LMFDB - Embedded newform 115.3.i.a.109.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [115,3,Mod(14,115)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(115, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 21])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("115.14"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	115.i (of order $22$, degree $10$, 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:	$3.13352304014$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$22$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			109.8
Character	$\chi$	$=$	115.109
Dual form			115.3.i.a.19.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.11696 - 0.510100i) q^{2} +(-1.12995 + 3.84825i) q^{3} +(-1.63204 - 1.88347i) q^{4} +(1.76717 - 4.67730i) q^{5} +(3.22510 - 3.72197i) q^{6} +(0.283825 - 1.97405i) q^{7} +(2.24596 + 7.64903i) q^{8} +(-5.96096 - 3.83087i) q^{9} +(-4.35975 + 4.32294i) q^{10} +(16.4790 - 7.52571i) q^{11} +(9.09219 - 4.15226i) q^{12} +(10.2222 - 1.46973i) q^{13} +(-1.32398 + 2.06016i) q^{14} +(16.0026 + 12.0856i) q^{15} +(-0.0255859 + 0.177954i) q^{16} +(-1.64738 + 1.90117i) q^{17} +(4.70404 + 7.31963i) q^{18} +(19.4865 - 16.8851i) q^{19} +(-11.6936 + 4.30511i) q^{20} +(7.27591 + 3.32280i) q^{21} -22.2453 q^{22} +(-12.5462 - 19.2768i) q^{23} -31.9732 q^{24} +(-18.7542 - 16.5312i) q^{25} +(-12.1676 - 3.57272i) q^{26} +(-5.80211 + 5.02756i) q^{27} +(-4.18127 + 2.68714i) q^{28} +(-2.83908 + 3.27647i) q^{29} +(-11.7094 - 21.6621i) q^{30} +(22.0740 - 6.48152i) q^{31} +(17.3592 - 27.0114i) q^{32} +(10.3404 + 71.9190i) q^{33} +(2.80985 - 1.28321i) q^{34} +(-8.73163 - 4.81601i) q^{35} +(2.51316 + 17.4794i) q^{36} +(-0.991092 - 0.636936i) q^{37} +(-30.3788 + 8.92002i) q^{38} +(-5.89468 + 40.9984i) q^{39} +(39.7458 + 3.01211i) q^{40} +(-62.7042 + 40.2975i) q^{41} +(-6.43197 - 7.42289i) q^{42} +(37.4854 + 11.0067i) q^{43} +(-41.0688 - 18.7555i) q^{44} +(-28.4522 + 21.1114i) q^{45} +(4.18053 + 27.9312i) q^{46} -32.4591i q^{47} +(-0.655900 - 0.299540i) q^{48} +(43.1989 + 12.6843i) q^{49} +(12.5152 + 28.0312i) q^{50} +(-5.45474 - 8.48774i) q^{51} +(-19.4513 - 16.8546i) q^{52} +(-5.79193 + 40.2837i) q^{53} +(9.04530 - 2.65594i) q^{54} +(-6.07880 - 90.3764i) q^{55} +(15.7370 - 2.26264i) q^{56} +(42.9595 + 94.0682i) q^{57} +(4.84248 - 2.21149i) q^{58} +(-8.19189 - 56.9758i) q^{59} +(-3.35394 - 49.8646i) q^{60} +(-3.43984 - 11.7150i) q^{61} +(-27.9621 - 4.02034i) q^{62} +(-9.25419 + 10.6799i) q^{63} +(-32.5631 + 20.9271i) q^{64} +(11.1900 - 50.4097i) q^{65} +(25.1360 - 85.6054i) q^{66} +(13.8867 - 30.4077i) q^{67} +6.26939 q^{68} +(88.3583 - 26.4990i) q^{69} +(7.29627 + 9.83331i) q^{70} +(-47.9828 + 105.068i) q^{71} +(15.9144 - 54.1995i) q^{72} +(-58.8347 + 50.9806i) q^{73} +(0.782112 + 1.21699i) q^{74} +(84.8073 - 53.4916i) q^{75} +(-63.6054 - 9.14508i) q^{76} +(-10.1789 - 34.6663i) q^{77} +(27.4974 - 42.7868i) q^{78} +(130.766 - 18.8013i) q^{79} +(0.787129 + 0.434148i) q^{80} +(-39.2831 - 86.0181i) q^{81} +(90.5940 - 13.0255i) q^{82} +(25.5210 + 16.4014i) q^{83} +(-5.61617 - 19.1269i) q^{84} +(5.98116 + 11.0650i) q^{85} +(-36.2553 - 31.4154i) q^{86} +(-9.40068 - 14.6277i) q^{87} +(94.5755 + 109.146i) q^{88} +(-22.6968 + 77.2981i) q^{89} +(42.5489 - 9.06717i) q^{90} -20.5963i q^{91} +(-15.8314 + 55.0908i) q^{92} +92.2702i q^{93} +(-16.5574 + 36.2556i) q^{94} +(-44.5409 - 120.983i) q^{95} +(84.3317 + 97.3240i) q^{96} +(-36.5228 + 23.4718i) q^{97} +(-41.7813 - 36.2037i) q^{98} +(-127.061 - 18.2686i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q + 26 q^{4} - 11 q^{5} - 14 q^{6} + 32 q^{9} - 11 q^{10} - 22 q^{11} - 22 q^{14} - 88 q^{15} - 142 q^{16} - 22 q^{19} - 99 q^{20} - 22 q^{21} - 88 q^{24} + 17 q^{25} + 34 q^{26} + 92 q^{29} + 341 q^{30}+ \cdots + 1628 q^{99}+O(q^{100}) $ 220 * q + 26 * q^4 - 11 * q^5 - 14 * q^6 + 32 * q^9 - 11 * q^10 - 22 * q^11 - 22 * q^14 - 88 * q^15 - 142 * q^16 - 22 * q^19 - 99 * q^20 - 22 * q^21 - 88 * q^24 + 17 * q^25 + 34 * q^26 + 92 * q^29 + 341 * q^30 - 152 * q^31 - 264 * q^34 - 13 * q^35 - 62 * q^36 - 118 * q^39 - 11 * q^40 - 80 * q^41 - 242 * q^44 + 226 * q^46 + 90 * q^49 - 211 * q^50 - 22 * q^51 + 658 * q^54 - 565 * q^55 + 770 * q^56 - 172 * q^59 - 891 * q^60 + 286 * q^61 - 474 * q^64 - 242 * q^65 - 44 * q^66 - 288 * q^69 + 790 * q^70 - 210 * q^71 + 506 * q^74 + 804 * q^75 - 2376 * q^76 + 462 * q^79 + 2398 * q^80 - 2408 * q^81 + 1034 * q^84 + 1197 * q^85 - 1518 * q^86 - 22 * q^89 + 154 * q^90 - 210 * q^94 - 338 * q^95 + 2772 * q^96 + 1628 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{7}{22}\right)$

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 $

$2$	−1.11696	−	0.510100i	−0.558482	−	0.255050i	0.116116	−	0.993236i	$-0.462956\pi$
$2$	−1.11696	−	0.510100i	−0.558482	−	0.255050i	−0.674598	+	0.738186i	$0.735683\pi$
$3$	−1.12995	+	3.84825i	−0.376649	+	1.28275i	0.525303	+	0.850915i	$0.323952\pi$
$3$	−1.12995	+	3.84825i	−0.376649	+	1.28275i	−0.901953	+	0.431835i	$0.857866\pi$
$4$	−1.63204	−	1.88347i	−0.408010	−	0.470868i
$5$	1.76717	−	4.67730i	0.353434	−	0.935460i
$5$	1.76717	−	4.67730i	0.353434	−	0.935460i
$6$	3.22510	−	3.72197i	0.537517	−	0.620328i
$7$	0.283825	−	1.97405i	0.0405464	−	0.282007i	−0.959454	−	0.281867i	$-0.909046\pi$
$7$	0.283825	−	1.97405i	0.0405464	−	0.282007i	1.00000		0.000139818i	$-4.45055e-5\pi$
$8$	2.24596	+	7.64903i	0.280745	+	0.956128i
$9$	−5.96096	−	3.83087i	−0.662329	−	0.425653i
$10$	−4.35975	+	4.32294i	−0.435975	+	0.432294i
$11$	16.4790	−	7.52571i	1.49809	−	0.684155i	0.513350	−	0.858180i	$-0.328404\pi$
$11$	16.4790	−	7.52571i	1.49809	−	0.684155i	0.984741	+	0.174024i	$0.0556772\pi$
$12$	9.09219	−	4.15226i	0.757683	−	0.346022i
$13$	10.2222	−	1.46973i	0.786325	−	0.113056i	0.262556	−	0.964917i	$-0.415435\pi$
$13$	10.2222	−	1.46973i	0.786325	−	0.113056i	0.523769	+	0.851860i	$0.324525\pi$
$14$	−1.32398	+	2.06016i	−0.0945702	+	0.147154i
$15$	16.0026	+	12.0856i	1.06684	+	0.805707i
$16$	−0.0255859	+	0.177954i	−0.00159912	+	0.0111221i
$17$	−1.64738	+	1.90117i	−0.0969044	+	0.111834i	−0.802130	−	0.597149i	$-0.796300\pi$
$17$	−1.64738	+	1.90117i	−0.0969044	+	0.111834i	0.705226	+	0.708983i	$0.250846\pi$
$18$	4.70404	+	7.31963i	0.261336	+	0.406646i
$19$	19.4865	−	16.8851i	1.02561	−	0.888692i	0.0317629	−	0.999495i	$-0.489888\pi$
$19$	19.4865	−	16.8851i	1.02561	−	0.888692i	0.993842	+	0.110803i	$0.0353424\pi$
$20$	−11.6936	+	4.30511i	−0.584682	+	0.215256i
$21$	7.27591	+	3.32280i	0.346472	+	0.158228i
$22$	−22.2453			−1.01115
$23$	−12.5462	−	19.2768i	−0.545486	−	0.838120i
$23$	−12.5462	−	19.2768i	−0.545486	−	0.838120i
$24$	−31.9732			−1.33222
$25$	−18.7542	−	16.5312i	−0.750169	−	0.661246i
$26$	−12.1676	−	3.57272i	−0.467983	−	0.137412i
$27$	−5.80211	+	5.02756i	−0.214893	+	0.186206i
$28$	−4.18127	+	2.68714i	−0.149331	+	0.0959693i
$29$	−2.83908	+	3.27647i	−0.0978994	+	0.112982i	−0.802585	−	0.596538i	$-0.796543\pi$
$29$	−2.83908	+	3.27647i	−0.0978994	+	0.112982i	0.704686	+	0.709520i	$0.251088\pi$
$30$	−11.7094	−	21.6621i	−0.390315	−	0.722070i
$31$	22.0740	−	6.48152i	0.712066	−	0.209081i	0.0944138	−	0.995533i	$-0.469902\pi$
