LMFDB - Embedded newform 380.2.k.c.343.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(267,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, 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("380.267");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			343.18
Character	$\chi$	$=$	380.343
Dual form			380.2.k.c.267.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.655429 - 1.25316i) q^{2} +(-0.124098 + 0.124098i) q^{3} +(-1.14082 - 1.64272i) q^{4} +(-0.0211435 - 2.23597i) q^{5} +(0.0741774 + 0.236853i) q^{6} +(-2.60801 - 2.60801i) q^{7} +(-2.80632 + 0.352951i) q^{8} +2.96920i q^{9} +(-2.81589 - 1.43902i) q^{10} +1.59093i q^{11} +(0.345433 + 0.0622840i) q^{12} +(-1.95339 - 1.95339i) q^{13} +(-4.97762 + 1.55889i) q^{14} +(0.280104 + 0.274856i) q^{15} +(-1.39704 + 3.74810i) q^{16} +(1.63902 - 1.63902i) q^{17} +(3.72088 + 1.94610i) q^{18} +1.00000 q^{19} +(-3.64894 + 2.58558i) q^{20} +0.647299 q^{21} +(1.99369 + 1.04274i) q^{22} +(3.32388 - 3.32388i) q^{23} +(0.304459 - 0.392060i) q^{24} +(-4.99911 + 0.0945526i) q^{25} +(-3.72823 + 1.16761i) q^{26} +(-0.740767 - 0.740767i) q^{27} +(-1.30894 + 7.25950i) q^{28} -2.83265i q^{29} +(0.528027 - 0.170866i) q^{30} -7.48876i q^{31} +(3.78132 + 4.20733i) q^{32} +(-0.197432 - 0.197432i) q^{33} +(-0.979691 - 3.12821i) q^{34} +(-5.77628 + 5.88657i) q^{35} +(4.87755 - 3.38734i) q^{36} +(-0.620175 + 0.620175i) q^{37} +(0.655429 - 1.25316i) q^{38} +0.484826 q^{39} +(0.848523 + 6.26738i) q^{40} +4.49344 q^{41} +(0.424259 - 0.811169i) q^{42} +(4.87104 - 4.87104i) q^{43} +(2.61345 - 1.81497i) q^{44} +(6.63903 - 0.0627794i) q^{45} +(-1.98679 - 6.34393i) q^{46} +(-9.05522 - 9.05522i) q^{47} +(-0.291763 - 0.638503i) q^{48} +6.60341i q^{49} +(-3.15807 + 6.32666i) q^{50} +0.406798i q^{51} +(-0.980395 + 5.43736i) q^{52} +(4.24526 + 4.24526i) q^{53} +(-1.41382 + 0.442780i) q^{54} +(3.55727 - 0.0336379i) q^{55} +(8.23940 + 6.39840i) q^{56} +(-0.124098 + 0.124098i) q^{57} +(-3.54977 - 1.85660i) q^{58} +0.166096 q^{59} +(0.131961 - 0.773693i) q^{60} +0.0704460 q^{61} +(-9.38462 - 4.90835i) q^{62} +(7.74370 - 7.74370i) q^{63} +(7.75085 - 1.98099i) q^{64} +(-4.32643 + 4.40903i) q^{65} +(-0.376816 + 0.118011i) q^{66} +(6.16238 + 6.16238i) q^{67} +(-4.56227 - 0.822610i) q^{68} +0.824976i q^{69} +(3.59087 + 11.0968i) q^{70} +8.99189i q^{71} +(-1.04798 - 8.33252i) q^{72} +(9.79301 + 9.79301i) q^{73} +(0.370698 + 1.18366i) q^{74} +(0.608647 - 0.632114i) q^{75} +(-1.14082 - 1.64272i) q^{76} +(4.14916 - 4.14916i) q^{77} +(0.317769 - 0.607565i) q^{78} +14.1076 q^{79} +(8.41018 + 3.04449i) q^{80} -8.72374 q^{81} +(2.94513 - 5.63100i) q^{82} +(4.60273 - 4.60273i) q^{83} +(-0.738454 - 1.06333i) q^{84} +(-3.69944 - 3.63013i) q^{85} +(-2.91157 - 9.29682i) q^{86} +(0.351527 + 0.351527i) q^{87} +(-0.561521 - 4.46466i) q^{88} -10.8550i q^{89} +(4.27275 - 8.36093i) q^{90} +10.1889i q^{91} +(-9.25216 - 1.66823i) q^{92} +(0.929342 + 0.929342i) q^{93} +(-17.2827 + 5.41259i) q^{94} +(-0.0211435 - 2.23597i) q^{95} +(-0.991377 - 0.0528679i) q^{96} +(3.24883 - 3.24883i) q^{97} +(8.27514 + 4.32807i) q^{98} -4.72379 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23}+ \cdots + 128 q^{99}+O(q^{100}) $ 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	0.655429	−	1.25316i	0.463459	−	0.886119i
$2$	0.655429	−	1.25316i	0.463459	−	0.886119i
$3$	−0.124098	+	0.124098i	−0.0716482	+	0.0716482i	−0.742023	−	0.670375i	$-0.766133\pi$
$3$	−0.124098	+	0.124098i	−0.0716482	+	0.0716482i	0.670375	+	0.742023i	$0.266133\pi$
$4$	−1.14082	−	1.64272i	−0.570412	−	0.821359i
$5$	−0.0211435	−	2.23597i	−0.00945568	−	0.999955i
$5$	−0.0211435	−	2.23597i	−0.00945568	−	0.999955i
$6$	0.0741774	+	0.236853i	0.0302828	+	0.0966947i
$7$	−2.60801	−	2.60801i	−0.985734	−	0.985734i	0.0141653	−	0.999900i	$-0.495491\pi$
$7$	−2.60801	−	2.60801i	−0.985734	−	0.985734i	−0.999900	+	0.0141653i	$0.995491\pi$
$8$	−2.80632	+	0.352951i	−0.992184	+	0.124787i
$9$			2.96920i			0.989733i
$10$	−2.81589	−	1.43902i	−0.890461	−	0.455059i
$11$			1.59093i			0.479684i	0.970812	+	0.239842i	$0.0770956\pi$
$11$			1.59093i			0.479684i	−0.970812	+	0.239842i	$0.922904\pi$
$12$	0.345433	+	0.0622840i	0.0997178	+	0.0179798i
$13$	−1.95339	−	1.95339i	−0.541774	−	0.541774i	0.382275	−	0.924049i	$-0.375141\pi$
$13$	−1.95339	−	1.95339i	−0.541774	−	0.541774i	−0.924049	+	0.382275i	$0.875141\pi$
$14$	−4.97762	+	1.55889i	−1.33032	+	0.416630i
$15$	0.280104	+	0.274856i	0.0723224	+	0.0709675i
$16$	−1.39704	+	3.74810i	−0.349260	+	0.937026i
$17$	1.63902	−	1.63902i	0.397520	−	0.397520i	−0.479838	−	0.877357i	$-0.659304\pi$
$17$	1.63902	−	1.63902i	0.397520	−	0.397520i	0.877357	+	0.479838i	$0.159304\pi$
$18$	3.72088	+	1.94610i	0.877021	+	0.458700i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−3.64894	+	2.58558i	−0.815928	+	0.578153i
$21$	0.647299			0.141252
$22$	1.99369	+	1.04274i	0.425057	+	0.222314i
$23$	3.32388	−	3.32388i	0.693077	−	0.693077i	−0.269831	−	0.962908i	$-0.586968\pi$
$23$	3.32388	−	3.32388i	0.693077	−	0.693077i	0.962908	+	0.269831i	$0.0869677\pi$
$24$	0.304459	−	0.392060i	0.0621474	−	0.0800289i
$25$	−4.99911	+	0.0945526i	−0.999821	+	0.0189105i
$26$	−3.72823	+	1.16761i	−0.731166	+	0.228986i
$27$	−0.740767	−	0.740767i	−0.142561	−	0.142561i
$28$	−1.30894	+	7.25950i	−0.247366	+	1.37192i
$29$		−	2.83265i		−	0.526010i	−0.964794	−	0.263005i	$-0.915286\pi$
$29$		−	2.83265i		−	0.526010i	0.964794	−	0.263005i	$-0.0847136\pi$
$30$	0.528027	−	0.170866i	0.0964041	−	0.0311958i
$31$		−	7.48876i		−	1.34502i	−0.740088	−	0.672510i	$-0.765216\pi$
$31$		−	7.48876i		−	1.34502i	0.740088	−	0.672510i	$-0.234784\pi$
$32$	3.78132	+	4.20733i	0.668449	+	0.743758i
$33$	−0.197432	−	0.197432i	−0.0343685	−	0.0343685i
$34$	−0.979691	−	3.12821i	−0.168016	−	0.536483i
$35$	−5.77628	+	5.88657i	−0.976370	+	0.995011i
$36$	4.87755	−	3.38734i	0.812926	−	0.564556i
$37$	−0.620175	+	0.620175i	−0.101956	+	0.101956i	−0.756245	−	0.654289i	$-0.772968\pi$
$37$	−0.620175	+	0.620175i	−0.101956	+	0.101956i	0.654289	+	0.756245i	$0.272968\pi$
$38$	0.655429	−	1.25316i	0.106325	−	0.203290i
$39$	0.484826			0.0776343
$40$	0.848523	+	6.26738i	0.134163	+	0.990959i
$41$	4.49344			0.701757			0.350879	−	0.936421i	$-0.385883\pi$
$41$	4.49344			0.701757			0.350879	+	0.936421i	$0.385883\pi$
$42$	0.424259	−	0.811169i	0.0654645	−	0.125166i
$43$	4.87104	−	4.87104i	0.742826	−	0.742826i	−0.230295	−	0.973121i	$-0.573969\pi$
$43$	4.87104	−	4.87104i	0.742826	−	0.742826i	0.973121	+	0.230295i	$0.0739690\pi$
$44$	2.61345	−	1.81497i	0.393992	−	0.273617i
$45$	6.63903	−	0.0627794i	0.989689	−	0.00935860i
$46$	−1.98679	−	6.34393i	−0.292936	−	0.935361i
$47$	−9.05522	−	9.05522i	−1.32084	−	1.32084i	−0.913096	−	0.407744i	$-0.866316\pi$
$47$	−9.05522	−	9.05522i	−1.32084	−	1.32084i	−0.407744	−	0.913096i	$-0.633684\pi$
$48$	−0.291763	−	0.638503i	−0.0421124	−	0.0921600i
$49$			6.60341i			0.943344i
$50$	−3.15807	+	6.32666i	−0.446619	+	0.894724i
$51$			0.406798i			0.0569631i
$52$	−0.980395	+	5.43736i	−0.135956	+	0.754026i
$53$	4.24526	+	4.24526i	0.583131	+	0.583131i	0.935762	−	0.352631i	$-0.114713\pi$
$53$	4.24526	+	4.24526i	0.583131	+	0.583131i	−0.352631	+	0.935762i	$0.614713\pi$
$54$	−1.41382	+	0.442780i	−0.192397	+	0.0602547i
$55$	3.55727	−	0.0336379i	0.479662	−	0.00453574i
$56$	8.23940	+	6.39840i	1.10104	+	0.855022i
$57$	−0.124098	+	0.124098i	−0.0164372	+	0.0164372i
$58$	−3.54977	−	1.85660i	−0.466107	−	0.243784i
$59$	0.166096			0.0216238			0.0108119	−	0.999942i	$-0.496558\pi$
$59$	0.166096			0.0216238			0.0108119	+	0.999942i	$0.496558\pi$
$60$	0.131961	−	0.773693i	0.0170361	−	0.0998834i
$61$	0.0704460			0.00901969			0.00450984	−	0.999990i	$-0.498564\pi$
$61$	0.0704460			0.00901969			0.00450984	+	0.999990i	$0.498564\pi$
$62$	−9.38462	−	4.90835i	−1.19185	−	0.623361i
$63$	7.74370	−	7.74370i	0.975614	−	0.975614i
$64$	7.75085	−	1.98099i	0.968856	−	0.247623i
$65$	−4.32643	+	4.40903i	−0.536627	+	0.546873i
$66$	−0.376816	+	0.118011i	−0.0463829	+	0.0145262i
$67$	6.16238	+	6.16238i	0.752854	+	0.752854i	0.975011	−	0.222157i	$-0.0713096\pi$
$67$	6.16238	+	6.16238i	0.752854	+	0.752854i	−0.222157	+	0.975011i	$0.571310\pi$
$68$	−4.56227	−	0.822610i	−0.553256	−	0.0997561i
$69$			0.824976i			0.0993154i
$70$	3.59087	+	11.0968i	0.429191	+	1.32633i
$71$			8.99189i			1.06714i	0.845755	+	0.533571i	$0.179150\pi$
$71$			8.99189i			1.06714i	−0.845755	+	0.533571i	$0.820850\pi$
$72$	−1.04798	−	8.33252i	−0.123506	−	0.981997i
$73$	9.79301	+	9.79301i	1.14618	+	1.14618i	0.987297	+	0.158888i	$0.0507910\pi$
$73$	9.79301	+	9.79301i	1.14618	+	1.14618i	0.158888	+	0.987297i	$0.449209\pi$
$74$	0.370698	+	1.18366i	0.0430928	+	0.137598i
$75$	0.608647	−	0.632114i	0.0702804	−	0.0729903i
$76$	−1.14082	−	1.64272i	−0.130862	−	0.188433i
