LMFDB - Embedded newform 104.2.r.a.29.7

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			29.7
Character	$\chi$	$=$	104.29
Dual form			104.2.r.a.61.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.332845 + 1.37449i) q^{2} +(-0.609172 + 0.351705i) q^{3} +(-1.77843 + 0.914983i) q^{4} +2.24007i q^{5} +(-0.686174 - 0.720235i) q^{6} +(0.471952 - 0.817445i) q^{7} +(-1.84957 - 2.13988i) q^{8} +(-1.25261 + 2.16958i) q^{9} +(-3.07895 + 0.745597i) 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} +(2.32561 - 3.25446i) q^{16} +(3.03119 - 5.25017i) q^{17} +(-3.39898 - 0.999558i) q^{18} +(-1.43961 - 0.831159i) q^{19} +(-2.04963 - 3.98380i) q^{20} +0.663952i q^{21} +(5.43884 + 5.70881i) q^{22} +(1.07746 + 1.86621i) q^{23} +(1.87931 + 0.653048i) q^{24} -0.0179136 q^{25} +(-4.91730 + 1.34912i) q^{26} -3.87243i q^{27} +(-0.0913848 + 1.88560i) q^{28} +(1.68452 - 0.972558i) q^{29} +(1.61338 - 1.53708i) q^{30} -1.91161 q^{31} +(5.24728 + 2.11329i) q^{32} +(-1.96092 + 3.39641i) q^{33} +(8.22520 + 2.41883i) q^{34} +(1.83113 + 1.05721i) q^{35} +(0.242544 - 5.00455i) 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} +(-0.912594 + 0.220993i) q^{42} +(-6.97919 - 4.02944i) q^{43} +(-6.03640 + 9.37576i) q^{44} +(-4.86001 - 2.80593i) q^{45} +(-2.20645 + 2.10211i) q^{46} -10.5778 q^{47} +(-0.272086 + 2.80046i) q^{48} +(3.05452 + 5.29059i) q^{49} +(-0.00596244 - 0.0246219i) q^{50} +4.26434i q^{51} +(-3.49105 - 6.30972i) q^{52} -10.3882i q^{53} +(5.32260 - 1.28892i) q^{54} +(6.24471 + 10.8162i) q^{55} +(-2.62214 + 0.502004i) q^{56} +1.16929 q^{57} +(1.89745 + 1.99164i) q^{58} +(-0.411368 - 0.237503i) q^{59} +(2.64970 + 1.70596i) q^{60} +(3.06666 + 1.77054i) q^{61} +(-0.636270 - 2.62748i) 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} +(-0.586933 + 12.1105i) q^{68} +(-1.31271 - 0.757894i) q^{69} +(-0.843631 + 2.86876i) q^{70} +(5.81695 - 10.0753i) q^{71} +(6.95942 - 1.33237i) q^{72} -1.91680 q^{73} +(-5.11561 - 5.36954i) q^{74} +(0.0109124 - 0.00630029i) q^{75} +(3.32074 + 0.160939i) q^{76} -5.26270i q^{77} +(2.52099 - 2.55129i) q^{78} +13.6120 q^{79} +(7.29022 + 5.20954i) q^{80} +(-2.39587 - 4.14976i) q^{81} +(0.679962 - 0.647806i) q^{82} +11.5623i q^{83} +(-0.607505 - 1.18079i) q^{84} +(11.7607 + 6.79007i) q^{85} +(3.21542 - 10.9340i) q^{86} +(-0.684108 + 1.18491i) q^{87} +(-14.8961 - 5.17627i) 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} +(-3.52077 - 14.5391i) q^{94} +(1.86185 - 3.22483i) q^{95} +(-3.93975 + 0.558140i) q^{96} +(0.640742 - 1.10980i) q^{97} +(-6.25516 + 5.95935i) 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 $

$2$	0.332845	+	1.37449i	0.235357	+	0.971909i
$2$	0.332845	+	1.37449i	0.235357	+	0.971909i
$3$	−0.609172	+	0.351705i	−0.351705	+	0.203057i	−0.665436	−	0.746455i	$-0.731754\pi$
$3$	−0.609172	+	0.351705i	−0.351705	+	0.203057i	0.313731	+	0.949512i	$0.398421\pi$
$4$	−1.77843	+	0.914983i	−0.889214	+	0.457491i
$5$			2.24007i			1.00179i	0.865508	+	0.500895i	$0.166996\pi$
$5$			2.24007i			1.00179i	−0.865508	+	0.500895i	$0.833004\pi$
$6$	−0.686174	−	0.720235i	−0.280129	−	0.294035i
$7$	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
$10$	−3.07895	+	0.745597i	−0.973648	+	0.235778i
$11$	4.82849	−	2.78773i	1.45584	−	0.840532i	0.457042	−	0.889445i	$-0.348909\pi$
$11$	4.82849	−	2.78773i	1.45584	−	0.840532i	0.998803	+	0.0489128i	$0.0155756\pi$
$12$	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
$16$	2.32561	−	3.25446i	0.581403	−	0.813616i
$17$	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	0.325692	−	0.945476i	$-0.394403\pi$
$19$	−1.43961	−	0.831159i	−0.330269	−	0.190681i	−0.655961	+	0.754795i	$0.727736\pi$
$20$	−2.04963	−	3.98380i	−0.458310	−	0.890806i
$21$			0.663952i			0.144886i
$22$	5.43884	+	5.70881i	1.15956	+	1.21712i
$23$	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	$0.761205\pi$
$24$	1.87931	+	0.653048i	0.383613	+	0.133303i
$25$	−0.0179136			−0.00358271
$26$	−4.91730	+	1.34912i	−0.964363	+	0.264584i
$27$		−	3.87243i		−	0.745249i
$28$	−0.0913848	+	1.88560i	−0.0172701	+	0.356344i
$29$	1.68452	−	0.972558i	0.312807	−	0.180599i	−0.335375	−	0.942085i	$-0.608863\pi$
$29$	1.68452	−	0.972558i	0.312807	−	0.180599i	0.648182	+	0.761485i	$0.275530\pi$
$30$	1.61338	−	1.53708i	0.294561	−	0.280631i
$31$	−1.91161			−0.343335			−0.171668	−	0.985155i	$-0.554916\pi$
$31$	−1.91161			−0.343335			−0.171668	+	0.985155i	$0.554916\pi$
$32$	5.24728	+	2.11329i	0.927598	+	0.373581i
$33$	−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
$36$	0.242544	−	5.00455i	0.0404240	−	0.834092i
$37$	−4.54154	+	2.62206i	−0.746624	+	0.431064i	−0.824473	−	0.565902i	$-0.808528\pi$
$37$	−4.54154	+	2.62206i	−0.746624	+	0.431064i	0.0778488	+	0.996965i	$0.475195\pi$
$38$	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	$0.849847\pi$
$42$	−0.912594	+	0.220993i	−0.140816	+	0.0341000i
$43$	−6.97919	−	4.02944i	−1.06432	−	0.614483i	−0.137693	−	0.990475i	$-0.543969\pi$
$43$	−6.97919	−	4.02944i	−1.06432	−	0.614483i	−0.926623	+	0.375992i	$0.877302\pi$
$44$	−6.03640	+	9.37576i	−0.910021	+	1.41345i
$45$	−4.86001	−	2.80593i	−0.724487	−	0.418283i
$46$	−2.20645	+	2.10211i	−0.325324	+	0.309939i
$47$	−10.5778			−1.54293			−0.771466	−	0.636270i	$-0.780476\pi$
$47$	−10.5778			−1.54293			−0.771466	+	0.636270i	$0.780476\pi$
$48$	−0.272086	+	2.80046i	−0.0392722	+	0.404211i
$49$	3.05452	+	5.29059i	0.436360	+	0.755798i
$50$	−0.00596244	−	0.0246219i	−0.000843216	−	0.00348207i
$51$			4.26434i			0.597127i
$52$	−3.49105	−	6.30972i	−0.484121	−	0.875001i
$53$		−	10.3882i		−	1.42693i	−0.700691	−	0.713465i	$-0.747125\pi$
$53$		−	10.3882i		−	1.42693i	0.700691	−	0.713465i	$-0.252875\pi$
$54$	5.32260	−	1.28892i	0.724314	−	0.175400i
$55$	6.24471	+	10.8162i	0.842037	+	1.45845i
$56$	−2.62214	+	0.502004i	−0.350399	+	0.0670831i
$57$	1.16929			0.154877
$58$	1.89745	+	1.99164i	0.249148	+	0.261515i
$59$	−0.411368	−	0.237503i	−0.0535555	−	0.0309203i	0.472983	−	0.881071i	$-0.343177\pi$
$59$	−0.411368	−	0.237503i	−0.0535555	−	0.0309203i	−0.526539	+	0.850151i	$0.676510\pi$
$60$	2.64970	+	1.70596i	0.342075	+	0.220238i
$61$	3.06666	+	1.77054i	0.392646	+	0.226694i	0.683306	−	0.730132i	$-0.260541\pi$
$61$	3.06666	+	1.77054i	0.392646	+	0.226694i	−0.290660	+	0.956826i	$0.593875\pi$
$62$	−0.636270	−	2.62748i	−0.0808064	−	0.333691i
$63$	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	−0.719484	−	0.694509i	$-0.755622\pi$
$67$	−3.91067	+	2.25783i	−0.477764	+	0.275837i	0.241720	+	0.970346i	$0.422288\pi$
$68$	−0.586933	+	12.1105i	−0.0711761	+	1.46862i
