LMFDB - Embedded newform 210.2.x.a.53.1

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			53.1
Character	$\chi$	$=$	210.53
Dual form			210.2.x.a.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-1.69017 + 0.378582i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.593376 - 2.15590i) q^{5} +(0.0717662 - 1.73056i) q^{6} +(2.64334 - 0.113038i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.71335 - 1.27974i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.69017 + 0.378582i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.593376 - 2.15590i) q^{5} +(0.0717662 - 1.73056i) q^{6} +(2.64334 - 0.113038i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.71335 - 1.27974i) q^{9} +(1.92886 + 1.13115i) q^{10} +(-3.54004 - 2.04384i) q^{11} +(1.65302 + 0.517224i) 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} +(7.20783 - 1.93133i) q^{17} +(0.533863 + 2.95212i) q^{18} +(2.12380 - 1.22618i) q^{19} +(-1.59183 + 1.57038i) q^{20} +(-4.42489 + 1.19177i) q^{21} +(2.89043 - 2.89043i) q^{22} +(-1.06215 - 0.284603i) q^{23} +(-0.927433 + 1.46283i) q^{24} +(-4.29581 - 2.55852i) q^{25} +(-4.52715 + 2.61375i) q^{26} +(-4.10154 + 3.19020i) q^{27} +(-2.34571 - 1.22377i) q^{28} -1.48870 q^{29} +(-3.68834 - 1.18160i) q^{30} +(2.62194 - 4.54133i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(6.75703 + 2.11425i) q^{33} +7.46210i q^{34} +(1.32479 - 5.76584i) q^{35} +(-2.98970 - 0.248392i) q^{36} +(-5.34010 - 1.43087i) q^{37} +(0.634717 + 2.36880i) q^{38} +(-7.64695 - 4.84816i) q^{39} +(-1.10487 - 1.94403i) q^{40} -6.74278i q^{41} +(-0.00591784 - 4.58257i) q^{42} +(1.27352 + 1.27352i) q^{43} +(2.04384 + 3.54004i) q^{44} +(-1.14894 - 6.60908i) q^{45} +(0.549811 - 0.952300i) q^{46} +(-0.796909 + 2.97410i) q^{47} +(-1.17295 - 1.27444i) q^{48} +(6.97444 - 0.597597i) q^{49} +(3.58318 - 3.48724i) q^{50} +(-11.4513 + 5.99303i) q^{51} +(-1.35298 - 5.04938i) q^{52} +(1.47542 + 5.50634i) q^{53} +(-2.01994 - 4.78747i) q^{54} +(-6.50689 + 6.41920i) q^{55} +(1.78919 - 1.94905i) q^{56} +(-3.12538 + 2.87649i) q^{57} +(0.385303 - 1.43797i) q^{58} +(-5.09134 + 8.81846i) q^{59} +(2.09595 - 3.25684i) q^{60} +(-0.814929 - 1.41150i) q^{61} +(3.70798 + 3.70798i) q^{62} +(7.02764 - 3.68948i) q^{63} -1.00000i q^{64} +(10.1624 - 5.77572i) q^{65} +(-3.79105 + 5.97958i) q^{66} +(0.909261 + 3.39341i) q^{67} +(-7.20783 - 1.93133i) q^{68} +(1.90296 + 0.0789157i) q^{69} +(5.22649 + 2.77196i) q^{70} +5.89777i q^{71} +(1.01372 - 2.82354i) q^{72} +(-5.38514 + 1.44294i) q^{73} +(2.76424 - 4.78780i) q^{74} +(8.22926 + 2.69802i) q^{75} -2.45236 q^{76} +(-9.58854 - 5.00240i) q^{77} +(6.66214 - 6.13159i) q^{78} +(-8.18814 + 4.72742i) q^{79} +(2.16375 - 0.564071i) q^{80} +(5.72455 - 6.94475i) q^{81} +(6.51303 + 1.74516i) q^{82} +(-6.31379 + 6.31379i) q^{83} +(4.42796 + 1.18034i) q^{84} +(0.113194 - 16.6854i) q^{85} +(-1.55973 + 0.900511i) q^{86} +(2.51615 - 0.563594i) q^{87} +(-3.94840 + 1.05797i) 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} +(-2.71226 + 8.66824i) q^{93} +(-2.66651 - 1.53951i) q^{94} +(-1.38331 - 5.30630i) q^{95} +(1.53459 - 0.803130i) q^{96} +(-5.21514 + 5.21514i) q^{97} +(-1.22788 + 6.89147i) 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 $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−1.69017	+	0.378582i	−0.975820	+	0.218574i
$3$	−1.69017	+	0.378582i	−0.975820	+	0.218574i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.593376	−	2.15590i	0.265366	−	0.964148i
$5$	0.593376	−	2.15590i	0.265366	−	0.964148i
$6$	0.0717662	−	1.73056i	0.0292984	−	0.706500i
$7$	2.64334	−	0.113038i	0.999087	−	0.0427245i
$7$	2.64334	−	0.113038i	0.999087	−	0.0427245i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.71335	−	1.27974i	0.904450	−	0.426579i
$10$	1.92886	+	1.13115i	0.609960	+	0.357700i
$11$	−3.54004	−	2.04384i	−1.06736	−	0.616242i	−0.139902	−	0.990165i	$-0.544679\pi$
$11$	−3.54004	−	2.04384i	−1.06736	−	0.616242i	−0.927459	+	0.373924i	$0.878012\pi$
$12$	1.65302	+	0.517224i	0.477186	+	0.149310i
$13$	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
$17$	7.20783	−	1.93133i	1.74816	−	0.468417i	0.763925	−	0.645305i	$-0.223270\pi$
$17$	7.20783	−	1.93133i	1.74816	−	0.468417i	0.984231	+	0.176888i	$0.0566032\pi$
$18$	0.533863	+	2.95212i	0.125833	+	0.695820i
$19$	2.12380	−	1.22618i	0.487234	−	0.281305i	−0.236192	−	0.971706i	$-0.575899\pi$
$19$	2.12380	−	1.22618i	0.487234	−	0.281305i	0.723426	+	0.690402i	$0.242566\pi$
$20$	−1.59183	+	1.57038i	−0.355944	+	0.351147i
$21$	−4.42489	+	1.19177i	−0.965591	+	0.260066i
$22$	2.89043	−	2.89043i	0.616242	−	0.616242i
$23$	−1.06215	−	0.284603i	−0.221474	−	0.0593438i	0.146376	−	0.989229i	$-0.453239\pi$
$23$	−1.06215	−	0.284603i	−0.221474	−	0.0593438i	−0.367850	+	0.929885i	$0.619906\pi$
$24$	−0.927433	+	1.46283i	−0.189311	+	0.298599i
$25$	−4.29581	−	2.55852i	−0.859162	−	0.511704i
$26$	−4.52715	+	2.61375i	−0.887848	+	0.512599i
$27$	−4.10154	+	3.19020i	−0.789342	+	0.613954i
$28$	−2.34571	−	1.22377i	−0.443298	−	0.231271i
$29$	−1.48870			−0.276444			−0.138222	−	0.990401i	$-0.544139\pi$
$29$	−1.48870			−0.276444			−0.138222	+	0.990401i	$0.544139\pi$
$30$	−3.68834	−	1.18160i	−0.673395	−	0.215729i
$31$	2.62194	−	4.54133i	0.470914	−	0.815647i	−0.528533	−	0.848913i	$-0.677258\pi$
$31$	2.62194	−	4.54133i	0.470914	−	0.815647i	0.999447	+	0.0332663i	$0.0105909\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	6.75703	+	2.11425i	1.17625	+	0.368043i
$34$			7.46210i			1.27974i
$35$	1.32479	−	5.76584i	0.223931	−	0.974605i
$36$	−2.98970	−	0.248392i	−0.498283	−	0.0413987i
$37$	−5.34010	−	1.43087i	−0.877906	−	0.235234i	−0.208403	−	0.978043i	$-0.566826\pi$
$37$	−5.34010	−	1.43087i	−0.877906	−	0.235234i	−0.669504	+	0.742809i	$0.733493\pi$
$38$	0.634717	+	2.36880i	0.102965	+	0.384269i
$39$	−7.64695	−	4.84816i	−1.22449	−	0.776328i
$40$	−1.10487	−	1.94403i	−0.174695	−	0.307378i
$41$		−	6.74278i		−	1.05305i	−0.850161	−	0.526523i	$-0.823495\pi$
$41$		−	6.74278i		−	1.05305i	0.850161	−	0.526523i	$-0.176505\pi$
$42$	−0.00591784	−	4.58257i	−0.000913142	−	0.707106i
$43$	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
$45$	−1.14894	−	6.60908i	−0.171275	−	0.985223i
$46$	0.549811	−	0.952300i	0.0810651	−	0.140409i
$47$	−0.796909	+	2.97410i	−0.116241	+	0.433818i	−0.999377	−	0.0353000i	$-0.988761\pi$
$47$	−0.796909	+	2.97410i	−0.116241	+	0.433818i	0.883136	+	0.469118i	$0.155428\pi$
$48$	−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
$51$	−11.4513	+	5.99303i	−1.60350	+	0.839193i
$52$	−1.35298	−	5.04938i	−0.187624	−	0.700224i
$53$	1.47542	+	5.50634i	0.202665	+	0.756355i	0.990149	+	0.140020i	$0.0447166\pi$
$53$	1.47542	+	5.50634i	0.202665	+	0.756355i	−0.787484	+	0.616335i	$0.788617\pi$
$54$	−2.01994	−	4.78747i	−0.274879	−	0.651492i
$55$	−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
$58$	0.385303	−	1.43797i	0.0505928	−	0.188815i
$59$	−5.09134	+	8.81846i	−0.662836	+	1.14807i	0.317031	+	0.948415i	$0.397314\pi$
$59$	−5.09134	+	8.81846i	−0.662836	+	1.14807i	−0.979867	+	0.199651i	$0.936019\pi$
$60$	2.09595	−	3.25684i	0.270585	−	0.420456i
$61$	−0.814929	−	1.41150i	−0.104341	−	0.180724i	0.809128	−	0.587633i	$-0.199940\pi$
$61$	−0.814929	−	1.41150i	−0.104341	−	0.180724i	−0.913469	+	0.406909i	$0.866607\pi$
$62$	3.70798	+	3.70798i	0.470914	+	0.470914i
$63$	7.02764	−	3.68948i	0.885399	−	0.464831i
$64$		−	1.00000i		−	0.125000i
$65$	10.1624	−	5.77572i	1.26050	−	0.716390i
$66$	−3.79105	+	5.97958i	−0.466646	+	0.736036i
$67$	0.909261	+	3.39341i	0.111084	+	0.414571i	0.998964	−	0.0455037i	$-0.0144893\pi$
$67$	0.909261	+	3.39341i	0.111084	+	0.414571i	−0.887880	+	0.460075i	$0.847823\pi$
$68$	−7.20783	−	1.93133i	−0.874078	−	0.234208i
$69$	1.90296	+	0.0789157i	0.229090	+	0.00950033i
$70$	5.22649	+	2.77196i	0.624685	+	0.331313i
$71$			5.89777i			0.699937i	0.936761	+	0.349969i	$0.113808\pi$
$71$			5.89777i			0.699937i	−0.936761	+	0.349969i	$0.886192\pi$
$72$	1.01372	−	2.82354i	0.119468	−	0.332757i
$73$	−5.38514	+	1.44294i	−0.630283	+	0.168884i	−0.559798	−	0.828629i	$-0.689121\pi$
$73$	−5.38514	+	1.44294i	−0.630283	+	0.168884i	−0.0704850	+	0.997513i	$0.522455\pi$
$74$	2.76424	−	4.78780i	0.321336	−	0.556570i
$75$	8.22926	+	2.69802i	0.950233	+	0.311540i
