LMFDB - Embedded newform 820.2.k.c.83.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(83,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.83"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [108] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			83.17
Character	$\chi$	$=$	820.83
Dual form			820.2.k.c.247.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.530735 - 1.31085i) q^{2} +(-0.00659099 + 0.00659099i) q^{3} +(-1.43664 + 1.39143i) q^{4} +(-1.13558 - 1.92625i) q^{5} +(0.0121378 + 0.00514171i) q^{6} +(-1.72131 - 1.72131i) q^{7} +(2.58642 + 1.14474i) q^{8} +2.99991i q^{9} +(-1.92233 + 2.51091i) q^{10} +4.72534i q^{11} +(0.000298009 - 0.0186397i) q^{12} +(3.18457 + 3.18457i) q^{13} +(-1.34281 + 3.16993i) q^{14} +(0.0201805 + 0.00521130i) q^{15} +(0.127870 - 3.99796i) q^{16} +(4.36940 - 4.36940i) q^{17} +(3.93243 - 1.59216i) q^{18} +1.01431 q^{19} +(4.31166 + 1.18725i) q^{20} +0.0226902 q^{21} +(6.19419 - 2.50790i) q^{22} +(1.07960 - 1.07960i) q^{23} +(-0.0245920 + 0.00950212i) q^{24} +(-2.42090 + 4.37484i) q^{25} +(2.48432 - 5.86465i) q^{26} +(-0.0395453 - 0.0395453i) q^{27} +(4.86797 + 0.0778282i) q^{28} +3.58169i q^{29} +(-0.00387930 - 0.0292194i) q^{30} -8.10943i q^{31} +(-5.30857 + 1.95424i) q^{32} +(-0.0311446 - 0.0311446i) q^{33} +(-8.04661 - 3.40862i) q^{34} +(-1.36099 + 5.27036i) q^{35} +(-4.17416 - 4.30980i) q^{36} +(4.37809 - 4.37809i) q^{37} +(-0.538331 - 1.32961i) q^{38} -0.0419789 q^{39} +(-0.732044 - 6.28205i) q^{40} +1.00000 q^{41} +(-0.0120425 - 0.0297434i) q^{42} +(-2.02742 + 2.02742i) q^{43} +(-6.57495 - 6.78861i) q^{44} +(5.77859 - 3.40665i) q^{45} +(-1.98817 - 0.842209i) q^{46} +(4.94300 + 4.94300i) q^{47} +(0.0255077 + 0.0271933i) q^{48} -1.07420i q^{49} +(7.01961 + 0.851550i) q^{50} +0.0575973i q^{51} +(-9.00618 - 0.143989i) q^{52} +(-2.72534 - 2.72534i) q^{53} +(-0.0308498 + 0.0728260i) q^{54} +(9.10219 - 5.36601i) q^{55} +(-2.48158 - 6.42247i) q^{56} +(-0.00668532 + 0.00668532i) q^{57} +(4.69505 - 1.90093i) q^{58} +2.91973 q^{59} +(-0.0362433 + 0.0205929i) q^{60} +14.1650 q^{61} +(-10.6302 + 4.30396i) q^{62} +(5.16378 - 5.16378i) q^{63} +(5.37915 + 5.92154i) q^{64} +(2.51795 - 9.75064i) q^{65} +(-0.0242963 + 0.0573554i) q^{66} +(6.79119 + 6.79119i) q^{67} +(-0.197561 + 12.3570i) q^{68} +0.0142313i q^{69} +(7.63097 - 1.01312i) q^{70} +14.7741i q^{71} +(-3.43411 + 7.75904i) q^{72} +(3.00629 + 3.00629i) q^{73} +(-8.06262 - 3.41540i) q^{74} +(-0.0128784 - 0.0447906i) q^{75} +(-1.45720 + 1.41134i) q^{76} +(8.13376 - 8.13376i) q^{77} +(0.0222797 + 0.0550280i) q^{78} +6.69329 q^{79} +(-7.84628 + 4.29370i) q^{80} -8.99922 q^{81} +(-0.530735 - 1.31085i) q^{82} +(7.11710 - 7.11710i) q^{83} +(-0.0325977 + 0.0315718i) q^{84} +(-13.3784 - 3.45475i) q^{85} +(3.73365 + 1.58161i) q^{86} +(-0.0236069 - 0.0236069i) q^{87} +(-5.40927 + 12.2217i) q^{88} -0.0121741i q^{89} +(-7.53250 - 5.76682i) q^{90} -10.9633i q^{91} +(-0.0488137 + 3.05318i) q^{92} +(0.0534491 + 0.0534491i) q^{93} +(3.85609 - 9.10294i) q^{94} +(-1.15184 - 1.95382i) q^{95} +(0.0221084 - 0.0478691i) q^{96} +(-10.4916 + 10.4916i) q^{97} +(-1.40811 + 0.570113i) q^{98} -14.1756 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 12 q^{2} - 4 q^{6} - 24 q^{8} + 4 q^{10} - 16 q^{13} + 52 q^{16} - 8 q^{17} + 18 q^{18} + 38 q^{20} + 72 q^{21} + 10 q^{22} - 12 q^{25} + 24 q^{26} - 58 q^{28} - 70 q^{30} - 38 q^{32} + 8 q^{33}+ \cdots + 122 q^{98}+O(q^{100}) $ 108 * q + 12 * q^2 - 4 * q^6 - 24 * q^8 + 4 * q^10 - 16 * q^13 + 52 * q^16 - 8 * q^17 + 18 * q^18 + 38 * q^20 + 72 * q^21 + 10 * q^22 - 12 * q^25 + 24 * q^26 - 58 * q^28 - 70 * q^30 - 38 * q^32 + 8 * q^33 + 72 * q^36 - 44 * q^37 + 56 * q^38 + 50 * q^40 + 108 * q^41 - 72 * q^42 - 4 * q^45 - 4 * q^46 - 94 * q^48 - 56 * q^50 - 50 * q^52 - 16 * q^53 - 32 * q^56 - 112 * q^57 + 68 * q^58 + 136 * q^60 + 8 * q^61 + 2 * q^62 - 48 * q^65 + 16 * q^66 - 16 * q^68 - 48 * q^70 - 42 * q^72 - 20 * q^73 - 12 * q^76 + 72 * q^77 + 100 * q^78 + 72 * q^80 - 52 * q^81 + 12 * q^82 - 32 * q^85 - 20 * q^86 - 38 * q^88 - 50 * q^90 + 8 * q^92 + 24 * q^93 + 44 * q^96 - 56 * q^97 + 122 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.530735	−	1.31085i	−0.375287	−	0.926909i
$2$	−0.530735	−	1.31085i	−0.375287	−	0.926909i
$3$	−0.00659099	+	0.00659099i	−0.00380531	+	0.00380531i	−0.709007	−	0.705202i	$-0.750856\pi$
$3$	−0.00659099	+	0.00659099i	−0.00380531	+	0.00380531i	0.705202	+	0.709007i	$0.250856\pi$
$4$	−1.43664	+	1.39143i	−0.718320	+	0.695713i
$5$	−1.13558	−	1.92625i	−0.507848	−	0.861447i
$5$	−1.13558	−	1.92625i	−0.507848	−	0.861447i
$6$	0.0121378	+	0.00514171i	0.00495525	+	0.00209909i
$7$	−1.72131	−	1.72131i	−0.650593	−	0.650593i	0.302542	−	0.953136i	$-0.402165\pi$
$7$	−1.72131	−	1.72131i	−0.650593	−	0.650593i	−0.953136	+	0.302542i	$0.902165\pi$
$8$	2.58642	+	1.14474i	0.914438	+	0.404726i
$9$			2.99991i			0.999971i
$10$	−1.92233	+	2.51091i	−0.607894	+	0.794018i
$11$			4.72534i			1.42474i	0.701803	+	0.712371i	$0.252379\pi$
$11$			4.72534i			1.42474i	−0.701803	+	0.712371i	$0.747621\pi$
$12$	0.000298009	−	0.0186397i	8.60277e−5	−	0.00538083i
$13$	3.18457	+	3.18457i	0.883242	+	0.883242i	0.993863	−	0.110621i	$-0.0352840\pi$
$13$	3.18457	+	3.18457i	0.883242	+	0.883242i	−0.110621	+	0.993863i	$0.535284\pi$
$14$	−1.34281	+	3.16993i	−0.358882	+	0.847200i
$15$	0.0201805	+	0.00521130i	0.00521059	+	0.00134555i
$16$	0.127870	−	3.99796i	0.0319675	−	0.999489i
$17$	4.36940	−	4.36940i	1.05974	−	1.05974i	0.0616368	−	0.998099i	$-0.480368\pi$
$17$	4.36940	−	4.36940i	1.05974	−	1.05974i	0.998099	−	0.0616368i	$-0.0196320\pi$
$18$	3.93243	−	1.59216i	0.926882	−	0.375276i
$19$	1.01431			0.232699			0.116350	−	0.993208i	$-0.462881\pi$
$19$	1.01431			0.232699			0.116350	+	0.993208i	$0.462881\pi$
$20$	4.31166	+	1.18725i	0.964117	+	0.265478i
$21$	0.0226902			0.00495142
$22$	6.19419	−	2.50790i	1.32061	−	0.534687i
$23$	1.07960	−	1.07960i	0.225112	−	0.225112i	−0.585535	−	0.810647i	$-0.699116\pi$
$23$	1.07960	−	1.07960i	0.225112	−	0.225112i	0.810647	+	0.585535i	$0.199116\pi$
$24$	−0.0245920	+	0.00950212i	−0.00501982	+	0.00193961i
$25$	−2.42090	+	4.37484i	−0.484180	+	0.874968i
$26$	2.48432	−	5.86465i	0.487216	−	1.15015i
$27$	−0.0395453	−	0.0395453i	−0.00761050	−	0.00761050i
$28$	4.86797	+	0.0778282i	0.919960	+	0.0147082i
$29$			3.58169i			0.665103i	0.943085	+	0.332551i	$0.107909\pi$
$29$			3.58169i			0.665103i	−0.943085	+	0.332551i	$0.892091\pi$
$30$	−0.00387930	−	0.0292194i	−0.000708260	−	0.00533471i
$31$		−	8.10943i		−	1.45650i	−0.685314	−	0.728248i	$-0.740335\pi$
$31$		−	8.10943i		−	1.45650i	0.685314	−	0.728248i	$-0.259665\pi$
$32$	−5.30857	+	1.95424i	−0.938432	+	0.345464i
$33$	−0.0311446	−	0.0311446i	−0.00542158	−	0.00542158i
$34$	−8.04661	−	3.40862i	−1.37998	−	0.584574i
$35$	−1.36099	+	5.27036i	−0.230049	+	0.890854i
$36$	−4.17416	−	4.30980i	−0.695693	−	0.718299i
$37$	4.37809	−	4.37809i	0.719754	−	0.719754i	−0.248801	−	0.968555i	$-0.580036\pi$
$37$	4.37809	−	4.37809i	0.719754	−	0.719754i	0.968555	+	0.248801i	$0.0800365\pi$
$38$	−0.538331	−	1.32961i	−0.0873289	−	0.215691i
$39$	−0.0419789			−0.00672201
$40$	−0.732044	−	6.28205i	−0.115746	−	0.993279i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	−0.0120425	−	0.0297434i	−0.00185820	−	0.00458951i
$43$	−2.02742	+	2.02742i	−0.309178	+	0.309178i	−0.844591	−	0.535413i	$-0.820156\pi$
$43$	−2.02742	+	2.02742i	−0.309178	+	0.309178i	0.535413	+	0.844591i	$0.320156\pi$
$44$	−6.57495	−	6.78861i	−0.991211	−	1.02342i
$45$	5.77859	−	3.40665i	0.861422	−	0.507833i
$46$	−1.98817	−	0.842209i	−0.293140	−	0.124177i
$47$	4.94300	+	4.94300i	0.721010	+	0.721010i	0.968811	−	0.247801i	$-0.0797078\pi$
$47$	4.94300	+	4.94300i	0.721010	+	0.721010i	−0.247801	+	0.968811i	$0.579708\pi$
$48$	0.0255077	+	0.0271933i	0.00368172	+	0.00392501i
$49$		−	1.07420i		−	0.153456i
$50$	7.01961	+	0.851550i	0.992722	+	0.120427i
$51$			0.0575973i			0.00806524i
$52$	−9.00618	−	0.143989i	−1.24893	−	0.0199677i
$53$	−2.72534	−	2.72534i	−0.374354	−	0.374354i	0.494706	−	0.869060i	$-0.335276\pi$
$53$	−2.72534	−	2.72534i	−0.374354	−	0.374354i	−0.869060	+	0.494706i	$0.835276\pi$
$54$	−0.0308498	+	0.0728260i	−0.00419812	+	0.00991036i
$55$	9.10219	−	5.36601i	1.22734	−	0.723553i
$56$	−2.48158	−	6.42247i	−0.331616	−	0.858239i
$57$	−0.00668532	+	0.00668532i	−0.000885492	+	0.000885492i
$58$	4.69505	−	1.90093i	0.616490	−	0.249604i
$59$	2.91973			0.380116			0.190058	−	0.981773i	$-0.439132\pi$
$59$	2.91973			0.380116			0.190058	+	0.981773i	$0.439132\pi$
$60$	−0.0362433	+	0.0205929i	−0.00467899	+	0.00265854i
$61$	14.1650			1.81365			0.906823	−	0.421513i	$-0.138501\pi$
$61$	14.1650			1.81365			0.906823	+	0.421513i	$0.138501\pi$
$62$	−10.6302	+	4.30396i	−1.35004	+	0.546603i
$63$	5.16378	−	5.16378i	0.650575	−	0.650575i
$64$	5.37915	+	5.92154i	0.672394	+	0.740193i
$65$	2.51795	−	9.75064i	0.312313	−	1.20942i
$66$	−0.0242963	+	0.0573554i	−0.00299067	+	0.00705996i
$67$	6.79119	+	6.79119i	0.829676	+	0.829676i	0.987472	−	0.157796i	$-0.0504387\pi$
$67$	6.79119	+	6.79119i	0.829676	+	0.829676i	−0.157796	+	0.987472i	$0.550439\pi$
