LMFDB - Embedded newform 105.3.w.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(17,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2]))

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

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

chi := DirichletCharacter("105.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.w (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.2
Character	$\chi$	$=$	105.17
Dual form			105.3.w.a.68.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.32412 - 0.890695i) q^{2} +(-2.80275 - 1.06987i) q^{3} +(6.79233 + 3.92155i) q^{4} +(3.30138 - 3.75512i) q^{5} +(8.36374 + 6.05276i) q^{6} +(3.32240 - 6.16130i) q^{7} +(-9.35192 - 9.35192i) q^{8} +(6.71077 + 5.99713i) q^{9} +(-14.3188 + 9.54193i) q^{10} +(-8.68269 - 5.01295i) q^{11} +(-14.8416 - 18.2580i) q^{12} +(-1.86963 - 1.86963i) q^{13} +(-16.5319 + 17.5217i) q^{14} +(-13.2704 + 6.99260i) q^{15} +(7.07097 + 12.2473i) q^{16} +(-21.3085 + 5.70960i) q^{17} +(-16.9658 - 25.9124i) q^{18} +(-2.05685 - 3.56257i) q^{19} +(37.1500 - 12.5595i) q^{20} +(-15.9036 + 13.7140i) q^{21} +(24.3973 + 24.3973i) q^{22} +(0.752160 - 2.80710i) q^{23} +(16.2057 + 36.2164i) q^{24} +(-3.20179 - 24.7941i) q^{25} +(4.54959 + 7.88012i) q^{26} +(-12.3924 - 23.9881i) q^{27} +(46.7287 - 28.8206i) q^{28} +34.1357 q^{29} +(50.3407 - 11.4243i) q^{30} +(-50.3808 - 29.0874i) q^{31} +(1.09601 + 4.09035i) q^{32} +(18.9722 + 23.3394i) q^{33} +75.9176 q^{34} +(-12.1679 - 32.8168i) q^{35} +(22.0637 + 67.0512i) q^{36} +(-13.3306 + 49.7505i) q^{37} +(3.66406 + 13.6744i) q^{38} +(3.23983 + 7.24034i) q^{39} +(-65.9918 + 4.24331i) q^{40} -9.22396 q^{41} +(65.0806 - 31.4218i) q^{42} +(-7.59676 + 7.59676i) q^{43} +(-39.3171 - 68.0993i) q^{44} +(44.6747 - 5.40090i) q^{45} +(-5.00054 + 8.66119i) q^{46} +(11.8264 - 44.1368i) q^{47} +(-6.71516 - 41.8910i) q^{48} +(-26.9233 - 40.9407i) q^{49} +(-11.4409 + 85.2705i) q^{50} +(65.8309 + 6.79473i) q^{51} +(-5.36728 - 20.0310i) q^{52} +(-65.7881 + 17.6279i) q^{53} +(19.8279 + 90.7771i) q^{54} +(-47.4891 + 16.0548i) q^{55} +(-88.6908 + 26.5492i) q^{56} +(1.95335 + 12.1855i) q^{57} +(-113.471 - 30.4045i) q^{58} +(33.4745 + 19.3265i) q^{59} +(-117.559 - 4.54457i) q^{60} +(21.5330 - 12.4321i) q^{61} +(141.564 + 141.564i) q^{62} +(59.2460 - 21.4222i) q^{63} -71.1408i q^{64} +(-13.1930 + 0.848318i) q^{65} +(-42.2775 - 94.4812i) q^{66} +(14.0279 - 3.75877i) q^{67} +(-167.125 - 44.7810i) q^{68} +(-5.11134 + 7.06287i) q^{69} +(11.2178 + 119.925i) q^{70} -79.7040i q^{71} +(-6.67386 - 118.843i) q^{72} +(108.835 - 29.1624i) q^{73} +(88.6251 - 153.503i) q^{74} +(-17.5526 + 72.9171i) q^{75} -32.2642i q^{76} +(-59.7337 + 36.8416i) q^{77} +(-4.32066 - 26.9534i) q^{78} +(-77.2623 + 44.6074i) q^{79} +(69.3339 + 13.8806i) q^{80} +(9.06881 + 80.4907i) q^{81} +(30.6615 + 8.21574i) q^{82} +(69.8011 - 69.8011i) q^{83} +(-161.803 + 30.7833i) q^{84} +(-48.9073 + 98.8655i) q^{85} +(32.0189 - 18.4861i) q^{86} +(-95.6737 - 36.5207i) q^{87} +(34.3191 + 128.081i) q^{88} +(28.9778 - 16.7303i) q^{89} +(-153.315 - 21.8383i) q^{90} +(-17.7310 + 5.30768i) q^{91} +(16.1171 - 16.1171i) q^{92} +(110.085 + 135.425i) q^{93} +(-78.6248 + 136.182i) q^{94} +(-20.1683 - 4.03768i) q^{95} +(1.30431 - 12.6368i) q^{96} +(90.5978 - 90.5978i) q^{97} +(53.0306 + 160.072i) q^{98} +(-28.2042 - 85.7120i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 6 q^{3} - 16 q^{7} - 60 q^{10} - 30 q^{12} - 20 q^{15} + 120 q^{16} + 46 q^{18} - 96 q^{21} - 80 q^{22} + 28 q^{25} - 136 q^{28} - 80 q^{30} - 24 q^{31} - 36 q^{33} - 272 q^{36} + 60 q^{37} - 72 q^{40}+ \cdots + 2184 q^{96}+O(q^{100}) $ 112 * q - 6 * q^3 - 16 * q^7 - 60 * q^10 - 30 * q^12 - 20 * q^15 + 120 * q^16 + 46 * q^18 - 96 * q^21 - 80 * q^22 + 28 * q^25 - 136 * q^28 - 80 * q^30 - 24 * q^31 - 36 * q^33 - 272 * q^36 + 60 * q^37 - 72 * q^40 + 338 * q^42 - 48 * q^43 + 384 * q^45 + 40 * q^46 + 176 * q^51 - 204 * q^52 + 344 * q^57 - 284 * q^58 - 214 * q^60 - 912 * q^61 + 132 * q^63 - 444 * q^66 - 36 * q^67 + 208 * q^70 - 638 * q^72 + 708 * q^73 + 42 * q^75 + 664 * q^78 + 8 * q^81 + 1104 * q^82 + 264 * q^85 + 246 * q^87 + 180 * q^88 + 632 * q^91 + 196 * q^93 + 2184 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−3.32412	−	0.890695i	−1.66206	−	0.445348i	−0.699107	−	0.715017i	$-0.746419\pi$
$2$	−3.32412	−	0.890695i	−1.66206	−	0.445348i	−0.962953	+	0.269670i	$0.913086\pi$
$3$	−2.80275	−	1.06987i	−0.934249	−	0.356622i
$3$	−2.80275	−	1.06987i	−0.934249	−	0.356622i
$4$	6.79233	+	3.92155i	1.69808	+	0.980389i
$5$	3.30138	−	3.75512i	0.660276	−	0.751023i
$5$	3.30138	−	3.75512i	0.660276	−	0.751023i
$6$	8.36374	+	6.05276i	1.39396	+	1.00879i
$7$	3.32240	−	6.16130i	0.474629	−	0.880186i
$7$	3.32240	−	6.16130i	0.474629	−	0.880186i
$8$	−9.35192	−	9.35192i	−1.16899	−	1.16899i
$9$	6.71077	+	5.99713i	0.745641	+	0.666348i
$10$	−14.3188	+	9.54193i	−1.43188	+	0.954193i
$11$	−8.68269	−	5.01295i	−0.789335	−	0.455723i	0.0503932	−	0.998729i	$-0.483953\pi$
$11$	−8.68269	−	5.01295i	−0.789335	−	0.455723i	−0.839729	+	0.543006i	$0.817286\pi$
$12$	−14.8416	−	18.2580i	−1.23680	−	1.52150i
$13$	−1.86963	−	1.86963i	−0.143817	−	0.143817i	0.631532	−	0.775350i	$-0.282426\pi$
$13$	−1.86963	−	1.86963i	−0.143817	−	0.143817i	−0.775350	+	0.631532i	$0.782426\pi$
$14$	−16.5319	+	17.5217i	−1.18085	+	1.25155i
$15$	−13.2704	+	6.99260i	−0.884693	+	0.466173i
$16$	7.07097	+	12.2473i	0.441935	+	0.765455i
$17$	−21.3085	+	5.70960i	−1.25344	+	0.335859i	−0.823665	−	0.567076i	$-0.808075\pi$
$17$	−21.3085	+	5.70960i	−1.25344	+	0.335859i	−0.429777	+	0.902935i	$0.641408\pi$
$18$	−16.9658	−	25.9124i	−0.942543	−	1.43958i
$19$	−2.05685	−	3.56257i	−0.108255	−	0.187504i	0.806808	−	0.590813i	$-0.201193\pi$
$19$	−2.05685	−	3.56257i	−0.108255	−	0.187504i	−0.915064	+	0.403310i	$0.867860\pi$
$20$	37.1500	−	12.5595i	1.85750	−	0.627973i
$21$	−15.9036	+	13.7140i	−0.757315	+	0.653049i
$22$	24.3973	+	24.3973i	1.10897	+	1.10897i
$23$	0.752160	−	2.80710i	0.0327026	−	0.122048i	−0.947645	−	0.319326i	$-0.896544\pi$
$23$	0.752160	−	2.80710i	0.0327026	−	0.122048i	0.980348	+	0.197278i	$0.0632102\pi$
$24$	16.2057	+	36.2164i	0.675239	+	1.50901i
$25$	−3.20179	−	24.7941i	−0.128072	−	0.991765i
$26$	4.54959	+	7.88012i	0.174984	+	0.303082i
$27$	−12.3924	−	23.9881i	−0.458979	−	0.888447i
$28$	46.7287	−	28.8206i	1.66888	−	1.02931i
$29$	34.1357			1.17709			0.588547	−	0.808463i	$-0.299700\pi$
$29$	34.1357			1.17709			0.588547	+	0.808463i	$0.299700\pi$
$30$	50.3407	−	11.4243i	1.67802	−	0.380812i
$31$	−50.3808	−	29.0874i	−1.62519	−	0.938302i	−0.985502	−	0.169665i	$-0.945731\pi$
$31$	−50.3808	−	29.0874i	−1.62519	−	0.938302i	−0.639685	−	0.768637i	$-0.720935\pi$
$32$	1.09601	+	4.09035i	0.0342502	+	0.127824i
$33$	18.9722	+	23.3394i	0.574914	+	0.707253i
$34$	75.9176			2.23287
$35$	−12.1679	−	32.8168i	−0.347654	−	0.937623i
$36$	22.0637	+	67.0512i	0.612880	+	1.86253i
$37$	−13.3306	+	49.7505i	−0.360287	+	1.34461i	0.513412	+	0.858142i	$0.328381\pi$
$37$	−13.3306	+	49.7505i	−0.360287	+	1.34461i	−0.873699	+	0.486467i	$0.838286\pi$
$38$	3.66406	+	13.6744i	0.0964226	+	0.359854i
$39$	3.23983	+	7.24034i	0.0830727	+	0.185650i
$40$	−65.9918	+	4.24331i	−1.64979	+	0.106083i
$41$	−9.22396			−0.224975			−0.112487	−	0.993653i	$-0.535882\pi$
$41$	−9.22396			−0.224975			−0.112487	+	0.993653i	$0.535882\pi$
$42$	65.0806	−	31.4218i	1.54954	−	0.748138i
$43$	−7.59676	+	7.59676i	−0.176669	+	0.176669i	−0.789902	−	0.613233i	$-0.789869\pi$
$43$	−7.59676	+	7.59676i	−0.176669	+	0.176669i	0.613233	+	0.789902i	$0.289869\pi$
$44$	−39.3171	−	68.0993i	−0.893571	−	1.54771i
$45$	44.6747	−	5.40090i	0.992771	−	0.120020i
$46$	−5.00054	+	8.66119i	−0.108707	+	0.188287i
$47$	11.8264	−	44.1368i	0.251626	−	0.939080i	−0.718311	−	0.695722i	$-0.755084\pi$
$47$	11.8264	−	44.1368i	0.251626	−	0.939080i	0.969937	−	0.243358i	$-0.0782489\pi$
$48$	−6.71516	−	41.8910i	−0.139899	−	0.872729i
$49$	−26.9233	−	40.9407i	−0.549455	−	0.835523i
$50$	−11.4409	+	85.2705i	−0.228817	+	1.70541i
$51$	65.8309	+	6.79473i	1.29080	+	0.133230i
$52$	−5.36728	−	20.0310i	−0.103217	−	0.385211i
$53$	−65.7881	+	17.6279i	−1.24128	+	0.332601i	−0.818964	−	0.573845i	$-0.805451\pi$
$53$	−65.7881	+	17.6279i	−1.24128	+	0.332601i	−0.422321	+	0.906447i	$0.638784\pi$
$54$	19.8279	+	90.7771i	0.367183	+	1.68106i
$55$	−47.4891	+	16.0548i	−0.863438	+	0.291906i
$56$	−88.6908	+	26.5492i	−1.58376	+	0.474092i
$57$	1.95335	+	12.1855i	0.0342694	+	0.213781i
$58$	−113.471	−	30.4045i	−1.95640	−	0.524216i
$59$	33.4745	+	19.3265i	0.567365	+	0.327568i	0.756096	−	0.654460i	$-0.227104\pi$
$59$	33.4745	+	19.3265i	0.567365	+	0.327568i	−0.188731	+	0.982029i	$0.560438\pi$
$60$	−117.559	−	4.54457i	−1.95931	−	0.0757428i
$61$	21.5330	−	12.4321i	0.353000	−	0.203805i	−0.313006	−	0.949751i	$-0.601336\pi$
$61$	21.5330	−	12.4321i	0.353000	−	0.203805i	0.666006	+	0.745946i	$0.268003\pi$
$62$	141.564	+	141.564i	2.28329	+	2.28329i
$63$	59.2460	−	21.4222i	0.940413	−	0.340035i
$64$		−	71.1408i		−	1.11157i
$65$	−13.1930	+	0.848318i	−0.202969	+	0.0130510i
$66$	−42.2775	−	94.4812i	−0.640569	−	1.43153i
$67$	14.0279	−	3.75877i	0.209372	−	0.0561010i	−0.152609	−	0.988287i	$-0.548767\pi$
$67$	14.0279	−	3.75877i	0.209372	−	0.0561010i	0.361980	+	0.932186i	$0.382101\pi$
$68$	−167.125	−	44.7810i	−2.45772	−	0.658545i