$76$	−2.45236			−0.281305
$77$	−9.58854	−	5.00240i	−1.09272	−	0.570076i
$78$	6.66214	−	6.13159i	0.754339	−	0.694266i
$79$	−8.18814	+	4.72742i	−0.921238	+	0.531877i	−0.884030	−	0.467431i	$-0.845180\pi$
$79$	−8.18814	+	4.72742i	−0.921238	+	0.531877i	−0.0372080	+	0.999308i	$0.511846\pi$
$80$	2.16375	−	0.564071i	0.241915	−	0.0630651i
$81$	5.72455	−	6.94475i	0.636061	−	0.771638i
$82$	6.51303	+	1.74516i	0.719243	+	0.192721i
$83$	−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	$0.413020\pi$
$84$	4.42796	+	1.18034i	0.483130	+	0.128786i
$85$	0.113194	−	16.6854i	0.0122776	−	1.80978i
$86$	−1.55973	+	0.900511i	−0.168190	+	0.0971046i
$87$	2.51615	−	0.563594i	0.269760	−	0.0604236i
$88$	−3.94840	+	1.05797i	−0.420901	+	0.112780i
$89$	6.71062	+	11.6231i	0.711325	+	1.23205i	0.964360	+	0.264594i	$0.0852378\pi$
$89$	6.71062	+	11.6231i	0.711325	+	1.23205i	−0.253035	+	0.967457i	$0.581429\pi$
$90$	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
$93$	−2.71226	+	8.66824i	−0.281248	+	0.898854i
$94$	−2.66651	−	1.53951i	−0.275029	−	0.158788i
$95$	−1.38331	−	5.30630i	−0.141924	−	0.544414i
$96$	1.53459	−	0.803130i	0.156624	−	0.0819691i
$97$	−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	$0.372160\pi$
$98$	−1.22788	+	6.89147i	−0.124035	+	0.696143i
$99$	−12.2209	−	1.01535i	−1.22825	−	0.102046i
$100$	2.44102	+	4.36365i	0.244102	+	0.436365i
$101$	−2.56058	−	1.47835i	−0.254787	−	0.147101i	0.367167	−	0.930155i	$-0.380328\pi$
$101$	−2.56058	−	1.47835i	−0.254787	−	0.147101i	−0.621954	+	0.783054i	$0.713661\pi$
$102$	−2.82501	−	12.6122i	−0.279718	−	1.24880i
$103$	2.68295	−	10.0129i	0.264359	−	0.986601i	−0.698283	−	0.715822i	$-0.746052\pi$
$103$	2.68295	−	10.0129i	0.264359	−	0.986601i	0.962642	−	0.270779i	$-0.0872813\pi$
$104$	5.22751			0.512599
$105$	−0.0562816	+	10.2468i	−0.00549252	+	0.999985i
$106$	−5.70059			−0.553690
$107$	0.329519	−	1.22978i	0.0318558	−	0.118887i	−0.948167	−	0.317772i	$-0.897065\pi$
$107$	0.329519	−	1.22978i	0.0318558	−	0.118887i	0.980023	+	0.198885i	$0.0637320\pi$
$108$	5.14714	−	0.712021i	0.495284	−	0.0685143i
$109$	2.57800	+	1.48841i	0.246927	+	0.142564i	0.618356	−	0.785898i	$-0.287799\pi$
$109$	2.57800	+	1.48841i	0.246927	+	0.142564i	−0.371429	+	0.928461i	$0.621132\pi$
$110$	−4.51637	−	7.94659i	−0.430619	−	0.757677i
$111$	9.56737	+	0.396758i	0.908095	+	0.0376586i
$112$	1.41956	+	2.23268i	0.134136	+	0.210968i
$113$	−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	$0.308822\pi$
$114$	−1.96956	−	3.76338i	−0.184467	−	0.352473i
$115$	−1.24383	+	2.12102i	−0.115988	+	0.197786i
$116$	1.28925	+	0.744349i	0.119704	+	0.0691110i
$117$	14.7601	+	5.29923i	1.36457	+	0.489914i
$118$	−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
$122$	1.57432	−	0.421838i	0.142532	−	0.0381914i
$123$	2.55269	+	11.3964i	0.230169	+	1.02758i
$124$	−4.54133	+	2.62194i	−0.407823	+	0.235457i
$125$	−8.06494	+	7.74317i	−0.721350	+	0.692570i
$126$	1.74488	+	7.74309i	0.155446	+	0.689809i
$127$	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	$0.137702\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−2.63459	−	1.67033i	−0.231963	−	0.147064i
$130$	2.94869	+	11.3110i	0.258617	+	0.992043i
$131$	12.5406	−	7.24030i	1.09567	−	0.632588i	0.160593	−	0.987021i	$-0.448659\pi$
$131$	12.5406	−	7.24030i	1.09567	−	0.632588i	0.935082	+	0.354433i	$0.115326\pi$
$132$	−4.79464	−	5.20951i	−0.417320	−	0.453429i
$133$	5.47532	−	3.48127i	0.474771	−	0.301865i
$134$	−3.51312			−0.303487
$135$	4.44399	+	10.7355i	0.382478	+	0.923965i
$136$	3.73105	−	6.46236i	0.319935	−	0.554143i
$137$	−11.5861	+	3.10449i	−0.989868	+	0.265234i	−0.717195	−	0.696872i	$-0.754574\pi$
$137$	−11.5861	+	3.10449i	−0.989868	+	0.265234i	−0.272673	+	0.962107i	$0.587908\pi$
$138$	−0.568750	+	1.81770i	−0.0484152	+	0.154733i
$139$		−	7.25394i		−	0.615271i	−0.951504	−	0.307636i	$-0.900462\pi$
$139$		−	7.25394i		−	0.615271i	0.951504	−	0.307636i	$-0.0995378\pi$
$140$	−4.03022	+	4.33097i	−0.340616	+	0.366034i
$141$	0.220970	−	5.32844i	0.0186090	−	0.448735i
$142$	−5.69681	−	1.52646i	−0.478066	−	0.128097i
$143$	−5.53055	−	20.6403i	−0.462488	−	1.72603i
$144$	2.46496	+	1.70996i	0.205413	+	0.142497i
$145$	−0.883357	+	3.20948i	−0.0733588	+	0.266533i
$146$		−	5.57511i		−	0.461399i
$147$	−11.5618	+	3.65044i	−0.953598	+	0.301083i
$148$	3.90922	+	3.90922i	0.321336	+	0.321336i
$149$	−5.71976	−	9.90691i	−0.468581	−	0.811606i	0.530774	−	0.847513i	$-0.321901\pi$
$149$	−5.71976	−	9.90691i	−0.468581	−	0.811606i	−0.999355	+	0.0359074i	$0.988568\pi$
$150$	−4.73597	+	7.25056i	−0.386691	+	0.592005i
$151$	−6.75854	+	11.7061i	−0.550002	+	0.952632i	0.448271	+	0.893897i	$0.352040\pi$
$151$	−6.75854	+	11.7061i	−0.550002	+	0.952632i	−0.998274	+	0.0587343i	$0.981294\pi$
$152$	0.634717	−	2.36880i	0.0514824	−	0.192135i
$153$	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
$156$	4.19837	+	8.02211i	0.336139	+	0.642283i
$157$	2.57312	+	9.60302i	0.205358	+	0.766405i	0.989340	+	0.145622i	$0.0465184\pi$
$157$	2.57312	+	9.60302i	0.205358	+	0.766405i	−0.783983	+	0.620783i	$0.786815\pi$
$158$	−2.44710	−	9.13268i	−0.194680	−	0.726557i
$159$	−4.57831	−	8.74809i	−0.363084	−	0.693769i
$160$	−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
$163$	3.00701	−	11.2223i	0.235527	−	0.879000i	−0.742383	−	0.669976i	$-0.766305\pi$
$163$	3.00701	−	11.2223i	0.235527	−	0.879000i	0.977910	−	0.209024i	$-0.0670288\pi$
$164$	−3.37139	+	5.83942i	−0.263261	+	0.455982i
$165$	8.56756	−	13.3129i	0.666984	−	1.03641i
$166$	−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	$0.421235\pi$
$168$	−2.28616	+	3.97158i	−0.176381	+	0.306414i
$169$			14.3268i			1.10206i
$170$	16.0875	+	4.42783i	1.23386	+	0.339599i
$171$	4.19344	−	6.04496i	0.320681	−	0.462270i
$172$	−0.466139	−	1.73965i	−0.0355428	−	0.132647i
$173$	−1.05488	−	0.282653i	−0.0802007	−	0.0214897i	0.218496	−	0.975838i	$-0.429885\pi$
$173$	−1.05488	−	0.282653i	−0.0802007	−	0.0214897i	−0.298696	+	0.954348i	$0.596552\pi$
$174$	−0.106838	+	2.57629i	−0.00809938	+	0.195308i
$175$	−11.6445	−	6.27743i	−0.880240	−	0.474529i
$176$		−	4.08768i		−	0.308121i
$177$	5.26673	−	16.8322i	0.395871	−	1.26519i
$178$	−12.9639	+	3.47367i	−0.971688	+	0.260363i
$179$	2.65439	−	4.59754i	0.198399	−	0.343637i	−0.749611	−	0.661879i	$-0.769759\pi$
$179$	2.65439	−	4.59754i	0.198399	−	0.343637i	0.948009	+	0.318242i	$0.103093\pi$
$180$	−2.30952	+	6.29810i	−0.172142	+	0.469433i
$181$	−13.7484			−1.02191			−0.510957	−	0.859607i	$-0.670709\pi$
$181$	−13.7484			−1.02191			−0.510957	+	0.859607i	$0.670709\pi$
$182$	−11.6713	+	7.42077i	−0.865137	+	0.550064i
$183$	1.91174	+	2.07716i	0.141320	+	0.153548i
$184$	−0.952300	+	0.549811i	−0.0702045	+	0.0405326i
$185$	−6.25351	+	10.6637i	−0.459767	+	0.784008i
$186$	−7.67089	−	4.86334i	−0.562457	−	0.356598i
$187$	−29.4633	−	7.89468i	−2.15457	−	0.577316i
$188$	2.17720	−	2.17720i	0.158788	−	0.158788i
$189$	−10.4811	+	8.89639i	−0.762390	+	0.647117i
$190$	5.48351	+	0.0372003i	0.397816	+	0.00269880i
$191$	−1.45963	+	0.842720i	−0.105615	+	0.0609771i	−0.551877	−	0.833925i	$-0.686088\pi$
$191$	−1.45963	+	0.842720i	−0.105615	+	0.0609771i	0.446262	+	0.894902i	$0.352755\pi$
$192$	0.378582	+	1.69017i	0.0273218	+	0.121978i
$193$	−3.28843	+	0.881131i	−0.236706	+	0.0634252i	−0.375222	−	0.926935i	$-0.622433\pi$
$193$	−3.28843	+	0.881131i	−0.236706	+	0.0634252i	0.138516	+	0.990360i	$0.455767\pi$
$194$	−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	$0.543713\pi$
$198$	4.14377	−	11.5417i	0.294485	−	0.820236i
$199$	−3.65684	−	2.11128i	−0.259226	−	0.149664i	0.364755	−	0.931103i	$-0.381153\pi$
$199$	−3.65684	−	2.11128i	−0.259226	−	0.149664i	−0.623982	+	0.781439i	$0.714486\pi$
$200$	−4.84674	+	1.22845i	−0.342716	+	0.0868646i
$201$	−2.82149	−	5.39121i	−0.199013	−	0.380267i
$202$	2.09070	−	2.09070i	0.147101	−	0.147101i
$203$	−3.93513	+	0.168280i	−0.276192	+	0.0118109i
$204$	12.9136	+	0.535527i	0.904135	+	0.0374944i
$205$	−14.5368	−	4.00100i	−1.01529	−	0.279442i
$206$	8.97733	+	5.18306i	0.625480	+	0.361121i
$207$	−3.24621	+	0.587047i	−0.225627	+	0.0408026i
$208$	−1.35298	+	5.04938i	−0.0938122	+	0.350112i
$209$	−10.0245			−0.693407
$210$	−9.88308	−	2.70643i	−0.681997	−	0.186761i
