LMFDB - Embedded newform 315.2.t.c.101.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(101,315)]

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, 1]))

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

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

chi := DirichletCharacter("315.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.t (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			101.11
Character	$\chi$	$=$	315.101
Dual form			315.2.t.c.131.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.645959i q^{2} +(0.803605 + 1.53435i) q^{3} +1.58274 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.991125 + 0.519096i) q^{6} +(-2.64433 + 0.0866018i) q^{7} +2.31430i q^{8} +(-1.70844 + 2.46602i) q^{9} +O(q^{10})$	\(q+0.645959i q^{2} +(0.803605 + 1.53435i) q^{3} +1.58274 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.991125 + 0.519096i) q^{6} +(-2.64433 + 0.0866018i) q^{7} +2.31430i q^{8} +(-1.70844 + 2.46602i) q^{9} +(-0.559417 - 0.322980i) q^{10} +(-1.35445 + 0.781994i) q^{11} +(1.27190 + 2.42847i) q^{12} +(0.956727 - 0.552367i) q^{13} +(-0.0559412 - 1.70813i) q^{14} +(-1.73059 - 0.0712304i) q^{15} +1.67053 q^{16} +(0.145248 - 0.251577i) q^{17} +(-1.59295 - 1.10358i) q^{18} +(5.30918 - 3.06526i) q^{19} +(-0.791368 + 1.37069i) q^{20} +(-2.25788 - 3.98773i) q^{21} +(-0.505136 - 0.874921i) q^{22} +(5.59325 + 3.22926i) q^{23} +(-3.55094 + 1.85979i) q^{24} +(-0.500000 - 0.866025i) 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} +(0.0460119 - 1.11789i) q^{30} -10.5950i q^{31} +5.70770i q^{32} +(-2.28830 - 1.44979i) 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} +(1.98003 + 3.42952i) q^{38} +(1.61635 + 1.02407i) q^{39} +(-2.00424 - 1.15715i) q^{40} +(0.348441 + 0.603517i) q^{41} +(2.57591 - 1.45850i) q^{42} +(-1.52356 + 2.63889i) q^{43} +(-2.14374 + 1.23769i) q^{44} +(-1.28142 - 2.71256i) q^{45} +(-2.08597 + 3.61301i) q^{46} -0.306045 q^{47} +(1.34245 + 2.56317i) q^{48} +(6.98500 - 0.458008i) q^{49} +(0.559417 - 0.322980i) q^{50} +(0.502728 + 0.0206921i) q^{51} +(1.51425 - 0.874251i) q^{52} +(-7.22102 - 4.16906i) q^{53} +(0.413173 - 3.33097i) q^{54} -1.56399i q^{55} +(-0.200423 - 6.11978i) q^{56} +(8.96966 + 5.68287i) q^{57} +(0.155155 - 0.268736i) q^{58} +5.52031 q^{59} +(-2.73906 - 0.112739i) q^{60} -2.24486i q^{61} +6.84392 q^{62} +(4.30411 - 6.66893i) q^{63} -0.345879 q^{64} +1.10473i q^{65} +(0.936502 - 1.47815i) q^{66} +7.93791 q^{67} +(0.229889 - 0.398180i) q^{68} +(-0.460043 + 11.1770i) q^{69} +(1.50726 + 0.805619i) q^{70} -10.5800i q^{71} +(-5.70711 - 3.95384i) q^{72} +(-10.9573 - 6.32622i) q^{73} +(-3.04733 + 1.75938i) q^{74} +(0.926980 - 1.46312i) q^{75} +(8.40304 - 4.85150i) q^{76} +(3.51390 - 2.18515i) q^{77} +(-0.661505 + 1.04410i) q^{78} +3.52487 q^{79} +(-0.835265 + 1.44672i) q^{80} +(-3.16249 - 8.42607i) q^{81} +(-0.389847 + 0.225078i) q^{82} +(0.398678 - 0.690530i) q^{83} +(-3.57363 - 6.31153i) q^{84} +(0.145248 + 0.251577i) q^{85} +(-1.70462 - 0.984160i) q^{86} +(0.0342180 - 0.831348i) q^{87} +(-1.80977 - 3.13461i) 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} +(16.2564 - 8.51418i) q^{93} -0.197692i q^{94} +6.13052i q^{95} +(-8.75758 + 4.58674i) 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} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9}+O(q^{10}) $ 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9	$ 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9} + 3 q^{11} + 12 q^{12} + 6 q^{13} - 15 q^{14} - q^{15} + 32 q^{16} - 3 q^{17} - 13 q^{18} + 16 q^{20} - q^{21} - 21 q^{22} - 9 q^{23} - 4 q^{24} - 16 q^{25} + 12 q^{26} + 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 19 q^{33} - 30 q^{34} + q^{35} + 18 q^{36} - q^{37} - 30 q^{38} + 21 q^{39} + 6 q^{41} + 19 q^{42} - 19 q^{43} + 21 q^{44} - 8 q^{45} + 6 q^{46} - 30 q^{47} - 35 q^{48} + 5 q^{49} + 36 q^{51} + 21 q^{52} - 24 q^{53} - 59 q^{54} + 30 q^{56} + 27 q^{57} + 30 q^{59} + 3 q^{60} - 32 q^{63} + 76 q^{64} + 26 q^{66} - 50 q^{67} - 3 q^{68} - 50 q^{69} + 9 q^{70} - 14 q^{72} + 12 q^{73} + 60 q^{74} + 2 q^{75} + 54 q^{76} - 27 q^{77} - 42 q^{78} + 4 q^{79} - 16 q^{80} - 23 q^{81} - 24 q^{82} - 42 q^{83} - 72 q^{84} - 3 q^{85} + 51 q^{86} + 34 q^{87} + 42 q^{88} + 30 q^{89} + 41 q^{90} - 57 q^{91} + 6 q^{92} - 33 q^{93} + 15 q^{96} - 42 q^{97} + 6 q^{98} - q^{99}+O(q^{100}) $ 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9 + 3 * q^11 + 12 * q^12 + 6 * q^13 - 15 * q^14 - q^15 + 32 * q^16 - 3 * q^17 - 13 * q^18 + 16 * q^20 - q^21 - 21 * q^22 - 9 * q^23 - 4 * q^24 - 16 * q^25 + 12 * q^26 + 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 19 * q^33 - 30 * q^34 + q^35 + 18 * q^36 - q^37 - 30 * q^38 + 21 * q^39 + 6 * q^41 + 19 * q^42 - 19 * q^43 + 21 * q^44 - 8 * q^45 + 6 * q^46 - 30 * q^47 - 35 * q^48 + 5 * q^49 + 36 * q^51 + 21 * q^52 - 24 * q^53 - 59 * q^54 + 30 * q^56 + 27 * q^57 + 30 * q^59 + 3 * q^60 - 32 * q^63 + 76 * q^64 + 26 * q^66 - 50 * q^67 - 3 * q^68 - 50 * q^69 + 9 * q^70 - 14 * q^72 + 12 * q^73 + 60 * q^74 + 2 * q^75 + 54 * q^76 - 27 * q^77 - 42 * q^78 + 4 * q^79 - 16 * q^80 - 23 * q^81 - 24 * q^82 - 42 * q^83 - 72 * q^84 - 3 * q^85 + 51 * q^86 + 34 * q^87 + 42 * q^88 + 30 * q^89 + 41 * q^90 - 57 * q^91 + 6 * q^92 - 33 * q^93 + 15 * 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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

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

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 $

$2$			0.645959i			0.456762i	0.973572	+	0.228381i	$0.0733432\pi$
$2$			0.645959i			0.456762i	−0.973572	+	0.228381i	$0.926657\pi$
$3$	0.803605	+	1.53435i	0.463962	+	0.885855i
$3$	0.803605	+	1.53435i	0.463962	+	0.885855i
$4$	1.58274			0.791368
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−0.991125	+	0.519096i	−0.404625	+	0.211920i
$7$	−2.64433	+	0.0866018i	−0.999464	+	0.0327324i
$7$	−2.64433	+	0.0866018i	−0.999464	+	0.0327324i
$8$			2.31430i			0.818229i
$9$	−1.70844	+	2.46602i	−0.569479	+	0.822006i
$10$	−0.559417	−	0.322980i	−0.176903	−	0.102135i
$11$	−1.35445	+	0.781994i	−0.408383	+	0.235780i	−0.690095	−	0.723719i	$-0.742431\pi$
$11$	−1.35445	+	0.781994i	−0.408383	+	0.235780i	0.281712	+	0.959499i	$0.409098\pi$
$12$	1.27190	+	2.42847i	0.367165	+	0.701038i
$13$	0.956727	−	0.552367i	0.265348	−	0.153199i	−0.361423	−	0.932402i	$-0.617709\pi$
$13$	0.956727	−	0.552367i	0.265348	−	0.153199i	0.626772	+	0.779203i	$0.284376\pi$
$14$	−0.0559412	−	1.70813i	−0.0149509	−	0.456517i
$15$	−1.73059	−	0.0712304i	−0.446835	−	0.0183916i
$16$	1.67053			0.417632
$17$	0.145248	−	0.251577i	0.0352278	−	0.0610164i	−0.847874	−	0.530198i	$-0.822118\pi$
$17$	0.145248	−	0.251577i	0.0352278	−	0.0610164i	0.883102	+	0.469181i	$0.155451\pi$
$18$	−1.59295	−	1.10358i	−0.375461	−	0.260116i
$19$	5.30918	−	3.06526i	1.21801	−	0.703219i	0.253518	−	0.967331i	$-0.418412\pi$
$19$	5.30918	−	3.06526i	1.21801	−	0.703219i	0.964492	+	0.264112i	$0.0850788\pi$
$20$	−0.791368	+	1.37069i	−0.176955	+	0.306496i
$21$	−2.25788	−	3.98773i	−0.492709	−	0.870194i
$22$	−0.505136	−	0.874921i	−0.107695	−	0.186534i
$23$	5.59325	+	3.22926i	1.16627	+	0.673348i	0.952799	−	0.303601i	$-0.0981890\pi$
$23$	5.59325	+	3.22926i	1.16627	+	0.673348i	0.213473	+	0.976949i	$0.431522\pi$
$24$	−3.55094	+	1.85979i	−0.724832	+	0.379627i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	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	$0.680869\pi$
$30$	0.0460119	−	1.11789i	0.00840058	−	0.204097i
$31$		−	10.5950i		−	1.90291i	−0.307781	−	0.951457i	$-0.599587\pi$
$31$		−	10.5950i		−	1.90291i	0.307781	−	0.951457i	$-0.400413\pi$
$32$			5.70770i			1.00899i
$33$	−2.28830	−	1.44979i	−0.398341	−	0.252375i
$34$	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	0.998240	−	0.0592957i	$-0.0188855\pi$
$37$	2.72367	+	4.71754i	0.447769	+	0.775558i	−0.550472	+	0.834854i	$0.685552\pi$
$38$	1.98003	+	3.42952i	0.321204	+	0.556341i
$39$	1.61635	+	1.02407i	0.258824	+	0.163982i
$40$	−2.00424	−	1.15715i	−0.316899	−	0.182962i
$41$	0.348441	+	0.603517i	0.0544173	+	0.0942535i	0.891951	−	0.452132i	$-0.149337\pi$
$41$	0.348441	+	0.603517i	0.0544173	+	0.0942535i	−0.837534	+	0.546386i	$0.816003\pi$
$42$	2.57591	−	1.45850i	0.397472	−	0.225051i
$43$	−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
$45$	−1.28142	−	2.71256i	−0.191022	−	0.404364i
$46$	−2.08597	+	3.61301i	−0.307560	+	0.532709i
$47$	−0.306045			−0.0446412			−0.0223206	−	0.999751i	$-0.507105\pi$
$47$	−0.306045			−0.0446412			−0.0223206	+	0.999751i	$0.507105\pi$
$48$	1.34245	+	2.56317i	0.193766	+	0.369962i
$49$	6.98500	−	0.458008i	0.997857	−	0.0654298i
