LMFDB - Embedded newform 570.2.k.a.533.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(77,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("570.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.k (of order $4$, degree $2$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			533.14
Character	$\chi$	$=$	570.533
Dual form			570.2.k.a.77.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.830420 + 1.52000i) q^{3} +1.00000i q^{4} +(2.23234 + 0.129088i) q^{5} +(-0.487608 + 1.66200i) q^{6} +(-2.47472 + 2.47472i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.62081 + 2.52448i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.830420 + 1.52000i) q^{3} +1.00000i q^{4} +(2.23234 + 0.129088i) q^{5} +(-0.487608 + 1.66200i) q^{6} +(-2.47472 + 2.47472i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.62081 + 2.52448i) q^{9} +(1.48722 + 1.66978i) q^{10} -0.319493i q^{11} +(-1.52000 + 0.830420i) q^{12} +(-3.95820 - 3.95820i) q^{13} -3.49979 q^{14} +(1.65756 + 3.50035i) q^{15} -1.00000 q^{16} +(4.30711 + 4.30711i) q^{17} +(-2.93116 + 0.638992i) q^{18} -1.00000i q^{19} +(-0.129088 + 2.23234i) q^{20} +(-5.81664 - 1.70652i) q^{21} +(0.225915 - 0.225915i) q^{22} +(2.89538 - 2.89538i) q^{23} +(-1.66200 - 0.487608i) q^{24} +(4.96667 + 0.576336i) q^{25} -5.59774i q^{26} +(-5.18316 - 0.367253i) q^{27} +(-2.47472 - 2.47472i) q^{28} +8.60087 q^{29} +(-1.30305 + 3.64720i) q^{30} -2.73939 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.485629 - 0.265313i) q^{33} +6.09118i q^{34} +(-5.84388 + 5.20497i) q^{35} +(-2.52448 - 1.62081i) q^{36} +(1.42898 - 1.42898i) q^{37} +(0.707107 - 0.707107i) q^{38} +(2.72950 - 9.30344i) q^{39} +(-1.66978 + 1.48722i) q^{40} -7.07028i q^{41} +(-2.90629 - 5.31968i) q^{42} +(6.45694 + 6.45694i) q^{43} +0.319493 q^{44} +(-3.94407 + 5.42626i) q^{45} +4.09469 q^{46} +(4.12471 + 4.12471i) q^{47} +(-0.830420 - 1.52000i) q^{48} -5.24852i q^{49} +(3.10444 + 3.91950i) q^{50} +(-2.97011 + 10.1235i) q^{51} +(3.95820 - 3.95820i) q^{52} +(-1.15569 + 1.15569i) q^{53} +(-3.40536 - 3.92473i) q^{54} +(0.0412426 - 0.713216i) q^{55} -3.49979i q^{56} +(1.52000 - 0.830420i) q^{57} +(6.08174 + 6.08174i) q^{58} -7.51199 q^{59} +(-3.50035 + 1.65756i) q^{60} +8.09546 q^{61} +(-1.93704 - 1.93704i) q^{62} +(-2.23634 - 10.2584i) q^{63} -1.00000i q^{64} +(-8.32509 - 9.34700i) q^{65} +(0.530996 + 0.155787i) q^{66} +(-11.1750 + 11.1750i) q^{67} +(-4.30711 + 4.30711i) q^{68} +(6.80536 + 1.99660i) q^{69} +(-7.81272 - 0.451781i) q^{70} -13.8007i q^{71} +(-0.638992 - 2.93116i) q^{72} +(-9.22508 - 9.22508i) q^{73} +2.02088 q^{74} +(3.24839 + 8.02795i) q^{75} +1.00000 q^{76} +(0.790656 + 0.790656i) q^{77} +(8.50858 - 4.64848i) q^{78} +3.00427i q^{79} +(-2.23234 - 0.129088i) q^{80} +(-3.74597 - 8.18338i) q^{81} +(4.99944 - 4.99944i) q^{82} +(-2.31688 + 2.31688i) q^{83} +(1.70652 - 5.81664i) q^{84} +(9.05894 + 10.1709i) q^{85} +9.13149i q^{86} +(7.14233 + 13.0733i) q^{87} +(0.225915 + 0.225915i) q^{88} +4.95832 q^{89} +(-6.62582 + 1.04807i) q^{90} +19.5909 q^{91} +(2.89538 + 2.89538i) q^{92} +(-2.27484 - 4.16388i) q^{93} +5.83322i q^{94} +(0.129088 - 2.23234i) q^{95} +(0.487608 - 1.66200i) q^{96} +(-2.21723 + 2.21723i) q^{97} +(3.71127 - 3.71127i) q^{98} +(0.806552 + 0.517836i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7}+O(q^{10}) $ 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7	$ 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} - 32 q^{21} - 4 q^{22} + 32 q^{25} + 28 q^{27} - 12 q^{28} - 8 q^{30} + 8 q^{31} + 36 q^{33} + 4 q^{36} - 32 q^{37} - 8 q^{40} + 12 q^{42} - 24 q^{43} - 28 q^{45} - 16 q^{46} - 4 q^{48} - 40 q^{51} - 8 q^{52} - 4 q^{55} + 4 q^{57} - 4 q^{58} - 24 q^{60} + 200 q^{61} + 28 q^{63} + 12 q^{70} - 68 q^{73} - 36 q^{75} + 36 q^{76} + 24 q^{78} - 92 q^{81} + 24 q^{82} + 24 q^{85} + 28 q^{87} - 4 q^{88} - 68 q^{90} + 64 q^{91} + 16 q^{93} - 4 q^{96} - 148 q^{97}+O(q^{100}) $ 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 - 32 * q^21 - 4 * q^22 + 32 * q^25 + 28 * q^27 - 12 * q^28 - 8 * q^30 + 8 * q^31 + 36 * q^33 + 4 * q^36 - 32 * q^37 - 8 * q^40 + 12 * q^42 - 24 * q^43 - 28 * q^45 - 16 * q^46 - 4 * q^48 - 40 * q^51 - 8 * q^52 - 4 * q^55 + 4 * q^57 - 4 * q^58 - 24 * q^60 + 200 * q^61 + 28 * q^63 + 12 * q^70 - 68 * q^73 - 36 * q^75 + 36 * q^76 + 24 * q^78 - 92 * q^81 + 24 * q^82 + 24 * q^85 + 28 * q^87 - 4 * q^88 - 68 * q^90 + 64 * q^91 + 16 * q^93 - 4 * q^96 - 148 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.830420	+	1.52000i	0.479443	+	0.877573i
$3$	0.830420	+	1.52000i	0.479443	+	0.877573i
$4$			1.00000i			0.500000i
$5$	2.23234	+	0.129088i	0.998332	+	0.0577299i
$5$	2.23234	+	0.129088i	0.998332	+	0.0577299i
$6$	−0.487608	+	1.66200i	−0.199065	+	0.678508i
$7$	−2.47472	+	2.47472i	−0.935358	+	0.935358i	−0.998034	−	0.0626759i	$-0.980037\pi$
$7$	−2.47472	+	2.47472i	−0.935358	+	0.935358i	0.0626759	+	0.998034i	$0.480037\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.62081	+	2.52448i	−0.540269	+	0.841492i
$10$	1.48722	+	1.66978i	0.470301	+	0.528031i
$11$		−	0.319493i		−	0.0963306i	−0.998839	−	0.0481653i	$-0.984663\pi$
$11$		−	0.319493i		−	0.0963306i	0.998839	−	0.0481653i	$-0.0153374\pi$
$12$	−1.52000	+	0.830420i	−0.438787	+	0.239721i
$13$	−3.95820	−	3.95820i	−1.09781	−	1.09781i	−0.994667	−	0.103141i	$-0.967111\pi$
$13$	−3.95820	−	3.95820i	−1.09781	−	1.09781i	−0.103141	−	0.994667i	$-0.532889\pi$
$14$	−3.49979			−0.935358
$15$	1.65756	+	3.50035i	0.427981	+	0.903788i
$16$	−1.00000			−0.250000
$17$	4.30711	+	4.30711i	1.04463	+	1.04463i	0.998956	+	0.0456719i	$0.0145429\pi$
$17$	4.30711	+	4.30711i	1.04463	+	1.04463i	0.0456719	+	0.998956i	$0.485457\pi$
$18$	−2.93116	+	0.638992i	−0.690881	+	0.150612i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−0.129088	+	2.23234i	−0.0288649	+	0.499166i
$21$	−5.81664	−	1.70652i	−1.26930	−	0.372394i
$22$	0.225915	−	0.225915i	0.0481653	−	0.0481653i
$23$	2.89538	−	2.89538i	0.603729	−	0.603729i	−0.337571	−	0.941300i	$-0.609605\pi$
$23$	2.89538	−	2.89538i	0.603729	−	0.603729i	0.941300	+	0.337571i	$0.109605\pi$
$24$	−1.66200	−	0.487608i	−0.339254	−	0.0995325i
$25$	4.96667	+	0.576336i	0.993335	+	0.115267i
$26$		−	5.59774i		−	1.09781i
$27$	−5.18316	−	0.367253i	−0.997499	−	0.0706778i
$28$	−2.47472	−	2.47472i	−0.467679	−	0.467679i
$29$	8.60087			1.59714			0.798571	−	0.601900i	$-0.205590\pi$
$29$	8.60087			1.59714			0.798571	+	0.601900i	$0.205590\pi$
$30$	−1.30305	+	3.64720i	−0.237903	+	0.665884i
$31$	−2.73939			−0.492009			−0.246005	−	0.969269i	$-0.579118\pi$
$31$	−2.73939			−0.492009			−0.246005	+	0.969269i	$0.579118\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	0.485629	−	0.265313i	0.0845372	−	0.0461850i
$34$			6.09118i			1.04463i
$35$	−5.84388	+	5.20497i	−0.987796	+	0.879800i
$36$	−2.52448	−	1.62081i	−0.420746	−	0.270134i
$37$	1.42898	−	1.42898i	0.234923	−	0.234923i	−0.579821	−	0.814744i	$-0.696878\pi$
$37$	1.42898	−	1.42898i	0.234923	−	0.234923i	0.814744	+	0.579821i	$0.196878\pi$
$38$	0.707107	−	0.707107i	0.114708	−	0.114708i
$39$	2.72950	−	9.30344i	0.437070	−	1.48974i
$40$	−1.66978	+	1.48722i	−0.264016	+	0.235151i
$41$		−	7.07028i		−	1.10419i	−0.833780	−	0.552096i	$-0.813828\pi$
$41$		−	7.07028i		−	1.10419i	0.833780	−	0.552096i	$-0.186172\pi$
$42$	−2.90629	−	5.31968i	−0.448451	−	0.820845i
$43$	6.45694	+	6.45694i	0.984674	+	0.984674i	0.999884	−	0.0152099i	$-0.00484166\pi$
$43$	6.45694	+	6.45694i	0.984674	+	0.984674i	−0.0152099	+	0.999884i	$0.504842\pi$
$44$	0.319493			0.0481653
$45$	−3.94407	+	5.42626i	−0.587947	+	0.808899i
$46$	4.09469			0.603729
$47$	4.12471	+	4.12471i	0.601650	+	0.601650i	0.940750	−	0.339100i	$-0.110123\pi$
$47$	4.12471	+	4.12471i	0.601650	+	0.601650i	−0.339100	+	0.940750i	$0.610123\pi$
$48$	−0.830420	−	1.52000i	−0.119861	−	0.219393i
$49$		−	5.24852i		−	0.749789i
$50$	3.10444	+	3.91950i	0.439034	+	0.554301i
$51$	−2.97011	+	10.1235i	−0.415898	+	1.41758i
$52$	3.95820	−	3.95820i	0.548904	−	0.548904i
$53$	−1.15569	+	1.15569i	−0.158747	+	0.158747i	−0.782011	−	0.623264i	$-0.785806\pi$
$53$	−1.15569	+	1.15569i	−0.158747	+	0.158747i	0.623264	+	0.782011i	$0.285806\pi$
$54$	−3.40536	−	3.92473i	−0.463411	−	0.534088i
$55$	0.0412426	−	0.713216i	0.00556116	−	0.0961700i
$56$		−	3.49979i		−	0.467679i
$57$	1.52000	−	0.830420i	0.201329	−	0.109992i
$58$	6.08174	+	6.08174i	0.798571	+	0.798571i
$59$	−7.51199			−0.977978			−0.488989	−	0.872290i	$-0.662634\pi$
$59$	−7.51199			−0.977978			−0.488989	+	0.872290i	$0.662634\pi$
$60$	−3.50035	+	1.65756i	−0.451894	+	0.213991i
$61$	8.09546			1.03652			0.518259	−	0.855224i	$-0.326581\pi$
$61$	8.09546			1.03652			0.518259	+	0.855224i	$0.326581\pi$
$62$	−1.93704	−	1.93704i	−0.246005	−	0.246005i
$63$	−2.23634	−	10.2584i	−0.281752	−	1.29244i
$64$		−	1.00000i		−	0.125000i
