LMFDB - Embedded newform 228.2.m.a.11.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [228,2,Mod(11,228)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("228.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	228.11
Dual form			228.2.m.a.83.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.735371 - 1.20799i) q^{2} +(1.37888 - 1.04818i) q^{3} +(-0.918459 + 1.77664i) q^{4} +(2.70326 + 1.56073i) q^{5} +(-2.28018 - 0.894872i) q^{6} +1.45593i q^{7} +(2.82156 - 0.197001i) q^{8} +(0.802644 - 2.89063i) q^{9} +(-0.102562 - 4.41321i) q^{10} -0.270221 q^{11} +(0.595782 + 3.41248i) q^{12} +(3.21847 + 5.57455i) q^{13} +(1.75874 - 1.07065i) q^{14} +(5.36340 - 0.681435i) q^{15} +(-2.31287 - 3.26353i) q^{16} +(-4.23572 - 2.44549i) q^{17} +(-4.08209 + 1.15611i) q^{18} +(-3.23274 - 2.92394i) q^{19} +(-5.25567 + 3.36924i) q^{20} +(1.52607 + 2.00756i) q^{21} +(0.198713 + 0.326423i) q^{22} +(-3.71597 - 6.43624i) q^{23} +(3.68411 - 3.22914i) q^{24} +(2.37173 + 4.10796i) q^{25} +(4.36721 - 7.98723i) q^{26} +(-1.92315 - 4.82716i) q^{27} +(-2.58665 - 1.33721i) q^{28} +(-0.679243 + 0.392161i) q^{29} +(-4.76725 - 5.97780i) q^{30} -0.616086i q^{31} +(-2.24149 + 5.19382i) q^{32} +(-0.372603 + 0.283240i) q^{33} +(0.160704 + 6.91503i) q^{34} +(-2.27231 + 3.93575i) q^{35} +(4.39841 + 4.08093i) q^{36} -6.98268 q^{37} +(-1.15481 + 6.05528i) q^{38} +(10.2810 + 4.31313i) q^{39} +(7.93486 + 3.87113i) q^{40} +(-1.16168 - 0.670695i) q^{41} +(1.30287 - 3.31977i) q^{42} +(5.94954 + 3.43497i) q^{43} +(0.248187 - 0.480084i) q^{44} +(6.68124 - 6.56142i) q^{45} +(-5.04228 + 9.22186i) q^{46} +(-0.780795 - 1.35238i) q^{47} +(-6.60994 - 2.07574i) q^{48} +4.88027 q^{49} +(3.21825 - 5.88589i) q^{50} +(-8.40387 + 1.06774i) q^{51} +(-12.8600 + 0.598049i) q^{52} +(7.14091 - 4.12281i) q^{53} +(-4.41692 + 5.87289i) q^{54} +(-0.730476 - 0.421741i) q^{55} +(0.286819 + 4.10799i) q^{56} +(-7.52238 - 0.643286i) q^{57} +(0.973220 + 0.532132i) q^{58} +(-6.09022 + 10.5486i) q^{59} +(-3.71540 + 10.1547i) q^{60} +(-1.39367 - 2.41391i) q^{61} +(-0.744223 + 0.453052i) q^{62} +(4.20856 + 1.16859i) q^{63} +(7.92238 - 1.11170i) q^{64} +20.0926i q^{65} +(0.616151 + 0.241813i) q^{66} +(-0.188511 + 0.108837i) q^{67} +(8.23508 - 5.27924i) q^{68} +(-11.8702 - 4.97984i) q^{69} +(6.42532 - 0.149323i) q^{70} +(-3.51569 + 6.08936i) q^{71} +(1.69525 - 8.31421i) q^{72} +(-0.410869 + 0.711646i) q^{73} +(5.13486 + 8.43498i) q^{74} +(7.57621 + 3.17840i) q^{75} +(8.16391 - 3.05788i) q^{76} -0.393422i q^{77} +(-2.35016 - 15.5911i) q^{78} +(5.16785 + 2.98366i) q^{79} +(-1.15879 - 12.4319i) q^{80} +(-7.71153 - 4.64030i) q^{81} +(0.0440742 + 1.89650i) q^{82} -6.63475 q^{83} +(-4.96833 + 0.867416i) q^{84} +(-7.63348 - 13.2216i) q^{85} +(-0.225726 - 9.71294i) q^{86} +(-0.525543 + 1.25271i) q^{87} +(-0.762444 + 0.0532337i) q^{88} +(-3.10403 + 1.79211i) q^{89} +(-12.8393 - 3.24577i) q^{90} +(-8.11615 + 4.68586i) q^{91} +(14.8478 - 0.690493i) q^{92} +(-0.645768 - 0.849511i) q^{93} +(-1.05948 + 1.93769i) q^{94} +(-4.17545 - 12.9496i) q^{95} +(2.35330 + 9.51115i) q^{96} +(7.11697 - 12.3269i) q^{97} +(-3.58881 - 5.89530i) q^{98} +(-0.216891 + 0.781110i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 8 q^{10} - 10 q^{12} - 4 q^{16} - 22 q^{18} + 4 q^{21} - 6 q^{22} + 11 q^{24} + 16 q^{25} + 6 q^{28} - 60 q^{30} - 30 q^{33} - 20 q^{34} - 11 q^{36} - 8 q^{37} + 36 q^{40} + 8 q^{42} - 28 q^{45}+ \cdots - 16 q^{97}+O(q^{100}) $ 72 * q + 3 * q^6 - 8 * q^10 - 10 * q^12 - 4 * q^16 - 22 * q^18 + 4 * q^21 - 6 * q^22 + 11 * q^24 + 16 * q^25 + 6 * q^28 - 60 * q^30 - 30 * q^33 - 20 * q^34 - 11 * q^36 - 8 * q^37 + 36 * q^40 + 8 * q^42 - 28 * q^45 - 8 * q^46 - 23 * q^48 - 16 * q^49 + 6 * q^52 - 22 * q^54 - 6 * q^57 - 80 * q^58 - 14 * q^60 - 40 * q^61 + 48 * q^64 - 15 * q^66 + 4 * q^69 + 72 * q^70 + 15 * q^72 - 4 * q^73 + 12 * q^76 + 44 * q^78 + 4 * q^81 - 6 * q^82 + 56 * q^84 - 52 * q^85 - 44 * q^88 + 20 * q^90 + 4 * q^93 + 56 * q^94 - 86 * q^96 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.735371	−	1.20799i	−0.519986	−	0.854175i
$2$	−0.735371	−	1.20799i	−0.519986	−	0.854175i
$3$	1.37888	−	1.04818i	0.796099	−	0.605166i
$3$	1.37888	−	1.04818i	0.796099	−	0.605166i
$4$	−0.918459	+	1.77664i	−0.459229	+	0.888318i
$5$	2.70326	+	1.56073i	1.20893	+	0.697978i	0.962526	−	0.271189i	$-0.0874167\pi$
$5$	2.70326	+	1.56073i	1.20893	+	0.697978i	0.246407	+	0.969166i	$0.420750\pi$
$6$	−2.28018	−	0.894872i	−0.930878	−	0.365330i
$7$			1.45593i			0.550289i	0.961403	+	0.275145i	$0.0887257\pi$
$7$			1.45593i			0.550289i	−0.961403	+	0.275145i	$0.911274\pi$
$8$	2.82156	−	0.197001i	0.997571	−	0.0696503i
$9$	0.802644	−	2.89063i	0.267548	−	0.963545i
$10$	−0.102562	−	4.41321i	−0.0324329	−	1.39558i
$11$	−0.270221			−0.0814747			−0.0407373	−	0.999170i	$-0.512971\pi$
$11$	−0.270221			−0.0814747			−0.0407373	+	0.999170i	$0.512971\pi$
$12$	0.595782	+	3.41248i	0.171988	+	0.985099i
$13$	3.21847	+	5.57455i	0.892643	+	1.54610i	0.836695	+	0.547669i	$0.184485\pi$
$13$	3.21847	+	5.57455i	0.892643	+	1.54610i	0.0559478	+	0.998434i	$0.482182\pi$
$14$	1.75874	−	1.07065i	0.470043	−	0.286143i
$15$	5.36340	−	0.681435i	1.38482	−	0.175946i
$16$	−2.31287	−	3.26353i	−0.578217	−	0.815883i
$17$	−4.23572	−	2.44549i	−1.02731	−	0.593119i	−0.111098	−	0.993809i	$-0.535437\pi$
$17$	−4.23572	−	2.44549i	−1.02731	−	0.593119i	−0.916213	+	0.400691i	$0.868770\pi$
$18$	−4.08209	+	1.15611i	−0.962157	+	0.272497i
$19$	−3.23274	−	2.92394i	−0.741641	−	0.670797i
$19$	−3.23274	−	2.92394i	−0.741641	−	0.670797i
$20$	−5.25567	+	3.36924i	−1.17520	+	0.753385i
$21$	1.52607	+	2.00756i	0.333016	+	0.438085i
$22$	0.198713	+	0.326423i	0.0423657	+	0.0695936i
$23$	−3.71597	−	6.43624i	−0.774833	−	1.34205i	−0.934889	−	0.354941i	$-0.884501\pi$
$23$	−3.71597	−	6.43624i	−0.774833	−	1.34205i	0.160056	−	0.987108i	$-0.448833\pi$
$24$	3.68411	−	3.22914i	0.752016	−	0.659145i
$25$	2.37173	+	4.10796i	0.474346	+	0.821592i
$26$	4.36721	−	7.98723i	0.856481	−	1.56642i
$27$	−1.92315	−	4.82716i	−0.370110	−	0.928988i
$28$	−2.58665	−	1.33721i	−0.488832	−	0.252709i
$29$	−0.679243	+	0.392161i	−0.126132	+	0.0728225i	−0.561739	−	0.827315i	$-0.689867\pi$
$29$	−0.679243	+	0.392161i	−0.126132	+	0.0728225i	0.435606	+	0.900137i	$0.356534\pi$
$30$	−4.76725	−	5.97780i	−0.870377	−	1.09139i
$31$		−	0.616086i		−	0.110652i	−0.998468	−	0.0553262i	$-0.982380\pi$
$31$		−	0.616086i		−	0.110652i	0.998468	−	0.0553262i	$-0.0176199\pi$
$32$	−2.24149	+	5.19382i	−0.396243	+	0.918146i
$33$	−0.372603	+	0.283240i	−0.0648619	+	0.0493057i
$34$	0.160704	+	6.91503i	0.0275604	+	1.18592i
$35$	−2.27231	+	3.93575i	−0.384090	+	0.665263i
$36$	4.39841	+	4.08093i	0.733068	+	0.680156i
$37$	−6.98268			−1.14795			−0.573973	−	0.818874i	$-0.694599\pi$
$37$	−6.98268			−1.14795			−0.573973	+	0.818874i	$0.694599\pi$
$38$	−1.15481	+	6.05528i	−0.187336	+	0.982296i
$39$	10.2810	+	4.31313i	1.64628	+	0.690654i
$40$	7.93486	+	3.87113i	1.25461	+	0.612080i
$41$	−1.16168	−	0.670695i	−0.181423	−	0.104745i	0.406538	−	0.913634i	$-0.366736\pi$
$41$	−1.16168	−	0.670695i	−0.181423	−	0.104745i	−0.587961	+	0.808889i	$0.700069\pi$
$42$	1.30287	−	3.31977i	0.201037	−	0.512252i
$43$	5.94954	+	3.43497i	0.907296	+	0.523828i	0.879560	−	0.475787i	$-0.157837\pi$
$43$	5.94954	+	3.43497i	0.907296	+	0.523828i	0.0277361	+	0.999615i	$0.491170\pi$
$44$	0.248187	−	0.480084i	0.0374156	−	0.0723754i
$45$	6.68124	−	6.56142i	0.995980	−	0.978118i
$46$	−5.04228	+	9.22186i	−0.743443	+	1.35969i
$47$	−0.780795	−	1.35238i	−0.113891	−	0.197264i	0.803445	−	0.595379i	$-0.202998\pi$
$47$	−0.780795	−	1.35238i	−0.113891	−	0.197264i	−0.917336	+	0.398114i	$0.869665\pi$
$48$	−6.60994	−	2.07574i	−0.954063	−	0.299607i
$49$	4.88027			0.697182
$50$	3.21825	−	5.88589i	0.455130	−	0.832390i
$51$	−8.40387	+	1.06774i	−1.17678	+	0.149513i
$52$	−12.8600	+	0.598049i	−1.78336	+	0.0829345i
$53$	7.14091	−	4.12281i	0.980879	−	0.566311i	0.0783438	−	0.996926i	$-0.475037\pi$
$53$	7.14091	−	4.12281i	0.980879	−	0.566311i	0.902535	+	0.430616i	$0.141703\pi$
$54$	−4.41692	+	5.87289i	−0.601066	+	0.799199i
$55$	−0.730476	−	0.421741i	−0.0984974	−	0.0568675i
$56$	0.286819	+	4.10799i	0.0383278	+	0.548953i
$57$	−7.52238	−	0.643286i	−0.996363	−	0.0852054i
$58$	0.973220	+	0.532132i	0.127790	+	0.0698723i
$59$	−6.09022	+	10.5486i	−0.792879	+	1.37331i	0.131299	+	0.991343i	$0.458085\pi$
$59$	−6.09022	+	10.5486i	−0.792879	+	1.37331i	−0.924177	+	0.381963i	$0.875248\pi$
$60$	−3.71540	+	10.1547i	−0.479656	+	1.31096i
$61$	−1.39367	−	2.41391i	−0.178441	−	0.309069i	0.762906	−	0.646510i	$-0.223772\pi$
$61$	−1.39367	−	2.41391i	−0.178441	−	0.309069i	−0.941347	+	0.337441i	$0.890439\pi$
$62$	−0.744223	+	0.453052i	−0.0945164	+	0.0575376i
$63$	4.20856	+	1.16859i	0.530228	+	0.147229i
$64$	7.92238	−	1.11170i	0.990298	−	0.138962i
$65$			20.0926i			2.49218i
$66$	0.616151	+	0.241813i	0.0758430	+	0.0297652i
$67$	−0.188511	+	0.108837i	−0.0230303	+	0.0132965i	−0.511471	−	0.859301i	$-0.670899\pi$
$67$	−0.188511	+	0.108837i	−0.0230303	+	0.0132965i	0.488441	+	0.872597i	$0.337566\pi$
$68$	8.23508	−	5.27924i	0.998650	−	0.640202i
$69$	−11.8702	−	4.97984i	−1.42901	−	0.599502i
$70$	6.42532	−	0.149323i	0.767972	−	0.0178475i
