LMFDB - Embedded newform 207.2.m.a.4.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,2,Mod(4,207)] 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("207.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([22, 12])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.m (of order $33$, degree $20$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			4.14
Character	$\chi$	$=$	207.4
Dual form			207.2.m.a.52.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.541462 - 0.760376i) q^{2} +(1.52956 - 0.812681i) q^{3} +(0.369144 + 1.06657i) q^{4} +(-0.806242 + 0.415647i) q^{5} +(0.210254 - 1.60308i) q^{6} +(-0.783251 + 0.615955i) q^{7} +(2.80218 + 0.822793i) q^{8} +(1.67910 - 2.48609i) q^{9} +(-0.120501 + 0.838104i) q^{10} +(4.29053 - 0.409696i) q^{11} +(1.43141 + 1.33139i) q^{12} +(-5.42615 - 4.26717i) q^{13} +(0.0442576 + 0.929082i) q^{14} +(-0.895406 + 1.29097i) q^{15} +(0.368550 - 0.289831i) q^{16} +(-0.698431 - 0.806032i) q^{17} +(-0.981193 - 2.62287i) q^{18} +(-4.69820 + 5.42201i) q^{19} +(-0.740937 - 0.706482i) q^{20} +(-0.697453 + 1.57867i) q^{21} +(2.01163 - 3.48425i) q^{22} +(-4.35352 + 2.01169i) q^{23} +(4.95476 - 1.01876i) q^{24} +(-2.42302 + 3.40266i) q^{25} +(-6.18271 + 1.81541i) q^{26} +(0.547888 - 5.16719i) q^{27} +(-0.946094 - 0.608017i) q^{28} +(1.09208 - 3.15536i) q^{29} +(0.496797 + 1.37986i) q^{30} +(4.39118 - 4.18698i) q^{31} +(0.257099 + 5.39717i) q^{32} +(6.22966 - 4.11348i) q^{33} +(-0.991061 + 0.0946349i) q^{34} +(0.375470 - 0.822165i) q^{35} +(3.27142 + 0.873157i) q^{36} +(-3.69780 + 2.37643i) q^{37} +(1.57888 + 6.50821i) q^{38} +(-11.7675 - 2.11716i) q^{39} +(-2.60122 + 0.501345i) q^{40} +(5.66270 - 2.91933i) q^{41} +(0.822742 + 1.38512i) q^{42} +(2.06724 + 1.97111i) q^{43} +(2.02079 + 4.42492i) q^{44} +(-0.320428 + 2.70230i) q^{45} +(-0.827624 + 4.39956i) q^{46} +(-3.75588 - 6.50538i) q^{47} +(0.328179 - 0.742828i) q^{48} +(-1.41623 + 5.83779i) q^{49} +(1.27533 + 3.68482i) q^{50} +(-1.72334 - 0.665272i) q^{51} +(2.54821 - 7.36258i) q^{52} +(1.56146 + 10.8602i) q^{53} +(-3.63235 - 3.21443i) q^{54} +(-3.28891 + 2.11366i) q^{55} +(-2.70161 + 1.08156i) q^{56} +(-2.77981 + 12.1114i) q^{57} +(-1.80794 - 2.53890i) q^{58} +(2.98941 + 2.35090i) q^{59} +(-1.70745 - 0.478460i) q^{60} +(-2.78681 - 11.4874i) q^{61} +(-0.806026 - 5.60604i) q^{62} +(0.216161 + 2.98148i) q^{63} +(5.03195 + 3.23384i) q^{64} +(6.14842 + 1.18501i) q^{65} +(0.245327 - 6.96418i) q^{66} +(-1.54306 - 0.147344i) q^{67} +(0.601870 - 1.04247i) q^{68} +(-5.02410 + 6.61501i) q^{69} +(-0.421852 - 0.730669i) q^{70} +(-3.19630 - 6.99892i) q^{71} +(6.75067 - 5.58490i) q^{72} +(0.832555 - 0.960819i) q^{73} +(-0.195234 + 4.09847i) q^{74} +(-0.940879 + 7.17371i) q^{75} +(-7.51728 - 3.00947i) q^{76} +(-3.10821 + 2.96367i) q^{77} +(-7.98147 + 7.80134i) q^{78} +(8.12970 - 3.25464i) q^{79} +(-0.176673 + 0.386861i) q^{80} +(-3.36125 - 8.34877i) q^{81} +(0.846350 - 5.88649i) q^{82} +(-8.01355 - 4.13127i) q^{83} +(-1.94123 - 0.161126i) q^{84} +(0.898129 + 0.359556i) q^{85} +(2.61812 - 0.504601i) q^{86} +(-0.893900 - 5.71383i) q^{87} +(12.3599 + 2.38218i) q^{88} +(13.7997 - 4.05196i) q^{89} +(1.88127 + 1.70684i) q^{90} +6.87842 q^{91} +(-3.75268 - 3.90074i) q^{92} +(3.31389 - 9.97286i) q^{93} +(-6.98020 - 0.666529i) q^{94} +(1.53425 - 6.32425i) q^{95} +(4.77942 + 8.04634i) q^{96} +(-0.614620 + 12.9025i) q^{97} +(3.67208 + 4.23781i) q^{98} +(6.18569 - 11.3545i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 9 q^{2} - 20 q^{3} + 11 q^{4} - 11 q^{5} - 17 q^{6} - 9 q^{7} - 50 q^{8} - 24 q^{9} - 44 q^{10} - 17 q^{11} - 30 q^{12} - 9 q^{13} - 21 q^{14} - 34 q^{15} + 11 q^{16} - 20 q^{17} + 3 q^{18} - 36 q^{19}+ \cdots - 220 q^{99}+O(q^{100}) $ 440 * q - 9 * q^2 - 20 * q^3 + 11 * q^4 - 11 * q^5 - 17 * q^6 - 9 * q^7 - 50 * q^8 - 24 * q^9 - 44 * q^10 - 17 * q^11 - 30 * q^12 - 9 * q^13 - 21 * q^14 - 34 * q^15 + 11 * q^16 - 20 * q^17 + 3 * q^18 - 36 * q^19 - 25 * q^20 + 3 * q^21 - 28 * q^22 - 5 * q^23 - 172 * q^24 + 11 * q^25 - 48 * q^26 + 31 * q^27 - 60 * q^28 + 9 * q^29 + 12 * q^30 - 3 * q^31 - 3 * q^32 - 44 * q^33 - 17 * q^34 - 56 * q^35 + 47 * q^36 - 48 * q^37 + 3 * q^38 - 64 * q^39 + 55 * q^40 - 9 * q^41 - 80 * q^42 - 9 * q^43 + 24 * q^44 - 56 * q^45 - 44 * q^46 - 12 * q^47 + 4 * q^48 - 53 * q^49 + 27 * q^50 + 14 * q^51 - 12 * q^52 - 84 * q^53 - 18 * q^54 - 68 * q^55 - 125 * q^56 + 27 * q^57 - 8 * q^58 + 81 * q^59 + 88 * q^60 + 3 * q^61 + 58 * q^62 + 43 * q^63 - 70 * q^64 - 84 * q^65 + 35 * q^66 - 3 * q^67 + 194 * q^68 + 33 * q^69 - 10 * q^70 + 86 * q^71 + 182 * q^72 - 36 * q^73 - 57 * q^74 + 55 * q^75 - 21 * q^76 + 91 * q^77 + 191 * q^78 - 9 * q^79 + 220 * q^80 - 228 * q^81 - 62 * q^82 - 68 * q^83 + 144 * q^84 + q^85 - 53 * q^86 + 160 * q^87 + 83 * q^88 - 28 * q^89 - 314 * q^90 - 108 * q^91 + q^92 + 132 * q^93 + 48 * q^94 - 3 * q^95 + 174 * q^96 - 36 * q^97 - 156 * q^98 - 220 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.541462	−	0.760376i	0.382871	−	0.537667i	−0.577500	−	0.816390i	$-0.695972\pi$
$2$	0.541462	−	0.760376i	0.382871	−	0.537667i	0.960372	+	0.278723i	$0.0899112\pi$
$3$	1.52956	−	0.812681i	0.883091	−	0.469201i
$3$	1.52956	−	0.812681i	0.883091	−	0.469201i
$4$	0.369144	+	1.06657i	0.184572	+	0.533286i
$5$	−0.806242	+	0.415647i	−0.360562	+	0.185883i	−0.628983	−	0.777419i	$-0.716529\pi$
$5$	−0.806242	+	0.415647i	−0.360562	+	0.185883i	0.268421	+	0.963302i	$0.413498\pi$
$6$	0.210254	−	1.60308i	0.0858359	−	0.654453i
$7$	−0.783251	+	0.615955i	−0.296041	+	0.232809i	−0.755121	−	0.655586i	$-0.772422\pi$
$7$	−0.783251	+	0.615955i	−0.296041	+	0.232809i	0.459080	+	0.888395i	$0.348179\pi$
$8$	2.80218	+	0.822793i	0.990719	+	0.290901i
$9$	1.67910	−	2.48609i	0.559700	−	0.828695i
$10$	−0.120501	+	0.838104i	−0.0381058	+	0.265032i
$11$	4.29053	−	0.409696i	1.29364	−	0.123528i	0.574566	−	0.818458i	$-0.305171\pi$
$11$	4.29053	−	0.409696i	1.29364	−	0.123528i	0.719077	+	0.694930i	$0.244565\pi$
$12$	1.43141	+	1.33139i	0.413213	+	0.384339i
$13$	−5.42615	−	4.26717i	−1.50494	−	1.18350i	−0.931223	−	0.364449i	$-0.881257\pi$
$13$	−5.42615	−	4.26717i	−1.50494	−	1.18350i	−0.573720	−	0.819052i	$-0.694500\pi$
$14$	0.0442576	+	0.929082i	0.0118283	+	0.248308i
$15$	−0.895406	+	1.29097i	−0.231193	+	0.333328i
$16$	0.368550	−	0.289831i	0.0921376	−	0.0724578i
$17$	−0.698431	−	0.806032i	−0.169394	−	0.195491i	0.664705	−	0.747106i	$-0.268557\pi$
$17$	−0.698431	−	0.806032i	−0.169394	−	0.195491i	−0.834099	+	0.551615i	$0.814012\pi$
$18$	−0.981193	−	2.62287i	−0.231269	−	0.618216i
$19$	−4.69820	+	5.42201i	−1.07784	+	1.24390i	−0.109574	+	0.993979i	$0.534949\pi$
$19$	−4.69820	+	5.42201i	−1.07784	+	1.24390i	−0.968267	+	0.249917i	$0.919597\pi$
$20$	−0.740937	−	0.706482i	−0.165678	−	0.157974i
$21$	−0.697453	+	1.57867i	−0.152197	+	0.344495i
$22$	2.01163	−	3.48425i	0.428882	−	0.742845i
$23$	−4.35352	+	2.01169i	−0.907771	+	0.419465i
$23$	−4.35352	+	2.01169i	−0.907771	+	0.419465i
$24$	4.95476	−	1.01876i	1.01139	−	0.207954i
$25$	−2.42302	+	3.40266i	−0.484604	+	0.680531i
$26$	−6.18271	+	1.81541i	−1.21253	+	0.356031i
$27$	0.547888	−	5.16719i	0.105441	−	0.994426i
$28$	−0.946094	−	0.608017i	−0.178795	−	0.114905i
$29$	1.09208	−	3.15536i	0.202795	−	0.585936i	−0.797044	−	0.603922i	$-0.793604\pi$
$29$	1.09208	−	3.15536i	0.202795	−	0.585936i	0.999838	+	0.0179852i	$0.00572518\pi$
$30$	0.496797	+	1.37986i	0.0907024	+	0.251927i
$31$	4.39118	−	4.18698i	0.788679	−	0.752004i	−0.184307	−	0.982869i	$-0.559004\pi$
$31$	4.39118	−	4.18698i	0.788679	−	0.752004i	0.972986	+	0.230865i	$0.0741556\pi$
$32$	0.257099	+	5.39717i	0.0454491	+	0.954093i
$33$	6.22966	−	4.11348i	1.08445	−	0.716066i
$34$	−0.991061	+	0.0946349i	−0.169966	+	0.0162297i
$35$	0.375470	−	0.822165i	0.0634660	−	0.138971i
$36$	3.27142	+	0.873157i	0.545237	+	0.145526i
$37$	−3.69780	+	2.37643i	−0.607915	+	0.390684i	−0.808075	−	0.589080i	$-0.799490\pi$
$37$	−3.69780	+	2.37643i	−0.607915	+	0.390684i	0.200159	+	0.979763i	$0.435854\pi$
$38$	1.57888	+	6.50821i	0.256127	+	1.05577i
$39$	−11.7675	−	2.11716i	−1.88430	−	0.339017i
$40$	−2.60122	+	0.501345i	−0.411289	+	0.0792695i
$41$	5.66270	−	2.91933i	0.884366	−	0.455922i	0.0446841	−	0.999001i	$-0.485772\pi$
$41$	5.66270	−	2.91933i	0.884366	−	0.455922i	0.839682	+	0.543079i	$0.182742\pi$
$42$	0.822742	+	1.38512i	0.126952	+	0.213728i
$43$	2.06724	+	1.97111i	0.315251	+	0.300592i	0.831139	−	0.556065i	$-0.187689\pi$
$43$	2.06724	+	1.97111i	0.315251	+	0.300592i	−0.515888	+	0.856656i	$0.672538\pi$
$44$	2.02079	+	4.42492i	0.304646	+	0.667082i
$45$	−0.320428	+	2.70230i	−0.0477665	+	0.402835i
$46$	−0.827624	+	4.39956i	−0.122027	+	0.648680i
$47$	−3.75588	−	6.50538i	−0.547852	−	0.948907i	−0.998421	−	0.0561658i	$-0.982112\pi$
$47$	−3.75588	−	6.50538i	−0.547852	−	0.948907i	0.450570	−	0.892741i	$-0.351221\pi$
$48$	0.328179	−	0.742828i	0.0473686	−	0.107218i
$49$	−1.41623	+	5.83779i	−0.202319	+	0.833969i
$50$	1.27533	+	3.68482i	0.180358	+	0.521112i
$51$	−1.72334	−	0.665272i	−0.241316	−	0.0931567i
$52$	2.54821	−	7.36258i	0.353374	−	1.02101i
$53$	1.56146	+	10.8602i	0.214483	+	1.49176i	0.757939	+	0.652325i	$0.226206\pi$
$53$	1.56146	+	10.8602i	0.214483	+	1.49176i	−0.543456	+	0.839438i	$0.682885\pi$
$54$	−3.63235	−	3.21443i	−0.494300	−	0.437429i
$55$	−3.28891	+	2.11366i	−0.443477	+	0.285005i
$56$	−2.70161	+	1.08156i	−0.361018	+	0.144530i
$57$	−2.77981	+	12.1114i	−0.368195	+	1.60420i
$58$	−1.80794	−	2.53890i	−0.237395	−	0.333374i
$59$	2.98941	+	2.35090i	0.389189	+	0.306061i	0.793512	−	0.608555i	$-0.208250\pi$
$59$	2.98941	+	2.35090i	0.389189	+	0.306061i	−0.404323	+	0.914616i	$0.632493\pi$
$60$	−1.70745	−	0.478460i	−0.220431	−	0.0617690i
$61$	−2.78681	−	11.4874i	−0.356814	−	1.47081i	−0.813702	−	0.581283i	$-0.802551\pi$
