LMFDB - Embedded newform 930.2.o.d.491.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(161,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("930.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.o (of order $6$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.1
Character	$\chi$	$=$	930.491
Dual form			930.2.o.d.161.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.72816 + 0.116014i) q^{3} -1.00000 q^{4} +(0.866025 - 0.500000i) q^{5} +(0.116014 + 1.72816i) q^{6} +(0.262744 - 0.455085i) q^{7} +1.00000i q^{8} +(2.97308 - 0.400981i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.72816 + 0.116014i) q^{3} -1.00000 q^{4} +(0.866025 - 0.500000i) q^{5} +(0.116014 + 1.72816i) q^{6} +(0.262744 - 0.455085i) q^{7} +1.00000i q^{8} +(2.97308 - 0.400981i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-0.205905 - 0.356638i) q^{11} +(1.72816 - 0.116014i) q^{12} +(1.67065 - 0.964551i) q^{13} +(-0.455085 - 0.262744i) q^{14} +(-1.43862 + 0.964551i) q^{15} +1.00000 q^{16} +(-1.92064 + 3.32664i) q^{17} +(-0.400981 - 2.97308i) q^{18} +(-1.20732 + 2.09115i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(-0.401267 + 0.816942i) q^{21} +(-0.356638 + 0.205905i) q^{22} +7.98075 q^{23} +(-0.116014 - 1.72816i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.964551 - 1.67065i) q^{26} +(-5.09144 + 1.03788i) q^{27} +(-0.262744 + 0.455085i) q^{28} +7.39923 q^{29} +(0.964551 + 1.43862i) q^{30} +(-1.00963 - 5.47546i) q^{31} -1.00000i q^{32} +(0.397212 + 0.592441i) q^{33} +(3.32664 + 1.92064i) q^{34} -0.525487i q^{35} +(-2.97308 + 0.400981i) q^{36} +(-3.96279 - 2.28792i) q^{37} +(2.09115 + 1.20732i) q^{38} +(-2.77525 + 1.86072i) q^{39} +(0.500000 + 0.866025i) q^{40} +(10.9569 - 6.32599i) q^{41} +(0.816942 + 0.401267i) q^{42} +(-8.27218 - 4.77595i) q^{43} +(0.205905 + 0.356638i) q^{44} +(2.37427 - 1.83380i) q^{45} -7.98075i q^{46} -11.2750i q^{47} +(-1.72816 + 0.116014i) q^{48} +(3.36193 + 5.82304i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(2.93323 - 5.97179i) q^{51} +(-1.67065 + 0.964551i) q^{52} +(-4.96807 - 8.60495i) q^{53} +(1.03788 + 5.09144i) q^{54} +(-0.356638 - 0.205905i) q^{55} +(0.455085 + 0.262744i) q^{56} +(1.84385 - 3.75391i) q^{57} -7.39923i q^{58} +(8.43537 + 4.87016i) q^{59} +(1.43862 - 0.964551i) q^{60} -3.42172i q^{61} +(-5.47546 + 1.00963i) q^{62} +(0.598677 - 1.45836i) q^{63} -1.00000 q^{64} +(0.964551 - 1.67065i) q^{65} +(0.592441 - 0.397212i) q^{66} +(-2.97699 - 5.15630i) q^{67} +(1.92064 - 3.32664i) q^{68} +(-13.7920 + 0.925878i) q^{69} -0.525487 q^{70} +(-5.72724 + 3.30663i) q^{71} +(0.400981 + 2.97308i) q^{72} +(0.0947842 - 0.0547237i) q^{73} +(-2.28792 + 3.96279i) q^{74} +(-0.763610 + 1.55464i) q^{75} +(1.20732 - 2.09115i) q^{76} -0.216401 q^{77} +(1.86072 + 2.77525i) q^{78} +(-13.7211 - 7.92191i) q^{79} +(0.866025 - 0.500000i) q^{80} +(8.67843 - 2.38430i) q^{81} +(-6.32599 - 10.9569i) q^{82} +(2.89939 + 5.02189i) q^{83} +(0.401267 - 0.816942i) q^{84} +3.84127i q^{85} +(-4.77595 + 8.27218i) q^{86} +(-12.7871 + 0.858414i) q^{87} +(0.356638 - 0.205905i) q^{88} +16.9361 q^{89} +(-1.83380 - 2.37427i) q^{90} -1.01372i q^{91} -7.98075 q^{92} +(2.38003 + 9.34534i) q^{93} -11.2750 q^{94} +2.41465i q^{95} +(0.116014 + 1.72816i) q^{96} +12.7503 q^{97} +(5.82304 - 3.36193i) q^{98} +(-0.755178 - 0.977751i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9}+O(q^{10}) $ 36 * q - 36 * q^4 - 8 * q^7 + 8 * q^9	$ 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9} - 18 q^{10} + 36 q^{16} - 4 q^{18} - 4 q^{19} + 72 q^{21} - 18 q^{22} + 18 q^{25} + 8 q^{28} + 52 q^{31} - 36 q^{33} + 18 q^{34} - 8 q^{36} - 54 q^{37} - 8 q^{39} + 18 q^{40} + 12 q^{42} - 18 q^{43} + 4 q^{45} - 62 q^{49} - 10 q^{51} - 18 q^{55} + 12 q^{57} + 88 q^{63} - 36 q^{64} - 4 q^{66} + 10 q^{67} + 46 q^{69} + 16 q^{70} + 4 q^{72} + 24 q^{73} + 4 q^{76} + 92 q^{78} + 42 q^{79} + 4 q^{81} - 12 q^{82} - 72 q^{84} - 16 q^{87} + 18 q^{88} + 8 q^{90} + 48 q^{93} - 92 q^{94} - 80 q^{97} - 18 q^{99}+O(q^{100}) $ 36 * q - 36 * q^4 - 8 * q^7 + 8 * q^9 - 18 * q^10 + 36 * q^16 - 4 * q^18 - 4 * q^19 + 72 * q^21 - 18 * q^22 + 18 * q^25 + 8 * q^28 + 52 * q^31 - 36 * q^33 + 18 * q^34 - 8 * q^36 - 54 * q^37 - 8 * q^39 + 18 * q^40 + 12 * q^42 - 18 * q^43 + 4 * q^45 - 62 * q^49 - 10 * q^51 - 18 * q^55 + 12 * q^57 + 88 * q^63 - 36 * q^64 - 4 * q^66 + 10 * q^67 + 46 * q^69 + 16 * q^70 + 4 * q^72 + 24 * q^73 + 4 * q^76 + 92 * q^78 + 42 * q^79 + 4 * q^81 - 12 * q^82 - 72 * q^84 - 16 * q^87 + 18 * q^88 + 8 * q^90 + 48 * q^93 - 92 * q^94 - 80 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.72816	+	0.116014i	−0.997754	+	0.0669806i
$3$	−1.72816	+	0.116014i	−0.997754	+	0.0669806i
$4$	−1.00000			−0.500000
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	0.116014	+	1.72816i	0.0473625	+	0.705519i
$7$	0.262744	−	0.455085i	0.0993077	−	0.172006i	−0.812091	−	0.583531i	$-0.801671\pi$
$7$	0.262744	−	0.455085i	0.0993077	−	0.172006i	0.911398	+	0.411525i	$0.135004\pi$
$8$			1.00000i			0.353553i
$9$	2.97308	−	0.400981i	0.991027	−	0.133660i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−0.205905	−	0.356638i	−0.0620828	−	0.107530i	0.833313	−	0.552801i	$-0.186441\pi$
$11$	−0.205905	−	0.356638i	−0.0620828	−	0.107530i	−0.895396	+	0.445270i	$0.853108\pi$
$12$	1.72816	−	0.116014i	0.498877	−	0.0334903i
$13$	1.67065	−	0.964551i	0.463356	−	0.267518i	−0.250099	−	0.968220i	$-0.580463\pi$
$13$	1.67065	−	0.964551i	0.463356	−	0.267518i	0.713454	+	0.700702i	$0.247130\pi$
$14$	−0.455085	−	0.262744i	−0.121627	−	0.0702212i
$15$	−1.43862	+	0.964551i	−0.371451	+	0.249046i
$16$	1.00000			0.250000
$17$	−1.92064	+	3.32664i	−0.465823	+	0.806828i	−0.999238	−	0.0390248i	$-0.987575\pi$
$17$	−1.92064	+	3.32664i	−0.465823	+	0.806828i	0.533416	+	0.845853i	$0.320908\pi$
$18$	−0.400981	−	2.97308i	−0.0945122	−	0.700762i
$19$	−1.20732	+	2.09115i	−0.276979	+	0.479742i	−0.970633	−	0.240567i	$-0.922667\pi$
$19$	−1.20732	+	2.09115i	−0.276979	+	0.479742i	0.693653	+	0.720309i	$0.256000\pi$
$20$	−0.866025	+	0.500000i	−0.193649	+	0.111803i
$21$	−0.401267	+	0.816942i	−0.0875636	+	0.178271i
$22$	−0.356638	+	0.205905i	−0.0760355	+	0.0438991i
$23$	7.98075			1.66410			0.832051	−	0.554700i	$-0.187167\pi$
$23$	7.98075			1.66410			0.832051	+	0.554700i	$0.187167\pi$
$24$	−0.116014	−	1.72816i	−0.0236812	−	0.352759i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−0.964551	−	1.67065i	−0.189164	−	0.327642i
$27$	−5.09144	+	1.03788i	−0.979849	+	0.199740i
$28$	−0.262744	+	0.455085i	−0.0496539	+	0.0860030i
$29$	7.39923			1.37400			0.687002	−	0.726656i	$-0.258927\pi$
$29$	7.39923			1.37400			0.687002	+	0.726656i	$0.258927\pi$
$30$	0.964551	+	1.43862i	0.176102	+	0.262656i
$31$	−1.00963	−	5.47546i	−0.181335	−	0.983421i
$31$	−1.00963	−	5.47546i	−0.181335	−	0.983421i
$32$		−	1.00000i		−	0.176777i
$33$	0.397212	+	0.592441i	0.0691458	+	0.103131i
$34$	3.32664	+	1.92064i	0.570514	+	0.329386i
$35$		−	0.525487i		−	0.0888235i
$36$	−2.97308	+	0.400981i	−0.495514	+	0.0668302i
$37$	−3.96279	−	2.28792i	−0.651479	−	0.376131i	0.137544	−	0.990496i	$-0.456079\pi$
$37$	−3.96279	−	2.28792i	−0.651479	−	0.376131i	−0.789023	+	0.614364i	$0.789413\pi$
$38$	2.09115	+	1.20732i	0.339229	+	0.195854i
$39$	−2.77525	+	1.86072i	−0.444396	+	0.297954i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	10.9569	−	6.32599i	1.71119	−	0.987954i	0.778218	−	0.627994i	$-0.216124\pi$
$41$	10.9569	−	6.32599i	1.71119	−	0.987954i	0.932968	−	0.359960i	$-0.117210\pi$
$42$	0.816942	+	0.401267i	0.126057	+	0.0619168i
$43$	−8.27218	−	4.77595i	−1.26150	−	0.728325i	−0.288132	−	0.957591i	$-0.593034\pi$
$43$	−8.27218	−	4.77595i	−1.26150	−	0.728325i	−0.973364	+	0.229265i	$0.926368\pi$
$44$	0.205905	+	0.356638i	0.0310414	+	0.0537652i
$45$	2.37427	−	1.83380i	0.353936	−	0.273367i
$46$		−	7.98075i		−	1.17670i
$47$		−	11.2750i		−	1.64462i	−0.569039	−	0.822311i	$-0.692685\pi$
$47$		−	11.2750i		−	1.64462i	0.569039	−	0.822311i	$-0.307315\pi$
$48$	−1.72816	+	0.116014i	−0.249439	+	0.0167452i
$49$	3.36193	+	5.82304i	0.480276	+	0.831862i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$	2.93323	−	5.97179i	0.410735	−	0.836218i
$52$	−1.67065	+	0.964551i	−0.231678	+	0.133759i
$53$	−4.96807	−	8.60495i	−0.682417	−	1.18198i	−0.974241	−	0.225509i	$-0.927596\pi$
$53$	−4.96807	−	8.60495i	−0.682417	−	1.18198i	0.291824	−	0.956472i	$-0.405738\pi$
$54$	1.03788	+	5.09144i	0.141237	+	0.692858i
$55$	−0.356638	−	0.205905i	−0.0480891	−	0.0277643i
$56$	0.455085	+	0.262744i	0.0608133	+	0.0351106i
$57$	1.84385	−	3.75391i	0.244224	−	0.497217i
$58$		−	7.39923i		−	0.971567i
$59$	8.43537	+	4.87016i	1.09819	+	0.634041i	0.935746	−	0.352676i	$-0.114728\pi$
$59$	8.43537	+	4.87016i	1.09819	+	0.634041i	0.162446	+	0.986717i	$0.448062\pi$
$60$	1.43862	−	0.964551i	0.185726	−	0.124523i
$61$		−	3.42172i		−	0.438106i	−0.975713	−	0.219053i	$-0.929703\pi$
$61$		−	3.42172i		−	0.438106i	0.975713	−	0.219053i	$-0.0702967\pi$
$62$	−5.47546	+	1.00963i	−0.695384	+	0.128223i
$63$	0.598677	−	1.45836i	0.0754263	−	0.183736i
$64$	−1.00000			−0.125000
