LMFDB - Embedded newform 221.2.m.c.69.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [221,2,Mod(69,221)] 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("221.69"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(221, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 221 = 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	221.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.76469388467$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			69.9
Character	$\chi$	$=$	221.69
Dual form			221.2.m.c.205.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.79032 + 1.03364i) q^{2} +(-1.71618 + 2.97252i) q^{3} +(1.13683 + 1.96904i) q^{4} +0.855003i q^{5} +(-6.14503 + 3.54783i) q^{6} +(2.31756 - 1.33804i) q^{7} +0.565718i q^{8} +(-4.39057 - 7.60469i) q^{9} +(-0.883766 + 1.53073i) q^{10} +(3.03733 + 1.75360i) q^{11} -7.80401 q^{12} +(-2.30992 + 2.76844i) q^{13} +5.53223 q^{14} +(-2.54151 - 1.46734i) q^{15} +(1.68890 - 2.92527i) q^{16} +(-0.500000 - 0.866025i) q^{17} -18.1531i q^{18} +(-3.51346 + 2.02850i) q^{19} +(-1.68354 + 0.971990i) q^{20} +9.18531i q^{21} +(3.62519 + 6.27901i) q^{22} +(1.92127 - 3.32775i) q^{23} +(-1.68160 - 0.970875i) q^{24} +4.26897 q^{25} +(-6.99707 + 2.56875i) q^{26} +19.8430 q^{27} +(5.26933 + 3.04225i) q^{28} +(-1.74263 + 3.01833i) q^{29} +(-3.03341 - 5.25402i) q^{30} +1.86067i q^{31} +(7.02720 - 4.05716i) q^{32} +(-10.4252 + 6.01900i) q^{33} -2.06728i q^{34} +(1.14403 + 1.98152i) q^{35} +(9.98263 - 17.2904i) q^{36} +(2.05094 + 1.18411i) q^{37} -8.38696 q^{38} +(-4.26497 - 11.6174i) q^{39} -0.483690 q^{40} +(-3.03627 - 1.75299i) q^{41} +(-9.49432 + 16.4446i) q^{42} +(0.136893 + 0.237105i) q^{43} +7.97416i q^{44} +(6.50203 - 3.75395i) q^{45} +(6.87939 - 3.97182i) q^{46} -11.1659i q^{47} +(5.79694 + 10.0406i) q^{48} +(0.0807251 - 0.139820i) q^{49} +(7.64281 + 4.41258i) q^{50} +3.43237 q^{51} +(-8.07715 - 1.40110i) q^{52} -4.06368 q^{53} +(35.5252 + 20.5105i) q^{54} +(-1.49933 + 2.59692i) q^{55} +(0.756955 + 1.31108i) q^{56} -13.9251i q^{57} +(-6.23974 + 3.60252i) q^{58} +(2.52098 - 1.45549i) q^{59} -6.67245i q^{60} +(-4.20010 - 7.27478i) q^{61} +(-1.92326 + 3.33119i) q^{62} +(-20.3508 - 11.7495i) q^{63} +10.0190 q^{64} +(-2.36702 - 1.97499i) q^{65} -24.8859 q^{66} +(-9.04904 - 5.22447i) q^{67} +(1.13683 - 1.96904i) q^{68} +(6.59452 + 11.4220i) q^{69} +4.73007i q^{70} +(3.25004 - 1.87641i) q^{71} +(4.30210 - 2.48382i) q^{72} +6.52175i q^{73} +(2.44789 + 4.23986i) q^{74} +(-7.32633 + 12.6896i) q^{75} +(-7.98840 - 4.61210i) q^{76} +9.38558 q^{77} +(4.37260 - 25.2074i) q^{78} +1.03719 q^{79} +(2.50111 + 1.44402i) q^{80} +(-20.8825 + 36.1695i) q^{81} +(-3.62392 - 6.27682i) q^{82} -13.7646i q^{83} +(-18.0863 + 10.4421i) q^{84} +(0.740455 - 0.427502i) q^{85} +0.565991i q^{86} +(-5.98136 - 10.3600i) q^{87} +(-0.992043 + 1.71827i) q^{88} +(1.00327 + 0.579239i) q^{89} +15.5209 q^{90} +(-1.64910 + 9.50680i) q^{91} +8.73662 q^{92} +(-5.53087 - 3.19325i) q^{93} +(11.5416 - 19.9906i) q^{94} +(-1.73437 - 3.00402i) q^{95} +27.8513i q^{96} +(2.17358 - 1.25492i) q^{97} +(0.289047 - 0.166881i) q^{98} -30.7972i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{3} + 14 q^{4} - 9 q^{6} - 3 q^{7} - 14 q^{9} + q^{10} + 6 q^{11} - 18 q^{12} + q^{13} - 12 q^{14} + 3 q^{15} - 24 q^{16} - 11 q^{17} + 3 q^{19} + 12 q^{20} - 11 q^{22} + 3 q^{23} + 57 q^{24}+ \cdots + 18 q^{98}+O(q^{100}) $ 22 * q - 3 * q^3 + 14 * q^4 - 9 * q^6 - 3 * q^7 - 14 * q^9 + q^10 + 6 * q^11 - 18 * q^12 + q^13 - 12 * q^14 + 3 * q^15 - 24 * q^16 - 11 * q^17 + 3 * q^19 + 12 * q^20 - 11 * q^22 + 3 * q^23 + 57 * q^24 - 48 * q^25 - 33 * q^26 + 6 * q^27 - 6 * q^28 - 15 * q^29 + 34 * q^30 + 33 * q^32 + 36 * q^33 - 6 * q^35 - 3 * q^36 + 12 * q^37 - 44 * q^38 - 17 * q^39 - 18 * q^40 - 9 * q^41 - 48 * q^42 + 42 * q^43 + 3 * q^45 + 48 * q^46 - 16 * q^48 + 22 * q^49 + 102 * q^50 + 6 * q^51 - 9 * q^52 - 16 * q^53 + 45 * q^54 - 38 * q^55 + 44 * q^56 - 93 * q^58 + 45 * q^59 + q^61 - 18 * q^62 + 27 * q^63 - 26 * q^64 + 18 * q^65 - 76 * q^66 - 21 * q^67 + 14 * q^68 - 9 * q^69 + 6 * q^71 + 57 * q^72 + 4 * q^74 + 27 * q^75 + 99 * q^76 - 22 * q^77 - 41 * q^78 + 52 * q^79 + 63 * q^80 - 75 * q^81 + 14 * q^82 - 126 * q^84 - 3 * q^85 - 31 * q^87 + 53 * q^88 - 3 * q^89 - 4 * q^90 + 11 * q^91 - 92 * q^92 + 66 * q^93 - 17 * q^94 + 9 * q^95 - 60 * q^97 + 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/221\mathbb{Z}\right)^\times$.

$n$	$105$	$171$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.79032	+	1.03364i	1.26595	+	0.730894i	0.974218	−	0.225607i	$-0.0724365\pi$
$2$	1.79032	+	1.03364i	1.26595	+	0.730894i	0.291728	+	0.956501i	$0.405770\pi$
$3$	−1.71618	+	2.97252i	−0.990839	+	1.71618i	−0.378462	+	0.925617i	$0.623547\pi$
$3$	−1.71618	+	2.97252i	−0.990839	+	1.71618i	−0.612377	+	0.790566i	$0.709786\pi$
$4$	1.13683	+	1.96904i	0.568413	+	0.984521i
$5$			0.855003i			0.382369i	0.981554	+	0.191185i	$0.0612329\pi$
$5$			0.855003i			0.382369i	−0.981554	+	0.191185i	$0.938767\pi$
$6$	−6.14503	+	3.54783i	−2.50870	+	1.44840i
$7$	2.31756	−	1.33804i	0.875956	−	0.505733i	0.00663284	−	0.999978i	$-0.497889\pi$
$7$	2.31756	−	1.33804i	0.875956	−	0.505733i	0.869323	+	0.494245i	$0.164555\pi$
$8$			0.565718i			0.200011i
$9$	−4.39057	−	7.60469i	−1.46352	−	2.53490i
$10$	−0.883766	+	1.53073i	−0.279471	+	0.484059i
$11$	3.03733	+	1.75360i	0.915788	+	0.528731i	0.882289	−	0.470708i	$-0.156002\pi$
$11$	3.03733	+	1.75360i	0.915788	+	0.528731i	0.0334992	+	0.999439i	$0.489335\pi$
$12$	−7.80401			−2.25282
$13$	−2.30992	+	2.76844i	−0.640658	+	0.767826i
$13$	−2.30992	+	2.76844i	−0.640658	+	0.767826i
$14$	5.53223			1.47855
$15$	−2.54151	−	1.46734i	−0.656215	−	0.378866i
$16$	1.68890	−	2.92527i	0.422226	−	0.731317i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$18$		−	18.1531i		−	4.27872i
$19$	−3.51346	+	2.02850i	−0.806044	+	0.465370i	−0.845580	−	0.533848i	$-0.820745\pi$
$19$	−3.51346	+	2.02850i	−0.806044	+	0.465370i	0.0395363	+	0.999218i	$0.487412\pi$
$20$	−1.68354	+	0.971990i	−0.376450	+	0.217344i
$21$			9.18531i			2.00440i
$22$	3.62519	+	6.27901i	0.772892	+	1.33869i
$23$	1.92127	−	3.32775i	0.400613	−	0.693883i	−0.593187	−	0.805065i	$-0.702130\pi$
$23$	1.92127	−	3.32775i	0.400613	−	0.693883i	0.993800	+	0.111182i	$0.0354637\pi$
$24$	−1.68160	−	0.970875i	−0.343256	−	0.198179i
$25$	4.26897			0.853794
$26$	−6.99707	+	2.56875i	−1.37224	+	0.503774i
$27$	19.8430			3.81878
$28$	5.26933	+	3.04225i	0.995810	+	0.574931i
$29$	−1.74263	+	3.01833i	−0.323599	+	0.560490i	−0.981228	−	0.192852i	$-0.938226\pi$
$29$	−1.74263	+	3.01833i	−0.323599	+	0.560490i	0.657629	+	0.753342i	$0.271560\pi$
$30$	−3.03341	−	5.25402i	−0.553822	−	0.959248i
$31$			1.86067i			0.334186i	0.985941	+	0.167093i	$0.0534380\pi$
$31$			1.86067i			0.334186i	−0.985941	+	0.167093i	$0.946562\pi$
$32$	7.02720	−	4.05716i	1.24225	−	0.717211i
$33$	−10.4252	+	6.01900i	−1.81480	+	1.04777i
$34$		−	2.06728i		−	0.354536i
$35$	1.14403	+	1.98152i	0.193377	+	0.334938i
$36$	9.98263	−	17.2904i	1.66377	−	2.88174i
$37$	2.05094	+	1.18411i	0.337172	+	0.194666i	0.659021	−	0.752125i	$-0.270971\pi$
$37$	2.05094	+	1.18411i	0.337172	+	0.194666i	−0.321849	+	0.946791i	$0.604304\pi$
$38$	−8.38696			−1.36054
$39$	−4.26497	−	11.6174i	−0.682942	−	1.86028i
$40$	−0.483690			−0.0764782
$41$	−3.03627	−	1.75299i	−0.474185	−	0.273771i	0.243805	−	0.969824i	$-0.421604\pi$
$41$	−3.03627	−	1.75299i	−0.474185	−	0.273771i	−0.717990	+	0.696053i	$0.754938\pi$
$42$	−9.49432	+	16.4446i	−1.46500	+	2.53746i
$43$	0.136893	+	0.237105i	0.0208759	+	0.0361581i	0.876275	−	0.481812i	$-0.160021\pi$
$43$	0.136893	+	0.237105i	0.0208759	+	0.0361581i	−0.855399	+	0.517970i	$0.826688\pi$
$44$			7.97416i			1.20215i
$45$	6.50203	−	3.75395i	0.969266	−	0.559606i
$46$	6.87939	−	3.97182i	1.01431	−	0.585612i
$47$		−	11.1659i		−	1.62872i	−0.580360	−	0.814360i	$-0.697088\pi$
$47$		−	11.1659i		−	1.62872i	0.580360	−	0.814360i	$-0.302912\pi$
$48$	5.79694	+	10.0406i	0.836716	+	1.44923i
$49$	0.0807251	−	0.139820i	0.0115322	−	0.0199743i
$50$	7.64281	+	4.41258i	1.08086	+	0.624033i
$51$	3.43237			0.480627
$52$	−8.07715	−	1.40110i	−1.12010	−	0.194298i
$53$	−4.06368			−0.558190			−0.279095	−	0.960264i	$-0.590034\pi$
$53$	−4.06368			−0.558190			−0.279095	+	0.960264i	$0.590034\pi$
$54$	35.5252	+	20.5105i	4.83437	+	2.79113i
$55$	−1.49933	+	2.59692i	−0.202170	+	0.350169i
$56$	0.756955	+	1.31108i	0.101152	+	0.175201i
$57$		−	13.9251i		−	1.84442i
$58$	−6.23974	+	3.60252i	−0.819318	+	0.473034i
$59$	2.52098	−	1.45549i	0.328204	−	0.189488i	−0.326840	−	0.945080i	$-0.605984\pi$
$59$	2.52098	−	1.45549i	0.328204	−	0.189488i	0.655043	+	0.755591i	$0.272650\pi$
$60$		−	6.67245i		−	0.861410i
