LMFDB - Embedded newform 315.2.bl.j.146.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(41,315)]

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([5, 0, 3]))

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

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

chi := DirichletCharacter("315.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bl (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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			146.4
Character	$\chi$	$=$	315.146
Dual form			315.2.bl.j.41.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13192 - 0.653515i) q^{2} +(0.957531 + 1.44331i) q^{3} +(-0.145837 - 0.252598i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.140627 - 2.25947i) q^{6} +(-2.56224 + 0.659483i) q^{7} +2.99529i q^{8} +(-1.16627 + 2.76402i) q^{9} +O(q^{10})$	\(q+(-1.13192 - 0.653515i) q^{2} +(0.957531 + 1.44331i) q^{3} +(-0.145837 - 0.252598i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.140627 - 2.25947i) q^{6} +(-2.56224 + 0.659483i) q^{7} +2.99529i q^{8} +(-1.16627 + 2.76402i) q^{9} +1.30703i q^{10} +(4.98971 + 2.88081i) q^{11} +(0.224932 - 0.452359i) q^{12} +(-3.14058 + 1.81321i) q^{13} +(3.33124 + 0.927980i) q^{14} +(0.771174 - 1.55090i) q^{15} +(1.66579 - 2.88523i) q^{16} +4.92433 q^{17} +(3.12645 - 2.36648i) q^{18} +3.02122i q^{19} +(-0.145837 + 0.252598i) q^{20} +(-3.40526 - 3.06662i) q^{21} +(-3.76530 - 6.52169i) q^{22} +(-5.93663 + 3.42751i) q^{23} +(-4.32312 + 2.86808i) q^{24} +(-0.500000 + 0.866025i) q^{25} +4.73984 q^{26} +(-5.10607 + 0.963357i) q^{27} +(0.540255 + 0.551040i) q^{28} +(7.16276 + 4.13542i) q^{29} +(-1.88644 + 1.25152i) q^{30} +(-3.18657 + 1.83977i) q^{31} +(1.41691 - 0.818053i) q^{32} +(0.619911 + 9.96014i) q^{33} +(-5.57395 - 3.21812i) q^{34} +(1.85225 + 1.88922i) q^{35} +(0.868272 - 0.108501i) q^{36} +2.80891 q^{37} +(1.97441 - 3.41978i) q^{38} +(-5.62422 - 2.79661i) q^{39} +(2.59399 - 1.49764i) q^{40} +(-5.57799 - 9.66136i) q^{41} +(1.85040 + 5.69656i) q^{42} +(-0.136193 + 0.235894i) q^{43} -1.68052i q^{44} +(2.97685 - 0.371994i) q^{45} +8.95972 q^{46} +(-1.88231 + 3.26026i) q^{47} +(5.75931 - 0.358455i) q^{48} +(6.13016 - 3.37951i) q^{49} +(1.13192 - 0.653515i) q^{50} +(4.71520 + 7.10732i) q^{51} +(0.916027 + 0.528869i) q^{52} +3.51435i q^{53} +(6.40923 + 2.24645i) q^{54} -5.76162i q^{55} +(-1.97534 - 7.67465i) q^{56} +(-4.36055 + 2.89291i) q^{57} +(-5.40512 - 9.36194i) q^{58} +(4.33885 + 7.51511i) q^{59} +(-0.504220 + 0.0313822i) q^{60} +(-7.81138 - 4.50990i) q^{61} +4.80926 q^{62} +(1.16543 - 7.85123i) q^{63} -8.80159 q^{64} +(3.14058 + 1.81321i) q^{65} +(5.80741 - 11.6792i) q^{66} +(1.65886 + 2.87323i) q^{67} +(-0.718152 - 1.24388i) q^{68} +(-10.6315 - 5.28642i) q^{69} +(-0.861964 - 3.34892i) q^{70} -6.95342i q^{71} +(-8.27904 - 3.49330i) q^{72} -2.88131i q^{73} +(-3.17946 - 1.83566i) q^{74} +(-1.72871 + 0.107593i) q^{75} +(0.763154 - 0.440607i) q^{76} +(-14.6847 - 4.09070i) q^{77} +(4.53855 + 6.84105i) q^{78} +(5.15417 - 8.92729i) q^{79} -3.33158 q^{80} +(-6.27964 - 6.44718i) q^{81} +14.5812i q^{82} +(-1.69417 + 2.93439i) q^{83} +(-0.278008 + 1.30739i) q^{84} +(-2.46216 - 4.26459i) q^{85} +(0.308320 - 0.178009i) q^{86} +(0.889887 + 14.2979i) q^{87} +(-8.62884 + 14.9456i) q^{88} +4.68832 q^{89} +(-3.61266 - 1.52435i) q^{90} +(6.85113 - 6.71705i) q^{91} +(1.73157 + 0.999720i) q^{92} +(-5.70659 - 2.83756i) q^{93} +(4.26126 - 2.46024i) q^{94} +(2.61645 - 1.51061i) q^{95} +(2.53744 + 1.26172i) q^{96} +(-4.00495 - 2.31226i) q^{97} +(-9.14742 - 0.180814i) q^{98} +(-13.7819 + 10.4319i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9	$ 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9} + 9 q^{11} - 18 q^{12} + 3 q^{13} + 18 q^{14} + 2 q^{15} - 18 q^{16} + 18 q^{17} + 2 q^{18} + 18 q^{20} + 8 q^{21} - 9 q^{22} + 9 q^{23} - 7 q^{24} - 12 q^{25} - 18 q^{26} - 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} - 42 q^{31} + 18 q^{32} + 13 q^{33} - 39 q^{34} - 9 q^{35} - 21 q^{36} - 12 q^{38} - 21 q^{39} - 6 q^{40} - 33 q^{41} - 65 q^{42} + 18 q^{43} + q^{45} - 30 q^{46} - 17 q^{48} + 9 q^{49} - 6 q^{50} - 12 q^{51} + 129 q^{52} + 52 q^{54} - 9 q^{56} + 6 q^{57} - 15 q^{58} + 12 q^{59} + 15 q^{60} - 15 q^{61} + 12 q^{62} + 46 q^{63} - 60 q^{64} - 3 q^{65} + 29 q^{66} - 15 q^{67} + 9 q^{68} + 61 q^{69} - 9 q^{70} + 61 q^{72} - 18 q^{74} - 7 q^{75} + 54 q^{76} - 45 q^{77} - 66 q^{78} + 21 q^{79} + 36 q^{80} + q^{81} - 30 q^{83} + 15 q^{84} - 9 q^{85} - 102 q^{86} + 10 q^{87} - 9 q^{88} + 102 q^{89} - 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} - 156 q^{94} - 18 q^{95} - 42 q^{96} - 45 q^{97} + 3 q^{98} + 23 q^{99}+O(q^{100}) $ 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9 + 9 * q^11 - 18 * q^12 + 3 * q^13 + 18 * q^14 + 2 * q^15 - 18 * q^16 + 18 * q^17 + 2 * q^18 + 18 * q^20 + 8 * q^21 - 9 * q^22 + 9 * q^23 - 7 * q^24 - 12 * q^25 - 18 * q^26 - 4 * q^27 - 9 * q^28 + 9 * q^29 - 5 * q^30 - 42 * q^31 + 18 * q^32 + 13 * q^33 - 39 * q^34 - 9 * q^35 - 21 * q^36 - 12 * q^38 - 21 * q^39 - 6 * q^40 - 33 * q^41 - 65 * q^42 + 18 * q^43 + q^45 - 30 * q^46 - 17 * q^48 + 9 * q^49 - 6 * q^50 - 12 * q^51 + 129 * q^52 + 52 * q^54 - 9 * q^56 + 6 * q^57 - 15 * q^58 + 12 * q^59 + 15 * q^60 - 15 * q^61 + 12 * q^62 + 46 * q^63 - 60 * q^64 - 3 * q^65 + 29 * q^66 - 15 * q^67 + 9 * q^68 + 61 * q^69 - 9 * q^70 + 61 * q^72 - 18 * q^74 - 7 * q^75 + 54 * q^76 - 45 * q^77 - 66 * q^78 + 21 * q^79 + 36 * q^80 + q^81 - 30 * q^83 + 15 * q^84 - 9 * q^85 - 102 * q^86 + 10 * q^87 - 9 * q^88 + 102 * q^89 - 37 * q^90 + 42 * q^91 - 3 * q^92 - 6 * q^93 - 156 * q^94 - 18 * q^95 - 42 * q^96 - 45 * q^97 + 3 * q^98 + 23 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.13192	−	0.653515i	−0.800389	−	0.462105i	0.0432184	−	0.999066i	$-0.486239\pi$
$2$	−1.13192	−	0.653515i	−0.800389	−	0.462105i	−0.843607	+	0.536961i	$0.819572\pi$
$3$	0.957531	+	1.44331i	0.552831	+	0.833293i
$3$	0.957531	+	1.44331i	0.552831	+	0.833293i
$4$	−0.145837	−	0.252598i	−0.0729187	−	0.126299i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.140627	−	2.25947i	−0.0574109	−	0.922424i
$7$	−2.56224	+	0.659483i	−0.968436	+	0.249261i
$7$	−2.56224	+	0.659483i	−0.968436	+	0.249261i
$8$			2.99529i			1.05899i
$9$	−1.16627	+	2.76402i	−0.388756	+	0.921341i
$10$			1.30703i			0.413319i
$11$	4.98971	+	2.88081i	1.50445	+	0.868596i	0.999987	+	0.00516464i	$0.00164396\pi$
$11$	4.98971	+	2.88081i	1.50445	+	0.868596i	0.504466	+	0.863432i	$0.331689\pi$
$12$	0.224932	−	0.452359i	0.0649324	−	0.130585i
$13$	−3.14058	+	1.81321i	−0.871039	+	0.502895i	−0.867693	−	0.497100i	$-0.834398\pi$
$13$	−3.14058	+	1.81321i	−0.871039	+	0.502895i	−0.00334565	+	0.999994i	$0.501065\pi$
$14$	3.33124	+	0.927980i	0.890310	+	0.248013i
$15$	0.771174	−	1.55090i	0.199116	−	0.400441i
$16$	1.66579	−	2.88523i	0.416447	−	0.721307i
$17$	4.92433			1.19433			0.597163	−	0.802120i	$-0.296295\pi$
$17$	4.92433			1.19433			0.597163	+	0.802120i	$0.296295\pi$
$18$	3.12645	−	2.36648i	0.736912	−	0.557785i
$19$			3.02122i			0.693116i	0.938029	+	0.346558i	$0.112650\pi$
$19$			3.02122i			0.693116i	−0.938029	+	0.346558i	$0.887350\pi$
$20$	−0.145837	+	0.252598i	−0.0326103	+	0.0564826i
$21$	−3.40526	−	3.06662i	−0.743089	−	0.669192i
$22$	−3.76530	−	6.52169i	−0.802765	−	1.39043i
$23$	−5.93663	+	3.42751i	−1.23787	+	0.714686i	−0.968659	−	0.248394i	$-0.920097\pi$
$23$	−5.93663	+	3.42751i	−1.23787	+	0.714686i	−0.269214	+	0.963080i	$0.586764\pi$
$24$	−4.32312	+	2.86808i	−0.882452	+	0.585444i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	4.73984			0.929560
$27$	−5.10607	+	0.963357i	−0.982663	+	0.185398i
$28$	0.540255	+	0.551040i	0.102099	+	0.104137i
$29$	7.16276	+	4.13542i	1.33009	+	0.767929i	0.985313	−	0.170755i	$-0.0546208\pi$
$29$	7.16276	+	4.13542i	1.33009	+	0.767929i	0.344778	+	0.938684i	$0.387954\pi$
$30$	−1.88644	+	1.25152i	−0.344416	+	0.228495i
$31$	−3.18657	+	1.83977i	−0.572325	+	0.330432i	−0.758077	−	0.652165i	$-0.773861\pi$
$31$	−3.18657	+	1.83977i	−0.572325	+	0.330432i	0.185753	+	0.982597i	$0.440528\pi$
$32$	1.41691	−	0.818053i	0.250476	−	0.144613i
$33$	0.619911	+	9.96014i	0.107913	+	1.73384i
$34$	−5.57395	−	3.21812i	−0.955924	−	0.551903i
$35$	1.85225	+	1.88922i	0.313087	+	0.319337i
$36$	0.868272	−	0.108501i	0.144712	−	0.0180836i
$37$	2.80891			0.461782			0.230891	−	0.972980i	$-0.425836\pi$
$37$	2.80891			0.461782			0.230891	+	0.972980i	$0.425836\pi$
$38$	1.97441	−	3.41978i	0.320292	−	0.554762i
$39$	−5.62422	−	2.79661i	−0.900596	−	0.447815i
$40$	2.59399	−	1.49764i	0.410146	−	0.236798i
$41$	−5.57799	−	9.66136i	−0.871136	−	1.50885i	−0.860823	−	0.508905i	$-0.830051\pi$
$41$	−5.57799	−	9.66136i	−0.871136	−	1.50885i	−0.0103128	−	0.999947i	$-0.503283\pi$
$42$	1.85040	+	5.69656i	0.285523	+	0.878999i
$43$	−0.136193	+	0.235894i	−0.0207693	+	0.0359735i	−0.876223	−	0.481905i	$-0.839945\pi$
$43$	−0.136193	+	0.235894i	−0.0207693	+	0.0359735i	0.855454	+	0.517879i	$0.173278\pi$
$44$		−	1.68052i		−	0.253348i
$45$	2.97685	−	0.371994i	0.443762	−	0.0554536i
$46$	8.95972			1.32104
$47$	−1.88231	+	3.26026i	−0.274564	+	0.475558i	−0.970025	−	0.243005i	$-0.921867\pi$
$47$	−1.88231	+	3.26026i	−0.274564	+	0.475558i	0.695461	+	0.718564i	$0.255200\pi$
$48$	5.75931	−	0.358455i	0.831285	−	0.0517385i
$49$	6.13016	−	3.37951i	0.875738	−	0.482787i
$50$	1.13192	−	0.653515i	0.160078	−	0.0924209i
