LMFDB - Embedded newform 483.2.v.a.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(41,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 12]))

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

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

chi := DirichletCharacter("483.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.v (of order $22$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$600$
Relative dimension:	$60$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			41.1
Character	$\chi$	$=$	483.41
Dual form			483.2.v.a.377.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.783018 + 2.66671i) q^{2} +(-1.29371 + 1.15165i) q^{3} +(-4.81573 - 3.09488i) q^{4} +(0.328519 - 2.28490i) q^{5} +(-2.05813 - 4.35173i) q^{6} +(-2.59187 + 0.531216i) q^{7} +(7.82307 - 6.77873i) q^{8} +(0.347391 - 2.97982i) q^{9} +(5.83594 + 2.66518i) q^{10} +(0.892863 + 3.04081i) q^{11} +(9.79441 - 1.54216i) q^{12} +(-1.39374 - 0.636498i) q^{13} +(0.612882 - 7.32773i) q^{14} +(2.20640 + 3.33435i) q^{15} +(7.19526 + 15.7554i) q^{16} +(-3.01474 + 1.93745i) q^{17} +(7.67431 + 3.25964i) q^{18} +(2.67355 - 4.16012i) q^{19} +(-8.65357 + 9.98675i) q^{20} +(2.74137 - 3.67218i) q^{21} -8.80810 q^{22} +(4.76812 + 0.514855i) q^{23} +(-2.31407 + 17.7792i) q^{24} +(-0.315385 - 0.0926055i) q^{25} +(2.78868 - 3.21830i) q^{26} +(2.98229 + 4.25511i) q^{27} +(14.1258 + 5.46336i) q^{28} +(2.38941 + 3.71800i) q^{29} +(-10.6194 + 3.27299i) q^{30} +(2.75156 - 2.38424i) q^{31} +(-27.1571 + 3.90460i) q^{32} +(-4.65707 - 2.90567i) q^{33} +(-2.80604 - 9.55650i) q^{34} +(0.362296 + 6.09669i) q^{35} +(-10.8951 + 13.2749i) q^{36} +(-0.721075 - 5.01519i) q^{37} +(9.00042 + 10.3870i) q^{38} +(2.53612 - 0.781654i) q^{39} +(-12.9187 - 20.1019i) q^{40} +(1.21612 - 8.45831i) q^{41} +(7.64611 + 10.1858i) q^{42} +(4.85917 - 5.60778i) q^{43} +(5.11117 - 17.4071i) q^{44} +(-6.69447 - 1.77268i) q^{45} +(-5.10649 + 12.3121i) q^{46} +4.42066 q^{47} +(-27.4534 - 12.0966i) q^{48} +(6.43562 - 2.75369i) q^{49} +(0.493905 - 0.768530i) q^{50} +(1.66893 - 5.97844i) q^{51} +(4.74197 + 7.37865i) q^{52} +(-4.10318 + 1.87386i) q^{53} +(-13.6823 + 4.62110i) q^{54} +(7.24128 - 1.04114i) q^{55} +(-16.6754 + 21.7254i) q^{56} +(1.33221 + 8.46101i) q^{57} +(-11.7858 + 3.46062i) q^{58} +(1.03142 - 2.25850i) q^{59} +(-0.306031 - 22.8859i) q^{60} +(1.37348 - 1.19012i) q^{61} +(4.20357 + 9.20453i) q^{62} +(0.682534 + 7.90785i) q^{63} +(5.92207 - 41.1889i) q^{64} +(-1.91220 + 2.97545i) q^{65} +(11.3952 - 10.1439i) q^{66} +(7.56177 + 2.22034i) q^{67} +20.5144 q^{68} +(-6.76151 + 4.82514i) q^{69} +(-16.5418 - 3.80768i) q^{70} +(0.378819 - 1.29014i) q^{71} +(-17.4817 - 25.6662i) q^{72} +(-3.09191 + 4.81110i) q^{73} +(13.9387 + 2.00408i) q^{74} +(0.514668 - 0.243410i) q^{75} +(-25.7502 + 11.7597i) q^{76} +(-3.92952 - 7.40710i) q^{77} +(0.0986206 + 7.37515i) q^{78} +(2.76204 - 6.04803i) q^{79} +(38.3634 - 11.2645i) q^{80} +(-8.75864 - 2.07032i) q^{81} +(21.6036 + 9.86605i) q^{82} +(1.61666 + 11.2441i) q^{83} +(-24.5667 + 9.20003i) q^{84} +(3.43649 + 7.52487i) q^{85} +(11.1495 + 17.3490i) q^{86} +(-7.37306 - 2.05825i) q^{87} +(27.5978 + 17.7360i) q^{88} +(-2.22215 + 2.56450i) q^{89} +(9.96912 - 16.4642i) q^{90} +(3.95050 + 0.909347i) q^{91} +(-21.3686 - 17.2362i) q^{92} +(-0.813914 + 6.25337i) q^{93} +(-3.46145 + 11.7886i) q^{94} +(-8.62716 - 7.47548i) q^{95} +(30.6368 - 36.3270i) q^{96} +(3.57783 + 0.514414i) q^{97} +(2.30410 + 19.3181i) q^{98} +(9.37124 - 1.60422i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 600 q + 20 q^{4} - 18 q^{7} - 26 q^{9} - 14 q^{15} - 116 q^{16} - 46 q^{18} - 50 q^{21} - 104 q^{22} - 88 q^{25} - 26 q^{28} + 26 q^{30} - 26 q^{36} - 56 q^{37} - 14 q^{39} + 5 q^{42} - 40 q^{43} - 44 q^{46}+ \cdots - 250 q^{99}+O(q^{100}) $ 600 * q + 20 * q^4 - 18 * q^7 - 26 * q^9 - 14 * q^15 - 116 * q^16 - 46 * q^18 - 50 * q^21 - 104 * q^22 - 88 * q^25 - 26 * q^28 + 26 * q^30 - 26 * q^36 - 56 * q^37 - 14 * q^39 + 5 * q^42 - 40 * q^43 - 44 * q^46 + 74 * q^49 + 14 * q^51 - 66 * q^57 - 76 * q^58 + 22 * q^60 - 44 * q^63 + 44 * q^64 - 92 * q^67 - 92 * q^70 + 178 * q^72 - 182 * q^78 + 68 * q^79 + 106 * q^81 - 87 * q^84 - 4 * q^85 - 220 * q^88 - 24 * q^91 - 44 * q^93 - 250 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	−0.783018	+	2.66671i	−0.553677	+	1.88565i	−0.0987737	+	0.995110i	$0.531492\pi$
$2$	−0.783018	+	2.66671i	−0.553677	+	1.88565i	−0.454903	+	0.890541i	$0.650326\pi$
$3$	−1.29371	+	1.15165i	−0.746926	+	0.664907i
$3$	−1.29371	+	1.15165i	−0.746926	+	0.664907i
$4$	−4.81573	−	3.09488i	−2.40787	−	1.54744i
$5$	0.328519	−	2.28490i	0.146918	−	1.02184i	−0.774307	−	0.632810i	$-0.781901\pi$
$5$	0.328519	−	2.28490i	0.146918	−	1.02184i	0.921225	−	0.389029i	$-0.127189\pi$
$6$	−2.05813	−	4.35173i	−0.840227	−	1.77659i
$7$	−2.59187	+	0.531216i	−0.979636	+	0.200781i
$7$	−2.59187	+	0.531216i	−0.979636	+	0.200781i
$8$	7.82307	−	6.77873i	2.76587	−	2.39664i
$9$	0.347391	−	2.97982i	0.115797	−	0.993273i
$10$	5.83594	+	2.66518i	1.84549	+	0.842805i
$11$	0.892863	+	3.04081i	0.269208	+	0.916840i	0.977503	+	0.210922i	$0.0676467\pi$
$11$	0.892863	+	3.04081i	0.269208	+	0.916840i	−0.708294	+	0.705917i	$0.750535\pi$
$12$	9.79441	−	1.54216i	2.82740	−	0.445183i
$13$	−1.39374	−	0.636498i	−0.386553	−	0.176533i	0.212653	−	0.977128i	$-0.431790\pi$
$13$	−1.39374	−	0.636498i	−0.386553	−	0.176533i	−0.599206	+	0.800595i	$0.704517\pi$
$14$	0.612882	−	7.32773i	0.163800	−	1.95842i
$15$	2.20640	+	3.33435i	0.569691	+	0.860925i
$16$	7.19526	+	15.7554i	1.79882	+	3.93886i
$17$	−3.01474	+	1.93745i	−0.731181	+	0.469902i	−0.852510	−	0.522711i	$-0.824921\pi$
$17$	−3.01474	+	1.93745i	−0.731181	+	0.469902i	0.121329	+	0.992612i	$0.461284\pi$
$18$	7.67431	+	3.25964i	1.80885	+	0.768305i
$19$	2.67355	−	4.16012i	0.613354	−	0.954398i	−0.386135	−	0.922442i	$-0.626190\pi$
$19$	2.67355	−	4.16012i	0.613354	−	0.954398i	0.999489	−	0.0319557i	$-0.0101736\pi$
$20$	−8.65357	+	9.98675i	−1.93500	+	2.23310i
$21$	2.74137	−	3.67218i	0.598215	−	0.801336i
$22$	−8.80810			−1.87789
$23$	4.76812	+	0.514855i	0.994221	+	0.107355i
$23$	4.76812	+	0.514855i	0.994221	+	0.107355i
$24$	−2.31407	+	17.7792i	−0.472358	+	3.62916i
$25$	−0.315385	−	0.0926055i	−0.0630771	−	0.0185211i
$26$	2.78868	−	3.21830i	0.546904	−	0.631161i
$27$	2.98229	+	4.25511i	0.573943	+	0.818896i
$28$	14.1258	+	5.46336i	2.66953	+	1.03248i
$29$	2.38941	+	3.71800i	0.443703	+	0.690415i	0.989015	−	0.147818i	$-0.0472251\pi$
$29$	2.38941	+	3.71800i	0.443703	+	0.690415i	−0.545312	+	0.838233i	$0.683589\pi$
$30$	−10.6194	+	3.27299i	−1.93883	+	0.597564i
$31$	2.75156	−	2.38424i	0.494195	−	0.428222i	−0.371772	−	0.928324i	$-0.621250\pi$
$31$	2.75156	−	2.38424i	0.494195	−	0.428222i	0.865967	+	0.500102i	$0.166704\pi$
$32$	−27.1571	+	3.90460i	−4.80074	+	0.690243i
$33$	−4.65707	−	2.90567i	−0.810692	−	0.505813i
$34$	−2.80604	−	9.55650i	−0.481232	−	1.63893i
$35$	0.362296	+	6.09669i	0.0612391	+	1.03053i
$36$	−10.8951	+	13.2749i	−1.81586	+	2.21248i
$37$	−0.721075	−	5.01519i	−0.118544	−	0.824492i	−0.959161	−	0.282861i	$-0.908716\pi$
$37$	−0.721075	−	5.01519i	−0.118544	−	0.824492i	0.840617	−	0.541630i	$-0.182193\pi$
$38$	9.00042	+	10.3870i	1.46006	+	1.68500i
$39$	2.53612	−	0.781654i	0.406104	−	0.125165i
$40$	−12.9187	−	20.1019i	−2.04263	−	3.17839i
$41$	1.21612	−	8.45831i	0.189926	−	1.32097i	−0.642267	−	0.766481i	$-0.722006\pi$
$41$	1.21612	−	8.45831i	0.189926	−	1.32097i	0.832193	−	0.554485i	$-0.187085\pi$
$42$	7.64611	+	10.1858i	1.17982	+	1.57171i
$43$	4.85917	−	5.60778i	0.741017	−	0.855179i	−0.252649	−	0.967558i	$-0.581302\pi$
$43$	4.85917	−	5.60778i	0.741017	−	0.855179i	0.993665	+	0.112379i	$0.0358472\pi$
$44$	5.11117	−	17.4071i	0.770538	−	2.62421i
$45$	−6.69447	−	1.77268i	−0.997952	−	0.264256i
$46$	−5.10649	+	12.3121i	−0.752911	+	1.81531i
$47$	4.42066			0.644820			0.322410	−	0.946600i	$-0.395507\pi$
$47$	4.42066			0.644820			0.322410	+	0.946600i	$0.395507\pi$
$48$	−27.4534	−	12.0966i	−3.96256	−	1.74599i
$49$	6.43562	−	2.75369i	0.919374	−	0.393384i
$50$	0.493905	−	0.768530i	0.0698487	−	0.108687i
$51$	1.66893	−	5.97844i	0.233697	−	0.837149i
$52$	4.74197	+	7.37865i	0.657593	+	1.02324i
$53$	−4.10318	+	1.87386i	−0.563615	+	0.257394i	−0.676784	−	0.736181i	$-0.736627\pi$
$53$	−4.10318	+	1.87386i	−0.563615	+	0.257394i	0.113169	+	0.993576i	$0.463900\pi$
$54$	−13.6823	+	4.62110i	−1.86193	+	0.628852i
$55$	7.24128	−	1.04114i	0.976414	−	0.140387i
$56$	−16.6754	+	21.7254i	−2.22835	+	2.90317i
$57$	1.33221	+	8.46101i	0.176456	+	1.12069i
$58$	−11.7858	+	3.46062i	−1.54755	+	0.454402i
$59$	1.03142	−	2.25850i	0.134280	−	0.294032i	−0.830533	−	0.556970i	$-0.811964\pi$
$59$	1.03142	−	2.25850i	0.134280	−	0.294032i	0.964813	+	0.262937i	$0.0846912\pi$
$60$	−0.306031	−	22.8859i	−0.0395084	−	2.95456i
$61$	1.37348	−	1.19012i	0.175856	−	0.152380i	−0.562486	−	0.826807i	$-0.690155\pi$
$61$	1.37348	−	1.19012i	0.175856	−	0.152380i	0.738341	+	0.674427i	$0.235609\pi$
$62$	4.20357	+	9.20453i	0.533853	+	1.16898i
$63$	0.682534	+	7.90785i	0.0859913	+	0.996296i
$64$	5.92207	−	41.1889i	0.740258	−	5.14861i
$65$	−1.91220	+	2.97545i	−0.237180	+	0.369059i
$66$	11.3952	−	10.1439i	1.40265	−	1.24862i
$67$	7.56177	+	2.22034i	0.923817	+	0.271257i	0.708846	−	0.705363i	$-0.249216\pi$
$67$	7.56177	+	2.22034i	0.923817	+	0.271257i	0.214971	+	0.976620i	$0.431034\pi$
$68$	20.5144			2.48773
