LMFDB - Embedded newform 273.2.cc.a.50.14

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			50.14
Character	$\chi$	$=$	273.50
Dual form			273.2.cc.a.71.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.307973 - 0.0825212i) q^{2} +(1.72958 + 0.0924370i) q^{3} +(-1.64401 - 0.949171i) q^{4} +(-2.80070 + 2.80070i) q^{5} +(-0.525037 - 0.171195i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.878890 + 0.878890i) q^{8} +(2.98291 + 0.319755i) q^{9} +O(q^{10})$	\(q+(-0.307973 - 0.0825212i) q^{2} +(1.72958 + 0.0924370i) q^{3} +(-1.64401 - 0.949171i) q^{4} +(-2.80070 + 2.80070i) q^{5} +(-0.525037 - 0.171195i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.878890 + 0.878890i) q^{8} +(2.98291 + 0.319755i) 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} +(-5.10293 + 4.58516i) q^{15} +(1.70020 + 2.94482i) q^{16} +(-1.68153 + 2.91250i) q^{17} +(-0.892270 - 0.344629i) q^{18} +(-0.852646 + 0.228466i) q^{19} +(7.26274 - 1.94604i) q^{20} +(0.358362 + 1.69457i) q^{21} +(0.680083 - 1.17794i) q^{22} +(-2.81588 - 4.87725i) q^{23} +(1.43887 + 1.60135i) 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} +(1.94994 - 0.991006i) q^{30} +(-1.32530 - 1.32530i) q^{31} +(-0.923996 - 3.44840i) q^{32} +(-2.29058 + 7.02495i) q^{33} +(0.758209 - 0.758209i) q^{34} +(-3.43015 - 1.98040i) q^{35} +(-4.60044 - 3.35697i) q^{36} +(-8.51301 - 2.28105i) q^{37} +0.281445 q^{38} +(5.72955 + 2.48441i) q^{39} -4.92302 q^{40} +(4.07157 + 1.09097i) q^{41} +(0.0294724 - 0.551456i) q^{42} +(7.76670 + 4.48411i) q^{43} +(5.72640 - 5.72640i) q^{44} +(-9.24978 + 7.45871i) q^{45} +(0.464740 + 1.73443i) q^{46} +(4.63695 + 4.63695i) q^{47} +(2.66842 + 5.25048i) 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} +(-1.51140 - 0.678544i) q^{54} +(-8.44839 - 14.6330i) q^{55} +(-0.621469 + 1.07642i) q^{56} +(-1.49584 + 0.316334i) q^{57} +(-0.279260 + 0.0748274i) q^{58} +(9.52199 - 2.55141i) q^{59} +(12.7414 - 2.69450i) q^{60} +(-2.31485 + 4.00944i) q^{61} +(0.298792 + 0.517522i) q^{62} +(0.463175 + 2.96403i) 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} +(-4.41946 - 8.69590i) q^{69} +(0.892969 + 0.892969i) q^{70} +(-3.10773 - 11.5982i) q^{71} +(2.34062 + 2.90268i) q^{72} +(5.88441 - 5.88441i) q^{73} +(2.43354 + 1.40501i) q^{74} +(0.987954 - 18.4855i) q^{75} +(1.61861 + 0.433706i) q^{76} -4.26601 q^{77} +(-1.55953 - 1.23794i) q^{78} +13.3054 q^{79} +(-13.0093 - 3.48584i) q^{80} +(8.79551 + 1.90760i) q^{81} +(-1.16391 - 0.671981i) q^{82} +(2.32987 - 2.32987i) q^{83} +(1.01929 - 3.12605i) q^{84} +(-3.44757 - 12.8665i) q^{85} +(-2.02190 - 2.02190i) q^{86} +(1.40012 - 0.711574i) 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} +(-2.16971 - 2.41472i) q^{93} +(-1.04541 - 1.81070i) q^{94} +(1.74814 - 3.02787i) q^{95} +(-1.27937 - 6.04970i) q^{96} +(13.4770 - 3.61115i) q^{97} +(0.307973 - 0.0825212i) q^{98} +(-4.61111 + 11.9385i) 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	0.148284	−	0.988945i	$-0.452625\pi$
$2$	−0.307973	−	0.0825212i	−0.217770	−	0.0583513i	−0.366054	+	0.930593i	$0.619292\pi$
$3$	1.72958	+	0.0924370i	0.998575	+	0.0533685i
$3$	1.72958	+	0.0924370i	0.998575	+	0.0533685i
$4$	−1.64401	−	0.949171i	−0.822006	−	0.474586i
$5$	−2.80070	+	2.80070i	−1.25251	+	1.25251i	−0.297922	+	0.954590i	$0.596293\pi$
$5$	−2.80070	+	2.80070i	−1.25251	+	1.25251i	−0.954590	+	0.297922i	$0.903707\pi$
$6$	−0.525037	−	0.171195i	−0.214346	−	0.0698902i
$7$	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
$9$	2.98291	+	0.319755i	0.994304	+	0.106585i
$10$	1.09366	−	0.631424i	0.345845	−	0.199674i
$11$	−1.10413	+	4.12065i	−0.332906	+	1.24242i	0.573215	+	0.819405i	$0.305696\pi$
$11$	−1.10413	+	4.12065i	−0.332906	+	1.24242i	−0.906121	+	0.423019i	$0.860971\pi$
$12$	−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
$15$	−5.10293	+	4.58516i	−1.31757	+	1.18388i
$16$	1.70020	+	2.94482i	0.425049	+	0.736206i
$17$	−1.68153	+	2.91250i	−0.407831	+	0.706384i	−0.994646	−	0.103337i	$-0.967048\pi$
$17$	−1.68153	+	2.91250i	−0.407831	+	0.706384i	0.586815	+	0.809721i	$0.300381\pi$
$18$	−0.892270	−	0.344629i	−0.210310	−	0.0812299i
$19$	−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
$21$	0.358362	+	1.69457i	0.0782009	+	0.369786i
$22$	0.680083	−	1.17794i	0.144994	−	0.251137i
$23$	−2.81588	−	4.87725i	−0.587152	−	1.01698i	−0.994603	−	0.103750i	$-0.966916\pi$
$23$	−2.81588	−	4.87725i	−0.587152	−	1.01698i	0.407451	−	0.913227i	$-0.366418\pi$
$24$	1.43887	+	1.60135i	0.293708	+	0.326875i
$25$		−	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	−0.425313	−	0.905046i	$-0.639836\pi$
$29$	0.785282	−	0.453383i	0.145823	−	0.0841911i	0.571136	+	0.820855i	$0.306503\pi$
$30$	1.94994	−	0.991006i	0.356009	−	0.180932i
$31$	−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
$33$	−2.29058	+	7.02495i	−0.398738	+	1.22289i
$34$	0.758209	−	0.758209i	0.130032	−	0.130032i
$35$	−3.43015	−	1.98040i	−0.579800	−	0.334748i
$36$	−4.60044	−	3.35697i	−0.766740	−	0.559496i
$37$	−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
$39$	5.72955	+	2.48441i	0.917462	+	0.397824i
$40$	−4.92302			−0.778397
$41$	4.07157	+	1.09097i	0.635872	+	0.170381i	0.562333	−	0.826911i	$-0.309904\pi$
$41$	4.07157	+	1.09097i	0.635872	+	0.170381i	0.0735391	+	0.997292i	$0.476571\pi$
$42$	0.0294724	−	0.551456i	0.00454769	−	0.0850915i
$43$	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
$45$	−9.24978	+	7.45871i	−1.37888	+	1.11188i
$46$	0.464740	+	1.73443i	0.0685222	+	0.255728i
$47$	4.63695	+	4.63695i	0.676369	+	0.676369i	0.959177	−	0.282808i	$-0.0912659\pi$
$47$	4.63695	+	4.63695i	0.676369	+	0.676369i	−0.282808	+	0.959177i	$0.591266\pi$
$48$	2.66842	+	5.25048i	0.385153	+	0.757841i
$49$	−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	$-0.926388\pi$
$53$		−	3.33723i		−	0.458404i	0.973379	−	0.229202i	$-0.0736116\pi$
$54$	−1.51140	−	0.678544i	−0.205675	−	0.0923381i
$55$	−8.44839	−	14.6330i	−1.13918	−	1.97312i
$56$	−0.621469	+	1.07642i	−0.0830473	+	0.143842i
$57$	−1.49584	+	0.316334i	−0.198129	+	0.0418995i
$58$	−0.279260	+	0.0748274i	−0.0366686	+	0.00982532i
$59$	9.52199	−	2.55141i	1.23966	−	0.332165i	0.421325	−	0.906910i	$-0.361565\pi$
$59$	9.52199	−	2.55141i	1.23966	−	0.332165i	0.818333	+	0.574744i	$0.194898\pi$
$60$	12.7414	−	2.69450i	1.64491	−	0.347858i
$61$	−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
$63$	0.463175	+	2.96403i	0.0583545	+	0.373433i
$64$		−	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
$69$	−4.41946	−	8.69590i	−0.532041	−	1.04686i
$70$	0.892969	+	0.892969i	0.106730	+	0.106730i
$71$	−3.10773	−	11.5982i	−0.368820	−	1.37645i	−0.862168	−	0.506622i	$-0.830894\pi$