$69$	−5.11134	+	7.06287i	−0.0740773	+	0.102360i
$70$	11.2178	+	119.925i	0.160254	+	1.71321i
$71$		−	79.7040i		−	1.12259i	−0.827615	−	0.561296i	$-0.810303\pi$
$71$		−	79.7040i		−	1.12259i	0.827615	−	0.561296i	$-0.189697\pi$
$72$	−6.67386	−	118.843i	−0.0926925	−	1.65060i
$73$	108.835	−	29.1624i	1.49090	−	0.399484i	0.580856	−	0.814006i	$-0.302718\pi$
$73$	108.835	−	29.1624i	1.49090	−	0.399484i	0.910039	+	0.414522i	$0.136051\pi$
$74$	88.6251	−	153.503i	1.19764	−	2.07437i
$75$	−17.5526	+	72.9171i	−0.234035	+	0.972228i
$76$		−	32.2642i		−	0.424529i
$77$	−59.7337	+	36.8416i	−0.775762	+	0.478463i
$78$	−4.32066	−	26.9534i	−0.0553931	−	0.345557i
$79$	−77.2623	+	44.6074i	−0.978004	+	0.564651i	−0.901667	−	0.432431i	$-0.857656\pi$
$79$	−77.2623	+	44.6074i	−0.978004	+	0.564651i	−0.0763371	+	0.997082i	$0.524323\pi$
$80$	69.3339	+	13.8806i	0.866673	+	0.173507i
$81$	9.06881	+	80.4907i	0.111961	+	0.993713i
$82$	30.6615	+	8.21574i	0.373921	+	0.100192i
$83$	69.8011	−	69.8011i	0.840977	−	0.840977i	−0.148009	−	0.988986i	$-0.547287\pi$
$83$	69.8011	−	69.8011i	0.840977	−	0.840977i	0.988986	+	0.148009i	$0.0472866\pi$
$84$	−161.803	+	30.7833i	−1.92623	+	0.366468i
$85$	−48.9073	+	98.8655i	−0.575380	+	1.16312i
$86$	32.0189	−	18.4861i	0.372313	−	0.214955i
$87$	−95.6737	−	36.5207i	−1.09970	−	0.419778i
$88$	34.3191	+	128.081i	0.389989	+	1.45546i
$89$	28.9778	−	16.7303i	0.325593	−	0.187981i	−0.328290	−	0.944577i	$-0.606472\pi$
$89$	28.9778	−	16.7303i	0.325593	−	0.187981i	0.653883	+	0.756596i	$0.273139\pi$
$90$	−153.315	−	21.8383i	−1.70350	−	0.242648i
$91$	−17.7310	+	5.30768i	−0.194846	+	0.0583261i
$92$	16.1171	−	16.1171i	0.175186	−	0.175186i
$93$	110.085	+	135.425i	1.18371	+	1.45619i
$94$	−78.6248	+	136.182i	−0.836434	+	1.44875i
$95$	−20.1683	−	4.03768i	−0.212298	−	0.0425019i
$96$	1.30431	−	12.6368i	0.0135865	−	0.131633i
$97$	90.5978	−	90.5978i	0.933998	−	0.933998i	−0.0639551	−	0.997953i	$-0.520371\pi$
$97$	90.5978	−	90.5978i	0.933998	−	0.933998i	0.997953	+	0.0639551i	$0.0203715\pi$
$98$	53.0306	+	160.072i	0.541128	+	1.63339i
$99$	−28.2042	−	85.7120i	−0.284891	−	0.865778i
$100$	75.4839	−	180.966i	0.754839	−	1.80966i
$101$	10.0452	−	17.3989i	0.0994578	−	0.172266i	−0.812003	−	0.583654i	$-0.801623\pi$
$101$	10.0452	−	17.3989i	0.0994578	−	0.172266i	0.911460	+	0.411388i	$0.134956\pi$
$102$	−212.778	−	81.2218i	−2.08606	−	0.796292i
$103$	3.49766	−	13.0534i	0.0339578	−	0.126732i	−0.946866	−	0.321628i	$-0.895770\pi$
$103$	3.49766	−	13.0534i	0.0339578	−	0.126732i	0.980824	+	0.194895i	$0.0624367\pi$
$104$			34.9692i			0.336242i
$105$	−1.00612	+	104.995i	−0.00958205	+	0.999954i
$106$	234.388			2.21121
$107$	98.6617	+	26.4363i	0.922072	+	0.247069i	0.688471	−	0.725264i	$-0.258282\pi$
$107$	98.6617	+	26.4363i	0.922072	+	0.247069i	0.233601	+	0.972332i	$0.424949\pi$
$108$	9.89696	−	211.533i	0.0916385	−	1.95863i
$109$	154.812	+	89.3809i	1.42030	+	0.820008i	0.996324	−	0.0856671i	$-0.0273022\pi$
$109$	154.812	+	89.3809i	1.42030	+	0.820008i	0.423972	+	0.905675i	$0.360635\pi$
$110$	172.159	−	11.0699i	1.56508	−	0.100636i
$111$	90.5888	−	125.176i	0.816115	−	1.12771i
$112$	98.9517	−	2.87599i	0.883498	−	0.0256785i
$113$	14.2399	+	14.2399i	0.126016	+	0.126016i	0.767302	−	0.641286i	$-0.221599\pi$
$113$	14.2399	+	14.2399i	0.126016	+	0.126016i	−0.641286	+	0.767302i	$0.721599\pi$
$114$	4.36042	−	42.2461i	0.0382493	−	0.370579i
$115$	−8.05782	−	12.0917i	−0.0700680	−	0.105146i
$116$	231.861	+	133.865i	1.99880	+	1.15401i
$117$	−1.33423	−	23.7590i	−0.0114037	−	0.203068i
$118$	−94.0593	−	94.0593i	−0.797113	−	0.797113i
$119$	−35.6169	+	150.258i	−0.299302	+	1.26267i
$120$	189.498	+	58.7095i	1.57915	+	0.489246i
$121$	−10.2406	−	17.7373i	−0.0846331	−	0.146589i
$122$	−82.6515	+	22.1464i	−0.677472	+	0.181528i
$123$	25.8524	+	9.86841i	0.210182	+	0.0802310i
$124$	−228.135	−	395.142i	−1.83980	−	3.18663i
$125$	−103.675	−	69.8317i	−0.829401	−	0.558654i
$126$	−216.021	+	18.4397i	−1.71446	+	0.146347i
$127$	−15.1169	−	15.1169i	−0.119031	−	0.119031i	0.645082	−	0.764113i	$-0.276823\pi$
$127$	−15.1169	−	15.1169i	−0.119031	−	0.119031i	−0.764113	+	0.645082i	$0.776823\pi$
$128$	−58.9807	+	220.119i	−0.460787	+	1.71968i
$129$	29.4193	−	13.1643i	0.228057	−	0.102048i
$130$	44.6107	+	8.93103i	0.343159	+	0.0687003i
$131$	−26.7467	−	46.3266i	−0.204173	−	0.353638i	0.745696	−	0.666286i	$-0.232117\pi$
$131$	−26.7467	−	46.3266i	−0.204173	−	0.353638i	−0.949869	+	0.312648i	$0.898784\pi$
$132$	37.3387	+	232.929i	0.282869	+	1.76461i
$133$	−28.7838	+	0.836588i	−0.216419	+	0.00629013i
$134$	−49.9784			−0.372973
$135$	−130.990	−	32.6587i	−0.970297	−	0.241916i
$136$	252.671	+	145.880i	1.85788	+	1.07265i
$137$	−3.44570	−	12.8595i	−0.0251511	−	0.0938652i	0.952209	−	0.305446i	$-0.0988055\pi$
$137$	−3.44570	−	12.8595i	−0.0251511	−	0.0938652i	−0.977361	+	0.211581i	$0.932139\pi$
$138$	23.2816	−	18.9252i	0.168707	−	0.137139i
$139$	−96.3062			−0.692850			−0.346425	−	0.938078i	$-0.612604\pi$
$139$	−96.3062			−0.692850			−0.346425	+	0.938078i	$0.612604\pi$
$140$	46.0445	−	270.620i	0.328889	−	1.93300i
$141$	−80.3669	+	111.051i	−0.569978	+	0.787599i
$142$	−70.9920	+	264.946i	−0.499944	+	1.86581i
$143$	6.86103	+	25.6057i	0.0479792	+	0.179061i
$144$	−25.9969	+	124.594i	−0.180534	+	0.865237i
$145$	112.695	−	128.184i	0.777206	−	0.884025i
$146$	−387.757			−2.65587
$147$	31.6581	+	143.551i	0.215361	+	0.976535i
$148$	−285.645	+	285.645i	−1.93004	+	1.93004i
$149$	36.6889	+	63.5470i	0.246234	+	0.426490i	0.962478	−	0.271360i	$-0.0874735\pi$
$149$	36.6889	+	63.5470i	0.246234	+	0.426490i	−0.716244	+	0.697850i	$0.754140\pi$
$150$	123.294	−	226.751i	0.821960	−	1.51167i
$151$	−3.67244	+	6.36085i	−0.0243208	+	0.0421249i	−0.877930	−	0.478790i	$-0.841076\pi$
$151$	−3.67244	+	6.36085i	−0.0243208	+	0.0421249i	0.853609	+	0.520915i	$0.174409\pi$
$152$	−14.0814	+	52.5524i	−0.0926406	+	0.345739i
$153$	−177.238	−	89.4742i	−1.15842	−	0.584799i
$154$	231.377	−	69.2614i	1.50245	−	0.449750i
$155$	−275.553	+	93.1573i	−1.77776	+	0.601015i
$156$	−6.38735	+	61.8840i	−0.0409445	+	0.396692i
$157$	−43.4860	−	162.292i	−0.276981	−	1.03371i	−0.954502	−	0.298204i	$-0.903612\pi$
$157$	−43.4860	−	162.292i	−0.276981	−	1.03371i	0.677521	−	0.735503i	$-0.263054\pi$
$158$	296.561	−	79.4632i	1.87697	−	0.502932i
$159$	203.247	+	20.9781i	1.27828	+	0.131938i
$160$	18.9781	+	9.38817i	0.118613	+	0.0586761i
$161$	−14.7964	−	13.9606i	−0.0919031	−	0.0867118i
$162$	41.5469	−	275.638i	0.256462	−	1.70147i
$163$	8.53573	+	2.28714i	0.0523664	+	0.0140315i	0.284907	−	0.958555i	$-0.408037\pi$
$163$	8.53573	+	2.28714i	0.0523664	+	0.0140315i	−0.232541	+	0.972587i	$0.574704\pi$
$164$	−62.6522	−	36.1723i	−0.382026	−	0.220563i
$165$	150.276	+	5.80935i	0.910766	+	0.0352082i
$166$	−294.199	+	169.856i	−1.77228	+	1.02323i
$167$	−91.2114	−	91.2114i	−0.546176	−	0.546176i	0.379156	−	0.925333i	$-0.376214\pi$
$167$	−91.2114	−	91.2114i	−0.546176	−	0.546176i	−0.925333	+	0.379156i	$0.876214\pi$
$168$	276.982	+	20.4769i	1.64870	+	0.121886i
$169$		−	162.009i		−	0.958633i
$170$	250.633	−	285.079i	1.47431	−	1.67694i
$171$	7.56216	−	36.2428i	0.0442232	−	0.211946i
$172$	−81.3908	+	21.8086i	−0.473202	+	0.126794i
$173$	−21.9478	−	5.88090i	−0.126866	−	0.0339936i	0.194827	−	0.980838i	$-0.437585\pi$
$173$	−21.9478	−	5.88090i	−0.126866	−	0.0339936i	−0.321693	+	0.946844i	$0.604252\pi$
$174$	285.502	+	206.615i	1.64082	+	1.18744i
$175$	−163.402	−	62.6489i	−0.933724	−	0.357993i
$176$		−	141.786i		−	0.805600i
$177$	−73.1438	−	89.9807i	−0.413242	−	0.508365i
$178$	−111.227	+	29.8033i	−0.624872	+	0.167434i
$179$	−12.6214	+	21.8609i	−0.0705105	+	0.122128i	−0.899125	−	0.437692i	$-0.855796\pi$
$179$	−12.6214	+	21.8609i	−0.0705105	+	0.122128i	0.828615	+	0.559819i	$0.189129\pi$
$180$	324.625	+	138.510i	1.80347	+	0.769498i
$181$			183.408i			1.01330i	0.862151	+	0.506652i	$0.169117\pi$
$181$			183.408i			1.01330i	−0.862151	+	0.506652i	$0.830883\pi$
$182$	63.6674	−	1.85046i	0.349821	−	0.0101674i
$183$	−73.6523	+	11.8065i	−0.402471	+	0.0645165i
$184$	−33.2859	+	19.2176i	−0.180902	+	0.104444i
$185$	142.810	+	214.303i	0.771944	+	1.15840i
$186$	−245.313	−	548.222i	−1.31889	−	2.94743i
$187$	213.637	+	57.2439i	1.14245	+	0.306117i
$188$	253.414	−	253.414i	1.34794	−	1.34794i
$189$	−188.970	−	3.34446i	−0.999843	−	0.0176955i
$190$	63.4456	+	31.3856i	0.333924	+	0.165187i
$191$	93.7259	−	54.1127i	0.490712	−	0.283312i	−0.234158	−	0.972199i	$-0.575233\pi$
$191$	93.7259	−	54.1127i	0.490712	−	0.283312i	0.724870	+	0.688886i	$0.241900\pi$
$192$	−76.1112	+	199.389i	−0.396412	+	1.03849i
$193$	54.6403	+	203.920i	0.283110	+	1.05658i	0.950209	+	0.311613i	$0.100869\pi$
$193$	54.6403	+	203.920i	0.283110	+	1.05658i	−0.667099	+	0.744969i	$0.732464\pi$
$194$	−381.853	+	220.463i	−1.96831	+	1.13641i
$195$	37.8842	+	11.7371i	0.194278	+	0.0601905i
$196$	−22.3209	−	383.664i	−0.113882	−	1.95747i
$197$	67.3795	−	67.3795i	0.342028	−	0.342028i	−0.515101	−	0.857129i	$-0.672246\pi$
$197$	67.3795	−	67.3795i	0.342028	−	0.342028i	0.857129	+	0.515101i	$0.172246\pi$
$198$	17.4108	+	310.038i	0.0879332	+	1.56585i
$199$	49.6723	−	86.0349i	0.249610	−	0.432336i	−0.713808	−	0.700341i	$-0.753031\pi$
$199$	49.6723	−	86.0349i	0.249610	−	0.432336i	0.963417	+	0.268005i	$0.0863644\pi$
$200$	−201.930	+	261.815i	−1.00965	+	1.30908i