$69$	−6.76151	+	4.82514i	−0.813990	+	0.580879i
$70$	−16.5418	−	3.80768i	−1.97712	−	0.455105i
$71$	0.378819	−	1.29014i	0.0449575	−	0.153111i	−0.933955	−	0.357390i	$-0.883667\pi$
$71$	0.378819	−	1.29014i	0.0449575	−	0.153111i	0.978913	+	0.204279i	$0.0654849\pi$
$72$	−17.4817	−	25.6662i	−2.06024	−	3.02479i
$73$	−3.09191	+	4.81110i	−0.361880	+	0.563097i	−0.973681	−	0.227915i	$-0.926809\pi$
$73$	−3.09191	+	4.81110i	−0.361880	+	0.563097i	0.611801	+	0.791012i	$0.290445\pi$
$74$	13.9387	+	2.00408i	1.62034	+	0.232970i
$75$	0.514668	−	0.243410i	0.0594287	−	0.0281065i
$76$	−25.7502	+	11.7597i	−2.95375	+	1.34893i
$77$	−3.92952	−	7.40710i	−0.447810	−	0.844117i
$78$	0.0986206	+	7.37515i	0.0111666	+	0.835071i
$79$	2.76204	−	6.04803i	0.310754	−	0.680457i	−0.688231	−	0.725491i	$-0.741613\pi$
$79$	2.76204	−	6.04803i	0.310754	−	0.680457i	0.998985	+	0.0450348i	$0.0143399\pi$
$80$	38.3634	−	11.2645i	4.28916	−	1.25941i
$81$	−8.75864	−	2.07032i	−0.973182	−	0.230036i
$82$	21.6036	+	9.86605i	2.38572	+	1.08952i
$83$	1.61666	+	11.2441i	0.177451	+	1.23420i	0.862634	+	0.505829i	$0.168813\pi$
$83$	1.61666	+	11.2441i	0.177451	+	1.23420i	−0.685183	+	0.728371i	$0.740278\pi$
$84$	−24.5667	+	9.20003i	−2.68044	+	1.00381i
$85$	3.43649	+	7.52487i	0.372740	+	0.816186i
$86$	11.1495	+	17.3490i	1.20228	+	1.87079i
$87$	−7.37306	−	2.05825i	−0.790475	−	0.220668i
$88$	27.5978	+	17.7360i	2.94193	+	1.89067i
$89$	−2.22215	+	2.56450i	−0.235548	+	0.271837i	−0.861201	−	0.508265i	$-0.830287\pi$
$89$	−2.22215	+	2.56450i	−0.235548	+	0.271837i	0.625653	+	0.780101i	$0.284833\pi$
$90$	9.96912	−	16.4642i	1.05084	−	1.73548i
$91$	3.95050	+	0.909347i	0.414125	+	0.0953255i
$92$	−21.3686	−	17.2362i	−2.22783	−	1.79699i
$93$	−0.813914	+	6.25337i	−0.0843989	+	0.648444i
$94$	−3.46145	+	11.7886i	−0.357022	+	1.21590i
$95$	−8.62716	−	7.47548i	−0.885128	−	0.766968i
$96$	30.6368	−	36.3270i	3.12685	−	3.70761i
$97$	3.57783	+	0.514414i	0.363274	+	0.0522309i	0.321535	−	0.946898i	$-0.395801\pi$
$97$	3.57783	+	0.514414i	0.363274	+	0.0522309i	0.0417386	+	0.999129i	$0.486710\pi$
$98$	2.30410	+	19.3181i	0.232749	+	1.95143i
$99$	9.37124	−	1.60422i	0.941845	−	0.161230i
$100$	1.23221	+	1.42204i	0.123221	+	0.142204i
$101$	−2.73862	−	19.0475i	−0.272503	−	1.89530i	−0.422098	−	0.906550i	$-0.638706\pi$
$101$	−2.73862	−	19.0475i	−0.272503	−	1.89530i	0.149595	−	0.988747i	$-0.452203\pi$
$102$	14.6360	+	9.13179i	1.44918	+	0.904182i
$103$	3.95664	+	13.4751i	0.389859	+	1.32774i	0.887681	+	0.460460i	$0.152315\pi$
$103$	3.95664	+	13.4751i	0.389859	+	1.32774i	−0.497821	+	0.867280i	$0.665866\pi$
$104$	−15.2179	+	4.46839i	−1.49224	+	0.438162i
$105$	−7.48998	−	7.47013i	−0.730947	−	0.729010i
$106$	−1.78418	−	12.4093i	−0.173295	−	1.20529i
$107$	2.88623	−	2.50094i	0.279023	−	0.241775i	−0.504095	−	0.863648i	$-0.668174\pi$
$107$	2.88623	−	2.50094i	0.279023	−	0.241775i	0.783118	+	0.621874i	$0.213628\pi$
$108$	−1.19287	−	29.7213i	−0.114784	−	2.85993i
$109$	−3.93751	+	2.53048i	−0.377145	+	0.242376i	−0.715456	−	0.698658i	$-0.753781\pi$
$109$	−3.93751	+	2.53048i	−0.377145	+	0.242376i	0.338311	+	0.941034i	$0.390145\pi$
$110$	−2.89363	+	20.1256i	−0.275897	+	1.91891i
$111$	6.70862	+	5.65779i	0.636754	+	0.537014i
$112$	−27.0187	−	37.0138i	−2.55303	−	3.49748i
$113$	1.96105	−	6.67872i	0.184480	−	0.628281i	−0.814370	−	0.580345i	$-0.802918\pi$
$113$	1.96105	−	6.67872i	0.184480	−	0.628281i	0.998850	−	0.0479356i	$-0.0152642\pi$
$114$	−23.6062	−	3.07249i	−2.21093	−	0.287765i
$115$	2.74281	−	10.7255i	0.255768	−	1.00016i
$116$		−	25.2998i		−	2.34903i
$117$	−2.38082	+	3.93197i	−0.220107	+	0.363510i
$118$	5.21516	+	4.51896i	0.480094	+	0.416004i
$119$	6.78461	−	6.62311i	0.621944	−	0.607140i
$120$	39.8635	+	11.1282i	3.63902	+	1.01586i
$121$	0.804451	−	0.516989i	0.0731319	−	0.0469990i
$122$	2.09826	+	4.59456i	0.189968	+	0.415972i
$123$	8.16773	+	12.3432i	0.736459	+	1.11295i
$124$	−20.6297	+	2.96611i	−1.85261	+	0.266364i
$125$	4.47951	−	9.80876i	0.400660	−	0.877322i
$126$	−21.6224	−	4.37186i	−1.92628	−	0.389477i
$127$	4.17205	−	1.22502i	0.370209	−	0.108703i	−0.0913354	−	0.995820i	$-0.529114\pi$
$127$	4.17205	−	1.22502i	0.370209	−	0.108703i	0.461545	+	0.887117i	$0.347295\pi$
$128$	55.2878	+	25.2491i	4.88680	+	2.23173i
$129$	0.171843	+	12.8509i	0.0151299	+	1.13146i
$130$	−6.43737	−	7.42912i	−0.564595	−	0.651577i
$131$	6.35002	+	13.9046i	0.554804	+	1.21485i	0.954502	+	0.298205i	$0.0963878\pi$
$131$	6.35002	+	13.9046i	0.554804	+	1.21485i	−0.399698	+	0.916647i	$0.630885\pi$
$132$	13.4345	+	28.4060i	1.16932	+	2.47243i
$133$	−4.71958	+	12.2028i	−0.409239	+	1.05811i
$134$	−11.8420	+	18.4265i	−1.02299	+	1.59181i
$135$	10.7022	−	5.41636i	0.921102	−	0.466166i
$136$	−10.4510	+	35.5929i	−0.896168	+	3.05207i
$137$			9.04558i			0.772816i	0.922328	+	0.386408i	$0.126284\pi$
$137$			9.04558i			0.772816i	−0.922328	+	0.386408i	$0.873716\pi$
$138$	−7.57288	−	21.8092i	−0.644646	−	1.85652i
$139$		−	18.0942i		−	1.53473i	−0.641210	−	0.767366i	$-0.721567\pi$
$139$		−	18.0942i		−	1.53473i	0.641210	−	0.767366i	$-0.278433\pi$
$140$	17.1238	−	30.4813i	1.44723	−	2.57614i
$141$	−5.71907	+	5.09107i	−0.481632	+	0.428745i
$142$	3.14381	+	2.02040i	0.263823	+	0.169548i
$143$	0.691055	−	4.80639i	0.0577889	−	0.401931i
$144$	49.4479	−	15.9673i	4.12066	−	1.33061i
$145$	9.28023	−	4.23814i	0.770681	−	0.351958i
$146$	−10.4088	−	12.0124i	−0.861439	−	0.994154i
$147$	−5.15455	+	10.9741i	−0.425141	+	0.905127i
$148$	−12.0489	+	26.3835i	−0.990415	+	2.16871i
$149$	−2.86638	−	9.76198i	−0.234823	−	0.799733i	−0.989612	−	0.143765i	$-0.954079\pi$
$149$	−2.86638	−	9.76198i	−0.234823	−	0.799733i	0.754789	−	0.655968i	$-0.227739\pi$
$150$	0.246109	+	1.56307i	0.0200947	+	0.127624i
$151$	4.54534	−	9.95292i	0.369895	−	0.809957i	−0.629560	−	0.776952i	$-0.716765\pi$
$151$	4.54534	−	9.95292i	0.369895	−	0.809957i	0.999455	−	0.0330052i	$-0.0105078\pi$
$152$	−7.28499	−	50.6682i	−0.590891	−	4.10974i
$153$	4.72597	+	9.65642i	0.382072	+	0.780675i
$154$	22.8295	−	4.67900i	1.83965	−	0.377045i
$155$	−4.54382	−	7.07032i	−0.364968	−	0.567901i
$156$	−14.6324	−	4.08476i	−1.17153	−	0.327042i
$157$	6.91128	−	10.7542i	0.551580	−	0.858276i	−0.447776	−	0.894146i	$-0.647784\pi$
$157$	6.91128	−	10.7542i	0.551580	−	0.858276i	0.999356	+	0.0358699i	$0.0114202\pi$
$158$	13.9656	+	12.1013i	1.11105	+	0.962727i
$159$	3.15030	−	7.14968i	0.249835	−	0.567006i
$160$			63.3341i			5.00700i
$161$	−12.6319	+	1.19846i	−0.995529	+	0.0944519i
$162$	12.3791	−	21.7357i	0.972596	−	1.70772i
$163$	−13.0760	−	3.83947i	−1.02419	−	0.300730i	−0.273845	−	0.961774i	$-0.588296\pi$
$163$	−13.0760	−	3.83947i	−1.02419	−	0.300730i	−0.750348	+	0.661044i	$0.770114\pi$
$164$	−32.0340	+	36.9692i	−2.50144	+	2.88681i
$165$	−8.16911	+	9.68638i	−0.635965	+	0.754084i
$166$	−31.2507	−	4.49317i	−2.42552	−	0.348737i
$167$	3.68461	−	2.36796i	0.285124	−	0.183238i	−0.390259	−	0.920705i	$-0.627615\pi$
$167$	3.68461	−	2.36796i	0.285124	−	0.183238i	0.675383	+	0.737467i	$0.263978\pi$
$168$	−3.44682	−	47.3107i	−0.265928	−	3.65010i
$169$	−6.97582	−	8.05053i	−0.536602	−	0.619271i
$170$	−22.7575	+	3.27203i	−1.74542	+	0.250954i
$171$	−11.4677	−	9.41188i	−0.876953	−	0.719745i
$172$	−40.7559	+	11.9670i	−3.10761	+	0.912476i
$173$	14.6905	−	4.31351i	1.11689	−	0.327950i	0.329350	−	0.944208i	$-0.393170\pi$
$173$	14.6905	−	4.31351i	1.11689	−	0.327950i	0.787544	+	0.616258i	$0.211352\pi$
$174$	11.2620	−	18.0502i	0.853770	−	1.36838i
$175$	0.866633	+	0.0724840i	0.0655113	+	0.00547928i
$176$	−41.4849	+	35.9469i	−3.12704	+	2.70960i
$177$	1.26665	+	4.10970i	0.0952069	+	0.308904i
$178$	−5.09880	−	7.93389i	−0.382171	−	0.594670i
$179$	−20.2388	−	2.90991i	−1.51272	−	0.217497i	−0.664560	−	0.747235i	$-0.731381\pi$
$179$	−20.2388	−	2.90991i	−1.51272	−	0.217497i	−0.848161	+	0.529738i	$0.822290\pi$
$180$	26.7525	+	29.2554i	1.99402	+	2.18057i
$181$	11.4427	+	9.91518i	0.850532	+	0.736990i	0.966610	−	0.256250i	$-0.0824871\pi$
$181$	11.4427	+	9.91518i	0.850532	+	0.736990i	−0.116079	+	0.993240i	$0.537033\pi$
$182$	−5.51828	+	9.82283i	−0.409042	+	0.728116i
$183$	−0.406276	+	3.12145i	−0.0300328	+	0.230744i
$184$	40.7914	−	28.2940i	3.00718	−	2.08586i
$185$	−11.6961			−0.859914
$186$	−16.0386	−	7.06697i	−1.17601	−	0.518176i
$187$	−8.58318	−	7.43737i	−0.627664	−	0.543874i
$188$	−21.2887	−	13.6814i	−1.55264	−	0.997821i
$189$	−9.99011	−	9.44446i	−0.726673	−	0.686983i
$190$	26.6902	−	17.1527i	1.93631	−	1.24439i
$191$	−8.52589	+	3.89364i	−0.616912	+	0.281734i	−0.699258	−	0.714870i	$-0.746486\pi$
$191$	−8.52589	+	3.89364i	−0.616912	+	0.281734i	0.0823459	+	0.996604i	$0.473759\pi$
$192$	39.7738	+	60.1068i	2.87043	+	4.33783i
$193$	−1.60123	−	11.1368i	−0.115259	−	0.801644i	−0.962664	−	0.270697i	$-0.912746\pi$
$193$	−1.60123	−	11.1368i	−0.115259	−	0.801644i	0.847405	−	0.530946i	$-0.178163\pi$
$194$	−4.17330	+	9.13825i	−0.299625	+	0.656088i
$195$	−0.952838	−	6.05157i	−0.0682342	−	0.433362i
$196$	−39.5146	−	6.65646i	−2.82247	−	0.475462i
$197$	1.71862	+	0.784867i	0.122447	+	0.0559195i	0.475696	−	0.879610i	$-0.342196\pi$
$197$	1.71862	+	0.784867i	0.122447	+	0.0559195i	−0.353250	+	0.935529i	$0.614923\pi$
$198$	−3.05985	+	26.2465i	−0.217454	+	1.86526i
$199$	5.23158	−	4.53319i	0.370857	−	0.321349i	−0.449415	−	0.893323i	$-0.648368\pi$
$199$	5.23158	−	4.53319i	0.370857	−	0.321349i	0.820272	+	0.571974i	$0.193822\pi$
$200$	−3.09503	+	1.41345i	−0.218852	+	0.0999462i
$201$	−12.3398	+	5.83606i	−0.870384	+	0.411644i
