LMFDB - Embedded newform 102.3.g.a.77.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [102,3,Mod(53,102)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(102, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("102.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 102 = 2 \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	102.g (of order $8$, degree $4$, 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:	$2.77929869648$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			77.6
Character	$\chi$	$=$	102.77
Dual form			102.3.g.a.53.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(2.40394 + 1.79473i) q^{3} +2.00000i q^{4} +(0.954492 + 0.395364i) q^{5} +(-0.609212 - 4.19867i) q^{6} +(1.41047 + 3.40519i) q^{7} +(2.00000 - 2.00000i) q^{8} +(2.55788 + 8.62886i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(2.40394 + 1.79473i) q^{3} +2.00000i q^{4} +(0.954492 + 0.395364i) q^{5} +(-0.609212 - 4.19867i) q^{6} +(1.41047 + 3.40519i) q^{7} +(2.00000 - 2.00000i) q^{8} +(2.55788 + 8.62886i) q^{9} +(-0.559128 - 1.34986i) q^{10} +(3.35908 + 8.10955i) q^{11} +(-3.58946 + 4.80789i) q^{12} -5.64347i q^{13} +(1.99471 - 4.81566i) q^{14} +(1.58497 + 2.66349i) q^{15} -4.00000 q^{16} +(16.6228 - 3.56128i) q^{17} +(6.07098 - 11.1867i) q^{18} +(9.80126 - 9.80126i) q^{19} +(-0.790727 + 1.90898i) q^{20} +(-2.72069 + 10.7173i) q^{21} +(4.75046 - 11.4686i) q^{22} +(0.279941 + 0.675838i) q^{23} +(8.39735 - 1.21842i) q^{24} +(-16.9229 - 16.9229i) q^{25} +(-5.64347 + 5.64347i) q^{26} +(-9.33748 + 25.3340i) q^{27} +(-6.81037 + 2.82095i) q^{28} +(-18.8633 - 7.81343i) q^{29} +(1.07851 - 4.24846i) q^{30} +(-25.6020 - 10.6047i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-6.47941 + 25.5235i) q^{33} +(-20.1841 - 13.0615i) q^{34} +3.80787i q^{35} +(-17.2577 + 5.11577i) q^{36} +(-25.0494 - 10.3758i) q^{37} -19.6025 q^{38} +(10.1285 - 13.5666i) q^{39} +(2.69971 - 1.11826i) q^{40} +(-23.6406 + 9.79227i) q^{41} +(13.4380 - 7.99660i) q^{42} +(-18.9042 - 18.9042i) q^{43} +(-16.2191 + 6.71817i) q^{44} +(-0.970058 + 9.24747i) q^{45} +(0.395897 - 0.955779i) q^{46} +35.3447 q^{47} +(-9.61577 - 7.17892i) q^{48} +(25.0424 - 25.0424i) q^{49} +33.8459i q^{50} +(46.3518 + 21.2723i) q^{51} +11.2869 q^{52} +(-65.1931 - 65.1931i) q^{53} +(34.6715 - 15.9965i) q^{54} +9.06856i q^{55} +(9.63132 + 3.98942i) q^{56} +(41.1523 - 5.97105i) q^{57} +(11.0499 + 26.6767i) q^{58} +(48.9566 - 48.9566i) q^{59} +(-5.32697 + 3.16995i) q^{60} +(45.5009 + 109.849i) q^{61} +(14.9973 + 36.2068i) q^{62} +(-25.7751 + 20.8809i) q^{63} -8.00000i q^{64} +(2.23122 - 5.38664i) q^{65} +(32.0029 - 19.0441i) q^{66} +61.8638 q^{67} +(7.12256 + 33.2456i) q^{68} +(-0.539984 + 2.12709i) q^{69} +(3.80787 - 3.80787i) q^{70} +(50.2353 - 121.279i) q^{71} +(22.3735 + 12.1420i) q^{72} +(-8.57649 + 20.7055i) q^{73} +(14.6736 + 35.4252i) q^{74} +(-10.3097 - 71.0538i) q^{75} +(19.6025 + 19.6025i) q^{76} +(-22.8766 + 22.8766i) q^{77} +(-23.6951 + 3.43807i) q^{78} +(-30.5974 + 12.6739i) q^{79} +(-3.81797 - 1.58145i) q^{80} +(-67.9145 + 44.1432i) q^{81} +(33.4329 + 13.8484i) q^{82} +(45.9605 + 45.9605i) q^{83} +(-21.4346 - 5.44139i) q^{84} +(17.2743 + 3.17283i) q^{85} +37.8083i q^{86} +(-31.3233 - 52.6376i) q^{87} +(22.9373 + 9.50092i) q^{88} -156.066 q^{89} +(10.2175 - 8.27741i) q^{90} +(19.2171 - 7.95996i) q^{91} +(-1.35168 + 0.559882i) q^{92} +(-42.5132 - 71.4419i) q^{93} +(-35.3447 - 35.3447i) q^{94} +(13.2303 - 5.48016i) q^{95} +(2.43685 + 16.7947i) q^{96} +(-43.4260 + 104.840i) q^{97} -50.0847 q^{98} +(-61.3840 + 49.7283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - 4 q^{3} + 8 q^{5} - 4 q^{6} + 48 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - 4 * q^3 + 8 * q^5 - 4 * q^6 + 48 * q^8 + 12 * q^9	$ 24 q - 24 q^{2} - 4 q^{3} + 8 q^{5} - 4 q^{6} + 48 q^{8} + 12 q^{9} - 16 q^{10} - 32 q^{11} + 16 q^{12} + 52 q^{15} - 96 q^{16} - 56 q^{17} - 16 q^{18} + 16 q^{20} + 96 q^{21} + 8 q^{23} - 24 q^{24} + 64 q^{25} - 8 q^{26} - 40 q^{27} - 16 q^{29} - 104 q^{30} + 24 q^{31} + 96 q^{32} + 64 q^{33} + 32 q^{34} + 8 q^{36} - 96 q^{37} - 60 q^{39} - 120 q^{41} - 128 q^{42} - 192 q^{43} + 64 q^{44} + 212 q^{45} + 48 q^{46} + 176 q^{47} + 16 q^{48} - 176 q^{49} - 96 q^{51} + 16 q^{52} - 16 q^{53} - 36 q^{54} + 76 q^{57} + 144 q^{58} + 32 q^{59} + 104 q^{60} + 88 q^{61} - 24 q^{62} - 24 q^{63} - 344 q^{65} - 32 q^{66} - 64 q^{67} + 48 q^{68} - 16 q^{69} + 176 q^{70} + 240 q^{71} + 16 q^{72} + 496 q^{73} + 72 q^{74} - 20 q^{75} - 48 q^{77} + 80 q^{78} - 96 q^{79} - 32 q^{80} - 224 q^{81} + 256 q^{82} + 64 q^{83} + 64 q^{84} + 392 q^{85} - 428 q^{87} - 128 q^{88} - 496 q^{89} - 264 q^{90} - 608 q^{91} - 112 q^{92} - 20 q^{93} - 176 q^{94} + 16 q^{95} + 16 q^{96} + 48 q^{97} + 352 q^{98} + 408 q^{99}+O(q^{100}) $ 24 * q - 24 * q^2 - 4 * q^3 + 8 * q^5 - 4 * q^6 + 48 * q^8 + 12 * q^9 - 16 * q^10 - 32 * q^11 + 16 * q^12 + 52 * q^15 - 96 * q^16 - 56 * q^17 - 16 * q^18 + 16 * q^20 + 96 * q^21 + 8 * q^23 - 24 * q^24 + 64 * q^25 - 8 * q^26 - 40 * q^27 - 16 * q^29 - 104 * q^30 + 24 * q^31 + 96 * q^32 + 64 * q^33 + 32 * q^34 + 8 * q^36 - 96 * q^37 - 60 * q^39 - 120 * q^41 - 128 * q^42 - 192 * q^43 + 64 * q^44 + 212 * q^45 + 48 * q^46 + 176 * q^47 + 16 * q^48 - 176 * q^49 - 96 * q^51 + 16 * q^52 - 16 * q^53 - 36 * q^54 + 76 * q^57 + 144 * q^58 + 32 * q^59 + 104 * q^60 + 88 * q^61 - 24 * q^62 - 24 * q^63 - 344 * q^65 - 32 * q^66 - 64 * q^67 + 48 * q^68 - 16 * q^69 + 176 * q^70 + 240 * q^71 + 16 * q^72 + 496 * q^73 + 72 * q^74 - 20 * q^75 - 48 * q^77 + 80 * q^78 - 96 * q^79 - 32 * q^80 - 224 * q^81 + 256 * q^82 + 64 * q^83 + 64 * q^84 + 392 * q^85 - 428 * q^87 - 128 * q^88 - 496 * q^89 - 264 * q^90 - 608 * q^91 - 112 * q^92 - 20 * q^93 - 176 * q^94 + 16 * q^95 + 16 * q^96 + 48 * q^97 + 352 * q^98 + 408 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/102\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{1}{8}\right)$

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 $

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	2.40394	+	1.79473i	0.801314	+	0.598244i
$3$	2.40394	+	1.79473i	0.801314	+	0.598244i
$4$			2.00000i			0.500000i
$5$	0.954492	+	0.395364i	0.190898	+	0.0790727i	0.476085	−	0.879399i	$-0.342056\pi$
$5$	0.954492	+	0.395364i	0.190898	+	0.0790727i	−0.285186	+	0.958472i	$0.592056\pi$
$6$	−0.609212	−	4.19867i	−0.101535	−	0.699779i
$7$	1.41047	+	3.40519i	0.201496	+	0.486455i	0.992036	−	0.125956i	$-0.0401998\pi$
$7$	1.41047	+	3.40519i	0.201496	+	0.486455i	−0.790539	+	0.612411i	$0.790200\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$	2.55788	+	8.62886i	0.284209	+	0.958762i
$10$	−0.559128	−	1.34986i	−0.0559128	−	0.134986i
$11$	3.35908	+	8.10955i	0.305371	+	0.737231i	0.999843	+	0.0177116i	$0.00563808\pi$
$11$	3.35908	+	8.10955i	0.305371	+	0.737231i	−0.694472	+	0.719520i	$0.744362\pi$
$12$	−3.58946	+	4.80789i	−0.299122	+	0.400657i
$13$		−	5.64347i		−	0.434113i	−0.976159	−	0.217056i	$-0.930354\pi$
$13$		−	5.64347i		−	0.434113i	0.976159	−	0.217056i	$-0.0696455\pi$
$14$	1.99471	−	4.81566i	0.142479	−	0.343976i
$15$	1.58497	+	2.66349i	0.105665	+	0.177566i
$16$	−4.00000			−0.250000
$17$	16.6228	−	3.56128i	0.977811	−	0.209487i
$17$	16.6228	−	3.56128i	0.977811	−	0.209487i
$18$	6.07098	−	11.1867i	0.337277	−	0.621486i
$19$	9.80126	−	9.80126i	0.515856	−	0.515856i	−0.400459	−	0.916315i	$-0.631149\pi$
$19$	9.80126	−	9.80126i	0.515856	−	0.515856i	0.916315	+	0.400459i	$0.131149\pi$
$20$	−0.790727	+	1.90898i	−0.0395364	+	0.0954492i
$21$	−2.72069	+	10.7173i	−0.129557	+	0.510347i
$22$	4.75046	−	11.4686i	0.215930	−	0.521301i
$23$	0.279941	+	0.675838i	0.0121714	+	0.0293842i	0.929848	−	0.367943i	$-0.119938\pi$
$23$	0.279941	+	0.675838i	0.0121714	+	0.0293842i	−0.917677	+	0.397327i	$0.869938\pi$
$24$	8.39735	−	1.21842i	0.349889	−	0.0507677i
$25$	−16.9229	−	16.9229i	−0.676917	−	0.676917i
$26$	−5.64347	+	5.64347i	−0.217056	+	0.217056i
$27$	−9.33748	+	25.3340i	−0.345832	+	0.938296i
$28$	−6.81037	+	2.82095i	−0.243228	+	0.100748i
$29$	−18.8633	−	7.81343i	−0.650459	−	0.269429i	0.0329587	−	0.999457i	$-0.489507\pi$
$29$	−18.8633	−	7.81343i	−0.650459	−	0.269429i	−0.683417	+	0.730028i	$0.739507\pi$
$30$	1.07851	−	4.24846i	0.0359505	−	0.141615i
$31$	−25.6020	−	10.6047i	−0.825872	−	0.342088i	−0.0706050	−	0.997504i	$-0.522493\pi$
$31$	−25.6020	−	10.6047i	−0.825872	−	0.342088i	−0.755267	+	0.655417i	$0.772493\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−6.47941	+	25.5235i	−0.196346	+	0.773441i
$34$	−20.1841	−	13.0615i	−0.593649	−	0.384162i
$35$			3.80787i			0.108796i
$36$	−17.2577	+	5.11577i	−0.479381	+	0.142105i
$37$	−25.0494	−	10.3758i	−0.677012	−	0.280427i	0.0175654	−	0.999846i	$-0.494408\pi$
$37$	−25.0494	−	10.3758i	−0.677012	−	0.280427i	−0.694577	+	0.719418i	$0.744408\pi$
$38$	−19.6025			−0.515856
$39$	10.1285	−	13.5666i	0.259705	−	0.347861i
$40$	2.69971	−	1.11826i	0.0674928	−	0.0279564i
$41$	−23.6406	+	9.79227i	−0.576601	+	0.238836i	−0.651874	−	0.758327i	$-0.726017\pi$
$41$	−23.6406	+	9.79227i	−0.576601	+	0.238836i	0.0752734	+	0.997163i	$0.476017\pi$
$42$	13.4380	−	7.99660i	0.319952	−	0.190395i
$43$	−18.9042	−	18.9042i	−0.439632	−	0.439632i	0.452256	−	0.891888i	$-0.350619\pi$
$43$	−18.9042	−	18.9042i	−0.439632	−	0.439632i	−0.891888	+	0.452256i	$0.850619\pi$
$44$	−16.2191	+	6.71817i	−0.368616	+	0.152686i
$45$	−0.970058	+	9.24747i	−0.0215568	+	0.205499i
$46$	0.395897	−	0.955779i	0.00860645	−	0.0207778i
$47$	35.3447			0.752016			0.376008	−	0.926616i	$-0.377297\pi$
