LMFDB - Embedded newform 387.2.f.c.259.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(130,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("387.130");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.f (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:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			259.16
Character	$\chi$	$=$	387.259
Dual form			387.2.f.c.130.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.887526 - 1.53724i) q^{2} +(-0.0779340 + 1.73030i) q^{3} +(-0.575406 - 0.996632i) q^{4} +(-1.84963 - 3.20365i) q^{5} +(2.59071 + 1.65549i) q^{6} +(0.0448503 - 0.0776831i) q^{7} +1.50735 q^{8} +(-2.98785 - 0.269698i) q^{9} +O(q^{10})$	\(q+(0.887526 - 1.53724i) q^{2} +(-0.0779340 + 1.73030i) q^{3} +(-0.575406 - 0.996632i) q^{4} +(-1.84963 - 3.20365i) q^{5} +(2.59071 + 1.65549i) q^{6} +(0.0448503 - 0.0776831i) q^{7} +1.50735 q^{8} +(-2.98785 - 0.269698i) q^{9} -6.56638 q^{10} +(2.40540 - 4.16628i) q^{11} +(1.76931 - 0.917952i) q^{12} +(-2.20207 - 3.81410i) q^{13} +(-0.0796117 - 0.137892i) q^{14} +(5.68742 - 2.95074i) q^{15} +(2.48863 - 4.31043i) q^{16} +4.51570 q^{17} +(-3.06639 + 4.35368i) q^{18} +0.457142 q^{19} +(-2.12858 + 3.68680i) q^{20} +(0.130919 + 0.0836586i) q^{21} +(-4.26972 - 7.39537i) q^{22} +(3.13921 + 5.43728i) q^{23} +(-0.117474 + 2.60817i) q^{24} +(-4.34227 + 7.52103i) q^{25} -7.81759 q^{26} +(0.699512 - 5.14885i) q^{27} -0.103229 q^{28} +(-2.41056 + 4.17521i) q^{29} +(0.511744 - 11.3618i) q^{30} +(1.62230 + 2.80991i) q^{31} +(-2.91009 - 5.04043i) q^{32} +(7.02144 + 4.48676i) q^{33} +(4.00780 - 6.94171i) q^{34} -0.331826 q^{35} +(1.45044 + 3.13298i) q^{36} -9.48421 q^{37} +(0.405726 - 0.702738i) q^{38} +(6.77115 - 3.51299i) q^{39} +(-2.78805 - 4.82904i) q^{40} +(-3.54390 - 6.13822i) q^{41} +(0.244798 - 0.127005i) q^{42} +(-0.500000 + 0.866025i) q^{43} -5.53633 q^{44} +(4.66241 + 10.0709i) q^{45} +11.1445 q^{46} +(-1.98801 + 3.44334i) q^{47} +(7.26437 + 4.64199i) q^{48} +(3.49598 + 6.05521i) q^{49} +(7.70775 + 13.3502i) q^{50} +(-0.351926 + 7.81349i) q^{51} +(-2.53417 + 4.38932i) q^{52} +8.18271 q^{53} +(-7.29419 - 5.64506i) q^{54} -17.7964 q^{55} +(0.0676053 - 0.117096i) q^{56} +(-0.0356269 + 0.790992i) q^{57} +(4.27886 + 7.41121i) q^{58} +(-4.89338 - 8.47559i) q^{59} +(-6.21338 - 3.97040i) q^{60} +(-5.86886 + 10.1652i) q^{61} +5.75934 q^{62} +(-0.154957 + 0.220010i) q^{63} -0.376622 q^{64} +(-8.14605 + 14.1094i) q^{65} +(13.1289 - 6.81153i) q^{66} +(3.11026 + 5.38713i) q^{67} +(-2.59836 - 4.50049i) q^{68} +(-9.65275 + 5.00802i) q^{69} +(-0.294505 + 0.510097i) q^{70} +13.8969 q^{71} +(-4.50375 - 0.406530i) q^{72} +11.2453 q^{73} +(-8.41748 + 14.5795i) q^{74} +(-12.6752 - 8.09955i) q^{75} +(-0.263042 - 0.455603i) q^{76} +(-0.215766 - 0.373718i) q^{77} +(0.609256 - 13.5268i) q^{78} +(4.64684 - 8.04856i) q^{79} -18.4122 q^{80} +(8.85453 + 1.61163i) q^{81} -12.5812 q^{82} +(-2.01802 + 3.49531i) q^{83} +(0.00804502 - 0.178616i) q^{84} +(-8.35237 - 14.4667i) q^{85} +(0.887526 + 1.53724i) q^{86} +(-7.03648 - 4.49637i) q^{87} +(3.62579 - 6.28006i) q^{88} +8.46429 q^{89} +(19.6194 + 1.77094i) q^{90} -0.395055 q^{91} +(3.61264 - 6.25728i) q^{92} +(-4.98841 + 2.58807i) q^{93} +(3.52883 + 6.11211i) q^{94} +(-0.845545 - 1.46453i) q^{95} +(8.94823 - 4.64250i) q^{96} +(0.339574 - 0.588160i) q^{97} +12.4111 q^{98} +(-8.31063 + 11.7995i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 4 q^{2} - 7 q^{3} - 22 q^{4} - 9 q^{5} - 7 q^{7} + 24 q^{8} - 3 q^{9}+O(q^{10}) $ 38 * q - 4 * q^2 - 7 * q^3 - 22 * q^4 - 9 * q^5 - 7 * q^7 + 24 * q^8 - 3 * q^9	\( 38 q - 4 q^{2} - 7 q^{3} - 22 q^{4} - 9 q^{5} - 7 q^{7} + 24 q^{8} - 3 q^{9} - 14 q^{10} - 5 q^{11} + 11 q^{12} + 5 q^{13} - 17 q^{14} - 5 q^{15} - 24 q^{16} + 42 q^{17} - 23 q^{18} - 8 q^{19} - 21 q^{20} + 20 q^{22} - 22 q^{23} - 14 q^{24} - 10 q^{25} + 34 q^{26} - 4 q^{27} - 2 q^{28} - 30 q^{29} + 63 q^{30} + 5 q^{31} - 48 q^{32} - q^{33} + 6 q^{34} + 106 q^{35} - 20 q^{36} - 2 q^{37} - 21 q^{38} + 25 q^{39} - 16 q^{40} - 29 q^{41} - 47 q^{42} - 19 q^{43} + 58 q^{44} - 37 q^{45} - 32 q^{47} + 45 q^{48} + 10 q^{49} + 11 q^{50} - 53 q^{51} - q^{52} + 76 q^{53} - 41 q^{54} + 4 q^{55} - 46 q^{56} + 23 q^{57} - 30 q^{58} - 30 q^{59} - 87 q^{60} + 10 q^{61} + 50 q^{62} + 21 q^{63} + 28 q^{64} - 8 q^{65} + 91 q^{66} - 3 q^{67} - 47 q^{68} - 40 q^{69} - 56 q^{70} + 42 q^{71} + 3 q^{72} + 16 q^{73} - 28 q^{74} + 19 q^{75} + 36 q^{76} - 49 q^{77} - 105 q^{78} - 4 q^{79} + 140 q^{80} + 77 q^{81} - 8 q^{82} - 29 q^{83} + 145 q^{84} + 4 q^{85} - 4 q^{86} - 24 q^{87} + 47 q^{88} + 108 q^{89} - 8 q^{90} + 8 q^{91} - 12 q^{92} - 4 q^{93} + 23 q^{94} - 33 q^{95} - 147 q^{96} + 4 q^{97} + 98 q^{98} + 85 q^{99}+O(q^{100}) \) 38 * q - 4 * q^2 - 7 * q^3 - 22 * q^4 - 9 * q^5 - 7 * q^7 + 24 * q^8 - 3 * q^9 - 14 * q^10 - 5 * q^11 + 11 * q^12 + 5 * q^13 - 17 * q^14 - 5 * q^15 - 24 * q^16 + 42 * q^17 - 23 * q^18 - 8 * q^19 - 21 * q^20 + 20 * q^22 - 22 * q^23 - 14 * q^24 - 10 * q^25 + 34 * q^26 - 4 * q^27 - 2 * q^28 - 30 * q^29 + 63 * q^30 + 5 * q^31 - 48 * q^32 - q^33 + 6 * q^34 + 106 * q^35 - 20 * q^36 - 2 * q^37 - 21 * q^38 + 25 * q^39 - 16 * q^40 - 29 * q^41 - 47 * q^42 - 19 * q^43 + 58 * q^44 - 37 * q^45 - 32 * q^47 + 45 * q^48 + 10 * q^49 + 11 * q^50 - 53 * q^51 - q^52 + 76 * q^53 - 41 * q^54 + 4 * q^55 - 46 * q^56 + 23 * q^57 - 30 * q^58 - 30 * q^59 - 87 * q^60 + 10 * q^61 + 50 * q^62 + 21 * q^63 + 28 * q^64 - 8 * q^65 + 91 * q^66 - 3 * q^67 - 47 * q^68 - 40 * q^69 - 56 * q^70 + 42 * q^71 + 3 * q^72 + 16 * q^73 - 28 * q^74 + 19 * q^75 + 36 * q^76 - 49 * q^77 - 105 * q^78 - 4 * q^79 + 140 * q^80 + 77 * q^81 - 8 * q^82 - 29 * q^83 + 145 * q^84 + 4 * q^85 - 4 * q^86 - 24 * q^87 + 47 * q^88 + 108 * q^89 - 8 * q^90 + 8 * q^91 - 12 * q^92 - 4 * q^93 + 23 * q^94 - 33 * q^95 - 147 * q^96 + 4 * q^97 + 98 * q^98 + 85 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.887526	−	1.53724i	0.627576	−	1.08699i	−0.360461	−	0.932774i	$-0.617381\pi$
$2$	0.887526	−	1.53724i	0.627576	−	1.08699i	0.988037	−	0.154219i	$-0.0492861\pi$
$3$	−0.0779340	+	1.73030i	−0.0449952	+	0.998987i
$3$	−0.0779340	+	1.73030i	−0.0449952	+	0.998987i
$4$	−0.575406	−	0.996632i	−0.287703	−	0.498316i
$5$	−1.84963	−	3.20365i	−0.827180	−	1.43272i	−0.900242	−	0.435390i	$-0.856610\pi$
$5$	−1.84963	−	3.20365i	−0.827180	−	1.43272i	0.0730618	−	0.997327i	$-0.476723\pi$
$6$	2.59071	+	1.65549i	1.05765	+	0.675850i
$7$	0.0448503	−	0.0776831i	0.0169518	−	0.0293614i	−0.857425	−	0.514609i	$-0.827937\pi$
$7$	0.0448503	−	0.0776831i	0.0169518	−	0.0293614i	0.874377	+	0.485247i	$0.161270\pi$
$8$	1.50735			0.532930
$9$	−2.98785	−	0.269698i	−0.995951	−	0.0898992i
$10$	−6.56638			−2.07647
$11$	2.40540	−	4.16628i	0.725256	−	1.25618i	−0.233612	−	0.972330i	$-0.575055\pi$
$11$	2.40540	−	4.16628i	0.725256	−	1.25618i	0.958868	−	0.283851i	$-0.0916121\pi$
$12$	1.76931	−	0.917952i	0.510757	−	0.264990i
$13$	−2.20207	−	3.81410i	−0.610745	−	1.05784i	−0.991115	−	0.133007i	$-0.957537\pi$
$13$	−2.20207	−	3.81410i	−0.610745	−	1.05784i	0.380370	−	0.924835i	$-0.375797\pi$
$14$	−0.0796117	−	0.137892i	−0.0212771	−	0.0368531i
$15$	5.68742	−	2.95074i	1.46849	−	0.761877i
$16$	2.48863	−	4.31043i	0.622157	−	1.07761i
$17$	4.51570			1.09522			0.547609	−	0.836735i	$-0.315538\pi$
$17$	4.51570			1.09522			0.547609	+	0.836735i	$0.315538\pi$
$18$	−3.06639	+	4.35368i	−0.722755	+	1.02617i
$19$	0.457142			0.104876			0.0524378	−	0.998624i	$-0.483301\pi$
$19$	0.457142			0.104876			0.0524378	+	0.998624i	$0.483301\pi$
$20$	−2.12858	+	3.68680i	−0.475964	+	0.824394i
$21$	0.130919	+	0.0836586i	0.0285690	+	0.0182558i
$22$	−4.26972	−	7.39537i	−0.910307	−	1.57670i
$23$	3.13921	+	5.43728i	0.654571	+	1.13375i	0.982001	+	0.188875i	$0.0604841\pi$
$23$	3.13921	+	5.43728i	0.654571	+	1.13375i	−0.327430	+	0.944875i	$0.606183\pi$
$24$	−0.117474	+	2.60817i	−0.0239793	+	0.532390i
$25$	−4.34227	+	7.52103i	−0.868453	+	1.50421i
$26$	−7.81759			−1.53316
$27$	0.699512	−	5.14885i	0.134621	−	0.990897i
$28$	−0.103229			−0.0195084
$29$	−2.41056	+	4.17521i	−0.447629	+	0.775316i	−0.998231	−	0.0594516i	$-0.981065\pi$
$29$	−2.41056	+	4.17521i	−0.447629	+	0.775316i	0.550602	+	0.834768i	$0.314398\pi$
$30$	0.511744	−	11.3618i	0.0934313	−	2.07437i
$31$	1.62230	+	2.80991i	0.291374	+	0.504674i	0.974135	−	0.225967i	$-0.0725543\pi$
$31$	1.62230	+	2.80991i	0.291374	+	0.504674i	−0.682761	+	0.730642i	$0.739221\pi$
$32$	−2.91009	−	5.04043i	−0.514436	−	0.891030i
$33$	7.02144	+	4.48676i	1.22228	+	0.781044i
$34$	4.00780	−	6.94171i	0.687332	−	1.19049i
$35$	−0.331826			−0.0560889
$36$	1.45044	+	3.13298i	0.241740	+	0.522163i
$37$	−9.48421			−1.55919			−0.779597	−	0.626282i	$-0.784576\pi$
$37$	−9.48421			−1.55919			−0.779597	+	0.626282i	$0.784576\pi$
$38$	0.405726	−	0.702738i	0.0658174	−	0.113999i
$39$	6.77115	−	3.51299i	1.08425	−	0.562529i
$40$	−2.78805	−	4.82904i	−0.440829	−	0.763538i
$41$	−3.54390	−	6.13822i	−0.553465	−	0.958629i	−0.998021	−	0.0628784i	$-0.979972\pi$
$41$	−3.54390	−	6.13822i	−0.553465	−	0.958629i	0.444556	−	0.895751i	$-0.353361\pi$
$42$	0.244798	−	0.127005i	0.0377731	−	0.0195974i
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i
$44$	−5.53633			−0.834634
$45$	4.66241	+	10.0709i	0.695030	+	1.50128i
$46$	11.1445			1.64317
