LMFDB - Embedded newform 273.2.cc.a.50.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(50,273)]

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([6, 0, 7]))

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

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

chi := DirichletCharacter("273.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cc (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:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			50.15
Character	$\chi$	$=$	273.50
Dual form			273.2.cc.a.71.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.307973 + 0.0825212i) q^{2} +(-0.784738 + 1.54408i) q^{3} +(-1.64401 - 0.949171i) q^{4} +(2.80070 - 2.80070i) q^{5} +(-0.369098 + 0.410778i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-0.878890 - 0.878890i) q^{8} +(-1.76837 - 2.42340i) q^{9} +O(q^{10})$	\(q+(0.307973 + 0.0825212i) q^{2} +(-0.784738 + 1.54408i) q^{3} +(-1.64401 - 0.949171i) q^{4} +(2.80070 - 2.80070i) q^{5} +(-0.369098 + 0.410778i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-0.878890 - 0.878890i) q^{8} +(-1.76837 - 2.42340i) q^{9} +(1.09366 - 0.631424i) q^{10} +(1.10413 - 4.12065i) q^{11} +(2.75572 - 1.79364i) q^{12} +(3.37979 + 1.25579i) q^{13} +0.318837i q^{14} +(2.12669 + 6.52233i) q^{15} +(1.70020 + 2.94482i) q^{16} +(1.68153 - 2.91250i) q^{17} +(-0.344629 - 0.892270i) q^{18} +(-0.852646 + 0.228466i) q^{19} +(-7.26274 + 1.94604i) q^{20} +(-1.69457 - 0.358362i) q^{21} +(0.680083 - 1.17794i) q^{22} +(2.81588 + 4.87725i) q^{23} +(2.04678 - 0.667378i) q^{24} -10.6879i q^{25} +(0.937256 + 0.665655i) q^{26} +(5.12963 - 0.828774i) q^{27} +(0.491327 - 1.83366i) q^{28} +(-0.785282 + 0.453383i) q^{29} +(0.116734 + 2.18420i) q^{30} +(-1.32530 - 1.32530i) q^{31} +(0.923996 + 3.44840i) q^{32} +(5.49617 + 4.93849i) q^{33} +(0.758209 - 0.758209i) q^{34} +(3.43015 + 1.98040i) q^{35} +(0.607004 + 5.66259i) q^{36} +(-8.51301 - 2.28105i) q^{37} -0.281445 q^{38} +(-4.59129 + 4.23320i) q^{39} -4.92302 q^{40} +(-4.07157 - 1.09097i) q^{41} +(-0.492311 - 0.250204i) q^{42} +(7.76670 + 4.48411i) q^{43} +(-5.72640 + 5.72640i) q^{44} +(-11.7399 - 1.83454i) q^{45} +(0.464740 + 1.73443i) q^{46} +(-4.63695 - 4.63695i) q^{47} +(-5.88126 + 0.314322i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(0.881975 - 3.29158i) q^{50} +(3.17757 + 4.88197i) q^{51} +(-4.36446 - 5.27254i) q^{52} +3.33723i q^{53} +(1.64818 + 0.168063i) q^{54} +(-8.44839 - 14.6330i) q^{55} +(0.621469 - 1.07642i) q^{56} +(0.316334 - 1.49584i) q^{57} +(-0.279260 + 0.0748274i) q^{58} +(-9.52199 + 2.55141i) q^{59} +(2.69450 - 12.7414i) q^{60} +(-2.31485 + 4.00944i) q^{61} +(-0.298792 - 0.517522i) q^{62} +(1.88314 - 2.33534i) q^{63} -5.66252i q^{64} +(12.9829 - 5.94869i) q^{65} +(1.28514 + 1.97448i) q^{66} +(-3.10288 + 11.5801i) q^{67} +(-5.52892 + 3.19212i) q^{68} +(-9.74060 + 0.520583i) q^{69} +(0.892969 + 0.892969i) q^{70} +(3.10773 + 11.5982i) q^{71} +(-0.575697 + 3.68410i) q^{72} +(5.88441 - 5.88441i) q^{73} +(-2.43354 - 1.40501i) q^{74} +(16.5029 + 8.38717i) q^{75} +(1.61861 + 0.433706i) q^{76} +4.26601 q^{77} +(-1.76333 + 0.924834i) q^{78} +13.3054 q^{79} +(13.0093 + 3.48584i) q^{80} +(-2.74573 + 8.57094i) q^{81} +(-1.16391 - 0.671981i) q^{82} +(-2.32987 + 2.32987i) q^{83} +(2.44575 + 2.19759i) q^{84} +(-3.44757 - 12.8665i) q^{85} +(2.02190 + 2.02190i) q^{86} +(-0.0838187 - 1.56833i) q^{87} +(-4.59200 + 2.65119i) q^{88} +(-0.372529 + 1.39030i) q^{89} +(-3.46419 - 1.53378i) q^{90} +(-0.338247 + 3.58965i) q^{91} -10.6910i q^{92} +(3.08638 - 1.00636i) q^{93} +(-1.04541 - 1.81070i) q^{94} +(-1.74814 + 3.02787i) q^{95} +(-6.04970 - 1.27937i) q^{96} +(13.4770 - 3.61115i) q^{97} +(-0.307973 + 0.0825212i) q^{98} +(-11.9385 + 4.61111i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{6}+O(q^{10}) $ 112 * q - 12 * q^6	$ 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) $ 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.307973	+	0.0825212i	0.217770	+	0.0583513i	0.366054	−	0.930593i	$-0.380708\pi$
$2$	0.307973	+	0.0825212i	0.217770	+	0.0583513i	−0.148284	+	0.988945i	$0.547375\pi$
$3$	−0.784738	+	1.54408i	−0.453069	+	0.891475i
$3$	−0.784738	+	1.54408i	−0.453069	+	0.891475i
$4$	−1.64401	−	0.949171i	−0.822006	−	0.474586i
$5$	2.80070	−	2.80070i	1.25251	−	1.25251i	0.297922	−	0.954590i	$-0.403707\pi$
$5$	2.80070	−	2.80070i	1.25251	−	1.25251i	0.954590	−	0.297922i	$-0.0962934\pi$
$6$	−0.369098	+	0.410778i	−0.150684	+	0.167699i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$8$	−0.878890	−	0.878890i	−0.310734	−	0.310734i
$9$	−1.76837	−	2.42340i	−0.589457	−	0.807800i
$10$	1.09366	−	0.631424i	0.345845	−	0.199674i
$11$	1.10413	−	4.12065i	0.332906	−	1.24242i	−0.573215	−	0.819405i	$-0.694304\pi$
$11$	1.10413	−	4.12065i	0.332906	−	1.24242i	0.906121	−	0.423019i	$-0.139029\pi$
$12$	2.75572	−	1.79364i	0.795507	−	0.517779i
$13$	3.37979	+	1.25579i	0.937385	+	0.348294i
$13$	3.37979	+	1.25579i	0.937385	+	0.348294i
$14$			0.318837i			0.0852129i
$15$	2.12669	+	6.52233i	0.549109	+	1.68406i
$16$	1.70020	+	2.94482i	0.425049	+	0.736206i
$17$	1.68153	−	2.91250i	0.407831	−	0.706384i	−0.586815	−	0.809721i	$-0.699619\pi$
$17$	1.68153	−	2.91250i	0.407831	−	0.706384i	0.994646	+	0.103337i	$0.0329519\pi$
$18$	−0.344629	−	0.892270i	−0.0812299	−	0.210310i
$19$	−0.852646	+	0.228466i	−0.195610	+	0.0524136i	−0.355294	−	0.934755i	$-0.615619\pi$
$19$	−0.852646	+	0.228466i	−0.195610	+	0.0524136i	0.159684	+	0.987168i	$0.448953\pi$
$20$	−7.26274	+	1.94604i	−1.62400	+	0.435149i
$21$	−1.69457	−	0.358362i	−0.369786	−	0.0782009i
$22$	0.680083	−	1.17794i	0.144994	−	0.251137i
$23$	2.81588	+	4.87725i	0.587152	+	1.01698i	0.994603	+	0.103750i	$0.0330842\pi$
$23$	2.81588	+	4.87725i	0.587152	+	1.01698i	−0.407451	+	0.913227i	$0.633582\pi$
$24$	2.04678	−	0.667378i	0.417796	−	0.136228i
$25$		−	10.6879i		−	2.13757i
$26$	0.937256	+	0.665655i	0.183811	+	0.130546i
$27$	5.12963	−	0.828774i	0.987198	−	0.159498i
$28$	0.491327	−	1.83366i	0.0928521	−	0.346529i
$29$	−0.785282	+	0.453383i	−0.145823	+	0.0841911i	−0.571136	−	0.820855i	$-0.693497\pi$
$29$	−0.785282	+	0.453383i	−0.145823	+	0.0841911i	0.425313	+	0.905046i	$0.360164\pi$
$30$	0.116734	+	2.18420i	0.0213126	+	0.398779i
$31$	−1.32530	−	1.32530i	−0.238031	−	0.238031i	0.578003	−	0.816034i	$-0.303832\pi$
$31$	−1.32530	−	1.32530i	−0.238031	−	0.238031i	−0.816034	+	0.578003i	$0.803832\pi$
$32$	0.923996	+	3.44840i	0.163341	+	0.609597i
$33$	5.49617	+	4.93849i	0.956761	+	0.859682i
$34$	0.758209	−	0.758209i	0.130032	−	0.130032i
$35$	3.43015	+	1.98040i	0.579800	+	0.334748i
$36$	0.607004	+	5.66259i	0.101167	+	0.943764i
$37$	−8.51301	−	2.28105i	−1.39953	−	0.375003i	−0.521354	−	0.853340i	$-0.674573\pi$
$37$	−8.51301	−	2.28105i	−1.39953	−	0.375003i	−0.878176	+	0.478337i	$0.841240\pi$
$38$	−0.281445			−0.0456565
$39$	−4.59129	+	4.23320i	−0.735196	+	0.677855i
$40$	−4.92302			−0.778397
$41$	−4.07157	−	1.09097i	−0.635872	−	0.170381i	−0.0735391	−	0.997292i	$-0.523429\pi$
$41$	−4.07157	−	1.09097i	−0.635872	−	0.170381i	−0.562333	+	0.826911i	$0.690096\pi$
$42$	−0.492311	−	0.250204i	−0.0759652	−	0.0386073i
$43$	7.76670	+	4.48411i	1.18441	+	0.683820i	0.957031	−	0.289986i	$-0.0936507\pi$
$43$	7.76670	+	4.48411i	1.18441	+	0.683820i	0.227380	+	0.973806i	$0.426984\pi$
$44$	−5.72640	+	5.72640i	−0.863288	+	0.863288i
$45$	−11.7399	−	1.83454i	−1.75008	−	0.273477i
$46$	0.464740	+	1.73443i	0.0685222	+	0.255728i
$47$	−4.63695	−	4.63695i	−0.676369	−	0.676369i	0.282808	−	0.959177i	$-0.408734\pi$
$47$	−4.63695	−	4.63695i	−0.676369	−	0.676369i	−0.959177	+	0.282808i	$0.908734\pi$
$48$	−5.88126	+	0.314322i	−0.848886	+	0.0453684i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	0.881975	−	3.29158i	0.124730	−	0.465499i
$51$	3.17757	+	4.88197i	0.444949	+	0.683612i
$52$	−4.36446	−	5.27254i	−0.605242	−	0.731169i
$53$			3.33723i			0.458404i	0.973379	+	0.229202i	$0.0736116\pi$
$53$			3.33723i			0.458404i	−0.973379	+	0.229202i	$0.926388\pi$
$54$	1.64818	+	0.168063i	0.224289	+	0.0228705i
$55$	−8.44839	−	14.6330i	−1.13918	−	1.97312i
$56$	0.621469	−	1.07642i	0.0830473	−	0.143842i
$57$	0.316334	−	1.49584i	0.0418995	−	0.198129i
$58$	−0.279260	+	0.0748274i	−0.0366686	+	0.00982532i
$59$	−9.52199	+	2.55141i	−1.23966	+	0.332165i	−0.818333	−	0.574744i	$-0.805102\pi$
$59$	−9.52199	+	2.55141i	−1.23966	+	0.332165i	−0.421325	+	0.906910i	$0.638435\pi$
$60$	2.69450	−	12.7414i	0.347858	−	1.64491i
$61$	−2.31485	+	4.00944i	−0.296387	+	0.513357i	−0.975307	−	0.220856i	$-0.929115\pi$
$61$	−2.31485	+	4.00944i	−0.296387	+	0.513357i	0.678920	+	0.734212i	$0.262448\pi$
$62$	−0.298792	−	0.517522i	−0.0379466	−	0.0657254i
$63$	1.88314	−	2.33534i	0.237253	−	0.294225i
$64$		−	5.66252i		−	0.707815i
$65$	12.9829	−	5.94869i	1.61033	−	0.737844i
$66$	1.28514	+	1.97448i	0.158190	+	0.243041i
$67$	−3.10288	+	11.5801i	−0.379077	+	1.41474i	0.468217	+	0.883613i	$0.344896\pi$
$67$	−3.10288	+	11.5801i	−0.379077	+	1.41474i	−0.847295	+	0.531123i	$0.821770\pi$
$68$	−5.52892	+	3.19212i	−0.670480	+	0.387102i
$69$	−9.74060	+	0.520583i	−1.17263	+	0.0626709i
$70$	0.892969	+	0.892969i	0.106730	+	0.106730i
$71$	3.10773	+	11.5982i	0.368820	+	1.37645i	0.862168	+	0.506622i	$0.169106\pi$