$31$	22.0740	−	6.48152i	0.712066	−	0.209081i	0.617652	+	0.786452i	$0.288084\pi$
$32$	17.3592	−	27.0114i	0.542475	−	0.844107i
$33$	10.3404	+	71.9190i	0.313345	+	2.17936i
$34$	2.80985	−	1.28321i	0.0826425	−	0.0377416i
$35$	−8.73163	−	4.81601i	−0.249475	−	0.137600i
$36$	2.51316	+	17.4794i	0.0698101	+	0.485540i
$37$	−0.991092	−	0.636936i	−0.0267863	−	0.0172145i	0.527179	−	0.849754i	$-0.323250\pi$
$37$	−0.991092	−	0.636936i	−0.0267863	−	0.0172145i	−0.553965	+	0.832540i	$0.686886\pi$
$38$	−30.3788	+	8.92002i	−0.799443	+	0.234737i
$39$	−5.89468	+	40.9984i	−0.151146	+	1.05124i
$40$	39.7458	+	3.01211i	0.993644	+	0.0753028i
$41$	−62.7042	+	40.2975i	−1.52937	+	0.982866i	−0.539328	+	0.842096i	$0.681322\pi$
$41$	−62.7042	+	40.2975i	−1.52937	+	0.982866i	−0.990042	+	0.140770i	$0.955042\pi$
$42$	−6.43197	−	7.42289i	−0.153142	−	0.176735i
$43$	37.4854	+	11.0067i	0.871753	+	0.255970i	0.686861	−	0.726789i	$-0.258988\pi$
$43$	37.4854	+	11.0067i	0.871753	+	0.255970i	0.184892	+	0.982759i	$0.440806\pi$
$44$	−41.0688	−	18.7555i	−0.933382	−	0.426261i
$45$	−28.4522	+	21.1114i	−0.632270	+	0.469142i
$46$	4.18053	+	27.9312i	0.0908812	+	0.607201i
$47$		−	32.4591i		−	0.690619i	−0.938489	−	0.345309i	$-0.887774\pi$
$47$		−	32.4591i		−	0.690619i	0.938489	−	0.345309i	$-0.112226\pi$
$48$	−0.655900	−	0.299540i	−0.0136646	−	0.00624041i
$49$	43.1989	+	12.6843i	0.881609	+	0.258864i
$50$	12.5152	+	28.0312i	0.250305	+	0.560624i
$51$	−5.45474	−	8.48774i	−0.106956	−	0.166426i
$52$	−19.4513	−	16.8546i	−0.374063	−	0.324127i
$53$	−5.79193	+	40.2837i	−0.109282	+	0.760070i	0.859317	+	0.511443i	$0.170889\pi$
$53$	−5.79193	+	40.2837i	−0.109282	+	0.760070i	−0.968599	+	0.248628i	$0.920020\pi$
$54$	9.04530	−	2.65594i	0.167506	−	0.0491841i
$55$	−6.07880	−	90.3764i	−0.110524	−	1.64321i
$56$	15.7370	−	2.26264i	0.281018	−	0.0404042i
$57$	42.9595	+	94.0682i	0.753676	+	1.65032i
$58$	4.84248	−	2.21149i	0.0834910	−	0.0381291i
$59$	−8.19189	−	56.9758i	−0.138846	−	0.965692i	−0.933487	−	0.358612i	$-0.883250\pi$
$59$	−8.19189	−	56.9758i	−0.138846	−	0.965692i	0.794641	−	0.607080i	$-0.207659\pi$
$60$	−3.35394	−	49.8646i	−0.0558990	−	0.831077i
$61$	−3.43984	−	11.7150i	−0.0563909	−	0.192050i	0.926480	−	0.376343i	$-0.122819\pi$
$61$	−3.43984	−	11.7150i	−0.0563909	−	0.192050i	−0.982871	+	0.184293i	$0.941000\pi$
$62$	−27.9621	−	4.02034i	−0.451002	−	0.0648443i
$63$	−9.25419	+	10.6799i	−0.146892	+	0.169522i
$64$	−32.5631	+	20.9271i	−0.508799	+	0.326985i
$65$	11.1900	−	50.4097i	0.172154	−	0.775533i
$66$	25.1360	−	85.6054i	0.380849	−	1.29705i
$67$	13.8867	−	30.4077i	0.207264	−	0.453846i	−0.777240	−	0.629204i	$-0.783381\pi$
$67$	13.8867	−	30.4077i	0.207264	−	0.453846i	0.984505	+	0.175358i	$0.0561084\pi$
$68$	6.26939			0.0921968
$69$	88.3583	−	26.4990i	1.28056	−	0.384044i
$70$	7.29627	+	9.83331i	0.104232	+	0.140476i
$71$	−47.9828	+	105.068i	−0.675814	+	1.47983i	0.191204	+	0.981550i	$0.438761\pi$
$71$	−47.9828	+	105.068i	−0.675814	+	1.47983i	−0.867018	+	0.498277i	$0.833966\pi$
$72$	15.9144	−	54.1995i	0.221033	−	0.752771i
$73$	−58.8347	+	50.9806i	−0.805955	+	0.698364i	−0.956976	−	0.290167i	$-0.906289\pi$
$73$	−58.8347	+	50.9806i	−0.805955	+	0.698364i	0.151021	+	0.988531i	$0.451744\pi$
$74$	0.782112	+	1.21699i	0.0105691	+	0.0164458i
$75$	84.8073	−	53.4916i	1.13076	−	0.713221i
$76$	−63.6054	−	9.14508i	−0.836914	−	0.120330i
$77$	−10.1789	−	34.6663i	−0.132194	−	0.450211i
$78$	27.4974	−	42.7868i	0.352531	−	0.548549i
$79$	130.766	−	18.8013i	1.65526	−	0.237991i	0.749571	−	0.661924i	$-0.230260\pi$
$79$	130.766	−	18.8013i	1.65526	−	0.237991i	0.905693	+	0.423933i	$0.139351\pi$
$80$	0.787129	+	0.434148i	0.00983911	+	0.00542685i
$81$	−39.2831	−	86.0181i	−0.484977	−	1.06195i
$82$	90.5940	−	13.0255i	1.10480	−	0.158847i
$83$	25.5210	+	16.4014i	0.307482	+	0.197607i	0.685277	−	0.728283i	$-0.259681\pi$
$83$	25.5210	+	16.4014i	0.307482	+	0.197607i	−0.377795	+	0.925889i	$0.623318\pi$
$84$	−5.61617	−	19.1269i	−0.0668592	−	0.227701i
$85$	5.98116	+	11.0650i	0.0703666	+	0.130176i
$86$	−36.2553	−	31.4154i	−0.421573	−	0.365295i
$87$	−9.40068	−	14.6277i	−0.108054	−	0.168135i
$88$	94.5755	+	109.146i	1.07472	+	1.24029i
$89$	−22.6968	+	77.2981i	−0.255020	+	0.868518i	0.728087	+	0.685485i	$0.240410\pi$
$89$	−22.6968	+	77.2981i	−0.255020	+	0.868518i	−0.983107	+	0.183033i	$0.941409\pi$
$90$	42.5489	−	9.06717i	0.472766	−	0.100746i
$91$		−	20.5963i		−	0.226333i
$92$	−15.8314	+	55.0908i	−0.172081	+	0.598813i
$93$			92.2702i			0.992152i
$94$	−16.5574	+	36.2556i	−0.176142	+	0.385698i
$95$	−44.5409	−	120.983i	−0.468852	−	1.27351i
$96$	84.3317	+	97.3240i	0.878456	+	1.01379i
$97$	−36.5228	+	23.4718i	−0.376524	+	0.241977i	−0.715191	−	0.698929i	$-0.753660\pi$
$97$	−36.5228	+	23.4718i	−0.376524	+	0.241977i	0.338667	+	0.940906i	$0.390024\pi$
$98$	−41.7813	−	36.2037i	−0.426339	−	0.369425i
$99$	−127.061	−	18.2686i	−1.28344	−	0.184531i
$100$	−0.528352	+	62.3025i	−0.00528352	+	0.623025i
$101$	−5.74329	−	3.69099i	−0.0568643	−	0.0365445i	0.511900	−	0.859045i	$-0.328942\pi$
$101$	−5.74329	−	3.69099i	−0.0568643	−	0.0365445i	−0.568764	+	0.822501i	$0.692578\pi$
$102$	1.76315	+	12.2629i	0.0172857	+	0.120225i
$103$	29.0991	+	63.7182i	0.282516	+	0.618624i	0.996686	−	0.0813490i	$-0.0259228\pi$
$103$	29.0991	+	63.7182i	0.282516	+	0.618624i	−0.714170	+	0.699973i	$0.753196\pi$
$104$	34.2007	+	74.8891i	0.328853	+	0.720088i
$105$	28.3995	−	28.1597i	0.270471	−	0.268187i
$106$	27.0181	−	42.0410i	0.254888	−	0.396613i
$107$	−92.4464	+	27.1447i	−0.863985	+	0.253689i	−0.683555	−	0.729899i	$-0.739567\pi$
$107$	−92.4464	+	27.1447i	−0.863985	+	0.253689i	−0.180430	+	0.983588i	$0.557749\pi$
$108$	18.9385	+	2.72295i	0.175357	+	0.0252125i
$109$	96.9146	+	83.9770i	0.889125	+	0.770431i	0.974139	−	0.225949i	$-0.0725482\pi$
$109$	96.9146	+	83.9770i	0.889125	+	0.770431i	−0.0850144	+	0.996380i	$0.527094\pi$
$110$	−39.3112	+	104.048i	−0.357375	+	0.945890i
$111$	3.57097	−	3.09426i	0.0321709	−	0.0278762i
$112$	0.344027	+	0.101016i	0.00307167	+	0.000901924i
$113$	87.0520	−	190.617i	0.770372	−	1.68688i	0.0445385	−	0.999008i	$-0.485818\pi$
$113$	87.0520	−	190.617i	0.770372	−	1.68688i	0.725833	−	0.687871i	$-0.241454\pi$
$114$		−	126.984i		−	1.11390i
$115$	−112.334	+	24.6169i	−0.976821	+	0.214060i
$116$	10.8046			0.0931435
$117$	−66.5646	−	30.3990i	−0.568928	−	0.259821i
$118$	−19.9133	+	67.8186i	−0.168757	+	0.574734i
$119$	3.28543	+	3.79159i	0.0276087	+	0.0318621i
$120$	−56.5020	+	149.548i	−0.470850	+	1.24623i
$121$	135.683	−	156.587i	1.12135	−	1.29410i
$122$	−2.13366	+	14.8399i	−0.0174890	+	0.121639i
$123$	−84.2225	−	286.835i	−0.684735	−	2.33199i
$124$	−48.2334	−	30.9977i	−0.388979	−	0.249982i
$125$	−110.463	+	58.5058i	−0.883704	+	0.468046i
$126$	15.7844	−	7.20850i	0.125273	−	0.0572103i
$127$	−4.36487	+	1.99337i	−0.0343691	+	0.0156958i	−0.432525	−	0.901622i	$-0.642377\pi$
$127$	−4.36487	+	1.99337i	−0.0343691	+	0.0156958i	0.398156	+	0.917318i	$0.369650\pi$
$128$	−80.0802	+	11.5138i	−0.625627	+	0.0899515i
$129$	−84.7131	+	131.816i	−0.656690	+	1.02183i
$130$	−38.2128	+	50.5977i	−0.293945	+	0.389213i
$131$	−24.0596	+	167.338i	−0.183661	+	1.27739i	0.664355	+	0.747418i	$0.268707\pi$
$131$	−24.0596	+	167.338i	−0.183661	+	1.27739i	−0.848015	+	0.529972i	$0.822203\pi$
