LMFDB - Embedded newform 930.2.o.d.161.4

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			161.4
Character	$\chi$	$=$	930.161
Dual form			930.2.o.d.491.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.763610 + 1.55464i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.55464 + 0.763610i) q^{6} +(0.262744 + 0.455085i) q^{7} +1.00000i q^{8} +(-1.83380 - 2.37427i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.763610 + 1.55464i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.55464 + 0.763610i) q^{6} +(0.262744 + 0.455085i) q^{7} +1.00000i q^{8} +(-1.83380 - 2.37427i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(0.205905 - 0.356638i) q^{11} +(0.763610 - 1.55464i) 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} +(-2.37427 + 1.83380i) q^{18} +(-1.20732 - 2.09115i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-0.908126 + 0.0609638i) q^{21} +(-0.356638 - 0.205905i) q^{22} -7.98075 q^{23} +(-1.55464 - 0.763610i) 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} +(1.83380 + 2.37427i) 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} +(0.0609638 + 0.908126i) q^{42} +(-8.27218 + 4.77595i) q^{43} +(-0.205905 + 0.356638i) q^{44} +(0.400981 + 2.97308i) q^{45} +7.98075i q^{46} -11.2750i q^{47} +(-0.763610 + 1.55464i) q^{48} +(3.36193 - 5.82304i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-6.63834 + 0.445641i) 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} +(4.17290 - 0.280133i) 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} +(6.09418 - 12.4072i) q^{69} -0.525487 q^{70} +(5.72724 + 3.30663i) q^{71} +(2.37427 - 1.83380i) q^{72} +(0.0947842 + 0.0547237i) q^{73} +(2.28792 + 3.96279i) q^{74} +(-1.72816 + 0.116014i) 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} +(-2.27435 + 8.70789i) q^{81} +(-6.32599 + 10.9569i) q^{82} +(-2.89939 + 5.02189i) q^{83} +(0.908126 - 0.0609638i) q^{84} -3.84127i q^{85} +(4.77595 + 8.27218i) q^{86} +(5.65013 - 11.5031i) q^{87} +(0.356638 + 0.205905i) q^{88} -16.9361 q^{89} +(2.97308 - 0.400981i) q^{90} +1.01372i q^{91} +7.98075 q^{92} +(-7.74139 - 5.75072i) q^{93} -11.2750 q^{94} +2.41465i q^{95} +(1.55464 + 0.763610i) q^{96} +12.7503 q^{97} +(-5.82304 - 3.36193i) q^{98} +(-1.22435 + 0.165128i) 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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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
$3$	−0.763610	+	1.55464i	−0.440870	+	0.897571i
$3$	−0.763610	+	1.55464i	−0.440870	+	0.897571i
$4$	−1.00000			−0.500000
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	1.55464	+	0.763610i	0.634678	+	0.311742i
$7$	0.262744	+	0.455085i	0.0993077	+	0.172006i	0.911398	−	0.411525i	$-0.135004\pi$
$7$	0.262744	+	0.455085i	0.0993077	+	0.172006i	−0.812091	+	0.583531i	$0.801671\pi$
$8$			1.00000i			0.353553i
$9$	−1.83380	−	2.37427i	−0.611267	−	0.791425i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	0.205905	−	0.356638i	0.0620828	−	0.107530i	−0.833313	−	0.552801i	$-0.813559\pi$
$11$	0.205905	−	0.356638i	0.0620828	−	0.107530i	0.895396	+	0.445270i	$0.146892\pi$
$12$	0.763610	−	1.55464i	0.220435	−	0.448785i
$13$	1.67065	+	0.964551i	0.463356	+	0.267518i	0.713454	−	0.700702i	$-0.247130\pi$
$13$	1.67065	+	0.964551i	0.463356	+	0.267518i	−0.250099	+	0.968220i	$0.580463\pi$
$14$	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	$-0.0124251\pi$
$17$	1.92064	+	3.32664i	0.465823	+	0.806828i	−0.533416	+	0.845853i	$0.679092\pi$
$18$	−2.37427	+	1.83380i	−0.559622	+	0.432231i
$19$	−1.20732	−	2.09115i	−0.276979	−	0.479742i	0.693653	−	0.720309i	$-0.256000\pi$
$19$	−1.20732	−	2.09115i	−0.276979	−	0.479742i	−0.970633	+	0.240567i	$0.922667\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$	−0.908126	+	0.0609638i	−0.198169	+	0.0133034i
$22$	−0.356638	−	0.205905i	−0.0760355	−	0.0438991i
$23$	−7.98075			−1.66410			−0.832051	−	0.554700i	$-0.812833\pi$
$23$	−7.98075			−1.66410			−0.832051	+	0.554700i	$0.812833\pi$
$24$	−1.55464	−	0.763610i	−0.317339	−	0.155871i
$25$	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	$-0.741073\pi$
$29$	−7.39923			−1.37400			−0.687002	+	0.726656i	$0.741073\pi$
$30$	−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
$36$	1.83380	+	2.37427i	0.305633	+	0.395712i
$37$	−3.96279	+	2.28792i	−0.651479	+	0.376131i	−0.789023	−	0.614364i	$-0.789413\pi$
$37$	−3.96279	+	2.28792i	−0.651479	+	0.376131i	0.137544	+	0.990496i	$0.456079\pi$
$38$	−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	−0.932968	−	0.359960i	$-0.882790\pi$
$41$	−10.9569	−	6.32599i	−1.71119	−	0.987954i	−0.778218	−	0.627994i	$-0.783876\pi$
$42$	0.0609638	+	0.908126i	0.00940692	+	0.140127i
$43$	−8.27218	+	4.77595i	−1.26150	+	0.728325i	−0.973364	−	0.229265i	$-0.926368\pi$
$43$	−8.27218	+	4.77595i	−1.26150	+	0.728325i	−0.288132	+	0.957591i	$0.593034\pi$
$44$	−0.205905	+	0.356638i	−0.0310414	+	0.0537652i
$45$	0.400981	+	2.97308i	0.0597748	+	0.443201i
$46$			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	$-0.307315\pi$
$48$	−0.763610	+	1.55464i	−0.110218	+	0.224393i
$49$	3.36193	−	5.82304i	0.480276	−	0.831862i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	−6.63834	+	0.445641i	−0.929553	+	0.0624022i
$52$	−1.67065	−	0.964551i	−0.231678	−	0.133759i
$53$	4.96807	−	8.60495i	0.682417	−	1.18198i	−0.291824	−	0.956472i	$-0.594262\pi$
$53$	4.96807	−	8.60495i	0.682417	−	1.18198i	0.974241	−	0.225509i	$-0.0724045\pi$
$54$	−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
$57$	4.17290	−	0.280133i	0.552715	−	0.0371045i
$58$			7.39923i			0.971567i
$59$	−8.43537	+	4.87016i	−1.09819	+	0.634041i	−0.935746	−	0.352676i	$-0.885272\pi$
$59$	−8.43537	+	4.87016i	−1.09819	+	0.634041i	−0.162446	+	0.986717i	$0.551938\pi$
$60$	−1.43862	+	0.964551i	−0.185726	+	0.124523i
$61$			3.42172i			0.438106i	0.975713	+	0.219053i	$0.0702967\pi$
$61$			3.42172i			0.438106i	−0.975713	+	0.219053i	$0.929703\pi$
$62$	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	−0.988566	−	0.150787i	$-0.951819\pi$
$67$	−2.97699	+	5.15630i	−0.363698	+	0.629943i	0.624869	+	0.780730i	$0.285153\pi$
$68$	−1.92064	−	3.32664i	−0.232911	−	0.403414i
$69$	6.09418	−	12.4072i	0.733653	−	1.49365i
$70$	−0.525487			−0.0628077
$71$	5.72724	+	3.30663i	0.679699	+	0.392424i	0.799742	−	0.600344i	$-0.204970\pi$
$71$	5.72724	+	3.30663i	0.679699	+	0.392424i	−0.120043	+	0.992769i	$0.538303\pi$
$72$	2.37427	−	1.83380i	0.279811	−	0.216115i
$73$	0.0947842	+	0.0547237i	0.0110937	+	0.00640493i	0.505537	−	0.862805i	$-0.331295\pi$
$73$	0.0947842	+	0.0547237i	0.0110937	+	0.00640493i	−0.494443	+	0.869210i	$0.664628\pi$
$74$	2.28792	+	3.96279i	0.265965	+	0.460665i