$71$	3.10773	+	11.5982i	0.368820	+	1.37645i	−0.493348	+	0.869832i	$0.664227\pi$
$72$	−0.575697	+	3.68410i	−0.0678466	+	0.434176i
$73$	5.88441	−	5.88441i	0.688718	−	0.688718i	−0.273231	−	0.961948i	$-0.588092\pi$
$73$	5.88441	−	5.88441i	0.688718	−	0.688718i	0.961948	+	0.273231i	$0.0880923\pi$
$74$	−2.43354	−	1.40501i	−0.282894	−	0.163329i
$75$	16.5029	+	8.38717i	1.90559	+	0.968468i
$76$	1.61861	+	0.433706i	0.185668	+	0.0497495i
$77$	4.26601			0.486157
$78$	−1.76333	+	0.924834i	−0.199657	+	0.104717i
$79$	13.3054			1.49698			0.748489	−	0.663147i	$-0.230780\pi$
$79$	13.3054			1.49698			0.748489	+	0.663147i	$0.230780\pi$
$80$	13.0093	+	3.48584i	1.45449	+	0.389728i
$81$	−2.74573	+	8.57094i	−0.305081	+	0.952326i
$82$	−1.16391	−	0.671981i	−0.128532	−	0.0742079i
$83$	−2.32987	+	2.32987i	−0.255736	+	0.255736i	−0.823318	−	0.567581i	$-0.807879\pi$
$83$	−2.32987	+	2.32987i	−0.255736	+	0.255736i	0.567581	+	0.823318i	$0.307879\pi$
$84$	2.44575	+	2.19759i	0.266854	+	0.239777i
$85$	−3.44757	−	12.8665i	−0.373941	−	1.39557i
$86$	2.02190	+	2.02190i	0.218027	+	0.218027i
$87$	−0.0838187	−	1.56833i	−0.00898631	−	0.168142i
$88$	−4.59200	+	2.65119i	−0.489509	+	0.282618i
$89$	−0.372529	+	1.39030i	−0.0394880	+	0.147371i	−0.982855	−	0.184379i	$-0.940973\pi$
$89$	−0.372529	+	1.39030i	−0.0394880	+	0.147371i	0.943367	+	0.331750i	$0.107639\pi$
$90$	−3.46419	−	1.53378i	−0.365157	−	0.161675i
$91$	−0.338247	+	3.58965i	−0.0354579	+	0.376298i
$92$		−	10.6910i		−	1.11462i
$93$	3.08638	−	1.00636i	0.320043	−	0.104354i
$94$	−1.04541	−	1.81070i	−0.107826	−	0.186760i
$95$	−1.74814	+	3.02787i	−0.179356	+	0.310653i
$96$	−6.04970	−	1.27937i	−0.617445	−	0.130575i
$97$	13.4770	−	3.61115i	1.36838	−	0.366657i	0.501494	−	0.865161i	$-0.332784\pi$
$97$	13.4770	−	3.61115i	1.36838	−	0.366657i	0.866887	+	0.498504i	$0.166117\pi$
$98$	−0.307973	+	0.0825212i	−0.0311100	+	0.00833590i
$99$	−11.9385	+	4.61111i	−1.19986	+	0.463434i
$100$	−10.1446	+	17.5710i	−1.01446	+	1.75710i
$101$	−1.38391	−	2.39700i	−0.137704	−	0.238511i	0.788923	−	0.614492i	$-0.210639\pi$
$101$	−1.38391	−	2.39700i	−0.137704	−	0.238511i	−0.926627	+	0.375981i	$0.877306\pi$
$102$	0.575740	+	1.76573i	0.0570068	+	0.174834i
$103$			7.33135i			0.722379i	0.932492	+	0.361190i	$0.117629\pi$
$103$			7.33135i			0.722379i	−0.932492	+	0.361190i	$0.882371\pi$
$104$	−1.86676	−	4.07417i	−0.183051	−	0.399505i
$105$	−5.74966	+	3.74233i	−0.561109	+	0.365214i
$106$	−0.275392	+	1.02778i	−0.0267485	+	0.0998267i
$107$	2.94617	−	1.70097i	0.284817	−	0.164439i	−0.350785	−	0.936456i	$-0.614085\pi$
$107$	2.94617	−	1.70097i	0.284817	−	0.164439i	0.635602	+	0.772017i	$0.280752\pi$
$108$	−9.21983	−	3.50639i	−0.887179	−	0.337402i
$109$	2.85124	+	2.85124i	0.273100	+	0.273100i	0.830347	−	0.557247i	$-0.188142\pi$
$109$	2.85124	+	2.85124i	0.273100	+	0.273100i	−0.557247	+	0.830347i	$0.688142\pi$
$110$	−1.39434	−	5.20376i	−0.132945	−	0.496159i
$111$	10.2026	−	11.3547i	0.968390	−	1.07774i
$112$	−2.40444	+	2.40444i	−0.227198	+	0.227198i
$113$	10.0683	+	5.81296i	0.947150	+	0.546837i	0.892194	−	0.451652i	$-0.149165\pi$
$113$	10.0683	+	5.81296i	0.947150	+	0.546837i	0.0549554	+	0.998489i	$0.482498\pi$
$114$	0.220861	−	0.434574i	0.0206855	−	0.0407016i
$115$	21.5462	+	5.77328i	2.00919	+	0.538361i
$116$	1.72135			0.159824
$117$	−2.93344	−	10.4113i	−0.271197	−	0.962524i
$118$	−3.14307			−0.289343
$119$	3.24847	+	0.870424i	0.297787	+	0.0797917i
$120$	3.86328	−	7.60153i	0.352668	−	0.693922i
$121$	−6.23441	−	3.59944i	−0.566765	−	0.327222i
$122$	−1.04378	+	1.04378i	−0.0944992	+	0.0944992i
$123$	4.87967	−	5.43070i	0.439985	−	0.489670i
$124$	0.920873	+	3.43675i	0.0826969	+	0.308629i
$125$	−15.9300	−	15.9300i	−1.42482	−	1.42482i
$126$	0.772670	−	0.563823i	0.0688349	−	0.0502293i
$127$	−12.5042	+	7.21932i	−1.10957	+	0.640611i	−0.938718	−	0.344685i	$-0.887986\pi$
$127$	−12.5042	+	7.21932i	−1.10957	+	0.640611i	−0.170853	+	0.985297i	$0.554652\pi$
$128$	2.31527	−	8.64070i	0.204643	−	0.763738i
$129$	−13.0187	+	8.47356i	−1.14623	+	0.746056i
$130$	4.48927	−	0.760675i	0.393735	−	0.0667156i
$131$			5.95803i			0.520555i	0.965534	+	0.260278i	$0.0838141\pi$
$131$			5.95803i			0.520555i	−0.965534	+	0.260278i	$0.916186\pi$
$132$	−4.34830	−	13.3358i	−0.378471	−	1.16073i
$133$	−0.441362	−	0.764461i	−0.0382709	−	0.0662872i
$134$	−1.91121	+	3.31031i	−0.165103	+	0.285967i
$135$	12.0454	−	16.6877i	1.03671	−	1.43625i
$136$	−4.03764	+	1.08188i	−0.346225	+	0.0927707i
$137$	−5.89659	+	1.57999i	−0.503780	+	0.134987i	−0.501754	−	0.865011i	$-0.667312\pi$
$137$	−5.89659	+	1.57999i	−0.503780	+	0.134987i	−0.00202619	+	0.999998i	$0.500645\pi$
$138$	−3.04280	−	0.643480i	−0.259021	−	0.0547767i
$139$	0.937719	−	1.62418i	0.0795363	−	0.137761i	−0.823514	−	0.567296i	$-0.807989\pi$
$139$	0.937719	−	1.62418i	0.0795363	−	0.137761i	0.903050	+	0.429536i	$0.141323\pi$
$140$	−3.75947	−	6.51159i	−0.317733	−	0.550330i
$141$	10.7986	−	3.52103i	0.909408	−	0.296525i
$142$			3.82839i			0.321272i
$143$	8.90639	−	12.5404i	0.744790	−	1.04868i
$144$	4.12991	−	9.32779i	0.344159	−	0.777316i
$145$	−0.929551	+	3.46913i	−0.0771950	+	0.288096i
$146$	2.29783	−	1.32665i	0.190170	−	0.109794i
$147$	−0.0924370	−	1.72958i	−0.00762407	−	0.142654i
$148$	11.8304	+	11.8304i	0.972452	+	0.972452i
$149$	0.519729	+	1.93966i	0.0425779	+	0.158903i	0.983942	−	0.178491i	$-0.0571214\pi$
$149$	0.519729	+	1.93966i	0.0425779	+	0.158903i	−0.941364	+	0.337393i	$0.890455\pi$
$150$	4.39034	+	3.94487i	0.358470	+	0.322097i
$151$	−8.37448	+	8.37448i	−0.681505	+	0.681505i	−0.960339	−	0.278834i	$-0.910052\pi$
$151$	−8.37448	+	8.37448i	−0.681505	+	0.681505i	0.278834	+	0.960339i	$0.410052\pi$
$152$	0.950178	+	0.548585i	0.0770696	+	0.0444961i
$153$	−10.0317	+	1.07535i	−0.811016	+	0.0869373i
$154$	1.31382	+	0.352037i	0.105871	+	0.0283679i
$155$	−7.42354			−0.596273
$156$	11.5662	−	2.60152i	0.926036	−	0.208288i
$157$	14.9848			1.19592			0.597960	−	0.801526i	$-0.295978\pi$
$157$	14.9848			1.19592			0.597960	+	0.801526i	$0.295978\pi$
$158$	4.09772	+	1.09798i	0.325997	+	0.0873506i
$159$	−5.15296	−	2.61885i	−0.408656	−	0.207689i
$160$	12.2458	+	7.07010i	0.968114	+	0.558941i
$161$	−3.98226	+	3.98226i	−0.313846	+	0.313846i
$162$	−1.55289	+	2.41304i	−0.122007	+	0.189586i
$163$	−1.42886	−	5.33256i	−0.111917	−	0.417679i	0.887121	−	0.461537i	$-0.152702\pi$
$163$	−1.42886	−	5.33256i	−0.111917	−	0.417679i	−0.999038	+	0.0438580i	$0.986035\pi$
$164$	5.65819	+	5.65819i	0.441830	+	0.441830i
$165$	29.2244	−	1.56189i	2.27512	−	0.121593i
$166$	−0.909801	+	0.525274i	−0.0706143	+	0.0407692i
$167$	−0.00150536	+	0.00561808i	−0.000116488	+	0.000434740i	−0.965984	−	0.258602i	$-0.916738\pi$
$167$	−0.00150536	+	0.00561808i	−0.000116488	+	0.000434740i	0.965868	+	0.259036i	$0.0834050\pi$
$168$	1.17438	+	1.80430i	0.0906055	+	0.139205i
$169$	9.84598	+	8.48862i	0.757383	+	0.652971i
$170$		−	4.24704i		−	0.325733i
$171$	2.06146	+	1.66229i	0.157644	+	0.127118i
$172$	−8.51237	−	14.7439i	−0.649062	−	1.12421i
$173$	−4.94215	+	8.56006i	−0.375745	+	0.650809i	−0.990438	−	0.137957i	$-0.955946\pi$
$173$	−4.94215	+	8.56006i	−0.375745	+	0.650809i	0.614693	+	0.788766i	$0.289280\pi$
$174$	0.103606	−	0.489919i	0.00785437	−	0.0371407i
$175$	10.3237	−	2.76622i	0.780397	−	0.209107i
$176$	14.0118	−	3.75446i	1.05618	−	0.283003i
$177$	3.53269	−	16.7049i	0.265533	−	1.25562i
$178$	−0.229458	+	0.397433i	−0.0171986	+	0.0297888i
$179$	−9.45512	−	16.3767i	−0.706708	−	1.22405i	−0.966071	−	0.258275i	$-0.916846\pi$
$179$	−9.45512	−	16.3767i	−0.706708	−	1.22405i	0.259363	−	0.965780i	$-0.416487\pi$
$180$	17.5593	+	14.1592i	1.30879	+	1.05536i
$181$			4.90602i			0.364662i	0.983237	+	0.182331i	$0.0583642\pi$
$181$			4.90602i			0.364662i	−0.983237	+	0.182331i	$0.941636\pi$
$182$	−0.400393	+	1.07760i	−0.0296791	+	0.0798773i
$183$	−4.37435	−	6.72069i	−0.323361	−	0.496807i
$184$	1.81172	−	6.76141i	0.133561	−	0.498458i
$185$	−30.2310	+	17.4539i	−2.22262	+	1.28323i
$186$	1.03357	−	0.0552388i	0.0757850	−	0.00405030i
$187$	−10.1448	−	10.1448i	−0.741859	−	0.741859i
$188$	3.22195	+	12.0245i	0.234985	+	0.876975i
$189$	2.12818	+	4.74034i	0.154802	+	0.344809i
$190$	−0.788245	+	0.788245i	−0.0571853	+	0.0571853i
$191$	16.0597	+	9.27208i	1.16204	+	0.670904i	0.951792	−	0.306744i	$-0.0992395\pi$
$191$	16.0597	+	9.27208i	1.16204	+	0.670904i	0.210248	+	0.977648i	$0.432573\pi$
$192$	8.74338	+	4.44359i	0.630999	+	0.320689i
$193$	−17.0645	−	4.57241i	−1.22833	−	0.329129i	−0.414399	−	0.910095i	$-0.636008\pi$
$193$	−17.0645	−	4.57241i	−1.22833	−	0.329129i	−0.813928	+	0.580966i	$0.802675\pi$
$194$	4.44855			0.319387
$195$	−1.00291	+	24.7148i	−0.0718197	+	1.76986i
$196$	1.89834			0.135596
$197$	−0.264368	−	0.0708371i	−0.0188354	−	0.00504693i	0.249389	−	0.968403i	$-0.419770\pi$
$197$	−0.264368	−	0.0708371i	−0.0188354	−	0.00504693i	−0.268224	+	0.963356i	$0.586437\pi$
$198$	−4.05725	+	0.434919i	−0.288336	+	0.0309084i
$199$	−16.2650	−	9.39062i	−1.15300	−	0.665683i	−0.203381	−	0.979100i	$-0.565193\pi$
$199$	−16.2650	−	9.39062i	−1.15300	−	0.665683i	−0.949616	+	0.313416i	$0.898526\pi$
$200$	−9.39345	+	9.39345i	−0.664217	+	0.664217i
$201$	−15.4457	−	13.8785i	−1.08945	−	0.978911i
$202$	−0.228404	−	0.852414i	−0.0160704	−	0.0599757i