$77$	4.14916	−	4.14916i	0.472841	−	0.472841i
$78$	0.317769	−	0.607565i	0.0359803	−	0.0687932i
$79$	14.1076			1.58723			0.793614	−	0.608422i	$-0.208197\pi$
$79$	14.1076			1.58723			0.793614	+	0.608422i	$0.208197\pi$
$80$	8.41018	+	3.04449i	0.940287	+	0.340384i
$81$	−8.72374			−0.969305
$82$	2.94513	−	5.63100i	0.325235	−	0.621840i
$83$	4.60273	−	4.60273i	0.505215	−	0.505215i	−0.407839	−	0.913054i	$-0.633717\pi$
$83$	4.60273	−	4.60273i	0.505215	−	0.505215i	0.913054	+	0.407839i	$0.133717\pi$
$84$	−0.738454	−	1.06333i	−0.0805719	−	0.116019i
$85$	−3.69944	−	3.63013i	−0.401261	−	0.393743i
$86$	−2.91157	−	9.29682i	−0.313963	−	1.00250i
$87$	0.351527	+	0.351527i	0.0376877	+	0.0376877i
$88$	−0.561521	−	4.46466i	−0.0598584	−	0.475934i
$89$		−	10.8550i		−	1.15063i	−0.817932	−	0.575315i	$-0.804879\pi$
$89$		−	10.8550i		−	1.15063i	0.817932	−	0.575315i	$-0.195121\pi$
$90$	4.27275	−	8.36093i	0.450387	−	0.881319i
$91$			10.1889i			1.06809i
$92$	−9.25216	−	1.66823i	−0.964605	−	0.173925i
$93$	0.929342	+	0.929342i	0.0963683	+	0.0963683i
$94$	−17.2827	+	5.41259i	−1.78258	+	0.558266i
$95$	−0.0211435	−	2.23597i	−0.00216928	−	0.229405i
$96$	−0.991377	−	0.0528679i	−0.101182	−	0.00539581i
$97$	3.24883	−	3.24883i	0.329869	−	0.329869i	−0.522668	−	0.852536i	$-0.675063\pi$
$97$	3.24883	−	3.24883i	0.329869	−	0.329869i	0.852536	+	0.522668i	$0.175063\pi$
$98$	8.27514	+	4.32807i	0.835915	+	0.437201i
$99$	−4.72379			−0.474759
$100$	5.85843	+	8.10425i	0.585843	+	0.810425i
$101$	−19.2696			−1.91740			−0.958700	−	0.284419i	$-0.908199\pi$
$101$	−19.2696			−1.91740			−0.958700	+	0.284419i	$0.908199\pi$
$102$	0.509783	+	0.266627i	0.0504761	+	0.0264000i
$103$	−1.20104	+	1.20104i	−0.118342	+	0.118342i	−0.763798	−	0.645456i	$-0.776668\pi$
$103$	−1.20104	+	1.20104i	−0.118342	+	0.118342i	0.645456	+	0.763798i	$0.276668\pi$
$104$	6.17130	+	4.79240i	0.605146	+	0.469933i
$105$	−0.0136862	−	1.44734i	−0.00133563	−	0.141246i
$106$	8.10246	−	2.53752i	0.786980	−	0.246466i
$107$	−7.40713	−	7.40713i	−0.716074	−	0.716074i	0.251725	−	0.967799i	$-0.419002\pi$
$107$	−7.40713	−	7.40713i	−0.716074	−	0.716074i	−0.967799	+	0.251725i	$0.919002\pi$
$108$	−0.371786	+	2.06196i	−0.0357751	+	0.198412i
$109$			4.29422i			0.411312i	0.978624	+	0.205656i	$0.0659328\pi$
$109$			4.29422i			0.411312i	−0.978624	+	0.205656i	$0.934067\pi$
$110$	2.28939	−	4.47988i	0.218284	−	0.427140i
$111$		−	0.153925i		−	0.0146099i
$112$	13.4186	−	6.13159i	1.26794	−	0.579381i
$113$	−4.11193	−	4.11193i	−0.386818	−	0.386818i	0.486733	−	0.873551i	$-0.338188\pi$
$113$	−4.11193	−	4.11193i	−0.386818	−	0.386818i	−0.873551	+	0.486733i	$0.838188\pi$
$114$	0.0741774	+	0.236853i	0.00694735	+	0.0221833i
$115$	−7.50237	−	7.36182i	−0.699600	−	0.686493i
$116$	−4.65325	+	3.23156i	−0.432043	+	0.300043i
$117$	5.80002	−	5.80002i	0.536212	−	0.536212i
$118$	0.108864	−	0.208145i	0.0100217	−	0.0191613i
$119$	−8.54913			−0.783698
$120$	−0.883071	−	0.672470i	−0.0806130	−	0.0613879i
$121$	8.46894			0.769904
$122$	0.0461724	−	0.0882802i	0.00418025	−	0.00799251i
$123$	−0.557628	+	0.557628i	−0.0502796	+	0.0502796i
$124$	−12.3019	+	8.54336i	−1.10474	+	0.767216i
$125$	0.317115	+	11.1758i	0.0283637	+	0.999598i
$126$	−4.62865	−	14.7795i	−0.412353	−	1.31667i
$127$	−1.43074	−	1.43074i	−0.126958	−	0.126958i	0.640773	−	0.767731i	$-0.278614\pi$
$127$	−1.43074	−	1.43074i	−0.126958	−	0.126958i	−0.767731	+	0.640773i	$0.778614\pi$
$128$	2.59764	−	11.0115i	0.229601	−	0.973285i
$129$			1.20897i			0.106444i
$130$	2.68956	+	8.31152i	0.235890	+	0.728968i
$131$			15.6098i			1.36383i	0.731429	+	0.681917i	$0.238854\pi$
$131$			15.6098i			1.36383i	−0.731429	+	0.681917i	$0.761146\pi$
$132$	−0.0990896	+	0.549559i	−0.00862464	+	0.0478330i
$133$	−2.60801	−	2.60801i	−0.226143	−	0.226143i
$134$	11.7615	−	3.68345i	1.01604	−	0.318201i
$135$	−1.64067	+	1.67199i	−0.141206	+	0.143902i
$136$	−4.02111	+	5.17809i	−0.344807	+	0.444018i
$137$	12.4864	−	12.4864i	1.06678	−	1.06678i	0.0691808	−	0.997604i	$-0.477961\pi$
$137$	12.4864	−	12.4864i	1.06678	−	1.06678i	0.997604	−	0.0691808i	$-0.0220385\pi$
$138$	1.03383	+	0.540714i	0.0880053	+	0.0460286i
$139$	−1.54135			−0.130736			−0.0653678	−	0.997861i	$-0.520822\pi$
$139$	−1.54135			−0.130736			−0.0653678	+	0.997861i	$0.520822\pi$
$140$	16.2597	+	2.77326i	1.37419	+	0.234383i
$141$	2.24747			0.189272
$142$	11.2683	+	5.89355i	0.945614	+	0.494576i
$143$	3.10772	−	3.10772i	0.259880	−	0.259880i
$144$	−11.1289	−	4.14809i	−0.927406	−	0.345674i
$145$	−6.33372	+	0.0598923i	−0.525987	+	0.00497379i
$146$	18.6908	−	5.85359i	1.54686	−	0.484446i
$147$	−0.819472	−	0.819472i	−0.0675889	−	0.0675889i
$148$	1.72628	+	0.311261i	0.141900	+	0.0255855i
$149$		−	4.77735i		−	0.391375i	−0.980666	−	0.195688i	$-0.937306\pi$
$149$		−	4.77735i		−	0.391375i	0.980666	−	0.195688i	$-0.0626939\pi$
$150$	−0.393216	−	1.17704i	−0.0321059	−	0.0961048i
$151$			23.0059i			1.87219i	0.351748	+	0.936095i	$0.385588\pi$
$151$			23.0059i			1.87219i	−0.351748	+	0.936095i	$0.614412\pi$
$152$	−2.80632	+	0.352951i	−0.227623	+	0.0286281i
$153$	4.86656	+	4.86656i	0.393438	+	0.393438i
$154$	−2.48008	−	7.91905i	−0.199851	−	0.638135i
$155$	−16.7446	+	0.158339i	−1.34496	+	0.0127181i
$156$	−0.553101	−	0.796432i	−0.0442835	−	0.0637656i
$157$	−8.05734	+	8.05734i	−0.643046	+	0.643046i	−0.951303	−	0.308257i	$-0.900254\pi$
$157$	−8.05734	+	8.05734i	−0.643046	+	0.643046i	0.308257	+	0.951303i	$0.400254\pi$
$158$	9.24653	−	17.6791i	0.735614	−	1.40647i
$159$	−1.05366			−0.0835605
$160$	9.32751	−	8.54386i	0.737404	−	0.675451i
$161$	−17.3374			−1.36638
$162$	−5.71780	+	10.9323i	−0.449233	+	0.858919i
$163$	−8.76560	+	8.76560i	−0.686575	+	0.686575i	−0.961473	−	0.274898i	$-0.911356\pi$
$163$	−8.76560	+	8.76560i	−0.686575	+	0.686575i	0.274898	+	0.961473i	$0.411356\pi$
$164$	−5.12623	−	7.38145i	−0.400291	−	0.576394i
$165$	−0.437277	+	0.445625i	−0.0340419	+	0.0346919i
$166$	−2.75120	−	8.78473i	−0.213534	−	0.681827i
$167$	6.17041	+	6.17041i	0.477481	+	0.477481i	0.904325	−	0.426844i	$-0.140375\pi$
$167$	6.17041	+	6.17041i	0.477481	+	0.477481i	−0.426844	+	0.904325i	$0.640375\pi$
$168$	−1.81653	+	0.228465i	−0.140148	+	0.0176264i
$169$		−	5.36850i		−	0.412961i
$170$	−6.97386	+	2.25670i	−0.534871	+	0.173081i
$171$			2.96920i			0.227060i
$172$	−13.5587	−	2.44474i	−1.03384	−	0.186410i
$173$	13.7767	+	13.7767i	1.04742	+	1.04742i	0.998818	+	0.0486014i	$0.0154764\pi$
$173$	13.7767	+	13.7767i	1.04742	+	1.04742i	0.0486014	+	0.998818i	$0.484524\pi$
$174$	0.670921	−	0.210119i	0.0508624	−	0.0159291i
$175$	13.2843	+	12.7911i	1.00420	+	0.966917i
$176$	−5.96297	−	2.22259i	−0.449476	−	0.167534i
$177$	−0.0206122	+	0.0206122i	−0.00154931	+	0.00154931i
$178$	−13.6031	−	7.11470i	−1.01959	−	0.533269i
$179$	−5.62503			−0.420435			−0.210217	−	0.977655i	$-0.567417\pi$
$179$	−5.62503			−0.420435			−0.210217	+	0.977655i	$0.567417\pi$
$180$	−7.67710	−	10.8344i	−0.572217	−	0.807551i
$181$	−2.11678			−0.157339			−0.0786696	−	0.996901i	$-0.525067\pi$
$181$	−2.11678			−0.157339			−0.0786696	+	0.996901i	$0.525067\pi$
$182$	12.7684	+	6.67813i	0.946455	+	0.495016i
$183$	−0.00874223	+	0.00874223i	−0.000646244	+	0.000646244i
$184$	−8.15470	+	10.5010i	−0.601173	+	0.774147i
$185$	1.39980	+	1.37358i	0.102916	+	0.100988i
$186$	1.77373	−	0.555497i	0.130056	−	0.0407310i
$187$	2.60756	+	2.60756i	0.190684	+	0.190684i
$188$	−4.54475	+	25.2056i	−0.331460	+	1.83831i
$189$			3.86385i			0.281054i
$190$	−2.81589	−	1.43902i	−0.204286	−	0.104398i
$191$			6.21119i			0.449426i	0.974425	+	0.224713i	$0.0721445\pi$
$191$			6.21119i			0.449426i	−0.974425	+	0.224713i	$0.927856\pi$
$192$	−0.716030	+	1.20770i	−0.0516750	+	0.0871585i
$193$	−9.39582	−	9.39582i	−0.676326	−	0.676326i	0.282841	−	0.959167i	$-0.408723\pi$
$193$	−9.39582	−	9.39582i	−0.676326	−	0.676326i	−0.959167	+	0.282841i	$0.908723\pi$
$194$	−1.94193	−	6.20068i	−0.139422	−	0.445183i
$195$	−0.0102509	−	1.08406i	−0.000734085	−	0.0776308i
$196$	10.8475	−	7.53333i	0.774824	−	0.538095i
$197$	−13.0636	+	13.0636i	−0.930744	+	0.930744i	−0.997752	−	0.0670085i	$-0.978655\pi$
$197$	−13.0636	+	13.0636i	−0.930744	+	0.930744i	0.0670085	+	0.997752i	$0.478655\pi$
$198$	−3.09611	+	5.91967i	−0.220031	+	0.420693i
$199$	14.4750			1.02610			0.513052	−	0.858358i	$-0.328515\pi$
$199$	14.4750			1.02610			0.513052	+	0.858358i	$0.328515\pi$
$200$	13.9957	−	2.02979i	0.989646	−	0.143528i
$201$	−1.52948			−0.107881
$202$	−12.6299	+	24.1480i	−0.888636	+	1.69904i
$203$	−7.38758	+	7.38758i	−0.518506	+	0.518506i
$204$	0.668254	−	0.464085i	0.0467871	−	0.0324925i
$205$	−0.0950072	−	10.0472i	−0.00663559	−	0.701726i
$206$	0.717900	+	2.29229i	0.0500185	+	0.159712i
$207$	9.86927	+	9.86927i	0.685962	+	0.685962i
$208$	10.0505	−	4.59256i	0.696877	−	0.318437i
