LMFDB - Embedded newform 1110.2.u.e.401.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(191,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("1110.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.u (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			401.14
Character	$\chi$	$=$	1110.401
Dual form			1110.2.u.e.191.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-1.55689 - 0.759006i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.63759 + 0.564190i) q^{6} +1.92521 q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.84782 + 2.36338i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.55689 - 0.759006i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.63759 + 0.564190i) q^{6} +1.92521 q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.84782 + 2.36338i) q^{9} +1.00000 q^{10} -5.18734 q^{11} +(-0.759006 + 1.55689i) q^{12} +(-3.96677 + 3.96677i) q^{13} +(1.36133 - 1.36133i) q^{14} +(-0.564190 - 1.63759i) q^{15} -1.00000 q^{16} +(-3.83800 - 3.83800i) q^{17} +(2.97777 + 0.364556i) q^{18} +(0.0989804 - 0.0989804i) q^{19} +(0.707107 - 0.707107i) q^{20} +(-2.99733 - 1.46124i) q^{21} +(-3.66800 + 3.66800i) q^{22} +(-1.07572 - 1.07572i) q^{23} +(0.564190 + 1.63759i) q^{24} +1.00000i q^{25} +5.60986i q^{26} +(-1.08303 - 5.08203i) q^{27} -1.92521i q^{28} +(-1.77763 + 1.77763i) q^{29} +(-1.55689 - 0.759006i) q^{30} +(-4.45832 - 4.45832i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(8.07612 + 3.93722i) q^{33} -5.42775 q^{34} +(1.36133 + 1.36133i) q^{35} +(2.36338 - 1.84782i) q^{36} +(-5.86944 + 1.59678i) q^{37} -0.139979i q^{38} +(9.18664 - 3.16503i) q^{39} -1.00000i q^{40} -12.4094 q^{41} +(-3.15269 + 1.08618i) q^{42} +(7.21797 - 7.21797i) q^{43} +5.18734i q^{44} +(-0.364556 + 2.97777i) q^{45} -1.52130 q^{46} +3.47762i q^{47} +(1.55689 + 0.759006i) q^{48} -3.29358 q^{49} +(0.707107 + 0.707107i) q^{50} +(3.06228 + 8.88841i) q^{51} +(3.96677 + 3.96677i) q^{52} -3.95819i q^{53} +(-4.35936 - 2.82772i) q^{54} +(-3.66800 - 3.66800i) q^{55} +(-1.36133 - 1.36133i) q^{56} +(-0.229228 + 0.0789750i) q^{57} +2.51395i q^{58} +(7.83820 + 7.83820i) q^{59} +(-1.63759 + 0.564190i) q^{60} +(9.10908 + 9.10908i) q^{61} -6.30502 q^{62} +(3.55743 + 4.54999i) q^{63} +1.00000i q^{64} -5.60986 q^{65} +(8.49472 - 2.92664i) q^{66} +9.29823i q^{67} +(-3.83800 + 3.83800i) q^{68} +(0.858304 + 2.49127i) q^{69} +1.92521 q^{70} +1.23955i q^{71} +(0.364556 - 2.97777i) q^{72} -6.92368i q^{73} +(-3.02123 + 5.27941i) q^{74} +(0.759006 - 1.55689i) q^{75} +(-0.0989804 - 0.0989804i) q^{76} -9.98669 q^{77} +(4.25792 - 8.73394i) q^{78} +(-0.761048 + 0.761048i) q^{79} +(-0.707107 - 0.707107i) q^{80} +(-2.17113 + 8.73420i) q^{81} +(-8.77480 + 8.77480i) q^{82} +9.18336i q^{83} +(-1.46124 + 2.99733i) q^{84} -5.42775i q^{85} -10.2078i q^{86} +(4.11681 - 1.41835i) q^{87} +(3.66800 + 3.66800i) q^{88} +(-5.54999 + 5.54999i) q^{89} +(1.84782 + 2.36338i) q^{90} +(-7.63685 + 7.63685i) q^{91} +(-1.07572 + 1.07572i) q^{92} +(3.55723 + 10.3250i) q^{93} +(2.45905 + 2.45905i) q^{94} +0.139979 q^{95} +(1.63759 - 0.564190i) q^{96} +(3.84448 - 3.84448i) q^{97} +(-2.32892 + 2.32892i) q^{98} +(-9.58527 - 12.2597i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 24 q^{7} - 8 q^{9}+O(q^{10}) $ 40 * q - 24 * q^7 - 8 * q^9	$ 40 q - 24 q^{7} - 8 q^{9} + 40 q^{10} - 8 q^{12} - 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 24 q^{31} + 24 q^{33} - 8 q^{34} + 16 q^{39} - 20 q^{42} - 32 q^{43} - 8 q^{45} + 72 q^{46} + 96 q^{49} + 20 q^{51} + 16 q^{52} + 24 q^{54} - 16 q^{57} + 40 q^{61} - 24 q^{63} - 44 q^{66} - 24 q^{70} + 8 q^{72} + 8 q^{75} - 16 q^{76} + 48 q^{79} + 24 q^{81} - 56 q^{82} - 8 q^{84} + 12 q^{87} - 8 q^{90} - 64 q^{91} + 12 q^{93} + 24 q^{94} + 8 q^{97}+O(q^{100}) $ 40 * q - 24 * q^7 - 8 * q^9 + 40 * q^10 - 8 * q^12 - 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 24 * q^31 + 24 * q^33 - 8 * q^34 + 16 * q^39 - 20 * q^42 - 32 * q^43 - 8 * q^45 + 72 * q^46 + 96 * q^49 + 20 * q^51 + 16 * q^52 + 24 * q^54 - 16 * q^57 + 40 * q^61 - 24 * q^63 - 44 * q^66 - 24 * q^70 + 8 * q^72 + 8 * q^75 - 16 * q^76 + 48 * q^79 + 24 * q^81 - 56 * q^82 - 8 * q^84 + 12 * q^87 - 8 * q^90 - 64 * q^91 + 12 * q^93 + 24 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−1.55689	−	0.759006i	−0.898871	−	0.438212i
$3$	−1.55689	−	0.759006i	−0.898871	−	0.438212i
$4$		−	1.00000i		−	0.500000i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$	−1.63759	+	0.564190i	−0.668542	+	0.230330i
$7$	1.92521			0.727659			0.363830	−	0.931466i	$-0.381469\pi$
$7$	1.92521			0.727659			0.363830	+	0.931466i	$0.381469\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	1.84782	+	2.36338i	0.615940	+	0.787793i
$10$	1.00000			0.316228
$11$	−5.18734			−1.56404			−0.782021	−	0.623252i	$-0.785811\pi$
$11$	−5.18734			−1.56404			−0.782021	+	0.623252i	$0.785811\pi$
$12$	−0.759006	+	1.55689i	−0.219106	+	0.449436i
$13$	−3.96677	+	3.96677i	−1.10018	+	1.10018i	−0.105797	+	0.994388i	$0.533739\pi$
$13$	−3.96677	+	3.96677i	−1.10018	+	1.10018i	−0.994388	+	0.105797i	$0.966261\pi$
$14$	1.36133	−	1.36133i	0.363830	−	0.363830i
$15$	−0.564190	−	1.63759i	−0.145673	−	0.422823i
$16$	−1.00000			−0.250000
$17$	−3.83800	−	3.83800i	−0.930851	−	0.930851i	0.0669078	−	0.997759i	$-0.478687\pi$
$17$	−3.83800	−	3.83800i	−0.930851	−	0.930851i	−0.997759	+	0.0669078i	$0.978687\pi$
$18$	2.97777	+	0.364556i	0.701867	+	0.0859267i
$19$	0.0989804	−	0.0989804i	0.0227077	−	0.0227077i	−0.695662	−	0.718369i	$-0.744889\pi$
$19$	0.0989804	−	0.0989804i	0.0227077	−	0.0227077i	0.718369	+	0.695662i	$0.244889\pi$
$20$	0.707107	−	0.707107i	0.158114	−	0.158114i
$21$	−2.99733	−	1.46124i	−0.654072	−	0.318869i
$22$	−3.66800	+	3.66800i	−0.782021	+	0.782021i
$23$	−1.07572	−	1.07572i	−0.224304	−	0.224304i	0.586004	−	0.810308i	$-0.300700\pi$
$23$	−1.07572	−	1.07572i	−0.224304	−	0.224304i	−0.810308	+	0.586004i	$0.800700\pi$
$24$	0.564190	+	1.63759i	0.115165	+	0.334271i
$25$			1.00000i			0.200000i
$26$			5.60986i			1.10018i
$27$	−1.08303	−	5.08203i	−0.208430	−	0.978037i
$28$		−	1.92521i		−	0.363830i
$29$	−1.77763	+	1.77763i	−0.330098	+	0.330098i	−0.852624	−	0.522526i	$-0.824990\pi$
$29$	−1.77763	+	1.77763i	−0.330098	+	0.330098i	0.522526	+	0.852624i	$0.324990\pi$
$30$	−1.55689	−	0.759006i	−0.284248	−	0.138575i
$31$	−4.45832	−	4.45832i	−0.800738	−	0.800738i	0.182472	−	0.983211i	$-0.441590\pi$
$31$	−4.45832	−	4.45832i	−0.800738	−	0.800738i	−0.983211	+	0.182472i	$0.941590\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	8.07612	+	3.93722i	1.40587	+	0.685382i
$34$	−5.42775			−0.930851
$35$	1.36133	+	1.36133i	0.230106	+	0.230106i
$36$	2.36338	−	1.84782i	0.393897	−	0.307970i
$37$	−5.86944	+	1.59678i	−0.964930	+	0.262508i
$37$	−5.86944	+	1.59678i	−0.964930	+	0.262508i
$38$		−	0.139979i		−	0.0227077i
$39$	9.18664	−	3.16503i	1.47104	−	0.506810i
$40$		−	1.00000i		−	0.158114i
$41$	−12.4094			−1.93803			−0.969014	−	0.247005i	$-0.920554\pi$
$41$	−12.4094			−1.93803			−0.969014	+	0.247005i	$0.920554\pi$
$42$	−3.15269	+	1.08618i	−0.486471	+	0.167601i
$43$	7.21797	−	7.21797i	1.10073	−	1.10073i	0.106408	−	0.994323i	$-0.466065\pi$
$43$	7.21797	−	7.21797i	1.10073	−	1.10073i	0.994323	−	0.106408i	$-0.0339349\pi$
$44$			5.18734i			0.782021i
$45$	−0.364556	+	2.97777i	−0.0543448	+	0.443899i
$46$	−1.52130			−0.224304
$47$			3.47762i			0.507263i	0.967301	+	0.253632i	$0.0816251\pi$
$47$			3.47762i			0.507263i	−0.967301	+	0.253632i	$0.918375\pi$
$48$	1.55689	+	0.759006i	0.224718	+	0.109553i
$49$	−3.29358			−0.470512
$50$	0.707107	+	0.707107i	0.100000	+	0.100000i
$51$	3.06228	+	8.88841i	0.428805	+	1.24463i
$52$	3.96677	+	3.96677i	0.550092	+	0.550092i
$53$		−	3.95819i		−	0.543699i	−0.962340	−	0.271849i	$-0.912365\pi$
$53$		−	3.95819i		−	0.543699i	0.962340	−	0.271849i	$-0.0876352\pi$
$54$	−4.35936	−	2.82772i	−0.593234	−	0.384804i
$55$	−3.66800	−	3.66800i	−0.494593	−	0.494593i
$56$	−1.36133	−	1.36133i	−0.181915	−	0.181915i
$57$	−0.229228	+	0.0789750i	−0.0303620	+	0.0104605i
$58$			2.51395i			0.330098i
$59$	7.83820	+	7.83820i	1.02045	+	1.02045i	0.999787	+	0.0206604i	$0.00657688\pi$
$59$	7.83820	+	7.83820i	1.02045	+	1.02045i	0.0206604	+	0.999787i	$0.493423\pi$
$60$	−1.63759	+	0.564190i	−0.211412	+	0.0728366i
$61$	9.10908	+	9.10908i	1.16630	+	1.16630i	0.983070	+	0.183228i	$0.0586547\pi$
$61$	9.10908	+	9.10908i	1.16630	+	1.16630i	0.183228	+	0.983070i	$0.441345\pi$
$62$	−6.30502			−0.800738
$63$	3.55743	+	4.54999i	0.448194	+	0.573245i
$64$			1.00000i			0.125000i
$65$	−5.60986			−0.695818
$66$	8.49472	−	2.92664i	1.04563	−	0.360245i
