LMFDB - Embedded newform 570.2.k.a.77.8

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			77.8
Character	$\chi$	$=$	570.77
Dual form			570.2.k.a.533.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.52000 - 0.830420i) q^{3} -1.00000i q^{4} +(-2.23234 + 0.129088i) q^{5} +(-0.487608 + 1.66200i) q^{6} +(-2.47472 - 2.47472i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.62081 - 2.52448i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.52000 - 0.830420i) 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} +(-0.830420 - 1.52000i) q^{12} +(-3.95820 + 3.95820i) q^{13} +3.49979 q^{14} +(-3.28596 + 2.04999i) q^{15} -1.00000 q^{16} +(-4.30711 + 4.30711i) q^{17} +(0.638992 + 2.93116i) 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} +(0.367253 - 5.18316i) q^{27} +(-2.47472 + 2.47472i) q^{28} -8.60087 q^{29} +(0.873962 - 3.77309i) q^{30} -2.73939 q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.265313 - 0.485629i) 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} +(5.31968 - 2.90629i) q^{42} +(6.45694 - 6.45694i) q^{43} -0.319493 q^{44} +(-3.29231 + 5.84472i) q^{45} +4.09469 q^{46} +(-4.12471 + 4.12471i) q^{47} +(-1.52000 + 0.830420i) 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} +(0.830420 + 1.52000i) q^{57} +(6.08174 - 6.08174i) q^{58} +7.51199 q^{59} +(2.04999 + 3.28596i) q^{60} +8.09546 q^{61} +(1.93704 - 1.93704i) q^{62} +(-10.2584 + 2.23634i) 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} +(2.93116 - 0.638992i) q^{72} +(-9.22508 + 9.22508i) q^{73} -2.02088 q^{74} +(7.07075 - 5.00045i) q^{75} +1.00000 q^{76} +(-0.790656 + 0.790656i) q^{77} +(-4.64848 - 8.50858i) 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} +(-13.0733 + 7.14233i) q^{87} +(0.225915 - 0.225915i) q^{88} -4.95832 q^{89} +(-1.80482 - 6.46085i) q^{90} +19.5909 q^{91} +(-2.89538 + 2.89538i) q^{92} +(-4.16388 + 2.27484i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

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

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
$3$	1.52000	−	0.830420i	0.877573	−	0.479443i
$3$	1.52000	−	0.830420i	0.877573	−	0.479443i
$4$		−	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	0.0626759	−	0.998034i	$-0.480037\pi$
$7$	−2.47472	−	2.47472i	−0.935358	−	0.935358i	−0.998034	+	0.0626759i	$0.980037\pi$
$8$	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	$-0.0153374\pi$
$12$	−0.830420	−	1.52000i	−0.239721	−	0.438787i
$13$	−3.95820	+	3.95820i	−1.09781	+	1.09781i	−0.103141	+	0.994667i	$0.532889\pi$
$13$	−3.95820	+	3.95820i	−1.09781	+	1.09781i	−0.994667	+	0.103141i	$0.967111\pi$
$14$	3.49979			0.935358
$15$	−3.28596	+	2.04999i	−0.848431	+	0.529306i
$16$	−1.00000			−0.250000
$17$	−4.30711	+	4.30711i	−1.04463	+	1.04463i	−0.0456719	+	0.998956i	$0.514543\pi$
$17$	−4.30711	+	4.30711i	−1.04463	+	1.04463i	−0.998956	+	0.0456719i	$0.985457\pi$
$18$	0.638992	+	2.93116i	0.150612	+	0.690881i
$19$			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	$-0.390395\pi$
$23$	−2.89538	−	2.89538i	−0.603729	−	0.603729i	−0.941300	+	0.337571i	$0.890395\pi$
$24$	1.66200	+	0.487608i	0.339254	+	0.0995325i
$25$	4.96667	−	0.576336i	0.993335	−	0.115267i
$26$		−	5.59774i		−	1.09781i
$27$	0.367253	−	5.18316i	0.0706778	−	0.997499i
$28$	−2.47472	+	2.47472i	−0.467679	+	0.467679i
$29$	−8.60087			−1.59714			−0.798571	−	0.601900i	$-0.794410\pi$
$29$	−8.60087			−1.59714			−0.798571	+	0.601900i	$0.794410\pi$
$30$	0.873962	−	3.77309i	0.159563	−	0.688868i
$31$	−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
$33$	−0.265313	−	0.485629i	−0.0461850	−	0.0845372i
$34$		−	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	0.814744	−	0.579821i	$-0.196878\pi$
$37$	1.42898	+	1.42898i	0.234923	+	0.234923i	−0.579821	+	0.814744i	$0.696878\pi$
$38$	−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	$-0.186172\pi$
$42$	5.31968	−	2.90629i	0.820845	−	0.448451i
$43$	6.45694	−	6.45694i	0.984674	−	0.984674i	−0.0152099	−	0.999884i	$-0.504842\pi$
$43$	6.45694	−	6.45694i	0.984674	−	0.984674i	0.999884	+	0.0152099i	$0.00484166\pi$
$44$	−0.319493			−0.0481653
$45$	−3.29231	+	5.84472i	−0.490789	+	0.871279i
$46$	4.09469			0.603729
$47$	−4.12471	+	4.12471i	−0.601650	+	0.601650i	−0.940750	−	0.339100i	$-0.889877\pi$
$47$	−4.12471	+	4.12471i	−0.601650	+	0.601650i	0.339100	+	0.940750i	$0.389877\pi$
$48$	−1.52000	+	0.830420i	−0.219393	+	0.119861i
$49$			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	$-0.214194\pi$
$53$	1.15569	+	1.15569i	0.158747	+	0.158747i	−0.623264	+	0.782011i	$0.714194\pi$
$54$	3.40536	+	3.92473i	0.463411	+	0.534088i
$55$	0.0412426	+	0.713216i	0.00556116	+	0.0961700i
$56$		−	3.49979i		−	0.467679i
$57$	0.830420	+	1.52000i	0.109992	+	0.201329i
$58$	6.08174	−	6.08174i	0.798571	−	0.798571i
$59$	7.51199			0.977978			0.488989	−	0.872290i	$-0.337366\pi$
$59$	7.51199			0.977978			0.488989	+	0.872290i	$0.337366\pi$
$60$	2.04999	+	3.28596i	0.264653	+	0.424216i
$61$	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
$63$	−10.2584	+	2.23634i	−1.29244	+	0.281752i
$64$			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	−0.867086	−	0.498158i	$-0.834010\pi$
$67$	−11.1750	−	11.1750i	−1.36524	−	1.36524i	−0.498158	−	0.867086i	$-0.665990\pi$
$68$	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	$-0.305426\pi$
$72$	2.93116	−	0.638992i	0.345440	−	0.0753059i
$73$	−9.22508	+	9.22508i	−1.07971	+	1.07971i	−0.0831788	+	0.996535i	$0.526507\pi$
$73$	−9.22508	+	9.22508i	−1.07971	+	1.07971i	−0.996535	+	0.0831788i	$0.973493\pi$
$74$	−2.02088			−0.234923
$75$	7.07075	−	5.00045i	0.816460	−	0.577403i
$76$	1.00000			0.114708
$77$	−0.790656	+	0.790656i	−0.0901036	+	0.0901036i
$78$	−4.64848	−	8.50858i	−0.526336	−	0.963407i
$79$		−	3.00427i		−	0.338007i	−0.985615	−	0.169004i	$-0.945945\pi$
$79$		−	3.00427i		−	0.338007i	0.985615	−	0.169004i	$-0.0540549\pi$