$71$	−3.51569	+	6.08936i	−0.417236	+	0.722674i	−0.995660	−	0.0930623i	$-0.970334\pi$
$71$	−3.51569	+	6.08936i	−0.417236	+	0.722674i	0.578424	+	0.815736i	$0.303668\pi$
$72$	1.69525	−	8.31421i	0.199787	−	0.979839i
$73$	−0.410869	+	0.711646i	−0.0480886	+	0.0832919i	−0.889068	−	0.457776i	$-0.848646\pi$
$73$	−0.410869	+	0.711646i	−0.0480886	+	0.0832919i	0.840979	+	0.541067i	$0.181980\pi$
$74$	5.13486	+	8.43498i	0.596916	+	0.980547i
$75$	7.57621	+	3.17840i	0.874826	+	0.367010i
$76$	8.16391	−	3.05788i	0.936464	−	0.350763i
$77$		−	0.393422i		−	0.0448346i
$78$	−2.35016	−	15.5911i	−0.266104	−	1.76534i
$79$	5.16785	+	2.98366i	0.581429	+	0.335688i	0.761701	−	0.647929i	$-0.224364\pi$
$79$	5.16785	+	2.98366i	0.581429	+	0.335688i	−0.180272	+	0.983617i	$0.557698\pi$
$80$	−1.15879	−	12.4319i	−0.129557	−	1.38993i
$81$	−7.71153	−	4.64030i	−0.856836	−	0.515589i
$82$	0.0440742	+	1.89650i	0.00486718	+	0.209433i
$83$	−6.63475			−0.728258			−0.364129	−	0.931349i	$-0.618633\pi$
$83$	−6.63475			−0.728258			−0.364129	+	0.931349i	$0.618633\pi$
$84$	−4.96833	+	0.867416i	−0.542089	+	0.0946429i
$85$	−7.63348	−	13.2216i	−0.827968	−	1.43408i
$86$	−0.225726	−	9.71294i	−0.0243407	−	1.04737i
$87$	−0.525543	+	1.25271i	−0.0563441	+	0.134305i
$88$	−0.762444	+	0.0532337i	−0.0812768	+	0.00567474i
$89$	−3.10403	+	1.79211i	−0.329027	+	0.189964i	−0.655409	−	0.755274i	$-0.727504\pi$
$89$	−3.10403	+	1.79211i	−0.329027	+	0.189964i	0.326382	+	0.945238i	$0.394170\pi$
$90$	−12.8393	−	3.24577i	−1.35338	−	0.342134i
$91$	−8.11615	+	4.68586i	−0.850804	+	0.491212i
$92$	14.8478	−	0.690493i	1.54799	−	0.0719888i
$93$	−0.645768	−	0.849511i	−0.0669630	−	0.0880902i
$94$	−1.05948	+	1.93769i	−0.109277	+	0.199857i
$95$	−4.17545	−	12.9496i	−0.428392	−	1.32860i
$96$	2.35330	+	9.51115i	0.240182	+	0.970728i
$97$	7.11697	−	12.3269i	0.722618	−	1.25161i	−0.237329	−	0.971429i	$-0.576272\pi$
$97$	7.11697	−	12.3269i	0.722618	−	1.25161i	0.959947	−	0.280182i	$-0.0903949\pi$
$98$	−3.58881	−	5.89530i	−0.362525	−	0.595515i
$99$	−0.216891	+	0.781110i	−0.0217984	+	0.0785045i
$100$	−9.47668	+	0.440710i	−0.947668	+	0.0440710i
$101$	1.74957	−	1.01011i	0.174088	−	0.100510i	−0.410424	−	0.911895i	$-0.634619\pi$
$101$	1.74957	−	1.01011i	0.174088	−	0.100510i	0.584512	+	0.811385i	$0.301286\pi$
$102$	7.46977	+	9.36658i	0.739618	+	0.927429i
$103$		−	0.991573i		−	0.0977026i	−0.998806	−	0.0488513i	$-0.984444\pi$
$103$		−	0.991573i		−	0.0977026i	0.998806	−	0.0488513i	$-0.0155560\pi$
$104$	10.1793	+	15.0949i	0.998162	+	1.48018i
$105$	0.992120	+	7.80872i	0.0968210	+	0.762053i
$106$	−10.2315	−	5.59432i	−0.993772	−	0.543369i
$107$	16.1522			1.56149			0.780746	−	0.624849i	$-0.214839\pi$
$107$	16.1522			1.56149			0.780746	+	0.624849i	$0.214839\pi$
$108$	10.3424	+	1.01682i	0.995202	+	0.0978436i
$109$	−2.96086	+	5.12836i	−0.283599	+	0.491208i	−0.972268	−	0.233867i	$-0.924862\pi$
$109$	−2.96086	+	5.12836i	−0.283599	+	0.491208i	0.688669	+	0.725075i	$0.258195\pi$
$110$	0.0277144	+	1.19254i	0.00264246	+	0.113704i
$111$	−9.62831	+	7.31910i	−0.913879	+	0.694698i
$112$	4.75147	−	3.36737i	0.448972	−	0.318186i
$113$		−	4.37597i		−	0.411657i	−0.978588	−	0.205828i	$-0.934011\pi$
$113$		−	4.37597i		−	0.411657i	0.978588	−	0.205828i	$-0.0659889\pi$
$114$	4.75466	+	9.55998i	0.445315	+	0.895374i
$115$		−	23.1984i		−	2.16326i
$116$	−0.0728705	−	1.56695i	−0.00676586	−	0.145488i
$117$	18.6973	−	4.82904i	1.72856	−	0.446445i
$118$	17.2211	−	0.400214i	1.58533	−	0.0368427i
$119$	3.56046	−	6.16690i	0.326387	−	0.565319i
$120$	14.9989	−	2.97930i	1.36921	−	0.271972i
$121$	−10.9270			−0.993362
$122$	−1.89110	+	3.45865i	−0.171212	+	0.313131i
$123$	−2.30483	+	0.292835i	−0.207819	+	0.0264040i
$124$	1.09456	+	0.565850i	0.0982944	+	0.0508148i
$125$		−	0.800774i		−	0.0716234i
$126$	−1.68321	−	5.94322i	−0.149952	−	0.529465i
$127$	−10.2611	+	5.92426i	−0.910527	+	0.525693i	−0.880601	−	0.473859i	$-0.842861\pi$
$127$	−10.2611	+	5.92426i	−0.910527	+	0.525693i	−0.0299262	+	0.999552i	$0.509527\pi$
$128$	−7.16881	−	8.75261i	−0.633639	−	0.773629i
$129$	11.8042	−	1.49976i	1.03930	−	0.132046i
$130$	24.2716	−	14.7755i	2.12876	−	1.29590i
$131$	0.893750	−	1.54802i	0.0780873	−	0.135251i	−0.824337	−	0.566099i	$-0.808452\pi$
$131$	0.893750	−	1.54802i	0.0780873	−	0.135251i	0.902425	+	0.430848i	$0.141785\pi$
$132$	−0.160993	−	0.922124i	−0.0140126	−	0.0802606i
$133$	4.25704	−	4.70663i	0.369133	−	0.408117i
$134$	0.270099	+	0.147683i	0.0233330	+	0.0127579i
$135$	2.33512	−	16.0506i	0.200975	−	1.38141i
$136$	−12.4331	−	6.06566i	−1.06613	−	0.520126i
$137$	−13.6110	+	7.85831i	−1.16287	+	0.671381i	−0.951989	−	0.306132i	$-0.900965\pi$
$137$	−13.6110	+	7.85831i	−1.16287	+	0.671381i	−0.210877	+	0.977513i	$0.567632\pi$
$138$	2.71344	+	18.0011i	0.230983	+	1.53235i
$139$	−2.27606	+	1.31408i	−0.193053	+	0.111459i	−0.593411	−	0.804900i	$-0.702219\pi$
$139$	−2.27606	+	1.31408i	−0.193053	+	0.111459i	0.400358	+	0.916359i	$0.368886\pi$
$140$	−4.90537	−	7.65188i	−0.414579	−	0.646702i
$141$	−2.49416	−	1.04636i	−0.210046	−	0.0881193i
$142$	9.94119	−	0.231031i	0.834246	−	0.0193877i
$143$	−0.869698	−	1.50636i	−0.0727278	−	0.125968i
$144$	−11.2901	+	4.06619i	−0.940841	+	0.338850i
$145$	−2.44822			−0.203314
$146$	1.16180	−	0.0270000i	0.0961513	−	0.00223453i
$147$	6.72933	−	5.11540i	0.555026	−	0.421911i
$148$	6.41331	−	12.4057i	0.527171	−	1.01974i
$149$	8.40819	+	4.85447i	0.688826	+	0.397694i	0.803172	−	0.595747i	$-0.203144\pi$
$149$	8.40819	+	4.85447i	0.688826	+	0.397694i	−0.114346	+	0.993441i	$0.536477\pi$
$150$	−1.73186	−	11.4893i	−0.141406	−	0.938094i
$151$			21.9757i			1.78836i	0.447707	+	0.894181i	$0.352241\pi$
$151$			21.9757i			1.78836i	−0.447707	+	0.894181i	$0.647759\pi$
$152$	−9.69737	−	7.61321i	−0.786561	−	0.617513i
$153$	−10.4688	+	10.2810i	−0.846352	+	0.831173i
$154$	−0.475249	+	0.289311i	−0.0382966	+	0.0233134i
$155$	0.961542	−	1.66544i	0.0772329	−	0.133771i
$156$	−17.1056	+	14.3042i	−1.36954	+	1.14525i
$157$	9.37366	−	16.2357i	0.748100	−	1.29575i	−0.200633	−	0.979667i	$-0.564300\pi$
$157$	9.37366	−	16.2357i	0.748100	−	1.29575i	0.948732	−	0.316080i	$-0.102367\pi$
$158$	−0.196069	−	8.43679i	−0.0155984	−	0.671195i
$159$	5.52505	−	13.1698i	0.438165	−	1.04443i
$160$	−14.1654	+	10.5419i	−1.11988	+	0.833408i
$161$	9.37071	−	5.41018i	0.738515	−	0.426382i
$162$	0.0654182	+	12.7278i	0.00513974	+	0.999987i
$163$		−	8.07011i		−	0.632100i	−0.948743	−	0.316050i	$-0.897643\pi$
$163$		−	8.07011i		−	0.632100i	0.948743	−	0.316050i	$-0.102357\pi$
$164$	2.25853	−	1.44787i	0.176362	−	0.113060i
$165$	−1.44930	+	0.184138i	−0.112828	+	0.0143351i
$166$	4.87900	+	8.01468i	0.378684	+	0.622060i
$167$	4.97016	+	8.60857i	0.384603	+	0.666151i	0.991714	−	0.128465i	$-0.0410051\pi$
$167$	4.97016	+	8.60857i	0.384603	+	0.666151i	−0.607111	+	0.794617i	$0.707672\pi$
$168$	4.70139	+	5.36380i	0.362720	+	0.413826i
$169$	−14.2171	+	24.6247i	−1.09362	+	1.89421i
$170$	−10.3580	+	18.9439i	−0.794425	+	1.45293i
$171$	−11.0468	+	6.99778i	−0.844768	+	0.535133i
$172$	−11.5671	+	7.41529i	−0.881983	+	0.565410i
$173$	−4.70695	−	2.71756i	−0.357863	−	0.206612i	0.310280	−	0.950645i	$-0.399577\pi$
$173$	−4.70695	−	2.71756i	−0.357863	−	0.206612i	−0.668143	+	0.744033i	$0.732910\pi$
$174$	1.89973	−	0.286361i	0.144018	−	0.0217089i
$175$	−5.98089	+	3.45307i	−0.452113	+	0.261028i
$176$	0.624985	+	0.881875i	0.0471100	+	0.0664738i
$177$	2.65907	+	20.9289i	0.199868	+	1.57311i
$178$	4.44746	+	2.43176i	0.333351	+	0.182268i
$179$	2.86834			0.214390			0.107195	−	0.994238i	$-0.465813\pi$
$179$	2.86834			0.214390			0.107195	+	0.994238i	$0.465813\pi$
$180$	5.52080	+	17.8965i	0.411496	+	1.33393i
$181$	1.77244	+	3.06996i	0.131745	+	0.228189i	0.924349	−	0.381548i	$-0.124609\pi$
$181$	1.77244	+	3.06996i	0.131745	+	0.228189i	−0.792604	+	0.609736i	$0.791275\pi$
$182$	11.6288	+	6.35835i	0.861987	+	0.471312i
$183$	−4.45191	−	1.86768i	−0.329095	−	0.138063i
$184$	−11.7528	−	17.4282i	−0.866425	−	1.28482i
$185$	−18.8760	−	10.8981i	−1.38779	−	0.801241i
$186$	−0.551319	+	1.40478i	−0.0404246	+	0.103004i
$187$	1.14458	+	0.660823i	0.0836999	+	0.0483242i
$188$	3.11981	−	0.145086i	0.227535	−	0.0105815i
$189$	7.02800	−	2.79996i	0.511212	−	0.203667i
$190$	−12.5724	+	14.5666i	−0.912097	+	1.05677i
$191$	−22.3910			−1.62015			−0.810077	−	0.586323i	$-0.800575\pi$
$191$	−22.3910			−1.62015			−0.810077	+	0.586323i	$0.800575\pi$
$192$	9.75879	−	9.83697i	0.704280	−	0.709922i
$193$	−1.51258	+	2.61987i	−0.108878	+	0.188582i	−0.915316	−	0.402736i	$-0.868059\pi$
$193$	−1.51258	+	2.61987i	−0.108878	+	0.188582i	0.806438	+	0.591319i	$0.201392\pi$
$194$	−20.1244	+	0.467686i	−1.44485	+	0.0335779i
$195$	21.0606	+	27.7054i	1.50818	+	1.98402i
$196$	−4.48233	+	8.67046i	−0.320166	+	0.619319i
$197$		−	8.82890i		−	0.629033i	−0.949252	−	0.314516i	$-0.898158\pi$
$197$		−	8.82890i		−	0.629033i	0.949252	−	0.314516i	$-0.101842\pi$
$198$	1.10306	−	0.312404i	0.0783914	−	0.0222016i
$199$	22.6989	−	13.1052i	1.60909	−	0.929006i	0.619511	−	0.784988i	$-0.287331\pi$
$199$	22.6989	−	13.1052i	1.60909	−	0.929006i	0.989575	−	0.144018i	$-0.0460022\pi$
$200$	7.50125	+	11.1236i	0.530418	+	0.786558i
$201$	−0.145854	+	0.347666i	−0.0102878	+	0.0245225i
$202$	−2.50678	−	1.37064i	−0.176377	−	0.0964382i
$203$	−0.570958	−	0.988929i	−0.0400734	−	0.0694092i