$65$	0.964551	−	1.67065i	0.119638	−	0.207219i
$66$	0.592441	−	0.397212i	0.0729244	−	0.0488935i
$67$	−2.97699	−	5.15630i	−0.363698	−	0.629943i	0.624869	−	0.780730i	$-0.285153\pi$
$67$	−2.97699	−	5.15630i	−0.363698	−	0.629943i	−0.988566	+	0.150787i	$0.951819\pi$
$68$	1.92064	−	3.32664i	0.232911	−	0.403414i
$69$	−13.7920	+	0.925878i	−1.66036	+	0.111463i
$70$	−0.525487			−0.0628077
$71$	−5.72724	+	3.30663i	−0.679699	+	0.392424i	−0.799742	−	0.600344i	$-0.795030\pi$
$71$	−5.72724	+	3.30663i	−0.679699	+	0.392424i	0.120043	+	0.992769i	$0.461697\pi$
$72$	0.400981	+	2.97308i	0.0472561	+	0.350381i
$73$	0.0947842	−	0.0547237i	0.0110937	−	0.00640493i	−0.494443	−	0.869210i	$-0.664628\pi$
$73$	0.0947842	−	0.0547237i	0.0110937	−	0.00640493i	0.505537	+	0.862805i	$0.331295\pi$
$74$	−2.28792	+	3.96279i	−0.265965	+	0.460665i
$75$	−0.763610	+	1.55464i	−0.0881740	+	0.179514i
$76$	1.20732	−	2.09115i	0.138490	−	0.239871i
$77$	−0.216401			−0.0246612
$78$	1.86072	+	2.77525i	0.210685	+	0.314236i
$79$	−13.7211	−	7.92191i	−1.54375	−	0.891284i	−0.998597	−	0.0529474i	$-0.983138\pi$
$79$	−13.7211	−	7.92191i	−1.54375	−	0.891284i	−0.545152	−	0.838337i	$-0.683528\pi$
$80$	0.866025	−	0.500000i	0.0968246	−	0.0559017i
$81$	8.67843	−	2.38430i	0.964270	−	0.264922i
$82$	−6.32599	−	10.9569i	−0.698589	−	1.20999i
$83$	2.89939	+	5.02189i	0.318249	+	0.551224i	0.980123	−	0.198391i	$-0.0635717\pi$
$83$	2.89939	+	5.02189i	0.318249	+	0.551224i	−0.661873	+	0.749616i	$0.730238\pi$
$84$	0.401267	−	0.816942i	0.0437818	−	0.0891357i
$85$			3.84127i			0.416644i
$86$	−4.77595	+	8.27218i	−0.515004	+	0.892013i
$87$	−12.7871	+	0.858414i	−1.37092	+	0.0920316i
$88$	0.356638	−	0.205905i	0.0380178	−	0.0219496i
$89$	16.9361			1.79522			0.897610	−	0.440790i	$-0.145302\pi$
$89$	16.9361			1.79522			0.897610	+	0.440790i	$0.145302\pi$
$90$	−1.83380	−	2.37427i	−0.193300	−	0.250270i
$91$		−	1.01372i		−	0.106267i
$92$	−7.98075			−0.832051
$93$	2.38003	+	9.34534i	0.246798	+	0.969067i
$94$	−11.2750			−1.16292
$95$			2.41465i			0.247738i
$96$	0.116014	+	1.72816i	0.0118406	+	0.176380i
$97$	12.7503			1.29460			0.647301	−	0.762235i	$-0.275898\pi$
$97$	12.7503			1.29460			0.647301	+	0.762235i	$0.275898\pi$
$98$	5.82304	−	3.36193i	0.588216	−	0.339606i
$99$	−0.755178	−	0.977751i	−0.0758983	−	0.0982676i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$		−	6.15786i		−	0.612730i	−0.951914	−	0.306365i	$-0.900887\pi$
$101$		−	6.15786i		−	0.612730i	0.951914	−	0.306365i	$-0.0991128\pi$
$102$	−5.97179	−	2.93323i	−0.591295	−	0.290433i
$103$	1.09180	+	1.89105i	0.107578	+	0.186331i	0.914789	−	0.403933i	$-0.132357\pi$
$103$	1.09180	+	1.89105i	0.107578	+	0.186331i	−0.807210	+	0.590264i	$0.799024\pi$
$104$	0.964551	+	1.67065i	0.0945821	+	0.163821i
$105$	0.0609638	+	0.908126i	0.00594946	+	0.0886241i
$106$	−8.60495	+	4.96807i	−0.835787	+	0.482542i
$107$	2.72873	+	1.57543i	0.263796	+	0.152303i	0.626065	−	0.779771i	$-0.284664\pi$
$107$	2.72873	+	1.57543i	0.263796	+	0.152303i	−0.362269	+	0.932074i	$0.617998\pi$
$108$	5.09144	−	1.03788i	0.489924	−	0.0998699i
$109$	15.3371			1.46903			0.734515	−	0.678593i	$-0.237410\pi$
$109$	15.3371			1.46903			0.734515	+	0.678593i	$0.237410\pi$
$110$	−0.205905	+	0.356638i	−0.0196323	+	0.0340041i
$111$	7.11377	+	3.49415i	0.675209	+	0.331650i
$112$	0.262744	−	0.455085i	0.0248269	−	0.0430015i
$113$	−16.4689	+	9.50830i	−1.54926	+	0.894466i	−0.551062	+	0.834464i	$0.685777\pi$
$113$	−16.4689	+	9.50830i	−1.54926	+	0.894466i	−0.998198	+	0.0600016i	$0.980889\pi$
$114$	−3.75391	−	1.84385i	−0.351586	−	0.172692i
$115$	6.91153	−	3.99037i	0.644504	−	0.372104i
$116$	−7.39923			−0.687002
$117$	4.58022	−	3.53759i	0.423441	−	0.327050i
$118$	4.87016	−	8.43537i	0.448335	−	0.776539i
$119$	1.00927	+	1.74811i	0.0925196	+	0.160249i
$120$	−0.964551	−	1.43862i	−0.0880511	−	0.131328i
$121$	5.41521	−	9.37941i	0.492291	−	0.852674i
$122$	−3.42172			−0.309788
$123$	−18.2014	+	12.2035i	−1.64117	+	1.10035i
$124$	1.00963	+	5.47546i	0.0906675	+	0.491711i
$125$		−	1.00000i		−	0.0894427i
$126$	−1.45836	−	0.598677i	−0.129921	−	0.0533344i
$127$	−1.69455	−	0.978350i	−0.150367	−	0.0868145i	0.422929	−	0.906163i	$-0.361002\pi$
$127$	−1.69455	−	0.978350i	−0.150367	−	0.0868145i	−0.573296	+	0.819348i	$0.694335\pi$
$128$			1.00000i			0.0883883i
$129$	14.8497	+	7.29392i	1.30745	+	0.642194i
$130$	−1.67065	−	0.964551i	−0.146526	−	0.0845968i
$131$	2.25900	+	1.30423i	0.197370	+	0.113952i	0.595428	−	0.803409i	$-0.296982\pi$
$131$	2.25900	+	1.30423i	0.197370	+	0.113952i	−0.398058	+	0.917360i	$0.630316\pi$
$132$	−0.397212	−	0.592441i	−0.0345729	−	0.0515653i
$133$	0.634434	+	1.09887i	0.0550124	+	0.0952842i
$134$	−5.15630	+	2.97699i	−0.445437	+	0.257173i
$135$	−3.89038	+	3.44455i	−0.334831	+	0.296460i
$136$	−3.32664	−	1.92064i	−0.285257	−	0.164693i
$137$	−0.986737	−	1.70908i	−0.0843027	−	0.146017i	0.820791	−	0.571228i	$-0.193533\pi$
$137$	−0.986737	−	1.70908i	−0.0843027	−	0.146017i	−0.905094	+	0.425212i	$0.860200\pi$
$138$	0.925878	+	13.7920i	0.0788159	+	1.17405i
$139$			6.85664i			0.581573i	0.956788	+	0.290787i	$0.0939169\pi$
$139$			6.85664i			0.581573i	−0.956788	+	0.290787i	$0.906083\pi$
$140$			0.525487i			0.0444118i
$141$	1.30805	+	19.4849i	0.110158	+	1.64093i
$142$	3.30663	+	5.72724i	0.277486	+	0.480620i
$143$	−0.687992	−	0.397212i	−0.0575328	−	0.0332166i
$144$	2.97308	−	0.400981i	0.247757	−	0.0334151i
$145$	6.40792	−	3.69962i	0.532149	−	0.307236i
$146$	−0.0547237	−	0.0947842i	−0.00452897	−	0.00784440i
$147$	−6.48551	−	9.67311i	−0.534916	−	0.797825i
$148$	3.96279	+	2.28792i	0.325739	+	0.188066i
$149$	3.48181	+	2.01022i	0.285241	+	0.164684i	0.635794	−	0.771859i	$-0.280673\pi$
$149$	3.48181	+	2.01022i	0.285241	+	0.164684i	−0.350553	+	0.936543i	$0.614006\pi$
$150$	1.55464	+	0.763610i	0.126936	+	0.0623485i
$151$		−	2.99192i		−	0.243479i	−0.992562	−	0.121739i	$-0.961153\pi$
$151$		−	2.99192i		−	0.243479i	0.992562	−	0.121739i	$-0.0388472\pi$
$152$	−2.09115	−	1.20732i	−0.169614	−	0.0979270i
$153$	−4.37629	+	10.6605i	−0.353802	+	0.861851i
$154$			0.216401i			0.0174381i
$155$	−3.61210	−	4.23707i	−0.290130	−	0.340330i
$156$	2.77525	−	1.86072i	0.222198	−	0.148977i
$157$	−0.0447155			−0.00356868			−0.00178434	−	0.999998i	$-0.500568\pi$
$157$	−0.0447155			−0.00356868			−0.00178434	+	0.999998i	$0.500568\pi$
$158$	−7.92191	+	13.7211i	−0.630233	+	1.09160i
$159$	9.58392	+	14.2944i	0.760054	+	1.13362i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	2.09689	−	3.63192i	0.165258	−	0.286235i
$162$	−2.38430	−	8.67843i	−0.187328	−	0.681842i
$163$	18.7599			1.46939			0.734696	−	0.678397i	$-0.237325\pi$
$163$	18.7599			1.46939			0.734696	+	0.678397i	$0.237325\pi$
$164$	−10.9569	+	6.32599i	−0.855593	+	0.493977i
$165$	0.640216	+	0.314462i	0.0498408	+	0.0244809i
$166$	5.02189	−	2.89939i	0.389774	−	0.225036i
$167$	−3.77154	+	6.53250i	−0.291851	+	0.505500i	−0.974247	−	0.225482i	$-0.927604\pi$
$167$	−3.77154	+	6.53250i	−0.291851	+	0.505500i	0.682397	+	0.730982i	$0.260938\pi$
$168$	−0.816942	−	0.401267i	−0.0630285	−	0.0309584i
$169$	−4.63928	+	8.03547i	−0.356868	+	0.618113i
$170$	3.84127			0.294612
$171$	−2.75096	+	6.70127i	−0.210371	+	0.512459i
$172$	8.27218	+	4.77595i	0.630748	+	0.364163i
$173$	6.51333	−	3.76048i	0.495200	−	0.285904i	−0.231529	−	0.972828i	$-0.574373\pi$
$173$	6.51333	−	3.76048i	0.495200	−	0.285904i	0.726729	+	0.686924i	$0.241040\pi$
$174$	0.858414	+	12.7871i	0.0650762	+	0.969385i
$175$	−0.262744	−	0.455085i	−0.0198615	−	0.0344012i
$176$	−0.205905	−	0.356638i	−0.0155207	−	0.0268826i
$177$	−15.1427	−	7.43781i	−1.13819	−	0.559060i
$178$		−	16.9361i		−	1.26941i
$179$	−4.31907	+	7.48085i	−0.322823	+	0.559145i	−0.981069	−	0.193657i	$-0.937965\pi$
$179$	−4.31907	+	7.48085i	−0.322823	+	0.559145i	0.658247	+	0.752802i	$0.271298\pi$
$180$	−2.37427	+	1.83380i	−0.176968	+	0.136683i
$181$	−21.2217	+	12.2524i	−1.57740	+	0.910711i	−0.582177	+	0.813062i	$0.697799\pi$
$181$	−21.2217	+	12.2524i	−1.57740	+	0.910711i	−0.995221	+	0.0976484i	$0.968868\pi$
$182$	−1.01372			−0.0751418
$183$	0.396966	+	5.91328i	0.0293446	+	0.437122i
$184$			7.98075i			0.588349i
$185$	−4.57584			−0.336422
$186$	9.34534	−	2.38003i	0.685234	−	0.174513i
$187$	1.58188			0.115678
$188$			11.2750i			0.822311i
$189$	−0.865421	+	2.58974i	−0.0629501	+	0.188376i
$190$	2.41465			0.175177
$191$	6.20798	−	3.58418i	0.449193	−	0.259342i	−0.258296	−	0.966066i	$-0.583161\pi$
$191$	6.20798	−	3.58418i	0.449193	−	0.259342i	0.707489	+	0.706724i	$0.249828\pi$
$192$	1.72816	−	0.116014i	0.124719	−	0.00837258i
$193$	−11.0532	+	19.1447i	−0.795627	+	1.37807i	0.126813	+	0.991927i	$0.459525\pi$
$193$	−11.0532	+	19.1447i	−0.795627	+	1.37807i	−0.922440	+	0.386140i	$0.873808\pi$
$194$		−	12.7503i		−	0.915422i
$195$	−1.47308	+	2.99906i	−0.105490	+	0.214767i
$196$	−3.36193	−	5.82304i	−0.240138	−	0.415931i
$197$	0.246916	+	0.427671i	0.0175920	+	0.0304703i	0.874687	−	0.484687i	$-0.161067\pi$
$197$	0.246916	+	0.427671i	0.0175920	+	0.0304703i	−0.857095	+	0.515158i	$0.827733\pi$
$198$	−0.977751	+	0.755178i	−0.0694857	+	0.0536682i
$199$	11.4412	−	6.60560i	0.811048	−	0.468259i	−0.0362718	−	0.999342i	$-0.511548\pi$