$47$	−1.98801	+	3.44334i	−0.289982	+	0.502263i	−0.973805	−	0.227385i	$-0.926983\pi$
$47$	−1.98801	+	3.44334i	−0.289982	+	0.502263i	0.683823	+	0.729648i	$0.260316\pi$
$48$	7.26437	+	4.64199i	1.04852	+	0.670014i
$49$	3.49598	+	6.05521i	0.499425	+	0.865030i
$50$	7.70775	+	13.3502i	1.09004	+	1.88801i
$51$	−0.351926	+	7.81349i	−0.0492795	+	1.09411i
$52$	−2.53417	+	4.38932i	−0.351427	+	0.608689i
$53$	8.18271			1.12398			0.561991	−	0.827143i	$-0.310036\pi$
$53$	8.18271			1.12398			0.561991	+	0.827143i	$0.310036\pi$
$54$	−7.29419	−	5.64506i	−0.992614	−	0.768196i
$55$	−17.7964			−2.39967
$56$	0.0676053	−	0.117096i	0.00903414	−	0.0156476i
$57$	−0.0356269	+	0.790992i	−0.00471890	+	0.104769i
$58$	4.27886	+	7.41121i	0.561842	+	0.973140i
$59$	−4.89338	−	8.47559i	−0.637064	−	1.10343i	−0.986074	−	0.166308i	$-0.946815\pi$
$59$	−4.89338	−	8.47559i	−0.637064	−	1.10343i	0.349010	−	0.937119i	$-0.386518\pi$
$60$	−6.21338	−	3.97040i	−0.802143	−	0.512576i
$61$	−5.86886	+	10.1652i	−0.751431	+	1.30152i	0.195698	+	0.980664i	$0.437303\pi$
$61$	−5.86886	+	10.1652i	−0.751431	+	1.30152i	−0.947129	+	0.320853i	$0.896031\pi$
$62$	5.75934			0.731437
$63$	−0.154957	+	0.220010i	−0.0195228	+	0.0277186i
$64$	−0.376622			−0.0470778
$65$	−8.14605	+	14.1094i	−1.01039	+	1.75005i
$66$	13.1289	−	6.81153i	1.61606	−	0.838441i
$67$	3.11026	+	5.38713i	0.379979	+	0.658143i	0.991059	−	0.133426i	$-0.0425979\pi$
$67$	3.11026	+	5.38713i	0.379979	+	0.658143i	−0.611080	+	0.791569i	$0.709265\pi$
$68$	−2.59836	−	4.50049i	−0.315097	−	0.545765i
$69$	−9.65275	+	5.00802i	−1.16205	+	0.602895i
$70$	−0.294505	+	0.510097i	−0.0352000	+	0.0609682i
$71$	13.8969			1.64925			0.824627	−	0.565676i	$-0.191385\pi$
$71$	13.8969			1.64925			0.824627	+	0.565676i	$0.191385\pi$
$72$	−4.50375	−	0.406530i	−0.530772	−	0.0479100i
$73$	11.2453			1.31616			0.658078	−	0.752949i	$-0.271369\pi$
$73$	11.2453			1.31616			0.658078	+	0.752949i	$0.271369\pi$
$74$	−8.41748	+	14.5795i	−0.978513	+	1.69483i
$75$	−12.6752	−	8.09955i	−1.46361	−	0.935256i
$76$	−0.263042	−	0.455603i	−0.0301730	−	0.0522612i
$77$	−0.215766	−	0.373718i	−0.0245889	−	0.0425892i
$78$	0.609256	−	13.5268i	0.0689847	−	1.53160i
$79$	4.64684	−	8.04856i	0.522810	−	0.905534i	−0.476838	−	0.878991i	$-0.658217\pi$
$79$	4.64684	−	8.04856i	0.522810	−	0.905534i	0.999648	−	0.0265422i	$-0.00844963\pi$
$80$	−18.4122			−2.05854
$81$	8.85453	+	1.61163i	0.983836	+	0.179070i
$82$	−12.5812			−1.38936
$83$	−2.01802	+	3.49531i	−0.221506	+	0.383660i	−0.955266	−	0.295750i	$-0.904431\pi$
$83$	−2.01802	+	3.49531i	−0.221506	+	0.383660i	0.733759	+	0.679409i	$0.237764\pi$
$84$	0.00804502	−	0.178616i	0.000877783	−	0.0194886i
$85$	−8.35237	−	14.4667i	−0.905942	−	1.56914i
$86$	0.887526	+	1.53724i	0.0957044	+	0.165765i
$87$	−7.03648	−	4.49637i	−0.754390	−	0.482061i
$88$	3.62579	−	6.28006i	0.386511	−	0.669456i
$89$	8.46429			0.897213			0.448607	−	0.893729i	$-0.351920\pi$
$89$	8.46429			0.897213			0.448607	+	0.893729i	$0.351920\pi$
$90$	19.6194	+	1.77094i	2.06806	+	0.186673i
$91$	−0.395055			−0.0414130
$92$	3.61264	−	6.25728i	0.376644	−	0.652367i
$93$	−4.98841	+	2.58807i	−0.517274	+	0.268371i
$94$	3.52883	+	6.11211i	0.363971	+	0.630416i
$95$	−0.845545	−	1.46453i	−0.0867510	−	0.150257i
$96$	8.94823	−	4.64250i	0.913275	−	0.473823i
$97$	0.339574	−	0.588160i	0.0344785	−	0.0597186i	−0.848271	−	0.529562i	$-0.822356\pi$
$97$	0.339574	−	0.588160i	0.0344785	−	0.0597186i	0.882750	+	0.469843i	$0.155690\pi$
$98$	12.4111			1.25371
$99$	−8.31063	+	11.7995i	−0.835250	+	1.18589i
$100$	9.99427			0.999427
$101$	−1.81569	+	3.14487i	−0.180668	+	0.312926i	−0.942108	−	0.335309i	$-0.891159\pi$
$101$	−1.81569	+	3.14487i	−0.180668	+	0.312926i	0.761440	+	0.648235i	$0.224493\pi$
$102$	11.6989	+	7.47568i	1.15836	+	0.740202i
$103$	2.72973	+	4.72803i	0.268968	+	0.465867i	0.968596	−	0.248641i	$-0.0799839\pi$
$103$	2.72973	+	4.72803i	0.268968	+	0.465867i	−0.699627	+	0.714508i	$0.746651\pi$
$104$	−3.31930	−	5.74920i	−0.325484	−	0.563756i
$105$	0.0258605	−	0.574158i	0.00252373	−	0.0560321i
$106$	7.26237	−	12.5788i	0.705384	−	1.22176i
$107$	−2.04706			−0.197896			−0.0989482	−	0.995093i	$-0.531548\pi$
$107$	−2.04706			−0.197896			−0.0989482	+	0.995093i	$0.531548\pi$
$108$	−5.53402	+	2.26552i	−0.532511	+	0.218000i
$109$	−1.75892			−0.168474			−0.0842371	−	0.996446i	$-0.526845\pi$
$109$	−1.75892			−0.168474			−0.0842371	+	0.996446i	$0.526845\pi$
$110$	−15.7948	+	27.3574i	−1.50598	+	2.60843i
$111$	0.739142	−	16.4105i	0.0701562	−	1.55761i
$112$	−0.223232	−	0.386649i	−0.0210934	−	0.0365349i
$113$	6.71065	+	11.6232i	0.631285	+	1.09342i	0.987289	+	0.158933i	$0.0508054\pi$
$113$	6.71065	+	11.6232i	0.631285	+	1.09342i	−0.356005	+	0.934484i	$0.615861\pi$
$114$	1.18433	+	0.756793i	0.110922	+	0.0708802i
$115$	11.6128	−	20.1139i	1.08290	−	1.87563i
$116$	5.54819			0.515137
$117$	5.55082	+	11.9899i	0.513173	+	1.10846i
$118$	−17.3720			−1.59922
$119$	0.202531	−	0.350793i	0.0185659	−	0.0321572i
$120$	8.57295	−	4.44780i	0.782600	−	0.406027i
$121$	−6.07193	−	10.5169i	−0.551994	−	0.956081i
$122$	10.4175	+	18.0437i	0.943160	+	1.63360i
$123$	10.8971	−	5.65363i	0.982562	−	0.509771i
$124$	1.86696	−	3.23368i	0.167658	−	0.290393i
$125$	13.6301			1.21911
$126$	0.200679	+	0.433471i	0.0178779	+	0.0386166i
$127$	5.69493			0.505344			0.252672	−	0.967552i	$-0.418691\pi$
$127$	5.69493			0.505344			0.252672	+	0.967552i	$0.418691\pi$
$128$	5.48592	−	9.50190i	0.484892	−	0.839857i
$129$	−1.45951	−	0.932641i	−0.128503	−	0.0821145i
$130$	14.4597	+	25.0449i	1.26820	+	2.19658i
$131$	0.210408	+	0.364437i	0.0183834	+	0.0318410i	0.875071	−	0.483995i	$-0.160815\pi$
$131$	0.210408	+	0.364437i	0.0183834	+	0.0318410i	−0.856687	+	0.515836i	$0.827481\pi$
$132$	0.431469	−	9.57950i	0.0375545	−	0.833789i
$133$	0.0205030	−	0.0355122i	0.00177784	−	0.00307930i
$134$	11.0418			0.953862
$135$	−17.7890	+	7.28248i	−1.53103	+	0.626776i
$136$	6.80675			0.583674
$137$	6.53263	−	11.3149i	0.558120	−	0.966693i	−0.439533	−	0.898226i	$-0.644856\pi$
$137$	6.53263	−	11.3149i	0.558120	−	0.966693i	0.997653	−	0.0684665i	$-0.0218106\pi$
$138$	−0.868538	+	19.2834i	−0.0739349	+	1.64151i
$139$	−3.71118	−	6.42796i	−0.314778	−	0.545212i	0.664612	−	0.747189i	$-0.268597\pi$
$139$	−3.71118	−	6.42796i	−0.314778	−	0.545212i	−0.979390	+	0.201977i	$0.935264\pi$
$140$	0.190935	+	0.330709i	0.0161369	+	0.0279500i
$141$	−5.80307	−	3.70821i	−0.488707	−	0.312287i
$142$	12.3338	−	21.3628i	1.03503	−	1.79273i
$143$	−21.1875			−1.77179
$144$	−8.59817	+	12.2078i	−0.716514	+	1.01731i
$145$	17.8346			1.48108
$146$	9.98046	−	17.2867i	0.825988	−	1.43065i
$147$	−10.7498	+	5.57717i	−0.886626	+	0.459997i
$148$	5.45727	+	9.45227i	0.448585	+	0.776972i
$149$	1.28740	+	2.22984i	0.105468	+	0.182676i	0.913929	−	0.405874i	$-0.133033\pi$
$149$	1.28740	+	2.22984i	0.105468	+	0.182676i	−0.808461	+	0.588549i	$0.799699\pi$
$150$	−23.7005	+	12.2963i	−1.93514	+	1.00399i
$151$	−9.06181	+	15.6955i	−0.737440	+	1.27728i	0.216205	+	0.976348i	$0.430632\pi$
$151$	−9.06181	+	15.6955i	−0.737440	+	1.27728i	−0.953645	+	0.300935i	$0.902701\pi$
$152$	0.689075			0.0558914
$153$	−13.4922	−	1.21787i	−1.09078	−	0.0984592i
$154$	−0.765993			−0.0617255
$155$	6.00131	−	10.3946i	0.482037	−	0.834913i
$156$	−7.39732	−	4.72695i	−0.592260	−	0.378459i
$157$	−3.35336	−	5.80818i	−0.267627	−	0.463543i	0.700622	−	0.713533i	$-0.252906\pi$
$157$	−3.35336	−	5.80818i	−0.267627	−	0.463543i	−0.968249	+	0.249990i	$0.919573\pi$
$158$	−8.24838	−	14.2866i	−0.656206	−	1.13658i
$159$	−0.637711	+	14.1585i	−0.0505738	+	1.12284i
$160$	−10.7652	+	18.6459i	−0.851063	+	1.47408i
$161$	0.563179			0.0443847
$162$	10.3361	−	12.1812i	0.812080	−	0.957043i
$163$	1.31744			0.103190			0.0515949	−	0.998668i	$-0.483570\pi$
$163$	1.31744			0.103190			0.0515949	+	0.998668i	$0.483570\pi$
$164$	−4.07837	+	7.06394i	−0.318467	+	0.551601i
$165$	1.38695	−	30.7931i	0.107974	−	2.39724i
$166$	3.58209	+	6.20436i	0.278024	+	0.481551i
$167$	−11.8993	−	20.6102i	−0.920795	−	1.59486i	−0.798188	−	0.602408i	$-0.794208\pi$
$167$	−11.8993	−	20.6102i	−0.920795	−	1.59486i	−0.122607	−	0.992455i	$-0.539125\pi$
$168$	0.197342	+	0.126103i	0.0152253	+	0.00972906i
$169$	−3.19826	+	5.53954i	−0.246020	+	0.426119i
$170$	−29.6518			−2.27419
$171$	−1.36587	−	0.123290i	−0.104451	−	0.00942824i
$172$	1.15081			0.0877486
$173$	2.23015	−	3.86273i	0.169555	−	0.293678i	−0.768709	−	0.639599i	$-0.779100\pi$
$173$	2.23015	−	3.86273i	0.169555	−	0.293678i	0.938263	+	0.345921i	$0.112434\pi$
$174$	−13.1571	+	6.82612i	−0.997434	+	0.517487i
$175$	0.389504	+	0.674641i	0.0294438	+	0.0509981i
$176$	−11.9723	−	20.7366i	−0.902447	−	1.56308i
$177$	15.0466	−	7.80647i	1.13097	−	0.586770i
$178$	7.51228	−	13.0117i	0.563069	−	0.975265i
$179$	−14.0146			−1.04750			−0.523749	−	0.851873i	$-0.675467\pi$
$179$	−14.0146			−1.04750			−0.523749	+	0.851873i	$0.675467\pi$
$180$	7.35420	−	10.4416i	0.548150	−	0.778267i
$181$	−22.6669			−1.68481			−0.842407	−	0.538842i	$-0.818862\pi$
$181$	−22.6669			−1.68481			−0.842407	+	0.538842i	$0.818862\pi$
$182$	−0.350622	+	0.607295i	−0.0259898	+	0.0450157i
$183$	−17.1314	−	10.9471i	−1.26639	−	0.809232i
$184$	4.73190	+	8.19590i	0.348841	+	0.604210i
$185$	17.5423	+	30.3841i	1.28973	+	2.23388i
$186$	−0.448848	+	9.96536i	−0.0329111	+	0.730696i
$187$	10.8621	−	18.8137i	0.794313	−	1.37579i
$188$	4.57566			0.333714