$61$	−4.20010	−	7.27478i	−0.537767	−	0.931440i	−0.999024	−	0.0441736i	$-0.985935\pi$
$61$	−4.20010	−	7.27478i	−0.537767	−	0.931440i	0.461256	−	0.887267i	$-0.347399\pi$
$62$	−1.92326	+	3.33119i	−0.244255	+	0.423061i
$63$	−20.3508	−	11.7495i	−2.56396	−	1.48030i
$64$	10.0190			1.25237
$65$	−2.36702	−	1.97499i	−0.293593	−	0.244968i
$66$	−24.8859			−3.06325
$67$	−9.04904	−	5.22447i	−1.10552	−	0.638270i	−0.167852	−	0.985812i	$-0.553683\pi$
$67$	−9.04904	−	5.22447i	−1.10552	−	0.638270i	−0.937664	+	0.347542i	$0.887016\pi$
$68$	1.13683	−	1.96904i	0.137860	−	0.238781i
$69$	6.59452	+	11.4220i	0.793887	+	1.37505i
$70$			4.73007i			0.565352i
$71$	3.25004	−	1.87641i	0.385709	−	0.222689i	−0.294590	−	0.955624i	$-0.595183\pi$
$71$	3.25004	−	1.87641i	0.385709	−	0.222689i	0.680299	+	0.732934i	$0.261850\pi$
$72$	4.30210	−	2.48382i	0.507008	−	0.292721i
$73$			6.52175i			0.763313i	0.924304	+	0.381656i	$0.124646\pi$
$73$			6.52175i			0.763313i	−0.924304	+	0.381656i	$0.875354\pi$
$74$	2.44789	+	4.23986i	0.284561	+	0.492874i
$75$	−7.32633	+	12.6896i	−0.845972	+	1.46527i
$76$	−7.98840	−	4.61210i	−0.916332	−	0.529045i
$77$	9.38558			1.06959
$78$	4.37260	−	25.2074i	0.495099	−	2.85417i
$79$	1.03719			0.116693			0.0583465	−	0.998296i	$-0.481417\pi$
$79$	1.03719			0.116693			0.0583465	+	0.998296i	$0.481417\pi$
$80$	2.50111	+	1.44402i	0.279633	+	0.161446i
$81$	−20.8825	+	36.1695i	−2.32027	+	4.01883i
$82$	−3.62392	−	6.27682i	−0.400196	−	0.693159i
$83$		−	13.7646i		−	1.51086i	−0.655231	−	0.755428i	$-0.727429\pi$
$83$		−	13.7646i		−	1.51086i	0.655231	−	0.755428i	$-0.272571\pi$
$84$	−18.0863	+	10.4421i	−1.97337	+	1.13933i
$85$	0.740455	−	0.427502i	0.0803136	−	0.0463691i
$86$			0.565991i			0.0610323i
$87$	−5.98136	−	10.3600i	−0.641269	−	1.11071i
$88$	−0.992043	+	1.71827i	−0.105752	+	0.183168i
$89$	1.00327	+	0.579239i	0.106346	+	0.0613992i	0.552230	−	0.833692i	$-0.313777\pi$
$89$	1.00327	+	0.579239i	0.106346	+	0.0613992i	−0.445883	+	0.895091i	$0.647110\pi$
$90$	15.5209			1.63605
$91$	−1.64910	+	9.50680i	−0.172873	+	0.996584i
$92$	8.73662			0.910856
$93$	−5.53087	−	3.19325i	−0.573524	−	0.331124i
$94$	11.5416	−	19.9906i	1.19042	−	2.06187i
$95$	−1.73437	−	3.00402i	−0.177943	−	0.308206i
$96$			27.8513i			2.84256i
$97$	2.17358	−	1.25492i	0.220694	−	0.127418i	−0.385578	−	0.922675i	$-0.625998\pi$
$97$	2.17358	−	1.25492i	0.220694	−	0.127418i	0.606272	+	0.795258i	$0.292664\pi$
$98$	0.289047	−	0.166881i	0.0291982	−	0.0168576i
$99$		−	30.7972i		−	3.09524i
$100$	4.85308	+	8.40578i	0.485308	+	0.840578i
$101$	3.61785	−	6.26630i	0.359989	−	0.623520i	−0.627969	−	0.778238i	$-0.716114\pi$
$101$	3.61785	−	6.26630i	0.359989	−	0.623520i	0.987959	+	0.154718i	$0.0494470\pi$
$102$	6.14503	+	3.54783i	0.608448	+	0.351288i
$103$	6.67757			0.657961			0.328980	−	0.944337i	$-0.393295\pi$
$103$	6.67757			0.657961			0.328980	+	0.944337i	$0.393295\pi$
$104$	−1.56615	−	1.30677i	−0.153574	−	0.128139i
$105$	−7.85347			−0.766421
$106$	−7.27529	−	4.20039i	−0.706638	−	0.407978i
$107$	0.165022	−	0.285827i	0.0159533	−	0.0276320i	−0.857939	−	0.513752i	$-0.828255\pi$
$107$	0.165022	−	0.285827i	0.0159533	−	0.0276320i	0.873892	+	0.486120i	$0.161588\pi$
$108$	22.5580	+	39.0716i	2.17065	+	3.75967i
$109$			17.1577i			1.64341i	0.569911	+	0.821707i	$0.306978\pi$
$109$			17.1577i			1.64341i	−0.569911	+	0.821707i	$0.693022\pi$
$110$	−5.36857	+	3.09955i	−0.511873	+	0.295530i
$111$	−7.03956	+	4.06429i	−0.668166	+	0.385766i
$112$		−	9.03931i		−	0.854135i
$113$	−0.858534	−	1.48702i	−0.0807641	−	0.139888i	0.822814	−	0.568310i	$-0.192403\pi$
$113$	−0.858534	−	1.48702i	−0.0807641	−	0.139888i	−0.903578	+	0.428423i	$0.859069\pi$
$114$	14.3936	−	24.9304i	1.34808	−	2.33494i
$115$	2.84523	+	1.64270i	0.265319	+	0.153182i
$116$	−7.92429			−0.735752
$117$	31.1950	+	5.41124i	2.88398	+	0.500270i
$118$	6.01781			0.553984
$119$	−2.31756	−	1.33804i	−0.212450	−	0.122658i
$120$	0.830101	−	1.43778i	0.0757775	−	0.131251i
$121$	0.650232	+	1.12623i	0.0591120	+	0.102385i
$122$		−	17.3656i		−	1.57220i
$123$	10.4216	−	6.01690i	0.939683	−	0.542526i
$124$	−3.66373	+	2.11526i	−0.329013	+	0.189956i
$125$			7.92500i			0.708833i
$126$	−24.2896	−	42.0709i	−2.16389	−	3.74797i
$127$	8.62746	−	14.9432i	0.765563	−	1.32599i	−0.174385	−	0.984678i	$-0.555794\pi$
$127$	8.62746	−	14.9432i	0.765563	−	1.32599i	0.939948	−	0.341317i	$-0.110873\pi$
$128$	3.88272	+	2.24169i	0.343187	+	0.198139i
$129$	−0.939730			−0.0827386
$130$	−2.19629	−	5.98252i	−0.192627	−	0.524702i
$131$	−13.8143			−1.20696			−0.603479	−	0.797379i	$-0.706219\pi$
$131$	−13.8143			−1.20696			−0.603479	+	0.797379i	$0.706219\pi$
$132$	−23.7033	−	13.6851i	−2.06311	−	1.19114i
$133$	−5.42844	+	9.40234i	−0.470706	+	0.815286i
$134$	−10.8004	−	18.7069i	−0.933016	−	1.61603i
$135$			16.9658i			1.46018i
$136$	0.489926	−	0.282859i	0.0420108	−	0.0242549i
$137$	−11.8237	+	6.82640i	−1.01016	+	0.583218i	−0.911240	−	0.411877i	$-0.864873\pi$
$137$	−11.8237	+	6.82640i	−1.01016	+	0.583218i	−0.0989242	+	0.995095i	$0.531540\pi$
$138$			27.2654i			2.32099i
$139$	11.0074	+	19.0653i	0.933633	+	1.61710i	0.777053	+	0.629435i	$0.216714\pi$
$139$	11.0074	+	19.0653i	0.933633	+	1.61710i	0.156581	+	0.987665i	$0.449953\pi$
$140$	−2.60113	+	4.50529i	−0.219836	+	0.380767i
$141$	33.1909	+	19.1628i	2.79518	+	1.61380i
$142$	7.75815			0.651049
$143$	−11.8707	+	4.35796i	−0.992680	+	0.364431i
$144$	−29.6610			−2.47175
$145$	−2.58068	−	1.48996i	−0.214314	−	0.123734i
$146$	−6.74114	+	11.6760i	−0.557901	+	0.966313i
$147$	0.277078	+	0.479913i	0.0228530	+	0.0395826i
$148$			5.38450i			0.442603i
$149$	−4.07022	+	2.34994i	−0.333446	+	0.192515i	−0.657370	−	0.753568i	$-0.728331\pi$
$149$	−4.07022	+	2.34994i	−0.333446	+	0.192515i	0.323924	+	0.946083i	$0.394998\pi$
$150$	−26.2329	+	15.1456i	−2.14191	+	1.23663i
$151$			15.0352i			1.22355i	0.791032	+	0.611775i	$0.209544\pi$
$151$			15.0352i			1.22355i	−0.791032	+	0.611775i	$0.790456\pi$
$152$	−1.14756	−	1.98763i	−0.0930792	−	0.161218i
$153$	−4.39057	+	7.60469i	−0.354956	+	0.614802i
$154$	16.8032	+	9.70132i	1.35404	+	0.781755i
$155$	−1.59088			−0.127782
$156$	18.0267	−	21.6049i	1.44329	−	1.72978i
$157$	−11.7869			−0.940698			−0.470349	−	0.882481i	$-0.655872\pi$
$157$	−11.7869			−0.940698			−0.470349	+	0.882481i	$0.655872\pi$
$158$	1.85690	+	1.07208i	0.147727	+	0.0852903i
$159$	6.97402	−	12.0794i	0.553076	−	0.957956i
$160$	3.46888	+	6.00828i	0.274239	+	0.474996i
$161$		−	10.2830i		−	0.810414i
$162$	−74.7725	+	43.1699i	−5.87468	+	3.39175i
$163$	−10.5472	+	6.08941i	−0.826118	+	0.476959i	−0.852522	−	0.522692i	$-0.824928\pi$
$163$	−10.5472	+	6.08941i	−0.826118	+	0.476959i	0.0264038	+	0.999651i	$0.491594\pi$
$164$		−	7.97138i		−	0.622460i
$165$	−5.14626	−	8.91359i	−0.400636	−	0.693922i
$166$	14.2276	−	24.6429i	1.10428	−	1.91266i
$167$	0.281107	+	0.162297i	0.0217527	+	0.0125589i	0.510837	−	0.859678i	$-0.329336\pi$
$167$	0.281107	+	0.162297i	0.0217527	+	0.0125589i	−0.489084	+	0.872237i	$0.662669\pi$
$168$	−5.19629			−0.400903
$169$	−2.32849	−	12.7898i	−0.179115	−	0.983828i
$170$	1.76753			0.135564
$171$	30.8522	+	17.8125i	2.35933	+	1.36216i
$172$	−0.311246	+	0.539094i	−0.0237323	+	0.0411055i
$173$	−5.73242	−	9.92885i	−0.435828	−	0.754876i	0.561535	−	0.827453i	$-0.310211\pi$
$173$	−5.73242	−	9.92885i	−0.435828	−	0.754876i	−0.997363	+	0.0725768i	$0.976878\pi$
$174$		−	24.7303i		−	1.87480i
$175$	9.89360	−	5.71207i	0.747886	−	0.431792i
$176$	10.2595	−	5.92333i	0.773339	−	0.446488i
$177$			9.99153i			0.751010i
$178$	1.19745	+	2.07404i	0.0897526	+	0.155456i
$179$	1.29736	−	2.24709i	0.0969692	−	0.167956i	−0.813460	−	0.581622i	$-0.802418\pi$
$179$	1.29736	−	2.24709i	0.0969692	−	0.167956i	0.910429	+	0.413666i	$0.135752\pi$
$180$	14.7834	+	8.53518i	1.10189	+	0.636175i
$181$	−13.5483			−1.00704			−0.503520	−	0.863984i	$-0.667962\pi$
$181$	−13.5483			−1.00704			−0.503520	+	0.863984i	$0.667962\pi$
$182$	−12.7790	+	15.3156i	−0.947245	+	1.13527i
$183$	28.8325			2.13136
$184$	1.88256	+	1.08690i	0.138784	+	0.0801273i
$185$	−1.01242	+	1.75356i	−0.0744344	+	0.128924i
$186$	−6.60134	−	11.4339i	−0.484034	−	0.838371i
$187$		−	3.50720i		−	0.256472i
$188$	21.9862	−	12.6937i	1.60351	−	0.925786i
$189$	45.9873	−	26.5508i	3.34508	−	1.93128i
$190$		−	7.17088i		−	0.520230i
$191$	8.14815	+	14.1130i	0.589579	+	1.02118i	0.994287	+	0.106735i	$0.0340398\pi$
$191$	8.14815	+	14.1130i	0.589579	+	1.02118i	−0.404708	+	0.914446i	$0.632627\pi$
$192$	−17.1944	+	29.7815i	−1.24090	+	2.14930i
$193$	−7.23588	−	4.17764i	−0.520850	−	0.300713i	0.216432	−	0.976298i	$-0.430558\pi$
$193$	−7.23588	−	4.17764i	−0.520850	−	0.300713i	−0.737282	+	0.675585i	$0.763891\pi$
$194$	5.18854			0.372516
$195$	9.93294	−	3.64656i	0.711313	−	0.261136i
$196$	0.367082			0.0262201