$51$	4.71520	+	7.10732i	0.660260	+	0.995223i
$52$	0.916027	+	0.528869i	0.127030	+	0.0733409i
$53$			3.51435i			0.482733i	0.970434	+	0.241367i	$0.0775957\pi$
$53$			3.51435i			0.482733i	−0.970434	+	0.241367i	$0.922404\pi$
$54$	6.40923	+	2.24645i	0.872186	+	0.305703i
$55$		−	5.76162i		−	0.776896i
$56$	−1.97534	−	7.67465i	−0.263966	−	1.02557i
$57$	−4.36055	+	2.89291i	−0.577569	+	0.383176i
$58$	−5.40512	−	9.36194i	−0.709727	−	1.22928i
$59$	4.33885	+	7.51511i	0.564870	+	0.978384i	0.997062	+	0.0766018i	$0.0244070\pi$
$59$	4.33885	+	7.51511i	0.564870	+	0.978384i	−0.432192	+	0.901782i	$0.642260\pi$
$60$	−0.504220	+	0.0313822i	−0.0650946	+	0.00405143i
$61$	−7.81138	−	4.50990i	−1.00014	−	0.577434i	−0.0918536	−	0.995773i	$-0.529279\pi$
$61$	−7.81138	−	4.50990i	−1.00014	−	0.577434i	−0.908291	+	0.418339i	$0.862613\pi$
$62$	4.80926			0.610776
$63$	1.16543	−	7.85123i	0.146831	−	0.989162i
$64$	−8.80159			−1.10020
$65$	3.14058	+	1.81321i	0.389540	+	0.224901i
$66$	5.80741	−	11.6792i	0.714842	−	1.43761i
$67$	1.65886	+	2.87323i	0.202662	+	0.351021i	0.949385	−	0.314114i	$-0.101707\pi$
$67$	1.65886	+	2.87323i	0.202662	+	0.351021i	−0.746723	+	0.665135i	$0.768374\pi$
$68$	−0.718152	−	1.24388i	−0.0870887	−	0.150842i
$69$	−10.6315	−	5.28642i	−1.27988	−	0.636411i
$70$	−0.861964	−	3.34892i	−0.103024	−	0.400273i
$71$		−	6.95342i		−	0.825220i	−0.910908	−	0.412610i	$-0.864617\pi$
$71$		−	6.95342i		−	0.825220i	0.910908	−	0.412610i	$-0.135383\pi$
$72$	−8.27904	−	3.49330i	−0.975694	−	0.411690i
$73$		−	2.88131i		−	0.337232i	−0.985682	−	0.168616i	$-0.946070\pi$
$73$		−	2.88131i		−	0.337232i	0.985682	−	0.168616i	$-0.0539298\pi$
$74$	−3.17946	−	1.83566i	−0.369605	−	0.213392i
$75$	−1.72871	+	0.107593i	−0.199614	+	0.0124238i
$76$	0.763154	−	0.440607i	0.0875398	−	0.0505411i
$77$	−14.6847	−	4.09070i	−1.67347	−	0.466178i
$78$	4.53855	+	6.84105i	0.513889	+	0.774596i
$79$	5.15417	−	8.92729i	0.579889	−	1.00440i	−0.415602	−	0.909547i	$-0.636429\pi$
$79$	5.15417	−	8.92729i	0.579889	−	1.00440i	0.995491	−	0.0948515i	$-0.0302376\pi$
$80$	−3.33158			−0.372481
$81$	−6.27964	−	6.44718i	−0.697738	−	0.716353i
$82$			14.5812i			1.61022i
$83$	−1.69417	+	2.93439i	−0.185959	+	0.322091i	−0.943899	−	0.330233i	$-0.892873\pi$
$83$	−1.69417	+	2.93439i	−0.185959	+	0.322091i	0.757940	+	0.652324i	$0.226206\pi$
$84$	−0.278008	+	1.30739i	−0.0303332	+	0.142648i
$85$	−2.46216	−	4.26459i	−0.267059	−	0.462560i
$86$	0.308320	−	0.178009i	0.0332470	−	0.0191952i
$87$	0.889887	+	14.2979i	0.0954059	+	1.53289i
$88$	−8.62884	+	14.9456i	−0.919838	+	1.59321i
$89$	4.68832			0.496961			0.248481	−	0.968637i	$-0.420069\pi$
$89$	4.68832			0.496961			0.248481	+	0.968637i	$0.420069\pi$
$90$	−3.61266	−	1.52435i	−0.380808	−	0.160680i
$91$	6.85113	−	6.71705i	0.718194	−	0.704138i
$92$	1.73157	+	0.999720i	0.180528	+	0.104228i
$93$	−5.70659	−	2.83756i	−0.591746	−	0.294241i
$94$	4.26126	−	2.46024i	0.439515	−	0.253754i
$95$	2.61645	−	1.51061i	0.268443	−	0.154985i
$96$	2.53744	+	1.26172i	0.258976	+	0.128774i
$97$	−4.00495	−	2.31226i	−0.406642	−	0.234775i	0.282704	−	0.959207i	$-0.408769\pi$
$97$	−4.00495	−	2.31226i	−0.406642	−	0.234775i	−0.689346	+	0.724433i	$0.742102\pi$
$98$	−9.14742	−	0.180814i	−0.924029	−	0.0182650i
$99$	−13.7819	+	10.4319i	−1.38514	+	1.04844i
$100$	0.291675			0.0291675
$101$	4.98278	−	8.63043i	0.495805	−	0.858760i	−0.504183	−	0.863597i	$-0.668206\pi$
$101$	4.98278	−	8.63043i	0.495805	−	0.858760i	0.999988	+	0.00483690i	$0.00153964\pi$
$102$	−0.692496	−	11.1264i	−0.0685673	−	1.10167i
$103$	8.37044	−	4.83267i	0.824763	−	0.476177i	−0.0272929	−	0.999627i	$-0.508689\pi$
$103$	8.37044	−	4.83267i	0.824763	−	0.476177i	0.852056	+	0.523450i	$0.175355\pi$
$104$	−5.43109	−	9.40692i	−0.532562	−	0.922425i
$105$	−0.953143	+	4.48236i	−0.0930172	+	0.437433i
$106$	2.29668	−	3.97797i	0.223073	−	0.386374i
$107$		−	9.46949i		−	0.915450i	−0.889094	−	0.457725i	$-0.848664\pi$
$107$		−	9.46949i		−	0.915450i	0.889094	−	0.457725i	$-0.151336\pi$
$108$	0.987998	+	1.14929i	0.0950702	+	0.110590i
$109$	−8.33627			−0.798470			−0.399235	−	0.916849i	$-0.630724\pi$
$109$	−8.33627			−0.798470			−0.399235	+	0.916849i	$0.630724\pi$
$110$	−3.76530	+	6.52169i	−0.359007	+	0.621819i
$111$	2.68962	+	4.05412i	0.255287	+	0.384800i
$112$	−2.36539	+	8.49121i	−0.223508	+	0.802344i
$113$	4.68004	−	2.70202i	0.440261	−	0.254185i	−0.263447	−	0.964674i	$-0.584859\pi$
$113$	4.68004	−	2.70202i	0.440261	−	0.254185i	0.703708	+	0.710489i	$0.251526\pi$
$114$	6.82636	−	0.424867i	0.639347	−	0.0397924i
$115$	5.93663	+	3.42751i	0.553594	+	0.319617i
$116$		−	2.41240i		−	0.223986i
$117$	−1.34901	−	10.7953i	−0.124716	−	0.998027i
$118$		−	11.3420i		−	1.04412i
$119$	−12.6173	+	3.24751i	−1.15663	+	0.297699i
$120$	4.64539	+	2.30989i	0.424064	+	0.210863i
$121$	11.0981	+	19.2225i	1.00892	+	1.74750i
$122$	5.89457	+	10.2097i	0.533670	+	0.924343i
$123$	8.60321	−	17.3018i	0.775725	−	1.56005i
$124$	0.929443	+	0.536614i	0.0834664	+	0.0481894i
$125$	1.00000			0.0894427
$126$	−6.45007	+	8.12534i	−0.574618	+	0.723863i
$127$	9.75881			0.865955			0.432977	−	0.901405i	$-0.357463\pi$
$127$	9.75881			0.865955			0.432977	+	0.901405i	$0.357463\pi$
$128$	7.12888	+	4.11586i	0.630110	+	0.363794i
$129$	−0.470877	+	0.0293070i	−0.0414584	+	0.00258033i
$130$	−2.36992	−	4.10482i	−0.207856	−	0.360017i
$131$	8.91007	+	15.4327i	0.778476	+	1.34836i	0.932820	+	0.360343i	$0.117340\pi$
$131$	8.91007	+	15.4327i	0.778476	+	1.34836i	−0.154344	+	0.988017i	$0.549326\pi$
$132$	2.42550	−	1.60915i	0.211113	−	0.140059i
$133$	−1.99244	−	7.74110i	−0.172767	−	0.671238i
$134$		−	4.33636i		−	0.374604i
$135$	3.38733	+	3.94031i	0.291535	+	0.339128i
$136$			14.7498i			1.26478i
$137$	1.19435	+	0.689559i	0.102040	+	0.0589130i	0.550152	−	0.835065i	$-0.314570\pi$
$137$	1.19435	+	0.689559i	0.102040	+	0.0589130i	−0.448111	+	0.893978i	$0.647903\pi$
$138$	8.57921	+	12.9316i	0.730311	+	1.10081i
$139$	10.5156	−	6.07121i	0.891926	−	0.514954i	0.0173539	−	0.999849i	$-0.494476\pi$
$139$	10.5156	−	6.07121i	0.891926	−	0.514954i	0.874572	+	0.484896i	$0.161142\pi$
$140$	0.207087	−	0.743394i	0.0175020	−	0.0628283i
$141$	−6.50793	+	0.405048i	−0.548067	+	0.0341112i
$142$	−4.54416	+	7.87072i	−0.381338	+	0.660496i
$143$	−20.8941			−1.74725
$144$	6.03208	+	7.96922i	0.502674	+	0.664102i
$145$		−	8.27085i		−	0.686856i
$146$	−1.88298	+	3.26142i	−0.155837	+	0.269917i
$147$	10.7475	+	5.61172i	0.886438	+	0.462847i
$148$	−0.409644	−	0.709525i	−0.0336726	−	0.0583226i
$149$	5.61055	−	3.23925i	0.459634	−	0.265370i	−0.252256	−	0.967661i	$-0.581173\pi$
$149$	5.61055	−	3.23925i	0.459634	−	0.265370i	0.711891	+	0.702290i	$0.247839\pi$
$150$	2.02707	+	1.00795i	0.165510	+	0.0822986i
$151$	−9.46471	+	16.3934i	−0.770227	+	1.33407i	0.167212	+	0.985921i	$0.446524\pi$
$151$	−9.46471	+	16.3934i	−0.770227	+	1.33407i	−0.937438	+	0.348151i	$0.886810\pi$
$152$	−9.04942			−0.734005
$153$	−5.74309	+	13.6110i	−0.464301	+	1.10038i
$154$	13.9486	+	14.2270i	1.12401	+	1.14644i
$155$	3.18657	+	1.83977i	0.255951	+	0.147774i
$156$	0.113805	+	1.82852i	0.00911172	+	0.146399i
$157$	0.754717	−	0.435736i	0.0602330	−	0.0347755i	−0.469581	−	0.882889i	$-0.655595\pi$
$157$	0.754717	−	0.435736i	0.0602330	−	0.0347755i	0.529814	+	0.848114i	$0.322262\pi$
$158$	−11.6682	+	6.73665i	−0.928274	+	0.535939i
$159$	−5.07229	+	3.36510i	−0.402259	+	0.266870i
$160$	−1.41691	−	0.818053i	−0.112016	−	0.0646727i
$161$	12.9507	−	12.6972i	1.02066	−	1.00068i
$162$	2.89473	+	11.4015i	0.227431	+	0.895789i
$163$	10.7991			0.845849			0.422924	−	0.906165i	$-0.361004\pi$
$163$	10.7991			0.845849			0.422924	+	0.906165i	$0.361004\pi$
$164$	−1.62696	+	2.81798i	−0.127044	+	0.220047i
$165$	8.31578	−	5.51693i	0.647382	−	0.429492i
$166$	3.83533	−	2.21433i	0.297679	−	0.171865i
$167$	3.22089	+	5.57874i	0.249240	+	0.431696i	0.963315	−	0.268373i	$-0.0864859\pi$
$167$	3.22089	+	5.57874i	0.249240	+	0.431696i	−0.714075	+	0.700069i	$0.753153\pi$
$168$	9.18542	−	10.1997i	0.708670	−	0.786927i
$169$	0.0754780	−	0.130732i	0.00580600	−	0.0100563i
$170$			6.43624i			0.493637i
$171$	−8.35072	−	3.52355i	−0.638596	−	0.269453i
$172$	0.0794484			0.00605788
$173$	2.37437	−	4.11252i	0.180520	−	0.312669i	−0.761538	−	0.648120i	$-0.775555\pi$
$173$	2.37437	−	4.11252i	0.180520	−	0.312669i	0.942058	+	0.335451i	$0.108889\pi$
$174$	8.33658	−	16.7656i	0.631994	−	1.27100i
$175$	0.709992	−	2.54871i	0.0536703	−	0.192664i
$176$	16.6236	−	9.59763i	1.25305	−	0.723448i
$177$	−6.69202	+	13.4582i	−0.503003	+	1.01158i
$178$	−5.30681	−	3.06389i	−0.397762	−	0.229648i
$179$			19.6922i			1.47186i	0.677056	+	0.735932i	$0.263256\pi$
$179$			19.6922i			1.47186i	−0.677056	+	0.735932i	$0.736744\pi$
$180$	−0.528101	−	0.697695i	−0.0393623	−	0.0520031i
$181$			26.6033i			1.97741i	0.149883	+	0.988704i	$0.452110\pi$
$181$			26.6033i			1.97741i	−0.149883	+	0.988704i	$0.547890\pi$
$182$	−12.1446	+	3.12585i	−0.900219	+	0.231703i
$183$	−0.970470	−	15.5926i	−0.0717392	−	1.15264i
$184$	−10.2664	−	17.7819i	−0.756848	−	1.31090i
$185$	−1.40446	−	2.43259i	−0.103258	−	0.178847i
$186$	4.60501	+	6.94123i	0.337656	+	0.508956i
$187$	24.5710	+	14.1860i	1.79681	+	1.03739i
$188$	1.09805			0.0800833
$189$	12.4477	−	5.83572i	0.905434	−	0.424486i
$190$	−3.94882			−0.286478
$191$	−9.69208	−	5.59572i	−0.701294	−	0.404892i	0.106535	−	0.994309i	$-0.466024\pi$
$191$	−9.69208	−	5.59572i	−0.701294	−	0.404892i	−0.807829	+	0.589417i	$0.799358\pi$
