LMFDB - Embedded newform 1110.2.u.e.401.10

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			401.10
Character	$\chi$	$=$	1110.401
Dual form			1110.2.u.e.191.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.55689 - 0.759006i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.564190 + 1.63759i) q^{6} +1.92521 q^{7} +(0.707107 + 0.707107i) q^{8} +(1.84782 - 2.36338i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.55689 - 0.759006i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.564190 + 1.63759i) 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} +(-1.63759 - 0.564190i) q^{15} -1.00000 q^{16} +(3.83800 + 3.83800i) q^{17} +(0.364556 + 2.97777i) 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} +(1.63759 + 0.564190i) 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} +(-3.16503 + 9.18664i) q^{39} -1.00000i q^{40} +12.4094 q^{41} +(-1.08618 + 3.15269i) q^{42} +(7.21797 - 7.21797i) q^{43} -5.18734i q^{44} +(-2.97777 + 0.364556i) 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} +(8.88841 + 3.06228i) q^{51} +(3.96677 + 3.96677i) q^{52} +3.95819i q^{53} +(2.82772 + 4.35936i) q^{54} +(-3.66800 - 3.66800i) q^{55} +(1.36133 + 1.36133i) q^{56} +(0.0789750 - 0.229228i) q^{57} +2.51395i q^{58} +(-7.83820 - 7.83820i) q^{59} +(-0.564190 + 1.63759i) 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} +(-2.92664 + 8.49472i) q^{66} +9.29823i q^{67} +(3.83800 - 3.83800i) q^{68} +(2.49127 + 0.858304i) q^{69} +1.92521 q^{70} -1.23955i q^{71} +(2.97777 - 0.364556i) 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} +(1.41835 - 4.11681i) 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} +(-10.3250 - 3.55723i) q^{93} +(2.45905 + 2.45905i) q^{94} -0.139979 q^{95} +(0.564190 - 1.63759i) 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
$6$	−0.564190	+	1.63759i	−0.230330	+	0.668542i
$7$	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	$-0.214189\pi$
$11$	5.18734			1.56404			0.782021	+	0.623252i	$0.214189\pi$
$12$	−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
$15$	−1.63759	−	0.564190i	−0.422823	−	0.145673i
$16$	−1.00000			−0.250000
$17$	3.83800	+	3.83800i	0.930851	+	0.930851i	0.997759	−	0.0669078i	$-0.0213133\pi$
$17$	3.83800	+	3.83800i	0.930851	+	0.930851i	−0.0669078	+	0.997759i	$0.521313\pi$
$18$	0.364556	+	2.97777i	0.0859267	+	0.701867i
$19$	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	0.810308	−	0.586004i	$-0.199300\pi$
$23$	1.07572	+	1.07572i	0.224304	+	0.224304i	−0.586004	+	0.810308i	$0.699300\pi$
$24$	1.63759	+	0.564190i	0.334271	+	0.115165i
$25$			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	−0.522526	−	0.852624i	$-0.675010\pi$
$29$	1.77763	−	1.77763i	0.330098	−	0.330098i	0.852624	+	0.522526i	$0.175010\pi$
$30$	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
$39$	−3.16503	+	9.18664i	−0.506810	+	1.47104i
$40$		−	1.00000i		−	0.158114i
$41$	12.4094			1.93803			0.969014	−	0.247005i	$-0.0794464\pi$
$41$	12.4094			1.93803			0.969014	+	0.247005i	$0.0794464\pi$
$42$	−1.08618	+	3.15269i	−0.167601	+	0.486471i
$43$	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
$45$	−2.97777	+	0.364556i	−0.443899	+	0.0543448i
$46$	−1.52130			−0.224304
$47$		−	3.47762i		−	0.507263i	−0.967301	−	0.253632i	$-0.918375\pi$
$47$		−	3.47762i		−	0.507263i	0.967301	−	0.253632i	$-0.0816251\pi$
$48$	−1.55689	+	0.759006i	−0.224718	+	0.109553i
$49$	−3.29358			−0.470512
$50$	−0.707107	−	0.707107i	−0.100000	−	0.100000i
$51$	8.88841	+	3.06228i	1.24463	+	0.428805i
$52$	3.96677	+	3.96677i	0.550092	+	0.550092i
$53$			3.95819i			0.543699i	0.962340	+	0.271849i	$0.0876352\pi$
$53$			3.95819i			0.543699i	−0.962340	+	0.271849i	$0.912365\pi$
$54$	2.82772	+	4.35936i	0.384804	+	0.593234i
$55$	−3.66800	−	3.66800i	−0.494593	−	0.494593i
$56$	1.36133	+	1.36133i	0.181915	+	0.181915i
$57$	0.0789750	−	0.229228i	0.0104605	−	0.0303620i
$58$			2.51395i			0.330098i
$59$	−7.83820	−	7.83820i	−1.02045	−	1.02045i	−0.999787	−	0.0206604i	$-0.993423\pi$
$59$	−7.83820	−	7.83820i	−1.02045	−	1.02045i	−0.0206604	−	0.999787i	$-0.506577\pi$
$60$	−0.564190	+	1.63759i	−0.0728366	+	0.211412i
$61$	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
$66$	−2.92664	+	8.49472i	−0.360245	+	1.04563i
$67$			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
$69$	2.49127	+	0.858304i	0.299913	+	0.103328i
$70$	1.92521			0.230106
$71$		−	1.23955i		−	0.147107i	−0.997291	−	0.0735537i	$-0.976566\pi$
