LMFDB - Embedded newform 104.2.r.a.29.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [104,2,Mod(29,104)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("104.29"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(104, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 104 = 2^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	104.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.830444181021$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.10
Character	$\chi$	$=$	104.29
Dual form			104.2.r.a.61.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.02392 + 0.975496i) q^{2} +(0.609172 - 0.351705i) q^{3} +(0.0968157 + 1.99766i) q^{4} -2.24007i q^{5} +(0.966829 + 0.234127i) q^{6} +(0.471952 - 0.817445i) q^{7} +(-1.84957 + 2.13988i) q^{8} +(-1.25261 + 2.16958i) q^{9} +(2.18518 - 2.29365i) q^{10} +(-4.82849 + 2.78773i) q^{11} +(0.761563 + 1.18286i) q^{12} +(-0.108823 - 3.60391i) q^{13} +(1.28065 - 0.376609i) q^{14} +(-0.787845 - 1.36459i) q^{15} +(-3.98125 + 0.386809i) q^{16} +(3.03119 - 5.25017i) q^{17} +(-3.39898 + 0.999558i) q^{18} +(1.43961 + 0.831159i) q^{19} +(4.47489 - 0.216874i) q^{20} -0.663952i q^{21} +(-7.66340 - 1.85577i) q^{22} +(1.07746 + 1.86621i) q^{23} +(-0.374101 + 1.95406i) q^{24} -0.0179136 q^{25} +(3.40417 - 3.79626i) q^{26} +3.87243i q^{27} +(1.67867 + 0.863656i) q^{28} +(-1.68452 + 0.972558i) q^{29} +(0.524461 - 2.16576i) q^{30} -1.91161 q^{31} +(-4.45381 - 3.48764i) q^{32} +(-1.96092 + 3.39641i) q^{33} +(8.22520 - 2.41883i) q^{34} +(-1.83113 - 1.05721i) q^{35} +(-4.45534 - 2.29223i) q^{36} +(4.54154 - 2.62206i) q^{37} +(0.663250 + 2.25537i) q^{38} +(-1.33381 - 2.15712i) q^{39} +(4.79348 + 4.14317i) q^{40} +(-0.332039 - 0.575109i) q^{41} +(0.647683 - 0.679833i) q^{42} +(6.97919 + 4.02944i) q^{43} +(-6.03640 - 9.37576i) q^{44} +(4.86001 + 2.80593i) q^{45} +(-0.717252 + 2.96190i) q^{46} -10.5778 q^{47} +(-2.28922 + 1.63586i) q^{48} +(3.05452 + 5.29059i) q^{49} +(-0.0183420 - 0.0174746i) q^{50} -4.26434i q^{51} +(7.18883 - 0.566307i) q^{52} +10.3882i q^{53} +(-3.77754 + 3.96505i) q^{54} +(6.24471 + 10.8162i) q^{55} +(0.876323 + 2.52184i) q^{56} +1.16929 q^{57} +(-2.67354 - 0.647422i) q^{58} +(0.411368 + 0.237503i) q^{59} +(2.64970 - 1.70596i) q^{60} +(-3.06666 - 1.77054i) q^{61} +(-1.95733 - 1.86477i) q^{62} +(1.18234 + 2.04787i) q^{63} +(-1.15816 - 7.91572i) q^{64} +(-8.07301 + 0.243772i) q^{65} +(-5.32101 + 1.56478i) q^{66} +(3.91067 - 2.25783i) q^{67} +(10.7815 + 5.54696i) q^{68} +(1.31271 + 0.757894i) q^{69} +(-0.843631 - 2.86876i) q^{70} +(5.81695 - 10.0753i) q^{71} +(-2.32585 - 6.69322i) q^{72} -1.91680 q^{73} +(7.20797 + 1.74548i) q^{74} +(-0.0109124 + 0.00630029i) q^{75} +(-1.52099 + 2.95631i) q^{76} +5.26270i q^{77} +(0.738558 - 3.50984i) q^{78} +13.6120 q^{79} +(0.866479 + 8.91829i) q^{80} +(-2.39587 - 4.14976i) q^{81} +(0.221035 - 0.912767i) q^{82} -11.5623i q^{83} +(1.32635 - 0.0642810i) q^{84} +(-11.7607 - 6.79007i) q^{85} +(3.21542 + 10.9340i) q^{86} +(-0.684108 + 1.18491i) q^{87} +(2.96524 - 15.4885i) q^{88} +(-0.373638 - 0.647161i) q^{89} +(2.23908 + 7.61396i) q^{90} +(-2.99736 - 1.61192i) q^{91} +(-3.62373 + 2.33306i) q^{92} +(-1.16450 + 0.672324i) q^{93} +(-10.8308 - 10.3186i) q^{94} +(1.86185 - 3.22483i) q^{95} +(-3.93975 - 0.558140i) q^{96} +(0.640742 - 1.10980i) q^{97} +(-2.03337 + 8.39680i) q^{98} -13.9677i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} - q^{4} - 8 q^{6} - 2 q^{7} - 10 q^{8} + 6 q^{9} - 3 q^{10} - 12 q^{12} + 8 q^{14} + 4 q^{15} - q^{16} + 6 q^{18} - 11 q^{20} - 2 q^{22} - 14 q^{23} - 18 q^{24} - 12 q^{25} - 3 q^{26} - 4 q^{28}+ \cdots - 17 q^{98}+O(q^{100}) $ 24 * q - q^2 - q^4 - 8 * q^6 - 2 * q^7 - 10 * q^8 + 6 * q^9 - 3 * q^10 - 12 * q^12 + 8 * q^14 + 4 * q^15 - q^16 + 6 * q^18 - 11 * q^20 - 2 * q^22 - 14 * q^23 - 18 * q^24 - 12 * q^25 - 3 * q^26 - 4 * q^28 + 14 * q^30 - 8 * q^31 - 21 * q^32 - 14 * q^33 + 14 * q^34 + 5 * q^36 + 12 * q^38 - 34 * q^39 + 54 * q^40 - 4 * q^41 + 22 * q^42 + 24 * q^46 - 8 * q^47 - 8 * q^48 + 6 * q^49 + 32 * q^50 - 4 * q^52 + 22 * q^54 + 8 * q^55 + 8 * q^56 - 52 * q^57 + 33 * q^58 + 56 * q^60 - 14 * q^62 + 32 * q^63 + 26 * q^64 + 30 * q^65 - 104 * q^66 + 23 * q^68 - 16 * q^70 + 30 * q^71 + 17 * q^72 - 12 * q^73 - 7 * q^74 + 14 * q^76 - 8 * q^78 - 48 * q^79 + 29 * q^80 + 8 * q^81 - q^82 + 60 * q^84 - 96 * q^86 - 26 * q^87 + 4 * q^88 - 22 * q^89 - 50 * q^90 - 80 * q^92 - 42 * q^94 + 60 * q^95 - 40 * q^96 + 2 * q^97 - 17 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/104\mathbb{Z}\right)^\times$.

$n$	$41$	$53$	$79$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.02392	+	0.975496i	0.724019	+	0.689780i
$2$	1.02392	+	0.975496i	0.724019	+	0.689780i
$3$	0.609172	−	0.351705i	0.351705	−	0.203057i	−0.313731	−	0.949512i	$-0.601579\pi$
$3$	0.609172	−	0.351705i	0.351705	−	0.203057i	0.665436	+	0.746455i	$0.268246\pi$
$4$	0.0968157	+	1.99766i	0.0484079	+	0.998828i
$5$		−	2.24007i		−	1.00179i	−0.865508	−	0.500895i	$-0.833004\pi$
$5$		−	2.24007i		−	1.00179i	0.865508	−	0.500895i	$-0.166996\pi$
$6$	0.966829	+	0.234127i	0.394706	+	0.0955819i
$7$	0.471952	−	0.817445i	0.178381	−	0.308965i	−0.762945	−	0.646463i	$-0.776247\pi$
$7$	0.471952	−	0.817445i	0.178381	−	0.308965i	0.941326	+	0.337498i	$0.109581\pi$
$8$	−1.84957	+	2.13988i	−0.653923	+	0.756561i
$9$	−1.25261	+	2.16958i	−0.417536	+	0.723193i
$10$	2.18518	−	2.29365i	0.691014	−	0.725315i
$11$	−4.82849	+	2.78773i	−1.45584	+	0.840532i	−0.998803	−	0.0489128i	$-0.984424\pi$
$11$	−4.82849	+	2.78773i	−1.45584	+	0.840532i	−0.457042	+	0.889445i	$0.651091\pi$
$12$	0.761563	+	1.18286i	0.219844	+	0.341463i
$13$	−0.108823	−	3.60391i	−0.0301821	−	0.999544i
$13$	−0.108823	−	3.60391i	−0.0301821	−	0.999544i
$14$	1.28065	−	0.376609i	0.342269	−	0.100653i
$15$	−0.787845	−	1.36459i	−0.203421	−	0.352335i
$16$	−3.98125	+	0.386809i	−0.995313	+	0.0967022i
$17$	3.03119	−	5.25017i	0.735170	−	1.27335i	−0.219478	−	0.975617i	$-0.570435\pi$
$17$	3.03119	−	5.25017i	0.735170	−	1.27335i	0.954649	−	0.297735i	$-0.0962312\pi$
$18$	−3.39898	+	0.999558i	−0.801148	+	0.235598i
$19$	1.43961	+	0.831159i	0.330269	+	0.190681i	0.655961	−	0.754795i	$-0.272264\pi$
$19$	1.43961	+	0.831159i	0.330269	+	0.190681i	−0.325692	+	0.945476i	$0.605597\pi$
$20$	4.47489	−	0.216874i	1.00062	−	0.0484945i
$21$		−	0.663952i		−	0.144886i
$22$	−7.66340	−	1.85577i	−1.63384	−	0.395651i
$23$	1.07746	+	1.86621i	0.224665	+	0.389131i	0.956219	−	0.292652i	$-0.0945379\pi$
$23$	1.07746	+	1.86621i	0.224665	+	0.389131i	−0.731554	+	0.681784i	$0.761205\pi$
$24$	−0.374101	+	1.95406i	−0.0763630	+	0.398870i
$25$	−0.0179136			−0.00358271
$26$	3.40417	−	3.79626i	0.667613	−	0.744508i
$27$			3.87243i			0.745249i
$28$	1.67867	+	0.863656i	0.317238	+	0.163216i
$29$	−1.68452	+	0.972558i	−0.312807	+	0.180599i	−0.648182	−	0.761485i	$-0.724470\pi$
$29$	−1.68452	+	0.972558i	−0.312807	+	0.180599i	0.335375	+	0.942085i	$0.391137\pi$
$30$	0.524461	−	2.16576i	0.0957530	−	0.395413i
$31$	−1.91161			−0.343335			−0.171668	−	0.985155i	$-0.554916\pi$
$31$	−1.91161			−0.343335			−0.171668	+	0.985155i	$0.554916\pi$
$32$	−4.45381	−	3.48764i	−0.787329	−	0.616533i
$33$	−1.96092	+	3.39641i	−0.341352	+	0.591239i
$34$	8.22520	−	2.41883i	1.41061	−	0.414826i
$35$	−1.83113	−	1.05721i	−0.309518	−	0.178700i
$36$	−4.45534	−	2.29223i	−0.742557	−	0.382038i
$37$	4.54154	−	2.62206i	0.746624	−	0.431064i	−0.0778488	−	0.996965i	$-0.524805\pi$
$37$	4.54154	−	2.62206i	0.746624	−	0.431064i	0.824473	+	0.565902i	$0.191472\pi$
$38$	0.663250	+	2.25537i	0.107593	+	0.365870i
$39$	−1.33381	−	2.15712i	−0.213580	−	0.345416i
$40$	4.79348	+	4.14317i	0.757915	+	0.655093i
$41$	−0.332039	−	0.575109i	−0.0518558	−	0.0898169i	0.838932	−	0.544236i	$-0.183180\pi$
$41$	−0.332039	−	0.575109i	−0.0518558	−	0.0898169i	−0.890788	+	0.454419i	$0.849847\pi$
$42$	0.647683	−	0.679833i	0.0999396	−	0.104900i
$43$	6.97919	+	4.02944i	1.06432	+	0.614483i	0.926623	−	0.375992i	$-0.122698\pi$
$43$	6.97919	+	4.02944i	1.06432	+	0.614483i	0.137693	+	0.990475i	$0.456031\pi$
$44$	−6.03640	−	9.37576i	−0.910021	−	1.41345i
$45$	4.86001	+	2.80593i	0.724487	+	0.418283i
$46$	−0.717252	+	2.96190i	−0.105753	+	0.436708i
$47$	−10.5778			−1.54293			−0.771466	−	0.636270i	$-0.780476\pi$
$47$	−10.5778			−1.54293			−0.771466	+	0.636270i	$0.780476\pi$
$48$	−2.28922	+	1.63586i	−0.330421	+	0.236116i
$49$	3.05452	+	5.29059i	0.436360	+	0.755798i
$50$	−0.0183420	−	0.0174746i	−0.00259395	−	0.00247128i
$51$		−	4.26434i		−	0.597127i
$52$	7.18883	−	0.566307i	0.996912	−	0.0785326i
$53$			10.3882i			1.42693i	0.700691	+	0.713465i	$0.252875\pi$
$53$			10.3882i			1.42693i	−0.700691	+	0.713465i	$0.747125\pi$
$54$	−3.77754	+	3.96505i	−0.514057	+	0.539574i
$55$	6.24471	+	10.8162i	0.842037	+	1.45845i
$56$	0.876323	+	2.52184i	0.117104	+	0.336996i
$57$	1.16929			0.154877
$58$	−2.67354	−	0.647422i	−0.351052	−	0.0850107i
$59$	0.411368	+	0.237503i	0.0535555	+	0.0309203i	0.526539	−	0.850151i	$-0.323490\pi$
$59$	0.411368	+	0.237503i	0.0535555	+	0.0309203i	−0.472983	+	0.881071i	$0.656823\pi$
$60$	2.64970	−	1.70596i	0.342075	−	0.220238i
$61$	−3.06666	−	1.77054i	−0.392646	−	0.226694i	0.290660	−	0.956826i	$-0.406125\pi$
$61$	−3.06666	−	1.77054i	−0.392646	−	0.226694i	−0.683306	+	0.730132i	$0.739459\pi$