$199$	11.4412	−	6.60560i	0.811048	−	0.468259i	0.847320	+	0.531083i	$0.178215\pi$
$200$	0.866025	+	0.500000i	0.0612372	+	0.0353553i
$201$	5.74293	+	8.56555i	0.405075	+	0.604167i
$202$	−6.15786			−0.433265
$203$	1.94410	−	3.36728i	0.136449	−	0.236337i
$204$	−2.93323	+	5.97179i	−0.205367	+	0.418109i
$205$	6.32599	−	10.9569i	0.441826	−	0.765266i
$206$	1.89105	−	1.09180i	0.131756	−	0.0760693i
$207$	23.7274	−	3.20013i	1.64917	−	0.222424i
$208$	1.67065	−	0.964551i	0.115839	−	0.0668796i
$209$	0.994378			0.0687825
$210$	0.908126	−	0.0609638i	0.0626667	−	0.00420690i
$211$	−0.344382	+	0.596487i	−0.0237082	+	0.0410639i	−0.877636	−	0.479328i	$-0.840881\pi$
$211$	−0.344382	+	0.596487i	−0.0237082	+	0.0410639i	0.853928	+	0.520391i	$0.174214\pi$
$212$	4.96807	+	8.60495i	0.341208	+	0.590990i
$213$	9.51399	−	6.37882i	0.651888	−	0.437070i
$214$	1.57543	−	2.72873i	0.107694	−	0.186532i
$215$	−9.55190			−0.651434
$216$	−1.03788	−	5.09144i	−0.0706187	−	0.346429i
$217$	−2.75707	−	0.979173i	−0.187162	−	0.0664706i
$218$		−	15.3371i		−	1.03876i
$219$	−0.157454	+	0.105568i	−0.0106397	+	0.00713360i
$220$	0.356638	+	0.205905i	0.0240445	+	0.0138821i
$221$			7.41021i			0.498465i
$222$	3.49415	−	7.11377i	0.234512	−	0.477445i
$223$	−1.23523	−	0.713160i	−0.0827171	−	0.0477567i	0.458071	−	0.888916i	$-0.348541\pi$
$223$	−1.23523	−	0.713160i	−0.0827171	−	0.0477567i	−0.540788	+	0.841159i	$0.681874\pi$
$224$	−0.455085	−	0.262744i	−0.0304067	−	0.0175553i
$225$	1.13928	−	2.77525i	0.0759521	−	0.185017i
$226$	9.50830	+	16.4689i	0.632483	+	1.09549i
$227$	−15.3135	+	8.84127i	−1.01639	+	0.586816i	−0.913058	−	0.407831i	$-0.866285\pi$
$227$	−15.3135	+	8.84127i	−1.01639	+	0.586816i	−0.103337	+	0.994646i	$0.532952\pi$
$228$	−1.84385	+	3.75391i	−0.122112	+	0.248609i
$229$	−12.9472	−	7.47510i	−0.855578	−	0.493968i	0.00695097	−	0.999976i	$-0.497787\pi$
$229$	−12.9472	−	7.47510i	−0.855578	−	0.493968i	−0.862529	+	0.506008i	$0.831121\pi$
$230$	−3.99037	−	6.91153i	−0.263118	−	0.455733i
$231$	0.373976	−	0.0251055i	0.0246058	−	0.00165182i
$232$			7.39923i			0.485783i
$233$		−	13.5860i		−	0.890049i	−0.895518	−	0.445025i	$-0.853195\pi$
$233$		−	13.5860i		−	0.890049i	0.895518	−	0.445025i	$-0.146805\pi$
$234$	−3.53759	−	4.58022i	−0.231260	−	0.299418i
$235$	−5.63748	−	9.76440i	−0.367749	−	0.636959i
$236$	−8.43537	−	4.87016i	−0.549096	−	0.317021i
$237$	24.6314	+	12.0985i	1.59998	+	0.785881i
$238$	1.74811	−	1.00927i	0.113313	−	0.0654212i
$239$	5.46206	+	9.46057i	0.353311	+	0.611953i	0.986827	−	0.161776i	$-0.0517223\pi$
$239$	5.46206	+	9.46057i	0.353311	+	0.611953i	−0.633516	+	0.773730i	$0.718389\pi$
$240$	−1.43862	+	0.964551i	−0.0928628	+	0.0622615i
$241$	15.2622	+	8.81166i	0.983127	+	0.567609i	0.903213	−	0.429193i	$-0.141202\pi$
$241$	15.2622	+	8.81166i	0.983127	+	0.567609i	0.0799144	+	0.996802i	$0.474535\pi$
$242$	−9.37941	−	5.41521i	−0.602931	−	0.348103i
$243$	−14.7211	+	5.12727i	−0.944360	+	0.328915i
$244$			3.42172i			0.219053i
$245$	5.82304	+	3.36193i	0.372020	+	0.214786i
$246$	12.2035	+	18.2014i	0.778066	+	1.16048i
$247$			4.65811i			0.296388i
$248$	5.47546	−	1.00963i	0.347692	−	0.0641116i
$249$	−5.59322	−	8.34227i	−0.354456	−	0.528670i
$250$	−1.00000			−0.0632456
$251$	−8.77380	+	15.1967i	−0.553797	+	0.959205i	0.444199	+	0.895928i	$0.353488\pi$
$251$	−8.77380	+	15.1967i	−0.553797	+	0.959205i	−0.997996	+	0.0632767i	$0.979845\pi$
$252$	−0.598677	+	1.45836i	−0.0377131	+	0.0918681i
$253$	−1.64328	−	2.84624i	−0.103312	−	0.178942i
$254$	−0.978350	+	1.69455i	−0.0613871	+	0.106326i
$255$	−0.445641	−	6.63834i	−0.0279071	−	0.415709i
$256$	1.00000			0.0625000
$257$	10.7798	−	6.22374i	0.672427	−	0.388226i	−0.124568	−	0.992211i	$-0.539755\pi$
$257$	10.7798	−	6.22374i	0.672427	−	0.388226i	0.796996	+	0.603985i	$0.206421\pi$
$258$	7.29392	−	14.8497i	0.454100	−	0.924505i
$259$	−2.08240	+	1.20227i	−0.129394	+	0.0747055i
$260$	−0.964551	+	1.67065i	−0.0598189	+	0.103609i
$261$	21.9985	−	2.96695i	1.36167	−	0.183650i
$262$	1.30423	−	2.25900i	0.0805759	−	0.139562i
$263$	−2.05549			−0.126747			−0.0633734	−	0.997990i	$-0.520186\pi$
$263$	−2.05549			−0.126747			−0.0633734	+	0.997990i	$0.520186\pi$
$264$	−0.592441	+	0.397212i	−0.0364622	+	0.0244467i
$265$	−8.60495	−	4.96807i	−0.528598	−	0.305186i
$266$	1.09887	−	0.634434i	0.0673761	−	0.0388996i
$267$	−29.2683	+	1.96482i	−1.79119	+	0.120245i
$268$	2.97699	+	5.15630i	0.181849	+	0.314971i
$269$	9.92480	+	17.1903i	0.605126	+	1.04811i	0.992032	+	0.125989i	$0.0402105\pi$
$269$	9.92480	+	17.1903i	0.605126	+	1.04811i	−0.386906	+	0.922119i	$0.626456\pi$
$270$	3.44455	+	3.89038i	0.209629	+	0.236761i
$271$			12.9670i			0.787686i	0.919178	+	0.393843i	$0.128855\pi$
$271$			12.9670i			0.787686i	−0.919178	+	0.393843i	$0.871145\pi$
$272$	−1.92064	+	3.32664i	−0.116456	+	0.201707i
$273$	0.117605	+	1.75187i	0.00711780	+	0.106028i
$274$	−1.70908	+	0.986737i	−0.103249	+	0.0596110i
$275$	−0.411810			−0.0248331
$276$	13.7920	−	0.925878i	0.830182	−	0.0557313i
$277$		−	11.7583i		−	0.706488i	−0.935531	−	0.353244i	$-0.885079\pi$
$277$		−	11.7583i		−	0.706488i	0.935531	−	0.353244i	$-0.114921\pi$
$278$	6.85664			0.411234
$279$	−5.19727	−	15.8741i	−0.311152	−	0.950360i
$280$	0.525487			0.0314039
$281$		−	16.6048i		−	0.990557i	−0.868734	−	0.495278i	$-0.835066\pi$
$281$		−	16.6048i		−	0.990557i	0.868734	−	0.495278i	$-0.164934\pi$
$282$	19.4849	−	1.30805i	1.16031	−	0.0778933i
$283$	−6.88072			−0.409017			−0.204508	−	0.978865i	$-0.565560\pi$
$283$	−6.88072			−0.409017			−0.204508	+	0.978865i	$0.565560\pi$
$284$	5.72724	−	3.30663i	0.339849	−	0.196212i
$285$	−0.280133	−	4.17290i	−0.0165936	−	0.247181i
$286$	−0.397212	+	0.687992i	−0.0234877	+	0.0406818i
$287$		−	6.64845i		−	0.392446i
$288$	−0.400981	−	2.97308i	−0.0236280	−	0.175191i
$289$	1.12232	+	1.94391i	0.0660185	+	0.114347i
$290$	−3.69962	−	6.40792i	−0.217249	−	0.376286i
$291$	−22.0347	+	1.47922i	−1.29169	+	0.0867132i
$292$	−0.0947842	+	0.0547237i	−0.00554683	+	0.00320246i
$293$	1.87383	+	1.08186i	0.109470	+	0.0632027i	0.553736	−	0.832693i	$-0.313202\pi$
$293$	1.87383	+	1.08186i	0.109470	+	0.0632027i	−0.444265	+	0.895895i	$0.646535\pi$
$294$	−9.67311	+	6.48551i	−0.564147	+	0.378243i
$295$	9.74033			0.567104
$296$	2.28792	−	3.96279i	0.132983	−	0.230333i
$297$	1.41850	+	1.60210i	0.0823098	+	0.0929632i
$298$	2.01022	−	3.48181i	0.116449	−	0.201696i
$299$	13.3331	−	7.69784i	0.771071	−	0.445178i
$300$	0.763610	−	1.55464i	0.0440870	−	0.0897571i
$301$	−4.34693	+	2.50970i	−0.250553	+	0.144657i
$302$	−2.99192			−0.172165
$303$	0.714397	+	10.6418i	0.0410410	+	0.611354i
$304$	−1.20732	+	2.09115i	−0.0692448	+	0.119936i
$305$	−1.71086	−	2.96329i	−0.0979634	−	0.169678i
$306$	10.6605	+	4.37629i	0.609421	+	0.250176i
$307$	12.0776	−	20.9190i	0.689303	−	1.19391i	−0.282761	−	0.959190i	$-0.591250\pi$
$307$	12.0776	−	20.9190i	0.689303	−	1.19391i	0.972064	−	0.234717i	$-0.0754164\pi$
$308$	0.216401			0.0123306
$309$	−2.10619	−	3.14138i	−0.119817	−	0.178707i
$310$	−4.23707	+	3.61210i	−0.240649	+	0.205153i
$311$		−	27.4654i		−	1.55742i	−0.627384	−	0.778710i	$-0.715874\pi$
$311$		−	27.4654i		−	1.55742i	0.627384	−	0.778710i	$-0.284126\pi$
$312$	−1.86072	−	2.77525i	−0.105342	−	0.157118i
$313$	27.6509	+	15.9643i	1.56292	+	0.902353i	0.996959	+	0.0779218i	$0.0248284\pi$
$313$	27.6509	+	15.9643i	1.56292	+	0.902353i	0.565962	+	0.824431i	$0.308505\pi$
$314$			0.0447155i			0.00252344i
$315$	−0.210710	−	1.56232i	−0.0118722	−	0.0880265i
$316$	13.7211	+	7.92191i	0.771875	+	0.445642i
$317$	−8.91264	−	5.14572i	−0.500584	−	0.289012i	0.228371	−	0.973574i	$-0.426660\pi$
$317$	−8.91264	−	5.14572i	−0.500584	−	0.289012i	−0.728955	+	0.684562i	$0.759994\pi$
$318$	14.2944	−	9.58392i	0.801589	−	0.537440i
$319$	−1.52354	−	2.63885i	−0.0853019	−	0.147747i
$320$	−0.866025	+	0.500000i	−0.0484123	+	0.0279508i
$321$	−4.89845	−	2.40603i	−0.273405	−	0.134292i
$322$	−3.63192	−	2.09689i	−0.202399	−	0.116855i
$323$	−4.63766	−	8.03267i	−0.258046	−	0.446950i
$324$	−8.67843	+	2.38430i	−0.482135	+	0.132461i
$325$		−	1.92910i		−	0.107007i
$326$		−	18.7599i		−	1.03902i
$327$	−26.5050	+	1.77932i	−1.46573	+	0.0983965i
$328$	6.32599	+	10.9569i	0.349294	+	0.604996i
$329$	−5.13106	−	2.96242i	−0.282885	−	0.163324i
$330$	0.314462	−	0.640216i	0.0173106	−	0.0352427i
$331$	−20.4858	+	11.8275i	−1.12600	+	0.650097i	−0.942926	−	0.333002i	$-0.891938\pi$
$331$	−20.4858	+	11.8275i	−1.12600	+	0.650097i	−0.183075	+	0.983099i	$0.558605\pi$
$332$	−2.89939	−	5.02189i	−0.159125	−	0.275612i
$333$	−12.6991	−	5.21316i	−0.695907	−	0.285680i
$334$	6.53250	+	3.77154i	0.357443	+	0.206370i
$335$	−5.15630	−	2.97699i	−0.281719	−	0.162651i
$336$	−0.401267	+	0.816942i	−0.0218909	+	0.0445679i
$337$		−	4.92368i		−	0.268210i	−0.990967	−	0.134105i	$-0.957184\pi$
$337$		−	4.92368i		−	0.268210i	0.990967	−	0.134105i	$-0.0428159\pi$
$338$	8.03547	+	4.63928i	0.437072	+	0.252344i
$339$	27.3578	−	18.3425i	1.48587	−	0.996228i
$340$		−	3.84127i		−	0.208322i
$341$	−1.74487	+	1.48750i	−0.0944900	+	0.0805526i
$342$	6.70127	+	2.75096i	0.362363	+	0.148755i