$192$	−8.42780	−	12.7034i	−0.608224	−	0.916788i
$193$	−0.463712	−	0.803173i	−0.0333787	−	0.0578137i	0.848853	−	0.528628i	$-0.177293\pi$
$193$	−0.463712	−	0.803173i	−0.0333787	−	0.0578137i	−0.882232	+	0.470815i	$0.843960\pi$
$194$	3.02219	+	5.23459i	0.216981	+	0.375822i
$195$	0.390179	+	6.26902i	0.0279413	+	0.448934i
$196$	−1.74767	−	1.05561i	−0.124833	−	0.0754005i
$197$			7.07291i			0.503924i	0.967737	+	0.251962i	$0.0810758\pi$
$197$			7.07291i			0.503924i	−0.967737	+	0.251962i	$0.918924\pi$
$198$	22.4174	−	2.80134i	1.59314	−	0.199082i
$199$		−	4.14124i		−	0.293565i	−0.989169	−	0.146782i	$-0.953108\pi$
$199$		−	4.14124i		−	0.293565i	0.989169	−	0.146782i	$-0.0468917\pi$
$200$	−2.59399	−	1.49764i	−0.183423	−	0.105899i
$201$	−2.55854	+	5.14545i	−0.180466	+	0.362932i
$202$	−11.2802	+	6.51264i	−0.793674	+	0.458228i
$203$	−21.0800	−	5.87223i	−1.47952	−	0.412150i
$204$	1.10764	−	2.22756i	0.0775504	−	0.155961i
$205$	−5.57799	+	9.66136i	−0.389584	+	0.674779i
$206$	−12.6329			−0.880175
$207$	−2.55003	−	20.4064i	−0.177239	−	1.41834i
$208$			12.0817i			0.837716i
$209$	−8.70356	+	15.0750i	−0.602038	+	1.04276i
$210$	4.00817	−	4.45078i	0.276590	−	0.307133i
$211$	−7.38983	−	12.7996i	−0.508737	−	0.881159i	−0.999949	−	0.0101183i	$-0.996779\pi$
$211$	−7.38983	−	12.7996i	−0.508737	−	0.881159i	0.491212	−	0.871040i	$-0.336554\pi$
$212$	0.887718	−	0.512524i	0.0609687	−	0.0352003i
$213$	10.0359	−	6.65812i	0.687650	−	0.456207i
$214$	−6.18845	+	10.7187i	−0.423034	+	0.732716i
$215$	0.272387			0.0185766
$216$	−2.88553	−	15.2941i	−0.196335	−	1.04063i
$217$	6.95147	−	6.81542i	0.471896	−	0.462661i
$218$	9.43599	+	5.44787i	0.639086	+	0.368977i
$219$	4.15862	−	2.75895i	0.281013	−	0.186432i
$220$	−1.45537	+	0.840260i	−0.0981212	+	0.0566503i
$221$	−15.4652	+	8.92886i	−1.04030	+	0.600620i
$222$	−0.395010	−	6.34664i	−0.0265113	−	0.425959i
$223$	5.55505	+	3.20721i	0.371994	+	0.214771i	0.674329	−	0.738431i	$-0.264433\pi$
$223$	5.55505	+	3.20721i	0.371994	+	0.214771i	−0.302335	+	0.953202i	$0.597766\pi$
$224$	−3.09097	+	3.03048i	−0.206524	+	0.202482i
$225$	−1.81058	−	2.39203i	−0.120705	−	0.159469i
$226$	−7.06324			−0.469840
$227$	2.28750	−	3.96207i	0.151827	−	0.262972i	−0.780072	−	0.625690i	$-0.784818\pi$
$227$	2.28750	−	3.96207i	0.151827	−	0.262972i	0.931899	+	0.362718i	$0.118151\pi$
$228$	1.36668	+	0.679570i	0.0905103	+	0.0450056i
$229$	−5.09205	+	2.93990i	−0.336492	+	0.194274i	−0.658720	−	0.752388i	$-0.728902\pi$
$229$	−5.09205	+	2.93990i	−0.336492	+	0.194274i	0.322227	+	0.946662i	$0.395568\pi$
$230$	−4.47986	−	7.75935i	−0.295393	−	0.511636i
$231$	−8.15690	−	25.1115i	−0.536685	−	1.65221i
$232$	−12.3868	+	21.4545i	−0.813232	+	1.40856i
$233$		−	9.82356i		−	0.643563i	−0.946814	−	0.321781i	$-0.895718\pi$
$233$		−	9.82356i		−	0.643563i	0.946814	−	0.321781i	$-0.104282\pi$
$234$	−5.52792	+	13.1010i	−0.361372	+	0.856441i
$235$	3.76463			0.245577
$236$	1.26553	−	2.19197i	0.0823792	−	0.142685i
$237$	17.8201	−	1.10911i	1.15754	−	0.0720443i
$238$	16.4041	+	4.56968i	1.06332	+	0.296208i
$239$	15.9544	−	9.21127i	1.03200	−	0.595827i	0.114445	−	0.993430i	$-0.463491\pi$
$239$	15.9544	−	9.21127i	1.03200	−	0.595827i	0.917558	+	0.397602i	$0.130158\pi$
$240$	−3.19009	−	4.80848i	−0.205919	−	0.310386i
$241$	−3.82945	−	2.21093i	−0.246677	−	0.142419i	0.371565	−	0.928407i	$-0.378821\pi$
$241$	−3.82945	−	2.21093i	−0.246677	−	0.142419i	−0.618241	+	0.785988i	$0.712155\pi$
$242$		−	29.0111i		−	1.86490i
$243$	3.29230	−	15.2368i	0.211201	−	0.977443i
$244$			2.63085i			0.168423i
$245$	−5.99182	−	3.61912i	−0.382804	−	0.231217i
$246$	−21.0451	+	13.9619i	−1.34179	+	0.890181i
$247$	−5.47812	−	9.48838i	−0.348564	−	0.603731i
$248$	−5.51063	−	9.54469i	−0.349925	−	0.606088i
$249$	−5.85744	+	0.364562i	−0.371200	+	0.0231032i
$250$	−1.13192	−	0.653515i	−0.0715889	−	0.0413319i
$251$	11.0078			0.694809			0.347405	−	0.937715i	$-0.387063\pi$
$251$	11.0078			0.694809			0.347405	+	0.937715i	$0.387063\pi$
$252$	−2.15317	+	0.850617i	−0.135637	+	0.0535839i
$253$	−39.4960			−2.48309
$254$	−11.0462	−	6.37753i	−0.693100	−	0.400162i
$255$	3.79752	−	7.63714i	0.237810	−	0.478256i
$256$	3.42204	+	5.92715i	0.213877	+	0.370447i
$257$	−2.36224	−	4.09152i	−0.147352	−	0.255222i	0.782896	−	0.622153i	$-0.213742\pi$
$257$	−2.36224	−	4.09152i	−0.147352	−	0.255222i	−0.930248	+	0.366931i	$0.880408\pi$
$258$	0.552147	+	0.274552i	0.0343752	+	0.0170928i
$259$	−7.19711	+	1.85243i	−0.447206	+	0.115104i
$260$		−	1.05774i		−	0.0655981i
$261$	−19.7841	+	14.9750i	−1.22461	+	0.926931i
$262$		−	23.2914i		−	1.43895i
$263$	3.45803	+	1.99649i	0.213231	+	0.123109i	0.602812	−	0.797883i	$-0.294047\pi$
$263$	3.45803	+	1.99649i	0.213231	+	0.123109i	−0.389581	+	0.920992i	$0.627380\pi$
$264$	−29.8335	+	1.85681i	−1.83612	+	0.114279i
$265$	3.04352	−	1.75718i	0.186962	−	0.107942i
$266$	−2.80363	+	10.0644i	−0.171902	+	0.617088i
$267$	4.48922	+	6.76669i	0.274735	+	0.414114i
$268$	0.483848	−	0.838049i	0.0295557	−	0.0511920i
$269$	21.2854			1.29779			0.648896	−	0.760877i	$-0.275231\pi$
$269$	21.2854			1.29779			0.648896	+	0.760877i	$0.275231\pi$
$270$	−1.25914	−	6.67378i	−0.0766285	−	0.406153i
$271$			8.91274i			0.541411i	0.962662	+	0.270705i	$0.0872569\pi$
$271$			8.91274i			0.541411i	−0.962662	+	0.270705i	$0.912743\pi$
$272$	8.20289	−	14.2078i	0.497373	−	0.861476i
$273$	16.2549	+	3.45650i	0.983793	+	0.209197i
$274$	−0.901273	−	1.56105i	−0.0544479	−	0.0943066i
$275$	−4.98971	+	2.88081i	−0.300891	+	0.173719i
$276$	0.215126	+	3.45644i	0.0129491	+	0.208053i
$277$	13.7461	−	23.8089i	0.825922	−	1.43054i	−0.0752903	−	0.997162i	$-0.523988\pi$
$277$	13.7461	−	23.8089i	0.825922	−	1.43054i	0.901212	−	0.433378i	$-0.142678\pi$
$278$	−15.8705			−0.951850
$279$	−1.36876	−	10.9534i	−0.0819458	−	0.655763i
$280$	−5.65877	+	5.54802i	−0.338176	+	0.331558i
$281$	−3.43914	−	1.98559i	−0.205162	−	0.118450i	0.393899	−	0.919154i	$-0.371126\pi$
$281$	−3.43914	−	1.98559i	−0.205162	−	0.118450i	−0.599061	+	0.800703i	$0.704459\pi$
$282$	7.63117	+	3.79455i	0.454429	+	0.225962i
$283$	−1.02668	+	0.592756i	−0.0610300	+	0.0352357i	−0.530205	−	0.847870i	$-0.677885\pi$
$283$	−1.02668	+	0.592756i	−0.0610300	+	0.0352357i	0.469175	+	0.883105i	$0.344552\pi$
$284$	−1.75642	+	1.01407i	−0.104224	+	0.0601740i
$285$	4.68561	+	2.32989i	0.277552	+	0.138011i
$286$	23.6504	+	13.6546i	1.39848	+	0.807412i
$287$	20.6637	+	21.0762i	1.21974	+	1.24409i
$288$	0.608621	+	4.87044i	0.0358634	+	0.286993i
$289$	7.24902			0.426413
$290$	−5.40512	+	9.36194i	−0.317399	+	0.549752i
$291$	−0.497567	−	7.99444i	−0.0291679	−	0.468642i
$292$	−0.727814	+	0.420204i	−0.0425921	+	0.0245906i
$293$	13.7335	+	23.7871i	0.802318	+	1.38966i	0.918087	+	0.396379i	$0.129733\pi$
$293$	13.7335	+	23.7871i	0.802318	+	1.38966i	−0.115769	+	0.993276i	$0.536933\pi$
$294$	−8.49797	−	13.3757i	−0.495612	−	0.780084i
$295$	4.33885	−	7.51511i	0.252618	−	0.437546i
$296$			8.41349i			0.489024i
$297$	−28.2530	−	9.90274i	−1.63941	−	0.574615i
$298$	−8.46760			−0.490515
$299$	12.4296	−	21.5287i	0.718824	−	1.24504i
$300$	0.279288	+	0.420976i	0.0161247	+	0.0243051i
$301$	0.193392	−	0.694234i	0.0111469	−	0.0400150i
$302$	21.4266	−	12.3706i	1.23296	−	0.711851i
$303$	17.2275	−	1.07223i	0.989696	−	0.0615978i
$304$	8.71692	+	5.03271i	0.499949	+	0.288646i
$305$			9.01980i			0.516473i
$306$	15.3957	−	11.6533i	0.880112	−	0.666177i
$307$		−	7.49498i		−	0.427761i	−0.976860	−	0.213881i	$-0.931390\pi$
$307$		−	7.49498i		−	0.427761i	0.976860	−	0.213881i	$-0.0686104\pi$
$308$	1.10827	+	4.30590i	0.0631498	+	0.245351i
$309$	14.9900	+	7.45367i	0.852750	+	0.424024i
$310$	−2.40463	−	4.16494i	−0.136574	−	0.236553i
$311$	9.95114	+	17.2359i	0.564278	+	0.977357i	0.997116	+	0.0758862i	$0.0241786\pi$
$311$	9.95114	+	17.2359i	0.564278	+	0.977357i	−0.432839	+	0.901471i	$0.642488\pi$
$312$	8.37663	−	16.8461i	0.474234	−	0.953725i
$313$	−28.3246	−	16.3532i	−1.60100	−	0.924339i	−0.991287	−	0.131718i	$-0.957951\pi$
$313$	−28.3246	−	16.3532i	−1.60100	−	0.924339i	−0.609715	−	0.792621i	$-0.708716\pi$
$314$	−1.13904			−0.0642797
$315$	−7.38208	+	2.91632i	−0.415933	+	0.164316i
$316$	−3.00669			−0.169139
$317$	−7.62204	−	4.40059i	−0.428097	−	0.247162i	0.270439	−	0.962737i	$-0.412831\pi$
$317$	−7.62204	−	4.40059i	−0.428097	−	0.247162i	−0.698535	+	0.715575i	$0.746165\pi$
$318$	7.94057	−	0.494214i	0.445285	−	0.0277142i
$319$	23.8267	+	41.2691i	1.33404	+	2.31063i
$320$	4.40079	+	7.62240i	0.246012	+	0.426105i
$321$	13.6674	−	9.06734i	0.762839	−	0.506089i
$322$	−22.9570	+	5.90879i	−1.27934	+	0.329284i
$323$			14.8775i			0.827806i
$324$	−0.712737	+	2.52646i	−0.0395965	+	0.140359i
$325$		−	3.62642i		−	0.201158i
$326$	−12.2237	−	7.05735i	−0.677007	−	0.390870i
$327$	−7.98224	−	12.0318i	−0.441419	−	0.665360i
$328$	28.9385	−	16.7077i	1.59786	−	0.922527i
$329$	2.67285	−	9.59493i	0.147359	−	0.528986i
$330$	−13.0182	+	0.810241i	−0.716628	+	0.0446023i
$331$	7.15743	−	12.3970i	0.393408	−	0.681402i	−0.599489	−	0.800383i	$-0.704629\pi$
$331$	7.15743	−	12.3970i	0.393408	−	0.681402i	0.992897	+	0.118981i	$0.0379628\pi$
$332$	0.988293			0.0542396
$333$	−3.27594	+	7.76389i	−0.179520	+	0.425459i
$334$		−	8.41959i		−	0.460700i
$335$	1.65886	−	2.87323i	0.0906332	−	0.156981i
$336$	−14.5204	+	4.71662i	−0.792151	+	0.257313i
$337$	−13.5173	−	23.4126i	−0.736332	−	1.27536i	−0.954136	−	0.299372i	$-0.903223\pi$
$337$	−13.5173	−	23.4126i	−0.736332	−	1.27536i	0.217804	−	0.975993i	$-0.430111\pi$
