LMFDB - Embedded newform 403.2.k.d.66.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			66.3
Character	$\chi$	$=$	403.66
Dual form			403.2.k.d.287.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.599354 - 1.84462i) q^{2} +(-0.251540 + 0.774160i) q^{3} +(-1.42537 + 1.03559i) q^{4} -3.24431 q^{5} +1.57879 q^{6} +(1.80822 - 1.31375i) q^{7} +(-0.373685 - 0.271498i) q^{8} +(1.89100 + 1.37389i) q^{9} +O(q^{10})$	\(q+(-0.599354 - 1.84462i) q^{2} +(-0.251540 + 0.774160i) q^{3} +(-1.42537 + 1.03559i) q^{4} -3.24431 q^{5} +1.57879 q^{6} +(1.80822 - 1.31375i) q^{7} +(-0.373685 - 0.271498i) q^{8} +(1.89100 + 1.37389i) q^{9} +(1.94449 + 5.98453i) q^{10} +(-4.60589 + 3.34638i) q^{11} +(-0.443176 - 1.36395i) q^{12} +(-0.309017 + 0.951057i) q^{13} +(-3.50714 - 2.54809i) q^{14} +(0.816074 - 2.51162i) q^{15} +(-1.36573 + 4.20327i) q^{16} +(0.131298 + 0.0953933i) q^{17} +(1.40093 - 4.31163i) q^{18} +(0.913366 + 2.81105i) q^{19} +(4.62434 - 3.35978i) q^{20} +(0.562214 + 1.73032i) q^{21} +(8.93336 + 6.49046i) q^{22} +(0.262498 + 0.190716i) q^{23} +(0.304180 - 0.221000i) q^{24} +5.52558 q^{25} +1.93955 q^{26} +(-3.51489 + 2.55372i) q^{27} +(-1.21688 + 3.74516i) q^{28} +(2.48786 + 7.65684i) q^{29} -5.12210 q^{30} +(4.25660 + 3.58906i) q^{31} +7.64820 q^{32} +(-1.43207 - 4.40744i) q^{33} +(0.0972707 - 0.299369i) q^{34} +(-5.86645 + 4.26223i) q^{35} -4.11816 q^{36} -6.49744 q^{37} +(4.63790 - 3.36963i) q^{38} +(-0.658540 - 0.478457i) q^{39} +(1.21235 + 0.880826i) q^{40} +(-1.57442 - 4.84556i) q^{41} +(2.85481 - 2.07414i) q^{42} +(-2.06691 - 6.36130i) q^{43} +(3.09962 - 9.53964i) q^{44} +(-6.13500 - 4.45734i) q^{45} +(0.194470 - 0.598516i) q^{46} +(-2.03315 + 6.25741i) q^{47} +(-2.91047 - 2.11458i) q^{48} +(-0.619387 + 1.90628i) q^{49} +(-3.31177 - 10.1926i) q^{50} +(-0.106876 + 0.0776501i) q^{51} +(-0.544442 - 1.67562i) q^{52} +(1.67411 + 1.21631i) q^{53} +(6.81731 + 4.95306i) q^{54} +(14.9430 - 10.8567i) q^{55} -1.03239 q^{56} -2.40595 q^{57} +(12.6329 - 9.17831i) q^{58} +(0.660375 - 2.03243i) q^{59} +(1.43780 + 4.42510i) q^{60} -10.2530 q^{61} +(4.06924 - 10.0029i) q^{62} +5.22431 q^{63} +(-1.85252 - 5.70148i) q^{64} +(1.00255 - 3.08553i) q^{65} +(-7.27175 + 5.28324i) q^{66} -7.78875 q^{67} -0.285936 q^{68} +(-0.213674 + 0.155243i) q^{69} +(11.3783 + 8.26680i) q^{70} +(-3.62555 - 2.63411i) q^{71} +(-0.333630 - 1.02681i) q^{72} +(2.13035 - 1.54779i) q^{73} +(3.89426 + 11.9853i) q^{74} +(-1.38990 + 4.27768i) q^{75} +(-4.21298 - 3.06091i) q^{76} +(-3.93218 + 12.1020i) q^{77} +(-0.487874 + 1.50152i) q^{78} +(-4.86100 - 3.53172i) q^{79} +(4.43084 - 13.6367i) q^{80} +(1.07404 + 3.30556i) q^{81} +(-7.99459 + 5.80841i) q^{82} +(-2.47937 - 7.63070i) q^{83} +(-2.59326 - 1.88411i) q^{84} +(-0.425971 - 0.309486i) q^{85} +(-10.4954 + 7.62534i) q^{86} -6.55341 q^{87} +2.62969 q^{88} +(-13.1566 + 9.55884i) q^{89} +(-4.54506 + 13.9883i) q^{90} +(0.690680 + 2.12570i) q^{91} -0.571660 q^{92} +(-3.84921 + 2.39250i) q^{93} +12.7611 q^{94} +(-2.96325 - 9.11994i) q^{95} +(-1.92383 + 5.92093i) q^{96} +(5.98552 - 4.34873i) q^{97} +3.88759 q^{98} -13.3073 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9}+O(q^{10}) $ 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9} - 19 q^{10} - 9 q^{11} + 15 q^{12} + 12 q^{13} - 25 q^{14} - 30 q^{15} - 21 q^{16} + 11 q^{17} + 17 q^{18} + 36 q^{19} + 30 q^{20} + 11 q^{21} + 15 q^{22} - 7 q^{23} - 20 q^{24} - 16 q^{25} + 8 q^{26} - 5 q^{27} - 9 q^{28} + 12 q^{29} + 18 q^{30} + 22 q^{31} - 76 q^{32} - 49 q^{33} - 26 q^{34} + 8 q^{35} + 2 q^{36} + 64 q^{37} - 27 q^{38} - 3 q^{39} - 24 q^{40} + 46 q^{41} + 20 q^{42} - 28 q^{43} - 23 q^{45} + 34 q^{46} + 5 q^{47} - 20 q^{48} - 11 q^{49} + 9 q^{50} + 59 q^{51} + 17 q^{52} + 23 q^{53} + 41 q^{54} - 10 q^{55} - 60 q^{56} + 24 q^{57} - 37 q^{58} + 71 q^{59} - 72 q^{60} + 22 q^{61} + 43 q^{62} - 106 q^{63} - 52 q^{64} + 2 q^{65} - 21 q^{66} - 56 q^{67} - 104 q^{68} - 12 q^{69} - 32 q^{70} - 36 q^{71} + 147 q^{72} - 12 q^{73} + 10 q^{74} + 34 q^{75} - 49 q^{76} - 30 q^{77} + 5 q^{78} - 70 q^{79} + q^{81} + 130 q^{82} + 11 q^{83} + 77 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} + 96 q^{88} - 40 q^{89} - 48 q^{90} + 10 q^{91} + 112 q^{92} + 50 q^{93} + 78 q^{94} + 41 q^{95} - 75 q^{96} - 47 q^{97} - 46 q^{98} + 46 q^{99}+O(q^{100}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9 - 19 * q^10 - 9 * q^11 + 15 * q^12 + 12 * q^13 - 25 * q^14 - 30 * q^15 - 21 * q^16 + 11 * q^17 + 17 * q^18 + 36 * q^19 + 30 * q^20 + 11 * q^21 + 15 * q^22 - 7 * q^23 - 20 * q^24 - 16 * q^25 + 8 * q^26 - 5 * q^27 - 9 * q^28 + 12 * q^29 + 18 * q^30 + 22 * q^31 - 76 * q^32 - 49 * q^33 - 26 * q^34 + 8 * q^35 + 2 * q^36 + 64 * q^37 - 27 * q^38 - 3 * q^39 - 24 * q^40 + 46 * q^41 + 20 * q^42 - 28 * q^43 - 23 * q^45 + 34 * q^46 + 5 * q^47 - 20 * q^48 - 11 * q^49 + 9 * q^50 + 59 * q^51 + 17 * q^52 + 23 * q^53 + 41 * q^54 - 10 * q^55 - 60 * q^56 + 24 * q^57 - 37 * q^58 + 71 * q^59 - 72 * q^60 + 22 * q^61 + 43 * q^62 - 106 * q^63 - 52 * q^64 + 2 * q^65 - 21 * q^66 - 56 * q^67 - 104 * q^68 - 12 * q^69 - 32 * q^70 - 36 * q^71 + 147 * q^72 - 12 * q^73 + 10 * q^74 + 34 * q^75 - 49 * q^76 - 30 * q^77 + 5 * q^78 - 70 * q^79 + q^81 + 130 * q^82 + 11 * q^83 + 77 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 + 96 * q^88 - 40 * q^89 - 48 * q^90 + 10 * q^91 + 112 * q^92 + 50 * q^93 + 78 * q^94 + 41 * q^95 - 75 * q^96 - 47 * q^97 - 46 * q^98 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.599354	−	1.84462i	−0.423807	−	1.30434i	−0.904132	−	0.427253i	$-0.859481\pi$
$2$	−0.599354	−	1.84462i	−0.423807	−	1.30434i	0.480325	−	0.877091i	$-0.340519\pi$
$3$	−0.251540	+	0.774160i	−0.145227	+	0.446961i	−0.997040	−	0.0768838i	$-0.975503\pi$
$3$	−0.251540	+	0.774160i	−0.145227	+	0.446961i	0.851813	+	0.523845i	$0.175503\pi$
$4$	−1.42537	+	1.03559i	−0.712684	+	0.517795i
$5$	−3.24431			−1.45090			−0.725451	−	0.688274i	$-0.758369\pi$
$5$	−3.24431			−1.45090			−0.725451	+	0.688274i	$0.758369\pi$
$6$	1.57879			0.644539
$7$	1.80822	−	1.31375i	0.683445	−	0.496552i	−0.191054	−	0.981580i	$-0.561191\pi$
$7$	1.80822	−	1.31375i	0.683445	−	0.496552i	0.874499	+	0.485028i	$0.161191\pi$
$8$	−0.373685	−	0.271498i	−0.132118	−	0.0959891i
$9$	1.89100	+	1.37389i	0.630333	+	0.457964i
$10$	1.94449	+	5.98453i	0.614902	+	1.89247i
$11$	−4.60589	+	3.34638i	−1.38873	+	1.00897i	−0.392726	+	0.919656i	$0.628468\pi$
$11$	−4.60589	+	3.34638i	−1.38873	+	1.00897i	−0.996003	+	0.0893150i	$0.971532\pi$
$12$	−0.443176	−	1.36395i	−0.127934	−	0.393740i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$14$	−3.50714	−	2.54809i	−0.937323	−	0.681005i
$15$	0.816074	−	2.51162i	0.210709	−	0.648497i
$16$	−1.36573	+	4.20327i	−0.341431	+	1.05082i
$17$	0.131298	+	0.0953933i	0.0318443	+	0.0231363i	0.603594	−	0.797292i	$-0.293735\pi$
$17$	0.131298	+	0.0953933i	0.0318443	+	0.0231363i	−0.571749	+	0.820428i	$0.693735\pi$
$18$	1.40093	−	4.31163i	0.330203	−	1.01626i
$19$	0.913366	+	2.81105i	0.209541	+	0.644900i	0.999496	+	0.0317358i	$0.0101035\pi$
$19$	0.913366	+	2.81105i	0.209541	+	0.644900i	−0.789956	+	0.613164i	$0.789897\pi$
$20$	4.62434	−	3.35978i	1.03403	−	0.751270i
$21$	0.562214	+	1.73032i	0.122685	+	0.377586i
$22$	8.93336	+	6.49046i	1.90460	+	1.38377i
$23$	0.262498	+	0.190716i	0.0547347	+	0.0397671i	0.614816	−	0.788670i	$-0.289230\pi$
$23$	0.262498	+	0.190716i	0.0547347	+	0.0397671i	−0.560082	+	0.828438i	$0.689230\pi$
$24$	0.304180	−	0.221000i	0.0620904	−	0.0451113i
$25$	5.52558			1.10512
$26$	1.93955			0.380377
$27$	−3.51489	+	2.55372i	−0.676441	+	0.491463i
$28$	−1.21688	+	3.74516i	−0.229968	+	0.707769i
$29$	2.48786	+	7.65684i	0.461983	+	1.42184i	0.862737	+	0.505653i	$0.168748\pi$
$29$	2.48786	+	7.65684i	0.461983	+	1.42184i	−0.400753	+	0.916186i	$0.631252\pi$
$30$	−5.12210			−0.935163
$31$	4.25660	+	3.58906i	0.764508	+	0.644614i
$31$	4.25660	+	3.58906i	0.764508	+	0.644614i
$32$	7.64820			1.35202
$33$	−1.43207	−	4.40744i	−0.249291	−	0.767238i
$34$	0.0972707	−	0.299369i	0.0166818	−	0.0513413i
$35$	−5.86645	+	4.26223i	−0.991611	+	0.720448i
$36$	−4.11816			−0.686360
$37$	−6.49744			−1.06817			−0.534086	−	0.845430i	$-0.679344\pi$
$37$	−6.49744			−1.06817			−0.534086	+	0.845430i	$0.679344\pi$
$38$	4.63790	−	3.36963i	0.752366	−	0.546626i
$39$	−0.658540	−	0.478457i	−0.105451	−	0.0766145i
$40$	1.21235	+	0.880826i	0.191690	+	0.139271i
$41$	−1.57442	−	4.84556i	−0.245883	−	0.756749i	−0.995490	−	0.0948664i	$-0.969758\pi$
$41$	−1.57442	−	4.84556i	−0.245883	−	0.756749i	0.749607	−	0.661883i	$-0.230242\pi$
$42$	2.85481	−	2.07414i	0.440507	−	0.320047i
$43$	−2.06691	−	6.36130i	−0.315201	−	0.970089i	−0.975672	−	0.219237i	$-0.929643\pi$
$43$	−2.06691	−	6.36130i	−0.315201	−	0.970089i	0.660471	−	0.750852i	$-0.270357\pi$
$44$	3.09962	−	9.53964i	0.467285	−	1.43815i
$45$	−6.13500	−	4.45734i	−0.914552	−	0.664461i
$46$	0.194470	−	0.598516i	0.0286730	−	0.0882464i
$47$	−2.03315	+	6.25741i	−0.296566	+	0.912737i	0.686125	+	0.727484i	$0.259310\pi$
$47$	−2.03315	+	6.25741i	−0.296566	+	0.912737i	−0.982691	+	0.185253i	$0.940690\pi$
$48$	−2.91047	−	2.11458i	−0.420090	−	0.305213i
$49$	−0.619387	+	1.90628i	−0.0884839	+	0.272325i
$50$	−3.31177	−	10.1926i	−0.468356	−	1.44145i
$51$	−0.106876	+	0.0776501i	−0.0149657	+	0.0108732i
$52$	−0.544442	−	1.67562i	−0.0755005	−	0.232367i