$204$	5.82164	−	15.9113i	0.407596	−	1.11401i
$205$	−2.09354	−	3.62612i	−0.146219	−	0.253259i
$206$	−1.19781	+	0.729174i	−0.0834551	+	0.0508039i
$207$	−21.5874	+	5.57549i	−1.50043	+	0.387523i
$208$	10.7488	−	23.3968i	0.745299	−	1.62227i
$209$	0.873553	+	0.790109i	0.0604249	+	0.0546530i
$210$	8.70325	−	6.94078i	0.600581	−	0.478959i
$211$	8.73343	+	5.04225i	0.601234	+	0.347123i	0.769527	−	0.638614i	$-0.220492\pi$
$211$	8.73343	+	5.04225i	0.601234	+	0.347123i	−0.168293	+	0.985737i	$0.553825\pi$
$212$	0.766091	+	16.4734i	0.0526153	+	1.13140i
$213$	1.53500	+	12.0816i	0.105176	+	0.827817i
$214$	−11.8779	−	19.5116i	−0.811953	−	1.33379i
$215$	10.7221	+	18.5712i	0.731240	+	1.26655i
$216$	−6.37723	−	13.2413i	−0.433915	−	0.900954i
$217$	0.896977			0.0608908
$218$	8.37232	−	0.194571i	0.567045	−	0.0131780i
$219$	0.179391	+	1.41194i	0.0121221	+	0.0954102i
$220$	1.42019	−	0.910439i	0.0957493	−	0.0613818i
$221$		−	31.4830i		−	2.11777i
$222$	15.9218	+	6.24861i	1.06860	+	0.419379i
$223$	17.6850	+	10.2104i	1.18427	+	0.683740i	0.956999	−	0.290090i	$-0.0936854\pi$
$223$	17.6850	+	10.2104i	1.18427	+	0.683740i	0.227274	+	0.973831i	$0.427019\pi$
$224$	−7.56183	−	3.26344i	−0.505246	−	0.218048i
$225$	13.7783	−	3.55858i	0.918550	−	0.237238i
$226$	−5.28611	+	3.21796i	−0.351627	+	0.214056i
$227$	−5.85358			−0.388516			−0.194258	−	0.980950i	$-0.562230\pi$
$227$	−5.85358			−0.388516			−0.194258	+	0.980950i	$0.562230\pi$
$228$	8.05188	−	12.7737i	0.533249	−	0.845958i
$229$	9.29195			0.614029			0.307015	−	0.951705i	$-0.400670\pi$
$229$	9.29195			0.614029			0.307015	+	0.951705i	$0.400670\pi$
$230$	−28.0234	+	17.0594i	−1.84781	+	1.12487i
$231$	−0.412377	−	0.542484i	−0.0271324	−	0.0356928i
$232$	−1.83927	+	1.24032i	−0.120754	+	0.0814308i
$233$	10.1031	+	5.83300i	0.661873	+	0.382133i	0.792990	−	0.609234i	$-0.208523\pi$
$233$	10.1031	+	5.83300i	0.661873	+	0.382133i	−0.131117	+	0.991367i	$0.541856\pi$
$234$	−19.5828	−	19.0349i	−1.28017	−	1.24435i
$235$		−	4.87443i		−	0.317973i
$236$	−13.1473	−	20.5085i	−0.855819	−	1.33499i
$237$	10.2533	−	1.30271i	0.666022	−	0.0846200i
$238$	−10.0678	+	0.233973i	−0.652598	+	0.0151662i
$239$	21.5943			1.39682			0.698410	−	0.715698i	$-0.253891\pi$
$239$	21.5943			1.39682			0.698410	+	0.715698i	$0.253891\pi$
$240$	−14.6287	−	15.9276i	−0.944279	−	1.02812i
$241$	7.40894	+	12.8327i	0.477252	+	0.826625i	0.999660	−	0.0260709i	$-0.00829956\pi$
$241$	7.40894	+	12.8327i	0.477252	+	0.826625i	−0.522408	+	0.852696i	$0.674966\pi$
$242$	8.03538	+	13.1996i	0.516534	+	0.848505i
$243$	−15.4972	+	1.68462i	−0.994143	+	0.108068i
$244$	5.56866	−	0.258969i	0.356497	−	0.0165788i
$245$	13.1926	+	7.61677i	0.842846	+	0.486617i
$246$	2.04864	+	2.56885i	0.130617	+	0.163784i
$247$	5.89518	−	27.4317i	0.375101	−	1.74544i
$248$	−0.121370	−	1.73832i	−0.00770697	−	0.110384i
$249$	−9.14855	+	6.95440i	−0.579766	+	0.440717i
$250$	−0.967324	+	0.588866i	−0.0611789	+	0.0372432i
$251$	−0.532539	−	0.922385i	−0.0336136	−	0.0582204i	0.848729	−	0.528828i	$-0.177368\pi$
$251$	−0.532539	−	0.922385i	−0.0336136	−	0.0582204i	−0.882343	+	0.470607i	$0.844035\pi$
$252$	−5.94155	+	6.40377i	−0.374282	+	0.403399i
$253$	1.00413	+	1.73921i	0.0631292	+	0.109343i
$254$	14.7021	+	8.03875i	0.922495	+	0.504396i
$255$	−24.3843	−	10.2298i	−1.52700	−	0.640614i
$256$	−5.30130	+	15.0962i	−0.331331	+	0.943515i
$257$	−5.08669	+	2.93680i	−0.317299	+	0.183193i	−0.650188	−	0.759773i	$-0.725310\pi$
$257$	−5.08669	+	2.93680i	−0.317299	+	0.183193i	0.332889	+	0.942966i	$0.391977\pi$
$258$	−10.4921	−	13.1564i	−0.653212	−	0.819083i
$259$		−	10.1663i		−	0.631702i
$260$	−35.6972	−	18.4542i	−2.21385	−	1.14448i
$261$	0.588404	+	2.27821i	0.0364213	+	0.141018i
$262$	−2.52723	+	0.0587321i	−0.156133	+	0.00362848i
$263$	−0.829810	+	1.43727i	−0.0511682	+	0.0886260i	−0.890475	−	0.455032i	$-0.849628\pi$
$263$	−0.829810	+	1.43727i	−0.0511682	+	0.0886260i	0.839307	+	0.543658i	$0.182961\pi$
$264$	−0.995524	+	0.872580i	−0.0612702	+	0.0537036i
$265$	25.7383			1.58109
$266$	−8.81605	−	1.68133i	−0.540547	−	0.103089i
$267$	−2.40164	+	5.72469i	−0.146978	+	0.350346i
$268$	−0.0202238	−	0.434877i	−0.00123537	−	0.0265643i
$269$	13.3036	+	7.68085i	0.811136	+	0.468310i	0.847350	−	0.531035i	$-0.178197\pi$
$269$	13.3036	+	7.68085i	0.811136	+	0.468310i	−0.0362143	+	0.999344i	$0.511530\pi$
$270$	−21.1060	+	8.98233i	−1.28447	+	0.546647i
$271$	−5.03114	−	2.90473i	−0.305620	−	0.176450i	0.339345	−	0.940662i	$-0.389795\pi$
$271$	−5.03114	−	2.90473i	−0.305620	−	0.176450i	−0.644965	+	0.764212i	$0.723128\pi$
$272$	1.81570	+	19.4795i	0.110093	+	1.18112i
$273$	−6.27961	+	14.9684i	−0.380059	+	0.905931i
$274$	19.5019	+	10.6631i	1.17815	+	0.644182i
$275$	−0.640891	−	1.11006i	−0.0386472	−	0.0669389i
$276$	19.7497	−	16.5153i	1.18879	−	0.994103i
$277$	0.252629			0.0151790			0.00758951	−	0.999971i	$-0.497584\pi$
$277$	0.252629			0.0151790			0.00758951	+	0.999971i	$0.497584\pi$
$278$	3.26114	+	1.78311i	0.195590	+	0.106944i
$279$	−1.78088	−	0.494498i	−0.106618	−	0.0296048i
$280$	−5.63610	+	11.5526i	−0.336821	+	0.690399i
$281$	−15.0804	+	8.70669i	−0.899623	+	0.519398i	−0.877078	−	0.480348i	$-0.840510\pi$
$281$	−15.0804	+	8.70669i	−0.899623	+	0.519398i	−0.0225454	+	0.999746i	$0.507177\pi$
$282$	0.570145	+	3.78237i	0.0339517	+	0.225237i
$283$	22.4320	+	12.9511i	1.33344	+	0.769863i	0.985826	−	0.167773i	$-0.0536576\pi$
$283$	22.4320	+	12.9511i	1.33344	+	0.769863i	0.347617	+	0.937637i	$0.386991\pi$
$284$	−7.58955	−	11.8389i	−0.450357	−	0.702511i
$285$	−19.3309	−	13.4793i	−1.14507	−	0.798447i
$286$	−1.18011	+	2.15832i	−0.0697815	+	0.127624i
$287$	0.976483	−	1.69132i	0.0576400	−	0.0998354i
$288$	13.2143	+	10.6481i	0.778661	+	0.627445i
$289$	3.46086	+	5.99438i	0.203580	+	0.352611i
$290$	1.80035	+	2.95742i	0.105720	+	0.173666i
$291$	−3.10737	−	24.4573i	−0.182157	−	1.43371i
$292$	−0.886970	−	1.38358i	−0.0519060	−	0.0809681i
$293$			9.41171i			0.549838i	0.961467	+	0.274919i	$0.0886511\pi$
$293$			9.41171i			0.549838i	−0.961467	+	0.274919i	$0.911349\pi$
$294$	−11.1279	−	4.36722i	−0.648991	−	0.254702i
$295$	−32.9268	+	19.0103i	−1.91707	+	1.10682i
$296$	−19.7020	+	1.37559i	−1.14516	+	0.0799548i
$297$	0.519674	+	1.30440i	0.0301546	+	0.0756890i
$298$	−0.319008	−	13.7268i	−0.0184796	−	0.795172i
$299$	23.9194	−	41.4297i	1.38330	−	2.39594i
$300$	−12.6053	+	10.5409i	−0.727767	+	0.608581i
$301$	−5.00107	+	8.66211i	−0.288257	+	0.499275i
$302$	26.5464	−	16.1603i	1.52757	−	0.929922i
$303$	1.35367	−	3.22669i	0.0777664	−	0.185368i
$304$	−2.06548	+	17.3128i	−0.118463	+	0.992958i
$305$		−	8.70055i		−	0.498192i
$306$	20.1178	+	5.08577i	1.15006	+	0.290734i
$307$	−11.8156	−	6.82174i	−0.674352	−	0.389338i	0.123371	−	0.992361i	$-0.460629\pi$
$307$	−11.8156	−	6.82174i	−0.674352	−	0.389338i	−0.797724	+	0.603023i	$0.793963\pi$
$308$	0.698968	+	0.361342i	0.0398274	+	0.0205894i
$309$	−1.03935	−	1.36726i	−0.0591263	−	0.0777809i
$310$	−2.71892	+	0.0631870i	−0.154424	+	0.00358878i
$311$	3.75137			0.212721			0.106360	−	0.994328i	$-0.466080\pi$
$311$	3.75137			0.212721			0.106360	+	0.994328i	$0.466080\pi$
$312$	29.8582	+	10.1444i	1.69039	+	0.574313i
$313$	−11.4412	−	19.8168i	−0.646696	−	1.12011i	−0.983907	−	0.178681i	$-0.942817\pi$
$313$	−11.4412	−	19.8168i	−0.646696	−	1.12011i	0.337212	−	0.941429i	$-0.390516\pi$
$314$	−26.5056	+	0.615983i	−1.49580	+	0.0347620i
$315$	9.55295	+	9.72741i	0.538248	+	0.548077i
$316$	−10.0473	+	6.44102i	−0.565207	+	0.362336i
$317$	20.7872	−	12.0015i	1.16753	−	0.674071i	0.214430	−	0.976739i	$-0.431211\pi$
$317$	20.7872	−	12.0015i	1.16753	−	0.674071i	0.953096	+	0.302668i	$0.0978774\pi$
$318$	−19.9719	+	3.01052i	−1.11997	+	0.168822i
$319$	0.183546	−	0.105970i	0.0102766	−	0.00593319i
$320$	23.1513	+	9.35946i	1.29420	+	0.523210i
$321$	22.2720	−	16.9304i	1.24310	−	0.944962i
$322$	−13.4264	−	7.34119i	−0.748222	−	0.409109i
$323$	6.54249	+	20.2906i	0.364034	+	1.12900i
$324$	15.3268	−	9.43865i	0.851491	−	0.524369i
$325$	−15.2667	+	26.4427i	−0.846843	+	1.46678i
$326$	−9.74858	+	5.93453i	−0.539924	+	0.328683i
$327$	1.29275	+	10.1749i	0.0714894	+	0.562675i
$328$	−3.40987	−	1.66355i	−0.188278	−	0.0918543i
$329$	1.96896	−	1.13678i	0.108552	−	0.0626728i
$330$	1.28821	+	1.61533i	0.0709137	+	0.0889208i
$331$		−	31.9375i		−	1.75544i	−0.479171	−	0.877722i	$-0.659063\pi$
$331$		−	31.9375i		−	1.75544i	0.479171	−	0.877722i	$-0.340937\pi$
$332$	6.09374	−	11.7875i	0.334438	−	0.646924i
$333$	−5.60461	+	20.1844i	−0.307131	+	1.10610i
$334$	6.74412	−	12.3344i	0.369022	−	0.674907i
$335$	−0.679457			−0.0371227
$336$	3.02213	−	9.62360i	0.164871	−	0.525010i
$337$	7.23189	−	12.5260i	0.393946	−	0.682335i	−0.599020	−	0.800734i	$-0.704443\pi$
$337$	7.23189	−	12.5260i	0.393946	−	0.682335i	0.992966	+	0.118400i	$0.0377764\pi$
$338$	40.2012	−	0.934266i	2.18665	−	0.0508173i
$339$	−4.58680	−	6.03396i	−0.249121	−	0.327720i
$340$	30.5010	−	1.41844i	1.65415	−	0.0769256i
$341$			0.166479i			0.00901536i
$342$	16.5767	+	8.19838i	0.896365	+	0.443317i
$343$			17.2968i			0.933941i
$344$	17.4637	+	8.51990i	0.941578	+	0.459362i
$345$	−24.3161	−	31.9879i	−1.30913	−	1.72217i
$346$	0.178582	+	7.68434i	0.00960064	+	0.413113i
$347$	9.69014	−	16.7838i	0.520194	−	0.901003i	−0.479530	−	0.877525i	$-0.659193\pi$
