LMFDB - Embedded newform 273.2.cg.b.115.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(19,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("273.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.1
Character	$\chi$	$=$	273.115
Dual form			273.2.cg.b.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.64088 + 0.707621i) q^{2} -1.00000i q^{3} +(4.74145 - 2.73748i) q^{4} +(-0.792066 - 0.212233i) q^{5} +(0.707621 + 2.64088i) q^{6} +(-1.19502 + 2.36049i) q^{7} +(-6.71797 + 6.71797i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-2.64088 + 0.707621i) q^{2} -1.00000i q^{3} +(4.74145 - 2.73748i) q^{4} +(-0.792066 - 0.212233i) q^{5} +(0.707621 + 2.64088i) q^{6} +(-1.19502 + 2.36049i) q^{7} +(-6.71797 + 6.71797i) q^{8} -1.00000 q^{9} +2.24193 q^{10} +(0.566870 - 0.566870i) q^{11} +(-2.73748 - 4.74145i) q^{12} +(2.33034 + 2.75128i) q^{13} +(1.48557 - 7.07939i) q^{14} +(-0.212233 + 0.792066i) q^{15} +(7.51260 - 13.0122i) q^{16} +(0.145326 + 0.251711i) q^{17} +(2.64088 - 0.707621i) q^{18} +(1.50629 - 1.50629i) q^{19} +(-4.33652 + 1.16197i) q^{20} +(2.36049 + 1.19502i) q^{21} +(-1.09590 + 1.89816i) q^{22} +(8.07890 + 4.66436i) q^{23} +(6.71797 + 6.71797i) q^{24} +(-3.74780 - 2.16379i) q^{25} +(-8.10100 - 5.61678i) q^{26} +1.00000i q^{27} +(0.795651 + 14.4635i) q^{28} +(2.87091 + 4.97256i) q^{29} -2.24193i q^{30} +(1.35027 + 5.03926i) q^{31} +(-5.71424 + 21.3259i) q^{32} +(-0.566870 - 0.566870i) q^{33} +(-0.561903 - 0.561903i) q^{34} +(1.44751 - 1.61604i) q^{35} +(-4.74145 + 2.73748i) q^{36} +(0.591680 + 2.20818i) q^{37} +(-2.91205 + 5.04382i) q^{38} +(2.75128 - 2.33034i) q^{39} +(6.74685 - 3.89530i) q^{40} +(8.80575 + 2.35949i) q^{41} +(-7.07939 - 1.48557i) q^{42} +(2.71857 + 1.56956i) q^{43} +(1.13599 - 4.23957i) q^{44} +(0.792066 + 0.212233i) q^{45} +(-24.6360 - 6.60119i) q^{46} +(1.25989 - 4.70196i) q^{47} +(-13.0122 - 7.51260i) q^{48} +(-4.14384 - 5.64168i) q^{49} +(11.4286 + 3.06229i) q^{50} +(0.251711 - 0.145326i) q^{51} +(18.5807 + 6.66578i) q^{52} +(-2.69075 + 4.66051i) q^{53} +(-0.707621 - 2.64088i) q^{54} +(-0.569307 + 0.328689i) q^{55} +(-7.82958 - 23.8858i) q^{56} +(-1.50629 - 1.50629i) q^{57} +(-11.1004 - 11.1004i) q^{58} +(3.22293 - 12.0281i) q^{59} +(1.16197 + 4.33652i) q^{60} +5.84594i q^{61} +(-7.13177 - 12.3526i) q^{62} +(1.19502 - 2.36049i) q^{63} -30.3120i q^{64} +(-1.26187 - 2.67377i) q^{65} +(1.89816 + 1.09590i) q^{66} +(8.97356 + 8.97356i) q^{67} +(1.37811 + 0.795651i) q^{68} +(4.66436 - 8.07890i) q^{69} +(-2.67916 + 5.29205i) q^{70} +(-6.43570 + 1.72444i) q^{71} +(6.71797 - 6.71797i) q^{72} +(-7.74069 + 2.07411i) q^{73} +(-3.12511 - 5.41284i) q^{74} +(-2.16379 + 3.74780i) q^{75} +(3.01857 - 11.2655i) q^{76} +(0.660669 + 2.01551i) q^{77} +(-5.61678 + 8.10100i) q^{78} +(2.75101 + 4.76489i) q^{79} +(-8.71210 + 8.71210i) q^{80} +1.00000 q^{81} -24.9245 q^{82} +(-3.51255 + 3.51255i) q^{83} +(14.4635 - 0.795651i) q^{84} +(-0.0616859 - 0.230215i) q^{85} +(-8.29005 - 2.22131i) q^{86} +(4.97256 - 2.87091i) q^{87} +7.61643i q^{88} +(-4.25897 + 1.14119i) q^{89} -2.24193 q^{90} +(-9.27917 + 2.21291i) q^{91} +51.0743 q^{92} +(5.03926 - 1.35027i) q^{93} +13.3088i q^{94} +(-1.51277 + 0.873398i) q^{95} +(21.3259 + 5.71424i) q^{96} +(-3.20349 - 11.9556i) q^{97} +(14.9355 + 11.9667i) q^{98} +(-0.566870 + 0.566870i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 8 * q^7 - 40 * q^9	$ 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} - 24 q^{34} + 26 q^{35} + 36 q^{37} - 8 q^{38} + 18 q^{39} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 32 q^{44} - 26 q^{46} - 4 q^{47} + 24 q^{48} - 14 q^{49} - 20 q^{50} + 2 q^{52} - 8 q^{53} - 42 q^{55} + 46 q^{56} - 14 q^{57} + 24 q^{58} + 14 q^{59} + 2 q^{60} + 24 q^{62} + 8 q^{63} + 28 q^{65} - 18 q^{66} - 44 q^{67} - 18 q^{68} + 4 q^{69} - 4 q^{70} - 6 q^{71} + 14 q^{73} - 20 q^{74} + 24 q^{75} - 64 q^{76} + 24 q^{77} + 8 q^{78} + 20 q^{80} + 40 q^{81} + 48 q^{82} - 12 q^{83} + 22 q^{84} + 2 q^{85} - 60 q^{86} + 18 q^{87} - 2 q^{89} - 14 q^{91} + 236 q^{92} - 8 q^{93} + 24 q^{95} + 16 q^{96} - 62 q^{97} - 88 q^{98} - 4 q^{99}+O(q^{100}) $ 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.64088	+	0.707621i	−1.86738	+	0.500363i	−0.867385	+	0.497638i	$0.834201\pi$
$2$	−2.64088	+	0.707621i	−1.86738	+	0.500363i	−0.999996	+	0.00272558i	$0.999132\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	4.74145	−	2.73748i	2.37072	−	1.36874i
$5$	−0.792066	−	0.212233i	−0.354223	−	0.0949137i	0.0773197	−	0.997006i	$-0.475364\pi$
$5$	−0.792066	−	0.212233i	−0.354223	−	0.0949137i	−0.431542	+	0.902093i	$0.642030\pi$
$6$	0.707621	+	2.64088i	0.288885	+	1.07813i
$7$	−1.19502	+	2.36049i	−0.451676	+	0.892182i
$7$	−1.19502	+	2.36049i	−0.451676	+	0.892182i
$8$	−6.71797	+	6.71797i	−2.37516	+	2.37516i
$9$	−1.00000			−0.333333
$10$	2.24193			0.708960
$11$	0.566870	−	0.566870i	0.170918	−	0.170918i	−0.616465	−	0.787382i	$-0.711436\pi$
$11$	0.566870	−	0.566870i	0.170918	−	0.170918i	0.787382	+	0.616465i	$0.211436\pi$
$12$	−2.73748	−	4.74145i	−0.790241	−	1.36874i
$13$	2.33034	+	2.75128i	0.646320	+	0.763066i
$13$	2.33034	+	2.75128i	0.646320	+	0.763066i
$14$	1.48557	−	7.07939i	0.397037	−	1.89205i
$15$	−0.212233	+	0.792066i	−0.0547984	+	0.204511i
$16$	7.51260	−	13.0122i	1.87815	−	3.25305i
$17$	0.145326	+	0.251711i	0.0352466	+	0.0610490i	0.883111	−	0.469165i	$-0.155445\pi$
$17$	0.145326	+	0.251711i	0.0352466	+	0.0610490i	−0.847864	+	0.530214i	$0.822112\pi$
$18$	2.64088	−	0.707621i	0.622460	−	0.166788i
$19$	1.50629	−	1.50629i	0.345568	−	0.345568i	−0.512888	−	0.858456i	$-0.671424\pi$
$19$	1.50629	−	1.50629i	0.345568	−	0.345568i	0.858456	+	0.512888i	$0.171424\pi$
$20$	−4.33652	+	1.16197i	−0.969676	+	0.259824i
$21$	2.36049	+	1.19502i	0.515101	+	0.260775i
$22$	−1.09590	+	1.89816i	−0.233647	+	0.404689i
$23$	8.07890	+	4.66436i	1.68457	+	0.972586i	0.958557	+	0.284902i	$0.0919612\pi$
$23$	8.07890	+	4.66436i	1.68457	+	0.972586i	0.726011	+	0.687683i	$0.241372\pi$
$24$	6.71797	+	6.71797i	1.37130	+	1.37130i
$25$	−3.74780	−	2.16379i	−0.749560	−	0.432759i
$26$	−8.10100	−	5.61678i	−1.58874	−	1.10154i
$27$			1.00000i			0.192450i
$28$	0.795651	+	14.4635i	0.150364	+	2.73334i
$29$	2.87091	+	4.97256i	0.533114	+	0.923380i	0.999252	+	0.0386684i	$0.0123116\pi$
$29$	2.87091	+	4.97256i	0.533114	+	0.923380i	−0.466138	+	0.884712i	$0.654355\pi$
$30$		−	2.24193i		−	0.409318i
$31$	1.35027	+	5.03926i	0.242515	+	0.905078i	0.974616	+	0.223882i	$0.0718731\pi$
$31$	1.35027	+	5.03926i	0.242515	+	0.905078i	−0.732101	+	0.681196i	$0.761460\pi$
$32$	−5.71424	+	21.3259i	−1.01015	+	3.76991i
$33$	−0.566870	−	0.566870i	−0.0986793	−	0.0986793i
$34$	−0.561903	−	0.561903i	−0.0963656	−	0.0963656i
$35$	1.44751	−	1.61604i	0.244674	−	0.273161i
$36$	−4.74145	+	2.73748i	−0.790241	+	0.456246i
$37$	0.591680	+	2.20818i	0.0972716	+	0.363022i	0.997354	−	0.0726971i	$-0.0231606\pi$
$37$	0.591680	+	2.20818i	0.0972716	+	0.363022i	−0.900082	+	0.435720i	$0.856494\pi$
$38$	−2.91205	+	5.04382i	−0.472397	+	0.818216i
$39$	2.75128	−	2.33034i	0.440557	−	0.373153i
$40$	6.74685	−	3.89530i	1.06677	−	0.615901i
$41$	8.80575	+	2.35949i	1.37523	+	0.368491i	0.869385	−	0.494135i	$-0.164515\pi$
$41$	8.80575	+	2.35949i	1.37523	+	0.368491i	0.505842	+	0.862626i	$0.331182\pi$
$42$	−7.07939	−	1.48557i	−1.09237	−	0.229229i
$43$	2.71857	+	1.56956i	0.414577	+	0.239356i	0.692755	−	0.721173i	$-0.256397\pi$
$43$	2.71857	+	1.56956i	0.414577	+	0.239356i	−0.278177	+	0.960530i	$0.589730\pi$
$44$	1.13599	−	4.23957i	0.171257	−	0.639140i
$45$	0.792066	+	0.212233i	0.118074	+	0.0316379i
$46$	−24.6360	−	6.60119i	−3.63238	−	0.973292i
$47$	1.25989	−	4.70196i	0.183773	−	0.685851i	−0.811117	−	0.584884i	$-0.801140\pi$
$47$	1.25989	−	4.70196i	0.183773	−	0.685851i	0.994890	−	0.100966i	$-0.0321934\pi$
$48$	−13.0122	−	7.51260i	−1.87815	−	1.08435i
$49$	−4.14384	−	5.64168i	−0.591977	−	0.805955i
$50$	11.4286	+	3.06229i	1.61625	+	0.433073i
$51$	0.251711	−	0.145326i	0.0352466	−	0.0203497i
$52$	18.5807	+	6.66578i	2.57668	+	0.924377i
$53$	−2.69075	+	4.66051i	−0.369602	+	0.640170i	−0.989503	−	0.144510i	$-0.953839\pi$
$53$	−2.69075	+	4.66051i	−0.369602	+	0.640170i	0.619901	+	0.784680i	$0.287173\pi$
$54$	−0.707621	−	2.64088i	−0.0962950	−	0.359378i
$55$	−0.569307	+	0.328689i	−0.0767653	+	0.0443205i
$56$	−7.82958	−	23.8858i	−1.04627	−	3.19188i
$57$	−1.50629	−	1.50629i	−0.199514	−	0.199514i
$58$	−11.1004	−	11.1004i	−1.45755	−	1.45755i
$59$	3.22293	−	12.0281i	0.419590	−	1.56593i	−0.355872	−	0.934535i	$-0.615816\pi$
$59$	3.22293	−	12.0281i	0.419590	−	1.56593i	0.775461	−	0.631395i	$-0.217517\pi$
$60$	1.16197	+	4.33652i	0.150009	+	0.559843i
$61$			5.84594i			0.748496i	0.927329	+	0.374248i	$0.122099\pi$
$61$			5.84594i			0.748496i	−0.927329	+	0.374248i	$0.877901\pi$
$62$	−7.13177	−	12.3526i	−0.905735	−	1.56878i
$63$	1.19502	−	2.36049i	0.150559	−	0.297394i
$64$		−	30.3120i		−	3.78901i
$65$	−1.26187	−	2.67377i	−0.156516	−	0.331640i
$66$	1.89816	+	1.09590i	0.233647	+	0.134896i
$67$	8.97356	+	8.97356i	1.09629	+	1.09629i	0.994840	+	0.101455i	$0.0323496\pi$
$67$	8.97356	+	8.97356i	1.09629	+	1.09629i	0.101455	+	0.994840i	$0.467650\pi$
$68$	1.37811	+	0.795651i	0.167120	+	0.0964868i