$53$	1.67411	+	1.21631i	0.229957	+	0.167073i	0.696797	−	0.717268i	$-0.254608\pi$
$53$	1.67411	+	1.21631i	0.229957	+	0.167073i	−0.466840	+	0.884342i	$0.654608\pi$
$54$	6.81731	+	4.95306i	0.927718	+	0.674027i
$55$	14.9430	−	10.8567i	2.01491	−	1.46392i
$56$	−1.03239			−0.137959
$57$	−2.40595			−0.318676
$58$	12.6329	−	9.17831i	1.65878	−	1.20517i
$59$	0.660375	−	2.03243i	0.0859735	−	0.264599i	−0.898823	−	0.438312i	$-0.855576\pi$
$59$	0.660375	−	2.03243i	0.0859735	−	0.264599i	0.984796	+	0.173713i	$0.0555765\pi$
$60$	1.43780	+	4.42510i	0.185619	+	0.571278i
$61$	−10.2530			−1.31277			−0.656383	−	0.754428i	$-0.727914\pi$
$61$	−10.2530			−1.31277			−0.656383	+	0.754428i	$0.727914\pi$
$62$	4.06924	−	10.0029i	0.516795	−	1.27037i
$63$	5.22431			0.658201
$64$	−1.85252	−	5.70148i	−0.231565	−	0.712685i
$65$	1.00255	−	3.08553i	0.124351	−	0.382712i
$66$	−7.27175	+	5.28324i	−0.895091	+	0.650321i
$67$	−7.78875			−0.951547			−0.475773	−	0.879568i	$-0.657832\pi$
$67$	−7.78875			−0.951547			−0.475773	+	0.879568i	$0.657832\pi$
$68$	−0.285936			−0.0346748
$69$	−0.213674	+	0.155243i	−0.0257233	+	0.0186891i
$70$	11.3783	+	8.26680i	1.35996	+	0.988071i
$71$	−3.62555	−	2.63411i	−0.430273	−	0.312612i	0.351485	−	0.936194i	$-0.385677\pi$
$71$	−3.62555	−	2.63411i	−0.430273	−	0.312612i	−0.781758	+	0.623582i	$0.785677\pi$
$72$	−0.333630	−	1.02681i	−0.0393186	−	0.121010i
$73$	2.13035	−	1.54779i	0.249339	−	0.181155i	−0.456095	−	0.889931i	$-0.650752\pi$
$73$	2.13035	−	1.54779i	0.249339	−	0.181155i	0.705434	+	0.708776i	$0.250752\pi$
$74$	3.89426	+	11.9853i	0.452699	+	1.39326i
$75$	−1.38990	+	4.27768i	−0.160492	+	0.493944i
$76$	−4.21298	−	3.06091i	−0.483262	−	0.351111i
$77$	−3.93218	+	12.1020i	−0.448113	+	1.37915i
$78$	−0.487874	+	1.50152i	−0.0552408	+	0.170014i
$79$	−4.86100	−	3.53172i	−0.546905	−	0.397350i	0.279738	−	0.960076i	$-0.409752\pi$
$79$	−4.86100	−	3.53172i	−0.546905	−	0.397350i	−0.826643	+	0.562726i	$0.809752\pi$
$80$	4.43084	−	13.6367i	0.495383	−	1.52463i
$81$	1.07404	+	3.30556i	0.119338	+	0.367284i
$82$	−7.99459	+	5.80841i	−0.882855	+	0.641431i
$83$	−2.47937	−	7.63070i	−0.272146	−	0.837578i	−0.989961	−	0.141344i	$-0.954858\pi$
$83$	−2.47937	−	7.63070i	−0.272146	−	0.837578i	0.717815	−	0.696234i	$-0.245142\pi$
$84$	−2.59326	−	1.88411i	−0.282948	−	0.205574i
$85$	−0.425971	−	0.309486i	−0.0462030	−	0.0335684i
$86$	−10.4954	+	7.62534i	−1.13175	+	0.822261i
$87$	−6.55341			−0.702599
$88$	2.62969			0.280326
$89$	−13.1566	+	9.55884i	−1.39460	+	1.01324i	−0.399256	+	0.916840i	$0.630731\pi$
$89$	−13.1566	+	9.55884i	−1.39460	+	1.01324i	−0.995343	+	0.0963959i	$0.969269\pi$
$90$	−4.54506	+	13.9883i	−0.479092	+	1.47449i
$91$	0.690680	+	2.12570i	0.0724030	+	0.222833i
$92$	−0.571660			−0.0595997
$93$	−3.84921	+	2.39250i	−0.399145	+	0.248091i
$94$	12.7611			1.31621
$95$	−2.96325	−	9.11994i	−0.304023	−	0.935686i
$96$	−1.92383	+	5.92093i	−0.196350	+	0.604302i
$97$	5.98552	−	4.34873i	0.607737	−	0.441547i	−0.240880	−	0.970555i	$-0.577436\pi$
$97$	5.98552	−	4.34873i	0.607737	−	0.441547i	0.848617	+	0.529008i	$0.177436\pi$
$98$	3.88759			0.392706
$99$	−13.3073			−1.33743
$100$	−7.87598	+	5.72223i	−0.787598	+	0.572223i
$101$	5.74670	+	4.17522i	0.571818	+	0.415450i	0.835765	−	0.549087i	$-0.185024\pi$
$101$	5.74670	+	4.17522i	0.571818	+	0.415450i	−0.263947	+	0.964537i	$0.585024\pi$
$102$	0.207292	+	0.150606i	0.0205249	+	0.0149122i
$103$	5.84534	+	17.9901i	0.575958	+	1.77262i	0.632893	+	0.774239i	$0.281867\pi$
$103$	5.84534	+	17.9901i	0.575958	+	1.77262i	−0.0569353	+	0.998378i	$0.518133\pi$
$104$	0.373685	−	0.271498i	0.0366429	−	0.0266226i
$105$	−1.82400	−	5.61369i	−0.178004	−	0.547840i
$106$	1.24025	−	3.81710i	0.120464	−	0.370750i
$107$	−10.0314	−	7.28824i	−0.969772	−	0.704581i	−0.0143727	−	0.999897i	$-0.504575\pi$
$107$	−10.0314	−	7.28824i	−0.969772	−	0.704581i	−0.955400	+	0.295316i	$0.904575\pi$
$108$	2.36541	−	7.27998i	0.227612	−	0.700516i
$109$	3.74406	−	11.5230i	0.358616	−	1.10371i	−0.595267	−	0.803528i	$-0.702954\pi$
$109$	3.74406	−	11.5230i	0.358616	−	1.10371i	0.953883	−	0.300178i	$-0.0970462\pi$
$110$	−28.9826	−	21.0571i	−2.76338	−	2.00772i
$111$	1.63436	−	5.03005i	0.155127	−	0.477432i
$112$	3.05252	+	9.39469i	0.288436	+	0.887714i
$113$	6.58340	−	4.78312i	0.619314	−	0.449958i	−0.233368	−	0.972388i	$-0.574975\pi$
$113$	6.58340	−	4.78312i	0.619314	−	0.449958i	0.852682	+	0.522431i	$0.174975\pi$
$114$	1.44202	+	4.43807i	0.135057	+	0.415663i
$115$	−0.851627	−	0.618743i	−0.0794146	−	0.0576981i
$116$	−11.4755	−	8.33741i	−1.06547	−	0.774109i
$117$	−1.89100	+	1.37389i	−0.174823	+	0.127016i
$118$	−4.14485			−0.381565
$119$	0.362739			0.0332522
$120$	−0.986855	+	0.716992i	−0.0900871	+	0.0654521i
$121$	6.61682	−	20.3645i	0.601529	−	1.85132i
$122$	6.14519	+	18.9129i	0.556359	+	1.71230i
$123$	4.14727			0.373946
$124$	−9.78402	−	0.707635i	−0.878631	−	0.0635475i
$125$	−1.70514			−0.152512
$126$	−3.13121	−	9.63686i	−0.278950	−	0.858520i
$127$	−0.813352	+	2.50324i	−0.0721733	+	0.222127i	−0.980636	−	0.195839i	$-0.937257\pi$
$127$	−0.813352	+	2.50324i	−0.0721733	+	0.222127i	0.908463	+	0.417966i	$0.137257\pi$
$128$	2.96829	−	2.15659i	0.262362	−	0.190617i
$129$	5.44457			0.479368
$130$	−6.29251			−0.551889
$131$	−0.197887	+	0.143774i	−0.0172895	+	0.0125616i	−0.596396	−	0.802690i	$-0.703401\pi$
$131$	−0.197887	+	0.143774i	−0.0172895	+	0.0125616i	0.579107	+	0.815252i	$0.303401\pi$
$132$	6.60553	+	4.79920i	0.574937	+	0.417716i
$133$	5.34460	+	3.88308i	0.463435	+	0.336706i
$134$	4.66821	+	14.3673i	0.403272	+	1.24114i
$135$	11.4034	−	8.28507i	0.981450	−	0.713065i
$136$	−0.0231649	−	0.0712941i	−0.00198637	−	0.00611342i
$137$	−4.88190	+	15.0249i	−0.417089	+	1.28367i	0.493281	+	0.869870i	$0.335798\pi$
$137$	−4.88190	+	15.0249i	−0.417089	+	1.28367i	−0.910369	+	0.413797i	$0.864202\pi$
$138$	0.414430	+	0.301101i	0.0352787	+	0.0256314i
$139$	−2.81694	+	8.66966i	−0.238930	+	0.735351i	0.757646	+	0.652666i	$0.226350\pi$
$139$	−2.81694	+	8.66966i	−0.238930	+	0.735351i	−0.996576	+	0.0826851i	$0.973650\pi$
$140$	3.94793	−	12.1505i	0.333661	−	1.02690i
$141$	−4.33281	−	3.14797i	−0.364889	−	0.265107i
$142$	−2.68596	+	8.26653i	−0.225401	+	0.693711i
$143$	−1.75929	−	5.41455i	−0.147120	−	0.452788i
$144$	−8.35743	+	6.07203i	−0.696452	+	0.506002i
$145$	−8.07139	−	24.8412i	−0.670293	−	2.06295i
$146$	−4.13192	−	3.00201i	−0.341960	−	0.248448i
$147$	−1.31996	−	0.959009i	−0.108869	−	0.0790978i
$148$	9.26124	−	6.72868i	0.761269	−	0.553094i
$149$	2.65842			0.217786			0.108893	−	0.994053i	$-0.465269\pi$
$149$	2.65842			0.217786			0.108893	+	0.994053i	$0.465269\pi$
$150$	8.72374			0.712291
$151$	−7.71583	+	5.60588i	−0.627906	+	0.456200i	−0.855674	−	0.517515i	$-0.826857\pi$
$151$	−7.71583	+	5.60588i	−0.627906	+	0.456200i	0.227768	+	0.973715i	$0.426857\pi$
$152$	0.421884	−	1.29843i	0.0342193	−	0.105316i
$153$	0.117224	+	0.360777i	0.00947697	+	0.0291671i
$154$	24.6804			1.98880
$155$	−13.8098	−	11.6440i	−1.10923	−	0.935272i
$156$	1.43415			0.114824
$157$	5.22607	+	16.0842i	0.417086	+	1.28366i	0.910372	+	0.413790i	$0.135795\pi$
$157$	5.22607	+	16.0842i	0.417086	+	1.28366i	−0.493287	+	0.869867i	$0.664205\pi$
$158$	−3.60123	+	11.0835i	−0.286499	+	0.881753i
$159$	−1.36273	+	0.990078i	−0.108071	+	0.0785183i
$160$	−24.8132			−1.96165
$161$	0.725210			0.0571545
$162$	5.45377	−	3.96240i	0.428489	−	0.311315i
$163$	−8.26860	−	6.00749i	−0.647647	−	0.470543i	0.214822	−	0.976653i	$-0.431083\pi$
$163$	−8.26860	−	6.00749i	−0.647647	−	0.470543i	−0.862469	+	0.506110i	$0.831083\pi$
$164$	7.26214	+	5.27625i	0.567078	+	0.412006i
$165$	4.64607	+	14.2991i	0.361696	+	1.11319i
$166$	−12.5897	+	9.14698i	−0.977153	+	0.709943i
$167$	6.60403	+	20.3251i	0.511035	+	1.57280i	0.790382	+	0.612614i	$0.209882\pi$
$167$	6.60403	+	20.3251i	0.511035	+	1.57280i	−0.279347	+	0.960190i	$0.590118\pi$
$168$	0.259687	−	0.799234i	0.0200353	−	0.0616622i
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	−0.315577	+	0.971246i	−0.0242036	+	0.0744911i
$171$	−2.13491	+	6.57057i	−0.163260	+	0.502464i
$172$	9.53381	+	6.92672i	0.726946	+	0.528157i
$173$	4.54409	−	13.9853i	0.345481	−	1.06328i	−0.615845	−	0.787867i	$-0.711185\pi$
$173$	4.54409	−	13.9853i	0.345481	−	1.06328i	0.961326	−	0.275413i	$-0.0888147\pi$
$174$	3.92781	+	12.0886i	0.297767	+	0.916431i
$175$	9.99148	−	7.25924i	0.755285	−	0.548747i
$176$	−7.77535	−	23.9301i	−0.586089	−	1.80380i
$177$	1.40731	+	1.02247i	0.105780	+	0.0768537i
$178$	25.5179	+	18.5398i	1.91265	+	1.38962i
$179$	16.6681	−	12.1101i	1.24583	−	0.905148i	0.247857	−	0.968797i	$-0.420274\pi$
$179$	16.6681	−	12.1101i	1.24583	−	0.905148i	0.997972	+	0.0636486i	$0.0202737\pi$
$180$	13.3606			0.995841
$181$	3.99756			0.297137			0.148568	−	0.988902i	$-0.452534\pi$
$181$	3.99756			0.297137			0.148568	+	0.988902i	$0.452534\pi$
$182$	3.50714	−	2.54809i	0.259967	−	0.188877i
$183$	2.57904	−	7.93748i	0.190648	−	0.586755i
$184$	−0.0463126	−	0.142536i	−0.00341421	−	0.0105079i
$185$	21.0797			1.54981
$186$	6.72029	+	5.66638i	0.492756	+	0.415479i
$187$	−0.923964			−0.0675670
$188$	−3.58212	−	11.0246i	−0.261253	−	0.804053i
$189$	−3.00076	+	9.23540i	−0.218273	+	0.671776i
$190$	−15.0468	+	10.9321i	−1.09161	+	0.793101i
$191$	12.4249			0.899036			0.449518	−	0.893271i	$-0.351596\pi$
$191$	12.4249			0.899036			0.449518	+	0.893271i	$0.351596\pi$