$75$	−1.72816	+	0.116014i	−0.199551	+	0.0133961i
$76$	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	−0.545152	+	0.838337i	$0.683528\pi$
$79$	−13.7211	+	7.92191i	−1.54375	+	0.891284i	−0.998597	+	0.0529474i	$0.983138\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	−2.27435	+	8.70789i	−0.252706	+	0.967543i
$82$	−6.32599	+	10.9569i	−0.698589	+	1.20999i
$83$	−2.89939	+	5.02189i	−0.318249	+	0.551224i	−0.980123	−	0.198391i	$-0.936428\pi$
$83$	−2.89939	+	5.02189i	−0.318249	+	0.551224i	0.661873	+	0.749616i	$0.269762\pi$
$84$	0.908126	−	0.0609638i	0.0990847	−	0.00665169i
$85$		−	3.84127i		−	0.416644i
$86$	4.77595	+	8.27218i	0.515004	+	0.892013i
$87$	5.65013	−	11.5031i	0.605757	−	1.23327i
$88$	0.356638	+	0.205905i	0.0380178	+	0.0219496i
$89$	−16.9361			−1.79522			−0.897610	−	0.440790i	$-0.854698\pi$
$89$	−16.9361			−1.79522			−0.897610	+	0.440790i	$0.854698\pi$
$90$	2.97308	−	0.400981i	0.313390	−	0.0422671i
$91$			1.01372i			0.106267i
$92$	7.98075			0.832051
$93$	−7.74139	−	5.75072i	−0.802745	−	0.596322i
$94$	−11.2750			−1.16292
$95$			2.41465i			0.247738i
$96$	1.55464	+	0.763610i	0.158670	+	0.0779356i
$97$	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
$99$	−1.22435	+	0.165128i	−0.123051	+	0.0165960i
$100$	−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	$-0.0991128\pi$
$102$	0.445641	+	6.63834i	0.0441250	+	0.657293i
$103$	1.09180	−	1.89105i	0.107578	−	0.186331i	−0.807210	−	0.590264i	$-0.799024\pi$
$103$	1.09180	−	1.89105i	0.107578	−	0.186331i	0.914789	+	0.403933i	$0.132357\pi$
$104$	−0.964551	+	1.67065i	−0.0945821	+	0.163821i
$105$	0.816942	+	0.401267i	0.0797254	+	0.0391596i
$106$	−8.60495	−	4.96807i	−0.835787	−	0.482542i
$107$	−2.72873	+	1.57543i	−0.263796	+	0.152303i	−0.626065	−	0.779771i	$-0.715336\pi$
$107$	−2.72873	+	1.57543i	−0.263796	+	0.152303i	0.362269	+	0.932074i	$0.382002\pi$
$108$	−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
$111$	−0.530860	−	7.90778i	−0.0503870	−	0.750573i
$112$	0.262744	+	0.455085i	0.0248269	+	0.0430015i
$113$	16.4689	+	9.50830i	1.54926	+	0.894466i	0.998198	+	0.0600016i	$0.0191106\pi$
$113$	16.4689	+	9.50830i	1.54926	+	0.894466i	0.551062	+	0.834464i	$0.314223\pi$
$114$	−0.280133	−	4.17290i	−0.0262368	−	0.390828i
$115$	6.91153	+	3.99037i	0.644504	+	0.372104i
$116$	7.39923			0.687002
$117$	−0.773534	−	5.73538i	−0.0715133	−	0.530236i
$118$	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	−0.573296	−	0.819348i	$-0.694335\pi$
$127$	−1.69455	+	0.978350i	−0.150367	+	0.0868145i	0.422929	+	0.906163i	$0.361002\pi$
$128$			1.00000i			0.0883883i
$129$	−1.10815	−	16.5072i	−0.0975674	−	1.45338i
$130$	−1.67065	+	0.964551i	−0.146526	+	0.0845968i
$131$	−2.25900	+	1.30423i	−0.197370	+	0.113952i	−0.595428	−	0.803409i	$-0.703018\pi$
$131$	−2.25900	+	1.30423i	−0.197370	+	0.113952i	0.398058	+	0.917360i	$0.369684\pi$
$132$	−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
$135$	−4.92826	−	1.64689i	−0.424157	−	0.141742i
$136$	−3.32664	+	1.92064i	−0.285257	+	0.164693i
$137$	0.986737	−	1.70908i	0.0843027	−	0.146017i	−0.820791	−	0.571228i	$-0.806467\pi$
$137$	0.986737	−	1.70908i	0.0843027	−	0.146017i	0.905094	+	0.425212i	$0.139800\pi$
$138$	−12.4072	−	6.09418i	−1.05617	−	0.518771i
$139$		−	6.85664i		−	0.581573i	−0.956788	−	0.290787i	$-0.906083\pi$
$139$		−	6.85664i		−	0.581573i	0.956788	−	0.290787i	$-0.0939169\pi$
$140$			0.525487i			0.0444118i
$141$	17.5285	+	8.60966i	1.47616	+	0.725065i
$142$	3.30663	−	5.72724i	0.277486	−	0.480620i
$143$	0.687992	−	0.397212i	0.0575328	−	0.0332166i
$144$	−1.83380	−	2.37427i	−0.152817	−	0.197856i
$145$	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	$-0.719327\pi$
$149$	−3.48181	+	2.01022i	−0.285241	+	0.164684i	0.350553	+	0.936543i	$0.385994\pi$
$150$	0.116014	+	1.72816i	0.00947249	+	0.141104i
$151$			2.99192i			0.243479i	0.992562	+	0.121739i	$0.0388472\pi$
$151$			2.99192i			0.243479i	−0.992562	+	0.121739i	$0.961153\pi$
$152$	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
$162$	8.70789	+	2.27435i	0.684156	+	0.178690i
$163$	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
$165$	−0.0477757	−	0.711675i	−0.00371933	−	0.0554038i
$166$	5.02189	+	2.89939i	0.389774	+	0.225036i
$167$	3.77154	+	6.53250i	0.291851	+	0.505500i	0.974247	−	0.225482i	$-0.0723956\pi$
$167$	3.77154	+	6.53250i	0.291851	+	0.505500i	−0.682397	+	0.730982i	$0.739062\pi$
$168$	−0.0609638	−	0.908126i	−0.00470346	−	0.0700635i
$169$	−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	$-0.425627\pi$
$173$	−6.51333	−	3.76048i	−0.495200	−	0.285904i	−0.726729	+	0.686924i	$0.758960\pi$
$174$	−11.5031	−	5.65013i	−0.872050	−	0.428335i
$175$	−0.262744	+	0.455085i	−0.0198615	+	0.0344012i
$176$	0.205905	−	0.356638i	0.0155207	−	0.0268826i
$177$	−1.13001	−	16.8329i	−0.0849370	−	1.26524i
$178$			16.9361i			1.26941i
$179$	4.31907	+	7.48085i	0.322823	+	0.559145i	0.981069	−	0.193657i	$-0.0620350\pi$
$179$	4.31907	+	7.48085i	0.322823	+	0.559145i	−0.658247	+	0.752802i	$0.728702\pi$
$180$	−0.400981	−	2.97308i	−0.0298874	−	0.221600i
$181$	−21.2217	−	12.2524i	−1.57740	−	0.910711i	−0.995221	−	0.0976484i	$-0.968868\pi$
$181$	−21.2217	−	12.2524i	−1.57740	−	0.910711i	−0.582177	−	0.813062i	$-0.697799\pi$
$182$	1.01372			0.0751418
$183$	−5.31953	−	2.61285i	−0.393231	−	0.193148i
$184$		−	7.98075i		−	0.588349i
$185$	4.57584			0.336422
$186$	−5.75072	+	7.74139i	−0.421664	+	0.567627i
$187$	1.58188			0.115678
$188$			11.2750i			0.822311i
$189$	1.81007	+	2.04434i	0.131663	+	0.148704i
$190$	2.41465			0.175177
$191$	−6.20798	−	3.58418i	−0.449193	−	0.259342i	0.258296	−	0.966066i	$-0.416839\pi$
$191$	−6.20798	−	3.58418i	−0.449193	−	0.259342i	−0.707489	+	0.706724i	$0.750172\pi$
$192$	0.763610	−	1.55464i	0.0551088	−	0.112196i
$193$	−11.0532	−	19.1447i	−0.795627	−	1.37807i	−0.922440	−	0.386140i	$-0.873808\pi$
$193$	−11.0532	−	19.1447i	−0.795627	−	1.37807i	0.126813	−	0.991927i	$-0.459525\pi$
$194$		−	12.7503i		−	0.915422i
$195$	3.33380	−	0.223803i	0.238738	−	0.0160268i
$196$	−3.36193	+	5.82304i	−0.240138	+	0.415931i
$197$	−0.246916	+	0.427671i	−0.0175920	+	0.0304703i	−0.874687	−	0.484687i	$-0.838933\pi$
$197$	−0.246916	+	0.427671i	−0.0175920	+	0.0304703i	0.857095	+	0.515158i	$0.172267\pi$
$198$	0.165128	+	1.22435i	0.0117352	+	0.0870105i
$199$	11.4412	+	6.60560i	0.811048	+	0.468259i	0.847320	−	0.531083i	$-0.178215\pi$
$199$	11.4412	+	6.60560i	0.811048	+	0.468259i	−0.0362718	+	0.999342i	$0.511548\pi$
$200$	−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
$204$	6.63834	−	0.445641i	0.464777	−	0.0312011i
$205$	6.32599	+	10.9569i	0.441826	+	0.765266i
$206$	−1.89105	−	1.09180i	−0.131756	−	0.0760693i
