LMFDB - Embedded newform 99.2.e.d.67.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(34,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("99.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.e (of order $3$, 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:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.3
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	99.67
Dual form			99.2.e.d.34.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 1.62760i) q^{2} +(-1.70574 + 0.300767i) q^{3} +(-0.766044 + 1.32683i) q^{4} +(-1.43969 + 2.49362i) q^{5} +(-2.09240 - 2.49362i) q^{6} +(0.326352 + 0.565258i) q^{7} +0.879385 q^{8} +(2.81908 - 1.02606i) q^{9} +O(q^{10})$	\(q+(0.939693 + 1.62760i) q^{2} +(-1.70574 + 0.300767i) q^{3} +(-0.766044 + 1.32683i) q^{4} +(-1.43969 + 2.49362i) q^{5} +(-2.09240 - 2.49362i) q^{6} +(0.326352 + 0.565258i) q^{7} +0.879385 q^{8} +(2.81908 - 1.02606i) q^{9} -5.41147 q^{10} +(0.500000 + 0.866025i) q^{11} +(0.907604 - 2.49362i) q^{12} +(3.37939 - 5.85327i) q^{13} +(-0.613341 + 1.06234i) q^{14} +(1.70574 - 4.68647i) q^{15} +(2.35844 + 4.08494i) q^{16} +0.184793 q^{17} +(4.31908 + 3.62414i) q^{18} -5.22668 q^{19} +(-2.20574 - 3.82045i) q^{20} +(-0.726682 - 0.866025i) q^{21} +(-0.939693 + 1.62760i) q^{22} +(1.59240 - 2.75811i) q^{23} +(-1.50000 + 0.264490i) q^{24} +(-1.64543 - 2.84997i) q^{25} +12.7023 q^{26} +(-4.50000 + 2.59808i) q^{27} -1.00000 q^{28} +(2.01114 + 3.48340i) q^{29} +(9.23055 - 1.62760i) q^{30} +(-0.553033 + 0.957882i) q^{31} +(-3.55303 + 6.15403i) q^{32} +(-1.11334 - 1.32683i) q^{33} +(0.173648 + 0.300767i) q^{34} -1.87939 q^{35} +(-0.798133 + 4.52644i) q^{36} +0.106067 q^{37} +(-4.91147 - 8.50692i) q^{38} +(-4.00387 + 11.0005i) q^{39} +(-1.26604 + 2.19285i) q^{40} +(2.80793 - 4.86348i) q^{41} +(0.726682 - 1.99654i) q^{42} +(-1.92989 - 3.34267i) q^{43} -1.53209 q^{44} +(-1.50000 + 8.50692i) q^{45} +5.98545 q^{46} +(-6.00387 - 10.3990i) q^{47} +(-5.25150 - 6.25849i) q^{48} +(3.28699 - 5.69323i) q^{49} +(3.09240 - 5.35619i) q^{50} +(-0.315207 + 0.0555796i) q^{51} +(5.17752 + 8.96773i) q^{52} -10.0719 q^{53} +(-8.45723 - 4.88279i) q^{54} -2.87939 q^{55} +(0.286989 + 0.497079i) q^{56} +(8.91534 - 1.57202i) q^{57} +(-3.77972 + 6.54666i) q^{58} +(-5.27719 + 9.14036i) q^{59} +(4.91147 + 5.85327i) q^{60} +(3.67365 + 6.36295i) q^{61} -2.07873 q^{62} +(1.50000 + 1.25865i) q^{63} -3.92127 q^{64} +(9.73055 + 16.8538i) q^{65} +(1.11334 - 3.05888i) q^{66} +(5.90420 - 10.2264i) q^{67} +(-0.141559 + 0.245188i) q^{68} +(-1.88666 + 5.18355i) q^{69} +(-1.76604 - 3.05888i) q^{70} -2.47565 q^{71} +(2.47906 - 0.902302i) q^{72} +10.4611 q^{73} +(0.0996702 + 0.172634i) q^{74} +(3.66385 + 4.36640i) q^{75} +(4.00387 - 6.93491i) q^{76} +(-0.326352 + 0.565258i) q^{77} +(-21.6668 + 3.82045i) q^{78} +(0.733956 + 1.27125i) q^{79} -13.5817 q^{80} +(6.89440 - 5.78509i) q^{81} +10.5544 q^{82} +(0.520945 + 0.902302i) q^{83} +(1.70574 - 0.300767i) q^{84} +(-0.266044 + 0.460802i) q^{85} +(3.62701 - 6.28217i) q^{86} +(-4.47818 - 5.33688i) q^{87} +(0.439693 + 0.761570i) q^{88} -3.01960 q^{89} +(-15.2554 + 5.55250i) q^{90} +4.41147 q^{91} +(2.43969 + 4.22567i) q^{92} +(0.655230 - 1.80023i) q^{93} +(11.2836 - 19.5437i) q^{94} +(7.52481 - 13.0334i) q^{95} +(4.20961 - 11.5658i) q^{96} +(2.86959 + 4.97027i) q^{97} +12.3550 q^{98} +(2.29813 + 1.92836i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} - 6 q^{8}+O(q^{10}) $ 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 - 6 * q^8	$ 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} - 6 q^{8} - 12 q^{10} + 3 q^{11} + 9 q^{12} + 9 q^{13} + 3 q^{14} + 6 q^{16} - 6 q^{17} + 9 q^{18} - 18 q^{19} - 3 q^{20} + 9 q^{21} + 6 q^{23} - 9 q^{24} + 6 q^{25} + 24 q^{26} - 27 q^{27} - 6 q^{28} + 6 q^{29} + 18 q^{30} + 9 q^{31} - 9 q^{32} + 9 q^{36} - 24 q^{37} - 9 q^{38} - 3 q^{40} + 6 q^{41} - 9 q^{42} - 3 q^{43} - 9 q^{45} - 12 q^{47} + 9 q^{48} + 12 q^{49} + 15 q^{50} - 9 q^{51} + 6 q^{52} + 6 q^{53} - 6 q^{55} - 6 q^{56} + 9 q^{57} + 3 q^{58} - 21 q^{59} + 9 q^{60} + 21 q^{61} - 30 q^{62} + 9 q^{63} - 6 q^{64} + 21 q^{65} - 3 q^{67} - 9 q^{68} - 18 q^{69} - 6 q^{70} + 24 q^{71} + 18 q^{72} - 12 q^{73} + 15 q^{74} + 18 q^{75} - 3 q^{77} - 45 q^{78} + 9 q^{79} - 18 q^{80} + 42 q^{82} + 3 q^{85} - 6 q^{86} + 27 q^{87} - 3 q^{88} - 24 q^{89} - 27 q^{90} + 6 q^{91} + 9 q^{92} - 9 q^{93} + 18 q^{94} + 18 q^{95} - 9 q^{96} + 3 q^{97} + 24 q^{98}+O(q^{100}) $ 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 - 6 * q^8 - 12 * q^10 + 3 * q^11 + 9 * q^12 + 9 * q^13 + 3 * q^14 + 6 * q^16 - 6 * q^17 + 9 * q^18 - 18 * q^19 - 3 * q^20 + 9 * q^21 + 6 * q^23 - 9 * q^24 + 6 * q^25 + 24 * q^26 - 27 * q^27 - 6 * q^28 + 6 * q^29 + 18 * q^30 + 9 * q^31 - 9 * q^32 + 9 * q^36 - 24 * q^37 - 9 * q^38 - 3 * q^40 + 6 * q^41 - 9 * q^42 - 3 * q^43 - 9 * q^45 - 12 * q^47 + 9 * q^48 + 12 * q^49 + 15 * q^50 - 9 * q^51 + 6 * q^52 + 6 * q^53 - 6 * q^55 - 6 * q^56 + 9 * q^57 + 3 * q^58 - 21 * q^59 + 9 * q^60 + 21 * q^61 - 30 * q^62 + 9 * q^63 - 6 * q^64 + 21 * q^65 - 3 * q^67 - 9 * q^68 - 18 * q^69 - 6 * q^70 + 24 * q^71 + 18 * q^72 - 12 * q^73 + 15 * q^74 + 18 * q^75 - 3 * q^77 - 45 * q^78 + 9 * q^79 - 18 * q^80 + 42 * q^82 + 3 * q^85 - 6 * q^86 + 27 * q^87 - 3 * q^88 - 24 * q^89 - 27 * q^90 + 6 * q^91 + 9 * q^92 - 9 * q^93 + 18 * q^94 + 18 * q^95 - 9 * q^96 + 3 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.939693	+	1.62760i	0.664463	+	1.15088i	0.979431	+	0.201781i	$0.0646730\pi$
$2$	0.939693	+	1.62760i	0.664463	+	1.15088i	−0.314968	+	0.949102i	$0.601994\pi$
$3$	−1.70574	+	0.300767i	−0.984808	+	0.173648i
$3$	−1.70574	+	0.300767i	−0.984808	+	0.173648i
$4$	−0.766044	+	1.32683i	−0.383022	+	0.663414i
$5$	−1.43969	+	2.49362i	−0.643850	+	1.11518i	0.340716	+	0.940166i	$0.389331\pi$
$5$	−1.43969	+	2.49362i	−0.643850	+	1.11518i	−0.984566	+	0.175015i	$0.944003\pi$
$6$	−2.09240	−	2.49362i	−0.854217	−	1.01802i
$7$	0.326352	+	0.565258i	0.123349	+	0.213647i	0.921087	−	0.389358i	$-0.127303\pi$
$7$	0.326352	+	0.565258i	0.123349	+	0.213647i	−0.797737	+	0.603005i	$0.793970\pi$
$8$	0.879385			0.310910
$9$	2.81908	−	1.02606i	0.939693	−	0.342020i
$10$	−5.41147			−1.71126
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	0.907604	−	2.49362i	0.262003	−	0.719846i
$13$	3.37939	−	5.85327i	0.937273	−	1.62340i	0.166743	−	0.986000i	$-0.446675\pi$
$13$	3.37939	−	5.85327i	0.937273	−	1.62340i	0.770530	−	0.637404i	$-0.219992\pi$
$14$	−0.613341	+	1.06234i	−0.163922	+	0.283922i
$15$	1.70574	−	4.68647i	0.440419	−	1.21004i
$16$	2.35844	+	4.08494i	0.589610	+	1.02123i
$17$	0.184793			0.0448188			0.0224094	−	0.999749i	$-0.492866\pi$
$17$	0.184793			0.0448188			0.0224094	+	0.999749i	$0.492866\pi$
$18$	4.31908	+	3.62414i	1.01802	+	0.854217i
$19$	−5.22668			−1.19908			−0.599541	−	0.800344i	$-0.704650\pi$
$19$	−5.22668			−1.19908			−0.599541	+	0.800344i	$0.704650\pi$
$20$	−2.20574	−	3.82045i	−0.493218	−	0.854278i
$21$	−0.726682	−	0.866025i	−0.158575	−	0.188982i
$22$	−0.939693	+	1.62760i	−0.200343	+	0.347004i
$23$	1.59240	−	2.75811i	0.332038	−	0.575106i	−0.650874	−	0.759186i	$-0.725597\pi$
$23$	1.59240	−	2.75811i	0.332038	−	0.575106i	0.982911	+	0.184080i	$0.0589306\pi$
$24$	−1.50000	+	0.264490i	−0.306186	+	0.0539889i
$25$	−1.64543	−	2.84997i	−0.329086	−	0.569994i
$26$	12.7023			2.49113
$27$	−4.50000	+	2.59808i	−0.866025	+	0.500000i
$28$	−1.00000			−0.188982
$29$	2.01114	+	3.48340i	0.373460	+	0.646852i	0.990095	−	0.140397i	$-0.0448379\pi$
$29$	2.01114	+	3.48340i	0.373460	+	0.646852i	−0.616635	+	0.787249i	$0.711505\pi$
$30$	9.23055	−	1.62760i	1.68526	−	0.297157i
$31$	−0.553033	+	0.957882i	−0.0993277	+	0.172041i	−0.911407	−	0.411507i	$-0.865003\pi$
$31$	−0.553033	+	0.957882i	−0.0993277	+	0.172041i	0.812079	+	0.583548i	$0.198336\pi$
$32$	−3.55303	+	6.15403i	−0.628094	+	1.08789i
$33$	−1.11334	−	1.32683i	−0.193808	−	0.230971i
$34$	0.173648	+	0.300767i	0.0297804	+	0.0515812i
$35$	−1.87939			−0.317674
$36$	−0.798133	+	4.52644i	−0.133022	+	0.754407i
$37$	0.106067			0.0174373			0.00871864	−	0.999962i	$-0.497225\pi$
$37$	0.106067			0.0174373			0.00871864	+	0.999962i	$0.497225\pi$
$38$	−4.91147	−	8.50692i	−0.796746	−	1.38001i
$39$	−4.00387	+	11.0005i	−0.641132	+	1.76150i
$40$	−1.26604	+	2.19285i	−0.200179	+	0.346721i
$41$	2.80793	−	4.86348i	0.438526	−	0.759549i	−0.559050	−	0.829134i	$-0.688834\pi$
$41$	2.80793	−	4.86348i	0.438526	−	0.759549i	0.997576	+	0.0695851i	$0.0221675\pi$
$42$	0.726682	−	1.99654i	0.112129	−	0.308073i
$43$	−1.92989	−	3.34267i	−0.294306	−	0.509753i	0.680517	−	0.732732i	$-0.261755\pi$
$43$	−1.92989	−	3.34267i	−0.294306	−	0.509753i	−0.974823	+	0.222979i	$0.928422\pi$
$44$	−1.53209			−0.230971
$45$	−1.50000	+	8.50692i	−0.223607	+	1.26814i
$46$	5.98545			0.882507
$47$	−6.00387	−	10.3990i	−0.875755	−	1.51685i	−0.855957	−	0.517047i	$-0.827031\pi$
$47$	−6.00387	−	10.3990i	−0.875755	−	1.51685i	−0.0197977	−	0.999804i	$-0.506302\pi$
$48$	−5.25150	−	6.25849i	−0.757988	−	0.903335i
$49$	3.28699	−	5.69323i	0.469570	−	0.813319i
$50$	3.09240	−	5.35619i	0.437331	−	0.757479i
$51$	−0.315207	+	0.0555796i	−0.0441379	+	0.00778270i
$52$	5.17752	+	8.96773i	0.717993	+	1.24360i