$61$	−2.78681	−	11.4874i	−0.356814	−	1.47081i	0.456887	−	0.889524i	$-0.348964\pi$
$62$	−0.806026	−	5.60604i	−0.102365	−	0.711967i
$63$	0.216161	+	2.98148i	0.0272338	+	0.375631i
$64$	5.03195	+	3.23384i	0.628994	+	0.404230i
$65$	6.14842	+	1.18501i	0.762618	+	0.146983i
$66$	0.245327	−	6.96418i	0.0301977	−	0.857232i
$67$	−1.54306	−	0.147344i	−0.188514	−	0.0180009i	0.000371875	−	1.00000i	$-0.499882\pi$
$67$	−1.54306	−	0.147344i	−0.188514	−	0.0180009i	−0.188886	+	0.981999i	$0.560488\pi$
$68$	0.601870	−	1.04247i	0.0729874	−	0.126418i
$69$	−5.02410	+	6.61501i	−0.604831	+	0.796354i
$70$	−0.421852	−	0.730669i	−0.0504210	−	0.0873317i
$71$	−3.19630	−	6.99892i	−0.379331	−	0.830619i	−0.998954	−	0.0457196i	$-0.985442\pi$
$71$	−3.19630	−	6.99892i	−0.379331	−	0.830619i	0.619623	−	0.784899i	$-0.287285\pi$
$72$	6.75067	−	5.58490i	0.795574	−	0.658187i
$73$	0.832555	−	0.960819i	0.0974432	−	0.112455i	−0.704933	−	0.709273i	$-0.749023\pi$
$73$	0.832555	−	0.960819i	0.0974432	−	0.112455i	0.802377	+	0.596818i	$0.203569\pi$
$74$	−0.195234	+	4.09847i	−0.0226955	+	0.476438i
$75$	−0.940879	+	7.17371i	−0.108643	+	0.828348i
$76$	−7.51728	−	3.00947i	−0.862292	−	0.345209i
$77$	−3.10821	+	2.96367i	−0.354213	+	0.337741i
$78$	−7.98147	+	7.80134i	−0.903723	+	0.883328i
$79$	8.12970	−	3.25464i	0.914662	−	0.366176i	0.133894	−	0.990996i	$-0.457252\pi$
$79$	8.12970	−	3.25464i	0.914662	−	0.366176i	0.780769	+	0.624820i	$0.214828\pi$
$80$	−0.176673	+	0.386861i	−0.0197527	+	0.0432523i
$81$	−3.36125	−	8.34877i	−0.373472	−	0.927642i
$82$	0.846350	−	5.88649i	0.0934637	−	0.650054i
$83$	−8.01355	−	4.13127i	−0.879601	−	0.453466i	−0.0415999	−	0.999134i	$-0.513245\pi$
$83$	−8.01355	−	4.13127i	−0.879601	−	0.453466i	−0.838001	+	0.545668i	$0.816276\pi$
$84$	−1.94123	−	0.161126i	−0.211806	−	0.0175803i
$85$	0.898129	+	0.359556i	0.0974157	+	0.0389994i
$86$	2.61812	−	0.504601i	0.282319	−	0.0544125i
$87$	−0.893900	−	5.71383i	−0.0958361	−	0.612587i
$88$	12.3599	+	2.38218i	1.31757	+	0.253941i
$89$	13.7997	−	4.05196i	1.46277	−	0.429507i	0.549027	−	0.835805i	$-0.314998\pi$
$89$	13.7997	−	4.05196i	1.46277	−	0.429507i	0.913741	+	0.406297i	$0.133180\pi$
$90$	1.88127	+	1.70684i	0.198303	+	0.179916i
$91$	6.87842			0.721055
$92$	−3.75268	−	3.90074i	−0.391244	−	0.406680i
$93$	3.31389	−	9.97286i	0.343634	−	1.03414i
$94$	−6.98020	−	0.666529i	−0.719953	−	0.0687472i
$95$	1.53425	−	6.32425i	0.157410	−	0.648854i
$96$	4.77942	+	8.04634i	0.487798	+	0.821227i
$97$	−0.614620	+	12.9025i	−0.0624052	+	1.31005i	0.722907	+	0.690946i	$0.242806\pi$
$97$	−0.614620	+	12.9025i	−0.0624052	+	1.31005i	−0.785312	+	0.619100i	$0.787497\pi$
$98$	3.67208	+	4.23781i	0.370936	+	0.428083i
$99$	6.18569	−	11.3545i	0.621685	−	1.14117i
$100$	−4.52362	−	1.32826i	−0.452362	−	0.132826i
$101$	6.03474	+	3.11113i	0.600480	+	0.309569i	0.731532	−	0.681807i	$-0.238805\pi$
$101$	6.03474	+	3.11113i	0.600480	+	0.309569i	−0.131053	+	0.991375i	$0.541836\pi$
$102$	−1.43898	+	0.950166i	−0.142480	+	0.0940804i
$103$	2.44849	+	3.43842i	0.241257	+	0.338798i	0.917396	−	0.397976i	$-0.130287\pi$
$103$	2.44849	+	3.43842i	0.241257	+	0.338798i	−0.676139	+	0.736774i	$0.736348\pi$
$104$	−11.6940	−	16.4220i	−1.14669	−	1.61031i
$105$	−0.0938539	−	1.56269i	−0.00915921	−	0.152503i
$106$	9.10331	+	4.69308i	0.884192	+	0.455832i
$107$	6.50947	+	1.91135i	0.629294	+	0.184777i	0.580800	−	0.814046i	$-0.302740\pi$
$107$	6.50947	+	1.91135i	0.629294	+	0.184777i	0.0484938	+	0.998823i	$0.484558\pi$
$108$	5.71343	−	1.32308i	0.549775	−	0.127313i
$109$	1.76205	+	2.03352i	0.168774	+	0.194775i	0.833835	−	0.552013i	$-0.186140\pi$
$109$	1.76205	+	2.03352i	0.168774	+	0.194775i	−0.665062	+	0.746789i	$0.731595\pi$
$110$	−0.173646	+	3.64528i	−0.0165565	+	0.347564i
$111$	−3.72473	+	6.64003i	−0.353535	+	0.630244i
$112$	−0.110144	+	0.454021i	−0.0104077	+	0.0429010i
$113$	−5.90093	−	0.563471i	−0.555113	−	0.0530069i	−0.186270	−	0.982499i	$-0.559640\pi$
$113$	−5.90093	−	0.563471i	−0.555113	−	0.0530069i	−0.368843	+	0.929492i	$0.620246\pi$
$114$	7.70408	+	8.67157i	0.721553	+	0.812167i
$115$	2.67384	−	3.43143i	0.249337	−	0.319983i
$116$	3.76856			0.349902
$117$	−19.7196	+	6.32487i	−1.82308	+	0.584734i
$118$	3.40622	−	1.00016i	0.313568	−	0.0920719i
$119$	1.04353	+	0.201123i	0.0956599	+	0.0184369i
$120$	−3.57129	+	2.88080i	−0.326013	+	0.262980i
$121$	7.43956	−	1.43386i	0.676324	−	0.130351i
$122$	−10.2437	−	4.10095i	−0.927419	−	0.371283i
$123$	6.28896	−	9.06725i	0.567056	−	0.817567i
$124$	6.08670	+	3.13791i	0.546601	+	0.281793i
$125$	1.18469	−	8.23970i	0.105962	−	0.736982i
$126$	2.38409	+	1.44999i	0.212392	+	0.129176i
$127$	1.55036	−	3.39481i	0.137572	−	0.301241i	−0.828289	−	0.560301i	$-0.810685\pi$
$127$	1.55036	−	3.39481i	0.137572	−	0.301241i	0.965861	+	0.259060i	$0.0834127\pi$
$128$	−4.84893	+	1.94122i	−0.428589	+	0.171581i
$129$	4.76385	+	1.33492i	0.419434	+	0.117533i
$130$	4.23019	−	4.03348i	0.371012	−	0.353759i
$131$	11.7870	+	4.71881i	1.02984	+	0.412284i	0.824172	−	0.566339i	$-0.191641\pi$
$131$	11.7870	+	4.71881i	1.02984	+	0.412284i	0.205663	+	0.978623i	$0.434065\pi$
$132$	6.68697	+	5.12592i	0.582026	+	0.446154i
$133$	0.340153	−	7.14068i	0.0294950	−	0.619175i
$134$	−0.947542	+	1.09352i	−0.0818552	+	0.0944659i
$135$	1.70599	+	4.39373i	0.146829	+	0.378152i
$136$	−1.29393	−	2.83331i	−0.110953	−	0.242954i
$137$	−5.76878	−	9.99182i	−0.492860	−	0.853659i	0.507106	−	0.861884i	$-0.330715\pi$
$137$	−5.76878	−	9.99182i	−0.492860	−	0.853659i	−0.999966	+	0.00822507i	$0.997382\pi$
$138$	2.30954	+	7.40198i	0.196601	+	0.630099i
$139$	5.59380	−	9.68875i	0.474460	−	0.821789i	−0.525112	−	0.851033i	$-0.675977\pi$
$139$	5.59380	−	9.68875i	0.474460	−	0.821789i	0.999572	+	0.0292439i	$0.00930995\pi$
$140$	1.01550	+	0.0969686i	0.0858255	+	0.00819534i
$141$	−11.0316	−	6.89803i	−0.929032	−	0.580919i
$142$	−7.05249	−	1.35926i	−0.591832	−	0.114066i
$143$	−25.0293	−	16.0853i	−2.09305	−	1.34512i
$144$	−0.101712	−	1.40290i	−0.00847603	−	0.116909i
$145$	0.431034	+	2.99791i	0.0357954	+	0.248963i
$146$	−0.279788	−	1.15330i	−0.0231554	−	0.0954479i
$147$	2.57805	+	10.0802i	0.212634	+	0.831399i
$148$	−3.89966	−	3.06673i	−0.320550	−	0.252084i
$149$	−5.01471	−	7.04218i	−0.410821	−	0.576918i	0.556380	−	0.830928i	$-0.312190\pi$
$149$	−5.01471	−	7.04218i	−0.410821	−	0.576918i	−0.967202	+	0.254010i	$0.918250\pi$
$150$	4.94527	+	4.59971i	0.403779	+	0.375565i
$151$	3.34730	−	1.34006i	0.272399	−	0.109052i	−0.231441	−	0.972849i	$-0.574344\pi$
$151$	3.34730	−	1.34006i	0.272399	−	0.109052i	0.503841	+	0.863797i	$0.331920\pi$
$152$	−17.6264	+	11.3278i	−1.42969	+	0.918805i
$153$	−3.17660	+	0.382950i	−0.256813	+	0.0309597i
$154$	0.570529	+	3.96812i	0.0459746	+	0.319760i
$155$	−1.80005	+	5.20090i	−0.144583	+	0.417746i
$156$	−2.08579	−	13.3324i	−0.166996	−	1.06745i
$157$	5.19734	+	15.0167i	0.414793	+	1.19847i	0.938113	+	0.346330i	$0.112572\pi$
$157$	5.19734	+	15.0167i	0.414793	+	1.19847i	−0.523320	+	0.852136i	$0.675307\pi$
$158$	1.92717	−	7.94389i	0.153317	−	0.631982i
$159$	11.2142	+	15.3423i	0.889345	+	1.21673i
$160$	−2.45060	−	4.24456i	−0.193737	−	0.335562i
$161$	2.17079	−	4.25723i	0.171082	−	0.335517i
$162$	−8.16820	−	1.96473i	−0.641754	−	0.154364i
$163$	2.06862	+	4.52965i	0.162027	+	0.354790i	0.973180	−	0.230044i	$-0.0738870\pi$
$163$	2.06862	+	4.52965i	0.162027	+	0.354790i	−0.811153	+	0.584834i	$0.801160\pi$
$164$	5.20403	+	4.96203i	0.406366	+	0.387470i
$165$	−3.31286	+	5.90580i	−0.257906	+	0.459766i
$166$	−7.48035	+	3.85639i	−0.580588	+	0.299314i
$167$	2.48064	−	0.478105i	0.191958	−	0.0369969i	−0.0923660	−	0.995725i	$-0.529443\pi$
$167$	2.48064	−	0.478105i	0.191958	−	0.0369969i	0.284324	+	0.958728i	$0.408231\pi$
$168$	−3.25331	+	3.84986i	−0.250998	+	0.297023i
$169$	8.16948	+	33.6751i	0.628422	+	2.59039i
$170$	0.759700	−	0.488230i	0.0582664	−	0.0374455i
$171$	5.59084	+	20.7842i	0.427542	+	1.58941i
$172$	−1.33922	+	2.93249i	−0.102115	+	0.223600i
$173$	2.24711	−	0.214573i	0.170845	−	0.0163137i	−0.00928312	−	0.999957i	$-0.502955\pi$
$173$	2.24711	−	0.214573i	0.170845	−	0.0163137i	0.180128	+	0.983643i	$0.442349\pi$
$174$	−4.82867	−	2.41412i	−0.366061	−	0.183014i
$175$	−0.198051	−	4.15761i	−0.0149713	−	0.314286i
$176$	1.46253	−	1.39452i	0.110243	−	0.105116i
$177$	6.48302	+	1.16640i	0.487293	+	0.0876722i
$178$	4.39100	−	12.6870i	0.329120	−	0.950929i
$179$	1.16430	+	0.748252i	0.0870241	+	0.0559270i	0.583429	−	0.812164i	$-0.301711\pi$
$179$	1.16430	+	0.748252i	0.0870241	+	0.0559270i	−0.496405	+	0.868091i	$0.665347\pi$
$180$	−3.00048	+	0.655779i	−0.223643	+	0.0488789i
$181$	5.05274	−	1.48362i	0.375567	−	0.110276i	−0.0885007	−	0.996076i	$-0.528208\pi$
$181$	5.05274	−	1.48362i	0.375567	−	0.110276i	0.464068	+	0.885800i	$0.346389\pi$
$182$	3.72440	−	5.23019i	0.276071	−	0.387688i
$183$	−13.5982	−	15.3058i	−1.00520	−	1.13144i
$184$	−13.8545	+	2.05505i	−1.02137	+	0.151501i
$185$	1.99357	−	3.45296i	0.146570	−	0.253867i
$186$	−5.78878	−	7.91972i	−0.424454	−	0.580702i
$187$	−3.32686	−	3.17216i	−0.243284	−	0.231971i
$188$	5.55199	−	6.40734i	0.404921	−	0.467304i
$189$	2.75362	+	4.38468i	0.200297	+	0.318938i
$190$	−3.97807	−	4.59094i	−0.288600	−	0.333062i
$191$	8.96175	−	7.04760i	0.648449	−	0.509946i	−0.238900	−	0.971044i	$-0.576787\pi$
$191$	8.96175	−	7.04760i	0.648449	−	0.509946i	0.887349	+	0.461098i	$0.152544\pi$
$192$	10.3247	+	0.856976i	0.745124	+	0.0618469i
$193$	0.00650509	+	0.136559i	0.000468247	+	0.00982971i	0.999089	−	0.0426665i	$-0.0135853\pi$
$193$	0.00650509	+	0.136559i	0.000468247	+	0.00982971i	−0.998621	+	0.0524962i	$0.983282\pi$
$194$	9.47793	+	7.45353i	0.680476	+	0.535132i
$195$	10.3674	−	3.18416i	0.742426	−	0.228023i
$196$	−6.74921	+	0.644472i	−0.482087	+	0.0460337i
$197$	−1.48623	+	10.3370i	−0.105890	+	0.736479i	0.865829	+	0.500339i	$0.166791\pi$
