LMFDB - Embedded newform 380.2.bb.a.219.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(59,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 1]))

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

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

chi := DirichletCharacter("380.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bb (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			219.15
Character	$\chi$	$=$	380.219
Dual form			380.2.bb.a.59.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.934972 - 1.06105i) q^{2} +(-0.912584 - 1.08758i) q^{3} +(-0.251654 + 1.98410i) q^{4} +(1.86792 - 1.22918i) q^{5} +(-0.300731 + 1.98515i) q^{6} +(-0.869878 + 1.50667i) q^{7} +(2.34052 - 1.58806i) q^{8} +(0.170934 - 0.969416i) q^{9} +(-3.05067 - 0.832706i) q^{10} +(1.98923 - 1.14848i) q^{11} +(2.38752 - 1.53697i) q^{12} +(-1.18014 - 0.990257i) q^{13} +(2.41197 - 0.485713i) q^{14} +(-3.04146 - 0.909772i) q^{15} +(-3.87334 - 0.998616i) q^{16} +(5.38638 - 0.949765i) q^{17} +(-1.18842 + 0.725008i) q^{18} +(-0.368312 - 4.34331i) q^{19} +(1.96875 + 4.01547i) q^{20} +(2.43246 - 0.428908i) q^{21} +(-3.07847 - 1.03687i) q^{22} +(-2.44934 + 0.891488i) q^{23} +(-3.86306 - 1.09625i) q^{24} +(1.97824 - 4.59201i) q^{25} +(0.0526880 + 2.17805i) q^{26} +(-4.89887 + 2.82836i) q^{27} +(-2.77049 - 2.10509i) q^{28} +(-8.70033 - 1.53410i) q^{29} +(1.87836 + 4.07775i) q^{30} +(2.00781 - 3.47763i) q^{31} +(2.56188 + 5.04349i) q^{32} +(-3.06440 - 1.11535i) q^{33} +(-6.04387 - 4.82722i) q^{34} +(0.227110 + 3.88358i) q^{35} +(1.88041 + 0.583109i) q^{36} -5.47065 q^{37} +(-4.26411 + 4.45167i) q^{38} +2.18719i q^{39} +(2.41989 - 5.84330i) q^{40} +(3.48030 + 4.14766i) q^{41} +(-2.72937 - 2.17994i) q^{42} +(-2.41969 - 0.880695i) q^{43} +(1.77811 + 4.23585i) q^{44} +(-0.872295 - 2.02090i) q^{45} +(3.23598 + 1.76536i) q^{46} +(1.38336 - 7.84540i) q^{47} +(2.44868 + 5.12387i) q^{48} +(1.98662 + 3.44093i) q^{49} +(-6.72195 + 2.19440i) q^{50} +(-5.94847 - 4.99136i) q^{51} +(2.26176 - 2.09232i) q^{52} +(-1.36045 + 0.495162i) q^{53} +(7.58134 + 2.55350i) q^{54} +(2.30402 - 4.59038i) q^{55} +(0.356724 + 4.90783i) q^{56} +(-4.38756 + 4.36420i) q^{57} +(6.50680 + 10.6658i) q^{58} +(-1.46082 - 8.28470i) q^{59} +(2.57048 - 5.80562i) q^{60} +(6.17019 - 2.24577i) q^{61} +(-5.56719 + 1.12110i) q^{62} +(1.31190 + 1.10082i) q^{63} +(2.95610 - 7.43381i) q^{64} +(-3.42161 - 0.399112i) q^{65} +(1.68168 + 4.29430i) q^{66} +(10.5222 + 1.85535i) q^{67} +(0.528926 + 10.9262i) q^{68} +(3.20479 + 1.85029i) q^{69} +(3.90833 - 3.87201i) q^{70} +(5.69952 + 2.07445i) q^{71} +(-1.13942 - 2.54040i) q^{72} +(4.66799 + 5.56309i) q^{73} +(5.11490 + 5.80463i) q^{74} +(-6.79946 + 2.03912i) q^{75} +(8.71027 + 0.362242i) q^{76} +3.99615i q^{77} +(2.32071 - 2.04496i) q^{78} +(0.266652 - 0.223748i) q^{79} +(-8.46256 + 2.89570i) q^{80} +(4.77166 + 1.73674i) q^{81} +(1.14689 - 7.57072i) q^{82} +(3.33647 - 5.77894i) q^{83} +(0.238860 + 4.93418i) q^{84} +(8.89389 - 8.39491i) q^{85} +(1.32788 + 3.39084i) q^{86} +(6.27133 + 10.8623i) q^{87} +(2.83197 - 5.84707i) q^{88} +(-6.63725 + 7.90997i) q^{89} +(-1.32870 + 2.81503i) q^{90} +(2.51857 - 0.916685i) q^{91} +(-1.15242 - 5.08410i) q^{92} +(-5.61448 + 0.989985i) q^{93} +(-9.61776 + 5.86742i) q^{94} +(-6.02669 - 7.66023i) q^{95} +(3.14724 - 7.38884i) q^{96} +(-0.978133 - 5.54727i) q^{97} +(1.79356 - 5.32509i) q^{98} +(-0.773329 - 2.12470i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40}+ \cdots + 24 q^{96}+O(q^{100}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$	$-1$

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 $

$2$	−0.934972	−	1.06105i	−0.661125	−	0.750276i
$2$	−0.934972	−	1.06105i	−0.661125	−	0.750276i
$3$	−0.912584	−	1.08758i	−0.526881	−	0.627912i	0.435313	−	0.900279i	$-0.356638\pi$
$3$	−0.912584	−	1.08758i	−0.526881	−	0.627912i	−0.962193	+	0.272368i	$0.912193\pi$
$4$	−0.251654	+	1.98410i	−0.125827	+	0.992052i
$5$	1.86792	−	1.22918i	0.835358	−	0.549706i
$5$	1.86792	−	1.22918i	0.835358	−	0.549706i
$6$	−0.300731	+	1.98515i	−0.122773	+	0.810434i
$7$	−0.869878	+	1.50667i	−0.328783	+	0.569469i	−0.982271	−	0.187468i	$-0.939972\pi$
$7$	−0.869878	+	1.50667i	−0.328783	+	0.569469i	0.653488	+	0.756937i	$0.273305\pi$
$8$	2.34052	−	1.58806i	0.827500	−	0.561466i
$9$	0.170934	−	0.969416i	0.0569781	−	0.323139i
$10$	−3.05067	−	0.832706i	−0.964707	−	0.263325i
$11$	1.98923	−	1.14848i	0.599775	−	0.346280i	−0.169178	−	0.985585i	$-0.554111\pi$
$11$	1.98923	−	1.14848i	0.599775	−	0.346280i	0.768953	+	0.639305i	$0.220778\pi$
$12$	2.38752	−	1.53697i	0.689217	−	0.443685i
$13$	−1.18014	−	0.990257i	−0.327312	−	0.274648i	0.464291	−	0.885683i	$-0.346309\pi$
$13$	−1.18014	−	0.990257i	−0.327312	−	0.274648i	−0.791604	+	0.611035i	$0.790754\pi$
$14$	2.41197	−	0.485713i	0.644625	−	0.129812i
$15$	−3.04146	−	0.909772i	−0.785301	−	0.234902i
$16$	−3.87334	−	0.998616i	−0.968335	−	0.249654i
$17$	5.38638	−	0.949765i	1.30639	−	0.230352i	0.523240	−	0.852185i	$-0.324723\pi$
$17$	5.38638	−	0.949765i	1.30639	−	0.230352i	0.783149	+	0.621834i	$0.213612\pi$
$18$	−1.18842	+	0.725008i	−0.280113	+	0.170886i
$19$	−0.368312	−	4.34331i	−0.0844966	−	0.996424i
$19$	−0.368312	−	4.34331i	−0.0844966	−	0.996424i
$20$	1.96875	+	4.01547i	0.440226	+	0.897887i
$21$	2.43246	−	0.428908i	0.530806	−	0.0935953i
$22$	−3.07847	−	1.03687i	−0.656331	−	0.221062i
$23$	−2.44934	+	0.891488i	−0.510723	+	0.185888i	−0.584511	−	0.811386i	$-0.698714\pi$
$23$	−2.44934	+	0.891488i	−0.510723	+	0.185888i	0.0737875	+	0.997274i	$0.476491\pi$
$24$	−3.86306	−	1.09625i	−0.788545	−	0.223772i
$25$	1.97824	−	4.59201i	0.395647	−	0.918403i
$26$	0.0526880	+	2.17805i	0.0103330	+	0.427151i
$27$	−4.89887	+	2.82836i	−0.942788	+	0.544319i
$28$	−2.77049	−	2.10509i	−0.523573	−	0.397825i
$29$	−8.70033	−	1.53410i	−1.61561	−	0.284876i	−0.708482	−	0.705729i	$-0.750620\pi$
$29$	−8.70033	−	1.53410i	−1.61561	−	0.284876i	−0.907129	+	0.420854i	$0.861731\pi$
$30$	1.87836	+	4.07775i	0.342941	+	0.744492i
$31$	2.00781	−	3.47763i	0.360614	−	0.624601i	−0.627448	−	0.778658i	$-0.715901\pi$
$31$	2.00781	−	3.47763i	0.360614	−	0.624601i	0.988062	+	0.154057i	$0.0492340\pi$
$32$	2.56188	+	5.04349i	0.452881	+	0.891571i
$33$	−3.06440	−	1.11535i	−0.533443	−	0.194157i
$34$	−6.04387	−	4.82722i	−1.03651	−	0.827861i
$35$	0.227110	+	3.88358i	0.0383887	+	0.656444i
$36$	1.88041	+	0.583109i	0.313401	+	0.0971849i
$37$	−5.47065			−0.899369			−0.449685	−	0.893187i	$-0.648464\pi$
$37$	−5.47065			−0.899369			−0.449685	+	0.893187i	$0.648464\pi$
$38$	−4.26411	+	4.45167i	−0.691730	+	0.722157i
$39$			2.18719i			0.350230i
$40$	2.41989	−	5.84330i	0.382618	−	0.923907i
$41$	3.48030	+	4.14766i	0.543532	+	0.647756i	0.965976	−	0.258633i	$-0.0832721\pi$
$41$	3.48030	+	4.14766i	0.543532	+	0.647756i	−0.422444	+	0.906389i	$0.638828\pi$
$42$	−2.72937	−	2.17994i	−0.421151	−	0.336372i
$43$	−2.41969	−	0.880695i	−0.368999	−	0.134305i	0.150864	−	0.988555i	$-0.451795\pi$
$43$	−2.41969	−	0.880695i	−0.368999	−	0.134305i	−0.519863	+	0.854250i	$0.674017\pi$
$44$	1.77811	+	4.23585i	0.268060	+	0.638579i
$45$	−0.872295	−	2.02090i	−0.130034	−	0.301258i
$46$	3.23598	+	1.76536i	0.477119	+	0.260288i
$47$	1.38336	−	7.84540i	0.201783	−	1.14437i	−0.700639	−	0.713516i	$-0.747102\pi$
$47$	1.38336	−	7.84540i	0.201783	−	1.14437i	0.902422	−	0.430853i	$-0.141787\pi$
$48$	2.44868	+	5.12387i	0.353436	+	0.739567i
$49$	1.98662	+	3.44093i	0.283803	+	0.491562i
$50$	−6.72195	+	2.19440i	−0.950627	+	0.310335i
$51$	−5.94847	−	4.99136i	−0.832952	−	0.698930i
$52$	2.26176	−	2.09232i	0.313650	−	0.290153i
$53$	−1.36045	+	0.495162i	−0.186872	+	0.0680157i	−0.433761	−	0.901028i	$-0.642814\pi$
$53$	−1.36045	+	0.495162i	−0.186872	+	0.0680157i	0.246889	+	0.969044i	$0.420592\pi$
$54$	7.58134	+	2.55350i	1.03169	+	0.347488i
$55$	2.30402	−	4.59038i	0.310675	−	0.618967i
$56$	0.356724	+	4.90783i	0.0476692	+	0.655836i
$57$	−4.38756	+	4.36420i	−0.581147	+	0.578053i
$58$	6.50680	+	10.6658i	0.854385	+	1.40049i
$59$	−1.46082	−	8.28470i	−0.190182	−	1.07858i	−0.919114	−	0.393991i	$-0.871094\pi$
$59$	−1.46082	−	8.28470i	−0.190182	−	1.07858i	0.728932	−	0.684586i	$-0.240017\pi$
$60$	2.57048	−	5.80562i	0.331847	−	0.749502i
$61$	6.17019	−	2.24577i	0.790012	−	0.287541i	0.0846712	−	0.996409i	$-0.473016\pi$
$61$	6.17019	−	2.24577i	0.790012	−	0.287541i	0.705341	+	0.708868i	$0.250794\pi$
$62$	−5.56719	+	1.12110i	−0.707034	+	0.142380i
$63$	1.31190	+	1.10082i	0.165284	+	0.138690i
$64$	2.95610	−	7.43381i	0.369513	−	0.929226i
$65$	−3.42161	−	0.399112i	−0.424399	−	0.0495038i
$66$	1.68168	+	4.29430i	0.207001	+	0.528591i
$67$	10.5222	+	1.85535i	1.28549	+	0.226667i	0.774310	−	0.632807i	$-0.218097\pi$
$67$	10.5222	+	1.85535i	1.28549	+	0.226667i	0.511180	+	0.859474i	$0.329208\pi$
$68$	0.528926	+	10.9262i	0.0641417	+	1.32499i
$69$	3.20479	+	1.85029i	0.385812	+	0.222748i
$70$	3.90833	−	3.87201i	0.467135	−	0.462794i
$71$	5.69952	+	2.07445i	0.676408	+	0.246192i	0.657304	−	0.753625i	$-0.271697\pi$
$71$	5.69952	+	2.07445i	0.676408	+	0.246192i	0.0191036	+	0.999818i	$0.493919\pi$
$72$	−1.13942	−	2.54040i	−0.134282	−	0.299389i
$73$	4.66799	+	5.56309i	0.546347	+	0.651111i	0.966598	−	0.256297i	$-0.0825025\pi$
$73$	4.66799	+	5.56309i	0.546347	+	0.651111i	−0.420251	+	0.907408i	$0.638058\pi$
$74$	5.11490	+	5.80463i	0.594596	+	0.674775i