$65$	−8.32509	−	9.34700i	−1.03260	−	1.15935i
$66$	0.530996	+	0.155787i	0.0653611	+	0.0191761i
$67$	−11.1750	+	11.1750i	−1.36524	+	1.36524i	−0.498158	+	0.867086i	$0.665990\pi$
$67$	−11.1750	+	11.1750i	−1.36524	+	1.36524i	−0.867086	+	0.498158i	$0.834010\pi$
$68$	−4.30711	+	4.30711i	−0.522314	+	0.522314i
$69$	6.80536	+	1.99660i	0.819270	+	0.240363i
$70$	−7.81272	−	0.451781i	−0.933798	−	0.0539981i
$71$		−	13.8007i		−	1.63784i	−0.573909	−	0.818919i	$-0.694574\pi$
$71$		−	13.8007i		−	1.63784i	0.573909	−	0.818919i	$-0.305426\pi$
$72$	−0.638992	−	2.93116i	−0.0753059	−	0.345440i
$73$	−9.22508	−	9.22508i	−1.07971	−	1.07971i	−0.996535	−	0.0831788i	$-0.973493\pi$
$73$	−9.22508	−	9.22508i	−1.07971	−	1.07971i	−0.0831788	−	0.996535i	$-0.526507\pi$
$74$	2.02088			0.234923
$75$	3.24839	+	8.02795i	0.375092	+	0.926988i
$76$	1.00000			0.114708
$77$	0.790656	+	0.790656i	0.0901036	+	0.0901036i
$78$	8.50858	−	4.64848i	0.963407	−	0.526336i
$79$			3.00427i			0.338007i	0.985615	+	0.169004i	$0.0540549\pi$
$79$			3.00427i			0.338007i	−0.985615	+	0.169004i	$0.945945\pi$
$80$	−2.23234	−	0.129088i	−0.249583	−	0.0144325i
$81$	−3.74597	−	8.18338i	−0.416219	−	0.909264i
$82$	4.99944	−	4.99944i	0.552096	−	0.552096i
$83$	−2.31688	+	2.31688i	−0.254311	+	0.254311i	−0.822735	−	0.568425i	$-0.807553\pi$
$83$	−2.31688	+	2.31688i	−0.254311	+	0.254311i	0.568425	+	0.822735i	$0.307553\pi$
$84$	1.70652	−	5.81664i	0.186197	−	0.634648i
$85$	9.05894	+	10.1709i	0.982580	+	1.10319i
$86$			9.13149i			0.984674i
$87$	7.14233	+	13.0733i	0.765739	+	1.40161i
$88$	0.225915	+	0.225915i	0.0240827	+	0.0240827i
$89$	4.95832			0.525580			0.262790	−	0.964853i	$-0.415357\pi$
$89$	4.95832			0.525580			0.262790	+	0.964853i	$0.415357\pi$
$90$	−6.62582	+	1.04807i	−0.698423	+	0.110476i
$91$	19.5909			2.05369
$92$	2.89538	+	2.89538i	0.301864	+	0.301864i
$93$	−2.27484	−	4.16388i	−0.235890	−	0.431774i
$94$			5.83322i			0.601650i
$95$	0.129088	−	2.23234i	0.0132441	−	0.229033i
$96$	0.487608	−	1.66200i	0.0497663	−	0.169627i
$97$	−2.21723	+	2.21723i	−0.225126	+	0.225126i	−0.810653	−	0.585527i	$-0.800888\pi$
$97$	−2.21723	+	2.21723i	−0.225126	+	0.225126i	0.585527	+	0.810653i	$0.300888\pi$
$98$	3.71127	−	3.71127i	0.374895	−	0.374895i
$99$	0.806552	+	0.517836i	0.0810615	+	0.0520445i
$100$	−0.576336	+	4.96667i	−0.0576336	+	0.496667i
$101$		−	6.77117i		−	0.673757i	−0.941548	−	0.336878i	$-0.890629\pi$
$101$		−	6.77117i		−	0.673757i	0.941548	−	0.336878i	$-0.109371\pi$
$102$	−9.25860	+	5.05823i	−0.916738	+	0.500840i
$103$	7.14069	+	7.14069i	0.703593	+	0.703593i	0.965180	−	0.261587i	$-0.0842458\pi$
$103$	7.14069	+	7.14069i	0.703593	+	0.703593i	−0.261587	+	0.965180i	$0.584246\pi$
$104$	5.59774			0.548904
$105$	−12.7644	−	4.56040i	−1.24568	−	0.445049i
$106$	−1.63440			−0.158747
$107$	4.96947	+	4.96947i	0.480416	+	0.480416i	0.905265	−	0.424848i	$-0.139673\pi$
$107$	4.96947	+	4.96947i	0.480416	+	0.480416i	−0.424848	+	0.905265i	$0.639673\pi$
$108$	0.367253	−	5.18316i	0.0353389	−	0.498750i
$109$		−	12.0861i		−	1.15764i	−0.815455	−	0.578820i	$-0.803513\pi$
$109$		−	12.0861i		−	1.15764i	0.815455	−	0.578820i	$-0.196487\pi$
$110$	0.533483	−	0.475157i	0.0508656	−	0.0453044i
$111$	3.35870	+	0.985397i	0.318794	+	0.0935298i
$112$	2.47472	−	2.47472i	0.233840	−	0.233840i
$113$	5.06883	−	5.06883i	0.476835	−	0.476835i	−0.427283	−	0.904118i	$-0.640529\pi$
$113$	5.06883	−	5.06883i	0.476835	−	0.476835i	0.904118	+	0.427283i	$0.140529\pi$
$114$	1.66200	+	0.487608i	0.155660	+	0.0456687i
$115$	6.83723	−	6.08971i	0.637575	−	0.567869i
$116$			8.60087i			0.798571i
$117$	16.4079	−	3.57691i	1.51691	−	0.330686i
$118$	−5.31178	−	5.31178i	−0.488989	−	0.488989i
$119$	−21.3178			−1.95420
$120$	−3.64720	−	1.30305i	−0.332942	−	0.118952i
$121$	10.8979			0.990720
$122$	5.72435	+	5.72435i	0.518259	+	0.518259i
$123$	10.7468	−	5.87130i	0.969010	−	0.529397i
$124$		−	2.73939i		−	0.246005i
$125$	11.0129	+	1.92771i	0.985024	+	0.172420i
$126$	5.67248	−	8.83514i	0.505345	−	0.787097i
$127$	11.4227	−	11.4227i	1.01360	−	1.01360i	0.0136950	−	0.999906i	$-0.495641\pi$
$127$	11.4227	−	11.4227i	1.01360	−	1.01360i	0.999906	−	0.0136950i	$-0.00435939\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−4.45259	+	15.1765i	−0.392028	+	1.33622i
$130$	0.722601	−	12.4961i	0.0633763	−	1.09598i
$131$		−	3.12384i		−	0.272931i	−0.990645	−	0.136466i	$-0.956426\pi$
$131$		−	3.12384i		−	0.272931i	0.990645	−	0.136466i	$-0.0435744\pi$
$132$	0.265313	+	0.485629i	0.0230925	+	0.0422686i
$133$	2.47472	+	2.47472i	0.214586	+	0.214586i
$134$	−15.8038			−1.36524
$135$	−11.5232	−	1.48892i	−0.991755	−	0.128145i
$136$	−6.09118			−0.522314
$137$	4.42417	+	4.42417i	0.377982	+	0.377982i	0.870374	−	0.492392i	$-0.163877\pi$
$137$	4.42417	+	4.42417i	0.377982	+	0.377982i	−0.492392	+	0.870374i	$0.663877\pi$
$138$	3.40031	+	6.22393i	0.289453	+	0.529816i
$139$		−	13.6045i		−	1.15392i	−0.816772	−	0.576960i	$-0.804239\pi$
$139$		−	13.6045i		−	1.15392i	0.816772	−	0.576960i	$-0.195761\pi$
$140$	−5.20497	−	5.84388i	−0.439900	−	0.493898i
$141$	−2.84432	+	9.69479i	−0.239535	+	0.816449i
$142$	9.75855	−	9.75855i	0.818919	−	0.818919i
$143$	−1.26462	+	1.26462i	−0.105753	+	0.105753i
$144$	1.62081	−	2.52448i	0.135067	−	0.210373i
$145$	19.2001	+	1.11027i	1.59448	+	0.0922028i
$146$		−	13.0462i		−	1.07971i
$147$	7.97776	−	4.35848i	0.657995	−	0.359481i
$148$	1.42898	+	1.42898i	0.117461	+	0.117461i
$149$	−15.4792			−1.26810			−0.634052	−	0.773291i	$-0.718609\pi$
$149$	−15.4792			−1.26810			−0.634052	+	0.773291i	$0.718609\pi$
$150$	−3.37966	+	7.97358i	−0.275948	+	0.651040i
$151$	−13.4794			−1.09694			−0.548469	−	0.836171i	$-0.684789\pi$
$151$	−13.4794			−1.09694			−0.548469	+	0.836171i	$0.684789\pi$
$152$	0.707107	+	0.707107i	0.0573539	+	0.0573539i
$153$	−17.8542	+	3.89221i	−1.44343	+	0.314667i
$154$			1.11816i			0.0901036i
$155$	−6.11525	−	0.353622i	−0.491189	−	0.0284036i
$156$	9.30344	+	2.72950i	0.744871	+	0.218535i
$157$	−5.84460	+	5.84460i	−0.466450	+	0.466450i	−0.900762	−	0.434313i	$-0.856991\pi$
$157$	−5.84460	+	5.84460i	−0.466450	+	0.466450i	0.434313	+	0.900762i	$0.356991\pi$
$158$	−2.12434	+	2.12434i	−0.169004	+	0.169004i
$159$	−2.71637	−	0.796945i	−0.215422	−	0.0632019i
$160$	−1.48722	−	1.66978i	−0.117575	−	0.132008i
$161$			14.3305i			1.12940i
$162$	3.13772	−	8.43532i	0.246523	−	0.662742i
$163$	−9.68901	−	9.68901i	−0.758902	−	0.758902i	0.217221	−	0.976123i	$-0.430301\pi$
$163$	−9.68901	−	9.68901i	−0.758902	−	0.758902i	−0.976123	+	0.217221i	$0.930301\pi$
$164$	7.07028			0.552096
$165$	1.11834	−	0.529579i	0.0870624	−	0.0412277i
$166$	−3.27656			−0.254311
$167$	9.29416	+	9.29416i	0.719204	+	0.719204i	0.968442	−	0.249239i	$-0.0801803\pi$
$167$	9.29416	+	9.29416i	0.719204	+	0.719204i	−0.249239	+	0.968442i	$0.580180\pi$
$168$	5.31968	−	2.90629i	0.410422	−	0.224225i
$169$			18.3347i			1.41036i
$170$	−0.786298	+	13.5976i	−0.0603063	+	1.04289i
$171$	2.52448	+	1.62081i	0.193052	+	0.123946i
$172$	−6.45694	+	6.45694i	−0.492337	+	0.492337i
$173$	4.33021	−	4.33021i	0.329220	−	0.329220i	−0.523070	−	0.852290i	$-0.675213\pi$
$173$	4.33021	−	4.33021i	0.329220	−	0.329220i	0.852290	+	0.523070i	$0.175213\pi$
$174$	−4.19385	+	14.2946i	−0.317935	+	1.08367i
$175$	−13.7174	+	10.8649i	−1.03694	+	0.821307i
$176$			0.319493i			0.0240827i
$177$	−6.23810	−	11.4182i	−0.468885	−	0.858247i
$178$	3.50606	+	3.50606i	0.262790	+	0.262790i
$179$	−8.41749			−0.629153			−0.314576	−	0.949232i	$-0.601862\pi$
$179$	−8.41749			−0.629153			−0.314576	+	0.949232i	$0.601862\pi$
$180$	−5.42626	−	3.94407i	−0.404450	−	0.293974i
$181$	−4.04233			−0.300464			−0.150232	−	0.988651i	$-0.548002\pi$
$181$	−4.04233			−0.300464			−0.150232	+	0.988651i	$0.548002\pi$
$182$	13.8529	+	13.8529i	1.02684	+	1.02684i
$183$	6.72263	+	12.3051i	0.496951	+	0.909619i
$184$			4.09469i			0.301864i
$185$	3.37443	−	3.00550i	0.248093	−	0.220969i
$186$	1.33575	−	4.55286i	0.0979418	−	0.333832i
$187$	1.37609	−	1.37609i	0.100630	−	0.100630i
$188$	−4.12471	+	4.12471i	−0.300825	+	0.300825i
$189$	13.7357	−	11.9180i	0.999128	−	0.866910i
$190$	1.66978	−	1.48722i	0.121139	−	0.107894i
$191$		−	12.7401i		−	0.921841i	−0.887441	−	0.460921i	$-0.847519\pi$
$191$		−	12.7401i		−	0.921841i	0.887441	−	0.460921i	$-0.152481\pi$
$192$	1.52000	−	0.830420i	0.109697	−	0.0599304i
$193$	0.0511200	+	0.0511200i	0.00367970	+	0.00367970i	0.708944	−	0.705265i	$-0.249172\pi$
$193$	0.0511200	+	0.0511200i	0.00367970	+	0.00367970i	−0.705265	+	0.708944i	$0.749172\pi$
$194$	−3.13564			−0.225126
$195$	7.29414	−	20.4161i	0.522344	−	1.46203i
$196$	5.24852			0.374895
$197$	−13.8117	−	13.8117i	−0.984041	−	0.984041i	0.0158340	−	0.999875i	$-0.494960\pi$
$197$	−13.8117	−	13.8117i	−0.984041	−	0.984041i	−0.999875	+	0.0158340i	$0.994960\pi$
$198$	0.204153	+	0.936483i	0.0145085	+	0.0665530i