$201$	−43.3381	−	4.47313i	−0.215612	−	0.0222544i
$202$	−48.8886	+	48.8886i	−0.242023	+	0.242023i
$203$	113.413	−	210.320i	0.558683	−	1.03606i
$204$	420.499	+	304.312i	2.06127	+	1.49172i
$205$	−30.4518	+	34.6370i	−0.148545	+	0.168961i
$206$	−23.2533	+	40.2758i	−0.112880	+	0.195514i
$207$	21.8821	−	14.3270i	0.105711	−	0.0692125i
$208$	9.67775	−	36.1179i	0.0465277	−	0.173644i
$209$			41.2436i			0.197338i
$210$	96.8631	−	348.120i	0.461253	−	1.65772i
$211$	251.373			1.19134			0.595671	−	0.803228i	$-0.296886\pi$
$211$	251.373			1.19134			0.595671	+	0.803228i	$0.296886\pi$
$212$	−515.983	−	138.257i	−2.43388	−	0.652157i
$213$	−85.2727	+	223.390i	−0.400341	+	1.04878i
$214$	−304.417	−	175.755i	−1.42251	−	0.821285i
$215$	3.44693	+	53.6065i	0.0160322	+	0.249332i
$216$	−108.441	+	340.228i	−0.502043	+	1.57513i
$217$	−346.601	+	213.771i	−1.59724	+	0.985121i
$218$	−435.003	−	435.003i	−1.99543	−	1.99543i
$219$	−336.238	−	34.7048i	−1.53533	−	0.158469i
$220$	−385.521	−	77.1811i	−1.75237	−	0.350823i
$221$	50.5138	+	29.1641i	0.228569	+	0.131964i
$222$	−412.622	+	335.413i	−1.85866	+	1.51087i
$223$	253.293	+	253.293i	1.13584	+	1.13584i	0.989187	+	0.146657i	$0.0468513\pi$
$223$	253.293	+	253.293i	1.13584	+	1.13584i	0.146657	+	0.989187i	$0.453149\pi$
$224$	28.8433	+	6.83697i	0.128765	+	0.0305222i
$225$	127.207	−	185.589i	0.565365	−	0.824841i
$226$	−34.6516	−	60.0183i	−0.153326	−	0.265568i
$227$	48.5877	−	13.0190i	0.214043	−	0.0573526i	−0.150204	−	0.988655i	$-0.547993\pi$
$227$	48.5877	−	13.0190i	0.214043	−	0.0573526i	0.364247	+	0.931302i	$0.381326\pi$
$228$	−34.5185	+	90.4285i	−0.151397	+	0.396616i
$229$	38.1511	+	66.0796i	0.166599	+	0.288557i	0.937222	−	0.348734i	$-0.113388\pi$
$229$	38.1511	+	66.0796i	0.166599	+	0.288557i	−0.770623	+	0.637291i	$0.780055\pi$
$230$	16.0151	+	47.3715i	0.0696308	+	0.205963i
$231$	206.834	−	39.3506i	0.895385	−	0.170349i
$232$	−319.234	−	319.234i	−1.37601	−	1.37601i
$233$	60.7902	−	226.872i	0.260902	−	0.973700i	−0.703809	−	0.710389i	$-0.748519\pi$
$233$	60.7902	−	226.872i	0.260902	−	0.973700i	0.964711	−	0.263311i	$-0.0848145\pi$
$234$	−16.7269	+	80.1662i	−0.0714825	+	0.342591i
$235$	−126.695	−	190.122i	−0.539129	−	0.809029i
$236$	151.580	+	262.544i	0.642289	+	1.11248i
$237$	264.271	−	42.3628i	1.11507	−	0.178746i
$238$	252.229	−	467.751i	1.05978	−	1.96534i
$239$	233.334			0.976294			0.488147	−	0.872761i	$-0.337673\pi$
$239$	233.334			0.976294			0.488147	+	0.872761i	$0.337673\pi$
$240$	−179.475	−	113.082i	−0.747812	−	0.471174i
$241$	56.1356	+	32.4099i	0.232928	+	0.134481i	0.611922	−	0.790918i	$-0.290397\pi$
$241$	56.1356	+	32.4099i	0.232928	+	0.134481i	−0.378994	+	0.925399i	$0.623730\pi$
$242$	18.2425	+	68.0820i	0.0753823	+	0.281331i
$243$	60.6968	−	235.297i	0.249781	−	0.968302i
$244$	195.013			0.799232
$245$	−242.621	−	34.0606i	−0.990289	−	0.139023i
$246$	−77.1468	−	55.8304i	−0.313605	−	0.226953i
$247$	−2.81513	+	10.5062i	−0.0113973	+	0.0425353i
$248$	199.134	+	743.180i	0.802961	+	2.99669i
$249$	−270.313	+	120.957i	−1.08559	+	0.485770i
$250$	282.430	+	324.472i	1.12972	+	1.29789i
$251$	−77.6902			−0.309523			−0.154761	−	0.987952i	$-0.549461\pi$
$251$	−77.6902			−0.309523			−0.154761	+	0.987952i	$0.549461\pi$
$252$	486.427	+	86.8299i	1.93027	+	0.344563i
$253$	−20.6026	+	20.6026i	−0.0814333	+	0.0814333i
$254$	36.7860	+	63.7151i	0.144827	+	0.250847i
$255$	242.848	−	224.771i	0.952344	−	0.881453i
$256$	249.836	−	432.729i	0.975923	−	1.69035i
$257$	65.6831	−	245.133i	0.255576	−	0.953824i	−0.712193	−	0.701984i	$-0.752298\pi$
$257$	65.6831	−	245.133i	0.255576	−	0.953824i	0.967769	−	0.251840i	$-0.0810355\pi$
$258$	−109.519	+	17.5559i	−0.424491	+	0.0680462i
$259$	262.238	+	247.425i	1.01250	+	0.955310i
$260$	−92.9380	−	45.9750i	−0.357454	−	0.176827i
$261$	229.077	+	204.716i	0.877689	+	0.784354i
$262$	47.6463	+	177.818i	0.181856	+	0.678696i
$263$	−173.820	+	46.5748i	−0.660911	+	0.177091i	−0.573657	−	0.819096i	$-0.694476\pi$
$263$	−173.820	+	46.5748i	−0.660911	+	0.177091i	−0.0872539	+	0.996186i	$0.527809\pi$
$264$	40.8415	−	395.694i	0.154703	−	1.49884i
$265$	−150.997	+	305.238i	−0.569799	+	1.15184i
$266$	96.4259	+	22.8567i	0.362503	+	0.0859273i
$267$	−99.1166	+	15.8885i	−0.371223	+	0.0595074i
$268$	110.022	+	29.4804i	0.410532	+	0.110002i
$269$	−183.948	−	106.202i	−0.683821	−	0.394804i	0.117472	−	0.993076i	$-0.462521\pi$
$269$	−183.948	−	106.202i	−0.683821	−	0.394804i	−0.801293	+	0.598272i	$0.795854\pi$
$270$	406.338	+	225.234i	1.50496	+	0.834198i
$271$	−160.462	+	92.6426i	−0.592109	+	0.341855i	−0.765931	−	0.642923i	$-0.777722\pi$
$271$	−160.462	+	92.6426i	−0.592109	+	0.341855i	0.173822	+	0.984777i	$0.444388\pi$
$272$	−220.599	−	220.599i	−0.811025	−	0.811025i
$273$	55.3739	+	4.09372i	0.202835	+	0.0149953i
$274$			45.8157i			0.167211i
$275$	−96.4916	+	231.330i	−0.350879	+	0.841200i
$276$	−62.4153	+	27.9290i	−0.226143	+	0.101192i
$277$	378.225	−	101.345i	1.36543	−	0.365867i	0.499626	−	0.866241i	$-0.333471\pi$
$277$	378.225	−	101.345i	1.36543	−	0.365867i	0.865809	+	0.500374i	$0.166804\pi$
$278$	320.133	+	85.7794i	1.15156	+	0.308559i
$279$	−163.653	−	497.339i	−0.586570	−	1.78258i
$280$	−193.107	+	420.693i	−0.689667	+	1.50248i
$281$			262.988i			0.935901i	0.883755	+	0.467951i	$0.155008\pi$
$281$			262.988i			0.935901i	−0.883755	+	0.467951i	$0.844992\pi$
$282$	366.062	−	297.566i	1.29809	−	1.05520i
$283$	−62.2585	+	16.6821i	−0.219995	+	0.0589474i	−0.367133	−	0.930169i	$-0.619661\pi$
$283$	−62.2585	+	16.6821i	−0.219995	+	0.0589474i	0.147138	+	0.989116i	$0.452994\pi$
$284$	312.564	−	541.376i	1.10058	−	1.90625i
$285$	52.2069	+	32.8940i	0.183182	+	0.115418i
$286$		−	91.2276i		−	0.318977i
$287$	−30.6457	+	56.8316i	−0.106779	+	0.198020i
$288$	−17.1753	+	34.0223i	−0.0596366	+	0.118133i
$289$	171.172	−	98.8264i	0.592292	−	0.341960i
$290$	−488.784	+	325.721i	−1.68546	+	1.12317i
$291$	−350.850	+	156.995i	−1.20567	+	0.539501i
$292$	853.608	+	228.724i	2.92331	+	0.783300i
$293$	208.783	−	208.783i	0.712571	−	0.712571i	−0.254501	−	0.967072i	$-0.581911\pi$
$293$	208.783	−	208.783i	0.712571	−	0.712571i	0.967072	+	0.254501i	$0.0819113\pi$
$294$	22.6247	−	505.377i	0.0769546	−	1.71897i
$295$	183.085	−	61.8965i	0.620629	−	0.209819i
$296$	589.930	−	340.596i	1.99301	−	1.15066i
$297$	−12.6514	+	270.404i	−0.0425972	+	0.910450i
$298$	−65.3572	−	243.916i	−0.219319	−	0.818511i
$299$	−6.65448	+	3.84197i	−0.0222558	+	0.0128494i
$300$	−405.172	+	426.444i	−1.35057	+	1.42148i
$301$	21.5664	+	72.0454i	0.0716493	+	0.239353i
$302$	17.8732	−	17.8732i	0.0591828	−	0.0591828i
$303$	−46.7687	+	38.0175i	−0.154352	+	0.125470i
$304$	29.0879	−	50.3817i	0.0956838	−	0.165729i
$305$	24.4047	−	121.902i	0.0800154	−	0.399679i
$306$	509.465	+	455.288i	1.66492	+	1.48787i
$307$	6.68824	−	6.68824i	0.0217858	−	0.0217858i	−0.696130	−	0.717916i	$-0.745096\pi$
$307$	6.68824	−	6.68824i	0.0217858	−	0.0217858i	0.717916	+	0.696130i	$0.245096\pi$
$308$	−550.208	+	15.9915i	−1.78639	+	0.0519206i
$309$	−23.7685	+	32.8434i	−0.0769206	+	0.106289i
$310$	998.944	−	64.2327i	3.22240	−	0.207202i
$311$	105.085	−	182.012i	0.337893	−	0.585247i	−0.646144	−	0.763216i	$-0.723619\pi$
$311$	105.085	−	182.012i	0.337893	−	0.585247i	0.984036	+	0.177969i	$0.0569526\pi$
$312$	37.4124	−	98.0097i	0.119911	−	0.314134i
$313$	15.1437	−	56.5169i	0.0483823	−	0.180565i	−0.937506	−	0.347969i	$-0.886872\pi$
$313$	15.1437	−	56.5169i	0.0483823	−	0.180565i	0.985888	+	0.167403i	$0.0535382\pi$
$314$			578.211i			1.84144i
$315$	115.151	−	293.198i	0.365558	−	0.930789i
$316$	−699.722			−2.21431
$317$	31.1577	+	8.34869i	0.0982894	+	0.0263366i	0.307629	−	0.951507i	$-0.400465\pi$
$317$	31.1577	+	8.34869i	0.0982894	+	0.0263366i	−0.209339	+	0.977843i	$0.567131\pi$
$318$	−656.931	−	250.765i	−2.06582	−	0.788568i
$319$	−296.390	−	171.121i	−0.929122	−	0.536429i
$320$	−267.142	−	234.863i	−0.834818	−	0.733946i
$321$	−248.240	−	179.649i	−0.773335	−	0.559655i
$322$	36.7504	+	59.5858i	0.114132	+	0.185049i
$323$	64.1694	+	64.1694i	0.198667	+	0.198667i
$324$	−254.050	+	582.284i	−0.784106	+	1.79717i
$325$	−40.3696	+	52.3419i	−0.124214	+	0.161052i
$326$	−26.3366	−	15.2055i	−0.0807872	−	0.0466425i
$327$	−338.274	−	416.140i	−1.03448	−	1.27260i
$328$	86.2617	+	86.2617i	0.262993	+	0.262993i
$329$	−232.648	−	219.506i	−0.707136	−	0.667192i
$330$	−494.362	−	153.161i	−1.49807	−	0.464125i
$331$	−191.576	−	331.819i	−0.578779	−	1.00247i	−0.995620	−	0.0934948i	$-0.970196\pi$
$331$	−191.576	−	331.819i	−0.578779	−	1.00247i	0.416841	−	0.908979i	$-0.363137\pi$
$332$	747.841	−	200.383i	2.25253	−	0.603564i
$333$	−387.819	+	253.919i	−1.16462	+	0.762519i
$334$	221.956	+	384.439i	0.664539	+	1.15102i
$335$	32.1969	−	65.0856i	0.0961100	−	0.194285i
$336$	−280.413	−	97.8046i	−0.834564	−	0.291085i
$337$	−210.927	−	210.927i	−0.625897	−	0.625897i	0.321136	−	0.947033i	$-0.395935\pi$
$337$	−210.927	−	210.927i	−0.625897	−	0.625897i	−0.947033	+	0.321136i	$0.895935\pi$
$338$	−144.301	+	538.537i	−0.426925	+	1.59331i
$339$	−24.6759	−	55.1454i	−0.0727904	−	0.162671i
$340$	−719.901	+	479.735i	−2.11736	+	1.41099i
$341$	291.627	+	505.113i	0.855212	+	1.48127i
$342$	−57.4188	+	113.740i	−0.167891	+	0.332573i
$343$	−341.698	+	29.8612i	−0.996203	+	0.0870588i
$344$	142.088			0.413048
$345$	9.64745	+	42.5109i	0.0279636	+	0.123220i
$346$	67.7191	+	39.0976i	0.195720	+	0.112999i