$132$	118.581	−	136.850i	0.898344	−	1.03674i
$133$	−27.8013	−	43.2597i	−0.209032	−	0.325261i
$134$	−31.0219	+	26.8806i	−0.231507	+	0.200602i
$135$	13.2621	+	36.0227i	0.0982375	+	0.266835i
$136$	−18.2421	−	8.33087i	−0.134133	−	0.0612564i
$137$	−252.401			−1.84235			−0.921173	−	0.389153i	$-0.872768\pi$
$137$	−252.401			−1.84235			−0.921173	+	0.389153i	$0.872768\pi$
$138$	−112.210	−	15.4731i	−0.813117	−	0.112124i
$139$	−92.0383			−0.662146			−0.331073	−	0.943605i	$-0.607411\pi$
$139$	−92.0383			−0.662146			−0.331073	+	0.943605i	$0.607411\pi$
$140$	5.17954	+	24.3057i	0.0369967	+	0.173612i
$141$	124.911	+	36.6771i	0.885891	+	0.260121i
$142$	107.190	−	92.8807i	0.754860	−	0.654090i
$143$	157.391	−	101.149i	1.10064	−	0.707337i
$144$	0.834236	−	0.962760i	0.00579330	−	0.00668583i
$145$	10.3079	+	19.0693i	0.0710890	+	0.131513i
$146$	91.7214	−	26.9318i	0.628229	−	0.184465i
$147$	−97.6249	+	151.907i	−0.664115	+	1.03338i
$148$	0.417848	+	2.90620i	0.00282330	+	0.0196365i
$149$	52.1263	−	23.8053i	0.349841	−	0.159767i	−0.232741	−	0.972539i	$-0.574770\pi$
$149$	52.1263	−	23.8053i	0.349841	−	0.159767i	0.582582	+	0.812772i	$0.302042\pi$
$150$	−122.013	+	16.4880i	−0.813418	+	0.109920i
$151$	10.1090	+	70.3097i	0.0669471	+	0.465627i	0.995526	+	0.0944913i	$0.0301225\pi$
$151$	10.1090	+	70.3097i	0.0669471	+	0.465627i	−0.928579	+	0.371136i	$0.878968\pi$
$152$	172.921	+	111.129i	1.13764	+	0.731115i
$153$	17.1031	−	5.02192i	0.111785	−	0.0328230i
$154$	−6.31377	+	43.9132i	−0.0409985	+	0.285151i
$155$	8.69254	−	114.701i	0.0560809	−	0.740005i
$156$	86.8397	−	55.8085i	0.556665	−	0.357747i
$157$	−6.25254	−	7.21582i	−0.0398251	−	0.0459606i	0.735488	−	0.677538i	$-0.236953\pi$
$157$	−6.25254	−	7.21582i	−0.0398251	−	0.0459606i	−0.775313	+	0.631578i	$0.782408\pi$
$158$	−155.651	−	45.7033i	−0.985134	−	0.289261i
$159$	−148.477	−	67.8073i	−0.933819	−	0.426461i
$160$	−95.6639	−	128.928i	−0.597899	−	0.805799i
$161$	−41.6141	+	19.2955i	−0.258473	+	0.119848i
$162$			116.117i			0.716774i
$163$	−167.867	−	76.6622i	−1.02986	−	0.470320i	−0.172483	−	0.985013i	$-0.555179\pi$
$163$	−167.867	−	76.6622i	−1.02986	−	0.470320i	−0.857375	+	0.514692i	$0.827906\pi$
$164$	178.235	+	52.3345i	1.08680	+	0.319113i
$165$	354.660	+	78.7279i	2.14945	+	0.477139i
$166$	−20.1397	−	31.3380i	−0.121323	−	0.188783i
$167$	198.809	+	172.269i	1.19047	+	1.03155i	0.998744	+	0.0501010i	$0.0159543\pi$
$167$	198.809	+	172.269i	1.19047	+	1.03155i	0.191727	+	0.981448i	$0.438591\pi$
$168$	−9.07478	+	63.1165i	−0.0540166	+	0.375694i
$169$	−59.8205	+	17.5649i	−0.353968	+	0.103934i
$170$	−1.03650	−	15.4101i	−0.00609706	−	0.0906479i
$171$	−180.843	+	26.0013i	−1.05756	+	0.152054i
$172$	−40.4468	−	88.5661i	−0.235156	−	0.514919i
$173$	92.4528	−	42.2218i	0.534409	−	0.244057i	−0.129883	−	0.991529i	$-0.541460\pi$
$173$	92.4528	−	42.2218i	0.534409	−	0.244057i	0.664292	+	0.747473i	$0.268733\pi$
$174$	3.03860	+	21.1339i	0.0174632	+	0.121459i
$175$	−37.9562	+	32.3297i	−0.216892	+	0.184741i
$176$	0.917599	+	3.12506i	0.00521363	+	0.0177560i
$177$	228.514	+	32.8553i	1.29104	+	0.185623i
$178$	64.7812	−	74.7615i	0.363939	−	0.420008i
$179$	−110.538	+	71.0385i	−0.617531	+	0.396863i	−0.811674	−	0.584110i	$-0.801444\pi$
$179$	−110.538	+	71.0385i	−0.617531	+	0.396863i	0.194143	+	0.980973i	$0.437807\pi$
$180$	86.1977	+	19.1343i	0.478876	+	0.106302i
$181$	−44.2716	+	150.775i	−0.244595	+	0.833013i	0.742080	+	0.670311i	$0.233839\pi$
$181$	−44.2716	+	150.775i	−0.244595	+	0.833013i	−0.986675	+	0.162702i	$0.947979\pi$
$182$	−10.5062	+	23.0053i	−0.0577262	+	0.126403i
$183$	48.9692			0.267591
$184$	119.270	−	139.261i	0.648208	−	0.756852i
$185$	−4.73057	+	3.51006i	−0.0255706	+	0.0189733i
$186$	47.0670	−	103.062i	0.253048	−	0.554099i
$187$	−12.8394	+	43.7271i	−0.0686601	+	0.233835i
$188$	−61.1358	+	52.9745i	−0.325190	+	0.281779i
$189$	8.27784	+	12.8806i	0.0437981	+	0.0681512i
$190$	−11.9629	+	157.854i	−0.0629626	+	0.830810i
$191$	−149.340	−	21.4718i	−0.781882	−	0.112418i	−0.260197	−	0.965556i	$-0.583787\pi$
$191$	−149.340	−	21.4718i	−0.781882	−	0.112418i	−0.521685	+	0.853138i	$0.674697\pi$
$192$	−43.7379	−	148.958i	−0.227801	−	0.775820i
$193$	−23.6126	+	36.7419i	−0.122345	+	0.190373i	−0.897024	−	0.441983i	$-0.854275\pi$
$193$	−23.6126	+	36.7419i	−0.122345	+	0.190373i	0.774679	+	0.632355i	$0.217912\pi$
$194$	52.7676	−	7.58683i	0.271998	−	0.0391074i
$195$	181.345	+	100.022i	0.929973	+	0.512935i
$196$	−46.6116	−	102.065i	−0.237814	−	0.520741i
$197$	−43.7335	+	6.28793i	−0.221997	+	0.0319184i	−0.252416	−	0.967619i	$-0.581225\pi$
$197$	−43.7335	+	6.28793i	−0.221997	+	0.0319184i	0.0304185	+	0.999537i	$0.490316\pi$
$198$	132.603	+	85.2189i	0.669713	+	0.430399i
$199$	−86.6668	−	295.160i	−0.435511	−	1.48322i	−0.826562	−	0.562846i	$-0.809706\pi$
$199$	−86.6668	−	295.160i	−0.435511	−	1.48322i	0.391050	−	0.920369i	$-0.372112\pi$
$200$	84.3260	−	180.580i	0.421630	−	0.902899i
$201$	101.325	+	87.7986i	0.504104	+	0.436809i
$202$	4.53227	+	7.05236i	0.0224370	+	0.0349127i
$203$	5.66211	+	6.53442i	0.0278922	+	0.0321893i
$204$	−7.08408	+	24.1262i	−0.0347259	+	0.118265i
$205$	77.6746	+	364.499i	0.378901	+	1.77804i
$206$		−	86.0144i		−	0.417545i
$207$	0.940320	+	162.971i	0.00454261	+	0.787298i
$208$			1.85669i			0.00892639i
$209$	194.045	−	424.900i	0.928447	−	2.03301i
$210$	−46.0854	+	16.9667i	−0.219454	+	0.0807940i
$211$	−170.541	−	196.815i	−0.808252	−	0.932772i	0.190552	−	0.981677i	$-0.438972\pi$
$211$	−170.541	−	196.815i	−0.808252	−	0.932772i	−0.998803	+	0.0489049i	$0.984427\pi$
$212$	85.3259	−	54.8357i	0.402481	−	0.258659i
$213$	−350.109	−	303.371i	−1.64370	−	1.42428i
$214$	117.106	+	16.8373i	0.547223	+	0.0786788i
$215$	117.725	−	155.880i	0.547556	−	0.725021i
$216$	−51.4872	−	33.0888i	−0.238367	−	0.153189i
$217$	−6.52966	−	45.4148i	−0.0300906	−	0.209285i
$218$	−65.4134	−	143.235i	−0.300061	−	0.657043i
$219$	−129.706	−	284.016i	−0.592264	−	1.29688i
$220$	−160.301	+	158.947i	−0.728639	+	0.722486i
$221$	−14.0456	+	21.8554i	−0.0635549	+	0.0988933i
$222$	−5.56703	+	1.63463i	−0.0250767	+	0.00736318i
$223$	332.585	+	47.8185i	1.49141	+	0.214433i	0.839291	−	0.543682i	$-0.182970\pi$
$223$	332.585	+	47.8185i	1.49141	+	0.214433i	0.652121	+	0.758115i	$0.273879\pi$
$224$	−48.3948	−	41.9344i	−0.216048	−	0.187207i
$225$	48.4644	+	170.387i	0.215397	+	0.757274i
$226$	−194.468	+	168.507i	−0.860477	+	0.745607i
$227$	−214.313	−	62.9279i	−0.944109	−	0.277215i	−0.226777	−	0.973947i	$-0.572819\pi$
$227$	−214.313	−	62.9279i	−0.944109	−	0.277215i	−0.717332	+	0.696731i	$0.754637\pi$
$228$	107.063	−	234.436i	0.469576	−	1.02823i
$229$			148.636i			0.649064i	0.945875	+	0.324532i	$0.105207\pi$
$229$			148.636i			0.649064i	−0.945875	+	0.324532i	$0.894793\pi$
$230$	138.030	+	29.8056i	0.600132	+	0.129590i
$231$	144.906			0.627299
$232$	−31.4383	−	14.3574i	−0.135510	−	0.0618853i
$233$	27.7799	−	94.6097i	0.119227	−	0.406050i	−0.878154	−	0.478378i	$-0.841225\pi$
$233$	27.7799	−	94.6097i	0.119227	−	0.406050i	0.997381	+	0.0723282i	$0.0230429\pi$
$234$	58.8437	+	67.9092i	0.251469	+	0.290210i
$235$	−151.821	−	57.3607i	−0.646046	−	0.244088i
$236$	−93.9429	+	108.416i	−0.398063	+	0.459389i
