LMFDB - Embedded newform 210.2.x.a.23.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(23,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

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

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

chi := DirichletCharacter("210.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.x (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:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.13
Character	$\chi$	$=$	210.23
Dual form			210.2.x.a.137.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(0.517224 - 1.65302i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.16375 + 0.564071i) q^{5} +(0.0717662 - 1.73056i) q^{6} +(0.113038 - 2.64334i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.46496 - 1.70996i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(0.517224 - 1.65302i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.16375 + 0.564071i) q^{5} +(0.0717662 - 1.73056i) q^{6} +(0.113038 - 2.64334i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.46496 - 1.70996i) q^{9} +(-1.94403 + 1.10487i) q^{10} +(3.54004 - 2.04384i) q^{11} +(-0.378582 - 1.69017i) q^{12} +(3.69641 + 3.69641i) q^{13} +(-0.574959 - 2.58252i) q^{14} +(-0.186722 + 3.86848i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.93133 + 7.20783i) q^{17} +(-2.82354 - 1.01372i) q^{18} +(-2.12380 - 1.22618i) q^{19} +(-1.59183 + 1.57038i) q^{20} +(-4.31102 - 1.55405i) q^{21} +(2.89043 - 2.89043i) q^{22} +(0.284603 + 1.06215i) q^{23} +(-0.803130 - 1.53459i) q^{24} +(4.36365 - 2.44102i) q^{25} +(4.52715 + 2.61375i) q^{26} +(-4.10154 + 3.19020i) q^{27} +(-1.22377 - 2.34571i) q^{28} -1.48870 q^{29} +(0.820877 + 3.78499i) q^{30} +(2.62194 + 4.54133i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-1.54752 - 6.90888i) q^{33} +7.46210i q^{34} +(1.24644 + 5.78328i) q^{35} +(-2.98970 - 0.248392i) q^{36} +(1.43087 + 5.34010i) q^{37} +(-2.36880 - 0.634717i) q^{38} +(8.02211 - 4.19837i) q^{39} +(-1.13115 + 1.92886i) q^{40} -6.74278i q^{41} +(-4.56635 - 0.385322i) q^{42} +(1.27352 + 1.27352i) q^{43} +(2.04384 - 3.54004i) q^{44} +(6.29810 + 2.30952i) q^{45} +(0.549811 + 0.952300i) q^{46} +(2.97410 - 0.796909i) q^{47} +(-1.17295 - 1.27444i) q^{48} +(-6.97444 - 0.597597i) q^{49} +(3.58318 - 3.48724i) q^{50} +(10.9158 + 6.92059i) q^{51} +(5.04938 + 1.35298i) q^{52} +(-5.50634 - 1.47542i) q^{53} +(-3.13610 + 4.14305i) q^{54} +(-6.50689 + 6.41920i) q^{55} +(-1.78919 - 1.94905i) q^{56} +(-3.12538 + 2.87649i) q^{57} +(-1.43797 + 0.385303i) q^{58} +(-5.09134 - 8.81846i) q^{59} +(1.77253 + 3.44356i) q^{60} +(-0.814929 + 1.41150i) q^{61} +(3.70798 + 3.70798i) q^{62} +(-4.79864 + 6.32242i) q^{63} -1.00000i q^{64} +(-10.0831 - 5.91307i) q^{65} +(-3.28294 - 6.27294i) q^{66} +(-3.39341 - 0.909261i) q^{67} +(1.93133 + 7.20783i) q^{68} +(1.90296 + 0.0789157i) q^{69} +(2.70080 + 5.26362i) q^{70} +5.89777i q^{71} +(-2.95212 + 0.533863i) q^{72} +(1.44294 - 5.38514i) q^{73} +(2.76424 + 4.78780i) q^{74} +(-1.77808 - 8.47576i) q^{75} -2.45236 q^{76} +(-5.00240 - 9.58854i) q^{77} +(6.66214 - 6.13159i) q^{78} +(8.18814 + 4.72742i) q^{79} +(-0.593376 + 2.15590i) q^{80} +(3.15205 + 8.42998i) q^{81} +(-1.74516 - 6.51303i) q^{82} +(-6.31379 + 6.31379i) q^{83} +(-4.51048 + 0.809665i) q^{84} +(0.113194 - 16.6854i) q^{85} +(1.55973 + 0.900511i) q^{86} +(-0.769989 + 2.46085i) q^{87} +(1.05797 - 3.94840i) q^{88} +(6.71062 - 11.6231i) q^{89} +(6.68125 + 0.600760i) q^{90} +(10.1887 - 9.35301i) q^{91} +(0.777550 + 0.777550i) q^{92} +(8.86304 - 1.98524i) q^{93} +(2.66651 - 1.53951i) q^{94} +(5.28704 + 1.45517i) q^{95} +(-1.46283 - 0.927433i) q^{96} +(-5.21514 + 5.21514i) q^{97} +(-6.89147 + 1.22788i) q^{98} +(-12.2209 - 1.01535i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) $ 64 * q + 8 * q^6 + 4 * q^7	$ 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43} - 28 q^{45} + 24 q^{46} - 16 q^{55} + 24 q^{57} - 28 q^{58} + 8 q^{60} + 24 q^{61} - 88 q^{63} - 16 q^{67} - 12 q^{70} + 8 q^{72} - 56 q^{73} + 8 q^{75} - 32 q^{76} - 16 q^{78} + 4 q^{81} + 16 q^{82} + 32 q^{85} + 76 q^{87} + 12 q^{88} + 40 q^{90} - 48 q^{91} + 84 q^{93} + 4 q^{96} + 104 q^{97}+O(q^{100}) $ 64 * q + 8 * q^6 + 4 * q^7 + 4 * q^10 - 24 * q^15 + 32 * q^16 - 8 * q^18 + 12 * q^21 - 24 * q^22 - 8 * q^25 - 72 * q^27 + 4 * q^28 - 12 * q^30 + 32 * q^31 - 20 * q^33 - 24 * q^36 - 8 * q^37 - 40 * q^42 - 64 * q^43 - 28 * q^45 + 24 * q^46 - 16 * q^55 + 24 * q^57 - 28 * q^58 + 8 * q^60 + 24 * q^61 - 88 * q^63 - 16 * q^67 - 12 * q^70 + 8 * q^72 - 56 * q^73 + 8 * q^75 - 32 * q^76 - 16 * q^78 + 4 * q^81 + 16 * q^82 + 32 * q^85 + 76 * q^87 + 12 * q^88 + 40 * q^90 - 48 * q^91 + 84 * q^93 + 4 * q^96 + 104 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	0.517224	−	1.65302i	0.298619	−	0.954372i
$3$	0.517224	−	1.65302i	0.298619	−	0.954372i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−2.16375	+	0.564071i	−0.967659	+	0.252260i
$5$	−2.16375	+	0.564071i	−0.967659	+	0.252260i
$6$	0.0717662	−	1.73056i	0.0292984	−	0.706500i
$7$	0.113038	−	2.64334i	0.0427245	−	0.999087i
$7$	0.113038	−	2.64334i	0.0427245	−	0.999087i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−2.46496	−	1.70996i	−0.821653	−	0.569988i
$10$	−1.94403	+	1.10487i	−0.614757	+	0.349391i
$11$	3.54004	−	2.04384i	1.06736	−	0.616242i	0.139902	−	0.990165i	$-0.455321\pi$
$11$	3.54004	−	2.04384i	1.06736	−	0.616242i	0.927459	+	0.373924i	$0.121988\pi$
$12$	−0.378582	−	1.69017i	−0.109287	−	0.487910i
$13$	3.69641	+	3.69641i	1.02520	+	1.02520i	0.999674	+	0.0255244i	$0.00812556\pi$
$13$	3.69641	+	3.69641i	1.02520	+	1.02520i	0.0255244	+	0.999674i	$0.491874\pi$
$14$	−0.574959	−	2.58252i	−0.153664	−	0.690208i
$15$	−0.186722	+	3.86848i	−0.0482114	+	0.998837i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.93133	+	7.20783i	−0.468417	+	1.74816i	0.176888	+	0.984231i	$0.443397\pi$
$17$	−1.93133	+	7.20783i	−0.468417	+	1.74816i	−0.645305	+	0.763925i	$0.723270\pi$
$18$	−2.82354	−	1.01372i	−0.665515	−	0.238936i
$19$	−2.12380	−	1.22618i	−0.487234	−	0.281305i	0.236192	−	0.971706i	$-0.424101\pi$
$19$	−2.12380	−	1.22618i	−0.487234	−	0.281305i	−0.723426	+	0.690402i	$0.757434\pi$
$20$	−1.59183	+	1.57038i	−0.355944	+	0.351147i
$21$	−4.31102	−	1.55405i	−0.940743	−	0.339122i
$22$	2.89043	−	2.89043i	0.616242	−	0.616242i
$23$	0.284603	+	1.06215i	0.0593438	+	0.221474i	0.989229	−	0.146376i	$-0.0467608\pi$
$23$	0.284603	+	1.06215i	0.0593438	+	0.221474i	−0.929885	+	0.367850i	$0.880094\pi$
$24$	−0.803130	−	1.53459i	−0.163938	−	0.313248i
$25$	4.36365	−	2.44102i	0.872729	−	0.488204i
$26$	4.52715	+	2.61375i	0.887848	+	0.512599i
$27$	−4.10154	+	3.19020i	−0.789342	+	0.613954i
$28$	−1.22377	−	2.34571i	−0.231271	−	0.443298i
$29$	−1.48870			−0.276444			−0.138222	−	0.990401i	$-0.544139\pi$
$29$	−1.48870			−0.276444			−0.138222	+	0.990401i	$0.544139\pi$
$30$	0.820877	+	3.78499i	0.149871	+	0.691042i
$31$	2.62194	+	4.54133i	0.470914	+	0.815647i	0.999447	−	0.0332663i	$-0.0105909\pi$
$31$	2.62194	+	4.54133i	0.470914	+	0.815647i	−0.528533	+	0.848913i	$0.677258\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−1.54752	−	6.90888i	−0.269389	−	1.20268i
$34$			7.46210i			1.27974i
$35$	1.24644	+	5.78328i	0.210687	+	0.977554i
$36$	−2.98970	−	0.248392i	−0.498283	−	0.0413987i
$37$	1.43087	+	5.34010i	0.235234	+	0.877906i	0.978043	+	0.208403i	$0.0668265\pi$
$37$	1.43087	+	5.34010i	0.235234	+	0.877906i	−0.742809	+	0.669504i	$0.766507\pi$
$38$	−2.36880	−	0.634717i	−0.384269	−	0.102965i
$39$	8.02211	−	4.19837i	1.28457	−	0.672277i
$40$	−1.13115	+	1.92886i	−0.178850	+	0.304980i
$41$		−	6.74278i		−	1.05305i	−0.850161	−	0.526523i	$-0.823495\pi$
$41$		−	6.74278i		−	1.05305i	0.850161	−	0.526523i	$-0.176505\pi$
$42$	−4.56635	−	0.385322i	−0.704603	−	0.0594565i
$43$	1.27352	+	1.27352i	0.194209	+	0.194209i	0.797512	−	0.603303i	$-0.206149\pi$
$43$	1.27352	+	1.27352i	0.194209	+	0.194209i	−0.603303	+	0.797512i	$0.706149\pi$
$44$	2.04384	−	3.54004i	0.308121	−	0.533681i
$45$	6.29810	+	2.30952i	0.938866	+	0.344284i
$46$	0.549811	+	0.952300i	0.0810651	+	0.140409i
$47$	2.97410	−	0.796909i	0.433818	−	0.116241i	−0.0353000	−	0.999377i	$-0.511239\pi$
$47$	2.97410	−	0.796909i	0.433818	−	0.116241i	0.469118	+	0.883136i	$0.344572\pi$
$48$	−1.17295	−	1.27444i	−0.169300	−	0.183949i
$49$	−6.97444	−	0.597597i	−0.996349	−	0.0853710i
$50$	3.58318	−	3.48724i	0.506738	−	0.493170i
$51$	10.9158	+	6.92059i	1.52851	+	0.969077i
$52$	5.04938	+	1.35298i	0.700224	+	0.187624i
$53$	−5.50634	−	1.47542i	−0.756355	−	0.202665i	−0.140020	−	0.990149i	$-0.544717\pi$
$53$	−5.50634	−	1.47542i	−0.756355	−	0.202665i	−0.616335	+	0.787484i	$0.711383\pi$
$54$	−3.13610	+	4.14305i	−0.426769	+	0.563798i
$55$	−6.50689	+	6.41920i	−0.877389	+	0.865565i
$56$	−1.78919	−	1.94905i	−0.239091	−	0.260453i
$57$	−3.12538	+	2.87649i	−0.413967	+	0.381000i
$58$	−1.43797	+	0.385303i	−0.188815	+	0.0505928i
$59$	−5.09134	−	8.81846i	−0.662836	−	1.14807i	−0.979867	−	0.199651i	$-0.936019\pi$
$59$	−5.09134	−	8.81846i	−0.662836	−	1.14807i	0.317031	−	0.948415i	$-0.397314\pi$
$60$	1.77253	+	3.44356i	0.228833	+	0.444562i
$61$	−0.814929	+	1.41150i	−0.104341	+	0.180724i	−0.913469	−	0.406909i	$-0.866607\pi$
$61$	−0.814929	+	1.41150i	−0.104341	+	0.180724i	0.809128	+	0.587633i	$0.199940\pi$
$62$	3.70798	+	3.70798i	0.470914	+	0.470914i
$63$	−4.79864	+	6.32242i	−0.604572	+	0.796550i
$64$		−	1.00000i		−	0.125000i
$65$	−10.0831	−	5.91307i	−1.25066	−	0.733426i
$66$	−3.28294	−	6.27294i	−0.404102	−	0.772146i