$343$	7.21171			0.389396
$344$	4.77595	−	8.27218i	0.257502	−	0.446006i
$345$	−11.4813	+	7.69784i	−0.618133	+	0.414438i
$346$	−3.76048	−	6.51333i	−0.202164	−	0.350159i
$347$	−3.52558	+	6.10648i	−0.189263	+	0.327813i	−0.945005	−	0.327057i	$-0.893943\pi$
$347$	−3.52558	+	6.10648i	−0.189263	+	0.327813i	0.755742	+	0.654870i	$0.227276\pi$
$348$	12.7871	−	0.858414i	0.685459	−	0.0460158i
$349$	−31.1919			−1.66967			−0.834833	−	0.550504i	$-0.814436\pi$
$349$	−31.1919			−1.66967			−0.834833	+	0.550504i	$0.814436\pi$
$350$	−0.455085	+	0.262744i	−0.0243253	+	0.0140442i
$351$	−7.50495	+	6.64490i	−0.400584	+	0.354678i
$352$	−0.356638	+	0.205905i	−0.0190089	+	0.0109748i
$353$	−9.28933	+	16.0896i	−0.494421	+	0.856363i	−0.999979	−	0.00642991i	$-0.997953\pi$
$353$	−9.28933	+	16.0896i	−0.494421	+	0.856363i	0.505558	+	0.862793i	$0.331287\pi$
$354$	−7.43781	+	15.1427i	−0.395315	+	0.804825i
$355$	−3.30663	+	5.72724i	−0.175497	+	0.303971i
$356$	−16.9361			−0.897610
$357$	−1.94698	−	2.90392i	−0.103045	−	0.153692i
$358$	7.48085	+	4.31907i	0.395375	+	0.228270i
$359$	12.1427	−	7.01060i	0.640868	−	0.370005i	−0.144081	−	0.989566i	$-0.546023\pi$
$359$	12.1427	−	7.01060i	0.640868	−	0.370005i	0.784949	+	0.619561i	$0.212689\pi$
$360$	1.83380	+	2.37427i	0.0966498	+	0.125135i
$361$	6.58473	+	11.4051i	0.346565	+	0.600268i
$362$	12.2524	+	21.2217i	0.643970	+	1.11539i
$363$	−8.27021	+	16.8374i	−0.434073	+	0.883733i
$364$			1.01372i			0.0531333i
$365$	0.0547237	−	0.0947842i	0.00286437	−	0.00496123i
$366$	5.91328	−	0.396966i	0.309092	−	0.0207498i
$367$	−0.308737	+	0.178249i	−0.0161159	+	0.00930454i	−0.508036	−	0.861336i	$-0.669628\pi$
$367$	−0.308737	+	0.178249i	−0.0161159	+	0.00930454i	0.491920	+	0.870640i	$0.336295\pi$
$368$	7.98075			0.416025
$369$	30.0393	−	23.2012i	1.56378	−	1.20781i
$370$			4.57584i			0.237886i
$371$	−5.22131			−0.271077
$372$	−2.38003	−	9.34534i	−0.123399	−	0.484533i
$373$	−25.2094			−1.30529			−0.652646	−	0.757663i	$-0.726341\pi$
$373$	−25.2094			−1.30529			−0.652646	+	0.757663i	$0.726341\pi$
$374$		−	1.58188i		−	0.0817968i
$375$	0.116014	+	1.72816i	0.00599093	+	0.0892419i
$376$	11.2750			0.581461
$377$	12.3615	−	7.13694i	0.636652	−	0.367571i
$378$	2.58974	+	0.865421i	0.133202	+	0.0445124i
$379$	12.6731	−	21.9505i	0.650975	−	1.12752i	−0.331912	−	0.943310i	$-0.607694\pi$
$379$	12.6731	−	21.9505i	0.650975	−	1.12752i	0.982887	−	0.184211i	$-0.0589730\pi$
$380$		−	2.41465i		−	0.123869i
$381$	3.04196	+	1.49415i	0.155844	+	0.0765479i
$382$	−3.58418	−	6.20798i	−0.183382	−	0.317628i
$383$	8.84004	+	15.3114i	0.451705	+	0.782376i	0.998492	−	0.0548956i	$-0.0174826\pi$
$383$	8.84004	+	15.3114i	0.451705	+	0.782376i	−0.546787	+	0.837272i	$0.684149\pi$
$384$	−0.116014	−	1.72816i	−0.00592031	−	0.0881899i
$385$	−0.187409	+	0.108201i	−0.00955124	+	0.00551441i
$386$	19.1447	+	11.0532i	0.974440	+	0.562593i
$387$	−26.5089	−	10.8823i	−1.34753	−	0.553178i
$388$	−12.7503			−0.647301
$389$	−10.8121	+	18.7271i	−0.548194	+	0.949500i	0.450204	+	0.892926i	$0.351351\pi$
$389$	−10.8121	+	18.7271i	−0.548194	+	0.949500i	−0.998398	+	0.0565746i	$0.981982\pi$
$390$	2.99906	+	1.47308i	0.151863	+	0.0745924i
$391$	−15.3281	+	26.5491i	−0.775176	+	1.34264i
$392$	−5.82304	+	3.36193i	−0.294108	+	0.169803i
$393$	−4.05523	−	1.99185i	−0.204559	−	0.100476i
$394$	0.427671	−	0.246916i	0.0215457	−	0.0124394i
$395$	−15.8438			−0.797189
$396$	0.755178	+	0.977751i	0.0379491	+	0.0491338i
$397$	3.04676	−	5.27715i	0.152913	−	0.264853i	−0.779384	−	0.626546i	$-0.784468\pi$
$397$	3.04676	−	5.27715i	0.152913	−	0.264853i	0.932297	+	0.361694i	$0.117801\pi$
$398$	−6.60560	−	11.4412i	−0.331109	−	0.573497i
$399$	−1.22389	−	1.82542i	−0.0612710	−	0.0913855i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	3.38331			0.168954			0.0844772	−	0.996425i	$-0.473078\pi$
$401$	3.38331			0.168954			0.0844772	+	0.996425i	$0.473078\pi$
$402$	8.56555	−	5.74293i	0.427211	−	0.286431i
$403$	−6.96810	−	8.17375i	−0.347106	−	0.407163i
$404$			6.15786i			0.306365i
$405$	6.32359	−	6.40408i	0.314222	−	0.318221i
$406$	−3.36728	−	1.94410i	−0.167115	−	0.0964841i
$407$			1.88438i			0.0934051i
$408$	5.97179	+	2.93323i	0.295648	+	0.145217i
$409$	0.373409	+	0.215588i	0.0184639	+	0.0106601i	0.509204	−	0.860646i	$-0.329940\pi$
$409$	0.373409	+	0.215588i	0.0184639	+	0.0106601i	−0.490740	+	0.871306i	$0.663273\pi$
$410$	−10.9569	−	6.32599i	−0.541125	−	0.312418i
$411$	1.90352	+	2.83909i	0.0938936	+	0.140042i
$412$	−1.09180	−	1.89105i	−0.0537891	−	0.0931655i
$413$	4.43268	−	2.55921i	0.218118	−	0.125930i
$414$	−3.20013	−	23.7274i	−0.157278	−	1.16614i
$415$	5.02189	+	2.89939i	0.246515	+	0.142325i
$416$	−0.964551	−	1.67065i	−0.0472910	−	0.0819105i
$417$	−0.795466	−	11.8494i	−0.0389541	−	0.580267i
$418$		−	0.994378i		−	0.0486366i
$419$			39.1620i			1.91319i	0.291422	+	0.956595i	$0.405872\pi$
$419$			39.1620i			1.91319i	−0.291422	+	0.956595i	$0.594128\pi$
$420$	−0.0609638	−	0.908126i	−0.00297473	−	0.0443120i
$421$	−11.5115	−	19.9385i	−0.561036	−	0.971743i	−0.997406	−	0.0719760i	$-0.977070\pi$
$421$	−11.5115	−	19.9385i	−0.561036	−	0.971743i	0.436370	−	0.899767i	$-0.356264\pi$
$422$	0.596487	+	0.344382i	0.0290365	+	0.0167643i
$423$	−4.52105	−	33.5214i	−0.219821	−	1.62986i
$424$	8.60495	−	4.96807i	0.417893	−	0.241271i
$425$	1.92064	+	3.32664i	0.0931645	+	0.161366i
$426$	−6.37882	−	9.51399i	−0.309055	−	0.460954i
$427$	−1.55717	−	0.899034i	−0.0753568	−	0.0435073i
$428$	−2.72873	−	1.57543i	−0.131898	−	0.0761514i
$429$	1.23504	+	0.606630i	0.0596284	+	0.0292884i
$430$			9.55190i			0.460633i
$431$	−11.5613	−	6.67493i	−0.556889	−	0.321520i	0.195007	−	0.980802i	$-0.437527\pi$
$431$	−11.5613	−	6.67493i	−0.556889	−	0.321520i	−0.751896	+	0.659282i	$0.770860\pi$
$432$	−5.09144	+	1.03788i	−0.244962	+	0.0499350i
$433$		−	7.69946i		−	0.370012i	−0.982737	−	0.185006i	$-0.940769\pi$
$433$		−	7.69946i		−	0.370012i	0.982737	−	0.185006i	$-0.0592305\pi$
$434$	−0.979173	+	2.75707i	−0.0470018	+	0.132344i
$435$	−10.6447	+	7.13694i	−0.510375	+	0.342190i
$436$	−15.3371			−0.734515
$437$	−9.63536	+	16.6889i	−0.460922	+	0.798340i
$438$	0.105568	+	0.157454i	0.00504422	+	0.00752343i
$439$	−9.41775	−	16.3120i	−0.449484	−	0.778530i	0.548868	−	0.835909i	$-0.315059\pi$
$439$	−9.41775	−	16.3120i	−0.449484	−	0.778530i	−0.998352	+	0.0573791i	$0.981726\pi$
$440$	0.205905	−	0.356638i	0.00981614	−	0.0170021i
$441$	12.3302	+	15.9643i	0.587154	+	0.760204i
$442$	7.41021			0.352468
$443$	−1.88105	+	1.08603i	−0.0893715	+	0.0515987i	−0.544020	−	0.839072i	$-0.683098\pi$
$443$	−1.88105	+	1.08603i	−0.0893715	+	0.0515987i	0.454648	+	0.890671i	$0.349765\pi$
$444$	−7.11377	−	3.49415i	−0.337605	−	0.165825i
$445$	14.6671	−	8.46804i	0.695286	−	0.401423i
$446$	−0.713160	+	1.23523i	−0.0337691	+	0.0584898i
$447$	−6.25034	−	3.07005i	−0.295631	−	0.145208i
$448$	−0.262744	+	0.455085i	−0.0124135	+	0.0215008i
$449$	−5.83596			−0.275416			−0.137708	−	0.990473i	$-0.543974\pi$
$449$	−5.83596			−0.275416			−0.137708	+	0.990473i	$0.543974\pi$
$450$	−2.77525	−	1.13928i	−0.130827	−	0.0537062i
$451$	−4.51218	−	2.60511i	−0.212470	−	0.122670i
$452$	16.4689	−	9.50830i	0.774630	−	0.447233i
$453$	0.347104	+	5.17051i	0.0163084	+	0.242932i
$454$	8.84127	+	15.3135i	0.414941	+	0.718700i
$455$	−0.506859	−	0.877906i	−0.0237619	−	0.0411569i
$456$	3.75391	+	1.84385i	0.175793	+	0.0863462i
$457$			4.51856i			0.211369i	0.994400	+	0.105685i	$0.0337034\pi$
$457$			4.51856i			0.211369i	−0.994400	+	0.105685i	$0.966297\pi$
$458$	−7.47510	+	12.9472i	−0.349288	+	0.604985i
$459$	6.32616	−	18.9308i	0.295280	−	0.883613i
$460$	−6.91153	+	3.99037i	−0.322252	+	0.186052i
$461$	−11.8557			−0.552176			−0.276088	−	0.961132i	$-0.589038\pi$
$461$	−11.8557			−0.552176			−0.276088	+	0.961132i	$0.589038\pi$
$462$	−0.0251055	−	0.373976i	−0.00116801	−	0.0173989i
$463$			21.1783i			0.984241i	0.870527	+	0.492121i	$0.163778\pi$
$463$			21.1783i			0.984241i	−0.870527	+	0.492121i	$0.836222\pi$
$464$	7.39923			0.343501
$465$	6.73384	+	6.90329i	0.312274	+	0.320132i
$466$	−13.5860			−0.629360
$467$			28.2481i			1.30717i	0.756854	+	0.653584i	$0.226735\pi$
$467$			28.2481i			1.30717i	−0.756854	+	0.653584i	$0.773265\pi$
$468$	−4.58022	+	3.53759i	−0.211721	+	0.163525i
$469$	−3.12874			−0.144472
$470$	−9.76440	+	5.63748i	−0.450398	+	0.260037i
$471$	0.0772756	−	0.00518762i	0.00356067	−	0.000239033i
$472$	−4.87016	+	8.43537i	−0.224167	+	0.388269i
$473$			3.93357i			0.180866i
$474$	12.0985	−	24.6314i	0.555702	−	1.13136i
$475$	1.20732	+	2.09115i	0.0553959	+	0.0959484i
$476$	−1.00927	−	1.74811i	−0.0462598	−	0.0801243i
$477$	−18.2209	−	23.5911i	−0.834278	−	1.08016i
$478$	9.46057	−	5.46206i	0.432716	−	0.249829i
$479$	13.4424	+	7.76095i	0.614197	+	0.354607i	0.774606	−	0.632444i	$-0.217948\pi$
$479$	13.4424	+	7.76095i	0.614197	+	0.354607i	−0.160409	+	0.987051i	$0.551281\pi$
$480$	0.964551	+	1.43862i	0.0440256	+	0.0656639i
$481$	−8.82726			−0.402488
$482$	8.81166	−	15.2622i	0.401360	−	0.695176i
$483$	−3.20241	+	6.51981i	−0.145715	+	0.296662i
$484$	−5.41521	+	9.37941i	−0.246146	+	0.426337i
$485$	11.0421	−	6.37517i	0.501397	−	0.289482i