$67$			9.29823i			1.13596i	0.823043	+	0.567980i	$0.192275\pi$
$67$			9.29823i			1.13596i	−0.823043	+	0.567980i	$0.807725\pi$
$68$	−3.83800	+	3.83800i	−0.465426	+	0.465426i
$69$	0.858304	+	2.49127i	0.103328	+	0.299913i
$70$	1.92521			0.230106
$71$			1.23955i			0.147107i	0.997291	+	0.0735537i	$0.0234340\pi$
$71$			1.23955i			0.147107i	−0.997291	+	0.0735537i	$0.976566\pi$
$72$	0.364556	−	2.97777i	0.0429633	−	0.350933i
$73$		−	6.92368i		−	0.810355i	−0.914238	−	0.405178i	$-0.867210\pi$
$73$		−	6.92368i		−	0.810355i	0.914238	−	0.405178i	$-0.132790\pi$
$74$	−3.02123	+	5.27941i	−0.351211	+	0.613719i
$75$	0.759006	−	1.55689i	0.0876425	−	0.179774i
$76$	−0.0989804	−	0.0989804i	−0.0113538	−	0.0113538i
$77$	−9.98669			−1.13809
$78$	4.25792	−	8.73394i	0.482114	−	0.988925i
$79$	−0.761048	+	0.761048i	−0.0856246	+	0.0856246i	−0.748622	−	0.662997i	$-0.769284\pi$
$79$	−0.761048	+	0.761048i	−0.0856246	+	0.0856246i	0.662997	+	0.748622i	$0.269284\pi$
$80$	−0.707107	−	0.707107i	−0.0790569	−	0.0790569i
$81$	−2.17113	+	8.73420i	−0.241236	+	0.970466i
$82$	−8.77480	+	8.77480i	−0.969014	+	0.969014i
$83$			9.18336i			1.00800i	0.863702	+	0.504002i	$0.168140\pi$
$83$			9.18336i			1.00800i	−0.863702	+	0.504002i	$0.831860\pi$
$84$	−1.46124	+	2.99733i	−0.159435	+	0.327036i
$85$		−	5.42775i		−	0.588722i
$86$		−	10.2078i		−	1.10073i
$87$	4.11681	−	1.41835i	0.441369	−	0.152063i
$88$	3.66800	+	3.66800i	0.391010	+	0.391010i
$89$	−5.54999	+	5.54999i	−0.588297	+	0.588297i	−0.937170	−	0.348873i	$-0.886565\pi$
$89$	−5.54999	+	5.54999i	−0.588297	+	0.588297i	0.348873	+	0.937170i	$0.386565\pi$
$90$	1.84782	+	2.36338i	0.194777	+	0.249122i
$91$	−7.63685	+	7.63685i	−0.800559	+	0.800559i
$92$	−1.07572	+	1.07572i	−0.112152	+	0.112152i
$93$	3.55723	+	10.3250i	0.368867	+	1.07065i
$94$	2.45905	+	2.45905i	0.253632	+	0.253632i
$95$	0.139979			0.0143616
$96$	1.63759	−	0.564190i	0.167135	−	0.0575824i
$97$	3.84448	−	3.84448i	0.390347	−	0.390347i	−0.484464	−	0.874811i	$-0.660985\pi$
$97$	3.84448	−	3.84448i	0.390347	−	0.390347i	0.874811	+	0.484464i	$0.160985\pi$
$98$	−2.32892	+	2.32892i	−0.235256	+	0.235256i
$99$	−9.58527	−	12.2597i	−0.963356	−	1.23214i
$100$	1.00000			0.100000
$101$	3.35861			0.334194			0.167097	−	0.985940i	$-0.446561\pi$
$101$	3.35861			0.334194			0.167097	+	0.985940i	$0.446561\pi$
$102$	8.45041	+	4.11969i	0.836716	+	0.407911i
$103$	−10.7788	−	10.7788i	−1.06207	−	1.06207i	−0.997942	−	0.0641240i	$-0.979575\pi$
$103$	−10.7788	−	10.7788i	−1.06207	−	1.06207i	−0.0641240	−	0.997942i	$-0.520425\pi$
$104$	5.60986			0.550092
$105$	−1.08618	−	3.15269i	−0.106000	−	0.307671i
$106$	−2.79886	−	2.79886i	−0.271849	−	0.271849i
$107$		−	11.3682i		−	1.09901i	−0.835492	−	0.549503i	$-0.814817\pi$
$107$		−	11.3682i		−	1.09901i	0.835492	−	0.549503i	$-0.185183\pi$
$108$	−5.08203	+	1.08303i	−0.489019	+	0.104215i
$109$	−11.3249	+	11.3249i	−1.08473	+	1.08473i	−0.0886661	+	0.996061i	$0.528260\pi$
$109$	−11.3249	+	11.3249i	−1.08473	+	1.08473i	−0.996061	+	0.0886661i	$0.971740\pi$
$110$	−5.18734			−0.494593
$111$	10.3500	+	1.96893i	0.982382	+	0.186883i
$112$	−1.92521			−0.181915
$113$	14.1216	−	14.1216i	1.32844	−	1.32844i	0.421716	−	0.906728i	$-0.361428\pi$
$113$	14.1216	−	14.1216i	1.32844	−	1.32844i	0.906728	−	0.421716i	$-0.138572\pi$
$114$	−0.106245	+	0.217933i	−0.00995078	+	0.0204113i
$115$		−	1.52130i		−	0.141862i
$116$	1.77763	+	1.77763i	0.165049	+	0.165049i
$117$	−16.7049	−	2.04511i	−1.54437	−	0.189070i
$118$	11.0849			1.02045
$119$	−7.38893	−	7.38893i	−0.677343	−	0.677343i
$120$	−0.759006	+	1.55689i	−0.0692875	+	0.142124i
$121$	15.9085			1.44623
$122$	12.8822			1.16630
$123$	19.3201	+	9.41884i	1.74204	+	0.849268i
$124$	−4.45832	+	4.45832i	−0.400369	+	0.400369i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	5.73281	+	0.701845i	0.510720	+	0.0625253i
$127$	6.10120			0.541394			0.270697	−	0.962665i	$-0.412746\pi$
$127$	6.10120			0.541394			0.270697	+	0.962665i	$0.412746\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−16.7161	+	5.75911i	−1.47177	+	0.507061i
$130$	−3.96677	+	3.96677i	−0.347909	+	0.347909i
$131$	5.14147	−	5.14147i	0.449212	−	0.449212i	−0.445880	−	0.895093i	$-0.647109\pi$
$131$	5.14147	−	5.14147i	0.449212	−	0.449212i	0.895093	+	0.445880i	$0.147109\pi$
$132$	3.93722	−	8.07612i	0.342691	−	0.702936i
$133$	0.190558	−	0.190558i	0.0165234	−	0.0165234i
$134$	6.57484	+	6.57484i	0.567980	+	0.567980i
$135$	2.82772	−	4.35936i	0.243371	−	0.375194i
$136$			5.42775i			0.465426i
$137$		−	2.67319i		−	0.228386i	−0.993459	−	0.114193i	$-0.963572\pi$
$137$		−	2.67319i		−	0.228386i	0.993459	−	0.114193i	$-0.0364282\pi$
$138$	2.36850	+	1.15468i	0.201620	+	0.0982928i
$139$		−	10.8710i		−	0.922067i	−0.887383	−	0.461034i	$-0.847479\pi$
$139$		−	10.8710i		−	0.922067i	0.887383	−	0.461034i	$-0.152521\pi$
$140$	1.36133	−	1.36133i	0.115053	−	0.115053i
$141$	2.63954	−	5.41428i	0.222289	−	0.455964i
$142$	0.876494	+	0.876494i	0.0735537	+	0.0735537i
$143$	20.5770	−	20.5770i	1.72073	−	1.72073i
$144$	−1.84782	−	2.36338i	−0.153985	−	0.196948i
$145$	−2.51395			−0.208772
$146$	−4.89578	−	4.89578i	−0.405178	−	0.405178i
$147$	5.12775	+	2.49985i	0.422930	+	0.206184i
$148$	1.59678	+	5.86944i	0.131254	+	0.482465i
$149$			9.44249i			0.773559i	0.922172	+	0.386779i	$0.126413\pi$
$149$			9.44249i			0.773559i	−0.922172	+	0.386779i	$0.873587\pi$
$150$	−0.564190	−	1.63759i	−0.0460659	−	0.133708i
$151$		−	12.4031i		−	1.00935i	−0.863310	−	0.504673i	$-0.831613\pi$
$151$		−	12.4031i		−	1.00935i	0.863310	−	0.504673i	$-0.168387\pi$
$152$	−0.139979			−0.0113538
$153$	1.97872	−	16.1626i	0.159970	−	1.30667i
$154$	−7.06166	+	7.06166i	−0.569045	+	0.569045i
$155$		−	6.30502i		−	0.506431i
$156$	−3.16503	−	9.18664i	−0.253405	−	0.735519i
$157$	7.28854			0.581689			0.290844	−	0.956770i	$-0.406064\pi$
$157$	7.28854			0.581689			0.290844	+	0.956770i	$0.406064\pi$
$158$			1.07628i			0.0856246i
$159$	−3.00429	+	6.16247i	−0.238256	+	0.488715i
$160$	−1.00000			−0.0790569
$161$	−2.07099	−	2.07099i	−0.163217	−	0.163217i
$162$	4.64079	+	7.71123i	0.364615	+	0.605851i
$163$	14.2334	+	14.2334i	1.11484	+	1.11484i	0.992486	+	0.122356i	$0.0390450\pi$
$163$	14.2334	+	14.2334i	1.11484	+	1.11484i	0.122356	+	0.992486i	$0.460955\pi$
$164$			12.4094i			0.969014i
$165$	2.92664	+	8.49472i	0.227839	+	0.661313i
$166$	6.49361	+	6.49361i	0.504002	+	0.504002i
$167$	−12.7580	−	12.7580i	−0.987247	−	0.987247i	0.0126725	−	0.999920i	$-0.495966\pi$
$167$	−12.7580	−	12.7580i	−0.987247	−	0.987247i	−0.999920	+	0.0126725i	$0.995966\pi$
$168$	1.08618	+	3.15269i	0.0838007	+	0.243235i
$169$		−	18.4706i		−	1.42081i
$170$	−3.83800	−	3.83800i	−0.294361	−	0.294361i
$171$	0.416826	+	0.0510303i	0.0318755	+	0.00390239i
$172$	−7.21797	−	7.21797i	−0.550365	−	0.550365i
$173$	−4.28631			−0.325882			−0.162941	−	0.986636i	$-0.552098\pi$
$173$	−4.28631			−0.325882			−0.162941	+	0.986636i	$0.552098\pi$
$174$	1.90810	−	3.91395i	0.144653	−	0.296716i
$175$			1.92521i			0.145532i
$176$	5.18734			0.391010
$177$	−6.25398	−	18.1525i	−0.470078	−	1.36442i
$178$			7.84887i			0.588297i
$179$	6.48181	−	6.48181i	0.484473	−	0.484473i	−0.422084	−	0.906557i	$-0.638701\pi$
$179$	6.48181	−	6.48181i	0.484473	−	0.484473i	0.906557	+	0.422084i	$0.138701\pi$
$180$	2.97777	+	0.364556i	0.221950	+	0.0271724i
$181$	−13.5004			−1.00347			−0.501737	−	0.865020i	$-0.667305\pi$
$181$	−13.5004			−1.00347			−0.501737	+	0.865020i	$0.667305\pi$
$182$			10.8001i			0.800559i
$183$	−7.26800	−	21.0957i	−0.537266	−	1.55944i
$184$			1.52130i			0.112152i
$185$	−5.27941	−	3.02123i	−0.388150	−	0.222125i
$186$	9.81623	+	4.78555i	0.719761	+	0.350894i
$187$	19.9090	+	19.9090i	1.45589	+	1.45589i
$188$	3.47762			0.253632
$189$	−2.08506	−	9.78395i	−0.151666	−	0.711678i
$190$	0.0989804	−	0.0989804i	0.00718079	−	0.00718079i
$191$	−9.94316	−	9.94316i	−0.719462	−	0.719462i	0.249033	−	0.968495i	$-0.419887\pi$
$191$	−9.94316	−	9.94316i	−0.719462	−	0.719462i	−0.968495	+	0.249033i	$0.919887\pi$
$192$	0.759006	−	1.55689i	0.0547765	−	0.112359i
$193$	−14.9338	+	14.9338i	−1.07496	+	1.07496i	−0.0780070	+	0.996953i	$0.524856\pi$
$193$	−14.9338	+	14.9338i	−1.07496	+	1.07496i	−0.996953	+	0.0780070i	$0.975144\pi$
$194$		−	5.43691i		−	0.390347i
$195$	8.73394	+	4.25792i	0.625451	+	0.304916i
$196$			3.29358i			0.235256i
$197$		−	10.0071i		−	0.712980i	−0.934299	−	0.356490i	$-0.883973\pi$
$197$		−	10.0071i		−	0.712980i	0.934299	−	0.356490i	$-0.116027\pi$
$198$	−15.4467	−	1.89108i	−1.09775	−	0.134393i
$199$	−12.2484	−	12.2484i	−0.868264	−	0.868264i	0.124016	−	0.992280i	$-0.460423\pi$
$199$	−12.2484	−	12.2484i	−0.868264	−	0.868264i	−0.992280	+	0.124016i	$0.960423\pi$