$71$		−	1.23955i		−	0.147107i	0.997291	−	0.0735537i	$-0.0234340\pi$
$72$	2.97777	−	0.364556i	0.350933	−	0.0429633i
$73$		−	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	$-0.831860\pi$
$83$		−	9.18336i		−	1.00800i	0.863702	−	0.504002i	$-0.168140\pi$
$84$	−1.46124	−	2.99733i	−0.159435	−	0.327036i
$85$		−	5.42775i		−	0.588722i
$86$			10.2078i			1.10073i
$87$	1.41835	−	4.11681i	0.152063	−	0.441369i
$88$	3.66800	+	3.66800i	0.391010	+	0.391010i
$89$	5.54999	−	5.54999i	0.588297	−	0.588297i	−0.348873	−	0.937170i	$-0.613435\pi$
$89$	5.54999	−	5.54999i	0.588297	−	0.588297i	0.937170	+	0.348873i	$0.113435\pi$
$90$	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
$93$	−10.3250	−	3.55723i	−1.07065	−	0.368867i
$94$	2.45905	+	2.45905i	0.253632	+	0.253632i
$95$	−0.139979			−0.0143616
$96$	0.564190	−	1.63759i	0.0575824	−	0.167135i
$97$	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	$-0.553439\pi$
$101$	−3.35861			−0.334194			−0.167097	+	0.985940i	$0.553439\pi$
$102$	−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
$105$	−3.15269	−	1.08618i	−0.307671	−	0.106000i
$106$	−2.79886	−	2.79886i	−0.271849	−	0.271849i
$107$			11.3682i			1.09901i	0.835492	+	0.549503i	$0.185183\pi$
$107$			11.3682i			1.09901i	−0.835492	+	0.549503i	$0.814817\pi$
$108$	−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
$111$	−7.92611	+	6.94095i	−0.752313	+	0.658805i
$112$	−1.92521			−0.181915
$113$	−14.1216	+	14.1216i	−1.32844	+	1.32844i	−0.421716	+	0.906728i	$0.638572\pi$
$113$	−14.1216	+	14.1216i	−1.32844	+	1.32844i	−0.906728	+	0.421716i	$0.861428\pi$
$114$	0.106245	+	0.217933i	0.00995078	+	0.0204113i
$115$		−	1.52130i		−	0.141862i
$116$	−1.77763	−	1.77763i	−0.165049	−	0.165049i
$117$	2.04511	+	16.7049i	0.189070	+	1.54437i
$118$	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
$126$	0.701845	+	5.73281i	0.0625253	+	0.510720i
$127$	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
$129$	5.75911	−	16.7161i	0.507061	−	1.47177i
$130$	−3.96677	+	3.96677i	−0.347909	+	0.347909i
$131$	−5.14147	+	5.14147i	−0.449212	+	0.449212i	−0.895093	−	0.445880i	$-0.852891\pi$
$131$	−5.14147	+	5.14147i	−0.449212	+	0.449212i	0.445880	+	0.895093i	$0.352891\pi$
$132$	−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
$135$	−4.35936	+	2.82772i	−0.375194	+	0.243371i
$136$			5.42775i			0.465426i
$137$			2.67319i			0.228386i	0.993459	+	0.114193i	$0.0364282\pi$
$137$			2.67319i			0.228386i	−0.993459	+	0.114193i	$0.963572\pi$
$138$	−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	$-0.873587\pi$
$149$		−	9.44249i		−	0.773559i	0.922172	−	0.386779i	$-0.126413\pi$
$150$	−1.63759	−	0.564190i	−0.133708	−	0.0460659i
$151$		−	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
$153$	16.1626	−	1.97872i	1.30667	−	0.159970i
$154$	−7.06166	+	7.06166i	−0.569045	+	0.569045i
$155$			6.30502i			0.506431i
$156$	9.18664	+	3.16503i	0.735519	+	0.253405i
$157$	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
$162$	7.71123	+	4.64079i	0.605851	+	0.364615i
$163$	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
$165$	−8.49472	−	2.92664i	−0.661313	−	0.227839i
$166$	6.49361	+	6.49361i	0.504002	+	0.504002i
$167$	12.7580	+	12.7580i	0.987247	+	0.987247i	0.999920	−	0.0126725i	$-0.00403390\pi$
$167$	12.7580	+	12.7580i	0.987247	+	0.987247i	−0.0126725	+	0.999920i	$0.504034\pi$
$168$	3.15269	+	1.08618i	0.243235	+	0.0838007i
$169$		−	18.4706i		−	1.42081i
$170$	3.83800	+	3.83800i	0.294361	+	0.294361i
$171$	−0.0510303	−	0.416826i	−0.00390239	−	0.0318755i
$172$	−7.21797	−	7.21797i	−0.550365	−	0.550365i
$173$	4.28631			0.325882			0.162941	−	0.986636i	$-0.447902\pi$
$173$	4.28631			0.325882			0.162941	+	0.986636i	$0.447902\pi$
$174$	1.90810	+	3.91395i	0.144653	+	0.296716i
$175$			1.92521i			0.145532i
$176$	−5.18734			−0.391010
$177$	−18.1525	−	6.25398i	−1.36442	−	0.470078i
$178$			7.84887i			0.588297i
$179$	−6.48181	+	6.48181i	−0.484473	+	0.484473i	−0.906557	−	0.422084i	$-0.861299\pi$
$179$	−6.48181	+	6.48181i	−0.484473	+	0.484473i	0.422084	+	0.906557i	$0.361299\pi$
$180$	0.364556	+	2.97777i	0.0271724	+	0.221950i
$181$	−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
$183$	21.0957	+	7.26800i	1.55944	+	0.537266i
$184$			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	0.968495	−	0.249033i	$-0.0801129\pi$
$191$	9.94316	+	9.94316i	0.719462	+	0.719462i	−0.249033	+	0.968495i	$0.580113\pi$
$192$	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	$0.116027\pi$