$209$			1.59093i			0.110047i
$210$	−1.82272	−	0.931477i	−0.125780	−	0.0642781i
$211$			14.2643i			0.981993i	0.871162	+	0.490996i	$0.163367\pi$
$211$			14.2643i			0.981993i	−0.871162	+	0.490996i	$0.836633\pi$
$212$	2.13066	−	11.8169i	0.146335	−	0.811585i
$213$	−1.11588	−	1.11588i	−0.0764587	−	0.0764587i
$214$	−14.1372	+	4.42747i	−0.966397	+	0.302656i
$215$	−10.9945	−	10.7885i	−0.749817	−	0.735769i
$216$	2.34028	+	1.81737i	0.159236	+	0.123657i
$217$	−19.5307	+	19.5307i	−1.32583	+	1.32583i
$218$	5.38135	+	2.81456i	0.364471	+	0.190626i
$219$	−2.43059			−0.164244
$220$	−4.11348	−	5.80521i	−0.277331	−	0.391387i
$221$	−6.40329			−0.430732
$222$	−0.192893	−	0.100887i	−0.0129461	−	0.00677111i
$223$	15.3529	−	15.3529i	1.02810	−	1.02810i	0.0285110	−	0.999593i	$-0.490923\pi$
$223$	15.3529	−	15.3529i	1.02810	−	1.02810i	0.999593	−	0.0285110i	$-0.00907656\pi$
$224$	1.11105	−	20.8345i	0.0742354	−	1.39206i
$225$	−0.280745	−	14.8433i	−0.0187164	−	0.989556i
$226$	−7.84798	+	2.45783i	−0.522040	+	0.163492i
$227$	−16.9471	−	16.9471i	−1.12482	−	1.12482i	−0.991006	−	0.133814i	$-0.957278\pi$
$227$	−16.9471	−	16.9471i	−1.12482	−	1.12482i	−0.133814	−	0.991006i	$-0.542722\pi$
$228$	0.345433	+	0.0622840i	0.0228768	+	0.00412486i
$229$		−	14.1088i		−	0.932333i	−0.884697	−	0.466166i	$-0.845635\pi$
$229$		−	14.1088i		−	0.932333i	0.884697	−	0.466166i	$-0.154365\pi$
$230$	−14.1428	+	4.57653i	−0.932550	+	0.301767i
$231$			1.02981i			0.0677563i
$232$	0.999788	+	7.94933i	0.0656393	+	0.521899i
$233$	−15.3804	−	15.3804i	−1.00760	−	1.00760i	−0.999971	−	0.00763101i	$-0.997571\pi$
$233$	−15.3804	−	15.3804i	−1.00760	−	1.00760i	−0.00763101	−	0.999971i	$-0.502429\pi$
$234$	−3.46685	−	11.0699i	−0.226635	−	0.723659i
$235$	−20.0557	+	20.4386i	−1.30829	+	1.33327i
$236$	−0.189486	−	0.272848i	−0.0123345	−	0.0177609i
$237$	−1.75073	+	1.75073i	−0.113722	+	0.113722i
$238$	−5.60335	+	10.7134i	−0.363211	+	0.694449i
$239$	−1.34233			−0.0868279			−0.0434140	−	0.999057i	$-0.513823\pi$
$239$	−1.34233			−0.0868279			−0.0434140	+	0.999057i	$0.513823\pi$
$240$	−1.42150	+	0.665873i	−0.0917577	+	0.0429819i
$241$	23.6295			1.52211			0.761055	−	0.648688i	$-0.224682\pi$
$241$	23.6295			1.52211			0.761055	+	0.648688i	$0.224682\pi$
$242$	5.55079	−	10.6129i	0.356818	−	0.682226i
$243$	3.30490	−	3.30490i	0.212010	−	0.212010i
$244$	−0.0803665	−	0.115723i	−0.00514494	−	0.00740840i
$245$	14.7650	−	0.139620i	0.943302	−	0.00891996i
$246$	0.333312	+	1.06428i	0.0212512	+	0.0678562i
$247$	−1.95339	−	1.95339i	−0.124292	−	0.124292i
$248$	2.64317	+	21.0158i	0.167841	+	1.33451i
$249$			1.14238i			0.0723955i
$250$	14.2130	+	6.92758i	0.898907	+	0.438139i
$251$		−	2.12114i		−	0.133885i	−0.997757	−	0.0669427i	$-0.978676\pi$
$251$		−	2.12114i		−	0.133885i	0.997757	−	0.0669427i	$-0.0213245\pi$
$252$	−21.5549	−	3.88650i	−1.35783	−	0.244827i
$253$	5.28807	+	5.28807i	0.332458	+	0.332458i
$254$	−2.73070	+	0.855200i	−0.171339	+	0.0536600i
$255$	0.909587	−	0.00860115i	0.0569606	−	0.000538625i
$256$	−12.0966	−	10.4725i	−0.756035	−	0.654531i
$257$	13.4566	−	13.4566i	0.839398	−	0.839398i	−0.149382	−	0.988780i	$-0.547728\pi$
$257$	13.4566	−	13.4566i	0.839398	−	0.839398i	0.988780	+	0.149382i	$0.0477283\pi$
$258$	1.51504	+	0.792398i	0.0943223	+	0.0493325i
$259$	3.23484			0.201003
$260$	12.1785	+	2.07717i	0.755277	+	0.128820i
$261$	8.41071			0.520610
$262$	19.5616	+	10.2311i	1.20852	+	0.632081i
$263$	4.28561	−	4.28561i	0.264262	−	0.264262i	−0.562521	−	0.826783i	$-0.690168\pi$
$263$	4.28561	−	4.28561i	0.264262	−	0.264262i	0.826783	+	0.562521i	$0.190168\pi$
$264$	0.623740	+	0.484373i	0.0383886	+	0.0298111i
$265$	9.40250	−	9.58202i	0.577591	−	0.588619i
$266$	−4.97762	+	1.55889i	−0.305197	+	0.0955816i
$267$	1.34709	+	1.34709i	0.0824405	+	0.0824405i
$268$	3.09285	−	17.1532i	0.188926	−	1.04780i
$269$		−	30.1647i		−	1.83917i	−0.392887	−	0.919587i	$-0.628524\pi$
$269$		−	30.1647i		−	1.83917i	0.392887	−	0.919587i	$-0.371476\pi$
$270$	1.01993	+	3.15190i	0.0620713	+	0.191818i
$271$		−	9.29213i		−	0.564457i	−0.959347	−	0.282228i	$-0.908926\pi$
$271$		−	9.29213i		−	0.564457i	0.959347	−	0.282228i	$-0.0910736\pi$
$272$	3.85343	+	8.43297i	0.233649	+	0.511324i
$273$	−1.26443	−	1.26443i	−0.0765268	−	0.0765268i
$274$	−7.46351	−	23.8314i	−0.450887	−	1.43971i
$275$	−0.150427	−	7.95323i	−0.00907107	−	0.479598i
$276$	1.35520	−	0.941153i	0.0815736	−	0.0566507i
$277$	−20.2079	+	20.2079i	−1.21418	+	1.21418i	−0.244535	+	0.969640i	$0.578635\pi$
$277$	−20.2079	+	20.2079i	−1.21418	+	1.21418i	−0.969640	+	0.244535i	$0.921365\pi$
$278$	−1.01025	+	1.93156i	−0.0605906	+	0.115847i
$279$	22.2356			1.33121
$280$	14.1324	−	18.5583i	0.844573	−	1.10907i
$281$	10.1316			0.604402			0.302201	−	0.953244i	$-0.402279\pi$
$281$	10.1316			0.604402			0.302201	+	0.953244i	$0.402279\pi$
$282$	1.47306	−	2.81645i	0.0877195	−	0.167717i
$283$	−9.78286	+	9.78286i	−0.581530	+	0.581530i	−0.935324	−	0.353793i	$-0.884892\pi$
$283$	−9.78286	+	9.78286i	−0.581530	+	0.581530i	0.353793	+	0.935324i	$0.384892\pi$
$284$	14.7711	−	10.2582i	0.876506	−	0.608711i
$285$	0.280104	+	0.274856i	0.0165919	+	0.0162811i
$286$	−1.85758	−	5.93136i	−0.109841	−	0.350728i
$287$	−11.7189	−	11.7189i	−0.691746	−	0.691746i
$288$	−12.4924	+	11.2275i	−0.736122	+	0.661586i
$289$			11.6273i			0.683956i
$290$	−4.07625	+	7.97642i	−0.239366	+	0.468392i
$291$			0.806348i			0.0472690i
$292$	4.91504	−	27.2592i	0.287631	−	1.59523i
$293$	0.409549	+	0.409549i	0.0239261	+	0.0239261i	0.718969	−	0.695043i	$-0.244614\pi$
$293$	0.409549	+	0.409549i	0.0239261	+	0.0239261i	−0.695043	+	0.718969i	$0.744614\pi$
$294$	−1.56404	+	0.489824i	−0.0912164	+	0.0285671i
$295$	−0.00351185	−	0.371385i	−0.000204468	−	0.0216229i
$296$	1.52152	−	1.95930i	0.0884364	−	0.113882i
$297$	1.17851	−	1.17851i	0.0683841	−	0.0683841i
$298$	−5.98678	−	3.13121i	−0.346805	−	0.181386i
$299$	−12.9857			−0.750983
$300$	−1.73274	−	0.278703i	−0.100040	−	0.0160909i
$301$	−25.4074			−1.46446
$302$	28.8300	+	15.0787i	1.65898	+	0.867682i
$303$	2.39133	−	2.39133i	0.137378	−	0.137378i
$304$	−1.39704	+	3.74810i	−0.0801257	+	0.214968i
$305$	−0.00148948	−	0.157515i	−8.52873e−5	−	0.00901928i
$306$	9.28828	−	2.90890i	0.530975	−	0.166291i
$307$	22.5342	+	22.5342i	1.28609	+	1.28609i	0.937141	+	0.348952i	$0.113462\pi$
$307$	22.5342	+	22.5342i	1.28609	+	1.28609i	0.348952	+	0.937141i	$0.386538\pi$
$308$	−11.5494	−	2.08243i	−0.658086	−	0.118658i
$309$		−	0.298094i		−	0.0169580i
$310$	−10.7765	+	21.0875i	−0.612064	+	1.19769i
$311$		−	3.85212i		−	0.218434i	−0.994018	−	0.109217i	$-0.965166\pi$
$311$		−	3.85212i		−	0.218434i	0.994018	−	0.109217i	$-0.0348343\pi$
$312$	−1.36058	+	0.171120i	−0.0770274	+	0.00968776i
$313$	8.59110	+	8.59110i	0.485598	+	0.485598i	0.906914	−	0.421316i	$-0.138432\pi$
$313$	8.59110	+	8.59110i	0.485598	+	0.485598i	−0.421316	+	0.906914i	$0.638432\pi$
$314$	4.81612	+	15.3782i	0.271790	+	0.867840i
$315$	−17.4784	−	17.1509i	−0.984795	−	0.966345i
$316$	−16.0943	−	23.1748i	−0.905374	−	1.30368i
$317$	14.2260	−	14.2260i	0.799013	−	0.799013i	−0.183927	−	0.982940i	$-0.558881\pi$
$317$	14.2260	−	14.2260i	0.799013	−	0.799013i	0.982940	+	0.183927i	$0.0588811\pi$
$318$	−0.690599	+	1.32040i	−0.0387269	+	0.0740446i
$319$	4.50655			0.252319
$320$	−4.59331	−	17.2888i	−0.256774	−	0.966472i
$321$	1.83842			0.102611
$322$	−11.3635	+	21.7266i	−0.633261	+	1.21077i
$323$	1.63902	−	1.63902i	0.0911973	−	0.0911973i
$324$	9.95226	+	14.3306i	0.552903	+	0.796147i
$325$	9.94993	+	9.58053i	0.551923	+	0.531432i
$326$	5.23948	+	16.7299i	0.290188	+	0.926586i
$327$	−0.532905	−	0.532905i	−0.0294697	−	0.0294697i
$328$	−12.6100	+	1.58597i	−0.696272	+	0.0875703i
$329$			47.2322i			2.60399i
$330$	0.271836	+	0.840054i	0.0149641	+	0.0462435i
$331$		−	30.6620i		−	1.68534i	−0.538431	−	0.842669i	$-0.680983\pi$
$331$		−	30.6620i		−	1.68534i	0.538431	−	0.842669i	$-0.319017\pi$
$332$	−12.8119	−	2.31008i	−0.703144	−	0.126782i
$333$	−1.84142	−	1.84142i	−0.100909	−	0.100909i
$334$	11.7768	−	3.68825i	0.644397	−	0.201812i
$335$	13.6486	−	13.9092i	0.745702	−	0.759939i
$336$	−0.904301	+	2.42614i	−0.0493337	+	0.132357i
$337$	1.70014	−	1.70014i	0.0926123	−	0.0926123i	−0.659283	−	0.751895i	$-0.729140\pi$
$337$	1.70014	−	1.70014i	0.0926123	−	0.0926123i	0.751895	+	0.659283i	$0.229140\pi$
$338$	−6.72759	−	3.51867i	−0.365933	−	0.191390i
$339$	1.02057			0.0554295
$340$	−1.74287	+	10.2185i	−0.0945202	+	0.554175i
$341$	11.9141			0.645185
$342$	3.72088	+	1.94610i	0.201202	+	0.105233i
$343$	−1.03431	+	1.03431i	−0.0558473	+	0.0558473i
$344$	−11.9504	+	15.3889i	−0.644325	+	0.829715i
$345$	1.84462	−	0.0174429i	0.0993110	−	0.000939095i
$346$	26.2940	−	8.23474i	1.41357	−	0.442702i
$347$	−3.07907	−	3.07907i	−0.165293	−	0.165293i	0.619614	−	0.784907i	$-0.287289\pi$
