LMFDB - Embedded newform 525.2.bb.a.41.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(41,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 2, 5]))

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

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

chi := DirichletCharacter("525.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bb (of order $10$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			41.6
Character	$\chi$	$=$	525.41
Dual form			525.2.bb.a.461.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.47080 + 2.02438i) q^{2} +(1.52339 + 0.824183i) q^{3} +(-1.31684 - 4.05281i) q^{4} +(-1.94672 - 1.10013i) q^{5} +(-3.90907 + 1.87172i) q^{6} +(-1.44927 - 2.21351i) q^{7} +(5.38165 + 1.74860i) q^{8} +(1.64144 + 2.51111i) q^{9} +O(q^{10})$	\(q+(-1.47080 + 2.02438i) q^{2} +(1.52339 + 0.824183i) q^{3} +(-1.31684 - 4.05281i) q^{4} +(-1.94672 - 1.10013i) q^{5} +(-3.90907 + 1.87172i) q^{6} +(-1.44927 - 2.21351i) q^{7} +(5.38165 + 1.74860i) q^{8} +(1.64144 + 2.51111i) q^{9} +(5.09032 - 2.32283i) q^{10} +(2.25031 - 3.09728i) q^{11} +(1.33420 - 7.25934i) q^{12} +(4.15662 + 5.72110i) q^{13} +(6.61257 + 0.321764i) q^{14} +(-2.05891 - 3.28038i) q^{15} +(-4.56011 + 3.31312i) q^{16} +(-0.789704 + 2.43046i) q^{17} +(-7.49768 - 0.370426i) q^{18} +(1.81182 + 0.588696i) q^{19} +(-1.89511 + 9.33839i) q^{20} +(-0.383461 - 4.56650i) q^{21} +(2.96033 + 9.11096i) q^{22} +(-2.15121 + 2.96089i) q^{23} +(6.75719 + 7.09927i) q^{24} +(2.57943 + 4.28329i) q^{25} -17.6953 q^{26} +(0.430950 + 5.17825i) q^{27} +(-7.06250 + 8.78844i) q^{28} +(7.87362 - 2.55829i) q^{29} +(9.66899 + 0.656769i) q^{30} +(-0.602544 - 0.195779i) q^{31} -2.78715i q^{32} +(5.98082 - 2.86371i) q^{33} +(-3.75868 - 5.17338i) q^{34} +(0.386164 + 5.90346i) q^{35} +(8.01553 - 9.95919i) q^{36} +(6.75673 - 4.90905i) q^{37} +(-3.85657 + 2.80196i) q^{38} +(1.61693 + 12.1413i) q^{39} +(-8.55287 - 9.32455i) q^{40} +(1.35750 - 0.986282i) q^{41} +(9.80835 + 5.94014i) q^{42} +5.55846 q^{43} +(-15.5160 - 5.04145i) q^{44} +(-0.432887 - 6.69422i) q^{45} +(-2.82997 - 8.70975i) q^{46} +(-1.59812 - 4.91850i) q^{47} +(-9.67745 + 1.28880i) q^{48} +(-2.79926 + 6.41593i) q^{49} +(-12.4648 - 1.07811i) q^{50} +(-3.20617 + 3.05168i) q^{51} +(17.7130 - 24.3798i) q^{52} +(12.2846 - 3.99151i) q^{53} +(-11.1166 - 6.74377i) q^{54} +(-7.78812 + 3.55391i) q^{55} +(-3.92888 - 14.4465i) q^{56} +(2.27492 + 2.39009i) q^{57} +(-6.40155 + 19.7020i) q^{58} +(-4.64495 + 3.37475i) q^{59} +(-10.5835 + 12.6641i) q^{60} +(2.04274 - 2.81159i) q^{61} +(1.28255 - 0.931830i) q^{62} +(3.17947 - 7.27262i) q^{63} +(-3.47797 - 2.52689i) q^{64} +(-1.79783 - 15.7102i) q^{65} +(-2.99936 + 16.3194i) q^{66} +(-0.328350 + 1.01056i) q^{67} +10.8901 q^{68} +(-5.71745 + 2.73760i) q^{69} +(-12.5188 - 7.90107i) q^{70} +(-2.44891 + 0.795701i) q^{71} +(4.44274 + 16.3841i) q^{72} +(-5.69357 + 7.83653i) q^{73} +20.8985i q^{74} +(0.399270 + 8.65105i) q^{75} -8.11819i q^{76} +(-10.1172 - 0.492294i) q^{77} +(-26.9568 - 14.5841i) q^{78} +(-2.10805 - 6.48790i) q^{79} +(12.5221 - 1.43299i) q^{80} +(-3.61132 + 8.24369i) q^{81} +4.19873i q^{82} +(0.642469 - 1.97732i) q^{83} +(-18.0022 + 7.56745i) q^{84} +(4.21115 - 3.86264i) q^{85} +(-8.17538 + 11.2524i) q^{86} +(14.1031 + 2.59202i) q^{87} +(17.5263 - 12.7336i) q^{88} +(-3.03690 - 2.20644i) q^{89} +(14.1884 + 8.96954i) q^{90} +(6.63967 - 17.4921i) q^{91} +(14.8327 + 4.81944i) q^{92} +(-0.756554 - 0.794854i) q^{93} +(12.3074 + 3.99893i) q^{94} +(-2.87946 - 3.13926i) q^{95} +(2.29712 - 4.24592i) q^{96} +(-0.233634 + 0.0759124i) q^{97} +(-8.87115 - 15.1033i) q^{98} +(11.4714 + 0.566747i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9}+O(q^{10}) $ 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9	$ 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9} + 8 q^{15} - 92 q^{16} - 16 q^{18} + 12 q^{21} - 48 q^{22} - 32 q^{25} - 36 q^{28} - 14 q^{30} - 8 q^{36} - 4 q^{37} - 26 q^{39} - 11 q^{42} - 20 q^{49} + 20 q^{51} - 168 q^{57} + 32 q^{58} + 76 q^{60} + 29 q^{63} + 68 q^{64} - 44 q^{67} + 30 q^{70} - 114 q^{72} - 124 q^{78} - 68 q^{79} - 2 q^{81} + 102 q^{84} + 72 q^{85} - 156 q^{88} + 70 q^{91} - 32 q^{93} - 36 q^{99}+O(q^{100}) $ 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9 + 8 * q^15 - 92 * q^16 - 16 * q^18 + 12 * q^21 - 48 * q^22 - 32 * q^25 - 36 * q^28 - 14 * q^30 - 8 * q^36 - 4 * q^37 - 26 * q^39 - 11 * q^42 - 20 * q^49 + 20 * q^51 - 168 * q^57 + 32 * q^58 + 76 * q^60 + 29 * q^63 + 68 * q^64 - 44 * q^67 + 30 * q^70 - 114 * q^72 - 124 * q^78 - 68 * q^79 - 2 * q^81 + 102 * q^84 + 72 * q^85 - 156 * q^88 + 70 * q^91 - 32 * q^93 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.47080	+	2.02438i	−1.04001	+	1.43146i	−0.142856	+	0.989743i	$0.545629\pi$
$2$	−1.47080	+	2.02438i	−1.04001	+	1.43146i	−0.897157	+	0.441712i	$0.854371\pi$
$3$	1.52339	+	0.824183i	0.879531	+	0.475842i
$3$	1.52339	+	0.824183i	0.879531	+	0.475842i
$4$	−1.31684	−	4.05281i	−0.658420	−	2.02641i
$5$	−1.94672	−	1.10013i	−0.870599	−	0.491993i
$5$	−1.94672	−	1.10013i	−0.870599	−	0.491993i
$6$	−3.90907	+	1.87172i	−1.59587	+	0.764126i
$7$	−1.44927	−	2.21351i	−0.547771	−	0.836628i
$7$	−1.44927	−	2.21351i	−0.547771	−	0.836628i
$8$	5.38165	+	1.74860i	1.90270	+	0.618225i
$9$	1.64144	+	2.51111i	0.547148	+	0.837036i
$10$	5.09032	−	2.32283i	1.60970	−	0.734545i
$11$	2.25031	−	3.09728i	0.678493	−	0.933865i	−0.321422	−	0.946936i	$-0.604161\pi$
$11$	2.25031	−	3.09728i	0.678493	−	0.933865i	0.999915	+	0.0130711i	$0.00416079\pi$
$12$	1.33420	−	7.25934i	0.385150	−	2.09559i
$13$	4.15662	+	5.72110i	1.15284	+	1.58675i	0.734742	+	0.678347i	$0.237303\pi$
$13$	4.15662	+	5.72110i	1.15284	+	1.58675i	0.418099	+	0.908402i	$0.362697\pi$
$14$	6.61257	+	0.321764i	1.76728	+	0.0859950i
$15$	−2.05891	−	3.28038i	−0.531608	−	0.846991i
$16$	−4.56011	+	3.31312i	−1.14003	+	0.828279i
$17$	−0.789704	+	2.43046i	−0.191531	+	0.589473i	0.808468	+	0.588540i	$0.200297\pi$
$17$	−0.789704	+	2.43046i	−0.191531	+	0.589473i	−1.00000		0.000933055i	$0.999703\pi$
$18$	−7.49768	−	0.370426i	−1.76722	−	0.0873102i
$19$	1.81182	+	0.588696i	0.415660	+	0.135056i	0.509378	−	0.860543i	$-0.329875\pi$
$19$	1.81182	+	0.588696i	0.415660	+	0.135056i	−0.0937184	+	0.995599i	$0.529875\pi$
$20$	−1.89511	+	9.33839i	−0.423758	+	2.08813i
$21$	−0.383461	−	4.56650i	−0.0836780	−	0.996493i
$22$	2.96033	+	9.11096i	0.631145	+	1.94246i
$23$	−2.15121	+	2.96089i	−0.448558	+	0.617388i	−0.972087	−	0.234620i	$-0.924615\pi$
$23$	−2.15121	+	2.96089i	−0.448558	+	0.617388i	0.523529	+	0.852008i	$0.324615\pi$
$24$	6.75719	+	7.09927i	1.37931	+	1.44913i
$25$	2.57943	+	4.28329i	0.515886	+	0.856657i
$26$	−17.6953			−3.47033
$27$	0.430950	+	5.17825i	0.0829364	+	0.996555i
$28$	−7.06250	+	8.78844i	−1.33469	+	1.66086i
$29$	7.87362	−	2.55829i	1.46209	−	0.475063i	0.533385	−	0.845873i	$-0.320920\pi$
$29$	7.87362	−	2.55829i	1.46209	−	0.475063i	0.928709	+	0.370809i	$0.120920\pi$
$30$	9.66899	+	0.656769i	1.76531	+	0.119909i
$31$	−0.602544	−	0.195779i	−0.108220	−	0.0351629i	0.254406	−	0.967097i	$-0.418120\pi$
$31$	−0.602544	−	0.195779i	−0.108220	−	0.0351629i	−0.362627	+	0.931935i	$0.618120\pi$
$32$		−	2.78715i		−	0.492703i
$33$	5.98082	−	2.86371i	1.04113	−	0.498507i
$34$	−3.75868	−	5.17338i	−0.644609	−	0.887228i
$35$	0.386164	+	5.90346i	0.0652737	+	0.997867i
$36$	8.01553	−	9.95919i	1.33592	−	1.65987i
$37$	6.75673	−	4.90905i	1.11080	−	0.807044i	0.128011	−	0.991773i	$-0.459141\pi$
$37$	6.75673	−	4.90905i	1.11080	−	0.807044i	0.982789	+	0.184729i	$0.0591408\pi$
$38$	−3.85657	+	2.80196i	−0.625619	+	0.454539i
$39$	1.61693	+	12.1413i	0.258916	+	1.94416i
$40$	−8.55287	−	9.32455i	−1.35233	−	1.47434i
$41$	1.35750	−	0.986282i	0.212006	−	0.154031i	−0.476715	−	0.879058i	$-0.658173\pi$
$41$	1.35750	−	0.986282i	0.212006	−	0.154031i	0.688721	+	0.725027i	$0.258173\pi$
$42$	9.80835	+	5.94014i	1.51346	+	0.916584i
$43$	5.55846			0.847657			0.423828	−	0.905743i	$-0.360686\pi$
$43$	5.55846			0.847657			0.423828	+	0.905743i	$0.360686\pi$
$44$	−15.5160	−	5.04145i	−2.33912	−	0.760027i
$45$	−0.432887	−	6.69422i	−0.0645310	−	0.997916i
$46$	−2.82997	−	8.70975i	−0.417256	−	1.28418i
$47$	−1.59812	−	4.91850i	−0.233109	−	0.717437i	−0.997367	−	0.0725252i	$-0.976894\pi$
$47$	−1.59812	−	4.91850i	−0.233109	−	0.717437i	0.764257	−	0.644911i	$-0.223106\pi$
$48$	−9.67745	+	1.28880i	−1.39682	+	0.186023i
$49$	−2.79926	+	6.41593i	−0.399894	+	0.916561i
$50$	−12.4648	−	1.07811i	−1.76279	−	0.152467i
$51$	−3.20617	+	3.05168i	−0.448954	+	0.427321i
$52$	17.7130	−	24.3798i	2.45635	−	3.38087i
$53$	12.2846	−	3.99151i	1.68742	−	0.548277i	0.701094	−	0.713069i	$-0.252695\pi$
$53$	12.2846	−	3.99151i	1.68742	−	0.548277i	0.986328	+	0.164792i	$0.0526954\pi$
$54$	−11.1166	−	6.74377i	−1.51278	−	0.917710i
$55$	−7.78812	+	3.55391i	−1.05015	+	0.479209i
$56$	−3.92888	−	14.4465i	−0.525019	−	1.93050i
$57$	2.27492	+	2.39009i	0.301320	+	0.316575i
$58$	−6.40155	+	19.7020i	−0.840565	+	2.58699i
$59$	−4.64495	+	3.37475i	−0.604721	+	0.439355i	−0.847551	−	0.530713i	$-0.821924\pi$
$59$	−4.64495	+	3.37475i	−0.604721	+	0.439355i	0.242831	+	0.970069i	$0.421924\pi$
$60$	−10.5835	+	12.6641i	−1.36633	+	1.63493i
$61$	2.04274	−	2.81159i	0.261546	−	0.359988i	−0.657967	−	0.753047i	$-0.728583\pi$
$61$	2.04274	−	2.81159i	0.261546	−	0.359988i	0.919513	+	0.393059i	$0.128583\pi$
$62$	1.28255	−	0.931830i	0.162884	−	0.118342i