$69$	−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	$-0.0758748\pi$
$72$	6.95942	−	1.33237i	0.820176	−	0.157021i
$73$	−1.91680			−0.224345			−0.112172	−	0.993689i	$-0.535781\pi$
$73$	−1.91680			−0.224345			−0.112172	+	0.993689i	$0.535781\pi$
$74$	−5.11561	−	5.36954i	−0.594678	−	0.624197i
$75$	0.0109124	−	0.00630029i	0.00126006	−	0.000727495i
$76$	3.32074	+	0.160939i	0.380915	+	0.0184609i
$77$		−	5.26270i		−	0.599741i
$78$	2.52099	−	2.55129i	0.285446	−	0.288876i
$79$	13.6120			1.53147			0.765737	−	0.643154i	$-0.222374\pi$
$79$	13.6120			1.53147			0.765737	+	0.643154i	$0.222374\pi$
$80$	7.29022	+	5.20954i	0.815072	+	0.582444i
$81$	−2.39587	−	4.14976i	−0.266207	−	0.461085i
$82$	0.679962	−	0.647806i	0.0750892	−	0.0715382i
$83$			11.5623i			1.26913i	0.772871	+	0.634564i	$0.218820\pi$
$83$			11.5623i			1.26913i	−0.772871	+	0.634564i	$0.781180\pi$
$84$	−0.607505	−	1.18079i	−0.0662842	−	0.128835i
$85$	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
$88$	−14.8961	−	5.17627i	−1.58792	−	0.551792i
$89$	−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
$94$	−3.52077	−	14.5391i	−0.363140	−	1.49959i
$95$	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	$0.145944\pi$
$98$	−6.25516	+	5.95935i	−0.631867	+	0.601985i
$99$			13.9677i			1.40381i
$100$	0.0318580	−	0.0163906i	0.00318580	−	0.00163906i
$101$	8.45583	−	4.88197i	0.841386	−	0.485775i	−0.0163490	−	0.999866i	$-0.505204\pi$
$101$	8.45583	−	4.88197i	0.841386	−	0.485775i	0.857735	+	0.514092i	$0.171871\pi$
$102$	−5.86127	+	1.41936i	−0.580353	+	0.140538i
$103$	−15.0755			−1.48544			−0.742719	−	0.669604i	$-0.766464\pi$
$103$	−15.0755			−1.48544			−0.742719	+	0.669604i	$0.766464\pi$
$104$	7.51065	−	6.89856i	0.736480	−	0.676460i
$105$	−1.48730			−0.145146
$106$	14.2785	−	3.45767i	1.38685	−	0.335838i
$107$	13.6044	−	7.85448i	1.31518	−	0.759321i	0.332233	−	0.943197i	$-0.392198\pi$
$107$	13.6044	−	7.85448i	1.31518	−	0.759321i	0.982949	+	0.183876i	$0.0588646\pi$
$108$	3.54320	+	6.88683i	0.340945	+	0.662686i
$109$		−	9.69920i		−	0.929015i	−0.885569	−	0.464508i	$-0.846231\pi$
$109$		−	9.69920i		−	0.929015i	0.885569	−	0.464508i	$-0.153769\pi$
$110$	−12.7881	+	12.1834i	−1.21930	+	1.16164i
$111$	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	$0.0509087\pi$
$114$	0.389193	+	1.60718i	0.0364513	+	0.150526i
$115$	−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
$120$	−1.46287	+	4.20979i	−0.133541	+	0.384300i
$121$	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
$124$	3.39966	−	1.74909i	0.305299	−	0.157073i
$125$			11.1602i			0.998201i
$126$	−2.42124	+	2.30674i	−0.215701	+	0.205500i
$127$	−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	$0.876957\pi$
$128$	−11.2655	+	1.04284i	−0.995743	+	0.0921746i
$129$	5.66870			0.499101
$130$	−3.02212	−	11.0151i	−0.265058	−	0.966089i
$131$			11.9145i			1.04098i	0.853869	+	0.520488i	$0.174250\pi$
$131$			11.9145i			1.04098i	−0.853869	+	0.520488i	$0.825750\pi$
$132$	0.379696	−	7.83448i	0.0330483	−	0.681904i
$133$	−1.35885	+	0.784534i	−0.117828	+	0.0680278i
$134$	−4.40500	−	4.62366i	−0.380534	−	0.399423i
$135$	8.67451			0.746583
$136$	−16.8411	+	3.22420i	−1.44411	+	0.276473i
$137$	−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	0.172024	−	0.985093i	$-0.444969\pi$
$139$	−7.01589	−	4.05062i	−0.595080	−	0.343570i	−0.767104	+	0.641523i	$0.778303\pi$
$140$	−4.22387	−	0.204708i	−0.356982	−	0.0173010i
$141$	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
$146$	−0.637998	−	2.63462i	−0.0528011	−	0.218043i
$147$	−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	0.622888	−	0.782311i	$-0.285959\pi$
$149$	3.13501	+	1.81000i	0.256830	+	0.148281i	−0.366058	+	0.930592i	$0.619293\pi$
$150$	0.0122918	+	0.0129020i	0.00100362	+	0.00105344i
$151$	−16.0939			−1.30970			−0.654850	−	0.755759i	$-0.727268\pi$
$151$	−16.0939			−1.30970			−0.654850	+	0.755759i	$0.727268\pi$
$152$	0.884084	+	4.61788i	0.0717087	+	0.374559i
$153$	7.59377	+	13.1528i	0.613920	+	1.06334i
$154$	7.23351	−	1.75167i	0.582893	−	0.141153i
$155$		−	4.28214i		−	0.343950i
$156$	4.34581	+	2.61588i	0.347943	+	0.209438i
$157$			15.4274i			1.23124i	0.788042	+	0.615621i	$0.211095\pi$
$157$			15.4274i			1.23124i	−0.788042	+	0.615621i	$0.788905\pi$
$158$	4.53070	+	18.7096i	0.360443	+	1.48845i
$159$	3.65359	+	6.32820i	0.289748	+	0.501859i
$160$	−4.73392	+	11.7543i	−0.374249	+	0.929258i
$161$	2.03403			0.160304
$162$	4.90634	−	4.67432i	0.385479	−	0.367249i
$163$	−4.33867	−	2.50493i	−0.339831	−	0.196201i	0.320366	−	0.947294i	$-0.396194\pi$
$163$	−4.33867	−	2.50493i	−0.339831	−	0.196201i	−0.660197	+	0.751092i	$0.729527\pi$
$164$	1.11672	+	0.718980i	0.0872014	+	0.0561429i
$165$	−7.60820	−	4.39260i	−0.592298	−	0.341963i
$166$	−15.8922	+	3.84846i	−1.23348	+	0.298698i
$167$	−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
$172$	16.0988	+	0.780226i	1.22753	+	0.0594916i
$173$	−18.9047	−	10.9146i	−1.43730	−	0.829825i	−0.439638	−	0.898175i	$-0.644893\pi$
$173$	−18.9047	−	10.9146i	−1.43730	−	0.829825i	−0.997661	+	0.0683503i	$0.978226\pi$
$174$	−1.85634	−	0.545905i	−0.140729	−	0.0413850i
$175$	−0.00845434	+	0.0146433i	−0.000639088	+	0.00110693i
$176$	2.15664	−	22.1973i	0.162563	−	1.67319i
$177$	0.334125			0.0251144
$178$	0.765150	−	0.728965i	0.0573504	−	0.0546383i
$179$	2.82862	−	1.63310i	0.211421	−	0.122064i	−0.390551	−	0.920581i	$-0.627715\pi$
$179$	2.82862	−	1.63310i	0.211421	−	0.122064i	0.601972	+	0.798517i	$0.294382\pi$
$180$	11.2105	+	0.543316i	0.835585	+	0.0404964i
$181$			13.1229i			0.975420i	0.873006	+	0.487710i	$0.162168\pi$
$181$			13.1229i			0.975420i	−0.873006	+	0.487710i	$0.837832\pi$
$182$	−1.21790	+	4.65635i	−0.0902768	+	0.345151i
$183$	−2.49083			−0.184128
$184$	2.00063	−	5.75731i	0.147488	−	0.424435i
$185$	−5.87359	−	10.1734i	−0.431835	−	0.747960i
$186$	1.31170	+	1.37681i	0.0961784	+	0.100952i
$187$		−	33.8005i		−	2.47174i
$188$	18.8119	−	9.67852i	1.37200	−	0.705878i
$189$	−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	$0.0726869\pi$
$192$	−2.07848	−	5.22936i	−0.150002	−	0.377397i
$193$	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	−0.700279	−	0.713869i	$-0.746941\pi$
$197$	−6.06608	+	3.50225i	−0.432190	+	0.249525i	0.268089	+	0.963394i	$0.413608\pi$
$198$	−19.1984	+	4.64909i	−1.36437	+	0.330396i
$199$	−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
$202$	9.52469	+	9.99748i	0.670155	+	0.703420i
$203$		−	1.83600i		−	0.128862i
$204$	−3.90179	−	7.58382i	−0.273180	−	0.530973i
$205$	1.28828	−	0.743791i	0.0899777	−	0.0519486i
$206$	−5.01782	−	20.7211i	−0.349608	−	1.44371i
$207$	−5.39851			−0.375223