$47$	35.3447			0.752016			0.376008	+	0.926616i	$0.377297\pi$
$48$	−9.61577	−	7.17892i	−0.200329	−	0.149561i
$49$	25.0424	−	25.0424i	0.511069	−	0.511069i
$50$			33.8459i			0.676917i
$51$	46.3518	+	21.2723i	0.908859	+	0.417104i
$52$	11.2869			0.217056
$53$	−65.1931	−	65.1931i	−1.23006	−	1.23006i	−0.963940	−	0.266119i	$-0.914259\pi$
$53$	−65.1931	−	65.1931i	−1.23006	−	1.23006i	−0.266119	−	0.963940i	$-0.585741\pi$
$54$	34.6715	−	15.9965i	0.642064	−	0.296232i
$55$			9.06856i			0.164883i
$56$	9.63132	+	3.98942i	0.171988	+	0.0712397i
$57$	41.1523	−	5.97105i	0.721970	−	0.104755i
$58$	11.0499	+	26.6767i	0.190515	+	0.459944i
$59$	48.9566	−	48.9566i	0.829773	−	0.829773i	−0.157712	−	0.987485i	$-0.550412\pi$
$59$	48.9566	−	48.9566i	0.829773	−	0.829773i	0.987485	+	0.157712i	$0.0504118\pi$
$60$	−5.32697	+	3.16995i	−0.0887829	+	0.0528324i
$61$	45.5009	+	109.849i	0.745917	+	1.80080i	0.579916	+	0.814676i	$0.303085\pi$
$61$	45.5009	+	109.849i	0.745917	+	1.80080i	0.166000	+	0.986126i	$0.446915\pi$
$62$	14.9973	+	36.2068i	0.241892	+	0.583980i
$63$	−25.7751	+	20.8809i	−0.409128	+	0.331442i
$64$		−	8.00000i		−	0.125000i
$65$	2.23122	−	5.38664i	0.0343265	−	0.0828714i
$66$	32.0029	−	19.0441i	0.484893	−	0.288547i
$67$	61.8638			0.923341			0.461670	−	0.887052i	$-0.347250\pi$
$67$	61.8638			0.923341			0.461670	+	0.887052i	$0.347250\pi$
$68$	7.12256	+	33.2456i	0.104744	+	0.488906i
$69$	−0.539984	+	2.12709i	−0.00782586	+	0.0308275i
$70$	3.80787	−	3.80787i	0.0543982	−	0.0543982i
$71$	50.2353	−	121.279i	0.707539	−	1.70815i	0.00147754	−	0.999999i	$-0.499530\pi$
$71$	50.2353	−	121.279i	0.707539	−	1.70815i	0.706061	−	0.708151i	$-0.250470\pi$
$72$	22.3735	+	12.1420i	0.310743	+	0.168638i
$73$	−8.57649	+	20.7055i	−0.117486	+	0.283637i	−0.971673	−	0.236330i	$-0.924055\pi$
$73$	−8.57649	+	20.7055i	−0.117486	+	0.283637i	0.854187	+	0.519966i	$0.174055\pi$
$74$	14.6736	+	35.4252i	0.198292	+	0.478720i
$75$	−10.3097	−	71.0538i	−0.137462	−	0.947385i
$76$	19.6025	+	19.6025i	0.257928	+	0.257928i
$77$	−22.8766	+	22.8766i	−0.297099	+	0.297099i
$78$	−23.6951	+	3.43807i	−0.303783	+	0.0440778i
$79$	−30.5974	+	12.6739i	−0.387309	+	0.160429i	−0.567837	−	0.823141i	$-0.692219\pi$
$79$	−30.5974	+	12.6739i	−0.387309	+	0.160429i	0.180528	+	0.983570i	$0.442219\pi$
$80$	−3.81797	−	1.58145i	−0.0477246	−	0.0197682i
$81$	−67.9145	+	44.1432i	−0.838450	+	0.544978i
$82$	33.4329	+	13.8484i	0.407718	+	0.168883i
$83$	45.9605	+	45.9605i	0.553741	+	0.553741i	0.927519	−	0.373777i	$-0.121938\pi$
$83$	45.9605	+	45.9605i	0.553741	+	0.553741i	−0.373777	+	0.927519i	$0.621938\pi$
$84$	−21.4346	−	5.44139i	−0.255174	−	0.0647784i
$85$	17.2743	+	3.17283i	0.203227	+	0.0373274i
$86$			37.8083i			0.439632i
$87$	−31.3233	−	52.6376i	−0.360038	−	0.605030i
$88$	22.9373	+	9.50092i	0.260651	+	0.107965i
$89$	−156.066			−1.75355			−0.876775	−	0.480901i	$-0.840310\pi$
$89$	−156.066			−1.75355			−0.876775	+	0.480901i	$0.840310\pi$
$90$	10.2175	−	8.27741i	0.113528	−	0.0919713i
$91$	19.2171	−	7.95996i	0.211176	−	0.0874721i
$92$	−1.35168	+	0.559882i	−0.0146921	+	0.00608568i
$93$	−42.5132	−	71.4419i	−0.457132	−	0.768192i
$94$	−35.3447	−	35.3447i	−0.376008	−	0.376008i
$95$	13.2303	−	5.48016i	0.139266	−	0.0576859i
$96$	2.43685	+	16.7947i	0.0253838	+	0.174945i
$97$	−43.4260	+	104.840i	−0.447691	+	1.08082i	0.525494	+	0.850798i	$0.323881\pi$
$97$	−43.4260	+	104.840i	−0.447691	+	1.08082i	−0.973185	+	0.230025i	$0.926119\pi$
$98$	−50.0847			−0.511069
$99$	−61.3840	+	49.7283i	−0.620040	+	0.502306i
$100$	33.8459	−	33.8459i	0.338459	−	0.338459i
$101$		−	30.8321i		−	0.305268i	−0.988283	−	0.152634i	$-0.951224\pi$
$101$		−	30.8321i		−	0.305268i	0.988283	−	0.152634i	$-0.0487756\pi$
$102$	−25.0795	−	67.6241i	−0.245877	−	0.662981i
$103$	64.5715			0.626907			0.313454	−	0.949603i	$-0.398514\pi$
$103$	64.5715			0.626907			0.313454	+	0.949603i	$0.398514\pi$
$104$	−11.2869	−	11.2869i	−0.108528	−	0.108528i
$105$	−6.83411	+	9.15391i	−0.0650867	+	0.0871801i
$106$			130.386i			1.23006i
$107$	144.466	+	59.8400i	1.35015	+	0.559252i	0.936335	−	0.351107i	$-0.114195\pi$
$107$	144.466	+	59.8400i	1.35015	+	0.559252i	0.413819	+	0.910359i	$0.364195\pi$
$108$	−50.6680	−	18.6750i	−0.469148	−	0.172916i
$109$	−31.5346	−	76.1314i	−0.289309	−	0.698453i	0.710679	−	0.703517i	$-0.248388\pi$
$109$	−31.5346	−	76.1314i	−0.289309	−	0.698453i	−0.999987	+	0.00506404i	$0.998388\pi$
$110$	9.06856	−	9.06856i	0.0824414	−	0.0824414i
$111$	−41.5956	−	69.8999i	−0.374735	−	0.629728i
$112$	−5.64190	−	13.6207i	−0.0503741	−	0.121614i
$113$	29.5003	+	71.2201i	0.261065	+	0.630267i	0.999005	−	0.0445998i	$-0.0142013\pi$
$113$	29.5003	+	71.2201i	0.261065	+	0.630267i	−0.737940	+	0.674866i	$0.764201\pi$
$114$	−47.1233	−	35.1812i	−0.413363	−	0.308607i
$115$			0.755760i			0.00657183i
$116$	15.6269	−	37.7266i	0.134714	−	0.325229i
$117$	48.6967	−	14.4353i	0.416211	−	0.123379i
$118$	−97.9132			−0.829773
$119$	35.5729	+	51.5806i	0.298932	+	0.433451i
$120$	8.49692	+	2.15703i	0.0708077	+	0.0179752i
$121$	31.0786	−	31.0786i	0.256848	−	0.256848i
$122$	64.3480	−	155.350i	0.527443	−	1.27336i
$123$	−74.4052	−	18.8885i	−0.604921	−	0.153565i
$124$	21.2094	−	51.2041i	0.171044	−	0.412936i
$125$	−19.3462	−	46.7058i	−0.154769	−	0.373646i
$126$	46.6559	+	4.89419i	0.370285	+	0.0388428i
$127$	−5.18300	−	5.18300i	−0.0408110	−	0.0408110i	0.686407	−	0.727218i	$-0.259187\pi$
$127$	−5.18300	−	5.18300i	−0.0408110	−	0.0408110i	−0.727218	+	0.686407i	$0.759187\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$	−11.5167	−	79.3724i	−0.0892764	−	0.615290i
$130$	−7.61786	+	3.15542i	−0.0585989	+	0.0242725i
$131$	45.9102	+	19.0166i	0.350460	+	0.145165i	0.550967	−	0.834527i	$-0.314259\pi$
$131$	45.9102	+	19.0166i	0.350460	+	0.145165i	−0.200507	+	0.979692i	$0.564259\pi$
$132$	−51.0471	−	12.9588i	−0.386720	−	0.0981728i
$133$	47.1995	+	19.5507i	0.354884	+	0.146998i
$134$	−61.8638	−	61.8638i	−0.461670	−	0.461670i
$135$	−18.9287	+	20.4894i	−0.140212	+	0.151773i
$136$	26.1230	−	40.3682i	0.192081	−	0.296825i
$137$			241.127i			1.76005i	0.474929	+	0.880024i	$0.342474\pi$
$137$			241.127i			1.76005i	−0.474929	+	0.880024i	$0.657526\pi$
$138$	2.66708	−	1.58711i	0.0193267	−	0.0115008i
$139$	−115.788	−	47.9610i	−0.833009	−	0.345044i	−0.0749156	−	0.997190i	$-0.523869\pi$
$139$	−115.788	−	47.9610i	−0.833009	−	0.345044i	−0.758093	+	0.652146i	$0.773869\pi$
$140$	−7.61575			−0.0543982
$141$	84.9667	+	63.4343i	0.602601	+	0.449889i
$142$	−171.514	+	71.0434i	−1.20784	+	0.500305i
$143$	45.7659	−	18.9569i	0.320042	−	0.132566i
$144$	−10.2315	−	34.5154i	−0.0710523	−	0.239691i
$145$	−14.9157	−	14.9157i	−0.102867	−	0.102867i
$146$	29.2820	−	12.1290i	0.200561	−	0.0830753i
$147$	105.145	−	15.2561i	0.715270	−	0.103783i
$148$	20.7516	−	50.0989i	0.140214	−	0.338506i
$149$	−222.772			−1.49512			−0.747558	−	0.664197i	$-0.768774\pi$
$149$	−222.772			−1.49512			−0.747558	+	0.664197i	$0.768774\pi$
$150$	−60.7442	+	81.3635i	−0.404961	+	0.542423i
$151$	−101.791	+	101.791i	−0.674111	+	0.674111i	−0.958661	−	0.284550i	$-0.908156\pi$
$151$	−101.791	+	101.791i	−0.674111	+	0.674111i	0.284550	+	0.958661i	$0.408156\pi$
$152$		−	39.2050i		−	0.257928i
$153$	73.2490	+	134.326i	0.478751	+	0.877950i
$154$	45.7532			0.297099
$155$	−20.2442	−	20.2442i	−0.130608	−	0.130608i
$156$	27.1331	+	20.2570i	0.173930	+	0.129853i
$157$		−	45.1566i		−	0.287622i	−0.989605	−	0.143811i	$-0.954064\pi$
$157$		−	45.1566i		−	0.287622i	0.989605	−	0.143811i	$-0.0459357\pi$
$158$	43.2713	+	17.9235i	0.273869	+	0.113440i
$159$	−39.7164	−	273.725i	−0.249789	−	1.72154i
$160$	2.23651	+	5.39942i	0.0139782	+	0.0337464i
$161$	−1.90650	+	1.90650i	−0.0118416	+	0.0118416i
$162$	112.058	+	23.7712i	0.691714	+	0.146736i
$163$	49.2800	+	118.973i	0.302332	+	0.729893i	0.999910	+	0.0133849i	$0.00426066\pi$
$163$	49.2800	+	118.973i	0.302332	+	0.729893i	−0.697579	+	0.716508i	$0.745739\pi$
$164$	−19.5845	−	47.2813i	−0.119418	−	0.288300i
$165$	−16.2756	+	21.8003i	−0.0986401	+	0.132123i
$166$		−	91.9211i		−	0.553741i
$167$	−90.3438	+	218.109i	−0.540981	+	1.30604i	0.383051	+	0.923727i	$0.374873\pi$
$167$	−90.3438	+	218.109i	−0.540981	+	1.30604i	−0.924032	+	0.382316i	$0.875127\pi$
$168$	15.9932	+	26.8760i	0.0951977	+	0.159976i
$169$	137.151			0.811546
$170$	−14.1015	−	20.4472i	−0.0829500	−	0.120277i
$171$	109.644	+	59.5032i	0.641194	+	0.347972i
$172$	37.8083	−	37.8083i	0.219816	−	0.219816i
$173$	115.092	−	277.857i	0.665272	−	1.60611i	−0.124153	−	0.992263i	$-0.539621\pi$
$173$	115.092	−	277.857i	0.665272	−	1.60611i	0.789426	−	0.613846i	$-0.210379\pi$
$174$	−21.3143	+	83.9609i	−0.122496	+	0.482534i
$175$	33.7564	−	81.4951i	0.192894	−	0.465686i
$176$	−13.4363	−	32.4382i	−0.0763428	−	0.184308i
$177$	205.553	−	29.8250i	1.16132	−	0.168503i
$178$	156.066	+	156.066i	0.876775	+	0.876775i
$179$	−61.4681	+	61.4681i	−0.343397	+	0.343397i	−0.857643	−	0.514246i	$-0.828072\pi$
$179$	−61.4681	+	61.4681i	−0.343397	+	0.343397i	0.514246	+	0.857643i	$0.328072\pi$
$180$	−18.4949	−	1.94012i	−0.102750	−	0.0107784i
$181$	−49.9859	+	20.7048i	−0.276165	+	0.114391i	−0.516468	−	0.856307i	$-0.672753\pi$
$181$	−49.9859	+	20.7048i	−0.276165	+	0.114391i	0.240302	+	0.970698i	$0.422753\pi$
$182$	−27.1770	−	11.2571i	−0.149324	−	0.0618521i
$183$	−87.7676	+	345.732i	−0.479605	+	1.88925i
$184$	1.91156	+	0.791793i	0.0103889	+	0.00430322i
$185$	−19.8073	−	19.8073i	−0.107066	−	0.107066i
$186$	−28.9287	+	113.955i	−0.155530	+	0.612662i
$187$	84.7177	+	122.841i	0.453036	+	0.656902i
$188$			70.6895i			0.376008i
$189$	−99.4373	+	3.93711i	−0.526123	+	0.0208313i