$63$	3.17947	−	7.27262i	0.400576	−	0.916263i
$64$	−3.47797	−	2.52689i	−0.434746	−	0.315861i
$65$	−1.79783	−	15.7102i	−0.222993	−	1.94861i
$66$	−2.99936	+	16.3194i	−0.369195	+	2.00878i
$67$	−0.328350	+	1.01056i	−0.0401143	+	0.123459i	−0.969108	−	0.246636i	$-0.920675\pi$
$67$	−0.328350	+	1.01056i	−0.0401143	+	0.123459i	0.928994	+	0.370095i	$0.120675\pi$
$68$	10.8901			1.32062
$69$	−5.71745	+	2.73760i	−0.688300	+	0.329568i
$70$	−12.5188	−	7.90107i	−1.49629	−	0.944359i
$71$	−2.44891	+	0.795701i	−0.290633	+	0.0944323i	−0.450705	−	0.892673i	$-0.648827\pi$
$71$	−2.44891	+	0.795701i	−0.290633	+	0.0944323i	0.160072	+	0.987105i	$0.448827\pi$
$72$	4.44274	+	16.3841i	0.523582	+	1.93089i
$73$	−5.69357	+	7.83653i	−0.666382	+	0.917196i	−0.999672	−	0.0256283i	$-0.991841\pi$
$73$	−5.69357	+	7.83653i	−0.666382	+	0.917196i	0.333289	+	0.942825i	$0.391841\pi$
$74$			20.8985i			2.42940i
$75$	0.399270	+	8.65105i	0.0461037	+	0.998937i
$76$		−	8.11819i		−	0.931220i
$77$	−10.1172	−	0.492294i	−1.15296	−	0.0561022i
$78$	−26.9568	−	14.5841i	−3.05226	−	1.65133i
$79$	−2.10805	−	6.48790i	−0.237174	−	0.729946i	−0.996826	−	0.0796160i	$-0.974631\pi$
$79$	−2.10805	−	6.48790i	−0.237174	−	0.729946i	0.759652	−	0.650330i	$-0.225369\pi$
$80$	12.5221	−	1.43299i	1.40001	−	0.160213i
$81$	−3.61132	+	8.24369i	−0.401258	+	0.915965i
$82$			4.19873i			0.463672i
$83$	0.642469	−	1.97732i	0.0705201	−	0.217039i	−0.909585	−	0.415518i	$-0.863600\pi$
$83$	0.642469	−	1.97732i	0.0705201	−	0.217039i	0.980105	+	0.198479i	$0.0636003\pi$
$84$	−18.0022	+	7.56745i	−1.96421	+	0.825676i
$85$	4.21115	−	3.86264i	0.456764	−	0.418963i
$86$	−8.17538	+	11.2524i	−0.881574	+	1.21338i
$87$	14.1031	+	2.59202i	1.51201	+	0.277894i
$88$	17.5263	−	12.7336i	1.86831	−	1.35740i
$89$	−3.03690	−	2.20644i	−0.321911	−	0.233882i	0.415080	−	0.909785i	$-0.363754\pi$
$89$	−3.03690	−	2.20644i	−0.321911	−	0.233882i	−0.736990	+	0.675903i	$0.763754\pi$
$90$	14.1884	+	8.96954i	1.49558	+	0.945472i
$91$	6.63967	−	17.4921i	0.696027	−	1.83367i
$92$	14.8327	+	4.81944i	1.54642	+	0.502462i
$93$	−0.756554	−	0.794854i	−0.0784510	−	0.0824226i
$94$	12.3074	+	3.99893i	1.26941	+	0.412458i
$95$	−2.87946	−	3.13926i	−0.295427	−	0.322082i
$96$	2.29712	−	4.24592i	0.234449	−	0.433347i
$97$	−0.233634	+	0.0759124i	−0.0237220	+	0.00770773i	−0.320854	−	0.947129i	$-0.603970\pi$
$97$	−0.233634	+	0.0759124i	−0.0237220	+	0.00770773i	0.297132	+	0.954836i	$0.403970\pi$
$98$	−8.87115	−	15.1033i	−0.896121	−	1.52567i
$99$	11.4714	+	0.566747i	1.15291	+	0.0569602i
$100$	13.9627	−	16.0944i	1.39627	−	1.60944i
$101$	−0.709721			−0.0706198			−0.0353099	−	0.999376i	$-0.511242\pi$
$101$	−0.709721			−0.0706198			−0.0353099	+	0.999376i	$0.511242\pi$
$102$	−1.46213	−	10.9789i	−0.144773	−	1.08708i
$103$	−4.31005	+	1.40042i	−0.424682	+	0.137988i	−0.513558	−	0.858055i	$-0.671673\pi$
$103$	−4.31005	+	1.40042i	−0.424682	+	0.137988i	0.0888754	+	0.996043i	$0.471673\pi$
$104$	12.3655	+	38.0572i	1.21254	+	3.73182i
$105$	−4.27726	+	9.31156i	−0.417417	+	0.908715i
$106$	−9.98787	+	30.7395i	−0.970108	+	2.98568i
$107$			0.120438i			0.0116432i	0.999983	+	0.00582158i	$0.00185308\pi$
$107$			0.120438i			0.0116432i	−0.999983	+	0.00582158i	$0.998147\pi$
$108$	20.4190	−	8.56548i	1.96482	−	0.824214i
$109$	2.10803	−	1.53158i	0.201913	−	0.146698i	−0.482234	−	0.876042i	$-0.660175\pi$
$109$	2.10803	−	1.53158i	0.201913	−	0.146698i	0.684147	+	0.729344i	$0.260175\pi$
$110$	4.26031	−	20.9932i	0.406204	−	2.00163i
$111$	14.3391	−	1.90963i	1.36101	−	0.181254i
$112$	13.9424	+	5.29227i	1.31744	+	0.500073i
$113$	5.72823	+	7.88424i	0.538867	+	0.741687i	0.988449	−	0.151552i	$-0.0484272\pi$
$113$	5.72823	+	7.88424i	0.538867	+	0.741687i	−0.449582	+	0.893239i	$0.648427\pi$
$114$	−8.18440	+	1.08997i	−0.766540	+	0.102085i
$115$	7.44516	−	3.39740i	0.694265	−	0.316810i
$116$	−20.7366	−	28.5415i	−1.92534	−	2.65001i
$117$	−7.54344	+	19.8286i	−0.697391	+	1.83316i
$118$		−	14.3667i		−	1.32257i
$119$	6.52434	−	1.77436i	0.598085	−	0.162656i
$120$	−5.34423	−	21.2541i	−0.487859	−	1.94022i
$121$	−1.13008	−	3.47803i	−0.102735	−	0.316184i
$122$	2.68728	+	8.27059i	0.243295	+	0.748784i
$123$	2.88088	−	0.383665i	0.259761	−	0.0345939i
$124$			2.69981i			0.242450i
$125$	−0.309255	−	11.1761i	−0.0276606	−	0.999617i
$126$	10.0462	+	17.1330i	0.894986	+	1.52633i
$127$	−9.86110	−	7.16451i	−0.875032	−	0.635748i	0.0569008	−	0.998380i	$-0.481878\pi$
$127$	−9.86110	−	7.16451i	−0.875032	−	0.635748i	−0.931932	+	0.362632i	$0.881878\pi$
$128$	15.5323	−	5.04674i	1.37287	−	0.446073i
$129$	8.46771	+	4.58119i	0.745540	+	0.403351i
$130$	34.4477	+	19.4671i	3.02127	+	1.70738i
$131$	−5.76081	+	17.7300i	−0.503325	+	1.54907i	0.300244	+	0.953862i	$0.402932\pi$
$131$	−5.76081	+	17.7300i	−0.503325	+	1.54907i	−0.803569	+	0.595212i	$0.797068\pi$
$132$	−19.4819	−	20.4681i	−1.69568	−	1.78152i
$133$	−1.32272	−	4.86366i	−0.114695	−	0.421733i
$134$	−1.56282	−	2.15103i	−0.135007	−	0.185821i
$135$	4.85781	−	10.5547i	0.418094	−	0.908404i
$136$	−8.49982	+	11.6990i	−0.728853	+	1.00318i
$137$	−6.45701	−	8.88731i	−0.551659	−	0.759294i	0.438577	−	0.898694i	$-0.355483\pi$
$137$	−6.45701	−	8.88731i	−0.551659	−	0.759294i	−0.990236	+	0.139400i	$0.955483\pi$
$138$	2.86728	−	15.6008i	0.244079	−	1.32803i
$139$	10.0569	−	13.8421i	0.853012	−	1.17407i	−0.130179	−	0.991491i	$-0.541555\pi$
$139$	10.0569	−	13.8421i	0.853012	−	1.17407i	0.983191	−	0.182580i	$-0.0584448\pi$
$140$	23.4171	−	9.33896i	1.97911	−	0.789287i
$141$	1.61919	−	8.80994i	0.136360	−	0.741931i
$142$	1.99106	−	6.12786i	0.167086	−	0.514238i
$143$	27.0735			2.26400
$144$	−15.8048	−	6.01264i	−1.31706	−	0.501053i
$145$	−18.1422	−	3.68172i	−1.50663	−	0.305750i
$146$	−7.49003	−	23.0519i	−0.619879	−	1.90779i
$147$	−9.55227	+	7.46687i	−0.787858	+	0.615857i
$148$	−28.7930	−	20.9194i	−2.36677	−	1.71956i
$149$		−	9.35988i		−	0.766791i	−0.923584	−	0.383396i	$-0.874755\pi$
$149$		−	9.35988i		−	0.766791i	0.923584	−	0.383396i	$-0.125245\pi$
$150$	−18.1003	−	11.9157i	−1.47788	−	0.972912i
$151$	−2.05744			−0.167432			−0.0837162	−	0.996490i	$-0.526679\pi$
$151$	−2.05744			−0.167432			−0.0837162	+	0.996490i	$0.526679\pi$
$152$	8.72118	+	6.33631i	0.707381	+	0.513943i
$153$	−7.39940	+	2.00643i	−0.598206	+	0.162210i
$154$	15.8769	−	19.7569i	1.27940	−	1.59206i
$155$	0.957603	+	1.04400i	0.0769165	+	0.0838563i
$156$	47.0772	−	22.5413i	3.76919	−	1.80475i
$157$			21.4282i			1.71015i	0.518501	+	0.855077i	$0.326490\pi$
$157$			21.4282i			1.71015i	−0.518501	+	0.855077i	$0.673510\pi$
$158$	16.2345	+	5.27492i	1.29155	+	0.419650i
$159$	22.0040	+	4.04414i	1.74503	+	0.320721i
$160$	−3.06623	+	5.42580i	−0.242406	+	0.428947i
$161$	9.67163	+	0.470616i	0.762231	+	0.0370897i
$162$	−11.3768	−	19.4355i	−0.893849	−	1.52700i
$163$	−11.8958	+	8.64282i	−0.931753	+	0.676958i	−0.946421	−	0.322934i	$-0.895331\pi$
$163$	−11.8958	+	8.64282i	−0.931753	+	0.676958i	0.0146683	+	0.999892i	$0.495331\pi$
$164$	−5.78483	−	4.20293i	−0.451719	−	0.328193i
$165$	−14.7934	−	1.00485i	−1.15167	−	0.0782273i
$166$	3.05790	+	4.20884i	0.237339	+	0.326669i
$167$	−0.784013	+	2.41294i	−0.0606688	+	0.186719i	−0.976798	−	0.214165i	$-0.931297\pi$
$167$	−0.784013	+	2.41294i	−0.0606688	+	0.186719i	0.916129	+	0.400884i	$0.131297\pi$
$168$	5.92135	−	25.2458i	0.456842	−	1.94776i
$169$	−11.4363	+	35.1972i	−0.879713	+	2.70748i
$170$	1.62571	+	14.2062i	0.124686	+	1.08956i
$171$	1.49572	+	5.51599i	0.114381	+	0.421818i
$172$	−7.31960	−	22.5274i	−0.558114	−	1.71770i
$173$	0.359971	+	0.261535i	0.0273681	+	0.0198841i	0.601385	−	0.798959i	$-0.294616\pi$
$173$	0.359971	+	0.261535i	0.0273681	+	0.0198841i	−0.574017	+	0.818843i	$0.694616\pi$
$174$	−25.9901	+	24.7377i	−1.97030	+	1.87536i
$175$	5.74282	−	11.9172i	0.434116	−	0.900857i
$176$			21.5795i			1.62661i
$177$	−9.85749	+	1.31278i	−0.740934	+	0.0986747i
$178$	8.93334	−	2.90262i	0.669582	−	0.217560i
$179$	−3.94627	+	1.28222i	−0.294958	+	0.0958377i	−0.452758	−	0.891633i	$-0.649560\pi$
$179$	−3.94627	+	1.28222i	−0.294958	+	0.0958377i	0.157800	+	0.987471i	$0.449560\pi$
$180$	−26.5604	+	10.5696i	−1.97970	+	0.787813i
$181$	−4.67959	−	1.52049i	−0.347831	−	0.113017i	0.129891	−	0.991528i	$-0.458537\pi$
$181$	−4.67959	−	1.52049i	−0.347831	−	0.113017i	−0.477722	+	0.878511i	$0.658537\pi$
$182$	25.6451	+	39.1687i	1.90094	+	2.90338i
$183$	5.42917	−	2.59956i	0.401335	−	0.192165i
$184$	−16.7545	+	12.1728i	−1.23516	+	0.897393i
$185$	−18.5541	+	2.12327i	−1.36412	+	0.156106i
$186$	2.72183	−	0.362483i	0.199574	−	0.0265785i
$187$	5.75074	+	7.91521i	0.420535	+	0.578817i
$188$	−17.8293	+	12.9537i	−1.30034	+	0.944749i
$189$	10.8376	−	8.45857i	0.788316	−	0.615271i
$190$	10.5902	−	1.21191i	0.768293	−	0.0879210i
$191$	0.242008	+	0.333096i	0.0175111	+	0.0241020i	0.817683	−	0.575669i	$-0.195258\pi$
$191$	0.242008	+	0.333096i	0.0175111	+	0.0241020i	−0.800172	+	0.599771i	$0.795258\pi$
$192$	−3.21568	−	6.71592i	−0.232072	−	0.484680i
$193$	12.8929			0.928054			0.464027	−	0.885821i	$-0.346404\pi$
$193$	12.8929			0.928054			0.464027	+	0.885821i	$0.346404\pi$
$194$	0.189954	−	0.584617i	0.0136379	−	0.0419731i
$195$	10.2093	−	25.4145i	0.731103	−	1.81997i
$196$	29.6887	+	2.89613i	2.12062	+	0.206866i
$197$	6.20065	−	2.01471i	0.441778	−	0.143542i	−0.0796779	−	0.996821i	$-0.525389\pi$
$197$	6.20065	−	2.01471i	0.441778	−	0.143542i	0.521456	+	0.853278i	$0.325389\pi$
$198$	−18.0194	+	22.3888i	−1.28058	+	1.59111i
