LMFDB - Embedded newform 285.2.k.d.248.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(77,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, 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("285.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.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:	$2.27573645761$
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			248.1
Character	$\chi$	$=$	285.248
Dual form			285.2.k.d.77.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91639 - 1.91639i) q^{2} +(-0.520717 + 1.65192i) q^{3} +5.34506i q^{4} +(0.478119 + 2.18435i) q^{5} +(4.16362 - 2.16783i) q^{6} +(-1.54943 + 1.54943i) q^{7} +(6.41043 - 6.41043i) q^{8} +(-2.45771 - 1.72037i) q^{9} +O(q^{10})$	\(q+(-1.91639 - 1.91639i) q^{2} +(-0.520717 + 1.65192i) q^{3} +5.34506i q^{4} +(0.478119 + 2.18435i) q^{5} +(4.16362 - 2.16783i) q^{6} +(-1.54943 + 1.54943i) q^{7} +(6.41043 - 6.41043i) q^{8} +(-2.45771 - 1.72037i) q^{9} +(3.26980 - 5.10232i) q^{10} +2.77537i q^{11} +(-8.82964 - 2.78327i) q^{12} +(-3.18746 - 3.18746i) q^{13} +5.93863 q^{14} +(-3.85735 - 0.347614i) q^{15} -13.8796 q^{16} +(-3.06903 - 3.06903i) q^{17} +(1.41302 + 8.00681i) q^{18} -1.00000i q^{19} +(-11.6755 + 2.55558i) q^{20} +(-1.75273 - 3.36636i) q^{21} +(5.31867 - 5.31867i) q^{22} +(1.05802 - 1.05802i) q^{23} +(7.25153 + 13.9276i) q^{24} +(-4.54280 + 2.08876i) q^{25} +12.2168i q^{26} +(4.12169 - 3.16412i) q^{27} +(-8.28182 - 8.28182i) q^{28} +0.341074 q^{29} +(6.72601 + 8.05833i) q^{30} +6.05973 q^{31} +(13.7778 + 13.7778i) q^{32} +(-4.58469 - 1.44518i) q^{33} +11.7629i q^{34} +(-4.12533 - 2.64370i) q^{35} +(9.19549 - 13.1366i) q^{36} +(-5.33202 + 5.33202i) q^{37} +(-1.91639 + 1.91639i) q^{38} +(6.92521 - 3.60568i) q^{39} +(17.0676 + 10.9377i) q^{40} +0.460773i q^{41} +(-3.09234 + 9.81016i) q^{42} +(-3.43474 - 3.43474i) q^{43} -14.8345 q^{44} +(2.58282 - 6.19105i) q^{45} -4.05513 q^{46} +(1.93023 + 1.93023i) q^{47} +(7.22733 - 22.9280i) q^{48} +2.19851i q^{49} +(12.7086 + 4.70289i) q^{50} +(6.66790 - 3.47171i) q^{51} +(17.0372 - 17.0372i) q^{52} +(-4.19597 + 4.19597i) q^{53} +(-13.9624 - 1.83507i) q^{54} +(-6.06238 + 1.32695i) q^{55} +19.8651i q^{56} +(1.65192 + 0.520717i) q^{57} +(-0.653630 - 0.653630i) q^{58} -12.0249 q^{59} +(1.85802 - 20.6178i) q^{60} -12.4849 q^{61} +(-11.6128 - 11.6128i) q^{62} +(6.47366 - 1.14246i) q^{63} -25.0478i q^{64} +(5.43856 - 8.48653i) q^{65} +(6.01652 + 11.5556i) q^{66} +(-2.96882 + 2.96882i) q^{67} +(16.4042 - 16.4042i) q^{68} +(1.19683 + 2.29869i) q^{69} +(2.83937 + 12.9721i) q^{70} -9.44996i q^{71} +(-26.7833 + 4.72666i) q^{72} +(11.0638 + 11.0638i) q^{73} +20.4364 q^{74} +(-1.08496 - 8.59202i) q^{75} +5.34506 q^{76} +(-4.30025 - 4.30025i) q^{77} +(-20.1812 - 6.36150i) q^{78} -1.95283i q^{79} +(-6.63609 - 30.3179i) q^{80} +(3.08066 + 8.45633i) q^{81} +(0.883018 - 0.883018i) q^{82} +(-1.98775 + 1.98775i) q^{83} +(17.9934 - 9.36846i) q^{84} +(5.23649 - 8.17121i) q^{85} +13.1646i q^{86} +(-0.177603 + 0.563429i) q^{87} +(17.7913 + 17.7913i) q^{88} +2.63417 q^{89} +(-16.8141 + 6.91475i) q^{90} +9.87752 q^{91} +(5.65516 + 5.65516i) q^{92} +(-3.15540 + 10.0102i) q^{93} -7.39814i q^{94} +(2.18435 - 0.478119i) q^{95} +(-29.9341 + 15.5855i) q^{96} +(-7.00016 + 7.00016i) q^{97} +(4.21319 - 4.21319i) q^{98} +(4.77465 - 6.82104i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7}+O(q^{10}) $ 36 * q - 2 * q^3 + 4 * q^6 + 4 * q^7	$ 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7} - 4 q^{10} - 18 q^{12} - 8 q^{13} - 8 q^{15} - 84 q^{16} + 8 q^{21} + 40 q^{22} - 20 q^{25} - 14 q^{27} + 36 q^{28} + 28 q^{30} - 28 q^{33} + 92 q^{36} - 4 q^{37} - 20 q^{40} - 100 q^{42} + 16 q^{43} + 28 q^{45} - 24 q^{46} - 58 q^{48} + 32 q^{51} + 148 q^{52} - 72 q^{55} - 2 q^{57} - 12 q^{58} + 58 q^{60} - 112 q^{61} - 64 q^{63} + 92 q^{66} - 8 q^{67} + 8 q^{70} - 88 q^{72} + 76 q^{73} + 80 q^{75} + 36 q^{76} - 36 q^{78} + 4 q^{81} + 20 q^{82} - 28 q^{85} - 4 q^{87} + 140 q^{88} + 76 q^{90} - 24 q^{91} - 48 q^{93} + 32 q^{96} + 32 q^{97}+O(q^{100}) $ 36 * q - 2 * q^3 + 4 * q^6 + 4 * q^7 - 4 * q^10 - 18 * q^12 - 8 * q^13 - 8 * q^15 - 84 * q^16 + 8 * q^21 + 40 * q^22 - 20 * q^25 - 14 * q^27 + 36 * q^28 + 28 * q^30 - 28 * q^33 + 92 * q^36 - 4 * q^37 - 20 * q^40 - 100 * q^42 + 16 * q^43 + 28 * q^45 - 24 * q^46 - 58 * q^48 + 32 * q^51 + 148 * q^52 - 72 * q^55 - 2 * q^57 - 12 * q^58 + 58 * q^60 - 112 * q^61 - 64 * q^63 + 92 * q^66 - 8 * q^67 + 8 * q^70 - 88 * q^72 + 76 * q^73 + 80 * q^75 + 36 * q^76 - 36 * q^78 + 4 * q^81 + 20 * q^82 - 28 * q^85 - 4 * q^87 + 140 * q^88 + 76 * q^90 - 24 * q^91 - 48 * q^93 + 32 * q^96 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.91639	−	1.91639i	−1.35509	−	1.35509i	−0.879865	−	0.475224i	$-0.842367\pi$
$2$	−1.91639	−	1.91639i	−1.35509	−	1.35509i	−0.475224	−	0.879865i	$-0.657633\pi$
$3$	−0.520717	+	1.65192i	−0.300636	+	0.953739i
$3$	−0.520717	+	1.65192i	−0.300636	+	0.953739i
$4$			5.34506i			2.67253i
$5$	0.478119	+	2.18435i	0.213821	+	0.976873i
$5$	0.478119	+	2.18435i	0.213821	+	0.976873i
$6$	4.16362	−	2.16783i	1.69979	−	0.885013i
$7$	−1.54943	+	1.54943i	−0.585631	+	0.585631i	−0.936445	−	0.350814i	$-0.885905\pi$
$7$	−1.54943	+	1.54943i	−0.585631	+	0.585631i	0.350814	+	0.936445i	$0.385905\pi$
$8$	6.41043	−	6.41043i	2.26643	−	2.26643i
$9$	−2.45771	−	1.72037i	−0.819236	−	0.573457i
$10$	3.26980	−	5.10232i	1.03400	−	1.61350i
$11$			2.77537i			0.836804i	0.908262	+	0.418402i	$0.137410\pi$
$11$			2.77537i			0.836804i	−0.908262	+	0.418402i	$0.862590\pi$
$12$	−8.82964	−	2.78327i	−2.54890	−	0.803459i
$13$	−3.18746	−	3.18746i	−0.884043	−	0.884043i	0.109900	−	0.993943i	$-0.464947\pi$
$13$	−3.18746	−	3.18746i	−0.884043	−	0.884043i	−0.993943	+	0.109900i	$0.964947\pi$
$14$	5.93863			1.58716
$15$	−3.85735	−	0.347614i	−0.995964	−	0.0897535i
$16$	−13.8796			−3.46990
$17$	−3.06903	−	3.06903i	−0.744349	−	0.744349i	0.229063	−	0.973412i	$-0.426434\pi$
$17$	−3.06903	−	3.06903i	−0.744349	−	0.744349i	−0.973412	+	0.229063i	$0.926434\pi$
$18$	1.41302	+	8.00681i	0.333053	+	1.88722i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−11.6755	+	2.55558i	−2.61072	+	0.571444i
$21$	−1.75273	−	3.36636i	−0.382477	−	0.734601i
$22$	5.31867	−	5.31867i	1.13394	−	1.13394i
$23$	1.05802	−	1.05802i	0.220611	−	0.220611i	−0.588144	−	0.808756i	$-0.700141\pi$
$23$	1.05802	−	1.05802i	0.220611	−	0.220611i	0.808756	+	0.588144i	$0.200141\pi$
$24$	7.25153	+	13.9276i	1.48021	+	2.84295i
$25$	−4.54280	+	2.08876i	−0.908561	+	0.417752i
$26$			12.2168i			2.39591i
$27$	4.12169	−	3.16412i	0.793220	−	0.608936i
$28$	−8.28182	−	8.28182i	−1.56512	−	1.56512i
$29$	0.341074			0.0633359			0.0316680	−	0.999498i	$-0.489918\pi$
$29$	0.341074			0.0633359			0.0316680	+	0.999498i	$0.489918\pi$
$30$	6.72601	+	8.05833i	1.22800	+	1.47124i
$31$	6.05973			1.08836			0.544180	−	0.838969i	$-0.316841\pi$
$31$	6.05973			1.08836			0.544180	+	0.838969i	$0.316841\pi$
$32$	13.7778	+	13.7778i	2.43559	+	2.43559i
$33$	−4.58469	−	1.44518i	−0.798093	−	0.251573i
$34$			11.7629i			2.01732i
$35$	−4.12533	−	2.64370i	−0.697307	−	0.446867i
$36$	9.19549	−	13.1366i	1.53258	−	2.18943i
$37$	−5.33202	+	5.33202i	−0.876579	+	0.876579i	−0.993179	−	0.116600i	$-0.962801\pi$
$37$	−5.33202	+	5.33202i	−0.876579	+	0.876579i	0.116600	+	0.993179i	$0.462801\pi$
$38$	−1.91639	+	1.91639i	−0.310879	+	0.310879i
$39$	6.92521	−	3.60568i	1.10892	−	0.577371i
$40$	17.0676	+	10.9377i	2.69862	+	1.72940i
$41$			0.460773i			0.0719606i	0.999352	+	0.0359803i	$0.0114554\pi$
$41$			0.460773i			0.0719606i	−0.999352	+	0.0359803i	$0.988545\pi$
$42$	−3.09234	+	9.81016i	−0.477159	+	1.51374i
$43$	−3.43474	−	3.43474i	−0.523794	−	0.523794i	0.394921	−	0.918715i	$-0.370772\pi$
$43$	−3.43474	−	3.43474i	−0.523794	−	0.523794i	−0.918715	+	0.394921i	$0.870772\pi$
$44$	−14.8345			−2.23639
$45$	2.58282	−	6.19105i	0.385024	−	0.922907i
$46$	−4.05513			−0.597896
$47$	1.93023	+	1.93023i	0.281553	+	0.281553i	0.833728	−	0.552175i	$-0.186202\pi$
$47$	1.93023	+	1.93023i	0.281553	+	0.281553i	−0.552175	+	0.833728i	$0.686202\pi$
$48$	7.22733	−	22.9280i	1.04318	−	3.30937i
$49$			2.19851i			0.314073i
$50$	12.7086	+	4.70289i	1.79727	+	0.665089i
$51$	6.66790	−	3.47171i	0.933693	−	0.486137i
$52$	17.0372	−	17.0372i	2.36263	−	2.36263i
$53$	−4.19597	+	4.19597i	−0.576360	+	0.576360i	−0.933899	−	0.357538i	$-0.883616\pi$
$53$	−4.19597	+	4.19597i	−0.576360	+	0.576360i	0.357538	+	0.933899i	$0.383616\pi$
$54$	−13.9624	−	1.83507i	−1.90005	−	0.249722i
$55$	−6.06238	+	1.32695i	−0.817451	+	0.178926i
$56$			19.8651i			2.65458i
$57$	1.65192	+	0.520717i	0.218803	+	0.0689706i
$58$	−0.653630	−	0.653630i	−0.0858258	−	0.0858258i
$59$	−12.0249			−1.56551			−0.782757	−	0.622327i	$-0.786187\pi$
$59$	−12.0249			−1.56551			−0.782757	+	0.622327i	$0.786187\pi$