$190$	−18.7104	−	7.75012i	−0.0984760	−	0.0407901i
$191$	−178.700			−0.935603			−0.467802	−	0.883833i	$-0.654954\pi$
$191$	−178.700			−0.935603			−0.467802	+	0.883833i	$0.654954\pi$
$192$	14.3578	−	19.2315i	0.0747804	−	0.100164i
$193$	80.3844	−	33.2963i	0.416499	−	0.172520i	−0.164585	−	0.986363i	$-0.552629\pi$
$193$	80.3844	−	33.2963i	0.416499	−	0.172520i	0.581085	+	0.813843i	$0.302629\pi$
$194$	148.266	−	61.4137i	0.764257	−	0.316565i
$195$	15.0313	−	8.94474i	0.0770836	−	0.0458705i
$196$	50.0847	+	50.0847i	0.255534	+	0.255534i
$197$	6.87192	−	2.84644i	0.0348828	−	0.0144489i	−0.365174	−	0.930939i	$-0.618990\pi$
$197$	6.87192	−	2.84644i	0.0348828	−	0.0144489i	0.400057	+	0.916490i	$0.368990\pi$
$198$	111.112	+	11.6557i	0.561173	+	0.0588670i
$199$	131.945	−	318.543i	0.663040	−	1.60072i	−0.129975	−	0.991517i	$-0.541490\pi$
$199$	131.945	−	318.543i	0.663040	−	1.60072i	0.793015	−	0.609202i	$-0.208510\pi$
$200$	−67.6917			−0.338459
$201$	148.717	+	111.029i	0.739886	+	0.552383i
$202$	−30.8321	+	30.8321i	−0.152634	+	0.152634i
$203$		−	75.2537i		−	0.370708i
$204$	−42.5446	+	92.7036i	−0.208552	+	0.454429i
$205$	−26.4363			−0.128958
$206$	−64.5715	−	64.5715i	−0.313454	−	0.313454i
$207$	−5.11565	+	4.14429i	−0.0247133	+	0.0200207i
$208$			22.5739i			0.108528i
$209$	112.407	+	46.5605i	0.537833	+	0.222778i
$210$	15.9880	−	2.31980i	0.0761334	−	0.0110467i
$211$	−37.5591	−	90.6756i	−0.178005	−	0.429742i	0.809543	−	0.587061i	$-0.199715\pi$
$211$	−37.5591	−	90.6756i	−0.178005	−	0.429742i	−0.987548	+	0.157318i	$0.949715\pi$
$212$	130.386	−	130.386i	0.615029	−	0.615029i
$213$	338.425	−	201.388i	1.58885	−	0.945484i
$214$	−84.6265	−	204.306i	−0.395451	−	0.954703i
$215$	−10.5699	−	25.5179i	−0.0491621	−	0.118688i
$216$	31.9930	+	69.3430i	0.148116	+	0.321032i
$217$		−	102.137i		−	0.470679i
$218$	−44.5967	+	107.666i	−0.204572	+	0.493881i
$219$	−57.7781	+	34.3823i	−0.263827	+	0.156997i
$220$	−18.1371			−0.0824414
$221$	−20.0980	−	93.8102i	−0.0909411	−	0.424480i
$222$	−28.3042	+	111.495i	−0.127497	+	0.502232i
$223$	−268.797	+	268.797i	−1.20537	+	1.20537i	−0.232858	+	0.972511i	$0.574808\pi$
$223$	−268.797	+	268.797i	−1.20537	+	1.20537i	−0.972511	+	0.232858i	$0.925192\pi$
$224$	−7.97885	+	19.2626i	−0.0356199	+	0.0859939i
$225$	102.739	−	189.312i	0.456616	−	0.841389i
$226$	41.7198	−	100.720i	0.184601	−	0.445666i
$227$	17.0090	+	41.0634i	0.0749296	+	0.180896i	0.956906	−	0.290397i	$-0.0937874\pi$
$227$	17.0090	+	41.0634i	0.0749296	+	0.180896i	−0.881977	+	0.471293i	$0.843787\pi$
$228$	11.9421	+	82.3046i	0.0523776	+	0.360985i
$229$	−251.947	−	251.947i	−1.10020	−	1.10020i	−0.994386	−	0.105818i	$-0.966254\pi$
$229$	−251.947	−	251.947i	−1.10020	−	1.10020i	−0.105818	−	0.994386i	$-0.533746\pi$
$230$	0.755760	−	0.755760i	0.00328591	−	0.00328591i
$231$	−96.0514	+	13.9367i	−0.415807	+	0.0603321i
$232$	−53.3535	+	22.0997i	−0.229972	+	0.0952574i
$233$	202.107	+	83.7154i	0.867412	+	0.359294i	0.771602	−	0.636106i	$-0.219456\pi$
$233$	202.107	+	83.7154i	0.867412	+	0.359294i	0.0958100	+	0.995400i	$0.469456\pi$
$234$	−63.1320	−	34.2614i	−0.269795	−	0.146416i
$235$	33.7363	+	13.9740i	0.143559	+	0.0594639i
$236$	97.9132	+	97.9132i	0.414887	+	0.414887i
$237$	−96.3006	−	24.4469i	−0.406332	−	0.103151i
$238$	16.0078	−	87.1535i	0.0672595	−	0.366191i
$239$			328.799i			1.37573i	0.725840	+	0.687863i	$0.241451\pi$
$239$			328.799i			1.37573i	−0.725840	+	0.687863i	$0.758549\pi$
$240$	−6.33989	−	10.6539i	−0.0264162	−	0.0443915i
$241$	−282.646	−	117.076i	−1.17280	−	0.485791i	−0.290685	−	0.956819i	$-0.593883\pi$
$241$	−282.646	−	117.076i	−1.17280	−	0.485791i	−0.882119	+	0.471027i	$0.843883\pi$
$242$	−62.1573			−0.256848
$243$	−242.488	−	15.7704i	−0.997892	−	0.0648986i
$244$	−219.698	+	91.0018i	−0.900401	+	0.372958i
$245$	33.8036	−	14.0019i	0.137974	−	0.0571506i
$246$	55.5167	+	93.2938i	0.225678	+	0.379243i
$247$	−55.3131	−	55.3131i	−0.223940	−	0.223940i
$248$	−72.4135	+	29.9947i	−0.291990	+	0.120946i
$249$	27.9997	+	192.973i	0.112449	+	0.774993i
$250$	−27.3596	+	66.0520i	−0.109439	+	0.264208i
$251$	−102.108			−0.406805			−0.203402	−	0.979095i	$-0.565200\pi$
$251$	−102.108			−0.406805			−0.203402	+	0.979095i	$0.565200\pi$
$252$	−41.7617	−	51.5501i	−0.165721	−	0.204564i
$253$	−4.54039	+	4.54039i	−0.0179462	+	0.0179462i
$254$			10.3660i			0.0408110i
$255$	35.8321	+	38.6301i	0.140518	+	0.151490i
$256$	16.0000			0.0625000
$257$	−35.3600	−	35.3600i	−0.137587	−	0.137587i	0.634959	−	0.772546i	$-0.281017\pi$
$257$	−35.3600	−	35.3600i	−0.137587	−	0.137587i	−0.772546	+	0.634959i	$0.781017\pi$
$258$	−67.8558	+	90.8891i	−0.263007	+	0.352283i
$259$		−	99.9328i		−	0.385841i
$260$	10.7733	+	4.46244i	0.0414357	+	0.0171632i
$261$	19.1709	−	182.755i	0.0734518	−	0.700209i
$262$	−26.8936	−	64.9268i	−0.102647	−	0.247812i
$263$	87.6913	−	87.6913i	0.333427	−	0.333427i	−0.520460	−	0.853886i	$-0.674239\pi$
$263$	87.6913	−	87.6913i	0.333427	−	0.333427i	0.853886	+	0.520460i	$0.174239\pi$
$264$	38.0883	+	64.0059i	0.144274	+	0.242447i
$265$	−36.4513	−	88.0013i	−0.137552	−	0.332080i
$266$	−27.6488	−	66.7502i	−0.103943	−	0.250941i
$267$	−375.174	−	280.096i	−1.40514	−	1.04905i
$268$			123.728i			0.461670i
$269$	110.968	−	267.900i	0.412520	−	0.995912i	−0.571939	−	0.820296i	$-0.693809\pi$
$269$	110.968	−	267.900i	0.412520	−	0.995912i	0.984459	−	0.175615i	$-0.0561915\pi$
$270$	39.4181	−	1.56072i	0.145993	−	0.00578044i
$271$	197.919			0.730328			0.365164	−	0.930943i	$-0.381013\pi$
$271$	197.919			0.730328			0.365164	+	0.930943i	$0.381013\pi$
$272$	−66.4912	+	14.2451i	−0.244453	+	0.0523718i
$273$	60.4827	+	15.3541i	0.221548	+	0.0562423i
$274$	241.127	−	241.127i	0.880024	−	0.880024i
$275$	80.3917	−	194.083i	0.292334	−	0.705756i
$276$	−4.25419	−	1.07997i	−0.0154137	−	0.00391293i
$277$	−139.797	+	337.500i	−0.504682	+	1.21841i	0.442226	+	0.896904i	$0.354189\pi$
$277$	−139.797	+	337.500i	−0.504682	+	1.21841i	−0.946908	+	0.321506i	$0.895811\pi$
$278$	67.8272	+	163.749i	0.243983	+	0.589026i
$279$	26.0196	−	248.042i	0.0932601	−	0.889040i
$280$	7.61575	+	7.61575i	0.0271991	+	0.0271991i
$281$	−274.117	+	274.117i	−0.975504	+	0.975504i	−0.999707	−	0.0242028i	$-0.992295\pi$
$281$	−274.117	+	274.117i	−0.975504	+	0.975504i	0.0242028	+	0.999707i	$0.492295\pi$
$282$	−21.5324	−	148.401i	−0.0763562	−	0.526245i
$283$	−45.8019	+	18.9718i	−0.161844	+	0.0670380i	−0.462135	−	0.886810i	$-0.652916\pi$
$283$	−45.8019	+	18.9718i	−0.161844	+	0.0670380i	0.300291	+	0.953848i	$0.402916\pi$
$284$	242.557	+	100.471i	0.854075	+	0.353769i
$285$	41.6403	+	10.5708i	0.146106	+	0.0370905i
$286$	−64.7228	−	26.8091i	−0.226304	−	0.0937380i
$287$	−66.6890	−	66.6890i	−0.232366	−	0.232366i
$288$	−24.2839	+	44.7470i	−0.0843191	+	0.155371i
$289$	263.635	−	118.397i	0.912230	−	0.409678i
$290$			29.8314i			0.102867i
$291$	−292.553	+	174.091i	−1.00534	+	0.598250i
$292$	−41.4110	−	17.1530i	−0.141818	−	0.0587431i
$293$	−182.352			−0.622360			−0.311180	−	0.950351i	$-0.600724\pi$
$293$	−182.352			−0.622360			−0.311180	+	0.950351i	$0.600724\pi$
$294$	−120.401	−	89.8886i	−0.409527	−	0.305744i
$295$	66.0844	−	27.3730i	0.224015	−	0.0927899i
$296$	−70.8505	+	29.3472i	−0.239360	+	0.0991461i
$297$	−236.813	+	9.37635i	−0.797349	+	0.0315702i
$298$	222.772	+	222.772i	0.747558	+	0.747558i
$299$	3.81407	−	1.57984i	0.0127561	−	0.00528374i
$300$	142.108	−	20.6193i	0.473692	−	0.0687310i
$301$	37.7084	−	91.0361i	0.125277	−	0.302445i
$302$	203.581			0.674111
$303$	55.3353	−	74.1186i	0.182625	−	0.244616i
$304$	−39.2050	+	39.2050i	−0.128964	+	0.128964i
$305$			122.839i			0.402752i
$306$	61.0775	−	207.575i	0.199600	−	0.678351i
$307$	−433.588			−1.41234			−0.706169	−	0.708043i	$-0.749578\pi$
$307$	−433.588			−1.41234			−0.706169	+	0.708043i	$0.749578\pi$
$308$	−45.7532	−	45.7532i	−0.148549	−	0.148549i
$309$	155.226	+	115.888i	0.502350	+	0.375043i
$310$			40.4885i			0.130608i
$311$	146.800	+	60.8066i	0.472026	+	0.195520i	0.605999	−	0.795465i	$-0.292773\pi$
$311$	146.800	+	60.8066i	0.472026	+	0.195520i	−0.133973	+	0.990985i	$0.542773\pi$
$312$	−6.87614	−	47.3901i	−0.0220389	−	0.151891i
$313$	199.716	+	482.158i	0.638071	+	1.54044i	0.829246	+	0.558884i	$0.188770\pi$
$313$	199.716	+	482.158i	0.638071	+	1.54044i	−0.191175	+	0.981556i	$0.561230\pi$
$314$	−45.1566	+	45.1566i	−0.143811	+	0.143811i
$315$	−32.8576	+	9.74010i	−0.104310	+	0.0309209i
$316$	−25.3477	−	61.1948i	−0.0802143	−	0.193654i
$317$	−38.2610	−	92.3701i	−0.120697	−	0.291388i	0.851971	−	0.523589i	$-0.175407\pi$
$317$	−38.2610	−	92.3701i	−0.120697	−	0.291388i	−0.972668	+	0.232201i	$0.925407\pi$
$318$	−234.008	+	313.441i	−0.735875	+	0.985664i
$319$		−	179.219i		−	0.561814i
$320$	3.16291	−	7.63594i	0.00988409	−	0.0238623i
$321$	239.893	+	403.130i	0.747329	+	1.25586i
$322$	3.81301			0.0118416
$323$	128.019	−	197.829i	0.396344	−	0.612475i
$324$	−88.2865	−	135.829i	−0.272489	−	0.419225i
$325$	−95.5040	+	95.5040i	−0.293858	+	0.293858i
$326$	69.6925	−	168.253i	0.213781	−	0.516112i
$327$	60.8278	−	239.612i	0.186018	−	0.732757i
$328$	−27.6967	+	66.8658i	−0.0844413	+	0.203859i
$329$	49.8528	+	120.355i	0.151528	+	0.365822i
$330$	38.0759	−	5.52468i	0.115382	−	0.0167414i
$331$	300.244	+	300.244i	0.907083	+	0.907083i	0.996036	−	0.0889530i	$-0.0283521\pi$
$331$	300.244	+	300.244i	0.907083	+	0.907083i	−0.0889530	+	0.996036i	$0.528352\pi$
$332$	−91.9211	+	91.9211i	−0.276871	+	0.276871i
$333$	25.4579	−	242.688i	0.0764503	−	0.728793i
$334$	308.453	−	127.765i	0.923512	−	0.382531i
$335$	59.0485	+	24.4587i	0.176264	+	0.0730110i