$208$	11.9819	+	8.02714i	0.830793	+	0.556582i
$209$	−9.26819			−0.641094
$210$	−0.495041	−	2.04427i	−0.0341610	−	0.141068i
$211$	−5.82236	+	3.36154i	−0.400828	+	0.231418i	−0.686841	−	0.726808i	$-0.741003\pi$
$211$	−5.82236	+	3.36154i	−0.400828	+	0.231418i	0.286013	+	0.958226i	$0.407670\pi$
$212$	9.50503	+	18.4747i	0.652808	+	1.26885i
$213$			8.18342i			0.560718i
$214$	15.3240	+	16.0847i	1.04753	+	1.09953i
$215$	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
$218$	13.3314	−	3.22833i	0.902918	−	0.218650i
$219$	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	$-0.412911\pi$
$224$	4.20397	−	3.29199i	0.280889	−	0.219956i
$225$	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	−0.173382	−	0.984855i	$-0.555469\pi$
$227$	−16.7688	−	9.68145i	−1.11298	−	0.642580i	−0.939600	+	0.342274i	$0.888803\pi$
$228$	−2.07950	+	1.06988i	−0.137718	+	0.0708547i
$229$		−	17.6044i		−	1.16333i	−0.813428	−	0.581666i	$-0.802401\pi$
$229$		−	17.6044i		−	1.16333i	0.813428	−	0.581666i	$-0.197599\pi$
$230$	−4.70887	−	4.94261i	−0.310494	−	0.325906i
$231$	1.85092	+	3.20589i	0.121782	+	0.210932i
$232$	−5.19680	−	1.80585i	−0.341186	−	0.118560i
$233$	15.3281			1.00417			0.502087	−	0.864817i	$-0.332566\pi$
$233$	15.3281			1.00417			0.502087	+	0.864817i	$0.332566\pi$
$234$	3.23243	−	12.3584i	0.211310	−	0.807893i
$235$		−	23.6950i		−	1.54569i
$236$	0.948900	+	0.0459881i	0.0617681	+	0.00299357i
$237$	−8.29207	+	4.78743i	−0.538628	+	0.310977i
$238$	5.85916	−	5.58208i	0.379793	−	0.361832i
$239$	−14.0854			−0.911111			−0.455556	−	0.890207i	$-0.650559\pi$
$239$	−14.0854			−0.911111			−0.455556	+	0.890207i	$0.650559\pi$
$240$	−6.27322	−	0.609491i	−0.404934	−	0.0393425i
$241$	−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
$244$	−7.07386	−	0.342832i	−0.452857	−	0.0219476i
$245$	−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
$250$	−15.3396	+	3.71463i	−0.970160	+	0.234934i
$251$	24.8381	+	14.3403i	1.56777	+	0.905151i	0.996429	+	0.0844378i	$0.0269094\pi$
$251$	24.8381	+	14.3403i	1.56777	+	0.905151i	0.571340	+	0.820714i	$0.306424\pi$
$252$	−3.97648	−	2.56018i	−0.250495	−	0.161276i
$253$	10.4050	+	6.00731i	0.654155	+	0.377677i
$254$	3.15289	−	3.00379i	0.197830	−	0.188475i
$255$	−9.55241			−0.598195
$256$	−5.18305	−	15.1372i	−0.323940	−	0.946077i
$257$	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	$0.715227\pi$
$258$	1.88680	+	7.79155i	0.117467	+	0.485081i
$259$			4.94994i			0.307574i
$260$	14.1342	−	7.82019i	0.876567	−	0.484988i
$261$			4.87293i			0.301627i
$262$	−16.3763	+	3.96569i	−1.01173	+	0.245001i
$263$	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	$0.658306\pi$
$264$	10.8948	−	2.08578i	0.670527	−	0.128371i
$265$	23.2703			1.42948
$266$	−1.53062	−	1.60660i	−0.0938483	−	0.0985068i
$267$	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	0.290247	−	0.956952i	$-0.406262\pi$
$269$	−6.45180	−	3.72495i	−0.393373	−	0.227114i	−0.683621	+	0.729837i	$0.739596\pi$
$270$	2.88727	+	11.9230i	0.175714	+	0.725610i
$271$	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
$276$	3.02802	+	0.146752i	0.182266	+	0.00883344i
$277$	13.9928	+	8.07878i	0.840749	+	0.485407i	0.857519	−	0.514453i	$-0.172005\pi$
$277$	13.9928	+	8.07878i	0.840749	+	0.485407i	−0.0167699	+	0.999859i	$0.505338\pi$
$278$	3.23233	−	10.9915i	0.193862	−	0.659225i
$279$	2.39450	−	4.14739i	0.143355	−	0.248298i
$280$	−1.12452	−	5.87378i	−0.0672032	−	0.351026i
$281$	27.7204			1.65366			0.826831	−	0.562450i	$-0.190141\pi$
$281$	27.7204			1.65366			0.826831	+	0.562450i	$0.190141\pi$
$282$	7.25822	+	7.61851i	0.432221	+	0.453676i
$283$	−3.28760	+	1.89810i	−0.195428	+	0.112830i	−0.594521	−	0.804080i	$-0.702658\pi$
$283$	−3.28760	+	1.89810i	−0.195428	+	0.112830i	0.399093	+	0.916910i	$0.369325\pi$
$284$	−1.12635	+	23.2405i	−0.0668363	+	1.37907i
$285$			2.61930i			0.155154i
$286$	−19.9822	+	20.2223i	−1.18157	+	1.19577i
$287$	−0.626827			−0.0370004
$288$	−11.1577	+	8.73727i	−0.657476	+	0.514849i
$289$	−9.87617	−	17.1060i	−0.580951	−	1.00624i
$290$	−4.46141	+	4.25043i	−0.261983	+	0.249594i
$291$			0.901409i			0.0528415i
$292$	3.40889	−	1.75384i	0.199490	−	0.102636i
$293$	−4.14791	−	2.39480i	−0.242324	−	0.139906i	0.373921	−	0.927461i	$-0.378013\pi$
$293$	−4.14791	−	2.39480i	−0.242324	−	0.139906i	−0.616244	+	0.787555i	$0.711347\pi$
$294$	1.71453	−	5.83024i	0.0999935	−	0.340026i
$295$	0.532024	−	0.921493i	0.0309756	−	0.0536514i
$296$	14.0108	+	4.86865i	0.814360	+	0.282984i
$297$	−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
$302$	−5.35677	−	22.1208i	−0.308247	−	1.27291i
$303$	−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
$306$	−15.5508	+	14.8154i	−0.888979	+	0.846939i
$307$			8.95981i			0.511363i	0.966761	+	0.255682i	$0.0822999\pi$
$307$			8.95981i			0.511363i	−0.966761	+	0.255682i	$0.917700\pi$
$308$	4.81528	+	9.35934i	0.274376	+	0.533298i
$309$	9.18359	−	5.30215i	0.522436	−	0.301629i
$310$	5.88575	−	1.42529i	0.334288	−	0.0809511i
$311$	9.35196			0.530301			0.265150	−	0.964207i	$-0.414578\pi$
$311$	9.35196			0.530301			0.265150	+	0.964207i	$0.414578\pi$
$312$	−2.14901	+	6.84394i	−0.121664	+	0.387462i
$313$	−11.7834			−0.666039			−0.333019	−	0.942920i	$-0.608067\pi$
$313$	−11.7834			−0.666039			−0.333019	+	0.942920i	$0.608067\pi$
$314$	−21.2048	+	5.13494i	−1.19665	+	0.289782i
$315$	−4.58738	+	2.64853i	−0.258470	+	0.149228i
$316$	−24.2080	+	12.4548i	−1.36181	+	0.700636i
$317$			0.828044i			0.0465076i	0.999730	+	0.0232538i	$0.00740258\pi$
$317$			0.828044i			0.0465076i	−0.999730	+	0.0232538i	$0.992597\pi$
$318$	−7.48195	+	7.12812i	−0.419567	+	0.399725i
$319$	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
$322$	0.677017	+	2.79575i	0.0377287	+	0.155801i
$323$	−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
$328$	−0.616532	+	1.77423i	−0.0340423	+	0.0979655i
$329$	−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	0.809524	−	0.587087i	$-0.199726\pi$
$331$	12.8419	+	7.41425i	0.705853	+	0.407524i	−0.103671	+	0.994612i	$0.533059\pi$
$332$	−10.5793	−	20.5627i	−0.580615	−	1.12853i
$333$		−	13.1376i		−	0.719937i
$334$	1.08986	−	1.03832i	0.0596343	−	0.0568142i
$335$	−5.05769	−	8.76018i	−0.276331	−	0.478620i
$336$	2.16081	+	1.54410i	0.117882	+	0.0842374i
$337$	5.53901			0.301729			0.150865	−	0.988554i	$-0.451794\pi$
$337$	5.53901			0.301729			0.150865	+	0.988554i	$0.451794\pi$
$338$	−5.39722	−	17.5747i	−0.293570	−	0.955938i
$339$			5.31941i			0.288911i
$340$	−27.1284	−	1.31477i	−1.47125	−	0.0713035i
$341$	−9.23019	+	5.32906i	−0.499843	+	0.288585i
$342$	4.06241	+	4.26407i	0.219670	+	0.230574i