$203$	−0.641180	−	0.641180i	−0.0450020	−	0.0450020i
$204$	−0.590140	−	11.0421i	−0.0413181	−	0.773100i
$205$	−14.4587	+	8.34776i	−1.00984	+	0.583033i
$206$	−0.604992	+	2.25786i	−0.0421518	+	0.157313i
$207$	6.84000	−	15.4488i	0.475413	−	1.07377i
$208$	2.04822	+	12.0880i	0.142019	+	0.838151i
$209$			3.76571i			0.260480i
$210$	−2.07956	+	0.678069i	−0.143503	+	0.0467912i
$211$	−2.61660	−	4.53208i	−0.180134	−	0.312001i	0.761792	−	0.647822i	$-0.224320\pi$
$211$	−2.61660	−	4.53208i	−0.180134	−	0.312001i	−0.941926	+	0.335820i	$0.890987\pi$
$212$	3.16760	−	5.48645i	0.217552	−	0.376811i
$213$	−20.3473	−	4.30297i	−1.39418	−	0.294835i
$214$	1.04771	−	0.280732i	0.0716198	−	0.0191905i
$215$	34.3109	−	9.19357i	2.33998	−	0.626996i
$216$	−5.23678	−	3.77998i	−0.356318	−	0.257195i
$217$	0.937128	−	1.62315i	0.0636164	−	0.110187i
$218$	0.642819	+	1.11339i	0.0435372	+	0.0754086i
$219$	4.46828	+	13.7037i	0.301938	+	0.926011i
$220$			32.0759i			2.16256i
$221$	9.34071	−	7.73198i	0.628324	−	0.520109i
$222$	4.07914	−	2.65503i	0.273774	−	0.178194i
$223$	0.991972	−	3.70209i	0.0664273	−	0.247910i	−0.924726	−	0.380634i	$-0.875706\pi$
$223$	0.991972	−	3.70209i	0.0664273	−	0.247910i	0.991153	+	0.132724i	$0.0423724\pi$
$224$	−3.09175	+	1.78502i	−0.206576	+	0.119267i
$225$	−25.9010	+	18.9001i	−1.72673	+	1.26001i
$226$	2.62109	+	2.62109i	0.174352	+	0.174352i
$227$	−5.66346	−	21.1363i	−0.375897	−	1.40287i	−0.852030	−	0.523494i	$-0.824628\pi$
$227$	−5.66346	−	21.1363i	−0.375897	−	1.40287i	0.476133	−	0.879374i	$-0.342038\pi$
$228$	−1.93987	+	2.15892i	−0.128471	+	0.142978i
$229$	8.95391	−	8.95391i	0.591691	−	0.591691i	−0.346397	−	0.938088i	$-0.612595\pi$
$229$	8.95391	−	8.95391i	0.591691	−	0.591691i	0.938088	+	0.346397i	$0.112595\pi$
$230$	6.15923	+	3.55603i	0.406127	+	0.234478i
$231$	−3.34771	+	6.58707i	−0.220263	+	0.433397i
$232$	1.08865	+	0.291703i	0.0714734	+	0.0191512i
$233$	−29.4939			−1.93221			−0.966104	−	0.258153i	$-0.916886\pi$
$233$	−29.4939			−1.93221			−0.966104	+	0.258153i	$0.916886\pi$
$234$	−0.0442700	−	3.44847i	−0.00289402	−	0.225434i
$235$	−25.9734			−1.69432
$236$	18.0760	+	4.84345i	1.17665	+	0.315282i
$237$	−10.4413	+	20.5447i	−0.678234	+	1.33452i
$238$	0.928613	+	0.536135i	0.0601930	+	0.0347525i
$239$	7.71928	−	7.71928i	0.499318	−	0.499318i	−0.411907	−	0.911226i	$-0.635137\pi$
$239$	7.71928	−	7.71928i	0.499318	−	0.499318i	0.911226	+	0.411907i	$0.135137\pi$
$240$	−15.5913	+	17.3520i	−1.00642	+	1.12006i
$241$	0.680541	+	2.53981i	0.0438375	+	0.163604i	0.984375	−	0.176087i	$-0.0563441\pi$
$241$	0.680541	+	2.53981i	0.0438375	+	0.163604i	−0.940537	+	0.339691i	$0.889677\pi$
$242$	−1.62300	−	1.62300i	−0.104331	−	0.104331i
$243$	−11.0795	−	10.9656i	−0.710753	−	0.703442i
$244$	7.61130	−	4.39439i	0.487263	−	0.281322i
$245$	−1.02513	+	3.82583i	−0.0654930	+	0.244423i
$246$	1.95096	−	1.26984i	0.124388	−	0.0809617i
$247$	−3.16867	−	0.298578i	−0.201618	−	0.0189981i
$248$			2.32958i			0.147929i
$249$	−1.76917	−	5.42585i	−0.112117	−	0.343849i
$250$	−3.59145	−	6.22058i	−0.227143	−	0.393424i
$251$	2.64931	−	4.58875i	0.167223	−	0.289639i	−0.770219	−	0.637779i	$-0.779853\pi$
$251$	2.64931	−	4.58875i	0.167223	−	0.289639i	0.937443	+	0.348140i	$0.113187\pi$
$252$	−5.31253	+	2.05191i	−0.334658	+	0.129258i
$253$	23.2065	−	6.21818i	1.45898	−	0.390933i
$254$	−4.44672	+	1.19149i	−0.279012	+	0.0747610i
$255$	22.5724	+	4.77351i	1.41354	+	0.298929i
$256$	−4.23643	+	7.33772i	−0.264777	+	0.458607i
$257$	3.49756	+	6.05795i	0.218172	+	0.377884i	0.954249	−	0.299013i	$-0.0966574\pi$
$257$	3.49756	+	6.05795i	0.218172	+	0.377884i	−0.736077	+	0.676897i	$0.763324\pi$
$258$	−4.70865	+	1.53532i	−0.293148	+	0.0955846i
$259$		−	8.81332i		−	0.547633i
$260$	−26.9904	−	2.54326i	−1.67387	−	0.157726i
$261$	2.48740	+	1.10130i	0.153966	+	0.0681689i
$262$	−0.491664	+	1.83491i	−0.0303751	+	0.113361i
$263$	−7.48278	+	4.32019i	−0.461408	+	0.266394i	−0.712636	−	0.701534i	$-0.752499\pi$
$263$	−7.48278	+	4.32019i	−0.461408	+	0.266394i	0.251228	+	0.967928i	$0.419166\pi$
$264$	−0.490137	−	9.17092i	−0.0301658	−	0.564431i
$265$	9.34659	+	9.34659i	0.574156	+	0.574156i
$266$	−0.0728434	−	0.271855i	−0.00446632	−	0.0166685i
$267$	−1.85439	−	1.66623i	−0.113487	−	0.101972i
$268$	16.0927	−	16.0927i	0.983018	−	0.983018i
$269$	3.30775	+	1.90973i	0.201677	+	0.116438i	0.597438	−	0.801915i	$-0.296186\pi$
$269$	3.30775	+	1.90973i	0.201677	+	0.116438i	−0.395760	+	0.918354i	$0.629519\pi$
$270$	5.08676	−	4.14537i	0.309570	−	0.252279i
$271$	−14.7134	−	3.94244i	−0.893775	−	0.239486i	−0.217434	−	0.976075i	$-0.569769\pi$
$271$	−14.7134	−	3.94244i	−0.893775	−	0.239486i	−0.676341	+	0.736589i	$0.736435\pi$
$272$	11.4357			0.693392
$273$	−5.27728	−	3.33922i	−0.319395	−	0.202099i
$274$	−1.94638			−0.117585
$275$	−44.0410	−	11.8007i	−2.65577	−	0.711612i
$276$	16.5078	+	8.38965i	0.993653	+	0.504998i
$277$	11.0354	+	6.37131i	0.663055	+	0.382815i	0.793440	−	0.608649i	$-0.208288\pi$
$277$	11.0354	+	6.37131i	0.663055	+	0.382815i	−0.130385	+	0.991463i	$0.541621\pi$
$278$	0.422821	−	0.422821i	0.0253591	−	0.0253591i
$279$	−0.868108	+	5.55535i	−0.0519723	+	0.332590i
$280$	−1.27417	−	4.75527i	−0.0761462	−	0.284182i
$281$	15.3354	+	15.3354i	0.914832	+	0.914832i	0.996647	−	0.0818157i	$-0.0260719\pi$
$281$	15.3354	+	15.3354i	0.914832	+	0.914832i	−0.0818157	+	0.996647i	$0.526072\pi$
$282$	3.61625	−	0.193269i	0.215344	−	0.0115090i
$283$	9.58487	−	5.53383i	0.569761	−	0.328952i	−0.187293	−	0.982304i	$-0.559971\pi$
$283$	9.58487	−	5.53383i	0.569761	−	0.328952i	0.757054	+	0.653352i	$0.226638\pi$
$284$	5.89954	−	22.0174i	0.350073	−	1.30649i
$285$	−3.30344	−	5.07536i	−0.195679	−	0.300638i
$286$	3.77778	−	3.12714i	0.223385	−	0.184912i
$287$		−	4.21520i		−	0.248815i
$288$	6.72288	−	8.33726i	0.396150	−	0.491278i
$289$	2.84491	+	4.92753i	0.167348	+	0.289855i
$290$	−0.572554	+	0.991692i	−0.0336215	+	0.0582342i
$291$	−5.00001	+	23.6434i	−0.293106	+	1.38600i
$292$	−15.2593	+	4.08873i	−0.892986	+	0.239275i
$293$	7.53874	−	2.02000i	0.440418	−	0.118010i	−0.0317946	−	0.999494i	$-0.510122\pi$
$293$	7.53874	−	2.02000i	0.440418	−	0.118010i	0.472212	+	0.881485i	$0.343456\pi$
$294$	0.114259	−	0.540293i	0.00666373	−	0.0315105i
$295$	−19.5225	+	33.8140i	−1.13665	+	1.96873i
$296$	5.47720	+	9.48679i	0.318356	+	0.551409i
$297$	2.24867	−	22.0525i	0.130481	−	1.27962i
$298$			0.640251i			0.0370887i
$299$	3.39229	+	20.0202i	0.196181	+	1.15780i
$300$	−19.1701	−	29.4527i	−1.10679	−	1.70045i
$301$	−2.32114	+	8.66263i	−0.133789	+	0.499306i
$302$	−3.27019	+	1.88804i	−0.188178	+	0.108645i
$303$	4.78717	−	0.255849i	0.275016	−	0.0146981i
$304$	−2.12246	−	2.12246i	−0.121731	−	0.121731i
$305$	4.74604	+	17.7125i	0.271758	+	1.01421i
$306$	−3.17824	−	0.496648i	−0.181688	−	0.0283915i
$307$	−0.0449453	+	0.0449453i	−0.00256516	+	0.00256516i	−0.708388	−	0.705823i	$-0.750577\pi$
$307$	−0.0449453	+	0.0449453i	−0.00256516	+	0.00256516i	0.705823	+	0.708388i	$0.250577\pi$
$308$	−7.01338	−	4.04918i	−0.399625	−	0.230723i
$309$	−11.3202	−	5.75319i	−0.643984	−	0.327288i
$310$	−2.28625	−	0.612599i	−0.129850	−	0.0347933i
$311$	−13.6132			−0.771936			−0.385968	−	0.922512i	$-0.626132\pi$
$311$	−13.6132			−0.771936			−0.385968	+	0.922512i	$0.626132\pi$
$312$	7.75576	+	0.314723i	0.439083	+	0.0178177i
$313$	7.49944			0.423893			0.211947	−	0.977281i	$-0.432020\pi$
$313$	7.49944			0.423893			0.211947	+	0.977281i	$0.432020\pi$
$314$	4.61493	+	1.23657i	0.260436	+	0.0697835i
$315$	−1.26648	−	11.8147i	−0.0713582	−	0.665682i
$316$	−21.8743	−	12.6291i	−1.23053	−	0.710444i
$317$	−16.3959	+	16.3959i	−0.920886	+	0.920886i	−0.997092	−	0.0762061i	$-0.975719\pi$
$317$	−16.3959	+	16.3959i	−0.920886	+	0.920886i	0.0762061	+	0.997092i	$0.475719\pi$
$318$	−1.37086	−	1.23177i	−0.0768741	−	0.0690740i
$319$	1.00118	+	3.73647i	0.0560555	+	0.209202i
$320$	−15.8590	−	15.8590i	−0.886546	−	0.886546i
$321$	0.314465	+	5.88394i	0.0175517	+	0.328410i
$322$	−1.55505	+	0.897809i	−0.0866596	+	0.0500329i
$323$	−0.768344	+	2.86750i	−0.0427518	+	0.159552i
$324$	12.6493	−	11.4846i	0.702739	−	0.638032i
$325$	13.4217	−	36.1227i	0.744503	−	2.00373i
$326$		−	1.76020i		−	0.0974884i
$327$	−6.64003	+	2.16507i	−0.367195	+	0.119729i
$328$	2.61961	+	4.53730i	0.144644	+	0.250531i
$329$	3.27882	−	5.67908i	0.180767	−	0.313098i
$330$	9.12922	+	1.93061i	0.502547	+	0.106277i
$331$	−7.04459	+	1.88759i	−0.387206	+	0.103751i	−0.447170	−	0.894449i	$-0.647568\pi$
$331$	−7.04459	+	1.88759i	−0.387206	+	0.103751i	0.0599641	+	0.998201i	$0.480901\pi$
$332$	6.04178	−	1.61889i	0.331586	−	0.0888482i
$333$	9.52626	+	24.6642i	0.522036	+	1.35159i
$334$	−0.000927222		0.00160600i	−5.07353e−5		8.78762e-5i
$335$	23.7422	+	41.1227i	1.29718	+	2.24677i
$336$	−1.82579	−	5.59950i	−0.0996051	−	0.305478i
$337$		−	27.2417i		−	1.48395i	−0.670427	−	0.741976i	$-0.733889\pi$
$337$		−	27.2417i		−	1.48395i	0.670427	−	0.741976i	$-0.266111\pi$
$338$	2.33181	+	3.42677i	0.126834	+	0.186392i
$339$	−16.8767	+	10.9847i	−0.916616	+	0.596606i
$340$	−6.54467	+	24.4250i	−0.354934	+	1.32463i
$341$	−6.92440	+	3.99780i	−0.374977	+	0.216493i
$342$	0.497700	+	0.682055i	0.0269125	+	0.0368813i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−2.88504	−	10.7671i	−0.155551	−	0.580524i