$50$	0.559417	−	0.322980i	0.0791135	−	0.0456762i
$51$	0.502728	+	0.0206921i	0.0703960	+	0.00289748i
$52$	1.51425	−	0.874251i	0.209988	−	0.121237i
$53$	−7.22102	−	4.16906i	−0.991883	−	0.572664i	−0.0860465	−	0.996291i	$-0.527423\pi$
$53$	−7.22102	−	4.16906i	−0.991883	−	0.572664i	−0.905837	+	0.423627i	$0.860757\pi$
$54$	0.413173	−	3.33097i	0.0562258	−	0.453288i
$55$		−	1.56399i		−	0.210888i
$56$	−0.200423	−	6.11978i	−0.0267826	−	0.817791i
$57$	8.96966	+	5.68287i	1.18806	+	0.752714i
$58$	0.155155	−	0.268736i	0.0203728	−	0.0352867i
$59$	5.52031			0.718683			0.359342	−	0.933206i	$-0.383001\pi$
$59$	5.52031			0.718683			0.359342	+	0.933206i	$0.383001\pi$
$60$	−2.73906	−	0.112739i	−0.353611	−	0.0145545i
$61$		−	2.24486i		−	0.287425i	−0.989619	−	0.143713i	$-0.954096\pi$
$61$		−	2.24486i		−	0.287425i	0.989619	−	0.143713i	$-0.0459041\pi$
$62$	6.84392			0.869179
$63$	4.30411	−	6.66893i	0.542267	−	0.840206i
$64$	−0.345879			−0.0432348
$65$			1.10473i			0.137025i
$66$	0.936502	−	1.47815i	0.115275	−	0.181947i
$67$	7.93791			0.969770			0.484885	−	0.874578i	$-0.338862\pi$
$67$	7.93791			0.969770			0.484885	+	0.874578i	$0.338862\pi$
$68$	0.229889	−	0.398180i	0.0278782	−	0.0482864i
$69$	−0.460043	+	11.1770i	−0.0553827	+	1.34556i
$70$	1.50726	+	0.805619i	0.180152	+	0.0962899i
$71$		−	10.5800i		−	1.25561i	−0.778369	−	0.627807i	$-0.783953\pi$
$71$		−	10.5800i		−	1.25561i	0.778369	−	0.627807i	$-0.216047\pi$
$72$	−5.70711	−	3.95384i	−0.672589	−	0.465964i
$73$	−10.9573	−	6.32622i	−1.28246	−	0.740428i	−0.305162	−	0.952301i	$-0.598711\pi$
$73$	−10.9573	−	6.32622i	−1.28246	−	0.740428i	−0.977297	+	0.211872i	$0.932044\pi$
$74$	−3.04733	+	1.75938i	−0.354245	+	0.204524i
$75$	0.926980	−	1.46312i	0.107038	−	0.168946i
$76$	8.40304	−	4.85150i	0.963895	−	0.556505i
$77$	3.51390	−	2.18515i	0.400447	−	0.249021i
$78$	−0.661505	+	1.04410i	−0.0749007	+	0.118221i
$79$	3.52487			0.396578			0.198289	−	0.980144i	$-0.436461\pi$
$79$	3.52487			0.396578			0.198289	+	0.980144i	$0.436461\pi$
$80$	−0.835265	+	1.44672i	−0.0933855	+	0.161748i
$81$	−3.16249	−	8.42607i	−0.351388	−	0.936230i
$82$	−0.389847	+	0.225078i	−0.0430514	+	0.0248557i
$83$	0.398678	−	0.690530i	0.0437605	−	0.0757955i	−0.843316	−	0.537419i	$-0.819399\pi$
$83$	0.398678	−	0.690530i	0.0437605	−	0.0757955i	0.887076	+	0.461623i	$0.152733\pi$
$84$	−3.57363	−	6.31153i	−0.389915	−	0.688644i
$85$	0.145248	+	0.251577i	0.0157544	+	0.0272873i
$86$	−1.70462	−	0.984160i	−0.183813	−	0.106125i
$87$	0.0342180	−	0.831348i	0.00366856	−	0.0891298i
$88$	−1.80977	−	3.13461i	−0.192922	−	0.334151i
$89$	5.51450	+	9.55140i	0.584536	+	1.01245i	0.994933	+	0.100539i	$0.0320568\pi$
$89$	5.51450	+	9.55140i	0.584536	+	1.01245i	−0.410397	+	0.911907i	$0.634610\pi$
$90$	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
$93$	16.2564	−	8.51418i	1.68571	−	0.882880i
$94$		−	0.197692i		−	0.0203904i
$95$			6.13052i			0.628978i
$96$	−8.75758	+	4.58674i	−0.893817	+	0.468132i
$97$	−7.45344	−	4.30325i	−0.756782	−	0.436928i	0.0713569	−	0.997451i	$-0.477267\pi$
$97$	−7.45344	−	4.30325i	−0.756782	−	0.436928i	−0.828139	+	0.560522i	$0.810600\pi$
$98$	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
$101$	−8.48453	−	14.6956i	−0.844242	−	1.46227i	−0.886278	−	0.463154i	$-0.846718\pi$
$101$	−8.48453	−	14.6956i	−0.844242	−	1.46227i	0.0420361	−	0.999116i	$-0.486616\pi$
$102$	−0.0133663	+	0.324742i	−0.00132346	+	0.0321542i
$103$	5.01289	+	2.89420i	0.493935	+	0.285174i	0.726206	−	0.687478i	$-0.241282\pi$
$103$	5.01289	+	2.89420i	0.493935	+	0.285174i	−0.232270	+	0.972651i	$0.574615\pi$
$104$	1.27834	+	2.21416i	0.125352	+	0.217116i
$105$	4.58241	+	0.0384849i	0.447198	+	0.00375575i
$106$	2.69304	−	4.66448i	0.261571	−	0.453055i
$107$	−6.14405	+	3.54727i	−0.593967	+	0.342927i	−0.766665	−	0.642048i	$-0.778085\pi$
$107$	−6.14405	+	3.54727i	−0.593967	+	0.342927i	0.172697	+	0.984975i	$0.444752\pi$
$108$	−8.16160	−	1.01236i	−0.785350	−	0.0974146i
$109$	−6.51984	+	11.2927i	−0.624488	+	1.08164i	0.364152	+	0.931340i	$0.381359\pi$
$109$	−6.51984	+	11.2927i	−0.624488	+	1.08164i	−0.988640	+	0.150305i	$0.951974\pi$
$110$	1.01027			0.0963257
$111$	−5.04958	+	7.97009i	−0.479285	+	0.756488i
$112$	−4.41744	+	0.144671i	−0.417409	+	0.0136701i
$113$	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	$0.0668476\pi$
$114$	−3.67090	+	5.79403i	−0.343811	+	0.542661i
$115$	−5.59325	+	3.22926i	−0.521573	+	0.301130i
$116$	−0.658459	−	0.380162i	−0.0611364	−	0.0352971i
$117$	−0.272362	+	3.30299i	−0.0251798	+	0.305362i
$118$			3.56590i			0.328267i
$119$	−0.362297	+	0.677832i	−0.0332117	+	0.0621368i
$120$	0.164849	−	4.00510i	0.0150485	−	0.365614i
$121$	−4.27697	+	7.40793i	−0.388816	+	0.673448i
$122$	1.45009			0.131285
$123$	−0.645995	+	1.01962i	−0.0582474	+	0.0919358i
$124$		−	16.7691i		−	1.50591i
$125$	1.00000			0.0894427
$126$	4.30785	+	2.78028i	0.383774	+	0.247687i
$127$	14.2360			1.26324			0.631620	−	0.775279i	$-0.282391\pi$
$127$	14.2360			1.26324			0.631620	+	0.775279i	$0.282391\pi$
$128$			11.1920i			0.989240i
$129$	−5.27332	−	0.217048i	−0.464290	−	0.0191100i
$130$	−0.713613			−0.0625880
$131$	−6.67914	+	11.5686i	−0.583559	+	1.01075i	0.411494	+	0.911412i	$0.365007\pi$
$131$	−6.67914	+	11.5686i	−0.583559	+	1.01075i	−0.995053	+	0.0993419i	$0.968326\pi$
$132$	−3.62177	−	2.29463i	−0.315235	−	0.199722i
$133$	−13.7738	+	8.56535i	−1.19434	+	0.742710i
$134$			5.12756i			0.442954i
$135$	3.13225	−	4.14596i	0.269581	−	0.356828i
$136$	0.582225	+	0.336148i	0.0499254	+	0.0288244i
$137$	−7.31343	+	4.22241i	−0.624828	+	0.360745i	−0.778746	−	0.627339i	$-0.784144\pi$
$137$	−7.31343	+	4.22241i	−0.624828	+	0.360745i	0.153918	+	0.988084i	$0.450811\pi$
$138$	−7.21990	−	0.297169i	−0.614599	−	0.0252967i
$139$	3.04415	−	1.75754i	0.258201	−	0.149073i	−0.365312	−	0.930885i	$-0.619038\pi$
$139$	3.04415	−	1.75754i	0.258201	−	0.149073i	0.623514	+	0.781812i	$0.285705\pi$
$140$	1.97394	−	3.69310i	0.166828	−	0.312124i
$141$	−0.245939	−	0.469578i	−0.0207118	−	0.0395456i
$142$	6.83424			0.573517
$143$	−0.863895	+	1.49631i	−0.0722425	+	0.125128i
$144$	−2.85399	+	4.11956i	−0.237833	+	0.343296i
$145$	0.416026	−	0.240193i	0.0345491	−	0.0199469i
$146$	4.08648	−	7.07799i	0.338199	−	0.585779i
$147$	6.31593	+	10.3494i	0.520929	+	0.853600i
$148$	4.31085	+	7.46662i	0.354350	+	0.613752i
$149$	−19.5847	−	11.3072i	−1.60444	−	0.926325i	−0.990584	−	0.136909i	$-0.956283\pi$
$149$	−19.5847	−	11.3072i	−1.60444	−	0.926325i	−0.613858	−	0.789416i	$-0.710383\pi$
$150$	0.945113	+	0.598791i	0.0771681	+	0.0488911i
$151$	−4.10711	−	7.11373i	−0.334232	−	0.578907i	0.649105	−	0.760699i	$-0.275144\pi$
$151$	−4.10711	−	7.11373i	−0.334232	−	0.578907i	−0.983337	+	0.181792i	$0.941810\pi$
$152$	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
$156$	2.55826	+	1.62083i	0.204825	+	0.129770i
$157$			3.78176i			0.301817i	0.988548	+	0.150909i	$0.0482199\pi$
$157$			3.78176i			0.301817i	−0.988548	+	0.150909i	$0.951780\pi$
$158$			2.27692i			0.181142i
$159$	0.593927	−	14.4298i	0.0471015	−	1.14436i
$160$	−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	0.894471	−	0.447126i	$-0.147552\pi$
$163$	0.766202	+	1.32710i	0.0600135	+	0.103946i	−0.834458	+	0.551072i	$0.814219\pi$
$164$	0.551490	+	0.955208i	0.0430641	+	0.0745892i
$165$	2.39970	−	1.25683i	0.186816	−	0.0978440i
$166$	0.446054	+	0.257529i	0.0346205	+	0.0199882i
$167$	−12.6284	−	21.8730i	−0.977213	−	1.69258i	−0.672431	−	0.740159i	$-0.734750\pi$
$167$	−12.6284	−	21.8730i	−0.977213	−	1.69258i	−0.304781	−	0.952422i	$-0.598583\pi$
$168$	9.22881	−	5.22541i	0.712018	−	0.403149i
$169$	−5.88978	+	10.2014i	−0.453060	+	0.784723i
$170$	−0.162508	+	0.0938243i	−0.0124638	+	0.00719599i
$171$	−1.51142	+	18.3293i	−0.115581	+	1.40168i
$172$	−2.41140	+	4.17667i	−0.183868	+	0.318468i
$173$	2.82376			0.214686			0.107343	−	0.994222i	$-0.465766\pi$
$173$	2.82376			0.214686			0.107343	+	0.994222i	$0.465766\pi$
$174$	0.537017	+	0.0221034i	0.0407111	+	0.00167566i
$175$	1.39717	+	2.24676i	0.105616	+	0.169839i
$176$	−2.26265	+	1.30634i	−0.170554	+	0.0984694i
$177$	4.43615	+	8.47007i	0.333442	+	0.636649i
$178$	−6.16981	+	3.56214i	−0.462447	+	0.266994i
$179$	16.8195	+	9.71074i	1.25715	+	0.725814i	0.972519	−	0.232823i	$-0.0747964\pi$
$179$	16.8195	+	9.71074i	1.25715	+	0.725814i	0.284629	+	0.958638i	$0.408130\pi$
$180$	−2.02814	−	4.29327i	−0.151169	−	0.320001i
$181$			25.8284i			1.91981i	0.280331	+	0.959903i	$0.409556\pi$
$181$			25.8284i			1.91981i	−0.280331	+	0.959903i	$0.590444\pi$
$182$	−0.997035	−	1.60332i	−0.0739052	−	0.118846i
$183$	3.44440	−	1.80398i	0.254617	−	0.133354i
$184$	−7.47349	+	12.9445i	−0.550953	+	0.954278i
$185$	−5.44734			−0.400496
