LMFDB - Embedded newform 65.2.o.a.63.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(2,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("65.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.o (of order $12$, degree $4$, 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:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			63.5
Root			$2.25081i$ of defining polynomial
Character	$\chi$	$=$	65.63
Dual form			65.2.o.a.32.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12540 + 1.94926i) q^{2} +(0.514229 - 1.91913i) q^{3} +(-1.53307 + 2.65535i) q^{4} +(-2.22228 + 0.247944i) q^{5} +(4.31958 - 1.15743i) q^{6} +(-1.10607 - 0.638592i) q^{7} -2.39966 q^{8} +(-0.820542 - 0.473740i) q^{9} +O(q^{10})$	\(q+(1.12540 + 1.94926i) q^{2} +(0.514229 - 1.91913i) q^{3} +(-1.53307 + 2.65535i) q^{4} +(-2.22228 + 0.247944i) q^{5} +(4.31958 - 1.15743i) q^{6} +(-1.10607 - 0.638592i) q^{7} -2.39966 q^{8} +(-0.820542 - 0.473740i) q^{9} +(-2.98427 - 4.05275i) q^{10} +(-5.27612 - 1.41373i) q^{11} +(4.30760 + 4.30760i) q^{12} +(3.50617 + 0.840691i) q^{13} -2.87469i q^{14} +(-0.666923 + 4.39234i) q^{15} +(0.365551 + 0.633152i) q^{16} +(3.11179 - 0.833802i) q^{17} -2.13259i q^{18} +(0.315395 + 1.17707i) q^{19} +(2.74852 - 6.28104i) q^{20} +(-1.79431 + 1.79431i) q^{21} +(-3.18204 - 11.8755i) q^{22} +(0.160006 + 0.0428736i) q^{23} +(-1.23397 + 4.60524i) q^{24} +(4.87705 - 1.10200i) q^{25} +(2.30714 + 7.78054i) q^{26} +(2.88358 - 2.88358i) q^{27} +(3.39137 - 1.95801i) q^{28} +(-8.41068 + 4.85591i) q^{29} +(-9.31234 + 3.64315i) q^{30} +(0.233305 + 0.233305i) q^{31} +(-3.22244 + 5.58143i) q^{32} +(-5.42627 + 9.39857i) q^{33} +(5.12732 + 5.12732i) q^{34} +(2.61634 + 1.14488i) q^{35} +(2.51589 - 1.45255i) q^{36} +(-1.14457 + 0.660816i) q^{37} +(-1.93947 + 1.93947i) q^{38} +(3.41637 - 6.29648i) q^{39} +(5.33270 - 0.594981i) q^{40} +(0.129579 - 0.483595i) q^{41} +(-5.51690 - 1.47825i) q^{42} +(-1.72444 - 6.43569i) q^{43} +(11.8426 - 11.8426i) q^{44} +(1.94093 + 0.849334i) q^{45} +(0.0965002 + 0.360144i) q^{46} -3.20027i q^{47} +(1.40308 - 0.375953i) q^{48} +(-2.68440 - 4.64952i) q^{49} +(7.63673 + 8.26642i) q^{50} -6.40069i q^{51} +(-7.60752 + 8.02127i) q^{52} +(4.49845 + 4.49845i) q^{53} +(8.86603 + 2.37565i) q^{54} +(12.0755 + 1.83353i) q^{55} +(2.65420 + 1.53240i) q^{56} +2.42113 q^{57} +(-18.9308 - 10.9297i) q^{58} +(-0.00222123 + 0.000595178i) q^{59} +(-10.6407 - 8.50465i) q^{60} +(-0.695993 + 1.20550i) q^{61} +(-0.192209 + 0.717332i) q^{62} +(0.605053 + 1.04798i) q^{63} -13.0440 q^{64} +(-8.00014 - 0.998915i) q^{65} -24.4270 q^{66} +(-3.03718 - 5.26055i) q^{67} +(-2.55655 + 9.54117i) q^{68} +(0.164560 - 0.285026i) q^{69} +(0.712764 + 6.38837i) q^{70} +(11.7428 - 3.14648i) q^{71} +(1.96902 + 1.13681i) q^{72} +7.34614 q^{73} +(-2.57620 - 1.48737i) q^{74} +(0.393034 - 9.92635i) q^{75} +(-3.60906 - 0.967044i) q^{76} +(4.93298 + 4.93298i) q^{77} +(16.1182 - 0.426708i) q^{78} +11.1774i q^{79} +(-0.969342 - 1.31640i) q^{80} +(-5.47236 - 9.47841i) q^{81} +(1.08848 - 0.291657i) q^{82} +2.65539i q^{83} +(-2.01373 - 7.51533i) q^{84} +(-6.70854 + 2.62449i) q^{85} +(10.6041 - 10.6041i) q^{86} +(4.99409 + 18.6382i) q^{87} +(12.6609 + 3.39247i) q^{88} +(1.86638 - 6.96542i) q^{89} +(0.528764 + 4.73922i) q^{90} +(-3.34123 - 3.16888i) q^{91} +(-0.359145 + 0.359145i) q^{92} +(0.567713 - 0.327769i) q^{93} +(6.23815 - 3.60160i) q^{94} +(-0.992745 - 2.53758i) q^{95} +(9.05440 + 9.05440i) q^{96} +(-2.09035 + 3.62059i) q^{97} +(6.04207 - 10.4652i) q^{98} +(3.65954 + 3.65954i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9} - 10 q^{10} - 16 q^{11} + 24 q^{12} + 2 q^{13} + 12 q^{15} - 2 q^{16} - 10 q^{17} + 20 q^{19} + 14 q^{20} + 4 q^{21} + 16 q^{22} - 2 q^{23} - 32 q^{24} - 18 q^{25} - 24 q^{26} + 4 q^{27} + 6 q^{28} + 14 q^{30} - 6 q^{32} - 18 q^{33} - 2 q^{34} - 20 q^{35} + 36 q^{36} + 42 q^{37} + 8 q^{38} - 4 q^{39} - 16 q^{40} + 10 q^{41} - 56 q^{42} - 22 q^{43} + 36 q^{44} + 52 q^{45} + 4 q^{46} + 28 q^{48} - 18 q^{49} + 44 q^{50} + 46 q^{52} - 10 q^{53} + 48 q^{54} + 26 q^{55} - 12 q^{57} - 90 q^{58} + 16 q^{59} - 92 q^{60} - 16 q^{61} - 40 q^{62} - 32 q^{63} - 20 q^{64} + 8 q^{65} - 32 q^{66} - 58 q^{67} + 28 q^{68} + 16 q^{69} + 32 q^{70} - 16 q^{71} - 66 q^{72} + 72 q^{73} - 18 q^{74} - 34 q^{75} - 64 q^{76} + 28 q^{77} + 32 q^{78} - 34 q^{80} - 14 q^{81} + 22 q^{82} + 40 q^{84} - 6 q^{85} + 60 q^{86} + 62 q^{87} + 50 q^{88} + 6 q^{89} - 46 q^{90} + 8 q^{91} - 8 q^{92} + 48 q^{93} + 48 q^{94} + 14 q^{95} + 56 q^{96} - 22 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9 - 10 * q^10 - 16 * q^11 + 24 * q^12 + 2 * q^13 + 12 * q^15 - 2 * q^16 - 10 * q^17 + 20 * q^19 + 14 * q^20 + 4 * q^21 + 16 * q^22 - 2 * q^23 - 32 * q^24 - 18 * q^25 - 24 * q^26 + 4 * q^27 + 6 * q^28 + 14 * q^30 - 6 * q^32 - 18 * q^33 - 2 * q^34 - 20 * q^35 + 36 * q^36 + 42 * q^37 + 8 * q^38 - 4 * q^39 - 16 * q^40 + 10 * q^41 - 56 * q^42 - 22 * q^43 + 36 * q^44 + 52 * q^45 + 4 * q^46 + 28 * q^48 - 18 * q^49 + 44 * q^50 + 46 * q^52 - 10 * q^53 + 48 * q^54 + 26 * q^55 - 12 * q^57 - 90 * q^58 + 16 * q^59 - 92 * q^60 - 16 * q^61 - 40 * q^62 - 32 * q^63 - 20 * q^64 + 8 * q^65 - 32 * q^66 - 58 * q^67 + 28 * q^68 + 16 * q^69 + 32 * q^70 - 16 * q^71 - 66 * q^72 + 72 * q^73 - 18 * q^74 - 34 * q^75 - 64 * q^76 + 28 * q^77 + 32 * q^78 - 34 * q^80 - 14 * q^81 + 22 * q^82 + 40 * q^84 - 6 * q^85 + 60 * q^86 + 62 * q^87 + 50 * q^88 + 6 * q^89 - 46 * q^90 + 8 * q^91 - 8 * q^92 + 48 * q^93 + 48 * q^94 + 14 * q^95 + 56 * q^96 - 22 * q^97 + 4 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	1.12540	+	1.94926i	0.795780	+	1.37833i	0.922342	+	0.386373i	$0.126272\pi$
$2$	1.12540	+	1.94926i	0.795780	+	1.37833i	−0.126562	+	0.991959i	$0.540394\pi$
$3$	0.514229	−	1.91913i	0.296890	−	1.10801i	−0.642815	−	0.766022i	$-0.722233\pi$
$3$	0.514229	−	1.91913i	0.296890	−	1.10801i	0.939705	−	0.341987i	$-0.111100\pi$
$4$	−1.53307	+	2.65535i	−0.766533	+	1.32767i
$5$	−2.22228	+	0.247944i	−0.993833	+	0.110884i
$5$	−2.22228	+	0.247944i	−0.993833	+	0.110884i
$6$	4.31958	−	1.15743i	1.76346	−	0.472518i
$7$	−1.10607	−	0.638592i	−0.418057	−	0.241365i	0.276189	−	0.961103i	$-0.410928\pi$
$7$	−1.10607	−	0.638592i	−0.418057	−	0.241365i	−0.694245	+	0.719738i	$0.744262\pi$
$8$	−2.39966			−0.848406
$9$	−0.820542	−	0.473740i	−0.273514	−	0.157913i
$10$	−2.98427	−	4.05275i	−0.943708	−	1.28159i
$11$	−5.27612	−	1.41373i	−1.59081	−	0.426257i	−0.648560	−	0.761163i	$-0.724629\pi$
$11$	−5.27612	−	1.41373i	−1.59081	−	0.426257i	−0.942251	+	0.334907i	$0.891295\pi$
$12$	4.30760	+	4.30760i	1.24350	+	1.24350i
$13$	3.50617	+	0.840691i	0.972437	+	0.233166i
$13$	3.50617	+	0.840691i	0.972437	+	0.233166i
$14$		−	2.87469i		−	0.768294i
$15$	−0.666923	+	4.39234i	−0.172199	+	1.13410i
$16$	0.365551	+	0.633152i	0.0913876	+	0.158288i
$17$	3.11179	−	0.833802i	0.754721	−	0.202227i	0.139110	−	0.990277i	$-0.455576\pi$
$17$	3.11179	−	0.833802i	0.754721	−	0.202227i	0.615611	+	0.788050i	$0.288909\pi$
$18$		−	2.13259i		−	0.502657i
$19$	0.315395	+	1.17707i	0.0723567	+	0.270039i	0.992621	−	0.121259i	$-0.0386931\pi$
$19$	0.315395	+	1.17707i	0.0723567	+	0.270039i	−0.920264	+	0.391297i	$0.872026\pi$
$20$	2.74852	−	6.28104i	0.614588	−	1.40448i
$21$	−1.79431	+	1.79431i	−0.391551	+	0.391551i
$22$	−3.18204	−	11.8755i	−0.678413	−	2.53187i
$23$	0.160006	+	0.0428736i	0.0333637	+	0.00893976i	0.275462	−	0.961312i	$-0.411169\pi$
$23$	0.160006	+	0.0428736i	0.0333637	+	0.00893976i	−0.242099	+	0.970252i	$0.577836\pi$
$24$	−1.23397	+	4.60524i	−0.251883	+	0.940042i
$25$	4.87705	−	1.10200i	0.975409	−	0.220401i
$26$	2.30714	+	7.78054i	0.452466	+	1.52589i
$27$	2.88358	−	2.88358i	0.554946	−	0.554946i
$28$	3.39137	−	1.95801i	0.640908	−	0.370029i
$29$	−8.41068	+	4.85591i	−1.56182	+	0.901719i	−0.564751	+	0.825262i	$0.691028\pi$
$29$	−8.41068	+	4.85591i	−1.56182	+	0.901719i	−0.997073	+	0.0764575i	$0.975639\pi$
$30$	−9.31234	+	3.64315i	−1.70019	+	0.665145i
$31$	0.233305	+	0.233305i	0.0419027	+	0.0419027i	0.727748	−	0.685845i	$-0.240567\pi$
$31$	0.233305	+	0.233305i	0.0419027	+	0.0419027i	−0.685845	+	0.727748i	$0.740567\pi$
$32$	−3.22244	+	5.58143i	−0.569652	+	0.986667i
$33$	−5.42627	+	9.39857i	−0.944592	+	1.63608i
$34$	5.12732	+	5.12732i	0.879328	+	0.879328i
$35$	2.61634	+	1.14488i	0.442242	+	0.193521i
$36$	2.51589	−	1.45255i	0.419315	−	0.242091i
$37$	−1.14457	+	0.660816i	−0.188166	+	0.108638i	−0.591124	−	0.806581i	$-0.701315\pi$
$37$	−1.14457	+	0.660816i	−0.188166	+	0.108638i	0.402958	+	0.915219i	$0.367982\pi$
$38$	−1.93947	+	1.93947i	−0.314623	+	0.314623i
$39$	3.41637	−	6.29648i	0.547057	−	1.00824i
$40$	5.33270	−	0.594981i	0.843175	−	0.0940747i
$41$	0.129579	−	0.483595i	0.0202368	−	0.0755249i	−0.955069	−	0.296384i	$-0.904219\pi$
$41$	0.129579	−	0.483595i	0.0202368	−	0.0755249i	0.975306	+	0.220859i	$0.0708860\pi$
$42$	−5.51690	−	1.47825i	−0.851277	−	0.228099i
$43$	−1.72444	−	6.43569i	−0.262974	−	0.981434i	−0.963479	−	0.267786i	$-0.913708\pi$
$43$	−1.72444	−	6.43569i	−0.262974	−	0.981434i	0.700504	−	0.713648i	$-0.252959\pi$
$44$	11.8426	−	11.8426i	1.78534	−	1.78534i
$45$	1.94093	+	0.849334i	0.289337	+	0.126611i
$46$	0.0965002	+	0.360144i	0.0142282	+	0.0531003i
$47$		−	3.20027i		−	0.466808i	−0.972380	−	0.233404i	$-0.925014\pi$
$47$		−	3.20027i		−	0.466808i	0.972380	−	0.233404i	$-0.0749864\pi$
$48$	1.40308	−	0.375953i	0.202517	−	0.0542642i
$49$	−2.68440	−	4.64952i	−0.383486	−	0.664217i
$50$	7.63673	+	8.26642i	1.08000	+	1.16905i
$51$		−	6.40069i		−	0.896276i
$52$	−7.60752	+	8.02127i	−1.05497	+	1.11235i
$53$	4.49845	+	4.49845i	0.617909	+	0.617909i	0.944995	−	0.327086i	$-0.106067\pi$
$53$	4.49845	+	4.49845i	0.617909	+	0.617909i	−0.327086	+	0.944995i	$0.606067\pi$
$54$	8.86603	+	2.37565i	1.20651	+	0.323285i
$55$	12.0755	+	1.83353i	1.62827	+	0.247232i