$189$	−0.368605	−	0.285268i	−0.0268121	−	0.0207502i
$190$	−3.00177			−0.217771
$191$	−1.92889	+	3.34094i	−0.139570	+	0.241742i	−0.927334	−	0.374235i	$-0.877905\pi$
$191$	−1.92889	+	3.34094i	−0.139570	+	0.241742i	0.787764	+	0.615977i	$0.211239\pi$
$192$	0.0293517	−	0.651668i	0.00211827	−	0.0470301i
$193$	7.02503	+	12.1677i	0.505673	+	0.875851i	0.999978	+	0.00656281i	$0.00208902\pi$
$193$	7.02503	+	12.1677i	0.505673	+	0.875851i	−0.494306	+	0.869288i	$0.664578\pi$
$194$	−0.602762	−	1.04401i	−0.0432758	−	0.0749559i
$195$	−23.7785	−	15.1947i	−1.70282	−	1.08811i
$196$	4.02321	−	6.96841i	0.287372	−	0.497743i
$197$	1.78785			0.127379			0.0636897	−	0.997970i	$-0.479713\pi$
$197$	1.78785			0.127379			0.0636897	+	0.997970i	$0.479713\pi$
$198$	10.7628	+	23.2478i	0.764877	+	1.65215i
$199$	−17.5450			−1.24373			−0.621865	−	0.783125i	$-0.713625\pi$
$199$	−17.5450			−1.24373			−0.621865	+	0.783125i	$0.713625\pi$
$200$	−6.54533	+	11.3368i	−0.462825	+	0.801636i
$201$	−9.56373	+	4.96183i	−0.674573	+	0.349981i
$202$	3.22295	+	5.58231i	0.226766	+	0.392770i
$203$	0.216229	+	0.374519i	0.0151763	+	0.0262861i
$204$	7.98968	−	4.14519i	0.559390	−	0.290221i
$205$	−13.1098	+	22.7069i	−0.915630	+	1.58592i
$206$	9.69083			0.675192
$207$	−7.91308	−	17.0924i	−0.549997	−	1.18801i
$208$	−21.9206			−1.51992
$209$	1.09961	−	1.90458i	0.0760618	−	0.131743i
$210$	−0.859667	−	0.549334i	−0.0593227	−	0.0379077i
$211$	5.52699	+	9.57302i	0.380493	+	0.659034i	0.991133	−	0.132875i	$-0.0424208\pi$
$211$	5.52699	+	9.57302i	0.380493	+	0.659034i	−0.610639	+	0.791909i	$0.709087\pi$
$212$	−4.70838	−	8.15515i	−0.323373	−	0.560098i
$213$	−1.08304	+	24.0457i	−0.0742085	+	1.64758i
$214$	−1.81682	+	3.14682i	−0.124195	+	0.215112i
$215$	3.69926			0.252288
$216$	1.05441	−	7.76114i	0.0717437	−	0.528079i
$217$	0.291043			0.0197573
$218$	−1.56109	+	2.70389i	−0.105730	+	0.183130i
$219$	−0.876387	+	19.4576i	−0.0592207	+	1.31482i
$220$	10.2402	+	17.7365i	0.690392	+	1.19579i
$221$	−9.94390	−	17.2233i	−0.668899	−	1.15857i
$222$	−24.5709	−	15.7010i	−1.64909	−	1.05378i
$223$	1.38127	−	2.39243i	0.0924968	−	0.160209i	−0.816064	−	0.577961i	$-0.803849\pi$
$223$	1.38127	−	2.39243i	0.0924968	−	0.160209i	0.908561	+	0.417752i	$0.137182\pi$
$224$	−0.522075			−0.0348826
$225$	15.0025	−	21.3006i	1.00016	−	1.42004i
$226$	23.8235			1.58472
$227$	−4.95711	+	8.58597i	−0.329015	+	0.569871i	−0.982317	−	0.187227i	$-0.940050\pi$
$227$	−4.95711	+	8.58597i	−0.329015	+	0.569871i	0.653302	+	0.757098i	$0.273383\pi$
$228$	0.808828	−	0.419635i	0.0535660	−	0.0277910i
$229$	−2.55779	−	4.43023i	−0.169024	−	0.292758i	0.769053	−	0.639185i	$-0.220728\pi$
$229$	−2.55779	−	4.43023i	−0.169024	−	0.292758i	−0.938077	+	0.346427i	$0.887395\pi$
$230$	−20.6133	−	35.7032i	−1.35920	−	2.35420i
$231$	0.663459	−	0.344214i	0.0436524	−	0.0226476i
$232$	−3.63356	+	6.29351i	−0.238555	+	0.413189i
$233$	14.9600			0.980063			0.490032	−	0.871705i	$-0.336985\pi$
$233$	14.9600			0.980063			0.490032	+	0.871705i	$0.336985\pi$
$234$	23.3578	+	2.10839i	1.52695	+	0.137830i
$235$	14.7084			0.959468
$236$	−5.63136	+	9.75381i	−0.366570	+	0.634919i
$237$	13.5642	+	8.66766i	0.881093	+	0.563025i
$238$	−0.359502	−	0.622676i	−0.0233031	−	0.0403621i
$239$	5.95980	+	10.3227i	0.385507	+	0.667718i	0.991839	−	0.127493i	$-0.0406931\pi$
$239$	5.95980	+	10.3227i	0.385507	+	0.667718i	−0.606332	+	0.795212i	$0.707360\pi$
$240$	1.43493	−	31.8585i	0.0926246	−	2.05646i
$241$	−8.84983	+	15.3284i	−0.570068	+	0.987387i	0.426490	+	0.904492i	$0.359750\pi$
$241$	−8.84983	+	15.3284i	−0.570068	+	0.987387i	−0.996558	+	0.0828945i	$0.973584\pi$
$242$	−21.5560			−1.38567
$243$	−3.47867	+	15.1954i	−0.223157	+	0.974783i
$244$	13.5079			0.864756
$245$	12.9325	−	22.3998i	0.826229	−	1.43107i
$246$	0.980505	−	21.7693i	0.0625147	−	1.38796i
$247$	−1.00666	−	1.74359i	−0.0640523	−	0.110942i
$248$	2.44538	+	4.23552i	0.155282	+	0.268956i
$249$	−5.89065	−	3.76417i	−0.373305	−	0.238545i
$250$	12.0970	−	20.9527i	0.765084	−	1.32516i
$251$	20.2883			1.28058			0.640292	−	0.768131i	$-0.278813\pi$
$251$	20.2883			1.28058			0.640292	+	0.768131i	$0.278813\pi$
$252$	0.308432	+	0.0278405i	0.0194294	+	0.00175379i
$253$	30.2043			1.89893
$254$	5.05440	−	8.75448i	0.317141	−	0.549305i
$255$	25.6827	−	13.3246i	1.60831	−	0.834421i
$256$	−10.1144	−	17.5187i	−0.632151	−	1.09492i
$257$	−13.4531	−	23.3015i	−0.839182	−	1.45351i	−0.890580	−	0.454827i	$-0.849701\pi$
$257$	−13.4531	−	23.3015i	−0.839182	−	1.45351i	0.0513980	−	0.998678i	$-0.483632\pi$
$258$	−2.72905	+	1.41588i	−0.169903	+	0.0881489i
$259$	−0.425370	+	0.736762i	−0.0264312	+	0.0457802i
$260$	18.7491			1.16277
$261$	8.32843	−	11.8248i	0.515517	−	0.731935i
$262$	0.746970			0.0461480
$263$	−9.87604	+	17.1058i	−0.608983	+	1.05479i	0.382426	+	0.923986i	$0.375089\pi$
$263$	−9.87604	+	17.1058i	−0.608983	+	1.05479i	−0.991408	+	0.130803i	$0.958245\pi$
$264$	10.5838	+	6.76313i	0.651387	+	0.416242i
$265$	−15.1350	−	26.2146i	−0.929735	−	1.61035i
$266$	−0.0363939	−	0.0630361i	−0.00223145	−	0.00386499i
$267$	−0.659656	+	14.6457i	−0.0403703	+	0.896304i
$268$	3.57933	−	6.19957i	0.218642	−	0.378699i
$269$	12.3187			0.751085			0.375542	−	0.926805i	$-0.377456\pi$
$269$	12.3187			0.751085			0.375542	+	0.926805i	$0.377456\pi$
$270$	−4.59327	+	33.8093i	−0.279537	+	2.05757i
$271$	10.3245			0.627168			0.313584	−	0.949560i	$-0.398470\pi$
$271$	10.3245			0.627168			0.313584	+	0.949560i	$0.398470\pi$
$272$	11.2379	−	19.4646i	0.681397	−	1.18021i
$273$	0.0307882	−	0.683562i	0.00186339	−	0.0413711i
$274$	−11.5958	−	20.0845i	−0.700526	−	1.21335i
$275$	20.8898	+	36.1822i	1.25970	+	2.18187i
$276$	10.5454	+	6.73860i	0.634759	+	0.405616i
$277$	−10.6063	+	18.3706i	−0.637269	+	1.10378i	0.348760	+	0.937212i	$0.386603\pi$
$277$	−10.6063	+	18.3706i	−0.637269	+	1.10378i	−0.986029	+	0.166571i	$0.946731\pi$
$278$	−13.1751			−0.790189
$279$	−4.08937	−	8.83312i	−0.244824	−	0.528825i
$280$	−0.500180			−0.0298914
$281$	−2.75338	+	4.76900i	−0.164253	+	0.284495i	−0.936390	−	0.350962i	$-0.885855\pi$
$281$	−2.75338	+	4.76900i	−0.164253	+	0.284495i	0.772137	+	0.635456i	$0.219188\pi$
$282$	−10.8508	+	5.62958i	−0.646155	+	0.335237i
$283$	4.75839	+	8.24177i	0.282857	+	0.489922i	0.972087	−	0.234620i	$-0.0753845\pi$
$283$	4.75839	+	8.24177i	0.282857	+	0.489922i	−0.689230	+	0.724542i	$0.742051\pi$
$284$	−7.99634	−	13.8501i	−0.474495	−	0.821850i
$285$	2.59996	−	1.34891i	0.154008	−	0.0799023i
$286$	−18.8045	+	32.5703i	−1.11193	+	1.92592i
$287$	−0.635781			−0.0375290
$288$	7.33553	+	15.8449i	0.432251	+	0.933670i
$289$	3.39152			0.199501
$290$	15.8286	−	27.4160i	0.929490	−	1.60992i
$291$	0.991226	+	0.633401i	0.0581067	+	0.0371307i
$292$	−6.47058	−	11.2074i	−0.378662	−	0.655862i
$293$	−3.30265	−	5.72035i	−0.192943	−	0.334187i	0.753281	−	0.657698i	$-0.228470\pi$
$293$	−3.30265	−	5.72035i	−0.192943	−	0.334187i	−0.946224	+	0.323512i	$0.895136\pi$
$294$	−0.967245	+	21.4749i	−0.0564109	+	1.25244i
$295$	−18.1019	+	31.3534i	−1.05393	+	1.82547i
$296$	−14.2961			−0.830941
$297$	−19.7690	−	15.2994i	−1.14711	−	0.887763i
$298$	4.57040			0.264756
$299$	13.8256	−	23.9466i	0.799553	−	1.38487i
$300$	−0.778893	+	17.2930i	−0.0449694	+	0.998414i
$301$	0.0448503	+	0.0776831i	0.00258513	+	0.00447758i
$302$	16.0852	+	27.8604i	0.925599	+	1.60318i
$303$	−5.30006	−	3.38678i	−0.304480	−	0.194565i
$304$	1.13766	−	1.97048i	0.0652491	−	0.113015i
$305$	43.4209			2.48627
$306$	−13.8469	+	19.6599i	−0.791573	+	1.12388i
$307$	9.30227			0.530908			0.265454	−	0.964123i	$-0.414478\pi$
$307$	9.30227			0.530908			0.265454	+	0.964123i	$0.414478\pi$
$308$	−0.248307	+	0.430080i	−0.0141486	+	0.0245061i
$309$	−8.39364	+	4.35477i	−0.477497	+	0.247734i
$310$	−10.6527	−	18.4509i	−0.605030	−	1.04794i
$311$	−11.3860	−	19.7211i	−0.645641	−	1.11828i	−0.984153	−	0.177321i	$-0.943257\pi$
$311$	−11.3860	−	19.7211i	−0.645641	−	1.11828i	0.338512	−	0.940962i	$-0.390076\pi$
$312$	10.2065	−	5.29532i	0.577830	−	0.299789i
$313$	−4.81844	+	8.34578i	−0.272354	+	0.471731i	−0.969464	−	0.245233i	$-0.921136\pi$
$313$	−4.81844	+	8.34578i	−0.272354	+	0.471731i	0.697110	+	0.716964i	$0.254469\pi$
$314$	−11.9048			−0.671825
$315$	0.991448	+	0.0894928i	0.0558618	+	0.00504235i
$316$	−10.6953			−0.601656
$317$	16.5490	−	28.6637i	0.929485	−	1.60992i	0.145302	−	0.989387i	$-0.453585\pi$
$317$	16.5490	−	28.6637i	0.929485	−	1.60992i	0.784184	−	0.620529i	$-0.213082\pi$
$318$	21.1991	+	13.5464i	1.18878	+	0.759643i
$319$	11.5967	+	20.0861i	0.649292	+	1.12461i
$320$	0.696612	+	1.20657i	0.0389418	+	0.0674491i
$321$	0.159535	−	3.54202i	0.00890439	−	0.197696i
$322$	0.499836	−	0.865742i	0.0278548	−	0.0482459i
$323$	2.06432			0.114862
$324$	−3.48874	−	9.75205i	−0.193819	−	0.541781i
$325$	38.2480			2.12162
$326$	1.16926	−	2.02522i	0.0647594	−	0.112167i
$327$	0.137080	−	3.04346i	0.00758053	−	0.168304i
$328$	−5.34192	−	9.25247i	−0.294958	−	0.510882i
$329$	0.178326	+	0.308870i	0.00983145	+	0.0170286i
$330$	−46.1055	−	29.4618i	−2.53802	−	1.62182i
$331$	−6.08451	+	10.5387i	−0.334435	+	0.579258i	−0.983376	−	0.181580i	$-0.941879\pi$
$331$	−6.08451	+	10.5387i	−0.334435	+	0.579258i	0.648941	+	0.760839i	$0.275212\pi$
$332$	4.64472			0.254912
$333$	28.3374	+	2.55787i	1.55288	+	0.140170i
$334$	−42.2437			−2.31147
$335$	11.5057	−	19.9284i	0.628622	−	1.08880i