$186$	5.49981	+	10.5009i	0.403266	+	0.769967i
$187$			0.454332i			0.0332241i
$188$	−0.484388			−0.0353276
$189$	13.6913	+	1.24481i	0.995892	+	0.0905469i
$190$	−3.96006			−0.287293
$191$		−	13.2335i		−	0.957543i	−0.877940	−	0.478771i	$-0.841082\pi$
$191$		−	13.2335i		−	0.957543i	0.877940	−	0.478771i	$-0.158918\pi$
$192$	−0.277950	−	0.530698i	−0.0200593	−	0.0382998i
$193$	−9.63604			−0.693618			−0.346809	−	0.937936i	$-0.612735\pi$
$193$	−9.63604			−0.693618			−0.346809	+	0.937936i	$0.612735\pi$
$194$	2.77972	−	4.81462i	0.199572	−	0.345669i
$195$	−1.69504	+	0.887770i	−0.121385	+	0.0635745i
$196$	11.0554	−	0.724907i	0.789673	−	0.0517790i
$197$		−	21.1621i		−	1.50774i	−0.657026	−	0.753868i	$-0.728186\pi$
$197$		−	21.1621i		−	1.50774i	0.657026	−	0.753868i	$-0.271814\pi$
$198$	3.02056	+	0.249073i	0.214662	+	0.0177008i
$199$	−3.72171	−	2.14873i	−0.263825	−	0.152319i	0.362253	−	0.932080i	$-0.382008\pi$
$199$	−3.72171	−	2.14873i	−0.263825	−	0.152319i	−0.626078	+	0.779760i	$0.715341\pi$
$200$	2.00424	−	1.15715i	0.141721	−	0.0818229i
$201$	6.37895	+	12.1795i	0.449936	+	0.859076i
$202$	9.49277	−	5.48066i	0.667909	−	0.385618i
$203$	1.12091	+	0.599121i	0.0786726	+	0.0420500i
$204$	0.795686	+	0.0327502i	0.0557092	+	0.00229297i
$205$	−0.696881			−0.0486723
$206$	−1.86953	+	3.23812i	−0.130256	+	0.225611i
$207$	−17.5191	+	8.27606i	−1.21766	+	0.575226i
$208$	1.59824	−	0.922745i	0.110818	−	0.0639809i
$209$	−4.79403	+	8.30350i	−0.331610	+	0.574365i
$210$	−0.0248597	+	2.96005i	−0.00171548	+	0.204263i
$211$	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	$0.714715\pi$
$212$	−11.4290	−	6.59852i	−0.784945	−	0.453188i
$213$	16.2334	−	8.50214i	1.11229	−	0.582557i
$214$	−2.29139	−	3.96880i	−0.156636	−	0.271302i
$215$	−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
$219$	0.901238	−	21.8961i	0.0609000	−	1.47960i
$220$		−	2.47538i		−	0.166890i
$221$		−	0.320921i		−	0.0215875i
$222$	−5.14835	−	3.26182i	−0.345535	−	0.218919i
$223$	−22.5466	−	13.0173i	−1.50983	−	0.871703i	−0.999934	−	0.0114694i	$-0.996349\pi$
$223$	−22.5466	−	13.0173i	−1.50983	−	0.871703i	−0.509900	−	0.860234i	$-0.670318\pi$
$224$	−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
$227$	−14.3986	−	24.9392i	−0.955671	−	1.65527i	−0.732826	−	0.680417i	$-0.761799\pi$
$227$	−14.3986	−	24.9392i	−0.955671	−	1.65527i	−0.222845	−	0.974854i	$-0.571534\pi$
$228$	14.1966	+	8.99448i	0.940193	+	0.595674i
$229$	0.398971	+	0.230346i	0.0263647	+	0.0152217i	0.513124	−	0.858314i	$-0.328488\pi$
$229$	0.398971	+	0.230346i	0.0263647	+	0.0152217i	−0.486760	+	0.873536i	$0.661821\pi$
$230$	−2.08597	−	3.61301i	−0.137545	−	0.238235i
$231$	6.17657	+	3.63555i	0.406388	+	0.239201i
$232$	0.555878	−	0.962809i	0.0364952	−	0.0632115i
$233$	−19.4028	+	11.2022i	−1.27112	+	0.733883i	−0.975199	−	0.221329i	$-0.928961\pi$
$233$	−19.4028	+	11.2022i	−1.27112	+	0.733883i	−0.295924	+	0.955212i	$0.595627\pi$
$234$	−2.13360	−	0.175934i	−0.139478	−	0.0115012i
$235$	0.153022	−	0.265042i	0.00998208	−	0.0172895i
$236$	8.73720			0.568743
$237$	2.83260	+	5.40837i	0.183997	+	0.351311i
$238$	−0.437852	−	0.234029i	−0.0283817	−	0.0151699i
$239$	−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	$0.615944\pi$
$240$	−2.89099	−	0.118992i	−0.186613	−	0.00768093i
$241$	2.01852	−	1.16539i	0.130024	−	0.0750695i	−0.433577	−	0.901117i	$-0.642749\pi$
$241$	2.01852	−	1.16539i	0.130024	−	0.0750695i	0.563601	+	0.826047i	$0.309415\pi$
$242$	−4.78522	−	2.76275i	−0.307606	−	0.177596i
$243$	10.3871	−	11.6236i	0.666334	−	0.745654i
$244$		−	3.55303i		−	0.227459i
$245$	−3.09585	+	6.27819i	−0.197787	+	0.401099i
$246$	−0.658631	−	0.417286i	−0.0419928	−	0.0266052i
$247$	3.38629	−	5.86523i	0.215465	−	0.373196i
$248$	24.5200			1.55702
$249$	1.37989	+	0.0567959i	0.0874470	+	0.00359929i
$250$			0.645959i			0.0408540i
$251$	8.29788			0.523758			0.261879	−	0.965101i	$-0.415658\pi$
$251$	8.29788			0.523758			0.261879	+	0.965101i	$0.415658\pi$
$252$	6.81228	−	10.5552i	0.429133	−	0.664912i
$253$	−10.1011			−0.635048
$254$			9.19586i			0.577000i
$255$	−0.269284	+	0.425029i	−0.0168632	+	0.0266164i
$256$	−7.92131			−0.495082
$257$	−8.44574	+	14.6285i	−0.526831	+	0.912498i	0.472680	+	0.881234i	$0.343287\pi$
$257$	−8.44574	+	14.6285i	−0.526831	+	0.912498i	−0.999511	+	0.0312639i	$0.990047\pi$
$258$	0.140204	−	3.40635i	0.00872873	−	0.212070i
$259$	−7.61084	−	12.2389i	−0.472915	−	0.760486i
$260$			1.74850i			0.108438i
$261$	1.30307	−	0.615573i	0.0806582	−	0.0381030i
$262$	−7.47285	−	4.31445i	−0.461674	−	0.266548i
$263$	13.5117	−	7.80096i	0.833165	−	0.481028i	−0.0217701	−	0.999763i	$-0.506930\pi$
$263$	13.5117	−	7.80096i	0.833165	−	0.481028i	0.854935	+	0.518735i	$0.173597\pi$
$264$	3.35524	−	5.29580i	0.206501	−	0.325934i
$265$	7.22102	−	4.16906i	0.443584	−	0.256103i
$266$	−5.53287	−	8.89731i	−0.339242	−	0.545529i
$267$	−10.2237	+	16.1367i	−0.625678	+	0.987551i
$268$	12.5636			0.767445
$269$	13.5334	−	23.4405i	0.825143	−	1.42919i	−0.0766668	−	0.997057i	$-0.524428\pi$
$269$	13.5334	−	23.4405i	0.825143	−	1.42919i	0.901810	−	0.432133i	$-0.142239\pi$
$270$	2.67812	+	2.02331i	0.162985	+	0.123134i
$271$	19.8992	−	11.4888i	1.20879	−	0.697896i	0.246296	−	0.969195i	$-0.420786\pi$
$271$	19.8992	−	11.4888i	1.20879	−	0.697896i	0.962495	+	0.271299i	$0.0874531\pi$
$272$	0.242641	−	0.420267i	0.0147123	−	0.0254824i
$273$	−4.36286	−	2.56799i	−0.264052	−	0.155422i
$274$	−2.72750	−	4.72417i	−0.164775	−	0.285398i
$275$	1.35445	+	0.781994i	0.0816766	+	0.0471560i
$276$	−0.728127	+	17.6903i	−0.0438281	+	1.06483i
$277$	8.99080	+	15.5725i	0.540205	+	0.935662i	0.998892	+	0.0470641i	$0.0149865\pi$
$277$	8.99080	+	15.5725i	0.540205	+	0.935662i	−0.458687	+	0.888598i	$0.651680\pi$
$278$	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	$0.646441\pi$
$282$	0.303328	−	0.158867i	0.0180629	−	0.00946037i
$283$			5.86042i			0.348366i	0.984713	+	0.174183i	$0.0557284\pi$
$283$			5.86042i			0.348366i	−0.984713	+	0.174183i	$0.944272\pi$
$284$		−	16.7453i		−	0.993653i
$285$	−9.40634	+	4.92652i	−0.557183	+	0.291822i
$286$	−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
$290$	0.155155	+	0.268736i	0.00911099	+	0.0157807i
$291$	0.613044	−	14.8943i	0.0359373	−	0.873118i
$292$	−17.3426	−	10.0127i	−1.01490	−	0.585951i
$293$	11.1730	+	19.3523i	0.652736	+	1.13057i	0.982456	+	0.186493i	$0.0597120\pi$
$293$	11.1730	+	19.3523i	0.652736	+	1.13057i	−0.329721	+	0.944078i	$0.606955\pi$
$294$	−6.68526	+	4.07983i	−0.389892	+	0.237941i
$295$	−2.76016	+	4.78073i	−0.160702	+	0.278345i
$296$	−10.9178	+	6.30339i	−0.634584	+	0.366377i
$297$	7.48460	−	3.16611i	0.434301	−	0.183716i
$298$	7.30401	−	12.6509i	0.423110	−	0.732848i
$299$	7.13495			0.412625
$300$	1.46717	−	2.31573i	0.0847068	−	0.133699i
$301$	3.80028	−	7.11005i	0.219044	−	0.409817i
$302$	4.59518	−	2.65303i	0.264423	−	0.152665i
$303$	15.7300	−	24.8277i	0.903663	−	1.42631i
$304$	8.86915	−	5.12061i	0.508681	−	0.293687i
$305$	1.94411	+	1.12243i	0.111319	+	0.0642702i
$306$	−0.509008	+	0.240456i	−0.0290980	+	0.0137459i
$307$		−	19.5900i		−	1.11806i	−0.829148	−	0.559029i	$-0.811174\pi$
$307$		−	19.5900i		−	1.11806i	0.829148	−	0.559029i	$-0.188826\pi$
$308$	5.56159	−	3.45852i	0.316901	−	0.197067i
$309$	−0.412309	+	10.0173i	−0.0234555	+	0.569865i
$310$	−3.42196	+	5.92701i	−0.194354	+	0.336632i
$311$	−14.3078			−0.811321			−0.405660	−	0.914024i	$-0.632958\pi$
$311$	−14.3078			−0.811321			−0.405660	+	0.914024i	$0.632958\pi$
$312$	−2.37000	+	3.74073i	−0.134175	+	0.211777i
$313$			5.81484i			0.328674i	0.986404	+	0.164337i	$0.0525485\pi$
$313$			5.81484i			0.328674i	−0.986404	+	0.164337i	$0.947452\pi$
$314$	−2.44286			−0.137859
$315$	3.62340	+	7.06194i	0.204156	+	0.397895i
$316$	5.57894			0.313840
$317$		−	15.3570i		−	0.862536i	−0.902224	−	0.431268i	$-0.858066\pi$
$317$		−	15.3570i		−	0.862536i	0.902224	−	0.431268i	$-0.141934\pi$
$318$	9.32107	+	0.383652i	0.522700	+	0.0215142i
$319$	0.751317			0.0420657
$320$	0.172939	−	0.299540i	0.00966760	−	0.0167448i
$321$	−10.3801	−	6.57649i	−0.579362	−	0.367064i
$322$	5.20311	−	9.73465i	0.289958	−	0.542491i
$323$		−	1.78089i		−	0.0990914i
$324$	−5.00539	−	13.3363i	−0.278077	−	0.740903i
$325$	−0.956727	−	0.552367i	−0.0530697	−	0.0306398i
$326$	−0.857252	+	0.494935i	−0.0474788	+	0.0274119i
$327$	−22.5663	−	0.928822i	−1.24792	−	0.0513640i
$328$	−1.39672	+	0.806396i	−0.0771209	+	0.0445258i
$329$	0.809284	−	0.0265040i	0.0446173	−	0.00146121i
$330$	0.811860	+	1.55011i	0.0446914	+	0.0853306i
$331$	26.7626			1.47101			0.735503	−	0.677521i	$-0.236946\pi$
$331$	26.7626			1.47101			0.735503	+	0.677521i	$0.236946\pi$
$332$	0.631002	−	1.09293i	0.0346307	−	0.0599822i