$347$	9.69014	−	16.7838i	0.520194	−	0.901003i	0.999724	−	0.0234773i	$-0.00747374\pi$
$348$	−1.74292	−	2.08426i	−0.0934305	−	0.111728i
$349$	−20.8864			−1.11803			−0.559013	−	0.829159i	$-0.688820\pi$
$349$	−20.8864			−1.11803			−0.559013	+	0.829159i	$0.688820\pi$
$350$	8.56943	+	4.68555i	0.458056	+	0.250453i
$351$	20.7197	−	26.2568i	1.10594	−	1.40148i
$352$	0.605696	−	1.40348i	0.0322837	−	0.0748056i
$353$		−	10.5185i		−	0.559846i	−0.960022	−	0.279923i	$-0.909691\pi$
$353$		−	10.5185i		−	0.559846i	0.960022	−	0.279923i	$-0.0903089\pi$
$354$	23.3264	−	18.6026i	1.23978	−	0.988718i
$355$	−19.0076	+	10.9741i	−1.00882	+	0.582443i
$356$	−0.333006	−	7.16071i	−0.0176493	−	0.379517i
$357$	−1.55455	−	12.2354i	−0.0822754	−	0.647568i
$358$	−2.10930	−	3.46492i	−0.111480	−	0.183127i
$359$	−3.08029	+	5.33522i	−0.162572	+	0.281582i	−0.935790	−	0.352557i	$-0.885312\pi$
$359$	−3.08029	+	5.33522i	−0.162572	+	0.281582i	0.773219	+	0.634140i	$0.218646\pi$
$360$	17.5589	−	19.8296i	0.925435	−	1.04511i
$361$	1.90118	+	18.9046i	0.100062	+	0.994981i
$362$	2.40507	−	4.39865i	0.126408	−	0.231188i
$363$	−15.0670	+	11.4534i	−0.790815	+	0.601149i
$364$	−0.870717	−	18.7232i	−0.0456379	−	0.981363i
$365$	−2.22137	+	1.28251i	−0.116272	+	0.0671296i
$366$	1.01767	+	6.75129i	0.0531947	+	0.352896i
$367$	−16.7215	+	9.65418i	−0.872857	+	0.503944i	−0.868297	−	0.496045i	$-0.834785\pi$
$367$	−16.7215	+	9.65418i	−0.872857	+	0.503944i	−0.00456047	+	0.999990i	$0.501452\pi$
$368$	−12.4104	+	27.0133i	−0.646935	+	1.40817i
$369$	−2.87115	+	2.81965i	−0.149466	+	0.146785i
$370$	0.716158	+	30.8160i	0.0372313	+	1.60205i
$371$	6.00251	+	10.3967i	0.311635	+	0.539767i
$372$	2.10238	−	0.367053i	0.109004	−	0.0190308i
$373$	22.9926			1.19051			0.595255	−	0.803537i	$-0.297051\pi$
$373$	22.9926			1.19051			0.595255	+	0.803537i	$0.297051\pi$
$374$	−0.0434255	−	1.86858i	−0.00224548	−	0.0966222i
$375$	−0.839355	−	1.10418i	−0.0433441	−	0.0570194i
$376$	−2.46948	−	3.66199i	−0.127354	−	0.188853i
$377$	−4.37224	−	2.52432i	−0.225182	−	0.130009i
$378$	−8.55051	−	6.43072i	−0.439791	−	0.330760i
$379$			14.3066i			0.734880i	0.930047	+	0.367440i	$0.119766\pi$
$379$			14.3066i			0.734880i	−0.930047	+	0.367440i	$0.880234\pi$
$380$	26.8416	+	4.47539i	1.37695	+	0.229583i
$381$	−7.93921	+	18.9243i	−0.406738	+	0.969524i
$382$	16.4657	+	27.0480i	0.842457	+	1.38390i
$383$	10.3085	−	17.8548i	0.526737	−	0.912336i	−0.472777	−	0.881182i	$-0.656748\pi$
$383$	10.3085	−	17.8548i	0.526737	−	0.912336i	0.999515	−	0.0311540i	$-0.00991822\pi$
$384$	−19.0593	−	4.55465i	−0.972613	−	0.232429i
$385$	0.614024	−	1.06352i	0.0312936	−	0.0542021i
$386$	4.27707	−	0.0993981i	0.217697	−	0.00505923i
$387$	14.7046	−	14.4409i	0.747477	−	0.734071i
$388$	15.3638	+	23.9660i	0.779981	+	1.21669i
$389$	−13.8755	+	8.01103i	−0.703516	+	0.406175i	−0.808656	−	0.588282i	$-0.799804\pi$
$389$	−13.8755	+	8.01103i	−0.703516	+	0.406175i	0.105140	+	0.994457i	$0.466471\pi$
$390$	17.9803	−	45.8147i	0.910468	−	2.31992i
$391$			36.3495i			1.83827i
$392$	13.7700	−	0.961418i	0.695489	−	0.0485589i
$393$	−0.390224	−	3.07135i	−0.0196842	−	0.154929i
$394$	−10.6652	+	6.49252i	−0.537304	+	0.327088i
$395$	9.31336	+	16.1312i	0.468606	+	0.811649i
$396$	−1.18854	−	1.10275i	−0.0597264	−	0.0554154i
$397$	5.72237	−	9.91144i	0.287198	−	0.497441i	−0.685942	−	0.727656i	$-0.740610\pi$
$397$	5.72237	−	9.91144i	0.287198	−	0.497441i	0.973140	+	0.230215i	$0.0739430\pi$
$398$	−32.5231	−	17.7828i	−1.63024	−	0.891371i
$399$	0.936579	−	10.9520i	0.0468876	−	0.548288i
$400$	7.92096	−	17.2414i	0.396048	−	0.862069i
$401$	23.8684	+	13.7804i	1.19193	+	0.688162i	0.958744	−	0.284270i	$-0.0917511\pi$
$401$	23.8684	+	13.7804i	1.19193	+	0.688162i	0.233187	+	0.972432i	$0.425084\pi$
$402$	0.527233	−	0.0794739i	0.0262960	−	0.00396380i
$403$	3.43440	−	1.98285i	0.171080	−	0.0987730i
$404$	0.187697	+	4.03609i	0.00933827	+	0.200803i
$405$	−13.6040	−	24.5795i	−0.675988	−	1.22136i
$406$	−0.774746	+	1.41694i	−0.0384500	+	0.0703215i
$407$	1.88687			0.0935285
$408$	−23.5017	+	4.66825i	−1.16351	+	0.231113i
$409$	−12.6975	−	21.9927i	−0.627850	−	1.08747i	−0.987982	−	0.154567i	$-0.950602\pi$
$409$	−12.6975	−	21.9927i	−0.627850	−	1.08747i	0.360132	−	0.932901i	$-0.382732\pi$
$410$	−2.84077	+	5.19551i	−0.140296	+	0.256588i
$411$	−10.5311	+	25.1025i	−0.519460	+	1.23821i
$412$	1.76166	+	0.910719i	0.0867909	+	0.0448679i
$413$	−15.3580	−	8.86692i	−0.755716	−	0.436313i
$414$	22.6099	+	21.9772i	1.11121	+	1.08012i
$415$	−17.9354	−	10.3550i	−0.880415	−	0.508308i
$416$	−36.1674	+	4.22086i	−1.77325	+	0.206945i
$417$	−1.76103	+	4.19768i	−0.0862379	+	0.205562i
$418$	0.312055	−	1.63626i	0.0152631	−	0.0800322i
$419$	−13.6284			−0.665793			−0.332897	−	0.942963i	$-0.608026\pi$
$419$	−13.6284			−0.665793			−0.332897	+	0.942963i	$0.608026\pi$
$420$	−14.7845	−	5.40936i	−0.721409	−	0.263950i
$421$	−0.367071	+	0.635786i	−0.0178900	+	0.0309863i	−0.874832	−	0.484427i	$-0.839028\pi$
$421$	−0.367071	+	0.635786i	−0.0178900	+	0.0309863i	0.856942	+	0.515413i	$0.172362\pi$
$422$	−0.331348	−	14.2578i	−0.0161298	−	0.694058i
$423$	−4.53593	+	1.17152i	−0.220544	+	0.0569610i
$424$	19.3363	−	13.0395i	0.939053	−	0.633254i
$425$		−	23.2002i		−	1.12537i
$426$	13.4656	−	10.7387i	0.652410	−	0.520292i
$427$	3.51448	−	2.02908i	0.170077	−	0.0981942i
$428$	−14.8351	+	28.6966i	−0.717083	+	1.38710i
$429$	−2.77815	−	1.16550i	−0.134130	−	0.0562708i
$430$	14.5490	−	26.6089i	0.701617	−	1.28319i
$431$	14.3970	+	24.9363i	0.693479	+	1.20114i	0.970691	+	0.240332i	$0.0772564\pi$
$431$	14.3970	+	24.9363i	0.693479	+	1.20114i	−0.277211	+	0.960809i	$0.589410\pi$
$432$	−11.3056	+	17.4408i	−0.543942	+	0.839123i
$433$	0.686496	+	1.18905i	0.0329909	+	0.0571419i	0.882049	−	0.471157i	$-0.156163\pi$
$433$	0.686496	+	1.18905i	0.0329909	+	0.0571419i	−0.849059	+	0.528299i	$0.822830\pi$
$434$	−0.659611	−	1.08354i	−0.0316623	−	0.0520114i
$435$	−3.37582	+	2.56618i	−0.161858	+	0.123039i
$436$	−6.39180	−	9.97056i	−0.306112	−	0.477503i
$437$	−6.80643	+	31.6719i	−0.325596	+	1.51507i
$438$	1.57369	−	1.25500i	0.0751937	−	0.0599664i
$439$	−16.1866	−	9.34532i	−0.772543	−	0.446028i	0.0612383	−	0.998123i	$-0.480495\pi$
$439$	−16.1866	−	9.34532i	−0.772543	−	0.446028i	−0.833781	+	0.552095i	$0.813828\pi$
$440$	−2.14416	−	1.04606i	−0.102219	−	0.0498690i
$441$	3.91712	−	14.1071i	0.186530	−	0.671766i
$442$	−38.0310	+	23.1517i	−1.80895	+	1.10121i
$443$	−9.01441	−	15.6134i	−0.428288	−	0.741816i	0.568433	−	0.822729i	$-0.307550\pi$
$443$	−9.01441	−	15.6134i	−0.428288	−	0.741816i	−0.996721	+	0.0809132i	$0.974216\pi$
$444$	−4.16016	−	23.8283i	−0.197432	−	1.13084i
$445$	−11.1880			−0.530361
$446$	−0.670970	−	28.8716i	−0.0317714	−	1.36711i
$447$	16.6823	−	2.11953i	0.789044	−	0.100250i
$448$	1.61855	+	11.5344i	0.0764695	+	0.544950i
$449$			20.7470i			0.979111i	0.871972	+	0.489555i	$0.162841\pi$
$449$			20.7470i			0.979111i	−0.871972	+	0.489555i	$0.837159\pi$
$450$	−14.4308	−	14.0271i	−0.680276	−	0.661242i
$451$	0.313909	+	0.181236i	0.0147814	+	0.00853405i
$452$	7.77451	+	4.01915i	0.365682	+	0.189045i
$453$	23.0345	+	30.3020i	1.08226	+	1.42371i
$454$	4.30455	+	7.07104i	0.202023	+	0.331860i
$455$	−29.2534			−1.37142
$456$	−21.3516	−	0.333155i	−0.999878	−	0.0156014i
$457$	20.5550			0.961523			0.480761	−	0.876852i	$-0.340360\pi$
$457$	20.5550			0.961523			0.480761	+	0.876852i	$0.340360\pi$
$458$	−6.83303	−	11.2245i	−0.319286	−	0.524488i
$459$	−3.65888	+	25.1495i	−0.170782	+	1.17388i
$460$	41.2151	+	21.3068i	1.92167	+	0.993434i
$461$	−22.2448	−	12.8430i	−1.03604	−	0.598159i	−0.117332	−	0.993093i	$-0.537434\pi$
$461$	−22.2448	−	12.8430i	−1.03604	−	0.598159i	−0.918710	+	0.394934i	$0.870768\pi$
$462$	−0.352063	+	0.897072i	−0.0163794	+	0.0417356i
$463$		−	1.93793i		−	0.0900634i	−0.998986	−	0.0450317i	$-0.985661\pi$
$463$		−	1.93793i		−	0.0900634i	0.998986	−	0.0450317i	$-0.0143389\pi$
$464$	2.85083	+	1.30972i	0.132346	+	0.0608020i
$465$	−0.419823	−	3.30431i	−0.0194688	−	0.153234i
$466$	−0.383311	−	16.4938i	−0.0177566	−	0.764059i
$467$	−24.5014			−1.13379			−0.566894	−	0.823791i	$-0.691855\pi$
$467$	−24.5014			−1.13379			−0.566894	+	0.823791i	$0.691855\pi$
$468$	−8.59324	+	37.6535i	−0.397223	+	1.74053i
$469$	−0.158459	−	0.274458i	−0.00731694	−	0.0126733i
$470$	−5.88824	+	3.58451i	−0.271604	+	0.165341i
$471$	−4.09267	−	32.2124i	−0.188580	−	1.48427i
$472$	−15.1058	+	30.9632i	−0.695302	+	1.42520i
$473$	−1.60769	−	0.928200i	−0.0739217	−	0.0426787i
$474$	−9.11362	−	11.4278i	−0.418602	−	0.524898i
$475$	4.34423	−	20.2147i	0.199327	−	0.927516i
$476$	7.68619	+	11.9897i	0.352296	+	0.549546i
$477$	−6.18591	−	23.9509i	−0.283234	−	1.09664i
$478$	−15.8798	−	26.0856i	−0.726327	−	1.19313i
$479$	5.72973	+	9.92419i	0.261798	+	0.453448i	0.966720	−	0.255838i	$-0.0823512\pi$
$479$	5.72973	+	9.92419i	0.261798	+	0.453448i	−0.704922	+	0.709285i	$0.749018\pi$
$480$	−8.48274	+	29.3839i	−0.387182	+	1.34119i
$481$	−22.4736	−	38.9253i	−1.02471	−	1.77484i
$482$	10.0534	−	18.3867i	0.457918	−	0.837490i
$483$	7.25029	−	17.2822i	0.329900	−	0.786367i
$484$	10.0360	−	19.4133i	0.456181	−	0.882421i
$485$	38.4780	−	22.2153i	1.74719	−	1.00874i
$486$	13.4312	+	17.4815i	0.609250	+	0.792978i
$487$		−	24.7999i		−	1.12379i	−0.827208	−	0.561895i	$-0.810072\pi$