$199$			3.67223i			0.260317i	0.991493	+	0.130159i	$0.0415487\pi$
$199$			3.67223i			0.260317i	−0.991493	+	0.130159i	$0.958451\pi$
$200$	6.39181	+	27.5615i	0.451969	+	1.94889i
$201$	−1.33309	+	1.26885i	−0.0940289	+	0.0894980i
$202$	1.04386	−	1.43675i	0.0734456	−	0.101089i
$203$	−17.0738	−	13.7207i	−1.19834	−	0.963004i
$204$	16.5899	+	8.97545i	1.16153	+	0.628407i
$205$	−3.72771	+	0.426587i	−0.260355	+	0.0297942i
$206$	3.50424	−	10.7849i	0.244152	−	0.751422i
$207$	−10.9662	−	0.541789i	−0.762203	−	0.0376570i
$208$	−37.9094	−	12.3175i	−2.62854	−	0.854065i
$209$	5.90051	−	4.28697i	0.408146	−	0.296536i
$210$	−12.5592	−	22.3542i	−0.866665	−	1.54259i
$211$	−10.5591	−	7.67164i	−0.726919	−	0.528138i	0.161668	−	0.986845i	$-0.448313\pi$
$211$	−10.5591	−	7.67164i	−0.726919	−	0.528138i	−0.888587	+	0.458708i	$0.848313\pi$
$212$	−32.3537	−	44.5311i	−2.22206	−	3.05841i
$213$	−4.38646	−	0.806191i	−0.300555	−	0.0552393i
$214$	−0.243812	−	0.177140i	−0.0166667	−	0.0121090i
$215$	−10.8208	−	6.11502i	−0.737969	−	0.417041i
$216$	−6.73549	+	28.6211i	−0.458292	+	1.94742i
$217$	0.439889	+	1.61747i	0.0298616	+	0.109801i
$218$			6.52011i			0.441597i
$219$	−15.1323	+	7.24556i	−1.02254	+	0.489609i
$220$	24.6590	+	26.8839i	1.66251	+	1.81251i
$221$	−17.1874	+	5.58453i	−1.15615	+	0.375656i
$222$	−17.2242	+	31.8365i	−1.15601	+	2.13673i
$223$	0.147004	−	0.202334i	0.00984411	−	0.0135493i	−0.804067	−	0.594539i	$-0.797334\pi$
$223$	0.147004	−	0.202334i	0.00984411	−	0.0135493i	0.813911	+	0.580990i	$0.197334\pi$
$224$	−6.16939	+	4.03932i	−0.412209	+	0.269888i
$225$	−6.52180	+	13.5080i	−0.434787	+	0.900533i
$226$	−24.3858			−1.62212
$227$	1.55846	+	1.13229i	0.103438	+	0.0751524i	0.638302	−	0.769786i	$-0.279637\pi$
$227$	1.55846	+	1.13229i	0.103438	+	0.0751524i	−0.534864	+	0.844938i	$0.679637\pi$
$228$	6.69088	−	12.3672i	0.443114	−	0.819037i
$229$	10.6475	−	3.45959i	0.703608	−	0.228616i	0.0647059	−	0.997904i	$-0.479389\pi$
$229$	10.6475	−	3.45959i	0.703608	−	0.228616i	0.638902	+	0.769288i	$0.279389\pi$
$230$	−4.07270	+	20.0688i	−0.268546	+	1.32330i
$231$	−15.0066	−	9.08834i	−0.987365	−	0.597969i
$232$	46.8465			3.07562
$233$	−15.1718	−	4.92961i	−0.993937	−	0.322950i	−0.233496	−	0.972358i	$-0.575017\pi$
$233$	−15.1718	−	4.92961i	−0.993937	−	0.322950i	−0.760440	+	0.649408i	$0.775017\pi$
$234$	−29.0458	−	44.4347i	−1.89878	−	2.90479i
$235$	−2.29990	+	11.3331i	−0.150029	+	0.739288i
$236$	19.7939	+	14.3811i	1.28847	+	0.936130i
$237$	2.13584	−	11.6210i	0.138738	−	0.754867i
$238$	−6.00401	+	15.8175i	−0.389182	+	1.02530i
$239$	10.8943	−	14.9948i	0.704695	−	0.969930i	−0.295200	−	0.955436i	$-0.595386\pi$
$239$	10.8943	−	14.9948i	0.704695	−	0.969930i	0.999895	−	0.0144943i	$-0.00461385\pi$
$240$	20.2571	+	8.13751i	1.30759	+	0.525274i
$241$	1.64668	+	2.26647i	0.106072	+	0.145996i	0.858753	−	0.512390i	$-0.171240\pi$
$241$	1.64668	+	2.26647i	0.106072	+	0.145996i	−0.752681	+	0.658386i	$0.771240\pi$
$242$	8.70298	+	2.82777i	0.559449	+	0.181776i
$243$	−12.2958	+	9.58197i	−0.788774	+	0.614684i
$244$	−14.0848	−	4.57644i	−0.901689	−	0.292977i
$245$	12.5077	−	9.41046i	0.799089	−	0.601212i
$246$	−3.46052	+	6.39631i	−0.220635	+	0.407814i
$247$	4.16307	+	12.8126i	0.264890	+	0.815246i
$248$	−2.90034	−	2.10722i	−0.184172	−	0.133809i
$249$	2.60840	−	2.48271i	0.165301	−	0.157336i
$250$	23.0795	+	15.8117i	1.45967	+	1.00002i
$251$	16.4681			1.03945			0.519727	−	0.854332i	$-0.326034\pi$
$251$	16.4681			1.03945			0.519727	+	0.854332i	$0.326034\pi$
$252$	−33.6614	−	3.30896i	−2.12047	−	0.208445i
$253$	4.32981	+	13.3258i	0.272213	+	0.837786i
$254$	29.0074	−	9.42509i	1.82009	−	0.591383i
$255$	9.59876	−	2.41356i	0.601098	−	0.151143i
$256$	−9.97140	+	30.6888i	−0.623212	+	1.91805i
$257$	5.66370			0.353292			0.176646	−	0.984274i	$-0.443475\pi$
$257$	5.66370			0.353292			0.176646	+	0.984274i	$0.443475\pi$
$258$	−21.7284	+	10.4039i	−1.35275	+	0.647717i
$259$	−20.6585	−	7.84158i	−1.28366	−	0.487252i
$260$	−61.3031	+	27.9741i	−3.80186	+	1.73488i
$261$	19.3483	+	15.5722i	1.19763	+	0.963895i
$262$	−27.4192	−	37.7393i	−1.69397	−	2.33154i
$263$	−1.67242	−	2.30188i	−0.103126	−	0.141940i	0.754335	−	0.656489i	$-0.227959\pi$
$263$	−1.67242	−	2.30188i	−0.103126	−	0.141940i	−0.857461	+	0.514549i	$0.827959\pi$
$264$	37.1942	−	4.95337i	2.28914	−	0.304859i
$265$	−28.3059	−	5.74431i	−1.73882	−	0.352870i
$266$	11.7914	+	4.47577i	0.722976	+	0.274427i
$267$	−2.80788	−	5.86422i	−0.171839	−	0.358885i
$268$	4.52798			0.276591
$269$	4.27697	−	13.1632i	0.260772	−	0.802572i	−0.731866	−	0.681449i	$-0.761350\pi$
$269$	4.27697	−	13.1632i	0.260772	−	0.802572i	0.992637	−	0.121124i	$-0.0386498\pi$
$270$	14.2219	+	25.3579i	0.865517	+	1.54323i
$271$	−23.9350	+	7.77695i	−1.45395	+	0.472416i	−0.926215	−	0.376995i	$-0.876958\pi$
$271$	−23.9350	+	7.77695i	−1.45395	+	0.472416i	−0.527732	+	0.849411i	$0.676958\pi$
$272$	−4.45125	−	13.6995i	−0.269897	−	0.830657i
$273$	24.5315	−	21.1751i	1.48472	−	1.28157i
$274$	27.4883			1.66063
$275$	19.0710	+	1.64949i	1.15003	+	0.0994678i
$276$	18.6239	+	19.5668i	1.12103	+	1.17778i
$277$	−21.3299	−	15.4971i	−1.28159	−	0.931129i	−0.281990	−	0.959417i	$-0.590994\pi$
$277$	−21.3299	−	15.4971i	−1.28159	−	0.931129i	−0.999600	+	0.0282882i	$0.990994\pi$
$278$	13.2300	+	40.7179i	0.793485	+	2.44210i
$279$	−0.497422	−	1.83441i	−0.0297799	−	0.109823i
$280$	−8.24462	+	32.4456i	−0.492710	+	1.93900i
$281$	17.1918	+	5.58595i	1.02558	+	0.333230i	0.773040	−	0.634358i	$-0.218735\pi$
$281$	17.1918	+	5.58595i	1.02558	+	0.333230i	0.252536	+	0.967587i	$0.418735\pi$
$282$	15.4532	+	16.2355i	0.920224	+	0.966811i
$283$	−3.23291	−	1.05044i	−0.192176	−	0.0624419i	0.211348	−	0.977411i	$-0.432215\pi$
$283$	−3.23291	−	1.05044i	−0.192176	−	0.0624419i	−0.403524	+	0.914969i	$0.632215\pi$
$284$	6.44965	+	8.87719i	0.382717	+	0.526764i
$285$	−1.79922	−	7.15553i	−0.106577	−	0.423857i
$286$	−39.8198	+	54.8072i	−2.35459	+	3.24082i
$287$	−4.15053	−	1.57546i	−0.244998	−	0.0929964i
$288$	6.99883	−	4.57495i	0.412410	−	0.269582i
$289$	8.46979	+	6.15366i	0.498223	+	0.361980i
$290$	34.1367	−	31.3116i	2.00458	−	1.83868i
$291$	−0.418482	−	0.0769131i	−0.0245319	−	0.00450873i
$292$	39.2575	+	12.7555i	2.29737	+	0.746461i
$293$	−17.1372			−1.00117			−0.500583	−	0.865689i	$-0.666881\pi$
$293$	−17.1372			−1.00117			−0.500583	+	0.865689i	$0.666881\pi$
$294$	−1.06633	−	30.3197i	−0.0621894	−	1.76828i
$295$	12.7551	−	1.45965i	0.742629	−	0.0849841i
$296$	44.9463	−	14.6040i	2.61245	−	0.848838i
$297$	17.0083	+	10.3179i	0.986919	+	0.598704i
$298$	18.9480	+	13.7665i	1.09763	+	0.797473i
$299$	−25.8813			−1.49675
$300$	34.5353	−	13.0102i	1.99390	−	0.751144i
$301$	−8.05568	−	12.3037i	−0.464322	−	0.709174i
$302$	3.02609	−	4.16506i	0.174132	−	0.239672i
$303$	−1.08118	−	0.584940i	−0.0621123	−	0.0336039i
$304$	−10.2125	+	3.31825i	−0.585728	+	0.190315i
$305$	−7.06976	+	3.22610i	−0.404813	+	0.184726i
$306$	6.82125	−	17.9303i	0.389945	−	1.02501i
$307$			9.29076i			0.530252i	0.964214	+	0.265126i	$0.0854135\pi$
$307$			9.29076i			0.530252i	−0.964214	+	0.265126i	$0.914586\pi$
$308$	11.3275	+	41.6512i	0.645443	+	2.37330i
$309$	−7.72010	−	1.41888i	−0.439181	−	0.0807174i
$310$	−3.52190	+	0.403035i	−0.200031	+	0.0228909i
$311$	−14.0572	−	10.2131i	−0.797109	−	0.579133i	0.112956	−	0.993600i	$-0.463968\pi$
$311$	−14.0572	−	10.2131i	−0.797109	−	0.579133i	−0.910064	+	0.414467i	$0.863968\pi$
$312$	−12.5286	+	68.1676i	−0.709291	+	3.85923i
$313$	1.83129	+	2.52056i	0.103511	+	0.142470i	0.857630	−	0.514267i	$-0.171936\pi$
$313$	1.83129	+	2.52056i	0.103511	+	0.142470i	−0.754119	+	0.656737i	$0.771936\pi$
$314$	−43.3788	−	31.5166i	−2.44801	−	1.77858i
$315$	−14.1904	+	10.6599i	−0.799536	+	0.600618i
$316$	−23.5183	+	17.0871i	−1.32301	+	0.961222i
$317$	7.30369	+	2.37311i	0.410216	+	0.133287i	0.506853	−	0.862032i	$-0.330809\pi$
$317$	7.30369	+	2.37311i	0.410216	+	0.133287i	−0.0966370	+	0.995320i	$0.530809\pi$
$318$	−40.5504	+	38.5965i	−2.27395	+	2.16438i
$319$	9.79429	−	30.1437i	0.548375	−	1.68773i
$320$	3.99072	+	8.74536i	0.223088	+	0.488880i
$321$	−0.0992628	+	0.183474i	−0.00554031	+	0.0102405i
$322$	−15.1777	+	18.8869i	−0.845823	+	1.05253i
$323$	−2.86160	+	3.93866i	−0.159224	+	0.219153i
$324$	38.1657	+	3.78041i	2.12031	+	0.210023i
$325$	−13.7834	+	32.5612i	−0.764566	+	1.80617i
$326$		−	36.7936i		−	2.03781i
$327$	4.47366	−	0.595784i	0.247394	−	0.0329469i
$328$	9.03021	−	2.93409i	0.498610	−	0.162008i
$329$	−8.57105	+	10.6657i	−0.472537	+	0.588017i
$330$	23.7924	−	28.4696i	1.30973	−	1.56720i
$331$	7.18710	−	22.1196i	0.395039	−	1.21581i	−0.533892	−	0.845553i	$-0.679271\pi$
$331$	7.18710	−	22.1196i	0.395039	−	1.21581i	0.928931	−	0.370252i	$-0.120729\pi$
$332$	−8.85972			−0.486241
$333$	23.4180	+	8.90895i	1.28330	+	0.488207i
$334$	−3.73160	−	5.13610i	−0.204184	−	0.281035i
$335$	1.75095	−	1.60604i	0.0956645	−	0.0877475i
$336$	16.8780	+	19.5533i	0.920769	+	1.06672i
$337$	7.45600	−	5.41710i	0.406154	−	0.295088i	−0.365889	−	0.930659i	$-0.619235\pi$
$337$	7.45600	−	5.41710i	0.406154	−	0.295088i	0.772043	+	0.635570i	$0.219235\pi$
$338$	−54.4322	−	74.9195i	−2.96072	−	4.07508i
$339$	2.22829	+	16.7319i	0.121024	+	0.908752i
$340$	−21.2000	−	11.9805i	−1.14973	−	0.649736i
$341$	−1.96229	+	1.42569i	−0.106264	+	0.0772053i
$342$	−13.3664	−	5.08500i	−0.722771	−	0.274965i
$343$	18.2586	−	3.10220i	0.985872	−	0.167503i
$344$	29.9137	+	9.71954i	1.61284	+	0.524042i