$80$	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	$-0.192447\pi$
$83$	2.31688	+	2.31688i	0.254311	+	0.254311i	−0.568425	+	0.822735i	$0.692447\pi$
$84$	−1.70652	+	5.81664i	−0.186197	+	0.634648i
$85$	9.05894	−	10.1709i	0.982580	−	1.10319i
$86$			9.13149i			0.984674i
$87$	−13.0733	+	7.14233i	−1.40161	+	0.765739i
$88$	0.225915	−	0.225915i	0.0240827	−	0.0240827i
$89$	−4.95832			−0.525580			−0.262790	−	0.964853i	$-0.584643\pi$
$89$	−4.95832			−0.525580			−0.262790	+	0.964853i	$0.584643\pi$
$90$	−1.80482	−	6.46085i	−0.190245	−	0.681034i
$91$	19.5909			2.05369
$92$	−2.89538	+	2.89538i	−0.301864	+	0.301864i
$93$	−4.16388	+	2.27484i	−0.431774	+	0.235890i
$94$		−	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	0.585527	−	0.810653i	$-0.300888\pi$
$97$	−2.21723	−	2.21723i	−0.225126	−	0.225126i	−0.810653	+	0.585527i	$0.800888\pi$
$98$	−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	$-0.109371\pi$
$102$	−5.05823	−	9.25860i	−0.500840	−	0.916738i
$103$	7.14069	−	7.14069i	0.703593	−	0.703593i	−0.261587	−	0.965180i	$-0.584246\pi$
$103$	7.14069	−	7.14069i	0.703593	−	0.703593i	0.965180	+	0.261587i	$0.0842458\pi$
$104$	−5.59774			−0.548904
$105$	13.2050	+	3.05868i	1.28868	+	0.298497i
$106$	−1.63440			−0.158747
$107$	−4.96947	+	4.96947i	−0.480416	+	0.480416i	−0.905265	−	0.424848i	$-0.860327\pi$
$107$	−4.96947	+	4.96947i	−0.480416	+	0.480416i	0.424848	+	0.905265i	$0.360327\pi$
$108$	−5.18316	−	0.367253i	−0.498750	−	0.0353389i
$109$			12.0861i			1.15764i	0.815455	+	0.578820i	$0.196487\pi$
$109$			12.0861i			1.15764i	−0.815455	+	0.578820i	$0.803513\pi$
$110$	−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	$-0.359471\pi$
$113$	−5.06883	−	5.06883i	−0.476835	−	0.476835i	−0.904118	+	0.427283i	$0.859471\pi$
$114$	−1.66200	−	0.487608i	−0.155660	−	0.0456687i
$115$	6.83723	+	6.08971i	0.637575	+	0.567869i
$116$			8.60087i			0.798571i
$117$	3.57691	+	16.4079i	0.330686	+	1.51691i
$118$	−5.31178	+	5.31178i	−0.488989	+	0.488989i
$119$	21.3178			1.95420
$120$	−3.77309	−	0.873962i	−0.344434	−	0.0797814i
$121$	10.8979			0.990720
$122$	−5.72435	+	5.72435i	−0.518259	+	0.518259i
$123$	−5.87130	−	10.7468i	−0.529397	−	0.969010i
$124$			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	0.999906	+	0.0136950i	$0.00435939\pi$
$127$	11.4227	+	11.4227i	1.01360	+	1.01360i	0.0136950	+	0.999906i	$0.495641\pi$
$128$	−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	$-0.0435744\pi$
$132$	−0.485629	+	0.265313i	−0.0422686	+	0.0230925i
$133$	2.47472	−	2.47472i	0.214586	−	0.214586i
$134$	15.8038			1.36524
$135$	−0.150749	+	11.6180i	−0.0129744	+	0.999916i
$136$	−6.09118			−0.522314
$137$	−4.42417	+	4.42417i	−0.377982	+	0.377982i	−0.870374	−	0.492392i	$-0.836123\pi$
$137$	−4.42417	+	4.42417i	−0.377982	+	0.377982i	0.492392	+	0.870374i	$0.336123\pi$
$138$	6.22393	−	3.40031i	0.529816	−	0.289453i
$139$			13.6045i			1.15392i	0.816772	+	0.576960i	$0.195761\pi$
$139$			13.6045i			1.15392i	−0.816772	+	0.576960i	$0.804239\pi$
$140$	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
$147$	4.35848	+	7.97776i	0.359481	+	0.657995i
$148$	1.42898	−	1.42898i	0.117461	−	0.117461i
$149$	15.4792			1.26810			0.634052	−	0.773291i	$-0.281391\pi$
$149$	15.4792			1.26810			0.634052	+	0.773291i	$0.281391\pi$
$150$	−1.46392	+	8.53563i	−0.119528	+	0.696931i
$151$	−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
$153$	3.89221	+	17.8542i	0.314667	+	1.44343i
$154$		−	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	0.434313	−	0.900762i	$-0.356991\pi$
$157$	−5.84460	−	5.84460i	−0.466450	−	0.466450i	−0.900762	+	0.434313i	$0.856991\pi$
$158$	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
$162$	8.43532	+	3.13772i	0.662742	+	0.246523i
$163$	−9.68901	+	9.68901i	−0.758902	+	0.758902i	−0.976123	−	0.217221i	$-0.930301\pi$
$163$	−9.68901	+	9.68901i	−0.758902	+	0.758902i	0.217221	+	0.976123i	$0.430301\pi$
$164$	−7.07028			−0.552096
$165$	0.654957	+	1.04984i	0.0509883	+	0.0817299i
$166$	−3.27656			−0.254311
$167$	−9.29416	+	9.29416i	−0.719204	+	0.719204i	−0.968442	−	0.249239i	$-0.919820\pi$
$167$	−9.29416	+	9.29416i	−0.719204	+	0.719204i	0.249239	+	0.968442i	$0.419820\pi$
$168$	−2.90629	−	5.31968i	−0.224225	−	0.410422i
$169$		−	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	$-0.324787\pi$
$173$	−4.33021	−	4.33021i	−0.329220	−	0.329220i	−0.852290	+	0.523070i	$0.824787\pi$
$174$	4.19385	−	14.2946i	0.317935	−	1.08367i
$175$	−13.7174	−	10.8649i	−1.03694	−	0.821307i
$176$			0.319493i			0.0240827i
$177$	11.4182	−	6.23810i	0.858247	−	0.468885i
$178$	3.50606	−	3.50606i	0.262790	−	0.262790i
$179$	8.41749			0.629153			0.314576	−	0.949232i	$-0.398138\pi$
$179$	8.41749			0.629153			0.314576	+	0.949232i	$0.398138\pi$
$180$	5.84472	+	3.29231i	0.435639	+	0.245394i
$181$	−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
$183$	12.3051	−	6.72263i	0.909619	−	0.496951i
$184$		−	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	$-0.152481\pi$
$192$	0.830420	+	1.52000i	0.0599304	+	0.109697i
$193$	0.0511200	−	0.0511200i	0.00367970	−	0.00367970i	−0.705265	−	0.708944i	$-0.749172\pi$
$193$	0.0511200	−	0.0511200i	0.00367970	−	0.00367970i	0.708944	+	0.705265i	$0.249172\pi$
$194$	3.13564			0.225126
$195$	4.89221	−	21.1208i	0.350339	−	1.51249i
$196$	5.24852			0.374895
$197$	13.8117	−	13.8117i	0.984041	−	0.984041i	−0.0158340	−	0.999875i	$-0.505040\pi$
$197$	13.8117	−	13.8117i	0.984041	−	0.984041i	0.999875	+	0.0158340i	$0.00504032\pi$
$198$	0.936483	−	0.204153i	0.0665530	−	0.0145085i
$199$			10.3363i			0.732719i	0.930473	+	0.366359i	$0.119396\pi$
$199$			10.3363i			0.732719i	−0.930473	+	0.366359i	$0.880604\pi$
$200$	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
$207$	−12.0022	+	2.61647i	−0.834209	+	0.181857i
$208$	3.95820	−	3.95820i	0.274452	−	0.274452i