$197$			10.0071i			0.712980i	−0.934299	+	0.356490i	$0.883973\pi$
$198$	1.89108	+	15.4467i	0.134393	+	1.09775i
$199$	−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
$204$	3.06228	−	8.88841i	0.214403	−	0.622313i
$205$	−8.77480	−	8.77480i	−0.612858	−	0.612858i
$206$	15.2435			1.06207
$207$	4.53009	−	0.554600i	0.314863	−	0.0385474i
$208$	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
$216$	4.35936	−	2.82772i	0.296617	−	0.192402i
$217$	−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
$222$	0.696619	−	10.5126i	0.0467540	−	0.705559i
$223$	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	0.0878367	−	0.996135i	$-0.472005\pi$
$227$	−13.6849	−	13.6849i	−0.908298	−	0.908298i	−0.996135	+	0.0878367i	$0.972005\pi$
$228$	−0.229228	−	0.0789750i	−0.0151810	−	0.00523024i
$229$	−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	$-0.665175\pi$
$233$	−15.1403			−0.991875			−0.495937	+	0.868358i	$0.665175\pi$
$234$	−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
$237$	−0.607229	+	1.76251i	−0.0394437	+	0.114487i
$238$	−10.4495			−0.677343
$239$	−5.80735	−	5.80735i	−0.375647	−	0.375647i	0.493882	−	0.869529i	$-0.335577\pi$
$239$	−5.80735	−	5.80735i	−0.375647	−	0.375647i	−0.869529	+	0.493882i	$0.835577\pi$
$240$	1.63759	+	0.564190i	0.105706	+	0.0364183i
$241$	−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
$246$	−7.00128	+	20.3215i	−0.446385	+	1.29565i
$247$			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	−0.377927	−	0.925835i	$-0.623363\pi$
$251$	8.68049	−	8.68049i	0.547908	−	0.547908i	0.925835	+	0.377927i	$0.123363\pi$
$252$	−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	0.879537	−	0.475830i	$-0.157852\pi$
$257$	6.47192	+	6.47192i	0.403707	+	0.403707i	−0.475830	+	0.879537i	$0.657852\pi$
$258$	7.74775	+	15.8924i	0.482354	+	0.989415i
$259$	−11.2999	+	3.07412i	−0.702140	+	0.191017i
$260$		−	5.60986i		−	0.347909i
$261$	−0.916476	−	7.48596i	−0.0567284	−	0.463369i
$262$		−	7.27114i		−	0.449212i
$263$	−21.9588			−1.35404			−0.677019	−	0.735966i	$-0.736728\pi$
$263$	−21.9588			−1.35404			−0.677019	+	0.735966i	$0.736728\pi$
$264$	8.49472	+	2.92664i	0.522814	+	0.180122i
$265$	2.79886	−	2.79886i	0.171933	−	0.171933i
$266$			0.269489i			0.0165234i
$267$	4.42825	−	12.8532i	0.271005	−	0.786603i
$268$	9.29823			0.567980
$269$		−	0.470491i		−	0.0286863i	−0.999897	−	0.0143432i	$-0.995434\pi$
$269$		−	0.470491i		−	0.0286863i	0.999897	−	0.0143432i	$-0.00456573\pi$
$270$	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
$273$	−6.09333	+	17.6862i	−0.368785	+	1.07042i
$274$	−1.89023	−	1.89023i	−0.114193	−	0.114193i
$275$			5.18734i			0.312808i
$276$	0.858304	−	2.49127i	0.0516638	−	0.149957i
$277$	−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
$279$	−18.7749	+	2.29853i	−1.12402	+	0.137610i
$280$		−	1.92521i		−	0.115053i
$281$	−16.4406	−	16.4406i	−0.980762	−	0.980762i	0.0190566	−	0.999818i	$-0.493934\pi$
$281$	−16.4406	−	16.4406i	−0.980762	−	0.980762i	−0.999818	+	0.0190566i	$0.993934\pi$
$282$	5.69490	+	1.96204i	0.339127	+	0.116838i
$283$	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
$288$	−0.364556	−	2.97777i	−0.0214817	−	0.175467i
$289$			12.4605i			0.732968i
$290$	1.77763	−	1.77763i	0.104386	−	0.104386i
$291$	3.06745	−	8.90341i	0.179817	−	0.521927i
$292$	−6.92368			−0.405178
$293$			22.5243i			1.31588i	0.753069	+	0.657942i	$0.228573\pi$
$293$			22.5243i			1.31588i	−0.753069	+	0.657942i	$0.771427\pi$
$294$	1.85821	−	5.39353i	0.108373	−	0.314557i
$295$			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
$309$	−24.9626	−	8.60024i	−1.42007	−	0.489250i
$310$	−4.45832	−	4.45832i	−0.253216	−	0.253216i
$311$	18.1688	−	18.1688i	1.03026	−	1.03026i	0.0307306	−	0.999528i	$-0.490217\pi$
$311$	18.1688	−	18.1688i	1.03026	−	1.03026i	0.999528	−	0.0307306i	$-0.00978340\pi$
$312$	−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
$315$	−5.73281	+	0.701845i	−0.323007	+	0.0395445i
$316$	0.761048	+	0.761048i	0.0428123	+	0.0428123i
$317$	11.6758			0.655777			0.327889	−	0.944716i	$-0.393663\pi$
$317$	11.6758			0.655777			0.327889	+	0.944716i	$0.393663\pi$
$318$	−6.48187	−	2.23317i	−0.363485	−	0.125230i
$319$	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
$327$	−9.03596	+	26.2273i	−0.499690	+	1.45037i
$328$	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
$333$	−7.07188	+	16.8223i	−0.387536	+	0.921854i
$334$	−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