$68$	−0.197561	+	12.3570i	−0.0239577	+	1.49850i
$69$			0.0142313i			0.00171324i
$70$	7.63097	−	1.01312i	0.912075	−	0.121091i
$71$			14.7741i			1.75337i	0.481069	+	0.876683i	$0.340249\pi$
$71$			14.7741i			1.75337i	−0.481069	+	0.876683i	$0.659751\pi$
$72$	−3.43411	+	7.75904i	−0.404714	+	0.914412i
$73$	3.00629	+	3.00629i	0.351859	+	0.351859i	0.860801	−	0.508942i	$-0.169963\pi$
$73$	3.00629	+	3.00629i	0.351859	+	0.351859i	−0.508942	+	0.860801i	$0.669963\pi$
$74$	−8.06262	−	3.41540i	−0.937260	−	0.397032i
$75$	−0.0128784	−	0.0447906i	−0.00148707	−	0.00517198i
$76$	−1.45720	+	1.41134i	−0.167153	+	0.161892i
$77$	8.13376	−	8.13376i	0.926928	−	0.926928i
$78$	0.0222797	+	0.0550280i	0.00252268	+	0.00623069i
$79$	6.69329			0.753054			0.376527	−	0.926406i	$-0.377118\pi$
$79$	6.69329			0.753054			0.376527	+	0.926406i	$0.377118\pi$
$80$	−7.84628	+	4.29370i	−0.877241	+	0.480050i
$81$	−8.99922			−0.999913
$82$	−0.530735	−	1.31085i	−0.0586099	−	0.144759i
$83$	7.11710	−	7.11710i	0.781203	−	0.781203i	−0.198831	−	0.980034i	$-0.563714\pi$
$83$	7.11710	−	7.11710i	0.781203	−	0.781203i	0.980034	+	0.198831i	$0.0637144\pi$
$84$	−0.0325977	+	0.0315718i	−0.00355670	+	0.00344476i
$85$	−13.3784	−	3.45475i	−1.45109	−	0.374721i
$86$	3.73365	+	1.58161i	0.402610	+	0.170550i
$87$	−0.0236069	−	0.0236069i	−0.00253092	−	0.00253092i
$88$	−5.40927	+	12.2217i	−0.576630	+	1.30284i
$89$		−	0.0121741i		−	0.00129045i	−1.00000		0.000645227i	$-0.999795\pi$
$89$		−	0.0121741i		−	0.00129045i	1.00000		0.000645227i	$-0.000205382\pi$
$90$	−7.53250	−	5.76682i	−0.793995	−	0.607876i
$91$		−	10.9633i		−	1.14926i
$92$	−0.0488137	+	3.05318i	−0.00508918	+	0.318316i
$93$	0.0534491	+	0.0534491i	0.00554242	+	0.00554242i
$94$	3.85609	−	9.10294i	0.397725	−	0.938896i
$95$	−1.15184	−	1.95382i	−0.118176	−	0.200458i
$96$	0.0221084	−	0.0478691i	0.00225643	−	0.00488562i
$97$	−10.4916	+	10.4916i	−1.06526	+	1.06526i	−0.0675478	+	0.997716i	$0.521518\pi$
$97$	−10.4916	+	10.4916i	−1.06526	+	1.06526i	−0.997716	+	0.0675478i	$0.978482\pi$
$98$	−1.40811	+	0.570113i	−0.142240	+	0.0575901i
$99$	−14.1756			−1.42470
$100$	−2.60930	−	9.65358i	−0.260930	−	0.965358i
$101$	−6.93633			−0.690191			−0.345096	−	0.938568i	$-0.612153\pi$
$101$	−6.93633			−0.690191			−0.345096	+	0.938568i	$0.612153\pi$
$102$	0.0755013	−	0.0305689i	0.00747574	−	0.00302677i
$103$	8.75999	−	8.75999i	0.863147	−	0.863147i	−0.128555	−	0.991702i	$-0.541034\pi$
$103$	8.75999	−	8.75999i	0.863147	−	0.863147i	0.991702	+	0.128555i	$0.0410339\pi$
$104$	4.59115	+	11.8821i	0.450199	+	1.16514i
$105$	−0.0257666	−	0.0437071i	−0.00251457	−	0.00426538i
$106$	−2.12607	+	5.01894i	−0.206502	+	0.487482i
$107$	11.4562	+	11.4562i	1.10751	+	1.10751i	0.993477	+	0.114036i	$0.0363780\pi$
$107$	11.4562	+	11.4562i	1.10751	+	1.10751i	0.114036	+	0.993477i	$0.463622\pi$
$108$	0.111837	+	0.00178803i	0.0107615	+	0.000172053i
$109$		−	15.6072i		−	1.49490i	−0.664319	−	0.747449i	$-0.731278\pi$
$109$		−	15.6072i		−	1.49490i	0.664319	−	0.747449i	$-0.268722\pi$
$110$	−11.8649	−	9.08365i	−1.13127	−	0.866092i
$111$			0.0577119i			0.00547777i
$112$	−7.10182	+	6.66161i	−0.671059	+	0.629463i
$113$	−4.50069	−	4.50069i	−0.423390	−	0.423390i	0.462979	−	0.886369i	$-0.346780\pi$
$113$	−4.50069	−	4.50069i	−0.423390	−	0.423390i	−0.886369	+	0.462979i	$0.846780\pi$
$114$	0.0123116	+	0.00521530i	0.00115308	+	0.000488457i
$115$	−3.30556	−	0.853607i	−0.308245	−	0.0795993i
$116$	−4.98365	−	5.14560i	−0.462721	−	0.477757i
$117$	−9.55344	+	9.55344i	−0.883216	+	0.883216i
$118$	−1.54960	−	3.82732i	−0.142652	−	0.352333i
$119$	−15.0422			−1.37891
$120$	0.0462298	+	0.0365800i	0.00422018	+	0.00333928i
$121$	−11.3288			−1.02989
$122$	−7.51788	−	18.5682i	−0.680637	−	1.68108i
$123$	−0.00659099	+	0.00659099i	−0.000594289	+	0.000594289i
$124$	11.2837	+	11.6503i	1.01330	+	1.04623i
$125$	11.1762	−	0.304724i	0.999629	−	0.0272554i
$126$	−9.50952	−	4.02832i	−0.847175	−	0.358871i
$127$	6.25233	+	6.25233i	0.554804	+	0.554804i	0.927824	−	0.373019i	$-0.121677\pi$
$127$	6.25233	+	6.25233i	0.554804	+	0.554804i	−0.373019	+	0.927824i	$0.621677\pi$
$128$	4.90733	−	10.1940i	0.433751	−	0.901033i
$129$		−	0.0267253i		−	0.00235304i
$130$	−14.1180	+	1.87437i	−1.23823	+	0.164393i
$131$			14.9773i			1.30857i	0.756248	+	0.654285i	$0.227030\pi$
$131$			14.9773i			1.30857i	−0.756248	+	0.654285i	$0.772970\pi$
$132$	0.0880790	+	0.00140819i	0.00766629	+	0.000122567i
$133$	−1.74594	−	1.74594i	−0.151393	−	0.151393i
$134$	5.29789	−	12.5065i	0.457668	−	1.08040i
$135$	−0.0312673	+	0.121081i	−0.00269106	+	0.0104210i
$136$	16.3029	−	6.29930i	1.39796	−	0.540160i
$137$	−8.57752	+	8.57752i	−0.732827	+	0.732827i	−0.971179	−	0.238352i	$-0.923393\pi$
$137$	−8.57752	+	8.57752i	−0.732827	+	0.732827i	0.238352	+	0.971179i	$0.423393\pi$
$138$	0.0186550	−	0.00755303i	0.00158802	−	0.000642957i
$139$	6.21163			0.526864			0.263432	−	0.964678i	$-0.415146\pi$
$139$	6.21163			0.526864			0.263432	+	0.964678i	$0.415146\pi$
$140$	−5.37807	−	9.46533i	−0.454530	−	0.799966i
$141$	−0.0651585			−0.00548733
$142$	19.3666	−	7.84115i	1.62521	−	0.658014i
$143$	−15.0482	+	15.0482i	−1.25839	+	1.25839i
$144$	11.9935	+	0.383598i	0.999460	+	0.0319665i
$145$	6.89924	−	4.06730i	0.572951	−	0.337771i
$146$	2.34524	−	5.53633i	0.194094	−	0.458190i
$147$	0.00708000	+	0.00708000i	0.000583949	+	0.000583949i
$148$	−0.197954	+	12.3815i	−0.0162717	+	1.01776i
$149$			8.04686i			0.659224i	0.944116	+	0.329612i	$0.106918\pi$
$149$			8.04686i			0.659224i	−0.944116	+	0.329612i	$0.893082\pi$
$150$	−0.0518787	+	0.0406536i	−0.00423588	+	0.00331935i
$151$			17.8088i			1.44926i	0.689140	+	0.724628i	$0.257988\pi$
$151$			17.8088i			1.44926i	−0.689140	+	0.724628i	$0.742012\pi$
$152$	2.62344	+	1.16112i	0.212789	+	0.0941793i
$153$	13.1078	+	13.1078i	1.05970	+	1.05970i
$154$	−14.9790	−	6.34524i	−1.20704	−	0.511314i
$155$	−15.6208	+	9.20893i	−1.25469	+	0.739679i
$156$	0.0603086	−	0.0584106i	0.00482856	−	0.00467659i
$157$	11.8246	−	11.8246i	0.943708	−	0.943708i	−0.0547899	−	0.998498i	$-0.517449\pi$
$157$	11.8246	−	11.8246i	0.943708	−	0.943708i	0.998498	+	0.0547899i	$0.0174489\pi$
$158$	−3.55237	−	8.77388i	−0.282611	−	0.698013i
$159$	0.0359254			0.00284907
$160$	9.79268	+	8.00646i	0.774180	+	0.632966i
$161$	−3.71665			−0.292913
$162$	4.77620	+	11.7966i	0.375254	+	0.926828i
$163$	2.93394	−	2.93394i	0.229804	−	0.229804i	−0.582807	−	0.812611i	$-0.698046\pi$
$163$	2.93394	−	2.93394i	0.229804	−	0.229804i	0.812611	+	0.582807i	$0.198046\pi$
$164$	−1.43664	+	1.39143i	−0.112183	+	0.108652i
$165$	−0.0246251	+	0.0953597i	−0.00191706	+	0.00742374i
$166$	−13.1067	−	5.55213i	−1.01728	−	0.430929i
$167$	−4.35719	−	4.35719i	−0.337169	−	0.337169i	0.518132	−	0.855301i	$-0.326628\pi$
$167$	−4.35719	−	4.35719i	−0.337169	−	0.337169i	−0.855301	+	0.518132i	$0.826628\pi$
$168$	0.0586865	+	0.0259744i	0.00452776	+	0.00200396i
$169$			7.28301i			0.560231i
$170$	2.57173	+	19.3706i	0.197243	+	1.48566i
$171$			3.04285i			0.232693i
$172$	0.0916688	−	5.73367i	0.00698968	−	0.437188i
$173$	−9.63563	−	9.63563i	−0.732583	−	0.732583i	0.238548	−	0.971131i	$-0.423329\pi$
$173$	−9.63563	−	9.63563i	−0.732583	−	0.732583i	−0.971131	+	0.238548i	$0.923329\pi$
$174$	−0.0184160	+	0.0434740i	−0.00139611	+	0.00329575i
$175$	11.6976	−	3.36333i	0.884253	−	0.254244i
$176$	18.8917	+	0.604228i	1.42401	+	0.0455454i
$177$	−0.0192439	+	0.0192439i	−0.00144646	+	0.00144646i
$178$	−0.0159584	+	0.00646124i	−0.00119613	+	0.000484290i
$179$	−24.6577			−1.84300			−0.921501	−	0.388377i	$-0.873036\pi$
$179$	−24.6577			−1.84300			−0.921501	+	0.388377i	$0.873036\pi$
$180$	−3.56166	+	12.9346i	−0.265470	+	0.964089i
$181$	16.6408			1.23690			0.618449	−	0.785825i	$-0.287761\pi$
$181$	16.6408			1.23690			0.618449	+	0.785825i	$0.287761\pi$
$182$	−14.3712	+	5.81859i	−1.06526	+	0.431303i
$183$	−0.0933614	+	0.0933614i	−0.00690148	+	0.00690148i
$184$	4.02816	−	1.55644i	0.296960	−	0.114742i
$185$	−13.4050	−	3.46163i	−0.985555	−	0.254504i
$186$	0.0416963	−	0.0984310i	0.00305732	−	0.00721731i
$187$	20.6469	+	20.6469i	1.50985	+	1.50985i
$188$	−13.9791	−	0.223496i	−1.01953	−	0.0163001i
$189$			0.136139i			0.00990269i
$190$	−1.94984	+	2.54684i	−0.141456	+	0.184767i
$191$		−	20.9259i		−	1.51415i	−0.653331	−	0.757073i	$-0.726629\pi$
$191$		−	20.9259i		−	1.51415i	0.653331	−	0.757073i	$-0.273371\pi$
$192$	−0.0744827	−	0.00357489i	−0.00537533	−	0.000257995i
$193$	12.1931	+	12.1931i	0.877681	+	0.877681i	0.993294	−	0.115613i	$-0.0368834\pi$
$193$	12.1931	+	12.1931i	0.877681	+	0.877681i	−0.115613	+	0.993294i	$0.536883\pi$
$194$	19.3212	+	8.18465i	1.38718	+	0.587623i
$195$	0.0476706	+	0.0808621i	0.00341376	+	0.00579065i
$196$	1.49466	+	1.54323i	0.106762	+	0.110231i
$197$	−3.76984	+	3.76984i	−0.268590	+	0.268590i	−0.828532	−	0.559942i	$-0.810823\pi$
$197$	−3.76984	+	3.76984i	−0.268590	+	0.268590i	0.559942	+	0.828532i	$0.310823\pi$
$198$	7.52349	+	18.5820i	0.534671	+	1.32057i
$199$	−12.5618			−0.890484			−0.445242	−	0.895410i	$-0.646882\pi$
$199$	−12.5618			−0.890484			−0.445242	+	0.895410i	$0.646882\pi$
$200$	−11.2695	+	8.54389i	−0.796875	+	0.604144i