$202$	52.9386	+	7.61142i	3.72475	+	0.535538i
$203$	−8.16812	−	8.36729i	−0.573289	−	0.587269i
$204$	−26.5397	+	23.6254i	−1.85815	+	1.65411i
$205$	−18.9269	−	5.55744i	−1.32191	−	0.388148i
$206$	−39.0323			−2.71951
$207$	3.19057	−	14.0293i	0.221760	−	0.975101i
$208$		−	26.5387i		−	1.84012i
$209$	15.0373	+	4.41534i	1.04015	+	0.305416i
$210$	25.7855	−	14.1244i	1.77937	−	0.974675i
$211$	7.37181	+	4.73757i	0.507496	+	0.326148i	0.769208	−	0.638998i	$-0.220651\pi$
$211$	7.37181	+	4.73757i	0.507496	+	0.326148i	−0.261712	+	0.965146i	$0.584287\pi$
$212$	25.5592	+	3.67486i	1.75541	+	0.252390i
$213$	0.995709	+	2.10534i	0.0682249	+	0.144255i
$214$	4.40931	+	9.65504i	0.301414	+	0.660005i
$215$	−11.2169	−	12.9450i	−0.764986	−	0.882841i
$216$	52.1749	+	13.0718i	3.55005	+	0.889426i
$217$	−5.86515	+	7.64133i	−0.398152	+	0.518727i
$218$	−3.66494	−	12.4816i	−0.248221	−	0.845362i
$219$	−1.54068	−	9.78499i	−0.104109	−	0.661209i
$220$	−38.0943	−	17.3971i	−2.56832	−	1.17291i
$221$	5.43493	−	0.781425i	0.365593	−	0.0525643i
$222$	−20.3407	+	13.4598i	−1.36518	+	0.903364i
$223$	−14.1060	+	6.44199i	−0.944606	+	0.431387i	−0.827333	−	0.561712i	$-0.810143\pi$
$223$	−14.1060	+	6.44199i	−0.944606	+	0.431387i	−0.117274	+	0.993100i	$0.537415\pi$
$224$	68.3136	−	24.5465i	4.56440	−	1.64008i
$225$	−0.385510	+	0.907621i	−0.0257006	+	0.0605081i
$226$	16.2747	+	10.4591i	1.08258	+	0.695729i
$227$	−15.1973	+	17.5386i	−1.00868	+	1.16408i	−0.0222720	+	0.999752i	$0.507090\pi$
$227$	−15.1973	+	17.5386i	−1.00868	+	1.16408i	−0.986406	+	0.164325i	$0.947455\pi$
$228$	19.7703	−	44.8690i	1.30932	−	2.97152i
$229$			0.117428i			0.00775989i	0.999992	+	0.00387994i	$0.00123503\pi$
$229$			0.117428i			0.00775989i	−0.999992	+	0.00387994i	$0.998765\pi$
$230$	26.4543	+	15.7126i	1.74434	+	1.03606i
$231$	13.6141	+	5.05723i	0.895741	+	0.332741i
$232$	43.8959	+	12.8890i	2.88190	+	0.846203i
$233$	−11.9492	−	10.3540i	−0.782818	−	0.678316i	0.168782	−	0.985653i	$-0.446016\pi$
$233$	−11.9492	−	10.3540i	−0.782818	−	0.678316i	−0.951601	+	0.307338i	$0.900562\pi$
$234$	−8.62120	−	9.42776i	−0.563586	−	0.616312i
$235$	1.45227	−	10.1008i	0.0947358	−	0.658902i
$236$	−11.9569	+	7.68422i	−0.778326	+	0.500200i
$237$	3.39194	+	11.0053i	0.220330	+	0.714873i
$238$	12.3495	+	23.2786i	0.800497	+	1.50893i
$239$	3.73639	−	0.537212i	0.241687	−	0.0347494i	−0.0204066	−	0.999792i	$-0.506496\pi$
$239$	3.73639	−	0.537212i	0.241687	−	0.0347494i	0.262094	+	0.965042i	$0.415587\pi$
$240$	−36.6584	+	58.7543i	−2.36629	+	3.79258i
$241$	2.60896	+	8.88532i	0.168058	+	0.572354i	0.999851	+	0.0172672i	$0.00549661\pi$
$241$	2.60896	+	8.88532i	0.168058	+	0.572354i	−0.831793	+	0.555086i	$0.812685\pi$
$242$	0.748763	+	2.55005i	0.0481323	+	0.163924i
$243$	13.7155	−	7.40851i	0.879848	−	0.475256i
$244$	−10.2976	+	1.48057i	−0.659236	+	0.0947839i
$245$	−4.17768	−	15.6094i	−0.266902	−	0.997248i
$246$	−39.3112	+	12.1161i	−2.50639	+	0.772491i
$247$	−6.37413	+	4.09641i	−0.405576	+	0.260648i
$248$	5.36353	−	37.3042i	0.340585	−	2.36882i
$249$	−15.0408	−	12.6848i	−0.953171	−	0.803868i
$250$	22.6496	+	19.6260i	1.43249	+	1.24126i
$251$	24.4319	+	7.17387i	1.54213	+	0.452810i	0.938737	−	0.344633i	$-0.111997\pi$
$251$	24.4319	+	7.17387i	1.54213	+	0.452810i	0.603393	+	0.797444i	$0.293815\pi$
$252$	21.1870	−	40.1945i	1.33465	−	2.53201i
$253$	2.69170	+	14.9586i	0.169226	+	0.940442i
$254$			12.0849i			0.758272i
$255$	−13.1119	−	5.77738i	−0.821097	−	0.361793i
$256$	−56.1228	+	64.7691i	−3.50767	+	4.04807i
$257$	11.4724	+	7.37285i	0.715628	+	0.459906i	0.847113	−	0.531412i	$-0.178338\pi$
$257$	11.4724	+	7.37285i	0.715628	+	0.459906i	−0.131486	+	0.991318i	$0.541975\pi$
$258$	−34.4043	−	9.60426i	−2.14192	−	0.597935i
$259$	4.53308	+	12.6157i	0.281672	+	0.783901i
$260$	18.4173	−	8.41091i	1.14219	−	0.521623i
$261$	11.9090	−	5.82842i	0.737150	−	0.360770i
$262$	−42.0518	+	6.04613i	−2.59797	+	0.373531i
$263$	−15.0755	−	6.88475i	−0.929595	−	0.424532i	−0.107708	−	0.994183i	$-0.534351\pi$
$263$	−15.0755	−	6.88475i	−0.929595	−	0.424532i	−0.821887	+	0.569651i	$0.807079\pi$
$264$	−56.1294	+	8.83774i	−3.45452	+	0.543925i
$265$	2.93361	+	9.99096i	0.180210	+	0.613740i
$266$	−28.8457	−	22.1407i	−1.76864	−	1.35754i
$267$	−0.0785857	−	5.87688i	−0.00480937	−	0.359659i
$268$	−29.5438	−	34.0953i	−1.80467	−	2.08270i
$269$	3.48906	+	7.63997i	0.212732	+	0.465817i	0.985675	−	0.168658i	$-0.0539434\pi$
$269$	3.48906	+	7.63997i	0.212732	+	0.465817i	−0.772943	+	0.634475i	$0.781216\pi$
$270$	6.06384	+	32.7809i	0.369034	+	1.99498i
$271$	0.597126	+	0.0858538i	0.0362728	+	0.00521525i	0.160427	−	0.987048i	$-0.448713\pi$
$271$	0.597126	+	0.0858538i	0.0362728	+	0.00521525i	−0.124155	+	0.992263i	$0.539622\pi$
$272$	−52.2172	−	33.5580i	−3.16613	−	2.03475i
$273$	−6.15807	+	3.37318i	−0.372704	+	0.204154i
$274$	−24.1220	−	7.08285i	−1.45726	−	0.427890i
$275$		−	1.04171i		−	0.0628176i
$276$	47.4949	−	2.31050i	2.85886	−	0.139075i
$277$	19.0295			1.14337			0.571686	−	0.820472i	$-0.306289\pi$
$277$	19.0295			1.14337			0.571686	+	0.820472i	$0.306289\pi$
$278$	48.2521	+	14.1681i	2.89397	+	0.849746i
$279$	−6.14874	−	9.02742i	−0.368115	−	0.540457i
$280$	44.1621	+	45.2389i	2.63919	+	2.70354i
$281$	−12.3339	−	1.77334i	−0.735776	−	0.105789i	−0.235768	−	0.971809i	$-0.575761\pi$
$281$	−12.3339	−	1.77334i	−0.735776	−	0.105789i	−0.500008	+	0.866021i	$0.666670\pi$
$282$	−9.09828	−	19.2375i	−0.541795	−	1.14558i
$283$	9.94351	−	4.54105i	0.591080	−	0.269937i	−0.0973378	−	0.995251i	$-0.531033\pi$
$283$	9.94351	−	4.54105i	0.591080	−	0.269937i	0.688418	+	0.725314i	$0.258305\pi$
$284$	−5.81712	+	5.04056i	−0.345183	+	0.299102i
$285$	19.7702	−	0.264368i	1.17109	−	0.0156598i
$286$	12.2762	+	5.60634i	0.725905	+	0.331510i
$287$	1.34116	+	22.5689i	0.0791659	+	1.33220i
$288$	2.20088	+	82.2797i	0.129688	+	4.84838i
$289$	−1.72714	+	3.78192i	−0.101597	+	0.222466i
$290$	4.03532	+	28.0662i	0.236962	+	1.64811i
$291$	−5.22112	+	3.45491i	−0.306067	+	0.202531i
$292$	29.7796	−	13.5999i	1.74272	−	0.795873i
$293$	2.18963	−	1.40719i	0.127919	−	0.0822087i	−0.475116	−	0.879923i	$-0.657594\pi$
$293$	2.18963	−	1.40719i	0.127919	−	0.0822087i	0.603036	+	0.797714i	$0.293958\pi$
$294$	−25.2286	−	22.3386i	−1.47136	−	1.30281i
$295$	−4.82162	−	3.09867i	−0.280725	−	0.180411i
$296$	−39.6376	−	34.3462i	−2.30389	−	1.99633i
$297$	−10.2762	+	12.8678i	−0.596286	+	0.746667i
$298$	28.2768			1.63803
$299$	−6.31779	−	3.75247i	−0.365367	−	0.217011i
$300$	−3.23183	−	0.420642i	−0.186590	−	0.0242858i
$301$	−9.61541	+	17.1159i	−0.554223	+	0.986546i
$302$	22.9825	+	19.9144i	1.32249	+	1.14595i
$303$	25.4791	+	21.4881i	1.46374	+	1.23446i
$304$	84.7814	+	12.1897i	4.86255	+	0.699129i
$305$	−2.26810	−	3.52924i	−0.129871	−	0.202084i
$306$	−29.4514	+	5.04166i	−1.68363	+	0.288212i
$307$	−19.1949	+	16.6325i	−1.09551	+	0.949266i	−0.998939	−	0.0460595i	$-0.985334\pi$
$307$	−19.1949	+	16.6325i	−1.09551	+	0.949266i	−0.0965731	+	0.995326i	$0.530788\pi$
$308$	−4.00061	+	47.8320i	−0.227956	+	2.72548i
$309$	−20.6374	−	12.8762i	−1.17402	−	0.732503i
$310$	22.4124	−	6.58087i	1.27294	−	0.373768i
$311$	−6.19693	+	1.81958i	−0.351396	+	0.103179i	−0.452667	−	0.891680i	$-0.649527\pi$
$311$	−6.19693	+	1.81958i	−0.351396	+	0.103179i	0.101271	+	0.994859i	$0.467709\pi$
$312$	14.5416	−	23.3066i	0.823257	−	1.31948i
$313$	5.84090	−	0.839795i	0.330147	−	0.0474680i	0.0247519	−	0.999694i	$-0.492120\pi$
$313$	5.84090	−	0.839795i	0.330147	−	0.0474680i	0.305395	+	0.952226i	$0.401211\pi$
$314$	23.2666	+	26.8511i	1.31301	+	1.51530i
$315$	18.2929	+	1.03836i	1.03069	+	0.0585048i
$316$	−32.0192	+	20.5775i	−1.80122	+	1.15757i
$317$	27.3502	+	3.93236i	1.53614	+	0.220863i	0.857837	−	0.513921i	$-0.171808\pi$
$317$	27.3502	+	3.93236i	1.53614	+	0.220863i	0.678300	+	0.734785i	$0.262717\pi$
$318$	16.5994	+	13.9993i	0.930848	+	0.785041i
$319$	−9.17232	+	10.5854i	−0.513551	+	0.592670i
$320$	−92.1670	−	27.0627i	−5.15229	−	1.51285i
$321$	−0.853750	+	6.55944i	−0.0476517	+	0.366112i
$322$	6.69501	−	34.6239i	0.373099	−	1.92952i
$323$			17.7216i			0.986054i
$324$	35.7719	+	37.0771i	1.98733	+	2.05984i
$325$	0.380621	+	0.329810i	0.0211130	+	0.0182945i
$326$	20.4775	−	31.8636i	1.13414	−	1.76476i
$327$	2.17977	−	7.80837i	0.120542	−	0.431804i
$328$	−47.8228	−	74.4137i	−2.64057	−	4.10881i
$329$	−11.4578	+	2.34832i	−0.631689	+	0.129467i
$330$	−19.4342	−	29.3693i	−1.06982	−	1.61673i
$331$	4.01654	+	27.9357i	0.220769	+	1.53548i	0.735140	+	0.677915i	$0.237116\pi$
$331$	4.01654	+	27.9357i	0.220769	+	1.53548i	−0.514371	+	0.857568i	$0.671975\pi$
$332$	27.0138	−	59.1519i	1.48257	−	3.24638i
$333$	−15.1948	+	0.406444i	−0.832672	+	0.0222730i
$334$	3.42954	+	11.6799i	0.187656	+	0.639098i
$335$	7.55743	−	16.5485i	0.412907	−	0.904140i
$336$	77.5816	+	16.7691i	4.23242	+	0.914829i
$337$	−19.1127	−	22.0573i	−1.04114	−	1.20154i	−0.979083	−	0.203463i	$-0.934780\pi$
$337$	−19.1127	−	22.0573i	−1.04114	−	1.20154i	−0.0620545	−	0.998073i	$-0.519765\pi$
$338$	26.9306	−	12.2988i	1.46483	−	0.668967i
$339$	5.15453	+	10.8988i	0.279956	+	0.591941i
$340$	6.73936	−	46.8733i	0.365493	−	2.54206i
$341$	9.70680	+	6.23818i	0.525653	+	0.337816i
$342$	34.0782	−	23.2113i	1.84274	−	1.25512i
$343$	−15.2175	+	10.5559i	−0.821668	+	0.569966i
$344$		−	76.8091i		−	4.14127i
$345$	8.80368	+	17.0345i	0.473974	+	0.917109i
$346$			42.5528i			2.28765i
$347$	−0.0622420	+	0.211977i	−0.00334133	+	0.0113795i	−0.961147	−	0.276038i	$-0.910978\pi$