$345$	−25.8225	+	28.7385i	−1.39024	+	1.54723i
$346$	−2.22844	+	2.22844i	−0.119802	+	0.119802i
$347$	−3.89383	−	2.24811i	−0.209032	−	0.120685i	0.391830	−	0.920038i	$-0.371842\pi$
$347$	−3.89383	−	2.24811i	−0.209032	−	0.120685i	−0.600861	+	0.799353i	$0.705176\pi$
$348$	−1.35081	+	2.65791i	−0.0724111	+	0.142479i
$349$	−23.9178	−	6.40875i	−1.28029	−	0.343053i	−0.446326	−	0.894871i	$-0.647268\pi$
$349$	−23.9178	−	6.40875i	−1.28029	−	0.343053i	−0.833965	+	0.551818i	$0.813934\pi$
$350$	3.40769			0.182149
$351$	18.3779	+	3.64067i	0.980937	+	0.194324i
$352$	15.2299			0.811755
$353$	22.8075	+	6.11126i	1.21392	+	0.325270i	0.808300	−	0.588771i	$-0.200388\pi$
$353$	22.8075	+	6.11126i	1.21392	+	0.325270i	0.405623	+	0.914041i	$0.367055\pi$
$354$	2.46648	−	4.85315i	0.131092	−	0.257942i
$355$	41.1870	+	23.7793i	2.18598	+	1.26207i
$356$	1.93207	−	1.93207i	0.102400	−	0.102400i
$357$	−3.89320	+	4.33284i	−0.206050	+	0.229318i
$358$	−1.56049	−	5.82385i	−0.0824747	−	0.307800i
$359$	3.81154	+	3.81154i	0.201165	+	0.201165i	0.800499	−	0.599334i	$-0.204568\pi$
$359$	3.81154	+	3.81154i	0.201165	+	0.201165i	−0.599334	+	0.800499i	$0.704568\pi$
$360$	8.70572	+	11.9304i	0.458832	+	0.628789i
$361$	−15.7797	+	9.11040i	−0.830509	+	0.479495i
$362$	−0.404851	+	1.51092i	−0.0212785	+	0.0794124i
$363$	10.4502	−	6.80182i	0.548494	−	0.357003i
$364$	3.96328	−	5.58038i	0.207732	−	0.292491i
$365$		−	32.9609i		−	1.72525i
$366$	−0.792584	−	2.43077i	−0.0414290	−	0.127058i
$367$	0.944880	+	1.63658i	0.0493223	+	0.0854288i	0.889633	−	0.456677i	$-0.150961\pi$
$367$	0.944880	+	1.63658i	0.0493223	+	0.0854288i	−0.840310	+	0.542106i	$0.817627\pi$
$368$	−9.57510	+	16.5846i	−0.499136	+	0.864530i
$369$	4.55618	+	11.7963i	0.237185	+	0.614090i
$370$	−10.7506	+	2.88063i	−0.558899	+	0.149757i
$371$	−3.22352	+	0.863739i	−0.167357	+	0.0448431i
$372$	−6.02926	−	1.27504i	−0.312603	−	0.0661080i
$373$	14.2103	−	24.6129i	0.735780	−	1.27441i	−0.218600	−	0.975814i	$-0.570149\pi$
$373$	14.2103	−	24.6129i	0.735780	−	1.27441i	0.954380	−	0.298594i	$-0.0965175\pi$
$374$	−2.28716	−	3.96148i	−0.118266	−	0.204843i
$375$	37.0981	−	12.0963i	1.91574	−	0.624651i
$376$			8.15074i			0.420342i
$377$	−3.22344	+	0.546189i	−0.166016	+	0.0281302i
$378$	0.264244	+	1.63552i	0.0135912	+	0.0841220i
$379$	0.193143	−	0.720819i	0.00992108	−	0.0370260i	−0.960788	−	0.277284i	$-0.910566\pi$
$379$	0.193143	−	0.720819i	0.00992108	−	0.0370260i	0.970709	+	0.240259i	$0.0772322\pi$
$380$	5.74794	−	3.31857i	0.294863	−	0.170239i
$381$	−1.33466	−	24.9728i	−0.0683769	−	1.27940i
$382$	4.18082	+	4.18082i	0.213909	+	0.213909i
$383$	−5.05678	−	18.8721i	−0.258389	−	0.964322i	−0.966173	−	0.257893i	$-0.916972\pi$
$383$	−5.05678	−	18.8721i	−0.258389	−	0.964322i	0.707784	−	0.706429i	$-0.249695\pi$
$384$	11.5251	+	10.3557i	0.588136	+	0.528460i
$385$	11.9478	−	11.9478i	0.608918	−	0.608918i
$386$	−4.87808	−	2.81636i	−0.248288	−	0.143349i
$387$	−2.86763	−	26.7514i	−0.145770	−	1.35985i
$388$	−25.5840	−	6.85520i	−1.29883	−	0.348020i
$389$	23.6751			1.20037			0.600187	−	0.799860i	$-0.295093\pi$
$389$	23.6751			1.20037			0.600187	+	0.799860i	$0.295093\pi$
$390$	−2.34836	+	7.52873i	−0.118914	+	0.381232i
$391$	18.9400			0.957835
$392$	1.20059	+	0.321696i	0.0606387	+	0.0162481i
$393$	−9.19968	−	4.67549i	−0.464062	−	0.235847i
$394$	−0.0755726	−	0.0436319i	−0.00380729	−	0.00219814i
$395$	37.2645	−	37.2645i	1.87498	−	1.87498i
$396$	24.0038	+	3.75095i	1.20623	+	0.188493i
$397$	−8.35316	−	31.1744i	−0.419233	−	1.56460i	−0.776203	−	0.630483i	$-0.782857\pi$
$397$	−8.35316	−	31.1744i	−0.419233	−	1.56460i	0.356970	−	0.934116i	$-0.383810\pi$
$398$	−4.23427	−	4.23427i	−0.212245	−	0.212245i
$399$	1.52674	−	0.0815963i	0.0764328	−	0.00408493i
$400$	31.4739	−	18.1714i	1.57369	−	0.908572i
$401$	−3.61704	+	13.4990i	−0.180627	+	0.674108i	0.814898	+	0.579604i	$0.196793\pi$
$401$	−3.61704	+	13.4990i	−0.180627	+	0.674108i	−0.995525	+	0.0945031i	$0.969874\pi$
$402$	−3.61159	−	5.54879i	−0.180130	−	0.276749i
$403$	−2.81494	−	6.14354i	−0.140222	−	0.306031i
$404$			5.25427i			0.261410i
$405$	16.3147	+	31.6946i	0.810683	+	1.57492i
$406$	−0.144555	−	0.250377i	−0.00717416	−	0.0124260i
$407$	−18.7989	+	32.5606i	−0.931825	+	1.61397i
$408$	1.49798	−	7.08344i	0.0741610	−	0.350683i
$409$	2.88993	−	0.774353i	0.142898	−	0.0382893i	−0.186661	−	0.982424i	$-0.559767\pi$
$409$	2.88993	−	0.774353i	0.142898	−	0.0382893i	0.329559	+	0.944135i	$0.393100\pi$
$410$	−5.14177	+	1.37773i	−0.253934	+	0.0680414i
$411$	2.18765	−	10.3447i	0.107909	−	0.510266i
$412$	6.95871	−	12.0528i	0.342831	−	0.593801i
$413$	−4.92895	−	8.53719i	−0.242538	−	0.420087i
$414$	3.38139	−	4.19337i	0.166186	−	0.206093i
$415$			13.0505i			0.640626i
$416$	−1.20756	+	12.8152i	−0.0592053	+	0.628318i
$417$	1.77200	+	2.72247i	0.0867750	+	0.133320i
$418$	−0.310751	+	1.15974i	−0.0151993	+	0.0567247i
$419$	31.9081	−	18.4221i	1.55881	−	0.899981i	0.561441	−	0.827517i	$-0.310247\pi$
$419$	31.9081	−	18.4221i	1.55881	−	0.899981i	0.997371	−	0.0724640i	$-0.0230862\pi$
$420$	13.0046	−	0.695028i	0.634561	−	0.0339139i
$421$	−1.40117	−	1.40117i	−0.0682890	−	0.0682890i	0.672137	−	0.740426i	$-0.265376\pi$
$421$	−1.40117	−	1.40117i	−0.0682890	−	0.0682890i	−0.740426	+	0.672137i	$0.765376\pi$
$422$	−0.431850	−	1.61169i	−0.0210221	−	0.0784556i
$423$	−3.03733	+	19.4370i	−0.147680	+	0.945061i
$424$	2.93306	−	2.93306i	0.142442	−	0.142442i
$425$	−31.1284	−	17.9720i	−1.50995	−	0.871768i
$426$	−5.91135	−	3.00429i	−0.286406	−	0.145558i
$427$	−4.47195	−	1.19826i	−0.216413	−	0.0579877i
$428$	−6.45805			−0.312162
$429$	12.3742	+	23.5931i	0.597432	+	1.13909i
$430$	11.3255			0.546164
$431$	16.5815	+	4.44299i	0.798701	+	0.214011i	0.635014	−	0.772501i	$-0.280994\pi$
$431$	16.5815	+	4.44299i	0.798701	+	0.214011i	0.163687	+	0.986512i	$0.447661\pi$
$432$	11.1620	+	13.6968i	0.537031	+	0.658987i
$433$	18.4248	+	10.6375i	0.885438	+	0.511208i	0.872447	−	0.488708i	$-0.162532\pi$
$433$	18.4248	+	10.6375i	0.885438	+	0.511208i	0.0129903	+	0.999916i	$0.495865\pi$
$434$	0.422555	−	0.422555i	0.0202833	−	0.0202833i
$435$	−4.62716	−	4.15766i	−0.221856	−	0.199345i
$436$	−1.98116	−	7.39380i	−0.0948805	−	0.354099i
$437$	−3.51523	−	3.51523i	−0.168156	−	0.168156i
$438$	0.245263	+	4.58911i	0.0117191	+	0.219276i
$439$	6.62632	−	3.82571i	0.316257	−	0.182591i	−0.333466	−	0.942762i	$-0.608218\pi$
$439$	6.62632	−	3.82571i	0.316257	−	0.182591i	0.649723	+	0.760171i	$0.274885\pi$
$440$	−5.43563	+	20.2860i	−0.259133	+	0.967099i
$441$	2.74315	+	1.21454i	0.130626	+	0.0578352i
$442$	3.51474	−	1.61044i	0.167179	−	0.0766007i
$443$		−	20.8460i		−	0.990426i	−0.868772	−	0.495213i	$-0.835090\pi$
$443$		−	20.8460i		−	0.990426i	0.868772	−	0.495213i	$-0.164910\pi$
$444$	−27.5508	+	8.98332i	−1.30750	+	0.426329i
$445$	2.85046	+	4.93715i	0.135125	+	0.234043i
$446$	0.611002	−	1.05829i	0.0289318	−	0.0501113i
$447$	−3.40284	−	0.719619i	−0.160949	−	0.0340368i
$448$	5.46957	−	1.46557i	0.258413	−	0.0692415i
$449$	−10.0905	+	2.70375i	−0.476202	+	0.127598i	−0.488933	−	0.872321i	$-0.662614\pi$
$449$	−10.0905	+	2.70375i	−0.476202	+	0.127598i	0.0127318	+	0.999919i	$0.495947\pi$
$450$	−9.53646	+	3.68335i	−0.449553	+	0.173635i
$451$	−8.99105	+	15.5729i	−0.423372	+	0.733301i
$452$	−11.0350	−	19.1132i	−0.519042	−	0.899007i
$453$	−6.35909	−	19.5026i	−0.298776	−	0.916314i
$454$		−	6.97678i		−	0.327436i
$455$	9.10621	+	11.0009i	0.426906	+	0.515729i
$456$	−1.59270	+	1.03666i	−0.0745851	+	0.0485458i
$457$	−0.979712	+	3.65633i	−0.0458290	+	0.171036i	−0.985047	−	0.172285i	$-0.944885\pi$
$457$	−0.979712	+	3.65633i	−0.0458290	+	0.171036i	0.939218	+	0.343321i	$0.111552\pi$
$458$	3.49645	−	2.01868i	0.163379	−	0.0943267i
$459$	6.21183	−	16.3336i	0.289944	−	0.762389i
$460$	−29.9424	−	29.9424i	−1.39607	−	1.39607i
$461$	−6.03635	−	22.5280i	−0.281141	−	1.04923i	−0.951613	−	0.307298i	$-0.900575\pi$
$461$	−6.03635	−	22.5280i	−0.281141	−	1.04923i	0.670473	−	0.741934i	$-0.266091\pi$
$462$	−1.57458	+	1.75239i	−0.0732560	+	0.0815283i
$463$	−5.24090	+	5.24090i	−0.243565	+	0.243565i	−0.818323	−	0.574758i	$-0.805096\pi$
$463$	−5.24090	+	5.24090i	−0.243565	+	0.243565i	0.574758	+	0.818323i	$0.305096\pi$
$464$	−2.67027	−	1.54168i	−0.123964	−	0.0715706i
$465$	5.82554	−	11.4625i	0.270153	−	0.531563i
$466$	−9.08333	−	2.43387i	−0.420777	−	0.112747i
$467$	−14.4447			−0.668420			−0.334210	−	0.942499i	$-0.608469\pi$
$467$	−14.4447			−0.668420			−0.334210	+	0.942499i	$0.608469\pi$
$468$	−5.05948	+	19.9006i	−0.233874	+	0.919907i
$469$	−11.9886			−0.553583
$470$	−7.99912	−	2.14336i	−0.368972	−	0.0988658i
$471$	−11.7592	+	23.1378i	−0.541834	+	1.06613i
$472$	10.6112	+	6.12637i	0.488420	+	0.281989i
$473$	27.0529	−	27.0529i	1.24389	−	1.24389i
$474$	−4.91101	+	5.46558i	−0.225570	+	0.251042i
$475$	2.44181	+	9.11296i	0.112038	+	0.418131i
$476$	−4.51434	−	4.51434i	−0.206914	−	0.206914i
$477$	8.08744	−	5.90146i	0.370299	−	0.270209i
$478$	3.01433	−	1.74033i	0.137872	−	0.0796007i
$479$	4.66397	−	17.4062i	0.213102	−	0.795308i	−0.773724	−	0.633523i	$-0.781608\pi$
$479$	4.66397	−	17.4062i	0.213102	−	0.795308i	0.986826	−	0.161785i	$-0.0517251\pi$
$480$	−20.5265	+	13.3603i	−0.936904	+	0.609811i
$481$	−25.9077	−	18.4001i	−1.18129	−	0.838970i