$201$	−0.0895213			−0.00631435
$202$	3.68136	+	9.09247i	0.259019	+	0.639744i
$203$	6.16519	−	6.16519i	0.432712	−	0.432712i
$204$	−0.0801424	−	0.0827466i	−0.00561109	−	0.00579342i
$205$	−1.13558	−	1.92625i	−0.0793126	−	0.134535i
$206$	−16.1322	−	6.83377i	−1.12399	−	0.476131i
$207$	3.23871	+	3.23871i	0.225106	+	0.225106i
$208$	13.1390	−	12.3246i	0.911025	−	0.854555i
$209$			4.79297i			0.331536i
$210$	−0.0436181	+	0.0569731i	−0.00300994	+	0.00393151i
$211$		−	20.0959i		−	1.38346i	−0.722157	−	0.691729i	$-0.756849\pi$
$211$		−	20.0959i		−	1.38346i	0.722157	−	0.691729i	$-0.243151\pi$
$212$	7.70744	+	0.123225i	0.529349	+	0.00846314i
$213$	−0.0973760	−	0.0973760i	−0.00667209	−	0.00667209i
$214$	8.93712	−	21.0975i	0.610929	−	1.44220i
$215$	6.20762	+	1.60302i	0.423356	+	0.109325i
$216$	−0.0570119	−	0.147550i	−0.00387917	−	0.0100395i
$217$	−13.9588	+	13.9588i	−0.947587	+	0.947587i
$218$	−20.4586	+	8.28329i	−1.38563	+	0.561015i
$219$	−0.0396288			−0.00267787
$220$	−5.61017	+	20.3740i	−0.378238	+	1.37362i
$221$	27.8294			1.87200
$222$	0.0756514	−	0.0306297i	0.00507739	−	0.00205573i
$223$	−2.18647	+	2.18647i	−0.146417	+	0.146417i	−0.776515	−	0.630098i	$-0.783015\pi$
$223$	−2.18647	+	2.18647i	−0.146417	+	0.146417i	0.630098	+	0.776515i	$0.283015\pi$
$224$	12.5015	+	5.77385i	0.835294	+	0.385781i
$225$	−13.1241	−	7.26250i	−0.874943	−	0.484166i
$226$	−3.51104	+	8.28840i	−0.233551	+	0.551336i
$227$	7.64226	+	7.64226i	0.507235	+	0.507235i	0.913677	−	0.406442i	$-0.133231\pi$
$227$	7.64226	+	7.64226i	0.507235	+	0.507235i	−0.406442	+	0.913677i	$0.633231\pi$
$228$	0.000302274	−	0.0189065i	2.00186e−5	−	0.00125211i
$229$		−	7.62451i		−	0.503842i	−0.967748	−	0.251921i	$-0.918938\pi$
$229$		−	7.62451i		−	0.503842i	0.967748	−	0.251921i	$-0.0810623\pi$
$230$	0.635428	+	4.78612i	0.0418989	+	0.315587i
$231$			0.107219i			0.00705449i
$232$	−4.10009	+	9.26376i	−0.269184	+	0.608195i
$233$	2.90969	+	2.90969i	0.190620	+	0.190620i	0.795964	−	0.605344i	$-0.206964\pi$
$233$	2.90969	+	2.90969i	0.190620	+	0.190620i	−0.605344	+	0.795964i	$0.706964\pi$
$234$	17.5934	+	7.45275i	1.15012	+	0.487202i
$235$	3.90828	−	15.1346i	0.254948	−	0.987276i
$236$	−4.19460	+	4.06258i	−0.273045	+	0.264452i
$237$	−0.0441154	+	0.0441154i	−0.00286560	+	0.00286560i
$238$	7.98341	+	19.7180i	0.517488	+	1.27813i
$239$	−10.8750			−0.703445			−0.351723	−	0.936104i	$-0.614404\pi$
$239$	−10.8750			−0.703445			−0.351723	+	0.936104i	$0.614404\pi$
$240$	0.0234150	−	0.0800144i	0.00151143	−	0.00516491i
$241$	−12.0958			−0.779159			−0.389579	−	0.920993i	$-0.627380\pi$
$241$	−12.0958			−0.779159			−0.389579	+	0.920993i	$0.627380\pi$
$242$	6.01259	+	14.8503i	0.386504	+	0.954615i
$243$	0.177950	−	0.177950i	0.0114155	−	0.0114155i
$244$	−20.3500	+	19.7096i	−1.30278	+	1.26178i
$245$	−2.06917	+	1.21984i	−0.132195	+	0.0779326i
$246$	0.0121378	+	0.00514171i	0.000773881	+	0.000327823i
$247$	3.23015	+	3.23015i	0.205530	+	0.205530i
$248$	9.28316	−	20.9744i	0.589481	−	1.33188i
$249$			0.0938174i			0.00594543i
$250$	−6.33104	−	14.4885i	−0.400410	−	0.916336i
$251$		−	14.4938i		−	0.914842i	−0.889250	−	0.457421i	$-0.848773\pi$
$251$		−	14.4938i		−	0.914842i	0.889250	−	0.457421i	$-0.151227\pi$
$252$	−0.233478	+	14.6035i	−0.0147077	+	0.919934i
$253$	5.10147	+	5.10147i	0.320727	+	0.320727i
$254$	4.87751	−	11.5142i	0.306042	−	0.722464i
$255$	0.110947	−	0.0654065i	0.00694777	−	0.00409592i
$256$	−15.9673	−	1.02244i	−0.997956	−	0.0639022i
$257$	−1.43900	+	1.43900i	−0.0897622	+	0.0897622i	−0.750562	−	0.660800i	$-0.770217\pi$
$257$	−1.43900	+	1.43900i	−0.0897622	+	0.0897622i	0.660800	+	0.750562i	$0.270217\pi$
$258$	−0.0350328	+	0.0141841i	−0.00218105	+	0.000883062i
$259$	−15.0721			−0.936534
$260$	9.94991	+	17.5117i	0.617067	+	1.08603i
$261$	−10.7448			−0.665084
$262$	19.6329	−	7.94897i	1.21293	−	0.491089i
$263$	−9.21669	+	9.21669i	−0.568326	+	0.568326i	−0.931659	−	0.363334i	$-0.881639\pi$
$263$	−9.21669	+	9.21669i	−0.568326	+	0.568326i	0.363334	+	0.931659i	$0.381639\pi$
$264$	−0.0449007	−	0.116206i	−0.00276345	−	0.00715195i
$265$	−2.15485	+	8.34455i	−0.132371	+	0.512601i
$266$	−1.36203	+	3.21530i	−0.0835115	+	0.197143i
$267$	8.02395e−5	0	8.02395e-5i	4.91058e−6	0	4.91058e-6i
$268$	−19.2059	−	0.307061i	−1.17319	−	0.0187567i
$269$			28.6499i			1.74681i	0.486991	+	0.873407i	$0.338094\pi$
$269$			28.6499i			1.74681i	−0.486991	+	0.873407i	$0.661906\pi$
$270$	0.175314	−	0.0232755i	0.0106693	−	0.00141650i
$271$			23.1779i			1.40796i	0.710220	+	0.703979i	$0.248595\pi$
$271$			23.1779i			1.40796i	−0.710220	+	0.703979i	$0.751405\pi$
$272$	−16.9100	−	18.0274i	−1.02532	−	1.09307i
$273$	0.0722587	+	0.0722587i	0.00437330	+	0.00437330i
$274$	15.7962	+	6.69143i	0.954284	+	0.404244i
$275$	−20.6726	−	11.4396i	−1.24660	−	0.689832i
$276$	−0.0198017	−	0.0204452i	−0.00119192	−	0.00123066i
$277$	11.8341	−	11.8341i	0.711041	−	0.711041i	−0.255712	−	0.966753i	$-0.582310\pi$
$277$	11.8341	−	11.8341i	0.711041	−	0.711041i	0.966753	+	0.255712i	$0.0823098\pi$
$278$	−3.29673	−	8.14250i	−0.197725	−	0.488355i
$279$	24.3276			1.45645
$280$	−9.55327	+	12.0734i	−0.570917	+	0.721524i
$281$	0.0358380			0.00213791			0.00106896	−	0.999999i	$-0.499660\pi$
$281$	0.0358380			0.00213791			0.00106896	+	0.999999i	$0.499660\pi$
$282$	0.0345819	+	0.0854128i	0.00205932	+	0.00508626i
$283$	3.90224	−	3.90224i	0.231964	−	0.231964i	−0.581548	−	0.813512i	$-0.697553\pi$
$283$	3.90224	−	3.90224i	0.231964	−	0.231964i	0.813512	+	0.581548i	$0.197553\pi$
$284$	−20.5571	−	21.2251i	−1.21984	−	1.25948i
$285$	0.0204694	+	0.00528588i	0.00121250	+	0.000313109i
$286$	27.7125	+	11.7393i	1.63867	+	0.694157i
$287$	−1.72131	−	1.72131i	−0.101606	−	0.101606i
$288$	−5.86255	−	15.9253i	−0.345454	−	0.938405i
$289$		−	21.1833i		−	1.24608i
$290$	−8.99328	−	6.88518i	−0.528104	−	0.404312i
$291$		−	0.138300i		−	0.00810731i
$292$	−8.50198	−	0.135928i	−0.497541	−	0.00795459i
$293$	−4.18576	−	4.18576i	−0.244535	−	0.244535i	0.574189	−	0.818723i	$-0.305318\pi$
$293$	−4.18576	−	4.18576i	−0.244535	−	0.244535i	−0.818723	+	0.574189i	$0.805318\pi$
$294$	0.00552319	−	0.0130384i	0.000322119	−	0.000760416i
$295$	−3.31559	−	5.62413i	−0.193041	−	0.327450i
$296$	16.3354	−	6.31183i	0.949473	−	0.366868i
$297$	0.186865	−	0.186865i	0.0108430	−	0.0108430i
$298$	10.5482	−	4.27075i	0.611041	−	0.247398i
$299$	6.87613			0.397657
$300$	0.0808244	+	0.0464287i	0.00466640	+	0.00268056i
$301$	6.97962			0.402298
$302$	23.3446	−	9.45173i	1.34333	−	0.543886i
$303$	0.0457173	−	0.0457173i	0.00262639	−	0.00262639i
$304$	0.129700	−	4.05518i	0.00743880	−	0.232580i
$305$	−16.0856	−	27.2854i	−0.921056	−	1.56236i
$306$	10.2256	−	24.1391i	0.584557	−	1.37994i
$307$	−13.9352	−	13.9352i	−0.795322	−	0.795322i	0.187032	−	0.982354i	$-0.440113\pi$
$307$	−13.9352	−	13.9352i	−0.795322	−	0.795322i	−0.982354	+	0.187032i	$0.940113\pi$
$308$	−0.367765	+	23.0028i	−0.0209553	+	1.31071i
$309$			0.115474i			0.00656908i
$310$	20.3620	+	15.5890i	1.15648	+	0.885395i
$311$		−	24.3964i		−	1.38340i	−0.722187	−	0.691698i	$-0.756863\pi$
$311$		−	24.3964i		−	1.38340i	0.722187	−	0.691698i	$-0.243137\pi$
$312$	−0.108575	−	0.0480548i	−0.00614686	−	0.00272057i
$313$	−0.378763	−	0.378763i	−0.0214089	−	0.0214089i	0.696321	−	0.717730i	$-0.254819\pi$
$313$	−0.378763	−	0.378763i	−0.0214089	−	0.0214089i	−0.717730	+	0.696321i	$0.754819\pi$
$314$	−21.7760	−	9.22453i	−1.22889	−	0.520570i
$315$	−15.8106	−	4.08284i	−0.890828	−	0.230042i
$316$	−9.61585	+	9.31322i	−0.540934	+	0.523909i
$317$	−7.32532	+	7.32532i	−0.411431	+	0.411431i	−0.882237	−	0.470806i	$-0.843963\pi$
$317$	−7.32532	+	7.32532i	−0.411431	+	0.411431i	0.470806	+	0.882237i	$0.343963\pi$
$318$	−0.0190669	−	0.0470927i	−0.00106922	−	0.00264082i
$319$	−16.9247			−0.947600
$320$	5.29792	−	17.0860i	0.296163	−	0.955138i
$321$	−0.151015			−0.00842885
$322$	1.97256	+	4.87196i	0.109926	+	0.271504i
$323$	4.43194	−	4.43194i	0.246600	−	0.246600i
$324$	12.9286	−	12.5217i	0.718258	−	0.695652i
$325$	−21.6415	+	6.22246i	−1.20046	+	0.345160i
$326$	−5.40309	−	2.28880i	−0.299250	−	0.126765i
$327$	0.102867	+	0.102867i	0.00568855	+	0.00568855i
$328$	2.58642	+	1.14474i	0.142811	+	0.0632075i
$329$		−	17.0168i		−	0.938169i
$330$	0.138071	−	0.0183310i	0.00760058	−	0.00100909i
$331$			8.92643i			0.490641i	0.969442	+	0.245321i	$0.0788932\pi$
$331$			8.92643i			0.490641i	−0.969442	+	0.245321i	$0.921107\pi$
$332$	−0.321797	+	20.1276i	−0.0176609	+	1.10465i
$333$	13.1339	+	13.1339i	0.719733	+	0.719733i
$334$	−3.39909	+	8.02412i	−0.185990	+	0.439060i
$335$	5.36959	−	20.7935i	0.293372	−	1.13607i
$336$	0.00290140	−	0.0907146i	0.000158284	−	0.00494888i
$337$	−2.53778	+	2.53778i	−0.138242	+	0.138242i	−0.772841	−	0.634600i	$-0.781165\pi$
$337$	−2.53778	+	2.53778i	−0.138242	+	0.138242i	0.634600	+	0.772841i	$0.281165\pi$
$338$	9.54691	−	3.86535i	0.519283	−	0.210247i
$339$	0.0593280			0.00322225
$340$	24.0270	−	13.6518i	1.30305	−	0.740373i
$341$	38.3198			2.07513
$342$	3.98871	−	1.61495i	0.215685	−	0.0873264i
$343$	−13.8982	+	13.8982i	−0.750431	+	0.750431i
$344$	−7.56461	+	2.92290i	−0.407857	+	0.157592i
