LMFDB - Embedded newform 285.2.k.d.77.2

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			77.2
Character	$\chi$	$=$	285.77
Dual form			285.2.k.d.248.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87817 + 1.87817i) q^{2} +(1.11989 + 1.32130i) q^{3} -5.05506i q^{4} +(-1.67041 + 1.48652i) q^{5} +(-4.58498 - 0.378288i) q^{6} +(2.61406 + 2.61406i) q^{7} +(5.73793 + 5.73793i) q^{8} +(-0.491688 + 2.95943i) q^{9} +O(q^{10})$	\(q+(-1.87817 + 1.87817i) q^{2} +(1.11989 + 1.32130i) q^{3} -5.05506i q^{4} +(-1.67041 + 1.48652i) q^{5} +(-4.58498 - 0.378288i) q^{6} +(2.61406 + 2.61406i) q^{7} +(5.73793 + 5.73793i) q^{8} +(-0.491688 + 2.95943i) q^{9} +(0.345374 - 5.92925i) q^{10} -1.96388i q^{11} +(6.67927 - 5.66112i) q^{12} +(-2.88991 + 2.88991i) q^{13} -9.81930 q^{14} +(-3.83482 - 0.542376i) q^{15} -11.4435 q^{16} +(-0.118891 + 0.118891i) q^{17} +(-4.63485 - 6.48180i) q^{18} +1.00000i q^{19} +(7.51444 + 8.44401i) q^{20} +(-0.526505 + 6.38143i) q^{21} +(3.68850 + 3.68850i) q^{22} +(-3.71671 - 3.71671i) q^{23} +(-1.15569 + 14.0074i) q^{24} +(0.580522 - 4.96619i) q^{25} -10.8555i q^{26} +(-4.46095 + 2.66457i) q^{27} +(13.2142 - 13.2142i) q^{28} +8.11307 q^{29} +(8.22112 - 6.18377i) q^{30} -5.06945 q^{31} +(10.0170 - 10.0170i) q^{32} +(2.59488 - 2.19933i) q^{33} -0.446595i q^{34} +(-8.25239 - 0.480695i) q^{35} +(14.9601 + 2.48551i) q^{36} +(0.362797 + 0.362797i) q^{37} +(-1.87817 - 1.87817i) q^{38} +(-7.05483 - 0.582064i) q^{39} +(-18.1142 - 1.05514i) q^{40} +3.68873i q^{41} +(-10.9966 - 12.9743i) q^{42} +(6.15556 - 6.15556i) q^{43} -9.92751 q^{44} +(-3.57793 - 5.67436i) q^{45} +13.9612 q^{46} +(-2.85613 + 2.85613i) q^{47} +(-12.8155 - 15.1203i) q^{48} +6.66661i q^{49} +(8.23703 + 10.4177i) q^{50} +(-0.290236 - 0.0239461i) q^{51} +(14.6087 + 14.6087i) q^{52} +(2.19294 + 2.19294i) q^{53} +(3.37390 - 13.3830i) q^{54} +(2.91934 + 3.28047i) q^{55} +29.9986i q^{56} +(-1.32130 + 1.11989i) q^{57} +(-15.2377 + 15.2377i) q^{58} +4.63152 q^{59} +(-2.74174 + 19.3852i) q^{60} -4.96370 q^{61} +(9.52129 - 9.52129i) q^{62} +(-9.02143 + 6.45083i) q^{63} +14.7403i q^{64} +(0.531421 - 9.12323i) q^{65} +(-0.742910 + 9.00434i) q^{66} +(10.1737 + 10.1737i) q^{67} +(0.601000 + 0.601000i) q^{68} +(0.748592 - 9.07321i) q^{69} +(16.4022 - 14.5966i) q^{70} +0.0158418i q^{71} +(-19.8023 + 14.1597i) q^{72} +(-6.43690 + 6.43690i) q^{73} -1.36279 q^{74} +(7.21196 - 4.79454i) q^{75} +5.05506 q^{76} +(5.13369 - 5.13369i) q^{77} +(14.3434 - 12.1570i) q^{78} +4.95634i q^{79} +(19.1153 - 17.0110i) q^{80} +(-8.51649 - 2.91023i) q^{81} +(-6.92807 - 6.92807i) q^{82} +(6.67296 + 6.67296i) q^{83} +(32.2585 + 2.66151i) q^{84} +(0.0218627 - 0.375330i) q^{85} +23.1224i q^{86} +(9.08576 + 10.7198i) q^{87} +(11.2686 - 11.2686i) q^{88} +9.02054 q^{89} +(17.3774 + 3.93745i) q^{90} -15.1088 q^{91} +(-18.7882 + 18.7882i) q^{92} +(-5.67723 - 6.69828i) q^{93} -10.7286i q^{94} +(-1.48652 - 1.67041i) q^{95} +(24.4535 + 2.01755i) q^{96} +(3.45173 + 3.45173i) q^{97} +(-12.5210 - 12.5210i) q^{98} +(5.81196 + 0.965613i) 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 $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.87817	+	1.87817i	−1.32807	+	1.32807i	−0.421014	+	0.907054i	$0.638326\pi$
$2$	−1.87817	+	1.87817i	−1.32807	+	1.32807i	−0.907054	+	0.421014i	$0.861674\pi$
$3$	1.11989	+	1.32130i	0.646569	+	0.762855i
$3$	1.11989	+	1.32130i	0.646569	+	0.762855i
$4$		−	5.05506i		−	2.52753i
$5$	−1.67041	+	1.48652i	−0.747029	+	0.664792i
$5$	−1.67041	+	1.48652i	−0.747029	+	0.664792i
$6$	−4.58498	−	0.378288i	−1.87181	−	0.154435i
$7$	2.61406	+	2.61406i	0.988021	+	0.988021i	0.999929	−	0.0119078i	$-0.00379044\pi$
$7$	2.61406	+	2.61406i	0.988021	+	0.988021i	−0.0119078	+	0.999929i	$0.503790\pi$
$8$	5.73793	+	5.73793i	2.02866	+	2.02866i
$9$	−0.491688	+	2.95943i	−0.163896	+	0.986478i
$10$	0.345374	−	5.92925i	0.109217	−	1.87499i
$11$		−	1.96388i		−	0.592131i	−0.955168	−	0.296065i	$-0.904325\pi$
$11$		−	1.96388i		−	0.592131i	0.955168	−	0.296065i	$-0.0956746\pi$
$12$	6.67927	−	5.66112i	1.92814	−	1.63422i
$13$	−2.88991	+	2.88991i	−0.801516	+	0.801516i	−0.983333	−	0.181816i	$-0.941802\pi$
$13$	−2.88991	+	2.88991i	−0.801516	+	0.801516i	0.181816	+	0.983333i	$0.441802\pi$
$14$	−9.81930			−2.62432
$15$	−3.83482	−	0.542376i	−0.990146	−	0.140041i
$16$	−11.4435			−2.86088
$17$	−0.118891	+	0.118891i	−0.0288353	+	0.0288353i	−0.721377	−	0.692542i	$-0.756491\pi$
$17$	−0.118891	+	0.118891i	−0.0288353	+	0.0288353i	0.692542	+	0.721377i	$0.256491\pi$
$18$	−4.63485	−	6.48180i	−1.09244	−	1.52777i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	7.51444	+	8.44401i	1.68028	+	1.88814i
$21$	−0.526505	+	6.38143i	−0.114893	+	1.39254i
$22$	3.68850	+	3.68850i	0.786390	+	0.786390i
$23$	−3.71671	−	3.71671i	−0.774987	−	0.774987i	0.203986	−	0.978974i	$-0.434610\pi$
$23$	−3.71671	−	3.71671i	−0.774987	−	0.774987i	−0.978974	+	0.203986i	$0.934610\pi$
$24$	−1.15569	+	14.0074i	−0.235904	+	2.85925i
$25$	0.580522	−	4.96619i	0.116104	−	0.993237i
$26$		−	10.8555i		−	2.12894i
$27$	−4.46095	+	2.66457i	−0.858510	+	0.512798i
$28$	13.2142	−	13.2142i	2.49725	−	2.49725i
$29$	8.11307			1.50656			0.753280	−	0.657700i	$-0.228471\pi$
$29$	8.11307			1.50656			0.753280	+	0.657700i	$0.228471\pi$
$30$	8.22112	−	6.18377i	1.50096	−	1.12900i
$31$	−5.06945			−0.910499			−0.455250	−	0.890364i	$-0.650450\pi$
$31$	−5.06945			−0.910499			−0.455250	+	0.890364i	$0.650450\pi$
$32$	10.0170	−	10.0170i	1.77077	−	1.77077i
$33$	2.59488	−	2.19933i	0.451710	−	0.382854i
$34$		−	0.446595i		−	0.0765904i
$35$	−8.25239	−	0.480695i	−1.39491	−	0.0812523i
$36$	14.9601	+	2.48551i	2.49335	+	0.414252i
$37$	0.362797	+	0.362797i	0.0596435	+	0.0596435i	0.736299	−	0.676656i	$-0.236572\pi$
$37$	0.362797	+	0.362797i	0.0596435	+	0.0596435i	−0.676656	+	0.736299i	$0.736572\pi$
$38$	−1.87817	−	1.87817i	−0.304680	−	0.304680i
$39$	−7.05483	−	0.582064i	−1.12968	−	0.0932048i
$40$	−18.1142	−	1.05514i	−2.86411	−	0.166832i
$41$			3.68873i			0.576083i	0.957618	+	0.288041i	$0.0930041\pi$
$41$			3.68873i			0.576083i	−0.957618	+	0.288041i	$0.906996\pi$
$42$	−10.9966	−	12.9743i	−1.69680	−	2.00198i
$43$	6.15556	−	6.15556i	0.938713	−	0.938713i	−0.0595140	−	0.998227i	$-0.518955\pi$
$43$	6.15556	−	6.15556i	0.938713	−	0.938713i	0.998227	+	0.0595140i	$0.0189551\pi$
$44$	−9.92751			−1.49663
$45$	−3.57793	−	5.67436i	−0.533367	−	0.845884i
$46$	13.9612			2.05847
$47$	−2.85613	+	2.85613i	−0.416610	+	0.416610i	−0.884033	−	0.467424i	$-0.845182\pi$
$47$	−2.85613	+	2.85613i	−0.416610	+	0.416610i	0.467424	+	0.884033i	$0.345182\pi$
$48$	−12.8155	−	15.1203i	−1.84976	−	2.18243i
$49$			6.66661i			0.952372i
$50$	8.23703	+	10.4177i	1.16489	+	1.47328i
$51$	−0.290236	−	0.0239461i	−0.0406411	−	0.00335313i
$52$	14.6087	+	14.6087i	2.02586	+	2.02586i
$53$	2.19294	+	2.19294i	0.301223	+	0.301223i	0.841492	−	0.540269i	$-0.181678\pi$
$53$	2.19294	+	2.19294i	0.301223	+	0.301223i	−0.540269	+	0.841492i	$0.681678\pi$
$54$	3.37390	−	13.3830i	0.459129	−	1.82119i
$55$	2.91934	+	3.28047i	0.393643	+	0.442339i
$56$			29.9986i			4.00873i
$57$	−1.32130	+	1.11989i	−0.175011	+	0.148333i
$58$	−15.2377	+	15.2377i	−2.00081	+	2.00081i
$59$	4.63152			0.602972			0.301486	−	0.953471i	$-0.402517\pi$
$59$	4.63152			0.602972			0.301486	+	0.953471i	$0.402517\pi$
$60$	−2.74174	+	19.3852i	−0.353958	+	2.50262i
$61$	−4.96370			−0.635537			−0.317768	−	0.948168i	$-0.602933\pi$
$61$	−4.96370			−0.635537			−0.317768	+	0.948168i	$0.602933\pi$
$62$	9.52129	−	9.52129i	1.20921	−	1.20921i
$63$	−9.02143	+	6.45083i	−1.13659	+	0.812728i
$64$			14.7403i			1.84254i
$65$	0.531421	−	9.12323i	0.0659146	−	1.13160i
$66$	−0.742910	+	9.00434i	−0.0914459	+	1.10836i
$67$	10.1737	+	10.1737i	1.24292	+	1.24292i	0.958784	+	0.284135i	$0.0917064\pi$
$67$	10.1737	+	10.1737i	1.24292	+	1.24292i	0.284135	+	0.958784i	$0.408294\pi$
$68$	0.601000	+	0.601000i	0.0728820	+	0.0728820i
$69$	0.748592	−	9.07321i	0.0901199	−	1.09229i
$70$	16.4022	−	14.5966i	1.96044	−	1.74463i
$71$			0.0158418i			0.00188007i	1.00000		0.000940037i	$0.000299223\pi$
$71$			0.0158418i			0.00188007i	−1.00000		0.000940037i	$0.999701\pi$
$72$	−19.8023	+	14.1597i	−2.33372	+	1.66874i
$73$	−6.43690	+	6.43690i	−0.753383	+	0.753383i	−0.975109	−	0.221726i	$-0.928831\pi$
$73$	−6.43690	+	6.43690i	−0.753383	+	0.753383i	0.221726	+	0.975109i	$0.428831\pi$
$74$	−1.36279			−0.158421
$75$	7.21196	−	4.79454i	0.832766	−	0.553626i
$76$	5.05506			0.579855
$77$	5.13369	−	5.13369i	0.585038	−	0.585038i