$336$	0.686414	−	0.356124i	0.0374470	−	0.0194282i
$337$	1.84427	+	3.19438i	0.100464	+	0.174009i	0.911876	−	0.410466i	$-0.134634\pi$
$337$	1.84427	+	3.19438i	0.100464	+	0.174009i	−0.811412	+	0.584475i	$0.801301\pi$
$338$	5.67707	+	9.83298i	0.308792	+	0.534844i
$339$	−20.6345	+	10.7056i	−1.12071	+	0.581447i
$340$	−9.61201	+	16.6485i	−0.521284	+	0.902891i
$341$	15.6092			0.845283
$342$	−1.40178	+	1.99025i	−0.0757994	+	0.107621i
$343$	1.25509			0.0677684
$344$	−0.753677	+	1.30541i	−0.0406355	+	0.0703828i
$345$	33.8980	+	21.6611i	1.82501	+	1.16619i
$346$	−3.95863	−	6.85655i	−0.212817	−	0.368610i
$347$	10.9502	+	18.9663i	0.587837	+	1.01816i	0.994515	+	0.104593i	$0.0333538\pi$
$347$	10.9502	+	18.9663i	0.587837	+	1.01816i	−0.406678	+	0.913572i	$0.633313\pi$
$348$	−0.432393	+	9.60002i	−0.0231787	+	0.514615i
$349$	3.95348	−	6.84762i	0.211625	−	0.366545i	−0.740598	−	0.671948i	$-0.765458\pi$
$349$	3.95348	−	6.84762i	0.211625	−	0.366545i	0.952223	+	0.305403i	$0.0987912\pi$
$350$	1.38278			0.0739128
$351$	−21.1786	+	8.67014i	−1.13043	+	0.462778i
$352$	−27.9998			−1.49239
$353$	4.71820	−	8.17216i	0.251124	−	0.434960i	−0.712711	−	0.701458i	$-0.752533\pi$
$353$	4.71820	−	8.17216i	0.251124	−	0.434960i	0.963836	+	0.266497i	$0.0858663\pi$
$354$	1.35387	−	30.0587i	0.0719574	−	1.59760i
$355$	−25.7041	−	44.5208i	−1.36423	−	2.36292i
$356$	−4.87040	−	8.43579i	−0.258131	−	0.447096i
$357$	0.591192	+	0.377777i	0.0312892	+	0.0199941i
$358$	−12.4383	+	21.5438i	−0.657384	+	1.13862i
$359$	−20.4163			−1.07753			−0.538765	−	0.842456i	$-0.681109\pi$
$359$	−20.4163			−1.07753			−0.538765	+	0.842456i	$0.681109\pi$
$360$	7.02789	+	15.1804i	0.370402	+	0.800077i
$361$	−18.7910			−0.989001
$362$	−20.1174	+	34.8444i	−1.05735	+	1.83138i
$363$	18.6706	−	9.68662i	0.979950	−	0.508416i
$364$	0.227317	+	0.393725i	0.0119147	+	0.0206368i
$365$	−20.7996	−	36.0259i	−1.08870	−	1.88568i
$366$	−32.0329	+	16.6192i	−1.67438	+	0.868701i
$367$	−2.01465	+	3.48947i	−0.105164	+	0.182149i	−0.913805	−	0.406153i	$-0.866870\pi$
$367$	−2.01465	+	3.48947i	−0.105164	+	0.182149i	0.808641	+	0.588302i	$0.200203\pi$
$368$	31.2493			1.62898
$369$	8.93320	+	19.2959i	0.465044	+	1.00450i
$370$	62.2769			3.23762
$371$	0.366997	−	0.635658i	0.0190536	−	0.0330017i
$372$	5.44972	+	3.48241i	0.282555	+	0.180555i
$373$	−4.64427	−	8.04412i	−0.240471	−	0.416509i	0.720377	−	0.693582i	$-0.243969\pi$
$373$	−4.64427	−	8.04412i	−0.240471	−	0.416509i	−0.960849	+	0.277074i	$0.910635\pi$
$374$	−19.2808	−	33.3952i	−0.996984	−	1.72683i
$375$	−1.06224	+	23.5840i	−0.0548541	+	1.21787i
$376$	−2.99664	+	5.19033i	−0.154540	+	0.267671i
$377$	21.2329			1.09355
$378$	−0.765673	+	0.313452i	−0.0393820	+	0.0161222i
$379$	29.2337			1.50164			0.750818	−	0.660509i	$-0.229660\pi$
$379$	29.2337			1.50164			0.750818	+	0.660509i	$0.229660\pi$
$380$	−0.973063	+	1.68539i	−0.0499171	+	0.0864589i
$381$	−0.443829	+	9.85392i	−0.0227380	+	0.504832i
$382$	3.42388	+	5.93034i	0.175181	+	0.303422i
$383$	−6.92866	−	12.0008i	−0.354038	−	0.613212i	0.632915	−	0.774221i	$-0.281858\pi$
$383$	−6.92866	−	12.0008i	−0.354038	−	0.613212i	−0.986953	+	0.161010i	$0.948525\pi$
$384$	16.0136	+	10.2328i	0.817188	+	0.522190i
$385$	−0.798176	+	1.38248i	−0.0406788	+	0.0704578i
$386$	24.9396			1.26939
$387$	1.72749	−	2.45271i	0.0878133	−	0.124678i
$388$	−0.781572			−0.0396783
$389$	−5.47168	+	9.47723i	−0.277425	+	0.480514i	−0.970744	−	0.240116i	$-0.922814\pi$
$389$	−5.47168	+	9.47723i	−0.277425	+	0.480514i	0.693319	+	0.720631i	$0.256148\pi$
$390$	−44.4619	+	23.0677i	−2.25142	+	1.16808i
$391$	14.1757	+	24.5531i	0.716898	+	1.24170i
$392$	5.26967	+	9.12734i	0.266159	+	0.461000i
$393$	−0.646982	+	0.335666i	−0.0326359	+	0.0169321i
$394$	1.58677	−	2.74836i	0.0799402	−	0.138460i
$395$	−34.3797			−1.72983
$396$	16.5418	+	1.49314i	0.831254	+	0.0750330i
$397$	−32.9079			−1.65160			−0.825799	−	0.563964i	$-0.809276\pi$
$397$	−32.9079			−1.65160			−0.825799	+	0.563964i	$0.809276\pi$
$398$	−15.5716	+	26.9708i	−0.780535	+	1.35193i
$399$	0.0598488	+	0.0382439i	0.00299619	+	0.00191459i
$400$	21.6126	+	37.4341i	1.08063	+	1.87170i
$401$	6.40291	+	11.0902i	0.319746	+	0.553817i	0.980435	−	0.196843i	$-0.0630690\pi$
$401$	6.40291	+	11.0902i	0.319746	+	0.553817i	−0.660689	+	0.750660i	$0.729736\pi$
$402$	−0.860528	+	19.1055i	−0.0429192	+	0.952896i
$403$	7.14485	−	12.3752i	0.355910	−	0.616455i
$404$	4.17904			0.207915
$405$	−11.2145	−	31.3478i	−0.557252	−	1.55768i
$406$	0.767634			0.0380970
$407$	−22.8133	+	39.5139i	−1.13082	+	1.95863i
$408$	−0.530477	+	11.7777i	−0.0262625	+	0.583083i
$409$	10.4185	+	18.0453i	0.515160	+	0.892283i	0.999845	+	0.0175947i	$0.00560085\pi$
$409$	10.4185	+	18.0453i	0.515160	+	0.892283i	−0.484685	+	0.874689i	$0.661066\pi$
$410$	23.2706	+	40.3059i	1.14925	+	1.99057i
$411$	19.0689	+	12.1852i	0.940601	+	0.601052i
$412$	3.14141	−	5.44108i	0.154766	−	0.268063i
$413$	−0.877879			−0.0431976
$414$	−33.2982	−	3.00566i	−1.63652	−	0.147720i
$415$	14.9303			0.732902
$416$	−12.8165	+	22.1988i	−0.628379	+	1.08838i
$417$	11.4115	−	5.92049i	0.558823	−	0.289928i
$418$	−1.95187	−	3.38074i	−0.0954690	−	0.165357i
$419$	−9.12325	−	15.8019i	−0.445700	−	0.771975i	0.552401	−	0.833579i	$-0.313712\pi$
$419$	−9.12325	−	15.8019i	−0.445700	−	0.771975i	−0.998101	+	0.0616036i	$0.980379\pi$
$420$	−0.587105	+	0.304600i	−0.0286478	+	0.0148630i
$421$	−10.3176	+	17.8706i	−0.502849	+	0.870960i	0.497146	+	0.867667i	$0.334381\pi$
$421$	−10.3176	+	17.8706i	−0.502849	+	0.870960i	−0.999995	+	0.00329287i	$0.998952\pi$
$422$	19.6214			0.955154
$423$	6.86856	−	9.75204i	0.333961	−	0.474160i
$424$	12.3342			0.599003
$425$	−19.6084	+	33.9627i	−0.951145	+	1.64743i
$426$	36.0028	+	23.0061i	1.74434	+	1.11465i
$427$	0.526441	+	0.911823i	0.0254763	+	0.0441262i
$428$	1.17789	+	2.04016i	0.0569354	+	0.0986150i
$429$	1.65123	−	36.6607i	0.0797219	−	1.76999i
$430$	3.28319	−	5.68666i	0.158330	−	0.274235i
$431$	−21.7596			−1.04812			−0.524062	−	0.851680i	$-0.675584\pi$
$431$	−21.7596			−1.04812			−0.524062	+	0.851680i	$0.675584\pi$
$432$	−20.4529	−	15.8288i	−0.984043	−	0.761562i
$433$	28.7635			1.38229			0.691144	−	0.722717i	$-0.257107\pi$
$433$	28.7635			1.38229			0.691144	+	0.722717i	$0.257107\pi$
$434$	0.258308	−	0.447403i	0.0123992	−	0.0214760i
$435$	−1.38992	+	30.8591i	−0.0666414	+	1.47958i
$436$	1.01209	+	1.75300i	0.0484705	+	0.0839534i
$437$	1.43507	+	2.48561i	0.0686486	+	0.118903i
$438$	29.1332	+	18.6164i	1.39204	+	0.889524i
$439$	13.1793	−	22.8273i	0.629015	−	1.08949i	−0.358735	−	0.933439i	$-0.616792\pi$
$439$	13.1793	−	22.8273i	0.629015	−	1.08949i	0.987750	−	0.156046i	$-0.0498749\pi$
$440$	−26.8255			−1.27886
$441$	−8.81239	−	19.0349i	−0.419637	−	0.906425i
$442$	−35.3019			−1.67914
$443$	7.54201	−	13.0632i	0.358332	−	0.620649i	−0.629350	−	0.777122i	$-0.716679\pi$
$443$	7.54201	−	13.0632i	0.358332	−	0.620649i	0.987682	+	0.156473i	$0.0500123\pi$
$444$	−16.7805	+	8.70604i	−0.796369	+	0.413170i
$445$	−15.6558	−	27.1167i	−0.742157	−	1.28545i
$446$	−2.45183	−	4.24669i	−0.116097	−	0.201087i
$447$	−3.95862	+	2.05380i	−0.187236	+	0.0971415i
$448$	−0.0168916	+	0.0292572i	−0.000798055	+	0.00138227i
$449$	−29.9757			−1.41464			−0.707320	−	0.706893i	$-0.750096\pi$
$449$	−29.9757			−1.41464			−0.707320	+	0.706893i	$0.750096\pi$
$450$	−19.4291	−	41.9673i	−0.915897	−	1.97836i
$451$	−34.0981			−1.60562
$452$	7.72269	−	13.3761i	0.363245	−	0.629159i
$453$	−26.4517	−	16.9028i	−1.24281	−	0.794164i
$454$	8.79914	+	15.2406i	0.412964	+	0.715275i
$455$	0.730706	+	1.26562i	0.0342560	+	0.0593332i
$456$	−0.0537024	+	1.19230i	−0.00251484	+	0.0558348i
$457$	10.6554	−	18.4557i	0.498439	−	0.863322i	−0.501559	−	0.865123i	$-0.667240\pi$
$457$	10.6554	−	18.4557i	0.498439	−	0.863322i	0.999998	+	0.00180135i	$0.000573387\pi$
$458$	−9.08043			−0.424301
$459$	3.15879	−	23.2507i	0.147439	−	1.08525i
$460$	−26.7282			−1.24621
$461$	−4.38481	+	7.59472i	−0.204221	+	0.353721i	−0.949884	−	0.312602i	$-0.898800\pi$
$461$	−4.38481	+	7.59472i	−0.204221	+	0.353721i	0.745663	+	0.666323i	$0.232133\pi$
$462$	0.0596969	−	1.32540i	0.00277735	−	0.0616630i
$463$	−15.7534	−	27.2856i	−0.732121	−	1.26807i	−0.955975	−	0.293448i	$-0.905197\pi$
$463$	−15.7534	−	27.2856i	−0.732121	−	1.26807i	0.223854	−	0.974623i	$-0.428136\pi$
$464$	11.9980	+	20.7811i	0.556991	+	0.964737i
$465$	17.5180	+	11.1941i	0.812378	+	0.519116i
$466$	13.2774	−	22.9971i	0.615064	−	1.06532i
$467$	19.0342			0.880796			0.440398	−	0.897803i	$-0.354837\pi$
$467$	19.0342			0.880796			0.440398	+	0.897803i	$0.354837\pi$
$468$	8.75552	−	12.4312i	0.404724	−	0.574631i
$469$	0.557985			0.0257654
$470$	13.0541	−	22.6103i	0.602139	−	1.04294i
$471$	10.3112	−	5.34964i	0.475116	−	0.246499i
$472$	−7.37606	−	12.7757i	−0.339510	−	0.588049i
$473$	2.40540	+	4.16628i	0.110601	+	0.191566i
$474$	25.3629	−	13.1587i	1.16496	−	0.604401i
$475$	−1.98503	+	3.43818i	−0.0910796	+	0.157755i
$476$	−0.466149			−0.0213659
$477$	−24.4487	−	2.20686i	−1.11943	−	0.101045i
$478$	21.1579			0.967741
$479$	−18.1095	+	31.3665i	−0.827443	+	1.43317i	0.0725947	+	0.997362i	$0.476872\pi$
$479$	−18.1095	+	31.3665i	−0.827443	+	1.43317i	−0.900038	+	0.435812i	$0.856461\pi$
$480$	−31.4239	−	20.0801i	−1.43430	−	0.916528i
$481$	20.8849	+	36.1737i	0.952270	+	1.64938i
$482$	15.7089	+	27.2086i	0.715522	+	1.23932i
$483$	−0.0438908	+	0.974467i	−0.00199710	+	0.0443398i