$75$	−6.79946	+	2.03912i	−0.785135	+	0.235457i
$76$	8.71027	+	0.362242i	0.999136	+	0.0415520i
$77$			3.99615i			0.455404i
$78$	2.32071	−	2.04496i	0.262769	−	0.231546i
$79$	0.266652	−	0.223748i	0.0300007	−	0.0251736i	−0.627664	−	0.778484i	$-0.715989\pi$
$79$	0.266652	−	0.223748i	0.0300007	−	0.0251736i	0.657665	+	0.753311i	$0.271544\pi$
$80$	−8.46256	+	2.89570i	−0.946143	+	0.323749i
$81$	4.77166	+	1.73674i	0.530185	+	0.192972i
$82$	1.14689	−	7.57072i	0.126653	−	0.836046i
$83$	3.33647	−	5.77894i	0.366225	−	0.634321i	−0.622747	−	0.782424i	$-0.713983\pi$
$83$	3.33647	−	5.77894i	0.366225	−	0.634321i	0.988972	+	0.148103i	$0.0473166\pi$
$84$	0.238860	+	4.93418i	0.0260617	+	0.538364i
$85$	8.89389	−	8.39491i	0.964678	−	0.910556i
$86$	1.32788	+	3.39084i	0.143189	+	0.365643i
$87$	6.27133	+	10.8623i	0.672357	+	1.16456i
$88$	2.83197	−	5.84707i	0.301889	−	0.623299i
$89$	−6.63725	+	7.90997i	−0.703547	+	0.838455i	−0.992923	−	0.118761i	$-0.962108\pi$
$89$	−6.63725	+	7.90997i	−0.703547	+	0.838455i	0.289376	+	0.957216i	$0.406552\pi$
$90$	−1.32870	+	2.81503i	−0.140058	+	0.296731i
$91$	2.51857	−	0.916685i	0.264018	−	0.0960947i
$92$	−1.15242	−	5.08410i	−0.120148	−	0.530054i
$93$	−5.61448	+	0.989985i	−0.582195	+	0.102657i
$94$	−9.61776	+	5.86742i	−0.991997	+	0.605178i
$95$	−6.02669	−	7.66023i	−0.618325	−	0.785923i
$96$	3.14724	−	7.38884i	0.321213	−	0.754121i
$97$	−0.978133	−	5.54727i	−0.0993143	−	0.563240i	−0.993340	−	0.115223i	$-0.963242\pi$
$97$	−0.978133	−	5.54727i	−0.0993143	−	0.563240i	0.894025	−	0.448016i	$-0.147869\pi$
$98$	1.79356	−	5.32509i	0.181177	−	0.537915i
$99$	−0.773329	−	2.12470i	−0.0777225	−	0.213541i
$100$	8.61320	+	5.08063i	0.861320	+	0.508063i
$101$	10.3394	+	8.67578i	1.02881	+	0.863272i	0.990709	−	0.136002i	$-0.0434252\pi$
$101$	10.3394	+	8.67578i	1.02881	+	0.863272i	0.0380993	+	0.999274i	$0.487870\pi$
$102$	0.265572	+	10.9784i	0.0262956	+	1.08702i
$103$	−9.07941	+	5.24200i	−0.894621	+	0.516510i	−0.875451	−	0.483307i	$-0.839436\pi$
$103$	−9.07941	+	5.24200i	−0.894621	+	0.516510i	−0.0191697	+	0.999816i	$0.506102\pi$
$104$	−4.33474	−	0.443577i	−0.425056	−	0.0434963i
$105$	4.01643	−	3.79109i	0.391963	−	0.369973i
$106$	1.79737	+	0.980539i	0.174576	+	0.0952383i
$107$	15.0503	+	8.68929i	1.45497	+	0.840025i	0.998757	−	0.0498476i	$-0.0158736\pi$
$107$	15.0503	+	8.68929i	1.45497	+	0.840025i	0.456209	+	0.889873i	$0.349207\pi$
$108$	−4.37895	−	10.4316i	−0.421364	−	1.00378i
$109$	5.32472	−	14.6295i	0.510016	−	1.40126i	−0.371205	−	0.928551i	$-0.621055\pi$
$109$	5.32472	−	14.6295i	0.510016	−	1.40126i	0.881220	−	0.472706i	$-0.156723\pi$
$110$	−7.02483	+	1.84720i	−0.669791	+	0.176123i
$111$	4.99243	+	5.94974i	0.473860	+	0.564724i
$112$	4.87392	−	4.96718i	0.460542	−	0.469355i
$113$	2.72712			0.256546			0.128273	−	0.991739i	$-0.459057\pi$
$113$	2.72712			0.256546			0.128273	+	0.991739i	$0.459057\pi$
$114$	8.73288	+	0.575013i	0.817909	+	0.0538549i
$115$	−3.47937	+	4.67591i	−0.324453	+	0.436031i
$116$	5.23329	−	16.8763i	0.485899	−	1.56692i
$117$	−1.16170	+	0.974780i	−0.107399	+	0.0901185i
$118$	−7.42466	+	9.29596i	−0.683495	+	0.855763i
$119$	−3.25451	+	8.94170i	−0.298341	+	0.819684i
$120$	−8.56338	+	2.70069i	−0.781726	+	0.246538i
$121$	−2.86198	+	4.95710i	−0.260180	+	0.450646i
$122$	−8.15183	−	4.44715i	−0.738032	−	0.402626i
$123$	1.33483	−	7.57018i	0.120357	−	0.682580i
$124$	6.39471	+	4.85887i	0.574262	+	0.436339i
$125$	−1.94923	−	11.0091i	−0.174344	−	0.984685i
$126$	−0.0585705	−	2.42123i	−0.00521787	−	0.215700i
$127$	4.85178	−	5.78213i	0.430526	−	0.513081i	−0.506548	−	0.862212i	$-0.669079\pi$
$127$	4.85178	−	5.78213i	0.430526	−	0.513081i	0.937074	+	0.349131i	$0.113523\pi$
$128$	−10.6515	+	3.81383i	−0.941470	+	0.337098i
$129$	1.25035	+	3.43530i	0.110087	+	0.302461i
$130$	2.77563	+	4.00366i	0.243439	+	0.351144i
$131$	5.19250	−	0.915578i	0.453671	−	0.0799944i	0.0578563	−	0.998325i	$-0.481573\pi$
$131$	5.19250	−	0.915578i	0.453671	−	0.0799944i	0.395814	+	0.918331i	$0.370462\pi$
$132$	2.98414	−	5.79940i	0.259736	−	0.504773i
$133$	6.86434	+	3.22322i	0.595213	+	0.279489i
$134$	−7.86934	−	12.8993i	−0.679807	−	1.11433i
$135$	−5.67412	+	11.3047i	−0.488350	+	0.972957i
$136$	11.0987	−	10.7769i	0.951703	−	0.924109i
$137$	6.37941	+	17.5273i	0.545030	+	1.49746i	0.840342	+	0.542057i	$0.182354\pi$
$137$	6.37941	+	17.5273i	0.545030	+	1.49746i	−0.295312	+	0.955401i	$0.595424\pi$
$138$	−1.03314	−	5.13041i	−0.0879470	−	0.436730i
$139$	−9.72900	+	11.5946i	−0.825203	+	0.983439i	−0.999999	−	0.00116587i	$-0.999629\pi$
$139$	−9.72900	+	11.5946i	−0.825203	+	0.983439i	0.174796	+	0.984605i	$0.444073\pi$
$140$	−7.76258	−	0.526708i	−0.656058	−	0.0445149i
$141$	−9.79489	+	5.65508i	−0.824879	+	0.476244i
$142$	−3.12779	−	7.98703i	−0.262478	−	0.670256i
$143$	−3.48486	−	0.614475i	−0.291419	−	0.0513850i
$144$	−1.63016	+	3.58418i	−0.135847	+	0.298682i
$145$	−18.1372	+	7.82869i	−1.50621	+	0.650137i
$146$	1.53828	−	10.1543i	0.127309	−	0.840376i
$147$	1.92931	−	5.30074i	0.159127	−	0.437198i
$148$	1.37671	−	10.8543i	0.113165	−	0.892221i
$149$	−11.7998	+	9.90122i	−0.966678	+	0.811139i	−0.982027	−	0.188743i	$-0.939559\pi$
$149$	−11.7998	+	9.90122i	−0.966678	+	0.811139i	0.0153483	+	0.999882i	$0.495114\pi$
$150$	8.52092	+	5.30805i	0.695730	+	0.433401i
$151$	−11.0414			−0.898538			−0.449269	−	0.893397i	$-0.648315\pi$
$151$	−11.0414			−0.898538			−0.449269	+	0.893397i	$0.648315\pi$
$152$	−7.75950	−	9.58072i	−0.629379	−	0.777099i
$153$		−	5.38399i		−	0.435270i
$154$	4.24012	−	3.73629i	0.341678	−	0.301079i
$155$	−0.524206	−	8.96389i	−0.0421052	−	0.719997i
$156$	−4.33960	−	0.550414i	−0.347446	−	0.0440684i
$157$	−1.41878	+	3.89806i	−0.113231	+	0.311099i	−0.983344	−	0.181752i	$-0.941823\pi$
$157$	−1.41878	+	3.89806i	−0.113231	+	0.311099i	0.870113	+	0.492851i	$0.164045\pi$
$158$	−0.486720	−	0.0737335i	−0.0387214	−	0.00586592i
$159$	1.78005	+	1.02771i	0.141167	+	0.0815027i
$160$	10.9847	+	6.27180i	0.868420	+	0.495830i
$161$	0.787449	−	4.46585i	0.0620597	−	0.351958i
$162$	−2.61860	−	6.68678i	−0.205737	−	0.525363i
$163$	4.08673	+	7.07843i	0.320098	+	0.554426i	0.980508	−	0.196480i	$-0.0629509\pi$
$163$	4.08673	+	7.07843i	0.320098	+	0.554426i	−0.660410	+	0.750905i	$0.729618\pi$
$164$	−9.10522	+	5.86150i	−0.710999	+	0.457707i
$165$	−7.09500	+	1.68331i	−0.552345	+	0.131046i
$166$	−9.25125	+	1.86298i	−0.718036	+	0.144596i
$167$	8.42722	+	23.1536i	0.652118	+	1.79168i	0.609774	+	0.792576i	$0.291260\pi$
$167$	8.42722	+	23.1536i	0.652118	+	1.79168i	0.0423441	+	0.999103i	$0.486517\pi$
$168$	5.01209	−	4.86677i	0.386691	−	0.375479i
$169$	−1.84530	−	10.4652i	−0.141946	−	0.805016i
$170$	−17.2230	−	1.58785i	−1.32094	−	0.121783i
$171$	−4.27343	−	0.385373i	−0.326798	−	0.0294702i
$172$	2.35631	−	4.57928i	0.179667	−	0.349167i
$173$	−0.867871	−	4.92194i	−0.0659830	−	0.374208i	−0.999862	−	0.0166187i	$-0.994710\pi$
$173$	−0.867871	−	4.92194i	−0.0659830	−	0.374208i	0.933879	−	0.357589i	$-0.116401\pi$
$174$	5.66188	−	16.8101i	0.429226	−	1.27437i
$175$	5.19784	+	6.97505i	0.392920	+	0.527264i
$176$	−8.85184	+	2.46198i	−0.667233	+	0.185579i
$177$	−7.67712	+	9.14923i	−0.577047	+	0.687698i
$178$	14.5985	−	0.353144i	1.09421	−	0.0264693i
$179$	12.7245	+	22.0396i	0.951077	+	1.64731i	0.743100	+	0.669181i	$0.233355\pi$
$179$	12.7245	+	22.0396i	0.951077	+	1.64731i	0.207978	+	0.978134i	$0.433312\pi$
$180$	4.22919	−	1.22216i	0.315225	−	0.0910942i
$181$	−7.47862	−	1.31868i	−0.555881	−	0.0980169i	−0.111352	−	0.993781i	$-0.535518\pi$
$181$	−7.47862	−	1.31868i	−0.555881	−	0.0980169i	−0.444530	+	0.895764i	$0.646629\pi$
$182$	−3.32744	−	1.81526i	−0.246647	−	0.134556i
$183$	−8.07326	−	4.66110i	−0.596793	−	0.344558i
$184$	−4.31701	+	5.97626i	−0.318254	+	0.440576i
$185$	−10.2187	+	6.72441i	−0.751296	+	0.494388i
$186$	6.29981	+	5.03164i	0.461924	+	0.368938i
$187$	9.62395	−	8.07545i	0.703773	−	0.590536i
$188$	15.2180	+	4.71905i	1.10988	+	0.344172i
$189$		−	9.84132i		−	0.715851i
$190$	−2.49310	+	13.5567i	−0.180869	+	0.983507i
$191$			18.2718i			1.32210i	0.750341	+	0.661051i	$0.229889\pi$
$191$			18.2718i			1.32210i	−0.750341	+	0.661051i	$0.770111\pi$
$192$	−10.7825	+	3.56899i	−0.778161	+	0.257570i
$193$	16.1324	−	13.5367i	1.16124	−	0.974394i	0.161316	−	0.986903i	$-0.448426\pi$
$193$	16.1324	−	13.5367i	1.16124	−	0.974394i	0.999922	+	0.0125087i	$0.00398175\pi$
$194$	−4.97140	+	6.22439i	−0.356926	+	0.446885i
$195$	2.68844	+	4.08548i	0.192523	+	0.292567i
$196$	−7.32711	+	3.07574i	−0.523365	+	0.219696i
$197$	−13.6369	−	7.87326i	−0.971588	−	0.560946i	−0.0718678	−	0.997414i	$-0.522896\pi$
$197$	−13.6369	−	7.87326i	−0.971588	−	0.560946i	−0.899720	+	0.436468i	$0.856229\pi$
$198$	−1.53138	+	2.80708i	−0.108830	+	0.199490i
$199$	−3.98026	−	0.701827i	−0.282153	−	0.0497512i	0.0307808	−	0.999526i	$-0.490201\pi$
$199$	−3.98026	−	0.701827i	−0.282153	−	0.0497512i	−0.312934	+	0.949775i	$0.601312\pi$
$200$	−2.66231	−	13.8893i	−0.188253	−	0.982120i
$201$	−7.58455	−	13.1368i	−0.534973	−	0.926600i
$202$	−0.461607	−	19.0822i	−0.0324786	−	1.34262i
$203$	9.87962	−	11.7741i	0.693413	−	0.826377i
$204$	11.4003	−	10.5463i	0.798183	−	0.738387i
$205$	11.5991	+	3.46958i	0.810119	+	0.242326i
$206$	14.0510	+	4.73258i	0.978981	+	0.329735i
$207$	0.445546	+	2.52682i	0.0309676	+	0.175626i
$208$	3.58220	+	5.01411i	0.248381	+	0.347666i