$56$	2.65420	+	1.53240i	0.354682	+	0.204776i
$57$	2.42113			0.320687
$58$	−18.9308	−	10.9297i	−2.48574	−	1.43514i
$59$	−0.00222123		0.000595178i	−0.000289180		7.74855e-5i	−0.258964	−	0.965887i	$-0.583381\pi$
$59$	−0.00222123		0.000595178i	−0.000289180		7.74855e-5i	0.258674	+	0.965965i	$0.416714\pi$
$60$	−10.6407	−	8.50465i	−1.37371	−	1.09795i
$61$	−0.695993	+	1.20550i	−0.0891128	+	0.154348i	−0.907136	−	0.420837i	$-0.861736\pi$
$61$	−0.695993	+	1.20550i	−0.0891128	+	0.154348i	0.818024	+	0.575185i	$0.195070\pi$
$62$	−0.192209	+	0.717332i	−0.0244105	+	0.0911013i
$63$	0.605053	+	1.04798i	0.0762295	+	0.132033i
$64$	−13.0440			−1.63050
$65$	−8.00014	−	0.998915i	−0.992295	−	0.123900i
$66$	−24.4270			−3.00675
$67$	−3.03718	−	5.26055i	−0.371050	−	0.642678i	0.618677	−	0.785645i	$-0.287669\pi$
$67$	−3.03718	−	5.26055i	−0.371050	−	0.642678i	−0.989727	+	0.142967i	$0.954336\pi$
$68$	−2.55655	+	9.54117i	−0.310027	+	1.15704i
$69$	0.164560	−	0.285026i	0.0198107	−	0.0343131i
$70$	0.712764	+	6.38837i	0.0851916	+	0.763557i
$71$	11.7428	−	3.14648i	1.39361	−	0.373418i	0.517567	−	0.855643i	$-0.326838\pi$
$71$	11.7428	−	3.14648i	1.39361	−	0.373418i	0.876048	+	0.482225i	$0.160171\pi$
$72$	1.96902	+	1.13681i	0.232051	+	0.133975i
$73$	7.34614			0.859801			0.429901	−	0.902876i	$-0.358549\pi$
$73$	7.34614			0.859801			0.429901	+	0.902876i	$0.358549\pi$
$74$	−2.57620	−	1.48737i	−0.299477	−	0.172903i
$75$	0.393034	−	9.92635i	0.0453837	−	1.14620i
$76$	−3.60906	−	0.967044i	−0.413987	−	0.110928i
$77$	4.93298	+	4.93298i	0.562166	+	0.562166i
$78$	16.1182	−	0.426708i	1.82503	−	0.0483152i
$79$			11.1774i			1.25756i	0.777584	+	0.628779i	$0.216445\pi$
$79$			11.1774i			1.25756i	−0.777584	+	0.628779i	$0.783555\pi$
$80$	−0.969342	−	1.31640i	−0.108376	−	0.147178i
$81$	−5.47236	−	9.47841i	−0.608040	−	1.05316i
$82$	1.08848	−	0.291657i	0.120202	−	0.0322081i
$83$			2.65539i			0.291467i	0.989324	+	0.145733i	$0.0465542\pi$
$83$			2.65539i			0.291467i	−0.989324	+	0.145733i	$0.953446\pi$
$84$	−2.01373	−	7.51533i	−0.219716	−	0.819990i
$85$	−6.70854	+	2.62449i	−0.727643	+	0.284666i
$86$	10.6041	−	10.6041i	1.14347	−	1.14347i
$87$	4.99409	+	18.6382i	0.535423	+	1.99823i
$88$	12.6609	+	3.39247i	1.34965	+	0.361639i
$89$	1.86638	−	6.96542i	0.197836	−	0.738333i	−0.793679	−	0.608337i	$-0.791837\pi$
$89$	1.86638	−	6.96542i	0.197836	−	0.738333i	0.991515	−	0.129996i	$-0.0414964\pi$
$90$	0.528764	+	4.73922i	0.0557367	+	0.499558i
$91$	−3.34123	−	3.16888i	−0.350256	−	0.332189i
$92$	−0.359145	+	0.359145i	−0.0374434	+	0.0374434i
$93$	0.567713	−	0.327769i	0.0588691	−	0.0339881i
$94$	6.23815	−	3.60160i	0.643416	−	0.371477i
$95$	−0.992745	−	2.53758i	−0.101853	−	0.260350i
$96$	9.05440	+	9.05440i	0.924111	+	0.924111i
$97$	−2.09035	+	3.62059i	−0.212243	+	0.367616i	−0.952416	−	0.304801i	$-0.901410\pi$
$97$	−2.09035	+	3.62059i	−0.212243	+	0.367616i	0.740173	+	0.672416i	$0.234743\pi$
$98$	6.04207	−	10.4652i	0.610341	−	1.05714i
$99$	3.65954	+	3.65954i	0.367797	+	0.367797i
$100$	−4.55063	+	14.6397i	−0.455063	+	1.46397i
$101$	−7.47319	+	4.31465i	−0.743610	+	0.429323i	−0.823380	−	0.567490i	$-0.807915\pi$
$101$	−7.47319	+	4.31465i	−0.743610	+	0.429323i	0.0797704	+	0.996813i	$0.474581\pi$
$102$	12.4766	−	7.20336i	1.23537	−	0.713239i
$103$	−1.07603	+	1.07603i	−0.106025	+	0.106025i	−0.758129	−	0.652104i	$-0.773886\pi$
$103$	−1.07603	+	1.07603i	−0.106025	+	0.106025i	0.652104	+	0.758129i	$0.273886\pi$
$104$	−8.41360	−	2.01737i	−0.825022	−	0.197819i
$105$	3.54258	−	4.43236i	0.345720	−	0.432554i
$106$	−3.70606	+	13.8312i	−0.359964	+	1.34340i
$107$	−14.0309	−	3.75956i	−1.35642	−	0.363451i	−0.493917	−	0.869509i	$-0.664435\pi$
$107$	−14.0309	−	3.75956i	−1.35642	−	0.363451i	−0.862499	+	0.506058i	$0.831102\pi$
$108$	3.23619	+	12.0776i	0.311403	+	1.16217i
$109$	4.72405	−	4.72405i	0.452481	−	0.452481i	−0.443696	−	0.896177i	$-0.646333\pi$
$109$	4.72405	−	4.72405i	0.452481	−	0.452481i	0.896177	+	0.443696i	$0.146333\pi$
$110$	10.0159	+	25.6018i	0.954974	+	2.44103i
$111$	0.679621	+	2.53638i	0.0645068	+	0.240743i
$112$		−	0.933751i		−	0.0882311i
$113$	−11.0065	+	2.94919i	−1.03541	+	0.277437i	−0.736209	−	0.676754i	$-0.763386\pi$
$113$	−11.0065	+	2.94919i	−1.03541	+	0.277437i	−0.299199	+	0.954191i	$0.596719\pi$
$114$	2.72475	+	4.71941i	0.255197	+	0.442013i
$115$	−0.366209	−	0.0556044i	−0.0341492	−	0.00518514i
$116$		−	29.7777i		−	2.76479i
$117$	−2.47869	−	2.35084i	−0.229155	−	0.217335i
$118$	−0.00365994	−	0.00365994i	−0.000336925	−	0.000336925i
$119$	−3.97433	−	1.06492i	−0.364326	−	0.0976210i
$120$	1.60039	−	10.5401i	0.146094	−	0.962175i
$121$	16.3126	+	9.41807i	1.48296	+	0.856188i
$122$	−3.13309			−0.283657
$123$	−0.861447	−	0.497357i	−0.0776741	−	0.0448452i
$124$	−0.977176	+	0.261833i	−0.0877530	+	0.0235133i
$125$	−10.5649	+	3.65819i	−0.944956	+	0.327199i
$126$	−1.36186	+	2.35881i	−0.121324	+	0.210139i
$127$	−0.135757	+	0.506651i	−0.0120465	+	0.0449580i	−0.971687	−	0.236270i	$-0.924075\pi$
$127$	−0.135757	+	0.506651i	−0.0120465	+	0.0449580i	0.959641	+	0.281228i	$0.0907417\pi$
$128$	−8.23486	−	14.2632i	−0.727865	−	1.26070i
$129$	−13.2377			−1.16551
$130$	−7.05624	−	16.7185i	−0.618873	−	1.46631i
$131$	5.09883			0.445486			0.222743	−	0.974877i	$-0.428499\pi$
$131$	5.09883			0.445486			0.222743	+	0.974877i	$0.428499\pi$
$132$	−16.6377	−	28.8173i	−1.44812	−	2.50822i
$133$	0.402818	−	1.50334i	0.0349287	−	0.130356i
$134$	6.83610	−	11.8405i	0.590549	−	1.02286i
$135$	−5.69316	+	7.12309i	−0.489989	+	0.613058i
$136$	−7.46723	+	2.00084i	−0.640310	+	0.171571i
$137$	3.29390	+	1.90173i	0.281417	+	0.162476i	0.634065	−	0.773280i	$-0.281385\pi$
$137$	3.29390	+	1.90173i	0.281417	+	0.162476i	−0.352648	+	0.935756i	$0.614719\pi$
$138$	0.740785			0.0630598
$139$	1.28017	+	0.739106i	0.108583	+	0.0626902i	0.553308	−	0.832977i	$-0.313365\pi$
$139$	1.28017	+	0.739106i	0.108583	+	0.0626902i	−0.444725	+	0.895667i	$0.646699\pi$
$140$	−7.05109	+	5.19211i	−0.595926	+	0.438813i
$141$	−6.14173	−	1.64567i	−0.517227	−	0.138591i
$142$	19.3487	+	19.3487i	1.62371	+	1.62371i
$143$	−17.3105	−	9.39238i	−1.44758	−	0.785431i
$144$		−	0.692704i		−	0.0577253i
$145$	17.4869	−	12.8766i	1.45221	−	1.06934i
$146$	8.26737	+	14.3195i	0.684213	+	1.18509i
$147$	−10.3034	+	2.76079i	−0.849811	+	0.227706i
$148$		−	4.05230i		−	0.333097i
$149$	4.45586	+	16.6295i	0.365038	+	1.36234i	0.867369	+	0.497665i	$0.165809\pi$
$149$	4.45586	+	16.6295i	0.365038	+	1.36234i	−0.502331	+	0.864675i	$0.667524\pi$
$150$	19.7913	−	10.4050i	1.61596	−	0.849567i
$151$	−10.0539	+	10.0539i	−0.818178	+	0.818178i	−0.985844	−	0.167666i	$-0.946377\pi$
$151$	−10.0539	+	10.0539i	−0.818178	+	0.818178i	0.167666	+	0.985844i	$0.446377\pi$
$152$	−0.756840	−	2.82457i	−0.0613879	−	0.229103i
$153$	−2.94836	−	0.790011i	−0.238361	−	0.0638686i
$154$	−4.06405	+	15.1672i	−0.327491	+	1.22221i
$155$	−0.576314	−	0.460621i	−0.0462907	−	0.0369980i
$156$	11.4818	+	18.7246i	0.919282	+	1.49916i
$157$	3.07230	−	3.07230i	0.245196	−	0.245196i	−0.573799	−	0.818996i	$-0.694531\pi$
$157$	3.07230	−	3.07230i	0.245196	−	0.245196i	0.818996	+	0.573799i	$0.194531\pi$
$158$	−21.7876	+	12.5791i	−1.73333	+	1.00074i
$159$	10.9463	−	6.31986i	0.868100	−	0.501198i
$160$	5.77728	−	13.2025i	0.456734	−	1.04375i
$161$	−0.149600	−	0.149600i	−0.0117902	−	0.0117902i
$162$	12.3172	−	21.3341i	0.967733	−	1.67616i
$163$	−4.60251	+	7.97177i	−0.360496	+	0.624398i	−0.988043	−	0.154182i	$-0.950726\pi$
$163$	−4.60251	+	7.97177i	−0.360496	+	0.624398i	0.627546	+	0.778579i	$0.284059\pi$
$164$	1.08546	+	1.08546i	0.0847602	+	0.0847602i
$165$	9.72836	−	22.2317i	0.757352	−	1.73073i
$166$	−5.17603	+	2.98838i	−0.401738	+	0.231944i
$167$	10.9455	−	6.31936i	0.846985	−	0.489007i	−0.0126474	−	0.999920i	$-0.504026\pi$
$167$	10.9455	−	6.31936i	0.846985	−	0.489007i	0.859632	+	0.510913i	$0.170693\pi$
$168$	4.30574	−	4.30574i	0.332195	−	0.332195i
$169$	11.5865	+	5.89521i	0.891267	+	0.453478i
$170$	−12.6656	−	10.1230i	−0.971409	−	0.776402i
$171$	0.298831	−	1.11525i	0.0228522	−	0.0852854i
$172$	19.7327	+	5.28736i	1.50460	+	0.403157i
$173$	−3.54983	−	13.2481i	−0.269888	−	1.00724i	−0.959190	−	0.282762i	$-0.908749\pi$
$173$	−3.54983	−	13.2481i	−0.269888	−	1.00724i	0.689302	−	0.724474i	$-0.257917\pi$
$174$	−30.7103	+	30.7103i	−2.32814	+	2.32814i
$175$	−6.09810	−	1.89555i	−0.460973	−	0.143290i
$176$	−1.03358	−	3.85738i	−0.0779092	−	0.290761i
$177$			0.00456889i			0.000343419i
$178$	15.6778	−	4.20086i	1.17510	−	0.314867i
$179$	6.32126	+	10.9487i	0.472473	+	0.818347i	0.999504	−	0.0314989i	$-0.0100281\pi$
$179$	6.32126	+	10.9487i	0.472473	+	0.818347i	−0.527031	+	0.849846i	$0.676695\pi$
$180$	−5.23085	+	3.85177i	−0.389885	+	0.287094i
$181$		−	8.16619i		−	0.606988i	−0.952833	−	0.303494i	$-0.901847\pi$
$181$		−	8.16619i		−	0.606988i	0.952833	−	0.303494i	$-0.0981533\pi$
$182$	2.41673	−	10.0792i	0.179140	−	0.747118i
$183$	1.95560	+	1.95560i	0.144562	+	0.144562i
$184$	−0.383960	−	0.102882i	−0.0283059	−	0.00758455i
$185$	2.37970	−	1.75231i	0.174959	−	0.128832i
$186$	1.27781	+	0.737745i	0.0936937	+	0.0540941i
$187$	−17.5970			−1.28682
$188$	8.49784	+	4.90623i	0.619769	+	0.357824i
$189$	−5.03089	+	1.34802i	−0.365943	+	0.0980542i
$190$	3.82916	−	4.79091i	0.277796	−	0.347569i
$191$	7.37692	−	12.7772i	0.533775	−	0.924526i	−0.465446	−	0.885076i	$-0.654106\pi$
$191$	7.37692	−	12.7772i	0.533775	−	0.924526i	0.999222	−	0.0394498i	$-0.0125605\pi$
$192$	−6.70758	+	25.0330i	−0.484078	+	1.80660i
$193$	7.54845	+	13.0743i	0.543349	+	0.941109i	0.998709	+	0.0508011i	$0.0161775\pi$
$193$	7.54845	+	13.0743i	0.543349	+	0.941109i	−0.455359	+	0.890308i	$0.650489\pi$
$194$	−9.40995			−0.675595
$195$	−6.03094	+	14.8396i	−0.431885	+	1.06269i
$196$	16.4614			1.17582
$197$	7.68576	+	13.3121i	0.547588	+	0.948450i	0.998439	+	0.0558510i	$0.0177872\pi$