$67$	−3.39341	−	0.909261i	−0.414571	−	0.111084i	0.0455037	−	0.998964i	$-0.485511\pi$
$67$	−3.39341	−	0.909261i	−0.414571	−	0.111084i	−0.460075	+	0.887880i	$0.652177\pi$
$68$	1.93133	+	7.20783i	0.234208	+	0.874078i
$69$	1.90296	+	0.0789157i	0.229090	+	0.00950033i
$70$	2.70080	+	5.26362i	0.322807	+	0.629123i
$71$			5.89777i			0.699937i	0.936761	+	0.349969i	$0.113808\pi$
$71$			5.89777i			0.699937i	−0.936761	+	0.349969i	$0.886192\pi$
$72$	−2.95212	+	0.533863i	−0.347910	+	0.0629163i
$73$	1.44294	−	5.38514i	0.168884	−	0.630283i	−0.828629	−	0.559798i	$-0.810879\pi$
$73$	1.44294	−	5.38514i	0.168884	−	0.630283i	0.997513	−	0.0704850i	$-0.0224547\pi$
$74$	2.76424	+	4.78780i	0.321336	+	0.556570i
$75$	−1.77808	−	8.47576i	−0.205315	−	0.978696i
$76$	−2.45236			−0.281305
$77$	−5.00240	−	9.58854i	−0.570076	−	1.09272i
$78$	6.66214	−	6.13159i	0.754339	−	0.694266i
$79$	8.18814	+	4.72742i	0.921238	+	0.531877i	0.884030	−	0.467431i	$-0.154820\pi$
$79$	8.18814	+	4.72742i	0.921238	+	0.531877i	0.0372080	+	0.999308i	$0.488154\pi$
$80$	−0.593376	+	2.15590i	−0.0663415	+	0.241037i
$81$	3.15205	+	8.42998i	0.350228	+	0.936665i
$82$	−1.74516	−	6.51303i	−0.192721	−	0.719243i
$83$	−6.31379	+	6.31379i	−0.693029	+	0.693029i	−0.962897	−	0.269868i	$-0.913020\pi$
$83$	−6.31379	+	6.31379i	−0.693029	+	0.693029i	0.269868	+	0.962897i	$0.413020\pi$
$84$	−4.51048	+	0.809665i	−0.492134	+	0.0883417i
$85$	0.113194	−	16.6854i	0.0122776	−	1.80978i
$86$	1.55973	+	0.900511i	0.168190	+	0.0971046i
$87$	−0.769989	+	2.46085i	−0.0825515	+	0.263831i
$88$	1.05797	−	3.94840i	0.112780	−	0.420901i
$89$	6.71062	−	11.6231i	0.711325	−	1.23205i	−0.253035	−	0.967457i	$-0.581429\pi$
$89$	6.71062	−	11.6231i	0.711325	−	1.23205i	0.964360	−	0.264594i	$-0.0852378\pi$
$90$	6.68125	+	0.600760i	0.704265	+	0.0633257i
$91$	10.1887	−	9.35301i	1.06806	−	0.980461i
$92$	0.777550	+	0.777550i	0.0810651	+	0.0810651i
$93$	8.86304	−	1.98524i	0.919055	−	0.205859i
$94$	2.66651	−	1.53951i	0.275029	−	0.158788i
$95$	5.28704	+	1.45517i	0.542439	+	0.149297i
$96$	−1.46283	−	0.927433i	−0.149299	−	0.0946557i
$97$	−5.21514	+	5.21514i	−0.529518	+	0.529518i	−0.920429	−	0.390911i	$-0.872160\pi$
$97$	−5.21514	+	5.21514i	−0.529518	+	0.529518i	0.390911	+	0.920429i	$0.372160\pi$
$98$	−6.89147	+	1.22788i	−0.696143	+	0.124035i
$99$	−12.2209	−	1.01535i	−1.22825	−	0.102046i
$100$	2.55852	−	4.29581i	0.255852	−	0.429581i
$101$	2.56058	−	1.47835i	0.254787	−	0.147101i	−0.367167	−	0.930155i	$-0.619672\pi$
$101$	2.56058	−	1.47835i	0.254787	−	0.147101i	0.621954	+	0.783054i	$0.286339\pi$
$102$	12.3350	+	3.85957i	1.22135	+	0.382155i
$103$	−10.0129	+	2.68295i	−0.986601	+	0.264359i	−0.715822	−	0.698283i	$-0.753948\pi$
$103$	−10.0129	+	2.68295i	−0.986601	+	0.264359i	−0.270779	+	0.962642i	$0.587281\pi$
$104$	5.22751			0.512599
$105$	10.2046	+	0.930855i	0.995865	+	0.0908421i
$106$	−5.70059			−0.553690
$107$	−1.22978	+	0.329519i	−0.118887	+	0.0318558i	−0.317772	−	0.948167i	$-0.602935\pi$
$107$	−1.22978	+	0.329519i	−0.118887	+	0.0318558i	0.198885	+	0.980023i	$0.436268\pi$
$108$	−1.95694	+	4.81356i	−0.188307	+	0.463185i
$109$	−2.57800	+	1.48841i	−0.246927	+	0.142564i	−0.618356	−	0.785898i	$-0.712201\pi$
$109$	−2.57800	+	1.48841i	−0.246927	+	0.142564i	0.371429	+	0.928461i	$0.378868\pi$
$110$	−4.62376	+	7.88458i	−0.440859	+	0.751765i
$111$	9.56737	+	0.396758i	0.908095	+	0.0376586i
$112$	−2.23268	−	1.41956i	−0.210968	−	0.134136i
$113$	−2.76230	+	2.76230i	−0.259856	+	0.259856i	−0.824995	−	0.565140i	$-0.808822\pi$
$113$	−2.76230	+	2.76230i	−0.259856	+	0.259856i	0.565140	+	0.824995i	$0.308822\pi$
$114$	−2.27440	+	3.58738i	−0.213017	+	0.335989i
$115$	−1.21494	−	2.13770i	−0.113294	−	0.199341i
$116$	−1.28925	+	0.744349i	−0.119704	+	0.0691110i
$117$	−2.79077	−	15.4322i	−0.258007	−	1.42671i
$118$	−7.20025	−	7.20025i	−0.662836	−	0.662836i
$119$	18.8344	+	5.91992i	1.72655	+	0.542678i
$120$	2.60340	+	2.86746i	0.237656	+	0.261762i
$121$	2.85458	−	4.94428i	0.259507	−	0.449480i
$122$	−0.421838	+	1.57432i	−0.0381914	+	0.142532i
$123$	−11.1460	−	3.48753i	−1.00500	−	0.314460i
$124$	4.54133	+	2.62194i	0.407823	+	0.235457i
$125$	−8.06494	+	7.74317i	−0.721350	+	0.692570i
$126$	−2.99877	+	7.34897i	−0.267152	+	0.654698i
$127$	5.50671	−	5.50671i	0.488642	−	0.488642i	−0.419236	−	0.907877i	$-0.637702\pi$
$127$	5.50671	−	5.50671i	0.488642	−	0.488642i	0.907877	+	0.419236i	$0.137702\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	2.76384	−	1.44646i	0.243343	−	0.127353i
$130$	−11.2700	−	3.10188i	−0.988443	−	0.272053i
$131$	−12.5406	−	7.24030i	−1.09567	−	0.632588i	−0.160593	−	0.987021i	$-0.551341\pi$
$131$	−12.5406	−	7.24030i	−1.09567	−	0.632588i	−0.935082	+	0.354433i	$0.884674\pi$
$132$	−4.79464	−	5.20951i	−0.417320	−	0.453429i
$133$	−3.48127	+	5.47532i	−0.301865	+	0.474771i
$134$	−3.51312			−0.303487
$135$	7.07522	−	9.21636i	0.608938	−	0.793218i
$136$	3.73105	+	6.46236i	0.319935	+	0.554143i
$137$	3.10449	−	11.5861i	0.265234	−	0.989868i	−0.696872	−	0.717195i	$-0.745426\pi$
$137$	3.10449	−	11.5861i	0.265234	−	0.989868i	0.962107	−	0.272673i	$-0.0879078\pi$
$138$	1.85855	−	0.416297i	0.158210	−	0.0354375i
$139$		−	7.25394i		−	0.615271i	−0.951504	−	0.307636i	$-0.900462\pi$
$139$		−	7.25394i		−	0.615271i	0.951504	−	0.307636i	$-0.0995378\pi$
$140$	3.97109	+	4.38525i	0.335619	+	0.370621i
$141$	0.220970	−	5.32844i	0.0186090	−	0.448735i
$142$	1.52646	+	5.69681i	0.128097	+	0.478066i
$143$	20.6403	+	5.53055i	1.72603	+	0.462488i
$144$	−2.71335	+	1.27974i	−0.226113	+	0.106645i
$145$	3.22117	−	0.839731i	0.267504	−	0.0697359i
$146$		−	5.57511i		−	0.461399i
$147$	−4.59519	+	11.2198i	−0.379005	+	0.925395i
$148$	3.90922	+	3.90922i	0.321336	+	0.321336i
$149$	−5.71976	+	9.90691i	−0.468581	+	0.811606i	−0.999355	−	0.0359074i	$-0.988568\pi$
$149$	−5.71976	+	9.90691i	−0.468581	+	0.811606i	0.530774	+	0.847513i	$0.321901\pi$
$150$	−3.91118	−	7.72675i	−0.319346	−	0.630887i
$151$	−6.75854	−	11.7061i	−0.550002	−	0.952632i	−0.998274	−	0.0587343i	$-0.981294\pi$
$151$	−6.75854	−	11.7061i	−0.550002	−	0.952632i	0.448271	−	0.893897i	$-0.352040\pi$
$152$	−2.36880	+	0.634717i	−0.192135	+	0.0514824i
$153$	17.0858	−	14.4645i	1.38130	−	1.16939i
$154$	−7.31365	−	7.96710i	−0.589350	−	0.642008i
$155$	−8.23486	−	8.34735i	−0.661440	−	0.670475i
$156$	4.84816	−	7.64695i	0.388164	−	0.612246i
$157$	−9.60302	−	2.57312i	−0.766405	−	0.205358i	−0.145622	−	0.989340i	$-0.546518\pi$
$157$	−9.60302	−	2.57312i	−0.766405	−	0.205358i	−0.620783	+	0.783983i	$0.713185\pi$
$158$	9.13268	+	2.44710i	0.726557	+	0.194680i
$159$	−5.28691	+	8.33898i	−0.419280	+	0.661324i
$160$	−0.0151692	+	2.23602i	−0.00119923	+	0.176773i
$161$	2.83980	−	0.632237i	0.223807	−	0.0498272i
$162$	5.22649	+	7.32693i	0.410632	+	0.575658i
$163$	−11.2223	+	3.00701i	−0.879000	+	0.235527i	−0.669976	−	0.742383i	$-0.733695\pi$
$163$	−11.2223	+	3.00701i	−0.879000	+	0.235527i	−0.209024	+	0.977910i	$0.567029\pi$
$164$	−3.37139	−	5.83942i	−0.263261	−	0.455982i
$165$	7.24556	+	14.0762i	0.564066	+	1.09583i
$166$	−4.46453	+	7.73279i	−0.346514	+	0.600181i
$167$	15.6944	+	15.6944i	1.21447	+	1.21447i	0.969541	+	0.244931i	$0.0787652\pi$
$167$	15.6944	+	15.6944i	1.21447	+	1.21447i	0.244931	+	0.969541i	$0.421235\pi$
$168$	−4.14723	+	1.94947i	−0.319966	+	0.150405i
$169$			14.3268i			1.10206i
$170$	−4.20915	−	16.1461i	−0.322827	−	1.23835i
$171$	3.13837	+	6.65411i	0.239997	+	0.508853i
$172$	1.73965	+	0.466139i	0.132647	+	0.0355428i
$173$	0.282653	+	1.05488i	0.0214897	+	0.0802007i	0.975838	−	0.218496i	$-0.0701149\pi$
$173$	0.282653	+	1.05488i	0.0214897	+	0.0802007i	−0.954348	+	0.298696i	$0.903448\pi$
$174$	−0.106838	+	2.57629i	−0.00809938	+	0.195308i
$175$	−5.95918	−	11.8105i	−0.450472	−	0.892791i
$176$		−	4.08768i		−	0.308121i
$177$	−17.2105	+	3.85498i	−1.29362	+	0.289758i
$178$	3.47367	−	12.9639i	0.260363	−	0.971688i
$179$	2.65439	+	4.59754i	0.198399	+	0.343637i	0.948009	−	0.318242i	$-0.103093\pi$
$179$	2.65439	+	4.59754i	0.198399	+	0.343637i	−0.749611	+	0.661879i	$0.769759\pi$
$180$	6.60908	−	1.14894i	0.492612	−	0.0856373i
$181$	−13.7484			−1.02191			−0.510957	−	0.859607i	$-0.670709\pi$
$181$	−13.7484			−1.02191			−0.510957	+	0.859607i	$0.670709\pi$
$182$	7.42077	−	11.6713i	0.550064	−	0.865137i
$183$	1.91174	+	2.07716i	0.141320	+	0.153548i
$184$	0.952300	+	0.549811i	0.0702045	+	0.0405326i
$185$	−6.10825	−	10.7475i	−0.449088	−	0.790174i
$186$	8.04722	−	4.21151i	0.590051	−	0.308803i
$187$	7.89468	+	29.4633i	0.577316	+	2.15457i
$188$	2.17720	−	2.17720i	0.158788	−	0.158788i
$189$	7.96913	+	11.2024i	0.579669	+	0.814852i
$190$	5.48351	+	0.0372003i	0.397816	+	0.00269880i
$191$	1.45963	+	0.842720i	0.105615	+	0.0609771i	0.551877	−	0.833925i	$-0.313912\pi$
$191$	1.45963	+	0.842720i	0.105615	+	0.0609771i	−0.446262	+	0.894902i	$0.647245\pi$
$192$	−1.65302	−	0.517224i	−0.119297	−	0.0373274i
$193$	0.881131	−	3.28843i	0.0634252	−	0.236706i	−0.926935	−	0.375222i	$-0.877567\pi$
$193$	0.881131	−	3.28843i	0.0634252	−	0.236706i	0.990360	+	0.138516i	$0.0442332\pi$
$194$	−3.68766	+	6.38722i	−0.264759	+	0.458576i
$195$	−14.9897	+	13.6093i	−1.07343	+	0.974580i
$196$	−6.33884	+	2.96969i	−0.452775	+	0.212121i
$197$	11.9821	+	11.9821i	0.853688	+	0.853688i	0.990585	−	0.136897i	$-0.0437130\pi$
$197$	11.9821	+	11.9821i	0.853688	+	0.853688i	−0.136897	+	0.990585i	$0.543713\pi$
$198$	−12.0673	+	2.18226i	−0.857587	+	0.155087i
$199$	3.65684	−	2.11128i	0.259226	−	0.149664i	−0.364755	−	0.931103i	$-0.618847\pi$