$60$	1.85802	−	20.6178i	0.239869	−	2.66175i
$61$	−12.4849			−1.59853			−0.799263	−	0.600981i	$-0.794777\pi$
$61$	−12.4849			−1.59853			−0.799263	+	0.600981i	$0.794777\pi$
$62$	−11.6128	−	11.6128i	−1.47482	−	1.47482i
$63$	6.47366	−	1.14246i	0.815604	−	0.143936i
$64$		−	25.0478i		−	3.13098i
$65$	5.43856	−	8.48653i	0.674570	−	1.05262i
$66$	6.01652	+	11.5556i	0.740582	+	1.42239i
$67$	−2.96882	+	2.96882i	−0.362699	+	0.362699i	−0.864806	−	0.502107i	$-0.832558\pi$
$67$	−2.96882	+	2.96882i	−0.362699	+	0.362699i	0.502107	+	0.864806i	$0.332558\pi$
$68$	16.4042	−	16.4042i	1.98930	−	1.98930i
$69$	1.19683	+	2.29869i	0.144082	+	0.276730i
$70$	2.83937	+	12.9721i	0.339369	+	1.55046i
$71$		−	9.44996i		−	1.12150i	−0.827984	−	0.560752i	$-0.810512\pi$
$71$		−	9.44996i		−	1.12150i	0.827984	−	0.560752i	$-0.189488\pi$
$72$	−26.7833	+	4.72666i	−3.15644	+	0.557042i
$73$	11.0638	+	11.0638i	1.29492	+	1.29492i	0.931706	+	0.363214i	$0.118321\pi$
$73$	11.0638	+	11.0638i	1.29492	+	1.29492i	0.363214	+	0.931706i	$0.381679\pi$
$74$	20.4364			2.37569
$75$	−1.08496	−	8.59202i	−0.125280	−	0.992121i
$76$	5.34506			0.613121
$77$	−4.30025	−	4.30025i	−0.490058	−	0.490058i
$78$	−20.1812	−	6.36150i	−2.28508	−	0.720298i
$79$		−	1.95283i		−	0.219710i	−0.993948	−	0.109855i	$-0.964961\pi$
$79$		−	1.95283i		−	0.219710i	0.993948	−	0.109855i	$-0.0350387\pi$
$80$	−6.63609	−	30.3179i	−0.741937	−	3.38965i
$81$	3.08066	+	8.45633i	0.342295	+	0.939593i
$82$	0.883018	−	0.883018i	0.0975130	−	0.0975130i
$83$	−1.98775	+	1.98775i	−0.218184	+	0.218184i	−0.807733	−	0.589549i	$-0.799306\pi$
$83$	−1.98775	+	1.98775i	−0.218184	+	0.218184i	0.589549	+	0.807733i	$0.299306\pi$
$84$	17.9934	−	9.36846i	1.96324	−	1.02218i
$85$	5.23649	−	8.17121i	0.567977	−	0.886292i
$86$			13.1646i			1.41957i
$87$	−0.177603	+	0.563429i	−0.0190411	+	0.0604059i
$88$	17.7913	+	17.7913i	1.89656	+	1.89656i
$89$	2.63417			0.279222			0.139611	−	0.990206i	$-0.455415\pi$
$89$	2.63417			0.279222			0.139611	+	0.990206i	$0.455415\pi$
$90$	−16.8141	+	6.91475i	−1.77236	+	0.728878i
$91$	9.87752			1.03545
$92$	5.65516	+	5.65516i	0.589591	+	0.589591i
$93$	−3.15540	+	10.0102i	−0.327200	+	1.03801i
$94$		−	7.39814i		−	0.763060i
$95$	2.18435	−	0.478119i	0.224110	−	0.0490540i
$96$	−29.9341	+	15.5855i	−3.05514	+	1.59069i
$97$	−7.00016	+	7.00016i	−0.710759	+	0.710759i	−0.966694	−	0.255935i	$-0.917617\pi$
$97$	−7.00016	+	7.00016i	−0.710759	+	0.710759i	0.255935	+	0.966694i	$0.417617\pi$
$98$	4.21319	−	4.21319i	0.425596	−	0.425596i
$99$	4.77465	−	6.82104i	0.479871	−	0.685540i
$100$	−11.1646	−	24.2816i	−1.11646	−	2.42816i
$101$			4.85779i			0.483369i	0.970355	+	0.241684i	$0.0776998\pi$
$101$			4.85779i			0.483369i	−0.970355	+	0.241684i	$0.922300\pi$
$102$	−19.4314	−	6.12513i	−1.92400	−	0.606479i
$103$	5.35243	+	5.35243i	0.527391	+	0.527391i	0.919793	−	0.392403i	$-0.128356\pi$
$103$	5.35243	+	5.35243i	0.527391	+	0.527391i	−0.392403	+	0.919793i	$0.628356\pi$
$104$	−40.8660			−4.00724
$105$	6.51532	−	5.43811i	0.635830	−	0.530705i
$106$	16.0822			1.56204
$107$	11.6658	+	11.6658i	1.12778	+	1.12778i	0.990538	+	0.137240i	$0.0438231\pi$
$107$	11.6658	+	11.6658i	1.12778	+	1.12778i	0.137240	+	0.990538i	$0.456177\pi$
$108$	16.9124	+	22.0307i	1.62740	+	2.11991i
$109$		−	8.24149i		−	0.789391i	−0.918812	−	0.394696i	$-0.870850\pi$
$109$		−	8.24149i		−	0.789391i	0.918812	−	0.394696i	$-0.129150\pi$
$110$	14.1608	+	9.07490i	1.35018	+	0.865258i
$111$	−6.03163	−	11.5846i	−0.572497	−	1.09956i
$112$	21.5055	−	21.5055i	2.03208	−	2.03208i
$113$	−1.81897	+	1.81897i	−0.171114	+	0.171114i	−0.787469	−	0.616355i	$-0.788609\pi$
$113$	−1.81897	+	1.81897i	−0.171114	+	0.171114i	0.616355	+	0.787469i	$0.288609\pi$
$114$	−2.16783	−	4.16362i	−0.203036	−	0.389958i
$115$	2.81694	+	1.80522i	0.262681	+	0.168338i
$116$			1.82306i			0.169267i
$117$	2.35024	+	13.3175i	0.217279	+	1.23120i
$118$	23.0444	+	23.0444i	2.12141	+	2.12141i
$119$	9.51052			0.871828
$120$	−26.9556	+	22.4989i	−2.46070	+	2.05386i
$121$	3.29735			0.299759
$122$	23.9259	+	23.9259i	2.16615	+	2.16615i
$123$	−0.761161	−	0.239932i	−0.0686316	−	0.0216339i
$124$			32.3897i			2.90868i
$125$	−6.73459	−	8.92442i	−0.602360	−	0.798224i
$126$	−14.5954	−	10.2166i	−1.30026	−	0.910170i
$127$	2.22493	−	2.22493i	0.197430	−	0.197430i	−0.601467	−	0.798897i	$-0.705417\pi$
$127$	2.22493	−	2.22493i	0.197430	−	0.197430i	0.798897	+	0.601467i	$0.205417\pi$
$128$	−20.4458	+	20.4458i	−1.80717	+	1.80717i
$129$	7.46247	−	3.88541i	0.657034	−	0.342091i
$130$	−26.6858	+	5.84109i	−2.34050	+	0.512297i
$131$			10.5155i			0.918741i	0.888245	+	0.459370i	$0.151925\pi$
$131$			10.5155i			0.918741i	−0.888245	+	0.459370i	$0.848075\pi$
$132$	7.72458	−	24.5055i	0.672338	−	2.13293i
$133$	1.54943	+	1.54943i	0.134353	+	0.134353i
$134$	11.3788			0.982977
$135$	8.88222	+	7.49041i	0.764460	+	0.644671i
$136$	−39.3476			−3.37403
$137$	−10.5193	−	10.5193i	−0.898728	−	0.898728i	0.0965958	−	0.995324i	$-0.469205\pi$
$137$	−10.5193	−	10.5193i	−0.898728	−	0.898728i	−0.995324	+	0.0965958i	$0.969205\pi$
$138$	2.11157	−	6.69877i	0.179749	−	0.570237i
$139$		−	4.15876i		−	0.352741i	−0.984324	−	0.176371i	$-0.943564\pi$
$139$		−	4.15876i		−	0.352741i	0.984324	−	0.176371i	$-0.0564357\pi$
$140$	14.1307	−	22.0501i	1.19427	−	1.86358i
$141$	−4.19370	+	2.18349i	−0.353174	+	0.183883i
$142$	−18.1098	+	18.1098i	−1.51974	+	1.51974i
$143$	8.84637	−	8.84637i	0.739771	−	0.739771i
$144$	34.1120	+	23.8780i	2.84266	+	1.98983i
$145$	0.163074	+	0.745027i	0.0135426	+	0.0618711i
$146$		−	42.4050i		−	3.50946i
$147$	−3.63177	−	1.14480i	−0.299543	−	0.0944215i
$148$	−28.5000	−	28.5000i	−2.34269	−	2.34269i
$149$	−7.19933			−0.589792			−0.294896	−	0.955529i	$-0.595285\pi$
$149$	−7.19933			−0.589792			−0.294896	+	0.955529i	$0.595285\pi$
$150$	−14.3864	+	18.5448i	−1.17465	+	1.51418i
$151$	−12.0309			−0.979064			−0.489532	−	0.871985i	$-0.662832\pi$
$151$	−12.0309			−0.979064			−0.489532	+	0.871985i	$0.662832\pi$
$152$	−6.41043	−	6.41043i	−0.519955	−	0.519955i
$153$	2.26291	+	12.8226i	0.182946	+	1.03665i
$154$			16.4819i			1.32815i
$155$	2.89727	+	13.2366i	0.232714	+	1.06319i
$156$	19.2726	+	37.0157i	1.54304	+	2.96363i
$157$	−16.2197	+	16.2197i	−1.29447	+	1.29447i	−0.362483	+	0.931990i	$0.618071\pi$
$157$	−16.2197	+	16.2197i	−1.29447	+	1.29447i	−0.931990	+	0.362483i	$0.881929\pi$
$158$	−3.74237	+	3.74237i	−0.297727	+	0.297727i
$159$	−4.74651	−	9.11633i	−0.376423	−	0.722972i
$160$	−23.5081	+	36.6829i	−1.85848	+	2.90004i
$161$			3.27865i			0.258394i
$162$	10.3019	−	22.1093i	0.809391	−	1.73707i
$163$	6.98240	+	6.98240i	0.546904	+	0.546904i	0.925544	−	0.378640i	$-0.123608\pi$
$163$	6.98240	+	6.98240i	0.546904	+	0.546904i	−0.378640	+	0.925544i	$0.623608\pi$
$164$	−2.46286			−0.192317
$165$	0.964756	−	10.7056i	0.0751061	−	0.833427i
$166$	7.61860			0.591318
$167$	3.03997	+	3.03997i	0.235240	+	0.235240i	0.814876	−	0.579636i	$-0.196805\pi$
$167$	3.03997	+	3.03997i	0.235240	+	0.235240i	−0.579636	+	0.814876i	$0.696805\pi$
$168$	−32.8156	−	10.3441i	−2.53178	−	0.798063i
$169$			7.31982i			0.563063i
$170$	−25.6943	+	5.62406i	−1.97066	+	0.431345i
$171$	−1.72037	+	2.45771i	−0.131560	+	0.187946i
$172$	18.3589	−	18.3589i	1.39986	−	1.39986i
$173$	7.67046	−	7.67046i	0.583175	−	0.583175i	−0.352600	−	0.935774i	$-0.614702\pi$
$173$	7.67046	−	7.67046i	0.583175	−	0.583175i	0.935774	+	0.352600i	$0.114702\pi$
$174$	1.42010	−	0.739391i	0.107658	−	0.0560531i
$175$	3.80238	−	10.2752i	0.287433	−	0.776730i
$176$		−	38.5209i		−	2.90362i
$177$	6.26159	−	19.8643i	0.470650	−	1.49309i
$178$	−5.04809	−	5.04809i	−0.378370	−	0.378370i
$179$	1.98934			0.148691			0.0743453	−	0.997233i	$-0.476313\pi$
$179$	1.98934			0.148691			0.0743453	+	0.997233i	$0.476313\pi$
$180$	33.0915	+	13.8053i	2.46650	+	1.02899i
$181$	4.67919			0.347801			0.173901	−	0.984763i	$-0.444363\pi$
$181$	4.67919			0.347801			0.173901	+	0.984763i	$0.444363\pi$
$182$	−18.9291	−	18.9291i	−1.40312	−	1.40312i
$183$	6.50109	−	20.6241i	0.480575	−	1.52458i
$184$		−	13.5647i		−	1.00000i
$185$	−14.1964	−	9.09769i	−1.04374	−	0.668875i
$186$	25.2304	−	13.1365i	1.84998	−	0.963212i
$187$	8.51768	−	8.51768i	0.622874	−	0.622874i
$188$	−10.3172	+	10.3172i	−0.752461	+	0.752461i
$189$	−1.48369	+	11.2889i	−0.107923	+	0.821146i
$190$	−5.10232	−	3.26980i	−0.370161	−	0.237217i
$191$			16.7170i			1.20960i	0.796377	+	0.604801i	$0.206747\pi$
$191$			16.7170i			1.20960i	−0.796377	+	0.604801i	$0.793253\pi$
$192$	41.3771	+	13.0428i	2.98614	+	0.941286i
$193$	−7.47975	−	7.47975i	−0.538404	−	0.538404i	0.384656	−	0.923060i	$-0.374320\pi$
$193$	−7.47975	−	7.47975i	−0.538404	−	0.538404i	−0.923060	+	0.384656i	$0.874320\pi$
$194$	26.8300			1.92628
$195$	11.1872	+	13.4032i	0.801129	+	0.959821i
$196$	−11.7512			−0.839369
$197$	7.94055	+	7.94055i	0.565741	+	0.565741i	0.930932	−	0.365192i	$-0.118997\pi$