$62$	−1.95733	−	1.86477i	−0.248581	−	0.236826i
$63$	1.18234	+	2.04787i	0.148961	+	0.258008i
$64$	−1.15816	−	7.91572i	−0.144770	−	0.989465i
$65$	−8.07301	+	0.243772i	−1.00133	+	0.0302362i
$66$	−5.32101	+	1.56478i	−0.654971	+	0.192611i
$67$	3.91067	−	2.25783i	0.477764	−	0.275837i	−0.241720	−	0.970346i	$-0.577712\pi$
$67$	3.91067	−	2.25783i	0.477764	−	0.275837i	0.719484	+	0.694509i	$0.244378\pi$
$68$	10.7815	+	5.54696i	1.30745	+	0.672668i
$69$	1.31271	+	0.757894i	0.158032	+	0.0912397i
$70$	−0.843631	−	2.86876i	−0.100833	−	0.342882i
$71$	5.81695	−	10.0753i	0.690345	−	1.19571i	−0.281379	−	0.959597i	$-0.590792\pi$
$71$	5.81695	−	10.0753i	0.690345	−	1.19571i	0.971725	−	0.236117i	$-0.0758748\pi$
$72$	−2.32585	−	6.69322i	−0.274104	−	0.788804i
$73$	−1.91680			−0.224345			−0.112172	−	0.993689i	$-0.535781\pi$
$73$	−1.91680			−0.224345			−0.112172	+	0.993689i	$0.535781\pi$
$74$	7.20797	+	1.74548i	0.837909	+	0.202908i
$75$	−0.0109124	+	0.00630029i	−0.00126006	+	0.000727495i
$76$	−1.52099	+	2.95631i	−0.174470	+	0.339112i
$77$			5.26270i			0.599741i
$78$	0.738558	−	3.50984i	0.0836253	−	0.397411i
$79$	13.6120			1.53147			0.765737	−	0.643154i	$-0.222374\pi$
$79$	13.6120			1.53147			0.765737	+	0.643154i	$0.222374\pi$
$80$	0.866479	+	8.91829i	0.0968753	+	0.997095i
$81$	−2.39587	−	4.14976i	−0.266207	−	0.461085i
$82$	0.221035	−	0.912767i	0.0244093	−	0.100798i
$83$		−	11.5623i		−	1.26913i	−0.772871	−	0.634564i	$-0.781180\pi$
$83$		−	11.5623i		−	1.26913i	0.772871	−	0.634564i	$-0.218820\pi$
$84$	1.32635	−	0.0642810i	0.144716	−	0.00701364i
$85$	−11.7607	−	6.79007i	−1.27563	−	0.736486i
$86$	3.21542	+	10.9340i	0.346727	+	1.17904i
$87$	−0.684108	+	1.18491i	−0.0733440	+	0.127036i
$88$	2.96524	−	15.4885i	0.316096	−	1.65108i
$89$	−0.373638	−	0.647161i	−0.0396056	−	0.0685989i	0.845543	−	0.533907i	$-0.179277\pi$
$89$	−0.373638	−	0.647161i	−0.0396056	−	0.0685989i	−0.885149	+	0.465308i	$0.845943\pi$
$90$	2.23908	+	7.61396i	0.236020	+	0.802581i
$91$	−2.99736	−	1.61192i	−0.314208	−	0.168975i
$92$	−3.62373	+	2.33306i	−0.377800	+	0.243239i
$93$	−1.16450	+	0.672324i	−0.120753	+	0.0697167i
$94$	−10.8308	−	10.3186i	−1.11711	−	1.06428i
$95$	1.86185	−	3.22483i	0.191022	−	0.330860i
$96$	−3.93975	−	0.558140i	−0.402099	−	0.0569650i
$97$	0.640742	−	1.10980i	0.0650575	−	0.112683i	−0.831662	−	0.555282i	$-0.812610\pi$
$97$	0.640742	−	1.10980i	0.0650575	−	0.112683i	0.896719	+	0.442599i	$0.145944\pi$
$98$	−2.03337	+	8.39680i	−0.205401	+	0.848205i
$99$		−	13.9677i		−	1.40381i
$100$	−0.00173431	−	0.0357851i	−0.000173431	−	0.00357851i
$101$	−8.45583	+	4.88197i	−0.841386	+	0.485775i	−0.857735	−	0.514092i	$-0.828129\pi$
$101$	−8.45583	+	4.88197i	−0.841386	+	0.485775i	0.0163490	+	0.999866i	$0.494796\pi$
$102$	4.15984	−	4.36633i	0.411886	−	0.432331i
$103$	−15.0755			−1.48544			−0.742719	−	0.669604i	$-0.766464\pi$
$103$	−15.0755			−1.48544			−0.742719	+	0.669604i	$0.766464\pi$
$104$	7.91320	+	6.43282i	0.775953	+	0.630790i
$105$	−1.48730			−0.145146
$106$	−10.1337	+	10.6367i	−0.984267	+	1.03312i
$107$	−13.6044	+	7.85448i	−1.31518	+	0.759321i	−0.982949	−	0.183876i	$-0.941135\pi$
$107$	−13.6044	+	7.85448i	−1.31518	+	0.759321i	−0.332233	+	0.943197i	$0.607802\pi$
$108$	−7.73577	+	0.374912i	−0.744375	+	0.0360759i
$109$			9.69920i			0.929015i	0.885569	+	0.464508i	$0.153769\pi$
$109$			9.69920i			0.929015i	−0.885569	+	0.464508i	$0.846231\pi$
$110$	−4.15704	+	17.1665i	−0.396359	+	1.63677i
$111$	1.84438	−	3.19457i	0.175061	−	0.303215i
$112$	−1.56277	+	3.43701i	−0.147668	+	0.324767i
$113$	3.78116	−	6.54916i	0.355701	−	0.616093i	−0.631536	−	0.775346i	$-0.717575\pi$
$113$	3.78116	−	6.54916i	0.355701	−	0.616093i	0.987238	+	0.159253i	$0.0509087\pi$
$114$	1.19726	+	1.14064i	0.112134	+	0.106831i
$115$	4.18044	−	2.41358i	0.389828	−	0.225067i
$116$	−2.10592	−	3.27093i	−0.195530	−	0.303698i
$117$	7.95528	+	4.27818i	0.735465	+	0.395518i
$118$	0.189523	+	0.644472i	0.0174470	+	0.0593284i
$119$	−2.86115	−	4.95566i	−0.262281	−	0.454284i
$120$	4.37723	+	0.838012i	0.399584	+	0.0764996i
$121$	10.0429	−	17.3948i	0.912989	−	1.58134i
$122$	−1.41286	−	4.80441i	−0.127914	−	0.434970i
$123$	−0.404538	−	0.233560i	−0.0364759	−	0.0210594i
$124$	−0.185074	−	3.81874i	−0.0166201	−	0.342933i
$125$		−	11.1602i		−	0.998201i
$126$	−0.787073	+	3.25022i	−0.0701180	+	0.289553i
$127$	−1.53962	−	2.66670i	−0.136619	−	0.236632i	0.789596	−	0.613628i	$-0.210290\pi$
$127$	−1.53962	−	2.66670i	−0.136619	−	0.236632i	−0.926215	+	0.376996i	$0.876957\pi$
$128$	6.53589	−	9.23483i	0.577697	−	0.816251i
$129$	5.66870			0.499101
$130$	−8.50390	−	7.62558i	−0.745841	−	0.668808i
$131$		−	11.9145i		−	1.04098i	−0.853869	−	0.520488i	$-0.825750\pi$
$131$		−	11.9145i		−	1.04098i	0.853869	−	0.520488i	$-0.174250\pi$
$132$	−6.97471	−	3.58842i	−0.607070	−	0.312331i
$133$	1.35885	−	0.784534i	0.117828	−	0.0680278i
$134$	6.20671	+	1.50301i	0.536178	+	0.129841i
$135$	8.67451			0.746583
$136$	5.62832	+	16.1969i	0.482624	+	1.38888i
$137$	−10.2342	+	17.7261i	−0.874365	+	1.51444i	−0.0169276	+	0.999857i	$0.505388\pi$
$137$	−10.2342	+	17.7261i	−0.874365	+	1.51444i	−0.857437	+	0.514588i	$0.827945\pi$
$138$	0.604786	+	2.05657i	0.0514828	+	0.175066i
$139$	7.01589	+	4.05062i	0.595080	+	0.343570i	0.767104	−	0.641523i	$-0.221697\pi$
$139$	7.01589	+	4.05062i	0.595080	+	0.343570i	−0.172024	+	0.985093i	$0.555031\pi$
$140$	1.93465	−	3.76033i	0.163508	−	0.317806i
$141$	−6.44370	+	3.72027i	−0.542658	+	0.313304i
$142$	15.7845	−	4.64182i	1.32460	−	0.389533i
$143$	10.5722	+	17.0981i	0.884090	+	1.42981i
$144$	4.14773	−	9.12216i	0.345644	−	0.760180i
$145$	2.17860	+	3.77344i	0.180923	+	0.313367i
$146$	−1.96265	−	1.86983i	−0.162430	−	0.154748i
$147$	3.72146	+	2.14858i	0.306941	+	0.177212i
$148$	5.67766	+	8.81857i	0.466701	+	0.724882i
$149$	−3.13501	−	1.81000i	−0.256830	−	0.148281i	0.366058	−	0.930592i	$-0.380707\pi$
$149$	−3.13501	−	1.81000i	−0.256830	−	0.148281i	−0.622888	+	0.782311i	$0.714041\pi$
$150$	−0.0173193	−	0.00419404i	−0.00141412	−	0.000342442i
$151$	−16.0939			−1.30970			−0.654850	−	0.755759i	$-0.727268\pi$
$151$	−16.0939			−1.30970			−0.654850	+	0.755759i	$0.727268\pi$
$152$	−4.44124	+	1.54330i	−0.360232	+	0.125178i
$153$	7.59377	+	13.1528i	0.613920	+	1.06334i
$154$	−5.13374	+	5.38857i	−0.413689	+	0.434224i
$155$			4.28214i			0.343950i
$156$	4.18006	−	2.87333i	0.334673	−	0.230050i
$157$		−	15.4274i		−	1.23124i	−0.788042	−	0.615621i	$-0.788905\pi$
$157$		−	15.4274i		−	1.23124i	0.788042	−	0.615621i	$-0.211095\pi$
$158$	13.9376	+	13.2785i	1.10882	+	1.05638i
$159$	3.65359	+	6.32820i	0.289748	+	0.501859i
$160$	−7.81255	+	9.97684i	−0.617636	+	0.788738i
$161$	2.03403			0.160304
$162$	1.59491	−	6.58618i	0.125308	−	0.517459i
$163$	4.33867	+	2.50493i	0.339831	+	0.196201i	0.660197	−	0.751092i	$-0.270473\pi$
$163$	4.33867	+	2.50493i	0.339831	+	0.196201i	−0.320366	+	0.947294i	$0.603806\pi$
$164$	1.11672	−	0.718980i	0.0872014	−	0.0561429i
$165$	7.60820	+	4.39260i	0.592298	+	0.341963i
$166$	11.2790	−	11.8388i	0.875418	−	0.918873i
$167$	−0.532199	−	0.921796i	−0.0411828	−	0.0713308i	0.844699	−	0.535241i	$-0.179779\pi$
$167$	−0.532199	−	0.921796i	−0.0411828	−	0.0713308i	−0.885882	+	0.463910i	$0.846446\pi$
$168$	1.42078	+	1.22803i	0.109615	+	0.0947445i
$169$	−12.9763	+	0.784378i	−0.998178	+	0.0603368i
$170$	−5.41835	−	18.4250i	−0.415569	−	1.41314i
$171$	−3.60653	+	2.08223i	−0.275798	+	0.159232i
$172$	−7.37373	+	14.3321i	−0.562241	+	1.09281i
$173$	18.9047	+	10.9146i	1.43730	+	0.829825i	0.997661	−	0.0683503i	$-0.0217736\pi$
$173$	18.9047	+	10.9146i	1.43730	+	0.829825i	0.439638	+	0.898175i	$0.355107\pi$
$174$	−1.85634	+	0.545905i	−0.140729	+	0.0413850i
$175$	−0.00845434	+	0.0146433i	−0.000639088	+	0.00110693i
$176$	18.1451	−	12.9664i	1.36774	−	0.977377i
$177$	0.334125			0.0251144
$178$	0.248728	−	1.02712i	0.0186429	−	0.0769861i
$179$	−2.82862	+	1.63310i	−0.211421	+	0.122064i	−0.601972	−	0.798517i	$-0.705618\pi$
$179$	−2.82862	+	1.63310i	−0.211421	+	0.122064i	0.390551	+	0.920581i	$0.372285\pi$
$180$	−5.13475	+	9.98028i	−0.382722	+	0.743886i
$181$		−	13.1229i		−	0.975420i	−0.873006	−	0.487710i	$-0.837832\pi$
$181$		−	13.1229i		−	0.975420i	0.873006	−	0.487710i	$-0.162168\pi$
$182$	−1.49663	−	4.57438i	−0.110938	−	0.339075i
$183$	−2.49083			−0.184128
$184$	−5.98629	−	1.14606i	−0.441315	−	0.0844890i
$185$	−5.87359	−	10.1734i	−0.431835	−	0.747960i
$186$	−1.84820	−	0.447559i	−0.135517	−	0.0328167i
$187$			33.8005i			2.47174i
$188$	−1.02410	−	21.1308i	−0.0746901	−	1.54112i
$189$	3.16550	+	1.82760i	0.230256	+	0.132938i
$190$	5.05219	−	1.48573i	0.366524	−	0.107786i
$191$	4.02136	−	6.96520i	0.290975	−	0.503984i	−0.683065	−	0.730357i	$-0.739354\pi$
$191$	4.02136	−	6.96520i	0.290975	−	0.503984i	0.974041	+	0.226373i	$0.0726869\pi$
$192$	−3.48952	−	4.41470i	−0.251834	−	0.318604i
$193$	0.417932	+	0.723880i	0.0300834	+	0.0521060i	0.880675	−	0.473721i	$-0.157089\pi$
$193$	0.417932	+	0.723880i	0.0300834	+	0.0521060i	−0.850592	+	0.525827i	$0.823756\pi$
$194$	1.73867	−	0.511300i	0.124829	−	0.0367092i
$195$	−4.83211	+	2.98782i	−0.346035	+	0.213962i
$196$	−10.2730	+	6.61409i	−0.733789	+	0.472435i
$197$	6.06608	−	3.50225i	0.432190	−	0.249525i	−0.268089	−	0.963394i	$-0.586392\pi$
$197$	6.06608	−	3.50225i	0.432190	−	0.249525i	0.700279	+	0.713869i	$0.253059\pi$