$199$	3.65684	−	2.11128i	0.259226	−	0.149664i	0.623982	+	0.781439i	$0.285514\pi$
$200$	1.35950	−	4.81163i	0.0961313	−	0.340233i
$201$	−3.25818	+	5.13909i	−0.229814	+	0.362483i
$202$	2.09070	−	2.09070i	0.147101	−	0.147101i
$203$	−0.168280	+	3.93513i	−0.0118109	+	0.276192i
$204$	12.9136	+	0.535527i	0.904135	+	0.0374944i
$205$	3.80341	+	14.5897i	0.265642	+	1.01899i
$206$	−8.97733	+	5.18306i	−0.625480	+	0.361121i
$207$	1.11471	−	3.10482i	0.0774775	−	0.215800i
$208$	5.04938	−	1.35298i	0.350112	−	0.0938122i
$209$	−10.0245			−0.693407
$210$	10.0978	−	1.74200i	0.696814	−	0.120210i
$211$	−1.74688			−0.120260			−0.0601302	−	0.998191i	$-0.519152\pi$
$211$	−1.74688			−0.120260			−0.0601302	+	0.998191i	$0.519152\pi$
$212$	−5.50634	+	1.47542i	−0.378177	+	0.101332i
$213$	9.74915	+	3.05047i	0.668001	+	0.209015i
$214$	−1.10259	+	0.636581i	−0.0753715	+	0.0435158i
$215$	−3.47393	−	2.03722i	−0.236920	−	0.138937i
$216$	−0.644418	+	5.15604i	−0.0438471	+	0.350824i
$217$	12.3006	−	6.41732i	0.835021	−	0.435636i
$218$	−2.10493	+	2.10493i	−0.142564	+	0.142564i
$219$	−8.15543	−	5.17054i	−0.551093	−	0.349393i
$220$	−2.42553	+	8.81264i	−0.163529	+	0.594148i
$221$	−33.7821	+	19.5041i	−2.27243	+	1.31199i
$222$	9.34406	−	2.09298i	0.627132	−	0.140472i
$223$	5.26364	+	5.26364i	0.352480	+	0.352480i	0.861031	−	0.508552i	$-0.169819\pi$
$223$	5.26364	+	5.26364i	0.352480	+	0.352480i	−0.508552	+	0.861031i	$0.669819\pi$
$224$	−2.52401	−	0.793332i	−0.168642	−	0.0530067i
$225$	−14.9303	−	1.44466i	−0.995351	−	0.0963106i
$226$	−1.95324	+	3.38312i	−0.129928	+	0.225042i
$227$	1.83391	−	6.84424i	0.121721	−	0.454268i	−0.877981	−	0.478696i	$-0.841110\pi$
$227$	1.83391	−	6.84424i	0.121721	−	0.454268i	0.999702	+	0.0244277i	$0.00777636\pi$
$228$	−1.26842	+	4.05380i	−0.0840030	+	0.268470i
$229$	2.52452	+	1.45753i	0.166825	+	0.0963164i	0.581088	−	0.813841i	$-0.302627\pi$
$229$	2.52452	+	1.45753i	0.166825	+	0.0963164i	−0.414263	+	0.910157i	$0.635961\pi$
$230$	−1.72682	−	1.75041i	−0.113863	−	0.115419i
$231$	−18.4374	+	3.30965i	−1.21309	+	0.217759i
$232$	−1.05267	+	1.05267i	−0.0691110	+	0.0691110i
$233$	7.18782	+	26.8253i	0.470890	+	1.75738i	0.636584	+	0.771207i	$0.280347\pi$
$233$	7.18782	+	26.8253i	0.470890	+	1.75738i	−0.165694	+	0.986177i	$0.552986\pi$
$234$	−6.68983	−	14.1841i	−0.437328	−	0.927241i
$235$	−5.98571	+	3.40192i	−0.390465	+	0.221917i
$236$	−8.81846	−	5.09134i	−0.574033	−	0.331418i
$237$	12.0496	−	11.0900i	0.782708	−	0.720375i
$238$	19.7248	+	0.843503i	1.27857	+	0.0546762i
$239$	6.40772			0.414481			0.207240	−	0.978290i	$-0.433552\pi$
$239$	6.40772			0.414481			0.207240	+	0.978290i	$0.433552\pi$
$240$	3.25684	+	2.09595i	0.210228	+	0.135293i
$241$	6.89013	+	11.9341i	0.443832	+	0.768740i	0.997970	−	0.0636847i	$-0.0202852\pi$
$241$	6.89013	+	11.9341i	0.443832	+	0.768740i	−0.554138	+	0.832425i	$0.686952\pi$
$242$	1.47764	−	5.51463i	0.0949863	−	0.354494i
$243$	15.5653	−	0.850221i	0.998511	−	0.0545417i
$244$			1.62986i			0.104341i
$245$	15.4281	−	2.64103i	0.985662	−	0.168729i
$246$	−11.6688	−	0.483904i	−0.743976	−	0.0308526i
$247$	−3.31799	−	12.3829i	−0.211119	−	0.787905i
$248$	5.06519	+	1.35721i	0.321640	+	0.0861832i
$249$	7.17119	+	13.7025i	0.454456	+	0.868359i
$250$	−5.78605	+	9.56669i	−0.365942	+	0.605051i
$251$		−	15.7442i		−	0.993767i	−0.867817	−	0.496884i	$-0.834478\pi$
$251$		−	15.7442i		−	0.993767i	0.867817	−	0.496884i	$-0.165522\pi$
$252$	−0.994534	+	7.87470i	−0.0626498	+	0.496059i
$253$	3.17838	+	3.17838i	0.199823	+	0.199823i
$254$	3.89384	−	6.74432i	0.244321	−	0.423176i
$255$	−27.5227	−	8.81718i	−1.72354	−	0.552153i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	24.8526	−	6.65924i	1.55026	−	0.415392i	0.620699	−	0.784049i	$-0.286849\pi$
$257$	24.8526	−	6.65924i	1.55026	−	0.415392i	0.929566	+	0.368656i	$0.120182\pi$
$258$	2.29529	−	2.11250i	0.142899	−	0.131519i
$259$	14.2774	−	3.17865i	0.887155	−	0.197511i
$260$	−11.6888	−	0.0792971i	−0.724908	−	0.00491780i
$261$	3.66958	+	2.54562i	0.227141	+	0.157570i
$262$	−13.9872	−	3.74786i	−0.864131	−	0.231543i
$263$	0.882836	+	0.236555i	0.0544380	+	0.0145866i	0.285935	−	0.958249i	$-0.407696\pi$
$263$	0.882836	+	0.236555i	0.0544380	+	0.0145866i	−0.231497	+	0.972836i	$0.574362\pi$
$264$	−5.97958	−	3.79105i	−0.368018	−	0.233323i
$265$	12.7466	+	0.0864734i	0.783018	+	0.00531202i
$266$	−1.94553	+	6.18978i	−0.119288	+	0.379520i
$267$	−15.7424	−	17.1046i	−0.963420	−	1.04678i
$268$	−3.39341	+	0.909261i	−0.207285	+	0.0555420i
$269$	4.05903	+	7.03044i	0.247483	+	0.428654i	0.962827	−	0.270119i	$-0.0870631\pi$
$269$	4.05903	+	7.03044i	0.247483	+	0.428654i	−0.715344	+	0.698773i	$0.753730\pi$
$270$	4.44877	−	10.7335i	0.270743	−	0.653221i
$271$	−0.143382	+	0.248344i	−0.00870982	+	0.0150858i	−0.870347	−	0.492438i	$-0.836106\pi$
$271$	−0.143382	+	0.248344i	−0.00870982	+	0.0150858i	0.861638	+	0.507524i	$0.169439\pi$
$272$	5.27650	+	5.27650i	0.319935	+	0.319935i
$273$	−10.1909	−	21.6797i	−0.616781	−	1.31211i
$274$		−	11.9948i		−	0.724634i
$275$	10.4584	−	17.5599i	0.630666	−	1.05890i
$276$	1.68747	−	0.883139i	0.101574	−	0.0531587i
$277$	−31.0992	−	8.33301i	−1.86857	−	0.500682i	−0.999987	−	0.00514027i	$-0.998364\pi$
$277$	−31.0992	−	8.33301i	−1.86857	−	0.500682i	−0.868584	−	0.495542i	$-0.834970\pi$
$278$	−1.87746	−	7.00677i	−0.112602	−	0.420238i
$279$	1.30254	−	15.6776i	0.0779808	−	0.938594i
$280$	4.97077	+	3.20803i	0.297060	+	0.191717i
$281$			6.43714i			0.384007i	0.981394	+	0.192004i	$0.0614986\pi$
$281$			6.43714i			0.384007i	−0.981394	+	0.192004i	$0.938501\pi$
$282$	−1.16566	−	5.20407i	−0.0694141	−	0.309898i
$283$	−0.508211	+	1.89667i	−0.0302100	+	0.112745i	−0.979384	−	0.202005i	$-0.935254\pi$
$283$	−0.508211	+	1.89667i	−0.0302100	+	0.112745i	0.949174	+	0.314751i	$0.101921\pi$
$284$	2.94889	+	5.10762i	0.174984	+	0.303082i
$285$	5.14001	−	7.98694i	0.304468	−	0.473106i
$286$	21.3684			1.26354
$287$	−17.8234	−	0.762193i	−1.05208	−	0.0449908i
$288$	−2.28968	+	1.93840i	−0.134920	+	0.114221i
$289$	−33.5003	−	19.3414i	−1.97061	−	1.13773i
$290$	2.89407	−	1.64482i	0.169946	−	0.0965871i
$291$	5.92335	+	11.3181i	0.347233	+	0.663481i
$292$	−1.44294	−	5.38514i	−0.0844419	−	0.315142i
$293$	−1.37301	+	1.37301i	−0.0802121	+	0.0802121i	−0.746075	−	0.665862i	$-0.768064\pi$
$293$	−1.37301	+	1.37301i	−0.0802121	+	0.0802121i	0.665862	+	0.746075i	$0.268064\pi$
$294$	−1.53471	+	12.0268i	−0.0895060	+	0.701419i
$295$	15.9906	+	16.2091i	0.931011	+	0.943730i
$296$	4.78780	+	2.76424i	0.278285	+	0.160668i
$297$	−7.99936	+	19.6763i	−0.464170	+	1.14174i
$298$	−2.96076	+	11.0497i	−0.171512	+	0.640093i
$299$	−2.87414	+	4.97815i	−0.166216	+	0.287894i
$300$	−5.77774	−	6.45118i	−0.333578	−	0.372459i
$301$	3.51028	−	3.22237i	0.202329	−	0.185734i
$302$	−9.55802	−	9.55802i	−0.550002	−	0.550002i
$303$	−1.11935	−	4.99733i	−0.0643052	−	0.287089i
$304$	−2.12380	+	1.22618i	−0.121809	+	0.0703262i
$305$	0.967119	−	3.51381i	0.0553770	−	0.201200i
$306$	12.7599	−	18.3938i	0.729436	−	1.05150i
$307$	10.0236	−	10.0236i	0.572077	−	0.572077i	−0.360631	−	0.932708i	$-0.617439\pi$
$307$	10.0236	−	10.0236i	0.572077	−	0.572077i	0.932708	+	0.360631i	$0.117439\pi$
$308$	−9.12648	−	5.80272i	−0.520029	−	0.330641i
$309$	−0.743938	+	17.9392i	−0.0423212	+	1.02053i
$310$	−10.1147	−	5.93158i	−0.574477	−	0.336891i
$311$	3.26860	−	1.88713i	0.185345	−	0.107009i	−0.404456	−	0.914557i	$-0.632539\pi$
$311$	3.26860	−	1.88713i	0.185345	−	0.107009i	0.589802	+	0.807548i	$0.299206\pi$
$312$	2.70379	−	8.64118i	0.153072	−	0.489211i
$313$	26.1427	−	7.00492i	1.47767	−	0.395941i	0.572119	−	0.820171i	$-0.306122\pi$
$313$	26.1427	−	7.00492i	1.47767	−	0.395941i	0.905555	+	0.424229i	$0.139455\pi$
$314$	−9.94178			−0.561047
$315$	6.81677	−	16.3869i	0.384082	−	0.923299i
$316$	9.45485			0.531877
$317$	−20.5304	+	5.50111i	−1.15310	+	0.308973i	−0.784208	−	0.620498i	$-0.786931\pi$
$317$	−20.5304	+	5.50111i	−1.15310	+	0.308973i	−0.368895	+	0.929471i	$0.620264\pi$
$318$	−2.94848	+	9.42319i	−0.165342	+	0.528426i
$319$	−5.27005	+	3.04266i	−0.295066	+	0.170356i
$320$	0.564071	+	2.16375i	0.0315325	+	0.120957i
$321$	−0.0913700	+	2.20329i	−0.00509978	+	0.122976i
$322$	2.57940	−	1.34569i	0.143744	−	0.0749922i
$323$	12.9399	−	12.9399i	0.719993	−	0.719993i
$324$	6.94475	+	5.72455i	0.385819	+	0.318031i
$325$	25.1528	+	7.10681i	1.39523	+	0.394215i
$326$	−10.0617	+	5.80910i	−0.557264	+	0.321736i
$327$	1.12697	+	5.03132i	0.0623215	+	0.278233i
$328$	−4.76787	−	4.76787i	−0.263261	−	0.263261i
$329$	−1.77031	−	7.95164i	−0.0976003	−	0.438388i
$330$	10.6419	+	11.7213i	0.585815	+	0.645235i
$331$	2.05157	−	3.55342i	0.112764	−	0.195313i	−0.804120	−	0.594468i	$-0.797363\pi$
$331$	2.05157	−	3.55342i	0.112764	−	0.195313i	0.916884	+	0.399154i	$0.130696\pi$
$332$	−2.31101	+	8.62480i	−0.126833	+	0.473348i
$333$	5.60432	−	15.6099i	0.307115	−	0.855415i
$334$	19.2217	+	11.0976i	1.05176	+	0.607236i
$335$	7.85539	+	0.0532912i	0.429186	+	0.00291161i
$336$	−3.50136	+	2.95643i	−0.191015	+	0.161287i
$337$	11.5744	−	11.5744i	0.630498	−	0.630498i	−0.317695	−	0.948193i	$-0.602909\pi$
$337$	11.5744	−	11.5744i	0.630498	−	0.630498i	0.948193	+	0.317695i	$0.102909\pi$
$338$	3.70806	+	13.8387i	0.201692	+	0.752724i
$339$	3.13742	+	5.99488i	0.170401	+	0.325597i
$340$	−8.24466	−	14.5065i	−0.447129	−	0.786728i
$341$	18.5635	+	10.7177i	1.00527	+	0.580393i
$342$	4.75364	+	5.61511i	0.257048	+	0.303630i
$343$	−2.36803	+	18.3682i	−0.127862	+	0.991792i
$344$	1.80102			0.0971046
$345$	−4.16206	+	0.902653i	−0.224078	+	0.0485972i