$78$	14.3434	−	12.1570i	1.62407	−	1.37651i
$79$			4.95634i			0.557632i	0.960345	+	0.278816i	$0.0899419\pi$
$79$			4.95634i			0.557632i	−0.960345	+	0.278816i	$0.910058\pi$
$80$	19.1153	−	17.0110i	2.13716	−	1.90189i
$81$	−8.51649	−	2.91023i	−0.946276	−	0.323359i
$82$	−6.92807	−	6.92807i	−0.765077	−	0.765077i
$83$	6.67296	+	6.67296i	0.732452	+	0.732452i	0.971105	−	0.238653i	$-0.0767058\pi$
$83$	6.67296	+	6.67296i	0.732452	+	0.732452i	−0.238653	+	0.971105i	$0.576706\pi$
$84$	32.2585	+	2.66151i	3.51969	+	0.290395i
$85$	0.0218627	−	0.375330i	0.00237134	−	0.0407102i
$86$			23.1224i			2.49335i
$87$	9.08576	+	10.7198i	0.974096	+	1.14929i
$88$	11.2686	−	11.2686i	1.20123	−	1.20123i
$89$	9.02054			0.956175			0.478088	−	0.878312i	$-0.341330\pi$
$89$	9.02054			0.956175			0.478088	+	0.878312i	$0.341330\pi$
$90$	17.3774	+	3.93745i	1.83174	+	0.415044i
$91$	−15.1088			−1.58383
$92$	−18.7882	+	18.7882i	−1.95880	+	1.95880i
$93$	−5.67723	−	6.69828i	−0.588701	−	0.694579i
$94$		−	10.7286i		−	1.10657i
$95$	−1.48652	−	1.67041i	−0.152514	−	0.171380i
$96$	24.4535	+	2.01755i	2.49577	+	0.205916i
$97$	3.45173	+	3.45173i	0.350470	+	0.350470i	0.860284	−	0.509814i	$-0.170286\pi$
$97$	3.45173	+	3.45173i	0.350470	+	0.350470i	−0.509814	+	0.860284i	$0.670286\pi$
$98$	−12.5210	−	12.5210i	−1.26482	−	1.26482i
$99$	5.81196	+	0.965613i	0.584124	+	0.0970478i
$100$	−25.1044	−	2.93458i	−2.51044	−	0.293458i
$101$			13.5211i			1.34540i	0.739914	+	0.672701i	$0.234866\pi$
$101$			13.5211i			1.34540i	−0.739914	+	0.672701i	$0.765134\pi$
$102$	0.590087	−	0.500138i	0.0584274	−	0.0495210i
$103$	−1.26800	+	1.26800i	−0.124940	+	0.124940i	−0.766812	−	0.641872i	$-0.778158\pi$
$103$	−1.26800	+	1.26800i	−0.124940	+	0.124940i	0.641872	+	0.766812i	$0.278158\pi$
$104$	−33.1642			−3.25201
$105$	−8.60664	−	11.4422i	−0.839922	−	1.11665i
$106$	−8.23743			−0.800090
$107$	1.50041	−	1.50041i	0.145050	−	0.145050i	−0.630852	−	0.775903i	$-0.717295\pi$
$107$	1.50041	−	1.50041i	0.145050	−	0.145050i	0.775903	+	0.630852i	$0.217295\pi$
$108$	13.4696	+	22.5503i	1.29611	+	2.16991i
$109$		−	10.4372i		−	0.999704i	−0.866111	−	0.499852i	$-0.833388\pi$
$109$		−	10.4372i		−	0.999704i	0.866111	−	0.499852i	$-0.166612\pi$
$110$	−11.6443	−	0.678272i	−1.11024	−	0.0646707i
$111$	−0.0730720	+	0.885659i	−0.00693569	+	0.0840631i
$112$	−29.9140	−	29.9140i	−2.82661	−	2.82661i
$113$	−4.14459	−	4.14459i	−0.389890	−	0.389890i	0.484758	−	0.874648i	$-0.338908\pi$
$113$	−4.14459	−	4.14459i	−0.389890	−	0.389890i	−0.874648	+	0.484758i	$0.838908\pi$
$114$	0.378288	−	4.58498i	0.0354299	−	0.429423i
$115$	11.7334	+	0.683460i	1.09414	+	0.0637330i
$116$		−	41.0121i		−	3.80787i
$117$	−7.13156	−	9.97342i	−0.659313	−	0.922043i
$118$	−8.69878	+	8.69878i	−0.800788	+	0.800788i
$119$	−0.621575			−0.0569797
$120$	−18.8918	−	25.1160i	−1.72458	−	2.29277i
$121$	7.14319			0.649381
$122$	9.32268	−	9.32268i	0.844036	−	0.844036i
$123$	−4.87393	+	4.13098i	−0.439468	+	0.372477i
$124$			25.6263i			2.30131i
$125$	6.41262	+	9.15851i	0.573562	+	0.819162i
$126$	4.82803	−	29.0596i	0.430115	−	2.58883i
$127$	10.4201	+	10.4201i	0.924635	+	0.924635i	0.997353	−	0.0727180i	$-0.0231673\pi$
$127$	10.4201	+	10.4201i	0.924635	+	0.924635i	−0.0727180	+	0.997353i	$0.523167\pi$
$128$	−7.65087	−	7.65087i	−0.676248	−	0.676248i
$129$	15.0269	+	1.23981i	1.32305	+	0.109159i
$130$	16.1369	+	18.1331i	1.41530	+	1.59038i
$131$		−	20.0635i		−	1.75296i	−0.481440	−	0.876479i	$-0.659886\pi$
$131$		−	20.0635i		−	1.75296i	0.481440	−	0.876479i	$-0.340114\pi$
$132$	−11.1177	−	13.1173i	−0.967674	−	1.14171i
$133$	−2.61406	+	2.61406i	−0.226668	+	0.226668i
$134$	−38.2160			−3.30136
$135$	3.49066	−	11.0822i	0.300428	−	0.953804i
$136$	−1.36437			−0.116994
$137$	3.84236	−	3.84236i	0.328275	−	0.328275i	−0.523655	−	0.851930i	$-0.675432\pi$
$137$	3.84236	−	3.84236i	0.328275	−	0.328275i	0.851930	+	0.523655i	$0.175432\pi$
$138$	15.6351	+	18.4470i	1.33095	+	1.57032i
$139$		−	17.5128i		−	1.48541i	−0.669617	−	0.742707i	$-0.733542\pi$
$139$		−	17.5128i		−	1.48541i	0.669617	−	0.742707i	$-0.266458\pi$
$140$	−2.42994	+	41.7163i	−0.205368	+	3.52567i
$141$	−6.97238	−	0.575261i	−0.587180	−	0.0484457i
$142$	−0.0297536	−	0.0297536i	−0.00249687	−	0.00249687i
$143$	5.67542	+	5.67542i	0.474602	+	0.474602i
$144$	5.62663	−	33.8663i	0.468886	−	2.82219i
$145$	−13.5521	+	12.0602i	−1.12544	+	1.00155i
$146$		−	24.1792i		−	2.00109i
$147$	−8.80861	+	7.46587i	−0.726522	+	0.615775i
$148$	1.83396	−	1.83396i	0.150751	−	0.150751i
$149$	3.14043			0.257274			0.128637	−	0.991692i	$-0.458940\pi$
$149$	3.14043			0.257274			0.128637	+	0.991692i	$0.458940\pi$
$150$	−4.54033	+	22.5503i	−0.370717	+	1.84122i
$151$	20.0025			1.62778			0.813890	−	0.581019i	$-0.197346\pi$
$151$	20.0025			1.62778			0.813890	+	0.581019i	$0.197346\pi$
$152$	−5.73793	+	5.73793i	−0.465407	+	0.465407i
$153$	−0.293392	−	0.410307i	−0.0237194	−	0.0331713i
$154$			19.2839i			1.55394i
$155$	8.46804	−	7.53583i	0.680169	−	0.605292i
$156$	−2.94237	+	35.6626i	−0.235578	+	2.85529i
$157$	−1.62416	−	1.62416i	−0.129622	−	0.129622i	0.639319	−	0.768941i	$-0.279216\pi$
$157$	−1.62416	−	1.62416i	−0.129622	−	0.129622i	−0.768941	+	0.639319i	$0.779216\pi$
$158$	−9.30886	−	9.30886i	−0.740573	−	0.740573i
$159$	−0.441686	+	5.35339i	−0.0350280	+	0.424552i
$160$	−1.84201	+	31.6230i	−0.145624	+	2.50002i
$161$		−	19.4314i		−	1.53141i
$162$	21.4613	−	10.5295i	1.68616	−	0.827276i
$163$	10.7499	−	10.7499i	0.842000	−	0.842000i	−0.147119	−	0.989119i	$-0.547000\pi$
$163$	10.7499	−	10.7499i	0.842000	−	0.842000i	0.989119	+	0.147119i	$0.0470000\pi$
$164$	18.6467			1.45607
$165$	−1.06516	+	7.53110i	−0.0829225	+	0.586296i
$166$	−25.0659			−1.94549
$167$	−2.85411	+	2.85411i	−0.220857	+	0.220857i	−0.808859	−	0.588002i	$-0.799915\pi$
$167$	−2.85411	+	2.85411i	−0.220857	+	0.220857i	0.588002	+	0.808859i	$0.299915\pi$
$168$	−39.6372	+	33.5951i	−3.05808	+	2.59192i
$169$		−	3.70314i		−	0.284857i
$170$	0.663872	+	0.745995i	0.0509166	+	0.0572152i
$171$	−2.95943	−	0.491688i	−0.226313	−	0.0376003i
$172$	−31.1167	−	31.1167i	−2.37263	−	2.37263i
$173$	−4.23581	−	4.23581i	−0.322043	−	0.322043i	0.527508	−	0.849550i	$-0.323127\pi$
$173$	−4.23581	−	4.23581i	−0.322043	−	0.322043i	−0.849550	+	0.527508i	$0.823127\pi$
$174$	−37.1983	−	3.06907i	−2.82000	−	0.232666i
$175$	14.4994	−	11.4644i	1.09605	−	0.866626i
$176$			22.4736i			1.69401i
$177$	5.18679	+	6.11964i	0.389863	+	0.459980i
$178$	−16.9421	+	16.9421i	−1.26987	+	1.26987i
$179$	−0.428761			−0.0320471			−0.0160235	−	0.999872i	$-0.505101\pi$
$179$	−0.428761			−0.0320471			−0.0160235	+	0.999872i	$0.505101\pi$
$180$	−28.6842	+	18.0867i	−2.13800	+	1.34810i
$181$	0.482909			0.0358943			0.0179472	−	0.999839i	$-0.494287\pi$
$181$	0.482909			0.0358943			0.0179472	+	0.999839i	$0.494287\pi$
$182$	28.3769	−	28.3769i	2.10343	−	2.10343i
$183$	−5.55880	−	6.55856i	−0.410919	−	0.484822i
$184$		−	42.6524i		−	3.14438i
$185$	−1.14532	−	0.0667143i	−0.0842060	−	0.00490493i
$186$	23.2433	+	1.91771i	1.70428	+	0.140613i
$187$	0.233487	+	0.233487i	0.0170742	+	0.0170742i
$188$	14.4379	+	14.4379i	1.05299	+	1.05299i
$189$	−18.6265	−	4.69582i	−1.35488	−	0.341571i
$190$	5.92925	+	0.345374i	0.430153	+	0.0250561i
$191$			18.7929i			1.35981i	0.733301	+	0.679904i	$0.237978\pi$
$191$			18.7929i			1.35981i	−0.733301	+	0.679904i	$0.762022\pi$
$192$	−19.4765	+	16.5076i	−1.40559	+	1.19133i
$193$	6.30712	−	6.30712i	0.453996	−	0.453996i	−0.442682	−	0.896679i	$-0.645973\pi$
$193$	6.30712	−	6.30712i	0.453996	−	0.453996i	0.896679	+	0.442682i	$0.145973\pi$
$194$	−12.9659			−0.930896
$195$	12.6497	−	9.51485i	0.905863	−	0.681373i
$196$	33.7001			2.40715
$197$	6.21578	−	6.21578i	0.442856	−	0.442856i	−0.450115	−	0.892971i	$-0.648617\pi$
$197$	6.21578	−	6.21578i	0.442856	−	0.442856i	0.892971	+	0.450115i	$0.148617\pi$
$198$	−12.7294	+	9.10227i	−0.904642	+	0.646870i
$199$			16.7946i			1.19054i	0.803527	+	0.595268i	$0.202954\pi$
$199$			16.7946i			1.19054i	−0.803527	+	0.595268i	$0.797046\pi$
$200$	31.8266	−	25.1646i	2.25048	−	1.77941i
$201$	−2.04912	+	24.8361i	−0.144534	+	1.75180i
$202$	−25.3950	−	25.3950i	−1.78679	−	1.78679i
$203$	21.2080	+	21.2080i	1.48851	+	1.48851i
$204$	−0.121049	+	1.46716i	−0.00847513	+	0.102722i
$205$	−5.48337	−	6.16168i	−0.382975	−	0.430350i
$206$		−	4.76305i		−	0.331857i
$207$	12.8268	−	9.17189i	0.891525	−	0.637491i
$208$	33.0707	−	33.0707i	2.29304	−	2.29304i
$209$	1.96388			0.135844
$210$	37.6552	+	5.32576i	2.59846	+	0.367512i