$197$	7.68576	+	13.3121i	0.547588	+	0.948450i	−0.450851	+	0.892599i	$0.648879\pi$
$198$	−3.01492	+	11.2518i	−0.214261	+	0.799633i
$199$	−5.72810	+	9.92136i	−0.406054	+	0.703307i	−0.994444	−	0.105271i	$-0.966429\pi$
$199$	−5.72810	+	9.92136i	−0.406054	+	0.703307i	0.588389	+	0.808578i	$0.299762\pi$
$200$	−11.7032	+	2.64443i	−0.827544	+	0.186989i
$201$	−11.6575	+	3.12361i	−0.822254	+	0.220322i
$202$	−16.8207	−	9.71144i	−1.18350	−	0.683294i
$203$	12.4038			0.870574
$204$	16.9961	+	9.81268i	1.18996	+	0.687025i
$205$	−0.168056	+	1.10681i	−0.0117375	+	0.0773031i
$206$	−3.30843	−	0.886492i	−0.230509	−	0.0617648i
$207$	−0.110981	−	0.110981i	−0.00771372	−	0.00771372i
$208$	0.749397	+	2.52726i	0.0519614	+	0.175234i
$209$		−	6.65626i		−	0.460423i
$210$	12.6266	+	1.91720i	0.871320	+	0.132299i
$211$	−1.59195	−	2.75735i	−0.109595	−	0.189823i	0.806011	−	0.591900i	$-0.201622\pi$
$211$	−1.59195	−	2.75735i	−0.109595	−	0.189823i	−0.915606	+	0.402076i	$0.868289\pi$
$212$	−18.8414	+	5.04852i	−1.29403	+	0.346734i
$213$		−	24.1539i		−	1.65500i
$214$	−8.46205	−	31.5808i	−0.578454	−	2.15882i
$215$	5.42788	+	13.8743i	0.370178	+	0.946222i
$216$	−6.91961	+	6.91961i	−0.470820	+	0.470820i
$217$	−0.109066	−	0.407038i	−0.00740386	−	0.0276316i
$218$	14.5248	+	3.89192i	0.983746	+	0.263594i
$219$	3.77760	−	14.0982i	0.255266	−	0.952667i
$220$	−23.3813	+	29.2539i	−1.57636	+	1.97230i
$221$	11.6115	−	0.307397i	0.781071	−	0.0206778i
$222$	−4.17921	+	4.17921i	−0.280490	+	0.280490i
$223$	−10.2862	+	5.93874i	−0.688815	+	0.397688i	−0.803168	−	0.595753i	$-0.796854\pi$
$223$	−10.2862	+	5.93874i	−0.688815	+	0.397688i	0.114353	+	0.993440i	$0.463521\pi$
$224$	7.12851	−	4.11565i	0.476294	−	0.274988i
$225$	−4.52388	−	1.40621i	−0.301592	−	0.0937475i
$226$	−18.1355	−	18.1355i	−1.20636	−	1.20636i
$227$	13.8333	−	23.9600i	0.918149	−	1.59028i	0.115924	−	0.993258i	$-0.463017\pi$
$227$	13.8333	−	23.9600i	0.918149	−	1.59028i	0.802225	−	0.597022i	$-0.203650\pi$
$228$	−3.71176	+	6.42896i	−0.245817	+	0.425768i
$229$	−12.9000	−	12.9000i	−0.852455	−	0.852455i	0.137980	−	0.990435i	$-0.455939\pi$
$229$	−12.9000	−	12.9000i	−0.852455	−	0.852455i	−0.990435	+	0.137980i	$0.955939\pi$
$230$	−0.303746	−	0.776413i	−0.0200284	−	0.0511952i
$231$	12.0037	−	6.93034i	0.789786	−	0.455983i
$232$	20.1827	−	11.6525i	1.32506	−	0.765024i
$233$	16.3545	−	16.3545i	1.07142	−	1.07142i	0.0741712	−	0.997246i	$-0.476369\pi$
$233$	16.3545	−	16.3545i	1.07142	−	1.07142i	0.997246	−	0.0741712i	$-0.0236311\pi$
$234$	1.79285	−	7.47724i	0.117202	−	0.488803i
$235$	0.793489	+	7.11190i	0.0517615	+	0.463929i
$236$	0.00182489	−	0.00681059i	0.000118790	−	0.000443332i
$237$	21.4509	+	5.74774i	1.39338	+	0.373356i
$238$	−2.39693	−	8.94546i	−0.155370	−	0.579848i
$239$	2.61794	−	2.61794i	0.169341	−	0.169341i	−0.617349	−	0.786690i	$-0.711793\pi$
$239$	2.61794	−	2.61794i	0.169341	−	0.169341i	0.786690	+	0.617349i	$0.211793\pi$
$240$	−3.02481	+	1.18336i	−0.195251	+	0.0763854i
$241$	5.38613	+	20.1013i	0.346951	+	1.29484i	0.890316	+	0.455343i	$0.150483\pi$
$241$	5.38613	+	20.1013i	0.346951	+	1.29484i	−0.543365	+	0.839496i	$0.682850\pi$
$242$			42.3965i			2.72535i
$243$	−9.18717	+	2.46169i	−0.589357	+	0.157918i
$244$	−2.13401	−	3.69621i	−0.136616	−	0.236625i
$245$	7.11831	+	9.66694i	0.454772	+	0.617598i
$246$		−	2.23891i		−	0.142748i
$247$	0.116277	+	4.39216i	0.00739850	+	0.279467i
$248$	−0.559851	−	0.559851i	−0.0355505	−	0.0355505i
$249$	5.09603	+	1.36548i	0.322948	+	0.0865336i
$250$	−19.0206	−	16.4768i	−1.20297	−	1.04208i
$251$	−2.05050	−	1.18386i	−0.129427	−	0.0747245i	0.433889	−	0.900966i	$-0.357141\pi$
$251$	−2.05050	−	1.18386i	−0.129427	−	0.0747245i	−0.563315	+	0.826242i	$0.690474\pi$
$252$	−3.71034			−0.233730
$253$	−0.783602	−	0.452413i	−0.0492647	−	0.0284430i
$254$	−1.14037	+	0.305562i	−0.0715533	+	0.0191727i
$255$	1.58701	+	14.2241i	0.0993827	+	0.890749i
$256$	5.49109	−	9.51085i	0.343193	−	0.594428i
$257$	0.225182	−	0.840391i	0.0140465	−	0.0524221i	−0.958547	−	0.284935i	$-0.908028\pi$
$257$	0.225182	−	0.840391i	0.0140465	−	0.0524221i	0.972593	+	0.232513i	$0.0746947\pi$
$258$	−14.8977	−	25.8036i	−0.927492	−	1.60646i
$259$	1.68797			0.104885
$260$	14.9172	−	19.7117i	0.925126	−	1.22247i
$261$	9.20175			0.569574
$262$	5.73824	+	9.93892i	0.354509	+	0.614028i
$263$	−3.93099	+	14.6707i	−0.242395	+	0.904632i	0.732279	+	0.681004i	$0.238457\pi$
$263$	−3.93099	+	14.6707i	−0.242395	+	0.904632i	−0.974675	+	0.223627i	$0.928210\pi$
$264$	13.0212	−	22.5533i	0.801398	−	1.38806i
$265$	−11.1122	−	8.88144i	−0.682615	−	0.545582i
$266$	3.38372	−	0.906665i	0.207469	−	0.0555912i
$267$	−12.4078	−	7.16363i	−0.759343	−	0.438407i
$268$	18.6248			1.13769
$269$	−21.1150	−	12.1908i	−1.28741	−	0.743285i	−0.309216	−	0.950992i	$-0.600067\pi$
$269$	−21.1150	−	12.1908i	−1.28741	−	0.743285i	−0.978191	+	0.207707i	$0.933400\pi$
$270$	−20.2918	−	3.08107i	−1.23492	−	0.187508i
$271$	−12.6697	−	3.39484i	−0.769630	−	0.206222i	−0.147422	−	0.989074i	$-0.547097\pi$
$271$	−12.6697	−	3.39484i	−0.769630	−	0.206222i	−0.622208	+	0.782852i	$0.713764\pi$
$272$	1.66544	+	1.66544i	0.100982	+	0.100982i
$273$	−7.79964	+	4.78271i	−0.472055	+	0.289463i
$274$			8.56086i			0.517181i
$275$	−27.2898	−	1.08054i	−1.64564	−	0.0651591i
$276$	0.504562	+	0.873927i	0.0303711	+	0.0526042i
$277$	11.8109	−	3.16472i	0.709647	−	0.190149i	0.114099	−	0.993469i	$-0.463602\pi$
$277$	11.8109	−	3.16472i	0.709647	−	0.190149i	0.595548	+	0.803320i	$0.296935\pi$
$278$			3.32717i			0.199550i
$279$	−0.0809104	−	0.301962i	−0.00484398	−	0.0180780i
$280$	−6.27831	−	2.74733i	−0.375201	−	0.164184i
$281$	−6.43529	+	6.43529i	−0.383897	+	0.383897i	−0.872504	−	0.488607i	$-0.837505\pi$
$281$	−6.43529	+	6.43529i	−0.383897	+	0.383897i	0.488607	+	0.872504i	$0.337505\pi$
$282$	−3.70409	−	13.8239i	−0.220575	−	0.823198i
$283$	26.4212	+	7.07953i	1.57057	+	0.420834i	0.935992	−	0.352021i	$-0.114505\pi$
$283$	26.4212	+	7.07953i	1.57057	+	0.420834i	0.634583	+	0.772855i	$0.281172\pi$
$284$	−9.64751	+	36.0050i	−0.572474	+	2.13650i
$285$	−5.38044	+	0.600307i	−0.318710	+	0.0355591i
$286$	−1.17312	−	44.3128i	−0.0693681	−	2.62027i
$287$	−0.452144	+	0.452144i	−0.0266892	+	0.0266892i
$288$	5.28829	−	3.05320i	0.311616	−	0.179911i
$289$	−5.73440	+	3.31076i	−0.337318	+	0.194750i
$290$	44.7795	+	19.5951i	2.62954	+	1.15066i
$291$	5.87346	+	5.87346i	0.344308	+	0.344308i
$292$	−11.2621	+	19.5066i	−0.659066	+	1.14154i
$293$	13.0620	−	22.6241i	0.763092	−	1.32171i	−0.178157	−	0.984002i	$-0.557013\pi$
$293$	13.0620	−	22.6241i	0.763092	−	1.32171i	0.941249	−	0.337713i	$-0.109653\pi$
$294$	−16.9770	−	16.9770i	−0.990118	−	0.990118i
$295$	0.00478863	−	0.00187339i	0.000278805	−	0.000109073i
$296$	2.74657	−	1.58573i	0.159641	−	0.0921688i
$297$	−19.2908	+	11.1375i	−1.11936	+	0.646265i
$298$	−27.4005	+	27.4005i	−1.58727	+	1.58727i
$299$	0.524967	+	0.284838i	0.0303596	+	0.0164726i
$300$	25.7554	+	16.2614i	1.48699	+	0.938852i
$301$	−2.20243	+	8.21957i	−0.126946	+	0.473768i
$302$	−30.9124	−	8.28296i	−1.77881	−	0.476631i
$303$	4.43743	+	16.5607i	0.254924	+	0.951388i
$304$	−0.629972	+	0.629972i	−0.0361314	+	0.0361314i
$305$	1.24780	−	2.85151i	0.0714485	−	0.163277i
$306$	−1.77816	−	6.63619i	−0.101651	−	0.379366i
$307$		−	14.7038i		−	0.839189i	−0.907712	−	0.419595i	$-0.862172\pi$
$307$		−	14.7038i		−	0.839189i	0.907712	−	0.419595i	$-0.137828\pi$
$308$	−20.6614	+	5.53620i	−1.17729	+	0.315454i
$309$	1.51172	+	2.61837i	0.0859985	+	0.148954i
$310$	0.249283	−	1.64177i	0.0141583	−	0.0932462i
$311$			31.8525i			1.80619i	0.429440	+	0.903095i	$0.358711\pi$
$311$			31.8525i			1.80619i	−0.429440	+	0.903095i	$0.641289\pi$
$312$	−8.19810	+	15.1094i	−0.464126	+	0.855401i
$313$	−11.9865	−	11.9865i	−0.677519	−	0.677519i	0.281919	−	0.959438i	$-0.409029\pi$
$313$	−11.9865	−	11.9865i	−0.677519	−	0.677519i	−0.959438	+	0.281919i	$0.909029\pi$
$314$	9.44628	+	2.53112i	0.533084	+	0.142840i
$315$	−1.60444	−	2.17889i	−0.0903998	−	0.122767i
$316$	−29.6799	−	17.1357i	−1.66963	−	0.963959i
$317$	15.5627			0.874088			0.437044	−	0.899440i	$-0.356025\pi$
$317$	15.5627			0.874088			0.437044	+	0.899440i	$0.356025\pi$
$318$	24.6380	+	14.2248i	1.38163	+	0.797686i
$319$	51.2407	−	13.7299i	2.86893	−	0.768728i
$320$	28.9874	−	3.23418i	1.62044	−	0.180796i
$321$	−14.4302	+	24.9938i	−0.805413	+	1.39502i
$322$	0.123249	−	0.459970i	0.00686837	−	0.0256331i
$323$	1.96289	+	3.39983i	0.109218	+	0.189171i
$324$	33.5580			1.86433
$325$	18.0262	+	0.236281i	0.999914	+	0.0131065i
$326$	−20.7187			−1.14750
$327$	−6.63680	−	11.4953i	−0.367016	−	0.635691i
$328$	−0.310945	+	1.16046i	−0.0171691	+	0.0640758i
$329$	−2.04367	+	3.53974i	−0.112671	+	0.195152i
$330$	54.2835	−	6.05653i	2.98821	−	0.333401i
$331$	−16.4820	+	4.41633i	−0.905930	+	0.242743i	−0.681561	−	0.731761i	$-0.738699\pi$
$331$	−16.4820	+	4.41633i	−0.905930	+	0.242743i	−0.224369	+	0.974504i	$0.572032\pi$
$332$	−7.05098	−	4.07089i	−0.386973	−	0.223419i
$333$	1.25222			0.0686212
$334$	24.6361	+	14.2237i	1.34803	+	0.778284i
$335$	8.05378	+	10.9374i	0.440025	+	0.597571i
$336$	−1.79199	−	0.480161i	−0.0977609	−	0.0261949i
$337$	−25.0560	−	25.0560i	−1.36489	−	1.36489i	−0.867568	−	0.497319i	$-0.834318\pi$
$337$	−25.0560	−	25.0560i	−1.36489	−	1.36489i	−0.497319	−	0.867568i	$-0.665682\pi$
$338$	1.54818	+	29.2195i	0.0842098	+	1.58933i
$339$			22.6395i			1.22961i
$340$	3.31569	−	21.8370i	0.179818	−	1.18428i
$341$	−0.901114	−	1.56077i	−0.0487980	−	0.0845207i
$342$	2.51022	−	0.672610i	0.135737	−	0.0363706i
$343$			15.7972i			0.852971i
$344$	4.13806	+	15.4435i	0.223109	+	0.832655i
$345$	−0.295027	+	0.674209i	−0.0158837	+	0.0362982i
$346$	21.8290	−	21.8290i	1.17354	−	1.17354i
$347$	3.33874	+	12.4604i	0.179233	+	0.668907i	0.995792	+	0.0916446i	$0.0292124\pi$
$347$	3.33874	+	12.4604i	0.179233	+	0.668907i	−0.816559	+	0.577262i	$0.804121\pi$