$345$	14.1420	+	0.960598i	0.761379	+	0.0517169i
$346$	−1.05889	+	0.344055i	−0.0569264	+	0.0184965i
$347$	−16.8487	+	5.47449i	−0.904488	+	0.293886i	−0.724088	−	0.689707i	$-0.757739\pi$
$347$	−16.8487	+	5.47449i	−0.904488	+	0.293886i	−0.180400	+	0.983593i	$0.557739\pi$
$348$	−8.06655	−	60.5705i	−0.432412	−	3.24692i
$349$		−	19.8667i		−	1.06344i	−0.846921	−	0.531719i	$-0.821546\pi$
$349$		−	19.8667i		−	1.06344i	0.846921	−	0.531719i	$-0.178454\pi$
$350$	15.6785	+	29.1535i	0.838049	+	1.55832i
$351$	−27.8340	+	23.9896i	−1.48567	+	1.28047i
$352$	−8.63258	−	6.27194i	−0.460118	−	0.334295i
$353$	−5.98362	−	18.4157i	−0.318476	−	0.980169i	−0.974300	−	0.225255i	$-0.927679\pi$
$353$	−5.98362	−	18.4157i	−0.318476	−	0.980169i	0.655824	−	0.754914i	$-0.272321\pi$
$354$	11.8408	−	21.8862i	0.629333	−	1.16324i
$355$	5.64272	+	1.14512i	0.299485	+	0.0607765i
$356$	−4.94317	+	15.2135i	−0.261987	+	0.806314i
$357$	11.4015	+	2.67420i	0.603432	+	0.141534i
$358$	3.20847	−	9.87465i	0.169573	−	0.521892i
$359$	3.09784	+	4.26381i	0.163498	+	0.225035i	0.882903	−	0.469555i	$-0.155586\pi$
$359$	3.09784	+	4.26381i	0.163498	+	0.225035i	−0.719405	+	0.694590i	$0.755586\pi$
$360$	9.37589	−	36.7829i	0.494153	−	1.93863i
$361$	−12.4352	−	9.03470i	−0.654484	−	0.475510i
$362$	9.96080	−	7.23694i	0.523528	−	0.380365i
$363$	1.14498	−	6.22979i	0.0600957	−	0.326979i
$364$	−79.6357	−	3.87503i	−4.17405	−	0.203107i
$365$	19.7050	−	8.99185i	1.03141	−	0.470655i
$366$	−2.72270	+	14.8142i	−0.142318	+	0.774348i
$367$	−30.4735	−	9.90143i	−1.59070	−	0.516851i	−0.625917	−	0.779890i	$-0.715275\pi$
$367$	−30.4735	−	9.90143i	−1.59070	−	0.516851i	−0.964785	+	0.263039i	$0.915275\pi$
$368$		−	20.6292i		−	1.07537i
$369$	4.70492	+	1.78990i	0.244929	+	0.0931787i
$370$	22.9910	−	40.6834i	1.19525	−	2.11503i
$371$	−26.6389	−	21.4074i	−1.38302	−	1.11142i
$372$	−2.22514	+	4.11287i	−0.115368	+	0.213242i
$373$	−20.1133	−	14.6132i	−1.04143	−	0.756642i	−0.0708642	−	0.997486i	$-0.522576\pi$
$373$	−20.1133	−	14.6132i	−1.04143	−	0.756642i	−0.970564	+	0.240844i	$0.922576\pi$
$374$	−24.4816			−1.26591
$375$	8.74000	−	17.2804i	0.451332	−	0.892356i
$376$		−	29.2641i		−	1.50918i
$377$	47.3639	+	34.4119i	2.43937	+	1.77230i
$378$	1.18351	+	34.3802i	0.0608734	+	1.76833i
$379$	−7.12654	−	21.9332i	−0.366066	−	1.12663i	−0.949311	−	0.314338i	$-0.898217\pi$
$379$	−7.12654	−	21.9332i	−0.366066	−	1.12663i	0.583245	−	0.812296i	$-0.301783\pi$
$380$	−8.93106	+	15.8038i	−0.458154	+	0.810720i
$381$	−9.11745	−	19.0417i	−0.467101	−	0.975537i
$382$	−1.03026			−0.0527127
$383$	0.795588	−	2.44857i	0.0406526	−	0.125116i	−0.928671	−	0.370906i	$-0.879047\pi$
$383$	0.795588	−	2.44857i	0.0406526	−	0.125116i	0.969323	+	0.245790i	$0.0790473\pi$
$384$	27.8212	+	5.11327i	1.41974	+	0.260935i
$385$	19.1537	+	12.0885i	0.976161	+	0.616089i
$386$	−18.9629	+	26.1002i	−0.965188	+	1.32847i
$387$	9.12390	+	13.9579i	0.463794	+	0.709519i
$388$	0.615317	+	0.846912i	0.0312380	+	0.0429954i
$389$	−20.2316	+	27.8464i	−1.02578	+	1.41187i	−0.117713	+	0.993048i	$0.537556\pi$
$389$	−20.2316	+	27.8464i	−1.02578	+	1.41187i	−0.908069	+	0.418820i	$0.862444\pi$
$390$	36.4329	+	58.0472i	1.84485	+	2.93934i
$391$	−5.49749	−	7.56665i	−0.278020	−	0.382662i
$392$	−26.2835	+	29.6335i	−1.32752	+	1.49672i
$393$	−23.3887	+	22.2617i	−1.17980	+	1.12295i
$394$	−5.04136	+	15.5157i	−0.253980	+	0.781671i
$395$	−3.03376	+	14.9492i	−0.152645	+	0.752178i
$396$	−12.8090	−	47.2376i	−0.643677	−	2.37378i
$397$	14.3718	−	4.66969i	0.721301	−	0.234365i	0.0747136	−	0.997205i	$-0.476196\pi$
$397$	14.3718	−	4.66969i	0.721301	−	0.234365i	0.646587	+	0.762840i	$0.276196\pi$
$398$	−7.43400	−	5.40112i	−0.372633	−	0.270734i
$399$	1.99352	−	8.49943i	0.0998009	−	0.425504i
$400$	−25.9535	−	10.9863i	−1.29768	−	0.549316i
$401$		−	9.08969i		−	0.453917i	−0.973904	−	0.226959i	$-0.927122\pi$
$401$		−	9.08969i		−	0.453917i	0.973904	−	0.226959i	$-0.0728782\pi$
$402$	−0.607937	−	4.56491i	−0.0303212	−	0.227677i
$403$	−1.38448	−	4.26100i	−0.0689659	−	0.212255i
$404$	0.934588	+	2.87637i	0.0464975	+	0.143105i
$405$	16.0994	−	12.0752i	0.799983	−	0.600022i
$406$	52.8880	−	14.3835i	2.62479	−	0.713839i
$407$		−	31.9744i		−	1.58491i
$408$	−22.5907	+	10.8167i	−1.11840	+	0.535509i
$409$	1.04421	+	1.43723i	0.0516328	+	0.0710665i	0.834053	−	0.551685i	$-0.186015\pi$
$409$	1.04421	+	1.43723i	0.0516328	+	0.0710665i	−0.782420	+	0.622751i	$0.786015\pi$
$410$	4.61914	−	8.17374i	0.228123	−	0.403672i
$411$	−2.51178	−	18.8606i	−0.123897	−	0.930325i
$412$	11.3513	+	15.6237i	0.559238	+	0.769725i
$413$	14.2018	+	5.39073i	0.698826	+	0.265261i
$414$	17.2259	−	21.4029i	0.846606	−	1.05190i
$415$	−3.42601	+	3.14248i	−0.168176	+	0.154258i
$416$	15.9456	−	11.5851i	0.781796	−	0.568008i
$417$	26.7290	−	12.7982i	1.30892	−	0.626731i
$418$			18.2502i			0.892644i
$419$	5.60302	−	17.2443i	0.273726	−	0.842440i	−0.715828	−	0.698276i	$-0.753951\pi$
$419$	5.60302	−	17.2443i	0.273726	−	0.842440i	0.989554	−	0.144164i	$-0.0460493\pi$
$420$	43.3705	+	5.07310i	2.11626	+	0.247542i
$421$	1.62785	+	5.01000i	0.0793365	+	0.244173i	0.982856	−	0.184374i	$-0.0590258\pi$
$421$	1.62785	+	5.01000i	0.0793365	+	0.244173i	−0.903520	+	0.428547i	$0.859026\pi$
$422$	31.0607	−	10.0922i	1.51201	−	0.491282i
$423$	9.72766	−	12.0865i	0.472975	−	0.587665i
$424$	73.0911			3.54962
$425$	−12.4473	+	2.88667i	−0.603785	+	0.140024i
$426$	8.08364	−	7.69413i	0.391654	−	0.372782i
$427$	−9.18397	−	0.446886i	−0.444443	−	0.0216263i
$428$	0.488112	−	0.158597i	0.0235938	−	0.00766608i
$429$	41.2436	+	22.3135i	1.99126	+	1.07731i
$430$	28.2943	−	12.9114i	1.36447	−	0.622642i
$431$	−10.5868	−	3.43985i	−0.509946	−	0.165692i	0.0427315	−	0.999087i	$-0.486394\pi$
$431$	−10.5868	−	3.43985i	−0.509946	−	0.165692i	−0.552678	+	0.833395i	$0.686394\pi$
$432$	−19.1213	−	22.1856i	−0.919975	−	1.06741i
$433$	1.29432	+	0.420550i	0.0622011	+	0.0202104i	0.339952	−	0.940443i	$-0.389589\pi$
$433$	1.29432	+	0.420550i	0.0622011	+	0.0202104i	−0.277751	+	0.960653i	$0.589589\pi$
$434$	−3.92138	−	1.48848i	−0.188232	−	0.0714492i
$435$	−24.6032	−	20.5612i	−1.17963	−	0.985833i
$436$	−8.98313	−	6.52663i	−0.430214	−	0.312569i
$437$	−5.64067	+	4.09819i	−0.269830	+	0.196043i
$438$	7.58877	−	41.2903i	0.362606	−	1.97293i
$439$	16.1747	−	22.2625i	0.771975	−	1.06253i	−0.224148	−	0.974555i	$-0.571960\pi$
$439$	16.1747	−	22.2625i	0.771975	−	1.06253i	0.996122	−	0.0879772i	$-0.0280403\pi$
$440$	−48.1273	+	5.50753i	−2.29438	+	0.262561i
$441$	−20.7059	+	3.50215i	−0.985996	+	0.166769i
$442$	13.9740	−	43.0076i	0.664677	−	2.04566i
$443$			35.4458i			1.68408i	0.539416	+	0.842040i	$0.318645\pi$
$443$			35.4458i			1.68408i	−0.539416	+	0.842040i	$0.681355\pi$
$444$	−26.6217	−	55.5991i	−1.26341	−	2.63862i
$445$	3.48462	+	7.63629i	0.165187	+	0.361995i
$446$	0.193387	+	0.595185i	0.00915715	+	0.0281828i
$447$	7.71426	−	14.2588i	0.364872	−	0.674416i
$448$	−0.552802	+	11.3606i	−0.0261175	+	0.536740i
$449$			33.9876i			1.60397i	0.597342	+	0.801987i	$0.296224\pi$
$449$			33.9876i			1.60397i	−0.597342	+	0.801987i	$0.703776\pi$
$450$	−17.7531	−	33.0702i	−0.836889	−	1.55894i
$451$		−	6.42400i		−	0.302494i
$452$	24.4102	−	33.5977i	1.14816	−	1.58030i
$453$	−3.13429	−	1.69571i	−0.147262	−	0.0796714i
$454$	−4.58436	+	1.48955i	−0.215155	+	0.0699080i
$455$	−32.1692	+	26.7478i	−1.50811	+	1.25395i
$456$	8.06350	+	16.8405i	0.377608	+	0.788630i
$457$	−32.7286			−1.53098			−0.765490	−	0.643447i	$-0.777503\pi$
$457$	−32.7286			−1.53098			−0.765490	+	0.643447i	$0.777503\pi$
$458$	−8.65684	+	26.6430i	−0.404508	+	1.24495i
$459$	−12.9258	−	3.04188i	−0.603327	−	0.141983i
$460$	−23.5731	−	25.7000i	−1.09910	−	1.19827i
$461$	25.3383	+	18.4093i	1.18012	+	0.857408i	0.992185	−	0.124774i	$-0.0398205\pi$
$461$	25.3383	+	18.4093i	1.18012	+	0.857408i	0.187935	+	0.982181i	$0.439821\pi$
$462$	40.4701	−	17.0121i	1.88284	−	0.791473i
$463$	22.0033	−	15.9863i	1.02258	−	0.742947i	0.0557689	−	0.998444i	$-0.482239\pi$
$463$	22.0033	−	15.9863i	1.02258	−	0.742947i	0.966810	+	0.255497i	$0.0822390\pi$
$464$	−27.4287	+	37.7523i	−1.27334	+	1.75261i
$465$	0.598355	+	2.37967i	0.0277480	+	0.110354i
$466$	32.2941	−	23.4630i	1.49599	−	1.08690i
$467$	−4.72298	+	14.5358i	−0.218554	+	0.672639i	0.780329	+	0.625370i	$0.215052\pi$
$467$	−4.72298	+	14.5358i	−0.218554	+	0.672639i	−0.998882	+	0.0472691i	$0.984948\pi$
$468$	90.2952	+	4.46107i	4.17389	+	0.206213i
$469$	2.71274	−	0.737759i	0.125263	−	0.0340666i
$470$	−19.5598	−	21.3246i	−0.902225	−	0.983629i
$471$	−17.6607	+	32.6435i	−0.813764	+	1.50413i
$472$	−30.8986	+	10.0396i	−1.42222	+	0.462108i
$473$	12.5082	−	17.2161i	0.575129	−	0.791597i
$474$	20.3840	+	21.4160i	0.936270	+	0.983668i
$475$	2.15191	+	9.27905i	0.0987364	+	0.425752i
$476$	−15.7827	−	24.1054i	−0.723397	−	1.10487i
$477$	30.1876	+	24.2961i	1.38220	+	1.11244i
$478$	14.3317	+	44.1086i	0.655519	+	2.01748i
$479$	−8.18580	−	25.1933i	−0.374019	−	1.15111i	−0.944138	−	0.329550i	$-0.893103\pi$
$479$	−8.18580	−	25.1933i	−0.374019	−	1.15111i	0.570119	−	0.821562i	$-0.306897\pi$
$480$	−9.14291	+	5.73848i	−0.417315	+	0.261925i
$481$	56.1704	+	18.2509i	2.56115	+	0.832168i
$482$	−7.01014			−0.319303
$483$	14.3458	+	8.68813i	0.652757	+	0.395323i
$484$	−12.6077	+	9.16001i	−0.573076	+	0.416364i
$485$	0.538334	+	0.109248i	0.0244445	+	0.00496069i
$486$	−1.31297	−	38.9845i	−0.0595574	−	1.76837i