$199$		−	10.3363i		−	0.732719i	−0.930473	−	0.366359i	$-0.880604\pi$
$199$		−	10.3363i		−	0.732719i	0.930473	−	0.366359i	$-0.119396\pi$
$200$	−3.91950	+	3.10444i	−0.277150	+	0.219517i
$201$	−26.2660	−	7.70608i	−1.85266	−	0.543545i
$202$	4.78794	−	4.78794i	0.336878	−	0.336878i
$203$	−21.2848	+	21.2848i	−1.49390	+	1.49390i
$204$	−10.1235	−	2.97011i	−0.708789	−	0.207949i
$205$	0.912688	−	15.7833i	0.0637449	−	1.10235i
$206$			10.0985i			0.703593i
$207$	2.61647	+	12.0022i	0.181857	+	0.834209i
$208$	3.95820	+	3.95820i	0.274452	+	0.274452i
$209$	−0.319493			−0.0220998
$210$	−5.80112	−	12.2505i	−0.400316	−	0.845365i
$211$	6.26053			0.430992			0.215496	−	0.976505i	$-0.430863\pi$
$211$	6.26053			0.430992			0.215496	+	0.976505i	$0.430863\pi$
$212$	−1.15569	−	1.15569i	−0.0793734	−	0.0793734i
$213$	20.9770	−	11.4603i	1.43732	−	0.785250i
$214$			7.02789i			0.480416i
$215$	13.5806	+	15.2476i	0.926187	+	1.03988i
$216$	3.92473	−	3.40536i	0.267044	−	0.231705i
$217$	6.77924	−	6.77924i	0.460205	−	0.460205i
$218$	8.54618	−	8.54618i	0.578820	−	0.578820i
$219$	6.36144	−	21.6828i	0.429866	−	1.46519i
$220$	0.713216	+	0.0412426i	0.0480850	+	0.00278058i
$221$		−	34.0969i		−	2.29360i
$222$	1.67818	+	3.07174i	0.112632	+	0.206162i
$223$	−8.21125	−	8.21125i	−0.549866	−	0.549866i	0.376536	−	0.926402i	$-0.377115\pi$
$223$	−8.21125	−	8.21125i	−0.549866	−	0.549866i	−0.926402	+	0.376536i	$0.877115\pi$
$224$	3.49979			0.233840
$225$	−9.50496	+	11.6041i	−0.633664	+	0.773608i
$226$	7.16840			0.476835
$227$	−3.64293	−	3.64293i	−0.241790	−	0.241790i	0.575800	−	0.817590i	$-0.304691\pi$
$227$	−3.64293	−	3.64293i	−0.241790	−	0.241790i	−0.817590	+	0.575800i	$0.804691\pi$
$228$	0.830420	+	1.52000i	0.0549959	+	0.100665i
$229$			21.7636i			1.43818i	0.694917	+	0.719090i	$0.255441\pi$
$229$			21.7636i			1.43818i	−0.694917	+	0.719090i	$0.744559\pi$
$230$	9.14073	+	0.528575i	0.602722	+	0.0348532i
$231$	−0.545222	+	1.85837i	−0.0358730	+	0.122272i
$232$	−6.08174	+	6.08174i	−0.399286	+	0.399286i
$233$	3.78119	−	3.78119i	0.247714	−	0.247714i	−0.572318	−	0.820032i	$-0.693956\pi$
$233$	3.78119	−	3.78119i	0.247714	−	0.247714i	0.820032	+	0.572318i	$0.193956\pi$
$234$	14.1314	+	9.07286i	0.923797	+	0.593111i
$235$	8.67529	+	9.74019i	0.565914	+	0.635380i
$236$		−	7.51199i		−	0.488989i
$237$	−4.56650	+	2.49481i	−0.296626	+	0.162055i
$238$	−15.0740	−	15.0740i	−0.977102	−	0.977102i
$239$	−14.2573			−0.922230			−0.461115	−	0.887340i	$-0.652550\pi$
$239$	−14.2573			−0.922230			−0.461115	+	0.887340i	$0.652550\pi$
$240$	−1.65756	−	3.50035i	−0.106995	−	0.225947i
$241$	−30.3058			−1.95217			−0.976084	−	0.217394i	$-0.930244\pi$
$241$	−30.3058			−1.95217			−0.976084	+	0.217394i	$0.930244\pi$
$242$	7.70600	+	7.70600i	0.495360	+	0.495360i
$243$	9.32802	−	12.4895i	0.598393	−	0.801203i
$244$			8.09546i			0.518259i
$245$	0.677521	−	11.7165i	0.0432852	−	0.748539i
$246$	11.7508	+	3.44752i	0.749204	+	0.219806i
$247$	−3.95820	+	3.95820i	−0.251854	+	0.251854i
$248$	1.93704	−	1.93704i	0.123002	−	0.123002i
$249$	−5.44564	−	1.59768i	−0.345103	−	0.101249i
$250$	6.42419	+	9.15039i	0.406302	+	0.578722i
$251$			26.1004i			1.64744i	0.566996	+	0.823720i	$0.308105\pi$
$251$			26.1004i			1.64744i	−0.566996	+	0.823720i	$0.691895\pi$
$252$	10.2584	−	2.23634i	0.646221	−	0.140876i
$253$	−0.925053	−	0.925053i	−0.0581576	−	0.0581576i
$254$	16.1541			1.01360
$255$	−7.93711	+	22.2157i	−0.497041	+	1.39120i
$256$	1.00000			0.0625000
$257$	−10.7603	−	10.7603i	−0.671212	−	0.671212i	0.286783	−	0.957995i	$-0.407414\pi$
$257$	−10.7603	−	10.7603i	−0.671212	−	0.671212i	−0.957995	+	0.286783i	$0.907414\pi$
$258$	−13.8799	+	7.58297i	−0.864124	+	0.472095i
$259$			7.07266i			0.439474i
$260$	9.34700	−	8.32509i	0.579677	−	0.516300i
$261$	−13.9404	+	21.7127i	−0.862886	+	1.34398i
$262$	2.20889	−	2.20889i	0.136466	−	0.136466i
$263$	−7.39717	+	7.39717i	−0.456129	+	0.456129i	−0.897383	−	0.441253i	$-0.854534\pi$
$263$	−7.39717	+	7.39717i	−0.456129	+	0.456129i	0.441253	+	0.897383i	$0.354534\pi$
$264$	−0.155787	+	0.530996i	−0.00958803	+	0.0326806i
$265$	−2.72909	+	2.43071i	−0.167646	+	0.149318i
$266$			3.49979i			0.214586i
$267$	4.11748	+	7.53664i	0.251986	+	0.461235i
$268$	−11.1750	−	11.1750i	−0.682622	−	0.682622i
$269$	−12.5829			−0.767193			−0.383596	−	0.923501i	$-0.625315\pi$
$269$	−12.5829			−0.767193			−0.383596	+	0.923501i	$0.625315\pi$
$270$	−7.09528	−	9.20092i	−0.431805	−	0.559950i
$271$	1.82465			0.110840			0.0554198	−	0.998463i	$-0.482350\pi$
$271$	1.82465			0.110840			0.0554198	+	0.998463i	$0.482350\pi$
$272$	−4.30711	−	4.30711i	−0.261157	−	0.261157i
$273$	16.2687	+	29.7782i	0.984626	+	1.80226i
$274$			6.25672i			0.377982i
$275$	0.184135	−	1.58682i	0.0111038	−	0.0956886i
$276$	−1.99660	+	6.80536i	−0.120181	+	0.409635i
$277$	−8.96703	+	8.96703i	−0.538777	+	0.538777i	−0.923170	−	0.384393i	$-0.874411\pi$
$277$	−8.96703	+	8.96703i	−0.538777	+	0.538777i	0.384393	+	0.923170i	$0.374411\pi$
$278$	9.61985	−	9.61985i	0.576960	−	0.576960i
$279$	4.44002	−	6.91553i	0.265817	−	0.414022i
$280$	0.451781	−	7.81272i	0.0269991	−	0.466899i
$281$		−	18.1779i		−	1.08440i	−0.840249	−	0.542200i	$-0.817591\pi$
$281$		−	18.1779i		−	1.08440i	0.840249	−	0.542200i	$-0.182409\pi$
$282$	−8.86649	+	4.84402i	−0.527992	+	0.288457i
$283$	14.1537	+	14.1537i	0.841353	+	0.841353i	0.989035	−	0.147682i	$-0.0471812\pi$
$283$	14.1537	+	14.1537i	0.841353	+	0.841353i	−0.147682	+	0.989035i	$0.547181\pi$
$284$	13.8007			0.818919
$285$	3.50035	−	1.65756i	0.207343	−	0.0981856i
$286$	−1.78844			−0.105753
$287$	17.4970	+	17.4970i	1.03282	+	1.03282i
$288$	2.93116	−	0.638992i	0.172720	−	0.0376529i
$289$			20.1024i			1.18250i
$290$	12.7914	+	14.3616i	0.751138	+	0.843341i
$291$	−5.21142	−	1.52896i	−0.305499	−	0.0896293i
$292$	9.22508	−	9.22508i	0.539857	−	0.539857i
$293$	19.2900	−	19.2900i	1.12694	−	1.12694i	0.136264	−	0.990673i	$-0.456491\pi$
$293$	19.2900	−	19.2900i	1.12694	−	1.12694i	0.990673	−	0.136264i	$-0.0435094\pi$
$294$	8.72304	+	2.55922i	0.508738	+	0.149257i
$295$	−16.7693	−	0.969707i	−0.976347	−	0.0564585i
$296$			2.02088i			0.117461i
$297$	−0.117334	+	1.65598i	−0.00680844	+	0.0960897i
$298$	−10.9454	−	10.9454i	−0.634052	−	0.634052i
$299$	−22.9210			−1.32556
$300$	−8.02795	+	3.24839i	−0.463494	+	0.187546i
$301$	−31.9583			−1.84205
$302$	−9.53138	−	9.53138i	−0.548469	−	0.548469i
$303$	10.2922	−	5.62291i	0.591271	−	0.323028i
$304$			1.00000i			0.0573539i
$305$	18.0718	+	1.04503i	1.03479	+	0.0598380i
$306$	−15.3770	−	9.87262i	−0.879047	−	0.564380i
$307$	−2.74294	+	2.74294i	−0.156548	+	0.156548i	−0.781035	−	0.624487i	$-0.785308\pi$
$307$	−2.74294	+	2.74294i	−0.156548	+	0.156548i	0.624487	+	0.781035i	$0.285308\pi$
$308$	−0.790656	+	0.790656i	−0.0450518	+	0.0450518i
$309$	−4.92409	+	16.7836i	−0.280121	+	0.954787i
$310$	−4.07409	−	4.57418i	−0.231392	−	0.259796i
$311$			8.60142i			0.487742i	0.969808	+	0.243871i	$0.0784173\pi$
$311$			8.60142i			0.487742i	−0.969808	+	0.243871i	$0.921583\pi$
$312$	4.64848	+	8.50858i	0.263168	+	0.481703i
$313$	−6.25964	−	6.25964i	−0.353816	−	0.353816i	0.507711	−	0.861527i	$-0.330492\pi$
$313$	−6.25964	−	6.25964i	−0.353816	−	0.353816i	−0.861527	+	0.507711i	$0.830492\pi$
$314$	−8.26551			−0.466450
$315$	−3.66802	−	23.1890i	−0.206669	−	1.30655i
$316$	−3.00427			−0.169004
$317$	19.7083	+	19.7083i	1.10693	+	1.10693i	0.993552	+	0.113376i	$0.0361664\pi$
$317$	19.7083	+	19.7083i	1.10693	+	1.10693i	0.113376	+	0.993552i	$0.463834\pi$
$318$	−1.35724	−	2.48429i	−0.0761100	−	0.139312i
$319$		−	2.74792i		−	0.153854i
$320$	0.129088	−	2.23234i	0.00721624	−	0.124792i
$321$	−3.42685	+	11.6803i	−0.191268	+	0.651933i
$322$	−10.1332	+	10.1332i	−0.564702	+	0.564702i
$323$	4.30711	−	4.30711i	0.239654	−	0.239654i
$324$	8.18338	−	3.74597i	0.454632	−	0.208110i
$325$	−17.3778	−	21.9403i	−0.963949	−	1.21703i
$326$		−	13.7023i		−	0.758902i
$327$	18.3709	−	10.0366i	1.01591	−	0.555023i
$328$	4.99944	+	4.99944i	0.276048	+	0.276048i
$329$	−20.4150			−1.12552
$330$	1.16525	+	0.416315i	0.0641451	+	0.0229174i
$331$	−17.7975			−0.978237			−0.489119	−	0.872217i	$-0.662682\pi$
$331$	−17.7975			−0.978237			−0.489119	+	0.872217i	$0.662682\pi$
$332$	−2.31688	−	2.31688i	−0.127155	−	0.127155i
$333$	1.29133	+	5.92352i	0.0707642	+	0.324607i
$334$			13.1439i			0.719204i
$335$	−26.3890	+	23.5038i	−1.44178	+	1.28415i
$336$	5.81664	+	1.70652i	0.317324	+	0.0930985i
$337$	−10.3711	+	10.3711i	−0.564952	+	0.564952i	−0.930710	−	0.365758i	$-0.880810\pi$
$337$	−10.3711	+	10.3711i	−0.564952	+	0.564952i	0.365758	+	0.930710i	$0.380810\pi$
$338$	−12.9646	+	12.9646i	−0.705182	+	0.705182i
$339$	11.9139	+	3.49537i	0.647073	+	0.189842i
$340$	−10.1709	+	9.05894i	−0.551596	+	0.491290i
$341$			0.875215i			0.0473956i
$342$	0.638992	+	2.93116i	0.0345527	+	0.158499i
$343$	−4.33442	−	4.33442i	−0.234037	−	0.234037i