$237$	−75.4065	+	524.464i	−0.318171	+	2.21293i
$238$	−1.73562	−	5.91097i	−0.00729251	−	0.0248360i
$239$	227.271	+	146.058i	0.950924	+	0.611122i	0.921472	−	0.388445i	$-0.126987\pi$
$239$	227.271	+	146.058i	0.950924	+	0.611122i	0.0294518	+	0.999566i	$0.490624\pi$
$240$	−2.56012	+	2.53850i	−0.0106672	+	0.0105771i
$241$	39.9056	−	18.2243i	0.165583	−	0.0756194i	−0.330899	−	0.943666i	$-0.607352\pi$
$241$	39.9056	−	18.2243i	0.165583	−	0.0756194i	0.496482	+	0.868047i	$0.334625\pi$
$242$	−231.428	+	105.689i	−0.956313	+	0.436733i
$243$	307.015	−	44.1420i	1.26343	−	0.181654i
$244$	−16.4510	+	25.5982i	−0.0674221	+	0.104911i
$245$	135.668	−	179.639i	0.553747	−	0.733219i
$246$	−52.2413	+	363.346i	−0.212363	+	1.47702i
$247$	174.379	−	201.244i	0.705987	−	0.814752i
$248$	99.1547	+	154.288i	0.399817	+	0.622128i
$249$	−91.9539	+	79.6785i	−0.369293	+	0.319994i
$250$	153.227	−	9.00161i	0.612908	−	0.0360065i
$251$	268.789	+	122.752i	1.07087	+	0.489051i	0.871259	−	0.490823i	$-0.163304\pi$
$251$	268.789	+	122.752i	1.07087	+	0.489051i	0.199614	+	0.979875i	$0.436031\pi$
$252$	35.2185			0.139756
$253$	−351.820	−	223.243i	−1.39059	−	0.882383i
$254$	5.89222			0.0231977
$255$	−49.3391	+	10.5142i	−0.193487	+	0.0412320i
$256$	243.880	+	71.6095i	0.952655	+	0.279725i
$257$	180.824	−	156.685i	0.703595	−	0.609669i	−0.227787	−	0.973711i	$-0.573149\pi$
$257$	180.824	−	156.685i	0.703595	−	0.609669i	0.931383	+	0.364042i	$0.118604\pi$
$258$	161.861	−	104.022i	0.627367	−	0.403184i
$259$	−1.53864	+	1.77568i	−0.00594068	+	0.00685591i
$260$	−113.208	+	61.1944i	−0.435414	+	0.235363i
$261$	29.4754	−	8.65476i	0.112933	−	0.0331600i
$262$	112.233	−	174.638i	0.428369	−	0.666556i
$263$	−35.6991	−	248.293i	−0.135738	−	0.944079i	−0.937884	−	0.346950i	$-0.887217\pi$
$263$	−35.6991	−	248.293i	−0.135738	−	0.944079i	0.802145	−	0.597129i	$-0.203692\pi$
$264$	−526.886	+	240.621i	−1.99578	+	0.911442i
$265$	178.184	+	98.2787i	0.672391	+	0.370863i
$266$	8.98627	+	62.5009i	0.0337830	+	0.234966i
$267$	−271.816	−	174.686i	−1.01804	−	0.654253i
$268$	−79.9356	+	23.4712i	−0.298267	+	0.0875792i
$269$	−21.3610	+	148.569i	−0.0794089	+	0.552301i	0.910815	+	0.412815i	$0.135454\pi$
$269$	−21.3610	+	148.569i	−0.0794089	+	0.552301i	−0.990224	+	0.139486i	$0.955455\pi$
$270$	3.56195	−	47.0010i	0.0131924	−	0.174078i
$271$	−30.7054	+	19.7332i	−0.113304	+	0.0728161i	−0.596066	−	0.802936i	$-0.703270\pi$
$271$	−30.7054	+	19.7332i	−0.113304	+	0.0728161i	0.482762	+	0.875752i	$0.339634\pi$
$272$	−0.296172	−	0.341800i	−0.00108887	−	0.00125662i
$273$	79.2596	+	23.2727i	0.290328	+	0.0852481i
$274$	281.923	+	128.750i	1.02892	+	0.469890i
$275$	−433.460	−	131.278i	−1.57622	−	0.477375i
$276$	−194.114	−	123.173i	−0.703313	−	0.446279i
$277$			6.31782i			0.0228080i	0.999935	+	0.0114040i	$0.00363009\pi$
$277$			6.31782i			0.0228080i	−0.999935	+	0.0114040i	$0.996370\pi$
$278$	102.803	+	46.9487i	0.369796	+	0.168880i
$279$	−156.412	−	45.9268i	−0.560617	−	0.164612i
$280$	17.2269	−	77.6050i	0.0615246	−	0.277161i
$281$	−195.535	−	304.259i	−0.695855	−	1.08277i	−0.991829	−	0.127575i	$-0.959281\pi$
$281$	−195.535	−	304.259i	−0.695855	−	1.08277i	0.295974	−	0.955196i	$-0.404356\pi$
$282$	−120.812	−	104.684i	−0.428410	−	0.371219i
$283$	−79.8956	+	555.686i	−0.282317	+	1.96356i	−0.0152249	+	0.999884i	$0.504846\pi$
$283$	−79.8956	+	555.686i	−0.282317	+	1.96356i	−0.267092	+	0.963671i	$0.586063\pi$
$284$	276.202	−	81.1002i	0.972542	−	0.285564i
$285$	515.902	−	34.7000i	1.81018	−	0.121754i
$286$	−227.396	+	32.6947i	−0.795092	+	0.114317i
$287$	61.7521	+	135.218i	0.215164	+	0.471144i
$288$	−206.955	+	94.5131i	−0.718593	+	0.328170i
$289$	40.2284	+	279.795i	0.139199	+	0.968147i
$290$	−1.78630	−	26.5578i	−0.00615966	−	0.0915786i
$291$	−49.0564	−	167.071i	−0.168579	−	0.574126i
$292$	192.041	+	27.6113i	0.657675	+	0.0945594i
$293$	−361.938	+	417.699i	−1.23528	+	1.42559i	−0.366486	+	0.930423i	$0.619439\pi$
$293$	−361.938	+	417.699i	−1.23528	+	1.42559i	−0.868797	+	0.495169i	$0.835106\pi$
$294$	186.531	−	119.876i	0.634460	−	0.407743i
$295$	−280.969	−	62.3700i	−0.952438	−	0.211424i
$296$	2.64599	−	9.01142i	0.00893916	−	0.0304440i
$297$	−57.7770	+	126.514i	−0.194535	+	0.425973i
$298$	−70.3662			−0.236128
$299$	−156.582	−	178.612i	−0.523684	−	0.597364i
$300$	−239.159	−	72.4319i	−0.797196	−	0.241440i
$301$	32.3670	−	70.8739i	0.107532	−	0.235461i
$302$	24.5736	−	83.6899i	0.0813695	−	0.277119i
$303$	20.6935	−	17.9310i	0.0682953	−	0.0591782i
$304$	2.50620	+	3.89972i	0.00824408	+	0.0128280i
$305$	−60.8735	−	4.61327i	−0.199585	−	0.0151255i
$306$	−21.6652	−	3.11499i	−0.0708013	−	0.0101797i
$307$	−159.800	−	544.229i	−0.520521	−	1.77273i	−0.627658	−	0.778489i	$-0.715986\pi$
$307$	−159.800	−	544.229i	−0.520521	−	1.77273i	0.107137	−	0.994244i	$-0.465832\pi$
$308$	−48.6806	+	75.7485i	−0.158054	+	0.245937i
$309$	−278.084	+	39.9825i	−0.899949	+	0.129393i
$310$	−68.2181	+	123.682i	−0.220058	+	0.398976i
$311$	202.232	+	442.825i	0.650262	+	1.42388i	0.891324	+	0.453366i	$0.149777\pi$
$311$	202.232	+	442.825i	0.650262	+	1.42388i	−0.241062	+	0.970510i	$0.577496\pi$
$312$	−326.837	+	46.9921i	−1.04755	+	0.150616i
$313$	51.3892	+	33.0258i	0.164183	+	0.105514i	0.620152	−	0.784482i	$-0.287071\pi$
$313$	51.3892	+	33.0258i	0.164183	+	0.105514i	−0.455969	+	0.889996i	$0.650707\pi$
$314$	3.30307	+	11.2492i	0.0105193	+	0.0358256i
$315$	33.5994	+	62.1578i	0.106665	+	0.197326i
$316$	−248.827	−	215.609i	−0.787426	−	0.682308i
$317$	187.085	+	291.111i	0.590175	+	0.918330i	0.999981	+	0.00615729i	$0.00195994\pi$
$317$	187.085	+	291.111i	0.590175	+	0.918330i	−0.409806	+	0.912173i	$0.634404\pi$
$318$	131.255	+	151.476i	0.412752	+	0.476341i
$319$	−22.1274	+	75.3591i	−0.0693650	+	0.236235i
$320$	40.3375	+	189.289i	0.126055	+	0.591528i
$321$		−	386.429i		−	1.20383i
$322$	56.3241	−	0.324983i	0.174919	−	0.00100926i
$323$			64.8634i			0.200815i
$324$	−97.9011	+	214.374i	−0.302164	+	0.661647i
$325$	−216.006	−	141.421i	−0.664635	−	0.435143i
$326$	148.396	+	171.258i	0.455202	+	0.525331i
$327$	−432.673	+	278.062i	−1.32316	+	0.850342i
$328$	−449.068	−	389.119i	−1.36911	−	1.18634i
$329$	−64.0757	−	9.21270i	−0.194759	−	0.0280021i
$330$	−355.983	−	268.848i	−1.07873	−	0.814691i
$331$	369.516	+	237.473i	1.11636	+	0.717442i	0.962670	−	0.270677i	$-0.0872475\pi$
$331$	369.516	+	237.473i	1.11636	+	0.717442i	0.153691	+	0.988119i	$0.450884\pi$
$332$	−10.7598	−	74.8357i	−0.0324089	−	0.225409i
$333$	3.46783	+	7.59350i	0.0104139	+	0.0228033i
$334$	−134.188	−	293.830i	−0.401760	−	0.879731i
$335$	−117.685	−	118.688i	−0.351300	−	0.354292i
$336$	−0.777466	+	1.20976i	−0.00231389	+	0.00360048i
$337$	−77.4580	+	22.7437i	−0.229846	+	0.0674888i	−0.394627	−	0.918841i	$-0.629126\pi$
$337$	−77.4580	+	22.7437i	−0.229846	+	0.0674888i	0.164781	+	0.986330i	$0.447308\pi$
$338$	75.7772	+	10.8951i	0.224193	+	0.0322341i
$339$	635.179	+	550.385i	1.87368	+	1.62356i
$340$	11.0791	−	29.3238i	0.0325855	−	0.0862464i
$341$	314.980	−	272.932i	0.923695	−	0.800386i
$342$	215.258	+	63.2055i	0.629410	+	0.184812i
$343$	77.8959	−	170.568i	0.227102	−	0.497284i
$344$			311.447i			0.905370i
$345$	32.2001	−	460.106i	0.0933337	−	1.33364i