$192$	4.87984			0.352172
$193$	20.5086	−	14.9004i	1.47624	−	1.07255i	0.497499	−	0.867465i	$-0.334252\pi$
$193$	20.5086	−	14.9004i	1.47624	−	1.07255i	0.978743	−	0.205088i	$-0.0657482\pi$
$194$	−11.6092	−	8.43458i	−0.833493	−	0.605568i
$195$	2.13651	+	1.55227i	0.152999	+	0.111160i
$196$	−1.09127	−	3.35858i	−0.0779477	−	0.239898i
$197$	19.3203	−	14.0370i	1.37652	−	1.00010i	0.379319	−	0.925266i	$-0.376158\pi$
$197$	19.3203	−	14.0370i	1.37652	−	1.00010i	0.997196	−	0.0748314i	$-0.0238419\pi$
$198$	7.97578	+	24.5469i	0.566814	+	1.74447i
$199$	0.759819	−	2.33848i	0.0538622	−	0.165771i	−0.920507	−	0.390727i	$-0.872224\pi$
$199$	0.759819	−	2.33848i	0.0538622	−	0.165771i	0.974369	+	0.224956i	$0.0722238\pi$
$200$	−2.06483	−	1.50018i	−0.146005	−	0.106079i
$201$	1.95918	−	6.02974i	0.138190	−	0.425305i
$202$	4.25740	−	13.1029i	0.299549	−	0.921918i
$203$	14.5578	+	10.5769i	1.02176	+	0.742350i
$204$	0.0719242	−	0.221360i	0.00503570	−	0.0154983i
$205$	5.10791	+	15.7205i	0.356752	+	1.09797i
$206$	29.6815	−	21.5649i	2.06801	−	1.50250i
$207$	0.234361	+	0.721288i	0.0162892	+	0.0501330i
$208$	−3.57552	−	2.59777i	−0.247917	−	0.180123i
$209$	−13.6137	−	9.89094i	−0.941680	−	0.684171i
$210$	−9.26191	+	6.72917i	−0.639132	+	0.464357i
$211$	−9.70880			−0.668381			−0.334191	−	0.942506i	$-0.608463\pi$
$211$	−9.70880			−0.668381			−0.334191	+	0.942506i	$0.608463\pi$
$212$	−3.64582			−0.250396
$213$	2.95119	−	2.14417i	0.202213	−	0.146916i
$214$	−7.43168	+	22.8724i	−0.508019	+	1.56352i
$215$	6.70571	+	20.6381i	0.457326	+	1.40750i
$216$	2.00679			0.136545
$217$	12.4120	+	0.897707i	0.842583	+	0.0609403i
$218$	−23.4996			−1.59160
$219$	0.662369	+	2.03856i	0.0447587	+	0.137753i
$220$	−10.0561	+	30.9496i	−0.677984	+	2.08662i
$221$	−0.131298	+	0.0953933i	−0.00883203	+	0.00641685i
$222$	−10.2581			−0.688479
$223$	−5.61766			−0.376186			−0.188093	−	0.982151i	$-0.560231\pi$
$223$	−5.61766			−0.376186			−0.188093	+	0.982151i	$0.560231\pi$
$224$	13.8297	−	10.0478i	0.924033	−	0.671349i
$225$	10.4489	+	7.59154i	0.696591	+	0.506103i
$226$	−12.7688	−	9.27709i	−0.849369	−	0.617103i
$227$	8.39508	+	25.8374i	0.557201	+	1.71489i	0.690058	+	0.723754i	$0.257585\pi$
$227$	8.39508	+	25.8374i	0.557201	+	1.71489i	−0.132857	+	0.991135i	$0.542415\pi$
$228$	3.42937	−	2.49158i	0.227115	−	0.165009i
$229$	8.41368	+	25.8947i	0.555992	+	1.71117i	0.693309	+	0.720640i	$0.256152\pi$
$229$	8.41368	+	25.8947i	0.555992	+	1.71117i	−0.137317	+	0.990527i	$0.543848\pi$
$230$	−0.630921	+	1.94178i	−0.0416017	+	0.128037i
$231$	−8.37979	−	6.08827i	−0.551349	−	0.400579i
$232$	1.14914	−	3.53670i	0.0754449	−	0.232196i
$233$	6.11876	−	18.8316i	0.400854	−	1.23370i	−0.523455	−	0.852053i	$-0.675357\pi$
$233$	6.11876	−	18.8316i	0.400854	−	1.23370i	0.924308	−	0.381647i	$-0.124643\pi$
$234$	3.66769	+	2.66473i	0.239764	+	0.174199i
$235$	6.59619	−	20.3010i	0.430288	−	1.32429i
$236$	1.16348	+	3.58083i	0.0757363	+	0.233092i
$237$	3.95685	−	2.87482i	0.257025	−	0.186740i
$238$	−0.217409	−	0.669115i	−0.0140925	−	0.0433723i
$239$	−14.4036	−	10.4648i	−0.931688	−	0.676911i	0.0147172	−	0.999892i	$-0.495315\pi$
$239$	−14.4036	−	10.4648i	−0.931688	−	0.676911i	−0.946406	+	0.322980i	$0.895315\pi$
$240$	9.44248	+	6.86036i	0.609510	+	0.442835i
$241$	−1.56950	+	1.14031i	−0.101100	+	0.0734537i	−0.637187	−	0.770709i	$-0.719902\pi$
$241$	−1.56950	+	1.14031i	−0.101100	+	0.0734537i	0.536087	+	0.844163i	$0.319902\pi$
$242$	−41.5306			−2.66969
$243$	−15.8631			−1.01762
$244$	14.6143	−	10.6179i	0.935587	−	0.679743i
$245$	2.00949	−	6.18456i	0.128381	−	0.395117i
$246$	−2.48568	−	7.65013i	−0.158481	−	0.487755i
$247$	−2.95572			−0.188068
$248$	−0.616206	−	2.49684i	−0.0391291	−	0.158549i
$249$	6.53104			0.413888
$250$	1.02198	+	3.14533i	0.0646357	+	0.198928i
$251$	−1.50516	+	4.63239i	−0.0950046	+	0.292394i	−0.987255	−	0.159147i	$-0.949126\pi$
$251$	−1.50516	+	4.63239i	−0.0950046	+	0.292394i	0.892250	+	0.451541i	$0.149126\pi$
$252$	−7.44656	+	5.41024i	−0.469089	+	0.340813i
$253$	−1.84725			−0.116135
$254$	5.10502			0.320317
$255$	0.346740	−	0.251921i	0.0217137	−	0.0157759i
$256$	−15.4571	−	11.2302i	−0.966067	−	0.701889i
$257$	−0.0593302	−	0.0431059i	−0.00370092	−	0.00268887i	0.585933	−	0.810359i	$-0.300728\pi$
$257$	−0.0593302	−	0.0431059i	−0.00370092	−	0.00268887i	−0.589634	+	0.807670i	$0.700728\pi$
$258$	−3.26323	−	10.0432i	−0.203160	−	0.625261i
$259$	−11.7488	+	8.53602i	−0.730036	+	0.530402i
$260$	1.76634	+	5.43624i	0.109544	+	0.337141i
$261$	−5.81513	+	17.8971i	−0.359947	+	1.10780i
$262$	0.383812	+	0.278856i	0.0237120	+	0.0172278i
$263$	1.58234	−	4.86996i	0.0975716	−	0.300294i	−0.890344	−	0.455289i	$-0.849536\pi$
$263$	1.58234	−	4.86996i	0.0975716	−	0.300294i	0.987915	+	0.154995i	$0.0495360\pi$
$264$	−0.661472	+	2.03580i	−0.0407108	+	0.125295i
$265$	−5.43134	−	3.94610i	−0.333645	−	0.242407i
$266$	3.95950	−	12.1861i	0.242773	−	0.747177i
$267$	−4.09066	−	12.5898i	−0.250344	−	0.770481i
$268$	11.1018	−	8.06595i	0.678152	−	0.492706i
$269$	−2.16680	−	6.66873i	−0.132112	−	0.406600i	0.863017	−	0.505174i	$-0.168572\pi$
$269$	−2.16680	−	6.66873i	−0.132112	−	0.406600i	−0.995130	+	0.0985744i	$0.968572\pi$
$270$	−22.1175	−	16.0693i	−1.34603	−	0.977946i
$271$	−7.39913	−	5.37579i	−0.449465	−	0.326556i	0.339919	−	0.940455i	$-0.389600\pi$
$271$	−7.39913	−	5.37579i	−0.449465	−	0.326556i	−0.789385	+	0.613899i	$0.789600\pi$
$272$	−0.580280	+	0.421598i	−0.0351847	+	0.0255632i
$273$	−1.81936			−0.110113
$274$	30.6413			1.85111
$275$	−25.4502	+	18.4907i	−1.53471	+	1.11503i
$276$	0.143795	−	0.442557i	0.00865546	−	0.0266388i
$277$	1.83184	+	5.63783i	0.110065	+	0.338745i	0.990886	−	0.134705i	$-0.0430087\pi$
$277$	1.83184	+	5.63783i	0.110065	+	0.338745i	−0.880821	+	0.473449i	$0.843009\pi$
$278$	17.6806			1.06041
$279$	3.11825	+	12.6350i	0.186685	+	0.756439i
$280$	3.34939			0.200165
$281$	0.454043	+	1.39740i	0.0270860	+	0.0833620i	0.963686	−	0.267039i	$-0.0860453\pi$
$281$	0.454043	+	1.39740i	0.0270860	+	0.0833620i	−0.936600	+	0.350401i	$0.886045\pi$
$282$	−3.20993	+	9.87915i	−0.191149	+	0.588295i
$283$	−23.9256	+	17.3830i	−1.42223	+	1.03331i	−0.430833	+	0.902432i	$0.641780\pi$
$283$	−23.9256	+	17.3830i	−1.42223	+	1.03331i	−0.991398	+	0.130879i	$0.958220\pi$
$284$	7.89560			0.468518
$285$	7.80567			0.462368
$286$	−8.93336	+	6.49046i	−0.528240	+	0.383789i
$287$	−9.21276	−	6.69347i	−0.543812	−	0.395103i
$288$	14.4627	+	10.5078i	0.852225	+	0.619178i
$289$	−5.24515	−	16.1429i	−0.308538	−	0.949583i
$290$	−40.9850	+	29.7773i	−2.40672	+	1.74858i
$291$	1.86102	+	5.72763i	0.109095	+	0.335759i
$292$	−1.43366	+	4.41234i	−0.0838983	+	0.258213i
$293$	18.2775	+	13.2794i	1.06778	+	0.775788i	0.975512	−	0.219946i	$-0.0705882\pi$
$293$	18.2775	+	13.2794i	1.06778	+	0.775788i	0.0922685	+	0.995734i	$0.470588\pi$
$294$	−0.977884	+	3.00962i	−0.0570313	+	0.175524i
$295$	−2.14246	+	6.59383i	−0.124739	+	0.383908i
$296$	2.42800	+	1.76404i	0.141124	+	0.102533i
$297$	7.64351	−	23.5243i	0.443522	−	1.36502i
$298$	−1.59333	−	4.90378i	−0.0922994	−	0.284068i
$299$	−0.262498	+	0.190716i	−0.0151807	+	0.0110294i
$300$	−2.44880	−	7.53664i	−0.141382	−	0.435128i
$301$	−12.0946	−	8.78725i	−0.697122	−	0.506489i
$302$	14.9652	+	10.8729i	0.861153	+	0.625664i
$303$	−4.67781	+	3.39863i	−0.268733	+	0.195246i
$304$	−13.0630			−0.749216
$305$	33.2640			1.90469
$306$	0.595239	−	0.432466i	0.0340275	−	0.0247225i
$307$	9.28251	−	28.5686i	0.529781	−	1.63050i	−0.224883	−	0.974386i	$-0.572200\pi$
$307$	9.28251	−	28.5686i	0.529781	−	1.63050i	0.754664	−	0.656112i	$-0.227800\pi$
$308$	−6.92792	−	21.3219i	−0.394755	−	1.21493i
$309$	−15.3975			−0.875936
$310$	−13.2019	+	32.4527i	−0.749818	+	1.84319i
$311$	−27.0700			−1.53500			−0.767499	−	0.641050i	$-0.778499\pi$
$311$	−27.0700			−1.53500			−0.767499	+	0.641050i	$0.778499\pi$
$312$	0.116186	+	0.357585i	0.00657776	+	0.0202443i
$313$	−7.50799	+	23.1072i	−0.424376	+	1.30610i	0.479214	+	0.877698i	$0.340922\pi$
$313$	−7.50799	+	23.1072i	−0.424376	+	1.30610i	−0.903590	+	0.428398i	$0.859078\pi$
$314$	26.5370	−	19.2802i	1.49757	−	1.08805i
$315$	−16.9493			−0.954984
$316$	10.5861			0.595517
$317$	16.5463	−	12.0216i	0.929334	−	0.675201i	−0.0164954	−	0.999864i	$-0.505251\pi$
$317$	16.5463	−	12.0216i	0.929334	−	0.675201i	0.945830	+	0.324663i	$0.105251\pi$
$318$	2.64307	+	1.92031i	0.148216	+	0.107685i
$319$	−37.0815	−	26.9413i	−2.07616	−	1.50842i
$320$	6.01017	+	18.4974i	0.335979	+	1.03404i
$321$	8.16556	−	5.93263i	0.455757	−	0.331127i
$322$	−0.434657	−	1.33774i	−0.0242225	−	0.0745492i
$323$	−0.148233	+	0.456213i	−0.00824789	+	0.0253844i
$324$	−4.95411	−	3.59937i	−0.275228	−	0.199965i
$325$	−1.70750	+	5.25514i	−0.0947149	+	0.291502i
$326$	−6.12573	+	18.8531i	−0.339273	+	1.04417i
$327$	7.97889	+	5.79700i	0.441234	+	0.320575i
$328$	−0.727224	+	2.23817i	−0.0401542	+	0.123582i
$329$	4.54428	+	13.9859i	0.250534	+	0.771065i
$330$	23.5918	−	17.1405i	1.29869	−	0.943552i
$331$	8.50208	+	26.1667i	0.467316	+	1.43825i	0.856046	+	0.516900i	$0.172914\pi$
$331$	8.50208	+	26.1667i	0.467316	+	1.43825i	−0.388729	+	0.921352i	$0.627086\pi$
$332$	11.4363	+	8.30895i	0.627648	+	0.456013i
$333$	−12.2866	−	8.92677i	−0.673304	−	0.489184i
$334$	33.5340	−	24.3639i	1.83490	−	1.33313i
$335$	25.2691			1.38060
$336$	−8.04082			−0.438663