$197$	7.94055	+	7.94055i	0.565741	+	0.565741i	−0.365192	+	0.930932i	$0.618997\pi$
$198$	−22.2218	+	3.92166i	−1.57924	+	0.278700i
$199$		−	2.10866i		−	0.149479i	−0.997203	−	0.0747396i	$-0.976187\pi$
$199$		−	2.10866i		−	0.149479i	0.997203	−	0.0747396i	$-0.0238126\pi$
$200$	−15.7315	+	42.5112i	−1.11238	+	3.00600i
$201$	−3.35835	−	6.45017i	−0.236879	−	0.454960i
$202$	9.30941	−	9.30941i	0.655007	−	0.655007i
$203$	−0.528472	+	0.528472i	−0.0370915	+	0.0370915i
$204$	18.5565	+	35.6404i	1.29922	+	2.49532i
$205$	−1.00649	+	0.220304i	−0.0702963	+	0.0153867i
$206$		−	20.5146i		−	1.42932i
$207$	−4.42047	+	0.780115i	−0.307244	+	0.0542217i
$208$	44.2406	+	44.2406i	3.06754	+	3.06754i
$209$	2.77537			0.191976
$210$	−22.9074	−	2.06435i	−1.58076	−	0.142454i
$211$	2.30777			0.158874			0.0794368	−	0.996840i	$-0.474688\pi$
$211$	2.30777			0.158874			0.0794368	+	0.996840i	$0.474688\pi$
$212$	−22.4277	−	22.4277i	−1.54034	−	1.54034i
$213$	15.6106	+	4.92075i	1.06962	+	0.337164i
$214$		−	44.7124i		−	3.05648i
$215$	5.86048	−	9.14491i	0.399682	−	0.623678i
$216$	6.13843	−	46.7052i	0.417667	−	3.17789i
$217$	−9.38915	+	9.38915i	−0.637377	+	0.637377i
$218$	−15.7939	+	15.7939i	−1.06970	+	1.06970i
$219$	−24.0377	+	12.5155i	−1.62432	+	0.845716i
$220$	−7.09266	−	32.4038i	−0.478187	−	2.18466i
$221$			19.5648i			1.31607i
$222$	−10.6416	+	33.7594i	−0.714217	+	2.26578i
$223$	10.1353	+	10.1353i	0.678708	+	0.678708i	0.959708	−	0.281000i	$-0.0906661\pi$
$223$	10.1353	+	10.1353i	0.678708	+	0.678708i	−0.281000	+	0.959708i	$0.590666\pi$
$224$	−42.6955			−2.85271
$225$	14.7583	+	2.68174i	0.983889	+	0.178783i
$226$	6.97169			0.463750
$227$	5.56895	+	5.56895i	0.369624	+	0.369624i	0.867340	−	0.497716i	$-0.165828\pi$
$227$	5.56895	+	5.56895i	0.369624	+	0.369624i	−0.497716	+	0.867340i	$0.665828\pi$
$228$	−2.78327	+	8.82964i	−0.184326	+	0.584757i
$229$		−	17.5759i		−	1.16145i	−0.814101	−	0.580723i	$-0.802770\pi$
$229$		−	17.5759i		−	1.16145i	0.814101	−	0.580723i	$-0.197230\pi$
$230$	−1.93883	−	8.85784i	−0.127843	−	0.584069i
$231$	9.34289	−	4.86447i	0.614717	−	0.320059i
$232$	2.18643	−	2.18643i	0.143546	−	0.143546i
$233$	−3.20196	+	3.20196i	−0.209767	+	0.209767i	−0.804169	−	0.594401i	$-0.797389\pi$
$233$	−3.20196	+	3.20196i	−0.209767	+	0.209767i	0.594401	+	0.804169i	$0.297389\pi$
$234$	21.0174	−	30.0253i	1.37395	−	1.96282i
$235$	−3.29343	+	5.13919i	−0.214840	+	0.335244i
$236$		−	64.2741i		−	4.18389i
$237$	3.22593	+	1.01687i	0.209546	+	0.0660529i
$238$	−18.2258	−	18.2258i	−1.18140	−	1.18140i
$239$	−3.93355			−0.254440			−0.127220	−	0.991875i	$-0.540605\pi$
$239$	−3.93355			−0.254440			−0.127220	+	0.991875i	$0.540605\pi$
$240$	53.5384	+	4.82474i	3.45589	+	0.311435i
$241$	13.4170			0.864268			0.432134	−	0.901809i	$-0.357761\pi$
$241$	13.4170			0.864268			0.432134	+	0.901809i	$0.357761\pi$
$242$	−6.31899	−	6.31899i	−0.406200	−	0.406200i
$243$	−15.5734	+	0.685655i	−0.999032	+	0.0439848i
$244$		−	66.7325i		−	4.27211i
$245$	−4.80232	+	1.05115i	−0.306809	+	0.0671554i
$246$	0.998876	+	1.91848i	0.0636860	+	0.122318i
$247$	−3.18746	+	3.18746i	−0.202813	+	0.202813i
$248$	38.8455	−	38.8455i	2.46669	−	2.46669i
$249$	−2.24856	−	4.31868i	−0.142497	−	0.273685i
$250$	−4.19654	+	30.0087i	−0.265413	+	1.89792i
$251$			22.6412i			1.42910i	0.699583	+	0.714551i	$0.253369\pi$
$251$			22.6412i			1.42910i	−0.699583	+	0.714551i	$0.746631\pi$
$252$	6.10650	+	34.6021i	0.384674	+	2.17973i
$253$	2.93638	+	2.93638i	0.184609	+	0.184609i
$254$	−8.52763			−0.535071
$255$	10.7715	+	12.9052i	0.674537	+	0.808153i
$256$	28.2683			1.76677
$257$	−17.9072	−	17.9072i	−1.11702	−	1.11702i	−0.992176	−	0.124844i	$-0.960157\pi$
$257$	−17.9072	−	17.9072i	−1.11702	−	1.11702i	−0.124844	−	0.992176i	$-0.539843\pi$
$258$	−21.7469	−	6.85502i	−1.35390	−	0.426775i
$259$		−	16.5232i		−	1.02670i
$260$	45.3610	+	29.0694i	2.81317	+	1.80281i
$261$	−0.838261	−	0.586774i	−0.0518871	−	0.0363204i
$262$	20.1517	−	20.1517i	1.24498	−	1.24498i
$263$	−17.9317	+	17.9317i	−1.10572	+	1.10572i	−0.112008	+	0.993707i	$0.535728\pi$
$263$	−17.9317	+	17.9317i	−1.10572	+	1.10572i	−0.993707	+	0.112008i	$0.964272\pi$
$264$	−38.6541	+	20.1256i	−2.37899	+	1.23865i
$265$	−11.1716	−	7.15931i	−0.686269	−	0.439793i
$266$		−	5.93863i		−	0.364120i
$267$	−1.37166	+	4.35145i	−0.0839441	+	0.266304i
$268$	−15.8685	−	15.8685i	−0.969323	−	0.969323i
$269$	−7.65484			−0.466724			−0.233362	−	0.972390i	$-0.574973\pi$
$269$	−7.65484			−0.466724			−0.233362	+	0.972390i	$0.574973\pi$
$270$	−2.66725	−	31.3763i	−0.162324	−	1.90950i
$271$	23.6973			1.43951			0.719754	−	0.694230i	$-0.244255\pi$
$271$	23.6973			1.43951			0.719754	+	0.694230i	$0.244255\pi$
$272$	42.5969	+	42.5969i	2.58281	+	2.58281i
$273$	−5.14339	+	16.3169i	−0.311292	+	0.987545i
$274$			40.3182i			2.43571i
$275$	−5.79708	−	12.6079i	−0.349577	−	0.760288i
$276$	−12.2866	+	6.39716i	−0.739568	+	0.385064i
$277$	−19.2242	+	19.2242i	−1.15507	+	1.15507i	−0.169547	+	0.985522i	$0.554230\pi$
$277$	−19.2242	+	19.2242i	−1.15507	+	1.15507i	−0.985522	+	0.169547i	$0.945770\pi$
$278$	−7.96978	+	7.96978i	−0.477996	+	0.477996i
$279$	−14.8930	−	10.4250i	−0.891624	−	0.624127i
$280$	−43.3924	+	9.49787i	−2.59319	+	0.567606i
$281$			13.1510i			0.784521i	0.919854	+	0.392260i	$0.128307\pi$
$281$			13.1510i			0.784521i	−0.919854	+	0.392260i	$0.871693\pi$
$282$	12.2212	+	3.85234i	0.727760	+	0.229403i
$283$	−6.91873	−	6.91873i	−0.411276	−	0.411276i	0.470907	−	0.882183i	$-0.343927\pi$
$283$	−6.91873	−	6.91873i	−0.411276	−	0.411276i	−0.882183	+	0.470907i	$0.843927\pi$
$284$	50.5106			2.99725
$285$	−0.347614	+	3.85735i	−0.0205909	+	0.228490i
$286$	−33.9061			−2.00491
$287$	−0.713937	−	0.713937i	−0.0421424	−	0.0421424i
$288$	−10.1589	−	57.5646i	−0.598617	−	3.39202i
$289$			1.83789i			0.108111i
$290$	1.11525	−	1.74027i	0.0654895	−	0.102192i
$291$	−7.91864	−	15.2088i	−0.464199	−	0.891558i
$292$	−59.1367	+	59.1367i	−3.46072	+	3.46072i
$293$	0.0332012	−	0.0332012i	0.00193964	−	0.00193964i	−0.706136	−	0.708076i	$-0.749563\pi$
$293$	0.0332012	−	0.0332012i	0.00193964	−	0.00193964i	0.708076	+	0.706136i	$0.249563\pi$
$294$	4.76599	+	9.15375i	0.277958	+	0.533857i
$295$	−5.74935	−	26.2667i	−0.334740	−	1.52931i
$296$			68.3612i			3.97341i
$297$	8.78159	+	11.4392i	0.509560	+	0.663770i
$298$	13.7967	+	13.7967i	0.799221	+	0.799221i
$299$	−6.74477			−0.390060
$300$	45.9249	−	5.79918i	2.65148	−	0.334816i
$301$	10.6438			0.613500
$302$	23.0559	+	23.0559i	1.32672	+	1.32672i
$303$	−8.02471	−	2.52954i	−0.461007	−	0.145318i
$304$			13.8796i			0.796049i
$305$	−5.96926	−	27.2714i	−0.341799	−	1.56156i
$306$	20.2365	−	28.9097i	1.15684	−	1.65266i
$307$	14.8603	−	14.8603i	0.848121	−	0.848121i	−0.141778	−	0.989899i	$-0.545282\pi$
$307$	14.8603	−	14.8603i	0.848121	−	0.848121i	0.989899	+	0.141778i	$0.0452818\pi$
$308$	22.9851	−	22.9851i	1.30970	−	1.30970i
$309$	−11.6289	+	6.05471i	−0.661546	+	0.344440i
$310$	19.8141	−	30.9187i	1.12537	−	1.75606i
$311$			20.7689i			1.17770i	0.808244	+	0.588848i	$0.200418\pi$
$311$			20.7689i			1.17770i	−0.808244	+	0.588848i	$0.799582\pi$
$312$	21.2796	−	67.5076i	1.20472	−	3.82186i
$313$	17.9949	+	17.9949i	1.01713	+	1.01713i	0.999851	+	0.0172821i	$0.00550135\pi$
$313$	17.9949	+	17.9949i	1.01713	+	1.01713i	0.0172821	+	0.999851i	$0.494499\pi$
$314$	62.1664			3.50825
$315$	5.59071	+	13.5945i	0.315001	+	0.765965i
$316$	10.4380			0.587183
$317$	−20.9864	−	20.9864i	−1.17871	−	1.17871i	−0.980073	−	0.198640i	$-0.936348\pi$
$317$	−20.9864	−	20.9864i	−1.17871	−	1.17871i	−0.198640	−	0.980073i	$-0.563652\pi$
$318$	−8.37426	+	26.5665i	−0.469605	+	1.48978i
$319$			0.946606i			0.0529998i
$320$	54.7134	−	11.9758i	3.05857	−	0.669470i
$321$	−25.3456	+	13.1965i	−1.41466	+	0.736555i
$322$	6.28316	−	6.28316i	0.350147	−	0.350147i
$323$	−3.06903	+	3.06903i	−0.170765	+	0.170765i
$324$	−45.1996	+	16.4663i	−2.51109	+	0.914795i
$325$	21.1379	+	7.82217i	1.17252	+	0.433896i
$326$		−	26.7619i		−	1.48221i
$327$	13.6143	+	4.29148i	0.752873	+	0.237320i
$328$	2.95375	+	2.95375i	0.163094	+	0.163094i
$329$	−5.98154			−0.329773
$330$	−22.3648	+	18.6671i	−1.23114	+	1.02759i
$331$	2.39369			0.131569			0.0657845	−	0.997834i	$-0.479045\pi$
$331$	2.39369			0.131569			0.0657845	+	0.997834i	$0.479045\pi$
$332$	−10.6247	−	10.6247i	−0.583105	−	0.583105i
$333$	22.2776	−	3.93150i	1.22081	−	0.215445i
$334$		−	11.6515i		−	0.637542i
$335$	−7.90439	−	5.06550i	−0.431863	−	0.276758i
$336$	24.3272	+	46.7237i	1.32716	+	2.54899i
$337$	1.11402	−	1.11402i	0.0606843	−	0.0606843i	−0.676113	−	0.736798i	$-0.736337\pi$
$337$	1.11402	−	1.11402i	0.0606843	−	0.0606843i	0.736798	+	0.676113i	$0.236337\pi$
$338$	14.0276	−	14.0276i	0.763001	−	0.763001i
$339$	−2.05763	−	3.95197i	−0.111755	−	0.214641i
$340$	43.6756	+	27.9894i	2.36864	+	1.51794i