$333$	−16.2867	−	1.34299i	−0.892508	−	0.0735954i
$334$	14.1290	−	8.15741i	0.773107	−	0.446354i
$335$	−3.96895	+	6.87443i	−0.216847	+	0.375590i
$336$	−3.77185	−	6.66162i	−0.205771	−	0.363421i
$337$	−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	$-0.428477\pi$
$338$	−6.58969	−	3.80456i	−0.358432	−	0.206941i
$339$	23.1046	+	14.6383i	1.25487	+	0.795043i
$340$	0.229889	+	0.398180i	0.0124675	+	0.0215943i
$341$	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
$345$	−9.44957	−	5.98692i	−0.508748	−	0.322325i
$346$			1.82403i			0.0980606i
$347$		−	6.42430i		−	0.344875i	−0.985020	−	0.172437i	$-0.944836\pi$
$347$		−	6.42430i		−	0.344875i	0.985020	−	0.172437i	$-0.0551642\pi$
$348$	0.0541581	−	1.31580i	0.00290318	−	0.0705345i
$349$	6.16611	+	3.56000i	0.330064	+	0.190563i	0.655870	−	0.754874i	$-0.272302\pi$
$349$	6.16611	+	3.56000i	0.330064	+	0.190563i	−0.325805	+	0.945437i	$0.605635\pi$
$350$	−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
$353$	6.40648	+	11.0963i	0.340982	+	0.590599i	0.984615	−	0.174735i	$-0.0559070\pi$
$353$	6.40648	+	11.0963i	0.340982	+	0.590599i	−0.643633	+	0.765334i	$0.722574\pi$
$354$	−5.47132	+	2.86557i	−0.290797	+	0.152303i
$355$	9.16254	+	5.29000i	0.486297	+	0.280764i
$356$	8.72801	+	15.1174i	0.462583	+	0.801218i
$357$	−1.33117	−	0.0111797i	−0.0704531	−	0.000591694i
$358$	−6.27274	+	10.8647i	−0.331524	+	0.574217i
$359$	20.5886	−	11.8868i	1.08662	−	0.627362i	0.153948	−	0.988079i	$-0.450801\pi$
$359$	20.5886	−	11.8868i	1.08662	−	0.627362i	0.932675	+	0.360717i	$0.117468\pi$
$360$	6.27768	−	2.96558i	0.330863	−	0.156300i
$361$	9.29162	−	16.0936i	0.489033	−	0.847030i
$362$	−16.6841			−0.876895
$363$	−14.8033	−	0.609300i	−0.776973	−	0.0319800i
$364$	−3.92846	+	2.44295i	−0.205907	+	0.128045i
$365$	10.9573	−	6.32622i	0.573533	−	0.331129i
$366$	1.16530	+	2.22494i	0.0609112	+	0.116299i
$367$	−17.1950	+	9.92751i	−0.897569	+	0.518212i	−0.876411	−	0.481564i	$-0.840069\pi$
$367$	−17.1950	+	9.92751i	−0.897569	+	0.518212i	−0.0211585	+	0.999776i	$0.506735\pi$
$368$	9.34369	+	5.39458i	0.487073	+	0.281212i
$369$	−2.08357	−	0.171809i	−0.108466	−	0.00894404i
$370$		−	3.51876i		−	0.182932i
$371$	19.4558	+	10.3990i	1.01010	+	0.539890i
$372$	25.7295	−	13.4757i	1.33401	−	0.698683i
$373$	1.65138	−	2.86027i	0.0855052	−	0.148099i	−0.820101	−	0.572219i	$-0.806083\pi$
$373$	1.65138	−	2.86027i	0.0855052	−	0.148099i	0.905606	+	0.424119i	$0.139416\pi$
$374$	−0.293480			−0.0151755
$375$	0.803605	+	1.53435i	0.0414980	+	0.0792333i
$376$		−	0.708280i		−	0.0365267i
$377$	−0.530698			−0.0273323
$378$	−0.804099	+	8.84399i	−0.0413584	+	0.454886i
$379$	−33.8286			−1.73766			−0.868828	−	0.495113i	$-0.835127\pi$
$379$	−33.8286			−1.73766			−0.868828	+	0.495113i	$0.835127\pi$
$380$			9.70300i			0.497753i
$381$	11.4401	+	21.8429i	0.586095	+	1.11905i
$382$	8.54830			0.437369
$383$	−12.5907	+	21.8078i	−0.643356	+	1.11433i	0.341322	+	0.939946i	$0.389125\pi$
$383$	−12.5907	+	21.8078i	−0.643356	+	1.11433i	−0.984679	+	0.174379i	$0.944208\pi$
$384$	−17.1724	+	8.99393i	−0.876323	+	0.458969i
$385$	0.135444	+	4.13571i	0.00690288	+	0.210775i
$386$		−	6.22449i		−	0.316818i
$387$	−3.90464	−	8.26551i	−0.198484	−	0.420160i
$388$	−11.7968	−	6.81091i	−0.598894	−	0.345771i
$389$	−3.97966	+	2.29766i	−0.201777	+	0.116496i	−0.597484	−	0.801881i	$-0.703833\pi$
$389$	−3.97966	+	2.29766i	−0.201777	+	0.116496i	0.395707	+	0.918377i	$0.370500\pi$
$390$	−0.573463	−	1.09493i	−0.0290384	−	0.0554439i
$391$	1.62482	−	0.938088i	0.0821705	−	0.0474411i
$392$	1.05997	+	16.1654i	0.0535365	+	0.816476i
$393$	−23.1176	−	0.951515i	−1.16613	−	0.0479976i
$394$	13.6698			0.688677
$395$	−1.76243	+	3.05262i	−0.0886776	+	0.153594i
$396$	0.610282	−	7.40102i	0.0306678	−	0.371915i
$397$	20.1504	−	11.6338i	1.01132	−	0.583884i	0.0997402	−	0.995014i	$-0.468199\pi$
$397$	20.1504	−	11.6338i	1.01132	−	0.583884i	0.911577	+	0.411129i	$0.134865\pi$
$398$	1.38799	−	2.40407i	0.0695737	−	0.120505i
$399$	−24.2109	−	14.2506i	−1.21206	−	0.713423i
$400$	−0.835265	−	1.44672i	−0.0417632	−	0.0723361i
$401$	2.50603	+	1.44685i	0.125145	+	0.0722525i	0.561266	−	0.827636i	$-0.310315\pi$
$401$	2.50603	+	1.44685i	0.125145	+	0.0722525i	−0.436121	+	0.899888i	$0.643648\pi$
$402$	−7.86746	+	4.12054i	−0.392393	+	0.205514i
$403$	−5.85231	−	10.1365i	−0.291525	−	0.504935i
$404$	−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
$408$	−0.0478878	+	1.16346i	−0.00237080	+	0.0576001i
$409$			11.5815i			0.572670i	0.958130	+	0.286335i	$0.0924371\pi$
$409$			11.5815i			0.572670i	−0.958130	+	0.286335i	$0.907563\pi$
$410$		−	0.450157i		−	0.0222317i
$411$	−12.3557	−	7.82818i	−0.609464	−	0.386136i
$412$	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
$416$	3.15274	+	5.46071i	0.154576	+	0.267733i
$417$	5.14297	+	3.25841i	0.251852	+	0.159565i
$418$	−5.36372	−	3.09675i	−0.262348	−	0.151467i
$419$	1.78552	+	3.09261i	0.0872285	+	0.151084i	0.906339	−	0.422552i	$-0.138866\pi$
$419$	1.78552	+	3.09261i	0.0872285	+	0.151084i	−0.819110	+	0.573636i	$0.805532\pi$
$420$	7.25276	+	0.0609115i	0.353898	+	0.00297218i
$421$	−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
$423$	0.522858	−	0.754712i	0.0254222	−	0.0366953i
$424$	9.64845	−	16.7116i	0.468570	−	0.811588i
$425$	−0.290496			−0.0140911
$426$	5.49203	+	10.4861i	0.266090	+	0.508053i
$427$	0.194409	+	5.93617i	0.00940812	+	0.287271i
$428$	−9.72441	+	5.61439i	−0.470047	+	0.271382i
$429$	−2.99009	−	0.123071i	−0.144363	−	0.00594193i
$430$	1.70462	−	0.984160i	0.0822039	−	0.0474604i
$431$	12.4615	+	7.19463i	0.600248	+	0.346553i	0.769139	−	0.639081i	$-0.220685\pi$
$431$	12.4615	+	7.19463i	0.600248	+	0.346553i	−0.168891	+	0.985635i	$0.554019\pi$
$432$	−8.61431	−	1.06852i	−0.414456	−	0.0514090i
$433$			23.9154i			1.14930i	0.818398	+	0.574651i	$0.194862\pi$
$433$			23.9154i			1.14930i	−0.818398	+	0.574651i	$0.805138\pi$
$434$	−18.0976	+	0.592696i	−0.868713	+	0.0284503i
$435$	0.702859	+	0.445308i	0.0336995	+	0.0213509i
$436$	−10.3192	+	17.8734i	−0.494200	+	0.855979i
$437$	39.5941			1.89404
$438$	14.1440	+	0.582163i	0.675827	+	0.0278168i
$439$			7.89141i			0.376636i	0.982108	+	0.188318i	$0.0603036\pi$
$439$			7.89141i			0.376636i	−0.982108	+	0.188318i	$0.939696\pi$
$440$	3.61954			0.172555
$441$	−10.8040	+	18.0076i	−0.514475	+	0.857505i
$442$	0.207302			0.00986033
$443$			19.1152i			0.908190i	0.890953	+	0.454095i	$0.150037\pi$
$443$			19.1152i			0.908190i	−0.890953	+	0.454095i	$0.849963\pi$
$444$	−7.99215	+	12.6146i	−0.379291	+	0.598660i
$445$	−11.0290			−0.522825
$446$	8.40865	−	14.5642i	0.398161	−	0.689635i
$447$	1.61084	−	39.1363i	0.0761900	−	1.85108i
$448$	0.914618	−	0.0299537i	0.0432117	−	0.00141518i
$449$			13.3687i			0.630910i	0.948941	+	0.315455i	$0.102157\pi$
$449$			13.3687i			0.630910i	−0.948941	+	0.315455i	$0.897843\pi$
$450$	−0.159255	+	1.93132i	−0.00750735	+	0.0910434i
$451$	−0.943893	−	0.544957i	−0.0444462	−	0.0256610i
$452$	21.6451	−	12.4968i	1.01810	−	0.587800i
$453$	7.61443	−	12.0184i	0.357757	−	0.564672i
$454$	16.1097	−	9.30093i	0.756065	−	0.436514i
$455$	−0.0956720	−	2.92128i	−0.00448517	−	0.136952i
$456$	−13.1519	+	20.7585i	−0.615893	+	0.972105i
$457$	5.54000			0.259150			0.129575	−	0.991570i	$-0.458639\pi$
$457$	5.54000			0.259150			0.129575	+	0.991570i	$0.458639\pi$
$458$	−0.148794	+	0.257719i	−0.00695269	+	0.0120424i
$459$	−0.909906	+	1.20439i	−0.0424708	+	0.0562159i
$460$	−8.85264	+	5.11107i	−0.412756	+	0.238305i
$461$	−4.27019	+	7.39619i	−0.198883	+	0.344475i	−0.948166	−	0.317774i	$-0.897065\pi$
$461$	−4.27019	+	7.39619i	−0.198883	+	0.344475i	0.749284	+	0.662249i	$0.230398\pi$
$462$	−2.34841	+	3.98981i	−0.109258	+	0.185623i
$463$	−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	$0.961736\pi$
$464$	−0.694984	−	0.401249i	−0.0322638	−	0.0186275i
$465$	−0.754684	+	18.3355i	−0.0349976	+	0.850289i
$466$	−7.23619	−	12.5334i	−0.335210	−	0.580601i
$467$	5.77689	+	10.0059i	0.267323	+	0.463016i	0.968170	−	0.250295i	$-0.0805277\pi$
$467$	5.77689	+	10.0059i	0.267323	+	0.463016i	−0.700847	+	0.713312i	$0.747194\pi$
$468$	−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
$471$	−5.80253	+	3.03904i	−0.267366	+	0.140032i
$472$			12.7757i			0.588048i
$473$		−	4.76567i		−	0.219126i
$474$	−3.49358	+	1.82974i	−0.160466	+	0.0840430i
$475$	−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
$479$	16.6342	+	28.8113i	0.760038	+	1.31642i	0.942831	+	0.333272i	$0.108153\pi$
$479$	16.6342	+	28.8113i	0.760038	+	1.31642i	−0.182793	+	0.983151i	$0.558514\pi$
$480$	0.406561	−	9.87766i	0.0185569	−	0.450851i
$481$	5.21162	+	3.00893i	0.237629	+	0.137195i
$482$	0.752796	+	1.30388i	0.0342889	+	0.0593901i
$483$	0.248556	−	29.5956i	0.0113097	−	1.34665i
