LMFDB - Embedded newform 403.2.bt.a.82.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(82,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 8]))

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

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

chi := DirichletCharacter("403.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bt (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$35$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			82.14
Character	$\chi$	$=$	403.82
Dual form			403.2.bt.a.231.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.136295 + 0.641215i) q^{2} +(-1.88071 + 0.399758i) q^{3} +(1.43451 + 0.638685i) q^{4} +(-1.94312 + 1.12186i) q^{5} -1.26043i q^{6} +(1.23396 + 1.69841i) q^{7} +(-1.37568 + 1.89347i) q^{8} +(0.636641 - 0.283451i) q^{9} +O(q^{10})$	\(q+(-0.136295 + 0.641215i) q^{2} +(-1.88071 + 0.399758i) q^{3} +(1.43451 + 0.638685i) q^{4} +(-1.94312 + 1.12186i) q^{5} -1.26043i q^{6} +(1.23396 + 1.69841i) q^{7} +(-1.37568 + 1.89347i) q^{8} +(0.636641 - 0.283451i) q^{9} +(-0.454518 - 1.39886i) q^{10} +(-0.250356 - 0.344586i) q^{11} +(-2.95322 - 0.627727i) q^{12} +(3.33628 - 1.36721i) q^{13} +(-1.25723 + 0.559753i) q^{14} +(3.20598 - 2.88668i) q^{15} +(1.07481 + 1.19369i) q^{16} +(-4.79106 - 3.48091i) q^{17} +(0.0949823 + 0.446857i) q^{18} +(-7.36179 + 2.39199i) q^{19} +(-3.50394 + 0.368279i) q^{20} +(-2.99968 - 2.70093i) q^{21} +(0.255076 - 0.113567i) q^{22} +(-3.78436 + 1.68491i) q^{23} +(1.83034 - 4.11101i) q^{24} +(0.0171474 - 0.0297001i) q^{25} +(0.421958 + 2.32561i) q^{26} +(3.58254 - 2.60286i) q^{27} +(0.685387 + 3.22449i) q^{28} +(1.44065 + 0.306219i) q^{29} +(1.41402 + 2.44916i) q^{30} +(4.61368 - 3.11672i) q^{31} +(-4.96569 + 2.86694i) q^{32} +(0.608600 + 0.547986i) q^{33} +(2.88501 - 2.59767i) q^{34} +(-4.30312 - 1.91587i) q^{35} +1.09430 q^{36} +(-7.86840 + 4.54282i) q^{37} +(-0.530409 - 5.04650i) q^{38} +(-5.72803 + 3.90503i) q^{39} +(0.548914 - 5.22256i) q^{40} +(2.44156 - 0.793311i) q^{41} +(2.14072 - 1.55532i) q^{42} +(0.915451 + 2.81747i) q^{43} +(-0.139057 - 0.654211i) q^{44} +(-0.919078 + 1.26500i) q^{45} +(-0.564600 - 2.65623i) q^{46} +(-10.3020 - 3.34733i) q^{47} +(-2.49859 - 1.81533i) q^{48} +(0.801204 - 2.46585i) q^{49} +(0.0167071 + 0.0150431i) q^{50} +(10.4021 + 4.63133i) q^{51} +(5.65914 + 0.169557i) q^{52} +(0.0461789 - 0.439363i) q^{53} +(1.18072 + 2.65193i) q^{54} +(0.873051 + 0.388707i) q^{55} -4.91342 q^{56} +(12.8892 - 7.44158i) q^{57} +(-0.392705 + 0.882029i) q^{58} +(9.93229 + 3.22720i) q^{59} +(6.44269 - 2.09336i) q^{60} +(1.92832 + 3.33995i) q^{61} +(1.36967 + 3.38316i) q^{62} +(1.26701 + 0.731506i) q^{63} +(-0.168801 - 0.519515i) q^{64} +(-4.94897 + 6.39949i) q^{65} +(-0.434326 + 0.315556i) q^{66} +12.0362i q^{67} +(-4.64962 - 8.05338i) q^{68} +(6.44374 - 4.68165i) q^{69} +(1.81498 - 2.49810i) q^{70} +(4.87151 + 10.9416i) q^{71} +(-0.339112 + 1.59540i) q^{72} +(-0.0417809 + 0.0938414i) q^{73} +(-1.84051 - 5.66450i) q^{74} +(-0.0203764 + 0.0627122i) q^{75} +(-12.0883 - 1.27053i) q^{76} +(0.276316 - 0.850414i) q^{77} +(-1.72327 - 4.20513i) q^{78} +(7.78491 - 3.46607i) q^{79} +(-3.42763 - 1.11371i) q^{80} +(-7.09614 + 7.88106i) q^{81} +(0.175912 + 1.67369i) q^{82} +(12.1751 + 10.9625i) q^{83} +(-2.57804 - 5.79036i) q^{84} +(13.2147 + 1.38892i) q^{85} +(-1.93138 + 0.202996i) q^{86} -2.83186 q^{87} +0.996874 q^{88} +(7.04005 - 0.739939i) q^{89} +(-0.685873 - 0.761740i) q^{90} +(6.43892 + 3.97927i) q^{91} -6.50482 q^{92} +(-7.43109 + 7.70601i) q^{93} +(3.55047 - 6.14959i) q^{94} +(11.6214 - 12.9068i) q^{95} +(8.19296 - 7.37697i) q^{96} +(-4.12865 + 9.27309i) q^{97} +(1.47194 + 0.849826i) q^{98} +(-0.257060 - 0.148414i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 9 q^{2} - 3 q^{3} - 35 q^{4} - 15 q^{7} + 45 q^{8} + 24 q^{9}+O(q^{10}) $ 280 * q - 9 * q^2 - 3 * q^3 - 35 * q^4 - 15 * q^7 + 45 * q^8 + 24 * q^9	\( 280 q - 9 q^{2} - 3 q^{3} - 35 q^{4} - 15 q^{7} + 45 q^{8} + 24 q^{9} + 3 q^{10} - 8 q^{12} - 6 q^{13} + 4 q^{14} - 45 q^{15} + 23 q^{16} + 27 q^{17} + 45 q^{18} - 15 q^{19} - 12 q^{20} - 76 q^{21} + 41 q^{22} - 10 q^{23} - 33 q^{24} + 96 q^{25} + 9 q^{26} - 24 q^{27} - 32 q^{28} + 13 q^{29} + 36 q^{30} + 2 q^{31} - 141 q^{32} - 93 q^{33} - 9 q^{34} - 43 q^{35} - 194 q^{36} + 3 q^{37} - 49 q^{38} + 50 q^{39} - 75 q^{40} - 15 q^{41} + 17 q^{42} + 33 q^{43} + 18 q^{44} - 15 q^{45} - 9 q^{46} - 59 q^{48} + 3 q^{49} + 36 q^{50} + 47 q^{51} - 56 q^{52} + 12 q^{53} - 33 q^{54} - 5 q^{55} - 50 q^{56} - 105 q^{57} - 3 q^{58} - 15 q^{59} + 90 q^{60} - 57 q^{61} - 72 q^{62} + 201 q^{63} + 13 q^{64} - 43 q^{65} + 22 q^{66} - 71 q^{68} - 7 q^{69} - 42 q^{71} + 90 q^{72} + 9 q^{73} - 113 q^{74} + 45 q^{75} + 14 q^{76} - 24 q^{77} + 61 q^{78} + 54 q^{79} + 30 q^{80} + 106 q^{81} + 16 q^{82} + 54 q^{83} + 60 q^{84} + 18 q^{85} + 84 q^{86} + 42 q^{87} - 98 q^{88} - 99 q^{89} + 11 q^{90} + 60 q^{91} + 266 q^{92} - 104 q^{93} + 33 q^{94} - 120 q^{95} + 204 q^{96} - 50 q^{97} - 15 q^{98} - 168 q^{99}+O(q^{100}) \) 280 * q - 9 * q^2 - 3 * q^3 - 35 * q^4 - 15 * q^7 + 45 * q^8 + 24 * q^9 + 3 * q^10 - 8 * q^12 - 6 * q^13 + 4 * q^14 - 45 * q^15 + 23 * q^16 + 27 * q^17 + 45 * q^18 - 15 * q^19 - 12 * q^20 - 76 * q^21 + 41 * q^22 - 10 * q^23 - 33 * q^24 + 96 * q^25 + 9 * q^26 - 24 * q^27 - 32 * q^28 + 13 * q^29 + 36 * q^30 + 2 * q^31 - 141 * q^32 - 93 * q^33 - 9 * q^34 - 43 * q^35 - 194 * q^36 + 3 * q^37 - 49 * q^38 + 50 * q^39 - 75 * q^40 - 15 * q^41 + 17 * q^42 + 33 * q^43 + 18 * q^44 - 15 * q^45 - 9 * q^46 - 59 * q^48 + 3 * q^49 + 36 * q^50 + 47 * q^51 - 56 * q^52 + 12 * q^53 - 33 * q^54 - 5 * q^55 - 50 * q^56 - 105 * q^57 - 3 * q^58 - 15 * q^59 + 90 * q^60 - 57 * q^61 - 72 * q^62 + 201 * q^63 + 13 * q^64 - 43 * q^65 + 22 * q^66 - 71 * q^68 - 7 * q^69 - 42 * q^71 + 90 * q^72 + 9 * q^73 - 113 * q^74 + 45 * q^75 + 14 * q^76 - 24 * q^77 + 61 * q^78 + 54 * q^79 + 30 * q^80 + 106 * q^81 + 16 * q^82 + 54 * q^83 + 60 * q^84 + 18 * q^85 + 84 * q^86 + 42 * q^87 - 98 * q^88 - 99 * q^89 + 11 * q^90 + 60 * q^91 + 266 * q^92 - 104 * q^93 + 33 * q^94 - 120 * q^95 + 204 * q^96 - 50 * q^97 - 15 * q^98 - 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{15}\right)$

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 $

$2$	−0.136295	+	0.641215i	−0.0963748	+	0.453408i	0.903326	+	0.428954i	$0.141118\pi$
$2$	−0.136295	+	0.641215i	−0.0963748	+	0.453408i	−0.999701	+	0.0244534i	$0.992215\pi$
$3$	−1.88071	+	0.399758i	−1.08583	+	0.230800i	−0.715861	−	0.698243i	$-0.753965\pi$
$3$	−1.88071	+	0.399758i	−1.08583	+	0.230800i	−0.369970	+	0.929044i	$0.620632\pi$
$4$	1.43451	+	0.638685i	0.717255	+	0.319343i
$5$	−1.94312	+	1.12186i	−0.868990	+	0.501712i	−0.867013	−	0.498286i	$-0.833963\pi$
$5$	−1.94312	+	1.12186i	−0.868990	+	0.501712i	−0.00197775	+	0.999998i	$0.500630\pi$
$6$		−	1.26043i		−	0.514567i
$7$	1.23396	+	1.69841i	0.466395	+	0.641937i	0.975819	−	0.218578i	$-0.0701418\pi$
$7$	1.23396	+	1.69841i	0.466395	+	0.641937i	−0.509425	+	0.860515i	$0.670142\pi$
$8$	−1.37568	+	1.89347i	−0.486378	+	0.669442i
$9$	0.636641	−	0.283451i	0.212214	−	0.0944836i
$10$	−0.454518	−	1.39886i	−0.143731	−	0.442359i
$11$	−0.250356	−	0.344586i	−0.0754853	−	0.103897i	0.769605	−	0.638521i	$-0.220453\pi$
$11$	−0.250356	−	0.344586i	−0.0754853	−	0.103897i	−0.845090	+	0.534624i	$0.820453\pi$
$12$	−2.95322	−	0.627727i	−0.852522	−	0.181209i
$13$	3.33628	−	1.36721i	0.925317	−	0.379195i
$13$	3.33628	−	1.36721i	0.925317	−	0.379195i
$14$	−1.25723	+	0.559753i	−0.336008	+	0.149600i
$15$	3.20598	−	2.88668i	0.827781	−	0.745337i
$16$	1.07481	+	1.19369i	0.268701	+	0.298423i
$17$	−4.79106	−	3.48091i	−1.16200	−	0.844245i	−0.171973	−	0.985102i	$-0.555014\pi$
$17$	−4.79106	−	3.48091i	−1.16200	−	0.844245i	−0.990030	+	0.140857i	$0.955014\pi$
$18$	0.0949823	+	0.446857i	0.0223875	+	0.105325i
$19$	−7.36179	+	2.39199i	−1.68891	+	0.548760i	−0.986607	−	0.163118i	$-0.947845\pi$
$19$	−7.36179	+	2.39199i	−1.68891	+	0.548760i	−0.702303	+	0.711878i	$0.747845\pi$
$20$	−3.50394	+	0.368279i	−0.783506	+	0.0823498i
$21$	−2.99968	−	2.70093i	−0.654585	−	0.589391i
$22$	0.255076	−	0.113567i	0.0543824	−	0.0242126i
$23$	−3.78436	+	1.68491i	−0.789093	+	0.351327i	−0.761394	−	0.648289i	$-0.775485\pi$
$23$	−3.78436	+	1.68491i	−0.789093	+	0.351327i	−0.0276993	+	0.999616i	$0.508818\pi$
$24$	1.83034	−	4.11101i	0.373617	−	0.839156i
$25$	0.0171474	−	0.0297001i	0.00342948	−	0.00594003i
$26$	0.421958	+	2.32561i	0.0827528	+	0.456091i
$27$	3.58254	−	2.60286i	0.689459	−	0.500922i
$28$	0.685387	+	3.22449i	0.129526	+	0.609372i
$29$	1.44065	+	0.306219i	0.267522	+	0.0568635i	0.339719	−	0.940527i	$-0.389668\pi$
$29$	1.44065	+	0.306219i	0.267522	+	0.0568635i	−0.0721977	+	0.997390i	$0.523001\pi$
$30$	1.41402	+	2.44916i	0.258164	+	0.447154i
$31$	4.61368	−	3.11672i	0.828642	−	0.559779i
$31$	4.61368	−	3.11672i	0.828642	−	0.559779i
$32$	−4.96569	+	2.86694i	−0.877818	+	0.506809i
$33$	0.608600	+	0.547986i	0.105944	+	0.0953921i
$34$	2.88501	−	2.59767i	0.494775	−	0.445497i
$35$	−4.30312	−	1.91587i	−0.727360	−	0.323841i
$36$	1.09430			0.182384
$37$	−7.86840	+	4.54282i	−1.29356	+	0.746835i	−0.979283	−	0.202497i	$-0.935094\pi$
$37$	−7.86840	+	4.54282i	−1.29356	+	0.746835i	−0.314274	+	0.949332i	$0.601761\pi$
$38$	−0.530409	−	5.04650i	−0.0860437	−	0.818651i
$39$	−5.72803	+	3.90503i	−0.917219	+	0.625305i
$40$	0.548914	−	5.22256i	0.0867909	−	0.825760i
$41$	2.44156	−	0.793311i	0.381308	−	0.123894i	−0.112090	−	0.993698i	$-0.535755\pi$
$41$	2.44156	−	0.793311i	0.381308	−	0.123894i	0.493398	+	0.869804i	$0.335755\pi$
$42$	2.14072	−	1.55532i	0.330320	−	0.239991i
$43$	0.915451	+	2.81747i	0.139605	+	0.429660i	0.996278	−	0.0862001i	$-0.0274724\pi$
$43$	0.915451	+	2.81747i	0.139605	+	0.429660i	−0.856673	+	0.515860i	$0.827472\pi$
$44$	−0.139057	−	0.654211i	−0.0209636	−	0.0986260i
$45$	−0.919078	+	1.26500i	−0.137008	+	0.188575i
$46$	−0.564600	−	2.65623i	−0.0832457	−	0.391640i
$47$	−10.3020	−	3.34733i	−1.50270	−	0.488258i	−0.561899	−	0.827206i	$-0.689929\pi$