$211$	3.99252			0.274856			0.137428	−	0.990512i	$-0.456116\pi$
$211$	3.99252			0.274856			0.137428	+	0.990512i	$0.456116\pi$
$212$	11.0854	−	11.0854i	0.761351	−	0.761351i
$213$	−0.0209318	+	0.0177411i	−0.00143422	+	0.00121560i
$214$			5.63606i			0.385273i
$215$	−1.13194	+	19.4326i	−0.0771974	+	1.32529i
$216$	−40.8857	−	10.3075i	−2.78192	−	0.701333i
$217$	−13.2518	−	13.2518i	−0.899593	−	0.899593i
$218$	19.6029	+	19.6029i	1.32767	+	1.32767i
$219$	−15.7137	−	1.29647i	−1.06184	−	0.0876076i
$220$	16.5830	−	14.7574i	1.11802	−	0.994945i
$221$		−	0.687167i		−	0.0462239i
$222$	−1.52618	−	1.80066i	−0.102430	−	0.120853i
$223$	−4.40499	+	4.40499i	−0.294980	+	0.294980i	−0.839044	−	0.544064i	$-0.816885\pi$
$223$	−4.40499	+	4.40499i	−0.294980	+	0.294980i	0.544064	+	0.839044i	$0.316885\pi$
$224$	52.3701			3.49913
$225$	14.4117	+	4.15983i	0.960777	+	0.277322i
$226$	15.5685			1.03560
$227$	−2.45504	+	2.45504i	−0.162947	+	0.162947i	−0.783871	−	0.620924i	$-0.786758\pi$
$227$	−2.45504	+	2.45504i	−0.162947	+	0.162947i	0.620924	+	0.783871i	$0.286758\pi$
$228$	5.66112	+	6.67927i	0.374917	+	0.442345i
$229$		−	12.6977i		−	0.839091i	−0.907734	−	0.419545i	$-0.862190\pi$
$229$		−	12.6977i		−	0.839091i	0.907734	−	0.419545i	$-0.137810\pi$
$230$	−23.3210	+	20.7536i	−1.53774	+	1.36845i
$231$	12.5323	+	1.03399i	0.824567	+	0.0680315i
$232$	46.5522	+	46.5522i	3.05630	+	3.05630i
$233$	−18.6113	−	18.6113i	−1.21926	−	1.21926i	−0.967890	−	0.251374i	$-0.919118\pi$
$233$	−18.6113	−	18.6113i	−1.21926	−	1.21926i	−0.251374	−	0.967890i	$-0.580882\pi$
$234$	32.1261	+	5.33751i	2.10015	+	0.348924i
$235$	0.525210	−	9.01660i	0.0342609	−	0.588178i
$236$		−	23.4126i		−	1.52403i
$237$	−6.54883	+	5.55056i	−0.425392	+	0.360548i
$238$	1.16743	−	1.16743i	0.0756729	−	0.0756729i
$239$	−1.67982			−0.108659			−0.0543293	−	0.998523i	$-0.517302\pi$
$239$	−1.67982			−0.108659			−0.0543293	+	0.998523i	$0.517302\pi$
$240$	43.8838	+	6.20669i	2.83268	+	0.400640i
$241$	−16.1063			−1.03750			−0.518749	−	0.854927i	$-0.673602\pi$
$241$	−16.1063			−1.03750			−0.518749	+	0.854927i	$0.673602\pi$
$242$	−13.4161	+	13.4161i	−0.862423	+	0.862423i
$243$	−5.69224	−	14.5120i	−0.365157	−	0.930946i
$244$			25.0918i			1.60634i
$245$	−9.91004	−	11.1359i	−0.633129	−	0.711450i
$246$	1.39540	−	16.9128i	0.0889675	−	1.07832i
$247$	−2.88991	−	2.88991i	−0.183880	−	0.183880i
$248$	−29.0881	−	29.0881i	−1.84710	−	1.84710i
$249$	−1.34402	+	16.2900i	−0.0851737	+	1.03234i
$250$	−29.2453	−	5.15725i	−1.84963	−	0.326173i
$251$		−	10.3835i		−	0.655402i	−0.944781	−	0.327701i	$-0.893726\pi$
$251$		−	10.3835i		−	0.655402i	0.944781	−	0.327701i	$-0.106274\pi$
$252$	32.6093	+	45.6039i	2.05419	+	2.87277i
$253$	−7.29915	+	7.29915i	−0.458894	+	0.458894i
$254$	−39.1415			−2.45596
$255$	0.520408	−	0.391441i	0.0325892	−	0.0245130i
$256$	−0.741396			−0.0463372
$257$	−18.1539	+	18.1539i	−1.13241	+	1.13241i	−0.142635	+	0.989775i	$0.545557\pi$
$257$	−18.1539	+	18.1539i	−1.13241	+	1.13241i	−0.989775	+	0.142635i	$0.954443\pi$
$258$	−30.5517	+	25.8946i	−1.90207	+	1.61212i
$259$			1.89675i			0.117858i
$260$	−46.1185	−	2.68636i	−2.86014	−	0.166601i
$261$	−3.98910	+	24.0101i	−0.246919	+	1.48619i
$262$	37.6827	+	37.6827i	2.32805	+	2.32805i
$263$	11.0145	+	11.0145i	0.679183	+	0.679183i	0.959815	−	0.280632i	$-0.0905441\pi$
$263$	11.0145	+	11.0145i	0.679183	+	0.679183i	−0.280632	+	0.959815i	$0.590544\pi$
$264$	27.5088	+	2.26963i	1.69305	+	0.139686i
$265$	−6.92295	−	0.403256i	−0.425273	−	0.0247718i
$266$		−	9.81930i		−	0.602060i
$267$	10.1020	+	11.9189i	0.618234	+	0.729423i
$268$	51.4288	−	51.4288i	3.14152	−	3.14152i
$269$	3.59002			0.218887			0.109444	−	0.993993i	$-0.465093\pi$
$269$	3.59002			0.218887			0.109444	+	0.993993i	$0.465093\pi$
$270$	14.2582	+	27.3703i	0.867728	+	1.66571i
$271$	−20.3081			−1.23363			−0.616813	−	0.787110i	$-0.711577\pi$
$271$	−20.3081			−1.23363			−0.616813	+	0.787110i	$0.711577\pi$
$272$	1.36053	−	1.36053i	0.0824941	−	0.0824941i
$273$	−16.9202	−	19.9633i	−1.02406	−	1.20823i
$274$			14.4332i			0.871943i
$275$	−9.75297	−	1.14007i	−0.588126	−	0.0687490i
$276$	−45.8656	−	3.78418i	−2.76079	−	0.227781i
$277$	−8.85319	−	8.85319i	−0.531936	−	0.531936i	0.389212	−	0.921148i	$-0.372747\pi$
$277$	−8.85319	−	8.85319i	−0.531936	−	0.531936i	−0.921148	+	0.389212i	$0.872747\pi$
$278$	32.8920	+	32.8920i	1.97273	+	1.97273i
$279$	2.49258	−	15.0027i	0.149227	−	0.898187i
$280$	−44.5934	−	50.1098i	−2.66497	−	2.99463i
$281$		−	12.9966i		−	0.775312i	−0.921804	−	0.387656i	$-0.873285\pi$
$281$		−	12.9966i		−	0.775312i	0.921804	−	0.387656i	$-0.126715\pi$
$282$	14.1758	−	12.0149i	0.844154	−	0.715476i
$283$	−8.49793	+	8.49793i	−0.505149	+	0.505149i	−0.913034	−	0.407884i	$-0.866267\pi$
$283$	−8.49793	+	8.49793i	−0.505149	+	0.505149i	0.407884	+	0.913034i	$0.366267\pi$
$284$	0.0800811			0.00475194
$285$	0.542376	−	3.83482i	0.0321276	−	0.227155i
$286$	−21.3188			−1.26061
$287$	−9.64255	+	9.64255i	−0.569182	+	0.569182i
$288$	24.7194	+	34.5699i	1.45661	+	2.03705i
$289$			16.9717i			0.998337i
$290$	2.80205	−	48.1044i	0.164542	−	2.82479i
$291$	−0.695222	+	8.42634i	−0.0407546	+	0.493961i
$292$	32.5389	+	32.5389i	1.90420	+	1.90420i
$293$	14.7298	+	14.7298i	0.860522	+	0.860522i	0.991399	−	0.130877i	$-0.0417792\pi$
$293$	14.7298	+	14.7298i	0.860522	+	0.860522i	−0.130877	+	0.991399i	$0.541779\pi$
$294$	2.52189	−	30.5663i	0.147080	−	1.78266i
$295$	−7.73652	+	6.88484i	−0.450438	+	0.400851i
$296$			4.16341i			0.241993i
$297$	5.23289	+	8.76074i	0.303643	+	0.508350i
$298$	−5.89828	+	5.89828i	−0.341678	+	0.341678i
$299$	21.4819			1.24233
$300$	−24.2367	−	36.4569i	−1.39931	−	2.10484i
$301$	32.1820			1.85494
$302$	−37.5681	+	37.5681i	−2.16180	+	2.16180i
$303$	−17.8655	+	15.1422i	−1.02635	+	0.869896i
$304$		−	11.4435i		−	0.656330i
$305$	8.29140	−	7.37863i	0.474764	−	0.422499i
$306$	1.32167	+	0.219585i	0.0755547	+	0.0125528i
$307$	−2.76684	−	2.76684i	−0.157912	−	0.157912i	0.623729	−	0.781641i	$-0.285617\pi$
$307$	−2.76684	−	2.76684i	−0.157912	−	0.157912i	−0.781641	+	0.623729i	$0.785617\pi$
$308$	−25.9511	−	25.9511i	−1.47870	−	1.47870i
$309$	−3.09544	−	0.255392i	−0.176093	−	0.0145287i
$310$	−1.75086	+	30.0580i	−0.0994419	+	1.70718i
$311$		−	23.7479i		−	1.34662i	−0.739360	−	0.673310i	$-0.764872\pi$
$311$		−	23.7479i		−	1.34662i	0.739360	−	0.673310i	$-0.235128\pi$
$312$	−37.1402	−	43.8199i	−2.10265	−	2.48081i
$313$	9.95192	−	9.95192i	0.562516	−	0.562516i	−0.367506	−	0.930021i	$-0.619788\pi$
$313$	9.95192	−	9.95192i	0.562516	−	0.562516i	0.930021	+	0.367506i	$0.119788\pi$
$314$	6.10091			0.344294
$315$	5.48018	−	24.1860i	0.308773	−	1.36273i
$316$	25.0546			1.40943
$317$	−2.31246	+	2.31246i	−0.129881	+	0.129881i	−0.769059	−	0.639178i	$-0.779275\pi$
$317$	−2.31246	+	2.31246i	−0.129881	+	0.129881i	0.639178	+	0.769059i	$0.279275\pi$
$318$	−9.22503	−	10.8842i	−0.517314	−	0.610353i
$319$		−	15.9331i		−	0.892080i
$320$	−21.9118	−	24.6224i	−1.22491	−	1.37643i
$321$	3.66280	+	0.302202i	0.204438	+	0.0168673i
$322$	36.4955	+	36.4955i	2.03381	+	2.03381i
$323$	−0.118891	−	0.118891i	−0.00661526	−	0.00661526i
$324$	−14.7114	+	43.0513i	−0.817300	+	2.39174i
$325$	12.6742	+	16.0295i	0.703036	+	0.889155i
$326$			40.3805i			2.23647i
$327$	13.7907	−	11.6885i	0.762629	−	0.646378i
$328$	−21.1657	+	21.1657i	−1.16868	+	1.16868i
$329$	−14.9322			−0.823239
$330$	−12.1442	−	16.1453i	−0.668514	−	0.888767i
$331$	3.05661			0.168006			0.0840032	−	0.996465i	$-0.473229\pi$
$331$	3.05661			0.168006			0.0840032	+	0.996465i	$0.473229\pi$
$332$	33.7322	−	33.7322i	1.85129	−	1.85129i
$333$	−1.25206	+	0.895292i	−0.0686123	+	0.0490617i
$334$		−	10.7210i		−	0.586627i
$335$	−32.1177	−	1.87083i	−1.75478	−	0.102214i
$336$	6.02506	−	73.0259i	0.328694	−	3.98389i
$337$	−24.0316	−	24.0316i	−1.30909	−	1.30909i	−0.922075	−	0.387011i	$-0.873507\pi$
$337$	−24.0316	−	24.0316i	−1.30909	−	1.30909i	−0.387011	−	0.922075i	$-0.626493\pi$
$338$	6.95512	+	6.95512i	0.378309	+	0.378309i
$339$	0.834774	−	10.1178i	0.0453387	−	0.549521i
$340$	−1.89731	−	0.110517i	−0.102896	−	0.00599363i
$341$			9.95576i			0.539135i
$342$	6.48180	−	4.63485i	0.350495	−	0.250624i
$343$	0.871510	−	0.871510i	0.0470571	−	0.0470571i
$344$	70.6402			3.80867
$345$	12.2370	+	16.2688i	0.658821	+	0.875880i
$346$	15.9112			0.855390
$347$	−3.65859	+	3.65859i	−0.196404	+	0.196404i	−0.798456	−	0.602053i	$-0.794350\pi$
$347$	−3.65859	+	3.65859i	−0.196404	+	0.196404i	0.602053	+	0.798456i	$0.294350\pi$
$348$	54.1894	−	45.9290i	2.90486	−	2.46206i