$339$	−11.2674	+	32.7041i	−0.611960	+	1.77624i
$340$	−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	−0.625640	−	0.780112i	$-0.715162\pi$
$347$	2.87749	−	2.87749i	0.154472	−	0.154472i	0.780112	+	0.625640i	$0.215162\pi$
$348$	−4.11681	−	1.41835i	−0.220684	−	0.0760313i
$349$	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
$351$	15.8631	+	24.4554i	0.846710	+	1.30533i
$352$	3.66800	−	3.66800i	0.195505	−	0.195505i
$353$	−8.81237	+	8.81237i	−0.469035	+	0.469035i	−0.901602	−	0.432567i	$-0.857608\pi$
$353$	−8.81237	+	8.81237i	−0.469035	+	0.469035i	0.432567	+	0.901602i	$0.357608\pi$
$354$	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
$357$	17.1120	+	5.89552i	0.905664	+	0.312024i
$358$		−	9.16666i		−	0.484473i
$359$		−	10.4710i		−	0.552637i	−0.961066	−	0.276319i	$-0.910886\pi$
$359$		−	10.4710i		−	0.552637i	0.961066	−	0.276319i	$-0.0891145\pi$
$360$	−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
$372$	−3.55723	+	10.3250i	−0.184434	+	0.535327i
$373$			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
$375$	0.564190	−	1.63759i	0.0291346	−	0.0845646i
$376$	2.45905	−	2.45905i	0.126816	−	0.126816i
$377$			14.1029i			0.726337i
$378$	5.44394	+	8.39266i	0.280006	+	0.431672i
$379$	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	0.785917	−	0.618332i	$-0.212191\pi$
$383$	3.27972	+	3.27972i	0.167586	+	0.167586i	−0.618332	+	0.785917i	$0.712191\pi$
$384$	−1.63759	−	0.564190i	−0.0835677	−	0.0287912i
$385$	−7.06166	−	7.06166i	−0.359895	−	0.359895i
$386$		−	21.1196i		−	1.07496i
$387$	−3.72130	−	30.3963i	−0.189164	−	1.54513i
$388$	−3.84448	−	3.84448i	−0.195174	−	0.195174i
$389$	−17.5886	−	17.5886i	−0.891778	−	0.891778i	0.102912	−	0.994690i	$-0.467184\pi$
$389$	−17.5886	−	17.5886i	−0.891778	−	0.891778i	−0.994690	+	0.102912i	$0.967184\pi$
$390$	−3.16503	+	9.18664i	−0.160267	+	0.465183i
$391$			8.25726i			0.417587i
$392$	−2.32892	−	2.32892i	−0.117628	−	0.117628i
$393$	−4.10230	+	11.9071i	−0.206934	+	0.600634i
$394$	−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
$399$	0.152043	−	0.441312i	0.00761167	−	0.0220932i
$400$		−	1.00000i		−	0.0500000i
$401$	19.3076	−	19.3076i	0.964177	−	0.964177i	−0.0352035	−	0.999380i	$-0.511208\pi$
$401$	19.3076	−	19.3076i	0.964177	−	0.964177i	0.999380	+	0.0352035i	$0.0112079\pi$
$402$	−15.2267	−	5.24597i	−0.759436	−	0.261645i
$403$	35.3703			1.76192
$404$			3.35861i			0.167097i
$405$	−4.64079	+	7.71123i	−0.230603	+	0.383174i
$406$			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	$0.222928\pi$
$419$			26.3846i			1.28897i	−0.764617	+	0.644485i	$0.777072\pi$
$420$	−1.08618	+	3.15269i	−0.0530002	+	0.153836i
$421$	−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
$426$	2.02987	+	0.699341i	0.0983475	+	0.0338832i
$427$	17.5369	+	17.5369i	0.848668	+	0.848668i
$428$	11.3682			0.549503
$429$	−16.4181	+	47.6542i	−0.792672	+	2.30077i
$430$	7.21797	−	7.21797i	0.348082	−	0.348082i
$431$	−16.8691	+	16.8691i	−0.812557	+	0.812557i	−0.985017	−	0.172460i	$-0.944828\pi$
$431$	−16.8691	+	16.8691i	−0.812557	+	0.812557i	0.172460	+	0.985017i	$0.444828\pi$
$432$	−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
$438$	11.3381	+	3.90627i	0.541756	+	0.186649i
$439$	−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	$-0.718603\pi$
$443$	−26.6898			−1.26807			−0.634035	+	0.773304i	$0.718603\pi$
$444$	6.94095	+	7.92611i	0.329403	+	0.376157i
$445$	−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	0.435039	−	0.900412i	$-0.356735\pi$
$449$	−9.86107	−	9.86107i	−0.465372	−	0.465372i	−0.900412	+	0.435039i	$0.856735\pi$
$450$	−2.97777	+	0.364556i	−0.140373	+	0.0171853i
$451$	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
$459$	23.6615	−	15.3481i	1.10442	−	0.716390i
$460$	−1.52130			−0.0709311
$461$	14.2328	+	14.2328i	0.662887	+	0.662887i	0.956060	−	0.293172i	$-0.0947110\pi$
$461$	14.2328	+	14.2328i	0.662887	+	0.662887i	−0.293172	+	0.956060i	$0.594711\pi$
$462$	−5.63439	+	16.3541i	−0.262136	+	0.760860i
$463$	−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	0.871828	−	0.489811i	$-0.162934\pi$
$467$	8.25546	+	8.25546i	0.382017	+	0.382017i	−0.489811	+	0.871828i	$0.662934\pi$
$468$	16.7049	−	2.04511i	0.772183	−	0.0945352i
$469$			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	0.968732	−	0.248110i	$-0.0798095\pi$
$479$	15.7716	+	15.7716i	0.720622	+	0.720622i	−0.248110	+	0.968732i	$0.579810\pi$
$480$	−1.55689	+	0.759006i	−0.0710620	+	0.0346437i