$209$	0.319493			0.0220998
$210$	−11.5002	+	7.17454i	−0.793587	+	0.495090i
$211$	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
$213$	−11.4603	−	20.9770i	−0.785250	−	1.43732i
$214$		−	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
$222$	−3.07174	+	1.67818i	−0.206162	+	0.112632i
$223$	−8.21125	+	8.21125i	−0.549866	+	0.549866i	−0.926402	−	0.376536i	$-0.877115\pi$
$223$	−8.21125	+	8.21125i	−0.549866	+	0.549866i	0.376536	+	0.926402i	$0.377115\pi$
$224$	−3.49979			−0.233840
$225$	6.59507	−	13.4724i	0.439671	−	0.898159i
$226$	7.16840			0.476835
$227$	3.64293	−	3.64293i	0.241790	−	0.241790i	−0.575800	−	0.817590i	$-0.695309\pi$
$227$	3.64293	−	3.64293i	0.241790	−	0.241790i	0.817590	+	0.575800i	$0.195309\pi$
$228$	1.52000	−	0.830420i	0.100665	−	0.0549959i
$229$		−	21.7636i		−	1.43818i	−0.694917	−	0.719090i	$-0.744559\pi$
$229$		−	21.7636i		−	1.43818i	0.694917	−	0.719090i	$-0.255441\pi$
$230$	−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	$-0.306044\pi$
$233$	−3.78119	−	3.78119i	−0.247714	−	0.247714i	−0.820032	+	0.572318i	$0.806044\pi$
$234$	−14.1314	−	9.07286i	−0.923797	−	0.593111i
$235$	8.67529	−	9.74019i	0.565914	−	0.635380i
$236$		−	7.51199i		−	0.488989i
$237$	−2.49481	−	4.56650i	−0.162055	−	0.296626i
$238$	−15.0740	+	15.0740i	−0.977102	+	0.977102i
$239$	14.2573			0.922230			0.461115	−	0.887340i	$-0.347450\pi$
$239$	14.2573			0.922230			0.461115	+	0.887340i	$0.347450\pi$
$240$	3.28596	−	2.04999i	0.212108	−	0.132326i
$241$	−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
$243$	−12.4895	−	9.32802i	−0.801203	−	0.598393i
$244$		−	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	$0.691895\pi$
$252$	2.23634	+	10.2584i	0.140876	+	0.646221i
$253$	−0.925053	+	0.925053i	−0.0581576	+	0.0581576i
$254$	−16.1541			−1.01360
$255$	5.32346	−	22.9825i	0.333368	−	1.43922i
$256$	1.00000			0.0625000
$257$	10.7603	−	10.7603i	0.671212	−	0.671212i	−0.286783	−	0.957995i	$-0.592586\pi$
$257$	10.7603	−	10.7603i	0.671212	−	0.671212i	0.957995	+	0.286783i	$0.0925860\pi$
$258$	7.58297	+	13.8799i	0.472095	+	0.864124i
$259$		−	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	$-0.145466\pi$
$263$	7.39717	+	7.39717i	0.456129	+	0.456129i	−0.441253	+	0.897383i	$0.645466\pi$
$264$	0.155787	−	0.530996i	0.00958803	−	0.0326806i
$265$	−2.72909	−	2.43071i	−0.167646	−	0.149318i
$266$			3.49979i			0.214586i
$267$	−7.53664	+	4.11748i	−0.461235	+	0.251986i
$268$	−11.1750	+	11.1750i	−0.682622	+	0.682622i
$269$	12.5829			0.767193			0.383596	−	0.923501i	$-0.374685\pi$
$269$	12.5829			0.767193			0.383596	+	0.923501i	$0.374685\pi$
$270$	−8.10855	−	8.32174i	−0.493471	−	0.506445i
$271$	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
$273$	29.7782	−	16.2687i	1.80226	−	0.984626i
$274$		−	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	0.384393	−	0.923170i	$-0.374411\pi$
$277$	−8.96703	−	8.96703i	−0.538777	−	0.538777i	−0.923170	+	0.384393i	$0.874411\pi$
$278$	−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	$-0.182409\pi$
$282$	−4.84402	−	8.86649i	−0.288457	−	0.527992i
$283$	14.1537	−	14.1537i	0.841353	−	0.841353i	−0.147682	−	0.989035i	$-0.547181\pi$
$283$	14.1537	−	14.1537i	0.841353	−	0.841353i	0.989035	+	0.147682i	$0.0471812\pi$
$284$	−13.8007			−0.818919
$285$	−2.04999	−	3.28596i	−0.121431	−	0.194643i
$286$	−1.78844			−0.105753
$287$	−17.4970	+	17.4970i	−1.03282	+	1.03282i
$288$	−0.638992	−	2.93116i	−0.0376529	−	0.172720i
$289$		−	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	−0.990673	−	0.136264i	$-0.956491\pi$
$293$	−19.2900	−	19.2900i	−1.12694	−	1.12694i	−0.136264	−	0.990673i	$-0.543509\pi$
$294$	−8.72304	−	2.55922i	−0.508738	−	0.149257i
$295$	−16.7693	+	0.969707i	−0.976347	+	0.0564585i
$296$			2.02088i			0.117461i
$297$	−1.65598	−	0.117334i	−0.0960897	−	0.00680844i
$298$	−10.9454	+	10.9454i	−0.634052	+	0.634052i
$299$	22.9210			1.32556
$300$	−5.00045	−	7.07075i	−0.288701	−	0.408230i
$301$	−31.9583			−1.84205
$302$	9.53138	−	9.53138i	0.548469	−	0.548469i
$303$	−5.62291	−	10.2922i	−0.323028	−	0.591271i
$304$		−	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	0.624487	−	0.781035i	$-0.285308\pi$
$307$	−2.74294	−	2.74294i	−0.156548	−	0.156548i	−0.781035	+	0.624487i	$0.785308\pi$
$308$	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	$0.921583\pi$
$312$	−8.50858	+	4.64848i	−0.481703	+	0.263168i
$313$	−6.25964	+	6.25964i	−0.353816	+	0.353816i	−0.861527	−	0.507711i	$-0.830492\pi$
$313$	−6.25964	+	6.25964i	−0.353816	+	0.353816i	0.507711	+	0.861527i	$0.330492\pi$
$314$	8.26551			0.466450
$315$	22.6116	−	6.31650i	1.27402	−	0.355894i
$316$	−3.00427			−0.169004
$317$	−19.7083	+	19.7083i	−1.10693	+	1.10693i	−0.113376	+	0.993552i	$0.536166\pi$
$317$	−19.7083	+	19.7083i	−1.10693	+	1.10693i	−0.993552	+	0.113376i	$0.963834\pi$
$318$	−2.48429	+	1.35724i	−0.139312	+	0.0761100i
$319$			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
$327$	10.0366	+	18.3709i	0.555023	+	1.01591i
$328$	4.99944	−	4.99944i	0.276048	−	0.276048i
$329$	20.4150			1.12552
$330$	−1.20547	−	0.279224i	−0.0663591	−	0.0153708i
$331$	−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
$333$	5.92352	−	1.29133i	0.324607	−	0.0707642i
$334$		−	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	0.365758	−	0.930710i	$-0.380810\pi$
$337$	−10.3711	−	10.3711i	−0.564952	−	0.564952i	−0.930710	+	0.365758i	$0.880810\pi$
$338$	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
$342$	−2.93116	+	0.638992i	−0.158499	+	0.0345527i
$343$	−4.33442	+	4.33442i	−0.234037	+	0.234037i
$344$	9.13149			0.492337
$345$	15.4496	+	3.57860i	0.831779	+	0.192665i
$346$	6.12384			0.329220
$347$	−5.55389	+	5.55389i	−0.298149	+	0.298149i	−0.840288	−	0.542140i	$-0.817614\pi$
$347$	−5.55389	+	5.55389i	−0.298149	+	0.298149i	0.542140	+	0.840288i	$0.317614\pi$
$348$	7.14233	+	13.0733i	0.382869	+	0.700805i