$343$	12.3737			0.668116
$344$	4.28601	+	22.3873i	0.231086	+	1.20704i
$345$	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	0.0753728	−	0.997155i	$-0.475985\pi$
$347$	−13.9803	−	8.07154i	−0.750503	−	0.433303i	−0.825876	+	0.563852i	$0.809319\pi$
$348$	0.132465	−	2.73322i	0.00710086	−	0.146516i
$349$	20.7087	−	11.9562i	1.10851	−	0.640000i	0.170068	−	0.985432i	$-0.445601\pi$
$349$	20.7087	−	11.9562i	1.10851	−	0.640000i	0.938444	+	0.345432i	$0.112268\pi$
$350$	−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	$0.880588\pi$
$354$	0.111212	+	0.459250i	0.00591084	+	0.0244089i
$355$	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
$358$	3.18617	+	3.34433i	0.168395	+	0.176753i
$359$	−8.55135			−0.451323			−0.225661	−	0.974206i	$-0.572454\pi$
$359$	−8.55135			−0.451323			−0.225661	+	0.974206i	$0.572454\pi$
$360$	2.98460	+	15.5896i	0.157302	+	0.821644i
$361$	−8.11835	−	14.0614i	−0.427282	−	0.740073i
$362$	−18.0373	+	4.36791i	−0.948019	+	0.229572i
$363$			14.1285i			0.741556i
$364$	−6.80546	−	0.124146i	−0.356703	−	0.00650701i
$365$		−	4.29377i		−	0.224746i
$366$	−0.829062	−	3.42362i	−0.0433358	−	0.178955i
$367$	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	$0.800593\pi$
$368$	8.57925	+	0.833539i	0.447224	+	0.0434512i
$369$	1.66366			0.0866066
$370$	12.0282	−	11.4593i	0.625314	−	0.595742i
$371$	−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	0.667047	−	0.745016i	$-0.267558\pi$
$373$	6.86329	+	3.96253i	0.355368	+	0.205172i	−0.311679	+	0.950187i	$0.600891\pi$
$374$	46.4584	−	11.2503i	2.40230	−	0.581741i
$375$	−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	−0.954890	−	0.296959i	$-0.904027\pi$
$379$	−22.8779	+	13.2086i	−1.17516	+	0.678479i	−0.220271	+	0.975439i	$0.570694\pi$
$380$	−0.360514	+	7.43868i	−0.0184940	+	0.381596i
$381$	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	$0.182077\pi$
$384$	6.49588	−	4.59742i	0.331491	−	0.234611i
$385$	11.7888			0.600814
$386$	−0.855857	+	0.815382i	−0.0435620	+	0.0415019i
$387$	17.4844	−	10.0946i	0.888780	−	0.513137i
$388$	−0.124068	+	2.55996i	−0.00629859	+	0.129962i
$389$		−	25.0808i		−	1.27165i	−0.771835	−	0.635823i	$-0.780661\pi$
$389$		−	25.0808i		−	1.27165i	0.771835	−	0.635823i	$-0.219339\pi$
$390$	5.71506	+	5.64719i	0.289393	+	0.285957i
$391$	13.0639			0.660669
$392$	5.67165	−	16.3216i	0.286462	−	0.824367i
$393$	−4.19040	−	7.25798i	−0.211378	−	0.366117i
$394$	−6.83286	−	7.17203i	−0.344235	−	0.361322i
$395$			30.4919i			1.53422i
$396$	−12.7802	−	24.8406i	−0.642230	−	1.24829i
$397$	−7.99993	−	4.61876i	−0.401505	−	0.231809i	0.285628	−	0.958341i	$-0.407798\pi$
$397$	−7.99993	−	4.61876i	−0.401505	−	0.231809i	−0.687133	+	0.726532i	$0.741131\pi$
$398$	−20.3991	−	5.99888i	−1.02251	−	0.300696i
$399$	0.551850	−	0.955832i	0.0276270	−	0.0478515i
$400$	−0.0416600	+	0.0582990i	−0.00208300	+	0.00291495i
$401$	−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
$406$	2.52356	−	0.611105i	0.125242	−	0.0303286i
$407$	−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	$0.939595\pi$
$410$	1.45113	+	1.52316i	0.0716662	+	0.0752236i
$411$		−	14.3977i		−	0.710184i
$412$	26.8108	−	13.7939i	1.32087	−	0.679575i
$413$	−0.388292	+	0.224180i	−0.0191066	+	0.0110312i
$414$	−1.79687	−	7.42019i	−0.0883113	−	0.364682i
$415$	−25.9004			−1.27140
$416$	−7.04509	+	19.1407i	−0.345414	+	0.938450i
$417$	5.69851			0.279057
$418$	−3.08487	−	12.7390i	−0.150886	−	0.623085i
$419$	−4.30501	+	2.48550i	−0.210314	+	0.121425i	−0.601457	−	0.798905i	$-0.705413\pi$
$419$	−4.30501	+	2.48550i	−0.210314	+	0.121425i	0.391144	+	0.920330i	$0.372080\pi$
$420$	2.64506	−	1.36085i	0.129066	−	0.0664029i
$421$		−	24.0575i		−	1.17249i	−0.810134	−	0.586244i	$-0.800606\pi$
$421$		−	24.0575i		−	1.17249i	0.810134	−	0.586244i	$-0.199394\pi$
$422$	−6.55834	−	6.88388i	−0.319255	−	0.335102i
$423$	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
$426$	−11.2480	+	2.72381i	−0.544967	+	0.131969i
$427$	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	$0.915340\pi$
$432$	−12.6027	−	9.00576i	−0.606346	−	0.433290i
$433$	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
$436$	8.87460	+	17.2493i	0.425016	+	0.826093i
$437$		−	3.58215i		−	0.171357i
$438$	1.31526	+	1.38055i	0.0628456	+	0.0659651i
$439$	−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	$0.933166\pi$
$440$	11.5952	−	33.3682i	0.552780	−	1.59077i
$441$	−15.3045			−0.728784
$442$	−7.82215	+	29.9061i	−0.372062	+	1.42249i
$443$			14.0440i			0.667248i	0.942706	+	0.333624i	$0.108272\pi$
$443$			14.0440i			0.667248i	−0.942706	+	0.333624i	$0.891728\pi$
$444$	−0.357131	+	7.36888i	−0.0169487	+	0.349712i
$445$	1.44969	−	0.836976i	0.0687217	−	0.0396765i
$446$	21.3672	−	20.3567i	1.01177	−	0.963918i
$447$	−2.54634			−0.120438
$448$	5.92407	+	4.68257i	0.279886	+	0.221231i
$449$	−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
$452$	−0.732151	+	15.1069i	−0.0344375	+	0.710569i
$453$	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	$0.594389\pi$
$458$	24.1970	−	5.85954i	1.13065	−	0.273798i
$459$	−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	−0.124190	−	0.992258i	$-0.539633\pi$
$461$	−22.4501	−	12.9616i	−1.04561	−	0.603681i	−0.921416	+	0.388577i	$0.872967\pi$
$462$	−3.79038	+	3.61113i	−0.176344	+	0.168005i
$463$	36.7003			1.70561			0.852803	−	0.522233i	$-0.174901\pi$
$463$	36.7003			1.70561			0.852803	+	0.522233i	$0.174901\pi$
$464$	0.752388	−	7.74400i	0.0349287	−	0.359506i
$465$	1.50605	+	2.60856i	0.0698415	+	0.120969i
$466$	5.10187	+	21.0682i	0.236340	+	0.975967i
$467$		−	27.9836i		−	1.29492i	−0.762097	−	0.647462i	$-0.775830\pi$
$467$		−	27.9836i		−	1.29492i	0.762097	−	0.647462i	$-0.224170\pi$
$468$	18.0623	+	0.329495i	0.834932	+	0.0152309i
$469$			4.26234i			0.196817i
$470$	32.5685	−	7.88678i	1.50227	−	0.363790i
$471$	−5.42590	−	9.39794i	−0.250012	−	0.433034i
$472$	0.252627	+	1.31956i	0.0116281	+	0.0607375i
$473$	−44.9319			−2.06597
$474$	−9.34023	−	9.80387i	−0.429011	−	0.450306i
$475$	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
$478$	−4.68827	−	19.3603i	−0.214437	−	0.885517i
$479$	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
$484$	−1.94462	+	40.1244i	−0.0883918	+	1.82384i
$485$	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	$0.251275\pi$
$488$	−1.88328	−	9.83703i	−0.0852521	−	0.445302i
$489$	3.52399			0.159360
$490$	−13.3494	−	14.0120i	−0.603062	−	0.632997i
$491$	−36.2077	+	20.9045i	−1.63403	+	0.943407i	−0.651197	+	0.758909i	$0.725733\pi$
$491$	−36.2077	+	20.9045i	−1.63403	+	0.943407i	−0.982833	+	0.184498i	$0.940934\pi$