$348$	−57.1472	−	15.3125i	−3.06341	−	0.820838i
$349$	6.94957	−	25.9362i	0.372002	−	1.38833i	−0.485674	−	0.874140i	$-0.661426\pi$
$349$	6.94957	−	25.9362i	0.372002	−	1.38833i	0.857676	−	0.514191i	$-0.171908\pi$
$350$	−3.16792	−	14.0200i	−0.169332	−	0.749402i
$351$	12.5345	−	7.68613i	0.669044	−	0.410255i
$352$	24.8926	−	24.8926i	1.32678	−	1.32678i
$353$	20.1885	−	11.6558i	1.07453	−	0.620378i	0.145111	−	0.989415i	$-0.453646\pi$
$353$	20.1885	−	11.6558i	1.07453	−	0.620378i	0.929414	+	0.369038i	$0.120313\pi$
$354$	−0.00890593	+	0.00514184i	−0.000473345	+	0.000273286i
$355$	−25.3156	+	9.90391i	−1.34361	+	0.525645i
$356$	15.6343	+	15.6343i	0.828617	+	0.828617i
$357$	−4.08743	+	7.07964i	−0.216330	+	0.374694i
$358$	−14.2279	+	24.6435i	−0.751970	+	1.30245i
$359$	−9.17222	−	9.17222i	−0.484091	−	0.484091i	0.422344	−	0.906435i	$-0.361207\pi$
$359$	−9.17222	−	9.17222i	−0.484091	−	0.484091i	−0.906435	+	0.422344i	$0.861207\pi$
$360$	−4.65757	−	2.03811i	−0.245476	−	0.107418i
$361$	15.1685	−	8.75751i	0.798340	−	0.460922i
$362$	15.9180	−	9.19026i	0.836631	−	0.483029i
$363$	26.4629	−	26.4629i	1.38894	−	1.38894i
$364$	13.5368	−	4.01402i	0.709521	−	0.210392i
$365$	−16.3252	+	1.82143i	−0.854499	+	0.0953382i
$366$	−1.61113	+	6.01280i	−0.0842149	+	0.314294i
$367$	−14.3602	−	3.84780i	−0.749595	−	0.200853i	−0.136256	−	0.990674i	$-0.543507\pi$
$367$	−14.3602	−	3.84780i	−0.749595	−	0.200853i	−0.613338	+	0.789820i	$0.710174\pi$
$368$	0.0313449	+	0.116981i	0.00163397	+	0.00609805i
$369$	−0.335423	+	0.335423i	−0.0174614	+	0.0174614i
$370$	6.09382	+	2.66660i	0.316803	+	0.138630i
$371$	−2.10294	−	7.84829i	−0.109179	−	0.407463i
$372$			2.00997i			0.104212i
$373$	−5.97055	+	1.59980i	−0.309144	+	0.0828348i	−0.410055	−	0.912061i	$-0.634491\pi$
$373$	−5.97055	+	1.59980i	−0.309144	+	0.0828348i	0.100912	+	0.994895i	$0.467824\pi$
$374$	−19.8037	−	34.3010i	−1.02403	−	1.77366i
$375$	1.58775	+	22.1566i	0.0819911	+	1.14416i
$376$			7.67955i			0.396043i
$377$	−33.5716	+	9.95486i	−1.72902	+	0.512701i
$378$	−8.28942	−	8.28942i	−0.426362	−	0.426362i
$379$	−17.6464	−	4.72834i	−0.906435	−	0.242878i	−0.224657	−	0.974438i	$-0.572126\pi$
$379$	−17.6464	−	4.72834i	−0.906435	−	0.242878i	−0.681778	+	0.731559i	$0.738793\pi$
$380$	8.26010	+	1.25420i	0.423734	+	0.0643389i
$381$	0.902517	+	0.521068i	0.0462373	+	0.0266951i
$382$	33.2081			1.69907
$383$	−8.87106	−	5.12171i	−0.453290	−	0.261707i	0.255929	−	0.966696i	$-0.417619\pi$
$383$	−8.87106	−	5.12171i	−0.453290	−	0.261707i	−0.709219	+	0.704989i	$0.750952\pi$
$384$	−31.6075	+	8.46920i	−1.61296	+	0.432192i
$385$	−12.1856	−	9.73936i	−0.621034	−	0.496364i
$386$	−16.9901	+	29.4277i	−0.864774	+	1.49783i
$387$	−1.63387	+	6.09769i	−0.0830543	+	0.309963i
$388$	−6.40929	−	11.1012i	−0.325382	−	0.563579i
$389$	3.41200			0.172995			0.0864977	−	0.996252i	$-0.472432\pi$
$389$	3.41200			0.172995			0.0864977	+	0.996252i	$0.472432\pi$
$390$	−35.7134	+	4.94469i	−1.80842	+	0.250384i
$391$	0.533655			0.0269881
$392$	6.44164	+	11.1572i	0.325352	+	0.563526i
$393$	2.62196	−	9.78529i	0.132260	−	0.493603i
$394$	−17.2992	+	29.9630i	−0.871519	+	1.50952i
$395$	−2.77138	−	24.8393i	−0.139443	−	1.24980i
$396$	−15.3277	+	4.10703i	−0.770244	+	0.206386i
$397$	−10.3335	−	5.96603i	−0.518622	−	0.299426i	0.217749	−	0.976005i	$-0.430129\pi$
$397$	−10.3335	−	5.96603i	−0.518622	−	0.299426i	−0.736371	+	0.676578i	$0.763462\pi$
$398$	−25.7857			−1.29252
$399$	−2.67795	−	1.54612i	−0.134065	−	0.0774027i
$400$	2.48054	+	2.68508i	0.124027	+	0.134254i
$401$	3.93721	+	1.05497i	0.196615	+	0.0526828i	0.355783	−	0.934569i	$-0.384214\pi$
$401$	3.93721	+	1.05497i	0.196615	+	0.0526828i	−0.159168	+	0.987252i	$0.550881\pi$
$402$	−19.2081	−	19.2081i	−0.958011	−	0.958011i
$403$	0.621869	+	1.01414i	0.0309775	+	0.0505181i
$404$		−	26.4586i		−	1.31636i
$405$	14.5112	+	19.7068i	0.721069	+	0.979240i
$406$	13.9592	+	24.1781i	0.692786	+	1.19994i
$407$	6.97310	−	1.86844i	0.345644	−	0.0926149i
$408$			15.3595i			0.760406i
$409$	1.79597	+	6.70266i	0.0888051	+	0.331425i	0.996008	−	0.0892692i	$-0.0284531\pi$
$409$	1.79597	+	6.70266i	0.0888051	+	0.331425i	−0.907202	+	0.420694i	$0.861786\pi$
$410$	−2.34659	+	0.918026i	−0.115890	+	0.0453381i
$411$	5.34348	−	5.34348i	0.263574	−	0.263574i
$412$	−1.20761	−	4.50687i	−0.0594948	−	0.222037i
$413$	0.00283692		0.000760151i	0.000139596		3.74046e-5i
$414$	0.0914320	−	0.341229i	0.00449364	−	0.0167705i
$415$	−0.658389	−	5.90102i	−0.0323190	−	0.289670i
$416$	−15.9907	+	16.8604i	−0.784008	+	0.826648i
$417$	2.07674	−	2.07674i	0.101698	−	0.101698i
$418$	12.9748	−	7.49098i	0.634616	−	0.366396i
$419$	18.3846	−	10.6144i	0.898147	−	0.518546i	0.0215487	−	0.999768i	$-0.493140\pi$
$419$	18.3846	−	10.6144i	0.898147	−	0.518546i	0.876599	+	0.481222i	$0.159807\pi$
$420$	6.33844	+	16.2019i	0.309284	+	0.790570i
$421$	−3.15727	−	3.15727i	−0.153876	−	0.153876i	0.625971	−	0.779847i	$-0.284703\pi$
$421$	−3.15727	−	3.15727i	−0.153876	−	0.153876i	−0.779847	+	0.625971i	$0.784703\pi$
$422$	3.58318	−	6.20625i	0.174427	−	0.302116i
$423$	−1.51610	+	2.62596i	−0.0737152	+	0.127678i
$424$	−10.7947	−	10.7947i	−0.524238	−	0.524238i
$425$	14.2575	−	7.49570i	0.691591	−	0.363595i
$426$	47.0822	−	27.1829i	2.28114	−	1.31702i
$427$	1.53964	−	0.888911i	0.0745084	−	0.0430174i
$428$	31.4932	−	31.4932i	1.52228	−	1.52228i
$429$	−26.9267	+	28.3912i	−1.30003	+	1.37074i
$430$	−20.9361	+	26.1946i	−1.00963	+	1.26321i
$431$	9.27711	−	34.6226i	0.446863	−	1.66771i	−0.264109	−	0.964493i	$-0.585078\pi$
$431$	9.27711	−	34.6226i	0.446863	−	1.66771i	0.710971	−	0.703221i	$-0.248256\pi$
$432$	2.87984	+	0.771651i	0.138556	+	0.0371261i
$433$	2.09465	+	7.81733i	0.100662	+	0.375677i	0.997817	−	0.0660397i	$-0.0210364\pi$
$433$	2.09465	+	7.81733i	0.100662	+	0.375677i	−0.897155	+	0.441716i	$0.854370\pi$
$434$	0.670679	−	0.670679i	0.0321936	−	0.0321936i
$435$	−15.7195	−	40.1810i	−0.753692	−	1.92653i
$436$	5.30171	+	19.7863i	0.253906	+	0.947590i
$437$			0.201861i			0.00965633i
$438$	31.7323	−	8.50264i	1.51623	−	0.406272i
$439$	−14.3336	−	24.8265i	−0.684104	−	1.18490i	−0.973717	−	0.227759i	$-0.926860\pi$
$439$	−14.3336	−	24.8265i	−0.684104	−	1.18490i	0.289613	−	0.957144i	$-0.406473\pi$
$440$	−28.9772	−	4.39983i	−1.38143	−	0.209754i
$441$			5.08683i			0.242230i
$442$	13.6668	+	22.2877i	0.650062	+	1.06012i
$443$	−17.1586	−	17.1586i	−0.815229	−	0.815229i	0.170184	−	0.985412i	$-0.445564\pi$
$443$	−17.1586	−	17.1586i	−0.815229	−	0.815229i	−0.985412	+	0.170184i	$0.945564\pi$
$444$	−7.77688	−	2.08381i	−0.369074	−	0.0988931i
$445$	−2.42058	+	15.9419i	−0.114746	+	0.755716i
$446$	−23.1523	−	13.3670i	−1.09629	−	0.632944i
$447$	34.2054			1.61786
$448$	14.4276	+	8.32978i	0.681640	+	0.393545i
$449$	−8.85389	+	2.37239i	−0.417841	+	0.111960i	−0.461613	−	0.887081i	$-0.652729\pi$
$449$	−8.85389	+	2.37239i	−0.417841	+	0.111960i	0.0437720	+	0.999042i	$0.486062\pi$
$450$	−2.35012	−	10.4008i	−0.110786	−	0.490297i
$451$	−1.36735	+	2.36832i	−0.0643860	+	0.111520i
$452$	9.04261	−	33.7475i	0.425329	−	1.58735i
$453$	14.1248	+	24.4648i	0.663639	+	1.14946i
$454$	62.2722			2.92258
$455$	8.21084	+	6.21370i	0.384930	+	0.291303i
$456$	−5.80989			−0.272073
$457$	10.7399	+	18.6021i	0.502391	+	0.870167i	0.999996	+	0.00276341i	$0.000879623\pi$
$457$	10.7399	+	18.6021i	0.502391	+	0.870167i	−0.497605	+	0.867404i	$0.665787\pi$
$458$	10.6277	−	39.6631i	0.496599	−	1.85333i
$459$	6.56877	−	11.3775i	0.306604	−	0.531054i
$460$	0.709072	−	0.887168i	0.0330607	−	0.0413644i
$461$	−4.90591	+	1.31453i	−0.228491	+	0.0612240i	−0.371248	−	0.928534i	$-0.621070\pi$
$461$	−4.90591	+	1.31453i	−0.228491	+	0.0612240i	0.142757	+	0.989758i	$0.454403\pi$
$462$	27.0180	+	15.5989i	1.25699	+	0.725725i
$463$	−20.0793			−0.933163			−0.466581	−	0.884478i	$-0.654515\pi$
$463$	−20.0793			−0.933163			−0.466581	+	0.884478i	$0.654515\pi$
$464$	−6.14905	−	3.55016i	−0.285463	−	0.164812i
$465$	−1.18035	+	0.869156i	−0.0547373	+	0.0403061i
$466$	50.2844	+	13.4737i	2.32938	+	0.624156i
$467$	21.4507	+	21.4507i	0.992618	+	0.992618i	0.999973	−	0.00735447i	$-0.00234102\pi$
$467$	21.4507	+	21.4507i	0.992618	+	0.992618i	−0.00735447	+	0.999973i	$0.502341\pi$
$468$	10.0423	−	2.97780i	0.464205	−	0.137649i
$469$			7.75807i			0.358234i
$470$	−12.9699	+	9.55047i	−0.598258	+	0.440530i
$471$	−4.31627	−	7.47600i	−0.198883	−	0.344476i
$472$	0.00533020	−	0.00142822i	0.000245342	−	6.57392e-5i
$473$			36.3934i			1.67337i
$474$	12.9371	+	48.2818i	0.594219	+	2.21766i
$475$	2.83533	+	5.39307i	0.130094	+	0.247451i
$476$	8.92064	−	8.92064i	0.408877	−	0.408877i
$477$	−1.56007	−	5.82226i	−0.0714306	−	0.266583i
$478$	8.04928	+	2.15680i	0.368166	+	0.0986497i
$479$	−8.05179	+	30.0497i	−0.367896	+	1.37300i	0.495557	+	0.868575i	$0.334964\pi$
$479$	−8.05179	+	30.0497i	−0.367896	+	1.37300i	−0.863453	+	0.504430i	$0.831703\pi$
$480$	−22.3664	−	17.8764i	−1.02088	−	0.815943i
$481$	−4.56859	+	1.35471i	−0.208310	+	0.0617693i
$482$	−33.1210	+	33.1210i	−1.50862	+	1.50862i
$483$	−0.364031	+	0.210173i	−0.0165640	+	0.00956321i
$484$	−50.0165	+	28.8770i	−2.27348	+	1.31259i
$485$	3.74764	−	8.56426i	0.170171	−	0.388883i
$486$	−15.1377	−	15.1377i	−0.686662	−	0.686662i
$487$	−9.71579	+	16.8282i	−0.440264	+	0.762560i	−0.997709	−	0.0676540i	$-0.978449\pi$
$487$	−9.71579	+	16.8282i	−0.440264	+	0.762560i	0.557445	+	0.830214i	$0.311782\pi$
$488$	1.67014	−	2.89277i	0.0756039	−	0.130950i
$489$	12.9321	+	12.9321i	0.584810	+	0.584810i
$490$	−10.8324	+	24.7546i	−0.489357	+	1.11830i
$491$	−30.5824	+	17.6568i	−1.38017	+	0.796839i	−0.992179	−	0.124825i	$-0.960163\pi$
$491$	−30.5824	+	17.6568i	−1.38017	+	0.796839i	−0.387987	+	0.921665i	$0.626830\pi$
$492$	2.64131	−	1.52496i	0.119079	−	0.0687506i
$493$	−22.1234	+	22.1234i	−0.996389	+	0.996389i
$494$	−8.43059	+	5.16961i	−0.379310	+	0.232592i
$495$	−9.03988	−	7.22515i	−0.406312	−	0.324746i