$345$	0.0274130	−	0.0161608i	0.00147587	−	0.000870067i
$346$	−7.51687	+	17.7448i	−0.404109	+	0.953966i
$347$	−1.67551	−	1.67551i	−0.0899461	−	0.0899461i	0.660702	−	0.750648i	$-0.270259\pi$
$347$	−1.67551	−	1.67551i	−0.0899461	−	0.0899461i	−0.750648	+	0.660702i	$0.770259\pi$
$348$	0.0667617	+	0.00106737i	0.00357880	+	5.72173e-5i
$349$			27.6566i			1.48043i	0.672373	+	0.740213i	$0.265275\pi$
$349$			27.6566i			1.48043i	−0.672373	+	0.740213i	$0.734725\pi$
$350$	−10.6171	−	13.5487i	−0.567509	−	0.724208i
$351$		−	0.251870i		−	0.0134438i
$352$	−9.23443	−	25.0848i	−0.492197	−	1.33702i
$353$	−2.47373	−	2.47373i	−0.131663	−	0.131663i	0.638204	−	0.769867i	$-0.279678\pi$
$353$	−2.47373	−	2.47373i	−0.131663	−	0.131663i	−0.769867	+	0.638204i	$0.779678\pi$
$354$	0.0354392	+	0.0150124i	0.00188357	+	0.000797899i
$355$	28.4587	−	16.7772i	1.51043	−	0.890443i
$356$	0.0169394	+	0.0174898i	0.000897786	+	0.000926959i
$357$	0.0991427	−	0.0991427i	0.00524719	−	0.00524719i
$358$	13.0867	+	32.3224i	0.691654	+	1.70829i
$359$	−26.5263			−1.40001			−0.700003	−	0.714140i	$-0.746818\pi$
$359$	−26.5263			−1.40001			−0.700003	+	0.714140i	$0.746818\pi$
$360$	18.8456	−	2.19607i	0.993250	−	0.115743i
$361$	−17.9712			−0.945851
$362$	−8.83183	−	21.8135i	−0.464191	−	1.14649i
$363$	0.0746679	−	0.0746679i	0.00391905	−	0.00391905i
$364$	15.2546	+	15.7503i	0.799556	+	0.825538i
$365$	2.37698	−	9.20476i	0.124417	−	0.481799i
$366$	0.171933	+	0.0728324i	0.00898707	+	0.00380701i
$367$	−2.55017	−	2.55017i	−0.133118	−	0.133118i	0.637408	−	0.770526i	$-0.280006\pi$
$367$	−2.55017	−	2.55017i	−0.133118	−	0.133118i	−0.770526	+	0.637408i	$0.780006\pi$
$368$	−4.17814	−	4.45424i	−0.217801	−	0.232193i
$369$			2.99991i			0.156169i
$370$	2.57684	+	19.4091i	0.133964	+	1.00903i
$371$			9.38230i			0.487105i
$372$	−0.151158	−	0.00241668i	−0.00783716	−	0.000125299i
$373$	−21.1488	−	21.1488i	−1.09504	−	1.09504i	−0.994981	−	0.100061i	$-0.968096\pi$
$373$	−21.1488	−	21.1488i	−1.09504	−	1.09504i	−0.100061	−	0.994981i	$-0.531904\pi$
$374$	16.1069	−	38.0229i	0.832867	−	1.96612i
$375$	−0.0716536	+	0.0756705i	−0.00370018	+	0.00390761i
$376$	7.12624	+	18.4431i	0.367508	+	0.951131i
$377$	−11.4061	+	11.4061i	−0.587446	+	0.587446i
$378$	0.178458	−	0.0722540i	0.00917889	−	0.00371635i
$379$	29.9467			1.53826			0.769130	−	0.639092i	$-0.220690\pi$
$379$	29.9467			1.53826			0.769130	+	0.639092i	$0.220690\pi$
$380$	4.37337	+	1.20425i	0.224349	+	0.0617765i
$381$	−0.0824180			−0.00422240
$382$	−27.4307	+	11.1061i	−1.40347	+	0.568238i
$383$	17.8548	−	17.8548i	0.912337	−	0.912337i	−0.0841188	−	0.996456i	$-0.526808\pi$
$383$	17.8548	−	17.8548i	0.912337	−	0.912337i	0.996456	+	0.0841188i	$0.0268075\pi$
$384$	0.0348445	+	0.0995328i	0.00177815	+	0.00507926i
$385$	−24.9042	−	6.43112i	−1.26924	−	0.327760i
$386$	9.51201	−	22.4547i	0.484148	−	1.14291i
$387$	−6.08207	−	6.08207i	−0.309169	−	0.309169i
$388$	0.474375	−	29.6710i	0.0240827	−	1.50632i
$389$			20.6434i			1.04666i	0.852129	+	0.523332i	$0.175311\pi$
$389$			20.6434i			1.04666i	−0.852129	+	0.523332i	$0.824689\pi$
$390$	0.0806974	−	0.105405i	0.00408627	−	0.00533740i
$391$		−	9.43441i		−	0.477119i
$392$	1.22967	−	2.77832i	0.0621078	−	0.140326i
$393$	−0.0987150	−	0.0987150i	−0.00497951	−	0.00497951i
$394$	6.94247	+	2.94090i	0.349757	+	0.148160i
$395$	−7.60079	−	12.8930i	−0.382437	−	0.648716i
$396$	20.3652	−	19.7243i	1.02339	−	0.991183i
$397$	1.08950	−	1.08950i	0.0546804	−	0.0546804i	−0.679238	−	0.733918i	$-0.737690\pi$
$397$	1.08950	−	1.08950i	0.0546804	−	0.0546804i	0.733918	+	0.679238i	$0.237690\pi$
$398$	6.66700	+	16.4666i	0.334187	+	0.825398i
$399$	0.0230150			0.00115219
$400$	17.1809	+	10.2381i	0.859043	+	0.511904i
$401$	3.07904			0.153760			0.0768800	−	0.997040i	$-0.475504\pi$
$401$	3.07904			0.153760			0.0768800	+	0.997040i	$0.475504\pi$
$402$	0.0475121	+	0.117349i	0.00236969	+	0.00585282i
$403$	25.8251	−	25.8251i	1.28644	−	1.28644i
$404$	9.96502	−	9.65139i	0.495778	−	0.480175i
$405$	10.2194	+	17.3348i	0.507804	+	0.861372i
$406$	−11.3537	−	4.80954i	−0.563475	−	0.238693i
$407$	20.6879	+	20.6879i	1.02546	+	1.02546i
$408$	−0.0659338	+	0.148971i	−0.00326421	+	0.00737516i
$409$		−	24.5461i		−	1.21372i	−0.794807	−	0.606862i	$-0.792428\pi$
$409$		−	24.5461i		−	1.21372i	0.794807	−	0.606862i	$-0.207572\pi$
$410$	−1.92233	+	2.51091i	−0.0949371	+	0.124005i
$411$		−	0.113069i		−	0.00557727i
$412$	−0.396079	+	24.7738i	−0.0195134	+	1.22052i
$413$	−5.02575	−	5.02575i	−0.247301	−	0.247301i
$414$	2.52655	−	5.96434i	0.124173	−	0.293132i
$415$	−21.7914	−	5.62728i	−1.06970	−	0.276232i
$416$	−23.1290	−	10.6821i	−1.13399	−	0.523734i
$417$	−0.0409408	+	0.0409408i	−0.00200488	+	0.00200488i
$418$	6.28285	−	2.54380i	0.307304	−	0.124421i
$419$	−31.9356			−1.56015			−0.780077	−	0.625683i	$-0.784820\pi$
$419$	−31.9356			−1.56015			−0.780077	+	0.625683i	$0.784820\pi$
$420$	0.0978326	+	0.0269391i	0.00477374	+	0.00131449i
$421$	14.1575			0.689995			0.344997	−	0.938604i	$-0.387880\pi$
$421$	14.1575			0.689995			0.344997	+	0.938604i	$0.387880\pi$
$422$	−26.3427	+	10.6656i	−1.28234	+	0.519193i
$423$	−14.8286	+	14.8286i	−0.720989	+	0.720989i
$424$	−3.92908	−	10.1687i	−0.190813	−	0.493835i
$425$	8.53754	+	29.6933i	0.414132	+	1.44034i
$426$	−0.0759642	+	0.179326i	−0.00368048	+	0.00868837i
$427$	−24.3824	−	24.3824i	−1.17995	−	1.17995i
$428$	−32.3989	−	0.517987i	−1.56606	−	0.0250379i
$429$		−	0.198365i		−	0.00957713i
$430$	−1.19329	−	8.98801i	−0.0575456	−	0.433441i
$431$		−	0.275508i		−	0.0132707i	−0.999978	−	0.00663537i	$-0.997888\pi$
$431$		−	0.275508i		−	0.0132707i	0.999978	−	0.00663537i	$-0.00211212\pi$
$432$	−0.163157	+	0.153044i	−0.00784990	+	0.00736333i
$433$	−18.8516	−	18.8516i	−0.905951	−	0.905951i	0.0899914	−	0.995943i	$-0.471316\pi$
$433$	−18.8516	−	18.8516i	−0.905951	−	0.905951i	−0.995943	+	0.0899914i	$0.971316\pi$
$434$	25.7063	+	10.8894i	1.23394	+	0.522710i
$435$	−0.0186652	+	0.0722803i	−0.000894930	+	0.00346558i
$436$	21.7162	+	22.4219i	1.04002	+	1.07382i
$437$	1.09505	−	1.09505i	0.0523834	−	0.0523834i
$438$	0.0210324	+	0.0519473i	0.00100497	+	0.00248214i
$439$	−26.1634			−1.24871			−0.624355	−	0.781141i	$-0.714638\pi$
$439$	−26.1634			−1.24871			−0.624355	+	0.781141i	$0.714638\pi$
$440$	29.6848	−	3.45915i	1.41517	−	0.164909i
$441$	3.22249			0.153452
$442$	−14.7700	−	36.4800i	−0.702538	−	1.73518i
$443$	18.3243	−	18.3243i	0.870612	−	0.870612i	−0.121927	−	0.992539i	$-0.538907\pi$
$443$	18.3243	−	18.3243i	0.870612	−	0.870612i	0.992539	+	0.121927i	$0.0389075\pi$
$444$	−0.0803018	−	0.0829112i	−0.00381095	−	0.00393479i
$445$	−0.0234504	+	0.0138247i	−0.00111166	+	0.000655355i
$446$	4.02657	+	1.70569i	0.190663	+	0.0807668i
$447$	−0.0530367	−	0.0530367i	−0.00250855	−	0.00250855i
$448$	0.933621	−	19.4520i	0.0441094	−	0.919020i
$449$		−	8.56026i		−	0.403984i	−0.979387	−	0.201992i	$-0.935259\pi$
$449$		−	8.56026i		−	0.403984i	0.979387	−	0.201992i	$-0.0647414\pi$
$450$	−2.55458	+	21.0582i	−0.120424	+	0.992693i
$451$			4.72534i			0.222507i
$452$	12.7283	+	0.203497i	0.598687	+	0.00957169i
$453$	−0.117377	−	0.117377i	−0.00551486	−	0.00551486i
$454$	5.96182	−	14.0739i	0.279802	−	0.660519i
$455$	−21.1180	+	12.4497i	−0.990028	+	0.583651i
$456$	−0.0249440	+	0.00963812i	−0.00116811	+	0.000451346i
$457$	12.9407	−	12.9407i	0.605341	−	0.605341i	−0.336384	−	0.941725i	$-0.609204\pi$
$457$	12.9407	−	12.9407i	0.605341	−	0.605341i	0.941725	+	0.336384i	$0.109204\pi$
$458$	−9.99456	+	4.04660i	−0.467015	+	0.189085i
$459$	−0.345579			−0.0161302
$460$	5.93663	−	3.37311i	0.276797	−	0.157272i
$461$	24.5960			1.14555			0.572776	−	0.819712i	$-0.305867\pi$
$461$	24.5960			1.14555			0.572776	+	0.819712i	$0.305867\pi$
$462$	0.140548	−	0.0569049i	0.00653887	−	0.00264746i
$463$	2.61590	−	2.61590i	0.121571	−	0.121571i	−0.643704	−	0.765275i	$-0.722603\pi$
$463$	2.61590	−	2.61590i	0.121571	−	0.121571i	0.765275	+	0.643704i	$0.222603\pi$
$464$	14.3194	+	0.457990i	0.664763	+	0.0212616i
$465$	0.0422606	−	0.163652i	0.00195979	−	0.00758920i
$466$	2.26988	−	5.35843i	0.105150	−	0.248225i
$467$	−9.80985	−	9.80985i	−0.453946	−	0.453946i	0.442716	−	0.896662i	$-0.354015\pi$
$467$	−9.80985	−	9.80985i	−0.453946	−	0.453946i	−0.896662	+	0.442716i	$0.854015\pi$
$468$	0.431955	−	27.0178i	0.0199671	−	1.24890i
$469$		−	23.3795i		−	1.07956i
$470$	−21.9135	+	2.90933i	−1.01079	+	0.134198i
$471$			0.155872i			0.00718220i
$472$	7.55165	+	3.34232i	0.347593	+	0.153843i
$473$	−9.58022	−	9.58022i	−0.440499	−	0.440499i
$474$	0.0812421	+	0.0344149i	0.00373157	+	0.00158073i
$475$	−2.45555	+	4.43746i	−0.112668	+	0.203604i
$476$	21.6102	−	20.9301i	0.990501	−	0.959328i
$477$	8.17579	−	8.17579i	0.374343	−	0.374343i
$478$	5.77175	+	14.2555i	0.263994	+	0.652030i
$479$	6.41212			0.292977			0.146489	−	0.989212i	$-0.453203\pi$
$479$	6.41212			0.292977			0.146489	+	0.989212i	$0.453203\pi$
$480$	−0.117314	+	0.0117730i	−0.00535462	+	0.000537361i
$481$	27.8847			1.27143
$482$	6.41967	+	15.8557i	0.292408	+	0.722209i
$483$	0.0244964	−	0.0244964i	0.00111462	−	0.00111462i
$484$	16.2754	−	15.7632i	0.739791	−	0.716508i