$484$	−6.76932	+	11.7248i	−0.307696	+	0.532946i
$485$	7.45344	−	4.30325i	0.338443	−	0.195400i
$486$	7.50836	+	6.70965i	0.340586	+	0.304356i
$487$	7.75103	−	13.4252i	0.351233	−	0.608353i	−0.635233	−	0.772321i	$-0.719096\pi$
$487$	7.75103	−	13.4252i	0.351233	−	0.608353i	0.986466	+	0.163968i	$0.0524292\pi$
$488$	5.19529			0.235180
$489$	−1.42051	+	2.24208i	−0.0642375	+	0.101391i
$490$	−4.05545	−	1.99979i	−0.183207	−	0.0903415i
$491$	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	$0.199308\pi$
$492$	−1.02244	+	1.61379i	−0.0460952	+	0.0727551i
$493$	−0.120854	+	0.0697750i	−0.00544298	+	0.00314251i
$494$	3.78870	+	2.18741i	0.170462	+	0.0984161i
$495$	3.85682	+	2.67197i	0.173351	+	0.120096i
$496$		−	17.6992i		−	0.794719i
$497$	0.916247	+	27.9770i	0.0410993	+	1.25494i
$498$	−0.0366878	+	0.891353i	−0.00164402	+	0.0399425i
$499$	−3.31186	+	5.73632i	−0.148259	+	0.256793i	−0.930584	−	0.366078i	$-0.880700\pi$
$499$	−3.31186	+	5.73632i	−0.148259	+	0.256793i	0.782325	+	0.622871i	$0.214034\pi$
$500$	1.58274			0.0707821
$501$	23.4125	−	36.9535i	1.04599	−	1.65096i
$502$			5.36009i			0.239233i
$503$	0.438495			0.0195515			0.00977576	−	0.999952i	$-0.496888\pi$
$503$	0.438495			0.0195515			0.00977576	+	0.999952i	$0.496888\pi$
$504$	15.4339	+	9.96102i	0.687481	+	0.443699i
$505$	16.9691			0.755113
$506$		−	6.52487i		−	0.290066i
$507$	−20.3855	−	0.839063i	−0.905354	−	0.0372641i
$508$	22.5318			0.999688
$509$	−0.172125	+	0.298128i	−0.00762929	+	0.0132143i	−0.869815	−	0.493378i	$-0.835762\pi$
$509$	−0.172125	+	0.298128i	−0.00762929	+	0.0132143i	0.862186	+	0.506593i	$0.169095\pi$
$510$	−0.274552	−	0.173946i	−0.0121573	−	0.00770248i
$511$	29.5227	+	15.7797i	1.30601	+	0.698053i
$512$			17.2671i			0.763105i
$513$	−29.3381	+	12.4105i	−1.29531	+	0.547938i
$514$	−9.44938	−	5.45560i	−0.416794	−	0.240636i
$515$	−5.01289	+	2.89420i	−0.220895	+	0.127534i
$516$	−8.34627	−	0.343530i	−0.367424	−	0.0151231i
$517$	0.414523	−	0.239325i	0.0182307	−	0.0105255i
$518$	7.90580	−	4.91629i	0.347361	−	0.216009i
$519$	2.26919	+	4.33262i	0.0996062	+	0.190181i
$520$	−2.55669			−0.112118
$521$	−6.15505	+	10.6609i	−0.269658	+	0.467061i	−0.968773	−	0.247948i	$-0.920244\pi$
$521$	−6.15505	+	10.6609i	−0.269658	+	0.467061i	0.699116	+	0.715008i	$0.253577\pi$
$522$	0.397635	+	0.841732i	0.0174040	+	0.0368416i
$523$	24.7952	−	14.3155i	1.08422	−	0.625974i	0.152187	−	0.988352i	$-0.451368\pi$
$523$	24.7952	−	14.3155i	1.08422	−	0.625974i	0.932031	+	0.362378i	$0.118035\pi$
$524$	−10.5713	+	18.3101i	−0.461810	+	0.799879i
$525$	−2.32454	+	3.94924i	−0.101451	+	0.172359i
$526$	5.03910	+	8.72798i	0.219715	+	0.380558i
$527$	−2.66545	−	1.53890i	−0.116109	−	0.0670355i
$528$	−3.82267	−	2.42191i	−0.166360	−	0.105400i
$529$	9.35627	+	16.2055i	0.406795	+	0.704589i
$530$	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
$534$	−10.4237	−	6.60407i	−0.451076	−	0.285786i
$535$		−	7.09453i		−	0.306723i
$536$			18.3707i			0.793494i
$537$	−1.38340	+	33.6105i	−0.0596980	+	1.45040i
$538$	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	−0.978046	−	0.208388i	$-0.933178\pi$
$541$	−15.5720	−	26.9715i	−0.669493	−	1.15960i	0.308553	−	0.951207i	$-0.400155\pi$
$542$	7.42131	+	12.8541i	0.318772	+	0.552130i
$543$	−39.6296	+	20.7558i	−1.70067	+	0.890717i
$544$	1.43592	+	0.829032i	0.0615648	+	0.0355444i
$545$	−6.51984	−	11.2927i	−0.279279	−	0.483726i
$546$	1.65882	−	2.81823i	0.0709909	−	0.120609i
$547$	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
$549$	5.53587	+	3.83521i	0.236265	+	0.163683i
$550$	−0.505136	+	0.874921i	−0.0215391	+	0.0373068i
$551$	−2.94501			−0.125462
$552$	−25.8670	−	1.06468i	−1.10097	−	0.0453157i
$553$	−9.32092	+	0.305260i	−0.396366	+	0.0129810i
$554$	−10.0592	+	5.80769i	−0.427375	+	0.246745i
$555$	−4.37751	−	8.35811i	−0.185815	−	0.354782i
$556$	4.81809	−	2.78172i	0.204332	−	0.117971i
$557$	−11.9288	−	6.88707i	−0.505438	−	0.291814i	0.225519	−	0.974239i	$-0.427592\pi$
$557$	−11.9288	−	6.88707i	−0.505438	−	0.291814i	−0.730956	+	0.682424i	$0.760926\pi$
$558$	−11.6924	+	16.8772i	−0.494979	+	0.714470i
$559$			3.36627i			0.142378i
$560$	2.08343	−	3.89795i	0.0880410	−	0.164718i
$561$	−0.697103	+	0.365104i	−0.0294317	+	0.0154147i
$562$	−0.687569	+	1.19091i	−0.0290034	+	0.0502353i
$563$	21.3677			0.900542			0.450271	−	0.892892i	$-0.351327\pi$
$563$	21.3677			0.900542			0.450271	+	0.892892i	$0.351327\pi$
$564$	−0.389257	−	0.743219i	−0.0163907	−	0.0312952i
$565$			15.7914i			0.664349i
$566$	−3.78559			−0.159120
$567$	9.09239	+	22.0075i	0.381844	+	0.924227i
$568$	24.4853			1.02738
$569$			10.3194i			0.432611i	0.976326	+	0.216306i	$0.0694007\pi$
$569$			10.3194i			0.432611i	−0.976326	+	0.216306i	$0.930599\pi$
$570$	−3.18233	−	6.07611i	−0.133293	−	0.254500i
$571$	−7.64951			−0.320122			−0.160061	−	0.987107i	$-0.551169\pi$
$571$	−7.64951			−0.320122			−0.160061	+	0.987107i	$0.551169\pi$
$572$	−1.36732	+	2.36826i	−0.0571705	+	0.0990221i
$573$	20.3048	−	10.6345i	0.848244	−	0.444263i
$574$	1.01139	−	0.628944i	0.0422148	−	0.0262516i
$575$		−	6.45853i		−	0.269339i
$576$	0.590912	−	0.852943i	0.0246213	−	0.0355393i
$577$	10.8976	+	6.29171i	0.453671	+	0.261927i	0.709379	−	0.704827i	$-0.248975\pi$
$577$	10.8976	+	6.29171i	0.453671	+	0.261927i	−0.255708	+	0.966754i	$0.582309\pi$
$578$	−9.46288	+	5.46340i	−0.393604	+	0.227247i
$579$	−7.74358	−	14.7850i	−0.321812	−	0.614445i
$580$	0.658459	−	0.380162i	0.0273410	−	0.0157854i
$581$	−0.994435	+	1.86052i	−0.0412561	+	0.0771873i
$582$	9.62109	+	0.396001i	0.398807	+	0.0164148i
$583$	13.0407			0.540091
$584$	14.6408	−	25.3586i	0.605840	−	1.04935i
$585$	−2.72429	−	1.88737i	−0.112636	−	0.0780330i
$586$	−12.5008	+	7.21732i	−0.516402	+	0.298145i
$587$	7.26812	−	12.5888i	0.299987	−	0.519593i	−0.676145	−	0.736768i	$-0.736351\pi$
$587$	7.26812	−	12.5888i	0.299987	−	0.519593i	0.976133	+	0.217175i	$0.0696842\pi$
$588$	9.99645	+	16.3803i	0.412247	+	0.675512i
$589$	−32.4764	−	56.2507i	−1.33816	−	2.31777i
$590$	−3.08816	−	1.78295i	−0.127137	−	0.0734028i
$591$	32.4700	−	17.0060i	1.33564	−	0.699532i
$592$	4.54997	+	7.88078i	0.187003	+	0.323898i
$593$	−9.78416	−	16.9467i	−0.401787	−	0.695916i	0.592154	−	0.805825i	$-0.298278\pi$
$593$	−9.78416	−	16.9467i	−0.401787	−	0.695916i	−0.993942	+	0.109908i	$0.964944\pi$
$594$	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
$597$	0.306110	−	7.43712i	0.0125282	−	0.304381i
$598$			4.60889i			0.188471i
$599$		−	43.1960i		−	1.76494i	−0.470369	−	0.882470i	$-0.655879\pi$
$599$		−	43.1960i		−	1.76494i	0.470369	−	0.882470i	$-0.344121\pi$
$600$	3.38609	+	2.14531i	0.138237	+	0.0875820i
$601$	−20.2611	−	11.6978i	−0.826468	−	0.477162i	0.0261737	−	0.999657i	$-0.491668\pi$
$601$	−20.2611	−	11.6978i	−0.826468	−	0.477162i	−0.852642	+	0.522496i	$0.825001\pi$
$602$	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
$605$	−4.27697	−	7.40793i	−0.173884	−	0.301175i
$606$	16.0377	+	10.1609i	0.651486	+	0.412759i
$607$	−12.5581	−	7.25043i	−0.509718	−	0.294286i	0.223000	−	0.974819i	$-0.428415\pi$
$607$	−12.5581	−	7.25043i	−0.509718	−	0.294286i	−0.732718	+	0.680533i	$0.761748\pi$
$608$	17.4956	+	30.3032i	0.709539	+	1.22896i
$609$	−0.0184876	+	2.20132i	−0.000749155	+	0.0892022i
$610$	−0.725045	+	1.25581i	−0.0293562	+	0.0508464i
$611$	−0.292801	+	0.169049i	−0.0118455	+	0.00683899i
$612$	0.589168	+	1.24718i	0.0238157	+	0.0504141i
$613$	8.99474	−	15.5793i	0.363294	−	0.629244i	−0.625207	−	0.780459i	$-0.714985\pi$
$613$	8.99474	−	15.5793i	0.363294	−	0.629244i	0.988501	+	0.151215i	$0.0483187\pi$
$614$	12.6543			0.510687
$615$	−0.560018	−	1.06926i	−0.0225821	−	0.0431166i
$616$	5.05710	+	8.13223i	0.203756	+	0.327657i
$617$	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	$0.313633\pi$
$618$	−6.47077	−	0.266335i	−0.260293	−	0.0107136i
$619$	−1.78031	+	1.02786i	−0.0715565	+	0.0413132i	−0.535351	−	0.844629i	$-0.679821\pi$
$619$	−1.78031	+	1.02786i	−0.0715565	+	0.0413132i	0.463795	+	0.885943i	$0.346487\pi$
$620$	14.5224	+	8.38453i	0.583235	+	0.336731i
$621$	−26.7768	−	20.2297i	−1.07452	−	0.811791i
$622$		−	9.24225i		−	0.370581i
$623$	−15.4094	−	24.7795i	−0.617363	−	0.992771i
$624$	2.70017	+	1.71073i	0.108093	+	0.0684841i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−3.75615			−0.150126
$627$	−16.5929	−	0.682961i	−0.662659	−	0.0272748i
$628$			5.98553i			0.238849i
$629$	1.58243			0.0630957
$630$	−4.56172	+	2.34057i	−0.181743	+	0.0932506i
$631$	16.2423			0.646597			0.323298	−	0.946297i	$-0.395208\pi$
$631$	16.2423			0.646597			0.323298	+	0.946297i	$0.395208\pi$
$632$			8.15760i			0.324492i
$633$	−9.80495	+	15.4758i	−0.389712	+	0.615109i
$634$	9.92001			0.393974