$338$	−0.170870	+	0.0986520i	−0.00929412	+	0.00536596i
$339$	8.38113	+	4.16746i	0.455201	+	0.226345i
$340$	−0.718152	+	1.24388i	−0.0389473	+	0.0674586i
$341$	−21.2001			−1.14805
$342$	7.14966	+	9.44570i	0.386609	+	0.510765i
$343$	−13.4782	+	12.7019i	−0.727756	+	0.685836i
$344$	−0.706569	−	0.407938i	−0.0380957	−	0.0219945i
$345$	0.737555	+	11.8503i	0.0397086	+	0.638000i
$346$	−5.37519	+	3.10337i	−0.288972	+	0.166838i
$347$	8.99376	−	5.19255i	0.482811	−	0.278751i	−0.238776	−	0.971075i	$-0.576746\pi$
$347$	8.99376	−	5.19255i	0.482811	−	0.278751i	0.721587	+	0.692324i	$0.243413\pi$
$348$	3.48183	−	2.30995i	0.186646	−	0.123826i
$349$	0.871278	+	0.503033i	0.0466385	+	0.0269267i	0.523138	−	0.852248i	$-0.324761\pi$
$349$	0.871278	+	0.503033i	0.0466385	+	0.0269267i	−0.476499	+	0.879175i	$0.658095\pi$
$350$	−2.46927	+	2.42094i	−0.131988	+	0.129405i
$351$	14.2892	−	12.2839i	0.762703	−	0.655665i
$352$	9.42661			0.502440
$353$	−3.86581	+	6.69578i	−0.205756	+	0.356381i	−0.950373	−	0.311111i	$-0.899299\pi$
$353$	−3.86581	+	6.69578i	−0.205756	+	0.356381i	0.744617	+	0.667492i	$0.232632\pi$
$354$	16.3700	−	10.8603i	0.870055	−	0.577220i
$355$	−6.02184	+	3.47671i	−0.319606	+	0.184525i
$356$	−0.683733	−	1.18426i	−0.0362378	−	0.0627657i
$357$	−16.7686	−	15.1011i	−0.887490	−	0.799233i
$358$	12.8691	−	22.2900i	0.680155	−	1.17806i
$359$		−	19.0140i		−	1.00352i	−0.865007	−	0.501760i	$-0.832686\pi$
$359$		−	19.0140i		−	1.00352i	0.865007	−	0.501760i	$-0.167314\pi$
$360$	1.11423	+	8.91651i	0.0587250	+	0.469941i
$361$	9.87222			0.519591
$362$	17.3856	−	30.1128i	0.913769	−	1.58269i
$363$	−17.1171	+	34.4241i	−0.898417	+	1.80680i
$364$	−2.69586	−	0.750985i	−0.141302	−	0.0393623i
$365$	−2.49529	+	1.44066i	−0.130610	+	0.0754074i
$366$	−9.09149	+	18.2838i	−0.475220	+	0.955709i
$367$	9.92332	+	5.72923i	0.517993	+	0.299063i	0.736113	−	0.676859i	$-0.236659\pi$
$367$	9.92332	+	5.72923i	0.517993	+	0.299063i	−0.218120	+	0.975922i	$0.569992\pi$
$368$			22.8380i			1.19052i
$369$	33.2097	−	4.14996i	1.72883	−	0.216038i
$370$			3.67133i			0.190863i
$371$	−2.31766	−	9.00462i	−0.120327	−	0.467497i
$372$	0.115472	+	1.85530i	0.00598695	+	0.0961926i
$373$	−7.14969	−	12.3836i	−0.370197	−	0.641200i	0.619399	−	0.785076i	$-0.287376\pi$
$373$	−7.14969	−	12.3836i	−0.370197	−	0.641200i	−0.989596	+	0.143877i	$0.954043\pi$
$374$	−18.5416	−	32.1149i	−0.958762	−	1.66062i
$375$	0.957531	+	1.44331i	0.0494467	+	0.0745320i
$376$	−9.76542	−	5.63807i	−0.503613	−	0.290761i
$377$	−29.9936			−1.54475
$378$	−17.9035	−	1.52916i	−0.920856	−	0.0786515i
$379$	6.30700			0.323969			0.161984	−	0.986793i	$-0.448211\pi$
$379$	6.30700			0.323969			0.161984	+	0.986793i	$0.448211\pi$
$380$	−0.763154	−	0.440607i	−0.0391490	−	0.0226027i
$381$	9.34437	+	14.0850i	0.478727	+	0.721594i
$382$	7.31377	+	12.6678i	0.374205	+	0.648142i
$383$	14.9406	+	25.8780i	0.763432	+	1.32230i	0.941072	+	0.338207i	$0.109820\pi$
$383$	14.9406	+	25.8780i	0.763432	+	1.32230i	−0.177640	+	0.984095i	$0.556846\pi$
$384$	0.885677	+	14.2302i	0.0451970	+	0.726183i
$385$	3.79969	+	14.7627i	0.193650	+	0.752374i
$386$			1.21217i			0.0616979i
$387$	−0.493178	−	0.651557i	−0.0250696	−	0.0331205i
$388$			1.34886i			0.0684779i
$389$	−6.79001	−	3.92022i	−0.344267	−	0.198763i	0.317890	−	0.948128i	$-0.397026\pi$
$389$	−6.79001	−	3.92022i	−0.344267	−	0.198763i	−0.662158	+	0.749365i	$0.730359\pi$
$390$	3.65525	−	7.35102i	0.185091	−	0.372233i
$391$	−29.2339	+	16.8782i	−1.47842	+	0.853568i
$392$	10.1226	+	18.3616i	0.511269	+	0.927400i
$393$	−13.7424	+	27.6372i	−0.693214	+	1.39411i
$394$	4.62225	−	8.00598i	0.232866	−	0.403335i
$395$	−10.3083			−0.518669
$396$	4.64499	+	1.95993i	0.233420	+	0.0984904i
$397$		−	0.325200i		−	0.0163213i	−0.999967	−	0.00816066i	$-0.997402\pi$
$397$		−	0.325200i		−	0.0163213i	0.999967	−	0.00816066i	$-0.00259765\pi$
$398$	−2.70636	+	4.68756i	−0.135658	+	0.234966i
$399$	9.26495	−	10.2881i	0.463828	−	0.515047i
$400$	1.66579	+	2.88523i	0.0832894	+	0.144261i
$401$	−0.562380	+	0.324690i	−0.0280839	+	0.0162142i	−0.513976	−	0.857804i	$-0.671828\pi$
$401$	−0.562380	+	0.324690i	−0.0280839	+	0.0162142i	0.485892	+	0.874019i	$0.338495\pi$
$402$	6.25869	−	4.15220i	0.312155	−	0.207093i
$403$	6.67178	−	11.5559i	0.332345	−	0.575638i
$404$	−2.90671			−0.144614
$405$	−2.44360	+	8.66192i	−0.121423	+	0.430414i
$406$	20.0233	+	20.4230i	0.993738	+	1.01357i
$407$	14.0156	+	8.09193i	0.694729	+	0.401102i
$408$	−21.2884	+	14.1234i	−1.05394	+	0.699211i
$409$	−18.7974	+	10.8527i	−0.929470	+	0.536630i	−0.886644	−	0.462453i	$-0.846969\pi$
$409$	−18.7974	+	10.8527i	−0.929470	+	0.536630i	−0.0428259	+	0.999083i	$0.513636\pi$
$410$	12.6277	−	7.29060i	0.623637	−	0.360057i
$411$	0.148384	+	2.38409i	0.00731923	+	0.117598i
$412$	−2.44145	−	1.40957i	−0.120281	−	0.0694445i
$413$	−16.0733	−	16.3941i	−0.790914	−	0.806702i
$414$	−10.4494	+	24.7649i	−0.513562	+	1.21713i
$415$	3.38834			0.166327
$416$	−2.96661	+	5.13831i	−0.145450	+	0.251927i
$417$	18.8317	+	9.36393i	0.922192	+	0.458554i
$418$	19.7035	−	11.3758i	0.963728	−	0.556409i
$419$	1.44983	+	2.51117i	0.0708287	+	0.122679i	0.899265	−	0.437405i	$-0.144102\pi$
$419$	1.44983	+	2.51117i	0.0708287	+	0.122679i	−0.828436	+	0.560084i	$0.810769\pi$
$420$	1.27124	−	0.412934i	0.0620301	−	0.0201491i
$421$	6.16736	−	10.6822i	0.300579	−	0.520618i	−0.675688	−	0.737187i	$-0.736153\pi$
$421$	6.16736	−	10.6822i	0.300579	−	0.520618i	0.976267	+	0.216569i	$0.0694868\pi$
$422$			19.3175i			0.940359i
$423$	−6.81616	−	9.00509i	−0.331413	−	0.437843i
$424$	−10.5265			−0.511212
$425$	−2.46216	+	4.26459i	−0.119433	+	0.206863i
$426$	−15.7110	+	0.977842i	−0.761203	+	0.0473766i
$427$	22.9888	+	6.40399i	1.11251	+	0.309911i
$428$	−2.39197	+	1.38101i	−0.115620	+	0.0667535i
$429$	−20.0067	−	30.1565i	−0.965934	−	1.45597i
$430$	−0.308320	−	0.178009i	−0.0148685	−	0.00858434i
$431$		−	25.3358i		−	1.22038i	−0.792254	−	0.610192i	$-0.791092\pi$
$431$		−	25.3358i		−	1.22038i	0.792254	−	0.610192i	$-0.208908\pi$
$432$	−5.72612	+	16.3369i	−0.275498	+	0.786011i
$433$		−	29.9796i		−	1.44073i	−0.693596	−	0.720365i	$-0.743974\pi$
$433$		−	29.9796i		−	1.44073i	0.693596	−	0.720365i	$-0.256026\pi$
$434$	−12.3225	+	3.17162i	−0.591498	+	0.152243i
$435$	11.9374	−	7.91959i	0.572353	−	0.379715i
$436$	1.21574	+	2.10572i	0.0582234	+	0.100846i
$437$	−10.3553	−	17.9359i	−0.495360	−	0.857989i
$438$	−6.51024	+	0.405192i	−0.311071	+	0.0193608i
$439$	−19.3472	−	11.1701i	−0.923391	−	0.533120i	−0.0386756	−	0.999252i	$-0.512314\pi$
$439$	−19.3472	−	11.1701i	−0.923391	−	0.533120i	−0.884715	+	0.466132i	$0.845647\pi$
$440$	17.2577			0.822728
$441$	2.19163	+	20.8853i	0.104363	+	0.994539i
$442$	23.3405			1.11020
$443$	11.3552	+	6.55595i	0.539504	+	0.311483i	0.744878	−	0.667201i	$-0.232508\pi$
$443$	11.3552	+	6.55595i	0.539504	+	0.311483i	−0.205374	+	0.978684i	$0.565841\pi$
$444$	0.631815	−	1.27063i	0.0299846	−	0.0603017i
$445$	−2.34416	−	4.06021i	−0.111124	−	0.192472i
$446$	−4.19192	−	7.26062i	−0.198493	−	0.343800i
$447$	10.0475	+	4.99606i	0.475231	+	0.236306i
$448$	22.5518	−	5.80450i	1.06547	−	0.274237i
$449$			29.0097i			1.36905i	0.728989	+	0.684526i	$0.239991\pi$
$449$			29.0097i			1.36905i	−0.728989	+	0.684526i	$0.760009\pi$
$450$	0.486207	+	3.89083i	0.0229200	+	0.183415i
$451$		−	64.2765i		−	3.02666i
$452$	−1.36505	−	0.788112i	−0.0642066	−	0.0370697i
$453$	−32.7234	+	2.03668i	−1.53748	+	0.0956914i
$454$	−5.17854	+	2.98983i	−0.243041	+	0.140320i
$455$	−9.24270	−	2.57473i	−0.433304	−	0.120705i
$456$	−8.66510	−	13.0611i	−0.405781	−	0.611642i
$457$	2.70505	−	4.68528i	0.126537	−	0.219168i	−0.795796	−	0.605565i	$-0.792947\pi$
$457$	2.70505	−	4.68528i	0.126537	−	0.219168i	0.922333	+	0.386397i	$0.126280\pi$
$458$	7.68507			0.359100
$459$	−25.1440	+	4.74389i	−1.17362	+	0.221426i
$460$		−	1.99944i		−	0.0932244i
$461$	6.99868	−	12.1221i	0.325961	−	0.564581i	−0.655745	−	0.754982i	$-0.727646\pi$
$461$	6.99868	−	12.1221i	0.325961	−	0.564581i	0.981706	+	0.190401i	$0.0609789\pi$
$462$	−7.17774	+	33.7548i	−0.333939	+	1.57042i
$463$	−5.11805	−	8.86472i	−0.237856	−	0.411978i	0.722243	−	0.691639i	$-0.243111\pi$
$463$	−5.11805	−	8.86472i	−0.237856	−	0.411978i	−0.960099	+	0.279661i	$0.909778\pi$
$464$	23.8633	−	13.7775i	1.10783	−	0.639603i
$465$	0.395893	+	6.36083i	0.0183591	+	0.294976i
$466$	−6.41984	+	11.1195i	−0.297393	+	0.515100i
$467$	−5.78707			−0.267794			−0.133897	−	0.990995i	$-0.542749\pi$
$467$	−5.78707			−0.267794			−0.133897	+	0.990995i	$0.542749\pi$
$468$	−2.53014	+	1.91512i	−0.116956	+	0.0885264i
$469$	−6.14525	−	6.26792i	−0.283761	−	0.289426i
$470$	−4.26126	−	2.46024i	−0.196557	−	0.113482i
$471$	1.35157	+	0.672057i	0.0622769	+	0.0309668i
$472$	−22.5099	+	12.9961i	−1.03610	+	0.598194i
$473$	−1.35913	+	0.784694i	−0.0624928	+	0.0360803i
$474$	−20.8957	−	10.3903i	−0.959773	−	0.477241i
$475$	−2.61645	−	1.51061i	−0.120051	−	0.0693116i
$476$	2.66039	+	2.71350i	0.121939	+	0.124373i
$477$	−9.71375	−	4.09867i	−0.444762	−	0.187665i
$478$	−24.0788			−1.10134
$479$	−5.91876	+	10.2516i	−0.270435	+	0.468407i	−0.968973	−	0.247165i	$-0.920501\pi$
$479$	−5.91876	+	10.2516i	−0.270435	+	0.468407i	0.698538	+	0.715573i	$0.253834\pi$
$480$	−0.176034	−	2.82834i	−0.00803481	−	0.129096i
$481$	−8.82160	+	5.09315i	−0.402230	+	0.232228i
$482$	2.88975	+	5.00520i	0.131625	+	0.227981i
$483$	30.7267	+	6.53382i	1.39811	+	0.297299i