$485$	32.1237	+	8.29542i	1.45866	+	0.376676i
$486$	−0.327709	−	0.138821i	−0.0148652	−	0.00629703i
$487$	12.1968	+	12.1968i	0.552692	+	0.552692i	0.927217	−	0.374525i	$-0.122194\pi$
$487$	12.1968	+	12.1968i	0.552692	+	0.552692i	−0.374525	+	0.927217i	$0.622194\pi$
$488$	36.6367	+	16.2152i	1.65847	+	0.734029i
$489$			0.0386751i			0.00174895i
$490$	2.69720	+	2.06496i	0.121847	+	0.0932852i
$491$			12.0929i			0.545743i	0.962051	+	0.272871i	$0.0879734\pi$
$491$			12.0929i			0.545743i	−0.962051	+	0.272871i	$0.912027\pi$
$492$	0.000298009	−	0.0186397i	1.34353e−5	−	0.000840344i
$493$	15.6498	+	15.6498i	0.704833	+	0.704833i
$494$	2.51988	−	5.94859i	0.113375	−	0.267640i
$495$	16.0976	+	27.3058i	0.723532	+	1.22730i
$496$	−32.4211	−	1.03695i	−1.45575	−	0.0465605i
$497$	25.4308	−	25.4308i	1.14073	−	1.14073i
$498$	0.122980	−	0.0497922i	0.00551088	−	0.00223124i
$499$	−1.70174			−0.0761804			−0.0380902	−	0.999274i	$-0.512127\pi$
$499$	−1.70174			−0.0761804			−0.0380902	+	0.999274i	$0.512127\pi$
$500$	−15.6322	+	15.9886i	−0.699091	+	0.715032i
$501$	0.0574363			0.00256607
$502$	−18.9992	+	7.69239i	−0.847975	+	0.343328i
$503$	25.9015	−	25.9015i	1.15489	−	1.15489i	0.169331	−	0.985559i	$-0.445839\pi$
$503$	25.9015	−	25.9015i	1.15489	−	1.15489i	0.985559	−	0.169331i	$-0.0541606\pi$
$504$	19.2669	−	7.44454i	0.858214	−	0.331606i
$505$	7.87678	+	13.3611i	0.350512	+	0.594563i
$506$	3.97972	−	9.39478i	0.176920	−	0.417649i
$507$	−0.0480022	−	0.0480022i	−0.00213185	−	0.00213185i
$508$	−17.6820	−	0.282696i	−0.784512	−	0.0125426i
$509$			17.9785i			0.796883i	0.917194	+	0.398441i	$0.130449\pi$
$509$			17.9785i			0.796883i	−0.917194	+	0.398441i	$0.869551\pi$
$510$	−0.144621	−	0.110721i	−0.00640395	−	0.00490281i
$511$		−	10.3495i		−	0.457835i
$512$	7.13415	+	21.4733i	0.315288	+	0.948996i
$513$	−0.0401113	−	0.0401113i	−0.00177096	−	0.00177096i
$514$	2.65003	+	1.12258i	0.116888	+	0.0495148i
$515$	−26.8217	−	6.92626i	−1.18190	−	0.305208i
$516$	0.0371863	+	0.0383947i	0.00163704	+	0.00169023i
$517$	−23.3573	+	23.3573i	−1.02725	+	1.02725i
$518$	7.99929	+	19.7572i	0.351469	+	0.868082i
$519$	0.127017			0.00557541
$520$	17.6744	−	22.3369i	0.775073	−	0.979537i
$521$	−1.66614			−0.0729951			−0.0364975	−	0.999334i	$-0.511620\pi$
$521$	−1.66614			−0.0729951			−0.0364975	+	0.999334i	$0.511620\pi$
$522$	5.70262	+	14.0847i	0.249597	+	0.616472i
$523$	7.31301	−	7.31301i	0.319776	−	0.319776i	−0.528905	−	0.848681i	$-0.677397\pi$
$523$	7.31301	−	7.31301i	0.319776	−	0.319776i	0.848681	+	0.528905i	$0.177397\pi$
$524$	−20.8398	−	21.5170i	−0.910389	−	0.939973i
$525$	−0.0549308	+	0.0992662i	−0.00239738	+	0.00433233i
$526$	16.9733	+	7.19005i	0.740071	+	0.313501i
$527$	−35.4333	−	35.4333i	−1.54350	−	1.54350i
$528$	−0.128497	+	0.120532i	−0.00559213	+	0.00524550i
$529$			20.6689i			0.898649i
$530$	12.0821	−	1.60407i	0.524812	−	0.0696765i
$531$			8.75893i			0.380105i
$532$	4.93765	+	0.0789422i	0.214074	+	0.00342258i
$533$	3.18457	+	3.18457i	0.137939	+	0.137939i
$534$	6.25958e−5	0	0.000147768i	2.70878e−6	0	6.39453e-6i
$535$	9.05808	−	35.0770i	0.391615	−	1.51651i
$536$	9.79076	+	25.3390i	0.422896	+	1.09448i
$537$	0.162518	−	0.162518i	0.00701319	−	0.00701319i
$538$	37.5556	−	15.2055i	1.61914	−	0.655556i
$539$	5.07593			0.218636
$540$	−0.123556	−	0.217456i	−0.00531700	−	0.00935784i
$541$	−18.3162			−0.787474			−0.393737	−	0.919223i	$-0.628818\pi$
$541$	−18.3162			−0.787474			−0.393737	+	0.919223i	$0.628818\pi$
$542$	30.3827	−	12.3013i	1.30505	−	0.528388i
$543$	−0.109679	+	0.109679i	−0.00470677	+	0.00470677i
$544$	−14.6564	+	31.7341i	−0.628389	+	1.36059i
$545$	−30.0634	+	17.7233i	−1.28777	+	0.759181i
$546$	0.0563699	−	0.133070i	0.00241241	−	0.00569489i
$547$	4.65077	+	4.65077i	0.198852	+	0.198852i	0.799508	−	0.600656i	$-0.205094\pi$
$547$	4.65077	+	4.65077i	0.198852	+	0.198852i	−0.600656	+	0.799508i	$0.705094\pi$
$548$	0.387829	−	24.2578i	0.0165672	−	1.03624i
$549$			42.4938i			1.81359i
$550$	−4.02386	+	33.1700i	−0.171578	+	1.41437i
$551$			3.63295i			0.154769i
$552$	−0.0162910	+	0.0368080i	−0.000693393	+	0.00156665i
$553$	−11.5212	−	11.5212i	−0.489932	−	0.489932i
$554$	−21.7934	−	9.23191i	−0.925915	−	0.392226i
$555$	0.111168	−	0.0655366i	0.00471880	−	0.00278187i
$556$	−8.92388	+	8.64302i	−0.378457	+	0.366546i
$557$	3.74758	−	3.74758i	0.158790	−	0.158790i	−0.623240	−	0.782030i	$-0.714184\pi$
$557$	3.74758	−	3.74758i	0.158790	−	0.158790i	0.782030	+	0.623240i	$0.214184\pi$
$558$	−12.9115	−	31.8897i	−0.546588	−	1.35000i
$559$	−12.9129			−0.546158
$560$	20.8967	+	6.11509i	0.883045	+	0.258410i
$561$	−0.272167			−0.0114909
$562$	−0.0190205	−	0.0469781i	−0.000802330	−	0.00198165i
$563$	−6.28565	+	6.28565i	−0.264908	+	0.264908i	−0.827045	−	0.562136i	$-0.809980\pi$
$563$	−6.28565	+	6.28565i	−0.264908	+	0.264908i	0.562136	+	0.827045i	$0.309980\pi$
$564$	0.0936092	−	0.0906631i	0.00394166	−	0.00381761i
$565$	−3.55856	+	13.7804i	−0.149710	+	0.579745i
$566$	−7.18630	−	3.04418i	−0.302063	−	0.127957i
$567$	15.4904	+	15.4904i	0.650537	+	0.650537i
$568$	−16.9125	+	38.2121i	−0.709632	+	1.60334i
$569$			7.13936i			0.299298i	0.988739	+	0.149649i	$0.0478143\pi$
$569$			7.13936i			0.299298i	−0.988739	+	0.149649i	$0.952186\pi$
$570$	−0.00393482	−	0.0296376i	−0.000164812	−	0.00124138i
$571$			30.6446i			1.28244i	0.767358	+	0.641219i	$0.221571\pi$
$571$			30.6446i			1.28244i	−0.767358	+	0.641219i	$0.778429\pi$
$572$	0.680397	−	42.5572i	0.0284488	−	1.77941i
$573$	0.137922	+	0.137922i	0.00576179	+	0.00576179i
$574$	−1.34281	+	3.16993i	−0.0560479	+	0.132310i
$575$	2.10947	+	7.33668i	0.0879711	+	0.305961i
$576$	−17.7641	+	16.1370i	−0.740172	+	0.672375i
$577$	1.97904	−	1.97904i	0.0823887	−	0.0823887i	−0.664711	−	0.747100i	$-0.731446\pi$
$577$	1.97904	−	1.97904i	0.0823887	−	0.0823887i	0.747100	+	0.664711i	$0.231446\pi$
$578$	−27.7681	+	11.2427i	−1.15500	+	0.467636i
$579$	−0.160730			−0.00667969
$580$	−4.25237	+	15.4430i	−0.176570	+	0.641237i
$581$	−24.5014			−1.01649
$582$	−0.181291	+	0.0734009i	−0.00751474	+	0.00304256i
$583$	12.8781	−	12.8781i	0.533358	−	0.533358i
$584$	4.33412	+	11.2169i	0.179347	+	0.464160i
$585$	29.2511	+	7.55362i	1.20938	+	0.312304i
$586$	−3.26536	+	7.70842i	−0.134891	+	0.318432i
$587$	14.9811	+	14.9811i	0.618338	+	0.618338i	0.945105	−	0.326767i	$-0.105959\pi$
$587$	14.9811	+	14.9811i	0.618338	+	0.618338i	−0.326767	+	0.945105i	$0.605959\pi$
$588$	−0.0200227		0.000320119i	−0.000825723		1.32015e-5i
$589$		−	8.22549i		−	0.338926i
$590$	−5.61268	+	7.33116i	−0.231070	+	0.301819i
$591$		−	0.0496939i		−	0.00204413i
$592$	−16.9436	−	18.0632i	−0.696377	−	0.742395i
$593$	−18.5219	−	18.5219i	−0.760602	−	0.760602i	0.215829	−	0.976431i	$-0.430755\pi$
$593$	−18.5219	−	18.5219i	−0.760602	−	0.760602i	−0.976431	+	0.215829i	$0.930755\pi$
$594$	−0.344127	−	0.145776i	−0.0141197	−	0.00598124i
$595$	17.0816	+	28.9750i	0.700279	+	1.18786i
$596$	−11.1966	−	11.5604i	−0.458631	−	0.473534i
$597$	0.0827948	−	0.0827948i	0.00338857	−	0.00338857i
$598$	−3.64940	−	9.01355i	−0.149235	−	0.368592i
$599$	5.76850			0.235694			0.117847	−	0.993032i	$-0.462401\pi$
$599$	5.76850			0.235694			0.117847	+	0.993032i	$0.462401\pi$
$600$	0.0179646	−	0.130590i	0.000733401	−	0.00533131i
$601$	−6.84895			−0.279374			−0.139687	−	0.990196i	$-0.544610\pi$
$601$	−6.84895			−0.279374			−0.139687	+	0.990196i	$0.544610\pi$
$602$	−3.70433	−	9.14921i	−0.150977	−	0.372894i
$603$	−20.3730	+	20.3730i	−0.829652	+	0.829652i
$604$	−24.7796	−	25.5848i	−1.00827	−	1.04103i
$605$	12.8648	+	21.8221i	0.523028	+	0.887196i
$606$	−0.0841921	−	0.0356646i	−0.00342007	−	0.00144878i
$607$	−26.0931	−	26.0931i	−1.05909	−	1.05909i	−0.998141	−	0.0609453i	$-0.980588\pi$
$607$	−26.0931	−	26.0931i	−1.05909	−	1.05909i	−0.0609453	−	0.998141i	$-0.519412\pi$
$608$	−5.38455	+	1.98221i	−0.218372	+	0.0803892i
$609$			0.0812694i			0.00329320i
$610$	−27.2298	+	35.5670i	−1.10250	+	1.44007i
$611$			31.4827i			1.27365i
$612$	−37.0698	−	0.592665i	−1.49846	−	0.0239571i
$613$	−6.25013	−	6.25013i	−0.252440	−	0.252440i	0.569530	−	0.821970i	$-0.307125\pi$
$613$	−6.25013	−	6.25013i	−0.252440	−	0.252440i	−0.821970	+	0.569530i	$0.807125\pi$
$614$	−10.8710	+	25.6628i	−0.438718	+	1.03567i
$615$	0.0201805	+	0.00521130i	0.000813757	+	0.000210140i
$616$	30.3483	−	11.7263i	1.22277	−	0.472467i
$617$	4.37662	−	4.37662i	0.176196	−	0.176196i	−0.613499	−	0.789695i	$-0.710239\pi$
$617$	4.37662	−	4.37662i	0.176196	−	0.176196i	0.789695	+	0.613499i	$0.210239\pi$
$618$	0.151369	−	0.0612861i	0.00608894	−	0.00246529i
$619$	−7.78672			−0.312975			−0.156487	−	0.987680i	$-0.550017\pi$
$619$	−7.78672			−0.312975			−0.156487	+	0.987680i	$0.550017\pi$
$620$	9.62794	−	34.9651i	0.386668	−	1.40423i
$621$	−0.0853863			−0.00342643
$622$	−31.9800	+	12.9481i	−1.28228	+	0.519170i
$623$	−0.0209554	+	0.0209554i	−0.000839561	+	0.000839561i
$624$	−0.00536784	+	0.167830i	−0.000214886	+	0.00671858i
$625$	−13.2785	−	21.1821i	−0.531139	−	0.847285i
$626$	−0.295477	+	0.697522i	−0.0118096	+	0.0278786i
$627$	−0.0315904	−	0.0315904i	−0.00126160	−	0.00126160i
$628$	−0.534646	+	33.4408i	−0.0213347	+	1.33443i