$484$	−6.98765	+	12.1030i	−0.317621	+	0.550135i
$485$	−2.51235			−0.114080
$486$	20.2715	+	18.8338i	0.919534	+	0.854320i
$487$	17.1775			0.778386			0.389193	−	0.921156i	$-0.372754\pi$
$487$	17.1775			0.778386			0.389193	+	0.921156i	$0.372754\pi$
$488$	−8.84645	+	15.3225i	−0.400460	+	0.693617i
$489$	−0.102673	+	2.27956i	−0.00464304	+	0.103085i
$490$	−22.9559	−	39.7608i	−1.03704	−	1.79621i
$491$	−21.2708	−	36.8422i	−0.959940	−	1.66266i	−0.722636	−	0.691228i	$-0.757070\pi$
$491$	−21.2708	−	36.8422i	−0.959940	−	1.66266i	−0.237303	−	0.971436i	$-0.576263\pi$
$492$	−11.9049	−	7.60731i	−0.536713	−	0.342964i
$493$	−10.8853	+	18.8540i	−0.490251	+	0.849140i
$494$	−3.57375			−0.160791
$495$	53.1731	+	4.79966i	2.38995	+	0.215729i
$496$	16.1492			0.725121
$497$	0.623279	−	1.07955i	0.0279579	−	0.0484245i
$498$	−11.0145	+	5.71454i	−0.493573	+	0.256075i
$499$	−4.14753	−	7.18374i	−0.185669	−	0.321588i	0.758133	−	0.652100i	$-0.226112\pi$
$499$	−4.14753	−	7.18374i	−0.185669	−	0.321588i	−0.943802	+	0.330512i	$0.892779\pi$
$500$	−7.84282	−	13.5842i	−0.350741	−	0.607502i
$501$	36.5891	−	18.9831i	1.63468	−	0.848101i
$502$	18.0064	−	31.1880i	0.803664	−	1.39199i
$503$	−25.8405			−1.15217			−0.576085	−	0.817390i	$-0.695420\pi$
$503$	−25.8405			−1.15217			−0.576085	+	0.817390i	$0.695420\pi$
$504$	−0.233575	+	0.331632i	−0.0104043	+	0.0147721i
$505$	13.4334			0.597780
$506$	26.8071	−	46.4313i	1.19172	−	2.06412i
$507$	−9.33580	−	5.96565i	−0.414617	−	0.264944i
$508$	−3.27690	−	5.67576i	−0.145389	−	0.251821i
$509$	12.3424	+	21.3777i	0.547069	+	0.947551i	0.998474	+	0.0552315i	$0.0175897\pi$
$509$	12.3424	+	21.3777i	0.547069	+	0.947551i	−0.451405	+	0.892319i	$0.649077\pi$
$510$	2.31088	−	51.3064i	0.102328	−	2.27189i
$511$	0.504353	−	0.873566i	0.0223113	−	0.0386443i
$512$	−13.9636			−0.617109
$513$	0.319777	−	2.35376i	0.0141185	−	0.103921i
$514$	−47.7599			−2.10660
$515$	10.0980	−	17.4902i	0.444971	−	0.770712i
$516$	−0.0896873	+	1.99125i	−0.00394827	+	0.0876597i
$517$	9.56395	+	16.5653i	0.420622	+	0.728539i
$518$	0.755054	+	1.30779i	0.0331752	+	0.0574611i
$519$	6.50986	+	4.15985i	0.285751	+	0.182597i
$520$	−12.2790	+	21.2678i	−0.538468	+	0.932655i
$521$	−39.1146			−1.71364			−0.856822	−	0.515613i	$-0.827564\pi$
$521$	−39.1146			−1.71364			−0.856822	+	0.515613i	$0.827564\pi$
$522$	−10.7858	−	23.2976i	−0.472083	−	1.01971i
$523$	2.94374			0.128721			0.0643603	−	0.997927i	$-0.479499\pi$
$523$	2.94374			0.128721			0.0643603	+	0.997927i	$0.479499\pi$
$524$	0.242140	−	0.419399i	0.0105779	−	0.0183215i
$525$	−1.19769	+	0.621381i	−0.0522713	+	0.0271193i
$526$	17.5305	+	30.3637i	0.764366	+	1.32392i
$527$	7.32582	+	12.6887i	0.319118	+	0.552728i
$528$	36.8136	−	19.0996i	1.60211	−	0.831201i
$529$	−8.20932	+	14.2190i	−0.356927	+	0.618215i
$530$	−53.7308			−2.33392
$531$	12.3349	+	26.6435i	0.535287	+	1.15623i
$532$	−0.0471902			−0.00204595
$533$	−15.6079	+	27.0336i	−0.676052	+	1.17096i
$534$	21.9286	+	14.0125i	0.948942	+	0.606381i
$535$	3.78630	+	6.55806i	0.163696	+	0.283530i
$536$	4.68826	+	8.12031i	0.202502	+	0.350744i
$537$	1.09221	−	24.2493i	0.0471324	−	1.04644i
$538$	10.9332	−	18.9368i	0.471363	−	0.816424i
$539$	33.6369			1.44885
$540$	17.4938	+	13.5387i	0.752815	+	0.582613i
$541$	−9.17458			−0.394446			−0.197223	−	0.980359i	$-0.563192\pi$
$541$	−9.17458			−0.394446			−0.197223	+	0.980359i	$0.563192\pi$
$542$	9.16325	−	15.8712i	0.393595	−	0.681727i
$543$	1.76652	−	39.2204i	0.0758085	−	1.68311i
$544$	−13.1411	−	22.7610i	−0.563420	−	0.975872i
$545$	3.25336	+	5.63498i	0.139358	+	0.241376i
$546$	−1.02347	−	0.654009i	−0.0438007	−	0.0279890i
$547$	8.91666	−	15.4441i	0.381249	−	0.660343i	−0.609992	−	0.792407i	$-0.708827\pi$
$547$	8.91666	−	15.4441i	0.381249	−	0.660343i	0.991241	+	0.132065i	$0.0421607\pi$
$548$	−15.0357			−0.642292
$549$	20.2768	−	28.7892i	0.865394	−	1.22869i
$550$	74.1610			3.16224
$551$	−1.10197	+	1.90866i	−0.0469454	+	0.0813118i
$552$	−14.5501	+	7.54886i	−0.619294	+	0.321301i
$553$	−0.416825	−	0.721961i	−0.0177252	−	0.0307009i
$554$	18.8267	+	32.6088i	0.799870	+	1.38542i
$555$	−53.9407	+	27.9854i	−2.28965	+	1.18791i
$556$	−4.27087	+	7.39737i	−0.181125	+	0.313718i
$557$	46.8931			1.98693			0.993463	−	0.114154i	$-0.0364159\pi$
$557$	46.8931			1.98693			0.993463	+	0.114154i	$0.0364159\pi$
$558$	−17.2081	−	1.55328i	−0.728475	−	0.0657556i
$559$	4.40415			0.186276
$560$	−0.825792	+	1.43031i	−0.0348961	+	0.0604418i
$561$	31.7067	+	20.2608i	1.33866	+	0.855413i
$562$	4.88740	+	8.46523i	0.206163	+	0.357084i
$563$	−14.2646	−	24.7071i	−0.601183	−	1.04128i	−0.992642	−	0.121084i	$-0.961363\pi$
$563$	−14.2646	−	24.7071i	−0.601183	−	1.04128i	0.391459	−	0.920195i	$-0.371970\pi$
$564$	−0.356599	+	7.91725i	−0.0150155	+	0.333376i
$565$	24.8244	−	42.9972i	1.04437	−	1.80891i
$566$	16.8928			0.710056
$567$	0.522325	−	0.615565i	0.0219356	−	0.0258513i
$568$	20.9475			0.878937
$569$	7.20081	−	12.4722i	0.301874	−	0.522860i	−0.674687	−	0.738104i	$-0.735721\pi$
$569$	7.20081	−	12.4722i	0.301874	−	0.522860i	0.976560	+	0.215244i	$0.0690546\pi$
$570$	0.233940	−	5.19396i	0.00979867	−	0.217551i
$571$	−4.92154	−	8.52435i	−0.205960	−	0.356733i	0.744478	−	0.667647i	$-0.232698\pi$
$571$	−4.92154	−	8.52435i	−0.205960	−	0.356733i	−0.950438	+	0.310914i	$0.899365\pi$
$572$	12.1914	+	21.1162i	0.509749	+	0.882911i
$573$	−5.63048	−	3.59792i	−0.235217	−	0.150305i
$574$	−0.564273	+	0.977349i	−0.0235523	+	0.0407938i
$575$	−54.5252			−2.27386
$576$	1.12529	+	0.101574i	0.0468871	+	0.00423226i
$577$	37.4871			1.56061			0.780304	−	0.625400i	$-0.215064\pi$
$577$	37.4871			1.56061			0.780304	+	0.625400i	$0.215064\pi$
$578$	3.01006	−	5.21358i	0.125202	−	0.216856i
$579$	−21.6012	+	11.2071i	−0.897717	+	0.465752i
$580$	−10.2621	−	17.7745i	−0.426111	−	0.738046i
$581$	0.181018	+	0.313532i	0.00750987	+	0.0130075i
$582$	1.85343	−	0.961593i	0.0768271	−	0.0398593i
$583$	19.6827	−	34.0915i	0.815175	−	1.41192i
$584$	16.9506			0.701419
$585$	28.1444	−	39.9597i	1.16363	−	1.65213i
$586$	−11.7247			−0.484345
$587$	5.83335	−	10.1037i	0.240768	−	0.417023i	−0.720165	−	0.693803i	$-0.755934\pi$
$587$	5.83335	−	10.1037i	0.240768	−	0.417023i	0.960933	+	0.276780i	$0.0892673\pi$
$588$	11.7439	+	7.50443i	0.484309	+	0.309477i
$589$	0.741623	+	1.28453i	0.0305580	+	0.0529281i
$590$	32.1318	+	55.6539i	1.32285	+	2.29124i
$591$	−0.139335	+	3.09352i	−0.00573146	+	0.127250i
$592$	−23.6027	+	40.8810i	−0.970063	+	1.68020i
$593$	−15.7994			−0.648805			−0.324402	−	0.945919i	$-0.605163\pi$
$593$	−15.7994			−0.648805			−0.324402	+	0.945919i	$0.605163\pi$
$594$	−41.0644	+	16.8110i	−1.68489	+	0.689764i
$595$	−1.49843			−0.0614295
$596$	1.48155	−	2.56613i	0.0606868	−	0.105113i
$597$	1.36735	−	30.3580i	0.0559619	−	1.24247i
$598$	−24.5411	−	42.5064i	−1.00356	−	1.73822i
$599$	−9.26903	−	16.0544i	−0.378722	−	0.655967i	0.612154	−	0.790738i	$-0.290303\pi$
$599$	−9.26903	−	16.0544i	−0.378722	−	0.655967i	−0.990877	+	0.134772i	$0.956970\pi$
$600$	−19.1060	−	12.2089i	−0.779999	−	0.498426i
$601$	−20.3049	+	35.1692i	−0.828256	+	1.43458i	0.0711491	+	0.997466i	$0.477333\pi$
$601$	−20.3049	+	35.1692i	−0.828256	+	1.43458i	−0.899405	+	0.437116i	$0.856000\pi$
$602$	0.159223			0.00648946
$603$	−7.84010	−	16.9348i	−0.319274	−	0.689638i
$604$	20.8569			0.848654
$605$	−22.4617	+	38.9047i	−0.913197	+	1.58170i
$606$	−9.91024	+	5.14161i	−0.402576	+	0.208864i
$607$	4.38698	+	7.59846i	0.178062	+	0.308412i	0.941217	−	0.337804i	$-0.109684\pi$
$607$	4.38698	+	7.59846i	0.178062	+	0.308412i	−0.763155	+	0.646216i	$0.776351\pi$
$608$	−1.33033	−	2.30419i	−0.0539519	−	0.0934474i
$609$	−0.664880	+	0.344952i	−0.0269423	+	0.0139782i
$610$	38.5372	−	66.7484i	1.56033	−	2.70256i
$611$	17.5110			0.708420
$612$	6.54974	+	14.1476i	0.264758	+	0.571882i
$613$	−13.3507			−0.539230			−0.269615	−	0.962968i	$-0.586897\pi$
$613$	−13.3507			−0.539230			−0.269615	+	0.962968i	$0.586897\pi$
$614$	8.25601	−	14.2998i	0.333185	−	0.577094i
$615$	−38.2680	−	24.4535i	−1.54311	−	0.986061i
$616$	−0.325236	−	0.563326i	−0.0131041	−	0.0226970i
$617$	14.2483	+	24.6788i	0.573615	+	0.993530i	0.996191	+	0.0872027i	$0.0277928\pi$
$617$	14.2483	+	24.6788i	0.573615	+	0.993530i	−0.422575	+	0.906328i	$0.638874\pi$
$618$	−0.755245	+	16.7680i	−0.0303804	+	0.674509i
$619$	−3.15880	+	5.47120i	−0.126963	+	0.219906i	−0.922498	−	0.386001i	$-0.873856\pi$
$619$	−3.15880	+	5.47120i	−0.126963	+	0.219906i	0.795536	+	0.605907i	$0.207190\pi$
$620$	−13.8128			−0.554734
$621$	30.1917	−	12.3599i	1.21155	−	0.495986i
$622$	−40.4215			−1.62075
$623$	0.379626	−	0.657532i	0.0152094	−	0.0263435i
$624$	1.70836	−	37.9291i	0.0683890	−	1.51838i
$625$	−3.49923	−	6.06085i	−0.139969	−	0.242434i
$626$	8.55298	+	14.8142i	0.341846	+	0.592095i
$627$	3.20980	+	2.05109i	0.128187	+	0.0819125i
$628$	−3.85908	+	6.68413i	−0.153994	+	0.266726i
$629$	−42.8278			−1.70766
$630$	1.01751	−	1.44467i	0.0405385	−	0.0575569i
$631$	−8.72945			−0.347514			−0.173757	−	0.984789i	$-0.555591\pi$
$631$	−8.72945			−0.347514			−0.173757	+	0.984789i	$0.555591\pi$
$632$	7.00443	−	12.1320i	0.278621	−	0.482586i
$633$	−16.9949	+	8.81726i	−0.675487	+	0.350455i
$634$	−29.3754	−	50.8796i	−1.16665	−	2.02069i
$635$	−10.5335	−	18.2446i	−0.418010	−	0.724015i
$636$	14.4778	−	7.51133i	0.574081	−	0.297844i
$637$	15.3968	−	26.6680i	0.610043	−	1.05663i