$336$	10.8828	−	42.8692i	0.0323892	−	0.127587i
$337$	467.688	+	193.723i	1.38780	+	0.574844i	0.946555	−	0.322543i	$-0.104538\pi$
$337$	467.688	+	193.723i	1.38780	+	0.574844i	0.441243	+	0.897388i	$0.354538\pi$
$338$	−137.151	−	137.151i	−0.405773	−	0.405773i
$339$	−56.9038	+	224.154i	−0.167858	+	0.661222i
$340$	−6.34566	+	34.5486i	−0.0186637	+	0.101614i
$341$		−	243.243i		−	0.713323i
$342$	−50.1409	−	169.147i	−0.146611	−	0.494583i
$343$	287.450	+	119.066i	0.838046	+	0.347130i
$344$	−75.6167			−0.219816
$345$	−1.35639	+	1.81680i	−0.00393155	+	0.00526610i
$346$	−392.949	+	162.765i	−1.13569	+	0.470419i
$347$	−349.502	+	144.769i	−1.00721	+	0.417201i	−0.824437	−	0.565954i	$-0.808508\pi$
$347$	−349.502	+	144.769i	−1.00721	+	0.417201i	−0.182775	+	0.983155i	$0.558508\pi$
$348$	105.275	−	62.6466i	0.302515	−	0.180019i
$349$	−133.010	−	133.010i	−0.381119	−	0.381119i	0.490386	−	0.871505i	$-0.336856\pi$
$349$	−133.010	−	133.010i	−0.381119	−	0.381119i	−0.871505	+	0.490386i	$0.836856\pi$
$350$	−115.251	+	47.7387i	−0.329290	+	0.136396i
$351$	142.972	+	52.6957i	0.407326	+	0.150130i
$352$	−19.0018	+	45.8745i	−0.0539825	+	0.130325i
$353$	538.747			1.52620			0.763098	−	0.646283i	$-0.223677\pi$
$353$	538.747			1.52620			0.763098	+	0.646283i	$0.223677\pi$
$354$	−235.378	−	175.728i	−0.664909	−	0.496406i
$355$	95.8983	−	95.8983i	0.270136	−	0.270136i
$356$		−	312.132i		−	0.876775i
$357$	−7.05820	+	187.841i	−0.0197709	+	0.526164i
$358$	122.936			0.343397
$359$	374.084	+	374.084i	1.04202	+	1.04202i	0.999078	+	0.0429384i	$0.0136719\pi$
$359$	374.084	+	374.084i	1.04202	+	1.04202i	0.0429384	+	0.999078i	$0.486328\pi$
$360$	16.5548	+	20.4351i	0.0459856	+	0.0567641i
$361$			168.871i			0.467786i
$362$	70.6907	+	29.2811i	0.195278	+	0.0808869i
$363$	130.489	−	18.9335i	0.359474	−	0.0521583i
$364$	15.9199	+	38.4341i	0.0437361	+	0.105588i
$365$	−16.3724	+	16.3724i	−0.0448558	+	0.0448558i
$366$	433.500	−	257.965i	1.18443	−	0.704822i
$367$	185.916	+	448.842i	0.506584	+	1.22300i	0.945838	+	0.324639i	$0.105243\pi$
$367$	185.916	+	448.842i	0.506584	+	1.22300i	−0.439254	+	0.898363i	$0.644757\pi$
$368$	−1.11976	−	2.70335i	−0.00304284	−	0.00734606i
$369$	−144.966	−	178.944i	−0.392862	−	0.484944i
$370$			39.6145i			0.107066i
$371$	130.042	−	313.948i	0.350516	−	0.846221i
$372$	142.884	−	85.0265i	0.384096	−	0.228566i
$373$	377.954			1.01328			0.506641	−	0.862157i	$-0.330887\pi$
$373$	377.954			1.01328			0.506641	+	0.862157i	$0.330887\pi$
$374$	38.1229	−	207.558i	0.101933	−	0.554969i
$375$	37.3172	−	146.999i	0.0995126	−	0.391998i
$376$	70.6895	−	70.6895i	0.188004	−	0.188004i
$377$	−44.0948	+	106.454i	−0.116962	+	0.282372i
$378$	103.374	+	95.5002i	0.273477	+	0.252646i
$379$	60.3656	−	145.735i	0.159276	−	0.384526i	−0.824015	−	0.566568i	$-0.808271\pi$
$379$	60.3656	−	145.735i	0.159276	−	0.384526i	0.983291	+	0.182042i	$0.0582708\pi$
$380$	10.9603	+	26.4606i	0.0288430	+	0.0696331i
$381$	−3.15754	−	21.7617i	−0.00828752	−	0.0571173i
$382$	178.700	+	178.700i	0.467802	+	0.467802i
$383$	−312.734	+	312.734i	−0.816539	+	0.816539i	−0.985605	−	0.169066i	$-0.945925\pi$
$383$	−312.734	+	312.734i	−0.816539	+	0.816539i	0.169066	+	0.985605i	$0.445925\pi$
$384$	−33.5894	+	4.87370i	−0.0874724	+	0.0126919i
$385$	−30.8801	+	12.7910i	−0.0802081	+	0.0332233i
$386$	−113.681	−	47.0881i	−0.294509	−	0.121990i
$387$	114.767	−	211.476i	0.296555	−	0.546450i
$388$	−209.679	−	86.8521i	−0.540411	−	0.223846i
$389$	−278.137	−	278.137i	−0.715005	−	0.715005i	0.252573	−	0.967578i	$-0.418723\pi$
$389$	−278.137	−	278.137i	−0.715005	−	0.715005i	−0.967578	+	0.252573i	$0.918723\pi$
$390$	−23.9760	−	6.08656i	−0.0614770	−	0.0156066i
$391$	7.06025	+	10.2374i	0.0180569	+	0.0261825i
$392$		−	100.169i		−	0.255534i
$393$	76.2358	+	128.111i	0.193984	+	0.325983i
$394$	−9.71836	−	4.02548i	−0.0246659	−	0.0102170i
$395$	−34.2158			−0.0866222
$396$	−99.4567	−	122.768i	−0.251153	−	0.310020i
$397$	182.296	−	75.5096i	0.459185	−	0.190201i	−0.141086	−	0.989997i	$-0.545059\pi$
$397$	182.296	−	75.5096i	0.459185	−	0.190201i	0.600271	+	0.799797i	$0.295059\pi$
$398$	−450.488	+	186.598i	−1.13188	+	0.468840i
$399$	78.3768	+	131.709i	0.196433	+	0.330098i
$400$	67.6917	+	67.6917i	0.169229	+	0.169229i
$401$	−360.244	+	149.218i	−0.898363	+	0.372114i	−0.783590	−	0.621278i	$-0.786614\pi$
$401$	−360.244	+	149.218i	−0.898363	+	0.372114i	−0.114772	+	0.993392i	$0.536614\pi$
$402$	−37.6882	−	259.746i	−0.0937517	−	0.646134i
$403$	−59.8473	+	144.484i	−0.148505	+	0.358522i
$404$	61.6642			0.152634
$405$	−82.2764	+	15.2835i	−0.203152	+	0.0377369i
$406$	−75.2537	+	75.2537i	−0.185354	+	0.185354i
$407$		−	237.993i		−	0.584749i
$408$	135.248	−	50.1589i	0.331491	−	0.122939i
$409$	−254.842			−0.623084			−0.311542	−	0.950232i	$-0.600846\pi$
$409$	−254.842			−0.623084			−0.311542	+	0.950232i	$0.600846\pi$
$410$	26.4363	+	26.4363i	0.0644788	+	0.0644788i
$411$	−432.757	+	579.654i	−1.05294	+	1.41035i
$412$			129.143i			0.313454i
$413$	235.758	+	97.6543i	0.570844	+	0.236451i
$414$	9.25994	+	0.971365i	0.0223670	+	0.00234629i
$415$	25.6978	+	62.0401i	0.0619225	+	0.149494i
$416$	22.5739	−	22.5739i	0.0542641	−	0.0542641i
$417$	−192.271	−	323.104i	−0.461082	−	0.774830i
$418$	−65.8465	−	158.968i	−0.157528	−	0.380305i
$419$	−44.8936	−	108.383i	−0.107145	−	0.258670i	0.861210	−	0.508250i	$-0.169707\pi$
$419$	−44.8936	−	108.383i	−0.107145	−	0.258670i	−0.968354	+	0.249580i	$0.919707\pi$
$420$	−18.3078	−	13.6682i	−0.0435900	−	0.0325434i
$421$		−	114.516i		−	0.272009i	−0.990708	−	0.136005i	$-0.956574\pi$
$421$		−	114.516i		−	0.272009i	0.990708	−	0.136005i	$-0.0434262\pi$
$422$	−53.1166	+	128.235i	−0.125869	+	0.303874i
$423$	90.4077	+	304.985i	0.213730	+	0.721004i
$424$	−260.773			−0.615029
$425$	−341.574	−	221.039i	−0.803703	−	0.520092i
$426$	−539.813	−	137.037i	−1.26717	−	0.321683i
$427$	−309.878	+	309.878i	−0.725710	+	0.725710i
$428$	−119.680	+	288.933i	−0.279626	+	0.675077i
$429$	144.041	+	36.5663i	0.335760	+	0.0852361i
$430$	−14.9480	+	36.0878i	−0.0347629	+	0.0839250i
$431$	213.799	+	516.157i	0.496054	+	1.19758i	0.951592	+	0.307364i	$0.0994471\pi$
$431$	213.799	+	516.157i	0.496054	+	1.19758i	−0.455538	+	0.890217i	$0.650553\pi$
$432$	37.3499	−	101.336i	0.0864581	−	0.234574i
$433$	−530.869	−	530.869i	−1.22602	−	1.22602i	−0.965455	−	0.260569i	$-0.916090\pi$
$433$	−530.869	−	530.869i	−1.22602	−	1.22602i	−0.260569	−	0.965455i	$-0.583910\pi$
$434$	−102.137	+	102.137i	−0.235340	+	0.235340i
$435$	−9.08684	−	62.6262i	−0.0208893	−	0.143968i
$436$	152.263	−	63.0693i	0.349226	−	0.144654i
$437$	9.36783	+	3.88028i	0.0214367	+	0.00887937i
$438$	92.1604	+	23.3959i	0.210412	+	0.0534152i
$439$	−314.234	−	130.160i	−0.715794	−	0.296492i	−0.00509417	−	0.999987i	$-0.501622\pi$
$439$	−314.234	−	130.160i	−0.715794	−	0.296492i	−0.710700	+	0.703495i	$0.751622\pi$
$440$	18.1371	+	18.1371i	0.0412207	+	0.0412207i
$441$	280.143	+	152.032i	0.635244	+	0.344743i
$442$	−73.7122	+	113.908i	−0.166770	+	0.257711i
$443$		−	779.173i		−	1.75885i	−0.476033	−	0.879427i	$-0.657926\pi$
$443$		−	779.173i		−	1.75885i	0.476033	−	0.879427i	$-0.342074\pi$
$444$	139.800	−	83.1912i	0.314864	−	0.187368i
$445$	−148.964	−	61.7028i	−0.334750	−	0.138658i
$446$	537.594			1.20537
$447$	−535.532	−	399.816i	−1.19806	−	0.894443i
$448$	27.2415	−	11.2838i	0.0608069	−	0.0251870i
$449$	−290.268	+	120.233i	−0.646477	+	0.267779i	−0.681735	−	0.731599i	$-0.738774\pi$
$449$	−290.268	+	120.233i	−0.646477	+	0.267779i	0.0352588	+	0.999378i	$0.488774\pi$
$450$	−292.051	+	86.5737i	−0.649003	+	0.192386i
$451$	−158.822	−	158.822i	−0.352155	−	0.352155i
$452$	−142.440	+	59.0007i	−0.315133	+	0.130532i
$453$	−427.386	+	62.0121i	−0.943457	+	0.136892i
$454$	24.0544	−	58.0724i	0.0529832	−	0.127913i
$455$	21.4896			0.0472299
$456$	70.3625	−	94.2467i	0.154304	−	0.206681i
$457$	42.6828	−	42.6828i	0.0933978	−	0.0933978i	−0.658864	−	0.752262i	$-0.728963\pi$
$457$	42.6828	−	42.6828i	0.0933978	−	0.0933978i	0.752262	+	0.658864i	$0.228963\pi$
$458$			503.893i			1.10020i
$459$	−64.9934	+	454.375i	−0.141598	+	0.989924i
$460$	−1.51152			−0.00328591
$461$	115.291	+	115.291i	0.250088	+	0.250088i	0.821007	−	0.570918i	$-0.193413\pi$
$461$	115.291	+	115.291i	0.250088	+	0.250088i	−0.570918	+	0.821007i	$0.693413\pi$
$462$	109.988	+	82.1147i	0.238070	+	0.177738i
$463$		−	527.993i		−	1.14037i	−0.821515	−	0.570187i	$-0.806871\pi$
$463$		−	527.993i		−	1.14037i	0.821515	−	0.570187i	$-0.193129\pi$
$464$	75.4532	+	31.2537i	0.162615	+	0.0673572i
$465$	−12.3330	−	84.9989i	−0.0265226	−	0.182793i
$466$	−118.391	−	285.822i	−0.254059	−	0.613353i
$467$	417.156	−	417.156i	0.893268	−	0.893268i	−0.101561	−	0.994829i	$-0.532384\pi$
$467$	417.156	−	417.156i	0.893268	−	0.893268i	0.994829	+	0.101561i	$0.0323839\pi$
$468$	28.8707	+	97.3934i	0.0616894	+	0.208105i
$469$	87.2573	+	210.658i	0.186050	+	0.449164i
$470$	−19.7622	−	47.7103i	−0.0420473	−	0.101511i
$471$	81.0439	−	108.554i	0.172068	−	0.230475i
$472$		−	195.826i		−	0.414887i
$473$	89.8036	−	216.805i	0.189860	−	0.458361i
$474$	71.8537	+	120.747i	0.151590	+	0.254741i
$475$	−331.732			−0.698383
$476$	−103.161	+	71.1457i	−0.216725	+	0.149466i
$477$	395.786	−	729.299i	0.829740	−	1.52893i
$478$	328.799	−	328.799i	0.687863	−	0.687863i
$479$	−122.711	+	296.252i	−0.256183	+	0.618480i	−0.998680	−	0.0513698i	$-0.983641\pi$
$479$	−122.711	+	296.252i	−0.256183	+	0.618480i	0.742497	+	0.669849i	$0.233641\pi$
$480$	−4.31406	+	16.9938i	−0.00898762	+	0.0354038i
$481$	−58.5556	+	141.366i	−0.121737	+	0.293899i
$482$	165.570	+	399.721i	0.343506	+	0.829298i
