LMFDB - Embedded newform 315.2.be.c.236.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(236,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 5]))

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

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

chi := DirichletCharacter("315.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.be (of order $6$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			236.11
Character	$\chi$	$=$	315.236
Dual form			315.2.be.c.311.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.559417 - 0.322980i) q^{2} +(1.73059 + 0.0712304i) q^{3} +(-0.791368 + 1.37069i) q^{4} -1.00000 q^{5} +(0.991125 - 0.519096i) q^{6} +(1.24717 + 2.33336i) q^{7} +2.31430i q^{8} +(2.98985 + 0.246540i) q^{9} +O(q^{10})$	\(q+(0.559417 - 0.322980i) q^{2} +(1.73059 + 0.0712304i) q^{3} +(-0.791368 + 1.37069i) q^{4} -1.00000 q^{5} +(0.991125 - 0.519096i) q^{6} +(1.24717 + 2.33336i) q^{7} +2.31430i q^{8} +(2.98985 + 0.246540i) q^{9} +(-0.559417 + 0.322980i) q^{10} -1.56399i q^{11} +(-1.46717 + 2.31573i) q^{12} +(-0.956727 + 0.552367i) q^{13} +(1.45131 + 0.902512i) q^{14} +(-1.73059 - 0.0712304i) q^{15} +(-0.835265 - 1.44672i) q^{16} +(-0.145248 - 0.251577i) q^{17} +(1.75220 - 0.827742i) q^{18} +(5.30918 + 3.06526i) q^{19} +(0.791368 - 1.37069i) q^{20} +(1.99212 + 4.12692i) q^{21} +(-0.505136 - 0.874921i) q^{22} -6.45853i q^{23} +(-0.164849 + 4.00510i) q^{24} +1.00000 q^{25} +(-0.356806 + 0.618007i) q^{26} +(5.15663 + 0.639628i) q^{27} +(-4.18528 - 0.137068i) q^{28} +(-0.416026 - 0.240193i) q^{29} +(-0.991125 + 0.519096i) q^{30} +(-9.17552 - 5.29749i) q^{31} +(-4.94301 - 2.85385i) q^{32} +(0.111403 - 2.70661i) q^{33} +(-0.162508 - 0.0938243i) q^{34} +(-1.24717 - 2.33336i) q^{35} +(-2.70401 + 3.90306i) q^{36} +(2.72367 - 4.71754i) q^{37} +3.96006 q^{38} +(-1.69504 + 0.887770i) q^{39} -2.31430i q^{40} +(-0.348441 - 0.603517i) q^{41} +(2.44734 + 1.66525i) q^{42} +(-1.52356 + 2.63889i) q^{43} +(2.14374 + 1.23769i) q^{44} +(-2.98985 - 0.246540i) q^{45} +(-2.08597 - 3.61301i) q^{46} +(-0.153022 - 0.265042i) q^{47} +(-1.34245 - 2.56317i) q^{48} +(-3.88915 + 5.82018i) q^{49} +(0.559417 - 0.322980i) q^{50} +(-0.233444 - 0.445721i) q^{51} -1.74850i q^{52} +(7.22102 - 4.16906i) q^{53} +(3.09130 - 1.30767i) q^{54} +1.56399i q^{55} +(-5.40010 + 2.88632i) q^{56} +(8.96966 + 5.68287i) q^{57} -0.310309 q^{58} +(2.76016 - 4.78073i) q^{59} +(1.46717 - 2.31573i) q^{60} +(1.94411 - 1.12243i) q^{61} -6.84392 q^{62} +(3.15358 + 7.28388i) q^{63} -0.345879 q^{64} +(0.956727 - 0.552367i) q^{65} +(-0.811860 - 1.55011i) q^{66} +(-3.96895 + 6.87443i) q^{67} +0.459779 q^{68} +(0.460043 - 11.1770i) q^{69} +(-1.45131 - 0.902512i) q^{70} -10.5800i q^{71} +(-0.570569 + 6.91942i) q^{72} +(-10.9573 + 6.32622i) q^{73} -3.51876i q^{74} +(1.73059 + 0.0712304i) q^{75} +(-8.40304 + 4.85150i) q^{76} +(3.64935 - 1.95055i) q^{77} +(-0.661505 + 1.04410i) q^{78} +(-1.76243 - 3.05262i) q^{79} +(0.835265 + 1.44672i) q^{80} +(8.87844 + 1.47424i) q^{81} +(-0.389847 - 0.225078i) q^{82} +(-0.398678 + 0.690530i) q^{83} +(-7.23323 - 0.535327i) q^{84} +(0.145248 + 0.251577i) q^{85} +1.96832i q^{86} +(-0.702859 - 0.445308i) q^{87} +3.61954 q^{88} +(-5.51450 + 9.55140i) q^{89} +(-1.75220 + 0.827742i) q^{90} +(-2.48207 - 1.54350i) q^{91} +(8.85264 + 5.11107i) q^{92} +(-15.5017 - 9.82133i) q^{93} +(-0.171207 - 0.0988462i) q^{94} +(-5.30918 - 3.06526i) q^{95} +(-8.35102 - 5.29092i) q^{96} +(7.45344 + 4.30325i) q^{97} +(-0.295855 + 4.51202i) q^{98} +(0.385586 - 4.67609i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9}+O(q^{10}) $ 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9	$ 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9} + 15 q^{12} - 6 q^{13} - 6 q^{14} - q^{15} - 16 q^{16} + 3 q^{17} + 41 q^{18} - 16 q^{20} - 17 q^{21} - 21 q^{22} - 26 q^{24} + 32 q^{25} - 12 q^{26} - 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 24 q^{31} - 19 q^{33} + 30 q^{34} - q^{35} + 18 q^{36} - q^{37} - 60 q^{38} - 36 q^{39} - 6 q^{41} + 44 q^{42} - 19 q^{43} - 21 q^{44} - 7 q^{45} + 6 q^{46} - 15 q^{47} + 35 q^{48} + 23 q^{49} - 9 q^{51} + 24 q^{53} - 58 q^{54} + 33 q^{56} + 27 q^{57} + 15 q^{59} - 15 q^{60} - 9 q^{61} - 11 q^{63} + 76 q^{64} + 6 q^{65} + 22 q^{66} + 25 q^{67} - 6 q^{68} + 50 q^{69} + 6 q^{70} + 61 q^{72} + 12 q^{73} + q^{75} - 54 q^{76} - 27 q^{77} - 42 q^{78} - 2 q^{79} + 16 q^{80} + 43 q^{81} - 24 q^{82} + 42 q^{83} - 36 q^{84} - 3 q^{85} - 55 q^{87} - 84 q^{88} - 30 q^{89} - 41 q^{90} - 57 q^{91} + 6 q^{92} - 48 q^{93} + 24 q^{94} - 9 q^{96} + 42 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) $ 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9 + 15 * q^12 - 6 * q^13 - 6 * q^14 - q^15 - 16 * q^16 + 3 * q^17 + 41 * q^18 - 16 * q^20 - 17 * q^21 - 21 * q^22 - 26 * q^24 + 32 * q^25 - 12 * q^26 - 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 24 * q^31 - 19 * q^33 + 30 * q^34 - q^35 + 18 * q^36 - q^37 - 60 * q^38 - 36 * q^39 - 6 * q^41 + 44 * q^42 - 19 * q^43 - 21 * q^44 - 7 * q^45 + 6 * q^46 - 15 * q^47 + 35 * q^48 + 23 * q^49 - 9 * q^51 + 24 * q^53 - 58 * q^54 + 33 * q^56 + 27 * q^57 + 15 * q^59 - 15 * q^60 - 9 * q^61 - 11 * q^63 + 76 * q^64 + 6 * q^65 + 22 * q^66 + 25 * q^67 - 6 * q^68 + 50 * q^69 + 6 * q^70 + 61 * q^72 + 12 * q^73 + q^75 - 54 * q^76 - 27 * q^77 - 42 * q^78 - 2 * q^79 + 16 * q^80 + 43 * q^81 - 24 * q^82 + 42 * q^83 - 36 * q^84 - 3 * q^85 - 55 * q^87 - 84 * q^88 - 30 * q^89 - 41 * q^90 - 57 * q^91 + 6 * q^92 - 48 * q^93 + 24 * q^94 - 9 * q^96 + 42 * q^97 - 6 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.559417	−	0.322980i	0.395568	−	0.228381i	−0.289002	−	0.957328i	$-0.593323\pi$
$2$	0.559417	−	0.322980i	0.395568	−	0.228381i	0.684570	+	0.728947i	$0.259990\pi$
$3$	1.73059	+	0.0712304i	0.999154	+	0.0411249i
$3$	1.73059	+	0.0712304i	0.999154	+	0.0411249i
$4$	−0.791368	+	1.37069i	−0.395684	+	0.685345i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.991125	−	0.519096i	0.404625	−	0.211920i
$7$	1.24717	+	2.33336i	0.471385	+	0.881928i
$7$	1.24717	+	2.33336i	0.471385	+	0.881928i
$8$			2.31430i			0.818229i
$9$	2.98985	+	0.246540i	0.996617	+	0.0821801i
$10$	−0.559417	+	0.322980i	−0.176903	+	0.102135i
$11$		−	1.56399i		−	0.471560i	−0.971806	−	0.235780i	$-0.924236\pi$
$11$		−	1.56399i		−	0.471560i	0.971806	−	0.235780i	$-0.0757645\pi$
$12$	−1.46717	+	2.31573i	−0.423534	+	0.668493i
$13$	−0.956727	+	0.552367i	−0.265348	+	0.153199i	−0.626772	−	0.779203i	$-0.715624\pi$
$13$	−0.956727	+	0.552367i	−0.265348	+	0.153199i	0.361423	+	0.932402i	$0.382291\pi$
$14$	1.45131	+	0.902512i	0.387880	+	0.241207i
$15$	−1.73059	−	0.0712304i	−0.446835	−	0.0183916i
$16$	−0.835265	−	1.44672i	−0.208816	−	0.361680i
$17$	−0.145248	−	0.251577i	−0.0352278	−	0.0610164i	0.847874	−	0.530198i	$-0.177882\pi$
$17$	−0.145248	−	0.251577i	−0.0352278	−	0.0610164i	−0.883102	+	0.469181i	$0.844549\pi$
$18$	1.75220	−	0.827742i	0.412998	−	0.195101i
$19$	5.30918	+	3.06526i	1.21801	+	0.703219i	0.964492	−	0.264112i	$-0.0850788\pi$
$19$	5.30918	+	3.06526i	1.21801	+	0.703219i	0.253518	+	0.967331i	$0.418412\pi$
$20$	0.791368	−	1.37069i	0.176955	−	0.306496i
$21$	1.99212	+	4.12692i	0.434717	+	0.900567i
$22$	−0.505136	−	0.874921i	−0.107695	−	0.186534i
$23$		−	6.45853i		−	1.34670i	−0.739326	−	0.673348i	$-0.764856\pi$
$23$		−	6.45853i		−	1.34670i	0.739326	−	0.673348i	$-0.235144\pi$
$24$	−0.164849	+	4.00510i	−0.0336496	+	0.817537i
$25$	1.00000			0.200000
$26$	−0.356806	+	0.618007i	−0.0699755	+	0.121201i
$27$	5.15663	+	0.639628i	0.992395	+	0.123096i
$28$	−4.18528	−	0.137068i	−0.790944	−	0.0259034i
$29$	−0.416026	−	0.240193i	−0.0772541	−	0.0446026i	0.460875	−	0.887465i	$-0.347536\pi$
$29$	−0.416026	−	0.240193i	−0.0772541	−	0.0446026i	−0.538129	+	0.842862i	$0.680869\pi$
$30$	−0.991125	+	0.519096i	−0.180954	+	0.0947736i
$31$	−9.17552	−	5.29749i	−1.64797	−	0.951457i	−0.977877	−	0.209182i	$-0.932920\pi$
$31$	−9.17552	−	5.29749i	−1.64797	−	0.951457i	−0.670095	−	0.742275i	$-0.733747\pi$
$32$	−4.94301	−	2.85385i	−0.873809	−	0.504494i
$33$	0.111403	−	2.70661i	0.0193928	−	0.471161i
$34$	−0.162508	−	0.0938243i	−0.0278700	−	0.0160907i
$35$	−1.24717	−	2.33336i	−0.210810	−	0.394410i
$36$	−2.70401	+	3.90306i	−0.450668	+	0.650510i
$37$	2.72367	−	4.71754i	0.447769	−	0.775558i	−0.550472	−	0.834854i	$-0.685552\pi$
$37$	2.72367	−	4.71754i	0.447769	−	0.775558i	0.998240	+	0.0592957i	$0.0188855\pi$
$38$	3.96006			0.642407
$39$	−1.69504	+	0.887770i	−0.271424	+	0.142157i
$40$		−	2.31430i		−	0.365923i
$41$	−0.348441	−	0.603517i	−0.0544173	−	0.0942535i	0.837534	−	0.546386i	$-0.183997\pi$
$41$	−0.348441	−	0.603517i	−0.0544173	−	0.0942535i	−0.891951	+	0.452132i	$0.850663\pi$
$42$	2.44734	+	1.66525i	0.377632	+	0.256954i
$43$	−1.52356	+	2.63889i	−0.232341	+	0.402427i	−0.958497	−	0.285104i	$-0.907972\pi$
$43$	−1.52356	+	2.63889i	−0.232341	+	0.402427i	0.726155	+	0.687531i	$0.241305\pi$
$44$	2.14374	+	1.23769i	0.323181	+	0.186589i
$45$	−2.98985	−	0.246540i	−0.445701	−	0.0367521i
$46$	−2.08597	−	3.61301i	−0.307560	−	0.532709i
$47$	−0.153022	−	0.265042i	−0.0223206	−	0.0386604i	0.854649	−	0.519206i	$-0.173772\pi$
$47$	−0.153022	−	0.265042i	−0.0223206	−	0.0386604i	−0.876970	+	0.480545i	$0.840439\pi$
$48$	−1.34245	−	2.56317i	−0.193766	−	0.369962i
$49$	−3.88915	+	5.82018i	−0.555592	+	0.831455i
$50$	0.559417	−	0.322980i	0.0791135	−	0.0456762i