$347$	−3.07907	−	3.07907i	−0.165293	−	0.165293i	−0.784907	+	0.619614i	$0.787289\pi$
$348$	0.176429	−	0.978491i	0.00945758	−	0.0524526i
$349$			29.1925i			1.56264i	0.624133	+	0.781318i	$0.285452\pi$
$349$			29.1925i			1.56264i	−0.624133	+	0.781318i	$0.714548\pi$
$350$	24.7362	−	8.26369i	1.32221	−	0.441713i
$351$			2.89402i			0.154471i
$352$	−6.69357	+	6.01581i	−0.356769	+	0.320644i
$353$	3.98871	+	3.98871i	0.212298	+	0.212298i	0.805243	−	0.592945i	$-0.202035\pi$
$353$	3.98871	+	3.98871i	0.212298	+	0.212298i	−0.592945	+	0.805243i	$0.702035\pi$
$354$	0.0123206	+	0.0393402i	0.000654830	+	0.00209091i
$355$	20.1056	−	0.190121i	1.06709	−	0.0100905i
$356$	−17.8317	+	12.3837i	−0.945080	+	0.656333i
$357$	1.06093	−	1.06093i	0.0561505	−	0.0561505i
$358$	−3.68681	+	7.04907i	−0.194854	+	0.372555i
$359$	−15.7000			−0.828613			−0.414306	−	0.910138i	$-0.635976\pi$
$359$	−15.7000			−0.828613			−0.414306	+	0.910138i	$0.635976\pi$
$360$	−18.6091	+	2.51944i	−0.980785	+	0.132786i
$361$	1.00000			0.0526316
$362$	−1.38740	+	2.65267i	−0.0729202	+	0.139421i
$363$	−1.05098	+	1.05098i	−0.0551622	+	0.0551622i
$364$	16.7375	−	11.6238i	0.877286	−	0.609252i
$365$	21.6898	−	22.1039i	1.13530	−	1.15697i
$366$	0.00522550	+	0.0166853i	0.000273141	+	0.000872156i
$367$	−12.9309	−	12.9309i	−0.674985	−	0.674985i	0.283876	−	0.958861i	$-0.408380\pi$
$367$	−12.9309	−	12.9309i	−0.674985	−	0.674985i	−0.958861	+	0.283876i	$0.908380\pi$
$368$	7.81466	+	17.1018i	0.407367	+	0.891495i
$369$			13.3419i			0.694552i
$370$	2.63879	−	0.853896i	0.137184	−	0.0443919i
$371$		−	22.1433i		−	1.14962i
$372$	0.466430	−	2.58686i	0.0241833	−	0.134123i
$373$	−16.0080	−	16.0080i	−0.828865	−	0.828865i	0.158495	−	0.987360i	$-0.449336\pi$
$373$	−16.0080	−	16.0080i	−0.828865	−	0.828865i	−0.987360	+	0.158495i	$0.949336\pi$
$374$	4.97676	−	1.55862i	0.257342	−	0.0805944i
$375$	−1.42626	−	1.34755i	−0.0736515	−	0.0695871i
$376$	28.6079	+	22.2158i	1.47534	+	1.14569i
$377$	−5.53329	+	5.53329i	−0.284979	+	0.284979i
$378$	4.84203	+	2.53248i	0.249047	+	0.130257i
$379$	26.0486			1.33803			0.669014	−	0.743250i	$-0.266717\pi$
$379$	26.0486			1.33803			0.669014	+	0.743250i	$0.266717\pi$
$380$	−3.64894	+	2.58558i	−0.187187	+	0.132637i
$381$	0.355105			0.0181926
$382$	7.78363	+	4.07100i	0.398245	+	0.208290i
$383$	19.9273	−	19.9273i	1.01824	−	1.01824i	0.0184082	−	0.999831i	$-0.494140\pi$
$383$	19.9273	−	19.9273i	1.01824	−	1.01824i	0.999831	−	0.0184082i	$-0.00585984\pi$
$384$	1.04414	+	1.68887i	0.0532836	+	0.0861846i
$385$	−9.36512	−	9.18966i	−0.477291	−	0.468349i
$386$	−17.9328	+	5.61618i	−0.912754	+	0.285856i
$387$	14.4631	+	14.4631i	0.735200	+	0.735200i
$388$	−9.04325	−	1.63056i	−0.459101	−	0.0827793i
$389$			15.8400i			0.803120i	0.915833	+	0.401560i	$0.131532\pi$
$389$			15.8400i			0.803120i	−0.915833	+	0.401560i	$0.868468\pi$
$390$	−1.36521	−	0.697676i	−0.0691303	−	0.0353282i
$391$		−	10.8958i		−	0.551024i
$392$	−2.33068	−	18.5313i	−0.117717	−	0.935971i
$393$	−1.93715	−	1.93715i	−0.0977162	−	0.0977162i
$394$	7.80853	+	24.9331i	0.393388	+	1.25611i
$395$	−0.298284	−	31.5441i	−0.0150083	−	1.58716i
$396$	5.38902	+	7.75985i	0.270808	+	0.389947i
$397$	10.7488	−	10.7488i	0.539467	−	0.539467i	−0.383905	−	0.923372i	$-0.625421\pi$
$397$	10.7488	−	10.7488i	0.539467	−	0.539467i	0.923372	+	0.383905i	$0.125421\pi$
$398$	9.48733	−	18.1395i	0.475557	−	0.909250i
$399$	0.647299			0.0324055
$400$	6.62955	−	18.8693i	0.331478	−	0.943463i
$401$	−17.4770			−0.872760			−0.436380	−	0.899763i	$-0.643740\pi$
$401$	−17.4770			−0.872760			−0.436380	+	0.899763i	$0.643740\pi$
$402$	−1.00247	+	1.91669i	−0.0499985	+	0.0955956i
$403$	−14.6285	+	14.6285i	−0.728698	+	0.728698i
$404$	21.9833	+	31.6546i	1.09371	+	1.57487i
$405$	0.184451	+	19.5060i	0.00916543	+	0.969261i
$406$	4.41579	+	14.0999i	0.219152	+	0.699764i
$407$	−0.986656	−	0.986656i	−0.0489067	−	0.0489067i
$408$	−0.143580	−	1.14160i	−0.00710826	−	0.0565179i
$409$		−	30.6758i		−	1.51682i	−0.651776	−	0.758411i	$-0.725976\pi$
$409$		−	30.6758i		−	1.51682i	0.651776	−	0.758411i	$-0.274024\pi$
$410$	−12.6530	−	6.46616i	−0.624888	−	0.319341i
$411$			3.09908i			0.152866i
$412$	3.34315	+	0.602794i	0.164705	+	0.0296975i
$413$	−0.433179	−	0.433179i	−0.0213153	−	0.0213153i
$414$	18.8364	−	5.89917i	0.925758	−	0.289928i
$415$	−10.3889	−	10.1942i	−0.509970	−	0.500416i
$416$	0.832178	−	15.6050i	0.0408009	−	0.765097i
$417$	0.191279	−	0.191279i	0.00936697	−	0.00936697i
$418$	1.99369	+	1.04274i	0.0975147	+	0.0510022i
$419$	31.7353			1.55037			0.775184	−	0.631735i	$-0.217657\pi$
$419$	31.7353			1.55037			0.775184	+	0.631735i	$0.217657\pi$
$420$	−2.36195	+	1.67364i	−0.115252	+	0.0816654i
$421$	27.0814			1.31987			0.659933	−	0.751324i	$-0.270585\pi$
$421$	27.0814			1.31987			0.659933	+	0.751324i	$0.270585\pi$
$422$	17.8754	+	9.34922i	0.870162	+	0.455113i
$423$	26.8868	−	26.8868i	1.30728	−	1.30728i
$424$	−13.4119	−	10.4152i	−0.651340	−	0.505806i
$425$	−8.03864	+	8.34858i	−0.389931	+	0.404966i
$426$	−2.12975	+	0.666996i	−0.103187	+	0.0323160i
$427$	−0.183724	−	0.183724i	−0.00889101	−	0.00889101i
$428$	−3.71758	+	20.6180i	−0.179696	+	0.996611i
$429$			0.771324i			0.0372399i
$430$	−20.7258	+	6.70675i	−0.999488	+	0.323428i
$431$			34.5665i			1.66501i	0.554017	+	0.832506i	$0.313094\pi$
$431$			34.5665i			1.66501i	−0.554017	+	0.832506i	$0.686906\pi$
$432$	3.81135	−	1.74159i	0.183374	−	0.0837924i
$433$	12.1303	+	12.1303i	0.582943	+	0.582943i	0.935711	−	0.352768i	$-0.114759\pi$
$433$	12.1303	+	12.1303i	0.582943	+	0.582943i	−0.352768	+	0.935711i	$0.614759\pi$
$434$	11.6741	+	37.2762i	0.560377	+	1.78931i
$435$	0.778571	−	0.793436i	0.0373296	−	0.0380424i
$436$	7.05419	−	4.89895i	0.337834	−	0.234617i
$437$	3.32388	−	3.32388i	0.159003	−	0.159003i
$438$	−1.59308	+	3.04592i	−0.0761203	+	0.145540i
$439$	13.6473			0.651351			0.325676	−	0.945482i	$-0.394408\pi$
$439$	13.6473			0.651351			0.325676	+	0.945482i	$0.394408\pi$
$440$	−9.97096	+	1.34994i	−0.475347	+	0.0643560i
$441$	−19.6068			−0.933659
$442$	−4.19690	+	8.02435i	−0.199626	+	0.381679i
$443$	−26.9614	+	26.9614i	−1.28097	+	1.28097i	−0.340859	+	0.940114i	$0.610718\pi$
$443$	−26.9614	+	26.9614i	−1.28097	+	1.28097i	−0.940114	+	0.340859i	$0.889282\pi$
$444$	−0.252856	+	0.175602i	−0.0120000	+	0.00833369i
$445$	−24.2715	+	0.229514i	−1.15058	+	0.0108800i
$446$	−9.17689	−	29.3023i	−0.434539	−	1.38751i
$447$	0.592860	+	0.592860i	0.0280413	+	0.0280413i
$448$	−25.3807	−	15.0478i	−1.19913	−	0.710944i
$449$			16.7867i			0.792214i	0.918204	+	0.396107i	$0.129639\pi$
$449$			16.7867i			0.792214i	−0.918204	+	0.396107i	$0.870361\pi$
$450$	−18.7851	−	9.37694i	−0.885538	−	0.442033i
$451$			7.14875i			0.336622i
$452$	−2.06375	+	11.4457i	−0.0970705	+	0.538361i
$453$	−2.85499	−	2.85499i	−0.134139	−	0.134139i
$454$	−32.3451	+	10.1298i	−1.51803	+	0.475417i
$455$	22.7821	−	0.215430i	1.06804	−	0.0100995i
$456$	0.304459	−	0.392060i	0.0142576	−	0.0183599i
$457$	−6.50673	+	6.50673i	−0.304372	+	0.304372i	−0.842722	−	0.538350i	$-0.819048\pi$
$457$	−6.50673	+	6.50673i	−0.304372	+	0.304372i	0.538350	+	0.842722i	$0.319048\pi$
$458$	−17.6805	−	9.24729i	−0.826157	−	0.432098i
$459$	−2.42826			−0.113341
$460$	−3.53449	+	20.7228i	−0.164796	+	0.966206i
$461$	22.0700			1.02790			0.513951	−	0.857820i	$-0.328181\pi$
$461$	22.0700			1.02790			0.513951	+	0.857820i	$0.328181\pi$
$462$	1.29051	+	0.674966i	0.0600401	+	0.0314023i
$463$	11.3477	−	11.3477i	0.527372	−	0.527372i	−0.392416	−	0.919788i	$-0.628361\pi$
$463$	11.3477	−	11.3477i	0.527372	−	0.527372i	0.919788	+	0.392416i	$0.128361\pi$
$464$	10.6171	+	3.95733i	0.492885	+	0.183714i
$465$	2.05833	−	2.09763i	0.0954527	−	0.0972752i
$466$	−29.3548	+	9.19333i	−1.35984	+	0.425873i
$467$	−9.63569	−	9.63569i	−0.445887	−	0.445887i	0.448098	−	0.893985i	$-0.352102\pi$
$467$	−9.63569	−	9.63569i	−0.445887	−	0.445887i	−0.893985	+	0.448098i	$0.852102\pi$
$468$	−16.1446	−	2.91099i	−0.746284	−	0.134560i
$469$		−	32.1431i		−	1.48423i
$470$	12.4678	+	38.5291i	0.575097	+	1.77722i
$471$		−	1.99980i		−	0.0921461i
$472$	−0.466118	+	0.0586237i	−0.0214548	+	0.00269837i
$473$	7.74948	+	7.74948i	0.356322	+	0.356322i
$474$	1.04646	+	3.34142i	0.0480657	+	0.153476i
$475$	−4.99911	+	0.0945526i	−0.229375	+	0.00433837i
$476$	9.75306	+	14.0438i	0.447031	+	0.643697i
$477$	−12.6050	+	12.6050i	−0.577144	+	0.577144i
$478$	−0.879801	+	1.68215i	−0.0402412	+	0.0769398i
$479$	3.41138			0.155870			0.0779350	−	0.996958i	$-0.475167\pi$
$479$	3.41138			0.155870			0.0779350	+	0.996958i	$0.475167\pi$
$480$	−0.0972497	+	2.21781i	−0.00443882	+	0.101229i
$481$	2.42289			0.110474
$482$	15.4875	−	29.6116i	0.705435	−	1.34877i
$483$	2.15154	−	2.15154i	0.0978986	−	0.0978986i
$484$	−9.66157	−	13.9121i	−0.439162	−	0.632367i
$485$	−7.33297	−	7.19559i	−0.332973	−	0.326735i