$47$	−10.3020	−	3.34733i	−1.50270	−	0.488258i	−0.940805	+	0.338947i	$0.889929\pi$
$48$	−2.49859	−	1.81533i	−0.360640	−	0.262020i
$49$	0.801204	−	2.46585i	0.114458	−	0.352265i
$50$	0.0167071	+	0.0150431i	0.00236274	+	0.00212742i
$51$	10.4021	+	4.63133i	1.45659	+	0.648516i
$52$	5.65914	+	0.169557i	0.784781	+	0.0235133i
$53$	0.0461789	−	0.439363i	0.00634317	−	0.0603512i	−0.990892	−	0.134656i	$-0.957007\pi$
$53$	0.0461789	−	0.439363i	0.00634317	−	0.0603512i	0.997236	+	0.0743047i	$0.0236738\pi$
$54$	1.18072	+	2.65193i	0.160675	+	0.360882i
$55$	0.873051	+	0.388707i	0.117722	+	0.0524133i
$56$	−4.91342			−0.656584
$57$	12.8892	−	7.44158i	1.70722	−	0.985661i
$58$	−0.392705	+	0.882029i	−0.0515647	+	0.115816i
$59$	9.93229	+	3.22720i	1.29307	+	0.420145i	0.873167	−	0.487422i	$-0.162063\pi$
$59$	9.93229	+	3.22720i	1.29307	+	0.420145i	0.419907	+	0.907567i	$0.362063\pi$
$60$	6.44269	−	2.09336i	0.831748	−	0.270251i
$61$	1.92832	+	3.33995i	0.246896	+	0.427636i	0.962663	−	0.270703i	$-0.0872561\pi$
$61$	1.92832	+	3.33995i	0.246896	+	0.427636i	−0.715767	+	0.698339i	$0.753923\pi$
$62$	1.36967	+	3.38316i	0.173948	+	0.429661i
$63$	1.26701	+	0.731506i	0.159628	+	0.0921611i
$64$	−0.168801	−	0.519515i	−0.0211001	−	0.0649394i
$65$	−4.94897	+	6.39949i	−0.613845	+	0.793759i
$66$	−0.434326	+	0.315556i	−0.0534618	+	0.0388423i
$67$			12.0362i			1.47046i	0.677818	+	0.735229i	$0.262926\pi$
$67$			12.0362i			1.47046i	−0.677818	+	0.735229i	$0.737074\pi$
$68$	−4.64962	−	8.05338i	−0.563850	−	0.976616i
$69$	6.44374	−	4.68165i	0.775735	−	0.563605i
$70$	1.81498	−	2.49810i	0.216931	−	0.298580i
$71$	4.87151	+	10.9416i	0.578142	+	1.29853i	0.931739	+	0.363129i	$0.118292\pi$
$71$	4.87151	+	10.9416i	0.578142	+	1.29853i	−0.353597	+	0.935398i	$0.615042\pi$
$72$	−0.339112	+	1.59540i	−0.0399647	+	0.188019i
$73$	−0.0417809	+	0.0938414i	−0.00489008	+	0.0109833i	−0.915974	−	0.401238i	$-0.868580\pi$
$73$	−0.0417809	+	0.0938414i	−0.00489008	+	0.0109833i	0.911084	+	0.412221i	$0.135247\pi$
$74$	−1.84051	−	5.66450i	−0.213955	−	0.658485i
$75$	−0.0203764	+	0.0627122i	−0.00235287	+	0.00724139i
$76$	−12.0883	−	1.27053i	−1.38662	−	0.145740i
$77$	0.276316	−	0.850414i	0.0314891	−	0.0969136i
$78$	−1.72327	−	4.20513i	−0.195121	−	0.476138i
$79$	7.78491	−	3.46607i	0.875871	−	0.389963i	0.0809804	−	0.996716i	$-0.474195\pi$
$79$	7.78491	−	3.46607i	0.875871	−	0.389963i	0.794891	+	0.606753i	$0.207528\pi$
$80$	−3.42763	−	1.11371i	−0.383221	−	0.124516i
$81$	−7.09614	+	7.88106i	−0.788460	+	0.875674i
$82$	0.175912	+	1.67369i	0.0194262	+	0.184828i
$83$	12.1751	+	10.9625i	1.33639	+	1.20329i	0.961039	+	0.276412i	$0.0891455\pi$
$83$	12.1751	+	10.9625i	1.33639	+	1.20329i	0.375354	+	0.926882i	$0.377521\pi$
$84$	−2.57804	−	5.79036i	−0.281287	−	0.631780i
$85$	13.2147	+	1.38892i	1.43334	+	0.150650i
$86$	−1.93138	+	0.202996i	−0.208266	+	0.0218896i
$87$	−2.83186			−0.303607
$88$	0.996874			0.106267
$89$	7.04005	−	0.739939i	0.746244	−	0.0784334i	0.276229	−	0.961092i	$-0.410915\pi$
$89$	7.04005	−	0.739939i	0.746244	−	0.0784334i	0.470015	+	0.882658i	$0.344249\pi$
$90$	−0.685873	−	0.761740i	−0.0722974	−	0.0802944i
$91$	6.43892	+	3.97927i	0.674982	+	0.417140i
$92$	−6.50482			−0.678175
$93$	−7.43109	+	7.70601i	−0.770568	+	0.799076i
$94$	3.55047	−	6.14959i	0.366203	−	0.634282i
$95$	11.6214	−	12.9068i	1.19233	−	1.32421i
$96$	8.19296	−	7.37697i	0.836190	−	0.752909i
$97$	−4.12865	+	9.27309i	−0.419201	+	0.941540i	0.573305	+	0.819342i	$0.305661\pi$
$97$	−4.12865	+	9.27309i	−0.419201	+	0.941540i	−0.992506	+	0.122198i	$0.961006\pi$
$98$	1.47194	+	0.849826i	0.148689	+	0.0858454i
$99$	−0.257060	−	0.148414i	−0.0258355	−	0.0149161i
$100$	0.0435671	−	0.0316534i	0.00435671	−	0.00316534i
$101$	−3.88885	+	1.73143i	−0.386955	+	0.172283i	−0.590988	−	0.806681i	$-0.701262\pi$
$101$	−3.88885	+	1.73143i	−0.386955	+	0.172283i	0.204033	+	0.978964i	$0.434595\pi$
$102$	−4.38743	+	6.03879i	−0.434421	+	0.597929i
$103$	7.77623	−	8.63638i	0.766215	−	0.850968i	−0.226177	−	0.974086i	$-0.572623\pi$
$103$	7.77623	−	8.63638i	0.766215	−	0.850968i	0.992392	+	0.123118i	$0.0392894\pi$
$104$	−2.00090	+	8.19798i	−0.196204	+	0.803878i
$105$	8.85882	+	1.88300i	0.864532	+	0.183762i
$106$	0.275433	+	0.0894935i	0.0267524	+	0.00869237i
$107$	−1.76111	+	16.7558i	−0.170252	+	1.61984i	0.492022	+	0.870583i	$0.336258\pi$
$107$	−1.76111	+	16.7558i	−0.170252	+	1.61984i	−0.662274	+	0.749261i	$0.730409\pi$
$108$	6.80159	−	1.44572i	0.654484	−	0.139115i
$109$	−6.89524	−	2.24040i	−0.660445	−	0.214591i	−0.0404307	−	0.999182i	$-0.512873\pi$
$109$	−6.89524	−	2.24040i	−0.660445	−	0.214591i	−0.620014	+	0.784591i	$0.712873\pi$
$110$	−0.368237	+	0.506835i	−0.0351100	+	0.0483248i
$111$	12.9822	−	11.6892i	1.23221	−	1.10949i
$112$	−0.701103	+	3.29843i	−0.0662480	+	0.311672i
$113$	−0.967176	−	9.20206i	−0.0909842	−	0.865657i	−0.940888	−	0.338719i	$-0.890007\pi$
$113$	−0.967176	−	9.20206i	−0.0909842	−	0.865657i	0.849903	−	0.526938i	$-0.176660\pi$
$114$	3.01493	+	9.27900i	0.282374	+	0.869058i
$115$	5.46324	−	7.51950i	0.509450	−	0.701197i
$116$	1.87105	+	1.35939i	0.173722	+	0.126217i
$117$	1.73647	−	1.81609i	0.160537	−	0.167898i
$118$	−3.42304	+	5.92889i	−0.315117	+	0.545798i
$119$		−	12.4325i		−	1.13968i
$120$	1.05541	+	10.0416i	0.0963456	+	0.916667i
$121$	3.34313	−	10.2891i	0.303921	−	0.935371i
$122$	−2.40444	+	0.781251i	−0.217688	+	0.0707312i
$123$	−4.27475	+	2.46803i	−0.385441	+	0.222534i
$124$	8.60898	−	1.52427i	0.773109	−	0.136883i
$125$		−	11.1417i		−	0.996541i
$126$	−0.641739	+	0.712723i	−0.0571707	+	0.0634945i
$127$	−17.2432	+	3.66515i	−1.53008	+	0.325229i	−0.894594	−	0.446880i	$-0.852535\pi$
$127$	−17.2432	+	3.66515i	−1.53008	+	0.325229i	−0.635490	+	0.772109i	$0.719202\pi$
$128$	−11.0488	+	1.16128i	−0.976587	+	0.102643i
$129$	−2.84801	−	4.93289i	−0.250753	−	0.434317i
$130$	−3.42893	−	4.04557i	−0.300737	−	0.354820i
$131$	1.31155	+	12.4785i	0.114590	+	1.09026i	0.889106	+	0.457701i	$0.151327\pi$
$131$	1.31155	+	12.4785i	0.114590	+	1.09026i	−0.774516	+	0.632554i	$0.782006\pi$
$132$	0.523052	+	1.17479i	0.0455258	+	0.102253i
$133$	−13.1467	−	9.55167i	−1.13997	−	0.828235i
$134$	−7.71781	−	1.64047i	−0.666717	−	0.141715i
$135$	−4.04125	+	9.07679i	−0.347815	+	0.781206i
$136$	13.1820	−	4.28309i	1.13035	−	0.367272i
$137$	−5.57614	+	5.02078i	−0.476402	+	0.428954i	−0.872027	−	0.489458i	$-0.837195\pi$
$137$	−5.57614	+	5.02078i	−0.476402	+	0.428954i	0.395625	+	0.918412i	$0.370528\pi$
$138$	2.12370	+	4.76991i	0.180781	+	0.406042i
$139$	−11.2542	+	2.39215i	−0.954566	+	0.202899i	−0.658764	−	0.752350i	$-0.728920\pi$
$139$	−11.2542	+	2.39215i	−0.954566	+	0.202899i	−0.295802	+	0.955249i	$0.595587\pi$
$140$	−4.94923	−	5.49667i	−0.418286	−	0.464554i
$141$	20.7133	+	2.17705i	1.74437	+	0.183341i
$142$	−7.67987	+	1.63241i	−0.644480	+	0.136989i
$143$	−1.30638	−	0.807345i	−0.109245	−	0.0675136i
$144$	1.02262	+	0.455299i	0.0852181	+	0.0379416i
$145$	−3.14289	+	1.02119i	−0.261003	+	0.0848049i
$146$	−0.0544780	−	0.0395806i	−0.00450863	−	0.00327571i
$147$	−0.521091	+	4.95785i	−0.0429789	+	0.408916i
$148$	−14.1887	+	1.49130i	−1.16631	+	0.122584i
$149$		−	0.987262i		−	0.0808797i	−0.999182	−	0.0404398i	$-0.987124\pi$
$149$		−	0.987262i		−	0.0808797i	0.999182	−	0.0404398i	$-0.0128759\pi$
$150$	−0.0374349	−	0.0216130i	−0.00305654	−	0.00176470i
$151$	10.0868	+	13.8833i	0.820855	+	1.12981i	0.989557	+	0.144143i	$0.0460426\pi$
$151$	10.0868	+	13.8833i	0.820855	+	1.12981i	−0.168702	+	0.985667i	$0.553957\pi$
$152$	5.59834	−	17.2299i	0.454085	−	1.39753i
$153$	−4.03685	−	0.858060i	−0.326360	−	0.0693700i
$154$	0.507638	+	0.293085i	0.0409066	+	0.0236174i
$155$	−5.46842	+	11.2321i	−0.439234	+	0.902182i
$156$	−10.7110	+	1.94340i	−0.857566	+	0.155596i
$157$	3.22468	+	9.92456i	0.257358	+	0.792066i	0.993356	+	0.115082i	$0.0367132\pi$
$157$	3.22468	+	9.92456i	0.257358	+	0.792066i	−0.735998	+	0.676984i	$0.763287\pi$
$158$	1.16145	+	5.46421i	0.0924003	+	0.434709i
$159$	0.0887896	+	0.844777i	0.00704148	+	0.0669952i
$160$	6.43262	−	11.1416i	0.508544	−	0.880823i
$161$	−7.53142	−	4.34826i	−0.593559	−	0.342691i
$162$	−4.08629	−	5.62430i	−0.321049	−	0.441887i
$163$	3.60099	+	0.378479i	0.282051	+	0.0296448i	0.244498	−	0.969650i	$-0.421377\pi$
$163$	3.60099	+	0.378479i	0.282051	+	0.0296448i	0.0375534	+	0.999295i	$0.488044\pi$
$164$	4.00912	+	0.421376i	0.313060	+	0.0329039i
$165$	−1.79735	−	0.382038i	−0.139923	−	0.0297416i
$166$	−8.68874	+	6.31274i	−0.674377	+	0.489964i
$167$	−7.18984	−	6.47376i	−0.556367	−	0.500955i	0.342298	−	0.939592i	$-0.388795\pi$
$167$	−7.18984	−	6.47376i	−0.556367	−	0.500955i	−0.898664	+	0.438637i	$0.855461\pi$
$168$	9.24074	−	1.96418i	0.712938	−	0.151540i
$169$	9.26149	−	9.12277i	0.712422	−	0.701751i
$170$	−2.69169	+	8.28418i	−0.206443	+	0.635367i
$171$	−4.00880	+	3.60954i	−0.306561	+	0.276029i
$172$	−0.486251	+	4.62637i	−0.0370763	+	0.352758i
$173$	−4.70567	−	5.22618i	−0.357765	−	0.397339i	0.537214	−	0.843446i	$-0.319477\pi$
$173$	−4.70567	−	5.22618i	−0.357765	−	0.397339i	−0.894980	+	0.446107i	$0.852810\pi$
$174$	0.385967	−	1.81583i	0.0292601	−	0.137658i
$175$	0.0716021	−	0.00752569i	0.00541261	−	0.000568888i
$176$	0.142245	−	0.669211i	0.0107221	−	0.0504437i
$177$	−19.9699	−	2.09892i	−1.50103	−	0.157765i
$178$	−0.485060	+	4.61504i	−0.0363568	+	0.345912i
$179$	6.91972	+	3.08086i	0.517204	+	0.230274i	0.648702	−	0.761042i	$-0.275312\pi$
$179$	6.91972	+	3.08086i	0.517204	+	0.230274i	−0.131498	+	0.991316i	$0.541979\pi$
$180$	−2.12636	+	1.22766i	−0.158490	+	0.0915041i
$181$	−6.52989	−	11.3101i	−0.485363	−	0.840673i	0.514496	−	0.857493i	$-0.327979\pi$
$181$	−6.52989	−	11.3101i	−0.485363	−	0.840673i	−0.999859	+	0.0168200i	$0.994646\pi$
$182$	−3.42916	+	3.58638i	−0.254186	+	0.265840i
$183$	−4.96179	−	5.51062i	−0.366786	−	0.407357i
$184$	2.01577	−	9.48346i	0.148605	−	0.699130i
$185$	10.1928	−	17.6545i	0.749392	−	1.29799i
$186$	−3.92839	−	5.81521i	−0.288044	−	0.426392i
$187$			2.52240i			0.184456i
$188$	−12.6405	−	11.3815i	−0.921901	−	0.830083i