$197$	−14.5673	−	8.41046i	−1.03788	−	0.599220i	−0.118648	−	0.992936i	$-0.537856\pi$
$197$	−14.5673	−	8.41046i	−1.03788	−	0.599220i	−0.919232	+	0.393716i	$0.871189\pi$
$198$	31.8333	−	55.1368i	2.26229	−	3.91840i
$199$	12.2923	+	21.2910i	0.871382	+	1.50928i	0.860568	+	0.509336i	$0.170109\pi$
$199$	12.2923	+	21.2910i	0.871382	+	1.50928i	0.0108135	+	0.999942i	$0.496558\pi$
$200$			2.41503i			0.170768i
$201$	31.0596	−	17.9323i	2.19078	−	1.26485i
$202$	12.9542	−	7.47911i	0.911454	−	0.526228i
$203$			9.32689i			0.654619i
$204$	3.90200	+	6.75847i	0.273195	+	0.473188i
$205$	1.49881	−	2.59602i	0.104682	−	0.181314i
$206$	11.9550	+	6.90221i	0.832943	+	0.480900i
$207$	−33.7419			−2.34523
$208$	4.19718	+	11.4328i	0.291022	+	0.792720i
$209$	−14.2287			−0.984221
$210$	−14.0602	−	8.11767i	−0.970247	−	0.560173i
$211$	−0.519665	+	0.900087i	−0.0357752	+	0.0619645i	−0.883359	−	0.468698i	$-0.844723\pi$
$211$	−0.519665	+	0.900087i	−0.0357752	+	0.0619645i	0.847583	+	0.530662i	$0.178057\pi$
$212$	−4.61970	−	8.00156i	−0.317282	−	0.549549i
$213$			12.8811i			0.882596i
$214$	0.590885	−	0.341148i	0.0403921	−	0.0233204i
$215$	−0.202725	+	0.117044i	−0.0138258	+	0.00798230i
$216$			11.2255i			0.763800i
$217$	2.48966	+	4.31221i	0.169009	+	0.292732i
$218$	−17.7349	+	30.7178i	−1.20116	+	2.08047i
$219$	−19.3860	−	11.1925i	−1.30998	−	0.756320i
$220$	−6.81793			−0.459665
$221$	3.55250	+	0.616235i	0.238967	+	0.0414524i
$222$	−16.8041			−1.12782
$223$	17.1024	+	9.87409i	1.14526	+	0.661218i	0.947728	−	0.319078i	$-0.103373\pi$
$223$	17.1024	+	9.87409i	1.14526	+	0.661218i	0.197534	+	0.980296i	$0.436707\pi$
$224$	10.8573	−	18.8054i	0.725435	−	1.25649i
$225$	−18.7432	−	32.4642i	−1.24955	−	2.16428i
$226$		−	3.54966i		−	0.236120i
$227$	−1.22371	+	0.706511i	−0.0812206	+	0.0468928i	−0.540060	−	0.841626i	$-0.681599\pi$
$227$	−1.22371	+	0.706511i	−0.0812206	+	0.0468928i	0.458840	+	0.888519i	$0.348265\pi$
$228$	27.4191	−	15.8304i	1.81587	−	1.04840i
$229$			3.39722i			0.224494i	0.993680	+	0.112247i	$0.0358049\pi$
$229$			3.39722i			0.224494i	−0.993680	+	0.112247i	$0.964195\pi$
$230$	3.39592	+	5.88190i	0.223920	+	0.387841i
$231$	−16.1074	+	27.8988i	−1.05979	+	1.83561i
$232$	−1.70752	−	0.985839i	−0.112104	−	0.0647235i
$233$	−20.4869			−1.34214			−0.671072	−	0.741392i	$-0.734166\pi$
$233$	−20.4869			−1.34214			−0.671072	+	0.741392i	$0.734166\pi$
$234$	50.2557	+	41.9322i	3.28532	+	2.74120i
$235$	9.54691			0.622772
$236$	5.73183	+	3.30927i	0.373110	+	0.215415i
$237$	−1.78001	+	3.08306i	−0.115624	+	0.200267i
$238$	−2.76611	−	4.79105i	−0.179301	−	0.310558i
$239$			2.31190i			0.149545i	0.997201	+	0.0747723i	$0.0238230\pi$
$239$			2.31190i			0.149545i	−0.997201	+	0.0747723i	$0.976177\pi$
$240$	−8.58474	+	4.95640i	−0.554142	+	0.319934i
$241$	18.6687	−	10.7784i	1.20256	−	0.694296i	0.241433	−	0.970417i	$-0.422383\pi$
$241$	18.6687	−	10.7784i	1.20256	−	0.694296i	0.961123	+	0.276122i	$0.0890493\pi$
$242$			2.68842i			0.172818i
$243$	−41.9118	−	72.5934i	−2.68864	−	4.65687i
$244$	9.54956	−	16.5403i	0.611348	−	1.05889i
$245$	0.119547	+	0.0690202i	0.00763755	+	0.00440954i
$246$	24.8773			1.58612
$247$	2.50006	−	14.4125i	0.159075	−	0.917045i
$248$	−1.05261			−0.0668410
$249$	40.9154	+	23.6225i	2.59291	+	1.49702i
$250$	−8.19160	+	14.1883i	−0.518082	+	0.897345i
$251$	−12.0116	−	20.8046i	−0.758163	−	1.31318i	−0.943786	−	0.330556i	$-0.892764\pi$
$251$	−12.0116	−	20.8046i	−0.758163	−	1.31318i	0.185623	−	0.982621i	$-0.440570\pi$
$252$		−	53.4288i		−	3.36570i
$253$	11.6711	−	6.73830i	0.733754	−	0.423633i
$254$	30.8918	−	17.8354i	1.93832	−	1.11909i
$255$			2.93468i			0.183777i
$256$	−5.38476	−	9.32667i	−0.336547	−	0.582917i
$257$	−13.7212	+	23.7659i	−0.855906	+	1.48247i	0.0198953	+	0.999802i	$0.493667\pi$
$257$	−13.7212	+	23.7659i	−0.855906	+	1.48247i	−0.875802	+	0.482671i	$0.839667\pi$
$258$	−1.68242	−	0.971344i	−0.104743	−	0.0604732i
$259$	6.33756			0.393797
$260$	1.19795	−	6.90599i	0.0742936	−	0.428291i
$261$	30.6046			1.89438
$262$	−24.7319	−	14.2790i	−1.52794	−	0.882159i
$263$	−0.283488	+	0.491015i	−0.0174806	+	0.0302773i	−0.874633	−	0.484785i	$-0.838898\pi$
$263$	−0.283488	+	0.491015i	−0.0174806	+	0.0302773i	0.857153	+	0.515062i	$0.172231\pi$
$264$	−3.40505	−	5.89773i	−0.209567	−	0.362980i
$265$		−	3.47446i		−	0.213435i
$266$	−19.4373	+	11.2221i	−1.19178	+	0.688072i
$267$	−3.44359	+	1.98816i	−0.210744	+	0.121673i
$268$		−	23.7573i		−	1.45121i
$269$	−1.07912	−	1.86908i	−0.0657949	−	0.113960i	0.831251	−	0.555897i	$-0.187625\pi$
$269$	−1.07912	−	1.86908i	−0.0657949	−	0.113960i	−0.897046	+	0.441937i	$0.854292\pi$
$270$	−17.5365	+	30.3742i	−1.06724	+	1.84851i
$271$	−0.783967	−	0.452624i	−0.0476226	−	0.0274949i	0.476000	−	0.879445i	$-0.342086\pi$
$271$	−0.783967	−	0.452624i	−0.0476226	−	0.0274949i	−0.523622	+	0.851951i	$0.675420\pi$
$272$	−3.37781			−0.204810
$273$	−25.4290	−	21.2174i	−1.53903	−	1.28413i
$274$	−28.2242			−1.70508
$275$	12.9663	+	7.48607i	0.781894	+	0.451427i
$276$	−14.9936	+	25.9698i	−0.902511	+	1.56320i
$277$	4.50673	+	7.80589i	0.270783	+	0.469011i	0.969063	−	0.246815i	$-0.0793840\pi$
$277$	4.50673	+	7.80589i	0.270783	+	0.469011i	−0.698279	+	0.715825i	$0.746051\pi$
$278$			45.5107i			2.72955i
$279$	14.1498	−	8.16939i	0.847127	−	0.489089i
$280$	−1.12098	+	0.647199i	−0.0669915	+	0.0386776i
$281$		−	12.3263i		−	0.735324i	−0.929960	−	0.367662i	$-0.880158\pi$
$281$		−	12.3263i		−	0.735324i	0.929960	−	0.367662i	$-0.119842\pi$
$282$	39.6149	+	68.6150i	2.35903	+	4.08596i
$283$	9.71443	−	16.8259i	0.577463	−	1.00019i	−0.418307	−	0.908306i	$-0.637376\pi$
$283$	9.71443	−	16.8259i	0.577463	−	1.00019i	0.995769	−	0.0918889i	$-0.0292905\pi$
$284$	7.38947	+	4.26631i	0.438484	+	0.253159i
$285$	11.9060			0.705251
$286$	−25.7569	−	4.46793i	−1.52304	−	0.264194i
$287$	−9.38232			−0.553821
$288$	−61.7068	−	35.6265i	−3.63611	−	2.09931i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	−3.08016	−	5.33500i	−0.180873	−	0.313282i
$291$			8.61468i			0.505002i
$292$	−12.8416	+	7.41409i	−0.751497	+	0.433877i
$293$	19.2457	−	11.1115i	1.12434	−	0.649140i	0.181838	−	0.983329i	$-0.441795\pi$
$293$	19.2457	−	11.1115i	1.12434	−	0.649140i	0.942506	+	0.334188i	$0.108462\pi$
$294$			1.14560i			0.0668126i
$295$	1.24445	+	2.15545i	0.0724545	+	0.125495i
$296$	−0.669871	+	1.16025i	−0.0389355	+	0.0674382i
$297$	60.2696	+	34.7966i	3.49719	+	2.01911i
$298$	−9.71599			−0.562832
$299$	4.77466	+	13.0058i	0.276125	+	0.752143i
$300$	−33.3151			−1.92345
$301$	0.634513	+	0.366336i	0.0365727	+	0.0211153i
$302$	−15.5410	+	26.9179i	−0.894286	+	1.54895i
$303$	12.4178	+	21.5082i	0.713383	+	1.23562i
$304$			13.7038i			0.785965i
$305$	6.21996	−	3.59110i	0.356154	−	0.205626i
$306$	−15.7210	+	9.07654i	−0.898711	+	0.518871i
$307$			4.26205i			0.243248i	0.992576	+	0.121624i	$0.0388103\pi$
$307$			4.26205i			0.243248i	−0.992576	+	0.121624i	$0.961190\pi$
$308$	10.6698	+	18.4806i	0.607967	+	1.05303i
$309$	−11.4599	+	19.8492i	−0.651933	+	1.12918i
$310$	−2.84818	−	1.64440i	−0.161766	−	0.0933954i
$311$	−22.8323			−1.29470			−0.647352	−	0.762191i	$-0.724124\pi$
$311$	−22.8323			−1.29470			−0.647352	+	0.762191i	$0.724124\pi$
$312$	6.57219	−	2.41277i	0.372077	−	0.136596i
$313$	−4.92761			−0.278525			−0.139262	−	0.990256i	$-0.544473\pi$
$313$	−4.92761			−0.278525			−0.139262	+	0.990256i	$0.544473\pi$
$314$	−21.1023	−	12.1834i	−1.19087	−	0.687551i
$315$	10.0459	−	17.4000i	0.566022	−	0.980380i
$316$	1.17911	+	2.04227i	0.0663299	+	0.114887i
$317$			6.26010i			0.351602i	0.984426	+	0.175801i	$0.0562516\pi$
$317$			6.26010i			0.351602i	−0.984426	+	0.175801i	$0.943748\pi$
$318$	24.9714	−	14.4173i	1.40033	−	0.808480i
$319$	−10.5859	+	6.11177i	−0.592697	+	0.342194i
$320$			8.56624i			0.478868i
$321$	0.566417	+	0.981064i	0.0316143	+	0.0547576i
$322$	10.6289	−	18.4098i	0.592327	−	1.02594i
$323$	3.51346	+	2.02850i	0.195494	+	0.112869i
$324$	−94.9589			−5.27550
$325$	−9.86100	+	11.8184i	−0.546990	+	0.655566i
$326$	−25.1770			−1.39443
$327$	−51.0016	−	29.4458i	−2.82040	−	1.62836i
$328$	0.991698	−	1.71767i	0.0547573	−	0.0948425i
$329$	−14.9405	−	25.8777i	−0.823698	−	1.42669i
$330$		−	21.2776i		−	1.17129i
$331$	−5.89473	+	3.40333i	−0.324004	+	0.187064i	−0.653176	−	0.757206i	$-0.726564\pi$
$331$	−5.89473	+	3.40333i	−0.324004	+	0.187064i	0.329172	+	0.944270i	$0.393230\pi$
$332$	27.1030	−	15.6479i	1.48747	−	0.858791i
$333$		−	20.7956i		−	1.13959i
$334$	0.335514	+	0.581127i	0.0183585	+	0.0317978i
$335$	4.46694	−	7.73696i	0.244055	−	0.422715i
$336$	26.8695	+	15.5131i	1.46585	+	0.846310i
$337$	−0.519772			−0.0283138			−0.0141569	−	0.999900i	$-0.504506\pi$
$337$	−0.519772			−0.0283138			−0.0141569	+	0.999900i	$0.504506\pi$
$338$	9.05128	−	25.3046i	0.492325	−	1.37639i
$339$	5.89361			0.320097