$198$	13.6255	−	14.3018i	0.968319	−	1.01638i
$199$	−7.51756	+	13.0208i	−0.532906	+	0.923019i	0.466356	+	0.884597i	$0.345567\pi$
$199$	−7.51756	+	13.0208i	−0.532906	+	0.923019i	−0.999262	+	0.0384223i	$0.987767\pi$
$200$	0.0331324	−	0.0383328i	0.00234282	−	0.00271054i
$201$	1.58818	−	2.75081i	0.112022	−	0.194027i
$202$	−13.4204	−	3.24988i	−0.944257	−	0.228661i
$203$			1.83600i			0.128862i
$204$	8.51867	−	0.412855i	0.596427	−	0.0289056i
$205$	−1.28828	+	0.743791i	−0.0899777	+	0.0519486i
$206$	−15.4361	−	14.7061i	−1.07549	−	1.02462i
$207$	−5.39851			−0.375223
$208$	1.82728	+	14.3060i	0.126699	+	0.991941i
$209$	−9.26819			−0.641094
$210$	−1.52287	−	1.45085i	−0.105088	−	0.100118i
$211$	5.82236	−	3.36154i	0.400828	−	0.231418i	−0.286013	−	0.958226i	$-0.592330\pi$
$211$	5.82236	−	3.36154i	0.400828	−	0.231418i	0.686841	+	0.726808i	$0.258997\pi$
$212$	−20.7521	+	1.00574i	−1.42526	+	0.0690746i
$213$		−	8.18342i		−	0.560718i
$214$	−21.5918	−	5.22865i	−1.47598	−	0.357423i
$215$	9.02622	−	15.6339i	0.615583	−	1.06622i
$216$	−8.28652	−	7.16233i	−0.563826	−	0.487335i
$217$	−0.902189	+	1.56264i	−0.0612446	+	0.106079i
$218$	−9.46153	+	9.93119i	−0.640816	+	0.672625i
$219$	−1.16766	+	0.674149i	−0.0789032	+	0.0455548i
$220$	−21.0024	+	13.5220i	−1.41598	+	0.911650i
$221$	−19.2510	−	10.3528i	−1.29496	−	0.696403i
$222$	5.00478	−	1.47178i	0.335899	−	0.0987797i
$223$	−10.4340	−	18.0723i	−0.698715	−	1.21021i	−0.968912	−	0.247404i	$-0.920422\pi$
$223$	−10.4340	−	18.0723i	−0.698715	−	1.21021i	0.270198	−	0.962805i	$-0.412911\pi$
$224$	−4.95293	+	1.99475i	−0.330932	+	0.133280i
$225$	0.0224386	−	0.0388649i	0.00149591	−	0.00259099i
$226$	10.2603	−	3.01730i	0.682503	−	0.200707i
$227$	16.7688	+	9.68145i	1.11298	+	0.642580i	0.939600	−	0.342274i	$-0.111197\pi$
$227$	16.7688	+	9.68145i	1.11298	+	0.642580i	0.173382	+	0.984855i	$0.444531\pi$
$228$	0.113206	+	2.33584i	0.00749724	+	0.154695i
$229$			17.6044i			1.16333i	0.813428	+	0.581666i	$0.197599\pi$
$229$			17.6044i			1.16333i	−0.813428	+	0.581666i	$0.802401\pi$
$230$	6.63486	+	1.60669i	0.437490	+	0.105942i
$231$	1.85092	+	3.20589i	0.121782	+	0.210932i
$232$	1.03449	−	5.40348i	0.0679174	−	0.354756i
$233$	15.3281			1.00417			0.502087	−	0.864817i	$-0.332566\pi$
$233$	15.3281			1.00417			0.502087	+	0.864817i	$0.332566\pi$
$234$	3.97220	+	12.1408i	0.259671	+	0.793672i
$235$			23.6950i			1.54569i
$236$	−0.434623	+	0.844765i	−0.0282915	+	0.0549895i
$237$	8.29207	−	4.78743i	0.538628	−	0.310977i
$238$	1.90464	−	7.86522i	0.123459	−	0.509827i
$239$	−14.0854			−0.911111			−0.455556	−	0.890207i	$-0.650559\pi$
$239$	−14.0854			−0.911111			−0.455556	+	0.890207i	$0.650559\pi$
$240$	3.66444	+	5.12802i	0.236539	+	0.331012i
$241$	−7.24993	+	12.5572i	−0.467009	+	0.808883i	−0.999290	−	0.0376849i	$-0.988002\pi$
$241$	−7.24993	+	12.5572i	−0.467009	+	0.808883i	0.532281	+	0.846568i	$0.321335\pi$
$242$	27.2516	−	8.01404i	1.75180	−	0.515162i
$243$	−12.9798	−	7.49392i	−0.832658	−	0.480735i
$244$	3.24003	−	6.29756i	0.207421	−	0.403160i
$245$	11.8513	−	6.84234i	0.757151	−	0.437141i
$246$	−0.186377	−	0.633771i	−0.0118829	−	0.0404078i
$247$	2.83876	−	5.27867i	0.180626	−	0.335874i
$248$	3.53566	−	4.09061i	0.224515	−	0.259754i
$249$	−4.06652	−	7.04342i	−0.257705	−	0.446359i
$250$	10.8868	−	11.4272i	0.688539	−	0.722717i
$251$	−24.8381	−	14.3403i	−1.56777	−	0.905151i	−0.996429	−	0.0844378i	$-0.973091\pi$
$251$	−24.8381	−	14.3403i	−1.56777	−	0.905151i	−0.571340	−	0.820714i	$-0.693576\pi$
$252$	−3.97648	+	2.56018i	−0.250495	+	0.161276i
$253$	−10.4050	−	6.00731i	−0.654155	−	0.377677i
$254$	1.02491	−	4.23238i	0.0643087	−	0.265563i
$255$	−9.55241			−0.598195
$256$	15.7008	−	3.07997i	0.981297	−	0.192498i
$257$	5.81269	+	10.0679i	0.362586	+	0.628017i	0.988386	−	0.151967i	$-0.0485607\pi$
$257$	5.81269	+	10.0679i	0.362586	+	0.628017i	−0.625800	+	0.779984i	$0.715227\pi$
$258$	5.80428	+	5.52979i	0.361359	+	0.344270i
$259$		−	4.94994i		−	0.307574i
$260$	−1.26857	−	16.1035i	−0.0786731	−	0.998696i
$261$		−	4.87293i		−	0.301627i
$262$	11.6226	−	12.1995i	0.718044	−	0.753687i
$263$	8.47469	+	14.6786i	0.522572	+	0.905121i	0.999655	+	0.0262631i	$0.00836075\pi$
$263$	8.47469	+	14.6786i	0.522572	+	0.905121i	−0.477083	+	0.878858i	$0.658306\pi$
$264$	−3.64105	−	10.4780i	−0.224091	−	0.644879i
$265$	23.2703			1.42948
$266$	2.15666	+	0.522257i	0.132234	+	0.0320216i
$267$	−0.455220	−	0.262821i	−0.0278590	−	0.0160844i
$268$	4.88897	+	7.59358i	0.298642	+	0.463852i
$269$	6.45180	+	3.72495i	0.393373	+	0.227114i	0.683621	−	0.729837i	$-0.260404\pi$
$269$	6.45180	+	3.72495i	0.393373	+	0.227114i	−0.290247	+	0.956952i	$0.593738\pi$
$270$	8.88198	+	8.46194i	0.540540	+	0.514978i
$271$	7.61248	+	13.1852i	0.462425	+	0.800944i	0.999081	−	0.0428569i	$-0.0136459\pi$
$271$	7.61248	+	13.1852i	0.462425	+	0.800944i	−0.536656	+	0.843801i	$0.680313\pi$
$272$	−10.0371	+	22.0747i	−0.608589	+	1.33848i
$273$	−2.39282	+	0.0722535i	−0.144820	+	0.00437298i
$274$	−27.7707	+	8.16669i	−1.67769	+	0.493368i
$275$	0.0864954	−	0.0499382i	0.00521587	−	0.00301138i
$276$	−1.38692	+	2.69572i	−0.0834828	+	0.162263i
$277$	−13.9928	−	8.07878i	−0.840749	−	0.485407i	0.0167699	−	0.999859i	$-0.494662\pi$
$277$	−13.9928	−	8.07878i	−0.840749	−	0.485407i	−0.857519	+	0.514453i	$0.827995\pi$
$278$	3.23233	+	10.9915i	0.193862	+	0.659225i
$279$	2.39450	−	4.14739i	0.143355	−	0.248298i
$280$	5.64911	−	1.96303i	0.337599	−	0.117313i
$281$	27.7204			1.65366			0.826831	−	0.562450i	$-0.190141\pi$
$281$	27.7204			1.65366			0.826831	+	0.562450i	$0.190141\pi$
$282$	−10.2269	−	2.47655i	−0.609005	−	0.147476i
$283$	3.28760	−	1.89810i	0.195428	−	0.112830i	−0.399093	−	0.916910i	$-0.630675\pi$
$283$	3.28760	−	1.89810i	0.195428	−	0.112830i	0.594521	+	0.804080i	$0.297342\pi$
$284$	20.6901	+	10.6448i	1.22773	+	0.631654i
$285$		−	2.61930i		−	0.155154i
$286$	−5.85405	+	27.8201i	−0.346157	+	1.64504i
$287$	−0.626827			−0.0370004
$288$	13.1456	−	5.29425i	0.774610	−	0.311967i
$289$	−9.87617	−	17.1060i	−0.580951	−	1.00624i
$290$	−1.45027	+	5.98891i	−0.0851629	+	0.351681i
$291$		−	0.901409i		−	0.0528415i
$292$	−0.185577	−	3.82911i	−0.0108600	−	0.224082i
$293$	4.14791	+	2.39480i	0.242324	+	0.139906i	0.616244	−	0.787555i	$-0.288653\pi$
$293$	4.14791	+	2.39480i	0.242324	+	0.139906i	−0.373921	+	0.927461i	$0.621987\pi$
$294$	1.71453	+	5.83024i	0.0999935	+	0.340026i
$295$	0.532024	−	0.921493i	0.0309756	−	0.0536514i
$296$	−2.78902	+	14.5680i	−0.162108	+	0.846749i
$297$	−10.7953	−	18.6980i	−0.626406	−	1.08497i
$298$	−1.44435	−	4.91148i	−0.0836687	−	0.284514i
$299$	6.60839	−	4.08614i	0.382173	−	0.236308i
$300$	−0.0136423	−	0.0211893i	−0.000787639	−	0.00122336i
$301$	6.58768	−	3.80340i	0.379708	−	0.219224i
$302$	−16.4788	−	15.6995i	−0.948249	−	0.903405i
$303$	−3.43403	+	5.94792i	−0.197280	+	0.341699i
$304$	−6.05295	−	2.75220i	−0.347160	−	0.157849i
$305$	−3.96613	+	6.86954i	−0.227100	+	0.393349i
$306$	−5.05510	+	20.8751i	−0.288981	+	1.19335i
$307$		−	8.95981i		−	0.511363i	−0.966761	−	0.255682i	$-0.917700\pi$
$307$		−	8.95981i		−	0.511363i	0.966761	−	0.255682i	$-0.0822999\pi$
$308$	−10.5131	+	0.509512i	−0.599037	+	0.0290322i
$309$	−9.18359	+	5.30215i	−0.522436	+	0.301629i
$310$	−4.17721	+	4.38456i	−0.237250	+	0.249026i
$311$	9.35196			0.530301			0.265150	−	0.964207i	$-0.414578\pi$
$311$	9.35196			0.530301			0.265150	+	0.964207i	$0.414578\pi$
$312$	7.08296	+	1.13558i	0.400993	+	0.0642894i
$313$	−11.7834			−0.666039			−0.333019	−	0.942920i	$-0.608067\pi$
$313$	−11.7834			−0.666039			−0.333019	+	0.942920i	$0.608067\pi$
$314$	15.0494	−	15.7964i	0.849286	−	0.891443i
$315$	4.58738	−	2.64853i	0.258470	−	0.149228i
$316$	1.31786	+	27.1922i	0.0741354	+	1.52968i
$317$		−	0.828044i		−	0.0465076i	−0.999730	−	0.0232538i	$-0.992597\pi$
$317$		−	0.828044i		−	0.0465076i	0.999730	−	0.0232538i	$-0.00740258\pi$
$318$	−2.43216	+	10.0436i	−0.136389	+	0.563218i
$319$	5.42246	−	9.39197i	0.303599	−	0.525850i
$320$	−17.7318	+	2.59436i	−0.991236	+	0.145029i
$321$	−5.52492	+	9.56945i	−0.308371	+	0.534114i
$322$	2.08268	+	1.98419i	0.116063	+	0.110574i
$323$	8.72745	−	5.03879i	0.485608	−	0.280366i
$324$	8.05784	−	5.18788i	0.447658	−	0.288216i
$325$	0.00194941	+	0.0645588i	0.000108134	+	0.00358108i
$326$	1.99889	+	6.79720i	0.110708	+	0.376462i
$327$	3.41126	+	5.90848i	0.188643	+	0.326740i
$328$	1.84479	+	0.353182i	0.101862	+	0.0195012i
$329$	−4.99222	+	8.64678i	−0.275230	+	0.476712i
$330$	3.50521	+	11.9194i	0.192956	+	0.656143i
$331$	−12.8419	−	7.41425i	−0.705853	−	0.407524i	0.103671	−	0.994612i	$-0.466941\pi$
$331$	−12.8419	−	7.41425i	−0.705853	−	0.407524i	−0.809524	+	0.587087i	$0.800274\pi$
$332$	23.0975	−	1.11941i	1.26764	−	0.0614357i
$333$			13.1376i			0.719937i
$334$	0.354280	−	1.46300i	0.0193853	−	0.0800519i
$335$	−5.05769	−	8.76018i	−0.276331	−	0.478620i
$336$	0.256823	+	2.64336i	0.0140108	+	0.144207i
$337$	5.53901			0.301729			0.150865	−	0.988554i	$-0.451794\pi$
$337$	5.53901			0.301729			0.150865	+	0.988554i	$0.451794\pi$
$338$	−14.0518	−	11.8552i	−0.764319	−	0.644838i
$339$		−	5.31941i		−	0.288911i
$340$	12.4256	−	24.1513i	0.673872	−	1.30979i
$341$	9.23019	−	5.32906i	0.499843	−	0.288585i
$342$	−5.72400	−	1.38612i	−0.309518	−	0.0749528i
$343$	12.3737			0.668116
$344$	−21.5310	+	7.48188i	−1.16087	+	0.403396i