$344$	−9.13149			−0.492337
$345$	14.9341	+	5.33558i	0.804027	+	0.287258i
$346$	6.12384			0.329220
$347$	5.55389	+	5.55389i	0.298149	+	0.298149i	0.840288	−	0.542140i	$-0.182386\pi$
$347$	5.55389	+	5.55389i	0.298149	+	0.298149i	−0.542140	+	0.840288i	$0.682386\pi$
$348$	−13.0733	+	7.14233i	−0.700805	+	0.382869i
$349$		−	10.2761i		−	0.550066i	−0.961435	−	0.275033i	$-0.911311\pi$
$349$		−	10.2761i		−	0.550066i	0.961435	−	0.275033i	$-0.0886889\pi$
$350$	−17.3823	−	2.01705i	−0.929123	−	0.107816i
$351$	19.0623	+	21.9696i	1.01747	+	1.17265i
$352$	−0.225915	+	0.225915i	−0.0120413	+	0.0120413i
$353$	−5.09591	+	5.09591i	−0.271228	+	0.271228i	−0.829594	−	0.558366i	$-0.811428\pi$
$353$	−5.09591	+	5.09591i	−0.271228	+	0.271228i	0.558366	+	0.829594i	$0.311428\pi$
$354$	3.66290	−	12.4849i	0.194681	−	0.663566i
$355$	1.78150	−	30.8078i	0.0945522	−	1.63511i
$356$			4.95832i			0.262790i
$357$	−17.7028	−	32.4031i	−0.936929	−	1.71496i
$358$	−5.95206	−	5.95206i	−0.314576	−	0.314576i
$359$	35.4806			1.87259			0.936297	−	0.351208i	$-0.114229\pi$
$359$	35.4806			1.87259			0.936297	+	0.351208i	$0.114229\pi$
$360$	−1.04807	−	6.62582i	−0.0552381	−	0.349212i
$361$	−1.00000			−0.0526316
$362$	−2.85836	−	2.85836i	−0.150232	−	0.150232i
$363$	9.04985	+	16.5649i	0.474994	+	0.869430i
$364$			19.5909i			1.02684i
$365$	−19.4026	−	21.7843i	−1.01558	−	1.14024i
$366$	−3.94741	+	13.4546i	−0.206334	+	0.703285i
$367$	−3.42185	+	3.42185i	−0.178619	+	0.178619i	−0.790754	−	0.612134i	$-0.790311\pi$
$367$	−3.42185	+	3.42185i	−0.178619	+	0.178619i	0.612134	+	0.790754i	$0.290311\pi$
$368$	−2.89538	+	2.89538i	−0.150932	+	0.150932i
$369$	17.8488	+	11.4596i	0.929170	+	0.596561i
$370$	4.51129	+	0.260871i	0.234531	+	0.0135621i
$371$		−	5.72005i		−	0.296970i
$372$	4.16388	−	2.27484i	0.215887	−	0.117945i
$373$	3.03363	+	3.03363i	0.157075	+	0.157075i	0.781269	−	0.624194i	$-0.214573\pi$
$373$	3.03363	+	3.03363i	0.157075	+	0.157075i	−0.624194	+	0.781269i	$0.714573\pi$
$374$	1.94609			0.100630
$375$	6.21520	+	18.3404i	0.320951	+	0.947096i
$376$	−5.83322			−0.300825
$377$	−34.0440	−	34.0440i	−1.75336	−	1.75336i
$378$	18.1400	+	1.28531i	0.933019	+	0.0661090i
$379$			19.3076i			0.991764i	0.868390	+	0.495882i	$0.165155\pi$
$379$			19.3076i			0.991764i	−0.868390	+	0.495882i	$0.834845\pi$
$380$	2.23234	+	0.129088i	0.114517	+	0.00662207i
$381$	26.8482	+	7.87689i	1.37547	+	0.403545i
$382$	9.00861	−	9.00861i	0.460921	−	0.460921i
$383$	−12.9987	+	12.9987i	−0.664204	+	0.664204i	−0.956368	−	0.292164i	$-0.905625\pi$
$383$	−12.9987	+	12.9987i	−0.664204	+	0.664204i	0.292164	+	0.956368i	$0.405625\pi$
$384$	1.66200	+	0.487608i	0.0848135	+	0.0248831i
$385$	1.66295	+	1.86708i	0.0847517	+	0.0951550i
$386$			0.0722945i			0.00367970i
$387$	−26.7659	+	5.83495i	−1.36058	+	0.296607i
$388$	−2.21723	−	2.21723i	−0.112563	−	0.112563i
$389$	−10.3234			−0.523419			−0.261709	−	0.965147i	$-0.584286\pi$
$389$	−10.3234			−0.523419			−0.261709	+	0.965147i	$0.584286\pi$
$390$	19.5941	−	9.27862i	0.992185	−	0.469841i
$391$	24.9415			1.26134
$392$	3.71127	+	3.71127i	0.187447	+	0.187447i
$393$	4.74825	−	2.59410i	0.239517	−	0.130855i
$394$		−	19.5326i		−	0.984041i
$395$	−0.387815	+	6.70655i	−0.0195131	+	0.337443i
$396$	−0.517836	+	0.806552i	−0.0260222	+	0.0405308i
$397$	−13.5127	+	13.5127i	−0.678181	+	0.678181i	−0.959588	−	0.281407i	$-0.909199\pi$
$397$	−13.5127	+	13.5127i	−0.678181	+	0.678181i	0.281407	+	0.959588i	$0.409199\pi$
$398$	7.30885	−	7.30885i	0.366359	−	0.366359i
$399$	−1.70652	+	5.81664i	−0.0854331	+	0.291196i
$400$	−4.96667	−	0.576336i	−0.248334	−	0.0288168i
$401$			17.9859i			0.898171i	0.893489	+	0.449086i	$0.148250\pi$
$401$			17.9859i			0.898171i	−0.893489	+	0.449086i	$0.851750\pi$
$402$	−13.1238	−	24.0219i	−0.654557	−	1.19810i
$403$	10.8431	+	10.8431i	0.540131	+	0.540131i
$404$	6.77117			0.336878
$405$	−7.30590	−	18.7516i	−0.363033	−	0.931776i
$406$	−30.1012			−1.49390
$407$	−0.456548	−	0.456548i	−0.0226302	−	0.0226302i
$408$	−5.05823	−	9.25860i	−0.250420	−	0.458369i
$409$		−	38.6156i		−	1.90942i	−0.297542	−	0.954709i	$-0.596167\pi$
$409$		−	38.6156i		−	1.90942i	0.297542	−	0.954709i	$-0.403833\pi$
$410$	11.8058	−	10.5151i	0.583048	−	0.519303i
$411$	−3.05082	+	10.3987i	−0.150486	+	0.512928i
$412$	−7.14069	+	7.14069i	−0.351796	+	0.351796i
$413$	18.5901	−	18.5901i	0.914759	−	0.914759i
$414$	−6.63670	+	10.3369i	−0.326176	+	0.508033i
$415$	−5.47114	+	4.87298i	−0.268568	+	0.239205i
$416$			5.59774i			0.274452i
$417$	20.6789	−	11.2975i	1.01265	−	0.553239i
$418$	−0.225915	−	0.225915i	−0.0110499	−	0.0110499i
$419$	1.37511			0.0671786			0.0335893	−	0.999436i	$-0.489306\pi$
$419$	1.37511			0.0671786			0.0335893	+	0.999436i	$0.489306\pi$
$420$	4.56040	−	12.7644i	0.222525	−	0.622840i
$421$	−3.07765			−0.149996			−0.0749978	−	0.997184i	$-0.523895\pi$
$421$	−3.07765			−0.149996			−0.0749978	+	0.997184i	$0.523895\pi$
$422$	4.42686	+	4.42686i	0.215496	+	0.215496i
$423$	−17.0981	+	3.72738i	−0.831337	+	0.181231i
$424$		−	1.63440i		−	0.0793734i
$425$	18.9097	+	23.8744i	0.917254	+	1.15808i
$426$	22.9367	+	6.72932i	1.11129	+	0.326036i
$427$	−20.0340	+	20.0340i	−0.969515	+	0.969515i
$428$	−4.96947	+	4.96947i	−0.240208	+	0.240208i
$429$	−2.97238	−	0.872056i	−0.143508	−	0.0421033i
$430$	−1.17877	+	20.3846i	−0.0568451	+	0.983032i
$431$			2.29824i			0.110702i	0.998467	+	0.0553512i	$0.0176278\pi$
$431$			2.29824i			0.110702i	−0.998467	+	0.0553512i	$0.982372\pi$
$432$	5.18316	+	0.367253i	0.249375	+	0.0176694i
$433$	−0.650645	−	0.650645i	−0.0312680	−	0.0312680i	0.691300	−	0.722568i	$-0.257038\pi$
$433$	−0.650645	−	0.650645i	−0.0312680	−	0.0312680i	−0.722568	+	0.691300i	$0.757038\pi$
$434$	9.58729			0.460205
$435$	14.2565	+	30.1061i	0.683547	+	1.44348i
$436$	12.0861			0.578820
$437$	−2.89538	−	2.89538i	−0.138505	−	0.138505i
$438$	19.8303	−	10.8338i	0.947527	−	0.517661i
$439$		−	18.3241i		−	0.874563i	−0.899325	−	0.437281i	$-0.855941\pi$
$439$		−	18.3241i		−	0.874563i	0.899325	−	0.437281i	$-0.144059\pi$
$440$	0.475157	+	0.533483i	0.0226522	+	0.0254328i
$441$	13.2498	+	8.50684i	0.630942	+	0.405088i
$442$	24.1101	−	24.1101i	1.14680	−	1.14680i
$443$	0.832433	−	0.832433i	0.0395501	−	0.0395501i	−0.687055	−	0.726605i	$-0.741097\pi$
$443$	0.832433	−	0.832433i	0.0395501	−	0.0395501i	0.726605	+	0.687055i	$0.241097\pi$
$444$	−0.985397	+	3.35870i	−0.0467649	+	0.159397i
$445$	11.0686	+	0.640059i	0.524704	+	0.0303417i
$446$		−	11.6125i		−	0.549866i
$447$	−12.8542	−	23.5284i	−0.607983	−	1.11285i
$448$	2.47472	+	2.47472i	0.116920	+	0.116920i
$449$	30.6819			1.44797			0.723984	−	0.689817i	$-0.242309\pi$
$449$	30.6819			1.44797			0.723984	+	0.689817i	$0.242309\pi$
$450$	−14.9264	+	1.48433i	−0.703636	+	0.0699720i
$451$	−2.25890			−0.106368
$452$	5.06883	+	5.06883i	0.238418	+	0.238418i
$453$	−11.1936	−	20.4887i	−0.525919	−	0.962643i
$454$		−	5.15188i		−	0.241790i
$455$	43.7336	+	2.52895i	2.05026	+	0.118559i
$456$	−0.487608	+	1.66200i	−0.0228343	+	0.0778302i
$457$	−3.78531	+	3.78531i	−0.177069	+	0.177069i	−0.790077	−	0.613008i	$-0.789959\pi$
$457$	−3.78531	+	3.78531i	−0.177069	+	0.177069i	0.613008	+	0.790077i	$0.289959\pi$
$458$	−15.3892	+	15.3892i	−0.719090	+	0.719090i
$459$	−20.7426	−	23.9062i	−0.968184	−	1.11585i
$460$	6.08971	+	6.83723i	0.283934	+	0.318788i
$461$		−	6.89618i		−	0.321187i	−0.987021	−	0.160593i	$-0.948659\pi$
$461$		−	6.89618i		−	0.321187i	0.987021	−	0.160593i	$-0.0513408\pi$
$462$	−1.69960	+	0.928539i	−0.0790725	+	0.0431996i
$463$	12.6005	+	12.6005i	0.585597	+	0.585597i	0.936436	−	0.350839i	$-0.114104\pi$
$463$	12.6005	+	12.6005i	0.585597	+	0.585597i	−0.350839	+	0.936436i	$0.614104\pi$
$464$	−8.60087			−0.399286
$465$	−4.54072	−	9.58884i	−0.210571	−	0.444672i
$466$	5.34741			0.247714
$467$	−26.3961	−	26.3961i	−1.22147	−	1.22147i	−0.967111	−	0.254355i	$-0.918137\pi$
$467$	−26.3961	−	26.3961i	−1.22147	−	1.22147i	−0.254355	−	0.967111i	$-0.581863\pi$
$468$	3.57691	+	16.4079i	0.165343	+	0.758454i
$469$		−	55.3101i		−	2.55398i
$470$	−0.752998	+	13.0217i	−0.0347332	+	0.600647i
$471$	−13.7373	−	4.03033i	−0.632980	−	0.185708i
$472$	5.31178	−	5.31178i	0.244494	−	0.244494i
$473$	2.06295	−	2.06295i	0.0948543	−	0.0948543i
$474$	−4.99310	−	1.46491i	−0.229340	−	0.0672854i
$475$	0.576336	−	4.96667i	0.0264441	−	0.227887i
$476$		−	21.3178i		−	0.977102i
$477$	−1.04437	−	4.79068i	−0.0478183	−	0.219350i
$478$	−10.0815	−	10.0815i	−0.461115	−	0.461115i
$479$	17.9400			0.819700			0.409850	−	0.912153i	$-0.365581\pi$
$479$	17.9400			0.819700			0.409850	+	0.912153i	$0.365581\pi$
$480$	1.30305	−	3.64720i	0.0594758	−	0.166471i
$481$	−11.3124			−0.515800
$482$	−21.4294	−	21.4294i	−0.976084	−	0.976084i
$483$	−21.7824	+	11.9004i	−0.991135	+	0.541485i
$484$			10.8979i			0.495360i
$485$	−5.23583	+	4.66339i	−0.237747	+	0.211754i
$486$	15.4273	−	2.23552i	0.699798	−	0.101405i