$346$	0.546044	+	0.945776i	0.0293555	+	0.0508452i
$347$	8.09375	−	30.2063i	0.434495	−	1.62156i	−0.307776	−	0.951459i	$-0.599585\pi$
$347$	8.09375	−	30.2063i	0.434495	−	1.62156i	0.742272	−	0.670099i	$-0.233748\pi$
$348$	0.563594	+	2.51615i	0.0302118	+	0.134880i
$349$		−	26.4465i		−	1.41565i	−0.706387	−	0.707826i	$-0.749676\pi$
$349$		−	26.4465i		−	1.41565i	0.706387	−	0.707826i	$-0.250324\pi$
$350$	−8.81291	−	9.86573i	−0.471070	−	0.527345i
$351$	−26.9532	−	3.36870i	−1.43866	−	0.179808i
$352$	−1.05797	−	3.94840i	−0.0563900	−	0.210450i
$353$	−19.2319	−	5.15317i	−1.02361	−	0.274276i	−0.292305	−	0.956325i	$-0.594422\pi$
$353$	−19.2319	−	5.15317i	−1.02361	−	0.274276i	−0.731306	+	0.682049i	$0.761089\pi$
$354$	−15.6263	+	8.17802i	−0.830528	+	0.434657i
$355$	−3.32677	−	12.7613i	−0.176566	−	0.677301i
$356$		−	13.4212i		−	0.711325i
$357$	19.5274	−	28.0717i	1.03350	−	1.48571i
$358$	3.75388	+	3.75388i	0.198399	+	0.198399i
$359$	14.1219	−	24.4599i	0.745327	−	1.29094i	−0.204715	−	0.978822i	$-0.565627\pi$
$359$	14.1219	−	24.4599i	0.745327	−	1.29094i	0.950042	−	0.312122i	$-0.101040\pi$
$360$	6.08651	−	2.82035i	0.320787	−	0.148646i
$361$	−6.49297	−	11.2462i	−0.341735	−	0.591903i
$362$	−13.2800	+	3.55836i	−0.697980	+	0.187023i
$363$	−6.69655	−	7.27599i	−0.351478	−	0.381890i
$364$	4.14715	−	13.1943i	0.217370	−	0.691568i
$365$	−0.0845700	+	12.4660i	−0.00442660	+	0.652502i
$366$	2.38420	+	1.51158i	0.124624	+	0.0790118i
$367$	21.1687	+	5.67214i	1.10500	+	0.296084i	0.764799	−	0.644269i	$-0.222838\pi$
$367$	21.1687	+	5.67214i	1.10500	+	0.296084i	0.340200	+	0.940353i	$0.389505\pi$
$368$	1.06215	+	0.284603i	0.0553685	+	0.0148360i
$369$	−11.5299	+	16.6207i	−0.600223	+	0.865238i
$370$	−8.68178	−	8.80038i	−0.451344	−	0.457510i
$371$	−4.52246	+	14.3883i	−0.234794	+	0.747005i
$372$	6.68300	−	6.15079i	0.346497	−	0.318903i
$373$	3.95292	−	1.05918i	0.204674	−	0.0548423i	−0.155025	−	0.987911i	$-0.549546\pi$
$373$	3.95292	−	1.05918i	0.204674	−	0.0548423i	0.359700	+	0.933068i	$0.382879\pi$
$374$	15.2513	+	26.4161i	0.788628	+	1.36594i
$375$	8.62825	+	17.3365i	0.445561	+	0.895252i
$376$	1.53951	−	2.66651i	0.0793942	−	0.137515i
$377$	−5.50283	−	5.50283i	−0.283410	−	0.283410i
$378$	10.5970	+	8.75809i	0.545050	+	0.450468i
$379$			12.0806i			0.620537i	0.950649	+	0.310269i	$0.100419\pi$
$379$			12.0806i			0.620537i	−0.950649	+	0.310269i	$0.899581\pi$
$380$	5.30630	−	1.38331i	0.272207	−	0.0709621i
$381$	−6.25451	−	11.9509i	−0.320428	−	0.612264i
$382$	1.62801	+	0.436224i	0.0832962	+	0.0223192i
$383$	−8.40909	−	31.3832i	−0.429684	−	1.60360i	−0.753476	−	0.657476i	$-0.771624\pi$
$383$	−8.40909	−	31.3832i	−0.429684	−	1.60360i	0.323791	−	0.946129i	$-0.395042\pi$
$384$	−1.73056	−	0.0717662i	−0.0883124	−	0.00366231i
$385$	16.2326	+	17.9255i	0.827289	+	0.913569i
$386$		−	3.40443i		−	0.173281i
$387$	−0.961499	−	5.31683i	−0.0488757	−	0.270270i
$388$	−1.90888	+	7.12402i	−0.0969085	+	0.361667i
$389$	0.0153183	+	0.0265320i	0.000776666	+	0.00134523i	0.866413	−	0.499327i	$-0.166419\pi$
$389$	0.0153183	+	0.0265320i	0.000776666	+	0.00134523i	−0.865637	+	0.500672i	$0.833086\pi$
$390$	−10.9566	+	17.0252i	−0.554808	+	0.862103i
$391$	−8.20548			−0.414969
$392$	−5.35424	+	4.50911i	−0.270430	+	0.227745i
$393$	−18.4546	+	16.9850i	−0.930914	+	0.856779i
$394$	14.6750	+	8.47261i	0.739316	+	0.426844i
$395$	−20.3837	−	5.61028i	−1.02562	−	0.282284i
$396$	−11.0913	+	5.23116i	−0.557360	+	0.262875i
$397$	5.93984	+	22.1678i	0.298112	+	1.11257i	0.938714	+	0.344696i	$0.112018\pi$
$397$	5.93984	+	22.1678i	0.298112	+	1.11257i	−0.640603	+	0.767873i	$0.721315\pi$
$398$	2.98580	−	2.98580i	0.149664	−	0.149664i
$399$	7.25023	+	8.58659i	0.362965	+	0.429867i
$400$	0.0678372	−	4.99954i	0.00339186	−	0.249977i
$401$	14.5458	+	8.39801i	0.726382	+	0.419377i	0.817097	−	0.576500i	$-0.195582\pi$
$401$	14.5458	+	8.39801i	0.726382	+	0.419377i	−0.0907151	+	0.995877i	$0.528915\pi$
$402$	−1.81707	+	5.80726i	−0.0906270	+	0.289640i
$403$	−7.09485	+	26.4783i	−0.353420	+	1.31898i
$404$	1.47835	−	2.56058i	0.0735507	−	0.127393i
$405$	−11.5754	−	16.4624i	−0.575185	−	0.818024i
$406$	0.855940	+	3.84459i	0.0424796	+	0.190804i
$407$	15.9797	+	15.9797i	0.792083	+	0.792083i
$408$	12.6122	−	2.82501i	0.624398	−	0.139859i
$409$	−24.6188	+	14.2137i	−1.21732	+	0.702822i	−0.964345	−	0.264650i	$-0.914744\pi$
$409$	−24.6188	+	14.2137i	−1.21732	+	0.702822i	−0.252979	+	0.967472i	$0.581410\pi$
$410$	7.44991	+	13.1082i	0.367925	+	0.647367i
$411$	−17.5464	−	11.1244i	−0.865499	−	0.548726i
$412$	−7.32996	+	7.32996i	−0.361121	+	0.361121i
$413$	−23.8857	+	12.4613i	−1.17534	+	0.613181i
$414$	0.273137	−	3.28754i	0.0134240	−	0.161574i
$415$	10.1001	−	17.2229i	0.495792	−	0.845440i
$416$	4.52715	−	2.61375i	0.221962	−	0.128150i
$417$	−11.9909	−	3.75191i	−0.587198	−	0.183732i
$418$	−9.68289	+	2.59452i	−0.473606	+	0.126902i
$419$	−20.1095			−0.982415			−0.491207	−	0.871043i	$-0.663444\pi$
$419$	−20.1095			−0.982415			−0.491207	+	0.871043i	$0.663444\pi$
$420$	9.30286	−	4.29615i	0.453933	−	0.209631i
$421$	0.466628			0.0227420			0.0113710	−	0.999935i	$-0.496380\pi$
$421$	0.466628			0.0227420			0.0113710	+	0.999935i	$0.496380\pi$
$422$	−1.68736	+	0.452127i	−0.0821394	+	0.0220092i
$423$	−8.69373	−	3.12126i	−0.422704	−	0.151761i
$424$	−4.93685	+	2.85029i	−0.239755	+	0.138422i
$425$	9.16681	+	36.1669i	0.444656	+	1.75435i
$426$	10.2065	+	0.423261i	0.494505	+	0.0205071i
$427$	3.63895	+	2.31368i	0.176101	+	0.111967i
$428$	−0.900261	+	0.900261i	−0.0435158	+	0.0435158i
$429$	19.8178	−	31.2583i	0.956811	−	1.50917i
$430$	−3.88282	−	1.06868i	−0.187246	−	0.0515365i
$431$	12.1781	−	7.03102i	0.586598	−	0.338672i	−0.177153	−	0.984183i	$-0.556689\pi$
$431$	12.1781	−	7.03102i	0.586598	−	0.338672i	0.763751	+	0.645511i	$0.223355\pi$
$432$	0.712021	+	5.14714i	0.0342571	+	0.247642i
$433$	−7.91330	−	7.91330i	−0.380289	−	0.380289i	0.490917	−	0.871206i	$-0.336662\pi$
$433$	−7.91330	−	7.91330i	−0.380289	−	0.380289i	−0.871206	+	0.490917i	$0.836662\pi$
$434$	10.2206	−	9.38229i	0.490603	−	0.450364i
$435$	0.277972	−	5.75900i	0.0133277	−	0.276123i
$436$	−1.48841	+	2.57800i	−0.0712818	+	0.123464i
$437$	0.697948	−	2.60478i	0.0333874	−	0.124603i
$438$	−9.21578	−	2.88358i	−0.440347	−	0.137783i
$439$	1.69708	+	0.979808i	0.0809971	+	0.0467637i	0.539952	−	0.841696i	$-0.318443\pi$
$439$	1.69708	+	0.979808i	0.0809971	+	0.0467637i	−0.458954	+	0.888460i	$0.651776\pi$
$440$	−0.0620069	+	9.14013i	−0.00295606	+	0.435739i
$441$	16.1699	+	13.3991i	0.769993	+	0.638052i
$442$	−27.5829	+	27.5829i	−1.31199	+	1.31199i
$443$	6.63929	+	24.7782i	0.315442	+	1.17725i	0.923577	+	0.383413i	$0.125251\pi$
$443$	6.63929	+	24.7782i	0.315442	+	1.17725i	−0.608135	+	0.793834i	$0.708082\pi$
$444$	8.48397	−	4.44008i	0.402631	−	0.210717i
$445$	−7.96385	+	28.9349i	−0.377523	+	1.37164i
$446$	6.44662	+	3.72196i	0.305256	+	0.176240i
$447$	13.4179	+	14.5790i	0.634647	+	0.689562i
$448$	−2.64334	−	0.113038i	−0.124886	−	0.00534056i
$449$	4.51616			0.213131			0.106565	−	0.994306i	$-0.466015\pi$
$449$	4.51616			0.213131			0.106565	+	0.994306i	$0.466015\pi$
$450$	−14.7954	+	2.46880i	−0.697464	+	0.116381i
$451$	−13.7812	−	23.8697i	−0.648930	−	1.12398i
$452$	−1.01107	+	3.77338i	−0.0475569	+	0.177485i
$453$	−22.8462	+	5.11732i	−1.07341	+	0.240433i
$454$		−	7.08568i		−	0.332547i
$455$	−16.7700	+	25.9847i	−0.786190	+	1.21818i
$456$	−0.175997	+	4.24396i	−0.00824179	+	0.198742i
$457$	7.48257	+	27.9253i	0.350020	+	1.30629i	0.886637	+	0.462466i	$0.153035\pi$
$457$	7.48257	+	27.9253i	0.350020	+	1.30629i	−0.536617	+	0.843826i	$0.680298\pi$
$458$	2.81574	+	0.754474i	0.131571	+	0.0352543i
$459$	−15.0730	−	35.7245i	−0.703546	−	1.66748i
$460$	−2.12102	−	1.24383i	−0.0988930	−	0.0579939i
$461$		−	28.5763i		−	1.33093i	−0.746428	−	0.665466i	$-0.768233\pi$
$461$		−	28.5763i		−	1.33093i	0.746428	−	0.665466i	$-0.231767\pi$
$462$	−16.9526	+	7.96884i	−0.788706	+	0.370744i
$463$	−26.2518	−	26.2518i	−1.22002	−	1.22002i	−0.967623	−	0.252401i	$-0.918780\pi$
$463$	−26.2518	−	26.2518i	−1.22002	−	1.22002i	−0.252401	−	0.967623i	$-0.581220\pi$
$464$	−0.744349	+	1.28925i	−0.0345555	+	0.0598519i
$465$	−18.0576	+	9.29495i	−0.837402	+	0.431043i
$466$	13.8858	+	24.0509i	0.643247	+	1.11414i
$467$	−30.0950	+	8.06394i	−1.39263	+	0.373154i	−0.875693	−	0.482868i	$-0.839595\pi$
$467$	−30.0950	+	8.06394i	−1.39263	+	0.373154i	−0.516938	+	0.856023i	$0.672928\pi$
$468$	−10.1330	−	11.9693i	−0.468397	−	0.553281i
$469$	−2.78707	+	8.86714i	−0.128695	+	0.409446i
$470$	−4.90127	+	4.83522i	−0.226079	+	0.223032i
$471$	−9.22034	+	14.5431i	−0.424851	+	0.670112i
$472$	−9.83572	−	2.63547i	−0.452726	−	0.121307i
$473$	7.11116	+	1.90543i	0.326971	+	0.0876117i
$474$	8.76874	−	13.8308i	0.402762	−	0.635271i
$475$	−12.2607	−	0.166361i	−0.562558	−	0.00763317i
$476$	19.2710	−	4.29040i	0.883286	−	0.196650i
$477$	11.0500	+	13.0525i	0.505945	+	0.597633i
$478$	6.18938	−	1.65844i	0.283096	−	0.0758552i
$479$	3.35100	+	5.80410i	0.153111	+	0.265196i	0.932370	−	0.361506i	$-0.117737\pi$
$479$	3.35100	+	5.80410i	0.153111	+	0.265196i	−0.779258	+	0.626703i	$0.784404\pi$
$480$	3.68834	+	1.18160i	0.168349	+	0.0539322i
$481$	−14.4501	+	25.0283i	−0.658867	+	1.14119i
$482$	9.74412	+	9.74412i	0.443832	+	0.443832i
$483$	0.423709	−	5.02125i	0.0192794	−	0.228475i
$484$		−	5.70916i		−	0.259507i
$485$	8.34257	−	14.2260i	0.378816	−	0.645969i
$486$	14.8148	−	4.84983i	0.672014	−	0.219993i
$487$	6.70741	+	1.79725i	0.303942	+	0.0814409i	0.407567	−	0.913176i	$-0.366377\pi$