$53$	−10.0719			−1.38348			−0.691742	−	0.722145i	$-0.743157\pi$
$53$	−10.0719			−1.38348			−0.691742	+	0.722145i	$0.743157\pi$
$54$	−8.45723	−	4.88279i	−1.15088	−	0.664463i
$55$	−2.87939			−0.388256
$56$	0.286989	+	0.497079i	0.0383505	+	0.0664250i
$57$	8.91534	−	1.57202i	1.18087	−	0.208219i
$58$	−3.77972	+	6.54666i	−0.496301	+	0.859618i
$59$	−5.27719	+	9.14036i	−0.687031	+	1.18997i	0.285762	+	0.958301i	$0.407753\pi$
$59$	−5.27719	+	9.14036i	−0.687031	+	1.18997i	−0.972794	+	0.231673i	$0.925580\pi$
$60$	4.91147	+	5.85327i	0.634069	+	0.755654i
$61$	3.67365	+	6.36295i	0.470362	+	0.814692i	0.999426	−	0.0338908i	$-0.0107899\pi$
$61$	3.67365	+	6.36295i	0.470362	+	0.814692i	−0.529063	+	0.848582i	$0.677457\pi$
$62$	−2.07873			−0.263998
$63$	1.50000	+	1.25865i	0.188982	+	0.158575i
$64$	−3.92127			−0.490159
$65$	9.73055	+	16.8538i	1.20693	+	2.09046i
$66$	1.11334	−	3.05888i	0.137043	−	0.376522i
$67$	5.90420	−	10.2264i	0.721313	−	1.24935i	−0.239161	−	0.970980i	$-0.576872\pi$
$67$	5.90420	−	10.2264i	0.721313	−	1.24935i	0.960474	−	0.278371i	$-0.0897943\pi$
$68$	−0.141559	+	0.245188i	−0.0171666	+	0.0297334i
$69$	−1.88666	+	5.18355i	−0.227127	+	0.624027i
$70$	−1.76604	−	3.05888i	−0.211083	−	0.365606i
$71$	−2.47565			−0.293806			−0.146903	−	0.989151i	$-0.546930\pi$
$71$	−2.47565			−0.293806			−0.146903	+	0.989151i	$0.546930\pi$
$72$	2.47906	−	0.902302i	0.292159	−	0.106337i
$73$	10.4611			1.22438			0.612190	−	0.790711i	$-0.290289\pi$
$73$	10.4611			1.22438			0.612190	+	0.790711i	$0.290289\pi$
$74$	0.0996702	+	0.172634i	0.0115864	+	0.0200683i
$75$	3.66385	+	4.36640i	0.423065	+	0.504189i
$76$	4.00387	−	6.93491i	0.459275	−	0.795488i
$77$	−0.326352	+	0.565258i	−0.0371912	+	0.0644171i
$78$	−21.6668	+	3.82045i	−2.45329	+	0.432581i
$79$	0.733956	+	1.27125i	0.0825765	+	0.143027i	0.904356	−	0.426779i	$-0.140352\pi$
$79$	0.733956	+	1.27125i	0.0825765	+	0.143027i	−0.821779	+	0.569806i	$0.807018\pi$
$80$	−13.5817			−1.51848
$81$	6.89440	−	5.78509i	0.766044	−	0.642788i
$82$	10.5544			1.16554
$83$	0.520945	+	0.902302i	0.0571811	+	0.0990406i	0.893199	−	0.449662i	$-0.148455\pi$
$83$	0.520945	+	0.902302i	0.0571811	+	0.0990406i	−0.836018	+	0.548702i	$0.815122\pi$
$84$	1.70574	−	0.300767i	0.186111	−	0.0328164i
$85$	−0.266044	+	0.460802i	−0.0288566	+	0.0499810i
$86$	3.62701	−	6.28217i	0.391111	−	0.677424i
$87$	−4.47818	−	5.33688i	−0.480111	−	0.572174i
$88$	0.439693	+	0.761570i	0.0468714	+	0.0811836i
$89$	−3.01960			−0.320077			−0.160038	−	0.987111i	$-0.551162\pi$
$89$	−3.01960			−0.320077			−0.160038	+	0.987111i	$0.551162\pi$
$90$	−15.2554	+	5.55250i	−1.60806	+	0.585285i
$91$	4.41147			0.462448
$92$	2.43969	+	4.22567i	0.254356	+	0.440557i
$93$	0.655230	−	1.80023i	0.0679442	−	0.186675i
$94$	11.2836	−	19.5437i	1.16381	−	2.01578i
$95$	7.52481	−	13.0334i	0.772030	−	1.33719i
$96$	4.20961	−	11.5658i	0.429641	−	1.18043i
$97$	2.86959	+	4.97027i	0.291362	+	0.504654i	0.974132	−	0.225979i	$-0.0725582\pi$
$97$	2.86959	+	4.97027i	0.291362	+	0.504654i	−0.682770	+	0.730633i	$0.739225\pi$
$98$	12.3550			1.24805
$99$	2.29813	+	1.92836i	0.230971	+	0.193808i
$100$	5.04189			0.504189
$101$	2.20961	+	3.82715i	0.219864	+	0.380816i	0.954766	−	0.297357i	$-0.0961053\pi$
$101$	2.20961	+	3.82715i	0.219864	+	0.380816i	−0.734902	+	0.678173i	$0.762772\pi$
$102$	−0.386659	−	0.460802i	−0.0382850	−	0.0456262i
$103$	−5.21941	+	9.04028i	−0.514284	+	0.890765i	0.485579	+	0.874193i	$0.338609\pi$
$103$	−5.21941	+	9.04028i	−0.514284	+	0.890765i	−0.999863	+	0.0165725i	$0.994725\pi$
$104$	2.97178	−	5.14728i	0.291407	−	0.504732i
$105$	3.20574	−	0.565258i	0.312848	−	0.0551635i
$106$	−9.46451	−	16.3930i	−0.919274	−	1.59223i
$107$	−8.31315			−0.803662			−0.401831	−	0.915714i	$-0.631626\pi$
$107$	−8.31315			−0.803662			−0.401831	+	0.915714i	$0.631626\pi$
$108$		−	7.96097i		−	0.766044i
$109$	−15.9881			−1.53139			−0.765693	−	0.643206i	$-0.777604\pi$
$109$	−15.9881			−1.53139			−0.765693	+	0.643206i	$0.777604\pi$
$110$	−2.70574	−	4.68647i	−0.257982	−	0.446838i
$111$	−0.180922	+	0.0319015i	−0.0171724	+	0.00302795i
$112$	−1.53936	+	2.66625i	−0.145456	+	0.251937i
$113$	2.53209	−	4.38571i	0.238199	−	0.412573i	−0.721999	−	0.691894i	$-0.756776\pi$
$113$	2.53209	−	4.38571i	0.238199	−	0.412573i	0.960198	+	0.279322i	$0.0901097\pi$
$114$	10.9363	+	13.0334i	1.02428	+	1.22069i
$115$	4.58512	+	7.94166i	0.427565	+	0.740564i
$116$	−6.16250			−0.572174
$117$	3.52094	−	19.9683i	0.325511	−	1.84607i
$118$	−19.8357			−1.82603
$119$	0.0603074	+	0.104455i	0.00552837	+	0.00957541i
$120$	1.50000	−	4.12122i	0.136931	−	0.376214i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−6.90420	+	11.9584i	−0.625077	+	1.08266i
$123$	−3.32682	+	9.14036i	−0.299969	+	0.824158i
$124$	−0.847296	−	1.46756i	−0.0760895	−	0.131791i
$125$	−4.92127			−0.440172
$126$	−0.639033	+	3.62414i	−0.0569296	+	0.322864i
$127$	7.80066			0.692197			0.346098	−	0.938198i	$-0.387506\pi$
$127$	7.80066			0.692197			0.346098	+	0.938198i	$0.387506\pi$
$128$	3.42127	+	5.92582i	0.302401	+	0.523774i
$129$	4.29726	+	5.12127i	0.378352	+	0.450903i
$130$	−18.2875	+	31.6748i	−1.60392	+	2.77806i
$131$	6.24897	−	10.8235i	0.545975	−	0.945657i	−0.452570	−	0.891729i	$-0.649493\pi$
$131$	6.24897	−	10.8235i	0.545975	−	0.945657i	0.998545	−	0.0539276i	$-0.0171740\pi$
$132$	2.61334	−	0.460802i	0.227462	−	0.0401077i
$133$	−1.70574	−	2.95442i	−0.147906	−	0.256181i
$134$	22.1925			1.91714
$135$		−	14.9617i		−	1.28770i
$136$	0.162504			0.0139346
$137$	−7.61334	−	13.1867i	−0.650452	−	1.12662i	−0.983013	−	0.183534i	$-0.941246\pi$
$137$	−7.61334	−	13.1867i	−0.650452	−	1.12662i	0.332562	−	0.943081i	$-0.392087\pi$
$138$	−10.2096	+	1.80023i	−0.869100	+	0.153246i
$139$	−7.25150	+	12.5600i	−0.615064	+	1.06532i	0.375309	+	0.926900i	$0.377536\pi$
$139$	−7.25150	+	12.5600i	−0.615064	+	1.06532i	−0.990373	+	0.138422i	$0.955797\pi$
$140$	1.43969	−	2.49362i	0.121676	−	0.210749i
$141$	13.3687	+	15.9322i	1.12585	+	1.34173i
$142$	−2.32635	−	4.02936i	−0.195223	−	0.338136i
$143$	6.75877			0.565197
$144$	10.8400	+	9.09586i	0.903335	+	0.757988i
$145$	−11.5817			−0.961809
$146$	9.83022	+	17.0264i	0.813555	+	1.40912i
$147$	−3.89440	+	10.6998i	−0.321205	+	0.882503i
$148$	−0.0812519	+	0.140732i	−0.00667887	+	0.0115681i
$149$	−7.30453	+	12.6518i	−0.598410	+	1.03648i	0.394645	+	0.918833i	$0.370867\pi$
$149$	−7.30453	+	12.6518i	−0.598410	+	1.03648i	−0.993056	+	0.117644i	$0.962466\pi$
$150$	−3.66385	+	10.0663i	−0.299152	+	0.821913i
$151$	10.5535	+	18.2792i	0.858832	+	1.48754i	0.873044	+	0.487641i	$0.162143\pi$
$151$	10.5535	+	18.2792i	0.858832	+	1.48754i	−0.0142125	+	0.999899i	$0.504524\pi$
$152$	−4.59627			−0.372806
$153$	0.520945	−	0.189608i	0.0421159	−	0.0153289i
$154$	−1.22668			−0.0988488
$155$	−1.59240	−	2.75811i	−0.127904	−	0.221537i
$156$	−11.5287	−	13.7394i	−0.923034	−	1.10003i
$157$	2.21554	−	3.83742i	0.176819	−	0.306260i	−0.763970	−	0.645252i	$-0.776753\pi$
$157$	2.21554	−	3.83742i	0.176819	−	0.306260i	0.940789	+	0.338992i	$0.110086\pi$
$158$	−1.37939	+	2.38917i	−0.109738	+	0.190072i
$159$	17.1800	−	3.02931i	1.36247	−	0.240240i
$160$	−10.2306	−	17.7198i	−0.808796	−	1.40088i
$161$	2.07873			0.163827
$162$	15.8944	+	5.78509i	1.24878	+	0.454519i
$163$	−2.12567			−0.166495			−0.0832476	−	0.996529i	$-0.526529\pi$
$163$	−2.12567			−0.166495			−0.0832476	+	0.996529i	$0.526529\pi$
$164$	4.30200	+	7.45129i	0.335930	+	0.581848i
$165$	4.91147	−	0.866025i	0.382358	−	0.0674200i
$166$	−0.979055	+	1.69577i	−0.0759894	+	0.131618i
$167$	−6.21554	+	10.7656i	−0.480973	+	0.833069i	−0.999762	−	0.0218332i	$-0.993050\pi$
$167$	−6.21554	+	10.7656i	−0.480973	+	0.833069i	0.518789	+	0.854902i	$0.326383\pi$
$168$	−0.639033	−	0.761570i	−0.0493025	−	0.0587564i
$169$	−16.3405	−	28.3026i	−1.25696	−	2.17712i
$170$	−1.00000			−0.0766965
$171$	−14.7344	+	5.36289i	−1.12677	+	0.410111i
$172$	5.91353			0.450903
$173$	−1.80200	−	3.12116i	−0.137004	−	0.237298i	0.789357	−	0.613934i	$-0.210414\pi$
$173$	−1.80200	−	3.12116i	−0.137004	−	0.237298i	−0.926361	+	0.376636i	$0.877081\pi$
$174$	4.47818	−	12.3037i	0.339490	−	0.932741i
$175$	1.07398	−	1.86018i	0.0811851	−	0.140617i
$176$	−2.35844	+	4.08494i	−0.177774	+	0.307914i
$177$	6.25237	−	17.1783i	0.469957	−	1.29120i
$178$	−2.83750	−	4.91469i	−0.212679	−	0.368371i
$179$	12.8726			0.962142			0.481071	−	0.876682i	$-0.340248\pi$
$179$	12.8726			0.962142			0.481071	+	0.876682i	$0.340248\pi$
$180$	−10.1382	−	8.50692i	−0.755654	−	0.634069i
$181$	−24.3405			−1.80921			−0.904607	−	0.426246i	$-0.859836\pi$
$181$	−24.3405			−1.80921			−0.904607	+	0.426246i	$0.859836\pi$
$182$	4.14543	+	7.18009i	0.307280	+	0.532224i
$183$	−8.18004	−	9.74860i	−0.604686	−	0.720637i
$184$	1.40033	−	2.42544i	0.103234	−	0.178806i
$185$	−0.152704	+	0.264490i	−0.0112270	+	0.0194457i
$186$	3.54576	−	0.625213i	0.259988	−	0.0458428i
$187$	0.0923963	+	0.160035i	0.00675668	+	0.0117029i
$188$	18.3969			1.34173
$189$	−2.93717	−	1.69577i	−0.213647	−	0.123349i
$190$	28.2841			2.05194
$191$	−2.97906	−	5.15988i	−0.215557	−	0.373355i	0.737888	−	0.674923i	$-0.235823\pi$
$191$	−2.97906	−	5.15988i	−0.215557	−	0.373355i	−0.953445	+	0.301568i	$0.902490\pi$
$192$	6.68866	−	1.17939i	0.482713	−	0.0851153i