$486$	−1.97544	−	6.30771i	−0.0896080	−	0.286123i
$487$	17.2633	+	17.2633i	0.782276	+	0.782276i	0.980214	−	0.197939i	$-0.0634247\pi$
$487$	17.2633	+	17.2633i	0.782276	+	0.782276i	−0.197939	+	0.980214i	$0.563425\pi$
$488$	−0.197694	+	0.0248640i	−0.00894918	+	0.00112554i
$489$		−	2.17559i		−	0.0983837i
$490$	9.50246	−	18.5945i	0.429277	−	0.840012i
$491$		−	33.3803i		−	1.50643i	−0.657773	−	0.753216i	$-0.728501\pi$
$491$		−	33.3803i		−	1.50643i	0.657773	−	0.753216i	$-0.271499\pi$
$492$	1.55218	+	0.279869i	0.0699777	+	0.0126175i
$493$	−4.64276	−	4.64276i	−0.209099	−	0.209099i
$494$	−3.72823	+	1.16761i	−0.167741	+	0.0525331i
$495$	0.0998777	+	10.5622i	0.00448917	+	0.474738i
$496$	28.0686	+	10.4621i	1.26032	+	0.469762i
$497$	23.4509	−	23.4509i	1.05192	−	1.05192i
$498$	1.43159	+	0.748751i	0.0641510	+	0.0335523i
$499$	−15.4619			−0.692169			−0.346084	−	0.938203i	$-0.612489\pi$
$499$	−15.4619			−0.692169			−0.346084	+	0.938203i	$0.612489\pi$
$500$	17.9970	−	13.2706i	0.804849	−	0.593479i
$501$	−1.53147			−0.0684212
$502$	−2.65813	−	1.39026i	−0.118638	−	0.0620503i
$503$	−27.4515	+	27.4515i	−1.22400	+	1.22400i	−0.257805	+	0.966197i	$0.582999\pi$
$503$	−27.4515	+	27.4515i	−1.22400	+	1.22400i	−0.966197	+	0.257805i	$0.917001\pi$
$504$	−18.9981	+	24.4644i	−0.846244	+	1.08973i
$505$	0.407428	+	43.0863i	0.0181303	+	1.91731i
$506$	10.0928	−	3.16084i	0.448678	−	0.140517i
$507$	0.666221	+	0.666221i	0.0295879	+	0.0295879i
$508$	−0.718079	+	3.98253i	−0.0318596	+	0.176696i
$509$			20.0213i			0.887429i	0.896168	+	0.443714i	$0.146340\pi$
$509$			20.0213i			0.887429i	−0.896168	+	0.443714i	$0.853660\pi$
$510$	0.585392	−	1.14550i	0.0259216	−	0.0507234i
$511$		−	51.0805i		−	2.25967i
$512$	−21.0522	+	8.29496i	−0.930383	+	0.366589i
$513$	−0.740767	−	0.740767i	−0.0327057	−	0.0327057i
$514$	−8.04342	−	25.6831i	−0.354780	−	1.13283i
$515$	2.71088	+	2.66009i	0.119456	+	0.117218i
$516$	1.98600	−	1.37923i	0.0874289	−	0.0607171i
$517$	14.4062	−	14.4062i	0.633585	−	0.633585i
$518$	2.12021	−	4.05378i	0.0931568	−	0.178113i
$519$	−3.41932			−0.150091
$520$	10.5852	−	13.9002i	0.464190	−	0.609562i
$521$	21.3299			0.934479			0.467239	−	0.884131i	$-0.345249\pi$
$521$	21.3299			0.934479			0.467239	+	0.884131i	$0.345249\pi$
$522$	5.51263	−	10.5400i	0.241281	−	0.461322i
$523$	−14.2835	+	14.2835i	−0.624575	+	0.624575i	−0.946698	−	0.322123i	$-0.895604\pi$
$523$	−14.2835	+	14.2835i	−0.624575	+	0.624575i	0.322123	+	0.946698i	$0.395604\pi$
$524$	25.6425	−	17.8080i	1.12020	−	0.777948i
$525$	−3.23591	+	0.0612037i	−0.141227	+	0.00267115i
$526$	−2.56164	−	8.17948i	−0.111693	−	0.356642i
$527$	−12.2742	−	12.2742i	−0.534672	−	0.534672i
$528$	1.01581	−	0.464175i	0.0442077	−	0.0202006i
$529$			0.903616i			0.0392877i
$530$	−5.84514	−	18.0632i	−0.253897	−	0.784615i
$531$			0.493171i			0.0214018i
$532$	−1.30894	+	7.25950i	−0.0567498	+	0.314739i
$533$	−8.77746	−	8.77746i	−0.380194	−	0.380194i
$534$	2.57104	−	0.805198i	0.111260	−	0.0348443i
$535$	−16.4055	+	16.7187i	−0.709271	+	0.722813i
$536$	−19.4686	−	15.1186i	−0.840916	−	0.653023i
$537$	0.698057	−	0.698057i	0.0301234	−	0.0301234i
$538$	−37.8012	−	19.7708i	−1.62973	−	0.852381i
$539$	−10.5056			−0.452507
$540$	4.61833	+	0.787704i	0.198741	+	0.0338974i
$541$	13.5259			0.581526			0.290763	−	0.956795i	$-0.406091\pi$
$541$	13.5259			0.581526			0.290763	+	0.956795i	$0.406091\pi$
$542$	−11.6445	−	6.09033i	−0.500175	−	0.261602i
$543$	0.262689	−	0.262689i	0.0112731	−	0.0112731i
$544$	13.0935	+	0.698247i	0.561380	+	0.0299371i
$545$	9.60174	−	0.0907951i	0.411293	−	0.00388923i
$546$	−2.41328	+	0.755789i	−0.103279	+	0.0323448i
$547$	−3.98128	−	3.98128i	−0.170227	−	0.170227i	0.616852	−	0.787079i	$-0.288408\pi$
$547$	−3.98128	−	3.98128i	−0.170227	−	0.170227i	−0.787079	+	0.616852i	$0.788408\pi$
$548$	−34.7564	−	6.26683i	−1.48472	−	0.267706i
$549$			0.209168i			0.00892708i
$550$	−10.0653	−	5.02427i	−0.429185	−	0.214236i
$551$		−	2.83265i		−	0.120675i
$552$	−0.291176	−	2.31515i	−0.0123933	−	0.0985391i
$553$	−36.7927	−	36.7927i	−1.56458	−	1.56458i
$554$	12.0789	+	38.5686i	0.513183	+	1.63862i
$555$	−0.344172	+	0.00325453i	−0.0146093	+	0.000138147i
$556$	1.75841	+	2.53200i	0.0745732	+	0.107381i
$557$	7.53148	−	7.53148i	0.319119	−	0.319119i	−0.529310	−	0.848429i	$-0.677549\pi$
$557$	7.53148	−	7.53148i	0.319119	−	0.319119i	0.848429	+	0.529310i	$0.177549\pi$
$558$	14.5739	−	27.8648i	0.616961	−	1.17961i
$559$	−19.0301			−0.804888
$560$	−13.9938	−	29.8739i	−0.591345	−	1.26240i
$561$	−0.647187			−0.0273243
$562$	6.64057	−	12.6966i	0.280115	−	0.535572i
$563$	−17.0950	+	17.0950i	−0.720470	+	0.720470i	−0.968701	−	0.248231i	$-0.920151\pi$
$563$	−17.0950	+	17.0950i	−0.720470	+	0.720470i	0.248231	+	0.968701i	$0.420151\pi$
$564$	−2.56397	−	3.69197i	−0.107963	−	0.155460i
$565$	−9.10720	+	9.28108i	−0.383143	+	0.390458i
$566$	5.84752	+	18.6715i	0.245790	+	0.784820i
$567$	22.7516	+	22.7516i	0.955477	+	0.955477i
$568$	−3.17370	−	25.2341i	−0.133166	−	1.05880i
$569$		−	41.8061i		−	1.75260i	−0.481762	−	0.876302i	$-0.660003\pi$
$569$		−	41.8061i		−	1.75260i	0.481762	−	0.876302i	$-0.339997\pi$
$570$	0.528027	−	0.170866i	0.0221166	−	0.00715680i
$571$			4.87808i			0.204141i	0.994777	+	0.102071i	$0.0325468\pi$
$571$			4.87808i			0.204141i	−0.994777	+	0.102071i	$0.967453\pi$
$572$	−8.65046	−	1.55974i	−0.361694	−	0.0652160i
$573$	−0.770798	−	0.770798i	−0.0322006	−	0.0322006i
$574$	−22.3666	+	7.00477i	−0.933565	+	0.292373i
$575$	−16.3022	+	16.9307i	−0.679847	+	0.706060i
$576$	5.88195	+	23.0138i	0.245081	+	0.958909i
$577$	−8.43373	+	8.43373i	−0.351101	+	0.351101i	−0.860519	−	0.509418i	$-0.829861\pi$
$577$	−8.43373	+	8.43373i	−0.351101	+	0.351101i	0.509418	+	0.860519i	$0.329861\pi$
$578$	14.5708	+	7.62085i	0.606066	+	0.316985i
$579$	2.33201			0.0969150
$580$	7.32405	+	10.3362i	0.304115	+	0.429187i
$581$	−24.0079			−0.996016
$582$	1.01048	+	0.528504i	0.0418859	+	0.0219072i
$583$	−6.75391	+	6.75391i	−0.279718	+	0.279718i
$584$	−30.9388	−	24.0258i	−1.28025	−	0.994197i
$585$	−13.0913	−	12.8460i	−0.541258	−	0.531118i
$586$	0.781661	−	0.244800i	0.0322901	−	0.0101126i
$587$	−3.58279	−	3.58279i	−0.147878	−	0.147878i	0.629292	−	0.777169i	$-0.283345\pi$
$587$	−3.58279	−	3.58279i	−0.147878	−	0.147878i	−0.777169	+	0.629292i	$0.783345\pi$
$588$	−0.411287	+	2.28103i	−0.0169612	+	0.0940683i
$589$		−	7.48876i		−	0.308569i
$590$	−0.467707	−	0.239016i	−0.0192552	−	0.00984012i
$591$		−	3.24234i		−	0.133372i
$592$	−1.45807	−	3.19089i	−0.0599264	−	0.131145i
$593$	0.629048	+	0.629048i	0.0258319	+	0.0258319i	0.719905	−	0.694073i	$-0.244185\pi$
$593$	0.629048	+	0.629048i	0.0258319	+	0.0258319i	−0.694073	+	0.719905i	$0.744185\pi$
$594$	−0.704432	−	2.24929i	−0.0289032	−	0.0922896i
$595$	0.180759	+	19.1156i	0.00741039	+	0.783662i
$596$	−7.84783	+	5.45011i	−0.321460	+	0.223245i
$597$	−1.79632	+	1.79632i	−0.0735185	+	0.0735185i
$598$	−8.51122	+	16.2732i	−0.348050	+	0.665460i
$599$	14.8776			0.607883			0.303941	−	0.952691i	$-0.401697\pi$
$599$	14.8776			0.607883			0.303941	+	0.952691i	$0.401697\pi$
$600$	−1.48495	+	1.98874i	−0.0606229	+	0.0811898i
$601$	4.49789			0.183473			0.0917364	−	0.995783i	$-0.470758\pi$
$601$	4.49789			0.183473			0.0917364	+	0.995783i	$0.470758\pi$
$602$	−16.6528	+	31.8396i	−0.678716	+	1.29768i
$603$	−18.2973	+	18.2973i	−0.745125	+	0.745125i
$604$	37.7921	−	26.2456i	1.53774	−	1.06792i
$605$	−0.179063	−	18.9363i	−0.00727996	−	0.769869i
$606$	−1.42937	−	4.56407i	−0.0580643	−	0.185402i
$607$	−30.8289	−	30.8289i	−1.25131	−	1.25131i	−0.955134	−	0.296174i	$-0.904289\pi$
$607$	−30.8289	−	30.8289i	−1.25131	−	1.25131i	−0.296174	−	0.955134i	$-0.595711\pi$
$608$	3.78132	+	4.20733i	0.153353	+	0.170630i
$609$		−	1.83357i		−	0.0743001i
$610$	−0.198368	−	0.101373i	−0.00803168	−	0.00410449i
$611$			35.3769i			1.43119i
$612$	2.44249	−	13.5463i	0.0987319	−	0.547576i
$613$	8.34078	+	8.34078i	0.336881	+	0.336881i	0.855192	−	0.518311i	$-0.173439\pi$
$613$	8.34078	+	8.34078i	0.336881	+	0.336881i	−0.518311	+	0.855192i	$0.673439\pi$
$614$	43.0085	−	13.4694i	1.73568	−	0.543580i
$615$	1.25863	+	1.23505i	0.0507528	+	0.0498019i
$616$	−10.1794	+	13.1083i	−0.410140	+	0.528149i
$617$	−12.8874	+	12.8874i	−0.518827	+	0.518827i	−0.917216	−	0.398389i	$-0.869569\pi$
$617$	−12.8874	+	12.8874i	−0.518827	+	0.518827i	0.398389	+	0.917216i	$0.369569\pi$
$618$	−0.373560	−	0.195380i	−0.0150268	−	0.00785932i
$619$	8.36882			0.336371			0.168186	−	0.985755i	$-0.446209\pi$
$619$	8.36882			0.336371			0.168186	+	0.985755i	$0.446209\pi$
$620$	19.3628	+	27.3260i	0.777628	+	1.09744i
$621$	−4.92445			−0.197611
$622$	−4.82733	−	2.52479i	−0.193558	−	0.101235i
$623$	−28.3100	+	28.3100i	−1.13422	+	1.13422i
$624$	−0.677321	+	1.81718i	−0.0271145	+	0.0727453i