$200$	0.707107	−	0.707107i	0.0500000	−	0.0500000i
$201$	7.05741	−	14.4763i	0.497791	−	1.02108i
$202$	2.37490	−	2.37490i	0.167097	−	0.167097i
$203$	−3.42231	+	3.42231i	−0.240199	+	0.240199i
$204$	8.88841	−	3.06228i	0.622313	−	0.214403i
$205$	−8.77480	−	8.77480i	−0.612858	−	0.612858i
$206$	−15.2435			−1.06207
$207$	0.554600	−	4.53009i	0.0385474	−	0.314863i
$208$	3.96677	−	3.96677i	0.275046	−	0.275046i
$209$	−0.513445	+	0.513445i	−0.0355157	+	0.0355157i
$210$	−2.99733	−	1.46124i	−0.206836	−	0.100835i
$211$	−22.1119			−1.52225			−0.761124	−	0.648606i	$-0.775352\pi$
$211$	−22.1119			−1.52225			−0.761124	+	0.648606i	$0.775352\pi$
$212$	−3.95819			−0.271849
$213$	0.940826	−	1.92984i	0.0644643	−	0.132231i
$214$	−8.03854	−	8.03854i	−0.549503	−	0.549503i
$215$	10.2078			0.696163
$216$	−2.82772	+	4.35936i	−0.192402	+	0.296617i
$217$	−8.58319	−	8.58319i	−0.582665	−	0.582665i
$218$			16.0158i			1.08473i
$219$	−5.25511	+	10.7794i	−0.355108	+	0.728405i
$220$	−3.66800	+	3.66800i	−0.247297	+	0.247297i
$221$	30.4489			2.04822
$222$	8.71083	−	5.92634i	0.584633	−	0.397750i
$223$	15.3186			1.02581			0.512904	−	0.858446i	$-0.328570\pi$
$223$	15.3186			1.02581			0.512904	+	0.858446i	$0.328570\pi$
$224$	−1.36133	+	1.36133i	−0.0909574	+	0.0909574i
$225$	−2.36338	+	1.84782i	−0.157559	+	0.123188i
$226$		−	19.9709i		−	1.32844i
$227$	13.6849	+	13.6849i	0.908298	+	0.908298i	0.996135	−	0.0878367i	$-0.0279954\pi$
$227$	13.6849	+	13.6849i	0.908298	+	0.908298i	−0.0878367	+	0.996135i	$0.527995\pi$
$228$	0.0789750	+	0.229228i	0.00523024	+	0.0151810i
$229$	−11.4150			−0.754322			−0.377161	−	0.926148i	$-0.623100\pi$
$229$	−11.4150			−0.754322			−0.377161	+	0.926148i	$0.623100\pi$
$230$	−1.07572	−	1.07572i	−0.0709311	−	0.0709311i
$231$	15.5482	+	7.57996i	1.02300	+	0.498725i
$232$	2.51395			0.165049
$233$	15.1403			0.991875			0.495937	−	0.868358i	$-0.334825\pi$
$233$	15.1403			0.991875			0.495937	+	0.868358i	$0.334825\pi$
$234$	−13.2582	+	10.3660i	−0.866718	+	0.677648i
$235$	−2.45905	+	2.45905i	−0.160411	+	0.160411i
$236$	7.83820	−	7.83820i	0.510223	−	0.510223i
$237$	1.76251	−	0.607229i	0.114487	−	0.0394437i
$238$	−10.4495			−0.677343
$239$	5.80735	+	5.80735i	0.375647	+	0.375647i	0.869529	−	0.493882i	$-0.164423\pi$
$239$	5.80735	+	5.80735i	0.375647	+	0.375647i	−0.493882	+	0.869529i	$0.664423\pi$
$240$	0.564190	+	1.63759i	0.0364183	+	0.105706i
$241$	−18.6269	+	18.6269i	−1.19987	+	1.19987i	−0.225659	+	0.974206i	$0.572453\pi$
$241$	−18.6269	+	18.6269i	−1.19987	+	1.19987i	−0.974206	+	0.225659i	$0.927547\pi$
$242$	11.2490	−	11.2490i	0.723113	−	0.723113i
$243$	10.0095	−	11.9503i	0.642111	−	0.766612i
$244$	9.10908	−	9.10908i	0.583149	−	0.583149i
$245$	−2.32892	−	2.32892i	−0.148789	−	0.148789i
$246$	20.3215	−	7.00128i	1.29565	−	0.446385i
$247$			0.785265i			0.0499652i
$248$			6.30502i			0.400369i
$249$	6.97022	−	14.2975i	0.441720	−	0.906067i
$250$			1.00000i			0.0632456i
$251$	−8.68049	+	8.68049i	−0.547908	+	0.547908i	−0.925835	−	0.377927i	$-0.876637\pi$
$251$	−8.68049	+	8.68049i	−0.547908	+	0.547908i	0.377927	+	0.925835i	$0.376637\pi$
$252$	4.54999	−	3.55743i	0.286622	−	0.224097i
$253$	5.58015	+	5.58015i	0.350821	+	0.350821i
$254$	4.31420	−	4.31420i	0.270697	−	0.270697i
$255$	−4.11969	+	8.45041i	−0.257985	+	0.529185i
$256$	1.00000			0.0625000
$257$	−6.47192	−	6.47192i	−0.403707	−	0.403707i	0.475830	−	0.879537i	$-0.342148\pi$
$257$	−6.47192	−	6.47192i	−0.403707	−	0.403707i	−0.879537	+	0.475830i	$0.842148\pi$
$258$	−7.74775	+	15.8924i	−0.482354	+	0.989415i
$259$	−11.2999	+	3.07412i	−0.702140	+	0.191017i
$260$			5.60986i			0.347909i
$261$	−7.48596	−	0.916476i	−0.463369	−	0.0567284i
$262$		−	7.27114i		−	0.449212i
$263$	21.9588			1.35404			0.677019	−	0.735966i	$-0.263272\pi$
$263$	21.9588			1.35404			0.677019	+	0.735966i	$0.263272\pi$
$264$	−2.92664	−	8.49472i	−0.180122	−	0.522814i
$265$	2.79886	−	2.79886i	0.171933	−	0.171933i
$266$		−	0.269489i		−	0.0165234i
$267$	12.8532	−	4.42825i	0.786603	−	0.271005i
$268$	9.29823			0.567980
$269$			0.470491i			0.0286863i	0.999897	+	0.0143432i	$0.00456573\pi$
$269$			0.470491i			0.0286863i	−0.999897	+	0.0143432i	$0.995434\pi$
$270$	−1.08303	−	5.08203i	−0.0659114	−	0.309283i
$271$	1.85985			0.112978			0.0564891	−	0.998403i	$-0.482009\pi$
$271$	1.85985			0.112978			0.0564891	+	0.998403i	$0.482009\pi$
$272$	3.83800	+	3.83800i	0.232713	+	0.232713i
$273$	17.6862	−	6.09333i	1.07042	−	0.368785i
$274$	−1.89023	−	1.89023i	−0.114193	−	0.114193i
$275$		−	5.18734i		−	0.312808i
$276$	2.49127	−	0.858304i	0.149957	−	0.0516638i
$277$	−20.9504	−	20.9504i	−1.25879	−	1.25879i	−0.951672	−	0.307118i	$-0.900635\pi$
$277$	−20.9504	−	20.9504i	−1.25879	−	1.25879i	−0.307118	−	0.951672i	$-0.599365\pi$
$278$	−7.68697	−	7.68697i	−0.461034	−	0.461034i
$279$	2.29853	−	18.7749i	0.137610	−	1.12402i
$280$		−	1.92521i		−	0.115053i
$281$	16.4406	+	16.4406i	0.980762	+	0.980762i	0.999818	−	0.0190566i	$-0.00606628\pi$
$281$	16.4406	+	16.4406i	0.980762	+	0.980762i	−0.0190566	+	0.999818i	$0.506066\pi$
$282$	−1.96204	−	5.69490i	−0.116838	−	0.339127i
$283$	3.56217	+	3.56217i	0.211749	+	0.211749i	0.805010	−	0.593261i	$-0.202160\pi$
$283$	3.56217	+	3.56217i	0.211749	+	0.211749i	−0.593261	+	0.805010i	$0.702160\pi$
$284$	1.23955			0.0735537
$285$	−0.217933	−	0.106245i	−0.0129092	−	0.00629342i
$286$		−	29.1003i		−	1.72073i
$287$	−23.8907			−1.41022
$288$	−2.97777	−	0.364556i	−0.175467	−	0.0214817i
$289$			12.4605i			0.732968i
$290$	−1.77763	+	1.77763i	−0.104386	+	0.104386i
$291$	−8.90341	+	3.06745i	−0.521927	+	0.179817i
$292$	−6.92368			−0.405178
$293$		−	22.5243i		−	1.31588i	−0.753069	−	0.657942i	$-0.771427\pi$
$293$		−	22.5243i		−	1.31588i	0.753069	−	0.657942i	$-0.228573\pi$
$294$	5.39353	−	1.85821i	0.314557	−	0.108373i
$295$			11.0849i			0.645387i
$296$	5.27941	+	3.02123i	0.306860	+	0.175605i
$297$	5.61807	+	26.3622i	0.325993	+	1.52969i
$298$	6.67685	+	6.67685i	0.386779	+	0.386779i
$299$	8.53430			0.493552
$300$	−1.55689	−	0.759006i	−0.0898871	−	0.0438212i
$301$	13.8961	−	13.8961i	0.800957	−	0.800957i
$302$	−8.77029	−	8.77029i	−0.504673	−	0.504673i
$303$	−5.22899	−	2.54921i	−0.300398	−	0.146448i
$304$	−0.0989804	+	0.0989804i	−0.00567691	+	0.00567691i
$305$			12.8822i			0.737632i
$306$	−10.0295	−	12.8278i	−0.573348	−	0.733318i
$307$			11.0158i			0.628707i	0.949306	+	0.314353i	$0.101788\pi$
$307$			11.0158i			0.628707i	−0.949306	+	0.314353i	$0.898212\pi$
$308$			9.98669i			0.569045i
$309$	8.60024	+	24.9626i	0.489250	+	1.42007i
$310$	−4.45832	−	4.45832i	−0.253216	−	0.253216i
$311$	−18.1688	+	18.1688i	−1.03026	+	1.03026i	−0.0307306	+	0.999528i	$0.509783\pi$
$311$	−18.1688	+	18.1688i	−1.03026	+	1.03026i	−0.999528	+	0.0307306i	$0.990217\pi$
$312$	−8.73394	−	4.25792i	−0.494462	−	0.241057i
$313$	3.51658	−	3.51658i	0.198769	−	0.198769i	−0.600703	−	0.799472i	$-0.705113\pi$
$313$	3.51658	−	3.51658i	0.198769	−	0.198769i	0.799472	+	0.600703i	$0.205113\pi$
$314$	5.15378	−	5.15378i	0.290844	−	0.290844i
$315$	−0.701845	+	5.73281i	−0.0395445	+	0.323007i
$316$	0.761048	+	0.761048i	0.0428123	+	0.0428123i
$317$	−11.6758			−0.655777			−0.327889	−	0.944716i	$-0.606337\pi$
$317$	−11.6758			−0.655777			−0.327889	+	0.944716i	$0.606337\pi$
$318$	2.23317	+	6.48187i	0.125230	+	0.363485i
$319$	9.22118	−	9.22118i	0.516287	−	0.516287i
$320$	−0.707107	+	0.707107i	−0.0395285	+	0.0395285i
$321$	−8.62854	+	17.6991i	−0.481598	+	0.987865i
$322$	−2.92882			−0.163217
$323$	−0.759773			−0.0422749
$324$	8.73420	+	2.17113i	0.485233	+	0.120618i
$325$	−3.96677	−	3.96677i	−0.220037	−	0.220037i
$326$	20.1290			1.11484
$327$	26.2273	−	9.03596i	1.45037	−	0.499690i
$328$	8.77480	+	8.77480i	0.484507	+	0.484507i
$329$			6.69513i			0.369115i
$330$	8.07612	+	3.93722i	0.444576	+	0.216737i
$331$	−0.607386	+	0.607386i	−0.0333850	+	0.0333850i	−0.723602	−	0.690217i	$-0.757515\pi$
$331$	−0.607386	+	0.607386i	−0.0333850	+	0.0333850i	0.690217	+	0.723602i	$0.257515\pi$
$332$	9.18336			0.504002
$333$	−14.6195	−	10.9212i	−0.801141	−	0.598476i
$334$	−18.0426			−0.987247
$335$	−6.57484	+	6.57484i	−0.359222	+	0.359222i
$336$	2.99733	+	1.46124i	0.163518	+	0.0797173i
$337$		−	1.97402i		−	0.107532i	−0.998554	−	0.0537659i	$-0.982878\pi$
$337$		−	1.97402i		−	0.107532i	0.998554	−	0.0537659i	$-0.0171225\pi$
$338$	−13.0607	−	13.0607i	−0.710406	−	0.710406i
$339$	−32.7041	+	11.2674i	−1.77624	+	0.611960i
$340$	−5.42775			−0.294361
$341$	23.1268	+	23.1268i	1.25239	+	1.25239i
$342$	0.330824	−	0.258657i	0.0178889	−	0.0139866i
$343$	−19.8173			−1.07003
$344$	−10.2078			−0.550365
$345$	−1.15468	+	2.36850i	−0.0621658	+	0.127516i
$346$	−3.03088	+	3.03088i	−0.162941	+	0.162941i