$487$	−16.1280	+	11.7176i	−0.730827	+	0.530977i	−0.889825	−	0.456302i	$-0.849174\pi$
$487$	−16.1280	+	11.7176i	−0.730827	+	0.530977i	0.158998	+	0.987279i	$0.449174\pi$
$488$	15.9097	−	11.5591i	0.720197	−	0.523254i
$489$	−25.2453	+	3.36207i	−1.14163	+	0.152038i
$490$	0.654018	+	39.1613i	0.0295455	+	1.76913i
$491$	18.7449	+	25.8001i	0.845944	+	1.16434i	0.984742	+	0.174021i	$0.0556762\pi$
$491$	18.7449	+	25.8001i	0.845944	+	1.16434i	−0.138798	+	0.990321i	$0.544324\pi$
$492$	−5.34858	−	11.1705i	−0.241133	−	0.503603i
$493$			21.1568i			0.952854i
$494$	−32.0607	−	10.4171i	−1.44248	−	0.468689i
$495$	−21.7080	−	13.7233i	−0.975702	−	0.616815i
$496$	3.39631	−	1.10353i	0.152499	−	0.0495498i
$497$	5.31042	+	4.26752i	0.238205	+	0.191424i
$498$	1.18953	+	8.93198i	0.0533040	+	0.400252i
$499$	3.75098			0.167917			0.0839585	−	0.996469i	$-0.473244\pi$
$499$	3.75098			0.167917			0.0839585	+	0.996469i	$0.473244\pi$
$500$	−44.8873	+	15.9704i	−2.00742	+	0.714219i
$501$	−3.18307	+	3.02969i	−0.142209	+	0.135357i
$502$	−24.2212	+	33.3376i	−1.08105	+	1.48793i
$503$	−0.518287	−	1.59512i	−0.0231093	−	0.0711230i	0.938837	−	0.344362i	$-0.111905\pi$
$503$	−0.518287	−	1.59512i	−0.0231093	−	0.0711230i	−0.961946	+	0.273239i	$0.911905\pi$
$504$	29.8277	−	33.5790i	1.32863	−	1.49573i
$505$	1.38163	+	0.780785i	0.0614816	+	0.0347445i
$506$	−33.3448	−	10.8344i	−1.48236	−	0.481647i
$507$	−46.4309	+	44.1936i	−2.06207	+	1.96271i
$508$	−16.0509	+	49.3997i	−0.712146	+	2.19176i
$509$	−24.9912	+	18.1572i	−1.10772	+	0.804802i	−0.982302	−	0.187302i	$-0.940026\pi$
$509$	−24.9912	+	18.1572i	−1.10772	+	0.804802i	−0.125413	+	0.992105i	$0.540026\pi$
$510$	−9.23189	+	22.9814i	−0.408795	+	1.01763i
$511$	25.5977	+	1.24557i	1.13238	+	0.0551008i
$512$	−28.2610	−	38.8980i	−1.24897	−	1.71906i
$513$	−2.26761	+	9.63576i	−0.100118	+	0.425429i
$514$	−8.33018	+	11.4655i	−0.367428	+	0.505722i
$515$	9.93111	+	2.01539i	0.437617	+	0.0888087i
$516$	7.41609	−	40.3507i	0.326475	−	1.77634i
$517$	−18.8302	−	6.11831i	−0.828152	−	0.269083i
$518$	46.2590	−	30.2874i	2.03250	−	1.33075i
$519$	0.332825	+	0.695102i	0.0146094	+	0.0305116i
$520$	17.7957	−	87.6905i	0.780391	−	3.84548i
$521$	8.51396	+	26.2033i	0.373003	+	1.14799i	0.944816	+	0.327602i	$0.106241\pi$
$521$	8.51396	+	26.2033i	0.373003	+	1.14799i	−0.571812	+	0.820385i	$0.693759\pi$
$522$	−59.9815	+	16.2647i	−2.62532	+	0.711885i
$523$	−10.3595	+	14.2587i	−0.452990	+	0.623487i	−0.973037	−	0.230651i	$-0.925915\pi$
$523$	−10.3595	+	14.2587i	−0.452990	+	0.623487i	0.520047	+	0.854138i	$0.325915\pi$
$524$	79.4423			3.47045
$525$	18.5705	−	13.4214i	0.810485	−	0.585760i
$526$	7.11968			0.310433
$527$	0.951663	−	1.30985i	0.0414551	−	0.0570581i
$528$	−17.7854	+	32.8740i	−0.774012	+	1.43066i
$529$	2.96825	+	9.13532i	0.129054	+	0.397188i
$530$	53.2610	−	48.8532i	2.31351	−	2.12205i
$531$	−16.0988	−	6.12450i	−0.698628	−	0.265781i
$532$	−17.9697	+	11.7654i	−0.779085	+	0.510095i
$533$	11.2852	+	3.66680i	0.488818	+	0.158827i
$534$	16.0013	+	2.94088i	0.692443	+	0.127265i
$535$	0.132497	−	0.234458i	0.00572835	−	0.0101365i
$536$	−3.53413	+	4.86431i	−0.152651	+	0.210106i
$537$	−7.06850	−	1.29912i	−0.305028	−	0.0560614i
$538$	20.3567	+	28.0186i	0.877641	+	1.20797i
$539$	13.5727	+	23.1079i	0.584619	+	0.995327i
$540$	−49.1732	−	5.78895i	−2.11608	−	0.249117i
$541$	28.2597	−	20.5319i	1.21498	−	0.882734i	0.219305	−	0.975656i	$-0.429621\pi$
$541$	28.2597	−	20.5319i	1.21498	−	0.882734i	0.995673	+	0.0929228i	$0.0296210\pi$
$542$	19.4601	−	59.8920i	0.835882	−	2.57258i
$543$	−5.87569	−	6.17314i	−0.252150	−	0.264915i
$544$	6.77405	+	2.20102i	0.290435	+	0.0943681i
$545$	−5.78868	+	0.662438i	−0.247960	+	0.0283757i
$546$	6.78544	+	80.8055i	0.290390	+	3.45816i
$547$	0.708608	+	2.18087i	0.0302979	+	0.0932474i	0.965062	−	0.262022i	$-0.0843892\pi$
$547$	0.708608	+	2.18087i	0.0302979	+	0.0932474i	−0.934764	+	0.355269i	$0.884389\pi$
$548$	−27.5158	+	37.8722i	−1.17542	+	1.61782i
$549$	10.4133	+	0.514471i	0.444427	+	0.0219571i
$550$	−31.3889	+	36.1810i	−1.33843	+	1.54276i
$551$	15.7716			0.671894
$552$	−35.5563	+	4.73524i	−1.51338	+	0.201545i
$553$	−11.3059	+	14.0689i	−0.480777	+	0.598270i
$554$	62.7441	−	20.3868i	2.66574	−	0.866151i
$555$	−30.0151	−	12.0574i	−1.27407	−	0.511807i
$556$	−69.3427	−	22.5308i	−2.94078	−	0.955519i
$557$			8.43645i			0.357464i	0.983898	+	0.178732i	$0.0571995\pi$
$557$			8.43645i			0.357464i	−0.983898	+	0.178732i	$0.942800\pi$
$558$	4.44516	+	1.69108i	0.188179	+	0.0715893i
$559$	23.1044	+	31.8005i	0.977213	+	1.34502i
$560$	−21.3198	−	25.6411i	−0.900926	−	1.08353i
$561$	2.23704	+	16.7976i	0.0944480	+	0.709196i
$562$	−36.5938	+	26.5869i	−1.54362	+	1.12150i
$563$	30.0720	−	21.8486i	1.26739	−	0.920809i	0.268290	−	0.963338i	$-0.413541\pi$
$563$	30.0720	−	21.8486i	1.26739	−	0.920809i	0.999095	+	0.0425286i	$0.0135414\pi$
$564$	−37.8373	+	5.03902i	−1.59324	+	0.212181i
$565$	−2.47758	−	21.6502i	−0.104233	−	0.910830i
$566$	6.88144	−	4.99966i	0.289249	−	0.210151i
$567$	23.4813	−	3.95359i	0.986120	−	0.166035i
$568$	−14.5706			−0.611367
$569$	−5.25856	−	1.70861i	−0.220450	−	0.0716287i	0.196709	−	0.980462i	$-0.436974\pi$
$569$	−5.25856	−	1.70861i	−0.220450	−	0.0716287i	−0.417160	+	0.908833i	$0.636974\pi$
$570$	17.1318	+	6.88204i	0.717574	+	0.288257i
$571$	2.37323	+	7.30406i	0.0993166	+	0.305665i	0.988355	−	0.152168i	$-0.0486256\pi$
$571$	2.37323	+	7.30406i	0.0993166	+	0.305665i	−0.889038	+	0.457834i	$0.848626\pi$
$572$	−35.6515	−	109.724i	−1.49066	−	4.58779i
$573$	0.0941415	+	0.706895i	0.00393282	+	0.0295310i
$574$	9.29393	−	6.08507i	0.387921	−	0.253986i
$575$	−18.2312	−	1.57685i	−0.760294	−	0.0657592i
$576$	0.636406	−	12.8813i	0.0265169	−	0.536721i
$577$	23.9031	−	32.8997i	0.995098	−	1.36963i	0.0668123	−	0.997766i	$-0.478717\pi$
$577$	23.9031	−	32.8997i	0.995098	−	1.36963i	0.928285	−	0.371869i	$-0.121283\pi$
$578$	−24.9147	+	8.09529i	−1.03632	+	0.336720i
$579$	19.6410	+	10.6261i	0.816252	+	0.441607i
$580$	8.96900	+	78.3751i	0.372417	+	3.25435i
$581$	−5.30792	+	1.44354i	−0.220210	+	0.0598883i
$582$	0.771205	−	0.734044i	0.0319675	−	0.0304271i
$583$	15.2813	−	47.0310i	0.632887	−	1.94783i
$584$	−44.3438	+	32.2176i	−1.83496	+	1.33318i
$585$	36.4990	−	30.3020i	1.50905	−	1.25283i
$586$	25.2054	−	34.6923i	1.04123	−	1.43312i
$587$	−22.1222	+	16.0727i	−0.913079	+	0.663391i	−0.941792	−	0.336197i	$-0.890859\pi$
$587$	−22.1222	+	16.0727i	−0.913079	+	0.663391i	0.0287127	+	0.999588i	$0.490859\pi$
$588$	42.8406	+	28.8809i	1.76672	+	1.19103i
$589$	−0.976448	−	0.709431i	−0.0402338	−	0.0292316i
$590$	−15.8053	+	27.9680i	−0.650693	+	1.15142i
$591$	11.1065	+	2.04127i	0.456861	+	0.0839667i
$592$	−14.5472	+	44.7717i	−0.597886	+	1.84010i
$593$	−29.7694			−1.22248			−0.611241	−	0.791444i	$-0.709329\pi$
$593$	−29.7694			−1.22248			−0.611241	+	0.791444i	$0.709329\pi$
$594$	−45.9031	+	19.2557i	−1.88343	+	0.790071i
$595$	−14.6531	−	3.72343i	−0.600718	−	0.152646i
$596$	−37.9339	+	12.3255i	−1.55383	+	0.504870i
$597$	−3.02659	+	5.59424i	−0.123870	+	0.228957i
$598$	38.0662	−	52.3937i	1.55664	−	2.14254i
$599$		−	5.27571i		−	0.215560i	−0.994175	−	0.107780i	$-0.965626\pi$
$599$		−	5.27571i		−	0.215560i	0.994175	−	0.107780i	$-0.0343742\pi$
$600$	−12.9785	+	47.2550i	−0.529846	+	1.92918i
$601$		−	18.4861i		−	0.754064i	−0.926200	−	0.377032i	$-0.876945\pi$
$601$		−	18.4861i		−	0.754064i	0.926200	−	0.377032i	$-0.123055\pi$
$602$	36.7557	+	1.78851i	1.49805	+	0.0728943i
$603$	−3.07658	+	0.834251i	−0.125288	+	0.0339733i
$604$	2.70932	+	8.33844i	0.110241	+	0.339286i
$605$	−1.62633	+	8.01398i	−0.0661199	+	0.325814i
$606$	2.77435	−	1.32840i	0.112700	−	0.0539625i
$607$			13.3258i			0.540876i	0.962737	+	0.270438i	$0.0871685\pi$
$607$			13.3258i			0.540876i	−0.962737	+	0.270438i	$0.912831\pi$
$608$	1.64078	−	5.04981i	0.0665426	−	0.204797i
$609$	−14.7017	−	34.9739i	−0.595742	−	1.41721i
$610$	3.86734	−	19.0569i	0.156584	−	0.771590i
$611$	21.4965	−	29.5873i	0.869654	−	1.19698i
$612$	17.8755	+	27.3462i	0.722575	+	1.10541i
$613$	−10.6807	+	7.75995i	−0.431388	+	0.313422i	−0.782204	−	0.623023i	$-0.785904\pi$
$613$	−10.6807	+	7.75995i	−0.431388	+	0.313422i	0.350816	+	0.936444i	$0.385904\pi$
$614$	−18.8081	−	13.6649i	−0.759032	−	0.551469i
$615$	−6.03035	−	2.42246i	−0.243167	−	0.0976829i
$616$	−53.5861	−	20.3402i	−2.15905	−	0.819532i
$617$	−25.8465	−	8.39804i	−1.04054	−	0.338093i	−0.261592	−	0.965179i	$-0.584247\pi$
$617$	−25.8465	−	8.39804i	−1.04054	−	0.338093i	−0.778950	+	0.627086i	$0.784247\pi$
$618$	14.2271	−	13.5416i	0.572298	−	0.544721i
$619$	28.1656	+	9.15157i	1.13207	+	0.367833i	0.814363	−	0.580356i	$-0.197086\pi$
$619$	28.1656	+	9.15157i	1.13207	+	0.367833i	0.317709	+	0.948188i	$0.397086\pi$
$620$	2.97014	−	5.25577i	0.119284	−	0.211077i
$621$	−16.2593	−	9.86351i	−0.652462	−	0.395809i
$622$	41.3506	−	13.4356i	1.65801	−	0.538719i
$623$	−0.482697	+	9.91992i	−0.0193389	+	0.397433i
$624$	−47.5989	−	50.0086i	−1.90548	−	2.00195i
$625$	−11.6931	+	22.0969i	−0.467723	+	0.883875i
$626$	−7.79603			−0.311592
$627$	12.5220	−	1.66763i	0.500082	−	0.0665989i
$628$	86.8444	−	28.2174i	3.46547	−	1.12600i
$629$	6.59544	+	20.2987i	0.262977	+	0.809361i
$630$	−0.708540	−	44.4053i	−0.0282289	−	1.76915i
$631$	−1.31272	+	4.04015i	−0.0522587	+	0.160836i	−0.973780	−	0.227492i	$-0.926947\pi$
$631$	−1.31272	+	4.04015i	−0.0522587	+	0.160836i	0.921521	+	0.388328i	$0.126947\pi$
$632$		−	38.6017i		−	1.53549i