$625$	24.9821	−	0.945357i	0.999285	−	0.0378143i
$626$	16.3969	−	5.13517i	0.655351	−	0.205243i
$627$	−0.197432	−	0.197432i	−0.00788466	−	0.00788466i
$628$	22.4279	+	4.04392i	0.894972	+	0.161370i
$629$			2.03295i			0.0810592i
$630$	−32.9487	+	10.6620i	−1.31271	+	0.424784i
$631$		−	31.5443i		−	1.25576i	−0.778311	−	0.627879i	$-0.783923\pi$
$631$		−	31.5443i		−	1.25576i	0.778311	−	0.627879i	$-0.216077\pi$
$632$	−39.5904	+	4.97929i	−1.57482	+	0.198066i
$633$	−1.77017	−	1.77017i	−0.0703580	−	0.0703580i
$634$	−8.50334	−	27.1516i	−0.337711	−	1.07833i
$635$	−3.16884	+	3.22935i	−0.125752	+	0.128153i
$636$	1.20204	+	1.73086i	0.0476640	+	0.0686332i
$637$	12.8991	−	12.8991i	0.511080	−	0.511080i
$638$	2.95373	−	5.64744i	0.116939	−	0.223584i
$639$	−26.6987			−1.05619
$640$	−24.6762	−	5.57542i	−0.975412	−	0.220388i
$641$	−22.5738			−0.891612			−0.445806	−	0.895130i	$-0.647083\pi$
$641$	−22.5738			−0.891612			−0.445806	+	0.895130i	$0.647083\pi$
$642$	1.20496	−	2.30384i	0.0475559	−	0.0909253i
$643$	−5.75048	+	5.75048i	−0.226777	+	0.226777i	−0.811345	−	0.584568i	$-0.801264\pi$
$643$	−5.75048	+	5.75048i	−0.226777	+	0.226777i	0.584568	+	0.811345i	$0.301264\pi$
$644$	19.7790	+	28.4805i	0.779400	+	1.12229i
$645$	2.70323	−	0.0255620i	0.106440	−	0.00100650i
$646$	−0.979691	−	3.12821i	−0.0385454	−	0.123078i
$647$	10.6270	+	10.6270i	0.417789	+	0.417789i	0.884441	−	0.466652i	$-0.154540\pi$
$647$	10.6270	+	10.6270i	0.417789	+	0.417789i	−0.466652	+	0.884441i	$0.654540\pi$
$648$	24.4816	−	3.07906i	0.961728	−	0.120957i
$649$			0.264247i			0.0103726i
$650$	18.5274	−	6.18950i	0.726705	−	0.242772i
$651$		−	4.84746i		−	0.189987i
$652$	24.3994	+	4.39939i	0.955555	+	0.172293i
$653$	−0.939598	−	0.939598i	−0.0367693	−	0.0367693i	0.688483	−	0.725252i	$-0.258277\pi$
$653$	−0.939598	−	0.939598i	−0.0367693	−	0.0367693i	−0.725252	+	0.688483i	$0.758277\pi$
$654$	−1.01710	+	0.318534i	−0.0397717	+	0.0124557i
$655$	34.9030	−	0.330046i	1.36377	−	0.0128960i
$656$	−6.27751	+	16.8419i	−0.245096	+	0.657565i
$657$	−29.0774	+	29.0774i	−1.13442	+	1.13442i
$658$	59.1895	+	30.9574i	2.30745	+	1.20684i
$659$	−0.526274			−0.0205007			−0.0102504	−	0.999947i	$-0.503263\pi$
$659$	−0.526274			−0.0205007			−0.0102504	+	0.999947i	$0.503263\pi$
$660$	1.23089	+	0.209941i	0.0479124	+	0.00817196i
$661$	24.1930			0.940998			0.470499	−	0.882400i	$-0.344074\pi$
$661$	24.1930			0.940998			0.470499	+	0.882400i	$0.344074\pi$
$662$	−38.4245	−	20.0968i	−1.49341	−	0.781085i
$663$	0.794637	−	0.794637i	0.0308611	−	0.0308611i
$664$	−11.2922	+	14.5413i	−0.438222	+	0.564311i
$665$	−5.77628	+	5.88657i	−0.223995	+	0.228271i
$666$	−3.51452	+	1.10068i	−0.136185	+	0.0426504i
$667$	−9.41540	−	9.41540i	−0.364566	−	0.364566i
$668$	3.09688	−	17.1756i	0.119822	−	0.664544i
$669$			3.81053i			0.147324i
$670$	−8.48475	−	26.2204i	−0.327794	−	1.01298i
$671$			0.112075i			0.00432660i
$672$	2.44764	+	2.72340i	0.0944198	+	0.105057i
$673$	14.4954	+	14.4954i	0.558758	+	0.558758i	0.928954	−	0.370196i	$-0.120709\pi$
$673$	14.4954	+	14.4954i	0.558758	+	0.558758i	−0.370196	+	0.928954i	$0.620709\pi$
$674$	−1.01623	−	3.24486i	−0.0391435	−	0.124988i
$675$	3.77322	+	3.63313i	0.145231	+	0.139839i
$676$	−8.81892	+	6.12451i	−0.339189	+	0.235558i
$677$	11.5440	−	11.5440i	0.443674	−	0.443674i	−0.449571	−	0.893245i	$-0.648423\pi$
$677$	11.5440	−	11.5440i	0.443674	−	0.443674i	0.893245	+	0.449571i	$0.148423\pi$
$678$	0.668909	−	1.27893i	0.0256893	−	0.0491171i
$679$	−16.9459			−0.650326
$680$	11.6631	+	8.88158i	0.447258	+	0.340593i
$681$	4.20622			0.161183
$682$	7.80885	−	14.9303i	0.299016	−	0.571710i
$683$	0.806416	−	0.806416i	0.0308567	−	0.0308567i	−0.691510	−	0.722367i	$-0.743054\pi$
$683$	0.806416	−	0.806416i	0.0308567	−	0.0308567i	0.722367	+	0.691510i	$0.243054\pi$
$684$	4.87755	−	3.38734i	0.186498	−	0.129518i
$685$	−28.1832	−	27.6552i	−1.07682	−	1.05665i
$686$	0.618237	+	1.97407i	0.0236044	+	0.0753702i
$687$	1.75087	+	1.75087i	0.0667999	+	0.0667999i
$688$	11.4521	+	25.0622i	0.436608	+	0.955487i
$689$		−	16.5853i		−	0.631851i
$690$	1.18716	−	2.32304i	0.0451944	−	0.0884365i
$691$		−	8.43610i		−	0.320924i	−0.987042	−	0.160462i	$-0.948702\pi$
$691$		−	8.43610i		−	0.320924i	0.987042	−	0.160462i	$-0.0512985\pi$
$692$	6.91440	−	38.3479i	0.262846	−	1.45777i
$693$	12.3197	+	12.3197i	0.467986	+	0.467986i
$694$	−5.87668	+	1.84045i	−0.223076	+	0.0698627i
$695$	0.0325896	+	3.44641i	0.00123619	+	0.130730i
$696$	−1.11057	−	0.862425i	−0.0420960	−	0.0326902i
$697$	7.36482	−	7.36482i	0.278962	−	0.278962i
$698$	36.5829	+	19.1336i	1.38468	+	0.724217i
$699$	3.81736			0.144386
$700$	5.85713	−	36.4148i	0.221379	−	1.37635i
$701$	−48.1260			−1.81769			−0.908847	−	0.417130i	$-0.863036\pi$
$701$	−48.1260			−1.81769			−0.908847	+	0.417130i	$0.863036\pi$
$702$	3.62668	+	1.89683i	0.136880	+	0.0715911i
$703$	−0.620175	+	0.620175i	−0.0233904	+	0.0233904i
$704$	3.15161	+	12.3311i	0.118781	+	0.464745i
$705$	−0.0475196	−	5.02528i	−0.00178969	−	0.189263i
$706$	7.61282	−	2.38418i	0.286512	−	0.0897297i
$707$	50.2554	+	50.2554i	1.89005	+	1.89005i
$708$	0.0573749	+	0.0103451i	0.00215628	+	0.000388793i
$709$			26.2454i			0.985666i	0.870124	+	0.492833i	$0.164039\pi$
$709$			26.2454i			0.985666i	−0.870124	+	0.492833i	$0.835961\pi$
$710$	12.9395	−	25.3201i	0.485612	−	0.950248i
$711$			41.8882i			1.57093i
$712$	3.83129	+	30.4627i	0.143584	+	1.14164i
$713$	−24.8918	−	24.8918i	−0.932203	−	0.932203i
$714$	−0.634153	−	2.02489i	−0.0237326	−	0.0757794i
$715$	−7.01446	−	6.88305i	−0.262326	−	0.257411i
$716$	6.41718	+	9.24034i	0.239821	+	0.345328i
$717$	0.166580	−	0.166580i	0.00622106	−	0.00622106i
$718$	−10.2902	+	19.6746i	−0.384028	+	0.734249i
$719$	−20.3968			−0.760673			−0.380336	−	0.924848i	$-0.624192\pi$
$719$	−20.3968			−0.760673			−0.380336	+	0.924848i	$0.624192\pi$
$720$	−9.03969	+	24.9715i	−0.336889	+	0.930633i
$721$	6.26465			0.233308
$722$	0.655429	−	1.25316i	0.0243926	−	0.0466378i
$723$	−2.93238	+	2.93238i	−0.109056	+	0.109056i
$724$	2.41488	+	3.47727i	0.0897482	+	0.129232i
$725$	0.267835	+	14.1607i	0.00994713	+	0.525916i
$726$	0.628204	+	2.00589i	0.0233148	+	0.0744456i
$727$	25.9245	+	25.9245i	0.961488	+	0.961488i	0.999285	−	0.0377979i	$-0.0120343\pi$
$727$	25.9245	+	25.9245i	0.961488	+	0.961488i	−0.0377979	+	0.999285i	$0.512034\pi$
$728$	−3.59620	−	28.5934i	−0.133284	−	1.05974i
$729$		−	25.3510i		−	0.938924i
$730$	−13.4836	−	41.6684i	−0.499051	−	1.54222i
$731$		−	15.9674i		−	0.590576i
$732$	0.0243343	+	0.00438766i	0.000899423	+	0.000162173i
$733$	16.2770	+	16.2770i	0.601204	+	0.601204i	0.940632	−	0.339428i	$-0.110234\pi$
$733$	16.2770	+	16.2770i	0.601204	+	0.601204i	−0.339428	+	0.940632i	$0.610234\pi$
$734$	−24.6797	+	7.72918i	−0.910945	+	0.285289i
$735$	−1.81499	+	1.84964i	−0.0669468	+	0.0682250i
$736$	26.5533	+	1.41603i	0.978769	+	0.0521955i
$737$	−9.80392	+	9.80392i	−0.361132	+	0.361132i
$738$	16.7196	+	8.74469i	0.615456	+	0.321896i
$739$	32.9152			1.21080			0.605402	−	0.795920i	$-0.293012\pi$
$739$	32.9152			1.21080			0.605402	+	0.795920i	$0.293012\pi$
$740$	0.659471	−	3.86650i	0.0242426	−	0.142135i
$741$	0.484826			0.0178105
$742$	−27.7492	−	14.5134i	−1.01870	−	0.532804i
$743$	30.7223	−	30.7223i	1.12709	−	1.12709i	0.136443	−	0.990648i	$-0.456433\pi$
$743$	30.7223	−	30.7223i	1.12709	−	1.12709i	0.990648	−	0.136443i	$-0.0435670\pi$
$744$	−2.93604	−	2.28002i	−0.107641	−	0.0835895i
$745$	−10.6820	+	0.101010i	−0.391358	+	0.00370072i
$746$	−30.5528	+	9.56851i	−1.11862	+	0.350328i
$747$	13.6664	+	13.6664i	0.500028	+	0.500028i
$748$	1.30872	−	7.25825i	0.0478514	−	0.265388i
$749$			38.6357i			1.41172i
$750$	−2.62351	+	0.904105i	−0.0957969	+	0.0330132i
$751$		−	15.8179i		−	0.577202i	−0.957449	−	0.288601i	$-0.906810\pi$
$751$		−	15.8179i		−	0.577202i	0.957449	−	0.288601i	$-0.0931902\pi$
$752$	46.5904	−	21.2894i	1.69898	−	0.776345i
$753$	0.263230	+	0.263230i	0.00959264	+	0.00959264i
$754$	3.30742	+	10.5608i	0.120449	+	0.384601i
$755$	51.4404	−	0.486425i	1.87211	−	0.0177028i
$756$	6.34722	−	4.40798i	0.230846	−	0.160317i
$757$	−11.8403	+	11.8403i	−0.430342	+	0.430342i	−0.888745	−	0.458403i	$-0.848422\pi$
$757$	−11.8403	+	11.8403i	−0.430342	+	0.430342i	0.458403	+	0.888745i	$0.348422\pi$
$758$	17.0730	−	32.6431i	0.620121	−	1.18565i
$759$	−1.31248			−0.0476400
$760$	0.848523	+	6.26738i	0.0307792	+	0.227342i
$761$	31.9316			1.15752			0.578759	−	0.815498i	$-0.303537\pi$
$761$	31.9316			1.15752			0.578759	+	0.815498i	$0.303537\pi$
$762$	0.232747	−	0.445004i	0.00843152	−	0.0161208i
$763$	11.1994	−	11.1994i	0.405444	−	0.405444i
$764$	10.2032	−	7.08588i	0.369140	−	0.256358i
$765$	10.7786	−	10.9844i	0.389701	−	0.397141i
$766$	−11.9112	−	38.0331i	−0.430369	−	1.37419i
$767$	−0.324451	−	0.324451i	−0.0117152	−	0.0117152i