$347$	118.460	+	442.099i	0.341383	+	1.27406i	0.896781	+	0.442475i	$0.145899\pi$
$347$	118.460	+	442.099i	0.341383	+	1.27406i	−0.555398	+	0.831585i	$0.687434\pi$
$348$	−506.630	−	623.250i	−1.45583	−	1.79095i
$349$	−426.370			−1.22169			−0.610846	−	0.791750i	$-0.709170\pi$
$349$	−426.370			−1.22169			−0.610846	+	0.791750i	$0.709170\pi$
$350$	487.366	+	353.793i	1.39247	+	1.01084i
$351$	−21.6795	+	68.0179i	−0.0617649	+	0.193783i
$352$	10.9885	−	41.0095i	0.0312172	−	0.116504i
$353$	−47.9722	−	179.035i	−0.135899	−	0.507181i	−0.999993	−	0.00385005i	$-0.998774\pi$
$353$	−47.9722	−	179.035i	−0.135899	−	0.507181i	0.864094	−	0.503331i	$-0.167892\pi$
$354$	162.993	+	364.255i	0.460433	+	1.02897i
$355$	−299.298	−	263.133i	−0.843092	−	0.741220i
$356$	262.436			0.737179
$357$	260.581	−	383.029i	0.729919	−	1.07291i
$358$	61.4264	−	61.4264i	0.171582	−	0.171582i
$359$	65.9692	+	114.262i	0.183758	+	0.318279i	0.943157	−	0.332346i	$-0.107840\pi$
$359$	65.9692	+	114.262i	0.183758	+	0.318279i	−0.759399	+	0.650625i	$0.774507\pi$
$360$	−468.303	−	367.285i	−1.30084	−	1.02024i
$361$	172.039	−	297.980i	0.476562	−	0.825429i
$362$	163.361	−	609.670i	0.451272	−	1.68417i
$363$	9.72531	+	60.6691i	0.0267915	+	0.167133i
$364$	−141.249	−	33.4815i	−0.388047	−	0.0919821i
$365$	249.799	−	504.965i	0.684380	−	1.38347i
$366$	255.345	+	26.3554i	0.697664	+	0.0720093i
$367$	4.06110	+	15.1562i	0.0110657	+	0.0412977i	0.971238	−	0.238111i	$-0.0765282\pi$
$367$	4.06110	+	15.1562i	0.0110657	+	0.0412977i	−0.960172	+	0.279409i	$0.909862\pi$
$368$	39.6978	−	10.6370i	0.107874	−	0.0289049i
$369$	−61.8999	−	55.3173i	−0.167750	−	0.149911i
$370$	−283.837	−	839.570i	−0.767127	−	2.26911i
$371$	−109.964	+	463.907i	−0.296399	+	1.25042i
$372$	216.656	+	1351.56i	0.582408	+	3.63322i
$373$	−316.635	−	84.8421i	−0.848887	−	0.227459i	−0.191951	−	0.981405i	$-0.561481\pi$
$373$	−316.635	−	84.8421i	−0.848887	−	0.227459i	−0.656936	+	0.753946i	$0.728148\pi$
$374$	−659.169	−	380.571i	−1.76248	−	1.01757i
$375$	215.864	+	306.639i	0.575638	+	0.817704i
$376$	−523.363	+	302.164i	−1.39192	+	0.803627i
$377$	−63.8210	−	63.8210i	−0.169286	−	0.169286i
$378$	625.181	+	179.432i	1.65392	+	0.474689i
$379$			494.008i			1.30345i	0.758454	+	0.651726i	$0.225955\pi$
$379$			494.008i			1.30345i	−0.758454	+	0.651726i	$0.774045\pi$
$380$	−121.156	−	106.516i	−0.318831	−	0.280307i
$381$	26.1958	+	58.5421i	0.0687555	+	0.153654i
$382$	−359.754	+	96.3958i	−0.941765	+	0.252345i
$383$	−293.013	−	78.5127i	−0.765048	−	0.204994i	−0.144865	−	0.989451i	$-0.546275\pi$
$383$	−293.013	−	78.5127i	−0.765048	−	0.204994i	−0.620183	+	0.784457i	$0.712941\pi$
$384$	400.806	−	553.836i	1.04377	−	1.44228i
$385$	−58.8591	+	345.935i	−0.152881	+	0.898533i
$386$		−	726.523i		−	1.88218i
$387$	−96.5388	+	5.42131i	−0.249454	+	0.0140086i
$388$	970.654	−	260.086i	2.50169	−	0.670325i
$389$	151.847	−	263.007i	0.390352	−	0.676110i	−0.602144	−	0.798388i	$-0.705687\pi$
$389$	151.847	−	263.007i	0.390352	−	0.676110i	0.992496	+	0.122278i	$0.0390199\pi$
$390$	−115.477	−	72.7590i	−0.296096	−	0.186561i
$391$			64.1097i			0.163963i
$392$	−131.089	+	634.658i	−0.334411	+	1.61903i
$393$	25.4008	+	158.457i	0.0646331	+	0.403199i
$394$	−283.992	+	163.963i	−0.720792	+	0.416149i
$395$	−87.5662	+	437.395i	−0.221687	+	1.10733i
$396$	144.552	−	692.789i	0.365031	−	1.74947i
$397$	−361.377	−	96.8306i	−0.910269	−	0.243906i	−0.226848	−	0.973930i	$-0.572842\pi$
$397$	−361.377	−	96.8306i	−0.910269	−	0.243906i	−0.683421	+	0.730024i	$0.739509\pi$
$398$	−241.748	+	241.748i	−0.607406	+	0.607406i
$399$	81.5687	+	28.4501i	0.204433	+	0.0713035i
$400$	281.021	−	214.532i	0.702552	−	0.536329i
$401$	−670.098	+	386.881i	−1.67107	+	0.964791i	−0.704025	+	0.710175i	$0.748616\pi$
$401$	−670.098	+	386.881i	−1.67107	+	0.964791i	−0.967042	+	0.254616i	$0.918051\pi$
$402$	140.077	+	53.4702i	0.348449	+	0.133011i
$403$	39.8107	+	148.576i	0.0987859	+	0.368674i
$404$	136.461	−	78.7859i	0.337775	−	0.195015i
$405$	332.192	+	231.676i	0.820226	+	0.572039i
$406$	−564.328	+	598.114i	−1.38997	+	1.47319i
$407$	365.143	−	365.143i	0.897156	−	0.897156i
$408$	−552.101	−	679.189i	−1.35319	−	1.66468i
$409$	122.966	−	212.984i	0.300651	−	0.520743i	−0.675632	−	0.737239i	$-0.736129\pi$
$409$	122.966	−	212.984i	0.300651	−	0.520743i	0.976284	+	0.216495i	$0.0694626\pi$
$410$	132.076	−	88.0144i	0.322138	−	0.214669i
$411$	−4.10057	+	39.7284i	−0.00997705	+	0.0966629i
$412$	74.9470	−	74.9470i	0.181910	−	0.181910i
$413$	230.292	−	142.036i	0.557609	−	0.343913i
$414$	−85.4997	+	28.1343i	−0.206521	+	0.0679573i
$415$	−31.6713	−	492.551i	−0.0763164	−	1.18687i
$416$	5.59830	−	9.69655i	0.0134575	−	0.0233090i
$417$	269.922	+	103.035i	0.647294	+	0.247086i
$418$	36.7355	−	137.099i	0.0878839	−	0.327987i
$419$			631.928i			1.50818i	0.656771	+	0.754090i	$0.271922\pi$
$419$			631.928i			1.50818i	−0.656771	+	0.754090i	$0.728078\pi$
$420$	−418.578	+	709.217i	−0.996615	+	1.68861i
$421$	687.942			1.63407			0.817033	−	0.576591i	$-0.195617\pi$
$421$	687.942			1.63407			0.817033	+	0.576591i	$0.195617\pi$
$422$	−835.595	−	223.897i	−1.98008	−	0.530562i
$423$	344.058	−	225.267i	0.813377	−	0.532546i
$424$	780.099	+	450.390i	1.83986	+	1.06224i
$425$	209.790	+	510.045i	0.493624	+	1.20011i
$426$	482.429	−	666.623i	1.13246	−	1.56484i
$427$	−5.05653	−	173.976i	−0.0118420	−	0.407438i
$428$	566.472	+	566.472i	1.32353	+	1.32353i
$429$	8.16499	−	79.1067i	0.0190326	−	0.184398i
$430$	36.2890	−	181.264i	0.0843931	−	0.421545i
$431$	−405.757	−	234.264i	−0.941432	−	0.543536i	−0.0510232	−	0.998697i	$-0.516248\pi$
$431$	−405.757	−	234.264i	−0.941432	−	0.543536i	−0.890409	+	0.455161i	$0.849582\pi$
$432$	206.162	−	321.392i	0.477227	−	0.743964i
$433$	−81.6205	−	81.6205i	−0.188500	−	0.188500i	0.606547	−	0.795047i	$-0.292554\pi$
$433$	−81.6205	−	81.6205i	−0.188500	−	0.188500i	−0.795047	+	0.606547i	$0.792554\pi$
$434$	1342.55	−	401.885i	3.09343	−	0.926003i
$435$	−452.995	+	238.697i	−1.04137	+	0.548729i
$436$	701.024	+	1214.21i	1.60785	+	2.78488i
$437$	−11.5476	+	3.09416i	−0.0264247	+	0.00708047i
$438$	1086.78	+	414.848i	2.48124	+	0.947142i
$439$	164.966	+	285.729i	0.375776	+	0.650863i	0.990443	−	0.137924i	$-0.0440428\pi$
$439$	164.966	+	285.729i	0.375776	+	0.650863i	−0.614667	+	0.788787i	$0.710709\pi$
$440$	594.257	+	293.970i	1.35059	+	0.668114i
$441$	64.8506	−	436.206i	0.147054	−	0.989129i
$442$	−141.937	−	141.937i	−0.321125	−	0.321125i
$443$	185.402	−	691.931i	0.418515	−	1.56192i	−0.359173	−	0.933271i	$-0.616941\pi$
$443$	185.402	−	691.931i	0.418515	−	1.56192i	0.777689	−	0.628650i	$-0.216392\pi$
$444$	1106.19	−	494.989i	2.49143	−	1.11484i
$445$	32.8423	−	164.048i	0.0738030	−	0.368647i
$446$	−616.370	−	1067.58i	−1.38200	−	2.39369i
$447$	−34.8427	−	217.358i	−0.0779479	−	0.486260i
$448$	−438.320	−	236.358i	−0.978392	−	0.527585i
$449$	−303.322			−0.675550			−0.337775	−	0.941227i	$-0.609674\pi$
$449$	−303.322			−0.675550			−0.337775	+	0.941227i	$0.609674\pi$
$450$	−588.155	+	503.618i	−1.30701	+	1.11915i
$451$	80.0888	+	46.2393i	0.177580	+	0.102526i
$452$	40.8794	+	152.564i	0.0904412	+	0.337531i
$453$	17.0982	−	13.8988i	0.0377443	−	0.0306818i
$454$	−173.107			−0.381294
$455$	−38.6057	+	84.1045i	−0.0848477	+	0.184845i
$456$	95.6906	−	132.226i	0.209848	−	0.289969i
$457$	108.752	−	405.868i	0.237969	−	0.888113i	−0.738819	−	0.673904i	$-0.764616\pi$
$457$	108.752	−	405.868i	0.237969	−	0.888113i	0.976788	−	0.214209i	$-0.0687173\pi$
$458$	−67.9620	−	253.638i	−0.148389	−	0.553794i
$459$	401.027	+	440.394i	0.873697	+	0.959465i
$460$	−7.31292	−	113.730i	−0.0158977	−	0.247240i
$461$	299.432			0.649526			0.324763	−	0.945795i	$-0.394715\pi$
$461$	299.432			0.649526			0.324763	+	0.945795i	$0.394715\pi$
$462$	−722.590	−	53.4201i	−1.56405	−	0.115628i
$463$	646.114	−	646.114i	1.39549	−	1.39549i	0.583076	−	0.812418i	$-0.301849\pi$
$463$	646.114	−	646.114i	1.39549	−	1.39549i	0.812418	−	0.583076i	$-0.198151\pi$
$464$	241.372	+	418.069i	0.520199	+	0.901012i
$465$	871.970	+	33.7084i	1.87520	+	0.0724913i
$466$	−404.148	+	700.005i	−0.867270	+	1.50216i
$467$	−162.967	+	608.200i	−0.348965	+	1.30236i	0.538946	+	0.842340i	$0.318823\pi$
$467$	−162.967	+	608.200i	−0.348965	+	1.30236i	−0.887911	+	0.460015i	$0.847844\pi$
$468$	84.1097	−	166.611i	0.179722	−	0.356007i
$469$	23.4475	−	98.9183i	0.0499946	−	0.210913i
$470$	251.809	+	744.834i	0.535765	+	1.58475i
$471$	−51.7507	+	501.388i	−0.109874	+	1.06452i
$472$	−132.311	−	493.791i	−0.280320	−	1.04617i
$473$	104.042	−	27.8781i	0.219963	−	0.0589389i
$474$	−916.200	−	94.5655i	−1.93291	−	0.199505i
$475$	−81.7453	+	62.4045i	−0.172095	+	0.131378i
$476$	−831.166	+	880.928i	−1.74615	+	1.85069i
$477$	−547.205	−	276.243i	−1.14718	−	0.579126i
$478$	−775.631	−	207.830i	−1.62266	−	0.434790i
$479$	735.072	+	424.394i	1.53460	+	0.886000i	0.999141	+	0.0414358i	$0.0131932\pi$
$479$	735.072	+	424.394i	1.53460	+	0.886000i	0.535455	+	0.844564i	$0.320140\pi$
$480$	−43.1466	−	46.6167i	−0.0898888	−	0.0971181i
$481$	117.938	−	68.0916i	0.245194	−	0.141563i
$482$	−157.734	−	157.734i	−0.327249	−	0.327249i
$483$	26.5346	+	54.9582i	0.0549370	+	0.113785i
$484$		−	160.636i		−	0.331893i
$485$	−41.1075	−	639.303i	−0.0847578	−	1.31815i
$486$	−411.342	+	728.095i	−0.846382	+	1.49814i
$487$	−351.301	+	94.1308i	−0.721357	+	0.193287i	−0.600777	−	0.799417i	$-0.705142\pi$