$197$	−1.48623	+	10.3370i	−0.105890	+	0.736479i	−0.971719	+	0.236140i	$0.924118\pi$
$198$	−5.28441	−	10.8515i	−0.375547	−	0.771182i
$199$	−11.6451	−	3.41932i	−0.825502	−	0.242389i	−0.158418	−	0.987372i	$-0.550639\pi$
$199$	−11.6451	−	3.41932i	−0.825502	−	0.242389i	−0.667084	+	0.744983i	$0.732458\pi$
$200$	−9.58941	+	7.54120i	−0.678074	+	0.533243i
$201$	−2.47994	+	1.02864i	−0.174921	+	0.0725547i
$202$	5.63321	−	2.90412i	0.396351	−	0.204333i
$203$	1.08819	+	3.14412i	0.0763759	+	0.220674i
$204$	0.0734007	−	2.08365i	0.00513907	−	0.145884i
$205$	−3.35210	+	4.70737i	−0.234121	+	0.328777i
$206$	3.94026			0.274531
$207$	−2.30877	+	14.2010i	−0.160471	+	0.987041i
$208$	−3.23657			−0.224416
$209$	−17.9364	+	25.1881i	−1.24069	+	1.74230i
$210$	−1.23905	−	0.774770i	−0.0855025	−	0.0534642i
$211$	−2.66981	−	7.71392i	−0.183797	−	0.531048i	0.815032	−	0.579416i	$-0.196719\pi$
$211$	−2.66981	−	7.71392i	−0.183797	−	0.531048i	−0.998830	+	0.0483678i	$0.984598\pi$
$212$	−11.0068	+	5.67439i	−0.755949	+	0.389719i
$213$	−10.5768	−	8.10769i	−0.724711	−	0.555530i
$214$	4.97797	−	3.91472i	0.340287	−	0.267605i
$215$	−2.48598	−	0.729950i	−0.169543	−	0.0497822i
$216$	5.78680	−	14.0286i	0.393742	−	0.954523i
$217$	−0.860402	+	5.98423i	−0.0584079	+	0.406236i
$218$	2.50032	−	0.238752i	0.169343	−	0.0161703i
$219$	0.492602	−	2.14623i	0.0332870	−	0.145029i
$220$	−3.46845	−	2.72762i	−0.233843	−	0.183896i
$221$	0.350313	+	7.35397i	0.0235646	+	0.494682i
$222$	3.03213	+	6.42752i	0.203503	+	0.431387i
$223$	4.22047	−	3.31902i	0.282624	−	0.222258i	−0.466776	−	0.884376i	$-0.654585\pi$
$223$	4.22047	−	3.31902i	0.282624	−	0.222258i	0.749400	+	0.662118i	$0.230342\pi$
$224$	−3.52579	−	4.06897i	−0.235577	−	0.271870i
$225$	4.39080	+	11.7372i	0.292720	+	0.782483i
$226$	−3.62358	+	4.18183i	−0.241037	+	0.278171i
$227$	−12.3037	−	11.7316i	−0.816627	−	0.778653i	0.161453	−	0.986880i	$-0.448382\pi$
$227$	−12.3037	−	11.7316i	−0.816627	−	0.778653i	−0.978080	+	0.208228i	$0.933230\pi$
$228$	−13.9439	+	1.50600i	−0.923455	+	0.0997370i
$229$	−14.0406	+	24.3190i	−0.927829	+	1.60705i	−0.140883	+	0.990026i	$0.544994\pi$
$229$	−14.0406	+	24.3190i	−0.927829	+	1.60705i	−0.786946	+	0.617022i	$0.788339\pi$
$230$	−1.16140	−	3.89111i	−0.0765803	−	0.256572i
$231$	−2.34567	+	7.05908i	−0.154334	+	0.464454i
$232$	5.65642	−	7.94333i	0.371362	−	0.521505i
$233$	11.0999	−	3.25923i	0.727180	−	0.213519i	0.102869	−	0.994695i	$-0.467198\pi$
$233$	11.0999	−	3.25923i	0.727180	−	0.213519i	0.624311	+	0.781176i	$0.285380\pi$
$234$	−5.86813	+	18.4190i	−0.383611	+	1.20409i
$235$	5.73209	+	3.68379i	0.373920	+	0.240304i
$236$	−1.40388	+	4.05625i	−0.0913849	+	0.264039i
$237$	9.78987	−	11.5850i	0.635920	−	0.752527i
$238$	0.717959	−	0.684572i	0.0465384	−	0.0443742i
$239$	−0.225134	−	4.72614i	−0.0145627	−	0.305709i	−0.994384	−	0.105833i	$-0.966249\pi$
$239$	−0.225134	−	4.72614i	−0.0145627	−	0.305709i	0.979821	−	0.199876i	$-0.0640539\pi$
$240$	0.0441620	+	0.735305i	0.00285064	+	0.0474637i
$241$	−19.5388	+	1.86573i	−1.25860	+	0.120182i	−0.702955	−	0.711234i	$-0.748136\pi$
$241$	−19.5388	+	1.86573i	−1.25860	+	0.120182i	−0.555650	+	0.831416i	$0.687530\pi$
$242$	2.93797	−	6.43325i	0.188860	−	0.413545i
$243$	−11.9261	−	10.0383i	−0.765060	−	0.643958i
$244$	11.2234	−	7.21283i	0.718503	−	0.461754i
$245$	−1.28463	−	5.29532i	−0.0820720	−	0.338306i
$246$	−3.48930	−	9.69154i	−0.222469	−	0.617910i
$247$	48.6298	−	9.37263i	3.09424	−	0.596366i
$248$	15.7499	−	8.11962i	1.00012	−	0.515597i
$249$	−15.6146	+	0.193434i	−0.989535	+	0.0122584i
$250$	−5.62381	−	5.36229i	−0.355681	−	0.339141i
$251$	−6.42018	−	14.0582i	−0.405238	−	0.887348i	−0.996712	−	0.0810237i	$-0.974181\pi$
$251$	−6.42018	−	14.0582i	−0.405238	−	0.887348i	0.591474	−	0.806324i	$-0.298546\pi$
$252$	−3.10017	+	1.33115i	−0.195292	+	0.0838544i
$253$	−17.8547	+	10.4148i	−1.12252	+	0.654774i
$254$	−1.74188	−	3.01702i	−0.109295	−	0.189305i
$255$	1.66595	−	0.179929i	0.104326	−	0.0112676i
$256$	−3.96983	+	16.3639i	−0.248115	+	1.02274i
$257$	8.69582	+	25.1249i	0.542430	+	1.56725i	0.799381	+	0.600825i	$0.205161\pi$
$257$	8.69582	+	25.1249i	0.542430	+	1.56725i	−0.256951	+	0.966425i	$0.582718\pi$
$258$	3.59449	−	2.89951i	0.223783	−	0.180516i
$259$	1.43253	−	4.13903i	0.0890132	−	0.257187i
$260$	1.00576	+	6.99518i	0.0623743	+	0.433823i
$261$	−6.01079	−	8.01318i	−0.372059	−	0.496004i
$262$	9.97028	−	6.40751i	0.615966	−	0.395857i
$263$	19.6807	−	7.87897i	1.21356	−	0.485838i	0.325494	−	0.945544i	$-0.394470\pi$
$263$	19.6807	−	7.87897i	1.21356	−	0.485838i	0.888071	+	0.459706i	$0.152045\pi$
$264$	20.8412	−	6.40098i	1.28268	−	0.393953i
$265$	−5.77292	−	8.10693i	−0.354628	−	0.498005i
$266$	−5.24543	−	4.12505i	−0.321618	−	0.252923i
$267$	17.8145	−	17.4125i	1.09023	−	1.06563i
$268$	−0.412457	−	1.70017i	−0.0251948	−	0.103854i
$269$	4.29552	+	29.8760i	0.261903	+	1.82157i	0.518526	+	0.855062i	$0.326481\pi$
$269$	4.29552	+	29.8760i	0.261903	+	1.82157i	−0.256624	+	0.966511i	$0.582610\pi$
$270$	4.26462	+	1.08184i	0.259536	+	0.0658386i
$271$	0.124257	+	0.0798549i	0.00754806	+	0.00485084i	0.544409	−	0.838820i	$-0.316754\pi$
$271$	0.124257	+	0.0798549i	0.00754806	+	0.00485084i	−0.536861	+	0.843670i	$0.680390\pi$
$272$	−0.491020	−	0.0946364i	−0.0297725	−	0.00573817i
$273$	10.5210	−	5.58996i	0.636757	−	0.338320i
$274$	−10.7211	−	1.02374i	−0.647686	−	0.0618465i
$275$	−9.00198	+	15.5919i	−0.542840	+	0.940227i
$276$	−8.91001	−	2.91668i	−0.536319	−	0.175563i
$277$	2.02504	+	3.50747i	0.121673	+	0.210744i	0.920428	−	0.390913i	$-0.127841\pi$
$277$	2.02504	+	3.50747i	0.121673	+	0.210744i	−0.798755	+	0.601657i	$0.794507\pi$
$278$	−4.33827	−	9.49948i	−0.260192	−	0.569741i
$279$	−3.03596	−	17.9472i	−0.181758	−	1.07447i
$280$	1.72860	−	1.99492i	0.103304	−	0.119219i
$281$	−0.315518	+	6.62353i	−0.0188222	+	0.395127i	0.969724	+	0.244205i	$0.0785271\pi$
$281$	−0.315518	+	6.62353i	−0.0188222	+	0.395127i	−0.988546	+	0.150922i	$0.951776\pi$
$282$	−11.2183	+	4.65318i	−0.668040	+	0.277093i
$283$	−8.02391	−	3.21229i	−0.476972	−	0.190951i	0.120704	−	0.992689i	$-0.461485\pi$
$283$	−8.02391	−	3.21229i	−0.476972	−	0.190951i	−0.597676	+	0.801738i	$0.703909\pi$
$284$	6.28496	−	5.99270i	0.372944	−	0.355601i
$285$	−2.79287	−	10.9202i	−0.165436	−	0.646854i
$286$	−25.7833	+	10.3221i	−1.52460	+	0.610358i
$287$	−2.63714	+	5.77454i	−0.155666	+	0.340860i
$288$	13.8495	+	8.42321i	0.816090	+	0.496343i
$289$	2.25747	−	15.7010i	0.132792	−	0.923591i
$290$	2.51293	+	1.29550i	0.147564	+	0.0760746i
$291$	9.54548	+	20.2346i	0.559566	+	1.18617i
$292$	1.33212	+	0.533299i	0.0779562	+	0.0312090i
$293$	8.50879	−	1.63994i	0.497089	−	0.0958060i	0.0654561	−	0.997855i	$-0.479150\pi$
$293$	8.50879	−	1.63994i	0.497089	−	0.0958060i	0.431633	+	0.902049i	$0.357938\pi$
$294$	9.06064	+	3.49774i	0.528428	+	0.203993i
$295$	−3.38733	−	0.652855i	−0.197218	−	0.0380107i
$296$	−12.3172	+	3.61666i	−0.715924	+	0.210214i
$297$	0.233754	−	22.3944i	0.0135638	−	1.29946i
$298$	−8.06998			−0.467482
$299$	32.2070	+	7.66150i	1.86258	+	0.443076i
$300$	−7.99860	+	1.64462i	−0.461799	+	0.0949520i
$301$	−2.83329	−	0.270546i	−0.163308	−	0.0155940i
$302$	0.793487	−	3.27080i	0.0456600	−	0.188213i
$303$	11.7589	−	0.145669i	0.675528	−	0.00836847i
$304$	−0.160055	+	3.35997i	−0.00917979	+	0.192707i
$305$	7.02153	+	8.10327i	0.402052	+	0.463992i
$306$	−1.42882	+	2.62276i	−0.0816802	+	0.149933i
$307$	−16.8402	−	4.94472i	−0.961120	−	0.282210i	−0.236710	−	0.971580i	$-0.576069\pi$
$307$	−16.8402	−	4.94472i	−0.961120	−	0.282210i	−0.724409	+	0.689370i	$0.757887\pi$
$308$	−4.30834	−	2.22111i	−0.245491	−	0.126559i
$309$	6.53945	+	3.26943i	0.372016	+	0.185991i
$310$	2.97998	+	4.18480i	0.169252	+	0.237681i
$311$	2.63792	+	3.70444i	0.149583	+	0.210060i	0.882568	−	0.470185i	$-0.155813\pi$
$311$	2.63792	+	3.70444i	0.149583	+	0.210060i	−0.732985	+	0.680245i	$0.761873\pi$
$312$	−31.2325	−	15.6148i	−1.76819	−	0.884017i
$313$	−4.77953	−	2.46402i	−0.270155	−	0.139275i	0.317827	−	0.948149i	$-0.397047\pi$
$313$	−4.77953	−	2.46402i	−0.270155	−	0.139275i	−0.587982	+	0.808874i	$0.700077\pi$
$314$	14.2325	+	4.17905i	0.803189	+	0.235837i
$315$	−1.41352	−	2.31395i	−0.0796428	−	0.130376i
$316$	6.47234	+	7.46948i	0.364098	+	0.420191i
$317$	−0.464274	+	9.74632i	−0.0260762	+	0.547408i	0.947598	+	0.319465i	$0.103503\pi$
$317$	−0.464274	+	9.74632i	−0.0260762	+	0.547408i	−0.973674	+	0.227943i	$0.926800\pi$
$318$	17.7380	−	0.219739i	0.994699	−	0.0123224i
$319$	3.39287	−	13.9856i	0.189964	−	0.783043i
$320$	−5.40110	−	0.515743i	−0.301931	−	0.0288309i
$321$	11.5099	−	2.36659i	0.642422	−	0.132090i
$322$	−2.06170	−	3.95574i	−0.114894	−	0.220445i
$323$	7.65168			0.425751
$324$	7.66379	−	6.66691i	0.425766	−	0.370384i
$325$	27.6674	−	8.12388i	1.53471	−	0.450632i
$326$	4.56432	+	0.879700i	0.252794	+	0.0487221i
$327$	4.34776	+	1.67840i	0.240432	+	0.0928155i
$328$	18.2699	−	3.52123i	1.00879	−	0.194428i
$329$	6.94882	+	2.78189i	0.383101	+	0.153370i
$330$	2.69685	+	5.71678i	0.148456	+	0.314699i
$331$	−0.0473066	−	0.0243882i	−0.00260021	−	0.00134050i	0.456926	−	0.889505i	$-0.348950\pi$
$331$	−0.0473066	−	0.0243882i	−0.00260021	−	0.00134050i	−0.459526	+	0.888164i	$0.651981\pi$
$332$	1.44814	−	10.0721i	0.0794772	−	0.552776i
$333$	−0.300963	+	13.1833i	−0.0164927	+	0.722442i
$334$	0.979634	−	2.14510i	0.0536032	−	0.117375i
$335$	1.30532	−	0.522571i	0.0713172	−	0.0285511i
$336$	0.200502	+	0.783964i	0.0109383	+	0.0427687i
$337$	13.9606	−	13.3114i	0.760480	−	0.725116i	−0.206923	−	0.978357i	$-0.566345\pi$
$337$	13.9606	−	13.3114i	0.760480	−	0.725116i	0.967403	+	0.253241i	$0.0814965\pi$
$338$	30.0292	+	12.0219i	1.63337	+	0.653904i
$339$	−9.48374	+	3.93371i	−0.515086	+	0.213650i
$340$	−0.0519539	+	1.09065i	−0.00281760	+	0.0591487i
$341$	17.1251	−	19.7634i	0.927375	−	1.07025i
$342$	18.8311	+	7.00272i	1.01827	+	0.378664i