$340$	1.68354	+	0.971990i	0.0913026	+	0.0527136i
$341$	−3.26287	+	5.65146i	−0.176694	+	0.306044i
$342$	36.8235	+	63.7802i	1.99119	+	3.44884i
$343$			18.3006i			0.988138i
$344$	−0.134134	+	0.0774425i	−0.00723204	+	0.00417542i
$345$	−9.76588	+	5.63833i	−0.525777	+	0.303558i
$346$		−	23.7011i		−	1.27418i
$347$	6.11815	+	10.5969i	0.328440	+	0.568874i	0.982202	−	0.187825i	$-0.0601439\pi$
$347$	6.11815	+	10.5969i	0.328440	+	0.568874i	−0.653763	+	0.756700i	$0.726811\pi$
$348$	13.5995	−	23.5551i	0.729012	−	1.26269i
$349$	−24.9029	−	14.3777i	−1.33302	−	0.769619i	−0.347258	−	0.937770i	$-0.612887\pi$
$349$	−24.9029	−	14.3777i	−1.33302	−	0.769619i	−0.985761	+	0.168150i	$0.946221\pi$
$350$	23.6169			1.26238
$351$	−45.8358	+	54.9340i	−2.44653	+	2.93216i
$352$	28.4585			1.51685
$353$	0.563002	+	0.325050i	0.0299656	+	0.0173006i	0.514908	−	0.857245i	$-0.327826\pi$
$353$	0.563002	+	0.325050i	0.0299656	+	0.0173006i	−0.484942	+	0.874546i	$0.661159\pi$
$354$	−10.3277	+	17.8880i	−0.548909	+	0.950738i
$355$	1.60434	+	2.77880i	0.0851495	+	0.147483i
$356$			2.63398i			0.139600i
$357$	7.95472	−	4.59266i	0.421008	−	0.243069i
$358$	4.64537	−	2.68201i	0.245516	−	0.141749i
$359$			7.56951i			0.399503i	0.979847	+	0.199752i	$0.0640135\pi$
$359$			7.56951i			0.399503i	−0.979847	+	0.199752i	$0.935986\pi$
$360$	2.12368	+	3.67831i	0.111928	+	0.193864i
$361$	−1.27038	+	2.20036i	−0.0668622	+	0.115809i
$362$	−24.2558	−	14.0041i	−1.27486	−	0.736040i
$363$	−4.46367			−0.234282
$364$	−20.5940	+	7.56044i	−1.07942	+	0.396275i
$365$	−5.57611			−0.291867
$366$	51.6194	+	29.8025i	2.69819	+	1.55780i
$367$	−10.8988	+	18.8773i	−0.568913	+	0.985386i	0.427761	+	0.903892i	$0.359303\pi$
$367$	−10.8988	+	18.8773i	−0.568913	+	0.985386i	−0.996674	+	0.0814943i	$0.974031\pi$
$368$	−6.48970	−	11.2405i	−0.338299	−	0.585951i
$369$			30.7865i			1.60268i
$370$	−3.62510	+	2.09295i	−0.188460	+	0.108807i
$371$	−9.41783	+	5.43739i	−0.488949	+	0.282295i
$372$		−	14.5207i		−	0.752862i
$373$	1.25035	+	2.16567i	0.0647406	+	0.112134i	0.896579	−	0.442884i	$-0.146045\pi$
$373$	1.25035	+	2.16567i	0.0647406	+	0.112134i	−0.831838	+	0.555018i	$0.812711\pi$
$374$	3.62519	−	6.27901i	0.187454	−	0.324680i
$375$	−23.5572	−	13.6007i	−1.21649	−	0.702340i
$376$	6.31677			0.325762
$377$	−4.33071	−	11.7965i	−0.223043	−	0.607551i
$378$	109.776			5.64626
$379$	9.98599	+	5.76541i	0.512946	+	0.296149i	0.734044	−	0.679102i	$-0.237631\pi$
$379$	9.98599	+	5.76541i	0.512946	+	0.296149i	−0.221098	+	0.975252i	$0.570964\pi$
$380$	3.94336	−	6.83011i	0.202290	−	0.350377i
$381$	29.6126	+	51.2905i	1.51710	+	2.62769i
$382$			33.6890i			1.72368i
$383$	22.8572	−	13.1966i	1.16795	−	0.674317i	0.214754	−	0.976668i	$-0.431105\pi$
$383$	22.8572	−	13.1966i	1.16795	−	0.674317i	0.953196	+	0.302352i	$0.0977717\pi$
$384$	−13.3269	+	7.69429i	−0.680086	+	0.392648i
$385$			8.02470i			0.408977i
$386$	−8.63636	−	14.9586i	−0.439579	−	0.761373i
$387$	1.20207	−	2.08205i	0.0611047	−	0.105836i
$388$	4.94197	+	2.85325i	0.250891	+	0.144852i
$389$	2.63435			0.133567			0.0667834	−	0.997767i	$-0.478726\pi$
$389$	2.63435			0.133567			0.0667834	+	0.997767i	$0.478726\pi$
$390$	21.5524	+	3.73859i	1.09135	+	0.189311i
$391$	−3.84255			−0.194326
$392$	0.0790986	+	0.0456676i	0.00399508	+	0.00230656i
$393$	23.7078	−	41.0631i	1.19590	−	2.07136i
$394$	−17.3868	−	30.1148i	−0.875933	−	1.51716i
$395$			0.886801i			0.0446198i
$396$	60.6410	−	35.0111i	3.04732	−	1.75937i
$397$	20.6324	−	11.9121i	1.03551	−	0.597853i	0.116953	−	0.993137i	$-0.462687\pi$
$397$	20.6324	−	11.9121i	1.03551	−	0.597853i	0.918559	+	0.395284i	$0.129354\pi$
$398$			50.8235i			2.54755i
$399$	−18.6324	−	32.2723i	−0.932787	−	1.61563i
$400$	7.20988	−	12.4879i	0.360494	−	0.624394i
$401$	16.2154	+	9.36199i	0.809760	+	0.467515i	0.846873	−	0.531796i	$-0.178483\pi$
$401$	16.2154	+	9.36199i	0.809760	+	0.467515i	−0.0371123	+	0.999311i	$0.511816\pi$
$402$	74.1422			3.69788
$403$	−5.15115	−	4.29801i	−0.256597	−	0.214099i
$404$	16.4515			0.818491
$405$	−30.9250	−	17.8546i	−1.53668	−	0.887201i
$406$	−9.64065	+	16.6981i	−0.478458	+	0.828713i
$407$	4.15291	+	7.19305i	0.205852	+	0.356546i
$408$			1.94175i			0.0961309i
$409$	−11.8226	+	6.82580i	−0.584591	+	0.337514i	−0.762956	−	0.646451i	$-0.776253\pi$
$409$	−11.8226	+	6.82580i	−0.584591	+	0.337514i	0.178365	+	0.983964i	$0.442919\pi$
$410$	5.36670	−	3.09847i	0.265043	−	0.153022i
$411$		−	46.8614i		−	2.31150i
$412$	7.59124	+	13.1484i	0.373994	+	0.647776i
$413$	3.89501	−	6.74636i	0.191661	−	0.331967i
$414$	−60.4088	−	34.8771i	−2.96893	−	1.71411i
$415$	11.7687			0.577705
$416$	−5.00032	+	28.8261i	−0.245161	+	1.41332i
$417$	−75.5627			−3.70032
$418$	−25.4739	−	14.7074i	−1.24597	−	0.719361i
$419$	15.6138	−	27.0438i	0.762782	−	1.32118i	−0.178629	−	0.983917i	$-0.557166\pi$
$419$	15.6138	−	27.0438i	0.762782	−	1.32118i	0.941411	−	0.337261i	$-0.109501\pi$
$420$	−8.92804	−	15.4638i	−0.435644	−	0.754557i
$421$			8.28513i			0.403792i	0.979407	+	0.201896i	$0.0647104\pi$
$421$			8.28513i			0.403792i	−0.979407	+	0.201896i	$0.935290\pi$
$422$	−1.86073	+	1.07429i	−0.0905791	+	0.0522958i
$423$	−84.9135	+	49.0248i	−4.12863	+	2.38367i
$424$		−	2.29890i		−	0.111644i
$425$	−2.13448	−	3.69704i	−0.103538	−	0.179333i
$426$	−13.3144	+	23.0612i	−0.645085	+	1.11732i
$427$	−19.4680	−	11.2398i	−0.942121	−	0.543934i
$428$	0.750408			0.0362723
$429$	7.41824	−	42.7650i	0.358156	−	2.06471i
$430$	−0.483924			−0.0233369
$431$	12.9168	+	7.45753i	0.622182	+	0.359217i	0.777718	−	0.628614i	$-0.216377\pi$
$431$	12.9168	+	7.45753i	0.622182	+	0.359217i	−0.155536	+	0.987830i	$0.549711\pi$
$432$	33.5129	−	58.0460i	1.61239	−	2.79274i
$433$	14.6411	+	25.3591i	0.703606	+	1.21868i	0.967192	+	0.254046i	$0.0817615\pi$
$433$	14.6411	+	25.3591i	0.703606	+	1.21868i	−0.263586	+	0.964636i	$0.584905\pi$
$434$			10.2936i			0.494111i
$435$	8.85785	−	5.11408i	0.424701	−	0.245202i
$436$	−33.7843	+	19.5054i	−1.61797	+	0.934138i
$437$			15.5892i			0.745733i
$438$	−23.1381	−	40.0763i	−1.10558	−	1.91492i
$439$	−13.0531	+	22.6087i	−0.622993	+	1.07905i	0.365933	+	0.930641i	$0.380750\pi$
$439$	−13.0531	+	22.6087i	−0.622993	+	1.07905i	−0.988925	+	0.148414i	$0.952583\pi$
$440$	−1.46913	−	0.848200i	−0.0700378	−	0.0404363i
$441$	−1.41772			−0.0675103
$442$	5.72314	+	4.77527i	0.272222	+	0.227136i
$443$	30.9964			1.47269			0.736343	−	0.676609i	$-0.236551\pi$
$443$	30.9964			1.47269			0.736343	+	0.676609i	$0.236551\pi$
$444$	−16.0055	−	9.24079i	−0.759588	−	0.438549i
$445$	−0.495251	+	0.857800i	−0.0234771	+	0.0406636i
$446$	20.4125	+	35.3555i	0.966561	+	1.67413i
$447$		−	16.1317i		−	0.763005i
$448$	23.2195	−	13.4058i	1.09702	−	0.633365i
$449$	20.1405	−	11.6281i	0.950487	−	0.548764i	0.0572550	−	0.998360i	$-0.481765\pi$
$449$	20.1405	−	11.6281i	0.950487	−	0.548764i	0.893232	+	0.449595i	$0.148432\pi$
$450$		−	77.4949i		−	3.65315i
$451$	−6.14809	−	10.6488i	−0.289502	−	0.501433i
$452$	1.95201	−	3.38098i	0.0918148	−	0.159028i
$453$	−44.6925	−	25.8032i	−2.09984	−	1.21234i
$454$	−2.92111			−0.137095
$455$	−8.12835	−	1.40999i	−0.381063	−	0.0661011i
$456$	7.87768			0.368906
$457$	−1.49254	−	0.861716i	−0.0698179	−	0.0403094i	0.464685	−	0.885476i	$-0.346168\pi$
$457$	−1.49254	−	0.861716i	−0.0698179	−	0.0403094i	−0.534503	+	0.845167i	$0.679501\pi$
$458$	−3.51150	+	6.08210i	−0.164082	+	0.284198i
$459$	−9.92148	−	17.1845i	−0.463095	−	0.802105i
$460$			7.46984i			0.348283i
$461$	5.48717	−	3.16802i	0.255563	−	0.147549i	−0.366746	−	0.930321i	$-0.619528\pi$
$461$	5.48717	−	3.16802i	0.255563	−	0.147549i	0.622309	+	0.782772i	$0.286195\pi$
$462$	−57.6747	+	33.2985i	−2.68327	+	1.54919i
$463$			10.7413i			0.499189i	0.968350	+	0.249595i	$0.0802974\pi$
$463$			10.7413i			0.499189i	−0.968350	+	0.249595i	$0.919703\pi$
$464$	5.88629	+	10.1953i	0.273264	+	0.473307i
$465$	2.73024	−	4.72891i	0.126612	−	0.219298i
$466$	−36.6781	−	21.1761i	−1.69908	−	0.980966i
$467$	−17.8199			−0.824605			−0.412302	−	0.911047i	$-0.635275\pi$
$467$	−17.8199			−0.824605			−0.412302	+	0.911047i	$0.635275\pi$
$468$	24.8083	+	67.5758i	1.14676	+	3.12369i
$469$	−27.9623			−1.29118
$470$	17.0920	+	9.86808i	0.788396	+	0.455181i
$471$	20.2285	−	35.0368i	0.932080	−	1.61441i
$472$	0.823395	+	1.42616i	0.0378998	+	0.0656444i
$473$			0.960219i			0.0441509i
$474$	−6.37356	+	3.67978i	−0.292747	+	0.169018i
$475$	−14.9989	+	8.65960i	−0.688195	+	0.397330i
$476$		−	6.08450i		−	0.278882i
$477$	17.8419	+	30.9030i	0.816923	+	1.41495i
$478$	−2.38968	+	4.13905i	−0.109301	+	0.189316i
$479$	16.6873	+	9.63443i	0.762463	+	0.440208i	0.830179	−	0.557496i	$-0.188238\pi$
$479$	16.6873	+	9.63443i	0.762463	+	0.440208i	−0.0677161	+	0.997705i	$0.521571\pi$
$480$	−23.8130			−1.08691
$481$	−8.01564	+	2.94269i	−0.365482	+	0.134175i
$482$	44.5639			2.02983