$71$	−3.10773	−	11.5982i	−0.368820	−	1.37645i	0.493348	−	0.869832i	$-0.335773\pi$
$72$	2.34062	+	2.90268i	0.275845	+	0.342084i
$73$	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
$75$	0.987954	−	18.4855i	0.114079	−	2.13453i
$76$	1.61861	+	0.433706i	0.185668	+	0.0497495i
$77$	−4.26601			−0.486157
$78$	−1.55953	−	1.23794i	−0.176582	−	0.140169i
$79$	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
$81$	8.79551	+	1.90760i	0.977279	+	0.211956i
$82$	−1.16391	−	0.671981i	−0.128532	−	0.0742079i
$83$	2.32987	−	2.32987i	0.255736	−	0.255736i	−0.567581	−	0.823318i	$-0.692121\pi$
$83$	2.32987	−	2.32987i	0.255736	−	0.255736i	0.823318	+	0.567581i	$0.192121\pi$
$84$	1.01929	−	3.12605i	0.111214	−	0.341080i
$85$	−3.44757	−	12.8665i	−0.373941	−	1.39557i
$86$	−2.02190	−	2.02190i	−0.218027	−	0.218027i
$87$	1.40012	−	0.711574i	0.150109	−	0.0762887i
$88$	−4.59200	+	2.65119i	−0.489509	+	0.282618i
$89$	0.372529	−	1.39030i	0.0394880	−	0.147371i	−0.943367	−	0.331750i	$-0.892361\pi$
$89$	0.372529	−	1.39030i	0.0394880	−	0.147371i	0.982855	+	0.184379i	$0.0590275\pi$
$90$	3.46419	−	1.53378i	0.365157	−	0.161675i
$91$	−0.338247	+	3.58965i	−0.0354579	+	0.376298i
$92$			10.6910i			1.11462i
$93$	−2.16971	−	2.41472i	−0.224988	−	0.250395i
$94$	−1.04541	−	1.81070i	−0.107826	−	0.186760i
$95$	1.74814	−	3.02787i	0.179356	−	0.310653i
$96$	−1.27937	−	6.04970i	−0.130575	−	0.617445i
$97$	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
$99$	−4.61111	+	11.9385i	−0.463434	+	1.19986i
$100$	−10.1446	+	17.5710i	−1.01446	+	1.75710i
$101$	1.38391	+	2.39700i	0.137704	+	0.238511i	0.926627	−	0.375981i	$-0.122694\pi$
$101$	1.38391	+	2.39700i	0.137704	+	0.238511i	−0.788923	+	0.614492i	$0.789361\pi$
$102$	1.38147	−	1.24130i	0.136786	−	0.122907i
$103$			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	−0.635602	−	0.772017i	$-0.719248\pi$
$107$	−2.94617	+	1.70097i	−0.284817	+	0.164439i	0.350785	+	0.936456i	$0.385915\pi$
$108$	−7.64654	−	6.23142i	−0.735788	−	0.599618i
$109$	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
$111$	−14.5131	−	4.73219i	−1.37752	−	0.449159i
$112$	−2.40444	+	2.40444i	−0.227198	+	0.227198i
$113$	−10.0683	−	5.81296i	−0.947150	−	0.546837i	−0.0549554	−	0.998489i	$-0.517502\pi$
$113$	−10.0683	−	5.81296i	−0.947150	−	0.546837i	−0.892194	+	0.451652i	$0.850835\pi$
$114$	0.486783	+	0.0260160i	0.0455914	+	0.00243662i
$115$	21.5462	+	5.77328i	2.00919	+	0.538361i
$116$	−1.72135			−0.159824
$117$	9.68007	+	4.82662i	0.894923	+	0.446221i
$118$	−3.14307			−0.289343
$119$	−3.24847	−	0.870424i	−0.297787	−	0.0797917i
$120$	−8.51476	−	0.455069i	−0.777288	−	0.0415419i
$121$	−6.23441	−	3.59944i	−0.566765	−	0.327222i
$122$	1.04378	−	1.04378i	0.0944992	−	0.0944992i
$123$	6.94127	+	2.26329i	0.625873	+	0.204074i
$124$	0.920873	+	3.43675i	0.0826969	+	0.308629i
$125$	15.9300	+	15.9300i	1.42482	+	1.42482i
$126$	0.101950	−	0.951064i	0.00908241	−	0.0847275i
$127$	−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	$-0.916186\pi$
$131$		−	5.95803i		−	0.520555i	0.965534	−	0.260278i	$-0.0838141\pi$
$132$	10.4336	−	9.37496i	0.908130	−	0.815985i
$133$	−0.441362	−	0.764461i	−0.0382709	−	0.0662872i
$134$	1.91121	−	3.31031i	0.165103	−	0.285967i
$135$	−16.6877	+	12.0454i	−1.43625	+	1.03671i
$136$	−4.03764	+	1.08188i	−0.346225	+	0.0927707i
$137$	5.89659	−	1.57999i	0.503780	−	0.134987i	0.00202619	−	0.999998i	$-0.499355\pi$
$137$	5.89659	−	1.57999i	0.503780	−	0.134987i	0.501754	+	0.865011i	$0.332688\pi$
$138$	0.643480	+	3.04280i	0.0547767	+	0.259021i
$139$	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
$141$	7.59136	+	8.44861i	0.639308	+	0.711502i
$142$			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
$147$	−1.54408	+	0.784738i	−0.127354	+	0.0647241i
$148$	11.8304	+	11.8304i	0.972452	+	0.972452i
$149$	−0.519729	−	1.93966i	−0.0425779	−	0.158903i	0.941364	−	0.337393i	$-0.109545\pi$
$149$	−0.519729	−	1.93966i	−0.0425779	−	0.158903i	−0.983942	+	0.178491i	$0.942879\pi$
$150$	−1.82971	+	5.61152i	−0.149395	+	0.458179i
$151$	−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
$153$	−5.94714	+	8.15004i	−0.480798	+	0.658892i
$154$	1.31382	+	0.352037i	0.105871	+	0.0283679i
$155$	7.42354			0.596273
$156$	−7.06132	−	9.52273i	−0.565358	−	0.762428i
$157$	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
$159$	0.308484	−	5.77202i	0.0244643	−	0.457751i
$160$	12.2458	+	7.07010i	0.968114	+	0.558941i
$161$	3.98226	−	3.98226i	0.313846	−	0.313846i
$162$	−2.55137	−	1.31331i	−0.200454	−	0.103183i
$163$	−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
$165$	−13.2596	−	26.0900i	−1.03226	−	2.03110i
$166$	−0.909801	+	0.525274i	−0.0706143	+	0.0407692i
$167$	0.00150536	−	0.00561808i	0.000116488	−	0.000434740i	−0.965868	−	0.259036i	$-0.916595\pi$
$167$	0.00150536	−	0.00561808i	0.000116488	−	0.000434740i	0.965984	+	0.258602i	$0.0832617\pi$
$168$	−1.17438	+	1.80430i	−0.0906055	+	0.139205i
$169$	9.84598	+	8.48862i	0.757383	+	0.652971i
$170$			4.24704i			0.325733i
$171$	−2.61642	+	0.408855i	−0.200083	+	0.0312660i
$172$	−8.51237	−	14.7439i	−0.649062	−	1.12421i
$173$	4.94215	−	8.56006i	0.375745	−	0.650809i	−0.614693	−	0.788766i	$-0.710720\pi$
$173$	4.94215	−	8.56006i	0.375745	−	0.650809i	0.990438	+	0.137957i	$0.0440535\pi$
$174$	−0.489919	+	0.103606i	−0.0371407	+	0.00785437i
$175$	10.3237	−	2.76622i	0.780397	−	0.209107i
$176$	−14.0118	+	3.75446i	−1.05618	+	0.283003i
$177$	16.7049	−	3.53269i	1.25562	−	0.265533i
$178$	−0.229458	+	0.397433i	−0.0171986	+	0.0297888i
$179$	9.45512	+	16.3767i	0.706708	+	1.22405i	0.966071	+	0.258275i	$0.0831541\pi$
$179$	9.45512	+	16.3767i	0.706708	+	1.22405i	−0.259363	+	0.965780i	$0.583513\pi$
$180$	22.2864	−	3.48258i	1.66113	−	0.259576i
$181$			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
$186$	0.468947	+	0.922717i	0.0343848	+	0.0676569i
$187$	−10.1448	−	10.1448i	−0.741859	−	0.741859i
$188$	−3.22195	−	12.0245i	−0.234985	−	0.876975i
$189$	0.527113	+	5.16935i	0.0383418	+	0.376015i
$190$	−0.788245	+	0.788245i	−0.0571853	+	0.0571853i
$191$	−16.0597	−	9.27208i	−1.16204	−	0.670904i	−0.210248	−	0.977648i	$-0.567427\pi$
$191$	−16.0597	−	9.27208i	−1.16204	−	0.670904i	−0.951792	+	0.306744i	$0.900761\pi$
$192$	0.523426	−	9.79379i	0.0377750	−	0.706806i
$193$	−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
$195$	−23.0048	+	9.08865i	−1.64741	+	0.650852i
$196$	1.89834			0.135596
$197$	0.264368	+	0.0708371i	0.0188354	+	0.00504693i	0.268224	−	0.963356i	$-0.413563\pi$
$197$	0.264368	+	0.0708371i	0.0188354	+	0.00504693i	−0.249389	+	0.968403i	$0.580230\pi$
$198$	2.40528	−	3.29622i	0.170936	−	0.234252i
$199$	−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
$201$	−6.43712	+	19.7419i	−0.454040	+	1.39249i