$209$	−5.72087	−	8.21683i	−0.395721	−	0.568370i
$210$	−7.77778	−	0.717064i	−0.536718	−	0.0494821i
$211$	−3.70732	−	21.0252i	−0.255222	−	1.44744i	−0.795502	−	0.605952i	$-0.792793\pi$
$211$	−3.70732	−	21.0252i	−0.255222	−	1.44744i	0.540279	−	0.841486i	$-0.318319\pi$
$212$	−0.640091	−	2.82388i	−0.0439616	−	0.193945i
$213$	−2.94516	−	8.09176i	−0.201799	−	0.554439i
$214$	−4.85183	−	24.0933i	−0.331664	−	1.64699i
$215$	−5.60231	+	1.32917i	−0.382074	+	0.0906484i
$216$	−6.97429	+	14.3996i	−0.474541	+	0.979766i
$217$	3.49310	+	6.05023i	0.237127	+	0.410717i
$218$	−20.5011	+	8.02843i	−1.38851	+	0.543754i
$219$	1.79035	−	10.1536i	0.120981	−	0.686115i
$220$	8.52799	+	5.72661i	0.574957	+	0.386088i
$221$	−7.29721	−	4.21304i	−0.490863	−	0.283400i
$222$	1.64519	−	10.8601i	0.110418	−	0.728879i
$223$	−2.79619	+	7.68248i	−0.187247	+	0.514457i	−0.997424	−	0.0717281i	$-0.977149\pi$
$223$	−2.79619	+	7.68248i	−0.187247	+	0.514457i	0.810177	+	0.586185i	$0.199371\pi$
$224$	−9.82741	−	0.527297i	−0.656622	−	0.0352315i
$225$	−4.11342	−	2.70267i	−0.274228	−	0.180178i
$226$	−2.54978	−	2.89361i	−0.169609	−	0.192480i
$227$		−	18.3515i		−	1.21803i	−0.793159	−	0.609015i	$-0.791565\pi$
$227$		−	18.3515i		−	1.21803i	0.793159	−	0.609015i	$-0.208435\pi$
$228$	−7.55488	−	9.80365i	−0.500334	−	0.649262i
$229$	7.74094			0.511536			0.255768	−	0.966738i	$-0.417672\pi$
$229$	7.74094			0.511536			0.255768	+	0.966738i	$0.417672\pi$
$230$	8.21449	−	0.680055i	0.541648	−	0.0448415i
$231$	4.34612	−	3.64682i	0.285953	−	0.239943i
$232$	−22.7996	+	10.2261i	−1.49687	+	0.671375i
$233$	6.69262	−	18.3878i	0.438448	−	1.20463i	−0.502053	−	0.864837i	$-0.667422\pi$
$233$	6.69262	−	18.3878i	0.438448	−	1.20463i	0.940501	−	0.339790i	$-0.110356\pi$
$234$	2.12045	+	0.321227i	0.138618	+	0.0209993i
$235$	−7.05941	−	16.3550i	−0.460505	−	1.06688i
$236$	16.8053	−	0.813532i	1.09393	−	0.0529564i
$237$	−0.486685	−	0.0858158i	−0.0316136	−	0.00557433i
$238$	12.5305	−	4.90704i	0.812229	−	0.318076i
$239$	8.95796	−	5.17188i	0.579442	−	0.334541i	−0.181469	−	0.983397i	$-0.558085\pi$
$239$	8.95796	−	5.17188i	0.579442	−	0.334541i	0.760912	+	0.648855i	$0.224752\pi$
$240$	10.8721	+	6.56110i	0.701790	+	0.423517i
$241$	2.26737	−	2.70215i	0.146054	−	0.174061i	−0.688057	−	0.725656i	$-0.741536\pi$
$241$	2.26737	−	2.70215i	0.146054	−	0.174061i	0.834112	+	0.551595i	$0.185981\pi$
$242$	7.93561	−	1.59804i	0.510120	−	0.102726i
$243$	3.33844	+	9.17228i	0.214161	+	0.588402i
$244$	2.90308	+	12.8075i	0.185851	+	0.819914i
$245$	7.94038	+	3.98547i	0.507292	+	0.254622i
$246$	−9.28036	+	5.66159i	−0.591694	+	0.360970i
$247$	−3.86633	+	5.49045i	−0.246009	+	0.349349i
$248$	−0.823374	−	11.3280i	−0.0522843	−	0.719330i
$249$	−9.32984	+	1.64510i	−0.591254	+	0.104254i
$250$	−9.85875	+	12.3614i	−0.623522	+	0.781806i
$251$	−1.78713	−	4.91010i	−0.112803	−	0.309923i	0.870426	−	0.492299i	$-0.163843\pi$
$251$	−1.78713	−	4.91010i	−0.112803	−	0.309923i	−0.983229	+	0.182376i	$0.941621\pi$
$252$	−2.51428	+	2.32592i	−0.158385	+	0.146519i
$253$	−3.84844	+	4.58640i	−0.241950	+	0.288344i
$254$	−10.6714	+	0.258146i	−0.669583	+	0.0161975i
$255$	−17.2465	−	2.01171i	−1.08002	−	0.125978i
$256$	14.0055	+	7.73596i	0.875346	+	0.483498i
$257$	−0.382032	+	2.16661i	−0.0238305	+	0.135149i	−0.994402	−	0.105664i	$-0.966303\pi$
$257$	−0.382032	+	2.16661i	−0.0238305	+	0.135149i	0.970571	+	0.240814i	$0.0774143\pi$
$258$	2.47599	−	4.53859i	0.154148	−	0.282560i
$259$	4.75880	−	8.24248i	0.295697	−	0.512163i
$260$	1.65294	−	6.68840i	0.102511	−	0.414797i
$261$	−2.97437	+	8.17201i	−0.184109	+	0.505835i
$262$	−5.82632	−	4.65346i	−0.359951	−	0.287492i
$263$	−6.44716	+	5.40981i	−0.397549	+	0.333583i	−0.819545	−	0.573014i	$-0.805774\pi$
$263$	−6.44716	+	5.40981i	−0.397549	+	0.333583i	0.421996	+	0.906597i	$0.361329\pi$
$264$	−8.94354	+	2.25596i	−0.550437	+	0.138845i
$265$	−1.93256	+	2.59715i	−0.118716	+	0.159542i
$266$	−2.99796	−	10.2970i	−0.183817	−	0.631351i
$267$	14.6597			0.897161
$268$	−6.32915	+	20.4102i	−0.386615	+	1.24675i
$269$	11.2619	+	13.4214i	0.686649	+	0.818316i	0.990946	−	0.134261i	$-0.0428660\pi$
$269$	11.2619	+	13.4214i	0.686649	+	0.818316i	−0.304297	+	0.952577i	$0.598422\pi$
$270$	17.3000	−	4.54909i	1.05285	−	0.276849i
$271$	−8.42074	+	23.1358i	−0.511524	+	1.40540i	0.368125	+	0.929776i	$0.380000\pi$
$271$	−8.42074	+	23.1358i	−0.511524	+	1.40540i	−0.879649	+	0.475624i	$0.842222\pi$
$272$	−21.8117	−	1.70017i	−1.32253	−	0.103088i
$273$	−3.29537	−	1.90258i	−0.199445	−	0.115150i
$274$	12.6328	−	23.1564i	0.763173	−	1.39893i
$275$	−1.33868	−	11.4065i	−0.0807253	−	0.687839i
$276$	−4.47766	+	5.89301i	−0.269524	+	0.354717i
$277$	4.16512	−	2.40473i	0.250258	−	0.144486i	−0.369625	−	0.929181i	$-0.620514\pi$
$277$	4.16512	−	2.40473i	0.250258	−	0.144486i	0.619882	+	0.784695i	$0.287180\pi$
$278$	21.3988	−	0.517645i	1.28341	−	0.0310463i
$279$	−3.02807	−	2.54085i	−0.181286	−	0.152117i
$280$	6.69893	+	8.72894i	0.400338	+	0.521654i
$281$	6.36744	+	17.4944i	0.379850	+	1.04363i	0.971418	+	0.237374i	$0.0762867\pi$
$281$	6.36744	+	17.4944i	0.379850	+	1.04363i	−0.591568	+	0.806255i	$0.701491\pi$
$282$	15.1583	+	5.10552i	0.902662	+	0.304030i
$283$	2.95087	+	16.7352i	0.175411	+	0.994806i	0.937668	+	0.347532i	$0.112980\pi$
$283$	2.95087	+	16.7352i	0.175411	+	0.994806i	−0.762257	+	0.647274i	$0.775909\pi$
$284$	−5.55024	+	10.7864i	−0.329346	+	0.640054i
$285$	−2.83122	+	13.5451i	−0.167707	+	0.802341i
$286$	2.60626	+	4.27213i	0.154111	+	0.252616i
$287$	−9.27661	+	1.63572i	−0.547581	+	0.0965533i
$288$	5.32715	−	1.62143i	0.313905	−	0.0955435i
$289$	12.1363	−	4.41725i	0.713899	−	0.259838i
$290$	25.2644	+	11.9249i	1.48358	+	0.700252i
$291$	−5.14044	+	6.12614i	−0.301338	+	0.359121i
$292$	−12.2125	+	7.86180i	−0.714681	+	0.460077i
$293$	11.8946	+	20.6020i	0.694887	+	1.20358i	0.970219	+	0.242230i	$0.0778790\pi$
$293$	11.8946	+	20.6020i	0.694887	+	1.20358i	−0.275332	+	0.961349i	$0.588788\pi$
$294$	−7.42821	+	2.90895i	−0.433222	+	0.169653i
$295$	−12.9121	−	13.6795i	−0.751770	−	0.796453i
$296$	−12.8042	+	8.68774i	−0.744228	+	0.504965i
$297$	−6.49664	+	11.2525i	−0.376973	+	0.652937i
$298$	21.5382	+	3.26283i	1.24767	+	0.189011i
$299$	3.77337	+	1.37340i	0.218220	+	0.0794256i
$300$	−2.33471	−	14.0040i	−0.134794	−	0.808521i
$301$	3.43175	−	2.87958i	0.197803	−	0.165976i
$302$	10.3234	+	11.7155i	0.594046	+	0.674151i
$303$		−	19.1622i		−	1.10084i
$304$	−2.91070	+	17.1909i	−0.166940	+	0.985967i
$305$	8.76497	−	11.7792i	0.501881	−	0.674474i
$306$	−5.71269	+	5.03389i	−0.326573	+	0.287768i
$307$	13.3169	+	15.8705i	0.760035	+	0.905775i	0.997850	−	0.0655355i	$-0.0208756\pi$
$307$	13.3169	+	15.8705i	0.760035	+	0.905775i	−0.237815	+	0.971311i	$0.576431\pi$
$308$	−7.92878	−	1.00565i	−0.451784	−	0.0573021i
$309$	13.9868	+	5.09078i	0.795681	+	0.289604i
$310$	−9.02102	+	8.93720i	−0.512360	+	0.507599i
$311$	22.7327	+	13.1247i	1.28905	+	0.744236i	0.978486	−	0.206315i	$-0.0661470\pi$
$311$	22.7327	+	13.1247i	1.28905	+	0.744236i	0.310569	+	0.950551i	$0.399480\pi$
$312$	3.47339	+	5.11916i	0.196642	+	0.289815i
$313$	−5.36045	−	0.945191i	−0.302990	−	0.0534254i	0.0200861	−	0.999798i	$-0.493606\pi$
$313$	−5.36045	−	0.945191i	−0.302990	−	0.0534254i	−0.323076	+	0.946373i	$0.604717\pi$
$314$	5.46256	−	2.13919i	0.308270	−	0.120721i
$315$	3.80363	+	0.443672i	0.214310	+	0.0249981i
$316$	0.376835	+	0.585373i	0.0211986	+	0.0329298i
$317$	−10.1806	−	8.54254i	−0.571799	−	0.479797i	0.310443	−	0.950592i	$-0.399523\pi$
$317$	−10.1806	−	8.54254i	−0.571799	−	0.479797i	−0.882242	+	0.470795i	$0.843967\pi$
$318$	−0.573842	−	2.84960i	−0.0321795	−	0.159798i
$319$	−19.0688	+	6.94048i	−1.06765	+	0.388592i
$320$	−3.61573	−	17.5193i	−0.202125	−	0.979360i
$321$	−4.28440	−	24.2980i	−0.239132	−	1.35618i
$322$	−5.47473	+	3.33992i	−0.305095	+	0.186126i
$323$	−6.10899	−	23.0449i	−0.339913	−	1.28225i
$324$	−4.64669	+	9.03042i	−0.258149	+	0.501690i
$325$	−6.88187	+	3.46027i	−0.381737	+	0.191941i
$326$	3.68959	−	10.9544i	0.204347	−	0.606706i
$327$	−20.7700	+	7.55966i	−1.14858	+	0.418050i
$328$	14.7325	+	4.18076i	0.813465	+	0.230844i
$329$	10.6171	+	8.90881i	0.585340	+	0.491159i
$330$	8.41971	+	5.95430i	0.463490	+	0.327774i
$331$	−11.1350	−	19.2864i	−0.612037	−	1.06008i	−0.990897	−	0.134625i	$-0.957017\pi$
$331$	−11.1350	−	19.2864i	−0.612037	−	1.06008i	0.378860	−	0.925454i	$-0.376316\pi$
$332$	10.6264	+	8.07420i	0.583198	+	0.443129i
$333$	−0.935121	+	5.30334i	−0.0512443	+	0.290621i
$334$	16.6879	−	30.5897i	0.913121	−	1.67379i
$335$	21.9351	−	9.46802i	1.19844	−	0.517293i
$336$	−9.85005	−	0.767785i	−0.537364	−	0.0418861i
$337$	2.71413	+	0.987863i	0.147848	+	0.0538123i	0.414884	−	0.909874i	$-0.363822\pi$
$337$	2.71413	+	0.987863i	0.147848	+	0.0538123i	−0.267036	+	0.963687i	$0.586044\pi$
$338$	−9.37881	+	11.7426i	−0.510140	+	0.638715i
$339$	−2.48872	−	2.96595i	−0.135169	−	0.161088i
$340$	14.4182	+	19.7590i	0.781937	+	1.07158i
$341$		−	9.22373i		−	0.499493i
$342$	3.58664	+	4.89464i	0.193943	+	0.264672i
$343$	−19.0908			−1.03081
$344$	−7.06194	+	1.78134i	−0.380754	+	0.0960432i
$345$	8.26062	−	0.483079i	0.444737	−	0.0260081i
$346$	−4.41099	+	5.52273i	−0.237136	+	0.296904i
$347$	3.47991	+	1.26658i	0.186811	+	0.0679938i	0.433732	−	0.901042i	$-0.357196\pi$
$347$	3.47991	+	1.26658i	0.186811	+	0.0679938i	−0.246921	+	0.969036i	$0.579419\pi$