$69$	4.66436	−	8.07890i	0.561523	−	0.972586i
$70$	−2.67916	+	5.29205i	−0.320220	+	0.632521i
$71$	−6.43570	+	1.72444i	−0.763778	+	0.204654i	−0.619621	−	0.784901i	$-0.712714\pi$
$71$	−6.43570	+	1.72444i	−0.763778	+	0.204654i	−0.144157	+	0.989555i	$0.546047\pi$
$72$	6.71797	−	6.71797i	0.791720	−	0.791720i
$73$	−7.74069	+	2.07411i	−0.905979	+	0.242756i	−0.681582	−	0.731742i	$-0.738708\pi$
$73$	−7.74069	+	2.07411i	−0.905979	+	0.242756i	−0.224397	+	0.974498i	$0.572041\pi$
$74$	−3.12511	−	5.41284i	−0.363286	−	0.629230i
$75$	−2.16379	+	3.74780i	−0.249853	+	0.432759i
$76$	3.01857	−	11.2655i	0.346254	−	1.29224i
$77$	0.660669	+	2.01551i	0.0752902	+	0.229689i
$78$	−5.61678	+	8.10100i	−0.635975	+	0.917257i
$79$	2.75101	+	4.76489i	0.309513	+	0.536092i	0.978256	−	0.207402i	$-0.0665008\pi$
$79$	2.75101	+	4.76489i	0.309513	+	0.536092i	−0.668743	+	0.743493i	$0.733167\pi$
$80$	−8.71210	+	8.71210i	−0.974042	+	0.974042i
$81$	1.00000			0.111111
$82$	−24.9245			−2.75245
$83$	−3.51255	+	3.51255i	−0.385552	+	0.385552i	−0.873098	−	0.487546i	$-0.837892\pi$
$83$	−3.51255	+	3.51255i	−0.385552	+	0.385552i	0.487546	+	0.873098i	$0.337892\pi$
$84$	14.4635	−	0.795651i	1.57810	−	0.0868126i
$85$	−0.0616859	−	0.230215i	−0.00669078	−	0.0249703i
$86$	−8.29005	−	2.22131i	−0.893939	−	0.239530i
$87$	4.97256	−	2.87091i	0.533114	−	0.307793i
$88$			7.61643i			0.811914i
$89$	−4.25897	+	1.14119i	−0.451450	+	0.120966i	−0.477378	−	0.878698i	$-0.658413\pi$
$89$	−4.25897	+	1.14119i	−0.451450	+	0.120966i	0.0259280	+	0.999664i	$0.491746\pi$
$90$	−2.24193			−0.236320
$91$	−9.27917	+	2.21291i	−0.972721	+	0.231976i
$92$	51.0743			5.32486
$93$	5.03926	−	1.35027i	0.522547	−	0.140016i
$94$			13.3088i			1.37270i
$95$	−1.51277	+	0.873398i	−0.155207	+	0.0896088i
$96$	21.3259	+	5.71424i	2.17656	+	0.583208i
$97$	−3.20349	−	11.9556i	−0.325265	−	1.21391i	−0.914045	−	0.405612i	$-0.867058\pi$
$97$	−3.20349	−	11.9556i	−0.325265	−	1.21391i	0.588780	−	0.808293i	$-0.299608\pi$
$98$	14.9355	+	11.9667i	1.50872	+	1.20882i
$99$	−0.566870	+	0.566870i	−0.0569725	+	0.0569725i
$100$	−23.6933			−2.36933
$101$	−12.2075			−1.21469			−0.607345	−	0.794438i	$-0.707765\pi$
$101$	−12.2075			−1.21469			−0.607345	+	0.794438i	$0.707765\pi$
$102$	−0.561903	+	0.561903i	−0.0556367	+	0.0556367i
$103$	−8.55111	−	14.8110i	−0.842566	−	1.45937i	−0.887719	−	0.460387i	$-0.847711\pi$
$103$	−8.55111	−	14.8110i	−0.842566	−	1.45937i	0.0451528	−	0.998980i	$-0.485623\pi$
$104$	−34.1381	−	2.82783i	−3.34752	−	0.277291i
$105$	−1.61604	−	1.44751i	−0.157709	−	0.141263i
$106$	3.80806	−	14.2119i	0.369871	−	1.38038i
$107$	3.30962	−	5.73242i	0.319953	−	0.554174i	−0.660525	−	0.750804i	$-0.729666\pi$
$107$	3.30962	−	5.73242i	0.319953	−	0.554174i	0.980478	+	0.196630i	$0.0629997\pi$
$108$	2.73748	+	4.74145i	0.263414	+	0.456246i
$109$	7.14245	−	1.91381i	0.684123	−	0.183310i	0.100014	−	0.994986i	$-0.468111\pi$
$109$	7.14245	−	1.91381i	0.684123	−	0.183310i	0.584108	+	0.811676i	$0.301444\pi$
$110$	1.27088	−	1.27088i	0.121174	−	0.121174i
$111$	2.20818	−	0.591680i	0.209591	−	0.0561598i
$112$	21.7375	+	33.2833i	2.05400	+	3.14498i
$113$	−5.57880	+	9.66277i	−0.524810	+	0.908997i	0.474773	+	0.880108i	$0.342530\pi$
$113$	−5.57880	+	9.66277i	−0.524810	+	0.908997i	−0.999583	+	0.0288885i	$0.990803\pi$
$114$	5.04382	+	2.91205i	0.472397	+	0.272739i
$115$	−5.40909	−	5.40909i	−0.504400	−	0.504400i
$116$	27.2245	+	15.7181i	2.52773	+	1.45939i
$117$	−2.33034	−	2.75128i	−0.215440	−	0.254355i
$118$			34.0454i			3.13414i
$119$	−0.767830	+	0.0422391i	−0.0703869	+	0.00387205i
$120$	−3.89530	−	6.74685i	−0.355590	−	0.615901i
$121$			10.3573i			0.941574i
$122$	−4.13671	−	15.4384i	−0.374520	−	1.39773i
$123$	2.35949	−	8.80575i	0.212748	−	0.793988i
$124$	20.1971	+	20.1971i	1.81375	+	1.81375i
$125$	5.40844	+	5.40844i	0.483745	+	0.483745i
$126$	−1.48557	+	7.07939i	−0.132346	+	0.630682i
$127$	6.08635	−	3.51395i	0.540076	−	0.311813i	−0.205034	−	0.978755i	$-0.565730\pi$
$127$	6.08635	−	3.51395i	0.540076	−	0.311813i	0.745110	+	0.666942i	$0.232397\pi$
$128$	10.0209	+	37.3986i	0.885734	+	3.30560i
$129$	1.56956	−	2.71857i	0.138192	−	0.239356i
$130$	5.22446	+	6.16816i	0.458215	+	0.540984i
$131$	1.77697	−	1.02593i	0.155254	−	0.0896361i	−0.420360	−	0.907357i	$-0.638096\pi$
$131$	1.77697	−	1.02593i	0.155254	−	0.0896361i	0.575614	+	0.817721i	$0.304763\pi$
$132$	−4.23957	−	1.13599i	−0.369008	−	0.0988753i
$133$	1.75554	+	5.35565i	0.152225	+	0.464394i
$134$	−30.0479	−	17.3482i	−2.59575	−	1.49865i
$135$	0.212233	−	0.792066i	0.0182661	−	0.0681702i
$136$	−2.66728	−	0.714696i	−0.228718	−	0.0612847i
$137$	−9.12079	−	2.44391i	−0.779242	−	0.208797i	−0.152791	−	0.988258i	$-0.548826\pi$
$137$	−9.12079	−	2.44391i	−0.779242	−	0.208797i	−0.626450	+	0.779461i	$0.715493\pi$
$138$	−6.60119	+	24.6360i	−0.561931	+	2.09715i
$139$	11.2360	+	6.48710i	0.953024	+	0.550229i	0.894019	−	0.448029i	$-0.147874\pi$
$139$	11.2360	+	6.48710i	0.953024	+	0.550229i	0.0590051	+	0.998258i	$0.481207\pi$
$140$	2.43943	−	11.6249i	0.206169	−	0.982484i
$141$	−4.70196	−	1.25989i	−0.395976	−	0.106101i
$142$	15.7756	−	9.10807i	1.32386	−	0.764333i
$143$	2.88061	+	0.238615i	0.240889	+	0.0199540i
$144$	−7.51260	+	13.0122i	−0.626050	+	1.08435i
$145$	−1.21860	−	4.54789i	−0.101200	−	0.377682i
$146$	18.9745	−	10.9549i	1.57034	−	0.906637i
$147$	−5.64168	+	4.14384i	−0.465318	+	0.341778i
$148$	8.85026	+	8.85026i	0.727487	+	0.727487i
$149$	−1.66901	−	1.66901i	−0.136731	−	0.136731i	0.635429	−	0.772160i	$-0.280823\pi$
$149$	−1.66901	−	1.66901i	−0.136731	−	0.136731i	−0.772160	+	0.635429i	$0.780823\pi$
$150$	3.06229	−	11.4286i	0.250035	−	0.933143i
$151$	−3.69311	−	13.7829i	−0.300541	−	1.12164i	−0.936716	−	0.350091i	$-0.886151\pi$
$151$	−3.69311	−	13.7829i	−0.300541	−	1.12164i	0.636174	−	0.771545i	$-0.280516\pi$
$152$			20.2385i			1.64156i
$153$	−0.145326	−	0.251711i	−0.0117489	−	0.0203497i
$154$	−3.17096	−	4.85522i	−0.255523	−	0.391244i
$155$		−	4.27800i		−	0.343617i
$156$	6.66578	−	18.5807i	0.533689	−	1.48765i
$157$	−19.5507	−	11.2876i	−1.56031	−	0.900848i	−0.997225	−	0.0744522i	$-0.976279\pi$
$157$	−19.5507	−	11.2876i	−1.56031	−	0.900848i	−0.563090	−	0.826396i	$-0.690387\pi$
$158$	−10.6368	−	10.6368i	−0.846219	−	0.846219i
$159$	4.66051	+	2.69075i	0.369602	+	0.213390i
$160$	9.05212	−	15.6787i	0.715633	−	1.23951i
$161$	−20.6646	+	13.4962i	−1.62860	+	1.06365i
$162$	−2.64088	+	0.707621i	−0.207487	+	0.0555959i
$163$	−10.0073	+	10.0073i	−0.783832	+	0.783832i	−0.980475	−	0.196643i	$-0.936996\pi$
$163$	−10.0073	+	10.0073i	−0.783832	+	0.783832i	0.196643	+	0.980475i	$0.436996\pi$
$164$	48.2111	−	12.9181i	3.76465	−	1.00874i
$165$	0.328689	+	0.569307i	0.0255884	+	0.0443205i
$166$	6.79065	−	11.7617i	0.527056	−	0.912889i
$167$	3.99207	−	14.8986i	0.308916	−	1.15289i	−0.620606	−	0.784123i	$-0.713113\pi$
$167$	3.99207	−	14.8986i	0.308916	−	1.15289i	0.929522	−	0.368767i	$-0.120220\pi$
$168$	−23.8858	+	7.82958i	−1.84283	+	0.604066i
$169$	−2.13903	+	12.8228i	−0.164541	+	0.986370i
$170$	0.325810	+	0.564319i	0.0249885	+	0.0432813i
$171$	−1.50629	+	1.50629i	−0.115189	+	0.115189i
$172$	17.1866			1.31046
$173$	−3.06425			−0.232971			−0.116485	−	0.993192i	$-0.537163\pi$
$173$	−3.06425			−0.232971			−0.116485	+	0.993192i	$0.537163\pi$
$174$	−11.1004	+	11.1004i	−0.841518	+	0.841518i
$175$	9.58633	−	6.26087i	0.724658	−	0.473277i
$176$	−3.11756	−	11.6349i	−0.234995	−	0.877012i
$177$	−12.0281	−	3.22293i	−0.904090	−	0.242250i
$178$	10.4399	−	6.02747i	0.782502	−	0.451778i
$179$		−	1.28907i		−	0.0963499i	−0.998839	−	0.0481749i	$-0.984659\pi$
$179$		−	1.28907i		−	0.0963499i	0.998839	−	0.0481749i	$-0.0153405\pi$
$180$	4.33652	−	1.16197i	0.323225	−	0.0866080i
$181$	14.2160			1.05667			0.528335	−	0.849036i	$-0.322817\pi$
$181$	14.2160			1.05667			0.528335	+	0.849036i	$0.322817\pi$
$182$	22.9392	−	12.4102i	1.70037	−	0.919902i
$183$	5.84594			0.432145
$184$	−85.6088	+	22.9388i	−6.31117	+	1.69107i
$185$		−	1.87460i		−	0.137823i
$186$	−12.3526	+	7.13177i	−0.905735	+	0.522927i
$187$	0.225068	+	0.0603068i	0.0164586	+	0.00441007i
$188$	−6.89781	−	25.7430i	−0.503075	−	1.87750i
$189$	−2.36049	−	1.19502i	−0.171700	−	0.0869251i
$190$	3.37700	−	3.37700i	0.244994	−	0.244994i
$191$	20.2815			1.46752			0.733758	−	0.679411i	$-0.237764\pi$
$191$	20.2815			1.46752			0.733758	+	0.679411i	$0.237764\pi$
$192$	−30.3120			−2.18758
$193$	−5.15026	+	5.15026i	−0.370724	+	0.370724i	−0.867741	−	0.497017i	$-0.834429\pi$
$193$	−5.15026	+	5.15026i	−0.370724	+	0.370724i	0.497017	+	0.867741i	$0.334429\pi$
$194$	16.9200	+	29.3064i	1.21479	+	2.10407i
$195$	−2.67377	+	1.26187i	−0.191472	+	0.0903644i
$196$	−35.0918	−	15.4061i	−2.50656	−	1.10043i
$197$	−4.20373	+	15.6885i	−0.299504	+	1.11776i	0.638071	+	0.769978i	$0.279733\pi$
$197$	−4.20373	+	15.6885i	−0.299504	+	1.11776i	−0.937574	+	0.347785i	$0.886934\pi$
$198$	1.09590	−	1.89816i	0.0778825	−	0.134896i
$199$	0.528554	+	0.915483i	0.0374682	+	0.0648968i	0.884151	−	0.467200i	$-0.154737\pi$
$199$	0.528554	+	0.915483i	0.0374682	+	0.0648968i	−0.846683	+	0.532097i	$0.821404\pi$
$200$	39.7139	−	10.6413i	2.80820	−	0.752455i
$201$	8.97356	−	8.97356i	0.632946	−	0.632946i
$202$	32.2384	−	8.63826i	2.26829	−	0.607786i