$202$	−0.228404	−	0.852414i	−0.0160704	−	0.0599757i
$203$	0.641180	+	0.641180i	0.0450020	+	0.0450020i
$204$	9.85779	−	5.00996i	0.690183	−	0.350767i
$205$	−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
$210$	1.46192	+	1.62701i	0.100882	+	0.112274i
$211$	−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
$213$	−4.30297	−	20.3473i	−0.294835	−	1.39418i
$214$	1.04771	−	0.280732i	0.0716198	−	0.0191905i
$215$	−34.3109	+	9.19357i	−2.33998	+	0.626996i
$216$	3.77998	+	5.23678i	0.257195	+	0.356318i
$217$	0.937128	−	1.62315i	0.0636164	−	0.110187i
$218$	−0.642819	−	1.11339i	−0.0435372	−	0.0754086i
$219$	10.7215	−	9.63363i	0.724492	−	0.650980i
$220$			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
$225$	3.41749	−	31.8809i	0.227833	−	2.12540i
$226$	2.62109	+	2.62109i	0.174352	+	0.174352i
$227$	5.66346	+	21.1363i	0.375897	+	1.40287i	0.852030	+	0.523494i	$0.175372\pi$
$227$	5.66346	+	21.1363i	0.375897	+	1.40287i	−0.476133	+	0.879374i	$0.657962\pi$
$228$	2.75944	+	0.899751i	0.182748	+	0.0595874i
$229$	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
$231$	−7.37842	−	0.394338i	−0.485465	−	0.0259455i
$232$	1.08865	+	0.291703i	0.0714734	+	0.0191512i
$233$	29.4939			1.93221			0.966104	−	0.258153i	$-0.0831137\pi$
$233$	29.4939			1.93221			0.966104	+	0.258153i	$0.0831137\pi$
$234$	−2.58291	−	2.28528i	−0.168850	−	0.149393i
$235$	−25.9734			−1.69432
$236$	−18.0760	−	4.84345i	−1.17665	−	0.315282i
$237$	23.0128	+	1.22991i	1.49484	+	0.0798915i
$238$	0.928613	+	0.536135i	0.0601930	+	0.0347525i
$239$	−7.71928	+	7.71928i	−0.499318	+	0.499318i	−0.911226	−	0.411907i	$-0.864863\pi$
$239$	−7.71928	+	7.71928i	−0.499318	+	0.499318i	0.411907	+	0.911226i	$0.364863\pi$
$240$	−22.1785	−	7.23158i	−1.43161	−	0.466797i
$241$	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
$243$	15.0362	+	4.11238i	0.964575	+	0.263809i
$244$	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
$249$	4.24507	−	3.81434i	0.269020	−	0.241724i
$250$	−3.59145	−	6.22058i	−0.227143	−	0.393424i
$251$	−2.64931	+	4.58875i	−0.167223	+	0.289639i	−0.937443	−	0.348140i	$-0.886813\pi$
$251$	−2.64931	+	4.58875i	−0.167223	+	0.289639i	0.770219	+	0.637779i	$0.220147\pi$
$252$	2.05191	−	5.31253i	0.129258	−	0.334658i
$253$	23.2065	−	6.21818i	1.45898	−	0.390933i
$254$	4.44672	−	1.19149i	0.279012	−	0.0747610i
$255$	−4.77351	−	22.5724i	−0.298929	−	1.41354i
$256$	−4.23643	+	7.33772i	−0.264777	+	0.458607i
$257$	−3.49756	−	6.05795i	−0.218172	−	0.377884i	0.736077	−	0.676897i	$-0.236676\pi$
$257$	−3.49756	−	6.05795i	−0.218172	−	0.377884i	−0.954249	+	0.299013i	$0.903343\pi$
$258$	−3.31015	−	3.68395i	−0.206081	−	0.229353i
$259$		−	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	−0.251228	−	0.967928i	$-0.580834\pi$
$263$	7.48278	−	4.32019i	0.461408	−	0.266394i	0.712636	+	0.701534i	$0.247501\pi$
$264$	−8.18732	+	4.16099i	−0.503895	+	0.256091i
$265$	9.34659	+	9.34659i	0.574156	+	0.574156i
$266$	0.0728434	+	0.271855i	0.00446632	+	0.0166685i
$267$	0.772834	−	2.37020i	0.0472967	−	0.145054i
$268$	16.0927	−	16.0927i	0.983018	−	0.983018i
$269$	−3.30775	−	1.90973i	−0.201677	−	0.116438i	0.395760	−	0.918354i	$-0.370481\pi$
$269$	−3.30775	−	1.90973i	−0.201677	−	0.116438i	−0.597438	+	0.801915i	$0.703814\pi$
$270$	6.13338	−	2.33258i	0.373265	−	0.141956i
$271$	−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
$273$	−0.916842	+	6.17733i	−0.0554898	+	0.373869i
$274$	−1.94638			−0.117585
$275$	44.0410	+	11.8007i	2.65577	+	0.711612i
$276$	−0.988245	+	18.4910i	−0.0594854	+	1.11303i
$277$	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
$279$	−3.52948	−	4.37702i	−0.211304	−	0.262045i
$280$	−1.27417	−	4.75527i	−0.0761462	−	0.284182i
$281$	−15.3354	−	15.3354i	−0.914832	−	0.914832i	0.0818157	−	0.996647i	$-0.473928\pi$
$281$	−15.3354	−	15.3354i	−0.914832	−	0.914832i	−0.996647	+	0.0818157i	$0.973928\pi$
$282$	−1.64075	−	3.22840i	−0.0977051	−	0.192248i
$283$	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
$288$	−1.65356	−	10.5817i	−0.0974367	−	0.623534i
$289$	2.84491	+	4.92753i	0.167348	+	0.289855i
$290$	0.572554	−	0.991692i	0.0336215	−	0.0582342i
$291$	23.6434	−	5.00001i	1.38600	−	0.293106i
$292$	−15.2593	+	4.08873i	−0.892986	+	0.239275i
$293$	−7.53874	+	2.02000i	−0.440418	+	0.118010i	−0.472212	−	0.881485i	$-0.656544\pi$
$293$	−7.53874	+	2.02000i	−0.440418	+	0.118010i	0.0317946	+	0.999494i	$0.489878\pi$
$294$	0.540293	−	0.114259i	0.0315105	−	0.00666373i
$295$	−19.5225	+	33.8140i	−1.13665	+	1.96873i
$296$	−5.47720	−	9.48679i	−0.318356	−	0.551409i
$297$	−9.07885	+	20.2224i	−0.526808	+	1.17342i
$298$			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
$303$	2.17201	+	4.27374i	0.124779	+	0.245520i
$304$	−2.12246	−	2.12246i	−0.121731	−	0.121731i
$305$	−4.74604	−	17.7125i	−0.271758	−	1.01421i
$306$	2.50411	−	2.01923i	0.143151	−	0.115432i
$307$	−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
$309$	−0.677688	+	12.6802i	−0.0385523	+	0.721350i
$310$	−2.28625	−	0.612599i	−0.129850	−	0.0347933i
$311$	13.6132			0.771936			0.385968	−	0.922512i	$-0.373868\pi$
$311$	13.6132			0.771936			0.385968	+	0.922512i	$0.373868\pi$
$312$	2.85211	+	7.21916i	0.161469	+	0.408705i
$313$	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
$315$	−9.59858	−	7.00415i	−0.540818	−	0.394639i
$316$	−21.8743	−	12.6291i	−1.23053	−	0.710444i
$317$	16.3959	−	16.3959i	0.920886	−	0.920886i	−0.0762061	−	0.997092i	$-0.524281\pi$
$317$	16.3959	−	16.3959i	0.920886	−	0.920886i	0.997092	+	0.0762061i	$0.0242807\pi$
$318$	−0.571319	+	1.75217i	−0.0320380	+	0.0982569i
$319$	1.00118	+	3.73647i	0.0560555	+	0.209202i
$320$	15.8590	+	15.8590i	0.886546	+	0.886546i
$321$	−5.25288	+	2.66964i	−0.293187	+	0.149005i
$322$	−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
$327$	4.66790	+	5.19502i	0.258135	+	0.287285i
$328$	2.61961	+	4.53730i	0.144644	+	0.250531i
$329$	−3.27882	+	5.67908i	−0.180767	+	0.313098i
$330$	1.93061	+	9.12922i	0.106277	+	0.502547i
$331$	−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
$333$	−24.6642	−	9.52626i	−1.35159	−	0.522036i
$334$	−0.000927222		0.00160600i	−5.07353e−5		8.78762e-5i
$335$	−23.7422	−	41.1227i	−1.29718	−	2.24677i
$336$	−4.38093	+	3.93642i	−0.239000	+	0.214749i
$337$		−	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
$342$	0.839527	+	0.0899935i	0.0453964	+	0.00486629i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	2.88504	+	10.7671i	0.155551	+	0.580524i
$345$	36.7322	+	11.9770i	1.97760	+	0.644821i
$346$	−2.22844	+	2.22844i	−0.119802	+	0.119802i
$347$	3.89383	+	2.24811i	0.209032	+	0.120685i	0.600861	−	0.799353i	$-0.294824\pi$
$347$	3.89383	+	2.24811i	0.209032	+	0.120685i	−0.391830	+	0.920038i	$0.628158\pi$