$492$	−0.933145	−	0.0452246i	−0.0420694	−	0.00203888i
$493$		−	11.7920i		−	0.531085i
$494$	8.20033	+	2.14485i	0.368950	+	0.0965016i
$495$	−31.2887			−1.40632
$496$	−4.44567	+	6.22126i	−0.199616	+	0.279343i
$497$	−5.49065	−	9.51008i	−0.246289	−	0.426585i
$498$	8.32757	−	7.93375i	0.373167	−	0.355520i
$499$			17.9011i			0.801363i	0.916217	+	0.400682i	$0.131227\pi$
$499$			17.9011i			0.801363i	−0.916217	+	0.400682i	$0.868773\pi$
$500$	−10.2114	−	19.8477i	−0.456668	−	0.887614i
$501$	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	$0.272114\pi$
$504$	2.19538	−	6.31776i	0.0977898	−	0.281415i
$505$	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	−0.475734	−	0.879589i	$-0.657818\pi$
$509$	1.08621	−	0.627122i	0.0481453	−	0.0277967i	0.523879	+	0.851792i	$0.324484\pi$
$510$	−3.17947	−	13.1297i	−0.140790	−	0.581391i
$511$	−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
$514$	−11.9034	+	11.3405i	−0.525038	+	0.500209i
$515$		−	33.7703i		−	1.48810i
$516$	−10.0814	+	5.18676i	−0.443807	+	0.228334i
$517$	−51.0749	+	29.4881i	−2.24627	+	1.29688i
$518$	−6.80363	+	1.64756i	−0.298934	+	0.0723898i
$519$	15.3550			0.674008
$520$	15.4533	+	16.8244i	0.677670	+	0.737798i
$521$	8.42526			0.369117			0.184559	−	0.982822i	$-0.440914\pi$
$521$	8.42526			0.369117			0.184559	+	0.982822i	$0.440914\pi$
$522$	−6.69778	+	1.62193i	−0.293154	+	0.0709900i
$523$	20.6677	−	11.9325i	0.903736	−	0.521772i	0.0253256	−	0.999679i	$-0.491938\pi$
$523$	20.6677	−	11.9325i	0.903736	−	0.521772i	0.878410	+	0.477907i	$0.158604\pi$
$524$	−10.9016	−	21.1891i	−0.476238	−	0.925651i
$525$		−	0.0118937i		−	0.000519086i
$526$	−17.3548	+	16.5341i	−0.756704	+	0.720919i
$527$	−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
$530$	7.74541	+	31.9847i	0.336439	+	1.38933i
$531$	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
$536$	12.0645	+	4.19234i	0.521109	+	0.181082i
$537$	−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
$540$	−15.4270	+	7.93702i	−0.663872	+	0.341555i
$541$			19.4928i			0.838059i	0.907973	+	0.419030i	$0.137630\pi$
$541$			19.4928i			0.838059i	−0.907973	+	0.419030i	$0.862370\pi$
$542$	−15.5891	+	14.8519i	−0.669610	+	0.637943i
$543$	−4.61541	−	7.99412i	−0.198066	−	0.343060i
$544$	27.0006	−	21.1433i	1.15764	−	0.906513i
$545$	21.7269			0.930678
$546$	−0.895751	−	3.26486i	−0.0383346	−	0.139723i
$547$		−	2.18538i		−	0.0934399i	−0.998908	−	0.0467200i	$-0.985123\pi$
$547$		−	2.18538i		−	0.0934399i	0.998908	−	0.0467200i	$-0.0148768\pi$
$548$	1.98166	−	40.8887i	0.0846523	−	1.74668i
$549$	−7.68265	+	4.43558i	−0.327887	+	0.189306i
$550$	−0.0974289	−	0.102265i	−0.00415438	−	0.00436060i
$551$	−3.23340			−0.137747
$552$	0.806154	+	4.21082i	0.0343122	+	0.179224i
$553$	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
$556$	16.1835	+	0.784328i	0.686333	+	0.0332629i
$557$	−29.5902	+	17.0839i	−1.25378	+	0.723869i	−0.971858	−	0.235568i	$-0.924305\pi$
$557$	−29.5902	+	17.0839i	−1.25378	+	0.723869i	−0.281921	+	0.959438i	$0.590972\pi$
$558$	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
$562$	9.22661	+	38.1014i	0.389201	+	1.60721i
$563$	−20.4379	−	11.7998i	−0.861353	−	0.497302i	0.00311215	−	0.999995i	$-0.499009\pi$
$563$	−20.4379	−	11.7998i	−0.861353	−	0.497302i	−0.864465	+	0.502693i	$0.832343\pi$
$564$	−8.05568	+	12.5121i	−0.339205	+	0.526855i
$565$	14.6706	+	8.47006i	0.617195	+	0.356338i
$566$	−3.70317	−	3.88699i	−0.155656	−	0.163382i
$567$	−4.52294			−0.189946
$568$	−32.3187	+	6.18736i	−1.35606	+	0.259616i
$569$	−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	$0.851880\pi$
$570$	−3.60019	+	0.871820i	−0.150795	+	0.0365165i
$571$			19.2497i			0.805577i	0.915293	+	0.402788i	$0.131959\pi$
$571$			19.2497i			0.805577i	−0.915293	+	0.402788i	$0.868041\pi$
$572$	−34.4463	−	20.7343i	−1.44027	−	0.866946i
$573$			5.65734i			0.236339i
$574$	−0.208636	−	0.861565i	−0.00870831	−	0.0359610i
$575$	−0.0193011	−	0.0334304i	−0.000804910	−	0.00139415i
$576$	−15.7231	−	12.4280i	−0.655128	−	0.517834i
$577$	6.64617			0.276683			0.138342	−	0.990385i	$-0.455823\pi$
$577$	6.64617			0.276683			0.138342	+	0.990385i	$0.455823\pi$
$578$	20.2248	−	19.2683i	0.841240	−	0.801457i
$579$	−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
$582$	−1.23898	+	0.300030i	−0.0513572	+	0.0124366i
$583$	−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	0.0593374	−	0.998238i	$-0.481101\pi$
$587$	23.1016	−	13.3377i	0.953505	−	0.550507i	0.894168	+	0.447731i	$0.147768\pi$
$588$	8.58426	+	0.416033i	0.354009	+	0.0171569i
$589$	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
$592$	−2.02847	+	20.8781i	−0.0833696	+	0.858087i
$593$	6.61409			0.271608			0.135804	−	0.990736i	$-0.456638\pi$
$593$	6.61409			0.271608			0.135804	+	0.990736i	$0.456638\pi$
$594$	22.1070	−	21.0615i	0.907060	−	0.864164i
$595$	11.1010	−	6.40917i	0.455097	−	0.262751i
$596$	−7.23150	−	0.350473i	−0.296214	−	0.0143559i
$597$		−	10.5759i		−	0.432841i
$598$	−7.81592	−	7.72310i	−0.319617	−	0.315821i
$599$	11.9319			0.487523			0.243762	−	0.969835i	$-0.421619\pi$
$599$	11.9319			0.487523			0.243762	+	0.969835i	$0.421619\pi$
$600$	−0.0336652	−	0.0116984i	−0.00137438	−	0.000477586i
$601$	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	$0.752537\pi$
$602$	−7.42040	−	7.78874i	−0.302433	−	0.317445i
$603$		−	11.3127i		−	0.460688i
$604$	28.6218	−	14.7256i	1.16460	−	0.599177i
$605$	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	$0.110073\pi$
$608$	−5.79756	−	7.40364i	−0.235122	−	0.300257i
$609$	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	0.272418	−	0.962179i	$-0.412177\pi$
$613$	30.7480	−	17.7523i	1.24190	−	0.717010i	0.969480	+	0.245169i	$0.0788433\pi$
$614$	−12.3151	+	2.98223i	−0.496999	+	0.120353i
$615$	−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	$0.00571178\pi$
$618$	10.3444	+	10.8579i	0.416115	+	0.436770i
$619$			21.6806i			0.871417i	0.900088	+	0.435708i	$0.143502\pi$
$619$			21.6806i			0.871417i	−0.900088	+	0.435708i	$0.856498\pi$
$620$	3.91809	+	7.61548i	0.157354	+	0.305845i
$621$	7.22675	−	4.17237i	0.290000	−	0.167431i
$622$	3.11275	+	12.8541i	0.124810	+	0.515404i
$623$	−0.705358			−0.0282596
$624$	−10.1222	−	0.675817i	−0.405212	−	0.0270543i
$625$	−25.0892			−1.00357
$626$	−3.92206	−	16.1962i	−0.156757	−	0.647329i
$627$	5.64592	−	3.25967i	0.225476	−	0.130179i
$628$	−14.1158	−	27.4365i	−0.563283	−	1.09484i
$629$			31.7918i			1.26762i
$630$	−5.16725	−	5.42375i	−0.205868	−	0.216087i
$631$	−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
$634$	−1.13814	+	0.275611i	−0.0452011	+	0.0109459i
$635$	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