$635$	−7.11799	+	12.3287i	−0.282469	+	0.489250i
$636$	0.940030	−	22.8386i	0.0372746	−	0.905610i
$637$	6.42975	−	4.29647i	0.254756	−	0.170232i
$638$			0.485320i			0.0192140i
$639$	26.0905	+	18.0752i	1.03212	+	0.715046i
$640$	−9.69253	−	5.59598i	−0.383131	−	0.221201i
$641$	−16.7872	+	9.69212i	−0.663056	+	0.382816i	−0.793440	−	0.608648i	$-0.791712\pi$
$641$	−16.7872	+	9.69212i	−0.663056	+	0.382816i	0.130384	+	0.991464i	$0.458379\pi$
$642$	4.24814	−	6.70513i	0.167661	−	0.264631i
$643$	15.3775	−	8.87823i	0.606431	−	0.350123i	−0.165136	−	0.986271i	$-0.552806\pi$
$643$	15.3775	−	8.87823i	0.606431	−	0.350123i	0.771567	+	0.636148i	$0.219473\pi$
$644$	−23.8520	−	12.7487i	−0.939899	−	0.502370i
$645$	2.82463	−	4.45830i	0.111220	−	0.175545i
$646$	1.15038			0.0452612
$647$	6.63329	−	11.4892i	0.260782	−	0.451687i	−0.705668	−	0.708542i	$-0.749353\pi$
$647$	6.63329	−	11.4892i	0.260782	−	0.451687i	0.966450	+	0.256855i	$0.0826864\pi$
$648$	19.5005	−	7.31895i	0.766051	−	0.287516i
$649$	−7.47700	+	4.31685i	−0.293498	+	0.169451i
$650$	0.356806	−	0.618007i	0.0139951	−	0.0242402i
$651$	−42.2499	+	23.9222i	−1.65590	+	0.937584i
$652$	1.21270	+	2.10045i	0.0474928	+	0.0822600i
$653$	−6.16973	−	3.56210i	−0.241440	−	0.139396i	0.374398	−	0.927268i	$-0.377849\pi$
$653$	−6.16973	−	3.56210i	−0.241440	−	0.139396i	−0.615839	+	0.787872i	$0.711183\pi$
$654$	0.599981	−	14.5769i	0.0234611	−	0.570002i
$655$	−6.67914	−	11.5686i	−0.260976	−	0.452023i
$656$	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	$0.621400\pi$
$660$	3.79809	−	1.98923i	0.147841	−	0.0774307i
$661$		−	42.8387i		−	1.66623i	−0.553099	−	0.833115i	$-0.686555\pi$
$661$		−	42.8387i		−	1.66623i	0.553099	−	0.833115i	$-0.313445\pi$
$662$			17.2876i			0.671900i
$663$	0.492403	−	0.257894i	0.0191234	−	0.0100158i
$664$	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
$668$	−19.9874	−	34.6192i	−0.773335	−	1.33946i
$669$	1.85445	−	45.0551i	0.0716973	−	1.74193i
$670$	−4.44060	−	2.56378i	−0.171555	−	0.0990475i
$671$	1.75547	+	3.04056i	0.0677691	+	0.117380i
$672$	22.7608	−	12.8873i	0.878015	−	0.497138i
$673$	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
$675$	2.02438	+	4.78559i	0.0779186	+	0.184197i
$676$	−9.32198	+	16.1461i	−0.358538	+	0.621005i
$677$	−22.4371			−0.862328			−0.431164	−	0.902274i	$-0.641897\pi$
$677$	−22.4371			−0.862328			−0.431164	+	0.902274i	$0.641897\pi$
$678$	−9.45574	+	14.9246i	−0.363146	+	0.573178i
$679$	20.0821	+	10.7337i	0.770679	+	0.411923i
$680$	−0.582225	+	0.336148i	−0.0223273	+	0.0128907i
$681$	26.6945	−	42.1337i	1.02294	−	1.61457i
$682$	−9.26977	+	5.35191i	−0.354958	+	0.204935i
$683$	8.46689	+	4.88836i	0.323977	+	0.187048i	0.653164	−	0.757217i	$-0.273441\pi$
$683$	8.46689	+	4.88836i	0.323977	+	0.187048i	−0.329187	+	0.944265i	$0.606775\pi$
$684$	−2.39218	+	29.0105i	−0.0914673	+	1.10925i
$685$		−	8.44482i		−	0.322660i
$686$	−1.17309	−	11.9057i	−0.0447887	−	0.454561i
$687$	−0.0328152	+	0.797266i	−0.00125198	+	0.0304176i
$688$	−2.54516	+	4.40835i	−0.0970333	+	0.168067i
$689$	−9.21139			−0.350926
$690$	3.86731	−	6.10404i	0.147226	−	0.232377i
$691$		−	25.1365i		−	0.956237i	−0.878295	−	0.478118i	$-0.841319\pi$
$691$		−	25.1365i		−	0.956237i	0.878295	−	0.478118i	$-0.158681\pi$
$692$	4.46927			0.169896
$693$	−0.614660	+	12.3985i	−0.0233490	+	0.470982i
$694$	4.14984			0.157526
$695$			3.51508i			0.133335i
$696$	1.92399	+	0.0791908i	0.0729286	+	0.00300172i
$697$	0.202441			0.00766801
$698$	−2.29962	+	3.98305i	−0.0870418	+	0.150761i
$699$	−32.7803	−	20.7685i	−1.23987	−	0.785537i
$700$	2.21135	+	3.55603i	0.0835810	+	0.134405i
$701$		−	27.0864i		−	1.02304i	−0.859271	−	0.511520i	$-0.829083\pi$
$701$		−	27.0864i		−	1.02304i	0.859271	−	0.511520i	$-0.170917\pi$
$702$	−1.44463	−	3.41506i	−0.0545239	−	0.128893i
$703$	28.9209	+	16.6975i	1.09077	+	0.629759i
$704$	0.468476	−	0.270475i	0.0176564	−	0.0101939i
$705$	0.529636	+	0.0217997i	0.0199473	+	0.000821023i
$706$	−7.16779	+	4.13832i	−0.269763	+	0.155748i
$707$	23.7086	+	38.1254i	0.891653	+	1.43385i
$708$	7.02126	+	13.4059i	0.263875	+	0.503824i
$709$	28.1080			1.05562			0.527809	−	0.849363i	$-0.323014\pi$
$709$	28.1080			1.05562			0.527809	+	0.849363i	$0.323014\pi$
$710$	−3.41712	+	5.91863i	−0.128242	+	0.222122i
$711$	−6.02201	+	8.69238i	−0.225843	+	0.325990i
$712$	−22.1048	+	12.7622i	−0.828413	+	0.478284i
$713$	34.2140	−	59.2603i	1.28132	−	2.21932i
$714$	0.00722164	−	0.859883i	0.000270263	−	0.0321803i
$715$	−0.863895	−	1.49631i	−0.0323078	−	0.0559588i
$716$	26.6208	+	15.3695i	0.994867	+	0.574387i
$717$	−35.0921	−	22.2332i	−1.31054	−	0.830313i
$718$	7.67840	+	13.2994i	0.286555	+	0.496328i
$719$	23.5658	+	40.8172i	0.878857	+	1.52222i	0.852597	+	0.522569i	$0.175026\pi$
$719$	23.5658	+	40.8172i	0.878857	+	1.52222i	0.0262598	+	0.999655i	$0.491640\pi$
$720$	−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
$723$	3.41021	+	2.16059i	0.126827	+	0.0803532i
$724$			40.8795i			1.51927i
$725$			0.480385i			0.0178411i
$726$	0.393583	−	9.56234i	0.0146072	−	0.354892i
$727$	−35.4549	−	20.4699i	−1.31495	−	0.759186i	−0.332038	−	0.943266i	$-0.607736\pi$
$727$	−35.4549	−	20.4699i	−1.31495	−	0.759186i	−0.982911	+	0.184080i	$0.941070\pi$
$728$	−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
$731$	0.442589	+	0.766587i	0.0163698	+	0.0283533i
$732$	5.45157	−	2.85523i	0.201496	−	0.105532i
$733$	21.2560	+	12.2721i	0.785108	+	0.453282i	0.838237	−	0.545305i	$-0.183586\pi$
$733$	21.2560	+	12.2721i	0.785108	+	0.453282i	−0.0531297	+	0.998588i	$0.516920\pi$
$734$	−6.41277	−	11.1072i	−0.236700	−	0.409976i
$735$	−12.1208	+	0.295078i	−0.447081	+	0.0108841i
$736$	−18.4317	+	31.9246i	−0.679400	+	1.17675i
$737$	−10.7515	+	6.20739i	−0.396037	+	0.228652i
$738$	0.110982	−	1.34590i	0.00408530	−	0.0495433i
$739$	11.8428	−	20.5123i	0.435644	−	0.754557i	−0.561704	−	0.827338i	$-0.689854\pi$
$739$	11.8428	−	20.5123i	0.435644	−	0.754557i	0.997348	+	0.0727809i	$0.0231874\pi$
$740$	−8.62171			−0.316940
$741$	11.7205	+	0.482414i	0.430565	+	0.0177219i
$742$	−6.71734	+	12.5677i	−0.246601	+	0.461374i
$743$	−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	$0.483827\pi$
$744$	19.7044	+	37.6221i	0.722398	+	1.37929i
$745$	19.5847	−	11.3072i	0.717528	−	0.414265i
$746$	1.84762	+	1.06672i	0.0676462	+	0.0390555i
$747$	1.02174	+	2.16287i	0.0373836	+	0.0791354i
$748$			0.719088i			0.0262925i
$749$	15.9397	−	9.91224i	0.582424	−	0.362185i
$750$	−0.991125	+	0.519096i	−0.0361908	+	0.0189547i
$751$	−13.2847	+	23.0098i	−0.484767	+	0.839641i	−0.999847	−	0.0175013i	$-0.994429\pi$
$751$	−13.2847	+	23.0098i	−0.484767	+	0.839641i	0.515080	+	0.857142i	$0.327762\pi$
$752$	−0.511257			−0.0186436
$753$	6.66822	+	12.7318i	0.243004	+	0.463973i
$754$		−	0.342809i		−	0.0124844i
$755$	8.21423			0.298946
$756$	21.6697	+	1.97021i	0.788118	+	0.0716560i
$757$	33.0625			1.20168			0.600838	−	0.799370i	$-0.294833\pi$
$757$	33.0625			1.20168			0.600838	+	0.799370i	$0.294833\pi$
$758$		−	21.8519i		−	0.793696i
$759$	−8.11726	−	15.4985i	−0.294638	−	0.562560i
$760$	−14.1879			−0.514648
$761$	17.8551	−	30.9259i	0.647247	−	1.12106i	−0.336531	−	0.941672i	$-0.609254\pi$
$761$	17.8551	−	30.9259i	0.647247	−	1.12106i	0.983778	−	0.179392i	$-0.0574130\pi$
$762$	−14.1096	+	7.38984i	−0.511138	+	0.267706i
$763$	16.2627	−	30.4263i	0.588748	−	1.10151i
$764$		−	20.9452i		−	0.757769i
$765$	−0.868540	−	0.0716190i	−0.0314021	−	0.00258939i
$766$	−14.0869	−	8.13310i	−0.508982	−	0.293861i
$767$	5.28143	−	3.04924i	0.190702	−	0.110102i
$768$	−6.36561	−	12.1540i	−0.229699	−	0.438571i
$769$	−30.7446	+	17.7504i	−1.10868	+	0.640095i	−0.938487	−	0.345316i	$-0.887772\pi$
$769$	−30.7446	+	17.7504i	−1.10868	+	0.640095i	−0.170191	+	0.985411i	$0.554439\pi$
$770$	−2.67150	+	0.0874914i	−0.0962740	+	0.00315297i
$771$	−29.2322	−	1.20319i	−1.05277	−	0.0433317i
$772$	−15.2513			−0.548907
$773$	−21.3697	+	37.0134i	−0.768615	+	1.33128i	0.169699	+	0.985496i	$0.445720\pi$
$773$	−21.3697	+	37.0134i	−0.768615	+	1.33128i	−0.938314	+	0.345784i	$0.887613\pi$
$774$	5.33918	−	2.52224i	0.191913	−	0.0906599i
$775$	−9.17552	+	5.29749i	−0.329594	+	0.190291i
$776$	9.95901	−	17.2495i	0.357508	−	0.619221i
$777$	12.6625	−	21.5129i	0.454266	−	0.771770i
$778$	−1.48419	−	2.57070i	−0.0532109	−	0.0921640i
$779$	3.69987	+	2.13612i	0.132562	+	0.0765345i
$780$	−2.68281	+	1.40511i	−0.0960599	+	0.0503109i
$781$	8.27349	+	14.3301i	0.296049	+	0.512771i
$782$	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
$786$	0.614640	−	14.9331i	0.0219235	−	0.532644i
$787$			33.4165i			1.19117i	0.803293	+	0.595584i	$0.203079\pi$
$787$			33.4165i			1.19117i	−0.803293	+	0.595584i	$0.796921\pi$
$788$		−	33.4940i		−	1.19318i