$348$	−23.1301	+	9.70943i	−1.23990	+	0.520480i
$349$	9.56687	−	16.5703i	0.512103	−	0.886988i	−0.487799	−	0.872956i	$-0.662200\pi$
$349$	9.56687	−	16.5703i	0.512103	−	0.886988i	0.999902	−	0.0140317i	$-0.00446658\pi$
$350$	2.54104	−	12.0366i	0.135824	−	0.643385i
$351$	8.58216	+	1.51327i	0.458082	+	0.0807722i
$352$	10.8885	+	7.09037i	0.580360	+	0.377918i
$353$	−14.5615	+	8.40708i	−0.775030	+	0.447464i	−0.834666	−	0.550756i	$-0.814339\pi$
$353$	−14.5615	+	8.40708i	−0.775030	+	0.447464i	0.0596360	+	0.998220i	$0.481006\pi$
$354$	16.8857	−	0.408472i	0.897464	−	0.0217100i
$355$	13.1961	−	3.13082i	0.700377	−	0.166167i
$356$	−14.0239	−	15.1596i	−0.743266	−	0.803456i
$357$	12.6948	−	4.62052i	0.671879	−	0.244544i
$358$	11.4880	−	34.1078i	0.607159	−	1.80265i
$359$	36.3146	−	6.40325i	1.91661	−	0.337950i	0.918293	−	0.395902i	$-0.129568\pi$
$359$	36.3146	−	6.40325i	1.91661	−	0.337950i	0.998319	+	0.0579513i	$0.0184568\pi$
$360$	−5.25095	−	3.34470i	−0.276749	−	0.176281i
$361$	−18.7287	+	3.19939i	−0.985721	+	0.168389i
$362$	5.59311	+	9.16812i	0.293968	+	0.481866i
$363$	8.00302	−	1.41115i	0.420050	−	0.0740661i
$364$	1.18499	+	5.22780i	0.0621104	+	0.274011i
$365$	15.5575	+	4.65360i	0.814315	+	0.243581i
$366$	2.60261	+	12.9241i	0.136041	+	0.675555i
$367$	−11.4899	−	9.64113i	−0.599765	−	0.503263i	0.291605	−	0.956539i	$-0.405811\pi$
$367$	−11.4899	−	9.64113i	−0.599765	−	0.503263i	−0.891370	+	0.453276i	$0.850255\pi$
$368$	10.3774	−	1.00708i	0.540959	−	0.0524978i
$369$	4.61571	−	2.66488i	0.240284	−	0.138728i
$370$	16.6892	+	4.55544i	0.867628	+	0.236826i
$371$	0.437375	−	2.48048i	0.0227074	−	0.128780i
$372$	−0.551325	−	11.3889i	−0.0285849	−	0.590485i
$373$	6.91588	−	11.9787i	0.358091	−	0.620231i	−0.629551	−	0.776959i	$-0.716761\pi$
$373$	6.91588	−	11.9787i	0.358091	−	0.620231i	0.987642	+	0.156728i	$0.0500945\pi$
$374$	−17.5666	−	2.66117i	−0.908347	−	0.137606i
$375$	−10.1944	+	12.1667i	−0.526437	+	0.628284i
$376$	−9.22123	−	20.5592i	−0.475549	−	1.06026i
$377$	8.74847	+	10.4260i	0.450569	+	0.536967i
$378$	−10.4421	+	9.20136i	−0.537085	+	0.473267i
$379$	−4.82805			−0.248000			−0.124000	−	0.992282i	$-0.539572\pi$
$379$	−4.82805			−0.248000			−0.124000	+	0.992282i	$0.539572\pi$
$380$	16.7153	−	10.0298i	0.857478	−	0.514520i
$381$	−10.7162			−0.549005
$382$	19.3873	−	17.0836i	0.991941	−	0.874075i
$383$	9.16024	+	10.9168i	0.468067	+	0.557820i	0.947499	−	0.319759i	$-0.103602\pi$
$383$	9.16024	+	10.9168i	0.468067	+	0.557820i	−0.479432	+	0.877579i	$0.659157\pi$
$384$	13.8682	+	8.10388i	0.707710	+	0.413549i
$385$	4.91199	+	7.46449i	0.250338	+	0.380425i
$386$	−29.4465	−	4.46086i	−1.49879	−	0.227052i
$387$	−1.26737	+	2.19514i	−0.0644239	+	0.111585i
$388$	11.2525	−	0.544725i	0.571260	−	0.0276542i
$389$	−1.83595	+	10.4122i	−0.0930863	+	0.527919i	0.902231	+	0.431254i	$0.141929\pi$
$389$	−1.83595	+	10.4122i	−0.0930863	+	0.527919i	−0.995317	+	0.0966649i	$0.969182\pi$
$390$	1.82128	−	6.67239i	0.0922242	−	0.337869i
$391$	−12.3464	+	7.12820i	−0.624384	+	0.360488i
$392$	10.1142	+	4.89870i	0.510843	+	0.247422i
$393$	−5.73435	−	4.81169i	−0.289260	−	0.242718i
$394$	4.39619	+	21.8307i	0.221477	+	1.09981i
$395$	0.223059	−	0.745707i	0.0112233	−	0.0375206i
$396$	4.41025	−	0.999675i	0.221623	−	0.0502356i
$397$	−20.2288	+	3.56689i	−1.01526	+	0.179017i	−0.656430	−	0.754387i	$-0.727934\pi$
$397$	−20.2288	+	3.56689i	−1.01526	+	0.179017i	−0.358826	+	0.933404i	$0.616823\pi$
$398$	2.97676	+	4.87944i	0.149211	+	0.244584i
$399$	−2.75878	−	10.4069i	−0.138112	−	0.520999i
$400$	−12.2480	+	15.8109i	−0.612402	+	0.790547i
$401$	13.5503	−	2.38928i	0.676670	−	0.119315i	0.175256	−	0.984523i	$-0.443925\pi$
$401$	13.5503	−	2.38928i	0.676670	−	0.119315i	0.501414	+	0.865208i	$0.332814\pi$
$402$	−6.84749	+	20.3302i	−0.341522	+	1.01398i
$403$	−5.81325	+	2.11585i	−0.289579	+	0.105398i
$404$	−19.8156	+	18.3311i	−0.985863	+	0.912008i
$405$	11.0478	−	2.62114i	0.548972	−	0.130245i
$406$	−21.7300	+	0.525659i	−1.07844	+	0.0260880i
$407$	−10.8824	+	6.28294i	−0.539419	+	0.311434i
$408$	−21.8491	−	2.23584i	−1.08169	−	0.110690i
$409$	31.9524	+	5.63407i	1.57994	+	0.278587i	0.893659	−	0.448746i	$-0.148129\pi$
$409$	31.9524	+	5.63407i	1.57994	+	0.278587i	0.686285	+	0.727333i	$0.259240\pi$
$410$	−7.16347	−	15.5512i	−0.353779	−	0.768020i
$411$	13.2405	−	22.9332i	0.653106	−	1.13121i
$412$	−8.11580	−	19.3337i	−0.399837	−	0.952501i
$413$	13.7531	+	5.00571i	0.676744	+	0.246315i
$414$	2.26451	−	2.83525i	0.111295	−	0.139345i
$415$	−0.871096	−	14.8957i	−0.0427604	−	0.731201i
$416$	1.97096	−	8.48895i	0.0966343	−	0.416205i
$417$	21.4885			1.05230
$418$	−3.36962	+	13.7526i	−0.164813	+	0.672663i
$419$		−	16.5448i		−	0.808267i	−0.914700	−	0.404134i	$-0.867573\pi$
$419$		−	16.5448i		−	0.808267i	0.914700	−	0.404134i	$-0.132427\pi$
$420$	6.51117	+	8.92305i	0.317712	+	0.435400i
$421$	−7.56489	−	9.01548i	−0.368690	−	0.439388i	0.549521	−	0.835480i	$-0.314810\pi$
$421$	−7.56489	−	9.01548i	−0.368690	−	0.439388i	−0.918211	+	0.396092i	$0.870366\pi$
$422$	−18.8426	+	23.5917i	−0.917243	+	1.14842i
$423$	−7.36900	−	2.68210i	−0.358293	−	0.130408i
$424$	−2.39781	+	3.31941i	−0.116448	+	0.161205i
$425$	6.29420	−	26.6132i	0.305314	−	1.29093i
$426$	−5.83212	+	10.6905i	−0.282567	+	0.517958i
$427$	−1.98368	+	11.2500i	−0.0959970	+	0.544426i
$428$	−21.0279	+	27.6746i	−1.01642	+	1.33770i
$429$	2.51194	+	4.35081i	0.121278	+	0.210059i
$430$	6.64832	+	4.70160i	0.320610	+	0.226731i
$431$	−14.6777	−	12.3160i	−0.706998	−	0.593242i	0.216757	−	0.976226i	$-0.430452\pi$
$431$	−14.6777	−	12.3160i	−0.706998	−	0.593242i	−0.923755	+	0.382984i	$0.874897\pi$
$432$	21.7994	−	6.06312i	1.04883	−	0.291712i
$433$	−17.2686	+	6.28527i	−0.829877	+	0.302051i	−0.721809	−	0.692093i	$-0.756689\pi$
$433$	−17.2686	+	6.28527i	−0.829877	+	0.302051i	−0.108069	+	0.994143i	$0.534467\pi$
$434$	3.15364	−	9.36316i	0.151380	−	0.449446i
$435$	25.0660	+	12.5812i	1.20182	+	0.603223i
$436$	27.6866	+	14.2464i	1.32595	+	0.682278i
$437$	4.77413	+	10.3099i	0.228378	+	0.493190i
$438$	−12.4474	+	7.59366i	−0.594759	+	0.362839i
$439$	0.186601	+	1.05827i	0.00890599	+	0.0505084i	0.988937	−	0.148337i	$-0.0473920\pi$
$439$	0.186601	+	1.05827i	0.00890599	+	0.0505084i	−0.980031	+	0.198845i	$0.936281\pi$
$440$	−1.89720	−	14.4028i	−0.0904457	−	0.686629i
$441$	3.67528	−	1.33769i	0.175013	−	0.0636996i
$442$	2.35243	+	11.6818i	0.111894	+	0.555646i
$443$	1.38195	+	1.15959i	0.0656585	+	0.0550940i	0.675026	−	0.737794i	$-0.264132\pi$
$443$	1.38195	+	1.15959i	0.0656585	+	0.0550940i	−0.609368	+	0.792888i	$0.708577\pi$
$444$	−13.0613	+	8.40822i	−0.619861	+	0.399036i
$445$	−2.67507	+	22.9335i	−0.126811	+	1.08715i
$446$	10.7659	−	4.21600i	0.509778	−	0.199634i
$447$	21.5366	+	3.79749i	1.01865	+	0.179615i
$448$	8.62887	+	10.9204i	0.407676	+	0.515940i
$449$	−16.6526	−	9.61441i	−0.785887	−	0.453732i	0.0526258	−	0.998614i	$-0.483241\pi$
$449$	−16.6526	−	9.61441i	−0.785887	−	0.453732i	−0.838512	+	0.544882i	$0.816574\pi$
$450$	0.978273	+	6.89147i	0.0461162	+	0.324867i
$451$	11.6866	+	4.25358i	0.550301	+	0.200293i
$452$	−0.686291	+	5.41089i	−0.0322804	+	0.254507i
$453$	10.0762	+	12.0084i	0.473422	+	0.564202i
$454$	−19.4718	+	17.1581i	−0.913858	+	0.805270i
$455$	3.57772	−	4.80807i	0.167726	−	0.225406i
$456$	−3.33855	+	17.1822i	−0.156342	+	0.804632i
$457$		−	18.2055i		−	0.851618i	−0.904813	−	0.425809i	$-0.859990\pi$
$457$		−	18.2055i		−	0.851618i	0.904813	−	0.425809i	$-0.140010\pi$
$458$	−7.23757	−	8.21353i	−0.338189	−	0.383793i
$459$	−23.7009	+	19.8874i	−1.10626	+	0.928265i
$460$	−8.40189	−	8.08015i	−0.391740	−	0.376739i
$461$	−14.2977	−	5.20394i	−0.665911	−	0.242372i	−0.0131245	−	0.999914i	$-0.504178\pi$
$461$	−14.2977	−	5.20394i	−0.665911	−	0.242372i	−0.652786	+	0.757542i	$0.726400\pi$
$462$	−7.93296	−	1.20177i	−0.369075	−	0.0559113i
$463$	9.01613	−	15.6164i	0.419015	−	0.725755i	−0.576826	−	0.816867i	$-0.695709\pi$
$463$	9.01613	−	15.6164i	0.419015	−	0.725755i	0.995841	+	0.0911121i	$0.0290421\pi$
$464$	32.1674	+	14.6304i	1.49333	+	0.679199i
$465$	−9.27053	+	8.75042i	−0.429910	+	0.405791i
$466$	−25.7678	+	10.0909i	−1.19367	+	0.467452i
$467$	−16.2072	−	28.0717i	−0.749979	−	1.29900i	−0.947832	−	0.318770i	$-0.896730\pi$
$467$	−16.2072	−	28.0717i	−0.749979	−	1.29900i	0.197853	−	0.980232i	$-0.436603\pi$
$468$	−1.64172	−	2.55024i	−0.0758885	−	0.117885i
$469$	−11.9484	+	14.2396i	−0.551727	+	0.657522i
$470$	−10.7531	+	22.7818i	−0.496003	+	1.05085i
$471$	5.53419	−	2.01428i	0.255002	−	0.0928132i
$472$	−16.5757	−	17.0707i	−0.762959	−	0.785741i
$473$	−5.82477	+	1.02706i	−0.267823	+	0.0472245i
$474$	0.363982	+	0.596633i	0.0167183	+	0.0274043i
$475$	−20.6731	−	6.90080i	−0.948549	−	0.316630i
$476$	−16.9222	−	8.70751i	−0.775630	−	0.399108i
$477$	0.247471	+	1.40348i	0.0113309	+	0.0642609i
$478$	−13.8631	−	4.66928i	−0.634082	−	0.213568i
$479$	−2.25454	−	6.19431i	−0.103013	−	0.283025i	0.877470	−	0.479632i	$-0.159230\pi$
$479$	−2.25454	−	6.19431i	−0.103013	−	0.283025i	−0.980482	+	0.196607i	$0.937008\pi$
$480$	−3.20344	−	17.6703i	−0.146216	−	0.806534i
$481$	6.45614	+	5.41735i	0.294375	+	0.247010i
$482$	−4.98705	+	0.120639i	−0.227154	+	0.00549495i
$483$	−5.57556	+	3.21905i	−0.253697	+	0.146472i
$484$	−9.11518	−	6.92595i	−0.414326	−	0.314816i
$485$	−8.64566	−	9.15954i	−0.392579	−	0.415913i