$487$		−	24.7999i		−	1.12379i	0.827208	−	0.561895i	$-0.189928\pi$
$488$	−4.40786	−	6.53642i	−0.199535	−	0.295890i
$489$	−8.45892	−	11.1278i	−0.382526	−	0.503214i
$490$	−0.500530	−	21.5377i	−0.0226116	−	0.972972i
$491$	−9.33950	+	16.1765i	−0.421486	+	0.730035i	−0.996085	−	0.0884001i	$-0.971825\pi$
$491$	−9.33950	+	16.1765i	−0.421486	+	0.730035i	0.574599	+	0.818435i	$0.305158\pi$
$492$	1.59663	−	4.36379i	0.0719815	−	0.196735i
$493$	3.83611			0.172770
$494$	−37.4722	+	13.0512i	−1.68595	+	0.587200i
$495$	−1.80541	+	1.77303i	−0.0811472	+	0.0796919i
$496$	−2.01062	+	1.42492i	−0.0902794	+	0.0639810i
$497$	−8.86567	−	5.11860i	−0.397680	−	0.229600i
$498$	15.1284	+	5.93725i	0.677919	+	0.266055i
$499$	31.9789	+	18.4630i	1.43157	+	0.826519i	0.997241	−	0.0742346i	$-0.0236514\pi$
$499$	31.9789	+	18.4630i	1.43157	+	0.826519i	0.434331	+	0.900753i	$0.356985\pi$
$500$	1.42268	+	0.735478i	0.0636244	+	0.0328916i
$501$	15.8766	+	6.66061i	0.709314	+	0.297574i
$502$	−0.722614	+	1.32159i	−0.0322518	+	0.0589857i
$503$	11.2056	+	19.4087i	0.499633	+	0.865389i	1.00000		0.000424029i	$-0.000134973\pi$
$503$	11.2056	+	19.4087i	0.499633	+	0.865389i	−0.500367	+	0.865813i	$0.666802\pi$
$504$	12.1049	+	2.46816i	0.539195	+	0.109941i
$505$	6.30604			0.280615
$506$	1.36253	−	2.49194i	0.0605718	−	0.110780i
$507$	6.20738	+	48.8567i	0.275680	+	2.16980i
$508$	−1.10083	−	23.6714i	−0.0488415	−	1.05025i
$509$	−36.8293	+	21.2634i	−1.63243	+	0.942483i	−0.649087	+	0.760714i	$0.724849\pi$
$509$	−36.8293	+	21.2634i	−1.63243	+	0.942483i	−0.983341	+	0.181769i	$0.941818\pi$
$510$	5.57406	+	36.9785i	0.246823	+	1.63744i
$511$	−1.03611	−	0.598196i	−0.0458346	−	0.0264626i
$512$	22.1345	−	4.69744i	0.978214	−	0.207599i
$513$	−7.89730	+	21.2281i	−0.348674	+	0.937244i
$514$	7.28823	+	3.98501i	0.321470	+	0.175771i
$515$	1.54757	−	2.68048i	0.0681942	−	0.118116i
$516$	−8.17714	+	22.3492i	−0.359979	+	0.983869i
$517$	0.210987	+	0.365440i	0.00927920	+	0.0160720i
$518$	−12.2807	+	7.47599i	−0.539584	+	0.328476i
$519$	−9.33882	+	1.18652i	−0.409929	+	0.0520826i
$520$	3.95826	+	56.6924i	0.173581	+	2.48613i
$521$		−	22.8263i		−	1.00004i	−0.866014	−	0.500019i	$-0.833326\pi$
$521$		−	22.8263i		−	1.00004i	0.866014	−	0.500019i	$-0.166674\pi$
$522$	2.31935	−	2.38611i	0.101515	−	0.104437i
$523$	−1.44861	+	0.836358i	−0.0633435	+	0.0365714i	−0.531337	−	0.847160i	$-0.678310\pi$
$523$	−1.44861	+	0.836358i	−0.0633435	+	0.0365714i	0.467994	+	0.883732i	$0.344977\pi$
$524$	1.92940	+	3.00966i	0.0842861	+	0.131478i
$525$	−4.62753	+	11.0304i	−0.201962	+	0.481407i
$526$	2.34642	−	0.0545303i	0.102309	−	0.00237763i
$527$	−1.50663	+	2.60957i	−0.0656300	+	0.113674i
$528$	1.78614	+	0.560908i	0.0777319	+	0.0244104i
$529$	−16.1168	+	27.9151i	−0.700731	+	1.21370i
$530$	−18.9272	−	31.0915i	−0.822144	−	1.35053i
$531$	25.6038	+	26.0713i	1.11111	+	1.13140i
$532$	4.45205	+	11.8861i	0.193021	+	0.515326i
$533$		−	8.63444i		−	0.373999i
$534$	8.68145	−	1.30862i	0.375683	−	0.0566296i
$535$	43.6635	+	25.2091i	1.88774	+	1.08989i
$536$	−0.510453	+	0.344226i	−0.0220482	+	0.0148683i
$537$	3.95511	−	3.00653i	0.170676	−	0.129742i
$538$	−0.504741	−	21.7189i	−0.0217609	−	0.936366i
$539$	−1.31875			−0.0568026
$540$	26.3713	+	18.8904i	1.13484	+	0.812915i
$541$	6.90152	+	11.9538i	0.296719	+	0.513933i	0.975383	−	0.220516i	$-0.0707741\pi$
$541$	6.90152	+	11.9538i	0.296719	+	0.513933i	−0.678664	+	0.734449i	$0.737441\pi$
$542$	0.190882	+	8.21360i	0.00819909	+	0.352804i
$543$	5.66186	+	2.37529i	0.242974	+	0.101933i
$544$	22.1957	−	16.5180i	0.951634	−	0.708203i
$545$	−16.0079	+	9.24219i	−0.685705	+	0.395892i
$546$	22.6995	−	3.42167i	0.971449	−	0.146434i
$547$	−33.4348	+	19.3036i	−1.42957	+	0.825362i	−0.997086	−	0.0762806i	$-0.975696\pi$
$547$	−33.4348	+	19.3036i	−1.42957	+	0.825362i	−0.432482	+	0.901642i	$0.642362\pi$
$548$	−1.46021	−	31.3993i	−0.0623773	−	1.34131i
$549$	−8.09634	+	2.09108i	−0.345543	+	0.0892452i
$550$	−0.869639	+	1.59049i	−0.0370815	+	0.0678187i
$551$	3.34247	+	0.718310i	0.142394	+	0.0306010i
$552$	−34.4735	−	11.7125i	−1.46729	−	0.498515i
$553$	−4.34400	+	7.52403i	−0.184726	+	0.319954i
$554$	−0.185776	−	0.305172i	−0.00789287	−	0.0129655i
$555$	−37.4509	+	4.75824i	−1.58970	+	0.201976i
$556$	−0.244180	−	5.25066i	−0.0103555	−	0.222678i
$557$	−19.1177	+	11.0376i	−0.810043	+	0.467679i	−0.846971	−	0.531639i	$-0.821576\pi$
$557$	−19.1177	+	11.0376i	−0.810043	+	0.467679i	0.0369276	+	0.999318i	$0.488243\pi$
$558$	0.712261	+	2.51492i	0.0301524	+	0.106465i
$559$			44.2214i			1.87036i
$560$	18.1000	−	1.68712i	0.764864	−	0.0712937i
$561$	2.27090	−	0.288525i	0.0958776	−	0.0121815i
$562$	21.6073	+	11.8143i	0.911448	+	0.498356i
$563$	−15.6539			−0.659733			−0.329866	−	0.944028i	$-0.607004\pi$
$563$	−15.6539			−0.659733			−0.329866	+	0.944028i	$0.607004\pi$
$564$	4.14978	−	3.47017i	0.174737	−	0.146121i
$565$	6.82969	−	11.8294i	0.287327	−	0.497665i
$566$	−0.851072	−	36.6214i	−0.0357732	−	1.53931i
$567$	6.75594	−	11.2274i	0.283723	−	0.471508i
$568$	−8.72012	+	17.8741i	−0.365888	+	0.749979i
$569$			3.11311i			0.130508i	0.997869	+	0.0652542i	$0.0207858\pi$
$569$			3.11311i			0.130508i	−0.997869	+	0.0652542i	$0.979214\pi$
$570$	−2.06745	+	33.2638i	−0.0865958	+	1.39327i
$571$		−	41.0259i		−	1.71688i	−0.512915	−	0.858439i	$-0.671434\pi$
$571$		−	41.0259i		−	1.71688i	0.512915	−	0.858439i	$-0.328566\pi$
$572$	3.47503	−	0.161605i	0.145299	−	0.00675706i
$573$	−30.8746	+	23.4697i	−1.28980	+	0.980463i
$574$	−2.76117	+	0.0641689i	−0.115249	+	0.00267836i
$575$	17.6265	−	30.5301i	0.735078	−	1.27319i
$576$	3.14534	−	23.7930i	0.131056	−	0.991375i
$577$	−18.3118			−0.762330			−0.381165	−	0.924507i	$-0.624477\pi$
$577$	−18.3118			−0.762330			−0.381165	+	0.924507i	$0.624477\pi$
$578$	4.69611	−	8.58876i	0.195333	−	0.357245i
$579$	0.660414	+	5.19795i	0.0274459	+	0.216019i
$580$	2.24859	−	4.34960i	0.0933677	−	0.180607i
$581$		−	9.65972i		−	0.400753i
$582$	−27.2590	+	21.7388i	−1.12992	+	0.901103i
$583$	−1.92962	+	1.11407i	−0.0799168	+	0.0461400i
$584$	−1.01910	+	2.08889i	−0.0421705	+	0.0864390i
$585$	58.0803	+	16.1272i	2.40133	+	0.666778i
$586$	11.3692	−	6.92110i	0.469658	−	0.285908i
$587$	0.820972	−	1.42196i	0.0338851	−	0.0586908i	−0.848586	−	0.529058i	$-0.822545\pi$
$587$	0.820972	−	1.42196i	0.0338851	−	0.0586908i	0.882471	+	0.470367i	$0.155879\pi$
$588$	2.90758	+	16.6538i	0.119907	+	0.686793i
$589$	−1.80140	+	1.99164i	−0.0742253	+	0.0820643i
$590$	47.1776	+	25.7955i	1.94227	+	1.06198i
$591$	−9.25426	−	12.1740i	−0.380669	−	0.500773i
$592$	16.1500	+	22.7882i	0.663762	+	0.936590i
$593$	16.8107	−	9.70567i	0.690333	−	0.398564i	−0.113404	−	0.993549i	$-0.536175\pi$
$593$	16.8107	−	9.70567i	0.690333	−	0.398564i	0.803737	+	0.594985i	$0.202842\pi$
$594$	1.19354	−	1.58698i	0.0489717	−	0.0651145i
$595$	19.2497	−	11.1138i	0.789160	−	0.455622i
$596$	−16.3472	+	10.4797i	−0.669607	+	0.429263i
$597$	17.5626	−	41.8632i	0.718789	−	1.71335i
$598$	−67.6362	+	1.57185i	−2.76585	+	0.0642777i
$599$	−5.62397	−	9.74101i	−0.229789	−	0.398007i	0.727956	−	0.685624i	$-0.240470\pi$
$599$	−5.62397	−	9.74101i	−0.229789	−	0.398007i	−0.957746	+	0.287617i	$0.907137\pi$
$600$	22.0029	+	7.47552i	0.898264	+	0.305187i
$601$	−7.87495			−0.321226			−0.160613	−	0.987017i	$-0.551347\pi$
$601$	−7.87495			−0.321226			−0.160613	+	0.987017i	$0.551347\pi$
$602$	14.1413	−	0.328642i	0.576358	−	0.0133944i
$603$	0.163300	+	0.632273i	0.00665010	+	0.0257481i
$604$	−39.0429	−	20.1838i	−1.58863	−	0.821268i
$605$	−29.5384	−	17.0540i	−1.20091	−	0.693345i
$606$	−4.89324	+	0.737596i	−0.198774	+	0.0299628i
$607$		−	17.9248i		−	0.727547i	−0.931487	−	0.363773i	$-0.881488\pi$
$607$		−	17.9248i		−	0.727547i	0.931487	−	0.363773i	$-0.118512\pi$
$608$	22.4325	−	10.2363i	0.909759	−	0.415136i
$609$	−1.82386	−	0.765152i	−0.0739065	−	0.0310055i
$610$	−10.5101	+	6.39813i	−0.425543	+	0.259053i
$611$	5.02593	−	8.70516i	0.203327	−	0.352173i
$612$	−8.65051	−	28.0419i	−0.349676	−	1.13353i
$613$	20.9233	−	36.2402i	0.845083	−	1.46373i	−0.0404659	−	0.999181i	$-0.512884\pi$
$613$	20.9233	−	36.2402i	0.845083	−	1.46373i	0.885549	−	0.464546i	$-0.153782\pi$
$614$	0.448286	+	19.2896i	0.0180913	+	0.778465i
$615$	−6.68757	−	2.80559i	−0.269669	−	0.113132i
$616$	−0.0775045	−	1.11006i	−0.00312275	−	0.0447257i
$617$	−4.14588	+	2.39362i	−0.166907	+	0.0963636i	−0.581126	−	0.813813i	$-0.697388\pi$
$617$	−4.14588	+	2.39362i	−0.166907	+	0.0963636i	0.414220	+	0.910177i	$0.364055\pi$
$618$	−0.887331	+	2.26096i	−0.0356937	+	0.0909492i
$619$		−	34.2768i		−	1.37770i	−0.724903	−	0.688851i	$-0.758115\pi$
$619$		−	34.2768i		−	1.37770i	0.724903	−	0.688851i	$-0.241885\pi$
$620$	2.07574	+	3.23795i	0.0833638	+	0.130039i
$621$	−23.9224	+	30.3154i	−0.959975	+	1.21652i
$622$	−2.75865	−	4.53161i	−0.110612	−	0.181701i
$623$	−2.60919	−	4.51925i	−0.104535	−	0.181060i
$624$	−9.70258	−	43.5282i	−0.388414	−	1.74252i
$625$	13.1084	−	22.7045i	0.524338	−	0.908179i
$626$	−15.5248	+	28.3935i	−0.620497	+	1.13483i
$627$	2.03270	+	0.173829i	0.0811784	+	0.00694208i
$628$	20.2355	+	31.5654i	0.807485	+	1.25960i
$629$	29.5767	+	17.0761i	1.17930	+	0.680869i
$630$	4.72560	−	18.6931i	0.188272	−	0.744750i
$631$	32.0248	−	18.4895i	1.27489	−	0.736057i	0.298985	−	0.954258i	$-0.403352\pi$