$346$	−124.804			−0.360704
$347$	453.087	+	206.918i	1.30573	+	0.596306i	0.942129	−	0.335250i	$-0.108821\pi$
$347$	453.087	+	206.918i	1.30573	+	0.596306i	0.363598	+	0.931556i	$0.381548\pi$
$348$	−12.2087	+	41.5789i	−0.0350824	+	0.119480i
$349$	−24.0188	−	27.7192i	−0.0688219	−	0.0794247i	0.720295	−	0.693668i	$-0.244007\pi$
$349$	−24.0188	−	27.7192i	−0.0688219	−	0.0794247i	−0.789116	+	0.614244i	$0.789461\pi$
$350$	58.8870	−	16.7497i	0.168249	−	0.0478563i
$351$	−51.9213	+	59.9204i	−0.147924	+	0.170713i
$352$	82.7820	−	575.762i	0.235176	−	1.63569i
$353$	161.449	+	549.845i	0.457363	+	1.55764i	0.789101	+	0.614264i	$0.210547\pi$
$353$	161.449	+	549.845i	0.457363	+	1.55764i	−0.331738	+	0.943372i	$0.607635\pi$
$354$	−238.482	−	153.263i	−0.673677	−	0.432946i
$355$	406.639	+	410.102i	1.14546	+	1.15522i
$356$	182.631	−	83.4047i	0.513008	−	0.234283i
$357$	−18.3034	+	8.35887i	−0.0512699	+	0.0234142i
$358$	159.704	−	22.9619i	0.446100	−	0.0641394i
$359$	146.125	−	227.375i	0.407033	−	0.633356i	−0.575857	−	0.817551i	$-0.695331\pi$
$359$	146.125	−	227.375i	0.407033	−	0.633356i	0.982890	+	0.184195i	$0.0589677\pi$
$360$	−225.384	−	170.216i	−0.626066	−	0.472823i
$361$	43.2398	−	300.739i	0.119778	−	0.833073i
$362$	126.360	−	145.828i	0.349062	−	0.402839i
$363$	449.269	+	699.077i	1.23766	+	1.92583i
$364$	−38.7925	+	33.6139i	−0.106573	+	0.0923460i
$365$	134.480	+	365.279i	0.368440	+	1.00076i
$366$	−54.6968	−	24.9792i	−0.149445	−	0.0682492i
$367$	74.6618			0.203438			0.101719	−	0.994813i	$-0.467566\pi$
$367$	74.6618			0.203438			0.101719	+	0.994813i	$0.467566\pi$
$368$	3.75138	−	1.73943i	0.0101940	−	0.00472670i
$369$	528.152			1.43131
$370$	7.07435	−	1.50754i	0.0191199	−	0.00407444i
$371$	77.8780	+	22.8671i	0.209914	+	0.0616363i
$372$	173.788	−	150.588i	0.467173	−	0.404808i
$373$	46.6674	−	29.9913i	0.125114	−	0.0804057i	−0.476587	−	0.879127i	$-0.658126\pi$
$373$	46.6674	−	29.9913i	0.125114	−	0.0804057i	0.601701	+	0.798722i	$0.294490\pi$
$374$	36.6464	−	42.2921i	0.0979849	−	0.113081i
$375$	−100.327	−	491.198i	−0.267540	−	1.30986i
$376$	248.280	−	72.9017i	0.660320	−	0.193887i
$377$	−24.2062	+	37.6656i	−0.0642074	+	0.0999086i
$378$	−2.67566	−	18.6097i	−0.00707848	−	0.0492319i
$379$	−434.982	+	198.649i	−1.14771	+	0.524141i	−0.896172	−	0.443707i	$-0.853663\pi$
$379$	−434.982	+	198.649i	−1.14771	+	0.524141i	−0.251537	+	0.967848i	$0.580936\pi$
$380$	−155.176	+	281.341i	−0.408357	+	0.740370i
$381$	−2.73891	−	19.0495i	−0.00718873	−	0.0499987i
$382$	155.854	+	100.161i	0.407995	+	0.262202i
$383$	628.902	−	184.662i	1.64204	−	0.482147i	0.675224	−	0.737613i	$-0.264047\pi$
$383$	628.902	−	184.662i	1.64204	−	0.482147i	0.966818	+	0.255466i	$0.0822289\pi$
$384$	46.1785	−	321.179i	0.120257	−	0.836403i
$385$	−180.132	−	13.6513i	−0.467876	−	0.0354578i
$386$	45.1165	−	28.9946i	0.116882	−	0.0751155i
$387$	−181.283	−	209.212i	−0.468433	−	0.540600i
$388$	103.815	+	30.4828i	0.267565	+	0.0785640i
$389$	−342.374	−	156.357i	−0.880138	−	0.401946i	−0.0765040	−	0.997069i	$-0.524376\pi$
$389$	−342.374	−	156.357i	−0.880138	−	0.401946i	−0.803634	+	0.595124i	$0.797103\pi$
$390$	−151.534	−	204.225i	−0.388549	−	0.523654i
$391$	57.3167	+	7.90363i	0.146590	+	0.0202139i
$392$			358.918i			0.915606i
$393$	−616.772	−	281.670i	−1.56939	−	0.716719i
$394$	52.0562	+	15.2851i	0.132122	+	0.0387946i
$395$	143.146	−	644.856i	0.362395	−	1.63255i
$396$	172.960	+	269.130i	0.436766	+	0.679622i
$397$	187.611	+	162.566i	0.472573	+	0.409487i	0.858318	−	0.513119i	$-0.171510\pi$
$397$	187.611	+	162.566i	0.472573	+	0.409487i	−0.385745	+	0.922606i	$0.626055\pi$
$398$	−53.7575	+	373.891i	−0.135069	+	0.939426i
$399$	197.888	−	58.1052i	0.495960	−	0.145627i
$400$	3.42163	−	2.91442i	0.00855407	−	0.00728606i
$401$	−373.485	+	53.6990i	−0.931384	+	0.133913i	−0.591272	−	0.806472i	$-0.701374\pi$
$401$	−373.485	+	53.6990i	−0.931384	+	0.133913i	−0.340112	+	0.940385i	$0.610465\pi$
$402$	−68.3902	−	149.754i	−0.170125	−	0.372522i
$403$	216.120	−	98.6985i	0.536277	−	0.244910i
$404$	2.42140	+	16.8412i	0.00599355	+	0.0416861i
$405$	−471.752	+	31.7305i	−1.16482	+	0.0783468i
$406$	−2.99116	−	10.1869i	−0.00736738	−	0.0250910i
$407$	−21.1256	−	3.03740i	−0.0519056	−	0.00746290i
$408$	52.6718	−	60.7865i	0.129098	−	0.148987i
$409$	175.537	−	112.811i	0.429187	−	0.275822i	−0.308162	−	0.951334i	$-0.599714\pi$
$409$	175.537	−	112.811i	0.429187	−	0.275822i	0.737349	+	0.675512i	$0.236077\pi$
$410$	99.1710	−	446.753i	0.241880	−	1.08964i
$411$	285.200	−	971.304i	0.693918	−	2.36327i
$412$	72.5206	−	158.798i	0.176021	−	0.385432i
$413$	−114.798			−0.277961
$414$	82.0811	−	182.512i	0.198263	−	0.440850i
$415$	121.814	−	90.3854i	0.293528	−	0.217796i
$416$	137.750	−	301.630i	0.331130	−	0.725073i
$417$	103.998	−	354.186i	0.249397	−	0.849367i
$418$	−433.483	+	375.615i	−1.03704	+	0.898601i
$419$	−66.6980	−	103.784i	−0.159184	−	0.247695i	0.752495	−	0.658597i	$-0.228850\pi$
$419$	−66.6980	−	103.784i	−0.159184	−	0.247695i	−0.911679	+	0.410903i	$0.865214\pi$
$420$	−99.3870	−	7.53200i	−0.236636	−	0.0179333i
$421$	275.863	+	39.6631i	0.655256	+	0.0942116i	0.461921	−	0.886921i	$-0.347160\pi$
$421$	275.863	+	39.6631i	0.655256	+	0.0942116i	0.193335	+	0.981133i	$0.438069\pi$
$422$	90.0928	+	306.828i	0.213490	+	0.727081i
$423$	−124.347	+	193.487i	−0.293964	+	0.457416i
$424$	−321.140	+	46.1729i	−0.757405	+	0.108898i
$425$	62.3238	−	8.42201i	0.146644	−	0.0198165i
$426$	236.309	+	517.445i	0.554716	+	1.21466i
$427$	−24.1023	+	3.46539i	−0.0564457	+	0.00811567i
$428$	202.002	+	129.819i	0.471968	+	0.303316i
$429$	211.403	+	719.974i	0.492782	+	1.67826i
$430$	−211.008	+	114.060i	−0.490717	+	0.265257i
$431$	161.921	+	140.305i	0.375687	+	0.325535i	0.822154	−	0.569266i	$-0.192772\pi$
$431$	161.921	+	140.305i	0.375687	+	0.325535i	−0.446467	+	0.894800i	$0.647318\pi$
$432$	−0.746221	−	1.16114i	−0.00172736	−	0.00268783i
$433$	376.038	+	433.971i	0.868448	+	1.00224i	0.999940	+	0.0109257i	$0.00347783\pi$
$433$	376.038	+	433.971i	0.868448	+	1.00224i	−0.131492	+	0.991317i	$0.541977\pi$
$434$	−15.8727	+	54.0574i	−0.0365730	+	0.124556i
$435$	−85.0309	+	18.1201i	−0.195473	+	0.0416554i
$436$		−	319.590i		−	0.733004i
$437$	−569.972	−	163.793i	−1.30428	−	0.374812i
$438$			383.398i			0.875339i
$439$	107.787	−	236.021i	0.245529	−	0.537633i	−0.746240	−	0.665677i	$-0.768143\pi$
$439$	107.787	−	236.021i	0.245529	−	0.537633i	0.991768	+	0.128045i	$0.0408701\pi$
$440$	677.639	−	249.478i	1.54009	−	0.566996i
$441$	−208.914	−	241.100i	−0.473729	−	0.546712i
$442$	26.8369	−	17.2470i	0.0607169	−	0.0390204i
$443$	−196.097	−	169.919i	−0.442657	−	0.383564i	0.404820	−	0.914396i	$-0.367334\pi$
$443$	−196.097	−	169.919i	−0.442657	−	0.383564i	−0.847477	+	0.530832i	$0.821879\pi$
$444$	−11.6559	−	1.67587i	−0.0262521	−	0.00377448i
$445$	321.437	+	242.758i	0.722330	+	0.545524i
$446$	−347.093	−	223.063i	−0.778235	−	0.500141i
$447$	32.7087	+	227.494i	0.0731737	+	0.508935i
$448$	32.0687	+	70.2207i	0.0715820	+	0.156743i
$449$	−201.047	−	440.232i	−0.447767	−	0.980473i	−0.990107	−	0.140314i	$-0.955189\pi$
$449$	−201.047	−	440.232i	−0.447767	−	0.980473i	0.542340	−	0.840159i	$-0.317538\pi$
$450$	32.7813	−	215.037i	0.0728472	−	0.477860i