$483$	30.5664	+	17.6475i	1.39082	+	0.802990i
$484$	−1.47840	+	2.56067i	−0.0672001	+	0.116394i
$485$	1.07296	+	1.85842i	0.0487206	+	0.0843865i
$486$		−	173.287i		−	7.86046i
$487$	11.3745	−	6.56706i	0.515427	−	0.297582i	−0.219635	−	0.975582i	$-0.570486\pi$
$487$	11.3745	−	6.56706i	0.515427	−	0.297582i	0.735062	+	0.678000i	$0.237153\pi$
$488$	4.11547	−	2.37607i	0.186299	−	0.107560i
$489$		−	41.8022i		−	1.89036i
$490$	0.142684	+	0.247136i	0.00644582	+	0.0111645i
$491$	−0.361104	+	0.625451i	−0.0162964	+	0.0282262i	−0.874059	−	0.485820i	$-0.838521\pi$
$491$	−0.361104	+	0.625451i	−0.0162964	+	0.0282262i	0.857762	+	0.514047i	$0.171854\pi$
$492$	23.6951	+	13.6804i	1.06826	+	0.616758i
$493$	3.48527			0.156969
$494$	19.3732	−	23.2188i	0.871643	−	1.04466i
$495$	26.3317			1.18352
$496$	5.44295	+	3.14249i	0.244396	+	0.141102i
$497$	5.02145	−	8.69740i	0.225243	−	0.390132i
$498$	48.8344	+	84.5836i	2.18832	+	3.79028i
$499$		−	5.47872i		−	0.245261i	−0.992452	−	0.122631i	$-0.960867\pi$
$499$		−	5.47872i		−	0.245261i	0.992452	−	0.122631i	$-0.0391331\pi$
$500$	−15.6046	+	9.00935i	−0.697861	+	0.402910i
$501$	−0.964861	+	0.557063i	−0.0431068	+	0.0248877i
$502$		−	49.6626i		−	2.21655i
$503$	14.9416	+	25.8796i	0.666213	+	1.15391i	0.978955	+	0.204076i	$0.0654190\pi$
$503$	14.9416	+	25.8796i	0.666213	+	1.15391i	−0.312743	+	0.949838i	$0.601248\pi$
$504$	6.64693	−	11.5128i	0.296078	−	0.512821i
$505$	5.35771	+	3.09327i	0.238415	+	0.137649i
$506$	27.8599			1.23852
$507$	42.0139	+	15.0281i	1.86590	+	0.667421i
$508$	39.2317			1.74063
$509$	30.5806	+	17.6557i	1.35546	+	0.782576i	0.989008	−	0.147860i	$-0.0472386\pi$
$509$	30.5806	+	17.6557i	1.35546	+	0.782576i	0.366453	+	0.930436i	$0.380572\pi$
$510$	−3.03341	+	5.25402i	−0.134322	+	0.232652i
$511$	8.72638	+	15.1145i	0.386033	+	0.668628i
$512$		−	31.2304i		−	1.38020i
$513$	−69.7176	+	40.2515i	−3.07811	+	1.77714i
$514$	−49.1307	+	28.3656i	−2.16706	+	1.25115i
$515$			5.70935i			0.251584i
$516$	−1.06831	−	1.85037i	−0.0470297	−	0.0814579i
$517$	19.5806	−	33.9146i	0.861154	−	1.49156i
$518$	11.3462	+	6.55076i	0.498525	+	0.287824i
$519$	39.3516			1.72734
$520$	1.11729	−	1.33907i	0.0489963	−	0.0587220i
$521$	−15.9319			−0.697987			−0.348994	−	0.937125i	$-0.613476\pi$
$521$	−15.9319			−0.697987			−0.348994	+	0.937125i	$0.613476\pi$
$522$	54.7920	+	31.6342i	2.39818	+	1.38459i
$523$	−8.47972	+	14.6873i	−0.370792	+	0.642231i	−0.989688	−	0.143243i	$-0.954247\pi$
$523$	−8.47972	+	14.6873i	−0.370792	+	0.642231i	0.618895	+	0.785473i	$0.287580\pi$
$524$	−15.7044	−	27.2008i	−0.686051	−	1.18827i
$525$			39.2118i			1.71134i
$526$	−1.01507	+	0.586049i	−0.0442590	+	0.0255530i
$527$	1.61139	−	0.930334i	0.0701931	−	0.0405260i
$528$			40.6621i			1.76959i
$529$	4.11741	+	7.13156i	0.179018	+	0.310068i
$530$	3.59135	−	6.22039i	0.155998	−	0.270197i
$531$	−22.1371	−	12.7808i	−0.960666	−	0.554641i
$532$	−24.6848			−1.07022
$533$	11.8666	−	4.35644i	0.513999	−	0.188699i
$534$	−8.22017			−0.355721
$535$	0.244383	+	0.141095i	0.0105656	+	0.00610006i
$536$	2.95557	−	5.11920i	0.127661	−	0.221116i
$537$	4.45301	+	7.71285i	0.192162	+	0.332834i
$538$		−	4.46168i		−	0.192356i
$539$	0.490377	−	0.283119i	0.0211220	−	0.0121948i
$540$	−33.4064	+	19.2872i	−1.43758	+	0.829988i
$541$		−	7.00625i		−	0.301222i	−0.988593	−	0.150611i	$-0.951876\pi$
$541$		−	7.00625i		−	0.301222i	0.988593	−	0.150611i	$-0.0481241\pi$
$542$	−0.935701	−	1.62068i	−0.0401918	−	0.0696142i
$543$	23.2514	−	40.2727i	0.997814	−	1.72826i
$544$	−7.02720	−	4.05716i	−0.301289	−	0.173949i
$545$	−14.6699			−0.628390
$546$	−23.5948	−	64.2703i	−1.00976	−	2.75051i
$547$	0.951573			0.0406863			0.0203432	−	0.999793i	$-0.493524\pi$
$547$	0.951573			0.0406863			0.0203432	+	0.999793i	$0.493524\pi$
$548$	−26.8829	−	15.5209i	−1.14838	−	0.663018i
$549$	−36.8816	+	63.8808i	−1.57407	+	2.72637i
$550$	15.4758	+	26.8049i	0.659891	+	1.14296i
$551$		−	14.1397i		−	0.602373i
$552$	−6.46165	+	3.73063i	−0.275026	+	0.158786i
$553$	2.40375	−	1.38781i	0.102218	−	0.0590155i
$554$			18.6334i			0.791656i
$555$	−3.47498	−	6.01885i	−0.147505	−	0.255486i
$556$	−25.0270	+	43.3480i	−1.06138	+	1.83836i
$557$	2.25251	+	1.30049i	0.0954420	+	0.0551035i	0.546961	−	0.837158i	$-0.315784\pi$
$557$	2.25251	+	1.30049i	0.0954420	+	0.0551035i	−0.451519	+	0.892261i	$0.649118\pi$
$558$	33.7769			1.42989
$559$	−0.972621	−	0.168716i	−0.0411375	−	0.00713592i
$560$	7.72864			0.326595
$561$	10.4252	+	6.01900i	0.440153	+	0.254122i
$562$	12.7409	−	22.0680i	0.537444	−	0.930880i
$563$	−20.8314	−	36.0811i	−0.877940	−	1.52064i	−0.853597	−	0.520934i	$-0.825584\pi$
$563$	−20.8314	−	36.0811i	−0.877940	−	1.52064i	−0.0243433	−	0.999704i	$-0.507749\pi$
$564$			87.1391i			3.66922i
$565$	1.27141	−	0.734050i	0.0534887	−	0.0308817i
$566$	34.7838	−	20.0825i	1.46207	−	0.844129i
$567$			111.767i			4.69376i
$568$	1.06152	+	1.83861i	0.0445404	+	0.0771462i
$569$	−6.13255	+	10.6219i	−0.257090	+	0.445293i	−0.965461	−	0.260547i	$-0.916097\pi$
$569$	−6.13255	+	10.6219i	−0.257090	+	0.445293i	0.708371	+	0.705840i	$0.249430\pi$
$570$	21.3155	+	12.3065i	0.892810	+	0.515464i
$571$	−33.3809			−1.39695			−0.698474	−	0.715636i	$-0.746137\pi$
$571$	−33.3809			−1.39695			−0.698474	+	0.715636i	$0.746137\pi$
$572$	−22.0760	−	18.4197i	−0.923042	−	0.770167i
$573$	−55.9348			−2.33671
$574$	−16.7973	−	9.69794i	−0.701107	−	0.404784i
$575$	8.20186	−	14.2060i	0.342041	−	0.592433i
$576$	−43.9889	−	76.1910i	−1.83287	−	3.17463i
$577$		−	42.3554i		−	1.76328i	−0.471923	−	0.881640i	$-0.656440\pi$
$577$		−	42.3554i		−	1.76328i	0.471923	−	0.881640i	$-0.343560\pi$
$578$	−1.79032	+	1.03364i	−0.0744674	+	0.0429938i
$579$	24.8362	−	14.3392i	1.03216	−	0.595916i
$580$		−	6.77530i		−	0.281329i
$581$	−18.4176	−	31.9002i	−0.764090	−	1.32344i
$582$	−8.90449	+	15.4230i	−0.369103	+	0.639305i
$583$	−12.3427	−	7.12608i	−0.511184	−	0.295132i
$584$	−3.68947			−0.152671
$585$	−4.62663	+	26.6718i	−0.191288	+	1.10274i
$586$	45.9412			1.89781
$587$	24.9213	+	14.3883i	1.02861	+	0.593871i	0.916587	−	0.399835i	$-0.130932\pi$
$587$	24.9213	+	14.3883i	1.02861	+	0.593871i	0.112027	+	0.993705i	$0.464266\pi$
$588$	−0.629979	+	1.09116i	−0.0259799	+	0.0449985i
$589$	−3.77437	−	6.53739i	−0.155520	−	0.269369i
$590$			5.14524i			0.211826i
$591$	50.0004	−	28.8678i	2.05674	−	1.18746i
$592$	6.92767	−	3.99969i	0.284725	−	0.164386i
$593$		−	14.7371i		−	0.605179i	−0.953121	−	0.302589i	$-0.902149\pi$
$593$		−	14.7371i		−	0.605179i	0.953121	−	0.302589i	$-0.0978511\pi$
$594$	71.9345	+	124.594i	2.95151	+	5.11216i
$595$	1.14403	−	1.98152i	0.0469008	−	0.0812345i
$596$	−9.25427	−	5.34296i	−0.379070	−	0.218856i
$597$	−84.3837			−3.45359
$598$	−4.89514	+	28.2197i	−0.200177	+	1.15399i
$599$	31.2011			1.27484			0.637422	−	0.770515i	$-0.280001\pi$
$599$	31.2011			1.27484			0.637422	+	0.770515i	$0.280001\pi$
$600$	−7.17872	−	4.14464i	−0.293070	−	0.169204i
$601$	−16.7076	+	28.9384i	−0.681518	+	1.18042i	0.293000	+	0.956112i	$0.405346\pi$
$601$	−16.7076	+	28.9384i	−0.681518	+	1.18042i	−0.974518	+	0.224311i	$0.927987\pi$
$602$	0.757321	+	1.31172i	0.0308661	+	0.0534616i
$603$			91.7535i			3.73649i
$604$	−29.6050	+	17.0925i	−1.20461	+	0.695482i
$605$	−0.962934	+	0.555950i	−0.0391488	+	0.0226026i
$606$			51.3421i			2.08563i
$607$	−8.59554	−	14.8879i	−0.348882	−	0.604282i	0.637169	−	0.770724i	$-0.280105\pi$
$607$	−8.59554	−	14.8879i	−0.348882	−	0.604282i	−0.986051	+	0.166442i	$0.946772\pi$
$608$	−16.4599	+	28.5094i	−0.667536	+	1.15621i
$609$	−27.7243	−	16.0067i	−1.12345	−	0.648622i
$610$	14.8476			0.601162
$611$	30.9122	+	25.7925i	1.25057	+	1.04345i
$612$	−19.9653			−0.807048
$613$	20.6664	+	11.9317i	0.834707	+	0.481918i	0.855461	−	0.517867i	$-0.173274\pi$
$613$	20.6664	+	11.9317i	0.834707	+	0.481918i	−0.0207548	+	0.999785i	$0.506607\pi$
$614$	−4.40543	+	7.63043i	−0.177789	+	0.307939i
$615$	5.14447	+	8.91049i	0.207445	+	0.359306i
$616$			5.30959i			0.213929i
$617$	19.5498	−	11.2871i	0.787046	−	0.454401i	−0.0518755	−	0.998654i	$-0.516520\pi$
$617$	19.5498	−	11.2871i	0.787046	−	0.454401i	0.838922	+	0.544252i	$0.183187\pi$
$618$	−41.0339	+	23.6909i	−1.65062	+	0.952988i
$619$		−	45.0388i		−	1.81026i	−0.425134	−	0.905131i	$-0.639773\pi$
$619$		−	45.0388i		−	1.81026i	0.425134	−	0.905131i	$-0.360227\pi$
$620$	−1.80855	−	3.13250i	−0.0726332	−	0.125804i
$621$	38.1238	−	66.0324i	1.52986	−	2.64979i
$622$	−40.8772	−	23.6004i	−1.63903	−	0.946292i
$623$	3.10019			0.124206
$624$	−41.1872	−	7.14455i	−1.64881	−	0.286011i
$625$	14.5689			0.582758
$626$	−8.82198	−	5.09337i	−0.352597	−	0.203572i
$627$	24.4191	−	42.2951i	0.975204	−	1.68910i
$628$	−13.3997	−	23.2089i	−0.534705	−	0.926137i
$629$		−	2.36822i		−	0.0944270i
$630$	35.9707	−	20.7677i	1.43311	−	0.827405i