$345$	1.69774	−	2.94056i	0.0914030	−	0.158315i
$346$	8.70969	+	29.6172i	0.468236	+	1.59223i
$347$	13.9803	+	8.07154i	0.750503	+	0.433303i	0.825876	−	0.563852i	$-0.190681\pi$
$347$	13.9803	+	8.07154i	0.750503	+	0.433303i	−0.0753728	+	0.997155i	$0.524015\pi$
$348$	−2.43327	−	1.25189i	−0.130437	−	0.0671085i
$349$	−20.7087	+	11.9562i	−1.10851	+	0.640000i	−0.938444	−	0.345432i	$-0.887732\pi$
$349$	−20.7087	+	11.9562i	−1.10851	+	0.640000i	−0.170068	+	0.985432i	$0.554399\pi$
$350$	−0.0229411	+	0.00674641i	−0.00122625	+	0.000360611i
$351$	13.9559	−	0.421410i	0.744909	−	0.0224932i
$352$	31.2278	+	4.42400i	1.66445	+	0.235800i
$353$	−2.77899	−	4.81335i	−0.147911	−	0.256189i	0.782544	−	0.622595i	$-0.213921\pi$
$353$	−2.77899	−	4.81335i	−0.147911	−	0.256189i	−0.930455	+	0.366406i	$0.880588\pi$
$354$	0.342116	+	0.325937i	0.0181833	+	0.0173234i
$355$	−22.5693	−	13.0304i	−1.19785	−	0.691581i
$356$	1.25663	−	0.809056i	0.0666013	−	0.0428799i
$357$	−3.48586	−	2.01256i	−0.184491	−	0.106516i
$358$	−4.48936	−	1.08714i	−0.237270	−	0.0574572i
$359$	−8.55135			−0.451323			−0.225661	−	0.974206i	$-0.572454\pi$
$359$	−8.55135			−0.451323			−0.225661	+	0.974206i	$0.572454\pi$
$360$	−14.9933	+	5.21006i	−0.790215	+	0.274594i
$361$	−8.11835	−	14.0614i	−0.427282	−	0.740073i
$362$	12.8014	−	13.4368i	0.672825	−	0.706223i
$363$		−	14.1285i		−	0.741556i
$364$	2.92986	−	6.14374i	0.153566	−	0.322020i
$365$			4.29377i			0.224746i
$366$	−2.55041	−	2.42980i	−0.133312	−	0.127008i
$367$	1.96700	+	3.40695i	0.102677	+	0.177841i	0.912787	−	0.408437i	$-0.133926\pi$
$367$	1.96700	+	3.40695i	0.102677	+	0.177841i	−0.810110	+	0.586278i	$0.800593\pi$
$368$	−5.01149	−	7.01308i	−0.261242	−	0.365582i
$369$	1.66366			0.0866066
$370$	3.90999	−	16.1463i	0.203271	−	0.839409i
$371$	8.49179	+	4.90274i	0.440872	+	0.254537i
$372$	−1.45581	−	2.26118i	−0.0754804	−	0.117236i
$373$	−6.86329	−	3.96253i	−0.355368	−	0.205172i	0.311679	−	0.950187i	$-0.399109\pi$
$373$	−6.86329	−	3.96253i	−0.355368	−	0.205172i	−0.667047	+	0.745016i	$0.732442\pi$
$374$	−32.9723	+	34.6090i	−1.70495	+	1.78959i
$375$	−3.92511	−	6.79849i	−0.202692	−	0.351073i
$376$	19.5644	−	22.6352i	1.00896	−	1.16732i
$377$	3.68832	+	5.96502i	0.189958	+	0.307214i
$378$	1.45839	+	4.95924i	0.0750116	+	0.255076i
$379$	22.8779	−	13.2086i	1.17516	−	0.678479i	0.220271	−	0.975439i	$-0.429306\pi$
$379$	22.8779	−	13.2086i	1.17516	−	0.678479i	0.954890	+	0.296959i	$0.0959726\pi$
$380$	6.62235	+	3.40713i	0.339719	+	0.174782i
$381$	−1.87579	−	1.08299i	−0.0960995	−	0.0554831i
$382$	10.9121	−	3.20897i	0.558310	−	0.164185i
$383$	−0.947088	+	1.64041i	−0.0483940	+	0.0838208i	−0.889208	−	0.457504i	$-0.848744\pi$
$383$	−0.947088	+	1.64041i	−0.0483940	+	0.0838208i	0.840814	+	0.541325i	$0.182077\pi$
$384$	0.733542	−	7.92430i	0.0374334	−	0.404385i
$385$	11.7888			0.600814
$386$	−0.278214	+	1.14888i	−0.0141607	+	0.0584767i
$387$	−17.4844	+	10.0946i	−0.888780	+	0.513137i
$388$	2.27903	+	1.17254i	0.115700	+	0.0595265i
$389$			25.0808i			1.27165i	0.771835	+	0.635823i	$0.219339\pi$
$389$			25.0808i			1.27165i	−0.771835	+	0.635823i	$0.780661\pi$
$390$	−7.86229	−	1.65442i	−0.398123	−	0.0837749i
$391$	13.0639			0.660669
$392$	−16.9708	−	3.24902i	−0.857154	−	0.164100i
$393$	−4.19040	−	7.25798i	−0.211378	−	0.366117i
$394$	9.62760	+	2.33141i	0.485031	+	0.117455i
$395$		−	30.4919i		−	1.53422i
$396$	27.9027	−	1.35230i	1.40216	−	0.0679554i
$397$	7.99993	+	4.61876i	0.401505	+	0.231809i	0.687133	−	0.726532i	$-0.258869\pi$
$397$	7.99993	+	4.61876i	0.401505	+	0.231809i	−0.285628	+	0.958341i	$0.592202\pi$
$398$	−20.3991	+	5.99888i	−1.02251	+	0.300696i
$399$	0.551850	−	0.955832i	0.0276270	−	0.0478515i
$400$	0.0713184	−	0.00692912i	0.00356592	−	0.000346456i
$401$	−2.21136	−	3.83018i	−0.110430	−	0.191270i	0.805514	−	0.592577i	$-0.201889\pi$
$401$	−2.21136	−	3.83018i	−0.110430	−	0.191270i	−0.915944	+	0.401307i	$0.868556\pi$
$402$	4.30957	−	1.26734i	0.214942	−	0.0632091i
$403$	0.208028	+	6.88927i	0.0103626	+	0.343179i
$404$	−10.5712	−	16.4192i	−0.525935	−	0.816884i
$405$	−9.29576	+	5.36691i	−0.461910	+	0.266684i
$406$	−1.79101	+	1.87992i	−0.0888865	+	0.0932987i
$407$	−14.6192	+	25.3212i	−0.724646	+	1.25512i
$408$	9.12516	+	7.88720i	0.451763	+	0.390475i
$409$	−13.2341	+	22.9221i	−0.654384	+	1.13343i	0.327664	+	0.944794i	$0.393738\pi$
$409$	−13.2341	+	22.9221i	−0.654384	+	1.13343i	−0.982048	+	0.188631i	$0.939595\pi$
$410$	−2.04466	−	0.495135i	−0.100979	−	0.0244530i
$411$			14.3977i			0.710184i
$412$	−1.45955	−	30.1157i	−0.0719068	−	1.48370i
$413$	0.388292	−	0.224180i	0.0191066	−	0.0110312i
$414$	−5.52764	−	5.26623i	−0.271668	−	0.258821i
$415$	−25.9004			−1.27140
$416$	−12.0844	+	16.4307i	−0.592489	+	0.805579i
$417$	5.69851			0.279057
$418$	−9.48986	−	9.04108i	−0.464164	−	0.442214i
$419$	4.30501	−	2.48550i	0.210314	−	0.121425i	−0.391144	−	0.920330i	$-0.627920\pi$
$419$	4.30501	−	2.48550i	0.210314	−	0.121425i	0.601457	+	0.798905i	$0.294587\pi$
$420$	−0.143994	−	2.97111i	−0.00702619	−	0.144975i
$421$			24.0575i			1.17249i	0.810134	+	0.586244i	$0.199394\pi$
$421$			24.0575i			1.17249i	−0.810134	+	0.586244i	$0.800606\pi$
$422$	9.24078	+	2.23774i	0.449834	+	0.108932i
$423$	13.2498	−	22.9494i	0.644229	−	1.11584i
$424$	−22.2295	−	19.2137i	−1.07956	−	0.933102i
$425$	−0.0542993	+	0.0940492i	−0.00263390	+	0.00456205i
$426$	7.98289	−	8.37915i	0.386772	−	0.405971i
$427$	−2.89464	+	1.67122i	−0.140081	+	0.0808760i
$428$	−17.0077	−	26.4164i	−0.822096	−	1.27688i
$429$	12.4538	+	6.69737i	0.601273	+	0.323352i
$430$	24.4929	−	7.20276i	1.18115	−	0.347348i
$431$	−5.28961	−	9.16188i	−0.254792	−	0.441312i	0.710047	−	0.704154i	$-0.248674\pi$
$431$	−5.28961	−	9.16188i	−0.254792	−	0.441312i	−0.964839	+	0.262842i	$0.915340\pi$
$432$	−1.49789	−	15.4171i	−0.0720672	−	0.741756i
$433$	6.11293	−	10.5879i	0.293769	−	0.508822i	−0.680929	−	0.732349i	$-0.738424\pi$
$433$	6.11293	−	10.5879i	0.293769	−	0.508822i	0.974698	+	0.223527i	$0.0717572\pi$
$434$	−2.44811	+	0.719930i	−0.117513	+	0.0345578i
$435$	2.65428	+	1.53245i	0.127263	+	0.0734753i
$436$	−19.3757	+	0.939036i	−0.927926	+	0.0449717i
$437$			3.58215i			0.171357i
$438$	−1.85322	−	0.448775i	−0.0885502	−	0.0214433i
$439$	−6.46417	−	11.1963i	−0.308518	−	0.534369i	0.669520	−	0.742794i	$-0.266500\pi$
$439$	−6.46417	−	11.1963i	−0.308518	−	0.534369i	−0.978038	+	0.208425i	$0.933166\pi$
$440$	−34.6953	−	6.64235i	−1.65403	−	0.316662i
$441$	−15.3045			−0.728784
$442$	−9.61234	−	29.3796i	−0.457212	−	1.39745i
$443$		−	14.0440i		−	0.667248i	−0.942706	−	0.333624i	$-0.891728\pi$
$443$		−	14.0440i		−	0.667248i	0.942706	−	0.333624i	$-0.108272\pi$
$444$	6.56021	+	3.37516i	0.311334	+	0.160178i
$445$	−1.44969	+	0.836976i	−0.0687217	+	0.0396765i
$446$	6.94584	−	28.6829i	0.328895	−	1.35817i
$447$	−2.54634			−0.120438
$448$	−7.01726	−	2.78911i	−0.331535	−	0.131773i
$449$	−0.857113	+	1.48456i	−0.0404497	+	0.0700609i	−0.885541	−	0.464560i	$-0.846212\pi$
$449$	−0.857113	+	1.48456i	−0.0404497	+	0.0700609i	0.845092	+	0.534621i	$0.179546\pi$
$450$	0.0608878	−	0.0179056i	0.00287028	−	0.000844079i
$451$	3.20650	+	1.85127i	0.150988	+	0.0871730i
$452$	13.4490	+	6.91939i	0.632589	+	0.325461i
$453$	−9.80393	+	5.66030i	−0.460629	+	0.265944i
$454$	7.72562	+	26.2709i	0.362581	+	1.23295i
$455$	−3.61080	+	6.71429i	−0.169277	+	0.314771i
$456$	−2.16269	+	2.50214i	−0.101277	+	0.117174i
$457$	14.5822	+	25.2571i	0.682126	+	1.18148i	0.974331	+	0.225121i	$0.0722778\pi$
$457$	14.5822	+	25.2571i	0.682126	+	1.18148i	−0.292205	+	0.956356i	$0.594389\pi$
$458$	−17.1730	+	18.0255i	−0.802443	+	0.842275i
$459$	20.3309	+	11.7380i	0.948964	+	0.547885i
$460$	5.22623	+	8.11740i	0.243674	+	0.378476i
$461$	22.4501	+	12.9616i	1.04561	+	0.603681i	0.921416	−	0.388577i	$-0.127033\pi$
$461$	22.4501	+	12.9616i	1.04561	+	0.603681i	0.124190	+	0.992258i	$0.460367\pi$
$462$	−1.23214	+	5.08813i	−0.0573243	+	0.236721i
$463$	36.7003			1.70561			0.852803	−	0.522233i	$-0.174901\pi$
$463$	36.7003			1.70561			0.852803	+	0.522233i	$0.174901\pi$
$464$	6.33030	−	4.52359i	0.293877	−	0.210002i
$465$	1.50605	+	2.60856i	0.0698415	+	0.120969i
$466$	15.6947	+	14.9525i	0.727042	+	0.692659i
$467$			27.9836i			1.29492i	0.762097	+	0.647462i	$0.224170\pi$
$467$			27.9836i			1.29492i	−0.762097	+	0.647462i	$0.775830\pi$
$468$	−7.77613	+	16.3061i	−0.359452	+	0.753749i
$469$		−	4.26234i		−	0.196817i
$470$	−23.1144	+	24.2618i	−1.06619	+	1.11911i
$471$	−5.42590	−	9.39794i	−0.250012	−	0.433034i
$472$	−1.26908	+	0.440997i	−0.0584143	+	0.0202986i
$473$	−44.9319			−2.06597
$474$	13.1605	+	3.18695i	0.604482	+	0.146381i
$475$	−0.0257885	−	0.0148890i	−0.00118326	−	0.000683155i
$476$	9.62269	−	6.19537i	0.441055	−	0.283965i
$477$	−22.5380	−	13.0123i	−1.03195	−	0.595794i
$478$	−14.4223	−	13.7403i	−0.659662	−	0.628466i
$479$	16.2482	+	28.1426i	0.742397	+	1.28587i	0.951401	+	0.307955i	$0.0996446\pi$
$479$	16.2482	+	28.1426i	0.742397	+	1.28587i	−0.209004	+	0.977915i	$0.567022\pi$
$480$	−1.25027	+	8.82532i	−0.0570669	+	0.402819i
$481$	−9.94388	−	16.0819i	−0.453402	−	0.733273i
$482$	−19.6729	+	5.78531i	−0.896074	+	0.263514i
$483$	1.23907	−	0.715379i	0.0563798	−	0.0325509i
$484$	35.7211	+	18.3781i	1.62369	+	0.835370i
$485$	−2.48602	−	1.43531i	−0.112885	−	0.0651739i