$487$	−351.301	+	94.1308i	−0.721357	+	0.193287i	−0.120580	+	0.992704i	$0.538475\pi$
$488$	−317.639	−	85.1111i	−0.650899	−	0.174408i
$489$	−21.4765	−	15.5424i	−0.0439193	−	0.0317840i
$490$	776.163	+	329.323i	1.58401	+	0.672087i
$491$			785.079i			1.59894i	0.600707	+	0.799469i	$0.294886\pi$
$491$			785.079i			1.59894i	−0.600707	+	0.799469i	$0.705114\pi$
$492$	136.899	+	168.411i	0.278249	+	0.342299i
$493$	−727.382	+	194.901i	−1.47542	+	0.395337i
$494$	18.7157	−	32.4165i	0.0378860	−	0.0656205i
$495$	−414.971	−	177.058i	−0.838326	−	0.357693i
$496$		−	822.703i		−	1.65868i
$497$	−491.080	−	264.809i	−0.988089	−	0.532815i
$498$	1006.29	−	161.309i	2.02066	−	0.323913i
$499$	28.6560	−	16.5445i	0.0574268	−	0.0331554i	−0.471012	−	0.882127i	$-0.656111\pi$
$499$	28.6560	−	16.5445i	0.0574268	−	0.0331554i	0.528438	+	0.848972i	$0.322778\pi$
$500$	−430.347	−	880.888i	−0.860694	−	1.76178i
$501$	158.058	+	353.227i	0.315486	+	0.705043i
$502$	258.252	+	69.1983i	0.514445	+	0.137845i
$503$	−409.855	+	409.855i	−0.814822	+	0.814822i	−0.985352	−	0.170530i	$-0.945452\pi$
$503$	−409.855	+	409.855i	−0.814822	+	0.814822i	0.170530	+	0.985352i	$0.445452\pi$
$504$	−754.402	−	353.725i	−1.49683	−	0.701836i
$505$	−32.1716	−	95.1612i	−0.0637061	−	0.188438i
$506$	86.8362	−	50.1349i	0.171613	−	0.0990809i
$507$	−173.328	+	454.070i	−0.341870	+	0.895602i
$508$	−43.3974	−	161.961i	−0.0854280	−	0.318821i
$509$	−549.812	+	317.434i	−1.08018	+	0.623643i	−0.930945	−	0.365159i	$-0.881015\pi$
$509$	−549.812	+	317.434i	−1.08018	+	0.623643i	−0.149236	+	0.988802i	$0.547681\pi$
$510$	−1007.46	+	530.861i	−1.97541	+	1.04090i
$511$	181.917	−	767.457i	0.356002	−	1.50187i
$512$	−571.363	+	571.363i	−1.11594	+	1.11594i
$513$	−59.9698	+	93.4889i	−0.116900	+	0.182240i
$514$	−436.677	+	756.347i	−0.849566	+	1.47149i
$515$	−37.4700	−	56.2284i	−0.0727574	−	0.109181i
$516$	251.450	+	25.9534i	0.487306	+	0.0502973i
$517$	−323.941	+	323.941i	−0.626577	+	0.626577i
$518$	−651.331	−	1056.05i	−1.25740	−	2.03870i
$519$	55.2224	+	39.9639i	0.106401	+	0.0770018i
$520$	131.313	+	115.446i	0.252526	+	0.222012i
$521$	497.225	−	861.219i	0.954366	−	1.65301i	0.218555	−	0.975825i	$-0.429866\pi$
$521$	497.225	−	861.219i	0.954366	−	1.65301i	0.735812	−	0.677186i	$-0.236801\pi$
$522$	−579.139	−	884.539i	−1.10946	−	1.69452i
$523$	−30.1997	+	112.707i	−0.0577433	+	0.215501i	−0.988769	−	0.149453i	$-0.952249\pi$
$523$	−30.1997	+	112.707i	−0.0577433	+	0.215501i	0.931026	+	0.364954i	$0.118915\pi$
$524$		−	419.554i		−	0.800676i
$525$	390.947	+	350.407i	0.744662	+	0.667442i
$526$	619.281			1.17734
$527$	1239.62	+	332.155i	2.35222	+	0.630274i
$528$	−151.692	+	397.389i	−0.287295	+	0.752631i
$529$	450.813	+	260.277i	0.852199	+	0.492017i
$530$	773.805	−	880.156i	1.46001	−	1.66067i
$531$	108.736	+	330.447i	0.204776	+	0.622311i
$532$	−198.790	−	107.195i	−0.373665	−	0.201494i
$533$	17.2454	+	17.2454i	0.0323553	+	0.0323553i
$534$	343.627	+	35.4675i	0.643497	+	0.0664185i
$535$	424.991	−	283.210i	0.794376	−	0.529364i
$536$	−166.340	−	96.0362i	−0.310335	−	0.179172i
$537$	58.7628	−	47.7673i	0.109428	−	0.0889521i
$538$	516.870	+	516.870i	0.960726	+	0.960726i
$539$	28.5329	+	490.440i	0.0529368	+	0.909907i
$540$	−761.656	−	735.513i	−1.41047	−	1.36206i
$541$	−10.0260	−	17.3656i	−0.0185324	−	0.0320991i	0.856610	−	0.515964i	$-0.172566\pi$
$541$	−10.0260	−	17.3656i	−0.0185324	−	0.0320991i	−0.875143	+	0.483865i	$0.839233\pi$
$542$	615.910	−	165.033i	1.13637	−	0.304488i
$543$	196.222	−	514.046i	0.361367	−	0.946677i
$544$	−46.7086	−	80.9016i	−0.0858613	−	0.148716i
$545$	846.730	−	286.258i	1.55363	−	0.525243i
$546$	−180.423	−	62.9293i	−0.330446	−	0.115255i
$547$	650.623	+	650.623i	1.18944	+	1.18944i	0.977223	+	0.212215i	$0.0680678\pi$
$547$	650.623	+	650.623i	1.18944	+	1.18944i	0.212215	+	0.977223i	$0.431932\pi$
$548$	27.0250	−	100.859i	0.0493157	−	0.184049i
$549$	219.060	+	45.7075i	0.399016	+	0.0832558i
$550$	526.794	−	683.024i	0.957808	−	1.24186i
$551$	−70.2121	−	121.611i	−0.127427	−	0.220710i
$552$	113.852	−	18.2506i	0.206254	−	0.0330627i
$553$	18.1433	+	624.240i	0.0328088	+	1.12883i
$554$	−1347.53			−2.43237
$555$	−170.983	−	753.425i	−0.308077	−	1.35752i
$556$	−654.143	−	377.670i	−1.17652	−	0.679262i
$557$	231.417	+	863.658i	0.415470	+	1.55055i	0.783893	+	0.620896i	$0.213231\pi$
$557$	231.417	+	863.658i	0.415470	+	1.55055i	−0.368424	+	0.929658i	$0.620102\pi$
$558$	101.025	+	1798.98i	0.181048	+	3.22398i
$559$	28.4062			0.0508161
$560$	315.878	−	381.070i	0.564067	−	0.680482i
$561$	−537.527	−	389.004i	−0.958160	−	0.693411i
$562$	234.242	−	874.204i	0.416801	−	1.55552i
$563$	159.909	+	596.790i	0.284031	+	1.06002i	0.949545	+	0.313632i	$0.101546\pi$
$563$	159.909	+	596.790i	0.284031	+	1.06002i	−0.665514	+	0.746386i	$0.731787\pi$
$564$	−981.373	+	439.135i	−1.74002	+	0.778608i
$565$	100.483	−	6.46114i	0.177847	−	0.0114357i
$566$	221.814			0.391897
$567$	526.058	+	211.547i	0.927792	+	0.373099i
$568$	−745.385	+	745.385i	−1.31230	+	1.31230i
$569$	−50.8317	−	88.0431i	−0.0893352	−	0.154733i	0.817895	−	0.575367i	$-0.195141\pi$
$569$	−50.8317	−	88.0431i	−0.0893352	−	0.154733i	−0.907230	+	0.420634i	$0.861808\pi$
$570$	−144.243	−	155.844i	−0.253059	−	0.273411i
$571$	−196.663	+	340.630i	−0.344419	+	0.596551i	−0.985248	−	0.171133i	$-0.945257\pi$
$571$	−196.663	+	340.630i	−0.344419	+	0.596551i	0.640829	+	0.767683i	$0.278591\pi$
$572$	−53.8118	+	200.828i	−0.0940766	+	0.351099i
$573$	−320.583	+	51.3898i	−0.559482	+	0.0896855i
$574$	152.490	−	161.619i	0.265661	−	0.281566i
$575$	−72.0078	−	9.66140i	−0.125231	−	0.0168024i
$576$	426.641	−	477.409i	0.740695	−	0.828835i
$577$	197.944	+	738.738i	0.343058	+	1.28031i	0.894865	+	0.446337i	$0.147272\pi$
$577$	197.944	+	738.738i	0.343058	+	1.28031i	−0.551808	+	0.833971i	$0.686062\pi$
$578$	−657.021	+	176.048i	−1.13672	+	0.304582i
$579$	65.0248	−	629.994i	0.112305	−	1.08807i
$580$	1268.14	−	428.726i	2.18645	−	0.739183i
$581$	−198.158	−	661.973i	−0.341064	−	1.13937i
$582$	1306.10	−	209.369i	2.24416	−	0.359741i
$583$	659.585	+	176.735i	1.13136	+	0.303148i
$584$	−1290.54	−	745.096i	−2.20983	−	1.27585i
$585$	−93.6226	−	73.4273i	−0.160039	−	0.125517i
$586$	−879.983	+	508.059i	−1.50168	+	0.866994i
$587$	−436.505	−	436.505i	−0.743621	−	0.743621i	0.229652	−	0.973273i	$-0.426241\pi$
$587$	−436.505	−	436.505i	−0.743621	−	0.743621i	−0.973273	+	0.229652i	$0.926241\pi$
$588$	−347.909	+	1099.19i	−0.591683	+	1.86937i
$589$			239.314i			0.406305i
$590$	−663.729	+	42.6782i	−1.12496	+	0.0723359i
$591$	−260.935	+	116.760i	−0.441514	+	0.197564i
$592$	−703.569	+	188.521i	−1.18846	+	0.318447i
$593$	333.633	+	89.3966i	0.562619	+	0.150753i	0.528909	−	0.848678i	$-0.322601\pi$
$593$	333.633	+	89.3966i	0.562619	+	0.150753i	0.0337095	+	0.999432i	$0.489268\pi$
$594$	282.902	−	887.586i	0.476266	−	1.49425i
$595$	446.651	+	629.804i	0.750673	+	1.05849i
$596$			575.509i			0.965620i
$597$	−231.265	+	187.991i	−0.387378	+	0.314893i
$598$	25.5423	−	6.84404i	0.0427129	−	0.0114449i
$599$	471.541	−	816.733i	0.787214	−	1.36349i	−0.140454	−	0.990087i	$-0.544856\pi$
$599$	471.541	−	816.733i	0.787214	−	1.36349i	0.927668	−	0.373407i	$-0.121811\pi$
$600$	846.065	−	517.764i	1.41011	−	0.862940i
$601$		−	657.422i		−	1.09388i	−0.837172	−	0.546940i	$-0.815793\pi$
$601$		−	657.422i		−	1.09388i	0.837172	−	0.546940i	$-0.184207\pi$
$602$	−7.51890	−	258.697i	−0.0124899	−	0.429729i
$603$	116.680	+	58.9030i	0.193499	+	0.0976833i
$604$	−49.8889	+	28.8034i	−0.0825975	+	0.0476877i
$605$	−100.414	−	20.1027i	−0.165973	−	0.0332277i
$606$	189.327	−	84.7181i	0.312420	−	0.139799i
$607$	−372.392	−	99.7822i	−0.613496	−	0.164386i	−0.0613268	−	0.998118i	$-0.519533\pi$
$607$	−372.392	−	99.7822i	−0.613496	−	0.164386i	−0.552169	+	0.833732i	$0.686200\pi$
$608$	12.3179	−	12.3179i	0.0202596	−	0.0202596i
$609$	−542.882	+	468.138i	−0.891431	+	0.768700i
$610$	−189.702	+	383.480i	−0.310986	+	0.628655i
$611$	−104.630	+	60.4083i	−0.171244	+	0.0988678i
$612$	−852.980	−	1302.79i	−1.39376	−	2.12874i
$613$	−118.479	−	442.171i	−0.193278	−	0.721324i	−0.992706	−	0.120561i	$-0.961531\pi$
$613$	−118.479	−	442.171i	−0.193278	−	0.721324i	0.799428	−	0.600762i	$-0.205136\pi$
$614$	−28.1897	+	16.2753i	−0.0459115	+	0.0265070i
$615$	122.406	−	64.4994i	0.199034	−	0.104877i
$616$	903.164	+	214.085i	1.46618	+	0.347540i
$617$	−209.106	+	209.106i	−0.338908	+	0.338908i	−0.855956	−	0.517048i	$-0.827031\pi$
$617$	−209.106	+	209.106i	−0.338908	+	0.338908i	0.517048	+	0.855956i	$0.327031\pi$
$618$	108.263	−	88.0050i	0.175182	−	0.142403i
$619$	−167.412	+	289.966i	−0.270455	+	0.468442i	−0.968978	−	0.247145i	$-0.920508\pi$
$619$	−167.412	+	289.966i	−0.270455	+	0.468442i	0.698523	+	0.715587i	$0.253841\pi$
$620$	−2236.97	−	447.839i	−3.60801	−	0.722321i
$621$	−76.6580	+	16.7439i	−0.123443	+	0.0269629i
$622$	−511.431	+	511.431i	−0.822236	+	0.822236i
$623$	−6.80476	−	234.126i	−0.0109226	−	0.375804i
$624$	−65.7656	+	90.8753i	−0.105394	+	0.145633i
$625$	−604.497	+	158.771i	−0.967195	+	0.254034i
$626$	−100.679	+	174.381i	−0.160829	+	0.278563i
$627$	44.1252	−	115.595i	0.0703751	−	0.184363i
$628$	341.066	−	1272.87i	0.543098	−	2.02687i
$629$		−	1136.22i		−	1.80640i
$630$	−643.925	+	872.062i	−1.02210	+	1.38423i
$631$	−780.395			−1.23676			−0.618380	−	0.785879i	$-0.712211\pi$