$347$	−2.87749	+	2.87749i	−0.154472	+	0.154472i	−0.780112	−	0.625640i	$-0.784838\pi$
$347$	−2.87749	+	2.87749i	−0.154472	+	0.154472i	0.625640	+	0.780112i	$0.284838\pi$
$348$	−1.41835	−	4.11681i	−0.0760313	−	0.220684i
$349$	5.35928			0.286876			0.143438	−	0.989659i	$-0.454184\pi$
$349$	5.35928			0.286876			0.143438	+	0.989659i	$0.454184\pi$
$350$	1.36133	+	1.36133i	0.0727659	+	0.0727659i
$351$	24.4554	+	15.8631i	1.30533	+	0.846710i
$352$	3.66800	−	3.66800i	0.195505	−	0.195505i
$353$	8.81237	−	8.81237i	0.469035	−	0.469035i	−0.432567	−	0.901602i	$-0.642392\pi$
$353$	8.81237	−	8.81237i	0.469035	−	0.469035i	0.901602	+	0.432567i	$0.142392\pi$
$354$	−17.2580	−	8.41350i	−0.917251	−	0.447172i
$355$	−0.876494	+	0.876494i	−0.0465195	+	0.0465195i
$356$	5.54999	+	5.54999i	0.294149	+	0.294149i
$357$	5.89552	+	17.1120i	0.312024	+	0.905664i
$358$		−	9.16666i		−	0.484473i
$359$			10.4710i			0.552637i	0.961066	+	0.276319i	$0.0891145\pi$
$359$			10.4710i			0.552637i	−0.961066	+	0.276319i	$0.910886\pi$
$360$	2.36338	−	1.84782i	0.124561	−	0.0973886i
$361$			18.9804i			0.998969i
$362$	−9.54619	+	9.54619i	−0.501737	+	0.501737i
$363$	−24.7678	−	12.0746i	−1.29997	−	0.633754i
$364$	7.63685	+	7.63685i	0.400280	+	0.400280i
$365$	4.89578	−	4.89578i	0.256257	−	0.256257i
$366$	−20.0562	−	9.77766i	−1.04835	−	0.511086i
$367$	−15.6683			−0.817877			−0.408938	−	0.912562i	$-0.634101\pi$
$367$	−15.6683			−0.817877			−0.408938	+	0.912562i	$0.634101\pi$
$368$	1.07572	+	1.07572i	0.0560760	+	0.0560760i
$369$	−22.9304	−	29.3282i	−1.19371	−	1.52677i
$370$	−5.86944	+	1.59678i	−0.305138	+	0.0830124i
$371$		−	7.62032i		−	0.395627i
$372$	10.3250	−	3.55723i	0.535327	−	0.184434i
$373$			4.20515i			0.217735i	0.994056	+	0.108867i	$0.0347224\pi$
$373$			4.20515i			0.217735i	−0.994056	+	0.108867i	$0.965278\pi$
$374$	28.1556			1.45589
$375$	1.63759	−	0.564190i	0.0845646	−	0.0291346i
$376$	2.45905	−	2.45905i	0.126816	−	0.126816i
$377$		−	14.1029i		−	0.726337i
$378$	−8.39266	−	5.44394i	−0.431672	−	0.280006i
$379$	10.8211			0.555842			0.277921	−	0.960604i	$-0.410355\pi$
$379$	10.8211			0.555842			0.277921	+	0.960604i	$0.410355\pi$
$380$		−	0.139979i		−	0.00718079i
$381$	−9.49890	−	4.63084i	−0.486643	−	0.237245i
$382$	−14.0617			−0.719462
$383$	−3.27972	−	3.27972i	−0.167586	−	0.167586i	0.618332	−	0.785917i	$-0.287809\pi$
$383$	−3.27972	−	3.27972i	−0.167586	−	0.167586i	−0.785917	+	0.618332i	$0.787809\pi$
$384$	−0.564190	−	1.63759i	−0.0287912	−	0.0835677i
$385$	−7.06166	−	7.06166i	−0.359895	−	0.359895i
$386$			21.1196i			1.07496i
$387$	30.3963	+	3.72130i	1.54513	+	0.189164i
$388$	−3.84448	−	3.84448i	−0.195174	−	0.195174i
$389$	17.5886	+	17.5886i	0.891778	+	0.891778i	0.994690	−	0.102912i	$-0.0328162\pi$
$389$	17.5886	+	17.5886i	0.891778	+	0.891778i	−0.102912	+	0.994690i	$0.532816\pi$
$390$	9.18664	−	3.16503i	0.465183	−	0.160267i
$391$			8.25726i			0.417587i
$392$	2.32892	+	2.32892i	0.117628	+	0.117628i
$393$	−11.9071	+	4.10230i	−0.600634	+	0.206934i
$394$	−7.07612	−	7.07612i	−0.356490	−	0.356490i
$395$	−1.07628			−0.0541537
$396$	−12.2597	+	9.58527i	−0.616071	+	0.481678i
$397$			29.2824i			1.46964i	0.678262	+	0.734820i	$0.262734\pi$
$397$			29.2824i			1.46964i	−0.678262	+	0.734820i	$0.737266\pi$
$398$	−17.3218			−0.868264
$399$	−0.441312	+	0.152043i	−0.0220932	+	0.00761167i
$400$		−	1.00000i		−	0.0500000i
$401$	−19.3076	+	19.3076i	−0.964177	+	0.964177i	−0.999380	−	0.0352035i	$-0.988792\pi$
$401$	−19.3076	+	19.3076i	−0.964177	+	0.964177i	0.0352035	+	0.999380i	$0.488792\pi$
$402$	−5.24597	−	15.2267i	−0.261645	−	0.759436i
$403$	35.3703			1.76192
$404$		−	3.35861i		−	0.167097i
$405$	−7.71123	+	4.64079i	−0.383174	+	0.230603i
$406$			4.83987i			0.240199i
$407$	30.4468	−	8.28302i	1.50919	−	0.410574i
$408$	4.11969	−	8.45041i	0.203955	−	0.418358i
$409$	6.57668	+	6.57668i	0.325196	+	0.325196i	0.850756	−	0.525560i	$-0.176144\pi$
$409$	6.57668	+	6.57668i	0.325196	+	0.325196i	−0.525560	+	0.850756i	$0.676144\pi$
$410$	−12.4094			−0.612858
$411$	−2.02897	+	4.16186i	−0.100082	+	0.205290i
$412$	−10.7788	+	10.7788i	−0.531033	+	0.531033i
$413$	15.0901	+	15.0901i	0.742538	+	0.742538i
$414$	−2.81109	−	3.59542i	−0.138158	−	0.176705i
$415$	−6.49361	+	6.49361i	−0.318759	+	0.318759i
$416$		−	5.60986i		−	0.275046i
$417$	−8.25116	+	16.9250i	−0.404061	+	0.828820i
$418$			0.726121i			0.0355157i
$419$		−	26.3846i		−	1.28897i	−0.764617	−	0.644485i	$-0.777072\pi$
$419$		−	26.3846i		−	1.28897i	0.764617	−	0.644485i	$-0.222928\pi$
$420$	−3.15269	+	1.08618i	−0.153836	+	0.0530002i
$421$	−21.6083	−	21.6083i	−1.05312	−	1.05312i	−0.998507	−	0.0546159i	$-0.982607\pi$
$421$	−21.6083	−	21.6083i	−1.05312	−	1.05312i	−0.0546159	−	0.998507i	$-0.517393\pi$
$422$	−15.6355	+	15.6355i	−0.761124	+	0.761124i
$423$	−8.21894	+	6.42601i	−0.399618	+	0.312444i
$424$	−2.79886	+	2.79886i	−0.135925	+	0.135925i
$425$	3.83800	−	3.83800i	0.186170	−	0.186170i
$426$	−0.699341	−	2.02987i	−0.0338832	−	0.0983475i
$427$	17.5369	+	17.5369i	0.848668	+	0.848668i
$428$	−11.3682			−0.549503
$429$	−47.6542	+	16.4181i	−2.30077	+	0.792672i
$430$	7.21797	−	7.21797i	0.348082	−	0.348082i
$431$	16.8691	−	16.8691i	0.812557	−	0.812557i	−0.172460	−	0.985017i	$-0.555172\pi$
$431$	16.8691	−	16.8691i	0.812557	−	0.812557i	0.985017	+	0.172460i	$0.0551715\pi$
$432$	1.08303	+	5.08203i	0.0521075	+	0.244509i
$433$	−20.9643			−1.00748			−0.503740	−	0.863855i	$-0.668043\pi$
$433$	−20.9643			−1.00748			−0.503740	+	0.863855i	$0.668043\pi$
$434$	−12.1385			−0.582665
$435$	3.91395	+	1.90810i	0.187659	+	0.0914866i
$436$	11.3249	+	11.3249i	0.542364	+	0.542364i
$437$	−0.212951			−0.0101868
$438$	3.90627	+	11.3381i	0.186649	+	0.541756i
$439$	−1.59624	−	1.59624i	−0.0761842	−	0.0761842i	0.667988	−	0.744172i	$-0.267156\pi$
$439$	−1.59624	−	1.59624i	−0.0761842	−	0.0761842i	−0.744172	+	0.667988i	$0.767156\pi$
$440$			5.18734i			0.247297i
$441$	−6.08595	−	7.78399i	−0.289807	−	0.370666i
$442$	21.5306	−	21.5306i	1.02411	−	1.02411i
$443$	26.6898			1.26807			0.634035	−	0.773304i	$-0.281397\pi$
$443$	26.6898			1.26807			0.634035	+	0.773304i	$0.281397\pi$
$444$	1.96893	−	10.3500i	0.0934414	−	0.491191i
$445$	−7.84887			−0.372072
$446$	10.8319	−	10.8319i	0.512904	−	0.512904i
$447$	7.16691	−	14.7009i	0.338983	−	0.695330i
$448$			1.92521i			0.0909574i
$449$	9.86107	+	9.86107i	0.465372	+	0.465372i	0.900412	−	0.435039i	$-0.143265\pi$
$449$	9.86107	+	9.86107i	0.465372	+	0.465372i	−0.435039	+	0.900412i	$0.643265\pi$
$450$	−0.364556	+	2.97777i	−0.0171853	+	0.140373i
$451$	64.3720			3.03116
$452$	−14.1216	−	14.1216i	−0.664222	−	0.664222i
$453$	−9.41400	+	19.3102i	−0.442308	+	0.907273i
$454$	19.3534			0.908298
$455$	−10.8001			−0.506318
$456$	0.217933	+	0.106245i	0.0102056	+	0.00497539i
$457$	6.55173	−	6.55173i	0.306477	−	0.306477i	−0.537064	−	0.843541i	$-0.680467\pi$
$457$	6.55173	−	6.55173i	0.306477	−	0.306477i	0.843541	+	0.537064i	$0.180467\pi$
$458$	−8.07160	+	8.07160i	−0.377161	+	0.377161i
$459$	−15.3481	+	23.6615i	−0.716390	+	1.10442i
$460$	−1.52130			−0.0709311
$461$	−14.2328	−	14.2328i	−0.662887	−	0.662887i	0.293172	−	0.956060i	$-0.405289\pi$
$461$	−14.2328	−	14.2328i	−0.662887	−	0.662887i	−0.956060	+	0.293172i	$0.905289\pi$
$462$	16.3541	−	5.63439i	0.760860	−	0.262136i
$463$	−3.29627	+	3.29627i	−0.153191	+	0.153191i	−0.779541	−	0.626351i	$-0.784548\pi$
$463$	−3.29627	+	3.29627i	−0.153191	+	0.153191i	0.626351	+	0.779541i	$0.284548\pi$
$464$	1.77763	−	1.77763i	0.0825245	−	0.0825245i
$465$	−4.78555	+	9.81623i	−0.221925	+	0.455217i
$466$	10.7058	−	10.7058i	0.495937	−	0.495937i
$467$	−8.25546	−	8.25546i	−0.382017	−	0.382017i	0.489811	−	0.871828i	$-0.337066\pi$
$467$	−8.25546	−	8.25546i	−0.382017	−	0.382017i	−0.871828	+	0.489811i	$0.837066\pi$
$468$	−2.04511	+	16.7049i	−0.0945352	+	0.772183i
$469$			17.9010i			0.826591i
$470$			3.47762i			0.160411i
$471$	−11.3475	−	5.53205i	−0.522863	−	0.254903i
$472$		−	11.0849i		−	0.510223i
$473$	−37.4421	+	37.4421i	−1.72159	+	1.72159i
$474$	0.816906	−	1.67566i	0.0375218	−	0.0769655i
$475$	0.0989804	+	0.0989804i	0.00454153	+	0.00454153i
$476$	−7.38893	+	7.38893i	−0.338671	+	0.338671i
$477$	9.35470	−	7.31401i	0.428322	−	0.334886i
$478$	8.21284			0.375647
$479$	−15.7716	−	15.7716i	−0.720622	−	0.720622i	0.248110	−	0.968732i	$-0.420190\pi$
$479$	−15.7716	−	15.7716i	−0.720622	−	0.720622i	−0.968732	+	0.248110i	$0.920190\pi$
$480$	1.55689	+	0.759006i	0.0710620	+	0.0346437i
$481$	16.9487	−	29.6168i	0.772793	−	1.35041i
$482$			26.3424i			1.19987i
$483$	1.65241	+	4.79620i	0.0751873	+	0.218235i
$484$		−	15.9085i		−	0.723113i
$485$	5.43691			0.246877