$482$			0.838353i			0.0381859i
$483$	−3.02390	−	9.27396i	−0.137592	−	0.421980i
$484$	6.83297	+	11.8351i	0.310590	+	0.537957i
$485$	27.6313	−	47.8588i	1.25467	−	2.17316i
$486$	−2.50731	−	4.29140i	−0.113734	−	0.194662i
$487$	−12.5422	+	3.36067i	−0.568341	+	0.152286i	−0.531536	−	0.847036i	$-0.678385\pi$
$487$	−12.5422	+	3.36067i	−0.568341	+	0.152286i	−0.0368052	+	0.999322i	$0.511718\pi$
$488$	5.55836	−	1.48936i	0.251615	−	0.0674201i
$489$	9.35519	+	1.97840i	0.423056	+	0.0894663i
$490$	−0.631424	+	1.09366i	−0.0285248	+	0.0494065i
$491$	13.0417	+	22.5888i	0.588562	+	1.01942i	0.994421	+	0.105483i	$0.0336389\pi$
$491$	13.0417	+	22.5888i	0.588562	+	1.01942i	−0.405859	+	0.913936i	$0.633028\pi$
$492$	−13.1769	+	4.29650i	−0.594061	+	0.193701i
$493$			3.04951i			0.137343i
$494$	−0.951227	−	0.353437i	−0.0427977	−	0.0159019i
$495$	−20.5218	+	46.3505i	−0.922387	+	2.08330i
$496$	1.64951	−	6.15604i	0.0740650	−	0.276415i
$497$	−10.3987	+	6.00368i	−0.466444	+	0.269302i
$498$	−0.0971095	−	1.81701i	−0.00435158	−	0.0814222i
$499$	−28.0638	−	28.0638i	−1.25631	−	1.25631i	−0.952842	−	0.303466i	$-0.901856\pi$
$499$	−28.0638	−	28.0638i	−1.25631	−	1.25631i	−0.303466	−	0.952842i	$-0.598144\pi$
$500$	11.0688	+	41.3094i	0.495013	+	1.84741i
$501$	−0.00749346	−	0.00673313i	−0.000334783	−	0.000300814i
$502$	1.19459	−	1.19459i	0.0533170	−	0.0533170i
$503$	−13.3566	−	7.71146i	−0.595543	−	0.343837i	0.171743	−	0.985142i	$-0.445060\pi$
$503$	−13.3566	−	7.71146i	−0.595543	−	0.343837i	−0.767286	+	0.641305i	$0.778393\pi$
$504$	−3.70757	+	0.397435i	−0.165148	+	0.0177032i
$505$	−10.5892	−	2.83737i	−0.471213	−	0.126261i
$506$	7.66013			0.340534
$507$	−20.8336	+	8.54164i	−0.925254	+	0.379347i
$508$	27.4095			1.21610
$509$	−12.9131	−	3.46005i	−0.572363	−	0.153364i	−0.0389830	−	0.999240i	$-0.512412\pi$
$509$	−12.9131	−	3.46005i	−0.572363	−	0.153364i	−0.533380	+	0.845876i	$0.679078\pi$
$510$	6.55777	+	3.33281i	0.290383	+	0.147579i
$511$	7.20690	+	4.16090i	0.318814	+	0.184068i
$512$	−14.5611	+	14.5611i	−0.643516	+	0.643516i
$513$	−4.18441	+	1.87860i	−0.184746	+	0.0829420i
$514$	0.577245	+	2.15431i	0.0254612	+	0.0950225i
$515$	20.5329	+	20.5329i	0.904789	+	0.904789i
$516$	29.4457	−	1.57372i	1.29627	−	0.0692790i
$517$	−24.2270	+	13.9875i	−1.06550	+	0.615169i
$518$	0.727286	−	2.71427i	0.0319551	−	0.119258i
$519$	−9.33913	−	14.3485i	−0.409942	−	0.629829i
$520$	−16.6388	−	6.18228i	−0.729658	−	0.271111i
$521$			17.5945i			0.770828i	0.922744	+	0.385414i	$0.125941\pi$
$521$			17.5945i			0.770828i	−0.922744	+	0.385414i	$0.874059\pi$
$522$	0.675171	+	0.544435i	0.0295514	+	0.0238293i
$523$	−9.03618	−	15.6511i	−0.395125	−	0.684376i	0.597993	−	0.801502i	$-0.295965\pi$
$523$	−9.03618	−	15.6511i	−0.395125	−	0.684376i	−0.993117	+	0.117126i	$0.962632\pi$
$524$	5.65519	−	9.79508i	0.247048	−	0.427900i
$525$	−3.83012	+	18.1114i	−0.167160	+	0.790444i
$526$	−2.66100	+	0.713014i	−0.116025	+	0.0310889i
$527$	−6.08846	+	1.63140i	−0.265218	+	0.0710648i
$528$	−5.19843	+	24.5817i	−0.226233	+	1.06978i
$529$	−4.35838	+	7.54894i	−0.189495	+	0.328215i
$530$	2.10721	+	3.64979i	0.0915313	+	0.158537i
$531$	23.0215	+	18.5638i	0.999048	+	0.805598i
$532$			1.67571i			0.0726513i
$533$	−12.3910	−	8.80030i	−0.536714	−	0.381183i
$534$	−0.433604	−	0.666182i	−0.0187639	−	0.0288285i
$535$	3.48743	−	13.0153i	0.150775	−	0.562699i
$536$	12.9047	−	7.45055i	0.557400	−	0.321815i
$537$	32.7068	−	1.74800i	1.41140	−	0.0754320i
$538$	0.861107	+	0.861107i	0.0371249	+	0.0371249i
$539$	1.10413	+	4.12065i	0.0475581	+	0.177489i
$540$	−35.6423	+	16.0017i	−1.53380	+	0.688602i
$541$	−7.57587	+	7.57587i	−0.325712	+	0.325712i	−0.850953	−	0.525241i	$-0.823975\pi$
$541$	−7.57587	+	7.57587i	−0.325712	+	0.325712i	0.525241	+	0.850953i	$0.323975\pi$
$542$	−4.20600	−	2.42834i	−0.180663	−	0.104306i
$543$	−7.57529	−	3.84994i	−0.325087	−	0.165217i
$544$	11.5972	+	3.10746i	0.497225	+	0.133231i
$545$	15.9710			0.684121
$546$	−1.34970	−	1.46388i	−0.0577620	−	0.0626481i
$547$	4.38105			0.187320			0.0936600	−	0.995604i	$-0.470143\pi$
$547$	4.38105			0.187320			0.0936600	+	0.995604i	$0.470143\pi$
$548$	11.1938	+	2.99936i	0.478173	+	0.128126i
$549$	13.8100	−	1.48037i	0.589397	−	0.0631807i
$550$	−12.5896	−	7.26863i	−0.536824	−	0.309935i
$551$	0.565985	−	0.565985i	0.0241118	−	0.0241118i
$552$	9.01845	+	8.10338i	0.383851	+	0.344903i
$553$	3.44370	+	12.8521i	0.146441	+	0.546525i
$554$	2.87285	+	2.87285i	0.122056	+	0.122056i
$555$	−3.22676	−	60.3758i	−0.136968	−	2.56281i
$556$	−3.08324	+	1.78011i	−0.130759	+	0.0754935i
$557$	−11.7601	+	43.8892i	−0.498291	+	1.85965i	0.0124674	+	0.999922i	$0.496031\pi$
$557$	−11.7601	+	43.8892i	−0.498291	+	1.85965i	−0.510758	+	0.859724i	$0.670635\pi$
$558$	−0.725789	+	1.63926i	−0.0307251	+	0.0693955i
$559$	20.6187	+	24.9087i	0.872079	+	1.05353i
$560$			13.4682i			0.569137i
$561$	23.6253	−	7.70335i	0.997462	−	0.325236i
$562$	3.45739	+	5.98838i	0.145841	+	0.252605i
$563$	−21.2250	+	36.7628i	−0.894527	+	1.54937i	−0.0601380	+	0.998190i	$0.519154\pi$
$563$	−21.2250	+	36.7628i	−0.894527	+	1.54937i	−0.834389	+	0.551176i	$0.814179\pi$
$564$	−21.0951	−	4.46112i	−0.888265	−	0.187847i
$565$	44.4788	−	11.9181i	1.87124	−	0.501396i
$566$	3.40854	−	0.913316i	0.143272	−	0.0383895i
$567$	−8.98954	−	0.433846i	−0.377525	−	0.0182198i
$568$	7.46219	−	12.9249i	0.313107	−	0.542317i
$569$	18.5359	+	32.1051i	0.777066	+	1.34592i	0.933626	+	0.358249i	$0.116626\pi$
$569$	18.5359	+	32.1051i	0.777066	+	1.34592i	−0.156561	+	0.987668i	$0.550041\pi$
$570$	−0.598548	−	1.83568i	−0.0250704	−	0.0768881i
$571$			5.39552i			0.225796i	0.993607	+	0.112898i	$0.0360133\pi$
$571$			5.39552i			0.225796i	−0.993607	+	0.112898i	$0.963987\pi$
$572$	−26.5452	+	12.1629i	−1.10991	+	0.508556i
$573$	−26.9195	+	17.5213i	−1.12458	+	0.731965i
$574$	0.347843	−	1.29817i	0.0145187	−	0.0541845i
$575$	52.1274	−	30.0958i	2.17386	−	1.25508i
$576$	−13.7225	+	10.0134i	−0.571772	+	0.417226i
$577$	23.2360	+	23.2360i	0.967327	+	0.967327i	0.999483	−	0.0321559i	$-0.0102373\pi$
$577$	23.2360	+	23.2360i	0.967327	+	0.967327i	−0.0321559	+	0.999483i	$0.510237\pi$
$578$	0.469531	+	1.75231i	0.0195299	+	0.0728866i
$579$	20.4513	−	22.7608i	0.849927	−	0.945905i
$580$	4.82099	−	4.82099i	0.200181	−	0.200181i
$581$	−2.85350	−	1.64747i	−0.118383	−	0.0683484i
$582$	−3.49095	+	6.86892i	−0.144704	+	0.284726i
$583$	13.7516	+	3.68472i	0.569532	+	0.152606i
$584$	−10.3435			−0.428017
$585$	−37.3746	−	20.9432i	−1.54525	−	0.865895i
$586$	2.48842			0.102796
$587$	−17.5723	−	4.70849i	−0.725287	−	0.194340i	−0.122758	−	0.992437i	$-0.539174\pi$
$587$	−17.5723	−	4.70849i	−0.725287	−	0.194340i	−0.602530	+	0.798097i	$0.705840\pi$
$588$	−1.48970	+	2.93119i	−0.0614343	+	0.120880i
$589$	1.43280	+	0.827226i	0.0590374	+	0.0340852i
$590$	−8.80279	+	8.80279i	−0.362405	+	0.362405i
$591$	0.316838	−	0.352616i	0.0130330	−	0.0145047i
$592$	−7.75648	−	28.9476i	−0.318789	−	1.18974i
$593$	−25.7189	−	25.7189i	−1.05615	−	1.05615i	−0.998327	−	0.0578202i	$-0.981585\pi$
$593$	−25.7189	−	25.7189i	−1.05615	−	1.05615i	−0.0578202	−	0.998327i	$-0.518415\pi$
$594$	2.51233	−	6.60602i	0.103082	−	0.271048i
$595$	11.5358	−	6.66019i	0.472921	−	0.273041i
$596$	0.986624	−	3.68213i	0.0404137	−	0.150826i
$597$	27.2637	−	17.7453i	1.11583	−	0.726268i
$598$	−0.607361	+	6.44564i	−0.0248369	+	0.263582i
$599$			25.0400i			1.02311i	0.859252	+	0.511553i	$0.170930\pi$
$599$			25.0400i			1.02311i	−0.859252	+	0.511553i	$0.829070\pi$
$600$	−7.13284	−	21.8756i	−0.291197	−	0.893069i
$601$	−3.59209	−	6.22167i	−0.146524	−	0.253787i	0.783416	−	0.621497i	$-0.213475\pi$
$601$	−3.59209	−	6.22167i	−0.146524	−	0.253787i	−0.929941	+	0.367710i	$0.880142\pi$
$602$	−1.42970	+	2.47632i	−0.0582703	+	0.100927i
$603$	33.5503	−	12.9584i	1.36627	−	0.527708i
$604$	21.7166	−	5.81893i	0.883634	−	0.236769i
$605$	−27.5417	+	7.37977i	−1.11973	+	0.300030i
$606$	1.49543	+	0.316248i	0.0607478	+	0.0128467i
$607$	−23.8542	+	41.3166i	−0.968210	+	1.67699i	−0.267479	+	0.963564i	$0.586191\pi$
$607$	−23.8542	+	41.3166i	−0.968210	+	1.67699i	−0.700731	+	0.713426i	$0.747143\pi$
$608$	−1.57568	−	2.72916i	−0.0639024	−	0.110682i
$609$	1.49319	−	0.486875i	0.0605072	−	0.0197292i
$610$			5.84662i			0.236723i
$611$	−9.84888	−	21.4950i	−0.398443	−	0.869593i
$612$	17.5130	+	7.75392i	0.707919	+	0.313433i
$613$	8.40096	−	31.3528i	0.339312	−	1.26633i	−0.559807	−	0.828623i	$-0.689125\pi$
$613$	8.40096	−	31.3528i	0.339312	−	1.26633i	0.899119	−	0.437705i	$-0.144209\pi$
$614$	−0.0175509	+	0.0101330i	−0.000708297	+	0.000408935i
$615$	−1.54328	−	28.8763i	−0.0622312	−	1.16440i
$616$	−3.74936	−	3.74936i	−0.151066	−	0.151066i
$617$	−1.68739	−	6.29744i	−0.0679319	−	0.253525i	0.923606	−	0.383343i	$-0.125227\pi$
$617$	−1.68739	−	6.29744i	−0.0679319	−	0.253525i	−0.991538	+	0.129818i	$0.958561\pi$
$618$	−3.01156	−	2.70599i	−0.121143	−	0.108851i
$619$	−16.0848	+	16.0848i	−0.646505	+	0.646505i	−0.952147	−	0.305642i	$-0.901129\pi$
$619$	−16.0848	+	16.0848i	−0.646505	+	0.646505i	0.305642	+	0.952147i	$0.401129\pi$
$620$	12.2044	+	7.04621i	0.490140	+	0.282983i
$621$	18.4866	+	22.6848i	0.741841	+	0.910309i
$622$	−4.19251	−	1.12338i	−0.168104	−	0.0450434i
$623$	−1.43934			−0.0576660