$483$	−8.00479	+	1.16147i	−0.0165731	+	0.00240469i
$484$	62.1573	+	62.1573i	0.128424	+	0.128424i
$485$	−82.8996	+	82.8996i	−0.170927	+	0.170927i
$486$	226.717	+	258.258i	0.466497	+	0.531395i
$487$	−277.363	+	114.888i	−0.569534	+	0.235909i	−0.648818	−	0.760943i	$-0.724736\pi$
$487$	−277.363	+	114.888i	−0.569534	+	0.235909i	0.0792844	+	0.996852i	$0.474736\pi$
$488$	310.700	+	128.696i	0.636680	+	0.263721i
$489$	−95.0573	+	374.448i	−0.194391	+	0.765741i
$490$	−47.8055	−	19.8017i	−0.0975622	−	0.0404116i
$491$	−395.352	−	395.352i	−0.805198	−	0.805198i	0.178705	−	0.983903i	$-0.442809\pi$
$491$	−395.352	−	395.352i	−0.805198	−	0.805198i	−0.983903	+	0.178705i	$0.942809\pi$
$492$	37.7770	−	148.810i	0.0767826	−	0.302460i
$493$	−341.387	−	62.7036i	−0.692468	−	0.127188i
$494$			110.626i			0.223940i
$495$	−78.2513	+	23.1963i	−0.158083	+	0.0468612i
$496$	102.408	+	42.4189i	0.206468	+	0.0855219i
$497$	483.832			0.973505
$498$	164.974	−	220.973i	0.331272	−	0.443721i
$499$	902.417	−	373.793i	1.80845	−	0.749085i	0.825712	−	0.564092i	$-0.190774\pi$
$499$	902.417	−	373.793i	1.80845	−	0.749085i	0.982740	−	0.184993i	$-0.0592262\pi$
$500$	93.4116	−	38.6924i	0.186823	−	0.0773847i
$501$	−608.629	+	362.179i	−1.21483	+	0.722913i
$502$	102.108	+	102.108i	0.203402	+	0.203402i
$503$	618.682	−	256.266i	1.22998	−	0.509476i	0.329413	−	0.944186i	$-0.393149\pi$
$503$	618.682	−	256.266i	1.22998	−	0.509476i	0.900571	+	0.434710i	$0.143149\pi$
$504$	−9.78839	+	93.3118i	−0.0194214	+	0.185142i
$505$	12.1899	−	29.4290i	0.0241384	−	0.0582752i
$506$	9.08078			0.0179462
$507$	329.704	+	246.150i	0.650304	+	0.485502i
$508$	10.3660	−	10.3660i	0.0204055	−	0.0204055i
$509$		−	592.622i		−	1.16429i	−0.813086	−	0.582144i	$-0.802214\pi$
$509$		−	592.622i		−	1.16429i	0.813086	−	0.582144i	$-0.197786\pi$
$510$	2.79795	−	74.4622i	0.00548618	−	0.146004i
$511$	−82.6029			−0.161650
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	156.786	+	339.824i	0.305626	+	0.662425i
$514$			70.7200i			0.137587i
$515$	61.6329	+	25.5292i	0.119676	+	0.0495713i
$516$	158.745	−	23.0333i	0.307645	−	0.0446382i
$517$	118.726	+	286.630i	0.229644	+	0.554410i
$518$	−99.9328	+	99.9328i	−0.192921	+	0.192921i
$519$	775.353	−	461.393i	1.49394	−	0.889003i
$520$	−6.31084	−	15.2357i	−0.0121362	−	0.0292995i
$521$	−39.9182	−	96.3711i	−0.0766184	−	0.184973i	0.880929	−	0.473248i	$-0.156918\pi$
$521$	−39.9182	−	96.3711i	−0.0766184	−	0.184973i	−0.957548	+	0.288274i	$0.906918\pi$
$522$	−201.926	+	163.584i	−0.386831	+	0.313379i
$523$		−	286.317i		−	0.547452i	−0.961808	−	0.273726i	$-0.911744\pi$
$523$		−	286.317i		−	0.547452i	0.961808	−	0.273726i	$-0.0882561\pi$
$524$	−38.0333	+	91.8204i	−0.0725826	+	0.175230i
$525$	227.410	−	135.326i	0.433162	−	0.257764i
$526$	−175.383			−0.333427
$527$	−463.344	−	85.1039i	−0.879210	−	0.161487i
$528$	25.9176	−	102.094i	0.0490864	−	0.193360i
$529$	373.681	−	373.681i	0.706391	−	0.706391i
$530$	−51.5500	+	124.453i	−0.0972641	+	0.234816i
$531$	547.665	+	297.214i	1.03138	+	0.559726i
$532$	−39.1014	+	94.3991i	−0.0734988	+	0.177442i
$533$	55.2624	+	133.415i	0.103682	+	0.250310i
$534$	95.0773	+	655.270i	0.178047	+	1.22710i
$535$	114.234	+	114.234i	0.213521	+	0.213521i
$536$	123.728	−	123.728i	0.230835	−	0.230835i
$537$	−258.085	+	37.4471i	−0.480604	+	0.0697339i
$538$	−378.868	+	156.932i	−0.704216	+	0.291696i
$539$	287.202	+	118.963i	0.532842	+	0.220710i
$540$	−40.9788	−	37.8574i	−0.0758867	−	0.0701062i
$541$	82.9985	+	34.3791i	0.153417	+	0.0635473i	0.458070	−	0.888916i	$-0.348541\pi$
$541$	82.9985	+	34.3791i	0.153417	+	0.0635473i	−0.304654	+	0.952463i	$0.598541\pi$
$542$	−197.919	−	197.919i	−0.365164	−	0.365164i
$543$	−157.323	−	39.9380i	−0.289729	−	0.0735506i
$544$	80.7363	+	52.2460i	0.148412	+	0.0960405i
$545$		−	85.1344i		−	0.156210i
$546$	−45.1286	−	75.8368i	−0.0826530	−	0.138895i
$547$	193.866	+	80.3020i	0.354417	+	0.146804i	0.552786	−	0.833323i	$-0.313565\pi$
$547$	193.866	+	80.3020i	0.354417	+	0.146804i	−0.198369	+	0.980127i	$0.563565\pi$
$548$	−482.253			−0.880024
$549$	−831.485	+	673.602i	−1.51454	+	1.22696i
$550$	−274.475	+	113.691i	−0.499045	+	0.206711i
$551$	−261.466	+	108.303i	−0.474529	+	0.196556i
$552$	3.17422	+	5.33416i	0.00575040	+	0.00966333i
$553$	−86.3137	−	86.3137i	−0.156083	−	0.156083i
$554$	477.296	−	197.703i	0.861546	−	0.356864i
$555$	−12.0668	−	83.1642i	−0.0217420	−	0.149845i
$556$	95.9221	−	231.576i	0.172522	−	0.416504i
$557$	443.367			0.795991			0.397996	−	0.917387i	$-0.369706\pi$
$557$	443.367			0.795991			0.397996	+	0.917387i	$0.369706\pi$
$558$	−274.062	+	222.023i	−0.491150	+	0.397890i
$559$	−106.685	+	106.685i	−0.190850	+	0.190850i
$560$		−	15.2315i		−	0.0271991i
$561$	−16.8093	+	447.347i	−0.0299631	+	0.797411i
$562$	548.233			0.975504
$563$	504.658	+	504.658i	0.896374	+	0.896374i	0.995113	−	0.0987398i	$-0.0314811\pi$
$563$	504.658	+	504.658i	0.896374	+	0.896374i	−0.0987398	+	0.995113i	$0.531481\pi$
$564$	−126.869	+	169.933i	−0.224944	+	0.301300i
$565$			79.6424i			0.140960i
$566$	64.7737	+	26.8301i	0.114441	+	0.0474031i
$567$	−246.108	−	168.999i	−0.434052	−	0.298057i
$568$	−142.087	−	343.028i	−0.250153	−	0.603922i
$569$	−416.928	+	416.928i	−0.732738	+	0.732738i	−0.971161	−	0.238423i	$-0.923369\pi$
$569$	−416.928	+	416.928i	−0.732738	+	0.732738i	0.238423	+	0.971161i	$0.423369\pi$
$570$	−31.0695	−	52.2111i	−0.0545078	−	0.0915983i
$571$	135.171	+	326.332i	0.236727	+	0.571510i	0.996941	−	0.0781633i	$-0.0249056\pi$
$571$	135.171	+	326.332i	0.236727	+	0.571510i	−0.760213	+	0.649674i	$0.774906\pi$
$572$	37.9138	+	91.5319i	0.0662828	+	0.160021i
$573$	−429.585	−	320.719i	−0.749712	−	0.559719i
$574$			133.378i			0.232366i
$575$	6.69973	−	16.1746i	0.0116517	−	0.0281297i
$576$	69.0309	−	20.4631i	0.119845	−	0.0355262i
$577$	−352.655			−0.611187			−0.305594	−	0.952162i	$-0.598855\pi$
$577$	−352.655			−0.611187			−0.305594	+	0.952162i	$0.598855\pi$
$578$	−382.031	−	145.238i	−0.660954	−	0.251276i
$579$	252.997	+	64.2259i	0.436956	+	0.110926i
$580$	29.8314	−	29.8314i	0.0514335	−	0.0514335i
$581$	−91.6780	+	221.330i	−0.157794	+	0.380947i
$582$	466.644	+	118.462i	0.801793	+	0.203543i
$583$	309.697	−	747.676i	0.531214	−	1.28246i
$584$	24.2580	+	58.5639i	0.0415376	+	0.100281i
$585$	52.1878	+	5.47449i	0.0892099	+	0.00935810i
$586$	182.352	+	182.352i	0.311180	+	0.311180i
$587$	−168.651	+	168.651i	−0.287310	+	0.287310i	−0.836016	−	0.548705i	$-0.815121\pi$
$587$	−168.651	+	168.651i	−0.287310	+	0.287310i	0.548705	+	0.836016i	$0.315121\pi$
$588$	30.5122	+	210.290i	0.0518916	+	0.357635i
$589$	−354.872	+	146.993i	−0.602499	+	0.249563i
$590$	−93.4574	−	38.7113i	−0.158402	−	0.0656124i
$591$	21.6283	+	5.49056i	0.0365961	+	0.00929029i
$592$	100.198	+	41.5033i	0.169253	+	0.0701069i
$593$	−280.118	−	280.118i	−0.472374	−	0.472374i	0.430308	−	0.902682i	$-0.358405\pi$
$593$	−280.118	−	280.118i	−0.472374	−	0.472374i	−0.902682	+	0.430308i	$0.858405\pi$
$594$	246.189	+	227.436i	0.414460	+	0.382889i
$595$	13.5609	+	63.2975i	0.0227914	+	0.106382i
$596$		−	445.545i		−	0.747558i
$597$	888.887	−	528.954i	1.48892	−	0.886020i
$598$	−5.39390	−	2.23423i	−0.00901991	−	0.00373617i
$599$	263.129			0.439280			0.219640	−	0.975581i	$-0.429512\pi$
$599$	263.129			0.439280			0.219640	+	0.975581i	$0.429512\pi$
$600$	−162.727	−	121.488i	−0.271212	−	0.202481i
$601$	188.819	−	78.2114i	0.314175	−	0.130135i	−0.220024	−	0.975495i	$-0.570613\pi$
$601$	188.819	−	78.2114i	0.314175	−	0.130135i	0.534199	+	0.845359i	$0.320613\pi$
$602$	−128.744	+	53.3277i	−0.213861	+	0.0885842i
$603$	158.240	+	533.814i	0.262422	+	0.885264i
$604$	−203.581	−	203.581i	−0.337055	−	0.337055i
$605$	41.9517	−	17.3769i	0.0693416	−	0.0287222i
$606$	−129.454	+	18.7833i	−0.213620	+	0.0309955i
$607$	−245.977	+	593.841i	−0.405234	+	0.978321i	0.581140	+	0.813803i	$0.302607\pi$
$607$	−245.977	+	593.841i	−0.405234	+	0.978321i	−0.986374	+	0.164518i	$0.947393\pi$
$608$	78.4101			0.128964
$609$	135.060	−	180.906i	0.221774	−	0.297054i
$610$	122.839	−	122.839i	0.201376	−	0.201376i
$611$		−	199.467i		−	0.326460i
$612$	−268.653	+	146.498i	−0.438975	+	0.239376i
$613$	171.969			0.280536			0.140268	−	0.990114i	$-0.455204\pi$
$613$	171.969			0.280536			0.140268	+	0.990114i	$0.455204\pi$
$614$	433.588	+	433.588i	0.706169	+	0.706169i
$615$	−63.5514	−	47.4461i	−0.103336	−	0.0771481i
$616$			91.5065i			0.148549i
$617$	−384.521	−	159.274i	−0.623211	−	0.258142i	0.0486545	−	0.998816i	$-0.484507\pi$
$617$	−384.521	−	159.274i	−0.623211	−	0.258142i	−0.671865	+	0.740673i	$0.734507\pi$
$618$	−39.3377	−	271.115i	−0.0636533	−	0.438697i
$619$	−203.795	−	492.004i	−0.329232	−	0.794836i	−0.998650	−	0.0519501i	$-0.983456\pi$
$619$	−203.795	−	492.004i	−0.329232	−	0.794836i	0.669418	−	0.742886i	$-0.266544\pi$
$620$	40.4885	−	40.4885i	0.0653040	−	0.0653040i
$621$	−19.7356	+	0.781411i	−0.0317804	+	0.00125831i
$622$	−85.9936	−	207.607i	−0.138253	−	0.333773i
$623$	−220.127	−	531.434i	−0.353334	−	0.853024i
$624$	−40.5140	+	54.2663i	−0.0649263	+	0.0869652i
$625$			546.087i			0.873739i
$626$	282.441	−	681.874i	0.451184	−	1.08926i
$627$	186.656	+	313.669i	0.297698	+	0.500270i
$628$	90.3132			0.143811
$629$	−453.343	−	83.2669i	−0.720736	−	0.132380i
$630$	42.5977	+	23.1175i	0.0676154	+	0.0366945i
$631$	54.1564	−	54.1564i	0.0858263	−	0.0858263i	−0.662890	−	0.748717i	$-0.730670\pi$
$631$	54.1564	−	54.1564i	0.0858263	−	0.0858263i	0.748717	+	0.662890i	$0.230670\pi$
$632$	−35.8471	+	86.5425i	−0.0567201	+	0.136934i
$633$	72.4485	−	285.388i	0.114453	−	0.450849i
$634$	−54.1092	+	130.631i	−0.0853457	+	0.206043i