$343$	−5.38409	−	11.7895i	−0.290714	−	0.636574i
$344$	4.17096	+	7.22431i	0.224883	+	0.389509i
$345$	1.30114	−	7.42155i	0.0700508	−	0.399563i
$346$	1.05357	−	1.82483i	0.0566401	−	0.0981036i
$347$	−20.9915	−	2.00445i	−1.12688	−	0.107604i	−0.485078	−	0.874471i	$-0.661209\pi$
$347$	−20.9915	−	2.00445i	−1.12688	−	0.107604i	−0.641807	+	0.766866i	$0.721815\pi$
$348$	5.76423	−	3.06264i	0.308995	−	0.164175i
$349$	−16.0178	−	3.08718i	−0.857414	−	0.165253i	−0.258446	−	0.966026i	$-0.583210\pi$
$349$	−16.0178	−	3.08718i	−0.857414	−	0.165253i	−0.598968	+	0.800773i	$0.704422\pi$
$350$	−3.26858	−	2.10059i	−0.174713	−	0.112281i
$351$	−25.0222	+	25.7000i	−1.33559	+	1.37176i
$352$	3.31429	+	23.0514i	0.176652	+	1.22864i
$353$	−0.109768	−	0.452470i	−0.00584237	−	0.0240826i	0.968816	−	0.247782i	$-0.0797017\pi$
$353$	−0.109768	−	0.452470i	−0.00584237	−	0.0240826i	−0.974658	+	0.223700i	$0.928187\pi$
$354$	4.39721	−	4.29797i	0.233709	−	0.228435i
$355$	5.48607	+	4.31429i	0.291170	+	0.228979i
$356$	9.41580	+	13.2226i	0.499037	+	0.700799i
$357$	1.75958	−	0.540424i	0.0931271	−	0.0286023i
$358$	1.19938	−	0.480159i	0.0633891	−	0.0253772i
$359$	−21.2843	+	13.6786i	−1.12334	+	0.721930i	−0.964161	−	0.265319i	$-0.914523\pi$
$359$	−21.2843	+	13.6786i	−1.12334	+	0.721930i	−0.159184	+	0.987249i	$0.550886\pi$
$360$	−3.12133	+	7.30867i	−0.164508	+	0.385201i
$361$	−4.62115	−	32.1408i	−0.243218	−	1.69162i
$362$	1.60776	−	4.64531i	0.0845018	−	0.244152i
$363$	10.2140	−	8.23916i	0.536095	−	0.432444i
$364$	2.53913	+	7.33634i	0.133087	+	0.384529i
$365$	−0.271879	+	1.12070i	−0.0142308	+	0.0586602i
$366$	−19.0011	+	2.05220i	−0.993202	+	0.107270i
$367$	4.72769	+	8.18860i	0.246783	+	0.427441i	0.962631	−	0.270815i	$-0.0872931\pi$
$367$	4.72769	+	8.18860i	0.246783	+	0.427441i	−0.715848	+	0.698256i	$0.753960\pi$
$368$	−1.02144	+	2.00319i	−0.0532463	+	0.104424i
$369$	2.25055	−	18.9798i	0.117159	−	0.988049i
$370$	−1.54611	−	3.38551i	−0.0803784	−	0.176004i
$371$	−7.91241	−	7.54447i	−0.410792	−	0.391689i
$372$	11.8601	−	0.146923i	0.614916	−	0.00761761i
$373$	−8.17180	+	4.21286i	−0.423120	+	0.218134i	−0.656617	−	0.754224i	$-0.728013\pi$
$373$	−8.17180	+	4.21286i	−0.423120	+	0.218134i	0.233497	+	0.972357i	$0.424983\pi$
$374$	−4.21340	+	0.812067i	−0.217870	+	0.0419910i
$375$	−4.88420	−	13.5659i	−0.252219	−	0.700539i
$376$	−5.17206	−	21.3195i	−0.266729	−	1.09947i
$377$	−19.3903	+	12.4614i	−0.998650	+	0.641794i
$378$	4.82499	+	0.280345i	0.248171	+	0.0144194i
$379$	−4.92465	+	10.7835i	−0.252962	+	0.553910i	−0.992926	−	0.118737i	$-0.962116\pi$
$379$	−4.92465	+	10.7835i	−0.252962	+	0.553910i	0.739963	+	0.672647i	$0.234843\pi$
$380$	7.31162	−	0.698175i	0.375078	−	0.0358156i
$381$	−0.387534	−	6.45252i	−0.0198540	−	0.330572i
$382$	−0.506384	−	10.6303i	−0.0259089	−	0.543894i
$383$	7.95942	−	7.58929i	0.406707	−	0.387794i	−0.458925	−	0.888475i	$-0.651765\pi$
$383$	7.95942	−	7.58929i	0.406707	−	0.387794i	0.865632	+	0.500681i	$0.166917\pi$
$384$	−5.83914	+	6.90985i	−0.297977	+	0.352617i
$385$	1.27413	−	3.68135i	0.0649355	−	0.187619i
$386$	0.107358	+	0.0689950i	0.00546439	+	0.00351175i
$387$	8.37146	−	1.82965i	0.425545	−	0.0930062i
$388$	−13.9883	+	4.10733i	−0.710148	+	0.208518i
$389$	2.71285	−	3.80967i	0.137547	−	0.193158i	−0.740057	−	0.672544i	$-0.765201\pi$
$389$	2.71285	−	3.80967i	0.137547	−	0.193158i	0.877604	+	0.479386i	$0.159141\pi$
$390$	3.19239	−	9.60724i	0.161653	−	0.486481i
$391$	4.66211	+	2.10405i	0.235773	+	0.106406i
$392$	−8.77182	+	15.1932i	−0.443044	+	0.767374i
$393$	21.8638	−	2.36138i	1.10288	−	0.119116i
$394$	7.05526	+	6.72717i	0.355439	+	0.338910i
$395$	−5.20172	+	6.00311i	−0.261727	+	0.302049i
$396$	14.3939	+	2.40602i	0.723318	+	0.120907i
$397$	−11.0337	−	12.7336i	−0.553766	−	0.639080i	0.407991	−	0.912986i	$-0.366230\pi$
$397$	−11.0337	−	12.7336i	−0.553766	−	0.639080i	−0.961756	+	0.273906i	$0.911684\pi$
$398$	−8.90537	+	7.00326i	−0.446386	+	0.351042i
$399$	−5.28281	−	11.1985i	−0.264471	−	0.560627i
$400$	0.0931909	+	1.95632i	0.00465954	+	0.0978158i
$401$	−30.2117	−	23.7588i	−1.50870	−	1.18646i	−0.928136	−	0.372242i	$-0.878589\pi$
$401$	−30.2117	−	23.7588i	−1.50870	−	1.18646i	−0.580565	−	0.814214i	$-0.697168\pi$
$402$	−0.560637	+	2.44265i	−0.0279620	+	0.121829i
$403$	−41.6937	+	3.98127i	−2.07691	+	0.198321i
$404$	−1.09055	+	7.58495i	−0.0542569	+	0.377365i
$405$	6.18012	+	5.33404i	0.307092	+	0.265051i
$406$	2.97992	+	0.874985i	0.147891	+	0.0434248i
$407$	−14.8919	+	11.7111i	−0.738165	+	0.580499i
$408$	−4.28171	−	3.28216i	−0.211976	−	0.162491i
$409$	−28.3330	+	14.6067i	−1.40097	+	0.722252i	−0.982550	−	0.185999i	$-0.940448\pi$
$409$	−28.3330	+	14.6067i	−1.40097	+	0.722252i	−0.418424	+	0.908252i	$0.637418\pi$
$410$	1.76434	+	5.09772i	0.0871344	+	0.251758i
$411$	−16.9438	−	10.5949i	−0.835778	−	0.522608i
$412$	−2.76348	+	3.88077i	−0.136147	+	0.191192i
$413$	−3.78951			−0.186470
$414$	9.54803	+	9.44485i	0.469260	+	0.464189i
$415$	8.17801			0.401443
$416$	21.6356	−	30.3829i	1.06077	−	1.48965i
$417$	0.682189	−	19.3655i	0.0334069	−	0.948332i
$418$	9.44060	+	27.2768i	0.461755	+	1.33415i
$419$	−18.0623	+	9.31177i	−0.882402	+	0.454910i	−0.838990	−	0.544147i	$-0.816853\pi$
$419$	−18.0623	+	9.31177i	−0.882402	+	0.454910i	−0.0434125	+	0.999057i	$0.513823\pi$
$420$	1.63207	−	0.676959i	0.0796370	−	0.0330322i
$421$	−11.1932	+	8.80244i	−0.545524	+	0.429005i	−0.852511	−	0.522709i	$-0.824922\pi$
$421$	−11.1932	+	8.80244i	−0.545524	+	0.429005i	0.306987	+	0.951714i	$0.400679\pi$
$422$	−7.31108	−	2.14673i	−0.355898	−	0.104501i
$423$	−22.4794	−	1.58574i	−1.09299	−	0.0771011i
$424$	−4.56021	+	31.7169i	−0.221463	+	1.54031i
$425$	4.43496	−	0.423488i	0.215127	−	0.0205422i
$426$	−11.8918	+	3.65236i	−0.576161	+	0.176957i
$427$	9.25848	+	7.28095i	0.448049	+	0.352350i
$428$	0.364337	+	7.64838i	0.0176109	+	0.369699i
$429$	−51.3560	−	4.26266i	−2.47949	−	0.205803i
$430$	−1.90110	+	1.49504i	−0.0916792	+	0.0720973i
$431$	8.00499	+	9.23825i	0.385587	+	0.444991i	0.915049	−	0.403343i	$-0.132152\pi$
$431$	8.00499	+	9.23825i	0.385587	+	0.444991i	−0.529462	+	0.848333i	$0.677606\pi$
$432$	−1.29569	−	2.06316i	−0.0623388	−	0.0992640i
$433$	14.5701	−	16.8148i	0.700193	−	0.808066i	−0.288585	−	0.957454i	$-0.593185\pi$
$433$	14.5701	−	16.8148i	0.700193	−	0.808066i	0.988779	+	0.149388i	$0.0477304\pi$
$434$	4.08439	+	3.89446i	0.196057	+	0.186940i
$435$	3.09563	+	4.23518i	0.148424	+	0.203061i
$436$	−1.51844	+	2.63002i	−0.0727201	+	0.125955i
$437$	9.54632	−	33.0561i	0.456662	−	1.58129i
$438$	−1.36522	−	1.53666i	−0.0652327	−	0.0734247i
$439$	−16.8737	+	23.6957i	−0.805336	+	1.13094i	0.183660	+	0.982990i	$0.441206\pi$
$439$	−16.8737	+	23.6957i	−0.805336	+	1.13094i	−0.988995	+	0.147946i	$0.952734\pi$
$440$	−10.9552	+	3.21674i	−0.522270	+	0.153352i
$441$	12.1352	+	13.3231i	0.577869	+	0.634433i
$442$	5.78147	+	3.71552i	0.274996	+	0.176729i
$443$	−2.16825	+	6.26474i	−0.103017	+	0.297647i	−0.984717	−	0.174163i	$-0.944278\pi$
$443$	−2.16825	+	6.26474i	−0.103017	+	0.297647i	0.881700	+	0.471810i	$0.156399\pi$
$444$	−8.45704	−	1.52156i	−0.401353	−	0.0722101i
$445$	−9.44173	+	9.00267i	−0.447581	+	0.426768i
$446$	−0.238478	−	5.00627i	−0.0112923	−	0.237054i
$447$	−13.3933	−	6.69607i	−0.633484	−	0.316713i
$448$	−5.93318	+	0.566550i	−0.280316	+	0.0267670i
$449$	6.11621	−	13.3926i	0.288642	−	0.632037i	−0.708652	−	0.705558i	$-0.750696\pi$
$449$	6.11621	−	13.3926i	0.288642	−	0.632037i	0.997294	+	0.0735211i	$0.0234236\pi$
$450$	11.3022	+	3.01660i	0.532789	+	0.142204i
$451$	23.1000	−	14.8454i	1.08773	−	0.699044i
$452$	−1.57731	−	6.50177i	−0.0741906	−	0.305818i
$453$	4.03085	−	4.76998i	0.189386	−	0.224113i
$454$	−15.5824	+	3.00327i	−0.731319	+	0.140950i
$455$	−5.54567	+	2.85899i	−0.259985	+	0.134032i
$456$	−17.7547	+	31.6511i	−0.831441	+	1.48220i
$457$	4.73612	+	4.51589i	0.221547	+	0.211244i	0.792721	−	0.609584i	$-0.208664\pi$
$457$	4.73612	+	4.51589i	0.221547	+	0.211244i	−0.571175	+	0.820829i	$0.693512\pi$
$458$	10.8892	+	23.8440i	0.508818	+	1.11416i
$459$	−4.54758	+	3.16731i	−0.212263	+	0.147837i
$460$	4.64690	+	1.58515i	0.216663	+	0.0739080i
$461$	−5.70793	−	9.88643i	−0.265845	−	0.460457i	0.701940	−	0.712236i	$-0.252318\pi$
$461$	−5.70793	−	9.88643i	−0.265845	−	0.460457i	−0.967785	+	0.251779i	$0.918984\pi$
$462$	4.09747	+	5.60581i	0.190632	+	0.260806i
$463$	−5.73272	+	23.6306i	−0.266422	+	1.09821i	0.668601	+	0.743621i	$0.266893\pi$
$463$	−5.73272	+	23.6306i	−0.266422	+	1.09821i	−0.935023	+	0.354586i	$0.884622\pi$
$464$	−0.512036	−	1.47943i	−0.0237707	−	0.0686808i
$465$	1.47339	+	9.41794i	0.0683268	+	0.436747i
$466$	3.53194	−	10.2049i	0.163614	−	0.472732i
$467$	−2.92006	−	20.3095i	−0.135124	−	0.939811i	−0.938731	−	0.344650i	$-0.887997\pi$
$467$	−2.92006	−	20.3095i	−0.135124	−	0.939811i	0.803607	−	0.595161i	$-0.202912\pi$
$468$	−14.0253	−	18.6976i	−0.648320	−	0.864297i
$469$	1.29936	−	0.835046i	0.0599987	−	0.0385588i
$470$	5.90477	−	2.36391i	0.272367	−	0.109039i
$471$	20.1535	+	18.7452i	0.928622	+	0.863733i
$472$	6.44256	+	9.04731i	0.296543	+	0.416436i
$473$	9.67711	+	7.61017i	0.444954	+	0.349916i
$474$	−3.50813	−	13.7168i	−0.161134	−	0.630035i
$475$	−7.06541	−	29.1240i	−0.324183	−	1.33630i
$476$	0.170699	+	1.18724i	0.00782399	+	0.0544171i
$477$	29.6212	+	14.3534i	1.35626	+	0.657199i
$478$	−3.71555	−	2.38784i	−0.169945	−	0.109217i
$479$	−30.3786	−	5.85500i	−1.38803	−	0.267522i	−0.560136	−	0.828400i	$-0.689251\pi$
$479$	−30.3786	−	5.85500i	−1.38803	−	0.267522i	−0.827898	+	0.560879i	$0.810463\pi$
$480$	−7.19781	−	4.50075i	−0.328533	−	0.205430i
$481$	30.2055	+	2.88428i	1.37725	+	0.131512i
$482$	−9.16085	+	15.8671i	−0.417265	+	0.722725i
$483$	−0.139418	−	8.27584i	−0.00634375	−	0.376564i
$484$	4.27559	+	7.40553i	0.194345	+	0.336615i
$485$	−4.86733	−	10.6580i	−0.221014	−	0.483953i