$207$	14.6351	+	18.9485i	1.01721	+	1.31701i
$208$	1.67065	+	0.964551i	0.115839	+	0.0668796i
$209$	−0.994378			−0.0687825
$210$	0.401267	−	0.816942i	0.0276901	−	0.0563744i
$211$	−0.344382	−	0.596487i	−0.0237082	−	0.0410639i	0.853928	−	0.520391i	$-0.174214\pi$
$211$	−0.344382	−	0.596487i	−0.0237082	−	0.0410639i	−0.877636	+	0.479328i	$0.840881\pi$
$212$	−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
$222$	−7.90778	+	0.530860i	−0.530736	+	0.0356290i
$223$	−1.23523	+	0.713160i	−0.0827171	+	0.0477567i	−0.540788	−	0.841159i	$-0.681874\pi$
$223$	−1.23523	+	0.713160i	−0.0827171	+	0.0477567i	0.458071	+	0.888916i	$0.348541\pi$
$224$	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	$-0.133715\pi$
$227$	15.3135	+	8.84127i	1.01639	+	0.586816i	0.103337	+	0.994646i	$0.467048\pi$
$228$	−4.17290	+	0.280133i	−0.276357	+	0.0185522i
$229$	−12.9472	+	7.47510i	−0.855578	+	0.493968i	−0.862529	−	0.506008i	$-0.831121\pi$
$229$	−12.9472	+	7.47510i	−0.855578	+	0.493968i	0.00695097	+	0.999976i	$0.497787\pi$
$230$	3.99037	−	6.91153i	0.263118	−	0.455733i
$231$	−0.165246	+	0.336425i	−0.0108724	+	0.0221352i
$232$		−	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	$-0.146805\pi$
$234$	−5.73538	+	0.773534i	−0.374934	+	0.0505675i
$235$	−5.63748	+	9.76440i	−0.367749	+	0.636959i
$236$	8.43537	−	4.87016i	0.549096	−	0.317021i
$237$	−1.83810	−	27.3807i	−0.119398	−	1.77857i
$238$	1.74811	+	1.00927i	0.113313	+	0.0654212i
$239$	−5.46206	+	9.46057i	−0.353311	+	0.611953i	−0.986827	−	0.161776i	$-0.948278\pi$
$239$	−5.46206	+	9.46057i	−0.353311	+	0.611953i	0.633516	+	0.773730i	$0.281611\pi$
$240$	1.43862	−	0.964551i	0.0928628	−	0.0622615i
$241$	15.2622	−	8.81166i	0.983127	−	0.567609i	0.0799144	−	0.996802i	$-0.474535\pi$
$241$	15.2622	−	8.81166i	0.983127	−	0.567609i	0.903213	+	0.429193i	$0.141202\pi$
$242$	9.37941	−	5.41521i	0.602931	−	0.348103i
$243$	−11.8009	−	10.1852i	−0.757028	−	0.653382i
$244$		−	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	0.997996	+	0.0632767i	$0.0201551\pi$
$251$	8.77380	+	15.1967i	0.553797	+	0.959205i	−0.444199	+	0.895928i	$0.646512\pi$
$252$	−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
$255$	5.97179	+	2.93323i	0.373968	+	0.183686i
$256$	1.00000			0.0625000
$257$	−10.7798	−	6.22374i	−0.672427	−	0.388226i	0.124568	−	0.992211i	$-0.460245\pi$
$257$	−10.7798	−	6.22374i	−0.672427	−	0.388226i	−0.796996	+	0.603985i	$0.793579\pi$
$258$	−16.5072	+	1.10815i	−1.02769	+	0.0689905i
$259$	−2.08240	−	1.20227i	−0.129394	−	0.0747055i
$260$	0.964551	+	1.67065i	0.0598189	+	0.103609i
$261$	13.5687	+	17.5678i	0.839883	+	1.08742i
$262$	1.30423	+	2.25900i	0.0805759	+	0.139562i
$263$	2.05549			0.126747			0.0633734	−	0.997990i	$-0.479814\pi$
$263$	2.05549			0.126747			0.0633734	+	0.997990i	$0.479814\pi$
$264$	−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
$267$	12.9325	−	26.3295i	0.791459	−	1.61134i
$268$	2.97699	−	5.15630i	0.181849	−	0.314971i
$269$	−9.92480	+	17.1903i	−0.605126	+	1.04811i	0.386906	+	0.922119i	$0.373544\pi$
$269$	−9.92480	+	17.1903i	−0.605126	+	1.04811i	−0.992032	+	0.125989i	$0.959790\pi$
$270$	−1.64689	+	4.92826i	−0.100227	+	0.299924i
$271$		−	12.9670i		−	0.787686i	−0.919178	−	0.393843i	$-0.871145\pi$
$271$		−	12.9670i		−	0.787686i	0.919178	−	0.393843i	$-0.128855\pi$
$272$	1.92064	+	3.32664i	0.116456	+	0.201707i
$273$	−1.57597	−	0.774085i	−0.0953818	−	0.0468498i
$274$	−1.70908	−	0.986737i	−0.103249	−	0.0596110i
$275$	0.411810			0.0248331
$276$	−6.09418	+	12.4072i	−0.366826	+	0.746824i
$277$			11.7583i			0.706488i	0.935531	+	0.353244i	$0.114921\pi$
$277$			11.7583i			0.706488i	−0.935531	+	0.353244i	$0.885079\pi$
$278$	−6.85664			−0.411234
$279$	14.8517	−	7.64376i	0.889148	−	0.457620i
$280$	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	$-0.164934\pi$
$282$	8.60966	−	17.5285i	0.512698	−	1.04381i
$283$	−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
$285$	−3.75391	−	1.84385i	−0.222362	−	0.109220i
$286$	−0.397212	−	0.687992i	−0.0234877	−	0.0406818i
$287$		−	6.64845i		−	0.392446i
$288$	−2.37427	+	1.83380i	−0.139905	+	0.108058i
$289$	1.12232	−	1.94391i	0.0660185	−	0.114347i
$290$	3.69962	−	6.40792i	0.217249	−	0.376286i
$291$	−9.73629	+	19.8222i	−0.570751	+	1.16200i
$292$	−0.0947842	−	0.0547237i	−0.00554683	−	0.00320246i
$293$	−1.87383	+	1.08186i	−0.109470	+	0.0632027i	−0.553736	−	0.832693i	$-0.686798\pi$
$293$	−1.87383	+	1.08186i	−0.109470	+	0.0632027i	0.444265	+	0.895895i	$0.353465\pi$
$294$	9.67311	−	6.48551i	0.564147	−	0.378243i
$295$	9.74033			0.567104
$296$	−2.28792	−	3.96279i	−0.132983	−	0.230333i
$297$	0.678208	−	2.02951i	0.0393536	−	0.117764i
$298$	2.01022	+	3.48181i	0.116449	+	0.201696i
$299$	−13.3331	−	7.69784i	−0.771071	−	0.445178i
$300$	1.72816	−	0.116014i	0.0997754	−	0.00669806i
$301$	−4.34693	−	2.50970i	−0.250553	−	0.144657i
$302$	2.99192			0.172165
$303$	9.57324	+	4.70220i	0.549969	+	0.270134i
$304$	−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	0.972064	+	0.234717i	$0.0754164\pi$
$307$	12.0776	+	20.9190i	0.689303	+	1.19391i	−0.282761	+	0.959190i	$0.591250\pi$
$308$	−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	0.565962	−	0.824431i	$-0.308505\pi$
$313$	27.6509	−	15.9643i	1.56292	−	0.902353i	0.996959	−	0.0779218i	$-0.0248284\pi$
$314$			0.0447155i			0.00252344i
$315$	−1.24765	+	0.963639i	−0.0702971	+	0.0542949i
$316$	13.7211	−	7.92191i	0.771875	−	0.445642i
$317$	8.91264	−	5.14572i	0.500584	−	0.289012i	−0.228371	−	0.973574i	$-0.573340\pi$
$317$	8.91264	−	5.14572i	0.500584	−	0.289012i	0.728955	+	0.684562i	$0.240006\pi$
$318$	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
$321$	−0.365544	−	5.44520i	−0.0204027	−	0.303921i
$322$	−3.63192	+	2.09689i	−0.202399	+	0.116855i
$323$	4.63766	−	8.03267i	0.258046	−	0.446950i
$324$	2.27435	−	8.70789i	0.126353	−	0.483772i
$325$			1.92910i			0.107007i
$326$		−	18.7599i		−	1.03902i
$327$	−11.7116	+	23.8437i	−0.647651	+	1.31856i
$328$	6.32599	−	10.9569i	0.349294	−	0.604996i
$329$	5.13106	−	2.96242i	0.282885	−	0.163324i
$330$	−0.711675	+	0.0477757i	−0.0391764	+	0.00262997i
$331$	−20.4858	−	11.8275i	−1.12600	−	0.650097i	−0.183075	−	0.983099i	$-0.558605\pi$
$331$	−20.4858	−	11.8275i	−1.12600	−	0.650097i	−0.942926	+	0.333002i	$0.891938\pi$
$332$	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
$336$	−0.908126	+	0.0609638i	−0.0495424	+	0.00332585i
$337$			4.92368i			0.268210i	0.990967	+	0.134105i	$0.0428159\pi$
$337$			4.92368i			0.268210i	−0.990967	+	0.134105i	$0.957184\pi$
$338$	−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	$-0.106057\pi$
$347$	3.52558	+	6.10648i	0.189263	+	0.327813i	−0.755742	+	0.654870i	$0.772724\pi$