$203$	−15.1685	+	0.834432i	−1.06462	+	0.0585657i
$204$	0.795651	−	1.37811i	0.0557067	−	0.0964868i
$205$	−6.47397	−	3.73775i	−0.452162	−	0.261056i
$206$	33.0630	+	33.0630i	2.30360	+	2.30360i
$207$	−8.07890	−	4.66436i	−0.561523	−	0.324195i
$208$	53.3071	−	9.65363i	3.69618	−	0.669359i
$209$		−	1.70774i		−	0.118127i
$210$	5.29205	+	2.67916i	0.365186	+	0.184879i
$211$	0.948161	+	1.64226i	0.0652741	+	0.113058i	0.896816	−	0.442405i	$-0.145875\pi$
$211$	0.948161	+	1.64226i	0.0652741	+	0.113058i	−0.831541	+	0.555463i	$0.812541\pi$
$212$			29.4634i			2.02356i
$213$	1.72444	+	6.43570i	0.118157	+	0.440967i
$214$	−4.68390	+	17.4806i	−0.320185	+	1.19495i
$215$	−1.82017	−	1.82017i	−0.124134	−	0.124134i
$216$	−6.71797	−	6.71797i	−0.457100	−	0.457100i
$217$	−13.5087	−	2.83474i	−0.917032	−	0.192435i
$218$	−17.5081	+	10.1083i	−1.18580	+	0.684620i
$219$	2.07411	+	7.74069i	0.140155	+	0.523067i
$220$	−1.79956	+	3.11693i	−0.121326	+	0.210143i
$221$	−0.353869	+	0.986404i	−0.0238038	+	0.0663527i
$222$	−5.41284	+	3.12511i	−0.363286	+	0.209743i
$223$	5.32451	+	1.42670i	0.356556	+	0.0955388i	0.432650	−	0.901562i	$-0.357578\pi$
$223$	5.32451	+	1.42670i	0.356556	+	0.0955388i	−0.0760947	+	0.997101i	$0.524245\pi$
$224$	−43.5108	−	38.9733i	−2.90719	−	2.60401i
$225$	3.74780	+	2.16379i	0.249853	+	0.144253i
$226$	7.89535	−	29.4658i	0.525191	−	1.96004i
$227$	15.4279	+	4.13390i	1.02399	+	0.274377i	0.731463	−	0.681881i	$-0.238838\pi$
$227$	15.4279	+	4.13390i	1.02399	+	0.274377i	0.292525	+	0.956258i	$0.405504\pi$
$228$	−11.2655	−	3.01857i	−0.746074	−	0.199910i
$229$	3.20721	−	11.9695i	0.211939	−	0.790966i	−0.775283	−	0.631614i	$-0.782393\pi$
$229$	3.20721	−	11.9695i	0.211939	−	0.790966i	0.987222	−	0.159352i	$-0.0509405\pi$
$230$	18.1123	+	10.4572i	1.19429	+	0.689524i
$231$	2.01551	−	0.660669i	0.132611	−	0.0434688i
$232$	−52.6921	−	14.1188i	−3.45941	−	0.926946i
$233$	−2.95409	+	1.70554i	−0.193529	+	0.111734i	−0.593633	−	0.804736i	$-0.702307\pi$
$233$	−2.95409	+	1.70554i	−0.193529	+	0.111734i	0.400105	+	0.916469i	$0.368974\pi$
$234$	8.10100	+	5.61678i	0.529579	+	0.367180i
$235$	−1.99582	+	3.45687i	−0.130193	+	0.225501i
$236$	−17.6454	−	65.8535i	−1.14862	−	4.28670i
$237$	4.76489	−	2.75101i	0.309513	−	0.178697i
$238$	1.99785	−	0.654880i	0.129502	−	0.0424496i
$239$	0.615965	+	0.615965i	0.0398435	+	0.0398435i	0.726748	−	0.686904i	$-0.241031\pi$
$239$	0.615965	+	0.615965i	0.0398435	+	0.0398435i	−0.686904	+	0.726748i	$0.741031\pi$
$240$	8.71210	+	8.71210i	0.562363	+	0.562363i
$241$	1.87818	−	7.00948i	0.120984	−	0.451520i	−0.878680	−	0.477411i	$-0.841575\pi$
$241$	1.87818	−	7.00948i	0.120984	−	0.451520i	0.999665	+	0.0258904i	$0.00824209\pi$
$242$	−7.32905	−	27.3524i	−0.471129	−	1.75828i
$243$		−	1.00000i		−	0.0641500i
$244$	16.0031	+	27.7182i	1.02450	+	1.77448i
$245$	2.08484	+	5.34805i	0.133196	+	0.341674i
$246$			24.9245i			1.58913i
$247$	7.65441	+	0.634052i	0.487038	+	0.0403438i
$248$	−42.9246	−	24.7826i	−2.72572	−	1.57369i
$249$	3.51255	+	3.51255i	0.222599	+	0.222599i
$250$	−18.1101	−	10.4559i	−1.14539	−	0.661289i
$251$	−7.68725	+	13.3147i	−0.485215	+	0.840417i	−0.999856	−	0.0169888i	$-0.994592\pi$
$251$	−7.68725	+	13.3147i	−0.485215	+	0.840417i	0.514641	+	0.857406i	$0.327925\pi$
$252$	−0.795651	−	14.4635i	−0.0501213	−	0.911115i
$253$	7.22376	−	1.93560i	0.454154	−	0.121690i
$254$	−13.5867	+	13.5867i	−0.852508	+	0.852508i
$255$	−0.230215	+	0.0616859i	−0.0144166	+	0.00386292i
$256$	−22.6161	−	39.1722i	−1.41350	−	2.44826i
$257$	11.1313	−	19.2801i	0.694354	−	1.20266i	−0.276044	−	0.961145i	$-0.589023\pi$
$257$	11.1313	−	19.2801i	0.694354	−	1.20266i	0.970398	−	0.241512i	$-0.0776432\pi$
$258$	−2.22131	+	8.29005i	−0.138293	+	0.516116i
$259$	−5.91946	−	1.24217i	−0.367817	−	0.0771847i
$260$	−13.3025	−	9.22319i	−0.824984	−	0.571998i
$261$	−2.87091	−	4.97256i	−0.177705	−	0.307793i
$262$	−3.96678	+	3.96678i	−0.245068	+	0.245068i
$263$	13.1804			0.812740			0.406370	−	0.913709i	$-0.366794\pi$
$263$	13.1804			0.812740			0.406370	+	0.913709i	$0.366794\pi$
$264$	7.61643			0.468759
$265$	3.12036	−	3.12036i	0.191682	−	0.191682i
$266$	−8.42593	−	12.9014i	−0.516627	−	0.791033i
$267$	1.14119	+	4.25897i	0.0698395	+	0.260645i
$268$	67.1126	+	17.9828i	4.09955	+	1.09847i
$269$	1.75759	−	1.01475i	0.107162	−	0.0618702i	−0.445461	−	0.895301i	$-0.646960\pi$
$269$	1.75759	−	1.01475i	0.107162	−	0.0618702i	0.552623	+	0.833431i	$0.313627\pi$
$270$			2.24193i			0.136439i
$271$	27.0730	−	7.25419i	1.64457	−	0.440661i	0.686484	−	0.727145i	$-0.259153\pi$
$271$	27.0730	−	7.25419i	1.64457	−	0.440661i	0.958085	+	0.286484i	$0.0924866\pi$
$272$	4.36709			0.264794
$273$	2.21291	+	9.27917i	0.133931	+	0.561601i
$274$	25.8162			1.55962
$275$	−3.35110	+	0.897926i	−0.202079	+	0.0541469i
$276$		−	51.0743i		−	3.07431i
$277$	−9.41668	+	5.43672i	−0.565794	+	0.326661i	−0.755468	−	0.655186i	$-0.772590\pi$
$277$	−9.41668	+	5.43672i	−0.565794	+	0.326661i	0.189674	+	0.981847i	$0.439257\pi$
$278$	−34.2633	−	9.18081i	−2.05497	−	0.550629i
$279$	−1.35027	−	5.03926i	−0.0808383	−	0.301693i
$280$	1.13217	+	20.5809i	0.0676603	+	1.22994i
$281$	−5.00498	+	5.00498i	−0.298572	+	0.298572i	−0.840454	−	0.541882i	$-0.817712\pi$
$281$	−5.00498	+	5.00498i	−0.298572	+	0.298572i	0.541882	+	0.840454i	$0.317712\pi$
$282$	13.3088			0.792528
$283$	−0.922161			−0.0548168			−0.0274084	−	0.999624i	$-0.508725\pi$
$283$	−0.922161			−0.0548168			−0.0274084	+	0.999624i	$0.508725\pi$
$284$	−25.7939	+	25.7939i	−1.53059	+	1.53059i
$285$	0.873398	+	1.51277i	0.0517357	+	0.0896088i
$286$	−7.77619	+	1.40823i	−0.459816	+	0.0832702i
$287$	−16.0926	+	17.9663i	−0.949919	+	1.06051i
$288$	5.71424	−	21.3259i	0.336715	−	1.25664i
$289$	8.45776	−	14.6493i	0.497515	−	0.861722i
$290$	6.43637	+	11.1481i	0.377956	+	0.654640i
$291$	−11.9556	+	3.20349i	−0.700849	+	0.187792i
$292$	−31.0242	+	31.0242i	−1.81556	+	1.81556i
$293$	−14.3112	+	3.83466i	−0.836067	+	0.224023i	−0.651359	−	0.758770i	$-0.725801\pi$
$293$	−14.3112	+	3.83466i	−0.836067	+	0.224023i	−0.184708	+	0.982793i	$0.559134\pi$
$294$	11.9667	−	14.9355i	0.697913	−	0.871058i
$295$	−5.10554	+	8.84306i	−0.297256	+	0.514863i
$296$	−18.8094	−	10.8596i	−1.09327	−	0.631201i
$297$	0.566870	+	0.566870i	0.0328931	+	0.0328931i
$298$	5.58868	+	3.22663i	0.323744	+	0.186913i
$299$	5.99366	+	33.0968i	0.346622	+	1.91404i
$300$			23.6933i			1.36794i
$301$	−6.95369	+	4.54149i	−0.400804	+	0.261767i
$302$	19.5061	+	33.7856i	1.12245	+	1.94414i
$303$			12.2075i			0.701301i
$304$	−8.28402	−	30.9164i	−0.475121	−	1.77318i
$305$	1.24070	−	4.63037i	0.0710425	−	0.265134i
$306$	0.561903	+	0.561903i	0.0321219	+	0.0321219i
$307$	2.59247	+	2.59247i	0.147960	+	0.147960i	0.777206	−	0.629246i	$-0.216636\pi$
$307$	2.59247	+	2.59247i	0.147960	+	0.147960i	−0.629246	+	0.777206i	$0.716636\pi$
$308$	8.64994	+	7.74788i	0.492876	+	0.441477i
$309$	−14.8110	+	8.55111i	−0.842566	+	0.486456i
$310$	3.02720	+	11.2977i	0.171933	+	0.641664i
$311$	−4.16328	+	7.21101i	−0.236078	+	0.408899i	−0.959585	−	0.281418i	$-0.909195\pi$
$311$	−4.16328	+	7.21101i	−0.236078	+	0.408899i	0.723508	+	0.690316i	$0.242529\pi$
$312$	−2.82783	+	34.1381i	−0.160094	+	1.93269i
$313$	8.01564	−	4.62783i	0.453071	−	0.261580i	−0.256056	−	0.966662i	$-0.582423\pi$
$313$	8.01564	−	4.62783i	0.453071	−	0.261580i	0.709126	+	0.705082i	$0.249090\pi$
$314$	59.6183	+	15.9747i	3.36445	+	0.901502i
$315$	−1.44751	+	1.61604i	−0.0815581	+	0.0910536i
$316$	26.0875	+	15.0616i	1.46754	+	0.847284i
$317$	−4.25100	+	15.8649i	−0.238760	+	0.891064i	0.737658	+	0.675175i	$0.235932\pi$
$317$	−4.25100	+	15.8649i	−0.238760	+	0.891064i	−0.976418	+	0.215889i	$0.930735\pi$
$318$	−14.2119	−	3.80806i	−0.796961	−	0.213545i
$319$	4.44622	+	1.19136i	0.248940	+	0.0667034i
$320$	−6.43323	+	24.0091i	−0.359628	+	1.34215i
$321$	−5.73242	−	3.30962i	−0.319953	−	0.184725i
$322$	45.0226	−	50.2644i	2.50901	−	2.80113i
$323$	0.598055	+	0.160248i	0.0332767	+	0.00891645i
$324$	4.74145	−	2.73748i	0.263414	−	0.152082i
$325$	−2.78046	−	15.3536i	−0.154232	−	0.851665i
$326$	19.3467	−	33.5094i	1.07151	−	1.85591i
$327$	−1.91381	−	7.14245i	−0.105834	−	0.394978i
$328$	−75.0078	+	43.3058i	−4.14161	+	2.39116i
$329$	9.59333	+	8.59289i	0.528898	+	0.473741i
$330$	−1.27088	−	1.27088i	−0.0699597	−	0.0699597i
$331$	15.3059	+	15.3059i	0.841291	+	0.841291i	0.989027	−	0.147736i	$-0.0471986\pi$
$331$	15.3059	+	15.3059i	0.841291	+	0.841291i	−0.147736	+	0.989027i	$0.547199\pi$
$332$	−7.03904	+	26.2701i	−0.386318	+	1.44176i
$333$	−0.591680	−	2.20818i	−0.0324239	−	0.121007i
$334$			42.1703i			2.30746i
$335$	−5.20316	−	9.01214i	−0.284279	−	0.492386i
$336$	33.2833	−	21.7375i	1.81575	−	1.18588i
$337$		−	29.6410i		−	1.61465i	−0.590110	−	0.807323i	$-0.700916\pi$
$337$		−	29.6410i		−	1.61465i	0.590110	−	0.807323i	$-0.299084\pi$
$338$	−3.42477	−	35.3771i	−0.186283	−	1.92426i
$339$	9.66277	+	5.57880i	0.524810	+	0.302999i
$340$	−0.922688	−	0.922688i	−0.0500398	−	0.0500398i
$341$	3.62203	+	2.09118i	0.196144	+	0.113244i
$342$	2.91205	−	5.04382i	0.157466	−	0.272739i
$343$	18.2691	−	3.03956i	0.986440	−	0.164121i
$344$	−28.8075	+	7.71896i	−1.55320	+	0.416178i
$345$	−5.40909	+	5.40909i	−0.291216	+	0.291216i
$346$	8.09231	−	2.16833i	0.435045	−	0.116570i