$481$	16.9487	−	29.6168i	0.772793	−	1.35041i
$482$		−	26.3424i		−	1.19987i
$483$	4.79620	+	1.65241i	0.218235	+	0.0751873i
$484$		−	15.9085i		−	0.723113i
$485$	−5.43691			−0.246877
$486$	15.5279	+	1.37234i	0.704361	+	0.0622506i
$487$	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
$489$	32.9630	+	11.3566i	1.49064	+	0.513562i
$490$	−3.29358			−0.148789
$491$			30.8895i			1.39402i	0.717059	+	0.697012i	$0.245488\pi$
$491$			30.8895i			1.39402i	−0.717059	+	0.697012i	$0.754512\pi$
$492$	−9.41884	−	19.3201i	−0.424634	−	0.871019i
$493$	13.6451			0.614544
$494$	−0.555266	−	0.555266i	−0.0249826	−	0.0249826i
$495$	−15.4467	+	1.89108i	−0.694277	+	0.0849975i
$496$	4.45832	+	4.45832i	0.200185	+	0.200185i
$497$		−	2.38639i		−	0.107044i
$498$	15.0385	+	5.18116i	0.673893	+	0.232173i
$499$	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
$501$	29.5463	+	10.1795i	1.32003	+	0.454784i
$502$			12.2761i			0.547908i
$503$	19.1000	+	19.1000i	0.851627	+	0.851627i	0.990333	−	0.138707i	$-0.0442946\pi$
$503$	19.1000	+	19.1000i	0.851627	+	0.851627i	−0.138707	+	0.990333i	$0.544295\pi$
$504$	5.73281	−	0.701845i	0.255360	−	0.0312627i
$505$	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	$-0.260135\pi$
$509$	30.8742			1.36848			0.684238	+	0.729259i	$0.260135\pi$
$510$	8.88841	+	3.06228i	0.393585	+	0.135600i
$511$		−	13.3295i		−	0.589662i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−0.395822	−	0.610220i	−0.0174760	−	0.0269419i
$514$	−9.15268			−0.403707
$515$			15.2435i			0.671709i
$516$	−16.7161	−	5.75911i	−0.735884	−	0.253531i
$517$		−	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	$-0.637594\pi$
$521$	−19.1245			−0.837858			−0.418929	+	0.908019i	$0.637594\pi$
$522$	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
$531$	−33.0082	+	4.04106i	−1.43244	+	0.175367i
$532$	−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
$537$	−5.17174	+	15.0112i	−0.223177	+	0.647781i
$538$	0.332687	+	0.332687i	0.0143432	+	0.0143432i
$539$	−17.0849			−0.735901
$540$	2.82772	+	4.35936i	0.121686	+	0.187597i
$541$	−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
$549$	38.3602	−	4.69628i	1.63717	−	0.200432i
$550$	−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
$555$	10.5126	+	0.696619i	0.446235	+	0.0295698i
$556$	−10.8710			−0.461034
$557$	−4.85816	+	4.85816i	−0.205847	+	0.205847i	−0.802500	−	0.596653i	$-0.796497\pi$
$557$	−4.85816	+	4.85816i	−0.205847	+	0.205847i	0.596653	+	0.802500i	$0.296497\pi$
$558$	11.6505	−	14.9012i	0.493207	−	0.630816i
$559$			57.2641i			2.42201i
$560$	1.36133	+	1.36133i	0.0575265	+	0.0575265i
$561$	46.1072	+	15.8851i	1.94665	+	0.670669i
$562$	23.2505			0.980762
$563$	18.9481	+	18.9481i	0.798568	+	0.798568i	0.982870	−	0.184302i	$-0.0590025\pi$
$563$	18.9481	+	18.9481i	0.798568	+	0.798568i	−0.184302	+	0.982870i	$0.559002\pi$
$564$	−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	−0.865276	−	0.501297i	$-0.832857\pi$
$569$	−8.68225	+	8.68225i	−0.363979	+	0.363979i	0.501297	+	0.865276i	$0.332857\pi$
$570$	0.0789750	−	0.229228i	0.00330790	−	0.00960132i
$571$	−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
$573$	23.0273	+	7.93350i	0.961980	+	0.331427i
$574$	−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
$579$	−11.9155	+	34.5852i	−0.495190	+	1.43731i
$580$			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	$-0.472058\pi$
$587$	26.2589	−	26.2589i	1.08382	−	1.08382i	0.996150	−	0.0876694i	$-0.0279419\pi$
$588$	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	$-0.636123\pi$
$593$		−	44.3173i		−	1.81989i	0.414727	−	0.909946i	$-0.363877\pi$
$594$	14.6683	+	22.6135i	0.601849	+	0.927842i
$595$		−	10.4495i		−	0.428389i
$596$	−9.44249			−0.386779
$597$	−28.3660	−	9.77279i	−1.16094	−	0.399974i
$598$	6.03466	−	6.03466i	0.246776	−	0.246776i
$599$			9.25641i			0.378207i	0.981957	+	0.189103i	$0.0605581\pi$
$599$			9.25641i			0.378207i	−0.981957	+	0.189103i	$0.939442\pi$
$600$	−0.564190	+	1.63759i	−0.0230330	+	0.0668542i
$601$	−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
$606$	1.89489	−	5.50001i	0.0769748	−	0.223423i
$607$	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
$609$	2.73061	−	7.92571i	0.110650	−	0.321166i
$610$	9.10908	+	9.10908i	0.368816	+	0.368816i
$611$	13.7949	+	13.7949i	0.558083	+	0.558083i
$612$	−1.97872	−	16.1626i	−0.0799850	−	0.653333i
$613$			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
$615$	−20.3215	−	7.00128i	−0.819443	−	0.282319i