$51$	−0.233444	−	0.445721i	−0.0326887	−	0.0624135i
$52$		−	1.74850i		−	0.242474i
$53$	7.22102	−	4.16906i	0.991883	−	0.572664i	0.0860465	−	0.996291i	$-0.472577\pi$
$53$	7.22102	−	4.16906i	0.991883	−	0.572664i	0.905837	+	0.423627i	$0.139243\pi$
$54$	3.09130	−	1.30767i	0.420672	−	0.177951i
$55$			1.56399i			0.210888i
$56$	−5.40010	+	2.88632i	−0.721619	+	0.385701i
$57$	8.96966	+	5.68287i	1.18806	+	0.752714i
$58$	−0.310309			−0.0407456
$59$	2.76016	−	4.78073i	0.359342	−	0.622398i	−0.628509	−	0.777802i	$-0.716335\pi$
$59$	2.76016	−	4.78073i	0.359342	−	0.622398i	0.987851	+	0.155404i	$0.0496679\pi$
$60$	1.46717	−	2.31573i	0.189410	−	0.298959i
$61$	1.94411	−	1.12243i	0.248918	−	0.143713i	−0.370351	−	0.928892i	$-0.620763\pi$
$61$	1.94411	−	1.12243i	0.248918	−	0.143713i	0.619269	+	0.785179i	$0.287429\pi$
$62$	−6.84392			−0.869179
$63$	3.15358	+	7.28388i	0.397314	+	0.917683i
$64$	−0.345879			−0.0432348
$65$	0.956727	−	0.552367i	0.118667	−	0.0685127i
$66$	−0.811860	−	1.55011i	−0.0999331	−	0.190805i
$67$	−3.96895	+	6.87443i	−0.484885	+	0.839845i	−0.999849	−	0.0173664i	$-0.994472\pi$
$67$	−3.96895	+	6.87443i	−0.484885	+	0.839845i	0.514964	+	0.857212i	$0.327805\pi$
$68$	0.459779			0.0557564
$69$	0.460043	−	11.1770i	0.0553827	−	1.34556i
$70$	−1.45131	−	0.902512i	−0.173465	−	0.107871i
$71$		−	10.5800i		−	1.25561i	−0.778369	−	0.627807i	$-0.783953\pi$
$71$		−	10.5800i		−	1.25561i	0.778369	−	0.627807i	$-0.216047\pi$
$72$	−0.570569	+	6.91942i	−0.0672422	+	0.815461i
$73$	−10.9573	+	6.32622i	−1.28246	+	0.740428i	−0.977297	−	0.211872i	$-0.932044\pi$
$73$	−10.9573	+	6.32622i	−1.28246	+	0.740428i	−0.305162	+	0.952301i	$0.598711\pi$
$74$		−	3.51876i		−	0.409047i
$75$	1.73059	+	0.0712304i	0.199831	+	0.00822497i
$76$	−8.40304	+	4.85150i	−0.963895	+	0.556505i
$77$	3.64935	−	1.95055i	0.415882	−	0.222286i
$78$	−0.661505	+	1.04410i	−0.0749007	+	0.118221i
$79$	−1.76243	−	3.05262i	−0.198289	−	0.343447i	0.749685	−	0.661795i	$-0.230205\pi$
$79$	−1.76243	−	3.05262i	−0.198289	−	0.343447i	−0.947974	+	0.318348i	$0.896872\pi$
$80$	0.835265	+	1.44672i	0.0933855	+	0.161748i
$81$	8.87844	+	1.47424i	0.986493	+	0.163804i
$82$	−0.389847	−	0.225078i	−0.0430514	−	0.0248557i
$83$	−0.398678	+	0.690530i	−0.0437605	+	0.0757955i	−0.887076	−	0.461623i	$-0.847267\pi$
$83$	−0.398678	+	0.690530i	−0.0437605	+	0.0757955i	0.843316	+	0.537419i	$0.180601\pi$
$84$	−7.23323	−	0.535327i	−0.789210	−	0.0584090i
$85$	0.145248	+	0.251577i	0.0157544	+	0.0272873i
$86$			1.96832i			0.212249i
$87$	−0.702859	−	0.445308i	−0.0753544	−	0.0477420i
$88$	3.61954			0.385844
$89$	−5.51450	+	9.55140i	−0.584536	+	1.01245i	0.410397	+	0.911907i	$0.365390\pi$
$89$	−5.51450	+	9.55140i	−0.584536	+	1.01245i	−0.994933	+	0.100539i	$0.967943\pi$
$90$	−1.75220	+	0.827742i	−0.184698	+	0.0872517i
$91$	−2.48207	−	1.54350i	−0.260192	−	0.161802i
$92$	8.85264	+	5.11107i	0.922951	+	0.532866i
$93$	−15.5017	−	9.82133i	−1.60745	−	1.01842i
$94$	−0.171207	−	0.0988462i	−0.0176586	−	0.0101952i
$95$	−5.30918	−	3.06526i	−0.544711	−	0.314489i
$96$	−8.35102	−	5.29092i	−0.852323	−	0.540002i
$97$	7.45344	+	4.30325i	0.756782	+	0.436928i	0.828139	−	0.560522i	$-0.189400\pi$
$97$	7.45344	+	4.30325i	0.756782	+	0.436928i	−0.0713569	+	0.997451i	$0.522733\pi$
$98$	−0.295855	+	4.51202i	−0.0298858	+	0.455783i
$99$	0.385586	−	4.67609i	0.0387529	−	0.469965i
$100$	−0.791368	+	1.37069i	−0.0791368	+	0.137069i
$101$	−16.9691			−1.68848			−0.844242	−	0.535962i	$-0.819949\pi$
$101$	−16.9691			−1.68848			−0.844242	+	0.535962i	$0.819949\pi$
$102$	−0.274552	−	0.173946i	−0.0271847	−	0.0172233i
$103$			5.78839i			0.570347i	0.958476	+	0.285174i	$0.0920513\pi$
$103$			5.78839i			0.570347i	−0.958476	+	0.285174i	$0.907949\pi$
$104$	−1.27834	−	2.21416i	−0.125352	−	0.217116i
$105$	−1.99212	−	4.12692i	−0.194411	−	0.402746i
$106$	2.69304	−	4.66448i	0.261571	−	0.453055i
$107$	6.14405	+	3.54727i	0.593967	+	0.342927i	0.766665	−	0.642048i	$-0.221915\pi$
$107$	6.14405	+	3.54727i	0.593967	+	0.342927i	−0.172697	+	0.984975i	$0.555248\pi$
$108$	−4.95753	+	6.56197i	−0.477038	+	0.631426i
$109$	−6.51984	−	11.2927i	−0.624488	−	1.08164i	−0.988640	−	0.150305i	$-0.951974\pi$
$109$	−6.51984	−	11.2927i	−0.624488	−	1.08164i	0.364152	−	0.931340i	$-0.381359\pi$
$110$	0.505136	+	0.874921i	0.0481628	+	0.0834205i
$111$	5.04958	−	7.97009i	0.479285	−	0.756488i
$112$	2.33401	−	3.75328i	0.220543	−	0.354651i
$113$	13.6757	−	7.89569i	1.28651	−	0.742764i	0.308476	−	0.951232i	$-0.400181\pi$
$113$	13.6757	−	7.89569i	1.28651	−	0.742764i	0.978029	+	0.208468i	$0.0668476\pi$
$114$	6.85323	+	0.282077i	0.641864	+	0.0264189i
$115$			6.45853i			0.602261i
$116$	0.658459	−	0.380162i	0.0611364	−	0.0352971i
$117$	−2.99665	+	1.41562i	−0.277041	+	0.130874i
$118$		−	3.56590i		−	0.328267i
$119$	0.405871	−	0.652675i	0.0372062	−	0.0598306i
$120$	0.164849	−	4.00510i	0.0150485	−	0.365614i
$121$	8.55394			0.777631
$122$	0.725045	−	1.25581i	0.0656425	−	0.113696i
$123$	−0.560018	−	1.06926i	−0.0504951	−	0.0964117i
$124$	14.5224	−	8.38453i	1.30415	−	0.752953i
$125$	−1.00000			−0.0894427
$126$	4.11671	+	3.05619i	0.366746	+	0.272267i
$127$	14.2360			1.26324			0.631620	−	0.775279i	$-0.282391\pi$
$127$	14.2360			1.26324			0.631620	+	0.775279i	$0.282391\pi$
$128$	9.69253	−	5.59598i	0.856707	−	0.494620i
$129$	−2.82463	+	4.45830i	−0.248695	+	0.392532i
$130$	0.356806	−	0.618007i	0.0312940	−	0.0542028i
$131$	−13.3583			−1.16712			−0.583559	−	0.812071i	$-0.698340\pi$
$131$	−13.3583			−1.16712			−0.583559	+	0.812071i	$0.698340\pi$
$132$	3.62177	+	2.29463i	0.315235	+	0.199722i
$133$	−0.530914	+	16.2111i	−0.0460361	+	1.40568i
$134$			5.12756i			0.442954i
$135$	−5.15663	−	0.639628i	−0.443812	−	0.0550504i
$136$	0.582225	−	0.336148i	0.0499254	−	0.0288244i
$137$		−	8.44482i		−	0.721490i	−0.932665	−	0.360745i	$-0.882523\pi$
$137$		−	8.44482i		−	0.721490i	0.932665	−	0.360745i	$-0.117477\pi$
$138$	−3.35260	−	6.40120i	−0.285392	−	0.544907i
$139$	−3.04415	+	1.75754i	−0.258201	+	0.149073i	−0.623514	−	0.781812i	$-0.714295\pi$
$139$	−3.04415	+	1.75754i	−0.258201	+	0.149073i	0.365312	+	0.930885i	$0.380962\pi$
$140$	4.18528	+	0.137068i	0.353721	+	0.0115844i
$141$	−0.245939	−	0.469578i	−0.0207118	−	0.0395456i
$142$	−3.41712	−	5.91863i	−0.286758	−	0.496680i
$143$	0.863895	+	1.49631i	0.0722425	+	0.125128i
$144$	−2.14064	−	4.53141i	−0.178387	−	0.377617i
$145$	0.416026	+	0.240193i	0.0345491	+	0.0199469i
$146$	−4.08648	+	7.07799i	−0.338199	+	0.585779i
$147$	−7.14508	+	9.79530i	−0.589316	+	0.807903i
$148$	4.31085	+	7.46662i	0.354350	+	0.613752i
$149$			22.6145i			1.85265i	0.376725	+	0.926325i	$0.377050\pi$
$149$			22.6145i			1.85265i	−0.376725	+	0.926325i	$0.622950\pi$
$150$	0.991125	−	0.519096i	0.0809250	−	0.0423840i
$151$	8.21423			0.668464			0.334232	−	0.942491i	$-0.391523\pi$
$151$	8.21423			0.668464			0.334232	+	0.942491i	$0.391523\pi$
$152$	−7.09393	+	12.2871i	−0.575394	+	0.996612i
$153$	−0.372246	−	0.787987i	−0.0300943	−	0.0637050i
$154$	1.41152	−	2.26984i	0.113743	−	0.182909i
$155$	9.17552	+	5.29749i	0.736996	+	0.425505i
$156$	0.124546	−	3.02593i	0.00997170	−	0.242269i
$157$	3.27510	+	1.89088i	0.261381	+	0.150909i	0.624965	−	0.780653i	$-0.285113\pi$
$157$	3.27510	+	1.89088i	0.261381	+	0.150909i	−0.363583	+	0.931562i	$0.618447\pi$
$158$	−1.97187	−	1.13846i	−0.156874	−	0.0905710i
$159$	12.7936	−	6.70055i	1.01459	−	0.531388i
$160$	4.94301	+	2.85385i	0.390779	+	0.225617i
$161$	15.0701	−	8.05486i	1.18769	−	0.634812i
$162$	5.44290	−	2.04284i	0.427634	−	0.160501i
$163$	0.766202	−	1.32710i	0.0600135	−	0.103946i	−0.834458	−	0.551072i	$-0.814219\pi$
$163$	0.766202	−	1.32710i	0.0600135	−	0.103946i	0.894471	+	0.447126i	$0.147552\pi$
$164$	1.10298			0.0861282
$165$	−0.111403	+	2.70661i	−0.00867274	+	0.210710i
$166$			0.515059i			0.0399763i
$167$	12.6284	+	21.8730i	0.977213	+	1.69258i	0.672431	+	0.740159i	$0.265250\pi$
$167$	12.6284	+	21.8730i	0.977213	+	1.69258i	0.304781	+	0.952422i	$0.401417\pi$
$168$	−9.55093	+	4.61037i	−0.736870	+	0.355698i
$169$	−5.88978	+	10.2014i	−0.453060	+	0.784723i
$170$	0.162508	+	0.0938243i	0.0124638	+	0.00719599i
$171$	15.1180	+	10.4736i	1.15610	+	0.800936i
$172$	−2.41140	−	4.17667i	−0.183868	−	0.318468i
$173$	1.41188	+	2.44545i	0.107343	+	0.185924i	0.914693	−	0.404149i	$-0.132432\pi$
$173$	1.41188	+	2.44545i	0.107343	+	0.185924i	−0.807350	+	0.590073i	$0.799099\pi$
$174$	−0.537017	−	0.0221034i	−0.0407111	−	0.00167566i
$175$	1.24717	+	2.33336i	0.0942770	+	0.176386i
$176$	−2.26265	+	1.30634i	−0.170554	+	0.0984694i
$177$	5.11722	−	8.07686i	0.384634	−	0.607094i
$178$			7.12429i			0.533988i
$179$	−16.8195	+	9.71074i	−1.25715	+	0.725814i	−0.972519	−	0.232823i	$-0.925204\pi$
$179$	−16.8195	+	9.71074i	−1.25715	+	0.725814i	−0.284629	+	0.958638i	$0.591870\pi$
$180$	2.70401	−	3.90306i	0.201545	−	0.290917i
$181$		−	25.8284i		−	1.91981i	−0.280331	−	0.959903i	$-0.590444\pi$
$181$		−	25.8284i		−	1.91981i	0.280331	−	0.959903i	$-0.409556\pi$
$182$	−1.88703	−	0.0618002i	−0.139876	−	0.00458093i
$183$	3.44440	−	1.80398i	0.254617	−	0.133354i
$184$	14.9470			1.10191
$185$	−2.72367	+	4.71754i	−0.200248	+	0.346840i
$186$	−11.8440	−	0.487495i	−0.868444	−	0.0357449i
$187$	−0.393463	+	0.227166i	−0.0287729	+	0.0166120i
$188$	0.484388			0.0353276
$189$	4.93870	+	12.8300i	0.359238	+	0.933246i
$190$	−3.96006			−0.287293
$191$	−11.4606	+	6.61675i	−0.829256	+	0.478771i	−0.853598	−	0.520932i	$-0.825584\pi$
$191$	−11.4606	+	6.61675i	−0.829256	+	0.478771i	0.0243416	+	0.999704i	$0.492251\pi$