$341$			16.8180i			0.910744i
$342$	8.00681	−	1.41302i	0.432958	−	0.0764076i
$343$	−14.2525	−	14.2525i	−0.769562	−	0.769562i
$344$	−44.0364			−2.37428
$345$	−4.44892	+	3.71336i	−0.239522	+	0.199920i
$346$	−29.3991			−1.58051
$347$	15.4836	+	15.4836i	0.831203	+	0.831203i	0.987681	−	0.156478i	$-0.0500141\pi$
$347$	15.4836	+	15.4836i	0.831203	+	0.831203i	−0.156478	+	0.987681i	$0.550014\pi$
$348$	−3.01156	−	0.949300i	−0.161437	−	0.0508878i
$349$		−	0.845815i		−	0.0452755i	−0.999744	−	0.0226377i	$-0.992794\pi$
$349$		−	0.845815i		−	0.0452755i	0.999744	−	0.0226377i	$-0.00720643\pi$
$350$	−26.9780	+	12.4044i	−1.44204	+	0.663042i
$351$	−23.2232	−	3.05221i	−1.23957	−	0.162915i
$352$	−38.2383	+	38.2383i	−2.03811	+	2.03811i
$353$	14.1758	−	14.1758i	0.754502	−	0.754502i	−0.220814	−	0.975316i	$-0.570871\pi$
$353$	14.1758	−	14.1758i	0.754502	−	0.754502i	0.975316	+	0.220814i	$0.0708713\pi$
$354$	−50.0673	+	26.0680i	−2.66105	+	1.38550i
$355$	20.6420	−	4.51820i	1.09557	−	0.239801i
$356$			14.0798i			0.746229i
$357$	−4.95229	+	15.7107i	−0.262103	+	0.831496i
$358$	−3.81235	−	3.81235i	−0.201489	−	0.201489i
$359$	−23.0208			−1.21499			−0.607496	−	0.794322i	$-0.707826\pi$
$359$	−23.0208			−1.21499			−0.607496	+	0.794322i	$0.707826\pi$
$360$	−23.1303	−	56.2443i	−1.21907	−	2.96433i
$361$	−1.00000			−0.0526316
$362$	−8.96712	−	8.96712i	−0.471301	−	0.471301i
$363$	−1.71698	+	5.44697i	−0.0901183	+	0.285892i
$364$			52.7960i			2.76726i
$365$	−18.8774	+	29.4571i	−0.988091	+	1.54185i
$366$	−51.9823	+	27.0651i	−2.71716	+	1.41472i
$367$	7.92943	−	7.92943i	0.413913	−	0.413913i	−0.469186	−	0.883099i	$-0.655453\pi$
$367$	7.92943	−	7.92943i	0.413913	−	0.413913i	0.883099	+	0.469186i	$0.155453\pi$
$368$	−14.6848	+	14.6848i	−0.765499	+	0.765499i
$369$	0.792699	−	1.13244i	0.0412663	−	0.0589527i
$370$	9.77104	+	44.6404i	0.507972	+	2.32074i
$371$		−	13.0027i		−	0.675069i
$372$	−53.5053	−	16.8658i	−2.77412	−	0.874453i
$373$	−6.69493	−	6.69493i	−0.346650	−	0.346650i	0.512210	−	0.858860i	$-0.328827\pi$
$373$	−6.69493	−	6.69493i	−0.346650	−	0.346650i	−0.858860	+	0.512210i	$0.828827\pi$
$374$	−32.6463			−1.68810
$375$	18.2493	−	6.47795i	0.942389	−	0.334520i
$376$	24.7473			1.27624
$377$	−1.08716	−	1.08716i	−0.0559917	−	0.0559917i
$378$	24.4772	−	18.7905i	1.25897	−	0.966481i
$379$			10.8622i			0.557952i	0.960298	+	0.278976i	$0.0899950\pi$
$379$			10.8622i			0.557952i	−0.960298	+	0.278976i	$0.910005\pi$
$380$	2.55558	+	11.6755i	0.131098	+	0.598941i
$381$	2.51685	+	4.83397i	0.128942	+	0.247652i
$382$	32.0363	−	32.0363i	1.63912	−	1.63912i
$383$	12.3305	−	12.3305i	0.630059	−	0.630059i	−0.318024	−	0.948083i	$-0.603019\pi$
$383$	12.3305	−	12.3305i	0.630059	−	0.630059i	0.948083	+	0.318024i	$0.103019\pi$
$384$	−23.1284	−	44.4214i	−1.18027	−	2.26687i
$385$	7.33723	−	11.4493i	0.373940	−	0.583510i
$386$			28.6682i			1.45917i
$387$	2.53257	+	14.3506i	0.128738	+	0.729483i
$388$	−37.4163	−	37.4163i	−1.89953	−	1.89953i
$389$	22.3582			1.13360			0.566802	−	0.823854i	$-0.308180\pi$
$389$	22.3582			1.13360			0.566802	+	0.823854i	$0.308180\pi$
$390$	4.24673	−	47.1245i	0.215042	−	2.38624i
$391$	−6.49416			−0.328424
$392$	14.0934	+	14.0934i	0.711823	+	0.711823i
$393$	−17.3708	−	5.47558i	−0.876239	−	0.276207i
$394$		−	30.4343i		−	1.53326i
$395$	4.26567	−	0.933684i	0.214629	−	0.0469788i
$396$	36.4589	+	25.5208i	1.83213	+	1.28247i
$397$	2.17078	−	2.17078i	0.108948	−	0.108948i	−0.650531	−	0.759479i	$-0.725454\pi$
$397$	2.17078	−	2.17078i	0.108948	−	0.108948i	0.759479	+	0.650531i	$0.225454\pi$
$398$	−4.04101	+	4.04101i	−0.202558	+	0.202558i
$399$	−3.36636	+	1.75273i	−0.168529	+	0.0877463i
$400$	63.0522	−	28.9911i	3.15261	−	1.44956i
$401$		−	31.8732i		−	1.59167i	−0.605512	−	0.795836i	$-0.707032\pi$
$401$		−	31.8732i		−	1.59167i	0.605512	−	0.795836i	$-0.292968\pi$
$402$	−5.92513	+	18.7969i	−0.295518	+	0.937504i
$403$	−19.3152	−	19.3152i	−0.962157	−	0.962157i
$404$	−25.9652			−1.29182
$405$	−16.9987	+	10.7724i	−0.844672	+	0.535284i
$406$	2.02551			0.100525
$407$	−14.7983	−	14.7983i	−0.733525	−	0.733525i
$408$	20.4890	−	64.9993i	1.01435	−	3.21794i
$409$			25.4247i			1.25717i	0.777740	+	0.628586i	$0.216366\pi$
$409$			25.4247i			1.25717i	−0.777740	+	0.628586i	$0.783634\pi$
$410$	2.35101	+	1.50664i	0.116108	+	0.0744074i
$411$	22.8548	−	11.8996i	1.12734	−	0.586962i
$412$	−28.6091	+	28.6091i	−1.40947	+	1.40947i
$413$	18.6319	−	18.6319i	0.916814	−	0.916814i
$414$	9.96633	+	6.97632i	0.489818	+	0.342868i
$415$	−5.29234	−	3.39158i	−0.259791	−	0.166486i
$416$		−	87.8322i		−	4.30633i
$417$	6.86995	+	2.16554i	0.336423	+	0.106047i
$418$	−5.31867	−	5.31867i	−0.260145	−	0.260145i
$419$	17.7057			0.864980			0.432490	−	0.901639i	$-0.357635\pi$
$419$	17.7057			0.864980			0.432490	+	0.901639i	$0.357635\pi$
$420$	29.0670	+	34.8248i	1.41833	+	1.69928i
$421$	−11.7072			−0.570573			−0.285286	−	0.958442i	$-0.592089\pi$
$421$	−11.7072			−0.570573			−0.285286	+	0.958442i	$0.592089\pi$
$422$	−4.42258	−	4.42258i	−0.215288	−	0.215288i
$423$	−1.42323	−	8.06466i	−0.0692000	−	0.392117i
$424$			53.7959i			2.61256i
$425$	20.3525	+	7.53153i	0.987240	+	0.365333i
$426$	−20.4859	−	39.3460i	−0.992545	−	1.90632i
$427$	19.3445	−	19.3445i	0.936147	−	0.936147i
$428$	−62.3546	+	62.3546i	−3.01402	+	3.01402i
$429$	10.0071	+	19.2200i	0.483146	+	0.927950i
$430$	−28.7561	+	6.29424i	−1.38674	+	0.303535i
$431$		−	21.6064i		−	1.04074i	−0.853940	−	0.520371i	$-0.825794\pi$
$431$		−	21.6064i		−	1.04074i	0.853940	−	0.520371i	$-0.174206\pi$
$432$	−57.2074	+	43.9167i	−2.75239	+	2.11294i
$433$	0.0582172	+	0.0582172i	0.00279774	+	0.00279774i	0.708504	−	0.705707i	$-0.249370\pi$
$433$	0.0582172	+	0.0582172i	0.00279774	+	0.00279774i	−0.705707	+	0.708504i	$0.749370\pi$
$434$	35.9865			1.72741
$435$	−1.31564	−	0.118562i	−0.0630803	−	0.00568462i
$436$	44.0513			2.10967
$437$	−1.05802	−	1.05802i	−0.0506117	−	0.0506117i
$438$	70.0499	+	22.0810i	3.34711	+	1.05507i
$439$		−	23.8132i		−	1.13654i	−0.822841	−	0.568272i	$-0.807612\pi$
$439$		−	23.8132i		−	1.13654i	0.822841	−	0.568272i	$-0.192388\pi$
$440$	−30.3561	+	47.3688i	−1.44717	+	2.25822i
$441$	3.78225	−	5.40329i	0.180107	−	0.257300i
$442$	37.4937	−	37.4937i	1.78340	−	1.78340i
$443$	2.17649	−	2.17649i	0.103408	−	0.103408i	−0.653510	−	0.756918i	$-0.726704\pi$
$443$	2.17649	−	2.17649i	0.103408	−	0.103408i	0.756918	+	0.653510i	$0.226704\pi$
$444$	61.9203	−	32.2394i	2.93861	−	1.53002i
$445$	1.25945	+	5.75396i	0.0597035	+	0.272764i
$446$		−	38.8462i		−	1.83942i
$447$	3.74881	−	11.8928i	0.177313	−	0.562508i
$448$	38.8100	+	38.8100i	1.83360	+	1.83360i
$449$	8.53457			0.402771			0.201386	−	0.979512i	$-0.435456\pi$
$449$	8.53457			0.402771			0.201386	+	0.979512i	$0.435456\pi$
$450$	−23.1434	−	33.4219i	−1.09099	−	1.57552i
$451$	−1.27881			−0.0602169
$452$	−9.72251	−	9.72251i	−0.457308	−	0.457308i
$453$	6.26471	−	19.8742i	0.294342	−	0.933771i
$454$		−	21.3445i		−	1.00175i
$455$	4.72263	+	21.5760i	0.221400	+	1.01150i
$456$	13.9276	−	7.25153i	0.652218	−	0.339584i
$457$	7.83972	−	7.83972i	0.366727	−	0.366727i	−0.499555	−	0.866282i	$-0.666503\pi$
$457$	7.83972	−	7.83972i	0.366727	−	0.366727i	0.866282	+	0.499555i	$0.166503\pi$
$458$	−33.6821	+	33.6821i	−1.57386	+	1.57386i
$459$	−22.3604	−	2.93881i	−1.04369	−	0.137172i
$460$	−9.64903	+	15.0567i	−0.449889	+	0.702023i
$461$			0.162959i			0.00758975i	0.999993	+	0.00379487i	$0.00120795\pi$
$461$			0.162959i			0.00758975i	−0.999993	+	0.00379487i	$0.998792\pi$
$462$	−27.2268	−	8.58238i	−1.26670	−	0.399288i
$463$	−0.535845	−	0.535845i	−0.0249028	−	0.0249028i	0.694546	−	0.719449i	$-0.255605\pi$
$463$	−0.535845	−	0.535845i	−0.0249028	−	0.0249028i	−0.719449	+	0.694546i	$0.755605\pi$
$464$	−4.73397			−0.219769
$465$	−23.3745	−	2.10645i	−1.08397	−	0.0976842i
$466$	12.2724			0.568507
$467$	18.3999	+	18.3999i	0.851446	+	0.851446i	0.990311	−	0.138865i	$-0.0443455\pi$
$467$	18.3999	+	18.3999i	0.851446	+	0.851446i	−0.138865	+	0.990311i	$0.544345\pi$
$468$	−71.1827	+	12.5622i	−3.29042	+	0.580686i
$469$		−	9.19997i		−	0.424815i
$470$	16.1602	−	3.53719i	0.745412	−	0.163158i
$471$	−18.3479	−	35.2396i	−0.845425	−	1.62376i
$472$	−77.0851	+	77.0851i	−3.54813	+	3.54813i
$473$	9.53267	−	9.53267i	0.438313	−	0.438313i
$474$	−4.23340	−	8.13083i	−0.194447	−	0.373462i
$475$	2.08876	+	4.54280i	0.0958389	+	0.208438i
$476$			50.8343i			2.32999i
$477$	17.5311	−	3.09385i	0.802693	−	0.141657i
$478$	7.53820	+	7.53820i	0.344789	+	0.344789i
$479$	13.7799			0.629620			0.314810	−	0.949155i	$-0.398059\pi$
$479$	13.7799			0.629620			0.314810	+	0.949155i	$0.398059\pi$
$480$	−48.3563	−	57.9350i	−2.20716	−	2.64436i
$481$	33.9912			1.54987
$482$	−25.7122	−	25.7122i	−1.17116	−	1.17116i
$483$	−5.41608	−	1.70725i	−0.246440	−	0.0776825i
$484$			17.6245i			0.801115i