$189$	8.84144	+	2.87276i	0.643120	+	0.208962i
$190$	6.69213	+	9.21093i	0.485498	+	0.668231i
$191$	1.32954	−	2.30284i	0.0962024	−	0.166627i	−0.813907	−	0.580995i	$-0.802664\pi$
$191$	1.32954	−	2.30284i	0.0962024	−	0.166627i	0.910110	+	0.414367i	$0.135997\pi$
$192$	0.525146	+	0.909580i	0.0378992	+	0.0656433i
$193$	−3.93981	+	8.84895i	−0.283593	+	0.636961i	−0.998030	−	0.0627390i	$-0.980016\pi$
$193$	−3.93981	+	8.84895i	−0.283593	+	0.636961i	0.714437	+	0.699700i	$0.246683\pi$
$194$	−5.38334	−	3.91122i	−0.386501	−	0.280809i
$195$	6.74935	−	14.0140i	0.483331	−	1.00356i
$196$	2.72424	−	3.02557i	0.194588	−	0.216112i
$197$	1.17619	+	1.61888i	0.0837997	+	0.115340i	0.848859	−	0.528620i	$-0.177290\pi$
$197$	1.17619	+	1.61888i	0.0837997	+	0.115340i	−0.765059	+	0.643960i	$0.777290\pi$
$198$	0.130201	−	0.144603i	0.00925299	−	0.0102765i
$199$	6.16975	+	6.85220i	0.437362	+	0.485740i	0.921019	−	0.389518i	$-0.127358\pi$
$199$	6.16975	+	6.85220i	0.437362	+	0.485740i	−0.483657	+	0.875258i	$0.660692\pi$
$200$	0.0326468	+	0.0733260i	0.00230848	+	0.00518493i
$201$	−4.81158	−	22.6367i	−0.339383	−	1.59667i
$202$	−0.580189	−	2.72957i	−0.0408219	−	0.192052i
$203$	1.25762	+	2.82467i	0.0882678	+	0.198253i
$204$	11.9640	+	13.2874i	0.837648	+	0.930303i
$205$	−3.85426	+	4.28059i	−0.269194	+	0.298970i
$206$	4.47792	+	6.16333i	0.311992	+	0.429420i
$207$	−1.93169	+	2.14536i	−0.134262	+	0.149113i
$208$	5.21787	+	2.51300i	0.361794	+	0.174246i
$209$	2.66732	+	1.93792i	0.184502	+	0.134049i
$210$	−2.41482	+	5.42377i	−0.166638	+	0.374276i
$211$	−7.53717	−	13.0548i	−0.518880	−	0.898727i	−0.999759	−	0.0219398i	$-0.993016\pi$
$211$	−7.53717	−	13.0548i	−0.518880	−	0.898727i	0.480879	−	0.876787i	$-0.340318\pi$
$212$	0.346859	−	0.600777i	0.0238224	−	0.0412615i
$213$	−13.5359	−	18.6306i	−0.927464	−	1.27655i
$214$	−10.5040	−	3.41297i	−0.718042	−	0.233306i
$215$	−4.93964	−	4.44768i	−0.336881	−	0.303329i
$216$			10.3641i			0.705190i
$217$	10.9866	+	3.98999i	0.745817	+	0.270858i
$218$	2.37636	−	4.11598i	0.160948	−	0.278769i
$219$	0.0410640	−	0.193191i	0.00277485	−	0.0130546i
$220$	1.00414	+	1.11521i	0.0676990	+	0.0751874i
$221$	−20.7434	−	5.06290i	−1.39535	−	0.340568i
$222$	5.72590	+	9.91754i	0.384297	+	0.665622i
$223$	−0.479400	+	0.276782i	−0.0321030	+	0.0185347i	−0.515966	−	0.856609i	$-0.672567\pi$
$223$	−0.479400	+	0.276782i	−0.0321030	+	0.0185347i	0.483863	+	0.875144i	$0.339233\pi$
$224$	−10.9967	−	4.89605i	−0.734749	−	0.327131i
$225$	0.00249820	−	0.0237688i	0.000166546	−	0.00158458i
$226$	6.03232	+	0.634023i	0.401264	+	0.0421746i
$227$	−1.93280	+	9.09313i	−0.128285	+	0.603532i	0.866293	+	0.499536i	$0.166496\pi$
$227$	−1.93280	+	9.09313i	−0.128285	+	0.603532i	−0.994578	+	0.103996i	$0.966837\pi$
$228$	23.2425	−	2.44289i	1.53927	−	0.161784i
$229$	−0.181396	+	0.853399i	−0.0119870	+	0.0563942i	−0.983735	−	0.179628i	$-0.942511\pi$
$229$	−0.181396	+	0.853399i	−0.0119870	+	0.0563942i	0.971748	+	0.236022i	$0.0758439\pi$
$230$	4.07701	+	4.52798i	0.268830	+	0.298566i
$231$	−0.179712	+	1.70984i	−0.0118242	+	0.112499i
$232$	−2.56169	+	2.30656i	−0.168183	+	0.151433i
$233$	7.86180	−	24.1961i	0.515044	−	1.58514i	−0.268158	−	0.963375i	$-0.586415\pi$
$233$	7.86180	−	24.1961i	0.515044	−	1.58514i	0.783202	−	0.621767i	$-0.213585\pi$
$234$	0.927833	+	1.36098i	0.0606543	+	0.0889698i
$235$	23.7733	−	5.05318i	1.55080	−	0.329633i
$236$	12.1868	+	10.9731i	0.793294	+	0.714285i
$237$	−13.2556	+	9.63076i	−0.861044	+	0.625585i
$238$	7.97190	+	1.69448i	0.516742	+	0.109837i
$239$	20.9040	+	2.19710i	1.35217	+	0.142119i	0.752744	−	0.658313i	$-0.228730\pi$
$239$	20.9040	+	2.19710i	1.35217	+	0.142119i	0.599424	+	0.800432i	$0.295396\pi$
$240$	6.89161	+	0.724338i	0.444852	+	0.0467558i
$241$	−0.0155637	−	0.0214216i	−0.00100255	−	0.00137989i	0.808515	−	0.588475i	$-0.200271\pi$
$241$	−0.0155637	−	0.0214216i	−0.00100255	−	0.00137989i	−0.809518	+	0.587095i	$0.800271\pi$
$242$	6.14187	+	3.54601i	0.394814	+	0.227946i
$243$	3.55290	−	6.15381i	0.227919	−	0.394767i
$244$	0.633019	+	6.02278i	0.0405249	+	0.385569i
$245$	1.20951	+	5.69029i	0.0772727	+	0.363539i
$246$	−0.999911	−	3.07741i	−0.0637520	−	0.196209i
$247$	−21.2906	+	18.0454i	−1.35469	+	1.14820i
$248$	−0.445574	+	13.0235i	−0.0282940	+	0.826992i
$249$	−27.2803	−	15.7503i	−1.72882	−	0.998133i
$250$	7.14421	+	1.51855i	0.451839	+	0.0960414i
$251$	−6.16749	+	18.9816i	−0.389289	+	1.19811i	0.544032	+	0.839064i	$0.316897\pi$
$251$	−6.16749	+	18.9816i	−0.389289	+	1.19811i	−0.933321	+	0.359043i	$0.883103\pi$
$252$	1.35033	+	1.85857i	0.0850629	+	0.117079i
$253$	1.52803	+	0.882210i	0.0960666	+	0.0554641i
$254$		−	11.5561i		−	0.725096i
$255$	−25.4083	+	2.67052i	−1.59113	+	0.167235i
$256$	0.875462	−	8.32946i	0.0547164	−	0.520592i
$257$	−2.83652	−	2.06086i	−0.176938	−	0.128553i	0.495792	−	0.868442i	$-0.334878\pi$
$257$	−2.83652	−	2.06086i	−0.176938	−	0.128553i	−0.672729	+	0.739889i	$0.734878\pi$
$258$	3.55121	−	1.15386i	0.221089	−	0.0718362i
$259$	−17.4249	−	7.75806i	−1.08273	−	0.482062i
$260$	−11.1866	+	6.01930i	−0.693764	+	0.373301i
$261$	1.00397	−	0.213401i	0.0621444	−	0.0132092i
$262$	−8.18019	−	0.859772i	−0.505374	−	0.0531169i
$263$	21.3218	+	23.6803i	1.31476	+	1.46019i	0.796042	+	0.605241i	$0.206923\pi$
$263$	21.3218	+	23.6803i	1.31476	+	1.46019i	0.518716	+	0.854946i	$0.326410\pi$
$264$	−1.87483	+	0.398508i	−0.115388	+	0.0245265i
$265$	0.403174	+	0.905543i	0.0247668	+	0.0556270i
$266$	7.91651	−	7.12806i	0.485392	−	0.437049i
$267$	−12.9445	+	4.20593i	−0.792192	+	0.257399i
$268$	−7.68736	+	17.2661i	−0.469580	+	1.05469i
$269$	−1.99906	−	0.424913i	−0.121885	−	0.0259074i	0.146565	−	0.989201i	$-0.453178\pi$
$269$	−1.99906	−	0.424913i	−0.121885	−	0.0259074i	−0.268450	+	0.963294i	$0.586511\pi$
$270$	−5.26938	−	3.82843i	−0.320684	−	0.232991i
$271$	−2.01905	−	4.53487i	−0.122649	−	0.275474i	0.841778	−	0.539824i	$-0.181509\pi$
$271$	−2.01905	−	4.53487i	−0.122649	−	0.275474i	−0.964427	+	0.264350i	$0.914842\pi$
$272$	−0.994323	−	9.46035i	−0.0602897	−	0.573618i
$273$	−13.7005	−	4.90985i	−0.829192	−	0.297158i
$274$	−2.45940	−	4.25981i	−0.148578	−	0.257345i
$275$	−0.0145272	+	0.00152687i	−0.000876024	+	9.20738e-5i
$276$	12.2337	−	2.60036i	0.736383	−	0.156523i
$277$	18.2384	−	20.2558i	1.09584	−	1.21706i	0.121355	−	0.992609i	$-0.461276\pi$
$277$	18.2384	−	20.2558i	1.09584	−	1.21706i	0.974487	−	0.224446i	$-0.0720573\pi$
$278$		−	7.54238i		−	0.452362i
$279$	2.05382	−	3.29198i	0.122959	−	0.197086i
$280$	9.54737	−	5.51218i	0.570565	−	0.329416i
$281$	4.63953	−	1.50747i	0.276771	−	0.0899284i	−0.167343	−	0.985899i	$-0.553519\pi$
$281$	4.63953	−	1.50747i	0.276771	−	0.0899284i	0.444114	+	0.895970i	$0.353519\pi$
$282$	−4.21907	+	12.9850i	−0.251242	+	0.773243i
$283$	−1.31570	−	12.5181i	−0.0782104	−	0.744123i	−0.961409	−	0.275123i	$-0.911281\pi$
$283$	−1.31570	−	12.5181i	−0.0782104	−	0.744123i	0.883198	−	0.468999i	$-0.155385\pi$
$284$			18.8072i			1.11600i
$285$	−16.6968	+	28.9198i	−0.989036	+	1.71306i
$286$	0.695734	−	0.727633i	0.0411396	−	0.0430259i
$287$	4.36016	+	3.16784i	0.257372	+	0.186992i
$288$	−2.34872	+	3.23274i	−0.138400	+	0.190491i
$289$	5.58425	+	17.1866i	0.328486	+	1.01097i
$290$	−0.226442	−	2.15445i	−0.0132971	−	0.126514i
$291$	4.05781	−	19.0905i	0.237873	−	1.11910i
$292$	−0.119870	+	0.107932i	−0.00701487	+	0.00631622i
$293$	−15.9366	+	21.9349i	−0.931027	+	1.28145i	0.0284302	+	0.999596i	$0.490949\pi$
$293$	−15.9366	+	21.9349i	−0.931027	+	1.28145i	−0.959458	+	0.281853i	$0.909051\pi$
$294$	−3.10803	−	1.00986i	−0.181264	−	0.0588962i
$295$	−22.9201	+	4.87182i	−1.33446	+	0.283648i
$296$	2.22275	−	21.1480i	0.129195	−	1.22921i
$297$	−1.79382	−	0.582848i	−0.104088	−	0.0338203i
$298$	0.633048	+	0.134558i	0.0366715	+	0.00779476i
$299$	−10.3221	+	10.7953i	−0.596940	+	0.624309i
$300$	−0.0692836	+	0.0769472i	−0.00400009	+	0.00444255i
$301$	−3.65557	+	5.03146i	−0.210704	+	0.290009i
$302$	−10.2770	+	4.57561i	−0.591374	+	0.263297i
$303$	6.62166	−	4.81092i	0.380404	−	0.276380i
$304$	−10.7678	−	6.21678i	−0.617575	−	0.356557i
$305$	−7.49392	−	4.32662i	−0.429100	−	0.247741i
$306$	1.10040	−	2.47154i	0.0629058	−	0.141289i
$307$	18.9173	−	17.0332i	1.07967	−	0.972137i	0.0799718	−	0.996797i	$-0.474517\pi$
$307$	18.9173	−	17.0332i	1.07967	−	0.972137i	0.999696	+	0.0246600i	$0.00785031\pi$
$308$	0.939525	−	1.04345i	0.0535344	−	0.0594560i
$309$	−11.1724	+	19.3512i	−0.635576	+	1.10085i
$310$	−6.45686	−	5.03731i	−0.366725	−	0.286100i
$311$	−17.2913			−0.980498			−0.490249	−	0.871583i	$-0.663094\pi$
$311$	−17.2913			−0.980498			−0.490249	+	0.871583i	$0.663094\pi$
$312$	0.485914	−	16.2179i	0.0275095	−	0.918159i
$313$	−11.6006	−	12.8838i	−0.655704	−	0.728233i	0.319978	−	0.947425i	$-0.396325\pi$
$313$	−11.6006	−	12.8838i	−0.655704	−	0.728233i	−0.975682	+	0.219192i	$0.929658\pi$
$314$	−6.80329	+	0.715054i	−0.383932	+	0.0403528i
$315$	−3.28260			−0.184953
$316$	13.3813			0.752755
$317$	−1.62782	+	0.171091i	−0.0914277	+	0.00960944i	−0.150132	−	0.988666i	$-0.547970\pi$
$317$	−1.62782	+	0.171091i	−0.0914277	+	0.00960944i	0.0587041	+	0.998275i	$0.481303\pi$
$318$	−0.553785	−	0.0582052i	−0.0310547	−	0.00326399i
$319$	−0.255157	−	0.573091i	−0.0142860	−	0.0320869i
$320$	0.910825	+	0.820110i	0.0509167	+	0.0458456i
$321$	−3.38613	−	32.2169i	−0.188995	−	1.79817i
$322$	3.81466	−	4.23661i	0.212583	−	0.236097i
$323$	43.5971	+	14.1656i	2.42581	+	0.788192i
$324$	−15.2130	+	6.77326i	−0.845167	+	0.376292i
$325$	0.0166021	−	0.122532i	0.000920921	−	0.00679685i
$326$	−0.733482	+	2.25742i	−0.0406238	+	0.125027i
$327$	13.8636	+	1.45712i	0.766659	+	0.0805791i
$328$	−1.85671	+	5.71436i	−0.102520	+	0.315523i
$329$	−7.02720	−	21.6275i	−0.387422	−	1.19236i
$330$	0.489937	−	1.10042i	0.0269702	−	0.0605760i
$331$	−0.218541	+	1.02816i	−0.0120121	+	0.0565126i	−0.983745	−	0.179569i	$-0.942530\pi$
$331$	−0.218541	+	1.02816i	−0.0120121	+	0.0565126i	0.971733	+	0.236081i	$0.0758631\pi$
$332$	10.4637	+	23.5019i	0.574272	+	1.28984i
$333$	−3.72168	+	5.12245i	−0.203947	+	0.280709i