$486$	−1.37234	−	15.5279i	−0.0622506	−	0.704361i
$487$	12.9849	−	12.9849i	0.588400	−	0.588400i	−0.348798	−	0.937198i	$-0.613410\pi$
$487$	12.9849	−	12.9849i	0.588400	−	0.588400i	0.937198	+	0.348798i	$0.113410\pi$
$488$		−	12.8822i		−	0.583149i
$489$	−11.3566	−	32.9630i	−0.513562	−	1.49064i
$490$	−3.29358			−0.148789
$491$		−	30.8895i		−	1.39402i	−0.717059	−	0.697012i	$-0.754512\pi$
$491$		−	30.8895i		−	1.39402i	0.717059	−	0.697012i	$-0.245488\pi$
$492$	9.41884	−	19.3201i	0.424634	−	0.871019i
$493$	13.6451			0.614544
$494$	0.555266	+	0.555266i	0.0249826	+	0.0249826i
$495$	1.89108	−	15.4467i	0.0849975	−	0.694277i
$496$	4.45832	+	4.45832i	0.200185	+	0.200185i
$497$			2.38639i			0.107044i
$498$	−5.18116	−	15.0385i	−0.232173	−	0.673893i
$499$	20.2463	+	20.2463i	0.906350	+	0.906350i	0.995976	−	0.0896254i	$-0.0285670\pi$
$499$	20.2463	+	20.2463i	0.906350	+	0.906350i	−0.0896254	+	0.995976i	$0.528567\pi$
$500$	0.707107	+	0.707107i	0.0316228	+	0.0316228i
$501$	10.1795	+	29.5463i	0.454784	+	1.32003i
$502$			12.2761i			0.547908i
$503$	−19.1000	−	19.1000i	−0.851627	−	0.851627i	0.138707	−	0.990333i	$-0.455705\pi$
$503$	−19.1000	−	19.1000i	−0.851627	−	0.851627i	−0.990333	+	0.138707i	$0.955705\pi$
$504$	0.701845	−	5.73281i	0.0312627	−	0.255360i
$505$	2.37490	+	2.37490i	0.105681	+	0.105681i
$506$	7.89152			0.350821
$507$	−14.0193	+	28.7566i	−0.622617	+	1.27713i
$508$		−	6.10120i		−	0.270697i
$509$	−30.8742			−1.36848			−0.684238	−	0.729259i	$-0.739865\pi$
$509$	−30.8742			−1.36848			−0.684238	+	0.729259i	$0.739865\pi$
$510$	3.06228	+	8.88841i	0.135600	+	0.393585i
$511$		−	13.3295i		−	0.589662i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−0.610220	−	0.395822i	−0.0269419	−	0.0174760i
$514$	−9.15268			−0.403707
$515$		−	15.2435i		−	0.671709i
$516$	5.75911	+	16.7161i	0.253531	+	0.735884i
$517$		−	18.0396i		−	0.793381i
$518$	−5.81649	+	10.1639i	−0.255562	+	0.446578i
$519$	6.67332	+	3.25333i	0.292926	+	0.142806i
$520$	3.96677	+	3.96677i	0.173954	+	0.173954i
$521$	19.1245			0.837858			0.418929	−	0.908019i	$-0.362406\pi$
$521$	19.1245			0.837858			0.418929	+	0.908019i	$0.362406\pi$
$522$	−5.94142	+	4.64533i	−0.260049	+	0.203321i
$523$	−5.56709	+	5.56709i	−0.243432	+	0.243432i	−0.818268	−	0.574836i	$-0.805066\pi$
$523$	−5.56709	+	5.56709i	−0.243432	+	0.243432i	0.574836	+	0.818268i	$0.305066\pi$
$524$	−5.14147	−	5.14147i	−0.224606	−	0.224606i
$525$	1.46124	−	2.99733i	0.0637738	−	0.130814i
$526$	15.5272	−	15.5272i	0.677019	−	0.677019i
$527$			34.2221i			1.49074i
$528$	−8.07612	−	3.93722i	−0.351468	−	0.171346i
$529$		−	20.6856i		−	0.899375i
$530$		−	3.95819i		−	0.171933i
$531$	−4.04106	+	33.0082i	−0.175367	+	1.43244i
$532$	−0.190558	−	0.190558i	−0.00826172	−	0.00826172i
$533$	49.2254	−	49.2254i	2.13219	−	2.13219i
$534$	5.95734	−	12.2198i	0.257799	−	0.528804i
$535$	8.03854	−	8.03854i	0.347536	−	0.347536i
$536$	6.57484	−	6.57484i	0.283990	−	0.283990i
$537$	−15.0112	+	5.17174i	−0.647781	+	0.223177i
$538$	0.332687	+	0.332687i	0.0143432	+	0.0143432i
$539$	17.0849			0.735901
$540$	−4.35936	−	2.82772i	−0.187597	−	0.121686i
$541$	−4.99094	+	4.99094i	−0.214577	+	0.214577i	−0.806209	−	0.591631i	$-0.798484\pi$
$541$	−4.99094	+	4.99094i	−0.214577	+	0.214577i	0.591631	+	0.806209i	$0.298484\pi$
$542$	1.31512	−	1.31512i	0.0564891	−	0.0564891i
$543$	21.0186	+	10.2469i	0.901994	+	0.439735i
$544$	5.42775			0.232713
$545$	−16.0158			−0.686042
$546$	8.19737	−	16.8146i	0.350815	−	0.719600i
$547$	−24.8167	−	24.8167i	−1.06108	−	1.06108i	−0.998009	−	0.0630758i	$-0.979909\pi$
$547$	−24.8167	−	24.8167i	−1.06108	−	1.06108i	−0.0630758	−	0.998009i	$-0.520091\pi$
$548$	−2.67319			−0.114193
$549$	−4.69628	+	38.3602i	−0.200432	+	1.63717i
$550$	−3.66800	−	3.66800i	−0.156404	−	0.156404i
$551$			0.351901i			0.0149915i
$552$	1.15468	−	2.36850i	0.0491464	−	0.100810i
$553$	−1.46517	+	1.46517i	−0.0623055	+	0.0623055i
$554$	−29.6284			−1.25879
$555$	5.92634	+	8.71083i	0.251559	+	0.369754i
$556$	−10.8710			−0.461034
$557$	4.85816	−	4.85816i	0.205847	−	0.205847i	−0.596653	−	0.802500i	$-0.703503\pi$
$557$	4.85816	−	4.85816i	0.205847	−	0.205847i	0.802500	+	0.596653i	$0.203503\pi$
$558$	−11.6505	−	14.9012i	−0.493207	−	0.630816i
$559$			57.2641i			2.42201i
$560$	−1.36133	−	1.36133i	−0.0575265	−	0.0575265i
$561$	−15.8851	−	46.1072i	−0.670669	−	1.94665i
$562$	23.2505			0.980762
$563$	−18.9481	−	18.9481i	−0.798568	−	0.798568i	0.184302	−	0.982870i	$-0.440998\pi$
$563$	−18.9481	−	18.9481i	−0.798568	−	0.798568i	−0.982870	+	0.184302i	$0.940998\pi$
$564$	−5.41428	−	2.63954i	−0.227982	−	0.111144i
$565$	19.9709			0.840182
$566$	5.03767			0.211749
$567$	−4.17986	+	16.8151i	−0.175538	+	0.706169i
$568$	0.876494	−	0.876494i	0.0367769	−	0.0367769i
$569$	8.68225	−	8.68225i	0.363979	−	0.363979i	−0.501297	−	0.865276i	$-0.667143\pi$
$569$	8.68225	−	8.68225i	0.363979	−	0.363979i	0.865276	+	0.501297i	$0.167143\pi$
$570$	−0.229228	+	0.0789750i	−0.00960132	+	0.00330790i
$571$	−1.59002			−0.0665404			−0.0332702	−	0.999446i	$-0.510592\pi$
$571$	−1.59002			−0.0665404			−0.0332702	+	0.999446i	$0.510592\pi$
$572$	−20.5770	−	20.5770i	−0.860367	−	0.860367i
$573$	7.93350	+	23.0273i	0.331427	+	0.961980i
$574$	−16.8933	+	16.8933i	−0.705112	+	0.705112i
$575$	1.07572	−	1.07572i	0.0448608	−	0.0448608i
$576$	−2.36338	+	1.84782i	−0.0984741	+	0.0769925i
$577$	−1.81221	+	1.81221i	−0.0754435	+	0.0754435i	−0.743822	−	0.668378i	$-0.766989\pi$
$577$	−1.81221	+	1.81221i	−0.0754435	+	0.0754435i	0.668378	+	0.743822i	$0.266989\pi$
$578$	8.81088	+	8.81088i	0.366484	+	0.366484i
$579$	34.5852	−	11.9155i	1.43731	−	0.495190i
$580$			2.51395i			0.104386i
$581$			17.6798i			0.733484i
$582$	−4.12665	+	8.46468i	−0.171055	+	0.350872i
$583$			20.5325i			0.850367i
$584$	−4.89578	+	4.89578i	−0.202589	+	0.202589i
$585$	−10.3660	−	13.2582i	−0.428582	−	0.548161i
$586$	−15.9271	−	15.9271i	−0.657942	−	0.657942i
$587$	−26.2589	+	26.2589i	−1.08382	+	1.08382i	−0.0876694	+	0.996150i	$0.527942\pi$
$587$	−26.2589	+	26.2589i	−1.08382	+	1.08382i	−0.996150	+	0.0876694i	$0.972058\pi$
$588$	2.49985	−	5.12775i	0.103092	−	0.211465i
$589$	−0.882573			−0.0363658
$590$	7.83820	+	7.83820i	0.322694	+	0.322694i
$591$	−7.59549	+	15.5800i	−0.312437	+	0.640877i
$592$	5.86944	−	1.59678i	0.241232	−	0.0656271i
$593$			44.3173i			1.81989i	0.414727	+	0.909946i	$0.363877\pi$
$593$			44.3173i			1.81989i	−0.414727	+	0.909946i	$0.636123\pi$
$594$	22.6135	+	14.6683i	0.927842	+	0.601849i
$595$		−	10.4495i		−	0.428389i
$596$	9.44249			0.386779
$597$	9.77279	+	28.3660i	0.399974	+	1.16094i
$598$	6.03466	−	6.03466i	0.246776	−	0.246776i
$599$		−	9.25641i		−	0.378207i	−0.981957	−	0.189103i	$-0.939442\pi$
$599$		−	9.25641i		−	0.378207i	0.981957	−	0.189103i	$-0.0605581\pi$
$600$	−1.63759	+	0.564190i	−0.0668542	+	0.0230330i
$601$	−1.16650			−0.0475826			−0.0237913	−	0.999717i	$-0.507574\pi$
$601$	−1.16650			−0.0475826			−0.0237913	+	0.999717i	$0.507574\pi$
$602$		−	19.6520i		−	0.800957i
$603$	−21.9752	+	17.1814i	−0.894901	+	0.699682i
$604$	−12.4031			−0.504673
$605$	11.2490	+	11.2490i	0.457337	+	0.457337i
$606$	−5.50001	+	1.89489i	−0.223423	+	0.0769748i
$607$	15.4706	+	15.4706i	0.627934	+	0.627934i	0.947548	−	0.319614i	$-0.103553\pi$
$607$	15.4706	+	15.4706i	0.627934	+	0.627934i	−0.319614	+	0.947548i	$0.603553\pi$
$608$			0.139979i			0.00567691i
$609$	7.92571	−	2.73061i	0.321166	−	0.110650i
$610$	9.10908	+	9.10908i	0.368816	+	0.368816i
$611$	−13.7949	−	13.7949i	−0.558083	−	0.558083i
$612$	−16.1626	−	1.97872i	−0.653333	−	0.0799850i
$613$			2.39296i			0.0966506i	0.998832	+	0.0483253i	$0.0153884\pi$
$613$			2.39296i			0.0966506i	−0.998832	+	0.0483253i	$0.984612\pi$
$614$	7.78937	+	7.78937i	0.314353	+	0.314353i
$615$	7.00128	+	20.3215i	0.282319	+	0.819443i
$616$	7.06166	+	7.06166i	0.284522	+	0.284522i
$617$	8.86781			0.357005			0.178502	−	0.983939i	$-0.442875\pi$
$617$	8.86781			0.357005			0.178502	+	0.983939i	$0.442875\pi$
$618$	23.7325	+	11.5699i	0.954661	+	0.465410i
$619$			17.1208i			0.688141i	0.938944	+	0.344071i	$0.111806\pi$
$619$			17.1208i			0.688141i	−0.938944	+	0.344071i	$0.888194\pi$
$620$	−6.30502			−0.253216
$621$	−4.30182	+	6.63191i	−0.172626	+	0.266129i
$622$			25.6946i			1.03026i
$623$	−10.6849	+	10.6849i	−0.428080	+	0.428080i
$624$	−9.18664	+	3.16503i	−0.367760	+	0.126703i
$625$	−1.00000			−0.0400000
$626$		−	4.97320i		−	0.198769i
$627$	1.18909	−	0.409670i	0.0474875	−	0.0163606i
$628$		−	7.28854i		−	0.290844i
$629$	28.6553	+	16.3985i	1.14256	+	0.653850i
$630$	3.55743	+	4.54999i	0.141731	+	0.181276i
$631$	−22.6451	−	22.6451i	−0.901487	−	0.901487i	0.0940780	−	0.995565i	$-0.470010\pi$