$631$	32.0248	−	18.4895i	1.27489	−	0.736057i	0.975904	+	0.218201i	$0.0700188\pi$
$632$	15.1692	+	7.40050i	0.603398	+	0.294376i
$633$	17.3276	−	2.20152i	0.688709	−	0.0875025i
$634$	−29.7839	−	16.2851i	−1.18287	−	0.646764i
$635$	−36.9846			−1.46769
$636$	18.3234	+	21.9119i	0.726571	+	0.868865i
$637$	15.7070	+	27.2053i	0.622334	+	1.07791i
$638$	−0.262984	−	0.143793i	−0.0104117	−	0.00569282i
$639$	14.7803	+	15.0502i	0.584698	+	0.595375i
$640$	−5.71869	−	34.8491i	−0.226051	−	1.37753i
$641$	36.6535	+	21.1619i	1.44773	+	0.835846i	0.998346	−	0.0574944i	$-0.0183111\pi$
$641$	36.6535	+	21.1619i	1.44773	+	0.835846i	0.449381	+	0.893340i	$0.351644\pi$
$642$	−36.8298	−	14.4542i	−1.45356	−	0.570460i
$643$	−32.8818	−	18.9843i	−1.29673	−	0.748667i	−0.316892	−	0.948462i	$-0.602639\pi$
$643$	−32.8818	−	18.9843i	−1.29673	−	0.748667i	−0.979838	+	0.199794i	$0.935973\pi$
$644$	1.00531	+	21.6174i	0.0396147	+	0.851843i
$645$	34.2505	+	14.3689i	1.34861	+	0.565774i
$646$	19.6996	−	22.8244i	0.775070	−	0.898012i
$647$	6.14775			0.241693			0.120847	−	0.992671i	$-0.461439\pi$
$647$	6.14775			0.241693			0.120847	+	0.992671i	$0.461439\pi$
$648$	−22.6727	−	11.5737i	−0.890666	−	0.454658i
$649$	1.64570	−	2.85044i	0.0645995	−	0.111890i
$650$	43.1690	−	1.00324i	1.69323	−	0.0393503i
$651$	1.23683	−	0.940192i	0.0484751	−	0.0368490i
$652$	14.3376	+	7.41207i	0.561506	+	0.290279i
$653$			18.8138i			0.736241i	0.929778	+	0.368120i	$0.119999\pi$
$653$			18.8138i			0.736241i	−0.929778	+	0.368120i	$0.880001\pi$
$654$	11.3405	−	9.04398i	0.443449	−	0.353647i
$655$	4.83207	−	2.78980i	0.188805	−	0.109006i
$656$	0.497970	+	5.34240i	0.0194425	+	0.208586i
$657$	1.72733	+	1.75887i	0.0673895	+	0.0686201i
$658$	−2.82113	−	1.54252i	−0.109979	−	0.0601338i
$659$	−19.9431	−	34.5425i	−0.776873	−	1.34558i	−0.933736	−	0.357963i	$-0.883471\pi$
$659$	−19.9431	−	34.5425i	−0.776873	−	1.34558i	0.156863	−	0.987620i	$-0.449862\pi$
$660$	1.00398	−	2.74400i	0.0390798	−	0.106810i
$661$	4.76337	+	8.25039i	0.185274	+	0.320903i	0.943669	−	0.330892i	$-0.107350\pi$
$661$	4.76337	+	8.25039i	0.185274	+	0.320903i	−0.758395	+	0.651795i	$0.774016\pi$
$662$	−38.5800	+	23.4859i	−1.49946	+	0.912806i
$663$	−32.9998	−	43.4114i	−1.28160	−	1.68596i
$664$	−18.7203	+	1.30705i	−0.726489	+	0.0507234i
$665$	18.8536	−	6.07916i	0.731113	−	0.235740i
$666$	28.5039	−	8.07272i	1.10450	−	0.312812i
$667$	5.04809	+	2.91451i	0.195463	+	0.112850i
$668$	−19.8592	+	0.923545i	−0.768375	+	0.0357330i
$669$	35.0879	−	4.45801i	1.35658	−	0.172357i
$670$	0.499653	+	0.820775i	0.0193033	+	0.0317093i
$671$	0.376599	+	0.652288i	0.0145384	+	0.0251813i
$672$	−13.8476	+	3.42623i	−0.534181	+	0.132170i
$673$	−24.5786			−0.947437			−0.473718	−	0.880676i	$-0.657089\pi$
$673$	−24.5786			−0.947437			−0.473718	+	0.880676i	$0.657089\pi$
$674$	−20.4493	+	0.475238i	−0.787679	+	0.0183055i
$675$	15.2686	−	19.3489i	0.587689	−	0.744741i
$676$	−30.6913	−	47.8754i	−1.18044	−	1.84136i
$677$			24.1522i			0.928246i	0.885771	+	0.464123i	$0.153630\pi$
$677$			24.1522i			0.928246i	−0.885771	+	0.464123i	$0.846370\pi$
$678$	−3.91594	+	9.97799i	−0.150391	+	0.383202i
$679$	17.9472	+	10.3618i	0.688748	+	0.397649i
$680$	−24.1430	−	35.8017i	−0.925841	−	1.37293i
$681$	−8.07141	+	6.13560i	−0.309297	+	0.235117i
$682$	0.201105	−	0.122424i	0.00770070	−	0.00468786i
$683$	41.7839			1.59882			0.799408	−	0.600789i	$-0.205147\pi$
$683$	41.7839			1.59882			0.799408	+	0.600789i	$0.205147\pi$
$684$	−2.28650	−	26.0533i	−0.0874264	−	0.996171i
$685$	−49.0587			−1.87444
$686$	20.8943	−	12.7196i	0.797749	−	0.485636i
$687$	12.8125	−	9.73962i	0.488828	−	0.371590i
$688$	−2.55036	−	27.3611i	−0.0972315	−	1.04313i
$689$	45.9656	+	26.5382i	1.75115	+	1.01103i
$690$	−20.7596	+	52.8965i	−0.790305	+	2.01373i
$691$		−	19.4316i		−	0.739211i	−0.929189	−	0.369606i	$-0.879493\pi$
$691$		−	19.4316i		−	0.739211i	0.929189	−	0.369606i	$-0.120507\pi$
$692$	9.15125	−	5.86656i	0.347878	−	0.223013i
$693$	−1.13724	−	0.315778i	−0.0432002	−	0.0119954i
$694$	−27.4005	+	0.636781i	−1.04011	+	0.0241719i
$695$	−8.20370			−0.311184
$696$	−1.23606	+	3.63813i	−0.0468529	+	0.137903i
$697$	3.28036	+	5.68174i	0.124252	+	0.215211i
$698$	15.3593	+	25.2305i	0.581357	+	0.954989i
$699$	20.0450	−	2.54677i	0.758170	−	0.0963277i
$700$	−0.641642	−	13.7974i	−0.0242518	−	0.521492i
$701$	10.1645	+	5.86846i	0.383907	+	0.221649i	0.679517	−	0.733660i	$-0.262190\pi$
$701$	10.1645	+	5.86846i	0.383907	+	0.221649i	−0.295610	+	0.955309i	$0.595523\pi$
$702$	−46.9545	−	5.72062i	−1.77218	−	0.215911i
$703$	22.5732	+	20.4169i	0.851364	+	0.770039i
$704$	−2.14079	+	0.300404i	−0.0806842	+	0.0113219i
$705$	−5.10927	−	6.72127i	−0.192426	−	0.253138i
$706$	−12.7063	+	7.73503i	−0.478206	+	0.291112i
$707$	1.47065	+	2.54724i	0.0553096	+	0.0957990i
$708$	−39.6253	−	14.4981i	−1.48921	−	0.544873i
$709$	9.62953	+	16.6788i	0.361645	+	0.626387i	0.988232	−	0.152965i	$-0.0488821\pi$
$709$	9.62953	+	16.6788i	0.361645	+	0.626387i	−0.626587	+	0.779351i	$0.715549\pi$
$710$	27.2342	+	14.8909i	1.02208	+	0.558847i
$711$	12.7726	−	12.5436i	0.479011	−	0.470420i
$712$	−8.40515	+	5.66805i	−0.314996	+	0.212419i
$713$	−3.96528	+	2.28936i	−0.148501	+	0.0857370i
$714$	−13.6371	+	10.8755i	−0.510354	+	0.407004i
$715$		−	5.42944i		−	0.203049i
$716$	−2.63445	+	5.09600i	−0.0984542	+	0.190446i
$717$	29.7761	−	22.6347i	1.11201	−	0.845308i
$718$	8.71003	−	0.202419i	0.325056	−	0.00755422i
$719$	−16.2499	+	28.1457i	−0.606021	+	1.04966i	0.385869	+	0.922554i	$0.373902\pi$
$719$	−16.2499	+	28.1457i	−0.606021	+	1.04966i	−0.991889	+	0.127105i	$0.959432\pi$
$720$	−36.8662	−	6.62876i	−1.37392	−	0.247039i
$721$	1.44366			0.0537647
$722$	21.4385	−	16.1985i	0.797857	−	0.602847i
$723$	23.6670	+	9.92887i	0.880185	+	0.369259i
$724$	−7.08212	+	0.329352i	−0.263205	+	0.0122403i
$725$	−3.22196	−	1.86020i	−0.119661	−	0.0690861i
$726$	24.9154	+	9.77825i	0.924699	+	0.362905i
$727$	18.3962	+	10.6210i	0.682276	+	0.393912i	0.800712	−	0.599049i	$-0.204455\pi$
$727$	18.3962	+	10.6210i	0.682276	+	0.393912i	−0.118436	+	0.992962i	$0.537788\pi$
$728$	−21.9771	+	14.8203i	−0.814524	+	0.549278i
$729$	−19.6030	+	18.5667i	−0.726037	+	0.687655i
$730$	3.18278	+	1.74026i	0.117800	+	0.0644100i
$731$	−16.8004	−	29.0991i	−0.621384	−	1.07627i
$732$	7.40709	−	6.19404i	0.273774	−	0.228938i
$733$	−9.76975			−0.360854			−0.180427	−	0.983588i	$-0.557748\pi$
$733$	−9.76975			−0.360854			−0.180427	+	0.983588i	$0.557748\pi$
$734$	23.9586	+	13.1000i	0.884330	+	0.483529i
$735$	26.1748	−	3.32559i	0.965473	−	0.122666i
$736$	41.7580	−	4.87330i	1.53922	−	0.179632i
$737$	0.0509396	−	0.0294100i	0.00187638	−	0.00108333i
$738$	5.51746	+	1.39481i	0.203100	+	0.0513437i
$739$	−1.65703	−	0.956687i	−0.0609549	−	0.0351923i	0.469213	−	0.883085i	$-0.344538\pi$
$739$	−1.65703	−	0.956687i	−0.0609549	−	0.0351923i	−0.530168	+	0.847893i	$0.677871\pi$
$740$	36.6987	−	23.5263i	1.34907	−	0.864845i
$741$	−20.6245	−	44.0043i	−0.757660	−	1.61654i
$742$	8.14494	−	14.8963i	0.299010	−	0.546862i
$743$	13.6139	−	23.5800i	0.499446	−	0.865067i	−0.500553	−	0.865706i	$-0.666870\pi$
$743$	13.6139	−	23.5800i	0.499446	−	0.865067i	1.00000		0.000639108i	$0.000203434\pi$
$744$	−1.98943	−	2.26973i	−0.0729359	−	0.0832123i
$745$	15.1530	+	26.2457i	0.555163	+	0.961570i
$746$	−16.9081	−	27.7747i	−0.619048	−	1.01690i
$747$	−5.32534	+	19.1786i	−0.194844	+	0.701709i
$748$	−2.22529	+	1.42656i	−0.0813647	+	0.0521602i
$749$			23.5164i			0.859272i
$750$	−0.716591	+	1.82591i	−0.0261662	+	0.0666727i
$751$	−27.2314	+	15.7220i	−0.993687	+	0.573705i	−0.906374	−	0.422476i	$-0.861161\pi$
$751$	−27.2314	+	15.7220i	−0.993687	+	0.573705i	−0.0873123	+	0.996181i	$0.527828\pi$
$752$	−2.60765	+	5.67602i	−0.0950913	+	0.206983i
$753$	−1.70113	−	0.713666i	−0.0619928	−	0.0260074i
$754$	0.165884	+	7.13792i	0.00604112	+	0.259948i
$755$	−34.2981	+	59.4061i	−1.24824	+	2.16201i
$756$	−1.48042	+	15.0579i	−0.0538423	+	0.547649i
$757$	21.5749	−	37.3689i	0.784154	−	1.35819i	−0.145349	−	0.989380i	$-0.546431\pi$
$757$	21.5749	−	37.3689i	0.784154	−	1.35819i	0.929503	−	0.368814i	$-0.120236\pi$
$758$	17.2822	−	10.5207i	0.627716	−	0.382127i
$759$	3.20758	+	1.34566i	0.116428	+	0.0488442i
$760$	−14.3324	−	35.7154i	−0.519889	−	1.29553i
$761$		−	13.0357i		−	0.472545i	−0.971687	−	0.236272i	$-0.924074\pi$
$761$		−	13.0357i		−	0.472545i	0.971687	−	0.236272i	$-0.0759257\pi$
$762$	28.6986	−	4.32596i	1.03964	−	0.156713i
$763$	−7.46653	−	4.31080i	−0.270306	−	0.156062i
$764$	20.5652	−	39.7806i	0.744023	−	1.43921i
$765$	−44.3457	+	11.4534i	−1.60332	+	0.414098i
$766$	−29.1488	+	0.677412i	−1.05319	+	0.0244759i
$767$	−78.4047			−2.83103
$768$	8.51367	+	26.3727i	0.307211	+	0.951642i
$769$	23.5634	+	40.8130i	0.849718	+	1.47175i	0.881460	+	0.472259i	$0.156561\pi$
$769$	23.5634	+	40.8130i	0.849718	+	1.47175i	−0.0317418	+	0.999496i	$0.510105\pi$
$770$	−1.73625	+	0.0403502i	−0.0625703	+	0.00145412i
$771$	−3.93567	+	9.38128i	−0.141740	+	0.337858i
$772$	−3.26531	−	5.09355i	−0.117521	−	0.183321i
$773$	20.3000	−	11.7202i	0.730140	−	0.421546i	−0.0883337	−	0.996091i	$-0.528154\pi$
$773$	20.3000	−	11.7202i	0.730140	−	0.421546i	0.818473	+	0.574545i	$0.194821\pi$
$774$	−28.2577	−	7.14354i	−1.01570	−	0.256769i
$775$	2.53086	−	1.46119i	0.0909110	−	0.0524875i