$334$	5.13101	−	3.72790i	0.280756	−	0.203982i
$335$	−13.5030	−	23.3878i	−0.737747	−	1.27781i
$336$		−	6.48367i		−	0.353713i
$337$	25.8902	−	18.8103i	1.41033	−	1.02466i	0.417052	−	0.908882i	$-0.363063\pi$
$337$	25.8902	−	18.8103i	1.41033	−	1.02466i	0.993275	−	0.115780i	$-0.0369369\pi$
$338$	4.58737	+	7.18199i	0.249520	+	0.390649i
$339$	5.49758	+	16.9198i	0.298587	+	0.918958i
$340$	18.0696	+	10.4325i	0.979960	+	0.565780i
$341$	−2.22904	−	0.809521i	−0.120709	−	0.0438380i
$342$	−1.76812	−	3.06247i	−0.0956087	−	0.165599i
$343$	19.1528	−	6.22314i	1.03416	−	0.336018i
$344$	−6.59416	−	2.14257i	−0.355533	−	0.115520i
$345$	−7.26881	+	16.3260i	−0.391339	+	0.878963i
$346$	3.99246	−	2.30505i	0.214636	−	0.123920i
$347$	−3.23279			−0.173545			−0.0867725	−	0.996228i	$-0.527655\pi$
$347$	−3.23279			−0.173545			−0.0867725	+	0.996228i	$0.527655\pi$
$348$	−4.06233	−	1.80867i	−0.217764	−	0.0969547i
$349$	8.29046	+	18.6207i	0.443778	+	0.996742i	0.987521	+	0.157490i	$0.0503402\pi$
$349$	8.29046	+	18.6207i	0.443778	+	0.996742i	−0.543742	+	0.839252i	$0.682993\pi$
$350$	−0.00493339	+	0.0469381i	−0.000263701	+	0.00250895i
$351$	8.39367	−	13.5819i	0.448021	−	0.724951i
$352$	2.23110	+	0.993350i	0.118918	+	0.0529457i
$353$	−2.23272	−	2.01035i	−0.118836	−	0.107000i	0.607570	−	0.794266i	$-0.292144\pi$
$353$	−2.23272	−	2.01035i	−0.118836	−	0.107000i	−0.726406	+	0.687266i	$0.758811\pi$
$354$	4.06765	−	12.5189i	0.216193	−	0.665374i
$355$	−21.7409	−	15.7957i	−1.15389	−	0.838347i
$356$	10.5716	+	3.43492i	0.560294	+	0.182051i
$357$	4.96999	+	23.3819i	0.263040	+	1.23750i
$358$	−2.91861	+	4.01712i	−0.154253	+	0.212312i
$359$	3.00797	+	14.1514i	0.158754	+	0.746881i	0.983432	+	0.181278i	$0.0580233\pi$
$359$	3.00797	+	14.1514i	0.158754	+	0.746881i	−0.824678	+	0.565603i	$0.808643\pi$
$360$	−1.13088	−	3.48049i	−0.0596026	−	0.183438i
$361$	33.1030	−	24.0507i	1.74226	−	1.26583i
$362$	8.14219	−	2.64556i	0.427944	−	0.139048i
$363$	−2.17432	+	20.6873i	−0.114122	+	1.08580i
$364$	6.69520	+	9.82074i	0.350924	+	0.514747i
$365$	−0.0240917	−	0.229218i	−0.00126102	−	0.0119978i
$366$	4.20976	−	2.43051i	0.220048	−	0.127045i
$367$	3.31576			0.173081			0.0865407	−	0.996248i	$-0.472419\pi$
$367$	3.31576			0.173081			0.0865407	+	0.996248i	$0.472419\pi$
$368$	−6.07871	−	2.70641i	−0.316874	−	0.141082i
$369$	1.32953	−	1.19712i	0.0692127	−	0.0623194i
$370$	9.93112	+	8.94202i	0.516294	+	0.464873i
$371$	0.803200	−	0.463728i	0.0417001	−	0.0240756i
$372$	−15.5817	+	6.30822i	−0.807872	+	0.327066i
$373$	13.2512	+	22.9518i	0.686121	+	1.18840i	0.973083	+	0.230455i	$0.0740213\pi$
$373$	13.2512	+	22.9518i	0.686121	+	1.18840i	−0.286962	+	0.957942i	$0.592645\pi$
$374$	−1.61740	−	0.343790i	−0.0836339	−	0.0177769i
$375$	4.45397	+	20.9543i	0.230002	+	1.08207i
$376$	20.5104	−	14.9017i	1.05774	−	0.768495i
$377$	5.22506	−	0.948033i	0.269105	−	0.0488262i
$378$	−3.04710	+	5.27773i	−0.156726	+	0.271457i
$379$	−5.39248	+	12.1117i	−0.276993	+	0.622136i	−0.997450	−	0.0713628i	$-0.977265\pi$
$379$	−5.39248	+	12.1117i	−0.276993	+	0.622136i	0.720458	+	0.693499i	$0.243932\pi$
$380$	24.9144	−	11.0926i	1.27808	−	0.569038i
$381$	30.9643	−	13.7862i	1.58635	−	0.706288i
$382$	1.29540	+	1.16639i	0.0662787	+	0.0596776i
$383$	16.7302	−	1.75842i	0.854876	−	0.0898510i	0.333056	−	0.942907i	$-0.391920\pi$
$383$	16.7302	−	1.75842i	0.854876	−	0.0898510i	0.521819	+	0.853056i	$0.325253\pi$
$384$	20.3154	−	6.60088i	1.03672	−	0.336850i
$385$	0.417131	+	1.96245i	0.0212589	+	0.100015i
$386$	−5.13711	−	3.73233i	−0.261472	−	0.189970i
$387$	1.38143	+	1.53423i	0.0702219	+	0.0779893i
$388$	−11.8452	+	10.6654i	−0.601347	+	0.541456i
$389$	−11.4514	+	5.09851i	−0.580611	+	0.258505i	−0.675959	−	0.736939i	$-0.736270\pi$
$389$	−11.4514	+	5.09851i	−0.580611	+	0.258505i	0.0953477	+	0.995444i	$0.469604\pi$
$390$	8.06609	+	6.23782i	0.408443	+	0.315864i
$391$	23.9961	+	5.10053i	1.21354	+	0.257945i
$392$	3.56681	+	4.90929i	0.180151	+	0.247956i
$393$	−7.45504	−	22.9443i	−0.376057	−	1.15738i
$394$	−1.19836	+	0.533543i	−0.0603724	+	0.0268795i
$395$	−11.2386	+	15.4686i	−0.565474	+	0.778309i
$396$	−0.273966	−	0.377082i	−0.0137673	−	0.0189491i
$397$			10.9385i			0.548988i	0.961589	+	0.274494i	$0.0885104\pi$
$397$			10.9385i			0.548988i	−0.961589	+	0.274494i	$0.911490\pi$
$398$	−5.23464	+	3.02222i	−0.262389	+	0.151490i
$399$	28.5436	+	12.7084i	1.42897	+	0.636218i
$400$	0.0538829	−	0.0114532i	0.00269415	−	0.000572658i
$401$	−1.97484	+	9.29087i	−0.0986186	+	0.463964i	0.900931	+	0.433962i	$0.142885\pi$
$401$	−1.97484	+	9.29087i	−0.0986186	+	0.463964i	−0.999550	+	0.0300021i	$0.990449\pi$
$402$	15.1708			0.756650
$403$	11.1313	−	16.7061i	0.554491	−	0.832190i
$404$	−6.68443			−0.332563
$405$	4.94720	−	23.2747i	0.245828	−	1.15653i
$406$	−1.98263	+	0.421420i	−0.0983961	+	0.0209147i
$407$	3.53530	+	1.57402i	0.175238	+	0.0780211i
$408$	−23.0793	+	13.3249i	−1.14260	+	0.659679i
$409$		−	1.08605i		−	0.0537016i	−0.999639	−	0.0268508i	$-0.991452\pi$
$409$		−	1.08605i		−	0.0537016i	0.999639	−	0.0268508i	$-0.00854790\pi$
$410$	−2.21947	−	3.05484i	−0.109612	−	0.150868i
$411$	8.48002	−	11.6718i	0.418289	−	0.575725i
$412$	16.6710	−	7.42241i	0.821322	−	0.365676i
$413$	6.77500	+	20.8513i	0.333376	+	1.02603i
$414$	−1.11236	−	1.53103i	−0.0546694	−	0.0752460i
$415$	−35.9562	−	7.64272i	−1.76502	−	0.375166i
$416$	−12.6472	+	16.3540i	−0.620080	+	0.801823i
$417$	20.2096	−	8.99788i	0.989667	−	0.440628i
$418$	−1.60616	+	1.44620i	−0.0785600	+	0.0707358i
$419$	10.4061	+	11.5572i	0.508371	+	0.564604i	0.941623	−	0.336669i	$-0.109300\pi$
$419$	10.4061	+	11.5572i	0.508371	+	0.564604i	−0.433251	+	0.901273i	$0.642634\pi$
$420$	11.5054	+	8.35918i	0.561407	+	0.407886i
$421$	3.74202	+	17.6048i	0.182375	+	0.858008i	0.970237	+	0.242156i	$0.0778546\pi$
$421$	3.74202	+	17.6048i	0.182375	+	0.858008i	−0.787862	+	0.615852i	$0.788812\pi$
$422$	9.39819	−	3.05366i	0.457497	−	0.148650i
$423$	−7.50749	+	0.789069i	−0.365027	+	0.0383659i
$424$	0.768392	+	0.691864i	0.0373164	+	0.0335999i
$425$	−0.185538	+	0.0826067i	−0.00899990	+	0.00400701i
$426$	13.7911	−	6.14018i	0.668179	−	0.297493i
$427$	−3.29311	+	7.39644i	−0.159365	+	0.357939i
$428$	−13.2280	+	22.9116i	−0.639400	+	1.10747i
$429$	2.77967	+	0.996149i	0.134204	+	0.0480945i
$430$	3.52516	−	2.56118i	0.169999	−	0.123511i
$431$	−4.70475	−	22.1341i	−0.226620	−	1.06616i	−0.933430	−	0.358760i	$-0.883200\pi$
$431$	−4.70475	−	22.1341i	−0.226620	−	1.06616i	0.706810	−	0.707403i	$-0.250134\pi$
$432$	6.95755	+	1.47887i	0.334745	+	0.0711523i
$433$	−18.9759	−	32.8672i	−0.911923	−	1.57950i	−0.811345	−	0.584567i	$-0.801264\pi$
$433$	−18.9759	−	32.8672i	−0.911923	−	1.57950i	−0.100577	−	0.994929i	$-0.532069\pi$
$434$	−4.05585	+	6.50094i	−0.194687	+	0.312055i
$435$	5.50265	−	3.17695i	0.263832	−	0.152323i
$436$	−8.46039	−	7.61777i	−0.405179	−	0.364825i
$437$	23.8294	−	21.4561i	1.13991	−	1.02638i
$438$	0.118280	+	0.0526618i	0.00565165	+	0.00251628i
$439$	−23.5628			−1.12459			−0.562297	−	0.826936i	$-0.690082\pi$
$439$	−23.5628			−1.12459			−0.562297	+	0.826936i	$0.690082\pi$
$440$	−1.93705	+	1.11835i	−0.0923451	+	0.0533155i
$441$	−0.188868	−	1.79696i	−0.00899374	−	0.0855697i
$442$	6.07363	−	12.6110i	0.288893	−	0.599842i
$443$	1.23616	−	11.7613i	0.0587318	−	0.558795i	−0.925103	−	0.379716i	$-0.876022\pi$
$443$	1.23616	−	11.7613i	0.0587318	−	0.558795i	0.983835	−	0.179079i	$-0.0573118\pi$
$444$	26.0888	−	8.47676i	1.23812	−	0.402289i
$445$	−12.8496	+	9.33575i	−0.609128	+	0.442557i
$446$	−0.112137	−	0.345123i	−0.00530985	−	0.0163420i
$447$	0.394666	+	1.85676i	0.0186671	+	0.0878216i
$448$	0.674054	−	0.927755i	0.0318460	−	0.0438323i
$449$	−1.43010	−	6.72811i	−0.0674908	−	0.317519i	0.931432	−	0.363914i	$-0.118560\pi$
$449$	−1.43010	−	6.72811i	−0.0674908	−	0.317519i	−0.998923	+	0.0463953i	$0.985227\pi$
$450$	0.0149004	+	0.00484143i	0.000702411	+	0.000228227i
$451$	−0.884625	−	0.642717i	−0.0416553	−	0.0302644i
$452$	4.48980	−	13.8182i	0.211182	−	0.649952i
$453$	−24.5204	−	22.0783i	−1.15207	−	1.03733i
$454$	−5.56723	−	2.47869i	−0.261283	−	0.116331i
$455$	−16.9758	−	0.508621i	−0.795837	−	0.0238445i
$456$	−3.64108	+	34.6425i	−0.170509	+	1.62229i
$457$	14.4078	+	32.3604i	0.673967	+	1.51375i	0.848552	+	0.529112i	$0.177475\pi$
$457$	14.4078	+	32.3604i	0.673967	+	1.51375i	−0.174585	+	0.984642i	$0.555858\pi$
$458$	−0.522489	−	0.232627i	−0.0244143	−	0.0108700i
$459$	−26.2245			−1.22405
$460$	12.6397	−	7.29751i	0.589327	−	0.340248i
$461$	13.8185	−	31.0369i	0.643592	−	1.44553i	−0.236931	−	0.971526i	$-0.576142\pi$
$461$	13.8185	−	31.0369i	0.643592	−	1.44553i	0.880523	−	0.474004i	$-0.157192\pi$
$462$	−1.07188	−	0.348276i	−0.0498686	−	0.0162033i
$463$	−10.4030	+	3.38013i	−0.483466	+	0.157088i	−0.540602	−	0.841279i	$-0.681803\pi$
$463$	−10.4030	+	3.38013i	−0.483466	+	0.157088i	0.0571353	+	0.998366i	$0.481803\pi$
$464$	1.18288	+	2.04882i	0.0549140	+	0.0951139i
$465$	5.79443	−	23.3104i	0.268710	−	1.08099i
$466$	14.4434	+	8.33891i	0.669078	+	0.386293i
$467$	3.73504	+	11.4953i	0.172837	+	0.531938i	0.999528	−	0.0307184i	$-0.00977952\pi$
$467$	3.73504	+	11.4953i	0.172837	+	0.531938i	−0.826691	+	0.562656i	$0.809780\pi$
$468$	3.65090	−	1.49614i	0.168763	−	0.0691591i
$469$	−20.4424	+	14.8523i	−0.943942	+	0.685814i
$470$			15.9325i			0.734913i
$471$	−10.0321	−	17.3762i	−0.462256	−	0.800651i
$472$	−19.7743	+	14.3669i	−0.910185	+	0.661288i
$473$	0.741671	−	1.02082i	0.0341021	−	0.0469375i
$474$	−4.36872	−	9.81231i	−0.200662	−	0.450695i
$475$	−0.0551929	+	0.259662i	−0.00253243	+	0.0119141i
$476$	7.94044	−	17.8345i	0.363950	−	0.817444i
$477$	−0.0951384	−	0.292806i	−0.00435609	−	0.0134067i
$478$	−4.25792	+	13.1045i	−0.194753	+	0.599387i
$479$	−19.7697	−	2.07788i	−0.903299	−	0.0949406i	−0.358522	−	0.933521i	$-0.616719\pi$
$479$	−19.7697	−	2.07788i	−0.903299	−	0.0949406i	−0.544777	+	0.838581i	$0.683386\pi$
$480$	−7.64397	+	23.5257i	−0.348898	+	1.07380i
$481$	−20.0402	+	25.9139i	−0.913753	+	1.18157i
$482$	0.0158571	−	0.00706005i	0.000722273	−	0.000321577i