$487$	6.70741	+	1.79725i	0.303942	+	0.0814409i	−0.103625	+	0.994616i	$0.533044\pi$
$488$	0.421838	+	1.57432i	0.0190957	+	0.0712662i
$489$	−0.833794	+	20.1060i	−0.0377055	+	0.909226i
$490$	14.2188	−	6.54412i	0.642340	−	0.295633i
$491$		−	18.8686i		−	0.851527i	−0.904835	−	0.425763i	$-0.860006\pi$
$491$		−	18.8686i		−	0.851527i	0.904835	−	0.425763i	$-0.139994\pi$
$492$	−11.3964	+	2.55269i	−0.513792	+	0.115084i
$493$	2.87517	−	10.7303i	0.129491	−	0.483267i
$494$	−6.40986	−	11.1022i	−0.288393	−	0.499512i
$495$	27.0158	−	4.69652i	1.21427	−	0.211093i
$496$	5.24387			0.235457
$497$	15.5898	+	0.666675i	0.699298	+	0.0299045i
$498$	10.4733	+	11.3795i	0.469320	+	0.509929i
$499$	33.7931	+	19.5105i	1.51279	+	0.873408i	0.999888	+	0.0149599i	$0.00476207\pi$
$499$	33.7931	+	19.5105i	1.51279	+	0.873408i	0.512900	+	0.858449i	$0.328571\pi$
$500$	−3.11286	+	10.7383i	−0.139211	+	0.480229i
$501$	34.0608	−	17.8257i	1.52172	−	0.796393i
$502$	−4.07491	−	15.2078i	−0.181872	−	0.678756i
$503$	23.7568	−	23.7568i	1.05926	−	1.05926i	0.0611349	−	0.998130i	$-0.480528\pi$
$503$	23.7568	−	23.7568i	1.05926	−	1.05926i	0.998130	−	0.0611349i	$-0.0194720\pi$
$504$	1.07748	+	7.86378i	0.0479946	+	0.350281i
$505$	−4.70656	+	4.64313i	−0.209439	+	0.206617i
$506$	3.89270	+	2.24745i	0.173052	+	0.0999114i
$507$	23.6826	+	7.41018i	1.05178	+	0.329098i
$508$	2.01560	−	7.52231i	0.0894277	−	0.333749i
$509$	9.24940	−	16.0204i	0.409972	−	0.710093i	−0.584914	−	0.811095i	$-0.698872\pi$
$509$	9.24940	−	16.0204i	0.409972	−	0.710093i	0.994886	+	0.101002i	$0.0322050\pi$
$510$	−28.8670	−	1.39334i	−1.27825	−	0.0616979i
$511$	−14.0716	−	4.42291i	−0.622492	−	0.195658i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	12.6226	−	1.74613i	0.557303	−	0.0770936i
$514$	22.2823	−	12.8647i	0.982829	−	0.567436i
$515$	20.1521	−	11.4532i	0.888007	−	0.504690i
$516$	1.67033	−	2.63459i	0.0735321	−	0.115981i
$517$	8.89969	−	8.89969i	0.391408	−	0.391408i
$518$	12.9682	−	6.76560i	0.569791	−	0.297263i
$519$	1.88993	+	0.0783751i	0.0829586	+	0.00344028i
$520$	−11.3110	+	2.94869i	−0.496022	+	0.129308i
$521$	25.4519	−	14.6946i	1.11507	−	0.643784i	0.174929	−	0.984581i	$-0.444030\pi$
$521$	25.4519	−	14.6946i	1.11507	−	0.643784i	0.940137	+	0.340797i	$0.110697\pi$
$522$	4.20340	+	1.50912i	0.183978	+	0.0660524i
$523$	−19.2076	+	5.14665i	−0.839888	+	0.225047i	−0.653023	−	0.757338i	$-0.726499\pi$
$523$	−19.2076	+	5.14665i	−0.839888	+	0.225047i	−0.186865	+	0.982386i	$0.559833\pi$
$524$	−14.4806			−0.632588
$525$	−22.6053	+	3.74197i	−0.986574	+	0.163313i
$526$	0.913979			0.0398514
$527$	−37.7970	+	10.1277i	−1.64646	+	0.441168i
$528$	−6.75703	−	2.11425i	−0.294062	−	0.0920108i
$529$	18.8714	−	10.8954i	0.820496	−	0.473714i
$530$	12.3347	−	3.21554i	0.535783	−	0.139674i
$531$	−2.52930	+	30.4432i	−0.109762	+	1.32112i
$532$	−0.277211	+	6.48241i	−0.0120186	+	0.281048i
$533$	24.9241	−	24.9241i	1.07958	−	1.07958i
$534$	−19.6330	−	12.4473i	−0.849603	−	0.538648i
$535$	2.47507	−	1.40668i	0.107006	−	0.0608161i
$536$	−3.04245	+	1.75656i	−0.131414	+	0.0758718i
$537$	8.97275	−	2.00981i	0.387203	−	0.0867297i
$538$	5.74033	+	5.74033i	0.247483	+	0.247483i
$539$	−25.9112	+	12.1391i	−1.11607	+	0.522870i
$540$	1.51914	−	11.5192i	0.0653734	−	0.495708i
$541$	8.30525	−	14.3851i	0.357071	−	0.618465i	−0.630399	−	0.776271i	$-0.717109\pi$
$541$	8.30525	−	14.3851i	0.357071	−	0.618465i	0.987470	+	0.157806i	$0.0504422\pi$
$542$	−0.0742198	+	0.276992i	−0.00318801	+	0.0118978i
$543$	−7.11102	+	22.7265i	−0.305163	+	0.975286i
$544$	6.46236	+	3.73105i	0.277072	+	0.159967i
$545$	4.73858	−	4.67472i	0.202978	−	0.200243i
$546$	−15.4548	−	18.3034i	−0.661403	−	0.783312i
$547$	3.70807	−	3.70807i	0.158545	−	0.158545i	−0.623376	−	0.781922i	$-0.714240\pi$
$547$	3.70807	−	3.70807i	0.158545	−	0.158545i	0.781922	+	0.623376i	$0.214240\pi$
$548$	−3.10449	−	11.5861i	−0.132617	−	0.494934i
$549$	4.42238	−	2.08579i	0.188742	−	0.0890192i
$550$	5.55721	−	19.6684i	0.236960	−	0.838664i
$551$	3.16170	+	1.82541i	0.134693	+	0.0777651i
$552$	1.40140	−	1.28980i	0.0596476	−	0.0548974i
$553$	13.4217	−	21.1096i	0.570751	−	0.897672i
$554$	−32.1963			−1.36789
$555$	−20.9252	+	4.53820i	−0.888226	+	0.192636i
$556$	−3.62697	−	6.28210i	−0.153818	−	0.266420i
$557$	−9.75350	+	36.4006i	−0.413269	+	1.54234i	0.375008	+	0.927022i	$0.377640\pi$
$557$	−9.75350	+	36.4006i	−0.413269	+	1.54234i	−0.788277	+	0.615320i	$0.789027\pi$
$558$	−2.79951	−	15.4805i	−0.118513	−	0.655343i
$559$			9.41486i			0.398206i
$560$	5.63169	+	1.81219i	0.237982	+	0.0765791i
$561$	52.7868	+	2.18906i	2.22866	+	0.0924223i
$562$	1.66605	+	6.21780i	0.0702782	+	0.262282i
$563$	−35.5103	−	9.51495i	−1.49658	−	0.401007i	−0.584627	−	0.811302i	$-0.698759\pi$
$563$	−35.5103	−	9.51495i	−1.49658	−	0.401007i	−0.911953	+	0.410295i	$0.865426\pi$
$564$	−2.47285	−	4.72505i	−0.104126	−	0.198960i
$565$	4.41880	−	7.53508i	0.185900	−	0.317003i
$566$			1.96358i			0.0825353i
$567$	22.6396	−	7.37901i	0.950773	−	0.309889i
$568$	4.17036	+	4.17036i	0.174984	+	0.174984i
$569$	−9.38493	+	16.2552i	−0.393437	+	0.681452i	−0.992900	−	0.118950i	$-0.962047\pi$
$569$	−9.38493	+	16.2552i	−0.393437	+	0.681452i	0.599464	+	0.800402i	$0.295381\pi$
$570$	2.89770	−	9.04512i	0.121371	−	0.378859i
$571$	−16.9888	−	29.4255i	−0.710960	−	1.23142i	−0.964497	−	0.264093i	$-0.914928\pi$
$571$	−16.9888	−	29.4255i	−0.710960	−	1.23142i	0.253538	−	0.967326i	$-0.418406\pi$
$572$	20.6403	−	5.53055i	0.863014	−	0.231244i
$573$	2.14799	−	1.97693i	0.0897336	−	0.0825875i
$574$	−17.4134	+	3.87682i	−0.726821	+	0.161815i
$575$	3.83464	+	3.94014i	0.159916	+	0.164315i
$576$	−1.70996	+	2.46496i	−0.0712485	+	0.102707i
$577$	−22.2872	−	5.97184i	−0.927829	−	0.248611i	−0.236900	−	0.971534i	$-0.576132\pi$
$577$	−22.2872	−	5.97184i	−0.927829	−	0.248611i	−0.690929	+	0.722923i	$0.742798\pi$
$578$	−37.3648	−	10.0119i	−1.55417	−	0.416439i
$579$	−4.98010	−	3.15738i	−0.206966	−	0.131216i
$580$	2.36975	−	2.33781i	0.0983986	−	0.0970725i
$581$	15.9758	+	17.4032i	0.662787	+	0.722005i
$582$	8.65087	+	9.39941i	0.358590	+	0.389618i
$583$	−22.5082	+	6.03105i	−0.932194	+	0.249781i
$584$	−2.78756	−	4.82819i	−0.115350	−	0.199792i
$585$	14.7434	+	31.8173i	0.609565	+	1.31548i
$586$	−0.970865	+	1.68159i	−0.0401061	+	0.0694657i
$587$	21.5670	+	21.5670i	0.890166	+	0.890166i	0.994538	−	0.104372i	$-0.0332834\pi$
$587$	21.5670	+	21.5670i	0.890166	+	0.890166i	−0.104372	+	0.994538i	$0.533283\pi$
$588$	1.63036	+	12.0142i	0.0672348	+	0.495459i
$589$		−	12.8599i		−	0.529881i
$590$	19.6410	+	11.5181i	0.808607	+	0.474192i
$591$	26.0041	−	13.6092i	1.06966	−	0.559809i
$592$	5.34010	+	1.43087i	0.219477	+	0.0588086i
$593$	0.694994	+	2.59375i	0.0285400	+	0.106513i	0.978727	−	0.205169i	$-0.0657744\pi$
$593$	0.694994	+	2.59375i	0.0285400	+	0.106513i	−0.950187	+	0.311682i	$0.899108\pi$
$594$	−2.63418	+	21.0763i	−0.108082	+	0.864769i
$595$	−44.0922	−	2.18530i	−1.80761	−	0.0895884i
$596$			11.4395i			0.468581i
$597$	−1.59858	−	7.13683i	−0.0654256	−	0.292091i
$598$	−1.48776	+	5.55241i	−0.0608392	+	0.227055i
$599$	8.81980	+	15.2764i	0.360367	+	0.624175i	0.988021	−	0.154318i	$-0.0493180\pi$
$599$	8.81980	+	15.2764i	0.360367	+	0.624175i	−0.627654	+	0.778493i	$0.715985\pi$
$600$	−7.25056	−	4.73597i	−0.296003	−	0.193345i
$601$	−25.1426			−1.02559			−0.512794	−	0.858512i	$-0.671390\pi$
$601$	−25.1426			−1.02559			−0.512794	+	0.858512i	$0.671390\pi$
$602$	2.55666	−	4.02110i	0.104202	−	0.163888i
$603$	6.80981	+	8.04390i	0.277317	+	0.327573i
$604$	−11.7061	−	6.75854i	−0.476316	−	0.275001i
$605$	−3.38768	+	12.3084i	−0.137729	+	0.500407i
$606$	−2.37462	−	4.53734i	−0.0964622	−	0.184317i
$607$	−11.1403	−	41.5761i	−0.452170	−	1.68752i	−0.696277	−	0.717773i	$-0.745161\pi$
$607$	−11.1403	−	41.5761i	−0.452170	−	1.68752i	0.244107	−	0.969748i	$-0.421505\pi$
$608$	−1.73408	+	1.73408i	−0.0703262	+	0.0703262i
$609$	6.41781	+	2.31351i	0.260063	+	0.0937482i
$610$	0.0247237	−	3.64439i	0.00100103	−	0.147557i
$611$	13.9392	+	8.04780i	0.563920	+	0.325579i
$612$	7.56447	−	21.0695i	0.305776	−	0.851685i
$613$	7.63014	−	28.4761i	0.308178	−	1.15014i	−0.621996	−	0.783020i	$-0.713678\pi$
$613$	7.63014	−	28.4761i	0.308178	−	1.15014i	0.930175	−	0.367117i	$-0.119655\pi$
$614$	7.08776	−	12.2764i	0.286039	−	0.495433i
$615$	26.0843	+	1.25902i	1.05182	+	0.0507687i
$616$	−10.3174	−	3.24289i	−0.415698	−	0.130660i
$617$	−21.8338	−	21.8338i	−0.878994	−	0.878994i	0.114437	−	0.993431i	$-0.463494\pi$
$617$	−21.8338	−	21.8338i	−0.878994	−	0.878994i	−0.993431	+	0.114437i	$0.963494\pi$
$618$	3.92443	+	17.5205i	0.157864	+	0.704779i
$619$	−22.7455	+	13.1321i	−0.914221	+	0.527826i	−0.881787	−	0.471648i	$-0.843659\pi$
$619$	−22.7455	+	13.1321i	−0.914221	+	0.527826i	−0.0324339	+	0.999474i	$0.510326\pi$
$620$	−11.3053	−	3.11159i	−0.454031	−	0.124964i
$621$	−4.55579	−	3.44852i	−0.182817	−	0.138384i
$622$	2.66880	−	2.66880i	0.107009	−	0.107009i
$623$	−29.9653	−	19.0523i	−1.20053	−	0.763314i
$624$	0.375159	−	9.04653i	0.0150184	−	0.362151i
$625$	13.0828	−	21.3035i	0.523313	−	0.852140i
$626$	23.4389	−	13.5325i	0.936807	−	0.540866i
$627$	−5.18489	+	16.5707i	−0.207065	+	0.661768i
$628$	−9.60302	+	2.57312i	−0.383202	+	0.102679i
$629$	−41.2540			−1.64490
$630$	2.34325	−	17.5929i	0.0933572	−	0.700917i
$631$	29.2208			1.16326			0.581631	−	0.813452i	$-0.302415\pi$
$631$	29.2208			1.16326			0.581631	+	0.813452i	$0.302415\pi$
$632$	9.13268	−	2.44710i	0.363279	−	0.0973402i
$633$	−0.903530	+	2.88764i	−0.0359121	+	0.114773i