$349$			10.2761i			0.550066i	0.961435	+	0.275033i	$0.0886889\pi$
$349$			10.2761i			0.550066i	−0.961435	+	0.275033i	$0.911311\pi$
$350$	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	$-0.188572\pi$
$353$	5.09591	+	5.09591i	0.271228	+	0.271228i	−0.558366	+	0.829594i	$0.688572\pi$
$354$	−3.66290	+	12.4849i	−0.194681	+	0.663566i
$355$	1.78150	+	30.8078i	0.0945522	+	1.63511i
$356$			4.95832i			0.262790i
$357$	32.4031	−	17.7028i	1.71496	−	0.936929i
$358$	−5.95206	+	5.95206i	−0.314576	+	0.314576i
$359$	−35.4806			−1.87259			−0.936297	−	0.351208i	$-0.885771\pi$
$359$	−35.4806			−1.87259			−0.936297	+	0.351208i	$0.885771\pi$
$360$	−6.46085	+	1.80482i	−0.340517	+	0.0951225i
$361$	−1.00000			−0.0526316
$362$	2.85836	−	2.85836i	0.150232	−	0.150232i
$363$	16.5649	−	9.04985i	0.869430	−	0.474994i
$364$		−	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	0.612134	−	0.790754i	$-0.290311\pi$
$367$	−3.42185	−	3.42185i	−0.178619	−	0.178619i	−0.790754	+	0.612134i	$0.790311\pi$
$368$	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
$372$	2.27484	+	4.16388i	0.117945	+	0.215887i
$373$	3.03363	−	3.03363i	0.157075	−	0.157075i	−0.624194	−	0.781269i	$-0.714573\pi$
$373$	3.03363	−	3.03363i	0.157075	−	0.157075i	0.781269	+	0.624194i	$0.214573\pi$
$374$	−1.94609			−0.100630
$375$	−15.1388	+	12.0755i	−0.781764	+	0.623574i
$376$	−5.83322			−0.300825
$377$	34.0440	−	34.0440i	1.75336	−	1.75336i
$378$	1.28531	−	18.1400i	0.0661090	−	0.933019i
$379$		−	19.3076i		−	0.991764i	−0.868390	−	0.495882i	$-0.834845\pi$
$379$		−	19.3076i		−	0.991764i	0.868390	−	0.495882i	$-0.165155\pi$
$380$	−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	$-0.0943752\pi$
$383$	12.9987	+	12.9987i	0.664204	+	0.664204i	−0.292164	+	0.956368i	$0.594375\pi$
$384$	−1.66200	−	0.487608i	−0.0848135	−	0.0248831i
$385$	1.66295	−	1.86708i	0.0847517	−	0.0951550i
$386$			0.0722945i			0.00367970i
$387$	−5.83495	−	26.7659i	−0.296607	−	1.36058i
$388$	−2.21723	+	2.21723i	−0.112563	+	0.112563i
$389$	10.3234			0.523419			0.261709	−	0.965147i	$-0.415714\pi$
$389$	10.3234			0.523419			0.261709	+	0.965147i	$0.415714\pi$
$390$	11.4753	+	18.3940i	0.581076	+	0.931414i
$391$	24.9415			1.26134
$392$	−3.71127	+	3.71127i	−0.187447	+	0.187447i
$393$	−2.59410	−	4.74825i	−0.130855	−	0.239517i
$394$			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	0.281407	−	0.959588i	$-0.409199\pi$
$397$	−13.5127	−	13.5127i	−0.678181	−	0.678181i	−0.959588	+	0.281407i	$0.909199\pi$
$398$	−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	$0.851750\pi$
$402$	24.0219	−	13.1238i	1.19810	−	0.654557i
$403$	10.8431	−	10.8431i	0.540131	−	0.540131i
$404$	−6.77117			−0.336878
$405$	9.41865	+	17.7845i	0.468017	+	0.883720i
$406$	−30.1012			−1.49390
$407$	0.456548	−	0.456548i	0.0226302	−	0.0226302i
$408$	−9.25860	+	5.05823i	−0.458369	+	0.250420i
$409$			38.6156i			1.90942i	0.297542	+	0.954709i	$0.403833\pi$
$409$			38.6156i			1.90942i	−0.297542	+	0.954709i	$0.596167\pi$
$410$	−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
$417$	11.2975	+	20.6789i	0.553239	+	1.01265i
$418$	−0.225915	+	0.225915i	−0.0110499	+	0.0110499i
$419$	−1.37511			−0.0671786			−0.0335893	−	0.999436i	$-0.510694\pi$
$419$	−1.37511			−0.0671786			−0.0335893	+	0.999436i	$0.510694\pi$
$420$	3.05868	−	13.2050i	0.149248	−	0.644339i
$421$	−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
$423$	3.72738	+	17.0981i	0.181231	+	0.831337i
$424$			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	$0.982372\pi$
$432$	−0.367253	+	5.18316i	−0.0176694	+	0.249375i
$433$	−0.650645	+	0.650645i	−0.0312680	+	0.0312680i	−0.722568	−	0.691300i	$-0.757038\pi$
$433$	−0.650645	+	0.650645i	−0.0312680	+	0.0312680i	0.691300	+	0.722568i	$0.257038\pi$
$434$	−9.58729			−0.460205
$435$	28.2621	−	17.6317i	1.35507	−	0.845376i
$436$	12.0861			0.578820
$437$	2.89538	−	2.89538i	0.138505	−	0.138505i
$438$	−10.8338	−	19.8303i	−0.517661	−	0.947527i
$439$			18.3241i			0.874563i	0.899325	+	0.437281i	$0.144059\pi$
$439$			18.3241i			0.874563i	−0.899325	+	0.437281i	$0.855941\pi$
$440$	−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	$-0.258903\pi$
$443$	−0.832433	−	0.832433i	−0.0395501	−	0.0395501i	−0.726605	+	0.687055i	$0.758903\pi$
$444$	0.985397	−	3.35870i	0.0467649	−	0.159397i
$445$	11.0686	−	0.640059i	0.524704	−	0.0303417i
$446$		−	11.6125i		−	0.549866i
$447$	23.5284	−	12.8542i	1.11285	−	0.607983i
$448$	2.47472	−	2.47472i	0.116920	−	0.116920i
$449$	−30.6819			−1.44797			−0.723984	−	0.689817i	$-0.757691\pi$
$449$	−30.6819			−1.44797			−0.723984	+	0.689817i	$0.757691\pi$
$450$	4.86299	+	14.1898i	0.229244	+	0.668915i
$451$	−2.25890			−0.106368
$452$	−5.06883	+	5.06883i	−0.238418	+	0.238418i
$453$	−20.4887	+	11.1936i	−0.962643	+	0.525919i
$454$			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	0.613008	−	0.790077i	$-0.289959\pi$
$457$	−3.78531	−	3.78531i	−0.177069	−	0.177069i	−0.790077	+	0.613008i	$0.789959\pi$
$458$	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	$-0.0513408\pi$
$462$	−0.928539	−	1.69960i	−0.0431996	−	0.0790725i
$463$	12.6005	−	12.6005i	0.585597	−	0.585597i	−0.350839	−	0.936436i	$-0.614104\pi$
$463$	12.6005	−	12.6005i	0.585597	−	0.585597i	0.936436	+	0.350839i	$0.114104\pi$
$464$	8.60087			0.399286
$465$	9.00153	−	5.61573i	0.417436	−	0.260423i
$466$	5.34741			0.247714
$467$	26.3961	−	26.3961i	1.22147	−	1.22147i	0.254355	−	0.967111i	$-0.418137\pi$
$467$	26.3961	−	26.3961i	1.22147	−	1.22147i	0.967111	−	0.254355i	$-0.0818630\pi$
$468$	16.4079	−	3.57691i	0.758454	−	0.165343i
$469$			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
$477$	4.79068	−	1.04437i	0.219350	−	0.0478183i
$478$	−10.0815	+	10.0815i	−0.461115	+	0.461115i
$479$	−17.9400			−0.819700			−0.409850	−	0.912153i	$-0.634419\pi$
$479$	−17.9400			−0.819700			−0.409850	+	0.912153i	$0.634419\pi$