$486$	6.61090	−	12.1181i	0.299877	−	0.549687i
$487$	−25.2833	−	14.5973i	−1.14570	−	0.661467i	−0.197861	−	0.980230i	$-0.563399\pi$
$487$	−25.2833	−	14.5973i	−1.14570	−	0.661467i	−0.947835	+	0.318763i	$0.896733\pi$
$488$	10.8751	−	15.0549i	0.492291	−	0.681505i
$489$	3.96884	−	10.9043i	0.179477	−	0.493109i
$490$	−3.19525	−	12.1514i	−0.144347	−	0.548946i
$491$	−24.9722	−	29.7607i	−1.12698	−	1.34308i	−0.932077	−	0.362259i	$-0.882006\pi$
$491$	−24.9722	−	29.7607i	−1.12698	−	1.34308i	−0.194902	−	0.980823i	$-0.562439\pi$
$492$	14.6841	+	4.55350i	0.662011	+	0.205288i
$493$	−48.3203			−2.17624
$494$	9.44055	−	1.03104i	0.424750	−	0.0463888i
$495$	−4.05616	−	3.01821i	−0.182311	−	0.135659i
$496$	−11.2498	+	11.4650i	−0.505129	+	0.514795i
$497$	−8.08341	+	6.78278i	−0.362590	+	0.304249i
$498$	10.4687	+	8.36130i	0.469113	+	0.374679i
$499$	6.50255	−	17.8656i	0.291094	−	0.799774i	−0.704813	−	0.709393i	$-0.748969\pi$
$499$	6.50255	−	17.8656i	0.291094	−	0.799774i	0.995907	−	0.0903814i	$-0.0288086\pi$
$500$	22.3338	−	1.09698i	0.998796	−	0.0490583i
$501$	17.4907	−	30.2948i	0.781428	−	1.35347i
$502$	−3.53895	+	6.48704i	−0.157951	+	0.289531i
$503$	−1.67324	+	9.48939i	−0.0746059	+	0.423111i	0.924513	+	0.381150i	$0.124472\pi$
$503$	−1.67324	+	9.48939i	−0.0746059	+	0.423111i	−0.999119	+	0.0419613i	$0.986639\pi$
$504$	4.81870	+	0.493102i	0.214642	+	0.0219645i
$505$	29.9772	+	3.49668i	1.33397	+	0.155600i
$506$	8.46458	−	0.204762i	0.376297	−	0.00910278i
$507$	−9.69772	+	11.5573i	−0.430691	+	0.513277i
$508$	10.2514	+	11.0815i	0.454831	+	0.491664i
$509$	5.52241	+	15.1727i	0.244777	+	0.672518i	0.999857	+	0.0168864i	$0.00537536\pi$
$509$	5.52241	+	15.1727i	0.244777	+	0.672518i	−0.755081	+	0.655632i	$0.772402\pi$
$510$	13.9905	+	20.1803i	0.619509	+	0.893599i
$511$	−12.4423	+	2.19392i	−0.550417	+	0.0970533i
$512$	−4.88654	−	22.0935i	−0.215957	−	0.976403i
$513$	14.0888	+	20.2356i	0.622034	+	0.893423i
$514$	2.65607	−	1.62037i	0.117154	−	0.0714713i
$515$	−10.5162	+	20.9518i	−0.463401	+	0.923249i
$516$	−7.13065	+	1.61631i	−0.313909	+	0.0711541i
$517$	−6.25848	−	17.1950i	−0.275248	−	0.756237i
$518$	−13.1950	+	2.65717i	−0.579756	+	0.116749i
$519$	−4.56097	+	5.43556i	−0.200204	+	0.238594i
$520$	−8.64218	+	4.49961i	−0.378985	+	0.197321i
$521$	−6.94349	+	4.00883i	−0.304200	+	0.175630i	−0.644328	−	0.764749i	$-0.722863\pi$
$521$	−6.94349	+	4.00883i	−0.304200	+	0.175630i	0.340128	+	0.940379i	$0.389530\pi$
$522$	11.4519	−	4.48465i	0.501234	−	0.196288i
$523$	9.73748	+	1.71698i	0.425790	+	0.0750783i	0.382437	−	0.923981i	$-0.375085\pi$
$523$	9.73748	+	1.71698i	0.425790	+	0.0750783i	0.0433531	+	0.999060i	$0.486196\pi$
$524$	0.509888	+	10.5329i	0.0222745	+	0.460130i
$525$	2.84242	−	12.0184i	0.124054	−	0.524524i
$526$	11.7680	+	1.78274i	0.513109	+	0.0777311i
$527$	7.51191	−	20.6388i	0.327224	−	0.899041i
$528$	10.7556	+	7.38028i	0.468079	+	0.321185i
$529$	−12.4145	+	10.4170i	−0.539760	+	0.452913i
$530$	4.56260	−	0.377725i	0.198187	−	0.0164073i
$531$	−8.28103			−0.359366
$532$	−8.12265	+	12.8084i	−0.352162	+	0.555315i
$533$		−	8.34122i		−	0.361298i
$534$	−13.7064	−	15.5547i	−0.593136	−	0.673118i
$535$	38.7934	−	2.26863i	1.67718	−	0.0980813i
$536$	27.5738	−	12.3674i	1.19101	−	0.534192i
$537$	12.3575	−	33.9519i	0.533264	−	1.46513i
$538$	3.71122	−	24.4980i	0.160002	−	1.05619i
$539$	7.90369	+	4.56320i	0.340436	+	0.196551i
$540$	−21.0019	−	14.1029i	−0.903776	−	0.606893i
$541$	−6.55009	+	37.1474i	−0.281610	+	1.59709i	0.435538	+	0.900170i	$0.356558\pi$
$541$	−6.55009	+	37.1474i	−0.281610	+	1.59709i	−0.717148	+	0.696920i	$0.754553\pi$
$542$	32.4214	−	12.6965i	1.39262	−	0.545361i
$543$	5.39070	+	9.33697i	0.231337	+	0.400688i
$544$	18.5894	+	24.7330i	0.797014	+	1.06042i
$545$	−8.03620	−	33.8718i	−0.344233	−	1.45091i
$546$	1.06234	+	5.27542i	0.0454642	+	0.225767i
$547$	2.99512	+	8.22902i	0.128062	+	0.351847i	0.987109	−	0.160049i	$-0.0511653\pi$
$547$	2.99512	+	8.22902i	0.128062	+	0.351847i	−0.859047	+	0.511897i	$0.828943\pi$
$548$	−36.3814	+	8.24660i	−1.55414	+	0.352278i
$549$	−1.12239	−	6.36537i	−0.0479023	−	0.271667i
$550$	−10.8513	+	12.0852i	−0.462699	+	0.515314i
$551$	−3.45865	+	38.3533i	−0.147343	+	1.63390i
$552$	10.4393	−	0.758775i	0.444325	−	0.0322956i
$553$	0.105160	+	0.596391i	0.00447185	+	0.0253611i
$554$	−6.44581	−	2.17104i	−0.273856	−	0.0922387i
$555$	16.6387	+	4.97704i	0.706275	+	0.211264i
$556$	−20.5565	−	22.2212i	−0.871790	−	0.942388i
$557$	24.4315	−	29.1163i	1.03520	−	1.23370i	0.0633722	−	0.997990i	$-0.479814\pi$
$557$	24.4315	−	29.1163i	1.03520	−	1.23370i	0.971824	−	0.235709i	$-0.0757411\pi$
$558$	0.135190	+	5.58856i	0.00572303	+	0.236583i
$559$	1.98346	+	3.43546i	0.0838915	+	0.145304i
$560$	2.99853	−	15.2692i	0.126711	−	0.645242i
$561$	−17.5653	−	3.09724i	−0.741609	−	0.130766i
$562$	12.6091	−	23.1130i	0.531881	−	0.974961i
$563$	8.52243	+	4.92043i	0.359178	+	0.207371i	0.668720	−	0.743514i	$-0.266843\pi$
$563$	8.52243	+	4.92043i	0.359178	+	0.207371i	−0.309542	+	0.950886i	$0.600176\pi$
$564$	−8.75535	−	20.8572i	−0.368667	−	0.878247i
$565$	5.09404	−	3.35212i	0.214308	−	0.141025i
$566$	14.9979	−	18.7780i	0.630410	−	0.789298i
$567$	−6.76747	+	5.67858i	−0.284207	+	0.238478i
$568$	16.6342	−	4.19589i	0.697956	−	0.176056i
$569$			14.7261i			0.617350i	0.951168	+	0.308675i	$0.0998855\pi$
$569$			14.7261i			0.617350i	−0.951168	+	0.308675i	$0.900114\pi$
$570$	17.0191	−	9.66020i	0.712852	−	0.404621i
$571$			9.73152i			0.407251i	0.979049	+	0.203626i	$0.0652726\pi$
$571$			9.73152i			0.407251i	−0.979049	+	0.203626i	$0.934727\pi$
$572$	2.09616	−	6.75969i	0.0876450	−	0.282637i
$573$	19.8720	−	16.6746i	0.830163	−	0.696590i
$574$	10.4089	+	8.31359i	0.434461	+	0.347003i
$575$	−0.751654	+	13.0110i	−0.0313461	+	0.542596i
$576$	−6.70115	−	4.13639i	−0.279215	−	0.172349i
$577$	−25.6009	−	14.7807i	−1.06578	−	0.615328i	−0.138754	−	0.990327i	$-0.544310\pi$
$577$	−25.6009	−	14.7807i	−1.06578	−	0.615328i	−0.927025	+	0.374999i	$0.877643\pi$
$578$	−16.0340	−	8.74721i	−0.666927	−	0.363836i
$579$	−29.4444	−	5.19184i	−1.22367	−	0.215766i
$580$	−10.9686	−	37.9562i	−0.455448	−	1.57605i
$581$	5.80465	+	10.0539i	0.240817	+	0.417108i
$582$	11.3063	−	0.273504i	0.468662	−	0.0113371i
$583$	−2.13755	+	2.54744i	−0.0885284	+	0.105504i
$584$	19.7601	+	5.60748i	0.817678	+	0.232039i
$585$	−0.971777	+	3.24874i	−0.0401780	+	0.134319i
$586$	10.7386	−	31.8830i	0.443609	−	1.31707i
$587$	−5.04001	−	28.5833i	−0.208023	−	1.17976i	−0.892611	−	0.450828i	$-0.851129\pi$
$587$	−5.04001	−	28.5833i	−0.208023	−	1.17976i	0.684587	−	0.728931i	$-0.259982\pi$
$588$	10.0317	+	5.16191i	0.413701	+	0.212874i
$589$	−15.8439	−	7.43970i	−0.652838	−	0.306547i
$590$	−2.44225	+	26.4903i	−0.100546	+	1.09059i
$591$	3.88204	+	22.0161i	0.159686	+	0.905623i
$592$	21.1897	+	5.46308i	0.870891	+	0.224531i
$593$	−7.21665	−	19.8276i	−0.296352	−	0.814221i	−0.995102	−	0.0988546i	$-0.968482\pi$
$593$	−7.21665	−	19.8276i	−0.296352	−	0.814221i	0.698750	−	0.715366i	$-0.253740\pi$
$594$	18.0137	−	3.62752i	0.739109	−	0.148839i
$595$	4.91179	+	20.7027i	0.201364	+	0.848729i
$596$	−16.6756	−	25.9037i	−0.683058	−	1.06106i
$597$	2.86903	+	4.96930i	0.117422	+	0.203380i
$598$	−2.07076	−	5.28783i	−0.0846796	−	0.216235i
$599$	−2.87403	+	16.2994i	−0.117430	+	0.665977i	0.868089	+	0.496409i	$0.165348\pi$
$599$	−2.87403	+	16.2994i	−0.117430	+	0.665977i	−0.985519	+	0.169568i	$0.945763\pi$
$600$	−12.6761	+	15.5706i	−0.517498	+	0.635667i
$601$	−17.4064	−	10.0496i	−0.710022	−	0.409931i	0.101047	−	0.994882i	$-0.467781\pi$
$601$	−17.4064	−	10.0496i	−0.710022	−	0.409931i	−0.811069	+	0.584950i	$0.801114\pi$
$602$	−6.26397	−	0.948932i	−0.255301	−	0.0386756i
$603$	3.59721	−	9.88324i	0.146490	−	0.402477i
$604$	2.77862	−	21.9073i	0.113060	−	0.891396i
$605$	0.747216	+	12.7774i	0.0303786	+	0.519473i
$606$	−20.3321	+	17.9162i	−0.825935	+	0.727794i
$607$		−	12.0712i		−	0.489957i	−0.969529	−	0.244978i	$-0.921219\pi$
$607$		−	12.0712i		−	0.489957i	0.969529	−	0.244978i	$-0.0787809\pi$
$608$	20.9619	−	12.9846i	0.850115	−	0.526596i
$609$	−21.8212			−0.884238
$610$	−20.6933	+	1.71314i	−0.837847	+	0.0693631i
$611$	−9.40152	+	7.88881i	−0.380345	+	0.319147i
$612$	10.6824	+	1.35490i	0.431811	+	0.0547688i
$613$	−0.753056	+	2.06900i	−0.0304156	+	0.0835663i	−0.953971	−	0.299899i	$-0.903047\pi$
$613$	−0.753056	+	2.06900i	−0.0304156	+	0.0835663i	0.923555	+	0.383465i	$0.125269\pi$
$614$	4.38842	−	28.9683i	0.177102	−	1.16907i
$615$	−6.81176	−	15.7812i	−0.274677	−	0.636360i
$616$	6.34615	+	9.35309i	0.255694	+	0.376847i
$617$	17.6184	+	3.10660i	0.709289	+	0.125067i	0.516642	−	0.856201i	$-0.327182\pi$
$617$	17.6184	+	3.10660i	0.709289	+	0.125067i	0.192647	+	0.981268i	$0.438293\pi$
$618$	−7.67569	−	19.6004i	−0.308762	−	0.788444i
$619$	35.1151	−	20.2737i	1.41139	−	0.814869i	0.415875	−	0.909422i	$-0.363475\pi$
$619$	35.1151	−	20.2737i	1.41139	−	0.814869i	0.995520	+	0.0945525i	$0.0301420\pi$
$620$	17.9172	+	1.21572i	0.719573	+	0.0488246i
$621$	9.47756	−	11.2949i	0.380321	−	0.453249i
$622$	−7.32846	−	36.3918i	−0.293844	−	1.45918i
$623$	−6.14414	−	16.8809i	−0.246160	−	0.676318i
$624$	2.18416	−	8.47171i	0.0874363	−	0.339140i
$625$	−17.1732	−	18.1682i	−0.686927	−	0.726727i
$626$	4.00897	+	6.57143i	0.160231	+	0.262647i
$627$	−3.71565	+	13.7204i	−0.148389	+	0.547941i