$348$	−2.97722	−	0.159117i	−0.159596	−	0.00852954i
$349$	−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
$351$	16.2963	+	9.24283i	0.869833	+	0.493346i
$352$	15.2299			0.811755
$353$	−22.8075	−	6.11126i	−1.21392	−	0.325270i	−0.405623	−	0.914041i	$-0.632945\pi$
$353$	−22.8075	−	6.11126i	−1.21392	−	0.325270i	−0.808300	+	0.588771i	$0.799612\pi$
$354$	−5.43619	−	0.290536i	−0.288930	−	0.0154418i
$355$	41.1870	+	23.7793i	2.18598	+	1.26207i
$356$	−1.93207	+	1.93207i	−0.102400	+	0.102400i
$357$	−5.53803	−	1.80575i	−0.293104	−	0.0955704i
$358$	−1.56049	−	5.82385i	−0.0824747	−	0.307800i
$359$	−3.81154	−	3.81154i	−0.201165	−	0.201165i	0.599334	−	0.800499i	$-0.295432\pi$
$359$	−3.81154	−	3.81154i	−0.201165	−	0.201165i	−0.800499	+	0.599334i	$0.795432\pi$
$360$	−14.6849	−	1.57416i	−0.773963	−	0.0829654i
$361$	−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
$366$	1.90178	−	1.70882i	0.0994078	−	0.0893212i
$367$	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
$369$	11.7963	+	4.55618i	0.614090	+	0.237185i
$370$	−10.7506	+	2.88063i	−0.558899	+	0.149757i
$371$	3.22352	−	0.863739i	0.167357	−	0.0448431i
$372$	1.27504	+	6.02926i	0.0661080	+	0.312603i
$373$	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
$375$	26.0797	+	29.0248i	1.34675	+	1.49883i
$376$			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
$381$	−22.2944	+	11.3306i	−1.14218	+	0.580482i
$382$	4.18082	+	4.18082i	0.213909	+	0.213909i
$383$	5.05678	+	18.8721i	0.258389	+	0.964322i	0.966173	+	0.257893i	$0.0830282\pi$
$383$	5.05678	+	18.8721i	0.258389	+	0.964322i	−0.707784	+	0.706429i	$0.750305\pi$
$384$	−4.80317	+	14.7308i	−0.245111	+	0.751728i
$385$	11.9478	−	11.9478i	0.608918	−	0.608918i
$386$	4.87808	+	2.81636i	0.248288	+	0.143349i
$387$	21.7336	+	15.8591i	1.10478	+	0.806165i
$388$	−25.5840	−	6.85520i	−1.29883	−	0.348020i
$389$	−23.6751			−1.20037			−0.600187	−	0.799860i	$-0.704907\pi$
$389$	−23.6751			−1.20037			−0.600187	+	0.799860i	$0.704907\pi$
$390$	7.83489	−	0.900675i	0.396735	−	0.0456075i
$391$	18.9400			0.957835
$392$	−1.20059	−	0.321696i	−0.0606387	−	0.0162481i
$393$	0.550742	−	10.3049i	0.0277813	−	0.519813i
$394$	−0.0755726	−	0.0436319i	−0.00380729	−	0.00219814i
$395$	−37.2645	+	37.2645i	−1.87498	+	1.87498i
$396$	18.9124	−	15.2503i	0.950384	−	0.766357i
$397$	−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
$399$	−0.692707	−	1.36300i	−0.0346787	−	0.0682352i
$400$	31.4739	−	18.1714i	1.57369	−	0.908572i
$401$	3.61704	−	13.4990i	0.180627	−	0.674108i	−0.814898	−	0.579604i	$-0.803207\pi$
$401$	3.61704	−	13.4990i	0.180627	−	0.674108i	0.995525	−	0.0945031i	$-0.0301262\pi$
$402$	3.61159	−	5.54879i	0.180130	−	0.276749i
$403$	−2.81494	−	6.14354i	−0.140222	−	0.306031i
$404$		−	5.25427i		−	0.261410i
$405$	−29.9762	+	19.2910i	−1.48953	+	0.958577i
$406$	−0.144555	−	0.250377i	−0.00717416	−	0.0124260i
$407$	18.7989	−	32.5606i	0.931825	−	1.61397i
$408$	−7.08344	+	1.49798i	−0.350683	+	0.0741610i
$409$	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
$411$	10.3447	−	2.18765i	0.510266	−	0.107909i
$412$	6.95871	−	12.0528i	0.342831	−	0.593801i
$413$	4.92895	+	8.53719i	0.242538	+	0.420087i
$414$	0.831685	+	5.32226i	0.0408751	+	0.261575i
$415$			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	$0.689753\pi$
$419$	−31.9081	+	18.4221i	−1.55881	+	0.899981i	−0.997371	+	0.0724640i	$0.976914\pi$
$420$	5.90040	+	11.6098i	0.287910	+	0.566503i
$421$	−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
$423$	12.3489	+	15.3143i	0.600425	+	0.744607i
$424$	2.93306	−	2.93306i	0.142442	−	0.142442i
$425$	31.1284	+	17.9720i	1.50995	+	0.871768i
$426$	−0.353885	+	6.62152i	−0.0171458	+	0.320814i
$427$	−4.47195	−	1.19826i	−0.216413	−	0.0579877i
$428$	6.45805			0.312162
$429$	−16.5635	+	20.8664i	−0.799695	+	1.00744i
$430$	11.3255			0.546164
$431$	−16.5815	−	4.44299i	−0.798701	−	0.214011i	−0.163687	−	0.986512i	$-0.552339\pi$
$431$	−16.5815	−	4.44299i	−0.798701	−	0.214011i	−0.635014	+	0.772501i	$0.719006\pi$
$432$	6.28078	+	16.5149i	0.302184	+	0.794576i
$433$	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
$435$	−1.92841	+	5.91422i	−0.0924602	+	0.283565i
$436$	−1.98116	−	7.39380i	−0.0948805	−	0.354099i
$437$	3.51523	+	3.51523i	0.168156	+	0.168156i
$438$	−4.09692	+	2.08215i	−0.195758	+	0.0994889i
$439$	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	$0.164910\pi$
$443$			20.8460i			0.990426i	−0.868772	+	0.495213i	$0.835090\pi$
$444$	19.3681	+	21.5552i	0.919168	+	1.02296i
$445$	2.85046	+	4.93715i	0.135125	+	0.234043i
$446$	−0.611002	+	1.05829i	−0.0289318	+	0.0501113i
$447$	−0.719619	−	3.40284i	−0.0340368	−	0.160949i
$448$	5.46957	−	1.46557i	0.258413	−	0.0692415i
$449$	10.0905	−	2.70375i	0.476202	−	0.127598i	−0.0127318	−	0.999919i	$-0.504053\pi$
$449$	10.0905	−	2.70375i	0.476202	−	0.127598i	0.488933	+	0.872321i	$0.337386\pi$
$450$	−3.68335	+	9.53646i	−0.173635	+	0.449553i
$451$	−8.99105	+	15.5729i	−0.423372	+	0.733301i
$452$	11.0350	+	19.1132i	0.519042	+	0.899007i
$453$	−15.2585	+	13.7102i	−0.716905	+	0.644163i
$454$		−	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
$459$	−11.0394	+	13.5464i	−0.515277	+	0.632293i
$460$	−29.9424	−	29.9424i	−1.39607	−	1.39607i
$461$	6.03635	+	22.5280i	0.281141	+	1.04923i	0.951613	+	0.307298i	$0.0994247\pi$
$461$	6.03635	+	22.5280i	0.281141	+	1.04923i	−0.670473	+	0.741934i	$0.733909\pi$
$462$	2.23982	+	0.730322i	0.104206	+	0.0339776i
$463$	−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
$465$	12.8396	+	0.686210i	0.595423	+	0.0318222i
$466$	−9.08333	−	2.43387i	−0.420777	−	0.112747i
$467$	14.4447			0.668420			0.334210	−	0.942499i	$-0.391531\pi$
$467$	14.4447			0.668420			0.334210	+	0.942499i	$0.391531\pi$
$468$	−11.3329	−	17.1231i	−0.523862	−	0.791514i
$469$	−11.9886			−0.553583
$470$	7.99912	+	2.14336i	0.368972	+	0.0988658i
$471$	25.9175	+	1.38515i	1.19422	+	0.0638245i
$472$	10.6112	+	6.12637i	0.488420	+	0.281989i
$473$	−27.0529	+	27.0529i	−1.24389	+	1.24389i
$474$	−6.98585	−	2.27783i	−0.320871	−	0.104624i
$475$	2.44181	+	9.11296i	0.112038	+	0.418131i
$476$	4.51434	+	4.51434i	0.206914	+	0.206914i
$477$	1.06710	−	9.95466i	0.0488590	−	0.455793i
$478$	3.01433	−	1.74033i	0.137872	−	0.0796007i
$479$	−4.66397	+	17.4062i	−0.213102	+	0.795308i	0.773724	+	0.633523i	$0.218392\pi$
$479$	−4.66397	+	17.4062i	−0.213102	+	0.795308i	−0.986826	+	0.161785i	$0.948275\pi$
$480$	20.5265	+	13.3603i	0.936904	+	0.609811i
$481$	−25.9077	−	18.4001i	−1.18129	−	0.838970i
$482$		−	0.838353i		−	0.0381859i
$483$	7.25575	−	6.51954i	0.330148	−	0.296649i
$484$	6.83297	+	11.8351i	0.310590	+	0.537957i
$485$	−27.6313	+	47.8588i	−1.25467	+	2.17316i