$486$	−14.0904	+	3.63297i	−0.639155	+	0.164795i
$487$	0.122915	−	0.141851i	0.00556981	−	0.00642790i	−0.752958	−	0.658069i	$-0.771374\pi$
$487$	0.122915	−	0.141851i	0.00556981	−	0.00642790i	0.758528	+	0.651641i	$0.225919\pi$
$488$	1.64261	−	34.4826i	0.0743574	−	1.56095i
$489$	6.84524	+	5.24724i	0.309552	+	0.237288i
$490$	−4.72201	−	1.89041i	−0.213319	−	0.0854000i
$491$	−7.70505	+	7.34675i	−0.347724	+	0.331554i	−0.843733	−	0.536763i	$-0.819647\pi$
$491$	−7.70505	+	7.34675i	−0.347724	+	0.331554i	0.496009	+	0.868318i	$0.334798\pi$
$492$	11.9924	+	3.36050i	0.540660	+	0.151503i
$493$	−3.30607	+	1.32355i	−0.148898	+	0.0596097i
$494$	19.2044	−	42.0519i	0.864049	−	1.89200i
$495$	−0.267683	+	11.7256i	−0.0120315	+	0.527025i
$496$	0.404853	−	2.81581i	0.0181784	−	0.126434i
$497$	6.81453	+	3.51313i	0.305673	+	0.157586i
$498$	−8.30762	+	11.9777i	−0.372273	+	0.536734i
$499$	25.2180	+	10.0958i	1.12891	+	0.451948i	0.859530	−	0.511085i	$-0.170756\pi$
$499$	25.2180	+	10.0958i	1.12891	+	0.451948i	0.269382	+	0.963033i	$0.413181\pi$
$500$	9.22556	−	1.77808i	0.412580	−	0.0795182i
$501$	3.40574	−	2.74726i	0.152157	−	0.122739i
$502$	−14.1658	−	2.73024i	−0.632252	−	0.121857i
$503$	19.5711	−	5.74658i	0.872630	−	0.256227i	0.185397	−	0.982664i	$-0.440643\pi$
$503$	19.5711	−	5.74658i	0.872630	−	0.256227i	0.687234	+	0.726436i	$0.258825\pi$
$504$	−1.84742	+	8.53249i	−0.0822906	+	0.380067i
$505$	−6.15859			−0.274054
$506$	−1.74846	+	19.2155i	−0.0777287	+	0.854234i
$507$	39.8628	+	44.8688i	1.77037	+	1.99269i
$508$	4.19312	+	0.400395i	0.186040	+	0.0177646i
$509$	−3.23913	+	13.3519i	−0.143572	+	0.591812i	0.853880	+	0.520470i	$0.174243\pi$
$509$	−3.23913	+	13.3519i	−0.143572	+	0.591812i	−0.997452	+	0.0713419i	$0.977272\pi$
$510$	0.765231	−	1.36417i	0.0338850	−	0.0604065i
$511$	−0.0602774	+	1.26538i	−0.00266652	+	0.0559771i
$512$	3.45242	+	3.98431i	0.152577	+	0.176083i
$513$	25.4425	+	27.2471i	1.12331	+	1.20299i
$514$	23.8128	+	6.99208i	1.05034	+	0.308408i
$515$	−3.40325	−	1.75449i	−0.149965	−	0.0773123i
$516$	0.334757	+	5.57377i	0.0147369	+	0.245372i
$517$	−18.7799	−	26.3727i	−0.825941	−	1.15987i
$518$	−2.37156	−	3.33039i	−0.104200	−	0.146329i
$519$	3.26271	−	2.15439i	0.143217	−	0.0945670i
$520$	16.2539	+	8.37949i	0.712783	+	0.367465i
$521$	30.1027	+	8.83896i	1.31882	+	0.387242i	0.864069	−	0.503374i	$-0.167908\pi$
$521$	30.1027	+	8.83896i	1.31882	+	0.387242i	0.454756	+	0.890616i	$0.349726\pi$
$522$	−9.34765	+	0.231634i	−0.409135	+	0.0101383i
$523$	−15.4109	−	17.7852i	−0.673874	−	0.777692i	0.311103	−	0.950376i	$-0.399301\pi$
$523$	−15.4109	−	17.7852i	−0.673874	−	0.777692i	−0.984977	+	0.172684i	$0.944756\pi$
$524$	−0.681842	+	14.3136i	−0.0297864	+	0.625293i
$525$	−3.68174	−	6.19835i	−0.160684	−	0.270518i
$526$	4.66537	−	19.2309i	0.203420	−	0.838507i
$527$	−6.44177	−	0.615115i	−0.280608	−	0.0267948i
$528$	1.10373	−	3.32158i	0.0480336	−	0.144553i
$529$	14.9062	−	17.5158i	0.648097	−	0.761557i
$530$	−9.29013			−0.403538
$531$	10.8641	−	3.48454i	0.471460	−	0.151216i
$532$	7.74162	−	2.27314i	0.335642	−	0.0985533i
$533$	−43.1839	−	8.32302i	−1.87050	−	0.360510i
$534$	−3.59416	−	22.9739i	−0.155534	−	0.994180i
$535$	−6.04265	+	1.16463i	−0.261247	+	0.0503512i
$536$	−4.20268	−	1.68250i	−0.181528	−	0.0726729i
$537$	2.38896	+	0.198289i	0.103091	+	0.00855680i
$538$	25.0429	+	12.9105i	1.07968	+	0.556611i
$539$	−3.68466	+	25.6274i	−0.158710	+	1.10385i
$540$	−4.05647	+	3.44149i	−0.174563	+	0.148098i
$541$	−7.68615	+	16.8303i	−0.330454	+	0.723592i	−0.999813	−	0.0193465i	$-0.993841\pi$
$541$	−7.68615	+	16.8303i	−0.330454	+	0.723592i	0.669359	+	0.742939i	$0.266569\pi$
$542$	0.128000	−	0.0512435i	0.00549807	−	0.00220110i
$543$	6.52275	−	6.37555i	0.279918	−	0.273601i
$544$	4.17072	−	3.97678i	0.178818	−	0.170503i
$545$	−2.26586	−	0.907115i	−0.0970589	−	0.0388565i
$546$	1.44622	−	11.0266i	0.0618924	−	0.471896i
$547$	0.345849	−	7.26027i	0.0147874	−	0.310427i	−0.979341	−	0.202217i	$-0.935185\pi$
$547$	0.345849	−	7.26027i	0.0147874	−	0.310427i	0.994128	−	0.108209i	$-0.0345117\pi$
$548$	8.52748	−	9.84124i	0.364276	−	0.420397i
$549$	−33.2379	−	12.3602i	−1.41856	−	0.527521i
$550$	6.98148	+	15.2873i	0.297691	+	0.651853i
$551$	11.9776	+	20.7458i	0.510263	+	0.883802i
$552$	−19.5212	+	14.4026i	−0.830878	+	0.613017i
$553$	−4.36288	+	7.55673i	−0.185529	+	0.321345i
$554$	3.76348	+	0.359369i	0.159895	+	0.0152681i
$555$	0.243124	−	6.90164i	0.0103201	−	0.292958i
$556$	12.3987	+	2.38965i	0.525821	+	0.101344i
$557$	−18.7022	−	12.0192i	−0.792438	−	0.509269i	0.0807023	−	0.996738i	$-0.474284\pi$
$557$	−18.7022	−	12.0192i	−0.792438	−	0.509269i	−0.873140	+	0.487469i	$0.837920\pi$
$558$	−15.2905	−	7.40925i	−0.647298	−	0.313658i
$559$	−2.80609	−	19.5168i	−0.118685	−	0.825473i
$560$	−0.0999094	−	0.411832i	−0.00422194	−	0.0174031i
$561$	−7.66659	−	2.14832i	−0.323684	−	0.0907023i
$562$	4.86554	+	3.82630i	0.205240	+	0.161403i
$563$	−24.7238	−	34.7197i	−1.04198	−	1.46326i	−0.879113	−	0.476613i	$-0.841864\pi$
$563$	−24.7238	−	34.7197i	−1.04198	−	1.46326i	−0.162870	−	0.986647i	$-0.552075\pi$
$564$	3.28498	−	14.3124i	0.138323	−	0.602661i
$565$	4.99178	−	1.99841i	0.210006	−	0.0840737i
$566$	−6.78719	+	4.36186i	−0.285287	+	0.183343i
$567$	7.77517	+	4.46881i	0.326527	+	0.187672i
$568$	−3.19793	−	22.2421i	−0.134182	−	0.933258i
$569$	10.2612	−	29.6477i	0.430171	−	1.24290i	−0.496833	−	0.867846i	$-0.665504\pi$
$569$	10.2612	−	29.6477i	0.430171	−	1.24290i	0.927004	−	0.375051i	$-0.122375\pi$
$570$	−9.81566	−	3.78921i	−0.411133	−	0.158713i
$571$	4.10218	+	11.8525i	0.171671	+	0.496011i	0.997713	−	0.0675982i	$-0.0215336\pi$
$571$	4.10218	+	11.8525i	0.171671	+	0.496011i	−0.826042	+	0.563609i	$0.809412\pi$
$572$	7.91677	−	32.6334i	0.331017	−	1.36447i
$573$	7.98007	−	18.0628i	0.333372	−	0.754582i
$574$	2.96291	+	5.13191i	0.123670	+	0.214202i
$575$	3.70359	−	19.6879i	0.154450	−	0.821041i
$576$	16.4887	−	7.07992i	0.687031	−	0.294997i
$577$	−10.0044	−	21.9065i	−0.416488	−	0.911980i	−0.995329	−	0.0965404i	$-0.969222\pi$
$577$	−10.0044	−	21.9065i	−0.416488	−	0.911980i	0.578842	−	0.815440i	$-0.303505\pi$
$578$	−10.7164	−	10.2180i	−0.445742	−	0.425015i
$579$	0.120929	+	0.203588i	0.00502562	+	0.00846083i
$580$	−3.03837	+	1.56639i	−0.126162	+	0.0650408i
$581$	8.82130	−	1.70017i	0.365969	−	0.0705348i
$582$	20.5544	+	3.69808i	0.852007	+	0.153290i
$583$	11.1489	+	45.9563i	0.461739	+	1.90331i
$584$	3.12352	−	2.00736i	0.129252	−	0.0830653i
$585$	13.2699	−	13.2958i	0.548641	−	0.549712i
$586$	3.36022	−	7.35785i	0.138809	−	0.303950i
$587$	−5.10852	+	0.487804i	−0.210851	+	0.0201338i	−0.199947	−	0.979807i	$-0.564077\pi$
$587$	−5.10852	+	0.487804i	−0.210851	+	0.0201338i	−0.0109041	+	0.999941i	$0.503471\pi$
$588$	−9.79957	+	6.47071i	−0.404127	+	0.266848i
$589$	2.07122	+	43.4803i	0.0853432	+	1.79157i
$590$	−2.33053	+	2.22215i	−0.0959463	+	0.0914846i
$591$	6.12738	+	17.0188i	0.252047	+	0.700062i
$592$	−0.674062	+	1.94757i	−0.0277038	+	0.0800448i
$593$	20.9549	+	13.4669i	0.860516	+	0.553020i	0.894838	−	0.446391i	$-0.147291\pi$
$593$	20.9549	+	13.4669i	0.860516	+	0.553020i	−0.0343221	+	0.999411i	$0.510927\pi$
$594$	−16.9016	−	12.3035i	−0.693482	−	0.504817i
$595$	−0.924931	+	0.271584i	−0.0379185	+	0.0111339i
$596$	5.65984	−	7.94814i	0.231836	−	0.325568i
$597$	−20.5907	+	4.23373i	−0.842723	+	0.173275i
$598$	23.2645	−	20.3411i	0.951356	−	0.831808i
$599$	1.63313	−	2.82867i	0.0667280	−	0.115576i	−0.830731	−	0.556674i	$-0.812077\pi$
$599$	1.63313	−	2.82867i	0.0667280	−	0.115576i	0.897459	+	0.441097i	$0.145411\pi$
$600$	−8.53898	+	19.3278i	−0.348603	+	0.789056i
$601$	16.2469	+	15.4914i	0.662726	+	0.631908i	0.944863	−	0.327467i	$-0.106195\pi$
$601$	16.2469	+	15.4914i	0.662726	+	0.631908i	−0.282137	+	0.959374i	$0.591043\pi$
$602$	−1.73983	+	2.00787i	−0.0709103	+	0.0818348i
$603$	−2.95725	+	3.58876i	−0.120429	+	0.146146i
$604$	2.66490	+	3.07546i	0.108433	+	0.125139i
$605$	−5.40211	+	4.24827i	−0.219627	+	0.172717i
$606$	6.25620	−	9.02003i	0.254141	−	0.366414i
$607$	−1.66527	−	34.9584i	−0.0675913	−	1.41892i	−0.736935	−	0.675964i	$-0.763728\pi$
$607$	−1.66527	−	34.9584i	−0.0675913	−	1.41892i	0.669343	−	0.742953i	$-0.266575\pi$
$608$	−30.4714	−	23.9630i	−1.23578	−	0.971827i
$609$	4.21961	+	3.92476i	0.170987	+	0.159039i
$610$	9.96343	−	0.951392i	0.403407	−	0.0385207i
$611$	−7.37959	+	51.3262i	−0.298546	+	2.07643i
$612$	−1.58107	−	3.24671i	−0.0639109	−	0.131240i
$613$	12.1044	+	3.55418i	0.488894	+	0.143552i	0.516883	−	0.856056i	$-0.327092\pi$
$613$	12.1044	+	3.55418i	0.488894	+	0.143552i	−0.0279892	+	0.999608i	$0.508910\pi$
$614$	−12.8782	+	10.1275i	−0.519720	+	0.408712i
$615$	−1.30165	+	9.92438i	−0.0524875	+	0.400190i
$616$	−11.1482	+	5.74731i	−0.449175	+	0.231566i
$617$	3.53648	+	10.2180i	0.142373	+	0.411360i	0.993533	−	0.113547i	$-0.0362213\pi$
$617$	3.53648	+	10.2180i	0.142373	+	0.411360i	−0.851159	+	0.524907i	$0.824100\pi$
$618$	6.02686	−	3.20217i	0.242436	−	0.128810i
$619$	10.5317	−	14.7897i	0.423305	−	0.594448i	−0.546762	−	0.837288i	$-0.684140\pi$
$619$	10.5317	−	14.7897i	0.423305	−	0.594448i	0.970066	+	0.242840i	$0.0780790\pi$
$620$	−6.21161			−0.249464
$621$	8.00952	+	23.5976i	0.321411	+	0.946940i
$622$	4.24511			0.170213
$623$	−8.31282	+	11.6737i	−0.333046	+	0.467698i
$624$	−4.95052	+	2.63030i	−0.198179	+	0.105296i
$625$	−4.36150	−	12.6017i	−0.174460	−	0.504069i
$626$	−4.46151	+	2.30007i	−0.178318	+	0.0919293i
$627$	−6.96485	+	53.1033i	−0.278149	+	2.12074i
$628$	−14.0979	+	11.0867i	−0.562566	+	0.442407i
$629$	4.49814	+	1.32077i	0.179353	+	0.0526627i
$630$	−2.52484	−	0.178106i	−0.100592	−	0.00709592i
$631$	6.10085	−	42.4323i	0.242871	−	1.68920i	−0.394698	−	0.918811i	$-0.629151\pi$
$631$	6.10085	−	42.4323i	0.242871	−	1.68920i	0.637569	−	0.770393i	$-0.279940\pi$