$348$	−5.65013	+	11.5031i	−0.302879	+	0.616633i
$349$	−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
$351$	9.50712	+	3.17703i	0.507453	+	0.169577i
$352$	−0.356638	−	0.205905i	−0.0190089	−	0.0109748i
$353$	9.28933	+	16.0896i	0.494421	+	0.856363i	0.999979	−	0.00642991i	$-0.00204672\pi$
$353$	9.28933	+	16.0896i	0.494421	+	0.856363i	−0.505558	+	0.862793i	$0.668713\pi$
$354$	−16.8329	+	1.13001i	−0.894656	+	0.0600595i
$355$	−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	$-0.453977\pi$
$359$	−12.1427	−	7.01060i	−0.640868	−	0.370005i	−0.784949	+	0.619561i	$0.787311\pi$
$360$	−2.97308	+	0.400981i	−0.156695	+	0.0211336i
$361$	6.58473	−	11.4051i	0.346565	−	0.600268i
$362$	−12.2524	+	21.2217i	−0.643970	+	1.11539i
$363$	−18.7167	+	1.25648i	−0.982372	+	0.0659480i
$364$		−	1.01372i		−	0.0531333i
$365$	−0.0547237	−	0.0947842i	−0.00286437	−	0.00496123i
$366$	−2.61285	+	5.31953i	−0.136576	+	0.278056i
$367$	−0.308737	−	0.178249i	−0.0161159	−	0.00930454i	0.491920	−	0.870640i	$-0.336295\pi$
$367$	−0.308737	−	0.178249i	−0.0161159	−	0.00930454i	−0.508036	+	0.861336i	$0.669628\pi$
$368$	−7.98075			−0.416025
$369$	5.07321	+	37.6154i	0.264101	+	1.95818i
$370$		−	4.57584i		−	0.237886i
$371$	5.22131			0.271077
$372$	7.74139	+	5.75072i	0.401373	+	0.298161i
$373$	−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
$375$	1.55464	+	0.763610i	0.0802812	+	0.0394326i
$376$	11.2750			0.581461
$377$	−12.3615	−	7.13694i	−0.636652	−	0.367571i
$378$	2.04434	−	1.81007i	0.105150	−	0.0930998i
$379$	12.6731	+	21.9505i	0.650975	+	1.12752i	0.982887	+	0.184211i	$0.0589730\pi$
$379$	12.6731	+	21.9505i	0.650975	+	1.12752i	−0.331912	+	0.943310i	$0.607694\pi$
$380$		−	2.41465i		−	0.123869i
$381$	−0.227004	−	3.38149i	−0.0116298	−	0.173239i
$382$	−3.58418	+	6.20798i	−0.183382	+	0.317628i
$383$	−8.84004	+	15.3114i	−0.451705	+	0.782376i	−0.998492	−	0.0548956i	$-0.982517\pi$
$383$	−8.84004	+	15.3114i	−0.451705	+	0.782376i	0.546787	+	0.837272i	$0.315851\pi$
$384$	−1.55464	−	0.763610i	−0.0793348	−	0.0389678i
$385$	−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	0.998398	+	0.0565746i	$0.0180179\pi$
$389$	10.8121	+	18.7271i	0.548194	+	0.949500i	−0.450204	+	0.892926i	$0.648649\pi$
$390$	−0.223803	−	3.33380i	−0.0113327	−	0.168814i
$391$	−15.3281	−	26.5491i	−0.775176	−	1.34264i
$392$	5.82304	+	3.36193i	0.294108	+	0.169803i
$393$	−0.302619	−	4.50786i	−0.0152651	−	0.227391i
$394$	0.427671	+	0.246916i	0.0215457	+	0.0124394i
$395$	15.8438			0.797189
$396$	1.22435	−	0.165128i	0.0615257	−	0.00829801i
$397$	3.04676	+	5.27715i	0.152913	+	0.264853i	0.932297	−	0.361694i	$-0.117801\pi$
$397$	3.04676	+	5.27715i	0.152913	+	0.264853i	−0.779384	+	0.626546i	$0.784468\pi$
$398$	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	$-0.526922\pi$
$401$	−3.38331			−0.168954			−0.0844772	+	0.996425i	$0.526922\pi$
$402$	−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
$408$	−0.445641	−	6.63834i	−0.0220625	−	0.328647i
$409$	0.373409	−	0.215588i	0.0184639	−	0.0106601i	−0.490740	−	0.871306i	$-0.663273\pi$
$409$	0.373409	−	0.215588i	0.0184639	−	0.0106601i	0.509204	+	0.860646i	$0.329940\pi$
$410$	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
$414$	18.9485	−	14.6351i	0.931267	−	0.719276i
$415$	5.02189	−	2.89939i	0.246515	−	0.142325i
$416$	0.964551	−	1.67065i	0.0472910	−	0.0819105i
$417$	10.6596	+	5.23580i	0.522003	+	0.256398i
$418$			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	$0.594128\pi$
$420$	−0.816942	−	0.401267i	−0.0398627	−	0.0195798i
$421$	−11.5115	+	19.9385i	−0.561036	+	0.971743i	0.436370	+	0.899767i	$0.356264\pi$
$421$	−11.5115	+	19.9385i	−0.561036	+	0.971743i	−0.997406	+	0.0719760i	$0.977070\pi$
$422$	−0.596487	+	0.344382i	−0.0290365	+	0.0167643i
$423$	−26.7698	+	20.6760i	−1.30159	+	1.00530i
$424$	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
$429$	0.0921643	+	1.37289i	0.00444973	+	0.0662839i
$430$		−	9.55190i		−	0.460633i
$431$	11.5613	−	6.67493i	0.556889	−	0.321520i	−0.195007	−	0.980802i	$-0.562473\pi$
$431$	11.5613	−	6.67493i	0.556889	−	0.321520i	0.751896	+	0.659282i	$0.229140\pi$
$432$	5.09144	−	1.03788i	0.244962	−	0.0499350i
$433$			7.69946i			0.370012i	0.982737	+	0.185006i	$0.0592305\pi$
$433$			7.69946i			0.370012i	−0.982737	+	0.185006i	$0.940769\pi$
$434$	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	−0.998352	−	0.0573791i	$-0.981726\pi$
$439$	−9.41775	+	16.3120i	−0.449484	+	0.778530i	0.548868	+	0.835909i	$0.315059\pi$
$440$	−0.205905	−	0.356638i	−0.00981614	−	0.0170021i
$441$	−19.9906	+	2.69614i	−0.951933	+	0.128388i
$442$	7.41021			0.352468
$443$	1.88105	+	1.08603i	0.0893715	+	0.0515987i	0.544020	−	0.839072i	$-0.316902\pi$
$443$	1.88105	+	1.08603i	0.0893715	+	0.0515987i	−0.454648	+	0.890671i	$0.650235\pi$
$444$	0.530860	+	7.90778i	0.0251935	+	0.375287i
$445$	14.6671	+	8.46804i	0.695286	+	0.401423i
$446$	0.713160	+	1.23523i	0.0337691	+	0.0584898i
$447$	−0.466427	−	6.94798i	−0.0220613	−	0.328628i
$448$	−0.262744	−	0.455085i	−0.0124135	−	0.0215008i
$449$	5.83596			0.275416			0.137708	−	0.990473i	$-0.456026\pi$
$449$	5.83596			0.275416			0.137708	+	0.990473i	$0.456026\pi$
$450$	−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
$453$	−4.65135	−	2.28466i	−0.218539	−	0.107342i
$454$	8.84127	−	15.3135i	0.414941	−	0.718700i
$455$	0.506859	−	0.877906i	0.0237619	−	0.0411569i
$456$	0.280133	+	4.17290i	0.0131184	+	0.195414i
$457$		−	4.51856i		−	0.211369i	−0.994400	−	0.105685i	$-0.966297\pi$
$457$		−	4.51856i		−	0.211369i	0.994400	−	0.105685i	$-0.0337034\pi$
$458$	7.47510	+	12.9472i	0.349288	+	0.604985i
$459$	13.2315	+	14.9440i	0.617592	+	0.697527i
$460$	−6.91153	−	3.99037i	−0.322252	−	0.186052i
$461$	11.8557			0.552176			0.276088	−	0.961132i	$-0.410962\pi$
$461$	11.8557			0.552176			0.276088	+	0.961132i	$0.410962\pi$
$462$	0.336425	+	0.165246i	0.0156519	+	0.00768794i
$463$		−	21.1783i		−	0.984241i	−0.870527	−	0.492121i	$-0.836222\pi$
$463$		−	21.1783i		−	0.984241i	0.870527	−	0.492121i	$-0.163778\pi$
$464$	−7.39923			−0.343501
$465$	3.82888	+	8.85097i	0.177560	+	0.410454i
$466$	−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	$0.773265\pi$
$468$	0.773534	+	5.73538i	0.0357566	+	0.265118i
$469$	−3.12874			−0.144472
$470$	9.76440	+	5.63748i	0.450398	+	0.260037i
$471$	0.0341452	−	0.0695164i	0.00157333	−	0.00320315i
$472$	−4.87016	−	8.43537i	−0.224167	−	0.388269i
$473$			3.93357i			0.180866i
$474$	−27.3807	+	1.83810i	−1.25764	+	0.0844268i
$475$	1.20732	−	2.09115i	0.0553959	−	0.0959484i
$476$	1.00927	−	1.74811i	0.0462598	−	0.0801243i
$477$	−29.5410	+	3.98421i	−1.35259	+	0.182424i
$478$	9.46057	+	5.46206i	0.432716	+	0.249829i