$480$	−0.873962	+	3.77309i	−0.0398907	+	0.172217i
$481$	−11.3124			−0.515800
$482$	21.4294	−	21.4294i	0.976084	−	0.976084i
$483$	11.9004	+	21.7824i	0.541485	+	0.991135i
$484$		−	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	0.877316	−	0.479913i	$-0.159332\pi$
$487$	8.76993	+	8.76993i	0.397403	+	0.397403i	−0.479913	+	0.877316i	$0.659332\pi$
$488$	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	$-0.0133506\pi$
$492$	−10.7468	+	5.87130i	−0.484505	+	0.264699i
$493$	37.0449	−	37.0449i	1.66842	−	1.66842i
$494$	5.59774			0.251854
$495$	1.86734	+	1.05187i	0.0839308	+	0.0472780i
$496$	2.73939			0.123002
$497$	−34.1529	+	34.1529i	−1.53197	+	1.53197i
$498$	−4.98038	+	2.72092i	−0.223176	+	0.121927i
$499$		−	6.79733i		−	0.304290i	−0.988358	−	0.152145i	$-0.951382\pi$
$499$		−	6.79733i		−	0.304290i	0.988358	−	0.152145i	$-0.0486181\pi$
$500$	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	−0.992052	−	0.125825i	$-0.959842\pi$
$503$	−25.0714	−	25.0714i	−1.11788	−	1.11788i	−0.125825	−	0.992052i	$-0.540158\pi$
$504$	−8.83514	−	5.67248i	−0.393548	−	0.252672i
$505$	0.874077	+	15.1156i	0.0388959	+	0.672633i
$506$		−	1.30822i		−	0.0581576i
$507$	−15.2255	−	27.8688i	−0.676189	−	1.23770i
$508$	11.4227	−	11.4227i	0.506801	−	0.506801i
$509$	−30.4865			−1.35129			−0.675644	−	0.737228i	$-0.736134\pi$
$509$	−30.4865			−1.35129			−0.675644	+	0.737228i	$0.736134\pi$
$510$	12.4869	+	20.0154i	0.552928	+	0.886295i
$511$	45.6590			2.01984
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	5.18316	+	0.367253i	0.228842	+	0.0162146i
$514$			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	$-0.0743729\pi$
$522$	−5.49589	−	25.2105i	−0.240548	−	1.10343i
$523$	−13.0333	+	13.0333i	−0.569906	+	0.569906i	−0.932102	−	0.362196i	$-0.882027\pi$
$523$	−13.0333	+	13.0333i	−0.569906	+	0.569906i	0.362196	+	0.932102i	$0.382027\pi$
$524$	−3.12384			−0.136466
$525$	−29.8729	−	5.12341i	−1.30376	−	0.223604i
$526$	−10.4612			−0.456129
$527$	11.7989	−	11.7989i	0.513967	−	0.513967i
$528$	0.265313	+	0.485629i	0.0115463	+	0.0211343i
$529$		−	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
$537$	12.7946	−	6.99005i	0.552127	−	0.301643i
$538$	−8.89745	+	8.89745i	−0.383596	+	0.383596i
$539$	1.67686			0.0722277
$540$	11.6180	+	0.150749i	0.499958	+	0.00648720i
$541$	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
$543$	−6.14435	+	3.35683i	−0.263679	+	0.144055i
$544$			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	0.504899	−	0.863178i	$-0.331530\pi$
$547$	−8.37945	−	8.37945i	−0.358279	−	0.358279i	−0.863178	+	0.504899i	$0.831530\pi$
$548$	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
$552$	−3.40031	−	6.22393i	−0.144727	−	0.264908i
$553$	−7.43475	+	7.43475i	−0.316158	+	0.316158i
$554$	12.6813			0.538777
$555$	−7.62496	−	1.76617i	−0.323662	−	0.0749699i
$556$	13.6045			0.576960
$557$	−10.8415	+	10.8415i	−0.459369	+	0.459369i	−0.898448	−	0.439079i	$-0.855305\pi$
$557$	−10.8415	+	10.8415i	−0.459369	+	0.459369i	0.439079	+	0.898448i	$0.355305\pi$
$558$	−1.75045	−	8.02959i	−0.0741024	−	0.339920i
$559$			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	$-0.0662002\pi$
$563$	18.3171	+	18.3171i	0.771973	+	0.771973i	−0.206478	+	0.978451i	$0.566200\pi$
$564$	9.69479	+	2.84432i	0.408225	+	0.119768i
$565$	11.9697	+	10.6610i	0.503567	+	0.448512i
$566$			20.0164i			0.841353i
$567$	−10.9814	+	29.5219i	−0.461174	+	1.23980i
$568$	9.75855	−	9.75855i	0.409460	−	0.409460i
$569$	−5.23426			−0.219432			−0.109716	−	0.993963i	$-0.534994\pi$
$569$	−5.23426			−0.219432			−0.109716	+	0.993963i	$0.534994\pi$
$570$	3.77309	+	0.873962i	0.158037	+	0.0366062i
$571$	−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
$573$	−10.5796	−	19.3650i	−0.441970	−	0.808983i
$574$		−	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	0.692581	−	0.721340i	$-0.256473\pi$
$577$	−0.690796	−	0.690796i	−0.0287582	−	0.0287582i	−0.721340	+	0.692581i	$0.756473\pi$
$578$	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
$582$	4.76617	−	2.60389i	0.197564	−	0.107935i
$583$	0.369236	−	0.369236i	0.0152922	−	0.0152922i
$584$	−13.0462			−0.539857
$585$	−10.1029	−	36.1662i	−0.417705	−	1.49529i
$586$	27.2802			1.12694
$587$	22.7297	−	22.7297i	0.938154	−	0.938154i	−0.0600421	−	0.998196i	$-0.519123\pi$
$587$	22.7297	−	22.7297i	0.938154	−	0.938154i	0.998196	+	0.0600421i	$0.0191235\pi$
$588$	7.97776	−	4.35848i	0.328997	−	0.179741i
$589$		−	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	0.935311	+	0.353828i	$0.115120\pi$
$593$	31.3926	+	31.3926i	1.28914	+	1.28914i	0.353828	+	0.935311i	$0.384880\pi$
$594$	1.25392	−	1.08799i	0.0514491	−	0.0446407i
$595$	−47.5886	+	2.75188i	−1.95094	+	0.112816i
$596$		−	15.4792i		−	0.634052i
$597$	8.58344	+	15.7111i	0.351297	+	0.643014i
$598$	−16.2076	+	16.2076i	−0.662778	+	0.662778i
$599$	−27.0824			−1.10656			−0.553278	−	0.832997i	$-0.686623\pi$
$599$	−27.0824			−1.10656			−0.553278	+	0.832997i	$0.686623\pi$
$600$	8.53563	+	1.46392i	0.348466	+	0.0597642i
$601$	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
$603$	−46.3236	+	10.0985i	−1.88644	+	0.411244i
$604$			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	0.836193	−	0.548435i	$-0.184776\pi$
$607$	7.08962	+	7.08962i	0.287759	+	0.287759i	−0.548435	+	0.836193i	$0.684776\pi$
$608$	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
$612$	17.8542	−	3.89221i	0.721714	−	0.157333i
$613$	24.9931	−	24.9931i	1.00946	−	1.00946i	0.00950519	−	0.999955i	$-0.496974\pi$
$613$	24.9931	−	24.9931i	1.00946	−	1.00946i	0.999955	−	0.00950519i	$-0.00302564\pi$
$614$	3.87911			0.156548
$615$	14.4940	+	23.2327i	0.584455	+	0.936832i
$616$	−1.11816			−0.0450518
$617$	−1.14572	+	1.14572i	−0.0461251	+	0.0461251i	−0.729793	−	0.683668i	$-0.760384\pi$
$617$	−1.14572	+	1.14572i	−0.0461251	+	0.0461251i	0.683668	+	0.729793i	$0.260384\pi$