$349$		−	24.5763i		−	1.31554i	−0.753219	−	0.657770i	$-0.771500\pi$
$349$		−	24.5763i		−	1.31554i	0.753219	−	0.657770i	$-0.228500\pi$
$350$	−5.70033	+	48.7645i	−0.304695	+	2.60657i
$351$	5.19135	−	20.5921i	0.277094	−	1.09912i
$352$	−19.6722	−	19.6722i	−1.04853	−	1.04853i
$353$	−24.7354	−	24.7354i	−1.31653	−	1.31653i	−0.916503	−	0.400029i	$-0.869000\pi$
$353$	−24.7354	−	24.7354i	−1.31653	−	1.31653i	−0.400029	−	0.916503i	$-0.631000\pi$
$354$	−21.2354	−	1.75205i	−1.12865	−	0.0931202i
$355$	−0.0235491	−	0.0264622i	−0.00124986	−	0.00140447i
$356$		−	45.5994i		−	2.41676i
$357$	−0.696097	−	0.821290i	−0.0368413	−	0.0434673i
$358$	0.805286	−	0.805286i	0.0425607	−	0.0425607i
$359$	28.2245			1.48963			0.744815	−	0.667271i	$-0.232538\pi$
$359$	28.2245			1.48963			0.744815	+	0.667271i	$0.232538\pi$
$360$	12.0291	−	53.0890i	0.633992	−	2.79804i
$361$	−1.00000			−0.0526316
$362$	−0.906985	+	0.906985i	−0.0476701	+	0.0476701i
$363$	7.99960	+	9.43833i	0.419870	+	0.495384i
$364$			76.3758i			4.00318i
$365$	1.18367	−	20.3208i	0.0619562	−	1.06364i
$366$	22.7585	+	1.87771i	1.18961	+	0.0981493i
$367$	1.22150	+	1.22150i	0.0637616	+	0.0637616i	0.738269	−	0.674507i	$-0.235644\pi$
$367$	1.22150	+	1.22150i	0.0637616	+	0.0637616i	−0.674507	+	0.738269i	$0.735644\pi$
$368$	42.5322	+	42.5322i	2.21714	+	2.21714i
$369$	−10.9165	−	1.81370i	−0.568293	−	0.0944176i
$370$	2.27642	−	2.02582i	0.118345	−	0.105317i
$371$			11.4649i			0.595230i
$372$	−33.8602	+	28.6987i	−1.75557	+	1.48796i
$373$	9.08310	−	9.08310i	0.470305	−	0.470305i	−0.431708	−	0.902013i	$-0.642089\pi$
$373$	9.08310	−	9.08310i	0.470305	−	0.470305i	0.902013	+	0.431708i	$0.142089\pi$
$374$	−0.877057			−0.0453515
$375$	−4.91974	+	18.7296i	−0.254054	+	0.967190i
$376$	−32.7765			−1.69032
$377$	−23.4460	+	23.4460i	−1.20753	+	1.20753i
$378$	43.8034	−	26.1643i	2.25300	−	1.34574i
$379$			4.33929i			0.222895i	0.993770	+	0.111447i	$0.0355486\pi$
$379$			4.33929i			0.222895i	−0.993770	+	0.111447i	$0.964451\pi$
$380$	−8.44401	+	7.51444i	−0.433168	+	0.385483i
$381$	−2.09874	+	25.4375i	−0.107522	+	1.30320i
$382$	−35.2963	−	35.2963i	−1.80592	−	1.80592i
$383$	−13.7042	−	13.7042i	−0.700251	−	0.700251i	0.264213	−	0.964464i	$-0.414888\pi$
$383$	−13.7042	−	13.7042i	−0.700251	−	0.700251i	−0.964464	+	0.264213i	$0.914888\pi$
$384$	1.54098	−	18.6773i	0.0786379	−	0.953120i
$385$	−0.944026	+	16.2067i	−0.0481120	+	0.825968i
$386$			23.6917i			1.20588i
$387$	15.1903	+	21.2436i	0.772169	+	1.07987i
$388$	17.4487	−	17.4487i	0.885823	−	0.885823i
$389$	−9.78146			−0.495940			−0.247970	−	0.968768i	$-0.579763\pi$
$389$	−9.78146			−0.495940			−0.247970	+	0.968768i	$0.579763\pi$
$390$	−5.88776	+	41.6288i	−0.298138	+	2.10796i
$391$	0.883765			0.0446939
$392$	−38.2525	+	38.2525i	−1.93204	+	1.93204i
$393$	26.5100	−	22.4690i	1.33725	−	1.13341i
$394$			23.3486i			1.17629i
$395$	−7.36769	−	8.27910i	−0.370709	−	0.416567i
$396$	4.88123	−	29.3798i	0.245291	−	1.47639i
$397$	−3.88246	−	3.88246i	−0.194855	−	0.194855i	0.602935	−	0.797790i	$-0.293998\pi$
$397$	−3.88246	−	3.88246i	−0.194855	−	0.194855i	−0.797790	+	0.602935i	$0.793998\pi$
$398$	−31.5431	−	31.5431i	−1.58111	−	1.58111i
$399$	−6.38143	−	0.526505i	−0.319471	−	0.0263582i
$400$	−6.64321	+	56.8306i	−0.332161	+	2.84153i
$401$		−	2.63083i		−	0.131377i	−0.997840	−	0.0656887i	$-0.979076\pi$
$401$		−	2.63083i		−	0.131377i	0.997840	−	0.0656887i	$-0.0209244\pi$
$402$	−42.7978	−	50.4950i	−2.13456	−	2.51846i
$403$	14.6502	−	14.6502i	0.729780	−	0.729780i
$404$	68.3501			3.40054
$405$	18.5521	−	7.79864i	0.921862	−	0.387518i
$406$	−79.6647			−3.95369
$407$	0.712489	−	0.712489i	0.0353168	−	0.0353168i
$408$	−1.52795	−	1.80275i	−0.0756448	−	0.0892495i
$409$		−	37.0209i		−	1.83057i	−0.402809	−	0.915284i	$-0.631966\pi$
$409$		−	37.0209i		−	1.83057i	0.402809	−	0.915284i	$-0.368034\pi$
$410$	21.8714	+	1.27399i	1.08015	+	0.0629180i
$411$	9.37995	+	0.773900i	0.462679	+	0.0381737i
$412$	6.40982	+	6.40982i	0.315789	+	0.315789i
$413$	12.1071	+	12.1071i	0.595749	+	0.595749i
$414$	−6.86457	+	41.3173i	−0.337375	+	2.03064i
$415$	−21.0660	−	1.22708i	−1.03409	−	0.0602350i
$416$			57.8965i			2.83861i
$417$	23.1397	−	19.6124i	1.13316	−	0.960423i
$418$	−3.68850	+	3.68850i	−0.180410	+	0.180410i
$419$	34.0978			1.66579			0.832893	−	0.553434i	$-0.186683\pi$
$419$	34.0978			1.66579			0.832893	+	0.553434i	$0.186683\pi$
$420$	−57.8412	+	43.5071i	−2.82236	+	2.12293i
$421$	6.65747			0.324465			0.162233	−	0.986753i	$-0.448131\pi$
$421$	6.65747			0.324465			0.162233	+	0.986753i	$0.448131\pi$
$422$	−7.49863	+	7.49863i	−0.365028	+	0.365028i
$423$	−7.04821	−	9.85686i	−0.342696	−	0.479257i
$424$			25.1658i			1.22216i
$425$	0.521415	+	0.659453i	0.0252923	+	0.0319882i
$426$	0.00599275	−	0.0726343i	0.000290350	−	0.00351914i
$427$	−12.9754	−	12.9754i	−0.627924	−	0.627924i
$428$	−7.58467	−	7.58467i	−0.366619	−	0.366619i
$429$	−1.14310	+	13.8548i	−0.0551894	+	0.668916i
$430$	−34.3719	−	38.6238i	−1.65756	−	1.86261i
$431$			36.4095i			1.75378i	0.480688	+	0.876892i	$0.340387\pi$
$431$			36.4095i			1.75378i	−0.480688	+	0.876892i	$0.659613\pi$
$432$	51.0489	−	30.4921i	2.45609	−	1.46705i
$433$	−11.5129	+	11.5129i	−0.553272	+	0.553272i	−0.927384	−	0.374111i	$-0.877948\pi$
$433$	−11.5129	+	11.5129i	−0.553272	+	0.553272i	0.374111	+	0.927384i	$0.377948\pi$
$434$	49.7784			2.38944
$435$	−31.1122	−	4.40034i	−1.49171	−	0.210980i
$436$	−52.7607			−2.52678
$437$	3.71671	−	3.71671i	0.177794	−	0.177794i
$438$	31.9481	−	27.0781i	1.52654	−	1.29384i
$439$			8.40975i			0.401376i	0.979655	+	0.200688i	$0.0643177\pi$
$439$			8.40975i			0.401376i	−0.979655	+	0.200688i	$0.935682\pi$
$440$	−2.07216	+	35.5740i	−0.0987864	+	1.69593i
$441$	−19.7294	−	3.27789i	−0.939494	−	0.156090i
$442$	1.29062	+	1.29062i	0.0613884	+	0.0613884i
$443$	22.7565	+	22.7565i	1.08119	+	1.08119i	0.996398	+	0.0847955i	$0.0270237\pi$
$443$	22.7565	+	22.7565i	1.08119	+	1.08119i	0.0847955	+	0.996398i	$0.472976\pi$
$444$	4.47706	+	0.369383i	0.212472	+	0.0175302i
$445$	−15.0680	+	13.4092i	−0.714291	+	0.635657i
$446$		−	16.5467i		−	0.783508i
$447$	3.51694	+	4.14947i	0.166346	+	0.196263i
$448$	−38.5321	+	38.5321i	−1.82047	+	1.82047i
$449$	4.04160			0.190735			0.0953675	−	0.995442i	$-0.469597\pi$
$449$	4.04160			0.190735			0.0953675	+	0.995442i	$0.469597\pi$
$450$	−34.8804	+	19.2547i	−1.64428	+	0.907675i
$451$	7.24420			0.341116
$452$	−20.9512	+	20.9512i	−0.985460	+	0.985460i
$453$	22.4006	+	26.4294i	1.05247	+	1.24176i
$454$		−	9.22197i		−	0.432808i
$455$	25.2378	−	22.4595i	1.18317	−	1.05292i
$456$	−14.0074	−	1.15569i	−0.655956	−	0.0541202i
$457$	−14.4297	−	14.4297i	−0.674995	−	0.674995i	0.283869	−	0.958863i	$-0.408382\pi$
$457$	−14.4297	−	14.4297i	−0.674995	−	0.674995i	−0.958863	+	0.283869i	$0.908382\pi$
$458$	23.8485	+	23.8485i	1.11437	+	1.11437i
$459$	0.213572	−	0.847159i	0.00996870	−	0.0395420i
$460$	3.45493	−	59.3129i	0.161087	−	2.76548i
$461$			3.12091i			0.145355i	0.997355	+	0.0726776i	$0.0231544\pi$
$461$			3.12091i			0.145355i	−0.997355	+	0.0726776i	$0.976846\pi$
$462$	−25.4799	+	21.5959i	−1.18543	+	1.00473i
$463$	−23.4962	+	23.4962i	−1.09196	+	1.09196i	−0.0966432	+	0.995319i	$0.530811\pi$
$463$	−23.4962	+	23.4962i	−1.09196	+	1.09196i	−0.995319	+	0.0966432i	$0.969189\pi$
$464$	−92.8420			−4.31008
$465$	19.4404	+	2.74955i	0.901527	+	0.127507i
$466$	69.9103			3.23853
$467$	−3.11320	+	3.11320i	−0.144061	+	0.144061i	−0.775459	−	0.631398i	$-0.782482\pi$
$467$	−3.11320	+	3.11320i	−0.144061	+	0.144061i	0.631398	+	0.775459i	$0.282482\pi$
$468$	−50.4162	+	36.0504i	−2.33049	+	1.66643i
$469$			53.1895i			2.45606i
$470$	15.9483	+	17.9212i	0.735640	+	0.826641i
$471$	0.327127	−	3.96490i	0.0150732	−	0.182693i
$472$	26.5753	+	26.5753i	1.22323	+	1.22323i
$473$	−12.0887	−	12.0887i	−0.555841	−	0.555841i
$474$	1.87492	−	22.7247i	0.0861180	−	1.04378i
$475$	4.96619	+	0.580522i	0.227864	+	0.0266362i
$476$			3.14210i			0.144018i
$477$	−7.56810	+	5.41161i	−0.346519	+	0.247781i
$478$	3.15499	−	3.15499i	0.144306	−	0.144306i
$479$	−16.2403			−0.742039			−0.371020	−	0.928625i	$-0.620992\pi$
$479$	−16.2403			−0.742039			−0.371020	+	0.928625i	$0.620992\pi$
$480$	−43.8464	+	32.9804i	−2.00131	+	1.50534i
$481$	−2.09690			−0.0956105
$482$	30.2504	−	30.2504i	1.37787	−	1.37787i
$483$	25.6748	−	21.7610i	1.16824	−	0.990162i
$484$		−	36.1093i		−	1.64133i
$485$	−10.8969	−	0.634733i	−0.494801	−	0.0288217i
$486$	37.9470	+	16.5651i	1.72131	+	0.751406i