$192$	−0.598573	−	0.0246371i	−0.0431982	−	0.00177803i
$193$	4.81802	−	8.34506i	0.346809	−	0.600691i	−0.638872	−	0.769313i	$-0.720599\pi$
$193$	4.81802	−	8.34506i	0.346809	−	0.600691i	0.985681	+	0.168623i	$0.0539319\pi$
$194$	5.55944			0.399145
$195$	1.69504	−	0.887770i	0.121385	−	0.0635745i
$196$	−4.89992	−	9.93673i	−0.349994	−	0.709766i
$197$		−	21.1621i		−	1.50774i	−0.657026	−	0.753868i	$-0.728186\pi$
$197$		−	21.1621i		−	1.50774i	0.657026	−	0.753868i	$-0.271814\pi$
$198$	−1.29458	−	2.74042i	−0.0920017	−	0.194753i
$199$	−3.72171	+	2.14873i	−0.263825	+	0.152319i	−0.626078	−	0.779760i	$-0.715341\pi$
$199$	−3.72171	+	2.14873i	−0.263825	+	0.152319i	0.362253	+	0.932080i	$0.382008\pi$
$200$			2.31430i			0.163646i
$201$	−7.35828	+	11.6141i	−0.519013	+	0.819194i
$202$	−9.49277	+	5.48066i	−0.667909	+	0.385618i
$203$	0.0416022	−	1.27030i	0.00291991	−	0.0891575i
$204$	0.795686	+	0.0327502i	0.0557092	+	0.00229297i
$205$	0.348441	+	0.603517i	0.0243361	+	0.0421514i
$206$	1.86953	+	3.23812i	0.130256	+	0.225611i
$207$	1.59229	−	19.3100i	0.110672	−	1.34214i
$208$	1.59824	+	0.922745i	0.110818	+	0.0639809i
$209$	4.79403	−	8.30350i	0.331610	−	0.574365i
$210$	−2.44734	−	1.66525i	−0.168882	−	0.114913i
$211$	5.28865	+	9.16022i	0.364086	+	0.630615i	0.988629	−	0.150375i	$-0.0480481\pi$
$211$	5.28865	+	9.16022i	0.364086	+	0.630615i	−0.624543	+	0.780990i	$0.714715\pi$
$212$			13.1970i			0.906376i
$213$	0.753617	−	18.3096i	0.0516370	−	1.25455i
$214$	4.58278			0.313272
$215$	1.52356	−	2.63889i	0.103906	−	0.179971i
$216$	−1.48029	+	11.9340i	−0.100721	+	0.812006i
$217$	0.917545	−	28.0167i	0.0622870	−	1.90189i
$218$	−7.29462	−	4.21155i	−0.494054	−	0.285242i
$219$	−19.4132	+	10.1676i	−1.31182	+	0.687061i
$220$	−2.14374	−	1.23769i	−0.144531	−	0.0834451i
$221$	0.277925	+	0.160460i	0.0186953	+	0.0107937i
$222$	0.250642	−	6.08951i	0.0168220	−	0.408701i
$223$	22.5466	+	13.0173i	1.50983	+	0.871703i	0.999934	+	0.0114694i	$0.00365089\pi$
$223$	22.5466	+	13.0173i	1.50983	+	0.871703i	0.509900	+	0.860234i	$0.329682\pi$
$224$	0.494297	−	15.0931i	0.0330266	−	1.00845i
$225$	2.98985	+	0.246540i	0.199323	+	0.0164360i
$226$	5.10029	−	8.83397i	0.339267	−	0.587627i
$227$	−28.7973			−1.91134			−0.955671	−	0.294437i	$-0.904868\pi$
$227$	−28.7973			−1.91134			−0.955671	+	0.294437i	$0.904868\pi$
$228$	−14.8878	+	7.79738i	−0.985966	+	0.516394i
$229$			0.460692i			0.0304434i	0.999884	+	0.0152217i	$0.00484540\pi$
$229$			0.460692i			0.0304434i	−0.999884	+	0.0152217i	$0.995155\pi$
$230$	2.08597	+	3.61301i	0.137545	+	0.238235i
$231$	6.45445	−	3.11566i	0.424671	−	0.204995i
$232$	0.555878	−	0.962809i	0.0364952	−	0.0632115i
$233$	19.4028	+	11.2022i	1.27112	+	0.733883i	0.975199	−	0.221329i	$-0.0710393\pi$
$233$	19.4028	+	11.2022i	1.27112	+	0.733883i	0.295924	+	0.955212i	$0.404373\pi$
$234$	−1.21916	+	1.75978i	−0.0796991	+	0.115041i
$235$	0.153022	+	0.265042i	0.00998208	+	0.0172895i
$236$	4.36860	+	7.56664i	0.284372	+	0.492546i
$237$	−2.83260	−	5.40837i	−0.183997	−	0.351311i
$238$	0.0162507	−	0.496205i	0.00105338	−	0.0321642i
$239$	−20.7712	+	11.9923i	−1.34358	+	0.775715i	−0.987331	−	0.158677i	$-0.949277\pi$
$239$	−20.7712	+	11.9923i	−1.34358	+	0.775715i	−0.356247	+	0.934392i	$0.615944\pi$
$240$	1.34245	+	2.56317i	0.0866546	+	0.165452i
$241$		−	2.33078i		−	0.150139i	−0.997178	−	0.0750695i	$-0.976082\pi$
$241$		−	2.33078i		−	0.150139i	0.997178	−	0.0750695i	$-0.0239179\pi$
$242$	4.78522	−	2.76275i	0.307606	−	0.177596i
$243$	15.2599	+	3.18371i	0.978922	+	0.204235i
$244$			3.55303i			0.227459i
$245$	3.88915	−	5.82018i	0.248468	−	0.371838i
$246$	−0.658631	−	0.417286i	−0.0419928	−	0.0266052i
$247$	−6.77259			−0.430929
$248$	12.2600	−	21.2349i	0.778510	−	1.34842i
$249$	−0.739132	+	1.16662i	−0.0468406	+	0.0739317i
$250$	−0.559417	+	0.322980i	−0.0353806	+	0.0204270i
$251$	−8.29788			−0.523758			−0.261879	−	0.965101i	$-0.584342\pi$
$251$	−8.29788			−0.523758			−0.261879	+	0.965101i	$0.584342\pi$
$252$	−12.4796	−	1.44165i	−0.786140	−	0.0908157i
$253$	−10.1011			−0.635048
$254$	7.96385	−	4.59793i	0.499696	−	0.288500i
$255$	0.233444	+	0.445721i	0.0146188	+	0.0279122i
$256$	3.96066	−	6.86006i	0.247541	−	0.428754i
$257$	−16.8915			−1.05366			−0.526831	−	0.849970i	$-0.676620\pi$
$257$	−16.8915			−1.05366			−0.526831	+	0.849970i	$0.676620\pi$
$258$	−0.140204	+	3.40635i	−0.00872873	+	0.212070i
$259$	14.4046	+	0.471750i	0.895057	+	0.0293131i
$260$			1.74850i			0.108438i
$261$	−1.18464	−	0.820708i	−0.0733273	−	0.0508005i
$262$	−7.47285	+	4.31445i	−0.461674	+	0.266548i
$263$			15.6019i			0.962056i	0.876705	+	0.481028i	$0.159736\pi$
$263$			15.6019i			0.962056i	−0.876705	+	0.481028i	$0.840264\pi$
$264$	6.26392	+	0.257821i	0.385518	+	0.0158678i
$265$	−7.22102	+	4.16906i	−0.443584	+	0.256103i
$266$	4.93886	+	9.24026i	0.302821	+	0.566557i
$267$	−10.2237	+	16.1367i	−0.625678	+	0.987551i
$268$	−6.28181	−	10.8804i	−0.383723	−	0.664627i
$269$	−13.5334	−	23.4405i	−0.825143	−	1.42919i	−0.901810	−	0.432133i	$-0.857761\pi$
$269$	−13.5334	−	23.4405i	−0.825143	−	1.42919i	0.0766668	−	0.997057i	$-0.475572\pi$
$270$	−3.09130	+	1.30767i	−0.188130	+	0.0795822i
$271$	19.8992	+	11.4888i	1.20879	+	0.697896i	0.962495	−	0.271299i	$-0.0874531\pi$
$271$	19.8992	+	11.4888i	1.20879	+	0.697896i	0.246296	+	0.969195i	$0.420786\pi$
$272$	−0.242641	+	0.420267i	−0.0147123	+	0.0254824i
$273$	−4.18549	−	2.84795i	−0.253317	−	0.172366i
$274$	−2.72750	−	4.72417i	−0.164775	−	0.285398i
$275$		−	1.56399i		−	0.0943120i
$276$	14.9562	+	9.47573i	0.900256	+	0.570372i
$277$	−17.9816			−1.08041			−0.540205	−	0.841534i	$-0.681653\pi$
$277$	−17.9816			−1.08041			−0.540205	+	0.841534i	$0.681653\pi$
$278$	−1.13530	+	1.96640i	−0.0680907	+	0.117937i
$279$	−26.1274	−	18.1008i	−1.56421	−	1.08367i
$280$	5.40010	−	2.88632i	0.322718	−	0.172491i
$281$	1.84362	+	1.06442i	0.109981	+	0.0634978i	0.553982	−	0.832529i	$-0.313108\pi$
$281$	1.84362	+	1.06442i	0.109981	+	0.0634978i	−0.444000	+	0.896027i	$0.646441\pi$
$282$	−0.289247	−	0.183257i	−0.0172244	−	0.0109128i
$283$	5.07527	+	2.93021i	0.301693	+	0.174183i	0.643203	−	0.765695i	$-0.277605\pi$
$283$	5.07527	+	2.93021i	0.301693	+	0.174183i	−0.341510	+	0.939878i	$0.610938\pi$
$284$	14.5019	+	8.37267i	0.860529	+	0.496827i
$285$	−8.96966	−	5.68287i	−0.531317	−	0.336624i
$286$	0.966555	+	0.558041i	0.0571536	+	0.0329976i
$287$	0.973659	−	1.56572i	0.0574733	−	0.0924218i
$288$	−14.0753	−	9.75124i	−0.829394	−	0.574597i
$289$	8.45781	−	14.6493i	0.497518	−	0.861726i
$290$	0.310309			0.0182220
$291$	12.5923	+	7.97805i	0.738174	+	0.467681i
$292$		−	20.0255i		−	1.17190i
$293$	−11.1730	−	19.3523i	−0.652736	−	1.13057i	−0.982456	−	0.186493i	$-0.940288\pi$
$293$	−11.1730	−	19.3523i	−0.652736	−	1.13057i	0.329721	−	0.944078i	$-0.393045\pi$
$294$	−0.833395	+	7.78737i	−0.0486046	+	0.454169i
$295$	−2.76016	+	4.78073i	−0.160702	+	0.278345i
$296$	10.9178	+	6.30339i	0.634584	+	0.366377i
$297$	1.00037	−	8.06491i	0.0580473	−	0.467974i
$298$	7.30401	+	12.6509i	0.423110	+	0.732848i
$299$	3.56747	+	6.17905i	0.206312	+	0.357344i
$300$	−1.46717	+	2.31573i	−0.0847068	+	0.133699i
$301$	−8.05762	−	0.263887i	−0.464434	−	0.0152102i
$302$	4.59518	−	2.65303i	0.264423	−	0.152665i
$303$	−29.3664	−	1.20871i	−1.68706	−	0.0694387i
$304$		−	10.2412i		−	0.587374i
$305$	−1.94411	+	1.12243i	−0.111319	+	0.0642702i
$306$	−0.462745	−	0.320586i	−0.0264534	−	0.0183267i
$307$			19.5900i			1.11806i	0.829148	+	0.559029i	$0.188826\pi$
$307$			19.5900i			1.11806i	−0.829148	+	0.559029i	$0.811174\pi$
$308$	−0.214373	+	6.54573i	−0.0122150	+	0.372978i
$309$	−0.412309	+	10.0173i	−0.0234555	+	0.569865i
$310$	6.84392			0.388709
$311$	−7.15390	+	12.3909i	−0.405660	+	0.702625i	−0.994398	−	0.105700i	$-0.966292\pi$
$311$	−7.15390	+	12.3909i	−0.405660	+	0.702625i	0.588738	+	0.808324i	$0.299625\pi$
$312$	−2.05457	−	3.92284i	−0.116317	−	0.222087i
$313$	−5.03580	+	2.90742i	−0.284640	+	0.164337i	−0.635522	−	0.772083i	$-0.719215\pi$
$313$	−5.03580	+	2.90742i	−0.284640	+	0.164337i	0.350882	+	0.936420i	$0.385882\pi$
$314$	2.44286			0.137859
$315$	−3.15358	−	7.28388i	−0.177684	−	0.410400i
$316$	5.57894			0.313840
$317$	−13.2996	+	7.67851i	−0.746978	+	0.431268i	−0.824601	−	0.565715i	$-0.808600\pi$
$317$	−13.2996	+	7.67851i	−0.746978	+	0.431268i	0.0776227	+	0.996983i	$0.475267\pi$
$318$	4.99279	−	7.88046i	0.279982	−	0.441914i
$319$	−0.375658	+	0.650659i	−0.0210328	+	0.0364299i
$320$	0.345879			0.0193352
$321$	10.3801	+	6.57649i	0.579362	+	0.367064i
$322$	5.82890	−	9.37335i	0.324832	−	0.522356i
$323$		−	1.78089i		−	0.0990914i
$324$	−9.04684	+	11.0029i	−0.502602	+	0.611273i
$325$	−0.956727	+	0.552367i	−0.0530697	+	0.0306398i
$326$		−	0.989870i		−	0.0548238i
$327$	−10.4788	−	20.0074i	−0.579477	−	1.10641i
$328$	1.39672	−	0.806396i	0.0771209	−	0.0445258i
$329$	0.427595	−	0.687609i	0.0235741	−	0.0379091i
$330$	0.811860	+	1.55011i	0.0446914	+	0.0853306i
$331$	−13.3813	−	23.1771i	−0.735503	−	1.27393i	−0.954502	−	0.298204i	$-0.903612\pi$
$331$	−13.3813	−	23.1771i	−0.735503	−	1.27393i	0.218999	−	0.975725i	$-0.429721\pi$
$332$	−0.631002	−	1.09293i	−0.0346307	−	0.0599822i
$333$	9.30644	−	13.4332i	0.509990	−	0.736137i
$334$	14.1290	+	8.15741i	0.773107	+	0.446354i
$335$	3.96895	−	6.87443i	0.216847	−	0.375590i
$336$	4.30655	−	6.32912i	0.234941	−	0.345282i
$337$	−13.4533	−	23.3019i	−0.732850	−	1.26933i	−0.955660	−	0.294471i	$-0.904856\pi$