$496$	−0.0624327	+	0.233002i	−0.00280331	+	0.0104621i
$497$	−14.9977	−	4.01863i	−0.672740	−	0.180260i
$498$	3.07343	+	11.4702i	0.137723	+	0.513991i
$499$	9.44430	−	9.44430i	0.422785	−	0.422785i	−0.463377	−	0.886161i	$-0.653362\pi$
$499$	9.44430	−	9.44430i	0.422785	−	0.422785i	0.886161	+	0.463377i	$0.153362\pi$
$500$	6.48295	−	33.6618i	0.289926	−	1.50540i
$501$	−6.49919	−	24.2553i	−0.290363	−	1.08365i
$502$		−	5.32928i		−	0.237857i
$503$	23.3052	−	6.24460i	1.03913	−	0.278433i	0.301375	−	0.953506i	$-0.402554\pi$
$503$	23.3052	−	6.24460i	1.03913	−	0.278433i	0.737751	+	0.675073i	$0.235888\pi$
$504$	−1.45192	−	2.51480i	−0.0646736	−	0.112018i
$505$	15.5377	−	11.4413i	0.691419	−	0.509130i
$506$		−	2.03659i		−	0.0905374i
$507$	17.2718	−	19.2044i	0.767066	−	0.852899i
$508$	−1.13721	−	1.13721i	−0.0504555	−	0.0504555i
$509$	−3.59537	−	0.963376i	−0.159362	−	0.0427009i	0.178256	−	0.983984i	$-0.442954\pi$
$509$	−3.59537	−	0.963376i	−0.159362	−	0.0427009i	−0.337618	+	0.941283i	$0.609621\pi$
$510$	−25.9404	+	19.1014i	−1.14866	+	0.845823i
$511$	−8.12538	−	4.69119i	−0.359446	−	0.207526i
$512$	−8.22064			−0.363304
$513$	4.30365	+	2.48471i	0.190011	+	0.109703i
$514$	1.89156	−	0.506841i	0.0834330	−	0.0223558i
$515$	2.12445	−	2.65804i	0.0936144	−	0.117127i
$516$	20.2942	−	35.1506i	0.893403	−	1.54742i
$517$	−4.52433	+	16.8850i	−0.198980	+	0.742603i
$518$	1.89964	+	3.29028i	0.0834656	+	0.144567i
$519$	−27.2503			−1.19615
$520$	19.1976	+	2.39705i	0.841869	+	0.105118i
$521$	45.2323			1.98166			0.990832	−	0.135103i	$-0.0431364\pi$
$521$	45.2323			1.98166			0.990832	+	0.135103i	$0.0431364\pi$
$522$	10.3557	+	17.9366i	0.453256	+	0.785062i
$523$	0.295439	−	1.10259i	0.0129187	−	0.0482131i	−0.959166	−	0.282845i	$-0.908722\pi$
$523$	0.295439	−	1.10259i	0.0129187	−	0.0482131i	0.972084	+	0.234632i	$0.0753885\pi$
$524$	−7.81683	+	13.5392i	−0.341480	+	0.591461i
$525$	−6.77362	+	10.7283i	−0.295625	+	0.468221i
$526$	−33.0208	+	8.84790i	−1.43978	+	0.385787i
$527$	0.920525	+	0.531466i	0.0400987	+	0.0231510i
$528$	−7.93430			−0.345296
$529$	−19.8948	−	11.4863i	−0.864992	−	0.499403i
$530$	4.80653	−	31.6557i	0.208782	−	1.37503i
$531$	0.00210457		0.000563919i	9.13307e−5		2.44720e-5i
$532$	3.37434	+	3.37434i	0.146296	+	0.146296i
$533$	0.860880	−	1.58663i	0.0372889	−	0.0687246i
$534$		−	32.2479i		−	1.39550i
$535$	32.1127	+	4.87592i	1.38835	+	0.210804i
$536$	7.28818	+	12.6235i	0.314801	+	0.545252i
$537$	24.2626	−	6.50114i	1.04701	−	0.280545i
$538$		−	54.8782i		−	2.36597i
$539$	7.59005	+	28.3265i	0.326927	+	1.22011i
$540$	−10.1863	−	26.0375i	−0.438349	−	1.12047i
$541$	22.3573	−	22.3573i	0.961218	−	0.961218i	−0.0380580	−	0.999276i	$-0.512117\pi$
$541$	22.3573	−	22.3573i	0.961218	−	0.961218i	0.999276	+	0.0380580i	$0.0121172\pi$
$542$	−7.64112	−	28.5171i	−0.328214	−	1.22491i
$543$	−15.6720	−	4.19929i	−0.672548	−	0.180209i
$544$	−5.37376	+	20.0551i	−0.230398	+	0.859857i
$545$	−9.32685	+	11.6694i	−0.399518	+	0.499864i
$546$	−18.1005	−	9.82101i	−0.774628	−	0.420300i
$547$	−5.20384	+	5.20384i	−0.222500	+	0.222500i	−0.809550	−	0.587050i	$-0.800289\pi$
$547$	−5.20384	+	5.20384i	−0.222500	+	0.222500i	0.587050	+	0.809550i	$0.300289\pi$
$548$	−10.0995	+	5.83096i	−0.431430	+	0.249086i
$549$	1.14218	−	0.659440i	0.0487472	−	0.0281442i
$550$	−28.6058	−	54.4109i	−1.21976	−	2.32009i
$551$	−8.36844	−	8.36844i	−0.356507	−	0.356507i
$552$	−0.394887	+	0.683964i	−0.0168075	+	0.0291114i
$553$	7.13781	−	12.3630i	0.303530	−	0.525730i
$554$	19.4608	+	19.4608i	0.826812	+	0.826812i
$555$	−2.13919	−	5.46804i	−0.0908035	−	0.232105i
$556$	−3.92517	+	2.26620i	−0.166464	+	0.0961081i
$557$	−5.70401	+	3.29321i	−0.241687	+	0.139538i	−0.615952	−	0.787784i	$-0.711228\pi$
$557$	−5.70401	+	3.29321i	−0.241687	+	0.139538i	0.374265	+	0.927322i	$0.377895\pi$
$558$	0.497544	−	0.497544i	0.0210627	−	0.0210627i
$559$	−0.635748	−	24.0144i	−0.0268893	−	1.01570i
$560$	0.231518	+	2.07505i	0.00978343	+	0.0876871i
$561$	−9.04887	+	33.7709i	−0.382044	+	1.42581i
$562$	−19.7863	−	5.30173i	−0.834636	−	0.223640i
$563$	7.59751	+	28.3543i	0.320197	+	1.19499i	0.919053	+	0.394134i	$0.128955\pi$
$563$	7.59751	+	28.3543i	0.320197	+	1.19499i	−0.598856	+	0.800856i	$0.704378\pi$
$564$	13.7855	−	13.7855i	0.580475	−	0.580475i
$565$	23.7284	−	9.28293i	0.998259	−	0.390536i
$566$	15.9347	+	59.4689i	0.669783	+	2.49967i
$567$			13.9784i			0.587039i
$568$	−28.1787	+	7.55046i	−1.18235	+	0.316810i
$569$	16.9543	+	29.3658i	0.710763	+	1.23108i	0.964571	+	0.263823i	$0.0849835\pi$
$569$	16.9543	+	29.3658i	0.710763	+	1.23108i	−0.253808	+	0.967255i	$0.581683\pi$
$570$	−7.22531	−	9.81226i	−0.302635	−	0.410990i
$571$			33.5525i			1.40413i	0.712113	+	0.702065i	$0.247738\pi$
$571$			33.5525i			1.40413i	−0.712113	+	0.702065i	$0.752262\pi$
$572$	51.4782	−	31.5662i	2.15241	−	1.31985i
$573$	−20.7277	−	20.7277i	−0.865910	−	0.865910i
$574$	−1.39019	−	0.372500i	−0.0580253	−	0.0155478i
$575$	0.827606	+	0.0327691i	0.0345136	+	0.00136656i
$576$	10.7031	+	6.17945i	0.445964	+	0.257477i
$577$	11.0413			0.459654			0.229827	−	0.973232i	$-0.426184\pi$
$577$	11.0413			0.459654			0.229827	+	0.973232i	$0.426184\pi$
$578$	−12.9070	−	7.45188i	−0.536862	−	0.309957i
$579$	28.9729	−	7.76326i	1.20407	−	0.322630i
$580$	7.38321	+	66.1743i	0.306571	+	2.74774i
$581$	1.69571	−	2.93706i	0.0703499	−	0.121850i
$582$	−4.83886	+	18.0589i	−0.200577	+	0.748565i
$583$	−17.3748	−	30.0940i	−0.719589	−	1.24636i
$584$	−17.6282			−0.729461
$585$	6.09122	+	4.60964i	0.251841	+	0.190585i
$586$	58.8002			2.42902
$587$	−11.7529	−	20.3567i	−0.485095	−	0.840209i	0.514758	−	0.857335i	$-0.327882\pi$
$587$	−11.7529	−	20.3567i	−0.485095	−	0.840209i	−0.999853	+	0.0171260i	$0.994548\pi$
$588$	8.46495	−	31.5916i	0.349089	−	1.30282i
$589$	−0.201033	+	0.348199i	−0.00828342	+	0.0143473i
$590$	0.00904086	+	0.00722594i	0.000372206	+	0.000297487i
$591$	29.4999	−	7.90448i	1.21346	−	0.325147i
$592$	−0.836794	−	0.483123i	−0.0343920	−	0.0198563i
$593$	−30.6582			−1.25898			−0.629491	−	0.777007i	$-0.716737\pi$
$593$	−30.6582			−1.25898			−0.629491	+	0.777007i	$0.716737\pi$
$594$	−43.4198	−	25.0684i	−1.78153	−	1.02857i
$595$	9.09612	+	1.38113i	0.372904	+	0.0566210i
$596$	−50.9882	−	13.6622i	−2.08856	−	0.559627i
$597$	16.0948	+	16.0948i	0.658717	+	0.658717i
$598$	0.0355767	+	1.34385i	0.00145484	+	0.0549542i
$599$		−	7.49378i		−	0.306188i	−0.988212	−	0.153094i	$-0.951076\pi$
$599$		−	7.49378i		−	0.306188i	0.988212	−	0.153094i	$-0.0489237\pi$
$600$	−0.943146	+	23.8198i	−0.0385038	+	0.972441i
$601$	7.04653	+	12.2049i	0.287434	+	0.497850i	0.973196	−	0.229975i	$-0.0738645\pi$
$601$	7.04653	+	12.2049i	0.287434	+	0.497850i	−0.685763	+	0.727825i	$0.740531\pi$
$602$	−18.5007	+	4.95724i	−0.754030	+	0.202042i
$603$			5.75533i			0.234375i
$604$	−11.2834	−	42.1101i	−0.459113	−	1.71343i
$605$	−38.5862	−	16.8850i	−1.56875	−	0.686471i
$606$	−27.2872	+	27.2872i	−1.10847	+	1.10847i
$607$	3.90296	+	14.5660i	0.158416	+	0.591218i	0.998789	+	0.0492080i	$0.0156697\pi$
$607$	3.90296	+	14.5660i	0.158416	+	0.591218i	−0.840372	+	0.542010i	$0.817664\pi$
$608$	−7.58608	−	2.03268i	−0.307656	−	0.0824363i
$609$	6.37837	−	23.8044i	0.258465	−	0.964604i
$610$	6.96260	−	0.776832i	0.281908	−	0.0314530i
$611$	2.69044	−	11.2207i	0.108844	−	0.453941i
$612$	6.61779	−	6.61779i	0.267508	−	0.267508i
$613$	10.3197	−	5.95807i	0.416808	−	0.240644i	−0.276903	−	0.960898i	$-0.589308\pi$
$613$	10.3197	−	5.95807i	0.416808	−	0.240644i	0.693711	+	0.720254i	$0.255975\pi$
$614$	28.6614	−	16.5477i	1.15668	−	0.667810i
$615$	2.03769	+	0.891675i	0.0821677	+	0.0359558i
$616$	−11.8375	−	11.8375i	−0.476945	−	0.476945i
$617$	19.4158	−	33.6292i	0.781652	−	1.35386i	−0.149326	−	0.988788i	$-0.547710\pi$
$617$	19.4158	−	33.6292i	0.781652	−	1.35386i	0.930979	−	0.365074i	$-0.118956\pi$
$618$	−3.40258	+	5.89344i	−0.136872	+	0.237069i
$619$	14.9567	+	14.9567i	0.601159	+	0.601159i	0.940620	−	0.339461i	$-0.110245\pi$
$619$	14.9567	+	14.9567i	0.601159	+	0.601159i	−0.339461	+	0.940620i	$0.610245\pi$
$620$	2.10664	−	0.824152i	0.0846046	−	0.0330987i
$621$	0.585021	−	0.337762i	0.0234761	−	0.0135539i
$622$	−62.0887	+	35.8469i	−2.48953	+	1.43733i
$623$	−6.51241	+	6.51241i	−0.260914	+	0.260914i
$624$	5.23549	−	0.138602i	0.209587	−	0.00554853i
$625$	22.5712	−	10.7490i	0.902847	−	0.429961i
$626$	9.87514	−	36.8545i	0.394690	−	1.47300i
$627$	−12.7742	−	3.42284i	−0.510153	−	0.136695i
$628$	3.44799	+	12.8681i	0.137590	+	0.513492i
$629$	−3.01067	+	3.01067i	−0.120043	+	0.120043i
$630$	2.44157	−	5.57959i	0.0972747	−	0.222296i
$631$	−10.1085	−	37.7256i	−0.402415	−	1.50183i	−0.808775	−	0.588119i	$-0.799869\pi$
$631$	−10.1085	−	37.7256i	−0.402415	−	1.50183i	0.406360	−	0.913713i	$-0.366798\pi$
$632$		−	26.8219i		−	1.06692i
$633$	−6.11032	+	1.63726i	−0.242864	+	0.0650751i
$634$	17.5143	+	30.3357i	0.695582	+	1.20478i
$635$	0.176068	−	1.15958i	0.00698704	−	0.0460165i
$636$			38.7550i			1.53674i
$637$	−5.50316	−	18.5588i	−0.218043	−	0.735325i
$638$	84.4296	+	84.4296i	3.34260	+	3.34260i
$639$	−11.1261	−	2.98122i	−0.440141	−	0.117935i
$640$	21.8366	+	29.6550i	0.863168	+	1.17222i
$641$	−7.55607	−	4.36250i	−0.298447	−	0.172308i	0.343298	−	0.939226i	$-0.388456\pi$
$641$	−7.55607	−	4.36250i	−0.298447	−	0.172308i	−0.641745	+	0.766918i	$0.721789\pi$
$642$	−64.9590			−2.56373
$643$	−12.8146	−	7.39852i	−0.505359	−	0.291769i	0.225565	−	0.974228i	$-0.427577\pi$
$643$	−12.8146	−	7.39852i	−0.505359	−	0.291769i	−0.730924	+	0.682459i	$0.760911\pi$
$644$	0.626588	−	0.167894i	0.0246910	−	0.00661594i
$645$	29.4178	−	3.28220i	1.15832	−	0.129237i
$646$	−4.41809	+	7.65235i	−0.173827	+	0.301078i
$647$	8.76765	−	32.7213i	0.344692	−	1.28641i	−0.548280	−	0.836295i	$-0.684717\pi$
$647$	8.76765	−	32.7213i	0.344692	−	1.28641i	0.892972	−	0.450113i	$-0.148616\pi$