$638$	41.1696			1.62992
$639$	−41.5218	−	3.74795i	−1.64258	−	0.148267i
$640$	−40.5877			−1.60437
$641$	−12.9501	+	22.4303i	−0.511499	+	0.885943i	0.488412	+	0.872613i	$0.337576\pi$
$641$	−12.9501	+	22.4303i	−0.511499	+	0.885943i	−0.999911	+	0.0133295i	$0.995757\pi$
$642$	−5.30334	−	3.38888i	−0.209306	−	0.133748i
$643$	12.5461	+	21.7305i	0.494771	+	0.856969i	0.999982	−	0.00602722i	$-0.00191854\pi$
$643$	12.5461	+	21.7305i	0.494771	+	0.856969i	−0.505211	+	0.862996i	$0.668585\pi$
$644$	−0.324057	−	0.561283i	−0.0127696	−	0.0221176i
$645$	−0.288298	+	6.40082i	−0.0113517	+	0.252032i
$646$	1.83214	−	3.17335i	0.0720844	−	0.124854i
$647$	39.8334			1.56601			0.783006	−	0.622014i	$-0.213685\pi$
$647$	39.8334			1.56601			0.783006	+	0.622014i	$0.213685\pi$
$648$	13.3469	+	2.42930i	0.524316	+	0.0954320i
$649$	−47.0822			−1.84814
$650$	33.9461	−	58.7963i	1.33147	−	2.30618i
$651$	−0.0226821	+	0.503591i	−0.000888983	+	0.0197373i
$652$	−0.758062	−	1.31300i	−0.0296880	−	0.0514211i
$653$	14.1805	+	24.5614i	0.554926	+	0.961160i	0.997909	+	0.0646301i	$0.0205867\pi$
$653$	14.1805	+	24.5614i	0.554926	+	0.961160i	−0.442983	+	0.896530i	$0.646080\pi$
$654$	−4.55686	−	2.91187i	−0.178187	−	0.113863i
$655$	0.778354	−	1.34815i	0.0304128	−	0.0526765i
$656$	−35.2778			−1.37737
$657$	−33.5991	−	3.03282i	−1.31083	−	0.118322i
$658$	0.633077			0.0246799
$659$	7.37678	−	12.7769i	0.287358	−	0.497719i	−0.685820	−	0.727771i	$-0.740556\pi$
$659$	7.37678	−	12.7769i	0.287358	−	0.497719i	0.973178	+	0.230052i	$0.0738896\pi$
$660$	−31.4875	+	16.3363i	−1.22565	+	0.635888i
$661$	17.2080	+	29.8051i	0.669312	+	1.15928i	0.978097	+	0.208150i	$0.0667443\pi$
$661$	17.2080	+	29.8051i	0.669312	+	1.15928i	−0.308785	+	0.951132i	$0.599922\pi$
$662$	10.8003	+	18.7067i	0.419767	+	0.727057i
$663$	30.5764	−	15.8636i	1.18749	−	0.616091i
$664$	−3.04186	+	5.26866i	−0.118047	+	0.204464i
$665$	−0.151692			−0.00588236
$666$	29.0823	−	41.2912i	1.12691	−	1.60000i
$667$	−30.2690			−1.17202
$668$	−13.6938	+	23.7184i	−0.529831	+	0.917694i
$669$	4.03197	+	2.57646i	0.155885	+	0.0996117i
$670$	−20.4232	−	35.3740i	−0.789016	−	1.36662i
$671$	28.2340	+	48.9027i	1.08996	+	1.88787i
$672$	0.0406873	−	0.903344i	0.00156955	−	0.0348472i
$673$	−0.242517	+	0.420052i	−0.00934835	+	0.0161918i	−0.870662	−	0.491882i	$-0.836309\pi$
$673$	−0.242517	+	0.420052i	−0.00934835	+	0.0161918i	0.861313	+	0.508074i	$0.169642\pi$
$674$	6.54737			0.252195
$675$	35.6872	+	27.6187i	1.37360	+	1.06305i
$676$	7.36118			0.283122
$677$	−7.60798	+	13.1774i	−0.292398	+	0.506449i	−0.974376	−	0.224924i	$-0.927787\pi$
$677$	−7.60798	+	13.1774i	−0.292398	+	0.506449i	0.681978	+	0.731373i	$0.261120\pi$
$678$	−1.85666	+	41.2217i	−0.0713046	+	1.58311i
$679$	−0.0304600	−	0.0527583i	−0.00116895	−	0.00202468i
$680$	−12.5900	−	21.8065i	−0.482804	−	0.836240i
$681$	−14.4699	−	9.24641i	−0.554490	−	0.354323i
$682$	13.8535	−	23.9950i	0.530479	−	0.918817i
$683$	15.8107			0.604978			0.302489	−	0.953153i	$-0.402182\pi$
$683$	15.8107			0.604978			0.302489	+	0.953153i	$0.402182\pi$
$684$	0.663057	+	1.43222i	0.0253526	+	0.0547622i
$685$	−48.3318			−1.84666
$686$	1.11392	−	1.92937i	0.0425298	−	0.0736638i
$687$	7.86494	−	4.08047i	0.300066	−	0.155680i
$688$	2.48863	+	4.31043i	0.0948780	+	0.164334i
$689$	−18.0189	−	31.2097i	−0.686467	−	1.18899i
$690$	63.3837	−	32.8846i	2.41298	−	1.25189i
$691$	−10.5608	+	18.2918i	−0.401750	+	0.695852i	−0.993937	−	0.109949i	$-0.964931\pi$
$691$	−10.5608	+	18.2918i	−0.401750	+	0.695852i	0.592187	+	0.805801i	$0.298265\pi$
$692$	−5.13296			−0.195126
$693$	0.543887	+	1.17481i	0.0206606	+	0.0446272i
$694$	38.8744			1.47565
$695$	−13.7286	+	23.7787i	−0.520757	+	0.901977i
$696$	−10.6065	−	6.77761i	−0.402037	−	0.256905i
$697$	−16.0032	−	27.7184i	−0.606164	−	1.04991i
$698$	−7.01763	−	12.1549i	−0.265621	−	0.460069i
$699$	−1.16589	+	25.8853i	−0.0440981	+	0.979070i
$700$	0.448246	−	0.776385i	0.0169421	−	0.0293446i
$701$	−40.9055			−1.54498			−0.772491	−	0.635026i	$-0.780989\pi$
$701$	−40.9055			−1.54498			−0.772491	+	0.635026i	$0.780989\pi$
$702$	−5.46850	+	40.2516i	−0.206395	+	1.51920i
$703$	−4.33563			−0.163522
$704$	−0.905928	+	1.56911i	−0.0341435	+	0.0591382i
$705$	−1.14628	+	25.4498i	−0.0431715	+	0.958497i
$706$	−8.37505	−	14.5060i	−0.315199	−	0.545941i
$707$	0.162869	+	0.282097i	0.00612532	+	0.0106094i
$708$	−16.4381	−	10.5041i	−0.617782	−	0.394767i
$709$	−16.0136	+	27.7364i	−0.601404	+	1.04166i	0.391205	+	0.920303i	$0.372058\pi$
$709$	−16.0136	+	27.7364i	−0.601404	+	1.04166i	−0.992609	+	0.121358i	$0.961275\pi$
$710$	−91.2522			−3.42463
$711$	−16.0547	+	22.7947i	−0.602100	+	0.854867i
$712$	12.7587			0.478152
$713$	−10.1855	+	17.6418i	−0.381450	+	0.660691i
$714$	1.10543	−	0.573518i	0.0413698	−	0.0214634i
$715$	39.1891	+	67.8774i	1.46559	+	2.53847i
$716$	8.06406	+	13.9674i	0.301368	+	0.521985i
$717$	−18.3258	+	9.50774i	−0.684388	+	0.355073i
$718$	−18.1200	+	31.3847i	−0.676232	+	1.17127i
$719$	−9.63404			−0.359289			−0.179644	−	0.983732i	$-0.557495\pi$
$719$	−9.63404			−0.359289			−0.179644	+	0.983732i	$0.557495\pi$
$720$	55.0128	+	4.96572i	2.05021	+	0.185061i
$721$	0.489718			0.0182380
$722$	−16.6775	+	28.8863i	−0.620673	+	1.07504i
$723$	−25.8329	−	16.5074i	−0.960736	−	0.613918i
$724$	13.0426	+	22.5905i	0.484726	+	0.839570i
$725$	−20.9346	−	36.2597i	−0.777490	−	1.34665i
$726$	1.67994	−	37.2983i	0.0623486	−	1.38427i
$727$	5.99536	−	10.3843i	0.222356	−	0.385131i	−0.733167	−	0.680048i	$-0.761959\pi$
$727$	5.99536	−	10.3843i	0.222356	−	0.385131i	0.955523	+	0.294917i	$0.0952920\pi$
$728$	−0.595488			−0.0220702
$729$	−26.0214	−	7.20337i	−0.963754	−	0.266792i
$730$	−73.8406			−2.73296
$731$	−2.25785	+	3.91071i	−0.0835095	+	0.144643i
$732$	−1.05273	+	23.3727i	−0.0389099	+	0.863880i
$733$	−0.0282171	−	0.0488735i	−0.00104222	−	0.00180518i	0.865504	−	0.500902i	$-0.166998\pi$
$733$	−0.0282171	−	0.0488735i	−0.00104222	−	0.00180518i	−0.866546	+	0.499097i	$0.833665\pi$
$734$	3.57610	+	6.19399i	0.131996	+	0.228624i
$735$	37.7504	+	24.1228i	1.39245	+	0.889784i
$736$	18.2708	−	31.6460i	0.673471	−	1.16649i
$737$	29.9257			1.10233
$738$	37.5909	+	3.39313i	1.38374	+	0.124903i
$739$	−6.30302			−0.231860			−0.115930	−	0.993257i	$-0.536985\pi$
$739$	−6.30302			−0.231860			−0.115930	+	0.993257i	$0.536985\pi$
$740$	20.1879	−	34.9664i	0.742121	−	1.28539i
$741$	3.09538	−	1.60594i	0.113712	−	0.0589956i
$742$	−0.651440	−	1.12833i	−0.0239151	−	0.0414222i
$743$	−26.3068	−	45.5647i	−0.965103	−	1.67161i	−0.709339	−	0.704868i	$-0.751006\pi$
$743$	−26.3068	−	45.5647i	−0.965103	−	1.67161i	−0.255764	−	0.966739i	$-0.582327\pi$
$744$	−7.51929	+	3.90114i	−0.275671	+	0.143023i
$745$	4.76243	−	8.24876i	0.174482	−	0.302211i
$746$	−16.4877			−0.603656
$747$	6.97221	−	9.89921i	0.255100	−	0.362193i
$748$	−25.0004			−0.914105
$749$	−0.0918112	+	0.159022i	−0.00335471	+	0.00581053i
$750$	35.3116	+	22.5644i	1.28940	+	0.823935i
$751$	1.10626	+	1.91609i	0.0403679	+	0.0699193i	0.885503	−	0.464633i	$-0.153814\pi$
$751$	1.10626	+	1.91609i	0.0403679	+	0.0699193i	−0.845136	+	0.534552i	$0.820480\pi$
$752$	9.89486	+	17.1384i	0.360828	+	0.624973i
$753$	−1.58115	+	35.1047i	−0.0576202	+	1.27929i
$754$	18.8447	−	32.6401i	0.686285	−	1.18868i
$755$	67.0440			2.43998
$756$	−0.0722097	+	0.531509i	−0.00262624	+	0.0193308i
$757$	−43.0907			−1.56616			−0.783079	−	0.621923i	$-0.786352\pi$
$757$	−43.0907			−1.56616			−0.783079	+	0.621923i	$0.786352\pi$
$758$	25.9457	−	44.9393i	0.942391	−	1.63227i
$759$	−2.35394	+	52.2624i	−0.0854426	+	1.89700i
$760$	−1.27453	−	2.20756i	−0.0462322	−	0.0800766i
$761$	20.8486	+	36.1109i	0.755763	+	1.30902i	0.944994	+	0.327087i	$0.106067\pi$
$761$	20.8486	+	36.1109i	0.755763	+	1.30902i	−0.189231	+	0.981933i	$0.560600\pi$
$762$	14.7539	+	9.42789i	0.534479	+	0.341536i
$763$	−0.0788883	+	0.136638i	−0.00285595	+	0.00494665i
$764$	4.43958			0.160618
$765$	21.0540	+	45.4771i	0.761209	+	1.64423i
$766$	−24.5975			−0.888743
$767$	−21.5512	+	37.3277i	−0.778168	+	1.34783i
$768$	31.1008	−	16.1357i	1.12225	−	0.582245i
$769$	−18.3752	−	31.8268i	−0.662627	−	1.14770i	−0.979923	−	0.199377i	$-0.936108\pi$
$769$	−18.3752	−	31.8268i	−0.662627	−	1.14770i	0.317296	−	0.948326i	$-0.397225\pi$
$770$	1.41680	+	2.45398i	0.0510581	+	0.0884352i
$771$	41.3669	−	21.4619i	1.48979	−	0.772931i
$772$	8.08449	−	14.0027i	0.290967	−	0.503970i
$773$	10.3042			0.370617			0.185309	−	0.982680i	$-0.440671\pi$
$773$	10.3042			0.370617			0.185309	+	0.982680i	$0.440671\pi$
$774$	−2.23721	−	4.83241i	−0.0804148	−	0.173697i
$775$	−28.1779			−1.01218
$776$	0.511858	−	0.886564i	0.0183746	−	0.0318258i
$777$	−1.24167	−	0.793435i	−0.0445445	−	0.0284643i
$778$	9.71252	+	16.8226i	0.348211	+	0.603119i
$779$	−1.62007	−	2.80604i	−0.0580450	−	0.100537i
$780$	−1.46119	+	32.4416i	−0.0523192	+	1.16159i
$781$	33.4276	−	57.8982i	1.19613	−	2.07176i
$782$	50.3254			1.79963
$783$	19.8113	+	15.3322i	0.707998	+	0.547928i
$784$	34.8007			1.24288
$785$	−12.4049	+	21.4860i	−0.442751	+	0.766868i
$786$	−0.0582143	+	1.29248i	−0.00207644	+	0.0461012i
$787$	3.37035	+	5.83762i	0.120140	+	0.208089i	0.919823	−	0.392334i	$-0.128332\pi$
$787$	3.37035	+	5.83762i	0.120140	+	0.208089i	−0.799683	+	0.600423i	$0.794999\pi$
$788$	−1.02874	−	1.78183i	−0.0366474	−	0.0634752i
$789$	−28.8284	−	18.4216i	−1.02632	−	0.655826i