$479$	−13.4424	+	7.76095i	−0.614197	+	0.354607i	−0.774606	−	0.632444i	$-0.782052\pi$
$479$	−13.4424	+	7.76095i	−0.614197	+	0.354607i	0.160409	+	0.987051i	$0.448719\pi$
$480$	−0.964551	−	1.43862i	−0.0440256	−	0.0656639i
$481$	−8.82726			−0.402488
$482$	−8.81166	−	15.2622i	−0.401360	−	0.695176i
$483$	7.24753	−	0.486537i	0.329774	−	0.0221382i
$484$	−5.41521	−	9.37941i	−0.246146	−	0.426337i
$485$	−11.0421	−	6.37517i	−0.501397	−	0.289482i
$486$	−10.1852	+	11.8009i	−0.462011	+	0.535300i
$487$	−3.99910	−	2.30888i	−0.181216	−	0.104625i	0.406648	−	0.913585i	$-0.366698\pi$
$487$	−3.99910	−	2.30888i	−0.181216	−	0.104625i	−0.587864	+	0.808960i	$0.700031\pi$
$488$	−3.42172			−0.154894
$489$	−14.3253	+	29.1649i	−0.647811	+	1.31888i
$490$	3.36193	+	5.82304i	0.151877	+	0.263058i
$491$	17.2463	−	29.8716i	0.778317	−	1.34808i	−0.154594	−	0.987978i	$-0.549407\pi$
$491$	17.2463	−	29.8716i	0.778317	−	1.34808i	0.932911	−	0.360106i	$-0.117260\pi$
$492$	−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	−0.674549	−	0.738230i	$-0.735662\pi$
$499$	−8.32095	+	4.80411i	−0.372497	+	0.215061i	0.302052	+	0.953292i	$0.402328\pi$
$500$			1.00000i			0.0447214i
$501$	−13.0357	+	0.875102i	−0.582391	+	0.0390967i
$502$	15.1967	−	8.77380i	0.678260	−	0.391594i
$503$	−8.03131	+	4.63688i	−0.358098	+	0.206748i	−0.668246	−	0.743940i	$-0.732955\pi$
$503$	−8.03131	+	4.63688i	−0.358098	+	0.206748i	0.310148	+	0.950688i	$0.399621\pi$
$504$	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
$507$	16.0348	−	1.07644i	0.712133	−	0.0478065i
$508$	1.69455	−	0.978350i	0.0751836	−	0.0434073i
$509$	10.3947	−	18.0042i	0.460739	−	0.798023i	−0.538259	−	0.842779i	$-0.680918\pi$
$509$	10.3947	−	18.0042i	0.460739	−	0.798023i	0.998998	+	0.0447566i	$0.0142512\pi$
$510$	2.93323	−	5.97179i	0.129886	−	0.264435i
$511$			0.0575132i			0.00254423i
$512$		−	1.00000i		−	0.0441942i
$513$	−8.31739	−	9.39391i	−0.367222	−	0.414751i
$514$	−6.22374	+	10.7798i	−0.274517	+	0.475478i
$515$	−1.89105	+	1.09180i	−0.0833297	+	0.0481105i
$516$	1.10815	+	16.5072i	0.0487837	+	0.726690i
$517$	−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	$-0.453345\pi$
$521$	24.5559	−	14.1773i	1.07581	−	0.621120i	0.929764	+	0.368157i	$0.120011\pi$
$522$	17.5678	−	13.5687i	0.768922	−	0.593887i
$523$			25.3776i			1.10968i	0.831956	+	0.554842i	$0.187221\pi$
$523$			25.3776i			1.10968i	−0.831956	+	0.554842i	$0.812779\pi$
$524$	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
$534$	−26.3295	−	12.9325i	−1.13939	−	0.559646i
$535$	3.15086			0.136224
$536$	−5.15630	−	2.97699i	−0.222718	−	0.128587i
$537$	−14.9281	+	1.00214i	−0.644195	+	0.0432457i
$538$	17.1903	+	9.92480i	0.741125	+	0.427889i
$539$	−1.38448	−	2.39799i	−0.0596337	−	0.103289i
$540$	4.92826	+	1.64689i	0.212079	+	0.0708710i
$541$	10.5846	+	18.3331i	0.455068	+	0.788201i	0.998692	−	0.0511278i	$-0.0162816\pi$
$541$	10.5846	+	18.3331i	0.455068	+	0.788201i	−0.543624	+	0.839329i	$0.682948\pi$
$542$	−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
$546$	−0.774085	+	1.57597i	−0.0331278	+	0.0674451i
$547$	−10.9017	+	18.8824i	−0.466125	+	0.807352i	−0.999252	−	0.0386835i	$-0.987684\pi$
$547$	−10.9017	+	18.8824i	−0.466125	+	0.807352i	0.533127	+	0.846035i	$0.321017\pi$
$548$	−0.986737	+	1.70908i	−0.0421513	+	0.0730083i
$549$	8.12409	−	6.27474i	0.346728	−	0.267800i
$550$		−	0.411810i		−	0.0175597i
$551$	8.93328	+	15.4729i	0.380570	+	0.659167i
$552$	12.4072	+	6.09418i	0.528085	+	0.259385i
$553$	−7.21029	−	4.16286i	−0.306613	−	0.177023i
$554$	11.7583			0.499563
$555$	−3.49415	+	7.11377i	−0.148319	+	0.301963i
$556$			6.85664i			0.290787i
$557$	23.9327			1.01406			0.507031	−	0.861928i	$-0.330743\pi$
$557$	23.9327			1.01406			0.507031	+	0.861928i	$0.330743\pi$
$558$	−7.64376	−	14.8517i	−0.323586	−	0.628723i
$559$	−18.4266			−0.779362
$560$		−	0.525487i		−	0.0222059i
$561$	−1.20794	+	2.45924i	−0.0509991	+	0.103829i
$562$	−16.6048			−0.700429
$563$	−18.4599	−	10.6578i	−0.777990	−	0.449173i	0.0577272	−	0.998332i	$-0.481615\pi$
$563$	−18.4599	−	10.6578i	−0.777990	−	0.449173i	−0.835718	+	0.549159i	$0.814948\pi$
$564$	−17.5285	−	8.60966i	−0.738082	−	0.362532i
$565$	−9.50830	−	16.4689i	−0.400017	−	0.692850i
$566$			6.88072i			0.289218i
$567$	−4.56040	+	1.25292i	−0.191519	+	0.0526176i
$568$	−3.30663	+	5.72724i	−0.138743	+	0.240310i
$569$	7.22407	−	12.5125i	0.302849	−	0.524550i	−0.673931	−	0.738794i	$-0.735396\pi$
$569$	7.22407	−	12.5125i	0.302849	−	0.524550i	0.976780	+	0.214244i	$0.0687289\pi$
$570$	−1.84385	+	3.75391i	−0.0772304	+	0.157234i
$571$	−10.6839	−	6.16838i	−0.447109	−	0.258139i	0.259499	−	0.965743i	$-0.416442\pi$
$571$	−10.6839	−	6.16838i	−0.447109	−	0.258139i	−0.706609	+	0.707605i	$0.749776\pi$
$572$	−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
$576$	1.83380	+	2.37427i	0.0764084	+	0.0989281i
$577$	8.28966	+	14.3581i	0.345103	+	0.597736i	0.985372	−	0.170414i	$-0.0545107\pi$
$577$	8.28966	+	14.3581i	0.345103	+	0.597736i	−0.640269	+	0.768150i	$0.721177\pi$
$578$	−1.94391	−	1.12232i	−0.0808559	−	0.0466822i
$579$	38.2034	−	2.56465i	1.58768	−	0.106583i
$580$	−6.40792	−	3.69962i	−0.266075	−	0.153618i
$581$	−3.04718			−0.126419
$582$	19.8222	+	9.73629i	0.821656	+	0.403582i
$583$	−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	$-0.485665\pi$
$587$	2.18146			0.0900383			0.0450192	+	0.998986i	$0.485665\pi$
$588$	−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	$0.626216\pi$
$594$	−2.02951	−	0.678208i	−0.0832717	−	0.0278272i
$595$	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	$-0.649106\pi$
$599$	−35.4872	−	20.4885i	−1.44997	−	0.837138i	−0.998479	+	0.0551389i	$0.982440\pi$
$600$	−0.116014	−	1.72816i	−0.00473625	−	0.0705519i
$601$	−0.626997	+	0.361997i	−0.0255757	+	0.0147662i	−0.512733	−	0.858548i	$-0.671367\pi$
$601$	−0.626997	+	0.361997i	−0.0255757	+	0.0147662i	0.487158	+	0.873314i	$0.338034\pi$
$602$	−2.50970	+	4.34693i	−0.102288	+	0.177167i
$603$	17.7017	−	2.38744i	0.720868	−	0.0972240i
$604$		−	2.99192i		−	0.121739i
$605$		−	10.8304i		−	0.440319i
$606$	4.70220	−	9.57324i	0.191014	−	0.388886i
$607$	19.1262	−	33.1276i	0.776309	−	1.34461i	−0.157747	−	0.987480i	$-0.550423\pi$
$607$	19.1262	−	33.1276i	0.776309	−	1.34461i	0.934056	−	0.357127i	$-0.116244\pi$
$608$	−2.09115	+	1.20732i	−0.0848072	+	0.0489635i
$609$	6.71944	−	0.451085i	0.272285	−	0.0182789i
$610$	−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	0.272206	−	0.962239i	$-0.412247\pi$
$613$	30.7414	−	17.7485i	1.24163	−	0.716857i	0.969426	+	0.245383i	$0.0789136\pi$
$614$	20.9190	−	12.0776i	0.844220	−	0.487411i
$615$	−21.8647	+	1.46781i	−0.881668	+	0.0591876i
$616$			0.216401i			0.00871905i