$483$	15.9027	+	5.16710i	0.723597	+	0.235111i
$484$	11.3672	−	12.6246i	0.516692	−	0.573845i
$485$	−2.38067	−	22.6505i	−0.108100	−	1.02851i
$486$	3.46167	+	3.11690i	0.157025	+	0.141386i
$487$	−10.9869	−	24.6770i	−0.497864	−	1.11822i	−0.971401	−	0.237446i	$-0.923690\pi$
$487$	−10.9869	−	24.6770i	−0.497864	−	1.11822i	0.473537	−	0.880774i	$-0.342977\pi$
$488$	−8.97684	−	0.943504i	−0.406362	−	0.0427104i
$489$	−6.92373	+	0.727713i	−0.313102	+	0.0329083i
$490$	−3.81355			−0.172279
$491$	−6.12076			−0.276226			−0.138113	−	0.990416i	$-0.544104\pi$
$491$	−6.12076			−0.276226			−0.138113	+	0.990416i	$0.544104\pi$
$492$	−7.70846	+	0.810191i	−0.347524	+	0.0365262i
$493$	−5.83631	−	6.48188i	−0.262854	−	0.291929i
$494$	−8.66921	−	16.1114i	−0.390046	−	0.724884i
$495$	0.665999			0.0299344
$496$	8.67921	+	2.15746i	0.389708	+	0.0968726i
$497$	−12.5720	+	21.7753i	−0.563931	+	0.976756i
$498$	13.8175	−	15.3459i	0.619176	−	0.687664i
$499$	3.09617	−	2.78780i	0.138603	−	0.124799i	−0.596913	−	0.802306i	$-0.703606\pi$
$499$	3.09617	−	2.78780i	0.138603	−	0.124799i	0.735516	+	0.677507i	$0.236940\pi$
$500$	7.11602	−	15.9828i	0.318238	−	0.714774i
$501$	16.1100	+	9.30110i	0.719740	+	0.415542i
$502$	−11.3307	−	6.54178i	−0.505713	−	0.291974i
$503$	28.0652	−	20.3905i	1.25136	−	0.909169i	0.253064	−	0.967450i	$-0.418562\pi$
$503$	28.0652	−	20.3905i	1.25136	−	0.909169i	0.998300	+	0.0582803i	$0.0185617\pi$
$504$	−3.12808	+	1.39271i	−0.139336	+	0.0620364i
$505$	5.61408	−	7.72712i	0.249823	−	0.343852i
$506$	−0.773949	+	0.859558i	−0.0344062	+	0.0382120i
$507$	−13.7713	+	20.8597i	−0.611605	+	0.926410i
$508$	−27.0764	−	5.75526i	−1.20132	−	0.255348i
$509$	6.57478	+	2.13628i	0.291422	+	0.0946888i	0.451080	−	0.892484i	$-0.351039\pi$
$509$	6.57478	+	2.13628i	0.291422	+	0.0946888i	−0.159658	+	0.987172i	$0.551039\pi$
$510$	1.75064	−	16.6562i	0.0775195	−	0.737548i
$511$	−0.210937	+	0.0448360i	−0.00933130	+	0.00198343i
$512$	−15.9102	−	5.16954i	−0.703138	−	0.228464i
$513$	−20.1478	+	27.7311i	−0.889549	+	1.22436i
$514$	1.70805	−	1.53794i	0.0753391	−	0.0678356i
$515$	−5.42134	+	25.5054i	−0.238893	+	1.12390i
$516$	−0.934930	−	8.89527i	−0.0411580	−	0.391592i
$517$	1.42573	+	4.38796i	0.0627037	+	0.192982i
$518$	7.34950	−	10.1157i	0.322918	−	0.444459i
$519$	10.9392	+	7.94781i	0.480179	+	0.348870i
$520$	−5.30900	−	18.1744i	−0.232815	−	0.797000i
$521$	1.40666	−	2.43640i	0.0616268	−	0.106741i	−0.833566	−	0.552420i	$-0.813704\pi$
$521$	1.40666	−	2.43640i	0.0616268	−	0.106741i	0.895193	+	0.445679i	$0.147038\pi$
$522$			0.672848i			0.0294498i
$523$	−1.28668	−	12.2419i	−0.0562625	−	0.535302i	−0.985960	−	0.166979i	$-0.946599\pi$
$523$	−1.28668	−	12.2419i	−0.0562625	−	0.535302i	0.929698	−	0.368323i	$-0.120068\pi$
$524$	−6.08843	+	18.7383i	−0.265974	+	0.818585i
$525$	−0.131655	+	0.0427772i	−0.00574588	+	0.00186695i
$526$	−18.0902	+	10.4444i	−0.788770	+	0.455396i
$527$	−32.9535	−	1.12744i	−1.43548	−	0.0491121i
$528$			1.31546i			0.0572480i
$529$	−3.90754	+	4.33976i	−0.169893	+	0.188685i
$530$	−0.635598	+	0.135101i	−0.0276086	+	0.00586839i
$531$	7.23805	−	0.760750i	0.314105	−	0.0330137i
$532$	−12.7586	−	22.0986i	−0.553157	−	0.958096i
$533$	7.06110	−	5.98483i	0.305850	−	0.259232i
$534$	−0.932639	−	8.87347i	−0.0403593	−	0.383993i
$535$	−15.3756	−	34.5343i	−0.664747	−	1.49305i
$536$	−22.7902	−	16.5580i	−0.984387	−	0.715199i
$537$	−14.2456	−	3.02800i	−0.614743	−	0.130668i
$538$	0.544921	−	1.22391i	0.0234932	−	0.0527666i
$539$	−1.05028	+	0.341258i	−0.0452390	+	0.0146990i
$540$	−11.5944	+	10.4397i	−0.498945	+	0.449252i
$541$	−7.09431	−	15.9341i	−0.305008	−	0.685060i	0.694395	−	0.719594i	$-0.255672\pi$
$541$	−7.09431	−	15.9341i	−0.305008	−	0.685060i	−0.999404	+	0.0345339i	$0.989005\pi$
$542$	3.18301	−	0.676570i	0.136722	−	0.0290612i
$543$	16.8021	+	18.6607i	0.721049	+	0.800806i
$544$	33.7705	+	3.54942i	1.44790	+	0.152180i
$545$	15.9117	−	3.38214i	0.681583	−	0.144875i
$546$	5.01558	−	8.11579i	0.214647	−	0.347324i
$547$	−27.6577	−	12.3140i	−1.18256	−	0.526509i	−0.281229	−	0.959641i	$-0.590742\pi$
$547$	−27.6577	−	12.3140i	−1.18256	−	0.526509i	−0.901331	+	0.433131i	$0.857409\pi$
$548$	−11.2057	+	3.64096i	−0.478685	+	0.155534i
$549$	2.17436	+	1.57976i	0.0927993	+	0.0674226i
$550$	0.00100093	−	0.00952317i	4.26796e−5	−	0.000406069i
$551$	−11.3382	+	1.19169i	−0.483024	+	0.0507679i
$552$			18.6415i			0.793434i
$553$	15.4931	+	8.94494i	0.658833	+	0.380377i
$554$	10.5026	+	14.4555i	0.446211	+	0.614156i
$555$	−12.1123	+	37.2778i	−0.514137	+	1.58235i
$556$	−17.6720	−	3.75631i	−0.749461	−	0.159303i
$557$	27.9309	+	16.1259i	1.18347	+	0.683277i	0.956815	−	0.290698i	$-0.0938876\pi$
$557$	27.9309	+	16.1259i	1.18347	+	0.683277i	0.226655	+	0.973975i	$0.427221\pi$
$558$	1.83094	+	1.76562i	0.0775100	+	0.0747447i
$559$	6.90627	+	8.14825i	0.292104	+	0.344634i
$560$	−2.33805	−	7.19579i	−0.0988008	−	0.304078i
$561$	−1.00835	−	4.74391i	−0.0425726	−	0.200288i
$562$	0.334273	+	3.18040i	0.0141005	+	0.134157i
$563$	4.68993	−	8.12320i	0.197657	−	0.342352i	−0.750111	−	0.661312i	$-0.770000\pi$
$563$	4.68993	−	8.12320i	0.197657	−	0.342352i	0.947768	+	0.318960i	$0.103333\pi$
$564$	28.3230	+	16.3523i	1.19261	+	0.688555i
$565$	12.2028	+	16.7957i	0.513375	+	0.706600i
$566$	8.20611	+	0.862497i	0.344928	+	0.0362534i
$567$	−22.1416	−	2.32718i	−0.929861	−	0.0977323i
$568$	−27.4192	−	5.82813i	−1.15048	−	0.244543i
$569$	−12.9338	+	9.39693i	−0.542211	+	0.393940i	−0.824906	−	0.565270i	$-0.808772\pi$
$569$	−12.9338	+	9.39693i	−0.542211	+	0.393940i	0.282694	+	0.959210i	$0.408772\pi$
$570$	−16.2681	−	14.6479i	−0.681397	−	0.613532i
$571$	18.3517	−	3.90078i	0.767995	−	0.163242i	0.192777	−	0.981243i	$-0.438251\pi$
$571$	18.3517	−	3.90078i	0.767995	−	0.163242i	0.575218	+	0.818000i	$0.304917\pi$
$572$	−1.35837	−	1.99251i	−0.0567965	−	0.0833110i
$573$	−1.57991	+	4.86247i	−0.0660018	+	0.203133i
$574$	−2.62554	+	2.36404i	−0.109588	+	0.0986733i
$575$	−0.0148499	+	0.141288i	−0.000619285	+	0.00589210i
$576$	−0.254722	−	0.282898i	−0.0106134	−	0.0117874i
$577$	−2.37995	+	11.1968i	−0.0990784	+	0.466127i	0.900437	+	0.434987i	$0.143247\pi$
$577$	−2.37995	+	11.1968i	−0.0990784	+	0.466127i	−0.999515	+	0.0311401i	$0.990086\pi$
$578$	−11.7814	+	1.23827i	−0.490041	+	0.0515054i
$579$	3.87221	−	18.2173i	0.160923	−	0.757085i
$580$	−5.16072	−	0.542414i	−0.214287	−	0.0225225i
$581$	−3.59516	+	34.2057i	−0.149152	+	1.41909i
$582$	11.6881	+	5.20386i	0.484486	+	0.215707i
$583$	−0.162960	+	0.0940848i	−0.00674910	+	0.00389659i
$584$	−0.120208	−	0.208207i	−0.00497426	−	0.00861566i
$585$	−1.33678	+	5.47697i	−0.0552689	+	0.226445i
$586$	−11.8929	−	13.2084i	−0.491291	−	0.545634i
$587$	6.43368	−	30.2681i	0.265546	−	1.24930i	−0.619947	−	0.784644i	$-0.712846\pi$
$587$	6.43368	−	30.2681i	0.265546	−	1.24930i	0.885493	−	0.464653i	$-0.153821\pi$
$588$	−3.91401	+	6.77927i	−0.161411	+	0.279572i
$589$	−26.5098	+	33.9805i	−1.09232	+	1.40014i
$590$		−	15.3607i		−	0.632391i
$591$	−2.85923	−	2.57446i	−0.117613	−	0.105899i
$592$	−13.8797	−	4.50980i	−0.570453	−	0.185352i
$593$	−2.70274	−	3.72001i	−0.110988	−	0.152762i	0.749909	−	0.661541i	$-0.230097\pi$
$593$	−2.70274	−	3.72001i	−0.110988	−	0.152762i	−0.860897	+	0.508779i	$0.830097\pi$
$594$	0.618219	−	1.07079i	0.0253658	−	0.0439349i
$595$	13.9475	+	24.1578i	0.571793	+	0.990375i
$596$	0.630549	−	1.41624i	0.0258283	−	0.0580113i
$597$	−14.3428	−	10.4206i	−0.587010	−	0.426488i
$598$	−5.51528	−	8.09000i	−0.225537	−	0.330825i
$599$	12.4787	−	13.8590i	0.509867	−	0.566265i	−0.432162	−	0.901796i	$-0.642249\pi$
$599$	12.4787	−	13.8590i	0.509867	−	0.566265i	0.942029	+	0.335531i	$0.108916\pi$
$600$	−0.0907120	−	0.124854i	−0.00370330	−	0.00509716i
$601$	0.198165	−	0.220084i	0.00808331	−	0.00897742i	−0.739090	−	0.673607i	$-0.764744\pi$
$601$	0.198165	−	0.220084i	0.00808331	−	0.00897742i	0.747173	+	0.664630i	$0.231411\pi$
$602$	−2.72802	−	3.02977i	−0.111186	−	0.123484i
$603$	3.41168	+	7.66275i	0.138934	+	0.312051i
$604$	5.60259	+	26.3581i	0.227966	+	1.07250i
$605$	5.04683	+	23.7435i	0.205183	+	0.965309i
$606$	2.18234	+	4.90161i	0.0886514	+	0.199114i
$607$	17.7130	+	19.6723i	0.718949	+	0.798474i	0.986271	−	0.165133i	$-0.0528055\pi$
$607$	17.7130	+	19.6723i	0.718949	+	0.798474i	−0.267322	+	0.963607i	$0.586139\pi$
$608$	29.6986	−	32.9837i	1.20444	−	1.33767i
$609$	−3.49441	−	4.80965i	−0.141601	−	0.194897i
$610$	3.79567	−	4.21552i	0.153682	−	0.170681i
$611$	−38.9469	+	2.91739i	−1.57562	+	0.118025i
$612$	−5.24288	−	3.80917i	−0.211931	−	0.153977i
$613$	−1.77832	+	3.99416i	−0.0718255	+	0.161323i	−0.945890	−	0.324487i	$-0.894808\pi$
$613$	−1.77832	+	3.99416i	−0.0718255	+	0.161323i	0.874065	+	0.485809i	$0.161475\pi$
$614$	8.34364	+	14.4516i	0.336722	+	0.583219i
$615$	5.53757	−	9.59135i	0.223296	−	0.386760i
$616$	1.23011	+	1.69310i	0.0495624	+	0.0682168i
$617$	−34.2959	−	11.1434i	−1.38070	−	0.448616i	−0.477800	−	0.878469i	$-0.658566\pi$
$617$	−34.2959	−	11.1434i	−1.38070	−	0.448616i	−0.902899	+	0.429852i	$0.858566\pi$
$618$	−10.8855	−	9.80138i	−0.437880	−	0.394269i
$619$		−	48.0418i		−	1.93096i	−0.260475	−	0.965481i	$-0.583879\pi$
$619$		−	48.0418i		−	1.93096i	0.260475	−	0.965481i	$-0.416121\pi$
$620$	−15.0183	+	12.6199i	−0.603148	+	0.506828i
$621$	−9.17202	+	15.8864i	−0.368061	+	0.637500i
$622$	2.35670	−	11.0874i	0.0944952	−	0.444565i
$623$	9.94389	+	11.0438i	0.398393	+	0.442461i
$624$	−10.8179	−	2.64036i	−0.433063	−	0.105699i
$625$	12.5851	+	21.7981i	0.503406	+	0.871925i
$626$	9.84236	−	5.68249i	0.393380	−	0.227118i
$627$	−5.79116	−	2.57839i	−0.231277	−	0.102971i
$628$	−1.71282	+	16.2964i	−0.0683491	+	0.650299i
$629$	53.5112	+	5.62425i	2.13363	+	0.224254i
$630$	0.447400	−	2.10485i	0.0178248	−	0.0838593i
$631$	−13.7351	+	1.44362i	−0.546785	+	0.0574695i	−0.373894	−	0.927471i	$-0.621978\pi$
$631$	−13.7351	+	1.44362i	−0.546785	+	0.0574695i	−0.172891	+	0.984941i	$0.555311\pi$
$632$	−4.14670	+	19.5087i	−0.164947	+	0.776014i
$633$	19.3940	+	21.5392i	0.770842	+	0.856107i