$631$	−22.6451	−	22.6451i	−0.901487	−	0.901487i	−0.995565	+	0.0940780i	$0.970010\pi$
$632$	1.07628			0.0428123
$633$	34.4259	+	16.7831i	1.36831	+	0.667068i
$634$	−8.25603	+	8.25603i	−0.327889	+	0.327889i
$635$	4.31420	+	4.31420i	0.171204	+	0.171204i
$636$	6.16247	+	3.00429i	0.244358	+	0.119128i
$637$	13.0649	−	13.0649i	0.517650	−	0.517650i
$638$		−	13.0407i		−	0.516287i
$639$	−2.92953	+	2.29046i	−0.115890	+	0.0906094i
$640$			1.00000i			0.0395285i
$641$			12.4293i			0.490929i	0.969406	+	0.245465i	$0.0789405\pi$
$641$			12.4293i			0.490929i	−0.969406	+	0.245465i	$0.921059\pi$
$642$	6.41383	+	18.6164i	0.253134	+	0.734732i
$643$	−10.0677	−	10.0677i	−0.397030	−	0.397030i	0.480154	−	0.877184i	$-0.340581\pi$
$643$	−10.0677	−	10.0677i	−0.397030	−	0.397030i	−0.877184	+	0.480154i	$0.840581\pi$
$644$	−2.07099	+	2.07099i	−0.0816084	+	0.0816084i
$645$	−15.8924	−	7.74775i	−0.625761	−	0.305067i
$646$	−0.537241	+	0.537241i	−0.0211375	+	0.0211375i
$647$	−23.6939	+	23.6939i	−0.931504	+	0.931504i	−0.997800	−	0.0662961i	$-0.978882\pi$
$647$	−23.6939	+	23.6939i	−0.931504	+	0.931504i	0.0662961	+	0.997800i	$0.478882\pi$
$648$	7.71123	−	4.64079i	0.302926	−	0.182308i
$649$	−40.6594	−	40.6594i	−1.59602	−	1.59602i
$650$	−5.60986			−0.220037
$651$	6.84840	+	19.8778i	0.268410	+	0.779072i
$652$	14.2334	−	14.2334i	0.557421	−	0.557421i
$653$	16.2030	−	16.2030i	0.634071	−	0.634071i	−0.315016	−	0.949087i	$-0.602010\pi$
$653$	16.2030	−	16.2030i	0.634071	−	0.634071i	0.949087	+	0.315016i	$0.102010\pi$
$654$	12.1561	−	24.9349i	0.475341	−	0.975031i
$655$	7.27114			0.284107
$656$	12.4094			0.484507
$657$	16.3633	−	12.7937i	0.638392	−	0.499130i
$658$	4.73417	+	4.73417i	0.184557	+	0.184557i
$659$	22.4489			0.874484			0.437242	−	0.899344i	$-0.355955\pi$
$659$	22.4489			0.874484			0.437242	+	0.899344i	$0.355955\pi$
$660$	8.49472	−	2.92664i	0.330656	−	0.113919i
$661$	20.3735	+	20.3735i	0.792436	+	0.792436i	0.981890	−	0.189453i	$-0.0606716\pi$
$661$	20.3735	+	20.3735i	0.792436	+	0.792436i	−0.189453	+	0.981890i	$0.560672\pi$
$662$			0.858974i			0.0333850i
$663$	−47.4057	−	23.1109i	−1.84108	−	0.897554i
$664$	6.49361	−	6.49361i	0.252001	−	0.252001i
$665$	0.269489			0.0104503
$666$	−18.0599	+	2.61509i	−0.699808	+	0.101333i
$667$	3.82448			0.148085
$668$	−12.7580	+	12.7580i	−0.493624	+	0.493624i
$669$	−23.8494	−	11.6269i	−0.922070	−	0.449522i
$670$			9.29823i			0.359222i
$671$	−47.2519	−	47.2519i	−1.82414	−	1.82414i
$672$	3.15269	−	1.08618i	0.121618	−	0.0419004i
$673$	27.9883			1.07887			0.539435	−	0.842027i	$-0.318638\pi$
$673$	27.9883			1.07887			0.539435	+	0.842027i	$0.318638\pi$
$674$	−1.39584	−	1.39584i	−0.0537659	−	0.0537659i
$675$	5.08203	−	1.08303i	0.195607	−	0.0416860i
$676$	−18.4706			−0.710406
$677$	−36.3628			−1.39754			−0.698769	−	0.715348i	$-0.746268\pi$
$677$	−36.3628			−1.39754			−0.698769	+	0.715348i	$0.746268\pi$
$678$	−15.1580	+	31.0925i	−0.582141	+	1.19410i
$679$	7.40140	−	7.40140i	0.284040	−	0.284040i
$680$	−3.83800	+	3.83800i	−0.147181	+	0.147181i
$681$	−10.9190	−	31.6928i	−0.418416	−	1.21447i
$682$	32.7063			1.25239
$683$	−31.9090	−	31.9090i	−1.22097	−	1.22097i	−0.967289	−	0.253677i	$-0.918360\pi$
$683$	−31.9090	−	31.9090i	−1.22097	−	1.22097i	−0.253677	−	0.967289i	$-0.581640\pi$
$684$	0.0510303	−	0.416826i	0.00195119	−	0.0159377i
$685$	1.89023	−	1.89023i	0.0722220	−	0.0722220i
$686$	−14.0129	+	14.0129i	−0.535016	+	0.535016i
$687$	17.7719	+	8.66403i	0.678039	+	0.330553i
$688$	−7.21797	+	7.21797i	−0.275183	+	0.275183i
$689$	15.7012	+	15.7012i	0.598169	+	0.598169i
$690$	0.858304	+	2.49127i	0.0326751	+	0.0948409i
$691$			35.8528i			1.36391i	0.731396	+	0.681953i	$0.238869\pi$
$691$			35.8528i			1.36391i	−0.731396	+	0.681953i	$0.761131\pi$
$692$			4.28631i			0.162941i
$693$	−18.4536	−	23.6023i	−0.700994	−	0.896579i
$694$			4.06939i			0.154472i
$695$	7.68697	−	7.68697i	0.291583	−	0.291583i
$696$	−3.91395	−	1.90810i	−0.148358	−	0.0723265i
$697$	47.6274	+	47.6274i	1.80402	+	1.80402i
$698$	3.78958	−	3.78958i	0.143438	−	0.143438i
$699$	−23.5718	−	11.4916i	−0.891568	−	0.434652i
$700$	1.92521			0.0727659
$701$	8.81865	+	8.81865i	0.333076	+	0.333076i	0.853753	−	0.520678i	$-0.174321\pi$
$701$	8.81865	+	8.81865i	0.333076	+	0.333076i	−0.520678	+	0.853753i	$0.674321\pi$
$702$	28.5095	−	6.07567i	1.07602	−	0.229312i
$703$	−0.422910	+	0.739009i	−0.0159503	+	0.0278722i
$704$		−	5.18734i		−	0.195505i
$705$	5.69490	−	1.96204i	0.214483	−	0.0738946i
$706$		−	12.4626i		−	0.469035i
$707$	6.46601			0.243179
$708$	−18.1525	+	6.25398i	−0.682212	+	0.235039i
$709$	26.8621	−	26.8621i	1.00883	−	1.00883i	0.00886777	−	0.999961i	$-0.497177\pi$
$709$	26.8621	−	26.8621i	1.00883	−	1.00883i	0.999961	−	0.00886777i	$-0.00282274\pi$
$710$			1.23955i			0.0465195i
$711$	−3.20492	−	0.392366i	−0.120194	−	0.0147149i
$712$	7.84887			0.294149
$713$			9.59185i			0.359218i
$714$	16.2688	+	7.93126i	0.608844	+	0.296820i
$715$	29.1003			1.08829
$716$	−6.48181	−	6.48181i	−0.242237	−	0.242237i
$717$	−4.63360	−	13.4492i	−0.173045	−	0.502271i
$718$	7.40410	+	7.40410i	0.276319	+	0.276319i
$719$			32.4752i			1.21112i	0.795799	+	0.605561i	$0.207051\pi$
$719$			32.4752i			1.21112i	−0.795799	+	0.605561i	$0.792949\pi$
$720$	0.364556	−	2.97777i	0.0135862	−	0.110975i
$721$	−20.7514	−	20.7514i	−0.772822	−	0.772822i
$722$	13.4212	+	13.4212i	0.499484	+	0.499484i
$723$	43.1380	−	14.8621i	1.60432	−	0.552729i
$724$			13.5004i			0.501737i
$725$	−1.77763	−	1.77763i	−0.0660196	−	0.0660196i
$726$	−26.0515	+	8.97541i	−0.966863	+	0.333109i
$727$	15.5520	+	15.5520i	0.576792	+	0.576792i	0.934018	−	0.357226i	$-0.116277\pi$
$727$	15.5520	+	15.5520i	0.576792	+	0.576792i	−0.357226	+	0.934018i	$0.616277\pi$
$728$	10.8001			0.400280
$729$	−24.6541	+	11.0080i	−0.913114	+	0.407705i
$730$		−	6.92368i		−	0.256257i
$731$	−55.4051			−2.04923
$732$	−21.0957	+	7.26800i	−0.779719	+	0.268633i
$733$		−	20.2890i		−	0.749390i	−0.927148	−	0.374695i	$-0.877747\pi$
$733$		−	20.2890i		−	0.749390i	0.927148	−	0.374695i	$-0.122253\pi$
$734$	−11.0791	+	11.0791i	−0.408938	+	0.408938i
$735$	1.85821	+	5.39353i	0.0685410	+	0.198943i
$736$	1.52130			0.0560760
$737$		−	48.2331i		−	1.77669i
$738$	−36.9524	−	4.52393i	−1.36024	−	0.166528i
$739$			16.8745i			0.620738i	0.950616	+	0.310369i	$0.100453\pi$
$739$			16.8745i			0.620738i	−0.950616	+	0.310369i	$0.899547\pi$
$740$	−3.02123	+	5.27941i	−0.111063	+	0.194075i
$741$	0.596021	−	1.22257i	0.0218954	−	0.0449123i
$742$	−5.38838	−	5.38838i	−0.197814	−	0.197814i
$743$	−19.1398			−0.702172			−0.351086	−	0.936343i	$-0.614187\pi$
$743$	−19.1398			−0.702172			−0.351086	+	0.936343i	$0.614187\pi$
$744$	4.78555	−	9.81623i	0.175447	−	0.359880i
$745$	−6.67685	+	6.67685i	−0.244621	+	0.244621i
$746$	2.97349	+	2.97349i	0.108867	+	0.108867i
$747$	−21.7038	+	16.9692i	−0.794099	+	0.620870i
$748$	19.9090	−	19.9090i	0.727945	−	0.727945i
$749$		−	21.8861i		−	0.799702i
$750$	0.759006	−	1.55689i	0.0277150	−	0.0568496i
$751$			3.29443i			0.120216i	0.998192	+	0.0601078i	$0.0191444\pi$
$751$			3.29443i			0.120216i	−0.998192	+	0.0601078i	$0.980856\pi$
$752$		−	3.47762i		−	0.126816i
$753$	20.1031	−	6.92603i	0.732599	−	0.252399i
$754$	−9.97227	−	9.97227i	−0.363169	−	0.363169i
$755$	8.77029	−	8.77029i	0.319183	−	0.319183i
$756$	−9.78395	+	2.08506i	−0.355839	+	0.0758330i
$757$	−26.1797	+	26.1797i	−0.951518	+	0.951518i	−0.998878	−	0.0473602i	$-0.984919\pi$
$757$	−26.1797	+	26.1797i	−0.951518	+	0.951518i	0.0473602	+	0.998878i	$0.484919\pi$
$758$	7.65167	−	7.65167i	0.277921	−	0.277921i
$759$	−4.45231	−	12.9230i	−0.161609	−	0.469077i
$760$	−0.0989804	−	0.0989804i	−0.00359040	−	0.00359040i
$761$	−13.0239			−0.472118			−0.236059	−	0.971739i	$-0.575856\pi$
$761$	−13.0239			−0.472118			−0.236059	+	0.971739i	$0.575856\pi$
$762$	−9.99124	+	3.44223i	−0.361944	+	0.124699i
$763$	−21.8027	+	21.8027i	−0.789312	+	0.789312i
$764$	−9.94316	+	9.94316i	−0.359731	+	0.359731i
$765$	12.8278	−	10.0295i	0.463791	−	0.362617i
$766$	−4.63822			−0.167586
$767$	−62.1847			−2.24536
$768$	−1.55689	−	0.759006i	−0.0561795	−	0.0273883i
$769$	−22.4249	−	22.4249i	−0.808662	−	0.808662i	0.175769	−	0.984431i	$-0.443759\pi$
$769$	−22.4249	−	22.4249i	−0.808662	−	0.808662i	−0.984431	+	0.175769i	$0.943759\pi$
$770$	−9.98669			−0.359895
$771$	5.16385	+	14.9883i	0.185971	+	0.539791i
$772$	14.9338	+	14.9338i	0.537480	+	0.537480i
$773$			20.2597i			0.728691i	0.931264	+	0.364345i	$0.118707\pi$
$773$			20.2597i			0.728691i	−0.931264	+	0.364345i	$0.881293\pi$
$774$	24.1248	−	18.8621i	0.867148	−	0.677984i
$775$	4.45832	−	4.45832i	0.160148	−	0.160148i
$776$	−5.43691			−0.195174