$211$	−1.74688			−0.120260			−0.0601302	−	0.998191i	$-0.519152\pi$
$211$	−1.74688			−0.120260			−0.0601302	+	0.998191i	$0.519152\pi$
$212$	1.47542	−	5.50634i	0.101332	−	0.378177i
$213$	−2.23279	−	9.96824i	−0.152988	−	0.683013i
$214$	1.10259	+	0.636581i	0.0753715	+	0.0435158i
$215$	3.50125	−	1.98990i	0.238783	−	0.135710i
$216$	−0.644418	+	5.15604i	−0.0438471	+	0.350824i
$217$	6.41732	−	12.3006i	0.435636	−	0.835021i
$218$	−2.10493	+	2.10493i	−0.142564	+	0.142564i
$219$	8.55554	−	4.47754i	0.578130	−	0.302564i
$220$	8.84474	−	2.30575i	0.596312	−	0.155453i
$221$	33.7821	+	19.5041i	2.27243	+	1.31199i
$222$	−2.85946	+	9.13869i	−0.191914	+	0.613348i
$223$	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
$227$	−6.84424	+	1.83391i	−0.454268	+	0.121721i	−0.478696	−	0.877981i	$-0.658890\pi$
$227$	−6.84424	+	1.83391i	−0.454268	+	0.121721i	0.0244277	+	0.999702i	$0.492224\pi$
$228$	4.14490	−	0.928418i	0.274503	−	0.0614860i
$229$	−2.52452	+	1.45753i	−0.166825	+	0.0963164i	−0.581088	−	0.813841i	$-0.697373\pi$
$229$	−2.52452	+	1.45753i	−0.166825	+	0.0963164i	0.414263	+	0.910157i	$0.364039\pi$
$230$	−1.72682	−	1.75041i	−0.113863	−	0.115419i
$231$	18.1001	+	4.82486i	1.19090	+	0.317453i
$232$	−1.05267	+	1.05267i	−0.0691110	+	0.0691110i
$233$	−26.8253	−	7.18782i	−1.75738	−	0.470890i	−0.771207	−	0.636584i	$-0.780347\pi$
$233$	−26.8253	−	7.18782i	−1.75738	−	0.470890i	−0.986177	+	0.165694i	$0.947014\pi$
$234$	−8.93885	+	12.8856i	−0.584351	+	0.842358i
$235$	5.93901	+	3.48282i	0.387418	+	0.227194i
$236$	8.81846	−	5.09134i	0.574033	−	0.331418i
$237$	12.0496	−	11.0900i	0.782708	−	0.720375i
$238$	0.843503	+	19.7248i	0.0546762	+	1.27857i
$239$	6.40772			0.414481			0.207240	−	0.978290i	$-0.433552\pi$
$239$	6.40772			0.414481			0.207240	+	0.978290i	$0.433552\pi$
$240$	−3.44356	+	1.77253i	−0.222281	+	0.114417i
$241$	6.89013	−	11.9341i	0.443832	−	0.768740i	−0.554138	−	0.832425i	$-0.686952\pi$
$241$	6.89013	−	11.9341i	0.443832	−	0.768740i	0.997970	+	0.0636847i	$0.0202852\pi$
$242$	−5.51463	+	1.47764i	−0.354494	+	0.0949863i
$243$	−7.04631	+	13.9050i	−0.452021	+	0.892007i
$244$			1.62986i			0.104341i
$245$	2.85011	−	15.3908i	0.182087	−	0.983282i
$246$	−11.6688	−	0.483904i	−0.743976	−	0.0308526i
$247$	12.3829	+	3.31799i	0.787905	+	0.211119i
$248$	−1.35721	−	5.06519i	−0.0861832	−	0.321640i
$249$	8.28110	−	13.0617i	0.524793	−	0.827750i
$250$	−5.39197	−	9.79422i	−0.341018	−	0.619441i
$251$		−	15.7442i		−	0.993767i	−0.867817	−	0.496884i	$-0.834478\pi$
$251$		−	15.7442i		−	0.993767i	0.867817	−	0.496884i	$-0.165522\pi$
$252$	−7.93086	−	0.318633i	−0.499597	−	0.0200720i
$253$	3.17838	+	3.17838i	0.199823	+	0.199823i
$254$	3.89384	+	6.74432i	0.244321	+	0.423176i
$255$	6.12546	+	28.2440i	0.383591	+	1.76871i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.65924	+	24.8526i	−0.415392	+	1.55026i	0.368656	+	0.929566i	$0.379818\pi$
$257$	−6.65924	+	24.8526i	−0.415392	+	1.55026i	−0.784049	+	0.620699i	$0.786849\pi$
$258$	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
$261$	−4.03936	+	1.90514i	−0.250030	+	0.117925i
$262$	3.74786	+	13.9872i	0.231543	+	0.864131i
$263$	−0.236555	−	0.882836i	−0.0145866	−	0.0544380i	0.958249	−	0.285935i	$-0.0923042\pi$
$263$	−0.236555	−	0.882836i	−0.0145866	−	0.0544380i	−0.972836	+	0.231497i	$0.925638\pi$
$264$	6.27294	−	3.28294i	0.386073	−	0.202051i
$265$	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
$268$	0.909261	−	3.39341i	0.0555420	−	0.207285i
$269$	4.05903	−	7.03044i	0.247483	−	0.428654i	−0.715344	−	0.698773i	$-0.753730\pi$
$269$	4.05903	−	7.03044i	0.247483	−	0.428654i	0.962827	+	0.270119i	$0.0870631\pi$
$270$	−11.5199	+	1.51401i	−0.701078	+	0.0921399i
$271$	−0.143382	−	0.248344i	−0.00870982	−	0.0150858i	0.861638	−	0.507524i	$-0.169439\pi$
$271$	−0.143382	−	0.248344i	−0.00870982	−	0.0150858i	−0.870347	+	0.492438i	$0.836106\pi$
$272$	5.27650	+	5.27650i	0.319935	+	0.319935i
$273$	−20.7615	−	11.9509i	−1.25654	−	0.723303i
$274$		−	11.9948i		−	0.724634i
$275$	9.97812	+	17.8372i	0.601704	+	1.07562i
$276$	−1.60856	−	1.01982i	−0.0968238	−	0.0613862i
$277$	8.33301	+	31.0992i	0.500682	+	1.86857i	0.495542	+	0.868584i	$0.334970\pi$
$277$	8.33301	+	31.0992i	0.500682	+	1.86857i	0.00514027	+	0.999987i	$0.498364\pi$
$278$	7.00677	+	1.87746i	0.420238	+	0.112602i
$279$	1.30254	−	15.6776i	0.0779808	−	0.938594i
$280$	−3.14030	−	5.01384i	−0.187669	−	0.299634i
$281$			6.43714i			0.384007i	0.981394	+	0.192004i	$0.0614986\pi$
$281$			6.43714i			0.384007i	−0.981394	+	0.192004i	$0.938501\pi$
$282$	5.08969	+	1.59254i	0.303086	+	0.0948345i
$283$	1.89667	−	0.508211i	0.112745	−	0.0302100i	−0.202005	−	0.979384i	$-0.564746\pi$
$283$	1.89667	−	0.508211i	0.112745	−	0.0302100i	0.314751	+	0.949174i	$0.398079\pi$
$284$	2.94889	−	5.10762i	0.174984	−	0.303082i
$285$	4.34689	+	8.44485i	0.257487	+	0.500230i
$286$	21.3684			1.26354
$287$	−0.762193	−	17.8234i	−0.0449908	−	1.05208i
$288$	−2.28968	+	1.93840i	−0.134920	+	0.114221i
$289$	33.5003	−	19.3414i	1.97061	−	1.13773i
$290$	−2.87149	−	1.68393i	−0.168620	−	0.0988839i
$291$	6.84012	−	10.7888i	0.400975	−	0.632453i
$292$	5.38514	+	1.44294i	0.315142	+	0.0844419i
$293$	−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	$0.268064\pi$
$294$	−0.533649	−	12.1126i	−0.0311231	−	0.706422i
$295$	15.9906	+	16.2091i	0.931011	+	0.943730i
$296$	−4.78780	+	2.76424i	−0.278285	+	0.160668i
$297$	21.0399	−	2.91052i	1.22086	−	0.168885i
$298$	11.0497	−	2.96076i	0.640093	−	0.171512i
$299$	−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
$303$	4.88749	+	1.52928i	0.280779	+	0.0878546i
$304$	2.12380	+	1.22618i	0.121809	+	0.0703262i
$305$	−3.52661	+	0.919356i	−0.201933	+	0.0526422i
$306$	9.54951	+	20.2473i	0.545909	+	1.15746i
$307$	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	$0.117439\pi$
$308$	5.80272	+	9.12648i	0.330641	+	0.520029i
$309$	−0.743938	+	17.9392i	−0.0423212	+	1.02053i
$310$	10.1943	−	5.79381i	0.578995	−	0.329066i
$311$	−3.26860	−	1.88713i	−0.185345	−	0.107009i	0.404456	−	0.914557i	$-0.367461\pi$
$311$	−3.26860	−	1.88713i	−0.185345	−	0.107009i	−0.589802	+	0.807548i	$0.700794\pi$
$312$	−8.83538	+	1.97904i	−0.500205	+	0.112041i
$313$	−7.00492	+	26.1427i	−0.395941	+	1.47767i	0.424229	+	0.905555i	$0.360545\pi$
$313$	−7.00492	+	26.1427i	−0.395941	+	1.47767i	−0.820171	+	0.572119i	$0.806122\pi$
$314$	−9.94178			−0.561047
$315$	−3.78413	−	17.3401i	−0.213211	−	0.977006i
$316$	9.45485			0.531877
$317$	5.50111	−	20.5304i	0.308973	−	1.15310i	−0.620498	−	0.784208i	$-0.713069\pi$
$317$	5.50111	−	20.5304i	0.308973	−	1.15310i	0.929471	−	0.368895i	$-0.120264\pi$
$318$	9.63496	−	2.15814i	0.540302	−	0.121022i
$319$	5.27005	+	3.04266i	0.295066	+	0.170356i
$320$	−2.15590	−	0.593376i	−0.120518	−	0.0331707i
$321$	−0.0913700	+	2.20329i	−0.00509978	+	0.122976i
$322$	1.34569	−	2.57940i	0.0749922	−	0.143744i
$323$	12.9399	−	12.9399i	0.719993	−	0.719993i
$324$	−8.42998	+	3.15205i	−0.468332	+	0.175114i
$325$	−6.42173	−	25.3364i	−0.356214	−	1.40541i
$326$	10.0617	+	5.80910i	0.557264	+	0.321736i
$327$	−4.92074	−	1.53968i	−0.272117	−	0.0851444i
$328$	−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	0.916884	−	0.399154i	$-0.130696\pi$
$331$	2.05157	+	3.55342i	0.112764	+	0.195313i	−0.804120	+	0.594468i	$0.797363\pi$
$332$	8.62480	−	2.31101i	0.473348	−	0.126833i
$333$	−16.3207	+	2.95145i	−0.894369	+	0.161738i
$334$	−19.2217	+	11.0976i	−1.05176	+	0.607236i
$335$	7.85539	+	0.0532912i	0.429186	+	0.00291161i
$336$	−3.24455	−	3.23618i	−0.177005	−	0.176548i
$337$	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	$0.102909\pi$
$338$	−13.8387	−	3.70806i	−0.752724	−	0.201692i
$339$	3.62301	−	5.71452i	0.196775	−	0.310370i
$340$	−8.44071	+	14.3934i	−0.457762	+	0.780589i
$341$	−18.5635	+	10.7177i	−1.00527	+	0.580393i
$342$	4.75364	+	5.61511i	0.257048	+	0.303630i
$343$	18.3682	−	2.36803i	0.991792	−	0.127862i
$344$	1.80102			0.0971046
$345$	1.29931	−	4.05577i	0.0699524	−	0.218356i
$346$	0.546044	−	0.945776i	0.0293555	−	0.0508452i
$347$	−30.2063	+	8.09375i	−1.62156	+	0.434495i	−0.951459	−	0.307776i	$-0.900415\pi$
$347$	−30.2063	+	8.09375i	−1.62156	+	0.434495i	−0.670099	+	0.742272i	$0.733748\pi$
$348$	−2.46085	−	0.769989i	−0.131915	−	0.0412758i
$349$		−	26.4465i		−	1.41565i	−0.706387	−	0.707826i	$-0.749676\pi$