$347$	−10.6740	−	18.4879i	−0.573011	−	0.992483i	−0.996255	−	0.0864677i	$-0.972442\pi$
$347$	−10.6740	−	18.4879i	−0.573011	−	0.992483i	0.423244	−	0.906016i	$-0.360891\pi$
$348$	15.7181	−	27.2245i	0.842577	−	1.45939i
$349$	0.717765	−	2.67873i	0.0384211	−	0.143389i	−0.944051	−	0.329800i	$-0.893019\pi$
$349$	0.717765	−	2.67873i	0.0384211	−	0.143389i	0.982472	+	0.186410i	$0.0596854\pi$
$350$	−20.8860	+	23.3177i	−1.11640	+	1.24638i
$351$	−2.75128	+	2.33034i	−0.146852	+	0.124384i
$352$	8.84974	+	15.3282i	0.471693	+	0.816996i
$353$	6.50619	−	6.50619i	0.346290	−	0.346290i	−0.512436	−	0.858725i	$-0.671257\pi$
$353$	6.50619	−	6.50619i	0.346290	−	0.346290i	0.858725	+	0.512436i	$0.171257\pi$
$354$	34.0454			1.80949
$355$	5.46349			0.289972
$356$	−17.0697	+	17.0697i	−0.904692	+	0.904692i
$357$	0.0422391	+	0.767830i	0.00223553	+	0.0406379i
$358$	0.912175	+	3.40428i	0.0482100	+	0.179922i
$359$	−20.4884	−	5.48985i	−1.08134	−	0.289743i	−0.326193	−	0.945303i	$-0.605766\pi$
$359$	−20.4884	−	5.48985i	−1.08134	−	0.289743i	−0.755143	+	0.655560i	$0.772433\pi$
$360$	−6.74685	+	3.89530i	−0.355590	+	0.205300i
$361$			14.4622i			0.761166i
$362$	−37.5428	+	10.0596i	−1.97320	+	0.528719i
$363$	10.3573			0.543618
$364$	−37.9389	+	35.8939i	−1.98854	+	1.88135i
$365$	6.57133			0.343959
$366$	−15.4384	+	4.13671i	−0.806979	+	0.216229i
$367$			4.94793i			0.258280i	0.991626	+	0.129140i	$0.0412217\pi$
$367$			4.94793i			0.258280i	−0.991626	+	0.129140i	$0.958778\pi$
$368$	121.387	−	70.0829i	6.32774	−	3.65332i
$369$	−8.80575	−	2.35949i	−0.458409	−	0.122830i
$370$	1.32650	+	4.95058i	0.0689616	+	0.257368i
$371$	−7.78559	−	11.9209i	−0.404208	−	0.618902i
$372$	20.1971	−	20.1971i	1.04717	−	1.04717i
$373$	15.7856			0.817346			0.408673	−	0.912681i	$-0.365992\pi$
$373$	15.7856			0.817346			0.408673	+	0.912681i	$0.365992\pi$
$374$	−0.637051			−0.0329411
$375$	5.40844	−	5.40844i	0.279291	−	0.279291i
$376$	23.1237	+	40.0515i	1.19252	+	2.06550i
$377$	−6.99068	+	19.4864i	−0.360038	+	1.00360i
$378$	7.07939	+	1.48557i	0.364124	+	0.0764097i
$379$	4.90908	−	18.3209i	0.252163	−	0.941084i	−0.717484	−	0.696575i	$-0.754707\pi$
$379$	4.90908	−	18.3209i	0.252163	−	0.941084i	0.969647	−	0.244509i	$-0.0786268\pi$
$380$	−4.78181	+	8.28235i	−0.245302	+	0.424875i
$381$	−3.51395	−	6.08635i	−0.180025	−	0.311813i
$382$	−53.5609	+	14.3516i	−2.74041	+	0.734291i
$383$	24.1091	−	24.1091i	1.23192	−	1.23192i	0.268690	−	0.963227i	$-0.413409\pi$
$383$	24.1091	−	24.1091i	1.23192	−	1.23192i	0.963227	−	0.268690i	$-0.0865908\pi$
$384$	37.3986	−	10.0209i	1.90849	−	0.511379i
$385$	−0.0955340	−	1.73663i	−0.00486886	−	0.0885071i
$386$	9.95676	−	17.2456i	0.506786	−	0.877779i
$387$	−2.71857	−	1.56956i	−0.138192	−	0.0797855i
$388$	−47.9173	−	47.9173i	−2.43263	−	2.43263i
$389$	−13.4365	−	7.75759i	−0.681260	−	0.393325i	0.119070	−	0.992886i	$-0.462009\pi$
$389$	−13.4365	−	7.75759i	−0.681260	−	0.393325i	−0.800330	+	0.599560i	$0.795342\pi$
$390$	6.16816	−	5.22446i	0.312337	−	0.264551i
$391$			2.71140i			0.137121i
$392$	65.7389	+	10.0625i	3.32031	+	0.508231i
$393$	−1.02593	−	1.77697i	−0.0517514	−	0.0896361i
$394$		−	44.4062i		−	2.23715i
$395$	−1.16771	−	4.35796i	−0.0587540	−	0.219273i
$396$	−1.13599	+	4.23957i	−0.0570857	+	0.213047i
$397$	−9.38202	−	9.38202i	−0.470870	−	0.470870i	0.431326	−	0.902196i	$-0.358046\pi$
$397$	−9.38202	−	9.38202i	−0.470870	−	0.470870i	−0.902196	+	0.431326i	$0.858046\pi$
$398$	−2.04366	−	2.04366i	−0.102439	−	0.102439i
$399$	5.35565	−	1.75554i	0.268118	−	0.0878869i
$400$	−56.3115	+	32.5114i	−2.81557	+	1.62557i
$401$	−4.29844	−	16.0420i	−0.214654	−	0.801100i	−0.986288	−	0.165033i	$-0.947227\pi$
$401$	−4.29844	−	16.0420i	−0.214654	−	0.801100i	0.771634	−	0.636067i	$-0.219440\pi$
$402$	−17.3482	+	30.0479i	−0.865249	+	1.49865i
$403$	−10.7178	+	15.4581i	−0.533892	+	0.770025i
$404$	−57.8811	+	33.4177i	−2.87969	+	1.66259i
$405$	−0.792066	−	0.212233i	−0.0393581	−	0.0105460i
$406$	39.4676	−	12.9372i	1.95874	−	0.642060i
$407$	1.58715	+	0.916344i	0.0786723	+	0.0454215i
$408$	−0.714696	+	2.66728i	−0.0353827	+	0.132050i
$409$	−34.7367	−	9.30766i	−1.71762	−	0.460234i	−0.740346	−	0.672226i	$-0.765338\pi$
$409$	−34.7367	−	9.30766i	−1.71762	−	0.460234i	−0.977271	+	0.211992i	$0.932005\pi$
$410$	19.7419	+	5.28982i	0.974981	+	0.261245i
$411$	−2.44391	+	9.12079i	−0.120549	+	0.449895i
$412$	−81.0893	−	46.8169i	−3.99498	−	2.30650i
$413$	24.5408	+	21.9816i	1.20758	+	1.08164i
$414$	24.6360	+	6.60119i	1.21079	+	0.324431i
$415$	3.52765	−	2.03669i	0.173165	−	0.0999771i
$416$	−71.9894	+	33.9750i	−3.52957	+	1.66576i
$417$	6.48710	−	11.2360i	0.317675	−	0.550229i
$418$	1.20844	+	4.50994i	0.0591065	+	0.220588i
$419$	17.3534	−	10.0190i	0.847767	−	0.489459i	−0.0121297	−	0.999926i	$-0.503861\pi$
$419$	17.3534	−	10.0190i	0.847767	−	0.489459i	0.859897	+	0.510468i	$0.170528\pi$
$420$	−11.6249	−	2.43943i	−0.567237	−	0.119032i
$421$	9.14971	+	9.14971i	0.445929	+	0.445929i	0.893999	−	0.448069i	$-0.147888\pi$
$421$	9.14971	+	9.14971i	0.445929	+	0.445929i	−0.448069	+	0.893999i	$0.647888\pi$
$422$	−3.66607	−	3.66607i	−0.178462	−	0.178462i
$423$	−1.25989	+	4.70196i	−0.0612577	+	0.228617i
$424$	−13.2328	−	49.3855i	−0.642642	−	2.39837i
$425$		−	1.25782i		−	0.0610132i
$426$	−9.10807	−	15.7756i	−0.441288	−	0.764333i
$427$	−13.7993	−	6.98604i	−0.667795	−	0.338078i
$428$		−	36.2400i		−	1.75173i
$429$	0.238615	−	2.88061i	0.0115205	−	0.139077i
$430$	6.09483	+	3.51885i	0.293919	+	0.169694i
$431$	8.69313	+	8.69313i	0.418734	+	0.418734i	0.884767	−	0.466033i	$-0.154317\pi$
$431$	8.69313	+	8.69313i	0.418734	+	0.418734i	−0.466033	+	0.884767i	$0.654317\pi$
$432$	13.0122	+	7.51260i	0.626050	+	0.361450i
$433$	11.2493	−	19.4844i	0.540609	−	0.936362i	−0.458261	−	0.888818i	$-0.651527\pi$
$433$	11.2493	−	19.4844i	0.540609	−	0.936362i	0.998869	−	0.0475437i	$-0.0151393\pi$
$434$	37.6808	−	2.07286i	1.80874	−	0.0995003i
$435$	−4.54789	+	1.21860i	−0.218055	+	0.0584276i
$436$	28.6265	−	28.6265i	1.37096	−	1.37096i
$437$	19.1951	−	5.14331i	0.918226	−	0.246038i
$438$	−10.9549	−	18.9745i	−0.523447	−	0.906637i
$439$	−8.42215	+	14.5876i	−0.401967	+	0.696228i	−0.993963	−	0.109713i	$-0.965007\pi$
$439$	−8.42215	+	14.5876i	−0.401967	+	0.696228i	0.591996	+	0.805941i	$0.298340\pi$
$440$	1.61646	−	6.03271i	0.0770617	−	0.287598i
$441$	4.14384	+	5.64168i	0.197326	+	0.268652i
$442$	0.236525	−	2.85538i	0.0112503	−	0.135816i
$443$	−6.31905	−	10.9449i	−0.300227	−	0.520008i	0.675960	−	0.736938i	$-0.263729\pi$
$443$	−6.31905	−	10.9449i	−0.300227	−	0.520008i	−0.976187	+	0.216930i	$0.930396\pi$
$444$	8.85026	−	8.85026i	0.420015	−	0.420015i
$445$	3.61558			0.171395
$446$	−15.0709			−0.713629
$447$	−1.66901	+	1.66901i	−0.0789416	+	0.0789416i
$448$	71.5513	+	36.2236i	3.38048	+	1.71140i
$449$	−2.81967	−	10.5232i	−0.133069	−	0.496618i	0.866930	−	0.498430i	$-0.166090\pi$
$449$	−2.81967	−	10.5232i	−0.133069	−	0.496618i	−0.999998	+	0.00181175i	$0.999423\pi$
$450$	−11.4286	−	3.06229i	−0.538751	−	0.144358i
$451$	6.32924	−	3.65419i	0.298032	−	0.172069i
$452$			61.0873i			2.87331i
$453$	−13.7829	+	3.69311i	−0.647577	+	0.173518i
$454$	−43.6685			−2.04947
$455$	7.81937	+	0.216578i	0.366578	+	0.0101534i
$456$	20.2385			0.947754
$457$	0.259222	−	0.0694582i	0.0121259	−	0.00324912i	−0.252751	−	0.967531i	$-0.581335\pi$
$457$	0.259222	−	0.0694582i	0.0121259	−	0.00324912i	0.264877	+	0.964282i	$0.414669\pi$
$458$			33.8794i			1.58308i
$459$	−0.251711	+	0.145326i	−0.0117489	+	0.00678322i
$460$	−40.4542	−	10.8397i	−1.88619	−	0.505402i
$461$	−8.32642	−	31.0746i	−0.387800	−	1.44729i	−0.833706	−	0.552209i	$-0.813785\pi$
$461$	−8.32642	−	31.0746i	−0.387800	−	1.44729i	0.445906	−	0.895080i	$-0.352882\pi$
$462$	−4.85522	+	3.17096i	−0.225885	+	0.147527i
$463$	23.1731	−	23.1731i	1.07695	−	1.07695i	0.0801653	−	0.996782i	$-0.474455\pi$
$463$	23.1731	−	23.1731i	1.07695	−	1.07695i	0.996782	−	0.0801653i	$-0.0255448\pi$
$464$	86.2719			4.00507
$465$	−4.27800			−0.198387
$466$	6.59451	−	6.59451i	0.305485	−	0.305485i
$467$	−3.81254	−	6.60352i	−0.176423	−	0.305574i	0.764230	−	0.644944i	$-0.223119\pi$
$467$	−3.81254	−	6.60352i	−0.176423	−	0.305574i	−0.940653	+	0.339370i	$0.889786\pi$
$468$	−18.5807	−	6.66578i	−0.858895	−	0.308126i
$469$	−31.9056	+	10.4584i	−1.47326	+	0.482924i
$470$	2.82457	−	10.5414i	0.130288	−	0.486241i
$471$	−11.2876	+	19.5507i	−0.520105	+	0.900848i
$472$	59.1531	+	102.456i	2.72274	+	4.71593i
$473$	2.43081	−	0.651334i	0.111769	−	0.0299484i
$474$	−10.6368	+	10.6368i	−0.488565	+	0.488565i
$475$	−8.90461	+	2.38598i	−0.408571	+	0.109476i
$476$	−3.52500	+	2.30219i	−0.161568	+	0.105521i
$477$	2.69075	−	4.66051i	0.123201	−	0.213390i
$478$	−2.06256	−	1.19082i	−0.0943392	−	0.0544667i
$479$	−4.06315	−	4.06315i	−0.185650	−	0.185650i	0.608162	−	0.793813i	$-0.291907\pi$
$479$	−4.06315	−	4.06315i	−0.185650	−	0.185650i	−0.793813	+	0.608162i	$0.791907\pi$
$480$	−15.6787	−	9.05212i	−0.715633	−	0.413171i
$481$	−4.69649	+	6.77368i	−0.214142	+	0.308853i
$482$			19.8402i			0.903697i
$483$	13.4962	+	20.6646i	0.614097	+	0.940274i
$484$	28.3529	+	49.1087i	1.28877	+	2.23221i
$485$			10.1495i			0.460865i
$486$	0.707621	+	2.64088i	0.0320983	+	0.119793i
$487$	1.00122	−	3.73662i	0.0453698	−	0.169322i	−0.939524	−	0.342484i	$-0.888732\pi$