$777$	19.9259	+	3.79060i	0.714839	+	0.135987i
$778$	24.8741			0.891778
$779$	−1.22829	+	1.22829i	−0.0440081	+	0.0440081i
$780$	4.25792	−	8.73394i	0.152458	−	0.312725i
$781$		−	6.42997i		−	0.230082i
$782$	5.83876	+	5.83876i	0.208794	+	0.208794i
$783$	10.9592	+	7.10875i	0.391651	+	0.254046i
$784$	3.29358			0.117628
$785$	5.15378	+	5.15378i	0.183946	+	0.183946i
$786$	−5.51884	+	11.3204i	−0.196850	+	0.403784i
$787$	−51.8393			−1.84787			−0.923936	−	0.382546i	$-0.875047\pi$
$787$	−51.8393			−1.84787			−0.923936	+	0.382546i	$0.875047\pi$
$788$	−10.0071			−0.356490
$789$	−34.1874	−	16.6669i	−1.21711	−	0.593356i
$790$	−0.761048	+	0.761048i	−0.0270769	+	0.0270769i
$791$	27.1869	−	27.1869i	0.966654	−	0.966654i
$792$	−1.89108	+	15.4467i	−0.0671964	+	0.548874i
$793$	−72.2673			−2.56629
$794$	20.7058	+	20.7058i	0.734820	+	0.734820i
$795$	−6.48187	+	2.23317i	−0.229888	+	0.0792023i
$796$	−12.2484	+	12.2484i	−0.434132	+	0.434132i
$797$	−15.4144	+	15.4144i	−0.546006	+	0.546006i	−0.925283	−	0.379277i	$-0.876173\pi$
$797$	−15.4144	+	15.4144i	−0.546006	+	0.546006i	0.379277	+	0.925283i	$0.376173\pi$
$798$	−0.204544	+	0.419565i	−0.00724077	+	0.0148524i
$799$	13.3471	−	13.3471i	0.472187	−	0.472187i
$800$	−0.707107	−	0.707107i	−0.0250000	−	0.0250000i
$801$	−23.3721	−	2.86135i	−0.825812	−	0.101101i
$802$			27.3051i			0.964177i
$803$			35.9155i			1.26743i
$804$	−14.4763	−	7.05741i	−0.510541	−	0.248896i
$805$		−	2.92882i		−	0.103227i
$806$	25.0106	−	25.0106i	0.880960	−	0.880960i
$807$	0.357105	−	0.732503i	0.0125707	−	0.0257853i
$808$	−2.37490	−	2.37490i	−0.0835485	−	0.0835485i
$809$	21.9588	−	21.9588i	0.772032	−	0.772032i	−0.206430	−	0.978461i	$-0.566185\pi$
$809$	21.9588	−	21.9588i	0.772032	−	0.772032i	0.978461	+	0.206430i	$0.0661845\pi$
$810$	−2.17113	+	8.73420i	−0.0762856	+	0.306888i
$811$	35.3528			1.24141			0.620703	−	0.784046i	$-0.286847\pi$
$811$	35.3528			1.24141			0.620703	+	0.784046i	$0.286847\pi$
$812$	3.42231	+	3.42231i	0.120099	+	0.120099i
$813$	−2.89559	−	1.41164i	−0.101553	−	0.0495084i
$814$	15.6721	−	27.3861i	0.549308	−	0.959882i
$815$			20.1290i			0.705088i
$816$	−3.06228	−	8.88841i	−0.107201	−	0.311157i
$817$		−	1.42888i		−	0.0499900i
$818$	9.30083			0.325196
$819$	−32.1603	−	3.93725i	−1.12377	−	0.137579i
$820$	−8.77480	+	8.77480i	−0.306429	+	0.306429i
$821$			11.3942i			0.397660i	0.980034	+	0.198830i	$0.0637141\pi$
$821$			11.3942i			0.397660i	−0.980034	+	0.198830i	$0.936286\pi$
$822$	1.50819	+	4.37758i	0.0526040	+	0.152686i
$823$	−24.7384			−0.862327			−0.431163	−	0.902274i	$-0.641897\pi$
$823$	−24.7384			−0.862327			−0.431163	+	0.902274i	$0.641897\pi$
$824$			15.2435i			0.531033i
$825$	−3.93722	+	8.07612i	−0.137076	+	0.281174i
$826$	21.3407			0.742538
$827$	−0.846501	−	0.846501i	−0.0294357	−	0.0294357i	0.692236	−	0.721671i	$-0.256626\pi$
$827$	−0.846501	−	0.846501i	−0.0294357	−	0.0294357i	−0.721671	+	0.692236i	$0.756626\pi$
$828$	−4.53009	−	0.554600i	−0.157431	−	0.0192737i
$829$	−12.4499	−	12.4499i	−0.432404	−	0.432404i	0.457041	−	0.889445i	$-0.348909\pi$
$829$	−12.4499	−	12.4499i	−0.432404	−	0.432404i	−0.889445	+	0.457041i	$0.848909\pi$
$830$			9.18336i			0.318759i
$831$	16.7160	+	48.5190i	0.579873	+	1.68311i
$832$	−3.96677	−	3.96677i	−0.137523	−	0.137523i
$833$	12.6408	+	12.6408i	0.437977	+	0.437977i
$834$	6.13332	+	17.8022i	0.212379	+	0.616441i
$835$		−	18.0426i		−	0.624390i
$836$	0.513445	+	0.513445i	0.0177579	+	0.0177579i
$837$	−17.8288	+	27.4859i	−0.616254	+	0.950050i
$838$	−18.6567	−	18.6567i	−0.644485	−	0.644485i
$839$	−24.1404			−0.833419			−0.416709	−	0.909040i	$-0.636817\pi$
$839$	−24.1404			−0.833419			−0.416709	+	0.909040i	$0.636817\pi$
$840$	−1.46124	+	2.99733i	−0.0504177	+	0.103418i
$841$			22.6800i			0.782071i
$842$	−30.5587			−1.05312
$843$	−13.1177	−	38.0747i	−0.451797	−	1.31136i
$844$			22.1119i			0.761124i
$845$	13.0607	−	13.0607i	0.449300	−	0.449300i
$846$	−1.26779	+	10.3555i	−0.0435874	+	0.356031i
$847$	30.6271			1.05236
$848$			3.95819i			0.135925i
$849$	−2.84220	−	8.24962i	−0.0975442	−	0.283126i
$850$		−	5.42775i		−	0.186170i
$851$	8.03159	+	4.59621i	0.275319	+	0.157556i
$852$	−1.92984	−	0.940826i	−0.0661154	−	0.0322322i
$853$	12.1090	+	12.1090i	0.414603	+	0.414603i	0.883339	−	0.468735i	$-0.155290\pi$
$853$	12.1090	+	12.1090i	0.414603	+	0.414603i	−0.468735	+	0.883339i	$0.655290\pi$
$854$	24.8009			0.848668
$855$	0.258657	+	0.330824i	0.00884587	+	0.0113140i
$856$	−8.03854	+	8.03854i	−0.274751	+	0.274751i
$857$	9.78821	+	9.78821i	0.334359	+	0.334359i	0.854239	−	0.519880i	$-0.174023\pi$
$857$	9.78821	+	9.78821i	0.334359	+	0.334359i	−0.519880	+	0.854239i	$0.674023\pi$
$858$	−22.0873	+	45.3059i	−0.754047	+	1.54672i
$859$	14.5905	−	14.5905i	0.497821	−	0.497821i	−0.412938	−	0.910759i	$-0.635498\pi$
$859$	14.5905	−	14.5905i	0.497821	−	0.497821i	0.910759	+	0.412938i	$0.135498\pi$
$860$		−	10.2078i		−	0.348082i
$861$	37.1952	+	18.1332i	1.26761	+	0.617978i
$862$		−	23.8565i		−	0.812557i
$863$			12.6373i			0.430178i	0.976595	+	0.215089i	$0.0690041\pi$
$863$			12.6373i			0.430178i	−0.976595	+	0.215089i	$0.930996\pi$
$864$	4.35936	+	2.82772i	0.148308	+	0.0962009i
$865$	−3.03088	−	3.03088i	−0.103053	−	0.103053i
$866$	−14.8240	+	14.8240i	−0.503740	+	0.503740i
$867$	9.45757	−	19.3996i	0.321196	−	0.658844i
$868$	−8.58319	+	8.58319i	−0.291332	+	0.291332i
$869$	3.94781	−	3.94781i	0.133920	−	0.133920i
$870$	4.11681	−	1.41835i	0.139573	−	0.0480864i
$871$	−36.8839	−	36.8839i	−1.24976	−	1.24976i
$872$	16.0158			0.542364
$873$	16.1899	+	1.98206i	0.547943	+	0.0670825i
$874$	−0.150579	+	0.150579i	−0.00509342	+	0.00509342i
$875$	−1.36133	+	1.36133i	−0.0460212	+	0.0460212i
$876$	10.7794	+	5.25511i	0.364203	+	0.177554i
$877$	−4.55805			−0.153914			−0.0769572	−	0.997034i	$-0.524520\pi$
$877$	−4.55805			−0.153914			−0.0769572	+	0.997034i	$0.524520\pi$
$878$	−2.25742			−0.0761842
$879$	−17.0961	+	35.0679i	−0.576637	+	1.18281i
$880$	3.66800	+	3.66800i	0.123648	+	0.123648i
$881$	−24.5294			−0.826416			−0.413208	−	0.910637i	$-0.635592\pi$
$881$	−24.5294			−0.826416			−0.413208	+	0.910637i	$0.635592\pi$
$882$	−9.80753	−	1.20070i	−0.330237	−	0.0404295i
$883$	−30.6747	−	30.6747i	−1.03229	−	1.03229i	−0.999461	−	0.0328243i	$-0.989550\pi$
$883$	−30.6747	−	30.6747i	−1.03229	−	1.03229i	−0.0328243	−	0.999461i	$-0.510450\pi$
$884$		−	30.4489i		−	1.02411i
$885$	8.41350	−	17.2580i	0.282817	−	0.580120i
$886$	18.8725	−	18.8725i	0.634035	−	0.634035i
$887$	54.5342			1.83108			0.915540	−	0.402227i	$-0.131764\pi$
$887$	54.5342			1.83108			0.915540	+	0.402227i	$0.131764\pi$
$888$	−5.92634	−	8.71083i	−0.198875	−	0.292316i
$889$	11.7461			0.393950
$890$	−5.54999	+	5.54999i	−0.186036	+	0.186036i
$891$	11.2624	−	45.3072i	0.377303	−	1.51785i
$892$		−	15.3186i		−	0.512904i
$893$	0.344216	+	0.344216i	0.0115188	+	0.0115188i
$894$	−5.32736	−	15.4629i	−0.178173	−	0.517156i
$895$	9.16666			0.306408
$896$	1.36133	+	1.36133i	0.0454787	+	0.0454787i
$897$	−13.2870	−	6.47759i	−0.443639	−	0.216280i
$898$	13.9457			0.465372
$899$	15.8505			0.528644
$900$	1.84782	+	2.36338i	0.0615940	+	0.0787793i
$901$	−15.1915	+	15.1915i	−0.506103	+	0.506103i
$902$	45.5178	−	45.5178i	1.51558	−	1.51558i
$903$	−32.1819	+	11.0875i	−1.07095	+	0.368968i
$904$	−19.9709			−0.664222
$905$	−9.54619	−	9.54619i	−0.317326	−	0.317326i
$906$	6.99768	+	20.3111i	0.232482	+	0.674791i
$907$	5.52271	−	5.52271i	0.183379	−	0.183379i	−0.609448	−	0.792826i	$-0.708609\pi$
$907$	5.52271	−	5.52271i	0.183379	−	0.183379i	0.792826	+	0.609448i	$0.208609\pi$
$908$	13.6849	−	13.6849i	0.454149	−	0.454149i
$909$	6.20610	+	7.93767i	0.205844	+	0.263276i
$910$	−7.63685	+	7.63685i	−0.253159	+	0.253159i
$911$	3.48960	+	3.48960i	0.115616	+	0.115616i	0.762548	−	0.646932i	$-0.223948\pi$
$911$	3.48960	+	3.48960i	0.115616	+	0.115616i	−0.646932	+	0.762548i	$0.723948\pi$
$912$	0.229228	−	0.0789750i	0.00759051	−	0.00261512i
$913$		−	47.6372i		−	1.57656i
$914$		−	9.26555i		−	0.306477i
$915$	9.77766	−	20.0562i	0.323239	−	0.663036i
$916$			11.4150i			0.377161i
$917$	9.89838	−	9.89838i	0.326873	−	0.326873i
$918$	5.87844	+	27.5840i	0.194017	+	0.910407i
$919$	23.9392	+	23.9392i	0.789680	+	0.789680i	0.981442	−	0.191762i	$-0.0614201\pi$
$919$	23.9392	+	23.9392i	0.789680	+	0.789680i	−0.191762	+	0.981442i	$0.561420\pi$
$920$	−1.07572	+	1.07572i	−0.0354656	+	0.0354656i
$921$	8.36109	−	17.1505i	0.275507	−	0.565127i
$922$	−20.1282			−0.662887
$923$	−4.91701	−	4.91701i	−0.161845	−	0.161845i
$924$	7.57996	−	15.5482i	0.249362	−	0.511498i
$925$	−1.59678	−	5.86944i	−0.0525017	−	0.192986i
$926$			4.66163i			0.153191i