$349$		−	26.4465i		−	1.41565i	0.706387	−	0.707826i	$-0.250324\pi$
$350$	9.07735	−	9.62298i	0.485205	−	0.514370i
$351$	−26.9532	−	3.36870i	−1.43866	−	0.179808i
$352$	3.94840	+	1.05797i	0.210450	+	0.0563900i
$353$	5.15317	+	19.2319i	0.274276	+	1.02361i	0.956325	+	0.292305i	$0.0944223\pi$
$353$	5.15317	+	19.2319i	0.274276	+	1.02361i	−0.682049	+	0.731306i	$0.738911\pi$
$354$	14.8955	+	9.44376i	0.791688	+	0.501930i
$355$	12.7150	+	3.49960i	0.674843	+	0.185739i
$356$		−	13.4212i		−	0.711325i
$357$	−29.5922	+	17.1360i	−1.56618	+	0.906935i
$358$	3.75388	+	3.75388i	0.198399	+	0.198399i
$359$	14.1219	+	24.4599i	0.745327	+	1.29094i	0.950042	+	0.312122i	$0.101040\pi$
$359$	14.1219	+	24.4599i	0.745327	+	1.29094i	−0.204715	+	0.978822i	$0.565627\pi$
$360$	−5.48575	−	3.86090i	−0.289124	−	0.203487i
$361$	−6.49297	+	11.2462i	−0.341735	+	0.591903i
$362$	3.55836	−	13.2800i	0.187023	−	0.697980i
$363$	−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
$366$	−2.50117	+	1.30899i	−0.130738	+	0.0684219i
$367$	−5.67214	−	21.1687i	−0.296084	−	1.10500i	−0.940353	−	0.340200i	$-0.889505\pi$
$367$	−5.67214	−	21.1687i	−0.296084	−	1.10500i	0.644269	−	0.764799i	$-0.277162\pi$
$368$	−0.284603	−	1.06215i	−0.0148360	−	0.0553685i
$369$	−8.62898	−	18.2955i	−0.449207	−	0.952428i
$370$	−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
$373$	−1.05918	+	3.95292i	−0.0548423	+	0.204674i	−0.987911	−	0.155025i	$-0.950454\pi$
$373$	−1.05918	+	3.95292i	−0.0548423	+	0.204674i	0.933068	+	0.359700i	$0.117121\pi$
$374$	15.2513	−	26.4161i	0.788628	−	1.36594i
$375$	10.6997	−	16.1405i	0.552530	−	0.833493i
$376$	1.53951	+	2.66651i	0.0793942	+	0.137515i
$377$	−5.50283	−	5.50283i	−0.283410	−	0.283410i
$378$	−5.88054	−	12.4266i	−0.302462	−	0.639153i
$379$			12.0806i			0.620537i	0.950649	+	0.310269i	$0.100419\pi$
$379$			12.0806i			0.620537i	−0.950649	+	0.310269i	$0.899581\pi$
$380$	−1.45517	+	5.28704i	−0.0746487	+	0.271219i
$381$	−7.22254	+	11.3920i	−0.370022	+	0.583631i
$382$	−0.436224	−	1.62801i	−0.0223192	−	0.0832962i
$383$	31.3832	+	8.40909i	1.60360	+	0.429684i	0.946129	−	0.323791i	$-0.104958\pi$
$383$	31.3832	+	8.40909i	1.60360	+	0.429684i	0.657476	+	0.753476i	$0.271624\pi$
$384$	−1.73056	−	0.0717662i	−0.0883124	−	0.00366231i
$385$	−16.4743	+	17.7036i	−0.839607	+	0.902261i
$386$		−	3.40443i		−	0.173281i
$387$	5.08526	+	1.82573i	0.258498	+	0.0928072i
$388$	7.12402	−	1.90888i	0.361667	−	0.0969085i
$389$	0.0153183	−	0.0265320i	0.000776666	−	0.00134523i	−0.865637	−	0.500672i	$-0.833086\pi$
$389$	0.0153183	−	0.0265320i	0.000776666	−	0.00134523i	0.866413	+	0.499327i	$0.166419\pi$
$390$	−9.26594	−	18.0013i	−0.469199	−	0.911529i
$391$	−8.20548			−0.414969
$392$	4.50911	−	5.35424i	0.227745	−	0.270430i
$393$	−18.4546	+	16.9850i	−0.930914	+	0.856779i
$394$	−14.6750	+	8.47261i	−0.739316	+	0.426844i
$395$	5.33321	+	20.4580i	0.268343	+	1.02935i
$396$	10.0760	+	6.98979i	0.506337	+	0.351250i
$397$	−22.1678	−	5.93984i	−1.11257	−	0.298112i	−0.344696	−	0.938714i	$-0.612018\pi$
$397$	−22.1678	−	5.93984i	−1.11257	−	0.298112i	−0.767873	+	0.640603i	$0.778685\pi$
$398$	2.98580	−	2.98580i	0.149664	−	0.149664i
$399$	−7.93628	+	7.95680i	−0.397311	+	0.398338i
$400$	0.0678372	−	4.99954i	0.00339186	−	0.249977i
$401$	−14.5458	+	8.39801i	−0.726382	+	0.419377i	−0.817097	−	0.576500i	$-0.804418\pi$
$401$	−14.5458	+	8.39801i	−0.726382	+	0.419377i	0.0907151	+	0.995877i	$0.471085\pi$
$402$	5.93776	−	1.33000i	0.296149	−	0.0663345i
$403$	26.4783	−	7.09485i	1.31898	−	0.353420i
$404$	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
$408$	−3.85957	+	12.3350i	−0.191077	+	0.610674i
$409$	24.6188	+	14.2137i	1.21732	+	0.702822i	0.964345	−	0.264650i	$-0.0852563\pi$
$409$	24.6188	+	14.2137i	1.21732	+	0.702822i	0.252979	+	0.967472i	$0.418590\pi$
$410$	7.62706	−	13.0059i	0.376674	−	0.642315i
$411$	18.4072	−	9.63341i	0.907960	−	0.475181i
$412$	−7.32996	+	7.32996i	−0.361121	+	0.361121i
$413$	−12.4613	+	23.8857i	−0.613181	+	1.17534i
$414$	0.273137	−	3.28754i	0.0134240	−	0.161574i
$415$	9.86545	+	17.3584i	0.484276	+	0.852088i
$416$	−4.52715	−	2.61375i	−0.221962	−	0.128150i
$417$	2.74621	+	12.2604i	0.134483	+	0.600394i
$418$	2.59452	−	9.68289i	0.126902	−	0.473606i
$419$	−20.1095			−0.982415			−0.491207	−	0.871043i	$-0.663444\pi$
$419$	−20.1095			−0.982415			−0.491207	+	0.871043i	$0.663444\pi$
$420$	5.17214	−	8.84585i	0.252375	−	0.431633i
$421$	0.466628			0.0227420			0.0113710	−	0.999935i	$-0.496380\pi$
$421$	0.466628			0.0227420			0.0113710	+	0.999935i	$0.496380\pi$
$422$	0.452127	−	1.68736i	0.0220092	−	0.0821394i
$423$	1.64377	+	9.08962i	0.0799230	+	0.441953i
$424$	4.93685	+	2.85029i	0.239755	+	0.138422i
$425$	−35.9048	−	10.1447i	−1.74164	−	0.492092i
$426$	10.2065	+	0.423261i	0.494505	+	0.0205071i
$427$	−2.31368	−	3.63895i	−0.111967	−	0.176101i
$428$	−0.900261	+	0.900261i	−0.0435158	+	0.0435158i
$429$	17.1616	+	32.7918i	0.828570	+	1.58321i
$430$	1.01591	+	3.89697i	0.0489913	+	0.187928i
$431$	−12.1781	−	7.03102i	−0.586598	−	0.338672i	0.177153	−	0.984183i	$-0.443311\pi$
$431$	−12.1781	−	7.03102i	−0.586598	−	0.338672i	−0.763751	+	0.645511i	$0.776645\pi$
$432$	−4.81356	−	1.95694i	−0.231593	−	0.0941533i
$433$	−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
$437$	−2.60478	+	0.697948i	−0.124603	+	0.0333874i
$438$	2.11064	+	9.42289i	0.100850	+	0.450243i
$439$	−1.69708	+	0.979808i	−0.0809971	+	0.0467637i	−0.539952	−	0.841696i	$-0.681557\pi$
$439$	−1.69708	+	0.979808i	−0.0809971	+	0.0467637i	0.458954	+	0.888460i	$0.348224\pi$
$440$	−0.0620069	+	9.14013i	−0.00295606	+	0.435739i
$441$	18.1594	−	10.5469i	0.864731	−	0.502235i
$442$	−27.5829	+	27.5829i	−1.31199	+	1.31199i
$443$	−24.7782	−	6.63929i	−1.17725	−	0.315442i	−0.383413	−	0.923577i	$-0.625251\pi$
$443$	−24.7782	−	6.63929i	−1.17725	−	0.315442i	−0.793834	+	0.608135i	$0.791918\pi$
$444$	−8.08721	−	5.12729i	−0.383802	−	0.243330i
$445$	29.0403	−	7.57054i	1.37664	−	0.358878i
$446$	−6.44662	+	3.72196i	−0.305256	+	0.176240i
$447$	13.4179	+	14.5790i	0.634647	+	0.689562i
$448$	−0.113038	−	2.64334i	−0.00534056	−	0.124886i
$449$	4.51616			0.213131			0.106565	−	0.994306i	$-0.466015\pi$
$449$	4.51616			0.213131			0.106565	+	0.994306i	$0.466015\pi$
$450$	5.25967	−	14.0476i	0.247943	−	0.662212i
$451$	−13.7812	+	23.8697i	−0.648930	+	1.12398i
$452$	3.77338	−	1.01107i	0.177485	−	0.0475569i
$453$	6.99135	−	22.3440i	0.328482	−	1.04981i
$454$		−	7.08568i		−	0.332547i
$455$	26.2099	−	16.4159i	1.22874	−	0.769590i
$456$	−0.175997	+	4.24396i	−0.00824179	+	0.198742i
$457$	−27.9253	−	7.48257i	−1.30629	−	0.350020i	−0.462466	−	0.886637i	$-0.653035\pi$
$457$	−27.9253	−	7.48257i	−1.30629	−	0.350020i	−0.843826	+	0.536617i	$0.819702\pi$
$458$	−0.754474	−	2.81574i	−0.0352543	−	0.131571i
$459$	−23.4019	+	30.9158i	−1.09231	+	1.44303i
$460$	2.13770	−	1.21494i	0.0996707	−	0.0566469i
$461$		−	28.5763i		−	1.33093i	−0.746428	−	0.665466i	$-0.768233\pi$
$461$		−	28.5763i		−	1.33093i	0.746428	−	0.665466i	$-0.231767\pi$
$462$	−9.34510	+	16.2346i	−0.434774	+	0.755301i
$463$	−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
$465$	17.0785	+	10.9909i	0.791995	+	0.509690i
$466$	13.8858	−	24.0509i	0.643247	−	1.11414i
$467$	8.06394	−	30.0950i	0.373154	−	1.39263i	−0.482868	−	0.875693i	$-0.660405\pi$
$467$	8.06394	−	30.0950i	0.373154	−	1.39263i	0.856023	−	0.516938i	$-0.172928\pi$
$468$	−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
$471$	−7.98455	−	15.2566i	−0.367908	−	0.702987i
$472$	2.63547	+	9.83572i	0.121307	+	0.452726i
$473$	−1.90543	−	7.11116i	−0.0876117	−	0.326971i
$474$	7.59348	+	14.5094i	0.348780	+	0.666437i
$475$	−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
$478$	−1.65844	+	6.18938i	−0.0758552	+	0.283096i
$479$	3.35100	−	5.80410i	0.153111	−	0.265196i	−0.779258	−	0.626703i	$-0.784404\pi$
$479$	3.35100	−	5.80410i	0.153111	−	0.265196i	0.932370	+	0.361506i	$0.117737\pi$
$480$	−0.820877	−	3.78499i	−0.0374677	−	0.172760i
$481$	−14.4501	−	25.0283i	−0.658867	−	1.14119i
$482$	9.74412	+	9.74412i	0.443832	+	0.443832i
$483$	5.03909	−	0.00650738i	0.229287	−	0.000296096i
$484$		−	5.70916i		−	0.259507i
$485$	8.14879	+	14.3379i	0.370017	+	0.651049i
$486$	−11.6075	−	10.4051i	−0.526527	−	0.471985i