$633$	−9.76282	−	20.3896i	−0.388037	−	0.810412i
$634$	−15.5464	+	11.2951i	−0.617425	+	0.448586i
$635$	11.3149	+	24.7958i	0.449018	+	0.983991i
$636$	−12.5856	−	94.5037i	−0.499053	−	3.74732i
$637$	−48.3417	+	10.6538i	−1.91537	+	0.422117i
$638$	46.6170	+	64.1628i	1.84559	+	2.54023i
$639$	−6.01785	−	4.84339i	−0.238062	−	0.191602i
$640$	−35.7890	−	7.26292i	−1.41469	−	0.287092i
$641$	25.5239	+	35.1306i	1.00813	+	1.38758i	0.920199	+	0.391450i	$0.128027\pi$
$641$	25.5239	+	35.1306i	1.00813	+	1.38758i	0.0879342	+	0.996126i	$0.471973\pi$
$642$	−0.225426	−	0.470799i	−0.00889684	−	0.0185810i
$643$		−	6.91080i		−	0.272535i	−0.990672	−	0.136268i	$-0.956489\pi$
$643$		−	6.91080i		−	0.272535i	0.990672	−	0.136268i	$-0.0435107\pi$
$644$	−10.8287	−	39.8170i	−0.426709	−	1.56901i
$645$	−11.4443	−	18.2339i	−0.450621	−	0.717958i
$646$	−3.76451	−	11.5860i	−0.148113	−	0.455844i
$647$	−7.41276	−	22.8141i	−0.291426	−	0.896916i	−0.984399	−	0.175952i	$-0.943700\pi$
$647$	−7.41276	−	22.8141i	−0.291426	−	0.896916i	0.692973	−	0.720963i	$-0.256300\pi$
$648$	−33.8498	+	38.0498i	−1.32975	+	1.49474i
$649$			21.9809i			0.862827i
$650$	−45.6437	−	75.7939i	−1.79029	−	2.97288i
$651$	−0.662971	+	2.82659i	−0.0259839	+	0.110783i
$652$	50.6927	+	36.8304i	1.98528	+	1.44239i
$653$	−27.2612	+	8.85770i	−1.06681	+	0.346629i	−0.789246	−	0.614077i	$-0.789528\pi$
$653$	−27.2612	+	8.85770i	−1.06681	+	0.346629i	−0.277568	+	0.960706i	$0.589528\pi$
$654$	−5.37376	+	9.93268i	−0.210131	+	0.388398i
$655$	30.7199	−	28.1776i	1.20033	−	1.10099i
$656$	−2.92269	+	8.99512i	−0.114112	+	0.351200i
$657$	−29.0240	−	1.43394i	−1.13234	−	0.0559435i
$658$	−8.98507	−	33.0381i	−0.350275	−	1.28796i
$659$	−8.50383	−	11.7045i	−0.331262	−	0.455943i	0.610602	−	0.791938i	$-0.290928\pi$
$659$	−8.50383	−	11.7045i	−0.331262	−	0.455943i	−0.941864	+	0.335995i	$0.890928\pi$
$660$	15.4081	+	61.2782i	0.599760	+	2.38525i
$661$	−22.6501	+	31.1752i	−0.880988	+	1.21258i	0.0951588	+	0.995462i	$0.469664\pi$
$661$	−22.6501	+	31.1752i	−0.880988	+	1.21258i	−0.976146	+	0.217113i	$0.930336\pi$
$662$	34.2078	+	47.0830i	1.32952	+	1.82993i
$663$	−30.7858	−	5.65815i	−1.19562	−	0.219744i
$664$	6.91508	−	9.51779i	0.268357	−	0.369362i
$665$	−2.77569	+	10.9233i	−0.107636	+	0.423589i
$666$	−52.4783	+	34.3037i	−2.03349	+	1.32924i
$667$	−9.36299	+	28.8163i	−0.362536	+	1.11577i
$668$	10.8116			0.418315
$669$	0.390705	−	0.187075i	0.0151055	−	0.00723274i
$670$	0.675951	+	5.90676i	0.0261143	+	0.228198i
$671$	−4.11150	−	12.6539i	−0.158723	−	0.488498i
$672$	−12.7275	+	1.06876i	−0.490975	+	0.0412284i
$673$	−13.5336	−	9.83271i	−0.521680	−	0.379023i	0.295556	−	0.955325i	$-0.404495\pi$
$673$	−13.5336	−	9.83271i	−0.521680	−	0.379023i	−0.817237	+	0.576302i	$0.804495\pi$
$674$			23.0613i			0.888287i
$675$	−21.0683	+	15.2028i	−0.810920	+	0.585157i
$676$	157.708			6.06568
$677$	−40.2168	−	29.2192i	−1.54566	−	1.12299i	−0.946659	−	0.322237i	$-0.895565\pi$
$677$	−40.2168	−	29.2192i	−1.54566	−	1.12299i	−0.598999	−	0.800750i	$-0.704435\pi$
$678$	−37.1491	−	20.0984i	−1.42670	−	0.771873i
$679$	0.506631	+	0.407135i	0.0194427	+	0.0156244i
$680$	29.4172	−	13.4238i	1.12810	−	0.514778i
$681$	1.44093	+	3.00937i	0.0552166	+	0.115319i
$682$		−	6.06933i		−	0.232407i
$683$	9.89335	+	3.21454i	0.378558	+	0.123001i	0.492114	−	0.870530i	$-0.336224\pi$
$683$	9.89335	+	3.21454i	0.378558	+	0.123001i	−0.113556	+	0.993532i	$0.536224\pi$
$684$	20.3856	−	13.3256i	0.779465	−	0.509515i
$685$	2.79279	+	24.4046i	0.106707	+	0.932453i
$686$	−20.5747	+	41.5251i	−0.785547	+	1.58544i
$687$	19.0717	+	3.50520i	0.727630	+	0.133732i
$688$	−25.3472	+	18.4158i	−0.966353	+	0.702096i
$689$	73.8984	+	53.6903i	2.81531	+	2.04544i
$690$	−22.7446	+	27.2159i	−0.865874	+	1.03609i
$691$	0.0570698	+	0.0785498i	0.00217104	+	0.00298817i	0.810101	−	0.586290i	$-0.199412\pi$
$691$	0.0570698	+	0.0785498i	0.00217104	+	0.00298817i	−0.807930	+	0.589278i	$0.799412\pi$
$692$	0.585926	−	1.80330i	0.0222736	−	0.0685510i
$693$	−15.3705	−	26.2133i	−0.583878	−	0.995762i
$694$	13.6987	−	42.1602i	0.519995	−	1.60038i
$695$	−34.8060	+	15.8828i	−1.32027	+	0.602469i
$696$	71.3655	+	38.6101i	2.70510	+	1.46351i
$697$	1.32509	+	4.07822i	0.0501915	+	0.154474i
$698$	40.2177	+	29.2199i	1.52226	+	1.10599i
$699$	−19.0497	−	20.0141i	−0.720525	−	0.757001i
$700$	−55.8606	−	7.58153i	−2.11133	−	0.286555i
$701$		−	21.3630i		−	0.806871i	−0.915008	−	0.403435i	$-0.867816\pi$
$701$		−	21.3630i		−	0.806871i	0.915008	−	0.403435i	$-0.132184\pi$
$702$	−7.62578	−	91.6306i	−0.287816	−	3.45837i
$703$	15.1319	−	4.91666i	0.570712	−	0.185435i
$704$	−15.6530	+	5.08596i	−0.589944	+	0.191684i
$705$	−12.8442	+	15.3692i	−0.483740	+	0.578836i
$706$	46.0812	+	14.9727i	1.73429	+	0.563504i
$707$	1.02857	+	1.57097i	0.0386835	+	0.0590826i
$708$	18.3012	+	38.2219i	0.687801	+	1.43647i
$709$	−2.86373	+	2.08062i	−0.107550	+	0.0781394i	−0.640260	−	0.768158i	$-0.721173\pi$
$709$	−2.86373	+	2.08062i	−0.107550	+	0.0781394i	0.532711	+	0.846298i	$0.321173\pi$
$710$	−10.6175	+	9.73879i	−0.398467	+	0.365490i
$711$	12.8316	−	15.9431i	0.481222	−	0.597912i
$712$	−12.4853	−	17.1846i	−0.467908	−	0.644020i
$713$	1.87588	−	1.36290i	0.0702522	−	0.0510412i
$714$	−22.1830	+	19.1478i	−0.830177	+	0.716590i
$715$	−52.7046	−	29.7844i	−1.97104	−	1.11387i
$716$	10.3932	+	14.3050i	0.388412	+	0.534604i
$717$	28.9547	−	13.8640i	1.08133	−	0.517759i
$718$	−13.1879			−0.492168
$719$	−7.38440	+	22.7268i	−0.275392	+	0.847568i	0.713724	+	0.700427i	$0.247007\pi$
$719$	−7.38440	+	22.7268i	−0.275392	+	0.847568i	−0.989115	+	0.147141i	$0.952993\pi$
$720$	24.1527	+	29.0922i	0.900120	+	1.08420i
$721$	9.34626	+	7.51077i	0.348073	+	0.279716i
$722$	36.5794	−	11.8854i	1.36134	−	0.442327i
$723$	0.640562	+	4.80989i	0.0238227	+	0.178882i
$724$			20.9678i			0.779260i
$725$	31.2673	+	27.1260i	1.16124	+	1.00744i
$726$	10.9274	+	11.4807i	0.405556	+	0.426087i
$727$	−19.0446	+	26.2126i	−0.706325	+	0.972172i	0.293544	+	0.955946i	$0.405165\pi$
$727$	−19.0446	+	26.2126i	−0.706325	+	0.972172i	−0.999868	+	0.0162268i	$0.994835\pi$
$728$	66.3192	−	82.5263i	2.45795	−	3.05863i
$729$	−26.6286	+	4.46313i	−0.986243	+	0.165301i
$730$	−10.7791	+	53.1156i	−0.398954	+	1.96590i
$731$	−4.38954	+	13.5096i	−0.162353	+	0.499671i
$732$	−17.6849	−	18.5802i	−0.653652	−	0.686744i
$733$	−33.4940	−	10.8829i	−1.23713	−	0.401968i	−0.383838	−	0.923400i	$-0.625398\pi$
$733$	−33.4940	−	10.8829i	−1.23713	−	0.401968i	−0.853293	+	0.521432i	$0.825398\pi$
$734$	64.8647	−	47.1270i	2.39420	−	1.73949i
$735$	26.8101	−	4.02717i	0.988906	−	0.148544i
$736$	8.25244	+	5.99575i	0.304189	+	0.221006i
$737$	2.39109	+	3.29105i	0.0880769	+	0.121227i
$738$	−10.5435	+	6.89198i	−0.388110	+	0.253697i
$739$	−39.7753	−	28.8984i	−1.46316	−	1.06305i	−0.982526	−	0.186124i	$-0.940407\pi$
$739$	−39.7753	−	28.8984i	−1.46316	−	1.06305i	−0.480632	−	0.876922i	$-0.659593\pi$
$740$	33.0379	+	72.4002i	1.21450	+	2.66148i
$741$	−4.21795	+	22.9497i	−0.154950	+	0.843080i
$742$	82.5173	−	22.4414i	3.02930	−	0.823851i
$743$		−	44.4264i		−	1.62985i	−0.579568	−	0.814924i	$-0.696779\pi$
$743$		−	44.4264i		−	1.62985i	0.579568	−	0.814924i	$-0.303221\pi$
$744$	−2.68162	−	5.60054i	−0.0983130	−	0.205326i
$745$	−10.2971	+	18.2211i	−0.377256	+	0.667568i
$746$	59.1653	−	19.2240i	2.16620	−	0.703840i
$747$	6.01983	−	1.63235i	0.220254	−	0.0597244i
$748$	24.5061	−	33.7297i	0.896031	−	1.23328i
$749$	0.266590	−	0.174546i	0.00974100	−	0.00637778i
$750$	22.1274	+	43.1091i	0.807977	+	1.57412i
$751$	8.08148			0.294898			0.147449	−	0.989070i	$-0.452894\pi$
$751$	8.08148			0.294898			0.147449	+	0.989070i	$0.452894\pi$
$752$	23.5831	+	17.1342i	0.859989	+	0.624818i
$753$	25.0873	+	13.5727i	0.914232	+	0.494616i
$754$	−139.326	+	45.2697i	−5.07395	+	1.64863i
$755$	4.00527	+	2.26345i	0.145767	+	0.0823756i
$756$	−48.5523	−	32.7840i	−1.76583	−	1.19234i
$757$	17.0397			0.619317			0.309659	−	0.950848i	$-0.399785\pi$
$757$	17.0397			0.619317			0.309659	+	0.950848i	$0.399785\pi$
$758$	54.8830	+	17.8326i	1.99344	+	0.647708i
$759$	−4.38690	+	23.8690i	−0.159234	+	0.866389i
$760$	−10.0069	−	21.9294i	−0.362989	−	0.795465i
$761$	26.5611	+	19.2978i	0.962840	+	0.699544i	0.953809	−	0.300415i	$-0.0971252\pi$
$761$	26.5611	+	19.2978i	0.962840	+	0.699544i	0.00903125	+	0.999959i	$0.497125\pi$
$762$	51.9577	+	9.54934i	1.88223	+	0.345936i
$763$	−6.44526	−	2.44649i	−0.233334	−	0.0885690i
$764$	1.03129	−	1.41945i	0.0373108	−	0.0513539i
$765$	16.6119	+	4.23434i	0.600604	+	0.153093i
$766$	3.78669	+	5.21193i	0.136819	+	0.188315i
$767$	−38.6146	−	12.5467i	−1.39429	−	0.453033i
$768$	−40.4835	+	38.5328i	−1.46082	+	1.39043i
$769$	−24.6495	−	8.00911i	−0.888884	−	0.288816i	−0.171243	−	0.985229i	$-0.554778\pi$
$769$	−24.6495	−	8.00911i	−0.888884	−	0.288816i	−0.717641	+	0.696413i	$0.754778\pi$
$770$	−52.6430	+	20.9945i	−1.89712	+	0.756590i
$771$	8.62804	+	4.66793i	0.310731	+	0.168111i
$772$	−16.9779	−	52.2527i	−0.611049	−	1.88062i
$773$	−11.1349	−	8.09001i	−0.400496	−	0.290977i	0.369247	−	0.929331i	$-0.379616\pi$
$773$	−11.1349	−	8.09001i	−0.400496	−	0.290977i	−0.769743	+	0.638354i	$0.779616\pi$
$774$	−41.6755	−	2.05900i	−1.49800	−	0.0740091i
$775$	−0.715645	−	3.08587i	−0.0257067	−	0.110848i
$776$	−1.39008			−0.0499009
$777$	−25.0082	−	28.9722i	−0.897163	−	1.03937i
$778$	−26.6151	−	81.9129i	−0.954199	−	2.93672i
$779$	3.04017	−	0.987811i	0.108925	−	0.0353920i
$780$	−116.444	−	7.90952i	−4.16938	−	0.283206i