$486$	5.12727	+	14.7211i	0.232578	+	0.667763i
$487$	−3.99910	+	2.30888i	−0.181216	+	0.104625i	−0.587864	−	0.808960i	$-0.700031\pi$
$487$	−3.99910	+	2.30888i	−0.181216	+	0.104625i	0.406648	+	0.913585i	$0.366698\pi$
$488$	3.42172			0.154894
$489$	−32.4202	+	2.17641i	−1.46609	+	0.0984208i
$490$	3.36193	−	5.82304i	0.151877	−	0.263058i
$491$	−17.2463	−	29.8716i	−0.778317	−	1.34808i	−0.932911	−	0.360106i	$-0.882740\pi$
$491$	−17.2463	−	29.8716i	−0.778317	−	1.34808i	0.154594	−	0.987978i	$-0.450593\pi$
$492$	18.2014	−	12.2035i	0.820585	−	0.550176i
$493$	−14.2112	+	24.6146i	−0.640042	+	1.10858i
$494$	4.65811			0.209578
$495$	−1.14288	−	0.469168i	−0.0513686	−	0.0210875i
$496$	−1.00963	−	5.47546i	−0.0453338	−	0.245855i
$497$			3.47518i			0.155883i
$498$	−8.34227	+	5.59322i	−0.373826	+	0.250638i
$499$	−8.32095	−	4.80411i	−0.372497	−	0.215061i	0.302052	−	0.953292i	$-0.402328\pi$
$499$	−8.32095	−	4.80411i	−0.372497	−	0.215061i	−0.674549	+	0.738230i	$0.735662\pi$
$500$			1.00000i			0.0447214i
$501$	5.75997	−	11.7268i	0.257337	−	0.523913i
$502$	15.1967	+	8.77380i	0.678260	+	0.391594i
$503$	8.03131	+	4.63688i	0.358098	+	0.206748i	0.668246	−	0.743940i	$-0.267045\pi$
$503$	8.03131	+	4.63688i	0.358098	+	0.206748i	−0.310148	+	0.950688i	$0.600379\pi$
$504$	1.45836	+	0.598677i	0.0649605	+	0.0266672i
$505$	−3.07893	−	5.33286i	−0.137011	−	0.237309i
$506$	−2.84624	+	1.64328i	−0.126531	+	0.0730526i
$507$	7.08520	−	14.4248i	0.314665	−	0.640628i
$508$	1.69455	+	0.978350i	0.0751836	+	0.0434073i
$509$	−10.3947	−	18.0042i	−0.460739	−	0.798023i	0.538259	−	0.842779i	$-0.319082\pi$
$509$	−10.3947	−	18.0042i	−0.460739	−	0.798023i	−0.998998	+	0.0447566i	$0.985749\pi$
$510$	−6.63834	+	0.445641i	−0.293950	+	0.0197333i
$511$		−	0.0575132i		−	0.00254423i
$512$		−	1.00000i		−	0.0441942i
$513$	3.97667	−	11.9000i	0.175574	−	0.525399i
$514$	−6.22374	−	10.7798i	−0.274517	−	0.475478i
$515$	1.89105	+	1.09180i	0.0833297	+	0.0481105i
$516$	−14.8497	−	7.29392i	−0.653723	−	0.321097i
$517$	−4.02108	+	2.32157i	−0.176847	+	0.102103i
$518$	1.20227	+	2.08240i	0.0528248	+	0.0914952i
$519$	−10.8198	+	7.25434i	−0.474938	+	0.318430i
$520$	1.67065	+	0.964551i	0.0732629	+	0.0422984i
$521$	−24.5559	−	14.1773i	−1.07581	−	0.621120i	−0.146048	−	0.989277i	$-0.546655\pi$
$521$	−24.5559	−	14.1773i	−1.07581	−	0.621120i	−0.929764	+	0.368157i	$0.879989\pi$
$522$	−2.96695	−	21.9985i	−0.129860	−	0.962849i
$523$		−	25.3776i		−	1.10968i	−0.831956	−	0.554842i	$-0.812779\pi$
$523$		−	25.3776i		−	1.10968i	0.831956	−	0.554842i	$-0.187221\pi$
$524$	−2.25900	−	1.30423i	−0.0986849	−	0.0569758i
$525$	0.506859	+	0.755979i	0.0221212	+	0.0329936i
$526$			2.05549i			0.0896235i
$527$	20.1540	+	7.15768i	0.877922	+	0.311794i
$528$	0.397212	+	0.592441i	0.0172864	+	0.0257827i
$529$	40.6924			1.76923
$530$	−4.96807	+	8.60495i	−0.215799	+	0.373775i
$531$	27.0319	+	11.0970i	1.17308	+	0.481567i
$532$	−0.634434	−	1.09887i	−0.0275062	−	0.0476421i
$533$	12.2035	−	21.1371i	0.528592	−	0.915548i
$534$	1.96482	+	29.2683i	0.0850260	+	1.26656i
$535$	3.15086			0.136224
$536$	5.15630	−	2.97699i	0.222718	−	0.128587i
$537$	6.59617	−	13.4292i	0.284646	−	0.579512i
$538$	17.1903	−	9.92480i	0.741125	−	0.427889i
$539$	1.38448	−	2.39799i	0.0596337	−	0.103289i
$540$	3.89038	−	3.44455i	0.167415	−	0.148230i
$541$	10.5846	−	18.3331i	0.455068	−	0.788201i	−0.543624	−	0.839329i	$-0.682948\pi$
$541$	10.5846	−	18.3331i	0.455068	−	0.788201i	0.998692	+	0.0511278i	$0.0162816\pi$
$542$	12.9670			0.556978
$543$	35.2531	−	23.6361i	1.51286	−	1.01432i
$544$	3.32664	+	1.92064i	0.142628	+	0.0823466i
$545$	13.2823	−	7.66856i	0.568953	−	0.328485i
$546$	1.75187	−	0.117605i	0.0749731	−	0.00503305i
$547$	−10.9017	−	18.8824i	−0.466125	−	0.807352i	0.533127	−	0.846035i	$-0.321017\pi$
$547$	−10.9017	−	18.8824i	−0.466125	−	0.807352i	−0.999252	+	0.0386835i	$0.987684\pi$
$548$	0.986737	+	1.70908i	0.0421513	+	0.0730083i
$549$	−1.37204	−	10.1730i	−0.0585574	−	0.434175i
$550$			0.411810i			0.0175597i
$551$	−8.93328	+	15.4729i	−0.380570	+	0.659167i
$552$	−0.925878	−	13.7920i	−0.0394080	−	0.587027i
$553$	−7.21029	+	4.16286i	−0.306613	+	0.177023i
$554$	−11.7583			−0.499563
$555$	7.90778	−	0.530860i	0.335667	−	0.0225338i
$556$		−	6.85664i		−	0.290787i
$557$	−23.9327			−1.01406			−0.507031	−	0.861928i	$-0.669257\pi$
$557$	−23.9327			−1.01406			−0.507031	+	0.861928i	$0.669257\pi$
$558$	−15.8741	+	5.19727i	−0.672006	+	0.220018i
$559$	−18.4266			−0.779362
$560$		−	0.525487i		−	0.0222059i
$561$	−2.73374	+	0.183519i	−0.115418	+	0.00774820i
$562$	−16.6048			−0.700429
$563$	18.4599	−	10.6578i	0.777990	−	0.449173i	−0.0577272	−	0.998332i	$-0.518385\pi$
$563$	18.4599	−	10.6578i	0.777990	−	0.449173i	0.835718	+	0.549159i	$0.185052\pi$
$564$	−1.30805	−	19.4849i	−0.0550789	−	0.820464i
$565$	−9.50830	+	16.4689i	−0.400017	+	0.692850i
$566$			6.88072i			0.289218i
$567$	1.19514	−	4.57588i	0.0501912	−	0.192169i
$568$	−3.30663	−	5.72724i	−0.138743	−	0.240310i
$569$	−7.22407	−	12.5125i	−0.302849	−	0.524550i	0.673931	−	0.738794i	$-0.264604\pi$
$569$	−7.22407	−	12.5125i	−0.302849	−	0.524550i	−0.976780	+	0.214244i	$0.931271\pi$
$570$	−4.17290	+	0.280133i	−0.174784	+	0.0117335i
$571$	−10.6839	+	6.16838i	−0.447109	+	0.258139i	−0.706609	−	0.707605i	$-0.749776\pi$
$571$	−10.6839	+	6.16838i	−0.447109	+	0.258139i	0.259499	+	0.965743i	$0.416442\pi$
$572$	0.687992	+	0.397212i	0.0287664	+	0.0166083i
$573$	−10.3126	+	6.91425i	−0.430814	+	0.288847i
$574$	−6.64845			−0.277501
$575$	3.99037	−	6.91153i	0.166410	−	0.288231i
$576$	−2.97308	+	0.400981i	−0.123878	+	0.0167076i
$577$	8.28966	−	14.3581i	0.345103	−	0.597736i	−0.640269	−	0.768150i	$-0.721177\pi$
$577$	8.28966	−	14.3581i	0.345103	−	0.597736i	0.985372	+	0.170414i	$0.0545107\pi$
$578$	1.94391	−	1.12232i	0.0808559	−	0.0466822i
$579$	16.8807	−	34.3675i	0.701536	−	1.42826i
$580$	−6.40792	+	3.69962i	−0.266075	+	0.153618i
$581$	3.04718			0.126419
$582$	1.47922	+	22.0347i	0.0613155	+	0.913366i
$583$	−2.04590	+	3.54361i	−0.0847326	+	0.146761i
$584$	0.0547237	+	0.0947842i	0.00226448	+	0.00392220i
$585$	2.19779	−	5.35375i	0.0908674	−	0.221350i
$586$	1.08186	−	1.87383i	0.0446911	−	0.0774072i
$587$	−2.18146			−0.0900383			−0.0450192	−	0.998986i	$-0.514335\pi$
$587$	−2.18146			−0.0900383			−0.0450192	+	0.998986i	$0.514335\pi$
$588$	6.48551	+	9.67311i	0.267458	+	0.398913i
$589$	12.6689	+	4.49937i	0.522015	+	0.185393i
$590$		−	9.74033i		−	0.401003i
$591$	−0.476326	−	0.710438i	−0.0195934	−	0.0292235i
$592$	−3.96279	−	2.28792i	−0.162870	−	0.0940329i
$593$			44.9244i			1.84482i	0.386210	+	0.922411i	$0.373784\pi$
$593$			44.9244i			1.84482i	−0.386210	+	0.922411i	$0.626216\pi$
$594$	1.60210	−	1.41850i	0.0657349	−	0.0582018i
$595$	1.74811	+	1.00927i	0.0716653	+	0.0413760i
$596$	−3.48181	−	2.01022i	−0.142620	−	0.0823419i
$597$	−19.0060	+	12.7429i	−0.777862	+	0.521532i
$598$	−7.69784	−	13.3331i	−0.314788	−	0.545229i
$599$	35.4872	−	20.4885i	1.44997	−	0.837138i	0.451488	−	0.892277i	$-0.350894\pi$
$599$	35.4872	−	20.4885i	1.44997	−	0.837138i	0.998479	+	0.0551389i	$0.0175602\pi$
$600$	−1.55464	−	0.763610i	−0.0634678	−	0.0311742i
$601$	−0.626997	−	0.361997i	−0.0255757	−	0.0147662i	0.487158	−	0.873314i	$-0.338034\pi$
$601$	−0.626997	−	0.361997i	−0.0255757	−	0.0147662i	−0.512733	+	0.858548i	$0.671367\pi$
$602$	2.50970	+	4.34693i	0.102288	+	0.177167i
$603$	−10.9184	−	14.1364i	−0.444633	−	0.575678i
$604$			2.99192i			0.121739i
$605$		−	10.8304i		−	0.440319i
$606$	10.6418	−	0.714397i	0.432292	−	0.0290204i
$607$	19.1262	+	33.1276i	0.776309	+	1.34461i	0.934056	+	0.357127i	$0.116244\pi$
$607$	19.1262	+	33.1276i	0.776309	+	1.34461i	−0.157747	+	0.987480i	$0.550423\pi$
$608$	2.09115	+	1.20732i	0.0848072	+	0.0489635i
$609$	−2.96907	+	6.04475i	−0.120313	+	0.244945i
$610$	−2.96329	+	1.71086i	−0.119980	+	0.0692706i
$611$	−10.8753	−	18.8365i	−0.439967	−	0.762044i
$612$	4.37629	−	10.6605i	0.176901	−	0.430926i
$613$	30.7414	+	17.7485i	1.24163	+	0.716857i	0.969426	−	0.245383i	$-0.0789136\pi$
$613$	30.7414	+	17.7485i	1.24163	+	0.716857i	0.272206	+	0.962239i	$0.412247\pi$
$614$	−20.9190	−	12.0776i	−0.844220	−	0.487411i
$615$	−9.66117	+	19.6693i	−0.389576	+	0.793141i
$616$		−	0.216401i		−	0.00871905i
$617$	38.0597	+	21.9738i	1.53223	+	0.884632i	0.999259	+	0.0384963i	$0.0122568\pi$
$617$	38.0597	+	21.9738i	1.53223	+	0.884632i	0.532968	+	0.846135i	$0.321077\pi$
$618$	−3.14138	+	2.10619i	−0.126365	+	0.0847236i
$619$		−	17.3926i		−	0.699066i	−0.936924	−	0.349533i	$-0.886340\pi$
$619$		−	17.3926i		−	0.699066i	0.936924	−	0.349533i	$-0.113660\pi$
$620$	3.61210	+	4.23707i	0.145065	+	0.170165i
$621$	−40.6335	+	8.28305i	−1.63057	+	0.332387i
$622$	−27.4654			−1.10126
$623$	4.44984	−	7.70735i	0.178279	−	0.308789i
$624$	−2.77525	+	1.86072i	−0.111099	+	0.0744884i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	15.9643	−	27.6509i	0.638060	−	1.10515i
$627$	−1.71844	+	0.115362i	−0.0686281	+	0.00460710i
$628$	0.0447155			0.00178434
$629$	15.2222	−	8.78852i	0.606947	−	0.350421i
$630$	−1.56232	+	0.210710i	−0.0622442	+	0.00839491i