$193$	−5.41147	+	9.37295i	−0.389526	+	0.674680i	−0.992386	−	0.123168i	$-0.960695\pi$
$193$	−5.41147	+	9.37295i	−0.389526	+	0.674680i	0.602859	+	0.797847i	$0.294028\pi$
$194$	−5.39306	+	9.34105i	−0.387199	+	0.670648i
$195$	−21.6668	−	25.8215i	−1.55159	−	1.84912i
$196$	5.03596	+	8.72254i	0.359711	+	0.623038i
$197$	3.07192			0.218865			0.109433	−	0.993994i	$-0.465097\pi$
$197$	3.07192			0.218865			0.109433	+	0.993994i	$0.465097\pi$
$198$	−0.979055	+	5.55250i	−0.0695784	+	0.394599i
$199$	1.54664			0.109638			0.0548191	−	0.998496i	$-0.482542\pi$
$199$	1.54664			0.109638			0.0548191	+	0.998496i	$0.482542\pi$
$200$	−1.44697	−	2.50622i	−0.102316	−	0.177216i
$201$	−6.99525	+	19.2193i	−0.493407	+	1.35562i
$202$	−4.15270	+	7.19269i	−0.292183	+	0.506076i
$203$	−1.31268	+	2.27363i	−0.0921322	+	0.159578i
$204$	0.167718	−	0.460802i	0.0117426	−	0.0322626i
$205$	8.08512	+	14.0038i	0.564689	+	0.978071i
$206$	−19.6186			−1.36689
$207$	1.65910	−	9.40923i	0.115315	−	0.653986i
$208$	31.8803			2.21050
$209$	−2.61334	−	4.52644i	−0.180769	−	0.313100i
$210$	3.93242	+	4.68647i	0.271363	+	0.323397i
$211$	7.92649	−	13.7291i	0.545682	−	0.945149i	−0.452882	−	0.891571i	$-0.649604\pi$
$211$	7.92649	−	13.7291i	0.545682	−	0.945149i	0.998564	−	0.0535783i	$-0.0170627\pi$
$212$	7.71554	−	13.3637i	0.529905	−	0.917823i
$213$	4.22281	−	0.744596i	0.289342	−	0.0510188i
$214$	−7.81180	−	13.5304i	−0.534004	−	0.924922i
$215$	11.1138			0.757955
$216$	−3.95723	+	2.28471i	−0.269256	+	0.155455i
$217$	−0.721934			−0.0490081
$218$	−15.0239	−	26.0222i	−1.01755	−	1.76245i
$219$	−17.8439	+	3.14636i	−1.20578	+	0.212611i
$220$	2.20574	−	3.82045i	0.148711	−	0.257575i
$221$	0.624485	−	1.08164i	0.0420074	−	0.0727590i
$222$	−0.221934	−	0.264490i	−0.0148952	−	0.0177514i
$223$	−3.12314	−	5.40944i	−0.209141	−	0.362243i	0.742303	−	0.670064i	$-0.233733\pi$
$223$	−3.12314	−	5.40944i	−0.209141	−	0.362243i	−0.951444	+	0.307821i	$0.900400\pi$
$224$	−4.63816			−0.309900
$225$	−7.56283	−	6.34597i	−0.504189	−	0.423065i
$226$	9.51754			0.633097
$227$	−1.63088	−	2.82477i	−0.108245	−	0.187487i	0.806814	−	0.590805i	$-0.201190\pi$
$227$	−1.63088	−	2.82477i	−0.108245	−	0.187487i	−0.915060	+	0.403319i	$0.867857\pi$
$228$	−4.74376	+	13.0334i	−0.314163	+	0.863155i
$229$	5.40760	−	9.36624i	0.357345	−	0.618939i	−0.630172	−	0.776456i	$-0.717016\pi$
$229$	5.40760	−	9.36624i	0.357345	−	0.618939i	0.987516	+	0.157517i	$0.0503489\pi$
$230$	−8.61721	+	14.9254i	−0.568202	+	0.984155i
$231$	0.386659	−	1.06234i	0.0254403	−	0.0698967i
$232$	1.76857	+	3.06325i	0.116112	+	0.201112i
$233$	−3.71688			−0.243501			−0.121750	−	0.992561i	$-0.538851\pi$
$233$	−3.71688			−0.243501			−0.121750	+	0.992561i	$0.538851\pi$
$234$	35.8089	−	13.0334i	2.34090	−	0.852018i
$235$	34.5749			2.25542
$236$	−8.08512	−	14.0038i	−0.526297	−	0.911573i
$237$	−1.63429	−	1.94767i	−0.106158	−	0.126514i
$238$	−0.113341	+	0.196312i	−0.00734679	+	0.0127250i
$239$	−4.02869	+	6.97789i	−0.260594	+	0.451362i	−0.966400	−	0.257043i	$-0.917252\pi$
$239$	−4.02869	+	6.97789i	−0.260594	+	0.451362i	0.705806	+	0.708405i	$0.250585\pi$
$240$	23.1668	−	4.08494i	1.49541	−	0.263682i
$241$	2.15998	+	3.74119i	0.139136	+	0.240991i	0.927170	−	0.374641i	$-0.122234\pi$
$241$	2.15998	+	3.74119i	0.139136	+	0.240991i	−0.788034	+	0.615632i	$0.788901\pi$
$242$	−1.87939			−0.120811
$243$	−10.0201	+	11.9415i	−0.642788	+	0.766044i
$244$	−11.2567			−0.720637
$245$	9.46451	+	16.3930i	0.604665	+	1.04731i
$246$	−18.0030	+	3.17441i	−1.14783	+	0.202393i
$247$	−17.6630	+	30.5932i	−1.12387	+	1.94660i
$248$	−0.486329	+	0.842347i	−0.0308819	+	0.0534891i
$249$	−1.15998	−	1.38241i	−0.0735106	−	0.0876065i
$250$	−4.62449	−	8.00984i	−0.292478	−	0.506587i
$251$	14.1753			0.894737			0.447368	−	0.894350i	$-0.352361\pi$
$251$	14.1753			0.894737			0.447368	+	0.894350i	$0.352361\pi$
$252$	−2.81908	+	1.02606i	−0.177585	+	0.0646357i
$253$	3.18479			0.200226
$254$	7.33022	+	12.6963i	0.459939	+	0.796638i
$255$	0.315207	−	0.866025i	0.0197391	−	0.0542326i
$256$	−10.3512	+	17.9287i	−0.646948	+	1.12055i
$257$	4.31655	−	7.47649i	0.269259	−	0.466370i	−0.699412	−	0.714719i	$-0.746555\pi$
$257$	4.31655	−	7.47649i	0.269259	−	0.466370i	0.968671	+	0.248349i	$0.0798879\pi$
$258$	−4.29726	+	11.8066i	−0.267535	+	0.735048i
$259$	0.0346151	+	0.0599551i	0.00215088	+	0.00372543i
$260$	−29.8161			−1.84912
$261$	9.24376	+	7.75643i	0.572174	+	0.480111i
$262$	23.4884			1.45112
$263$	−0.599670	−	1.03866i	−0.0369773	−	0.0640465i	0.846945	−	0.531681i	$-0.178440\pi$
$263$	−0.599670	−	1.03866i	−0.0369773	−	0.0640465i	−0.883922	+	0.467635i	$0.845106\pi$
$264$	−0.979055	−	1.16679i	−0.0602567	−	0.0718111i
$265$	14.5005	−	25.1155i	0.890757	−	1.54284i
$266$	3.20574	−	5.55250i	0.196556	−	0.340446i
$267$	5.15064	−	0.908198i	0.315214	−	0.0555808i
$268$	9.04576	+	15.6677i	0.552558	+	0.957058i
$269$	27.9213			1.70239			0.851195	−	0.524849i	$-0.175878\pi$
$269$	27.9213			1.70239			0.851195	+	0.524849i	$0.175878\pi$
$270$	24.3516	−	14.0594i	1.48199	−	0.855629i
$271$	−13.4311			−0.815880			−0.407940	−	0.913009i	$-0.633753\pi$
$271$	−13.4311			−0.815880			−0.407940	+	0.913009i	$0.633753\pi$
$272$	0.435822	+	0.754866i	0.0264256	+	0.0457705i
$273$	−7.52481	+	1.32683i	−0.455423	+	0.0803033i
$274$	14.3084	−	24.7829i	0.864402	−	1.49719i
$275$	1.64543	−	2.84997i	0.0992231	−	0.171860i
$276$	−5.43242	−	6.47410i	−0.326993	−	0.389695i
$277$	4.24035	+	7.34451i	0.254778	+	0.441289i	0.964835	−	0.262855i	$-0.0846642\pi$
$277$	4.24035	+	7.34451i	0.254778	+	0.441289i	−0.710057	+	0.704144i	$0.751331\pi$
$278$	−27.2567			−1.63475
$279$	−0.576199	+	3.26779i	−0.0344962	+	0.195637i
$280$	−1.65270			−0.0987679
$281$	1.26945	+	2.19875i	0.0757289	+	0.131166i	0.901403	−	0.432981i	$-0.142538\pi$
$281$	1.26945	+	2.19875i	0.0757289	+	0.131166i	−0.825674	+	0.564147i	$0.809205\pi$
$282$	−13.3687	+	36.7302i	−0.796095	+	2.18725i
$283$	2.33750	−	4.04866i	0.138950	−	0.240668i	−0.788150	−	0.615484i	$-0.788961\pi$
$283$	2.33750	−	4.04866i	0.138950	−	0.240668i	0.927099	+	0.374816i	$0.122294\pi$
$284$	1.89646	−	3.28476i	0.112534	−	0.194915i
$285$	−8.91534	+	24.4947i	−0.528099	+	1.45094i
$286$	6.35117	+	11.0005i	0.375552	+	0.650476i
$287$	3.66550			0.216367
$288$	−3.70187	+	20.9943i	−0.218135	+	1.23710i
$289$	−16.9659			−0.997991
$290$	−10.8833	−	18.8504i	−0.639087	−	1.10693i
$291$	−6.38965	−	7.61489i	−0.374568	−	0.446393i
$292$	−8.01367	+	13.8801i	−0.468965	+	0.812271i
$293$	−3.92262	+	6.79417i	−0.229162	+	0.396920i	−0.957560	−	0.288234i	$-0.906932\pi$
$293$	−3.92262	+	6.79417i	−0.229162	+	0.396920i	0.728398	+	0.685154i	$0.240265\pi$
$294$	−21.0744	+	3.71599i	−1.22909	+	0.216721i
$295$	−15.1951	−	26.3186i	−0.884691	−	1.53233i
$296$	0.0932736			0.00542142
$297$	−4.50000	−	2.59808i	−0.261116	−	0.150756i
$298$	−27.4561			−1.59049
$299$	−10.7626	−	18.6414i	−0.622420	−	1.07806i
$300$	−8.60014	+	1.51644i	−0.496529	+	0.0875515i
$301$	1.25965	−	2.18177i	0.0726049	−	0.125755i
$302$	−19.8341	+	34.3537i	−1.14132	+	1.97683i
$303$	−4.92009	−	5.86354i	−0.282652	−	0.336851i
$304$	−12.3268	−	21.3507i	−0.706992	−	1.22455i
$305$	−21.1557			−1.21137
$306$	0.798133	+	0.669713i	0.0456262	+	0.0382850i
$307$	26.4047			1.50699			0.753497	−	0.657451i	$-0.228365\pi$
$307$	26.4047			1.50699			0.753497	+	0.657451i	$0.228365\pi$
$308$	−0.500000	−	0.866025i	−0.0284901	−	0.0493464i
$309$	6.18392	−	16.9902i	0.351791	−	0.966537i
$310$	2.99273	−	5.18355i	0.169975	−	0.294406i
$311$	9.57057	−	16.5767i	0.542697	−	0.939980i	−0.456050	−	0.889954i	$-0.650736\pi$
$311$	9.57057	−	16.5767i	0.542697	−	0.939980i	0.998748	−	0.0500257i	$-0.0159303\pi$
$312$	−3.52094	+	9.67372i	−0.199334	+	0.547666i
$313$	4.48545	+	7.76903i	0.253533	+	0.439132i	0.964496	−	0.264098i	$-0.0850741\pi$
$313$	4.48545	+	7.76903i	0.253533	+	0.439132i	−0.710963	+	0.703229i	$0.751741\pi$
$314$	8.32770			0.469959
$315$	−5.29813	+	1.92836i	−0.298516	+	0.108651i
$316$	−2.24897			−0.126514
$317$	−3.13903	−	5.43696i	−0.176306	−	0.305370i	0.764307	−	0.644853i	$-0.223081\pi$
$317$	−3.13903	−	5.43696i	−0.176306	−	0.305370i	−0.940612	+	0.339483i	$0.889748\pi$
$318$	21.0744	+	25.1155i	1.18180	+	1.40841i
$319$	−2.01114	+	3.48340i	−0.112602	+	0.195033i
$320$	5.64543	−	9.77817i	0.315589	−	0.546616i
$321$	14.1800	−	2.50032i	0.791453	−	0.139555i
$322$	1.95336	+	3.38332i	0.108857	+	0.188545i
$323$	−0.965852			−0.0537414
$324$	2.39440	+	13.5793i	0.133022	+	0.754407i
$325$	−22.2422			−1.23377
$326$	−1.99747	−	3.45973i	−0.110630	−	0.191617i
$327$	27.2716	−	4.80871i	1.50812	−	0.265922i
$328$	2.46926	−	4.27688i	0.136342	−	0.236151i
$329$	3.91875	−	6.78747i	0.216048	−	0.374205i
$330$	6.02481	+	7.18009i	0.331655	+	0.395251i
$331$	5.93629	+	10.2820i	0.326288	+	0.565147i	0.981772	−	0.190062i	$-0.0608688\pi$
$331$	5.93629	+	10.2820i	0.326288	+	0.565147i	−0.655484	+	0.755209i	$0.727535\pi$
$332$	−1.59627			−0.0876065
$333$	0.299011	−	0.108831i	0.0163857	−	0.00596390i
$334$	−23.3628			−1.27835
$335$	17.0005	+	29.4457i	0.928835	+	1.60879i
$336$	1.82383	−	5.01092i	0.0994978	−	0.273368i
$337$	−4.52094	+	7.83051i	−0.246272	+	0.426555i	−0.962488	−	0.271323i	$-0.912539\pi$
$337$	−4.52094	+	7.83051i	−0.246272	+	0.426555i	0.716217	+	0.697878i	$0.245872\pi$