$337$	−13.4533	−	23.3019i	−0.732850	−	1.26933i	0.222810	−	0.974862i	$-0.428477\pi$
$338$			7.60912i			0.413881i
$339$	24.2295	−	12.6900i	1.31596	−	0.689229i
$340$	−0.459779			−0.0249350
$341$	−8.28521	+	14.3504i	−0.448669	+	0.777118i
$342$	11.8400	+	0.976316i	0.640234	+	0.0527931i
$343$	−18.4310	−	1.81604i	−0.995181	−	0.0980570i
$344$	−6.10719	−	3.52599i	−0.329278	−	0.190108i
$345$	−0.460043	+	11.1770i	−0.0247679	+	0.601751i
$346$	1.57966	+	0.912016i	0.0849229	+	0.0490303i
$347$	5.56361	+	3.21215i	0.298670	+	0.172437i	0.641845	−	0.766834i	$-0.278169\pi$
$347$	5.56361	+	3.21215i	0.298670	+	0.172437i	−0.343175	+	0.939271i	$0.611502\pi$
$348$	1.16660	−	0.611000i	0.0625363	−	0.0327530i
$349$	−6.16611	−	3.56000i	−0.330064	−	0.190563i	0.325805	−	0.945437i	$-0.394365\pi$
$349$	−6.16611	−	3.56000i	−0.330064	−	0.190563i	−0.655870	+	0.754874i	$0.727698\pi$
$350$	1.45131	+	0.902512i	0.0775760	+	0.0482413i
$351$	−5.28680	+	2.23640i	−0.282189	+	0.119370i
$352$	−4.46338	+	7.73081i	−0.237899	+	0.412053i
$353$	12.8130			0.681965			0.340982	−	0.940070i	$-0.389240\pi$
$353$	12.8130			0.681965			0.340982	+	0.940070i	$0.389240\pi$
$354$	0.254000	−	6.17109i	0.0134999	−	0.327990i
$355$			10.5800i			0.561528i
$356$	−8.72801	−	15.1174i	−0.462583	−	0.801218i
$357$	0.748885	−	1.10060i	0.0396352	−	0.0582499i
$358$	−6.27274	+	10.8647i	−0.331524	+	0.574217i
$359$	−20.5886	−	11.8868i	−1.08662	−	0.627362i	−0.153948	−	0.988079i	$-0.549199\pi$
$359$	−20.5886	−	11.8868i	−1.08662	−	0.627362i	−0.932675	+	0.360717i	$0.882532\pi$
$360$	0.570569	−	6.91942i	0.0300716	−	0.364685i
$361$	9.29162	+	16.0936i	0.489033	+	0.847030i
$362$	−8.34203	−	14.4488i	−0.438447	−	0.759413i
$363$	14.8033	+	0.609300i	0.776973	+	0.0319800i
$364$	4.07989	−	2.18068i	0.213844	−	0.114298i
$365$	10.9573	−	6.32622i	0.573533	−	0.331129i
$366$	1.34420	−	2.12165i	0.0702627	−	0.110900i
$367$			19.8550i			1.03642i	0.855252	+	0.518212i	$0.173402\pi$
$367$			19.8550i			1.03642i	−0.855252	+	0.518212i	$0.826598\pi$
$368$	−9.34369	+	5.39458i	−0.487073	+	0.281212i
$369$	−0.892995	−	1.89033i	−0.0464874	−	0.0984067i
$370$			3.51876i			0.182932i
$371$	18.7337	+	11.6497i	0.972607	+	0.604824i
$372$	25.7295	−	13.4757i	1.33401	−	0.698683i
$373$	−3.30276			−0.171010			−0.0855052	−	0.996338i	$-0.527250\pi$
$373$	−3.30276			−0.171010			−0.0855052	+	0.996338i	$0.527250\pi$
$374$	−0.146740	+	0.254161i	−0.00758775	+	0.0131424i
$375$	−1.73059	−	0.0712304i	−0.0893671	−	0.00367832i
$376$	0.613388	−	0.354140i	0.0316331	−	0.0182634i
$377$	0.530698			0.0273323
$378$	6.90663	+	5.58223i	0.355239	+	0.287119i
$379$	−33.8286			−1.73766			−0.868828	−	0.495113i	$-0.835127\pi$
$379$	−33.8286			−1.73766			−0.868828	+	0.495113i	$0.835127\pi$
$380$	8.40304	−	4.85150i	0.431067	−	0.248877i
$381$	24.6366	+	1.01403i	1.26217	+	0.0519505i
$382$	−4.27415	+	7.40305i	−0.218685	+	0.378773i
$383$	−25.1815			−1.28671			−0.643356	−	0.765567i	$-0.722459\pi$
$383$	−25.1815			−1.28671			−0.643356	+	0.765567i	$0.722459\pi$
$384$	17.1724	−	8.99393i	0.876323	−	0.458969i
$385$	−3.64935	+	1.95055i	−0.185988	+	0.0994095i
$386$		−	6.22449i		−	0.316818i
$387$	−5.20583	+	7.51427i	−0.264627	+	0.381972i
$388$	−11.7968	+	6.81091i	−0.598894	+	0.345771i
$389$		−	4.59532i		−	0.232992i	−0.993191	−	0.116496i	$-0.962834\pi$
$389$		−	4.59532i		−	0.232992i	0.993191	−	0.116496i	$-0.0371662\pi$
$390$	0.661505	−	1.04410i	0.0334966	−	0.0528700i
$391$	−1.62482	+	0.938088i	−0.0821705	+	0.0474411i
$392$	−13.4697	−	9.00066i	−0.680320	−	0.454602i
$393$	−23.1176	−	0.951515i	−1.16613	−	0.0479976i
$394$	−6.83492	−	11.8384i	−0.344338	−	0.596412i
$395$	1.76243	+	3.05262i	0.0886776	+	0.153594i
$396$	6.10433	+	4.22903i	0.306754	+	0.212517i
$397$	20.1504	+	11.6338i	1.01132	+	0.583884i	0.911577	−	0.411129i	$-0.134865\pi$
$397$	20.1504	+	11.6338i	1.01132	+	0.583884i	0.0997402	+	0.995014i	$0.468199\pi$
$398$	−1.38799	+	2.40407i	−0.0695737	+	0.120505i
$399$	−2.07352	+	28.0169i	−0.103806	+	1.40260i
$400$	−0.835265	−	1.44672i	−0.0417632	−	0.0723361i
$401$		−	2.89371i		−	0.144505i	−0.997386	−	0.0722525i	$-0.976981\pi$
$401$		−	2.89371i		−	0.144505i	0.997386	−	0.0722525i	$-0.0230187\pi$
$402$	−0.365238	+	8.87369i	−0.0182164	+	0.442579i
$403$	11.7046			0.583049
$404$	13.4288	−	23.2593i	0.668106	−	1.15719i
$405$	−8.87844	−	1.47424i	−0.441173	−	0.0732555i
$406$	−0.387008	−	0.724063i	−0.0192069	−	0.0359347i
$407$	−7.37817	−	4.25979i	−0.365722	−	0.211150i
$408$	1.03153	−	0.540260i	0.0510685	−	0.0267469i
$409$	10.0299	+	5.79077i	0.495947	+	0.286335i	0.727038	−	0.686597i	$-0.240896\pi$
$409$	10.0299	+	5.79077i	0.495947	+	0.286335i	−0.231091	+	0.972932i	$0.574230\pi$
$410$	0.389847	+	0.225078i	0.0192532	+	0.0111158i
$411$	0.601527	−	14.6145i	0.0296712	−	0.720879i
$412$	−7.93409	−	4.58075i	−0.390885	−	0.225677i
$413$	14.5975	+	0.478069i	0.718298	+	0.0235242i
$414$	−5.34599	−	11.3166i	−0.262741	−	0.556182i
$415$	0.398678	−	0.690530i	0.0195703	−	0.0338968i
$416$	6.30548			0.309152
$417$	−5.39335	+	2.82474i	−0.264113	+	0.138328i
$418$		−	6.19349i		−	0.302934i
$419$	−1.78552	−	3.09261i	−0.0872285	−	0.151084i	0.819110	−	0.573636i	$-0.194468\pi$
$419$	−1.78552	−	3.09261i	−0.0872285	−	0.151084i	−0.906339	+	0.422552i	$0.861134\pi$
$420$	7.23323	+	0.535327i	0.352945	+	0.0261213i
$421$	−13.3432	+	23.1110i	−0.650306	+	1.12636i	0.332743	+	0.943018i	$0.392026\pi$
$421$	−13.3432	+	23.1110i	−0.650306	+	1.12636i	−0.983049	+	0.183345i	$0.941307\pi$
$422$	5.91713	+	3.41625i	0.288041	+	0.166301i
$423$	−0.392171	−	0.830164i	−0.0190680	−	0.0403640i
$424$	9.64845	+	16.7116i	0.468570	+	0.811588i
$425$	−0.145248	−	0.251577i	−0.00704556	−	0.0122033i
$426$	−5.49203	−	10.4861i	−0.266090	−	0.508053i
$427$	5.04367	+	3.13645i	0.244080	+	0.151783i
$428$	−9.72441	+	5.61439i	−0.470047	+	0.271382i
$429$	1.38846	+	2.65103i	0.0670355	+	0.127993i
$430$		−	1.96832i		−	0.0949208i
$431$	−12.4615	+	7.19463i	−0.600248	+	0.346553i	−0.769139	−	0.639081i	$-0.779315\pi$
$431$	−12.4615	+	7.19463i	−0.600248	+	0.346553i	0.168891	+	0.985635i	$0.445981\pi$
$432$	−3.38179	−	7.99447i	−0.162707	−	0.384634i
$433$		−	23.9154i		−	1.14930i	−0.818398	−	0.574651i	$-0.805138\pi$
$433$		−	23.9154i		−	1.14930i	0.818398	−	0.574651i	$-0.194862\pi$
$434$	−8.53552	−	15.9693i	−0.409718	−	0.766553i
$435$	0.702859	+	0.445308i	0.0336995	+	0.0213509i
$436$	20.6384			0.988400
$437$	19.7971	−	34.2895i	0.947021	−	1.64029i
$438$	−7.57617	+	11.9580i	−0.362003	+	0.571375i
$439$	−6.83416	+	3.94570i	−0.326177	+	0.188318i	−0.654142	−	0.756371i	$-0.726970\pi$
$439$	−6.83416	+	3.94570i	−0.326177	+	0.188318i	0.327966	+	0.944690i	$0.393637\pi$
$440$	−3.61954			−0.172555
$441$	−13.0629	+	16.4427i	−0.622042	+	0.782984i
$442$	0.207302			0.00986033
$443$	16.5542	−	9.55760i	0.786516	−	0.454095i	−0.0522186	−	0.998636i	$-0.516629\pi$
$443$	16.5542	−	9.55760i	0.786516	−	0.454095i	0.838735	+	0.544540i	$0.183296\pi$
$444$	6.92845	+	13.2287i	0.328810	+	0.627806i
$445$	5.51450	−	9.55140i	0.261413	−	0.452780i
$446$	16.8173			0.796322
$447$	−1.61084	+	39.1363i	−0.0761900	+	1.85108i
$448$	−0.431369	−	0.807060i	−0.0203802	−	0.0381300i
$449$			13.3687i			0.630910i	0.948941	+	0.315455i	$0.102157\pi$
$449$			13.3687i			0.630910i	−0.948941	+	0.315455i	$0.897843\pi$
$450$	1.75220	−	0.827742i	0.0825996	−	0.0390201i
$451$	−0.943893	+	0.544957i	−0.0444462	+	0.0256610i
$452$			24.9936i			1.17560i
$453$	14.2154	+	0.585102i	0.667899	+	0.0274905i
$454$	−16.1097	+	9.30093i	−0.756065	+	0.436514i
$455$	2.48207	+	1.54350i	0.116361	+	0.0723602i
$456$	−13.1519	+	20.7585i	−0.615893	+	0.972105i
$457$	−2.77000	−	4.79778i	−0.129575	−	0.224431i	0.793937	−	0.608000i	$-0.208028\pi$
$457$	−2.77000	−	4.79778i	−0.129575	−	0.224431i	−0.923512	+	0.383569i	$0.874695\pi$
$458$	0.148794	+	0.257719i	0.00695269	+	0.0120424i
$459$	−0.588075	−	1.39019i	−0.0274490	−	0.0648887i
$460$	−8.85264	−	5.11107i	−0.412756	−	0.238305i
$461$	4.27019	−	7.39619i	0.198883	−	0.344475i	−0.749284	−	0.662249i	$-0.769602\pi$
$461$	4.27019	−	7.39619i	0.198883	−	0.344475i	0.948166	+	0.317774i	$0.102935\pi$
$462$	2.60443	−	3.82761i	0.121169	−	0.178076i
$463$	−8.44641	−	14.6296i	−0.392538	−	0.679896i	0.600245	−	0.799816i	$-0.295070\pi$
$463$	−8.44641	−	14.6296i	−0.392538	−	0.679896i	−0.992784	+	0.119920i	$0.961736\pi$
$464$			0.802498i			0.0372550i
$465$	15.5017	+	9.82133i	0.718873	+	0.455453i
$466$	14.4724			0.670420
$467$	−5.77689	+	10.0059i	−0.267323	+	0.463016i	−0.968170	−	0.250295i	$-0.919472\pi$
$467$	−5.77689	+	10.0059i	−0.267323	+	0.463016i	0.700847	+	0.713312i	$0.252806\pi$
$468$	0.431077	−	5.22776i	0.0199265	−	0.241654i
$469$	−20.9905	−	0.687437i	−0.969250	−	0.0317429i
$470$	0.171207	+	0.0988462i	0.00789717	+	0.00455943i
$471$	5.53315	+	3.50561i	0.254954	+	0.161530i
$472$	11.0641	+	6.38783i	0.509264	+	0.294024i
$473$	4.12719	+	2.38284i	0.189769	+	0.109563i
$474$	−3.33140	−	2.11066i	−0.153016	−	0.0969458i
$475$	5.30918	+	3.06526i	0.243602	+	0.140644i
$476$	0.573421	+	1.07283i	0.0262827	+	0.0491731i
$477$	22.6176	−	10.6846i	1.03559	−	0.489214i
$478$	−7.74651	+	13.4173i	−0.354317	+	0.613695i
$479$	33.2685			1.52008			0.760038	−	0.649879i	$-0.225181\pi$
$479$	33.2685			1.52008			0.760038	+	0.649879i	$0.225181\pi$
$480$	8.35102	+	5.29092i	0.381170	+	0.241496i
$481$			6.01786i			0.274391i
$482$	−0.752796	−	1.30388i	−0.0342889	−	0.0593901i
$483$	26.6538	−	12.8662i	1.21279	−	0.585432i
$484$	−6.76932	+	11.7248i	−0.307696	+	0.532946i