$616$	7.06166	+	7.06166i	0.284522	+	0.284522i
$617$	−8.86781			−0.357005			−0.178502	−	0.983939i	$-0.557125\pi$
$617$	−8.86781			−0.357005			−0.178502	+	0.983939i	$0.557125\pi$
$618$	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
$621$	6.63191	−	4.30182i	0.266129	−	0.172626i
$622$			25.6946i			1.03026i
$623$	10.6849	−	10.6849i	0.428080	−	0.428080i
$624$	3.16503	−	9.18664i	0.126703	−	0.367760i
$625$	−1.00000			−0.0400000
$626$			4.97320i			0.198769i
$627$	0.409670	−	1.18909i	0.0163606	−	0.0474875i
$628$		−	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	$-0.921059\pi$
$641$		−	12.4293i		−	0.490929i	0.969406	−	0.245465i	$-0.0789405\pi$
$642$	−18.6164	−	6.41383i	−0.734732	−	0.253134i
$643$	−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	−0.0662961	−	0.997800i	$-0.521118\pi$
$647$	23.6939	−	23.6939i	0.931504	−	0.931504i	0.997800	+	0.0662961i	$0.0211182\pi$
$648$	4.64079	−	7.71123i	0.182308	−	0.302926i
$649$	−40.6594	−	40.6594i	−1.59602	−	1.59602i
$650$	5.60986			0.220037
$651$	−19.8778	−	6.84840i	−0.779072	−	0.268410i
$652$	14.2334	−	14.2334i	0.557421	−	0.557421i
$653$	−16.2030	+	16.2030i	−0.634071	+	0.634071i	−0.949087	−	0.315016i	$-0.897990\pi$
$653$	−16.2030	+	16.2030i	−0.634071	+	0.634071i	0.315016	+	0.949087i	$0.397990\pi$
$654$	−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	$-0.644045\pi$
$659$	−22.4489			−0.874484			−0.437242	+	0.899344i	$0.644045\pi$
$660$	−2.92664	+	8.49472i	−0.113919	+	0.330656i
$661$	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
$666$	−6.89457	−	16.8957i	−0.267159	−	0.654695i
$667$	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
$672$	1.08618	−	3.15269i	0.0419004	−	0.121618i
$673$	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	$-0.253732\pi$
$677$	36.3628			1.39754			0.698769	+	0.715348i	$0.253732\pi$
$678$	−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
$681$	−31.6928	−	10.9190i	−1.21447	−	0.418416i
$682$	32.7063			1.25239
$683$	31.9090	+	31.9090i	1.22097	+	1.22097i	0.967289	+	0.253677i	$0.0816399\pi$
$683$	31.9090	+	31.9090i	1.22097	+	1.22097i	0.253677	+	0.967289i	$0.418360\pi$
$684$	−0.416826	+	0.0510303i	−0.0159377	+	0.00195119i
$685$	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
$690$	2.49127	+	0.858304i	0.0948409	+	0.0326751i
$691$			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	0.520678	−	0.853753i	$-0.325679\pi$
$701$	−8.81865	−	8.81865i	−0.333076	−	0.333076i	−0.853753	+	0.520678i	$0.825679\pi$
$702$	−28.5095	−	6.07567i	−1.07602	−	0.229312i
$703$	−0.422910	+	0.739009i	−0.0159503	+	0.0278722i
$704$			5.18734i			0.195505i
$705$	−1.96204	+	5.69490i	−0.0738946	+	0.214483i
$706$		−	12.4626i		−	0.469035i
$707$	−6.46601			−0.243179
$708$	−6.25398	+	18.1525i	−0.235039	+	0.682212i
$709$	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
$711$	0.392366	+	3.20492i	0.0147149	+	0.120194i
$712$	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
$717$	−13.4492	−	4.63360i	−0.502271	−	0.173045i
$718$	7.40410	+	7.40410i	0.276319	+	0.276319i
$719$		−	32.4752i		−	1.21112i	−0.795799	−	0.605561i	$-0.792949\pi$
$719$		−	32.4752i		−	1.21112i	0.795799	−	0.605561i	$-0.207051\pi$
$720$	2.97777	−	0.364556i	0.110975	−	0.0135862i
$721$	−20.7514	−	20.7514i	−0.772822	−	0.772822i
$722$	−13.4212	−	13.4212i	−0.499484	−	0.499484i
$723$	−14.8621	+	43.1380i	−0.552729	+	1.60432i
$724$			13.5004i			0.501737i
$725$	1.77763	+	1.77763i	0.0660196	+	0.0660196i
$726$	−8.97541	+	26.0515i	−0.333109	+	0.966863i
$727$	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
$732$	7.26800	−	21.0957i	0.268633	−	0.779719i
$733$		−	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
$735$	5.39353	+	1.85821i	0.198943	+	0.0685410i
$736$	1.52130			0.0560760
$737$			48.2331i			1.77669i
$738$	4.52393	+	36.9524i	0.166528	+	1.36024i
$739$			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	$-0.385813\pi$
$743$	19.1398			0.702172			0.351086	+	0.936343i	$0.385813\pi$
$744$	−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
$753$	6.92603	−	20.1031i	0.252399	−	0.732599i
$754$	−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
$759$	12.9230	+	4.45231i	0.469077	+	0.161609i
$760$	−0.0989804	−	0.0989804i	−0.00359040	−	0.00359040i
$761$	13.0239			0.472118			0.236059	−	0.971739i	$-0.424144\pi$
$761$	13.0239			0.472118			0.236059	+	0.971739i	$0.424144\pi$
$762$	−3.44223	+	9.99124i	−0.124699	+	0.361944i