$628$	−7.37713	−	3.79597i	−0.294379	−	0.151476i
$629$	−29.4670	+	5.19583i	−1.17493	+	0.207171i
$630$	−3.08553	−	4.45066i	−0.122930	−	0.177318i
$631$	13.2184	+	36.3172i	0.526216	+	1.44577i	0.863493	+	0.504361i	$0.168272\pi$
$631$	13.2184	+	36.3172i	0.526216	+	1.44577i	−0.337277	+	0.941405i	$0.609506\pi$
$632$	0.268780	−	0.947149i	0.0106915	−	0.0376756i
$633$	−19.4833	+	23.2193i	−0.774391	+	0.922884i
$634$	0.454518	+	18.7892i	0.0180512	+	0.746213i
$635$	1.95546	−	16.7642i	0.0775999	−	0.665269i
$636$	−2.48704	+	3.27317i	−0.0986176	+	0.129790i
$637$	1.06291	−	6.02806i	0.0421140	−	0.238840i
$638$	25.1930	+	13.7438i	0.997401	+	0.544123i
$639$	2.98525	−	5.17061i	0.118095	−	0.204546i
$640$	−15.2083	+	20.2165i	−0.601160	+	0.799129i
$641$	−1.75540	+	4.82293i	−0.0693343	+	0.190494i	−0.969520	−	0.245011i	$-0.921208\pi$
$641$	−1.75540	+	4.82293i	−0.0693343	+	0.190494i	0.900186	+	0.435506i	$0.143430\pi$
$642$	−21.7756	+	27.2639i	−0.859415	+	1.07602i
$643$	−29.6773	+	24.9022i	−1.17036	+	0.982049i	−0.999994	−	0.00333236i	$-0.998939\pi$
$643$	−29.6773	+	24.9022i	−1.17036	+	0.982049i	−0.170365	+	0.985381i	$0.554495\pi$
$644$	8.66254	+	2.68623i	0.341352	+	0.105852i
$645$	6.55815	+	4.87996i	0.258227	+	0.192148i
$646$	−18.7401	+	28.0283i	−0.737318	+	1.10276i
$647$	27.4359			1.07862			0.539308	−	0.842108i	$-0.318686\pi$
$647$	27.4359			1.07862			0.539308	+	0.842108i	$0.318686\pi$
$648$	13.9263	−	3.51282i	0.547075	−	0.137997i
$649$	−12.4207	−	14.8024i	−0.487556	−	0.581046i
$650$	10.1059	+	4.06676i	0.396385	+	0.159511i
$651$	3.39233	−	9.32036i	0.132956	−	0.365294i
$652$	−15.0728	+	6.32719i	−0.590296	+	0.247792i
$653$	7.98181	+	4.60830i	0.312352	+	0.180337i	0.647979	−	0.761658i	$-0.275615\pi$
$653$	7.98181	+	4.60830i	0.312352	+	0.180337i	−0.335626	+	0.941995i	$0.608948\pi$
$654$	27.4405	+	14.9699i	1.07301	+	0.585370i
$655$	8.57375	−	8.09274i	0.335004	−	0.316209i
$656$	−9.33847	−	19.5408i	−0.364606	−	0.762940i
$657$	6.19087	−	3.57430i	0.241529	−	0.139447i
$658$	−0.474006	−	19.5948i	−0.0184787	−	0.763884i
$659$	25.5973	+	21.4787i	0.997129	+	0.836691i	0.986584	−	0.163254i	$-0.0521989\pi$
$659$	25.5973	+	21.4787i	0.997129	+	0.836691i	0.0105451	+	0.999944i	$0.496643\pi$
$660$	−1.55438	−	14.5008i	−0.0605041	−	0.564444i
$661$	9.38080	+	25.7735i	0.364871	+	1.00247i	0.977284	+	0.211936i	$0.0679769\pi$
$661$	9.38080	+	25.7735i	0.364871	+	1.00247i	−0.612413	+	0.790538i	$0.709801\pi$
$662$	−10.0529	+	29.8471i	−0.390718	+	1.16004i
$663$	2.07731	+	11.7810i	0.0806761	+	0.457537i
$664$	−1.36824	−	18.8243i	−0.0530979	−	0.730523i
$665$	16.7839	−	2.41678i	0.650853	−	0.0937187i
$666$	6.50142	−	3.96626i	0.251925	−	0.153690i
$667$	22.6777	−	3.99869i	0.878085	−	0.154830i
$668$	−48.0599	+	10.8938i	−1.85949	+	0.421493i
$669$	10.9070	−	3.96984i	0.421690	−	0.153483i
$670$	−30.5548	−	14.4219i	−1.18043	−	0.557168i
$671$	9.69470	−	11.5537i	0.374260	−	0.446025i
$672$	8.39486	+	11.1692i	0.323839	+	0.430863i
$673$	0.0628497	+	0.108859i	0.00242268	+	0.00419620i	0.867234	−	0.497900i	$-0.165896\pi$
$673$	0.0628497	+	0.108859i	0.00242268	+	0.00419620i	−0.864812	+	0.502097i	$0.832562\pi$
$674$	−1.48947	−	3.80345i	−0.0573721	−	0.146504i
$675$	3.29676	+	28.0908i	0.126892	+	1.08122i
$676$	21.2285	−	1.02765i	0.816479	−	0.0395251i
$677$	−9.60120	+	16.6298i	−0.369004	+	0.639134i	−0.989410	−	0.145147i	$-0.953635\pi$
$677$	−9.60120	+	16.6298i	−0.369004	+	0.639134i	0.620406	+	0.784281i	$0.286968\pi$
$678$	−0.820129	+	5.41374i	−0.0314969	+	0.207913i
$679$	9.20877	+	3.35172i	0.353400	+	0.128627i
$680$	7.48470	−	33.7726i	0.287025	−	1.29512i
$681$	−19.9586	+	16.7473i	−0.764815	+	0.641756i
$682$	−9.78684	+	8.62393i	−0.374758	+	0.330228i
$683$		−	15.0197i		−	0.574715i	−0.957823	−	0.287357i	$-0.907223\pi$
$683$		−	15.0197i		−	0.574715i	0.957823	−	0.287357i	$-0.0927767\pi$
$684$	1.84005	−	8.38196i	0.0703560	−	0.320492i
$685$	33.4604	+	24.8981i	1.27846	+	0.951308i
$686$	17.8493	+	20.2563i	0.681491	+	0.773388i
$687$	−7.06426	−	8.41886i	−0.269518	−	0.321199i
$688$	8.49280	+	5.82757i	0.323785	+	0.222174i
$689$	2.09586	+	0.762829i	0.0798458	+	0.0290615i
$690$	−8.23602	−	8.31327i	−0.313540	−	0.316481i
$691$	33.3764	+	19.2699i	1.26970	+	0.733060i	0.974931	−	0.222509i	$-0.0714246\pi$
$691$	33.3764	+	19.2699i	1.26970	+	0.733060i	0.294767	+	0.955569i	$0.404758\pi$
$692$	9.98404	−	0.483319i	0.379536	−	0.0183730i
$693$	3.87394	+	0.683079i	0.147159	+	0.0259480i
$694$	−1.90971	−	4.87658i	−0.0724916	−	0.185112i
$695$	−3.92117	+	33.6164i	−0.148738	+	1.27514i
$696$	31.9282	+	15.4641i	1.21023	+	0.586165i
$697$	22.6855	+	19.0354i	0.859276	+	0.721018i
$698$	−26.5267	+	5.34184i	−1.00405	+	0.202192i
$699$	−26.1057	+	9.50171i	−0.987409	+	0.359388i
$700$	−15.1473	+	8.55775i	−0.572513	+	0.323453i
$701$	−8.19094	−	46.4532i	−0.309368	−	1.75451i	−0.602198	−	0.798347i	$-0.705708\pi$
$701$	−8.19094	−	46.4532i	−0.309368	−	1.75451i	0.292830	−	0.956164i	$-0.405403\pi$
$702$	−6.41843	−	10.5210i	−0.242248	−	0.397088i
$703$	2.01491	+	23.7607i	0.0759937	+	0.896153i
$704$	−2.65723	−	18.1826i	−0.100148	−	0.685281i
$705$	−11.3449	+	22.6029i	−0.427275	+	0.851275i
$706$	22.5349	+	7.59008i	0.848113	+	0.285657i
$707$	−22.0656	+	8.03121i	−0.829861	+	0.302045i
$708$	−16.2211	−	17.5346i	−0.609624	−	0.658992i
$709$	−7.15207	−	6.00130i	−0.268602	−	0.225384i	0.498531	−	0.866872i	$-0.333873\pi$
$709$	−7.15207	−	6.00130i	−0.268602	−	0.225384i	−0.767133	+	0.641488i	$0.778317\pi$
$710$	−15.6599	−	11.0745i	−0.587707	−	0.415619i
$711$	−0.171325	−	0.296743i	−0.00642519	−	0.0111287i
$712$	−2.97310	+	29.0538i	−0.111422	+	1.08884i
$713$	−1.81755	+	10.3079i	−0.0680679	+	0.386032i
$714$	−16.7719	−	9.14974i	−0.627671	−	0.342420i
$715$	−7.26473	+	3.13573i	−0.271686	+	0.117270i
$716$	−46.9310	+	19.7005i	−1.75389	+	0.736242i
$717$	−13.7997	−	5.02268i	−0.515359	−	0.187575i
$718$	−40.7473	−	32.5448i	−1.52068	−	1.21456i
$719$	−5.37015	−	6.39989i	−0.200273	−	0.238676i	0.656556	−	0.754278i	$-0.272013\pi$
$719$	−5.37015	−	6.39989i	−0.200273	−	0.238676i	−0.856828	+	0.515602i	$0.827568\pi$
$720$	1.36059	+	8.69872i	0.0507064	+	0.324182i
$721$		−	18.2396i		−	0.679278i
$722$	20.9055	+	16.8807i	0.778023	+	0.628236i
$723$	−5.00796			−0.186248
$724$	4.49843	−	14.5065i	0.167183	−	0.539130i
$725$	−24.2559	+	36.9172i	−0.900842	+	1.37107i
$726$	−8.97990	−	7.17222i	−0.333275	−	0.266186i
$727$	−4.19333	−	1.52625i	−0.155522	−	0.0566053i	0.263086	−	0.964772i	$-0.415260\pi$
$727$	−4.19333	−	1.52625i	−0.155522	−	0.0566053i	−0.418608	+	0.908167i	$0.637482\pi$
$728$	4.43902	−	6.14518i	0.164521	−	0.227756i
$729$	14.5458	−	25.1940i	0.538733	−	0.933113i
$730$	−9.60808	−	20.8582i	−0.355611	−	0.771998i
$731$	−13.8698	−	2.44562i	−0.512994	−	0.0904546i
$732$	11.2798	−	14.8452i	0.416912	−	0.548695i
$733$	−23.5838	+	13.6161i	−0.871087	+	0.502922i	−0.867709	−	0.497072i	$-0.834408\pi$
$733$	−23.5838	+	13.6161i	−0.871087	+	0.502922i	−0.00337737	+	0.999994i	$0.501075\pi$
$734$	0.512970	+	21.2055i	0.0189341	+	0.782709i
$735$	−2.91177	−	12.2728i	−0.107402	−	0.452690i
$736$	−10.7711	−	10.0693i	−0.397030	−	0.371161i
$737$	23.0619	−	8.39383i	0.849494	−	0.309191i
$738$	−7.14314	−	2.40591i	−0.262943	−	0.0885628i
$739$	−40.6553	+	7.16863i	−1.49553	+	0.263702i	−0.860765	−	0.509002i	$-0.830015\pi$
$739$	−40.6553	+	7.16863i	−1.49553	+	0.263702i	−0.634766	+	0.772705i	$0.718903\pi$
$740$	−10.7703	−	21.9672i	−0.395926	−	0.807532i
$741$	9.49962	−	0.805567i	0.348977	−	0.0295932i
$742$	−3.04084	+	1.85510i	−0.111633	+	0.0681029i
$743$	47.6586	−	8.40349i	1.74842	−	0.308294i	0.794259	−	0.607579i	$-0.207859\pi$
$743$	47.6586	−	8.40349i	1.74842	−	0.308294i	0.954164	+	0.299285i	$0.0967481\pi$
$744$	−11.5687	+	11.2332i	−0.424128	+	0.411831i
$745$	−9.87071	+	32.9987i	−0.361635	+	1.20898i
$746$	−19.1761	+	3.86161i	−0.702087	+	0.141384i
$747$	−5.03188	−	4.22225i	−0.184107	−	0.154484i
$748$	13.6006	+	21.1271i	0.497288	+	0.772485i
$749$	−26.1838	+	15.1172i	−0.956736	+	0.552372i
$750$	22.4409	−	0.558722i	0.819427	−	0.0204016i
$751$	1.70684	−	9.67995i	0.0622833	−	0.353226i	−0.937700	−	0.347446i	$-0.887049\pi$
$751$	1.70684	−	9.67995i	0.0622833	−	0.353226i	0.999983	−	0.00578021i	$-0.00183991\pi$
$752$	−13.1928	+	29.0065i	−0.481090	+	1.05776i
$753$	−3.70920	+	6.42452i	−0.135171	+	0.234122i
$754$	2.88295	−	19.0306i	0.104991	−	0.693053i
$755$	−20.6245	+	13.5719i	−0.750601	+	0.493931i
$756$	19.5262	+	2.47661i	0.710161	+	0.0900734i
$757$	−8.78222	−	10.4662i	−0.319195	−	0.380402i	0.582459	−	0.812860i	$-0.302091\pi$
$757$	−8.78222	−	10.4662i	−0.319195	−	0.380402i	−0.901654	+	0.432458i	$0.857646\pi$
$758$	4.51409	+	5.12280i	0.163959	+	0.186069i
$759$	8.50008			0.308533
$760$	−26.2705	−	8.35818i	−0.952932	−	0.303183i
$761$	29.7646			1.07897			0.539483	−	0.841996i	$-0.318620\pi$
$761$	29.7646			1.07897			0.539483	+	0.841996i	$0.318620\pi$
$762$	10.0193	+	11.3704i	0.362961	+	0.411905i
$763$	17.4101	+	20.7485i	0.630288	+	0.751147i
$764$	−36.2532	−	4.59818i	−1.31159	−	0.166356i
$765$	−6.61790	−	10.0569i	−0.239271	−	0.363607i
$766$	3.01865	−	19.9263i	0.109068	−	0.719968i
$767$	−6.48001	+	11.2237i	−0.233980	+	0.405265i
$768$	−4.36778	−	22.2918i	−0.157609	−	0.804385i
$769$	−5.73370	+	32.5174i	−0.206763	+	1.17261i	0.687879	+	0.725825i	$0.258542\pi$
$769$	−5.73370	+	32.5174i	−0.206763	+	1.17261i	−0.894642	+	0.446784i	$0.852569\pi$