$487$	8.76993	−	8.76993i	0.397403	−	0.397403i	−0.479913	−	0.877316i	$-0.659332\pi$
$487$	8.76993	−	8.76993i	0.397403	−	0.397403i	0.877316	+	0.479913i	$0.159332\pi$
$488$	−5.72435	+	5.72435i	−0.259129	+	0.259129i
$489$	6.68136	−	22.7732i	0.302142	−	1.02984i
$490$	8.76389	−	7.80573i	0.395912	−	0.352627i
$491$		−	1.85820i		−	0.0838595i	−0.999121	−	0.0419298i	$-0.986649\pi$
$491$		−	1.85820i		−	0.0838595i	0.999121	−	0.0419298i	$-0.0133506\pi$
$492$	5.87130	+	10.7468i	0.264699	+	0.484505i
$493$	37.0449	+	37.0449i	1.66842	+	1.66842i
$494$	−5.59774			−0.251854
$495$	1.73365	+	1.26010i	0.0779218	+	0.0566373i
$496$	2.73939			0.123002
$497$	34.1529	+	34.1529i	1.53197	+	1.53197i
$498$	−2.72092	−	4.98038i	−0.121927	−	0.223176i
$499$			6.79733i			0.304290i	0.988358	+	0.152145i	$0.0486181\pi$
$499$			6.79733i			0.304290i	−0.988358	+	0.152145i	$0.951382\pi$
$500$	−1.92771	+	11.0129i	−0.0862100	+	0.492512i
$501$	−6.40908	+	21.8452i	−0.286337	+	0.975971i
$502$	−18.4557	+	18.4557i	−0.823720	+	0.823720i
$503$	25.0714	−	25.0714i	1.11788	−	1.11788i	0.125825	−	0.992052i	$-0.459842\pi$
$503$	25.0714	−	25.0714i	1.11788	−	1.11788i	0.992052	−	0.125825i	$-0.0401579\pi$
$504$	8.83514	+	5.67248i	0.393548	+	0.252672i
$505$	0.874077	−	15.1156i	0.0388959	−	0.672633i
$506$		−	1.30822i		−	0.0581576i
$507$	−27.8688	+	15.2255i	−1.23770	+	0.676189i
$508$	11.4227	+	11.4227i	0.506801	+	0.506801i
$509$	30.4865			1.35129			0.675644	−	0.737228i	$-0.263866\pi$
$509$	30.4865			1.35129			0.675644	+	0.737228i	$0.263866\pi$
$510$	−21.3213	+	10.0965i	−0.944122	+	0.447081i
$511$	45.6590			2.01984
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−0.367253	+	5.18316i	−0.0162146	+	0.228842i
$514$		−	15.2174i		−	0.671212i
$515$	15.0187	+	16.8622i	0.661801	+	0.743038i
$516$	−15.1765	−	4.45259i	−0.668109	−	0.196014i
$517$	1.31781	−	1.31781i	0.0579574	−	0.0579574i
$518$	−5.00112	+	5.00112i	−0.219737	+	0.219737i
$519$	10.1778	+	2.98603i	0.446756	+	0.131072i
$520$	12.4961	+	0.722601i	0.547988	+	0.0316882i
$521$		−	10.5695i		−	0.463058i	−0.972828	−	0.231529i	$-0.925627\pi$
$521$		−	10.5695i		−	0.463058i	0.972828	−	0.231529i	$-0.0743729\pi$
$522$	−25.2105	+	5.49589i	−1.10343	+	0.240548i
$523$	−13.0333	−	13.0333i	−0.569906	−	0.569906i	0.362196	−	0.932102i	$-0.382027\pi$
$523$	−13.0333	−	13.0333i	−0.569906	−	0.569906i	−0.932102	+	0.362196i	$0.882027\pi$
$524$	3.12384			0.136466
$525$	−27.9058	−	11.8281i	−1.21791	−	0.516220i
$526$	−10.4612			−0.456129
$527$	−11.7989	−	11.7989i	−0.513967	−	0.513967i
$528$	−0.485629	+	0.265313i	−0.0211343	+	0.0115463i
$529$			6.23354i			0.271023i
$530$	−3.64853	−	0.210981i	−0.158482	−	0.00916443i
$531$	12.1755	−	18.9638i	0.528371	−	0.822961i
$532$	−2.47472	+	2.47472i	−0.107293	+	0.107293i
$533$	−27.9856	+	27.9856i	−1.21219	+	1.21219i
$534$	−2.41771	+	8.24071i	−0.104625	+	0.356610i
$535$	10.4520	+	11.7350i	0.451881	+	0.507350i
$536$		−	15.8038i		−	0.682622i
$537$	−6.99005	−	12.7946i	−0.301643	−	0.552127i
$538$	−8.89745	−	8.89745i	−0.383596	−	0.383596i
$539$	−1.67686			−0.0722277
$540$	1.48892	−	11.5232i	0.0640727	−	0.495878i
$541$	4.01245			0.172509			0.0862544	−	0.996273i	$-0.472510\pi$
$541$	4.01245			0.172509			0.0862544	+	0.996273i	$0.472510\pi$
$542$	1.29022	+	1.29022i	0.0554198	+	0.0554198i
$543$	−3.35683	−	6.14435i	−0.144055	−	0.263679i
$544$		−	6.09118i		−	0.261157i
$545$	1.56017	−	26.9803i	0.0668305	−	1.15571i
$546$	−9.55269	+	32.5601i	−0.408817	+	1.39344i
$547$	−8.37945	+	8.37945i	−0.358279	+	0.358279i	−0.863178	−	0.504899i	$-0.831530\pi$
$547$	−8.37945	+	8.37945i	−0.358279	+	0.358279i	0.504899	+	0.863178i	$0.331530\pi$
$548$	−4.42417	+	4.42417i	−0.188991	+	0.188991i
$549$	−13.1212	+	20.4368i	−0.559998	+	0.872221i
$550$	1.25225	−	0.991845i	0.0533962	−	0.0422924i
$551$		−	8.60087i		−	0.366410i
$552$	−6.22393	+	3.40031i	−0.264908	+	0.144727i
$553$	−7.43475	−	7.43475i	−0.316158	−	0.316158i
$554$	−12.6813			−0.538777
$555$	7.37055	+	2.63331i	0.312863	+	0.111778i
$556$	13.6045			0.576960
$557$	10.8415	+	10.8415i	0.459369	+	0.459369i	0.898448	−	0.439079i	$-0.144695\pi$
$557$	10.8415	+	10.8415i	0.459369	+	0.459369i	−0.439079	+	0.898448i	$0.644695\pi$
$558$	8.02959	−	1.75045i	0.339920	−	0.0741024i
$559$		−	51.1158i		−	2.16197i
$560$	5.84388	−	5.20497i	0.246949	−	0.219950i
$561$	3.23439	+	0.948927i	0.136556	+	0.0400637i
$562$	12.8537	−	12.8537i	0.542200	−	0.542200i
$563$	−18.3171	+	18.3171i	−0.771973	+	0.771973i	−0.978451	−	0.206478i	$-0.933800\pi$
$563$	−18.3171	+	18.3171i	−0.771973	+	0.771973i	0.206478	+	0.978451i	$0.433800\pi$
$564$	−9.69479	−	2.84432i	−0.408225	−	0.119768i
$565$	11.9697	−	10.6610i	0.503567	−	0.448512i
$566$			20.0164i			0.841353i
$567$	29.5219	+	10.9814i	1.23980	+	0.461174i
$568$	9.75855	+	9.75855i	0.409460	+	0.409460i
$569$	5.23426			0.219432			0.109716	−	0.993963i	$-0.465006\pi$
$569$	5.23426			0.219432			0.109716	+	0.993963i	$0.465006\pi$
$570$	3.64720	+	1.30305i	0.152764	+	0.0545787i
$571$	−36.1118			−1.51123			−0.755616	−	0.655015i	$-0.772662\pi$
$571$	−36.1118			−1.51123			−0.755616	+	0.655015i	$0.772662\pi$
$572$	−1.26462	−	1.26462i	−0.0528763	−	0.0528763i
$573$	19.3650	−	10.5796i	0.808983	−	0.441970i
$574$			24.7445i			1.03282i
$575$	16.0491	−	12.7117i	0.669295	−	0.530114i
$576$	2.52448	+	1.62081i	0.105187	+	0.0675336i
$577$	−0.690796	+	0.690796i	−0.0287582	+	0.0287582i	−0.721340	−	0.692581i	$-0.756473\pi$
$577$	−0.690796	+	0.690796i	−0.0287582	+	0.0287582i	0.692581	+	0.721340i	$0.256473\pi$
$578$	−14.2146	+	14.2146i	−0.591248	+	0.591248i
$579$	−0.0352514	+	0.120153i	−0.00146500	+	0.00499341i
$580$	−1.11027	+	19.2001i	−0.0461014	+	0.797239i
$581$		−	11.4673i		−	0.475743i
$582$	−2.60389	−	4.76617i	−0.107935	−	0.197564i
$583$	0.369236	+	0.369236i	0.0152922	+	0.0152922i
$584$	13.0462			0.539857
$585$	37.0897	−	5.86682i	1.53347	−	0.242563i
$586$	27.2802			1.12694
$587$	−22.7297	−	22.7297i	−0.938154	−	0.938154i	0.0600421	−	0.998196i	$-0.480877\pi$
$587$	−22.7297	−	22.7297i	−0.938154	−	0.938154i	−0.998196	+	0.0600421i	$0.980877\pi$
$588$	4.35848	+	7.97776i	0.179741	+	0.328997i
$589$			2.73939i			0.112875i
$590$	−11.1720	−	12.5434i	−0.459944	−	0.516403i
$591$	9.52427	−	32.4632i	0.391776	−	1.33536i
$592$	−1.42898	+	1.42898i	−0.0587307	+	0.0587307i
$593$	−31.3926	+	31.3926i	−1.28914	+	1.28914i	−0.353828	+	0.935311i	$0.615120\pi$
$593$	−31.3926	+	31.3926i	−1.28914	+	1.28914i	−0.935311	+	0.353828i	$0.884880\pi$
$594$	−1.25392	+	1.08799i	−0.0514491	+	0.0446407i
$595$	−47.5886	−	2.75188i	−1.95094	−	0.112816i
$596$		−	15.4792i		−	0.634052i
$597$	15.7111	−	8.58344i	0.643014	−	0.351297i
$598$	−16.2076	−	16.2076i	−0.662778	−	0.662778i
$599$	27.0824			1.10656			0.553278	−	0.832997i	$-0.313377\pi$
$599$	27.0824			1.10656			0.553278	+	0.832997i	$0.313377\pi$
$600$	−7.97358	−	3.37966i	−0.325520	−	0.137974i
$601$	10.0478			0.409860			0.204930	−	0.978777i	$-0.434303\pi$
$601$	10.0478			0.409860			0.204930	+	0.978777i	$0.434303\pi$
$602$	−22.5979	−	22.5979i	−0.921023	−	0.921023i
$603$	−10.0985	−	46.3236i	−0.411244	−	1.88644i
$604$		−	13.4794i		−	0.548469i
$605$	24.3279	+	1.40679i	0.989068	+	0.0571942i
$606$	11.2537	+	3.30168i	0.457149	+	0.134121i
$607$	7.08962	−	7.08962i	0.287759	−	0.287759i	−0.548435	−	0.836193i	$-0.684776\pi$
$607$	7.08962	−	7.08962i	0.287759	−	0.287759i	0.836193	+	0.548435i	$0.184776\pi$
$608$	−0.707107	+	0.707107i	−0.0286770	+	0.0286770i
$609$	−50.0282	−	14.6776i	−2.02725	−	0.594766i
$610$	12.0397	+	13.5176i	0.487475	+	0.547313i
$611$		−	32.6528i		−	1.32099i
$612$	−3.89221	−	17.8542i	−0.157333	−	0.721714i
$613$	24.9931	+	24.9931i	1.00946	+	1.00946i	0.999955	+	0.00950519i	$0.00302564\pi$
$613$	24.9931	+	24.9931i	1.00946	+	1.00946i	0.00950519	+	0.999955i	$0.496974\pi$
$614$	−3.87911			−0.156548
$615$	24.7485	−	11.7194i	0.997956	−	0.472574i
$616$	−1.11816			−0.0450518
$617$	1.14572	+	1.14572i	0.0461251	+	0.0461251i	0.729793	−	0.683668i	$-0.239616\pi$
$617$	1.14572	+	1.14572i	0.0461251	+	0.0461251i	−0.683668	+	0.729793i	$0.739616\pi$
$618$	−15.3497	+	8.38596i	−0.617454	+	0.337333i
$619$			38.1788i			1.53454i	0.641327	+	0.767268i	$0.278384\pi$
$619$			38.1788i			1.53454i	−0.641327	+	0.767268i	$0.721616\pi$
$620$	0.353622	−	6.11525i	0.0142018	−	0.245594i
$621$	−16.0706	+	13.9439i	−0.644889	+	0.559549i
$622$	−6.08212	+	6.08212i	−0.243871	+	0.243871i
$623$	−12.2705	+	12.2705i	−0.491606	+	0.491606i
$624$	−2.72950	+	9.30344i	−0.109268	+	0.372436i
$625$	24.3357	+	5.72495i	0.973427	+	0.228998i
$626$		−	8.85247i		−	0.353816i
$627$	−0.265313	−	0.485629i	−0.0105956	−	0.0193942i
$628$	−5.84460	−	5.84460i	−0.233225	−	0.233225i
$629$	12.3095			0.490814
$630$	13.8034	−	18.9908i	0.549941	−	0.756611i
$631$	37.8573			1.50707			0.753537	−	0.657405i	$-0.228346\pi$
$631$	37.8573			1.50707			0.753537	+	0.657405i	$0.228346\pi$