$487$	−1.79725	−	6.70741i	−0.0814409	−	0.303942i	0.913176	−	0.407567i	$-0.133623\pi$
$487$	−1.79725	−	6.70741i	−0.0814409	−	0.303942i	−0.994616	+	0.103625i	$0.966956\pi$
$488$	−1.57432	−	0.421838i	−0.0712662	−	0.0190957i
$489$	−0.833794	+	20.1060i	−0.0377055	+	0.909226i
$490$	14.1287	+	6.73643i	0.638270	+	0.304321i
$491$		−	18.8686i		−	0.851527i	−0.904835	−	0.425763i	$-0.860006\pi$
$491$		−	18.8686i		−	0.851527i	0.904835	−	0.425763i	$-0.139994\pi$
$492$	3.48753	−	11.1460i	0.157230	−	0.502499i
$493$	−10.7303	+	2.87517i	−0.483267	+	0.129491i
$494$	−6.40986	+	11.1022i	−0.288393	+	0.499512i
$495$	−9.44061	+	25.7447i	−0.424324	+	1.15714i
$496$	5.24387			0.235457
$497$	0.666675	+	15.5898i	0.0299045	+	0.699298i
$498$	10.4733	+	11.3795i	0.469320	+	0.509929i
$499$	−33.7931	+	19.5105i	−1.51279	+	0.873408i	−0.512900	+	0.858449i	$0.671429\pi$
$499$	−33.7931	+	19.5105i	−1.51279	+	0.873408i	−0.999888	+	0.0149599i	$0.995238\pi$
$500$	10.8560	−	2.67331i	0.485496	−	0.119554i
$501$	−32.4679	−	20.5846i	−1.45056	−	0.919653i
$502$	15.2078	+	4.07491i	0.678756	+	0.181872i
$503$	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	$-0.0194720\pi$
$504$	2.36043	−	7.57815i	0.105142	−	0.337558i
$505$	−4.70656	+	4.64313i	−0.209439	+	0.206617i
$506$	−3.89270	+	2.24745i	−0.173052	+	0.0999114i
$507$	−5.42388	−	24.2148i	−0.240883	−	1.07542i
$508$	−7.52231	+	2.01560i	−0.333749	+	0.0894277i
$509$	9.24940	+	16.0204i	0.409972	+	0.710093i	0.994886	−	0.101002i	$-0.0322050\pi$
$509$	9.24940	+	16.0204i	0.409972	+	0.710093i	−0.584914	+	0.811095i	$0.698872\pi$
$510$	−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
$513$	−4.79912	+	11.8046i	−0.211886	+	0.521185i
$514$	−22.2823	−	12.8647i	−0.982829	−	0.567436i
$515$	−19.9948	−	11.7256i	−0.881078	−	0.516691i
$516$	1.44646	+	2.76384i	0.0636767	+	0.121671i
$517$	8.89969	−	8.89969i	0.391408	−	0.391408i
$518$	6.76560	−	12.9682i	0.297263	−	0.569791i
$519$	1.88993	+	0.0783751i	0.0829586	+	0.00344028i
$520$	3.10188	−	11.2700i	0.136026	−	0.494222i
$521$	−25.4519	−	14.6946i	−1.11507	−	0.643784i	−0.174929	−	0.984581i	$-0.555970\pi$
$521$	−25.4519	−	14.6946i	−1.11507	−	0.643784i	−0.940137	+	0.340797i	$0.889303\pi$
$522$	−0.794760	−	4.39481i	−0.0347857	−	0.192356i
$523$	5.14665	−	19.2076i	0.225047	−	0.839888i	−0.757338	−	0.653023i	$-0.773501\pi$
$523$	5.14665	−	19.2076i	0.225047	−	0.839888i	0.982386	−	0.186865i	$-0.0598327\pi$
$524$	−14.4806			−0.632588
$525$	22.0577	+	6.20154i	0.962676	+	0.270657i
$526$	0.913979			0.0398514
$527$	10.1277	−	37.7970i	0.441168	−	1.64646i
$528$	1.54752	+	6.90888i	0.0673473	+	0.300671i
$529$	−18.8714	−	10.8954i	−0.820496	−	0.473714i
$530$	−3.38259	+	12.2899i	−0.146930	+	0.533839i
$531$	−2.52930	+	30.4432i	−0.109762	+	1.32112i
$532$	−6.48241	+	0.277211i	−0.281048	+	0.0120186i
$533$	24.9241	−	24.9241i	1.07958	−	1.07958i
$534$	20.5962	−	10.7790i	0.891284	−	0.466453i
$535$	−2.45575	−	1.44013i	−0.106172	−	0.0622623i
$536$	3.04245	+	1.75656i	0.131414	+	0.0758718i
$537$	−2.74583	+	8.77554i	−0.118491	+	0.378692i
$538$	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	0.987470	−	0.157806i	$-0.0504422\pi$
$541$	8.30525	+	14.3851i	0.357071	+	0.618465i	−0.630399	+	0.776271i	$0.717109\pi$
$542$	0.276992	−	0.0742198i	0.0118978	−	0.00318801i
$543$	23.2372	−	5.20491i	0.997204	−	0.223364i
$544$	−6.46236	+	3.73105i	−0.277072	+	0.159967i
$545$	4.73858	−	4.67472i	0.202978	−	0.200243i
$546$	16.9172	−	16.9609i	0.723988	−	0.725860i
$547$	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	$0.214240\pi$
$548$	11.5861	+	3.10449i	0.494934	+	0.132617i
$549$	−4.01753	−	2.78700i	−0.171464	−	0.118946i
$550$	−19.8120	+	5.02152i	−0.844785	+	0.214118i
$551$	−3.16170	+	1.82541i	−0.134693	+	0.0777651i
$552$	1.40140	−	1.28980i	0.0596476	−	0.0548974i
$553$	−21.1096	+	13.4217i	−0.897672	+	0.570751i
$554$	−32.1963			−1.36789
$555$	6.53242	−	20.3909i	0.277286	−	0.865545i
$556$	−3.62697	+	6.28210i	−0.153818	+	0.266420i
$557$	36.4006	−	9.75350i	1.54234	−	0.413269i	0.615320	−	0.788277i	$-0.289027\pi$
$557$	36.4006	−	9.75350i	1.54234	−	0.413269i	0.927022	+	0.375008i	$0.122360\pi$
$558$	14.8063	+	5.31582i	0.626800	+	0.225036i
$559$			9.41486i			0.398206i
$560$	5.65576	−	1.73562i	0.239000	−	0.0733432i
$561$	52.7868	+	2.18906i	2.22866	+	0.0924223i
$562$	−6.21780	−	1.66605i	−0.262282	−	0.0702782i
$563$	9.51495	+	35.5103i	0.401007	+	1.49658i	0.811302	+	0.584627i	$0.198759\pi$
$563$	9.51495	+	35.5103i	0.401007	+	1.49658i	−0.410295	+	0.911953i	$0.634574\pi$
$564$	−2.85558	+	4.50408i	−0.120242	+	0.189656i
$565$	4.31617	+	7.59433i	0.181582	+	0.319496i
$566$			1.96358i			0.0825353i
$567$	14.3469	−	19.0044i	0.602513	−	0.798109i
$568$	4.17036	+	4.17036i	0.174984	+	0.174984i
$569$	−9.38493	−	16.2552i	−0.393437	−	0.681452i	0.599464	−	0.800402i	$-0.295381\pi$
$569$	−9.38493	−	16.2552i	−0.393437	−	0.681452i	−0.992900	+	0.118950i	$0.962047\pi$
$570$	−9.28216	+	2.01308i	−0.388787	+	0.0843188i
$571$	−16.9888	+	29.4255i	−0.710960	+	1.23142i	0.253538	+	0.967326i	$0.418406\pi$
$571$	−16.9888	+	29.4255i	−0.710960	+	1.23142i	−0.964497	+	0.264093i	$0.914928\pi$
$572$	−5.53055	+	20.6403i	−0.231244	+	0.863014i
$573$	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
$576$	−1.27974	−	2.71335i	−0.0533223	−	0.113056i
$577$	5.97184	+	22.2872i	0.248611	+	0.927829i	0.971534	+	0.236900i	$0.0761315\pi$
$577$	5.97184	+	22.2872i	0.248611	+	0.927829i	−0.722923	+	0.690929i	$0.757202\pi$
$578$	10.0119	+	37.3648i	0.416439	+	1.55417i
$579$	5.22442	−	2.73420i	0.217119	−	0.113629i
$580$	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
$583$	6.03105	−	22.5082i	0.249781	−	0.932194i
$584$	−2.78756	+	4.82819i	−0.115350	+	0.199792i
$585$	20.1829	−	28.6768i	0.834459	−	1.18564i
$586$	−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	$0.533283\pi$
$588$	11.8380	+	2.61951i	0.488191	+	0.108027i
$589$		−	12.8599i		−	0.529881i
$590$	−19.7955	+	11.2506i	−0.814966	+	0.463178i
$591$	−24.7880	−	15.7156i	−1.01964	−	0.646452i
$592$	−1.43087	−	5.34010i	−0.0588086	−	0.219477i
$593$	−2.59375	−	0.694994i	−0.106513	−	0.0285400i	0.205169	−	0.978727i	$-0.434226\pi$
$593$	−2.59375	−	0.694994i	−0.106513	−	0.0285400i	−0.311682	+	0.950187i	$0.600892\pi$
$594$	−2.63418	+	21.0763i	−0.108082	+	0.864769i
$595$	−1.58688	−	44.1178i	−0.0650556	−	1.80865i
$596$			11.4395i			0.468581i
$597$	6.97997	+	2.18400i	0.285671	+	0.0893854i
$598$	5.55241	−	1.48776i	0.227055	−	0.0608392i
$599$	8.81980	−	15.2764i	0.360367	−	0.624175i	−0.627654	−	0.778493i	$-0.715985\pi$
$599$	8.81980	−	15.2764i	0.360367	−	0.624175i	0.988021	+	0.154318i	$0.0493180\pi$
$600$	7.72675	−	3.91118i	0.315443	−	0.159673i
$601$	−25.1426			−1.02559			−0.512794	−	0.858512i	$-0.671390\pi$
$601$	−25.1426			−1.02559			−0.512794	+	0.858512i	$0.671390\pi$
$602$	−4.02110	+	2.55666i	−0.163888	+	0.104202i
$603$	6.80981	+	8.04390i	0.277317	+	0.327573i
$604$	11.7061	−	6.75854i	0.476316	−	0.275001i
$605$	12.3532	−	3.22038i	0.502230	−	0.130927i
$606$	−2.74214	+	4.32515i	−0.111392	+	0.175697i
$607$	41.5761	+	11.1403i	1.68752	+	0.452170i	0.969748	−	0.244107i	$-0.0784947\pi$
$607$	41.5761	+	11.1403i	1.68752	+	0.452170i	0.717773	+	0.696277i	$0.245161\pi$
$608$	−1.73408	+	1.73408i	−0.0703262	+	0.0703262i
$609$	6.58733	−	1.77419i	0.266932	−	0.0718938i
$610$	0.0247237	−	3.64439i	0.00100103	−	0.147557i
$611$	−13.9392	+	8.04780i	−0.563920	+	0.325579i
$612$	−22.0290	+	3.98373i	−0.890468	+	0.161033i
$613$	−28.4761	+	7.63014i	−1.15014	+	0.308178i	−0.783020	−	0.621996i	$-0.786322\pi$
$613$	−28.4761	+	7.63014i	−1.15014	+	0.308178i	−0.367117	+	0.930175i	$0.619655\pi$
$614$	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	$0.963494\pi$
$618$	−17.1354	−	5.36161i	−0.689288	−	0.215675i
$619$	22.7455	+	13.1321i	0.914221	+	0.527826i	0.881787	−	0.471648i	$-0.156341\pi$
$619$	22.7455	+	13.1321i	0.914221	+	0.527826i	0.0324339	+	0.999474i	$0.489674\pi$
$620$	2.95792	+	11.3464i	0.118793	+	0.455684i
$621$	5.26440	−	2.22117i	0.211253	−	0.0891323i
$622$	2.66880	−	2.66880i	0.107009	−	0.107009i
$623$	19.0523	+	29.9653i	0.763314	+	1.20053i
$624$	0.375159	−	9.04653i	0.0150184	−	0.362151i
$625$	11.9080	+	21.9818i	0.476319	+	0.879273i
$626$	−23.4389	−	13.5325i	−0.936807	−	0.540866i