$485$	−7.45344	−	4.30325i	−0.338443	−	0.195400i
$486$	9.56491	−	3.14761i	0.433873	−	0.142778i
$487$	7.75103	+	13.4252i	0.351233	+	0.608353i	0.986466	−	0.163968i	$-0.0524292\pi$
$487$	7.75103	+	13.4252i	0.351233	+	0.608353i	−0.635233	+	0.772321i	$0.719096\pi$
$488$	2.59765	+	4.49925i	0.117590	+	0.203672i
$489$	1.42051	−	2.24208i	0.0642375	−	0.101391i
$490$	0.295855	−	4.51202i	0.0133653	−	0.203832i
$491$	15.6866	−	9.05665i	0.707926	−	0.408721i	−0.102367	−	0.994747i	$-0.532642\pi$
$491$	15.6866	−	9.05665i	0.707926	−	0.408721i	0.810292	+	0.586026i	$0.199308\pi$
$492$	1.90880	+	0.0785656i	0.0860554	+	0.00354201i
$493$			0.139550i			0.00628502i
$494$	−3.78870	+	2.18741i	−0.170462	+	0.0984161i
$495$	−0.385586	+	4.67609i	−0.0173308	+	0.210175i
$496$			17.6992i			0.794719i
$497$	24.6869	−	13.1950i	1.10736	−	0.591878i
$498$	−0.0366878	+	0.891353i	−0.00164402	+	0.0399425i
$499$	6.62373			0.296519			0.148259	−	0.988949i	$-0.452633\pi$
$499$	6.62373			0.296519			0.148259	+	0.988949i	$0.452633\pi$
$500$	0.791368	−	1.37069i	0.0353911	−	0.0612991i
$501$	20.2965	+	38.7526i	0.906779	+	1.73134i
$502$	−4.64198	+	2.68005i	−0.207182	+	0.119616i
$503$	−0.438495			−0.0195515			−0.00977576	−	0.999952i	$-0.503112\pi$
$503$	−0.438495			−0.0195515			−0.00977576	+	0.999952i	$0.503112\pi$
$504$	−16.8571	+	7.29833i	−0.750875	+	0.325094i
$505$	16.9691			0.755113
$506$	−5.65070	+	3.26243i	−0.251204	+	0.145033i
$507$	−10.9194	+	17.2349i	−0.484948	+	0.765427i
$508$	−11.2659	+	19.5131i	−0.499844	+	0.865755i
$509$	−0.344249			−0.0152586			−0.00762929	−	0.999971i	$-0.502429\pi$
$509$	−0.344249			−0.0152586			−0.00762929	+	0.999971i	$0.502429\pi$
$510$	0.274552	+	0.173946i	0.0121573	+	0.00770248i
$511$	−28.4270	−	17.6776i	−1.25754	−	0.782009i
$512$			17.2671i			0.763105i
$513$	25.4169	+	19.2023i	1.12218	+	0.847803i
$514$	−9.44938	+	5.45560i	−0.416794	+	0.240636i
$515$		−	5.78839i		−	0.255067i
$516$	−3.87563	−	7.39985i	−0.170615	−	0.325760i
$517$	−0.414523	+	0.239325i	−0.0182307	+	0.0105255i
$518$	8.21054	−	4.38848i	0.360750	−	0.192819i
$519$	2.26919	+	4.33262i	0.0996062	+	0.190181i
$520$	1.27834	+	2.21416i	0.0560591	+	0.0970971i
$521$	6.15505	+	10.6609i	0.269658	+	0.467061i	0.968773	−	0.247948i	$-0.0797561\pi$
$521$	6.15505	+	10.6609i	0.269658	+	0.467061i	−0.699116	+	0.715008i	$0.746423\pi$
$522$	−0.927779	−	0.0765038i	−0.0406078	−	0.00334848i
$523$	24.7952	+	14.3155i	1.08422	+	0.625974i	0.932031	−	0.362378i	$-0.118035\pi$
$523$	24.7952	+	14.3155i	1.08422	+	0.625974i	0.152187	+	0.988352i	$0.451368\pi$
$524$	10.5713	−	18.3101i	0.461810	−	0.799879i
$525$	1.99212	+	4.12692i	0.0869434	+	0.180113i
$526$	5.03910	+	8.72798i	0.219715	+	0.380558i
$527$			3.07780i			0.134071i
$528$	−4.00877	+	2.09957i	−0.174459	+	0.0913721i
$529$	−18.7125			−0.813589
$530$	−2.69304	+	4.66448i	−0.116978	+	0.202612i
$531$	9.43110	−	13.6132i	0.409275	−	0.590762i
$532$	−21.8003	−	13.5567i	−0.945163	−	0.587757i
$533$	0.666725	+	0.384934i	0.0288791	+	0.0166733i
$534$	−0.507465	+	12.3292i	−0.0219602	+	0.533536i
$535$	−6.14405	−	3.54727i	−0.265630	−	0.153362i
$536$	−15.9095	−	9.18535i	−0.687186	−	0.396747i
$537$	−29.7993	+	15.6072i	−1.28593	+	0.673500i
$538$	−15.1416	−	8.74199i	−0.652800	−	0.376894i
$539$	9.10270	+	6.08258i	0.392081	+	0.261995i
$540$	4.95753	−	6.56197i	0.213338	−	0.282382i
$541$	−15.5720	+	26.9715i	−0.669493	+	1.15960i	0.308553	+	0.951207i	$0.400155\pi$
$541$	−15.5720	+	26.9715i	−0.669493	+	1.15960i	−0.978046	+	0.208388i	$0.933178\pi$
$542$	14.8426			0.637545
$543$	1.83976	−	44.6982i	0.0789518	−	1.91818i
$544$			1.65806i			0.0710889i
$545$	6.51984	+	11.2927i	0.279279	+	0.483726i
$546$	−3.26126	−	0.241364i	−0.139569	−	0.0103294i
$547$	12.6256	−	21.8681i	0.539831	−	0.935014i	−0.459082	−	0.888394i	$-0.651822\pi$
$547$	12.6256	−	21.8681i	0.539831	−	0.935014i	0.998913	−	0.0466202i	$-0.0148451\pi$
$548$	11.5752	+	6.68296i	0.494469	+	0.285482i
$549$	6.08932	−	2.87660i	0.259886	−	0.122770i
$550$	−0.505136	−	0.874921i	−0.0215391	−	0.0373068i
$551$	−1.47251	−	2.55045i	−0.0627308	−	0.108653i
$552$	25.8670	+	1.06468i	1.10097	+	0.0453157i
$553$	4.92482	−	7.91953i	0.209425	−	0.336772i
$554$	−10.0592	+	5.80769i	−0.427375	+	0.246745i
$555$	−5.04958	+	7.97009i	−0.214343	+	0.338312i
$556$		−	5.56345i		−	0.235943i
$557$	11.9288	−	6.88707i	0.505438	−	0.291814i	−0.225519	−	0.974239i	$-0.572408\pi$
$557$	11.9288	−	6.88707i	0.505438	−	0.291814i	0.730956	+	0.682424i	$0.239074\pi$
$558$	−20.4623	−	1.68730i	−0.866239	−	0.0714293i
$559$		−	3.36627i		−	0.142378i
$560$	−2.33401	+	3.75328i	−0.0986298	+	0.158605i
$561$	−0.697103	+	0.365104i	−0.0294317	+	0.0154147i
$562$	1.37514			0.0580067
$563$	10.6839	−	18.5050i	0.450271	−	0.779893i	−0.548131	−	0.836392i	$-0.684661\pi$
$563$	10.6839	−	18.5050i	0.450271	−	0.779893i	0.998403	+	0.0564996i	$0.0179940\pi$
$564$	0.838275	+	0.0345031i	0.0352978	+	0.00145284i
$565$	−13.6757	+	7.89569i	−0.575343	+	0.332174i
$566$	3.78559			0.159120
$567$	7.63296	+	22.5552i	0.320554	+	0.947230i
$568$	24.4853			1.02738
$569$	8.93685	−	5.15969i	0.374652	−	0.216306i	−0.300837	−	0.953676i	$-0.597266\pi$
$569$	8.93685	−	5.15969i	0.374652	−	0.216306i	0.675489	+	0.737370i	$0.263933\pi$
$570$	−6.85323	−	0.282077i	−0.287050	−	0.0118149i
$571$	3.82476	−	6.62467i	0.160061	−	0.277234i	−0.774829	−	0.632170i	$-0.782164\pi$
$571$	3.82476	−	6.62467i	0.160061	−	0.277234i	0.934890	+	0.354937i	$0.115498\pi$
$572$	−2.73464			−0.114341
$573$	−20.3048	+	10.6345i	−0.848244	+	0.444263i
$574$	0.0389844	−	1.19036i	0.00162718	−	0.0496849i
$575$		−	6.45853i		−	0.269339i
$576$	−1.03413	−	0.0852731i	−0.0430886	−	0.00355304i
$577$	10.8976	−	6.29171i	0.453671	−	0.261927i	−0.255708	−	0.966754i	$-0.582309\pi$
$577$	10.8976	−	6.29171i	0.453671	−	0.261927i	0.709379	+	0.704827i	$0.248975\pi$
$578$		−	10.9268i		−	0.454495i
$579$	8.93242	−	14.0986i	0.371219	−	0.585920i
$580$	−0.658459	+	0.380162i	−0.0273410	+	0.0157854i
$581$	−2.10847	−	0.0690524i	−0.0874742	−	0.00286478i
$582$	9.62109	+	0.396001i	0.398807	+	0.0164148i
$583$	−6.52035	−	11.2936i	−0.270045	−	0.467732i
$584$	−14.6408	−	25.3586i	−0.605840	−	1.04935i
$585$	2.99665	−	1.41562i	0.123896	−	0.0585288i
$586$	−12.5008	−	7.21732i	−0.516402	−	0.298145i
$587$	−7.26812	+	12.5888i	−0.299987	+	0.519593i	−0.976133	−	0.217175i	$-0.930316\pi$
$587$	−7.26812	+	12.5888i	−0.299987	+	0.519593i	0.676145	+	0.736768i	$0.263649\pi$
$588$	−7.77194	−	17.5454i	−0.320509	−	0.723559i
$589$	−32.4764	−	56.2507i	−1.33816	−	2.31777i
$590$			3.56590i			0.146806i
$591$	1.50738	−	36.6228i	0.0620055	−	1.50646i
$592$	−9.09995			−0.374005
$593$	9.78416	−	16.9467i	0.401787	−	0.695916i	−0.592154	−	0.805825i	$-0.701722\pi$
$593$	9.78416	−	16.9467i	0.401787	−	0.695916i	0.993942	+	0.109908i	$0.0350558\pi$
$594$	−2.04518	−	4.83475i	−0.0839147	−	0.198372i
$595$	−0.405871	+	0.652675i	−0.0166391	+	0.0267570i
$596$	−30.9974	−	17.8964i	−1.26970	−	0.733064i
$597$	−6.59379	+	3.45346i	−0.269866	+	0.141341i
$598$	3.99141	+	2.30444i	0.163221	+	0.0942357i
$599$	37.4088	+	21.5980i	1.52848	+	0.882470i	0.999426	+	0.0338837i	$0.0107876\pi$
$599$	37.4088	+	21.5980i	1.52848	+	0.882470i	0.529057	+	0.848586i	$0.322546\pi$
$600$	−0.164849	+	4.00510i	−0.00672991	+	0.163507i
$601$	20.2611	+	11.6978i	0.826468	+	0.477162i	0.852642	−	0.522496i	$-0.174999\pi$
$601$	20.2611	+	11.6978i	0.826468	+	0.477162i	−0.0261737	+	0.999657i	$0.508332\pi$
$602$	−4.59280	+	2.45482i	−0.187189	+	0.100051i
$603$	−13.5614	+	19.5750i	−0.552263	+	0.797157i
$604$	−6.50048	+	11.2592i	−0.264501	+	0.458129i
$605$	−8.55394			−0.347767
$606$	−16.8184	+	8.80857i	−0.683203	+	0.357824i
$607$		−	14.5009i		−	0.588572i	−0.955717	−	0.294286i	$-0.904918\pi$
$607$		−	14.5009i		−	0.588572i	0.955717	−	0.294286i	$-0.0950818\pi$
$608$	−17.4956	−	30.3032i	−0.709539	−	1.22896i
$609$	0.162480	−	2.19540i	0.00658402	−	0.0889620i
$610$	−0.725045	+	1.25581i	−0.0293562	+	0.0508464i
$611$	0.292801	+	0.169049i	0.0118455	+	0.00683899i
$612$	1.37467	+	0.113354i	0.0555678	+	0.00458207i
$613$	8.99474	+	15.5793i	0.363294	+	0.629244i	0.988501	−	0.151215i	$-0.0483187\pi$
$613$	8.99474	+	15.5793i	0.363294	+	0.629244i	−0.625207	+	0.780459i	$0.714985\pi$
$614$	6.32716	+	10.9590i	0.255343	+	0.442268i
$615$	0.560018	+	1.06926i	0.0225821	+	0.0431166i
$616$	4.51417	+	8.44569i	0.181881	+	0.340287i
$617$	2.66102	−	1.53634i	0.107129	−	0.0618508i	−0.445478	−	0.895293i	$-0.646966\pi$
$617$	2.66102	−	1.53634i	0.107129	−	0.0618508i	0.552607	+	0.833442i	$0.313633\pi$
$618$	3.00473	+	5.73702i	0.120868	+	0.230777i
$619$			2.05572i			0.0826263i	0.999146	+	0.0413132i	$0.0131541\pi$
$619$			2.05572i			0.0826263i	−0.999146	+	0.0413132i	$0.986846\pi$
$620$	−14.5224	+	8.38453i	−0.583235	+	0.336731i
$621$	4.13105	−	33.3043i	0.165773	−	1.33645i
$622$			9.24225i			0.370581i
$623$	−29.1644	−	0.955132i	−1.16845	−	0.0382666i
$624$	2.70017	+	1.71073i	0.108093	+	0.0684841i
$625$	1.00000			0.0400000
$626$	−1.87807	+	3.25292i	−0.0750630	+	0.130013i
$627$	8.88794	−	14.0284i	0.354950	−	0.560242i
$628$	−5.18362	+	2.99276i	−0.206849	+	0.119424i
$629$	−1.58243			−0.0630957
$630$	−4.11671	−	3.05619i	−0.164014	−	0.121761i
$631$	16.2423			0.646597			0.323298	−	0.946297i	$-0.395208\pi$
$631$	16.2423			0.646597			0.323298	+	0.946297i	$0.395208\pi$
$632$	7.06469	−	4.07880i	0.281018	−	0.162246i
$633$	8.49998	+	16.2293i	0.337844	+	0.645055i
$634$	−4.96000	+	8.59098i	−0.196987	+	0.341191i
$635$	−14.2360			−0.564938