$451$	−730.035	+	1135.96i	−1.61870	+	2.51875i
$452$	−501.095	+	147.135i	−1.10862	+	0.325519i
$453$	−281.992	−	40.5443i	−0.622499	−	0.0895018i
$454$	207.280	+	179.609i	0.456564	+	0.395615i
$455$	−96.3350	−	36.3971i	−0.211725	−	0.0799937i
$456$	−623.045	+	539.872i	−1.36633	+	1.18393i
$457$	−117.413	−	34.4756i	−0.256921	−	0.0754389i	0.150735	−	0.988574i	$-0.451836\pi$
$457$	−117.413	−	34.4756i	−0.256921	−	0.0754389i	−0.407657	+	0.913135i	$0.633654\pi$
$458$	75.8190	−	166.020i	0.165544	−	0.362490i
$459$		−	19.3131i		−	0.0420764i
$460$	229.699	+	171.403i	0.499346	+	0.372615i
$461$	−379.831			−0.823929			−0.411965	−	0.911200i	$-0.635157\pi$
$461$	−379.831			−0.823929			−0.411965	+	0.911200i	$0.635157\pi$
$462$	−161.855	−	73.9166i	−0.350335	−	0.159993i
$463$	−60.0233	+	204.421i	−0.129640	+	0.441513i	−0.998572	−	0.0534179i	$-0.982988\pi$
$463$	−60.0233	+	204.421i	−0.129640	+	0.441513i	0.868932	+	0.494931i	$0.164807\pi$
$464$	−0.510421	−	0.589057i	−0.00110005	−	0.00126952i
$465$	431.575	+	163.057i	0.928118	+	0.350660i
$466$	−79.2895	+	91.5050i	−0.170149	+	0.196363i
$467$	8.47094	−	58.9167i	0.0181391	−	0.126160i	−0.978740	−	0.205106i	$-0.934246\pi$
$467$	8.47094	−	58.9167i	0.0181391	−	0.126160i	0.996879	+	0.0789456i	$0.0251553\pi$
$468$	51.3802	+	174.985i	0.109787	+	0.373900i
$469$	−56.0847	−	36.0435i	−0.119584	−	0.0768517i
$470$	140.319	+	141.514i	0.298550	+	0.301093i
$471$	34.8333	−	15.9078i	0.0739561	−	0.0337746i
$472$	417.411	−	190.625i	0.884345	−	0.403867i
$473$	700.555	−	100.725i	1.48109	−	0.212948i
$474$	351.755	−	547.342i	0.742100	−	1.15473i
$475$	−644.585	−	5.46635i	−1.35702	−	0.0115081i
$476$	1.77941	−	12.3761i	0.00373825	−	0.0260001i
$477$	188.847	−	217.941i	0.395906	−	0.456900i
$478$	−179.349	−	279.072i	−0.375207	−	0.583833i
$479$	−116.331	+	100.802i	−0.242863	+	0.210442i	−0.767784	−	0.640709i	$-0.778640\pi$
$479$	−116.331	+	100.802i	−0.242863	+	0.210442i	0.524921	+	0.851151i	$0.324095\pi$
$480$	604.242	−	222.457i	1.25884	−	0.463451i
$481$	−11.0673	−	5.05426i	−0.0230089	−	0.0105078i
$482$	−53.8693			−0.111762
$483$	−27.2320	−	181.944i	−0.0563810	−	0.376697i
$484$	−516.366			−1.06687
$485$	45.2425	+	212.307i	0.0932836	+	0.437745i
$486$	−365.441	−	107.303i	−0.751936	−	0.220788i
$487$	178.023	−	154.258i	0.365550	−	0.316751i	−0.452646	−	0.891690i	$-0.649520\pi$
$487$	178.023	−	154.258i	0.365550	−	0.316751i	0.818196	+	0.574939i	$0.194974\pi$
$488$	81.8829	−	52.6229i	0.167793	−	0.107834i
$489$	484.696	−	559.369i	0.991199	−	1.14390i
$490$	−243.170	+	131.445i	−0.496265	+	0.268256i
$491$	11.5912	−	3.40348i	0.0236073	−	0.00693173i	−0.269908	−	0.962886i	$-0.586993\pi$
$491$	11.5912	−	3.40348i	0.0236073	−	0.00693173i	0.293515	+	0.955955i	$0.405175\pi$
$492$	−402.792	+	626.757i	−0.818683	+	1.27390i
$493$	−1.55211	−	10.7952i	−0.00314830	−	0.0218969i
$494$	−297.429	+	135.831i	−0.602083	+	0.274962i
$495$	−309.985	+	562.017i	−0.626233	+	1.13539i
$496$	0.588628	+	4.09400i	0.00118675	+	0.00825403i
$497$	193.790	+	124.541i	0.389919	+	0.250586i
$498$	143.353	−	42.0923i	0.287858	−	0.0845226i
$499$	−62.5282	+	434.893i	−0.125307	+	0.871529i	0.826085	+	0.563546i	$0.190563\pi$
$499$	−62.5282	+	434.893i	−0.125307	+	0.871529i	−0.951392	+	0.307983i	$0.900346\pi$
$500$	290.474	+	112.570i	0.580948	+	0.225141i
$501$	−887.576	+	570.411i	−1.77161	+	1.13854i
$502$	−237.612	−	274.219i	−0.473330	−	0.546252i
$503$	−540.518	−	158.710i	−1.07459	−	0.315528i	−0.303877	−	0.952711i	$-0.598281\pi$
$503$	−540.518	−	158.710i	−1.07459	−	0.315528i	−0.770712	+	0.637184i	$0.780099\pi$
$504$	−102.475	−	46.7989i	−0.203324	−	0.0928550i
$505$	−27.4132	+	20.3405i	−0.0542836	+	0.0402782i
$506$	279.093	+	428.817i	0.551568	+	0.847465i
$507$		−	250.052i		−	0.493199i
$508$	10.8781	+	4.96786i	0.0214136	+	0.00977925i
$509$	−552.882	−	162.341i	−1.08621	−	0.318941i	−0.310851	−	0.950459i	$-0.600614\pi$
$509$	−552.882	−	162.341i	−1.08621	−	0.318941i	−0.775361	+	0.631518i	$0.782432\pi$
$510$	60.4732	+	13.4239i	0.118575	+	0.0263215i
$511$	83.9392	+	130.612i	0.164265	+	0.255601i
$512$	8.69529	+	7.53451i	0.0169830	+	0.0147158i
$513$	−28.1718	+	195.939i	−0.0549157	+	0.381947i
$514$	−281.899	+	82.7729i	−0.548441	+	0.161037i
$515$	349.452	−	23.5045i	0.678548	−	0.0456397i
$516$	386.527	−	55.5742i	0.749083	−	0.107702i
$517$	−244.278	−	534.893i	−0.472490	−	1.03461i
$518$	2.62438	−	1.19851i	0.00506636	−	0.00231373i
$519$	58.0131	+	403.490i	0.111779	+	0.777437i
$520$	410.717	−	27.6252i	0.789841	−	0.0531254i
$521$	85.0544	+	289.669i	0.163252	+	0.555986i	0.999965	+	0.00834425i	$0.00265609\pi$
$521$	85.0544	+	289.669i	0.163252	+	0.555986i	−0.836713	+	0.547642i	$0.815526\pi$
$522$	−37.3377	−	5.36836i	−0.0715282	−	0.0102842i
$523$	229.053	−	264.341i	0.437960	−	0.505432i	−0.493264	−	0.869879i	$-0.664196\pi$
$523$	229.053	−	264.341i	0.437960	−	0.505432i	0.931224	+	0.364447i	$0.118742\pi$
$524$	354.443	−	227.786i	0.676417	−	0.434707i
$525$	−81.5244	−	182.596i	−0.155285	−	0.347801i
$526$	−86.7795	+	295.544i	−0.164980	+	0.561871i
$527$	−24.0417	+	52.6440i	−0.0456200	+	0.0998938i
$528$	−13.0628			−0.0247402
$529$	−214.187	+	483.699i	−0.404891	+	0.914365i
$530$	−148.893	−	200.665i	−0.280929	−	0.378614i
$531$	−169.436	+	371.013i	−0.319088	+	0.698705i
$532$	−36.1056	+	122.964i	−0.0678677	+	0.231136i
$533$	−581.750	+	504.089i	−1.09146	+	0.945758i
$534$	214.501	+	333.771i	0.401688	+	0.625039i
$535$	−36.4045	+	480.369i	−0.0680458	+	0.897886i
$536$	263.778	+	37.9255i	0.492123	+	0.0707566i
$537$	−148.472	−	505.648i	−0.276483	−	0.941616i
$538$	99.6445	−	155.050i	0.185213	−	0.288197i
$539$	807.332	−	116.077i	1.49783	−	0.215356i
$540$	46.2036	−	83.7692i	0.0855623	−	0.155128i
$541$	−306.464	−	671.063i	−0.566477	−	1.24041i	−0.948652	−	0.316322i	$-0.897552\pi$
$541$	−306.464	−	671.063i	−0.566477	−	1.24041i	0.382175	−	0.924090i	$-0.375175\pi$
$542$	44.3627	−	6.37839i	0.0818500	−	0.0117682i
$543$	−530.197	−	340.737i	−0.976421	−	0.627508i
$544$	22.7563	+	77.5008i	0.0418314	+	0.142465i
$545$	564.050	−	304.897i	1.03495	−	0.559444i
$546$	−76.6587	−	66.4251i	−0.140401	−	0.121658i
$547$	−430.689	−	670.165i	−0.787366	−	1.22516i	−0.970268	−	0.242034i	$-0.922186\pi$
$547$	−430.689	−	670.165i	−0.787366	−	1.22516i	0.182902	−	0.983131i	$-0.441451\pi$
$548$	411.929	+	475.391i	0.751695	+	0.867502i
$549$	−24.3741	+	83.0104i	−0.0443972	+	0.151203i
$550$	417.193	+	367.740i	0.758533	+	0.668619i
$551$			111.785i			0.202877i
$552$	401.141	+	616.339i	0.726705	+	1.11656i
$553$		−	263.474i		−	0.476445i
$554$	3.22272	−	7.05677i	0.00581718	−	0.0127379i
$555$	−8.16228	−	22.1706i	−0.0147068	−	0.0399470i
$556$	150.210	+	173.352i	0.270162	+	0.311783i
$557$	−150.562	+	96.7602i	−0.270308	+	0.173717i	−0.668772	−	0.743467i	$-0.733180\pi$
$557$	−150.562	+	96.7602i	−0.270308	+	0.173717i	0.398464	+	0.917184i	$0.369543\pi$
$558$	151.279	+	131.084i	0.271110	+	0.234918i
$559$	399.361	+	57.4194i	0.714420	+	0.102718i
$560$	1.08043	−	1.43061i	0.00192935	−	0.00255465i
$561$	−153.765	−	98.8186i	−0.274091	−	0.176147i
$562$	63.2032	+	439.588i	0.112461	+	0.782185i
$563$	−103.500	−	226.634i	−0.183837	−	0.402547i	0.795166	−	0.606391i	$-0.207384\pi$