$627$	16.9431	−	3.79508i	0.676641	−	0.151561i
$628$	2.57312	−	9.60302i	0.102679	−	0.383202i
$629$	−41.2540			−1.64490
$630$	17.7287	+	0.832773i	0.706328	+	0.0331785i
$631$	29.2208			1.16326			0.581631	−	0.813452i	$-0.302415\pi$
$631$	29.2208			1.16326			0.581631	+	0.813452i	$0.302415\pi$
$632$	−2.44710	+	9.13268i	−0.0973402	+	0.363279i
$633$	2.95253	−	0.661339i	0.117353	−	0.0262858i
$634$	18.4071	+	10.6273i	0.731038	+	0.422065i
$635$	−8.60437	−	15.1395i	−0.341454	−	0.600792i
$636$	−0.409110	+	9.86523i	−0.0162223	+	0.391182i
$637$	27.9893	+	23.5714i	1.10898	+	0.933934i
$638$	−4.30297	+	4.30297i	−0.170356	+	0.170356i
$639$	7.54759	+	16.0027i	0.298578	+	0.633058i
$640$	1.13115	−	1.92886i	0.0447124	−	0.0762450i
$641$	40.0771	+	23.1385i	1.58295	+	0.913916i	0.994426	+	0.105435i	$0.0336235\pi$
$641$	40.0771	+	23.1385i	1.58295	+	0.913916i	0.588522	+	0.808481i	$0.299710\pi$
$642$	−2.10456	−	0.658509i	−0.0830605	−	0.0259893i
$643$	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
$647$	−1.85517	+	0.497092i	−0.0729343	+	0.0195427i	−0.295102	−	0.955466i	$-0.595354\pi$
$647$	−1.85517	+	0.497092i	−0.0729343	+	0.0195427i	0.222167	+	0.975009i	$0.428687\pi$
$648$	−0.862807	−	8.95855i	−0.0338943	−	0.351925i
$649$	36.0471	−	20.8118i	1.41497	−	0.816935i
$650$	26.1351	+	0.354619i	1.02510	+	0.0139093i
$651$	−6.18956	+	23.2196i	−0.242588	+	0.910050i
$652$	−8.21531	+	8.21531i	−0.321736	+	0.321736i
$653$	47.9356	+	12.8443i	1.87586	+	0.502636i	0.999791	+	0.0204570i	$0.00651211\pi$
$653$	47.9356	+	12.8443i	1.87586	+	0.502636i	0.876073	+	0.482179i	$0.160155\pi$
$654$	2.76080	−	4.35457i	0.107956	−	0.170277i
$655$	−8.16809	−	31.3324i	−0.319154	−	1.22426i
$656$	5.83942	−	3.37139i	0.227991	−	0.131631i
$657$	−12.7652	+	10.8068i	−0.498018	+	0.421612i
$658$	−7.22250	−	3.76802i	−0.281562	−	0.146893i
$659$	23.0084			0.896279			0.448139	−	0.893964i	$-0.352087\pi$
$659$	23.0084			0.896279			0.448139	+	0.893964i	$0.352087\pi$
$660$	−14.0762	+	7.24556i	−0.547915	+	0.282033i
$661$	15.1551	−	26.2494i	0.589465	−	1.02098i	−0.404838	−	0.914389i	$-0.632672\pi$
$661$	15.1551	−	26.2494i	0.589465	−	1.02098i	0.994303	−	0.106594i	$-0.0339947\pi$
$662$	−3.96332	+	1.06197i	−0.154039	+	0.0412746i
$663$	−64.4813	−	20.1759i	−2.50425	−	0.783569i
$664$			8.92905i			0.346514i
$665$	−4.25635	−	13.8700i	−0.165054	−	0.537854i
$666$	1.37323	−	16.5285i	0.0532115	−	0.640465i
$667$	1.58122	+	0.423688i	0.0612252	+	0.0164052i
$668$	−5.74456	−	21.4390i	−0.222264	−	0.829499i
$669$	−10.8892	−	6.90373i	−0.421000	−	0.266914i
$670$	−2.08460	+	7.57393i	−0.0805351	+	0.292606i
$671$			6.66235i			0.257197i
$672$	3.96566	−	2.29641i	0.152979	−	0.0885860i
$673$	−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
$675$	25.7816	−	3.21061i	0.992335	−	0.123576i
$676$	7.16342	−	12.4074i	0.275516	−	0.477208i
$677$	6.87791	−	25.6687i	0.264340	−	0.986529i	−0.698314	−	0.715792i	$-0.746066\pi$
$677$	6.87791	−	25.6687i	0.264340	−	0.986529i	0.962653	−	0.270737i	$-0.0872675\pi$
$678$	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
$681$	10.8736	−	5.69072i	0.416679	−	0.218069i
$682$	−5.54787	−	20.7049i	−0.212439	−	0.792832i
$683$	−5.07317	−	18.9333i	−0.194119	−	0.724464i	−0.992493	−	0.122301i	$-0.960973\pi$
$683$	−5.07317	−	18.9333i	−0.194119	−	0.724464i	0.798374	−	0.602163i	$-0.205694\pi$
$684$	−6.65411	+	3.13837i	−0.254426	+	0.119999i
$685$	−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
$688$	−0.466139	+	1.73965i	−0.0177714	+	0.0663237i
$689$	−14.8999	+	25.8074i	−0.567642	+	0.983185i
$690$	3.58129	+	2.30475i	0.136337	+	0.0877402i
$691$	17.1906	+	29.7749i	0.653960	+	1.13269i	0.982154	+	0.188081i	$0.0602267\pi$
$691$	17.1906	+	29.7749i	0.653960	+	1.13269i	−0.328194	+	0.944610i	$0.606440\pi$
$692$	0.772223	+	0.772223i	0.0293555	+	0.0293555i
$693$	−32.4188	−	1.30247i	−1.23149	−	0.0494768i
$694$		−	31.2718i		−	1.18706i
$695$	−15.6388	−	4.30432i	−0.593213	−	0.163272i
$696$	1.38067	−	2.17771i	0.0523341	−	0.0825459i
$697$	−13.0226	−	48.6008i	−0.493264	−	1.84089i
$698$	25.5454	+	6.84487i	0.966908	+	0.259082i
$699$	48.0605	+	1.99306i	1.81782	+	0.0753846i
$700$	6.94570	+	11.2587i	0.262523	+	0.425537i
$701$		−	13.1621i		−	0.497124i	−0.968616	−	0.248562i	$-0.920042\pi$
$701$		−	13.1621i		−	0.497124i	0.968616	−	0.248562i	$-0.0799581\pi$
$702$	10.2299	−	25.1629i	0.386104	−	0.949714i
$703$	−13.0958	+	3.50902i	−0.493919	+	0.132345i
$704$	−2.04384	+	3.54004i	−0.0770302	+	0.133420i
$705$	−11.3565	−	3.63816i	−0.427709	−	0.137021i
$706$	−19.9103			−0.749335
$707$	−6.93558	−	3.61833i	−0.260839	−	0.136081i
$708$	−12.9772	+	11.9437i	−0.487714	+	0.448874i
$709$	6.02363	−	3.47774i	0.226222	−	0.130609i	−0.382606	−	0.923912i	$-0.624973\pi$
$709$	6.02363	−	3.47774i	0.226222	−	0.130609i	0.608828	+	0.793302i	$0.291640\pi$
$710$	−6.67124	+	11.3760i	−0.250367	+	0.426934i
$711$	−16.1674	+	23.3058i	−0.606327	+	0.874037i
$712$	12.9639	+	3.47367i	0.485844	+	0.130181i
$713$	−4.07737	+	4.07737i	−0.152699	+	0.152699i
$714$	−8.89312	−	33.0190i	−0.332817	−	1.23570i
$715$	−47.7801	−	0.324142i	−1.78687	−	0.0121222i
$716$	−4.59754	+	2.65439i	−0.171818	+	0.0991993i
$717$	−10.8301	+	2.42585i	−0.404459	+	0.0905949i
$718$	−27.2815	+	7.31005i	−1.01814	+	0.272808i
$719$	−8.04406	−	13.9327i	−0.299993	−	0.519603i	0.676141	−	0.736772i	$-0.263651\pi$
$719$	−8.04406	−	13.9327i	−0.299993	−	0.519603i	−0.976134	+	0.217169i	$0.930318\pi$
$720$	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
$723$	−7.12748	+	22.7791i	−0.265074	+	0.847163i
$724$	11.9065	+	6.87422i	0.442501	+	0.255478i
$725$	6.39516	+	3.80886i	0.237510	+	0.141458i
$726$	8.76126	−	4.58520i	0.325161	−	0.170173i
$727$	−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	$0.379075\pi$
$728$	13.8181	−	0.590909i	0.512131	−	0.0219005i
$729$	6.64528	−	26.1695i	0.246122	−	0.969239i
$730$	−12.0194	−	3.30814i	−0.444857	−	0.122440i
$731$	11.6389	+	6.71970i	0.430479	+	0.248537i
$732$	−0.617035	−	2.75474i	−0.0228063	−	0.101818i
$733$	−1.94770	+	7.26892i	−0.0719400	+	0.268484i	−0.992522	−	0.122066i	$-0.961048\pi$
$733$	−1.94770	+	7.26892i	−0.0719400	+	0.268484i	0.920582	+	0.390549i	$0.127715\pi$
$734$	21.9155			0.808915
$735$	1.00951	+	27.0921i	0.0372363	+	0.999306i
$736$	1.09962			0.0405326
$737$	3.71677	−	13.8712i	0.136909	−	0.510952i
$738$	19.9055	−	3.59972i	0.732731	−	0.132508i
$739$	−35.8593	−	20.7034i	−1.31911	−	0.761586i	−0.335522	−	0.942033i	$-0.608913\pi$
$739$	−35.8593	−	20.7034i	−1.31911	−	0.761586i	−0.983585	+	0.180446i	$0.942246\pi$
$740$	10.7475	−	6.10825i	0.395087	−	0.224544i
$741$	−22.1853	−	0.920023i	−0.814999	−	0.0337979i
$742$	−15.0686	+	0.644385i	−0.553184	+	0.0236561i
$743$	−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	$0.992444\pi$
$744$	4.21151	+	8.04722i	0.154402	+	0.295026i
$745$	−24.7523	+	6.45270i	−0.906853	+	0.236409i
$746$	−3.54409	−	2.04618i	−0.129758	−	0.0749160i
$747$	−9.05155	+	25.2115i	−0.331179	+	0.922442i
$748$	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	−0.884065	−	0.467363i	$-0.845204\pi$
$751$	−23.2055	−	40.1931i	−0.846781	−	1.46667i	0.0372844	−	0.999305i	$-0.488129\pi$
$752$	−2.97410	+	0.796909i	−0.108454	+	0.0290603i
$753$	5.96048	+	26.6104i	0.217212	+	0.969738i
$754$	6.73956	−	3.89109i	0.245440	−	0.141705i
$755$	21.2269	+	21.5169i	0.772526	+	0.783079i
$756$	13.5251	−	2.46393i	0.491904	−	0.0896124i
$757$	−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	$0.336870\pi$
$758$	−11.6689	−	3.12668i	−0.423835	−	0.113566i
$759$	−6.57527	−	4.16872i	−0.238667	−	0.151315i
$760$	−4.73026	−	2.77397i	−0.171585	−	0.100623i
$761$	−22.6579	+	13.0816i	−0.821350	+	0.474207i	−0.850882	−	0.525357i	$-0.823932\pi$
$761$	−22.6579	+	13.0816i	−0.821350	+	0.474207i	0.0295319	+	0.999564i	$0.490598\pi$
$762$	−9.13452	−	9.92491i	−0.330909	−	0.359542i
$763$	6.98276	+	3.64295i	0.252793	+	0.131884i
$764$	1.68544			0.0609771
$765$	−21.0457	−	45.4181i	−0.760910	−	1.64210i
$766$	−16.2451	+	28.1374i	−0.586960	+	1.01664i
$767$	−51.4163	+	13.7770i	−1.85653	+	0.497457i
$768$	0.517224	−	1.65302i	0.0186637	−	0.0596483i
$769$			51.0736i			1.84176i	0.389843	+	0.920881i	$0.372529\pi$
$769$			51.0736i			1.84176i	−0.389843	+	0.920881i	$0.627471\pi$