$629$		−	38.2593i		−	1.52550i
$630$	3.03928	+	22.8922i	0.121088	+	0.912048i
$631$		−	27.3674i		−	1.08948i	−0.838605	−	0.544740i	$-0.816628\pi$
$631$		−	27.3674i		−	1.08948i	0.838605	−	0.544740i	$-0.183372\pi$
$632$	17.3117	+	7.66206i	0.688621	+	0.304780i
$633$	0.132452	+	0.132452i	0.00526449	+	0.00526449i
$634$	13.4902	+	5.71457i	0.535763	+	0.226954i
$635$	4.94353	−	19.1436i	0.196178	−	0.759691i
$636$	−0.0516118	+	0.0499875i	−0.00204654	+	0.00198213i
$637$	3.42085	−	3.42085i	0.135539	−	0.135539i
$638$	8.98252	+	22.1857i	0.355622	+	0.878339i
$639$	−44.3211			−1.75331
$640$	−25.2090	+	2.12339i	−0.996471	+	0.0839345i
$641$	24.7840			0.978910			0.489455	−	0.872029i	$-0.337196\pi$
$641$	24.7840			0.978910			0.489455	+	0.872029i	$0.337196\pi$
$642$	0.0801492	+	0.197958i	0.00316323	+	0.00781278i
$643$	27.0677	−	27.0677i	1.06744	−	1.06744i	0.0698898	−	0.997555i	$-0.477735\pi$
$643$	27.0677	−	27.0677i	1.06744	−	1.06744i	0.997555	−	0.0698898i	$-0.0222648\pi$
$644$	5.33949	−	5.17144i	0.210405	−	0.203783i
$645$	−0.0514798	+	0.0303488i	−0.00202701	+	0.00119498i
$646$	−8.16178	−	3.45741i	−0.321121	−	0.136030i
$647$	11.7277	+	11.7277i	0.461063	+	0.461063i	0.899004	−	0.437941i	$-0.144292\pi$
$647$	11.7277	+	11.7277i	0.461063	+	0.461063i	−0.437941	+	0.899004i	$0.644292\pi$
$648$	−23.2758	−	10.3017i	−0.914359	−	0.404690i
$649$			13.7967i			0.541568i
$650$	19.6426	+	25.0663i	0.770447	+	0.983180i
$651$		−	0.184005i		−	0.00721172i
$652$	−0.132657	+	8.29737i	−0.00519524	+	0.324950i
$653$	−19.5058	−	19.5058i	−0.763321	−	0.763321i	0.213600	−	0.976921i	$-0.431481\pi$
$653$	−19.5058	−	19.5058i	−0.763321	−	0.763321i	−0.976921	+	0.213600i	$0.931481\pi$
$654$	0.0802476	−	0.189438i	0.00313793	−	0.00740760i
$655$	28.8500	−	17.0079i	1.12726	−	0.664555i
$656$	0.127870	−	3.99796i	0.00499248	−	0.156094i
$657$	−9.01860	+	9.01860i	−0.351849	+	0.351849i
$658$	−22.3065	+	9.03144i	−0.869597	+	0.352082i
$659$	−15.1678			−0.590855			−0.295427	−	0.955365i	$-0.595462\pi$
$659$	−15.1678			−0.590855			−0.295427	+	0.955365i	$0.595462\pi$
$660$	−0.0973085	−	0.171262i	−0.00378773	−	0.00666635i
$661$	18.9229			0.736016			0.368008	−	0.929823i	$-0.380040\pi$
$661$	18.9229			0.736016			0.368008	+	0.929823i	$0.380040\pi$
$662$	11.7012	−	4.73757i	0.454780	−	0.184131i
$663$	−0.183423	+	0.183423i	−0.00712355	+	0.00712355i
$664$	26.5550	−	10.2606i	1.03053	−	0.398189i
$665$	−1.38047	+	5.34580i	−0.0535322	+	0.207301i
$666$	10.2459	−	24.1871i	0.397021	−	0.937233i
$667$	3.86679	+	3.86679i	0.149723	+	0.149723i
$668$	12.3224	+	0.197008i	0.476769	+	0.00762249i
$669$		−	0.0288220i		−	0.00111432i
$670$	−30.1070	+	3.99714i	−1.16313	+	0.154423i
$671$			66.9345i			2.58398i
$672$	−0.120453	+	0.0443421i	−0.00464657	+	0.00171053i
$673$	8.50604	+	8.50604i	0.327884	+	0.327884i	0.851781	−	0.523898i	$-0.175523\pi$
$673$	8.50604	+	8.50604i	0.327884	+	0.327884i	−0.523898	+	0.851781i	$0.675523\pi$
$674$	4.67353	+	1.97975i	0.180018	+	0.0762572i
$675$	0.268740	−	0.0772692i	0.0103438	−	0.00297409i
$676$	−10.1338	−	10.4631i	−0.389760	−	0.402425i
$677$	36.1877	−	36.1877i	1.39081	−	1.39081i	0.567289	−	0.823519i	$-0.307992\pi$
$677$	36.1877	−	36.1877i	1.39081	−	1.39081i	0.823519	−	0.567289i	$-0.192008\pi$
$678$	−0.0314875	−	0.0777699i	−0.00120927	−	0.00298674i
$679$	36.1187			1.38611
$680$	−30.6474	−	24.2502i	−1.17527	−	0.929952i
$681$	−0.100740			−0.00386037
$682$	−20.3377	−	50.2314i	−0.778769	−	1.92346i
$683$	−34.2497	+	34.2497i	−1.31053	+	1.31053i	−0.389502	+	0.921026i	$0.627353\pi$
$683$	−34.2497	+	34.2497i	−1.31053	+	1.31053i	−0.921026	+	0.389502i	$0.872647\pi$
$684$	−4.23390	−	4.37148i	−0.161887	−	0.167148i
$685$	26.2630	+	6.78199i	1.00346	+	0.259127i
$686$	25.5946	+	10.8421i	0.977208	+	0.413955i
$687$	0.0502530	+	0.0502530i	0.00191727	+	0.00191727i
$688$	7.84627	+	8.36477i	0.299136	+	0.318904i
$689$		−	17.3581i		−	0.661291i
$690$	−0.0357333	−	0.0273572i	−0.00136035	−	0.00104147i
$691$			38.1736i			1.45219i	0.687593	+	0.726096i	$0.258667\pi$
$691$			38.1736i			1.45219i	−0.687593	+	0.726096i	$0.741333\pi$
$692$	27.2502	+	0.435671i	1.03590	+	0.0165617i
$693$	24.4006	+	24.4006i	0.926901	+	0.926901i
$694$	−1.30709	+	3.08559i	−0.0496163	+	0.117127i
$695$	−7.05382	−	11.9652i	−0.267567	−	0.453865i
$696$	−0.0340336	−	0.0880809i	−0.00129004	−	0.00333870i
$697$	4.36940	−	4.36940i	0.165503	−	0.165503i
$698$	36.2536	−	14.6784i	1.37222	−	0.555584i
$699$	−0.0383554			−0.00145074
$700$	−12.1254	+	21.1082i	−0.458296	+	0.797815i
$701$	−45.4820			−1.71783			−0.858916	−	0.512117i	$-0.828862\pi$
$701$	−45.4820			−1.71783			−0.858916	+	0.512117i	$0.828862\pi$
$702$	−0.330163	+	0.133676i	−0.0124612	+	0.00504529i
$703$	4.44075	−	4.44075i	0.167486	−	0.167486i
$704$	−27.9813	+	25.4183i	−1.05458	+	0.957989i
$705$	0.0739928	+	0.125512i	0.00278673	+	0.00472704i
$706$	−1.92979	+	4.55558i	−0.0726285	+	0.171452i
$707$	11.9396	+	11.9396i	0.449034	+	0.449034i
$708$	0.000870104	−	0.0544230i	3.27005e−5	−	0.00204534i
$709$			33.8933i			1.27289i	0.771323	+	0.636444i	$0.219595\pi$
$709$			33.8933i			1.27289i	−0.771323	+	0.636444i	$0.780405\pi$
$710$	−37.0964	−	28.4007i	−1.39220	−	1.06586i
$711$			20.0793i			0.753032i
$712$	0.0139362	−	0.0314874i	0.000522280	−	0.00118004i
$713$	−8.75494	−	8.75494i	−0.327875	−	0.327875i
$714$	−0.182580	−	0.0773424i	−0.00683287	−	0.00289447i
$715$	46.0750	+	11.8981i	1.72311	+	0.444965i
$716$	35.4242	−	34.3093i	1.32386	−	1.28220i
$717$	0.0716770	−	0.0716770i	0.00267683	−	0.00267683i
$718$	14.0785	+	34.7719i	0.525403	+	1.29768i
$719$	13.2343			0.493557			0.246778	−	0.969072i	$-0.420628\pi$
$719$	13.2343			0.493557			0.246778	+	0.969072i	$0.420628\pi$
$720$	−12.8807	−	23.5382i	−0.480036	−	0.877216i
$721$	−30.1573			−1.12312
$722$	9.53793	+	23.5575i	0.354965	+	0.876718i
$723$	0.0797232	−	0.0797232i	0.00296494	−	0.00296494i
$724$	−23.9068	+	23.1544i	−0.888488	+	0.860525i
$725$	−15.6693	−	8.67092i	−0.581944	−	0.322030i
$726$	−0.137507	−	0.0582493i	−0.00510337	−	0.00216184i
$727$	−19.9663	−	19.9663i	−0.740510	−	0.740510i	0.232166	−	0.972676i	$-0.425419\pi$
$727$	−19.9663	−	19.9663i	−0.740510	−	0.740510i	−0.972676	+	0.232166i	$0.925419\pi$
$728$	12.5501	−	28.3556i	0.465136	−	1.05093i
$729$		−	26.9953i		−	0.999826i
$730$	−13.3276	+	1.76943i	−0.493276	+	0.0654896i
$731$			17.7172i			0.655294i
$732$	0.00422130	−	0.264032i	0.000156024	−	0.00975892i
$733$	−5.89265	−	5.89265i	−0.217650	−	0.217650i	0.589857	−	0.807507i	$-0.299184\pi$
$733$	−5.89265	−	5.89265i	−0.217650	−	0.217650i	−0.807507	+	0.589857i	$0.799184\pi$
$734$	−1.98942	+	4.69634i	−0.0734307	+	0.173345i
$735$	0.00559795	−	0.0216778i	0.000206483	−	0.000799598i
$736$	−3.62134	+	7.84093i	−0.133484	+	0.289021i
$737$	−32.0907	+	32.0907i	−1.18207	+	1.18207i
$738$	3.93243	−	1.59216i	0.144755	−	0.0586082i
$739$	12.4032			0.456257			0.228129	−	0.973631i	$-0.426739\pi$
$739$	12.4032			0.456257			0.228129	+	0.973631i	$0.426739\pi$
$740$	24.0748	−	13.6789i	0.885006	−	0.502848i
$741$	−0.0425798			−0.00156421
$742$	12.2988	−	4.97952i	0.451502	−	0.182804i
$743$	−16.2565	+	16.2565i	−0.596393	+	0.596393i	−0.939351	−	0.342958i	$-0.888571\pi$
$743$	−16.2565	+	16.2565i	−0.596393	+	0.596393i	0.342958	+	0.939351i	$0.388571\pi$
$744$	0.0770568	+	0.199427i	0.00282504	+	0.00731135i
$745$	15.5003	−	9.13787i	0.567886	−	0.334786i
$746$	−16.4984	+	38.9472i	−0.604050	+	1.42596i
$747$	21.3507	+	21.3507i	0.781180	+	0.781180i
$748$	−58.3907	−	0.933540i	−2.13498	−	0.0341336i
$749$		−	39.4393i		−	1.44108i
$750$	0.137222	+	0.0537660i	0.00501062	+	0.00196326i
$751$			3.99139i			0.145648i	0.997345	+	0.0728240i	$0.0232011\pi$
$751$			3.99139i			0.145648i	−0.997345	+	0.0728240i	$0.976799\pi$
$752$	20.3939	−	19.1298i	0.743691	−	0.697593i
$753$	0.0955286	+	0.0955286i	0.00348126	+	0.00348126i
$754$	21.0054	+	8.89807i	0.764970	+	0.324049i
$755$	34.3042	−	20.2233i	1.24846	−	0.736002i
$756$	−0.189428	−	0.195583i	−0.00688943	−	0.00711330i
$757$	14.5412	−	14.5412i	0.528509	−	0.528509i	−0.391619	−	0.920128i	$-0.628085\pi$
$757$	14.5412	−	14.5412i	0.528509	−	0.528509i	0.920128	+	0.391619i	$0.128085\pi$
$758$	−15.8938	−	39.2556i	−0.577289	−	1.42583i
$759$	−0.0672475			−0.00244093
$760$	−0.742521	−	6.37196i	−0.0269341	−	0.231135i
$761$	−0.266259			−0.00965187			−0.00482594	−	0.999988i	$-0.501536\pi$
$761$	−0.266259			−0.00965187			−0.00482594	+	0.999988i	$0.501536\pi$
$762$	0.0437421	+	0.108037i	0.00158461	+	0.00391378i
$763$	−26.8648	+	26.8648i	−0.972571	+	0.972571i
$764$	29.1168	+	30.0630i	1.05341	+	1.08764i
$765$	10.3640	−	40.1340i	0.374710	−	1.45105i
$766$	−32.8811	−	13.9287i	−1.18804	−	0.503265i
$767$	9.29808	+	9.29808i	0.335734	+	0.335734i
$768$	0.111979	−	0.0985014i	0.00404070	−	0.00355436i
$769$			7.85734i			0.283343i	0.989914	+	0.141671i	$0.0452476\pi$
$769$			7.85734i			0.283343i	−0.989914	+	0.141671i	$0.954752\pi$
$770$	4.78734	+	36.0589i	0.172524	+	1.29947i
$771$		−	0.0189688i		−	0.000683145i
$772$	−34.4830	−	0.551307i	−1.24107	−	0.0198420i
$773$	4.06175	+	4.06175i	0.146091	+	0.146091i	0.776369	−	0.630278i	$-0.217059\pi$