$487$	1.00122	−	3.73662i	0.0453698	−	0.169322i	0.984893	+	0.173162i	$0.0553984\pi$
$488$	−39.2729	−	39.2729i	−1.77780	−	1.77780i
$489$	10.0073	+	10.0073i	0.452546	+	0.452546i
$490$	−9.29019	−	12.6482i	−0.419688	−	0.571390i
$491$	−33.9925	+	19.6256i	−1.53406	+	0.885691i	−0.534893	+	0.844920i	$0.679648\pi$
$491$	−33.9925	+	19.6256i	−1.53406	+	0.885691i	−0.999169	+	0.0407714i	$0.987018\pi$
$492$	−12.9181	−	48.2111i	−0.582394	−	2.17352i
$493$	−0.834432	+	1.44528i	−0.0375809	+	0.0650921i
$494$	−20.6630	+	3.74196i	−0.929673	+	0.168359i
$495$	0.569307	−	0.328689i	0.0255884	−	0.0147735i
$496$	75.7159	+	20.2880i	3.39974	+	0.910959i
$497$	3.62028	−	17.2522i	0.162392	−	0.773866i
$498$	−11.7617	−	6.79065i	−0.527056	−	0.304296i
$499$	2.97967	−	11.1203i	0.133388	−	0.497811i	−0.866611	−	0.498984i	$-0.833707\pi$
$499$	2.97967	−	11.1203i	0.133388	−	0.497811i	0.999999	+	0.00117270i	$0.000373282\pi$
$500$	40.4493	+	10.8384i	1.80895	+	0.484706i
$501$	−14.8986	−	3.99207i	−0.665621	−	0.178353i
$502$	10.8793	−	40.6022i	0.485568	−	1.81216i
$503$	−12.9603	−	7.48266i	−0.577873	−	0.333635i	0.182414	−	0.983222i	$-0.441609\pi$
$503$	−12.9603	−	7.48266i	−0.577873	−	0.333635i	−0.760288	+	0.649586i	$0.774942\pi$
$504$	7.82958	+	23.8858i	0.348757	+	1.06396i
$505$	9.66913	+	2.59083i	0.430271	+	0.115291i
$506$	−17.7074	+	10.2234i	−0.787190	+	0.454484i
$507$	12.8228	+	2.13903i	0.569481	+	0.0949976i
$508$	19.2387	−	33.3225i	0.853581	−	1.47845i
$509$	7.07706	+	26.4120i	0.313685	+	1.17069i	0.925207	+	0.379462i	$0.123891\pi$
$509$	7.07706	+	26.4120i	0.313685	+	1.17069i	−0.611522	+	0.791227i	$0.709442\pi$
$510$	0.564319	−	0.325810i	0.0249885	−	0.0144271i
$511$	4.35438	−	20.7504i	0.192626	−	0.917945i
$512$	32.6898	+	32.6898i	1.44470	+	1.44470i
$513$	1.50629	+	1.50629i	0.0665045	+	0.0665045i
$514$	−15.7535	+	58.7930i	−0.694859	+	2.59325i
$515$	3.62966	+	13.5461i	0.159942	+	0.596912i
$516$		−	17.1866i		−	0.756597i
$517$	−1.95120	−	3.37959i	−0.0858139	−	0.148634i
$518$	16.5115	−	0.908316i	0.725476	−	0.0399091i
$519$			3.06425i			0.134506i
$520$	26.4395	+	9.48508i	1.15945	+	0.415948i
$521$	6.87190	+	3.96750i	0.301064	+	0.173819i	0.642921	−	0.765933i	$-0.277723\pi$
$521$	6.87190	+	3.96750i	0.301064	+	0.173819i	−0.341857	+	0.939752i	$0.611056\pi$
$522$	11.1004	+	11.1004i	0.485851	+	0.485851i
$523$	−2.98599	−	1.72396i	−0.130568	−	0.0753837i	0.433293	−	0.901253i	$-0.357351\pi$
$523$	−2.98599	−	1.72396i	−0.130568	−	0.0753837i	−0.563861	+	0.825869i	$0.690685\pi$
$524$	5.61693	−	9.72881i	0.245377	−	0.425005i
$525$	−6.26087	−	9.58633i	−0.273247	−	0.418382i
$526$	−34.8079	+	9.32675i	−1.51770	+	0.406665i
$527$	−1.07221	+	1.07221i	−0.0467062	+	0.0467062i
$528$	−11.6349	+	3.11756i	−0.506343	+	0.135674i
$529$	32.0124	+	55.4472i	1.39185	+	2.41075i
$530$	−6.03246	+	10.4485i	−0.262033	+	0.453855i
$531$	−3.22293	+	12.0281i	−0.139863	+	0.521977i
$532$	22.9848	+	20.5878i	0.996516	+	0.892594i
$533$	14.0288	+	29.7255i	0.607654	+	1.28755i
$534$	−6.02747	−	10.4399i	−0.260834	−	0.451778i
$535$	−3.83804	+	3.83804i	−0.165933	+	0.165933i
$536$	−120.568			−5.20775
$537$	−1.28907			−0.0556276
$538$	−3.92353	+	3.92353i	−0.169155	+	0.169155i
$539$	−5.54711	−	0.849081i	−0.238931	−	0.0365725i
$540$	−1.16197	−	4.33652i	−0.0500031	−	0.186614i
$541$	−2.58494	−	0.692633i	−0.111135	−	0.0297786i	0.202823	−	0.979215i	$-0.434988\pi$
$541$	−2.58494	−	0.692633i	−0.111135	−	0.0297786i	−0.313958	+	0.949437i	$0.601655\pi$
$542$	−66.3633	+	38.3149i	−2.85055	+	1.64576i
$543$		−	14.2160i		−	0.610068i
$544$	−6.19838	+	1.66085i	−0.265754	+	0.0712085i
$545$	−6.06346			−0.259730
$546$	−12.4102	−	22.9392i	−0.531106	−	0.981709i
$547$	−34.9374			−1.49382			−0.746908	−	0.664927i	$-0.768463\pi$
$547$	−34.9374			−1.49382			−0.746908	+	0.664927i	$0.768463\pi$
$548$	−49.9359	+	13.3803i	−2.13316	+	0.571577i
$549$		−	5.84594i		−	0.249499i
$550$	8.21446	−	4.74262i	0.350266	−	0.202226i
$551$	11.8146	+	3.16570i	0.503317	+	0.134863i
$552$	22.9388	+	85.6088i	0.976341	+	3.64375i
$553$	−14.5350	+	0.799584i	−0.618091	+	0.0340018i
$554$	21.0211	−	21.0211i	0.893103	−	0.893103i
$555$	−1.87460			−0.0795722
$556$	71.0331			3.01248
$557$	−1.19623	+	1.19623i	−0.0506861	+	0.0506861i	−0.731996	−	0.681309i	$-0.761411\pi$
$557$	−1.19623	+	1.19623i	−0.0506861	+	0.0506861i	0.681309	+	0.731996i	$0.261411\pi$
$558$	7.13177	+	12.3526i	0.301912	+	0.522927i
$559$	2.01688	+	11.1371i	0.0853049	+	0.471051i
$560$	−10.1537	−	30.9760i	−0.429071	−	1.30897i
$561$	0.0603068	−	0.225068i	0.00254616	−	0.00950239i
$562$	9.67591	−	16.7592i	0.408154	−	0.706943i
$563$	−9.17247	−	15.8872i	−0.386574	−	0.669565i	0.605412	−	0.795912i	$-0.293008\pi$
$563$	−9.17247	−	15.8872i	−0.386574	−	0.669565i	−0.991986	+	0.126347i	$0.959675\pi$
$564$	−25.7430	+	6.89781i	−1.08398	+	0.290450i
$565$	6.46954	−	6.46954i	0.272176	−	0.272176i
$566$	2.43531	−	0.652540i	0.102364	−	0.0274283i
$567$	−1.19502	+	2.36049i	−0.0501862	+	0.0991313i
$568$	31.6501	−	54.8196i	1.32801	−	2.30018i
$569$	12.4249	+	7.17349i	0.520877	+	0.300728i	0.737293	−	0.675573i	$-0.236104\pi$
$569$	12.4249	+	7.17349i	0.520877	+	0.300728i	−0.216416	+	0.976301i	$0.569437\pi$
$570$	−3.37700	−	3.37700i	−0.141447	−	0.141447i
$571$	−5.06747	−	2.92571i	−0.212067	−	0.122437i	0.390205	−	0.920728i	$-0.372404\pi$
$571$	−5.06747	−	2.92571i	−0.212067	−	0.122437i	−0.602272	+	0.798291i	$0.705738\pi$
$572$	14.3115	−	6.75423i	0.598393	−	0.282408i
$573$		−	20.2815i		−	0.847271i
$574$	29.7854	−	58.8341i	1.24322	−	2.45569i
$575$	−20.1854	−	34.9622i	−0.841790	−	1.45802i
$576$			30.3120i			1.26300i
$577$	2.67664	+	9.98937i	0.111430	+	0.415863i	0.998995	−	0.0448197i	$-0.0142713\pi$
$577$	2.67664	+	9.98937i	0.111430	+	0.415863i	−0.887565	+	0.460683i	$0.847605\pi$
$578$	−11.9698	+	44.6718i	−0.497877	+	1.85810i
$579$	5.15026	+	5.15026i	0.214037	+	0.214037i
$580$	−18.2277	−	18.2277i	−0.756864	−	0.756864i
$581$	−4.09376	−	12.4889i	−0.169838	−	0.518127i
$582$	29.3064	−	16.9200i	1.21479	−	0.701358i
$583$	1.11660	+	4.16720i	0.0462448	+	0.172588i
$584$	38.0679	−	65.9355i	1.57526	−	2.72843i
$585$	1.26187	+	2.67377i	0.0521719	+	0.110547i
$586$	35.0805	−	20.2537i	1.44916	−	0.836674i
$587$	−28.5050	−	7.63789i	−1.17653	−	0.315250i	−0.382979	−	0.923757i	$-0.625102\pi$
$587$	−28.5050	−	7.63789i	−1.17653	−	0.315250i	−0.793548	+	0.608507i	$0.791769\pi$
$588$	−15.4061	+	35.0918i	−0.635336	+	1.44716i
$589$	9.62451	+	5.55671i	0.396571	+	0.228960i
$590$	7.22558	−	26.9662i	0.297472	−	1.11018i
$591$	15.6885	+	4.20373i	0.645341	+	0.172919i
$592$	33.1783	+	8.89011i	1.36362	+	0.365381i
$593$	−7.03528	+	26.2560i	−0.288904	+	1.07821i	0.657034	+	0.753861i	$0.271811\pi$
$593$	−7.03528	+	26.2560i	−0.288904	+	1.07821i	−0.945939	+	0.324345i	$0.894856\pi$
$594$	−1.89816	−	1.09590i	−0.0778825	−	0.0449655i
$595$	0.617136	+	0.129503i	0.0253001	+	0.00530911i
$596$	−12.4824	−	3.34465i	−0.511300	−	0.137002i
$597$	0.915483	−	0.528554i	0.0374682	−	0.0216323i
$598$	−39.2485	−	83.1634i	−1.60499	−	3.40080i
$599$	14.5684	−	25.2331i	0.595247	−	1.03100i	−0.398265	−	0.917270i	$-0.630388\pi$
$599$	14.5684	−	25.2331i	0.595247	−	1.03100i	0.993512	−	0.113727i	$-0.0362790\pi$
$600$	−10.6413	−	39.7139i	−0.434430	−	1.62131i
$601$	22.2556	−	12.8493i	0.907826	−	0.524133i	0.0280947	−	0.999605i	$-0.491056\pi$
$601$	22.2556	−	12.8493i	0.907826	−	0.524133i	0.879731	+	0.475472i	$0.157723\pi$
$602$	15.1502	−	16.9141i	0.617476	−	0.689366i
$603$	−8.97356	−	8.97356i	−0.365432	−	0.365432i
$604$	−55.2410	−	55.2410i	−2.24773	−	2.24773i
$605$	2.19817	−	8.20368i	0.0893683	−	0.333527i
$606$	−8.63826	−	32.2384i	−0.350905	−	1.30960i
$607$			20.8561i			0.846524i	0.906007	+	0.423262i	$0.139115\pi$
$607$			20.8561i			0.846524i	−0.906007	+	0.423262i	$0.860885\pi$
$608$	23.5157	+	40.7303i	0.953687	+	1.65183i
$609$	0.834432	+	15.1685i	0.0338129	+	0.614658i
$610$			13.1062i			0.530654i
$611$	15.8723	−	7.49086i	0.642126	−	0.303048i
$612$	−1.37811	−	0.795651i	−0.0557067	−	0.0321623i
$613$	−1.99834	−	1.99834i	−0.0807123	−	0.0807123i	0.665598	−	0.746310i	$-0.268177\pi$
$613$	−1.99834	−	1.99834i	−0.0807123	−	0.0807123i	−0.746310	+	0.665598i	$0.768177\pi$
$614$	−8.68088	−	5.01191i	−0.350332	−	0.202264i
$615$	−3.73775	+	6.47397i	−0.150721	+	0.261056i
$616$	−17.9785	−	9.10180i	−0.724375	−	0.366722i
$617$	28.1706	−	7.54830i	1.13411	−	0.303883i	0.357528	−	0.933902i	$-0.383620\pi$
$617$	28.1706	−	7.54830i	1.13411	−	0.303883i	0.776579	+	0.630019i	$0.216953\pi$
$618$	33.0630	−	33.0630i	1.32999	−	1.32999i
$619$	−44.5517	+	11.9376i	−1.79069	+	0.479813i	−0.992462	−	0.122549i	$-0.960893\pi$
$619$	−44.5517	+	11.9376i	−1.79069	+	0.479813i	−0.798223	+	0.602362i	$0.794226\pi$
$620$	−11.7109	−	20.2839i	−0.470322	−	0.814621i
$621$	−4.66436	+	8.07890i	−0.187174	+	0.324195i
$622$	5.89204	−	21.9894i	0.236249	−	0.881694i
$623$	2.39580	−	11.4170i	0.0959857	−	0.457412i
$624$	−9.65363	−	53.3071i	−0.386455	−	2.13399i
$625$	7.68298	+	13.3073i	0.307319	+	0.532293i
$626$	−17.8936	+	17.8936i	−0.715170	+	0.715170i
$627$	−1.70774			−0.0682008
$628$	−123.598			−4.93210
$629$	−0.469838	+	0.469838i	−0.0187337	+	0.0187337i
$630$	2.67916	−	5.29205i	0.106740	−	0.210840i
