 - 12 * q^13 - 12 * q^14 - 30 * q^15 + 30 * q^17 - 12 * q^18 - 6 * q^19 + 60 * q^20 - 30 * q^21 - 12 * q^22 - 12 * q^23 - 18 * q^24 + 36 * q^25 + 12 * q^26 + 120 * q^28 - 6 * q^29 - 72 * q^30 - 18 * q^31 - 18 * q^32 - 60 * q^33 - 60 * q^34 - 36 * q^35 + 60 * q^36 - 6 * q^37 + 48 * q^38 + 78 * q^39 - 18 * q^40 + 54 * q^42 - 24 * q^43 + 48 * q^44 + 36 * q^47 + 30 * q^48 - 18 * q^49 + 132 * q^50 - 18 * q^51 - 24 * q^53 - 6 * q^54 + 72 * q^55 + 24 * q^56 - 6 * q^57 - 18 * q^58 - 66 * q^60 - 36 * q^61 - 36 * q^62 + 12 * q^63 - 84 * q^64 + 24 * q^65 + 156 * q^66 - 54 * q^67 - 84 * q^68 - 6 * q^69 - 162 * q^70 + 48 * q^71 - 72 * q^72 - 36 * q^73 + 144 * q^74 + 6 * q^75 - 180 * q^76 - 24 * q^77 - 198 * q^78 - 36 * q^79 - 126 * q^80 - 48 * q^81 + 30 * q^82 - 48 * q^83 - 126 * q^84 - 6 * q^85 - 120 * q^86 + 6 * q^87 + 6 * q^88 + 6 * q^89 + 210 * q^90 + 48 * q^91 + 96 * q^92 + 144 * q^93 - 6 * q^94 - 12 * q^95 + 162 * q^96 - 18 * q^97 + 186 * q^98 + 78 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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