$634$	0.112157	−	1.06710i	0.00445433	−	0.0423801i
$635$	29.3938	−	26.4663i	1.16646	−	1.05028i
$636$	−0.412177	+	1.26855i	−0.0163439	+	0.0503013i
$637$	−0.698294	−	9.32218i	−0.0276674	−	0.369358i
$638$	0.402251	−	0.0855011i	0.0159253	−	0.00338502i
$639$	6.20280	+	5.58503i	0.245379	+	0.220940i
$640$	20.1664	−	14.6518i	0.797147	−	0.579161i
$641$	35.5073	+	7.54732i	1.40246	+	0.298101i	0.846180	−	0.532897i	$-0.178897\pi$
$641$	35.5073	+	7.54732i	1.40246	+	0.298101i	0.556275	+	0.830998i	$0.312230\pi$
$642$	21.1195	+	2.21975i	0.833519	+	0.0876064i
$643$	−18.2833	−	1.92165i	−0.721024	−	0.0757826i	−0.263093	−	0.964771i	$-0.584743\pi$
$643$	−18.2833	−	1.92165i	−0.721024	−	0.0757826i	−0.457931	+	0.888988i	$0.651409\pi$
$644$	−8.02672	−	11.0478i	−0.316297	−	0.435346i
$645$	11.0680	+	6.39014i	0.435804	+	0.251612i
$646$	−15.0252	+	26.0244i	−0.591159	+	1.02392i
$647$	0.409158	+	3.89288i	0.0160857	+	0.153045i	0.999616	−	0.0276961i	$-0.00881708\pi$
$647$	0.409158	+	3.89288i	0.0160857	+	0.153045i	−0.983531	+	0.180741i	$0.942150\pi$
$648$	−5.16048	−	24.2782i	−0.202723	−	0.953736i
$649$	−1.37457	−	4.23048i	−0.0539564	−	0.166061i
$650$	0.0763065	+	0.0273460i	0.00299299	+	0.00107260i
$651$	−22.2576	−	3.11206i	−0.872345	−	0.121971i
$652$	4.92393	+	2.84283i	0.192836	+	0.111334i
$653$	10.7018	+	2.27473i	0.418793	+	0.0890171i	0.412488	−	0.910963i	$-0.364660\pi$
$653$	10.7018	+	2.27473i	0.418793	+	0.0890171i	0.00630453	+	0.999980i	$0.497993\pi$
$654$	−2.82386	+	8.69095i	−0.110422	+	0.339843i
$655$	−16.5477	−	22.7759i	−0.646572	−	0.889930i
$656$	3.57117	+	2.06182i	0.139431	+	0.0805004i
$657$			0.0715861i			0.00279284i
$658$	14.8257	−	1.55824i	0.577964	−	0.0607465i
$659$	−1.89268	+	18.0076i	−0.0737283	+	0.701478i	0.893757	+	0.448551i	$0.148060\pi$
$659$	−1.89268	+	18.0076i	−0.0737283	+	0.701478i	−0.967485	+	0.252927i	$0.918607\pi$
$660$	−2.33431	−	1.69598i	−0.0908629	−	0.0660158i
$661$	−40.7091	+	13.2272i	−1.58340	+	0.514477i	−0.962929	−	0.269753i	$-0.913058\pi$
$661$	−40.7091	+	13.2272i	−1.58340	+	0.514477i	−0.620469	+	0.784231i	$0.713058\pi$
$662$	−0.629483	−	0.280264i	−0.0244656	−	0.0108928i
$663$	41.0364	+	1.22951i	1.59372	+	0.0477504i
$664$	−37.5063	+	7.97221i	−1.45553	+	0.309382i
$665$	36.2614	+	3.81122i	1.40616	+	0.147793i
$666$	−2.77735	−	3.08456i	−0.107620	−	0.119524i
$667$	−5.96788	+	1.26851i	−0.231077	+	0.0491170i
$668$	−6.17920	−	13.8787i	−0.239081	−	0.536984i
$669$	0.790969	−	0.712191i	0.0305806	−	0.0275349i
$670$	16.8370	−	5.47068i	0.650471	−	0.211351i
$671$	0.668132	−	1.50065i	0.0257929	−	0.0579319i
$672$	22.6389	+	4.81205i	0.873315	+	0.185629i
$673$	−29.2099	−	21.2222i	−1.12596	−	0.818057i	−0.140857	−	0.990030i	$-0.544986\pi$
$673$	−29.2099	−	21.2222i	−1.12596	−	0.818057i	−0.985102	+	0.171973i	$0.944986\pi$
$674$	8.53277	+	19.1649i	0.328670	+	0.738205i
$675$	−0.0158743	−	0.151034i	−0.000611003	−	0.00581331i
$676$	19.1123	−	7.17153i	0.735087	−	0.275828i
$677$	−8.01811	−	13.8878i	−0.308161	−	0.533751i	0.669799	−	0.742542i	$-0.266380\pi$
$677$	−8.01811	−	13.8878i	−0.308161	−	0.533751i	−0.977960	+	0.208792i	$0.933047\pi$
$678$	−11.5985	+	1.21905i	−0.445439	+	0.0468175i
$679$	−20.8441	+	4.43055i	−0.799922	+	0.170029i
$680$	−20.8092	+	23.1109i	−0.797995	+	0.886263i
$681$		−	17.8742i		−	0.684942i
$682$	0.822884	−	1.31896i	0.0315098	−	0.0505057i
$683$	39.1076	−	22.5788i	1.49641	−	0.863953i	0.496419	−	0.868083i	$-0.334648\pi$
$683$	39.1076	−	22.5788i	1.49641	−	0.863953i	0.999991	+	0.00412984i	$0.00131457\pi$
$684$	−8.05603	+	2.61756i	−0.308030	+	0.100085i
$685$	5.20250	−	16.0116i	0.198777	−	0.611773i
$686$	1.37994	+	13.1293i	0.0526865	+	0.501278i
$687$		−	1.67751i		−	0.0640011i
$688$	−2.37926	+	4.12100i	−0.0907084	+	0.157112i
$689$	−0.446635	−	1.52897i	−0.0170154	−	0.0582493i
$690$	−9.47779	−	6.88601i	−0.360813	−	0.262146i
$691$	−20.0339	+	27.5743i	−0.762125	+	1.04897i	0.234910	+	0.972017i	$0.424521\pi$
$691$	−20.0339	+	27.5743i	−0.762125	+	1.04897i	−0.997034	+	0.0769576i	$0.975479\pi$
$692$	−3.41245	−	10.5024i	−0.129722	−	0.399243i
$693$	−0.0651362	−	0.619730i	−0.00247432	−	0.0235416i
$694$	0.440611	−	2.07291i	0.0167254	−	0.0786867i
$695$	19.1845	−	17.2738i	0.727711	−	0.655234i
$696$	3.89574	−	5.36203i	0.147668	−	0.203247i
$697$	−14.4591	−	4.69805i	−0.547678	−	0.177951i
$698$	−13.0698	+	2.77807i	−0.494700	+	0.105152i
$699$	−5.11320	+	48.6488i	−0.193399	+	1.84007i
$700$	0.107521	+	0.0349355i	0.00406389	+	0.00132044i
$701$	39.7682	+	8.45299i	1.50202	+	0.319265i	0.884221	−	0.467068i	$-0.154690\pi$
$701$	39.7682	+	8.45299i	1.50202	+	0.319265i	0.617802	+	0.786333i	$0.288023\pi$
$702$	7.56494	+	7.23330i	0.285520	+	0.273003i
$703$	47.0591	−	52.2644i	1.77487	−	1.97119i
$704$	−0.136757	+	0.188230i	−0.00515424	+	0.00709420i
$705$	−42.6908	+	19.0072i	−1.60783	+	0.715851i
$706$	1.59338	−	1.15766i	0.0599675	−	0.0435689i
$707$	−7.73936	−	4.46832i	−0.291069	−	0.168049i
$708$	−27.3065	−	15.7654i	−1.02624	−	0.592500i
$709$	−3.62581	+	8.14371i	−0.136170	+	0.305843i	−0.968741	−	0.248076i	$-0.920202\pi$
$709$	−3.62581	+	8.14371i	−0.136170	+	0.305843i	0.832570	+	0.553919i	$0.186868\pi$
$710$	13.0916	−	11.7877i	0.491318	−	0.442385i
$711$	3.97373	−	4.41328i	0.149027	−	0.165511i
$712$	−8.28384	+	14.3480i	−0.310450	+	0.537715i
$713$	−12.2085	+	19.5684i	−0.457211	+	0.732842i
$714$	−15.6702			−0.586444
$715$	3.44418	+	0.103193i	0.128805	+	0.00385920i
$716$	7.95871	+	8.83904i	0.297431	+	0.330330i
$717$	−40.1928	+	4.22443i	−1.50103	+	0.157764i
$718$	−9.48405			−0.353941
$719$	−19.6259			−0.731924			−0.365962	−	0.930630i	$-0.619260\pi$
$719$	−19.6259			−0.731924			−0.365962	+	0.930630i	$0.619260\pi$
$720$	−2.49785	+	0.262535i	−0.0930895	+	0.00978410i
$721$	24.2637	+	2.55022i	0.903627	+	0.0949750i
$722$	10.9099	+	24.5041i	0.406026	+	0.911948i
$723$	0.0378344	+	0.0340662i	0.00140708	+	0.00126694i
$724$	−2.14360	−	20.3950i	−0.0796663	−	0.757974i
$725$	0.0337981	−	0.0375366i	0.00125523	−	0.00139407i
$726$	−12.9686	−	4.21377i	−0.481311	−	0.156388i
$727$	13.4070	−	5.96916i	0.497236	−	0.221384i	−0.142766	−	0.989756i	$-0.545600\pi$
$727$	13.4070	−	5.96916i	0.497236	−	0.221384i	0.640003	+	0.768372i	$0.278933\pi$
$728$	−16.3925	+	6.71767i	−0.607548	+	0.248973i
$729$	5.60943	−	17.2641i	0.207757	−	0.639410i
$730$	0.150261	+	0.0157931i	0.00556142	+	0.000584529i
$731$	5.42138	−	16.6853i	0.200517	−	0.617127i
$732$	−3.59818	−	11.0741i	−0.132993	−	0.409309i
$733$	−9.45584	+	21.2382i	−0.349259	+	0.784449i	0.650431	+	0.759565i	$0.274588\pi$
$733$	−9.45584	+	21.2382i	−0.349259	+	0.784449i	−0.999690	+	0.0248839i	$0.992078\pi$
$734$	−0.451920	+	2.12612i	−0.0166807	+	0.0784764i
$735$	−4.54948	−	10.2183i	−0.167810	−	0.376907i
$736$	13.9614	−	19.2163i	0.514625	−	0.708321i
$737$	4.14751	−	3.01335i	0.152776	−	0.110998i
$738$	0.586402	+	1.01568i	0.0215857	+	0.0373876i
$739$		−	12.7140i		−	0.467693i	−0.972274	−	0.233846i	$-0.924869\pi$
$739$		−	12.7140i		−	0.467693i	0.972274	−	0.233846i	$-0.0751313\pi$
$740$	25.8974	−	18.8156i	0.952007	−	0.691674i
$741$	32.8277	−	42.4494i	1.20596	−	1.55942i
$742$	0.187878	+	0.578228i	0.00689720	+	0.0212274i
$743$	−17.5288	−	10.1203i	−0.643071	−	0.371277i	0.142726	−	0.989762i	$-0.454413\pi$
$743$	−17.5288	−	10.1203i	−0.643071	−	0.371277i	−0.785796	+	0.618485i	$0.787747\pi$
$744$	−4.36824	−	24.6716i	−0.160148	−	0.904503i
$745$	1.10757	+	1.91837i	0.0405783	+	0.0702836i
$746$	−16.5231	+	5.36867i	−0.604953	+	0.196561i
$747$	10.8585	+	3.52815i	0.397292	+	0.129088i
$748$	−1.61102	+	3.61841i	−0.0589047	+	0.132302i
$749$	−30.6313	+	17.6850i	−1.11924	+	0.646195i
$750$	−14.0433			−0.512787
$751$	37.8908	+	16.8701i	1.38266	+	0.615598i	0.957212	−	0.289387i	$-0.0934515\pi$
$751$	37.8908	+	16.8701i	1.38266	+	0.615598i	0.425443	+	0.904985i	$0.360118\pi$
$752$	−7.07699	−	15.8952i	−0.258071	−	0.579637i
$753$	4.01124	−	38.1644i	0.146178	−	1.39079i
$754$	−0.104254	+	3.47960i	−0.00379672	+	0.126720i
$755$	−35.1751	−	15.6610i	−1.28015	−	0.569962i
$756$	10.8483	+	9.76790i	0.394551	+	0.355255i
$757$	−5.11008	+	15.7272i	−0.185729	+	0.571615i	−0.999960	−	0.00892576i	$-0.997159\pi$
$757$	−5.11008	+	15.7272i	−0.185729	+	0.571615i	0.814231	+	0.580541i	$0.197159\pi$
$758$	−7.03124	−	5.10850i	−0.255386	−	0.185549i
$759$	−3.22646	−	1.04834i	−0.117113	−	0.0380524i
$760$	8.45133	+	39.7604i	0.306562	+	1.44226i
$761$	5.43012	−	7.47392i	0.196842	−	0.270929i	−0.699174	−	0.714951i	$-0.746449\pi$
$761$	5.43012	−	7.47392i	0.196842	−	0.270929i	0.896016	+	0.444022i	$0.146449\pi$
$762$	4.61965	+	21.7338i	0.167352	+	0.787331i
$763$	−4.70337	−	14.4755i	−0.170274	−	0.524048i
$764$	3.37803	−	2.45428i	0.122213	−	0.0887929i
$765$	8.80672	−	2.86148i	0.318408	−	0.103457i
$766$	−1.15272	+	10.9674i	−0.0416493	+	0.396267i
$767$	37.5491	−	2.81268i	1.35582	−	0.101560i
$768$	1.68328	+	16.0153i	0.0607400	+	0.577903i
$769$	−9.77754	+	5.64507i	−0.352587	+	0.203566i	−0.665824	−	0.746109i	$-0.731920\pi$
$769$	−9.77754	+	5.64507i	−0.352587	+	0.203566i	0.313237	+	0.949675i	$0.398587\pi$
$770$	−1.31520			−0.0473966
$771$	6.15853	+	2.74196i	0.221794	+	0.0987491i
$772$	−11.3034	+	10.1776i	−0.406818	+	0.366300i
$773$	8.56190	+	7.70917i	0.307950	+	0.277280i	0.808585	−	0.588379i	$-0.200234\pi$
$773$	8.56190	+	7.70917i	0.307950	+	0.277280i	−0.500635	+	0.865658i	$0.666900\pi$
$774$	−1.17205	+	0.676685i	−0.0421286	+	0.0243229i
$775$	−0.0134543	−	0.190471i	−0.000483292	−	0.00684190i
$776$	−11.8786	−	20.5743i	−0.426416	−	0.738575i
$777$	35.8726	+	7.62495i	1.28692	+	0.273543i
$778$	−1.70847	−	8.03774i	−0.0612518	−	0.288167i
$779$	−16.0767	+	11.6804i	−0.576006	+	0.418493i
$780$	18.6325	−	15.7925i	0.667152	−	0.565463i
$781$	2.55070	−	4.41795i	0.0912714	−	0.158087i
$782$	−6.54108	+	14.6915i	−0.233908	+	0.525367i
$783$	5.95822	−	2.65277i	0.212929	−	0.0948023i
$784$	3.80461	−	1.69392i	0.135879	−	0.0604971i
$785$	−17.3999	−	15.6670i	−0.621030	−	0.559178i
$786$	15.7283	−	1.65311i	0.561010	−	0.0589645i
$787$	−27.2775	+	8.86299i	−0.972337	+	0.315932i	−0.751759	−	0.659438i	$-0.770794\pi$