$632$	25.4587	−	2.43101i	1.01269	−	0.0967006i
$633$	−10.3526	−	9.62918i	−0.411478	−	0.382726i
$634$	7.15948	+	5.63028i	0.284339	+	0.223607i
$635$	0.161078	+	3.38144i	0.00639219	+	0.134189i
$636$	−12.2241	+	17.6243i	−0.484715	+	0.698850i
$637$	32.5955	−	25.6334i	1.29148	−	1.01563i
$638$	−8.79721	−	10.1525i	−0.348285	−	0.401942i
$639$	−22.7668	−	3.80561i	−0.900641	−	0.150548i
$640$	3.10255	−	3.58054i	0.122639	−	0.141533i
$641$	23.1607	+	22.0837i	0.914791	+	0.872252i	0.992188	−	0.124749i	$-0.0398124\pi$
$641$	23.1607	+	22.0837i	0.914791	+	0.872252i	−0.0773970	+	0.997000i	$0.524661\pi$
$642$	4.43268	−	10.0333i	0.174944	−	0.395983i
$643$	20.8499	−	36.1131i	0.822240	−	1.42416i	−0.0817698	−	0.996651i	$-0.526057\pi$
$643$	20.8499	−	36.1131i	0.822240	−	1.42416i	0.904010	−	0.427511i	$-0.140609\pi$
$644$	5.34198	+	0.743772i	0.210503	+	0.0293087i
$645$	−4.39567	+	0.903808i	−0.173079	+	0.0355874i
$646$	4.14309	−	5.81816i	0.163008	−	0.228912i
$647$	−10.4509	+	3.06865i	−0.410865	+	0.120641i	−0.480632	−	0.876922i	$-0.659593\pi$
$647$	−10.4509	+	3.06865i	−0.410865	+	0.120641i	0.0697667	+	0.997563i	$0.477775\pi$
$648$	−2.54949	−	26.1603i	−0.100153	−	1.02768i
$649$	13.7893	+	8.86186i	0.541278	+	0.347858i
$650$	8.80362	−	25.4364i	0.345307	−	0.997698i
$651$	3.54723	+	9.85246i	0.139027	+	0.386148i
$652$	−4.06758	+	3.87843i	−0.159299	+	0.151891i
$653$	1.62114	+	34.0320i	0.0634402	+	1.33177i	0.776254	+	0.630421i	$0.217118\pi$
$653$	1.62114	+	34.0320i	0.0634402	+	1.33177i	−0.712813	+	0.701354i	$0.752579\pi$
$654$	3.63036	−	2.39715i	0.141958	−	0.0937359i
$655$	−11.4645	+	1.09473i	−0.447956	+	0.0427746i
$656$	1.24088	−	2.71715i	0.0484482	−	0.106087i
$657$	−0.990737	−	3.68311i	−0.0386523	−	0.143692i
$658$	5.87780	−	3.77743i	0.229141	−	0.147260i
$659$	0.795769	+	3.28021i	0.0309988	+	0.127779i	0.985209	−	0.171360i	$-0.0548160\pi$
$659$	0.795769	+	3.28021i	0.0309988	+	0.127779i	−0.954210	+	0.299138i	$0.903301\pi$
$660$	−7.52189	−	1.35331i	−0.292789	−	0.0526776i
$661$	−36.3912	+	7.01383i	−1.41545	+	0.272806i	−0.838915	−	0.544263i	$-0.816809\pi$
$661$	−36.3912	+	7.01383i	−1.41545	+	0.272806i	−0.576540	+	0.817069i	$0.695597\pi$
$662$	−0.0441590	+	0.0227655i	−0.00171629	+	0.000884807i
$663$	6.51226	+	10.9636i	0.252915	+	0.425793i
$664$	−19.0562	−	18.1700i	−0.739524	−	0.705134i
$665$	2.69375	+	5.89850i	0.104459	+	0.228734i
$666$	9.86134	+	7.36711i	0.382119	+	0.285470i
$667$	1.59320	+	15.9339i	0.0616890	+	0.616962i
$668$	1.42565	+	2.46930i	0.0551600	+	0.0955400i
$669$	3.75816	−	8.50653i	0.145299	−	0.328881i
$670$	0.309429	−	1.27549i	0.0119543	−	0.0492763i
$671$	−16.6632	−	48.1452i	−0.643276	−	1.85862i
$672$	−8.69968	−	3.35840i	−0.335597	−	0.129553i
$673$	14.6510	−	42.3313i	0.564755	−	1.63175i	−0.194460	−	0.980910i	$-0.562295\pi$
$673$	14.6510	−	42.3313i	0.564755	−	1.63175i	0.759214	−	0.650841i	$-0.225583\pi$
$674$	−2.56254	−	17.8229i	−0.0987054	−	0.686511i
$675$	16.2546	+	14.3845i	0.625641	+	0.553659i
$676$	−32.9012	+	21.1443i	−1.26543	+	0.813243i
$677$	15.5421	−	6.22214i	0.597333	−	0.239136i	−0.0532374	−	0.998582i	$-0.516954\pi$
$677$	15.5421	−	6.22214i	0.597333	−	0.239136i	0.650571	+	0.759446i	$0.274530\pi$
$678$	−2.14398	+	9.34117i	−0.0823391	+	0.358745i
$679$	−7.46594	−	10.4844i	−0.286516	−	0.402356i
$680$	2.22087	+	1.74651i	0.0851666	+	0.0669758i
$681$	−28.3533	−	7.94514i	−1.08650	−	0.304459i
$682$	−5.75505	−	23.7226i	−0.220372	−	0.908387i
$683$	−6.07390	−	42.2449i	−0.232411	−	1.61646i	−0.687619	−	0.726071i	$-0.741344\pi$
$683$	−6.07390	−	42.2449i	−0.232411	−	1.61646i	0.455208	−	0.890385i	$-0.349565\pi$
$684$	−20.1041	+	13.6354i	−0.768698	+	0.521363i
$685$	8.80410	+	5.65805i	0.336387	+	0.216183i
$686$	−11.8797	−	2.28963i	−0.453571	−	0.0874186i
$687$	−1.71231	+	48.6079i	−0.0653288	+	1.85451i
$688$	1.33317	+	0.127302i	0.0508267	+	0.00485336i
$689$	37.8696	−	65.5921i	1.44272	−	2.49886i
$690$	−4.93866	−	5.00784i	−0.188011	−	0.190645i
$691$	11.1990	+	19.3972i	0.426030	+	0.737905i	0.996516	−	0.0834022i	$-0.0265786\pi$
$691$	11.1990	+	19.3972i	0.426030	+	0.737905i	−0.570486	+	0.821307i	$0.693245\pi$
$692$	1.05837	+	2.31750i	0.0402330	+	0.0880980i
$693$	2.14895	+	12.7036i	0.0816317	+	0.482568i
$694$	−12.8902	+	14.8761i	−0.489307	+	0.564690i
$695$	−0.482862	+	10.1365i	−0.0183160	+	0.384500i
$696$	2.19643	−	16.7467i	0.0832556	−	0.634780i
$697$	−6.30808	−	2.52537i	−0.238935	−	0.0956553i
$698$	−11.0204	+	10.5080i	−0.417130	+	0.397733i
$699$	14.3293	−	14.0059i	0.541983	−	0.529751i
$700$	4.36128	−	1.74599i	0.164841	−	0.0659923i
$701$	1.22273	−	2.67740i	0.0461819	−	0.101124i	−0.885135	−	0.465335i	$-0.845934\pi$
$701$	1.22273	−	2.67740i	0.0461819	−	0.101124i	0.931317	+	0.364211i	$0.118661\pi$
$702$	5.99312	+	32.9418i	0.226196	+	1.24331i
$703$	4.48797	−	31.2145i	0.169267	−	1.17728i
$704$	22.9146	+	11.8133i	0.863627	+	0.445231i
$705$	11.7613	+	0.976215i	0.442957	+	0.0367664i
$706$	−0.403483	−	0.161530i	−0.0151853	−	0.00607927i
$707$	−6.64304	+	1.28034i	−0.249837	+	0.0481521i
$708$	1.14912	+	7.34518i	0.0431864	+	0.276049i
$709$	−7.42394	−	1.43085i	−0.278812	−	0.0537366i	0.0479282	−	0.998851i	$-0.484738\pi$
$709$	−7.42394	−	1.43085i	−0.278812	−	0.0537366i	−0.326740	+	0.945114i	$0.605950\pi$
$710$	6.25098	−	1.83545i	0.234595	−	0.0688833i
$711$	5.55926	−	25.6760i	0.208489	−	0.962925i
$712$	42.0032			1.57414
$713$	−10.6942	+	27.0618i	−0.400500	+	1.01347i
$714$	0.541821	−	1.63056i	0.0202772	−	0.0610224i
$715$	26.8655	+	2.56534i	1.00471	+	0.0959384i
$716$	−0.368269	+	1.51803i	−0.0137629	+	0.0567313i
$717$	−4.18520	−	7.04595i	−0.156299	−	0.263136i
$718$	−1.12376	+	23.5906i	−0.0419382	+	0.880392i
$719$	29.0662	+	33.5442i	1.08399	+	1.25099i	0.966157	+	0.257955i	$0.0830487\pi$
$719$	29.0662	+	33.5442i	1.08399	+	1.25099i	0.117831	+	0.993034i	$0.462406\pi$
$720$	0.665117	+	1.08880i	0.0247874	+	0.0405773i
$721$	−4.03570	−	1.18499i	−0.150297	−	0.0441313i
$722$	−26.9413	−	13.8892i	−1.00265	−	0.516903i
$723$	−28.3695	+	18.7325i	−1.05507	+	0.696671i
$724$	3.44758	+	4.84144i	0.128128	+	0.179931i
$725$	8.09048	+	11.3615i	0.300473	+	0.421955i
$726$	−0.734385	−	12.2277i	−0.0272556	−	0.453811i
$727$	36.6182	+	18.8780i	1.35809	+	0.700146i	0.974716	−	0.223446i	$-0.0717306\pi$
$727$	36.6182	+	18.8780i	1.35809	+	0.700146i	0.383377	+	0.923592i	$0.374761\pi$
$728$	19.2746	+	5.65952i	0.714363	+	0.209756i
$729$	−26.3996	−	5.66208i	−0.977764	−	0.209707i
$730$	0.704943	+	0.813547i	0.0260911	+	0.0301107i
$731$	0.144953	−	3.04295i	0.00536130	−	0.112547i
$732$	11.3051	−	20.1535i	0.417848	−	0.744894i
$733$	−5.98539	+	24.6721i	−0.221075	+	0.911285i	0.747837	+	0.663882i	$0.231092\pi$
$733$	−5.98539	+	24.6721i	−0.221075	+	0.911285i	−0.968913	+	0.247403i	$0.920423\pi$
$734$	8.78628	+	0.838988i	0.324307	+	0.0309676i
$735$	−6.26832	−	7.05551i	−0.231211	−	0.260246i
$736$	−11.9767	−	22.9795i	−0.441467	−	0.847034i
$737$	−6.68089			−0.246094
$738$	−13.2132	−	11.9881i	−0.486385	−	0.441288i
$739$	−37.5977	+	11.0397i	−1.38305	+	0.406101i	−0.886831	−	0.462094i	$-0.847098\pi$
$739$	−37.5977	+	11.0397i	−1.38305	+	0.406101i	−0.496223	+	0.868195i	$0.665280\pi$
$740$	4.41875	+	0.851644i	0.162436	+	0.0313070i
$741$	66.7652	−	53.8565i	2.45268	−	1.97847i
$742$	−10.0209	+	1.93137i	−0.367879	+	0.0709029i
$743$	35.3234	+	14.1414i	1.29589	+	0.518797i	0.914114	−	0.405458i	$-0.132888\pi$
$743$	35.3234	+	14.1414i	1.29589	+	0.518797i	0.381777	+	0.924254i	$0.375312\pi$
$744$	17.4917	−	25.2191i	0.641277	−	0.924576i
$745$	6.97013	+	3.59335i	0.255366	+	0.131650i
$746$	−1.22136	+	8.49475i	−0.0447172	+	0.311015i
$747$	−23.7262	+	12.9856i	−0.868098	+	0.475116i
$748$	2.15524	−	4.71933i	0.0788035	−	0.172556i
$749$	−6.27586	+	2.51247i	−0.229315	+	0.0918038i
$750$	−12.9598	−	3.63158i	−0.473224	−	0.132607i
$751$	−27.5330	+	26.2527i	−1.00469	+	0.957974i	−0.999117	−	0.0420103i	$-0.986624\pi$
$751$	−27.5330	+	26.2527i	−1.00469	+	0.957974i	−0.00557721	+	0.999984i	$0.501775\pi$
$752$	−3.26969	−	1.30899i	−0.119233	−	0.0477339i
$753$	−21.2449	−	16.2853i	−0.774207	−	0.593471i
$754$	−1.02376	+	21.4913i	−0.0372830	+	0.782666i
$755$	−2.14174	+	2.47170i	−0.0779460	+	0.0899545i
$756$	−3.66009	+	4.55552i	−0.133116	+	0.165683i
$757$	−0.263834	−	0.577715i	−0.00958920	−	0.0209974i	0.904777	−	0.425886i	$-0.140038\pi$
$757$	−0.263834	−	0.577715i	−0.00958920	−	0.0209974i	−0.914366	+	0.404889i	$0.867310\pi$
$758$	5.53300	+	9.58343i	0.200968	+	0.348086i
$759$	−18.8459	+	30.4402i	−0.684063	+	1.10491i
$760$	9.50277	−	16.4593i	0.344702	−	0.597041i
$761$	32.7583	+	3.12804i	1.18749	+	0.113391i	0.670041	−	0.742324i	$-0.266276\pi$
$761$	32.7583	+	3.12804i	1.18749	+	0.113391i	0.517447	+	0.855715i	$0.326882\pi$
$762$	−5.11618	−	3.19912i	−0.185340	−	0.115892i
$763$	−2.63268	−	0.507408i	−0.0953095	−	0.0183694i
$764$	10.8249	+	6.95677i	0.391633	+	0.251687i
$765$	2.40194	−	1.62909i	0.0868422	−	0.0589000i
$766$	−1.46100	−	10.1615i	−0.0527880	−	0.367148i
$767$	−6.18931	−	25.5127i	−0.223483	−	0.921210i
$768$	7.22651	+	28.2557i	0.260764	+	1.01959i
$769$	−2.18339	−	1.71704i	−0.0787352	−	0.0619180i	0.578016	−	0.816026i	$-0.303827\pi$
$769$	−2.18339	−	1.71704i	−0.0787352	−	0.0619180i	−0.656751	+	0.754108i	$0.728070\pi$
$770$	−2.10932	−	2.96213i	−0.0760146	−	0.106748i
$771$	33.7193	+	31.3631i	1.21437	+	1.12951i
$772$	−0.143248	+	0.0573480i	−0.00515562	+	0.00206400i
$773$	−41.3810	+	26.5940i	−1.48837	+	0.956518i	−0.492073	+	0.870554i	$0.663761\pi$
$773$	−41.3810	+	26.5940i	−1.48837	+	0.956518i	−0.996298	+	0.0859643i	$0.972603\pi$
$774$	3.14160	−	7.35614i	0.112923	−	0.264411i
$775$	3.60694	+	25.0868i	0.129565	+	0.901145i
$776$	−12.3383	+	35.6492i	−0.442920	+	1.27973i
$777$	−1.17257	−	7.49508i	−0.0420656	−	0.268884i
$778$	−1.42788	−	4.12558i	−0.0511919	−	0.147909i
$779$	−10.7759	+	44.4188i	−0.386086	+	1.59147i