$337$	−4.44505	+	3.22952i	−0.242137	+	0.175923i	−0.702235	−	0.711945i	$-0.747814\pi$
$337$	−4.44505	+	3.22952i	−0.242137	+	0.175923i	0.460098	+	0.887868i	$0.347814\pi$
$338$	−0.599354	+	1.84462i	−0.0326005	+	0.100334i
$339$	2.04691	+	6.29974i	0.111173	+	0.342155i
$340$	0.927665			0.0503097
$341$	−31.6158	−	2.28663i	−1.71209	−	0.123828i
$342$	13.3998			0.724577
$343$	6.21915	+	19.1406i	0.335802	+	1.03349i
$344$	−0.954708	+	2.93829i	−0.0514744	+	0.158422i
$345$	0.693224	−	0.503657i	0.0373219	−	0.0271160i
$346$	−28.5211			−1.53330
$347$	0.464869			0.0249555			0.0124777	−	0.999922i	$-0.496028\pi$
$347$	0.464869			0.0249555			0.0124777	+	0.999922i	$0.496028\pi$
$348$	9.34102	−	6.78665i	0.500731	−	0.363803i
$349$	12.2195	+	8.87800i	0.654096	+	0.475228i	0.864664	−	0.502351i	$-0.167531\pi$
$349$	12.2195	+	8.87800i	0.654096	+	0.475228i	−0.210568	+	0.977579i	$0.567531\pi$
$350$	−19.3790	−	14.0797i	−1.03585	−	0.752589i
$351$	−1.34257	−	4.13200i	−0.0716611	−	0.220550i
$352$	−35.2268	+	25.5938i	−1.87759	+	1.36415i
$353$	−8.55345	−	26.3248i	−0.455254	−	1.40113i	−0.870837	−	0.491573i	$-0.836422\pi$
$353$	−8.55345	−	26.3248i	−0.455254	−	1.40113i	0.415582	−	0.909556i	$-0.363578\pi$
$354$	1.04260	−	3.20878i	0.0554133	−	0.170545i
$355$	11.7624	+	8.54589i	0.624284	+	0.453569i
$356$	8.85398	−	27.2497i	0.469260	−	1.44423i
$357$	−0.0912432	+	0.280818i	−0.00482910	+	0.0148624i
$358$	−32.3285	−	23.4880i	−1.70862	−	1.24138i
$359$	−9.95770	+	30.6466i	−0.525547	+	1.61747i	0.237684	+	0.971343i	$0.423612\pi$
$359$	−9.95770	+	30.6466i	−0.525547	+	1.61747i	−0.763231	+	0.646126i	$0.776388\pi$
$360$	1.08240	+	3.33128i	0.0570475	+	0.175574i
$361$	8.30354	−	6.03288i	0.437029	−	0.317520i
$362$	−2.39596	−	7.37399i	−0.125929	−	0.387568i
$363$	14.1010	+	10.2450i	0.740109	+	0.537721i
$364$	−3.18582	−	2.31464i	−0.166983	−	0.121320i
$365$	−6.91152	+	5.02152i	−0.361766	+	0.262838i
$366$	−16.1874			−0.846129
$367$	−31.4682			−1.64263			−0.821314	−	0.570476i	$-0.806759\pi$
$367$	−31.4682			−1.64263			−0.821314	+	0.570476i	$0.806759\pi$
$368$	−1.16013	+	0.842886i	−0.0604761	+	0.0439385i
$369$	3.68005	−	11.3260i	0.191576	−	0.589610i
$370$	−12.6342	−	38.8841i	−0.656821	−	2.02149i
$371$	4.62510			0.240123
$372$	3.00889	−	7.39640i	0.156004	−	0.383485i
$373$	8.78302			0.454767			0.227384	−	0.973805i	$-0.426983\pi$
$373$	8.78302			0.454767			0.227384	+	0.973805i	$0.426983\pi$
$374$	0.553781	+	1.70436i	0.0286354	+	0.0881306i
$375$	0.428910	−	1.32005i	0.0221488	−	0.0681670i
$376$	2.45864	−	1.78630i	0.126794	−	0.0921216i
$377$	−8.05087			−0.414641
$378$	18.8343			0.968733
$379$	−15.9922	+	11.6190i	−0.821463	+	0.596828i	−0.917131	−	0.398586i	$-0.869501\pi$
$379$	−15.9922	+	11.6190i	−0.821463	+	0.596828i	0.0956683	+	0.995413i	$0.469501\pi$
$380$	13.6682	+	9.93056i	0.701166	+	0.509427i
$381$	−1.73332	−	1.25933i	−0.0888006	−	0.0645174i
$382$	−7.44692	−	22.9193i	−0.381018	−	1.17265i
$383$	−8.41322	+	6.11256i	−0.429895	+	0.312337i	−0.781607	−	0.623771i	$-0.785600\pi$
$383$	−8.41322	+	6.11256i	−0.429895	+	0.312337i	0.351712	+	0.936108i	$0.385600\pi$
$384$	0.922901	+	2.84040i	0.0470966	+	0.144948i
$385$	12.7572	−	39.2627i	0.650169	−	2.00101i
$386$	−39.7775	−	28.9000i	−2.02462	−	1.47097i
$387$	4.83121	−	14.8689i	0.245584	−	0.755830i
$388$	−4.02806	+	12.3971i	−0.204494	+	0.629367i
$389$	3.79648	+	2.75830i	0.192489	+	0.139852i	0.679856	−	0.733346i	$-0.262042\pi$
$389$	3.79648	+	2.75830i	0.192489	+	0.139852i	−0.487366	+	0.873198i	$0.662042\pi$
$390$	1.58282	−	4.87141i	0.0801490	−	0.246673i
$391$	0.0162723	+	0.0500811i	0.000822928	+	0.00253271i
$392$	0.749007	−	0.544185i	0.0378306	−	0.0274855i
$393$	−0.0615272	−	0.189361i	−0.00310364	−	0.00955201i
$394$	−37.4727	−	27.2255i	−1.88785	−	1.37160i
$395$	15.7706	+	11.4580i	0.793506	+	0.576516i
$396$	18.9678	−	13.7809i	0.953168	−	0.692517i
$397$	23.8564			1.19732			0.598659	−	0.801004i	$-0.295701\pi$
$397$	23.8564			1.19732			0.598659	+	0.801004i	$0.295701\pi$
$398$	−4.76902			−0.239049
$399$	−4.35050	+	3.16082i	−0.217798	+	0.158239i
$400$	−7.54642	+	23.2255i	−0.377321	+	1.16128i
$401$	8.12673	+	25.0115i	0.405830	+	1.24901i	0.920201	+	0.391447i	$0.128025\pi$
$401$	8.12673	+	25.0115i	0.405830	+	1.24901i	−0.514371	+	0.857568i	$0.671975\pi$
$402$	−12.2968			−0.613310
$403$	−4.72876	+	2.93919i	−0.235556	+	0.146411i
$404$	−12.5150			−0.622644
$405$	−3.48453	−	10.7243i	−0.173148	−	0.532894i
$406$	10.7850	−	33.1929i	0.535252	−	1.64734i
$407$	29.9265	−	21.7429i	1.48340	−	1.07775i
$408$	0.0610199			0.00302094
$409$	32.3075			1.59751			0.798753	−	0.601659i	$-0.205494\pi$
$409$	32.3075			1.59751			0.798753	+	0.601659i	$0.205494\pi$
$410$	25.9370	−	18.8443i	1.28094	−	0.930654i
$411$	−10.4037	−	7.55874i	−0.513177	−	0.372845i
$412$	−26.9621	−	19.5891i	−1.32833	−	0.965087i
$413$	−1.47600	−	4.54265i	−0.0726291	−	0.223529i
$414$	1.19004	−	0.864614i	0.0584872	−	0.0424935i
$415$	8.04384	+	24.7564i	0.394857	+	1.21524i
$416$	−2.36342	+	7.27387i	−0.115876	+	0.356631i
$417$	−6.00313	−	4.36153i	−0.293975	−	0.213585i
$418$	−10.0856	+	31.0403i	−0.493303	+	1.51823i
$419$	8.51731	−	26.2136i	0.416098	−	1.28062i	−0.495167	−	0.868798i	$-0.664893\pi$
$419$	8.51731	−	26.2136i	0.416098	−	1.28062i	0.911265	−	0.411820i	$-0.135107\pi$
$420$	8.41335	+	6.11266i	0.410530	+	0.298267i
$421$	−11.0255	+	33.9329i	−0.537349	+	1.65379i	0.201169	+	0.979556i	$0.435526\pi$
$421$	−11.0255	+	33.9329i	−0.537349	+	1.65379i	−0.738518	+	0.674233i	$0.764474\pi$
$422$	5.81900	+	17.9090i	0.283265	+	0.871799i
$423$	−12.4417	+	9.03942i	−0.604936	+	0.439512i
$424$	−0.295364	−	0.909036i	−0.0143441	−	0.0441467i
$425$	0.725495	+	0.527103i	0.0351917	+	0.0255682i
$426$	−5.72399	−	4.15872i	−0.277328	−	0.201491i
$427$	−18.5398	+	13.4699i	−0.897202	+	0.651856i
$428$	21.8461			1.05597
$429$	4.63426			0.223744
$430$	34.0503	−	24.7390i	1.64205	−	1.19302i
$431$	−1.06592	+	3.28055i	−0.0513434	+	0.158019i	−0.973441	−	0.228939i	$-0.926474\pi$
$431$	−1.06592	+	3.28055i	−0.0513434	+	0.158019i	0.922097	+	0.386958i	$0.126474\pi$
$432$	−5.93360	−	18.2617i	−0.285480	−	0.878618i
$433$	10.7779			0.517950			0.258975	−	0.965884i	$-0.416615\pi$
$433$	10.7779			0.517950			0.258975	+	0.965884i	$0.416615\pi$
$434$	−5.78326	−	23.4335i	−0.277606	−	1.12485i
$435$	21.2613			1.01940
$436$	6.59648	+	20.3019i	0.315914	+	0.972283i
$437$	−0.296356	+	0.912090i	−0.0141766	+	0.0436312i
$438$	3.36338	−	2.44364i	0.160709	−	0.116762i
$439$	−4.99059			−0.238188			−0.119094	−	0.992883i	$-0.537999\pi$
$439$	−4.99059			−0.238188			−0.119094	+	0.992883i	$0.537999\pi$
$440$	−8.53154			−0.406725
$441$	−3.79028	+	2.75380i	−0.180490	+	0.131133i
$442$	0.254658	+	0.185020i	0.0121129	+	0.00880050i
$443$	0.725264	+	0.526935i	0.0344584	+	0.0250355i	0.604881	−	0.796316i	$-0.293221\pi$
$443$	0.725264	+	0.526935i	0.0344584	+	0.0250355i	−0.570423	+	0.821351i	$0.693221\pi$
$444$	2.87951	+	8.86221i	0.136655	+	0.420582i
$445$	42.6842	−	31.0119i	2.02343	−	1.47010i
$446$	3.36697	+	10.3625i	0.159430	+	0.490677i
$447$	−0.668699	+	2.05804i	−0.0316284	+	0.0973421i
$448$	−10.8401	−	7.87580i	−0.512147	−	0.372097i
$449$	−5.17423	+	15.9246i	−0.244187	+	0.751530i	0.751582	+	0.659640i	$0.229291\pi$
$449$	−5.17423	+	15.9246i	−0.244187	+	0.751530i	−0.995769	+	0.0918909i	$0.970709\pi$
$450$	7.74096	−	23.8242i	0.364912	−	1.12308i
$451$	23.4667	+	17.0495i	1.10500	+	0.802831i
$452$	−4.43041	+	13.6354i	−0.208389	+	0.641355i
$453$	−2.39901	−	7.38339i	−0.112715	−	0.346902i
$454$	42.6286	−	30.9715i	2.00066	−	1.45356i
$455$	−2.24078	−	6.89643i	−0.105050	−	0.323309i
$456$	0.899069	+	0.653212i	0.0421028	+	0.0305894i
$457$	16.4286	+	11.9361i	0.768496	+	0.558345i	0.901505	−	0.432770i	$-0.142464\pi$
$457$	16.4286	+	11.9361i	0.768496	+	0.558345i	−0.133008	+	0.991115i	$0.542464\pi$
$458$	42.7231	−	31.0401i	1.99632	−	1.45041i
$459$	−0.705104			−0.0329115
$460$	1.85465			0.0864733
$461$	−4.64460	+	3.37450i	−0.216321	+	0.157166i	−0.690669	−	0.723171i	$-0.742684\pi$
$461$	−4.64460	+	3.37450i	−0.216321	+	0.157166i	0.474348	+	0.880337i	$0.342684\pi$
$462$	−6.20810	+	19.1066i	−0.288827	+	0.888918i
$463$	−1.66530	−	5.12526i	−0.0773929	−	0.238191i	0.904874	−	0.425680i	$-0.139965\pi$
$463$	−1.66530	−	5.12526i	−0.0773929	−	0.238191i	−0.982267	+	0.187489i	$0.939965\pi$
$464$	−35.5815			−1.65183
$465$	12.4880	−	7.76202i	0.579119	−	0.359955i
$466$	−38.4045			−1.77905
$467$	3.16806	+	9.75030i	0.146601	+	0.451190i	0.997213	−	0.0746025i	$-0.0237688\pi$
$467$	3.16806	+	9.75030i	0.146601	+	0.451190i	−0.850613	+	0.525793i	$0.823769\pi$
$468$	1.27258	−	3.91660i	0.0588251	−	0.181045i
$469$	−14.0838	+	10.2325i	−0.650330	+	0.472492i
$470$	−41.4011			−1.90969
$471$	−13.7663			−0.634317
$472$	−0.798573	+	0.580197i	−0.0367573	+	0.0267057i
$473$	30.8073	+	22.3828i	1.41652	+	1.02916i
$474$	−7.67452	−	5.57586i	−0.352502	−	0.256108i
$475$	5.04688	+	15.5327i	0.231567	+	0.712689i
$476$	−0.517036	+	0.375649i	−0.0236983	+	0.0172178i
$477$	1.49466	+	4.60009i	0.0684358	+	0.210624i
$478$	−10.6708	+	32.8412i	−0.488069	+	1.50212i
$479$	1.48920	+	1.08197i	0.0680432	+	0.0494363i	0.621287	−	0.783583i	$-0.286610\pi$
$479$	1.48920	+	1.08197i	0.0680432	+	0.0494363i	−0.553244	+	0.833019i	$0.686610\pi$
$480$	6.24150	−	19.2093i	0.284884	−	0.876783i
$481$	2.00782	−	6.17943i	0.0915486	−	0.281758i
$482$	3.04412	+	2.21168i	0.138656	+	0.100739i