$486$	−4.29140	−	2.50731i	−0.194662	−	0.113734i
$487$	−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
$489$	−1.97840	−	9.35519i	−0.0894663	−	0.423056i
$490$	−0.631424	+	1.09366i	−0.0285248	+	0.0494065i
$491$	−13.0417	−	22.5888i	−0.588562	−	1.01942i	−0.994421	−	0.105483i	$-0.966361\pi$
$491$	−13.0417	−	22.5888i	−0.588562	−	1.01942i	0.405859	−	0.913936i	$-0.366972\pi$
$492$	−9.26328	−	10.3093i	−0.417621	−	0.464781i
$493$			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
$498$	−1.62213	+	0.824406i	−0.0726894	+	0.0369425i
$499$	−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
$501$	0.00312297	−	0.00957779i	0.000139524	−	0.000427904i
$502$	1.19459	−	1.19459i	0.0533170	−	0.0533170i
$503$	13.3566	+	7.71146i	0.595543	+	0.343837i	0.767286	−	0.641305i	$-0.221607\pi$
$503$	13.3566	+	7.71146i	0.595543	+	0.343837i	−0.171743	+	0.985142i	$0.554940\pi$
$504$	−2.19797	+	3.01213i	−0.0979056	+	0.134171i
$505$	−10.5892	−	2.83737i	−0.471213	−	0.126261i
$506$	−7.66013			−0.340534
$507$	16.2448	+	15.5919i	0.721455	+	0.692461i
$508$	27.4095			1.21610
$509$	12.9131	+	3.46005i	0.572363	+	0.153364i	0.533380	−	0.845876i	$-0.320922\pi$
$509$	12.9131	+	3.46005i	0.572363	+	0.153364i	0.0389830	+	0.999240i	$0.487588\pi$
$510$	−0.392583	+	7.34560i	−0.0173839	+	0.325269i
$511$	7.20690	+	4.16090i	0.318814	+	0.184068i
$512$	14.5611	−	14.5611i	0.643516	−	0.643516i
$513$	−4.56311	+	0.465295i	−0.201466	+	0.0205433i
$514$	0.577245	+	2.15431i	0.0254612	+	0.0950225i
$515$	−20.5329	−	20.5329i	−0.904789	−	0.904789i
$516$	−13.3600	−	26.2876i	−0.588140	−	1.15725i
$517$	−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	$-0.874059\pi$
$521$		−	17.5945i		−	0.770828i	0.922744	−	0.385414i	$-0.125941\pi$
$522$	−0.856933	+	0.133909i	−0.0375069	+	0.00586103i
$523$	−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
$525$	18.1114	−	3.83012i	0.790444	−	0.167160i
$526$	−2.66100	+	0.713014i	−0.116025	+	0.0310889i
$527$	6.08846	−	1.63140i	0.265218	−	0.0710648i
$528$	−24.5817	+	5.19843i	−1.06978	+	0.226233i
$529$	−4.35838	+	7.54894i	−0.189495	+	0.328215i
$530$	−2.10721	−	3.64979i	−0.0915313	−	0.158537i
$531$	29.2191	−	4.56593i	1.26800	−	0.198144i
$532$			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
$537$	14.8396	+	29.1989i	0.640375	+	1.26003i
$538$	0.861107	+	0.861107i	0.0371249	+	0.0371249i
$539$	−1.10413	−	4.12065i	−0.0475581	−	0.177489i
$540$	38.8680	−	3.96333i	1.67261	−	0.170555i
$541$	−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
$543$	−0.453498	+	8.48537i	−0.0194615	+	0.364142i
$544$	11.5972	+	3.10746i	0.497225	+	0.133231i
$545$	−15.9710			−0.684121
$546$	0.792123	−	1.82679i	0.0338998	−	0.0781796i
$547$	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
$549$	−8.18704	+	11.2196i	−0.349414	+	0.478842i
$550$	−12.5896	−	7.26863i	−0.536824	−	0.309935i
$551$	−0.565985	+	0.565985i	−0.0241118	+	0.0241118i
$552$	3.75852	−	11.5270i	0.159973	−	0.490620i
$553$	3.44370	+	12.8521i	0.146441	+	0.546525i
$554$	−2.87285	−	2.87285i	−0.122056	−	0.122056i
$555$	53.9003	−	27.3934i	2.28794	−	1.16279i
$556$	−3.08324	+	1.78011i	−0.130759	+	0.0754935i
$557$	11.7601	−	43.8892i	0.498291	−	1.85965i	−0.0124674	−	0.999922i	$-0.503969\pi$
$557$	11.7601	−	43.8892i	0.498291	−	1.85965i	0.510758	−	0.859724i	$-0.329365\pi$
$558$	0.725789	+	1.63926i	0.0307251	+	0.0693955i
$559$	20.6187	+	24.9087i	0.872079	+	1.05353i
$560$		−	13.4682i		−	0.569137i
$561$	−16.6085	−	18.4840i	−0.701210	−	0.780393i
$562$	3.45739	+	5.98838i	0.145841	+	0.252605i
$563$	21.2250	−	36.7628i	0.894527	−	1.54937i	0.0601380	−	0.998190i	$-0.480846\pi$
$563$	21.2250	−	36.7628i	0.894527	−	1.54937i	0.834389	−	0.551176i	$-0.185821\pi$
$564$	−4.46112	−	21.0951i	−0.187847	−	0.888265i
$565$	44.4788	−	11.9181i	1.87124	−	0.501396i
$566$	−3.40854	+	0.913316i	−0.143272	+	0.0383895i
$567$	0.433846	+	8.98954i	0.0182198	+	0.377525i
$568$	7.46219	−	12.9249i	0.313107	−	0.542317i
$569$	−18.5359	−	32.1051i	−0.777066	−	1.34592i	−0.933626	−	0.358249i	$-0.883374\pi$
$569$	−18.5359	−	32.1051i	−0.777066	−	1.34592i	0.156561	−	0.987668i	$-0.449959\pi$
$570$	−1.43620	+	1.29047i	−0.0601557	+	0.0540519i
$571$			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
$576$	1.81062	−	16.8908i	0.0754424	−	0.703783i
$577$	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
$579$	−29.0917	−	9.48574i	−1.20901	−	0.394214i
$580$	4.82099	−	4.82099i	0.200181	−	0.200181i
$581$	2.85350	+	1.64747i	0.118383	+	0.0683484i
$582$	−7.69413	−	0.411211i	−0.318932	−	0.0170452i
$583$	13.7516	+	3.68472i	0.569532	+	0.152606i
$584$	10.3435			0.428017
$585$	−40.6289	+	13.5931i	−1.67980	+	0.562005i
$586$	2.48842			0.102796
$587$	17.5723	+	4.70849i	0.725287	+	0.194340i	0.602530	−	0.798097i	$-0.294160\pi$
$587$	17.5723	+	4.70849i	0.725287	+	0.194340i	0.122758	+	0.992437i	$0.460826\pi$
$588$	3.28334	+	0.175477i	0.135403	+	0.00723655i
$589$	1.43280	+	0.827226i	0.0590374	+	0.0340852i
$590$	8.80279	−	8.80279i	0.362405	−	0.362405i
$591$	0.450698	+	0.146956i	0.0185392	+	0.00604496i
$592$	−7.75648	−	28.9476i	−0.318789	−	1.18974i
$593$	25.7189	+	25.7189i	1.05615	+	1.05615i	0.998327	+	0.0578202i	$0.0184150\pi$
$593$	25.7189	+	25.7189i	1.05615	+	1.05615i	0.0578202	+	0.998327i	$0.481585\pi$
$594$	4.46482	−	5.47875i	0.183194	−	0.224796i
$595$	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	$-0.829070\pi$
$599$		−	25.0400i		−	1.02311i	0.859252	−	0.511553i	$-0.170930\pi$
$600$	17.1150	−	15.3784i	0.698719	−	0.627822i
$601$	−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
$603$	−12.9584	+	33.5503i	−0.527708	+	1.36627i
$604$	21.7166	−	5.81893i	0.883634	−	0.236769i
$605$	27.5417	−	7.37977i	1.11973	−	0.300030i
$606$	−0.316248	−	1.49543i	−0.0128467	−	0.0607478i
$607$	−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
$609$	1.04971	+	1.16824i	0.0425362	+	0.0473396i
$610$			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
$615$	−25.7792	+	13.1016i	−1.03952	+	0.528308i
$616$	−3.74936	−	3.74936i	−0.151066	−	0.151066i
$617$	1.68739	+	6.29744i	0.0679319	+	0.253525i	0.991538	−	0.129818i	$-0.0414393\pi$
$617$	1.68739	+	6.29744i	0.0679319	+	0.253525i	−0.923606	+	0.383343i	$0.874773\pi$
$618$	1.25509	−	3.84923i	0.0504872	−	0.154839i
$619$	−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
$621$	−10.4023	−	27.3522i	−0.417430	−	1.09761i
$622$	−4.19251	−	1.12338i	−0.168104	−	0.0450434i
$623$	1.43934			0.0576660
$624$	2.42519	+	21.0965i	0.0970853	+	0.844536i
$625$	−35.7911			−1.43164
$626$	−2.30963	−	0.618863i	−0.0923113	−	0.0247347i
$627$	0.348091	−	6.51311i	0.0139014	−	0.260109i
$628$	−24.6353	−	14.2232i	−0.983054	−	0.567567i
$629$	20.9584	−	20.9584i	0.835668	−	0.835668i