$484$	3.23704	−	5.60672i	0.147138	−	0.254851i
$485$			4.62452i			0.209989i
$486$	−13.6841	+	15.0953i	−0.620724	+	0.684737i
$487$	20.5456			0.931012			0.465506	−	0.885045i	$-0.345872\pi$
$487$	20.5456			0.931012			0.465506	+	0.885045i	$0.345872\pi$
$488$	13.5084	−	23.3973i	0.611499	−	1.05915i
$489$	10.3404	+	15.5864i	0.467611	+	0.704840i
$490$	4.41712	+	8.01230i	0.199545	+	0.361959i
$491$	6.02013	−	3.47573i	0.271685	−	0.156857i	−0.357968	−	0.933734i	$-0.616530\pi$
$491$	6.02013	−	3.47573i	0.271685	−	0.156857i	0.629653	+	0.776876i	$0.283197\pi$
$492$	−5.62507	+	0.350100i	−0.253598	+	0.0157837i
$493$	35.2718	+	20.3642i	1.58856	+	0.917157i
$494$			14.3201i			0.644292i
$495$	15.9252	+	6.71958i	0.715786	+	0.302023i
$496$			12.2586i			0.550429i
$497$	4.58567	+	17.8164i	0.205695	+	0.799173i
$498$	6.86840	+	3.41527i	0.307780	+	0.153042i
$499$	13.4054	+	23.2188i	0.600108	+	1.03942i	0.992804	+	0.119750i	$0.0382092\pi$
$499$	13.4054	+	23.2188i	0.600108	+	1.03942i	−0.392696	+	0.919668i	$0.628457\pi$
$500$	−0.145837	−	0.252598i	−0.00652205	−	0.0112965i
$501$	−4.96774	+	9.99055i	−0.221942	+	0.446345i
$502$	−12.4600	−	7.19379i	−0.556117	−	0.321075i
$503$	14.8532			0.662273			0.331137	−	0.943583i	$-0.392568\pi$
$503$	14.8532			0.662273			0.331137	+	0.943583i	$0.392568\pi$
$504$	23.5167	+	3.49080i	1.04752	+	0.155493i
$505$	−9.96556			−0.443462
$506$	44.7064	+	25.8112i	1.98744	+	1.14745i
$507$	0.260959	−	0.0162418i	0.0115896	−	0.000721326i
$508$	−1.42320	−	2.46506i	−0.0631443	−	0.109369i
$509$	−19.6497	−	34.0343i	−0.870958	−	1.50854i	−0.861007	−	0.508593i	$-0.830166\pi$
$509$	−19.6497	−	34.0343i	−0.870958	−	1.50854i	−0.00995035	−	0.999950i	$-0.503167\pi$
$510$	−9.28947	+	6.16290i	−0.411345	+	0.272898i
$511$	1.90018	+	7.38262i	0.0840589	+	0.326588i
$512$		−	25.4089i		−	1.12292i
$513$	−2.91051	−	15.4266i	−0.128502	−	0.681100i
$514$			6.17503i			0.272369i
$515$	−8.37044	−	4.83267i	−0.368845	−	0.212953i
$516$	0.0760743	+	0.114668i	0.00334899	+	0.00504799i
$517$	−18.7844	+	10.8452i	−0.826136	+	0.476970i
$518$	9.35714	+	2.60661i	0.411129	+	0.114528i
$519$	8.20916	−	0.510932i	0.360342	−	0.0224274i
$520$	−5.43109	+	9.40692i	−0.238169	+	0.412521i
$521$	39.4804			1.72967			0.864835	−	0.502056i	$-0.167423\pi$
$521$	39.4804			1.72967			0.864835	+	0.502056i	$0.167423\pi$
$522$	32.1804	−	4.02134i	1.40850	−	0.176009i
$523$		−	15.0977i		−	0.660177i	−0.943950	−	0.330089i	$-0.892921\pi$
$523$		−	15.0977i		−	0.660177i	0.943950	−	0.330089i	$-0.107079\pi$
$524$	2.59884	−	4.50133i	0.113531	−	0.196641i
$525$	4.35841	−	1.41573i	0.190216	−	0.0617876i
$526$	−2.60948	−	4.51974i	−0.113779	−	0.197070i
$527$	−15.6917	+	9.05962i	−0.683542	+	0.394643i
$528$	29.7699	+	14.8029i	1.29557	+	0.644213i
$529$	11.9957	−	20.7772i	0.521553	−	0.903356i
$530$	−4.59336			−0.199523
$531$	−25.8322	+	3.22805i	−1.12102	+	0.140086i
$532$	−1.66481	+	1.63223i	−0.0721788	+	0.0707661i
$533$	35.0362	+	20.2282i	1.51759	+	0.876179i
$534$	−0.659307	−	10.5931i	−0.0285310	−	0.458409i
$535$	−8.20082	+	4.73475i	−0.354552	+	0.204701i
$536$	−8.60614	+	4.96876i	−0.371729	+	0.214618i
$537$	−28.4219	+	18.8559i	−1.22649	+	0.813692i
$538$	−24.0933	−	13.9103i	−1.03874	−	0.599716i
$539$	40.3234	+	0.797061i	1.73685	+	0.0343319i
$540$	0.501314	−	1.43028i	0.0215731	−	0.0615493i
$541$	−36.6140			−1.57416			−0.787080	−	0.616851i	$-0.788408\pi$
$541$	−36.6140			−1.57416			−0.787080	+	0.616851i	$0.788408\pi$
$542$	5.82461	−	10.0885i	0.250188	−	0.433339i
$543$	−38.3967	+	25.4735i	−1.64776	+	1.09317i
$544$	6.97733	−	4.02836i	0.299150	−	0.172715i
$545$	4.16813	+	7.21942i	0.178543	+	0.309246i
$546$	−16.1404	−	14.5353i	−0.690746	−	0.622054i
$547$	13.0028	−	22.5215i	0.555960	−	0.962951i	−0.441868	−	0.897080i	$-0.645684\pi$
$547$	13.0028	−	22.5215i	0.555960	−	0.962951i	0.997828	−	0.0658711i	$-0.0209826\pi$
$548$		−	0.402254i		−	0.0171834i
$549$	21.5756	−	16.3311i	0.920825	−	0.696993i
$550$	7.53060			0.321106
$551$	−12.4940	+	21.6403i	−0.532264	+	0.921907i
$552$	15.8343	−	31.8443i	0.673955	−	1.35538i
$553$	−7.31884	+	26.2730i	−0.311229	+	1.11724i
$554$	−31.1189	+	17.9665i	−1.32212	+	0.763325i
$555$	2.16616	−	4.35634i	0.0919484	−	0.184916i
$556$	−3.06715	−	1.77082i	−0.130076	−	0.0750995i
$557$		−	5.40214i		−	0.228896i	−0.993429	−	0.114448i	$-0.963490\pi$
$557$		−	5.40214i		−	0.228896i	0.993429	−	0.114448i	$-0.0365099\pi$
$558$	−5.60888	+	13.2929i	−0.237443	+	0.562733i
$559$		−	0.987790i		−	0.0417791i
$560$	8.53630	−	2.19712i	0.360725	−	0.0928452i
$561$	3.05264	+	49.0470i	0.128883	+	2.07077i
$562$	2.59522	+	4.49506i	0.109473	+	0.189613i
$563$	−0.653430	−	1.13177i	−0.0275388	−	0.0476986i	0.851928	−	0.523660i	$-0.175434\pi$
$563$	−0.653430	−	1.13177i	−0.0275388	−	0.0476986i	−0.879466	+	0.475961i	$0.842100\pi$
$564$	1.05141	+	1.58482i	0.0442726	+	0.0667329i
$565$	−4.68004	−	2.70202i	−0.196891	−	0.113675i
$566$	1.54950			0.0651303
$567$	20.3418	+	12.3779i	0.854274	+	0.519823i
$568$	20.8275			0.873902
$569$	0.0109445	+	0.00631883i	0.000458818	+	0.000264899i	0.500229	−	0.865893i	$-0.333249\pi$
$569$	0.0109445	+	0.00631883i	0.000458818	+	0.000264899i	−0.499771	+	0.866158i	$0.666582\pi$
$570$	−3.78112	−	5.69936i	−0.158374	−	0.238720i
$571$	−1.19240	−	2.06530i	−0.0499004	−	0.0864301i	0.839996	−	0.542592i	$-0.182557\pi$
$571$	−1.19240	−	2.06530i	−0.0499004	−	0.0864301i	−0.889897	+	0.456162i	$0.849224\pi$
$572$	3.04714	+	5.27780i	0.127407	+	0.220676i
$573$	−1.20412	−	19.3467i	−0.0503030	−	0.808221i
$574$	−9.61605	−	37.3605i	−0.401366	−	1.55940i
$575$		−	6.85503i		−	0.285874i
$576$	10.2650	−	24.3278i	0.427709	−	1.01366i
$577$			14.0085i			0.583181i	0.956543	+	0.291590i	$0.0941844\pi$
$577$			14.0085i			0.583181i	−0.956543	+	0.291590i	$0.905816\pi$
$578$	−8.20531	−	4.73734i	−0.341296	−	0.197047i
$579$	0.715206	−	1.43834i	0.0297229	−	0.0597755i
$580$	−2.08920	+	1.20620i	−0.0867493	+	0.0500847i
$581$	2.40569	−	8.63588i	0.0998049	−	0.358277i
$582$	−4.66128	+	9.37424i	−0.193216	+	0.388575i
$583$	−10.1242	+	17.5356i	−0.419300	+	0.726250i
$584$	8.63036			0.357127
$585$	−8.67451	+	6.56593i	−0.358647	+	0.271468i
$586$		−	35.9001i		−	1.48302i
$587$	−22.1238	+	38.3196i	−0.913148	+	1.58162i	−0.103558	+	0.994623i	$0.533023\pi$
$587$	−22.1238	+	38.3196i	−0.913148	+	1.58162i	−0.809590	+	0.586996i	$0.800311\pi$
$588$	−0.149879	−	3.53319i	−0.00618091	−	0.145706i
$589$	−5.55834	−	9.62733i	−0.229028	−	0.396687i
$590$	−9.82246	+	5.67100i	−0.404384	+	0.233471i
$591$	−10.2084	+	6.77254i	−0.419917	+	0.278585i
$592$	4.67905	−	8.10435i	0.192308	−	0.333087i
$593$	−10.0021			−0.410736			−0.205368	−	0.978685i	$-0.565839\pi$
$593$	−10.0021			−0.410736			−0.205368	+	0.978685i	$0.565839\pi$
$594$	25.5086	+	29.6729i	1.04663	+	1.21749i
$595$	9.12109	+	9.30316i	0.373928	+	0.381393i
$596$	−1.63646	−	0.944809i	−0.0670319	−	0.0387009i
$597$	5.97708	−	3.96537i	0.244626	−	0.162292i
$598$	−28.1387	+	16.2459i	−1.15068	+	0.664343i
$599$	−23.6768	+	13.6698i	−0.967407	+	0.558532i	−0.898445	−	0.439087i	$-0.855302\pi$
$599$	−23.6768	+	13.6698i	−0.967407	+	0.558532i	−0.0689620	+	0.997619i	$0.521969\pi$
$600$	−0.322272	−	5.17797i	−0.0131567	−	0.211390i
$601$	34.6432	+	20.0013i	1.41313	+	0.815869i	0.995682	−	0.0928341i	$-0.0295926\pi$
$601$	34.6432	+	20.0013i	1.41313	+	0.815869i	0.417444	+	0.908703i	$0.362926\pi$
$602$	−0.672597	+	0.659433i	−0.0274130	+	0.0268765i
$603$	−9.87634	+	1.23417i	−0.402196	+	0.0502594i
$604$	5.52124			0.224656
$605$	11.0981	−	19.2225i	0.451202	−	0.781505i
$606$	−20.2009	−	10.0448i	−0.820606	−	0.408041i
$607$	19.4976	−	11.2569i	0.791381	−	0.456904i	−0.0490673	−	0.998795i	$-0.515625\pi$
$607$	19.4976	−	11.2569i	0.791381	−	0.456904i	0.840449	+	0.541891i	$0.182292\pi$
$608$	2.47152	+	4.28080i	0.100233	+	0.173609i
$609$	−11.7093	−	36.0477i	−0.474485	−	1.46073i
$610$	5.89457	−	10.2097i	0.238664	−	0.413379i
$611$		−	13.6521i		−	0.552306i
$612$	4.27566	−	0.534296i	0.172833	−	0.0215977i
$613$	31.9991			1.29243			0.646216	−	0.763154i	$-0.276350\pi$
$613$	31.9991			1.29243			0.646216	+	0.763154i	$0.276350\pi$
$614$	−4.89808	+	8.48373i	−0.197670	+	0.342375i
$615$	−19.2854	+	1.20031i	−0.777663	+	0.0484011i
$616$	12.2528	−	43.9848i	0.493680	−	1.77220i
$617$	−0.991996	+	0.572729i	−0.0399363	+	0.0230572i	−0.519835	−	0.854267i	$-0.674007\pi$
$617$	−0.991996	+	0.572729i	−0.0399363	+	0.0230572i	0.479899	+	0.877324i	$0.340673\pi$
$618$	−12.0964	−	18.2331i	−0.486588	−	0.733444i
$619$	7.02781	+	4.05751i	0.282471	+	0.163085i	0.634542	−	0.772889i	$-0.281189\pi$
$619$	7.02781	+	4.05751i	0.282471	+	0.163085i	−0.352070	+	0.935974i	$0.614522\pi$
$620$		−	1.07323i		−	0.0431019i
$621$	27.0109	−	23.2202i	1.08391	−	0.931795i
$622$		−	26.0129i		−	1.04302i
$623$	−12.0126	+	3.09187i	−0.481275	+	0.123873i
$624$	−17.4376	+	11.5686i	−0.698063	+	0.463115i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	21.3741	+	37.0211i	0.854283	+	1.47966i
$627$	−30.0918	+	1.87289i	−1.20175	+	0.0747959i
$628$	−0.220132	−	0.127093i	−0.00878423	−	0.00507158i
$629$	13.8320			0.551518
$630$	10.2618	+	1.52325i	0.408839	+	0.0606879i
$631$	−19.8404			−0.789835			−0.394917	−	0.918717i	$-0.629227\pi$
$631$	−19.8404			−0.789835			−0.394917	+	0.918717i	$0.629227\pi$
$632$	26.7398	+	15.4382i	1.06365	+	0.614099i
$633$	11.3977	−	22.9218i	0.453018	−	0.911059i
$634$	5.75170	+	9.96223i	0.228429	+	0.395651i
$635$	−4.87941	−	8.45138i	−0.193633	−	0.335383i