$632$	−2.12434	−	2.12434i	−0.0845018	−	0.0845018i
$633$	5.19886	+	9.51601i	0.206636	+	0.378227i
$634$			27.8717i			1.10693i
$635$	26.9739	−	24.0248i	1.07043	−	0.953396i
$636$	0.796945	−	2.71637i	0.0316009	−	0.107711i
$637$	−20.7747	+	20.7747i	−0.823124	+	0.823124i
$638$	1.94307	−	1.94307i	0.0769269	−	0.0769269i
$639$	34.8395	+	22.3682i	1.37823	+	0.884873i
$640$	1.66978	−	1.48722i	0.0660039	−	0.0587876i
$641$			43.9989i			1.73785i	0.494942	+	0.868926i	$0.335189\pi$
$641$			43.9989i			1.73785i	−0.494942	+	0.868926i	$0.664811\pi$
$642$	−10.6824	+	5.83609i	−0.421601	+	0.230332i
$643$	−17.5175	−	17.5175i	−0.690823	−	0.690823i	0.271590	−	0.962413i	$-0.412450\pi$
$643$	−17.5175	−	17.5175i	−0.690823	−	0.690823i	−0.962413	+	0.271590i	$0.912450\pi$
$644$	−14.3305			−0.564702
$645$	−11.8988	+	33.3044i	−0.468514	+	1.31136i
$646$	6.09118			0.239654
$647$	−11.7619	−	11.7619i	−0.462407	−	0.462407i	0.437037	−	0.899444i	$-0.356028\pi$
$647$	−11.7619	−	11.7619i	−0.462407	−	0.462407i	−0.899444	+	0.437037i	$0.856028\pi$
$648$	8.43532	+	3.13772i	0.331371	+	0.123261i
$649$			2.40003i			0.0942092i
$650$	3.22618	−	27.8022i	0.126541	−	1.09049i
$651$	15.9341	+	4.67484i	0.624505	+	0.183221i
$652$	9.68901	−	9.68901i	0.379451	−	0.379451i
$653$	−4.52948	+	4.52948i	−0.177252	+	0.177252i	−0.790157	−	0.612905i	$-0.790001\pi$
$653$	−4.52948	+	4.52948i	−0.177252	+	0.177252i	0.612905	+	0.790157i	$0.290001\pi$
$654$	20.0871	+	5.89329i	0.785468	+	0.230446i
$655$	0.403251	−	6.97348i	0.0157563	−	0.272476i
$656$			7.07028i			0.276048i
$657$	38.2406	−	8.33643i	1.49191	−	0.325235i
$658$	−14.4356	−	14.4356i	−0.562758	−	0.562758i
$659$	2.17251			0.0846292			0.0423146	−	0.999104i	$-0.486527\pi$
$659$	2.17251			0.0846292			0.0423146	+	0.999104i	$0.486527\pi$
$660$	0.529579	+	1.11834i	0.0206139	+	0.0435312i
$661$	−13.3844			−0.520595			−0.260297	−	0.965529i	$-0.583821\pi$
$661$	−13.3844			−0.520595			−0.260297	+	0.965529i	$0.583821\pi$
$662$	−12.5847	−	12.5847i	−0.489119	−	0.489119i
$663$	51.8273	−	28.3147i	2.01280	−	1.09965i
$664$		−	3.27656i		−	0.127155i
$665$	5.20497	+	5.84388i	0.201840	+	0.226616i
$666$	−3.27546	+	5.10167i	−0.126921	+	0.197686i
$667$	24.9028	−	24.9028i	0.964241	−	0.964241i
$668$	−9.29416	+	9.29416i	−0.359602	+	0.359602i
$669$	5.66232	−	19.2999i	0.218918	−	0.746177i
$670$	−35.2795	−	2.04009i	−1.36297	−	0.0788154i
$671$		−	2.58644i		−	0.0998484i
$672$	2.90629	+	5.31968i	0.112113	+	0.205211i
$673$	5.79495	+	5.79495i	0.223379	+	0.223379i	0.809920	−	0.586541i	$-0.199511\pi$
$673$	5.79495	+	5.79495i	0.223379	+	0.223379i	−0.586541	+	0.809920i	$0.699511\pi$
$674$	−14.6670			−0.564952
$675$	−25.5314	−	4.81126i	−0.982704	−	0.185186i
$676$	−18.3347			−0.705182
$677$	−3.09214	−	3.09214i	−0.118841	−	0.118841i	0.645185	−	0.764026i	$-0.276780\pi$
$677$	−3.09214	−	3.09214i	−0.118841	−	0.118841i	−0.764026	+	0.645185i	$0.776780\pi$
$678$	5.95278	+	10.8960i	0.228615	+	0.418458i
$679$		−	10.9741i		−	0.421146i
$680$	−13.5976	−	0.786298i	−0.521443	−	0.0301531i
$681$	2.51210	−	8.56242i	0.0962638	−	0.328113i
$682$	−0.618871	+	0.618871i	−0.0236978	+	0.0236978i
$683$	−28.9452	+	28.9452i	−1.10756	+	1.10756i	−0.114089	+	0.993471i	$0.536395\pi$
$683$	−28.9452	+	28.9452i	−1.10756	+	1.10756i	−0.993471	+	0.114089i	$0.963605\pi$
$684$	−1.62081	+	2.52448i	−0.0619731	+	0.0965258i
$685$	9.30513	+	10.4473i	0.355531	+	0.399173i
$686$		−	6.12979i		−	0.234037i
$687$	−33.0807	+	18.0729i	−1.26211	+	0.689525i
$688$	−6.45694	−	6.45694i	−0.246169	−	0.246169i
$689$	9.14894			0.348547
$690$	6.78721	+	14.3329i	0.258385	+	0.545643i
$691$	14.2335			0.541468			0.270734	−	0.962654i	$-0.412734\pi$
$691$	14.2335			0.541468			0.270734	+	0.962654i	$0.412734\pi$
$692$	4.33021	+	4.33021i	0.164610	+	0.164610i
$693$	−3.27749	+	0.714493i	−0.124502	+	0.0271413i
$694$			7.85439i			0.298149i
$695$	1.75618	−	30.3699i	0.0666157	−	1.15200i
$696$	−14.2946	−	4.19385i	−0.541837	−	0.158968i
$697$	30.4525	−	30.4525i	1.15347	−	1.15347i
$698$	7.26629	−	7.26629i	0.275033	−	0.275033i
$699$	8.88739	+	2.60744i	0.336152	+	0.0986224i
$700$	−10.8649	−	13.7174i	−0.410654	−	0.518470i
$701$		−	32.5972i		−	1.23118i	−0.788067	−	0.615589i	$-0.788918\pi$
$701$		−	32.5972i		−	1.23118i	0.788067	−	0.615589i	$-0.211082\pi$
$702$	−2.05579	+	29.0140i	−0.0775906	+	1.09506i
$703$	−1.42898	−	1.42898i	−0.0538949	−	0.0538949i
$704$	−0.319493			−0.0120413
$705$	−7.60097	+	21.2749i	−0.286269	+	0.801259i
$706$	−7.20671			−0.271228
$707$	16.7568	+	16.7568i	0.630204	+	0.630204i
$708$	11.4182	−	6.23810i	0.429123	−	0.234442i
$709$		−	15.6457i		−	0.587587i	−0.955869	−	0.293794i	$-0.905082\pi$
$709$		−	15.6457i		−	0.587587i	0.955869	−	0.293794i	$-0.0949178\pi$
$710$	23.0441	−	20.5247i	0.864830	−	0.770277i
$711$	−7.58422	−	4.86934i	−0.284430	−	0.182615i
$712$	−3.50606	+	3.50606i	−0.131395	+	0.131395i
$713$	−7.93158	+	7.93158i	−0.297040	+	0.297040i
$714$	10.3947	−	35.4302i	0.389014	−	1.32594i
$715$	−2.98630	+	2.65981i	−0.111681	+	0.0994711i
$716$		−	8.41749i		−	0.314576i
$717$	−11.8396	−	21.6712i	−0.442157	−	0.809324i
$718$	25.0886	+	25.0886i	0.936297	+	0.936297i
$719$	−11.4282			−0.426200			−0.213100	−	0.977030i	$-0.568356\pi$
$719$	−11.4282			−0.426200			−0.213100	+	0.977030i	$0.568356\pi$
$720$	3.94407	−	5.42626i	0.146987	−	0.202225i
$721$	−35.3425			−1.31622
$722$	−0.707107	−	0.707107i	−0.0263158	−	0.0263158i
$723$	−25.1665	−	46.0648i	−0.935953	−	1.71317i
$724$		−	4.04233i		−	0.150232i
$725$	42.7177	+	4.95699i	1.58650	+	0.184098i
$726$	−5.31391	+	18.1123i	−0.197218	+	0.672212i
$727$	−22.6001	+	22.6001i	−0.838192	+	0.838192i	−0.988621	−	0.150429i	$-0.951935\pi$
$727$	−22.6001	+	22.6001i	−0.838192	+	0.838192i	0.150429	+	0.988621i	$0.451935\pi$
$728$	−13.8529	+	13.8529i	−0.513422	+	0.513422i
$729$	26.7303	+	3.80706i	0.990009	+	0.141002i
$730$	1.68411	−	29.1236i	0.0623317	−	1.07791i
$731$			55.6216i			2.05724i
$732$	−12.3051	+	6.72263i	−0.454810	+	0.248475i
$733$	31.3451	+	31.3451i	1.15776	+	1.15776i	0.984957	+	0.172801i	$0.0552819\pi$
$733$	31.3451	+	31.3451i	1.15776	+	1.15776i	0.172801	+	0.984957i	$0.444718\pi$
$734$	−4.83923			−0.178619
$735$	18.3717	−	8.69977i	0.677650	−	0.320896i
$736$	−4.09469			−0.150932
$737$	3.57033	+	3.57033i	0.131515	+	0.131515i
$738$	4.51785	+	20.7241i	0.166304	+	0.762865i
$739$		−	43.9564i		−	1.61696i	−0.588523	−	0.808481i	$-0.700290\pi$
$739$		−	43.9564i		−	1.61696i	0.588523	−	0.808481i	$-0.299710\pi$
$740$	3.00550	+	3.37443i	0.110484	+	0.124046i
$741$	−9.30344	−	2.72950i	−0.341770	−	0.100271i
$742$	4.04469	−	4.04469i	0.148485	−	0.148485i
$743$	17.5022	−	17.5022i	0.642094	−	0.642094i	−0.308976	−	0.951070i	$-0.599986\pi$
$743$	17.5022	−	17.5022i	0.642094	−	0.642094i	0.951070	+	0.308976i	$0.0999863\pi$
$744$	4.55286	+	1.33575i	0.166916	+	0.0489709i
$745$	−34.5548	−	1.99817i	−1.26599	−	0.0732075i
$746$			4.29019i			0.157075i
$747$	−2.09370	−	9.60412i	−0.0766043	−	0.351396i
$748$	1.37609	+	1.37609i	0.0503149	+	0.0503149i
$749$	−24.5961			−0.898723
$750$	−8.57383	+	17.3634i	−0.313072	+	0.634024i
$751$	−1.27690			−0.0465948			−0.0232974	−	0.999729i	$-0.507416\pi$
$751$	−1.27690			−0.0465948			−0.0232974	+	0.999729i	$0.507416\pi$
$752$	−4.12471	−	4.12471i	−0.150413	−	0.150413i
$753$	−39.6726	+	21.6743i	−1.44575	+	0.789854i
$754$		−	48.1455i		−	1.75336i
$755$	−30.0906	−	1.74003i	−1.09511	−	0.0633261i
$756$	11.9180	+	13.7357i	0.433455	+	0.499564i
$757$	31.4744	−	31.4744i	1.14396	−	1.14396i	0.156236	−	0.987720i	$-0.450064\pi$
$757$	31.4744	−	31.4744i	1.14396	−	1.14396i	0.987720	−	0.156236i	$-0.0499360\pi$
$758$	−13.6525	+	13.6525i	−0.495882	+	0.495882i
$759$	0.637899	−	2.17426i	0.0231543	−	0.0789208i
$760$	1.48722	+	1.66978i	0.0539472	+	0.0605693i
$761$			35.4794i			1.28613i	0.765813	+	0.643063i	$0.222337\pi$
$761$			35.4794i			1.28613i	−0.765813	+	0.643063i	$0.777663\pi$
$762$	13.4147	+	24.5543i	0.485964	+	0.889509i
$763$	29.9098	+	29.9098i	1.08281	+	1.08281i
$764$	12.7401			0.460921
$765$	−40.3591	+	6.38397i	−1.45919	+	0.230813i
$766$	−18.3830			−0.664204
$767$	29.7340	+	29.7340i	1.07363	+	1.07363i
$768$	0.830420	+	1.52000i	0.0299652	+	0.0548483i
$769$			32.3859i			1.16786i	0.811803	+	0.583932i	$0.198487\pi$
$769$			32.3859i			1.16786i	−0.811803	+	0.583932i	$0.801513\pi$
$770$	−0.144341	+	2.49610i	−0.00520167	+	0.0899534i
$771$	7.42014	−	25.2913i	0.267230	−	0.910845i
$772$	−0.0511200	+	0.0511200i	−0.00183985	+	0.00183985i
$773$	−34.7488	+	34.7488i	−1.24983	+	1.24983i	−0.294032	+	0.955796i	$0.594997\pi$
$773$	−34.7488	+	34.7488i	−1.24983	+	1.24983i	−0.955796	+	0.294032i	$0.905003\pi$
$774$	−23.0523	−	14.8004i	−0.828596	−	0.531989i
$775$	−13.6057	−	1.57881i	−0.488730	−	0.0567125i
$776$		−	3.13564i		−	0.112563i
$777$	−10.7504	+	5.87327i	−0.385670	+	0.210702i
$778$	−7.29977	−	7.29977i	−0.261709	−	0.261709i