$487$	24.5020	+	24.5020i	1.11029	+	1.11029i	0.993111	+	0.117181i	$0.0373859\pi$
$487$	24.5020	+	24.5020i	1.11029	+	1.11029i	0.117181	+	0.993111i	$0.462614\pi$
$488$	−28.4813	−	28.4813i	−1.28929	−	1.28929i
$489$	26.2427	+	2.16517i	1.18674	+	0.0979125i
$490$	39.5280	+	2.30247i	1.78569	+	0.104015i
$491$		−	13.8631i		−	0.625634i	−0.949813	−	0.312817i	$-0.898727\pi$
$491$		−	13.8631i		−	0.625634i	0.949813	−	0.312817i	$-0.101273\pi$
$492$	20.8823	+	24.6380i	0.941448	+	1.11077i
$493$	−0.964570	+	0.964570i	−0.0434420	+	0.0434420i
$494$	10.8555			0.488411
$495$	−11.1437	+	7.02662i	−0.500874	+	0.315823i
$496$	58.0122			2.60483
$497$	−0.0414113	+	0.0414113i	−0.00185755	+	0.00185755i
$498$	−28.0711	−	33.1197i	−1.25790	−	1.48413i
$499$			9.59691i			0.429617i	0.976656	+	0.214808i	$0.0689127\pi$
$499$			9.59691i			0.429617i	−0.976656	+	0.214808i	$0.931087\pi$
$500$	46.2968	−	32.4162i	2.07046	−	1.44970i
$501$	−6.96743	−	0.574853i	−0.311282	−	0.0256825i
$502$	19.5020	+	19.5020i	0.870419	+	0.870419i
$503$	1.44429	+	1.44429i	0.0643976	+	0.0643976i	0.738572	−	0.674174i	$-0.235500\pi$
$503$	1.44429	+	1.44429i	0.0643976	+	0.0643976i	−0.674174	+	0.738572i	$0.735500\pi$
$504$	−88.7787	−	14.7499i	−3.95452	−	0.657013i
$505$	−20.0994	−	22.5858i	−0.894412	−	1.00505i
$506$		−	27.4181i		−	1.21888i
$507$	4.89297	−	4.14711i	0.217304	−	0.184180i
$508$	52.6742	−	52.6742i	2.33704	−	2.33704i
$509$	−7.68992			−0.340850			−0.170425	−	0.985371i	$-0.554514\pi$
$509$	−7.68992			−0.340850			−0.170425	+	0.985371i	$0.554514\pi$
$510$	−0.242222	+	1.71261i	−0.0107258	+	0.0758356i
$511$	−33.6529			−1.48872
$512$	16.6942	−	16.6942i	0.737787	−	0.737787i
$513$	−2.66457	−	4.46095i	−0.117644	−	0.196956i
$514$		−	68.1924i		−	3.00784i
$515$	0.233171	−	4.00299i	0.0102747	−	0.176393i
$516$	6.26730	−	75.9619i	0.275902	−	3.34404i
$517$	5.60909	+	5.60909i	0.246687	+	0.246687i
$518$	−3.56242	−	3.56242i	−0.156524	−	0.156524i
$519$	0.853146	−	10.3404i	0.0374490	−	0.453895i
$520$	55.3977	−	49.2991i	2.42935	−	2.16191i
$521$		−	30.8124i		−	1.34992i	−0.737856	−	0.674958i	$-0.764162\pi$
$521$		−	30.8124i		−	1.34992i	0.737856	−	0.674958i	$-0.235838\pi$
$522$	−37.6029	−	52.5873i	−1.64583	−	2.30168i
$523$	−4.40699	+	4.40699i	−0.192704	+	0.192704i	−0.796864	−	0.604159i	$-0.793509\pi$
$523$	−4.40699	+	4.40699i	−0.192704	+	0.192704i	0.604159	+	0.796864i	$0.293509\pi$
$524$	−101.422			−4.43065
$525$	31.3857	+	6.31928i	1.36978	+	0.275796i
$526$	−41.3743			−1.80400
$527$	0.602711	−	0.602711i	0.0262545	−	0.0262545i
$528$	−29.6945	+	25.1680i	−1.29229	+	1.09530i
$529$			4.62786i			0.201211i
$530$	13.7599	−	12.2451i	0.597691	−	0.531893i
$531$	−2.27726	+	13.7067i	−0.0988246	+	0.594819i
$532$	13.2142	+	13.2142i	0.572909	+	0.572909i
$533$	−10.6601	−	10.6601i	−0.461740	−	0.461740i
$534$	−41.3590	−	3.41236i	−1.78978	−	0.147667i
$535$	−0.275909	+	4.73669i	−0.0119286	+	0.204785i
$536$			116.752i			5.04293i
$537$	−0.480165	−	0.566523i	−0.0207207	−	0.0244473i
$538$	−6.74268	+	6.74268i	−0.290697	+	0.290697i
$539$	13.0924			0.563929
$540$	−56.0212	−	17.6455i	−2.41077	−	0.759341i
$541$	30.7416			1.32169			0.660843	−	0.750524i	$-0.270199\pi$
$541$	30.7416			1.32169			0.660843	+	0.750524i	$0.270199\pi$
$542$	38.1420	−	38.1420i	1.63834	−	1.63834i
$543$	0.540805	+	0.638069i	0.0232082	+	0.0273822i
$544$			2.38186i			0.102122i
$545$	15.5151	+	17.4344i	0.664595	+	0.746808i
$546$	69.2735	+	5.71546i	2.96463	+	0.244599i
$547$	−24.7815	−	24.7815i	−1.05958	−	1.05958i	−0.998109	−	0.0614735i	$-0.980420\pi$
$547$	−24.7815	−	24.7815i	−1.05958	−	1.05958i	−0.0614735	−	0.998109i	$-0.519580\pi$
$548$	−19.4234	−	19.4234i	−0.829725	−	0.829725i
$549$	2.44059	−	14.6897i	0.104162	−	0.626943i
$550$	20.4590	−	16.1765i	0.872375	−	0.689768i
$551$			8.11307i			0.345629i
$552$	56.3568	−	47.7661i	2.39870	−	2.03306i
$553$	−12.9562	+	12.9562i	−0.550952	+	0.550952i
$554$	33.2556			1.41290
$555$	−1.19449	−	1.58804i	−0.0507033	−	0.0674083i
$556$	−88.5281			−3.75443
$557$	20.4367	−	20.4367i	0.865930	−	0.865930i	−0.126089	−	0.992019i	$-0.540242\pi$
$557$	20.4367	−	20.4367i	0.865930	−	0.865930i	0.992019	+	0.126089i	$0.0402423\pi$
$558$	23.4961	+	32.8591i	0.994670	+	1.39104i
$559$			35.5780i			1.50479i
$560$	94.4363	+	5.50084i	3.99066	+	0.232453i
$561$	−0.0470272	+	0.569987i	−0.00198549	+	0.0240649i
$562$	24.4098	+	24.4098i	1.02967	+	1.02967i
$563$	−19.1295	−	19.1295i	−0.806211	−	0.806211i	0.177847	−	0.984058i	$-0.443087\pi$
$563$	−19.1295	−	19.1295i	−0.806211	−	0.806211i	−0.984058	+	0.177847i	$0.943087\pi$
$564$	−2.90798	+	35.2458i	−0.122448	+	1.48411i
$565$	13.0842	+	0.762143i	0.550455	+	0.0320636i
$566$		−	31.9211i		−	1.34175i
$567$	−14.6551	−	29.8701i	−0.615455	−	1.25443i
$568$	−0.0908990	+	0.0908990i	−0.00381404	+	0.00381404i
$569$	−17.8694			−0.749123			−0.374562	−	0.927202i	$-0.622207\pi$
$569$	−17.8694			−0.749123			−0.374562	+	0.927202i	$0.622207\pi$
$570$	6.18377	+	8.22112i	0.259010	+	0.344345i
$571$	38.3869			1.60644			0.803221	−	0.595682i	$-0.203118\pi$
$571$	38.3869			1.60644			0.803221	+	0.595682i	$0.203118\pi$
$572$	28.6896	−	28.6896i	1.19957	−	1.19957i
$573$	−24.8312	+	21.0460i	−1.03734	+	0.879210i
$574$		−	36.2207i		−	1.51182i
$575$	−20.6155	+	16.3002i	−0.859726	+	0.679767i
$576$	−43.6231	−	7.24764i	−1.81763	−	0.301985i
$577$	21.9754	+	21.9754i	0.914850	+	0.914850i	0.996649	−	0.0817993i	$-0.0260666\pi$
$577$	21.9754	+	21.9754i	0.914850	+	0.914850i	−0.0817993	+	0.996649i	$0.526067\pi$
$578$	−31.8758	−	31.8758i	−1.32586	−	1.32586i
$579$	15.3969	+	1.27033i	0.639874	+	0.0527933i
$580$	60.9652	+	68.5069i	2.53144	+	2.84459i
$581$			34.8870i			1.44736i
$582$	−14.5204	−	17.1319i	−0.601889	−	0.710139i
$583$	4.30666	−	4.30666i	0.178364	−	0.178364i
$584$	−73.8689			−3.05672
$585$	26.7383	+	6.05848i	1.10549	+	0.250487i
$586$	−55.3301			−2.28566
$587$	13.7985	−	13.7985i	0.569525	−	0.569525i	−0.362471	−	0.931995i	$-0.618067\pi$
$587$	13.7985	−	13.7985i	0.569525	−	0.569525i	0.931995	+	0.362471i	$0.118067\pi$
$588$	37.7404	+	44.5281i	1.55639	+	1.83631i
$589$		−	5.06945i		−	0.208883i
$590$	1.59961	−	27.4614i	0.0658547	−	1.13057i
$591$	15.1739	+	1.25194i	0.624172	+	0.0514978i
$592$	−4.15167	−	4.15167i	−0.170633	−	0.170633i
$593$	21.3842	+	21.3842i	0.878144	+	0.878144i	0.993343	−	0.115198i	$-0.0367504\pi$
$593$	21.3842	+	21.3842i	0.878144	+	0.878144i	−0.115198	+	0.993343i	$0.536750\pi$
$594$	−26.2824	−	6.62591i	−1.07838	−	0.271864i
$595$	1.03828	−	0.923983i	0.0425655	−	0.0378796i
$596$		−	15.8751i		−	0.650269i
$597$	−22.1907	+	18.8081i	−0.908206	+	0.769764i
$598$	−40.3467	+	40.3467i	−1.64990	+	1.64990i
$599$	44.7670			1.82913			0.914564	−	0.404441i	$-0.132534\pi$
$599$	44.7670			1.82913			0.914564	+	0.404441i	$0.132534\pi$
$600$	68.8924	+	13.8710i	2.81252	+	0.566280i
$601$	21.1545			0.862909			0.431455	−	0.902135i	$-0.358001\pi$
$601$	21.1545			0.862909			0.431455	+	0.902135i	$0.358001\pi$
$602$	−60.4433	+	60.4433i	−2.46348	+	2.46348i
$603$	−35.1108	+	25.1062i	−1.42982	+	1.02240i
$604$		−	101.114i		−	4.11426i
$605$	−11.9320	+	10.6185i	−0.485107	+	0.431703i
$606$	5.11487	−	61.9941i	0.207778	−	2.51834i
$607$	−25.4585	−	25.4585i	−1.03333	−	1.03333i	−0.999425	−	0.0339018i	$-0.989207\pi$
$607$	−25.4585	−	25.4585i	−1.03333	−	1.03333i	−0.0339018	−	0.999425i	$-0.510793\pi$
$608$	10.0170	+	10.0170i	0.406244	+	0.406244i
$609$	−4.27157	+	51.7730i	−0.173093	+	2.09795i
$610$	−1.71433	+	29.4310i	−0.0694113	+	1.19163i
$611$		−	16.5079i		−	0.667839i
$612$	−2.07412	+	1.48312i	−0.0838415	+	0.0599514i
$613$	−18.5170	+	18.5170i	−0.747894	+	0.747894i	−0.974083	−	0.226190i	$-0.927373\pi$
$613$	−18.5170	+	18.5170i	−0.747894	+	0.747894i	0.226190	+	0.974083i	$0.427373\pi$
$614$	10.3932			0.419435
$615$	2.00068	−	14.1456i	0.0806752	−	0.570406i
$616$	58.9134			2.37369
$617$	0.509575	−	0.509575i	0.0205147	−	0.0205147i	−0.696775	−	0.717290i	$-0.745382\pi$
$617$	0.509575	−	0.509575i	0.0205147	−	0.0205147i	0.717290	+	0.696775i	$0.245382\pi$
$618$	6.29343	−	5.33410i	0.253159	−	0.214569i
$619$		−	5.94443i		−	0.238927i	−0.992839	−	0.119463i	$-0.961883\pi$
$619$		−	5.94443i		−	0.238927i	0.992839	−	0.119463i	$-0.0381174\pi$
$620$	−38.0941	−	42.8064i	−1.52989	−	1.71915i
$621$	26.4835	+	6.67659i	1.06275	+	0.267923i
$622$	44.6027	+	44.6027i	1.78840	+	1.78840i
$623$	23.5802	+	23.5802i	0.944722	+	0.944722i
$624$	80.7320	+	6.66085i	3.23186	+	0.266648i
$625$	−24.3260	−	5.76596i	−0.973039	−	0.230639i
$626$			37.3828i			1.49412i
$627$	2.19933	+	2.59488i	0.0878326	+	0.103629i