$624$	−20.2721	−	6.32329i	−0.811535	−	0.253134i
$625$	−35.7911			−1.43164
$626$	2.30963	+	0.618863i	0.0923113	+	0.0247347i
$627$	−5.81457	−	2.95510i	−0.232211	−	0.118015i
$628$	−24.6353	−	14.2232i	−0.983054	−	0.567567i
$629$	−20.9584	+	20.9584i	−0.835668	+	0.835668i
$630$	0.584919	−	3.74312i	0.0233037	−	0.149129i
$631$	1.00345	+	3.74492i	0.0399467	+	0.149083i	0.983019	−	0.183506i	$-0.0587446\pi$
$631$	1.00345	+	3.74492i	0.0399467	+	0.149083i	−0.943072	+	0.332589i	$0.892078\pi$
$632$	−11.6940	−	11.6940i	−0.465163	−	0.465163i
$633$	9.05125	−	0.483741i	0.359755	−	0.0192270i
$634$	−6.40251	+	3.69649i	−0.254276	+	0.146806i
$635$	−14.8015	+	55.2398i	−0.587378	+	2.19212i
$636$	5.98578	+	9.19647i	0.237352	+	0.364664i
$637$	−3.55488	+	0.602349i	−0.140849	+	0.0238659i
$638$			1.23335i			0.0488288i
$639$	22.6115	−	28.0412i	0.894496	−	1.10929i
$640$	−17.7157	−	30.6844i	−0.700273	−	1.21291i
$641$	10.0013	−	17.3227i	0.395027	−	0.684206i	−0.598078	−	0.801438i	$-0.704069\pi$
$641$	10.0013	−	17.3227i	0.395027	−	0.684206i	0.993105	+	0.117232i	$0.0374020\pi$
$642$	−0.388703	+	1.83805i	−0.0153409	+	0.0725419i
$643$	−37.8353	+	10.1379i	−1.49208	+	0.399801i	−0.910439	−	0.413644i	$-0.864256\pi$
$643$	−37.8353	+	10.1379i	−1.49208	+	0.399801i	−0.581641	+	0.813446i	$0.697589\pi$
$644$	10.3267	−	2.76704i	0.406930	−	0.109037i
$645$	−12.7294	+	60.1933i	−0.501221	+	2.37011i
$646$	−0.473259	+	0.819709i	−0.0186201	+	0.0322510i
$647$	−17.0940	−	29.6076i	−0.672034	−	1.16400i	−0.977327	−	0.211738i	$-0.932088\pi$
$647$	−17.0940	−	29.6076i	−0.672034	−	1.16400i	0.305293	−	0.952258i	$-0.401246\pi$
$648$	9.94610	−	5.11972i	0.390720	−	0.201122i
$649$			42.0539i			1.65076i
$650$	7.11442	−	10.0173i	0.279051	−	0.392909i
$651$	1.77088	+	2.72075i	0.0694063	+	0.106635i
$652$	−2.71246	+	10.1230i	−0.106228	+	0.396449i
$653$	13.2606	−	7.65599i	0.518926	−	0.299602i	−0.217569	−	0.976045i	$-0.569813\pi$
$653$	13.2606	−	7.65599i	0.518926	−	0.299602i	0.736495	+	0.676443i	$0.236479\pi$
$654$	−2.22362	+	0.118840i	−0.0869503	+	0.00464703i
$655$	16.6867	+	16.6867i	0.652002	+	0.652002i
$656$	−3.70973	−	13.8449i	−0.144841	−	0.540553i
$657$	−24.6661	−	3.85445i	−0.962315	−	0.150376i
$658$	1.47843	−	1.47843i	0.0576353	−	0.0576353i
$659$	−28.8971	−	16.6837i	−1.12567	−	0.649906i	−0.182827	−	0.983145i	$-0.558525\pi$
$659$	−28.8971	−	16.6837i	−1.12567	−	0.649906i	−0.942842	+	0.333239i	$0.891858\pi$
$660$	−49.5278	−	25.1712i	−1.92787	−	0.979787i
$661$	19.0048	+	5.09232i	0.739200	+	0.198068i	0.608723	−	0.793383i	$-0.291682\pi$
$661$	19.0048	+	5.09232i	0.739200	+	0.198068i	0.130478	+	0.991451i	$0.458349\pi$
$662$	−2.32531			−0.0903758
$663$	4.60879	+	20.4904i	0.178990	+	0.795781i
$664$	4.09540			0.158932
$665$	−3.37715	−	0.904905i	−0.130960	−	0.0350907i
$666$	0.898516	+	8.38203i	0.0348168	+	0.324797i
$667$	−4.42252	−	2.55335i	−0.171241	−	0.0988659i
$668$	0.00780736	−	0.00780736i	0.000302076	−	0.000302076i
$669$	4.93789	+	4.43686i	0.190910	+	0.171539i
$670$	3.91847	+	14.6239i	0.151384	+	0.564972i
$671$	13.9656	+	13.9656i	0.539138	+	0.539138i
$672$	−0.330004	−	6.17469i	−0.0127302	−	0.238194i
$673$	23.8982	−	13.7976i	0.921209	−	0.531860i	0.0371881	−	0.999308i	$-0.488160\pi$
$673$	23.8982	−	13.7976i	0.921209	−	0.531860i	0.884020	+	0.467448i	$0.154827\pi$
$674$	2.24802	−	8.38973i	0.0865905	−	0.323160i
$675$	−8.85782	−	54.8248i	−0.340937	−	2.11021i
$676$	−8.12976	−	23.3009i	−0.312683	−	0.896189i
$677$		−	20.3837i		−	0.783409i	−0.920091	−	0.391705i	$-0.871886\pi$
$677$		−	20.3837i		−	0.783409i	0.920091	−	0.391705i	$-0.128114\pi$
$678$	−6.10404	+	1.99030i	−0.234424	+	0.0764371i
$679$	6.97620	+	12.0831i	0.267722	+	0.463708i
$680$	−8.27820	+	14.3383i	−0.317454	+	0.549847i
$681$	37.0805	+	7.84164i	1.42093	+	0.300492i
$682$	−2.46243	+	0.659807i	−0.0942915	+	0.0252653i
$683$	−12.6624	+	3.39288i	−0.484514	+	0.129825i	−0.492804	−	0.870141i	$-0.664028\pi$
$683$	−12.6624	+	3.39288i	−0.484514	+	0.129825i	0.00828973	+	0.999966i	$0.497361\pi$
$684$	−1.81127	−	4.68950i	−0.0692555	−	0.179308i
$685$	−12.0895	+	20.9397i	−0.461917	+	0.800064i
$686$	−0.159419	−	0.276121i	−0.00608663	−	0.0105424i
$687$	6.79909	+	20.8520i	0.259401	+	0.795555i
$688$			30.4954i			1.16263i
$689$	−4.19087	+	11.2791i	−0.159659	+	0.429701i
$690$	−10.3242	+	6.71979i	−0.393035	+	0.255818i
$691$	−1.42922	+	5.33391i	−0.0543700	+	0.202911i	−0.987768	−	0.155932i	$-0.950162\pi$
$691$	−1.42922	+	5.33391i	−0.0543700	+	0.202911i	0.933398	+	0.358843i	$0.116829\pi$
$692$	16.2499	−	9.38190i	0.617730	−	0.356646i
$693$	−7.54390	−	10.3383i	−0.286569	−	0.392718i
$694$	−1.01368	−	1.01368i	−0.0384788	−	0.0384788i
$695$	−1.92256	−	7.17510i	−0.0729270	−	0.272167i
$696$	−1.30472	+	1.45205i	−0.0494552	+	0.0550399i
$697$	−10.0239	+	10.0239i	−0.379683	+	0.379683i
$698$	−6.83718	−	3.94745i	−0.258791	−	0.149413i
$699$	23.1450	−	45.5409i	0.875424	−	1.72252i
$700$	−19.5979	−	5.25124i	−0.740730	−	0.198478i
$701$	−48.9927			−1.85043			−0.925214	−	0.379445i	$-0.876115\pi$
$701$	−48.9927			−1.85043			−0.925214	+	0.379445i	$0.876115\pi$
$702$	5.35946	+	2.63779i	0.202280	+	0.0995570i
$703$	7.77973			0.293418
$704$	−23.3333	−	6.25213i	−0.879406	−	0.235636i
$705$	20.3824	−	40.1051i	0.767644	−	1.51044i
$706$	6.51980	+	3.76421i	0.245376	+	0.141668i
$707$	1.95714	−	1.95714i	0.0736059	−	0.0736059i
$708$	−21.6636	+	24.1100i	−0.814169	+	0.906108i
$709$	−2.16356	−	8.07450i	−0.0812541	−	0.303244i	0.913324	−	0.407233i	$-0.133506\pi$
$709$	−2.16356	−	8.07450i	−0.0812541	−	0.303244i	−0.994579	+	0.103988i	$0.966840\pi$
$710$	10.7222	+	10.7222i	0.402397	+	0.402397i
$711$	−23.5289	−	32.2444i	−0.882404	−	1.20926i
$712$	1.54933	−	0.894506i	0.0580636	−	0.0335230i
$713$	2.73193	−	10.1957i	0.102312	−	0.381832i
$714$	−1.55655	+	1.01313i	−0.0582526	+	0.0379153i
$715$	−10.1778	−	60.0661i	−0.380627	−	2.24634i
$716$			35.8981i			1.34157i
$717$	5.86157	+	17.9768i	0.218904	+	0.671356i
$718$	0.859320	+	1.48839i	0.0320695	+	0.0555461i
$719$	−4.54570	+	7.87338i	−0.169526	+	0.293627i	−0.938253	−	0.345949i	$-0.887557\pi$
$719$	−4.54570	+	7.87338i	−0.169526	+	0.293627i	0.768727	+	0.639577i	$0.220890\pi$
$720$	−14.5577	−	37.6910i	−0.542534	−	1.40466i
$721$	−7.08154	+	1.89749i	−0.263730	+	0.0706663i
$722$	−5.61152	+	1.50360i	−0.208839	+	0.0559583i
$723$	−4.45572	−	0.942278i	−0.165710	−	0.0350437i
$724$	4.65666	−	8.06556i	0.173063	−	0.299754i
$725$	4.84569	+	8.39299i	0.179964	+	0.311708i
$726$	3.77968	−	1.23241i	0.140277	−	0.0457392i
$727$			19.1974i			0.711991i	0.934488	+	0.355996i	$0.115858\pi$
$727$			19.1974i			0.711991i	−0.934488	+	0.355996i	$0.884142\pi$
$728$	3.45219	−	2.85762i	0.127947	−	0.105911i
$729$	25.6263	−	8.50261i	0.949121	−	0.314911i
$730$	2.71998	−	10.1511i	0.100671	−	0.375709i
$731$	26.1199	−	15.0803i	0.966079	−	0.557766i
$732$	0.812408	+	15.2009i	0.0300274	+	0.561842i
$733$	33.9403	+	33.9403i	1.25361	+	1.25361i	0.954088	+	0.299527i	$0.0968289\pi$
$733$	33.9403	+	33.9403i	1.25361	+	1.25361i	0.299527	+	0.954088i	$0.403171\pi$
$734$	0.155945	+	0.581996i	0.00575604	+	0.0214818i
$735$	−5.10293	−	4.58516i	−0.188225	−	0.169126i
$736$	−14.2168	+	14.2168i	−0.524040	+	0.524040i
$737$	44.2917	+	25.5718i	1.63150	+	0.941950i
$738$	0.429738	+	4.00892i	0.0158189	+	0.147570i
$739$	18.1874	+	4.87331i	0.669035	+	0.179267i	0.577320	−	0.816518i	$-0.304098\pi$
$739$	18.1874	+	4.87331i	0.669035	+	0.179267i	0.0917151	+	0.995785i	$0.470765\pi$
$740$	66.2668			2.43602
$741$	2.94761	−	4.65838i	0.108283	−	0.171130i
$742$	−1.06403			−0.0390619
$743$	42.8653	+	11.4857i	1.57257	+	0.421370i	0.936617	−	0.350354i	$-0.113939\pi$
$743$	42.8653	+	11.4857i	1.57257	+	0.421370i	0.635957	+	0.771724i	$0.280605\pi$
$744$	−3.59707	−	1.82811i	−0.131875	−	0.0670219i
$745$	6.88801	+	3.97679i	0.252357	+	0.145698i
$746$	6.40747	−	6.40747i	0.234594	−	0.234594i
$747$	9.76628	+	1.52613i	0.357329	+	0.0558382i
$748$	7.04901	+	26.3072i	0.257737	+	0.961888i
$749$	2.40554	+	2.40554i	0.0878964	+	0.0878964i
$750$	12.4234	−	0.663966i	0.453639	−	0.0242446i
$751$	1.42630	−	0.823475i	0.0520465	−	0.0300490i	−0.473751	−	0.880659i	$-0.657100\pi$
$751$	1.42630	−	0.823475i	0.0520465	−	0.0300490i	0.525797	+	0.850610i	$0.323767\pi$
$752$	5.77128	−	21.5387i	0.210457	−	0.785437i
$753$	5.00638	+	7.69172i	0.182443	+	0.280302i
$754$	−1.03781	−	0.0977908i	−0.0377947	−	0.00356133i
$755$			46.9088i			1.70719i
$756$	1.00064	−	9.81319i	0.0363930	−	0.356902i
$757$	13.6190	+	23.5888i	0.494991	+	0.857349i	0.999983	−	0.00577485i	$-0.00183820\pi$
$757$	13.6190	+	23.5888i	0.494991	+	0.857349i	−0.504993	+	0.863124i	$0.668505\pi$
$758$	0.118966	−	0.206055i	0.00432103	−	0.00748424i
$759$	−8.60970	+	40.7124i	−0.312512	+	1.47777i
$760$	4.19759	−	1.12474i	0.152263	−	0.0407986i
$761$	6.34882	−	1.70116i	0.230144	−	0.0616670i	−0.141904	−	0.989880i	$-0.545322\pi$
$761$	6.34882	−	1.70116i	0.230144	−	0.0616670i	0.372048	+	0.928213i	$0.378656\pi$
$762$	1.64975	−	7.80110i	0.0597640	−	0.282604i
$763$	−2.01613	+	3.49205i	−0.0729889	+	0.126421i
$764$	−17.6016	−	30.4868i	−0.636803	−	1.10298i
$765$	−25.0841	+	31.1076i	−0.906917	+	1.12470i
$766$		−	6.22941i		−	0.225078i
$767$	−35.3864	−	3.33440i	−1.27773	−	0.120398i
$768$	−8.00554	−	12.2996i	−0.288875	−	0.443823i