$631$	−780.395			−1.23676			−0.618380	+	0.785879i	$0.712211\pi$
$632$	1139.72	+	305.386i	1.80335	+	0.483206i
$633$	−704.536	−	268.936i	−1.11301	−	0.424860i
$634$	−96.1359	−	55.5041i	−0.151634	−	0.0875459i
$635$	−106.673	+	6.85911i	−0.167988	+	0.0108018i
$636$	1298.25	+	939.533i	2.04128	+	1.47725i
$637$	−26.2072	+	126.880i	−0.0411416	+	0.199184i
$638$	832.819	+	832.819i	1.30536	+	1.30536i
$639$	477.996	−	534.875i	0.748037	−	0.837050i
$640$	631.855	+	948.176i	0.987273	+	1.48152i
$641$	−147.398	−	85.1004i	−0.229950	−	0.132762i	0.380599	−	0.924740i	$-0.375718\pi$
$641$	−147.398	−	85.1004i	−0.229950	−	0.132762i	−0.610549	+	0.791978i	$0.709051\pi$
$642$	665.168	+	818.282i	1.03609	+	1.27458i
$643$	409.723	+	409.723i	0.637206	+	0.637206i	0.949865	−	0.312659i	$-0.101220\pi$
$643$	409.723	+	409.723i	0.637206	+	0.637206i	−0.312659	+	0.949865i	$0.601220\pi$
$644$	−45.7549	−	152.850i	−0.0710479	−	0.237345i
$645$	47.6910	−	153.933i	0.0739395	−	0.238656i
$646$	−156.151	−	270.462i	−0.241720	−	0.418672i
$647$	−631.529	+	169.218i	−0.976088	+	0.261542i	−0.711396	−	0.702791i	$-0.751937\pi$
$647$	−631.529	+	169.218i	−0.976088	+	0.261542i	−0.264692	+	0.964333i	$0.585270\pi$
$648$	667.932	−	837.553i	1.03076	−	1.29252i
$649$	−193.766	−	335.612i	−0.298561	−	0.517122i
$650$	180.814	−	138.034i	0.278175	−	0.212359i
$651$	1200.14	−	228.329i	1.84354	−	0.350736i
$652$	49.0083	+	49.0083i	0.0751662	+	0.0751662i
$653$	−236.867	+	884.001i	−0.362737	+	1.35375i	0.507725	+	0.861519i	$0.330487\pi$
$653$	−236.867	+	884.001i	−0.362737	+	1.35375i	−0.870462	+	0.492235i	$0.836180\pi$
$654$	753.808	+	1684.60i	1.15261	+	2.57584i
$655$	−262.263	−	52.5048i	−0.400401	−	0.0801600i
$656$	−65.2223	−	112.968i	−0.0994243	−	0.172208i
$657$	905.259	+	456.998i	1.37787	+	0.695584i
$658$	577.836	+	936.883i	0.878170	+	1.42383i
$659$	−506.439			−0.768496			−0.384248	−	0.923230i	$-0.625539\pi$
$659$	−506.439			−0.768496			−0.384248	+	0.923230i	$0.625539\pi$
$660$	997.945	+	628.776i	1.51204	+	0.952691i
$661$	−934.886	−	539.757i	−1.41435	−	0.816576i	−0.418557	−	0.908191i	$-0.637464\pi$
$661$	−934.886	−	539.757i	−1.41435	−	0.816576i	−0.995795	+	0.0916145i	$0.970797\pi$
$662$	341.271	+	1273.64i	0.515515	+	1.92393i
$663$	−110.376	−	135.783i	−0.166479	−	0.204800i
$664$	−1305.55			−1.96619
$665$	−91.8847	+	110.848i	−0.138172	+	0.166689i
$666$	1515.32	−	498.628i	2.27526	−	0.748690i
$667$	25.6755	−	95.8223i	0.0384940	−	0.143662i
$668$	−261.848	−	977.229i	−0.391988	−	1.46292i
$669$	−438.926	−	980.907i	−0.656093	−	1.46623i
$670$	−164.998	+	187.675i	−0.246265	+	0.280111i
$671$	−249.286			−0.371514
$672$	−73.5257	−	50.0208i	−0.109413	−	0.0744357i
$673$	−342.826	+	342.826i	−0.509400	+	0.509400i	−0.914342	−	0.404942i	$-0.867292\pi$
$673$	−342.826	+	342.826i	−0.509400	+	0.509400i	0.404942	+	0.914342i	$0.367292\pi$
$674$	513.276	+	889.019i	0.761536	+	1.31902i
$675$	−555.085	+	384.064i	−0.822348	+	0.568984i
$676$	635.327	−	1100.42i	0.939833	−	1.62784i
$677$	52.0099	−	194.104i	0.0768241	−	0.286711i	−0.916817	−	0.399308i	$-0.869250\pi$
$677$	52.0099	−	194.104i	0.0768241	−	0.286711i	0.993641	+	0.112597i	$0.0359169\pi$
$678$	32.9080	+	205.289i	0.0485368	+	0.302786i
$679$	−257.198	−	859.202i	−0.378789	−	1.26539i
$680$	1381.96	−	467.205i	2.03229	−	0.687067i
$681$	−150.108	−	15.4934i	−0.220423	−	0.0227509i
$682$	−519.502	−	1938.81i	−0.761733	−	2.84283i
$683$	−929.024	+	248.931i	−1.36021	+	0.364468i	−0.863894	−	0.503674i	$-0.831981\pi$
$683$	−929.024	+	248.931i	−1.36021	+	0.364468i	−0.496317	+	0.868141i	$0.665315\pi$
$684$	193.493	−	216.518i	0.282884	−	0.316547i
$685$	−59.6646	−	29.5152i	−0.0871016	−	0.0430879i
$686$	1162.44	+	205.086i	1.69452	+	0.298960i
$687$	−36.2314	−	226.021i	−0.0527385	−	0.328997i
$688$	−146.756	−	39.3231i	−0.213308	−	0.0571557i
$689$	155.957	+	90.0415i	0.226352	+	0.130684i
$690$	5.79497	−	149.904i	0.00839850	−	0.217252i
$691$	269.606	−	155.657i	0.390168	−	0.225263i	−0.292065	−	0.956398i	$-0.594342\pi$
$691$	269.606	−	155.657i	0.390168	−	0.225263i	0.682233	+	0.731135i	$0.261009\pi$
$692$	−126.015	−	126.015i	−0.182102	−	0.182102i
$693$	−621.803	−	110.995i	−0.897263	−	0.160166i
$694$		−	1575.10i		−	2.26960i
$695$	−317.943	+	361.641i	−0.457472	+	0.520346i
$696$	553.194	+	1236.27i	0.794820	+	1.77625i
$697$	196.549	−	52.6651i	0.281993	−	0.0755597i
$698$	1417.31	+	379.766i	2.03052	+	0.544077i
$699$	−413.103	+	570.827i	−0.590991	+	0.816634i
$700$	−864.198	−	1066.32i	−1.23457	−	1.52332i
$701$		−	1307.35i		−	1.86497i	−0.361204	−	0.932487i	$-0.617634\pi$
$701$		−	1307.35i		−	1.86497i	0.361204	−	0.932487i	$-0.382366\pi$
$702$	132.648	−	206.790i	0.188958	−	0.294573i
$703$	204.659	−	54.8382i	0.291122	−	0.0780060i
$704$	−356.625	+	617.693i	−0.506570	+	0.877405i
$705$	151.689	+	668.410i	0.215162	+	0.948099i
$706$			637.862i			0.903487i
$707$	−73.8253	−	119.698i	−0.104420	−	0.169304i
$708$	−143.953	−	898.016i	−0.203323	−	1.26838i
$709$	773.408	−	446.528i	1.09084	−	0.629799i	0.157043	−	0.987592i	$-0.449804\pi$
$709$	773.408	−	446.528i	1.09084	−	0.629799i	0.933801	+	0.357793i	$0.116471\pi$
$710$	760.530	+	1141.27i	1.07117	+	1.60742i
$711$	−786.006	−	164.002i	−1.10549	−	0.230664i
$712$	−427.459	−	114.537i	−0.600363	−	0.160867i
$713$	−119.546	+	119.546i	−0.167666	+	0.167666i
$714$	−1207.37	+	1041.14i	−1.69099	+	1.45817i
$715$	118.803	+	58.7702i	0.166158	+	0.0821961i
$716$	−171.457	+	98.9909i	−0.239465	+	0.138255i
$717$	−653.976	−	249.637i	−0.912101	−	0.348168i
$718$	−117.517	−	438.579i	−0.163673	−	0.610835i
$719$	290.477	−	167.707i	0.404001	−	0.233250i	−0.284208	−	0.958763i	$-0.591731\pi$
$719$	290.477	−	167.707i	0.404001	−	0.233250i	0.688209	+	0.725513i	$0.258397\pi$
$720$	382.040	+	508.954i	0.530611	+	0.706880i
$721$	−68.8055	−	64.9189i	−0.0954306	−	0.0900400i
$722$	−837.286	+	837.286i	−1.15968	+	1.15968i
$723$	−122.660	−	150.894i	−0.169654	−	0.208706i
$724$	−719.244	+	1245.77i	−0.993431	+	1.72067i
$725$	−109.295	−	846.365i	−0.150752	−	1.16740i
$726$	21.7096	−	210.334i	0.0299030	−	0.289716i
$727$	−511.166	+	511.166i	−0.703118	+	0.703118i	−0.965078	−	0.261961i	$-0.915631\pi$
$727$	−511.166	+	511.166i	−0.703118	+	0.703118i	0.261961	+	0.965078i	$0.415631\pi$
$728$	215.456	+	116.182i	0.295955	+	0.159590i
$729$	−421.855	+	594.541i	−0.578676	+	0.815557i
$730$	−1280.13	+	1456.07i	−1.75360	+	1.99462i
$731$	118.501	−	205.250i	0.162108	−	0.280780i
$732$	−546.571	−	208.638i	−0.746681	−	0.285024i
$733$	52.3209	−	195.264i	0.0713791	−	0.266390i	−0.921009	−	0.389542i	$-0.872633\pi$
$733$	52.3209	−	195.264i	0.0713791	−	0.266390i	0.992388	+	0.123151i	$0.0393001\pi$
$734$		−	53.9984i		−	0.0735673i
$735$	643.564	+	355.035i	0.875598	+	0.483041i
$736$	12.3064			0.0167206
$737$	−140.643	−	37.6851i	−0.190831	−	0.0511330i
$738$	156.492	+	239.015i	0.212048	+	0.323869i
$739$	264.287	+	152.586i	0.357629	+	0.206477i	0.668040	−	0.744125i	$-0.267133\pi$
$739$	264.287	+	152.586i	0.357629	+	0.206477i	−0.310411	+	0.950602i	$0.600467\pi$
$740$	129.608	+	2015.66i	0.175146	+	2.72386i
$741$	19.1304	−	26.4344i	0.0258170	−	0.0356740i
$742$	778.733	−	1444.14i	1.04951	−	1.94628i
$743$	787.429	+	787.429i	1.05980	+	1.05980i	0.998095	+	0.0617024i	$0.0196530\pi$
$743$	787.429	+	787.429i	1.05980	+	1.05980i	0.0617024	+	0.998095i	$0.480347\pi$
$744$	236.981	−	2295.99i	0.318522	−	3.08601i
$745$	359.750	+	72.0217i	0.482886	+	0.0966734i
$746$	976.964	+	564.050i	1.30960	+	0.756100i
$747$	887.025	−	49.8125i	1.18745	−	0.0666834i
$748$	1226.61	+	1226.61i	1.63985	+	1.63985i
$749$	490.676	−	520.053i	0.655108	−	0.694329i
$750$	−444.437	−	1211.57i	−0.592583	−	1.61543i
$751$	−119.523	−	207.021i	−0.159152	−	0.275660i	0.775411	−	0.631457i	$-0.217543\pi$
$751$	−119.523	−	207.021i	−0.159152	−	0.275660i	−0.934563	+	0.355797i	$0.884209\pi$
$752$	624.179	−	167.248i	0.830025	−	0.222405i
$753$	217.746	+	83.1182i	0.289171	+	0.110383i
$754$	155.304	+	268.994i	0.205973	+	0.356756i
$755$	11.7616	+	34.7900i	0.0155783	+	0.0460795i
$756$	−1270.43	−	763.774i	−1.68047	−	1.01028i
$757$	−868.776	−	868.776i	−1.14766	−	1.14766i	−0.987012	−	0.160645i	$-0.948643\pi$
$757$	−868.776	−	868.776i	−1.14766	−	1.14766i	−0.160645	−	0.987012i	$-0.551357\pi$
$758$	440.011	−	1642.14i	0.580489	−	2.16642i
$759$	79.7860	−	35.7018i	0.105120	−	0.0470380i
$760$	150.852	+	226.373i	0.198490	+	0.297859i
$761$	289.949	+	502.207i	0.381011	+	0.659930i	0.991207	−	0.132320i	$-0.0422427\pi$
$761$	289.949	+	502.207i	0.381011	+	0.659930i	−0.610196	+	0.792250i	$0.708909\pi$
$762$	−34.9349	−	217.933i	−0.0458464	−	0.286002i
$763$	1065.05	−	656.886i	1.39587	−	0.860925i
$764$	848.823			1.11103
$765$	−921.115	+	370.160i	−1.20407	+	0.483869i
$766$	904.080	+	521.971i	1.18026	+	0.681424i
$767$	−26.4515	−	98.7182i	−0.0344869	−	0.128707i
$768$	−1163.19	+	945.538i	−1.51457	+	1.23117i
$769$	1014.55			1.31931			0.659654	−	0.751570i	$-0.270703\pi$
$769$	1014.55			1.31931			0.659654	+	0.751570i	$0.270703\pi$
$770$	503.777	−	1097.50i	0.654256	−	1.42533i
$771$	−446.352	+	616.772i	−0.578927	+	0.799964i
$772$	−428.550	+	1599.37i	−0.555116	+	2.07172i
$773$	8.55711	+	31.9356i	0.0110700	+	0.0413138i	0.971240	−	0.238103i	$-0.0765256\pi$
$773$	8.55711	+	31.9356i	0.0110700	+	0.0413138i	−0.960170	+	0.279417i	$0.909859\pi$
$774$	325.735	+	67.9656i	0.420847	+	0.0878108i
$775$	−559.887	+	1342.28i	−0.722435	+	1.73197i