$483$	−0.182419	+	0.561428i	−0.00830036	+	0.0255459i
$484$	11.6579	+	35.8792i	0.529903	+	1.63087i
$485$	−19.4189	+	14.1087i	−0.881767	+	0.640641i
$486$	9.50763	+	29.2615i	0.431275	+	1.32733i
$487$	−15.5777	−	11.3179i	−0.705893	−	0.512861i	0.175953	−	0.984399i	$-0.443699\pi$
$487$	−15.5777	−	11.3179i	−0.705893	−	0.512861i	−0.881846	+	0.471537i	$0.843699\pi$
$488$	3.83140	+	2.78368i	0.173440	+	0.126011i
$489$	6.73064	−	4.89010i	0.304370	−	0.221138i
$490$	−12.6126			−0.569778
$491$	33.8384			1.52711			0.763553	−	0.645746i	$-0.223453\pi$
$491$	33.8384			1.52711			0.763553	+	0.645746i	$0.223453\pi$
$492$	−5.91138	+	4.29487i	−0.266506	+	0.193628i
$493$	−0.403761	+	1.24265i	−0.0181845	+	0.0559661i
$494$	1.77152	+	5.45218i	0.0797044	+	0.245305i
$495$	43.1731			1.94049
$496$	−20.8991	+	12.9900i	−0.938399	+	0.583267i
$497$	−10.0164			−0.449296
$498$	−3.91440	−	12.0473i	−0.175409	−	0.539852i
$499$	5.85686	−	18.0256i	0.262189	−	0.806935i	−0.730139	−	0.683299i	$-0.760545\pi$
$499$	5.85686	−	18.0256i	0.262189	−	0.806935i	0.992328	−	0.123636i	$-0.0394554\pi$
$500$	2.43045	−	1.76582i	0.108693	−	0.0789700i
$501$	−17.3961			−0.777198
$502$	9.44713			0.421646
$503$	25.0465	−	18.1974i	1.11677	−	0.811380i	0.133052	−	0.991109i	$-0.457522\pi$
$503$	25.0465	−	18.1974i	1.11677	−	0.811380i	0.983716	+	0.179729i	$0.0575221\pi$
$504$	−1.95225	−	1.41839i	−0.0869600	−	0.0631801i
$505$	−18.6441	−	13.5457i	−0.829652	−	0.602777i
$506$	1.10715	+	3.40747i	0.0492190	+	0.151481i
$507$	0.658540	−	0.478457i	0.0292468	−	0.0212490i
$508$	−1.43301	−	4.41034i	−0.0635794	−	0.195677i
$509$	−1.81133	+	5.57471i	−0.0802860	+	0.247095i	−0.983141	−	0.182851i	$-0.941467\pi$
$509$	−1.81133	+	5.57471i	−0.0802860	+	0.247095i	0.902855	+	0.429946i	$0.141467\pi$
$510$	−0.672519	−	0.488614i	−0.0297797	−	0.0216362i
$511$	1.81874	−	5.59750i	0.0804563	−	0.247619i
$512$	−9.18368	+	28.2645i	−0.405865	+	1.24912i
$513$	−10.3890	−	7.54807i	−0.458687	−	0.333255i
$514$	−0.0439543	+	0.135277i	−0.00193874	+	0.00596683i
$515$	−18.9641	−	58.3655i	−0.835659	−	2.57189i
$516$	−7.76052	+	5.63835i	−0.341638	+	0.248214i
$517$	−11.5752	−	35.6247i	−0.509075	−	1.56677i
$518$	22.7874	+	16.5560i	1.00122	+	0.727430i
$519$	9.68382	+	7.03571i	0.425072	+	0.308833i
$520$	−1.21235	+	0.880826i	−0.0531652	+	0.0386268i
$521$	−25.7720			−1.12909			−0.564545	−	0.825402i	$-0.690948\pi$
$521$	−25.7720			−1.12909			−0.564545	+	0.825402i	$0.690948\pi$
$522$	36.4987			1.59751
$523$	11.7662	−	8.54865i	0.514500	−	0.373806i	−0.300028	−	0.953930i	$-0.596996\pi$
$523$	11.7662	−	8.54865i	0.514500	−	0.373806i	0.814528	+	0.580124i	$0.196996\pi$
$524$	0.133172	−	0.409860i	0.00581763	−	0.0179048i
$525$	3.10656	+	9.56099i	0.135581	+	0.417276i
$526$	−9.93161			−0.433039
$527$	0.216509	+	0.877286i	0.00943129	+	0.0382152i
$528$	20.4815			0.891343
$529$	−7.07486	−	21.7742i	−0.307603	−	0.946703i
$530$	−4.02376	+	12.3839i	−0.174781	+	0.537921i
$531$	4.04110	−	2.93603i	0.175369	−	0.127413i
$532$	−11.6393			−0.504628
$533$	5.09492			0.220686
$534$	−20.7716	+	15.0914i	−0.898874	+	0.653070i
$535$	32.5450	+	23.6453i	1.40704	+	1.02228i
$536$	2.91054	+	2.11463i	0.125716	+	0.0913382i
$537$	5.18244	+	15.9499i	0.223639	+	0.688289i
$538$	−11.0026	+	7.99386i	−0.474356	+	0.344640i
$539$	−3.52629	−	10.8528i	−0.151888	−	0.467464i
$540$	−7.67413	+	23.6185i	−0.330242	+	1.01638i
$541$	−28.6305	−	20.8013i	−1.23092	−	0.894316i	−0.233961	−	0.972246i	$-0.575169\pi$
$541$	−28.6305	−	20.8013i	−1.23092	−	0.894316i	−0.996959	+	0.0779301i	$0.975169\pi$
$542$	−5.48159	+	16.8706i	−0.235454	+	0.724654i
$543$	−1.00555	+	3.09475i	−0.0431521	+	0.132809i
$544$	1.00419	+	0.729586i	0.0430543	+	0.0312808i
$545$	−12.1469	+	37.3843i	−0.520316	+	1.60137i
$546$	1.09044	+	3.35603i	0.0466666	+	0.143625i
$547$	18.7531	−	13.6249i	0.801825	−	0.582560i	−0.109624	−	0.993973i	$-0.534965\pi$
$547$	18.7531	−	13.6249i	0.801825	−	0.582560i	0.911449	+	0.411413i	$0.134965\pi$
$548$	−8.60118	−	26.4717i	−0.367424	−	1.13082i
$549$	−19.3885	−	14.0865i	−0.827480	−	0.601199i
$550$	49.3620	+	35.8636i	2.10480	+	1.52923i
$551$	−19.2514	+	13.9870i	−0.820139	+	0.595866i
$552$	0.121995			0.00519245
$553$	−13.4296			−0.571084
$554$	9.30174	−	6.75811i	0.395193	−	0.287125i
$555$	−5.30239	+	16.3191i	−0.225074	+	0.692706i
$556$	−4.96304	−	15.2747i	−0.210480	−	0.647790i
$557$	−18.4048			−0.779835			−0.389917	−	0.920850i	$-0.627496\pi$
$557$	−18.4048			−0.779835			−0.389917	+	0.920850i	$0.627496\pi$
$558$	21.4379	−	13.3248i	0.907538	−	0.564085i
$559$	6.68867			0.282900
$560$	−9.90333	−	30.4793i	−0.418492	−	1.28799i
$561$	0.232414	−	0.715296i	0.00981252	−	0.0301998i
$562$	2.30554	−	1.67508i	0.0972535	−	0.0706588i
$563$	−20.1329			−0.848502			−0.424251	−	0.905545i	$-0.639463\pi$
$563$	−20.1329			−0.848502			−0.424251	+	0.905545i	$0.639463\pi$
$564$	9.43587			0.397322
$565$	−21.3586	+	15.5179i	−0.898563	+	0.652844i
$566$	46.4049	+	33.7152i	1.95054	+	1.41715i
$567$	6.28479	+	4.56617i	0.263937	+	0.191761i
$568$	0.639656	+	1.96866i	0.0268394	+	0.0826031i
$569$	10.9230	−	7.93601i	0.457915	−	0.332695i	−0.334798	−	0.942290i	$-0.608668\pi$
$569$	10.9230	−	7.93601i	0.457915	−	0.332695i	0.792713	+	0.609595i	$0.208668\pi$
$570$	−4.67835	−	14.3985i	−0.195955	−	0.603087i
$571$	9.62125	−	29.6112i	0.402637	−	1.23919i	−0.520216	−	0.854035i	$-0.674148\pi$
$571$	9.62125	−	29.6112i	0.402637	−	1.23919i	0.922852	−	0.385154i	$-0.125852\pi$
$572$	8.11490	+	5.89582i	0.339301	+	0.246517i
$573$	−3.12536	+	9.61888i	−0.130564	+	0.401834i
$574$	−6.82520	+	21.0058i	−0.284878	+	0.876766i
$575$	1.45045	+	1.05382i	0.0604881	+	0.0439472i
$576$	4.33010	−	13.3267i	0.180421	−	0.555278i
$577$	−0.292095	−	0.898977i	−0.0121601	−	0.0374249i	0.944792	−	0.327670i	$-0.106263\pi$
$577$	−0.292095	−	0.898977i	−0.0121601	−	0.0374249i	−0.956952	+	0.290245i	$0.906263\pi$
$578$	−26.6339	+	19.3506i	−1.10782	+	0.804880i
$579$	6.37654	+	19.6250i	0.265000	+	0.815587i
$580$	37.2300	+	27.0492i	1.54589	+	1.12316i
$581$	−14.5081	−	10.5408i	−0.601897	−	0.437304i
$582$	9.44989	−	6.86575i	0.391711	−	0.284594i
$583$	−11.7810			−0.487920
$584$	−1.21630			−0.0503310
$585$	6.13500	−	4.45734i	0.253651	−	0.184288i
$586$	13.5407	−	41.6740i	0.559361	−	1.72154i
$587$	11.8037	+	36.3281i	0.487191	+	1.49942i	0.828782	+	0.559571i	$0.189034\pi$
$587$	11.8037	+	36.3281i	0.487191	+	1.49942i	−0.341591	+	0.939849i	$0.610966\pi$
$588$	2.87457			0.118545
$589$	−6.20120	+	15.2437i	−0.255516	+	0.628104i
$590$	13.4472			0.553613
$591$	6.00708	+	18.4879i	0.247098	+	0.760490i
$592$	8.87372	−	27.3105i	0.364708	−	1.12245i
$593$	−12.6990	+	9.22638i	−0.521487	+	0.378882i	−0.817164	−	0.576406i	$-0.804455\pi$
$593$	−12.6990	+	9.22638i	−0.521487	+	0.378882i	0.295677	+	0.955288i	$0.404455\pi$
$594$	−47.9746			−1.96842
$595$	−1.17684			−0.0482457
$596$	−3.78923	+	2.75304i	−0.155213	+	0.112769i
$597$	1.61924	+	1.17644i	0.0662709	+	0.0481486i
$598$	0.509128	+	0.369903i	0.0208198	+	0.0151265i
$599$	3.60254	+	11.0875i	0.147196	+	0.453022i	0.997287	−	0.0736136i	$-0.0234532\pi$
$599$	3.60254	+	11.0875i	0.147196	+	0.453022i	−0.850091	+	0.526636i	$0.823453\pi$
$600$	1.68077	−	1.22115i	0.0686171	−	0.0498532i
$601$	−0.689953	−	2.12346i	−0.0281438	−	0.0866176i	0.935998	−	0.352005i	$-0.114500\pi$
$601$	−0.689953	−	2.12346i	−0.0281438	−	0.0866176i	−0.964142	+	0.265388i	$0.914500\pi$
$602$	−8.96020	+	27.5766i	−0.365190	+	1.12394i
$603$	−14.7285	−	10.7009i	−0.599792	−	0.435774i
$604$	5.19250	−	15.9809i	0.211280	−	0.650253i
$605$	−21.4671	+	66.0688i	−0.872760	+	2.68608i
$606$	9.07285	+	6.59181i	0.368559	+	0.267774i
$607$	−5.07613	+	15.6227i	−0.206034	+	0.634107i	0.793635	+	0.608394i	$0.208186\pi$
$607$	−5.07613	+	15.6227i	−0.206034	+	0.634107i	−0.999669	+	0.0257135i	$0.991814\pi$
$608$	6.98561	+	21.4995i	0.283304	+	0.871919i
$609$	−11.8500	+	8.60956i	−0.480188	+	0.348877i
$610$	−19.9369	−	61.3595i	−0.807222	−	2.48437i
$611$	−5.32287	−	3.86729i	−0.215340	−	0.156454i
$612$	−0.540704	−	0.392845i	−0.0218567	−	0.0158798i
$613$	−6.53415	+	4.74734i	−0.263912	+	0.191743i	−0.711870	−	0.702311i	$-0.752151\pi$
$613$	−6.53415	+	4.74734i	−0.263912	+	0.191743i	0.447958	+	0.894055i	$0.352151\pi$
$614$	−58.2618			−2.35125
$615$	−13.4550			−0.542559
$616$	4.75507	−	3.45476i	0.191587	−	0.139196i
$617$	3.54185	−	10.9007i	0.142590	−	0.438846i	−0.854103	−	0.520103i	$-0.825894\pi$
$617$	3.54185	−	10.9007i	0.142590	−	0.438846i	0.996693	+	0.0812572i	$0.0258935\pi$
$618$	9.22858	+	28.4026i	0.371228	+	1.14252i
$619$	10.7300			0.431276			0.215638	−	0.976473i	$-0.430817\pi$
$619$	10.7300			0.431276			0.215638	+	0.976473i	$0.430817\pi$
$620$	31.7424	+	2.29579i	1.27481	+	0.0922012i
$621$	−1.40969			−0.0565689
$622$	16.2245	+	49.9339i	0.650543	+	2.00217i
$623$	−11.2322	+	34.5691i	−0.450008	+	1.38498i
$624$	2.91047	−	2.11458i	0.116512	−	0.0846510i
$625$	−22.0959			−0.883835
$626$	47.1240			1.88345
$627$	11.0816	−	8.05122i	0.442555	−	0.321535i
$628$	−24.1057	−	17.5138i	−0.961922	−	0.698877i
$629$	−0.853097	−	0.619812i	−0.0340152	−	0.0247135i
$630$	10.1586	+	31.2650i	0.404729	+	1.24563i
$631$	16.3136	−	11.8525i	0.649432	−	0.471840i	−0.213645	−	0.976911i	$-0.568534\pi$
$631$	16.3136	−	11.8525i	0.649432	−	0.471840i	0.863078	+	0.505071i	$0.168534\pi$
$632$	0.857628	+	2.63951i	0.0341146	+	0.104994i