$769$	13.6977	−	51.1203i	0.493950	−	1.84345i	−0.0418835	−	0.999123i	$-0.513336\pi$
$769$	13.6977	−	51.1203i	0.493950	−	1.84345i	0.535833	−	0.844324i	$-0.319998\pi$
$770$	4.66556	−	2.69366i	0.168135	−	0.0970729i
$771$	−12.0986	+	0.646608i	−0.435722	+	0.0232870i
$772$	23.7142	+	23.7142i	0.853493	+	0.853493i
$773$	0.943142	+	3.51985i	0.0339224	+	0.126600i	0.980811	−	0.194963i	$-0.0624585\pi$
$773$	0.943142	+	3.51985i	0.0339224	+	0.126600i	−0.946888	+	0.321563i	$0.895792\pi$
$774$	1.32440	−	8.47535i	0.0476047	−	0.304640i
$775$	−14.1646	+	14.1646i	−0.508808	+	0.508808i
$776$	−15.0186	−	8.67099i	−0.539136	−	0.311270i
$777$	13.6085	+	6.91615i	0.488201	+	0.248115i
$778$	7.29129	+	1.95370i	0.261406	+	0.0700434i
$779$	3.72086			0.133313
$780$	25.1074	−	39.6795i	0.898988	−	1.42075i
$781$	51.2235			1.83292
$782$	5.83300	+	1.56295i	0.208588	+	0.0558909i
$783$	−3.65246	+	2.97651i	−0.130528	+	0.106372i
$784$	−2.94482	−	1.70020i	−0.105172	−	0.0607213i
$785$	41.9681	−	41.9681i	1.49790	−	1.49790i
$786$	−2.44743	−	2.19910i	−0.0872969	−	0.0784391i
$787$	−10.3308	−	38.5550i	−0.368253	−	1.37434i	−0.862957	−	0.505277i	$-0.831390\pi$
$787$	−10.3308	−	38.5550i	−0.368253	−	1.37434i	0.494705	−	0.869061i	$-0.335276\pi$
$788$	0.367387	+	0.367387i	0.0130876	+	0.0130876i
$789$	−0.798690	−	14.9442i	−0.0284341	−	0.532029i
$790$	14.5516	−	8.40137i	0.517723	−	0.298907i
$791$	−3.00901	+	11.2298i	−0.106988	+	0.399285i
$792$	14.5453	+	6.43996i	0.516844	+	0.228834i
$793$	−12.8587	+	10.6441i	−0.456627	+	0.377983i
$794$		−	10.2902i		−	0.365186i
$795$	−21.7665	+	7.09726i	−0.771979	+	0.251714i
$796$	17.8266	+	30.8766i	0.631847	+	1.09439i
$797$	21.4930	−	37.2270i	0.761323	−	1.31865i	−0.180846	−	0.983511i	$-0.557884\pi$
$797$	21.4930	−	37.2270i	0.761323	−	1.31865i	0.942169	−	0.335138i	$-0.108783\pi$
$798$	0.476930	+	0.100859i	0.0168831	+	0.00357038i
$799$	−21.3023	+	5.70793i	−0.753620	+	0.201932i
$800$	36.8560	−	9.87554i	1.30306	−	0.349153i
$801$	4.02801	−	1.55577i	0.142323	−	0.0549706i
$802$	−2.22791	+	3.85885i	−0.0786701	+	0.136261i
$803$	−17.7505	−	30.7447i	−0.626401	−	1.08496i
$804$	12.2199	+	37.4770i	0.430961	+	1.32171i
$805$			22.3062i			0.786192i
$806$	−0.359953	−	2.12434i	−0.0126788	−	0.0748266i
$807$	−5.54450	+	3.60880i	−0.195176	+	0.127036i
$808$	−0.890396	+	3.32300i	−0.0313240	+	0.116903i
$809$	−14.3225	+	8.26907i	−0.503551	+	0.290725i	−0.730179	−	0.683256i	$-0.760563\pi$
$809$	−14.3225	+	8.26907i	−0.503551	+	0.290725i	0.226628	+	0.973981i	$0.427230\pi$
$810$	2.40901	+	11.1074i	0.0846440	+	0.390274i
$811$	−16.6951	−	16.6951i	−0.586245	−	0.586245i	0.350367	−	0.936612i	$-0.386057\pi$
$811$	−16.6951	−	16.6951i	−0.586245	−	0.586245i	−0.936612	+	0.350367i	$0.886057\pi$
$812$	0.445519	+	1.66270i	0.0156346	+	0.0583493i
$813$	17.6336	−	19.6249i	0.618438	−	0.688275i
$814$	−8.47649	+	8.47649i	−0.297101	+	0.297101i
$815$	−18.9367	−	10.9331i	−0.663325	−	0.382971i
$816$	−8.97405	+	17.6577i	−0.314155	+	0.618142i
$817$	−7.64671	−	2.04893i	−0.267525	−	0.0716830i
$818$	0.953920			0.0333530
$819$	9.29730	−	5.52813i	0.324874	−	0.193168i
$820$	31.6938			1.10680
$821$	−42.8169	−	11.4728i	−1.49432	−	0.400402i	−0.583128	−	0.812381i	$-0.698171\pi$
$821$	−42.8169	−	11.4728i	−1.49432	−	0.400402i	−0.911194	+	0.411978i	$0.864838\pi$
$822$	1.52740	−	3.00536i	0.0532740	−	0.104824i
$823$	15.7479	+	9.09207i	0.548938	+	0.316930i	0.748694	−	0.662916i	$-0.230681\pi$
$823$	15.7479	+	9.09207i	0.548938	+	0.316930i	−0.199755	+	0.979846i	$0.564015\pi$
$824$	6.44345	−	6.44345i	0.224468	−	0.224468i
$825$	52.7819	−	58.7423i	1.83763	−	2.04515i
$826$	−0.813485	−	3.03597i	−0.0283048	−	0.105635i
$827$	37.0427	+	37.0427i	1.28810	+	1.28810i	0.935940	+	0.352159i	$0.114553\pi$
$827$	37.0427	+	37.0427i	1.28810	+	1.28810i	0.352159	+	0.935940i	$0.385447\pi$
$828$	−25.9086	+	18.9057i	−0.900386	+	0.657018i
$829$	−36.1141	+	20.8505i	−1.25429	+	0.724166i	−0.971959	−	0.235150i	$-0.924442\pi$
$829$	−36.1141	+	20.8505i	−1.25429	+	0.724166i	−0.282334	+	0.959316i	$0.591109\pi$
$830$	−1.07695	+	4.01922i	−0.0373814	+	0.139509i
$831$	−18.4977	+	12.0398i	−0.641680	+	0.417656i
$832$	7.11094	−	19.1381i	0.246527	−	0.663495i
$833$			3.36306i			0.116523i
$834$	0.321066	+	0.984675i	0.0111176	+	0.0340965i
$835$	0.0115185	+	0.0199506i	0.000398615	+	0.000690421i
$836$	3.57431	−	6.19088i	0.123620	−	0.214116i
$837$	−7.89667	−	5.69993i	−0.272949	−	0.197018i
$838$	11.3471	−	3.04043i	0.391978	−	0.105030i
$839$	24.4688	−	6.55640i	0.844757	−	0.226352i	0.189616	−	0.981858i	$-0.439276\pi$
$839$	24.4688	−	6.55640i	0.844757	−	0.226352i	0.655141	+	0.755506i	$0.272609\pi$
$840$	8.34241	+	1.76422i	0.287840	+	0.0608714i
$841$	−14.0889	+	24.4027i	−0.485824	+	0.841471i
$842$	−0.315898	−	0.547151i	−0.0108866	−	0.0188561i
$843$	−35.7133	+	11.6448i	−1.23003	+	0.401068i
$844$			9.93440i			0.341956i
$845$	51.3497	−	3.80155i	1.76649	−	0.130777i
$846$	−2.53938	+	5.73544i	−0.0873058	+	0.197189i
$847$	1.86321	−	6.95358i	0.0640206	−	0.238928i
$848$	−9.82756	+	5.67395i	−0.337480	+	0.194844i
$849$	1.02306	+	19.1424i	0.0351113	+	0.656966i
$850$	−8.10363	−	8.10363i	−0.277952	−	0.277952i
$851$	−12.8464	−	47.9433i	−0.440368	−	1.64347i
$852$	29.3670	+	26.3872i	1.00610	+	0.904012i
$853$	16.3128	−	16.3128i	0.558541	−	0.558541i	−0.370351	−	0.928892i	$-0.620763\pi$
$853$	16.3128	−	16.3128i	0.558541	−	0.558541i	0.928892	+	0.370351i	$0.120763\pi$
$854$	−1.27836	−	0.738062i	−0.0437446	−	0.0252560i
$855$	10.4291	−	1.11795i	0.356668	−	0.0382332i
$856$	−4.08432	−	1.09439i	−0.139599	−	0.0374055i
$857$	38.5550			1.31701			0.658506	−	0.752575i	$-0.271189\pi$
$857$	38.5550			1.31701			0.658506	+	0.752575i	$0.271189\pi$
$858$	1.86399	+	8.28719i	0.0636356	+	0.282920i
$859$	−39.3924			−1.34405			−0.672025	−	0.740529i	$-0.734575\pi$
$859$	−39.3924			−1.34405			−0.672025	+	0.740529i	$0.734575\pi$
$860$	−65.1338	−	17.4525i	−2.22104	−	0.595127i
$861$	6.50860	+	3.30783i	0.221813	+	0.112730i
$862$	4.74001	+	2.73664i	0.161445	+	0.0932105i
$863$	−16.9671	+	16.9671i	−0.577565	+	0.577565i	−0.934232	−	0.356666i	$-0.883913\pi$
$863$	−16.9671	+	16.9671i	−0.577565	+	0.577565i	0.356666	+	0.934232i	$0.383913\pi$
$864$	7.59770	+	16.9232i	0.258479	+	0.575741i
$865$	10.1327	+	37.8157i	0.344521	+	1.28577i
$866$	4.79651	+	4.79651i	0.162992	+	0.162992i
$867$	−9.84102	+	0.525950i	−0.334218	+	0.0178622i
$868$	−3.08130	+	1.77899i	−0.104586	+	0.0603829i
$869$	14.6909	−	54.8271i	0.498354	−	1.85988i
$870$	−1.08195	−	1.66229i	−0.0366815	−	0.0563568i
$871$	−25.0293	+	35.2418i	−0.848086	+	1.19412i
$872$		−	5.01186i		−	0.169723i
$873$	−32.5836	−	26.2743i	−1.10279	−	0.889250i
$874$	−0.792517	−	1.37268i	−0.0268073	−	0.0464316i
$875$	11.2642	−	19.5102i	0.380800	−	0.659565i
$876$	5.66127	−	26.7703i	0.191277	−	0.904483i
$877$	51.7120	−	13.8562i	1.74619	−	0.467890i	0.762384	−	0.647125i	$-0.224029\pi$
$877$	51.7120	−	13.8562i	1.74619	−	0.467890i	0.983806	+	0.179235i	$0.0573622\pi$
$878$	2.35643	−	0.631404i	0.0795258	−	0.0213089i
$879$	−2.79690	+	13.2256i	−0.0943370	+	0.446088i
$880$	28.7278	−	49.7581i	0.968415	−	1.67734i
$881$	−13.5812	−	23.5233i	−0.457561	−	0.792519i	0.541270	−	0.840849i	$-0.317944\pi$
$881$	−13.5812	−	23.5233i	−0.457561	−	0.792519i	−0.998831	+	0.0483295i	$0.984610\pi$
$882$	0.744593	+	0.600414i	0.0250717	+	0.0202170i
$883$		−	28.4422i		−	0.957157i	−0.878045	−	0.478578i	$-0.841152\pi$
$883$		−	28.4422i		−	0.957157i	0.878045	−	0.478578i	$-0.158848\pi$
$884$	−22.6952	+	3.84554i	−0.763323	+	0.129340i
$885$	−36.8915	−	56.6795i	−1.24009	−	1.90526i
$886$	1.72024	−	6.42003i	0.0577926	−	0.215685i
$887$	−0.320813	+	0.185221i	−0.0107718	+	0.00621913i	−0.505376	−	0.862899i	$-0.668646\pi$
$887$	−0.320813	+	0.185221i	−0.0107718	+	0.00621913i	0.494604	+	0.869118i	$0.335313\pi$
$888$	−18.9465	+	1.01259i	−0.635804	+	0.0339804i
$889$	−10.2097	−	10.2097i	−0.342421	−	0.342421i
$890$	0.470447	+	1.75573i	0.0157694	+	0.0588523i
$891$	32.2862	+	20.7776i	1.08163	+	0.696075i
$892$	−5.14473	+	5.14473i	−0.172258	+	0.172258i
$893$	5.01306	+	2.89429i	0.167756	+	0.0968538i
$894$	−0.988599	−	0.502430i	−0.0330637	−	0.0168038i
$895$	−72.3473	−	19.3854i	−2.41830	−	0.647983i
$896$	8.94552			0.298849
$897$	−33.5749	−	10.4727i	−1.12103	−	0.349673i
$898$	−3.33073			−0.111148
$899$	1.64160	+	0.439866i	0.0547505	+	0.0146704i
$900$	60.5209	−	6.48758i	2.01736	−	0.216253i
$901$	9.71967	+	5.61166i	0.323809	+	0.186951i
$902$	−4.05410	+	4.05410i	−0.134987	+	0.134987i
$903$	−11.5543	−	10.3819i	−0.384503	−	0.345489i
$904$	−3.74001	−	13.9579i	−0.124391	−	0.464233i
$905$	13.7403	+	13.7403i	0.456743	+	0.456743i
$906$	−0.349050	−	6.53105i	−0.0115964	−	0.216980i
$907$	10.5533	−	6.09298i	0.350418	−	0.202314i	−0.314451	−	0.949274i	$-0.601821\pi$
$907$	10.5533	−	6.09298i	0.350418	−	0.202314i	0.664869	+	0.746960i	$0.268487\pi$
$908$	−10.7512	+	40.1240i	−0.356791	+	1.33156i
$909$	−3.36163	+	7.59255i	−0.111498	+	0.251829i
$910$	1.89667	+	4.13943i	0.0628738	+	0.137221i
$911$			30.5875i			1.01341i	0.862119	+	0.506705i	$0.169137\pi$
$911$			30.5875i			1.01341i	−0.862119	+	0.506705i	$0.830863\pi$
$912$	4.94282	−	1.61167i	0.163673	−	0.0533677i
$913$	7.02812	+	12.1731i	0.232597	+	0.402869i
$914$	−0.603450	+	1.04521i	−0.0199604	+	0.0345724i