$486$	−5.98001	−	20.3349i	−0.271259	−	0.922412i
$487$	−5.79695	+	10.0406i	−0.262685	+	0.454983i	−0.966954	−	0.254949i	$-0.917941\pi$
$487$	−5.79695	+	10.0406i	−0.262685	+	0.454983i	0.704270	+	0.709933i	$0.251275\pi$
$488$	9.46076	−	3.28755i	0.428268	−	0.148820i
$489$	3.52399			0.159360
$490$	18.8094	+	4.55488i	0.849723	+	0.205769i
$491$	36.2077	−	20.9045i	1.63403	−	0.943407i	0.651197	−	0.758909i	$-0.274267\pi$
$491$	36.2077	−	20.9045i	1.63403	−	0.943407i	0.982833	−	0.184498i	$-0.0590661\pi$
$492$	0.427407	−	0.830739i	0.0192690	−	0.0374526i
$493$			11.7920i			0.531085i
$494$	8.05597	−	2.63573i	0.362455	−	0.118587i
$495$	−31.2887			−1.40632
$496$	7.61061	−	0.739428i	0.341726	−	0.0332013i
$497$	−5.49065	−	9.51008i	−0.246289	−	0.426585i
$498$	2.70705	−	11.1788i	0.121306	−	0.500932i
$499$		−	17.9011i		−	0.801363i	−0.916217	−	0.400682i	$-0.868773\pi$
$499$		−	17.9011i		−	0.801363i	0.916217	−	0.400682i	$-0.131227\pi$
$500$	22.2943	−	1.08049i	0.997030	−	0.0483208i
$501$	−0.648402	−	0.374355i	−0.0289684	−	0.0167249i
$502$	−11.4433	−	38.9128i	−0.510739	−	1.73676i
$503$	−7.29456	+	12.6345i	−0.325248	+	0.563346i	−0.981563	−	0.191141i	$-0.938781\pi$
$503$	−7.29456	+	12.6345i	−0.325248	+	0.563346i	0.656314	+	0.754488i	$0.272114\pi$
$504$	−6.56903	−	1.25763i	−0.292608	−	0.0560192i
$505$	10.9360	+	18.9416i	0.486644	+	0.842892i
$506$	−4.79373	−	16.3010i	−0.213107	−	0.724668i
$507$	−7.62893	+	5.04166i	−0.338813	+	0.223908i
$508$	5.17810	−	3.33381i	0.229741	−	0.147914i
$509$	−1.08621	+	0.627122i	−0.0481453	+	0.0277967i	−0.523879	−	0.851792i	$-0.675516\pi$
$509$	−1.08621	+	0.627122i	−0.0481453	+	0.0277967i	0.475734	+	0.879589i	$0.342182\pi$
$510$	−9.78089	−	9.31834i	−0.433105	−	0.412623i
$511$	−0.904639	+	1.56688i	−0.0400189	+	0.0693147i
$512$	19.0808	+	12.1624i	0.843259	+	0.537507i
$513$	−3.21860	+	5.57478i	−0.142105	+	0.246133i
$514$	−3.86945	+	15.9789i	−0.170674	+	0.704801i
$515$			33.7703i			1.48810i
$516$	0.548819	+	11.3241i	0.0241604	+	0.498516i
$517$	51.0749	−	29.4881i	2.24627	−	1.29688i
$518$	4.82865	−	5.06833i	0.212159	−	0.222690i
$519$	15.3550			0.674008
$520$	14.4100	−	17.7261i	0.631919	−	0.777342i
$521$	8.42526			0.369117			0.184559	−	0.982822i	$-0.440914\pi$
$521$	8.42526			0.369117			0.184559	+	0.982822i	$0.440914\pi$
$522$	4.75352	−	4.98948i	0.208056	−	0.218384i
$523$	−20.6677	+	11.9325i	−0.903736	+	0.521772i	−0.878410	−	0.477907i	$-0.841396\pi$
$523$	−20.6677	+	11.9325i	−0.903736	+	0.521772i	−0.0253256	+	0.999679i	$0.508062\pi$
$524$	23.8011	−	1.15351i	1.03976	−	0.0503914i
$525$			0.0118937i			0.000519086i
$526$	−5.64152	+	23.2967i	−0.245982	+	1.01578i
$527$	−5.79445	+	10.0363i	−0.252410	+	0.437187i
$528$	6.49315	−	14.2805i	0.282578	−	0.621478i
$529$	9.17818	−	15.8971i	0.399051	−	0.691177i
$530$	23.8269	+	22.7001i	1.03497	+	0.986029i
$531$	−1.03056	+	0.594997i	−0.0447227	+	0.0258207i
$532$	1.69879	+	2.63857i	0.0736518	+	0.114396i
$533$	−2.03651	+	1.25922i	−0.0882109	+	0.0545431i
$534$	−0.209727	−	0.713172i	−0.00907576	−	0.0308620i
$535$	17.5946	+	30.4747i	0.760680	+	1.31754i
$536$	−2.40160	+	12.5444i	−0.103733	+	0.541834i
$537$	−1.14874	+	1.98968i	−0.0495719	+	0.0858611i
$538$	2.97244	+	10.1077i	0.128151	+	0.435776i
$539$	−29.4975	−	17.0304i	−1.27055	−	0.733550i
$540$	0.839829	+	17.3287i	0.0361405	+	0.745707i
$541$		−	19.4928i		−	0.838059i	−0.907973	−	0.419030i	$-0.862370\pi$
$541$		−	19.4928i		−	0.838059i	0.907973	−	0.419030i	$-0.137630\pi$
$542$	−5.06756	+	20.9265i	−0.217670	+	0.898871i
$543$	−4.61541	−	7.99412i	−0.198066	−	0.343060i
$544$	−31.8110	+	12.8116i	−1.36388	+	0.549291i
$545$	21.7269			0.930678
$546$	−2.52054	−	2.26021i	−0.107869	−	0.0967280i
$547$			2.18538i			0.0934399i	0.998908	+	0.0467200i	$0.0148768\pi$
$547$			2.18538i			0.0934399i	−0.998908	+	0.0467200i	$0.985123\pi$
$548$	−36.4015	−	18.7282i	−1.55500	−	0.800029i
$549$	7.68265	−	4.43558i	0.327887	−	0.189306i
$550$	0.137279	+	0.0332434i	0.00585358	+	0.00141750i
$551$	−3.23340			−0.137747
$552$	−4.04976	+	1.40726i	−0.172369	+	0.0598970i
$553$	6.42423	−	11.1271i	0.273186	−	0.473172i
$554$	−6.44672	−	21.9220i	−0.273895	−	0.931375i
$555$	−7.15605	−	4.13155i	−0.303757	−	0.175374i
$556$	−7.41250	+	14.4075i	−0.314360	+	0.611014i
$557$	29.5902	−	17.0839i	1.25378	−	0.723869i	0.281921	−	0.959438i	$-0.409028\pi$
$557$	29.5902	−	17.0839i	1.25378	−	0.723869i	0.971858	+	0.235568i	$0.0756951\pi$
$558$	6.49753	−	1.91076i	0.275062	−	0.0808891i
$559$	13.7622	−	25.5908i	0.582080	−	1.08238i
$560$	7.69915	+	3.50071i	0.325348	+	0.147932i
$561$	11.8878	+	20.5903i	0.501904	+	0.869324i
$562$	28.3834	+	27.0412i	1.19728	+	1.14066i
$563$	20.4379	+	11.7998i	0.861353	+	0.497302i	0.864465	−	0.502693i	$-0.167657\pi$
$563$	20.4379	+	11.7998i	0.861353	+	0.497302i	−0.00311215	+	0.999995i	$0.500991\pi$
$564$	−8.05568	−	12.5121i	−0.339205	−	0.526855i
$565$	−14.6706	−	8.47006i	−0.617195	−	0.356338i
$566$	5.21782	+	1.26355i	0.219321	+	0.0531108i
$567$	−4.52294			−0.189946
$568$	10.8009	+	31.0825i	0.453198	+	1.30419i
$569$	−1.38906	−	2.40592i	−0.0582323	−	0.100861i	0.835440	−	0.549582i	$-0.185213\pi$
$569$	−1.38906	−	2.40592i	−0.0582323	−	0.100861i	−0.893672	+	0.448721i	$0.851880\pi$
$570$	2.55511	−	2.68194i	0.107022	−	0.112334i
$571$		−	19.2497i		−	0.805577i	−0.915293	−	0.402788i	$-0.868041\pi$
$571$		−	19.2497i		−	0.805577i	0.915293	−	0.402788i	$-0.131959\pi$
$572$	−33.1325	+	22.7749i	−1.38534	+	0.952268i
$573$		−	5.65734i		−	0.236339i
$574$	−0.641819	−	0.611467i	−0.0267890	−	0.0255221i
$575$	−0.0193011	−	0.0334304i	−0.000804910	−	0.00139415i
$576$	18.6245	+	7.40257i	0.776021	+	0.308440i
$577$	6.64617			0.276683			0.138342	−	0.990385i	$-0.455823\pi$
$577$	6.64617			0.276683			0.138342	+	0.990385i	$0.455823\pi$
$578$	6.57447	−	27.1493i	0.273462	−	1.12926i
$579$	0.509185	+	0.293978i	0.0211610	+	0.0122173i
$580$	−7.32711	+	4.71742i	−0.304242	+	0.195880i
$581$	−9.45154	−	5.45685i	−0.392116	−	0.226388i
$582$	0.879321	−	0.922969i	0.0364490	−	0.0382583i
$583$	−28.9595	−	50.1594i	−1.19938	−	2.07739i
$584$	3.54526	−	4.10172i	0.146704	−	0.169730i
$585$	9.58342	−	17.8204i	0.396226	−	0.736782i
$586$	1.91101	+	6.49835i	0.0789430	+	0.268444i
$587$	−23.1016	+	13.3377i	−0.953505	+	0.550507i	−0.894168	−	0.447731i	$-0.852232\pi$
$587$	−23.1016	+	13.3377i	−0.953505	+	0.550507i	−0.0593374	+	0.998238i	$0.518899\pi$
$588$	−3.93183	+	7.64220i	−0.162146	+	0.315159i
$589$	−2.75197	−	1.58885i	−0.113393	−	0.0654675i
$590$	1.44366	−	0.424546i	0.0594346	−	0.0174783i
$591$	2.46352	−	4.26694i	0.101336	−	0.175519i
$592$	−17.0668	+	12.1958i	−0.701440	+	0.501244i
$593$	6.61409			0.271608			0.135804	−	0.990736i	$-0.456638\pi$
$593$	6.61409			0.271608			0.135804	+	0.990736i	$0.456638\pi$
$594$	7.18632	−	29.6759i	0.294858	−	1.21762i
$595$	−11.1010	+	6.40917i	−0.455097	+	0.262751i
$596$	3.31223	−	6.43790i	0.135674	−	0.263707i
$597$			10.5759i			0.432841i
$598$	10.7525	+	2.26259i	0.439701	+	0.0925241i
$599$	11.9319			0.487523			0.243762	−	0.969835i	$-0.421619\pi$
$599$	11.9319			0.487523			0.243762	+	0.969835i	$0.421619\pi$
$600$	0.00670147	−	0.0350041i	0.000273586	−	0.00142904i
$601$	6.15610	+	10.6627i	0.251113	+	0.434940i	0.963832	−	0.266509i	$-0.0858702\pi$
$601$	6.15610	+	10.6627i	0.251113	+	0.434940i	−0.712720	+	0.701449i	$0.752537\pi$
$602$	10.4555	+	2.53189i	0.426132	+	0.103192i
$603$			11.3127i			0.460688i
$604$	−1.55814	−	32.1500i	−0.0633998	−	1.30817i
$605$	−38.9655	−	22.4968i	−1.58417	−	0.914623i
$606$	−9.31834	+	2.74030i	−0.378532	+	0.111317i
$607$	4.35738	−	7.54720i	0.176860	−	0.306331i	−0.763943	−	0.645284i	$-0.776739\pi$
$607$	4.35738	−	7.54720i	0.176860	−	0.306331i	0.940804	+	0.338952i	$0.110073\pi$
$608$	−3.51296	−	8.72265i	−0.142469	−	0.353750i
$609$	0.645732	+	1.11844i	0.0261664	+	0.0453215i
$610$	−10.7622	+	3.16490i	−0.435749	+	0.128143i
$611$	1.15111	+	38.1215i	0.0465690	+	1.54223i
$612$	−25.5395	+	16.4431i	−1.03237	+	0.664674i
$613$	−30.7480	+	17.7523i	−1.24190	+	0.717010i	−0.969480	−	0.245169i	$-0.921157\pi$
$613$	−30.7480	+	17.7523i	−1.24190	+	0.717010i	−0.272418	+	0.962179i	$0.587823\pi$
$614$	8.74025	−	9.17411i	0.352728	−	0.370237i
$615$	−0.523191	+	0.906193i	−0.0210971	+	0.0365412i
$616$	−11.2615	−	9.73375i	−0.453740	−	0.392184i
$617$	12.0318	−	20.8396i	0.484380	−	0.838971i	−0.515459	−	0.856914i	$-0.672378\pi$
$617$	12.0318	−	20.8396i	0.484380	−	0.838971i	0.999839	+	0.0179431i	$0.00571178\pi$
$618$	−14.5755	−	3.52959i	−0.586311	−	0.141981i
$619$		−	21.6806i		−	0.871417i	−0.900088	−	0.435708i	$-0.856498\pi$
$619$		−	21.6806i		−	0.871417i	0.900088	−	0.435708i	$-0.143502\pi$
$620$	−8.55424	+	0.414579i	−0.343547	+	0.0166499i
$621$	−7.22675	+	4.17237i	−0.290000	+	0.167431i
$622$	9.57564	+	9.12280i	0.383948	+	0.365791i
$623$	−0.705358			−0.0282596
$624$	6.14462	+	8.07213i	0.245981	+	0.323144i
$625$	−25.0892			−1.00357
$626$	−12.0653	−	11.4947i	−0.482225	−	0.459420i
$627$	−5.64592	+	3.25967i	−0.225476	+	0.130179i
$628$	30.8187	−	1.49362i	1.22980	−	0.0596018i
$629$		−	31.7918i		−	1.26762i
$630$	7.28073	+	1.76310i	0.290071	+	0.0702435i
$631$	−9.48379	+	16.4264i	−0.377544	+	0.653925i	−0.990704	−	0.136033i	$-0.956565\pi$
$631$	−9.48379	+	16.4264i	−0.377544	+	0.653925i	0.613161	+	0.789958i	$0.289898\pi$
$632$	−25.1765	+	29.1281i	−1.00147	+	1.15865i