$634$	−18.4071	+	10.6273i	−0.731038	+	0.422065i
$635$	−8.80899	+	15.0213i	−0.349574	+	0.596104i
$636$	−0.409110	+	9.86523i	−0.0162223	+	0.391182i
$637$	−23.5714	−	27.9893i	−0.933934	−	1.10898i
$638$	−4.30297	+	4.30297i	−0.170356	+	0.170356i
$639$	10.0850	−	14.5378i	0.398956	−	0.575106i
$640$	1.10487	+	1.94403i	0.0436739	+	0.0768446i
$641$	−40.0771	+	23.1385i	−1.58295	+	0.913916i	−0.588522	+	0.808481i	$0.700290\pi$
$641$	−40.0771	+	23.1385i	−1.58295	+	0.913916i	−0.994426	+	0.105435i	$0.966377\pi$
$642$	0.481996	+	2.15186i	0.0190229	+	0.0849272i
$643$	26.7885	+	26.7885i	1.05644	+	1.05644i	0.998309	+	0.0581268i	$0.0185128\pi$
$643$	26.7885	+	26.7885i	1.05644	+	1.05644i	0.0581268	+	0.998309i	$0.481487\pi$
$644$	2.14322	−	1.96743i	0.0844546	−	0.0775277i
$645$	−5.16436	+	4.68878i	−0.203347	+	0.184620i
$646$	9.14987	−	15.8480i	0.359997	−	0.623532i
$647$	0.497092	−	1.85517i	0.0195427	−	0.0729343i	−0.955466	−	0.295102i	$-0.904646\pi$
$647$	0.497092	−	1.85517i	0.0195427	−	0.0729343i	0.975009	+	0.222167i	$0.0713131\pi$
$648$	8.18973	+	3.73206i	0.321723	+	0.146609i
$649$	−36.0471	−	20.8118i	−1.41497	−	0.816935i
$650$	26.1351	+	0.354619i	1.02510	+	0.0139093i
$651$	−4.24578	−	23.6524i	−0.166405	−	0.927011i
$652$	−8.21531	+	8.21531i	−0.321736	+	0.321736i
$653$	−12.8443	−	47.9356i	−0.502636	−	1.87586i	−0.482179	−	0.876073i	$-0.660155\pi$
$653$	−12.8443	−	47.9356i	−0.502636	−	1.87586i	−0.0204570	−	0.999791i	$-0.506512\pi$
$654$	2.39077	+	4.56820i	0.0934865	+	0.178631i
$655$	31.2187	+	8.59244i	1.21982	+	0.335734i
$656$	−5.83942	−	3.37139i	−0.227991	−	0.131631i
$657$	−12.7652	+	10.8068i	−0.498018	+	0.421612i
$658$	−3.76802	−	7.22250i	−0.146893	−	0.281562i
$659$	23.0084			0.896279			0.448139	−	0.893964i	$-0.352087\pi$
$659$	23.0084			0.896279			0.448139	+	0.893964i	$0.352087\pi$
$660$	13.3129	+	8.56756i	0.518205	+	0.333492i
$661$	15.1551	+	26.2494i	0.589465	+	1.02098i	0.994303	+	0.106594i	$0.0339947\pi$
$661$	15.1551	+	26.2494i	0.589465	+	1.02098i	−0.404838	+	0.914389i	$0.632672\pi$
$662$	1.06197	−	3.96332i	0.0412746	−	0.154039i
$663$	14.7678	+	65.9304i	0.573533	+	2.56053i
$664$			8.92905i			0.346514i
$665$	4.44414	−	13.8109i	0.172336	−	0.535565i
$666$	1.37323	−	16.5285i	0.0532115	−	0.640465i
$667$	−0.423688	−	1.58122i	−0.0164052	−	0.0612252i
$668$	21.4390	+	5.74456i	0.829499	+	0.222264i
$669$	11.4234	−	5.97843i	0.441654	−	0.231140i
$670$	7.60151	−	1.98165i	0.293672	−	0.0765577i
$671$			6.66235i			0.257197i
$672$	−2.61687	+	3.76191i	−0.100948	+	0.145119i
$673$	−15.1720	−	15.1720i	−0.584839	−	0.584839i	0.351390	−	0.936229i	$-0.385709\pi$
$673$	−15.1720	−	15.1720i	−0.584839	−	0.584839i	−0.936229	+	0.351390i	$0.885709\pi$
$674$	8.18434	−	14.1757i	0.315249	−	0.546027i
$675$	−10.1103	+	23.9328i	−0.389147	+	0.921176i
$676$	7.16342	+	12.4074i	0.275516	+	0.477208i
$677$	−25.6687	+	6.87791i	−0.986529	+	0.264340i	−0.715792	−	0.698314i	$-0.753934\pi$
$677$	−25.6687	+	6.87791i	−0.986529	+	0.264340i	−0.270737	+	0.962653i	$0.587267\pi$
$678$	4.58210	+	4.97858i	0.175975	+	0.191201i
$679$	13.1959	+	14.3749i	0.506411	+	0.551658i
$680$	−11.7183	−	11.8784i	−0.449376	−	0.455515i
$681$	−10.3651	−	6.57149i	−0.397193	−	0.251820i
$682$	20.7049	+	5.54787i	0.792832	+	0.212439i
$683$	18.9333	+	5.07317i	0.724464	+	0.194119i	0.602163	−	0.798374i	$-0.294306\pi$
$683$	18.9333	+	5.07317i	0.724464	+	0.194119i	0.122301	+	0.992493i	$0.460973\pi$
$684$	6.04496	+	4.19344i	0.231135	+	0.160340i
$685$	−0.181952	+	26.8206i	−0.00695203	+	1.02476i
$686$	2.46671	+	18.3553i	0.0941795	+	0.700807i
$687$	3.71507	−	3.41922i	0.141739	−	0.130451i
$688$	1.73965	−	0.466139i	0.0663237	−	0.0177714i
$689$	−14.8999	−	25.8074i	−0.567642	−	0.983185i
$690$	−3.78661	+	1.94912i	−0.144154	+	0.0742016i
$691$	17.1906	−	29.7749i	0.653960	−	1.13269i	−0.328194	−	0.944610i	$-0.606440\pi$
$691$	17.1906	−	29.7749i	0.653960	−	1.13269i	0.982154	−	0.188081i	$-0.0602267\pi$
$692$	0.772223	+	0.772223i	0.0293555	+	0.0293555i
$693$	−4.06534	+	32.1893i	−0.154430	+	1.22277i
$694$		−	31.2718i		−	1.18706i
$695$	4.09174	+	15.6957i	0.155209	+	0.595373i
$696$	1.19562	+	2.28455i	0.0453198	+	0.0865955i
$697$	48.6008	+	13.0226i	1.84089	+	0.493264i
$698$	−6.84487	−	25.5454i	−0.259082	−	0.966908i
$699$	48.0605	+	1.99306i	1.81782	+	0.0753846i
$700$	−11.0661	−	7.24861i	−0.418258	−	0.273972i
$701$		−	13.1621i		−	0.497124i	−0.968616	−	0.248562i	$-0.920042\pi$
$701$		−	13.1621i		−	0.497124i	0.968616	−	0.248562i	$-0.0799581\pi$
$702$	−26.9067	+	3.72210i	−1.01553	+	0.140481i
$703$	3.50902	−	13.0958i	0.132345	−	0.493919i
$704$	−2.04384	−	3.54004i	−0.0770302	−	0.133420i
$705$	2.52750	+	11.6541i	0.0951910	+	0.438917i
$706$	−19.9103			−0.749335
$707$	−3.61833	−	6.93558i	−0.136081	−	0.260839i
$708$	−12.9772	+	11.9437i	−0.487714	+	0.448874i
$709$	−6.02363	−	3.47774i	−0.226222	−	0.130609i	0.382606	−	0.923912i	$-0.375027\pi$
$709$	−6.02363	−	3.47774i	−0.226222	−	0.130609i	−0.608828	+	0.793302i	$0.708360\pi$
$710$	−6.51628	−	11.4655i	−0.244552	−	0.430291i
$711$	−12.0997	−	25.6543i	−0.453775	−	0.962113i
$712$	−3.47367	−	12.9639i	−0.130181	−	0.485844i
$713$	−4.07737	+	4.07737i	−0.152699	+	0.152699i
$714$	11.5965	−	32.1693i	0.433987	−	1.20390i
$715$	−47.7801	−	0.324142i	−1.78687	−	0.0121222i
$716$	4.59754	+	2.65439i	0.171818	+	0.0991993i
$717$	3.31422	−	10.5921i	0.123772	−	0.395569i
$718$	7.31005	−	27.2815i	0.272808	−	1.01814i
$719$	−8.04406	+	13.9327i	−0.299993	+	0.519603i	−0.976134	−	0.217169i	$-0.930318\pi$
$719$	−8.04406	+	13.9327i	−0.299993	+	0.519603i	0.676141	+	0.736772i	$0.263651\pi$
$720$	5.14916	−	4.29955i	0.191898	−	0.160235i
$721$	5.96010	+	26.7708i	0.221966	+	0.996995i
$722$	−9.18245	−	9.18245i	−0.341735	−	0.341735i
$723$	23.2910	−	5.21696i	0.866201	−	0.194021i
$724$	−11.9065	+	6.87422i	−0.442501	+	0.255478i
$725$	−6.49615	+	3.63394i	−0.241261	+	0.134961i
$726$	−8.35153	−	5.29487i	−0.309954	−	0.196511i
$727$	−15.0421	+	15.0421i	−0.557879	+	0.557879i	−0.928703	−	0.370824i	$-0.879075\pi$
$727$	−15.0421	+	15.0421i	−0.557879	+	0.557879i	0.370824	+	0.928703i	$0.379075\pi$
$728$	0.590909	−	13.8181i	0.0219005	−	0.512131i
$729$	6.64528	−	26.1695i	0.246122	−	0.969239i
$730$	3.14476	+	12.0632i	0.116393	+	0.446477i
$731$	−11.6389	+	6.71970i	−0.430479	+	0.248537i
$732$	2.69419	+	0.843001i	0.0995801	+	0.0311582i
$733$	7.26892	−	1.94770i	0.268484	−	0.0719400i	−0.122066	−	0.992522i	$-0.538952\pi$
$733$	7.26892	−	1.94770i	0.268484	−	0.0719400i	0.390549	+	0.920582i	$0.372285\pi$
$734$	21.9155			0.808915
$735$	3.61407	−	26.8689i	0.133307	−	0.991075i
$736$	1.09962			0.0405326
$737$	−13.8712	+	3.71677i	−0.510952	+	0.136909i
$738$	−6.83529	+	19.0385i	−0.251610	+	0.700817i
$739$	35.8593	−	20.7034i	1.31911	−	0.761586i	0.335522	−	0.942033i	$-0.391087\pi$
$739$	35.8593	−	20.7034i	1.31911	−	0.761586i	0.983585	+	0.180446i	$0.0577541\pi$
$740$	−10.6637	−	6.25351i	−0.392004	−	0.229883i
$741$	−22.1853	−	0.920023i	−0.814999	−	0.0337979i
$742$	−0.644385	+	15.0686i	−0.0236561	+	0.553184i
$743$	−27.8973	+	27.8973i	−1.02345	+	1.02345i	−0.0237355	+	0.999718i	$0.507556\pi$
$743$	−27.8973	+	27.8973i	−1.02345	+	1.02345i	−0.999718	+	0.0237355i	$0.992444\pi$
$744$	4.86334	−	7.67089i	0.178299	−	0.281228i
$745$	6.78793	−	24.6625i	0.248691	−	0.903562i
$746$	3.54409	−	2.04618i	0.129758	−	0.0749160i
$747$	26.3596	−	4.76689i	0.964447	−	0.174411i
$748$	21.5687	+	21.5687i	0.788628	+	0.788628i
$749$	0.732016	+	3.28797i	0.0267473	+	0.120140i
$750$	12.8213	+	14.5126i	0.468166	+	0.529925i
$751$	−23.2055	+	40.1931i	−0.846781	+	1.46667i	0.0372844	+	0.999305i	$0.488129\pi$
$751$	−23.2055	+	40.1931i	−0.846781	+	1.46667i	−0.884065	+	0.467363i	$0.845204\pi$
$752$	0.796909	−	2.97410i	0.0290603	−	0.108454i
$753$	−26.0256	−	8.14329i	−0.948424	−	0.296758i
$754$	−6.73956	−	3.89109i	−0.245440	−	0.141705i
$755$	21.2269	+	21.5169i	0.772526	+	0.783079i
$756$	12.5027	+	5.71697i	0.454717	+	0.207924i
$757$	−10.4877	+	10.4877i	−0.381181	+	0.381181i	−0.871528	−	0.490346i	$-0.836870\pi$
$757$	−10.4877	+	10.4877i	−0.381181	+	0.381181i	0.490346	+	0.871528i	$0.336870\pi$
$758$	3.12668	+	11.6689i	0.113566	+	0.423835i
$759$	6.89786	−	3.60999i	0.250376	−	0.131034i
$760$	4.76746	−	2.70954i	0.172934	−	0.0982854i
$761$	22.6579	+	13.0816i	0.821350	+	0.474207i	0.850882	−	0.525357i	$-0.176068\pi$
$761$	22.6579	+	13.0816i	0.821350	+	0.474207i	−0.0295319	+	0.999564i	$0.509402\pi$
$762$	−9.13452	−	9.92491i	−0.330909	−	0.359542i
$763$	3.64295	+	6.98276i	0.131884	+	0.252793i
$764$	1.68544			0.0609771
$765$	−28.8104	+	40.9352i	−1.04164	+	1.48002i
$766$	−16.2451	−	28.1374i	−0.586960	−	1.01664i
$767$	13.7770	−	51.4163i	0.497457	−	1.85653i
$768$	−1.69017	+	0.378582i	−0.0609888	+	0.0136609i
$769$			51.0736i			1.84176i	0.389843	+	0.920881i	$0.372529\pi$
$769$			51.0736i			1.84176i	−0.389843	+	0.920881i	$0.627471\pi$
$770$	20.3189	+	13.1134i	0.732243	+	0.472575i
$771$	1.84650	−	44.5263i	0.0665000	−	1.60357i
$772$	−0.881131	−	3.28843i	−0.0317126	−	0.118353i
$773$	35.3002	+	9.45865i	1.26966	+	0.340204i	0.829900	−	0.557912i	$-0.188397\pi$
$773$	35.3002	+	9.45865i	1.26966	+	0.340204i	0.439759	+	0.898116i	$0.355064\pi$
$774$	−2.30483	−	4.88681i	−0.0828455	−	0.175653i
$775$	22.5267	+	13.4166i	0.809183	+	0.481937i
$776$			7.37533i			0.264759i
$777$	2.13024	−	25.2449i	0.0764221	−	0.905657i
$778$	0.0216633	+	0.0216633i	0.000776666	+	0.000776666i
$779$	−8.26786	+	14.3203i	−0.296227	+	0.513080i
$780$	−6.17680	+	19.2808i	−0.221165	+	0.690364i
$781$	12.0541	+	20.8784i	0.431330	+	0.747086i