$640$	−2.33603	−	25.2356i	−0.0923395	−	0.997525i
$641$	−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	0.562794	−	0.826597i	$-0.309726\pi$
$643$	3.25429	+	1.87887i	0.128337	+	0.0740952i	−0.434457	+	0.900692i	$0.643060\pi$
$644$	−3.61738	+	1.86110i	−0.142545	+	0.0733377i
$645$			12.6983i			0.499994i
$646$	−9.83064	−	10.3186i	−0.386781	−	0.405981i
$647$	−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	$-0.562559\pi$
$648$	−4.44866	+	12.8022i	−0.174760	+	0.502916i
$649$	−2.64838			−0.103958
$650$	0.0880864	−	0.0241675i	0.00345503	−	0.000947929i
$651$		−	1.26922i		−	0.0497446i
$652$	10.0080	+	0.485034i	0.391943	+	0.0189954i
$653$	21.5793	−	12.4588i	0.844463	−	0.487551i	−0.0143156	−	0.999898i	$-0.504557\pi$
$653$	21.5793	−	12.4588i	0.844463	−	0.487551i	0.858779	+	0.512346i	$0.171224\pi$
$654$	−6.98570	+	6.65534i	−0.273163	+	0.260245i
$655$	−26.6894			−1.04284
$656$	−2.64387	−	0.256872i	−0.103226	−	0.0100291i
$657$	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	0.533843	−	0.845583i	$-0.320747\pi$
$659$	1.75765	+	1.01478i	0.0684684	+	0.0395302i	−0.465375	+	0.885114i	$0.654081\pi$
$660$	17.5498	+	0.850545i	0.683125	+	0.0331074i
$661$	−9.61763	+	5.55274i	−0.374082	+	0.215977i	−0.675240	−	0.737598i	$-0.735960\pi$
$661$	−9.61763	+	5.55274i	−0.374082	+	0.215977i	0.301158	+	0.953574i	$0.402627\pi$
$662$	−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
$666$	18.0575	−	4.37280i	0.699714	−	0.169442i
$667$	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
$670$	10.3573	−	9.86751i	0.400138	−	0.381215i
$671$	19.7432			0.762176
$672$	−1.40313	+	3.48395i	−0.0541267	+	0.134396i
$673$	−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	$-0.394757\pi$
$674$	1.84363	+	7.61330i	0.0710141	+	0.293253i
$675$			0.0693689i			0.00267001i
$676$	22.3598	−	13.2681i	0.859990	−	0.510310i
$677$			28.8974i			1.11062i	0.831645	+	0.555308i	$0.187400\pi$
$677$			28.8974i			1.11062i	−0.831645	+	0.555308i	$0.812600\pi$
$678$	−7.31146	+	1.77054i	−0.280795	+	0.0679972i
$679$	−0.604799	−	1.04754i	−0.0232100	−	0.0402010i
$680$	−7.22243	−	37.7253i	−0.276968	−	1.44670i
$681$	13.6201			0.521922
$682$	−10.3969	−	10.9130i	−0.398120	−	0.417882i
$683$	18.5350	+	10.7012i	0.709221	+	0.409469i	0.810773	−	0.585361i	$-0.199047\pi$
$683$	18.5350	+	10.7012i	0.709221	+	0.409469i	−0.101551	+	0.994830i	$0.532381\pi$
$684$	−4.50875	+	7.00301i	−0.172396	+	0.267767i
$685$	−39.7078	−	22.9253i	−1.51716	−	0.875930i
$686$	4.11852	+	17.0075i	0.157246	+	0.649348i
$687$	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	$-0.273543\pi$
$691$	42.9878	−	24.8190i	1.63533	−	0.944159i	0.982411	−	0.186733i	$-0.0597900\pi$
$692$	43.6074	+	2.11342i	1.65770	+	0.0803401i
$693$	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
$696$	3.80087	−	0.727669i	0.144072	−	0.0275822i
$697$	−4.02589			−0.152491
$698$	23.3264	+	24.4843i	0.882918	+	0.926744i
$699$	−9.33742	+	5.39096i	−0.353174	+	0.203905i
$700$	0.00163703	−	0.0337777i	6.18738e−5	−	0.00127668i
$701$			23.3855i			0.883258i	0.897198	+	0.441629i	$0.145599\pi$
$701$			23.3855i			0.883258i	−0.897198	+	0.441629i	$0.854401\pi$
$702$	5.22437	+	19.0419i	0.197181	+	0.718690i
$703$	8.71738			0.328782
$704$	16.4747	+	41.4496i	0.620915	+	1.56219i
$705$	8.33367	+	14.4343i	0.313864	+	0.543629i
$706$	5.69091	−	5.42178i	0.214180	−	0.204051i
$707$		−	9.21623i		−	0.346612i
$708$	−0.594217	+	0.305718i	−0.0223320	+	0.0114896i
$709$	−41.1118	−	23.7359i	−1.54399	−	0.891421i	−0.998581	−	0.0532487i	$-0.983042\pi$
$709$	−41.1118	−	23.7359i	−1.54399	−	0.891421i	−0.545405	−	0.838172i	$-0.683624\pi$
$710$	−10.3980	+	35.3583i	−0.390230	+	1.32697i
$711$	−17.0505	+	29.5324i	−0.639445	+	1.10755i
$712$	−0.693774	+	1.99651i	−0.0260003	+	0.0748224i
$713$	−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
$718$	−2.84628	−	11.7537i	−0.106222	−	0.438645i
$719$	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
$722$	16.6250	−	15.8388i	0.618720	−	0.589460i
$723$		−	10.1993i		−	0.379318i
$724$	−12.0073	−	23.3382i	−0.446246	−	0.867357i
$725$	−0.0301757	+	0.0174220i	−0.00112070	+	0.000647036i
$726$	−19.4195	+	4.70262i	−0.720725	+	0.174531i
$727$	27.1042			1.00524			0.502619	−	0.864508i	$-0.332370\pi$
$727$	27.1042			1.00524			0.502619	+	0.864508i	$0.332370\pi$
$728$	−2.09453	−	9.39533i	−0.0776284	−	0.348214i
$729$	3.83260			0.141948
$730$	5.90173	−	1.42916i	0.218433	−	0.0528956i
$731$	−42.3104	+	24.4279i	−1.56491	+	0.903500i
$732$	4.42977	−	2.27907i	0.163729	−	0.0842368i
$733$			21.1225i			0.780179i	0.920777	+	0.390090i	$0.127556\pi$
$733$			21.1225i			0.780179i	−0.920777	+	0.390090i	$0.872444\pi$
$734$	−4.02810	+	3.83760i	−0.148680	+	0.141649i
$735$	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
$738$	0.553741	+	2.28668i	0.0203835	+	0.0841737i
$739$	25.6746	−	14.8233i	0.944457	−	0.545283i	0.0531023	−	0.998589i	$-0.483089\pi$
$739$	25.6746	−	14.8233i	0.944457	−	0.545283i	0.891355	+	0.453307i	$0.149756\pi$
$740$	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	$0.768386\pi$
$744$	−3.59252	−	1.24837i	−0.131708	−	0.0457676i
$745$	−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
$748$	30.9269	+	60.1118i	1.13080	+	2.19790i
$749$		−	14.8277i		−	0.541794i
$750$	8.03798	−	7.65786i	0.293506	−	0.279625i
$751$	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	$0.595814\pi$
$752$	−24.5999	+	34.4251i	−0.897066	+	1.25535i
$753$	−20.1742			−0.735190
$754$	−6.97120	+	7.05498i	−0.253876	+	0.256927i
$755$		−	36.0514i		−	1.31204i
$756$	7.30183	+	0.353881i	0.265565	+	0.0128705i
$757$	17.2083	−	9.93522i	0.625446	−	0.361102i	−0.153540	−	0.988142i	$-0.549067\pi$
$757$	17.2083	−	9.93522i	0.625446	−	0.361102i	0.778986	+	0.627041i	$0.215734\pi$
$758$	−25.7698	−	27.0490i	−0.936003	−	0.982464i
$759$	−8.45122			−0.306760
$760$	−10.3444	+	1.98041i	−0.375230	+	0.0718370i
$761$	−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
$764$	−0.778662	+	16.0666i	−0.0281710	+	0.581269i
$765$	−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	$0.894392\pi$
$770$	3.92385	+	16.2036i	0.141406	+	0.583936i
$771$	−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	0.0415022	−	0.999138i	$-0.486786\pi$
$773$	−22.3264	−	12.8902i	−0.803026	−	0.463627i	−0.844528	+	0.535511i	$0.820119\pi$
$774$	19.6945	+	20.6721i	0.707903	+	0.743042i
$775$	0.0342437			0.00123007
$776$	−3.55993	+	0.681542i	−0.127794	+	0.0244659i
$777$	−1.74092	−	3.01536i	−0.0624552	−	0.108176i
$778$	34.4732	−	8.34802i	1.23592	−	0.299291i
$779$			1.10391i			0.0395517i
$780$	−5.85976	+	9.73492i	−0.209813	+	0.348566i