$618$	8.38596	+	15.3497i	0.337333	+	0.617454i
$619$		−	38.1788i		−	1.53454i	−0.641327	−	0.767268i	$-0.721616\pi$
$619$		−	38.1788i		−	1.53454i	0.641327	−	0.767268i	$-0.278384\pi$
$620$	−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
$627$	0.485629	−	0.265313i	0.0193942	−	0.0105956i
$628$	−5.84460	+	5.84460i	−0.233225	+	0.233225i
$629$	−12.3095			−0.490814
$630$	−11.5224	+	20.4553i	−0.459063	+	0.814958i
$631$	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
$633$	9.51601	−	5.19886i	0.378227	−	0.206636i
$634$		−	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	$0.664811\pi$
$642$	−5.83609	−	10.6824i	−0.230332	−	0.421601i
$643$	−17.5175	+	17.5175i	−0.690823	+	0.690823i	−0.962413	−	0.271590i	$-0.912450\pi$
$643$	−17.5175	+	17.5175i	−0.690823	+	0.690823i	0.271590	+	0.962413i	$0.412450\pi$
$644$	14.3305			0.564702
$645$	−7.98058	+	34.4539i	−0.314235	+	1.35662i
$646$	6.09118			0.239654
$647$	11.7619	−	11.7619i	0.462407	−	0.462407i	−0.437037	−	0.899444i	$-0.643972\pi$
$647$	11.7619	−	11.7619i	0.462407	−	0.462407i	0.899444	+	0.437037i	$0.143972\pi$
$648$	3.13772	−	8.43532i	0.123261	−	0.331371i
$649$		−	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	$-0.209999\pi$
$653$	4.52948	+	4.52948i	0.177252	+	0.177252i	−0.612905	+	0.790157i	$0.709999\pi$
$654$	−20.0871	−	5.89329i	−0.785468	−	0.230446i
$655$	0.403251	+	6.97348i	0.0157563	+	0.272476i
$656$			7.07028i			0.276048i
$657$	8.33643	+	38.2406i	0.325235	+	1.49191i
$658$	−14.4356	+	14.4356i	−0.562758	+	0.562758i
$659$	−2.17251			−0.0846292			−0.0423146	−	0.999104i	$-0.513473\pi$
$659$	−2.17251			−0.0846292			−0.0423146	+	0.999104i	$0.513473\pi$
$660$	1.04984	−	0.654957i	0.0408650	−	0.0254942i
$661$	−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
$663$	−28.3147	−	51.8273i	−1.09965	−	2.01280i
$664$			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
$672$	−5.31968	+	2.90629i	−0.205211	+	0.112113i
$673$	5.79495	−	5.79495i	0.223379	−	0.223379i	−0.586541	−	0.809920i	$-0.699511\pi$
$673$	5.79495	−	5.79495i	0.223379	−	0.223379i	0.809920	+	0.586541i	$0.199511\pi$
$674$	14.6670			0.564952
$675$	−1.16322	−	25.9547i	−0.0447723	−	0.998997i
$676$	−18.3347			−0.705182
$677$	3.09214	−	3.09214i	0.118841	−	0.118841i	−0.645185	−	0.764026i	$-0.723220\pi$
$677$	3.09214	−	3.09214i	0.118841	−	0.118841i	0.764026	+	0.645185i	$0.223220\pi$
$678$	10.8960	−	5.95278i	0.418458	−	0.228615i
$679$			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	0.993471	+	0.114089i	$0.0363947\pi$
$683$	28.9452	+	28.9452i	1.10756	+	1.10756i	0.114089	+	0.993471i	$0.463605\pi$
$684$	1.62081	−	2.52448i	0.0619731	−	0.0965258i
$685$	9.30513	−	10.4473i	0.355531	−	0.399173i
$686$		−	6.12979i		−	0.234037i
$687$	−18.0729	−	33.0807i	−0.689525	−	1.26211i
$688$	−6.45694	+	6.45694i	−0.246169	+	0.246169i
$689$	−9.14894			−0.348547
$690$	−13.4550	+	8.39407i	−0.512222	+	0.319557i
$691$	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
$693$	0.714493	+	3.27749i	0.0271413	+	0.124502i
$694$		−	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	$-0.211082\pi$
$702$	−29.0140	−	2.05579i	−1.09506	−	0.0775906i
$703$	−1.42898	+	1.42898i	−0.0538949	+	0.0538949i
$704$	0.319493			0.0120413
$705$	5.09801	−	22.0092i	0.192002	−	0.828916i
$706$	−7.20671			−0.271228
$707$	−16.7568	+	16.7568i	−0.630204	+	0.630204i
$708$	−6.23810	−	11.4182i	−0.234442	−	0.429123i
$709$			15.6457i			0.587587i	0.955869	+	0.293794i	$0.0949178\pi$
$709$			15.6457i			0.587587i	−0.955869	+	0.293794i	$0.905082\pi$
$710$	−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
$717$	21.6712	−	11.8396i	0.809324	−	0.442157i
$718$	25.0886	−	25.0886i	0.936297	−	0.936297i
$719$	11.4282			0.426200			0.213100	−	0.977030i	$-0.431644\pi$
$719$	11.4282			0.426200			0.213100	+	0.977030i	$0.431644\pi$
$720$	3.29231	−	5.84472i	0.122697	−	0.217820i
$721$	−35.3425			−1.31622
$722$	0.707107	−	0.707107i	0.0263158	−	0.0263158i
$723$	−46.0648	+	25.1665i	−1.71317	+	0.935953i
$724$			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	0.150429	−	0.988621i	$-0.451935\pi$
$727$	−22.6001	−	22.6001i	−0.838192	−	0.838192i	−0.988621	+	0.150429i	$0.951935\pi$
$728$	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
$732$	−6.72263	−	12.3051i	−0.248475	−	0.454810i
$733$	31.3451	−	31.3451i	1.15776	−	1.15776i	0.172801	−	0.984957i	$-0.444718\pi$
$733$	31.3451	−	31.3451i	1.15776	−	1.15776i	0.984957	−	0.172801i	$-0.0552819\pi$
$734$	4.83923			0.178619
$735$	−10.7594	−	17.2464i	−0.396868	−	0.636145i
$736$	−4.09469			−0.150932
$737$	−3.57033	+	3.57033i	−0.131515	+	0.131515i
$738$	20.7241	−	4.51785i	0.762865	−	0.166304i
$739$			43.9564i			1.61696i	0.588523	+	0.808481i	$0.299710\pi$
$739$			43.9564i			1.61696i	−0.588523	+	0.808481i	$0.700290\pi$
$740$	−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	$-0.400014\pi$
$743$	−17.5022	−	17.5022i	−0.642094	−	0.642094i	−0.951070	+	0.308976i	$0.900014\pi$
$744$	−4.55286	−	1.33575i	−0.166916	−	0.0489709i
$745$	−34.5548	+	1.99817i	−1.26599	+	0.0732075i
$746$			4.29019i			0.157075i
$747$	9.60412	−	2.09370i	0.351396	−	0.0766043i
$748$	1.37609	−	1.37609i	0.0503149	−	0.0503149i
$749$	24.5961			0.898723
$750$	2.16612	−	19.2434i	0.0790954	−	0.702669i
$751$	−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
$753$	21.6743	+	39.6726i	0.789854	+	1.44575i
$754$			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	0.987720	+	0.156236i	$0.0499360\pi$
$757$	31.4744	+	31.4744i	1.14396	+	1.14396i	0.156236	+	0.987720i	$0.450064\pi$
$758$	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	$0.777663\pi$
$762$	−24.5543	+	13.4147i	−0.889509	+	0.485964i
$763$	29.9098	−	29.9098i	1.08281	−	1.08281i
$764$	−12.7401			−0.460921
$765$	−10.9935	−	39.3542i	−0.397471	−	1.42285i
$766$	−18.3830			−0.664204
$767$	−29.7340	+	29.7340i	−1.07363	+	1.07363i