$485$	−18.6377	−	11.9439i	−0.846297	−	0.542346i
$486$	31.1586	+	28.5306i	1.41338	+	1.29417i
$487$	−0.179630	+	0.179630i	−0.00813983	+	0.00813983i	−0.711165	−	0.703025i	$-0.751832\pi$
$487$	−0.179630	+	0.179630i	−0.00813983	+	0.00813983i	0.703025	+	0.711165i	$0.251832\pi$
$488$	−80.0335	+	80.0335i	−3.62295	+	3.62295i
$489$	−15.1703	+	7.89855i	−0.686023	+	0.357185i
$490$	11.2175	+	7.18869i	0.506755	+	0.324752i
$491$		−	28.1070i		−	1.26845i	−0.773148	−	0.634225i	$-0.781319\pi$
$491$		−	28.1070i		−	1.26845i	0.773148	−	0.634225i	$-0.218681\pi$
$492$	1.28245	−	4.06846i	0.0578174	−	0.183420i
$493$	−1.04677	−	1.04677i	−0.0471440	−	0.0471440i
$494$	12.2168			0.549660
$495$	17.1824	+	7.16827i	0.772292	+	0.322190i
$496$	−84.1066			−3.77650
$497$	14.6421	+	14.6421i	0.656787	+	0.656787i
$498$	−3.96714	+	12.5854i	−0.177772	+	0.563963i
$499$			24.5089i			1.09717i	0.836096	+	0.548584i	$0.184833\pi$
$499$			24.5089i			1.09717i	−0.836096	+	0.548584i	$0.815167\pi$
$500$	47.7016	−	35.9968i	2.13328	−	1.60983i
$501$	−6.60477	+	3.43884i	−0.295079	+	0.153636i
$502$	43.3893	−	43.3893i	1.93656	−	1.93656i
$503$	9.04409	−	9.04409i	0.403256	−	0.403256i	−0.476123	−	0.879379i	$-0.657958\pi$
$503$	9.04409	−	9.04409i	0.403256	−	0.403256i	0.879379	+	0.476123i	$0.157958\pi$
$504$	34.1753	−	48.8226i	1.52229	−	2.17473i
$505$	−10.6111	+	2.32260i	−0.472190	+	0.103354i
$506$		−	11.2545i		−	0.500322i
$507$	−12.0918	−	3.81155i	−0.537015	−	0.169277i
$508$	11.8924	+	11.8924i	0.527639	+	0.527639i
$509$	−23.6478			−1.04817			−0.524086	−	0.851665i	$-0.675593\pi$
$509$	−23.6478			−1.04817			−0.524086	+	0.851665i	$0.675593\pi$
$510$	4.08894	−	45.3736i	0.181061	−	2.00918i
$511$	−34.2853			−1.51669
$512$	−13.2814	−	13.2814i	−0.586961	−	0.586961i
$513$	−3.16412	−	4.12169i	−0.139699	−	0.181977i
$514$			68.6342i			3.02733i
$515$	−9.13251	+	14.2507i	−0.402426	+	0.627961i
$516$	20.7678	+	39.8874i	0.914250	+	1.75594i
$517$	−5.35710	+	5.35710i	−0.235605	+	0.235605i
$518$	−31.6649	+	31.6649i	−1.39128	+	1.39128i
$519$	8.67689	+	16.6652i	0.380873	+	0.731520i
$520$	−19.5388	−	89.2658i	−0.856833	−	3.91457i
$521$			31.8364i			1.39478i	0.716693	+	0.697389i	$0.245655\pi$
$521$			31.8364i			1.39478i	−0.716693	+	0.697389i	$0.754345\pi$
$522$	0.481946	+	2.73092i	0.0210942	+	0.119529i
$523$	10.3448	+	10.3448i	0.452346	+	0.452346i	0.896132	−	0.443787i	$-0.146365\pi$
$523$	10.3448	+	10.3448i	0.452346	+	0.452346i	−0.443787	+	0.896132i	$0.646365\pi$
$524$	−56.2059			−2.45536
$525$	14.9938	+	11.6317i	0.654385	+	0.507649i
$526$	68.7281			2.99669
$527$	−18.5975	−	18.5975i	−0.810120	−	0.810120i
$528$	63.6336	+	20.0585i	2.76930	+	0.872934i
$529$			20.7612i			0.902661i
$530$	7.68919	+	35.1292i	0.333997	+	1.52591i
$531$	29.5538	+	20.6874i	1.28253	+	0.897755i
$532$	−8.28182	+	8.28182i	−0.359063	+	0.359063i
$533$	1.46869	−	1.46869i	0.0636162	−	0.0636162i
$534$	10.9677	−	5.71043i	0.474618	−	0.247115i
$535$	−19.9046	+	31.0599i	−0.860553	+	1.34284i
$536$			38.0628i			1.64406i
$537$	−1.03589	+	3.28625i	−0.0447018	+	0.141812i
$538$	14.6696	+	14.6696i	0.632452	+	0.632452i
$539$	−6.10166			−0.262817
$540$	−40.0367	+	47.4760i	−1.72291	+	2.04304i
$541$	−13.8983			−0.597535			−0.298767	−	0.954326i	$-0.596575\pi$
$541$	−13.8983			−0.597535			−0.298767	+	0.954326i	$0.596575\pi$
$542$	−45.4131	−	45.4131i	−1.95066	−	1.95066i
$543$	−2.43653	+	7.72966i	−0.104562	+	0.331712i
$544$		−	84.5687i		−	3.62585i
$545$	18.0023	−	3.94041i	0.771135	−	0.168789i
$546$	41.1262	−	21.4128i	1.76004	−	0.916382i
$547$	−27.6535	+	27.6535i	−1.18238	+	1.18238i	−0.203253	+	0.979126i	$0.565151\pi$
$547$	−27.6535	+	27.6535i	−1.18238	+	1.18238i	−0.979126	+	0.203253i	$0.934849\pi$
$548$	56.2266	−	56.2266i	2.40188	−	2.40188i
$549$	30.6842	+	21.4786i	1.30957	+	0.916686i
$550$	−13.0522	+	35.2711i	−0.556550	+	1.50396i
$551$		−	0.341074i		−	0.0145303i
$552$	22.4078	+	7.06335i	0.953740	+	0.300636i
$553$	3.02578	+	3.02578i	0.128669	+	0.128669i
$554$	73.6818			3.13044
$555$	22.4210	−	18.7140i	0.951718	−	0.794365i
$556$	22.2288			0.942712
$557$	−10.7082	−	10.7082i	−0.453720	−	0.453720i	0.442867	−	0.896587i	$-0.353961\pi$
$557$	−10.7082	−	10.7082i	−0.453720	−	0.453720i	−0.896587	+	0.442867i	$0.853961\pi$
$558$	8.56254	+	48.5191i	0.362481	+	2.05398i
$559$			21.8962i			0.926112i
$560$	57.2578	+	36.6934i	2.41958	+	1.55058i
$561$	9.63526	+	18.5059i	0.406801	+	0.781318i
$562$	25.2023	−	25.2023i	1.06310	−	1.06310i
$563$	8.16092	−	8.16092i	0.343942	−	0.343942i	−0.513905	−	0.857847i	$-0.671802\pi$
$563$	8.16092	−	8.16092i	0.343942	−	0.343942i	0.857847	+	0.513905i	$0.171802\pi$
$564$	−11.6709	−	22.4156i	−0.491434	−	0.943868i
$565$	−4.84296	−	3.10359i	−0.203745	−	0.130569i
$566$			26.5179i			1.11463i
$567$	−17.8758	−	8.32926i	−0.750713	−	0.349796i
$568$	−60.5783	−	60.5783i	−2.54181	−	2.54181i
$569$	15.6913			0.657812			0.328906	−	0.944363i	$-0.393320\pi$
$569$	15.6913			0.657812			0.328906	+	0.944363i	$0.393320\pi$
$570$	8.05833	−	6.72601i	0.337526	−	0.281722i
$571$	−2.89052			−0.120965			−0.0604823	−	0.998169i	$-0.519264\pi$
$571$	−2.89052			−0.120965			−0.0604823	+	0.998169i	$0.519264\pi$
$572$	47.2844	+	47.2844i	1.97706	+	1.97706i
$573$	−27.6153	−	8.70484i	−1.15364	−	0.363650i
$574$			2.73636i			0.114213i
$575$	−2.59642	+	7.01630i	−0.108278	+	0.292600i
$576$	−43.0916	+	61.5603i	−1.79548	+	2.56501i
$577$	33.4230	−	33.4230i	1.39142	−	1.39142i	0.569265	−	0.822154i	$-0.307228\pi$
$577$	33.4230	−	33.4230i	1.39142	−	1.39142i	0.822154	−	0.569265i	$-0.192772\pi$
$578$	3.52210	−	3.52210i	0.146500	−	0.146500i
$579$	16.2508	−	8.46115i	0.675361	−	0.351633i
$580$	−3.98222	+	0.871641i	−0.165353	+	0.0361929i
$581$		−	6.15979i		−	0.255551i
$582$	−13.9708	+	44.3212i	−0.579110	+	1.83717i
$583$	−11.6453	−	11.6453i	−0.482301	−	0.482301i
$584$	141.847			5.86969
$585$	−27.9664	+	11.5011i	−1.15627	+	0.475511i
$586$	−0.127253			−0.00525676
$587$	32.6911	+	32.6911i	1.34931	+	1.34931i	0.886413	+	0.462895i	$0.153189\pi$
$587$	32.6911	+	32.6911i	1.34931	+	1.34931i	0.462895	+	0.886413i	$0.346811\pi$
$588$	6.11903	−	19.4120i	0.252345	−	0.800539i
$589$		−	6.05973i		−	0.249687i
$590$	−39.3192	+	61.3552i	−1.61875	+	2.52595i
$591$	−17.2520	+	8.98241i	−0.709651	+	0.369487i
$592$	74.0063	−	74.0063i	3.04164	−	3.04164i
$593$	3.73463	−	3.73463i	0.153363	−	0.153363i	−0.626255	−	0.779618i	$-0.715413\pi$
$593$	3.73463	−	3.73463i	0.153363	−	0.153363i	0.779618	+	0.626255i	$0.215413\pi$
$594$	5.09299	−	38.7508i	0.208968	−	1.58997i
$595$	4.54716	+	20.7743i	0.186415	+	0.851665i
$596$		−	38.4809i		−	1.57624i
$597$	3.48335	+	1.09802i	0.142564	+	0.0449388i
$598$	12.9256	+	12.9256i	0.528566	+	0.528566i
$599$	18.9926			0.776015			0.388007	−	0.921656i	$-0.373163\pi$
$599$	18.9926			0.776015			0.388007	+	0.921656i	$0.373163\pi$
$600$	−62.0336	−	48.1235i	−2.53251	−	1.96463i
$601$	−34.2389			−1.39663			−0.698316	−	0.715789i	$-0.746067\pi$
$601$	−34.2389			−1.39663			−0.698316	+	0.715789i	$0.746067\pi$
$602$	−20.3977	−	20.3977i	−0.831347	−	0.831347i
$603$	12.4039	−	2.18902i	0.505128	−	0.0891438i
$604$		−	64.3061i		−	2.61658i
$605$	1.57652	+	7.20257i	0.0640948	+	0.292826i
$606$	10.5309	+	20.2260i	0.427787	+	0.821625i
$607$	−0.971775	+	0.971775i	−0.0394431	+	0.0394431i	−0.726553	−	0.687110i	$-0.758879\pi$
$607$	−0.971775	+	0.971775i	−0.0394431	+	0.0394431i	0.687110	+	0.726553i	$0.258879\pi$
$608$	13.7778	−	13.7778i	0.558762	−	0.558762i
$609$	−0.597812	−	1.14818i	−0.0242246	−	0.0465266i
$610$	−40.8231	+	63.7020i	−1.65288	+	2.57922i
$611$		−	12.3051i		−	0.497811i
$612$	−68.5379	+	12.0954i	−2.77048	+	0.488928i
$613$	−0.868747	−	0.868747i	−0.0350884	−	0.0350884i	0.689345	−	0.724433i	$-0.257898\pi$
$613$	−0.868747	−	0.868747i	−0.0350884	−	0.0350884i	−0.724433	+	0.689345i	$0.757898\pi$
$614$	−56.9560			−2.29856
$615$	0.160171	−	1.77736i	0.00645872	−	0.0716701i
$616$	−55.1329			−2.22137
$617$	21.7676	+	21.7676i	0.876329	+	0.876329i	0.993153	−	0.116823i	$-0.0372711\pi$
$617$	21.7676	+	21.7676i	0.876329	+	0.876329i	−0.116823	+	0.993153i	$0.537271\pi$
$618$	33.8886	+	10.6823i	1.36320	+	0.429706i
$619$		−	38.6157i		−	1.55210i	−0.630674	−	0.776048i	$-0.717222\pi$
$619$		−	38.6157i		−	1.55210i	0.630674	−	0.776048i	$-0.282778\pi$
$620$	−70.7505	+	15.4861i	−2.84141	+	0.621937i
$621$	1.01312	−	7.70850i	0.0406552	−	0.309332i
$622$	39.8012	−	39.8012i	1.59588	−	1.59588i
$623$	−4.08147	+	4.08147i	−0.163521	+	0.163521i
$624$	−96.1190	+	50.0453i	−3.84784	+	2.00342i
$625$	16.2742	−	18.9777i	0.650966	−	0.759107i
$626$		−	68.9704i		−	2.75661i
$627$	−1.44518	+	4.58469i	−0.0577149	+	0.183095i
$628$	−86.6954	−	86.6954i	−3.45952	−	3.45952i
$629$	32.7283			1.30496
$630$	15.3384	−	36.7663i	0.611097	−	1.46480i
$631$	−28.7544			−1.14469			−0.572347	−	0.820011i	$-0.693967\pi$
$631$	−28.7544			−1.14469			−0.572347	+	0.820011i	$0.693967\pi$