$636$	1.58975	+	0.790491i	0.0630376	+	0.0313450i
$637$	−13.1245	+	21.7289i	−0.520011	+	0.860930i
$638$		−	62.2844i		−	2.46586i
$639$	19.2194	+	8.10955i	0.760309	+	0.320809i
$640$		−	8.23172i		−	0.325387i
$641$	26.4557	+	15.2742i	1.04494	+	0.603294i	0.921228	−	0.389024i	$-0.127188\pi$
$641$	26.4557	+	15.2742i	1.04494	+	0.603294i	0.123709	+	0.992319i	$0.460521\pi$
$642$	−21.3960	+	1.33167i	−0.844434	+	0.0525569i
$643$	−31.1031	+	17.9574i	−1.22658	+	0.708169i	−0.966314	−	0.257367i	$-0.917145\pi$
$643$	−31.1031	+	17.9574i	−1.22658	+	0.708169i	−0.260271	+	0.965536i	$0.583812\pi$
$644$	−5.09599	−	1.41959i	−0.200810	−	0.0559395i
$645$	0.260819	+	0.393138i	0.0102697	+	0.0154798i
$646$	9.72266	−	16.8401i	0.382533	−	0.662566i
$647$	−5.35102			−0.210370			−0.105185	−	0.994453i	$-0.533544\pi$
$647$	−5.35102			−0.210370			−0.105185	+	0.994453i	$0.533544\pi$
$648$	19.3111	−	18.8093i	0.758613	−	0.738900i
$649$			49.9976i			1.96258i
$650$	−2.36992	+	4.10482i	−0.0929560	+	0.161004i
$651$	16.4930	+	3.50712i	0.646411	+	0.137455i
$652$	−1.57491	−	2.72782i	−0.0616782	−	0.106830i
$653$	29.5953	−	17.0869i	1.15815	−	0.668660i	0.207293	−	0.978279i	$-0.433535\pi$
$653$	29.5953	−	17.0869i	1.15815	−	0.668660i	0.950861	+	0.309619i	$0.100201\pi$
$654$	1.17231	+	18.8355i	0.0458409	+	0.736528i
$655$	8.91007	−	15.4327i	0.348145	−	0.603005i
$656$	−37.1670			−1.45113
$657$	7.96402	+	3.36038i	0.310706	+	0.131101i
$658$	−9.29589	+	9.11395i	−0.362391	+	0.355299i
$659$	−16.6480	−	9.61174i	−0.648515	−	0.374420i	0.139372	−	0.990240i	$-0.455492\pi$
$659$	−16.6480	−	9.61174i	−0.648515	−	0.374420i	−0.787887	+	0.615820i	$0.788825\pi$
$660$	−2.60632	−	1.29597i	−0.101451	−	0.0504457i
$661$	14.1032	−	8.14247i	0.548550	−	0.316705i	−0.199987	−	0.979799i	$-0.564090\pi$
$661$	14.1032	−	8.14247i	0.548550	−	0.316705i	0.748537	+	0.663093i	$0.230757\pi$
$662$	−16.2033	+	9.35496i	−0.629758	+	0.363591i
$663$	−27.6955	−	13.7714i	−1.07560	−	0.534837i
$664$	−8.78933	−	5.07452i	−0.341092	−	0.196930i
$665$	−5.70777	+	5.59606i	−0.221338	+	0.217006i
$666$	8.78192	−	6.64723i	0.340292	−	0.257575i
$667$	−56.6969			−2.19531
$668$	0.939453	−	1.62718i	0.0363485	−	0.0629575i
$669$	0.690148	+	11.0887i	0.0266827	+	0.428712i
$670$	−3.75539	+	2.16818i	−0.145084	+	0.0837640i
$671$	−25.9843	−	45.0062i	−1.00311	−	1.73744i
$672$	−7.33361	−	1.55944i	−0.282900	−	0.0601568i
$673$	−7.55471	+	13.0851i	−0.291213	+	0.504395i	−0.974097	−	0.226131i	$-0.927392\pi$
$673$	−7.55471	+	13.0851i	−0.291213	+	0.504395i	0.682884	+	0.730527i	$0.260725\pi$
$674$			35.3349i			1.36105i
$675$	1.71874	−	4.90366i	0.0661545	−	0.188742i
$676$	−0.0440301			−0.00169347
$677$	19.8465	−	34.3752i	0.762764	−	1.32115i	−0.178656	−	0.983912i	$-0.557175\pi$
$677$	19.8465	−	34.3752i	0.762764	−	1.32115i	0.941420	−	0.337235i	$-0.109492\pi$
$678$	−6.76328	−	10.1944i	−0.259742	−	0.391515i
$679$	11.7866	+	3.28337i	0.452327	+	0.126004i
$680$	12.7737	−	7.37489i	0.489848	−	0.282814i
$681$	7.90884	−	0.492240i	0.303067	−	0.0188627i
$682$	23.9968	+	13.8545i	0.918884	+	0.530518i
$683$		−	9.81578i		−	0.375591i	−0.982208	−	0.187795i	$-0.939866\pi$
$683$		−	9.81578i		−	0.375591i	0.982208	−	0.187795i	$-0.0601342\pi$
$684$	0.327807	+	2.62324i	0.0125340	+	0.100302i
$685$		−	1.37912i		−	0.0526934i
$686$	23.5571	−	5.56928i	0.899416	−	0.212636i
$687$	−9.11898	−	4.53435i	−0.347911	−	0.172996i
$688$	0.453739	+	0.785898i	0.0172986	+	0.0299621i
$689$	−6.37227	−	11.0371i	−0.242764	−	0.420480i
$690$	6.90951	−	13.8956i	0.263040	−	0.528998i
$691$	−33.1911	−	19.1629i	−1.26265	−	0.728990i	−0.289062	−	0.957310i	$-0.593343\pi$
$691$	−33.1911	−	19.1629i	−1.26265	−	0.728990i	−0.973586	+	0.228320i	$0.926677\pi$
$692$	−1.38509			−0.0526531
$693$	28.4330	−	35.8179i	1.08008	−	1.36061i
$694$	−13.5736			−0.515248
$695$	−10.5156	−	6.07121i	−0.398881	−	0.230294i
$696$	−42.8262	+	2.66547i	−1.62332	+	0.101034i
$697$	−27.4679	−	47.5757i	−1.04042	−	1.80206i
$698$	−0.657479	−	1.13879i	−0.0248859	−	0.0431037i
$699$	14.1784	−	9.40637i	0.536277	−	0.355781i
$700$	−0.747342	+	0.192355i	−0.0282469	+	0.00727033i
$701$			0.509304i			0.0192362i	0.999954	+	0.00961808i	$0.00306158\pi$
$701$			0.509304i			0.0192362i	−0.999954	+	0.00961808i	$0.996938\pi$
$702$	−24.2020	+	4.56616i	−0.913444	+	0.172339i
$703$			8.48634i			0.320068i
$704$	−43.9173	−	25.3557i	−1.65520	−	0.955628i
$705$	3.60475	+	5.43351i	0.135763	+	0.204638i
$706$	8.75158	−	5.05273i	0.329370	−	0.190162i
$707$	−7.07547	+	25.3993i	−0.266100	+	0.955239i
$708$	4.37547	−	0.272326i	0.164440	−	0.0102346i
$709$	−8.37903	+	14.5129i	−0.314681	+	0.545044i	−0.979370	−	0.202077i	$-0.935231\pi$
$709$	−8.37903	+	14.5129i	−0.314681	+	0.545044i	0.664688	+	0.747121i	$0.268564\pi$
$710$	9.08833			0.341079
$711$	18.6641	+	24.6578i	0.699958	+	0.924741i
$712$			14.0429i			0.526279i
$713$	12.6117	−	21.8440i	0.472310	−	0.818065i
$714$	9.11199	+	28.0518i	0.341008	+	1.04981i
$715$	10.4470	+	18.0948i	0.390697	+	0.676707i
$716$	4.97421	−	2.87186i	0.185895	−	0.107326i
$717$	28.5715	+	14.2070i	1.06702	+	0.530570i
$718$	−12.4259	+	21.5223i	−0.463731	+	0.803205i
$719$	0.103522			0.00386073			0.00193037	−	0.999998i	$-0.499386\pi$
$719$	0.103522			0.00386073			0.00193037	+	0.999998i	$0.499386\pi$
$720$	3.88551	−	9.20855i	0.144804	−	0.343182i
$721$	−18.2600	+	17.9026i	−0.680038	+	0.666729i
$722$	−11.1746	−	6.45164i	−0.415874	−	0.240105i
$723$	−0.475763	−	7.64411i	−0.0176938	−	0.284287i
$724$	6.71994	−	3.87976i	0.249745	−	0.144190i
$725$	−7.16276	+	4.13542i	−0.266018	+	0.153586i
$726$	41.8719	−	27.7790i	1.55401	−	1.03098i
$727$	42.0055	+	24.2519i	1.55790	+	0.899453i	0.997458	+	0.0712586i	$0.0227016\pi$
$727$	42.0055	+	24.2519i	1.55790	+	0.899453i	0.560441	+	0.828195i	$0.310632\pi$
$728$	20.1195	+	20.5211i	0.745677	+	0.760562i
$729$	25.1439	−	9.83793i	0.931255	−	0.364368i
$730$	3.76596			0.139384
$731$	−0.670661	+	1.16162i	−0.0248053	+	0.0429640i
$732$	−3.79713	+	2.51912i	−0.140346	+	0.0931095i
$733$	9.42982	−	5.44431i	0.348298	−	0.201090i	−0.315637	−	0.948880i	$-0.602218\pi$
$733$	9.42982	−	5.44431i	0.348298	−	0.201090i	0.663936	+	0.747790i	$0.268885\pi$
$734$	−7.48827	−	12.9701i	−0.276397	−	0.478734i
$735$	−0.513856	−	12.1135i	−0.0189539	−	0.446812i
$736$	−5.60777	+	9.71295i	−0.206705	+	0.358024i
$737$			19.1154i			0.704126i
$738$	−40.3027	−	17.0056i	−1.48356	−	0.625984i
$739$	−44.1464			−1.62395			−0.811975	−	0.583692i	$-0.801607\pi$
$739$	−44.1464			−1.62395			−0.811975	+	0.583692i	$0.801607\pi$
$740$	−0.409644	+	0.709525i	−0.0150588	+	0.0260827i
$741$	8.44917	−	16.9920i	0.310388	−	0.624217i
$742$	−3.26125	+	11.7071i	−0.119724	+	0.429782i
$743$	−40.8891	+	23.6073i	−1.50008	+	0.866069i	−0.500076	+	0.865981i	$0.666695\pi$
$743$	−40.8891	+	23.6073i	−1.50008	+	0.866069i	−1.00000		8.81124e-5i	$0.999972\pi$
$744$	8.49931	−	17.0929i	0.311600	−	0.626655i
$745$	−5.61055	−	3.23925i	−0.205555	−	0.118677i
$746$			18.6897i			0.684278i
$747$	−6.13486	−	8.10500i	−0.224463	−	0.296546i
$748$		−	8.27543i		−	0.302580i
$749$	6.24497	+	24.2631i	0.228186	+	0.886555i
$750$	−0.140627	−	2.25947i	−0.00513499	−	0.0825041i
$751$	13.1860	+	22.8389i	0.481166	+	0.833403i	0.999766	−	0.0216131i	$-0.00688020\pi$
$751$	13.1860	+	22.8389i	0.481166	+	0.833403i	−0.518601	+	0.855017i	$0.673547\pi$
$752$	6.27107	+	10.8618i	0.228682	+	0.396089i
$753$	10.5404	+	15.8877i	0.384112	+	0.578980i
$754$	33.9504	+	19.6013i	1.23640	+	0.713836i
$755$	18.9294			0.688912
$756$	−3.28943	−	2.29319i	−0.119635	−	0.0834024i
$757$	−29.2002			−1.06130			−0.530649	−	0.847592i	$-0.678052\pi$
$757$	−29.2002			−1.06130			−0.530649	+	0.847592i	$0.678052\pi$
$758$	−7.13902	−	4.12172i	−0.259301	−	0.149708i
$759$	−37.8187	−	57.0049i	−1.37273	−	2.06915i
$760$	4.52471	+	7.83703i	0.164129	+	0.284279i
$761$	17.7331	+	30.7147i	0.642826	+	1.11341i	0.984799	+	0.173697i	$0.0555713\pi$
$761$	17.7331	+	30.7147i	0.642826	+	1.11341i	−0.341974	+	0.939710i	$0.611095\pi$
$762$	−1.37236	−	22.0497i	−0.0497153	−	0.798778i
$763$	21.3595	−	5.49763i	0.773267	−	0.199028i
$764$			3.26426i			0.118097i
$765$	14.6590	−	1.83182i	0.529996	−	0.0662296i
$766$		−	39.0557i		−	1.41114i
$767$	−27.2530	−	15.7345i	−0.984048	−	0.568140i
$768$	−5.27798	+	10.6145i	−0.190453	+	0.383017i
$769$	−29.0445	+	16.7688i	−1.04737	+	0.604700i	−0.921912	−	0.387399i	$-0.873374\pi$
$769$	−29.0445	+	16.7688i	−1.04737	+	0.604700i	−0.125459	+	0.992099i	$0.540040\pi$
$770$	5.34666	−	19.1933i	0.192680	−	0.691678i
$771$	3.64340	−	7.32719i	0.131214	−	0.263882i
$772$	−0.135253	+	0.234265i	−0.00486787	+	0.00843140i
$773$	−29.1971			−1.05015			−0.525073	−	0.851057i	$-0.675962\pi$
$773$	−29.1971			−1.05015			−0.525073	+	0.851057i	$0.675962\pi$
$774$	0.132436	+	1.05981i	0.00476033	+	0.0380941i
$775$		−	3.67953i		−	0.132173i
$776$	6.92589	−	11.9960i	0.248625	−	0.430631i
$777$	−9.56508	−	8.61387i	−0.343145	−	0.309021i
$778$	5.12384	+	8.87475i	0.183698	+	0.318175i
$779$	29.1891	−	16.8523i	1.04581	−	0.603798i
$780$	1.52664	−	1.01282i	0.0546625	−	0.0362647i
$781$	20.0315	−	34.6955i	0.716783	−	1.24150i
$782$	44.1206			1.57775
$783$	−40.5575	−	14.2155i	−1.44941	−	0.508019i
$784$	0.460890	−	23.3165i	0.0164604	−	0.832731i
$785$	−0.754717	−	0.435736i	−0.0269370	−	0.0155521i
$786$	33.6167	−	22.3023i	1.19907	−	0.795496i
$787$	−20.7541	+	11.9824i	−0.739803	+	0.427126i	−0.821998	−	0.569491i	$-0.807140\pi$
$787$	−20.7541	+	11.9824i	−0.739803	+	0.427126i	0.0821945	+	0.996616i	$0.473807\pi$