$338$	30.7101	−	53.1914i	1.67041	−	2.89323i
$339$	−3.00000	+	8.24243i	−0.162938	+	0.447667i
$340$	−0.407604	−	0.705990i	−0.0221054	−	0.0382877i
$341$	−1.10607			−0.0598969
$342$	−22.5744	−	18.9422i	−1.22069	−	1.02428i
$343$	8.85978			0.478383
$344$	−1.69712	−	2.93950i	−0.0915025	−	0.158487i
$345$	−10.2096	−	12.1673i	−0.549667	−	0.655067i
$346$	3.38666	−	5.86587i	0.182068	−	0.315351i
$347$	9.48158	−	16.4226i	0.508998	−	0.881610i	−0.490948	−	0.871189i	$-0.663349\pi$
$347$	9.48158	−	16.4226i	0.508998	−	0.881610i	0.999946	−	0.0104213i	$-0.00331727\pi$
$348$	10.5116	−	1.85348i	0.563482	−	0.0993570i
$349$	11.0642	+	19.1637i	0.592252	+	1.02581i	0.993928	+	0.110029i	$0.0350943\pi$
$349$	11.0642	+	19.1637i	0.592252	+	1.02581i	−0.401677	+	0.915782i	$0.631572\pi$
$350$	4.03684			0.215778
$351$			35.1196i			1.87455i
$352$	−7.10607			−0.378755
$353$	12.2208	+	21.1670i	0.650445	+	1.12660i	0.983015	+	0.183525i	$0.0587509\pi$
$353$	12.2208	+	21.1670i	0.650445	+	1.12660i	−0.332570	+	0.943079i	$0.607916\pi$
$354$	33.8346	−	5.96595i	1.79829	−	0.317086i
$355$	3.56418	−	6.17334i	0.189167	−	0.327647i
$356$	2.31315	−	4.00649i	0.122597	−	0.212344i
$357$	−0.134285	−	0.160035i	−0.00710713	−	0.00846995i
$358$	12.0963	+	20.9513i	0.639308	+	1.10731i
$359$	−4.68685			−0.247363			−0.123681	−	0.992322i	$-0.539470\pi$
$359$	−4.68685			−0.247363			−0.123681	+	0.992322i	$0.539470\pi$
$360$	−1.31908	+	7.48086i	−0.0695215	+	0.394276i
$361$	8.31820			0.437800
$362$	−22.8726	−	39.6165i	−1.20216	−	2.08220i
$363$	0.592396	−	1.62760i	0.0310927	−	0.0854266i
$364$	−3.37939	+	5.85327i	−0.177128	+	0.306795i
$365$	−15.0608	+	26.0860i	−0.788317	+	1.36541i
$366$	8.18004	−	22.4745i	0.427578	−	1.17476i
$367$	4.50134	+	7.79656i	0.234968	+	0.406977i	0.959263	−	0.282513i	$-0.0911680\pi$
$367$	4.50134	+	7.79656i	0.234968	+	0.406977i	−0.724295	+	0.689490i	$0.757835\pi$
$368$	15.0223			0.783091
$369$	2.92556	−	16.5916i	0.152298	−	0.863727i
$370$	−0.573978			−0.0298397
$371$	−3.28699	−	5.69323i	−0.170652	−	0.295578i
$372$	1.88666	+	2.24843i	0.0978187	+	0.116576i
$373$	−5.13950	+	8.90187i	−0.266113	+	0.460922i	−0.967855	−	0.251510i	$-0.919073\pi$
$373$	−5.13950	+	8.90187i	−0.266113	+	0.460922i	0.701741	+	0.712432i	$0.252406\pi$
$374$	−0.173648	+	0.300767i	−0.00897913	+	0.0155523i
$375$	8.39440	−	1.48016i	0.433485	−	0.0764351i
$376$	−5.27972	−	9.14473i	−0.272281	−	0.471604i
$377$	27.1857			1.40014
$378$		−	6.37402i		−	0.327844i
$379$	14.2540			0.732180			0.366090	−	0.930579i	$-0.380696\pi$
$379$	14.2540			0.732180			0.366090	+	0.930579i	$0.380696\pi$
$380$	11.5287	+	19.9683i	0.591409	+	1.02435i
$381$	−13.3059	+	2.34618i	−0.681681	+	0.120199i
$382$	5.59879	−	9.69739i	0.286459	−	0.496162i
$383$	−7.41740	+	12.8473i	−0.379012	+	0.656467i	−0.990919	−	0.134462i	$-0.957069\pi$
$383$	−7.41740	+	12.8473i	−0.379012	+	0.656467i	0.611907	+	0.790930i	$0.290403\pi$
$384$	−7.61809	−	9.07888i	−0.388759	−	0.463305i
$385$	−0.939693	−	1.62760i	−0.0478912	−	0.0829499i
$386$	−20.3405			−1.03530
$387$	−8.87030	−	7.44307i	−0.450903	−	0.378352i
$388$	−8.79292			−0.446393
$389$	−5.46064	−	9.45810i	−0.276865	−	0.479545i	0.693739	−	0.720227i	$-0.255962\pi$
$389$	−5.46064	−	9.45810i	−0.276865	−	0.479545i	−0.970604	+	0.240682i	$0.922629\pi$
$390$	21.6668	−	59.5292i	1.09714	−	3.01438i
$391$	0.294263	−	0.509678i	0.0148815	−	0.0257755i
$392$	2.89053	−	5.00654i	0.145994	−	0.252869i
$393$	−7.40373	+	20.3416i	−0.373469	+	1.02610i
$394$	2.88666	+	4.99984i	0.145428	+	0.251888i
$395$	−4.22668			−0.212667
$396$	−4.31908	+	1.57202i	−0.217042	+	0.0789968i
$397$	−34.5945			−1.73625			−0.868124	−	0.496347i	$-0.834674\pi$
$397$	−34.5945			−1.73625			−0.868124	+	0.496347i	$0.834674\pi$
$398$	1.45336	+	2.51730i	0.0728505	+	0.126181i
$399$	3.79813	+	4.52644i	0.190144	+	0.226605i
$400$	7.76130	−	13.4430i	0.388065	−	0.672148i
$401$	−8.62061	+	14.9313i	−0.430493	+	0.745636i	−0.996916	−	0.0784791i	$-0.974994\pi$
$401$	−8.62061	+	14.9313i	−0.430493	+	0.745636i	0.566423	+	0.824115i	$0.308327\pi$
$402$	−37.8546	+	6.67479i	−1.88802	+	0.332908i
$403$	3.73783	+	6.47410i	0.186194	+	0.322498i
$404$	−6.77063			−0.336851
$405$	4.50000	+	25.5208i	0.223607	+	1.26814i
$406$	−4.93407			−0.244874
$407$	0.0530334	+	0.0918566i	0.00262877	+	0.00455316i
$408$	−0.277189	+	0.0488759i	−0.0137229	+	0.00241972i
$409$	2.21167	−	3.83072i	0.109360	−	0.189417i	−0.806151	−	0.591710i	$-0.798453\pi$
$409$	2.21167	−	3.83072i	0.109360	−	0.189417i	0.915511	+	0.402293i	$0.131787\pi$
$410$	−15.1951	+	26.3186i	−0.750431	+	1.29978i
$411$	16.9525	+	20.2032i	0.836204	+	0.996550i
$412$	−7.99660	−	13.8505i	−0.393964	−	0.682366i
$413$	−6.88888			−0.338980
$414$	16.8735	−	6.14144i	0.829285	−	0.301835i
$415$	−3.00000			−0.147264
$416$	24.0141	+	41.5937i	1.17739	+	2.03930i
$417$	8.59152	−	23.6050i	0.420728	−	1.15594i
$418$	4.91147	−	8.50692i	0.240228	−	0.416087i
$419$	8.75877	−	15.1706i	0.427894	−	0.741134i	−0.568792	−	0.822481i	$-0.692589\pi$
$419$	8.75877	−	15.1706i	0.427894	−	0.741134i	0.996686	+	0.0813475i	$0.0259223\pi$
$420$	−1.70574	+	4.68647i	−0.0832314	+	0.228677i
$421$	−4.95858	−	8.58851i	−0.241666	−	0.418578i	0.719523	−	0.694469i	$-0.244361\pi$
$421$	−4.95858	−	8.58851i	−0.241666	−	0.418578i	−0.961189	+	0.275891i	$0.911027\pi$
$422$	29.7939			1.45034
$423$	−27.5954	−	23.1553i	−1.34173	−	1.12585i
$424$	−8.85710			−0.430139
$425$	−0.304063	−	0.526653i	−0.0147492	−	0.0255464i
$426$	5.18004	+	6.17334i	0.250974	+	0.299099i
$427$	−2.39780	+	4.15312i	−0.116038	+	0.200983i
$428$	6.36824	−	11.0301i	0.307821	−	0.533161i
$429$	−11.5287	+	2.03282i	−0.556610	+	0.0981454i
$430$	10.4436	+	18.0888i	0.503633	+	0.872319i
$431$	−2.38238			−0.114755			−0.0573776	−	0.998353i	$-0.518274\pi$
$431$	−2.38238			−0.114755			−0.0573776	+	0.998353i	$0.518274\pi$
$432$	−21.2260	−	12.2548i	−1.02123	−	0.589610i
$433$	31.1661			1.49775			0.748874	−	0.662712i	$-0.230595\pi$
$433$	31.1661			1.49775			0.748874	+	0.662712i	$0.230595\pi$
$434$	−0.678396	−	1.17502i	−0.0325640	−	0.0564026i
$435$	19.7554	−	3.48340i	0.947197	−	0.167016i
$436$	12.2476	−	21.2135i	0.586555	−	1.01594i
$437$	−8.32295	+	14.4158i	−0.398141	+	0.689600i
$438$	−21.8888	−	26.0860i	−1.04589	−	1.24644i
$439$	−4.02734	−	6.97556i	−0.192215	−	0.332925i	0.753769	−	0.657139i	$-0.228234\pi$
$439$	−4.02734	−	6.97556i	−0.192215	−	0.332925i	−0.945984	+	0.324214i	$0.894900\pi$
$440$	−2.53209			−0.120713
$441$	3.42468	−	19.4223i	0.163080	−	0.924872i
$442$	2.34730			0.111650
$443$	5.81773	+	10.0766i	0.276409	+	0.478754i	0.970490	−	0.241143i	$-0.0775223\pi$
$443$	5.81773	+	10.0766i	0.276409	+	0.478754i	−0.694081	+	0.719897i	$0.744189\pi$
$444$	0.0962667	−	0.264490i	0.00456861	−	0.0125522i
$445$	4.34730	−	7.52974i	0.206082	−	0.356944i
$446$	5.86959	−	10.1664i	0.277933	−	0.481394i
$447$	8.65435	−	23.7776i	0.409337	−	1.12464i
$448$	−1.27972	−	2.21653i	−0.0604609	−	0.104721i
$449$	−25.7442			−1.21494			−0.607472	−	0.794341i	$-0.707817\pi$
$449$	−25.7442			−1.21494			−0.607472	+	0.794341i	$0.707817\pi$
$450$	3.22193	−	18.2725i	0.151883	−	0.861374i
$451$	5.61587			0.264441
$452$	3.87939	+	6.71929i	0.182471	+	0.316049i
$453$	−23.4993	−	28.0054i	−1.10409	−	1.31581i
$454$	3.06506	−	5.30883i	0.143850	−	0.249156i
$455$	−6.35117	+	11.0005i	−0.297747	+	0.515713i
$456$	7.84002	−	1.38241i	0.367143	−	0.0647372i
$457$	−19.2160	−	33.2831i	−0.898887	−	1.55692i	−0.828919	−	0.559368i	$-0.811044\pi$
$457$	−19.2160	−	33.2831i	−0.898887	−	1.55692i	−0.0699675	−	0.997549i	$-0.522290\pi$
$458$	20.3259			0.949769
$459$	−0.831566	+	0.480105i	−0.0388142	+	0.0224094i
$460$	−14.0496			−0.655067
$461$	−2.79948	−	4.84884i	−0.130385	−	0.225833i	0.793440	−	0.608648i	$-0.208288\pi$
$461$	−2.79948	−	4.84884i	−0.130385	−	0.225833i	−0.923825	+	0.382815i	$0.874955\pi$
$462$	2.09240	−	0.368946i	0.0973471	−	0.0171649i
$463$	−4.64677	+	8.04845i	−0.215954	+	0.374043i	−0.953567	−	0.301180i	$-0.902619\pi$
$463$	−4.64677	+	8.04845i	−0.215954	+	0.374043i	0.737613	+	0.675223i	$0.235953\pi$
$464$	−9.48633	+	16.4308i	−0.440392	+	0.762781i
$465$	3.54576	+	4.22567i	0.164431	+	0.195961i
$466$	−3.49273	−	6.04958i	−0.161797	−	0.280241i
$467$	17.0642			0.789636			0.394818	−	0.918759i	$-0.370808\pi$
$467$	17.0642			0.789636			0.394818	+	0.918759i	$0.370808\pi$
$468$	23.7973	+	19.9683i	1.10003	+	0.923034i
$469$	7.70739			0.355894
$470$	32.4898	+	56.2740i	1.49864	+	2.59572i
$471$	−2.62495	+	7.21200i	−0.120951	+	0.332311i
$472$	−4.64068	+	8.03790i	−0.213605	+	0.369974i
$473$	1.92989	−	3.34267i	0.0887365	−	0.153696i
$474$	1.63429	−	4.49016i	0.0750652	−	0.206240i
$475$	8.60014	+	14.8959i	0.394601	+	0.683470i
$476$	−0.184793			−0.00846995
$477$	−28.3935	+	10.3344i	−1.30005	+	0.473180i
$478$	−15.1429			−0.692620
$479$	19.7101	+	34.1389i	0.900576	+	1.55984i	0.826748	+	0.562573i	$0.190188\pi$
$479$	19.7101	+	34.1389i	0.900576	+	1.55984i	0.0738286	+	0.997271i	$0.476478\pi$
$480$	22.7802	+	27.1484i	1.03977	+	1.23915i
$481$	0.358441	−	0.620838i	0.0163435	−	0.0283078i
$482$	−4.05943	+	7.03114i	−0.184902	+	0.320260i
$483$	−3.54576	+	0.625213i	−0.161338	+	0.0284482i
$484$	−0.766044	−	1.32683i	−0.0348202	−	0.0603104i
$485$	−16.5253			−0.750374