$635$	−2.89796	−	6.99629i	−0.00456372	−	0.0110178i
$636$	547.449	−	79.4329i	0.860769	−	0.124894i
$637$	−141.326	−	141.326i	−0.221862	−	0.221862i
$638$	−179.219	+	179.219i	−0.280907	+	0.280907i
$639$	1174.99	+	123.256i	1.83880	+	0.192890i
$640$	−10.7988	+	4.47303i	−0.0168732	+	0.00698911i
$641$	797.831	+	330.472i	1.24467	+	0.515557i	0.905170	−	0.425050i	$-0.139744\pi$
$641$	797.831	+	330.472i	1.24467	+	0.515557i	0.339496	+	0.940608i	$0.389744\pi$
$642$	163.238	−	643.023i	0.254264	−	1.00159i
$643$	−1102.46	−	456.654i	−1.71456	−	0.710192i	−0.999943	−	0.0106717i	$-0.996603\pi$
$643$	−1102.46	−	456.654i	−1.71456	−	0.710192i	−0.714613	−	0.699520i	$-0.753397\pi$
$644$	−3.81301	−	3.81301i	−0.00592082	−	0.00592082i
$645$	20.3884	−	80.3136i	0.0316100	−	0.124517i
$646$	−325.849	+	69.8101i	−0.504410	+	0.108065i
$647$			515.560i			0.796846i	0.917202	+	0.398423i	$0.130442\pi$
$647$			515.560i			0.796846i	−0.917202	+	0.398423i	$0.869558\pi$
$648$	−47.5425	+	224.115i	−0.0733680	+	0.345857i
$649$	561.465	+	232.567i	0.865124	+	0.358346i
$650$	191.008			0.293858
$651$	183.309	−	245.533i	0.281581	−	0.377162i
$652$	−237.945	+	98.5601i	−0.364946	+	0.151166i
$653$	−408.511	+	169.211i	−0.625591	+	0.259128i	−0.672878	−	0.739753i	$-0.734942\pi$
$653$	−408.511	+	169.211i	−0.625591	+	0.259128i	0.0472877	+	0.998881i	$0.484942\pi$
$654$	−300.439	+	178.784i	−0.459388	+	0.273370i
$655$	36.3024	+	36.3024i	0.0554236	+	0.0554236i
$656$	94.5626	−	39.1691i	0.144150	−	0.0597090i
$657$	−200.602	−	21.0431i	−0.305331	−	0.0320291i
$658$	70.5026	−	170.208i	0.107147	−	0.258675i
$659$	688.676			1.04503			0.522516	−	0.852630i	$-0.324994\pi$
$659$	688.676			1.04503			0.522516	+	0.852630i	$0.324994\pi$
$660$	−43.6006	−	32.5512i	−0.0660615	−	0.0493200i
$661$	341.896	−	341.896i	0.517240	−	0.517240i	−0.399495	−	0.916735i	$-0.630815\pi$
$661$	341.896	−	341.896i	0.517240	−	0.517240i	0.916735	+	0.399495i	$0.130815\pi$
$662$		−	600.489i		−	0.907083i
$663$	120.050	−	261.585i	0.181070	−	0.394547i
$664$	183.842			0.276871
$665$	37.3219	+	37.3219i	0.0561232	+	0.0561232i
$666$	−268.146	+	217.230i	−0.402622	+	0.326172i
$667$		−	14.9358i		−	0.0223925i
$668$	−436.219	−	180.688i	−0.653022	−	0.270490i
$669$	−1128.59	+	163.755i	−1.68698	+	0.244775i
$670$	−34.5898	−	83.5072i	−0.0516266	−	0.124638i
$671$	−737.983	+	737.983i	−1.09983	+	1.09983i
$672$	−53.7520	+	31.9864i	−0.0799880	+	0.0475988i
$673$	−276.791	−	668.232i	−0.411279	−	0.992915i	−0.984795	−	0.173720i	$-0.944421\pi$
$673$	−276.791	−	668.232i	−0.411279	−	0.992915i	0.573516	−	0.819194i	$-0.305579\pi$
$674$	−273.965	−	661.410i	−0.406476	−	0.981321i
$675$	586.743	−	270.708i	0.869249	−	0.401049i
$676$			274.303i			0.405773i
$677$	−227.816	+	549.996i	−0.336508	+	0.812402i	0.661538	+	0.749912i	$0.269904\pi$
$677$	−227.816	+	549.996i	−0.336508	+	0.812402i	−0.998046	+	0.0624901i	$0.980096\pi$
$678$	281.058	−	167.250i	0.414540	−	0.246682i
$679$	−418.250			−0.615980
$680$	40.8943	−	28.2030i	0.0601387	−	0.0414750i
$681$	−32.8090	+	129.241i	−0.0481778	+	0.189781i
$682$	−243.243	+	243.243i	−0.356661	+	0.356661i
$683$	−53.1302	+	128.268i	−0.0777895	+	0.187800i	−0.957990	−	0.286802i	$-0.907408\pi$
$683$	−53.1302	+	128.268i	−0.0777895	+	0.187800i	0.880201	+	0.474602i	$0.157408\pi$
$684$	−119.006	+	219.288i	−0.173986	+	0.320597i
$685$	−95.3326	+	230.153i	−0.139172	+	0.335990i
$686$	−168.384	−	406.515i	−0.245458	−	0.592588i
$687$	−153.489	−	1057.84i	−0.223419	−	1.53980i
$688$	75.6167	+	75.6167i	0.109908	+	0.109908i
$689$	−367.915	+	367.915i	−0.533984	+	0.533984i
$690$	3.17319	−	0.460418i	0.00459883	−	0.000667273i
$691$	651.445	−	269.837i	0.942757	−	0.390503i	0.142253	−	0.989830i	$-0.454565\pi$
$691$	651.445	−	269.837i	0.942757	−	0.390503i	0.800504	+	0.599328i	$0.204565\pi$
$692$	555.714	+	230.184i	0.803055	+	0.332636i
$693$	−255.915	−	138.883i	−0.369285	−	0.200409i
$694$	494.271	+	204.734i	0.712206	+	0.295005i
$695$	−91.5569	−	91.5569i	−0.131737	−	0.131737i
$696$	−167.922	−	42.6286i	−0.241267	−	0.0612480i
$697$	−358.100	+	246.966i	−0.513774	+	0.354327i
$698$			266.021i			0.381119i
$699$	335.607	+	563.975i	0.480124	+	0.806831i
$700$	162.990	+	67.5127i	0.232843	+	0.0964468i
$701$	197.974			0.282417			0.141208	−	0.989980i	$-0.454901\pi$
$701$	197.974			0.282417			0.141208	+	0.989980i	$0.454901\pi$
$702$	−90.2758	−	195.667i	−0.128598	−	0.278728i
$703$	−347.212	+	143.820i	−0.493900	+	0.204580i
$704$	64.8764	−	26.8727i	0.0921539	−	0.0381714i
$705$	56.0205	+	94.1403i	0.0794616	+	0.133532i
$706$	−538.747	−	538.747i	−0.763098	−	0.763098i
$707$	104.989	−	43.4879i	0.148499	−	0.0615104i
$708$	59.6499	+	411.106i	0.0842513	+	0.580658i
$709$	−92.3879	+	223.044i	−0.130307	+	0.314590i	−0.975545	−	0.219801i	$-0.929459\pi$
$709$	−92.3879	+	223.044i	−0.130307	+	0.314590i	0.845237	+	0.534391i	$0.179459\pi$
$710$	−191.797			−0.270136
$711$	−187.626	−	231.602i	−0.263890	−	0.325742i
$712$	−312.132	+	312.132i	−0.438388	+	0.438388i
$713$		−	20.2715i		−	0.0284313i
$714$	194.899	−	180.782i	0.272967	−	0.253197i
$715$	51.1781			0.0715777
$716$	−122.936	−	122.936i	−0.171699	−	0.171699i
$717$	−590.105	+	790.413i	−0.823020	+	1.10239i
$718$		−	748.168i		−	1.04202i
$719$	−552.385	−	228.805i	−0.768268	−	0.318227i	−0.0360975	−	0.999348i	$-0.511493\pi$
$719$	−552.385	−	228.805i	−0.768268	−	0.318227i	−0.732171	+	0.681121i	$0.761493\pi$
$720$	3.88023	−	36.9899i	0.00538921	−	0.0513748i
$721$	91.0764	+	219.878i	0.126320	+	0.304962i
$722$	168.871	−	168.871i	0.233893	−	0.233893i
$723$	−469.345	−	788.716i	−0.649163	−	1.09089i
$724$	−41.4097	−	99.9718i	−0.0571957	−	0.138083i
$725$	186.996	+	451.448i	0.257926	+	0.622687i
$726$	−149.422	−	111.556i	−0.205816	−	0.153658i
$727$		−	234.085i		−	0.321988i	−0.986955	−	0.160994i	$-0.948530\pi$
$727$		−	234.085i		−	0.321988i	0.986955	−	0.160994i	$-0.0514700\pi$
$728$	22.5142	−	54.3540i	0.0309261	−	0.0746621i
$729$	−554.623	−	473.111i	−0.760800	−	0.648987i
$730$	32.7448			0.0448558
$731$	−381.563	−	246.917i	−0.521974	−	0.337780i
$732$	−691.465	−	175.535i	−0.944624	−	0.239802i
$733$	301.803	−	301.803i	0.411737	−	0.411737i	−0.470606	−	0.882343i	$-0.655965\pi$
$733$	301.803	−	301.803i	0.411737	−	0.411737i	0.882343	+	0.470606i	$0.155965\pi$
$734$	262.925	−	634.758i	0.358209	−	0.864793i
$735$	106.392	+	27.0086i	0.144750	+	0.0367463i
$736$	−1.58359	+	3.82312i	−0.00215161	+	0.00519445i
$737$	207.806	+	501.688i	0.281962	+	0.680716i
$738$	−33.9781	+	323.910i	−0.0460408	+	0.438903i
$739$	237.687	+	237.687i	0.321633	+	0.321633i	0.849393	−	0.527760i	$-0.176968\pi$
$739$	237.687	+	237.687i	0.321633	+	0.321633i	−0.527760	+	0.849393i	$0.676968\pi$
$740$	39.6145	−	39.6145i	0.0535331	−	0.0535331i
$741$	−33.6974	−	232.241i	−0.0454756	−	0.313416i
$742$	−443.990	+	183.906i	−0.598369	+	0.247852i
$743$	404.645	+	167.609i	0.544609	+	0.225585i	0.637988	−	0.770046i	$-0.279767\pi$
$743$	404.645	+	167.609i	0.544609	+	0.225585i	−0.0933790	+	0.995631i	$0.529767\pi$
$744$	−227.910	−	57.8573i	−0.306331	−	0.0777652i
$745$	−212.634	−	88.0760i	−0.285415	−	0.118223i
$746$	−377.954	−	377.954i	−0.506641	−	0.506641i
$747$	−279.025	+	514.149i	−0.373528	+	0.688285i
$748$	−245.681	+	169.435i	−0.328451	+	0.226518i
$749$			576.338i			0.769477i
$750$	−184.317	+	109.682i	−0.245755	+	0.146243i
$751$	531.600	+	220.196i	0.707856	+	0.293203i	0.707417	−	0.706797i	$-0.249860\pi$
$751$	531.600	+	220.196i	0.707856	+	0.293203i	0.000438658		1.00000i	$0.499860\pi$
$752$	−141.379			−0.188004
$753$	−245.462	−	183.256i	−0.325978	−	0.243368i
$754$	150.549	−	62.3595i	0.199667	−	0.0827049i
$755$	−137.403	+	56.9141i	−0.181990	+	0.0753829i
$756$	−7.87423	−	198.875i	−0.0104156	−	0.263062i
$757$	393.693	+	393.693i	0.520070	+	0.520070i	0.917592	−	0.397522i	$-0.130130\pi$
$757$	393.693	+	393.693i	0.520070	+	0.520070i	−0.397522	+	0.917592i	$0.630130\pi$
$758$	−206.101	+	85.3698i	−0.271901	+	0.112625i
$759$	−19.0636	+	2.76606i	−0.0251168	+	0.00364435i
$760$	15.5002	−	37.4209i	0.0203951	−	0.0492380i
$761$	14.5975			0.0191819			0.00959097	−	0.999954i	$-0.496947\pi$
$761$	14.5975			0.0191819			0.00959097	+	0.999954i	$0.496947\pi$
$762$	−18.6042	+	24.9192i	−0.0244149	+	0.0327024i
$763$	214.763	−	214.763i	0.281471	−	0.281471i
$764$		−	357.400i		−	0.467802i
$765$	16.8078	+	157.173i	0.0219710	+	0.205456i
$766$	625.469			0.816539
$767$	−276.285	−	276.285i	−0.360215	−	0.360215i
$768$	38.4631	+	28.7157i	0.0500821	+	0.0373902i
$769$			757.613i			0.985192i	0.870258	+	0.492596i	$0.163952\pi$
$769$			757.613i			0.985192i	−0.870258	+	0.492596i	$0.836048\pi$
$770$	43.6711	+	18.0892i	0.0567157	+	0.0234924i
$771$	−21.5417	−	148.465i	−0.0279400	−	0.192562i
$772$	66.5926	+	160.769i	0.0862598	+	0.208250i
$773$	173.130	−	173.130i	0.223972	−	0.223972i	−0.586197	−	0.810169i	$-0.699375\pi$
$773$	173.130	−	173.130i	0.223972	−	0.223972i	0.810169	+	0.586197i	$0.199375\pi$
$774$	−326.243	+	96.7093i	−0.421502	+	0.124947i
$775$	253.799	+	612.724i	0.327482	+	0.790612i
$776$	122.827	+	296.532i	0.158283	+	0.382128i
$777$	179.353	−	240.233i	0.230827	−	0.309180i
$778$			556.274i			0.715005i
$779$	−135.731	+	327.685i	−0.174238	+	0.420648i
$780$	17.8895	+	30.0626i	0.0229352	+	0.0385418i
$781$	1152.26			1.47536
$782$	3.17711	−	17.2976i	0.00406280	−	0.0221197i
$783$	374.081	−	404.925i	0.477754	−	0.517146i
$784$	−100.169	+	100.169i	−0.127767	+	0.127767i
$785$	17.8533	−	43.1016i	0.0227430	−	0.0549065i
$786$	51.8756	−	204.347i	0.0659994	−	0.259984i
$787$	−280.196	+	676.453i	−0.356031	+	0.859534i	0.639820	+	0.768525i	$0.279009\pi$