$347$	−0.0622420	+	0.211977i	−0.00334133	+	0.0113795i	0.957805	+	0.287417i	$0.0927967\pi$
$348$	29.1366	+	32.7308i	1.56189	+	1.75455i
$349$	15.3199	−	23.8383i	0.820057	−	1.27603i	−0.138279	−	0.990393i	$-0.544157\pi$
$349$	15.3199	−	23.8383i	0.820057	−	1.27603i	0.958337	−	0.285641i	$-0.0922065\pi$
$350$	−0.871883	+	2.25430i	−0.0466041	+	0.120498i
$351$	−1.44816	−	7.82872i	−0.0772972	−	0.417866i
$352$	−36.1208	−	79.0934i	−1.92524	−	4.21569i
$353$	−3.00117	−	3.46353i	−0.159736	−	0.184345i	0.670240	−	0.742145i	$-0.266191\pi$
$353$	−3.00117	−	3.46353i	−0.159736	−	0.184345i	−0.829976	+	0.557799i	$0.811646\pi$
$354$	−11.9512	+	0.159812i	−0.635199	+	0.00849389i
$355$	−2.82339	−	1.28940i	−0.149850	−	0.0684342i
$356$	18.6381	−	5.47265i	0.987819	−	0.290050i
$357$	−1.14982	+	16.3819i	−0.0608548	+	0.867024i
$358$	23.6072	−	51.6927i	1.24768	−	2.73204i
$359$	1.20320	−	0.172994i	0.0635023	−	0.00913025i	−0.110490	−	0.993877i	$-0.535242\pi$
$359$	1.20320	−	0.172994i	0.0635023	−	0.00913025i	0.173993	+	0.984747i	$0.444333\pi$
$360$	−64.3878	+	31.5122i	−3.39354	+	1.66084i
$361$	−2.26588	−	4.96159i	−0.119257	−	0.261136i
$362$	−35.4008	+	22.7507i	−1.86063	+	1.19575i
$363$	−0.445337	+	1.59529i	−0.0233741	+	0.0837308i
$364$	−16.2103	−	16.6055i	−0.849648	−	0.870366i
$365$	9.97714	+	8.64524i	0.522227	+	0.452513i
$366$	−8.00589	−	3.52757i	−0.418475	−	0.184389i
$367$			0.634511i			0.0331212i	0.999863	+	0.0165606i	$0.00527164\pi$
$367$			0.634511i			0.0331212i	−0.999863	+	0.0165606i	$0.994728\pi$
$368$	26.1961	+	78.8282i	1.36556	+	4.10920i
$369$	−24.7818	−	6.56216i	−1.29009	−	0.341612i
$370$	9.15825	−	31.1901i	0.476115	−	1.62150i
$371$	9.63950	−	7.03648i	0.500458	−	0.365316i
$372$	23.2730	−	27.5956i	1.20665	−	1.43076i
$373$	0.248073	−	1.72538i	0.0128447	−	0.0893370i	−0.982391	−	0.186838i	$-0.940176\pi$
$373$	0.248073	−	1.72538i	0.0128447	−	0.0893370i	0.995235	+	0.0975013i	$0.0310850\pi$
$374$	26.5541	−	17.0653i	1.37308	−	0.882425i
$375$	5.50108	+	17.8486i	0.284075	+	0.921696i
$376$	34.5831	−	29.9665i	1.78349	−	1.54540i
$377$	−0.963712	−	6.70276i	−0.0496337	−	0.345210i
$378$	33.0081	−	19.2456i	1.69775	−	0.989886i
$379$	23.3447	−	6.85463i	1.19914	−	0.352099i	0.379615	−	0.925145i	$-0.376056\pi$
$379$	23.3447	−	6.85463i	1.19914	−	0.352099i	0.819523	+	0.573046i	$0.194238\pi$
$380$	18.4104	+	62.7000i	0.944432	+	3.21644i
$381$	−3.98663	+	6.38958i	−0.204241	+	0.327348i
$382$	−3.70731	−	25.7849i	−0.189682	−	1.31927i
$383$	−15.1513	−	17.4855i	−0.774193	−	0.893466i	0.222483	−	0.974937i	$-0.428584\pi$
$383$	−15.1513	−	17.4855i	−0.774193	−	0.893466i	−0.996676	+	0.0814703i	$0.974038\pi$
$384$	−100.605	+	31.0073i	−5.13397	+	1.58233i
$385$	−18.2154	+	6.54518i	−0.928344	+	0.333573i
$386$	30.9524	+	4.45029i	1.57544	+	0.226514i
$387$	−15.0221	−	16.4275i	−0.763618	−	0.835059i
$388$	−15.6378	−	13.5503i	−0.793890	−	0.687910i
$389$	−5.80741	+	19.7782i	−0.294448	+	1.00280i	0.670839	+	0.741603i	$0.265934\pi$
$389$	−5.80741	+	19.7782i	−0.294448	+	1.00280i	−0.965286	+	0.261193i	$0.915884\pi$
$390$	16.8839	+	2.19754i	0.854949	+	0.111277i
$391$	−15.3721	+	7.68585i	−0.777402	+	0.388690i
$392$	31.6798	−	65.1676i	1.60007	−	3.29146i
$393$	−24.2284	−	10.6756i	−1.22216	−	0.538511i
$394$	−3.43873	+	3.96850i	−0.173241	+	0.199930i
$395$	−12.9118	−	8.29789i	−0.649662	−	0.417512i
$396$	−50.0943	−	21.2774i	−2.51733	−	1.06923i
$397$	−19.4051	−	30.1949i	−0.973915	−	1.51544i	−0.852426	−	0.522848i	$-0.824870\pi$
$397$	−19.4051	−	30.1949i	−0.973915	−	1.51544i	−0.121489	−	0.992593i	$-0.538767\pi$
$398$	7.99230	+	17.5007i	0.400618	+	0.877231i
$399$	−7.94755	−	21.2222i	−0.397875	−	1.06244i
$400$	−0.810241	−	5.63535i	−0.0405121	−	0.281768i
$401$	2.20708	+	1.00794i	0.110216	+	0.0503341i	0.469760	−	0.882794i	$-0.344340\pi$
$401$	2.20708	+	1.00794i	0.110216	+	0.0503341i	−0.359544	+	0.933128i	$0.617068\pi$
$402$	−5.90079	−	37.4765i	−0.294305	−	1.86916i
$403$	−5.35251	+	1.57164i	−0.266628	+	0.0782889i
$404$	−45.7614	+	100.203i	−2.27671	+	4.98531i
$405$	−7.60786	+	19.3325i	−0.378038	+	0.960639i
$406$	28.7089	−	15.2303i	1.42480	−	0.755866i
$407$	14.6064	−	6.67053i	0.724014	−	0.330646i
$408$	−27.4701	−	58.0830i	−1.35997	−	2.87554i
$409$	−1.28308	−	0.184479i	−0.0634441	−	0.00912188i	0.110520	−	0.993874i	$-0.464748\pi$
$409$	−1.28308	−	0.184479i	−0.0634441	−	0.00912188i	−0.173964	+	0.984752i	$0.555658\pi$
$410$	29.6402	−	46.1210i	1.46382	−	2.27775i
$411$	−10.4174	−	11.7024i	−0.513851	−	0.577236i
$412$	22.6497	−	77.1378i	1.11587	−	3.80030i
$413$	−1.47357	+	6.40167i	−0.0725096	+	0.315006i
$414$	34.9137	+	19.4935i	1.71592	+	0.958053i
$415$	26.2228			1.28722
$416$	40.3351	+	11.8435i	1.97759	+	0.580673i
$417$	20.8383	+	23.4087i	1.02045	+	1.14633i
$418$	−23.5489	+	36.6428i	−1.15181	+	1.79226i
$419$	−1.79768	+	12.5031i	−0.0878223	+	0.610818i	0.897615	+	0.440780i	$0.145298\pi$
$419$	−1.79768	+	12.5031i	−0.0878223	+	0.610818i	−0.985438	+	0.170038i	$0.945611\pi$
$420$	12.9505	+	59.1548i	0.631922	+	2.88646i
$421$	7.47689	+	16.3721i	0.364401	+	0.797928i	0.999671	+	0.0256376i	$0.00816158\pi$
$421$	7.47689	+	16.3721i	0.364401	+	0.797928i	−0.635270	+	0.772290i	$0.719111\pi$
$422$	−18.4060	+	15.9489i	−0.895990	+	0.776380i
$423$	1.53570	−	13.1728i	0.0746681	−	0.640482i
$424$	−19.3971	+	42.4737i	−0.942006	+	2.06270i
$425$	1.13022	−	0.331863i	0.0548239	−	0.0160977i
$426$	−6.39399	+	1.00675i	−0.309790	+	0.0487774i
$427$	−2.92767	+	3.81427i	−0.141680	+	0.184585i
$428$	−21.6394	+	3.11128i	−1.04598	+	0.150390i
$429$	4.64127	+	7.01395i	0.224083	+	0.338637i
$430$	43.3036	−	19.7761i	2.08829	−	0.953688i
$431$	6.07000	+	9.44511i	0.292382	+	0.454955i	0.956105	−	0.293023i	$-0.0946613\pi$
$431$	6.07000	+	9.44511i	0.292382	+	0.454955i	−0.663724	+	0.747978i	$0.731025\pi$
$432$	−45.5826	+	77.6039i	−2.19309	+	3.73372i
$433$	−1.71705	+	2.67178i	−0.0825162	+	0.128398i	−0.880058	−	0.474865i	$-0.842497\pi$
$433$	−1.71705	+	2.67178i	−0.0825162	+	0.128398i	0.797542	+	0.603263i	$0.206133\pi$
$434$	−15.7847	−	21.6240i	−0.757690	−	1.03798i
$435$	−7.12509	+	16.1705i	−0.341622	+	0.775318i
$436$	26.7936			1.28318
$437$	14.8897	−	18.4595i	0.712269	−	0.883036i
$438$	27.3001	+	3.55328i	1.30445	+	0.169782i
$439$	9.10173	−	30.9976i	0.434402	−	1.47944i	−0.393899	−	0.919154i	$-0.628874\pi$
$439$	9.10173	−	30.9976i	0.434402	−	1.47944i	0.828301	−	0.560283i	$-0.189308\pi$
$440$	49.5915	−	57.2316i	2.36418	−	2.72841i
$441$	−5.96982	−	20.1336i	−0.284277	−	0.958742i
$442$	−2.17181	+	15.1053i	−0.103302	+	0.718484i
$443$	−1.13678	−	1.76887i	−0.0540102	−	0.0840416i	0.813198	−	0.581987i	$-0.197724\pi$
$443$	−1.13678	−	1.76887i	−0.0540102	−	0.0840416i	−0.867209	+	0.497945i	$0.834088\pi$
$444$	−14.7967	−	48.0088i	−0.702222	−	2.27840i
$445$	5.12961	+	5.91989i	0.243167	+	0.280630i
$446$	−6.13370	−	42.6608i	−0.290439	−	2.02005i
$447$	14.9507	+	9.32814i	0.707143	+	0.441206i
$448$	6.53094	+	109.902i	0.308558	+	5.19239i
$449$	−6.84074	−	23.2974i	−0.322834	−	1.09947i	−0.947812	−	0.318830i	$-0.896710\pi$
$449$	−6.84074	−	23.2974i	−0.322834	−	1.09947i	0.624977	−	0.780643i	$-0.285108\pi$
$450$	−2.11850	−	1.73873i	−0.0998672	−	0.0819643i
$451$	26.8060	−	3.85412i	1.26224	−	0.181483i
$452$	−30.1138	+	26.0937i	−1.41643	+	1.22735i
$453$	5.58193	+	18.1109i	0.262262	+	0.850924i
$454$	−34.8706	−	54.2598i	−1.63656	−	2.54654i
$455$	3.37559	−	8.72778i	0.158250	−	0.409164i
$456$	67.7769	+	57.1604i	3.17394	+	2.67678i
$457$	−24.5896	+	28.3779i	−1.15025	+	1.32746i	−0.213718	+	0.976895i	$0.568557\pi$
$457$	−24.5896	+	28.3779i	−1.15025	+	1.32746i	−0.936537	+	0.350569i	$0.885988\pi$
$458$	−0.313148	−	0.0919485i	−0.0146324	−	0.00429647i
$459$	−17.2349	−	7.04997i	−0.804456	−	0.329064i
$460$	−46.4029	+	43.1626i	−2.16355	+	2.01247i
$461$	11.1746			0.520451			0.260226	−	0.965548i	$-0.416203\pi$
$461$	11.1746			0.520451			0.260226	+	0.965548i	$0.416203\pi$
$462$	−24.1462	+	32.3449i	−1.12338	+	1.50482i
$463$	11.7093	−	13.5133i	0.544179	−	0.628016i	−0.415338	−	0.909667i	$-0.636337\pi$
$463$	11.7093	−	13.5133i	0.544179	−	0.628016i	0.959517	+	0.281651i	$0.0908821\pi$
$464$	−41.3862	+	64.3982i	−1.92131	+	2.98961i
$465$	14.0209	+	3.91407i	0.650206	+	0.181510i
$466$	36.9677	−	23.7577i	1.71250	−	1.10055i
$467$	4.34397	+	9.51198i	0.201015	+	0.440162i	0.983114	−	0.182992i	$-0.0585783\pi$
$467$	4.34397	+	9.51198i	0.201015	+	0.440162i	−0.782099	+	0.623154i	$0.785851\pi$
$468$	23.6344	−	11.5669i	1.09250	−	0.534682i
$469$	−20.7786	−	1.73790i	−0.959468	−	0.0802487i
$470$	25.7987	+	11.7819i	1.19001	+	0.543457i
$471$	3.44385	+	21.8722i	0.158684	+	1.00782i
$472$	−7.24089	−	24.6602i	−0.333289	−	1.13508i
$473$	21.3908	+	9.76885i	0.983550	+	0.449172i
$474$	−32.0040	+	0.427958i	−1.46999	+	0.0196568i
$475$	−1.22845	+	1.06446i	−0.0563651	+	0.0488406i
$476$	−53.1706	+	10.8976i	−2.43707	+	0.499489i
$477$	4.15836	+	12.8777i	0.190398	+	0.589629i
$478$	−1.49307	+	10.3845i	−0.0682915	+	0.474978i
$479$	−13.2334	−	8.50458i	−0.604649	−	0.388584i	0.202198	−	0.979345i	$-0.435191\pi$
$479$	−13.2334	−	8.50458i	−0.604649	−	0.388584i	−0.806847	+	0.590761i	$0.798828\pi$
$480$	−72.9389	−	81.9362i	−3.32919	−	3.73986i
$481$	−2.18717	+	7.44881i	−0.0997262	+	0.339636i
$482$	−25.7375			−1.17231
$483$	14.9618	−	16.0980i	0.680785	−	0.732483i
$484$	−5.47405			−0.248820
$485$	2.35077	−	8.00600i	0.106743	−	0.363534i
$486$	9.01692	+	42.3762i	0.409016	+	1.92222i