$770$	3.32762	−	12.1910i	0.119919	−	0.439331i
$771$	2.70499	−	1.56173i	0.0974178	−	0.0562442i
$772$	22.7985	+	35.4150i	0.820535	+	1.27461i
$773$	40.4821	+	33.9685i	1.45604	+	1.22176i	0.928021	+	0.372528i	$0.121509\pi$
$773$	40.4821	+	33.9685i	1.45604	+	1.22176i	0.528017	+	0.849234i	$0.322936\pi$
$774$	3.51411	−	0.707659i	0.126312	−	0.0254363i
$775$	−11.9974	−	16.0995i	−0.430960	−	0.578310i
$776$	−11.0988	−	11.4302i	−0.398422	−	0.410319i
$777$	−13.3071	+	2.34640i	−0.477390	+	0.0841768i
$778$	12.7644	−	7.78707i	0.457626	−	0.279180i
$779$	16.7327	−	16.6437i	0.599513	−	0.596321i
$780$	−8.78258	+	4.30602i	−0.314467	+	0.154180i
$781$	13.7201	−	2.41922i	0.490944	−	0.0865666i
$782$	19.1069	+	6.43548i	0.683262	+	0.230132i
$783$	46.9608	−	17.0923i	1.67824	−	0.610830i
$784$	−4.25870	−	15.3118i	−0.152096	−	0.546849i
$785$	2.14126	+	9.02520i	0.0764247	+	0.322123i
$786$	0.256013	+	10.5832i	0.00913167	+	0.377491i
$787$	−22.7850	+	13.1549i	−0.812198	+	0.468923i	−0.847719	−	0.530446i	$-0.822024\pi$
$787$	−22.7850	+	13.1549i	−0.812198	+	0.468923i	0.0355204	+	0.999369i	$0.488691\pi$
$788$	19.0531	−	25.0757i	0.678740	−	0.893283i
$789$	11.7671	+	2.07487i	0.418922	+	0.0738672i
$790$	−0.999785	+	0.460539i	−0.0355708	+	0.0163852i
$791$	−2.37226	+	4.10888i	−0.0843479	+	0.146095i
$792$	−5.18416	−	3.74482i	−0.184211	−	0.133067i
$793$	−9.50559	−	3.45975i	−0.337553	−	0.122859i
$794$	22.6980	+	18.1289i	0.805523	+	0.643369i
$795$	4.58822	−	0.268318i	0.162727	−	0.00951625i
$796$	2.39415	−	7.72063i	0.0848582	−	0.273650i
$797$	−32.8644			−1.16412			−0.582058	−	0.813147i	$-0.697752\pi$
$797$	−32.8644			−1.16412			−0.582058	+	0.813147i	$0.697752\pi$
$798$	−8.46290	+	12.6574i	−0.299583	+	0.448067i
$799$		−	43.5722i		−	1.54147i
$800$	28.2278	−	1.78700i	0.998002	−	0.0631799i
$801$	6.53352	+	7.78634i	0.230851	+	0.275117i
$802$	−15.2043	−	12.1436i	−0.536883	−	0.428807i
$803$	15.6748	+	5.70516i	0.553151	+	0.201331i
$804$	27.9735	−	11.7426i	0.986550	−	0.414130i
$805$	−4.01844	−	9.30975i	−0.141631	−	0.328126i
$806$	7.68025	+	4.18989i	0.270525	+	0.147583i
$807$	4.31935	−	24.4963i	0.152048	−	0.862310i
$808$	37.9773	+	3.88624i	1.33604	+	0.136718i
$809$	−17.2593	−	29.8939i	−0.606803	−	1.05101i	−0.991764	−	0.128081i	$-0.959118\pi$
$809$	−17.2593	−	29.8939i	−0.606803	−	1.05101i	0.384961	−	0.922933i	$-0.374215\pi$
$810$	−13.1106	−	9.27163i	−0.460659	−	0.325772i
$811$	−10.5725	−	8.87135i	−0.371249	−	0.311515i	0.438006	−	0.898972i	$-0.355685\pi$
$811$	−10.5725	−	8.87135i	−0.371249	−	0.311515i	−0.809256	+	0.587457i	$0.800129\pi$
$812$	20.8747	+	22.5652i	0.732559	+	0.791883i
$813$	32.8466	−	11.9552i	1.15198	−	0.419286i
$814$	16.8412	+	5.67236i	0.590284	+	0.198816i
$815$	16.3343	+	8.19860i	0.572167	+	0.287184i
$816$	18.0560	+	25.2735i	0.632086	+	0.884748i
$817$	−2.93393	+	10.8338i	−0.102645	+	0.379028i
$818$	−23.8966	−	39.1708i	−0.835524	−	1.36957i
$819$	−0.458140	−	2.59824i	−0.0160087	−	0.0907898i
$820$	−9.80297	+	22.1408i	−0.342335	+	0.773189i
$821$	−8.46877	+	3.08238i	−0.295562	+	0.107576i	−0.485545	−	0.874212i	$-0.661379\pi$
$821$	−8.46877	+	3.08238i	−0.295562	+	0.107576i	0.189983	+	0.981787i	$0.439157\pi$
$822$	−36.7128	+	7.39309i	−1.28051	+	0.257864i
$823$	−8.53939	−	7.16540i	−0.297665	−	0.249770i	0.481707	−	0.876332i	$-0.340017\pi$
$823$	−8.53939	−	7.16540i	−0.297665	−	0.249770i	−0.779371	+	0.626562i	$0.784461\pi$
$824$	−12.9259	+	26.6877i	−0.450296	+	0.929710i
$825$	−11.1838	+	11.8653i	−0.389370	+	0.413097i
$826$	−7.54743	−	19.2729i	−0.262609	−	0.670590i
$827$	−23.1319	−	4.07879i	−0.804377	−	0.141833i	−0.243681	−	0.969855i	$-0.578355\pi$
$827$	−23.1319	−	4.07879i	−0.804377	−	0.141833i	−0.560695	+	0.828022i	$0.689466\pi$
$828$	−5.12560	+	0.248126i	−0.178127	+	0.00862297i
$829$	−23.3384	−	13.4744i	−0.810576	−	0.467986i	0.0365797	−	0.999331i	$-0.488354\pi$
$829$	−23.3384	−	13.4744i	−0.810576	−	0.467986i	−0.847156	+	0.531344i	$0.821687\pi$
$830$	−14.9906	+	14.8513i	−0.520333	+	0.515498i
$831$	−6.41634	−	2.33536i	−0.222580	−	0.0810127i
$832$	−10.8500	+	5.84565i	−0.376156	+	0.202661i
$833$	13.9688	+	16.6474i	0.483990	+	0.576797i
$834$	−20.0911	−	22.8004i	−0.695699	−	0.789512i
$835$	44.2013	+	32.8904i	1.52965	+	1.13822i
$836$	17.7427	−	9.28299i	0.613645	−	0.321059i
$837$			22.7153i			0.785155i
$838$	−17.5549	+	15.4689i	−0.606423	+	0.534366i
$839$	−24.6010	+	20.6427i	−0.849320	+	0.712664i	−0.959640	−	0.281232i	$-0.909257\pi$
$839$	−24.6010	+	20.6427i	−0.849320	+	0.712664i	0.110319	+	0.993896i	$0.464813\pi$
$840$	3.38004	−	15.2515i	0.116623	−	0.526226i
$841$	46.0911	+	16.7758i	1.58935	+	0.578476i
$842$	−2.49292	+	16.4560i	−0.0859116	+	0.567110i
$843$	13.2157	−	22.8902i	0.455171	−	0.788380i
$844$	42.6492	−	2.06461i	1.46805	−	0.0710670i
$845$	−16.3105	−	17.2800i	−0.561098	−	0.594449i
$846$	4.04397	+	10.3266i	0.139035	+	0.355035i
$847$	−4.97915	−	8.62415i	−0.171086	−	0.296329i
$848$	5.76395	−	0.559367i	0.197935	−	0.0192087i
$849$	15.5079	−	18.4816i	0.532230	−	0.634287i
$850$	−34.1228	+	18.2041i	−1.17040	+	0.624397i
$851$	13.3995	−	4.87702i	0.459329	−	0.167182i
$852$	16.7961	−	3.80718i	0.575424	−	0.130432i
$853$	10.4096	−	1.83550i	0.356419	−	0.0628464i	0.00742836	−	0.999972i	$-0.497635\pi$
$853$	10.4096	−	1.83550i	0.356419	−	0.0628464i	0.348991	+	0.937126i	$0.386524\pi$
$854$	13.7915	−	8.41366i	0.471936	−	0.287910i
$855$	−8.45612	+	4.53297i	−0.289193	+	0.155024i
$856$	49.0247	−	3.56335i	1.67563	−	0.121793i
$857$	1.51810	+	8.60955i	0.0518572	+	0.294097i	0.999696	−	0.0246531i	$-0.00784813\pi$
$857$	1.51810	+	8.60955i	0.0518572	+	0.294097i	−0.947839	+	0.318750i	$0.896737\pi$
$858$	2.26783	−	6.73318i	0.0774225	−	0.229867i
$859$	15.8719	+	43.6076i	0.541541	+	1.48787i	0.844862	+	0.534984i	$0.179682\pi$
$859$	15.8719	+	43.6076i	0.541541	+	1.48787i	−0.303321	+	0.952888i	$0.598096\pi$
$860$	−1.22736	−	11.4501i	−0.0418526	−	0.390444i
$861$	10.2446	+	8.59628i	0.349137	+	0.292960i
$862$	0.655291	+	27.0889i	0.0223193	+	0.922651i
$863$	2.47919	−	1.43136i	0.0843926	−	0.0487241i	−0.457210	−	0.889359i	$-0.651151\pi$
$863$	2.47919	−	1.43136i	0.0843926	−	0.0487241i	0.541602	+	0.840635i	$0.317818\pi$
$864$	−26.8151	−	17.4614i	−0.912269	−	0.594050i
$865$	−7.67106	−	8.12701i	−0.260824	−	0.276327i
$866$	22.8147	+	12.4463i	0.775274	+	0.422943i
$867$	−15.8795	−	9.16802i	−0.539295	−	0.311362i
$868$	−12.8833	+	5.40812i	−0.437289	+	0.183563i
$869$	0.273462	−	0.751331i	0.00927656	−	0.0254871i
$870$	−10.0867	−	38.3594i	−0.341971	−	1.30050i
$871$	−10.5804	−	12.6092i	−0.358503	−	0.427248i
$872$	−10.7700	−	42.6968i	−0.364719	−	1.44590i
$873$	−5.54481			−0.187663
$874$	6.47565	−	14.7051i	0.219042	−	0.497407i
$875$	18.2827	+	6.63974i	0.618069	+	0.224464i
$876$	19.6952	+	6.10743i	0.665439	+	0.206351i
$877$	31.2242	−	26.2002i	1.05436	−	0.884717i	0.0608191	−	0.998149i	$-0.480629\pi$
$877$	31.2242	−	26.2002i	1.05436	−	0.884717i	0.993546	+	0.113432i	$0.0361843\pi$
$878$	0.948409	−	1.18744i	0.0320072	−	0.0400743i
$879$	11.5514	−	31.7372i	0.389619	−	1.07047i
$880$	−13.5083	+	15.4793i	−0.455365	+	0.521807i
$881$	−20.5699	+	35.6280i	−0.693016	+	1.20034i	0.277829	+	0.960631i	$0.410385\pi$
$881$	−20.5699	+	35.6280i	−0.693016	+	1.20034i	−0.970845	+	0.239709i	$0.922948\pi$
$882$	−4.85564	−	2.64895i	−0.163498	−	0.0891948i
$883$	−9.05789	+	51.3698i	−0.304822	+	1.72873i	0.319518	+	0.947580i	$0.396479\pi$
$883$	−9.05789	+	51.3698i	−0.304822	+	1.72873i	−0.624340	+	0.781152i	$0.714632\pi$
$884$	10.1955	−	13.4182i	0.342912	−	0.451303i
$885$	−3.09418	+	26.5266i	−0.104010	+	0.891681i
$886$	−0.0616979	−	2.55051i	−0.00207278	−	0.0856860i
$887$	−15.1464	+	18.0507i	−0.508565	+	0.606085i	−0.957838	−	0.287310i	$-0.907239\pi$
$887$	−15.1464	+	18.0507i	−0.508565	+	0.606085i	0.449272	+	0.893395i	$0.351683\pi$
$888$	21.1335	+	5.99722i	0.709193	+	0.201253i
$889$	4.49132	+	12.3398i	0.150634	+	0.413863i
$890$	26.8348	−	18.6038i	0.899503	−	0.623602i
$891$	11.4865	−	2.02539i	0.384814	−	0.0678530i
$892$	−14.5392	−	7.48127i	−0.486807	−	0.250491i
$893$	−34.5845	−	3.11879i	−1.15733	−	0.104366i
$894$	−16.1068	−	26.4020i	−0.538693	−	0.883015i
$895$	50.8590	+	25.5273i	1.70003	+	0.853285i
$896$	3.51932	−	19.3659i	0.117572	−	0.646970i
$897$	−1.94985	−	5.35717i	−0.0651036	−	0.178871i
$898$	5.36839	+	26.6585i	0.179145	+	0.889605i
$899$	−22.8037	+	27.1764i	−0.760545	+	0.906382i
$900$	6.39753	−	7.48133i	0.213251	−	0.249378i
$901$	−6.85760	+	3.95923i	−0.228460	+	0.131901i
$902$	−6.41340	−	16.3771i	−0.213543	−	0.545297i
$903$	−6.26352	−	1.10443i	−0.208437	−	0.0367531i
$904$	6.38289	−	4.33084i	0.212292	−	0.144042i
$905$	−15.5903	+	6.72938i	−0.518241	+	0.223692i
$906$	3.32050	−	21.9189i	0.110316	−	0.728206i
$907$	9.21713	−	25.3238i	0.306050	−	0.840865i	−0.687367	−	0.726310i	$-0.741234\pi$
$907$	9.21713	−	25.3238i	0.306050	−	0.840865i	0.993417	−	0.114555i	$-0.0365441\pi$
$908$	36.4112	+	4.61822i	1.20835	+	0.153261i
$909$	10.1778	−	8.54019i	0.337576	−	0.283260i
$910$	−8.44667	+	0.699276i	−0.280004	+	0.0231808i
$911$	14.4933			0.480184			0.240092	−	0.970750i	$-0.422822\pi$
$911$	14.4933			0.480184			0.240092	+	0.970750i	$0.422822\pi$
$912$	21.3527	−	12.5226i	0.707058	−	0.414663i
$913$		−	15.3275i		−	0.507266i
$914$	−19.3170	+	17.0216i	−0.638948	+	0.563026i
$915$	−20.8095	+	1.21693i	−0.687941	+	0.0402306i