$633$	2.36454	−	4.09551i	0.0939821	−	0.162782i
$634$	0.807754	−	0.847849i	0.0320800	−	0.0336724i
$635$	−5.97360	+	3.44886i	−0.237055	+	0.136864i
$636$	−12.2878	+	7.91128i	−0.487244	+	0.313703i
$637$	18.7344	−	11.5840i	0.742284	−	0.458973i
$638$	14.7140	−	4.32702i	0.582532	−	0.171309i
$639$	14.5727	+	25.2407i	0.576488	+	0.998506i
$640$	−20.6867	−	14.6409i	−0.817712	−	0.578731i
$641$	−12.4294	+	21.5284i	−0.490934	+	0.850322i	−0.999946	−	0.0104375i	$-0.996678\pi$
$641$	−12.4294	+	21.5284i	−0.490934	+	0.850322i	0.509012	+	0.860759i	$0.330011\pi$
$642$	−14.9920	+	4.40879i	−0.591688	+	0.174001i
$643$	−3.25429	−	1.87887i	−0.128337	−	0.0740952i	0.434457	−	0.900692i	$-0.356940\pi$
$643$	−3.25429	−	1.87887i	−0.128337	−	0.0740952i	−0.562794	+	0.826597i	$0.690274\pi$
$644$	0.196926	+	4.06329i	0.00775998	+	0.160116i
$645$		−	12.6983i		−	0.499994i
$646$	13.8515	+	3.35428i	0.544980	+	0.131972i
$647$	−24.0878	−	41.7213i	−0.946989	−	1.64023i	−0.751718	−	0.659484i	$-0.770775\pi$
$647$	−24.0878	−	41.7213i	−0.946989	−	1.64023i	−0.195271	−	0.980749i	$-0.562559\pi$
$648$	13.3113	+	2.54843i	0.522918	+	0.100112i
$649$	−2.64838			−0.103958
$650$	−0.0609808	+	0.0680046i	−0.00239186	+	0.00266736i
$651$			1.26922i			0.0497446i
$652$	−4.58394	+	8.90969i	−0.179521	+	0.348930i
$653$	−21.5793	+	12.4588i	−0.844463	+	0.487551i	−0.858779	−	0.512346i	$-0.828776\pi$
$653$	−21.5793	+	12.4588i	−0.844463	+	0.487551i	0.0143156	+	0.999898i	$0.495443\pi$
$654$	−2.27084	+	9.37747i	−0.0887970	+	0.366688i
$655$	−26.6894			−1.04284
$656$	1.54439	+	2.16122i	0.0602983	+	0.0843814i
$657$	2.40100	−	4.15865i	0.0936719	−	0.162244i
$658$	−13.5465	+	3.98370i	−0.528098	+	0.155301i
$659$	−1.75765	−	1.01478i	−0.0684684	−	0.0395302i	0.465375	−	0.885114i	$-0.345919\pi$
$659$	−1.75765	−	1.01478i	−0.0684684	−	0.0395302i	−0.533843	+	0.845583i	$0.679253\pi$
$660$	−8.03830	+	15.6238i	−0.312890	+	0.608157i
$661$	9.61763	−	5.55274i	0.374082	−	0.215977i	−0.301158	−	0.953574i	$-0.597373\pi$
$661$	9.61763	−	5.55274i	0.374082	−	0.215977i	0.675240	+	0.737598i	$0.264040\pi$
$662$	−5.91644	−	20.1188i	−0.229949	−	0.781938i
$663$	−15.3683	+	0.464059i	−0.596855	+	0.0180226i
$664$	24.7419	+	21.3853i	0.960172	+	0.829911i
$665$	−1.75741	−	3.04393i	−0.0681495	−	0.118038i
$666$	−12.8157	+	13.4519i	−0.496598	+	0.521249i
$667$	−3.62999	−	2.09578i	−0.140554	−	0.0811488i
$668$	1.78991	−	1.15240i	0.0692536	−	0.0445875i
$669$	−12.7122	−	7.33941i	−0.491483	−	0.283758i
$670$	3.36686	−	13.9035i	0.130073	−	0.537137i
$671$	19.7432			0.762176
$672$	−2.31562	+	2.95712i	−0.0893271	+	0.114073i
$673$	−17.0389	−	29.5122i	−0.656800	−	1.13761i	−0.981439	−	0.191773i	$-0.938576\pi$
$673$	−17.0389	−	29.5122i	−0.656800	−	1.13761i	0.324639	−	0.945838i	$-0.394757\pi$
$674$	5.67149	+	5.40328i	0.218458	+	0.208127i
$675$		−	0.0693689i		−	0.00267001i
$676$	−2.82323	−	25.8463i	−0.108586	−	0.994087i
$677$		−	28.8974i		−	1.11062i	−0.831645	−	0.555308i	$-0.812600\pi$
$677$		−	28.8974i		−	1.11062i	0.831645	−	0.555308i	$-0.187400\pi$
$678$	5.18906	−	5.44664i	0.199285	−	0.209177i
$679$	−0.604799	−	1.04754i	−0.0232100	−	0.0402010i
$680$	36.2823	−	12.6078i	1.39136	−	0.483488i
$681$	13.6201			0.521922
$682$	14.6494	+	3.54750i	0.560956	+	0.135841i
$683$	−18.5350	−	10.7012i	−0.709221	−	0.409469i	0.101551	−	0.994830i	$-0.467619\pi$
$683$	−18.5350	−	10.7012i	−0.709221	−	0.409469i	−0.810773	+	0.585361i	$0.800953\pi$
$684$	−4.50875	−	7.00301i	−0.172396	−	0.267767i
$685$	39.7078	+	22.9253i	1.51716	+	0.875930i
$686$	12.6696	+	12.0705i	0.483729	+	0.460853i
$687$	6.19156	+	10.7241i	0.236223	+	0.409150i
$688$	−29.3445	−	13.3426i	−1.11875	−	0.508682i
$689$	37.4381	−	1.13048i	1.42628	−	0.0430678i
$690$	4.60685	−	1.35476i	0.175380	−	0.0515749i
$691$	−42.9878	+	24.8190i	−1.63533	+	0.944159i	−0.652921	+	0.757426i	$0.726457\pi$
$691$	−42.9878	+	24.8190i	−1.63533	+	0.944159i	−0.982411	+	0.186733i	$0.940210\pi$
$692$	−19.9734	+	38.8218i	−0.759276	+	1.47578i
$693$	−11.4178	−	6.59210i	−0.433728	−	0.250413i
$694$	6.44094	+	21.9023i	0.244495	+	0.831401i
$695$	9.07368	−	15.7161i	0.344184	−	0.596145i
$696$	−1.27025	−	3.65548i	−0.0481489	−	0.138561i
$697$	−4.02589			−0.152491
$698$	−32.8672	−	7.95912i	−1.24404	−	0.301257i
$699$	9.33742	−	5.39096i	0.353174	−	0.203905i
$700$	−0.0300709	−	0.0154712i	−0.00113657	−	0.000584755i
$701$		−	23.3855i		−	0.883258i	−0.897198	−	0.441629i	$-0.854401\pi$
$701$		−	23.3855i		−	0.883258i	0.897198	−	0.441629i	$-0.145599\pi$
$702$	14.7007	+	13.1824i	0.554844	+	0.497538i
$703$	8.71738			0.328782
$704$	27.6591	+	34.9924i	1.04244	+	1.31882i
$705$	8.33367	+	14.4343i	0.313864	+	0.543629i
$706$	1.84995	−	7.63936i	0.0696236	−	0.287511i
$707$			9.21623i			0.346612i
$708$	0.0323485	+	0.667466i	0.00121573	+	0.0250849i
$709$	41.1118	+	23.7359i	1.54399	+	0.891421i	0.998581	+	0.0532487i	$0.0169576\pi$
$709$	41.1118	+	23.7359i	1.54399	+	0.891421i	0.545405	+	0.838172i	$0.316376\pi$
$710$	−10.3980	−	35.3583i	−0.390230	−	1.32697i
$711$	−17.0505	+	29.5324i	−0.639445	+	1.10755i
$712$	2.07592	+	0.397430i	0.0777983	+	0.0148943i
$713$	−2.05968	−	3.56746i	−0.0771355	−	0.133603i
$714$	−1.60599	−	5.46114i	−0.0601026	−	0.204378i
$715$	38.3009	−	23.6824i	1.43237	−	0.885672i
$716$	−3.53624	−	5.49250i	−0.132155	−	0.205264i
$717$	−8.58045	+	4.95392i	−0.320443	+	0.185008i
$718$	−8.75588	−	8.34180i	−0.326766	−	0.311313i
$719$	22.6840	−	39.2899i	0.845972	−	1.46527i	−0.0388023	−	0.999247i	$-0.512354\pi$
$719$	22.6840	−	39.2899i	0.845972	−	1.46527i	0.884774	−	0.466020i	$-0.154312\pi$
$720$	−20.4343	−	9.29121i	−0.761541	−	0.346263i
$721$	−7.11493	+	12.3234i	−0.264974	+	0.458948i
$722$	5.40431	−	22.3171i	0.201128	−	0.830558i
$723$			10.1993i			0.379318i
$724$	26.2151	−	1.27051i	0.974276	−	0.0472180i
$725$	0.0301757	−	0.0174220i	0.00112070	−	0.000647036i
$726$	13.7823	−	14.4665i	0.511510	−	0.536901i
$727$	27.1042			1.00524			0.502619	−	0.864508i	$-0.332370\pi$
$727$	27.1042			1.00524			0.502619	+	0.864508i	$0.332370\pi$
$728$	8.99313	−	3.43262i	0.333308	−	0.127222i
$729$	3.83260			0.141948
$730$	−4.18855	+	4.39647i	−0.155025	+	0.162721i
$731$	42.3104	−	24.4279i	1.56491	−	0.903500i
$732$	−0.241152	−	4.97583i	−0.00891323	−	0.183912i
$733$		−	21.1225i		−	0.780179i	−0.920777	−	0.390090i	$-0.872444\pi$
$733$		−	21.1225i		−	0.780179i	0.920777	−	0.390090i	$-0.127556\pi$
$734$	−1.30941	+	5.40723i	−0.0483314	+	0.199585i
$735$	4.81298	−	8.33632i	0.177529	−	0.307490i
$736$	1.70987	−	12.0695i	0.0630268	−	0.444888i
$737$	−12.5884	+	21.8038i	−0.463701	+	0.803153i
$738$	1.70345	+	1.62289i	0.0627049	+	0.0597395i
$739$	−25.6746	+	14.8233i	−0.944457	+	0.545283i	−0.891355	−	0.453307i	$-0.850244\pi$
$739$	−25.6746	+	14.8233i	−0.944457	+	0.545283i	−0.0531023	+	0.998589i	$0.516911\pi$
$740$	19.7542	−	12.7184i	0.726179	−	0.467536i
$741$	−0.127246	−	4.21402i	−0.00467451	−	0.154806i
$742$	3.91230	+	13.3037i	0.143625	+	0.488394i
$743$	5.52318	+	9.56643i	0.202626	+	0.350958i	0.949374	−	0.314149i	$-0.101719\pi$
$743$	5.52318	+	9.56643i	0.202626	+	0.350958i	−0.746748	+	0.665107i	$0.768386\pi$
$744$	0.715135	−	3.73540i	0.0262181	−	0.136946i
$745$	−4.05452	+	7.02264i	−0.148546	+	0.257290i
$746$	−3.16202	−	10.7524i	−0.115770	−	0.393674i
$747$	25.0853	+	14.4830i	0.917824	+	0.529906i
$748$	−67.5218	+	3.27242i	−2.46884	+	0.119652i
$749$			14.8277i			0.541794i
$750$	2.61291	−	10.7900i	0.0954099	−	0.393996i
$751$	18.6034	+	32.2220i	0.678846	+	1.17580i	0.975329	+	0.220758i	$0.0708530\pi$
$751$	18.6034	+	32.2220i	0.678846	+	1.17580i	−0.296483	+	0.955038i	$0.595814\pi$
$752$	42.1130	−	4.09159i	1.53570	−	0.149205i
$753$	−20.1742			−0.735190
$754$	−2.04231	+	9.70563i	−0.0743765	+	0.353458i
$755$			36.0514i			1.31204i
$756$	−3.34444	+	6.50051i	−0.121636	+	0.236421i
$757$	−17.2083	+	9.93522i	−0.625446	+	0.361102i	−0.778986	−	0.627041i	$-0.784266\pi$
$757$	−17.2083	+	9.93522i	−0.625446	+	0.361102i	0.153540	+	0.988142i	$0.450933\pi$
$758$	36.3100	+	8.79283i	1.31884	+	0.319370i
$759$	−8.45122			−0.306760
$760$	3.45710	+	9.94869i	0.125402	+	0.360877i
$761$	−4.52926	+	7.84491i	−0.164186	+	0.284378i	−0.936366	−	0.351026i	$-0.885833\pi$
$761$	−4.52926	+	7.84491i	−0.164186	+	0.284378i	0.772180	+	0.635404i	$0.219166\pi$
$762$	−0.864204	−	2.93871i	−0.0313068	−	0.106458i
$763$	7.92857	+	4.57756i	0.287033	+	0.165719i
$764$	14.3034	+	7.35895i	0.517479	+	0.266237i
$765$	29.4632	−	17.0106i	1.06524	−	0.615018i
$766$	−2.56995	+	0.755759i	−0.0928560	+	0.0273067i
$767$	0.811174	−	1.50838i	0.0292898	−	0.0544644i
$768$	8.48121	−	7.39827i	0.306039	−	0.266962i
$769$	−5.28678	−	9.15697i	−0.190646	−	0.330209i	0.754818	−	0.655934i	$-0.227725\pi$
$769$	−5.28678	−	9.15697i	−0.190646	−	0.330209i	−0.945465	+	0.325725i	$0.894392\pi$
$770$	12.0708	+	11.4999i	0.435001	+	0.414429i
$771$	7.08185	+	4.08871i	0.255047	+	0.147251i
$772$	−1.40560	+	0.904968i	−0.0505887	+	0.0325705i
$773$	22.3264	+	12.8902i	0.803026	+	0.463627i	0.844528	−	0.535511i	$-0.179881\pi$
$773$	22.3264	+	12.8902i	0.803026	+	0.463627i	−0.0415022	+	0.999138i	$0.513214\pi$
$774$	−27.7498	−	6.71988i	−0.997445	−	0.241541i
$775$	0.0342437			0.00123007
$776$	1.18973	+	3.42376i	0.0427089	+	0.122906i
$777$	−1.74092	−	3.01536i	−0.0624552	−	0.108176i
$778$	−24.4662	+	25.6807i	−0.877156	+	0.920697i
$779$		−	1.10391i		−	0.0395517i