$633$	2.44215	−	7.51616i	0.0970667	−	0.298741i
$634$	−32.0924	−	23.3165i	−1.27455	−	0.926017i
$635$	2.63877	−	8.12130i	0.104716	−	0.322284i
$636$	0.917070	−	2.82245i	0.0363642	−	0.111917i
$637$	−1.62158	−	1.17814i	−0.0642492	−	0.0466798i
$638$	−27.4715	+	84.5486i	−1.08761	+	3.34731i
$639$	−3.23692	−	9.96222i	−0.128051	−	0.394099i
$640$	−9.63006	+	6.99665i	−0.380662	+	0.276567i
$641$	−11.1978	−	34.4634i	−0.442288	−	1.36122i	−0.885431	−	0.464771i	$-0.846137\pi$
$641$	−11.1978	−	34.4634i	−0.442288	−	1.36122i	0.443143	−	0.896451i	$-0.353863\pi$
$642$	−15.8375	−	11.5066i	−0.625057	−	0.454130i
$643$	−26.4864	−	19.2435i	−1.04452	−	0.758889i	−0.0733577	−	0.997306i	$-0.523371\pi$
$643$	−26.4864	−	19.2435i	−1.04452	−	0.758889i	−0.971163	+	0.238417i	$0.923371\pi$
$644$	−1.03369	+	0.751020i	−0.0407331	+	0.0295943i
$645$	−17.6639			−0.695516
$646$	0.930385			0.0366055
$647$	−19.6354	+	14.2660i	−0.771949	+	0.560854i	−0.902552	−	0.430581i	$-0.858309\pi$
$647$	−19.6354	+	14.2660i	−0.771949	+	0.560854i	0.130603	+	0.991435i	$0.458309\pi$
$648$	0.496100	−	1.52684i	0.0194887	−	0.0599799i
$649$	3.75965	+	11.5710i	0.147579	+	0.454201i
$650$	10.7171			0.420360
$651$	−3.81709	+	9.38308i	−0.149603	+	0.367752i
$652$	18.0071			0.705213
$653$	9.23845	+	28.4330i	0.361528	+	1.11267i	0.952126	+	0.305704i	$0.0988919\pi$
$653$	9.23845	+	28.4330i	0.361528	+	1.11267i	−0.590598	+	0.806966i	$0.701108\pi$
$654$	5.91110	−	18.1925i	0.231142	−	0.711382i
$655$	0.642009	−	0.466447i	0.0250854	−	0.0182256i
$656$	22.5174			0.879158
$657$	6.15498			0.240129
$658$	23.0750	−	16.7650i	0.899556	−	0.653566i
$659$	−1.69014	−	1.22796i	−0.0658385	−	0.0478345i	0.554379	−	0.832264i	$-0.312956\pi$
$659$	−1.69014	−	1.22796i	−0.0658385	−	0.0478345i	−0.620218	+	0.784430i	$0.712956\pi$
$660$	−21.4304	−	15.5701i	−0.834178	−	0.606065i
$661$	−3.78048	−	11.6351i	−0.147043	−	0.452553i	0.850225	−	0.526420i	$-0.176466\pi$
$661$	−3.78048	−	11.6351i	−0.147043	−	0.452553i	−0.997268	+	0.0738668i	$0.976466\pi$
$662$	43.1719	−	31.3662i	1.67792	−	1.21908i
$663$	−0.0408231	−	0.125641i	−0.00158544	−	0.00487947i
$664$	−1.14522	+	3.52462i	−0.0444432	+	0.136782i
$665$	−17.3396	−	12.5979i	−0.672399	−	0.488527i
$666$	−9.10246	+	28.0145i	−0.352713	+	1.08554i
$667$	−0.807224	+	2.48438i	−0.0312559	+	0.0961956i
$668$	−30.4617	−	22.1317i	−1.17860	−	0.856301i
$669$	1.41307	−	4.34897i	0.0546323	−	0.168141i
$670$	−15.1452	−	46.6120i	−0.585108	−	1.80078i
$671$	47.2243	−	34.3105i	1.82308	−	1.32454i
$672$	4.29992	+	13.2338i	0.165873	+	0.510505i
$673$	8.69724	+	6.31892i	0.335254	+	0.243576i	0.742657	−	0.669672i	$-0.233565\pi$
$673$	8.69724	+	6.31892i	0.335254	+	0.243576i	−0.407403	+	0.913249i	$0.633565\pi$
$674$	8.62140	+	6.26381i	0.332084	+	0.241273i
$675$	−19.4218	+	14.1108i	−0.747546	+	0.543124i
$676$	1.76185			0.0677635
$677$	34.9052			1.34152			0.670758	−	0.741677i	$-0.265969\pi$
$677$	34.9052			1.34152			0.670758	+	0.741677i	$0.265969\pi$
$678$	10.3938	−	7.55155i	0.399172	−	0.290016i
$679$	5.11000	−	15.7270i	0.196104	−	0.603546i
$680$	0.0751541	+	0.231301i	0.00288203	+	0.00886997i
$681$	−22.1140			−0.847410
$682$	14.7311	+	59.6897i	0.564082	+	2.28564i
$683$	−18.2965			−0.700096			−0.350048	−	0.936732i	$-0.613835\pi$
$683$	−18.2965			−0.700096			−0.350048	+	0.936732i	$0.613835\pi$
$684$	−3.76139	−	11.5764i	−0.143820	−	0.442633i
$685$	15.8384	−	48.7456i	0.605155	−	1.86247i
$686$	31.5796	−	22.9439i	1.20572	−	0.876004i
$687$	−22.1630			−0.845571
$688$	29.5611			1.12701
$689$	−1.67411	+	1.21631i	−0.0637785	+	0.0463378i
$690$	−1.34454	−	0.976867i	−0.0511859	−	0.0371887i
$691$	14.6402	+	10.6368i	0.556941	+	0.404641i	0.830338	−	0.557260i	$-0.188147\pi$
$691$	14.6402	+	10.6368i	0.556941	+	0.404641i	−0.273397	+	0.961901i	$0.588147\pi$
$692$	8.00601	+	24.6400i	0.304343	+	0.936671i
$693$	−24.0626	+	17.4825i	−0.914062	+	0.664105i
$694$	−0.278621	−	0.857507i	−0.0105763	−	0.0325505i
$695$	9.13905	−	28.1271i	0.346664	−	1.06692i
$696$	2.44891	+	1.77924i	0.0928258	+	0.0674419i
$697$	0.255517	−	0.786399i	0.00967838	−	0.0297870i
$698$	9.05273	−	27.8614i	0.342651	−	1.05457i
$699$	13.0396	+	9.47380i	0.493202	+	0.358332i
$700$	−6.72394	+	20.6942i	−0.254141	+	0.782166i
$701$	−7.87859	−	24.2478i	−0.297570	−	0.915827i	−0.982346	−	0.187073i	$-0.940100\pi$
$701$	−7.87859	−	24.2478i	−0.297570	−	0.915827i	0.684776	−	0.728754i	$-0.259900\pi$
$702$	−6.81731	+	4.95306i	−0.257303	+	0.186941i
$703$	−5.93454	−	18.2646i	−0.223825	−	0.688864i
$704$	27.6118	+	20.0612i	1.04066	+	0.756084i
$705$	14.0570	+	10.2130i	0.529418	+	0.384644i
$706$	−43.4328	+	31.5557i	−1.63461	+	1.18762i
$707$	15.8765			0.597099
$708$	−3.06480			−0.115182
$709$	40.8886	−	29.7073i	1.53560	−	1.11568i	0.582583	−	0.812771i	$-0.302042\pi$
$709$	40.8886	−	29.7073i	1.53560	−	1.11568i	0.953019	−	0.302910i	$-0.0979581\pi$
$710$	8.71409	−	26.8192i	0.327034	−	1.00651i
$711$	−4.33995	−	13.3570i	−0.162761	−	0.500926i
$712$	7.51165			0.281511
$713$	0.432859	+	1.75392i	0.0162107	+	0.0656850i
$714$	0.572689			0.0214324
$715$	5.70771	+	17.5665i	0.213456	+	0.656950i
$716$	−11.2171	+	34.5226i	−0.419201	+	1.29017i
$717$	11.7245	−	8.51834i	0.437859	−	0.318123i
$718$	62.4996			2.33247
$719$	31.2057			1.16377			0.581887	−	0.813269i	$-0.302314\pi$
$719$	31.2057			1.16377			0.581887	+	0.813269i	$0.302314\pi$
$720$	27.1141	−	19.6996i	1.01048	−	0.734159i
$721$	34.2042	+	24.8508i	1.27383	+	0.925493i
$722$	−16.1051	−	11.7011i	−0.599371	−	0.435469i
$723$	−0.487989	−	1.50188i	−0.0181485	−	0.0558553i
$724$	−5.69800	+	4.13984i	−0.211765	+	0.153856i
$725$	13.7468	+	42.3084i	0.510545	+	1.57130i
$726$	10.4466	−	32.1513i	0.387710	−	1.19325i
$727$	−16.9704	−	12.3297i	−0.629399	−	0.457285i	0.226793	−	0.973943i	$-0.427176\pi$
$727$	−16.9704	−	12.3297i	−0.629399	−	0.457285i	−0.856192	+	0.516658i	$0.827176\pi$
$728$	0.319026	−	0.981860i	0.0118239	−	0.0363901i
$729$	0.768085	−	2.36392i	0.0284476	−	0.0875527i
$730$	13.4052	+	9.73948i	0.496150	+	0.360474i
$731$	0.335445	−	1.03239i	0.0124069	−	0.0381844i
$732$	4.54389	+	13.9847i	0.167947	+	0.516888i
$733$	−26.1261	+	18.9817i	−0.964990	+	0.701106i	−0.954304	−	0.298837i	$-0.903401\pi$
$733$	−26.1261	+	18.9817i	−0.964990	+	0.701106i	−0.0106858	+	0.999943i	$0.503401\pi$
$734$	18.8606	+	58.0470i	0.696158	+	2.14255i
$735$	4.28238	+	3.11133i	0.157958	+	0.114763i
$736$	2.00764	+	1.45863i	0.0740025	+	0.0537660i
$737$	35.8741	−	26.0641i	1.32144	−	0.960083i
$738$	−23.0979			−0.850245
$739$	8.35652			0.307400			0.153700	−	0.988118i	$-0.450881\pi$
$739$	8.35652			0.307400			0.153700	+	0.988118i	$0.450881\pi$
$740$	−30.0464	+	21.8300i	−1.10453	+	0.802485i
$741$	0.743480	−	2.28820i	0.0273124	−	0.0840590i
$742$	−2.77207	−	8.53156i	−0.101766	−	0.313203i
$743$	−23.2947			−0.854601			−0.427300	−	0.904110i	$-0.640535\pi$
$743$	−23.2947			−0.854601			−0.427300	+	0.904110i	$0.640535\pi$
$744$	2.08795	+	0.151012i	0.0765481	+	0.00553638i
$745$	−8.62476			−0.315987
$746$	−5.26413	−	16.2013i	−0.192734	−	0.593173i
$747$	5.79528	−	17.8360i	0.212038	−	0.652586i
$748$	1.31699	−	0.956849i	0.0481539	−	0.0349859i
$749$	−27.7140			−1.01265
$750$	−2.69206			−0.0983000
$751$	−33.1211	+	24.0639i	−1.20861	+	0.878104i	−0.995103	−	0.0988389i	$-0.968487\pi$
$751$	−33.1211	+	24.0639i	−1.20861	+	0.878104i	−0.213503	+	0.976943i	$0.568487\pi$
$752$	−23.5249	−	17.0918i	−0.857863	−	0.623274i
$753$	−3.20761	−	2.33046i	−0.116892	−	0.0849268i
$754$	4.82532	+	14.8508i	0.175728	+	0.540835i
$755$	25.0326	−	18.1872i	0.911029	−	0.661901i
$756$	−5.28690	−	16.2714i	−0.192283	−	0.591785i
$757$	12.5014	−	38.4755i	0.454373	−	1.39842i	−0.417498	−	0.908678i	$-0.637093\pi$
$757$	12.5014	−	38.4755i	0.454373	−	1.39842i	0.871870	−	0.489737i	$-0.162907\pi$
$758$	31.0176	+	22.5356i	1.12661	+	0.818530i
$759$	0.464656	−	1.43006i	0.0168660	−	0.0519081i
$760$	−1.36873	+	4.21250i	−0.0496489	+	0.152804i
$761$	−12.3540	−	8.97574i	−0.447834	−	0.325370i	0.340906	−	0.940097i	$-0.389266\pi$
$761$	−12.3540	−	8.97574i	−0.447834	−	0.325370i	−0.788740	+	0.614727i	$0.789266\pi$
$762$	−1.28411	+	3.95210i	−0.0465186	+	0.143169i
$763$	−8.36831	−	25.7550i	−0.302953	−	0.932394i
$764$	−17.7101	+	12.8671i	−0.640728	+	0.465516i
$765$	−0.380310	−	1.17047i	−0.0137501	−	0.0423186i
$766$	16.3179	+	11.8556i	0.589588	+	0.428361i
$767$	1.72888	+	1.25611i	0.0624264	+	0.0453554i
$768$	12.5821	−	9.14140i	0.454016	−	0.329862i
$769$	4.15376			0.149788			0.0748941	−	0.997191i	$-0.476138\pi$
$769$	4.15376			0.149788			0.0748941	+	0.997191i	$0.476138\pi$
$770$	−80.0709			−2.88556
$771$	0.0482948	−	0.0350882i	0.00173929	−	0.00126367i
$772$	−13.8016	+	42.4771i	−0.496732	+	1.52878i
$773$	4.17806	+	12.8588i	0.150275	+	0.462497i	0.997652	−	0.0684944i	$-0.0218195\pi$
$773$	4.17806	+	12.8588i	0.150275	+	0.462497i	−0.847377	+	0.530992i	$0.821820\pi$
$774$	−30.3231			−1.08994
$775$	23.5202	+	19.8316i	0.844870	+	0.712373i
$776$	−3.41737			−0.122677
$777$	−3.65295	−	11.2426i	−0.131049	−	0.403327i
$778$	2.81259	−	8.65627i	0.100836	−	0.310342i
$779$	12.1831	−	8.85154i	0.436505	−	0.317139i
$780$	−4.65282			−0.166598
$781$	25.5136			0.912949
$782$	0.0826278	−	0.0600326i	0.00295476	−	0.00214676i
$783$	−28.2980	−	20.5597i	−1.01129	−	0.734743i
$784$	−7.16669	−	5.20691i	−0.255953	−	0.185961i
$785$	−16.9550	−	52.1821i	−0.605150	−	1.86246i