$789$	22.8274	+	14.4627i	0.812678	+	0.514885i
$790$	−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
$794$	7.51497	+	13.0163i	0.266696	+	0.461931i
$795$	12.1996	+	7.72927i	0.432676	+	0.274129i
$796$	−5.89049	−	3.40087i	−0.208783	−	0.120541i
$797$	−6.99751	−	12.1200i	−0.247865	−	0.429314i	0.715069	−	0.699054i	$-0.246395\pi$
$797$	−6.99751	−	12.1200i	−0.247865	−	0.429314i	−0.962933	+	0.269740i	$0.913062\pi$
$798$	9.20531	−	15.6393i	0.325864	−	0.553624i
$799$	−0.0444524	+	0.0769938i	−0.00157261	+	0.00272384i
$800$	4.94301	−	2.85385i	0.174762	−	0.100899i
$801$	−32.9751	−	2.71910i	−1.16512	−	0.0960745i
$802$	−0.934609	+	1.61879i	−0.0330022	+	0.0571615i
$803$	19.7883			0.698313
$804$	10.0962	+	19.2769i	0.356065	+	0.679845i
$805$	14.5108	−	9.02363i	0.511437	−	0.318041i
$806$	6.54777	−	3.78036i	0.230635	−	0.133157i
$807$	46.8412	+	1.92797i	1.64889	+	0.0678678i
$808$	34.0101	−	19.6357i	1.19647	−	0.690783i
$809$	−15.2148	−	8.78427i	−0.534924	−	0.308839i	0.208095	−	0.978109i	$-0.433274\pi$
$809$	−15.2148	−	8.78427i	−0.534924	−	0.308839i	−0.743019	+	0.669270i	$0.766607\pi$
$810$	−0.952298	+	5.73511i	−0.0334603	+	0.201511i
$811$			14.4173i			0.506261i	0.967432	+	0.253131i	$0.0814603\pi$
$811$			14.4173i			0.506261i	−0.967432	+	0.253131i	$0.918540\pi$
$812$	1.77411	+	0.948251i	0.0622590	+	0.0332771i
$813$	33.6189	+	21.2998i	1.17907	+	0.747017i
$814$	2.75165	−	4.76599i	0.0964452	−	0.167048i
$815$	−1.53240			−0.0536777
$816$	0.839822	+	0.0345668i	0.0293997	+	0.00121008i
$817$			18.6805i			0.653547i
$818$	−7.48120			−0.261574
$819$	0.434170	−	8.75780i	0.0151711	−	0.306022i
$820$	−1.10298			−0.0385177
$821$		−	1.82571i		−	0.0637178i	−0.999492	−	0.0318589i	$-0.989857\pi$
$821$		−	1.82571i		−	0.0637178i	0.999492	−	0.0318589i	$-0.0101427\pi$
$822$	5.05668	−	7.98131i	0.176372	−	0.278380i
$823$	−38.7585			−1.35104			−0.675519	−	0.737343i	$-0.736080\pi$
$823$	−38.7585			−1.35104			−0.675519	+	0.737343i	$0.736080\pi$
$824$	−6.69804	+	11.6013i	−0.233337	+	0.404152i
$825$	−0.111403	+	2.70661i	−0.00387857	+	0.0942322i
$826$	−0.308813	−	9.42942i	−0.0107450	−	0.328091i
$827$			39.0575i			1.35816i	0.734064	+	0.679081i	$0.237621\pi$
$827$			39.0575i			1.35816i	−0.734064	+	0.679081i	$0.762379\pi$
$828$	−27.7282	+	13.0988i	−0.963620	+	0.455215i
$829$	22.4944	+	12.9872i	0.781263	+	0.451063i	0.836878	−	0.547390i	$-0.184378\pi$
$829$	22.4944	+	12.9872i	0.781263	+	0.451063i	−0.0556144	+	0.998452i	$0.517712\pi$
$830$	−0.446054	+	0.257529i	−0.0154828	+	0.00893897i
$831$	−16.6686	+	26.3092i	−0.578227	+	0.912654i
$832$	−0.330912	+	0.191052i	−0.0114723	+	0.00662353i
$833$	0.899333	−	1.82379i	0.0311600	−	0.0631906i
$834$	−2.10480	+	3.32215i	−0.0728832	+	0.115037i
$835$	25.2567			0.874046
$836$	−7.58768	+	13.1423i	−0.262426	+	0.454534i
$837$	−6.77684	+	54.6344i	−0.234242	+	1.88844i
$838$	−1.99770	+	1.15337i	−0.0690095	+	0.0398426i
$839$	−6.12667	+	10.6117i	−0.211516	+	0.366357i	−0.952189	−	0.305509i	$-0.901173\pi$
$839$	−6.12667	+	10.6117i	−0.211516	+	0.366357i	0.740673	+	0.671866i	$0.234507\pi$
$840$	−0.0890657	+	10.6051i	−0.00307306	+	0.365910i
$841$	−14.3846	−	24.9149i	−0.496021	−	0.859134i
$842$	−14.9288	−	8.61913i	−0.514480	−	0.297035i
$843$	−0.151638	+	3.68413i	−0.00522267	+	0.126888i
$844$	8.37055	+	14.4982i	0.288126	+	0.499049i
$845$	−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
$849$	−8.99191	+	4.70946i	−0.308602	+	0.161628i
$850$		−	0.187649i		−	0.00643629i
$851$			35.1818i			1.20602i
$852$	25.6932	−	13.4567i	0.880233	−	0.461017i
$853$	7.81229	+	4.51043i	0.267488	+	0.154434i	0.627745	−	0.778419i	$-0.283978\pi$
$853$	7.81229	+	4.51043i	0.267488	+	0.154434i	−0.360258	+	0.932853i	$0.617311\pi$
$854$	−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
$857$	8.59732	+	14.8910i	0.293679	+	0.508667i	0.974677	−	0.223619i	$-0.0717870\pi$
$857$	8.59732	+	14.8910i	0.293679	+	0.508667i	−0.680998	+	0.732285i	$0.738454\pi$
$858$	0.0794989	−	1.93147i	0.00271405	−	0.0659394i
$859$	−7.61868	−	4.39865i	−0.259946	−	0.150080i	0.364364	−	0.931257i	$-0.381286\pi$
$859$	−7.61868	−	4.39865i	−0.259946	−	0.150080i	−0.624310	+	0.781177i	$0.714620\pi$
$860$	−2.41140	−	4.17667i	−0.0822281	−	0.142423i
$861$	1.61993	−	2.75215i	0.0552069	−	0.0937932i
$862$	−4.64744	+	8.04960i	−0.158292	+	0.274170i
$863$	−4.64329	+	2.68081i	−0.158059	+	0.0912557i	−0.576943	−	0.816784i	$-0.695755\pi$
$863$	−4.64329	+	2.68081i	−0.158059	+	0.0912557i	0.418884	+	0.908040i	$0.362421\pi$
$864$	3.65080	−	29.4325i	0.124203	−	1.00131i
$865$	−1.41188	+	2.44545i	−0.0480053	+	0.0831476i
$866$	−15.4484			−0.524958
$867$	−15.6804	+	24.7495i	−0.532535	+	0.840537i
$868$	1.45223	+	44.3430i	0.0492920	+	1.50510i
$869$	−4.77427	+	2.75642i	−0.161956	+	0.0935053i
$870$	−0.287650	+	0.454018i	−0.00975226	+	0.0153927i
$871$	7.59441	−	4.38464i	0.257327	−	0.148568i
$872$	−26.1347	−	15.0889i	−0.885033	−	0.510974i
$873$	23.3456	−	11.0285i	0.790129	−	0.373258i
$874$			25.5762i			0.865127i
$875$	−2.64433	+	0.0866018i	−0.0893948	+	0.00292768i
$876$	1.42642	−	34.6558i	0.0481943	−	1.17091i
$877$	−12.0597	+	20.8881i	−0.407229	+	0.705341i	−0.994578	−	0.103993i	$-0.966838\pi$
$877$	−12.0597	+	20.8881i	−0.407229	+	0.705341i	0.587349	+	0.809333i	$0.300171\pi$
$878$	−5.09753			−0.172033
$879$	−20.7144	+	32.6949i	−0.698678	+	1.10277i
$880$		−	2.61269i		−	0.0880737i
$881$	6.19597			0.208748			0.104374	−	0.994538i	$-0.466716\pi$
$881$	6.19597			0.208748			0.104374	+	0.994538i	$0.466716\pi$
$882$	−11.6322	−	6.97892i	−0.391676	−	0.234993i
$883$	−18.1365			−0.610340			−0.305170	−	0.952298i	$-0.598713\pi$
$883$	−18.1365			−0.610340			−0.305170	+	0.952298i	$0.598713\pi$
$884$		−	0.507933i		−	0.0170836i
$885$	−9.55337	−	0.393214i	−0.321133	−	0.0132177i
$886$	−12.3476			−0.414827
$887$	1.64063	−	2.84166i	0.0550870	−	0.0954135i	−0.837167	−	0.546948i	$-0.815790\pi$
$887$	1.64063	−	2.84166i	0.0550870	−	0.0954135i	0.892254	+	0.451534i	$0.149123\pi$
$888$	−18.4452	−	11.6862i	−0.618980	−	0.392165i
$889$	−37.6447	+	1.23286i	−1.26256	+	0.0413489i
$890$		−	7.12429i		−	0.238807i
$891$	10.8726	+	8.93967i	0.364245	+	0.299490i
$892$	−35.6854	−	20.6030i	−1.19484	−	0.689838i
$893$	−1.62485	+	0.938106i	−0.0543734	+	0.0313925i
$894$	25.2804	+	1.04053i	0.845504	+	0.0348007i
$895$	−16.8195	+	9.71074i	−0.562213	+	0.324594i
$896$	−0.969245	−	29.5953i	−0.0323802	−	0.988710i
$897$	5.73368	+	10.9475i	0.191442	+	0.365526i
$898$	−8.63566			−0.288176
$899$	−2.54484	+	4.40778i	−0.0848750	+	0.147008i
$900$	4.73215	+	0.390209i	0.157738	+	0.0130070i
$901$	−2.09768	+	1.21109i	−0.0698838	+	0.0403474i
$902$	0.352020	−	0.609716i	0.0117210	−	0.0203013i
$903$	13.9632	+	0.117269i	0.464666	+	0.00390245i
$904$	18.2730	+	31.6498i	0.607751	+	1.05266i
$905$	−22.3680	−	12.9142i	−0.743538	−	0.429282i
$906$	7.76337	+	4.91861i	0.257921	+	0.163410i
$907$	21.7374	+	37.6503i	0.721778	+	1.25016i	0.960286	+	0.279016i	$0.0900082\pi$
$907$	21.7374	+	37.6503i	0.721778	+	1.25016i	−0.238508	+	0.971140i	$0.576658\pi$
$908$	−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	$0.365047\pi$
$912$	14.9841	+	9.49340i	0.496173	+	0.314358i
$913$			1.24705i			0.0412714i
$914$			3.57861i			0.118370i
$915$	−0.159902	+	3.88493i	−0.00528621	+	0.128432i
$916$	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	0.786529	−	0.617553i	$-0.211876\pi$
$919$	−4.29115	−	7.43249i	−0.141552	−	0.245175i	−0.928081	+	0.372378i	$0.878543\pi$
$920$	−7.47349	−	12.9445i	−0.246394	−	0.426766i
$921$	30.0578	−	15.7426i	0.990438	−	0.518736i
$922$	−4.77764	−	2.75837i	−0.157343	−	0.0908421i
$923$	−5.84404	−	10.1222i	−0.192359	−	0.333175i
$924$	9.77589	+	5.75411i	0.321603	+	0.189296i
$925$	2.72367	−	4.71754i	0.0895537	−	0.155112i
$926$	9.45013	−	5.45604i	0.310551	−	0.179297i
$927$	−15.7014	+	7.41734i	−0.515700	+	0.243617i
$928$	1.37095	−	2.37455i	0.0450035	−	0.0779484i
$929$	7.06743			0.231875			0.115937	−	0.993257i	$-0.463013\pi$
$929$	7.06743			0.231875			0.115937	+	0.993257i	$0.463013\pi$
$930$	−11.8440	−	0.487495i	−0.388380	−	0.0159856i
$931$	35.6807	−	23.8425i	1.16939	−	0.781406i
$932$	−30.7096	+	17.7302i	−1.00593	+	0.580772i
$933$	−11.4978	−	21.9531i	−0.376422	−	0.718713i
$934$	−6.46338	+	3.73163i	−0.211488	+	0.122103i
$935$	−0.393463	−	0.227166i	−0.0128676	−	0.00742913i
$936$	−7.64412	−	0.630327i	−0.249856	−	0.0206029i
$937$			29.9370i			0.978001i	0.872284	+	0.489000i	$0.162638\pi$
$937$			29.9370i			0.978001i	−0.872284	+	0.489000i	$0.837362\pi$
$938$	−0.444056	−	13.5590i	−0.0144990	−	0.442717i
$939$	−8.92198	+	4.67284i	−0.291158	+	0.152492i
$940$	0.242194	−	0.419492i	0.00789950	−	0.0136823i
$941$	−54.3888			−1.77302			−0.886512	−	0.462705i	$-0.846879\pi$