$773$	4.06175	+	4.06175i	0.146091	+	0.146091i	−0.630278	+	0.776369i	$0.717059\pi$
$774$	−4.74470	+	11.2006i	−0.170545	+	0.402599i
$775$	35.4775	+	19.6321i	1.27439	+	0.705207i
$776$	−39.1459	+	15.1256i	−1.40526	+	0.542978i
$777$	0.0993399	−	0.0993399i	0.00356380	−	0.00356380i
$778$	27.0604	−	10.9562i	0.970162	−	0.392799i
$779$	1.01431			0.0363415
$780$	−0.180999	−	0.0498396i	−0.00648080	−	0.00178455i
$781$	−69.8127			−2.49809
$782$	−12.3671	+	5.00717i	−0.442246	+	0.179056i
$783$	0.141639	−	0.141639i	0.00506177	−	0.00506177i
$784$	−4.29458	−	0.137357i	−0.153378	−	0.00490561i
$785$	−36.2051	−	9.34938i	−1.29221	−	0.333694i
$786$	−0.0770087	+	0.181792i	−0.00274681	+	0.00648430i
$787$	−36.6753	−	36.6753i	−1.30733	−	1.30733i	−0.923334	−	0.383998i	$-0.874547\pi$
$787$	−36.6753	−	36.6753i	−1.30733	−	1.30733i	−0.383998	−	0.923334i	$-0.625453\pi$
$788$	0.170452	−	10.6614i	0.00607209	−	0.379795i
$789$		−	0.121494i		−	0.00432531i
$790$	−12.8667	+	16.8062i	−0.457777	+	0.597939i
$791$			15.4942i			0.550909i
$792$	−36.6641	−	16.2273i	−1.30280	−	0.576613i
$793$	45.1095	+	45.1095i	1.60189	+	1.60189i
$794$	−2.00640	−	0.849932i	−0.0712046	−	0.0301629i
$795$	−0.0407962	−	0.0692013i	−0.00144689	−	0.00245432i
$796$	18.0468	−	17.4788i	0.639653	−	0.619521i
$797$	2.65247	−	2.65247i	0.0939554	−	0.0939554i	−0.658567	−	0.752522i	$-0.728837\pi$
$797$	2.65247	−	2.65247i	0.0939554	−	0.0939554i	0.752522	+	0.658567i	$0.228837\pi$
$798$	−0.0122149	−	0.0301691i	−0.000432402	−	0.00106798i
$799$	43.1959			1.52816
$800$	4.30206	−	27.9552i	0.152101	−	0.988365i
$801$	0.0365213			0.00129042
$802$	−1.63416	−	4.03615i	−0.0577040	−	0.142521i
$803$	−14.2057	+	14.2057i	−0.501309	+	0.501309i
$804$	0.128610	−	0.124562i	0.00453572	−	0.00439297i
$805$	4.22056	+	7.15921i	0.148755	+	0.252329i
$806$	−47.5590	−	20.1464i	−1.67519	−	0.709628i
$807$	−0.188831	−	0.188831i	−0.00664716	−	0.00664716i
$808$	−17.9403	−	7.94028i	−0.631137	−	0.279338i
$809$			21.1509i			0.743626i	0.928308	+	0.371813i	$0.121264\pi$
$809$			21.1509i			0.743626i	−0.928308	+	0.371813i	$0.878736\pi$
$810$	17.2995	−	22.5962i	0.607841	−	0.793949i
$811$		−	41.5073i		−	1.45752i	−0.684769	−	0.728760i	$-0.740097\pi$
$811$		−	41.5073i		−	1.45752i	0.684769	−	0.728760i	$-0.259903\pi$
$812$	−0.278757	+	17.4356i	−0.00978244	+	0.611868i
$813$	−0.152765	−	0.152765i	−0.00535772	−	0.00535772i
$814$	16.1389	−	38.0986i	0.565669	−	1.33535i
$815$	−8.98324	−	2.31978i	−0.314669	−	0.0812583i
$816$	0.230272	+	0.00736496i	0.00806112	+	0.000257825i
$817$	−2.05643	+	2.05643i	−0.0719455	+	0.0719455i
$818$	−32.1761	+	13.0275i	−1.12501	+	0.455494i
$819$	32.8888			1.14923
$820$	4.31166	+	1.18725i	0.150570	+	0.0414607i
$821$	22.0579			0.769826			0.384913	−	0.922953i	$-0.374232\pi$
$821$	22.0579			0.769826			0.384913	+	0.922953i	$0.374232\pi$
$822$	−0.148216	+	0.0600095i	−0.00516962	+	0.00209307i
$823$	15.8580	−	15.8580i	0.552774	−	0.552774i	−0.374467	−	0.927240i	$-0.622174\pi$
$823$	15.8580	−	15.8580i	0.552774	−	0.552774i	0.927240	+	0.374467i	$0.122174\pi$
$824$	32.6849	−	12.6291i	1.13863	−	0.439957i
$825$	0.211651	−	0.0608547i	0.00736874	−	0.00211869i
$826$	−3.92065	+	9.25534i	−0.136417	+	0.322034i
$827$	31.5043	+	31.5043i	1.09551	+	1.09551i	0.994929	+	0.100585i	$0.0320713\pi$
$827$	31.5043	+	31.5043i	1.09551	+	1.09551i	0.100585	+	0.994929i	$0.467929\pi$
$828$	−9.15927	−	0.146437i	−0.318307	−	0.00508903i
$829$		−	24.6665i		−	0.856705i	−0.903612	−	0.428352i	$-0.859094\pi$
$829$		−	24.6665i		−	0.856705i	0.903612	−	0.428352i	$-0.140906\pi$
$830$	4.18896	+	31.5518i	0.145401	+	1.09518i
$831$			0.155997i			0.00541146i
$832$	−1.72728	+	35.9879i	−0.0598827	+	1.24766i
$833$	−4.69359	−	4.69359i	−0.162623	−	0.162623i
$834$	0.0753958	+	0.0319384i	0.00261074	+	0.00110594i
$835$	−3.44510	+	13.3410i	−0.119223	+	0.461684i
$836$	−6.66906	−	6.88577i	−0.230654	−	0.238149i
$837$	−0.320690	+	0.320690i	−0.0110847	+	0.0110847i
$838$	16.9493	+	41.8626i	0.585505	+	1.44612i
$839$	−2.81130			−0.0970567			−0.0485284	−	0.998822i	$-0.515453\pi$
$839$	−2.81130			−0.0970567			−0.0485284	+	0.998822i	$0.515453\pi$
$840$	−0.0166102	−	0.142541i	−0.000573108	−	0.00491814i
$841$	16.1715			0.557638
$842$	−7.51389	−	18.5583i	−0.258946	−	0.639562i
$843$	−0.000236208	0	0.000236208i	−8.13542e−6	0	8.13542e-6i
$844$	27.9620	+	28.8706i	0.962490	+	0.993766i
$845$	14.0289	−	8.27046i	0.482609	−	0.284512i
$846$	27.3080	+	11.5679i	0.938869	+	0.397714i
$847$	19.5003	+	19.5003i	0.670040	+	0.670040i
$848$	−11.2443	+	10.5473i	−0.386130	+	0.362196i
$849$			0.0514392i			0.00176539i
$850$	34.3922	−	26.9507i	1.17964	−	0.924402i
$851$		−	9.45317i		−	0.324051i
$852$	0.275386	+	0.00440282i	0.00943456	+	0.000150838i
$853$	−20.6790	−	20.6790i	−0.708036	−	0.708036i	0.258086	−	0.966122i	$-0.416908\pi$
$853$	−20.6790	−	20.6790i	−0.708036	−	0.708036i	−0.966122	+	0.258086i	$0.916908\pi$
$854$	−19.0210	+	44.9021i	−0.650884	+	1.53652i
$855$	5.86130	−	3.45541i	0.200452	−	0.118172i
$856$	16.5162	+	42.7449i	0.564513	+	1.46099i
$857$	−20.2633	+	20.2633i	−0.692181	+	0.692181i	−0.962711	−	0.270531i	$-0.912801\pi$
$857$	−20.2633	+	20.2633i	−0.692181	+	0.692181i	0.270531	+	0.962711i	$0.412801\pi$
$858$	−0.260026	+	0.105279i	−0.00887713	+	0.00359417i
$859$	7.80943			0.266454			0.133227	−	0.991086i	$-0.457466\pi$
$859$	7.80943			0.266454			0.133227	+	0.991086i	$0.457466\pi$
$860$	−11.1486	+	6.33448i	−0.380164	+	0.216004i
$861$	0.0226902			0.000773281
$862$	−0.361149	+	0.146222i	−0.0123008	+	0.00498033i
$863$	−30.2725	+	30.2725i	−1.03049	+	1.03049i	−0.0309674	+	0.999520i	$0.509859\pi$
$863$	−30.2725	+	30.2725i	−1.03049	+	1.03049i	−0.999520	+	0.0309674i	$0.990141\pi$
$864$	0.287210	+	0.132648i	0.00977109	+	0.00451279i
$865$	−7.61860	+	29.5027i	−0.259040	+	1.00312i
$866$	−14.7064	+	34.7168i	−0.499743	+	1.17973i
$867$	0.139619	+	0.139619i	0.00474171	+	0.00474171i
$868$	0.631143	−	39.4765i	0.0214224	−	1.33992i
$869$			31.6280i			1.07291i
$870$	0.104655	−	0.0138944i	0.00354813	−	0.000471066i
$871$			43.2541i			1.46561i
$872$	17.8661	−	40.3668i	0.605024	−	1.36699i
$873$	−31.4740	−	31.4740i	−1.06523	−	1.06523i
$874$	−2.01663	−	0.854263i	−0.0682135	−	0.0288959i
$875$	−19.7622	−	18.7131i	−0.668084	−	0.632620i
$876$	0.0569323	−	0.0551405i	0.00192357	−	0.00186303i
$877$	34.7106	−	34.7106i	1.17209	−	1.17209i	0.190385	−	0.981709i	$-0.439026\pi$
$877$	34.7106	−	34.7106i	1.17209	−	1.17209i	0.981709	−	0.190385i	$-0.0609738\pi$
$878$	13.8858	+	34.2962i	0.468624	+	1.15744i
$879$	0.0551765			0.00186106
$880$	−20.2892	−	37.0763i	−0.683948	−	1.24984i
$881$	−29.7775			−1.00323			−0.501614	−	0.865091i	$-0.667260\pi$
$881$	−29.7775			−1.00323			−0.501614	+	0.865091i	$0.667260\pi$
$882$	−1.71029	−	4.22419i	−0.0575885	−	0.142236i
$883$	39.7970	−	39.7970i	1.33928	−	1.33928i	0.442516	−	0.896761i	$-0.354086\pi$
$883$	39.7970	−	39.7970i	1.33928	−	1.33928i	0.896761	−	0.442516i	$-0.145914\pi$
$884$	−39.9808	+	38.7225i	−1.34470	+	1.30238i
$885$	0.0589216	+	0.0152156i	0.00198063	+	0.000511466i
$886$	−33.7456	−	14.2950i	−1.13371	−	0.480249i
$887$	−5.97784	−	5.97784i	−0.200716	−	0.200716i	0.599591	−	0.800307i	$-0.295330\pi$
$887$	−5.97784	−	5.97784i	−0.200716	−	0.200716i	−0.800307	+	0.599591i	$0.795330\pi$
$888$	−0.0660649	+	0.149267i	−0.00221699	+	0.00500908i
$889$		−	21.5244i		−	0.721904i
$890$	0.0305681	+	0.0234027i	0.00102464	+	0.000784459i
$891$		−	42.5243i		−	1.42462i
$892$	0.0988604	−	6.18348i	0.00331009	−	0.207038i
$893$	5.01374	+	5.01374i	0.167779	+	0.167779i
$894$	−0.0413746	+	0.0976715i	−0.00138377	+	0.00326662i
$895$	28.0008	+	47.4969i	0.935965	+	1.58765i
$896$	−25.9941	+	9.10002i	−0.868402	+	0.304010i
$897$	−0.0453205	+	0.0453205i	−0.00151321	+	0.00151321i
$898$	−11.2212	+	4.54323i	−0.374456	+	0.151610i
$899$	29.0454			0.968720
$900$	28.9599	−	7.82767i	0.965330	−	0.260922i
$901$	−23.8162			−0.793433
$902$	6.19419	−	2.50790i	0.206244	−	0.0835040i
$903$	−0.0460026	+	0.0460026i	−0.00153087	+	0.00153087i
$904$	−6.48858	−	16.7928i	−0.215807	−	0.558520i
$905$	−18.8970	−	32.0543i	−0.628156	−	1.06552i
$906$	−0.0915674	+	0.216160i	−0.00304212	+	0.00718143i
$907$	−13.2056	−	13.2056i	−0.438485	−	0.438485i	0.453017	−	0.891502i	$-0.350348\pi$
$907$	−13.2056	−	13.2056i	−0.438485	−	0.438485i	−0.891502	+	0.453017i	$0.850348\pi$
$908$	−21.6128	−	0.345542i	−0.717247	−	0.0114672i
$909$		−	20.8084i		−	0.690171i
$910$	27.5277	+	21.0750i	0.912535	+	0.698630i
$911$		−	52.2104i		−	1.72981i	−0.501938	−	0.864903i	$-0.667380\pi$
$911$		−	52.2104i		−	1.72981i	0.501938	−	0.864903i	$-0.332620\pi$
$912$	0.0258728	+	0.0275825i	0.000856733	+	0.000913346i
$913$	33.6307	+	33.6307i	1.11301	+	1.11301i
$914$	−23.8314	−	10.0952i	−0.788273	−	0.333920i
$915$	0.285857	+	0.0738181i	0.00945016	+	0.00244035i
$916$	10.6089	+	10.9537i	0.350529	+	0.361920i
$917$	25.7805	−	25.7805i	0.851347	−	0.851347i
$918$	0.183411	+	0.453001i	0.00605346	+	0.0149513i
$919$	−9.17638			−0.302701			−0.151350	−	0.988480i	$-0.548362\pi$
$919$	−9.17638			−0.302701			−0.151350	+	0.988480i	$0.548362\pi$
$920$	−7.57241	−	5.99178i	−0.249655	−	0.197543i
$921$	0.183693			0.00605289