$786$	−0.312423	+	0.226989i	−0.0111438	+	0.00809642i
$787$	−10.2698	−	31.6072i	−0.366079	−	1.12667i	−0.949303	−	0.314363i	$-0.898209\pi$
$787$	−10.2698	−	31.6072i	−0.366079	−	1.12667i	0.583224	−	0.812311i	$-0.301791\pi$
$788$	−13.0019	+	40.0159i	−0.463175	+	1.42551i
$789$	3.37210	+	2.44998i	0.120050	+	0.0872214i
$790$	11.6835	−	35.9582i	0.415682	−	1.27934i
$791$	5.62043	−	17.2979i	0.199839	−	0.615043i
$792$	4.97274	+	3.61291i	0.176699	+	0.128379i
$793$	3.16836	−	9.75120i	0.112512	−	0.346275i
$794$	−14.2984	−	44.0060i	−0.507432	−	1.56171i
$795$	4.42111	−	3.21212i	0.156801	−	0.113922i
$796$	1.33869	+	4.12006i	0.0474486	+	0.146032i
$797$	5.81927	+	4.22795i	0.206129	+	0.149762i	0.686061	−	0.727544i	$-0.259338\pi$
$797$	5.81927	+	4.22795i	0.206129	+	0.149762i	−0.479931	+	0.877306i	$0.659338\pi$
$798$	8.43801	+	6.13058i	0.298702	+	0.217020i
$799$	−0.863863	+	0.627633i	−0.0305613	+	0.0222041i
$800$	42.2607			1.49414
$801$	−38.0120			−1.34309
$802$	41.2660	−	29.9815i	1.45715	−	1.05868i
$803$	−4.63267	+	14.2579i	−0.163484	+	0.503151i
$804$	3.45178	+	10.6235i	0.121735	+	0.374662i
$805$	−2.35281			−0.0829256
$806$	8.25589	+	6.96116i	0.290801	+	0.245196i
$807$	5.70770			0.200921
$808$	−1.01389	−	3.12044i	−0.0356686	−	0.109777i
$809$	−15.5173	+	47.7574i	−0.545560	+	1.67906i	0.174096	+	0.984729i	$0.444300\pi$
$809$	−15.5173	+	47.7574i	−0.545560	+	1.67906i	−0.719655	+	0.694331i	$0.755700\pi$
$810$	−17.6938	+	12.8553i	−0.621695	+	0.451688i
$811$	30.6035			1.07463			0.537317	−	0.843380i	$-0.319438\pi$
$811$	30.6035			1.07463			0.537317	+	0.843380i	$0.319438\pi$
$812$	−31.7035			−1.11257
$813$	6.02289	−	4.37589i	0.211232	−	0.153469i
$814$	−58.0439	−	42.1714i	−2.03444	−	1.47811i
$815$	26.8259	+	19.4902i	0.939672	+	0.682712i
$816$	−0.180421	−	0.555279i	−0.00631600	−	0.0194386i
$817$	15.9941	−	11.6204i	0.559563	−	0.406546i
$818$	−19.3636	−	59.5952i	−0.677034	−	2.08370i
$819$	−1.61440	+	4.96861i	−0.0564117	+	0.173617i
$820$	−23.5607	−	17.1178i	−0.822774	−	0.597780i
$821$	5.52664	−	17.0092i	0.192881	−	0.593627i	−0.807114	−	0.590396i	$-0.798972\pi$
$821$	5.52664	−	17.0092i	0.192881	−	0.593627i	0.999995	−	0.00323084i	$-0.00102841\pi$
$822$	−7.70751	+	23.7213i	−0.268830	+	0.827374i
$823$	−2.51565	−	1.82772i	−0.0876899	−	0.0637105i	0.543076	−	0.839683i	$-0.317259\pi$
$823$	−2.51565	−	1.82772i	−0.0876899	−	0.0637105i	−0.630766	+	0.775973i	$0.717259\pi$
$824$	2.69996	−	8.30963i	0.0940577	−	0.289480i
$825$	−7.91299	−	24.3537i	−0.275495	−	0.847886i
$826$	−7.49483	+	5.44531i	−0.260778	+	0.189467i
$827$	−2.23384	−	6.87505i	−0.0776782	−	0.239069i	0.904676	−	0.426101i	$-0.140113\pi$
$827$	−2.23384	−	6.87505i	−0.0776782	−	0.239069i	−0.982354	+	0.187032i	$0.940113\pi$
$828$	−1.08101	−	0.785400i	−0.0375677	−	0.0272945i
$829$	30.9298	+	22.4718i	1.07424	+	0.780478i	0.976669	−	0.214751i	$-0.0688940\pi$
$829$	30.9298	+	22.4718i	1.07424	+	0.780478i	0.0975669	+	0.995229i	$0.468894\pi$
$830$	40.8451	−	29.6757i	1.41775	−	1.03006i
$831$	−4.82536			−0.167390
$832$	5.99489			0.207835
$833$	−0.263170	+	0.191204i	−0.00911830	+	0.00662483i
$834$	−4.44737	+	13.6876i	−0.154000	+	0.473963i
$835$	−21.4255	−	65.9410i	−0.741461	−	2.28198i
$836$	29.6475			1.02538
$837$	−24.1269	−	1.74500i	−0.833949	−	0.0603159i
$838$	−53.4590			−1.84671
$839$	6.33597	+	19.5001i	0.218742	+	0.673218i	0.998867	+	0.0475943i	$0.0151555\pi$
$839$	6.33597	+	19.5001i	0.218742	+	0.673218i	−0.780125	+	0.625624i	$0.784845\pi$
$840$	−0.842506	+	2.59297i	−0.0290692	+	0.0894658i
$841$	−28.9762	+	21.0525i	−0.999180	+	0.725947i
$842$	69.2016			2.38484
$843$	−1.19602			−0.0411932
$844$	13.8386	−	10.0543i	0.476344	−	0.346085i
$845$	2.62471	+	1.90696i	0.0902926	+	0.0656014i
$846$	24.1313	+	17.5324i	0.829651	+	0.602776i
$847$	−14.7892	−	45.5164i	−0.508163	−	1.56396i
$848$	−7.39887	+	5.37559i	−0.254078	+	0.184599i
$849$	−7.43896	−	22.8948i	−0.255305	−	0.785747i
$850$	0.537477	−	1.65418i	0.0184353	−	0.0567380i
$851$	−1.70557	−	1.23917i	−0.0584660	−	0.0424781i
$852$	−1.98606	+	6.11246i	−0.0680412	+	0.209409i
$853$	3.99702	−	12.3016i	0.136855	−	0.421197i	−0.859019	−	0.511944i	$-0.828925\pi$
$853$	3.99702	−	12.3016i	0.136855	−	0.421197i	0.995874	+	0.0907470i	$0.0289255\pi$
$854$	35.9588	+	26.1256i	1.23048	+	0.894000i
$855$	6.92631	−	21.3170i	0.236875	−	0.729025i
$856$	1.76984	+	5.44702i	0.0604920	+	0.186175i
$857$	−20.9348	+	15.2100i	−0.715119	+	0.519565i	−0.884821	−	0.465931i	$-0.845720\pi$
$857$	−20.9348	+	15.2100i	−0.715119	+	0.519565i	0.169702	+	0.985495i	$0.445720\pi$
$858$	−2.77756	−	8.54846i	−0.0948244	−	0.291839i
$859$	24.1249	+	17.5278i	0.823131	+	0.598040i	0.917608	−	0.397487i	$-0.130118\pi$
$859$	24.1249	+	17.5278i	0.823131	+	0.598040i	−0.0944765	+	0.995527i	$0.530118\pi$
$860$	−30.9307	−	22.4725i	−1.05473	−	0.766304i
$861$	7.49919	−	5.44848i	0.255572	−	0.185684i
$862$	6.69024			0.227870
$863$	−32.3374			−1.10078			−0.550389	−	0.834909i	$-0.685520\pi$
$863$	−32.3374			−1.10078			−0.550389	+	0.834909i	$0.685520\pi$
$864$	−26.8826	+	19.5313i	−0.914564	+	0.664470i
$865$	−14.7425	+	45.3726i	−0.501259	+	1.54272i
$866$	−6.45974	−	19.8811i	−0.219511	−	0.675586i
$867$	13.8166			0.469235
$868$	−18.6214	+	11.5742i	−0.632050	+	0.392854i
$869$	34.2077			1.16042
$870$	−12.7431	−	39.2191i	−0.432030	−	1.32965i
$871$	2.40686	−	7.40754i	0.0815532	−	0.250995i
$872$	−4.52758	+	3.28948i	−0.153323	+	0.111396i
$873$	17.2933			0.585290
$874$	1.86008			0.0629182
$875$	−3.08327	+	2.24013i	−0.104234	+	0.0757301i
$876$	−3.05523	−	2.21976i	−0.103227	−	0.0749986i
$877$	14.6163	+	10.6193i	0.493556	+	0.358589i	0.806550	−	0.591166i	$-0.201332\pi$
$877$	14.6163	+	10.6193i	0.493556	+	0.358589i	−0.312994	+	0.949755i	$0.601332\pi$
$878$	2.99113	+	9.20575i	0.100946	+	0.310679i
$879$	−14.8778	+	10.8094i	−0.501817	+	0.364592i
$880$	25.2257	+	77.6366i	0.850357	+	2.61713i
$881$	1.22293	−	3.76379i	0.0412016	−	0.126805i	−0.928340	−	0.371732i	$-0.878764\pi$
$881$	1.22293	−	3.76379i	0.0412016	−	0.126805i	0.969542	+	0.244927i	$0.0787640\pi$
$882$	7.35143	+	5.34113i	0.247536	+	0.179845i
$883$	0.447353	−	1.37681i	0.0150546	−	0.0463333i	−0.943247	−	0.332092i	$-0.892246\pi$
$883$	0.447353	−	1.37681i	0.0150546	−	0.0463333i	0.958302	+	0.285759i	$0.0922456\pi$
$884$	0.0883590	−	0.271941i	0.00297183	−	0.00914637i
$885$	−4.56576	−	3.31722i	−0.153476	−	0.111507i
$886$	0.537306	−	1.65366i	0.0180512	−	0.0555558i
$887$	3.39318	+	10.4431i	0.113932	+	0.350646i	0.991723	−	0.128398i	$-0.0409835\pi$
$887$	3.39318	+	10.4431i	0.113932	+	0.350646i	−0.877791	+	0.479044i	$0.840983\pi$
$888$	−1.97639	+	1.43593i	−0.0663233	+	0.0481867i
$889$	1.81791	+	5.59496i	0.0609709	+	0.187649i
$890$	−82.7881	−	60.1491i	−2.77506	−	2.01620i
$891$	−16.0086	−	11.6309i	−0.536307	−	0.389650i
$892$	8.00723	−	5.81760i	0.268102	−	0.194788i
$893$	−19.4469			−0.650766
$894$	4.19710			0.140372
$895$	−54.0764	+	39.2888i	−1.80758	+	1.31328i
$896$	2.53411	−	7.79919i	0.0846587	−	0.260553i
$897$	−0.0816160	−	0.251188i	−0.00272508	−	0.00838694i
$898$	32.4761			1.08374
$899$	−16.8910	+	41.5212i	−0.563347	+	1.38481i
$900$	−22.7552			−0.758507
$901$	0.103779	+	0.319398i	0.00345737	+	0.0106407i
$902$	17.3851	−	53.5058i	0.578860	−	1.78155i
$903$	9.84501	−	7.15282i	0.327622	−	0.238031i
$904$	−3.75873			−0.125013
$905$	−12.9694			−0.431116
$906$	−12.1817	+	8.85052i	−0.404710	+	0.294039i
$907$	2.90044	+	2.10729i	0.0963075	+	0.0699715i	0.634897	−	0.772597i	$-0.281043\pi$
$907$	2.90044	+	2.10729i	0.0963075	+	0.0699715i	−0.538589	+	0.842568i	$0.681043\pi$
$908$	−38.7231	−	28.1339i	−1.28507	−	0.933658i
$909$	5.13071	+	15.7907i	0.170175	+	0.523744i
$910$	−11.3783	+	8.26680i	−0.377186	+	0.274042i
$911$	−10.4744	−	32.2368i	−0.347032	−	1.06805i	−0.960487	−	0.278324i	$-0.910221\pi$
$911$	−10.4744	−	32.2368i	−0.347032	−	1.06805i	0.613456	−	0.789729i	$-0.289779\pi$
$912$	3.28587	−	10.1129i	0.108806	−	0.334871i
$913$	36.9549	+	26.8493i	1.22303	+	0.888582i
$914$	12.1710	−	37.4584i	0.402580	−	1.23901i
$915$	−8.36723	+	25.7517i	−0.276612	+	0.851324i
$916$	−38.8089	−	28.1963i	−1.28228	−	0.931631i
$917$	−0.168942	+	0.519950i	−0.00557895	+	0.0171703i
$918$	0.422607	+	1.30065i	0.0139481	+	0.0429279i
$919$	−34.0601	+	24.7461i	−1.12354	+	0.816298i	−0.984742	−	0.174022i	$-0.944323\pi$
$919$	−34.0601	+	24.7461i	−1.12354	+	0.816298i	−0.138797	+	0.990321i	$0.544323\pi$
$920$	0.150253	+	0.462431i	0.00495369	+	0.0152459i
$921$	19.7818	+	14.3723i	0.651831	+	0.473583i
$922$	9.00843	+	6.54501i	0.296677	+	0.215548i
$923$	3.62555	−	2.63411i	0.119336	−	0.0867029i
$924$	18.2492			0.600356
$925$	−35.9021			−1.18045
$926$	−8.45606	+	6.14369i	−0.277883	+	0.201894i
$927$	−13.6629	+	42.0501i	−0.448749	+	1.38111i
$928$	19.0276	+	58.5610i	0.624612	+	1.92236i
$929$	11.2438			0.368896			0.184448	−	0.982842i	$-0.440950\pi$
$929$	11.2438			0.368896			0.184448	+	0.982842i	$0.440950\pi$
$930$	−21.8027	−	18.3835i	−0.714940	−	0.602819i
$931$	−5.92437			−0.194163
$932$	10.7804	+	33.1785i	0.353122	+	1.08680i
$933$	6.80918	−	20.9565i	0.222922	−	0.686085i
$934$	16.0868	−	11.6878i	0.526377	−	0.382435i
$935$	2.99763			0.0980330
$936$	1.07965			0.0352894
$937$	15.2395	−	11.0721i	0.497853	−	0.361711i	−0.310344	−	0.950624i	$-0.600444\pi$
$937$	15.2395	−	11.0721i	0.497853	−	0.361711i	0.808196	+	0.588913i	$0.200444\pi$
$938$	27.3162	+	19.8464i	0.891907	+	0.648008i