$563$	−103.500	−	226.634i	−0.183837	−	0.402547i	−0.979003	+	0.203845i	$0.934656\pi$
$564$	−134.779	−	295.124i	−0.238969	−	0.523270i
$565$	−737.738	−	744.021i	−1.30573	−	1.31685i
$566$	372.696	−	579.926i	0.658473	−	1.02460i
$567$	−180.953	+	53.1326i	−0.319141	+	0.0937084i
$568$	−911.433	−	131.044i	−1.60464	−	0.230712i
$569$	−261.751	−	226.809i	−0.460020	−	0.398609i	0.393785	−	0.919203i	$-0.371165\pi$
$569$	−261.751	−	226.809i	−0.460020	−	0.398609i	−0.853805	+	0.520593i	$0.825711\pi$
$570$	−593.944	−	224.403i	−1.04201	−	0.393689i
$571$	644.533	−	558.491i	1.12878	−	0.978093i	0.128872	−	0.991661i	$-0.458864\pi$
$571$	644.533	−	558.491i	1.12878	−	0.978093i	0.999908	+	0.0135682i	$0.00431903\pi$
$572$	−447.380	−	131.363i	−0.782134	−	0.229655i
$573$	251.375	−	550.434i	0.438699	−	0.960617i
$574$		−	182.534i		−	0.318003i
$575$	−83.3734	+	568.923i	−0.144997	+	0.989432i
$576$	274.276			0.476174
$577$	693.646	+	316.777i	1.20216	+	0.549008i	0.912876	−	0.408236i	$-0.133856\pi$
$577$	693.646	+	316.777i	1.20216	+	0.549008i	0.289283	+	0.957244i	$0.406583\pi$
$578$	97.7896	−	333.041i	0.169186	−	0.576195i
$579$	−114.711	−	132.384i	−0.198119	−	0.228642i
$580$	19.0936	−	50.5365i	0.0329200	−	0.0871319i
$581$	39.6205	−	45.7245i	0.0681937	−	0.0786997i
$582$	−30.4286	+	211.635i	−0.0522828	+	0.363635i
$583$	207.718	+	707.424i	0.356292	+	1.21342i
$584$	−522.092	−	335.528i	−0.893993	−	0.574535i
$585$	−259.816	+	257.622i	−0.444130	+	0.440380i
$586$	617.339	−	281.929i	1.05348	−	0.481108i
$587$	−392.910	+	179.436i	−0.669352	+	0.305683i	−0.720952	−	0.692985i	$-0.756295\pi$
$587$	−392.910	+	179.436i	−0.669352	+	0.305683i	0.0516000	+	0.998668i	$0.483568\pi$
$588$	445.441	−	64.0447i	0.757553	−	0.108920i
$589$	320.704	−	499.025i	0.544489	−	0.847242i
$590$	282.017	+	212.987i	0.477996	+	0.360996i
$591$	25.2191	−	175.402i	0.0426718	−	0.296789i
$592$	0.138703	−	0.160072i	0.000234296	−	0.000270392i
$593$	−409.679	−	637.473i	−0.690858	−	1.07500i	−0.992579	−	0.121600i	$-0.961197\pi$
$593$	−409.679	−	637.473i	−0.690858	−	1.07500i	0.301721	−	0.953396i	$-0.402439\pi$
$594$	129.070	−	111.839i	0.217289	−	0.188282i
$595$	23.5403	−	8.66657i	0.0395636	−	0.0145657i
$596$	−129.909	−	59.3273i	−0.217968	−	0.0995425i
$597$	1233.78			2.06663
$598$	83.7858	+	279.375i	0.140110	+	0.467182i
$599$	−942.991			−1.57428			−0.787138	−	0.616777i	$-0.788438\pi$
$599$	−942.991			−1.57428			−0.787138	+	0.616777i	$0.788438\pi$
$600$	599.632	+	528.553i	0.999387	+	0.880922i
$601$	6.06354	+	1.78042i	0.0100891	+	0.00296242i	0.286773	−	0.957999i	$-0.407417\pi$
$601$	6.06354	+	1.78042i	0.0100891	+	0.00296242i	−0.276684	+	0.960961i	$0.589236\pi$
$602$	−72.3055	+	62.6531i	−0.120109	+	0.104075i
$603$	−199.266	+	128.060i	−0.330458	+	0.212372i
$604$	115.928	−	133.788i	0.191934	−	0.221504i
$605$	−492.627	−	911.345i	−0.814260	−	1.50635i
$606$	−32.2605	+	9.47252i	−0.0532351	+	0.0156312i
$607$	100.141	−	155.822i	0.164976	−	0.256708i	−0.748916	−	0.662665i	$-0.769425\pi$
$607$	100.141	−	155.822i	0.164976	−	0.256708i	0.913892	+	0.405957i	$0.133062\pi$
$608$	−117.822	−	819.471i	−0.193786	−	1.34781i
$609$	−31.5440	+	14.4056i	−0.0517963	+	0.0236546i
$610$	65.6402	+	36.2044i	0.107607	+	0.0593515i
$611$	−47.7062	−	331.804i	−0.0780789	−	0.543051i
$612$	−37.3715	−	24.0172i	−0.0610646	−	0.0392438i
$613$	−959.841	+	281.835i	−1.56581	+	0.459763i	−0.945778	−	0.324815i	$-0.894698\pi$
$613$	−959.841	+	281.835i	−1.56581	+	0.459763i	−0.620031	+	0.784577i	$0.712880\pi$
$614$	−99.1205	+	689.398i	−0.161434	+	1.12280i
$615$	−1490.45	−	112.953i	−2.42350	−	0.183663i
$616$	242.302	−	155.718i	0.393347	−	0.252789i
$617$	−340.022	−	392.406i	−0.551088	−	0.635990i	0.410048	−	0.912064i	$-0.365512\pi$
$617$	−340.022	−	392.406i	−0.551088	−	0.635990i	−0.961136	+	0.276074i	$0.910966\pi$
$618$	331.005	+	97.1918i	0.535606	+	0.157268i
$619$	−106.257	−	48.5259i	−0.171659	−	0.0783940i	0.327732	−	0.944771i	$-0.393716\pi$
$619$	−106.257	−	48.5259i	−0.171659	−	0.0783940i	−0.499391	+	0.866377i	$0.666443\pi$
$620$	−230.222	+	170.824i	−0.371326	+	0.275522i
$621$	169.709	+	48.7693i	0.273284	+	0.0785335i
$622$		−	597.778i		−	0.961058i
$623$	146.148	+	66.7436i	0.234587	+	0.107133i
$624$	−7.14501	−	2.09796i	−0.0114503	−	0.00336212i
$625$	78.4421	+	620.058i	0.125507	+	0.992093i
$626$	−40.5534	−	63.1023i	−0.0647817	−	0.100802i
$627$	1415.86	+	1226.85i	2.25815	+	1.95670i
$628$	−3.38641	+	23.5530i	−0.00539237	+	0.0375048i
$629$	2.84362	−	0.834964i	0.00452087	−	0.00132745i
$630$	−5.82257	−	86.5670i	−0.00924218	−	0.137408i
$631$	445.166	−	64.0052i	0.705493	−	0.101435i	0.219776	−	0.975550i	$-0.429467\pi$
$631$	445.166	−	64.0052i	0.705493	−	0.101435i	0.485718	+	0.874116i	$0.338558\pi$
$632$	437.506	+	958.005i	0.692256	+	1.51583i
$633$	950.096	−	433.894i	1.50094	−	0.685457i
$634$	−60.4720	−	420.592i	−0.0953817	−	0.663394i
$635$	1.61012	+	23.9384i	0.00253562	+	0.0376983i
$636$	114.607	+	390.317i	0.180200	+	0.613706i
$637$	460.231	+	66.1712i	0.722498	+	0.103879i
$638$	63.1562	−	72.8862i	0.0989909	−	0.114242i
$639$	688.525	−	442.488i	1.07750	−	0.692470i
$640$	−87.6618	+	394.906i	−0.136972	+	0.617040i
$641$	−86.7258	+	295.361i	−0.135298	+	0.460782i	−0.999071	−	0.0430993i	$-0.986277\pi$
$641$	−86.7258	+	295.361i	−0.135298	+	0.460782i	0.863773	+	0.503881i	$0.168095\pi$
$642$	−197.117	+	431.627i	−0.307036	+	0.672316i
$643$	848.757			1.32000			0.659998	−	0.751267i	$-0.270557\pi$
$643$	848.757			1.32000			0.659998	+	0.751267i	$0.270557\pi$
$644$	104.258	+	46.8881i	0.161892	+	0.0728076i
$645$	466.841	+	629.170i	0.723784	+	0.975457i
$646$	33.0868	−	72.4500i	0.0512180	−	0.112152i
$647$	−317.319	+	1080.69i	−0.490447	+	1.67031i	0.227159	+	0.973858i	$0.427056\pi$
$647$	−317.319	+	1080.69i	−0.490447	+	1.67031i	−0.717605	+	0.696450i	$0.754762\pi$
$648$	569.727	−	493.671i	0.879208	−	0.761838i
$649$	−563.777	−	877.255i	−0.868686	−	1.35170i
$650$	169.132	+	268.147i	0.260203	+	0.412534i
$651$	182.146	+	26.1886i	0.279793	+	0.0402282i
$652$	129.574	+	441.288i	0.198733	+	0.676823i
$653$	205.778	−	320.196i	0.315127	−	0.490347i	−0.647171	−	0.762345i	$-0.724048\pi$
$653$	205.778	−	320.196i	0.315127	−	0.490347i	0.962298	+	0.271998i	$0.0876845\pi$
$654$	625.119	−	89.8785i	0.955839	−	0.137429i
$655$	740.172	+	408.248i	1.13003	+	0.623280i
$656$	−5.56676	−	12.1895i	−0.00848591	−	0.0185816i
$657$	546.011	−	78.5046i	0.831068	−	0.119489i
$658$	66.8708	+	42.9753i	0.101627	+	0.0653119i
$659$	295.141	+	1005.16i	0.447861	+	1.52528i	0.806177	+	0.591675i	$0.201533\pi$
$659$	295.141	+	1005.16i	0.447861	+	1.52528i	−0.358315	+	0.933601i	$0.616649\pi$
$660$	−430.536	−	796.478i	−0.652328	−	1.20679i
$661$	−28.5390	−	24.7292i	−0.0431754	−	0.0374117i	0.633006	−	0.774147i	$-0.281821\pi$
$661$	−28.5390	−	24.7292i	−0.0431754	−	0.0374117i	−0.676181	+	0.736735i	$0.736366\pi$
$662$	−291.600	−	453.739i	−0.440484	−	0.685406i
$663$	−68.2343	−	78.7465i	−0.102917	−	0.118773i
$664$	−68.1353	+	232.048i	−0.102613	+	0.349469i
$665$	−251.468	+	53.5878i	−0.378147	+	0.0805832i
$666$		−	10.2506i		−	0.0153913i
$667$	98.7794	+	13.6211i	0.148095	+	0.0204214i
$668$		−	655.600i		−	0.981437i
$669$	−559.821	+	1225.84i	−0.836803	+	1.83234i