$776$	−1694.53			−2.18367
$777$	−470.275	−	974.030i	−0.605245	−	1.25358i
$778$	−739.016	+	739.016i	−0.949892	+	0.949892i
$779$	18.9723	+	32.8610i	0.0243547	+	0.0421836i
$780$	211.294	+	228.288i	0.270890	+	0.292676i
$781$	−399.552	+	692.045i	−0.511591	+	0.886101i
$782$	57.1022	−	213.108i	0.0730207	−	0.272517i
$783$	−423.025	−	818.850i	−0.540262	−	1.04579i
$784$	311.038	−	619.227i	0.396732	−	0.789830i
$785$	−752.990	−	372.493i	−0.959222	−	0.474513i
$786$	56.7016	−	549.355i	0.0721394	−	0.698924i
$787$	294.434	+	1098.84i	0.374122	+	1.39624i	0.854623	+	0.519248i	$0.173788\pi$
$787$	294.434	+	1098.84i	0.374122	+	1.39624i	−0.480501	+	0.876994i	$0.659545\pi$
$788$	721.896	−	193.432i	0.916112	−	0.245471i
$789$	537.001	+	55.4265i	0.680610	+	0.0702491i
$790$	680.666	−	1375.96i	0.861603	−	1.74172i
$791$	135.047	−	40.4255i	0.170729	−	0.0511068i
$792$	−537.808	+	1065.33i	−0.679051	+	1.34512i
$793$	−63.5020	−	17.0153i	−0.0800782	−	0.0214569i
$794$	1115.01	+	643.753i	1.40430	+	0.810772i
$795$	749.770	−	693.958i	0.943106	−	0.872903i
$796$	674.781	−	389.585i	0.847715	−	0.489429i
$797$	−3.85146	−	3.85146i	−0.00483245	−	0.00483245i	0.704686	−	0.709519i	$-0.251088\pi$
$797$	−3.85146	−	3.85146i	−0.00483245	−	0.00483245i	−0.709519	+	0.704686i	$0.751088\pi$
$798$	−245.804	−	167.224i	−0.308025	−	0.209554i
$799$			1008.01i			1.26159i
$800$	97.9075	−	40.2710i	0.122384	−	0.0503387i
$801$	294.797	+	61.5102i	0.368037	+	0.0767918i
$802$	2572.08	−	689.187i	3.20708	−	0.859335i
$803$	−1091.17	−	292.379i	−1.35887	−	0.364108i
$804$	−276.825	−	200.336i	−0.344309	−	0.249174i
$805$	−101.272	+	9.47300i	−0.125804	+	0.0117677i
$806$		−	529.343i		−	0.656753i
$807$	401.936	+	494.458i	0.498062	+	0.612711i
$808$	−256.655	+	68.7705i	−0.317642	+	0.0851120i
$809$	144.501	−	250.284i	0.178617	−	0.309374i	−0.762790	−	0.646646i	$-0.776171\pi$
$809$	144.501	−	250.284i	0.178617	−	0.309374i	0.941407	+	0.337272i	$0.109504\pi$
$810$	−897.892	−	1066.00i	−1.10851	−	1.31605i
$811$		−	477.193i		−	0.588400i	−0.955744	−	0.294200i	$-0.904947\pi$
$811$		−	477.193i		−	0.588400i	0.955744	−	0.294200i	$-0.0950532\pi$
$812$	1595.12	−	983.813i	1.96443	−	1.21159i
$813$	548.849	−	87.9809i	0.675090	−	0.108218i
$814$	−1539.01	+	888.547i	−1.89067	+	1.09158i
$815$	36.7681	−	24.5019i	0.0451143	−	0.0300637i
$816$	382.271	+	854.294i	0.468469	+	1.04693i
$817$	42.6894	+	11.4386i	0.0522514	+	0.0140007i
$818$	−598.459	+	598.459i	−0.731612	+	0.731612i
$819$	−150.819	−	70.7164i	−0.184151	−	0.0863448i
$820$	−342.670	+	115.848i	−0.417890	+	0.141278i
$821$	384.865	−	222.202i	0.468776	−	0.270648i	−0.246951	−	0.969028i	$-0.579429\pi$
$821$	384.865	−	222.202i	0.468776	−	0.270648i	0.715727	+	0.698380i	$0.246095\pi$
$822$	49.0167	−	128.410i	0.0596310	−	0.156216i
$823$	113.633	+	424.086i	0.138072	+	0.515292i	0.999966	+	0.00820411i	$0.00261148\pi$
$823$	113.633	+	424.086i	0.138072	+	0.515292i	−0.861894	+	0.507088i	$0.830722\pi$
$824$	−154.784	+	89.3648i	−0.187845	+	0.108452i
$825$	517.934	−	545.126i	0.627799	−	0.660759i
$826$	−892.031	+	267.025i	−1.07994	+	0.323275i
$827$	612.628	−	612.628i	0.740784	−	0.740784i	−0.231945	−	0.972729i	$-0.574509\pi$
$827$	612.628	−	612.628i	0.740784	−	0.740784i	0.972729	+	0.231945i	$0.0745090\pi$
$828$	204.815	−	11.5017i	0.247361	−	0.0138910i
$829$	749.851	−	1298.78i	0.904525	−	1.56668i	0.0829717	−	0.996552i	$-0.473559\pi$
$829$	749.851	−	1298.78i	0.904525	−	1.56668i	0.821553	−	0.570132i	$-0.193108\pi$
$830$	−333.433	+	1665.51i	−0.401727	+	2.00664i
$831$	−1168.50	−	120.606i	−1.40613	−	0.145134i
$832$	−133.007	+	133.007i	−0.159864	+	0.159864i
$833$	807.450	+	718.664i	0.969328	+	0.862741i
$834$	−805.479	−	582.918i	−0.965803	−	0.698942i
$835$	−643.633	+	41.3860i	−0.770818	+	0.0495640i
$836$	−161.739	+	280.140i	−0.193468	+	0.335096i
$837$	−73.4088	+	1569.00i	−0.0877046	+	1.87455i
$838$	562.855	−	2100.60i	0.671665	−	2.50669i
$839$			1060.78i			1.26434i	0.774829	+	0.632171i	$0.217836\pi$
$839$			1060.78i			1.26434i	−0.774829	+	0.632171i	$0.782164\pi$
$840$	991.315	−	972.497i	1.18014	−	1.15773i
$841$	324.247			0.385549
$842$	−2286.80	−	612.747i	−2.71592	−	0.727728i
$843$	281.363	−	737.089i	0.333763	−	0.874364i
$844$	1707.41	+	985.774i	2.02300	+	1.16798i
$845$	−608.363	−	534.853i	−0.719956	−	0.632962i
$846$	−1344.34	+	442.363i	−1.58905	+	0.522888i
$847$	−143.308	+	4.16518i	−0.169195	+	0.00491757i
$848$	−681.078	−	681.078i	−0.803158	−	0.803158i
$849$	192.343	+	19.8526i	0.226552	+	0.0233835i
$850$	−243.072	−	1882.31i	−0.285967	−	2.21448i
$851$	129.628	+	74.8407i	0.152324	+	0.0879444i
$852$	−1455.24	+	1182.94i	−1.70802	+	1.38842i
$853$	40.3652	+	40.3652i	0.0473214	+	0.0473214i	0.730372	−	0.683050i	$-0.239347\pi$
$853$	40.3652	+	40.3652i	0.0473214	+	0.0473214i	−0.683050	+	0.730372i	$0.739347\pi$
$854$	−138.151	+	582.820i	−0.161769	+	0.682459i
$855$	−111.130	−	148.048i	−0.129977	−	0.173156i
$856$	−675.446	−	1169.91i	−0.789072	−	1.36671i
$857$	−493.821	+	132.319i	−0.576221	+	0.154398i	−0.535148	−	0.844758i	$-0.679744\pi$
$857$	−493.821	+	132.319i	−0.576221	+	0.154398i	−0.0410728	+	0.999156i	$0.513078\pi$
$858$	−97.6014	+	255.688i	−0.113755	+	0.298004i
$859$	55.7529	+	96.5669i	0.0649045	+	0.112418i	0.896652	−	0.442737i	$-0.145992\pi$
$859$	55.7529	+	96.5669i	0.0649045	+	0.112418i	−0.831747	+	0.555155i	$0.812659\pi$
$860$	−186.808	+	377.630i	−0.217219	+	0.439105i
$861$	146.694	−	126.498i	0.170377	−	0.146920i
$862$	1140.13	+	1140.13i	1.32265	+	1.32265i
$863$	43.5340	−	162.471i	0.0504449	−	0.188263i	−0.936106	−	0.351719i	$-0.885597\pi$
$863$	43.5340	−	162.471i	0.0504449	−	0.188263i	0.986551	+	0.163456i	$0.0522641\pi$
$864$	84.5375	−	76.9805i	0.0978443	−	0.0890978i
$865$	−94.5415	+	63.0015i	−0.109297	+	0.0728341i
$866$	198.617	+	344.015i	0.229350	+	0.397246i
$867$	−585.484	+	93.8535i	−0.675298	+	0.108251i
$868$	−3192.55	+	92.7900i	−3.67805	+	0.106901i
$869$	894.460			1.02930
$870$	1718.42	−	389.978i	1.97519	−	0.448251i
$871$	−33.2544	−	19.1995i	−0.0381796	−	0.0220430i
$872$	−611.909	−	2283.67i	−0.701730	−	2.61889i
$873$	1151.31	−	64.6538i	1.31879	−	0.0740593i
$874$	41.1415			0.0470726
$875$	−774.705	+	406.765i	−0.885377	+	0.464874i
$876$	−2147.74	−	1554.30i	−2.45176	−	1.77432i
$877$	−386.850	+	1443.75i	−0.441107	+	1.64623i	0.284909	+	0.958554i	$0.408036\pi$
$877$	−386.850	+	1443.75i	−0.441107	+	1.64623i	−0.726016	+	0.687678i	$0.758630\pi$
$878$	−293.868	−	1096.73i	−0.334702	−	1.24912i
$879$	−808.537	+	361.796i	−0.919838	+	0.411600i
$880$	−532.422	−	468.088i	−0.605025	−	0.531919i
$881$	−1173.25			−1.33172			−0.665861	−	0.746076i	$-0.731936\pi$
$881$	−1173.25			−1.33172			−0.665861	+	0.746076i	$0.731936\pi$
$882$	−604.097	+	1392.24i	−0.684918	+	1.57850i
$883$	445.237	−	445.237i	0.504232	−	0.504232i	−0.408518	−	0.912750i	$-0.633954\pi$
$883$	445.237	−	445.237i	0.504232	−	0.504232i	0.912750	+	0.408518i	$0.133954\pi$
$884$	228.738	+	396.185i	0.258753	+	0.448173i
$885$	−579.363	−	22.3969i	−0.654648	−	0.0253072i
$886$	−1232.60	+	2134.92i	−1.39120	+	2.40962i
$887$	231.405	−	863.617i	0.260885	−	0.973638i	−0.703835	−	0.710363i	$-0.748531\pi$
$887$	231.405	−	863.617i	0.260885	−	0.973638i	0.964721	−	0.263275i	$-0.0848026\pi$
$888$	−2017.82	+	323.458i	−2.27231	+	0.364254i
$889$	−143.365	+	42.9155i	−0.161265	+	0.0482739i
$890$	−255.289	+	516.063i	−0.286841	+	0.579846i
$891$	324.755	−	744.337i	0.364483	−	0.835396i
$892$	727.149	+	2713.76i	0.815189	+	3.04233i
$893$	−181.566	+	48.6504i	−0.203321	+	0.0544797i
$894$	−77.7785	+	753.559i	−0.0870006	+	0.842907i
$895$	40.4221	+	119.566i	0.0451644	+	0.133593i
$896$	1160.26	+	1094.72i	1.29494	+	1.22179i
$897$	22.7612	−	3.64864i	0.0253748	−	0.00406761i
$898$	1008.28	+	270.168i	1.12281	+	0.300855i
$899$	−1719.78	−	992.918i	−1.91300	−	1.10447i
$900$	1591.83	−	761.733i	1.76870	−	0.846370i
$901$	1301.20	−	751.247i	1.44417	−	0.833793i
$902$	−225.040	−	225.040i	−0.249490	−	0.249490i
$903$	16.6338	−	224.998i	0.0184206	−	0.249167i
$904$		−	266.340i		−	0.294624i
$905$	688.718	+	605.499i	0.761014	+	0.669060i
$906$	−69.2161	+	30.9721i	−0.0763974	+	0.0341856i
$907$	−161.765	+	43.3449i	−0.178352	+	0.0477893i	−0.346890	−	0.937906i	$-0.612762\pi$
$907$	−161.765	+	43.3449i	−0.178352	+	0.0477893i	0.168538	+	0.985695i	$0.446096\pi$
$908$	381.079	+	102.110i	0.419690	+	0.112456i
$909$	171.754	−	56.5171i	0.188949	−	0.0621750i
$910$	203.242	−	245.188i	0.223342	−	0.269437i
$911$			282.131i			0.309694i	0.987938	+	0.154847i	$0.0494884\pi$
$911$			282.131i			0.309694i	−0.987938	+	0.154847i	$0.950512\pi$
$912$	−135.428	+	110.087i	−0.148495	+	0.120709i
$913$	−955.970	+	256.151i	−1.04706	+	0.280560i
$914$	−723.009	+	1252.29i	−0.791038	+	1.37012i
$915$	−198.819	+	315.551i	−0.217289	+	0.344864i
$916$			598.446i			0.653326i
$917$	−374.295	+	10.8787i	−0.408174	+	0.0118634i
$918$	−940.804	−	1821.12i	−1.02484	−	1.98379i
$919$	−344.416	+	198.849i	−0.374772	+	0.216375i	−0.675541	−	0.737322i	$-0.736090\pi$
$919$	−344.416	+	198.849i	−0.374772	+	0.216375i	0.300769	+	0.953697i	$0.402757\pi$
$920$	−37.7250	+	188.437i	−0.0410054	+	0.204823i
$921$	−25.9010	+	11.5899i	−0.0281226	+	0.0125840i
$922$	−995.346	−	266.702i	−1.07955	−	0.289265i
$923$	−149.017	+	149.017i	−0.161448	+	0.161448i
$924$	1559.20	+	543.829i	1.68745	+	0.588559i
$925$	1276.20	+	171.230i	1.37968	+	0.185114i