$782$	−7.92588	+	2.12373i	−0.283429	+	0.0759446i
$783$	6.10595	−	4.74924i	0.218209	−	0.169724i
$784$	−4.00476	+	5.74125i	−0.143027	+	0.205045i
$785$	22.2300	+	0.150809i	0.793422	+	0.00538260i
$786$	−13.4298	+	21.1826i	−0.479025	+	0.755560i
$787$	13.2276	+	3.54432i	0.471513	+	0.126342i	0.486748	−	0.873542i	$-0.338183\pi$
$787$	13.2276	+	3.54432i	0.471513	+	0.126342i	−0.0152350	+	0.999884i	$0.504850\pi$
$788$	16.3678	+	4.38575i	0.583080	+	0.156236i
$789$	0.847654	−	1.33699i	0.0301773	−	0.0475983i
$790$	−21.1412	−	0.143423i	−0.752170	−	0.00510275i
$791$	6.98945	+	7.61394i	0.248516	+	0.270721i
$792$	−9.35947	+	7.92355i	−0.332574	+	0.281551i
$793$	−8.22978	+	2.20516i	−0.292248	+	0.0783076i
$794$	11.4749	+	19.8751i	0.407228	+	0.705340i
$795$	6.73579	−	21.0257i	0.238894	−	0.745704i
$796$	2.11128	−	3.65684i	0.0748322	−	0.129613i
$797$	0.268242	+	0.268242i	0.00950163	+	0.00950163i	0.711842	−	0.702340i	$-0.247861\pi$
$797$	0.268242	+	0.268242i	0.00950163	+	0.00950163i	−0.702340	+	0.711842i	$0.747861\pi$
$798$	9.22556	+	6.41751i	0.326581	+	0.227177i
$799$			22.9759i			0.812830i
$800$	−1.22845	−	4.84674i	−0.0434323	−	0.171358i
$801$	−36.4166	+	17.1757i	−1.28672	+	0.606872i
$802$	16.2237	+	4.34713i	0.572879	+	0.153503i
$803$	−5.89830	−	22.0128i	−0.208147	−	0.776814i
$804$	−0.252123	+	6.07967i	−0.00889170	+	0.214413i
$805$	−5.78799	+	2.96985i	−0.204000	+	0.104674i
$806$			27.4124i			0.965560i
$807$	13.7209	−	3.07335i	0.482999	−	0.108187i
$808$	0.765250	−	2.85595i	0.0269214	−	0.100472i
$809$	12.6754	+	21.9544i	0.445642	+	0.771875i	0.998097	−	0.0616679i	$-0.0196420\pi$
$809$	12.6754	+	21.9544i	0.445642	+	0.771875i	−0.552454	+	0.833543i	$0.686309\pi$
$810$	−15.4417	−	12.9055i	−0.542567	−	0.453454i
$811$	44.0597			1.54714			0.773572	−	0.633708i	$-0.218468\pi$
$811$	44.0597			1.54714			0.773572	+	0.633708i	$0.218468\pi$
$812$	1.82183	+	3.49206i	0.0639336	+	0.122547i
$813$	0.336358	+	0.365462i	0.0117966	+	0.0128173i
$814$	19.5710	+	11.2993i	0.685964	+	0.396041i
$815$	22.5861	−	12.8366i	0.791158	−	0.449647i
$816$	11.4513	−	5.99303i	0.400875	−	0.209798i
$817$	−1.14314	−	4.26626i	−0.0399934	−	0.149257i
$818$	−20.1012	+	20.1012i	−0.702822	+	0.702822i
$819$	−41.1080	+	5.63251i	−1.43643	+	0.196816i
$820$	10.5887	+	10.7334i	0.369774	+	0.374825i
$821$	−39.8047	−	22.9813i	−1.38919	−	0.802051i	−0.395969	−	0.918264i	$-0.629591\pi$
$821$	−39.8047	−	22.9813i	−1.38919	−	0.802051i	−0.993224	+	0.116213i	$0.962925\pi$
$822$	−19.8277	−	6.20401i	−0.691571	−	0.216390i
$823$	−5.37097	+	20.0447i	−0.187220	+	0.698716i	0.806924	+	0.590655i	$0.201131\pi$
$823$	−5.37097	+	20.0447i	−0.187220	+	0.698716i	−0.994144	+	0.108061i	$0.965536\pi$
$824$	−5.18306	+	8.97733i	−0.180561	+	0.312740i
$825$	−23.6176	−	26.3704i	−0.822258	−	0.918099i
$826$	−19.8466	+	18.2188i	−0.690550	+	0.633912i
$827$	−15.6135	−	15.6135i	−0.542934	−	0.542934i	0.381454	−	0.924388i	$-0.375423\pi$
$827$	−15.6135	−	15.6135i	−0.542934	−	0.542934i	−0.924388	+	0.381454i	$0.875423\pi$
$828$	−0.587047	−	3.24621i	−0.0204013	−	0.112814i
$829$	12.2584	−	7.07737i	0.425751	−	0.245807i	−0.271784	−	0.962358i	$-0.587614\pi$
$829$	12.2584	−	7.07737i	0.425751	−	0.245807i	0.697535	+	0.716551i	$0.254280\pi$
$830$	5.29829	−	19.2501i	0.183906	−	0.668182i
$831$	−29.8599	+	47.0976i	−1.03583	+	1.63380i
$832$	3.69641	−	3.69641i	0.128150	−	0.128150i
$833$	17.7773	−	49.1165i	0.615949	−	1.70178i
$834$	−12.5534	−	0.520588i	−0.434689	−	0.0180265i
$835$	−42.8116	−	25.1061i	−1.48156	−	0.868832i
$836$	−8.68144	+	5.01223i	−0.300254	+	0.173352i
$837$	−25.2417	−	10.2620i	−0.872481	−	0.354705i
$838$	−19.4243	+	5.20473i	−0.671002	+	0.179794i
$839$	−7.87337			−0.271819			−0.135909	−	0.990721i	$-0.543396\pi$
$839$	−7.87337			−0.271819			−0.135909	+	0.990721i	$0.543396\pi$
$840$	7.87394	−	6.55752i	0.271677	−	0.226256i
$841$	−26.7838			−0.923579
$842$	0.450728	−	0.120772i	0.0155331	−	0.00416208i
$843$	10.6407	+	3.32944i	0.366486	+	0.114672i
$844$	−1.51285	+	0.873442i	−0.0520743	+	0.0300651i
$845$	−8.08136	−	30.9997i	−0.278007	−	1.06642i
$846$	−9.20534	−	0.764804i	−0.316486	−	0.0262945i
$847$	−12.7467	−	8.10451i	−0.437982	−	0.278474i
$848$	−4.03092	+	4.03092i	−0.138422	+	0.138422i
$849$	2.87238	+	1.82109i	0.0985797	+	0.0624995i
$850$	18.2151	+	32.5619i	0.624774	+	1.11687i
$851$	−5.26476	+	3.03961i	−0.180474	+	0.104197i
$852$	9.96824	−	2.23279i	0.341506	−	0.0764942i
$853$	7.40770	+	7.40770i	0.253635	+	0.253635i	0.822459	−	0.568824i	$-0.192602\pi$
$853$	7.40770	+	7.40770i	0.253635	+	0.253635i	−0.568824	+	0.822459i	$0.692602\pi$
$854$	4.11378	+	1.29302i	0.140771	+	0.0442462i
$855$	−10.5440	−	12.6276i	−0.360599	−	0.431854i
$856$	−0.636581	+	1.10259i	−0.0217579	+	0.0376858i
$857$	9.42103	−	35.1598i	0.321816	−	1.20103i	−0.595657	−	0.803239i	$-0.703108\pi$
$857$	9.42103	−	35.1598i	0.321816	−	1.20103i	0.917474	−	0.397796i	$-0.130225\pi$
$858$	11.0522	−	35.3224i	0.377317	−	1.20589i
$859$	−18.8699	−	10.8945i	−0.643831	−	0.371716i	0.142258	−	0.989830i	$-0.454564\pi$
$859$	−18.8699	−	10.8945i	−0.643831	−	0.371716i	−0.786089	+	0.618114i	$0.787897\pi$
$860$	−4.02712	−	0.0273201i	−0.137324	−	0.000931607i
$861$	−10.4786	+	29.0683i	−0.357110	+	0.990645i
$862$	9.94337	−	9.94337i	0.338672	−	0.338672i
$863$	7.91226	+	29.5289i	0.269336	+	1.00518i	0.959542	+	0.281564i	$0.0908532\pi$
$863$	7.91226	+	29.5289i	0.269336	+	1.00518i	−0.690206	+	0.723613i	$0.742480\pi$
$864$	2.01994	+	4.78747i	0.0687196	+	0.162873i
$865$	−1.20662	−	2.12305i	−0.0410262	−	0.0721860i
$866$	−9.69177	−	5.59555i	−0.329340	−	0.190144i
$867$	−49.2990	+	45.3729i	−1.67428	+	1.54095i
$868$	7.44400	−	11.7079i	0.252666	−	0.397391i
$869$	38.6484			1.31106
$870$	−1.22204	−	5.63471i	−0.0414309	−	0.191034i
$871$	−9.18242	−	15.9044i	−0.311134	−	0.538901i
$872$	−0.770456	+	2.87538i	−0.0260909	+	0.0973727i
$873$	21.7728	−	3.93741i	0.736899	−	0.133261i
$874$		−	2.69666i		−	0.0912161i
$875$	19.5562	+	22.1936i	0.661119	+	0.750281i
$876$	−9.64808	−	0.400105i	−0.325978	−	0.0135183i
$877$	5.41309	+	20.2019i	0.182787	+	0.682171i	0.995093	+	0.0989398i	$0.0315451\pi$
$877$	5.41309	+	20.2019i	0.182787	+	0.682171i	−0.812306	+	0.583231i	$0.801788\pi$
$878$	1.89284	+	0.507186i	0.0638804	+	0.0171167i
$879$	1.55946	+	2.97977i	0.0525993	+	0.100505i
$880$	2.30575	+	8.84474i	0.0777267	+	0.298156i
$881$		−	42.7328i		−	1.43971i	−0.694127	−	0.719853i	$-0.744209\pi$
$881$		−	42.7328i		−	1.43971i	0.694127	−	0.719853i	$-0.255791\pi$
$882$	19.0868	+	8.75747i	0.642687	+	0.294879i
$883$	11.2379	+	11.2379i	0.378184	+	0.378184i	0.870447	−	0.492263i	$-0.163830\pi$
$883$	11.2379	+	11.2379i	0.378184	+	0.378184i	−0.492263	+	0.870447i	$0.663830\pi$
$884$	−19.5041	+	33.7821i	−0.655993	+	1.13621i
$885$	35.0647	−	18.0492i	1.17869	−	0.606716i
$886$	12.8261	+	22.2155i	0.430902	+	0.746344i
$887$	−1.49243	+	0.399896i	−0.0501110	+	0.0134272i	−0.283787	−	0.958887i	$-0.591591\pi$
$887$	−1.49243	+	0.399896i	−0.0501110	+	0.0134272i	0.233676	+	0.972314i	$0.424924\pi$
$888$	7.04571	−	6.48461i	0.236438	−	0.217609i
$889$	−13.9336	−	15.1786i	−0.467319	−	0.509073i
$890$	−0.203590	+	30.0101i	−0.00682434	+	1.00594i
$891$	28.3879	+	23.4002i	0.951031	+	0.783935i
$892$	7.19027	+	1.92663i	0.240748	+	0.0645082i
$893$	−7.29357	−	1.95431i	−0.244070	−	0.0653984i
$894$	16.7341	+	10.6094i	0.559670	+	0.354831i
$895$	−8.33679	−	8.45068i	−0.278668	−	0.282475i
$896$	−2.58252	+	0.574959i	−0.0862760	+	0.0192080i
$897$	6.74242	+	7.32583i	0.225123	+	0.244602i
$898$	4.36227	−	1.16887i	0.145571	−	0.0390056i
$899$	−3.90327	−	6.76066i	−0.130181	−	0.225481i
$900$	−13.6523	+	6.21402i	−0.455077	+	0.207134i
$901$	21.2692	−	36.8393i	0.708579	−	1.22729i
$902$	−19.4895	−	19.4895i	−0.648930	−	0.648930i
$903$	−3.51105	−	7.46926i	−0.116840	−	0.248561i
$904$			3.90649i			0.129928i
$905$	29.7482	−	7.75510i	0.988864	−	0.257788i
$906$	−20.7432	+	10.8560i	−0.689148	+	0.360666i
$907$	8.33811	+	2.23419i	0.276862	+	0.0741851i	0.394579	−	0.918862i	$-0.370891\pi$
$907$	8.33811	+	2.23419i	0.276862	+	0.0741851i	−0.117716	+	0.993047i	$0.537557\pi$
$908$	−1.83391	−	6.84424i	−0.0608604	−	0.227134i
$909$	−8.83964	−	0.734421i	−0.293192	−	0.0243592i
$910$	−9.47324	+	29.4397i	−0.314035	+	0.975917i
$911$			49.6817i			1.64603i	0.568020	+	0.823015i	$0.307710\pi$
$911$			49.6817i			1.64603i	−0.568020	+	0.823015i	$0.692290\pi$
$912$	0.928418	+	4.14490i	0.0307430	+	0.137251i
$913$	−9.44668	+	35.2555i	−0.312639	+	1.16679i
$914$	14.4552	+	25.0372i	0.478136	+	0.828156i
$915$	−5.30819	−	3.41609i	−0.175483	−	0.112933i
$916$	2.91506			0.0963164
$917$	−20.5561	+	32.3305i	−0.678822	+	1.06765i
$918$	−23.8056	−	30.6061i	−0.785700	−	1.01015i
$919$	28.8152	+	16.6365i	0.950525	+	0.548786i	0.893244	−	0.449572i	$-0.148424\pi$
$919$	28.8152	+	16.6365i	0.950525	+	0.548786i	0.0572812	+	0.998358i	$0.481757\pi$
$920$	−2.37067	−	0.652489i	−0.0781588	−	0.0215119i
$921$	−11.3848	−	21.7537i	−0.375141	−	0.716808i
$922$	−7.39609	−	27.6026i	−0.243577	−	0.909043i
$923$	−21.8006	+	21.8006i	−0.717575	+	0.717575i
$924$	−14.3125	+	12.0850i	−0.470845	+	0.397566i
$925$	19.2791	+	19.8095i	0.633893	+	0.651332i
$926$	−32.1517	−	18.5628i	−1.05657	−	0.610012i
$927$	29.2692	+	10.5083i	0.961325	+	0.345139i
$928$	−0.385303	+	1.43797i	−0.0126482	+	0.0472037i
$929$	−12.5625	+	21.7588i	−0.412161	+	0.713884i	−0.995126	−	0.0986138i	$-0.968559\pi$
$929$	−12.5625	+	21.7588i	−0.412161	+	0.713884i	0.582965	+	0.812497i	$0.301892\pi$
$930$	−15.0366	+	13.6519i	−0.493070	+	0.447663i