$787$	−27.2775	+	8.86299i	−0.972337	+	0.315932i	−0.220578	+	0.975369i	$0.570794\pi$
$788$	0.653295	+	3.07351i	0.0232727	+	0.109489i
$789$	−49.5666	−	36.0122i	−1.76462	−	1.28207i
$790$	−8.38693	−	9.31463i	−0.298394	−	0.331400i
$791$	14.4354	−	12.9977i	0.513263	−	0.462144i
$792$	0.634650	−	0.282565i	0.0225513	−	0.0100405i
$793$	10.9998	+	8.50657i	0.390615	+	0.302077i
$794$	−7.01395	−	1.49086i	−0.248916	−	0.0529086i
$795$	−1.12025	−	1.54189i	−0.0397312	−	0.0546854i
$796$	4.47417	+	13.7701i	0.158583	+	0.488068i
$797$	−12.4887	+	5.56034i	−0.442373	+	0.196957i	−0.615821	−	0.787886i	$-0.711176\pi$
$797$	−12.4887	+	5.56034i	−0.442373	+	0.196957i	0.173448	+	0.984843i	$0.444509\pi$
$798$	−12.0392	+	16.5705i	−0.426183	+	0.586590i
$799$	37.7059	+	51.8977i	1.33394	+	1.83601i
$800$			0.196642i			0.00695235i
$801$	4.27225	−	2.46658i	0.150952	−	0.0871524i
$802$	−5.68829	−	2.53259i	−0.200861	−	0.0894289i
$803$	0.0427965	−	0.00909669i	0.00151026	−	0.000321015i
$804$	7.55546	−	35.5456i	0.266461	−	1.25360i
$805$	19.5126			0.687729
$806$	9.19506	+	9.41453i	0.323882	+	0.331613i
$807$	3.92951			0.138325
$808$	2.07143	−	9.74530i	0.0728726	−	0.342839i
$809$	33.2302	−	7.06329i	1.16831	−	0.248332i	0.417391	−	0.908727i	$-0.362944\pi$
$809$	33.2302	−	7.06329i	1.16831	−	0.248332i	0.750919	+	0.660395i	$0.229611\pi$
$810$	14.2498	+	6.34444i	0.500689	+	0.222921i
$811$	−16.5951	+	9.58121i	−0.582734	+	0.336442i	−0.762219	−	0.647319i	$-0.775890\pi$
$811$	−16.5951	+	9.58121i	−0.582734	+	0.336442i	0.179485	+	0.983761i	$0.442557\pi$
$812$			4.85524i			0.170386i
$813$	5.61011	+	7.72165i	0.196755	+	0.270810i
$814$	−1.49112	+	2.05236i	−0.0522639	+	0.0719351i
$815$	−7.42176	+	3.30438i	−0.259973	+	0.115747i
$816$	5.65189	+	17.3947i	0.197856	+	0.608937i
$817$	−13.4787	−	18.5519i	−0.471560	−	0.649047i
$818$	0.696391	+	0.148022i	0.0243487	+	0.00517548i
$819$	5.22720	+	0.708247i	0.182653	+	0.0247481i
$820$	−8.26293	+	3.67889i	−0.288554	+	0.128473i
$821$	−12.5282	+	11.2804i	−0.437237	+	0.393690i	−0.858140	−	0.513416i	$-0.828380\pi$
$821$	−12.5282	+	11.2804i	−0.437237	+	0.393690i	0.420903	+	0.907106i	$0.361713\pi$
$822$	6.32833	+	7.02832i	0.220726	+	0.245141i
$823$	9.45849	+	6.87199i	0.329702	+	0.239543i	0.740304	−	0.672272i	$-0.234681\pi$
$823$	9.45849	+	6.87199i	0.329702	+	0.239543i	−0.410602	+	0.911815i	$0.634681\pi$
$824$	5.65506	+	26.6050i	0.197003	+	0.926828i
$825$	0.0267111	−	0.00867897i	0.000929962	−	0.000302163i
$826$	−14.2936	+	1.50231i	−0.497337	+	0.0522722i
$827$	1.65932	+	1.49406i	0.0577004	+	0.0519536i	0.697476	−	0.716608i	$-0.254306\pi$
$827$	1.65932	+	1.49406i	0.0577004	+	0.0519536i	−0.639776	+	0.768561i	$0.720973\pi$
$828$	−4.14124	+	1.84380i	−0.143918	+	0.0640764i
$829$	−17.4867	+	7.78559i	−0.607339	+	0.270405i	−0.687277	−	0.726395i	$-0.741194\pi$
$829$	−17.4867	+	7.78559i	−0.607339	+	0.270405i	0.0799384	+	0.996800i	$0.474528\pi$
$830$	9.80126	−	22.0140i	0.340207	−	0.764117i
$831$	−26.2038	+	45.3864i	−0.909001	+	1.57444i
$832$	−1.27345	−	1.50246i	−0.0441490	−	0.0520885i
$833$	−12.4220	+	9.02513i	−0.430398	+	0.312702i
$834$	3.01513	+	14.1851i	0.104405	+	0.491188i
$835$	21.2334	+	4.51330i	0.734812	+	0.156189i
$836$	2.58857	+	4.48354i	0.0895276	+	0.155066i
$837$	8.41630	−	23.1745i	0.290910	−	0.801029i
$838$	−8.82892	+	5.09738i	−0.304990	+	0.176086i
$839$	−2.15010	−	1.93596i	−0.0742299	−	0.0668369i	0.631181	−	0.775636i	$-0.282571\pi$
$839$	−2.15010	−	1.93596i	−0.0742299	−	0.0668369i	−0.705411	+	0.708799i	$0.749237\pi$
$840$	−15.7523	+	14.1835i	−0.543507	+	0.489376i
$841$	−24.5111	−	10.9131i	−0.845211	−	0.376312i
$842$	−11.7985			−0.406604
$843$	−8.12300	+	4.68982i	−0.279771	+	0.161526i
$844$	−2.47426	−	23.5411i	−0.0851677	−	0.810317i
$845$	−7.76171	+	28.1168i	−0.267011	+	0.967246i
$846$	0.517267	−	4.92146i	0.0177840	−	0.169203i
$847$	21.6003	−	7.01837i	0.742196	−	0.241154i
$848$	0.574098	−	0.417106i	0.0197146	−	0.0143235i
$849$	7.47866	+	23.0170i	0.256667	+	0.789940i
$850$	−0.0276809	−	0.130228i	−0.000949447	−	0.00446680i
$851$	22.1226	−	30.4492i	0.758354	−	1.04378i
$852$	−7.51832	−	35.3709i	−0.257573	−	1.21179i
$853$	22.3304	+	7.25559i	0.764579	+	0.248427i	0.665243	−	0.746627i	$-0.268328\pi$
$853$	22.3304	+	7.25559i	0.764579	+	0.248427i	0.0993363	+	0.995054i	$0.468328\pi$
$854$	−4.29388	−	3.11969i	−0.146934	−	0.106753i
$855$	3.74018	−	11.5111i	0.127912	−	0.393671i
$856$	−29.3038	−	26.3853i	−1.00158	−	0.901831i
$857$	17.4932	+	7.78846i	0.597555	+	0.266049i	0.683146	−	0.730282i	$-0.260611\pi$
$857$	17.4932	+	7.78846i	0.597555	+	0.266049i	−0.0855909	+	0.996330i	$0.527278\pi$
$858$	−1.01760	+	1.64660i	−0.0347403	+	0.0562138i
$859$	−2.80808	+	26.7171i	−0.0958103	+	0.911575i	0.836025	+	0.548692i	$0.184874\pi$
$859$	−2.80808	+	26.7171i	−0.0958103	+	0.911575i	−0.931835	+	0.362883i	$0.881793\pi$
$860$	−4.24531	−	9.53511i	−0.144764	−	0.325145i
$861$	−9.46659	−	4.21480i	−0.322621	−	0.143640i
$862$	14.8340			0.505247
$863$	5.82536	−	3.36327i	0.198298	−	0.114487i	−0.397564	−	0.917575i	$-0.630144\pi$
$863$	5.82536	−	3.36327i	0.198298	−	0.114487i	0.595861	+	0.803087i	$0.296811\pi$
$864$	−10.3275	+	23.1959i	−0.351349	+	0.789142i
$865$	15.0067	+	4.87598i	0.510244	+	0.165788i
$866$	23.6613	−	7.68801i	0.804042	−	0.261249i
$867$	−17.3728	−	30.0907i	−0.590013	−	1.02193i
$868$	13.2120	+	12.7406i	0.448444	+	0.432446i
$869$	−3.14336	−	1.81482i	−0.106631	−	0.0615635i
$870$	1.28713	+	3.96138i	0.0436378	+	0.134303i
$871$	16.4560	+	40.1562i	0.557591	+	1.36064i
$872$	13.7278	−	9.97383i	0.464882	−	0.337757i
$873$			7.07390i			0.239415i
$874$	10.5101	+	18.2041i	0.355511	+	0.615763i
$875$	18.9231	−	13.7484i	0.639717	−	0.464781i
$876$	0.182295	−	0.250908i	0.00615918	−	0.00847738i
$877$	−18.8880	−	42.4232i	−0.637804	−	1.43253i	−0.885937	−	0.463805i	$-0.846484\pi$
$877$	−18.8880	−	42.4232i	−0.637804	−	1.43253i	0.248134	−	0.968726i	$-0.420183\pi$
$878$	3.21149	−	15.1089i	0.108382	−	0.509899i
$879$	21.2036	−	47.6240i	0.715179	−	1.60632i
$880$	0.474363	+	1.45994i	0.0159908	+	0.0492145i
$881$	8.71660	−	26.8270i	0.293670	−	0.903823i	−0.689995	−	0.723814i	$-0.742387\pi$
$881$	8.71660	−	26.8270i	0.293670	−	0.903823i	0.983665	−	0.180009i	$-0.0576127\pi$
$882$	1.17798	+	0.123811i	0.0396647	+	0.00416893i
$883$	2.48767	−	7.65626i	0.0837168	−	0.257654i	−0.900433	−	0.434996i	$-0.856750\pi$
$883$	2.48767	−	7.65626i	0.0837168	−	0.257654i	0.984149	+	0.177342i	$0.0567499\pi$
$884$	−26.5231	−	20.5113i	−0.892068	−	0.689870i
$885$	41.1586	−	18.3250i	1.38353	−	0.615988i
$886$	7.37303	+	2.39564i	0.247702	+	0.0804832i
$887$	−15.3500	+	17.0479i	−0.515402	+	0.572412i	−0.943522	−	0.331310i	$-0.892509\pi$
$887$	−15.3500	+	17.0479i	−0.515402	+	0.572412i	0.428120	+	0.903722i	$0.359176\pi$
$888$	4.27375	+	40.6620i	0.143418	+	1.36453i
$889$	−27.5024	−	24.7632i	−0.922399	−	0.830532i
$890$	−4.23490	−	9.51175i	−0.141954	−	0.318835i
$891$	4.49227	+	0.472156i	0.150497	+	0.0158178i
$892$	−0.864481	+	0.0908606i	−0.0289450	+	0.00304224i
$893$	83.8481			2.80587
$894$	−1.24437			−0.0416180
$895$	−16.9021	+	1.77649i	−0.564976	+	0.0593814i
$896$	−15.6062	−	17.3324i	−0.521365	−	0.579035i
$897$	15.0973	−	24.4292i	0.504085	−	0.815668i
$898$	4.50908			0.150470
$899$	7.60109	−	3.07729i	0.253511	−	0.102633i
$900$	0.0187644	−	0.0325010i	0.000625481	−	0.00108337i
$901$	−1.75063	+	1.94427i	−0.0583220	+	0.0647731i
$902$	0.532690	−	0.479636i	0.0177366	−	0.0159701i
$903$	4.86372	−	10.9241i	0.161854	−	0.363531i
$904$	18.7543	+	10.8278i	0.623760	+	0.360128i
$905$	25.3767	+	14.6513i	0.843551	+	0.487024i
$906$	17.4989	−	12.7137i	0.581363	−	0.422385i
$907$	−27.6577	+	12.3140i	−0.918360	+	0.408880i	−0.810803	−	0.585319i	$-0.800969\pi$
$907$	−27.6577	+	12.3140i	−0.918360	+	0.408880i	−0.107557	+	0.994199i	$0.534303\pi$
$908$	−8.58028	+	11.8097i	−0.284746	+	0.391920i
$909$	−1.98502	+	2.20459i	−0.0658391	+	0.0731217i
$910$	2.63984	−	10.8158i	0.0875099	−	0.358541i
$911$	19.6918	+	4.18561i	0.652417	+	0.138675i	0.522218	−	0.852812i	$-0.325105\pi$
$911$	19.6918	+	4.18561i	0.652417	+	0.138675i	0.130199	+	0.991488i	$0.458438\pi$
$912$	22.7363	+	7.38748i	0.752875	+	0.244624i
$913$	0.729414	−	6.93992i	0.0241401	−	0.229678i
$914$	−22.7137	+	4.82794i	−0.751301	+	0.159694i
$915$	15.8235	+	5.14137i	0.523109	+	0.169968i
$916$	−0.805267	+	1.10836i	−0.0266068	+	0.0366211i
$917$	−19.5752	+	17.6256i	−0.646431	+	0.582049i
$918$	3.57426	−	16.8155i	0.117968	−	0.554996i
$919$	1.31770	+	12.5370i	0.0434668	+	0.413559i	0.994521	+	0.104535i	$0.0333356\pi$
$919$	1.31770	+	12.5370i	0.0434668	+	0.413559i	−0.951054	+	0.309024i	$0.899998\pi$
$920$	6.72224	+	20.6889i	0.221626	+	0.682094i
$921$	−28.7689	+	39.5970i	−0.947966	+	1.30476i
$922$	18.0179	+	13.0908i	0.593389	+	0.431122i
$923$	31.2121	+	29.8438i	1.02736	+	0.982320i
$924$	−1.34985	+	2.33801i	−0.0444068	+	0.0769148i
$925$			0.311590i			0.0102450i
$926$	−0.749522	−	7.13123i	−0.0246308	−	0.234347i
$927$	2.50268	−	7.70245i	0.0821987	−	0.252982i
$928$	−8.03172	+	2.60966i	−0.263654	+	0.0856664i
$929$	48.5516	−	28.0313i	1.59293	−	0.919677i	0.600125	−	0.799906i	$-0.295118\pi$
$929$	48.5516	−	28.0313i	1.59293	−	0.919677i	0.992802	−	0.119770i	$-0.0382158\pi$
$930$	14.1572	+	6.89255i	0.464233	+	0.226016i
$931$			20.0695i			0.657753i
$932$	26.7315	−	29.6884i	0.875621	−	0.972476i
$933$	32.5199	−	6.91232i	1.06465	−	0.226299i
$934$	−7.88001	+	0.828222i	−0.257842	+	0.0271003i
$935$	−2.82979	−	4.90133i	−0.0925439	−	0.160291i
$936$	1.04987	+	5.78632i	0.0343160	+	0.189132i
$937$	3.53726	+	33.6548i	0.115557	+	1.09945i	0.886557	+	0.462619i	$0.153090\pi$
$937$	3.53726	+	33.6548i	0.115557	+	1.09945i	−0.771000	+	0.636835i	$0.780243\pi$
$938$	−6.73732	−	15.1323i	−0.219981	−	0.494086i
$939$	26.9678	+	19.5932i	0.880060	+	0.639401i
$940$	37.3305	+	7.93483i	1.21759	+	0.258806i
$941$	12.2123	−	27.4293i	0.398109	−	0.894168i	−0.597614	−	0.801784i	$-0.703884\pi$
$941$	12.2123	−	27.4293i	0.398109	−	0.894168i	0.995723	−	0.0923844i	$-0.0294489\pi$
$942$	12.5092	−	4.06448i	0.407571	−	0.132428i