$768$	2.80078	−	0.201544i	0.101064	−	0.00727259i
$769$		−	2.26915i		−	0.0818278i	−0.999163	−	0.0409139i	$-0.986973\pi$
$769$		−	2.26915i		−	0.0818278i	0.999163	−	0.0409139i	$-0.0130269\pi$
$770$	−17.6543	+	5.71282i	−0.636217	+	0.205876i
$771$			3.33987i			0.120283i
$772$	−4.71569	+	26.1537i	−0.169722	+	0.941291i
$773$	3.66627	+	3.66627i	0.131866	+	0.131866i	0.769959	−	0.638093i	$-0.220276\pi$
$773$	3.66627	+	3.66627i	0.131866	+	0.131866i	−0.638093	+	0.769959i	$0.720276\pi$
$774$	27.6041	−	8.64504i	0.992209	−	0.310739i
$775$	0.708081	+	37.4371i	0.0254350	+	1.34478i
$776$	−7.97057	+	10.2639i	−0.286127	+	0.368454i
$777$	−0.401439	+	0.401439i	−0.0144015	+	0.0144015i
$778$	19.8501	+	10.3820i	0.711660	+	0.372213i
$779$	4.49344			0.160994
$780$	−1.76910	+	1.25356i	−0.0633440	+	0.0448845i
$781$	−14.3055			−0.511890
$782$	−13.6542	−	7.14142i	−0.488272	−	0.255377i
$783$	−2.09834	+	2.09834i	−0.0749884	+	0.0749884i
$784$	−24.7503	−	9.22523i	−0.883938	−	0.329472i
$785$	18.1863	+	17.8456i	0.649097	+	0.636936i
$786$	−3.69722	+	1.15789i	−0.131876	+	0.0413007i
$787$	−12.4937	−	12.4937i	−0.445354	−	0.445354i	0.448453	−	0.893806i	$-0.351975\pi$
$787$	−12.4937	−	12.4937i	−0.445354	−	0.445354i	−0.893806	+	0.448453i	$0.851975\pi$
$788$	36.3631	+	6.55653i	1.29538	+	0.233567i
$789$			1.06367i			0.0378678i
$790$	−39.7253	−	20.3011i	−1.41336	−	0.722282i
$791$			21.4479i			0.762599i
$792$	13.2565	−	1.66727i	0.471048	−	0.0592438i
$793$	−0.137609	−	0.137609i	−0.00488663	−	0.00488663i
$794$	−6.42490	−	20.5151i	−0.228011	−	0.728053i
$795$	0.0222781	+	2.35595i	0.000790122	+	0.0835568i
$796$	−16.5134	−	23.7783i	−0.585302	−	0.842799i
$797$	−38.2984	+	38.2984i	−1.35660	+	1.35660i	−0.478525	+	0.878074i	$0.658829\pi$
$797$	−38.2984	+	38.2984i	−1.35660	+	1.35660i	−0.878074	+	0.478525i	$0.841171\pi$
$798$	0.424259	−	0.811169i	0.0150186	−	0.0287151i
$799$	−29.6833			−1.05012
$800$	−19.3010	−	20.6754i	−0.682394	−	0.730985i
$801$	32.2307			1.13882
$802$	−11.4549	+	21.9015i	−0.404488	+	0.773369i
$803$	−15.5800	+	15.5800i	−0.549806	+	0.549806i
$804$	1.74487	+	2.51250i	0.0615368	+	0.0886092i
$805$	0.366575	+	38.7659i	0.0129201	+	1.36632i
$806$	8.74392	+	27.9198i	0.307991	+	0.983434i
$807$	3.74339	+	3.74339i	0.131773	+	0.131773i
$808$	54.0767	−	6.80124i	1.90241	−	0.239267i
$809$		−	2.00239i		−	0.0704003i	−0.999380	−	0.0352002i	$-0.988793\pi$
$809$		−	2.00239i		−	0.0704003i	0.999380	−	0.0352002i	$-0.0112069\pi$
$810$	24.5651	+	12.5537i	0.863128	+	0.441091i
$811$		−	16.2430i		−	0.570367i	−0.958473	−	0.285184i	$-0.907945\pi$
$811$		−	16.2430i		−	0.570367i	0.958473	−	0.285184i	$-0.0920546\pi$
$812$	20.5636	+	3.70777i	0.721642	+	0.130117i
$813$	1.15314	+	1.15314i	0.0404423	+	0.0404423i
$814$	−1.88312	+	0.589755i	−0.0660034	+	0.0206709i
$815$	19.7849	+	19.4143i	0.693036	+	0.680052i
$816$	−1.52472	−	0.568313i	−0.0533759	−	0.0198949i
$817$	4.87104	−	4.87104i	0.170416	−	0.170416i
$818$	−38.4418	−	20.1058i	−1.34408	−	0.702984i
$819$	−30.2530			−1.05713
$820$	−16.3963	+	11.6181i	−0.572584	+	0.405723i
$821$	10.5576			0.368463			0.184232	−	0.982883i	$-0.441020\pi$
$821$	10.5576			0.368463			0.184232	+	0.982883i	$0.441020\pi$
$822$	3.88365	+	2.03123i	0.135458	+	0.0708472i
$823$	34.7707	−	34.7707i	1.21203	−	1.21203i	0.241674	−	0.970358i	$-0.422304\pi$
$823$	34.7707	−	34.7707i	1.21203	−	1.21203i	0.970358	−	0.241674i	$-0.0776965\pi$
$824$	2.94659	−	3.79441i	0.102649	−	0.132185i
$825$	1.00565	+	0.968314i	0.0350122	+	0.0337124i
$826$	−0.826761	+	0.258925i	−0.0287667	+	0.00900914i
$827$	19.5183	+	19.5183i	0.678719	+	0.678719i	0.959710	−	0.280991i	$-0.0906631\pi$
$827$	19.5183	+	19.5183i	0.678719	+	0.678719i	−0.280991	+	0.959710i	$0.590663\pi$
$828$	4.95331	−	27.4715i	0.172140	−	0.954701i
$829$			21.3600i			0.741862i	0.928660	+	0.370931i	$0.120961\pi$
$829$			21.3600i			0.741862i	−0.928660	+	0.370931i	$0.879039\pi$
$830$	−19.5842	+	6.33733i	−0.679778	+	0.219972i
$831$		−	5.01553i		−	0.173987i
$832$	−19.0101	−	11.2708i	−0.659057	−	0.390745i
$833$	10.8231	+	10.8231i	0.374998	+	0.374998i
$834$	−0.114333	−	0.365073i	−0.00395904	−	0.0126414i
$835$	13.6664	−	13.9273i	0.472944	−	0.481974i
$836$	2.61345	−	1.81497i	0.0903880	−	0.0627721i
$837$	−5.54743	+	5.54743i	−0.191747	+	0.191747i
$838$	20.8002	−	39.7694i	0.718532	−	1.37381i
$839$	−20.3438			−0.702345			−0.351173	−	0.936311i	$-0.614217\pi$
$839$	−20.3438			−0.702345			−0.351173	+	0.936311i	$0.614217\pi$
$840$	0.549248	+	4.05686i	0.0189509	+	0.139975i
$841$	20.9761			0.723313
$842$	17.7499	−	33.9373i	0.611703	−	1.16956i
$843$	−1.25732	+	1.25732i	−0.0433043	+	0.0433043i
$844$	23.4322	−	16.2730i	0.806568	−	0.560141i
$845$	−12.0038	+	0.113509i	−0.412943	+	0.00390483i
$846$	−16.0711	−	51.3158i	−0.552535	−	1.76427i
$847$	−22.0871	−	22.0871i	−0.758920	−	0.758920i
$848$	−21.8425	+	9.98088i	−0.750073	+	0.342745i
$849$		−	2.42807i		−	0.0833312i
$850$	5.19336	+	15.5456i	0.178131	+	0.533210i
$851$			4.12278i			0.141327i
$852$	−0.560051	+	3.10609i	−0.0191870	+	0.106413i
$853$	−23.0651	−	23.0651i	−0.789733	−	0.789733i	0.191717	−	0.981450i	$-0.438594\pi$
$853$	−23.0651	−	23.0651i	−0.789733	−	0.789733i	−0.981450	+	0.191717i	$0.938594\pi$
$854$	−0.350653	+	0.109817i	−0.0119991	+	0.00375788i
$855$	6.63903	−	0.0627794i	0.227050	−	0.00214701i
$856$	23.4011	+	18.1724i	0.799834	+	0.621120i
$857$	−21.3897	+	21.3897i	−0.730657	+	0.730657i	−0.970750	−	0.240093i	$-0.922822\pi$
$857$	−21.3897	+	21.3897i	−0.730657	+	0.730657i	0.240093	+	0.970750i	$0.422822\pi$
$858$	0.966593	+	0.505549i	0.0329990	+	0.0172591i
$859$	−31.5338			−1.07592			−0.537959	−	0.842971i	$-0.680805\pi$
$859$	−31.5338			−1.07592			−0.537959	+	0.842971i	$0.680805\pi$
$860$	−5.17968	+	30.3686i	−0.176626	+	1.03556i
$861$	2.90860			0.0991247
$862$	43.3174	+	22.6559i	1.47540	+	0.771664i
$863$	−11.4012	+	11.4012i	−0.388100	+	0.388100i	−0.874009	−	0.485909i	$-0.838489\pi$
$863$	−11.4012	+	11.4012i	−0.388100	+	0.388100i	0.485909	+	0.874009i	$0.338489\pi$
$864$	0.315579	−	5.91773i	0.0107362	−	0.201325i
$865$	30.5129	−	31.0954i	1.03747	−	1.05728i
$866$	23.1517	−	7.25064i	0.786727	−	0.246387i
$867$	−1.44292	−	1.44292i	−0.0490042	−	0.0490042i
$868$	54.3646	+	9.80234i	1.84526	+	0.332713i
$869$			22.4442i			0.761367i
$870$	−0.484005	−	1.49572i	−0.0164093	−	0.0507095i
$871$		−	24.0751i		−	0.815754i
$872$	−1.51565	−	12.0510i	−0.0513264	−	0.408097i
$873$	9.64642	+	9.64642i	0.326482	+	0.326482i
$874$	−1.98679	−	6.34393i	−0.0672041	−	0.214587i
$875$	28.3196	−	29.9737i	0.957379	−	1.01330i
$876$	2.77288	+	3.99277i	0.0936868	+	0.134903i
$877$	8.28156	−	8.28156i	0.279649	−	0.279649i	−0.553320	−	0.832969i	$-0.686639\pi$
$877$	8.28156	−	8.28156i	0.279649	−	0.279649i	0.832969	+	0.553320i	$0.186639\pi$
$878$	8.94486	−	17.1023i	0.301874	−	0.577174i
$879$	−0.101649			−0.00342852
$880$	−4.84357	+	13.3800i	−0.163277	+	0.451040i
$881$	−29.7548			−1.00246			−0.501232	−	0.865313i	$-0.667120\pi$
$881$	−29.7548			−1.00246			−0.501232	+	0.865313i	$0.667120\pi$
$882$	−12.8509	+	24.5705i	−0.432712	+	0.827333i
$883$	−17.9126	+	17.9126i	−0.602807	+	0.602807i	−0.941056	−	0.338250i	$-0.890165\pi$
$883$	−17.9126	+	17.9126i	−0.602807	+	0.602807i	0.338250	+	0.941056i	$0.390165\pi$
$884$	7.30503	+	10.5188i	0.245695	+	0.353785i
$885$	0.0465240	+	0.0456524i	0.00156389	+	0.00153459i
$886$	16.1157	+	51.4582i	0.541416	+	1.72877i
$887$	−22.7676	−	22.7676i	−0.764463	−	0.764463i	0.212663	−	0.977126i	$-0.431786\pi$
$887$	−22.7676	−	22.7676i	−0.764463	−	0.764463i	−0.977126	+	0.212663i	$0.931786\pi$
$888$	0.0543282	+	0.431964i	0.00182313	+	0.0144957i
$889$			7.46278i			0.250294i
$890$	−15.6206	+	30.5665i	−0.523605	+	1.02459i
$891$		−	13.8789i		−	0.464960i
$892$	−42.7354	−	7.70550i	−1.43089	−	0.257999i
$893$	−9.05522	−	9.05522i	−0.303021	−	0.303021i
$894$	1.13153	−	0.354371i	0.0378439	−	0.0118519i
$895$	0.118933	+	12.5774i	0.00397550	+	0.420416i
$896$	−35.4926	+	21.9433i	−1.18573	+	0.733075i
$897$	1.61150	−	1.61150i	0.0538065	−	0.0538065i
$898$	21.0364	+	11.0025i	0.701995	+	0.367158i
$899$	−21.2130			−0.707495
$900$	−24.0631	+	17.3948i	−0.802104	+	0.579828i
$901$	13.9161			0.463612
$902$	8.95854	+	4.68550i	0.298287	+	0.156010i
$903$	3.15302	−	3.15302i	0.104926	−	0.104926i
$904$	12.9907	+	10.0881i	0.432064	+	0.335524i
$905$	0.0447563	+	4.73306i	0.00148775	+	0.157332i
$906$	−5.44900	+	1.70652i	−0.181031	+	0.0566952i
$907$	14.2857	+	14.2857i	0.474350	+	0.474350i	0.903319	−	0.428969i	$-0.141123\pi$
$907$	14.2857	+	14.2857i	0.474350	+	0.474350i	−0.428969	+	0.903319i	$0.641123\pi$
$908$	−8.50564	+	47.1730i	−0.282270	+	1.56549i
$909$		−	57.2154i		−	1.89771i
$910$	14.6621	−	28.6909i	0.486044	−	0.951094i
$911$			57.1661i			1.89400i	0.321235	+	0.946999i	$0.395902\pi$