$487$	−6.30080	−	4.04928i	−0.285516	−	0.183490i	0.390041	−	0.920797i	$-0.372461\pi$
$487$	−6.30080	−	4.04928i	−0.285516	−	0.183490i	−0.675558	+	0.737307i	$0.736097\pi$
$488$	2.67728	−	18.6209i	0.121195	−	0.842927i
$489$	21.3384	−	10.0919i	0.964954	−	0.456370i
$490$	44.8970	+	1.08175i	2.02824	+	0.0488684i
$491$	−10.2500	+	8.88168i	−0.462576	+	0.400825i	−0.854728	−	0.519076i	$-0.826276\pi$
$491$	−10.2500	+	8.88168i	−0.462576	+	0.400825i	0.392152	+	0.919900i	$0.371731\pi$
$492$	−1.13287	−	84.7196i	−0.0510738	−	3.81946i
$493$	−14.4069	−	6.57941i	−0.648854	−	0.296322i
$494$	−5.93288	−	20.2055i	−0.266933	−	0.909090i
$495$	−0.586852	−	21.9394i	−0.0263771	−	0.986102i
$496$	57.3629	+	26.1968i	2.57567	+	1.17627i
$497$	−0.296509	+	3.54511i	−0.0133002	+	0.159020i
$498$	45.6040	−	30.1770i	2.04356	−	1.35227i
$499$	12.2822	+	26.8944i	0.549829	+	1.20396i	0.956862	+	0.290544i	$0.0938362\pi$
$499$	12.2822	+	26.8944i	0.549829	+	1.20396i	−0.407033	+	0.913414i	$0.633436\pi$
$500$	−51.9291	+	33.3728i	−2.32234	+	1.49248i
$501$	−2.03977	+	7.30685i	−0.0911301	+	0.326446i
$502$	−38.2613	+	59.5357i	−1.70768	+	2.65721i
$503$	−7.51548	+	8.67332i	−0.335099	+	0.386724i	−0.898144	−	0.439702i	$-0.855084\pi$
$503$	−7.51548	+	8.67332i	−0.335099	+	0.386724i	0.563045	+	0.826426i	$0.309630\pi$
$504$	58.9447	+	57.2370i	2.62561	+	2.54954i
$505$	−44.4214			−1.97672
$506$	−41.9980	−	4.53489i	−1.86704	−	0.201601i
$507$	18.2961	+	2.38135i	0.812560	+	0.105760i
$508$	−23.8828	−	7.01262i	−1.05963	−	0.311135i
$509$	−5.29279	+	6.10821i	−0.234599	+	0.270742i	−0.860826	−	0.508899i	$-0.830053\pi$
$509$	−5.29279	+	6.10821i	−0.234599	+	0.270742i	0.626227	+	0.779640i	$0.284598\pi$
$510$	25.6734	−	30.4418i	1.13684	−	1.34799i
$511$	5.45810	−	14.1122i	0.241452	−	0.624289i
$512$	−63.0548	−	98.1151i	−2.78665	−	4.33612i
$513$	25.6751	−	1.03047i	1.13358	−	0.0454965i
$514$	−28.6444	+	24.8205i	−1.26345	+	1.09478i
$515$	32.0891	−	4.61371i	1.41401	−	0.203304i
$516$	38.9446	−	62.4186i	1.71444	−	2.74782i
$517$	3.94704	+	13.4424i	0.173591	+	0.591196i
$518$	−37.1919	+	2.21013i	−1.63412	+	0.0971074i
$519$	−14.0376	+	22.4987i	−0.616181	+	0.987586i
$520$	5.21045	+	36.2394i	0.228493	+	1.58920i
$521$	15.5574	+	17.9542i	0.681582	+	0.786588i	0.986142	−	0.165905i	$-0.0530547\pi$
$521$	15.5574	+	17.9542i	0.681582	+	0.786588i	−0.304559	+	0.952493i	$0.598509\pi$
$522$	6.21775	+	36.3217i	0.272143	+	1.58976i
$523$	18.5645	+	28.8870i	0.811771	+	1.26314i	0.961607	+	0.274430i	$0.0884890\pi$
$523$	18.5645	+	28.8870i	0.811771	+	1.26314i	−0.149836	+	0.988711i	$0.547875\pi$
$524$	12.4531	−	86.6135i	0.544018	−	3.78373i
$525$	−1.20465	+	0.904286i	−0.0525753	+	0.0394663i
$526$	30.1640	−	34.8112i	1.31521	−	1.51784i
$527$	−3.67588	+	12.5189i	−0.160124	+	0.545331i
$528$	12.2713	−	94.2812i	0.534038	−	4.10306i
$529$	22.4698	+	4.90977i	0.976950	+	0.213468i
$530$	−28.9401			−1.25708
$531$	−6.37163	−	3.85804i	−0.276505	−	0.167425i
$532$	60.4943	−	44.1586i	2.62276	−	1.91452i
$533$	−7.07865	+	11.0146i	−0.306610	+	0.477095i
$534$	15.7335	+	4.39213i	0.680854	+	0.190066i
$535$	−4.76621	−	7.41637i	−0.206061	−	0.320638i
$536$	74.2073	−	33.8893i	3.20527	−	1.46380i
$537$	29.5345	−	19.5435i	1.27451	−	0.843366i
$538$	−23.1056	+	3.32208i	−0.996153	+	0.143225i
$539$	14.1196	+	17.1108i	0.608173	+	0.737016i
$540$	−68.3022	−	7.03843i	−2.93926	−	0.302886i
$541$	−7.66517	+	2.25070i	−0.329551	+	0.0967650i	−0.442323	−	0.896856i	$-0.645845\pi$
$541$	−7.66517	+	2.25070i	−0.329551	+	0.0967650i	0.112771	+	0.993621i	$0.464027\pi$
$542$	−0.696508	+	1.52514i	−0.0299176	+	0.0655103i
$543$	−26.2225	+	0.350647i	−1.12531	+	0.0150477i
$544$	74.3066	−	64.3870i	3.18587	−	2.76057i
$545$	4.48836	+	9.82814i	0.192260	+	0.420991i
$546$	−4.17341	−	19.0631i	−0.178605	−	0.815824i
$547$	−3.77240	+	26.2376i	−0.161296	+	1.12184i	0.734898	+	0.678178i	$0.237230\pi$
$547$	−3.77240	+	26.2376i	−0.161296	+	1.12184i	−0.896194	+	0.443663i	$0.853679\pi$
$548$	27.9950	−	43.5611i	1.19589	−	1.86084i
$549$	−3.06922	−	4.50615i	−0.130991	−	0.192318i
$550$	2.77795	+	0.815679i	0.118452	+	0.0347807i
$551$	21.8556			0.931078
$552$	−20.1875	+	83.5819i	−0.859236	+	3.55748i
$553$	−3.94606	+	17.1430i	−0.167803	+	0.728993i
$554$	−14.9004	+	50.7462i	−0.633059	+	2.15600i
$555$	15.1314	−	13.4698i	0.642292	−	0.571763i
$556$	−55.9995	+	87.1369i	−2.37491	+	3.69543i
$557$	2.82928	+	0.406789i	0.119881	+	0.0172362i	0.201994	−	0.979387i	$-0.435258\pi$
$557$	2.82928	+	0.406789i	0.119881	+	0.0172362i	−0.0821134	+	0.996623i	$0.526167\pi$
$558$	28.8881	−	9.32830i	1.22293	−	0.394898i
$559$	−10.3417	+	4.72291i	−0.437409	+	0.199758i
$560$	−93.4491	+	49.5754i	−3.94895	+	2.09494i
$561$	19.6694	−	0.263020i	0.830445	−	0.0111047i
$562$	14.3866	−	31.5023i	0.606863	−	1.32884i
$563$	−37.7291	+	11.0782i	−1.59009	+	0.466893i	−0.952766	−	0.303704i	$-0.901777\pi$
$563$	−37.7291	+	11.0782i	−1.59009	+	0.466893i	−0.637323	+	0.770596i	$0.719958\pi$
$564$	43.2978	−	6.81737i	1.82317	−	0.287063i
$565$	−14.6160	−	6.67489i	−0.614899	−	0.280815i
$566$	4.32373	+	30.0722i	0.181740	+	1.26403i
$567$	23.8011	+	0.713285i	0.999551	+	0.0299552i
$568$	−5.78198	−	12.6608i	−0.242606	−	0.531234i
$569$	−9.75515	−	15.1793i	−0.408957	−	0.636350i	0.574285	−	0.818656i	$-0.305280\pi$
$569$	−9.75515	−	15.1793i	−0.408957	−	0.636350i	−0.983242	+	0.182306i	$0.941644\pi$
$570$	−14.7754	+	52.9286i	−0.618875	+	2.21693i
$571$	7.68936	+	4.94165i	0.321790	+	0.206802i	0.691556	−	0.722323i	$-0.256926\pi$
$571$	7.68936	+	4.94165i	0.321790	+	0.206802i	−0.369766	+	0.929125i	$0.620562\pi$
$572$	−18.2032	+	21.0076i	−0.761113	+	0.878371i
$573$	6.54594	−	14.8561i	0.273460	−	0.620624i
$574$	−61.2349	−	14.0954i	−2.55590	−	0.588329i
$575$	−1.45612	−	0.603931i	−0.0607242	−	0.0251857i
$576$	−120.678	−	31.9553i	−5.02826	−	1.33147i
$577$	−9.82120	+	33.4479i	−0.408862	+	1.39246i	0.455791	+	0.890087i	$0.349356\pi$
$577$	−9.82120	+	33.4479i	−0.408862	+	1.39246i	−0.864653	+	0.502369i	$0.832462\pi$
$578$	−8.73291	−	7.56711i	−0.363241	−	0.314750i
$579$	14.8973	+	12.5638i	0.619109	+	0.522132i
$580$	−57.8077	−	8.31149i	−2.40033	−	0.345116i
$581$	−10.1632	−	28.2845i	−0.421641	−	1.17344i
$582$	−5.12504	−	16.6285i	−0.212440	−	0.689272i
$583$	−9.36164	−	10.8039i	−0.387719	−	0.447452i
$584$	8.42495	+	58.5968i	0.348627	+	2.42475i
$585$	8.20201	+	6.73166i	0.339111	+	0.278320i
$586$	2.03805	+	6.94095i	0.0841910	+	0.286728i
$587$	2.20991	−	0.648887i	0.0912126	−	0.0267824i	−0.235808	−	0.971800i	$-0.575774\pi$
$587$	2.20991	−	0.648887i	0.0912126	−	0.0267824i	0.327020	+	0.945017i	$0.393955\pi$
$588$	58.7865	−	36.8955i	2.42431	−	1.52155i
$589$	−2.56231	−	17.8212i	−0.105578	−	0.734311i
$590$	12.0387	−	10.4316i	0.495624	−	0.429461i
$591$	−3.12730	+	0.963860i	−0.128640	+	0.0396479i
$592$	73.8281	−	47.4464i	3.03432	−	1.95004i
$593$	1.46769	−	10.2080i	0.0602709	−	0.419193i	−0.937240	−	0.348684i	$-0.886629\pi$
$593$	1.46769	−	10.2080i	0.0602709	−	0.419193i	0.997511	−	0.0705090i	$-0.0224624\pi$
$594$	−26.2683	−	37.4794i	−1.07780	−	1.53780i
$595$	−12.9043	−	17.6780i	−0.529024	−	0.724727i
$596$	−16.4085	+	55.8822i	−0.672118	+	2.28903i
$597$	−1.54751	+	11.8896i	−0.0633352	+	0.486610i
$598$	14.9537	−	13.9095i	0.611502	−	0.568801i
$599$		−	15.2575i		−	0.623405i	−0.950180	−	0.311703i	$-0.899101\pi$
$599$		−	15.2575i		−	0.623405i	0.950180	−	0.311703i	$-0.100899\pi$
$600$	2.37628	−	5.39300i	0.0970111	−	0.220168i
$601$	−31.8021	−	27.5567i	−1.29724	−	1.12406i	−0.984719	−	0.174150i	$-0.944282\pi$
$601$	−31.8021	−	27.5567i	−1.29724	−	1.12406i	−0.312518	−	0.949912i	$-0.601172\pi$
$602$	−38.1142	−	39.0436i	−1.55342	−	1.59130i
$603$	9.24309	−	21.7614i	0.376408	−	0.886192i
$604$	−52.6923	+	33.8633i	−2.14402	+	1.37788i
$605$	−0.916992	−	2.00793i	−0.0372810	−	0.0816341i
$606$	−77.2531	+	51.1199i	−3.13819	+	2.07660i
$607$	11.7656	−	1.69164i	0.477552	−	0.0686616i	0.100664	−	0.994920i	$-0.467903\pi$
$607$	11.7656	−	1.69164i	0.477552	−	0.0686616i	0.376888	+	0.926259i	$0.376994\pi$
$608$	−56.3623	+	123.416i	−2.28579	+	5.00518i
$609$	20.2034	+	1.41804i	0.818684	+	0.0574619i
$610$	11.1874	−	3.28493i	0.452966	−	0.133003i
$611$	−6.16123	−	2.81374i	−0.249257	−	0.113832i
$612$	7.12650	−	61.1291i	0.288072	−	2.47100i
$613$	−3.34273	−	3.85772i	−0.135012	−	0.155812i	0.684218	−	0.729278i	$-0.260144\pi$
$613$	−3.34273	−	3.85772i	−0.135012	−	0.155812i	−0.819229	+	0.573466i	$0.805598\pi$
$614$	−29.3241	−	64.2109i	−1.18343	−	2.59134i
$615$	30.8862	−	14.6075i	1.24545	−	0.589030i
$616$	−80.9516	−	31.3091i	−3.26163	−	1.26148i
$617$	−21.0021	+	32.6799i	−0.845512	+	1.31564i	0.101628	+	0.994823i	$0.467595\pi$
$617$	−21.0021	+	32.6799i	−0.845512	+	1.31564i	−0.947140	+	0.320821i	$0.896041\pi$
$618$	50.4966	−	44.9517i	2.03127	−	1.80822i
$619$	2.03990	−	6.94726i	0.0819905	−	0.279234i	−0.908285	−	0.418351i	$-0.862608\pi$
$619$	2.03990	−	6.94726i	0.0819905	−	0.279234i	0.990276	+	0.139117i	$0.0444264\pi$
$620$			48.1113i			1.93220i
$621$	12.0292	+	21.8243i	0.482713	+	0.875778i
$622$		−	17.9502i		−	0.719738i
$623$	4.39724	−	7.82731i	0.176172	−	0.313594i
$624$	30.5633	+	34.3334i	1.22351	+	1.37444i
$625$	−22.3230	−	14.3462i	−0.892922	−	0.573846i
$626$	−2.33404	+	16.2336i	−0.0932869	+	0.648825i
$627$	−24.5389	+	11.6055i	−0.979988	+	0.463480i
$628$	−66.5658	+	30.3996i	−2.65626	+	1.21308i
$629$	11.8905	+	13.7224i	0.474107	+	0.547149i
$630$	−17.0927	+	47.9688i	−0.680988	+	1.91112i