$631$	−9.07320	+	5.23841i	−0.361198	+	0.208538i	−0.669606	−	0.742716i	$-0.733537\pi$
$631$	−9.07320	+	5.23841i	−0.361198	+	0.208538i	0.308408	+	0.951254i	$0.400204\pi$
$632$			0.586757i			0.0233399i
$633$	−1.78368	−	3.08943i	−0.0708950	−	0.122794i
$634$	−6.47069	+	11.2076i	−0.256984	+	0.445109i
$635$	12.7765	+	7.37651i	0.507019	+	0.292728i
$636$	31.7130			1.25750
$637$	0.200614	+	0.546456i	0.00794861	+	0.0216514i
$638$	−25.2695			−1.00043
$639$	−28.5391	−	16.4770i	−1.12899	−	0.651821i
$640$	−1.91665	+	3.31974i	−0.0757623	+	0.131224i
$641$	−13.9984	−	24.2460i	−0.552904	−	0.957658i	−0.998063	−	0.0622064i	$-0.980186\pi$
$641$	−13.9984	−	24.2460i	−0.552904	−	0.957658i	0.445159	−	0.895451i	$-0.353147\pi$
$642$			2.34189i			0.0924270i
$643$	16.0677	−	9.27671i	0.633649	−	0.365838i	−0.148515	−	0.988910i	$-0.547449\pi$
$643$	16.0677	−	9.27671i	0.633649	−	0.365838i	0.782164	+	0.623073i	$0.214116\pi$
$644$	20.2477	−	11.6900i	0.797869	−	0.460650i
$645$		−	0.803472i		−	0.0316367i
$646$	4.19348	+	7.26332i	0.164990	+	0.285771i
$647$	7.67896	−	13.3003i	0.301891	−	0.522891i	−0.674673	−	0.738117i	$-0.735715\pi$
$647$	7.67896	−	13.3003i	0.301891	−	0.522891i	0.976564	+	0.215226i	$0.0690488\pi$
$648$	−20.4617	−	11.8136i	−0.803812	−	0.464081i
$649$	10.2094			0.400753
$650$	−29.8703	+	10.9659i	−1.17161	+	0.430119i
$651$	−17.0908			−0.669842
$652$	−23.9806	−	13.8452i	−0.939153	−	0.542220i
$653$	−23.2842	+	40.3295i	−0.911183	+	1.57821i	−0.0987866	+	0.995109i	$0.531496\pi$
$653$	−23.2842	+	40.3295i	−0.911183	+	1.57821i	−0.812396	+	0.583106i	$0.801837\pi$
$654$	−60.8728	−	105.435i	−2.38031	−	4.12283i
$655$		−	11.8112i		−	0.461503i
$656$	−10.2559	+	5.92127i	−0.400427	+	0.231187i
$657$	49.5958	−	28.6342i	1.93492	−	1.11713i
$658$		−	61.7725i		−	2.40814i
$659$	20.2757	+	35.1185i	0.789829	+	1.36802i	0.926071	+	0.377348i	$0.123164\pi$
$659$	20.2757	+	35.1185i	0.789829	+	1.36802i	−0.136243	+	0.990676i	$0.543503\pi$
$660$	11.7008	−	20.2664i	0.455454	−	0.788869i
$661$	−20.1968	−	11.6606i	−0.785565	−	0.453546i	0.0528338	−	0.998603i	$-0.483175\pi$
$661$	−20.1968	−	11.6606i	−0.785565	−	0.453546i	−0.838399	+	0.545057i	$0.816508\pi$
$662$	−14.0713			−0.546895
$663$	−7.92851	+	9.50229i	−0.307918	+	0.369038i
$664$	7.78685			0.302189
$665$	−8.03903	−	4.64134i	−0.311740	−	0.179983i
$666$	21.4952	−	37.2308i	0.832923	−	1.44266i
$667$	6.69616	+	11.5981i	0.259276	+	0.449080i
$668$			0.738014i			0.0285546i
$669$	−58.7018	+	33.8915i	−2.26954	+	1.31032i
$670$	15.9945	−	9.23442i	0.617921	−	0.356757i
$671$		−	29.4612i		−	1.13734i
$672$	37.2663	+	64.5471i	1.43758	+	2.48996i
$673$	6.65206	−	11.5217i	0.256418	−	0.444129i	−0.708862	−	0.705347i	$-0.750791\pi$
$673$	6.65206	−	11.5217i	0.256418	−	0.444129i	0.965280	+	0.261218i	$0.0841243\pi$
$674$	−0.930557	−	0.537257i	−0.0358437	−	0.0206944i
$675$	84.7090			3.26045
$676$	22.5365	−	19.1246i	0.866788	−	0.735563i
$677$	−13.9848			−0.537479			−0.268740	−	0.963213i	$-0.586607\pi$
$677$	−13.9848			−0.537479			−0.268740	+	0.963213i	$0.586607\pi$
$678$	10.5514	+	6.09187i	0.405225	+	0.233957i
$679$	3.35827	−	5.81670i	0.128879	−	0.223225i
$680$	0.241845	+	0.418888i	0.00927434	+	0.0160636i
$681$		−	4.85001i		−	0.185853i
$682$	−11.6832	+	6.74527i	−0.447371	+	0.258290i
$683$	38.9757	−	22.5026i	1.49136	−	0.861039i	0.491412	−	0.870927i	$-0.336481\pi$
$683$	38.9757	−	22.5026i	1.49136	−	0.861039i	0.999951	+	0.00988781i	$0.00314744\pi$
$684$			80.9990i			3.09707i
$685$	−5.83659	−	10.1093i	−0.223005	−	0.386255i
$686$	−18.9162	+	32.7638i	−0.722224	+	1.25093i
$687$	−10.0983	−	5.83025i	−0.385273	−	0.222438i
$688$	0.924793			0.0352574
$689$	9.38680	−	11.2501i	0.357609	−	0.428593i
$690$	−23.3120			−0.887475
$691$	−3.98130	−	2.29860i	−0.151456	−	0.0874430i	0.422357	−	0.906430i	$-0.361203\pi$
$691$	−3.98130	−	2.29860i	−0.151456	−	0.0874430i	−0.573813	+	0.818987i	$0.694536\pi$
$692$	13.0335	−	22.5748i	0.495461	−	0.858163i
$693$	−41.2080	−	71.3744i	−1.56536	−	2.71129i
$694$			25.2959i			0.960219i
$695$	−16.3009	+	9.41134i	−0.618329	+	0.356993i
$696$	5.86085	−	3.38376i	0.222155	−	0.128261i
$697$			3.50598i			0.132798i
$698$	−29.7227	−	51.4812i	−1.12502	−	1.94859i
$699$	35.1593	−	60.8978i	1.32985	−	2.30336i
$700$	22.4946	+	12.9873i	0.850216	+	0.490872i
$701$	3.55300			0.134195			0.0670975	−	0.997746i	$-0.478626\pi$
$701$	3.55300			0.134195			0.0670975	+	0.997746i	$0.478626\pi$
$702$	−138.843	+	50.9717i	−5.24028	+	1.92380i
$703$	−9.60785			−0.362367
$704$	30.4308	+	17.5693i	1.14691	+	0.662166i
$705$	−16.3843	+	28.3784i	−0.617067	+	1.06879i
$706$	0.671969	+	1.16388i	0.0252899	+	0.0438034i
$707$		−	19.3634i		−	0.728234i
$708$	−19.6737	+	11.3586i	−0.739385	+	0.426884i
$709$	−7.08462	+	4.09031i	−0.266068	+	0.153615i	−0.627100	−	0.778939i	$-0.715758\pi$
$709$	−7.08462	+	4.09031i	−0.266068	+	0.153615i	0.361031	+	0.932554i	$0.382425\pi$
$710$			6.63324i			0.248941i
$711$	−4.55385	−	7.88751i	−0.170783	−	0.295805i
$712$	−0.327686	+	0.567568i	−0.0122805	+	0.0212705i
$713$	6.19183	+	3.57486i	0.231886	+	0.133879i
$714$	18.9886			0.710632
$715$	−3.72607	−	10.1495i	−0.139347	−	0.379570i
$716$	5.89949			0.220474
$717$	−6.87217	−	3.96765i	−0.256646	−	0.148175i
$718$	−7.82415	+	13.5518i	−0.291995	+	0.505750i
$719$	−11.5826	−	20.0616i	−0.431957	−	0.748171i	0.565085	−	0.825033i	$-0.308843\pi$
$719$	−11.5826	−	20.0616i	−0.431957	−	0.748171i	−0.997042	+	0.0768619i	$0.975510\pi$
$720$		−	25.3602i		−	0.945120i
$721$	15.4757	−	8.93489i	0.576344	−	0.332753i
$722$	−4.54877	+	2.62624i	−0.169288	+	0.0977384i
$723$			73.9906i			2.75174i
$724$	−15.4021	−	26.6772i	−0.572415	−	0.991452i
$725$	−7.43926	+	12.8852i	−0.276287	+	0.478543i
$726$	−7.99138	−	4.61383i	−0.296588	−	0.171235i
$727$	25.9102			0.960957			0.480479	−	0.877006i	$-0.340463\pi$
$727$	25.9102			0.960957			0.480479	+	0.877006i	$0.340463\pi$
$728$	−5.37817	−	0.932925i	−0.199328	−	0.0345765i
$729$	162.418			6.01550
$730$	−9.98302	−	5.76370i	−0.369488	−	0.213324i
$731$	0.136893	−	0.237105i	0.00506315	−	0.00876964i
$732$	32.7776	+	56.7725i	1.21149	+	2.09837i
$733$		−	17.4154i		−	0.643253i	−0.946867	−	0.321627i	$-0.895770\pi$
$733$		−	17.4154i		−	0.643253i	0.946867	−	0.321627i	$-0.104230\pi$
$734$	−39.0247	+	22.5309i	−1.44043	+	0.831631i
$735$	−0.410327	+	0.236903i	−0.0151352	+	0.00873829i
$736$		−	31.1797i		−	1.14930i
$737$	−18.3233	−	31.7368i	−0.674946	−	1.16904i
$738$	−31.8222	+	55.1176i	−1.17139	+	2.02891i
$739$	−21.1183	−	12.1927i	−0.776850	−	0.448515i	0.0584626	−	0.998290i	$-0.481380\pi$
$739$	−21.1183	−	12.1927i	−0.776850	−	0.448515i	−0.835313	+	0.549775i	$0.814713\pi$
$740$	−4.60377			−0.169238
$741$	38.5508	+	32.1659i	1.41620	+	1.18165i
$742$	−22.4812			−0.825312
$743$	−38.9018	−	22.4600i	−1.42717	−	0.823976i	−0.430272	−	0.902699i	$-0.641582\pi$
$743$	−38.9018	−	22.4600i	−1.42717	−	0.823976i	−0.996896	+	0.0787235i	$0.974916\pi$
$744$	1.80648	−	3.12891i	0.0662287	−	0.114711i
$745$	−2.00921	−	3.48005i	−0.0736117	−	0.127499i
$746$			5.16964i			0.189274i
$747$	−104.675	+	60.4342i	−3.82986	+	2.21117i
$748$	6.90582	−	3.98708i	0.252502	−	0.145782i
$749$		−	0.883229i		−	0.0322725i
$750$	−28.1166	−	48.6993i	−1.02667	−	1.77825i
$751$	−7.20712	+	12.4831i	−0.262991	+	0.455515i	−0.967035	−	0.254642i	$-0.918042\pi$
$751$	−7.20712	+	12.4831i	−0.262991	+	0.455515i	0.704044	+	0.710156i	$0.251376\pi$
$752$	−32.6634	−	18.8582i	−1.19111	−	0.687688i
$753$	82.4562			3.00487
$754$	4.43999	−	25.5959i	0.161695	−	0.932147i
$755$	−12.8552			−0.467848
$756$	104.559	+	60.3672i	3.80278	+	2.19554i
$757$	16.7078	−	28.9388i	0.607256	−	1.05180i	−0.384435	−	0.923152i	$-0.625604\pi$
$757$	16.7078	−	28.9388i	0.607256	−	1.05180i	0.991691	−	0.128646i	$-0.0410630\pi$
$758$	11.9187	+	20.6438i	0.432908	+	0.749818i
$759$			46.2566i			1.67901i
$760$	1.69943	−	0.981166i	0.0616448	−	0.0355906i
$761$	−6.00648	+	3.46785i	−0.217735	+	0.125709i	−0.604901	−	0.796301i	$-0.706787\pi$
$761$	−6.00648	+	3.46785i	−0.217735	+	0.125709i	0.387166	+	0.922010i	$0.373454\pi$
$762$			122.435i			4.43536i
$763$	22.9578	+	39.7641i	0.831129	+	1.43956i
$764$	−18.5261	+	32.0881i	−0.670249	+	1.16091i
$765$	−6.50203	−	3.75395i	−0.235081	−	0.135724i
$766$	54.5623			1.97142
$767$	−1.79385	+	10.3412i	−0.0647720	+	0.373401i
$768$	36.9649			1.33386
$769$	23.3813	+	13.4992i	0.843150	+	0.486793i	0.858334	−	0.513092i	$-0.171500\pi$
$769$	23.3813	+	13.4992i	0.843150	+	0.486793i	−0.0151834	+	0.999885i	$0.504833\pi$
$770$	−8.29466	+	14.3668i	−0.298919	+	0.517743i
$771$	−47.0963	−	81.5731i	−1.69613	−	2.93778i
$772$		−	18.9970i		−	0.683717i
$773$	−30.7397	+	17.7476i	−1.10563	+	0.638337i	−0.937694	−	0.347461i	$-0.887044\pi$
$773$	−30.7397	+	17.7476i	−1.10563	+	0.638337i	−0.167937	+	0.985798i	$0.553711\pi$