$648$	13.1318	+	22.7449i	0.515865	+	0.893505i
$649$	0.0125609			0.000493060
$650$	19.8262	+	35.4036i	0.777647	+	1.38864i
$651$	−0.837243			−0.0328141
$652$	−14.1119	−	24.4425i	−0.552664	−	0.957242i
$653$	−5.24059	+	19.5581i	−0.205080	+	0.765369i	0.784345	+	0.620325i	$0.212999\pi$
$653$	−5.24059	+	19.5581i	−0.205080	+	0.765369i	−0.989425	+	0.145044i	$0.953667\pi$
$654$	14.9382	−	25.8737i	0.584128	−	1.01174i
$655$	−11.3310	+	1.26422i	−0.442739	+	0.0493973i
$656$	0.353557	−	0.0947353i	0.0138041	−	0.00369879i
$657$	−6.02782	−	3.48016i	−0.235168	−	0.135774i
$658$	−9.19981			−0.358646
$659$	26.2317	+	15.1449i	1.02184	+	0.589961i	0.914637	−	0.404276i	$-0.132477\pi$
$659$	26.2317	+	15.1449i	1.02184	+	0.589961i	0.107205	+	0.994237i	$0.465810\pi$
$660$	44.1186	+	59.9148i	1.71731	+	2.33218i
$661$	−21.1339	−	5.66280i	−0.822012	−	0.220257i	−0.176786	−	0.984249i	$-0.556570\pi$
$661$	−21.1339	−	5.66280i	−0.822012	−	0.220257i	−0.645226	+	0.763992i	$0.723237\pi$
$662$	−27.1574	−	27.1574i	−1.05550	−	1.05550i
$663$	5.38101	−	22.4419i	0.208981	−	0.871572i
$664$		−	6.37202i		−	0.247282i
$665$	−0.522430	+	3.44071i	−0.0202590	+	0.133425i
$666$	1.40925	+	2.44090i	0.0546074	+	0.0945829i
$667$	−1.55395	+	0.416380i	−0.0601693	+	0.0161223i
$668$			38.7520i			1.49936i
$669$	6.10774	+	22.7944i	0.236139	+	0.881282i
$670$	−12.2559	+	28.0078i	−0.473488	+	1.08204i
$671$	5.37640	−	5.37640i	0.207553	−	0.207553i
$672$	−4.23277	−	15.7969i	−0.163283	−	0.609379i
$673$	0.554664	+	0.148622i	0.0213807	+	0.00572895i	0.269494	−	0.963002i	$-0.413144\pi$
$673$	0.554664	+	0.148622i	0.0213807	+	0.00572895i	−0.248113	+	0.968731i	$0.579810\pi$
$674$	20.6424	−	77.0386i	0.795117	−	2.96742i
$675$	10.8857	−	17.2411i	0.418989	−	0.663610i
$676$	−33.4167	+	21.7284i	−1.28526	+	0.835707i
$677$	−11.5229	+	11.5229i	−0.442862	+	0.442862i	−0.892973	−	0.450111i	$-0.851385\pi$
$677$	−11.5229	+	11.5229i	−0.442862	+	0.442862i	0.450111	+	0.892973i	$0.351385\pi$
$678$	−44.1302	+	25.4786i	−1.69481	+	0.978498i
$679$	4.62416	−	2.66976i	0.177459	−	0.102456i
$680$	16.0982	−	6.29788i	0.617337	−	0.241513i
$681$	−38.8688	−	38.8688i	−1.48946	−	1.48946i
$682$	2.02823	−	3.51300i	0.0776650	−	0.134520i
$683$	−10.0529	+	17.4121i	−0.384663	+	0.666256i	−0.991722	−	0.128400i	$-0.959016\pi$
$683$	−10.0529	+	17.4121i	−0.384663	+	0.666256i	0.607059	+	0.794657i	$0.292349\pi$
$684$	2.50325	+	2.50325i	0.0957143	+	0.0957143i
$685$	−7.79148	−	3.40948i	−0.297697	−	0.130269i
$686$	−30.7929	+	17.7783i	−1.17568	+	0.678777i
$687$	−31.3902	+	18.1232i	−1.19761	+	0.691442i
$688$	3.44440	−	3.44440i	0.131317	−	0.131317i
$689$	11.9905	+	19.5541i	0.456802	+	0.744953i
$690$	−1.64623	+	0.183673i	−0.0626709	+	0.00699232i
$691$	−11.2156	+	41.8571i	−0.426661	+	1.59232i	0.333608	+	0.942712i	$0.391734\pi$
$691$	−11.2156	+	41.8571i	−0.426661	+	1.59232i	−0.760269	+	0.649608i	$0.774933\pi$
$692$	40.6205	+	10.8842i	1.54416	+	0.413756i
$693$	−1.71077	−	6.38467i	−0.0649867	−	0.242534i
$694$	−20.5310	+	20.5310i	−0.779346	+	0.779346i
$695$	−3.02815	−	1.32509i	−0.114864	−	0.0502635i
$696$	−11.9841	−	44.7253i	−0.454256	−	1.69531i
$697$		−	1.61289i		−	0.0610926i
$698$	58.3773	−	15.6421i	2.20961	−	0.592064i
$699$	−22.9764	−	39.7962i	−0.869046	−	1.50523i
$700$	14.3821	−	13.2866i	0.543593	−	0.502186i
$701$			8.03468i			0.303466i	0.988422	+	0.151733i	$0.0484853\pi$
$701$			8.03468i			0.303466i	−0.988422	+	0.151733i	$0.951515\pi$
$702$	29.0886	+	15.7830i	1.09788	+	0.595692i
$703$	−1.13882	−	1.13882i	−0.0429514	−	0.0429514i
$704$	68.8216	+	18.4407i	2.59381	+	0.695010i
$705$	14.0567	+	2.13434i	0.529405	+	0.0803837i
$706$	45.4404	+	26.2350i	1.71017	+	0.987369i
$707$	11.0212			0.414495
$708$	−0.0121320	−	0.00700440i	−0.000455948	−	0.000263242i
$709$	−21.9526	+	5.88217i	−0.824446	+	0.220910i	−0.646289	−	0.763092i	$-0.723680\pi$
$709$	−21.9526	+	5.88217i	−0.824446	+	0.220910i	−0.178157	+	0.984002i	$0.557013\pi$
$710$	−47.7956	−	38.2008i	−1.79374	−	1.43365i
$711$	5.29519	−	9.17153i	0.198585	−	0.343959i
$712$	−4.47866	+	16.7146i	−0.167845	+	0.626406i
$713$	0.0273276	+	0.0473328i	0.00102343	+	0.00177263i
$714$	−18.4000			−0.688604
$715$	40.7975	+	16.5805i	1.52574	+	0.620074i
$716$	−38.7636			−1.44866
$717$	−3.67794	−	6.37039i	−0.137355	−	0.237906i
$718$	7.55655	−	28.2014i	0.282008	−	1.05247i
$719$	−21.4786	+	37.2021i	−0.801018	+	1.38740i	0.117928	+	0.993022i	$0.462375\pi$
$719$	−21.4786	+	37.2021i	−0.801018	+	1.38740i	−0.918946	+	0.394382i	$0.870959\pi$
$720$	0.171752	+	1.53938i	0.00640081	+	0.0573693i
$721$	1.87732	−	0.503026i	0.0699149	−	0.0187336i
$722$	34.1413	+	19.7115i	1.27061	+	0.733585i
$723$	41.3467			1.53770
$724$	21.6841	+	12.5193i	0.805882	+	0.465276i
$725$	−35.6680	+	32.9511i	−1.32468	+	1.22377i
$726$	81.3643	+	21.8015i	3.01971	+	0.809129i
$727$	1.42786	+	1.42786i	0.0529563	+	0.0529563i	0.733089	−	0.680133i	$-0.238078\pi$
$727$	1.42786	+	1.42786i	0.0529563	+	0.0529563i	−0.680133	+	0.733089i	$0.738078\pi$
$728$	8.01779	+	7.60422i	0.297159	+	0.281831i
$729$		−	13.9369i		−	0.516183i
$730$	−21.9229	−	29.7721i	−0.811401	−	1.10191i
$731$	−10.7322	−	18.5887i	−0.396945	−	0.687528i
$732$	−8.19086	+	2.19473i	−0.302743	+	0.0811197i
$733$			32.1064i			1.18588i	0.805247	+	0.592939i	$0.202033\pi$
$733$			32.1064i			1.18588i	−0.805247	+	0.592939i	$0.797967\pi$
$734$	−8.66065	−	32.3220i	−0.319670	−	1.19303i
$735$	22.2125	−	8.68992i	0.819322	−	0.320532i
$736$	−0.754907	+	0.754907i	−0.0278262	+	0.0278262i
$737$	8.58752	+	32.0491i	0.316325	+	1.18054i
$738$	−1.03131	−	0.276339i	−0.0379631	−	0.0101722i
$739$	−5.31771	+	19.8460i	−0.195615	+	0.730046i	0.796492	+	0.604650i	$0.206687\pi$
$739$	−5.31771	+	19.8460i	−0.195615	+	0.730046i	−0.992107	+	0.125396i	$0.959980\pi$
$740$	1.00474	+	9.00534i	0.0369351	+	0.331043i
$741$	8.48891	+	2.03543i	0.311848	+	0.0747733i
$742$	12.9317	−	12.9317i	0.474736	−	0.474736i
$743$	19.4891	−	11.2520i	0.714985	−	0.412797i	−0.0979193	−	0.995194i	$-0.531219\pi$
$743$	19.4891	−	11.2520i	0.714985	−	0.412797i	0.812904	+	0.582398i	$0.197885\pi$
$744$	−1.36232	+	0.786533i	−0.0499449	+	0.0288357i
$745$	−14.0253	−	35.8505i	−0.513849	−	1.31346i
$746$	−9.83771	−	9.83771i	−0.360184	−	0.360184i
$747$	1.25796	−	2.17886i	0.0460265	−	0.0797202i
$748$	26.9773	−	46.7261i	0.986389	−	1.70848i
$749$	13.1184	+	13.1184i	0.479334	+	0.479334i
$750$	−41.4020	+	28.0300i	−1.51179	+	1.02351i
$751$	1.44204	−	0.832560i	0.0526207	−	0.0303806i	−0.473459	−	0.880816i	$-0.656995\pi$
$751$	1.44204	−	0.832560i	0.0526207	−	0.0303806i	0.526080	+	0.850435i	$0.323661\pi$
$752$	2.02626	−	1.16986i	0.0738901	−	0.0426605i
$753$	−3.32640	+	3.32640i	−0.121221	+	0.121221i
$754$	−57.1861	−	54.2364i	−2.08260	−	1.97517i
$755$	19.8498	−	24.8355i	0.722410	−	0.903855i
$756$	4.13321	−	15.4254i	0.150324	−	0.561015i
$757$	37.6990	+	10.1014i	1.37019	+	0.367143i	0.867550	−	0.497350i	$-0.165694\pi$
$757$	37.6990	+	10.1014i	1.37019	+	0.367143i	0.502645	+	0.864493i	$0.332360\pi$
$758$	−10.6426	−	39.7186i	−0.386556	−	1.44265i
$759$	−1.27119	+	1.27119i	−0.0461412	+	0.0461412i
$760$	2.38225	+	6.08932i	0.0864131	+	0.220883i
$761$	−4.20973	−	15.7109i	−0.152603	−	0.569521i	−0.999299	−	0.0374441i	$-0.988078\pi$
$761$	−4.20973	−	15.7109i	−0.152603	−	0.569521i	0.846696	−	0.532077i	$-0.178588\pi$
$762$			2.34565i			0.0849739i
$763$	−8.24188	+	2.20841i	−0.298376	+	0.0799496i
$764$	22.6186	+	39.1766i	0.818313	+	1.41736i
$765$	6.74796	+	1.02460i	0.243973	+	0.0370443i
$766$		−	23.0560i		−	0.833045i
$767$	−0.00828839		0.000219424i	−0.000299276		7.92293e-6i
$768$	−15.4289	−	15.4289i	−0.556741	−	0.556741i
$769$	−38.5504	−	10.3296i	−1.39016	−	0.372493i	−0.515362	−	0.856973i	$-0.672342\pi$
$769$	−38.5504	−	10.3296i	−1.39016	−	0.372493i	−0.874803	+	0.484479i	$0.839009\pi$
$770$	5.27082	−	34.7135i	0.189947	−	1.25099i
$771$	−1.49702	−	0.864306i	−0.0539139	−	0.0311272i
$772$	−46.2891			−1.66598
$773$	−17.8304	−	10.2944i	−0.641313	−	0.370262i	0.143807	−	0.989606i	$-0.454066\pi$
$773$	−17.8304	−	10.2944i	−0.641313	−	0.370262i	−0.785120	+	0.619343i	$0.787399\pi$
$774$	−13.7247	+	3.67753i	−0.493325	+	0.132186i
$775$	1.39494	+	0.880735i	0.0501077	+	0.0316369i
$776$	5.01612	−	8.68818i	0.180068	−	0.311887i
$777$	0.868001	−	3.23942i	0.0311394	−	0.116214i
$778$	3.83988	+	6.65087i	0.137666	+	0.238445i
$779$	0.610095			0.0218589
$780$	−30.1585	−	38.7643i	−1.07985	−	1.38799i
$781$	−66.4048			−2.37615
$782$	0.600577	+	1.04023i	0.0214766	+	0.0371986i
$783$	−10.2505	+	38.2553i	−0.366322	+	1.36713i
$784$	1.96257	−	3.39927i	0.0700917	−	0.121402i
$785$	−6.06575	+	7.58927i	−0.216496	+	0.270873i
$786$	22.0248	−	5.90153i	0.785599	−	0.210501i
$787$	24.8106	+	14.3244i	0.884404	+	0.510611i	0.872108	−	0.489314i	$-0.162753\pi$
$787$	24.8106	+	14.3244i	0.884404	+	0.510611i	0.0122960	+	0.999924i	$0.496086\pi$
$788$	−47.1311			−1.67898
$789$	26.1334	+	15.0881i	0.930375	+	0.537152i
$790$	45.2993	−	33.3564i	1.61168	−	1.18677i
$791$	14.0574	+	3.76666i	0.499822	+	0.133927i
$792$	−8.78163	−	8.78163i	−0.312042	−	0.312042i
$793$	−3.45372	+	3.64156i	−0.122645	+	0.129316i
$794$		−	26.8568i		−	0.953111i
$795$	−22.7588	+	16.7586i	−0.807171	+	0.594365i
$796$	−17.5631	−	30.4202i	−0.622508	−	1.07822i
$797$	−8.48530	+	2.27363i	−0.300565	+	0.0805361i	−0.405950	−	0.913895i	$-0.633059\pi$
$797$	−8.48530	+	2.27363i	−0.300565	+	0.0805361i	0.105385	+	0.994432i	$0.466393\pi$
$798$		−	6.96002i		−	0.246382i
$799$	−2.66840	−	9.95859i	−0.0944011	−	0.352310i
$800$	−9.56524	+	30.7720i	−0.338182	+	1.08796i
$801$	−4.83124	+	4.83124i	−0.170703	+	0.170703i
$802$	2.37454	+	8.86190i	0.0838479	+	0.312924i
$803$	−38.7592	−	10.3855i	−1.36778	−	0.366496i
$804$	9.57739	−	35.7433i	0.337768	−	1.26057i
$805$	0.369546	+	0.295361i	0.0130248	+	0.0104101i
$806$	−1.27697	+	2.35350i	−0.0449794	+	0.0828985i
$807$	−34.2536	+	34.2536i	−1.20578	+	1.20578i