$628$	−8.21023	+	8.21023i	−0.327624	+	0.327624i
$629$	−0.0862666			−0.00343967
$630$	35.1328	+	55.7183i	1.39973	+	2.21987i
$631$	−23.7519			−0.945549			−0.472775	−	0.881183i	$-0.656748\pi$
$631$	−23.7519			−0.945549			−0.472775	+	0.881183i	$0.656748\pi$
$632$	−28.4391	+	28.4391i	−1.13125	+	1.13125i
$633$	4.47118	+	5.27533i	0.177714	+	0.209675i
$634$		−	8.68640i		−	0.344981i
$635$	−32.8955	−	1.91614i	−1.30542	−	0.0760396i
$636$	27.0617	+	2.23275i	1.07307	+	0.0885342i
$637$	−19.2659	−	19.2659i	−0.763342	−	0.763342i
$638$	29.9250	+	29.9250i	1.18474	+	1.18474i
$639$	−0.0468827	−	0.00778921i	−0.00185465	−	0.000308136i
$640$	24.1532	+	1.40691i	0.954740	+	0.0556129i
$641$			33.5684i			1.32587i	0.748676	+	0.662936i	$0.230690\pi$
$641$			33.5684i			1.32587i	−0.748676	+	0.662936i	$0.769310\pi$
$642$	−7.44695	+	6.31178i	−0.293908	+	0.249106i
$643$	20.0512	−	20.0512i	0.790744	−	0.790744i	−0.190871	−	0.981615i	$-0.561131\pi$
$643$	20.0512	−	20.0512i	0.790744	−	0.790744i	0.981615	+	0.190871i	$0.0611313\pi$
$644$	−98.2268			−3.87068
$645$	−26.9441	+	20.2668i	−1.06092	+	0.798005i
$646$	0.446595			0.0175710
$647$	−7.32994	+	7.32994i	−0.288170	+	0.288170i	−0.836356	−	0.548187i	$-0.815318\pi$
$647$	−7.32994	+	7.32994i	−0.288170	+	0.288170i	0.548187	+	0.836356i	$0.315318\pi$
$648$	−32.1683	−	65.5657i	−1.26369	−	2.57566i
$649$		−	9.09572i		−	0.357038i
$650$	−53.9104	−	6.30185i	−2.11454	−	0.247179i
$651$	2.66909	−	32.3503i	0.104610	−	1.26791i
$652$	−54.3416	−	54.3416i	−2.12818	−	2.12818i
$653$	−0.929053	−	0.929053i	−0.0363567	−	0.0363567i	0.688695	−	0.725051i	$-0.258184\pi$
$653$	−0.929053	−	0.929053i	−0.0363567	−	0.0363567i	−0.725051	+	0.688695i	$0.758184\pi$
$654$	−3.94827	+	47.8545i	−0.154390	+	1.87126i
$655$	29.8248	+	33.5142i	1.16535	+	1.30951i
$656$		−	42.2120i		−	1.64810i
$657$	−15.8846	−	22.2145i	−0.619719	−	0.866671i
$658$	28.0452	−	28.0452i	1.09332	−	1.09332i
$659$	−0.146567			−0.00570943			−0.00285471	−	0.999996i	$-0.500909\pi$
$659$	−0.146567			−0.00570943			−0.00285471	+	0.999996i	$0.500909\pi$
$660$	38.0702	+	5.38444i	1.48188	+	0.209589i
$661$	20.9876			0.816323			0.408162	−	0.912910i	$-0.366170\pi$
$661$	20.9876			0.816323			0.408162	+	0.912910i	$0.366170\pi$
$662$	−5.74083	+	5.74083i	−0.223124	+	0.223124i
$663$	0.907957	−	0.769552i	0.0352621	−	0.0298869i
$664$			76.5779i			2.97180i
$665$	0.480695	−	8.25239i	0.0186406	−	0.320014i
$666$	0.670068	−	4.03309i	0.0259646	−	0.156279i
$667$	−30.1539	−	30.1539i	−1.16756	−	1.16756i
$668$	14.4277	+	14.4277i	0.558224	+	0.558224i
$669$	−10.7534	−	0.887222i	−0.415752	−	0.0343020i
$670$	63.8364	−	56.8089i	2.46621	−	2.19472i
$671$			9.74809i			0.376321i
$672$	58.6488	+	69.1969i	2.26243	+	2.66933i
$673$	31.6581	−	31.6581i	1.22033	−	1.22033i	0.252815	−	0.967515i	$-0.418644\pi$
$673$	31.6581	−	31.6581i	1.22033	−	1.22033i	0.967515	−	0.252815i	$-0.0813562\pi$
$674$	90.2711			3.47711
$675$	10.6431	+	23.7007i	0.409653	+	0.912242i
$676$	−18.7196			−0.719983
$677$	9.02858	−	9.02858i	0.346997	−	0.346997i	−0.511993	−	0.858990i	$-0.671093\pi$
$677$	9.02858	−	9.02858i	0.346997	−	0.346997i	0.858990	+	0.511993i	$0.171093\pi$
$678$	17.4350	+	20.5707i	0.669589	+	0.790014i
$679$			18.0460i			0.692543i
$680$	2.27906	−	2.02817i	0.0873980	−	0.0777767i
$681$	−5.99323	−	0.494476i	−0.229661	−	0.0189484i
$682$	−18.6986	−	18.6986i	−0.716007	−	0.716007i
$683$	−26.5061	−	26.5061i	−1.01423	−	1.01423i	−0.999897	−	0.0143293i	$-0.995439\pi$
$683$	−26.5061	−	26.5061i	−1.01423	−	1.01423i	−0.0143293	−	0.999897i	$-0.504561\pi$
$684$	−2.48551	+	14.9601i	−0.0950358	+	0.572014i
$685$	−0.706566	+	12.1301i	−0.0269965	+	0.463465i
$686$			3.27369i			0.124990i
$687$	16.7776	−	14.2201i	0.640105	−	0.542530i
$688$	−70.4411	+	70.4411i	−2.68554	+	2.68554i
$689$	−12.6748			−0.482871
$690$	−53.5388	−	7.57224i	−2.03819	−	0.288270i
$691$	41.3985			1.57487			0.787437	−	0.616396i	$-0.211408\pi$
$691$	41.3985			1.57487			0.787437	+	0.616396i	$0.211408\pi$
$692$	−21.4123	+	21.4123i	−0.813973	+	0.813973i
$693$	12.6686	+	17.7170i	0.481241	+	0.673012i
$694$		−	13.7429i		−	0.521675i
$695$	26.0331	+	29.2535i	0.987491	+	1.10965i
$696$	−9.37621	+	113.643i	−0.355404	+	4.30763i
$697$	−0.438556	−	0.438556i	−0.0166115	−	0.0166115i
$698$	46.1586	+	46.1586i	1.74713	+	1.74713i
$699$	3.74854	−	45.4337i	0.141783	−	1.71846i
$700$	−57.9531	−	73.2954i	−2.19042	−	2.77031i
$701$		−	51.1074i		−	1.93030i	−0.261694	−	0.965151i	$-0.584281\pi$
$701$		−	51.1074i		−	1.93030i	0.261694	−	0.965151i	$-0.415719\pi$
$702$	28.9252	+	48.4257i	1.09171	+	1.82771i
$703$	−0.362797	+	0.362797i	−0.0136832	+	0.0136832i
$704$	28.9482			1.09103
$705$	12.5018	−	9.40365i	0.470847	−	0.354162i
$706$	92.9146			3.49689
$707$	−35.3450	+	35.3450i	−1.32929	+	1.32929i
$708$	30.9351	−	26.2196i	1.16261	−	0.985391i
$709$			16.2520i			0.610355i	0.952295	+	0.305178i	$0.0987158\pi$
$709$			16.2520i			0.610355i	−0.952295	+	0.305178i	$0.901284\pi$
$710$	0.0939299	+	0.00547134i	0.00352513	+	0.000205336i
$711$	−14.6680	−	2.43697i	−0.550091	−	0.0913935i
$712$	51.7592	+	51.7592i	1.93976	+	1.93976i
$713$	18.8417	+	18.8417i	0.705626	+	0.705626i
$714$	2.84991	+	0.235134i	0.106655	+	0.00879968i
$715$	−17.9169	−	1.04364i	−0.670053	−	0.0390301i
$716$			2.16741i			0.0809999i
$717$	−1.88122	−	2.21955i	−0.0702553	−	0.0828907i
$718$	−53.0104	+	53.0104i	−1.97833	+	1.97833i
$719$	10.5713			0.394244			0.197122	−	0.980379i	$-0.436840\pi$
$719$	10.5713			0.394244			0.197122	+	0.980379i	$0.436840\pi$
$720$	40.9441	+	64.9346i	1.52590	+	2.41997i
$721$	−6.62926			−0.246887
$722$	1.87817	−	1.87817i	0.0698983	−	0.0698983i
$723$	−18.0373	−	21.2813i	−0.670815	−	0.791461i
$724$		−	2.44113i		−	0.0907239i
$725$	4.70982	−	40.2910i	0.174918	−	1.49637i
$726$	−32.7514	−	2.70218i	−1.21552	−	0.100287i
$727$	−6.13560	−	6.13560i	−0.227557	−	0.227557i	0.584114	−	0.811671i	$-0.301442\pi$
$727$	−6.13560	−	6.13560i	−0.227557	−	0.227557i	−0.811671	+	0.584114i	$0.801442\pi$
$728$	−86.6930	−	86.6930i	−3.21306	−	3.21306i
$729$	12.8001	−	23.7730i	0.474077	−	0.880483i
$730$	35.9429	+	40.3892i	1.33031	+	1.49487i
$731$			1.46368i			0.0541361i
$732$	−33.1539	+	28.1001i	−1.22540	+	1.03861i
$733$	−10.0183	+	10.0183i	−0.370034	+	0.370034i	−0.867490	−	0.497455i	$-0.834268\pi$
$733$	−10.0183	+	10.0183i	−0.370034	+	0.370034i	0.497455	+	0.867490i	$0.334268\pi$
$734$	−4.58836			−0.169359
$735$	3.61581	−	25.5652i	0.133371	−	0.942987i
$736$	−74.4607			−2.74466
$737$	19.9799	−	19.9799i	0.735971	−	0.735971i
$738$	23.9096	−	17.0967i	0.880124	−	0.629338i
$739$			9.87022i			0.363082i	0.983383	+	0.181541i	$0.0581085\pi$
$739$			9.87022i			0.363082i	−0.983383	+	0.181541i	$0.941892\pi$
$740$	−0.337245	+	5.78969i	−0.0123974	+	0.212833i
$741$	0.582064	−	7.05483i	0.0213827	−	0.259166i
$742$	−21.5331	−	21.5331i	−0.790506	−	0.790506i
$743$	−8.21613	−	8.21613i	−0.301421	−	0.301421i	0.540149	−	0.841569i	$-0.318368\pi$
$743$	−8.21613	−	8.21613i	−0.301421	−	0.301421i	−0.841569	+	0.540149i	$0.818368\pi$
$744$	5.85871	−	71.0097i	0.214791	−	2.60334i
$745$	−5.24580	+	4.66832i	−0.192191	+	0.171034i
$746$			34.1192i			1.24919i
$747$	−23.0292	+	16.4672i	−0.842594	+	0.602502i
$748$	1.18029	−	1.18029i	0.0431557	−	0.0431557i
$749$	7.84433			0.286626
$750$	−25.9372	−	44.4174i	−0.947093	−	1.62190i
$751$	−8.64862			−0.315593			−0.157796	−	0.987472i	$-0.550439\pi$
$751$	−8.64862			−0.315593			−0.157796	+	0.987472i	$0.550439\pi$
$752$	32.6842	−	32.6842i	1.19187	−	1.19187i
$753$	13.7198	−	11.6284i	0.499977	−	0.423763i
$754$		−	88.0714i		−	3.20737i
$755$	−33.4123	+	29.7341i	−1.21600	+	1.08213i
$756$	−23.7377	+	94.1582i	−0.863331	+	3.42450i
$757$	1.46815	+	1.46815i	0.0533608	+	0.0533608i	0.733284	−	0.679923i	$-0.237987\pi$
$757$	1.46815	+	1.46815i	0.0533608	+	0.0533608i	−0.679923	+	0.733284i	$0.737987\pi$
$758$	−8.14994	−	8.14994i	−0.296019	−	0.296019i
$759$	−17.8187	−	1.47014i	−0.646776	−	0.0533628i
$760$	1.05514	−	18.1142i	0.0382739	−	0.657071i
$761$		−	11.2911i		−	0.409304i	−0.978835	−	0.204652i	$-0.934394\pi$
$761$		−	11.2911i		−	0.409304i	0.978835	−	0.204652i	$-0.0656062\pi$
$762$	−43.8342	−	51.7178i	−1.58795	−	1.87354i
$763$	27.2835	−	27.2835i	0.987729	−	0.987729i
$764$	94.9993			3.43695
$765$	1.10001	+	0.249246i	0.0397711	+	0.00901151i
$766$	51.4776			1.85996
$767$	−13.3847	+	13.3847i	−0.483292	+	0.483292i
$768$	−0.830283	−	0.979609i	−0.0299602	−	0.0353486i
$769$		−	27.8835i		−	1.00550i	−0.864431	−	0.502752i	$-0.832321\pi$
$769$		−	27.8835i		−	1.00550i	0.864431	−	0.502752i	$-0.167679\pi$