$781$	−3.04630	+	9.37554i	−0.109005	+	0.335483i
$782$	23.4035			0.836908
$783$	16.6406	+	39.6691i	0.594687	+	1.41766i
$784$	−8.49178	−	38.5316i	−0.303278	−	1.37613i
$785$	23.5738	−	41.7146i	0.841383	−	1.48886i
$786$	−10.6661	−	80.0902i	−0.380447	−	2.85672i
$787$	−18.8308	−	25.9183i	−0.671244	−	0.923889i	0.328543	−	0.944489i	$-0.393442\pi$
$787$	−18.8308	−	25.9183i	−0.671244	−	0.923889i	−0.999788	+	0.0206002i	$0.993442\pi$
$788$	−16.3305	−	22.4770i	−0.581750	−	0.800711i
$789$	−0.650571	−	4.88504i	−0.0231609	−	0.173912i
$790$	−25.8010	−	28.1289i	−0.917957	−	1.00078i
$791$	9.15011	−	24.1059i	0.325340	−	0.857106i
$792$	60.7438	+	23.1089i	2.15844	+	0.821138i
$793$	24.5763			0.872731
$794$	−11.6848	+	35.9622i	−0.414679	+	1.27625i
$795$	−38.3866	−	32.0801i	−1.36143	−	1.13776i
$796$	14.8829	−	4.83574i	0.527509	−	0.171398i
$797$	−4.70123	−	14.4689i	−0.166526	−	0.512514i	0.832620	−	0.553845i	$-0.186840\pi$
$797$	−4.70123	−	14.4689i	−0.166526	−	0.512514i	−0.999146	+	0.0413312i	$0.986840\pi$
$798$	14.2740	+	16.5366i	0.505295	+	0.585390i
$799$	13.2162			0.467557
$800$	11.9382	−	7.18926i	0.422078	−	0.254179i
$801$	0.555698	−	11.2477i	0.0196346	−	0.397419i
$802$	18.4010	+	13.3691i	0.649762	+	0.472080i
$803$	11.4596	+	35.2692i	0.404402	+	1.24462i
$804$	6.89789	+	3.73189i	0.243270	+	0.131614i
$805$	−18.3102	−	11.5562i	−0.645350	−	0.407303i
$806$	10.6622	+	3.46435i	0.375560	+	0.122027i
$807$	17.3644	−	16.5276i	0.611255	−	0.581801i
$808$	−3.81947	−	1.24102i	−0.134368	−	0.0436589i
$809$	10.4762	+	14.4192i	0.368323	+	0.506954i	0.952444	−	0.304713i	$-0.0985606\pi$
$809$	10.4762	+	14.4192i	0.368323	+	0.506954i	−0.584121	+	0.811667i	$0.698561\pi$
$810$	0.765937	+	50.3515i	0.0269123	+	1.76917i
$811$	32.4921	−	44.7215i	1.14095	−	1.57038i	0.375584	−	0.926788i	$-0.377442\pi$
$811$	32.4921	−	44.7215i	1.14095	−	1.57038i	0.765366	−	0.643595i	$-0.222558\pi$
$812$	−33.1240	+	87.2648i	−1.16242	+	3.06239i
$813$	−42.8720	−	7.87948i	−1.50359	−	0.276345i
$814$	64.7284	+	47.0279i	2.26873	+	1.64833i
$815$	32.6661	−	3.73820i	1.14424	−	0.130943i
$816$	4.50994	−	24.5384i	0.157879	−	0.859017i
$817$	10.0709	+	3.27224i	0.352337	+	0.114481i
$818$	−4.44533			−0.155427
$819$	54.8233	−	12.0394i	1.91568	−	0.420692i
$820$	6.63768	+	14.5460i	0.231798	+	0.507968i
$821$	27.9982	−	9.09716i	0.977144	−	0.317493i	0.223447	−	0.974716i	$-0.428269\pi$
$821$	27.9982	−	9.09716i	0.977144	−	0.317493i	0.753696	+	0.657223i	$0.228269\pi$
$822$	41.8754	+	22.6554i	1.46057	+	0.790197i
$823$	35.0800	+	25.4871i	1.22281	+	0.888425i	0.996330	−	0.0855907i	$-0.0272777\pi$
$823$	35.0800	+	25.4871i	1.22281	+	0.888425i	0.226481	+	0.974015i	$0.427278\pi$
$824$	−25.6440			−0.893350
$825$	27.6932	+	18.2308i	0.964153	+	0.634717i
$826$	−31.8009	+	20.8212i	−1.10650	+	0.724463i
$827$	−15.4948	+	21.3267i	−0.538806	+	0.741603i	−0.988440	−	0.151610i	$-0.951554\pi$
$827$	−15.4948	+	21.3267i	−0.538806	+	0.741603i	0.449634	+	0.893213i	$0.351554\pi$
$828$	12.2449	+	45.1574i	0.425541	+	1.56933i
$829$	37.1613	−	12.0745i	1.29067	−	0.419363i	0.418342	−	0.908290i	$-0.362611\pi$
$829$	37.1613	−	12.0745i	1.29067	−	0.419363i	0.872325	+	0.488927i	$0.162611\pi$
$830$	−1.32261	−	11.5575i	−0.0459083	−	0.401167i
$831$	−19.7214	−	41.1879i	−0.684126	−	1.42879i
$832$		−	30.4011i		−	1.05397i
$833$	−13.3831	−	11.8702i	−0.463696	−	0.411277i
$834$	−13.4045	+	72.9333i	−0.464158	+	2.52547i
$835$	4.18080	−	3.83481i	0.144683	−	0.132709i
$836$	−25.1443	−	18.2684i	−0.869634	−	0.631826i
$837$	0.754124	−	3.20450i	0.0260663	−	0.110764i
$838$	26.6682	+	36.7056i	0.921238	+	1.26797i
$839$	−13.1041	−	9.52069i	−0.452404	−	0.328691i	0.338140	−	0.941096i	$-0.390202\pi$
$839$	−13.1041	−	9.52069i	−0.452404	−	0.328691i	−0.790544	+	0.612405i	$0.790202\pi$
$840$	−39.3009	+	42.6323i	−1.35601	+	1.47095i
$841$	31.9875	−	23.2403i	1.10302	−	0.801389i
$842$	−12.5364	−	4.07333i	−0.432033	−	0.140376i
$843$	21.5860	+	22.6788i	0.743460	+	0.781098i
$844$	−17.1871	+	52.8964i	−0.591604	+	1.82077i
$845$	60.9847	−	55.9377i	2.09794	−	1.92432i
$846$	10.1602	+	37.4693i	0.349316	+	1.28822i
$847$	−6.06087	+	7.54203i	−0.208254	+	0.259147i
$848$	−42.7949	+	58.9021i	−1.46958	+	2.02271i
$849$	−4.05923	−	4.26473i	−0.139313	−	0.146365i
$850$	12.4638	−	29.4439i	0.427506	−	1.00992i
$851$			30.5663i			1.04780i
$852$	2.50892	+	18.8391i	0.0859542	+	0.645418i
$853$	8.68447	−	2.82176i	0.297351	−	0.0966151i	−0.156542	−	0.987671i	$-0.550035\pi$
$853$	8.68447	−	2.82176i	0.297351	−	0.0966151i	0.453893	+	0.891056i	$0.350035\pi$
$854$	14.4125	−	17.9346i	0.493184	−	0.613709i
$855$	3.15655	−	12.3836i	0.107952	−	0.423509i
$856$	−0.210598	+	0.648153i	−0.00719809	+	0.0221534i
$857$	37.7325			1.28892			0.644459	−	0.764638i	$-0.277082\pi$
$857$	37.7325			1.28892			0.644459	+	0.764638i	$0.277082\pi$
$858$	−105.832	+	50.6741i	−3.61305	+	1.72998i
$859$	−29.6184	−	40.7663i	−1.01057	−	1.39093i	−0.918610	−	0.395165i	$-0.870688\pi$
$859$	−29.6184	−	40.7663i	−1.01057	−	1.39093i	−0.0919576	−	0.995763i	$-0.529312\pi$
$860$	−10.5339	+	51.9070i	−0.359202	+	1.77001i
$861$	−5.02441	−	5.82083i	−0.171231	−	0.198374i
$862$	22.5346	−	16.3723i	0.767531	−	0.557644i
$863$	13.9342	+	19.1788i	0.474325	+	0.652853i	0.977402	−	0.211389i	$-0.0677986\pi$
$863$	13.9342	+	19.1788i	0.474325	+	0.652853i	−0.503077	+	0.864242i	$0.667799\pi$
$864$	14.4326	−	1.20112i	0.491006	−	0.0408630i
$865$	−0.413041	−	0.905149i	−0.0140438	−	0.0307760i
$866$	−2.75504	+	2.00166i	−0.0936202	+	0.0680191i
$867$	7.83106	+	16.3551i	0.265957	+	0.555448i
$868$	5.97606	−	3.91274i	0.202841	−	0.132807i
$869$	−24.8386	−	8.07055i	−0.842592	−	0.273775i
$870$	77.8101	−	19.5650i	2.63801	−	0.663314i
$871$	−7.14633	+	2.32198i	−0.242144	+	0.0786774i
$872$	14.0228	−	4.55629i	0.474872	−	0.154295i
$873$	−0.574122	−	0.462075i	−0.0194311	−	0.0156389i
$874$		−	17.4465i		−	0.590136i
$875$	−24.2901	+	16.8816i	−0.821157	+	0.570703i
$876$	49.2917	+	51.7871i	1.66541	+	1.74972i
$877$	37.4765	+	27.2283i	1.26549	+	0.919433i	0.999013	−	0.0444078i	$-0.0141401\pi$
$877$	37.4765	+	27.2283i	1.26549	+	0.919433i	0.266478	+	0.963841i	$0.414140\pi$
$878$	21.2782	+	65.4875i	0.718103	+	2.21010i
$879$	−26.1067	−	14.1242i	−0.880556	−	0.476397i
$880$	23.7402	−	42.0092i	0.800282	−	1.41613i
$881$	6.31282	−	19.4289i	0.212684	−	0.654575i	−0.786625	−	0.617430i	$-0.788174\pi$
$881$	6.31282	−	19.4289i	0.212684	−	0.654575i	0.999310	−	0.0371448i	$-0.0118263\pi$
$882$	23.3646	−	47.0677i	0.786726	−	1.58485i
$883$	−12.5708	+	38.6891i	−0.423042	+	1.30199i	0.481814	+	0.876273i	$0.339978\pi$
$883$	−12.5708	+	38.6891i	−0.423042	+	1.30199i	−0.904856	+	0.425717i	$0.860022\pi$
$884$	45.2661	+	62.3035i	1.52246	+	2.09549i
$885$	20.6340	+	8.28890i	0.693604	+	0.278628i
$886$	−71.7558	−	52.1337i	−2.41068	−	1.75146i
$887$	7.67730	−	5.57789i	0.257779	−	0.187287i	−0.451389	−	0.892328i	$-0.649071\pi$
$887$	7.67730	−	5.57789i	0.257779	−	0.187287i	0.709167	+	0.705040i	$0.249071\pi$
$888$	80.5072	+	14.7965i	2.70165	+	0.496537i
$889$	−1.56736	+	32.2109i	−0.0525677	+	1.08032i
$890$	−20.5840	−	4.17725i	−0.689976	−	0.140022i
$891$	17.4064	+	29.7361i	0.583137	+	0.996196i
$892$	−1.01360	−	0.329339i	−0.0339379	−	0.0110271i
$893$		−	9.85224i		−	0.329693i
$894$	17.5191	+	36.5884i	0.585925	+	1.22370i
$895$	9.09289	+	1.84528i	0.303942	+	0.0616811i
$896$	−33.6814	−	27.0668i	−1.12522	−	0.904237i
$897$	−39.4274	−	21.3309i	−1.31644	−	0.712219i
$898$	−68.8039	−	49.9890i	−2.29602	−	1.66815i
$899$	−5.24506			−0.174933
$900$	63.3336	+	8.64379i	2.11112	+	0.288126i
$901$			33.0094i			1.09970i
$902$	13.0046	+	9.44842i	0.433007	+	0.314598i
$903$	−2.13145	−	25.3827i	−0.0709302	−	0.844684i
$904$	17.0409	+	52.4466i	0.566773	+	1.74435i
$905$	7.43711	+	8.10812i	0.247218	+	0.269523i
$906$	8.04269	−	3.85096i	0.267200	−	0.127940i
$907$	39.2642			1.30374			0.651872	−	0.758329i	$-0.273984\pi$
$907$	39.2642			1.30374			0.651872	+	0.758329i	$0.273984\pi$
$908$	2.53671	−	7.80718i	0.0841835	−	0.259090i
$909$	−1.16497	−	1.78218i	−0.0386395	−	0.0591113i
$910$	−6.83328	−	104.463i	−0.226521	−	3.46293i
$911$	15.1668	−	20.8753i	0.502499	−	0.691631i	−0.480133	−	0.877196i	$-0.659412\pi$
$911$	15.1668	−	20.8753i	0.502499	−	0.691631i	0.982632	+	0.185565i	$0.0594115\pi$
$912$	−18.2925	−	3.36200i	−0.605726	−	0.111327i
$913$	−4.67855	−	6.43947i	−0.154837	−	0.213115i
$914$	48.1373	−	66.2553i	1.59224	−	2.19153i
$915$	−13.4289	−	0.912163i	−0.443946	−	0.0301552i
$916$	−28.0421	−	38.5967i	−0.926538	−	1.27527i
$917$	47.5944	−	12.9438i	1.57171	−	0.427442i
$918$	25.1693	−	21.6929i	0.830710	−	0.715972i
$919$	15.4693	−	47.6095i	0.510284	−	1.57049i	−0.281418	−	0.959585i	$-0.590805\pi$
$919$	15.4693	−	47.6095i	0.510284	−	1.57049i	0.791702	−	0.610907i	$-0.209195\pi$
$920$	46.0079	−	5.26500i	1.51684	−	0.173582i
$921$	−7.65729	+	14.1535i	−0.252316	+	0.466373i
$922$	−74.5350	+	24.2179i	−2.45468	+	0.797574i
$923$	−14.7315	−	10.7031i	−0.484893	−	0.352296i
$924$	−17.0720	+	72.7870i	−0.561629	+	2.39452i
$925$	38.4554	+	16.2785i	1.26441	+	0.535233i
$926$			68.0557i			2.23645i
$927$	−10.5913	−	8.52429i	−0.347865	−	0.279975i
$928$	−7.13035	−	21.9450i	−0.234065	−	0.720378i
$929$	−4.82999	−	14.8652i	−0.158467	−	0.487711i	0.840029	−	0.542542i	$-0.182538\pi$
$929$	−4.82999	−	14.8652i	−0.158467	−	0.487711i	−0.998496	+	0.0548310i	$0.982538\pi$
$930$	−5.69741	−	2.28871i	−0.186826	−	0.0750499i