$617$	−38.0597	+	21.9738i	−1.53223	+	0.884632i	−0.532968	+	0.846135i	$0.678923\pi$
$617$	−38.0597	+	21.9738i	−1.53223	+	0.884632i	−0.999259	+	0.0384963i	$0.987743\pi$
$618$	3.14138	−	2.10619i	0.126365	−	0.0847236i
$619$			17.3926i			0.699066i	0.936924	+	0.349533i	$0.113660\pi$
$619$			17.3926i			0.699066i	−0.936924	+	0.349533i	$0.886340\pi$
$620$	−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
$627$	0.759316	−	1.54590i	0.0303242	−	0.0617372i
$628$	0.0447155			0.00178434
$629$	−15.2222	−	8.78852i	−0.606947	−	0.350421i
$630$	0.963639	+	1.24765i	0.0383923	+	0.0497076i
$631$	3.13351	+	1.80913i	0.124743	+	0.0720205i	0.561073	−	0.827766i	$-0.310389\pi$
$631$	3.13351	+	1.80913i	0.124743	+	0.0720205i	−0.436330	+	0.899787i	$0.643722\pi$
$632$	−7.92191	−	13.7211i	−0.315117	−	0.545798i
$633$	1.19030	−	0.0799062i	0.0473100	−	0.00317599i
$634$	−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
$639$	−2.65179	−	19.6617i	−0.104903	−	0.777806i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−6.46266	+	11.1937i	−0.255260	+	0.442123i	−0.964966	−	0.262375i	$-0.915494\pi$
$641$	−6.46266	+	11.1937i	−0.255260	+	0.442123i	0.709706	+	0.704498i	$0.248828\pi$
$642$	−5.44520	+	0.365544i	−0.214905	+	0.0144269i
$643$		−	26.4746i		−	1.04406i	−0.852928	−	0.522028i	$-0.825176\pi$
$643$		−	26.4746i		−	1.04406i	0.852928	−	0.522028i	$-0.174824\pi$
$644$	2.09689	+	3.63192i	0.0826291	+	0.143118i
$645$	−7.29392	+	14.8497i	−0.287198	+	0.584708i
$646$	−8.03267	−	4.63766i	−0.316041	−	0.182466i
$647$	−36.7796			−1.44596			−0.722978	−	0.690871i	$-0.757227\pi$
$647$	−36.7796			−1.44596			−0.722978	+	0.690871i	$0.757227\pi$
$648$	−8.70789	−	2.27435i	−0.342078	−	0.0893449i
$649$			4.01117i			0.157452i
$650$	1.92910			0.0756656
$651$	0.583068	−	5.03396i	0.0228522	−	0.197296i
$652$	−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	$0.961801\pi$
$654$	23.8437	+	11.7116i	0.932362	+	0.457959i
$655$	2.60847			0.101921
$656$	−10.9569	−	6.32599i	−0.427796	−	0.246988i
$657$	−0.0438864	−	0.325396i	−0.00171217	−	0.0126949i
$658$	−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	$0.832409\pi$
$660$	0.0477757	+	0.711675i	0.00185967	+	0.0277019i
$661$	3.22830	−	5.59158i	0.125566	−	0.217487i	−0.796388	−	0.604786i	$-0.793259\pi$
$661$	3.22830	−	5.59158i	0.125566	−	0.217487i	0.921954	+	0.387299i	$0.126592\pi$
$662$	−11.8275	+	20.4858i	−0.459688	+	0.796203i
$663$	−11.5202	−	5.65851i	−0.447407	−	0.219758i
$664$	−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
$669$	−0.165473	−	2.46491i	−0.00639755	−	0.0952989i
$670$	−2.97699	−	5.15630i	−0.115011	−	0.199205i
$671$	1.22031	+	0.704549i	0.0471097	+	0.0271988i
$672$	0.0609638	+	0.908126i	0.00235173	+	0.0350317i
$673$	4.80470	+	2.77400i	0.185208	+	0.106930i	0.589737	−	0.807595i	$-0.299231\pi$
$673$	4.80470	+	2.77400i	0.185208	+	0.106930i	−0.404529	+	0.914525i	$0.632565\pi$
$674$	4.92368			0.189653
$675$	3.44455	+	3.89038i	0.132581	+	0.149741i
$676$	4.63928	+	8.03547i	0.178434	+	0.309057i
$677$	12.3039	−	21.3109i	0.472876	−	0.819045i	−0.526642	−	0.850087i	$-0.676549\pi$
$677$	12.3039	−	21.3109i	0.472876	−	0.819045i	0.999518	+	0.0310417i	$0.00988248\pi$
$678$	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
$687$	−1.73443	−	25.8363i	−0.0661726	−	0.985718i
$688$	−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	−0.191133	−	0.981564i	$-0.561216\pi$
$691$	19.8333	−	34.3522i	0.754493	−	1.30682i	0.945626	−	0.325256i	$-0.105450\pi$
$692$	6.51333	+	3.76048i	0.247600	+	0.142952i
$693$	−0.396836	−	0.513795i	−0.0150746	−	0.0195175i
$694$	6.10648	−	3.52558i	0.231799	−	0.133829i
$695$	−3.42832	+	5.93803i	−0.130044	+	0.225242i
$696$	11.5031	+	5.65013i	0.436025	+	0.214167i
$697$		−	48.5997i		−	1.84084i
$698$			31.1919i			1.18063i
$699$	21.1213	+	10.3744i	0.798882	+	0.392396i
$700$	0.262744	−	0.455085i	0.00993077	−	0.0172006i
$701$	21.5025	−	12.4145i	0.812138	−	0.468888i	−0.0355597	−	0.999368i	$-0.511321\pi$
$701$	21.5025	−	12.4145i	0.812138	−	0.468888i	0.847698	+	0.530479i	$0.177988\pi$
$702$	3.17703	−	9.50712i	0.119909	−	0.358823i
$703$	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
$708$	1.13001	+	16.8329i	0.0424685	+	0.632618i
$709$		−	3.30912i		−	0.124277i	−0.998068	−	0.0621384i	$-0.980208\pi$
$709$		−	3.30912i		−	0.124277i	0.998068	−	0.0621384i	$-0.0197920\pi$
$710$	−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	−0.907214	−	0.420669i	$-0.861796\pi$
$719$	−21.9318	−	37.9869i	−0.817917	−	1.41667i	0.0892975	−	0.996005i	$-0.471538\pi$
$720$	0.400981	+	2.97308i	0.0149437	+	0.110800i
$721$	1.14745			0.0427334
$722$	−11.4051	−	6.58473i	−0.424454	−	0.245058i
$723$	2.04455	+	30.4559i	0.0760376	+	1.13267i
$724$	21.2217	+	12.2524i	0.788699	+	0.455355i
$725$	−3.69962	−	6.40792i	−0.137400	−	0.237984i
$726$	1.25648	+	18.7167i	0.0466323	+	0.694642i
$727$	5.52326	+	9.56657i	0.204847	+	0.354805i	0.950084	−	0.311995i	$-0.100997\pi$
$727$	5.52326	+	9.56657i	0.204847	+	0.354805i	−0.745237	+	0.666799i	$0.767664\pi$
$728$	−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
$732$	5.31953	+	2.61285i	0.196615	+	0.0965739i
$733$	−20.5336	+	35.5652i	−0.758426	+	1.31363i	0.185228	+	0.982696i	$0.440698\pi$
$733$	−20.5336	+	35.5652i	−0.758426	+	1.31363i	−0.943653	+	0.330936i	$0.892636\pi$
$734$	−0.178249	+	0.308737i	−0.00657930	+	0.0113957i
$735$	−0.780061	−	11.6199i	−0.0287730	−	0.428607i
$736$			7.98075i			0.294174i
$737$	1.22596	+	2.12342i	0.0451587	+	0.0782172i
$738$	37.6154	−	5.07321i	1.38464	−	0.186747i
$739$	−29.3903	−	16.9685i	−1.08114	−	0.624196i	−0.149935	−	0.988696i	$-0.547907\pi$
$739$	−29.3903	−	16.9685i	−1.08114	−	0.624196i	−0.931203	+	0.364500i	$0.881240\pi$
$740$	−4.57584			−0.168211
$741$	7.24167	+	3.55698i	0.266029	+	0.130669i
$742$		−	5.22131i		−	0.191680i
$743$	32.4341			1.18989			0.594946	−	0.803766i	$-0.297173\pi$
$743$	32.4341			1.18989			0.594946	+	0.803766i	$0.297173\pi$
$744$	5.75072	−	7.74139i	0.210832	−	0.283813i
$745$	4.02044			0.147298
$746$			25.2094i			0.922981i
$747$	17.2402	−	2.32520i	0.630788	−	0.0850747i
$748$	−1.58188			−0.0578391
$749$	−1.43391	−	0.827869i	−0.0523940	−	0.0302497i
$750$	0.763610	−	1.55464i	0.0278831	−	0.0567674i
$751$	−24.1637	−	41.8527i	−0.881744	−	1.52723i	−0.849400	−	0.527749i	$-0.823036\pi$
$751$	−24.1637	−	41.8527i	−0.881744	−	1.52723i	−0.0323439	−	0.999477i	$-0.510297\pi$
$752$		−	11.2750i		−	0.411155i
$753$	−30.3251	+	2.03576i	−1.10511	+	0.0741874i
$754$	−7.13694	+	12.3615i	−0.259912	+	0.450181i
$755$	1.49596	−	2.59108i	0.0544435	−	0.0942989i
$756$	−1.81007	−	2.04434i	−0.0658315	−	0.0743521i
$757$	−26.3664	−	15.2226i	−0.958303	−	0.553276i	−0.0626525	−	0.998035i	$-0.519956\pi$