$630$	2.37811	+	2.94918i	0.0947464	+	0.117498i
$631$	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
$633$	−4.10669	−	8.08048i	−0.163226	−	0.321170i
$634$	−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
$639$	−5.56150	−	35.5901i	−0.220010	−	1.40792i
$640$	−17.7157	−	30.6844i	−0.700273	−	1.21291i
$641$	−10.0013	+	17.3227i	−0.395027	+	0.684206i	−0.993105	−	0.117232i	$-0.962598\pi$
$641$	−10.0013	+	17.3227i	−0.395027	+	0.684206i	0.598078	+	0.801438i	$0.295931\pi$
$642$	1.83805	−	0.388703i	0.0725419	−	0.0153409i
$643$	−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
$645$	−60.1933	+	12.7294i	−2.37011	+	0.501221i
$646$	−0.473259	+	0.819709i	−0.0186201	+	0.0322510i
$647$	17.0940	+	29.6076i	0.672034	+	1.16400i	0.977327	+	0.211738i	$0.0679123\pi$
$647$	17.0940	+	29.6076i	0.672034	+	1.16400i	−0.305293	+	0.952258i	$0.598754\pi$
$648$	6.05372	+	9.40686i	0.237812	+	0.369536i
$649$			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	−0.736495	−	0.676443i	$-0.763521\pi$
$653$	−13.2606	+	7.65599i	−0.518926	+	0.299602i	0.217569	+	0.976045i	$0.430187\pi$
$654$	−1.00889	−	1.98513i	−0.0394507	−	0.0776247i
$655$	16.6867	+	16.6867i	0.652002	+	0.652002i
$656$	3.70973	+	13.8449i	0.144841	+	0.540553i
$657$	19.4342	−	15.6711i	0.758201	−	0.611387i
$658$	1.47843	−	1.47843i	0.0576353	−	0.0576353i
$659$	28.8971	+	16.6837i	1.12567	+	0.649906i	0.942842	−	0.333239i	$-0.108142\pi$
$659$	28.8971	+	16.6837i	1.12567	+	0.649906i	0.182827	+	0.983145i	$0.441475\pi$
$660$	−2.96500	+	55.4779i	−0.115412	+	2.15947i
$661$	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
$663$	−16.8702	+	12.5097i	−0.655186	+	0.485835i
$664$	4.09540			0.158932
$665$	3.37715	+	0.904905i	0.130960	+	0.0350907i
$666$	6.80979	+	4.96915i	0.263874	+	0.192551i
$667$	−4.42252	−	2.55335i	−0.171241	−	0.0988659i
$668$	−0.00780736	+	0.00780736i	−0.000302076	+	0.000302076i
$669$	2.05791	−	6.31137i	0.0795633	−	0.244012i
$670$	3.91847	+	14.6239i	0.151384	+	0.564972i
$671$	−13.9656	−	13.9656i	−0.539138	−	0.539138i
$672$	5.51244	−	2.80155i	0.212647	−	0.108072i
$673$	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	$0.128114\pi$
$677$			20.3837i			0.783409i	−0.920091	+	0.391705i	$0.871886\pi$
$678$	4.29110	+	4.77567i	0.164799	+	0.183409i
$679$	6.97620	+	12.0831i	0.267722	+	0.463708i
$680$	8.27820	−	14.3383i	0.317454	−	0.549847i
$681$	7.84164	+	37.0805i	0.300492	+	1.42093i
$682$	−2.46243	+	0.659807i	−0.0942915	+	0.0252653i
$683$	12.6624	−	3.39288i	0.484514	−	0.129825i	−0.00828973	−	0.999966i	$-0.502639\pi$
$683$	12.6624	−	3.39288i	0.484514	−	0.129825i	0.492804	+	0.870141i	$0.335972\pi$
$684$	4.68950	+	1.81127i	0.179308	+	0.0692555i
$685$	−12.0895	+	20.9397i	−0.461917	+	0.800064i
$686$	0.159419	+	0.276121i	0.00608663	+	0.0105424i
$687$	16.3142	−	14.6589i	0.622426	−	0.559270i
$688$			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
$693$	−12.7251	−	1.36408i	−0.483388	−	0.0518171i
$694$	−1.01368	−	1.01368i	−0.0384788	−	0.0384788i
$695$	1.92256	+	7.17510i	0.0729270	+	0.272167i
$696$	1.85595	+	0.605156i	0.0703494	+	0.0229384i
$697$	−10.0239	+	10.0239i	−0.379683	+	0.379683i
$698$	6.83718	+	3.94745i	0.258791	+	0.149413i
$699$	51.0121	+	2.72633i	1.92945	+	0.103119i
$700$	−19.5979	−	5.25124i	−0.740730	−	0.198478i
$701$	48.9927			1.85043			0.925214	−	0.379445i	$-0.123885\pi$
$701$	48.9927			1.85043			0.925214	+	0.379445i	$0.123885\pi$
$702$	−4.25610	−	4.19134i	−0.160636	−	0.158192i
$703$	7.77973			0.293418
$704$	23.3333	+	6.25213i	0.879406	+	0.235636i
$705$	−44.9232	−	2.40091i	−1.69191	−	0.0904233i
$706$	6.51980	+	3.76421i	0.245376	+	0.141668i
$707$	−1.95714	+	1.95714i	−0.0736059	+	0.0736059i
$708$	−30.8162	−	10.0480i	−1.15814	−	0.377629i
$709$	−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
$711$	39.6889	+	4.25448i	1.48845	+	0.159555i
$712$	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
$717$	−14.0647	+	12.6376i	−0.525255	+	0.471959i
$718$	0.859320	+	1.48839i	0.0320695	+	0.0555461i
$719$	4.54570	−	7.87338i	0.169526	−	0.293627i	−0.768727	−	0.639577i	$-0.779110\pi$
$719$	4.54570	−	7.87338i	0.169526	−	0.293627i	0.938253	+	0.345949i	$0.112443\pi$
$720$	−37.6910	−	14.5577i	−1.40466	−	0.542534i
$721$	−7.08154	+	1.89749i	−0.263730	+	0.0706663i
$722$	5.61152	−	1.50360i	0.208839	−	0.0559583i
$723$	0.942278	+	4.45572i	0.0350437	+	0.165710i
$724$	4.65666	−	8.06556i	0.173063	−	0.299754i
$725$	−4.84569	−	8.39299i	−0.179964	−	0.311708i
$726$	2.65709	+	2.95714i	0.0986139	+	0.109750i
$727$			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
$732$	13.5706	−	6.89689i	0.501583	−	0.254916i
$733$	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
$735$	2.12669	−	6.52233i	0.0784442	−	0.240580i
$736$	−14.2168	+	14.2168i	−0.524040	+	0.524040i
$737$	−44.2917	−	25.5718i	−1.63150	−	0.941950i
$738$	−3.25696	−	2.37662i	−0.119890	−	0.0874848i
$739$	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
$741$	−5.45288	−	0.809318i	−0.200316	−	0.0297310i
$742$	−1.06403			−0.0390619
$743$	−42.8653	−	11.4857i	−1.57257	−	0.421370i	−0.635957	−	0.771724i	$-0.719395\pi$
$743$	−42.8653	−	11.4857i	−1.57257	−	0.421370i	−0.936617	+	0.350354i	$0.886061\pi$
$744$	0.215340	−	4.02921i	0.00789474	−	0.147718i
$745$	6.88801	+	3.97679i	0.252357	+	0.145698i
$746$	−6.40747	+	6.40747i	−0.234594	+	0.234594i
$747$	7.69478	−	6.20481i	0.281537	−	0.227022i
$748$	7.04901	+	26.3072i	0.257737	+	0.961888i
$749$	−2.40554	−	2.40554i	−0.0878964	−	0.0878964i
$750$	−5.63670	−	11.0910i	−0.205823	−	0.404986i
$751$	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
$756$	4.04002	−	8.99879i	0.146934	−	0.327283i
$757$	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
$759$	40.7124	−	8.60970i	1.47777	−	0.312512i
$760$	4.19759	−	1.12474i	0.152263	−	0.0407986i
$761$	−6.34882	+	1.70116i	−0.230144	+	0.0616670i	−0.372048	−	0.928213i	$-0.621344\pi$
$761$	−6.34882	+	1.70116i	−0.230144	+	0.0616670i	0.141904	+	0.989880i	$0.454678\pi$
$762$	7.80110	−	1.64975i	0.282604	−	0.0597640i
$763$	−2.01613	+	3.49205i	−0.0729889	+	0.126421i
$764$	17.6016	+	30.4868i	0.636803	+	1.10298i
$765$	−6.16966	−	39.4820i	−0.223065	−	1.42747i
$766$		−	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
$771$	−5.48934	−	10.8010i	−0.197694	−	0.388989i
$772$	23.7142	+	23.7142i	0.853493	+	0.853493i
$773$	−0.943142	−	3.51985i	−0.0339224	−	0.126600i	0.946888	−	0.321563i	$-0.104208\pi$
$773$	−0.943142	−	3.51985i	−0.0339224	−	0.126600i	−0.980811	+	0.194963i	$0.937541\pi$
$774$	−5.38464	−	6.67767i	−0.193547	−	0.240024i
$775$	−14.1646	+	14.1646i	−0.508808	+	0.508808i
$776$	15.0186	+	8.67099i	0.539136	+	0.311270i
$777$	0.814677	−	15.2434i	0.0292264	−	0.546852i