$631$	−3.87044	−	14.4447i	−0.154080	−	0.575034i	−0.999182	−	0.0404298i	$-0.987127\pi$
$631$	−3.87044	−	14.4447i	−0.154080	−	0.575034i	0.845102	−	0.534604i	$-0.179539\pi$
$632$	−50.4916	−	13.5292i	−2.00845	−	0.538162i
$633$	1.64226	−	0.948161i	0.0652741	−	0.0376860i
$634$		−	44.9054i		−	1.78342i
$635$	−5.56657	+	1.49156i	−0.220902	+	0.0591906i
$636$	29.4634			1.16830
$637$	5.86526	−	24.5479i	0.232390	−	0.972623i
$638$	−12.5849			−0.498243
$639$	6.43570	−	1.72444i	0.254593	−	0.0682179i
$640$		−	31.7490i		−	1.25499i
$641$	14.6146	−	8.43773i	0.577241	−	0.333270i	−0.182795	−	0.983151i	$-0.558514\pi$
$641$	14.6146	−	8.43773i	0.577241	−	0.333270i	0.760036	+	0.649881i	$0.225181\pi$
$642$	17.4806	+	4.68390i	0.689903	+	0.184859i
$643$	4.07102	+	15.1933i	0.160545	+	0.599164i	0.998566	+	0.0535258i	$0.0170459\pi$
$643$	4.07102	+	15.1933i	0.160545	+	0.599164i	−0.838021	+	0.545638i	$0.816287\pi$
$644$	−61.0349	+	120.560i	−2.40511	+	4.75074i
$645$	−1.82017	+	1.82017i	−0.0716691	+	0.0716691i
$646$	−1.69278			−0.0666017
$647$	9.80443			0.385452			0.192726	−	0.981253i	$-0.438267\pi$
$647$	9.80443			0.385452			0.192726	+	0.981253i	$0.438267\pi$
$648$	−6.71797	+	6.71797i	−0.263907	+	0.263907i
$649$	−4.99140	−	8.64536i	−0.195930	−	0.339360i
$650$	18.2074	+	38.5795i	0.714152	+	1.51321i
$651$	−2.83474	+	13.5087i	−0.111102	+	0.529449i
$652$	−20.0543	+	74.8438i	−0.785389	+	2.93111i
$653$	1.81468	−	3.14312i	0.0710140	−	0.123000i	−0.828332	−	0.560238i	$-0.810710\pi$
$653$	1.81468	−	3.14312i	0.0710140	−	0.123000i	0.899346	+	0.437238i	$0.144043\pi$
$654$	10.1083	+	17.5081i	0.395265	+	0.684620i
$655$	−1.62521	+	0.435474i	−0.0635023	+	0.0170154i
$656$	96.8563	−	96.8563i	3.78160	−	3.78160i
$657$	7.74069	−	2.07411i	0.301993	−	0.0809188i
$658$	−31.4153	−	15.9043i	−1.22470	−	0.620015i
$659$	5.04765	−	8.74278i	0.196628	−	0.340570i	−0.750805	−	0.660524i	$-0.770334\pi$
$659$	5.04765	−	8.74278i	0.196628	−	0.340570i	0.947433	+	0.319954i	$0.103667\pi$
$660$	3.11693	+	1.79956i	0.121326	+	0.0700477i
$661$	21.7446	+	21.7446i	0.845766	+	0.845766i	0.989602	−	0.143836i	$-0.0459437\pi$
$661$	21.7446	+	21.7446i	0.845766	+	0.845766i	−0.143836	+	0.989602i	$0.545944\pi$
$662$	−51.2519	−	29.5903i	−1.99196	−	1.15006i
$663$	0.986404	+	0.353869i	0.0383088	+	0.0137431i
$664$		−	47.1944i		−	1.83150i
$665$	−0.253854	−	4.61461i	−0.00984405	−	0.178947i
$666$	3.12511	+	5.41284i	0.121095	+	0.209743i
$667$			53.5637i			2.07400i
$668$	−21.8564	−	81.5693i	−0.845650	−	3.15601i
$669$	1.42670	−	5.32451i	0.0551593	−	0.205857i
$670$	20.1181	+	20.1181i	0.777229	+	0.777229i
$671$	3.31389	+	3.31389i	0.127931	+	0.127931i
$672$	−38.9733	+	43.5108i	−1.50343	+	1.67847i
$673$	−6.14654	+	3.54871i	−0.236932	+	0.136793i	−0.613766	−	0.789488i	$-0.710346\pi$
$673$	−6.14654	+	3.54871i	−0.236932	+	0.136793i	0.376834	+	0.926281i	$0.377013\pi$
$674$	20.9746	+	78.2781i	0.807910	+	3.01516i
$675$	2.16379	−	3.74780i	0.0832845	−	0.144253i
$676$	24.9600	+	66.6542i	0.960002	+	2.56362i
$677$	11.0871	−	6.40112i	0.426111	−	0.246015i	−0.271578	−	0.962417i	$-0.587545\pi$
$677$	11.0871	−	6.40112i	0.426111	−	0.246015i	0.697688	+	0.716401i	$0.254212\pi$
$678$	−29.4658	−	7.89535i	−1.13163	−	0.303219i
$679$	32.0493	+	6.72539i	1.22994	+	0.258097i
$680$	1.96098	+	1.13217i	0.0752002	+	0.0434168i
$681$	4.13390	−	15.4279i	0.158412	−	0.591200i
$682$	−11.0451	−	2.95952i	−0.422938	−	0.113326i
$683$	21.3543	+	5.72186i	0.817098	+	0.218941i	0.643077	−	0.765801i	$-0.277657\pi$
$683$	21.3543	+	5.72186i	0.817098	+	0.218941i	0.174021	+	0.984742i	$0.444324\pi$
$684$	−3.01857	+	11.2655i	−0.115418	+	0.430746i
$685$	6.70559	+	3.87147i	0.256207	+	0.147921i
$686$	−46.0956	+	20.9547i	−1.75994	+	0.800055i
$687$	−11.9695	−	3.20721i	−0.456664	−	0.122363i
$688$	40.8470	−	23.5830i	1.55728	−	0.899094i
$689$	−19.0927	+	3.45759i	−0.727374	+	0.131724i
$690$	10.4572	−	18.1123i	0.398097	−	0.689524i
$691$	−3.23842	−	12.0860i	−0.123195	−	0.459772i	0.876574	−	0.481268i	$-0.159824\pi$
$691$	−3.23842	−	12.0860i	−0.123195	−	0.459772i	−0.999769	+	0.0214965i	$0.993157\pi$
$692$	−14.5290	+	8.38832i	−0.552310	+	0.318876i
$693$	−0.660669	−	2.01551i	−0.0250967	−	0.0765630i
$694$	41.2712	+	41.2712i	1.56663	+	1.56663i
$695$	−7.52286	−	7.52286i	−0.285358	−	0.285358i
$696$	−14.1188	+	52.6921i	−0.535172	+	1.99729i
$697$	0.685790	+	2.55940i	0.0259762	+	0.0969443i
$698$			7.58211i			0.286987i
$699$	1.70554	+	2.95409i	0.0645096	+	0.111734i
$700$	28.3141	−	55.9279i	1.07017	−	2.11388i
$701$			35.5823i			1.34393i	0.740585	+	0.671963i	$0.234549\pi$
$701$			35.5823i			1.34393i	−0.740585	+	0.671963i	$0.765451\pi$
$702$	5.61678	−	8.10100i	0.211992	−	0.305752i
$703$	4.21741	+	2.43492i	0.159063	+	0.0918349i
$704$	−17.1830	−	17.1830i	−0.647608	−	0.647608i
$705$	3.45687	+	1.99582i	0.130193	+	0.0751671i
$706$	−12.5781	+	21.7860i	−0.473384	+	0.819925i
$707$	14.5882	−	28.8157i	0.548646	−	1.08372i
$708$	−65.8535	+	17.6454i	−2.47492	+	0.663154i
$709$	−10.3917	+	10.3917i	−0.390269	+	0.390269i	−0.874783	−	0.484514i	$-0.838996\pi$
$709$	−10.3917	+	10.3917i	−0.390269	+	0.390269i	0.484514	+	0.874783i	$0.338996\pi$
$710$	−14.4284	+	3.86607i	−0.541488	+	0.145091i
$711$	−2.75101	−	4.76489i	−0.103171	−	0.178697i
$712$	20.9452	−	36.2781i	0.784953	−	1.35958i
$713$	−12.5962	+	47.0098i	−0.471733	+	1.76053i
$714$	−0.654880	−	1.99785i	−0.0245083	−	0.0747678i
$715$	−2.23099	−	0.800361i	−0.0834344	−	0.0299318i
$716$	−3.52881	−	6.11208i	−0.131878	−	0.228419i
$717$	0.615965	−	0.615965i	0.0230036	−	0.0230036i
$718$	57.9920			2.16424
$719$	−19.3966			−0.723372			−0.361686	−	0.932300i	$-0.617799\pi$
$719$	−19.3966			−0.723372			−0.361686	+	0.932300i	$0.617799\pi$
$720$	8.71210	−	8.71210i	0.324681	−	0.324681i
$721$	45.1799	−	2.48539i	1.68259	−	0.0925608i
$722$	−10.2337	−	38.1928i	−0.380860	−	1.42139i
$723$	−7.00948	−	1.87818i	−0.260685	−	0.0698504i
$724$	67.4046	−	38.9161i	2.50507	−	1.44630i
$725$		−	24.8482i		−	0.922839i
$726$	−27.3524	+	7.32905i	−1.01514	+	0.272007i
$727$	−48.0775			−1.78309			−0.891547	−	0.452928i	$-0.850379\pi$
$727$	−48.0775			−1.78309			−0.891547	+	0.452928i	$0.850379\pi$
$728$	47.4709	−	77.2035i	1.75939	−	2.86135i
$729$	−1.00000			−0.0370370
$730$	−17.3541	+	4.65001i	−0.642303	+	0.172105i
$731$			0.912392i			0.0337460i
$732$	27.7182	−	16.0031i	1.02450	−	0.591493i
$733$	20.6455	+	5.53194i	0.762558	+	0.204327i	0.619082	−	0.785327i	$-0.287505\pi$
$733$	20.6455	+	5.53194i	0.762558	+	0.204327i	0.143477	+	0.989654i	$0.454172\pi$
$734$	−3.50126	−	13.0669i	−0.129234	−	0.482307i
$735$	5.34805	−	2.08484i	0.197266	−	0.0769005i
$736$	−145.636	+	145.636i	−5.36822	+	5.36822i
$737$	10.1737			0.374752
$738$	24.9245			0.917485
$739$	10.9912	−	10.9912i	0.404317	−	0.404317i	−0.475434	−	0.879751i	$-0.657709\pi$
$739$	10.9912	−	10.9912i	0.404317	−	0.404317i	0.879751	+	0.475434i	$0.157709\pi$
$740$	−5.13167	−	8.88831i	−0.188644	−	0.326741i
$741$	0.634052	−	7.65441i	0.0232925	−	0.281192i
$742$	28.9963	+	25.9724i	1.06449	+	0.953476i
$743$	−1.89512	+	7.07267i	−0.0695250	+	0.259471i	−0.991936	−	0.126738i	$-0.959549\pi$
$743$	−1.89512	+	7.07267i	−0.0695250	+	0.259471i	0.922411	+	0.386209i	$0.126216\pi$
$744$	−24.7826	+	42.9246i	−0.908573	+	1.57369i
$745$	0.967747	+	1.67619i	0.0354555	+	0.0614108i
$746$	−41.6878	+	11.1702i	−1.52630	+	0.408970i
$747$	3.51255	−	3.51255i	0.128517	−	0.128517i
$748$	1.23224	−	0.330177i	0.0450551	−	0.0120725i
$749$	9.57627	+	14.6627i	0.349909	+	0.535763i
$750$	−10.4559	+	18.1101i	−0.381795	+	0.661289i
$751$	13.2187	+	7.63184i	0.482358	+	0.278490i	0.721399	−	0.692520i	$-0.243500\pi$
$751$	13.2187	+	7.63184i	0.482358	+	0.278490i	−0.239040	+	0.971010i	$0.576833\pi$
$752$	−51.7178	−	51.7178i	−1.88595	−	1.88595i
$753$	13.3147	+	7.68725i	0.485215	+	0.280139i
$754$	4.67254	−	56.4079i	0.170164	−	2.05425i
$755$			11.7008i			0.425834i
$756$	−14.4635	+	0.795651i	−0.526032	+	0.0289375i
$757$	−14.8601	−	25.7384i	−0.540098	−	0.935477i	−0.998898	−	0.0469377i	$-0.985054\pi$
$757$	−14.8601	−	25.7384i	−0.540098	−	0.935477i	0.458800	−	0.888540i	$-0.348280\pi$
$758$			51.8571i			1.88354i
$759$	−1.93560	−	7.22376i	−0.0702579	−	0.262206i
$760$	4.29528	−	16.0302i	0.155806	−	0.581477i
$761$	1.72595	+	1.72595i	0.0625658	+	0.0625658i	0.737697	−	0.675132i	$-0.235913\pi$
$761$	1.72595	+	1.72595i	0.0625658	+	0.0625658i	−0.675132	+	0.737697i	$0.735913\pi$
$762$	13.5867	+	13.5867i	0.492196	+	0.492196i
$763$	−4.01785	+	19.1467i	−0.145456	+	0.693159i
$764$	96.1636	−	55.5201i	3.47908	−	2.00865i
$765$	0.0616859	+	0.230215i	0.00223026	+	0.00832344i
$766$	−46.6090	+	80.7292i	−1.68405	+	2.91686i
$767$	40.6032	−	19.1625i	1.46610	−	0.691917i
$768$	−39.1722	+	22.6161i	−1.41350	+	0.816087i
$769$	−39.3287	−	10.5381i	−1.41823	−	0.380013i	−0.533374	−	0.845880i	$-0.679076\pi$
$769$	−39.3287	−	10.5381i	−1.41823	−	0.380013i	−0.884855	+	0.465867i	$0.845743\pi$
$770$	1.48117	+	4.51863i	0.0533777	+	0.162840i
$771$	−19.2801	−	11.1313i	−0.694354	−	0.400886i
$772$	−10.3210	+	38.5184i	−0.371460	+	1.38631i
$773$	27.1613	+	7.27785i	0.976925	+	0.261766i	0.711749	−	0.702434i	$-0.247903\pi$
$773$	27.1613	+	7.27785i	0.976925	+	0.261766i	0.265176	+	0.964200i	$0.414570\pi$
$774$	8.29005	+	2.22131i	0.297980	+	0.0798434i