$757$	−26.3664	−	15.2226i	−0.958303	−	0.553276i	−0.895650	+	0.444759i	$0.853289\pi$
$758$	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	$-0.135790\pi$
$761$	2.67170	+	4.62752i	0.0968491	+	0.167748i	−0.813530	+	0.581523i	$0.802457\pi$
$762$	−3.38149	+	0.227004i	−0.122499	+	0.00822350i
$763$	4.02973	+	6.97970i	0.145886	+	0.252682i
$764$	6.20798	+	3.58418i	0.224597	+	0.129671i
$765$	−9.12023	+	7.04413i	−0.329743	+	0.254681i
$766$	15.3114	+	8.84004i	0.553224	+	0.319404i
$767$	−18.7901			−0.678471
$768$	−0.763610	+	1.55464i	−0.0275544	+	0.0560982i
$769$	−23.4231	−	40.5700i	−0.844658	−	1.46299i	−0.885918	−	0.463842i	$-0.846471\pi$
$769$	−23.4231	−	40.5700i	−0.844658	−	1.46299i	0.0412605	−	0.999148i	$-0.486863\pi$
$770$	−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	$-0.729204\pi$
$773$	−36.6683			−1.31887			−0.659434	+	0.751762i	$0.729204\pi$
$774$	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
$780$	−3.33380	+	0.223803i	−0.119369	+	0.00801342i
$781$	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
$786$	−4.50786	+	0.302619i	−0.160790	+	0.0107940i
$787$	−42.2310	+	24.3821i	−1.50537	+	0.869126i	−0.505390	+	0.862891i	$0.668651\pi$
$787$	−42.2310	+	24.3821i	−1.50537	+	0.869126i	−0.999981	+	0.00623537i	$0.998015\pi$
$788$	0.246916	−	0.427671i	0.00879601	−	0.0152351i
$789$	−1.56959	+	3.19554i	−0.0558789	+	0.113764i
$790$		−	15.8438i		−	0.563698i
$791$			9.99298i			0.355309i
$792$	−0.165128	−	1.22435i	−0.00586758	−	0.0435052i
$793$	−3.30042	+	5.71650i	−0.117201	+	0.202999i
$794$	5.27715	−	3.04676i	0.187279	−	0.108126i
$795$	−1.15273	−	17.1713i	−0.0408831	−	0.609002i
$796$	−11.4412	−	6.60560i	−0.405524	−	0.234129i
$797$	−18.4262	+	31.9152i	−0.652690	+	1.13049i	0.329777	+	0.944059i	$0.393026\pi$
$797$	−18.4262	+	31.9152i	−0.652690	+	1.13049i	−0.982468	+	0.186434i	$0.940307\pi$
$798$	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
$801$	31.0574	+	40.2109i	1.09736	+	1.42078i
$802$			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	0.920161	+	0.391540i	$0.128057\pi$
$809$	22.7306	+	39.3705i	0.799164	+	1.38419i	−0.120997	+	0.992653i	$0.538609\pi$
$810$	−6.40408	−	6.32359i	−0.225016	−	0.222188i
$811$	17.8903	−	30.9870i	0.628214	−	1.08810i	−0.359696	−	0.933070i	$-0.617119\pi$
$811$	17.8903	−	30.9870i	0.628214	−	1.08810i	0.987910	−	0.155029i	$-0.0495472\pi$
$812$	1.94410	+	3.36728i	0.0682246	+	0.118168i
$813$	20.1589	+	9.90169i	0.707004	+	0.347267i
$814$	1.88438			0.0660474
$815$	−16.2466	−	9.37997i	−0.569093	−	0.328566i
$816$	−6.63834	+	0.445641i	−0.232388	+	0.0156005i
$817$	19.9744	+	11.5322i	0.698817	+	0.403462i
$818$	−0.215588	−	0.373409i	−0.00753784	−	0.0130559i
$819$	2.40685	−	1.85896i	0.0841020	−	0.0649573i
$820$	−6.32599	−	10.9569i	−0.220913	−	0.382633i
$821$	42.8036			1.49385			0.746927	−	0.664906i	$-0.231528\pi$
$821$	42.8036			1.49385			0.746927	+	0.664906i	$0.231528\pi$
$822$	2.83909	−	1.90352i	0.0990246	−	0.0663928i
$823$	−40.3479	+	23.2949i	−1.40644	+	0.812008i	−0.995043	−	0.0994493i	$-0.968292\pi$
$823$	−40.3479	+	23.2949i	−1.40644	+	0.812008i	−0.411396	+	0.911457i	$0.634959\pi$
$824$	1.89105	+	1.09180i	0.0658780	+	0.0380347i
$825$	−0.314462	+	0.640216i	−0.0109482	+	0.0222895i
$826$	−2.55921	+	4.43268i	−0.0890462	+	0.154233i
$827$	−11.9976	+	20.7805i	−0.417198	+	0.722607i	−0.995656	−	0.0931042i	$-0.970321\pi$
$827$	−11.9976	+	20.7805i	−0.417198	+	0.722607i	0.578459	+	0.815712i	$0.303654\pi$
$828$	−14.6351	−	18.9485i	−0.508605	−	0.658505i
$829$		−	32.5316i		−	1.12987i	−0.825136	−	0.564934i	$-0.808902\pi$
$829$		−	32.5316i		−	1.12987i	0.825136	−	0.564934i	$-0.191098\pi$
$830$	−2.89939	−	5.02189i	−0.100639	−	0.174312i
$831$	−18.2799	−	8.97875i	−0.634123	−	0.311470i
$832$	−1.67065	−	0.964551i	−0.0579194	−	0.0334398i
$833$	25.8282			0.894894
$834$	5.23580	−	10.6596i	0.181301	−	0.369112i
$835$		−	7.54308i		−	0.261039i
$836$	0.994378			0.0343913
$837$	0.542383	+	28.9259i	0.0187475	+	0.999824i
$838$	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	$-0.0850444\pi$
$840$	−0.401267	+	0.816942i	−0.0138450	+	0.0281872i
$841$	25.7486			0.887884
$842$	19.9385	+	11.5115i	0.687126	+	0.396713i
$843$	25.8144	+	12.6796i	0.889095	+	0.436707i
$844$	0.344382	+	0.596487i	0.0118541	+	0.0205319i
$845$			9.27856i			0.319192i
$846$	20.6760	+	26.7698i	0.710856	+	0.920366i
$847$	−2.84562	+	4.92876i	−0.0977767	+	0.169354i
$848$	4.96807	−	8.60495i	0.170604	−	0.295495i
$849$	5.25419	−	10.6970i	0.180323	−	0.367121i
$850$	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
$855$	5.73304	−	4.42799i	0.196066	−	0.151434i
$856$	−1.57543	−	2.72873i	−0.0538472	−	0.0932660i
$857$	−33.4700	−	19.3239i	−1.14331	−	0.660093i	−0.196065	−	0.980591i	$-0.562816\pi$
$857$	−33.4700	−	19.3239i	−1.14331	−	0.660093i	−0.947249	+	0.320498i	$0.896150\pi$
$858$	1.37289	−	0.0921643i	0.0468698	−	0.00314644i
$859$	20.0638	+	11.5838i	0.684568	+	0.395236i	0.801574	−	0.597895i	$-0.203996\pi$
$859$	20.0638	+	11.5838i	0.684568	+	0.395236i	−0.117006	+	0.993131i	$0.537330\pi$
$860$	−9.55190			−0.325717
$861$	10.3359	+	5.07682i	0.352248	+	0.173018i
$862$	−6.67493	−	11.5613i	−0.227349	−	0.393780i
$863$	6.41727	−	11.1150i	0.218447	−	0.378361i	−0.735887	−	0.677105i	$-0.763234\pi$
$863$	6.41727	−	11.1150i	0.218447	−	0.378361i	0.954333	+	0.298744i	$0.0965677\pi$
$864$	−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
$873$	−23.3816	−	30.2728i	−0.791347	−	1.02458i
$874$	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	−0.868184	−	0.496243i	$-0.834713\pi$
$877$	−0.128327	+	0.222269i	−0.00433330	+	0.00750550i	0.863851	+	0.503748i	$0.168046\pi$
$878$	16.3120	+	9.41775i	0.550504	+	0.317834i
$879$	−0.251021	−	3.73924i	−0.00846672	−	0.126122i
$880$	−0.356638	+	0.205905i	−0.0120223	+	0.00694106i
$881$	23.3047	−	40.3649i	0.785155	−	1.35993i	−0.143752	−	0.989614i	$-0.545917\pi$
$881$	23.3047	−	40.3649i	0.785155	−	1.35993i	0.928907	−	0.370314i	$-0.120750\pi$
$882$	2.69614	+	19.9906i	0.0907839	+	0.673118i
$883$		−	17.2463i		−	0.580384i	−0.956968	−	0.290192i	$-0.906281\pi$
$883$		−	17.2463i		−	0.580384i	0.956968	−	0.290192i	$-0.0937192\pi$
$884$		−	7.41021i		−	0.249232i
$885$	−7.43781	+	15.1427i	−0.250019	+	0.509016i
$886$	1.08603	−	1.88105i	0.0364858	−	0.0631952i
$887$	8.35780	−	4.82538i	0.280628	−	0.162020i	−0.353080	−	0.935593i	$-0.614866\pi$
$887$	8.35780	−	4.82538i	0.280628	−	0.162020i	0.633707	+	0.773573i	$0.281532\pi$
$888$	7.90778	−	0.530860i	0.265368	−	0.0178145i
$889$	−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
$894$	−6.94798	+	0.466427i	−0.232375	+	0.0155997i
$895$		−	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
$906$	−2.28466	+	4.65135i	−0.0759026	+	0.154531i