$770$	−12.8365	−	20.4950i	−0.462597	−	0.738588i
$771$	1.84650	−	44.5263i	0.0665000	−	1.60357i
$772$	3.28843	+	0.881131i	0.118353	+	0.0317126i
$773$	−9.45865	−	35.3002i	−0.340204	−	1.26966i	−0.898116	−	0.439759i	$-0.855064\pi$
$773$	−9.45865	−	35.3002i	−0.340204	−	1.26966i	0.557912	−	0.829900i	$-0.311603\pi$
$774$	−3.07968	+	4.43945i	−0.110697	+	0.159573i
$775$	−22.8824	+	12.8004i	−0.821961	+	0.459804i
$776$			7.37533i			0.264759i
$777$	25.3346	−	0.0327166i	0.908875	−	0.00117370i
$778$	0.0216633	+	0.0216633i	0.000776666	+	0.000776666i
$779$	−8.26786	−	14.3203i	−0.296227	−	0.513080i
$780$	19.7861	−	4.29114i	0.708455	−	0.153647i
$781$	12.0541	−	20.8784i	0.431330	−	0.747086i
$782$	2.12373	−	7.92588i	0.0759446	−	0.283429i
$783$	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
$786$	−11.6298	−	22.2219i	−0.414822	−	0.792627i
$787$	−3.54432	−	13.2276i	−0.126342	−	0.471513i	0.873542	−	0.486748i	$-0.161817\pi$
$787$	−3.54432	−	13.2276i	−0.126342	−	0.471513i	−0.999884	+	0.0152350i	$0.995150\pi$
$788$	−4.38575	−	16.3678i	−0.156236	−	0.583080i
$789$	0.734044	+	1.40259i	0.0261327	+	0.0499334i
$790$	−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
$793$	2.20516	−	8.22978i	0.0783076	−	0.292248i
$794$	11.4749	−	19.8751i	0.407228	−	0.705340i
$795$	−21.5767	+	4.67948i	−0.765246	+	0.165964i
$796$	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	$0.747861\pi$
$798$	−5.63162	−	9.72523i	−0.199357	−	0.344269i
$799$			22.9759i			0.812830i
$800$	4.81163	+	1.35950i	0.170117	+	0.0480656i
$801$	33.0828	+	22.9498i	1.16892	+	0.810893i
$802$	−4.34713	−	16.2237i	−0.153503	−	0.572879i
$803$	22.0128	+	5.89830i	0.776814	+	0.208147i
$804$	−0.252123	+	6.07967i	−0.00889170	+	0.214413i
$805$	−3.04811	+	5.74716i	−0.107432	+	0.202561i
$806$			27.4124i			0.965560i
$807$	−4.19885	+	13.4193i	−0.147807	+	0.472383i
$808$	−2.85595	+	0.765250i	−0.100472	+	0.0269214i
$809$	12.6754	−	21.9544i	0.445642	−	0.771875i	−0.552454	−	0.833543i	$-0.686309\pi$
$809$	12.6754	−	21.9544i	0.445642	−	0.771875i	0.998097	+	0.0616679i	$0.0196420\pi$
$810$	18.8974	−	6.92016i	0.663987	−	0.243150i
$811$	44.0597			1.54714			0.773572	−	0.633708i	$-0.218468\pi$
$811$	44.0597			1.54714			0.773572	+	0.633708i	$0.218468\pi$
$812$	3.49206	+	1.82183i	0.122547	+	0.0639336i
$813$	0.336358	+	0.365462i	0.0117966	+	0.0128173i
$814$	−19.5710	+	11.2993i	−0.685964	+	0.396041i
$815$	−22.4099	−	13.1419i	−0.784985	−	0.460340i
$816$	−10.9158	−	6.92059i	−0.382128	−	0.242269i
$817$	4.26626	+	1.14314i	0.149257	+	0.0399934i
$818$	−20.1012	+	20.1012i	−0.702822	+	0.702822i
$819$	39.6148	+	12.3392i	1.38425	+	0.431166i
$820$	10.5887	+	10.7334i	0.369774	+	0.374825i
$821$	39.8047	−	22.9813i	1.38919	−	0.802051i	0.395969	−	0.918264i	$-0.370409\pi$
$821$	39.8047	−	22.9813i	1.38919	−	0.802051i	0.993224	+	0.116213i	$0.0370754\pi$
$822$	4.54102	+	20.2733i	0.158386	+	0.707113i
$823$	20.0447	−	5.37097i	0.698716	−	0.187220i	0.108061	−	0.994144i	$-0.465536\pi$
$823$	20.0447	−	5.37097i	0.698716	−	0.187220i	0.590655	+	0.806924i	$0.298869\pi$
$824$	−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	$0.875423\pi$
$828$	3.10482	+	1.11471i	0.107900	+	0.0387388i
$829$	−12.2584	−	7.07737i	−0.425751	−	0.245807i	0.271784	−	0.962358i	$-0.412386\pi$
$829$	−12.2584	−	7.07737i	−0.425751	−	0.245807i	−0.697535	+	0.716551i	$0.745720\pi$
$830$	−19.3203	+	5.03662i	−0.670616	+	0.174824i
$831$	−25.8578	−	49.4082i	−0.896997	−	1.71395i
$832$	3.69641	−	3.69641i	0.128150	−	0.128150i
$833$	49.1165	−	17.7773i	1.70178	−	0.615949i
$834$	−12.5534	−	0.520588i	−0.434689	−	0.0180265i
$835$	43.1483	−	24.5229i	1.49321	−	0.848651i
$836$	8.68144	+	5.01223i	0.300254	+	0.173352i
$837$	3.73375	+	26.9909i	0.129057	+	0.932944i
$838$	5.20473	−	19.4243i	0.179794	−	0.671002i
$839$	−7.87337			−0.271819			−0.135909	−	0.990721i	$-0.543396\pi$
$839$	−7.87337			−0.271819			−0.135909	+	0.990721i	$0.543396\pi$
$840$	7.20578	+	7.28538i	0.248623	+	0.251369i
$841$	−26.7838			−0.923579
$842$	−0.120772	+	0.450728i	−0.00416208	+	0.0155331i
$843$	−2.43698	−	10.8799i	−0.0839342	−	0.374722i
$844$	1.51285	+	0.873442i	0.0520743	+	0.0300651i
$845$	30.8872	+	8.50120i	1.06255	+	0.292450i
$846$	−9.20534	−	0.764804i	−0.316486	−	0.0262945i
$847$	8.10451	+	12.7467i	0.278474	+	0.437982i
$848$	−4.03092	+	4.03092i	−0.138422	+	0.138422i
$849$	−3.01329	+	1.57701i	−0.103416	+	0.0541228i
$850$	19.0919	−	32.0557i	0.654847	−	1.09950i
$851$	5.26476	+	3.03961i	0.180474	+	0.104197i
$852$	−3.05047	+	9.74915i	−0.104507	+	0.334000i
$853$	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
$857$	−35.1598	+	9.42103i	−1.20103	+	0.321816i	−0.803239	−	0.595657i	$-0.796892\pi$
$857$	−35.1598	+	9.42103i	−1.20103	+	0.321816i	−0.397796	+	0.917474i	$0.630225\pi$
$858$	−36.1162	+	8.08969i	−1.23299	+	0.276177i
$859$	18.8699	−	10.8945i	0.643831	−	0.371716i	−0.142258	−	0.989830i	$-0.545436\pi$
$859$	18.8699	−	10.8945i	0.643831	−	0.371716i	0.786089	+	0.618114i	$0.212103\pi$
$860$	−4.02712	−	0.0273201i	−0.137324	−	0.000931607i
$861$	8.03586	+	29.8361i	0.273862	+	1.01681i
$862$	9.94337	−	9.94337i	0.338672	−	0.338672i
$863$	−29.5289	−	7.91226i	−1.00518	−	0.269336i	−0.281564	−	0.959542i	$-0.590853\pi$
$863$	−29.5289	−	7.91226i	−1.00518	−	0.269336i	−0.723613	+	0.690206i	$0.757520\pi$
$864$	3.13610	−	4.14305i	0.106692	−	0.140949i
$865$	−1.23531	+	2.10649i	−0.0420018	+	0.0716227i
$866$	9.69177	−	5.59555i	0.329340	−	0.190144i
$867$	−49.2990	+	45.3729i	−1.67428	+	1.54095i
$868$	−11.7079	+	7.44400i	−0.397391	+	0.252666i
$869$	38.6484			1.31106
$870$	5.49082	+	1.75904i	0.186156	+	0.0596370i
$871$	−9.18242	+	15.9044i	−0.311134	+	0.538901i
$872$	2.87538	−	0.770456i	0.0973727	−	0.0260909i
$873$	−7.47651	+	20.8245i	−0.253042	+	0.704803i
$874$		−	2.69666i		−	0.0912161i
$875$	−20.4431	+	21.3795i	−0.691102	+	0.722757i
$876$	−9.64808	−	0.400105i	−0.325978	−	0.0135183i
$877$	−20.2019	−	5.41309i	−0.682171	−	0.182787i	−0.0989398	−	0.995093i	$-0.531545\pi$
$877$	−20.2019	−	5.41309i	−0.682171	−	0.182787i	−0.583231	+	0.812306i	$0.698212\pi$
$878$	−0.507186	−	1.89284i	−0.0171167	−	0.0638804i
$879$	1.80082	−	2.84042i	0.0607403	−	0.0958049i
$880$	−8.81264	−	2.42553i	−0.297074	−	0.0817647i
$881$		−	42.7328i		−	1.43971i	−0.694127	−	0.719853i	$-0.744209\pi$
$881$		−	42.7328i		−	1.43971i	0.694127	−	0.719853i	$-0.255791\pi$
$882$	5.48757	+	20.2703i	0.184776	+	0.682538i
$883$	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
$885$	−33.1634	−	21.3424i	−1.11477	−	0.717415i
$886$	12.8261	−	22.2155i	0.430902	−	0.746344i
$887$	0.399896	−	1.49243i	0.0134272	−	0.0501110i	−0.958887	−	0.283787i	$-0.908409\pi$
$887$	0.399896	−	1.49243i	0.0134272	−	0.0501110i	0.972314	+	0.233676i	$0.0750757\pi$
$888$	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
$891$	−34.4591	+	12.8846i	−1.15442	+	0.431650i
$892$	−1.92663	−	7.19027i	−0.0645082	−	0.240748i
$893$	1.95431	+	7.29357i	0.0653984	+	0.244070i
$894$	−17.5550	+	9.18742i	−0.587128	+	0.307273i
$895$	−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
$898$	−1.16887	+	4.36227i	−0.0390056	+	0.145571i
$899$	−3.90327	+	6.76066i	−0.130181	+	0.225481i
$900$	12.2077	+	8.71625i	0.406922	+	0.290542i
$901$	21.2692	+	36.8393i	0.708579	+	1.22729i
$902$	−19.4895	−	19.4895i	−0.648930	−	0.648930i
$903$	−7.15291	−	4.11743i	−0.238034	−	0.137019i
$904$			3.90649i			0.129928i
$905$	−8.15799	+	29.6402i	−0.271181	+	0.985275i
$906$	19.7732	+	12.5362i	0.656920	+	0.416487i
$907$	−2.23419	−	8.33811i	−0.0741851	−	0.276862i	0.918862	−	0.394579i	$-0.129109\pi$
$907$	−2.23419	−	8.33811i	−0.0741851	−	0.276862i	−0.993047	+	0.117716i	$0.962443\pi$
$908$	6.84424	+	1.83391i	0.227134	+	0.0608604i
$909$	−8.83964	−	0.734421i	−0.293192	−	0.0243592i
$910$	9.07295	+	29.5655i	0.300765	+	0.980088i
$911$			49.6817i			1.64603i	0.568020	+	0.823015i	$0.307710\pi$
$911$			49.6817i			1.64603i	−0.568020	+	0.823015i	$0.692290\pi$
$912$	−4.05380	−	1.26842i	−0.134235	−	0.0420015i
$913$	35.2555	−	9.44668i	1.16679	−	0.312639i
$914$	14.4552	−	25.0372i	0.478136	−	0.828156i
$915$	5.61252	−	2.88898i	0.185544	−	0.0955067i
$916$	2.91506			0.0963164
$917$	32.3305	−	20.5561i	1.06765	−	0.678822i
$918$	−23.8056	−	30.6061i	−0.785700	−	1.01015i
$919$	−28.8152	+	16.6365i	−0.950525	+	0.548786i	−0.893244	−	0.449572i	$-0.851576\pi$