$776$	17.6525	−	36.1832i	0.633688	−	1.29890i
$777$	−10.6561	−	14.0181i	−0.382285	−	0.502898i
$778$	19.8808	+	10.8703i	0.712763	+	0.389720i
$779$	1.79433	+	5.56485i	0.0642884	+	0.199381i
$780$	−68.5656	+	11.9708i	−2.45504	+	0.428624i
$781$	0.950013	−	1.64547i	0.0339941	−	0.0588796i
$782$	43.9096	−	26.7303i	1.57021	−	0.955875i
$783$	3.19931	+	2.52463i	0.114334	+	0.0902230i
$784$	−11.2874	−	15.9269i	−0.403122	−	0.568819i
$785$	50.6788	−	29.2594i	1.80881	−	1.04431i
$786$	−3.42319	+	2.72997i	−0.122101	+	0.0973747i
$787$		−	1.54593i		−	0.0551063i	−0.999620	−	0.0275531i	$-0.991228\pi$
$787$		−	1.54593i		−	0.0551063i	0.999620	−	0.0275531i	$-0.00877155\pi$
$788$	15.6857	+	8.10898i	0.558781	+	0.288870i
$789$	0.362306	+	2.85162i	0.0128985	+	0.101520i
$790$	12.6375	−	23.1128i	0.449622	−	0.822317i
$791$	6.37110			0.226530
$792$	−0.458092	+	2.24667i	−0.0162776	+	0.0798321i
$793$	8.97097	−	15.5382i	0.318568	−	0.551777i
$794$	−16.1809	+	0.376042i	−0.574240	+	0.0133452i
$795$	35.4901	−	26.9783i	1.25870	−	0.956822i
$796$	2.43519	+	52.3644i	0.0863129	+	1.85601i
$797$		−	16.5283i		−	0.585463i	−0.956195	−	0.292732i	$-0.905436\pi$
$797$		−	16.5283i		−	0.585463i	0.956195	−	0.292732i	$-0.0945642\pi$
$798$	−13.9186	+	6.92244i	−0.492715	+	0.245052i
$799$			7.63771i			0.270203i
$800$	−26.6522	+	3.11040i	−0.942297	+	0.109969i
$801$	2.68891	+	10.4110i	0.0950080	+	0.367856i
$802$	−0.905571	−	38.9664i	−0.0319768	−	1.37595i
$803$	0.111025	−	0.192302i	0.00391800	−	0.00678618i
$804$	−0.483715	−	0.578447i	−0.0170593	−	0.0204003i
$805$	33.7752			1.19042
$806$	−4.92082	−	2.69058i	−0.173329	−	0.0947716i
$807$	26.3950	−	3.35357i	0.929150	−	0.118051i
$808$	4.73751	−	3.19476i	0.166665	−	0.112391i
$809$		−	38.2090i		−	1.34336i	−0.740843	−	0.671679i	$-0.765574\pi$
$809$		−	38.2090i		−	1.34336i	0.740843	−	0.671679i	$-0.234426\pi$
$810$	−19.6877	+	34.5085i	−0.691755	+	1.21250i
$811$	−7.83754	+	4.52501i	−0.275213	+	0.158894i	−0.631254	−	0.775576i	$-0.717460\pi$
$811$	−7.83754	+	4.52501i	−0.275213	+	0.158894i	0.356041	+	0.934470i	$0.384126\pi$
$812$	2.28137	−	0.106094i	0.0800603	−	0.00372318i
$813$	−9.98204	+	1.26825i	−0.350085	+	0.0444793i
$814$	−1.38755	−	2.27931i	−0.0486335	−	0.0798897i
$815$	12.5952	−	21.8156i	0.441192	−	0.764167i
$816$	22.9216	+	24.9568i	0.802417	+	0.873662i
$817$	−9.18967	−	28.5004i	−0.321506	−	0.997104i
$818$	−17.2295	+	31.5112i	−0.602415	+	1.10176i
$819$	7.03073	+	27.2219i	0.245674	+	0.951210i
$820$	8.36512	−	0.389017i	0.292123	−	0.0135851i
$821$	−32.0275	+	18.4911i	−1.11777	+	0.645342i	−0.940830	−	0.338880i	$-0.889952\pi$
$821$	−32.0275	+	18.4911i	−1.11777	+	0.645342i	−0.176936	+	0.984222i	$0.556619\pi$
$822$	38.0677	−	5.73823i	1.32776	−	0.200144i
$823$	−14.0553	+	8.11483i	−0.489937	+	0.282865i	−0.724548	−	0.689224i	$-0.757952\pi$
$823$	−14.0553	+	8.11483i	−0.489937	+	0.282865i	0.234611	+	0.972089i	$0.424618\pi$
$824$	−0.195341	−	2.79778i	−0.00680501	−	0.0974653i
$825$	−2.04725	−	0.858870i	−0.0712761	−	0.0299020i
$826$	0.582683	+	25.0727i	0.0202741	+	0.872390i
$827$	−2.44055	−	4.22715i	−0.0848661	−	0.146992i	0.820468	−	0.571692i	$-0.193713\pi$
$827$	−2.44055	−	4.22715i	−0.0848661	−	0.146992i	−0.905334	+	0.424700i	$0.860380\pi$
$828$	9.92155	−	43.4738i	0.344798	−	1.51082i
$829$	32.0995			1.11486			0.557431	−	0.830223i	$-0.311787\pi$
$829$	32.0995			1.11486			0.557431	+	0.830223i	$0.311787\pi$
$830$	0.680472	+	29.2805i	0.0236195	+	1.01634i
$831$	0.348346	−	0.264801i	0.0120840	−	0.00918583i
$832$	31.6952	+	40.5858i	1.09883	+	1.40706i
$833$	−20.6714	−	11.9347i	−0.716223	−	0.413512i
$834$	6.36575	−	0.959559i	0.220428	−	0.0332268i
$835$			31.0282i			1.07378i
$836$	−2.20606	+	0.826303i	−0.0762981	+	0.0285783i
$837$	−2.97395	+	1.18482i	−0.102795	+	0.0409535i
$838$	10.0220	+	16.4630i	0.346203	+	0.568704i
$839$	−17.8443	+	30.9072i	−0.616053	+	1.06703i	0.374146	+	0.927370i	$0.377936\pi$
$839$	−17.8443	+	30.9072i	−0.616053	+	1.06703i	−0.990199	+	0.139665i	$0.955397\pi$
$840$	4.33765	+	21.8373i	0.149663	+	0.753459i
$841$	−14.1924	+	24.5820i	−0.489394	+	0.847655i
$842$	1.03795	−	0.0241218i	0.0357703	−	0.000831293i
$843$	−11.6680	+	27.8125i	−0.401868	+	0.957914i
$844$	−16.9795	+	10.8850i	−0.584460	+	0.374678i
$845$	−76.8649	+	44.3780i	−2.64423	+	1.52665i
$846$	4.75076	+	4.61783i	0.163335	+	0.158764i
$847$		−	15.9089i		−	0.546636i
$848$	−29.9709	−	13.7691i	−1.02920	−	0.472833i
$849$	44.5062	−	5.65464i	1.52745	−	0.194067i
$850$	−28.0255	+	17.0607i	−0.961267	+	0.585179i
$851$	25.9474	+	44.9423i	0.889466	+	1.54060i
$852$	−22.8744	−	8.36931i	−0.783665	−	0.286728i
$853$	−19.2055	+	33.2650i	−0.657585	+	1.13897i	0.323654	+	0.946176i	$0.395089\pi$
$853$	−19.2055	+	33.2650i	−0.657585	+	1.13897i	−0.981239	+	0.192795i	$0.938245\pi$
$854$	−5.03555	−	2.75331i	−0.172313	−	0.0942162i
$855$	−40.7839	+	1.67581i	−1.39478	+	0.0573115i
$856$	45.5743	−	3.18200i	1.55770	−	0.108758i
$857$	−38.1323	−	22.0157i	−1.30258	−	0.752042i	−0.321730	−	0.946831i	$-0.604264\pi$
$857$	−38.1323	−	22.0157i	−1.30258	−	0.752042i	−0.980845	+	0.194789i	$0.937598\pi$
$858$	0.635063	+	4.21304i	0.0216807	+	0.143831i
$859$	4.46967	−	2.58057i	0.152503	−	0.0880478i	−0.421807	−	0.906686i	$-0.638604\pi$
$859$	4.46967	−	2.58057i	0.152503	−	0.0880478i	0.574310	+	0.818638i	$0.305271\pi$
$860$	−42.8421	+	1.99236i	−1.46090	+	0.0679387i
$861$	−0.426346	−	3.35566i	−0.0145298	−	0.114361i
$862$	19.5356	−	35.7288i	0.665385	−	1.21693i
$863$	43.2729			1.47303			0.736513	−	0.676423i	$-0.236471\pi$
$863$	43.2729			1.47303			0.736513	+	0.676423i	$0.236471\pi$
$864$	29.3821	+	0.831548i	0.999600	+	0.0282898i
$865$	−8.48272	−	14.6925i	−0.288421	−	0.499560i
$866$	0.931521	−	1.70367i	0.0316544	−	0.0578930i
$867$	11.0553	+	4.63796i	0.375458	+	0.157513i
$868$	−0.823837	+	1.59360i	−0.0279628	+	0.0540904i
$869$	−1.39646	−	0.806248i	−0.0473717	−	0.0273501i
$870$	5.58238	+	2.19085i	0.189260	+	0.0742767i
$871$	−1.21343	−	0.700576i	−0.0411156	−	0.0237381i
$872$	−7.34395	+	15.0533i	−0.248698	+	0.509768i
$873$	−29.9203	−	30.4667i	−1.01265	−	1.03114i
$874$	43.2645	−	15.0686i	1.46344	−	0.509701i
$875$	1.16587			0.0394136
$876$	−2.67327	−	0.978098i	−0.0903214	−	0.0330469i
$877$	−11.5484	+	20.0024i	−0.389962	+	0.675434i	−0.992444	−	0.122699i	$-0.960845\pi$
$877$	−11.5484	+	20.0024i	−0.389962	+	0.675434i	0.602482	+	0.798132i	$0.294178\pi$
$878$	0.614121	+	26.4254i	0.0207256	+	0.891815i
$879$	9.86516	+	12.9777i	0.332743	+	0.437726i
$880$	0.313129	+	3.35936i	0.0105556	+	0.113244i
$881$			45.5990i			1.53627i	0.640288	+	0.768135i	$0.278815\pi$
$881$			45.5990i			1.53627i	−0.640288	+	0.768135i	$0.721185\pi$
$882$	−19.9217	+	5.64211i	−0.670798	+	0.189980i
$883$	−25.7298	+	14.8551i	−0.865877	+	0.499914i	−0.865976	−	0.500086i	$-0.833302\pi$
$883$	−25.7298	+	14.8551i	−0.865877	+	0.499914i	9.87523e−5		1.00000i	$0.499969\pi$
$884$	55.9337	+	28.9158i	1.88126	+	0.972544i
$885$	−25.4761	+	60.7262i	−0.856370	+	2.04129i
$886$	−12.2319	+	22.3709i	−0.410937	+	0.751566i
$887$	−14.1582	−	24.5228i	−0.475387	−	0.823394i	0.524216	−	0.851585i	$-0.324359\pi$
$887$	−14.1582	−	24.5228i	−0.475387	−	0.823394i	−0.999603	+	0.0281914i	$0.991025\pi$
$888$	−25.7250	+	22.5481i	−0.863274	+	0.756663i
$889$	−8.62530	−	14.9395i	−0.289283	−	0.501053i
$890$	8.22732	+	13.5149i	0.275780	+	0.453021i
$891$	2.08382	+	1.25391i	0.0698104	+	0.0420074i
$892$	−34.3831	+	22.0419i	−1.15123	+	0.738017i
$893$	−1.43016	+	6.65487i	−0.0478585	+	0.222697i
$894$	−14.8280	−	18.5933i	−0.495923	−	0.621853i
$895$	7.75386	+	4.47670i	0.259183	+	0.149639i
$896$	12.7432	−	10.4373i	0.425720	−	0.348685i
$897$	−10.4436	−	82.1986i	−0.348701	−	2.74453i
$898$	25.0621	−	15.2567i	0.836332	−	0.509124i
$899$	0.241605	+	0.418472i	0.00805798	+	0.0139568i
$900$	−6.33247	+	27.7473i	−0.211082	+	0.924911i
$901$	−40.3291			−1.34356
$902$	−0.0119098	−	0.512473i	−0.000396552	−	0.0170635i
$903$	2.18354	+	17.1861i	0.0726636	+	0.571916i
$904$	−0.862070	−	12.3471i	−0.0286720	−	0.410657i
$905$			11.0652i			0.367820i
$906$	19.6655	−	50.1086i	0.653342	−	1.66475i
$907$	21.3988	+	12.3546i	0.710535	+	0.410228i	0.811259	−	0.584687i	$-0.198783\pi$
$907$	21.3988	+	12.3546i	0.710535	+	0.410228i	−0.100724	+	0.994914i	$0.532116\pi$
$908$	5.37627	−	10.3997i	0.178418	−	0.345125i
$909$	−1.51559	−	5.86812i	−0.0502688	−	0.194633i
$910$	21.5121	+	35.3377i	0.713119	+	1.17143i
$911$	37.1771			1.23173			0.615866	−	0.787851i	$-0.288806\pi$
$911$	37.1771			1.23173			0.615866	+	0.787851i	$0.288806\pi$
$912$	15.2989	+	26.0374i	0.506596	+	0.862183i
$913$	1.79285			0.0593346
$914$	−15.1156	−	24.8302i	−0.499978	−	0.821308i
$915$	−9.11972	−	11.9970i	−0.301489	−	0.396610i
$916$	−8.53427	+	16.5084i	−0.281980	+	0.545453i
$917$	2.25381	+	1.30124i	0.0744273	+	0.0429706i
$918$	33.0709	−	14.0744i	1.09150	−	0.464523i
$919$			29.1327i			0.960999i	0.876995	+	0.480500i	$0.159545\pi$
$919$			29.1327i			0.960999i	−0.876995	+	0.480500i	$0.840455\pi$
$920$	−4.57011	−	65.4557i	−0.150672	−	2.15801i
$921$	−23.4428	+	2.97847i	−0.772465	+	0.0981439i
$922$	0.843969	+	36.3157i	0.0277946	+	1.19599i
$923$	−45.2606			−1.48977
$924$	1.34255	−	0.234394i	0.0441666	−	0.00771100i
$925$	−16.5610	−	28.6846i	−0.544524	−	0.943143i
$926$	−2.34099	+	1.42510i	−0.0769299	+	0.0468317i