$768$	1.52000	−	0.830420i	0.0548483	−	0.0299652i
$769$		−	32.3859i		−	1.16786i	−0.811803	−	0.583932i	$-0.801513\pi$
$769$		−	32.3859i		−	1.16786i	0.811803	−	0.583932i	$-0.198487\pi$
$770$	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	0.955796	+	0.294032i	$0.0949971\pi$
$773$	34.7488	+	34.7488i	1.24983	+	1.24983i	0.294032	+	0.955796i	$0.405003\pi$
$774$	23.0523	+	14.8004i	0.828596	+	0.531989i
$775$	−13.6057	+	1.57881i	−0.488730	+	0.0567125i
$776$		−	3.13564i		−	0.112563i
$777$	−5.87327	−	10.7504i	−0.210702	−	0.385670i
$778$	−7.29977	+	7.29977i	−0.261709	+	0.261709i
$779$	7.07028			0.253319
$780$	−21.1208	−	4.89221i	−0.756245	−	0.175169i
$781$	−4.40921			−0.157774
$782$	−17.6363	+	17.6363i	−0.630672	+	0.630672i
$783$	−3.15869	+	44.5797i	−0.112882	+	1.59315i
$784$		−	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	0.819197	−	0.573512i	$-0.194420\pi$
$787$	6.89231	+	6.89231i	0.245684	+	0.245684i	−0.573512	+	0.819197i	$0.694420\pi$
$788$	−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
$792$	−0.204153	−	0.936483i	−0.00725426	−	0.0332765i
$793$	−32.0435	+	32.0435i	−1.13790	+	1.13790i
$794$	19.1098			0.678181
$795$	−6.16673	−	1.42840i	−0.218711	−	0.0506602i
$796$	10.3363			0.366359
$797$	27.7333	−	27.7333i	0.982365	−	0.982365i	−0.0174819	−	0.999847i	$-0.505565\pi$
$797$	27.7333	−	27.7333i	0.982365	−	0.982365i	0.999847	+	0.0174819i	$0.00556495\pi$
$798$	2.90629	+	5.31968i	0.102882	+	0.188315i
$799$		−	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
$807$	19.1260	−	10.4491i	0.673268	−	0.367825i
$808$	4.78794	−	4.78794i	0.168439	−	0.168439i
$809$	−40.8048			−1.43462			−0.717309	−	0.696755i	$-0.754627\pi$
$809$	−40.8048			−1.43462			−0.717309	+	0.696755i	$0.754627\pi$
$810$	−19.2355	−	5.91556i	−0.675868	−	0.207852i
$811$	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
$813$	2.77347	−	1.51522i	0.0972698	−	0.0531412i
$814$			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	$0.992149\pi$
$822$	−5.19570	−	9.51022i	−0.181221	−	0.331707i
$823$	−28.8276	+	28.8276i	−1.00487	+	1.00487i	−0.00487736	+	0.999988i	$0.501553\pi$
$823$	−28.8276	+	28.8276i	−1.00487	+	1.00487i	−0.999988	+	0.00487736i	$0.998447\pi$
$824$	10.0985			0.351796
$825$	−1.59761	−	2.25905i	−0.0556216	−	0.0786501i
$826$	26.2904			0.914759
$827$	−21.4341	+	21.4341i	−0.745336	+	0.745336i	−0.973599	−	0.228263i	$-0.926695\pi$
$827$	−21.4341	+	21.4341i	−0.745336	+	0.745336i	0.228263	+	0.973599i	$0.426695\pi$
$828$	2.61647	+	12.0022i	0.0909287	+	0.417104i
$829$		−	5.00012i		−	0.173661i	−0.996223	−	0.0868306i	$-0.972326\pi$
$829$		−	5.00012i		−	0.173661i	0.996223	−	0.0868306i	$-0.0276739\pi$
$830$	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
$837$	−1.00605	+	14.1987i	−0.0347741	+	0.490779i
$838$	0.972351	−	0.972351i	0.0335893	−	0.0335893i
$839$	43.4500			1.50006			0.750029	−	0.661404i	$-0.230039\pi$
$839$	43.4500			1.50006			0.750029	+	0.661404i	$0.230039\pi$
$840$	7.17454	+	11.5002i	0.247545	+	0.396793i
$841$	44.9750			1.55086
$842$	2.17623	−	2.17623i	0.0749978	−	0.0749978i
$843$	−15.0953	−	27.6304i	−0.519908	−	0.951640i
$844$		−	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
$852$	−20.9770	+	11.4603i	−0.718662	+	0.392625i
$853$	−13.6676	+	13.6676i	−0.467969	+	0.467969i	−0.901256	−	0.433287i	$-0.857354\pi$
$853$	−13.6676	+	13.6676i	−0.467969	+	0.467969i	0.433287	+	0.901256i	$0.357354\pi$
$854$	28.3324			0.969515
$855$	−5.84472	−	3.29231i	−0.199885	−	0.112595i
$856$	−7.02789			−0.240208
$857$	8.79374	−	8.79374i	0.300388	−	0.300388i	−0.540777	−	0.841166i	$-0.681870\pi$
$857$	8.79374	−	8.79374i	0.300388	−	0.300388i	0.841166	+	0.540777i	$0.181870\pi$
$858$	−2.71843	+	1.48515i	−0.0928056	+	0.0507023i
$859$			15.9374i			0.543777i	0.962329	+	0.271889i	$0.0876483\pi$
$859$			15.9374i			0.543777i	−0.962329	+	0.271889i	$0.912352\pi$
$860$	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	$-0.214790\pi$
$863$	4.58621	+	4.58621i	0.156116	+	0.156116i	−0.624727	+	0.780843i	$0.714790\pi$
$864$	−3.40536	−	3.92473i	−0.115853	−	0.133522i
$865$	10.2255	+	9.10751i	0.347676	+	0.309665i
$866$		−	0.920152i		−	0.0312680i
$867$	−16.6935	−	30.5557i	−0.566940	−	1.03773i
$868$	6.77924	−	6.77924i	0.230102	−	0.230102i
$869$	−0.959843			−0.0325604
$870$	−7.51684	+	32.4519i	−0.254845	+	1.10022i
$871$	88.4659			2.99755
$872$	−8.54618	+	8.54618i	−0.289410	+	0.289410i
$873$	−9.19105	+	2.00365i	−0.311070	+	0.0678131i
$874$			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	0.0624587	−	0.998048i	$-0.480106\pi$
$877$	−27.7067	−	27.7067i	−0.935589	−	0.935589i	−0.998048	+	0.0624587i	$0.980106\pi$
$878$	−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	$0.765000\pi$
$882$	−15.3843	+	3.35376i	−0.518015	+	0.112927i
$883$	14.0072	−	14.0072i	0.471379	−	0.471379i	−0.430982	−	0.902361i	$-0.641833\pi$
$883$	14.0072	−	14.0072i	0.471379	−	0.471379i	0.902361	+	0.430982i	$0.141833\pi$
$884$	−34.0969			−1.14680
$885$	−24.6841	+	15.3995i	−0.829747	+	0.517649i
$886$	1.17724			0.0395501
$887$	−2.74648	+	2.74648i	−0.0922178	+	0.0922178i	−0.751711	−	0.659493i	$-0.770771\pi$
$887$	−2.74648	+	2.74648i	−0.0922178	+	0.0922178i	0.659493	+	0.751711i	$0.270771\pi$
$888$	1.67818	+	3.07174i	0.0563160	+	0.103081i
$889$		−	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
$897$	34.8400	−	19.0341i	1.16327	−	0.635529i
$898$	21.6954	−	21.6954i	0.723984	−	0.723984i
$899$	23.5612			0.785809
$900$	−13.4724	−	6.59507i	−0.449079	−	0.219836i
$901$	−9.95541			−0.331663
$902$	1.59729	−	1.59729i	0.0531838	−	0.0531838i
$903$	−48.5767	+	26.5388i	−1.61653	+	0.883156i
$904$		−	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	−0.972240	−	0.233987i	$-0.924823\pi$
$907$	−36.3273	−	36.3273i	−1.20623	−	1.20623i	−0.233987	−	0.972240i	$-0.575177\pi$
$908$	−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	$-0.111035\pi$