$775$	5.84339	−	21.8078i	0.209901	−	0.783361i
$776$	101.838	+	58.7963i	3.65578	+	2.11066i
$777$	−1.24217	+	5.91946i	−0.0445626	+	0.212359i
$778$	40.9737	+	10.9789i	1.46898	+	0.393611i
$779$	16.8182	−	9.70997i	0.602573	−	0.347896i
$780$	−9.22319	+	13.3025i	−0.330243	+	0.476305i
$781$	−2.67067	+	4.62574i	−0.0955641	+	0.165522i
$782$	−1.91864	−	7.16048i	−0.0686106	−	0.256058i
$783$	−4.97256	+	2.87091i	−0.177705	+	0.102598i
$784$	−104.542	+	11.5368i	−3.73363	+	0.412029i
$785$	13.0898	+	13.0898i	0.467196	+	0.467196i
$786$	3.96678	+	3.96678i	0.141490	+	0.141490i
$787$	0.536271	−	2.00139i	0.0191160	−	0.0713418i	−0.955709	−	0.294313i	$-0.904909\pi$
$787$	0.536271	−	2.00139i	0.0191160	−	0.0713418i	0.974825	+	0.222972i	$0.0715757\pi$
$788$	23.0152	+	85.8941i	0.819884	+	3.05985i
$789$		−	13.1804i		−	0.469236i
$790$	6.16756	+	10.6825i	0.219432	+	0.380068i
$791$	−16.1421	−	24.7159i	−0.573947	−	0.878798i
$792$		−	7.61643i		−	0.270638i
$793$	−16.0838	+	13.6230i	−0.571153	+	0.483768i
$794$	31.4157	+	18.1378i	1.11490	+	0.643688i
$795$	−3.12036	−	3.12036i	−0.110668	−	0.110668i
$796$	5.01222	+	2.89381i	0.177654	+	0.102568i
$797$	11.7487	−	20.3493i	0.416159	−	0.720809i	−0.579390	−	0.815050i	$-0.696709\pi$
$797$	11.7487	−	20.3493i	0.416159	−	0.720809i	0.995549	+	0.0942412i	$0.0300425\pi$
$798$	−12.9014	+	8.42593i	−0.456703	+	0.298275i
$799$	1.36663	−	0.366187i	0.0483479	−	0.0129548i
$800$	67.5606	−	67.5606i	2.38863	−	2.38863i
$801$	4.25897	−	1.14119i	0.150483	−	0.0403219i
$802$	22.7033	+	39.3233i	0.801682	+	1.38855i
$803$	−3.21221	+	5.56371i	−0.113356	+	0.196339i
$804$	17.9828	−	67.1126i	0.634203	−	2.36688i
$805$	19.2321	−	6.30413i	0.677842	−	0.222191i
$806$	17.3659	−	48.4072i	0.611688	−	1.70507i
$807$	−1.01475	−	1.75759i	−0.0357207	−	0.0618702i
$808$	82.0095	−	82.0095i	2.88508	−	2.88508i
$809$	−43.5704			−1.53185			−0.765927	−	0.642928i	$-0.777720\pi$
$809$	−43.5704			−1.53185			−0.765927	+	0.642928i	$0.777720\pi$
$810$	2.24193			0.0787733
$811$	−9.71904	+	9.71904i	−0.341282	+	0.341282i	−0.856849	−	0.515567i	$-0.827581\pi$
$811$	−9.71904	+	9.71904i	−0.341282	+	0.341282i	0.515567	+	0.856849i	$0.327581\pi$
$812$	−69.6363	+	45.4798i	−2.44375	+	1.59603i
$813$	−7.25419	−	27.0730i	−0.254416	−	0.949492i
$814$	−4.83990	−	1.29685i	−0.169639	−	0.0454545i
$815$	10.0503	−	5.80256i	0.352048	−	0.203255i
$816$		−	4.36709i		−	0.152879i
$817$	6.45919	−	1.73073i	0.225978	−	0.0605507i
$818$	98.3215			3.43773
$819$	9.27917	−	2.21291i	0.324240	−	0.0773254i
$820$	−40.9280			−1.42927
$821$	7.97298	−	2.13635i	0.278259	−	0.0745592i	−0.116991	−	0.993133i	$-0.537325\pi$
$821$	7.97298	−	2.13635i	0.278259	−	0.0745592i	0.395250	+	0.918574i	$0.370658\pi$
$822$		−	25.8162i		−	0.900445i
$823$	5.75470	−	3.32248i	0.200596	−	0.115814i	−0.396337	−	0.918105i	$-0.629719\pi$
$823$	5.75470	−	3.32248i	0.200596	−	0.115814i	0.596934	+	0.802291i	$0.296386\pi$
$824$	156.946	+	42.0535i	5.46746	+	1.46500i
$825$	0.897926	+	3.35110i	0.0312618	+	0.116670i
$826$	−80.3639	−	40.6851i	−2.79622	−	1.41561i
$827$	31.3947	−	31.3947i	1.09170	−	1.09170i	0.0963527	−	0.995347i	$-0.469282\pi$
$827$	31.3947	−	31.3947i	1.09170	−	1.09170i	0.995347	−	0.0963527i	$-0.0307177\pi$
$828$	−51.0743			−1.77495
$829$	−17.1664			−0.596213			−0.298106	−	0.954533i	$-0.596355\pi$
$829$	−17.1664			−0.596213			−0.298106	+	0.954533i	$0.596355\pi$
$830$	−7.87487	+	7.87487i	−0.273341	+	0.273341i
$831$	5.43672	+	9.41668i	0.188598	+	0.326661i
$832$	83.3968	−	70.6374i	2.89126	−	2.44891i
$833$	0.817869	−	1.86293i	0.0283375	−	0.0645468i
$834$	−9.18081	+	34.2633i	−0.317906	+	1.18644i
$835$	−6.32397	+	10.9534i	−0.218850	+	0.379059i
$836$	−4.67491	−	8.09718i	−0.161685	−	0.280047i
$837$	−5.03926	+	1.35027i	−0.174182	+	0.0466720i
$838$	−38.7384	+	38.7384i	−1.33820	+	1.33820i
$839$	2.14438	−	0.574586i	0.0740324	−	0.0198369i	−0.221613	−	0.975135i	$-0.571132\pi$
$839$	2.14438	−	0.574586i	0.0740324	−	0.0198369i	0.295645	+	0.955298i	$0.404465\pi$
$840$	20.5809	−	1.13217i	0.710107	−	0.0390637i
$841$	−1.98420	+	3.43674i	−0.0684208	+	0.118508i
$842$	−30.6378	−	17.6887i	−1.05585	−	0.609594i
$843$	5.00498	+	5.00498i	0.172381	+	0.172381i
$844$	8.99131	+	5.19113i	0.309494	+	0.178686i
$845$	4.41568	−	9.70254i	0.151904	−	0.333777i
$846$		−	13.3088i		−	0.457566i
$847$	−24.4484	−	12.3772i	−0.840056	−	0.425287i
$848$	40.4290	+	70.0251i	1.38834	+	2.40467i
$849$			0.922161i			0.0316485i
$850$	0.890059	+	3.32174i	0.0305288	+	0.113935i
$851$	−5.51961	+	20.5995i	−0.189210	+	0.706141i
$852$	25.7939	+	25.7939i	0.883686	+	0.883686i
$853$	20.3713	+	20.3713i	0.697499	+	0.697499i	0.963870	−	0.266371i	$-0.0858248\pi$
$853$	20.3713	+	20.3713i	0.697499	+	0.697499i	−0.266371	+	0.963870i	$0.585825\pi$
$854$	41.3857	+	8.68459i	1.41619	+	0.297180i
$855$	1.51277	−	0.873398i	0.0517357	−	0.0298696i
$856$	16.2763	+	60.7441i	0.556314	+	2.07619i
$857$	21.8286	−	37.8083i	0.745652	−	1.29151i	−0.204238	−	0.978921i	$-0.565472\pi$
$857$	21.8286	−	37.8083i	0.745652	−	1.29151i	0.949890	−	0.312585i	$-0.101195\pi$
$858$	1.40823	+	7.77619i	0.0480761	+	0.265475i
$859$	−34.3572	+	19.8362i	−1.17225	+	0.676801i	−0.954210	−	0.299138i	$-0.903301\pi$
$859$	−34.3572	+	19.8362i	−1.17225	+	0.676801i	−0.218044	+	0.975939i	$0.569968\pi$
$860$	−13.6129	−	3.64757i	−0.464196	−	0.124381i
$861$	17.9663	+	16.0926i	0.612288	+	0.548436i
$862$	−29.1089	−	16.8060i	−0.991454	−	0.572416i
$863$	−7.51704	+	28.0540i	−0.255883	+	0.954968i	0.711714	+	0.702469i	$0.247919\pi$
$863$	−7.51704	+	28.0540i	−0.255883	+	0.954968i	−0.967597	+	0.252499i	$0.918748\pi$
$864$	−21.3259	−	5.71424i	−0.725520	−	0.194403i
$865$	2.42709	+	0.650337i	0.0825235	+	0.0221121i
$866$	−15.9205	+	59.4162i	−0.541001	+	2.01904i
$867$	−14.6493	−	8.45776i	−0.497515	−	0.287241i
$868$	−71.8110	+	23.5391i	−2.43742	+	0.798968i
$869$	4.26053	+	1.14161i	0.144529	+	0.0387263i
$870$	11.1481	−	6.43637i	0.377956	−	0.218213i
$871$	−3.77729	+	45.6002i	−0.127988	+	1.54510i
$872$	−35.1258	+	60.8397i	−1.18951	+	2.06029i
$873$	3.20349	+	11.9556i	0.108422	+	0.404635i
$874$	−47.0524	+	27.1657i	−1.59157	+	0.918893i
$875$	−19.2298	+	6.30337i	−0.650085	+	0.213093i
$876$	31.0242	+	31.0242i	1.04821	+	1.04821i
$877$	−17.0288	−	17.0288i	−0.575021	−	0.575021i	0.358506	−	0.933527i	$-0.383286\pi$
$877$	−17.0288	−	17.0288i	−0.575021	−	0.575021i	−0.933527	+	0.358506i	$0.883286\pi$
$878$	11.9194	−	44.4837i	0.402259	−	1.50125i
$879$	3.83466	+	14.3112i	0.129340	+	0.482703i
$880$			9.87725i			0.332962i
$881$	−16.4202	−	28.4406i	−0.553209	−	0.958187i	−0.998040	−	0.0625724i	$-0.980070\pi$
$881$	−16.4202	−	28.4406i	−0.553209	−	0.958187i	0.444831	−	0.895615i	$-0.353264\pi$
$882$	−14.9355	−	11.9667i	−0.502906	−	0.402940i
$883$		−	23.2851i		−	0.783606i	−0.920049	−	0.391803i	$-0.871851\pi$
$883$		−	23.2851i		−	0.783606i	0.920049	−	0.391803i	$-0.128149\pi$
$884$	1.02241	+	5.64569i	0.0343872	+	0.189885i
$885$	8.84306	+	5.10554i	0.297256	+	0.171621i
$886$	24.4327	+	24.4327i	0.820831	+	0.820831i
$887$	34.5243	+	19.9326i	1.15921	+	0.669272i	0.951115	−	0.308835i	$-0.0999392\pi$
$887$	34.5243	+	19.9326i	1.15921	+	0.669272i	0.208098	+	0.978108i	$0.433273\pi$
$888$	−10.8596	+	18.8094i	−0.364424	+	0.631201i
$889$	1.02134	+	18.5660i	0.0342545	+	0.622685i
$890$	−9.54830	+	2.55846i	−0.320060	+	0.0857597i
$891$	0.566870	−	0.566870i	0.0189908	−	0.0189908i
$892$	29.1514	−	7.81111i	0.976063	−	0.261535i
$893$	−5.18477	−	8.98029i	−0.173502	−	0.300514i
$894$	3.22663	−	5.58868i	0.107915	−	0.186913i
$895$	−0.273585	+	1.02103i	−0.00914492	+	0.0341293i
$896$	−100.254	−	21.0379i	−3.34927	−	0.702827i
$897$	33.0968	−	5.99366i	1.10507	−	0.200123i
$898$	14.8928	+	25.7951i	0.496979	+	0.860793i
$899$	−21.1815	+	21.1815i	−0.706443	+	0.706443i
$900$	23.6933			0.789778
$901$	−1.56414			−0.0521090
$902$	−14.1290	+	14.1290i	−0.470443	+	0.470443i
$903$	4.54149	+	6.95369i	0.151131	+	0.231404i
$904$	−27.4360	−	102.392i	−0.912507	−	3.40552i
$905$	−11.2600	−	3.01712i	−0.374296	−	0.100292i
$906$	33.7856	−	19.5061i	1.12245	−	0.648047i
$907$			14.0338i			0.465985i	0.972479	+	0.232992i	$0.0748517\pi$
$907$			14.0338i			0.465985i	−0.972479	+	0.232992i	$0.925148\pi$
$908$	84.4673	−	22.6329i	2.80314	−	0.751100i
$909$	12.2075			0.404897
$910$	−20.8032	+	4.96119i	−0.689621	+	0.164462i
$911$	−11.6160			−0.384856			−0.192428	−	0.981311i	$-0.561636\pi$
$911$	−11.6160			−0.384856			−0.192428	+	0.981311i	$0.561636\pi$
$912$	−30.9164	+	8.28402i	−1.02374	+	0.274311i
$913$			3.98231i			0.131795i
$914$	−0.635422	+	0.366861i	−0.0210179	+	0.0121347i
$915$	−4.63037	−	1.24070i	−0.153075	−	0.0410164i
$916$	−17.5593	−	65.5324i	−0.580177	−	2.16525i
$917$	0.298188	+	5.42053i	0.00984705	+	0.179002i
$918$	0.561903	−	0.561903i	0.0185456	−	0.0185456i
$919$	−18.8503			−0.621813			−0.310906	−	0.950441i	$-0.600633\pi$
$919$	−18.8503			−0.621813			−0.310906	+	0.950441i	$0.600633\pi$
$920$	72.6762			2.39606
$921$	2.59247	−	2.59247i	0.0854248	−	0.0854248i
$922$	43.9781	+	76.1722i	1.44834	+	2.50860i
$923$	−19.7418	−	13.6879i	−0.649809	−	0.450541i
$924$	7.74788	−	8.64994i	0.254887	−	0.284562i
$925$	2.56055	−	9.55609i	0.0841903	−	0.314202i
$926$	−44.7996	+	77.5952i	−1.47221	+	2.54994i
$927$	8.55111	+	14.8110i	0.280855	+	0.486456i