$941$	−54.3888			−1.77302			−0.886512	+	0.462705i	$0.846879\pi$
$942$	−1.96310	−	3.74819i	−0.0639611	−	0.122123i
$943$			4.50082i			0.146567i
$944$	9.22185			0.300146
$945$	−7.92367	+	11.2346i	−0.257757	+	0.365460i
$946$	3.07843			0.100088
$947$		−	16.3917i		−	0.532660i	−0.963882	−	0.266330i	$-0.914189\pi$
$947$		−	16.3917i		−	0.532660i	0.963882	−	0.266330i	$-0.0858110\pi$
$948$	4.48326	+	8.56002i	0.145610	+	0.278016i
$949$	−13.9776			−0.453731
$950$	1.98003	−	3.42952i	0.0642407	−	0.111268i
$951$	23.5630	−	12.3410i	0.764082	−	0.400184i
$952$	−1.56871	−	0.838465i	−0.0508421	−	0.0271748i
$953$			17.4072i			0.563873i	0.959433	+	0.281937i	$0.0909768\pi$
$953$			17.4072i			0.563873i	−0.959433	+	0.281937i	$0.909023\pi$
$954$	6.90181	+	14.6101i	0.223454	+	0.473018i
$955$	11.4606	+	6.61675i	0.370855	+	0.214113i
$956$	−32.8753	+	18.9806i	−1.06326	+	0.613876i
$957$	0.603762	+	1.15278i	0.0195169	+	0.0372641i
$958$	−18.6109	+	10.7450i	−0.601292	+	0.347156i
$959$	18.9735	−	11.7988i	0.612685	−	0.381004i
$960$	0.598573	+	0.0246371i	0.0193188	+	0.000795158i
$961$	−81.2536			−2.62108
$962$	−1.94365	+	3.36649i	−0.0626657	+	0.108540i
$963$	1.74909	−	21.2116i	0.0563636	−	0.683534i
$964$	3.19478	−	1.84451i	0.102897	−	0.0594077i
$965$	4.81802	−	8.34506i	0.155098	−	0.268637i
$966$	19.1176	+	0.160557i	0.615098	+	0.00516584i
$967$	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	$0.796192\pi$
$968$	−17.1442	−	9.89820i	−0.551035	−	0.318140i
$969$	2.73250	−	1.43113i	0.0877807	−	0.0459746i
$970$	2.77972	+	4.81462i	0.0892515	+	0.154588i
$971$	−11.7556	−	20.3614i	−0.377256	−	0.653427i	0.613406	−	0.789768i	$-0.289799\pi$
$971$	−11.7556	−	20.3614i	−0.377256	−	0.653427i	−0.990662	+	0.136341i	$0.956466\pi$
$972$	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
$975$	0.0786906	−	1.91184i	0.00252011	−	0.0612278i
$976$		−	3.75011i		−	0.120038i
$977$		−	56.8610i		−	1.81914i	−0.415546	−	0.909572i	$-0.636409\pi$
$977$		−	56.8610i		−	1.81914i	0.415546	−	0.909572i	$-0.363591\pi$
$978$	−1.44829	−	0.917589i	−0.0463113	−	0.0293413i
$979$	−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
$983$	−22.9502	−	39.7510i	−0.731999	−	1.26786i	−0.956028	−	0.293277i	$-0.905254\pi$
$983$	−22.9502	−	39.7510i	−0.731999	−	1.26786i	0.224029	−	0.974583i	$-0.428079\pi$
$984$	−2.35970	−	1.49503i	−0.0752246	−	0.0476597i
$985$	18.3269	+	10.5810i	0.583944	+	0.337140i
$986$	−0.0450718	−	0.0780666i	−0.00143538	−	0.00248615i
$987$	0.691012	+	1.22042i	0.0219951	+	0.0388465i
$988$	5.35961	−	9.28312i	0.170512	−	0.295335i
$989$	−17.0433	+	9.83998i	−0.541947	+	0.312893i
$990$	−1.72599	+	2.49135i	−0.0548554	+	0.0791803i
$991$	−13.6765	+	23.6884i	−0.434449	+	0.752488i	−0.997251	−	0.0741040i	$-0.976390\pi$
$991$	−13.6765	+	23.6884i	−0.434449	+	0.752488i	0.562801	+	0.826592i	$0.309724\pi$
$992$	60.4729			1.92002
$993$	21.5066	+	41.0631i	0.682491	+	1.30310i
$994$	−18.0720	+	0.591858i	−0.573210	+	0.0187726i
$995$	3.72171	−	2.14873i	0.117986	−	0.0681193i
$996$	2.18400	+	0.0898929i	0.0692028	+	0.00284837i
$997$	−12.0810	+	6.97496i	−0.382609	+	0.220899i	−0.678953	−	0.734182i	$-0.737566\pi$
$997$	−12.0810	+	6.97496i	−0.382609	+	0.220899i	0.296344	+	0.955081i	$0.404233\pi$
$998$	−3.70543	−	2.13933i	−0.117293	−	0.0677193i
$999$	−11.0275	−	26.0687i	−0.348895	−	0.824778i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.c.101.11	✓	32	1.1	even	1	trivial
315.2.t.c.131.6	yes	32	63.5	even	6	inner
315.2.be.c.236.11	yes	32	7.5	odd	6
315.2.be.c.311.11	yes	32	9.5	odd	6
945.2.t.c.341.11		32	63.40	odd	6
945.2.t.c.521.6		32	3.2	odd	2
945.2.be.c.206.6		32	9.4	even	3
945.2.be.c.656.6		32	21.5	even	6

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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.645959i q^{2} +(0.803605 + 1.53435i) q^{3} +1.58274 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.991125 + 0.519096i) q^{6} +(-2.64433 + 0.0866018i) q^{7} +2.31430i q^{8} +(-1.70844 + 2.46602i) q^{9} +O(q^{10})\)	\(q+0.645959i q^{2} +(0.803605 + 1.53435i) q^{3} +1.58274 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.991125 + 0.519096i) q^{6} +(-2.64433 + 0.0866018i) q^{7} +2.31430i q^{8} +(-1.70844 + 2.46602i) q^{9} +(-0.559417 - 0.322980i) q^{10} +(-1.35445 + 0.781994i) q^{11} +(1.27190 + 2.42847i) q^{12} +(0.956727 - 0.552367i) q^{13} +(-0.0559412 - 1.70813i) q^{14} +(-1.73059 - 0.0712304i) q^{15} +1.67053 q^{16} +(0.145248 - 0.251577i) q^{17} +(-1.59295 - 1.10358i) q^{18} +(5.30918 - 3.06526i) q^{19} +(-0.791368 + 1.37069i) q^{20} +(-2.25788 - 3.98773i) q^{21} +(-0.505136 - 0.874921i) q^{22} +(5.59325 + 3.22926i) q^{23} +(-3.55094 + 1.85979i) q^{24} +(-0.500000 - 0.866025i) 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} +(0.0460119 - 1.11789i) q^{30} -10.5950i q^{31} +5.70770i q^{32} +(-2.28830 - 1.44979i) 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} +(1.98003 + 3.42952i) q^{38} +(1.61635 + 1.02407i) q^{39} +(-2.00424 - 1.15715i) q^{40} +(0.348441 + 0.603517i) q^{41} +(2.57591 - 1.45850i) q^{42} +(-1.52356 + 2.63889i) q^{43} +(-2.14374 + 1.23769i) q^{44} +(-1.28142 - 2.71256i) q^{45} +(-2.08597 + 3.61301i) q^{46} -0.306045 q^{47} +(1.34245 + 2.56317i) q^{48} +(6.98500 - 0.458008i) q^{49} +(0.559417 - 0.322980i) q^{50} +(0.502728 + 0.0206921i) q^{51} +(1.51425 - 0.874251i) q^{52} +(-7.22102 - 4.16906i) q^{53} +(0.413173 - 3.33097i) q^{54} -1.56399i q^{55} +(-0.200423 - 6.11978i) q^{56} +(8.96966 + 5.68287i) q^{57} +(0.155155 - 0.268736i) q^{58} +5.52031 q^{59} +(-2.73906 - 0.112739i) q^{60} -2.24486i q^{61} +6.84392 q^{62} +(4.30411 - 6.66893i) q^{63} -0.345879 q^{64} +1.10473i q^{65} +(0.936502 - 1.47815i) q^{66} +7.93791 q^{67} +(0.229889 - 0.398180i) q^{68} +(-0.460043 + 11.1770i) q^{69} +(1.50726 + 0.805619i) q^{70} -10.5800i q^{71} +(-5.70711 - 3.95384i) q^{72} +(-10.9573 - 6.32622i) q^{73} +(-3.04733 + 1.75938i) q^{74} +(0.926980 - 1.46312i) q^{75} +(8.40304 - 4.85150i) q^{76} +(3.51390 - 2.18515i) q^{77} +(-0.661505 + 1.04410i) q^{78} +3.52487 q^{79} +(-0.835265 + 1.44672i) q^{80} +(-3.16249 - 8.42607i) q^{81} +(-0.389847 + 0.225078i) q^{82} +(0.398678 - 0.690530i) q^{83} +(-3.57363 - 6.31153i) q^{84} +(0.145248 + 0.251577i) q^{85} +(-1.70462 - 0.984160i) q^{86} +(0.0342180 - 0.831348i) q^{87} +(-1.80977 - 3.13461i) 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} +(16.2564 - 8.51418i) q^{93} -0.197692i q^{94} +6.13052i q^{95} +(-8.75758 + 4.58674i) q^{96} +(-7.45344 - 4.30325i) q^{97} +(0.295855 + 4.51202i) q^{98} +(0.385586 - 4.67609i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9}+O(q^{10}) \) 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9	\( 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9} + 3 q^{11} + 12 q^{12} + 6 q^{13} - 15 q^{14} - q^{15} + 32 q^{16} - 3 q^{17} - 13 q^{18} + 16 q^{20} - q^{21} - 21 q^{22} - 9 q^{23} - 4 q^{24} - 16 q^{25} + 12 q^{26} + 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 19 q^{33} - 30 q^{34} + q^{35} + 18 q^{36} - q^{37} - 30 q^{38} + 21 q^{39} + 6 q^{41} + 19 q^{42} - 19 q^{43} + 21 q^{44} - 8 q^{45} + 6 q^{46} - 30 q^{47} - 35 q^{48} + 5 q^{49} + 36 q^{51} + 21 q^{52} - 24 q^{53} - 59 q^{54} + 30 q^{56} + 27 q^{57} + 30 q^{59} + 3 q^{60} - 32 q^{63} + 76 q^{64} + 26 q^{66} - 50 q^{67} - 3 q^{68} - 50 q^{69} + 9 q^{70} - 14 q^{72} + 12 q^{73} + 60 q^{74} + 2 q^{75} + 54 q^{76} - 27 q^{77} - 42 q^{78} + 4 q^{79} - 16 q^{80} - 23 q^{81} - 24 q^{82} - 42 q^{83} - 72 q^{84} - 3 q^{85} + 51 q^{86} + 34 q^{87} + 42 q^{88} + 30 q^{89} + 41 q^{90} - 57 q^{91} + 6 q^{92} - 33 q^{93} + 15 q^{96} - 42 q^{97} + 6 q^{98} - q^{99}+O(q^{100}) \) 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9 + 3 * q^11 + 12 * q^12 + 6 * q^13 - 15 * q^14 - q^15 + 32 * q^16 - 3 * q^17 - 13 * q^18 + 16 * q^20 - q^21 - 21 * q^22 - 9 * q^23 - 4 * q^24 - 16 * q^25 + 12 * q^26 + 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 19 * q^33 - 30 * q^34 + q^35 + 18 * q^36 - q^37 - 30 * q^38 + 21 * q^39 + 6 * q^41 + 19 * q^42 - 19 * q^43 + 21 * q^44 - 8 * q^45 + 6 * q^46 - 30 * q^47 - 35 * q^48 + 5 * q^49 + 36 * q^51 + 21 * q^52 - 24 * q^53 - 59 * q^54 + 30 * q^56 + 27 * q^57 + 30 * q^59 + 3 * q^60 - 32 * q^63 + 76 * q^64 + 26 * q^66 - 50 * q^67 - 3 * q^68 - 50 * q^69 + 9 * q^70 - 14 * q^72 + 12 * q^73 + 60 * q^74 + 2 * q^75 + 54 * q^76 - 27 * q^77 - 42 * q^78 + 4 * q^79 - 16 * q^80 - 23 * q^81 - 24 * q^82 - 42 * q^83 - 72 * q^84 - 3 * q^85 + 51 * q^86 + 34 * q^87 + 42 * q^88 + 30 * q^89 + 41 * q^90 - 57 * q^91 + 6 * q^92 - 33 * q^93 + 15 * q^96 - 42 * q^97 + 6 * q^98 - q^99

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