$486$	−28.8516	−	5.08732i	−1.30874	−	0.230766i
$487$	−34.9522			−1.58384			−0.791919	−	0.610627i	$-0.790918\pi$
$487$	−34.9522			−1.58384			−0.791919	+	0.610627i	$0.790918\pi$
$488$	3.23055	+	5.59548i	0.146240	+	0.253295i
$489$	3.62583	−	0.639332i	0.163966	−	0.0289116i
$490$	−17.7875	+	30.8088i	−0.803555	+	1.39180i
$491$	12.0235	−	20.8253i	0.542612	−	0.939831i	−0.456141	−	0.889907i	$-0.650769\pi$
$491$	12.0235	−	20.8253i	0.542612	−	0.939831i	0.998753	−	0.0499236i	$-0.0158978\pi$
$492$	−9.57919	−	11.4160i	−0.431863	−	0.514675i
$493$	0.371644	+	0.643707i	0.0167380	+	0.0289911i
$494$	−66.3911			−2.98707
$495$	−8.11721	+	2.95442i	−0.364842	+	0.132791i
$496$	−5.21719			−0.234259
$497$	−0.807934	−	1.39938i	−0.0362408	−	0.0627709i
$498$	1.15998	−	3.18701i	0.0519798	−	0.142813i
$499$	−13.5608	+	23.4879i	−0.607064	+	1.05147i	0.384658	+	0.923059i	$0.374319\pi$
$499$	−13.5608	+	23.4879i	−0.607064	+	1.05147i	−0.991722	+	0.128406i	$0.959014\pi$
$500$	3.76991	−	6.52968i	0.168596	−	0.292016i
$501$	7.36412	−	20.2328i	0.329005	−	0.903933i
$502$	13.3204	+	23.0716i	0.594520	+	1.02974i
$503$	16.2867			0.726190			0.363095	−	0.931752i	$-0.381720\pi$
$503$	16.2867			0.726190			0.363095	+	0.931752i	$0.381720\pi$
$504$	1.31908	+	1.10684i	0.0587564	+	0.0493025i
$505$	−12.7246			−0.566238
$506$	2.99273	+	5.18355i	0.133043	+	0.230437i
$507$	36.3851	+	43.3620i	1.61592	+	1.92578i
$508$	−5.97565	+	10.3501i	−0.265127	+	0.459213i
$509$	−10.6655	+	18.4732i	−0.472740	+	0.818809i	−0.999513	−	0.0311963i	$-0.990068\pi$
$509$	−10.6655	+	18.4732i	−0.472740	+	0.818809i	0.526773	+	0.850006i	$0.323402\pi$
$510$	1.70574	−	0.300767i	0.0755313	−	0.0133182i
$511$	3.41400	+	5.91322i	0.151026	+	0.261586i
$512$	−25.2226			−1.11469
$513$	23.5201	−	13.5793i	1.03844	−	0.599541i
$514$	16.2249			0.715651
$515$	−15.0287	−	26.0304i	−0.662243	−	1.14704i
$516$	−10.0869	+	1.77860i	−0.444052	+	0.0782984i
$517$	6.00387	−	10.3990i	0.264050	−	0.457348i
$518$	−0.0650551	+	0.112679i	−0.00285836	+	0.00495082i
$519$	4.01249	+	4.78190i	0.176129	+	0.209902i
$520$	8.55690	+	14.8210i	0.375245	+	0.649944i
$521$	−39.4671			−1.72908			−0.864542	−	0.502560i	$-0.832392\pi$
$521$	−39.4671			−1.72908			−0.864542	+	0.502560i	$0.832392\pi$
$522$	−3.93804	+	22.3338i	−0.172363	+	0.977522i
$523$	4.68779			0.204983			0.102491	−	0.994734i	$-0.467319\pi$
$523$	4.68779			0.204983			0.102491	+	0.994734i	$0.467319\pi$
$524$	9.57398	+	16.5826i	0.418241	+	0.724415i
$525$	−1.27244	+	3.49600i	−0.0555339	+	0.152578i
$526$	1.12701	−	1.95204i	0.0491400	−	0.0851130i
$527$	−0.102196	+	0.177009i	−0.00445175	+	0.00771065i
$528$	2.79426	−	7.67717i	0.121605	−	0.334106i
$529$	6.42855	+	11.1346i	0.279502	+	0.484112i
$530$	54.5039			2.36750
$531$	−5.49825	+	31.1821i	−0.238604	+	1.35319i
$532$	5.22668			0.226605
$533$	−18.9782	−	32.8712i	−0.822036	−	1.42381i
$534$	6.31820	+	7.52974i	0.273415	+	0.325844i
$535$	11.9684	−	20.7298i	0.517438	−	0.896229i
$536$	5.19207	−	8.99292i	0.224263	−	0.388435i
$537$	−21.9572	+	3.87165i	−0.947525	+	0.167074i
$538$	26.2374	+	45.4445i	1.13118	+	1.95925i
$539$	6.57398			0.283161
$540$	19.8516	+	11.4613i	0.854278	+	0.493218i
$541$	0.200274			0.00861046			0.00430523	−	0.999991i	$-0.498630\pi$
$541$	0.200274			0.00861046			0.00430523	+	0.999991i	$0.498630\pi$
$542$	−12.6211	−	21.8604i	−0.542122	−	0.938983i
$543$	41.5185	−	7.32083i	1.78173	−	0.314167i
$544$	−0.656574	+	1.13722i	−0.0281504	+	0.0487579i
$545$	23.0180	−	39.8684i	0.985983	−	1.70777i
$546$	−9.23055	−	11.0005i	−0.395031	−	0.470780i
$547$	−17.9697	−	31.1245i	−0.768330	−	1.33079i	−0.938468	−	0.345366i	$-0.887755\pi$
$547$	−17.9697	−	31.1245i	−0.768330	−	1.33079i	0.170138	−	0.985420i	$-0.445579\pi$
$548$	23.3286			0.996550
$549$	16.8851	+	14.1683i	0.720637	+	0.604686i
$550$	6.18479			0.263720
$551$	−10.5116	−	18.2066i	−0.447810	−	0.775629i
$552$	−1.65910	+	4.55834i	−0.0706160	+	0.194016i
$553$	−0.479055	+	0.829748i	−0.0203715	+	0.0352845i
$554$	−7.96926	+	13.8032i	−0.338581	+	0.586440i
$555$	0.180922	−	0.497079i	0.00767972	−	0.0210998i
$556$	−11.1099	−	19.2430i	−0.471166	−	0.816084i
$557$	16.6186			0.704151			0.352075	−	0.935972i	$-0.385476\pi$
$557$	16.6186			0.704151			0.352075	+	0.935972i	$0.385476\pi$
$558$	−5.86009	+	2.13290i	−0.248077	+	0.0902928i
$559$	−26.0874			−1.10338
$560$	−4.43242	−	7.67717i	−0.187304	−	0.324420i
$561$	−0.205737	−	0.245188i	−0.00868623	−	0.0103518i
$562$	−2.38578	+	4.13230i	−0.100638	+	0.174310i
$563$	6.46316	−	11.1945i	0.272390	−	0.471793i	−0.697083	−	0.716990i	$-0.745519\pi$
$563$	6.46316	−	11.1945i	0.272390	−	0.471793i	0.969473	+	0.245197i	$0.0788526\pi$
$564$	−31.3803	+	5.53320i	−1.32135	+	0.232990i
$565$	7.29086	+	12.6281i	0.306729	+	0.531270i
$566$	8.78611			0.369308
$567$	5.52007	+	2.00914i	0.231821	+	0.0843760i
$568$	−2.17705			−0.0913471
$569$	−6.73648	−	11.6679i	−0.282408	−	0.489145i	0.689569	−	0.724220i	$-0.257800\pi$
$569$	−6.73648	−	11.6679i	−0.282408	−	0.489145i	−0.971977	+	0.235075i	$0.924467\pi$
$570$	−48.2452	+	8.50692i	−2.02077	+	0.356316i
$571$	−0.427204	+	0.739939i	−0.0178779	+	0.0309655i	−0.874826	−	0.484437i	$-0.839024\pi$
$571$	−0.427204	+	0.739939i	−0.0178779	+	0.0309655i	0.856948	+	0.515403i	$0.172358\pi$
$572$	−5.17752	+	8.96773i	−0.216483	+	0.374959i
$573$	6.63341	+	7.90539i	0.277115	+	0.330252i
$574$	3.44444	+	5.96595i	0.143768	+	0.249014i
$575$	−10.4807			−0.437076
$576$	−11.0544	+	4.02346i	−0.460599	+	0.167644i
$577$	−2.22668			−0.0926980			−0.0463490	−	0.998925i	$-0.514759\pi$
$577$	−2.22668			−0.0926980			−0.0463490	+	0.998925i	$0.514759\pi$
$578$	−15.9427	−	27.6135i	−0.663128	−	1.14857i
$579$	6.41147	−	17.6154i	0.266452	−	0.732070i
$580$	8.87211	−	15.3669i	0.368394	−	0.638078i
$581$	−0.340022	+	0.588936i	−0.0141065	+	0.0244332i
$582$	6.38965	−	17.5554i	0.264860	−	0.727696i
$583$	−5.03596	−	8.72254i	−0.208568	−	0.361251i
$584$	9.19934			0.380671
$585$	44.7242	+	37.5281i	1.84912	+	1.55159i
$586$	−14.7442			−0.609078
$587$	−2.41993	−	4.19144i	−0.0998812	−	0.172999i	0.811754	−	0.583999i	$-0.198513\pi$
$587$	−2.41993	−	4.19144i	−0.0998812	−	0.172999i	−0.911635	+	0.411000i	$0.865180\pi$
$588$	−11.2135	−	13.3637i	−0.462436	−	0.551110i
$589$	2.89053	−	5.00654i	0.119102	−	0.206291i
$590$	28.5574	−	49.4628i	1.17569	−	2.03635i
$591$	−5.23989	+	0.923933i	−0.215540	+	0.0380055i
$592$	0.250152	+	0.433277i	0.0102812	+	0.0178076i
$593$	42.2523			1.73509			0.867546	−	0.497356i	$-0.165696\pi$
$593$	42.2523			1.73509			0.867546	+	0.497356i	$0.165696\pi$
$594$		−	9.76557i		−	0.400686i
$595$	−0.347296			−0.0142378
$596$	−11.1912	−	19.3837i	−0.458409	−	0.793988i
$597$	−2.63816	+	0.465178i	−0.107973	+	0.0190385i
$598$	20.2271	−	35.0344i	0.827150	−	1.43267i
$599$	1.18227	−	2.04775i	0.0483061	−	0.0836686i	−0.840861	−	0.541251i	$-0.817951\pi$
$599$	1.18227	−	2.04775i	0.0483061	−	0.0836686i	0.889167	+	0.457582i	$0.151284\pi$
$600$	3.22193	+	3.83975i	0.131535	+	0.156757i
$601$	6.14455	+	10.6427i	0.250642	+	0.434124i	0.963703	−	0.266978i	$-0.0860251\pi$
$601$	6.14455	+	10.6427i	0.250642	+	0.434124i	−0.713061	+	0.701102i	$0.752692\pi$
$602$	4.73473			0.192973
$603$	6.15152	−	34.8870i	0.250509	−	1.42071i
$604$	−32.3378			−1.31581
$605$	−1.43969	−	2.49362i	−0.0585318	−	0.101380i
$606$	4.92009	−	13.5178i	0.199865	−	0.549125i
$607$	−7.08765	+	12.2762i	−0.287679	+	0.498274i	−0.973255	−	0.229726i	$-0.926217\pi$
$607$	−7.08765	+	12.2762i	−0.287679	+	0.498274i	0.685576	+	0.728001i	$0.259550\pi$
$608$	18.5706	−	32.1652i	0.753136	−	1.30447i
$609$	1.55525	−	4.27303i	0.0630221	−	0.173152i
$610$	−19.8799	−	34.4329i	−0.804912	−	1.39415i
$611$	−81.1576			−3.28328
$612$	−0.147489	+	0.836452i	−0.00596189	+	0.0338116i
$613$	28.5749			1.15413			0.577065	−	0.816698i	$-0.304198\pi$
$613$	28.5749			1.15413			0.577065	+	0.816698i	$0.304198\pi$
$614$	24.8123	+	42.9761i	1.00134	+	1.73437i
$615$	−18.0030	−	21.4551i	−0.725951	−	0.865154i
$616$	−0.286989	+	0.497079i	−0.0115631	+	0.0200279i
$617$	−9.03983	+	15.6574i	−0.363930	+	0.630345i	−0.988604	−	0.150541i	$-0.951899\pi$
$617$	−9.03983	+	15.6574i	−0.363930	+	0.630345i	0.624674	+	0.780886i	$0.285232\pi$
$618$	33.4641	−	5.90062i	1.34612	−	0.237358i
$619$	−7.73190	−	13.3920i	−0.310771	−	0.538271i	0.667758	−	0.744378i	$-0.267254\pi$
$619$	−7.73190	−	13.3920i	−0.310771	−	0.538271i	−0.978530	+	0.206107i	$0.933921\pi$
$620$	4.87939			0.195961
$621$			16.5487i			0.664075i
$622$	35.9736			1.44241
$623$	−0.985452	−	1.70685i	−0.0394813	−	0.0683836i
$624$	−54.3794	+	9.58856i	−2.17692	+	0.383850i
$625$	15.3123	−	26.5216i	0.612491	−	1.06087i
$626$	−8.42989	+	14.6010i	−0.336926	+	0.583573i
$627$	5.81908	+	6.93491i	0.232392	+	0.276954i
$628$	3.39440	+	5.87927i	0.135451	+	0.234609i
$629$	0.0196004			0.000781518
$630$	−8.11721	−	6.81115i	−0.323397	−	0.271363i
$631$	9.35235			0.372311			0.186156	−	0.982520i	$-0.440397\pi$
$631$	9.35235			0.372311			0.186156	+	0.982520i	$0.440397\pi$
$632$	0.645430	+	1.11792i	0.0256738	+	0.0444684i
$633$	−9.39124	+	25.8022i	−0.373268	+	1.02555i
$634$	5.89945	−	10.2182i	0.234297	−	0.405815i
$635$	−11.2306	+	19.4519i	−0.445671	+	0.771925i
$636$	−9.14131	+	25.1155i	−0.362477	+	0.995896i
$637$	−22.2160	−	38.4792i	−0.880230	−	1.52460i