$779$	−7.07028			−0.253319
$780$	20.4161	+	7.29414i	0.731013	+	0.261172i
$781$	−4.40921			−0.157774
$782$	17.6363	+	17.6363i	0.630672	+	0.630672i
$783$	−44.5797	−	3.15869i	−1.59315	−	0.112882i
$784$			5.24852i			0.187447i
$785$	−13.8016	+	12.2927i	−0.492600	+	0.438744i
$786$	5.19182	+	1.52321i	0.185186	+	0.0543311i
$787$	6.89231	−	6.89231i	0.245684	−	0.245684i	−0.573512	−	0.819197i	$-0.694420\pi$
$787$	6.89231	−	6.89231i	0.245684	−	0.245684i	0.819197	+	0.573512i	$0.194420\pi$
$788$	13.8117	−	13.8117i	0.492020	−	0.492020i
$789$	−17.3865	−	5.10095i	−0.618975	−	0.181599i
$790$	−5.01648	+	4.46802i	−0.178478	+	0.158965i
$791$			25.0879i			0.892023i
$792$	−0.936483	+	0.204153i	−0.0332765	+	0.00725426i
$793$	−32.0435	−	32.0435i	−1.13790	−	1.13790i
$794$	−19.1098			−0.678181
$795$	−5.96098	−	2.12970i	−0.211414	−	0.0755328i
$796$	10.3363			0.366359
$797$	−27.7333	−	27.7333i	−0.982365	−	0.982365i	0.0174819	−	0.999847i	$-0.494435\pi$
$797$	−27.7333	−	27.7333i	−0.982365	−	0.982365i	−0.999847	+	0.0174819i	$0.994435\pi$
$798$	−5.31968	+	2.90629i	−0.188315	+	0.102882i
$799$			35.5312i			1.25700i
$800$	−3.10444	−	3.91950i	−0.109758	−	0.138575i
$801$	−8.03647	+	12.5172i	−0.283955	+	0.442272i
$802$	−12.7179	+	12.7179i	−0.449086	+	0.449086i
$803$	−2.94734	+	2.94734i	−0.104009	+	0.104009i
$804$	7.70608	−	26.2660i	0.271772	−	0.926329i
$805$	−1.84990	+	31.9906i	−0.0652004	+	1.12752i
$806$			15.3344i			0.540131i
$807$	−10.4491	−	19.1260i	−0.367825	−	0.673268i
$808$	4.78794	+	4.78794i	0.168439	+	0.168439i
$809$	40.8048			1.43462			0.717309	−	0.696755i	$-0.245373\pi$
$809$	40.8048			1.43462			0.717309	+	0.696755i	$0.245373\pi$
$810$	8.09336	−	18.4255i	0.284372	−	0.647405i
$811$	27.8185			0.976838			0.488419	−	0.872609i	$-0.337574\pi$
$811$	27.8185			0.976838			0.488419	+	0.872609i	$0.337574\pi$
$812$	−21.2848	−	21.2848i	−0.746950	−	0.746950i
$813$	1.51522	+	2.77347i	0.0531412	+	0.0972698i
$814$		−	0.645656i		−	0.0226302i
$815$	−20.3784	−	22.8799i	−0.713825	−	0.801447i
$816$	2.97011	−	10.1235i	0.103974	−	0.354394i
$817$	6.45694	−	6.45694i	0.225900	−	0.225900i
$818$	27.3053	−	27.3053i	0.954709	−	0.954709i
$819$	−31.7531	+	49.4568i	−1.10954	+	1.72816i
$820$	15.7833	+	0.912688i	0.551176	+	0.0318725i
$821$			1.41329i			0.0493241i	0.999696	+	0.0246620i	$0.00785096\pi$
$821$			1.41329i			0.0493241i	−0.999696	+	0.0246620i	$0.992149\pi$
$822$	−9.51022	+	5.19570i	−0.331707	+	0.181221i
$823$	−28.8276	−	28.8276i	−1.00487	−	1.00487i	−0.999988	−	0.00487736i	$-0.998447\pi$
$823$	−28.8276	−	28.8276i	−1.00487	−	1.00487i	−0.00487736	−	0.999988i	$-0.501553\pi$
$824$	−10.0985			−0.351796
$825$	2.56487	−	1.03784i	0.0892973	−	0.0361328i
$826$	26.2904			0.914759
$827$	21.4341	+	21.4341i	0.745336	+	0.745336i	0.973599	−	0.228263i	$-0.0733047\pi$
$827$	21.4341	+	21.4341i	0.745336	+	0.745336i	−0.228263	+	0.973599i	$0.573305\pi$
$828$	−12.0022	+	2.61647i	−0.417104	+	0.0909287i
$829$			5.00012i			0.173661i	0.996223	+	0.0868306i	$0.0276739\pi$
$829$			5.00012i			0.173661i	−0.996223	+	0.0868306i	$0.972326\pi$
$830$	−7.31440	−	0.422965i	−0.253886	−	0.0146813i
$831$	−21.0763	−	6.18350i	−0.731128	−	0.214503i
$832$	−3.95820	+	3.95820i	−0.137226	+	0.137226i
$833$	22.6060	−	22.6060i	0.783251	−	0.783251i
$834$	22.6107	+	6.63367i	0.782944	+	0.229705i
$835$	19.5479	+	21.9475i	0.676485	+	0.759524i
$836$		−	0.319493i		−	0.0110499i
$837$	14.1987	+	1.00605i	0.490779	+	0.0347741i
$838$	0.972351	+	0.972351i	0.0335893	+	0.0335893i
$839$	−43.4500			−1.50006			−0.750029	−	0.661404i	$-0.769961\pi$
$839$	−43.4500			−1.50006			−0.750029	+	0.661404i	$0.769961\pi$
$840$	12.2505	−	5.80112i	0.422683	−	0.200158i
$841$	44.9750			1.55086
$842$	−2.17623	−	2.17623i	−0.0749978	−	0.0749978i
$843$	27.6304	−	15.0953i	0.951640	−	0.519908i
$844$			6.26053i			0.215496i
$845$	−2.36679	+	40.9293i	−0.0814201	+	1.40801i
$846$	−14.7258	−	9.45451i	−0.506284	−	0.325053i
$847$	−26.9694	+	26.9694i	−0.926678	+	0.926678i
$848$	1.15569	−	1.15569i	0.0396867	−	0.0396867i
$849$	−9.76016	+	33.2673i	−0.334968	+	1.14173i
$850$	−3.51057	+	30.2529i	−0.120411	+	1.03767i
$851$		−	8.27488i		−	0.283659i
$852$	11.4603	+	20.9770i	0.392625	+	0.718662i
$853$	−13.6676	−	13.6676i	−0.467969	−	0.467969i	0.433287	−	0.901256i	$-0.357354\pi$
$853$	−13.6676	−	13.6676i	−0.467969	−	0.467969i	−0.901256	+	0.433287i	$0.857354\pi$
$854$	−28.3324			−0.969515
$855$	5.42626	+	3.94407i	0.185574	+	0.134884i
$856$	−7.02789			−0.240208
$857$	−8.79374	−	8.79374i	−0.300388	−	0.300388i	0.540777	−	0.841166i	$-0.318130\pi$
$857$	−8.79374	−	8.79374i	−0.300388	−	0.300388i	−0.841166	+	0.540777i	$0.818130\pi$
$858$	−1.48515	−	2.71843i	−0.0507023	−	0.0928056i
$859$		−	15.9374i		−	0.543777i	−0.962329	−	0.271889i	$-0.912352\pi$
$859$		−	15.9374i		−	0.543777i	0.962329	−	0.271889i	$-0.0876483\pi$
$860$	−15.2476	+	13.5806i	−0.519939	+	0.463094i
$861$	−12.0656	+	41.1253i	−0.411195	+	1.40155i
$862$	−1.62510	+	1.62510i	−0.0553512	+	0.0553512i
$863$	−4.58621	+	4.58621i	−0.156116	+	0.156116i	−0.780843	−	0.624727i	$-0.785210\pi$
$863$	−4.58621	+	4.58621i	−0.156116	+	0.156116i	0.624727	+	0.780843i	$0.285210\pi$
$864$	3.40536	+	3.92473i	0.115853	+	0.133522i
$865$	10.2255	−	9.10751i	0.347676	−	0.309665i
$866$		−	0.920152i		−	0.0312680i
$867$	−30.5557	+	16.6935i	−1.03773	+	0.566940i
$868$	6.77924	+	6.77924i	0.230102	+	0.230102i
$869$	0.959843			0.0325604
$870$	−11.2074	+	31.3691i	−0.379965	+	1.06351i
$871$	88.4659			2.99755
$872$	8.54618	+	8.54618i	0.289410	+	0.289410i
$873$	−2.00365	−	9.19105i	−0.0678131	−	0.311070i
$874$		−	4.09469i		−	0.138505i
$875$	−32.0245	+	22.4833i	−1.08262	+	0.760075i
$876$	21.6828	+	6.36144i	0.732594	+	0.214933i
$877$	−27.7067	+	27.7067i	−0.935589	+	0.935589i	−0.998048	−	0.0624587i	$-0.980106\pi$
$877$	−27.7067	+	27.7067i	−0.935589	+	0.935589i	0.0624587	+	0.998048i	$0.480106\pi$
$878$	12.9571	−	12.9571i	0.437281	−	0.437281i
$879$	45.3397	+	13.3021i	1.52927	+	0.448667i
$880$	−0.0412426	+	0.713216i	−0.00139029	+	0.0240425i
$881$			39.9522i			1.34602i	0.739632	+	0.673011i	$0.235000\pi$
$881$			39.9522i			1.34602i	−0.739632	+	0.673011i	$0.765000\pi$
$882$	3.35376	+	15.3843i	0.112927	+	0.518015i
$883$	14.0072	+	14.0072i	0.471379	+	0.471379i	0.902361	−	0.430982i	$-0.141833\pi$
$883$	14.0072	+	14.0072i	0.471379	+	0.471379i	−0.430982	+	0.902361i	$0.641833\pi$
$884$	34.0969			1.14680
$885$	−12.4516	−	26.2946i	−0.418556	−	0.883884i
$886$	1.17724			0.0395501
$887$	2.74648	+	2.74648i	0.0922178	+	0.0922178i	0.751711	−	0.659493i	$-0.229229\pi$
$887$	2.74648	+	2.74648i	0.0922178	+	0.0922178i	−0.659493	+	0.751711i	$0.729229\pi$
$888$	−3.07174	+	1.67818i	−0.103081	+	0.0563160i
$889$			56.5361i			1.89616i
$890$	7.37412	+	8.27930i	0.247181	+	0.277523i
$891$	−2.61453	+	1.19681i	−0.0875900	+	0.0400946i
$892$	8.21125	−	8.21125i	0.274933	−	0.274933i
$893$	4.12471	−	4.12471i	0.138028	−	0.138028i
$894$	7.54777	−	25.7264i	0.252435	−	0.860418i
$895$	−18.7907	−	1.08660i	−0.628103	−	0.0363209i
$896$			3.49979i			0.116920i
$897$	−19.0341	−	34.8400i	−0.635529	−	1.16327i
$898$	21.6954	+	21.6954i	0.723984	+	0.723984i
$899$	−23.5612			−0.785809
$900$	−11.6041	−	9.50496i	−0.386804	−	0.316832i
$901$	−9.95541			−0.331663
$902$	−1.59729	−	1.59729i	−0.0531838	−	0.0531838i
$903$	−26.5388	−	48.5767i	−0.883156	−	1.61653i
$904$			7.16840i			0.238418i
$905$	−9.02386	−	0.521816i	−0.299963	−	0.0173458i
$906$	6.57266	−	22.4027i	0.218362	−	0.744281i
$907$	−36.3273	+	36.3273i	−1.20623	+	1.20623i	−0.233987	+	0.972240i	$0.575177\pi$
$907$	−36.3273	+	36.3273i	−1.20623	+	1.20623i	−0.972240	+	0.233987i	$0.924823\pi$
$908$	3.64293	−	3.64293i	0.120895	−	0.120895i
$909$	17.0937	+	10.9748i	0.566961	+	0.364010i
$910$	29.1361	+	32.7125i	0.965851	+	1.08441i
$911$		−	20.6327i		−	0.683591i	−0.939774	−	0.341795i	$-0.888965\pi$
$911$		−	20.6327i		−	0.683591i	0.939774	−	0.341795i	$-0.111035\pi$
$912$	−1.52000	+	0.830420i	−0.0503323	+	0.0274979i
$913$	0.740226	+	0.740226i	0.0244979	+	0.0244979i
$914$	−5.35324			−0.177069
$915$	13.4187	+	28.3370i	0.443610	+	0.936791i
$916$	−21.7636			−0.719090
$917$	7.73065	+	7.73065i	0.255289	+	0.255289i
$918$	2.23700	−	31.5715i	0.0738320	−	1.04202i
$919$		−	18.3864i		−	0.606510i	−0.952909	−	0.303255i	$-0.901927\pi$
$919$		−	18.3864i		−	0.606510i	0.952909	−	0.303255i	$-0.0980734\pi$
$920$	−0.528575	+	9.14073i	−0.0174266	+	0.301361i
$921$	−6.44707	−	1.89148i	−0.212438	−	0.0623265i
$922$	4.87633	−	4.87633i	0.160593	−	0.160593i
$923$	−54.6259	+	54.6259i	−1.79803	+	1.79803i
$924$	−1.85837	−	0.545222i	−0.0611360	−	0.0179365i
$925$	7.92084	−	6.27370i	0.260436	−	0.206278i
$926$			17.8199i			0.585597i
$927$	−29.6002	+	6.45283i	−0.972197	+	0.211939i
$928$	−6.08174	−	6.08174i	−0.199643	−	0.199643i
$929$	40.9856			1.34469			0.672346	−	0.740237i	$-0.265287\pi$