$788$	1.78660	−	1.03150i	0.0636451	−	0.0367455i
$789$	0.429618	+	6.90270i	0.0152948	+	0.245743i
$790$	11.6682	+	6.73665i	0.415137	+	0.239679i
$791$	−10.2095	+	10.0096i	−0.363006	+	0.355902i
$792$	−31.2464	−	41.2809i	−1.11029	−	1.46685i
$793$	32.7096			1.16155
$794$	−0.212523	+	0.368100i	−0.00754215	+	0.0130634i
$795$	5.45041	+	2.71018i	0.193306	+	0.0961201i
$796$	−1.04607	+	0.603948i	−0.0370769	+	0.0214064i
$797$	−16.1948	−	28.0502i	−0.573648	−	0.993588i	−0.996187	−	0.0872431i	$-0.972194\pi$
$797$	−16.1948	−	28.0502i	−0.573648	−	0.993588i	0.422539	−	0.906345i	$-0.361139\pi$
$798$	−17.2106	+	5.59048i	−0.609248	+	0.197901i
$799$	−9.26913	+	16.0546i	−0.327918	+	0.567971i
$800$			1.63611i			0.0578451i
$801$	−5.46784	+	12.9586i	−0.193197	+	0.457871i
$802$	0.848759			0.0299707
$803$	8.30051	−	14.3769i	0.292919	−	0.507350i
$804$	1.67286	−	0.104117i	0.0589973	−	0.00367194i
$805$	−17.4715	−	4.86701i	−0.615788	−	0.171540i
$806$	−15.1038	+	8.72020i	−0.532010	+	0.307156i
$807$	20.3814	+	30.7213i	0.717460	+	1.08144i
$808$	25.8506	+	14.9249i	0.909421	+	0.525055i
$809$			4.89038i			0.171937i	0.996298	+	0.0859683i	$0.0273984\pi$
$809$			4.89038i			0.171937i	−0.996298	+	0.0859683i	$0.972602\pi$
$810$	8.42665	−	8.20767i	0.296082	−	0.288388i
$811$			8.79200i			0.308729i	0.988014	+	0.154364i	$0.0493330\pi$
$811$			8.79200i			0.308729i	−0.988014	+	0.154364i	$0.950667\pi$
$812$	1.59094	+	6.18115i	0.0558309	+	0.216916i
$813$	−12.8638	+	8.53423i	−0.451154	+	0.299309i
$814$	−10.5764	−	18.3188i	−0.370702	−	0.642075i
$815$	−5.39954	−	9.35227i	−0.189137	−	0.327596i
$816$	28.3608	−	1.76515i	0.992825	−	0.0617926i
$817$	−0.712688	−	0.411470i	−0.0249338	−	0.0143955i
$818$	28.3695			0.991916
$819$	10.5758	+	26.7706i	0.369549	+	0.935439i
$820$	3.25392			0.113632
$821$	−37.8062	−	21.8274i	−1.31945	−	0.761783i	−0.335807	−	0.941931i	$-0.609009\pi$
$821$	−37.8062	−	21.8274i	−1.31945	−	0.761783i	−0.983640	+	0.180148i	$0.942342\pi$
$822$	1.39008	−	2.79557i	0.0484845	−	0.0975067i
$823$	0.415923	+	0.720400i	0.0144982	+	0.0251116i	0.873183	−	0.487392i	$-0.162052\pi$
$823$	0.415923	+	0.720400i	0.0144982	+	0.0251116i	−0.858685	+	0.512503i	$0.828718\pi$
$824$	14.4752	+	25.0718i	0.504269	+	0.873419i
$825$	−8.93569	−	4.44321i	−0.311101	−	0.154693i
$826$	7.47986	+	29.0610i	0.260258	+	1.01116i
$827$			31.2225i			1.08571i	0.839826	+	0.542856i	$0.182657\pi$
$827$			31.2225i			1.08571i	−0.839826	+	0.542856i	$0.817343\pi$
$828$	−4.78272	+	3.62015i	−0.166211	+	0.125809i
$829$		−	17.2401i		−	0.598772i	−0.954132	−	0.299386i	$-0.903218\pi$
$829$		−	17.2401i		−	0.598772i	0.954132	−	0.299386i	$-0.0967819\pi$
$830$	−3.83533	−	2.21433i	−0.133126	−	0.0768604i
$831$	47.5259	−	2.95797i	1.64865	−	0.102611i
$832$	27.6421	−	15.9591i	0.958316	−	0.553284i
$833$	30.1869	−	16.6418i	1.04592	−	0.576605i
$834$	−15.1965	−	22.9060i	−0.526212	−	0.793170i
$835$	3.22089	−	5.57874i	0.111463	−	0.193060i
$836$	5.07722			0.175599
$837$	14.4985	−	12.4638i	0.501141	−	0.430811i
$838$		−	3.78993i		−	0.130921i
$839$	−23.3177	+	40.3874i	−0.805016	+	1.39433i	0.111265	+	0.993791i	$0.464510\pi$
$839$	−23.3177	+	40.3874i	−0.805016	+	1.39433i	−0.916280	+	0.400537i	$0.868823\pi$
$840$	−13.4259	−	2.85494i	−0.463239	−	0.0985046i
$841$	19.7034	+	34.1274i	0.679429	+	1.17681i
$842$	−13.9619	+	8.06092i	−0.481160	+	0.277798i
$843$	−0.427272	−	6.86500i	−0.0147160	−	0.236443i
$844$	−2.15543	+	3.73331i	−0.0741930	+	0.128506i
$845$	−0.150956			−0.00519305
$846$	1.83039	+	14.6475i	0.0629300	+	0.503592i
$847$	−41.1129	−	41.9336i	−1.41266	−	1.44086i
$848$	10.1397	+	5.85417i	0.348199	+	0.201033i
$849$	−1.83861	−	0.914236i	−0.0631009	−	0.0313765i
$850$	5.57395	−	3.21812i	0.191185	−	0.110381i
$851$	−16.6755	+	9.62758i	−0.571627	+	0.330029i
$852$	−3.14544	−	1.56405i	−0.107761	−	0.0535835i
$853$	−29.6463	−	17.1163i	−1.01507	−	0.586051i	−0.102398	−	0.994743i	$-0.532652\pi$
$853$	−29.6463	−	17.1163i	−1.01507	−	0.586051i	−0.912672	+	0.408692i	$0.865985\pi$
$854$	−21.8364	−	22.2723i	−0.747228	−	0.762144i
$855$	1.12388	+	8.99371i	0.0384358	+	0.307579i
$856$	28.3638			0.969456
$857$	−4.58831	+	7.94718i	−0.156734	+	0.271471i	−0.933689	−	0.358085i	$-0.883430\pi$
$857$	−4.58831	+	7.94718i	−0.156734	+	0.271471i	0.776955	+	0.629556i	$0.216763\pi$
$858$	2.93828	+	47.2095i	0.100311	+	1.61171i
$859$	14.7502	−	8.51605i	0.503271	−	0.290564i	−0.226792	−	0.973943i	$-0.572824\pi$
$859$	14.7502	−	8.51605i	0.503271	−	0.290564i	0.730063	+	0.683379i	$0.239490\pi$
$860$	−0.0397242	−	0.0688043i	−0.00135458	−	0.00234621i
$861$	−10.6332	+	50.0051i	−0.362380	+	1.70417i
$862$	−16.5573	+	28.6781i	−0.563945	+	0.976781i
$863$		−	48.0982i		−	1.63728i	−0.574307	−	0.818640i	$-0.694728\pi$
$863$		−	48.0982i		−	1.63728i	0.574307	−	0.818640i	$-0.305272\pi$
$864$	−6.44676	+	5.54202i	−0.219323	+	0.188543i
$865$	−4.74873			−0.161462
$866$	−19.5921	+	33.9346i	−0.665768	+	1.15314i
$867$	6.94116	+	10.4626i	0.235734	+	0.355327i
$868$	−2.73534	−	0.761983i	−0.0928436	−	0.0258634i
$869$	51.4356	−	29.6963i	1.74483	−	1.00738i
$870$	−18.6877	+	1.16311i	−0.633573	+	0.0394331i
$871$	−10.4195	−	6.01573i	−0.353053	−	0.203835i
$872$		−	24.9695i		−	0.845574i
$873$	11.0620	−	8.37307i	0.374392	−	0.283385i
$874$			27.0693i			0.915633i
$875$	−2.56224	+	0.659483i	−0.0866196	+	0.0222946i
$876$	−1.30339	−	0.648101i	−0.0440374	−	0.0218973i
$877$	20.2172	+	35.0172i	0.682685	+	1.18245i	0.974158	+	0.225867i	$0.0725214\pi$
$877$	20.2172	+	35.0172i	0.682685	+	1.18245i	−0.291473	+	0.956579i	$0.594145\pi$
$878$	14.5997	+	25.2873i	0.492714	+	0.853406i
$879$	−21.1818	+	42.5985i	−0.714444	+	1.43681i
$880$	−16.6236	−	9.59763i	−0.560381	−	0.323536i
$881$	−47.9451			−1.61531			−0.807656	−	0.589653i	$-0.799264\pi$
$881$	−47.9451			−1.61531			−0.807656	+	0.589653i	$0.799264\pi$
$882$	11.1681	−	25.0728i	0.376050	−	0.844245i
$883$	22.4684			0.756122			0.378061	−	0.925781i	$-0.376591\pi$
$883$	22.4684			0.756122			0.378061	+	0.925781i	$0.376591\pi$
$884$	4.51082	+	2.60432i	0.151715	+	0.0875929i
$885$	15.0012	−	0.933661i	0.504259	−	0.0313847i
$886$	−8.56882	−	14.8416i	−0.287875	−	0.498614i
$887$	−4.00551	−	6.93775i	−0.134492	−	0.232947i	0.790911	−	0.611931i	$-0.209607\pi$
$887$	−4.00551	−	6.93775i	−0.134492	−	0.232947i	−0.925403	+	0.378984i	$0.876274\pi$
$888$	−12.1432	+	8.05618i	−0.407501	+	0.270348i
$889$	−25.0044	+	6.43577i	−0.838622	+	0.215849i
$890$			6.12777i			0.205403i
$891$	−12.7605	−	50.2600i	−0.427492	−	1.68377i
$892$		−	1.87093i		−	0.0626433i
$893$	−9.84997	−	5.68689i	−0.329617	−	0.190304i
$894$	−8.10799	−	12.2213i	−0.271172	−	0.408743i
$895$	17.0539	−	9.84610i	0.570050	−	0.329119i
$896$	−20.9803	−	5.84445i	−0.700901	−	0.195249i
$897$	42.9743	−	2.67469i	1.43487	−	0.0893052i
$898$	18.9582	−	32.8366i	0.632645	−	1.09577i
$899$	−30.4329			−1.01499
$900$	−0.340171	+	0.806196i	−0.0113390	+	0.0268732i
$901$			17.3058i			0.576541i
$902$	−42.0056	+	72.7558i	−1.39863	+	2.42250i
$903$	1.18717	−	0.385627i	0.0395066	−	0.0128329i
$904$	8.09333	+	14.0181i	0.269180	+	0.466234i
$905$	23.0391	−	13.3016i	0.765847	−	0.442162i
$906$	38.3713	+	19.0799i	1.27480	+	0.633886i
$907$	5.25834	−	9.10772i	0.174600	−	0.302417i	−0.765423	−	0.643528i	$-0.777470\pi$
$907$	5.25834	−	9.10772i	0.174600	−	0.302417i	0.940023	+	0.341111i	$0.110803\pi$
$908$	−1.33442			−0.0442841
$909$	18.0434	+	23.8379i	0.598463	+	0.790654i
$910$	8.77937	+	8.95463i	0.291033	+	0.296843i
$911$	25.7026	+	14.8394i	0.851567	+	0.491652i	0.861179	−	0.508302i	$-0.169726\pi$
$911$	25.7026	+	14.8394i	0.851567	+	0.491652i	−0.00961242	+	0.999954i	$0.503060\pi$
$912$	1.08297	+	17.4002i	0.0358608	+	0.576177i
$913$	−16.9068	+	9.76115i	−0.559534	+	0.323047i
$914$	−6.12380	+	3.53558i	−0.202557	+	0.116947i
$915$	−13.0183	+	8.63675i	−0.430373	+	0.285522i
$916$	1.48523	+	0.857495i	0.0490732	+	0.0283324i
$917$	−33.0073	−	33.6662i	−1.09000	−	1.11176i
$918$	31.5612	+	11.0622i	1.04167	+	0.365109i
$919$	7.29885			0.240767			0.120383	−	0.992727i	$-0.461588\pi$
$919$	7.29885			0.240767			0.120383	+	0.992727i	$0.461588\pi$
$920$	−10.2664	+	17.7819i	−0.338473	+	0.586252i
$921$	10.8176	−	7.17668i	0.356451	−	0.236480i
$922$	−15.8439	+	9.14747i	−0.521791	+	0.301256i
$923$	12.6080	+	21.8378i	0.414999	+	0.718799i
$924$	−5.15352	+	5.72261i	−0.169538	+	0.188260i
$925$	−1.40446	+	2.43259i	−0.0461782	+	0.0799830i
$926$			13.3789i			0.439657i
$927$	3.59545	+	28.7723i	0.118090	+	0.945005i
$928$	13.5320			0.444209
$929$	−12.1110	+	20.9768i	−0.397348	+	0.688227i	−0.993398	−	0.114720i	$-0.963403\pi$
$929$	−12.1110	+	20.9768i	−0.397348	+	0.688227i	0.596050	+	0.802948i	$0.296736\pi$
$930$	3.70878	−	7.45868i	0.121616	−	0.244580i
$931$	10.2102	+	18.5206i	0.334627	+	0.606988i
$932$	−2.48141	+	1.43264i	−0.0812813	+	0.0469278i
$933$	−15.3481	+	30.8665i	−0.502475	+	1.01052i
$934$	6.55050	+	3.78193i	0.214339	+	0.123749i
$935$		−	28.3721i		−	0.927867i
$936$	32.3350	−	4.04067i	1.05690	−	0.132073i
$937$			21.2312i			0.693594i	0.937940	+	0.346797i	$0.112731\pi$
$937$			21.2312i			0.693594i	−0.937940	+	0.346797i	$0.887269\pi$
$938$	2.85975	+	11.1108i	0.0933743	+	0.362780i
$939$	−3.51899	−	56.5398i	−0.114838	−	1.84511i
$940$	−0.549024	−	0.950937i	−0.0179072	−	0.0310161i
$941$	−2.03848	−	3.53075i	−0.0664524	−	0.115099i	0.830885	−	0.556444i	$-0.187835\pi$
$941$	−2.03848	−	3.53075i	−0.0664524	−	0.115099i	−0.897337	+	0.441345i	$0.854501\pi$