$632$	−12.5185	−	12.5185i	−0.497958	−	0.497958i
$633$	−1.20170	+	3.81226i	−0.0477631	+	0.151524i
$634$			80.4360i			3.19452i
$635$	5.92381	+	3.79625i	0.235079	+	0.150649i
$636$	48.7274	−	25.3704i	1.93217	−	1.00600i
$637$	7.00766	−	7.00766i	0.277654	−	0.277654i
$638$	1.81406	−	1.81406i	0.0718194	−	0.0718194i
$639$	−16.2574	+	23.2252i	−0.643134	+	0.918776i
$640$	−54.4363	−	34.8853i	−2.15179	−	1.37896i
$641$			15.2356i			0.601769i	0.953661	+	0.300885i	$0.0972819\pi$
$641$			15.2356i			0.601769i	−0.953661	+	0.300885i	$0.902718\pi$
$642$	73.8615	+	23.2825i	2.91508	+	0.918887i
$643$	14.6770	+	14.6770i	0.578805	+	0.578805i	0.934574	−	0.355769i	$-0.115781\pi$
$643$	14.6770	+	14.6770i	0.578805	+	0.578805i	−0.355769	+	0.934574i	$0.615781\pi$
$644$	−17.5246			−0.690566
$645$	12.0551	+	14.4430i	0.474667	+	0.568692i
$646$	11.7629			0.462805
$647$	−8.15999	−	8.15999i	−0.320802	−	0.320802i	0.528273	−	0.849075i	$-0.322840\pi$
$647$	−8.15999	−	8.15999i	−0.320802	−	0.320802i	−0.849075	+	0.528273i	$0.822840\pi$
$648$	73.9571	+	34.4604i	2.90531	+	1.35373i
$649$		−	33.3736i		−	1.31003i
$650$	−25.5180	−	55.4986i	−1.00090	−	2.17683i
$651$	−10.6211	−	20.3993i	−0.416273	−	0.799510i
$652$	−37.3214	+	37.3214i	−1.46162	+	1.46162i
$653$	18.7646	−	18.7646i	0.734317	−	0.734317i	−0.237154	−	0.971472i	$-0.576215\pi$
$653$	18.7646	−	18.7646i	0.734317	−	0.734317i	0.971472	+	0.237154i	$0.0762147\pi$
$654$	−17.8661	−	34.3144i	−0.698621	−	1.34180i
$655$	−22.9695	+	5.02764i	−0.897493	+	0.196446i
$656$		−	6.39533i		−	0.249696i
$657$	−8.15776	−	46.2254i	−0.318265	−	1.80343i
$658$	11.4629	+	11.4629i	0.446872	+	0.446872i
$659$	−19.8613			−0.773688			−0.386844	−	0.922145i	$-0.626435\pi$
$659$	−19.8613			−0.773688			−0.386844	+	0.922145i	$0.626435\pi$
$660$	57.2219	+	5.15668i	2.22736	+	0.200724i
$661$	1.81809			0.0707156			0.0353578	−	0.999375i	$-0.488743\pi$
$661$	1.81809			0.0707156			0.0353578	+	0.999375i	$0.488743\pi$
$662$	−4.58723	−	4.58723i	−0.178288	−	0.178288i
$663$	−32.3196	−	10.1877i	−1.25519	−	0.395659i
$664$			25.4847i			0.988999i
$665$	−2.64370	+	4.12533i	−0.102518	+	0.159973i
$666$	−50.2268	−	35.1582i	−1.94625	−	1.36235i
$667$	0.360862	−	0.360862i	0.0139726	−	0.0139726i
$668$	−16.2488	+	16.2488i	−0.628686	+	0.628686i
$669$	−22.0203	+	11.4651i	−0.851354	+	0.443266i
$670$	5.44041	+	24.8553i	0.210181	+	0.960244i
$671$		−	34.6501i		−	1.33765i
$672$	22.2323	−	70.5297i	0.857628	−	2.72074i
$673$	−26.1329	−	26.1329i	−1.00735	−	1.00735i	−0.999973	−	0.00737644i	$-0.997652\pi$
$673$	−26.1329	−	26.1329i	−1.00735	−	1.00735i	−0.00737644	−	0.999973i	$-0.502348\pi$
$674$	−4.26976			−0.164465
$675$	−12.1149	+	22.9832i	−0.466304	+	0.884624i
$676$	−39.1249			−1.50480
$677$	−23.2430	−	23.2430i	−0.893303	−	0.893303i	0.101530	−	0.994832i	$-0.467626\pi$
$677$	−23.2430	−	23.2430i	−0.893303	−	0.893303i	−0.994832	+	0.101530i	$0.967626\pi$
$678$	−3.63028	+	11.5167i	−0.139420	+	0.442297i
$679$		−	21.6926i		−	0.832485i
$680$	−18.8128	−	85.9491i	−0.721439	−	3.29600i
$681$	−12.0993	+	6.29964i	−0.463647	+	0.241403i
$682$	32.2297	−	32.2297i	1.23414	−	1.23414i
$683$	−6.69635	+	6.69635i	−0.256229	+	0.256229i	−0.823518	−	0.567290i	$-0.807992\pi$
$683$	−6.69635	+	6.69635i	−0.256229	+	0.256229i	0.567290	+	0.823518i	$0.307992\pi$
$684$	−13.1366	−	9.19549i	−0.502291	−	0.351598i
$685$	17.9485	−	28.0075i	0.685776	−	1.07011i
$686$			54.6265i			2.08565i
$687$	29.0340	+	9.15205i	1.10772	+	0.349172i
$688$	47.6728	+	47.6728i	1.81751	+	1.81751i
$689$	26.7490			1.01905
$690$	15.6421	+	1.40962i	0.595483	+	0.0536633i
$691$	14.0822			0.535713			0.267856	−	0.963459i	$-0.413685\pi$
$691$	14.0822			0.535713			0.267856	+	0.963459i	$0.413685\pi$
$692$	40.9991	+	40.9991i	1.55855	+	1.55855i
$693$	3.17073	+	17.9668i	0.120446	+	0.682501i
$694$		−	59.3451i		−	2.25271i
$695$	9.08420	−	1.98838i	0.344583	−	0.0754236i
$696$	2.47331	+	4.75034i	0.0937506	+	0.180061i
$697$	1.41412	−	1.41412i	0.0535638	−	0.0535638i
$698$	−1.62091	+	1.62091i	−0.0613523	+	0.0613523i
$699$	−3.62208	−	6.95671i	−0.137000	−	0.263127i
$700$	54.9215	+	20.3240i	2.07584	+	0.768173i
$701$			8.36037i			0.315767i	0.987458	+	0.157883i	$0.0504670\pi$
$701$			8.36037i			0.315767i	−0.987458	+	0.157883i	$0.949533\pi$
$702$	38.6555	+	50.3539i	1.45896	+	1.90049i
$703$	5.33202	+	5.33202i	0.201101	+	0.201101i
$704$	69.5169			2.62002
$705$	−6.77461	−	8.11656i	−0.255147	−	0.305687i
$706$	−54.3326			−2.04484
$707$	−7.52683	−	7.52683i	−0.283076	−	0.283076i
$708$	106.176	+	33.4686i	3.99034	+	1.25783i
$709$			18.9746i			0.712607i	0.934370	+	0.356303i	$0.115963\pi$
$709$			18.9746i			0.712607i	−0.934370	+	0.356303i	$0.884037\pi$
$710$	−48.2167	−	30.8995i	−1.80954	−	1.15964i
$711$	−3.35959	+	4.79948i	−0.125994	+	0.179995i
$712$	16.8862	−	16.8862i	0.632836	−	0.632836i
$713$	6.41129	−	6.41129i	0.240105	−	0.240105i
$714$	39.5982	−	20.6172i	1.48192	−	0.771579i
$715$	23.5532	+	15.0940i	0.880840	+	0.564483i
$716$			10.6332i			0.397380i
$717$	2.04827	−	6.49793i	0.0764939	−	0.242670i
$718$	44.1168	+	44.1168i	1.64642	+	1.64642i
$719$	16.5292			0.616434			0.308217	−	0.951316i	$-0.400268\pi$
$719$	16.5292			0.616434			0.308217	+	0.951316i	$0.400268\pi$
$720$	−35.8485	+	85.9291i	−1.33599	+	3.20239i
$721$	−16.5865			−0.617713
$722$	1.91639	+	1.91639i	0.0713205	+	0.0713205i
$723$	−6.98648	+	22.1639i	−0.259830	+	0.824286i
$724$			25.0105i			0.929510i
$725$	−1.54943	+	0.712423i	−0.0575445	+	0.0264587i
$726$	13.7289	−	7.14809i	0.509527	−	0.265290i
$727$	−4.61397	+	4.61397i	−0.171123	+	0.171123i	−0.787472	−	0.616350i	$-0.788611\pi$
$727$	−4.61397	+	4.61397i	−0.171123	+	0.171123i	0.616350	+	0.787472i	$0.288611\pi$
$728$	63.3192	−	63.3192i	2.34677	−	2.34677i
$729$	6.97667	−	26.0831i	0.258395	−	0.966039i
$730$	92.6275	−	20.2746i	3.42830	−	0.750398i
$731$			21.0827i			0.779771i
$732$	110.237	+	34.7488i	4.07448	+	1.28435i
$733$	−29.2126	−	29.2126i	−1.07899	−	1.07899i	−0.996600	−	0.0823910i	$-0.973744\pi$
$733$	−29.2126	−	29.2126i	−1.07899	−	1.07899i	−0.0823910	−	0.996600i	$-0.526256\pi$
$734$	−30.3917			−1.12178
$735$	0.764232	−	8.48042i	0.0281891	−	0.312805i
$736$	29.1542			1.07464
$737$	−8.23955	−	8.23955i	−0.303508	−	0.303508i
$738$	−3.68932	+	0.651083i	−0.135806	+	0.0239667i
$739$			49.6356i			1.82587i	0.408101	+	0.912937i	$0.366191\pi$
$739$			49.6356i			1.82587i	−0.408101	+	0.912937i	$0.633809\pi$
$740$	48.6277	−	75.8805i	1.78759	−	2.78942i
$741$	−3.60568	−	6.92521i	−0.132458	−	0.254404i
$742$	−24.9183	+	24.9183i	−0.914779	+	0.914779i
$743$	0.289869	−	0.289869i	0.0106343	−	0.0106343i	−0.701770	−	0.712404i	$-0.747606\pi$
$743$	0.289869	−	0.289869i	0.0106343	−	0.0106343i	0.712404	+	0.701770i	$0.247606\pi$
$744$	43.9423	+	84.3973i	1.61100	+	3.09416i
$745$	−3.44214	−	15.7259i	−0.126110	−	0.576152i
$746$			25.6601i			0.939484i
$747$	8.30499	−	1.46565i	0.303864	−	0.0536252i
$748$	45.5275	+	45.5275i	1.66465	+	1.66465i
$749$	−36.1508			−1.32092
$750$	−47.3869	−	22.5584i	−1.73032	−	0.823717i
$751$	−43.9824			−1.60494			−0.802471	−	0.596691i	$-0.796482\pi$
$751$	−43.9824			−1.60494			−0.802471	+	0.596691i	$0.796482\pi$
$752$	−26.7908	−	26.7908i	−0.976961	−	0.976961i
$753$	−37.4016	−	11.7897i	−1.36299	−	0.429640i
$754$			4.16684i			0.151747i
$755$	−5.75222	−	26.2798i	−0.209345	−	0.956421i
$756$	−60.3398	−	7.93042i	−2.19454	−	0.288427i
$757$	10.7580	−	10.7580i	0.391005	−	0.391005i	−0.484040	−	0.875046i	$-0.660831\pi$
$757$	10.7580	−	10.7580i	0.391005	−	0.391005i	0.875046	+	0.484040i	$0.160831\pi$
$758$	20.8161	−	20.8161i	0.756075	−	0.756075i
$759$	−6.37970	+	3.32165i	−0.231568	+	0.120568i
$760$	10.9377	−	17.0676i	0.396752	−	0.619107i
$761$		−	43.6178i		−	1.58114i	−0.612370	−	0.790571i	$-0.709784\pi$
$761$		−	43.6178i		−	1.58114i	0.612370	−	0.790571i	$-0.290216\pi$
$762$	4.44048	−	14.0870i	0.160862	−	0.510318i
$763$	12.7696	+	12.7696i	0.462292	+	0.462292i
$764$	−89.3536			−3.23270
$765$	−26.9273	+	11.0737i	−0.973557	+	0.400372i
$766$	−47.2600			−1.70757
$767$	38.3290	+	38.3290i	1.38398	+	1.38398i
$768$	−14.7198	+	46.6971i	−0.531155	+	1.68504i
$769$		−	30.3590i		−	1.09477i	−0.836880	−	0.547386i	$-0.815623\pi$
$769$		−	30.3590i		−	1.09477i	0.836880	−	0.547386i	$-0.184377\pi$
$770$	−36.0022	+	7.88028i	−1.29743	+	0.283986i
$771$	38.9059	−	20.2568i	1.40116	−	0.729530i
$772$	39.9797	−	39.9797i	1.43890	−	1.43890i
$773$	23.7753	−	23.7753i	0.855137	−	0.855137i	−0.135624	−	0.990760i	$-0.543304\pi$
$773$	23.7753	−	23.7753i	0.855137	−	0.855137i	0.990760	+	0.135624i	$0.0433038\pi$
$774$	22.6480	−	32.3547i	0.814064	−	1.16297i
$775$	−27.5282	+	12.6573i	−0.988841	+	0.454665i
$776$			89.7482i			3.22177i
$777$	27.2951	+	8.60393i	0.979208	+	0.308664i
$778$	−42.8469	−	42.8469i	−1.53614	−	1.53614i
$779$	0.460773			0.0165089
$780$	−71.6408	+	59.7961i	−2.56515	+	2.14104i