$774$	4.30418	−	2.48502i	0.154711	−	0.0893222i
$775$			7.94314i			0.285326i
$776$	0.709930	+	1.22963i	0.0254850	+	0.0441413i
$777$	−10.8764	+	18.8385i	−0.390189	+	0.675827i
$778$	4.71632	+	2.72297i	0.169088	+	0.0976232i
$779$	14.2238			0.509619
$780$	18.4723	+	15.4129i	0.661413	+	0.551869i
$781$	13.1619			0.470970
$782$	−6.87939	−	3.97182i	−0.246006	−	0.142032i
$783$	−34.5791	+	59.8927i	−1.23575	+	2.14039i
$784$	−0.272674	−	0.472285i	−0.00973835	−	0.0168673i
$785$		−	10.0778i		−	0.359694i
$786$	84.8890	−	49.0107i	3.02789	−	1.74815i
$787$	19.9149	−	11.4979i	0.709890	−	0.409855i	−0.101130	−	0.994873i	$-0.532246\pi$
$787$	19.9149	−	11.4979i	0.709890	−	0.409855i	0.811020	+	0.585018i	$0.198912\pi$
$788$		−	38.2449i		−	1.36242i
$789$	−0.973034	−	1.68534i	−0.0346409	−	0.0599998i
$790$	−0.916634	+	1.58766i	−0.0326124	+	0.0564863i
$791$	−3.97941	−	2.29751i	−0.141492	−	0.0816902i
$792$	17.4225			0.619082
$793$	29.8417	+	5.17649i	1.05971	+	0.183823i
$794$	49.2515			1.74787
$795$	10.3279	+	5.96281i	0.366293	+	0.211479i
$796$	−27.9485	+	48.4083i	−0.990610	+	1.71579i
$797$	−5.47050	−	9.47518i	−0.193775	−	0.335628i	0.752723	−	0.658337i	$-0.228740\pi$
$797$	−5.47050	−	9.47518i	−0.193775	−	0.335628i	−0.946498	+	0.322709i	$0.895407\pi$
$798$		−	77.0369i		−	2.72708i
$799$	−9.66999	+	5.58297i	−0.342100	+	0.197511i
$800$	29.9989	−	17.3199i	1.06062	−	0.612350i
$801$		−	10.1727i		−	0.359436i
$802$	19.3539	+	33.5219i	0.683409	+	1.18370i
$803$	−11.4365	+	19.8087i	−0.403587	+	0.699033i
$804$	70.6188	+	40.7718i	2.49053	+	1.43791i
$805$	8.79200			0.309877
$806$	−4.77960	−	13.0192i	−0.168354	−	0.458583i
$807$	7.40785			0.260768
$808$	3.54496	+	2.04668i	0.124711	+	0.0720020i
$809$	−2.41014	+	4.17449i	−0.0847361	+	0.146767i	−0.905279	−	0.424818i	$-0.860338\pi$
$809$	−2.41014	+	4.17449i	−0.0847361	+	0.146767i	0.820543	+	0.571585i	$0.193671\pi$
$810$	−36.9104	−	63.9307i	−1.29690	−	2.24630i
$811$			41.4343i			1.45495i	0.686132	+	0.727477i	$0.259307\pi$
$811$			41.4343i			1.45495i	−0.686132	+	0.727477i	$0.740693\pi$
$812$	−18.3650	+	10.6031i	−0.644486	+	0.372094i
$813$	2.69086	−	1.55357i	0.0943727	−	0.0544861i
$814$			17.1705i			0.601824i
$815$	−5.20646	−	9.01786i	−0.182374	−	0.315882i
$816$	5.79694	−	10.0406i	0.202933	−	0.351491i
$817$	−0.961934	−	0.555373i	−0.0336538	−	0.0194300i
$818$	−28.2217			−0.986748
$819$	79.5367	−	29.1994i	2.77924	−	1.02031i
$820$	6.81556			0.238010
$821$	26.1109	+	15.0751i	0.911275	+	0.526125i	0.880841	−	0.473412i	$-0.156978\pi$
$821$	26.1109	+	15.0751i	0.911275	+	0.526125i	0.0304340	+	0.999537i	$0.490311\pi$
$822$	48.4378	−	83.8968i	1.68946	−	2.92624i
$823$	−13.0729	−	22.6429i	−0.455692	−	0.789282i	0.543035	−	0.839710i	$-0.317275\pi$
$823$	−13.0729	−	22.6429i	−0.455692	−	0.789282i	−0.998728	+	0.0504276i	$0.983942\pi$
$824$			3.77762i			0.131600i
$825$	−44.5049	+	25.6949i	−1.54946	+	0.894582i
$826$	13.9466	−	8.05209i	0.485265	−	0.280168i
$827$		−	6.03471i		−	0.209847i	−0.994480	−	0.104924i	$-0.966540\pi$
$827$		−	6.03471i		−	0.209847i	0.994480	−	0.104924i	$-0.0334598\pi$
$828$	−38.3587	−	66.4393i	−1.33306	−	2.30892i
$829$	2.01165	−	3.48428i	0.0698674	−	0.121014i	−0.828975	−	0.559285i	$-0.811076\pi$
$829$	2.01165	−	3.48428i	0.0698674	−	0.121014i	0.898843	+	0.438271i	$0.144409\pi$
$830$	21.0698	+	12.1647i	0.731343	+	0.422241i
$831$	−30.9375			−1.07321
$832$	−23.1430	+	27.7369i	−0.802341	+	0.961603i
$833$	−0.161450			−0.00559392
$834$	−135.281	−	78.1047i	−4.68441	−	2.70454i
$835$	−0.138765	+	0.240347i	−0.00480214	+	0.00831756i
$836$	−16.1756	−	28.0169i	−0.559444	−	0.968985i
$837$			36.9212i			1.27618i
$838$	55.9072	−	32.2780i	1.93128	−	1.11503i
$839$	16.2762	−	9.39704i	0.561915	−	0.324422i	−0.191999	−	0.981395i	$-0.561497\pi$
$839$	16.2762	−	9.39704i	0.561915	−	0.324422i	0.753914	+	0.656973i	$0.228164\pi$
$840$		−	4.44285i		−	0.153293i
$841$	8.42645	+	14.5950i	0.290567	+	0.503277i
$842$	−8.56384	+	14.8330i	−0.295130	+	0.511179i
$843$	36.6400	+	21.1541i	1.26195	+	0.728587i
$844$	−2.36308			−0.0813405
$845$	10.9353	−	1.99087i	0.376185	−	0.0684880i
$846$	−202.696			−6.96884
$847$	3.01390	+	1.74008i	0.103559	+	0.0597898i
$848$	−6.86317	+	11.8874i	−0.235682	+	0.408214i
$849$	33.3435	+	57.7526i	1.14434	+	1.98206i
$850$		−	8.82516i		−	0.302701i
$851$	7.88082	−	4.55000i	0.270151	−	0.155972i
$852$	−25.3634	+	14.6435i	−0.868934	+	0.501679i
$853$		−	2.11437i		−	0.0723945i	−0.999345	−	0.0361973i	$-0.988476\pi$
$853$		−	2.11437i		−	0.0723945i	0.999345	−	0.0361973i	$-0.0115245\pi$
$854$	−23.2359	−	40.2458i	−0.795116	−	1.37718i
$855$	−15.2298	+	26.3787i	−0.520847	+	0.902134i
$856$	0.161698	+	0.0933561i	0.00552671	+	0.00319085i
$857$	4.46306			0.152455			0.0762275	−	0.997090i	$-0.475712\pi$
$857$	4.46306			0.152455			0.0762275	+	0.997090i	$0.475712\pi$
$858$	57.4846	−	68.8952i	1.96249	−	2.35204i
$859$	−12.0691			−0.411792			−0.205896	−	0.978574i	$-0.566011\pi$
$859$	−12.0691			−0.411792			−0.205896	+	0.978574i	$0.566011\pi$
$860$	−0.460927	−	0.266116i	−0.0157175	−	0.00907449i
$861$	16.1018	−	27.8891i	0.548747	−	0.950457i
$862$	15.4168	+	26.7027i	0.525099	+	0.909498i
$863$			3.58900i			0.122171i	0.998133	+	0.0610854i	$0.0194562\pi$
$863$			3.58900i			0.122171i	−0.998133	+	0.0610854i	$0.980544\pi$
$864$	139.441	−	80.5061i	4.74387	−	2.73887i
$865$	8.48920	−	4.90124i	0.288641	−	0.166647i
$866$			60.5346i			2.05705i
$867$	−1.71618	−	2.97252i	−0.0582846	−	0.100952i
$868$	−5.66062	+	9.80448i	−0.192134	+	0.332786i
$869$	3.15028	+	1.81882i	0.106866	+	0.0616992i
$870$	21.1445			0.716866
$871$	35.3662	−	12.9836i	1.19834	−	0.439932i
$872$	−9.70643			−0.328701
$873$	−19.0865	−	11.0196i	−0.645981	−	0.372957i
$874$	−16.1137	+	27.9097i	−0.545052	+	0.944058i
$875$	10.6040	+	18.3667i	0.358481	+	0.620907i
$876$		−	50.8958i		−	1.71961i
$877$	−2.91940	+	1.68551i	−0.0985811	+	0.0569158i	−0.548480	−	0.836164i	$-0.684793\pi$
$877$	−2.91940	+	1.68551i	−0.0985811	+	0.0569158i	0.449899	+	0.893079i	$0.351460\pi$
$878$	−46.7386	+	26.9845i	−1.57735	+	0.910684i
$879$			76.2774i			2.57277i
$880$	5.06446	+	8.77191i	0.170723	+	0.295701i
$881$	−13.9709	+	24.1983i	−0.470692	+	0.815262i	−0.999438	−	0.0335181i	$-0.989329\pi$
$881$	−13.9709	+	24.1983i	−0.470692	+	0.815262i	0.528747	+	0.848780i	$0.322662\pi$
$882$	−2.53816	−	1.46541i	−0.0854644	−	0.0493429i
$883$	3.44081			0.115792			0.0578962	−	0.998323i	$-0.481561\pi$
$883$	3.44081			0.115792			0.0578962	+	0.998323i	$0.481561\pi$
$884$	2.82518	+	7.69557i	0.0950212	+	0.258830i
$885$	−8.54279			−0.287163
$886$	55.4935	+	32.0392i	1.86434	+	1.07638i
$887$	−8.00624	+	13.8672i	−0.268823	+	0.465615i	−0.968558	−	0.248787i	$-0.919968\pi$
$887$	−8.00624	+	13.8672i	−0.268823	+	0.465615i	0.699735	+	0.714402i	$0.253301\pi$
$888$	−2.29924	−	3.98240i	−0.0771575	−	0.133641i
$889$		−	46.1757i		−	1.54868i
$890$	−1.77331	+	1.02382i	−0.0594416	+	0.0343186i
$891$	−126.854	+	73.2390i	−4.24976	+	2.45360i
$892$			44.9005i			1.50338i
$893$	22.6501	+	39.2311i	0.757957	+	1.31282i
$894$	16.6744	−	28.8809i	0.557676	−	0.965923i
$895$	1.92127	+	1.10925i	0.0642210	+	0.0370780i
$896$	11.9979			0.400822
$897$	−46.8540	−	8.12754i	−1.56441	−	0.271371i
$898$	48.0771			1.60435
$899$	−5.61612	−	3.24247i	−0.187308	−	0.108142i
$900$	42.6155	−	73.8123i	1.42052	−	2.46041i
$901$	2.03184	+	3.51925i	0.0676904	+	0.117243i
$902$		−	25.4197i		−	0.846382i
$903$	−2.17788	+	1.25740i	−0.0724754	+	0.0418437i
$904$	0.841236	−	0.485688i	0.0279791	−	0.0161537i
$905$		−	11.5839i		−	0.385061i
$906$	−53.3425	−	92.3920i	−1.77219	−	3.06952i
$907$	−22.7116	+	39.3376i	−0.754125	+	1.30618i	0.191682	+	0.981457i	$0.438606\pi$
$907$	−22.7116	+	39.3376i	−0.754125	+	1.30618i	−0.945808	+	0.324727i	$0.894728\pi$
$908$	−2.78230	−	1.60636i	−0.0923338	−	0.0533089i
$909$	−63.5376			−2.10741
$910$	−13.0949	−	10.9261i	−0.434092	−	0.362197i
$911$	14.2141			0.470934			0.235467	−	0.971882i	$-0.424338\pi$
$911$	14.2141			0.470934			0.235467	+	0.971882i	$0.424338\pi$
$912$	−40.7347	−	23.5182i	−1.34886	−	0.778764i
$913$	24.1375	−	41.8074i	0.798836	−	1.38362i
$914$	−1.78141	−	3.08549i	−0.0589238	−	0.102059i
$915$			24.6519i			0.814967i
$916$	−6.68926	+	3.86205i	−0.221019	+	0.127606i
$917$	−32.0154	+	18.4841i	−1.05724	+	0.610399i
$918$		−	41.0210i		−	1.35389i
$919$	−4.63829	−	8.03376i	−0.153003	−	0.265009i	0.779327	−	0.626617i	$-0.215561\pi$
$919$	−4.63829	−	8.03376i	−0.153003	−	0.265009i	−0.932330	+	0.361608i	$0.882228\pi$
$920$	−0.929302	+	1.60960i	−0.0306382	+	0.0530669i
$921$	−12.6690	−	7.31446i	−0.417459	−	0.241020i
$922$	13.0984			0.431372
$923$	−2.31262	+	13.3319i	−0.0761209	+	0.438825i
$924$	−73.2452			−2.40959
$925$	8.75538	+	5.05492i	0.287875	+	0.166205i
$926$	−11.1026	+	19.2303i	−0.364855	+	0.631947i
$927$	−29.3183	−	50.7808i	−0.962940	−	1.66786i