$790$	−30.5129	+	52.8499i	−1.08560	+	1.88032i
$791$	1.20390			0.0428057
$792$	−12.5271	+	17.7860i	−0.445129	+	0.631999i
$793$	51.6947			1.83573
$794$	−29.2066	+	50.5873i	−1.03650	+	1.79528i
$795$	46.5385	−	24.1450i	1.65055	−	0.856335i
$796$	10.0955	+	17.4859i	0.357825	+	0.619771i
$797$	18.9731	+	32.8624i	0.672063	+	1.16405i	0.977318	+	0.211776i	$0.0679249\pi$
$797$	18.9731	+	32.8624i	0.672063	+	1.16405i	−0.305255	+	0.952271i	$0.598742\pi$
$798$	0.111907	−	0.0580596i	0.00396148	−	0.00205529i
$799$	−8.97727	+	15.5491i	−0.317593	+	0.550087i
$800$	50.5456			1.78706
$801$	−25.2901	−	2.28280i	−0.893580	−	0.0806588i
$802$	22.7310			0.802660
$803$	27.0494	−	46.8509i	0.954551	−	1.65333i
$804$	10.4482	+	6.67645i	0.368478	+	0.235460i
$805$	−1.04167	−	1.80423i	−0.0367142	−	0.0635908i
$806$	−12.6825	−	21.9667i	−0.446722	−	0.773745i
$807$	−0.960045	+	21.3150i	−0.0337952	+	0.750324i
$808$	−2.73689	+	4.74043i	−0.0962835	+	0.166768i
$809$	−13.5355			−0.475884			−0.237942	−	0.971279i	$-0.576473\pi$
$809$	−13.5355			−0.475884			−0.237942	+	0.971279i	$0.576473\pi$
$810$	−58.1422	−	10.5826i	−2.04291	−	0.371835i
$811$	−21.9654			−0.771309			−0.385654	−	0.922643i	$-0.626024\pi$
$811$	−21.9654			−0.771309			−0.385654	+	0.922643i	$0.626024\pi$
$812$	0.248838	−	0.431001i	0.00873252	−	0.0151252i
$813$	−0.804628	+	17.8644i	−0.0282195	+	0.626533i
$814$	40.4949	+	70.1392i	1.41935	+	2.45838i
$815$	−2.43677	−	4.22062i	−0.0853565	−	0.147842i
$816$	32.8037	+	20.9618i	1.14836	+	0.733811i
$817$	−0.228571	+	0.395897i	−0.00799669	+	0.0138507i
$818$	36.9867			1.29321
$819$	1.18037	+	0.106545i	0.0412453	+	0.00372300i
$820$	30.1739			1.05372
$821$	−4.48947	+	7.77600i	−0.156684	+	0.271384i	−0.933671	−	0.358132i	$-0.883414\pi$
$821$	−4.48947	+	7.77600i	−0.156684	+	0.271384i	0.776987	+	0.629516i	$0.216747\pi$
$822$	35.6558	−	18.4989i	1.24364	−	0.645222i
$823$	−17.8366	−	30.8940i	−0.621746	−	1.07690i	−0.989161	−	0.146838i	$-0.953090\pi$
$823$	−17.8366	−	30.8940i	−0.621746	−	1.07690i	0.367414	−	0.930057i	$-0.380243\pi$
$824$	4.11467	+	7.12682i	0.143341	+	0.248274i
$825$	−64.2340	+	33.3257i	−2.23634	+	1.16025i
$826$	−0.779141	+	1.34951i	−0.0271098	+	0.0469555i
$827$	−14.9924			−0.521337			−0.260668	−	0.965428i	$-0.583943\pi$
$827$	−14.9924			−0.521337			−0.260668	+	0.965428i	$0.583943\pi$
$828$	−12.4816	+	17.7215i	−0.433766	+	0.615865i
$829$	3.42729			0.119035			0.0595174	−	0.998227i	$-0.481044\pi$
$829$	3.42729			0.119035			0.0595174	+	0.998227i	$0.481044\pi$
$830$	13.2511	−	22.9515i	0.459951	−	0.796659i
$831$	−30.9600	−	19.7837i	−1.07399	−	0.686289i
$832$	0.829350	+	1.43648i	0.0287525	+	0.0498008i
$833$	15.7868	+	27.3435i	0.546979	+	0.947396i
$834$	1.02679	−	22.7968i	0.0355547	−	0.789389i
$835$	−44.0186	+	76.2424i	−1.52333	+	2.63848i
$836$	−2.53089			−0.0875328
$837$	15.6026	−	6.38742i	0.539305	−	0.220782i
$838$	−32.3885			−1.11884
$839$	28.0222	−	48.5358i	0.967433	−	1.67564i	0.264502	−	0.964385i	$-0.414792\pi$
$839$	28.0222	−	48.5358i	0.967433	−	1.67564i	0.702931	−	0.711258i	$-0.251874\pi$
$840$	0.0389810	−	0.865459i	0.00134497	−	0.0298612i
$841$	2.87844	+	4.98560i	0.0992565	+	0.171917i
$842$	18.3143	+	31.7213i	0.631152	+	1.09319i
$843$	−8.03720	−	5.13584i	−0.276816	−	0.176888i
$844$	6.36052	−	11.0167i	0.218938	−	0.379212i
$845$	23.6624			0.814010
$846$	−8.89520	−	19.2138i	−0.305823	−	0.660584i
$847$	−1.08931			−0.0374292
$848$	20.3637	−	35.2710i	0.699293	−	1.21121i
$849$	−14.6315	+	7.59111i	−0.502153	+	0.260526i
$850$	34.8059	+	60.2855i	1.19383	+	2.06778i
$851$	−29.7729	−	51.5683i	−1.02060	−	1.76774i
$852$	24.5879	−	12.7566i	0.842368	−	0.437036i
$853$	10.4191	−	18.0464i	0.356744	−	0.617899i	−0.630671	−	0.776050i	$-0.717220\pi$
$853$	10.4191	−	18.0464i	0.356744	−	0.617899i	0.987415	+	0.158152i	$0.0505535\pi$
$854$	1.86892			0.0639532
$855$	2.13138	+	4.60383i	0.0728918	+	0.157448i
$856$	−3.08564			−0.105465
$857$	−11.1473	+	19.3077i	−0.380785	+	0.659539i	−0.991175	−	0.132562i	$-0.957680\pi$
$857$	−11.1473	+	19.3077i	−0.380785	+	0.659539i	0.610389	+	0.792101i	$0.291013\pi$
$858$	−54.8908	−	35.0756i	−1.87394	−	1.19746i
$859$	−15.1810	−	26.2943i	−0.517970	−	0.897151i	−0.999782	−	0.0208763i	$-0.993354\pi$
$859$	−15.1810	−	26.2943i	−0.517970	−	0.897151i	0.481812	−	0.876275i	$-0.339979\pi$
$860$	−2.12858	−	3.68680i	−0.0725839	−	0.125719i
$861$	0.0495490	−	1.10009i	0.00168862	−	0.0374910i
$862$	−19.3122	+	33.4498i	−0.657777	+	1.13930i
$863$	−11.2552			−0.383131			−0.191565	−	0.981480i	$-0.561356\pi$
$863$	−11.2552			−0.383131			−0.191565	+	0.981480i	$0.561356\pi$
$864$	−27.9881	+	11.4578i	−0.952173	+	0.389802i
$865$	−16.4998			−0.561010
$866$	25.5284	−	44.2165i	0.867490	−	1.50254i
$867$	−0.264314	+	5.86833i	−0.00897659	+	0.199299i
$868$	−0.167468	−	0.290063i	−0.00568423	−	0.00984538i
$869$	−22.3550	−	38.7201i	−0.758343	−	1.31349i
$870$	46.2042	+	29.5249i	1.56647	+	1.00099i
$871$	13.6980	−	23.7257i	0.464141	−	0.803915i
$872$	−2.65132			−0.0897849
$873$	−1.17322	+	1.66575i	−0.0397076	+	0.0563772i
$874$	5.09464			0.172329
$875$	0.611313	−	1.05882i	0.0206661	−	0.0357948i
$876$	19.8964	−	10.3226i	0.672236	−	0.348768i
$877$	−1.81204	−	3.13854i	−0.0611881	−	0.105981i	0.833809	−	0.552054i	$-0.186156\pi$
$877$	−1.81204	−	3.13854i	−0.0611881	−	0.105981i	−0.894997	+	0.446073i	$0.852822\pi$
$878$	−23.3940	−	40.5196i	−0.789509	−	1.36747i
$879$	10.1553	−	5.26875i	0.342530	−	0.177710i
$880$	−44.2887	+	76.7103i	−1.49297	+	2.58590i
$881$	−44.6822			−1.50538			−0.752692	−	0.658373i	$-0.771245\pi$
$881$	−44.6822			−1.50538			−0.752692	+	0.658373i	$0.771245\pi$
$882$	−37.0825	−	3.34724i	−1.24863	−	0.112708i
$883$	54.4600			1.83273			0.916363	−	0.400348i	$-0.131111\pi$
$883$	54.4600			1.83273			0.916363	+	0.400348i	$0.131111\pi$
$884$	−11.4436	+	19.8208i	−0.384888	+	0.666646i
$885$	−52.8399	−	33.7651i	−1.77620	−	1.13500i
$886$	−13.3875	−	23.1878i	−0.449761	−	0.779009i
$887$	−3.53223	−	6.11800i	−0.118601	−	0.205422i	0.800613	−	0.599182i	$-0.204507\pi$
$887$	−3.53223	−	6.11800i	−0.118601	−	0.205422i	−0.919213	+	0.393760i	$0.871174\pi$
$888$	1.11415	−	24.7364i	0.0373884	−	0.830100i
$889$	0.255420	−	0.442400i	0.00856650	−	0.0148376i
$890$	−55.5798			−1.86304
$891$	28.0132	−	33.0138i	0.938479	−	1.10600i
$892$	−3.17917			−0.106446
$893$	−0.908806	+	1.57410i	−0.0304120	+	0.0526752i
$894$	−0.356190	+	7.90815i	−0.0119128	+	0.264488i
$895$	25.9218	+	44.8978i	0.866469	+	1.50077i
$896$	−0.492091	−	0.852327i	−0.0164396	−	0.0284742i
$897$	40.3572	+	25.7886i	1.34749	+	0.861055i
$898$	−26.6042	+	46.0799i	−0.887795	+	1.53771i
$899$	−15.6426			−0.521710
$900$	−29.8614	−	2.69543i	−0.995380	−	0.0898477i
$901$	36.9506			1.23100
$902$	−30.2629	+	52.4170i	−1.00765	+	1.74529i
$903$	−0.137910	+	0.0715503i	−0.00458936	+	0.00238104i
$904$	10.1153	+	17.5202i	0.336430	+	0.582715i
$905$	41.9253	+	72.6168i	1.39364	+	2.41386i
$906$	−49.4603	+	25.6609i	−1.64321	+	0.852526i
$907$	14.0197	−	24.2828i	0.465516	−	0.806297i	−0.533709	−	0.845668i	$-0.679202\pi$
$907$	14.0197	−	24.2828i	0.465516	−	0.806297i	0.999225	+	0.0393716i	$0.0125356\pi$
$908$	11.4094			0.378635
$909$	6.27319	−	8.90673i	0.208068	−	0.295417i
$910$	2.59408			0.0859930
$911$	21.5130	−	37.2616i	0.712758	−	1.23453i	−0.251061	−	0.967971i	$-0.580779\pi$
$911$	21.5130	−	37.2616i	0.712758	−	1.23453i	0.963818	−	0.266561i	$-0.0858873\pi$
$912$	3.32085	+	2.12205i	0.109964	+	0.0702682i
$913$	9.70829	+	16.8153i	0.321297	+	0.556504i
$914$	−18.9139	−	32.7599i	−0.625617	−	1.08360i
$915$	−3.38396	+	75.1311i	−0.111870	+	2.48376i
$916$	−2.94354	+	5.09836i	−0.0972572	+	0.168454i
$917$	0.0377475			0.00124653
$918$	−32.9384	−	25.4914i	−1.08713	−	0.841341i
$919$	9.18522			0.302993			0.151496	−	0.988458i	$-0.451591\pi$
$919$	9.18522			0.302993			0.151496	+	0.988458i	$0.451591\pi$
$920$	17.5045	−	30.3188i	0.577108	−	0.999580i
$921$	−0.724963	+	16.0957i	−0.0238883	+	0.530371i
$922$	7.78328	+	13.4810i	0.256329	+	0.443974i
$923$	−30.6019	−	53.0041i	−1.00727	−	1.74465i
$924$	−0.724814	−	0.463162i	−0.0238446	−	0.0152369i
$925$	41.1830	−	71.3310i	1.35409	−	2.34535i
$926$	−55.9261			−1.83785
$927$	−6.88089	−	14.8629i	−0.225998	−	0.488161i
$928$	28.0598			0.921107
$929$	−0.265051	+	0.459082i	−0.00869604	+	0.0150620i	−0.870341	−	0.492450i	$-0.836101\pi$
$929$	−0.265051	+	0.459082i	−0.00869604	+	0.0150620i	0.861645	+	0.507512i	$0.169435\pi$
$930$	32.7558	−	16.9943i	1.07410	−	0.557265i
$931$	1.59816	+	2.76809i	0.0523776	+	0.0907206i
$932$	−8.60808	−	14.9096i	−0.281967	−	0.488381i
$933$	35.0108	−	18.1642i	1.14620	−	0.594670i
$934$	16.8933	−	29.2601i	0.552766	−	0.957419i
$935$	−80.3633			−2.62816
$936$	8.36704	+	18.0730i	0.273485	+	0.590734i
$937$	−36.8282			−1.20313			−0.601563	−	0.798825i	$-0.705455\pi$
$937$	−36.8282			−1.20313			−0.601563	+	0.798825i	$0.705455\pi$
$938$	0.495227	−	0.857758i	0.0161697	−	0.0280068i
$939$	−14.0652	−	8.98775i	−0.458999	−	0.293304i
$940$	−8.46328	−	14.6588i	−0.276042	−	0.478119i
$941$	13.6057	+	23.5658i	0.443535	+	0.768224i	0.997949	−	0.0640165i	$-0.0203910\pi$
$941$	13.6057	+	23.5658i	0.443535	+	0.768224i	−0.554414	+	0.832241i	$0.687058\pi$
$942$	0.927785	−	20.5988i	0.0302289	−	0.671144i
$943$	22.2501	−	38.5384i	0.724564	−	1.25498i
$944$	−48.7112			−1.58542
$945$	−0.232117	+	1.70852i	−0.00755075	+	0.0555783i