$927$	−2.86627	−	0.795880i	−0.0941408	−	0.0261401i
$928$	−0.514299	−	4.40689i	−0.0168827	−	0.144663i
$929$	−14.1822	−	8.18808i	−0.465302	−	0.268642i	0.248969	−	0.968511i	$-0.419908\pi$
$929$	−14.1822	−	8.18808i	−0.465302	−	0.268642i	−0.714271	+	0.699869i	$0.753242\pi$
$930$	−3.68284	+	2.93704i	−0.120765	+	0.0963092i
$931$	−15.7766	−	14.2696i	−0.517058	−	0.467668i
$932$	−19.6424	+	12.5921i	−0.643407	+	0.412467i
$933$	5.17271	−	3.93211i	0.169347	−	0.128731i
$934$	18.0176	+	29.5973i	0.589553	+	0.968453i
$935$	2.06273	+	3.57275i	0.0674584	+	0.116841i
$936$	51.8041	−	17.3088i	1.69327	−	0.565755i
$937$	3.09777	+	5.36550i	0.101200	+	0.175283i	0.912179	−	0.409791i	$-0.134399\pi$
$937$	3.09777	+	5.36550i	0.101200	+	0.175283i	−0.810979	+	0.585075i	$0.801065\pi$
$938$	−0.215016	+	0.393244i	−0.00702052	+	0.0128399i
$939$	−36.5476	−	15.3326i	−1.19269	−	0.500360i
$940$	8.66008	+	4.47696i	0.282461	+	0.146022i
$941$	30.0415	−	17.3445i	0.979325	−	0.565414i	0.0772590	−	0.997011i	$-0.475383\pi$
$941$	30.0415	−	17.3445i	0.979325	−	0.565414i	0.902066	+	0.431597i	$0.142050\pi$
$942$	−35.9025	+	28.6319i	−1.16977	+	0.932879i
$943$			9.96911i			0.324639i
$944$	48.5115	−	4.52180i	1.57891	−	0.147172i
$945$	23.3685	+	3.39977i	0.760177	+	0.110594i
$946$	0.0609960	+	2.62464i	0.00198315	+	0.0853343i
$947$	22.4714	−	38.9217i	0.730223	−	1.26478i	−0.226564	−	0.973996i	$-0.572749\pi$
$947$	22.4714	−	38.9217i	0.730223	−	1.26478i	0.956788	−	0.290788i	$-0.0939173\pi$
$948$	−7.10278	+	19.4128i	−0.230688	+	0.630499i
$949$	−5.28948			−0.171704
$950$	−27.6137	+	9.61756i	−0.895908	+	0.312035i
$951$	16.0834	−	38.3374i	0.521541	−	1.24317i
$952$	8.83116	−	18.1017i	0.286220	−	0.586679i
$953$	19.5921	+	11.3115i	0.634651	+	0.366416i	0.782551	−	0.622587i	$-0.213918\pi$
$953$	19.5921	+	11.3115i	0.634651	+	0.366416i	−0.147900	+	0.989002i	$0.547251\pi$
$954$	−24.3834	+	25.0853i	−0.789442	+	0.812166i
$955$	−60.5286	−	34.9462i	−1.95866	−	1.13083i
$956$	−19.8335	+	38.3652i	−0.641461	+	1.24082i
$957$	0.142013	−	0.338509i	0.00459061	−	0.0109424i
$958$	7.77480	−	14.2194i	0.251192	−	0.459408i
$959$	−11.4411	−	19.8166i	−0.369454	−	0.639913i
$960$	41.7333	−	11.3611i	1.34694	−	0.366677i
$961$	30.6204			0.987756
$962$	−30.4949	+	55.7723i	−0.983194	+	1.79817i
$963$	12.9645	−	46.6901i	0.417774	−	1.50457i
$964$	−29.6038	+	1.37671i	−0.953474	+	0.0443410i
$965$	−8.17779	+	4.72145i	−0.263252	+	0.151989i
$966$	−26.2083	+	3.95058i	−0.843238	+	0.127108i
$967$	−37.0426	−	21.3865i	−1.19121	−	0.687745i	−0.232628	−	0.972566i	$-0.574732\pi$
$967$	−37.0426	−	21.3865i	−1.19121	−	0.687745i	−0.958581	+	0.284821i	$0.908066\pi$
$968$	−30.8311	+	2.15262i	−0.990949	+	0.0691880i
$969$	30.2895	+	21.1207i	0.973039	+	0.678494i
$970$	−55.1313	−	30.1444i	−1.77016	−	0.967877i
$971$	−1.73178	+	2.99953i	−0.0555755	+	0.0962596i	−0.892475	−	0.451097i	$-0.851033\pi$
$971$	−1.73178	+	2.99953i	−0.0555755	+	0.0962596i	0.836899	+	0.547357i	$0.184366\pi$
$972$	11.2406	−	29.0801i	0.360541	−	0.932743i
$973$	−1.91321	−	3.31378i	−0.0613347	−	0.106235i
$974$	−29.9579	+	18.2371i	−0.959914	+	0.584355i
$975$	6.66565	+	52.4636i	0.213472	+	1.68018i
$976$	−4.65449	+	10.1313i	−0.148987	+	0.324296i
$977$			7.12317i			0.227891i	0.993487	+	0.113945i	$0.0363489\pi$
$977$			7.12317i			0.227891i	−0.993487	+	0.113945i	$0.963651\pi$
$978$	−7.22172	+	18.4013i	−0.230925	+	0.588408i
$979$	0.838774	−	0.484266i	0.0268073	−	0.0154772i
$980$	−25.6491	+	16.4428i	−0.819331	+	0.525246i
$981$	12.4477	+	12.6750i	0.397424	+	0.404682i
$982$	26.4090	−	0.613738i	0.842744	−	0.0195852i
$983$	−15.2423	+	26.4004i	−0.486154	+	0.842043i	−0.999873	−	0.0159152i	$-0.994934\pi$
$983$	−15.2423	+	26.4004i	−0.486154	+	0.842043i	0.513720	+	0.857958i	$0.328267\pi$
$984$	−6.44551	+	1.28030i	−0.205475	+	0.0408146i
$985$	13.7795	−	23.8668i	0.439051	−	0.760459i
$986$	−2.82096	−	4.63396i	−0.0898377	−	0.147575i
$987$	1.52342	−	3.63132i	0.0484911	−	0.115586i
$988$	43.3216	+	35.6684i	1.37824	+	1.13476i
$989$		−	51.0569i		−	1.62352i
$990$	3.46944	+	0.877073i	0.110266	+	0.0278752i
$991$	−5.94043	−	3.42971i	−0.188704	−	0.108948i	0.402672	−	0.915344i	$-0.368082\pi$
$991$	−5.94043	−	3.42971i	−0.188704	−	0.108948i	−0.591376	+	0.806396i	$0.701415\pi$
$992$	3.19984	+	1.38095i	0.101595	+	0.0438452i
$993$	−33.4762	−	44.0381i	−1.06233	−	1.39751i
$994$	0.336365	+	14.4737i	0.0106688	+	0.459077i
$995$	81.8148			2.59370
$996$	−3.95286	−	22.6410i	−0.125251	−	0.717406i
$997$	−8.09482	−	14.0206i	−0.256365	−	0.444038i	0.708900	−	0.705309i	$-0.249192\pi$
$997$	−8.09482	−	14.0206i	−0.256365	−	0.444038i	−0.965266	+	0.261271i	$0.915858\pi$
$998$	−1.21328	−	52.2072i	−0.0384058	−	1.65259i
$999$	13.4287	+	33.7066i	0.424866	+	1.06643i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.m.a.11.12	yes	72
3.2	odd	2	inner	228.2.m.a.11.25	yes	72
4.3	odd	2	inner	228.2.m.a.11.1	✓	72
12.11	even	2	inner	228.2.m.a.11.36	yes	72
19.7	even	3	inner	228.2.m.a.83.36	yes	72
57.26	odd	6	inner	228.2.m.a.83.1	yes	72
76.7	odd	6	inner	228.2.m.a.83.25	yes	72
228.83	even	6	inner	228.2.m.a.83.12	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.m.a.11.1	✓	72	4.3	odd	2	inner
228.2.m.a.11.12	yes	72	1.1	even	1	trivial
228.2.m.a.11.25	yes	72	3.2	odd	2	inner
228.2.m.a.11.36	yes	72	12.11	even	2	inner
228.2.m.a.83.1	yes	72	57.26	odd	6	inner
228.2.m.a.83.12	yes	72	228.83	even	6	inner
228.2.m.a.83.25	yes	72	76.7	odd	6	inner
228.2.m.a.83.36	yes	72	19.7	even	3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.735371 - 1.20799i) q^{2} +(1.37888 - 1.04818i) q^{3} +(-0.918459 + 1.77664i) q^{4} +(2.70326 + 1.56073i) q^{5} +(-2.28018 - 0.894872i) q^{6} +1.45593i q^{7} +(2.82156 - 0.197001i) q^{8} +(0.802644 - 2.89063i) q^{9} +(-0.102562 - 4.41321i) q^{10} -0.270221 q^{11} +(0.595782 + 3.41248i) q^{12} +(3.21847 + 5.57455i) q^{13} +(1.75874 - 1.07065i) q^{14} +(5.36340 - 0.681435i) q^{15} +(-2.31287 - 3.26353i) q^{16} +(-4.23572 - 2.44549i) q^{17} +(-4.08209 + 1.15611i) q^{18} +(-3.23274 - 2.92394i) q^{19} +(-5.25567 + 3.36924i) q^{20} +(1.52607 + 2.00756i) q^{21} +(0.198713 + 0.326423i) q^{22} +(-3.71597 - 6.43624i) q^{23} +(3.68411 - 3.22914i) q^{24} +(2.37173 + 4.10796i) q^{25} +(4.36721 - 7.98723i) q^{26} +(-1.92315 - 4.82716i) q^{27} +(-2.58665 - 1.33721i) q^{28} +(-0.679243 + 0.392161i) q^{29} +(-4.76725 - 5.97780i) q^{30} -0.616086i q^{31} +(-2.24149 + 5.19382i) q^{32} +(-0.372603 + 0.283240i) q^{33} +(0.160704 + 6.91503i) q^{34} +(-2.27231 + 3.93575i) q^{35} +(4.39841 + 4.08093i) q^{36} -6.98268 q^{37} +(-1.15481 + 6.05528i) q^{38} +(10.2810 + 4.31313i) q^{39} +(7.93486 + 3.87113i) q^{40} +(-1.16168 - 0.670695i) q^{41} +(1.30287 - 3.31977i) q^{42} +(5.94954 + 3.43497i) q^{43} +(0.248187 - 0.480084i) q^{44} +(6.68124 - 6.56142i) q^{45} +(-5.04228 + 9.22186i) q^{46} +(-0.780795 - 1.35238i) q^{47} +(-6.60994 - 2.07574i) q^{48} +4.88027 q^{49} +(3.21825 - 5.88589i) q^{50} +(-8.40387 + 1.06774i) q^{51} +(-12.8600 + 0.598049i) q^{52} +(7.14091 - 4.12281i) q^{53} +(-4.41692 + 5.87289i) q^{54} +(-0.730476 - 0.421741i) q^{55} +(0.286819 + 4.10799i) q^{56} +(-7.52238 - 0.643286i) q^{57} +(0.973220 + 0.532132i) q^{58} +(-6.09022 + 10.5486i) q^{59} +(-3.71540 + 10.1547i) q^{60} +(-1.39367 - 2.41391i) q^{61} +(-0.744223 + 0.453052i) q^{62} +(4.20856 + 1.16859i) q^{63} +(7.92238 - 1.11170i) q^{64} +20.0926i q^{65} +(0.616151 + 0.241813i) q^{66} +(-0.188511 + 0.108837i) q^{67} +(8.23508 - 5.27924i) q^{68} +(-11.8702 - 4.97984i) q^{69} +(6.42532 - 0.149323i) q^{70} +(-3.51569 + 6.08936i) q^{71} +(1.69525 - 8.31421i) q^{72} +(-0.410869 + 0.711646i) q^{73} +(5.13486 + 8.43498i) q^{74} +(7.57621 + 3.17840i) q^{75} +(8.16391 - 3.05788i) q^{76} -0.393422i q^{77} +(-2.35016 - 15.5911i) q^{78} +(5.16785 + 2.98366i) q^{79} +(-1.15879 - 12.4319i) q^{80} +(-7.71153 - 4.64030i) q^{81} +(0.0440742 + 1.89650i) q^{82} -6.63475 q^{83} +(-4.96833 + 0.867416i) q^{84} +(-7.63348 - 13.2216i) q^{85} +(-0.225726 - 9.71294i) q^{86} +(-0.525543 + 1.25271i) q^{87} +(-0.762444 + 0.0532337i) q^{88} +(-3.10403 + 1.79211i) q^{89} +(-12.8393 - 3.24577i) q^{90} +(-8.11615 + 4.68586i) q^{91} +(14.8478 - 0.690493i) q^{92} +(-0.645768 - 0.849511i) q^{93} +(-1.05948 + 1.93769i) q^{94} +(-4.17545 - 12.9496i) q^{95} +(2.35330 + 9.51115i) q^{96} +(7.11697 - 12.3269i) q^{97} +(-3.58881 - 5.89530i) q^{98} +(-0.216891 + 0.781110i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} - 8 q^{10} - 10 q^{12} - 4 q^{16} - 22 q^{18} + 4 q^{21} - 6 q^{22} + 11 q^{24} + 16 q^{25} + 6 q^{28} - 60 q^{30} - 30 q^{33} - 20 q^{34} - 11 q^{36} - 8 q^{37} + 36 q^{40} + 8 q^{42} - 28 q^{45}+ \cdots - 16 q^{97}+O(q^{100}) \) 72 * q + 3 * q^6 - 8 * q^10 - 10 * q^12 - 4 * q^16 - 22 * q^18 + 4 * q^21 - 6 * q^22 + 11 * q^24 + 16 * q^25 + 6 * q^28 - 60 * q^30 - 30 * q^33 - 20 * q^34 - 11 * q^36 - 8 * q^37 + 36 * q^40 + 8 * q^42 - 28 * q^45 - 8 * q^46 - 23 * q^48 - 16 * q^49 + 6 * q^52 - 22 * q^54 - 6 * q^57 - 80 * q^58 - 14 * q^60 - 40 * q^61 + 48 * q^64 - 15 * q^66 + 4 * q^69 + 72 * q^70 + 15 * q^72 - 4 * q^73 + 12 * q^76 + 44 * q^78 + 4 * q^81 - 6 * q^82 + 56 * q^84 - 52 * q^85 - 44 * q^88 + 20 * q^90 + 4 * q^93 + 56 * q^94 - 86 * q^96 - 16 * q^97

Introduction

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