$778$	7.29129	+	1.95370i	0.261406	+	0.0700434i
$779$	−3.72086			−0.133313
$780$	46.4470	+	6.89368i	1.66307	+	0.246833i
$781$	51.2235			1.83292
$782$	−5.83300	−	1.56295i	−0.208588	−	0.0558909i
$783$	4.40396	−	1.67487i	0.157385	−	0.0598548i
$784$	−2.94482	−	1.70020i	−0.105172	−	0.0607213i
$785$	−41.9681	+	41.9681i	−1.49790	+	1.49790i
$786$	−1.01999	+	3.12819i	−0.0363817	+	0.111579i
$787$	−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
$789$	13.3414	−	6.78043i	0.474968	−	0.241390i
$790$	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
$795$	15.3017	+	17.0297i	0.542696	+	0.603980i
$796$	17.8266	+	30.8766i	0.631847	+	1.09439i
$797$	−21.4930	+	37.2270i	−0.761323	+	1.31865i	0.180846	+	0.983511i	$0.442116\pi$
$797$	−21.4930	+	37.2270i	−0.761323	+	1.31865i	−0.942169	+	0.335138i	$0.891217\pi$
$798$	0.100859	+	0.476930i	0.00357038	+	0.0168831i
$799$	−21.3023	+	5.70793i	−0.753620	+	0.201932i
$800$	−36.8560	+	9.87554i	−1.30306	+	0.349153i
$801$	1.55577	−	4.02801i	0.0549706	−	0.142323i
$802$	−2.22791	+	3.85885i	−0.0786701	+	0.136261i
$803$	17.7505	+	30.7447i	0.626401	+	1.08496i
$804$	29.3212	−	26.3461i	1.03408	−	0.929155i
$805$			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	−0.226628	−	0.973981i	$-0.572770\pi$
$809$	14.3225	−	8.26907i	0.503551	−	0.290725i	0.730179	+	0.683256i	$0.239437\pi$
$810$	10.8238	−	3.46744i	0.380309	−	0.121833i
$811$	−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
$813$	−25.0836	−	8.17884i	−0.879721	−	0.286845i
$814$	−8.47649	+	8.47649i	−0.297101	+	0.297101i
$815$	18.9367	+	10.9331i	0.663325	+	0.382971i
$816$	−19.7790	−	1.05708i	−0.692404	−	0.0370053i
$817$	−7.64671	−	2.04893i	−0.267525	−	0.0716830i
$818$	−0.953920			−0.0333530
$819$	−2.15677	+	10.5995i	−0.0753636	+	0.370375i
$820$	31.6938			1.10680
$821$	42.8169	+	11.4728i	1.49432	+	0.400402i	0.911194	−	0.411978i	$-0.135162\pi$
$821$	42.8169	+	11.4728i	1.49432	+	0.400402i	0.583128	+	0.812381i	$0.301829\pi$
$822$	−3.36642	−	0.179917i	−0.117417	−	0.00627533i
$823$	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
$825$	75.0817	+	24.4814i	2.61401	+	0.852332i
$826$	−0.813485	−	3.03597i	−0.0283048	−	0.105635i
$827$	−37.0427	−	37.0427i	−1.28810	−	1.28810i	−0.935940	−	0.352159i	$-0.885447\pi$
$827$	−37.0427	−	37.0427i	−1.28810	−	1.28810i	−0.352159	−	0.935940i	$-0.614553\pi$
$828$	−3.41850	+	31.8904i	−0.118801	+	1.10827i
$829$	−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
$834$	−0.770389	+	0.692220i	−0.0266764	+	0.0239696i
$835$	0.0115185	+	0.0199506i	0.000398615	+	0.000690421i
$836$	−3.57431	+	6.19088i	−0.123620	+	0.214116i
$837$	−5.69993	−	7.89667i	−0.197018	−	0.272949i
$838$	11.3471	−	3.04043i	0.391978	−	0.105030i
$839$	−24.4688	+	6.55640i	−0.844757	+	0.226352i	−0.655141	−	0.755506i	$-0.727391\pi$
$839$	−24.4688	+	6.55640i	−0.844757	+	0.226352i	−0.189616	+	0.981858i	$0.560724\pi$
$840$	−1.76422	−	8.34241i	−0.0608714	−	0.287840i
$841$	−14.0889	+	24.4027i	−0.485824	+	0.841471i
$842$	0.315898	+	0.547151i	0.0108866	+	0.0188561i
$843$	−25.1062	−	27.9414i	−0.864705	−	0.962351i
$844$			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
$849$	17.0894	−	8.68521i	0.586505	−	0.298076i
$850$	−8.10363	−	8.10363i	−0.277952	−	0.277952i
$851$	12.8464	+	47.9433i	0.440368	+	1.64347i
$852$	−12.2390	+	37.5355i	−0.419300	+	1.28595i
$853$	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
$855$	6.18273	−	8.47289i	0.211445	−	0.289767i
$856$	−4.08432	−	1.09439i	−0.139599	−	0.0374055i
$857$	−38.5550			−1.31701			−0.658506	−	0.752575i	$-0.728811\pi$
$857$	−38.5550			−1.31701			−0.658506	+	0.752575i	$0.728811\pi$
$858$	6.82305	−	5.05944i	0.232935	−	0.172727i
$859$	−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
$861$	−0.389640	+	7.29053i	−0.0132789	+	0.248461i
$862$	4.74001	+	2.73664i	0.161445	+	0.0932105i
$863$	16.9671	−	16.9671i	0.577565	−	0.577565i	−0.356666	−	0.934232i	$-0.616087\pi$
$863$	16.9671	−	16.9671i	0.577565	−	0.577565i	0.934232	+	0.356666i	$0.116087\pi$
$864$	−1.88182	−	18.4548i	−0.0640207	−	0.627845i
$865$	10.1327	+	37.8157i	0.344521	+	1.28577i
$866$	−4.79651	−	4.79651i	−0.162992	−	0.162992i
$867$	4.46502	+	8.78554i	0.151640	+	0.298373i
$868$	−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
$873$	41.3553	−	6.46240i	1.39967	−	0.218719i
$874$	−0.792517	−	1.37268i	−0.0268073	−	0.0464316i
$875$	−11.2642	+	19.5102i	−0.380800	+	0.659565i
$876$	−26.7703	+	5.66127i	−0.904483	+	0.191277i
$877$	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
$879$	−13.2256	+	2.79690i	−0.446088	+	0.0943370i
$880$	28.7278	−	49.7581i	0.968415	−	1.67734i
$881$	13.5812	+	23.5233i	0.457561	+	0.792519i	0.998831	−	0.0483295i	$-0.0153898\pi$
$881$	13.5812	+	23.5233i	0.457561	+	0.792519i	−0.541270	+	0.840849i	$0.682056\pi$
$882$	0.945043	−	0.147677i	0.0318213	−	0.00497256i
$883$		−	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	−0.494604	−	0.869118i	$-0.664687\pi$
$887$	0.320813	−	0.185221i	0.0107718	−	0.00621913i	0.505376	+	0.862899i	$0.331354\pi$
$888$	−8.59634	−	16.9145i	−0.288474	−	0.567613i
$889$	−10.2097	−	10.2097i	−0.342421	−	0.342421i
$890$	−0.470447	−	1.75573i	−0.0157694	−	0.0588523i
$891$	−17.5719	+	34.1370i	−0.588681	+	1.14363i
$892$	−5.14473	+	5.14473i	−0.172258	+	0.172258i
$893$	−5.01306	−	2.89429i	−0.167756	−	0.0968538i
$894$	−0.0591829	+	1.10737i	−0.00197937	+	0.0370359i
$895$	−72.3473	−	19.3854i	−2.41830	−	0.647983i
$896$	−8.94552			−0.298849
$897$	−4.01663	−	34.9402i	−0.134111	−	1.16662i
$898$	−3.33073			−0.111148
$899$	−1.64160	−	0.439866i	−0.0547505	−	0.0146704i
$900$	−35.8789	+	49.1689i	−1.19596	+	1.63896i
$901$	9.71967	+	5.61166i	0.323809	+	0.186951i
$902$	4.05410	−	4.05410i	0.134987	−	0.134987i
$903$	−4.81536	+	14.7682i	−0.160245	+	0.491454i
$904$	−3.74001	−	13.9579i	−0.124391	−	0.464233i
$905$	−13.7403	−	13.7403i	−0.456743	−	0.456743i
$906$	5.83058	−	2.96324i	0.193708	−	0.0984471i
$907$	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	$-0.830863\pi$
$911$		−	30.5875i		−	1.01341i	0.862119	−	0.506705i	$-0.169137\pi$
$912$	−3.47477	−	3.86716i	−0.115061	−	0.128054i
$913$	7.02812	+	12.1731i	0.232597	+	0.402869i
$914$	0.603450	−	1.04521i	0.0199604	−	0.0345724i
$915$	−6.57138	−	31.0739i	−0.217243	−	1.02727i
$916$	−23.2192	+	6.22155i	−0.767182	+	0.205566i
$917$	5.75501	−	1.54205i	0.190047	−	0.0509230i
$918$	4.51772	−	3.26095i	0.149107	−	0.107627i
$919$	−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
$921$	−0.0818912	+	0.0735820i	−0.00269841	+	0.00242461i
$922$		−	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
$927$	−2.34423	+	21.8688i	−0.0769948	+	0.718265i
$928$	−2.28904	−	2.28904i	−0.0751415	−	0.0751415i