$946$	8.53944			0.277641
$947$	1.71551	−	2.97135i	0.0557466	−	0.0965559i	−0.836805	−	0.547500i	$-0.815579\pi$
$947$	1.71551	−	2.97135i	0.0557466	−	0.0965559i	0.892552	+	0.450945i	$0.148913\pi$
$948$	0.833525	−	18.5060i	0.0270716	−	0.601047i
$949$	−24.7629	−	42.8905i	−0.803837	−	1.39229i
$950$	3.52354	+	6.10295i	0.114319	+	0.198006i
$951$	48.3070	+	30.8686i	1.56646	+	1.00098i
$952$	0.305285	−	0.528769i	0.00989435	−	0.0171375i
$953$	27.0518			0.876293			0.438146	−	0.898904i	$-0.355635\pi$
$953$	27.0518			0.876293			0.438146	+	0.898904i	$0.355635\pi$
$954$	−25.0914	+	35.6249i	−0.812363	+	1.15340i
$955$	14.2709			0.461797
$956$	6.85861	−	11.8795i	0.221823	−	0.384209i
$957$	−35.6587	+	18.5004i	−1.15268	+	0.598032i
$958$	32.1453	+	55.6772i	1.03857	+	1.79885i
$959$	−0.585982	−	1.01495i	−0.0189223	−	0.0327744i
$960$	−2.14201	+	1.11131i	−0.0691330	+	0.0358675i
$961$	10.2363	−	17.7298i	0.330203	−	0.571928i
$962$	74.1437			2.39049
$963$	6.11630	+	0.552087i	0.197095	+	0.0177907i
$964$	20.3690			0.656041
$965$	25.9874	−	45.0115i	0.836565	−	1.44897i
$966$	1.45904	+	0.932336i	0.0469437	+	0.0299974i
$967$	10.7214	+	18.5700i	0.344777	+	0.597171i	0.985313	−	0.170757i	$-0.0546212\pi$
$967$	10.7214	+	18.5700i	0.344777	+	0.597171i	−0.640536	+	0.767928i	$0.721288\pi$
$968$	−9.15255	−	15.8527i	−0.294174	−	0.509524i
$969$	−0.160880	+	3.57188i	−0.00516822	+	0.114745i
$970$	−2.22977	+	3.86208i	−0.0715937	+	0.124004i
$971$	−27.1957			−0.872751			−0.436376	−	0.899765i	$-0.643738\pi$
$971$	−27.1957			−0.872751			−0.436376	+	0.899765i	$0.643738\pi$
$972$	17.1458	−	5.27654i	0.549953	−	0.169245i
$973$	−0.665791			−0.0213443
$974$	15.2455	−	26.4059i	0.488496	−	0.846100i
$975$	−2.98082	+	66.1803i	−0.0954625	+	2.11947i
$976$	29.2108	+	50.5947i	0.935016	+	1.61950i
$977$	−9.95284	−	17.2388i	−0.318420	−	0.551519i	0.661739	−	0.749734i	$-0.269819\pi$
$977$	−9.95284	−	17.2388i	−0.318420	−	0.551519i	−0.980158	+	0.198216i	$0.936485\pi$
$978$	3.41311	+	2.18100i	0.109139	+	0.0697407i
$979$	20.3600	−	35.2646i	0.650710	−	1.12706i
$980$	−29.7658			−0.950834
$981$	5.25540	+	0.474377i	0.167792	+	0.0151457i
$982$	−75.5137			−2.40974
$983$	−4.05129	+	7.01704i	−0.129216	+	0.223809i	−0.923373	−	0.383904i	$-0.874579\pi$
$983$	−4.05129	+	7.01704i	−0.129216	+	0.223809i	0.794157	+	0.607713i	$0.207913\pi$
$984$	16.4258	−	8.52202i	0.523636	−	0.271672i
$985$	−3.30687	−	5.72767i	−0.105366	−	0.182499i
$986$	19.3221	+	33.4668i	0.615340	+	1.06580i
$987$	−0.548335	+	0.284486i	−0.0174537	+	0.00905529i
$988$	−1.15848	+	2.00654i	−0.0368561	+	0.0638366i
$989$	−6.27843			−0.199642
$990$	54.5708	−	77.4801i	1.73437	−	2.46248i
$991$	−33.1910			−1.05435			−0.527174	−	0.849757i	$-0.676748\pi$
$991$	−33.1910			−1.05435			−0.527174	+	0.849757i	$0.676748\pi$
$992$	9.44209	−	16.3542i	0.299787	−	0.519246i
$993$	−17.7609	−	11.3493i	−0.563624	−	0.360160i
$994$	−1.10635	−	1.91626i	−0.0350914	−	0.0607801i
$995$	32.4517	+	56.2080i	1.02879	+	1.78191i
$996$	−0.361981	+	8.03674i	−0.0114698	+	0.254654i
$997$	−1.17342	+	2.03242i	−0.0371626	+	0.0643674i	−0.884008	−	0.467471i	$-0.845165\pi$
$997$	−1.17342	+	2.03242i	−0.0371626	+	0.0643674i	0.846846	+	0.531838i	$0.178499\pi$
$998$	−14.7242			−0.466086
$999$	−6.63432	+	48.8328i	−0.209901	+	1.54500i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.f.c.259.16	yes	38
3.2	odd	2		1161.2.f.c.775.4		38
9.2	odd	6		3483.2.a.r.1.16		19
9.4	even	3	inner	387.2.f.c.130.16	✓	38
9.5	odd	6		1161.2.f.c.388.4		38
9.7	even	3		3483.2.a.s.1.4		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.f.c.130.16	✓	38	9.4	even	3	inner
387.2.f.c.259.16	yes	38	1.1	even	1	trivial
1161.2.f.c.388.4		38	9.5	odd	6
1161.2.f.c.775.4		38	3.2	odd	2
3483.2.a.r.1.16		19	9.2	odd	6
3483.2.a.s.1.4		19	9.7	even	3

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.887526 - 1.53724i) q^{2} +(-0.0779340 + 1.73030i) q^{3} +(-0.575406 - 0.996632i) q^{4} +(-1.84963 - 3.20365i) q^{5} +(2.59071 + 1.65549i) q^{6} +(0.0448503 - 0.0776831i) q^{7} +1.50735 q^{8} +(-2.98785 - 0.269698i) q^{9} +O(q^{10})\)	\(q+(0.887526 - 1.53724i) q^{2} +(-0.0779340 + 1.73030i) q^{3} +(-0.575406 - 0.996632i) q^{4} +(-1.84963 - 3.20365i) q^{5} +(2.59071 + 1.65549i) q^{6} +(0.0448503 - 0.0776831i) q^{7} +1.50735 q^{8} +(-2.98785 - 0.269698i) q^{9} -6.56638 q^{10} +(2.40540 - 4.16628i) q^{11} +(1.76931 - 0.917952i) q^{12} +(-2.20207 - 3.81410i) q^{13} +(-0.0796117 - 0.137892i) q^{14} +(5.68742 - 2.95074i) q^{15} +(2.48863 - 4.31043i) q^{16} +4.51570 q^{17} +(-3.06639 + 4.35368i) q^{18} +0.457142 q^{19} +(-2.12858 + 3.68680i) q^{20} +(0.130919 + 0.0836586i) q^{21} +(-4.26972 - 7.39537i) q^{22} +(3.13921 + 5.43728i) q^{23} +(-0.117474 + 2.60817i) q^{24} +(-4.34227 + 7.52103i) q^{25} -7.81759 q^{26} +(0.699512 - 5.14885i) q^{27} -0.103229 q^{28} +(-2.41056 + 4.17521i) q^{29} +(0.511744 - 11.3618i) q^{30} +(1.62230 + 2.80991i) q^{31} +(-2.91009 - 5.04043i) q^{32} +(7.02144 + 4.48676i) q^{33} +(4.00780 - 6.94171i) q^{34} -0.331826 q^{35} +(1.45044 + 3.13298i) q^{36} -9.48421 q^{37} +(0.405726 - 0.702738i) q^{38} +(6.77115 - 3.51299i) q^{39} +(-2.78805 - 4.82904i) q^{40} +(-3.54390 - 6.13822i) q^{41} +(0.244798 - 0.127005i) q^{42} +(-0.500000 + 0.866025i) q^{43} -5.53633 q^{44} +(4.66241 + 10.0709i) q^{45} +11.1445 q^{46} +(-1.98801 + 3.44334i) q^{47} +(7.26437 + 4.64199i) q^{48} +(3.49598 + 6.05521i) q^{49} +(7.70775 + 13.3502i) q^{50} +(-0.351926 + 7.81349i) q^{51} +(-2.53417 + 4.38932i) q^{52} +8.18271 q^{53} +(-7.29419 - 5.64506i) q^{54} -17.7964 q^{55} +(0.0676053 - 0.117096i) q^{56} +(-0.0356269 + 0.790992i) q^{57} +(4.27886 + 7.41121i) q^{58} +(-4.89338 - 8.47559i) q^{59} +(-6.21338 - 3.97040i) q^{60} +(-5.86886 + 10.1652i) q^{61} +5.75934 q^{62} +(-0.154957 + 0.220010i) q^{63} -0.376622 q^{64} +(-8.14605 + 14.1094i) q^{65} +(13.1289 - 6.81153i) q^{66} +(3.11026 + 5.38713i) q^{67} +(-2.59836 - 4.50049i) q^{68} +(-9.65275 + 5.00802i) q^{69} +(-0.294505 + 0.510097i) q^{70} +13.8969 q^{71} +(-4.50375 - 0.406530i) q^{72} +11.2453 q^{73} +(-8.41748 + 14.5795i) q^{74} +(-12.6752 - 8.09955i) q^{75} +(-0.263042 - 0.455603i) q^{76} +(-0.215766 - 0.373718i) q^{77} +(0.609256 - 13.5268i) q^{78} +(4.64684 - 8.04856i) q^{79} -18.4122 q^{80} +(8.85453 + 1.61163i) q^{81} -12.5812 q^{82} +(-2.01802 + 3.49531i) q^{83} +(0.00804502 - 0.178616i) q^{84} +(-8.35237 - 14.4667i) q^{85} +(0.887526 + 1.53724i) q^{86} +(-7.03648 - 4.49637i) q^{87} +(3.62579 - 6.28006i) q^{88} +8.46429 q^{89} +(19.6194 + 1.77094i) q^{90} -0.395055 q^{91} +(3.61264 - 6.25728i) q^{92} +(-4.98841 + 2.58807i) q^{93} +(3.52883 + 6.11211i) q^{94} +(-0.845545 - 1.46453i) q^{95} +(8.94823 - 4.64250i) q^{96} +(0.339574 - 0.588160i) q^{97} +12.4111 q^{98} +(-8.31063 + 11.7995i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 4 q^{2} - 7 q^{3} - 22 q^{4} - 9 q^{5} - 7 q^{7} + 24 q^{8} - 3 q^{9}+O(q^{10}) \) 38 * q - 4 * q^2 - 7 * q^3 - 22 * q^4 - 9 * q^5 - 7 * q^7 + 24 * q^8 - 3 * q^9	\( 38 q - 4 q^{2} - 7 q^{3} - 22 q^{4} - 9 q^{5} - 7 q^{7} + 24 q^{8} - 3 q^{9} - 14 q^{10} - 5 q^{11} + 11 q^{12} + 5 q^{13} - 17 q^{14} - 5 q^{15} - 24 q^{16} + 42 q^{17} - 23 q^{18} - 8 q^{19} - 21 q^{20} + 20 q^{22} - 22 q^{23} - 14 q^{24} - 10 q^{25} + 34 q^{26} - 4 q^{27} - 2 q^{28} - 30 q^{29} + 63 q^{30} + 5 q^{31} - 48 q^{32} - q^{33} + 6 q^{34} + 106 q^{35} - 20 q^{36} - 2 q^{37} - 21 q^{38} + 25 q^{39} - 16 q^{40} - 29 q^{41} - 47 q^{42} - 19 q^{43} + 58 q^{44} - 37 q^{45} - 32 q^{47} + 45 q^{48} + 10 q^{49} + 11 q^{50} - 53 q^{51} - q^{52} + 76 q^{53} - 41 q^{54} + 4 q^{55} - 46 q^{56} + 23 q^{57} - 30 q^{58} - 30 q^{59} - 87 q^{60} + 10 q^{61} + 50 q^{62} + 21 q^{63} + 28 q^{64} - 8 q^{65} + 91 q^{66} - 3 q^{67} - 47 q^{68} - 40 q^{69} - 56 q^{70} + 42 q^{71} + 3 q^{72} + 16 q^{73} - 28 q^{74} + 19 q^{75} + 36 q^{76} - 49 q^{77} - 105 q^{78} - 4 q^{79} + 140 q^{80} + 77 q^{81} - 8 q^{82} - 29 q^{83} + 145 q^{84} + 4 q^{85} - 4 q^{86} - 24 q^{87} + 47 q^{88} + 108 q^{89} - 8 q^{90} + 8 q^{91} - 12 q^{92} - 4 q^{93} + 23 q^{94} - 33 q^{95} - 147 q^{96} + 4 q^{97} + 98 q^{98} + 85 q^{99}+O(q^{100}) \) 38 * q - 4 * q^2 - 7 * q^3 - 22 * q^4 - 9 * q^5 - 7 * q^7 + 24 * q^8 - 3 * q^9 - 14 * q^10 - 5 * q^11 + 11 * q^12 + 5 * q^13 - 17 * q^14 - 5 * q^15 - 24 * q^16 + 42 * q^17 - 23 * q^18 - 8 * q^19 - 21 * q^20 + 20 * q^22 - 22 * q^23 - 14 * q^24 - 10 * q^25 + 34 * q^26 - 4 * q^27 - 2 * q^28 - 30 * q^29 + 63 * q^30 + 5 * q^31 - 48 * q^32 - q^33 + 6 * q^34 + 106 * q^35 - 20 * q^36 - 2 * q^37 - 21 * q^38 + 25 * q^39 - 16 * q^40 - 29 * q^41 - 47 * q^42 - 19 * q^43 + 58 * q^44 - 37 * q^45 - 32 * q^47 + 45 * q^48 + 10 * q^49 + 11 * q^50 - 53 * q^51 - q^52 + 76 * q^53 - 41 * q^54 + 4 * q^55 - 46 * q^56 + 23 * q^57 - 30 * q^58 - 30 * q^59 - 87 * q^60 + 10 * q^61 + 50 * q^62 + 21 * q^63 + 28 * q^64 - 8 * q^65 + 91 * q^66 - 3 * q^67 - 47 * q^68 - 40 * q^69 - 56 * q^70 + 42 * q^71 + 3 * q^72 + 16 * q^73 - 28 * q^74 + 19 * q^75 + 36 * q^76 - 49 * q^77 - 105 * q^78 - 4 * q^79 + 140 * q^80 + 77 * q^81 - 8 * q^82 - 29 * q^83 + 145 * q^84 + 4 * q^85 - 4 * q^86 - 24 * q^87 + 47 * q^88 + 108 * q^89 - 8 * q^90 + 8 * q^91 - 12 * q^92 - 4 * q^93 + 23 * q^94 - 33 * q^95 - 147 * q^96 + 4 * q^97 + 98 * q^98 + 85 * q^99

Introduction

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