$781$		−	64.8644i		−	2.32103i
$782$	4.34825	+	17.9561i	0.155493	+	0.642110i
$783$	−3.76616	−	6.52318i	−0.134592	−	0.233119i
$784$	24.3217	+	2.36303i	0.868631	+	0.0843940i
$785$	−34.5585			−1.23345
$786$	8.58125	−	8.17543i	0.306083	−	0.291608i
$787$	12.1719	+	7.02745i	0.433881	+	0.250502i	0.700999	−	0.713162i	$-0.252738\pi$
$787$	12.1719	+	7.02745i	0.433881	+	0.250502i	−0.267117	+	0.963664i	$0.586071\pi$
$788$	7.58358	−	11.7789i	0.270154	−	0.419604i
$789$	−10.3251	−	5.96119i	−0.367583	−	0.212224i
$790$	−41.9108	+	10.1491i	−1.49112	+	0.361088i
$791$	−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
$796$	1.45564	−	30.0350i	0.0515936	−	1.06456i
$797$	19.1331	+	11.0465i	0.677731	+	0.391288i	0.798999	−	0.601332i	$-0.205363\pi$
$797$	19.1331	+	11.0465i	0.677731	+	0.391288i	−0.121269	+	0.992620i	$0.538696\pi$
$798$	1.49746	+	0.440366i	0.0530095	+	0.0155888i
$799$	−32.0633	+	55.5353i	−1.13432	+	1.96470i
$800$	−0.0939975	−	0.0378566i	−0.00332331	−	0.00133843i
$801$	1.87209			0.0661470
$802$	4.52849	−	4.31434i	0.159907	−	0.152345i
$803$	−9.25526	+	5.34353i	−0.326611	+	0.188569i
$804$	−0.307522	+	6.34527i	−0.0108454	+	0.223780i
$805$			4.55637i			0.160591i
$806$	9.39997	−	2.57899i	0.331100	−	0.0908411i
$807$	5.24034			0.184469
$808$	−26.0865	−	9.06487i	−0.917720	−	0.318901i
$809$	−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	$0.855994\pi$
$810$	10.4708	+	10.9906i	0.367906	+	0.386169i
$811$			18.7132i			0.657109i	0.944485	+	0.328555i	$0.106561\pi$
$811$			18.7132i			0.657109i	−0.944485	+	0.328555i	$0.893439\pi$
$812$	1.67991	+	3.26520i	0.0589533	+	0.114586i
$813$	−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
$816$	13.8781	+	9.91720i	0.485831	+	0.347171i
$817$	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	−0.608506	−	0.793549i	$-0.708231\pi$
$821$	−6.46202	+	3.73085i	−0.225526	+	0.130208i	0.382980	+	0.923757i	$0.374898\pi$
$822$	19.7894	−	4.79219i	0.690235	−	0.167147i
$823$	−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
$826$	−0.437374	−	0.459085i	−0.0152182	−	0.0159736i
$827$			19.2616i			0.669792i	0.942255	+	0.334896i	$0.108701\pi$
$827$			19.2616i			0.669792i	−0.942255	+	0.334896i	$0.891299\pi$
$828$	9.60087	−	4.93955i	0.333653	−	0.171661i
$829$	18.7148	−	10.8050i	0.649993	−	0.375273i	−0.138461	−	0.990368i	$-0.544215\pi$
$829$	18.7148	−	10.8050i	0.649993	−	0.375273i	0.788453	+	0.615094i	$0.210882\pi$
$830$	−8.62081	−	35.5997i	−0.299233	−	1.23568i
$831$	−11.3654			−0.394261
$832$	−28.6536	−	3.31248i	−0.993384	−	0.114840i
$833$	37.0353			1.28320
$834$	1.89672	+	7.83252i	0.0656781	+	0.271218i
$835$	2.06489	−	1.19216i	0.0714584	−	0.0412565i
$836$	16.4828	−	8.48023i	0.570070	−	0.293295i
$837$			7.40257i			0.255870i
$838$	−4.84919	−	5.08989i	−0.167512	−	0.175827i
$839$	−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
$842$	33.0667	−	8.00741i	1.13955	−	0.275954i
$843$	−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
$848$	−33.8080	−	24.1590i	−1.16097	−	0.829622i
$849$	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
$852$	−7.48768	−	14.5536i	−0.256524	−	0.498599i
$853$		−	40.2417i		−	1.37785i	−0.724833	−	0.688924i	$-0.758083\pi$
$853$		−	40.2417i		−	1.37785i	0.724833	−	0.688924i	$-0.241917\pi$
$854$	3.26054	+	3.42238i	0.111573	+	0.117112i
$855$	4.66434	+	8.07888i	0.159517	+	0.276292i
$856$	−41.9699	−	14.5842i	−1.43450	−	0.498479i
$857$	7.37621			0.251966			0.125983	−	0.992032i	$-0.459791\pi$
$857$	7.37621			0.251966			0.125983	+	0.992032i	$0.459791\pi$
$858$	5.06027	−	19.3467i	0.172755	−	0.660486i
$859$			31.9493i			1.09010i	0.838405	+	0.545048i	$0.183489\pi$
$859$			31.9493i			1.09010i	−0.838405	+	0.545048i	$0.816511\pi$
$860$	−1.74776	+	36.0625i	−0.0595981	+	1.22972i
$861$	0.381845	−	0.220458i	0.0130132	−	0.00751320i
$862$	10.8323	−	10.3200i	0.368948	−	0.351500i
$863$	−16.1143			−0.548536			−0.274268	−	0.961653i	$-0.588436\pi$
$863$	−16.1143			−0.548536			−0.274268	+	0.961653i	$0.588436\pi$
$864$	8.18357	−	20.3197i	0.278411	−	0.691291i
$865$	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
$868$	0.174692	−	3.60452i	0.00592944	−	0.122346i
$869$	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
$874$	4.92362	−	1.19230i	0.166544	−	0.0403302i
$875$	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	0.496931	−	0.867790i	$-0.334460\pi$
$877$	−0.181562	−	0.104825i	−0.00613091	−	0.00353968i	−0.503062	+	0.864250i	$0.667793\pi$
$878$	13.2376	−	12.6115i	0.446746	−	0.425619i
$879$	3.36906			0.113635
$880$	49.7236	+	4.83102i	1.67618	+	0.162854i
$881$	−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	$-0.403480\pi$
$882$	−5.09402	−	21.0358i	−0.171524	−	0.708312i
$883$			4.69019i			0.157837i	0.996881	+	0.0789187i	$0.0251467\pi$
$883$			4.69019i			0.157837i	−0.996881	+	0.0789187i	$0.974853\pi$
$884$	−43.7091	−	0.797345i	−1.47010	−	0.0268176i
$885$			0.748463i			0.0251593i
$886$	−19.3032	+	4.67446i	−0.648505	+	0.157042i
$887$	−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	$0.961833\pi$
$888$	−10.2473	+	1.96183i	−0.343877	+	0.0658346i
$889$	−2.90651			−0.0974813
$890$	1.63293	+	1.71399i	0.0547361	+	0.0574531i
$891$	−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
$894$	−0.847538	−	3.49992i	−0.0283459	−	0.117055i
$895$	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
$900$	−0.00434483	+	0.0896493i	−0.000144828	+	0.00298831i
$901$	−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
$904$	−21.0079	+	4.02193i	−0.698713	+	0.133767i
$905$	−29.3963			−0.977166
$906$	11.0432	+	11.5914i	0.366886	+	0.385097i
$907$	−3.93422	+	2.27142i	−0.130634	+	0.0754213i	−0.563893	−	0.825848i	$-0.690697\pi$
$907$	−3.93422	+	2.27142i	−0.130634	+	0.0754213i	0.433259	+	0.901269i	$0.357363\pi$
$908$	38.6804	+	1.87463i	1.28365	+	0.0622119i
$909$			24.4608i			0.811313i
$910$	−10.4305	−	2.72818i	−0.345769	−	0.0904384i
$911$	−29.5451			−0.978873			−0.489436	−	0.872039i	$-0.662797\pi$
$911$	−29.5451			−0.978873			−0.489436	+	0.872039i	$0.662797\pi$
$912$	2.71932	−	3.80542i	0.0900457	−	0.126010i
$913$	32.2326	+	55.8285i	1.06674	+	1.84765i
$914$	−29.8619	+	28.4497i	−0.987745	+	0.941033i
$915$		−	5.57964i		−	0.184457i
$916$	16.1077	+	31.3082i	0.532214	+	1.03445i
$917$	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	$-0.00495905\pi$
$920$	12.8968	+	4.48154i	0.425194	+	0.147752i
$921$	−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
$926$	12.2155	+	50.4440i	0.401426	+	1.65769i
$927$	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	$0.0387098\pi$
$930$	−3.08415	+	2.93830i	−0.101133	+	0.0963505i