$931$	−8.84879	+	9.97660i	−0.290007	+	0.326970i
$932$			67.9799i			2.22676i
$933$	−12.9971	−	27.1443i	−0.425505	−	0.888663i
$934$	−22.4796	−	30.9405i	−0.735554	−	1.01240i
$935$	−2.48731	−	21.7352i	−0.0813438	−	0.710818i
$936$	−75.2685	+	93.5201i	−2.46023	+	3.05680i
$937$	4.25004	+	5.84968i	0.138843	+	0.191101i	0.872776	−	0.488121i	$-0.162317\pi$
$937$	4.25004	+	5.84968i	0.138843	+	0.191101i	−0.733933	+	0.679222i	$0.762317\pi$
$938$	−2.49640	+	6.57673i	−0.0815103	+	0.214738i
$939$	0.712374	+	5.34911i	0.0232474	+	0.174562i
$940$	48.9594	−	5.60276i	1.59688	−	0.182742i
$941$	−15.7611	+	11.4511i	−0.513796	+	0.373295i	−0.814262	−	0.580498i	$-0.802858\pi$
$941$	−15.7611	+	11.4511i	−0.513796	+	0.373295i	0.300465	+	0.953793i	$0.402858\pi$
$942$	−40.1075	−	83.7641i	−1.30677	−	2.72918i
$943$			6.14111i			0.199982i
$944$	10.0005	−	30.7785i	0.325490	−	1.00176i
$945$	−30.4032	+	4.54375i	−0.989016	+	0.147808i
$946$	16.4549	+	50.6429i	0.534994	+	1.64654i
$947$	14.0950	−	4.57974i	0.458026	−	0.148822i	−0.0709115	−	0.997483i	$-0.522591\pi$
$947$	14.0950	−	4.57974i	0.458026	−	0.148822i	0.528937	+	0.848661i	$0.322591\pi$
$948$	−49.9105	+	6.64688i	−1.62102	+	0.215881i
$949$	−68.4996			−2.22359
$950$	−21.9494	−	9.29134i	−0.712132	−	0.301451i
$951$	9.17051	+	9.63476i	0.297374	+	0.312429i
$952$	38.2143	+	1.85949i	1.23853	+	0.0602663i
$953$	−31.2589	+	10.1566i	−1.01257	+	0.329005i	−0.767879	−	0.640595i	$-0.778688\pi$
$953$	−31.2589	+	10.1566i	−1.01257	+	0.329005i	−0.244695	+	0.969600i	$0.578688\pi$
$954$	−93.5847	+	25.3766i	−3.02992	+	0.821596i
$955$	−0.104674	−	0.914685i	−0.00338716	−	0.0295985i
$956$	−75.1170	−	24.4070i	−2.42946	−	0.789379i
$957$	39.7645	−	37.8484i	1.28540	−	1.22347i
$958$	63.0406	+	20.4831i	2.03675	+	0.661780i
$959$	−10.3142	+	27.1727i	−0.333064	+	0.877453i
$960$	−1.12835	+	16.6117i	−0.0364175	+	0.536140i
$961$	−24.7548	−	17.9854i	−0.798542	−	0.580175i
$962$	−119.562	+	86.8671i	−3.85484	+	2.80071i
$963$	−0.302432	+	0.197692i	−0.00974574	+	0.00637053i
$964$	7.01715	−	9.65828i	0.226007	−	0.311072i
$965$	−25.0989	−	14.1839i	−0.807963	−	0.456596i
$966$	−38.6879	+	16.2629i	−1.24476	+	0.523251i
$967$	−16.7151	+	51.4437i	−0.537521	+	1.65432i	0.200618	+	0.979669i	$0.435705\pi$
$967$	−16.7151	+	51.4437i	−0.537521	+	1.65432i	−0.738139	+	0.674649i	$0.764295\pi$
$968$		−	20.6936i		−	0.665117i
$969$	−7.60552	+	3.64164i	−0.244324	+	0.116986i
$970$	−1.01294	+	0.929112i	−0.0325236	+	0.0298320i
$971$	−6.41859	−	19.7544i	−0.205982	−	0.633949i	−0.999672	−	0.0256251i	$-0.991842\pi$
$971$	−6.41859	−	19.7544i	−0.205982	−	0.633949i	0.793689	−	0.608323i	$-0.208158\pi$
$972$	55.0255	+	37.2145i	1.76494	+	1.19366i
$973$	−45.2147	−	2.20012i	−1.44952	−	0.0705326i
$974$		−	49.8835i		−	1.59837i
$975$	−47.8339	+	38.2434i	−1.53191	+	1.22477i
$976$			19.5890i			0.627029i
$977$	−14.2235	+	19.5770i	−0.455051	+	0.626324i	−0.973473	−	0.228801i	$-0.926520\pi$
$977$	−14.2235	+	19.5770i	−0.455051	+	0.626324i	0.518422	+	0.855125i	$0.326520\pi$
$978$	30.3247	−	56.0510i	0.969675	−	1.79231i
$979$	−13.6679	+	4.44097i	−0.436828	+	0.141934i
$980$	−54.6095	−	38.2994i	−1.74444	−	1.22343i
$981$	7.30617	+	2.77950i	0.233268	+	0.0887426i
$982$	−79.7992			−2.54650
$983$	−13.6220	+	41.9243i	−0.434476	+	1.33718i	0.459147	+	0.888360i	$0.348155\pi$
$983$	−13.6220	+	41.9243i	−0.434476	+	1.33718i	−0.893623	+	0.448818i	$0.851845\pi$
$984$	16.1748	+	2.97277i	0.515633	+	0.0947686i
$985$	−14.2874	−	2.89944i	−0.455233	−	0.0923837i
$986$	−42.8295	−	31.1174i	−1.36397	−	0.990981i
$987$	−21.8475	+	9.18386i	−0.695414	+	0.292325i
$988$	46.4450	−	33.7443i	1.47761	−	1.07355i
$989$	−11.9574	+	16.4580i	−0.380224	+	0.523333i
$990$	59.7093	−	23.7611i	1.89769	−	0.755178i
$991$	−3.13364	+	2.27672i	−0.0995434	+	0.0723225i	−0.636444	−	0.771323i	$-0.719595\pi$
$991$	−3.13364	+	2.27672i	−0.0995434	+	0.0723225i	0.536900	+	0.843646i	$0.319595\pi$
$992$	−0.545664	+	1.67938i	−0.0173249	+	0.0533204i
$993$	29.1794	−	27.7734i	0.925980	−	0.881361i
$994$	−16.4497	+	4.47366i	−0.521751	+	0.141896i
$995$	4.03993	−	7.14880i	0.128074	−	0.226632i
$996$	−13.4968	−	7.30204i	−0.427663	−	0.231374i
$997$	16.6348	−	5.40497i	0.526829	−	0.171177i	−0.0335134	−	0.999438i	$-0.510670\pi$
$997$	16.6348	−	5.40497i	0.526829	−	0.171177i	0.560342	+	0.828261i	$0.310670\pi$
$998$	−5.51695	+	7.59343i	−0.174636	+	0.240366i
$999$	28.3321	+	32.8725i	0.896389	+	1.04004i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bb.a.41.6	yes	304
3.2	odd	2	inner	525.2.bb.a.41.72	yes	304
7.6	odd	2	inner	525.2.bb.a.41.5	✓	304
21.20	even	2	inner	525.2.bb.a.41.71	yes	304
25.11	even	5	inner	525.2.bb.a.461.71	yes	304
75.11	odd	10	inner	525.2.bb.a.461.5	yes	304
175.111	odd	10	inner	525.2.bb.a.461.72	yes	304
525.461	even	10	inner	525.2.bb.a.461.6	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bb.a.41.5	✓	304	7.6	odd	2	inner
525.2.bb.a.41.6	yes	304	1.1	even	1	trivial
525.2.bb.a.41.71	yes	304	21.20	even	2	inner
525.2.bb.a.41.72	yes	304	3.2	odd	2	inner
525.2.bb.a.461.5	yes	304	75.11	odd	10	inner
525.2.bb.a.461.6	yes	304	525.461	even	10	inner
525.2.bb.a.461.71	yes	304	25.11	even	5	inner
525.2.bb.a.461.72	yes	304	175.111	odd	10	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.47080 + 2.02438i) q^{2} +(1.52339 + 0.824183i) q^{3} +(-1.31684 - 4.05281i) q^{4} +(-1.94672 - 1.10013i) q^{5} +(-3.90907 + 1.87172i) q^{6} +(-1.44927 - 2.21351i) q^{7} +(5.38165 + 1.74860i) q^{8} +(1.64144 + 2.51111i) q^{9} +O(q^{10})\)	\(q+(-1.47080 + 2.02438i) q^{2} +(1.52339 + 0.824183i) q^{3} +(-1.31684 - 4.05281i) q^{4} +(-1.94672 - 1.10013i) q^{5} +(-3.90907 + 1.87172i) q^{6} +(-1.44927 - 2.21351i) q^{7} +(5.38165 + 1.74860i) q^{8} +(1.64144 + 2.51111i) q^{9} +(5.09032 - 2.32283i) q^{10} +(2.25031 - 3.09728i) q^{11} +(1.33420 - 7.25934i) q^{12} +(4.15662 + 5.72110i) q^{13} +(6.61257 + 0.321764i) q^{14} +(-2.05891 - 3.28038i) q^{15} +(-4.56011 + 3.31312i) q^{16} +(-0.789704 + 2.43046i) q^{17} +(-7.49768 - 0.370426i) q^{18} +(1.81182 + 0.588696i) q^{19} +(-1.89511 + 9.33839i) q^{20} +(-0.383461 - 4.56650i) q^{21} +(2.96033 + 9.11096i) q^{22} +(-2.15121 + 2.96089i) q^{23} +(6.75719 + 7.09927i) q^{24} +(2.57943 + 4.28329i) q^{25} -17.6953 q^{26} +(0.430950 + 5.17825i) q^{27} +(-7.06250 + 8.78844i) q^{28} +(7.87362 - 2.55829i) q^{29} +(9.66899 + 0.656769i) q^{30} +(-0.602544 - 0.195779i) q^{31} -2.78715i q^{32} +(5.98082 - 2.86371i) q^{33} +(-3.75868 - 5.17338i) q^{34} +(0.386164 + 5.90346i) q^{35} +(8.01553 - 9.95919i) q^{36} +(6.75673 - 4.90905i) q^{37} +(-3.85657 + 2.80196i) q^{38} +(1.61693 + 12.1413i) q^{39} +(-8.55287 - 9.32455i) q^{40} +(1.35750 - 0.986282i) q^{41} +(9.80835 + 5.94014i) q^{42} +5.55846 q^{43} +(-15.5160 - 5.04145i) q^{44} +(-0.432887 - 6.69422i) q^{45} +(-2.82997 - 8.70975i) q^{46} +(-1.59812 - 4.91850i) q^{47} +(-9.67745 + 1.28880i) q^{48} +(-2.79926 + 6.41593i) q^{49} +(-12.4648 - 1.07811i) q^{50} +(-3.20617 + 3.05168i) q^{51} +(17.7130 - 24.3798i) q^{52} +(12.2846 - 3.99151i) q^{53} +(-11.1166 - 6.74377i) q^{54} +(-7.78812 + 3.55391i) q^{55} +(-3.92888 - 14.4465i) q^{56} +(2.27492 + 2.39009i) q^{57} +(-6.40155 + 19.7020i) q^{58} +(-4.64495 + 3.37475i) q^{59} +(-10.5835 + 12.6641i) q^{60} +(2.04274 - 2.81159i) q^{61} +(1.28255 - 0.931830i) q^{62} +(3.17947 - 7.27262i) q^{63} +(-3.47797 - 2.52689i) q^{64} +(-1.79783 - 15.7102i) q^{65} +(-2.99936 + 16.3194i) q^{66} +(-0.328350 + 1.01056i) q^{67} +10.8901 q^{68} +(-5.71745 + 2.73760i) q^{69} +(-12.5188 - 7.90107i) q^{70} +(-2.44891 + 0.795701i) q^{71} +(4.44274 + 16.3841i) q^{72} +(-5.69357 + 7.83653i) q^{73} +20.8985i q^{74} +(0.399270 + 8.65105i) q^{75} -8.11819i q^{76} +(-10.1172 - 0.492294i) q^{77} +(-26.9568 - 14.5841i) q^{78} +(-2.10805 - 6.48790i) q^{79} +(12.5221 - 1.43299i) q^{80} +(-3.61132 + 8.24369i) q^{81} +4.19873i q^{82} +(0.642469 - 1.97732i) q^{83} +(-18.0022 + 7.56745i) q^{84} +(4.21115 - 3.86264i) q^{85} +(-8.17538 + 11.2524i) q^{86} +(14.1031 + 2.59202i) q^{87} +(17.5263 - 12.7336i) q^{88} +(-3.03690 - 2.20644i) q^{89} +(14.1884 + 8.96954i) q^{90} +(6.63967 - 17.4921i) q^{91} +(14.8327 + 4.81944i) q^{92} +(-0.756554 - 0.794854i) q^{93} +(12.3074 + 3.99893i) q^{94} +(-2.87946 - 3.13926i) q^{95} +(2.29712 - 4.24592i) q^{96} +(-0.233634 + 0.0759124i) q^{97} +(-8.87115 - 15.1033i) q^{98} +(11.4714 + 0.566747i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9}+O(q^{10}) \) 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9	\( 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9} + 8 q^{15} - 92 q^{16} - 16 q^{18} + 12 q^{21} - 48 q^{22} - 32 q^{25} - 36 q^{28} - 14 q^{30} - 8 q^{36} - 4 q^{37} - 26 q^{39} - 11 q^{42} - 20 q^{49} + 20 q^{51} - 168 q^{57} + 32 q^{58} + 76 q^{60} + 29 q^{63} + 68 q^{64} - 44 q^{67} + 30 q^{70} - 114 q^{72} - 124 q^{78} - 68 q^{79} - 2 q^{81} + 102 q^{84} + 72 q^{85} - 156 q^{88} + 70 q^{91} - 32 q^{93} - 36 q^{99}+O(q^{100}) \) 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9 + 8 * q^15 - 92 * q^16 - 16 * q^18 + 12 * q^21 - 48 * q^22 - 32 * q^25 - 36 * q^28 - 14 * q^30 - 8 * q^36 - 4 * q^37 - 26 * q^39 - 11 * q^42 - 20 * q^49 + 20 * q^51 - 168 * q^57 + 32 * q^58 + 76 * q^60 + 29 * q^63 + 68 * q^64 - 44 * q^67 + 30 * q^70 - 114 * q^72 - 124 * q^78 - 68 * q^79 - 2 * q^81 + 102 * q^84 + 72 * q^85 - 156 * q^88 + 70 * q^91 - 32 * q^93 - 36 * q^99

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