$770$	−28.6659	−	32.2119i	−1.03305	−	1.16084i
$771$	−44.3173	−	3.65643i	−1.59605	−	0.131683i
$772$	−31.8829	−	31.8829i	−1.14749	−	1.14749i
$773$	−23.9989	−	23.9989i	−0.863180	−	0.863180i	0.128526	−	0.991706i	$-0.458975\pi$
$773$	−23.9989	−	23.9989i	−0.863180	−	0.863180i	−0.991706	+	0.128526i	$0.958975\pi$
$774$	−68.4291	−	11.3690i	−2.45963	−	0.408650i
$775$	−2.94293	+	25.1758i	−0.105713	+	0.904342i
$776$			39.6115i			1.42197i
$777$	−2.50618	+	2.12415i	−0.0899087	+	0.0762035i
$778$	18.3713	−	18.3713i	0.658641	−	0.658641i
$779$	−3.68873			−0.132162
$780$	−48.0981	−	63.9449i	−1.72219	−	2.28960i
$781$	0.0311113			0.00111325
$782$	−1.65986	+	1.65986i	−0.0593566	+	0.0593566i
$783$	−36.1920	+	21.6179i	−1.29340	+	0.772560i
$784$		−	76.2893i		−	2.72462i
$785$	5.12736	+	0.298665i	0.183003	+	0.0106598i
$786$	−7.58978	+	91.9909i	−0.270718	+	3.28121i
$787$	29.8650	+	29.8650i	1.06457	+	1.06457i	0.997766	+	0.0668081i	$0.0212815\pi$
$787$	29.8650	+	29.8650i	1.06457	+	1.06457i	0.0668081	+	0.997766i	$0.478718\pi$
$788$	−31.4211	−	31.4211i	−1.11933	−	1.11933i
$789$	−2.21846	+	26.8886i	−0.0789793	+	0.957258i
$790$	29.3874	+	1.71179i	1.04556	+	0.0609028i
$791$		−	21.6684i		−	0.770440i
$792$	27.8080	+	38.8892i	0.988113	+	1.38187i
$793$	14.3446	−	14.3446i	0.509393	−	0.509393i
$794$	14.5839			0.517562
$795$	−7.22012	−	9.59892i	−0.256071	−	0.340439i
$796$	84.8976			3.00911
$797$	−10.0124	+	10.0124i	−0.354658	+	0.354658i	−0.861839	−	0.507182i	$-0.830687\pi$
$797$	−10.0124	+	10.0124i	−0.354658	+	0.354658i	0.507182	+	0.861839i	$0.330687\pi$
$798$	12.9743	−	10.9966i	0.459285	−	0.389274i
$799$		−	0.679136i		−	0.0240261i
$800$	−43.9312	−	55.5615i	−1.55320	−	1.96439i
$801$	−4.43529	+	26.6957i	−0.156713	+	0.943246i
$802$	4.94115	+	4.94115i	0.174478	+	0.174478i
$803$	12.6413	+	12.6413i	0.446101	+	0.446101i
$804$	125.548	+	10.3584i	4.42773	+	0.365313i
$805$	28.8851	+	32.4583i	1.01807	+	1.14401i
$806$			55.0313i			1.93839i
$807$	4.02043	+	4.74351i	0.141526	+	0.166979i
$808$	−77.5832	+	77.5832i	−2.72937	+	2.72937i
$809$	−24.9450			−0.877020			−0.438510	−	0.898726i	$-0.644494\pi$
$809$	−24.9450			−0.877020			−0.438510	+	0.898726i	$0.644494\pi$
$810$	−20.1969	+	49.4913i	−0.709646	+	1.73895i
$811$	15.0374			0.528033			0.264017	−	0.964518i	$-0.414953\pi$
$811$	15.0374			0.528033			0.264017	+	0.964518i	$0.414953\pi$
$812$	107.208	−	107.208i	3.76226	−	3.76226i
$813$	−22.7428	−	26.8331i	−0.797625	−	0.941078i
$814$			2.67635i			0.0938061i
$815$	−1.97679	+	33.9368i	−0.0692439	+	1.18875i
$816$	3.32131	+	0.274028i	0.116269	+	0.00959288i
$817$	6.15556	+	6.15556i	0.215356	+	0.215356i
$818$	69.5317	+	69.5317i	2.43112	+	2.43112i
$819$	7.42880	−	44.7134i	0.259583	−	1.56241i
$820$	−31.1477	+	27.7187i	−1.08772	+	0.967980i
$821$		−	8.96002i		−	0.312707i	−0.987701	−	0.156353i	$-0.950026\pi$
$821$		−	8.96002i		−	0.312707i	0.987701	−	0.156353i	$-0.0499739\pi$
$822$	−19.0707	+	16.1636i	−0.665166	+	0.563772i
$823$	8.13076	−	8.13076i	0.283420	−	0.283420i	−0.551051	−	0.834472i	$-0.685773\pi$
$823$	8.13076	−	8.13076i	0.283420	−	0.283420i	0.834472	+	0.551051i	$0.185773\pi$
$824$	−14.5514			−0.506922
$825$	−9.41588	−	14.1634i	−0.327819	−	0.493106i
$826$	−45.4783			−1.58239
$827$	−38.0057	+	38.0057i	−1.32159	+	1.32159i	−0.409096	+	0.912492i	$0.634156\pi$
$827$	−38.0057	+	38.0057i	−1.32159	+	1.32159i	−0.912492	+	0.409096i	$0.865844\pi$
$828$	−46.3645	−	64.8403i	−1.61128	−	2.25336i
$829$			41.7308i			1.44937i	0.689080	+	0.724685i	$0.258015\pi$
$829$			41.7308i			1.44937i	−0.689080	+	0.724685i	$0.741985\pi$
$830$	41.8703	−	37.2610i	1.45334	−	1.29335i
$831$	1.78314	−	21.6124i	0.0618566	−	0.749724i
$832$	−42.5982	−	42.5982i	−1.47683	−	1.47683i
$833$	−0.792598	−	0.792598i	−0.0274619	−	0.0274619i
$834$	−6.62486	+	80.2958i	−0.229400	+	2.78042i
$835$	0.524837	−	9.01021i	0.0181627	−	0.311811i
$836$		−	9.92751i		−	0.343350i
$837$	22.6145	−	13.5079i	0.781672	−	0.466902i
$838$	−64.0415	+	64.0415i	−2.21228	+	2.21228i
$839$	−39.2304			−1.35438			−0.677192	−	0.735806i	$-0.736803\pi$
$839$	−39.2304			−1.35438			−0.677192	+	0.735806i	$0.736803\pi$
$840$	16.2705	−	115.039i	0.561386	−	3.96922i
$841$	36.8219			1.26972
$842$	−12.5039	+	12.5039i	−0.430912	+	0.430912i
$843$	17.1725	−	14.5548i	0.591451	−	0.501293i
$844$		−	20.1824i		−	0.694707i
$845$	5.50478	+	6.18574i	0.189370	+	0.212796i
$846$	31.7506	+	5.27513i	1.09161	+	0.181363i
$847$	18.6727	+	18.6727i	0.641603	+	0.641603i
$848$	−25.0949	−	25.0949i	−0.861763	−	0.861763i
$849$	−20.7451	−	1.71159i	−0.711970	−	0.0587416i
$850$	−2.21787	−	0.259258i	−0.0760724	−	0.00889249i
$851$		−	2.69683i		−	0.0924460i
$852$	0.0896822	+	0.105812i	0.00307246	+	0.00362504i
$853$	11.1471	−	11.1471i	0.381670	−	0.381670i	−0.490033	−	0.871704i	$-0.663015\pi$
$853$	11.1471	−	11.1471i	0.381670	−	0.381670i	0.871704	+	0.490033i	$0.163015\pi$
$854$	48.7401			1.66785
$855$	5.67436	−	3.57793i	0.194059	−	0.122363i
$856$	17.2185			0.588517
$857$	−15.5408	+	15.5408i	−0.530865	+	0.530865i	−0.920830	−	0.389965i	$-0.872487\pi$
$857$	−15.5408	+	15.5408i	−0.530865	+	0.530865i	0.389965	+	0.920830i	$0.372487\pi$
$858$	−23.8748	−	28.1686i	−0.815071	−	0.961662i
$859$			1.44068i			0.0491555i	0.999698	+	0.0245777i	$0.00782413\pi$
$859$			1.44068i			0.0491555i	−0.999698	+	0.0245777i	$0.992176\pi$
$860$	98.2331	+	5.72200i	3.34972	+	0.195119i
$861$	−23.5394	−	1.94213i	−0.802219	−	0.0661877i
$862$	−68.3833	−	68.3833i	−2.32914	−	2.32914i
$863$	−10.2849	−	10.2849i	−0.350102	−	0.350102i	0.510045	−	0.860148i	$-0.329629\pi$
$863$	−10.2849	−	10.2849i	−0.350102	−	0.350102i	−0.860148	+	0.510045i	$0.829629\pi$
$864$	−17.9943	+	71.3764i	−0.612178	+	2.42828i
$865$	13.3721	+	0.778917i	0.454667	+	0.0264840i
$866$		−	43.2462i		−	1.46957i
$867$	−22.4248	+	19.0065i	−0.761587	+	0.645494i
$868$	−66.9888	+	66.9888i	−2.27375	+	2.27375i
$869$	9.73363			0.330191
$870$	66.6986	−	50.1694i	2.26129	−	1.70090i
$871$	−58.8023			−1.99244
$872$	59.8880	−	59.8880i	2.02806	−	2.02806i
$873$	−11.9123	+	8.51799i	−0.403171	+	0.288290i
$874$			13.9612i			0.472246i
$875$	−7.17792	+	40.7038i	−0.242658	+	1.37604i
$876$	−6.55375	+	79.4339i	−0.221431	+	2.68382i
$877$	5.21645	+	5.21645i	0.176147	+	0.176147i	0.789674	−	0.613527i	$-0.210250\pi$
$877$	5.21645	+	5.21645i	0.176147	+	0.176147i	−0.613527	+	0.789674i	$0.710250\pi$
$878$	−15.7950	−	15.7950i	−0.533054	−	0.533054i
$879$	−2.96676	+	35.9582i	−0.100066	+	1.21284i
$880$	−33.4075	−	37.5401i	−1.12617	−	1.26548i
$881$		−	20.6917i		−	0.697120i	−0.937286	−	0.348560i	$-0.886671\pi$
$881$		−	20.6917i		−	0.697120i	0.937286	−	0.348560i	$-0.113329\pi$
$882$	43.2116	−	30.8987i	1.45501	−	1.04041i
$883$	−20.5807	+	20.5807i	−0.692596	+	0.692596i	−0.962802	−	0.270206i	$-0.912908\pi$
$883$	−20.5807	+	20.5807i	−0.692596	+	0.692596i	0.270206	+	0.962802i	$0.412908\pi$
$884$	−3.47367			−0.116832
$885$	−17.7610	−	2.51203i	−0.597030	−	0.0844408i
$886$	−85.4812			−2.87180
$887$	3.75118	−	3.75118i	0.125952	−	0.125952i	−0.641321	−	0.767273i	$-0.721613\pi$
$887$	3.75118	−	3.75118i	0.125952	−	0.125952i	0.767273	+	0.641321i	$0.221613\pi$
$888$	−5.50113	+	4.66257i	−0.184606	+	0.156465i
$889$			54.4775i			1.82712i
$890$	3.11546	−	53.4850i	0.104431	−	1.79282i
$891$	−5.71533	+	16.7253i	−0.191471	+	0.560319i
$892$	22.2675	+	22.2675i	0.745571	+	0.745571i
$893$	−2.85613	−	2.85613i	−0.0955768	−	0.0955768i
$894$	−14.3988	−	1.18799i	−0.481569	−	0.0397322i
$895$	0.716205	−	0.637361i	0.0239401	−	0.0213046i
$896$		−	39.9996i		−	1.33629i
$897$	24.0574	+	28.3841i	0.803253	+	0.947718i
$898$	−7.59082	+	7.59082i	−0.253309	+	0.253309i
$899$	−41.1288			−1.37172
$900$	21.0282	−	72.8518i	0.700939	−	2.42839i
$901$	−0.521441			−0.0173717
$902$	−13.6059	+	13.6059i	−0.453026	+	0.453026i
$903$	36.0403	+	42.5222i	1.19935	+	1.41505i
$904$		−	47.5627i		−	1.58191i
$905$	−0.806654	+	0.717853i	−0.0268141	+	0.0238622i
$906$	−91.7111	−	7.56670i	−3.04690	−	0.251387i
$907$	8.90010	+	8.90010i	0.295523	+	0.295523i	0.839257	−	0.543734i	$-0.182990\pi$
$907$	8.90010	+	8.90010i	0.295523	+	0.295523i	−0.543734	+	0.839257i	$0.682990\pi$
$908$	12.4104	+	12.4104i	0.411852	+	0.411852i
$909$	−40.0149	−	6.64817i	−1.32721	−	0.220506i
$910$	−5.21818	+	89.5837i	−0.172981	+	2.96967i
$911$		−	47.7271i		−	1.58127i	−0.612288	−	0.790635i	$-0.709751\pi$
$911$		−	47.7271i		−	1.58127i	0.612288	−	0.790635i	$-0.290249\pi$
$912$	15.1203	−	12.8155i	0.500685	−	0.424363i
$913$	13.1049	−	13.1049i	0.433707	−	0.433707i