$808$	17.9331	−	10.3537i	0.630884	−	0.364241i
$809$	0.820571	−	0.473757i	0.0288497	−	0.0166564i	−0.485506	−	0.874233i	$-0.661365\pi$
$809$	0.820571	−	0.473757i	0.0288497	−	0.0166564i	0.514356	+	0.857577i	$0.328031\pi$
$810$	−22.0827	+	50.4642i	−0.775905	+	1.77313i
$811$	28.8041	+	28.8041i	1.01145	+	1.01145i	0.999934	+	0.0115151i	$0.00366545\pi$
$811$	28.8041	+	28.8041i	1.01145	+	1.01145i	0.0115151	+	0.999934i	$0.496335\pi$
$812$	−19.0158	+	32.9363i	−0.667324	+	1.15584i
$813$	−13.0302	+	22.5690i	−0.456991	+	0.791531i
$814$	11.4896	+	11.4896i	0.402711	+	0.402711i
$815$	8.25150	−	18.8567i	0.289037	−	0.660520i
$816$	4.05261	−	2.33978i	0.141870	−	0.0819086i
$817$	7.03139	−	4.05958i	0.245997	−	0.142027i
$818$	−11.0440	+	11.0440i	−0.386145	+	0.386145i
$819$	1.24039	+	4.18307i	0.0433427	+	0.146168i
$820$	−2.68133	−	2.14306i	−0.0936361	−	0.0748390i
$821$	0.348249	−	1.29968i	0.0121540	−	0.0453592i	−0.959583	−	0.281427i	$-0.909192\pi$
$821$	0.348249	−	1.29968i	0.0121540	−	0.0453592i	0.971737	+	0.236068i	$0.0758588\pi$
$822$	16.4294	+	4.40224i	0.573041	+	0.153546i
$823$	−8.55907	−	31.9429i	−0.298350	−	1.11346i	−0.938520	−	0.345225i	$-0.887803\pi$
$823$	−8.55907	−	31.9429i	−0.298350	−	1.11346i	0.640169	−	0.768234i	$-0.278864\pi$
$824$	2.58211	−	2.58211i	0.0899520	−	0.0899520i
$825$	−16.1069	+	51.8170i	−0.560771	+	1.80404i
$826$	0.00171095	+	0.00638537i	5.95317e−5	+	0.000222175i
$827$			26.4195i			0.918697i	0.888256	+	0.459349i	$0.151917\pi$
$827$			26.4195i			0.918697i	−0.888256	+	0.459349i	$0.848083\pi$
$828$	0.464834	−	0.124552i	0.0161541	−	0.00432848i
$829$	−1.23034	−	2.13101i	−0.0427314	−	0.0740130i	0.843869	−	0.536550i	$-0.180273\pi$
$829$	−1.23034	−	2.13101i	−0.0427314	−	0.0740130i	−0.886600	+	0.462537i	$0.846939\pi$
$830$	10.7616	−	7.92439i	0.373542	−	0.275060i
$831$		−	24.2940i		−	0.842748i
$832$	−45.7344	−	10.9660i	−1.58556	−	0.380176i
$833$	−12.2301	−	12.2301i	−0.423747	−	0.423747i
$834$	6.38526	+	1.71093i	0.221104	+	0.0592445i
$835$	−22.7570	+	16.7573i	−0.787539	+	0.579909i
$836$	17.6747	+	10.2045i	0.611292	+	0.352929i
$837$	1.34551			0.0465075
$838$	41.3802	+	23.8909i	1.42946	+	0.825297i
$839$	−48.6308	+	13.0306i	−1.67892	+	0.449866i	−0.967494	−	0.252893i	$-0.918618\pi$
$839$	−48.6308	+	13.0306i	−1.67892	+	0.449866i	−0.711428	+	0.702759i	$0.751951\pi$
$840$	−8.50096	+	10.6361i	−0.293311	+	0.366981i
$841$	32.6597	−	56.5682i	1.12619	−	1.95063i
$842$	2.60113	−	9.70754i	0.0896408	−	0.334544i
$843$	9.04093	+	15.6594i	0.311386	+	0.539337i
$844$	9.76228			0.336032
$845$	−27.2101	−	10.2280i	−0.936055	−	0.351854i
$846$	−6.82488			−0.234644
$847$	−12.0286	−	20.8342i	−0.413308	−	0.715870i
$848$	−1.20379	+	4.49261i	−0.0413384	+	0.154277i
$849$	27.1730	−	47.0651i	0.932576	−	1.61527i
$850$	30.6565	+	19.3559i	1.05151	+	0.663900i
$851$	−0.211470	+	0.0566632i	−0.00724909	+	0.00194239i
$852$	64.1371	+	37.0296i	2.19730	+	1.26861i
$853$	42.9612			1.47096			0.735481	−	0.677545i	$-0.236956\pi$
$853$	42.9612			1.47096			0.735481	+	0.677545i	$0.236956\pi$
$854$	3.46543	+	2.00077i	0.118585	+	0.0684649i
$855$	−0.387565	+	2.55249i	−0.0132544	+	0.0872934i
$856$	33.6693	+	9.02166i	1.15079	+	0.308354i
$857$	−29.0789	−	29.0789i	−0.993316	−	0.993316i	0.00666151	−	0.999978i	$-0.497880\pi$
$857$	−29.0789	−	29.0789i	−0.993316	−	0.993316i	−0.999978	+	0.00666151i	$0.997880\pi$
$858$	−85.6451	−	20.5355i	−2.92388	−	0.701072i
$859$			42.1283i			1.43740i	0.695321	+	0.718700i	$0.255262\pi$
$859$			42.1283i			1.43740i	−0.695321	+	0.718700i	$0.744738\pi$
$860$	−45.1625	−	6.85738i	−1.54003	−	0.233835i
$861$	0.635216	+	1.10023i	0.0216481	+	0.0374956i
$862$	77.9289	−	20.8810i	2.65427	−	0.711209i
$863$			6.80768i			0.231736i	0.993265	+	0.115868i	$0.0369650\pi$
$863$			6.80768i			0.231736i	−0.993265	+	0.115868i	$0.963035\pi$
$864$	6.80234	+	25.3867i	0.231420	+	0.863672i
$865$	11.1735	+	28.5609i	0.379910	+	0.971099i
$866$	−12.8806	+	12.8806i	−0.437702	+	0.437702i
$867$	3.40497	+	12.7075i	0.115639	+	0.431570i
$868$	1.24803	+	0.334410i	0.0423610	+	0.0113506i
$869$	15.8019	−	58.9734i	0.536042	−	2.00054i
$870$	60.6323	−	75.8612i	2.05563	−	2.57194i
$871$	−6.22637	−	20.9977i	−0.210973	−	0.711480i
$872$	−11.3361	+	11.3361i	−0.383888	+	0.383888i
$873$	3.43044	−	1.98056i	0.116103	−	0.0670320i
$874$	−0.393479	+	0.227175i	−0.0133096	+	0.00768432i
$875$	14.0217	+	2.70044i	0.474019	+	0.0912917i
$876$	31.6443	+	31.6443i	1.06916	+	1.06916i
$877$	−23.8407	+	41.2933i	−0.805043	+	1.39437i	0.111219	+	0.993796i	$0.464524\pi$
$877$	−23.8407	+	41.2933i	−0.805043	+	1.39437i	−0.916262	+	0.400579i	$0.868809\pi$
$878$	32.2621	−	55.8796i	1.08879	−	1.88585i
$879$	−36.7017	−	36.7017i	−1.23792	−	1.23792i
$880$	3.25332	+	8.31591i	0.109669	+	0.280329i
$881$	4.43737	−	2.56192i	0.149499	−	0.0863133i	−0.423385	−	0.905950i	$-0.639158\pi$
$881$	4.43737	−	2.56192i	0.149499	−	0.0863133i	0.572884	+	0.819637i	$0.305825\pi$
$882$	−9.91554	+	5.72474i	−0.333873	+	0.192762i
$883$	14.8283	−	14.8283i	0.499014	−	0.499014i	−0.412117	−	0.911131i	$-0.635211\pi$
$883$	14.8283	−	14.8283i	0.499014	−	0.499014i	0.911131	+	0.412117i	$0.135211\pi$
$884$	−16.9849	+	31.3037i	−0.571263	+	1.05286i
$885$	−0.00113283	−	0.0101533i	−3.80796e−5	−	0.000341301i
$886$	14.1361	−	52.7568i	0.474913	−	1.77240i
$887$	10.1735	+	2.72597i	0.341592	+	0.0915293i	0.425537	−	0.904941i	$-0.360085\pi$
$887$	10.1735	+	2.72597i	0.341592	+	0.0915293i	−0.0839449	+	0.996470i	$0.526752\pi$
$888$	−1.63086	−	6.08644i	−0.0547280	−	0.204248i
$889$	0.473700	−	0.473700i	0.0158874	−	0.0158874i
$890$	−33.7989	+	13.2227i	−1.13294	+	0.443226i
$891$	15.4729	+	57.7457i	0.518362	+	1.93455i
$892$		−	36.4179i		−	1.21936i
$893$	3.76695	−	1.00935i	0.126056	−	0.0337767i
$894$	38.4949	+	66.6751i	1.28746	+	2.22995i
$895$	−16.7623	−	22.7638i	−0.560301	−	0.760911i
$896$			21.0349i			0.702725i
$897$	0.816594	−	0.861006i	0.0272653	−	0.0287481i
$898$	−14.5886	−	14.5886i	−0.486828	−	0.486828i
$899$	−3.09515	−	0.829344i	−0.103229	−	0.0276602i
$900$	10.6694	−	9.85667i	0.355646	−	0.328556i
$901$	17.7490	+	10.2474i	0.591307	+	0.341391i
$902$	−6.15528			−0.204948
$903$	14.6418	+	8.45347i	0.487250	+	0.281314i
$904$	26.4119	−	7.07704i	0.878446	−	0.235379i
$905$	2.02476	+	18.1476i	0.0673053	+	0.603245i
$906$	−31.7921	+	55.0656i	−1.05622	+	1.82943i
$907$	5.57417	−	20.8031i	0.185087	−	0.690755i	−0.809525	−	0.587086i	$-0.800275\pi$
$907$	5.57417	−	20.8031i	0.185087	−	0.690755i	0.994612	−	0.103669i	$-0.0330582\pi$
$908$	42.4147	+	73.4645i	1.40758	+	2.43800i
$909$	8.17608			0.271184
$910$	−2.87158	+	22.9979i	−0.0951918	+	0.762374i
$911$	−16.6400			−0.551309			−0.275654	−	0.961257i	$-0.588895\pi$
$911$	−16.6400			−0.551309			−0.275654	+	0.961257i	$0.588895\pi$
$912$	0.885047	+	1.53295i	0.0293068	+	0.0507609i
$913$	3.75401	−	14.0102i	0.124240	−	0.463669i
$914$	−24.1734	+	41.8696i	−0.799586	+	1.38492i
$915$	−4.83077	−	3.86101i	−0.159700	−	0.127641i
$916$	54.0305	−	14.4774i	1.78522	−	0.478347i
$917$	−5.63968	−	3.25607i	−0.186239	−	0.107525i
$918$	29.5701			0.975958
$919$	−5.95358	−	3.43730i	−0.196390	−	0.113386i	0.398580	−	0.917133i	$-0.369503\pi$
$919$	−5.95358	−	3.43730i	−0.196390	−	0.113386i	−0.594971	+	0.803747i	$0.702836\pi$
$920$	0.878776	+	0.133431i	0.0289724	+	0.00439911i
$921$	−28.2184	−	7.56111i	−0.929829	−	0.249147i
$922$	−8.08349	−	8.08349i	−0.266216	−	0.266216i
$923$	43.8175	−	1.16001i	1.44227	−	0.0381821i
$924$			42.4987i			1.39810i
$925$	−4.85389	+	4.48415i	−0.159595	+	0.147438i
$926$	−22.5973	−	39.1396i	−0.742593	−	1.28621i
$927$	1.39269	−	0.373170i	0.0457419	−	0.0122565i
$928$		−	62.5915i		−	2.05467i
$929$	−11.5057	−	42.9399i	−0.377490	−	1.40881i	−0.849672	−	0.527312i	$-0.823200\pi$
$929$	−11.5057	−	42.9399i	−0.377490	−	1.40881i	0.472182	−	0.881501i	$-0.343467\pi$
$930$	−3.02257	−	1.32265i	−0.0991141	−	0.0433714i
$931$	4.62617	−	4.62617i	0.151617	−	0.151617i
$932$	18.3543	+	68.4993i	0.601216	+	2.24377i
$933$	61.1290	+	16.3795i	2.00127	+	0.536240i
$934$	−17.6722	+	65.9535i	−0.578252	+	2.15806i
$935$	39.1054	−	4.36307i	1.27888	−	0.142688i
$936$	5.94800	+	5.64120i	0.194417	+	0.184388i
$937$	13.1724	−	13.1724i	0.430323	−	0.430323i	−0.458415	−	0.888738i	$-0.651583\pi$
$937$	13.1724	−	13.1724i	0.430323	−	0.430323i	0.888738	+	0.458415i	$0.151583\pi$
$938$	−15.1225	+	8.73096i	−0.493766	+	0.285076i
$939$	−29.1675	+	16.8399i	−0.951846	+	0.549548i
$940$	−20.1010	−	8.79602i	−0.655624	−	0.286895i
$941$	40.0251	+	40.0251i	1.30478	+	1.30478i	0.925130	+	0.379650i	$0.123955\pi$
$941$	40.0251	+	40.0251i	1.30478	+	1.30478i	0.379650	+	0.925130i	$0.376045\pi$
$942$	9.71510	−	16.8270i	0.316535	−	0.548255i
$943$	0.0414669	−	0.0718228i	0.00135035	−	0.00233887i
$944$	−0.00118881	−	0.00118881i	−3.86925e−5	−	3.86925e-5i
$945$	10.8458	−	4.24306i	0.352814	−	0.138027i
$946$	−70.9401	+	40.9573i	−2.30646	+	1.33164i
$947$	51.0040	−	29.4472i	1.65741	−	0.956904i	0.683501	−	0.729949i	$-0.260456\pi$
$947$	51.0040	−	29.4472i	1.65741	−	0.956904i	0.973905	−	0.226955i	$-0.0728770\pi$
$948$	−48.1479	+	48.1479i	−1.56377	+	1.56377i
$949$	25.7568	+	6.17584i	0.836102	+	0.200476i
$950$	−7.32157	+	11.5962i	−0.237543	+	0.376229i
$951$	8.00278	−	29.8668i	0.259508	−	0.968497i
$952$	9.53703	+	2.55544i	0.309097	+	0.0828223i
$953$	−4.62094	−	17.2456i	−0.149687	−	0.558640i	−0.999502	−	0.0315583i	$-0.989953\pi$
$953$	−4.62094	−	17.2456i	−0.149687	−	0.558640i	0.849815	−	0.527081i	$-0.176714\pi$
$954$	9.59336	−	9.59336i	0.310596	−	0.310596i
$955$	−13.2255	+	30.2236i	−0.427969	+	0.978012i
$956$	2.93807	+	10.9650i	0.0950240	+	0.354634i
$957$		−	105.398i		−	3.40703i
$958$	−67.6360	+	18.1230i	−2.18522	+	0.585528i
$959$	−2.42886	−	4.20691i	−0.0784320	−	0.135848i
$960$	8.69932	−	57.2935i	0.280769	−	1.84914i
$961$		−	30.8911i		−	0.996488i
$962$	−7.78218	−	7.38076i	−0.250908	−	0.237965i