$780$	7.22321	+	9.88218i	0.258632	+	0.353839i
$781$	−16.5812	−	28.7195i	−0.593323	−	1.02767i
$782$	4.12423	−	2.40570i	0.147482	−	0.0860276i
$783$	−15.7060	−	7.37178i	−0.561287	−	0.263446i
$784$	1.17002	+	2.56199i	0.0417864	+	0.0914995i
$785$	−10.4320	−	9.94687i	−0.372333	−	0.355019i
$786$	10.0429	−	17.9033i	0.358217	−	0.638590i
$787$	6.58998	−	3.39737i	0.234908	−	0.121103i	−0.336754	−	0.941593i	$-0.609329\pi$
$787$	6.58998	−	3.39737i	0.234908	−	0.121103i	0.571662	+	0.820489i	$0.306299\pi$
$788$	−11.5738	+	2.23066i	−0.412298	+	0.0794640i
$789$	23.6997	−	28.0455i	0.843732	−	0.998446i
$790$	1.74809	+	7.20572i	0.0621942	+	0.256368i
$791$	4.96898	−	3.19337i	0.176677	−	0.113543i
$792$	26.6758	−	26.7279i	0.947884	−	0.949734i
$793$	−33.8970	+	74.2240i	−1.20372	+	2.63577i
$794$	−15.6566	+	1.49503i	−0.555633	+	0.0530565i
$795$	−15.4184	−	7.70849i	−0.546833	−	0.273392i
$796$	−0.651783	−	13.6826i	−0.0231018	−	0.484967i
$797$	−8.09654	+	7.72004i	−0.286794	+	0.273458i	−0.819795	−	0.572657i	$-0.805913\pi$
$797$	−8.09654	+	7.72004i	−0.286794	+	0.273458i	0.533001	+	0.846115i	$0.321064\pi$
$798$	−11.3755	−	2.04665i	−0.402690	−	0.0724505i
$799$	−2.62032	+	7.57092i	−0.0927003	+	0.267840i
$800$	−18.9877	−	12.2026i	−0.671315	−	0.431428i
$801$	13.0976	−	41.1110i	0.462780	−	1.45258i
$802$	−34.4241	+	10.1078i	−1.21556	+	0.356920i
$803$	3.17846	−	4.46352i	0.112165	−	0.157514i
$804$	−2.01257	−	2.26532i	−0.0709780	−	0.0798915i
$805$	0.0193214	+	4.33464i	0.000680990	+	0.152776i
$806$	−19.5483	+	33.8586i	−0.688559	+	1.19262i
$807$	30.8499	+	42.2062i	1.08597	+	1.48573i
$808$	14.3506	+	13.6833i	0.504852	+	0.481376i
$809$	26.5406	−	30.6295i	0.933117	−	1.07687i	−0.0637650	−	0.997965i	$-0.520311\pi$
$809$	26.5406	−	30.6295i	0.933117	−	1.07687i	0.996882	−	0.0789092i	$-0.0251437\pi$
$810$	7.40217	−	1.81104i	0.260086	−	0.0636334i
$811$	3.47430	+	4.00956i	0.121999	+	0.140795i	0.813463	−	0.581616i	$-0.197579\pi$
$811$	3.47430	+	4.00956i	0.121999	+	0.140795i	−0.691464	+	0.722411i	$0.743034\pi$
$812$	−2.95173	+	2.32127i	−0.103585	+	0.0814604i
$813$	0.254954	+	0.0211618i	0.00894164	+	0.000742176i
$814$	0.841468	+	17.6646i	0.0294935	+	0.619144i
$815$	−3.55054	−	2.79218i	−0.124370	−	0.0978058i
$816$	−0.827953	+	0.254291i	−0.0289842	+	0.00890195i
$817$	−20.3997	+	1.94794i	−0.713695	+	0.0681496i
$818$	−4.23465	+	29.4527i	−0.148061	+	1.02979i
$819$	11.5496	−	17.1004i	0.403574	−	0.597535i
$820$	−6.25816	−	1.83756i	−0.218544	−	0.0641704i
$821$	13.9451	−	10.9665i	0.486686	−	0.382734i	−0.344449	−	0.938805i	$-0.611934\pi$
$821$	13.9451	−	10.9665i	0.486686	−	0.382734i	0.831135	+	0.556071i	$0.187692\pi$
$822$	−17.2305	+	7.14697i	−0.600984	+	0.249279i
$823$	−0.115546	+	0.0595683i	−0.00402769	+	0.00207642i	−0.460239	−	0.887795i	$-0.652236\pi$
$823$	−0.115546	+	0.0595683i	−0.00402769	+	0.00207642i	0.456211	+	0.889871i	$0.349206\pi$
$824$	4.03199	+	11.6497i	0.140461	+	0.405836i
$825$	−1.09783	+	31.1645i	−0.0382216	+	1.08501i
$826$	−2.05188	+	2.88146i	−0.0713939	+	0.100259i
$827$	−48.4442			−1.68457			−0.842285	−	0.539033i	$-0.818790\pi$
$827$	−48.4442			−1.68457			−0.842285	+	0.539033i	$0.818790\pi$
$828$	−15.9987	+	2.77976i	−0.555994	+	0.0966035i
$829$	−42.0914			−1.46190			−0.730948	−	0.682433i	$-0.760922\pi$
$829$	−42.0914			−1.46190			−0.730948	+	0.682433i	$0.760922\pi$
$830$	4.42808	−	6.21836i	0.153701	−	0.215843i
$831$	5.94787	+	3.71917i	0.206329	+	0.129017i
$832$	−13.5048	−	39.0195i	−0.468194	−	1.35276i
$833$	5.69458	−	2.93576i	0.197306	−	0.101718i
$834$	−14.3557	−	11.0044i	−0.497097	−	0.381051i
$835$	−1.80128	+	1.41654i	−0.0623357	+	0.0490214i
$836$	−33.4861	−	9.83240i	−1.15814	−	0.340061i
$837$	−19.2290	−	24.9840i	−0.664653	−	0.863574i
$838$	−2.69960	+	18.7761i	−0.0932562	+	0.648611i
$839$	−14.0564	+	1.34223i	−0.485282	+	0.0463388i	−0.334830	−	0.942279i	$-0.608679\pi$
$839$	−14.0564	+	1.34223i	−0.485282	+	0.0463388i	−0.150452	+	0.988617i	$0.548073\pi$
$840$	1.02277	−	4.45614i	0.0352890	−	0.153752i
$841$	14.0319	+	11.0348i	0.483857	+	0.380509i
$842$	0.632473	+	13.2772i	0.0217965	+	0.457564i
$843$	4.90022	+	10.3875i	0.168772	+	0.357764i
$844$	7.24190	−	5.69510i	0.249277	−	0.196033i
$845$	−20.5835	−	23.7546i	−0.708094	−	0.817184i
$846$	−13.3775	+	16.2342i	−0.459928	+	0.558144i
$847$	−4.94385	+	5.70551i	−0.169873	+	0.196044i
$848$	3.72310	+	3.54997i	0.127852	+	0.121906i
$849$	−14.8836	+	1.60749i	−0.510804	+	0.0551690i
$850$	2.07935	−	3.60154i	0.0713212	−	0.123532i
$851$	11.3178	−	17.7847i	0.387970	−	0.609651i
$852$	4.74306	−	14.2738i	0.162495	−	0.489014i
$853$	−4.60513	+	6.46700i	−0.157677	+	0.221426i	−0.885855	−	0.463961i	$-0.846428\pi$
$853$	−4.60513	+	6.46700i	−0.157677	+	0.221426i	0.728179	+	0.685387i	$0.240367\pi$
$854$	10.5494	−	3.09758i	0.360992	−	0.105997i
$855$	−13.1465	−	14.4333i	−0.449600	−	0.493609i
$856$	16.6680	+	10.7119i	0.569701	+	0.366125i
$857$	−12.1890	+	35.2178i	−0.416368	+	1.20302i	0.520661	+	0.853764i	$0.325686\pi$
$857$	−12.1890	+	35.2178i	−0.416368	+	1.20302i	−0.937029	+	0.349253i	$0.886435\pi$
$858$	−31.0485	+	36.7418i	−1.05998	+	1.25435i
$859$	15.9956	−	15.2517i	0.545762	−	0.520383i	−0.366267	−	0.930510i	$-0.619364\pi$
$859$	15.9956	−	15.2517i	0.545762	−	0.520383i	0.912028	+	0.410127i	$0.134516\pi$
$860$	−0.139141	−	2.92094i	−0.00474468	−	0.0996031i
$861$	0.659191	+	10.9757i	0.0224652	+	0.374049i
$862$	11.3589	−	1.08465i	0.386887	−	0.0369432i
$863$	13.0269	−	28.5249i	0.443440	−	0.970998i	−0.547514	−	0.836796i	$-0.684426\pi$
$863$	13.0269	−	28.5249i	0.443440	−	0.970998i	0.990954	−	0.134201i	$-0.0428469\pi$
$864$	28.0290	+	1.62856i	0.953567	+	0.0554049i
$865$	−1.72253	+	1.10700i	−0.0585677	+	0.0376392i
$866$	−4.89641	−	20.1833i	−0.166387	−	0.685856i
$867$	−9.30701	−	25.8503i	−0.316083	−	0.877922i
$868$	−6.70022	+	1.29136i	−0.227420	+	0.0438317i
$869$	33.5473	−	17.2948i	1.13801	−	0.586687i
$870$	4.89650	−	0.0606581i	0.166007	−	0.00205650i
$871$	7.74411	+	7.38399i	0.262399	+	0.250197i
$872$	3.26442	+	7.14807i	0.110547	+	0.242064i
$873$	31.0446	+	23.1925i	1.05070	+	0.784947i
$874$	−19.9661	−	25.1574i	−0.675365	−	0.850963i
$875$	4.14738	+	7.18347i	0.140207	+	0.242846i
$876$	2.47095	−	0.266873i	0.0834857	−	0.00901681i
$877$	12.9593	−	53.4191i	0.437605	−	1.80383i	−0.143086	−	0.989710i	$-0.545703\pi$
$877$	12.9593	−	53.4191i	0.437605	−	1.80383i	0.580691	−	0.814124i	$-0.302782\pi$
$878$	8.88124	+	25.6607i	0.299727	+	0.866005i
$879$	11.6820	−	9.42331i	0.394022	−	0.317840i
$880$	−0.599527	+	1.73222i	−0.0202100	+	0.0583931i
$881$	2.97571	+	20.6965i	0.100254	+	0.697284i	0.976515	+	0.215448i	$0.0691210\pi$
$881$	2.97571	+	20.6965i	0.100254	+	0.697284i	−0.876261	+	0.481837i	$0.839970\pi$
$882$	16.7013	−	2.01341i	0.562363	−	0.0677949i
$883$	−7.25419	+	4.66199i	−0.244123	+	0.156888i	−0.656981	−	0.753907i	$-0.728167\pi$
$883$	−7.25419	+	4.66199i	−0.244123	+	0.156888i	0.412858	+	0.910795i	$0.364531\pi$
$884$	−7.71423	+	3.08831i	−0.259458	+	0.103871i
$885$	−5.71169	+	1.75424i	−0.191996	+	0.0589682i
$886$	3.58954	+	5.04080i	0.120593	+	0.169349i
$887$	4.27306	+	3.36037i	0.143475	+	0.112830i	0.687317	−	0.726358i	$-0.258788\pi$
$887$	4.27306	+	3.36037i	0.143475	+	0.112830i	−0.543842	+	0.839188i	$0.683031\pi$
$888$	−15.9007	+	15.5419i	−0.533593	+	0.521551i
$889$	0.876734	+	3.61394i	0.0294047	+	0.121208i
$890$	1.73309	+	12.0539i	0.0580931	+	0.404047i
$891$	−17.8420	−	34.4436i	−0.597729	−	1.15390i
$892$	5.09794	+	3.27624i	0.170692	+	0.109697i
$893$	52.9181	+	10.1991i	1.77084	+	0.341301i
$894$	−12.3435	+	6.55832i	−0.412829	+	0.219343i
$895$	−1.24972	−	0.119334i	−0.0417735	−	0.00398888i
$896$	2.60223	−	4.50719i	0.0869343	−	0.150575i
$897$	55.4889	−	14.4553i	1.85272	−	0.482650i
$898$	−6.87175	−	11.9022i	−0.229313	−	0.397182i
$899$	−8.41592	−	18.4283i	−0.280687	−	0.614618i
$900$	−10.8978	+	9.01584i	−0.363259	+	0.300528i
$901$	7.66310	−	8.84368i	0.255295	−	0.294626i
$902$	1.21962	−	25.6029i	0.0406088	−	0.852483i
$903$	−4.55354	+	1.88874i	−0.151532	+	0.0628534i
$904$	−16.0718	−	6.43419i	−0.534541	−	0.213998i
$905$	−3.45707	+	3.29631i	−0.114917	+	0.109573i
$906$	−1.44443	−	5.64773i	−0.0479880	−	0.187633i
$907$	−41.2007	+	16.4943i	−1.36805	+	0.547683i	−0.935307	−	0.353836i	$-0.884877\pi$
$907$	−41.2007	+	16.4943i	−1.36805	+	0.547683i	−0.432739	+	0.901519i	$0.642453\pi$
$908$	7.97073	−	17.4535i	0.264518	−	0.579214i
$909$	17.8675	−	9.77900i	0.592627	−	0.324349i
$910$	−0.828858	+	5.76484i	−0.0274764	+	0.191102i
$911$	−9.47383	−	4.88410i	−0.313882	−	0.161817i	0.294086	−	0.955779i	$-0.404985\pi$
$911$	−9.47383	−	4.88410i	−0.313882	−	0.161817i	−0.607968	+	0.793962i	$0.708015\pi$
$912$	2.48577	+	5.26934i	0.0823120	+	0.174485i
$913$	−36.0749	−	14.4422i	−1.19391	−	0.477968i
$914$	5.99820	−	1.15606i	0.198403	−	0.0382390i
$915$	17.3252	+	6.68817i	0.572754	+	0.221104i
$916$	−31.1210	−	5.99809i	−1.02827	−	0.198182i
$917$	−12.1388	+	3.56426i	−0.400857	+	0.117702i
$918$	−0.0539944	+	5.17285i	−0.00178208	+	0.170729i
$919$	−14.1788			−0.467717			−0.233858	−	0.972271i	$-0.575135\pi$
$919$	−14.1788			−0.467717			−0.233858	+	0.972271i	$0.575135\pi$
$920$	10.3159	−	7.41546i	0.340106	−	0.244480i
$921$	−29.7765	+	6.12244i	−0.981170	+	0.201741i
$922$	−10.6080	−	1.01294i	−0.349357	−	0.0333596i
$923$	−12.5220	+	51.6163i	−0.412166	+	1.69897i
$924$	−8.39491	+	0.103997i	−0.276172	+	0.00342124i
$925$	0.873666	−	18.3405i	0.0287260	−	0.603032i
$926$	14.8641	+	17.1541i	0.488465	+	0.563719i
$927$	12.6595	−	0.313701i	0.415792	−	0.0103033i
$928$	17.3108	+	5.08291i	0.568255	+	0.166855i
$929$	−21.3670	−	11.0155i	−0.701030	−	0.361406i	0.0705763	−	0.997506i	$-0.477516\pi$
$929$	−21.3670	−	11.0155i	−0.701030	−	0.361406i	−0.771606	+	0.636100i	$0.780546\pi$
$930$	7.95896	+	3.97912i	0.260985	+	0.130481i
$931$	−24.9988	−	35.1059i	−0.819303	−	1.15055i