$922$	−13.0540	−	32.2416i	−0.429910	−	1.06182i
$923$	−47.0493	+	47.0493i	−1.54865	+	1.54865i
$924$	−0.149187	−	0.154035i	−0.00490790	−	0.00506738i
$925$	8.55452	+	29.7524i	0.281271	+	0.978252i
$926$	−4.81739	−	2.04069i	−0.158309	−	0.0670614i
$927$	26.2792	+	26.2792i	0.863122	+	0.863122i
$928$	−6.99947	−	19.0137i	−0.229769	−	0.624154i
$929$			51.0539i			1.67502i	0.546418	+	0.837512i	$0.315991\pi$
$929$			51.0539i			1.67502i	−0.546418	+	0.837512i	$0.684009\pi$
$930$	−0.236953	+	0.0314589i	−0.00776998	+	0.00103158i
$931$		−	1.08957i		−	0.0357092i
$932$	−8.22879	−	0.131560i	−0.269543	−	0.00430940i
$933$	0.160797	+	0.160797i	0.00526424	+	0.00526424i
$934$	−7.65278	+	18.0657i	−0.250407	+	0.591126i
$935$	16.3249	−	63.2174i	0.533881	−	2.06743i
$936$	−35.6454	+	13.7731i	−1.16511	+	0.450186i
$937$	−34.8590	+	34.8590i	−1.13879	+	1.13879i	−0.150128	+	0.988667i	$0.547969\pi$
$937$	−34.8590	+	34.8590i	−1.13879	+	1.13879i	−0.988667	+	0.150128i	$0.952031\pi$
$938$	−30.6469	+	12.4083i	−1.00066	+	0.405146i
$939$	0.00499284			0.000162935
$940$	15.4439	+	27.1811i	0.503726	+	0.886551i
$941$	6.06019			0.197557			0.0987783	−	0.995109i	$-0.468507\pi$
$941$	6.06019			0.197557			0.0987783	+	0.995109i	$0.468507\pi$
$942$	0.204324	−	0.0827267i	0.00665724	−	0.00269538i
$943$	1.07960	−	1.07960i	0.0351566	−	0.0351566i
$944$	0.373345	−	11.6729i	0.0121513	−	0.379922i
$945$	0.262239	−	0.154598i	0.00853064	−	0.00502906i
$946$	−7.47364	+	17.6428i	−0.242989	+	0.573616i
$947$	24.7188	+	24.7188i	0.803254	+	0.803254i	0.983603	−	0.180349i	$-0.0577226\pi$
$947$	24.7188	+	24.7188i	0.803254	+	0.803254i	−0.180349	+	0.983603i	$0.557723\pi$
$948$	0.00199466	−	0.124761i	6.47835e−5	−	0.00405206i
$949$			19.1475i			0.621554i
$950$	7.12007	+	0.863738i	0.231006	+	0.0280234i
$951$		−	0.0965621i		−	0.00313124i
$952$	−38.9054	−	17.2193i	−1.26093	−	0.558082i
$953$	−25.0940	−	25.0940i	−0.812876	−	0.812876i	0.172188	−	0.985064i	$-0.444916\pi$
$953$	−25.0940	−	25.0940i	−0.812876	−	0.812876i	−0.985064	+	0.172188i	$0.944916\pi$
$954$	−15.0564	−	6.37803i	−0.487468	−	0.206496i
$955$	−40.3086	+	23.7631i	−1.30436	+	0.768956i
$956$	15.6235	−	15.1318i	0.505299	−	0.489396i
$957$	0.111550	−	0.111550i	0.00360591	−	0.00360591i
$958$	−3.40314	−	8.40531i	−0.109950	−	0.271563i
$959$	29.5291			0.953545
$960$	0.0776952	+	0.147532i	0.00250760	+	0.00476158i
$961$	−34.7628			−1.12138
$962$	−14.7994	−	36.5526i	−0.477152	−	1.17850i
$963$	−34.3676	+	34.3676i	−1.10748	+	1.10748i
$964$	17.3773	−	16.8304i	0.559685	−	0.542071i
$965$	9.64075	−	37.3334i	0.310347	−	1.20180i
$966$	−0.0451121	−	0.0191099i	−0.00145146	−	0.000614851i
$967$	27.6514	+	27.6514i	0.889209	+	0.889209i	0.994447	−	0.105238i	$-0.0335606\pi$
$967$	27.6514	+	27.6514i	0.889209	+	0.889209i	−0.105238	+	0.994447i	$0.533561\pi$
$968$	−29.3010	−	12.9685i	−0.941771	−	0.416823i
$969$			0.0584217i			0.00187677i
$970$	−6.17513	−	46.5119i	−0.198272	−	1.49341i
$971$			0.527059i			0.0169141i	0.999964	+	0.00845706i	$0.00269200\pi$
$971$			0.527059i			0.0169141i	−0.999964	+	0.00845706i	$0.997308\pi$
$972$	−0.00804592	+	0.503254i	−0.000258073	+	0.0161419i
$973$	−10.6921	−	10.6921i	−0.342774	−	0.342774i
$974$	9.51490	−	22.4615i	0.304877	−	0.719713i
$975$	0.101627	−	0.183651i	0.00325467	−	0.00588155i
$976$	1.81128	−	56.6311i	0.0579776	−	1.81272i
$977$	17.5673	−	17.5673i	0.562028	−	0.562028i	−0.367855	−	0.929883i	$-0.619908\pi$
$977$	17.5673	−	17.5673i	0.562028	−	0.562028i	0.929883	+	0.367855i	$0.119908\pi$
$978$	0.0506971	−	0.0205262i	0.00162112	−	0.000656357i
$979$	0.0575268			0.00183857
$980$	1.27534	−	4.63157i	0.0407393	−	0.147950i
$981$	46.8202			1.49485
$982$	15.8519	−	6.41810i	0.505854	−	0.204810i
$983$	−35.1624	+	35.1624i	−1.12151	+	1.12151i	−0.129990	+	0.991515i	$0.541495\pi$
$983$	−35.1624	+	35.1624i	−1.12151	+	1.12151i	−0.991515	+	0.129990i	$0.958505\pi$
$984$	−0.0245920	+	0.00950212i	−0.000783965	+	0.000302917i
$985$	11.5426	+	2.98070i	0.367779	+	0.0949730i
$986$	12.2086	−	28.8205i	0.388802	−	0.917830i
$987$	0.112158	+	0.112158i	0.00357002	+	0.00357002i
$988$	−9.13508	−	0.146050i	−0.290626	−	0.00464647i
$989$			4.37760i			0.139199i
$990$	27.2502	−	35.5936i	0.866067	−	1.13124i
$991$		−	23.0666i		−	0.732735i	−0.930470	−	0.366368i	$-0.880601\pi$
$991$		−	23.0666i		−	0.732735i	0.930470	−	0.366368i	$-0.119399\pi$
$992$	15.8478	+	43.0495i	0.503167	+	1.36682i
$993$	−0.0588340	−	0.0588340i	−0.00186704	−	0.00186704i
$994$	−46.8329	−	19.8389i	−1.48545	−	0.629251i
$995$	14.2650	+	24.1973i	0.452231	+	0.767105i
$996$	−0.130540	−	0.134782i	−0.00413631	−	0.00427072i
$997$	−6.95249	+	6.95249i	−0.220188	+	0.220188i	−0.808577	−	0.588390i	$-0.799762\pi$
$997$	−6.95249	+	6.95249i	−0.220188	+	0.220188i	0.588390	+	0.808577i	$0.299762\pi$
$998$	0.903174	+	2.23072i	0.0285895	+	0.0706123i
$999$	−0.346266			−0.0109554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.k.c.83.17	✓	108
4.3	odd	2	inner	820.2.k.c.83.48	yes	108
5.2	odd	4	inner	820.2.k.c.247.48	yes	108
20.7	even	4	inner	820.2.k.c.247.17	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.k.c.83.17	✓	108	1.1	even	1	trivial
820.2.k.c.83.48	yes	108	4.3	odd	2	inner
820.2.k.c.247.17	yes	108	20.7	even	4	inner
820.2.k.c.247.48	yes	108	5.2	odd	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.530735 - 1.31085i) q^{2} +(-0.00659099 + 0.00659099i) q^{3} +(-1.43664 + 1.39143i) q^{4} +(-1.13558 - 1.92625i) q^{5} +(0.0121378 + 0.00514171i) q^{6} +(-1.72131 - 1.72131i) q^{7} +(2.58642 + 1.14474i) q^{8} +2.99991i q^{9} +(-1.92233 + 2.51091i) q^{10} +4.72534i q^{11} +(0.000298009 - 0.0186397i) q^{12} +(3.18457 + 3.18457i) q^{13} +(-1.34281 + 3.16993i) q^{14} +(0.0201805 + 0.00521130i) q^{15} +(0.127870 - 3.99796i) q^{16} +(4.36940 - 4.36940i) q^{17} +(3.93243 - 1.59216i) q^{18} +1.01431 q^{19} +(4.31166 + 1.18725i) q^{20} +0.0226902 q^{21} +(6.19419 - 2.50790i) q^{22} +(1.07960 - 1.07960i) q^{23} +(-0.0245920 + 0.00950212i) q^{24} +(-2.42090 + 4.37484i) q^{25} +(2.48432 - 5.86465i) q^{26} +(-0.0395453 - 0.0395453i) q^{27} +(4.86797 + 0.0778282i) q^{28} +3.58169i q^{29} +(-0.00387930 - 0.0292194i) q^{30} -8.10943i q^{31} +(-5.30857 + 1.95424i) q^{32} +(-0.0311446 - 0.0311446i) q^{33} +(-8.04661 - 3.40862i) q^{34} +(-1.36099 + 5.27036i) q^{35} +(-4.17416 - 4.30980i) q^{36} +(4.37809 - 4.37809i) q^{37} +(-0.538331 - 1.32961i) q^{38} -0.0419789 q^{39} +(-0.732044 - 6.28205i) q^{40} +1.00000 q^{41} +(-0.0120425 - 0.0297434i) q^{42} +(-2.02742 + 2.02742i) q^{43} +(-6.57495 - 6.78861i) q^{44} +(5.77859 - 3.40665i) q^{45} +(-1.98817 - 0.842209i) q^{46} +(4.94300 + 4.94300i) q^{47} +(0.0255077 + 0.0271933i) q^{48} -1.07420i q^{49} +(7.01961 + 0.851550i) q^{50} +0.0575973i q^{51} +(-9.00618 - 0.143989i) q^{52} +(-2.72534 - 2.72534i) q^{53} +(-0.0308498 + 0.0728260i) q^{54} +(9.10219 - 5.36601i) q^{55} +(-2.48158 - 6.42247i) q^{56} +(-0.00668532 + 0.00668532i) q^{57} +(4.69505 - 1.90093i) q^{58} +2.91973 q^{59} +(-0.0362433 + 0.0205929i) q^{60} +14.1650 q^{61} +(-10.6302 + 4.30396i) q^{62} +(5.16378 - 5.16378i) q^{63} +(5.37915 + 5.92154i) q^{64} +(2.51795 - 9.75064i) q^{65} +(-0.0242963 + 0.0573554i) q^{66} +(6.79119 + 6.79119i) q^{67} +(-0.197561 + 12.3570i) q^{68} +0.0142313i q^{69} +(7.63097 - 1.01312i) q^{70} +14.7741i q^{71} +(-3.43411 + 7.75904i) q^{72} +(3.00629 + 3.00629i) q^{73} +(-8.06262 - 3.41540i) q^{74} +(-0.0128784 - 0.0447906i) q^{75} +(-1.45720 + 1.41134i) q^{76} +(8.13376 - 8.13376i) q^{77} +(0.0222797 + 0.0550280i) q^{78} +6.69329 q^{79} +(-7.84628 + 4.29370i) q^{80} -8.99922 q^{81} +(-0.530735 - 1.31085i) q^{82} +(7.11710 - 7.11710i) q^{83} +(-0.0325977 + 0.0315718i) q^{84} +(-13.3784 - 3.45475i) q^{85} +(3.73365 + 1.58161i) q^{86} +(-0.0236069 - 0.0236069i) q^{87} +(-5.40927 + 12.2217i) q^{88} -0.0121741i q^{89} +(-7.53250 - 5.76682i) q^{90} -10.9633i q^{91} +(-0.0488137 + 3.05318i) q^{92} +(0.0534491 + 0.0534491i) q^{93} +(3.85609 - 9.10294i) q^{94} +(-1.15184 - 1.95382i) q^{95} +(0.0221084 - 0.0478691i) q^{96} +(-10.4916 + 10.4916i) q^{97} +(-1.40811 + 0.570113i) q^{98} -14.1756 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 12 q^{2} - 4 q^{6} - 24 q^{8} + 4 q^{10} - 16 q^{13} + 52 q^{16} - 8 q^{17} + 18 q^{18} + 38 q^{20} + 72 q^{21} + 10 q^{22} - 12 q^{25} + 24 q^{26} - 58 q^{28} - 70 q^{30} - 38 q^{32} + 8 q^{33}+ \cdots + 122 q^{98}+O(q^{100}) \) 108 * q + 12 * q^2 - 4 * q^6 - 24 * q^8 + 4 * q^10 - 16 * q^13 + 52 * q^16 - 8 * q^17 + 18 * q^18 + 38 * q^20 + 72 * q^21 + 10 * q^22 - 12 * q^25 + 24 * q^26 - 58 * q^28 - 70 * q^30 - 38 * q^32 + 8 * q^33 + 72 * q^36 - 44 * q^37 + 56 * q^38 + 50 * q^40 + 108 * q^41 - 72 * q^42 - 4 * q^45 - 4 * q^46 - 94 * q^48 - 56 * q^50 - 50 * q^52 - 16 * q^53 - 32 * q^56 - 112 * q^57 + 68 * q^58 + 136 * q^60 + 8 * q^61 + 2 * q^62 - 48 * q^65 + 16 * q^66 - 16 * q^68 - 48 * q^70 - 42 * q^72 - 20 * q^73 - 12 * q^76 + 72 * q^77 + 100 * q^78 + 72 * q^80 - 52 * q^81 + 12 * q^82 - 32 * q^85 - 20 * q^86 - 38 * q^88 - 50 * q^90 + 8 * q^92 + 24 * q^93 + 44 * q^96 - 56 * q^97 + 122 * q^98

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