$631$	3.13351	−	1.80913i	0.124743	−	0.0720205i	−0.436330	−	0.899787i	$-0.643722\pi$
$631$	3.13351	−	1.80913i	0.124743	−	0.0720205i	0.561073	+	0.827766i	$0.310389\pi$
$632$	7.92191	−	13.7211i	0.315117	−	0.545798i
$633$	0.525947	−	1.07078i	0.0209045	−	0.0425596i
$634$	−5.14572	+	8.91264i	−0.204363	+	0.353966i
$635$	−1.95670			−0.0776493
$636$	−9.58392	−	14.2944i	−0.380027	−	0.566809i
$637$	11.2332	+	6.48551i	0.445077	+	0.256965i
$638$	−2.63885	+	1.52354i	−0.104473	+	0.0603175i
$639$	−15.7017	+	12.1274i	−0.621148	+	0.479752i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	6.46266	+	11.1937i	0.255260	+	0.442123i	0.964966	−	0.262375i	$-0.0845057\pi$
$641$	6.46266	+	11.1937i	0.255260	+	0.442123i	−0.709706	+	0.704498i	$0.751172\pi$
$642$	−2.40603	+	4.89845i	−0.0949584	+	0.193327i
$643$			26.4746i			1.04406i	0.852928	+	0.522028i	$0.174824\pi$
$643$			26.4746i			1.04406i	−0.852928	+	0.522028i	$0.825176\pi$
$644$	−2.09689	+	3.63192i	−0.0826291	+	0.143118i
$645$	16.5072	−	1.10815i	0.649971	−	0.0436334i
$646$	−8.03267	+	4.63766i	−0.316041	+	0.182466i
$647$	36.7796			1.44596			0.722978	−	0.690871i	$-0.242773\pi$
$647$	36.7796			1.44596			0.722978	+	0.690871i	$0.242773\pi$
$648$	2.38430	+	8.67843i	0.0936641	+	0.340921i
$649$		−	4.01117i		−	0.157452i
$650$	−1.92910			−0.0756656
$651$	4.87827	+	1.37231i	0.191194	+	0.0537851i
$652$	−18.7599			−0.734696
$653$			6.11852i			0.239436i	0.992808	+	0.119718i	$0.0381991\pi$
$653$			6.11852i			0.239436i	−0.992808	+	0.119718i	$0.961801\pi$
$654$	1.77932	+	26.5050i	0.0695769	+	1.03643i
$655$	2.60847			0.101921
$656$	10.9569	−	6.32599i	0.427796	−	0.246988i
$657$	0.259858	−	0.200705i	0.0101380	−	0.00783024i
$658$	−2.96242	+	5.13106i	−0.115487	+	0.200030i
$659$			25.8000i			1.00502i	0.864570	+	0.502512i	$0.167591\pi$
$659$			25.8000i			1.00502i	−0.864570	+	0.502512i	$0.832409\pi$
$660$	−0.640216	−	0.314462i	−0.0249204	−	0.0122404i
$661$	3.22830	+	5.59158i	0.125566	+	0.217487i	0.921954	−	0.387299i	$-0.126592\pi$
$661$	3.22830	+	5.59158i	0.125566	+	0.217487i	−0.796388	+	0.604786i	$0.793259\pi$
$662$	11.8275	+	20.4858i	0.459688	+	0.796203i
$663$	−0.859687	−	12.8060i	−0.0333875	−	0.497345i
$664$	−5.02189	+	2.89939i	−0.194887	+	0.112518i
$665$	1.09887	+	0.634434i	0.0426124	+	0.0246023i
$666$	−5.21316	+	12.6991i	−0.202006	+	0.492081i
$667$	59.0514			2.28648
$668$	3.77154	−	6.53250i	0.145925	−	0.252750i
$669$	2.21741	+	1.08915i	0.0857301	+	0.0421090i
$670$	−2.97699	+	5.15630i	−0.115011	+	0.199205i
$671$	−1.22031	+	0.704549i	−0.0471097	+	0.0271988i
$672$	0.816942	+	0.401267i	0.0315142	+	0.0154792i
$673$	4.80470	−	2.77400i	0.185208	−	0.106930i	−0.404529	−	0.914525i	$-0.632565\pi$
$673$	4.80470	−	2.77400i	0.185208	−	0.106930i	0.589737	+	0.807595i	$0.299231\pi$
$674$	−4.92368			−0.189653
$675$	−1.64689	+	4.92826i	−0.0633889	+	0.189689i
$676$	4.63928	−	8.03547i	0.178434	−	0.309057i
$677$	−12.3039	−	21.3109i	−0.472876	−	0.819045i	0.526642	−	0.850087i	$-0.323451\pi$
$677$	−12.3039	−	21.3109i	−0.472876	−	0.819045i	−0.999518	+	0.0310417i	$0.990118\pi$
$678$	−18.3425	−	27.3578i	−0.704439	−	1.05067i
$679$	3.35007	−	5.80249i	0.128564	−	0.222679i
$680$	−3.84127			−0.147306
$681$	25.4385	−	17.0557i	0.974807	−	0.653577i
$682$	1.48750	+	1.74487i	0.0569593	+	0.0668145i
$683$			14.3202i			0.547949i	0.961737	+	0.273975i	$0.0883384\pi$
$683$			14.3202i			0.547949i	−0.961737	+	0.273975i	$0.911662\pi$
$684$	2.75096	−	6.70127i	0.105186	−	0.256229i
$685$	−1.70908	−	0.986737i	−0.0653006	−	0.0377013i
$686$		−	7.21171i		−	0.275344i
$687$	23.2421	+	11.4161i	0.886743	+	0.435552i
$688$	−8.27218	−	4.77595i	−0.315374	−	0.182081i
$689$	−16.5998	−	9.58392i	−0.632403	−	0.365118i
$690$	7.69784	+	11.4813i	0.293052	+	0.437086i
$691$	19.8333	+	34.3522i	0.754493	+	1.30682i	0.945626	+	0.325256i	$0.105450\pi$
$691$	19.8333	+	34.3522i	0.754493	+	1.30682i	−0.191133	+	0.981564i	$0.561216\pi$
$692$	−6.51333	+	3.76048i	−0.247600	+	0.142952i
$693$	−0.643378	+	0.0867728i	−0.0244399	+	0.00329622i
$694$	6.10648	+	3.52558i	0.231799	+	0.133829i
$695$	3.42832	+	5.93803i	0.130044	+	0.225242i
$696$	−0.858414	−	12.7871i	−0.0325381	−	0.484692i
$697$			48.5997i			1.84084i
$698$			31.1919i			1.18063i
$699$	1.57617	+	23.4788i	0.0596160	+	0.888050i
$700$	0.262744	+	0.455085i	0.00993077	+	0.0172006i
$701$	−21.5025	−	12.4145i	−0.812138	−	0.468888i	0.0355597	−	0.999368i	$-0.488679\pi$
$701$	−21.5025	−	12.4145i	−0.812138	−	0.468888i	−0.847698	+	0.530479i	$0.822012\pi$
$702$	6.64490	+	7.50495i	0.250795	+	0.283256i
$703$	9.56875	−	5.52452i	0.360892	−	0.208361i
$704$	0.205905	+	0.356638i	0.00776034	+	0.0134413i
$705$	10.8753	+	16.2204i	0.409587	+	0.610897i
$706$	16.0896	+	9.28933i	0.605540	+	0.349609i
$707$	−2.80235	−	1.61794i	−0.105393	−	0.0608488i
$708$	15.1427	+	7.43781i	0.569097	+	0.279530i
$709$			3.30912i			0.124277i	0.998068	+	0.0621384i	$0.0197920\pi$
$709$			3.30912i			0.124277i	−0.998068	+	0.0621384i	$0.980208\pi$
$710$	5.72724	+	3.30663i	0.214940	+	0.124095i
$711$	−43.9706	−	18.0506i	−1.64903	−	0.676949i
$712$			16.9361i			0.634706i
$713$	−8.05761	−	43.6983i	−0.301760	−	1.63651i
$714$	−2.90392	+	1.94698i	−0.108676	+	0.0728641i
$715$	−0.794425			−0.0297098
$716$	4.31907	−	7.48085i	0.161411	−	0.279573i
$717$	−10.5369	−	15.7157i	−0.393507	−	0.586914i
$718$	−7.01060	−	12.1427i	−0.261633	−	0.453162i
$719$	21.9318	−	37.9869i	0.817917	−	1.41667i	−0.0892975	−	0.996005i	$-0.528462\pi$
$719$	21.9318	−	37.9869i	0.817917	−	1.41667i	0.907214	−	0.420669i	$-0.138204\pi$
$720$	2.37427	−	1.83380i	0.0884840	−	0.0683417i
$721$	1.14745			0.0427334
$722$	11.4051	−	6.58473i	0.424454	−	0.245058i
$723$	−27.3979	−	13.4573i	−1.01894	−	0.500484i
$724$	21.2217	−	12.2524i	0.788699	−	0.455355i
$725$	3.69962	−	6.40792i	0.137400	−	0.237984i
$726$	16.8374	+	8.27021i	0.624894	+	0.306936i
$727$	5.52326	−	9.56657i	0.204847	−	0.354805i	−0.745237	−	0.666799i	$-0.767664\pi$
$727$	5.52326	−	9.56657i	0.204847	−	0.354805i	0.950084	+	0.311995i	$0.100997\pi$
$728$	1.01372			0.0375709
$729$	24.8456	−	10.5686i	0.920208	−	0.391430i
$730$	−0.0947842	−	0.0547237i	−0.00350812	−	0.00202542i
$731$	31.7757	−	18.3457i	1.17527	−	0.678541i
$732$	−0.396966	−	5.91328i	−0.0146723	−	0.218561i
$733$	−20.5336	−	35.5652i	−0.758426	−	1.31363i	−0.943653	−	0.330936i	$-0.892636\pi$
$733$	−20.5336	−	35.5652i	−0.758426	−	1.31363i	0.185228	−	0.982696i	$-0.440698\pi$
$734$	0.178249	+	0.308737i	0.00657930	+	0.0113957i
$735$	−10.4532	−	5.13441i	−0.385571	−	0.189385i
$736$		−	7.98075i		−	0.294174i
$737$	−1.22596	+	2.12342i	−0.0451587	+	0.0782172i
$738$	−23.2012	−	30.0393i	−0.854048	−	1.10576i
$739$	−29.3903	+	16.9685i	−1.08114	+	0.624196i	−0.931203	−	0.364500i	$-0.881240\pi$
$739$	−29.3903	+	16.9685i	−1.08114	+	0.624196i	−0.149935	+	0.988696i	$0.547907\pi$
$740$	4.57584			0.168211
$741$	−0.540405	−	8.04996i	−0.0198523	−	0.295723i
$742$			5.22131i			0.191680i
$743$	−32.4341			−1.18989			−0.594946	−	0.803766i	$-0.702827\pi$
$743$	−32.4341			−1.18989			−0.594946	+	0.803766i	$0.702827\pi$
$744$	−9.34534	+	2.38003i	−0.342617	+	0.0872563i
$745$	4.02044			0.147298
$746$			25.2094i			0.922981i
$747$	10.6338	+	13.7679i	0.389071	+	0.503741i
$748$	−1.58188			−0.0578391
$749$	1.43391	−	0.827869i	0.0523940	−	0.0302497i
$750$	1.72816	−	0.116014i	0.0631035	−	0.00423623i
$751$	−24.1637	+	41.8527i	−0.881744	+	1.52723i	−0.0323439	+	0.999477i	$0.510297\pi$
$751$	−24.1637	+	41.8527i	−0.881744	+	1.52723i	−0.849400	+	0.527749i	$0.823036\pi$
$752$		−	11.2750i		−	0.411155i
$753$	13.3995	−	27.2802i	0.488305	−	0.994145i
$754$	−7.13694	−	12.3615i	−0.259912	−	0.450181i
$755$	−1.49596	−	2.59108i	−0.0544435	−	0.0942989i
$756$	0.865421	−	2.58974i	0.0314751	−	0.0941878i
$757$	−26.3664	+	15.2226i	−0.958303	+	0.553276i	−0.895650	−	0.444759i	$-0.853289\pi$
$757$	−26.3664	+	15.2226i	−0.958303	+	0.553276i	−0.0626525	+	0.998035i	$0.519956\pi$
$758$	−21.9505	−	12.6731i	−0.797278	−	0.460309i
$759$	3.17005	+	4.72812i	0.115066	+	0.171620i
$760$	−2.41465			−0.0875885
$761$	−2.67170	+	4.62752i	−0.0968491	+	0.167748i	−0.910379	−	0.413776i	$-0.864210\pi$
$761$	−2.67170	+	4.62752i	−0.0968491	+	0.167748i	0.813530	+	0.581523i	$0.197543\pi$
$762$	1.49415	−	3.04196i	0.0541275	−	0.110199i
$763$	4.02973	−	6.97970i	0.145886	−	0.252682i
$764$	−6.20798	+	3.58418i	−0.224597	+	0.129671i
$765$	1.54028	+	11.4204i	0.0556889	+	0.412906i
$766$	15.3114	−	8.84004i	0.553224	−	0.319404i
$767$	18.7901			0.678471
$768$	−1.72816	+	0.116014i	−0.0623596	+	0.00418629i
$769$	−23.4231	+	40.5700i	−0.844658	+	1.46299i	0.0412605	+	0.999148i	$0.486863\pi$
$769$	−23.4231	+	40.5700i	−0.844658	+	1.46299i	−0.885918	+	0.463842i	$0.846471\pi$
$770$	0.108201	+	0.187409i	0.00389928	+	0.00675374i
$771$	−17.9072	+	12.0062i	−0.644914	+	0.432394i
$772$	11.0532	−	19.1447i	0.397813	−	0.689033i
$773$	36.6683			1.31887			0.659434	−	0.751762i	$-0.270796\pi$
$773$	36.6683			1.31887			0.659434	+	0.751762i	$0.270796\pi$
$774$	−10.8823	+	26.5089i	−0.391156	+	0.952844i
$775$	−5.24670	−	1.86336i	−0.188467	−	0.0669340i
$776$			12.7503i			0.457711i
$777$	3.45923	−	2.31931i	0.124099	−	0.0832046i