$912$	−0.830420	−	1.52000i	−0.0274979	−	0.0503323i
$913$	0.740226	−	0.740226i	0.0244979	−	0.0244979i
$914$	5.35324			0.177069
$915$	−26.6013	+	16.5956i	−0.879413	+	0.548634i
$916$	−21.7636			−0.719090
$917$	−7.73065	+	7.73065i	−0.255289	+	0.255289i
$918$	−31.5715	−	2.23700i	−1.04202	−	0.0738320i
$919$			18.3864i			0.606510i	0.952909	+	0.303255i	$0.0980734\pi$
$919$			18.3864i			0.606510i	−0.952909	+	0.303255i	$0.901927\pi$
$920$	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
$927$	−6.45283	−	29.6002i	−0.211939	−	0.972197i
$928$	−6.08174	+	6.08174i	−0.199643	+	0.199643i
$929$	−40.9856			−1.34469			−0.672346	−	0.740237i	$-0.734713\pi$
$929$	−40.9856			−1.34469			−0.672346	+	0.740237i	$0.734713\pi$
$930$	−2.39412	+	10.3360i	−0.0785064	+	0.338930i
$931$	−5.24852			−0.172013
$932$	−3.78119	+	3.78119i	−0.123857	+	0.123857i
$933$	7.14279	+	13.0742i	0.233844	+	0.428029i
$934$			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	0.248492	−	0.968634i	$-0.420065\pi$
$937$	−22.0439	−	22.0439i	−0.720142	−	0.720142i	−0.968634	+	0.248492i	$0.920065\pi$
$938$	−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	$0.852176\pi$
$942$	12.5636	−	6.86384i	0.409344	−	0.223636i
$943$	−20.4712	+	20.4712i	−0.666633	+	0.666633i
$944$	−7.51199			−0.244494
$945$	29.1243	−	28.3782i	0.947415	−	0.923144i
$946$	2.91744			0.0948543
$947$	18.6928	−	18.6928i	0.607435	−	0.607435i	−0.334840	−	0.942275i	$-0.608682\pi$
$947$	18.6928	−	18.6928i	0.607435	−	0.607435i	0.942275	+	0.334840i	$0.108682\pi$
$948$	−4.56650	+	2.49481i	−0.148313	+	0.0810276i
$949$		−	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	$-0.393684\pi$
$953$	−19.0445	−	19.0445i	−0.616913	−	0.616913i	−0.944738	+	0.327825i	$0.893684\pi$
$954$	−2.64904	+	4.12600i	−0.0857660	+	0.133584i
$955$	1.64459	+	28.4402i	0.0532178	+	0.920304i
$956$		−	14.2573i		−	0.461115i
$957$	2.28192	+	4.17683i	0.0737641	+	0.135018i
$958$	12.6855	−	12.6855i	0.409850	−	0.409850i
$959$	21.8972			0.707097
$960$	−2.04999	−	3.28596i	−0.0661632	−	0.106054i
$961$	−23.4957			−0.757927
$962$	7.99906	−	7.99906i	0.257900	−	0.257900i
$963$	4.49076	+	20.5998i	0.144713	+	0.663821i
$964$			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	0.799120	−	0.601171i	$-0.205299\pi$
$967$	6.15556	+	6.15556i	0.197950	+	0.197950i	−0.601171	+	0.799120i	$0.705299\pi$
$968$	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	$-0.135936\pi$
$972$	−9.32802	+	12.4895i	−0.299196	+	0.400602i
$973$	33.6675	−	33.6675i	1.07933	−	1.07933i
$974$	−12.4026			−0.397403
$975$	−8.19464	+	47.7803i	−0.262439	+	1.53019i
$976$	−8.09546			−0.259129
$977$	−30.9999	+	30.9999i	−0.991776	+	0.991776i	−0.999966	−	0.00819042i	$-0.997393\pi$
$977$	−30.9999	+	30.9999i	−0.991776	+	0.991776i	0.00819042	+	0.999966i	$0.497393\pi$
$978$	−11.3787	−	20.8276i	−0.363850	−	0.665992i
$979$			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	$-0.307546\pi$
$983$	−7.97240	−	7.97240i	−0.254280	−	0.254280i	−0.822723	+	0.568443i	$0.807546\pi$
$984$	3.44752	−	11.7508i	0.109903	−	0.374602i
$985$	−29.0494	+	32.6152i	−0.925591	+	1.03921i
$986$			52.3895i			1.66842i
$987$	31.0309	−	16.9530i	0.987723	−	0.539621i
$988$	−3.95820	+	3.95820i	−0.125927	+	0.125927i
$989$	−37.3906			−1.18895
$990$	−2.06419	+	0.576628i	−0.0656044	+	0.0183264i
$991$	−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
$993$	−27.0522	+	14.7794i	−0.858475	+	0.469009i
$994$		−	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	0.897249	−	0.441524i	$-0.145562\pi$
$997$	14.3896	+	14.3896i	0.455725	+	0.455725i	−0.441524	+	0.897249i	$0.645562\pi$
$998$	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.77.8	✓	36
3.2	odd	2	inner	570.2.k.a.77.14	yes	36
5.3	odd	4	inner	570.2.k.a.533.14	yes	36
15.8	even	4	inner	570.2.k.a.533.8	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.a.77.8	✓	36	1.1	even	1	trivial
570.2.k.a.77.14	yes	36	3.2	odd	2	inner
570.2.k.a.533.8	yes	36	15.8	even	4	inner
570.2.k.a.533.14	yes	36	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.52000 - 0.830420i) q^{3} -1.00000i q^{4} +(-2.23234 + 0.129088i) q^{5} +(-0.487608 + 1.66200i) q^{6} +(-2.47472 - 2.47472i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.62081 - 2.52448i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.52000 - 0.830420i) 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} +(-0.830420 - 1.52000i) q^{12} +(-3.95820 + 3.95820i) q^{13} +3.49979 q^{14} +(-3.28596 + 2.04999i) q^{15} -1.00000 q^{16} +(-4.30711 + 4.30711i) q^{17} +(0.638992 + 2.93116i) 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} +(0.367253 - 5.18316i) q^{27} +(-2.47472 + 2.47472i) q^{28} -8.60087 q^{29} +(0.873962 - 3.77309i) q^{30} -2.73939 q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.265313 - 0.485629i) 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} +(5.31968 - 2.90629i) q^{42} +(6.45694 - 6.45694i) q^{43} -0.319493 q^{44} +(-3.29231 + 5.84472i) q^{45} +4.09469 q^{46} +(-4.12471 + 4.12471i) q^{47} +(-1.52000 + 0.830420i) 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} +(0.830420 + 1.52000i) q^{57} +(6.08174 - 6.08174i) q^{58} +7.51199 q^{59} +(2.04999 + 3.28596i) q^{60} +8.09546 q^{61} +(1.93704 - 1.93704i) q^{62} +(-10.2584 + 2.23634i) 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} +(2.93116 - 0.638992i) q^{72} +(-9.22508 + 9.22508i) q^{73} -2.02088 q^{74} +(7.07075 - 5.00045i) q^{75} +1.00000 q^{76} +(-0.790656 + 0.790656i) q^{77} +(-4.64848 - 8.50858i) 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} +(-13.0733 + 7.14233i) q^{87} +(0.225915 - 0.225915i) q^{88} -4.95832 q^{89} +(-1.80482 - 6.46085i) q^{90} +19.5909 q^{91} +(-2.89538 + 2.89538i) q^{92} +(-4.16388 + 2.27484i) 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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