$963$	9.73187	+	9.73187i	0.313605	+	0.313605i
$964$	−61.6333	−	16.5146i	−1.98507	−	0.531899i
$965$	−20.0165	−	27.1832i	−0.644353	−	0.875057i
$966$	−0.819363	−	0.473059i	−0.0263626	−	0.0152204i
$967$	−23.2093			−0.746360			−0.373180	−	0.927759i	$-0.621733\pi$
$967$	−23.2093			−0.746360			−0.373180	+	0.927759i	$0.621733\pi$
$968$	−39.1446	−	22.6001i	−1.25815	−	0.726395i
$969$	7.53407	−	2.01875i	0.242029	−	0.0648515i
$970$	20.9115	−	2.33314i	0.671429	−	0.0749127i
$971$	−21.1932	+	36.7078i	−0.680123	+	1.17801i	0.294820	+	0.955553i	$0.404740\pi$
$971$	−21.1932	+	36.7078i	−0.680123	+	1.17801i	−0.974943	+	0.222455i	$0.928593\pi$
$972$	7.54788	−	28.1691i	0.242098	−	0.903523i
$973$	−0.943975	−	1.63501i	−0.0302624	−	0.0524161i
$974$	−43.7367			−1.40141
$975$	9.72304	−	34.4731i	0.311387	−	1.10402i
$976$	−1.01768			−0.0325752
$977$	12.2049	+	21.1395i	0.390469	+	0.676312i	0.992511	−	0.122152i	$-0.0389796\pi$
$977$	12.2049	+	21.1395i	0.390469	+	0.676312i	−0.602043	+	0.798464i	$0.705646\pi$
$978$	−10.6541	+	39.7618i	−0.340682	+	1.27144i
$979$	−19.6945	+	34.1118i	−0.629438	+	1.09022i
$980$	−36.5819	+	4.08152i	−1.16857	+	0.130379i
$981$	−6.11424	+	1.63831i	−0.195213	+	0.0523071i
$982$	−68.8352	−	39.7420i	−2.19662	−	1.26822i
$983$	−4.47004			−0.142572			−0.0712860	−	0.997456i	$-0.522710\pi$
$983$	−4.47004			−0.142572			−0.0712860	+	0.997456i	$0.522710\pi$
$984$	2.06718	+	1.19349i	0.0658992	+	0.0380469i
$985$	−20.3806	−	27.6776i	−0.649379	−	0.881883i
$986$	−68.0220	−	18.2264i	−2.16626	−	0.580448i
$987$	5.74230	+	5.74230i	0.182779	+	0.182779i
$988$	−11.8410	−	6.42472i	−0.376712	−	0.204398i
$989$		−	1.10369i		−	0.0350952i
$990$	3.91016	−	25.7522i	0.124273	−	0.818460i
$991$	24.7675	+	42.8986i	0.786766	+	1.36272i	0.927938	+	0.372734i	$0.121580\pi$
$991$	24.7675	+	42.8986i	0.786766	+	1.36272i	−0.141172	+	0.989985i	$0.545087\pi$
$992$	−2.05398	+	0.550363i	−0.0652140	+	0.0174740i
$993$			33.9020i			1.07585i
$994$	−9.04516	−	33.7570i	−0.286895	−	1.07071i
$995$	10.2695	−	23.4683i	0.325565	−	0.743995i
$996$	−11.4384	+	11.4384i	−0.362439	+	0.362439i
$997$	−9.06967	−	33.8485i	−0.287239	−	1.07199i	−0.947187	−	0.320681i	$-0.896088\pi$
$997$	−9.06967	−	33.8485i	−0.287239	−	1.07199i	0.659948	−	0.751311i	$-0.270578\pi$
$998$	29.0380	+	7.78071i	0.919182	+	0.246294i
$999$	−1.39494	+	5.20597i	−0.0441338	+	0.164710i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.o.a.63.5	yes	20
3.2	odd	2		585.2.cf.a.388.1		20
5.2	odd	4		65.2.t.a.37.1	yes	20
5.3	odd	4		325.2.x.b.232.5		20
5.4	even	2		325.2.s.b.193.1		20
13.2	odd	12		845.2.f.e.408.10		20
13.3	even	3		845.2.k.e.268.1		20
13.4	even	6		845.2.o.f.488.1		20
13.5	odd	4		845.2.t.f.418.5		20
13.6	odd	12		65.2.t.a.58.1	yes	20
13.7	odd	12		845.2.t.g.188.5		20
13.8	odd	4		845.2.t.e.418.1		20
13.9	even	3		845.2.o.e.488.5		20
13.10	even	6		845.2.k.d.268.10		20
13.11	odd	12		845.2.f.d.408.1		20
13.12	even	2		845.2.o.g.258.1		20
15.2	even	4		585.2.dp.a.37.5		20
39.32	even	12		585.2.dp.a.253.5		20
65.2	even	12		845.2.k.e.577.1		20
65.7	even	12		845.2.o.g.357.1		20
65.12	odd	4		845.2.t.g.427.5		20
65.17	odd	12		845.2.t.e.657.1		20
65.19	odd	12		325.2.x.b.318.5		20
65.22	odd	12		845.2.t.f.657.5		20
65.32	even	12	inner	65.2.o.a.32.5	✓	20
65.37	even	12		845.2.k.d.577.10		20
65.42	odd	12		845.2.f.e.437.1		20
65.47	even	4		845.2.o.f.587.1		20
65.57	even	4		845.2.o.e.587.5		20
65.58	even	12		325.2.s.b.32.1		20
65.62	odd	12		845.2.f.d.437.10		20
195.32	odd	12		585.2.cf.a.487.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.5	✓	20	65.32	even	12	inner
65.2.o.a.63.5	yes	20	1.1	even	1	trivial
65.2.t.a.37.1	yes	20	5.2	odd	4
65.2.t.a.58.1	yes	20	13.6	odd	12
325.2.s.b.32.1		20	65.58	even	12
325.2.s.b.193.1		20	5.4	even	2
325.2.x.b.232.5		20	5.3	odd	4
325.2.x.b.318.5		20	65.19	odd	12
585.2.cf.a.388.1		20	3.2	odd	2
585.2.cf.a.487.1		20	195.32	odd	12
585.2.dp.a.37.5		20	15.2	even	4
585.2.dp.a.253.5		20	39.32	even	12
845.2.f.d.408.1		20	13.11	odd	12
845.2.f.d.437.10		20	65.62	odd	12
845.2.f.e.408.10		20	13.2	odd	12
845.2.f.e.437.1		20	65.42	odd	12
845.2.k.d.268.10		20	13.10	even	6
845.2.k.d.577.10		20	65.37	even	12
845.2.k.e.268.1		20	13.3	even	3
845.2.k.e.577.1		20	65.2	even	12
845.2.o.e.488.5		20	13.9	even	3
845.2.o.e.587.5		20	65.57	even	4
845.2.o.f.488.1		20	13.4	even	6
845.2.o.f.587.1		20	65.47	even	4
845.2.o.g.258.1		20	13.12	even	2
845.2.o.g.357.1		20	65.7	even	12
845.2.t.e.418.1		20	13.8	odd	4
845.2.t.e.657.1		20	65.17	odd	12
845.2.t.f.418.5		20	13.5	odd	4
845.2.t.f.657.5		20	65.22	odd	12
845.2.t.g.188.5		20	13.7	odd	12
845.2.t.g.427.5		20	65.12	odd	4

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.12540 + 1.94926i) q^{2} +(0.514229 - 1.91913i) q^{3} +(-1.53307 + 2.65535i) q^{4} +(-2.22228 + 0.247944i) q^{5} +(4.31958 - 1.15743i) q^{6} +(-1.10607 - 0.638592i) q^{7} -2.39966 q^{8} +(-0.820542 - 0.473740i) q^{9} +O(q^{10})\)	\(q+(1.12540 + 1.94926i) q^{2} +(0.514229 - 1.91913i) q^{3} +(-1.53307 + 2.65535i) q^{4} +(-2.22228 + 0.247944i) q^{5} +(4.31958 - 1.15743i) q^{6} +(-1.10607 - 0.638592i) q^{7} -2.39966 q^{8} +(-0.820542 - 0.473740i) q^{9} +(-2.98427 - 4.05275i) q^{10} +(-5.27612 - 1.41373i) q^{11} +(4.30760 + 4.30760i) q^{12} +(3.50617 + 0.840691i) q^{13} -2.87469i q^{14} +(-0.666923 + 4.39234i) q^{15} +(0.365551 + 0.633152i) q^{16} +(3.11179 - 0.833802i) q^{17} -2.13259i q^{18} +(0.315395 + 1.17707i) q^{19} +(2.74852 - 6.28104i) q^{20} +(-1.79431 + 1.79431i) q^{21} +(-3.18204 - 11.8755i) q^{22} +(0.160006 + 0.0428736i) q^{23} +(-1.23397 + 4.60524i) q^{24} +(4.87705 - 1.10200i) q^{25} +(2.30714 + 7.78054i) q^{26} +(2.88358 - 2.88358i) q^{27} +(3.39137 - 1.95801i) q^{28} +(-8.41068 + 4.85591i) q^{29} +(-9.31234 + 3.64315i) q^{30} +(0.233305 + 0.233305i) q^{31} +(-3.22244 + 5.58143i) q^{32} +(-5.42627 + 9.39857i) q^{33} +(5.12732 + 5.12732i) q^{34} +(2.61634 + 1.14488i) q^{35} +(2.51589 - 1.45255i) q^{36} +(-1.14457 + 0.660816i) q^{37} +(-1.93947 + 1.93947i) q^{38} +(3.41637 - 6.29648i) q^{39} +(5.33270 - 0.594981i) q^{40} +(0.129579 - 0.483595i) q^{41} +(-5.51690 - 1.47825i) q^{42} +(-1.72444 - 6.43569i) q^{43} +(11.8426 - 11.8426i) q^{44} +(1.94093 + 0.849334i) q^{45} +(0.0965002 + 0.360144i) q^{46} -3.20027i q^{47} +(1.40308 - 0.375953i) q^{48} +(-2.68440 - 4.64952i) q^{49} +(7.63673 + 8.26642i) q^{50} -6.40069i q^{51} +(-7.60752 + 8.02127i) q^{52} +(4.49845 + 4.49845i) q^{53} +(8.86603 + 2.37565i) q^{54} +(12.0755 + 1.83353i) q^{55} +(2.65420 + 1.53240i) q^{56} +2.42113 q^{57} +(-18.9308 - 10.9297i) q^{58} +(-0.00222123 + 0.000595178i) q^{59} +(-10.6407 - 8.50465i) q^{60} +(-0.695993 + 1.20550i) q^{61} +(-0.192209 + 0.717332i) q^{62} +(0.605053 + 1.04798i) q^{63} -13.0440 q^{64} +(-8.00014 - 0.998915i) q^{65} -24.4270 q^{66} +(-3.03718 - 5.26055i) q^{67} +(-2.55655 + 9.54117i) q^{68} +(0.164560 - 0.285026i) q^{69} +(0.712764 + 6.38837i) q^{70} +(11.7428 - 3.14648i) q^{71} +(1.96902 + 1.13681i) q^{72} +7.34614 q^{73} +(-2.57620 - 1.48737i) q^{74} +(0.393034 - 9.92635i) q^{75} +(-3.60906 - 0.967044i) q^{76} +(4.93298 + 4.93298i) q^{77} +(16.1182 - 0.426708i) q^{78} +11.1774i q^{79} +(-0.969342 - 1.31640i) q^{80} +(-5.47236 - 9.47841i) q^{81} +(1.08848 - 0.291657i) q^{82} +2.65539i q^{83} +(-2.01373 - 7.51533i) q^{84} +(-6.70854 + 2.62449i) q^{85} +(10.6041 - 10.6041i) q^{86} +(4.99409 + 18.6382i) q^{87} +(12.6609 + 3.39247i) q^{88} +(1.86638 - 6.96542i) q^{89} +(0.528764 + 4.73922i) q^{90} +(-3.34123 - 3.16888i) q^{91} +(-0.359145 + 0.359145i) q^{92} +(0.567713 - 0.327769i) q^{93} +(6.23815 - 3.60160i) q^{94} +(-0.992745 - 2.53758i) q^{95} +(9.05440 + 9.05440i) q^{96} +(-2.09035 + 3.62059i) q^{97} +(6.04207 - 10.4652i) q^{98} +(3.65954 + 3.65954i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9} - 10 q^{10} - 16 q^{11} + 24 q^{12} + 2 q^{13} + 12 q^{15} - 2 q^{16} - 10 q^{17} + 20 q^{19} + 14 q^{20} + 4 q^{21} + 16 q^{22} - 2 q^{23} - 32 q^{24} - 18 q^{25} - 24 q^{26} + 4 q^{27} + 6 q^{28} + 14 q^{30} - 6 q^{32} - 18 q^{33} - 2 q^{34} - 20 q^{35} + 36 q^{36} + 42 q^{37} + 8 q^{38} - 4 q^{39} - 16 q^{40} + 10 q^{41} - 56 q^{42} - 22 q^{43} + 36 q^{44} + 52 q^{45} + 4 q^{46} + 28 q^{48} - 18 q^{49} + 44 q^{50} + 46 q^{52} - 10 q^{53} + 48 q^{54} + 26 q^{55} - 12 q^{57} - 90 q^{58} + 16 q^{59} - 92 q^{60} - 16 q^{61} - 40 q^{62} - 32 q^{63} - 20 q^{64} + 8 q^{65} - 32 q^{66} - 58 q^{67} + 28 q^{68} + 16 q^{69} + 32 q^{70} - 16 q^{71} - 66 q^{72} + 72 q^{73} - 18 q^{74} - 34 q^{75} - 64 q^{76} + 28 q^{77} + 32 q^{78} - 34 q^{80} - 14 q^{81} + 22 q^{82} + 40 q^{84} - 6 q^{85} + 60 q^{86} + 62 q^{87} + 50 q^{88} + 6 q^{89} - 46 q^{90} + 8 q^{91} - 8 q^{92} + 48 q^{93} + 48 q^{94} + 14 q^{95} + 56 q^{96} - 22 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9 - 10 * q^10 - 16 * q^11 + 24 * q^12 + 2 * q^13 + 12 * q^15 - 2 * q^16 - 10 * q^17 + 20 * q^19 + 14 * q^20 + 4 * q^21 + 16 * q^22 - 2 * q^23 - 32 * q^24 - 18 * q^25 - 24 * q^26 + 4 * q^27 + 6 * q^28 + 14 * q^30 - 6 * q^32 - 18 * q^33 - 2 * q^34 - 20 * q^35 + 36 * q^36 + 42 * q^37 + 8 * q^38 - 4 * q^39 - 16 * q^40 + 10 * q^41 - 56 * q^42 - 22 * q^43 + 36 * q^44 + 52 * q^45 + 4 * q^46 + 28 * q^48 - 18 * q^49 + 44 * q^50 + 46 * q^52 - 10 * q^53 + 48 * q^54 + 26 * q^55 - 12 * q^57 - 90 * q^58 + 16 * q^59 - 92 * q^60 - 16 * q^61 - 40 * q^62 - 32 * q^63 - 20 * q^64 + 8 * q^65 - 32 * q^66 - 58 * q^67 + 28 * q^68 + 16 * q^69 + 32 * q^70 - 16 * q^71 - 66 * q^72 + 72 * q^73 - 18 * q^74 - 34 * q^75 - 64 * q^76 + 28 * q^77 + 32 * q^78 - 34 * q^80 - 14 * q^81 + 22 * q^82 + 40 * q^84 - 6 * q^85 + 60 * q^86 + 62 * q^87 + 50 * q^88 + 6 * q^89 - 46 * q^90 + 8 * q^91 - 8 * q^92 + 48 * q^93 + 48 * q^94 + 14 * q^95 + 56 * q^96 - 22 * q^97 + 4 * q^98 - 60 * q^99

Introduction

L-functions

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