$778$	18.7271	+	10.8121i	0.671398	+	0.387632i
$779$			30.5501i			1.09457i
$780$	1.47308	−	2.99906i	0.0527448	−	0.107383i
$781$	2.35854	+	1.36170i	0.0843952	+	0.0487256i
$782$	26.5491	+	15.3281i	0.949393	+	0.548132i
$783$	−37.6728	+	7.67951i	−1.34632	+	0.274443i
$784$	3.36193	+	5.82304i	0.120069	+	0.207966i
$785$	−0.0387247	+	0.0223577i	−0.00138215	+	0.000797982i
$786$	−1.99185	+	4.05523i	−0.0710470	+	0.144645i
$787$	−42.2310	−	24.3821i	−1.50537	−	0.869126i	−0.999981	−	0.00623537i	$-0.998015\pi$
$787$	−42.2310	−	24.3821i	−1.50537	−	0.869126i	−0.505390	−	0.862891i	$-0.668651\pi$
$788$	−0.246916	−	0.427671i	−0.00879601	−	0.0152351i
$789$	3.55221	−	0.238465i	0.126462	−	0.00848958i
$790$			15.8438i			0.563698i
$791$			9.99298i			0.355309i
$792$	0.977751	−	0.755178i	0.0347429	−	0.0268341i
$793$	−3.30042	−	5.71650i	−0.117201	−	0.202999i
$794$	−5.27715	−	3.04676i	−0.187279	−	0.108126i
$795$	15.4471	+	7.58733i	0.547852	+	0.269095i
$796$	−11.4412	+	6.60560i	−0.405524	+	0.234129i
$797$	18.4262	+	31.9152i	0.652690	+	1.13049i	0.982468	+	0.186434i	$0.0596930\pi$
$797$	18.4262	+	31.9152i	0.652690	+	1.13049i	−0.329777	+	0.944059i	$0.606974\pi$
$798$	−1.82542	+	1.22389i	−0.0646193	+	0.0433252i
$799$	37.5077	+	21.6551i	1.32693	+	0.766102i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$	50.3523	−	6.79105i	1.77911	−	0.239950i
$802$		−	3.38331i		−	0.119469i
$803$	−0.0390331	−	0.0225358i	−0.00137745	−	0.000795271i
$804$	−5.74293	−	8.56555i	−0.202537	−	0.302084i
$805$		−	4.19378i		−	0.147811i
$806$	−8.17375	+	6.96810i	−0.287908	+	0.245441i
$807$	−19.1460	−	28.5561i	−0.673970	−	1.00522i
$808$	6.15786			0.216633
$809$	−22.7306	+	39.3705i	−0.799164	+	1.38419i	0.120997	+	0.992653i	$0.461391\pi$
$809$	−22.7306	+	39.3705i	−0.799164	+	1.38419i	−0.920161	+	0.391540i	$0.871943\pi$
$810$	−6.40408	−	6.32359i	−0.225016	−	0.222188i
$811$	17.8903	+	30.9870i	0.628214	+	1.08810i	0.987910	+	0.155029i	$0.0495472\pi$
$811$	17.8903	+	30.9870i	0.628214	+	1.08810i	−0.359696	+	0.933070i	$0.617119\pi$
$812$	−1.94410	+	3.36728i	−0.0682246	+	0.118168i
$813$	−1.50435	−	22.4090i	−0.0527597	−	0.785917i
$814$	1.88438			0.0660474
$815$	16.2466	−	9.37997i	0.569093	−	0.328566i
$816$	2.93323	−	5.97179i	0.102684	−	0.209054i
$817$	19.9744	−	11.5322i	0.698817	−	0.403462i
$818$	0.215588	−	0.373409i	0.00753784	−	0.0130559i
$819$	−0.406482	−	3.01387i	−0.0142036	−	0.105313i
$820$	−6.32599	+	10.9569i	−0.220913	+	0.382633i
$821$	−42.8036			−1.49385			−0.746927	−	0.664906i	$-0.768472\pi$
$821$	−42.8036			−1.49385			−0.746927	+	0.664906i	$0.768472\pi$
$822$	2.83909	−	1.90352i	0.0990246	−	0.0663928i
$823$	−40.3479	−	23.2949i	−1.40644	−	0.812008i	−0.411396	−	0.911457i	$-0.634959\pi$
$823$	−40.3479	−	23.2949i	−1.40644	−	0.812008i	−0.995043	+	0.0994493i	$0.968292\pi$
$824$	−1.89105	+	1.09180i	−0.0658780	+	0.0380347i
$825$	0.711675	−	0.0477757i	0.0247773	−	0.00166334i
$826$	−2.55921	−	4.43268i	−0.0890462	−	0.154233i
$827$	11.9976	+	20.7805i	0.417198	+	0.722607i	0.995656	−	0.0931042i	$-0.0296790\pi$
$827$	11.9976	+	20.7805i	0.417198	+	0.722607i	−0.578459	+	0.815712i	$0.696346\pi$
$828$	−23.7274	+	3.20013i	−0.824585	+	0.111212i
$829$			32.5316i			1.12987i	0.825136	+	0.564934i	$0.191098\pi$
$829$			32.5316i			1.12987i	−0.825136	+	0.564934i	$0.808902\pi$
$830$	2.89939	−	5.02189i	0.100639	−	0.174312i
$831$	1.36413	+	20.3202i	0.0473210	+	0.704902i
$832$	−1.67065	+	0.964551i	−0.0579194	+	0.0334398i
$833$	−25.8282			−0.894894
$834$	−11.8494	+	0.795466i	−0.410311	+	0.0275447i
$835$			7.54308i			0.261039i
$836$	−0.994378			−0.0343913
$837$	10.8233	+	26.8301i	0.374109	+	0.927385i
$838$	39.1620			1.35283
$839$		−	15.2942i		−	0.528015i	−0.964521	−	0.264008i	$-0.914956\pi$
$839$		−	15.2942i		−	0.528015i	0.964521	−	0.264008i	$-0.0850444\pi$
$840$	−0.908126	+	0.0609638i	−0.0313333	+	0.00210345i
$841$	25.7486			0.887884
$842$	−19.9385	+	11.5115i	−0.687126	+	0.396713i
$843$	1.92638	+	28.6957i	0.0663481	+	0.988332i
$844$	0.344382	−	0.596487i	0.0118541	−	0.0205319i
$845$			9.27856i			0.319192i
$846$	−33.5214	+	4.52105i	−1.15249	+	0.155437i
$847$	−2.84562	−	4.92876i	−0.0977767	−	0.169354i
$848$	−4.96807	−	8.60495i	−0.170604	−	0.295495i
$849$	11.8910	−	0.798259i	0.408098	−	0.0273962i
$850$	3.32664	−	1.92064i	0.114103	−	0.0658773i
$851$	−31.6260	−	18.2593i	−1.08413	−	0.625921i
$852$	−9.51399	+	6.37882i	−0.325944	+	0.218535i
$853$	−25.0289			−0.856972			−0.428486	−	0.903548i	$-0.640953\pi$
$853$	−25.0289			−0.856972			−0.428486	+	0.903548i	$0.640953\pi$
$854$	−0.899034	+	1.55717i	−0.0307643	+	0.0532853i
$855$	0.968229	+	7.17895i	0.0331127	+	0.245515i
$856$	−1.57543	+	2.72873i	−0.0538472	+	0.0932660i
$857$	33.4700	−	19.3239i	1.14331	−	0.660093i	0.196065	−	0.980591i	$-0.437184\pi$
$857$	33.4700	−	19.3239i	1.14331	−	0.660093i	0.947249	+	0.320498i	$0.103850\pi$
$858$	0.606630	−	1.23504i	0.0207100	−	0.0421637i
$859$	20.0638	−	11.5838i	0.684568	−	0.395236i	−0.117006	−	0.993131i	$-0.537330\pi$
$859$	20.0638	−	11.5838i	0.684568	−	0.395236i	0.801574	+	0.597895i	$0.203996\pi$
$860$	9.55190			0.325717
$861$	0.771313	+	11.4896i	0.0262863	+	0.391564i
$862$	−6.67493	+	11.5613i	−0.227349	+	0.393780i
$863$	−6.41727	−	11.1150i	−0.218447	−	0.378361i	0.735887	−	0.677105i	$-0.236766\pi$
$863$	−6.41727	−	11.1150i	−0.218447	−	0.378361i	−0.954333	+	0.298744i	$0.903432\pi$
$864$	1.03788	+	5.09144i	0.0353094	+	0.173214i
$865$	3.76048	−	6.51333i	0.127860	−	0.221460i
$866$	−7.69946			−0.261638
$867$	−2.16506	−	3.22918i	−0.0735293	−	0.109669i
$868$	2.75707	+	0.979173i	0.0935812	+	0.0332353i
$869$			6.52465i			0.221334i
$870$	7.13694	+	10.6447i	0.241965	+	0.360890i
$871$	−9.94704	−	5.74293i	−0.337043	−	0.194592i
$872$			15.3371i			0.519380i
$873$	37.9078	−	5.11265i	1.28299	−	0.173037i
$874$	16.6889	+	9.63536i	0.564511	+	0.325921i
$875$	−0.455085	−	0.262744i	−0.0153847	−	0.00888235i
$876$	0.157454	−	0.105568i	0.00531987	−	0.00356680i
$877$	−0.128327	−	0.222269i	−0.00433330	−	0.00750550i	0.863851	−	0.503748i	$-0.168046\pi$
$877$	−0.128327	−	0.222269i	−0.00433330	−	0.00750550i	−0.868184	+	0.496243i	$0.834713\pi$
$878$	−16.3120	+	9.41775i	−0.550504	+	0.317834i
$879$	−3.36379	−	1.65223i	−0.113458	−	0.0557284i
$880$	−0.356638	−	0.205905i	−0.0120223	−	0.00694106i
$881$	−23.3047	−	40.3649i	−0.785155	−	1.35993i	−0.928907	−	0.370314i	$-0.879250\pi$
$881$	−23.3047	−	40.3649i	−0.785155	−	1.35993i	0.143752	−	0.989614i	$-0.454083\pi$
$882$	15.9643	−	12.3302i	0.537546	−	0.415180i
$883$			17.2463i			0.580384i	0.956968	+	0.290192i	$0.0937192\pi$
$883$			17.2463i			0.580384i	−0.956968	+	0.290192i	$0.906281\pi$
$884$		−	7.41021i		−	0.249232i
$885$	−16.8329	+	1.13001i	−0.565830	+	0.0379850i
$886$	1.08603	+	1.88105i	0.0364858	+	0.0631952i
$887$	−8.35780	−	4.82538i	−0.280628	−	0.162020i	0.353080	−	0.935593i	$-0.385134\pi$
$887$	−8.35780	−	4.82538i	−0.280628	−	0.162020i	−0.633707	+	0.773573i	$0.718468\pi$
$888$	−3.49415	+	7.11377i	−0.117256	+	0.238723i
$889$	−0.890465	+	0.514110i	−0.0298652	+	0.0172427i
$890$	−8.46804	−	14.6671i	−0.283849	−	0.491641i
$891$	−2.63727	−	2.60412i	−0.0883517	−	0.0872413i
$892$	1.23523	+	0.713160i	0.0413585	+	0.0238784i
$893$	23.5776	+	13.6125i	0.788994	+	0.455526i
$894$	−3.07005	+	6.25034i	−0.102678	+	0.209043i
$895$			8.63814i			0.288741i
$896$	0.455085	+	0.262744i	0.0152033	+	0.00877765i
$897$	−22.1486	+	14.8499i	−0.739521	+	0.495825i
$898$			5.83596i			0.194749i
$899$	−7.47049	−	40.5142i	−0.249155	−	1.35122i
$900$	−1.13928	+	2.77525i	−0.0379760	+	0.0925085i
$901$	38.1674			1.27154
$902$	−2.60511	+	4.51218i	−0.0867406	+	0.150239i
$903$	7.22103	−	4.84147i	0.240301	−	0.161114i
$904$	−9.50830	−	16.4689i	−0.316241	−	0.547746i
$905$	−12.2524	+	21.2217i	−0.407282	+	0.705434i
$906$	5.17051	−	0.347104i	0.171779	−	0.0115317i
$907$	−1.56482			−0.0519589			−0.0259795	−	0.999662i	$-0.508270\pi$
$907$	−1.56482			−0.0519589			−0.0259795	+	0.999662i	$0.508270\pi$
$908$	15.3135	−	8.84127i	0.508197	−	0.293408i
$909$	−2.46919	−	18.3078i	−0.0818977	−	0.607232i
$910$	−0.877906	+	0.506859i	−0.0291023	+	0.0168022i
$911$	−5.84896	+	10.1307i	−0.193785	+	0.335645i	−0.946501	−	0.322700i	$-0.895410\pi$
$911$	−5.84896	+	10.1307i	−0.193785	+	0.335645i	0.752717	+	0.658344i	$0.228743\pi$
$912$	1.84385	−	3.75391i	0.0610560	−	0.124304i
$913$	1.19400	−	2.06807i	0.0395156	−	0.0684430i
$914$	4.51856			0.149461
$915$	3.30042	+	4.92256i	0.109109	+	0.162735i
$916$	12.9472	+	7.47510i	0.427789	+	0.246984i
$917$	1.18708	−	0.685359i	0.0392007	−	0.0226325i
$918$	−18.9308	−	6.32616i	−0.624809	−	0.208794i
$919$	21.8201	+	37.7935i	0.719779	+	1.24669i	0.961087	+	0.276245i	$0.0890901\pi$
$919$	21.8201	+	37.7935i	0.719779	+	1.24669i	−0.241308	+	0.970448i	$0.577577\pi$
$920$	3.99037	+	6.91153i	0.131559	+	0.227866i
$921$	−18.4451	+	37.5525i	−0.607786	+	1.23740i
$922$			11.8557i			0.390447i
$923$	−6.37882	+	11.0484i	−0.209961	+	0.363664i
$924$	−0.373976	+	0.0251055i	−0.0123029	+	0.000825911i
$925$	−3.96279	+	2.28792i	−0.130296	+	0.0752263i
$926$	21.1783			0.695964
$927$	4.00429	+	5.18446i	0.131518	+	0.170280i