$638$	−7.55943			−0.299281
$639$	−6.97906	+	2.54017i	−0.276087	+	0.100488i
$640$	−19.7023			−0.778803
$641$	−0.607411	−	1.05207i	−0.0239913	−	0.0415541i	0.853780	−	0.520633i	$-0.174304\pi$
$641$	−0.607411	−	1.05207i	−0.0239913	−	0.0415541i	−0.877772	+	0.479079i	$0.840971\pi$
$642$	17.3944	+	20.7298i	0.686502	+	0.818141i
$643$	15.9013	−	27.5418i	0.627085	−	1.08614i	−0.361049	−	0.932547i	$-0.617581\pi$
$643$	15.9013	−	27.5418i	0.627085	−	1.08614i	0.988134	−	0.153596i	$-0.0490853\pi$
$644$	−1.59240	+	2.75811i	−0.0627492	+	0.108685i
$645$	−18.9572	+	3.34267i	−0.746440	+	0.131618i
$646$	−0.907604	−	1.57202i	−0.0357092	−	0.0618501i
$647$	30.6854			1.20637			0.603184	−	0.797602i	$-0.293898\pi$
$647$	30.6854			1.20637			0.603184	+	0.797602i	$0.293898\pi$
$648$	6.06283	−	5.08732i	0.238171	−	0.199849i
$649$	−10.5544			−0.414296
$650$	−20.9008	−	36.2012i	−0.819797	−	1.41993i
$651$	1.23143	−	0.217134i	0.0482635	−	0.00851016i
$652$	1.62836	−	2.82039i	0.0637713	−	0.110455i
$653$	−3.63176	+	6.29039i	−0.142122	+	0.246162i	−0.928295	−	0.371844i	$-0.878726\pi$
$653$	−3.63176	+	6.29039i	−0.142122	+	0.246162i	0.786174	+	0.618006i	$0.212059\pi$
$654$	33.4535	+	39.8684i	1.30814	+	1.55898i
$655$	17.9932	+	31.1651i	0.703052	+	1.21772i
$656$	26.4894			1.03424
$657$	29.4907	−	10.7337i	1.15054	−	0.418762i
$658$	14.7297			0.574223
$659$	−12.7939	−	22.1596i	−0.498378	−	0.863216i	0.501621	−	0.865088i	$-0.332737\pi$
$659$	−12.7939	−	22.1596i	−0.498378	−	0.863216i	−0.999998	+	0.00187222i	$0.999404\pi$
$660$	−2.61334	+	7.18009i	−0.101724	+	0.279485i
$661$	−3.87804	+	6.71696i	−0.150838	+	0.261260i	−0.931536	−	0.363649i	$-0.881531\pi$
$661$	−3.87804	+	6.71696i	−0.150838	+	0.261260i	0.780698	+	0.624909i	$0.214864\pi$
$662$	−11.1566	+	19.3238i	−0.433613	+	0.751039i
$663$	−0.739885	+	2.03282i	−0.0287348	+	0.0789481i
$664$	0.458111	+	0.793471i	0.0177782	+	0.0307927i
$665$	9.82295			0.380918
$666$	0.458111	+	0.384401i	0.0177514	+	0.0148952i
$667$	12.8102			0.496011
$668$	−9.52276	−	16.4939i	−0.368446	−	0.638168i
$669$	6.95424	+	8.28774i	0.268866	+	0.320423i
$670$	−31.9504	+	55.3398i	−1.23435	+	2.13796i
$671$	−3.67365	+	6.36295i	−0.141820	+	0.245639i
$672$	7.91147	−	1.39501i	0.305192	−	0.0538135i
$673$	21.3025	+	36.8970i	0.821150	+	1.42227i	0.904827	+	0.425780i	$0.140000\pi$
$673$	21.3025	+	36.8970i	0.821150	+	1.42227i	−0.0836766	+	0.996493i	$0.526666\pi$
$674$	−16.9932			−0.654553
$675$	14.8089	+	8.54990i	0.569994	+	0.329086i
$676$	50.0702			1.92578
$677$	−11.4256	−	19.7897i	−0.439122	−	0.760581i	0.558500	−	0.829504i	$-0.311377\pi$
$677$	−11.4256	−	19.7897i	−0.439122	−	0.760581i	−0.997622	+	0.0689230i	$0.978044\pi$
$678$	−16.2344	+	2.86257i	−0.623479	+	0.109936i
$679$	−1.87299	+	3.24411i	−0.0718787	+	0.124498i
$680$	−0.233956	+	0.405223i	−0.00897179	+	0.0155396i
$681$	3.63145	+	4.32780i	0.139158	+	0.165842i
$682$	−1.03936	−	1.80023i	−0.0397993	−	0.0689343i
$683$	−12.3946			−0.474265			−0.237132	−	0.971477i	$-0.576208\pi$
$683$	−12.3946			−0.474265			−0.237132	+	0.971477i	$0.576208\pi$
$684$	4.17159	−	23.6583i	0.159505	−	0.904596i
$685$	43.8435			1.67517
$686$	8.32547	+	14.4201i	0.317868	+	0.550564i
$687$	−6.40689	+	17.6028i	−0.244438	+	0.671588i
$688$	9.10307	−	15.7670i	0.347051	−	0.601111i
$689$	−34.0369	+	58.9536i	−1.29670	+	2.24595i
$690$	10.2096	−	28.0507i	0.388673	−	1.06787i
$691$	−8.21823	−	14.2344i	−0.312636	−	0.541501i	0.666296	−	0.745687i	$-0.267879\pi$
$691$	−8.21823	−	14.2344i	−0.312636	−	0.541501i	−0.978932	+	0.204186i	$0.934545\pi$
$692$	5.52166			0.209902
$693$	−0.340022	+	1.92836i	−0.0129164	+	0.0732524i
$694$	35.6391			1.35284
$695$	−20.8799	−	36.1650i	−0.792018	−	1.37182i
$696$	−3.93804	−	4.69318i	−0.149271	−	0.177894i
$697$	0.518885	−	0.898735i	0.0196542	−	0.0340420i
$698$	−20.7939	+	36.0160i	−0.787059	+	1.36323i
$699$	6.34002	−	1.11792i	0.239802	−	0.0422835i
$700$	1.64543	+	2.84997i	0.0621914	+	0.107719i
$701$	23.8084			0.899231			0.449615	−	0.893222i	$-0.351561\pi$
$701$	23.8084			0.899231			0.449615	+	0.893222i	$0.351561\pi$
$702$	−57.1605	+	33.0016i	−2.15738	+	1.24557i
$703$	−0.554378			−0.0209087
$704$	−1.96064	−	3.39592i	−0.0738943	−	0.127989i
$705$	−58.9757	+	10.3990i	−2.22115	+	0.391649i
$706$	−22.9675	+	39.7809i	−0.864393	+	1.49717i
$707$	−1.44222	+	2.49800i	−0.0542402	+	0.0939468i
$708$	18.0030	+	21.4551i	0.676594	+	0.806333i
$709$	21.2811	+	36.8599i	0.799227	+	1.38430i	0.920120	+	0.391636i	$0.128091\pi$
$709$	21.2811	+	36.8599i	0.799227	+	1.38430i	−0.120893	+	0.992666i	$0.538576\pi$
$710$	13.3969			0.502778
$711$	3.37346	+	2.83067i	0.126514	+	0.106158i
$712$	−2.65539			−0.0995150
$713$	1.76130	+	3.05066i	0.0659611	+	0.114248i
$714$	0.134285	−	0.368946i	0.00502550	−	0.0138075i
$715$	−9.73055	+	16.8538i	−0.363902	+	0.630297i
$716$	−9.86097	+	17.0797i	−0.368522	+	0.638298i
$717$	4.77316	−	13.1141i	0.178257	−	0.489756i
$718$	−4.40420	−	7.62830i	−0.164363	−	0.284686i
$719$	14.9391			0.557135			0.278568	−	0.960417i	$-0.410140\pi$
$719$	14.9391			0.557135			0.278568	+	0.960417i	$0.410140\pi$
$720$	−38.2879	+	13.9357i	−1.42691	+	0.519352i
$721$	−6.81345			−0.253746
$722$	7.81655	+	13.5387i	0.290902	+	0.503857i
$723$	−4.80958	−	5.73184i	−0.178870	−	0.213169i
$724$	18.6459	−	32.2956i	0.692969	−	1.20026i
$725$	6.61839	−	11.4634i	0.245801	−	0.425740i
$726$	3.20574	−	0.565258i	0.118976	−	0.0209787i
$727$	−22.1013	−	38.2806i	−0.819693	−	1.41975i	−0.905909	−	0.423473i	$-0.860811\pi$
$727$	−22.1013	−	38.2806i	−0.819693	−	1.41975i	0.0862163	−	0.996276i	$-0.472522\pi$
$728$	3.87939			0.143780
$729$	13.5000	−	23.3827i	0.500000	−	0.866025i
$730$	−56.6100			−2.09523
$731$	−0.356630	−	0.617701i	−0.0131904	−	0.0228465i
$732$	19.2010	−	3.38565i	0.709689	−	0.125137i
$733$	−13.4932	+	23.3709i	−0.498382	+	0.863224i	−0.999998	−	0.00186678i	$-0.999406\pi$
$733$	−13.4932	+	23.3709i	−0.498382	+	0.863224i	0.501616	+	0.865091i	$0.332739\pi$
$734$	−8.45976	+	14.6527i	−0.312255	+	0.540842i
$735$	−21.0744	−	25.1155i	−0.777343	−	0.926401i
$736$	11.3157	+	19.5993i	0.417101	+	0.722441i
$737$	11.8084			0.434968
$738$	29.7536	−	10.8294i	1.09525	−	0.398637i
$739$	10.5689			0.388784			0.194392	−	0.980924i	$-0.437727\pi$
$739$	10.5689			0.388784			0.194392	+	0.980924i	$0.437727\pi$
$740$	−0.233956	−	0.405223i	−0.00860038	−	0.0148963i
$741$	20.9270	−	57.4963i	0.768771	−	2.11218i
$742$	6.17752	−	10.6998i	0.226784	−	0.392801i
$743$	−21.8803	+	37.8978i	−0.802711	+	1.39034i	0.115114	+	0.993352i	$0.463277\pi$
$743$	−21.8803	+	37.8978i	−0.802711	+	1.39034i	−0.917825	+	0.396984i	$0.870057\pi$
$744$	0.576199	−	1.58310i	0.0211245	−	0.0580391i
$745$	−21.0326	−	36.4295i	−0.770573	−	1.33467i
$746$	−19.3182			−0.707290
$747$	2.39440	+	2.00914i	0.0876065	+	0.0735106i
$748$	−0.283119			−0.0103518
$749$	−2.71301	−	4.69907i	−0.0991313	−	0.171700i
$750$	10.2973	+	12.2718i	0.376003	+	0.448102i
$751$	−3.03091	+	5.24968i	−0.110599	+	0.191564i	−0.916012	−	0.401151i	$-0.868610\pi$
$751$	−3.03091	+	5.24968i	−0.110599	+	0.191564i	0.805413	+	0.592714i	$0.201944\pi$
$752$	28.3195	−	49.0509i	1.03271	−	1.78870i
$753$	−24.1793	+	4.26347i	−0.881144	+	0.155369i
$754$	25.5462	+	44.2474i	0.930339	+	1.61139i
$755$	−60.7752			−2.21184
$756$	4.50000	−	2.59808i	0.163663	−	0.0944911i
$757$	20.7192			0.753054			0.376527	−	0.926406i	$-0.377118\pi$
$757$	20.7192			0.753054			0.376527	+	0.926406i	$0.377118\pi$
$758$	13.3944	+	23.1998i	0.486507	+	0.842654i
$759$	−5.43242	+	0.957882i	−0.197184	+	0.0347689i
$760$	6.61721	−	11.4613i	0.240031	−	0.415747i
$761$	23.7788	−	41.1862i	0.861982	−	1.49300i	−0.00803057	−	0.999968i	$-0.502556\pi$
$761$	23.7788	−	41.1862i	0.861982	−	1.49300i	0.870013	−	0.493029i	$-0.164110\pi$
$762$	−16.3221	−	19.4519i	−0.591286	−	0.704668i
$763$	−5.21776	−	9.03742i	−0.188896	−	0.327177i
$764$	9.12836			0.330252
$765$	−0.277189	+	1.57202i	−0.0100218	+	0.0568364i
$766$	−27.8803			−1.00736
$767$	35.6673	+	61.7776i	1.28787	+	2.23066i
$768$	12.2640	−	33.6950i	0.442538	−	1.21586i
$769$	−20.8384	+	36.0932i	−0.751453	+	1.30155i	0.195665	+	0.980671i	$0.437313\pi$
$769$	−20.8384	+	36.0932i	−0.751453	+	1.30155i	−0.947118	+	0.320884i	$0.896020\pi$
$770$	1.76604	−	3.05888i	0.0636438	−	0.110234i
$771$	−5.11422	+	14.0512i	−0.184184	+	0.506042i
$772$	−8.29086	−	14.3602i	−0.298395	−	0.516835i
$773$	−40.1652			−1.44464			−0.722321	−	0.691558i	$-0.756925\pi$
$773$	−40.1652			−1.44464			−0.722321	+	0.691558i	$0.756925\pi$
$774$	3.77894	−	21.4315i	0.135831	−	0.770338i
$775$	3.63991			0.130749
$776$	2.52347	+	4.37078i	0.0905873	+	0.156902i
$777$	−0.0770768	−	0.0918566i	−0.00276512	−	0.00329534i
$778$	10.2626	−	17.7754i	0.367934	−	0.637280i
$779$	−14.6762	+	25.4199i	−0.525829	+	0.910762i
$780$	50.8585	−	8.96773i	1.82103	−	0.321096i
$781$	−1.23783	−	2.14398i	−0.0442929	−	0.0767175i
$782$	1.10607			0.0395529
$783$	−18.1003	−	10.4502i	−0.646852	−	0.373460i
$784$	31.0087			1.10745
$785$	6.37939	+	11.0494i	0.227690	+	0.394371i
$786$	−40.0651	+	7.06456i	−1.42908	+	0.251985i
$787$	11.2408	−	19.4697i	0.400692	−	0.694019i	−0.593118	−	0.805116i	$-0.702103\pi$
$787$	11.2408	−	19.4697i	0.400692	−	0.694019i	0.993810	+	0.111097i	$0.0354364\pi$