$927$	5.55711	−	45.3916i	0.182520	−	1.49086i
$928$		−	2.51395i		−	0.0825245i
$929$	39.0723			1.28192			0.640961	−	0.767574i	$-0.278536\pi$
$929$	39.0723			1.28192			0.640961	+	0.767574i	$0.278536\pi$
$930$	3.55723	+	10.3250i	0.116646	+	0.338571i
$931$	−0.326000	+	0.326000i	−0.0106842	+	0.0106842i
$932$		−	15.1403i		−	0.495937i
$933$	42.0771	−	14.4966i	1.37754	−	0.474598i
$934$	−11.6750			−0.382017
$935$			28.1556i			0.920786i
$936$	10.3660	+	13.2582i	0.338824	+	0.433359i
$937$	−5.26195			−0.171900			−0.0859502	−	0.996299i	$-0.527393\pi$
$937$	−5.26195			−0.171900			−0.0859502	+	0.996299i	$0.527393\pi$
$938$	12.6579	+	12.6579i	0.413296	+	0.413296i
$939$	−8.14404	+	2.80583i	−0.265771	+	0.0915647i
$940$	2.45905	+	2.45905i	0.0802053	+	0.0802053i
$941$			48.3770i			1.57704i	0.615007	+	0.788522i	$0.289153\pi$
$941$			48.3770i			1.57704i	−0.615007	+	0.788522i	$0.710847\pi$
$942$	−11.9356	+	4.11212i	−0.388883	+	0.133980i
$943$	13.3491	+	13.3491i	0.434708	+	0.434708i
$944$	−7.83820	−	7.83820i	−0.255112	−	0.255112i
$945$	5.44394	−	8.39266i	0.177091	−	0.273013i
$946$			52.9511i			1.72159i
$947$	9.05959	+	9.05959i	0.294397	+	0.294397i	0.838814	−	0.544417i	$-0.183249\pi$
$947$	9.05959	+	9.05959i	0.294397	+	0.294397i	−0.544417	+	0.838814i	$0.683249\pi$
$948$	−0.607229	−	1.76251i	−0.0197219	−	0.0572436i
$949$	27.4647	+	27.4647i	0.891540	+	0.891540i
$950$	0.139979			0.00454153
$951$	18.1779	+	8.86199i	0.589460	+	0.287370i
$952$			10.4495i			0.338671i
$953$	9.84569			0.318933			0.159467	−	0.987203i	$-0.449023\pi$
$953$	9.84569			0.318933			0.159467	+	0.987203i	$0.449023\pi$
$954$	1.44298	−	11.7866i	0.0467182	−	0.381604i
$955$		−	14.0617i		−	0.455027i
$956$	5.80735	−	5.80735i	0.187823	−	0.187823i
$957$	−21.3553	+	7.35744i	−0.690319	+	0.237832i
$958$	−22.3044			−0.720622
$959$		−	5.14644i		−	0.166187i
$960$	1.63759	−	0.564190i	0.0528529	−	0.0182091i
$961$			8.75329i			0.282364i
$962$	−8.95769	−	32.9267i	−0.288808	−	1.06160i
$963$	26.8674	−	21.0064i	0.865789	−	0.676922i
$964$	18.6269	+	18.6269i	0.599933	+	0.599933i
$965$	−21.1196			−0.679864
$966$	4.55986	+	2.22299i	0.146711	+	0.0715236i
$967$	23.0717	−	23.0717i	0.741937	−	0.741937i	−0.231013	−	0.972951i	$-0.574204\pi$
$967$	23.0717	−	23.0717i	0.741937	−	0.741937i	0.972951	+	0.231013i	$0.0742041\pi$
$968$	−11.2490	−	11.2490i	−0.361557	−	0.361557i
$969$	1.18288	+	0.576672i	0.0379997	+	0.0185254i
$970$	3.84448	−	3.84448i	0.123439	−	0.123439i
$971$			8.02634i			0.257577i	0.991672	+	0.128789i	$0.0411089\pi$
$971$			8.02634i			0.257577i	−0.991672	+	0.128789i	$0.958891\pi$
$972$	−11.9503	−	10.0095i	−0.383306	−	0.321055i
$973$		−	20.9289i		−	0.670951i
$974$		−	18.3634i		−	0.588400i
$975$	3.16503	+	9.18664i	0.101362	+	0.294208i
$976$	−9.10908	−	9.10908i	−0.291575	−	0.291575i
$977$	−17.8008	+	17.8008i	−0.569499	+	0.569499i	−0.931988	−	0.362489i	$-0.881927\pi$
$977$	−17.8008	+	17.8008i	−0.569499	+	0.569499i	0.362489	+	0.931988i	$0.381927\pi$
$978$	−31.3387	−	15.2780i	−1.00210	−	0.488538i
$979$	28.7897	−	28.7897i	0.920122	−	0.920122i
$980$	−2.32892	+	2.32892i	−0.0743945	+	0.0743945i
$981$	−47.6914	−	5.83866i	−1.52267	−	0.186414i
$982$	−21.8422	−	21.8422i	−0.697012	−	0.697012i
$983$	49.9878			1.59436			0.797181	−	0.603740i	$-0.206323\pi$
$983$	49.9878			1.59436			0.797181	+	0.603740i	$0.206323\pi$
$984$	−7.00128	−	20.3215i	−0.223193	−	0.647827i
$985$	7.07612	−	7.07612i	0.225464	−	0.225464i
$986$	9.64854	−	9.64854i	0.307272	−	0.307272i
$987$	5.08165	−	10.4236i	0.161751	−	0.331787i
$988$	0.785265			0.0249826
$989$	−15.5291			−0.493796
$990$	−9.58527	−	12.2597i	−0.304640	−	0.389637i
$991$	7.00029	+	7.00029i	0.222372	+	0.222372i	0.809496	−	0.587125i	$-0.199740\pi$
$991$	7.00029	+	7.00029i	0.222372	+	0.222372i	−0.587125	+	0.809496i	$0.699740\pi$
$992$	6.30502			0.200185
$993$	1.40664	−	0.484624i	0.0446385	−	0.0153791i
$994$	1.68743	+	1.68743i	0.0535221	+	0.0535221i
$995$		−	17.3218i		−	0.549138i
$996$	−14.2975	−	6.97022i	−0.453033	−	0.220860i
$997$	−4.54972	+	4.54972i	−0.144091	+	0.144091i	−0.775473	−	0.631381i	$-0.782488\pi$
$997$	−4.54972	+	4.54972i	−0.144091	+	0.144091i	0.631381	+	0.775473i	$0.282488\pi$
$998$	28.6326			0.906350
$999$	14.4717	+	28.0993i	0.457863	+	0.889023i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.u.e.401.14	yes	40
3.2	odd	2	inner	1110.2.u.e.401.10	yes	40
37.6	odd	4	inner	1110.2.u.e.191.10	✓	40
111.80	even	4	inner	1110.2.u.e.191.14	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.e.191.10	✓	40	37.6	odd	4	inner
1110.2.u.e.191.14	yes	40	111.80	even	4	inner
1110.2.u.e.401.10	yes	40	3.2	odd	2	inner
1110.2.u.e.401.14	yes	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.55689 - 0.759006i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.63759 + 0.564190i) q^{6} +1.92521 q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.84782 + 2.36338i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.55689 - 0.759006i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.63759 + 0.564190i) q^{6} +1.92521 q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.84782 + 2.36338i) q^{9} +1.00000 q^{10} -5.18734 q^{11} +(-0.759006 + 1.55689i) q^{12} +(-3.96677 + 3.96677i) q^{13} +(1.36133 - 1.36133i) q^{14} +(-0.564190 - 1.63759i) q^{15} -1.00000 q^{16} +(-3.83800 - 3.83800i) q^{17} +(2.97777 + 0.364556i) q^{18} +(0.0989804 - 0.0989804i) q^{19} +(0.707107 - 0.707107i) q^{20} +(-2.99733 - 1.46124i) q^{21} +(-3.66800 + 3.66800i) q^{22} +(-1.07572 - 1.07572i) q^{23} +(0.564190 + 1.63759i) q^{24} +1.00000i q^{25} +5.60986i q^{26} +(-1.08303 - 5.08203i) q^{27} -1.92521i q^{28} +(-1.77763 + 1.77763i) q^{29} +(-1.55689 - 0.759006i) q^{30} +(-4.45832 - 4.45832i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(8.07612 + 3.93722i) q^{33} -5.42775 q^{34} +(1.36133 + 1.36133i) q^{35} +(2.36338 - 1.84782i) q^{36} +(-5.86944 + 1.59678i) q^{37} -0.139979i q^{38} +(9.18664 - 3.16503i) q^{39} -1.00000i q^{40} -12.4094 q^{41} +(-3.15269 + 1.08618i) q^{42} +(7.21797 - 7.21797i) q^{43} +5.18734i q^{44} +(-0.364556 + 2.97777i) q^{45} -1.52130 q^{46} +3.47762i q^{47} +(1.55689 + 0.759006i) q^{48} -3.29358 q^{49} +(0.707107 + 0.707107i) q^{50} +(3.06228 + 8.88841i) q^{51} +(3.96677 + 3.96677i) q^{52} -3.95819i q^{53} +(-4.35936 - 2.82772i) q^{54} +(-3.66800 - 3.66800i) q^{55} +(-1.36133 - 1.36133i) q^{56} +(-0.229228 + 0.0789750i) q^{57} +2.51395i q^{58} +(7.83820 + 7.83820i) q^{59} +(-1.63759 + 0.564190i) q^{60} +(9.10908 + 9.10908i) q^{61} -6.30502 q^{62} +(3.55743 + 4.54999i) q^{63} +1.00000i q^{64} -5.60986 q^{65} +(8.49472 - 2.92664i) q^{66} +9.29823i q^{67} +(-3.83800 + 3.83800i) q^{68} +(0.858304 + 2.49127i) q^{69} +1.92521 q^{70} +1.23955i q^{71} +(0.364556 - 2.97777i) q^{72} -6.92368i q^{73} +(-3.02123 + 5.27941i) q^{74} +(0.759006 - 1.55689i) q^{75} +(-0.0989804 - 0.0989804i) q^{76} -9.98669 q^{77} +(4.25792 - 8.73394i) q^{78} +(-0.761048 + 0.761048i) q^{79} +(-0.707107 - 0.707107i) q^{80} +(-2.17113 + 8.73420i) q^{81} +(-8.77480 + 8.77480i) q^{82} +9.18336i q^{83} +(-1.46124 + 2.99733i) q^{84} -5.42775i q^{85} -10.2078i q^{86} +(4.11681 - 1.41835i) q^{87} +(3.66800 + 3.66800i) q^{88} +(-5.54999 + 5.54999i) q^{89} +(1.84782 + 2.36338i) q^{90} +(-7.63685 + 7.63685i) q^{91} +(-1.07572 + 1.07572i) q^{92} +(3.55723 + 10.3250i) q^{93} +(2.45905 + 2.45905i) q^{94} +0.139979 q^{95} +(1.63759 - 0.564190i) q^{96} +(3.84448 - 3.84448i) q^{97} +(-2.32892 + 2.32892i) q^{98} +(-9.58527 - 12.2597i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 24 q^{7} - 8 q^{9}+O(q^{10}) \) 40 * q - 24 * q^7 - 8 * q^9	\( 40 q - 24 q^{7} - 8 q^{9} + 40 q^{10} - 8 q^{12} - 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 24 q^{31} + 24 q^{33} - 8 q^{34} + 16 q^{39} - 20 q^{42} - 32 q^{43} - 8 q^{45} + 72 q^{46} + 96 q^{49} + 20 q^{51} + 16 q^{52} + 24 q^{54} - 16 q^{57} + 40 q^{61} - 24 q^{63} - 44 q^{66} - 24 q^{70} + 8 q^{72} + 8 q^{75} - 16 q^{76} + 48 q^{79} + 24 q^{81} - 56 q^{82} - 8 q^{84} + 12 q^{87} - 8 q^{90} - 64 q^{91} + 12 q^{93} + 24 q^{94} + 8 q^{97}+O(q^{100}) \) 40 * q - 24 * q^7 - 8 * q^9 + 40 * q^10 - 8 * q^12 - 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 24 * q^31 + 24 * q^33 - 8 * q^34 + 16 * q^39 - 20 * q^42 - 32 * q^43 - 8 * q^45 + 72 * q^46 + 96 * q^49 + 20 * q^51 + 16 * q^52 + 24 * q^54 - 16 * q^57 + 40 * q^61 - 24 * q^63 - 44 * q^66 - 24 * q^70 + 8 * q^72 + 8 * q^75 - 16 * q^76 + 48 * q^79 + 24 * q^81 - 56 * q^82 - 8 * q^84 + 12 * q^87 - 8 * q^90 - 64 * q^91 + 12 * q^93 + 24 * q^94 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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