$915$	−31.0739	−	6.57138i	−1.02727	−	0.217243i
$916$	−23.2192	+	6.22155i	−0.767182	+	0.205566i
$917$	−5.75501	+	1.54205i	−0.190047	+	0.0509230i
$918$	3.26095	−	4.51772i	0.107627	−	0.149107i
$919$	−23.4658	+	40.6439i	−0.774065	+	1.34072i	0.161253	+	0.986913i	$0.448446\pi$
$919$	−23.4658	+	40.6439i	−0.774065	+	1.34072i	−0.935318	+	0.353807i	$0.884887\pi$
$920$	−13.8626	−	24.0108i	−0.457037	−	0.791612i
$921$	−0.0341289	−	0.104670i	−0.00112459	−	0.00344898i
$922$		−	7.43614i		−	0.244896i
$923$	−4.06145	+	43.1022i	−0.133684	+	1.41873i
$924$	11.7559	−	7.65168i	0.386742	−	0.251722i
$925$	−24.3796	+	90.9859i	−0.801596	+	2.99160i
$926$	−2.04654	+	1.18157i	−0.0672535	+	0.0388288i
$927$	17.7668	−	12.9645i	0.583538	−	0.425812i
$928$	−2.28904	−	2.28904i	−0.0751415	−	0.0751415i
$929$	8.96251	+	33.4485i	0.294050	+	1.09741i	0.941969	+	0.335701i	$0.108973\pi$
$929$	8.96251	+	33.4485i	0.294050	+	1.09741i	−0.647918	+	0.761710i	$0.724360\pi$
$930$	2.74001	−	3.04943i	0.0898485	−	0.0999947i
$931$	0.624180	−	0.624180i	0.0204567	−	0.0204567i
$932$	48.4883	+	27.9947i	1.58829	+	0.916998i
$933$	10.6828	−	21.0199i	0.349740	−	0.688162i
$934$	−4.44857	−	1.19199i	−0.145562	−	0.0390032i
$935$	−56.8249			−1.85837
$936$	−6.57220	+	11.7285i	−0.214819	+	0.383359i
$937$	−36.6710			−1.19799			−0.598994	−	0.800754i	$-0.704433\pi$
$937$	−36.6710			−1.19799			−0.598994	+	0.800754i	$0.704433\pi$
$938$	−3.69217	−	0.989315i	−0.120554	−	0.0323023i
$939$	−5.88510	+	11.5797i	−0.192053	+	0.377891i
$940$	42.7007	+	24.6532i	1.39274	+	0.804100i
$941$	−15.0046	+	15.0046i	−0.489136	+	0.489136i	−0.908033	−	0.418898i	$-0.862417\pi$
$941$	−15.0046	+	15.0046i	−0.489136	+	0.489136i	0.418898	+	0.908033i	$0.362417\pi$
$942$	−5.53087	+	6.15544i	−0.180206	+	0.200555i
$943$	−6.14410	−	22.9301i	−0.200080	−	0.746707i
$944$	−23.7027	−	23.7027i	−0.771457	−	0.771457i
$945$	19.2367	+	7.31589i	0.625769	+	0.237986i
$946$	10.5640	−	6.09913i	0.343465	−	0.198300i
$947$	7.70012	−	28.7372i	0.250220	−	0.933835i	−0.720467	−	0.693489i	$-0.756073\pi$
$947$	7.70012	−	28.7372i	0.250220	−	0.933835i	0.970687	−	0.240346i	$-0.0772608\pi$
$948$	36.6660	−	23.8651i	1.19086	−	0.775103i
$949$	27.2776	−	12.4985i	0.885470	−	0.405718i
$950$			3.00805i			0.0975940i
$951$	−12.4501	−	38.1831i	−0.403722	−	1.23817i
$952$	−2.09004	−	3.62005i	−0.0677385	−	0.117327i
$953$	−3.95695	+	6.85364i	−0.128178	+	0.222011i	−0.922971	−	0.384870i	$-0.874246\pi$
$953$	−3.95695	+	6.85364i	−0.128178	+	0.222011i	0.794793	+	0.606881i	$0.207580\pi$
$954$	2.97771	−	1.15011i	0.0964070	−	0.0372361i
$955$	70.9468	−	19.0101i	2.29578	−	0.615154i
$956$	−20.0175	+	5.36367i	−0.647412	+	0.173474i
$957$	−6.55507	−	1.38624i	−0.211895	−	0.0448108i
$958$	2.87276	−	4.97576i	0.0928145	−	0.160759i
$959$	−3.05230	−	5.28674i	−0.0985639	−	0.170718i
$960$	36.9328	−	12.0424i	1.19200	−	0.388668i
$961$		−	27.4872i		−	0.886683i
$962$	−6.46048	−	7.80466i	−0.208294	−	0.251632i
$963$	−9.33205	−	4.13180i	−0.300721	−	0.133145i
$964$	1.29190	−	4.82143i	0.0416093	−	0.155288i
$965$	−60.5984	+	34.9865i	−1.95073	+	1.12626i
$966$	−0.165981	−	3.10567i	−0.00534037	−	0.0999232i
$967$	−5.86653	−	5.86653i	−0.188655	−	0.188655i	0.606459	−	0.795114i	$-0.292589\pi$
$967$	−5.86653	−	5.86653i	−0.188655	−	0.188655i	−0.795114	+	0.606459i	$0.792589\pi$
$968$	2.31585	+	8.64287i	0.0744342	+	0.277792i
$969$	−3.82470	−	3.43662i	−0.122867	−	0.110400i
$970$	12.4591	−	12.4591i	0.400036	−	0.400036i
$971$	−7.72705	−	4.46121i	−0.247973	−	0.143167i	0.370863	−	0.928688i	$-0.379062\pi$
$971$	−7.72705	−	4.46121i	−0.247973	−	0.143167i	−0.618836	+	0.785520i	$0.712395\pi$
$972$	7.80671	+	28.5439i	0.250400	+	0.915547i
$973$	1.81153	+	0.485399i	0.0580751	+	0.0155612i
$974$	−4.13999			−0.132654
$975$	45.2439	+	49.0711i	1.44896	+	1.57153i
$976$	−15.7428			−0.503915
$977$	17.6211	+	4.72156i	0.563749	+	0.151056i	0.529428	−	0.848355i	$-0.322407\pi$
$977$	17.6211	+	4.72156i	0.563749	+	0.151056i	0.0343206	+	0.999411i	$0.489073\pi$
$978$	2.71789	+	1.38130i	0.0869085	+	0.0441690i
$979$	5.31761	+	3.07013i	0.169952	+	0.0981216i
$980$	5.31669	−	5.31669i	0.169835	−	0.169835i
$981$	1.86764	−	11.9518i	0.0596293	−	0.381590i
$982$	2.15243	+	8.03296i	0.0686867	+	0.256342i
$983$	19.2028	+	19.2028i	0.612473	+	0.612473i	0.943590	−	0.331117i	$-0.107425\pi$
$983$	19.2028	+	19.2028i	0.612473	+	0.612473i	−0.331117	+	0.943590i	$0.607425\pi$
$984$	−9.06167	+	0.484298i	−0.288876	+	0.0154389i
$985$	−0.938808	+	0.542021i	−0.0299129	+	0.0172702i
$986$	−0.251649	+	0.939167i	−0.00801414	+	0.0299092i
$987$	6.19595	+	9.51936i	0.197219	+	0.303004i
$988$	4.92593	+	3.49848i	0.156715	+	0.111301i
$989$			50.5069i			1.60603i
$990$	−10.1451	+	12.5812i	−0.322432	+	0.399858i
$991$	2.29925	+	3.98242i	0.0730382	+	0.126506i	0.900231	−	0.435412i	$-0.143397\pi$
$991$	2.29925	+	3.98242i	0.0730382	+	0.126506i	−0.827193	+	0.561918i	$0.810064\pi$
$992$	3.34559	−	5.79474i	0.106223	−	0.183983i
$993$	2.61357	−	12.3587i	0.0829390	−	0.392191i
$994$	−3.69794	+	0.990861i	−0.117292	+	0.0314282i
$995$	−71.8538	+	19.2532i	−2.27792	+	0.610367i
$996$	−2.24152	+	10.5994i	−0.0710253	+	0.335855i
$997$	4.27026	−	7.39631i	0.135240	−	0.234243i	−0.790449	−	0.612528i	$-0.790153\pi$
$997$	4.27026	−	7.39631i	0.135240	−	0.234243i	0.925689	+	0.378285i	$0.123486\pi$
$998$	−6.32704	−	10.9588i	−0.200279	−	0.346893i
$999$	−45.5591	−	4.64561i	−1.44143	−	0.146981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cc.a.50.15	yes	112
3.2	odd	2	inner	273.2.cc.a.50.14	✓	112
13.6	odd	12	inner	273.2.cc.a.71.14	yes	112
39.32	even	12	inner	273.2.cc.a.71.15	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cc.a.50.14	✓	112	3.2	odd	2	inner
273.2.cc.a.50.15	yes	112	1.1	even	1	trivial
273.2.cc.a.71.14	yes	112	13.6	odd	12	inner
273.2.cc.a.71.15	yes	112	39.32	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.307973 + 0.0825212i) q^{2} +(-0.784738 + 1.54408i) q^{3} +(-1.64401 - 0.949171i) q^{4} +(2.80070 - 2.80070i) q^{5} +(-0.369098 + 0.410778i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-0.878890 - 0.878890i) q^{8} +(-1.76837 - 2.42340i) q^{9} +O(q^{10})\)	\(q+(0.307973 + 0.0825212i) q^{2} +(-0.784738 + 1.54408i) q^{3} +(-1.64401 - 0.949171i) q^{4} +(2.80070 - 2.80070i) q^{5} +(-0.369098 + 0.410778i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-0.878890 - 0.878890i) q^{8} +(-1.76837 - 2.42340i) q^{9} +(1.09366 - 0.631424i) q^{10} +(1.10413 - 4.12065i) q^{11} +(2.75572 - 1.79364i) q^{12} +(3.37979 + 1.25579i) q^{13} +0.318837i q^{14} +(2.12669 + 6.52233i) q^{15} +(1.70020 + 2.94482i) q^{16} +(1.68153 - 2.91250i) q^{17} +(-0.344629 - 0.892270i) q^{18} +(-0.852646 + 0.228466i) q^{19} +(-7.26274 + 1.94604i) q^{20} +(-1.69457 - 0.358362i) q^{21} +(0.680083 - 1.17794i) q^{22} +(2.81588 + 4.87725i) q^{23} +(2.04678 - 0.667378i) q^{24} -10.6879i q^{25} +(0.937256 + 0.665655i) q^{26} +(5.12963 - 0.828774i) q^{27} +(0.491327 - 1.83366i) q^{28} +(-0.785282 + 0.453383i) q^{29} +(0.116734 + 2.18420i) q^{30} +(-1.32530 - 1.32530i) q^{31} +(0.923996 + 3.44840i) q^{32} +(5.49617 + 4.93849i) q^{33} +(0.758209 - 0.758209i) q^{34} +(3.43015 + 1.98040i) q^{35} +(0.607004 + 5.66259i) q^{36} +(-8.51301 - 2.28105i) q^{37} -0.281445 q^{38} +(-4.59129 + 4.23320i) q^{39} -4.92302 q^{40} +(-4.07157 - 1.09097i) q^{41} +(-0.492311 - 0.250204i) q^{42} +(7.76670 + 4.48411i) q^{43} +(-5.72640 + 5.72640i) q^{44} +(-11.7399 - 1.83454i) q^{45} +(0.464740 + 1.73443i) q^{46} +(-4.63695 - 4.63695i) q^{47} +(-5.88126 + 0.314322i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(0.881975 - 3.29158i) q^{50} +(3.17757 + 4.88197i) q^{51} +(-4.36446 - 5.27254i) q^{52} +3.33723i q^{53} +(1.64818 + 0.168063i) q^{54} +(-8.44839 - 14.6330i) q^{55} +(0.621469 - 1.07642i) q^{56} +(0.316334 - 1.49584i) q^{57} +(-0.279260 + 0.0748274i) q^{58} +(-9.52199 + 2.55141i) q^{59} +(2.69450 - 12.7414i) q^{60} +(-2.31485 + 4.00944i) q^{61} +(-0.298792 - 0.517522i) q^{62} +(1.88314 - 2.33534i) q^{63} -5.66252i q^{64} +(12.9829 - 5.94869i) q^{65} +(1.28514 + 1.97448i) q^{66} +(-3.10288 + 11.5801i) q^{67} +(-5.52892 + 3.19212i) q^{68} +(-9.74060 + 0.520583i) q^{69} +(0.892969 + 0.892969i) q^{70} +(3.10773 + 11.5982i) q^{71} +(-0.575697 + 3.68410i) q^{72} +(5.88441 - 5.88441i) q^{73} +(-2.43354 - 1.40501i) q^{74} +(16.5029 + 8.38717i) q^{75} +(1.61861 + 0.433706i) q^{76} +4.26601 q^{77} +(-1.76333 + 0.924834i) q^{78} +13.3054 q^{79} +(13.0093 + 3.48584i) q^{80} +(-2.74573 + 8.57094i) q^{81} +(-1.16391 - 0.671981i) q^{82} +(-2.32987 + 2.32987i) q^{83} +(2.44575 + 2.19759i) q^{84} +(-3.44757 - 12.8665i) q^{85} +(2.02190 + 2.02190i) q^{86} +(-0.0838187 - 1.56833i) q^{87} +(-4.59200 + 2.65119i) q^{88} +(-0.372529 + 1.39030i) q^{89} +(-3.46419 - 1.53378i) q^{90} +(-0.338247 + 3.58965i) q^{91} -10.6910i q^{92} +(3.08638 - 1.00636i) q^{93} +(-1.04541 - 1.81070i) q^{94} +(-1.74814 + 3.02787i) q^{95} +(-6.04970 - 1.27937i) q^{96} +(13.4770 - 3.61115i) q^{97} +(-0.307973 + 0.0825212i) q^{98} +(-11.9385 + 4.61111i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{6}+O(q^{10}) \) 112 * q - 12 * q^6	\( 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) \) 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more