$928$		−	7.39923i		−	0.242892i
$929$	−27.4000			−0.898965			−0.449482	−	0.893289i	$-0.648392\pi$
$929$	−27.4000			−0.898965			−0.449482	+	0.893289i	$0.648392\pi$
$930$	6.90329	−	6.73384i	0.226368	−	0.220811i
$931$	−16.2358			−0.532106
$932$			13.5860i			0.445025i
$933$	3.18637	+	47.4646i	0.104317	+	1.55392i
$934$	28.2481			0.924308
$935$	1.36994	−	0.790938i	0.0448020	−	0.0258664i
$936$	3.53759	+	4.58022i	0.115630	+	0.149709i
$937$	−25.3058	+	43.8309i	−0.826704	+	1.43189i	0.0739057	+	0.997265i	$0.476454\pi$
$937$	−25.3058	+	43.8309i	−0.826704	+	1.43189i	−0.900610	+	0.434628i	$0.856880\pi$
$938$			3.12874i			0.102157i
$939$	−49.6373	−	24.3809i	−1.61985	−	0.795641i
$940$	5.63748	+	9.76440i	0.183874	+	0.318480i
$941$	27.2058	+	47.1218i	0.886883	+	1.53613i	0.843540	+	0.537066i	$0.180467\pi$
$941$	27.2058	+	47.1218i	0.886883	+	1.53613i	0.0433429	+	0.999060i	$0.486199\pi$
$942$	−0.00518762	−	0.0772756i	−0.000169022	−	0.00251777i
$943$	87.4446	−	50.4861i	2.84759	−	1.64406i
$944$	8.43537	+	4.87016i	0.274548	+	0.158510i
$945$	0.545392	+	2.67549i	0.0177416	+	0.0870336i
$946$	3.93357			0.127891
$947$	−26.6487	+	46.1569i	−0.865967	+	1.49990i	0.000117103		1.00000i	$0.499963\pi$
$947$	−26.6487	+	46.1569i	−0.865967	+	1.49990i	−0.866084	+	0.499899i	$0.833371\pi$
$948$	−24.6314	−	12.0985i	−0.799991	−	0.392941i
$949$	0.105568	−	0.182849i	0.00342687	−	0.00593552i
$950$	2.09115	−	1.20732i	0.0678458	−	0.0391708i
$951$	15.9995	+	7.85864i	0.518818	+	0.254834i
$952$	−1.74811	+	1.00927i	−0.0566564	+	0.0327106i
$953$	−49.6593			−1.60862			−0.804311	−	0.594208i	$-0.797466\pi$
$953$	−49.6593			−1.60862			−0.804311	+	0.594208i	$0.797466\pi$
$954$	−23.5911	+	18.2209i	−0.763791	+	0.589924i
$955$	3.58418	−	6.20798i	0.115981	−	0.200885i
$956$	−5.46206	−	9.46057i	−0.176656	−	0.305977i
$957$	2.93907	+	4.38361i	0.0950065	+	0.141702i
$958$	7.76095	−	13.4424i	0.250745	−	0.434303i
$959$	−1.03704			−0.0334876
$960$	1.43862	−	0.964551i	0.0464314	−	0.0311308i
$961$	−28.9613	+	11.0564i	−0.934235	+	0.356658i
$962$			8.82726i			0.284602i
$963$	8.74445	+	3.58972i	0.281786	+	0.115677i
$964$	−15.2622	−	8.81166i	−0.491564	−	0.283804i
$965$			22.1064i			0.711630i
$966$	6.51981	+	3.20241i	0.209772	+	0.103036i
$967$	23.5613	+	13.6031i	0.757681	+	0.437447i	0.828463	−	0.560044i	$-0.189216\pi$
$967$	23.5613	+	13.6031i	0.757681	+	0.437447i	−0.0707815	+	0.997492i	$0.522549\pi$
$968$	9.37941	+	5.41521i	0.301466	+	0.174051i
$969$	8.94653	+	13.3437i	0.287404	+	0.428662i
$970$	−6.37517	−	11.0421i	−0.204695	−	0.354541i
$971$	33.2074	−	19.1723i	1.06568	−	0.615269i	0.138680	−	0.990337i	$-0.455714\pi$
$971$	33.2074	−	19.1723i	1.06568	−	0.615269i	0.926997	+	0.375068i	$0.122381\pi$
$972$	14.7211	−	5.12727i	0.472180	−	0.164457i
$973$	3.12036	+	1.80154i	0.100034	+	0.0577547i
$974$	2.30888	+	3.99910i	0.0739813	+	0.128139i
$975$	0.223803	+	3.33380i	0.00716742	+	0.106767i
$976$		−	3.42172i		−	0.109526i
$977$			15.2310i			0.487284i	0.969865	+	0.243642i	$0.0783422\pi$
$977$			15.2310i			0.487284i	−0.969865	+	0.243642i	$0.921658\pi$
$978$	2.17641	+	32.4202i	0.0695940	+	1.03668i
$979$	−3.48723	−	6.04005i	−0.111452	−	0.193041i
$980$	−5.82304	−	3.36193i	−0.186010	−	0.107393i
$981$	45.5985	−	6.14990i	1.45585	−	0.196351i
$982$	−29.8716	+	17.2463i	−0.953240	+	0.550353i
$983$	7.23306	+	12.5280i	0.230699	+	0.399582i	0.958014	−	0.286722i	$-0.0925655\pi$
$983$	7.23306	+	12.5280i	0.230699	+	0.399582i	−0.727315	+	0.686304i	$0.759232\pi$
$984$	−12.2035	−	18.2014i	−0.389033	−	0.580241i
$985$	0.427671	+	0.246916i	0.0136267	+	0.00786739i
$986$	24.6146	+	14.2112i	0.783888	+	0.452578i
$987$	9.21099	+	4.52427i	0.293189	+	0.144009i
$988$		−	4.65811i		−	0.148194i
$989$	−66.0182	−	38.1156i	−2.09926	−	1.21201i
$990$	−0.469168	+	1.14288i	−0.0149111	+	0.0363231i
$991$		−	53.2402i		−	1.69123i	−0.533793	−	0.845615i	$-0.679234\pi$
$991$		−	53.2402i		−	1.69123i	0.533793	−	0.845615i	$-0.320766\pi$
$992$	−5.47546	+	1.00963i	−0.173846	+	0.0320558i
$993$	34.0306	−	22.8164i	1.07993	−	0.724057i
$994$	3.47518			0.110226
$995$	6.60560	−	11.4412i	0.209412	−	0.362712i
$996$	5.59322	+	8.34227i	0.177228	+	0.264335i
$997$	6.53214	+	11.3140i	0.206875	+	0.358318i	0.950728	−	0.310025i	$-0.100337\pi$
$997$	6.53214	+	11.3140i	0.206875	+	0.358318i	−0.743854	+	0.668343i	$0.767004\pi$
$998$	−4.80411	+	8.32095i	−0.152071	+	0.263395i
$999$	22.5509	+	7.53591i	0.713479	+	0.238426i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.o.d.491.1	yes	36
3.2	odd	2	inner	930.2.o.d.491.13	yes	36
31.6	odd	6	inner	930.2.o.d.161.4	✓	36
93.68	even	6	inner	930.2.o.d.161.10	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.o.d.161.4	✓	36	31.6	odd	6	inner
930.2.o.d.161.10	yes	36	93.68	even	6	inner
930.2.o.d.491.1	yes	36	1.1	even	1	trivial
930.2.o.d.491.13	yes	36	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.72816 + 0.116014i) q^{3} -1.00000 q^{4} +(0.866025 - 0.500000i) q^{5} +(0.116014 + 1.72816i) q^{6} +(0.262744 - 0.455085i) q^{7} +1.00000i q^{8} +(2.97308 - 0.400981i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.72816 + 0.116014i) q^{3} -1.00000 q^{4} +(0.866025 - 0.500000i) q^{5} +(0.116014 + 1.72816i) q^{6} +(0.262744 - 0.455085i) q^{7} +1.00000i q^{8} +(2.97308 - 0.400981i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-0.205905 - 0.356638i) q^{11} +(1.72816 - 0.116014i) q^{12} +(1.67065 - 0.964551i) q^{13} +(-0.455085 - 0.262744i) q^{14} +(-1.43862 + 0.964551i) q^{15} +1.00000 q^{16} +(-1.92064 + 3.32664i) q^{17} +(-0.400981 - 2.97308i) q^{18} +(-1.20732 + 2.09115i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(-0.401267 + 0.816942i) q^{21} +(-0.356638 + 0.205905i) q^{22} +7.98075 q^{23} +(-0.116014 - 1.72816i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.964551 - 1.67065i) q^{26} +(-5.09144 + 1.03788i) q^{27} +(-0.262744 + 0.455085i) q^{28} +7.39923 q^{29} +(0.964551 + 1.43862i) q^{30} +(-1.00963 - 5.47546i) q^{31} -1.00000i q^{32} +(0.397212 + 0.592441i) q^{33} +(3.32664 + 1.92064i) q^{34} -0.525487i q^{35} +(-2.97308 + 0.400981i) q^{36} +(-3.96279 - 2.28792i) q^{37} +(2.09115 + 1.20732i) q^{38} +(-2.77525 + 1.86072i) q^{39} +(0.500000 + 0.866025i) q^{40} +(10.9569 - 6.32599i) q^{41} +(0.816942 + 0.401267i) q^{42} +(-8.27218 - 4.77595i) q^{43} +(0.205905 + 0.356638i) q^{44} +(2.37427 - 1.83380i) q^{45} -7.98075i q^{46} -11.2750i q^{47} +(-1.72816 + 0.116014i) q^{48} +(3.36193 + 5.82304i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(2.93323 - 5.97179i) q^{51} +(-1.67065 + 0.964551i) q^{52} +(-4.96807 - 8.60495i) q^{53} +(1.03788 + 5.09144i) q^{54} +(-0.356638 - 0.205905i) q^{55} +(0.455085 + 0.262744i) q^{56} +(1.84385 - 3.75391i) q^{57} -7.39923i q^{58} +(8.43537 + 4.87016i) q^{59} +(1.43862 - 0.964551i) q^{60} -3.42172i q^{61} +(-5.47546 + 1.00963i) q^{62} +(0.598677 - 1.45836i) q^{63} -1.00000 q^{64} +(0.964551 - 1.67065i) q^{65} +(0.592441 - 0.397212i) q^{66} +(-2.97699 - 5.15630i) q^{67} +(1.92064 - 3.32664i) q^{68} +(-13.7920 + 0.925878i) q^{69} -0.525487 q^{70} +(-5.72724 + 3.30663i) q^{71} +(0.400981 + 2.97308i) q^{72} +(0.0947842 - 0.0547237i) q^{73} +(-2.28792 + 3.96279i) q^{74} +(-0.763610 + 1.55464i) q^{75} +(1.20732 - 2.09115i) q^{76} -0.216401 q^{77} +(1.86072 + 2.77525i) q^{78} +(-13.7211 - 7.92191i) q^{79} +(0.866025 - 0.500000i) q^{80} +(8.67843 - 2.38430i) q^{81} +(-6.32599 - 10.9569i) q^{82} +(2.89939 + 5.02189i) q^{83} +(0.401267 - 0.816942i) q^{84} +3.84127i q^{85} +(-4.77595 + 8.27218i) q^{86} +(-12.7871 + 0.858414i) q^{87} +(0.356638 - 0.205905i) q^{88} +16.9361 q^{89} +(-1.83380 - 2.37427i) q^{90} -1.01372i q^{91} -7.98075 q^{92} +(2.38003 + 9.34534i) q^{93} -11.2750 q^{94} +2.41465i q^{95} +(0.116014 + 1.72816i) q^{96} +12.7503 q^{97} +(5.82304 - 3.36193i) q^{98} +(-0.755178 - 0.977751i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9}+O(q^{10}) \) 36 * q - 36 * q^4 - 8 * q^7 + 8 * q^9	\( 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9} - 18 q^{10} + 36 q^{16} - 4 q^{18} - 4 q^{19} + 72 q^{21} - 18 q^{22} + 18 q^{25} + 8 q^{28} + 52 q^{31} - 36 q^{33} + 18 q^{34} - 8 q^{36} - 54 q^{37} - 8 q^{39} + 18 q^{40} + 12 q^{42} - 18 q^{43} + 4 q^{45} - 62 q^{49} - 10 q^{51} - 18 q^{55} + 12 q^{57} + 88 q^{63} - 36 q^{64} - 4 q^{66} + 10 q^{67} + 46 q^{69} + 16 q^{70} + 4 q^{72} + 24 q^{73} + 4 q^{76} + 92 q^{78} + 42 q^{79} + 4 q^{81} - 12 q^{82} - 72 q^{84} - 16 q^{87} + 18 q^{88} + 8 q^{90} + 48 q^{93} - 92 q^{94} - 80 q^{97} - 18 q^{99}+O(q^{100}) \) 36 * q - 36 * q^4 - 8 * q^7 + 8 * q^9 - 18 * q^10 + 36 * q^16 - 4 * q^18 - 4 * q^19 + 72 * q^21 - 18 * q^22 + 18 * q^25 + 8 * q^28 + 52 * q^31 - 36 * q^33 + 18 * q^34 - 8 * q^36 - 54 * q^37 - 8 * q^39 + 18 * q^40 + 12 * q^42 - 18 * q^43 + 4 * q^45 - 62 * q^49 - 10 * q^51 - 18 * q^55 + 12 * q^57 + 88 * q^63 - 36 * q^64 - 4 * q^66 + 10 * q^67 + 46 * q^69 + 16 * q^70 + 4 * q^72 + 24 * q^73 + 4 * q^76 + 92 * q^78 + 42 * q^79 + 4 * q^81 - 12 * q^82 - 72 * q^84 - 16 * q^87 + 18 * q^88 + 8 * q^90 + 48 * q^93 - 92 * q^94 - 80 * q^97 - 18 * q^99

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