$781$	26.2271			0.938479
$782$	12.4453	+	12.4453i	0.445044	+	0.445044i
$783$	1.40580	−	1.07920i	0.0502393	−	0.0385675i
$784$		−	30.5144i		−	1.08980i
$785$	−43.1845	−	27.6746i	−1.54132	−	0.987750i
$786$	22.7957	+	43.7824i	0.813097	+	1.56167i
$787$	−23.9413	+	23.9413i	−0.853417	+	0.853417i	−0.990552	−	0.137135i	$-0.956210\pi$
$787$	−23.9413	+	23.9413i	−0.853417	+	0.853417i	0.137135	+	0.990552i	$0.456210\pi$
$788$	−42.4427	+	42.4427i	−1.51196	+	1.51196i
$789$	−20.2845	−	38.9591i	−0.722146	−	1.38698i
$790$	−9.96397	−	6.38537i	−0.354502	−	0.227181i
$791$		−	5.63675i		−	0.200420i
$792$	−13.1182	−	74.3334i	−0.466135	−	2.64132i
$793$	39.7951	+	39.7951i	1.41317	+	1.41317i
$794$	−8.32009			−0.295269
$795$	17.6439	−	14.7267i	0.625765	−	0.522304i
$796$	11.2709			0.399488
$797$	−23.3654	−	23.3654i	−0.827645	−	0.827645i	0.159546	−	0.987191i	$-0.448997\pi$
$797$	−23.3654	−	23.3654i	−0.827645	−	0.827645i	−0.987191	+	0.159546i	$0.948997\pi$
$798$	9.81016	+	3.09234i	0.347276	+	0.109468i
$799$		−	11.8479i		−	0.419148i
$800$	−91.3682	−	33.8112i	−3.23035	−	1.19541i
$801$	−6.47402	−	4.53175i	−0.228748	−	0.160121i
$802$	−61.0814	+	61.0814i	−2.15686	+	2.15686i
$803$	−30.7061	+	30.7061i	−1.08359	+	1.08359i
$804$	34.4766	−	17.9506i	1.21590	−	0.633068i
$805$	−7.16173	+	1.56758i	−0.252418	+	0.0552501i
$806$			74.0306i			2.60762i
$807$	3.98600	−	12.6452i	0.140314	−	0.445133i
$808$	31.1406	+	31.1406i	1.09552	+	1.09552i
$809$	−27.0018			−0.949331			−0.474666	−	0.880166i	$-0.657431\pi$
$809$	−27.0018			−0.949331			−0.474666	+	0.880166i	$0.657431\pi$
$810$	53.2201	+	11.9320i	1.86996	+	0.419249i
$811$	39.6623			1.39273			0.696366	−	0.717687i	$-0.254799\pi$
$811$	39.6623			1.39273			0.696366	+	0.717687i	$0.254799\pi$
$812$	−2.82472	−	2.82472i	−0.0991282	−	0.0991282i
$813$	−12.3396	+	39.1461i	−0.432768	+	1.37291i
$814$			56.7185i			1.98798i
$815$	−11.9136	+	18.5905i	−0.417316	+	0.651195i
$816$	−92.5477	+	48.1859i	−3.23982	+	1.68684i
$817$	−3.43474	+	3.43474i	−0.120166	+	0.120166i
$818$	48.7235	−	48.7235i	1.70358	−	1.70358i
$819$	−24.2761	−	16.9930i	−0.848274	−	0.593783i
$820$	−1.17754	−	5.37976i	−0.0411214	−	0.187869i
$821$			47.6707i			1.66372i	0.554987	+	0.831859i	$0.312723\pi$
$821$			47.6707i			1.66372i	−0.554987	+	0.831859i	$0.687277\pi$
$822$	−66.6026	−	20.9944i	−2.32303	−	0.732263i
$823$	−29.4943	−	29.4943i	−1.02811	−	1.02811i	−0.999593	−	0.0285131i	$-0.990923\pi$
$823$	−29.4943	−	29.4943i	−1.02811	−	1.02811i	−0.0285131	−	0.999593i	$-0.509077\pi$
$824$	68.6228			2.39059
$825$	23.8460	−	3.01116i	0.830211	−	0.104835i
$826$	−71.4116			−2.48473
$827$	15.3766	+	15.3766i	0.534695	+	0.534695i	0.921966	−	0.387271i	$-0.126582\pi$
$827$	15.3766	+	15.3766i	0.534695	+	0.534695i	−0.387271	+	0.921966i	$0.626582\pi$
$828$	−4.16977	−	23.6277i	−0.144909	−	0.821119i
$829$			54.0919i			1.87869i	0.342973	+	0.939345i	$0.388566\pi$
$829$			54.0919i			1.87869i	−0.342973	+	0.939345i	$0.611434\pi$
$830$	3.64260	+	16.6417i	0.126436	+	0.577643i
$831$	−21.7465	−	41.7672i	−0.754379	−	1.44889i
$832$	−79.8390	+	79.8390i	−2.76792	+	2.76792i
$833$	6.74729	−	6.74729i	0.233780	−	0.233780i
$834$	−9.01547	−	17.3155i	−0.312180	−	0.599586i
$835$	−5.18690	+	8.09384i	−0.179500	+	0.280099i
$836$			14.8345i			0.513062i
$837$	24.9763	−	19.1737i	0.863309	−	0.662741i
$838$	−33.9309	−	33.9309i	−1.17212	−	1.17212i
$839$	−44.2660			−1.52823			−0.764116	−	0.645079i	$-0.776825\pi$
$839$	−44.2660			−1.52823			−0.764116	+	0.645079i	$0.776825\pi$
$840$	6.90538	−	76.6266i	0.238258	−	2.64387i
$841$	−28.8837			−0.995989
$842$	22.4355	+	22.4355i	0.773177	+	0.773177i
$843$	−21.7244	−	6.84793i	−0.748228	−	0.235855i
$844$			12.3352i			0.424595i
$845$	−15.9891	+	3.49974i	−0.550041	+	0.120395i
$846$	−12.7275	+	18.1825i	−0.437582	+	0.625126i
$847$	−5.10902	+	5.10902i	−0.175548	+	0.175548i
$848$	58.2383	−	58.2383i	1.99991	−	1.99991i
$849$	15.0319	−	7.82652i	0.515894	−	0.268606i
$850$	−24.5699	−	53.4365i	−0.842739	−	1.83286i
$851$			11.2827i			0.386767i
$852$	−26.3017	+	83.4397i	−0.901083	+	2.85860i
$853$	25.8036	+	25.8036i	0.883500	+	0.883500i	0.993888	−	0.110389i	$-0.0352096\pi$
$853$	25.8036	+	25.8036i	0.883500	+	0.883500i	−0.110389	+	0.993888i	$0.535210\pi$
$854$	−74.1431			−2.53712
$855$	−6.19105	−	2.58282i	−0.211729	−	0.0883306i
$856$	149.566			5.11206
$857$	11.5385	+	11.5385i	0.394149	+	0.394149i	0.876163	−	0.482014i	$-0.160095\pi$
$857$	11.5385	+	11.5385i	0.394149	+	0.394149i	−0.482014	+	0.876163i	$0.660095\pi$
$858$	17.6555	−	56.0103i	0.602748	−	1.91216i
$859$			7.36205i			0.251190i	0.992082	+	0.125595i	$0.0400840\pi$
$859$			7.36205i			0.251190i	−0.992082	+	0.125595i	$0.959916\pi$
$860$	48.8802	+	31.3247i	1.66680	+	1.06816i
$861$	1.55113	−	0.807610i	0.0528623	−	0.0275233i
$862$	−41.4061	+	41.4061i	−1.41030	+	1.41030i
$863$	25.2214	−	25.2214i	0.858547	−	0.858547i	−0.132620	−	0.991167i	$-0.542339\pi$
$863$	25.2214	−	25.2214i	0.858547	−	0.858547i	0.991167	+	0.132620i	$0.0423390\pi$
$864$	100.382	+	13.1932i	3.41507	+	0.448840i
$865$	20.4224	+	13.0876i	0.694382	+	0.444992i
$866$		−	0.223133i		−	0.00758238i
$867$	−3.03605	−	0.957019i	−0.103110	−	0.0325021i
$868$	−50.1856	−	50.1856i	−1.70341	−	1.70341i
$869$	5.41981			0.183855
$870$	2.29407	+	2.74849i	0.0777762	+	0.0931826i
$871$	18.9260			0.641282
$872$	−52.8315	−	52.8315i	−1.78910	−	1.78910i
$873$	29.2472	−	5.16149i	0.989869	−	0.174690i
$874$			4.05513i			0.137167i
$875$	24.2626	+	3.39299i	0.820226	+	0.114704i
$876$	−66.8959	−	128.483i	−2.26020	−	4.34103i
$877$	−18.2079	+	18.2079i	−0.614837	+	0.614837i	−0.944203	−	0.329365i	$-0.893165\pi$
$877$	−18.2079	+	18.2079i	−0.614837	+	0.614837i	0.329365	+	0.944203i	$0.393165\pi$
$878$	−45.6353	+	45.6353i	−1.54012	+	1.54012i
$879$	0.0375575	+	0.0721343i	0.00126678	+	0.00243303i
$880$	84.1433	−	18.4176i	2.83647	−	0.620856i
$881$			2.75574i			0.0928432i	0.998922	+	0.0464216i	$0.0147818\pi$
$881$			2.75574i			0.0928432i	−0.998922	+	0.0464216i	$0.985218\pi$
$882$	−17.6030	+	3.10654i	−0.592725	+	0.104603i
$883$	29.7060	+	29.7060i	0.999685	+	0.999685i	1.00000		0.000314913i	$-0.000100240\pi$
$883$	29.7060	+	29.7060i	0.999685	+	0.999685i	−0.000314913		1.00000i	$0.500100\pi$
$884$	−104.575			−3.51725
$885$	46.3844	+	4.18004i	1.55920	+	0.140510i
$886$	−8.34199			−0.280255
$887$	11.3767	+	11.3767i	0.381992	+	0.381992i	0.871819	−	0.489827i	$-0.162940\pi$
$887$	11.3767	+	11.3767i	0.381992	+	0.381992i	−0.489827	+	0.871819i	$0.662940\pi$
$888$	−112.927	−	35.5968i	−3.78960	−	1.19455i
$889$			6.89475i			0.231243i
$890$	8.61322	−	13.4404i	0.288716	−	0.450523i
$891$	−23.4694	+	8.54994i	−0.786255	+	0.286434i
$892$	−54.1737	+	54.1737i	−1.81387	+	1.81387i
$893$	1.93023	−	1.93023i	0.0645928	−	0.0645928i
$894$	−29.9753	+	15.6069i	−1.00252	+	0.521974i
$895$	0.951143	+	4.34543i	0.0317932	+	0.145252i
$896$		−	63.3588i		−	2.11667i
$897$	3.51211	−	11.1418i	0.117266	−	0.372015i
$898$	−16.3555	−	16.3555i	−0.545791	−	0.545791i
$899$	2.06682			0.0689323
$900$	−14.3341	+	78.8842i	−0.477802	+	2.62947i
$901$	25.7551			0.858026
$902$	2.45070	+	2.45070i	0.0815993	+	0.0815993i
$903$	−5.54242	+	17.5828i	−0.184440	+	0.585118i
$904$			23.3208i			0.775637i
$905$	2.23721	+	10.2210i	0.0743673	+	0.339757i
$906$	−50.0922	+	26.0810i	−1.66420	+	0.866484i
$907$	3.71801	−	3.71801i	0.123454	−	0.123454i	−0.642680	−	0.766135i	$-0.722178\pi$
$907$	3.71801	−	3.71801i	0.123454	−	0.123454i	0.766135	+	0.642680i	$0.222178\pi$
$908$	−29.7664	+	29.7664i	−0.987832	+	0.987832i
$909$	8.35720	−	11.9390i	0.277191	−	0.395993i
$910$	32.2976	−	50.3983i	1.07065	−	1.67069i
$911$			16.7808i			0.555973i	0.960585	+	0.277986i	$0.0896670\pi$
$911$			16.7808i			0.555973i	−0.960585	+	0.277986i	$0.910333\pi$
$912$	−22.9280	−	7.22733i	−0.759223	−	0.239321i
$913$	−5.51674	−	5.51674i	−0.182578	−	0.182578i
$914$	−30.0479			−0.993895
$915$	48.1586	+	4.33992i	1.59207	+	0.143473i
$916$	93.9441			3.10400
$917$	−16.2930	−	16.2930i	−0.538043	−	0.538043i
$918$	37.2192	+	48.4830i	1.22842	+	1.60018i
$919$		−	29.7043i		−	0.979856i	−0.871763	−	0.489928i	$-0.837023\pi$
$919$		−	29.7043i		−	0.979856i	0.871763	−	0.489928i	$-0.162977\pi$
$920$	29.6300	−	6.48552i	0.976874	−	0.213821i
$921$	16.8101	+	32.2861i	0.553910	+	1.06386i
$922$	0.312292	−	0.312292i	0.0102848	−	0.0102848i
$923$	−30.1214	+	30.1214i	−0.991457	+	0.991457i
$924$	26.0009	+	49.9384i	0.855367	+	1.64285i
$925$	13.0850	−	35.3597i	0.430233	−	1.16262i
$926$			2.05377i			0.0674911i
$927$	−3.94655	−	22.3629i	−0.129622	−	0.734493i
$928$	4.69924	+	4.69924i	0.154260	+	0.154260i
$929$	29.7808			0.977078			0.488539	−	0.872542i	$-0.337530\pi$
$929$	29.7808			0.977078			0.488539	+	0.872542i	$0.337530\pi$
$930$	40.7578	+	48.8313i	1.33650	+	1.60124i
$931$	2.19851			0.0720532
$932$	−17.1147	−	17.1147i	−0.560610	−	0.560610i