$787$	−280.196	+	676.453i	−0.356031	+	0.859534i	−0.995850	+	0.0910086i	$0.970991\pi$
$788$	5.69289	+	13.7438i	0.00722447	+	0.0174414i
$789$	368.187	−	53.4226i	0.466650	−	0.0677092i
$790$	34.2158	+	34.2158i	0.0433111	+	0.0433111i
$791$	−200.908	+	200.908i	−0.253993	+	0.253993i
$792$	−23.3113	+	222.225i	−0.0294335	+	0.280587i
$793$	619.929	−	256.783i	0.781751	−	0.323812i
$794$	−257.806	−	106.787i	−0.324693	−	0.134492i
$795$	70.3117	−	276.970i	0.0884424	−	0.348390i
$796$	637.086	+	263.890i	0.800360	+	0.331520i
$797$	251.220	+	251.220i	0.315206	+	0.315206i	0.846923	−	0.531716i	$-0.178453\pi$
$797$	251.220	+	251.220i	0.315206	+	0.315206i	−0.531716	+	0.846923i	$0.678453\pi$
$798$	53.3324	−	210.086i	0.0668326	−	0.263266i
$799$	587.528	−	125.873i	0.735329	−	0.157538i
$800$		−	135.383i		−	0.169229i
$801$	−399.199	−	1346.67i	−0.498375	−	1.68124i
$802$	509.461	+	211.026i	0.635238	+	0.263124i
$803$	−196.721			−0.244983
$804$	−222.058	+	297.434i	−0.276191	+	0.369943i
$805$	−2.57350	+	1.06598i	−0.00319690	+	0.00132420i
$806$	204.332	−	84.6369i	0.253513	−	0.105009i
$807$	747.569	−	444.859i	0.926356	−	0.551251i
$808$	−61.6642	−	61.6642i	−0.0763171	−	0.0763171i
$809$	598.127	−	247.753i	0.739342	−	0.306245i	0.0189573	−	0.999820i	$-0.493965\pi$
$809$	598.127	−	247.753i	0.739342	−	0.306245i	0.720385	+	0.693575i	$0.243965\pi$
$810$	97.5599	+	66.9930i	0.120444	+	0.0827074i
$811$	−354.236	+	855.201i	−0.436789	+	1.05450i	0.540262	+	0.841497i	$0.318325\pi$
$811$	−354.236	+	855.201i	−0.436789	+	1.05450i	−0.977051	+	0.213005i	$0.931675\pi$
$812$	150.507			0.185354
$813$	475.786	+	355.211i	0.585223	+	0.436914i
$814$	−237.993	+	237.993i	−0.292374	+	0.292374i
$815$			133.042i			0.163242i
$816$	−185.407	−	85.0893i	−0.227215	−	0.104276i
$817$	−370.569			−0.453573
$818$	254.842	+	254.842i	0.311542	+	0.311542i
$819$	117.840	+	145.461i	0.143883	+	0.177608i
$820$		−	52.8726i		−	0.0644788i
$821$	1131.66	+	468.748i	1.37839	+	0.570948i	0.944050	−	0.329802i	$-0.106982\pi$
$821$	1131.66	+	468.748i	1.37839	+	0.570948i	0.434339	+	0.900749i	$0.356982\pi$
$822$	1012.41	−	146.897i	1.23164	−	0.178707i
$823$	21.1046	+	50.9510i	0.0256435	+	0.0619089i	0.936183	−	0.351514i	$-0.114333\pi$
$823$	21.1046	+	50.9510i	0.0256435	+	0.0619089i	−0.910539	+	0.413423i	$0.864333\pi$
$824$	129.143	−	129.143i	0.156727	−	0.156727i
$825$	541.583	−	322.282i	0.656465	−	0.390645i
$826$	−138.104	−	333.413i	−0.167196	−	0.403647i
$827$	−338.042	−	816.106i	−0.408757	−	0.986828i	−0.985465	−	0.169877i	$-0.945663\pi$
$827$	−338.042	−	816.106i	−0.408757	−	0.986828i	0.576708	−	0.816950i	$-0.304337\pi$
$828$	−8.28857	−	10.2313i	−0.0100104	−	0.0123566i
$829$			741.823i			0.894841i	0.894324	+	0.447420i	$0.147657\pi$
$829$			741.823i			0.894841i	−0.894324	+	0.447420i	$0.852343\pi$
$830$	36.3422	−	87.7379i	0.0437858	−	0.105708i
$831$	−941.785	+	560.432i	−1.13331	+	0.674407i
$832$	−45.1477			−0.0542641
$833$	327.091	−	505.457i	0.392667	−	0.606791i
$834$	−130.833	+	515.375i	−0.156874	+	0.617956i
$835$	−172.465	+	172.465i	−0.206545	+	0.206545i
$836$	−93.1210	+	224.814i	−0.111389	+	0.268916i
$837$	507.718	−	549.581i	0.606593	−	0.656608i
$838$	−63.4891	+	153.276i	−0.0757626	+	0.182907i
$839$	−45.9757	−	110.995i	−0.0547982	−	0.132294i	0.894109	−	0.447849i	$-0.147810\pi$
$839$	−45.9757	−	110.995i	−0.0547982	−	0.132294i	−0.948908	+	0.315554i	$0.897810\pi$
$840$	4.63961	+	31.9760i	0.00552334	+	0.0380667i
$841$	−299.903	−	299.903i	−0.356602	−	0.356602i
$842$	−114.516	+	114.516i	−0.136005	+	0.136005i
$843$	−1150.93	+	166.995i	−1.36527	+	0.198096i
$844$	181.351	−	75.1182i	0.214871	−	0.0890026i
$845$	130.910	+	54.2246i	0.154923	+	0.0641711i
$846$	214.577	−	395.392i	0.253637	−	0.467367i
$847$	149.664	+	61.9929i	0.176699	+	0.0731912i
$848$	260.773	+	260.773i	0.307515	+	0.307515i
$849$	−144.154	−	36.5950i	−0.169793	−	0.0431037i
$850$	120.535	+	562.613i	0.141805	+	0.661897i
$851$		−	19.8340i		−	0.0233067i
$852$	402.776	+	676.850i	0.472742	+	0.794425i
$853$	−892.763	−	369.794i	−1.04662	−	0.433522i	−0.207933	−	0.978143i	$-0.566674\pi$
$853$	−892.763	−	369.794i	−1.04662	−	0.433522i	−0.838682	+	0.544621i	$0.816674\pi$
$854$	619.756			0.725710
$855$	81.1291	+	100.145i	0.0948878	+	0.117128i
$856$	408.613	−	169.253i	0.477352	−	0.197725i
$857$	920.120	−	381.126i	1.07365	−	0.444721i	0.225374	−	0.974272i	$-0.427640\pi$
$857$	920.120	−	381.126i	1.07365	−	0.444721i	0.848278	+	0.529551i	$0.177640\pi$
$858$	−107.475	−	180.608i	−0.125262	−	0.210498i
$859$	980.624	+	980.624i	1.14159	+	1.14159i	0.988160	+	0.153428i	$0.0490314\pi$
$859$	980.624	+	980.624i	1.14159	+	1.14159i	0.153428	+	0.988160i	$0.450969\pi$
$860$	51.0358	−	21.1397i	0.0593440	−	0.0245811i
$861$	−40.6278	−	280.005i	−0.0471867	−	0.325210i
$862$	302.358	−	729.957i	0.350763	−	0.846818i
$863$	−662.958			−0.768202			−0.384101	−	0.923291i	$-0.625488\pi$
$863$	−662.958			−0.768202			−0.384101	+	0.923291i	$0.625488\pi$
$864$	−138.686	+	63.9861i	−0.160516	+	0.0740580i
$865$	219.709	−	219.709i	0.253999	−	0.253999i
$866$			1061.74i			1.22602i
$867$	846.253	+	188.534i	0.976070	+	0.217455i
$868$	204.275			0.235340
$869$	−205.558	−	205.558i	−0.236546	−	0.236546i
$870$	−53.5394	+	71.7131i	−0.0615395	+	0.0824288i
$871$		−	349.126i		−	0.400834i
$872$	−215.332	−	89.1934i	−0.246940	−	0.102286i
$873$	−1015.73	−	106.549i	−1.16349	−	0.122050i
$874$	−5.48755	−	13.2481i	−0.00627866	−	0.0151580i
$875$	131.755	−	131.755i	0.150577	−	0.150577i
$876$	−68.7646	−	115.556i	−0.0784984	−	0.131914i
$877$	−195.883	−	472.904i	−0.223356	−	0.539229i	0.771986	−	0.635640i	$-0.219264\pi$
$877$	−195.883	−	472.904i	−0.223356	−	0.539229i	−0.995342	+	0.0964110i	$0.969264\pi$
$878$	184.074	+	444.393i	0.209651	+	0.506143i
$879$	−438.363	−	327.272i	−0.498706	−	0.372323i
$880$		−	36.2742i		−	0.0412207i
$881$	459.119	−	1108.41i	0.521133	−	1.25813i	−0.416066	−	0.909334i	$-0.636592\pi$
$881$	459.119	−	1108.41i	0.521133	−	1.25813i	0.937200	−	0.348793i	$-0.113408\pi$
$882$	−128.111	−	432.174i	−0.145251	−	0.489994i
$883$	−9.82185			−0.0111233			−0.00556163	−	0.999985i	$-0.501770\pi$
$883$	−9.82185			−0.0111233			−0.00556163	+	0.999985i	$0.501770\pi$
$884$	187.620	−	40.1959i	0.212240	−	0.0454705i
$885$	207.990	+	52.8004i	0.235017	+	0.0596615i
$886$	−779.173	+	779.173i	−0.879427	+	0.879427i
$887$	198.426	−	479.043i	0.223705	−	0.540072i	−0.771683	−	0.636008i	$-0.780585\pi$
$887$	198.426	−	479.043i	0.223705	−	0.540072i	0.995387	+	0.0959364i	$0.0305845\pi$
$888$	−222.991	−	56.6085i	−0.251116	−	0.0637483i
$889$	10.3386	−	24.9595i	0.0116295	−	0.0280760i
$890$	87.2609	+	210.667i	0.0980460	+	0.236704i
$891$	−586.112	−	402.475i	−0.657814	−	0.451711i
$892$	−537.594	−	537.594i	−0.602684	−	0.602684i
$893$	346.423	−	346.423i	0.387932	−	0.387932i
$894$	135.716	+	935.348i	0.151807	+	1.04625i
$895$	−82.9731	+	34.3686i	−0.0927073	+	0.0384006i
$896$	−38.5253	−	15.9577i	−0.0429970	−	0.0178099i
$897$	12.0042	+	3.04738i	0.0133826	+	0.00339730i
$898$	410.501	+	170.035i	0.457128	+	0.189349i
$899$	400.080	+	400.080i	0.445028	+	0.445028i
$900$	378.625	+	205.477i	0.420694	+	0.228308i
$901$	−1315.86	−	851.521i	−1.46045	−	0.945084i
$902$			317.644i			0.352155i
$903$	254.034	−	151.169i	0.281322	−	0.167408i
$904$	201.441	+	83.4396i	0.222833	+	0.0923004i
$905$	−55.8971			−0.0617647
$906$	489.398	+	365.374i	0.540174	+	0.403282i
$907$	772.632	−	320.035i	0.851855	−	0.352850i	0.0863380	−	0.996266i	$-0.472484\pi$
$907$	772.632	−	320.035i	0.851855	−	0.352850i	0.765517	+	0.643416i	$0.222484\pi$
$908$	−82.1268	+	34.0180i	−0.0904480	+	0.0374648i
$909$	266.046	−	78.8649i	0.292680	−	0.0867601i
$910$	−21.4896	−	21.4896i	−0.0236149	−	0.0236149i
$911$	−1324.73	+	548.723i	−1.45415	+	0.602331i	−0.963183	−	0.268845i	$-0.913358\pi$
$911$	−1324.73	+	548.723i	−1.45415	+	0.602331i	−0.490971	+	0.871176i	$0.663358\pi$
$912$	−164.609	+	23.8842i	−0.180492	+	0.0261888i
$913$	−218.334	+	527.104i	−0.239139	+	0.577332i
$914$	−85.3656			−0.0933978
$915$	−220.463	+	295.299i	−0.240944	+	0.322731i
$916$	503.893	−	503.893i	0.550102	−	0.550102i
$917$			183.155i			0.199733i
$918$	519.369	−	389.382i	0.565761	−	0.424163i
$919$	−1199.39			−1.30510			−0.652552	−	0.757744i	$-0.726301\pi$
$919$	−1199.39			−1.30510			−0.652552	+	0.757744i	$0.726301\pi$
$920$	1.51152	+	1.51152i	0.00164296	+	0.00164296i
$921$	−1042.32	−	778.174i	−1.13173	−	0.844923i
$922$		−	230.581i		−	0.250088i
$923$	−684.432	−	283.501i	−0.741530	−	0.307152i
$924$	−27.8734	−	192.103i	−0.0301660	−	0.207904i
$925$	248.321	+	599.499i	0.268455	+	0.648107i
$926$	−527.993	+	527.993i	−0.570187	+	0.570187i
$927$	165.166	+	557.178i	0.178173	+	0.601055i
$928$	−44.1995	−	106.707i	−0.0476287	−	0.114986i
$929$	−178.154	−	430.102i	−0.191770	−	0.462973i	0.798524	−	0.601963i	$-0.205615\pi$
$929$	−178.154	−	430.102i	−0.191770	−	0.462973i	−0.990294	+	0.138990i	$0.955615\pi$
$930$	−72.6659	+	97.3319i	−0.0781353	+	0.104658i
$931$		−	490.894i		−	0.527276i
$932$	−167.431	+	404.214i	−0.179647	+	0.433706i
$933$	243.768	+	409.643i	0.261273	+	0.439060i
$934$	−834.312			−0.893268
$935$	32.2957	+	150.745i	0.0345408	+	0.161224i
$936$	68.5227	−	126.264i	0.0732080	−	0.134897i
$937$	192.699	−	192.699i	0.205655	−	0.205655i	−0.596762	−	0.802418i	$-0.703547\pi$
$937$	192.699	−	192.699i	0.205655	−	0.205655i	0.802418	+	0.596762i	$0.203547\pi$
$938$	123.401	−	297.915i	0.131557	−	0.317607i
$939$	−385.237	+	1517.52i	−0.410263	+	1.61610i
$940$	−27.9480	+	67.4725i	−0.0297320	+	0.0717793i
$941$	354.392	+	855.578i	0.376612	+	0.909222i	0.992596	+	0.121463i	$0.0387587\pi$