$931$		−	10.1552i		−	0.332822i
$932$	−27.2599	+	14.0249i	−0.892926	+	0.459401i
$933$	−5.69695	+	3.28913i	−0.186510	+	0.107681i
$934$	38.4630	−	9.31419i	1.25855	−	0.304770i
$935$	75.7155			2.47616
$936$	5.55908	+	24.9361i	0.181704	+	0.815063i
$937$	−9.97996			−0.326031			−0.163016	−	0.986623i	$-0.552122\pi$
$937$	−9.97996			−0.326031			−0.163016	+	0.986623i	$0.552122\pi$
$938$	−5.85854	+	1.41870i	−0.191288	+	0.0463222i
$939$	7.17813	−	4.14430i	0.234249	−	0.135244i
$940$	21.6806	+	42.1399i	0.707142	+	1.37445i
$941$		−	12.2242i		−	0.398498i	−0.979949	−	0.199249i	$-0.936150\pi$
$941$		−	12.2242i		−	0.398498i	0.979949	−	0.199249i	$-0.0638502\pi$
$942$	11.1114	−	10.5859i	0.362028	−	0.344907i
$943$	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
$946$	−14.9554	−	61.7583i	−0.486241	−	2.00794i
$947$	−2.80497	+	1.61945i	−0.0911494	+	0.0526251i	−0.544882	−	0.838513i	$-0.683426\pi$
$947$	−2.80497	+	1.61945i	−0.0911494	+	0.0526251i	0.453732	+	0.891138i	$0.350092\pi$
$948$	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
$952$	−5.31260	+	15.2884i	−0.172182	+	0.495499i
$953$	−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
$956$	25.0499	−	12.8879i	0.810173	−	0.416826i
$957$			7.62843i			0.246592i
$958$	−33.2736	+	31.7000i	−1.07502	+	1.02418i
$959$	9.66009	+	16.7318i	0.311941	+	0.540297i
$960$	11.7141	−	4.65595i	0.378072	−	0.150270i
$961$	−27.3457			−0.882121
$962$	18.7946	−	19.0205i	0.605964	−	0.613246i
$963$			39.3543i			1.26817i
$964$	1.40381	−	28.9657i	0.0452138	−	0.932922i
$965$	−1.62154	+	0.936197i	−0.0521993	+	0.0301373i
$966$	−1.39570	−	1.46498i	−0.0449059	−	0.0471349i
$967$	44.1828			1.42082			0.710411	−	0.703787i	$-0.248509\pi$
$967$	44.1828			1.42082			0.710411	+	0.703787i	$0.248509\pi$
$968$	−55.7978	+	10.6824i	−1.79341	+	0.343345i
$969$	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	0.927195	−	0.374578i	$-0.122212\pi$
$971$	33.2299	+	19.1853i	1.06640	+	0.615686i	0.139204	+	0.990264i	$0.455546\pi$
$972$	−29.9405	−	1.45106i	−0.960343	−	0.0465427i
$973$	−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	$0.926728\pi$
$978$	1.17294	+	4.84368i	0.0375066	+	0.154884i
$979$	−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
$982$	−40.7845	−	42.8090i	−1.30149	−	1.36609i
$983$	18.8329			0.600677			0.300339	−	0.953833i	$-0.402900\pi$
$983$	18.8329			0.600677			0.300339	+	0.953833i	$0.402900\pi$
$984$	−0.248432	−	1.29765i	−0.00791973	−	0.0413675i
$985$	−7.84529	−	13.5884i	−0.249972	−	0.432964i
$986$	16.2080	−	3.92491i	0.516167	−	0.124995i
$987$		−	7.02316i		−	0.223550i
$988$	−0.218634	+	11.9851i	−0.00695568	+	0.381298i
$989$		−	17.3662i		−	0.552212i
$990$	−10.4143	−	43.0059i	−0.330988	−	1.36682i
$991$	−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	$-0.456433\pi$
$992$	−10.0308	−	4.03979i	−0.318477	−	0.128264i
$993$	−10.4305			−0.331003
$994$	11.2439	−	10.7122i	0.356636	−	0.339771i
$995$	−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	0.983427	−	0.181306i	$-0.0580324\pi$
$997$	41.6202	+	24.0294i	1.31812	+	0.761020i	0.334698	+	0.942325i	$0.391366\pi$
$998$	−24.6048	+	5.95829i	−0.778852	+	0.188606i
$999$	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.29.7	✓	24
3.2	odd	2		936.2.be.a.757.6		24
4.3	odd	2		416.2.z.a.81.8		24
8.3	odd	2		416.2.z.a.81.5		24
8.5	even	2	inner	104.2.r.a.29.10	yes	24
13.9	even	3	inner	104.2.r.a.61.10	yes	24
24.5	odd	2		936.2.be.a.757.3		24
39.35	odd	6		936.2.be.a.685.3		24
52.35	odd	6		416.2.z.a.113.5		24
104.35	odd	6		416.2.z.a.113.8		24
104.61	even	6	inner	104.2.r.a.61.7	yes	24
312.269	odd	6		936.2.be.a.685.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.r.a.29.7	✓	24	1.1	even	1	trivial
104.2.r.a.29.10	yes	24	8.5	even	2	inner
104.2.r.a.61.7	yes	24	104.61	even	6	inner
104.2.r.a.61.10	yes	24	13.9	even	3	inner
416.2.z.a.81.5		24	8.3	odd	2
416.2.z.a.81.8		24	4.3	odd	2
416.2.z.a.113.5		24	52.35	odd	6
416.2.z.a.113.8		24	104.35	odd	6
936.2.be.a.685.3		24	39.35	odd	6
936.2.be.a.685.6		24	312.269	odd	6
936.2.be.a.757.3		24	24.5	odd	2
936.2.be.a.757.6		24	3.2	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+(0.332845 + 1.37449i) q^{2} +(-0.609172 + 0.351705i) q^{3} +(-1.77843 + 0.914983i) q^{4} +2.24007i q^{5} +(-0.686174 - 0.720235i) q^{6} +(0.471952 - 0.817445i) q^{7} +(-1.84957 - 2.13988i) q^{8} +(-1.25261 + 2.16958i) q^{9} +(-3.07895 + 0.745597i) 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} +(2.32561 - 3.25446i) q^{16} +(3.03119 - 5.25017i) q^{17} +(-3.39898 - 0.999558i) q^{18} +(-1.43961 - 0.831159i) q^{19} +(-2.04963 - 3.98380i) q^{20} +0.663952i q^{21} +(5.43884 + 5.70881i) q^{22} +(1.07746 + 1.86621i) q^{23} +(1.87931 + 0.653048i) q^{24} -0.0179136 q^{25} +(-4.91730 + 1.34912i) q^{26} -3.87243i q^{27} +(-0.0913848 + 1.88560i) q^{28} +(1.68452 - 0.972558i) q^{29} +(1.61338 - 1.53708i) q^{30} -1.91161 q^{31} +(5.24728 + 2.11329i) q^{32} +(-1.96092 + 3.39641i) q^{33} +(8.22520 + 2.41883i) q^{34} +(1.83113 + 1.05721i) q^{35} +(0.242544 - 5.00455i) 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} +(-0.912594 + 0.220993i) q^{42} +(-6.97919 - 4.02944i) q^{43} +(-6.03640 + 9.37576i) q^{44} +(-4.86001 - 2.80593i) q^{45} +(-2.20645 + 2.10211i) q^{46} -10.5778 q^{47} +(-0.272086 + 2.80046i) q^{48} +(3.05452 + 5.29059i) q^{49} +(-0.00596244 - 0.0246219i) q^{50} +4.26434i q^{51} +(-3.49105 - 6.30972i) q^{52} -10.3882i q^{53} +(5.32260 - 1.28892i) q^{54} +(6.24471 + 10.8162i) q^{55} +(-2.62214 + 0.502004i) q^{56} +1.16929 q^{57} +(1.89745 + 1.99164i) q^{58} +(-0.411368 - 0.237503i) q^{59} +(2.64970 + 1.70596i) q^{60} +(3.06666 + 1.77054i) q^{61} +(-0.636270 - 2.62748i) 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} +(-0.586933 + 12.1105i) q^{68} +(-1.31271 - 0.757894i) q^{69} +(-0.843631 + 2.86876i) q^{70} +(5.81695 - 10.0753i) q^{71} +(6.95942 - 1.33237i) q^{72} -1.91680 q^{73} +(-5.11561 - 5.36954i) q^{74} +(0.0109124 - 0.00630029i) q^{75} +(3.32074 + 0.160939i) q^{76} -5.26270i q^{77} +(2.52099 - 2.55129i) q^{78} +13.6120 q^{79} +(7.29022 + 5.20954i) q^{80} +(-2.39587 - 4.14976i) q^{81} +(0.679962 - 0.647806i) q^{82} +11.5623i q^{83} +(-0.607505 - 1.18079i) q^{84} +(11.7607 + 6.79007i) q^{85} +(3.21542 - 10.9340i) q^{86} +(-0.684108 + 1.18491i) q^{87} +(-14.8961 - 5.17627i) 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} +(-3.52077 - 14.5391i) q^{94} +(1.86185 - 3.22483i) q^{95} +(-3.93975 + 0.558140i) q^{96} +(0.640742 - 1.10980i) q^{97} +(-6.25516 + 5.95935i) 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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