$928$	−122.449	+	32.8101i	−4.01959	+	1.07704i
$929$	16.5508	−	16.5508i	0.543015	−	0.543015i	−0.381396	−	0.924412i	$-0.624557\pi$
$929$	16.5508	−	16.5508i	0.543015	−	0.543015i	0.924412	+	0.381396i	$0.124557\pi$
$930$	11.2977	−	3.02720i	0.370465	−	0.0992658i
$931$	−14.7399	−	2.25619i	−0.483080	−	0.0739437i
$932$	−9.33777	+	16.1735i	−0.305869	+	0.529781i
$933$	7.21101	+	4.16328i	0.236078	+	0.136300i
$934$	14.7412	+	14.7412i	0.482348	+	0.482348i
$935$	−0.165470	−	0.0955340i	−0.00541144	−	0.00312429i
$936$	34.1381	+	2.82783i	1.11584	+	0.0924305i
$937$			6.34230i			0.207194i	0.994619	+	0.103597i	$0.0330352\pi$
$937$			6.34230i			0.207194i	−0.994619	+	0.103597i	$0.966965\pi$
$938$	76.8582	−	50.1964i	2.50951	−	1.63897i
$939$	−4.62783	−	8.01564i	−0.151024	−	0.261580i
$940$			21.8541i			0.712802i
$941$	11.3483	+	42.3526i	0.369945	+	1.38065i	0.860592	+	0.509295i	$0.170094\pi$
$941$	11.3483	+	42.3526i	0.369945	+	1.38065i	−0.490647	+	0.871359i	$0.663239\pi$
$942$	15.9747	−	59.6183i	0.520483	−	1.94247i
$943$	60.1353	+	60.1353i	1.95827	+	1.95827i
$944$	−132.300	−	132.300i	−4.30600	−	4.30600i
$945$	1.61604	+	1.44751i	0.0525698	+	0.0470876i
$946$	−5.95857	+	3.44018i	−0.193730	+	0.111850i
$947$	−14.5258	−	54.2110i	−0.472025	−	1.76162i	−0.632478	−	0.774579i	$-0.717962\pi$
$947$	−14.5258	−	54.2110i	−0.472025	−	1.76162i	0.160452	−	0.987044i	$-0.448705\pi$
$948$	15.0616	−	26.0875i	0.489179	−	0.847284i
$949$	−23.7449	−	16.4634i	−0.770792	−	0.534424i
$950$	21.8276	−	12.6022i	0.708180	−	0.408868i
$951$	15.8649	+	4.25100i	0.514456	+	0.137848i
$952$	4.87450	−	5.44202i	0.157983	−	0.176377i
$953$	2.39079	+	1.38032i	0.0774453	+	0.0447130i	0.538223	−	0.842803i	$-0.319096\pi$
$953$	2.39079	+	1.38032i	0.0774453	+	0.0447130i	−0.460777	+	0.887516i	$0.652429\pi$
$954$	−3.80806	+	14.2119i	−0.123290	+	0.460126i
$955$	−16.0643	−	4.30441i	−0.519828	−	0.139287i
$956$	4.60676	+	1.23438i	0.148993	+	0.0399226i
$957$	1.19136	−	4.44622i	0.0385112	−	0.143726i
$958$	13.6055	+	7.85511i	0.439572	+	0.253787i
$959$	16.6684	−	18.6090i	0.538250	−	0.600917i
$960$	24.0091	+	6.43323i	0.774891	+	0.207632i
$961$	3.27586	−	1.89132i	0.105673	−	0.0610103i
$962$	7.60966	−	21.2118i	0.245345	−	0.683896i
$963$	−3.30962	+	5.73242i	−0.106651	+	0.184725i
$964$	−10.2830	−	38.3766i	−0.331192	−	1.23603i
$965$	5.17240	−	2.98629i	0.166505	−	0.0961320i
$966$	−50.2644	−	45.0226i	−1.61723	−	1.44858i
$967$	3.57988	+	3.57988i	0.115121	+	0.115121i	0.762321	−	0.647200i	$-0.224060\pi$
$967$	3.57988	+	3.57988i	0.115121	+	0.115121i	−0.647200	+	0.762321i	$0.724060\pi$
$968$	−69.5802	−	69.5802i	−2.23639	−	2.23639i
$969$	0.160248	−	0.598055i	0.00514792	−	0.0192123i
$970$	−7.18199	−	26.8036i	−0.230600	−	0.860610i
$971$			16.6292i			0.533655i	0.963744	+	0.266828i	$0.0859755\pi$
$971$			16.6292i			0.533655i	−0.963744	+	0.266828i	$0.914025\pi$
$972$	−2.73748	−	4.74145i	−0.0878046	−	0.152082i
$973$	−28.7400	+	18.7702i	−0.921362	+	0.601746i
$974$			10.5764i			0.338891i
$975$	−15.3536	+	2.78046i	−0.491709	+	0.0890460i
$976$	76.0686	+	43.9182i	2.43490	+	1.40579i
$977$	2.06788	+	2.06788i	0.0661573	+	0.0661573i	0.739411	−	0.673254i	$-0.235104\pi$
$977$	2.06788	+	2.06788i	0.0661573	+	0.0661573i	−0.673254	+	0.739411i	$0.735104\pi$
$978$	−33.5094	−	19.3467i	−1.07151	−	0.618638i
$979$	−1.76737	+	3.06118i	−0.0564855	+	0.0978358i
$980$	24.5253	+	19.6503i	0.783432	+	0.627705i
$981$	−7.14245	+	1.91381i	−0.228041	+	0.0611034i
$982$	75.8826	−	75.8826i	2.42151	−	2.42151i
$983$	−52.9906	+	14.1988i	−1.69014	+	0.452871i	−0.970426	−	0.241401i	$-0.922393\pi$
$983$	−52.9906	+	14.1988i	−1.69014	+	0.452871i	−0.719713	+	0.694272i	$0.755727\pi$
$984$	43.3058	+	75.0078i	1.38054	+	2.39116i
$985$	6.65927	−	11.5342i	0.212182	−	0.367510i
$986$	1.18092	−	4.40726i	0.0376083	−	0.140356i
$987$	8.59289	−	9.59333i	0.273515	−	0.305359i
$988$	38.0287	−	17.9474i	1.20985	−	0.570984i
$989$	14.6420	+	25.3607i	0.465589	+	0.806424i
$990$	−1.27088	+	1.27088i	−0.0403912	+	0.0403912i
$991$	−54.6627			−1.73642			−0.868209	−	0.496199i	$-0.834729\pi$
$991$	−54.6627			−1.73642			−0.868209	+	0.496199i	$0.834729\pi$
$992$	−115.182			−3.65704
$993$	15.3059	−	15.3059i	0.485719	−	0.485719i
$994$	2.64727	+	48.1226i	0.0839664	+	1.52636i
$995$	−0.224354	−	0.837299i	−0.00711249	−	0.0265442i
$996$	26.2701	+	7.03904i	0.832399	+	0.223041i
$997$	−26.9243	+	15.5447i	−0.852700	+	0.492307i	−0.861561	−	0.507654i	$-0.830513\pi$
$997$	−26.9243	+	15.5447i	−0.852700	+	0.492307i	0.00886064	+	0.999961i	$0.497180\pi$
$998$			31.4757i			0.996346i
$999$	−2.20818	+	0.591680i	−0.0698637	+	0.0187199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.b.115.1	yes	40
3.2	odd	2		819.2.gh.d.388.10		40
7.5	odd	6		273.2.bt.b.271.10	yes	40
13.6	odd	12		273.2.bt.b.136.10	✓	40
21.5	even	6		819.2.et.d.271.1		40
39.32	even	12		819.2.et.d.136.1		40
91.19	even	12	inner	273.2.cg.b.19.1	yes	40
273.110	odd	12		819.2.gh.d.19.10		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.136.10	✓	40	13.6	odd	12
273.2.bt.b.271.10	yes	40	7.5	odd	6
273.2.cg.b.19.1	yes	40	91.19	even	12	inner
273.2.cg.b.115.1	yes	40	1.1	even	1	trivial
819.2.et.d.136.1		40	39.32	even	12
819.2.et.d.271.1		40	21.5	even	6
819.2.gh.d.19.10		40	273.110	odd	12
819.2.gh.d.388.10		40	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.64088 + 0.707621i) q^{2} -1.00000i q^{3} +(4.74145 - 2.73748i) q^{4} +(-0.792066 - 0.212233i) q^{5} +(0.707621 + 2.64088i) q^{6} +(-1.19502 + 2.36049i) q^{7} +(-6.71797 + 6.71797i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-2.64088 + 0.707621i) q^{2} -1.00000i q^{3} +(4.74145 - 2.73748i) q^{4} +(-0.792066 - 0.212233i) q^{5} +(0.707621 + 2.64088i) q^{6} +(-1.19502 + 2.36049i) q^{7} +(-6.71797 + 6.71797i) q^{8} -1.00000 q^{9} +2.24193 q^{10} +(0.566870 - 0.566870i) q^{11} +(-2.73748 - 4.74145i) q^{12} +(2.33034 + 2.75128i) q^{13} +(1.48557 - 7.07939i) q^{14} +(-0.212233 + 0.792066i) q^{15} +(7.51260 - 13.0122i) q^{16} +(0.145326 + 0.251711i) q^{17} +(2.64088 - 0.707621i) q^{18} +(1.50629 - 1.50629i) q^{19} +(-4.33652 + 1.16197i) q^{20} +(2.36049 + 1.19502i) q^{21} +(-1.09590 + 1.89816i) q^{22} +(8.07890 + 4.66436i) q^{23} +(6.71797 + 6.71797i) q^{24} +(-3.74780 - 2.16379i) q^{25} +(-8.10100 - 5.61678i) q^{26} +1.00000i q^{27} +(0.795651 + 14.4635i) q^{28} +(2.87091 + 4.97256i) q^{29} -2.24193i q^{30} +(1.35027 + 5.03926i) q^{31} +(-5.71424 + 21.3259i) q^{32} +(-0.566870 - 0.566870i) q^{33} +(-0.561903 - 0.561903i) q^{34} +(1.44751 - 1.61604i) q^{35} +(-4.74145 + 2.73748i) q^{36} +(0.591680 + 2.20818i) q^{37} +(-2.91205 + 5.04382i) q^{38} +(2.75128 - 2.33034i) q^{39} +(6.74685 - 3.89530i) q^{40} +(8.80575 + 2.35949i) q^{41} +(-7.07939 - 1.48557i) q^{42} +(2.71857 + 1.56956i) q^{43} +(1.13599 - 4.23957i) q^{44} +(0.792066 + 0.212233i) q^{45} +(-24.6360 - 6.60119i) q^{46} +(1.25989 - 4.70196i) q^{47} +(-13.0122 - 7.51260i) q^{48} +(-4.14384 - 5.64168i) q^{49} +(11.4286 + 3.06229i) q^{50} +(0.251711 - 0.145326i) q^{51} +(18.5807 + 6.66578i) q^{52} +(-2.69075 + 4.66051i) q^{53} +(-0.707621 - 2.64088i) q^{54} +(-0.569307 + 0.328689i) q^{55} +(-7.82958 - 23.8858i) q^{56} +(-1.50629 - 1.50629i) q^{57} +(-11.1004 - 11.1004i) q^{58} +(3.22293 - 12.0281i) q^{59} +(1.16197 + 4.33652i) q^{60} +5.84594i q^{61} +(-7.13177 - 12.3526i) q^{62} +(1.19502 - 2.36049i) q^{63} -30.3120i q^{64} +(-1.26187 - 2.67377i) q^{65} +(1.89816 + 1.09590i) q^{66} +(8.97356 + 8.97356i) q^{67} +(1.37811 + 0.795651i) q^{68} +(4.66436 - 8.07890i) q^{69} +(-2.67916 + 5.29205i) q^{70} +(-6.43570 + 1.72444i) q^{71} +(6.71797 - 6.71797i) q^{72} +(-7.74069 + 2.07411i) q^{73} +(-3.12511 - 5.41284i) q^{74} +(-2.16379 + 3.74780i) q^{75} +(3.01857 - 11.2655i) q^{76} +(0.660669 + 2.01551i) q^{77} +(-5.61678 + 8.10100i) q^{78} +(2.75101 + 4.76489i) q^{79} +(-8.71210 + 8.71210i) q^{80} +1.00000 q^{81} -24.9245 q^{82} +(-3.51255 + 3.51255i) q^{83} +(14.4635 - 0.795651i) q^{84} +(-0.0616859 - 0.230215i) q^{85} +(-8.29005 - 2.22131i) q^{86} +(4.97256 - 2.87091i) q^{87} +7.61643i q^{88} +(-4.25897 + 1.14119i) q^{89} -2.24193 q^{90} +(-9.27917 + 2.21291i) q^{91} +51.0743 q^{92} +(5.03926 - 1.35027i) q^{93} +13.3088i q^{94} +(-1.51277 + 0.873398i) q^{95} +(21.3259 + 5.71424i) q^{96} +(-3.20349 - 11.9556i) q^{97} +(14.9355 + 11.9667i) q^{98} +(-0.566870 + 0.566870i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 8 * q^7 - 40 * q^9	\( 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} - 24 q^{34} + 26 q^{35} + 36 q^{37} - 8 q^{38} + 18 q^{39} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 32 q^{44} - 26 q^{46} - 4 q^{47} + 24 q^{48} - 14 q^{49} - 20 q^{50} + 2 q^{52} - 8 q^{53} - 42 q^{55} + 46 q^{56} - 14 q^{57} + 24 q^{58} + 14 q^{59} + 2 q^{60} + 24 q^{62} + 8 q^{63} + 28 q^{65} - 18 q^{66} - 44 q^{67} - 18 q^{68} + 4 q^{69} - 4 q^{70} - 6 q^{71} + 14 q^{73} - 20 q^{74} + 24 q^{75} - 64 q^{76} + 24 q^{77} + 8 q^{78} + 20 q^{80} + 40 q^{81} + 48 q^{82} - 12 q^{83} + 22 q^{84} + 2 q^{85} - 60 q^{86} + 18 q^{87} - 2 q^{89} - 14 q^{91} + 236 q^{92} - 8 q^{93} + 24 q^{95} + 16 q^{96} - 62 q^{97} - 88 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

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