$914$	54.2030			1.79288
$915$	19.0349	+	2.69219i	0.629274	+	0.0890012i
$916$	−64.1878			−2.12083
$917$	52.4472	−	52.4472i	1.73196	−	1.73196i
$918$	1.18999	+	1.99224i	0.0392754	+	0.0657536i
$919$			24.3417i			0.802957i	0.915868	+	0.401479i	$0.131504\pi$
$919$			24.3417i			0.802957i	−0.915868	+	0.401479i	$0.868496\pi$
$920$	63.4036	+	71.2469i	2.09036	+	2.34894i
$921$	0.557276	−	6.75439i	0.0183629	−	0.222565i
$922$	−5.86160	−	5.86160i	−0.193042	−	0.193042i
$923$	−0.0457813	−	0.0457813i	−0.00150691	−	0.00150691i
$924$	5.22688	−	63.3517i	0.171952	−	2.08412i
$925$	2.01233	−	1.59111i	0.0661651	−	0.0523153i
$926$		−	88.2599i		−	2.90040i
$927$	−3.12910	−	4.37603i	−0.102773	−	0.143728i
$928$	81.2688	−	81.2688i	2.66778	−	2.66778i
$929$	−48.8166			−1.60162			−0.800811	−	0.598917i	$-0.795598\pi$
$929$	−48.8166			−1.60162			−0.800811	+	0.598917i	$0.795598\pi$
$930$	−41.6765	+	31.3483i	−1.36663	+	1.02795i
$931$	−6.66661			−0.218489
$932$	−94.0810	+	94.0810i	−3.08173	+	3.08173i
$933$	31.3782	−	26.5951i	1.02728	−	0.870684i
$934$		−	11.6942i		−	0.382647i
$935$	−0.737101	−	0.0429355i	−0.0241058	−	0.00140414i
$936$	16.3064	−	98.1471i	0.532991	−	3.20804i
$937$	−7.04288	−	7.04288i	−0.230081	−	0.230081i	0.582646	−	0.812726i	$-0.302018\pi$
$937$	−7.04288	−	7.04288i	−0.230081	−	0.230081i	−0.812726	+	0.582646i	$0.802018\pi$
$938$	−99.8990	−	99.8990i	−3.26182	−	3.26182i
$939$	24.2946	+	2.00444i	0.792823	+	0.0654125i
$940$	−45.5794	−	2.65497i	−1.48664	−	0.0865955i
$941$		−	14.9283i		−	0.486650i	−0.969945	−	0.243325i	$-0.921762\pi$
$941$		−	14.9283i		−	0.486650i	0.969945	−	0.243325i	$-0.0782381\pi$
$942$	6.83236	+	8.06116i	0.222610	+	0.262647i
$943$	13.7099	−	13.7099i	0.446457	−	0.446457i
$944$	−53.0008			−1.72503
$945$	38.0943	−	19.8448i	1.23921	−	0.645550i
$946$	45.4095			1.47639
$947$	12.4386	−	12.4386i	0.404199	−	0.404199i	−0.475511	−	0.879710i	$-0.657737\pi$
$947$	12.4386	−	12.4386i	0.404199	−	0.404199i	0.879710	+	0.475511i	$0.157737\pi$
$948$	28.0584	+	33.1047i	0.911295	+	1.07519i
$949$		−	37.2041i		−	1.20770i
$950$	−10.4177	+	8.23703i	−0.337994	+	0.267244i
$951$	−5.64517	−	0.465759i	−0.183057	−	0.0151033i
$952$	−3.56655	−	3.56655i	−0.115593	−	0.115593i
$953$	16.8670	+	16.8670i	0.546377	+	0.546377i	0.925391	−	0.379014i	$-0.123737\pi$
$953$	16.8670	+	16.8670i	0.546377	+	0.546377i	−0.379014	+	0.925391i	$0.623737\pi$
$954$	4.05024	−	24.3781i	0.131131	−	0.789271i
$955$	−27.9360	−	31.3918i	−0.903989	−	1.01582i
$956$			8.49159i			0.274638i
$957$	21.0524	−	17.8433i	0.680528	−	0.576792i
$958$	30.5021	−	30.5021i	0.985478	−	0.985478i
$959$	20.0883			0.648685
$960$	7.99481	−	56.5265i	0.258031	−	1.82439i
$961$	−5.30072			−0.170991
$962$	3.93834	−	3.93834i	0.126977	−	0.126977i
$963$	3.70264	+	5.17810i	0.119316	+	0.166862i
$964$			81.4183i			2.62231i
$965$	−1.15981	+	19.9111i	−0.0373355	+	0.640961i
$966$	−7.35066	+	89.0926i	−0.236503	+	2.86651i
$967$	−29.8123	−	29.8123i	−0.958699	−	0.958699i	0.0404809	−	0.999180i	$-0.487111\pi$
$967$	−29.8123	−	29.8123i	−0.958699	−	0.958699i	−0.999180	+	0.0404809i	$0.987111\pi$
$968$	40.9871	+	40.9871i	1.31738	+	1.31738i
$969$	0.0239461	−	0.290236i	0.000769260	−	0.00932371i
$970$	21.6583	−	19.2740i	0.695406	−	0.618852i
$971$			27.4941i			0.882327i	0.897427	+	0.441163i	$0.145434\pi$
$971$			27.4941i			0.882327i	−0.897427	+	0.441163i	$0.854566\pi$
$972$	−73.3591	+	28.7746i	−2.35299	+	0.922945i
$973$	45.7794	−	45.7794i	1.46762	−	1.46762i
$974$	−92.0380			−2.94909
$975$	−6.98612	+	34.6977i	−0.223735	+	1.11122i
$976$	56.8021			1.81819
$977$	5.79323	−	5.79323i	0.185342	−	0.185342i	−0.608337	−	0.793679i	$-0.708163\pi$
$977$	5.79323	−	5.79323i	0.185342	−	0.185342i	0.793679	+	0.608337i	$0.208163\pi$
$978$	−53.3549	+	45.2217i	−1.70610	+	1.44603i
$979$		−	17.7152i		−	0.566181i
$980$	−56.2929	+	50.0958i	−1.79821	+	1.60025i
$981$	30.8882	+	5.13185i	0.986185	+	0.163847i
$982$	26.0373	+	26.0373i	0.830884	+	0.830884i
$983$	16.5249	+	16.5249i	0.527063	+	0.527063i	0.919695	−	0.392633i	$-0.128436\pi$
$983$	16.5249	+	16.5249i	0.527063	+	0.527063i	−0.392633	+	0.919695i	$0.628436\pi$
$984$	−51.6695	−	4.26303i	−1.64716	−	0.135900i
$985$	−1.14301	+	19.6228i	−0.0364193	+	0.625233i
$986$		−	3.62326i		−	0.115388i
$987$	−16.7224	−	19.7300i	−0.532281	−	0.628012i
$988$	−14.6087	+	14.6087i	−0.464763	+	0.464763i
$989$	−45.7568			−1.45498
$990$	7.73266	−	34.1271i	0.245760	−	1.08463i
$991$	−26.7493			−0.849718			−0.424859	−	0.905259i	$-0.639676\pi$
$991$	−26.7493			−0.849718			−0.424859	+	0.905259i	$0.639676\pi$
$992$	−50.7807	+	50.7807i	−1.61229	+	1.61229i
$993$	3.42307	+	4.03871i	0.108628	+	0.128164i
$994$		−	0.155555i		−	0.00493391i
$995$	−24.9655	−	28.0538i	−0.791458	−	0.889365i
$996$	82.3469	+	6.79409i	2.60926	+	0.215279i
$997$	2.62584	+	2.62584i	0.0831611	+	0.0831611i	0.747464	−	0.664303i	$-0.231271\pi$
$997$	2.62584	+	2.62584i	0.0831611	+	0.0831611i	−0.664303	+	0.747464i	$0.731271\pi$
$998$	−18.0247	−	18.0247i	−0.570560	−	0.570560i
$999$	−2.58512	−	0.651719i	−0.0817896	−	0.0206195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.k.d.77.2	✓	36
3.2	odd	2	inner	285.2.k.d.77.17	yes	36
5.3	odd	4	inner	285.2.k.d.248.17	yes	36
15.8	even	4	inner	285.2.k.d.248.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.k.d.77.2	✓	36	1.1	even	1	trivial
285.2.k.d.77.17	yes	36	3.2	odd	2	inner
285.2.k.d.248.2	yes	36	15.8	even	4	inner
285.2.k.d.248.17	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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.87817 + 1.87817i) q^{2} +(1.11989 + 1.32130i) q^{3} -5.05506i q^{4} +(-1.67041 + 1.48652i) q^{5} +(-4.58498 - 0.378288i) q^{6} +(2.61406 + 2.61406i) q^{7} +(5.73793 + 5.73793i) q^{8} +(-0.491688 + 2.95943i) q^{9} +O(q^{10})\)	\(q+(-1.87817 + 1.87817i) q^{2} +(1.11989 + 1.32130i) q^{3} -5.05506i q^{4} +(-1.67041 + 1.48652i) q^{5} +(-4.58498 - 0.378288i) q^{6} +(2.61406 + 2.61406i) q^{7} +(5.73793 + 5.73793i) q^{8} +(-0.491688 + 2.95943i) q^{9} +(0.345374 - 5.92925i) q^{10} -1.96388i q^{11} +(6.67927 - 5.66112i) q^{12} +(-2.88991 + 2.88991i) q^{13} -9.81930 q^{14} +(-3.83482 - 0.542376i) q^{15} -11.4435 q^{16} +(-0.118891 + 0.118891i) q^{17} +(-4.63485 - 6.48180i) q^{18} +1.00000i q^{19} +(7.51444 + 8.44401i) q^{20} +(-0.526505 + 6.38143i) q^{21} +(3.68850 + 3.68850i) q^{22} +(-3.71671 - 3.71671i) q^{23} +(-1.15569 + 14.0074i) q^{24} +(0.580522 - 4.96619i) q^{25} -10.8555i q^{26} +(-4.46095 + 2.66457i) q^{27} +(13.2142 - 13.2142i) q^{28} +8.11307 q^{29} +(8.22112 - 6.18377i) q^{30} -5.06945 q^{31} +(10.0170 - 10.0170i) q^{32} +(2.59488 - 2.19933i) q^{33} -0.446595i q^{34} +(-8.25239 - 0.480695i) q^{35} +(14.9601 + 2.48551i) q^{36} +(0.362797 + 0.362797i) q^{37} +(-1.87817 - 1.87817i) q^{38} +(-7.05483 - 0.582064i) q^{39} +(-18.1142 - 1.05514i) q^{40} +3.68873i q^{41} +(-10.9966 - 12.9743i) q^{42} +(6.15556 - 6.15556i) q^{43} -9.92751 q^{44} +(-3.57793 - 5.67436i) q^{45} +13.9612 q^{46} +(-2.85613 + 2.85613i) q^{47} +(-12.8155 - 15.1203i) q^{48} +6.66661i q^{49} +(8.23703 + 10.4177i) q^{50} +(-0.290236 - 0.0239461i) q^{51} +(14.6087 + 14.6087i) q^{52} +(2.19294 + 2.19294i) q^{53} +(3.37390 - 13.3830i) q^{54} +(2.91934 + 3.28047i) q^{55} +29.9986i q^{56} +(-1.32130 + 1.11989i) q^{57} +(-15.2377 + 15.2377i) q^{58} +4.63152 q^{59} +(-2.74174 + 19.3852i) q^{60} -4.96370 q^{61} +(9.52129 - 9.52129i) q^{62} +(-9.02143 + 6.45083i) q^{63} +14.7403i q^{64} +(0.531421 - 9.12323i) q^{65} +(-0.742910 + 9.00434i) q^{66} +(10.1737 + 10.1737i) q^{67} +(0.601000 + 0.601000i) q^{68} +(0.748592 - 9.07321i) q^{69} +(16.4022 - 14.5966i) q^{70} +0.0158418i q^{71} +(-19.8023 + 14.1597i) q^{72} +(-6.43690 + 6.43690i) q^{73} -1.36279 q^{74} +(7.21196 - 4.79454i) q^{75} +5.05506 q^{76} +(5.13369 - 5.13369i) q^{77} +(14.3434 - 12.1570i) q^{78} +4.95634i q^{79} +(19.1153 - 17.0110i) q^{80} +(-8.51649 - 2.91023i) q^{81} +(-6.92807 - 6.92807i) q^{82} +(6.67296 + 6.67296i) q^{83} +(32.2585 + 2.66151i) q^{84} +(0.0218627 - 0.375330i) q^{85} +23.1224i q^{86} +(9.08576 + 10.7198i) q^{87} +(11.2686 - 11.2686i) q^{88} +9.02054 q^{89} +(17.3774 + 3.93745i) q^{90} -15.1088 q^{91} +(-18.7882 + 18.7882i) q^{92} +(-5.67723 - 6.69828i) q^{93} -10.7286i q^{94} +(-1.48652 - 1.67041i) q^{95} +(24.4535 + 2.01755i) q^{96} +(3.45173 + 3.45173i) q^{97} +(-12.5210 - 12.5210i) q^{98} +(5.81196 + 0.965613i) 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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