$763$	−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
$771$	14.9883	+	5.16385i	0.539791	+	0.185971i
$772$	14.9338	+	14.9338i	0.537480	+	0.537480i
$773$		−	20.2597i		−	0.728691i	−0.931264	−	0.364345i	$-0.881293\pi$
$773$		−	20.2597i		−	0.728691i	0.931264	−	0.364345i	$-0.118707\pi$
$774$	24.1248	+	18.8621i	0.867148	+	0.677984i
$775$	4.45832	−	4.45832i	0.160148	−	0.160148i
$776$	5.43691			0.195174
$777$	−15.2594	+	13.3627i	−0.547428	+	0.479386i
$778$	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
$783$	−7.10875	−	10.9592i	−0.254046	−	0.391651i
$784$	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
$792$	15.4467	−	1.89108i	0.548874	−	0.0671964i
$793$	−72.2673			−2.56629
$794$	−20.7058	−	20.7058i	−0.734820	−	0.734820i
$795$	2.23317	−	6.48187i	0.0792023	−	0.229888i
$796$	−12.2484	+	12.2484i	−0.434132	+	0.434132i
$797$	15.4144	−	15.4144i	0.546006	−	0.546006i	−0.379277	−	0.925283i	$-0.623827\pi$
$797$	15.4144	−	15.4144i	0.546006	−	0.546006i	0.925283	+	0.379277i	$0.123827\pi$
$798$	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
$801$	−2.86135	−	23.3721i	−0.101101	−	0.825812i
$802$			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	−0.978461	−	0.206430i	$-0.933815\pi$
$809$	−21.9588	+	21.9588i	−0.772032	+	0.772032i	0.206430	+	0.978461i	$0.433815\pi$
$810$	−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
$816$	−8.88841	−	3.06228i	−0.311157	−	0.107201i
$817$		−	1.42888i		−	0.0499900i
$818$	−9.30083			−0.325196
$819$	3.93725	+	32.1603i	0.137579	+	1.12377i
$820$	−8.77480	+	8.77480i	−0.306429	+	0.306429i
$821$		−	11.3942i		−	0.397660i	−0.980034	−	0.198830i	$-0.936286\pi$
$821$		−	11.3942i		−	0.397660i	0.980034	−	0.198830i	$-0.0637141\pi$
$822$	−4.37758	−	1.50819i	−0.152686	−	0.0526040i
$823$	−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	0.721671	−	0.692236i	$-0.243374\pi$
$827$	0.846501	+	0.846501i	0.0294357	+	0.0294357i	−0.692236	+	0.721671i	$0.743374\pi$
$828$	−0.554600	−	4.53009i	−0.0192737	−	0.157431i
$829$	−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
$831$	−48.5190	−	16.7160i	−1.68311	−	0.579873i
$832$	−3.96677	−	3.96677i	−0.137523	−	0.137523i
$833$	−12.6408	−	12.6408i	−0.437977	−	0.437977i
$834$	17.8022	+	6.13332i	0.616441	+	0.212379i
$835$		−	18.0426i		−	0.624390i
$836$	−0.513445	−	0.513445i	−0.0177579	−	0.0177579i
$837$	−27.4859	+	17.8288i	−0.950050	+	0.616254i
$838$	−18.6567	−	18.6567i	−0.644485	−	0.644485i
$839$	24.1404			0.833419			0.416709	−	0.909040i	$-0.363183\pi$
$839$	24.1404			0.833419			0.416709	+	0.909040i	$0.363183\pi$
$840$	−1.46124	−	2.99733i	−0.0504177	−	0.103418i
$841$			22.6800i			0.782071i
$842$	30.5587			1.05312
$843$	−38.0747	−	13.1177i	−1.31136	−	0.451797i
$844$			22.1119i			0.761124i
$845$	−13.0607	+	13.0607i	−0.449300	+	0.449300i
$846$	10.3555	−	1.26779i	0.356031	−	0.0435874i
$847$	30.6271			1.05236
$848$		−	3.95819i		−	0.135925i
$849$	8.24962	+	2.84220i	0.283126	+	0.0975442i
$850$		−	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	0.519880	−	0.854239i	$-0.325977\pi$
$857$	−9.78821	−	9.78821i	−0.334359	−	0.334359i	−0.854239	+	0.519880i	$0.825977\pi$
$858$	−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	$-0.930996\pi$
$863$		−	12.6373i		−	0.430178i	0.976595	−	0.215089i	$-0.0690041\pi$
$864$	−2.82772	−	4.35936i	−0.0962009	−	0.148308i
$865$	−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
$870$	1.41835	−	4.11681i	0.0480864	−	0.139573i
$871$	−36.8839	−	36.8839i	−1.24976	−	1.24976i
$872$	−16.0158			−0.542364
$873$	−1.98206	−	16.1899i	−0.0670825	−	0.547943i
$874$	−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	$-0.364408\pi$
$881$	24.5294			0.826416			0.413208	+	0.910637i	$0.364408\pi$
$882$	−1.20070	−	9.80753i	−0.0404295	−	0.330237i
$883$	−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	$-0.868236\pi$
$887$	−54.5342			−1.83108			−0.915540	+	0.402227i	$0.868236\pi$
$888$	−10.5126	−	0.696619i	−0.352780	−	0.0233770i
$889$	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
$894$	15.4629	+	5.32736i	0.517156	+	0.178173i
$895$	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
$903$	11.0875	−	32.1819i	0.368968	−	1.07095i
$904$	−19.9709			−0.664222
$905$	9.54619	+	9.54619i	0.317326	+	0.317326i
$906$	20.3111	+	6.99768i	0.674791	+	0.232482i
$907$	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	0.646932	−	0.762548i	$-0.276052\pi$
$911$	−3.48960	−	3.48960i	−0.115616	−	0.115616i	−0.762548	+	0.646932i	$0.776052\pi$