$907$	−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
$909$	−14.6204	+	11.2923i	−0.484929	+	0.374542i
$910$	−0.877906	−	0.506859i	−0.0291023	−	0.0168022i
$911$	5.84896	+	10.1307i	0.193785	+	0.335645i	0.946501	−	0.322700i	$-0.104590\pi$
$911$	5.84896	+	10.1307i	0.193785	+	0.335645i	−0.752717	+	0.658344i	$0.771257\pi$
$912$	4.17290	−	0.280133i	0.138179	−	0.00927612i
$913$	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
$918$	14.9440	−	13.2315i	0.493226	−	0.436703i
$919$	21.8201	−	37.7935i	0.719779	−	1.24669i	−0.241308	−	0.970448i	$-0.577577\pi$
$919$	21.8201	−	37.7935i	0.719779	−	1.24669i	0.961087	−	0.276245i	$-0.0890901\pi$
$920$	−3.99037	+	6.91153i	−0.131559	+	0.227866i
$921$	−41.7440	+	2.80233i	−1.37551	+	0.0923399i
$922$		−	11.8557i		−	0.390447i
$923$	6.37882	+	11.0484i	0.209961	+	0.363664i
$924$	0.165246	−	0.336425i	0.00543619	−	0.0110676i
$925$	−3.96279	−	2.28792i	−0.130296	−	0.0752263i
$926$	−21.1783			−0.695964
$927$	−6.49202	+	0.875583i	−0.213226	+	0.0287579i
$928$			7.39923i			0.242892i
$929$	27.4000			0.898965			0.449482	−	0.893289i	$-0.351608\pi$
$929$	27.4000			0.898965			0.449482	+	0.893289i	$0.351608\pi$
$930$	8.85097	−	3.82888i	0.290235	−	0.125554i
$931$	−16.2358			−0.532106
$932$			13.5860i			0.445025i
$933$	42.6988	+	20.9728i	1.39789	+	0.686620i
$934$	28.2481			0.924308
$935$	−1.36994	−	0.790938i	−0.0448020	−	0.0258664i
$936$	5.73538	−	0.773534i	0.187467	−	0.0252838i
$937$	−25.3058	−	43.8309i	−0.826704	−	1.43189i	−0.900610	−	0.434628i	$-0.856880\pi$
$937$	−25.3058	−	43.8309i	−0.826704	−	1.43189i	0.0739057	−	0.997265i	$-0.476454\pi$
$938$			3.12874i			0.102157i
$939$	3.70415	+	55.1776i	0.120880	+	1.80065i
$940$	5.63748	−	9.76440i	0.183874	−	0.318480i
$941$	−27.2058	+	47.1218i	−0.886883	+	1.53613i	−0.0433429	+	0.999060i	$0.513801\pi$
$941$	−27.2058	+	47.1218i	−0.886883	+	1.53613i	−0.843540	+	0.537066i	$0.819533\pi$
$942$	−0.0695164	−	0.0341452i	−0.00226497	−	0.00111251i
$943$	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	0.866084	+	0.499899i	$0.166629\pi$
$947$	26.6487	+	46.1569i	0.865967	+	1.49990i	−0.000117103		1.00000i	$0.500037\pi$
$948$	1.83810	+	27.3807i	0.0596988	+	0.889283i
$949$	0.105568	+	0.182849i	0.00342687	+	0.00593552i
$950$	−2.09115	−	1.20732i	−0.0678458	−	0.0391708i
$951$	1.19395	+	17.7853i	0.0387164	+	0.576726i
$952$	−1.74811	−	1.00927i	−0.0566564	−	0.0327106i
$953$	49.6593			1.60862			0.804311	−	0.594208i	$-0.202534\pi$
$953$	49.6593			1.60862			0.804311	+	0.594208i	$0.202534\pi$
$954$	3.98421	+	29.5410i	0.128993	+	0.956424i
$955$	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
$966$	−0.486537	−	7.24753i	−0.0156541	−	0.233185i
$967$	23.5613	−	13.6031i	0.757681	−	0.437447i	−0.0707815	−	0.997492i	$-0.522549\pi$
$967$	23.5613	−	13.6031i	0.757681	−	0.437447i	0.828463	+	0.560044i	$0.189216\pi$
$968$	−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	$-0.544286\pi$
$971$	−33.2074	−	19.1723i	−1.06568	−	0.615269i	−0.926997	+	0.375068i	$0.877619\pi$
$972$	11.8009	+	10.1852i	0.378514	+	0.326691i
$973$	3.12036	−	1.80154i	0.100034	−	0.0577547i
$974$	−2.30888	+	3.99910i	−0.0739813	+	0.128139i
$975$	−2.99906	−	1.47308i	−0.0960467	−	0.0471764i
$976$			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	$0.921658\pi$
$978$	29.1649	+	14.3253i	0.932591	+	0.458071i
$979$	−3.48723	+	6.04005i	−0.111452	+	0.193041i
$980$	5.82304	−	3.36193i	0.186010	−	0.107393i
$981$	−28.1252	−	36.4145i	−0.897969	−	1.16263i
$982$	−29.8716	−	17.2463i	−0.953240	−	0.550353i
$983$	−7.23306	+	12.5280i	−0.230699	+	0.399582i	−0.958014	−	0.286722i	$-0.907435\pi$
$983$	−7.23306	+	12.5280i	−0.230699	+	0.399582i	0.727315	+	0.686304i	$0.240768\pi$
$984$	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
$987$	0.687364	+	10.2391i	0.0218790	+	0.325914i
$988$			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	$0.320766\pi$
$991$			53.2402i			1.69123i	−0.533793	+	0.845615i	$0.679234\pi$
$992$	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	−0.743854	−	0.668343i	$-0.767004\pi$
$997$	6.53214	−	11.3140i	0.206875	−	0.358318i	0.950728	+	0.310025i	$0.100337\pi$
$998$	4.80411	+	8.32095i	0.152071	+	0.263395i
$999$	−17.8017	+	15.7617i	−0.563222	+	0.498678i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.o.d.161.4	✓	36	1.1	even	1	trivial
930.2.o.d.161.10	yes	36	3.2	odd	2	inner
930.2.o.d.491.1	yes	36	31.26	odd	6	inner
930.2.o.d.491.13	yes	36	93.26	even	6	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.763610 + 1.55464i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.55464 + 0.763610i) q^{6} +(0.262744 + 0.455085i) q^{7} +1.00000i q^{8} +(-1.83380 - 2.37427i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.763610 + 1.55464i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.55464 + 0.763610i) q^{6} +(0.262744 + 0.455085i) q^{7} +1.00000i q^{8} +(-1.83380 - 2.37427i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(0.205905 - 0.356638i) q^{11} +(0.763610 - 1.55464i) 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} +(-2.37427 + 1.83380i) q^{18} +(-1.20732 - 2.09115i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-0.908126 + 0.0609638i) q^{21} +(-0.356638 - 0.205905i) q^{22} -7.98075 q^{23} +(-1.55464 - 0.763610i) 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} +(1.83380 + 2.37427i) 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} +(0.0609638 + 0.908126i) q^{42} +(-8.27218 + 4.77595i) q^{43} +(-0.205905 + 0.356638i) q^{44} +(0.400981 + 2.97308i) q^{45} +7.98075i q^{46} -11.2750i q^{47} +(-0.763610 + 1.55464i) q^{48} +(3.36193 - 5.82304i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-6.63834 + 0.445641i) 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} +(4.17290 - 0.280133i) 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} +(6.09418 - 12.4072i) q^{69} -0.525487 q^{70} +(5.72724 + 3.30663i) q^{71} +(2.37427 - 1.83380i) q^{72} +(0.0947842 + 0.0547237i) q^{73} +(2.28792 + 3.96279i) q^{74} +(-1.72816 + 0.116014i) 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} +(-2.27435 + 8.70789i) q^{81} +(-6.32599 + 10.9569i) q^{82} +(-2.89939 + 5.02189i) q^{83} +(0.908126 - 0.0609638i) q^{84} -3.84127i q^{85} +(4.77595 + 8.27218i) q^{86} +(5.65013 - 11.5031i) q^{87} +(0.356638 + 0.205905i) q^{88} -16.9361 q^{89} +(2.97308 - 0.400981i) q^{90} +1.01372i q^{91} +7.98075 q^{92} +(-7.74139 - 5.75072i) q^{93} -11.2750 q^{94} +2.41465i q^{95} +(1.55464 + 0.763610i) q^{96} +12.7503 q^{97} +(-5.82304 - 3.36193i) q^{98} +(-1.22435 + 0.165128i) 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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