$916$	−1.94804	+	15.3588i	−0.0643651	+	0.507470i
$917$	−3.13736	+	8.61984i	−0.103605	+	0.284652i
$918$	43.2612	+	6.55366i	1.42783	+	0.216303i
$919$	27.7245	+	16.0067i	0.914547	+	0.528014i	0.881891	−	0.471453i	$-0.156270\pi$
$919$	27.7245	+	16.0067i	0.914547	+	0.528014i	0.0326556	+	0.999467i	$0.489604\pi$
$920$	−0.717911	+	16.4695i	−0.0236688	+	0.542985i
$921$	5.10753	−	28.9663i	0.168299	−	0.954470i
$922$	7.84632	+	20.0361i	0.258405	+	0.659855i
$923$	−4.67200	−	8.09213i	−0.153781	−	0.266356i
$924$	6.14196	+	9.54089i	0.202056	+	0.313872i
$925$	−10.8222	+	25.1213i	−0.355833	+	0.825983i
$926$	−24.9996	+	5.03433i	−0.821538	+	0.165438i
$927$	3.52970	+	9.69777i	0.115930	+	0.318516i
$928$	−14.5520	−	47.8102i	−0.477693	−	1.56945i
$929$	5.90367	+	33.4814i	0.193693	+	1.09849i	0.914267	+	0.405111i	$0.132767\pi$
$929$	5.90367	+	33.4814i	0.193693	+	1.09849i	−0.720574	+	0.693378i	$0.756122\pi$
$930$	17.9523	+	1.65509i	0.588680	+	0.0542727i
$931$	14.2133	−	9.89586i	0.465824	−	0.324324i
$932$	34.7992	+	17.9062i	1.13988	+	0.586538i
$933$	−6.47137	−	36.7010i	−0.211863	−	1.20154i
$934$	−14.6322	+	43.4429i	−0.478780	+	1.42149i
$935$	8.05057	−	26.9138i	0.263282	−	0.880177i
$936$	−1.17097	+	4.12635i	−0.0382743	+	0.134874i
$937$	8.27223	−	9.85846i	0.270242	−	0.322062i	−0.613807	−	0.789456i	$-0.710363\pi$
$937$	8.27223	−	9.85846i	0.270242	−	0.322062i	0.884049	+	0.467394i	$0.154807\pi$
$938$	26.2803	−	0.635733i	0.858083	−	0.0207574i
$939$	3.86389	+	6.69245i	0.126093	+	0.218400i
$940$	34.2265	−	9.89081i	1.11634	−	0.322603i
$941$	57.4727	+	10.1340i	1.87356	+	0.330358i	0.990346	−	0.138619i	$-0.0442664\pi$
$941$	57.4727	+	10.1340i	1.87356	+	0.330358i	0.883210	+	0.468978i	$0.155378\pi$
$942$	−7.31157	−	3.98876i	−0.238224	−	0.129961i
$943$	−12.2220	−	7.05640i	−0.398004	−	0.229788i
$944$	−2.61500	+	33.5483i	−0.0851110	+	1.09190i
$945$	−12.0968	−	18.3828i	−0.393507	−	0.597992i
$946$	6.53576	+	5.22010i	0.212496	+	0.169720i
$947$	−35.3209	+	29.6378i	−1.14778	+	0.963099i	−0.999665	−	0.0258718i	$-0.991764\pi$
$947$	−35.3209	+	29.6378i	−1.14778	+	0.963099i	−0.148111	+	0.988971i	$0.547319\pi$
$948$	0.292744	−	0.944039i	0.00950788	−	0.0306610i
$949$		−	11.1877i		−	0.363170i
$950$	12.0067	+	28.3873i	0.389550	+	0.921005i
$951$			18.8679i			0.611835i
$952$	6.58273	+	26.0966i	0.213348	+	0.845796i
$953$	39.2854	−	32.9644i	1.27258	−	1.06782i	0.278358	−	0.960477i	$-0.410210\pi$
$953$	39.2854	−	32.9644i	1.27258	−	1.06782i	0.994222	−	0.107344i	$-0.0342347\pi$
$954$	1.25778	−	1.57479i	0.0407222	−	0.0509858i
$955$	22.4593	+	34.1302i	0.726767	+	1.10443i
$956$	8.00724	+	19.0751i	0.258973	+	0.616931i
$957$	24.9502	+	14.4050i	0.806525	+	0.465647i
$958$	−4.46453	+	8.18369i	−0.144243	+	0.264403i
$959$	−31.9572	−	5.63492i	−1.03195	−	0.181961i
$960$	−15.7539	+	19.9202i	−0.508456	+	0.642922i
$961$	7.43738	+	12.8819i	0.239916	+	0.415546i
$962$	−0.288238	−	11.9154i	−0.00929315	−	0.384167i
$963$	10.9961	−	13.1047i	0.354346	−	0.422293i
$964$	4.79075	+	5.17871i	0.154300	+	0.166795i
$965$	13.4950	−	45.1151i	0.434420	−	1.45231i
$966$	8.62856	+	2.90622i	0.277619	+	0.0935062i
$967$	−7.98220	−	45.2693i	−0.256690	−	1.45576i	−0.791696	−	0.610915i	$-0.790802\pi$
$967$	−7.98220	−	45.2693i	−0.256690	−	1.45576i	0.535006	−	0.844848i	$-0.320309\pi$
$968$	1.17366	+	16.1472i	0.0377228	+	0.518992i
$969$	−19.4881	+	27.6744i	−0.626048	+	0.889030i
$970$	−1.63528	+	17.7374i	−0.0525057	+	0.569513i
$971$	−9.36806	−	53.1289i	−0.300635	−	1.70499i	−0.643369	−	0.765556i	$-0.722464\pi$
$971$	−9.36806	−	53.1289i	−0.300635	−	1.70499i	0.342734	−	0.939432i	$-0.388647\pi$
$972$	−19.0389	+	4.31556i	−0.610673	+	0.138422i
$973$	−9.00618	−	24.7443i	−0.288725	−	0.793265i
$974$	8.15069	+	40.4749i	0.261165	+	1.29690i
$975$	10.0436	+	4.32677i	0.321652	+	0.138567i
$976$	−26.1419	+	2.53696i	−0.836782	+	0.0812062i
$977$	7.52849	+	13.0397i	0.240858	+	0.417178i	0.960959	−	0.276691i	$-0.0892380\pi$
$977$	7.52849	+	13.0397i	0.240858	+	0.417178i	−0.720101	+	0.693869i	$0.755905\pi$
$978$	−15.2808	+	5.98407i	−0.488625	+	0.191350i
$979$	−4.11855	+	23.3575i	−0.131630	+	0.746508i
$980$	−9.90581	+	14.7516i	−0.316429	+	0.471222i
$981$	−13.2719	−	7.66256i	−0.423741	−	0.244647i
$982$	−8.22929	+	54.3222i	−0.262607	+	1.73349i
$983$	−3.91167	+	10.7472i	−0.124763	+	0.342783i	−0.986312	−	0.164891i	$-0.947273\pi$
$983$	−3.91167	+	10.7472i	−0.124763	+	0.342783i	0.861549	+	0.507675i	$0.169495\pi$
$984$	−8.89774	−	19.8380i	−0.283650	−	0.632411i
$985$	−35.1502	+	2.05557i	−1.11998	+	0.0654961i
$986$	45.1782	+	51.2703i	1.43877	+	1.63278i
$987$		−	19.6769i		−	0.626324i
$988$	−9.92064	−	9.05290i	−0.315618	−	0.288011i
$989$	6.71178			0.213422
$990$	0.589920	+	7.12573i	0.0187489	+	0.226471i
$991$	−8.97494	+	7.53087i	−0.285098	+	0.239226i	−0.774110	−	0.633051i	$-0.781802\pi$
$991$	−8.97494	+	7.53087i	−0.285098	+	0.239226i	0.489011	+	0.872277i	$0.337358\pi$
$992$	22.6832	+	1.21708i	0.720191	+	0.0386424i
$993$	−10.8138	+	29.7107i	−0.343166	+	0.942840i
$994$	14.7546	+	2.23519i	0.467989	+	0.0708958i
$995$	−8.29746	+	3.58149i	−0.263047	+	0.113541i
$996$	−0.916162	−	18.9254i	−0.0290297	−	0.599673i
$997$	−58.2344	−	10.2683i	−1.84430	−	0.325200i	−0.861201	−	0.508265i	$-0.830287\pi$
$997$	−58.2344	−	10.2683i	−1.84430	−	0.325200i	−0.983101	+	0.183064i	$0.941398\pi$
$998$	−25.0360	+	9.80431i	−0.792501	+	0.310350i
$999$	26.8000	−	15.4730i	0.847914	−	0.489543i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bb.a.219.15	yes	336
4.3	odd	2	inner	380.2.bb.a.219.36	yes	336
5.4	even	2	inner	380.2.bb.a.219.42	yes	336
19.2	odd	18	inner	380.2.bb.a.59.21	yes	336
20.19	odd	2	inner	380.2.bb.a.219.21	yes	336
76.59	even	18	inner	380.2.bb.a.59.42	yes	336
95.59	odd	18	inner	380.2.bb.a.59.36	yes	336
380.59	even	18	inner	380.2.bb.a.59.15	✓	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bb.a.59.15	✓	336	380.59	even	18	inner
380.2.bb.a.59.21	yes	336	19.2	odd	18	inner
380.2.bb.a.59.36	yes	336	95.59	odd	18	inner
380.2.bb.a.59.42	yes	336	76.59	even	18	inner
380.2.bb.a.219.15	yes	336	1.1	even	1	trivial
380.2.bb.a.219.21	yes	336	20.19	odd	2	inner
380.2.bb.a.219.36	yes	336	4.3	odd	2	inner
380.2.bb.a.219.42	yes	336	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.934972 - 1.06105i) q^{2} +(-0.912584 - 1.08758i) q^{3} +(-0.251654 + 1.98410i) q^{4} +(1.86792 - 1.22918i) q^{5} +(-0.300731 + 1.98515i) q^{6} +(-0.869878 + 1.50667i) q^{7} +(2.34052 - 1.58806i) q^{8} +(0.170934 - 0.969416i) q^{9} +(-3.05067 - 0.832706i) q^{10} +(1.98923 - 1.14848i) q^{11} +(2.38752 - 1.53697i) q^{12} +(-1.18014 - 0.990257i) q^{13} +(2.41197 - 0.485713i) q^{14} +(-3.04146 - 0.909772i) q^{15} +(-3.87334 - 0.998616i) q^{16} +(5.38638 - 0.949765i) q^{17} +(-1.18842 + 0.725008i) q^{18} +(-0.368312 - 4.34331i) q^{19} +(1.96875 + 4.01547i) q^{20} +(2.43246 - 0.428908i) q^{21} +(-3.07847 - 1.03687i) q^{22} +(-2.44934 + 0.891488i) q^{23} +(-3.86306 - 1.09625i) q^{24} +(1.97824 - 4.59201i) q^{25} +(0.0526880 + 2.17805i) q^{26} +(-4.89887 + 2.82836i) q^{27} +(-2.77049 - 2.10509i) q^{28} +(-8.70033 - 1.53410i) q^{29} +(1.87836 + 4.07775i) q^{30} +(2.00781 - 3.47763i) q^{31} +(2.56188 + 5.04349i) q^{32} +(-3.06440 - 1.11535i) q^{33} +(-6.04387 - 4.82722i) q^{34} +(0.227110 + 3.88358i) q^{35} +(1.88041 + 0.583109i) q^{36} -5.47065 q^{37} +(-4.26411 + 4.45167i) q^{38} +2.18719i q^{39} +(2.41989 - 5.84330i) q^{40} +(3.48030 + 4.14766i) q^{41} +(-2.72937 - 2.17994i) q^{42} +(-2.41969 - 0.880695i) q^{43} +(1.77811 + 4.23585i) q^{44} +(-0.872295 - 2.02090i) q^{45} +(3.23598 + 1.76536i) q^{46} +(1.38336 - 7.84540i) q^{47} +(2.44868 + 5.12387i) q^{48} +(1.98662 + 3.44093i) q^{49} +(-6.72195 + 2.19440i) q^{50} +(-5.94847 - 4.99136i) q^{51} +(2.26176 - 2.09232i) q^{52} +(-1.36045 + 0.495162i) q^{53} +(7.58134 + 2.55350i) q^{54} +(2.30402 - 4.59038i) q^{55} +(0.356724 + 4.90783i) q^{56} +(-4.38756 + 4.36420i) q^{57} +(6.50680 + 10.6658i) q^{58} +(-1.46082 - 8.28470i) q^{59} +(2.57048 - 5.80562i) q^{60} +(6.17019 - 2.24577i) q^{61} +(-5.56719 + 1.12110i) q^{62} +(1.31190 + 1.10082i) q^{63} +(2.95610 - 7.43381i) q^{64} +(-3.42161 - 0.399112i) q^{65} +(1.68168 + 4.29430i) q^{66} +(10.5222 + 1.85535i) q^{67} +(0.528926 + 10.9262i) q^{68} +(3.20479 + 1.85029i) q^{69} +(3.90833 - 3.87201i) q^{70} +(5.69952 + 2.07445i) q^{71} +(-1.13942 - 2.54040i) q^{72} +(4.66799 + 5.56309i) q^{73} +(5.11490 + 5.80463i) q^{74} +(-6.79946 + 2.03912i) q^{75} +(8.71027 + 0.362242i) q^{76} +3.99615i q^{77} +(2.32071 - 2.04496i) q^{78} +(0.266652 - 0.223748i) q^{79} +(-8.46256 + 2.89570i) q^{80} +(4.77166 + 1.73674i) q^{81} +(1.14689 - 7.57072i) q^{82} +(3.33647 - 5.77894i) q^{83} +(0.238860 + 4.93418i) q^{84} +(8.89389 - 8.39491i) q^{85} +(1.32788 + 3.39084i) q^{86} +(6.27133 + 10.8623i) q^{87} +(2.83197 - 5.84707i) q^{88} +(-6.63725 + 7.90997i) q^{89} +(-1.32870 + 2.81503i) q^{90} +(2.51857 - 0.916685i) q^{91} +(-1.15242 - 5.08410i) q^{92} +(-5.61448 + 0.989985i) q^{93} +(-9.61776 + 5.86742i) q^{94} +(-6.02669 - 7.66023i) q^{95} +(3.14724 - 7.38884i) q^{96} +(-0.978133 - 5.54727i) q^{97} +(1.79356 - 5.32509i) q^{98} +(-0.773329 - 2.12470i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40}+ \cdots + 24 q^{96}+O(q^{100}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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