$911$			57.1661i			1.89400i	−0.321235	+	0.946999i	$0.604098\pi$
$912$	−0.291763	−	0.638503i	−0.00966124	−	0.0211430i
$913$	7.32263	+	7.32263i	0.242344	+	0.242344i
$914$	3.88928	+	12.4187i	0.128646	+	0.410773i
$915$	0.0197322	+	0.0193625i	0.000652326	+	0.000640104i
$916$	−23.1767	+	16.0956i	−0.765779	+	0.531814i
$917$	40.7105	−	40.7105i	1.34438	−	1.34438i
$918$	−1.59155	+	3.04300i	−0.0525290	+	0.100434i
$919$	−37.2279			−1.22804			−0.614018	−	0.789292i	$-0.710448\pi$
$919$	−37.2279			−1.22804			−0.614018	+	0.789292i	$0.710448\pi$
$920$	23.6524	+	18.0116i	0.779797	+	0.593826i
$921$	−5.59290			−0.184292
$922$	14.4653	−	27.6572i	0.476390	−	0.910843i
$923$	17.5647	−	17.5647i	0.578150	−	0.578150i
$924$	1.69168	−	1.17483i	0.0556522	−	0.0386490i
$925$	3.04168	−	3.15896i	0.100010	−	0.103866i
$926$	−6.78288	−	21.6581i	−0.222899	−	0.711730i
$927$	−3.56613	−	3.56613i	−0.117127	−	0.117127i
$928$	11.9179	−	10.7112i	0.391225	−	0.351611i
$929$		−	25.9201i		−	0.850412i	−0.905097	−	0.425206i	$-0.860202\pi$
$929$		−	25.9201i		−	0.850412i	0.905097	−	0.425206i	$-0.139798\pi$
$930$	−1.27958	−	3.95427i	−0.0419590	−	0.129665i
$931$			6.60341i			0.216418i
$932$	−7.71930	+	42.8119i	−0.252854	+	1.40235i
$933$	0.478041	+	0.478041i	0.0156504	+	0.0156504i
$934$	−18.3906	+	5.75956i	−0.601759	+	0.188458i
$935$	5.77529	−	5.88555i	0.188872	−	0.192478i
$936$	−14.2296	+	18.3238i	−0.465108	+	0.598933i
$937$	3.72764	−	3.72764i	0.121777	−	0.121777i	−0.643592	−	0.765369i	$-0.722557\pi$
$937$	3.72764	−	3.72764i	0.121777	−	0.121777i	0.765369	+	0.643592i	$0.222557\pi$
$938$	−40.2804	−	21.0675i	−1.31520	−	0.687879i
$939$	−2.13228			−0.0695843
$940$	56.4550	+	9.62898i	1.84136	+	0.314063i
$941$	−13.4372			−0.438041			−0.219020	−	0.975720i	$-0.570286\pi$
$941$	−13.4372			−0.438041			−0.219020	+	0.975720i	$0.570286\pi$
$942$	−2.50608	−	1.31073i	−0.0816523	−	0.0427059i
$943$	14.9357	−	14.9357i	0.486372	−	0.486372i
$944$	−0.232042	+	0.622544i	−0.00755233	+	0.0202621i
$945$	8.63945	−	0.0816956i	0.281041	−	0.00265756i
$946$	14.7906	−	4.63211i	0.480884	−	0.150603i
$947$	−1.34091	−	1.34091i	−0.0435736	−	0.0435736i	0.684984	−	0.728558i	$-0.259809\pi$
$947$	−1.34091	−	1.34091i	−0.0435736	−	0.0435736i	−0.728558	+	0.684984i	$0.759809\pi$
$948$	4.87322	+	0.878677i	0.158275	+	0.0285381i
$949$		−	38.2592i		−	1.24195i
$950$	−3.15807	+	6.32666i	−0.102461	+	0.205264i
$951$			3.53085i			0.114496i
$952$	23.9916	−	3.01743i	0.777572	−	0.0977954i
$953$	−27.0674	−	27.0674i	−0.876799	−	0.876799i	0.116403	−	0.993202i	$-0.462864\pi$
$953$	−27.0674	−	27.0674i	−0.876799	−	0.876799i	−0.993202	+	0.116403i	$0.962864\pi$
$954$	7.53442	+	24.0578i	0.243936	+	0.778901i
$955$	13.8880	−	0.131327i	0.449406	−	0.00424963i
$956$	1.53136	+	2.20506i	0.0495277	+	0.0713169i
$957$	−0.559255	+	0.559255i	−0.0180782	+	0.0180782i
$958$	2.23592	−	4.27501i	0.0722393	−	0.138119i
$959$	−65.1292			−2.10313
$960$	2.71553	+	1.57548i	0.0876433	+	0.0508486i
$961$	−25.0815			−0.809081
$962$	1.58804	−	3.03628i	0.0512003	−	0.0978935i
$963$	21.9932	−	21.9932i	0.708722	−	0.708722i
$964$	−26.9571	−	38.8166i	−0.868230	−	1.25020i
$965$	−20.8101	+	21.2074i	−0.669900	+	0.682691i
$966$	−1.28605	−	4.10642i	−0.0413778	−	0.132122i
$967$	4.25304	+	4.25304i	0.136768	+	0.136768i	0.772177	−	0.635408i	$-0.219168\pi$
$967$	4.25304	+	4.25304i	0.136768	+	0.136768i	−0.635408	+	0.772177i	$0.719168\pi$
$968$	−23.7665	+	2.98912i	−0.763886	+	0.0960741i
$969$			0.406798i			0.0130682i
$970$	−13.8235	+	4.47319i	−0.443845	+	0.143626i
$971$		−	30.4453i		−	0.977038i	−0.872553	−	0.488519i	$-0.837537\pi$
$971$		−	30.4453i		−	0.977038i	0.872553	−	0.488519i	$-0.162463\pi$
$972$	−9.19933	−	1.65871i	−0.295069	−	0.0532030i
$973$	4.01986	+	4.01986i	0.128871	+	0.128871i
$974$	32.9486	−	10.3188i	1.05574	−	0.330637i
$975$	−2.42370	+	0.0458415i	−0.0776204	+	0.00146810i
$976$	−0.0984158	+	0.264039i	−0.00315021	+	0.00845168i
$977$	−21.8518	+	21.8518i	−0.699101	+	0.699101i	−0.964217	−	0.265116i	$-0.914590\pi$
$977$	−21.8518	+	21.8518i	−0.699101	+	0.699101i	0.265116	+	0.964217i	$0.414590\pi$
$978$	−2.72637	−	1.42595i	−0.0871796	−	0.0455968i
$979$	17.2696			0.551938
$980$	−17.0736	−	24.0955i	−0.545398	−	0.769701i
$981$	−12.7504			−0.407089
$982$	−41.8309	−	21.8784i	−1.33488	−	0.698169i
$983$	−0.567980	+	0.567980i	−0.0181158	+	0.0181158i	−0.716107	−	0.697991i	$-0.754078\pi$
$983$	−0.567980	+	0.567980i	−0.0181158	+	0.0181158i	0.697991	+	0.716107i	$0.254078\pi$
$984$	1.36807	−	1.76170i	0.0436124	−	0.0561609i
$985$	29.4860	+	28.9336i	0.939503	+	0.921901i
$986$	−8.86113	+	2.77512i	−0.282196	+	0.0883779i
$987$	−5.86143	−	5.86143i	−0.186571	−	0.186571i
$988$	−0.980395	+	5.43736i	−0.0311905	+	0.172985i
$989$		−	32.3815i		−	1.02967i
$990$	13.3017	+	6.79764i	0.422754	+	0.216043i
$991$		−	42.0926i		−	1.33712i	−0.743660	−	0.668558i	$-0.766912\pi$
$991$		−	42.0926i		−	1.33712i	0.743660	−	0.668558i	$-0.233088\pi$
$992$	31.5077	−	28.3174i	1.00037	−	0.899077i
$993$	3.80511	+	3.80511i	0.120751	+	0.120751i
$994$	−14.0174	−	44.7582i	−0.444604	−	1.41964i
$995$	−0.306052	−	32.3656i	−0.00970251	−	1.02606i
$996$	1.87661	−	1.30326i	0.0594627	−	0.0412953i
$997$	15.5483	−	15.5483i	0.492419	−	0.492419i	−0.416649	−	0.909068i	$-0.636795\pi$
$997$	15.5483	−	15.5483i	0.492419	−	0.492419i	0.909068	+	0.416649i	$0.136795\pi$
$998$	−10.1342	+	19.3762i	−0.320792	+	0.613344i
$999$	0.918811			0.0290699

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.k.c.343.18	yes	52
4.3	odd	2		380.2.k.d.343.22	yes	52
5.2	odd	4		380.2.k.d.267.22	yes	52
20.7	even	4	inner	380.2.k.c.267.18	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.k.c.267.18	✓	52	20.7	even	4	inner
380.2.k.c.343.18	yes	52	1.1	even	1	trivial
380.2.k.d.267.22	yes	52	5.2	odd	4
380.2.k.d.343.22	yes	52	4.3	odd	2

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.655429 - 1.25316i) q^{2} +(-0.124098 + 0.124098i) q^{3} +(-1.14082 - 1.64272i) q^{4} +(-0.0211435 - 2.23597i) q^{5} +(0.0741774 + 0.236853i) q^{6} +(-2.60801 - 2.60801i) q^{7} +(-2.80632 + 0.352951i) q^{8} +2.96920i q^{9} +(-2.81589 - 1.43902i) q^{10} +1.59093i q^{11} +(0.345433 + 0.0622840i) q^{12} +(-1.95339 - 1.95339i) q^{13} +(-4.97762 + 1.55889i) q^{14} +(0.280104 + 0.274856i) q^{15} +(-1.39704 + 3.74810i) q^{16} +(1.63902 - 1.63902i) q^{17} +(3.72088 + 1.94610i) q^{18} +1.00000 q^{19} +(-3.64894 + 2.58558i) q^{20} +0.647299 q^{21} +(1.99369 + 1.04274i) q^{22} +(3.32388 - 3.32388i) q^{23} +(0.304459 - 0.392060i) q^{24} +(-4.99911 + 0.0945526i) q^{25} +(-3.72823 + 1.16761i) q^{26} +(-0.740767 - 0.740767i) q^{27} +(-1.30894 + 7.25950i) q^{28} -2.83265i q^{29} +(0.528027 - 0.170866i) q^{30} -7.48876i q^{31} +(3.78132 + 4.20733i) q^{32} +(-0.197432 - 0.197432i) q^{33} +(-0.979691 - 3.12821i) q^{34} +(-5.77628 + 5.88657i) q^{35} +(4.87755 - 3.38734i) q^{36} +(-0.620175 + 0.620175i) q^{37} +(0.655429 - 1.25316i) q^{38} +0.484826 q^{39} +(0.848523 + 6.26738i) q^{40} +4.49344 q^{41} +(0.424259 - 0.811169i) q^{42} +(4.87104 - 4.87104i) q^{43} +(2.61345 - 1.81497i) q^{44} +(6.63903 - 0.0627794i) q^{45} +(-1.98679 - 6.34393i) q^{46} +(-9.05522 - 9.05522i) q^{47} +(-0.291763 - 0.638503i) q^{48} +6.60341i q^{49} +(-3.15807 + 6.32666i) q^{50} +0.406798i q^{51} +(-0.980395 + 5.43736i) q^{52} +(4.24526 + 4.24526i) q^{53} +(-1.41382 + 0.442780i) q^{54} +(3.55727 - 0.0336379i) q^{55} +(8.23940 + 6.39840i) q^{56} +(-0.124098 + 0.124098i) q^{57} +(-3.54977 - 1.85660i) q^{58} +0.166096 q^{59} +(0.131961 - 0.773693i) q^{60} +0.0704460 q^{61} +(-9.38462 - 4.90835i) q^{62} +(7.74370 - 7.74370i) q^{63} +(7.75085 - 1.98099i) q^{64} +(-4.32643 + 4.40903i) q^{65} +(-0.376816 + 0.118011i) q^{66} +(6.16238 + 6.16238i) q^{67} +(-4.56227 - 0.822610i) q^{68} +0.824976i q^{69} +(3.59087 + 11.0968i) q^{70} +8.99189i q^{71} +(-1.04798 - 8.33252i) q^{72} +(9.79301 + 9.79301i) q^{73} +(0.370698 + 1.18366i) q^{74} +(0.608647 - 0.632114i) q^{75} +(-1.14082 - 1.64272i) q^{76} +(4.14916 - 4.14916i) q^{77} +(0.317769 - 0.607565i) q^{78} +14.1076 q^{79} +(8.41018 + 3.04449i) q^{80} -8.72374 q^{81} +(2.94513 - 5.63100i) q^{82} +(4.60273 - 4.60273i) q^{83} +(-0.738454 - 1.06333i) q^{84} +(-3.69944 - 3.63013i) q^{85} +(-2.91157 - 9.29682i) q^{86} +(0.351527 + 0.351527i) q^{87} +(-0.561521 - 4.46466i) q^{88} -10.8550i q^{89} +(4.27275 - 8.36093i) q^{90} +10.1889i q^{91} +(-9.25216 - 1.66823i) q^{92} +(0.929342 + 0.929342i) q^{93} +(-17.2827 + 5.41259i) q^{94} +(-0.0211435 - 2.23597i) q^{95} +(-0.991377 - 0.0528679i) q^{96} +(3.24883 - 3.24883i) q^{97} +(8.27514 + 4.32807i) q^{98} -4.72379 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23}+ \cdots + 128 q^{99}+O(q^{100}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

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