$941$	354.392	+	855.578i	0.376612	+	0.909222i	−0.615984	+	0.787759i	$0.711241\pi$
$942$	−189.598	+	27.5099i	−0.201272	+	0.0292038i
$943$	−13.2360	−	13.2360i	−0.0140360	−	0.0140360i
$944$	−195.826	+	195.826i	−0.207443	+	0.207443i
$945$	−96.4687	−	35.5559i	−0.102083	−	0.0376253i
$946$	−306.609	+	127.001i	−0.324110	+	0.134251i
$947$	−602.356	−	249.504i	−0.636067	−	0.263468i	0.0412612	−	0.999148i	$-0.486862\pi$
$947$	−602.356	−	249.504i	−0.636067	−	0.263468i	−0.677329	+	0.735681i	$0.736862\pi$
$948$	48.8937	−	192.601i	0.0515757	−	0.203166i
$949$	116.851	+	48.4011i	0.123130	+	0.0510022i
$950$	331.732	+	331.732i	0.349192	+	0.349192i
$951$	73.8024	−	290.721i	0.0776050	−	0.305700i
$952$	174.307	+	32.0155i	0.183096	+	0.0336297i
$953$		−	608.994i		−	0.639029i	−0.947581	−	0.319514i	$-0.896480\pi$
$953$		−	608.994i		−	0.639029i	0.947581	−	0.319514i	$-0.103520\pi$
$954$	−1125.08	+	333.513i	−1.17933	+	0.349594i
$955$	−170.568	−	70.6516i	−0.178605	−	0.0739807i
$956$	−657.597			−0.687863
$957$	321.649	−	430.832i	0.336102	−	0.450190i
$958$	418.963	−	173.540i	0.437331	−	0.181148i
$959$	−821.081	+	340.103i	−0.856184	+	0.354643i
$960$	21.3079	−	12.6798i	0.0221957	−	0.0132081i
$961$	−136.525	−	136.525i	−0.142066	−	0.142066i
$962$	199.921	−	82.8101i	0.207818	−	0.0860811i
$963$	−146.822	+	1399.64i	−0.152464	+	1.45342i
$964$	234.151	−	565.291i	0.242896	−	0.586402i
$965$	89.8904			0.0931506
$966$	9.16625	+	6.84332i	0.00948887	+	0.00708418i
$967$	−891.695	+	891.695i	−0.922125	+	0.922125i	−0.997179	−	0.0750546i	$-0.976087\pi$
$967$	−891.695	+	891.695i	−0.922125	+	0.922125i	0.0750546	+	0.997179i	$0.476087\pi$
$968$		−	124.315i		−	0.128424i
$969$	662.801	−	245.810i	0.684006	−	0.253674i
$970$	165.799			0.170927
$971$	−916.590	−	916.590i	−0.943965	−	0.943965i	0.0545462	−	0.998511i	$-0.482629\pi$
$971$	−916.590	−	916.590i	−0.943965	−	0.943965i	−0.998511	+	0.0545462i	$0.982629\pi$
$972$	31.5407	−	484.975i	0.0324493	−	0.498946i
$973$		−	461.928i		−	0.474746i
$974$	392.251	+	162.475i	0.402721	+	0.166813i
$975$	−400.990	+	58.1822i	−0.411272	+	0.0596740i
$976$	−182.004	−	439.396i	−0.186479	−	0.450200i
$977$	790.076	−	790.076i	0.808675	−	0.808675i	−0.175758	−	0.984433i	$-0.556238\pi$
$977$	790.076	−	790.076i	0.808675	−	0.808675i	0.984433	+	0.175758i	$0.0562377\pi$
$978$	469.505	−	279.390i	0.480066	−	0.285675i
$979$	−524.239	−	1265.62i	−0.535484	−	1.29277i
$980$	28.0038	+	67.6072i	0.0285753	+	0.0689869i
$981$	576.265	−	466.843i	0.587426	−	0.475885i
$982$			790.704i			0.805198i
$983$	−58.1499	+	140.386i	−0.0591555	+	0.142814i	−0.950694	−	0.310132i	$-0.899627\pi$
$983$	−58.1499	+	140.386i	−0.0591555	+	0.142814i	0.891538	+	0.452946i	$0.149627\pi$
$984$	−186.588	+	111.033i	−0.189621	+	0.112839i
$985$	7.68457			0.00780160
$986$	278.683	+	404.090i	0.282640	+	0.409828i
$987$	−96.1622	+	378.800i	−0.0974287	+	0.383789i
$988$	110.626	−	110.626i	0.111970	−	0.111970i
$989$	7.48410	−	18.0682i	0.00756734	−	0.0182692i
$990$	101.448	+	55.0550i	0.102472	+	0.0556111i
$991$	621.952	−	1501.52i	0.627600	−	1.51516i	−0.214996	−	0.976615i	$-0.568974\pi$
$991$	621.952	−	1501.52i	0.627600	−	1.51516i	0.842596	−	0.538546i	$-0.181026\pi$
$992$	−59.9893	−	144.827i	−0.0604731	−	0.145995i
$993$	182.913	+	1260.63i	0.184202	+	1.26951i
$994$	−483.832	−	483.832i	−0.486752	−	0.486752i
$995$	251.881	−	251.881i	0.253146	−	0.253146i
$996$	−385.947	+	55.9994i	−0.387497	+	0.0562243i
$997$	1438.07	−	595.670i	1.44240	−	0.597462i	0.482022	−	0.876159i	$-0.339903\pi$
$997$	1438.07	−	595.670i	1.44240	−	0.597462i	0.960379	+	0.278697i	$0.0899025\pi$
$998$	−1276.21	−	528.624i	−1.27877	−	0.529683i
$999$	496.759	−	537.718i	0.497257	−	0.538257i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	102.3.g.a.77.6	yes	24
3.2	odd	2		102.3.g.b.77.6	yes	24
17.2	even	8		102.3.g.b.53.6	yes	24
51.2	odd	8	inner	102.3.g.a.53.6	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.3.g.a.53.6	✓	24	51.2	odd	8	inner
102.3.g.a.77.6	yes	24	1.1	even	1	trivial
102.3.g.b.53.6	yes	24	17.2	even	8
102.3.g.b.77.6	yes	24	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 102 = 2 \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	102.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(2.40394 + 1.79473i) q^{3} +2.00000i q^{4} +(0.954492 + 0.395364i) q^{5} +(-0.609212 - 4.19867i) q^{6} +(1.41047 + 3.40519i) q^{7} +(2.00000 - 2.00000i) q^{8} +(2.55788 + 8.62886i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(2.40394 + 1.79473i) q^{3} +2.00000i q^{4} +(0.954492 + 0.395364i) q^{5} +(-0.609212 - 4.19867i) q^{6} +(1.41047 + 3.40519i) q^{7} +(2.00000 - 2.00000i) q^{8} +(2.55788 + 8.62886i) q^{9} +(-0.559128 - 1.34986i) q^{10} +(3.35908 + 8.10955i) q^{11} +(-3.58946 + 4.80789i) q^{12} -5.64347i q^{13} +(1.99471 - 4.81566i) q^{14} +(1.58497 + 2.66349i) q^{15} -4.00000 q^{16} +(16.6228 - 3.56128i) q^{17} +(6.07098 - 11.1867i) q^{18} +(9.80126 - 9.80126i) q^{19} +(-0.790727 + 1.90898i) q^{20} +(-2.72069 + 10.7173i) q^{21} +(4.75046 - 11.4686i) q^{22} +(0.279941 + 0.675838i) q^{23} +(8.39735 - 1.21842i) q^{24} +(-16.9229 - 16.9229i) q^{25} +(-5.64347 + 5.64347i) q^{26} +(-9.33748 + 25.3340i) q^{27} +(-6.81037 + 2.82095i) q^{28} +(-18.8633 - 7.81343i) q^{29} +(1.07851 - 4.24846i) q^{30} +(-25.6020 - 10.6047i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-6.47941 + 25.5235i) q^{33} +(-20.1841 - 13.0615i) q^{34} +3.80787i q^{35} +(-17.2577 + 5.11577i) q^{36} +(-25.0494 - 10.3758i) q^{37} -19.6025 q^{38} +(10.1285 - 13.5666i) q^{39} +(2.69971 - 1.11826i) q^{40} +(-23.6406 + 9.79227i) q^{41} +(13.4380 - 7.99660i) q^{42} +(-18.9042 - 18.9042i) q^{43} +(-16.2191 + 6.71817i) q^{44} +(-0.970058 + 9.24747i) q^{45} +(0.395897 - 0.955779i) q^{46} +35.3447 q^{47} +(-9.61577 - 7.17892i) q^{48} +(25.0424 - 25.0424i) q^{49} +33.8459i q^{50} +(46.3518 + 21.2723i) q^{51} +11.2869 q^{52} +(-65.1931 - 65.1931i) q^{53} +(34.6715 - 15.9965i) q^{54} +9.06856i q^{55} +(9.63132 + 3.98942i) q^{56} +(41.1523 - 5.97105i) q^{57} +(11.0499 + 26.6767i) q^{58} +(48.9566 - 48.9566i) q^{59} +(-5.32697 + 3.16995i) q^{60} +(45.5009 + 109.849i) q^{61} +(14.9973 + 36.2068i) q^{62} +(-25.7751 + 20.8809i) q^{63} -8.00000i q^{64} +(2.23122 - 5.38664i) q^{65} +(32.0029 - 19.0441i) q^{66} +61.8638 q^{67} +(7.12256 + 33.2456i) q^{68} +(-0.539984 + 2.12709i) q^{69} +(3.80787 - 3.80787i) q^{70} +(50.2353 - 121.279i) q^{71} +(22.3735 + 12.1420i) q^{72} +(-8.57649 + 20.7055i) q^{73} +(14.6736 + 35.4252i) q^{74} +(-10.3097 - 71.0538i) q^{75} +(19.6025 + 19.6025i) q^{76} +(-22.8766 + 22.8766i) q^{77} +(-23.6951 + 3.43807i) q^{78} +(-30.5974 + 12.6739i) q^{79} +(-3.81797 - 1.58145i) q^{80} +(-67.9145 + 44.1432i) q^{81} +(33.4329 + 13.8484i) q^{82} +(45.9605 + 45.9605i) q^{83} +(-21.4346 - 5.44139i) q^{84} +(17.2743 + 3.17283i) q^{85} +37.8083i q^{86} +(-31.3233 - 52.6376i) q^{87} +(22.9373 + 9.50092i) q^{88} -156.066 q^{89} +(10.2175 - 8.27741i) q^{90} +(19.2171 - 7.95996i) q^{91} +(-1.35168 + 0.559882i) q^{92} +(-42.5132 - 71.4419i) q^{93} +(-35.3447 - 35.3447i) q^{94} +(13.2303 - 5.48016i) q^{95} +(2.43685 + 16.7947i) q^{96} +(-43.4260 + 104.840i) q^{97} -50.0847 q^{98} +(-61.3840 + 49.7283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - 4 q^{3} + 8 q^{5} - 4 q^{6} + 48 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - 4 * q^3 + 8 * q^5 - 4 * q^6 + 48 * q^8 + 12 * q^9	\( 24 q - 24 q^{2} - 4 q^{3} + 8 q^{5} - 4 q^{6} + 48 q^{8} + 12 q^{9} - 16 q^{10} - 32 q^{11} + 16 q^{12} + 52 q^{15} - 96 q^{16} - 56 q^{17} - 16 q^{18} + 16 q^{20} + 96 q^{21} + 8 q^{23} - 24 q^{24} + 64 q^{25} - 8 q^{26} - 40 q^{27} - 16 q^{29} - 104 q^{30} + 24 q^{31} + 96 q^{32} + 64 q^{33} + 32 q^{34} + 8 q^{36} - 96 q^{37} - 60 q^{39} - 120 q^{41} - 128 q^{42} - 192 q^{43} + 64 q^{44} + 212 q^{45} + 48 q^{46} + 176 q^{47} + 16 q^{48} - 176 q^{49} - 96 q^{51} + 16 q^{52} - 16 q^{53} - 36 q^{54} + 76 q^{57} + 144 q^{58} + 32 q^{59} + 104 q^{60} + 88 q^{61} - 24 q^{62} - 24 q^{63} - 344 q^{65} - 32 q^{66} - 64 q^{67} + 48 q^{68} - 16 q^{69} + 176 q^{70} + 240 q^{71} + 16 q^{72} + 496 q^{73} + 72 q^{74} - 20 q^{75} - 48 q^{77} + 80 q^{78} - 96 q^{79} - 32 q^{80} - 224 q^{81} + 256 q^{82} + 64 q^{83} + 64 q^{84} + 392 q^{85} - 428 q^{87} - 128 q^{88} - 496 q^{89} - 264 q^{90} - 608 q^{91} - 112 q^{92} - 20 q^{93} - 176 q^{94} + 16 q^{95} + 16 q^{96} + 48 q^{97} + 352 q^{98} + 408 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 4 * q^3 + 8 * q^5 - 4 * q^6 + 48 * q^8 + 12 * q^9 - 16 * q^10 - 32 * q^11 + 16 * q^12 + 52 * q^15 - 96 * q^16 - 56 * q^17 - 16 * q^18 + 16 * q^20 + 96 * q^21 + 8 * q^23 - 24 * q^24 + 64 * q^25 - 8 * q^26 - 40 * q^27 - 16 * q^29 - 104 * q^30 + 24 * q^31 + 96 * q^32 + 64 * q^33 + 32 * q^34 + 8 * q^36 - 96 * q^37 - 60 * q^39 - 120 * q^41 - 128 * q^42 - 192 * q^43 + 64 * q^44 + 212 * q^45 + 48 * q^46 + 176 * q^47 + 16 * q^48 - 176 * q^49 - 96 * q^51 + 16 * q^52 - 16 * q^53 - 36 * q^54 + 76 * q^57 + 144 * q^58 + 32 * q^59 + 104 * q^60 + 88 * q^61 - 24 * q^62 - 24 * q^63 - 344 * q^65 - 32 * q^66 - 64 * q^67 + 48 * q^68 - 16 * q^69 + 176 * q^70 + 240 * q^71 + 16 * q^72 + 496 * q^73 + 72 * q^74 - 20 * q^75 - 48 * q^77 + 80 * q^78 - 96 * q^79 - 32 * q^80 - 224 * q^81 + 256 * q^82 + 64 * q^83 + 64 * q^84 + 392 * q^85 - 428 * q^87 - 128 * q^88 - 496 * q^89 - 264 * q^90 - 608 * q^91 - 112 * q^92 - 20 * q^93 - 176 * q^94 + 16 * q^95 + 16 * q^96 + 48 * q^97 + 352 * q^98 + 408 * q^99

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