$943$	−7.90309	+	7.11597i	−0.257360	+	0.231728i
$944$	6.82300	+	15.3247i	0.222070	+	0.498777i
$945$	−20.4028	+	4.33676i	−0.663704	+	0.141075i
$946$	0.553482	+	0.614704i	0.0179952	+	0.0199857i
$947$	38.5801	+	4.05494i	1.25369	+	0.131768i	0.707994	−	0.706218i	$-0.249600\pi$
$947$	38.5801	+	4.05494i	1.25369	+	0.131768i	0.545692	+	0.837986i	$0.316267\pi$
$948$	−25.1663	+	5.34927i	−0.817364	+	0.173736i
$949$	−0.0110919	+	0.370204i	−0.000360058	+	0.0120173i
$950$	−0.158977	−	0.0707811i	−0.00515789	−	0.00229644i
$951$	2.99308	−	0.972509i	0.0970571	−	0.0315358i
$952$	23.5405	+	17.1032i	0.762952	+	0.554317i
$953$	−6.13876	+	58.4064i	−0.198854	+	1.89197i	0.207471	+	0.978241i	$0.433477\pi$
$953$	−6.13876	+	58.4064i	−0.198854	+	1.89197i	−0.406325	+	0.913729i	$0.633190\pi$
$954$	0.200719	−	0.0210964i	0.00649850	−	0.000683020i
$955$			5.96626i			0.193064i
$956$	28.5838	+	16.5028i	0.924465	+	0.533740i
$957$	0.708974	+	0.975819i	0.0229179	+	0.0315438i
$958$	4.02686	−	12.3934i	0.130102	−	0.400413i
$959$	−15.4081	−	3.27509i	−0.497553	−	0.105758i
$960$	−2.04085	−	1.17828i	−0.0658680	−	0.0380289i
$961$	11.5722	−	28.7591i	0.373296	−	0.927712i
$962$	−13.8850	−	16.3820i	−0.447670	−	0.528176i
$963$	3.62825	+	11.1666i	0.116919	+	0.359839i
$964$	−0.00864465	−	0.0406699i	−0.000278425	−	0.00130989i
$965$	−2.27178	−	21.6145i	−0.0731310	−	0.695795i
$966$	−5.48067	+	9.49280i	−0.176338	+	0.305426i
$967$	−35.1928	−	20.3186i	−1.13172	−	0.653401i	−0.187356	−	0.982292i	$-0.559992\pi$
$967$	−35.1928	−	20.3186i	−1.13172	−	0.653401i	−0.944368	+	0.328891i	$0.893325\pi$
$968$	14.8830	+	20.4846i	0.478356	+	0.658401i
$969$	−87.6564	−	9.21306i	−2.81593	−	0.295966i
$970$	14.8483	+	1.56062i	0.476751	+	0.0501086i
$971$	2.71809	+	0.577748i	0.0872276	+	0.0185408i	0.251319	−	0.967904i	$-0.419136\pi$
$971$	2.71809	+	0.577748i	0.0872276	+	0.0185408i	−0.164091	+	0.986445i	$0.552469\pi$
$972$	9.02702	−	6.55851i	0.289542	−	0.210364i
$973$	−17.9501	−	16.1623i	−0.575453	−	0.518140i
$974$	17.3207	−	3.68163i	0.554991	−	0.117967i
$975$	0.0177592	+	0.237084i	0.000568750	+	0.00759277i
$976$	−1.91430	+	5.89161i	−0.0612753	+	0.188586i
$977$	0.816578	−	0.735250i	0.0261246	−	0.0235227i	−0.655965	−	0.754791i	$-0.727738\pi$
$977$	0.816578	−	0.735250i	0.0261246	−	0.0235227i	0.682090	+	0.731269i	$0.261071\pi$
$978$	0.477045	−	4.53878i	0.0152542	−	0.145134i
$979$	−2.01749	−	2.24065i	−0.0644794	−	0.0716116i
$980$	−1.89925	+	8.93527i	−0.0606693	+	0.285427i
$981$	−5.02484	+	0.528132i	−0.160431	+	0.0168619i
$982$	0.834226	−	3.92472i	0.0266212	−	0.125243i
$983$	−14.5135	−	1.52543i	−0.462909	−	0.0486537i	−0.129796	−	0.991541i	$-0.541432\pi$
$983$	−14.5135	−	1.52543i	−0.462909	−	0.0486537i	−0.333113	+	0.942887i	$0.608099\pi$
$984$	1.20758	−	11.4893i	0.0384961	−	0.366266i
$985$	−4.10163	−	1.82616i	−0.130689	−	0.0581864i
$986$	4.95174	−	2.85889i	0.157695	−	0.0910455i
$987$	21.8619	+	37.8660i	0.695873	+	1.20529i
$988$	−42.0669	+	12.2884i	−1.33833	+	0.390945i
$989$	−8.21156	−	9.11987i	−0.261113	−	0.289995i
$990$	−0.0907720	+	0.427049i	−0.00288492	+	0.0135725i
$991$	13.3604	−	23.1410i	0.424408	−	0.735097i	−0.571957	−	0.820284i	$-0.693816\pi$
$991$	13.3604	−	23.1410i	0.424408	−	0.735097i	0.996365	+	0.0851872i	$0.0271488\pi$
$992$	−13.9747	+	28.7038i	−0.443696	+	0.911347i
$993$		−	2.02103i		−	0.0641355i
$994$	−12.2492	−	11.0292i	−0.388520	−	0.349825i
$995$	−19.6758	−	6.39305i	−0.623765	−	0.202673i
$996$	−29.0744	−	40.0174i	−0.921256	−	1.26800i
$997$	4.03636	−	6.99118i	0.127833	−	0.221413i	−0.795004	−	0.606604i	$-0.792531\pi$
$997$	4.03636	−	6.99118i	0.127833	−	0.221413i	0.922837	+	0.385191i	$0.125865\pi$
$998$	1.36559	+	2.36527i	0.0432270	+	0.0748714i
$999$	−16.3645	+	36.7552i	−0.517749	+	1.16288i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bt.a.82.14	yes	280
13.10	even	6		403.2.bp.a.361.22	yes	280
31.14	even	15		403.2.bp.a.355.22	✓	280
403.231	even	30	inner	403.2.bt.a.231.14	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bp.a.355.22	✓	280	31.14	even	15
403.2.bp.a.361.22	yes	280	13.10	even	6
403.2.bt.a.82.14	yes	280	1.1	even	1	trivial
403.2.bt.a.231.14	yes	280	403.231	even	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bt (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.136295 + 0.641215i) q^{2} +(-1.88071 + 0.399758i) q^{3} +(1.43451 + 0.638685i) q^{4} +(-1.94312 + 1.12186i) q^{5} -1.26043i q^{6} +(1.23396 + 1.69841i) q^{7} +(-1.37568 + 1.89347i) q^{8} +(0.636641 - 0.283451i) q^{9} +O(q^{10})\)	\(q+(-0.136295 + 0.641215i) q^{2} +(-1.88071 + 0.399758i) q^{3} +(1.43451 + 0.638685i) q^{4} +(-1.94312 + 1.12186i) q^{5} -1.26043i q^{6} +(1.23396 + 1.69841i) q^{7} +(-1.37568 + 1.89347i) q^{8} +(0.636641 - 0.283451i) q^{9} +(-0.454518 - 1.39886i) q^{10} +(-0.250356 - 0.344586i) q^{11} +(-2.95322 - 0.627727i) q^{12} +(3.33628 - 1.36721i) q^{13} +(-1.25723 + 0.559753i) q^{14} +(3.20598 - 2.88668i) q^{15} +(1.07481 + 1.19369i) q^{16} +(-4.79106 - 3.48091i) q^{17} +(0.0949823 + 0.446857i) q^{18} +(-7.36179 + 2.39199i) q^{19} +(-3.50394 + 0.368279i) q^{20} +(-2.99968 - 2.70093i) q^{21} +(0.255076 - 0.113567i) q^{22} +(-3.78436 + 1.68491i) q^{23} +(1.83034 - 4.11101i) q^{24} +(0.0171474 - 0.0297001i) q^{25} +(0.421958 + 2.32561i) q^{26} +(3.58254 - 2.60286i) q^{27} +(0.685387 + 3.22449i) q^{28} +(1.44065 + 0.306219i) q^{29} +(1.41402 + 2.44916i) q^{30} +(4.61368 - 3.11672i) q^{31} +(-4.96569 + 2.86694i) q^{32} +(0.608600 + 0.547986i) q^{33} +(2.88501 - 2.59767i) q^{34} +(-4.30312 - 1.91587i) q^{35} +1.09430 q^{36} +(-7.86840 + 4.54282i) q^{37} +(-0.530409 - 5.04650i) q^{38} +(-5.72803 + 3.90503i) q^{39} +(0.548914 - 5.22256i) q^{40} +(2.44156 - 0.793311i) q^{41} +(2.14072 - 1.55532i) q^{42} +(0.915451 + 2.81747i) q^{43} +(-0.139057 - 0.654211i) q^{44} +(-0.919078 + 1.26500i) q^{45} +(-0.564600 - 2.65623i) q^{46} +(-10.3020 - 3.34733i) q^{47} +(-2.49859 - 1.81533i) q^{48} +(0.801204 - 2.46585i) q^{49} +(0.0167071 + 0.0150431i) q^{50} +(10.4021 + 4.63133i) q^{51} +(5.65914 + 0.169557i) q^{52} +(0.0461789 - 0.439363i) q^{53} +(1.18072 + 2.65193i) q^{54} +(0.873051 + 0.388707i) q^{55} -4.91342 q^{56} +(12.8892 - 7.44158i) q^{57} +(-0.392705 + 0.882029i) q^{58} +(9.93229 + 3.22720i) q^{59} +(6.44269 - 2.09336i) q^{60} +(1.92832 + 3.33995i) q^{61} +(1.36967 + 3.38316i) q^{62} +(1.26701 + 0.731506i) q^{63} +(-0.168801 - 0.519515i) q^{64} +(-4.94897 + 6.39949i) q^{65} +(-0.434326 + 0.315556i) q^{66} +12.0362i q^{67} +(-4.64962 - 8.05338i) q^{68} +(6.44374 - 4.68165i) q^{69} +(1.81498 - 2.49810i) q^{70} +(4.87151 + 10.9416i) q^{71} +(-0.339112 + 1.59540i) q^{72} +(-0.0417809 + 0.0938414i) q^{73} +(-1.84051 - 5.66450i) q^{74} +(-0.0203764 + 0.0627122i) q^{75} +(-12.0883 - 1.27053i) q^{76} +(0.276316 - 0.850414i) q^{77} +(-1.72327 - 4.20513i) q^{78} +(7.78491 - 3.46607i) q^{79} +(-3.42763 - 1.11371i) q^{80} +(-7.09614 + 7.88106i) q^{81} +(0.175912 + 1.67369i) q^{82} +(12.1751 + 10.9625i) q^{83} +(-2.57804 - 5.79036i) q^{84} +(13.2147 + 1.38892i) q^{85} +(-1.93138 + 0.202996i) q^{86} -2.83186 q^{87} +0.996874 q^{88} +(7.04005 - 0.739939i) q^{89} +(-0.685873 - 0.761740i) q^{90} +(6.43892 + 3.97927i) q^{91} -6.50482 q^{92} +(-7.43109 + 7.70601i) q^{93} +(3.55047 - 6.14959i) q^{94} +(11.6214 - 12.9068i) q^{95} +(8.19296 - 7.37697i) q^{96} +(-4.12865 + 9.27309i) q^{97} +(1.47194 + 0.849826i) q^{98} +(-0.257060 - 0.148414i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 9 q^{2} - 3 q^{3} - 35 q^{4} - 15 q^{7} + 45 q^{8} + 24 q^{9}+O(q^{10}) \) 280 * q - 9 * q^2 - 3 * q^3 - 35 * q^4 - 15 * q^7 + 45 * q^8 + 24 * q^9	\( 280 q - 9 q^{2} - 3 q^{3} - 35 q^{4} - 15 q^{7} + 45 q^{8} + 24 q^{9} + 3 q^{10} - 8 q^{12} - 6 q^{13} + 4 q^{14} - 45 q^{15} + 23 q^{16} + 27 q^{17} + 45 q^{18} - 15 q^{19} - 12 q^{20} - 76 q^{21} + 41 q^{22} - 10 q^{23} - 33 q^{24} + 96 q^{25} + 9 q^{26} - 24 q^{27} - 32 q^{28} + 13 q^{29} + 36 q^{30} + 2 q^{31} - 141 q^{32} - 93 q^{33} - 9 q^{34} - 43 q^{35} - 194 q^{36} + 3 q^{37} - 49 q^{38} + 50 q^{39} - 75 q^{40} - 15 q^{41} + 17 q^{42} + 33 q^{43} + 18 q^{44} - 15 q^{45} - 9 q^{46} - 59 q^{48} + 3 q^{49} + 36 q^{50} + 47 q^{51} - 56 q^{52} + 12 q^{53} - 33 q^{54} - 5 q^{55} - 50 q^{56} - 105 q^{57} - 3 q^{58} - 15 q^{59} + 90 q^{60} - 57 q^{61} - 72 q^{62} + 201 q^{63} + 13 q^{64} - 43 q^{65} + 22 q^{66} - 71 q^{68} - 7 q^{69} - 42 q^{71} + 90 q^{72} + 9 q^{73} - 113 q^{74} + 45 q^{75} + 14 q^{76} - 24 q^{77} + 61 q^{78} + 54 q^{79} + 30 q^{80} + 106 q^{81} + 16 q^{82} + 54 q^{83} + 60 q^{84} + 18 q^{85} + 84 q^{86} + 42 q^{87} - 98 q^{88} - 99 q^{89} + 11 q^{90} + 60 q^{91} + 266 q^{92} - 104 q^{93} + 33 q^{94} - 120 q^{95} + 204 q^{96} - 50 q^{97} - 15 q^{98} - 168 q^{99}+O(q^{100}) \) 280 * q - 9 * q^2 - 3 * q^3 - 35 * q^4 - 15 * q^7 + 45 * q^8 + 24 * q^9 + 3 * q^10 - 8 * q^12 - 6 * q^13 + 4 * q^14 - 45 * q^15 + 23 * q^16 + 27 * q^17 + 45 * q^18 - 15 * q^19 - 12 * q^20 - 76 * q^21 + 41 * q^22 - 10 * q^23 - 33 * q^24 + 96 * q^25 + 9 * q^26 - 24 * q^27 - 32 * q^28 + 13 * q^29 + 36 * q^30 + 2 * q^31 - 141 * q^32 - 93 * q^33 - 9 * q^34 - 43 * q^35 - 194 * q^36 + 3 * q^37 - 49 * q^38 + 50 * q^39 - 75 * q^40 - 15 * q^41 + 17 * q^42 + 33 * q^43 + 18 * q^44 - 15 * q^45 - 9 * q^46 - 59 * q^48 + 3 * q^49 + 36 * q^50 + 47 * q^51 - 56 * q^52 + 12 * q^53 - 33 * q^54 - 5 * q^55 - 50 * q^56 - 105 * q^57 - 3 * q^58 - 15 * q^59 + 90 * q^60 - 57 * q^61 - 72 * q^62 + 201 * q^63 + 13 * q^64 - 43 * q^65 + 22 * q^66 - 71 * q^68 - 7 * q^69 - 42 * q^71 + 90 * q^72 + 9 * q^73 - 113 * q^74 + 45 * q^75 + 14 * q^76 - 24 * q^77 + 61 * q^78 + 54 * q^79 + 30 * q^80 + 106 * q^81 + 16 * q^82 + 54 * q^83 + 60 * q^84 + 18 * q^85 + 84 * q^86 + 42 * q^87 - 98 * q^88 - 99 * q^89 + 11 * q^90 + 60 * q^91 + 266 * q^92 - 104 * q^93 + 33 * q^94 - 120 * q^95 + 204 * q^96 - 50 * q^97 - 15 * q^98 - 168 * q^99

Introduction

L-functions

Modular forms

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Database

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