$636$	−0.940030	+	22.8386i	−0.0372746	+	0.905610i
$637$	0.505977	−	7.71656i	0.0200475	−	0.305741i
$638$			0.485320i			0.0192140i
$639$	2.60840	−	31.6326i	0.103187	−	1.25137i
$640$	−9.69253	+	5.59598i	−0.383131	+	0.221201i
$641$		−	19.3842i		−	0.765631i	−0.923825	−	0.382816i	$-0.874954\pi$
$641$		−	19.3842i		−	0.765631i	0.923825	−	0.382816i	$-0.125046\pi$
$642$	7.93089	+	0.326433i	0.313007	+	0.0128833i
$643$	−15.3775	+	8.87823i	−0.606431	+	0.350123i	−0.771567	−	0.636148i	$-0.780527\pi$
$643$	−15.3775	+	8.87823i	−0.606431	+	0.350123i	0.165136	+	0.986271i	$0.447194\pi$
$644$	−0.885257	+	27.0308i	−0.0348840	+	1.06516i
$645$	2.82463	−	4.45830i	0.111220	−	0.175545i
$646$	−0.575191	−	0.996261i	−0.0226306	−	0.0391973i
$647$	−6.63329	−	11.4892i	−0.260782	−	0.451687i	0.705668	−	0.708542i	$-0.250647\pi$
$647$	−6.63329	−	11.4892i	−0.260782	−	0.451687i	−0.966450	+	0.256855i	$0.917314\pi$
$648$	−3.41183	+	20.5474i	−0.134029	+	0.807177i
$649$	−7.47700	−	4.31685i	−0.293498	−	0.169451i
$650$	−0.356806	+	0.618007i	−0.0139951	+	0.0242402i
$651$	3.58353	−	48.4199i	0.140449	−	1.89772i
$652$	1.21270	+	2.10045i	0.0474928	+	0.0822600i
$653$			7.12420i			0.278791i	0.990237	+	0.139396i	$0.0445160\pi$
$653$			7.12420i			0.278791i	−0.990237	+	0.139396i	$0.955484\pi$
$654$	−12.3240	−	7.80805i	−0.481906	−	0.305319i
$655$	13.3583			0.521951
$656$	−0.582080	+	1.00819i	−0.0227264	+	0.0393633i
$657$	−34.3205	+	16.2130i	−1.33897	+	0.632531i
$658$	0.0171205	−	0.522764i	0.000667427	−	0.0203795i
$659$	6.30181	+	3.63835i	0.245484	+	0.141730i	0.617695	−	0.786418i	$-0.288067\pi$
$659$	6.30181	+	3.63835i	0.245484	+	0.141730i	−0.372211	+	0.928148i	$0.621400\pi$
$660$	−3.62177	−	2.29463i	−0.140977	−	0.0893183i
$661$	−37.0994	−	21.4193i	−1.44300	−	0.833115i	−0.444949	−	0.895556i	$-0.646778\pi$
$661$	−37.0994	−	21.4193i	−1.44300	−	0.833115i	−0.998049	+	0.0624404i	$0.980112\pi$
$662$	−14.9715	−	8.64378i	−0.581883	−	0.335950i
$663$	0.469544	+	0.297487i	0.0182356	+	0.0115534i
$664$	−1.59809	−	0.922660i	−0.0620181	−	0.0358061i
$665$	0.530914	−	16.2111i	0.0205880	−	0.628641i
$666$	0.867517	−	10.5206i	0.0336156	−	0.407664i
$667$	−1.55129	+	2.68691i	−0.0600662	+	0.104038i
$668$	−39.9748			−1.54667
$669$	38.0916	+	24.1336i	1.47271	+	0.933057i
$670$		−	5.12756i		−	0.198095i
$671$	−1.75547	−	3.04056i	−0.0677691	−	0.117380i
$672$	1.93051	−	26.0846i	0.0744709	−	1.00624i
$673$	10.9329	−	18.9364i	0.421433	−	0.729944i	−0.574647	−	0.818402i	$-0.694860\pi$
$673$	10.9329	−	18.9364i	0.421433	−	0.729944i	0.996080	+	0.0884576i	$0.0281938\pi$
$674$	−15.0520	−	8.69030i	−0.579783	−	0.334738i
$675$	5.15663	+	0.639628i	0.198479	+	0.0246193i
$676$	−9.32198	−	16.1461i	−0.358538	−	0.621005i
$677$	−11.2186	−	19.4311i	−0.431164	−	0.746798i	0.565810	−	0.824536i	$-0.308564\pi$
$677$	−11.2186	−	19.4311i	−0.431164	−	0.746798i	−0.996974	+	0.0777379i	$0.975230\pi$
$678$	9.45574	−	14.9246i	0.363146	−	0.573178i
$679$	−0.745338	+	22.7584i	−0.0286035	+	0.873389i
$680$	−0.582225	+	0.336148i	−0.0223273	+	0.0128907i
$681$	−49.8361	−	2.05124i	−1.90972	−	0.0786037i
$682$			10.7038i			0.409870i
$683$	−8.46689	+	4.88836i	−0.323977	+	0.187048i	−0.653164	−	0.757217i	$-0.726559\pi$
$683$	−8.46689	+	4.88836i	−0.323977	+	0.187048i	0.329187	+	0.944265i	$0.393225\pi$
$684$	−26.3199	+	12.4336i	−1.00637	+	0.475410i
$685$			8.44482i			0.322660i
$686$	−10.8972	+	4.93691i	−0.416056	+	0.188492i
$687$	−0.0328152	+	0.797266i	−0.00125198	+	0.0304176i
$688$	5.09032			0.194067
$689$	−4.60570	+	7.97730i	−0.175463	+	0.303911i
$690$	3.35260	+	6.40120i	0.127631	+	0.243690i
$691$	21.7688	−	12.5682i	0.828125	−	0.478118i	−0.0250851	−	0.999685i	$-0.507986\pi$
$691$	21.7688	−	12.5682i	0.828125	−	0.478118i	0.853210	+	0.521567i	$0.174652\pi$
$692$	−4.46927			−0.169896
$693$	11.3919	−	4.93216i	0.432743	−	0.187357i
$694$	4.14984			0.157526
$695$	3.04415	−	1.75754i	0.115471	−	0.0666673i
$696$	1.03058	−	1.62663i	0.0390639	−	0.0616572i
$697$	−0.101221	+	0.175319i	−0.00383400	+	0.00664069i
$698$	−4.59923			−0.174084
$699$	32.7803	+	20.7685i	1.23987	+	0.785537i
$700$	−4.18528	−	0.137068i	−0.158189	−	0.00518068i
$701$		−	27.0864i		−	1.02304i	−0.859271	−	0.511520i	$-0.829083\pi$
$701$		−	27.0864i		−	1.02304i	0.859271	−	0.511520i	$-0.170917\pi$
$702$	−2.23521	+	2.95861i	−0.0843627	+	0.111666i
$703$	28.9209	−	16.6975i	1.09077	−	0.629759i
$704$			0.540950i			0.0203878i
$705$	0.245939	+	0.469578i	0.00926260	+	0.0176853i
$706$	7.16779	−	4.13832i	0.269763	−	0.155748i
$707$	−21.1632	−	39.5949i	−0.795926	−	1.48912i
$708$	7.02126	+	13.4059i	0.263875	+	0.503824i
$709$	−14.0540	−	24.3423i	−0.527809	−	0.914193i	−0.999474	−	0.0324149i	$-0.989680\pi$
$709$	−14.0540	−	24.3423i	−0.527809	−	0.914193i	0.471665	−	0.881778i	$-0.343653\pi$
$710$	3.41712	+	5.91863i	0.128242	+	0.222122i
$711$	−4.51682	−	9.56141i	−0.169394	−	0.358581i
$712$	−22.1048	−	12.7622i	−0.828413	−	0.478284i
$713$	−34.2140	+	59.2603i	−1.28132	+	2.21932i
$714$	0.0634681	−	0.857568i	0.00237523	−	0.0320937i
$715$	−0.863895	−	1.49631i	−0.0323078	−	0.0559588i
$716$		−	30.7391i		−	1.14877i
$717$	−36.8005	+	19.2741i	−1.37434	+	0.719804i
$718$	−15.3568			−0.573110
$719$	−23.5658	+	40.8172i	−0.878857	+	1.52222i	−0.0262598	+	0.999655i	$0.508360\pi$
$719$	−23.5658	+	40.8172i	−0.878857	+	1.52222i	−0.852597	+	0.522569i	$0.824974\pi$
$720$	2.14064	+	4.53141i	0.0797771	+	0.168876i
$721$	−13.5064	+	7.21909i	−0.503005	+	0.268853i
$722$	10.3958	+	6.00201i	0.386891	+	0.223372i
$723$	0.166023	−	4.03362i	0.00617445	−	0.150012i
$724$	35.4027	+	20.4397i	1.31573	+	0.759637i
$725$	−0.416026	−	0.240193i	−0.0154508	−	0.00892053i
$726$	8.47802	−	4.44032i	0.314649	−	0.164796i
$727$	35.4549	+	20.4699i	1.31495	+	0.759186i	0.982911	−	0.184080i	$-0.0589305\pi$
$727$	35.4549	+	20.4699i	1.31495	+	0.759186i	0.332038	+	0.943266i	$0.392264\pi$
$728$	3.57212	−	5.74426i	0.132391	−	0.212896i
$729$	26.1818	+	6.59665i	0.969695	+	0.244320i
$730$	4.08648	−	7.07799i	0.151247	−	0.261968i
$731$	0.885179			0.0327395
$732$	−0.253083	+	6.14882i	−0.00935423	+	0.227267i
$733$			24.5443i			0.906564i	0.891367	+	0.453282i	$0.149747\pi$
$733$			24.5443i			0.906564i	−0.891367	+	0.453282i	$0.850253\pi$
$734$	6.41277	+	11.1072i	0.236700	+	0.409976i
$735$	7.14508	−	9.79530i	0.263550	−	0.361305i
$736$	−18.4317	+	31.9246i	−0.679400	+	1.17675i
$737$	10.7515	+	6.20739i	0.396037	+	0.228652i
$738$	−1.11009	−	0.769064i	−0.0408631	−	0.0283096i
$739$	11.8428	+	20.5123i	0.435644	+	0.754557i	0.997348	−	0.0727809i	$-0.0231874\pi$
$739$	11.8428	+	20.5123i	0.435644	+	0.754557i	−0.561704	+	0.827338i	$0.689854\pi$
$740$	−4.31085	−	7.46662i	−0.158470	−	0.274478i
$741$	−11.7205	−	0.482414i	−0.430565	−	0.0177219i
$742$	14.2426	+	0.466444i	0.522862	+	0.0171237i
$743$	−21.4991	+	12.4125i	−0.788726	+	0.455371i	−0.839514	−	0.543339i	$-0.817160\pi$
$743$	−21.4991	+	12.4125i	−0.788726	+	0.455371i	0.0507881	+	0.998709i	$0.483827\pi$
$744$	22.7295	−	35.8756i	0.833305	−	1.31526i
$745$		−	22.6145i		−	0.828530i
$746$	−1.84762	+	1.06672i	−0.0676462	+	0.0390555i
$747$	−1.36223	+	1.96629i	−0.0498414	+	0.0719429i
$748$		−	0.719088i		−	0.0262925i
$749$	−0.614400	+	18.7603i	−0.0224497	+	0.685487i
$750$	−0.991125	+	0.519096i	−0.0361908	+	0.0189547i
$751$	26.5695			0.969534			0.484767	−	0.874643i	$-0.338904\pi$
$751$	26.5695			0.969534			0.484767	+	0.874643i	$0.338904\pi$
$752$	−0.255628	+	0.442761i	−0.00932181	+	0.0161458i
$753$	−14.3602	−	0.591061i	−0.523315	−	0.0215395i
$754$	0.296881	−	0.171404i	0.0108118	−	0.00624218i
$755$	−8.21423			−0.298946
$756$	−21.4943	−	3.38383i	−0.781740	−	0.123069i
$757$	33.0625			1.20168			0.600838	−	0.799370i	$-0.294833\pi$
$757$	33.0625			1.20168			0.600838	+	0.799370i	$0.294833\pi$
$758$	−18.9243	+	10.9259i	−0.687361	+	0.396848i
$759$	−17.4807	−	0.719502i	−0.634511	−	0.0261163i
$760$	7.09393	−	12.2871i	0.257324	−	0.445698i
$761$	35.7102			1.29449			0.647247	−	0.762280i	$-0.275920\pi$
$761$	35.7102			1.29449			0.647247	+	0.762280i	$0.275920\pi$
$762$	14.1096	−	7.38984i	0.511138	−	0.267706i
$763$	18.2186	−	29.2970i	0.659558	−	1.06062i
$764$		−	20.9452i		−	0.757769i
$765$	0.372246	+	0.787987i	0.0134586	+	0.0284897i
$766$	−14.0869	+	8.13310i	−0.508982	+	0.293861i
$767$			6.09847i			0.220203i
$768$	7.34290	−	11.5898i	0.264964	−	0.418211i
$769$	30.7446	−	17.7504i	1.10868	−	0.640095i	0.170191	−	0.985411i	$-0.445561\pi$
$769$	30.7446	−	17.7504i	1.10868	−	0.640095i	0.938487	+	0.345316i	$0.112228\pi$
$770$	−1.41152	+	2.26984i	−0.0508676	+	0.0817993i
$771$	−29.2322	−	1.20319i	−1.05277	−	0.0433317i
$772$	7.62566	+	13.2080i	0.274454	+	0.475368i
$773$	21.3697	+	37.0134i	0.768615	+	1.33128i	0.938314	+	0.345784i	$0.112387\pi$
$773$	21.3697	+	37.0134i	0.768615	+	1.33128i	−0.169699	+	0.985496i	$0.554280\pi$
$774$	−0.485271	+	5.88499i	−0.0174427	+	0.211532i
$775$	−9.17552	−	5.29749i	−0.329594	−	0.190291i
$776$	−9.95901	+	17.2495i	−0.357508	+	0.619221i
$777$	24.8948	+	1.84245i	0.893095	+	0.0660974i
$778$	−1.48419	−	2.57070i	−0.0532109	−	0.0921640i
$779$		−	4.27224i		−	0.153069i
$780$	−0.124546	+	3.02593i	−0.00445948	+	0.108346i
$781$	−16.5470			−0.592097
$782$	−0.605966	+	1.04956i	−0.0216693	+	0.0375324i
$783$	−1.99166	−	1.50469i	−0.0711761	−	0.0537731i
$784$	11.6687	+	0.765117i	0.416738	+	0.0273256i
$785$	−3.27510	−	1.89088i	−0.116893	−	0.0674884i
$786$	−13.2397	+	6.93423i	−0.472245	+	0.247336i
$787$	28.9395	+	16.7082i	1.03158	+	0.595584i	0.917437	−	0.397880i	$-0.130254\pi$