$912$	−0.0789750	+	0.229228i	−0.00261512	+	0.00759051i
$913$		−	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
$927$	−45.3916	+	5.55711i	−1.49086	+	0.182520i
$928$		−	2.51395i		−	0.0825245i
$929$	−39.0723			−1.28192			−0.640961	−	0.767574i	$-0.721464\pi$
$929$	−39.0723			−1.28192			−0.640961	+	0.767574i	$0.721464\pi$
$930$	−10.3250	−	3.55723i	−0.338571	−	0.116646i
$931$	−0.326000	+	0.326000i	−0.0106842	+	0.0106842i
$932$			15.1403i			0.495937i
$933$	14.4966	−	42.0771i	0.474598	−	1.37754i
$934$	−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
$939$	2.80583	−	8.14404i	0.0915647	−	0.265771i
$940$	2.45905	+	2.45905i	0.0802053	+	0.0802053i
$941$		−	48.3770i		−	1.57704i	−0.615007	−	0.788522i	$-0.710847\pi$
$941$		−	48.3770i		−	1.57704i	0.615007	−	0.788522i	$-0.289153\pi$
$942$	−4.11212	+	11.9356i	−0.133980	+	0.388883i
$943$	13.3491	+	13.3491i	0.434708	+	0.434708i
$944$	7.83820	+	7.83820i	0.255112	+	0.255112i
$945$	−8.39266	+	5.44394i	−0.273013	+	0.177091i
$946$			52.9511i			1.72159i
$947$	−9.05959	−	9.05959i	−0.294397	−	0.294397i	0.544417	−	0.838814i	$-0.316751\pi$
$947$	−9.05959	−	9.05959i	−0.294397	−	0.294397i	−0.838814	+	0.544417i	$0.816751\pi$
$948$	1.76251	+	0.607229i	0.0572436	+	0.0197219i
$949$	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	$-0.550977\pi$
$953$	−9.84569			−0.318933			−0.159467	+	0.987203i	$0.550977\pi$
$954$	−11.7866	+	1.44298i	−0.381604	+	0.0467182i
$955$		−	14.0617i		−	0.455027i
$956$	−5.80735	+	5.80735i	−0.187823	+	0.187823i
$957$	7.35744	−	21.3553i	0.237832	−	0.690319i
$958$	−22.3044			−0.720622
$959$			5.14644i			0.166187i
$960$	0.564190	−	1.63759i	0.0182091	−	0.0528529i
$961$			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	$-0.958891\pi$
$971$		−	8.02634i		−	0.257577i	0.991672	−	0.128789i	$-0.0411089\pi$
$972$	−11.9503	+	10.0095i	−0.383306	+	0.321055i
$973$		−	20.9289i		−	0.670951i
$974$			18.3634i			0.588400i
$975$	−9.18664	−	3.16503i	−0.294208	−	0.101362i
$976$	−9.10908	−	9.10908i	−0.291575	−	0.291575i
$977$	17.8008	−	17.8008i	0.569499	−	0.569499i	−0.362489	−	0.931988i	$-0.618073\pi$
$977$	17.8008	−	17.8008i	0.569499	−	0.569499i	0.931988	+	0.362489i	$0.118073\pi$
$978$	−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
$981$	5.83866	+	47.6914i	0.186414	+	1.52267i
$982$	−21.8422	−	21.8422i	−0.697012	−	0.697012i
$983$	−49.9878			−1.59436			−0.797181	−	0.603740i	$-0.793677\pi$
$983$	−49.9878			−1.59436			−0.797181	+	0.603740i	$0.793677\pi$
$984$	20.3215	+	7.00128i	0.647827	+	0.223193i
$985$	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
$993$	−0.484624	+	1.40664i	−0.0153791	+	0.0446385i
$994$	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
$999$	1.75806	+	31.5580i	0.0556226	+	0.998452i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.55689 - 0.759006i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.564190 + 1.63759i) q^{6} +1.92521 q^{7} +(0.707107 + 0.707107i) q^{8} +(1.84782 - 2.36338i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.55689 - 0.759006i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.564190 + 1.63759i) 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} +(-1.63759 - 0.564190i) q^{15} -1.00000 q^{16} +(3.83800 + 3.83800i) q^{17} +(0.364556 + 2.97777i) 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} +(1.63759 + 0.564190i) 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} +(-3.16503 + 9.18664i) q^{39} -1.00000i q^{40} +12.4094 q^{41} +(-1.08618 + 3.15269i) q^{42} +(7.21797 - 7.21797i) q^{43} -5.18734i q^{44} +(-2.97777 + 0.364556i) 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} +(8.88841 + 3.06228i) q^{51} +(3.96677 + 3.96677i) q^{52} +3.95819i q^{53} +(2.82772 + 4.35936i) q^{54} +(-3.66800 - 3.66800i) q^{55} +(1.36133 + 1.36133i) q^{56} +(0.0789750 - 0.229228i) q^{57} +2.51395i q^{58} +(-7.83820 - 7.83820i) q^{59} +(-0.564190 + 1.63759i) 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} +(-2.92664 + 8.49472i) q^{66} +9.29823i q^{67} +(3.83800 - 3.83800i) q^{68} +(2.49127 + 0.858304i) q^{69} +1.92521 q^{70} -1.23955i q^{71} +(2.97777 - 0.364556i) 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} +(1.41835 - 4.11681i) 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} +(-10.3250 - 3.55723i) q^{93} +(2.45905 + 2.45905i) q^{94} -0.139979 q^{95} +(0.564190 - 1.63759i) 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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