$932$	7.57368	+	10.6357i	0.248084	+	0.348385i
$933$	7.04539	+	3.52238i	0.230656	+	0.115317i
$934$	−17.0240	−	8.77646i	−0.557041	−	0.287175i
$935$	4.00075	+	1.17473i	0.130839	+	0.0384177i
$936$	−60.4619	+	1.49824i	−1.97626	+	0.0489715i
$937$	26.8579	+	30.9956i	0.877408	+	1.01258i	0.999798	+	0.0201008i	$0.00639872\pi$
$937$	26.8579	+	30.9956i	0.877408	+	1.01258i	−0.122390	+	0.992482i	$0.539056\pi$
$938$	0.0686026	−	1.44015i	0.00223995	−	0.0470224i
$939$	−9.31303	+	0.115370i	−0.303919	+	0.00376496i
$940$	−1.81306	+	7.47354i	−0.0591355	+	0.243760i
$941$	−6.58931	−	0.629202i	−0.214805	−	0.0205114i	−0.0129015	−	0.999917i	$-0.504107\pi$
$941$	−6.58931	−	0.629202i	−0.214805	−	0.0205114i	−0.201904	+	0.979405i	$0.564713\pi$
$942$	25.1657	−	5.17441i	0.819944	−	0.168591i
$943$	−18.7799	+	24.1009i	−0.611558	+	0.784834i
$944$	1.78311			0.0580354
$945$	−4.04256	−	2.39058i	−0.131505	−	0.0777655i
$946$	11.0264	−	3.23764i	0.358498	−	0.105265i
$947$	39.1623	+	7.54792i	1.27260	+	0.245274i	0.780442	−	0.625229i	$-0.214994\pi$
$947$	39.1623	+	7.54792i	1.27260	+	0.245274i	0.492163	+	0.870503i	$0.336206\pi$
$948$	15.9701	+	6.16506i	0.518686	+	0.200232i
$949$	−8.61755	+	1.66090i	−0.279737	+	0.0539150i
$950$	−25.9709	−	10.3972i	−0.842606	−	0.337329i
$951$	7.21051	+	15.2849i	0.233817	+	0.495646i
$952$	2.75866	+	1.42219i	0.0894087	+	0.0460934i
$953$	2.27380	−	15.8146i	0.0736556	−	0.512286i	−0.919278	−	0.393610i	$-0.871226\pi$
$953$	2.27380	−	15.8146i	0.0736556	−	0.512286i	0.992933	−	0.118676i	$-0.0378649\pi$
$954$	26.9528	−	14.7515i	0.872628	−	0.477596i
$955$	−4.29603	+	9.40699i	−0.139016	+	0.304403i
$956$	4.95767	−	1.98475i	0.160342	−	0.0641914i
$957$	−6.17623	−	24.1491i	−0.199649	−	0.780630i
$958$	−20.9009	+	19.9289i	−0.675276	+	0.643874i
$959$	10.6729	+	4.27279i	0.344646	+	0.137976i
$960$	−8.68044	+	3.60051i	−0.280160	+	0.116206i
$961$	0.276605	−	5.80666i	0.00892275	−	0.187312i
$962$	18.5483	−	21.4058i	0.598020	−	0.690151i
$963$	15.6818	−	12.9737i	0.505340	−	0.418073i
$964$	−9.20257	−	20.1508i	−0.296395	−	0.649014i
$965$	−0.0620048	−	0.107396i	−0.00199601	−	0.00345718i
$966$	−6.36824	−	4.37504i	−0.204895	−	0.140765i
$967$	4.85715	−	8.41284i	0.156196	−	0.270539i	−0.777298	−	0.629132i	$-0.783410\pi$
$967$	4.85715	−	8.41284i	0.156196	−	0.270539i	0.933494	+	0.358594i	$0.116744\pi$
$968$	22.0267	+	2.10330i	0.707966	+	0.0676026i
$969$	11.7037	−	6.21838i	0.375977	−	0.199763i
$970$	−10.7395	−	2.06988i	−0.344826	−	0.0664597i
$971$	−12.6937	−	8.15777i	−0.407361	−	0.261795i	0.320875	−	0.947122i	$-0.396023\pi$
$971$	−12.6937	−	8.15777i	−0.407361	−	0.261795i	−0.728236	+	0.685326i	$0.759660\pi$
$972$	6.30414	−	16.4256i	0.202205	−	0.526853i
$973$	1.58649	+	11.0343i	0.0508604	+	0.353742i
$974$	−0.0413068	−	0.170269i	−0.00132355	−	0.00545576i
$975$	35.7168	−	34.9107i	1.14385	−	1.11804i
$976$	−4.35648	−	3.42597i	−0.139447	−	0.109663i
$977$	9.99884	+	14.0414i	0.319891	+	0.449224i	0.942942	−	0.332957i	$-0.108046\pi$
$977$	9.99884	+	14.0414i	0.319891	+	0.449224i	−0.623051	+	0.782181i	$0.714107\pi$
$978$	7.69631	−	2.36378i	0.246101	−	0.0755854i
$979$	57.5480	−	23.0388i	1.83924	−	0.736322i
$980$	5.17363	−	3.32489i	0.165265	−	0.106210i
$981$	8.01415	−	0.966135i	0.255872	−	0.0308463i
$982$	1.41431	+	9.83673i	0.0451324	+	0.313903i
$983$	−18.8388	+	54.4311i	−0.600864	+	1.73608i	0.0731048	+	0.997324i	$0.476709\pi$
$983$	−18.8388	+	54.4311i	−0.600864	+	1.73608i	−0.673969	+	0.738759i	$0.735412\pi$
$984$	25.0832	−	20.2335i	0.799625	−	0.645021i
$985$	−3.09827	−	8.95185i	−0.0987190	−	0.285230i
$986$	−0.783713	+	3.23051i	−0.0249585	+	0.102880i
$987$	12.8894	−	1.39211i	0.410275	−	0.0443114i
$988$	27.9480	+	48.4074i	0.889144	+	1.54004i
$989$	−12.9650	−	4.42263i	−0.412264	−	0.140631i
$990$	8.77090	+	6.55248i	0.278758	+	0.208252i
$991$	25.1194	+	55.0037i	0.797943	+	1.74725i	0.652366	+	0.757904i	$0.273776\pi$
$991$	25.1194	+	55.0037i	0.797943	+	1.74725i	0.145577	+	0.989347i	$0.453496\pi$
$992$	23.7268	+	22.6235i	0.753326	+	0.718295i
$993$	−0.0921781	+	0.00114191i	−0.00292518	+	3.62373e-5i
$994$	6.36111	−	3.27938i	0.201762	−	0.104016i
$995$	10.8100	−	2.08346i	0.342701	−	0.0660502i
$996$	−5.97035	−	16.5827i	−0.189178	−	0.525443i
$997$	−4.27637	−	17.6275i	−0.135434	−	0.558267i	−0.998578	−	0.0533091i	$-0.983023\pi$
$997$	−4.27637	−	17.6275i	−0.135434	−	0.558267i	0.863144	−	0.504958i	$-0.168492\pi$
$998$	21.3311	−	13.7087i	0.675225	−	0.433941i
$999$	10.2535	+	20.4093i	0.324406	+	0.645721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.m.a.4.14	✓	440
3.2	odd	2		621.2.q.a.280.9		440
9.2	odd	6		621.2.q.a.73.14		440
9.7	even	3	inner	207.2.m.a.142.9	yes	440
23.6	even	11	inner	207.2.m.a.121.9	yes	440
69.29	odd	22		621.2.q.a.604.14		440
207.29	odd	66		621.2.q.a.397.9		440
207.52	even	33	inner	207.2.m.a.52.14	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.m.a.4.14	✓	440	1.1	even	1	trivial
207.2.m.a.52.14	yes	440	207.52	even	33	inner
207.2.m.a.121.9	yes	440	23.6	even	11	inner
207.2.m.a.142.9	yes	440	9.7	even	3	inner
621.2.q.a.73.14		440	9.2	odd	6
621.2.q.a.280.9		440	3.2	odd	2
621.2.q.a.397.9		440	207.29	odd	66
621.2.q.a.604.14		440	69.29	odd	22

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.541462 - 0.760376i) q^{2} +(1.52956 - 0.812681i) q^{3} +(0.369144 + 1.06657i) q^{4} +(-0.806242 + 0.415647i) q^{5} +(0.210254 - 1.60308i) q^{6} +(-0.783251 + 0.615955i) q^{7} +(2.80218 + 0.822793i) q^{8} +(1.67910 - 2.48609i) q^{9} +(-0.120501 + 0.838104i) q^{10} +(4.29053 - 0.409696i) q^{11} +(1.43141 + 1.33139i) q^{12} +(-5.42615 - 4.26717i) q^{13} +(0.0442576 + 0.929082i) q^{14} +(-0.895406 + 1.29097i) q^{15} +(0.368550 - 0.289831i) q^{16} +(-0.698431 - 0.806032i) q^{17} +(-0.981193 - 2.62287i) q^{18} +(-4.69820 + 5.42201i) q^{19} +(-0.740937 - 0.706482i) q^{20} +(-0.697453 + 1.57867i) q^{21} +(2.01163 - 3.48425i) q^{22} +(-4.35352 + 2.01169i) q^{23} +(4.95476 - 1.01876i) q^{24} +(-2.42302 + 3.40266i) q^{25} +(-6.18271 + 1.81541i) q^{26} +(0.547888 - 5.16719i) q^{27} +(-0.946094 - 0.608017i) q^{28} +(1.09208 - 3.15536i) q^{29} +(0.496797 + 1.37986i) q^{30} +(4.39118 - 4.18698i) q^{31} +(0.257099 + 5.39717i) q^{32} +(6.22966 - 4.11348i) q^{33} +(-0.991061 + 0.0946349i) q^{34} +(0.375470 - 0.822165i) q^{35} +(3.27142 + 0.873157i) q^{36} +(-3.69780 + 2.37643i) q^{37} +(1.57888 + 6.50821i) q^{38} +(-11.7675 - 2.11716i) q^{39} +(-2.60122 + 0.501345i) q^{40} +(5.66270 - 2.91933i) q^{41} +(0.822742 + 1.38512i) q^{42} +(2.06724 + 1.97111i) q^{43} +(2.02079 + 4.42492i) q^{44} +(-0.320428 + 2.70230i) q^{45} +(-0.827624 + 4.39956i) q^{46} +(-3.75588 - 6.50538i) q^{47} +(0.328179 - 0.742828i) q^{48} +(-1.41623 + 5.83779i) q^{49} +(1.27533 + 3.68482i) q^{50} +(-1.72334 - 0.665272i) q^{51} +(2.54821 - 7.36258i) q^{52} +(1.56146 + 10.8602i) q^{53} +(-3.63235 - 3.21443i) q^{54} +(-3.28891 + 2.11366i) q^{55} +(-2.70161 + 1.08156i) q^{56} +(-2.77981 + 12.1114i) q^{57} +(-1.80794 - 2.53890i) q^{58} +(2.98941 + 2.35090i) q^{59} +(-1.70745 - 0.478460i) q^{60} +(-2.78681 - 11.4874i) q^{61} +(-0.806026 - 5.60604i) q^{62} +(0.216161 + 2.98148i) q^{63} +(5.03195 + 3.23384i) q^{64} +(6.14842 + 1.18501i) q^{65} +(0.245327 - 6.96418i) q^{66} +(-1.54306 - 0.147344i) q^{67} +(0.601870 - 1.04247i) q^{68} +(-5.02410 + 6.61501i) q^{69} +(-0.421852 - 0.730669i) q^{70} +(-3.19630 - 6.99892i) q^{71} +(6.75067 - 5.58490i) q^{72} +(0.832555 - 0.960819i) q^{73} +(-0.195234 + 4.09847i) q^{74} +(-0.940879 + 7.17371i) q^{75} +(-7.51728 - 3.00947i) q^{76} +(-3.10821 + 2.96367i) q^{77} +(-7.98147 + 7.80134i) q^{78} +(8.12970 - 3.25464i) q^{79} +(-0.176673 + 0.386861i) q^{80} +(-3.36125 - 8.34877i) q^{81} +(0.846350 - 5.88649i) q^{82} +(-8.01355 - 4.13127i) q^{83} +(-1.94123 - 0.161126i) q^{84} +(0.898129 + 0.359556i) q^{85} +(2.61812 - 0.504601i) q^{86} +(-0.893900 - 5.71383i) q^{87} +(12.3599 + 2.38218i) q^{88} +(13.7997 - 4.05196i) q^{89} +(1.88127 + 1.70684i) q^{90} +6.87842 q^{91} +(-3.75268 - 3.90074i) q^{92} +(3.31389 - 9.97286i) q^{93} +(-6.98020 - 0.666529i) q^{94} +(1.53425 - 6.32425i) q^{95} +(4.77942 + 8.04634i) q^{96} +(-0.614620 + 12.9025i) q^{97} +(3.67208 + 4.23781i) q^{98} +(6.18569 - 11.3545i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 9 q^{2} - 20 q^{3} + 11 q^{4} - 11 q^{5} - 17 q^{6} - 9 q^{7} - 50 q^{8} - 24 q^{9} - 44 q^{10} - 17 q^{11} - 30 q^{12} - 9 q^{13} - 21 q^{14} - 34 q^{15} + 11 q^{16} - 20 q^{17} + 3 q^{18} - 36 q^{19}+ \cdots - 220 q^{99}+O(q^{100}) \) 440 * q - 9 * q^2 - 20 * q^3 + 11 * q^4 - 11 * q^5 - 17 * q^6 - 9 * q^7 - 50 * q^8 - 24 * q^9 - 44 * q^10 - 17 * q^11 - 30 * q^12 - 9 * q^13 - 21 * q^14 - 34 * q^15 + 11 * q^16 - 20 * q^17 + 3 * q^18 - 36 * q^19 - 25 * q^20 + 3 * q^21 - 28 * q^22 - 5 * q^23 - 172 * q^24 + 11 * q^25 - 48 * q^26 + 31 * q^27 - 60 * q^28 + 9 * q^29 + 12 * q^30 - 3 * q^31 - 3 * q^32 - 44 * q^33 - 17 * q^34 - 56 * q^35 + 47 * q^36 - 48 * q^37 + 3 * q^38 - 64 * q^39 + 55 * q^40 - 9 * q^41 - 80 * q^42 - 9 * q^43 + 24 * q^44 - 56 * q^45 - 44 * q^46 - 12 * q^47 + 4 * q^48 - 53 * q^49 + 27 * q^50 + 14 * q^51 - 12 * q^52 - 84 * q^53 - 18 * q^54 - 68 * q^55 - 125 * q^56 + 27 * q^57 - 8 * q^58 + 81 * q^59 + 88 * q^60 + 3 * q^61 + 58 * q^62 + 43 * q^63 - 70 * q^64 - 84 * q^65 + 35 * q^66 - 3 * q^67 + 194 * q^68 + 33 * q^69 - 10 * q^70 + 86 * q^71 + 182 * q^72 - 36 * q^73 - 57 * q^74 + 55 * q^75 - 21 * q^76 + 91 * q^77 + 191 * q^78 - 9 * q^79 + 220 * q^80 - 228 * q^81 - 62 * q^82 - 68 * q^83 + 144 * q^84 + q^85 - 53 * q^86 + 160 * q^87 + 83 * q^88 - 28 * q^89 - 314 * q^90 - 108 * q^91 + q^92 + 132 * q^93 + 48 * q^94 - 3 * q^95 + 174 * q^96 - 36 * q^97 - 156 * q^98 - 220 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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