$787$	28.9395	+	16.7082i	1.03158	+	0.595584i	0.114144	+	0.993464i	$0.463587\pi$
$788$	29.0067	+	16.7470i	1.03332	+	0.596588i
$789$	−1.11133	+	27.0005i	−0.0395644	+	0.961242i
$790$	1.97187	+	1.13846i	0.0701560	+	0.0405046i
$791$	35.4794	+	22.0632i	1.26150	+	0.784477i
$792$	10.8219	+	0.892363i	0.384539	+	0.0317087i
$793$	−1.23999	+	2.14772i	−0.0440333	+	0.0762678i
$794$	15.0299			0.533392
$795$	−12.7936	+	6.70055i	−0.453741	+	0.237644i
$796$		−	6.80175i		−	0.241082i
$797$	6.99751	+	12.1200i	0.247865	+	0.429314i	0.962933	−	0.269740i	$-0.0869379\pi$
$797$	6.99751	+	12.1200i	0.247865	+	0.429314i	−0.715069	+	0.699054i	$0.753605\pi$
$798$	7.88894	+	16.3429i	0.279265	+	0.578531i
$799$	−0.0444524	+	0.0769938i	−0.00157261	+	0.00272384i
$800$	−4.94301	−	2.85385i	−0.174762	−	0.100899i
$801$	−18.8424	+	27.1977i	−0.665762	+	0.960984i
$802$	−0.934609	−	1.61879i	−0.0330022	−	0.0571615i
$803$	9.89413	+	17.1371i	0.349156	+	0.604756i
$804$	−10.0962	−	19.2769i	−0.356065	−	0.679845i
$805$	−15.0701	+	8.05486i	−0.531150	+	0.283897i
$806$	6.54777	−	3.78036i	0.230635	−	0.133157i
$807$	−21.7510	−	41.5297i	−0.765670	−	1.46191i
$808$		−	39.2715i		−	1.38157i
$809$	15.2148	−	8.78427i	0.534924	−	0.308839i	−0.208095	−	0.978109i	$-0.566726\pi$
$809$	15.2148	−	8.78427i	0.534924	−	0.308839i	0.743019	+	0.669270i	$0.233393\pi$
$810$	−5.44290	+	2.04284i	−0.191244	+	0.0717780i
$811$		−	14.4173i		−	0.506261i	−0.967432	−	0.253131i	$-0.918540\pi$
$811$		−	14.4173i		−	0.506261i	0.967432	−	0.253131i	$-0.0814603\pi$
$812$	1.70826	+	1.06230i	0.0599483	+	0.0372794i
$813$	33.6189	+	21.2998i	1.17907	+	0.747017i
$814$	−5.50330			−0.192890
$815$	−0.766202	+	1.32710i	−0.0268389	+	0.0464863i
$816$	−0.449847	+	0.710024i	−0.0157478	+	0.0248558i
$817$	−16.1778	+	9.34024i	−0.565988	+	0.326774i
$818$	7.48120			0.261574
$819$	−7.04049	−	5.22676i	−0.246015	−	0.182638i
$820$	−1.10298			−0.0385177
$821$	−1.58111	+	0.912857i	−0.0551813	+	0.0318589i	−0.527337	−	0.849656i	$-0.676809\pi$
$821$	−1.58111	+	0.912857i	−0.0551813	+	0.0318589i	0.472156	+	0.881515i	$0.343476\pi$
$822$	−4.38367	−	8.36987i	−0.152898	−	0.291933i
$823$	19.3793	−	33.5659i	0.675519	−	1.17003i	−0.300798	−	0.953688i	$-0.597253\pi$
$823$	19.3793	−	33.5659i	0.675519	−	1.17003i	0.976317	−	0.216345i	$-0.0694137\pi$
$824$	−13.3961			−0.466675
$825$	0.111403	−	2.70661i	0.00387857	−	0.0942322i
$826$	8.32052	−	4.44727i	0.289508	−	0.154740i
$827$			39.0575i			1.35816i	0.734064	+	0.679081i	$0.237621\pi$
$827$			39.0575i			1.35816i	−0.734064	+	0.679081i	$0.762379\pi$
$828$	25.2080	+	17.4639i	0.876038	+	0.606912i
$829$	22.4944	−	12.9872i	0.781263	−	0.451063i	−0.0556144	−	0.998452i	$-0.517712\pi$
$829$	22.4944	−	12.9872i	0.781263	−	0.451063i	0.836878	+	0.547390i	$0.184378\pi$
$830$		−	0.515059i		−	0.0178779i
$831$	−31.1187	−	1.28084i	−1.07950	−	0.0444317i
$832$	0.330912	−	0.191052i	0.0114723	−	0.00662353i
$833$	2.02911	+	0.133050i	0.0703047	+	0.00460989i
$834$	−2.10480	+	3.32215i	−0.0728832	+	0.115037i
$835$	−12.6284	−	21.8730i	−0.437023	−	0.756946i
$836$	7.58768	+	13.1423i	0.262426	+	0.454534i
$837$	−43.9264	−	33.1861i	−1.51832	−	1.14708i
$838$	−1.99770	−	1.15337i	−0.0690095	−	0.0398426i
$839$	6.12667	−	10.6117i	0.211516	−	0.366357i	−0.740673	−	0.671866i	$-0.765493\pi$
$839$	6.12667	−	10.6117i	0.211516	−	0.366357i	0.952189	+	0.305509i	$0.0988266\pi$
$840$	9.55093	−	4.61037i	0.329538	−	0.159073i
$841$	−14.3846	−	24.9149i	−0.496021	−	0.859134i
$842$			17.2383i			0.594070i
$843$	3.11473	+	1.97339i	0.107277	+	0.0679670i
$844$	−16.7411			−0.576252
$845$	5.88978	−	10.2014i	0.202615	−	0.350939i
$846$	−0.487513	−	0.337745i	−0.0167610	−	0.0116119i
$847$	10.6682	+	19.9594i	0.366564	+	0.685814i
$848$	−12.0629	−	6.96453i	−0.414243	−	0.239163i
$849$	8.57447	+	5.43249i	0.294275	+	0.186443i
$850$	−0.162508	−	0.0938243i	−0.00557399	−	0.00321815i
$851$	−30.4683	−	17.5909i	−1.04444	−	0.603008i
$852$	24.5004	+	15.5226i	0.839369	+	0.531796i
$853$	−7.81229	−	4.51043i	−0.267488	−	0.154434i	0.360258	−	0.932853i	$-0.382689\pi$
$853$	−7.81229	−	4.51043i	−0.267488	−	0.154434i	−0.627745	+	0.778419i	$0.716022\pi$
$854$	3.83452	+	0.125580i	0.131215	+	0.00429727i
$855$	−15.1180	−	10.4736i	−0.517024	−	0.358190i
$856$	−8.20944	+	14.2192i	−0.280593	+	0.486001i
$857$	17.1946			0.587358			0.293679	−	0.955904i	$-0.405120\pi$
$857$	17.1946			0.587358			0.293679	+	0.955904i	$0.405120\pi$
$858$	1.63296	+	1.03459i	0.0557482	+	0.0353202i
$859$		−	8.79729i		−	0.300160i	−0.988674	−	0.150080i	$-0.952047\pi$
$859$		−	8.79729i		−	0.300160i	0.988674	−	0.150080i	$-0.0479531\pi$
$860$	2.41140	+	4.17667i	0.0822281	+	0.142423i
$861$	1.79653	−	2.64027i	0.0612255	−	0.0899800i
$862$	−4.64744	+	8.04960i	−0.158292	+	0.274170i
$863$	4.64329	+	2.68081i	0.158059	+	0.0912557i	0.576943	−	0.816784i	$-0.304245\pi$
$863$	4.64329	+	2.68081i	0.158059	+	0.0912557i	−0.418884	+	0.908040i	$0.637579\pi$
$864$	−23.6639	−	17.8779i	−0.805062	−	0.608220i
$865$	−1.41188	−	2.44545i	−0.0480053	−	0.0831476i
$866$	−7.72420	−	13.3787i	−0.262479	−	0.454627i
$867$	15.6804	−	24.7495i	0.532535	−	0.840537i
$868$	37.6760	+	23.4292i	1.27881	+	0.795238i
$869$	−4.77427	+	2.75642i	−0.161956	+	0.0935053i
$870$	0.537017	+	0.0221034i	0.0182066	+	0.000749377i
$871$		−	8.76927i		−	0.297135i
$872$	26.1347	−	15.0889i	0.885033	−	0.510974i
$873$	21.2238	+	14.7036i	0.718316	+	0.497643i
$874$		−	25.5762i		−	0.865127i
$875$	−1.24717	−	2.33336i	−0.0421620	−	0.0788820i
$876$	1.42642	−	34.6558i	0.0481943	−	1.17091i
$877$	24.1195			0.814457			0.407229	−	0.913326i	$-0.366495\pi$
$877$	24.1195			0.814457			0.407229	+	0.913326i	$0.366495\pi$
$878$	−2.54876	+	4.41459i	−0.0860166	+	0.148985i
$879$	−17.9574	−	34.2866i	−0.605689	−	1.15646i
$880$	2.26265	−	1.30634i	0.0762741	−	0.0440369i
$881$	−6.19597			−0.208748			−0.104374	−	0.994538i	$-0.533284\pi$
$881$	−6.19597			−0.208748			−0.104374	+	0.994538i	$0.533284\pi$
$882$	−1.99696	+	13.4173i	−0.0672411	+	0.451786i
$883$	−18.1365			−0.610340			−0.305170	−	0.952298i	$-0.598713\pi$
$883$	−18.1365			−0.610340			−0.305170	+	0.952298i	$0.598713\pi$
$884$	−0.439883	+	0.253967i	−0.0147949	+	0.00854182i
$885$	−5.11722	+	8.07686i	−0.172013	+	0.271501i
$886$	6.17382	−	10.6934i	0.207413	−	0.359251i
$887$	3.28126			0.110174			0.0550870	−	0.998482i	$-0.482456\pi$
$887$	3.28126			0.110174			0.0550870	+	0.998482i	$0.482456\pi$
$888$	18.4452	+	11.6862i	0.618980	+	0.392165i
$889$	17.7547	+	33.2177i	0.595472	+	1.11409i
$890$		−	7.12429i		−	0.238807i
$891$	2.30569	−	13.8858i	0.0772436	−	0.465191i
$892$	−35.6854	+	20.6030i	−1.19484	+	0.689838i
$893$		−	1.87621i		−	0.0627850i
$894$	11.7391	+	22.4138i	0.392614	+	0.749629i
$895$	16.8195	−	9.71074i	0.562213	−	0.324594i
$896$	25.1457	+	15.6370i	0.840058	+	0.522397i
$897$	5.73368	+	10.9475i	0.191442	+	0.365526i
$898$	4.31783	+	7.47870i	0.144088	+	0.249567i
$899$	2.54484	+	4.40778i	0.0848750	+	0.147008i
$900$	−2.70401	+	3.90306i	−0.0901335	+	0.130102i
$901$	−2.09768	−	1.21109i	−0.0698838	−	0.0403474i
$902$	−0.352020	+	0.609716i	−0.0117210	+	0.0203013i
$903$	−13.9256	−	1.03063i	−0.463415	−	0.0342971i
$904$	18.2730	+	31.6498i	0.607751	+	1.05266i
$905$			25.8284i			0.858564i
$906$	8.14133	−	4.26398i	0.270477	−	0.141661i
$907$	−43.4748			−1.44356			−0.721778	−	0.692125i	$-0.756675\pi$
$907$	−43.4748			−1.44356			−0.721778	+	0.692125i	$0.756675\pi$
$908$	22.7892	−	39.4721i	0.756288	−	1.30993i
$909$	−50.7350	−	4.18356i	−1.68277	−	0.138760i
$910$	1.88703	+	0.0618002i	0.0625544	+	0.00204866i
$911$	42.4497	+	24.5084i	1.40642	+	0.811998i	0.995041	−	0.0994652i	$-0.0317132\pi$
$911$	42.4497	+	24.5084i	1.40642	+	0.811998i	0.411381	+	0.911463i	$0.365047\pi$
$912$	0.729485	−	17.7233i	0.0241557	−	0.586877i
$913$	1.07998	+	0.623527i	0.0357421	+	0.0206357i
$914$	−3.09917	−	1.78931i	−0.102511	−	0.0591850i
$915$	−3.44440	+	1.80398i	−0.113868	+	0.0596379i
$916$	−0.631466	−	0.364577i	−0.0208642	−	0.0120460i
$917$	−16.6600	−	31.1697i	−0.550162	−	1.02931i
$918$	−0.777984	−	0.587762i	−0.0256773	−	0.0193990i
$919$	−4.29115	+	7.43249i	−0.141552	+	0.245175i	−0.928081	−	0.372378i	$-0.878543\pi$
$919$	−4.29115	+	7.43249i	−0.141552	+	0.245175i	0.786529	+	0.617553i	$0.211876\pi$
$920$	−14.9470			−0.492787
$921$	−1.39540	+	33.9021i	−0.0459800	+	1.11711i
$922$		−	5.51674i		−	0.181684i
$923$	5.84404	+	10.1222i	0.192359	+	0.333175i
$924$	−0.837245	+	11.3127i	−0.0275433	+	0.372160i
$925$	2.72367	−	4.71754i	0.0895537	−	0.155112i
$926$	−9.45013	−	5.45604i	−0.310551	−	0.179297i
$927$	−1.42707	+	17.3064i	−0.0468712	+	0.568418i
$928$	1.37095	+	2.37455i	0.0450035	+	0.0779484i
$929$	3.53371	+	6.12057i	0.115937	+	0.200809i	0.918154	−	0.396224i	$-0.129679\pi$
$929$	3.53371	+	6.12057i	0.115937	+	0.200809i	−0.802217	+	0.597033i	$0.796346\pi$
$930$	11.8440	+	0.487495i	0.388380	+	0.0159856i
$931$	−38.4886	+	18.9792i	−1.26141	+	0.622018i
$932$	−30.7096	+	17.7302i	−1.00593	+	0.580772i
$933$	−13.2630	+	20.9340i	−0.434213	+	0.685347i
$934$			7.46327i			0.244206i
$935$	0.393463	−	0.227166i	0.0128676	−	0.00742913i
$936$	−3.27618	−	6.93516i	−0.107085	−	0.226683i
$937$		−	29.9370i		−	0.978001i	−0.872284	−	0.489000i	$-0.837362\pi$
$937$		−	29.9370i		−	0.978001i	0.872284	−	0.489000i	$-0.162638\pi$
$938$	−11.9645	+	6.39493i	−0.390653	+	0.208802i
$939$	−8.92198	+	4.67284i	−0.291158	+	0.152492i
$940$	−0.484388			−0.0157990
$941$	−27.1944	+	47.1021i	−0.886512	+	1.53548i	−0.0425418	+	0.999095i	$0.513546\pi$