$631$	11.0313	−	24.1552i	0.439150	−	0.961605i	−0.552603	−	0.833444i	$-0.686366\pi$
$631$	11.0313	−	24.1552i	0.439150	−	0.961605i	0.991753	−	0.128160i	$-0.0409072\pi$
$632$	−19.3903	−	66.0373i	−0.771305	−	2.62682i
$633$	−14.9931	+	2.36070i	−0.595920	+	0.0938295i
$634$	−31.9021	+	69.8559i	−1.26700	+	2.77433i
$635$	−1.42846	−	9.93516i	−0.0566867	−	0.394265i
$636$	−37.2985	+	24.6811i	−1.47898	+	0.978670i
$637$	−10.7223	−	0.258342i	−0.424832	−	0.0102359i
$638$	−21.0462	−	32.7485i	−0.833227	−	1.29653i
$639$	−3.71278	−	1.57699i	−0.146875	−	0.0623849i
$640$	75.8548	−	118.032i	2.99843	−	4.66564i
$641$	24.8743	+	21.5537i	0.982477	+	0.851321i	0.988889	−	0.148658i	$-0.0474955\pi$
$641$	24.8743	+	21.5537i	0.982477	+	0.851321i	−0.00641177	+	0.999979i	$0.502041\pi$
$642$	−16.8236	−	7.41286i	−0.663976	−	0.292562i
$643$			44.4492i			1.75290i	0.481489	+	0.876452i	$0.340096\pi$
$643$			44.4492i			1.75290i	−0.481489	+	0.876452i	$0.659904\pi$
$644$	64.5407	+	33.3227i	2.54326	+	1.31310i
$645$	29.4196	+	3.82914i	1.15840	+	0.150772i
$646$	−47.2583	−	13.8763i	−1.85935	−	0.545955i
$647$	24.9141	−	28.7524i	0.979473	−	1.13037i	−0.0119832	−	0.999928i	$-0.503814\pi$
$647$	24.9141	−	28.7524i	0.979473	−	1.13037i	0.991456	−	0.130443i	$-0.0416401\pi$
$648$	−82.5536	+	43.1762i	−3.24301	+	1.69612i
$649$	7.78861	+	1.11983i	0.305730	+	0.0439573i
$650$	−1.17754	+	0.756759i	−0.0461869	+	0.0296825i
$651$	−1.21233	−	16.6403i	−0.0475149	−	0.652185i
$652$	51.0879	+	58.9586i	2.00076	+	2.30900i
$653$	8.40847	−	1.20896i	0.329049	−	0.0473101i	0.0241893	−	0.999707i	$-0.492300\pi$
$653$	8.40847	−	1.20896i	0.329049	−	0.0473101i	0.304860	+	0.952397i	$0.401390\pi$
$654$	19.1159	+	11.9269i	0.747490	+	0.466379i
$655$	33.8568	−	9.94125i	1.32289	−	0.388437i
$656$	142.015	−	41.6992i	5.54474	−	1.62808i
$657$	13.2621	+	10.8847i	0.517404	+	0.424651i
$658$	2.70934	−	32.3934i	0.105621	−	1.26283i
$659$	17.0091	−	14.7385i	0.662582	−	0.574131i	−0.257297	−	0.966332i	$-0.582832\pi$
$659$	17.0091	−	14.7385i	0.662582	−	0.574131i	0.919879	+	0.392202i	$0.128286\pi$
$660$	69.3185	−	21.3646i	2.69822	−	0.831614i
$661$	6.85632	+	10.6686i	0.266680	+	0.414962i	0.948606	−	0.316459i	$-0.102494\pi$
$661$	6.85632	+	10.6686i	0.266680	+	0.414962i	−0.681926	+	0.731421i	$0.738857\pi$
$662$	−77.6414	−	11.1631i	−3.01762	−	0.433868i
$663$	−6.13131	+	7.27009i	−0.238121	+	0.282347i
$664$	88.8679	+	77.0045i	3.44874	+	2.98835i
$665$	26.3316	+	14.7926i	1.02110	+	0.573633i
$666$	10.8140	−	40.8385i	0.419032	−	1.58246i
$667$	9.47877	+	18.9580i	0.367019	+	0.734058i
$668$	−25.0726			−0.970090
$669$	10.8302	−	24.5793i	0.418719	−	0.950290i
$670$	38.2124	+	33.1113i	1.47627	+	1.27920i
$671$	4.84527	+	3.11387i	0.187050	+	0.120210i
$672$	−60.1092	+	110.430i	−2.31876	+	4.25992i
$673$	−8.07944	+	5.19234i	−0.311439	+	0.200150i	−0.687018	−	0.726641i	$-0.741081\pi$
$673$	−8.07944	+	5.19234i	−0.311439	+	0.200150i	0.375578	+	0.926791i	$0.377444\pi$
$674$	73.7860	−	33.6969i	2.84213	−	1.29796i
$675$	−0.546525	−	1.61817i	−0.0210358	−	0.0622836i
$676$	8.67825	+	60.3585i	0.333779	+	2.32148i
$677$	17.4952	−	38.3092i	0.672395	−	1.47234i	−0.198109	−	0.980180i	$-0.563480\pi$
$677$	17.4952	−	38.3092i	0.672395	−	1.47234i	0.870505	−	0.492160i	$-0.163793\pi$
$678$	−33.1001	+	5.21170i	−1.27120	+	0.200154i
$679$	−9.54655	+	0.567303i	−0.366363	+	0.0217711i
$680$	77.8930	+	35.5725i	2.98706	+	1.36414i
$681$	−0.537446	−	40.1919i	−0.0205950	−	1.54016i
$682$	−24.2360	+	21.0006i	−0.928046	+	0.804156i
$683$	38.9601	−	17.7925i	1.49077	−	0.680810i	0.507277	−	0.861783i	$-0.330652\pi$
$683$	38.9601	−	17.7925i	1.49077	−	0.680810i	0.983488	+	0.180973i	$0.0579247\pi$
$684$	26.0965	+	80.8162i	0.997824	+	3.09008i
$685$	20.6683	+	2.97165i	0.789694	+	0.113541i
$686$	−16.2340	−	48.8462i	−0.619818	−	1.86496i
$687$	−0.135237	−	0.151919i	−0.00515960	−	0.00579606i
$688$	123.316	+	36.2088i	4.70138	+	1.38045i
$689$	6.91146			0.263306
$690$	−52.3197	+	10.1386i	−1.99178	+	0.385968i
$691$		−	24.3874i		−	0.927740i	−0.885903	−	0.463870i	$-0.846461\pi$
$691$		−	24.3874i		−	0.927740i	0.885903	−	0.463870i	$-0.153539\pi$
$692$	−84.0951	−	24.6926i	−3.19682	−	0.938670i
$693$	−23.4369	+	9.13609i	−0.890294	+	0.347051i
$694$	−0.516545	−	0.331963i	−0.0196078	−	0.0126012i
$695$	−41.3435	−	5.94430i	−1.56825	−	0.225480i
$696$	−71.6323	+	33.8781i	−2.71522	+	1.28415i
$697$	12.7213	+	27.8558i	0.481854	+	1.05511i
$698$	51.5741	+	59.5197i	1.95211	+	2.25285i
$699$	27.3831	−	0.366167i	1.03572	−	0.0138497i
$700$	−3.94914	−	3.03119i	−0.149264	−	0.114568i
$701$	−8.87647	−	30.2305i	−0.335260	−	1.14179i	−0.938802	−	0.344458i	$-0.888063\pi$
$701$	−8.87647	−	30.2305i	−0.335260	−	1.14179i	0.603542	−	0.797331i	$-0.293756\pi$
$702$	22.0109	+	2.26819i	0.830747	+	0.0856072i
$703$	−22.7916	−	10.4086i	−0.859603	−	0.392567i
$704$	130.535	−	18.7681i	4.91973	−	0.707351i
$705$	9.75376	+	14.7400i	0.367348	+	0.555141i
$706$	11.5862	−	5.29124i	0.436053	−	0.199139i
$707$	17.2165	+	47.9139i	0.647493	+	1.80199i
$708$	6.61922	−	23.7114i	0.248766	−	0.891127i
$709$	21.1148	+	13.5696i	0.792981	+	0.509618i	0.873318	−	0.487150i	$-0.161963\pi$
$709$	21.1148	+	13.5696i	0.792981	+	0.509618i	−0.0803373	+	0.996768i	$0.525600\pi$
$710$	5.64922	−	6.51955i	0.212012	−	0.244674i
$711$	−17.0625	−	10.3314i	−0.639895	−	0.387458i
$712$			35.1257i			1.31639i
$713$	14.3473	−	9.95168i	0.537311	−	0.372693i
$714$	−42.7856	−	15.8936i	−1.60121	−	0.594802i
$715$	−10.7551	−	3.15799i	−0.402218	−	0.118102i
$716$	88.4590	+	76.6502i	3.30587	+	2.86455i
$717$	−4.21514	+	4.99803i	−0.157417	+	0.186655i
$718$	−0.480800	+	3.34404i	−0.0179433	+	0.124798i
$719$	−27.4676	+	17.6523i	−1.02437	+	0.658321i	−0.941073	−	0.338204i	$-0.890181\pi$
$719$	−27.4676	+	17.6523i	−1.02437	+	0.658321i	−0.0832950	+	0.996525i	$0.526544\pi$
$720$	−20.2391	−	118.229i	−0.754267	−	4.40614i
$721$	−17.4133	−	32.8239i	−0.648505	−	1.22243i
$722$	15.0054	−	2.15745i	0.558442	−	0.0802919i
$723$	−13.6081	−	8.49044i	−0.506089	−	0.315763i
$724$	−24.4188	−	83.1628i	−0.907518	−	3.09072i
$725$	−0.409279	−	1.39388i	−0.0152002	−	0.0517672i
$726$	−3.90546	−	2.43672i	−0.144945	−	0.0904353i
$727$	−37.2977	+	5.36260i	−1.38329	+	0.198888i	−0.793453	−	0.608631i	$-0.791719\pi$
$727$	−37.2977	+	5.36260i	−1.38329	+	0.198888i	−0.589842	+	0.807519i	$0.700810\pi$
$728$	37.0693	−	19.6655i	1.37388	−	0.728853i
$729$	−9.21185	+	25.3799i	−0.341180	+	0.939998i
$730$	−30.8667	+	19.8368i	−1.14243	+	0.734193i
$731$	−3.78430	+	26.3204i	−0.139967	+	0.973495i
$732$	11.6170	−	13.7747i	0.429378	−	0.509128i
$733$	−8.98240	−	7.78329i	−0.331772	−	0.287482i	0.473004	−	0.881060i	$-0.343170\pi$
$733$	−8.98240	−	7.78329i	−0.331772	−	0.287482i	−0.804777	+	0.593578i	$0.797715\pi$
$734$	−1.69206	−	0.496833i	−0.0624550	−	0.0183384i
$735$	23.3813	+	15.3828i	0.862434	+	0.567405i
$736$	−131.499	+	4.63563i	−4.84710	+	0.170871i
$737$			24.9764i			0.920017i
$738$	36.9039	−	60.9476i	1.35845	−	2.24351i
$739$	32.5350	−	37.5474i	1.19682	−	1.38120i	0.291443	−	0.956588i	$-0.405865\pi$
$739$	32.5350	−	37.5474i	1.19682	−	1.38120i	0.905375	−	0.424614i	$-0.139590\pi$
$740$	56.3253	+	36.1981i	2.07056	+	1.33067i
$741$	3.52866	−	12.6404i	0.129629	−	0.464355i
$742$	11.2164	+	31.2155i	0.411766	+	1.14596i
$743$	−3.08830	+	1.41038i	−0.113299	+	0.0517418i	−0.471258	−	0.881995i	$-0.656200\pi$
$743$	−3.08830	+	1.41038i	−0.113299	+	0.0517418i	0.357959	+	0.933737i	$0.383473\pi$
$744$	36.0226	+	54.4379i	1.32065	+	1.99579i
$745$	−23.2468	+	3.34239i	−0.851698	+	0.122456i
$746$	4.40686	+	2.01255i	0.161347	+	0.0736845i
$747$	34.0670	−	0.911251i	1.24645	−	0.0333409i
$748$	18.3165	+	62.3803i	0.669718	+	2.28085i
$749$	−6.15222	+	8.01533i	−0.224797	+	0.292874i
$750$	−51.9045	+	0.694067i	−1.89528	+	0.0253437i
$751$	8.15612	+	9.41266i	0.297621	+	0.343473i	0.884789	−	0.465992i	$-0.154303\pi$
$751$	8.15612	+	9.41266i	0.297621	+	0.343473i	−0.587168	+	0.809465i	$0.699757\pi$
$752$	31.8078	+	69.6494i	1.15991	+	2.53985i
$753$	−39.8697	+	18.8562i	−1.45293	+	0.687158i
$754$	18.6289	+	2.67844i	0.678426	+	0.0975430i
$755$	−21.2482	−	13.6554i	−0.773301	−	0.496971i
$756$	18.8802	+	76.4002i	0.686666	+	2.77865i
$757$	30.6528	+	9.00047i	1.11409	+	0.327128i	0.786438	−	0.617669i	$-0.211923\pi$
$757$	30.6528	+	9.00047i	1.11409	+	0.327128i	0.327657	+	0.944797i	$0.393741\pi$
$758$			67.6210i			2.45611i
$759$	−20.7095	−	16.2523i	−0.751705	−	0.589921i
$760$	−118.165			−4.28630
$761$	−15.2475	−	4.47706i	−0.552720	−	0.162293i	−0.00656669	−	0.999978i	$-0.502090\pi$
$761$	−15.2475	−	4.47706i	−0.552720	−	0.162293i	−0.546153	+	0.837685i	$0.683908\pi$
$762$	−13.9176	−	15.6344i	−0.504181	−	0.566373i
$763$	8.86130	−	8.65036i	0.320800	−	0.313164i
$764$	53.1088	+	7.63589i	1.92141	+	0.276257i
$765$	23.6165	−	7.62605i	0.853858	−	0.275721i
$766$	58.4925	−	26.7126i	2.11342	−	0.965166i
$767$	−2.87507	+	2.49126i	−0.103813	+	0.0899542i
$768$	−1.98476	−	148.427i	−0.0716190	−	5.35588i
$769$	27.0063	+	12.3334i	0.973873	+	0.444753i	0.837819	−	0.545949i	$-0.183831\pi$
$769$	27.0063	+	12.3334i	0.973873	+	0.444753i	0.136054	+	0.990701i	$0.456558\pi$
$770$	−3.19114	−	53.7003i	−0.115001	−	1.93522i
$771$	−23.3330	+	3.67384i	−0.840316	+	0.132310i
$772$	−26.7560	+	58.5874i	−0.962969	+	2.10861i
$773$	−5.64336	−	39.2504i	−0.202977	−	1.41174i	−0.795387	−	0.606102i	$-0.792732\pi$
$773$	−5.64336	−	39.2504i	−0.202977	−	1.41174i	0.592410	−	0.805637i	$-0.298177\pi$
$774$	55.5701	−	27.1967i	1.99743	−	0.977565i