$788$	−2.35323	+	4.07591i	−0.0838302	+	0.145198i
$789$	1.33527	+	1.59132i	0.0475370	+	0.0566524i
$790$	−3.97178	−	6.87933i	−0.141310	−	0.244755i
$791$	3.30541			0.117527
$792$	2.02094	+	1.69577i	0.0718111	+	0.0602567i
$793$	49.6587			1.76343
$794$	−32.5082	−	56.3059i	−1.15367	−	1.99822i
$795$	−17.1800	+	47.2018i	−0.609313	+	1.67407i
$796$	−1.18479	+	2.05212i	−0.0419939	+	0.0727355i
$797$	19.9688	−	34.5871i	0.707333	−	1.22514i	−0.258510	−	0.966009i	$-0.583232\pi$
$797$	19.9688	−	34.5871i	0.707333	−	1.22514i	0.965843	−	0.259128i	$-0.0834351\pi$
$798$	−3.79813	+	10.4353i	−0.134452	+	0.369405i
$799$	−1.10947	−	1.92166i	−0.0392502	−	0.0679834i
$800$	23.3851			0.826787
$801$	−8.51249	+	3.09829i	−0.300774	+	0.109473i
$802$	−32.4029			−1.14419
$803$	5.23055	+	9.05958i	0.184582	+	0.319706i
$804$	−20.1420	−	24.0043i	−0.710354	−	0.846568i
$805$	−2.99273	+	5.18355i	−0.105480	+	0.182696i
$806$	−7.02481	+	12.1673i	−0.247439	+	0.428576i
$807$	−47.6264	+	8.39781i	−1.67653	+	0.295617i
$808$	1.94310	+	3.36554i	0.0683579	+	0.118399i
$809$	17.9240			0.630173			0.315086	−	0.949063i	$-0.397966\pi$
$809$	17.9240			0.630173			0.315086	+	0.949063i	$0.397966\pi$
$810$	−37.3089	+	31.3059i	−1.31090	+	1.09998i
$811$	26.8972			0.944490			0.472245	−	0.881467i	$-0.343444\pi$
$811$	26.8972			0.944490			0.472245	+	0.881467i	$0.343444\pi$
$812$	−2.01114	−	3.48340i	−0.0705773	−	0.122244i
$813$	22.9099	−	4.03963i	0.803485	−	0.141676i
$814$	−0.0996702	+	0.172634i	−0.00349344	+	0.00605081i
$815$	3.06031	−	5.30061i	0.107198	−	0.185672i
$816$	−0.970437	−	1.15652i	−0.0339721	−	0.0404864i
$817$	10.0869	+	17.4711i	0.352897	+	0.611236i
$818$	8.31315			0.290662
$819$	12.4363	−	4.52644i	0.434559	−	0.158167i
$820$	−24.7743			−0.865154
$821$	6.00387	+	10.3990i	0.209537	+	0.362928i	0.951569	−	0.307436i	$-0.0994712\pi$
$821$	6.00387	+	10.3990i	0.209537	+	0.362928i	−0.742032	+	0.670364i	$0.766138\pi$
$822$	−16.9525	+	46.5766i	−0.591286	+	1.62454i
$823$	6.47952	−	11.2229i	0.225862	−	0.391204i	−0.730716	−	0.682682i	$-0.760814\pi$
$823$	6.47952	−	11.2229i	0.225862	−	0.391204i	0.956578	+	0.291477i	$0.0941468\pi$
$824$	−4.58987	+	7.94989i	−0.159896	+	0.276947i
$825$	−1.94949	+	5.35619i	−0.0678726	+	0.186479i
$826$	−6.47343	−	11.2123i	−0.225239	−	0.390126i
$827$	−23.3678			−0.812579			−0.406290	−	0.913744i	$-0.633178\pi$
$827$	−23.3678			−0.812579			−0.406290	+	0.913744i	$0.633178\pi$
$828$	11.2135	+	9.40923i	0.389695	+	0.326993i
$829$	−54.3164			−1.88649			−0.943244	−	0.332100i	$-0.892243\pi$
$829$	−54.3164			−1.88649			−0.943244	+	0.332100i	$0.892243\pi$
$830$	−2.81908	−	4.88279i	−0.0978516	−	0.169484i
$831$	−9.44191	−	11.2524i	−0.327536	−	0.390343i
$832$	−13.2515	+	22.9523i	−0.459413	+	0.795727i
$833$	0.607411	−	1.05207i	0.0210455	−	0.0364520i
$834$	46.4928	−	8.19793i	1.60991	−	0.283871i
$835$	−17.8969	−	30.9984i	−0.619349	−	1.07274i
$836$	8.00774			0.276954
$837$		−	5.74729i		−	0.198655i
$838$	32.9222			1.13728
$839$	22.3790	+	38.7615i	0.772608	+	1.33820i	0.936129	+	0.351656i	$0.114381\pi$
$839$	22.3790	+	38.7615i	0.772608	+	1.33820i	−0.163521	+	0.986540i	$0.552285\pi$
$840$	2.81908	−	0.497079i	0.0972674	−	0.0171509i
$841$	6.41060	−	11.1035i	0.221055	−	0.382879i
$842$	9.31908	−	16.1411i	0.321157	−	0.556260i
$843$	−2.82666	−	3.36868i	−0.0973552	−	0.116023i
$844$	12.1441	+	21.0342i	0.418017	+	0.724026i
$845$	94.1011			3.23718
$846$	11.7562	−	66.6730i	0.404188	−	2.29226i
$847$	−0.652704			−0.0224272
$848$	−23.7540	−	41.1432i	−0.815716	−	1.41286i
$849$	−2.76945	+	7.60900i	−0.0950472	+	0.261140i
$850$	0.571452	−	0.989783i	0.0196006	−	0.0339493i
$851$	0.168900	−	0.292544i	0.00578983	−	0.0100283i
$852$	−2.24691	+	6.17334i	−0.0769779	+	0.211495i
$853$	−7.06402	−	12.2352i	−0.241867	−	0.418926i	0.719379	−	0.694618i	$-0.244427\pi$
$853$	−7.06402	−	12.2352i	−0.241867	−	0.418926i	−0.961246	+	0.275691i	$0.911093\pi$
$854$	−9.01279			−0.308411
$855$	7.84002	−	44.4630i	0.268123	−	1.52060i
$856$	−7.31046			−0.249866
$857$	9.47906	+	16.4182i	0.323798	+	0.560835i	0.981268	−	0.192645i	$-0.0617067\pi$
$857$	9.47906	+	16.4182i	0.323798	+	0.560835i	−0.657470	+	0.753481i	$0.728373\pi$
$858$	−14.1420	−	16.8538i	−0.482801	−	0.575380i
$859$	−19.0587	+	33.0107i	−0.650275	+	1.12631i	0.332781	+	0.943004i	$0.392013\pi$
$859$	−19.0587	+	33.0107i	−0.650275	+	1.12631i	−0.983056	+	0.183305i	$0.941320\pi$
$860$	−8.51367	+	14.7461i	−0.290314	+	0.502838i
$861$	−6.25237	+	1.10246i	−0.213080	+	0.0375718i
$862$	−2.23870	−	3.87755i	−0.0762505	−	0.132070i
$863$	−37.9665			−1.29239			−0.646197	−	0.763171i	$-0.723641\pi$
$863$	−37.9665			−1.29239			−0.646197	+	0.763171i	$0.723641\pi$
$864$		−	36.9242i		−	1.25619i
$865$	10.3773			0.352840
$866$	29.2866	+	50.7258i	0.995198	+	1.72373i
$867$	28.9393	−	5.10278i	0.982830	−	0.173299i
$868$	0.553033	−	0.957882i	0.0187712	−	0.0325126i
$869$	−0.733956	+	1.27125i	−0.0248977	+	0.0431241i
$870$	24.2335	+	28.8804i	0.821594	+	0.979138i
$871$	−39.9051	−	69.1177i	−1.35213	−	2.34196i
$872$	−14.0597			−0.476123
$873$	13.1894	+	11.0672i	0.446393	+	0.374568i
$874$	−31.2841			−1.05820
$875$	−1.60607	−	2.78179i	−0.0542950	−	0.0940416i
$876$	9.49454	−	26.0860i	0.320791	−	0.881365i
$877$	−12.5488	+	21.7351i	−0.423741	+	0.733941i	−0.996302	−	0.0859209i	$-0.972617\pi$
$877$	−12.5488	+	21.7351i	−0.423741	+	0.733941i	0.572561	+	0.819862i	$0.305950\pi$
$878$	7.56893	−	13.1098i	0.255439	−	0.442433i
$879$	4.64749	−	12.7689i	0.156756	−	0.430683i
$880$	−6.79086	−	11.7621i	−0.228920	−	0.396501i
$881$	−7.51485			−0.253182			−0.126591	−	0.991955i	$-0.540404\pi$
$881$	−7.51485			−0.253182			−0.126591	+	0.991955i	$0.540404\pi$
$882$	34.8298	−	12.6770i	1.17278	−	0.426857i
$883$	−28.9231			−0.973341			−0.486671	−	0.873586i	$-0.661789\pi$
$883$	−28.9231			−0.973341			−0.486671	+	0.873586i	$0.661789\pi$
$884$	0.956767	+	1.65717i	0.0321795	+	0.0557366i
$885$	33.8346	+	40.3225i	1.13734	+	1.35542i
$886$	−10.9338	+	18.9378i	−0.367327	+	0.636229i
$887$	−0.825008	+	1.42896i	−0.0277010	+	0.0479796i	−0.879544	−	0.475818i	$-0.842152\pi$
$887$	−0.825008	+	1.42896i	−0.0277010	+	0.0479796i	0.851843	+	0.523798i	$0.175485\pi$
$888$	−0.159100	+	0.0280537i	−0.00533906	+	0.000941419i
$889$	2.54576	+	4.40938i	0.0853820	+	0.147886i
$890$	16.3405			0.547734
$891$	8.45723	+	3.07818i	0.283328	+	0.103123i
$892$	9.56986			0.320423
$893$	31.3803	+	54.3523i	1.05010	+	1.81883i
$894$	46.8328	−	8.25789i	1.56632	−	0.276185i
$895$	−18.5326	+	32.0993i	−0.619475	+	1.07296i
$896$	−2.23308	+	3.86780i	−0.0746019	+	0.129214i
$897$	23.9650	+	28.5603i	0.800167	+	0.953602i
$898$	−24.1917	−	41.9012i	−0.807286	−	1.39826i
$899$	−4.44892			−0.148380
$900$	14.2135	−	5.17328i	0.473783	−	0.172443i
$901$	−1.86122			−0.0620061
$902$	5.27719	+	9.14036i	0.175711	+	0.304341i
$903$	−1.49242	+	4.10039i	−0.0496647	+	0.136453i
$904$	2.22668	−	3.85673i	0.0740583	−	0.128273i
$905$	35.0428	−	60.6959i	1.16486	−	2.01760i
$906$	23.4993	−	64.5638i	0.780711	−	2.14499i
$907$	−13.9213	−	24.1124i	−0.462248	−	0.800638i	0.536824	−	0.843694i	$-0.319624\pi$
$907$	−13.9213	−	24.1124i	−0.462248	−	0.800638i	−0.999073	+	0.0430565i	$0.986290\pi$
$908$	4.99731			0.165842
$909$	10.1559	+	8.52185i	0.336851	+	0.282652i
$910$	−23.8726			−0.791368
$911$	8.52188	+	14.7603i	0.282342	+	0.489031i	0.971961	−	0.235141i	$-0.0755552\pi$
$911$	8.52188	+	14.7603i	0.282342	+	0.489031i	−0.689619	+	0.724173i	$0.742222\pi$
$912$	27.4479	+	32.7111i	0.908891	+	1.08317i
$913$	−0.520945	+	0.902302i	−0.0172407	+	0.0298619i
$914$	36.1143	−	62.5518i	1.19455	−	2.06903i
$915$	36.0861	−	6.36295i	1.19297	−	0.210352i
$916$	8.28493	+	14.3499i	0.273742	+	0.474135i
$917$	8.15745			0.269383
$918$	−1.56283	−	0.902302i	−0.0515812	−	0.0297804i
$919$	47.4638			1.56569			0.782843	−	0.622219i	$-0.213769\pi$
$919$	47.4638			1.56569			0.782843	+	0.622219i	$0.213769\pi$
$920$	4.03209	+	6.98378i	0.132934	+	0.230249i
$921$	−45.0394	+	7.94166i	−1.48410	+	0.261687i
$922$	5.26130	−	9.11283i	0.173272	−	0.300115i
$923$	−8.36618	+	14.4907i	−0.275376	+	0.476966i
$924$	1.11334	+	1.32683i	0.0366262	+	0.0436494i
$925$	−0.174526	−	0.302287i	−0.00573836	−	0.00993914i
$926$	−17.4662			−0.573974
$927$	−5.43804	+	30.8407i	−0.178609	+	1.01294i
$928$	−28.5827			−0.938272
$929$	−14.4561	−	25.0386i	−0.474288	−	0.821490i	0.525279	−	0.850930i	$-0.323961\pi$
$929$	−14.4561	−	25.0386i	−0.474288	−	0.821490i	−0.999567	+	0.0294398i	$0.990628\pi$
$930$	−3.54576	+	9.74189i	−0.116270	+	0.319449i
$931$	−17.1800	+	29.7567i	−0.563053	+	0.975237i
$932$	2.84730	−	4.93166i	0.0932663	−	0.161542i
$933$	−11.3391	+	31.1540i	−0.371227	+	1.01994i
$934$	16.0351	+	27.7736i	0.524684	+	0.908779i
$935$	−0.532089			−0.0174012
$936$	3.09627	−	17.5598i	0.101205	−	0.573960i
$937$	−4.87258			−0.159180			−0.0795901	−	0.996828i	$-0.525361\pi$
$937$	−4.87258			−0.159180			−0.0795901	+	0.996828i	$0.525361\pi$
$938$	7.24257	+	12.5445i	0.236478	+	0.409593i
$939$	−9.98767	−	11.9028i	−0.325935	−	0.388435i
$940$	−26.4859	+	45.8750i	−0.863875	+	1.49628i
$941$	27.1391	−	47.0063i	0.884709	−	1.53236i	0.0386622	−	0.999252i	$-0.487690\pi$
$941$	27.1391	−	47.0063i	0.884709	−	1.53236i	0.846047	−	0.533109i	$-0.178976\pi$
$942$	−14.2049	+	2.50470i	−0.462819	+	0.0816075i