$941$	−27.1944	+	47.1021i	−0.886512	+	1.53548i	−0.843970	+	0.536390i	$0.819788\pi$
$942$	4.22758	+	0.174006i	0.137742	+	0.00566942i
$943$	−3.89783	+	2.25041i	−0.126931	+	0.0732835i
$944$	−9.22185			−0.300146
$945$	−4.93870	−	12.8300i	−0.160656	−	0.417360i
$946$	3.07843			0.100088
$947$	−14.1957	+	8.19587i	−0.461297	+	0.266330i	−0.712589	−	0.701581i	$-0.752478\pi$
$947$	−14.1957	+	8.19587i	−0.461297	+	0.266330i	0.251293	+	0.967911i	$0.419144\pi$
$948$	9.65483	+	0.397390i	0.313574	+	0.0129066i
$949$	6.98879	−	12.1049i	0.226866	−	0.392943i
$950$	3.96006			0.128481
$951$	−23.5630	+	12.3410i	−0.764082	+	0.400184i
$952$	1.51049	+	0.939308i	0.0489551	+	0.0304432i
$953$			17.4072i			0.563873i	0.959433	+	0.281937i	$0.0909768\pi$
$953$			17.4072i			0.563873i	−0.959433	+	0.281937i	$0.909023\pi$
$954$	9.20178	−	13.2822i	0.297918	−	0.430026i
$955$	11.4606	−	6.61675i	0.370855	−	0.214113i
$956$		−	37.9612i		−	1.22775i
$957$	−0.696456	+	1.09926i	−0.0225132	+	0.0355341i
$958$	18.6109	−	10.7450i	0.601292	−	0.347156i
$959$	19.7048	−	10.5321i	0.636302	−	0.340099i
$960$	0.598573	+	0.0246371i	0.0193188	+	0.000795158i
$961$	40.6268	+	70.3676i	1.31054	+	2.26992i
$962$	1.94365	+	3.36649i	0.0626657	+	0.108540i
$963$	17.4952	+	12.1206i	0.563776	+	0.390580i
$964$	3.19478	+	1.84451i	0.102897	+	0.0594077i
$965$	−4.81802	+	8.34506i	−0.155098	+	0.268637i
$966$	10.7551	−	15.8062i	0.346039	−	0.508556i
$967$	3.62017	+	6.27032i	0.116417	+	0.201640i	0.918345	−	0.395780i	$-0.129526\pi$
$967$	3.62017	+	6.27032i	0.116417	+	0.201640i	−0.801928	+	0.597420i	$0.796192\pi$
$968$			19.7964i			0.636280i
$969$	0.126853	−	3.08198i	0.00407512	−	0.0990076i
$970$	−5.55944			−0.178503
$971$	11.7556	−	20.3614i	0.377256	−	0.653427i	−0.613406	−	0.789768i	$-0.710201\pi$
$971$	11.7556	−	20.3614i	0.377256	−	0.653427i	0.990662	+	0.136341i	$0.0435342\pi$
$972$	−16.4401	+	18.3971i	−0.527316	+	0.590087i
$973$	−7.89754	−	4.91115i	−0.253183	−	0.157444i
$974$	8.67212	+	5.00685i	0.277873	+	0.160430i
$975$	−1.69504	+	0.887770i	−0.0542848	+	0.0284314i
$976$	−3.24769	−	1.87506i	−0.103956	−	0.0600191i
$977$	49.2431	+	28.4305i	1.57543	+	0.909572i	0.995486	+	0.0949131i	$0.0302573\pi$
$977$	49.2431	+	28.4305i	1.57543	+	0.909572i	0.579940	+	0.814659i	$0.303076\pi$
$978$	0.0705088	−	1.71305i	0.00225462	−	0.0547774i
$979$	14.9383	+	8.62462i	0.477429	+	0.275644i
$980$	4.89992	+	9.93673i	0.156522	+	0.317417i
$981$	−16.7093	−	35.3709i	−0.533486	−	1.12931i
$982$	5.85023	−	10.1329i	0.186688	−	0.323354i
$983$	−45.9005			−1.46400			−0.731999	−	0.681306i	$-0.761412\pi$
$983$	−45.9005			−1.46400			−0.731999	+	0.681306i	$0.761412\pi$
$984$	2.47458	−	1.29605i	0.0788868	−	0.0413165i
$985$			21.1621i			0.674280i
$986$	0.0450718	+	0.0780666i	0.00143538	+	0.00248615i
$987$	0.788969	−	1.15951i	0.0251132	−	0.0369075i
$988$	5.35961	−	9.28312i	0.170512	−	0.295335i
$989$	17.0433	+	9.83998i	0.541947	+	0.312893i
$990$	1.29458	+	2.74042i	0.0411444	+	0.0870963i
$991$	−13.6765	−	23.6884i	−0.434449	−	0.752488i	0.562801	−	0.826592i	$-0.309724\pi$
$991$	−13.6765	−	23.6884i	−0.434449	−	0.752488i	−0.997251	+	0.0741040i	$0.976390\pi$
$992$	30.2365	+	52.3711i	0.960009	+	1.66278i
$993$	−21.5066	−	41.0631i	−0.682491	−	1.30310i
$994$	9.54857	−	15.3549i	0.302862	−	0.487028i
$995$	3.72171	−	2.14873i	0.117986	−	0.0681193i
$996$	−1.01415	−	1.93635i	−0.0321347	−	0.0613556i
$997$			13.9499i			0.441799i	0.975297	+	0.220899i	$0.0708992\pi$
$997$			13.9499i			0.441799i	−0.975297	+	0.220899i	$0.929101\pi$
$998$	3.70543	−	2.13933i	0.117293	−	0.0677193i
$999$	17.0624	−	22.5845i	0.539832	−	0.714541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.be.c.236.11	yes	32
3.2	odd	2		945.2.be.c.656.6		32
7.3	odd	6		315.2.t.c.101.11	✓	32
9.4	even	3		945.2.t.c.341.11		32
9.5	odd	6		315.2.t.c.131.6	yes	32
21.17	even	6		945.2.t.c.521.6		32
63.31	odd	6		945.2.be.c.206.6		32
63.59	even	6	inner	315.2.be.c.311.11	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.c.101.11	✓	32	7.3	odd	6
315.2.t.c.131.6	yes	32	9.5	odd	6
315.2.be.c.236.11	yes	32	1.1	even	1	trivial
315.2.be.c.311.11	yes	32	63.59	even	6	inner
945.2.t.c.341.11		32	9.4	even	3
945.2.t.c.521.6		32	21.17	even	6
945.2.be.c.206.6		32	63.31	odd	6
945.2.be.c.656.6		32	3.2	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.559417 - 0.322980i) q^{2} +(1.73059 + 0.0712304i) q^{3} +(-0.791368 + 1.37069i) q^{4} -1.00000 q^{5} +(0.991125 - 0.519096i) q^{6} +(1.24717 + 2.33336i) q^{7} +2.31430i q^{8} +(2.98985 + 0.246540i) q^{9} +O(q^{10})\)	\(q+(0.559417 - 0.322980i) q^{2} +(1.73059 + 0.0712304i) q^{3} +(-0.791368 + 1.37069i) q^{4} -1.00000 q^{5} +(0.991125 - 0.519096i) q^{6} +(1.24717 + 2.33336i) q^{7} +2.31430i q^{8} +(2.98985 + 0.246540i) q^{9} +(-0.559417 + 0.322980i) q^{10} -1.56399i q^{11} +(-1.46717 + 2.31573i) q^{12} +(-0.956727 + 0.552367i) q^{13} +(1.45131 + 0.902512i) q^{14} +(-1.73059 - 0.0712304i) q^{15} +(-0.835265 - 1.44672i) q^{16} +(-0.145248 - 0.251577i) q^{17} +(1.75220 - 0.827742i) q^{18} +(5.30918 + 3.06526i) q^{19} +(0.791368 - 1.37069i) q^{20} +(1.99212 + 4.12692i) q^{21} +(-0.505136 - 0.874921i) q^{22} -6.45853i q^{23} +(-0.164849 + 4.00510i) q^{24} +1.00000 q^{25} +(-0.356806 + 0.618007i) q^{26} +(5.15663 + 0.639628i) q^{27} +(-4.18528 - 0.137068i) q^{28} +(-0.416026 - 0.240193i) q^{29} +(-0.991125 + 0.519096i) q^{30} +(-9.17552 - 5.29749i) q^{31} +(-4.94301 - 2.85385i) q^{32} +(0.111403 - 2.70661i) q^{33} +(-0.162508 - 0.0938243i) q^{34} +(-1.24717 - 2.33336i) q^{35} +(-2.70401 + 3.90306i) q^{36} +(2.72367 - 4.71754i) q^{37} +3.96006 q^{38} +(-1.69504 + 0.887770i) q^{39} -2.31430i q^{40} +(-0.348441 - 0.603517i) q^{41} +(2.44734 + 1.66525i) q^{42} +(-1.52356 + 2.63889i) q^{43} +(2.14374 + 1.23769i) q^{44} +(-2.98985 - 0.246540i) q^{45} +(-2.08597 - 3.61301i) q^{46} +(-0.153022 - 0.265042i) q^{47} +(-1.34245 - 2.56317i) q^{48} +(-3.88915 + 5.82018i) q^{49} +(0.559417 - 0.322980i) q^{50} +(-0.233444 - 0.445721i) q^{51} -1.74850i q^{52} +(7.22102 - 4.16906i) q^{53} +(3.09130 - 1.30767i) q^{54} +1.56399i q^{55} +(-5.40010 + 2.88632i) q^{56} +(8.96966 + 5.68287i) q^{57} -0.310309 q^{58} +(2.76016 - 4.78073i) q^{59} +(1.46717 - 2.31573i) q^{60} +(1.94411 - 1.12243i) q^{61} -6.84392 q^{62} +(3.15358 + 7.28388i) q^{63} -0.345879 q^{64} +(0.956727 - 0.552367i) q^{65} +(-0.811860 - 1.55011i) q^{66} +(-3.96895 + 6.87443i) q^{67} +0.459779 q^{68} +(0.460043 - 11.1770i) q^{69} +(-1.45131 - 0.902512i) q^{70} -10.5800i q^{71} +(-0.570569 + 6.91942i) q^{72} +(-10.9573 + 6.32622i) q^{73} -3.51876i q^{74} +(1.73059 + 0.0712304i) q^{75} +(-8.40304 + 4.85150i) q^{76} +(3.64935 - 1.95055i) q^{77} +(-0.661505 + 1.04410i) q^{78} +(-1.76243 - 3.05262i) q^{79} +(0.835265 + 1.44672i) q^{80} +(8.87844 + 1.47424i) q^{81} +(-0.389847 - 0.225078i) q^{82} +(-0.398678 + 0.690530i) q^{83} +(-7.23323 - 0.535327i) q^{84} +(0.145248 + 0.251577i) q^{85} +1.96832i q^{86} +(-0.702859 - 0.445308i) q^{87} +3.61954 q^{88} +(-5.51450 + 9.55140i) q^{89} +(-1.75220 + 0.827742i) q^{90} +(-2.48207 - 1.54350i) q^{91} +(8.85264 + 5.11107i) q^{92} +(-15.5017 - 9.82133i) q^{93} +(-0.171207 - 0.0988462i) q^{94} +(-5.30918 - 3.06526i) q^{95} +(-8.35102 - 5.29092i) q^{96} +(7.45344 + 4.30325i) q^{97} +(-0.295855 + 4.51202i) q^{98} +(0.385586 - 4.67609i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9}+O(q^{10}) \) 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9	\( 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9} + 15 q^{12} - 6 q^{13} - 6 q^{14} - q^{15} - 16 q^{16} + 3 q^{17} + 41 q^{18} - 16 q^{20} - 17 q^{21} - 21 q^{22} - 26 q^{24} + 32 q^{25} - 12 q^{26} - 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 24 q^{31} - 19 q^{33} + 30 q^{34} - q^{35} + 18 q^{36} - q^{37} - 60 q^{38} - 36 q^{39} - 6 q^{41} + 44 q^{42} - 19 q^{43} - 21 q^{44} - 7 q^{45} + 6 q^{46} - 15 q^{47} + 35 q^{48} + 23 q^{49} - 9 q^{51} + 24 q^{53} - 58 q^{54} + 33 q^{56} + 27 q^{57} + 15 q^{59} - 15 q^{60} - 9 q^{61} - 11 q^{63} + 76 q^{64} + 6 q^{65} + 22 q^{66} + 25 q^{67} - 6 q^{68} + 50 q^{69} + 6 q^{70} + 61 q^{72} + 12 q^{73} + q^{75} - 54 q^{76} - 27 q^{77} - 42 q^{78} - 2 q^{79} + 16 q^{80} + 43 q^{81} - 24 q^{82} + 42 q^{83} - 36 q^{84} - 3 q^{85} - 55 q^{87} - 84 q^{88} - 30 q^{89} - 41 q^{90} - 57 q^{91} + 6 q^{92} - 48 q^{93} + 24 q^{94} - 9 q^{96} + 42 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) \) 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9 + 15 * q^12 - 6 * q^13 - 6 * q^14 - q^15 - 16 * q^16 + 3 * q^17 + 41 * q^18 - 16 * q^20 - 17 * q^21 - 21 * q^22 - 26 * q^24 + 32 * q^25 - 12 * q^26 - 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 24 * q^31 - 19 * q^33 + 30 * q^34 - q^35 + 18 * q^36 - q^37 - 60 * q^38 - 36 * q^39 - 6 * q^41 + 44 * q^42 - 19 * q^43 - 21 * q^44 - 7 * q^45 + 6 * q^46 - 15 * q^47 + 35 * q^48 + 23 * q^49 - 9 * q^51 + 24 * q^53 - 58 * q^54 + 33 * q^56 + 27 * q^57 + 15 * q^59 - 15 * q^60 - 9 * q^61 - 11 * q^63 + 76 * q^64 + 6 * q^65 + 22 * q^66 + 25 * q^67 - 6 * q^68 + 50 * q^69 + 6 * q^70 + 61 * q^72 + 12 * q^73 + q^75 - 54 * q^76 - 27 * q^77 - 42 * q^78 - 2 * q^79 + 16 * q^80 + 43 * q^81 - 24 * q^82 + 42 * q^83 - 36 * q^84 - 3 * q^85 - 55 * q^87 - 84 * q^88 - 30 * q^89 - 41 * q^90 - 57 * q^91 + 6 * q^92 - 48 * q^93 + 24 * q^94 - 9 * q^96 + 42 * q^97 - 6 * q^98 - q^99

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