$926$	−2723.25	+	1572.27i	−2.94087	+	1.69791i
$927$	101.755	−	66.6226i	0.109768	−	0.0718691i
$928$	37.4130	+	139.627i	0.0403157	+	0.150460i
$929$	−826.901	+	477.411i	−0.890098	+	0.513898i	−0.873974	−	0.485972i	$-0.838466\pi$
$929$	−826.901	+	477.411i	−0.890098	+	0.513898i	−0.0161233	+	0.999870i	$0.505132\pi$
$930$	−2868.51	−	888.710i	−3.08442	−	0.955602i
$931$	−90.4768	+	180.125i	−0.0971824	+	0.193475i
$932$	1302.60	−	1302.60i	1.39764	−	1.39764i
$933$	−489.254	+	397.706i	−0.524388	+	0.426266i
$934$	1083.44	−	1876.58i	1.16000	−	2.00918i
$935$	920.255	−	613.249i	0.984230	−	0.655881i
$936$	−209.715	+	234.670i	−0.224054	+	0.250716i
$937$	664.538	−	664.538i	0.709219	−	0.709219i	−0.257152	−	0.966371i	$-0.582784\pi$
$937$	664.538	−	664.538i	0.709219	−	0.709219i	0.966371	+	0.257152i	$0.0827842\pi$
$938$	−166.048	+	307.932i	−0.177024	+	0.328286i
$939$	−102.909	+	142.201i	−0.109595	+	0.151439i
$940$	−114.983	−	1788.21i	−0.122322	−	1.90235i
$941$	550.294	−	953.137i	0.584797	−	1.01290i	−0.410104	−	0.912039i	$-0.634508\pi$
$941$	550.294	−	953.137i	0.584797	−	1.01290i	0.994901	−	0.100859i	$-0.0321591\pi$
$942$	618.609	−	1620.58i	0.656698	−	1.72036i
$943$	−6.93789	+	25.8926i	−0.00735726	+	0.0274577i
$944$			546.629i			0.579056i
$945$	−636.422	+	698.564i	−0.673462	+	0.739222i
$946$	−370.680			−0.391840
$947$	1188.87	+	318.558i	1.25541	+	0.336386i	0.824424	−	0.565972i	$-0.191499\pi$
$947$	1188.87	+	318.558i	1.25541	+	0.336386i	0.430986	+	0.902358i	$0.358166\pi$
$948$	1961.14	+	748.610i	2.06872	+	0.789672i
$949$	−258.004	−	148.959i	−0.271869	−	0.156964i
$950$	327.314	−	134.630i	0.344541	−	0.141716i
$951$	−78.3952	−	56.7339i	−0.0824345	−	0.0596571i
$952$	1738.29	−	1072.11i	1.82593	−	1.12617i
$953$	−136.949	−	136.949i	−0.143703	−	0.143703i	0.631595	−	0.775298i	$-0.282400\pi$
$953$	−136.949	−	136.949i	−0.143703	−	0.143703i	−0.775298	+	0.631595i	$0.782400\pi$
$954$	1572.93	+	1405.66i	1.64877	+	1.47344i
$955$	106.225	−	530.598i	0.111231	−	0.555600i
$956$	1584.88	+	915.033i	1.65783	+	0.957147i
$957$	647.629	+	796.706i	0.676728	+	0.832503i
$958$	−2065.46	−	2065.46i	−2.15601	−	2.15601i
$959$	−90.6795	−	21.4945i	−0.0945563	−	0.0224135i
$960$	497.459	+	944.066i	0.518186	+	0.983403i
$961$	1211.65	+	2098.64i	1.26082	+	2.18381i
$962$	−452.689	+	121.298i	−0.470571	+	0.126089i
$963$	503.554	+	769.096i	0.522901	+	0.798645i
$964$	254.195	+	440.278i	0.263687	+	0.456720i
$965$	946.132	+	468.037i	0.980448	+	0.485013i
$966$	−39.2531	−	206.322i	−0.0406347	−	0.213584i
$967$	−998.741	−	998.741i	−1.03282	−	1.03282i	−0.999443	−	0.0333815i	$-0.989372\pi$
$967$	−998.741	−	998.741i	−1.03282	−	1.03282i	−0.0333815	−	0.999443i	$-0.510628\pi$
$968$	−70.1080	+	261.647i	−0.0724256	+	0.270296i
$969$	−111.198	−	248.503i	−0.114755	−	0.256453i
$970$	−432.778	+	2161.73i	−0.446162	+	2.22859i
$971$	388.004	+	672.042i	0.399592	+	0.692114i	0.993676	−	0.112290i	$-0.0358185\pi$
$971$	388.004	+	672.042i	0.399592	+	0.692114i	−0.594084	+	0.804403i	$0.702485\pi$
$972$	1335.01	−	1360.19i	1.37346	−	1.39938i
$973$	−319.968	+	593.371i	−0.328847	+	0.609837i
$974$	1251.61			1.28502
$975$	169.145	−	103.511i	0.173482	−	0.106165i
$976$	304.518	+	175.814i	0.312007	+	0.180137i
$977$	−435.769	−	1626.31i	−0.446028	−	1.66460i	−0.713208	−	0.700953i	$-0.752758\pi$
$977$	−435.769	−	1626.31i	−0.446028	−	1.66460i	0.267180	−	0.963647i	$-0.413908\pi$
$978$	57.5471	+	70.7937i	0.0588416	+	0.0723862i
$979$	−335.473			−0.342670
$980$	−1514.39	−	1182.80i	−1.54530	−	1.20694i
$981$	502.880	+	1528.24i	0.512620	+	1.55784i
$982$	699.266	−	2609.70i	0.712084	−	2.65753i
$983$	−281.543	−	1050.73i	−0.286412	−	1.06891i	−0.947801	−	0.318862i	$-0.896699\pi$
$983$	−281.543	−	1050.73i	−0.286412	−	1.06891i	0.661389	−	0.750043i	$-0.269967\pi$
$984$	−149.481	−	334.058i	−0.151912	−	0.339490i
$985$	−30.5725	−	475.463i	−0.0310381	−	0.482704i
$986$	2591.50			2.62830
$987$	417.210	+	864.122i	0.422705	+	0.875504i
$988$	−60.3220	+	60.3220i	−0.0610547	+	0.0610547i
$989$	15.6109	+	27.0388i	0.0157845	+	0.0273396i
$990$	1221.71	+	958.174i	1.23405	+	0.967853i
$991$	884.108	−	1531.32i	0.892137	−	1.54523i	0.0548284	−	0.998496i	$-0.482539\pi$
$991$	884.108	−	1531.32i	0.892137	−	1.54523i	0.837309	−	0.546731i	$-0.184128\pi$
$992$	63.7599	−	237.955i	0.0642741	−	0.239874i
$993$	181.936	+	1134.96i	0.183218	+	1.14297i
$994$	1396.55	+	1317.66i	1.40498	+	1.32561i
$995$	−159.084	−	470.559i	−0.159883	−	0.472924i
$996$	−2310.39	−	238.467i	−2.31967	−	0.239425i
$997$	−26.8272	−	100.120i	−0.0269079	−	0.100422i	0.951166	−	0.308680i	$-0.0998872\pi$
$997$	−26.8272	−	100.120i	−0.0269079	−	0.100422i	−0.978074	+	0.208258i	$0.933221\pi$
$998$	−109.992	+	29.4723i	−0.110212	+	0.0295313i
$999$	1358.62	−	296.755i	1.35998	−	0.297052i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.w.a.17.2	✓	112
3.2	odd	2	inner	105.3.w.a.17.27	yes	112
5.3	odd	4	inner	105.3.w.a.38.2	yes	112
7.5	odd	6	inner	105.3.w.a.47.27	yes	112
15.8	even	4	inner	105.3.w.a.38.27	yes	112
21.5	even	6	inner	105.3.w.a.47.2	yes	112
35.33	even	12	inner	105.3.w.a.68.27	yes	112
105.68	odd	12	inner	105.3.w.a.68.2	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.w.a.17.2	✓	112	1.1	even	1	trivial
105.3.w.a.17.27	yes	112	3.2	odd	2	inner
105.3.w.a.38.2	yes	112	5.3	odd	4	inner
105.3.w.a.38.27	yes	112	15.8	even	4	inner
105.3.w.a.47.2	yes	112	21.5	even	6	inner
105.3.w.a.47.27	yes	112	7.5	odd	6	inner
105.3.w.a.68.2	yes	112	105.68	odd	12	inner
105.3.w.a.68.27	yes	112	35.33	even	12	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.32412 - 0.890695i) q^{2} +(-2.80275 - 1.06987i) q^{3} +(6.79233 + 3.92155i) q^{4} +(3.30138 - 3.75512i) q^{5} +(8.36374 + 6.05276i) q^{6} +(3.32240 - 6.16130i) q^{7} +(-9.35192 - 9.35192i) q^{8} +(6.71077 + 5.99713i) q^{9} +(-14.3188 + 9.54193i) q^{10} +(-8.68269 - 5.01295i) q^{11} +(-14.8416 - 18.2580i) q^{12} +(-1.86963 - 1.86963i) q^{13} +(-16.5319 + 17.5217i) q^{14} +(-13.2704 + 6.99260i) q^{15} +(7.07097 + 12.2473i) q^{16} +(-21.3085 + 5.70960i) q^{17} +(-16.9658 - 25.9124i) q^{18} +(-2.05685 - 3.56257i) q^{19} +(37.1500 - 12.5595i) q^{20} +(-15.9036 + 13.7140i) q^{21} +(24.3973 + 24.3973i) q^{22} +(0.752160 - 2.80710i) q^{23} +(16.2057 + 36.2164i) q^{24} +(-3.20179 - 24.7941i) q^{25} +(4.54959 + 7.88012i) q^{26} +(-12.3924 - 23.9881i) q^{27} +(46.7287 - 28.8206i) q^{28} +34.1357 q^{29} +(50.3407 - 11.4243i) q^{30} +(-50.3808 - 29.0874i) q^{31} +(1.09601 + 4.09035i) q^{32} +(18.9722 + 23.3394i) q^{33} +75.9176 q^{34} +(-12.1679 - 32.8168i) q^{35} +(22.0637 + 67.0512i) q^{36} +(-13.3306 + 49.7505i) q^{37} +(3.66406 + 13.6744i) q^{38} +(3.23983 + 7.24034i) q^{39} +(-65.9918 + 4.24331i) q^{40} -9.22396 q^{41} +(65.0806 - 31.4218i) q^{42} +(-7.59676 + 7.59676i) q^{43} +(-39.3171 - 68.0993i) q^{44} +(44.6747 - 5.40090i) q^{45} +(-5.00054 + 8.66119i) q^{46} +(11.8264 - 44.1368i) q^{47} +(-6.71516 - 41.8910i) q^{48} +(-26.9233 - 40.9407i) q^{49} +(-11.4409 + 85.2705i) q^{50} +(65.8309 + 6.79473i) q^{51} +(-5.36728 - 20.0310i) q^{52} +(-65.7881 + 17.6279i) q^{53} +(19.8279 + 90.7771i) q^{54} +(-47.4891 + 16.0548i) q^{55} +(-88.6908 + 26.5492i) q^{56} +(1.95335 + 12.1855i) q^{57} +(-113.471 - 30.4045i) q^{58} +(33.4745 + 19.3265i) q^{59} +(-117.559 - 4.54457i) q^{60} +(21.5330 - 12.4321i) q^{61} +(141.564 + 141.564i) q^{62} +(59.2460 - 21.4222i) q^{63} -71.1408i q^{64} +(-13.1930 + 0.848318i) q^{65} +(-42.2775 - 94.4812i) q^{66} +(14.0279 - 3.75877i) q^{67} +(-167.125 - 44.7810i) q^{68} +(-5.11134 + 7.06287i) q^{69} +(11.2178 + 119.925i) q^{70} -79.7040i q^{71} +(-6.67386 - 118.843i) q^{72} +(108.835 - 29.1624i) q^{73} +(88.6251 - 153.503i) q^{74} +(-17.5526 + 72.9171i) q^{75} -32.2642i q^{76} +(-59.7337 + 36.8416i) q^{77} +(-4.32066 - 26.9534i) q^{78} +(-77.2623 + 44.6074i) q^{79} +(69.3339 + 13.8806i) q^{80} +(9.06881 + 80.4907i) q^{81} +(30.6615 + 8.21574i) q^{82} +(69.8011 - 69.8011i) q^{83} +(-161.803 + 30.7833i) q^{84} +(-48.9073 + 98.8655i) q^{85} +(32.0189 - 18.4861i) q^{86} +(-95.6737 - 36.5207i) q^{87} +(34.3191 + 128.081i) q^{88} +(28.9778 - 16.7303i) q^{89} +(-153.315 - 21.8383i) q^{90} +(-17.7310 + 5.30768i) q^{91} +(16.1171 - 16.1171i) q^{92} +(110.085 + 135.425i) q^{93} +(-78.6248 + 136.182i) q^{94} +(-20.1683 - 4.03768i) q^{95} +(1.30431 - 12.6368i) q^{96} +(90.5978 - 90.5978i) q^{97} +(53.0306 + 160.072i) q^{98} +(-28.2042 - 85.7120i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 6 q^{3} - 16 q^{7} - 60 q^{10} - 30 q^{12} - 20 q^{15} + 120 q^{16} + 46 q^{18} - 96 q^{21} - 80 q^{22} + 28 q^{25} - 136 q^{28} - 80 q^{30} - 24 q^{31} - 36 q^{33} - 272 q^{36} + 60 q^{37} - 72 q^{40}+ \cdots + 2184 q^{96}+O(q^{100}) \) 112 * q - 6 * q^3 - 16 * q^7 - 60 * q^10 - 30 * q^12 - 20 * q^15 + 120 * q^16 + 46 * q^18 - 96 * q^21 - 80 * q^22 + 28 * q^25 - 136 * q^28 - 80 * q^30 - 24 * q^31 - 36 * q^33 - 272 * q^36 + 60 * q^37 - 72 * q^40 + 338 * q^42 - 48 * q^43 + 384 * q^45 + 40 * q^46 + 176 * q^51 - 204 * q^52 + 344 * q^57 - 284 * q^58 - 214 * q^60 - 912 * q^61 + 132 * q^63 - 444 * q^66 - 36 * q^67 + 208 * q^70 - 638 * q^72 + 708 * q^73 + 42 * q^75 + 664 * q^78 + 8 * q^81 + 1104 * q^82 + 264 * q^85 + 246 * q^87 + 180 * q^88 + 632 * q^91 + 196 * q^93 + 2184 * q^96

Introduction

L-functions

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