$775$	−1.08860	+	0.497145i	−0.0391035	+	0.0178580i
$776$	31.4767	−	20.2288i	1.12995	−	0.726173i
$777$	−20.3934	−	11.1005i	−0.731609	−	0.398230i
$778$	−48.1956	−	30.9734i	−1.72790	−	1.11045i
$779$	−31.9363	−	27.6729i	−1.14424	−	0.991486i
$780$	−14.1403	+	32.0917i	−0.506304	+	1.14907i
$781$	4.26130			0.152481
$782$	−8.45932	−	47.0112i	−0.302505	−	1.68112i
$783$	−8.69455	+	21.2554i	−0.310718	+	0.759605i
$784$	89.6915	+	81.5824i	3.20327	+	2.91366i
$785$	−22.3017	−	19.3245i	−0.795982	−	0.689723i
$786$	47.4399	−	56.2510i	1.69213	−	2.00641i
$787$	6.70153	+	0.963535i	0.238884	+	0.0343463i	0.260717	−	0.965415i	$-0.416041\pi$
$787$	6.70153	+	0.963535i	0.238884	+	0.0343463i	−0.0218330	+	0.999762i	$0.506950\pi$
$788$	−5.84734	−	9.09864i	−0.208303	−	0.324126i
$789$	27.4322	−	8.45485i	0.976613	−	0.301001i
$790$	32.2382	−	27.9346i	1.14698	−	0.993868i
$791$	−1.53495	+	18.3521i	−0.0545765	+	0.652527i
$792$	62.4373	−	76.0751i	2.21861	−	2.70321i
$793$	−2.67178	+	0.784504i	−0.0948775	+	0.0278586i
$794$	95.7158	−	28.1047i	3.39683	−	0.997398i
$795$	−15.3014	−	9.54694i	−0.542684	−	0.338595i
$796$	−39.2236	+	5.63950i	−1.39024	+	0.199887i
$797$	−8.70235	−	10.0430i	−0.308253	−	0.355743i	0.580393	−	0.814336i	$-0.302899\pi$
$797$	−8.70235	−	10.0430i	−0.308253	−	0.355743i	−0.888646	+	0.458594i	$0.848353\pi$
$798$	62.8165	−	4.57649i	2.22368	−	0.162006i
$799$	−13.3271	+	8.56482i	−0.471480	+	0.303002i
$800$	8.92654	+	1.28344i	0.315601	+	0.0453766i
$801$	6.86979	+	7.51250i	0.242732	+	0.265441i
$802$	−4.41607	+	5.09641i	−0.155937	+	0.179961i
$803$	−17.3903	−	5.10626i	−0.613691	−	0.180196i
$804$	77.4872	+	10.0854i	2.73276	+	0.355686i
$805$	−1.41144	+	29.2563i	−0.0497469	+	1.03115i
$806$		−	15.5042i		−	0.546113i
$807$	−13.3124	−	5.86575i	−0.468620	−	0.206484i
$808$	−150.542	−	130.446i	−5.29606	−	4.58906i
$809$	−12.7835	+	19.8915i	−0.449444	+	0.699349i	−0.989860	−	0.142050i	$-0.954631\pi$
$809$	−12.7835	+	19.8915i	−0.449444	+	0.699349i	0.540415	+	0.841398i	$0.318267\pi$
$810$	−45.5971	−	35.4257i	−1.60212	−	1.24473i
$811$	−0.707806	−	1.10137i	−0.0248544	−	0.0386742i	0.828604	−	0.559835i	$-0.189136\pi$
$811$	−0.707806	−	1.10137i	−0.0248544	−	0.0386742i	−0.853458	+	0.521161i	$0.825499\pi$
$812$	13.4397	+	65.5740i	0.471640	+	2.30120i
$813$	−0.871384	+	0.576612i	−0.0305608	+	0.0202227i
$814$	6.35130	+	44.1743i	0.222613	+	1.54831i
$815$	−13.0685	+	28.6161i	−0.457771	+	1.00238i
$816$	106.201	−	16.7217i	3.71779	−	0.585377i
$817$	−10.3378	−	35.2074i	−0.361675	−	1.23175i
$818$	1.49662	−	3.27715i	0.0523282	−	0.114583i
$819$	4.08206	−	11.4559i	0.142639	−	0.400301i
$820$	73.9472	+	85.3397i	2.58235	+	2.98019i
$821$	−43.2392	+	19.7467i	−1.50906	+	0.689164i	−0.986549	−	0.163469i	$-0.947732\pi$
$821$	−43.2392	+	19.7467i	−1.50906	+	0.689164i	−0.522511	+	0.852633i	$0.675004\pi$
$822$	39.3639	−	18.6170i	1.37297	−	0.649341i
$823$	−4.94775	+	34.4124i	−0.172468	+	1.19954i	0.701181	+	0.712983i	$0.252656\pi$
$823$	−4.94775	+	34.4124i	−0.172468	+	1.19954i	−0.873649	+	0.486557i	$0.838253\pi$
$824$	122.297	+	78.5955i	4.26042	+	2.73801i
$825$	1.19969	+	1.34768i	0.0417679	+	0.0469201i
$826$	−15.9176	−	8.94220i	−0.553843	−	0.311139i
$827$		−	34.2214i		−	1.18999i	−0.803728	−	0.594997i	$-0.797153\pi$
$827$		−	34.2214i		−	1.18999i	0.803728	−	0.594997i	$-0.202847\pi$
$828$	−58.7839	+	57.6867i	−2.04288	+	2.00475i
$829$			3.94347i			0.136962i	0.997652	+	0.0684811i	$0.0218153\pi$
$829$			3.94347i			0.136962i	−0.997652	+	0.0684811i	$0.978185\pi$
$830$	−20.5329	+	69.9286i	−0.712707	+	2.42726i
$831$	−24.6187	+	21.9154i	−0.854015	+	0.760237i
$832$	−34.4704	+	53.6370i	−1.19505	+	1.85953i
$833$	−14.0666	+	20.7704i	−0.487377	+	0.719650i
$834$	−78.7411	+	37.2402i	−2.72658	+	1.28952i
$835$	−4.20008	−	9.19689i	−0.145350	−	0.318272i
$836$	−58.7505	−	67.8017i	−2.03193	−	2.34497i
$837$	18.3512	+	4.59768i	0.634309	+	0.158919i
$838$	−31.9346	−	14.5841i	−1.10316	−	0.503798i
$839$	−3.97127	+	1.16607i	−0.137104	+	0.0402573i	−0.349564	−	0.936912i	$-0.613670\pi$
$839$	−3.97127	+	1.16607i	−0.137104	+	0.0402573i	0.212461	+	0.977170i	$0.431852\pi$
$840$	−109.233	−	7.66685i	−3.76889	−	0.264531i
$841$	3.93281	−	8.61166i	0.135614	−	0.296954i
$842$	−49.5143	+	7.11907i	−1.70637	+	0.245340i
$843$	17.9987	−	11.9101i	0.619910	−	0.410206i
$844$	−20.8384	−	45.6298i	−0.717288	−	1.57064i
$845$	−20.6863	+	13.2943i	−0.711632	+	0.457338i
$846$	33.9255	+	14.4098i	1.16638	+	0.495418i
$847$	−1.81040	+	1.76731i	−0.0622062	+	0.0607254i
$848$	−59.0469	−	51.1644i	−2.02768	−	1.75699i
$849$	−7.63434	+	17.3263i	−0.262010	+	0.594637i
$850$			3.27383i			0.112292i
$851$	−0.856076	−	24.2842i	−0.0293459	−	0.832453i
$852$	1.72071	−	13.2204i	0.0589505	−	0.452922i
$853$	−0.429722	+	1.46350i	−0.0147134	+	0.0501092i	−0.966522	−	0.256582i	$-0.917404\pi$
$853$	−0.429722	+	1.46350i	−0.0147134	+	0.0501092i	0.951809	+	0.306691i	$0.0992218\pi$
$854$	−7.87914	−	10.7939i	−0.269619	−	0.369359i
$855$	−25.2726	+	23.1105i	−0.864304	+	0.790361i
$856$	5.62605	−	39.1300i	0.192294	−	1.33744i
$857$	11.5127	−	7.39877i	0.393267	−	0.252737i	−0.329031	−	0.944319i	$-0.606722\pi$
$857$	11.5127	−	7.39877i	0.393267	−	0.252737i	0.722298	+	0.691582i	$0.243086\pi$
$858$	−22.3384	+	6.88489i	−0.762620	+	0.235046i
$859$	−22.5246	+	19.5176i	−0.768528	+	0.665933i	−0.948157	−	0.317801i	$-0.897056\pi$
$859$	−22.5246	+	19.5176i	−0.768528	+	0.665933i	0.179630	+	0.983734i	$0.442510\pi$
$860$	13.9544	+	97.0546i	0.475839	+	3.30954i
$861$	−27.7266	−	27.6531i	−0.944920	−	0.942417i
$862$	−29.9403	+	8.79127i	−1.01977	+	0.299432i
$863$	−1.33351	−	4.54152i	−0.0453932	−	0.154595i	0.933678	−	0.358114i	$-0.116580\pi$
$863$	−1.33351	−	4.54152i	−0.0453932	−	0.154595i	−0.979071	+	0.203519i	$0.934762\pi$
$864$	−97.6050	−	103.912i	−3.32059	−	3.53515i
$865$	−5.02984	−	34.9833i	−0.171020	−	1.18947i
$866$	−5.78040	−	6.67093i	−0.196426	−	0.226688i
$867$	−2.12103	−	6.88179i	−0.0720339	−	0.233718i
$868$	51.8940	−	18.6466i	1.76140	−	0.632908i
$869$	20.8571	+	2.99879i	0.707527	+	0.101727i
$870$	−37.5431	−	31.6624i	−1.27283	−	1.07346i
$871$	−9.12587	−	7.90761i	−0.309218	−	0.267939i
$872$	−13.6500	+	46.4875i	−0.462246	+	1.57426i
$873$	2.77577	−	10.4826i	0.0939455	−	0.354782i
$874$	37.5672	+	54.1605i	1.27073	+	1.83201i
$875$	−6.39976	+	27.8027i	−0.216351	+	0.939901i
$876$	−22.8639	+	51.8901i	−0.772501	+	1.75321i
$877$	22.5572	−	26.0324i	0.761702	−	0.879051i	−0.233945	−	0.972250i	$-0.575164\pi$
$877$	22.5572	−	26.0324i	0.761702	−	0.879051i	0.995648	+	0.0931985i	$0.0297091\pi$
$878$	75.5350	+	48.5434i	2.54918	+	1.63826i
$879$	−1.21216	+	4.34219i	−0.0408851	+	0.146458i
$880$	68.5065	+	106.598i	2.30935	+	3.59342i
$881$	0.374052	+	0.819060i	0.0126021	+	0.0275948i	0.915828	−	0.401570i	$-0.131535\pi$
$881$	0.374052	+	0.819060i	0.0126021	+	0.0275948i	−0.903226	+	0.429165i	$0.858808\pi$
$882$	58.3650	−	0.154848i	1.96525	−	0.00521399i
$883$	−3.70150	−	25.7445i	−0.124565	−	0.866371i	−0.952281	−	0.305223i	$-0.901269\pi$
$883$	−3.70150	−	25.7445i	−0.124565	−	0.866371i	0.827715	−	0.561148i	$-0.189640\pi$
$884$	−28.5916	−	13.0573i	−0.961640	−	0.439166i
$885$	9.80638	−	1.54404i	0.329638	−	0.0519025i
$886$	5.60719	−	1.64642i	0.188377	−	0.0553125i
$887$	−11.5425	+	25.2746i	−0.387560	+	0.848638i	0.610822	+	0.791768i	$0.290839\pi$
$887$	−11.5425	+	25.2746i	−0.387560	+	0.848638i	−0.998382	+	0.0568697i	$0.981888\pi$
$888$	90.8346	−	1.21464i	3.04821	−	0.0407607i
$889$	−10.1627	+	5.39137i	−0.340845	+	0.180821i
$890$	−19.8032	+	9.04383i	−0.663805	+	0.303150i
$891$	−1.52480	−	28.4819i	−0.0510829	−	0.954179i
$892$	87.8679	+	12.6335i	2.94203	+	0.423001i
$893$	11.8189	−	18.3905i	0.395503	−	0.615415i
$894$	−36.5821	+	32.5651i	−1.22349	+	1.08914i
$895$	−13.2977	+	45.2878i	−0.444493	+	1.51380i
$896$	−156.712	−	36.0727i	−5.23537	−	1.20510i
$897$	12.4949	−	2.42128i	0.417194	−	0.0808443i
$898$	67.4839			2.25197
$899$	15.4392	+	4.53336i	0.514927	+	0.151196i
$900$	4.66549	−	3.17775i	0.155516	−	0.105925i
$901$	8.73949	−	13.5989i	0.291155	−	0.453046i
$902$	−10.7117	+	74.5017i	−0.356661	+	2.48063i
$903$	−7.27202	−	33.2167i	−0.241998	−	1.10538i
$904$	−29.9318	−	65.5415i	−0.995517	−	2.17988i
$905$	26.4144	−	22.8882i	0.878044	−	0.760829i
$906$	−52.6673	+	0.704268i	−1.74975	+	0.0233977i
$907$	15.0360	−	32.9243i	0.499263	−	1.09323i	−0.477445	−	0.878661i	$-0.658437\pi$
$907$	15.0360	−	32.9243i	0.499263	−	1.09323i	0.976708	−	0.214572i	$-0.0688356\pi$
$908$	127.466	−	37.4274i	4.23010	−	1.24207i
$909$	−57.7095	+	1.54366i	−1.91410	+	0.0512000i
$910$	20.6313	+	15.8357i	0.683922	+	0.524949i
$911$	46.3607	−	6.66566i	1.53600	−	0.220843i	0.678218	−	0.734861i	$-0.262753\pi$
$911$	46.3607	−	6.66566i	1.53600	−	0.220843i	0.857779	+	0.514018i	$0.171844\pi$
$912$	−123.721	+	81.8687i	−4.09682	+	2.71095i
$913$	−32.7477	+	14.9554i	−1.08379	+	0.494951i
$914$	−56.4217	−	87.7939i	−1.86626	−	2.90396i
$915$	6.99874	+	1.95376i	0.231371	+	0.0645892i
$916$	0.363427	−	0.565504i	0.0120080	−	0.0186848i
$917$	−23.8448	−	32.6658i	−0.787425	−	1.07872i
$918$	32.2955	−	40.4403i	1.06591	−	1.33473i
$919$	−21.8054			−0.719292			−0.359646	−	0.933089i	$-0.617103\pi$
$919$	−21.8054			−0.719292			−0.359646	+	0.933089i	$0.617103\pi$
$920$	−51.2483	−	102.499i	−1.68961	−	3.37931i
$921$	5.67787	−	43.6236i	0.187092	−	1.43745i
$922$	−8.74988	+	29.7994i	−0.288162	+	0.981389i
$923$	−1.34914	+	1.55700i	−0.0444076	+	0.0512491i
$924$	−49.9102	−	66.4883i	−1.64193	−	2.18730i