$929$	−8.96251	−	33.4485i	−0.294050	−	1.09741i	−0.941969	−	0.335701i	$-0.891027\pi$
$929$	−8.96251	−	33.4485i	−0.294050	−	1.09741i	0.647918	−	0.761710i	$-0.275640\pi$
$930$	−3.89763	−	1.27088i	−0.127808	−	0.0416736i
$931$	0.624180	−	0.624180i	0.0204567	−	0.0204567i
$932$	−48.4883	−	27.9947i	−1.58829	−	0.916998i
$933$	23.5452	+	1.25837i	0.770835	+	0.0411971i
$934$	−4.44857	−	1.19199i	−0.145562	−	0.0390032i
$935$	56.8249			1.85837
$936$	4.26565	+	12.7498i	0.139427	+	0.416739i
$937$	−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
$939$	12.9709	+	0.693226i	0.423289	+	0.0226226i
$940$	42.7007	+	24.6532i	1.39274	+	0.804100i
$941$	15.0046	−	15.0046i	0.489136	−	0.489136i	−0.418898	−	0.908033i	$-0.637583\pi$
$941$	15.0046	−	15.0046i	0.489136	−	0.489136i	0.908033	+	0.418898i	$0.137583\pi$
$942$	−7.86760	−	2.56533i	−0.256340	−	0.0835831i
$943$	−6.14410	−	22.9301i	−0.200080	−	0.746707i
$944$	23.7027	+	23.7027i	0.771457	+	0.771457i
$945$	−15.9541	−	13.0015i	−0.518986	−	0.422939i
$946$	10.5640	−	6.09913i	0.343465	−	0.198300i
$947$	−7.70012	+	28.7372i	−0.250220	+	0.933835i	0.720467	+	0.693489i	$0.243927\pi$
$947$	−7.70012	+	28.7372i	−0.250220	+	0.933835i	−0.970687	+	0.240346i	$0.922739\pi$
$948$	−36.6660	−	23.8651i	−1.19086	−	0.775103i
$949$	27.2776	−	12.4985i	0.885470	−	0.405718i
$950$		−	3.00805i		−	0.0975940i
$951$	29.8737	−	26.8425i	0.968720	−	0.870427i
$952$	−2.09004	−	3.62005i	−0.0677385	−	0.117327i
$953$	3.95695	−	6.85364i	0.128178	−	0.222011i	−0.794793	−	0.606881i	$-0.792420\pi$
$953$	3.95695	−	6.85364i	0.128178	−	0.222011i	0.922971	+	0.384870i	$0.125754\pi$
$954$	−1.15011	+	2.97771i	−0.0372361	+	0.0964070i
$955$	70.9468	−	19.0101i	2.29578	−	0.615154i
$956$	20.0175	−	5.36367i	0.647412	−	0.173474i
$957$	1.38624	+	6.55507i	0.0448108	+	0.211895i
$958$	2.87276	−	4.97576i	0.0928145	−	0.160759i
$959$	3.05230	+	5.28674i	0.0985639	+	0.170718i
$960$	25.9635	+	28.8954i	0.837969	+	0.932596i
$961$		−	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
$966$	−2.77258	+	1.40909i	−0.0892062	+	0.0453367i
$967$	−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
$969$	1.59398	−	4.88855i	0.0512059	−	0.157043i
$970$	12.4591	−	12.4591i	0.400036	−	0.400036i
$971$	7.72705	+	4.46121i	0.247973	+	0.143167i	0.618836	−	0.785520i	$-0.287605\pi$
$971$	7.72705	+	4.46121i	0.247973	+	0.143167i	−0.370863	+	0.928688i	$0.620938\pi$
$972$	−20.8164	−	21.0328i	−0.667687	−	0.674626i
$973$	1.81153	+	0.485399i	0.0580751	+	0.0155612i
$974$	4.13999			0.132654
$975$	26.5530	−	61.2366i	0.850378	−	1.96114i
$976$	−15.7428			−0.503915
$977$	−17.6211	−	4.72156i	−0.563749	−	0.151056i	−0.0343206	−	0.999411i	$-0.510927\pi$
$977$	−17.6211	−	4.72156i	−0.563749	−	0.151056i	−0.529428	+	0.848355i	$0.677593\pi$
$978$	−0.162707	+	3.04441i	−0.00520281	+	0.0973495i
$979$	5.31761	+	3.07013i	0.169952	+	0.0981216i
$980$	−5.31669	+	5.31669i	−0.169835	+	0.169835i
$981$	7.59331	+	9.41670i	0.242436	+	0.300652i
$982$	2.15243	+	8.03296i	0.0686867	+	0.256342i
$983$	−19.2028	−	19.2028i	−0.612473	−	0.612473i	0.331117	−	0.943590i	$-0.392575\pi$
$983$	−19.2028	−	19.2028i	−0.612473	−	0.612473i	−0.943590	+	0.331117i	$0.892575\pi$
$984$	4.11142	+	8.08979i	0.131067	+	0.257893i
$985$	−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
$990$	2.49527	+	15.9682i	0.0793050	+	0.507503i
$991$	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
$993$	−12.3587	+	2.61357i	−0.392191	+	0.0829390i
$994$	−3.69794	+	0.990861i	−0.117292	+	0.0314282i
$995$	71.8538	−	19.2532i	2.27792	−	0.610367i
$996$	−10.5994	+	2.24152i	−0.335855	+	0.0710253i
$997$	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
$999$	−41.7781	−	18.7563i	−1.32180	−	0.593424i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.307973 - 0.0825212i) q^{2} +(1.72958 + 0.0924370i) q^{3} +(-1.64401 - 0.949171i) q^{4} +(-2.80070 + 2.80070i) q^{5} +(-0.525037 - 0.171195i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.878890 + 0.878890i) q^{8} +(2.98291 + 0.319755i) q^{9} +O(q^{10})\)	\(q+(-0.307973 - 0.0825212i) q^{2} +(1.72958 + 0.0924370i) q^{3} +(-1.64401 - 0.949171i) q^{4} +(-2.80070 + 2.80070i) q^{5} +(-0.525037 - 0.171195i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.878890 + 0.878890i) q^{8} +(2.98291 + 0.319755i) 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} +(-5.10293 + 4.58516i) q^{15} +(1.70020 + 2.94482i) q^{16} +(-1.68153 + 2.91250i) q^{17} +(-0.892270 - 0.344629i) q^{18} +(-0.852646 + 0.228466i) q^{19} +(7.26274 - 1.94604i) q^{20} +(0.358362 + 1.69457i) q^{21} +(0.680083 - 1.17794i) q^{22} +(-2.81588 - 4.87725i) q^{23} +(1.43887 + 1.60135i) 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} +(1.94994 - 0.991006i) q^{30} +(-1.32530 - 1.32530i) q^{31} +(-0.923996 - 3.44840i) q^{32} +(-2.29058 + 7.02495i) q^{33} +(0.758209 - 0.758209i) q^{34} +(-3.43015 - 1.98040i) q^{35} +(-4.60044 - 3.35697i) q^{36} +(-8.51301 - 2.28105i) q^{37} +0.281445 q^{38} +(5.72955 + 2.48441i) q^{39} -4.92302 q^{40} +(4.07157 + 1.09097i) q^{41} +(0.0294724 - 0.551456i) q^{42} +(7.76670 + 4.48411i) q^{43} +(5.72640 - 5.72640i) q^{44} +(-9.24978 + 7.45871i) q^{45} +(0.464740 + 1.73443i) q^{46} +(4.63695 + 4.63695i) q^{47} +(2.66842 + 5.25048i) 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} +(-1.51140 - 0.678544i) q^{54} +(-8.44839 - 14.6330i) q^{55} +(-0.621469 + 1.07642i) q^{56} +(-1.49584 + 0.316334i) q^{57} +(-0.279260 + 0.0748274i) q^{58} +(9.52199 - 2.55141i) q^{59} +(12.7414 - 2.69450i) q^{60} +(-2.31485 + 4.00944i) q^{61} +(0.298792 + 0.517522i) q^{62} +(0.463175 + 2.96403i) 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} +(-4.41946 - 8.69590i) q^{69} +(0.892969 + 0.892969i) q^{70} +(-3.10773 - 11.5982i) q^{71} +(2.34062 + 2.90268i) q^{72} +(5.88441 - 5.88441i) q^{73} +(2.43354 + 1.40501i) q^{74} +(0.987954 - 18.4855i) q^{75} +(1.61861 + 0.433706i) q^{76} -4.26601 q^{77} +(-1.55953 - 1.23794i) q^{78} +13.3054 q^{79} +(-13.0093 - 3.48584i) q^{80} +(8.79551 + 1.90760i) q^{81} +(-1.16391 - 0.671981i) q^{82} +(2.32987 - 2.32987i) q^{83} +(1.01929 - 3.12605i) q^{84} +(-3.44757 - 12.8665i) q^{85} +(-2.02190 - 2.02190i) q^{86} +(1.40012 - 0.711574i) 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} +(-2.16971 - 2.41472i) q^{93} +(-1.04541 - 1.81070i) q^{94} +(1.74814 - 3.02787i) q^{95} +(-1.27937 - 6.04970i) q^{96} +(13.4770 - 3.61115i) q^{97} +(0.307973 - 0.0825212i) q^{98} +(-4.61111 + 11.9385i) 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

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Representations

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Database

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