$931$	14.0796	+	9.82110i	0.461440	+	0.321873i
$932$	19.6375	+	19.6375i	0.643247	+	0.643247i
$933$	−1.42887	−	6.37914i	−0.0467789	−	0.208844i
$934$	−26.9825	+	15.5783i	−0.882893	+	0.509738i
$935$	−33.7015	−	59.2982i	−1.10216	−	1.93926i
$936$	−12.8856	−	8.93885i	−0.421179	−	0.292175i
$937$	8.91661	−	8.91661i	0.291293	−	0.291293i	−0.546298	−	0.837591i	$-0.683963\pi$
$937$	8.91661	−	8.91661i	0.291293	−	0.291293i	0.837591	+	0.546298i	$0.183963\pi$
$938$	−0.397117	+	9.28634i	−0.0129663	+	0.303210i
$939$	1.94235	−	46.8376i	0.0633861	−	1.52849i
$940$	−3.48282	+	5.93901i	−0.113597	+	0.193709i
$941$	−32.5006	+	18.7642i	−1.05949	+	0.611696i	−0.925291	−	0.379259i	$-0.876179\pi$
$941$	−32.5006	+	18.7642i	−1.05949	+	0.611696i	−0.134197	+	0.990955i	$0.542846\pi$
$942$	−5.14212	+	16.4340i	−0.167539	+	0.535448i
$943$	7.16186	−	1.91901i	0.233222	−	0.0624917i
$944$	−10.1827			−0.331418
$945$	−23.5622	−	19.7440i	−0.766477	−	0.642272i
$946$	7.36201			0.239360
$947$	55.4649	−	14.8618i	1.80237	−	0.482943i	0.808024	−	0.589149i	$-0.200537\pi$
$947$	55.4649	−	14.8618i	1.80237	−	0.482943i	0.994344	+	0.106206i	$0.0338704\pi$
$948$	4.89027	−	15.6291i	0.158829	−	0.507609i
$949$	25.2394	−	14.5720i	0.819305	−	0.473026i
$950$	−11.8859	+	3.01260i	−0.385631	+	0.0977417i
$951$	−1.52537	+	36.7825i	−0.0494634	+	1.19276i
$952$	17.5039	−	9.13192i	0.567306	−	0.295967i
$953$	22.8327	−	22.8327i	0.739622	−	0.739622i	−0.232883	−	0.972505i	$-0.574816\pi$
$953$	22.8327	−	22.8327i	0.739622	−	0.739622i	0.972505	+	0.232883i	$0.0748158\pi$
$954$	14.0517	+	9.74780i	0.454941	+	0.315597i
$955$	−3.63364	−	1.00010i	−0.117582	−	0.0323625i
$956$	5.54924	−	3.20386i	0.179475	−	0.103620i
$957$	2.30379	+	10.2852i	0.0744711	+	0.332474i
$958$	4.73903	+	4.73903i	0.153111	+	0.153111i
$959$	−30.2751	−	9.51588i	−0.977633	−	0.307284i
$960$	3.86848	+	0.186722i	0.124855	+	0.00602642i
$961$	1.75089	−	3.03263i	0.0564803	−	0.0978268i
$962$	−7.47991	+	27.9154i	−0.241162	+	0.900028i
$963$	3.59482	+	1.29063i	0.115842	+	0.0415899i
$964$	11.9341	+	6.89013i	0.384370	+	0.221916i
$965$	−0.0516425	+	7.61236i	−0.00166243	+	0.245051i
$966$	−0.890325	−	4.95982i	−0.0286457	−	0.159580i
$967$	10.9688	−	10.9688i	0.352734	−	0.352734i	−0.508392	−	0.861126i	$-0.669760\pi$
$967$	10.9688	−	10.9688i	0.352734	−	0.352734i	0.861126	+	0.508392i	$0.169760\pi$
$968$	−1.47764	−	5.51463i	−0.0474932	−	0.177247i
$969$	−14.6971	−	28.0827i	−0.472138	−	0.902146i
$970$	4.37634	−	15.9005i	0.140516	−	0.510533i
$971$	29.4378	+	16.9959i	0.944702	+	0.545424i	0.891431	−	0.453156i	$-0.149702\pi$
$971$	29.4378	+	16.9959i	0.944702	+	0.545424i	0.0532711	+	0.998580i	$0.483035\pi$
$972$	13.0548	−	8.51894i	0.418733	−	0.273245i
$973$	−19.1746	−	0.819974i	−0.614710	−	0.0262872i
$974$	6.94402			0.222501
$975$	24.7573	−	37.9023i	0.792869	−	1.21385i
$976$	0.814929	+	1.41150i	0.0260852	+	0.0451810i
$977$	−6.37466	+	23.7906i	−0.203943	+	0.761127i	0.785826	+	0.618448i	$0.212238\pi$
$977$	−6.37466	+	23.7906i	−0.203943	+	0.761127i	−0.989769	+	0.142679i	$0.954428\pi$
$978$	4.39844	+	19.6367i	0.140647	+	0.627913i
$979$		−	54.8618i		−	1.75339i
$980$	12.0406	−	10.0012i	0.384622	−	0.319478i
$981$	8.89978	+	0.739417i	0.284148	+	0.0236078i
$982$	−4.88355	−	18.2256i	−0.155840	−	0.581604i
$983$	10.2091	+	2.73551i	0.325618	+	0.0872492i	0.417925	−	0.908481i	$-0.362757\pi$
$983$	10.2091	+	2.73551i	0.325618	+	0.0872492i	−0.0923068	+	0.995731i	$0.529424\pi$
$984$	−10.3474	+	5.41533i	−0.329864	+	0.172634i
$985$	−32.6850	−	19.1675i	−1.04143	−	0.610728i
$986$		−	11.1088i		−	0.353776i
$987$	−14.0599	−	1.18641i	−0.447531	−	0.0377640i
$988$	−9.06491	−	9.06491i	−0.288393	−	0.288393i
$989$	−0.990221	+	1.71511i	−0.0314872	+	0.0545374i
$990$	24.8797	−	11.5287i	0.790730	−	0.366406i
$991$	19.0277	+	32.9570i	0.604435	+	1.04691i	0.992140	+	0.125129i	$0.0399346\pi$
$991$	19.0277	+	32.9570i	0.604435	+	1.04691i	−0.387705	+	0.921784i	$0.626732\pi$
$992$	5.06519	−	1.35721i	0.160820	−	0.0430916i
$993$	−4.81275	−	5.22919i	−0.152728	−	0.165943i
$994$	15.2311	−	3.39098i	0.483102	−	0.107555i
$995$	−6.72158	+	6.63100i	−0.213088	+	0.210217i
$996$	13.0617	+	8.28110i	0.413875	+	0.262397i
$997$	−18.9410	−	5.07524i	−0.599869	−	0.160734i	−0.0539091	−	0.998546i	$-0.517168\pi$
$997$	−18.9410	−	5.07524i	−0.599869	−	0.160734i	−0.545960	+	0.837812i	$0.683835\pi$
$998$	37.6913	+	10.0994i	1.19310	+	0.319690i
$999$	−22.9047	−	17.3379i	−0.724674	−	0.548545i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.x.a.23.13	yes	64
3.2	odd	2	inner	210.2.x.a.23.5	✓	64
5.2	odd	4	inner	210.2.x.a.107.10	yes	64
7.4	even	3	inner	210.2.x.a.53.1	yes	64
15.2	even	4	inner	210.2.x.a.107.1	yes	64
21.11	odd	6	inner	210.2.x.a.53.10	yes	64
35.32	odd	12	inner	210.2.x.a.137.5	yes	64
105.32	even	12	inner	210.2.x.a.137.13	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.x.a.23.5	✓	64	3.2	odd	2	inner
210.2.x.a.23.13	yes	64	1.1	even	1	trivial
210.2.x.a.53.1	yes	64	7.4	even	3	inner
210.2.x.a.53.10	yes	64	21.11	odd	6	inner
210.2.x.a.107.1	yes	64	15.2	even	4	inner
210.2.x.a.107.10	yes	64	5.2	odd	4	inner
210.2.x.a.137.5	yes	64	35.32	odd	12	inner
210.2.x.a.137.13	yes	64	105.32	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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.517224 - 1.65302i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.16375 + 0.564071i) q^{5} +(0.0717662 - 1.73056i) q^{6} +(0.113038 - 2.64334i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.46496 - 1.70996i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.517224 - 1.65302i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.16375 + 0.564071i) q^{5} +(0.0717662 - 1.73056i) q^{6} +(0.113038 - 2.64334i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.46496 - 1.70996i) q^{9} +(-1.94403 + 1.10487i) q^{10} +(3.54004 - 2.04384i) q^{11} +(-0.378582 - 1.69017i) q^{12} +(3.69641 + 3.69641i) q^{13} +(-0.574959 - 2.58252i) q^{14} +(-0.186722 + 3.86848i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.93133 + 7.20783i) q^{17} +(-2.82354 - 1.01372i) q^{18} +(-2.12380 - 1.22618i) q^{19} +(-1.59183 + 1.57038i) q^{20} +(-4.31102 - 1.55405i) q^{21} +(2.89043 - 2.89043i) q^{22} +(0.284603 + 1.06215i) q^{23} +(-0.803130 - 1.53459i) q^{24} +(4.36365 - 2.44102i) q^{25} +(4.52715 + 2.61375i) q^{26} +(-4.10154 + 3.19020i) q^{27} +(-1.22377 - 2.34571i) q^{28} -1.48870 q^{29} +(0.820877 + 3.78499i) q^{30} +(2.62194 + 4.54133i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-1.54752 - 6.90888i) q^{33} +7.46210i q^{34} +(1.24644 + 5.78328i) q^{35} +(-2.98970 - 0.248392i) q^{36} +(1.43087 + 5.34010i) q^{37} +(-2.36880 - 0.634717i) q^{38} +(8.02211 - 4.19837i) q^{39} +(-1.13115 + 1.92886i) q^{40} -6.74278i q^{41} +(-4.56635 - 0.385322i) q^{42} +(1.27352 + 1.27352i) q^{43} +(2.04384 - 3.54004i) q^{44} +(6.29810 + 2.30952i) q^{45} +(0.549811 + 0.952300i) q^{46} +(2.97410 - 0.796909i) q^{47} +(-1.17295 - 1.27444i) q^{48} +(-6.97444 - 0.597597i) q^{49} +(3.58318 - 3.48724i) q^{50} +(10.9158 + 6.92059i) q^{51} +(5.04938 + 1.35298i) q^{52} +(-5.50634 - 1.47542i) q^{53} +(-3.13610 + 4.14305i) q^{54} +(-6.50689 + 6.41920i) q^{55} +(-1.78919 - 1.94905i) q^{56} +(-3.12538 + 2.87649i) q^{57} +(-1.43797 + 0.385303i) q^{58} +(-5.09134 - 8.81846i) q^{59} +(1.77253 + 3.44356i) q^{60} +(-0.814929 + 1.41150i) q^{61} +(3.70798 + 3.70798i) q^{62} +(-4.79864 + 6.32242i) q^{63} -1.00000i q^{64} +(-10.0831 - 5.91307i) q^{65} +(-3.28294 - 6.27294i) q^{66} +(-3.39341 - 0.909261i) q^{67} +(1.93133 + 7.20783i) q^{68} +(1.90296 + 0.0789157i) q^{69} +(2.70080 + 5.26362i) q^{70} +5.89777i q^{71} +(-2.95212 + 0.533863i) q^{72} +(1.44294 - 5.38514i) q^{73} +(2.76424 + 4.78780i) q^{74} +(-1.77808 - 8.47576i) q^{75} -2.45236 q^{76} +(-5.00240 - 9.58854i) q^{77} +(6.66214 - 6.13159i) q^{78} +(8.18814 + 4.72742i) q^{79} +(-0.593376 + 2.15590i) q^{80} +(3.15205 + 8.42998i) q^{81} +(-1.74516 - 6.51303i) q^{82} +(-6.31379 + 6.31379i) q^{83} +(-4.51048 + 0.809665i) q^{84} +(0.113194 - 16.6854i) q^{85} +(1.55973 + 0.900511i) q^{86} +(-0.769989 + 2.46085i) q^{87} +(1.05797 - 3.94840i) q^{88} +(6.71062 - 11.6231i) q^{89} +(6.68125 + 0.600760i) q^{90} +(10.1887 - 9.35301i) q^{91} +(0.777550 + 0.777550i) q^{92} +(8.86304 - 1.98524i) q^{93} +(2.66651 - 1.53951i) q^{94} +(5.28704 + 1.45517i) q^{95} +(-1.46283 - 0.927433i) q^{96} +(-5.21514 + 5.21514i) q^{97} +(-6.89147 + 1.22788i) q^{98} +(-12.2209 - 1.01535i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) \) 64 * q + 8 * q^6 + 4 * q^7	\( 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43} - 28 q^{45} + 24 q^{46} - 16 q^{55} + 24 q^{57} - 28 q^{58} + 8 q^{60} + 24 q^{61} - 88 q^{63} - 16 q^{67} - 12 q^{70} + 8 q^{72} - 56 q^{73} + 8 q^{75} - 32 q^{76} - 16 q^{78} + 4 q^{81} + 16 q^{82} + 32 q^{85} + 76 q^{87} + 12 q^{88} + 40 q^{90} - 48 q^{91} + 84 q^{93} + 4 q^{96} + 104 q^{97}+O(q^{100}) \) 64 * q + 8 * q^6 + 4 * q^7 + 4 * q^10 - 24 * q^15 + 32 * q^16 - 8 * q^18 + 12 * q^21 - 24 * q^22 - 8 * q^25 - 72 * q^27 + 4 * q^28 - 12 * q^30 + 32 * q^31 - 20 * q^33 - 24 * q^36 - 8 * q^37 - 40 * q^42 - 64 * q^43 - 28 * q^45 + 24 * q^46 - 16 * q^55 + 24 * q^57 - 28 * q^58 + 8 * q^60 + 24 * q^61 - 88 * q^63 - 16 * q^67 - 12 * q^70 + 8 * q^72 - 56 * q^73 + 8 * q^75 - 32 * q^76 - 16 * q^78 + 4 * q^81 + 16 * q^82 + 32 * q^85 + 76 * q^87 + 12 * q^88 + 40 * q^90 - 48 * q^91 + 84 * q^93 + 4 * q^96 + 104 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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