$919$	−28.8152	+	16.6365i	−0.950525	+	0.548786i	−0.0572812	+	0.998358i	$0.518243\pi$
$920$	0.620265	+	2.37931i	0.0204495	+	0.0784434i
$921$	−13.1468	+	20.7363i	−0.433203	+	0.683286i
$922$	27.6026	+	7.39609i	0.909043	+	0.243577i
$923$	−21.8006	+	21.8006i	−0.717575	+	0.717575i
$924$	−13.2627	−	13.2285i	−0.436311	−	0.435186i
$925$	19.2791	+	19.8095i	0.633893	+	0.651332i
$926$	32.1517	−	18.5628i	1.05657	−	0.610012i
$927$	−5.53409	−	30.6020i	−0.181763	−	1.00510i
$928$	1.43797	−	0.385303i	0.0472037	−	0.0126482i
$929$	−12.5625	−	21.7588i	−0.412161	−	0.713884i	0.582965	−	0.812497i	$-0.301892\pi$
$929$	−12.5625	−	21.7588i	−0.412161	−	0.713884i	−0.995126	+	0.0986138i	$0.968559\pi$
$930$	−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
$933$	6.23893	+	1.95213i	0.204253	+	0.0639100i
$934$	26.9825	+	15.5783i	0.882893	+	0.509738i
$935$	−34.5030	+	58.8355i	−1.12837	+	1.92413i
$936$	14.1841	−	6.68983i	0.463621	−	0.218664i
$937$	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	$0.183963\pi$
$938$	−9.28634	+	0.397117i	−0.303210	+	0.0129663i
$939$	1.94235	−	46.8376i	0.0633861	−	1.52849i
$940$	−3.40192	−	5.98571i	−0.110958	−	0.195232i
$941$	32.5006	+	18.7642i	1.05949	+	0.611696i	0.925291	−	0.379259i	$-0.123821\pi$
$941$	32.5006	+	18.7642i	1.05949	+	0.611696i	0.134197	+	0.990955i	$0.457154\pi$
$942$	16.8033	−	3.76378i	0.547481	−	0.122631i
$943$	−1.91901	+	7.16186i	−0.0624917	+	0.233222i
$944$	−10.1827			−0.331418
$945$	12.9605	+	27.8752i	0.421604	+	0.906780i
$946$	7.36201			0.239360
$947$	−14.8618	+	55.4649i	−0.482943	+	1.80237i	0.106206	+	0.994344i	$0.466130\pi$
$947$	−14.8618	+	55.4649i	−0.482943	+	1.80237i	−0.589149	+	0.808024i	$0.700537\pi$
$948$	−15.9803	+	3.57943i	−0.519016	+	0.116255i
$949$	−25.2394	−	14.5720i	−0.819305	−	0.473026i
$950$	3.33399	−	11.7998i	0.108169	−	0.382837i
$951$	−1.52537	+	36.7825i	−0.0494634	+	1.19276i
$952$	9.13192	−	17.5039i	0.295967	−	0.567306i
$953$	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	$0.0748158\pi$
$954$	−15.4677	+	7.29525i	−0.500785	+	0.236192i
$955$	0.950708	+	3.64687i	0.0307642	+	0.118010i
$956$	−5.54924	−	3.20386i	−0.179475	−	0.103620i
$957$	−10.0592	−	3.14747i	−0.325167	−	0.101743i
$958$	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
$962$	27.9154	−	7.47991i	0.900028	−	0.241162i
$963$	−0.679694	−	3.75852i	−0.0219028	−	0.121117i
$964$	−11.9341	+	6.89013i	−0.384370	+	0.221916i
$965$	−0.0516425	+	7.61236i	−0.00166243	+	0.245051i
$966$	−1.29793	+	4.86907i	−0.0417601	+	0.156660i
$967$	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	$0.169760\pi$
$968$	5.51463	+	1.47764i	0.177247	+	0.0474932i
$969$	−16.9718	+	26.7694i	−0.545212	+	0.859956i
$970$	−15.9584	+	4.16021i	−0.512393	+	0.133576i
$971$	−29.4378	+	16.9959i	−0.944702	+	0.545424i	−0.891431	−	0.453156i	$-0.850298\pi$
$971$	−29.4378	+	16.9959i	−0.944702	+	0.545424i	−0.0532711	+	0.998580i	$0.516965\pi$
$972$	13.0548	−	8.51894i	0.418733	−	0.273245i
$973$	−0.819974	−	19.1746i	−0.0262872	−	0.614710i
$974$	6.94402			0.222501
$975$	20.4457	+	40.3917i	0.654787	+	1.29357i
$976$	0.814929	−	1.41150i	0.0260852	−	0.0451810i
$977$	23.7906	−	6.37466i	0.761127	−	0.203943i	0.142679	−	0.989769i	$-0.454428\pi$
$977$	23.7906	−	6.37466i	0.761127	−	0.203943i	0.618448	+	0.785826i	$0.287762\pi$
$978$	−19.2051	−	6.00921i	−0.614112	−	0.192153i
$979$		−	54.8618i		−	1.75339i
$980$	−10.1637	+	11.9038i	−0.324667	+	0.380252i
$981$	8.89978	+	0.739417i	0.284148	+	0.0236078i
$982$	18.2256	+	4.88355i	0.581604	+	0.155840i
$983$	−2.73551	−	10.2091i	−0.0872492	−	0.325618i	0.908481	−	0.417925i	$-0.137243\pi$
$983$	−2.73551	−	10.2091i	−0.0872492	−	0.325618i	−0.995731	+	0.0923068i	$0.970576\pi$
$984$	9.86353	+	6.25348i	0.314438	+	0.199354i
$985$	32.9421	−	18.7223i	1.04962	−	0.596542i
$986$		−	11.1088i		−	0.353776i
$987$	−0.0182211	−	14.1098i	−0.000579985	−	0.449121i
$988$	−9.06491	−	9.06491i	−0.288393	−	0.288393i
$989$	−0.990221	−	1.71511i	−0.0314872	−	0.0545374i
$990$	−22.4240	−	15.7821i	−0.712682	−	0.501589i
$991$	19.0277	−	32.9570i	0.604435	−	1.04691i	−0.387705	−	0.921784i	$-0.626732\pi$
$991$	19.0277	−	32.9570i	0.604435	−	1.04691i	0.992140	−	0.125129i	$-0.0399346\pi$
$992$	−1.35721	+	5.06519i	−0.0430916	+	0.160820i
$993$	−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
$996$	−13.7025	+	7.17119i	−0.434180	+	0.227228i
$997$	5.07524	+	18.9410i	0.160734	+	0.599869i	0.998546	+	0.0539091i	$0.0171681\pi$
$997$	5.07524	+	18.9410i	0.160734	+	0.599869i	−0.837812	+	0.545960i	$0.816165\pi$
$998$	−10.0994	−	37.6913i	−0.319690	−	1.19310i
$999$	26.4674	−	11.1672i	0.837391	−	0.353314i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.x.a.23.5	✓	64	21.2	odd	6	inner
210.2.x.a.23.13	yes	64	7.2	even	3	inner
210.2.x.a.53.1	yes	64	1.1	even	1	trivial
210.2.x.a.53.10	yes	64	3.2	odd	2	inner
210.2.x.a.107.1	yes	64	105.2	even	12	inner
210.2.x.a.107.10	yes	64	35.2	odd	12	inner
210.2.x.a.137.5	yes	64	5.2	odd	4	inner
210.2.x.a.137.13	yes	64	15.2	even	4	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)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.69017 + 0.378582i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.593376 - 2.15590i) q^{5} +(0.0717662 - 1.73056i) q^{6} +(2.64334 - 0.113038i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.71335 - 1.27974i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.69017 + 0.378582i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.593376 - 2.15590i) q^{5} +(0.0717662 - 1.73056i) q^{6} +(2.64334 - 0.113038i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.71335 - 1.27974i) q^{9} +(1.92886 + 1.13115i) q^{10} +(-3.54004 - 2.04384i) q^{11} +(1.65302 + 0.517224i) 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} +(7.20783 - 1.93133i) q^{17} +(0.533863 + 2.95212i) q^{18} +(2.12380 - 1.22618i) q^{19} +(-1.59183 + 1.57038i) q^{20} +(-4.42489 + 1.19177i) q^{21} +(2.89043 - 2.89043i) q^{22} +(-1.06215 - 0.284603i) q^{23} +(-0.927433 + 1.46283i) q^{24} +(-4.29581 - 2.55852i) q^{25} +(-4.52715 + 2.61375i) q^{26} +(-4.10154 + 3.19020i) q^{27} +(-2.34571 - 1.22377i) q^{28} -1.48870 q^{29} +(-3.68834 - 1.18160i) q^{30} +(2.62194 - 4.54133i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(6.75703 + 2.11425i) q^{33} +7.46210i q^{34} +(1.32479 - 5.76584i) q^{35} +(-2.98970 - 0.248392i) q^{36} +(-5.34010 - 1.43087i) q^{37} +(0.634717 + 2.36880i) q^{38} +(-7.64695 - 4.84816i) q^{39} +(-1.10487 - 1.94403i) q^{40} -6.74278i q^{41} +(-0.00591784 - 4.58257i) q^{42} +(1.27352 + 1.27352i) q^{43} +(2.04384 + 3.54004i) q^{44} +(-1.14894 - 6.60908i) q^{45} +(0.549811 - 0.952300i) q^{46} +(-0.796909 + 2.97410i) q^{47} +(-1.17295 - 1.27444i) q^{48} +(6.97444 - 0.597597i) q^{49} +(3.58318 - 3.48724i) q^{50} +(-11.4513 + 5.99303i) q^{51} +(-1.35298 - 5.04938i) q^{52} +(1.47542 + 5.50634i) q^{53} +(-2.01994 - 4.78747i) q^{54} +(-6.50689 + 6.41920i) q^{55} +(1.78919 - 1.94905i) q^{56} +(-3.12538 + 2.87649i) q^{57} +(0.385303 - 1.43797i) q^{58} +(-5.09134 + 8.81846i) q^{59} +(2.09595 - 3.25684i) q^{60} +(-0.814929 - 1.41150i) q^{61} +(3.70798 + 3.70798i) q^{62} +(7.02764 - 3.68948i) q^{63} -1.00000i q^{64} +(10.1624 - 5.77572i) q^{65} +(-3.79105 + 5.97958i) q^{66} +(0.909261 + 3.39341i) q^{67} +(-7.20783 - 1.93133i) q^{68} +(1.90296 + 0.0789157i) q^{69} +(5.22649 + 2.77196i) q^{70} +5.89777i q^{71} +(1.01372 - 2.82354i) q^{72} +(-5.38514 + 1.44294i) q^{73} +(2.76424 - 4.78780i) q^{74} +(8.22926 + 2.69802i) q^{75} -2.45236 q^{76} +(-9.58854 - 5.00240i) q^{77} +(6.66214 - 6.13159i) q^{78} +(-8.18814 + 4.72742i) q^{79} +(2.16375 - 0.564071i) q^{80} +(5.72455 - 6.94475i) q^{81} +(6.51303 + 1.74516i) q^{82} +(-6.31379 + 6.31379i) q^{83} +(4.42796 + 1.18034i) q^{84} +(0.113194 - 16.6854i) q^{85} +(-1.55973 + 0.900511i) q^{86} +(2.51615 - 0.563594i) q^{87} +(-3.94840 + 1.05797i) 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} +(-2.71226 + 8.66824i) q^{93} +(-2.66651 - 1.53951i) q^{94} +(-1.38331 - 5.30630i) q^{95} +(1.53459 - 0.803130i) q^{96} +(-5.21514 + 5.21514i) q^{97} +(-1.22788 + 6.89147i) 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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