$925$	−0.237017	+	1.64849i	−0.00779308	+	0.0542021i
$926$	26.8675	+	41.8066i	0.882919	+	1.37385i
$927$	41.5278	−	7.10896i	1.36395	−	0.233489i
$928$	−79.4069	−	91.6404i	−2.60666	−	3.00824i
$929$	−6.00589	−	41.7719i	−0.197047	−	1.37049i	−0.812795	−	0.582549i	$-0.802055\pi$
$929$	−6.00589	−	41.7719i	−0.197047	−	1.37049i	0.615748	−	0.787943i	$-0.288854\pi$
$930$	−21.4163	+	34.3251i	−0.702269	+	1.12556i
$931$	5.75026	−	34.1351i	0.188457	−	1.11873i
$932$	25.4996	+	86.8437i	0.835268	+	2.84466i
$933$	5.92153	−	9.49074i	0.193862	−	0.310713i
$934$	−28.7671	+	4.13609i	−0.941289	+	0.135337i
$935$	−19.8134	+	17.1684i	−0.647967	+	0.561467i
$936$	8.02842	+	46.8990i	0.262417	+	1.53294i
$937$	−0.526204	−	0.818790i	−0.0171903	−	0.0267487i	0.832552	−	0.553947i	$-0.186879\pi$
$937$	−0.526204	−	0.818790i	−0.0171903	−	0.0267487i	−0.849742	+	0.527198i	$0.823243\pi$
$938$	20.9045	−	54.0498i	0.682556	−	1.76479i
$939$	−6.58930	+	7.81315i	−0.215034	+	0.254972i
$940$	−38.2545	+	44.1480i	−1.24772	+	1.43995i
$941$	−9.11700	−	2.67699i	−0.297206	−	0.0872674i	0.129730	−	0.991549i	$-0.458589\pi$
$941$	−9.11700	−	2.67699i	−0.297206	−	0.0872674i	−0.426936	+	0.904282i	$0.640407\pi$
$942$	−61.0235	−	7.94258i	−1.98825	−	0.258783i
$943$	10.1534	−	39.7041i	0.330641	−	1.29294i
$944$	43.0051			1.39970
$945$	−24.8616	+	19.7237i	−0.808748	+	0.641613i
$946$	−42.8001	+	49.3939i	−1.39155	+	1.60593i
$947$	6.20625	−	9.65711i	0.201676	−	0.313814i	−0.725653	−	0.688061i	$-0.758462\pi$
$947$	6.20625	−	9.65711i	0.201676	−	0.313814i	0.927329	+	0.374247i	$0.122099\pi$
$948$	17.7256	−	63.4964i	0.575699	−	2.06227i
$949$	7.37156	−	4.73741i	0.239291	−	0.153783i
$950$	−1.87670	−	4.10941i	−0.0608883	−	0.133327i
$951$	−39.9120	+	26.4105i	−1.29423	+	0.856420i
$952$	8.18021	−	97.8041i	0.265122	−	3.16985i
$953$	−46.9016	−	21.4192i	−1.51929	−	0.693837i	−0.531136	−	0.847287i	$-0.678234\pi$
$953$	−46.9016	−	21.4192i	−1.51929	−	0.693837i	−0.988156	+	0.153449i	$0.950962\pi$
$954$	−37.5972	+	1.00568i	−1.21725	+	0.0325601i
$955$	6.09567	+	20.7600i	0.197251	+	0.671777i
$956$	−19.6561	−	8.97664i	−0.635723	−	0.290325i
$957$	−0.324376	−	24.2578i	−0.0104856	−	0.784144i
$958$	33.0412	−	28.6304i	1.06751	−	0.925006i
$959$	−4.80516	−	23.4450i	−0.155167	−	0.757079i
$960$	150.405	−	71.1331i	4.85429	−	2.29581i
$961$	−2.52528	+	17.5637i	−0.0814606	+	0.566571i
$962$	−18.1512	−	11.6651i	−0.585220	−	0.376098i
$963$	−6.44969	−	9.46926i	−0.207838	−	0.305143i
$964$	14.9349	−	50.8638i	0.481022	−	1.63821i
$965$	−25.9725			−0.836085
$966$	31.2133	+	52.5038i	1.00427	+	1.68928i
$967$	13.7459			0.442037			0.221019	−	0.975270i	$-0.429062\pi$
$967$	13.7459			0.442037			0.221019	+	0.975270i	$0.429062\pi$
$968$	2.78875	−	9.49760i	0.0896338	−	0.305265i
$969$	−20.4091	−	22.9266i	−0.655634	−	0.736509i
$970$	19.5090	+	12.5377i	0.626396	+	0.402560i
$971$	−7.41754	+	51.5902i	−0.238040	+	1.65561i	0.423647	+	0.905827i	$0.360750\pi$
$971$	−7.41754	+	51.5902i	−0.238040	+	1.65561i	−0.661688	+	0.749780i	$0.730159\pi$
$972$	−88.9785	−	6.77037i	−2.85399	−	0.217160i
$973$	9.61194	+	46.8979i	0.308145	+	1.50348i
$974$	15.7319	−	13.6318i	0.504082	−	0.436790i
$975$	−0.872240	+	0.0116636i	−0.0279340	+	0.000373534i
$976$	28.6334	+	13.0765i	0.916534	+	0.418567i
$977$	8.38974	+	28.5728i	0.268411	+	0.914125i	0.977841	+	0.209349i	$0.0671345\pi$
$977$	8.38974	+	28.5728i	0.268411	+	0.914125i	−0.709430	+	0.704776i	$0.751047\pi$
$978$	10.2038	+	64.8054i	0.326282	+	2.07225i
$979$	−9.78225	−	4.46740i	−0.312642	−	0.142779i
$980$	−28.1907	+	88.1002i	−0.900518	+	2.81426i
$981$	6.17253	+	12.6121i	0.197074	+	0.402674i
$982$	−15.6590	−	34.2883i	−0.499697	−	1.09418i
$983$	26.7866	−	17.2147i	0.854359	−	0.549063i	−0.0385726	−	0.999256i	$-0.512281\pi$
$983$	26.7866	−	17.2147i	0.854359	−	0.549063i	0.892931	+	0.450193i	$0.148645\pi$
$984$	147.568	+	41.1948i	4.70429	+	1.31324i
$985$	2.35794	−	3.66903i	0.0751304	−	0.116905i
$986$	28.8263	−	33.2673i	0.918015	−	1.05945i
$987$	12.1186	−	16.2335i	0.385741	−	0.516717i
$988$	43.3740			1.37991
$989$	26.0563	−	24.2368i	0.828542	−	0.770685i
$990$	58.9656	+	15.6140i	1.87405	+	0.496244i
$991$	−13.3358	−	3.91574i	−0.423625	−	0.124387i	0.0629696	−	0.998015i	$-0.479943\pi$
$991$	−13.3358	−	3.91574i	−0.423625	−	0.124387i	−0.486594	+	0.873628i	$0.661761\pi$
$992$	−65.4149	+	75.4929i	−2.07693	+	2.39690i
$993$	−37.3684	−	31.5151i	−1.18585	−	1.00010i
$994$	−9.22162	−	3.56659i	−0.292492	−	0.113125i
$995$	−8.63922	−	13.4429i	−0.273882	−	0.426168i
$996$	33.1744	+	107.636i	1.05117	+	3.41058i
$997$	37.6630	−	32.6352i	1.19280	−	1.03357i	0.194185	−	0.980965i	$-0.437794\pi$
$997$	37.6630	−	32.6352i	1.19280	−	1.03357i	0.998616	−	0.0526021i	$-0.0167515\pi$
$998$	−81.3368	+	11.6945i	−2.57467	+	0.370182i
$999$	19.1897	−	18.0250i	0.607135	−	0.570286i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.v.a.41.1	✓	600
3.2	odd	2	inner	483.2.v.a.41.60	yes	600
7.6	odd	2	inner	483.2.v.a.41.2	yes	600
21.20	even	2	inner	483.2.v.a.41.59	yes	600
23.9	even	11	inner	483.2.v.a.377.59	yes	600
69.32	odd	22	inner	483.2.v.a.377.2	yes	600
161.55	odd	22	inner	483.2.v.a.377.60	yes	600
483.377	even	22	inner	483.2.v.a.377.1	yes	600

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.v.a.41.1	✓	600	1.1	even	1	trivial
483.2.v.a.41.2	yes	600	7.6	odd	2	inner
483.2.v.a.41.59	yes	600	21.20	even	2	inner
483.2.v.a.41.60	yes	600	3.2	odd	2	inner
483.2.v.a.377.1	yes	600	483.377	even	22	inner
483.2.v.a.377.2	yes	600	69.32	odd	22	inner
483.2.v.a.377.59	yes	600	23.9	even	11	inner
483.2.v.a.377.60	yes	600	161.55	odd	22	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.v (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.783018 + 2.66671i) q^{2} +(-1.29371 + 1.15165i) q^{3} +(-4.81573 - 3.09488i) q^{4} +(0.328519 - 2.28490i) q^{5} +(-2.05813 - 4.35173i) q^{6} +(-2.59187 + 0.531216i) q^{7} +(7.82307 - 6.77873i) q^{8} +(0.347391 - 2.97982i) q^{9} +(5.83594 + 2.66518i) q^{10} +(0.892863 + 3.04081i) q^{11} +(9.79441 - 1.54216i) q^{12} +(-1.39374 - 0.636498i) q^{13} +(0.612882 - 7.32773i) q^{14} +(2.20640 + 3.33435i) q^{15} +(7.19526 + 15.7554i) q^{16} +(-3.01474 + 1.93745i) q^{17} +(7.67431 + 3.25964i) q^{18} +(2.67355 - 4.16012i) q^{19} +(-8.65357 + 9.98675i) q^{20} +(2.74137 - 3.67218i) q^{21} -8.80810 q^{22} +(4.76812 + 0.514855i) q^{23} +(-2.31407 + 17.7792i) q^{24} +(-0.315385 - 0.0926055i) q^{25} +(2.78868 - 3.21830i) q^{26} +(2.98229 + 4.25511i) q^{27} +(14.1258 + 5.46336i) q^{28} +(2.38941 + 3.71800i) q^{29} +(-10.6194 + 3.27299i) q^{30} +(2.75156 - 2.38424i) q^{31} +(-27.1571 + 3.90460i) q^{32} +(-4.65707 - 2.90567i) q^{33} +(-2.80604 - 9.55650i) q^{34} +(0.362296 + 6.09669i) q^{35} +(-10.8951 + 13.2749i) q^{36} +(-0.721075 - 5.01519i) q^{37} +(9.00042 + 10.3870i) q^{38} +(2.53612 - 0.781654i) q^{39} +(-12.9187 - 20.1019i) q^{40} +(1.21612 - 8.45831i) q^{41} +(7.64611 + 10.1858i) q^{42} +(4.85917 - 5.60778i) q^{43} +(5.11117 - 17.4071i) q^{44} +(-6.69447 - 1.77268i) q^{45} +(-5.10649 + 12.3121i) q^{46} +4.42066 q^{47} +(-27.4534 - 12.0966i) q^{48} +(6.43562 - 2.75369i) q^{49} +(0.493905 - 0.768530i) q^{50} +(1.66893 - 5.97844i) q^{51} +(4.74197 + 7.37865i) q^{52} +(-4.10318 + 1.87386i) q^{53} +(-13.6823 + 4.62110i) q^{54} +(7.24128 - 1.04114i) q^{55} +(-16.6754 + 21.7254i) q^{56} +(1.33221 + 8.46101i) q^{57} +(-11.7858 + 3.46062i) q^{58} +(1.03142 - 2.25850i) q^{59} +(-0.306031 - 22.8859i) q^{60} +(1.37348 - 1.19012i) q^{61} +(4.20357 + 9.20453i) q^{62} +(0.682534 + 7.90785i) q^{63} +(5.92207 - 41.1889i) q^{64} +(-1.91220 + 2.97545i) q^{65} +(11.3952 - 10.1439i) q^{66} +(7.56177 + 2.22034i) q^{67} +20.5144 q^{68} +(-6.76151 + 4.82514i) q^{69} +(-16.5418 - 3.80768i) q^{70} +(0.378819 - 1.29014i) q^{71} +(-17.4817 - 25.6662i) q^{72} +(-3.09191 + 4.81110i) q^{73} +(13.9387 + 2.00408i) q^{74} +(0.514668 - 0.243410i) q^{75} +(-25.7502 + 11.7597i) q^{76} +(-3.92952 - 7.40710i) q^{77} +(0.0986206 + 7.37515i) q^{78} +(2.76204 - 6.04803i) q^{79} +(38.3634 - 11.2645i) q^{80} +(-8.75864 - 2.07032i) q^{81} +(21.6036 + 9.86605i) q^{82} +(1.61666 + 11.2441i) q^{83} +(-24.5667 + 9.20003i) q^{84} +(3.43649 + 7.52487i) q^{85} +(11.1495 + 17.3490i) q^{86} +(-7.37306 - 2.05825i) q^{87} +(27.5978 + 17.7360i) q^{88} +(-2.22215 + 2.56450i) q^{89} +(9.96912 - 16.4642i) q^{90} +(3.95050 + 0.909347i) q^{91} +(-21.3686 - 17.2362i) q^{92} +(-0.813914 + 6.25337i) q^{93} +(-3.46145 + 11.7886i) q^{94} +(-8.62716 - 7.47548i) q^{95} +(30.6368 - 36.3270i) q^{96} +(3.57783 + 0.514414i) q^{97} +(2.30410 + 19.3181i) q^{98} +(9.37124 - 1.60422i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 600 q + 20 q^{4} - 18 q^{7} - 26 q^{9} - 14 q^{15} - 116 q^{16} - 46 q^{18} - 50 q^{21} - 104 q^{22} - 88 q^{25} - 26 q^{28} + 26 q^{30} - 26 q^{36} - 56 q^{37} - 14 q^{39} + 5 q^{42} - 40 q^{43} - 44 q^{46}+ \cdots - 250 q^{99}+O(q^{100}) \) 600 * q + 20 * q^4 - 18 * q^7 - 26 * q^9 - 14 * q^15 - 116 * q^16 - 46 * q^18 - 50 * q^21 - 104 * q^22 - 88 * q^25 - 26 * q^28 + 26 * q^30 - 26 * q^36 - 56 * q^37 - 14 * q^39 + 5 * q^42 - 40 * q^43 - 44 * q^46 + 74 * q^49 + 14 * q^51 - 66 * q^57 - 76 * q^58 + 22 * q^60 - 44 * q^63 + 44 * q^64 - 92 * q^67 - 92 * q^70 + 178 * q^72 - 182 * q^78 + 68 * q^79 + 106 * q^81 - 87 * q^84 - 4 * q^85 - 220 * q^88 - 24 * q^91 - 44 * q^93 - 250 * q^99

Introduction

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