$929$	40.9856			1.34469			0.672346	+	0.740237i	$0.265287\pi$
$930$	3.56956	−	9.99110i	0.117051	−	0.327621i
$931$	−5.24852			−0.172013
$932$	3.78119	+	3.78119i	0.123857	+	0.123857i
$933$	−13.0742	+	7.14279i	−0.428029	+	0.233844i
$934$		−	37.3297i		−	1.22147i
$935$	3.24954	−	2.89426i	0.106271	−	0.0946526i
$936$	−9.07286	+	14.1314i	−0.296556	+	0.461898i
$937$	−22.0439	+	22.0439i	−0.720142	+	0.720142i	−0.968634	−	0.248492i	$-0.920065\pi$
$937$	−22.0439	+	22.0439i	−0.720142	+	0.720142i	0.248492	+	0.968634i	$0.420065\pi$
$938$	39.1102	−	39.1102i	1.27699	−	1.27699i
$939$	4.31653	−	14.7128i	0.140865	−	0.480134i
$940$	−9.74019	+	8.67529i	−0.317690	+	0.282957i
$941$			27.4786i			0.895776i	0.894090	+	0.447888i	$0.147824\pi$
$941$			27.4786i			0.895776i	−0.894090	+	0.447888i	$0.852176\pi$
$942$	−6.86384	−	12.5636i	−0.223636	−	0.409344i
$943$	−20.4712	−	20.4712i	−0.666633	−	0.666633i
$944$	7.51199			0.244494
$945$	32.2013	−	24.8320i	1.04751	−	0.807785i
$946$	2.91744			0.0948543
$947$	−18.6928	−	18.6928i	−0.607435	−	0.607435i	0.334840	−	0.942275i	$-0.391318\pi$
$947$	−18.6928	−	18.6928i	−0.607435	−	0.607435i	−0.942275	+	0.334840i	$0.891318\pi$
$948$	−2.49481	−	4.56650i	−0.0810276	−	0.148313i
$949$			73.0294i			2.37064i
$950$	3.91950	−	3.10444i	0.127165	−	0.100721i
$951$	−13.5905	+	46.3228i	−0.440701	+	1.50212i
$952$	15.0740	−	15.0740i	0.488551	−	0.488551i
$953$	19.0445	−	19.0445i	0.616913	−	0.616913i	−0.327825	−	0.944738i	$-0.606316\pi$
$953$	19.0445	−	19.0445i	0.616913	−	0.616913i	0.944738	+	0.327825i	$0.106316\pi$
$954$	2.64904	−	4.12600i	0.0857660	−	0.133584i
$955$	1.64459	−	28.4402i	0.0532178	−	0.920304i
$956$		−	14.2573i		−	0.461115i
$957$	4.17683	−	2.28192i	0.135018	−	0.0737641i
$958$	12.6855	+	12.6855i	0.409850	+	0.409850i
$959$	−21.8972			−0.707097
$960$	3.50035	−	1.65756i	0.112973	−	0.0534976i
$961$	−23.4957			−0.757927
$962$	−7.99906	−	7.99906i	−0.257900	−	0.257900i
$963$	−20.5998	+	4.49076i	−0.663821	+	0.144713i
$964$		−	30.3058i		−	0.976084i
$965$	0.107518	+	0.120716i	0.00346113	+	0.00388599i
$966$	−23.8173	−	6.98768i	−0.766310	−	0.224825i
$967$	6.15556	−	6.15556i	0.197950	−	0.197950i	−0.601171	−	0.799120i	$-0.705299\pi$
$967$	6.15556	−	6.15556i	0.197950	−	0.197950i	0.799120	+	0.601171i	$0.205299\pi$
$968$	−7.70600	+	7.70600i	−0.247680	+	0.247680i
$969$	10.1235	+	2.97011i	0.325215	+	0.0954135i
$970$	−6.99980	−	0.404773i	−0.224750	−	0.0129965i
$971$		−	25.8132i		−	0.828385i	−0.910189	−	0.414193i	$-0.864064\pi$
$971$		−	25.8132i		−	0.828385i	0.910189	−	0.414193i	$-0.135936\pi$
$972$	12.4895	+	9.32802i	0.400602	+	0.299196i
$973$	33.6675	+	33.6675i	1.07933	+	1.07933i
$974$	12.4026			0.397403
$975$	18.9185	−	44.6340i	0.605876	−	1.42943i
$976$	−8.09546			−0.259129
$977$	30.9999	+	30.9999i	0.991776	+	0.991776i	0.999966	−	0.00819042i	$-0.00260712\pi$
$977$	30.9999	+	30.9999i	0.991776	+	0.991776i	−0.00819042	+	0.999966i	$0.502607\pi$
$978$	20.8276	−	11.3787i	0.665992	−	0.363850i
$979$		−	1.58415i		−	0.0506295i
$980$	11.7165	+	0.677521i	0.374269	+	0.0216426i
$981$	30.5111	+	19.5893i	0.974146	+	0.625437i
$982$	1.31395	−	1.31395i	0.0419298	−	0.0419298i
$983$	7.97240	−	7.97240i	0.254280	−	0.254280i	−0.568443	−	0.822723i	$-0.692454\pi$
$983$	7.97240	−	7.97240i	0.254280	−	0.254280i	0.822723	+	0.568443i	$0.192454\pi$
$984$	−3.44752	+	11.7508i	−0.109903	+	0.374602i
$985$	−29.0494	−	32.6152i	−0.925591	−	1.03921i
$986$			52.3895i			1.66842i
$987$	−16.9530	−	31.0309i	−0.539621	−	0.987723i
$988$	−3.95820	−	3.95820i	−0.125927	−	0.125927i
$989$	37.3906			1.18895
$990$	0.334850	+	2.11690i	0.0106422	+	0.0672796i
$991$	−14.1534			−0.449597			−0.224799	−	0.974405i	$-0.572172\pi$
$991$	−14.1534			−0.449597			−0.224799	+	0.974405i	$0.572172\pi$
$992$	1.93704	+	1.93704i	0.0615011	+	0.0615011i
$993$	−14.7794	−	27.0522i	−0.469009	−	0.858475i
$994$			48.2994i			1.53197i
$995$	1.33429	−	23.0741i	0.0422998	−	0.731497i
$996$	1.59768	−	5.44564i	0.0506243	−	0.172552i
$997$	14.3896	−	14.3896i	0.455725	−	0.455725i	−0.441524	−	0.897249i	$-0.645562\pi$
$997$	14.3896	−	14.3896i	0.455725	−	0.455725i	0.897249	+	0.441524i	$0.145562\pi$
$998$	−4.80644	+	4.80644i	−0.152145	+	0.152145i
$999$	−7.93142	+	6.88183i	−0.250939	+	0.217731i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.k.a.533.14	yes	36
3.2	odd	2	inner	570.2.k.a.533.8	yes	36
5.2	odd	4	inner	570.2.k.a.77.8	✓	36
15.2	even	4	inner	570.2.k.a.77.14	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.a.77.8	✓	36	5.2	odd	4	inner
570.2.k.a.77.14	yes	36	15.2	even	4	inner
570.2.k.a.533.8	yes	36	3.2	odd	2	inner
570.2.k.a.533.14	yes	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.830420 + 1.52000i) q^{3} +1.00000i q^{4} +(2.23234 + 0.129088i) q^{5} +(-0.487608 + 1.66200i) q^{6} +(-2.47472 + 2.47472i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.62081 + 2.52448i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.830420 + 1.52000i) q^{3} +1.00000i q^{4} +(2.23234 + 0.129088i) q^{5} +(-0.487608 + 1.66200i) q^{6} +(-2.47472 + 2.47472i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.62081 + 2.52448i) q^{9} +(1.48722 + 1.66978i) q^{10} -0.319493i q^{11} +(-1.52000 + 0.830420i) q^{12} +(-3.95820 - 3.95820i) q^{13} -3.49979 q^{14} +(1.65756 + 3.50035i) q^{15} -1.00000 q^{16} +(4.30711 + 4.30711i) q^{17} +(-2.93116 + 0.638992i) q^{18} -1.00000i q^{19} +(-0.129088 + 2.23234i) q^{20} +(-5.81664 - 1.70652i) q^{21} +(0.225915 - 0.225915i) q^{22} +(2.89538 - 2.89538i) q^{23} +(-1.66200 - 0.487608i) q^{24} +(4.96667 + 0.576336i) q^{25} -5.59774i q^{26} +(-5.18316 - 0.367253i) q^{27} +(-2.47472 - 2.47472i) q^{28} +8.60087 q^{29} +(-1.30305 + 3.64720i) q^{30} -2.73939 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.485629 - 0.265313i) q^{33} +6.09118i q^{34} +(-5.84388 + 5.20497i) q^{35} +(-2.52448 - 1.62081i) q^{36} +(1.42898 - 1.42898i) q^{37} +(0.707107 - 0.707107i) q^{38} +(2.72950 - 9.30344i) q^{39} +(-1.66978 + 1.48722i) q^{40} -7.07028i q^{41} +(-2.90629 - 5.31968i) q^{42} +(6.45694 + 6.45694i) q^{43} +0.319493 q^{44} +(-3.94407 + 5.42626i) q^{45} +4.09469 q^{46} +(4.12471 + 4.12471i) q^{47} +(-0.830420 - 1.52000i) q^{48} -5.24852i q^{49} +(3.10444 + 3.91950i) q^{50} +(-2.97011 + 10.1235i) q^{51} +(3.95820 - 3.95820i) q^{52} +(-1.15569 + 1.15569i) q^{53} +(-3.40536 - 3.92473i) q^{54} +(0.0412426 - 0.713216i) q^{55} -3.49979i q^{56} +(1.52000 - 0.830420i) q^{57} +(6.08174 + 6.08174i) q^{58} -7.51199 q^{59} +(-3.50035 + 1.65756i) q^{60} +8.09546 q^{61} +(-1.93704 - 1.93704i) q^{62} +(-2.23634 - 10.2584i) q^{63} -1.00000i q^{64} +(-8.32509 - 9.34700i) q^{65} +(0.530996 + 0.155787i) q^{66} +(-11.1750 + 11.1750i) q^{67} +(-4.30711 + 4.30711i) q^{68} +(6.80536 + 1.99660i) q^{69} +(-7.81272 - 0.451781i) q^{70} -13.8007i q^{71} +(-0.638992 - 2.93116i) q^{72} +(-9.22508 - 9.22508i) q^{73} +2.02088 q^{74} +(3.24839 + 8.02795i) q^{75} +1.00000 q^{76} +(0.790656 + 0.790656i) q^{77} +(8.50858 - 4.64848i) q^{78} +3.00427i q^{79} +(-2.23234 - 0.129088i) q^{80} +(-3.74597 - 8.18338i) q^{81} +(4.99944 - 4.99944i) q^{82} +(-2.31688 + 2.31688i) q^{83} +(1.70652 - 5.81664i) q^{84} +(9.05894 + 10.1709i) q^{85} +9.13149i q^{86} +(7.14233 + 13.0733i) q^{87} +(0.225915 + 0.225915i) q^{88} +4.95832 q^{89} +(-6.62582 + 1.04807i) q^{90} +19.5909 q^{91} +(2.89538 + 2.89538i) q^{92} +(-2.27484 - 4.16388i) q^{93} +5.83322i q^{94} +(0.129088 - 2.23234i) q^{95} +(0.487608 - 1.66200i) q^{96} +(-2.21723 + 2.21723i) q^{97} +(3.71127 - 3.71127i) q^{98} +(0.806552 + 0.517836i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7}+O(q^{10}) \) 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7	\( 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} - 32 q^{21} - 4 q^{22} + 32 q^{25} + 28 q^{27} - 12 q^{28} - 8 q^{30} + 8 q^{31} + 36 q^{33} + 4 q^{36} - 32 q^{37} - 8 q^{40} + 12 q^{42} - 24 q^{43} - 28 q^{45} - 16 q^{46} - 4 q^{48} - 40 q^{51} - 8 q^{52} - 4 q^{55} + 4 q^{57} - 4 q^{58} - 24 q^{60} + 200 q^{61} + 28 q^{63} + 12 q^{70} - 68 q^{73} - 36 q^{75} + 36 q^{76} + 24 q^{78} - 92 q^{81} + 24 q^{82} + 24 q^{85} + 28 q^{87} - 4 q^{88} - 68 q^{90} + 64 q^{91} + 16 q^{93} - 4 q^{96} - 148 q^{97}+O(q^{100}) \) 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 - 32 * q^21 - 4 * q^22 + 32 * q^25 + 28 * q^27 - 12 * q^28 - 8 * q^30 + 8 * q^31 + 36 * q^33 + 4 * q^36 - 32 * q^37 - 8 * q^40 + 12 * q^42 - 24 * q^43 - 28 * q^45 - 16 * q^46 - 4 * q^48 - 40 * q^51 - 8 * q^52 - 4 * q^55 + 4 * q^57 - 4 * q^58 - 24 * q^60 + 200 * q^61 + 28 * q^63 + 12 * q^70 - 68 * q^73 - 36 * q^75 + 36 * q^76 + 24 * q^78 - 92 * q^81 + 24 * q^82 + 24 * q^85 + 28 * q^87 - 4 * q^88 - 68 * q^90 + 64 * q^91 + 16 * q^93 - 4 * q^96 - 148 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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