$928$			28.2806i			0.928356i
$929$	−16.3374	+	9.43243i	−0.536014	+	0.309468i	−0.743462	−	0.668778i	$-0.766818\pi$
$929$	−16.3374	+	9.43243i	−0.536014	+	0.309468i	0.207448	+	0.978246i	$0.433484\pi$
$930$	9.77599	−	5.64417i	0.320567	−	0.185080i
$931$			0.655003i			0.0214669i
$932$	−23.2901	−	40.3396i	−0.762892	−	1.32137i
$933$	39.1845	−	67.8695i	1.28284	−	2.22195i
$934$	−31.9032	−	18.4193i	−1.04391	−	0.602699i
$935$	2.99867			0.0980670
$936$	−3.06123	+	17.6475i	−0.100060	+	0.576828i
$937$	16.4276			0.536665			0.268333	−	0.963326i	$-0.413527\pi$
$937$	16.4276			0.536665			0.268333	+	0.963326i	$0.413527\pi$
$938$	−50.0614	−	28.9030i	−1.63456	−	0.943715i
$939$	8.45667	−	14.6474i	0.275973	−	0.477999i
$940$	10.8532	+	18.7983i	0.353992	+	0.613132i
$941$		−	2.79307i		−	0.0910516i	−0.998963	−	0.0455258i	$-0.985504\pi$
$941$		−	2.79307i		−	0.0910516i	0.998963	−	0.0455258i	$-0.0144963\pi$
$942$	72.4309	−	41.8180i	2.35993	−	1.36250i
$943$	−11.6670	+	6.73595i	−0.379930	+	0.219353i
$944$		−	9.83272i		−	0.320028i
$945$	22.7010	+	39.3193i	0.738464	+	1.27906i
$946$	−0.992522	+	1.71910i	−0.0322697	+	0.0558927i
$947$	11.7667	+	6.79352i	0.382367	+	0.220760i	0.678848	−	0.734279i	$-0.262480\pi$
$947$	11.7667	+	6.79352i	0.382367	+	0.220760i	−0.296481	+	0.955039i	$0.595813\pi$
$948$	−8.09424			−0.262889
$949$	−18.0550	−	15.0647i	−0.586092	−	0.489022i
$950$	−35.8037			−1.16162
$951$	−18.6082	−	10.7435i	−0.603414	−	0.348381i
$952$	0.756955	−	1.31108i	0.0245331	−	0.0424925i
$953$	−15.8006	−	27.3674i	−0.511831	−	0.886518i	−0.999906	−	0.0137160i	$-0.995634\pi$
$953$	−15.8006	−	27.3674i	−0.511831	−	0.886518i	0.488075	−	0.872802i	$-0.337699\pi$
$954$			73.7683i			2.38834i
$955$	−12.0667	+	6.96669i	−0.390468	+	0.225437i
$956$	−4.55224	+	2.62823i	−0.147230	+	0.0850032i
$957$		−	41.9557i		−	1.35623i
$958$	19.9171	+	34.4974i	0.643492	+	1.11456i
$959$	−18.2680	+	31.6412i	−0.589906	+	1.02175i
$960$	−25.4633	−	14.7012i	−0.821824	−	0.474480i
$961$	27.5379			0.888320
$962$	−17.3922	−	3.01695i	−0.560748	−	0.0972702i
$963$	−2.89817			−0.0933922
$964$	42.4461	+	24.5063i	1.36710	+	0.789294i
$965$	3.57190	−	6.18670i	0.114983	−	0.199157i
$966$	36.4824	+	63.1893i	1.17380	+	2.03308i
$967$		−	36.9730i		−	1.18897i	−0.804106	−	0.594486i	$-0.797356\pi$
$967$		−	36.9730i		−	1.18897i	0.804106	−	0.594486i	$-0.202644\pi$
$968$	−0.637131	+	0.367848i	−0.0204782	+	0.0118231i
$969$	−12.0595	+	6.96255i	−0.387407	+	0.223669i
$970$			4.43622i			0.142438i
$971$	18.6956	+	32.3817i	0.599970	+	1.03918i	0.992825	+	0.119578i	$0.0381541\pi$
$971$	18.6956	+	32.3817i	0.599970	+	1.03918i	−0.392855	+	0.919600i	$0.628513\pi$
$972$	95.2929	−	165.052i	3.05652	−	5.29405i
$973$	51.0205	+	29.4567i	1.63564	+	0.944339i
$974$	27.1519			0.870004
$975$	−18.2070	−	49.5945i	−0.583092	−	1.58829i
$976$	−28.3742			−0.908238
$977$	40.5667	+	23.4212i	1.29785	+	0.749311i	0.980032	−	0.198842i	$-0.0637180\pi$
$977$	40.5667	+	23.4212i	1.29785	+	0.749311i	0.317814	+	0.948153i	$0.397051\pi$
$978$	43.2084	−	74.8392i	1.38165	−	2.39309i
$979$	2.03151	+	3.51867i	0.0649272	+	0.112457i
$980$			0.313856i			0.0100258i
$981$	130.479	−	75.3322i	4.16588	−	2.40517i
$982$	−1.29298	+	0.746504i	−0.0412608	+	0.0238219i
$983$			7.36507i			0.234909i	0.993078	+	0.117455i	$0.0374735\pi$
$983$			7.36507i			0.234909i	−0.993078	+	0.117455i	$0.962527\pi$
$984$	3.40387	+	5.89567i	0.108511	+	0.187947i
$985$	7.19097	−	12.4551i	0.229123	−	0.396853i
$986$	6.23974	+	3.60252i	0.198714	+	0.114728i
$987$	102.563			3.26461
$988$	31.2209	−	11.4618i	0.993270	−	0.364647i
$989$	1.05203			0.0334527
$990$	47.1422	+	27.2175i	1.49828	+	0.865030i
$991$	0.192424	−	0.333289i	0.00611256	−	0.0105873i	−0.862953	−	0.505284i	$-0.831388\pi$
$991$	0.192424	−	0.333289i	0.00611256	−	0.0105873i	0.869066	+	0.494697i	$0.164721\pi$
$992$	7.54903	+	13.0753i	0.239682	+	0.415141i
$993$		−	23.3629i		−	0.741400i
$994$	17.9800	−	10.3807i	0.570290	−	0.329257i
$995$	−18.2039	+	10.5100i	−0.577101	+	0.333189i
$996$			107.419i			3.40369i
$997$	6.21564	+	10.7658i	0.196851	+	0.340956i	0.947506	−	0.319739i	$-0.103595\pi$
$997$	6.21564	+	10.7658i	0.196851	+	0.340956i	−0.750655	+	0.660695i	$0.770262\pi$
$998$	5.66303	−	9.80866i	0.179260	−	0.310488i
$999$	40.6967	+	23.4962i	1.28759	+	0.743388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	221.2.m.c.69.9	✓	22
13.6	odd	12		2873.2.a.x.1.5		22
13.7	odd	12		2873.2.a.x.1.18		22
13.10	even	6	inner	221.2.m.c.205.9	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
221.2.m.c.69.9	✓	22	1.1	even	1	trivial
221.2.m.c.205.9	yes	22	13.10	even	6	inner
2873.2.a.x.1.5		22	13.6	odd	12
2873.2.a.x.1.18		22	13.7	odd	12

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:	\( N \)	\(=\)	\( 221 = 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	221.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.79032 + 1.03364i) q^{2} +(-1.71618 + 2.97252i) q^{3} +(1.13683 + 1.96904i) q^{4} +0.855003i q^{5} +(-6.14503 + 3.54783i) q^{6} +(2.31756 - 1.33804i) q^{7} +0.565718i q^{8} +(-4.39057 - 7.60469i) q^{9} +(-0.883766 + 1.53073i) q^{10} +(3.03733 + 1.75360i) q^{11} -7.80401 q^{12} +(-2.30992 + 2.76844i) q^{13} +5.53223 q^{14} +(-2.54151 - 1.46734i) q^{15} +(1.68890 - 2.92527i) q^{16} +(-0.500000 - 0.866025i) q^{17} -18.1531i q^{18} +(-3.51346 + 2.02850i) q^{19} +(-1.68354 + 0.971990i) q^{20} +9.18531i q^{21} +(3.62519 + 6.27901i) q^{22} +(1.92127 - 3.32775i) q^{23} +(-1.68160 - 0.970875i) q^{24} +4.26897 q^{25} +(-6.99707 + 2.56875i) q^{26} +19.8430 q^{27} +(5.26933 + 3.04225i) q^{28} +(-1.74263 + 3.01833i) q^{29} +(-3.03341 - 5.25402i) q^{30} +1.86067i q^{31} +(7.02720 - 4.05716i) q^{32} +(-10.4252 + 6.01900i) q^{33} -2.06728i q^{34} +(1.14403 + 1.98152i) q^{35} +(9.98263 - 17.2904i) q^{36} +(2.05094 + 1.18411i) q^{37} -8.38696 q^{38} +(-4.26497 - 11.6174i) q^{39} -0.483690 q^{40} +(-3.03627 - 1.75299i) q^{41} +(-9.49432 + 16.4446i) q^{42} +(0.136893 + 0.237105i) q^{43} +7.97416i q^{44} +(6.50203 - 3.75395i) q^{45} +(6.87939 - 3.97182i) q^{46} -11.1659i q^{47} +(5.79694 + 10.0406i) q^{48} +(0.0807251 - 0.139820i) q^{49} +(7.64281 + 4.41258i) q^{50} +3.43237 q^{51} +(-8.07715 - 1.40110i) q^{52} -4.06368 q^{53} +(35.5252 + 20.5105i) q^{54} +(-1.49933 + 2.59692i) q^{55} +(0.756955 + 1.31108i) q^{56} -13.9251i q^{57} +(-6.23974 + 3.60252i) q^{58} +(2.52098 - 1.45549i) q^{59} -6.67245i q^{60} +(-4.20010 - 7.27478i) q^{61} +(-1.92326 + 3.33119i) q^{62} +(-20.3508 - 11.7495i) q^{63} +10.0190 q^{64} +(-2.36702 - 1.97499i) q^{65} -24.8859 q^{66} +(-9.04904 - 5.22447i) q^{67} +(1.13683 - 1.96904i) q^{68} +(6.59452 + 11.4220i) q^{69} +4.73007i q^{70} +(3.25004 - 1.87641i) q^{71} +(4.30210 - 2.48382i) q^{72} +6.52175i q^{73} +(2.44789 + 4.23986i) q^{74} +(-7.32633 + 12.6896i) q^{75} +(-7.98840 - 4.61210i) q^{76} +9.38558 q^{77} +(4.37260 - 25.2074i) q^{78} +1.03719 q^{79} +(2.50111 + 1.44402i) q^{80} +(-20.8825 + 36.1695i) q^{81} +(-3.62392 - 6.27682i) q^{82} -13.7646i q^{83} +(-18.0863 + 10.4421i) q^{84} +(0.740455 - 0.427502i) q^{85} +0.565991i q^{86} +(-5.98136 - 10.3600i) q^{87} +(-0.992043 + 1.71827i) q^{88} +(1.00327 + 0.579239i) q^{89} +15.5209 q^{90} +(-1.64910 + 9.50680i) q^{91} +8.73662 q^{92} +(-5.53087 - 3.19325i) q^{93} +(11.5416 - 19.9906i) q^{94} +(-1.73437 - 3.00402i) q^{95} +27.8513i q^{96} +(2.17358 - 1.25492i) q^{97} +(0.289047 - 0.166881i) q^{98} -30.7972i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{3} + 14 q^{4} - 9 q^{6} - 3 q^{7} - 14 q^{9} + q^{10} + 6 q^{11} - 18 q^{12} + q^{13} - 12 q^{14} + 3 q^{15} - 24 q^{16} - 11 q^{17} + 3 q^{19} + 12 q^{20} - 11 q^{22} + 3 q^{23} + 57 q^{24}+ \cdots + 18 q^{98}+O(q^{100}) \) 22 * q - 3 * q^3 + 14 * q^4 - 9 * q^6 - 3 * q^7 - 14 * q^9 + q^10 + 6 * q^11 - 18 * q^12 + q^13 - 12 * q^14 + 3 * q^15 - 24 * q^16 - 11 * q^17 + 3 * q^19 + 12 * q^20 - 11 * q^22 + 3 * q^23 + 57 * q^24 - 48 * q^25 - 33 * q^26 + 6 * q^27 - 6 * q^28 - 15 * q^29 + 34 * q^30 + 33 * q^32 + 36 * q^33 - 6 * q^35 - 3 * q^36 + 12 * q^37 - 44 * q^38 - 17 * q^39 - 18 * q^40 - 9 * q^41 - 48 * q^42 + 42 * q^43 + 3 * q^45 + 48 * q^46 - 16 * q^48 + 22 * q^49 + 102 * q^50 + 6 * q^51 - 9 * q^52 - 16 * q^53 + 45 * q^54 - 38 * q^55 + 44 * q^56 - 93 * q^58 + 45 * q^59 + q^61 - 18 * q^62 + 27 * q^63 - 26 * q^64 + 18 * q^65 - 76 * q^66 - 21 * q^67 + 14 * q^68 - 9 * q^69 + 6 * q^71 + 57 * q^72 + 4 * q^74 + 27 * q^75 + 99 * q^76 - 22 * q^77 - 41 * q^78 + 52 * q^79 + 63 * q^80 - 75 * q^81 + 14 * q^82 - 126 * q^84 - 3 * q^85 - 31 * q^87 + 53 * q^88 - 3 * q^89 - 4 * q^90 + 11 * q^91 - 92 * q^92 + 66 * q^93 - 17 * q^94 + 9 * q^95 - 60 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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