$933$	−34.3087	−	10.8147i	−1.12322	−	0.354058i
$934$		−	70.5226i		−	2.30757i
$935$	22.6781	+	14.5332i	0.741653	+	0.475285i
$936$	100.437	+	70.3046i	3.28288	+	2.29798i
$937$	−5.04610	+	5.04610i	−0.164849	+	0.164849i	−0.784711	−	0.619862i	$-0.787189\pi$
$937$	−5.04610	+	5.04610i	−0.164849	+	0.164849i	0.619862	+	0.784711i	$0.287189\pi$
$938$	−17.6307	+	17.6307i	−0.575662	+	0.575662i
$939$	−39.0965	+	20.3560i	−1.27587	+	0.664292i
$940$	−27.4693	−	17.6036i	−0.895950	−	0.574166i
$941$		−	23.3773i		−	0.762078i	−0.924559	−	0.381039i	$-0.875566\pi$
$941$		−	23.3773i		−	0.762078i	0.924559	−	0.381039i	$-0.124434\pi$
$942$	−32.3711	+	102.694i	−1.05471	+	3.34596i
$943$	0.487504	+	0.487504i	0.0158753	+	0.0158753i
$944$	166.901			5.43217
$945$	−25.3683	+	2.15652i	−0.825231	+	0.0701518i
$946$	−36.5365			−1.18791
$947$	0.993307	+	0.993307i	0.0322781	+	0.0322781i	0.723062	−	0.690784i	$-0.242734\pi$
$947$	0.993307	+	0.993307i	0.0322781	+	0.0322781i	−0.690784	+	0.723062i	$0.742734\pi$
$948$	−5.43524	+	17.2428i	−0.176528	+	0.560020i
$949$		−	70.5309i		−	2.28953i
$950$	4.70289	−	12.7086i	0.152582	−	0.412323i
$951$	45.5959	−	23.7399i	1.47855	−	0.769821i
$952$	60.9665	−	60.9665i	1.97594	−	1.97594i
$953$	−27.4515	+	27.4515i	−0.889242	+	0.889242i	−0.994450	−	0.105208i	$-0.966449\pi$
$953$	−27.4515	+	27.4515i	−0.889242	+	0.889242i	0.105208	+	0.994450i	$0.466449\pi$
$954$	−39.5253	−	27.6673i	−1.27968	−	0.895762i
$955$	−36.5159	+	7.99273i	−1.18163	+	0.258639i
$956$		−	21.0251i		−	0.680000i
$957$	−1.56372	−	0.492914i	−0.0505479	−	0.0159336i
$958$	−26.4076	−	26.4076i	−0.853190	−	0.853190i
$959$	32.5980			1.05265
$960$	−8.70698	+	96.6183i	−0.281017	+	3.11834i
$961$	5.72035			0.184527
$962$	−65.1403	−	65.1403i	−2.10021	−	2.10021i
$963$	−8.60166	−	48.7407i	−0.277184	−	1.57065i
$964$			71.7150i			2.30978i
$965$	12.7622	−	19.9146i	0.410830	−	0.641075i
$966$	7.10755	+	13.6510i	0.228682	+	0.439215i
$967$	−11.7616	+	11.7616i	−0.378227	+	0.378227i	−0.870462	−	0.492235i	$-0.836180\pi$
$967$	−11.7616	+	11.7616i	−0.378227	+	0.378227i	0.492235	+	0.870462i	$0.336180\pi$
$968$	21.1374	−	21.1374i	0.679382	−	0.679382i
$969$	−3.47171	−	6.66790i	−0.111527	−	0.214204i
$970$	12.8279	+	58.6063i	0.411880	+	1.88173i
$971$		−	10.8719i		−	0.348896i	−0.984666	−	0.174448i	$-0.944186\pi$
$971$		−	10.8719i		−	0.348896i	0.984666	−	0.174448i	$-0.0558142\pi$
$972$	−3.66487	−	83.2407i	−0.117551	−	2.66995i
$973$	6.44372	+	6.44372i	0.206576	+	0.206576i
$974$	0.688482			0.0220604
$975$	−23.9285	+	30.8450i	−0.766324	+	0.987831i
$976$	173.285			5.54672
$977$	−33.2307	−	33.2307i	−1.06314	−	1.06314i	−0.997867	−	0.0652771i	$-0.979207\pi$
$977$	−33.2307	−	33.2307i	−1.06314	−	1.06314i	−0.0652771	−	0.997867i	$-0.520793\pi$
$978$	44.2087	+	13.9354i	1.41364	+	0.445605i
$979$			7.31079i			0.233654i
$980$	−5.61845	−	25.6687i	−0.179475	−	0.819957i
$981$	−14.1784	+	20.2552i	−0.452682	+	0.646698i
$982$	−53.8638	+	53.8638i	−1.71886	+	1.71886i
$983$	−35.1193	+	35.1193i	−1.12013	+	1.12013i	−0.128409	+	0.991721i	$0.540987\pi$
$983$	−35.1193	+	35.1193i	−1.12013	+	1.12013i	−0.991721	+	0.128409i	$0.959013\pi$
$984$	−6.41744	+	3.34130i	−0.204581	+	0.106517i
$985$	−13.5484	+	21.1415i	−0.431689	+	0.673624i
$986$			4.01202i			0.127769i
$987$	3.11469	−	9.88105i	0.0991416	−	0.314517i
$988$	−17.0372	−	17.0372i	−0.542025	−	0.542025i
$989$	−7.26803			−0.231110
$990$	−19.1910	−	46.6653i	−0.609929	−	1.48312i
$991$	62.4789			1.98471			0.992354	−	0.123425i	$-0.0393880\pi$
$991$	62.4789			1.98471			0.992354	+	0.123425i	$0.0393880\pi$
$992$	83.4896	+	83.4896i	2.65080	+	2.65080i
$993$	−1.24643	+	3.95419i	−0.0395544	+	0.125483i
$994$		−	56.1197i		−	1.78001i
$995$	4.60607	−	1.00819i	0.146022	−	0.0319618i
$996$	23.0836	−	12.0187i	0.731432	−	0.380827i
$997$	24.1417	−	24.1417i	0.764577	−	0.764577i	−0.212569	−	0.977146i	$-0.568183\pi$
$997$	24.1417	−	24.1417i	0.764577	−	0.764577i	0.977146	+	0.212569i	$0.0681831\pi$
$998$	46.9684	−	46.9684i	1.48676	−	1.48676i
$999$	−5.10578	+	38.8481i	−0.161540	+	1.22910i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.k.d.248.1	yes	36
3.2	odd	2	inner	285.2.k.d.248.18	yes	36
5.2	odd	4	inner	285.2.k.d.77.18	yes	36
15.2	even	4	inner	285.2.k.d.77.1	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.k.d.77.1	✓	36	15.2	even	4	inner
285.2.k.d.77.18	yes	36	5.2	odd	4	inner
285.2.k.d.248.1	yes	36	1.1	even	1	trivial
285.2.k.d.248.18	yes	36	3.2	odd	2	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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.91639 - 1.91639i) q^{2} +(-0.520717 + 1.65192i) q^{3} +5.34506i q^{4} +(0.478119 + 2.18435i) q^{5} +(4.16362 - 2.16783i) q^{6} +(-1.54943 + 1.54943i) q^{7} +(6.41043 - 6.41043i) q^{8} +(-2.45771 - 1.72037i) q^{9} +O(q^{10})\)	\(q+(-1.91639 - 1.91639i) q^{2} +(-0.520717 + 1.65192i) q^{3} +5.34506i q^{4} +(0.478119 + 2.18435i) q^{5} +(4.16362 - 2.16783i) q^{6} +(-1.54943 + 1.54943i) q^{7} +(6.41043 - 6.41043i) q^{8} +(-2.45771 - 1.72037i) q^{9} +(3.26980 - 5.10232i) q^{10} +2.77537i q^{11} +(-8.82964 - 2.78327i) q^{12} +(-3.18746 - 3.18746i) q^{13} +5.93863 q^{14} +(-3.85735 - 0.347614i) q^{15} -13.8796 q^{16} +(-3.06903 - 3.06903i) q^{17} +(1.41302 + 8.00681i) q^{18} -1.00000i q^{19} +(-11.6755 + 2.55558i) q^{20} +(-1.75273 - 3.36636i) q^{21} +(5.31867 - 5.31867i) q^{22} +(1.05802 - 1.05802i) q^{23} +(7.25153 + 13.9276i) q^{24} +(-4.54280 + 2.08876i) q^{25} +12.2168i q^{26} +(4.12169 - 3.16412i) q^{27} +(-8.28182 - 8.28182i) q^{28} +0.341074 q^{29} +(6.72601 + 8.05833i) q^{30} +6.05973 q^{31} +(13.7778 + 13.7778i) q^{32} +(-4.58469 - 1.44518i) q^{33} +11.7629i q^{34} +(-4.12533 - 2.64370i) q^{35} +(9.19549 - 13.1366i) q^{36} +(-5.33202 + 5.33202i) q^{37} +(-1.91639 + 1.91639i) q^{38} +(6.92521 - 3.60568i) q^{39} +(17.0676 + 10.9377i) q^{40} +0.460773i q^{41} +(-3.09234 + 9.81016i) q^{42} +(-3.43474 - 3.43474i) q^{43} -14.8345 q^{44} +(2.58282 - 6.19105i) q^{45} -4.05513 q^{46} +(1.93023 + 1.93023i) q^{47} +(7.22733 - 22.9280i) q^{48} +2.19851i q^{49} +(12.7086 + 4.70289i) q^{50} +(6.66790 - 3.47171i) q^{51} +(17.0372 - 17.0372i) q^{52} +(-4.19597 + 4.19597i) q^{53} +(-13.9624 - 1.83507i) q^{54} +(-6.06238 + 1.32695i) q^{55} +19.8651i q^{56} +(1.65192 + 0.520717i) q^{57} +(-0.653630 - 0.653630i) q^{58} -12.0249 q^{59} +(1.85802 - 20.6178i) q^{60} -12.4849 q^{61} +(-11.6128 - 11.6128i) q^{62} +(6.47366 - 1.14246i) q^{63} -25.0478i q^{64} +(5.43856 - 8.48653i) q^{65} +(6.01652 + 11.5556i) q^{66} +(-2.96882 + 2.96882i) q^{67} +(16.4042 - 16.4042i) q^{68} +(1.19683 + 2.29869i) q^{69} +(2.83937 + 12.9721i) q^{70} -9.44996i q^{71} +(-26.7833 + 4.72666i) q^{72} +(11.0638 + 11.0638i) q^{73} +20.4364 q^{74} +(-1.08496 - 8.59202i) q^{75} +5.34506 q^{76} +(-4.30025 - 4.30025i) q^{77} +(-20.1812 - 6.36150i) q^{78} -1.95283i q^{79} +(-6.63609 - 30.3179i) q^{80} +(3.08066 + 8.45633i) q^{81} +(0.883018 - 0.883018i) q^{82} +(-1.98775 + 1.98775i) q^{83} +(17.9934 - 9.36846i) q^{84} +(5.23649 - 8.17121i) q^{85} +13.1646i q^{86} +(-0.177603 + 0.563429i) q^{87} +(17.7913 + 17.7913i) q^{88} +2.63417 q^{89} +(-16.8141 + 6.91475i) q^{90} +9.87752 q^{91} +(5.65516 + 5.65516i) q^{92} +(-3.15540 + 10.0102i) q^{93} -7.39814i q^{94} +(2.18435 - 0.478119i) q^{95} +(-29.9341 + 15.5855i) q^{96} +(-7.00016 + 7.00016i) q^{97} +(4.21319 - 4.21319i) q^{98} +(4.77465 - 6.82104i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7}+O(q^{10}) \) 36 * q - 2 * q^3 + 4 * q^6 + 4 * q^7	\( 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7} - 4 q^{10} - 18 q^{12} - 8 q^{13} - 8 q^{15} - 84 q^{16} + 8 q^{21} + 40 q^{22} - 20 q^{25} - 14 q^{27} + 36 q^{28} + 28 q^{30} - 28 q^{33} + 92 q^{36} - 4 q^{37} - 20 q^{40} - 100 q^{42} + 16 q^{43} + 28 q^{45} - 24 q^{46} - 58 q^{48} + 32 q^{51} + 148 q^{52} - 72 q^{55} - 2 q^{57} - 12 q^{58} + 58 q^{60} - 112 q^{61} - 64 q^{63} + 92 q^{66} - 8 q^{67} + 8 q^{70} - 88 q^{72} + 76 q^{73} + 80 q^{75} + 36 q^{76} - 36 q^{78} + 4 q^{81} + 20 q^{82} - 28 q^{85} - 4 q^{87} + 140 q^{88} + 76 q^{90} - 24 q^{91} - 48 q^{93} + 32 q^{96} + 32 q^{97}+O(q^{100}) \) 36 * q - 2 * q^3 + 4 * q^6 + 4 * q^7 - 4 * q^10 - 18 * q^12 - 8 * q^13 - 8 * q^15 - 84 * q^16 + 8 * q^21 + 40 * q^22 - 20 * q^25 - 14 * q^27 + 36 * q^28 + 28 * q^30 - 28 * q^33 + 92 * q^36 - 4 * q^37 - 20 * q^40 - 100 * q^42 + 16 * q^43 + 28 * q^45 - 24 * q^46 - 58 * q^48 + 32 * q^51 + 148 * q^52 - 72 * q^55 - 2 * q^57 - 12 * q^58 + 58 * q^60 - 112 * q^61 - 64 * q^63 + 92 * q^66 - 8 * q^67 + 8 * q^70 - 88 * q^72 + 76 * q^73 + 80 * q^75 + 36 * q^76 - 36 * q^78 + 4 * q^81 + 20 * q^82 - 28 * q^85 - 4 * q^87 + 140 * q^88 + 76 * q^90 - 24 * q^91 - 48 * q^93 + 32 * q^96 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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