$942$	−1.09067	−	1.64398i	−0.0355358	−	0.0535639i
$943$	66.2289	+	38.2373i	2.15671	+	1.24518i
$944$	28.9104			0.940954
$945$	−11.2777	−	7.86213i	−0.366864	−	0.255755i
$946$	2.05124			0.0666914
$947$	−18.2207	−	10.5197i	−0.592093	−	0.341845i	0.173832	−	0.984775i	$-0.444385\pi$
$947$	−18.2207	−	10.5197i	−0.592093	−	0.341845i	−0.765925	+	0.642930i	$0.777718\pi$
$948$	−2.87900	−	4.33957i	−0.0935054	−	0.140943i
$949$	5.22443	+	9.04899i	0.169592	+	0.293743i
$950$	1.97441	+	3.41978i	0.0640584	+	0.110952i
$951$	−0.946947	−	15.2146i	−0.0307069	−	0.493369i
$952$	−9.72723	−	37.7925i	−0.315261	−	1.22486i
$953$		−	45.0425i		−	1.45907i	−0.683944	−	0.729535i	$-0.739737\pi$
$953$		−	45.0425i		−	1.45907i	0.683944	−	0.729535i	$-0.260263\pi$
$954$	8.31665	+	10.9874i	0.269261	+	0.355732i
$955$			11.1914i			0.362147i
$956$	−4.65349	−	2.68670i	−0.150505	−	0.0868940i
$957$	−36.7491	+	73.9057i	−1.18793	+	2.38903i
$958$	13.3991	−	7.73599i	0.432906	−	0.249939i
$959$	−3.51497	−	0.979162i	−0.113504	−	0.0316188i
$960$	−6.78756	+	13.6504i	−0.219068	+	0.440564i
$961$	−8.73052	+	15.1217i	−0.281630	+	0.487797i
$962$	13.3138			0.429254
$963$	26.1739	+	11.0440i	0.843442	+	0.355887i
$964$			1.28975i			0.0415400i
$965$	−0.463712	+	0.803173i	−0.0149274	+	0.0258551i
$966$	−30.5102	−	27.4761i	−0.981650	−	0.884029i
$967$	17.2648	+	29.9034i	0.555197	+	0.961630i	0.997888	+	0.0649554i	$0.0206905\pi$
$967$	17.2648	+	29.9034i	0.555197	+	0.961630i	−0.442691	+	0.896674i	$0.645976\pi$
$968$	−57.5768	+	33.2420i	−1.85059	+	1.06844i
$969$	−21.4728	+	14.2457i	−0.689805	+	0.457637i
$970$	3.02219	−	5.23459i	0.0970368	−	0.168073i
$971$	−52.4564			−1.68341			−0.841704	−	0.539940i	$-0.818447\pi$
$971$	−52.4564			−1.68341			−0.841704	+	0.539940i	$0.818447\pi$
$972$	−4.32893	+	1.39047i	−0.138851	+	0.0445994i
$973$	−22.9398	+	22.4908i	−0.735415	+	0.721022i
$974$	−23.2560	−	13.4269i	−0.745171	−	0.430225i
$975$	5.23404	−	3.47242i	0.167624	−	0.111206i
$976$	−26.0242	+	15.0251i	−0.833014	+	0.480941i
$977$	28.8591	−	16.6618i	0.923286	−	0.533059i	0.0386041	−	0.999255i	$-0.487709\pi$
$977$	28.8591	−	16.6618i	0.923286	−	0.533059i	0.884682	+	0.466195i	$0.154376\pi$
$978$	−1.51865	−	24.4002i	−0.0485609	−	0.780231i
$979$	23.3933	+	13.5062i	0.747654	+	0.431659i
$980$	−0.0403503	+	2.04133i	−0.00128894	+	0.0652078i
$981$	9.72232	−	23.0416i	0.310410	−	0.735663i
$982$	−9.08575			−0.289938
$983$	10.6537	−	18.4527i	0.339800	−	0.588550i	−0.644595	−	0.764524i	$-0.722974\pi$
$983$	10.6537	−	18.4527i	0.339800	−	0.588550i	0.984395	+	0.175974i	$0.0563074\pi$
$984$	51.8239	+	25.7691i	1.65208	+	0.821488i
$985$	6.12532	−	3.53646i	0.195169	−	0.112681i
$986$	−26.6166	−	46.1013i	−0.847645	−	1.46816i
$987$	16.4078	−	5.32970i	0.522265	−	0.169646i
$988$	−1.59783	+	2.76752i	−0.0508337	+	0.0880466i
$989$		−	1.86722i		−	0.0593741i
$990$	−13.6348	−	18.0134i	−0.433341	−	0.572504i
$991$	6.50275			0.206567			0.103283	−	0.994652i	$-0.467065\pi$
$991$	6.50275			0.206567			0.103283	+	0.994652i	$0.467065\pi$
$992$	−3.01005	+	5.21356i	−0.0955692	+	0.165531i
$993$	24.7462	−	1.54018i	0.785296	−	0.0488762i
$994$	6.45264	−	23.1635i	0.204665	−	0.734701i
$995$	−3.58642	+	2.07062i	−0.113697	+	0.0656431i
$996$	0.946322	+	1.42641i	0.0299854	+	0.0451975i
$997$	18.8609	+	10.8893i	0.597330	+	0.344869i	0.767991	−	0.640461i	$-0.221257\pi$
$997$	18.8609	+	10.8893i	0.597330	+	0.344869i	−0.170660	+	0.985330i	$0.554590\pi$
$998$		−	35.0425i		−	1.10925i
$999$	−14.3425	+	2.70598i	−0.453776	+	0.0856135i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bl.j.146.4	yes	24
3.2	odd	2		945.2.bl.j.251.9		24
7.6	odd	2		315.2.bl.i.146.4	yes	24
9.4	even	3		945.2.bl.i.881.9		24
9.5	odd	6		315.2.bl.i.41.4	✓	24
21.20	even	2		945.2.bl.i.251.9		24
63.13	odd	6		945.2.bl.j.881.9		24
63.41	even	6	inner	315.2.bl.j.41.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bl.i.41.4	✓	24	9.5	odd	6
315.2.bl.i.146.4	yes	24	7.6	odd	2
315.2.bl.j.41.4	yes	24	63.41	even	6	inner
315.2.bl.j.146.4	yes	24	1.1	even	1	trivial
945.2.bl.i.251.9		24	21.20	even	2
945.2.bl.i.881.9		24	9.4	even	3
945.2.bl.j.251.9		24	3.2	odd	2
945.2.bl.j.881.9		24	63.13	odd	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.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13192 - 0.653515i) q^{2} +(0.957531 + 1.44331i) q^{3} +(-0.145837 - 0.252598i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.140627 - 2.25947i) q^{6} +(-2.56224 + 0.659483i) q^{7} +2.99529i q^{8} +(-1.16627 + 2.76402i) q^{9} +O(q^{10})\)	\(q+(-1.13192 - 0.653515i) q^{2} +(0.957531 + 1.44331i) q^{3} +(-0.145837 - 0.252598i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.140627 - 2.25947i) q^{6} +(-2.56224 + 0.659483i) q^{7} +2.99529i q^{8} +(-1.16627 + 2.76402i) q^{9} +1.30703i q^{10} +(4.98971 + 2.88081i) q^{11} +(0.224932 - 0.452359i) q^{12} +(-3.14058 + 1.81321i) q^{13} +(3.33124 + 0.927980i) q^{14} +(0.771174 - 1.55090i) q^{15} +(1.66579 - 2.88523i) q^{16} +4.92433 q^{17} +(3.12645 - 2.36648i) q^{18} +3.02122i q^{19} +(-0.145837 + 0.252598i) q^{20} +(-3.40526 - 3.06662i) q^{21} +(-3.76530 - 6.52169i) q^{22} +(-5.93663 + 3.42751i) q^{23} +(-4.32312 + 2.86808i) q^{24} +(-0.500000 + 0.866025i) q^{25} +4.73984 q^{26} +(-5.10607 + 0.963357i) q^{27} +(0.540255 + 0.551040i) q^{28} +(7.16276 + 4.13542i) q^{29} +(-1.88644 + 1.25152i) q^{30} +(-3.18657 + 1.83977i) q^{31} +(1.41691 - 0.818053i) q^{32} +(0.619911 + 9.96014i) q^{33} +(-5.57395 - 3.21812i) q^{34} +(1.85225 + 1.88922i) q^{35} +(0.868272 - 0.108501i) q^{36} +2.80891 q^{37} +(1.97441 - 3.41978i) q^{38} +(-5.62422 - 2.79661i) q^{39} +(2.59399 - 1.49764i) q^{40} +(-5.57799 - 9.66136i) q^{41} +(1.85040 + 5.69656i) q^{42} +(-0.136193 + 0.235894i) q^{43} -1.68052i q^{44} +(2.97685 - 0.371994i) q^{45} +8.95972 q^{46} +(-1.88231 + 3.26026i) q^{47} +(5.75931 - 0.358455i) q^{48} +(6.13016 - 3.37951i) q^{49} +(1.13192 - 0.653515i) q^{50} +(4.71520 + 7.10732i) q^{51} +(0.916027 + 0.528869i) q^{52} +3.51435i q^{53} +(6.40923 + 2.24645i) q^{54} -5.76162i q^{55} +(-1.97534 - 7.67465i) q^{56} +(-4.36055 + 2.89291i) q^{57} +(-5.40512 - 9.36194i) q^{58} +(4.33885 + 7.51511i) q^{59} +(-0.504220 + 0.0313822i) q^{60} +(-7.81138 - 4.50990i) q^{61} +4.80926 q^{62} +(1.16543 - 7.85123i) q^{63} -8.80159 q^{64} +(3.14058 + 1.81321i) q^{65} +(5.80741 - 11.6792i) q^{66} +(1.65886 + 2.87323i) q^{67} +(-0.718152 - 1.24388i) q^{68} +(-10.6315 - 5.28642i) q^{69} +(-0.861964 - 3.34892i) q^{70} -6.95342i q^{71} +(-8.27904 - 3.49330i) q^{72} -2.88131i q^{73} +(-3.17946 - 1.83566i) q^{74} +(-1.72871 + 0.107593i) q^{75} +(0.763154 - 0.440607i) q^{76} +(-14.6847 - 4.09070i) q^{77} +(4.53855 + 6.84105i) q^{78} +(5.15417 - 8.92729i) q^{79} -3.33158 q^{80} +(-6.27964 - 6.44718i) q^{81} +14.5812i q^{82} +(-1.69417 + 2.93439i) q^{83} +(-0.278008 + 1.30739i) q^{84} +(-2.46216 - 4.26459i) q^{85} +(0.308320 - 0.178009i) q^{86} +(0.889887 + 14.2979i) q^{87} +(-8.62884 + 14.9456i) q^{88} +4.68832 q^{89} +(-3.61266 - 1.52435i) q^{90} +(6.85113 - 6.71705i) q^{91} +(1.73157 + 0.999720i) q^{92} +(-5.70659 - 2.83756i) q^{93} +(4.26126 - 2.46024i) q^{94} +(2.61645 - 1.51061i) q^{95} +(2.53744 + 1.26172i) q^{96} +(-4.00495 - 2.31226i) q^{97} +(-9.14742 - 0.180814i) q^{98} +(-13.7819 + 10.4319i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9	\( 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9} + 9 q^{11} - 18 q^{12} + 3 q^{13} + 18 q^{14} + 2 q^{15} - 18 q^{16} + 18 q^{17} + 2 q^{18} + 18 q^{20} + 8 q^{21} - 9 q^{22} + 9 q^{23} - 7 q^{24} - 12 q^{25} - 18 q^{26} - 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} - 42 q^{31} + 18 q^{32} + 13 q^{33} - 39 q^{34} - 9 q^{35} - 21 q^{36} - 12 q^{38} - 21 q^{39} - 6 q^{40} - 33 q^{41} - 65 q^{42} + 18 q^{43} + q^{45} - 30 q^{46} - 17 q^{48} + 9 q^{49} - 6 q^{50} - 12 q^{51} + 129 q^{52} + 52 q^{54} - 9 q^{56} + 6 q^{57} - 15 q^{58} + 12 q^{59} + 15 q^{60} - 15 q^{61} + 12 q^{62} + 46 q^{63} - 60 q^{64} - 3 q^{65} + 29 q^{66} - 15 q^{67} + 9 q^{68} + 61 q^{69} - 9 q^{70} + 61 q^{72} - 18 q^{74} - 7 q^{75} + 54 q^{76} - 45 q^{77} - 66 q^{78} + 21 q^{79} + 36 q^{80} + q^{81} - 30 q^{83} + 15 q^{84} - 9 q^{85} - 102 q^{86} + 10 q^{87} - 9 q^{88} + 102 q^{89} - 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} - 156 q^{94} - 18 q^{95} - 42 q^{96} - 45 q^{97} + 3 q^{98} + 23 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9 + 9 * q^11 - 18 * q^12 + 3 * q^13 + 18 * q^14 + 2 * q^15 - 18 * q^16 + 18 * q^17 + 2 * q^18 + 18 * q^20 + 8 * q^21 - 9 * q^22 + 9 * q^23 - 7 * q^24 - 12 * q^25 - 18 * q^26 - 4 * q^27 - 9 * q^28 + 9 * q^29 - 5 * q^30 - 42 * q^31 + 18 * q^32 + 13 * q^33 - 39 * q^34 - 9 * q^35 - 21 * q^36 - 12 * q^38 - 21 * q^39 - 6 * q^40 - 33 * q^41 - 65 * q^42 + 18 * q^43 + q^45 - 30 * q^46 - 17 * q^48 + 9 * q^49 - 6 * q^50 - 12 * q^51 + 129 * q^52 + 52 * q^54 - 9 * q^56 + 6 * q^57 - 15 * q^58 + 12 * q^59 + 15 * q^60 - 15 * q^61 + 12 * q^62 + 46 * q^63 - 60 * q^64 - 3 * q^65 + 29 * q^66 - 15 * q^67 + 9 * q^68 + 61 * q^69 - 9 * q^70 + 61 * q^72 - 18 * q^74 - 7 * q^75 + 54 * q^76 - 45 * q^77 - 66 * q^78 + 21 * q^79 + 36 * q^80 + q^81 - 30 * q^83 + 15 * q^84 - 9 * q^85 - 102 * q^86 + 10 * q^87 - 9 * q^88 + 102 * q^89 - 37 * q^90 + 42 * q^91 - 3 * q^92 - 6 * q^93 - 156 * q^94 - 18 * q^95 - 42 * q^96 - 45 * q^97 + 3 * q^98 + 23 * q^99

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