$780$	−6.43646	−	9.36362i	−0.230462	−	0.335272i
$781$			64.8644i			2.32103i
$782$	13.3763	+	12.7438i	0.478337	+	0.455716i
$783$	−3.76616	−	6.52318i	−0.134592	−	0.233119i
$784$	−14.2073	−	19.8817i	−0.507403	−	0.710059i
$785$	−34.5585			−1.23345
$786$	2.78951	−	11.5193i	0.0994985	−	0.410880i
$787$	−12.1719	−	7.02745i	−0.433881	−	0.250502i	0.267117	−	0.963664i	$-0.413929\pi$
$787$	−12.1719	−	7.02745i	−0.433881	−	0.250502i	−0.700999	+	0.713162i	$0.747262\pi$
$788$	7.58358	+	11.7789i	0.270154	+	0.419604i
$789$	10.3251	+	5.96119i	0.367583	+	0.212224i
$790$	29.7447	−	31.2212i	1.05827	−	1.11080i
$791$	−3.56905	−	6.18178i	−0.126901	−	0.219799i
$792$	29.8892	+	25.8343i	1.06207	+	0.917983i
$793$	−6.04714	+	11.2447i	−0.214740	+	0.399309i
$794$	3.68569	+	12.5331i	0.130800	+	0.444784i
$795$	14.1756	−	8.18429i	0.502757	−	0.290267i
$796$	−26.7389	−	13.7569i	−0.947734	−	0.487599i
$797$	−19.1331	−	11.0465i	−0.677731	−	0.391288i	0.121269	−	0.992620i	$-0.461304\pi$
$797$	−19.1331	−	11.0465i	−0.677731	−	0.391288i	−0.798999	+	0.601332i	$0.794637\pi$
$798$	1.49746	−	0.440366i	0.0530095	−	0.0155888i
$799$	−32.0633	+	55.5353i	−1.13432	+	1.96470i
$800$	0.0797835	+	0.0624759i	0.00282077	+	0.00220886i
$801$	1.87209			0.0661470
$802$	1.47208	−	6.07896i	0.0519809	−	0.214656i
$803$	9.25526	−	5.34353i	0.326611	−	0.188569i
$804$	5.64893	+	2.90631i	0.199222	+	0.102498i
$805$		−	4.55637i		−	0.160591i
$806$	−6.50745	+	7.25698i	−0.229215	+	0.255616i
$807$	5.24034			0.184469
$808$	5.19284	−	27.1240i	0.182683	−	0.954219i
$809$	−2.02317	−	3.50424i	−0.0711310	−	0.123202i	0.828266	−	0.560335i	$-0.189328\pi$
$809$	−2.02317	−	3.50424i	−0.0711310	−	0.123202i	−0.899397	+	0.437132i	$0.855994\pi$
$810$	−14.7535	−	3.57270i	−0.518385	−	0.125532i
$811$		−	18.7132i		−	0.657109i	−0.944485	−	0.328555i	$-0.893439\pi$
$811$		−	18.7132i		−	0.657109i	0.944485	−	0.328555i	$-0.106561\pi$
$812$	−3.66770	+	0.177754i	−0.128711	+	0.00623794i
$813$	9.27462	+	5.35470i	0.325275	+	0.187798i
$814$	−39.6695	+	11.6658i	−1.39042	+	0.408888i
$815$	5.61122	−	9.71893i	0.196553	−	0.340439i
$816$	1.64948	+	16.9774i	0.0577435	+	0.594328i
$817$	6.69820	+	11.6016i	0.234340	+	0.405889i
$818$	−35.9110	+	10.5606i	−1.25560	+	0.369241i
$819$	7.25169	−	4.48390i	0.253394	−	0.156680i
$820$	−1.61056	−	2.50154i	−0.0562434	−	0.0873575i
$821$	6.46202	−	3.73085i	0.225526	−	0.130208i	−0.382980	−	0.923757i	$-0.625102\pi$
$821$	6.46202	−	3.73085i	0.225526	−	0.130208i	0.608506	+	0.793549i	$0.291769\pi$
$822$	−14.0449	+	14.7420i	−0.489871	+	0.514187i
$823$	−9.81336	+	16.9972i	−0.342072	+	0.592486i	−0.984817	−	0.173594i	$-0.944462\pi$
$823$	−9.81336	+	16.9972i	−0.342072	+	0.592486i	0.642745	+	0.766080i	$0.277795\pi$
$824$	27.8833	−	32.2598i	0.971361	−	1.12382i
$825$	0.0351270	−	0.0608418i	0.00122297	−	0.00211824i
$826$	0.616266	+	0.149235i	0.0214426	+	0.00519254i
$827$		−	19.2616i		−	0.669792i	−0.942255	−	0.334896i	$-0.891299\pi$
$827$		−	19.2616i		−	0.669792i	0.942255	−	0.334896i	$-0.108701\pi$
$828$	−0.522661	−	10.7844i	−0.0181637	−	0.374783i
$829$	−18.7148	+	10.8050i	−0.649993	+	0.375273i	−0.788453	−	0.615094i	$-0.789118\pi$
$829$	−18.7148	+	10.8050i	−0.649993	+	0.375273i	0.138461	+	0.990368i	$0.455785\pi$
$830$	−26.5198	−	25.2657i	−0.920517	−	0.876985i
$831$	−11.3654			−0.394261
$832$	−28.4015	+	5.03531i	−0.984645	+	0.174568i
$833$	37.0353			1.28320
$834$	5.83480	+	5.55887i	0.202043	+	0.192488i
$835$	−2.06489	+	1.19216i	−0.0714584	+	0.0412565i
$836$	−0.897306	−	18.5146i	−0.0310340	−	0.640342i
$837$		−	7.40257i		−	0.255870i
$838$	6.83257	+	1.65457i	0.236027	+	0.0571563i
$839$	−21.0839	+	36.5183i	−0.727895	+	1.26075i	0.229876	+	0.973220i	$0.426168\pi$
$839$	−21.0839	+	36.5183i	−0.727895	+	1.26075i	−0.957771	+	0.287532i	$0.907165\pi$
$840$	2.75087	−	3.18264i	0.0949140	−	0.109812i
$841$	−12.6083	+	21.8382i	−0.434768	+	0.753040i
$842$	−23.4680	+	24.6329i	−0.808759	+	0.848905i
$843$	16.8865	−	9.74942i	0.581602	−	0.335788i
$844$	7.27889	+	11.3056i	0.250550	+	0.389155i
$845$	1.75706	+	29.0679i	0.0604448	+	0.999965i
$846$	35.9538	−	10.5731i	1.23612	−	0.363512i
$847$	−9.47952	−	16.4190i	−0.325720	−	0.564164i
$848$	−4.01825	−	41.3581i	−0.137987	−	1.42024i
$849$	1.33514	−	2.31253i	0.0458220	−	0.0793660i
$850$	−0.147343	+	0.0433299i	−0.00505381	+	0.00148620i
$851$	9.78661	+	5.65030i	0.335481	+	0.193690i
$852$	16.3476	−	0.792283i	0.560061	−	0.0271432i
$853$			40.2417i			1.37785i	0.724833	+	0.688924i	$0.241917\pi$
$853$			40.2417i			1.37785i	−0.724833	+	0.688924i	$0.758083\pi$
$854$	−4.59414	−	1.11252i	−0.157208	−	0.0380695i
$855$	4.66434	+	8.07888i	0.159517	+	0.276292i
$856$	8.35462	−	43.6391i	0.285555	−	1.49155i
$857$	7.37621			0.251966			0.125983	−	0.992032i	$-0.459791\pi$
$857$	7.37621			0.251966			0.125983	+	0.992032i	$0.459791\pi$
$858$	6.21837	+	19.0061i	0.212292	+	0.648859i
$859$		−	31.9493i		−	1.09010i	−0.838405	−	0.545048i	$-0.816511\pi$
$859$		−	31.9493i		−	1.09010i	0.838405	−	0.545048i	$-0.183489\pi$
$860$	32.1050	+	16.5177i	1.09477	+	0.563248i
$861$	−0.381845	+	0.220458i	−0.0130132	+	0.00751320i
$862$	3.52124	−	14.5410i	0.119934	−	0.495269i
$863$	−16.1143			−0.548536			−0.274268	−	0.961653i	$-0.588436\pi$
$863$	−16.1143			−0.548536			−0.274268	+	0.961653i	$0.588436\pi$
$864$	13.5056	−	17.2470i	0.459470	−	0.586756i
$865$	24.4496	−	42.3479i	0.831310	−	1.43987i
$866$	16.5876	−	4.87801i	0.563669	−	0.165761i
$867$	−12.0326	−	6.94700i	−0.408647	−	0.235933i
$868$	−3.20896	−	1.65097i	−0.108919	−	0.0560377i
$869$	−65.7256	+	37.9467i	−2.22959	+	1.28725i
$870$	1.22287	+	4.15834i	0.0414591	+	0.140981i
$871$	−8.56257	−	13.8480i	−0.290132	−	0.469221i
$872$	−20.7551	−	17.9394i	−0.702857	−	0.607504i
$873$	1.60519	+	2.78028i	0.0543276	+	0.0940982i
$874$	−3.49437	+	3.66783i	−0.118199	+	0.124066i
$875$	−9.12287	−	5.26709i	−0.308409	−	0.178060i
$876$	−1.45977	−	2.26732i	−0.0493209	−	0.0766055i
$877$	0.181562	+	0.104825i	0.00613091	+	0.00353968i	0.503062	−	0.864250i	$-0.332207\pi$
$877$	0.181562	+	0.104825i	0.00613091	+	0.00353968i	−0.496931	+	0.867790i	$0.665540\pi$
$878$	4.30314	−	17.7698i	0.145224	−	0.599703i
$879$	3.36906			0.113635
$880$	−29.0456	−	40.6464i	−0.979126	−	1.37019i
$881$	−20.1008	−	34.8157i	−0.677214	−	1.17297i	−0.975816	−	0.218592i	$-0.929854\pi$
$881$	−20.1008	−	34.8157i	−0.677214	−	1.17297i	0.298602	−	0.954378i	$-0.403480\pi$
$882$	−15.6705	−	14.9294i	−0.527654	−	0.502700i
$883$		−	4.69019i		−	0.157837i	−0.996881	−	0.0789187i	$-0.974853\pi$
$883$		−	4.69019i		−	0.157837i	0.996881	−	0.0789187i	$-0.0251467\pi$
$884$	18.8175	−	39.4591i	0.632900	−	1.32715i
$885$		−	0.748463i		−	0.0251593i
$886$	13.6998	−	14.3799i	0.460254	−	0.483101i
$887$	−11.6991	−	20.2635i	−0.392819	−	0.680382i	0.600002	−	0.799999i	$-0.295167\pi$
$887$	−11.6991	−	20.2635i	−0.392819	−	0.680382i	−0.992820	+	0.119617i	$0.961833\pi$
$888$	3.42466	+	9.85534i	0.114924	+	0.330723i
$889$	−2.90651			−0.0974813
$890$	−2.30083	−	0.557167i	−0.0771239	−	0.0186763i
$891$	23.1368	+	13.3581i	0.775113	+	0.447512i
$892$	35.0920	−	22.5933i	1.17497	−	0.756479i
$893$	−15.2279	−	8.79184i	−0.509583	−	0.294208i
$894$	−2.60725	−	2.48395i	−0.0871994	−	0.0830756i
$895$	3.65827	+	6.33631i	0.122282	+	0.211799i
$896$	−4.46434	−	9.70113i	−0.149143	−	0.324092i
$897$	2.58853	−	4.81337i	0.0864284	−	0.160714i
$898$	−2.32580	+	0.683961i	−0.0776129	+	0.0228241i
$899$	3.22015	−	1.85915i	0.107398	−	0.0620062i
$900$	0.0798110	+	0.0410619i	0.00266037	+	0.00136873i
$901$	54.5398	+	31.4886i	1.81698	+	1.04904i
$902$	1.47728	+	5.02348i	0.0491881	+	0.167263i
$903$	2.67535	−	4.63385i	0.0890302	−	0.154205i
$904$	7.02087	+	20.2044i	0.233511	+	0.671987i
$905$	−29.3963			−0.977166
$906$	−15.5600	−	3.76801i	−0.516947	−	0.125184i
$907$	3.93422	−	2.27142i	0.130634	−	0.0754213i	−0.433259	−	0.901269i	$-0.642637\pi$
$907$	3.93422	−	2.27142i	0.130634	−	0.0754213i	0.563893	+	0.825848i	$0.309303\pi$
$908$	−17.7167	+	34.4355i	−0.587950	+	1.14278i
$909$		−	24.4608i		−	0.811313i
$910$	−10.2469	+	3.35256i	−0.339682	+	0.111136i
$911$	−29.5451			−0.978873			−0.489436	−	0.872039i	$-0.662797\pi$
$911$	−29.5451			−0.978873			−0.489436	+	0.872039i	$0.662797\pi$
$912$	−4.65525	+	0.452293i	−0.154151	+	0.0149769i
$913$	32.2326	+	55.8285i	1.06674	+	1.84765i
$914$	−9.70722	+	40.0860i	−0.321086	+	1.32593i
$915$			5.57964i			0.184457i
$916$	−35.1675	+	1.70438i	−1.16197	+	0.0563144i
$917$	−9.73946	−	5.62308i	−0.321625	−	0.185691i
$918$	9.36675	+	31.8515i	0.309149	+	1.05126i
$919$	15.5647	−	26.9588i	0.513431	−	0.889288i	−0.486448	−	0.873710i	$-0.661708\pi$
$919$	15.5647	−	26.9588i	0.513431	−	0.889288i	0.999879	−	0.0155787i	$-0.00495905\pi$
$920$	−2.56726	+	13.4097i	−0.0846402	+	0.442105i
$921$	−3.15121	−	5.45806i	−0.103836	−	0.179849i
$922$	10.3431	+	35.1716i	0.340632	+	1.15831i
$923$	−36.9433	−	19.8673i	−1.21600	−	0.653942i
$924$	−6.22506	+	4.00788i	−0.204789	+	0.131850i
$925$	−0.0813551	+	0.0469704i	−0.00267494	+	0.00154438i
$926$	37.5781	+	35.8009i	1.23489	+	1.17649i
$927$	18.8837	−	32.7076i	0.620223	−	1.07426i
$928$	10.8945	+	1.54341i	0.357628	+	0.0506648i
$929$	11.9251	−	20.6548i	0.391249	−	0.677663i	−0.601366	−	0.798974i	$-0.705376\pi$
$929$	11.9251	−	20.6548i	0.391249	−	0.677663i	0.992615	+	0.121311i	$0.0387098\pi$
$930$	−1.00256	+	4.14010i	−0.0328754	+	0.135759i