$943$	−8.94269	−	15.4892i	−0.291214	−	0.504397i
$944$	−49.7837			−1.62032
$945$	8.45723	−	4.88279i	0.275114	−	0.158837i
$946$	7.25402			0.235849
$947$	10.7253	+	18.5768i	0.348527	+	0.603666i	0.985988	−	0.166817i	$-0.0533488\pi$
$947$	10.7253	+	18.5768i	0.348527	+	0.603666i	−0.637461	+	0.770482i	$0.720015\pi$
$948$	3.83615	−	0.676417i	0.124592	−	0.0219690i
$949$	35.3521	−	61.2316i	1.14758	−	1.98766i
$950$	−16.1630	+	27.9951i	−0.524396	+	0.908281i
$951$	6.98963	+	8.32991i	0.226654	+	0.270116i
$952$	0.0530334	+	0.0918566i	0.00171882	+	0.00297709i
$953$	−13.0601			−0.423057			−0.211528	−	0.977372i	$-0.567844\pi$
$953$	−13.0601			−0.423057			−0.211528	+	0.977372i	$0.567844\pi$
$954$	−43.5014	−	36.5020i	−1.40841	−	1.18180i
$955$	17.1557			0.555145
$956$	−6.17230	−	10.6907i	−0.199627	−	0.345763i
$957$	2.38279	−	6.54666i	0.0770246	−	0.211623i
$958$	−37.0428	+	64.1601i	−1.19680	+	2.07292i
$959$	4.96926	−	8.60700i	0.160466	−	0.277935i
$960$	−6.68866	+	18.3770i	−0.215876	+	0.593114i
$961$	14.8883	+	25.7873i	0.480268	+	0.831849i
$962$	1.34730			0.0434386
$963$	−23.4354	+	8.52979i	−0.755196	+	0.274869i
$964$	−6.61856			−0.213169
$965$	−15.5817	−	26.9883i	−0.501593	−	0.868785i
$966$	−4.34952	−	5.18355i	−0.139943	−	0.166778i
$967$	−5.59240	+	9.68631i	−0.179839	+	0.311491i	−0.941825	−	0.336103i	$-0.890891\pi$
$967$	−5.59240	+	9.68631i	−0.179839	+	0.311491i	0.761986	+	0.647593i	$0.224224\pi$
$968$	−0.439693	+	0.761570i	−0.0141323	+	0.0244778i
$969$	1.64749	−	0.290497i	0.0529250	−	0.00933210i
$970$	−15.5287	−	26.8965i	−0.498596	−	0.863594i
$971$	28.4935			0.914400			0.457200	−	0.889364i	$-0.348852\pi$
$971$	28.4935			0.914400			0.457200	+	0.889364i	$0.348852\pi$
$972$	−8.16843	−	22.4426i	−0.262003	−	0.719846i
$973$	−9.46616			−0.303471
$974$	−32.8444	−	56.8881i	−1.05240	−	1.82281i
$975$	37.9393	−	6.68972i	1.21503	−	0.214242i
$976$	−17.3282	+	30.0133i	−0.554661	+	0.960701i
$977$	9.96363	−	17.2575i	0.318765	−	0.552117i	−0.661466	−	0.749975i	$-0.730065\pi$
$977$	9.96363	−	17.2575i	0.318765	−	0.552117i	0.980231	+	0.197859i	$0.0633987\pi$
$978$	4.44774	+	5.30061i	0.142223	+	0.169495i
$979$	−1.50980	−	2.61505i	−0.0482534	−	0.0835774i
$980$	−29.0009			−0.926401
$981$	−45.0718	+	16.4048i	−1.43903	+	0.523765i
$982$	45.1935			1.44218
$983$	21.5141	+	37.2636i	0.686194	+	1.18852i	0.973060	+	0.230553i	$0.0740534\pi$
$983$	21.5141	+	37.2636i	0.686194	+	1.18852i	−0.286865	+	0.957971i	$0.592613\pi$
$984$	−2.92556	+	8.03790i	−0.0932633	+	0.256239i
$985$	−4.42262	+	7.66020i	−0.140916	+	0.244074i
$986$	−0.698463	+	1.20977i	−0.0222436	+	0.0385270i
$987$	−4.64290	+	12.7563i	−0.147785	+	0.406037i
$988$	−27.0612	−	46.8714i	−0.860933	−	1.49118i
$989$	−12.2926			−0.390882
$990$	−12.4363	−	10.4353i	−0.395251	−	0.331655i
$991$	−21.1516			−0.671902			−0.335951	−	0.941879i	$-0.609058\pi$
$991$	−21.1516			−0.671902			−0.335951	+	0.941879i	$0.609058\pi$
$992$	−3.92989	−	6.80677i	−0.124774	−	0.216115i
$993$	−13.2182	−	15.7529i	−0.419468	−	0.499902i
$994$	1.51842	−	2.62998i	0.0481613	−	0.0834178i
$995$	−2.22668	+	3.85673i	−0.0705906	+	0.122266i
$996$	2.72281	−	0.480105i	0.0862756	−	0.0152127i
$997$	13.4204	+	23.2448i	0.425028	+	0.736170i	0.996423	−	0.0845048i	$-0.0269308\pi$
$997$	13.4204	+	23.2448i	0.425028	+	0.736170i	−0.571395	+	0.820675i	$0.693597\pi$
$998$	−50.9718			−1.61349
$999$	−0.477301	+	0.275570i	−0.0151011	+	0.00871864i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.e.d.67.3	yes	6
3.2	odd	2		297.2.e.d.199.1		6
9.2	odd	6		297.2.e.d.100.1		6
9.4	even	3		891.2.a.l.1.1		3
9.5	odd	6		891.2.a.k.1.3		3
9.7	even	3	inner	99.2.e.d.34.3	✓	6
11.10	odd	2		1089.2.e.h.364.1		6
99.32	even	6		9801.2.a.bd.1.1		3
99.43	odd	6		1089.2.e.h.727.1		6
99.76	odd	6		9801.2.a.be.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.e.d.34.3	✓	6	9.7	even	3	inner
99.2.e.d.67.3	yes	6	1.1	even	1	trivial
297.2.e.d.100.1		6	9.2	odd	6
297.2.e.d.199.1		6	3.2	odd	2
891.2.a.k.1.3		3	9.5	odd	6
891.2.a.l.1.1		3	9.4	even	3
1089.2.e.h.364.1		6	11.10	odd	2
1089.2.e.h.727.1		6	99.43	odd	6
9801.2.a.bd.1.1		3	99.32	even	6
9801.2.a.be.1.3		3	99.76	odd	6

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 1.62760i) q^{2} +(-1.70574 + 0.300767i) q^{3} +(-0.766044 + 1.32683i) q^{4} +(-1.43969 + 2.49362i) q^{5} +(-2.09240 - 2.49362i) q^{6} +(0.326352 + 0.565258i) q^{7} +0.879385 q^{8} +(2.81908 - 1.02606i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 1.62760i) q^{2} +(-1.70574 + 0.300767i) q^{3} +(-0.766044 + 1.32683i) q^{4} +(-1.43969 + 2.49362i) q^{5} +(-2.09240 - 2.49362i) q^{6} +(0.326352 + 0.565258i) q^{7} +0.879385 q^{8} +(2.81908 - 1.02606i) q^{9} -5.41147 q^{10} +(0.500000 + 0.866025i) q^{11} +(0.907604 - 2.49362i) q^{12} +(3.37939 - 5.85327i) q^{13} +(-0.613341 + 1.06234i) q^{14} +(1.70574 - 4.68647i) q^{15} +(2.35844 + 4.08494i) q^{16} +0.184793 q^{17} +(4.31908 + 3.62414i) q^{18} -5.22668 q^{19} +(-2.20574 - 3.82045i) q^{20} +(-0.726682 - 0.866025i) q^{21} +(-0.939693 + 1.62760i) q^{22} +(1.59240 - 2.75811i) q^{23} +(-1.50000 + 0.264490i) q^{24} +(-1.64543 - 2.84997i) q^{25} +12.7023 q^{26} +(-4.50000 + 2.59808i) q^{27} -1.00000 q^{28} +(2.01114 + 3.48340i) q^{29} +(9.23055 - 1.62760i) q^{30} +(-0.553033 + 0.957882i) q^{31} +(-3.55303 + 6.15403i) q^{32} +(-1.11334 - 1.32683i) q^{33} +(0.173648 + 0.300767i) q^{34} -1.87939 q^{35} +(-0.798133 + 4.52644i) q^{36} +0.106067 q^{37} +(-4.91147 - 8.50692i) q^{38} +(-4.00387 + 11.0005i) q^{39} +(-1.26604 + 2.19285i) q^{40} +(2.80793 - 4.86348i) q^{41} +(0.726682 - 1.99654i) q^{42} +(-1.92989 - 3.34267i) q^{43} -1.53209 q^{44} +(-1.50000 + 8.50692i) q^{45} +5.98545 q^{46} +(-6.00387 - 10.3990i) q^{47} +(-5.25150 - 6.25849i) q^{48} +(3.28699 - 5.69323i) q^{49} +(3.09240 - 5.35619i) q^{50} +(-0.315207 + 0.0555796i) q^{51} +(5.17752 + 8.96773i) q^{52} -10.0719 q^{53} +(-8.45723 - 4.88279i) q^{54} -2.87939 q^{55} +(0.286989 + 0.497079i) q^{56} +(8.91534 - 1.57202i) q^{57} +(-3.77972 + 6.54666i) q^{58} +(-5.27719 + 9.14036i) q^{59} +(4.91147 + 5.85327i) q^{60} +(3.67365 + 6.36295i) q^{61} -2.07873 q^{62} +(1.50000 + 1.25865i) q^{63} -3.92127 q^{64} +(9.73055 + 16.8538i) q^{65} +(1.11334 - 3.05888i) q^{66} +(5.90420 - 10.2264i) q^{67} +(-0.141559 + 0.245188i) q^{68} +(-1.88666 + 5.18355i) q^{69} +(-1.76604 - 3.05888i) q^{70} -2.47565 q^{71} +(2.47906 - 0.902302i) q^{72} +10.4611 q^{73} +(0.0996702 + 0.172634i) q^{74} +(3.66385 + 4.36640i) q^{75} +(4.00387 - 6.93491i) q^{76} +(-0.326352 + 0.565258i) q^{77} +(-21.6668 + 3.82045i) q^{78} +(0.733956 + 1.27125i) q^{79} -13.5817 q^{80} +(6.89440 - 5.78509i) q^{81} +10.5544 q^{82} +(0.520945 + 0.902302i) q^{83} +(1.70574 - 0.300767i) q^{84} +(-0.266044 + 0.460802i) q^{85} +(3.62701 - 6.28217i) q^{86} +(-4.47818 - 5.33688i) q^{87} +(0.439693 + 0.761570i) q^{88} -3.01960 q^{89} +(-15.2554 + 5.55250i) q^{90} +4.41147 q^{91} +(2.43969 + 4.22567i) q^{92} +(0.655230 - 1.80023i) q^{93} +(11.2836 - 19.5437i) q^{94} +(7.52481 - 13.0334i) q^{95} +(4.20961 - 11.5658i) q^{96} +(2.86959 + 4.97027i) q^{97} +12.3550 q^{98} +(2.29813 + 1.92836i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} - 6 q^{8}+O(q^{10}) \) 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 - 6 * q^8	\( 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} - 6 q^{8} - 12 q^{10} + 3 q^{11} + 9 q^{12} + 9 q^{13} + 3 q^{14} + 6 q^{16} - 6 q^{17} + 9 q^{18} - 18 q^{19} - 3 q^{20} + 9 q^{21} + 6 q^{23} - 9 q^{24} + 6 q^{25} + 24 q^{26} - 27 q^{27} - 6 q^{28} + 6 q^{29} + 18 q^{30} + 9 q^{31} - 9 q^{32} + 9 q^{36} - 24 q^{37} - 9 q^{38} - 3 q^{40} + 6 q^{41} - 9 q^{42} - 3 q^{43} - 9 q^{45} - 12 q^{47} + 9 q^{48} + 12 q^{49} + 15 q^{50} - 9 q^{51} + 6 q^{52} + 6 q^{53} - 6 q^{55} - 6 q^{56} + 9 q^{57} + 3 q^{58} - 21 q^{59} + 9 q^{60} + 21 q^{61} - 30 q^{62} + 9 q^{63} - 6 q^{64} + 21 q^{65} - 3 q^{67} - 9 q^{68} - 18 q^{69} - 6 q^{70} + 24 q^{71} + 18 q^{72} - 12 q^{73} + 15 q^{74} + 18 q^{75} - 3 q^{77} - 45 q^{78} + 9 q^{79} - 18 q^{80} + 42 q^{82} + 3 q^{85} - 6 q^{86} + 27 q^{87} - 3 q^{88} - 24 q^{89} - 27 q^{90} + 6 q^{91} + 9 q^{92} - 9 q^{93} + 18 q^{94} + 18 q^{95} - 9 q^{96} + 3 q^{97} + 24 q^{98}+O(q^{100}) \) 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 - 6 * q^8 - 12 * q^10 + 3 * q^11 + 9 * q^12 + 9 * q^13 + 3 * q^14 + 6 * q^16 - 6 * q^17 + 9 * q^18 - 18 * q^19 - 3 * q^20 + 9 * q^21 + 6 * q^23 - 9 * q^24 + 6 * q^25 + 24 * q^26 - 27 * q^27 - 6 * q^28 + 6 * q^29 + 18 * q^30 + 9 * q^31 - 9 * q^32 + 9 * q^36 - 24 * q^37 - 9 * q^38 - 3 * q^40 + 6 * q^41 - 9 * q^42 - 3 * q^43 - 9 * q^45 - 12 * q^47 + 9 * q^48 + 12 * q^49 + 15 * q^50 - 9 * q^51 + 6 * q^52 + 6 * q^53 - 6 * q^55 - 6 * q^56 + 9 * q^57 + 3 * q^58 - 21 * q^59 + 9 * q^60 + 21 * q^61 - 30 * q^62 + 9 * q^63 - 6 * q^64 + 21 * q^65 - 3 * q^67 - 9 * q^68 - 18 * q^69 - 6 * q^70 + 24 * q^71 + 18 * q^72 - 12 * q^73 + 15 * q^74 + 18 * q^75 - 3 * q^77 - 45 * q^78 + 9 * q^79 - 18 * q^80 + 42 * q^82 + 3 * q^85 - 6 * q^86 + 27 * q^87 - 3 * q^88 - 24 * q^89 - 27 * q^90 + 6 * q^91 + 9 * q^92 - 9 * q^93 + 18 * q^94 + 18 * q^95 - 9 * q^96 + 3 * q^97 + 24 * q^98

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