$939$	−16.0001	−	11.6248i	−0.522144	−	0.379360i
$940$	11.6215	+	35.7673i	0.379052	+	1.16660i
$941$	−26.2320	+	19.0587i	−0.855138	+	0.621294i	−0.926558	−	0.376152i	$-0.877247\pi$
$941$	−26.2320	+	19.0587i	−0.855138	+	0.621294i	0.0714195	+	0.997446i	$0.477247\pi$
$942$	8.25088	+	25.3936i	0.268828	+	0.827368i
$943$	0.510845	−	1.57222i	0.0166354	−	0.0511985i
$944$	7.64095	+	5.55147i	0.248692	+	0.180685i
$945$	9.73542	−	29.9625i	0.316693	−	0.974681i
$946$	22.8233	−	70.2430i	0.742050	−	2.28380i
$947$	−2.68231	−	1.94881i	−0.0871632	−	0.0633278i	0.543350	−	0.839506i	$-0.317156\pi$
$947$	−2.68231	−	1.94881i	−0.0871632	−	0.0633278i	−0.630513	+	0.776178i	$0.717156\pi$
$948$	−2.66283	+	8.19536i	−0.0864848	+	0.266173i
$949$	0.813721	+	2.50438i	0.0264145	+	0.0812955i
$950$	25.6271	−	18.6191i	0.831452	−	0.604085i
$951$	5.14459	+	15.8334i	0.166825	+	0.513434i
$952$	−0.135550	−	0.0984829i	−0.00439320	−	0.00319185i
$953$	29.2733	+	21.2683i	0.948255	+	0.688947i	0.950393	−	0.311050i	$-0.100681\pi$
$953$	29.2733	+	21.2683i	0.948255	+	0.688947i	−0.00213881	+	0.999998i	$0.500681\pi$
$954$	7.58960	−	5.51417i	0.245722	−	0.178528i
$955$	−40.3104			−1.30441
$956$	31.3676			1.01450
$957$	30.1843	−	21.9302i	0.975720	−	0.708902i
$958$	1.10326	−	3.39549i	0.0356447	−	0.109703i
$959$	10.9115	+	33.5821i	0.352350	+	1.08442i
$960$	−15.8317			−0.510967
$961$	5.23731	+	30.5544i	0.168945	+	0.985625i
$962$	−12.6021			−0.406308
$963$	−8.95613	−	27.5641i	−0.288607	−	0.888241i
$964$	1.05622	−	3.25072i	0.0340186	−	0.104698i
$965$	−66.5364	+	48.3415i	−2.14188	+	1.55617i
$966$	1.14496			0.0368384
$967$	1.48420			0.0477287			0.0238643	−	0.999715i	$-0.492403\pi$
$967$	1.48420			0.0477287			0.0238643	+	0.999715i	$0.492403\pi$
$968$	−8.00153	+	5.81346i	−0.257179	+	0.186852i
$969$	−0.315896	−	0.229512i	−0.0101480	−	0.00737298i
$970$	37.6639	+	27.3644i	1.20932	+	0.878619i
$971$	−10.9803	−	33.7938i	−0.352373	−	1.08449i	−0.957517	−	0.288377i	$-0.906884\pi$
$971$	−10.9803	−	33.7938i	−0.352373	−	1.08449i	0.605143	−	0.796116i	$-0.293116\pi$
$972$	22.6108	−	16.4277i	0.725242	−	0.526919i
$973$	6.29612	+	19.3775i	0.201844	+	0.621213i
$974$	−11.5406	+	35.5184i	−0.369785	+	1.13808i
$975$	−3.63881	−	2.64375i	−0.116535	−	0.0846678i
$976$	14.0028	−	43.0962i	0.448219	−	1.37948i
$977$	3.73009	−	11.4800i	0.119336	−	0.367279i	−0.873491	−	0.486841i	$-0.838149\pi$
$977$	3.73009	−	11.4800i	0.119336	−	0.367279i	0.992827	+	0.119562i	$0.0381491\pi$
$978$	−13.0544	−	9.48459i	−0.417434	−	0.303284i
$979$	28.6105	−	88.0540i	0.914395	−	2.81422i
$980$	3.54042	+	10.8963i	0.113094	+	0.348069i
$981$	22.9114	−	16.6461i	0.731505	−	0.531470i
$982$	−20.2812	−	62.4190i	−0.647198	−	1.99187i
$983$	0.625845	+	0.454703i	0.0199614	+	0.0145028i	0.597721	−	0.801704i	$-0.296073\pi$
$983$	0.625845	+	0.454703i	0.0199614	+	0.0145028i	−0.577760	+	0.816207i	$0.696073\pi$
$984$	−1.54977	−	1.12598i	−0.0494049	−	0.0358948i
$985$	−62.6812	+	45.5405i	−1.99719	+	1.45104i
$986$	2.53421			0.0807057
$987$	−11.9704			−0.381021
$988$	4.21298	−	3.06091i	0.134033	−	0.0973805i
$989$	0.670642	−	2.06402i	0.0213252	−	0.0656321i
$990$	−25.8759	−	79.6380i	−0.822391	−	2.53106i
$991$	54.5006			1.73127			0.865634	−	0.500677i	$-0.166915\pi$
$991$	54.5006			1.73127			0.865634	+	0.500677i	$0.166915\pi$
$992$	32.5553	+	27.4498i	1.03363	+	0.871533i
$993$	−22.3958			−0.710710
$994$	6.00335	+	18.4764i	0.190415	+	0.586036i
$995$	−2.46509	+	7.58678i	−0.0781487	+	0.240517i
$996$	−9.30914	+	6.76348i	−0.294971	+	0.214309i
$997$	2.72095			0.0861733			0.0430866	−	0.999071i	$-0.486281\pi$
$997$	2.72095			0.0861733			0.0430866	+	0.999071i	$0.486281\pi$
$998$	−36.7606			−1.16364
$999$	22.8378	−	16.5926i	0.722556	−	0.524967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.d.66.3	✓	48
31.8	even	5	inner	403.2.k.d.287.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.d.66.3	✓	48	1.1	even	1	trivial
403.2.k.d.287.3	yes	48	31.8	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.599354 - 1.84462i) q^{2} +(-0.251540 + 0.774160i) q^{3} +(-1.42537 + 1.03559i) q^{4} -3.24431 q^{5} +1.57879 q^{6} +(1.80822 - 1.31375i) q^{7} +(-0.373685 - 0.271498i) q^{8} +(1.89100 + 1.37389i) q^{9} +O(q^{10})\)	\(q+(-0.599354 - 1.84462i) q^{2} +(-0.251540 + 0.774160i) q^{3} +(-1.42537 + 1.03559i) q^{4} -3.24431 q^{5} +1.57879 q^{6} +(1.80822 - 1.31375i) q^{7} +(-0.373685 - 0.271498i) q^{8} +(1.89100 + 1.37389i) q^{9} +(1.94449 + 5.98453i) q^{10} +(-4.60589 + 3.34638i) q^{11} +(-0.443176 - 1.36395i) q^{12} +(-0.309017 + 0.951057i) q^{13} +(-3.50714 - 2.54809i) q^{14} +(0.816074 - 2.51162i) q^{15} +(-1.36573 + 4.20327i) q^{16} +(0.131298 + 0.0953933i) q^{17} +(1.40093 - 4.31163i) q^{18} +(0.913366 + 2.81105i) q^{19} +(4.62434 - 3.35978i) q^{20} +(0.562214 + 1.73032i) q^{21} +(8.93336 + 6.49046i) q^{22} +(0.262498 + 0.190716i) q^{23} +(0.304180 - 0.221000i) q^{24} +5.52558 q^{25} +1.93955 q^{26} +(-3.51489 + 2.55372i) q^{27} +(-1.21688 + 3.74516i) q^{28} +(2.48786 + 7.65684i) q^{29} -5.12210 q^{30} +(4.25660 + 3.58906i) q^{31} +7.64820 q^{32} +(-1.43207 - 4.40744i) q^{33} +(0.0972707 - 0.299369i) q^{34} +(-5.86645 + 4.26223i) q^{35} -4.11816 q^{36} -6.49744 q^{37} +(4.63790 - 3.36963i) q^{38} +(-0.658540 - 0.478457i) q^{39} +(1.21235 + 0.880826i) q^{40} +(-1.57442 - 4.84556i) q^{41} +(2.85481 - 2.07414i) q^{42} +(-2.06691 - 6.36130i) q^{43} +(3.09962 - 9.53964i) q^{44} +(-6.13500 - 4.45734i) q^{45} +(0.194470 - 0.598516i) q^{46} +(-2.03315 + 6.25741i) q^{47} +(-2.91047 - 2.11458i) q^{48} +(-0.619387 + 1.90628i) q^{49} +(-3.31177 - 10.1926i) q^{50} +(-0.106876 + 0.0776501i) q^{51} +(-0.544442 - 1.67562i) q^{52} +(1.67411 + 1.21631i) q^{53} +(6.81731 + 4.95306i) q^{54} +(14.9430 - 10.8567i) q^{55} -1.03239 q^{56} -2.40595 q^{57} +(12.6329 - 9.17831i) q^{58} +(0.660375 - 2.03243i) q^{59} +(1.43780 + 4.42510i) q^{60} -10.2530 q^{61} +(4.06924 - 10.0029i) q^{62} +5.22431 q^{63} +(-1.85252 - 5.70148i) q^{64} +(1.00255 - 3.08553i) q^{65} +(-7.27175 + 5.28324i) q^{66} -7.78875 q^{67} -0.285936 q^{68} +(-0.213674 + 0.155243i) q^{69} +(11.3783 + 8.26680i) q^{70} +(-3.62555 - 2.63411i) q^{71} +(-0.333630 - 1.02681i) q^{72} +(2.13035 - 1.54779i) q^{73} +(3.89426 + 11.9853i) q^{74} +(-1.38990 + 4.27768i) q^{75} +(-4.21298 - 3.06091i) q^{76} +(-3.93218 + 12.1020i) q^{77} +(-0.487874 + 1.50152i) q^{78} +(-4.86100 - 3.53172i) q^{79} +(4.43084 - 13.6367i) q^{80} +(1.07404 + 3.30556i) q^{81} +(-7.99459 + 5.80841i) q^{82} +(-2.47937 - 7.63070i) q^{83} +(-2.59326 - 1.88411i) q^{84} +(-0.425971 - 0.309486i) q^{85} +(-10.4954 + 7.62534i) q^{86} -6.55341 q^{87} +2.62969 q^{88} +(-13.1566 + 9.55884i) q^{89} +(-4.54506 + 13.9883i) q^{90} +(0.690680 + 2.12570i) q^{91} -0.571660 q^{92} +(-3.84921 + 2.39250i) q^{93} +12.7611 q^{94} +(-2.96325 - 9.11994i) q^{95} +(-1.92383 + 5.92093i) q^{96} +(5.98552 - 4.34873i) q^{97} +3.88759 q^{98} -13.3073 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9}+O(q^{10}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9} - 19 q^{10} - 9 q^{11} + 15 q^{12} + 12 q^{13} - 25 q^{14} - 30 q^{15} - 21 q^{16} + 11 q^{17} + 17 q^{18} + 36 q^{19} + 30 q^{20} + 11 q^{21} + 15 q^{22} - 7 q^{23} - 20 q^{24} - 16 q^{25} + 8 q^{26} - 5 q^{27} - 9 q^{28} + 12 q^{29} + 18 q^{30} + 22 q^{31} - 76 q^{32} - 49 q^{33} - 26 q^{34} + 8 q^{35} + 2 q^{36} + 64 q^{37} - 27 q^{38} - 3 q^{39} - 24 q^{40} + 46 q^{41} + 20 q^{42} - 28 q^{43} - 23 q^{45} + 34 q^{46} + 5 q^{47} - 20 q^{48} - 11 q^{49} + 9 q^{50} + 59 q^{51} + 17 q^{52} + 23 q^{53} + 41 q^{54} - 10 q^{55} - 60 q^{56} + 24 q^{57} - 37 q^{58} + 71 q^{59} - 72 q^{60} + 22 q^{61} + 43 q^{62} - 106 q^{63} - 52 q^{64} + 2 q^{65} - 21 q^{66} - 56 q^{67} - 104 q^{68} - 12 q^{69} - 32 q^{70} - 36 q^{71} + 147 q^{72} - 12 q^{73} + 10 q^{74} + 34 q^{75} - 49 q^{76} - 30 q^{77} + 5 q^{78} - 70 q^{79} + q^{81} + 130 q^{82} + 11 q^{83} + 77 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} + 96 q^{88} - 40 q^{89} - 48 q^{90} + 10 q^{91} + 112 q^{92} + 50 q^{93} + 78 q^{94} + 41 q^{95} - 75 q^{96} - 47 q^{97} - 46 q^{98} + 46 q^{99}+O(q^{100}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9 - 19 * q^10 - 9 * q^11 + 15 * q^12 + 12 * q^13 - 25 * q^14 - 30 * q^15 - 21 * q^16 + 11 * q^17 + 17 * q^18 + 36 * q^19 + 30 * q^20 + 11 * q^21 + 15 * q^22 - 7 * q^23 - 20 * q^24 - 16 * q^25 + 8 * q^26 - 5 * q^27 - 9 * q^28 + 12 * q^29 + 18 * q^30 + 22 * q^31 - 76 * q^32 - 49 * q^33 - 26 * q^34 + 8 * q^35 + 2 * q^36 + 64 * q^37 - 27 * q^38 - 3 * q^39 - 24 * q^40 + 46 * q^41 + 20 * q^42 - 28 * q^43 - 23 * q^45 + 34 * q^46 + 5 * q^47 - 20 * q^48 - 11 * q^49 + 9 * q^50 + 59 * q^51 + 17 * q^52 + 23 * q^53 + 41 * q^54 - 10 * q^55 - 60 * q^56 + 24 * q^57 - 37 * q^58 + 71 * q^59 - 72 * q^60 + 22 * q^61 + 43 * q^62 - 106 * q^63 - 52 * q^64 + 2 * q^65 - 21 * q^66 - 56 * q^67 - 104 * q^68 - 12 * q^69 - 32 * q^70 - 36 * q^71 + 147 * q^72 - 12 * q^73 + 10 * q^74 + 34 * q^75 - 49 * q^76 - 30 * q^77 + 5 * q^78 - 70 * q^79 + q^81 + 130 * q^82 + 11 * q^83 + 77 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 + 96 * q^88 - 40 * q^89 - 48 * q^90 + 10 * q^91 + 112 * q^92 + 50 * q^93 + 78 * q^94 + 41 * q^95 - 75 * q^96 - 47 * q^97 - 46 * q^98 + 46 * q^99

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