$931$			10.1552i			0.332822i
$932$	1.48400	+	30.6202i	0.0486100	+	1.00300i
$933$	5.69695	−	3.28913i	0.186510	−	0.107681i
$934$	−27.2978	+	28.6529i	−0.893213	+	0.937550i
$935$	75.7155			2.47616
$936$	−23.8686	+	9.11052i	−0.780171	+	0.297787i
$937$	−9.97996			−0.326031			−0.163016	−	0.986623i	$-0.552122\pi$
$937$	−9.97996			−0.326031			−0.163016	+	0.986623i	$0.552122\pi$
$938$	4.15790	−	4.36429i	0.135760	−	0.142499i
$939$	−7.17813	+	4.14430i	−0.234249	+	0.135244i
$940$	−47.3345	+	2.29405i	−1.54388	+	0.0748238i
$941$			12.2242i			0.398498i	0.979949	+	0.199249i	$0.0638502\pi$
$941$			12.2242i			0.398498i	−0.979949	+	0.199249i	$0.936150\pi$
$942$	3.61197	−	14.9157i	0.117684	−	0.485979i
$943$	0.715515	−	1.23931i	0.0233004	−	0.0403575i
$944$	−1.72963	−	0.786440i	−0.0562946	−	0.0255965i
$945$	4.09395	−	7.09093i	0.133176	−	0.230668i
$946$	−46.0066	−	43.8309i	−1.49580	−	1.42507i
$947$	2.80497	−	1.61945i	0.0911494	−	0.0526251i	−0.453732	−	0.891138i	$-0.649908\pi$
$947$	2.80497	−	1.61945i	0.0911494	−	0.0526251i	0.544882	+	0.838513i	$0.316574\pi$
$948$	10.3664	+	16.1012i	0.336686	+	0.522943i
$949$	0.208593	+	6.90798i	0.00677120	+	0.224242i
$950$	−0.0118812	−	0.0404017i	−0.000385476	−	0.00131080i
$951$	−0.291228	−	0.504421i	−0.00944370	−	0.0163570i
$952$	15.8964	+	3.04334i	0.515205	+	0.0986351i
$953$	−3.08301	+	5.33994i	−0.0998686	+	0.172977i	−0.911630	−	0.411012i	$-0.865176\pi$
$953$	−3.08301	+	5.33994i	−0.0998686	+	0.172977i	0.811762	+	0.583989i	$0.198509\pi$
$954$	−10.3836	−	35.3093i	−0.336182	−	1.14318i
$955$	−15.6025	−	9.00813i	−0.504886	−	0.291496i
$956$	−1.36369	−	28.1379i	−0.0441050	−	0.910043i
$957$		−	7.62843i		−	0.246592i
$958$	−10.8162	+	44.6658i	−0.349457	+	1.44309i
$959$	9.66009	+	16.7318i	0.311941	+	0.540297i
$960$	−9.88924	+	7.81677i	−0.319174	+	0.252285i
$961$	−27.3457			−0.882121
$962$	5.50615	−	26.1668i	0.177525	−	0.843652i
$963$		−	39.3543i		−	1.26817i
$964$	−25.7869	−	13.2671i	−0.830541	−	0.427305i
$965$	1.62154	−	0.936197i	0.0521993	−	0.0301373i
$966$	1.96656	+	0.476221i	0.0632730	+	0.0153222i
$967$	44.1828			1.42082			0.710411	−	0.703787i	$-0.248509\pi$
$967$	44.1828			1.42082			0.710411	+	0.703787i	$0.248509\pi$
$968$	18.6477	+	53.6635i	0.599359	+	1.72481i
$969$	3.54434	−	6.13898i	0.113861	−	0.197212i
$970$	−1.14535	−	3.89474i	−0.0367749	−	0.125053i
$971$	−33.2299	−	19.1853i	−1.06640	−	0.615686i	−0.139204	−	0.990264i	$-0.544454\pi$
$971$	−33.2299	−	19.1853i	−1.06640	−	0.615686i	−0.927195	+	0.374578i	$0.877788\pi$
$972$	13.7136	−	26.6548i	0.439864	−	0.854953i
$973$	6.62233	−	3.82340i	0.212302	−	0.122573i
$974$	−15.7302	+	4.62586i	−0.504027	+	0.148222i
$975$	0.0238932	+	0.0386418i	0.000765195	+	0.00123753i
$976$	12.8940	+	5.86275i	0.412728	+	0.187662i
$977$	−9.04005	−	15.6578i	−0.289217	−	0.500938i	0.684406	−	0.729101i	$-0.260062\pi$
$977$	−9.04005	−	15.6578i	−0.289217	−	0.500938i	−0.973623	+	0.228163i	$0.926728\pi$
$978$	3.60828	+	3.43764i	0.115380	+	0.109924i
$979$	3.60822	+	2.08321i	0.115319	+	0.0665796i
$980$	14.8160	+	23.0123i	0.473281	+	0.735102i
$981$	−21.0432	−	12.1493i	−0.671857	−	0.387897i
$982$	57.4660	+	13.9159i	1.83381	+	0.444075i
$983$	18.8329			0.600677			0.300339	−	0.953833i	$-0.402900\pi$
$983$	18.8329			0.600677			0.300339	+	0.953833i	$0.402900\pi$
$984$	1.24801	−	0.433675i	0.0397852	−	0.0138251i
$985$	−7.84529	−	13.5884i	−0.249972	−	0.432964i
$986$	−11.5031	+	12.0741i	−0.366332	+	0.384516i
$987$			7.02316i			0.223550i
$988$	10.8198	+	5.15980i	0.344224	+	0.164155i
$989$			17.3662i			0.552212i
$990$	−32.0370	−	30.5220i	−1.01820	−	0.970052i
$991$	−24.8600	−	43.0588i	−0.789704	−	1.36781i	−0.926148	−	0.377160i	$-0.876901\pi$
$991$	−24.8600	−	43.0588i	−0.789704	−	1.36781i	0.136444	−	0.990648i	$-0.456433\pi$
$992$	8.51395	+	6.66700i	0.270318	+	0.211677i
$993$	−10.4305			−0.331003
$994$	3.65507	−	15.0936i	0.115932	−	0.478741i
$995$	29.1675	+	16.8399i	0.924671	+	0.533859i
$996$	13.6766	−	8.80542i	0.433361	−	0.279011i
$997$	−41.6202	−	24.0294i	−1.31812	−	0.761020i	−0.334698	−	0.942325i	$-0.608634\pi$
$997$	−41.6202	−	24.0294i	−1.31812	−	0.761020i	−0.983427	+	0.181306i	$0.941968\pi$
$998$	17.4624	−	18.3293i	0.552764	−	0.580202i
$999$	10.1537	+	17.5868i	0.321250	+	0.556421i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	104.2.r.a.29.10	yes	24
3.2	odd	2		936.2.be.a.757.3		24
4.3	odd	2		416.2.z.a.81.5		24
8.3	odd	2		416.2.z.a.81.8		24
8.5	even	2	inner	104.2.r.a.29.7	✓	24
13.9	even	3	inner	104.2.r.a.61.7	yes	24
24.5	odd	2		936.2.be.a.757.6		24
39.35	odd	6		936.2.be.a.685.6		24
52.35	odd	6		416.2.z.a.113.8		24
104.35	odd	6		416.2.z.a.113.5		24
104.61	even	6	inner	104.2.r.a.61.10	yes	24
312.269	odd	6		936.2.be.a.685.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.r.a.29.7	✓	24	8.5	even	2	inner
104.2.r.a.29.10	yes	24	1.1	even	1	trivial
104.2.r.a.61.7	yes	24	13.9	even	3	inner
104.2.r.a.61.10	yes	24	104.61	even	6	inner
416.2.z.a.81.5		24	4.3	odd	2
416.2.z.a.81.8		24	8.3	odd	2
416.2.z.a.113.5		24	104.35	odd	6
416.2.z.a.113.8		24	52.35	odd	6
936.2.be.a.685.3		24	312.269	odd	6
936.2.be.a.685.6		24	39.35	odd	6
936.2.be.a.757.3		24	3.2	odd	2
936.2.be.a.757.6		24	24.5	odd	2

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:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02392 + 0.975496i) q^{2} +(0.609172 - 0.351705i) q^{3} +(0.0968157 + 1.99766i) q^{4} -2.24007i q^{5} +(0.966829 + 0.234127i) q^{6} +(0.471952 - 0.817445i) q^{7} +(-1.84957 + 2.13988i) q^{8} +(-1.25261 + 2.16958i) q^{9} +(2.18518 - 2.29365i) q^{10} +(-4.82849 + 2.78773i) q^{11} +(0.761563 + 1.18286i) q^{12} +(-0.108823 - 3.60391i) q^{13} +(1.28065 - 0.376609i) q^{14} +(-0.787845 - 1.36459i) q^{15} +(-3.98125 + 0.386809i) q^{16} +(3.03119 - 5.25017i) q^{17} +(-3.39898 + 0.999558i) q^{18} +(1.43961 + 0.831159i) q^{19} +(4.47489 - 0.216874i) q^{20} -0.663952i q^{21} +(-7.66340 - 1.85577i) q^{22} +(1.07746 + 1.86621i) q^{23} +(-0.374101 + 1.95406i) q^{24} -0.0179136 q^{25} +(3.40417 - 3.79626i) q^{26} +3.87243i q^{27} +(1.67867 + 0.863656i) q^{28} +(-1.68452 + 0.972558i) q^{29} +(0.524461 - 2.16576i) q^{30} -1.91161 q^{31} +(-4.45381 - 3.48764i) q^{32} +(-1.96092 + 3.39641i) q^{33} +(8.22520 - 2.41883i) q^{34} +(-1.83113 - 1.05721i) q^{35} +(-4.45534 - 2.29223i) q^{36} +(4.54154 - 2.62206i) q^{37} +(0.663250 + 2.25537i) q^{38} +(-1.33381 - 2.15712i) q^{39} +(4.79348 + 4.14317i) q^{40} +(-0.332039 - 0.575109i) q^{41} +(0.647683 - 0.679833i) q^{42} +(6.97919 + 4.02944i) q^{43} +(-6.03640 - 9.37576i) q^{44} +(4.86001 + 2.80593i) q^{45} +(-0.717252 + 2.96190i) q^{46} -10.5778 q^{47} +(-2.28922 + 1.63586i) q^{48} +(3.05452 + 5.29059i) q^{49} +(-0.0183420 - 0.0174746i) q^{50} -4.26434i q^{51} +(7.18883 - 0.566307i) q^{52} +10.3882i q^{53} +(-3.77754 + 3.96505i) q^{54} +(6.24471 + 10.8162i) q^{55} +(0.876323 + 2.52184i) q^{56} +1.16929 q^{57} +(-2.67354 - 0.647422i) q^{58} +(0.411368 + 0.237503i) q^{59} +(2.64970 - 1.70596i) q^{60} +(-3.06666 - 1.77054i) q^{61} +(-1.95733 - 1.86477i) q^{62} +(1.18234 + 2.04787i) q^{63} +(-1.15816 - 7.91572i) q^{64} +(-8.07301 + 0.243772i) q^{65} +(-5.32101 + 1.56478i) q^{66} +(3.91067 - 2.25783i) q^{67} +(10.7815 + 5.54696i) q^{68} +(1.31271 + 0.757894i) q^{69} +(-0.843631 - 2.86876i) q^{70} +(5.81695 - 10.0753i) q^{71} +(-2.32585 - 6.69322i) q^{72} -1.91680 q^{73} +(7.20797 + 1.74548i) q^{74} +(-0.0109124 + 0.00630029i) q^{75} +(-1.52099 + 2.95631i) q^{76} +5.26270i q^{77} +(0.738558 - 3.50984i) q^{78} +13.6120 q^{79} +(0.866479 + 8.91829i) q^{80} +(-2.39587 - 4.14976i) q^{81} +(0.221035 - 0.912767i) q^{82} -11.5623i q^{83} +(1.32635 - 0.0642810i) q^{84} +(-11.7607 - 6.79007i) q^{85} +(3.21542 + 10.9340i) q^{86} +(-0.684108 + 1.18491i) q^{87} +(2.96524 - 15.4885i) q^{88} +(-0.373638 - 0.647161i) q^{89} +(2.23908 + 7.61396i) q^{90} +(-2.99736 - 1.61192i) q^{91} +(-3.62373 + 2.33306i) q^{92} +(-1.16450 + 0.672324i) q^{93} +(-10.8308 - 10.3186i) q^{94} +(1.86185 - 3.22483i) q^{95} +(-3.93975 - 0.558140i) q^{96} +(0.640742 - 1.10980i) q^{97} +(-2.03337 + 8.39680i) q^{98} -13.9677i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} - q^{4} - 8 q^{6} - 2 q^{7} - 10 q^{8} + 6 q^{9} - 3 q^{10} - 12 q^{12} + 8 q^{14} + 4 q^{15} - q^{16} + 6 q^{18} - 11 q^{20} - 2 q^{22} - 14 q^{23} - 18 q^{24} - 12 q^{25} - 3 q^{26} - 4 q^{28}+ \cdots - 17 q^{98}+O(q^{100}) \) 24 * q - q^2 - q^4 - 8 * q^6 - 2 * q^7 - 10 * q^8 + 6 * q^9 - 3 * q^10 - 12 * q^12 + 8 * q^14 + 4 * q^15 - q^16 + 6 * q^18 - 11 * q^20 - 2 * q^22 - 14 * q^23 - 18 * q^24 - 12 * q^25 - 3 * q^26 - 4 * q^28 + 14 * q^30 - 8 * q^31 - 21 * q^32 - 14 * q^33 + 14 * q^34 + 5 * q^36 + 12 * q^38 - 34 * q^39 + 54 * q^40 - 4 * q^41 + 22 * q^42 + 24 * q^46 - 8 * q^47 - 8 * q^48 + 6 * q^49 + 32 * q^50 - 4 * q^52 + 22 * q^54 + 8 * q^55 + 8 * q^56 - 52 * q^57 + 33 * q^58 + 56 * q^60 - 14 * q^62 + 32 * q^63 + 26 * q^64 + 30 * q^65 - 104 * q^66 + 23 * q^68 - 16 * q^70 + 30 * q^71 + 17 * q^72 - 12 * q^73 - 7 * q^74 + 14 * q^76 - 8 * q^78 - 48 * q^79 + 29 * q^80 + 8 * q^81 - q^82 + 60 * q^84 - 96 * q^86 - 26 * q^87 + 4 * q^88 - 22 * q^89 - 50 * q^90 - 80 * q^92 - 42 * q^94 + 60 * q^95 - 40 * q^96 + 2 * q^97 - 17 * q^98

Introduction

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