$670$	70.9077	+	192.601i	0.105832	+	0.287464i
$671$	−144.849	−	167.165i	−0.215871	−	0.249128i
$672$	216.057	−	138.852i	0.321514	−	0.206625i
$673$	−421.286	−	365.046i	−0.625982	−	0.542416i	0.283070	−	0.959099i	$-0.408647\pi$
$673$	−421.286	−	365.046i	−0.625982	−	0.542416i	−0.909052	+	0.416683i	$0.863193\pi$
$674$	98.1194	+	14.1074i	0.145578	+	0.0209309i
$675$	191.925	+	1.62761i	0.284334	+	0.00241127i
$676$	130.712	+	84.0038i	0.193362	+	0.124266i
$677$	−98.8083	−	687.227i	−0.145950	−	1.01511i	−0.922761	−	0.385372i	$-0.874073\pi$
$677$	−98.8083	−	687.227i	−0.145950	−	1.01511i	0.776811	−	0.629734i	$-0.216836\pi$
$678$	−428.719	−	938.765i	−0.632330	−	1.38461i
$679$	35.9683	+	78.7595i	0.0529724	+	0.115993i
$680$	−71.2027	+	70.6015i	−0.104710	+	0.103826i
$681$	484.325	−	753.624i	0.711196	−	1.10664i
$682$	−491.043	+	144.183i	−0.720005	+	0.211413i
$683$	−23.8582	−	3.43030i	−0.0349315	−	0.00502240i	0.124827	−	0.992179i	$-0.460162\pi$
$683$	−23.8582	−	3.43030i	−0.0349315	−	0.00502240i	−0.159758	+	0.987156i	$0.551072\pi$
$684$	344.116	+	298.178i	0.503093	+	0.435933i
$685$	−446.036	+	1180.56i	−0.651147	+	1.72344i
$686$	−174.014	+	150.784i	−0.253664	+	0.219801i
$687$	−571.987	−	167.950i	−0.832586	−	0.244469i
$688$	−2.91778	+	6.38906i	−0.00424097	+	0.00928642i
$689$			420.302i			0.610017i
$690$	−270.667	+	497.497i	−0.392270	+	0.721010i
$691$	204.104			0.295375			0.147688	−	0.989034i	$-0.452817\pi$
$691$	204.104			0.295375			0.147688	+	0.989034i	$0.452817\pi$
$692$	−230.410	−	105.225i	−0.332963	−	0.152059i
$693$	−72.1260	+	245.638i	−0.104078	+	0.354457i
$694$	−400.533	−	462.240i	−0.577137	−	0.666051i
$695$	−162.647	+	430.490i	−0.234025	+	0.619411i
$696$	90.7745	−	104.759i	0.130423	−	0.150516i
$697$	26.6848	−	185.597i	0.0382852	−	0.266279i
$698$	12.6886	+	43.2133i	0.0181785	+	0.0619102i
$699$	332.692	+	213.808i	0.475954	+	0.305877i
$700$	122.838	+	18.7260i	0.175483	+	0.0267514i
$701$	−519.439	+	237.220i	−0.740996	+	0.338402i	−0.749893	−	0.661559i	$-0.769895\pi$
$701$	−519.439	+	237.220i	−0.740996	+	0.338402i	0.00889692	+	0.999960i	$0.497168\pi$
$702$	88.5595	−	40.4438i	0.126153	−	0.0576122i
$703$	−30.0677	+	4.32308i	−0.0427705	+	0.00614947i
$704$	−379.117	+	589.918i	−0.538518	+	0.837951i
$705$	392.288	−	519.430i	0.556437	−	0.736780i
$706$	100.143	−	696.512i	0.141846	−	0.986561i
$707$	−8.91628	+	10.2899i	−0.0126114	+	0.0145544i
$708$	−311.061	−	484.020i	−0.439351	−	0.683644i
$709$	250.364	−	216.942i	0.353123	−	0.305983i	−0.460177	−	0.887827i	$-0.652214\pi$
$709$	250.364	−	216.942i	0.353123	−	0.305983i	0.813300	+	0.581844i	$0.197669\pi$
$710$	−245.008	−	665.496i	−0.345082	−	0.937318i
$711$	−851.515	−	388.874i	−1.19763	−	0.546939i
$712$	−642.231			−0.902010
$713$	−401.887	−	344.198i	−0.563657	−	0.482746i
$714$	24.7080			0.0346051
$715$	−194.968	−	914.914i	−0.272683	−	1.27960i
$716$	314.201	+	92.2578i	0.438829	+	0.128852i
$717$	−818.872	+	709.557i	−1.14208	+	0.989619i
$718$	−279.200	+	179.431i	−0.388858	+	0.249904i
$719$	253.095	−	292.087i	0.352010	−	0.406241i	−0.551937	−	0.833886i	$-0.686111\pi$
$719$	253.095	−	292.087i	0.352010	−	0.406241i	0.903947	+	0.427645i	$0.140657\pi$
$720$	−3.02888	−	5.60333i	−0.00420677	−	0.00778240i
$721$	134.042	−	39.3582i	0.185911	−	0.0545884i
$722$	−201.704	+	313.858i	−0.279369	+	0.434707i
$723$	25.0403	+	174.159i	0.0346339	+	0.240884i
$724$	356.234	−	162.687i	0.492036	−	0.224705i
$725$	107.409	−	14.5145i	0.148150	−	0.0200200i
$726$	−145.218	−	1010.02i	−0.200025	−	1.39121i
$727$	389.916	+	250.584i	0.536336	+	0.344682i	0.780604	−	0.625026i	$-0.214911\pi$
$727$	389.916	+	250.584i	0.536336	+	0.344682i	−0.244269	+	0.969708i	$0.578548\pi$
$728$	157.542	−	46.2584i	0.216403	−	0.0635417i
$729$	−55.9207	+	388.937i	−0.0767088	+	0.533521i
$730$	36.1190	−	476.601i	0.0494781	−	0.652879i
$731$	−82.6781	+	53.1340i	−0.113103	+	0.0726867i
$732$	−79.9196	−	92.2322i	−0.109180	−	0.126000i
$733$	132.493	+	38.9033i	0.180754	+	0.0530741i	0.370857	−	0.928690i	$-0.379064\pi$
$733$	132.493	+	38.9033i	0.180754	+	0.0530741i	−0.190103	+	0.981764i	$0.560882\pi$
$734$	−83.3945	−	38.0850i	−0.113616	−	0.0518869i
$735$	537.996	+	725.067i	0.731967	+	0.986485i
$736$	−738.484	+	4.26096i	−1.00338	+	0.00578935i
$737$		−	605.595i		−	0.821703i
$738$	−589.926	−	269.410i	−0.799358	−	0.365054i
$739$	−910.837	−	267.446i	−1.23253	−	0.361903i	−0.400324	−	0.916374i	$-0.631102\pi$
$739$	−910.837	−	267.446i	−1.23253	−	0.361903i	−0.832203	+	0.554471i	$0.812921\pi$
$740$	14.3316	+	3.18134i	0.0193670	+	0.00429911i
$741$	577.397	+	898.448i	0.779214	+	1.21248i
$742$	−75.3224	−	65.2672i	−0.101513	−	0.0879612i
$743$	159.539	−	1109.62i	0.214723	−	1.49343i	−0.542378	−	0.840135i	$-0.682476\pi$
$743$	159.539	−	1109.62i	0.214723	−	1.49343i	0.757101	−	0.653298i	$-0.226615\pi$
$744$	−705.777	+	207.235i	−0.948625	+	0.278541i
$745$	−19.2284	−	285.878i	−0.0258100	−	0.383729i
$746$	−67.4243	+	9.69416i	−0.0903811	+	0.0129948i
$747$	−89.2981	−	195.535i	−0.119542	−	0.261761i
$748$	103.313	−	47.1816i	0.138119	−	0.0630769i
$749$	27.3463	+	190.198i	0.0365104	+	0.253936i
$750$	−138.498	+	599.827i	−0.184664	+	0.799769i
$751$	2.03559	+	6.93258i	0.00271050	+	0.00923113i	0.960837	−	0.277114i	$-0.0893779\pi$
$751$	2.03559	+	6.93258i	0.00271050	+	0.00923113i	−0.958127	+	0.286345i	$0.907560\pi$
$752$	5.77622	+	0.830495i	0.00768115	+	0.00110438i
$753$	−776.098	+	895.665i	−1.03067	+	1.18946i
$754$	46.2506	−	29.7235i	0.0613403	−	0.0394210i
$755$	346.724	+	76.9663i	0.459237	+	0.101942i
$756$	10.7505	−	36.6127i	0.0142202	−	0.0484295i
$757$	290.404	−	635.895i	0.383624	−	0.840020i	−0.615047	−	0.788490i	$-0.710863\pi$
$757$	290.404	−	635.895i	0.383624	−	0.840020i	0.998671	−	0.0515296i	$-0.0164097\pi$
$758$	587.190			0.774656
$759$	1256.63	−	1101.64i	1.65564	−	1.45143i
$760$	825.366	−	612.418i	1.08601	−	0.805813i
$761$	227.353	−	497.833i	0.298755	−	0.654183i	−0.699410	−	0.714720i	$-0.746554\pi$
$761$	227.353	−	497.833i	0.298755	−	0.654183i	0.998166	+	0.0605370i	$0.0192813\pi$
$762$	−6.65790	+	22.6747i	−0.00873740	+	0.0297569i
$763$	193.281	−	167.479i	0.253317	−	0.219501i
$764$	203.286	+	316.320i	0.266082	+	0.414031i
$765$	6.73503	−	88.8708i	0.00880396	−	0.116171i
$766$	−796.656	−	114.542i	−1.04002	−	0.149533i
$767$	−167.479	−	570.380i	−0.218355	−	0.743650i
$768$	−551.142	+	857.594i	−0.717633	+	1.11666i
$769$	621.573	−	89.3688i	0.808288	−	0.116214i	0.274232	−	0.961664i	$-0.411576\pi$
$769$	621.573	−	89.3688i	0.808288	−	0.116214i	0.534056	+	0.845449i	$0.320667\pi$
$770$	194.238	+	107.133i	0.252257	+	0.139134i
$771$	398.641	+	872.902i	0.517044	+	1.13217i
$772$	107.739	−	15.4905i	0.139558	−	0.0200655i
$773$	−478.081	−	307.244i	−0.618475	−	0.397470i	0.193552	−	0.981090i	$-0.437999\pi$
$773$	−478.081	−	307.244i	−0.618475	−	0.397470i	−0.812027	+	0.583620i	$0.801636\pi$
$774$	95.7678	+	326.155i	0.123731	+	0.421389i
$775$	−521.128	−	243.353i	−0.672424	−	0.314004i
$776$	−261.565	−	226.647i	−0.337068	−	0.292071i
$777$	−5.09469	−	7.92749i	−0.00655687	−	0.0102027i
$778$	302.661	+	349.290i	0.389025	+	0.448958i
$779$	−541.455	+	1844.03i	−0.695064	+	2.36717i
$780$	−107.572	−	504.798i	−0.137913	−	0.647177i
$781$			2092.52i			2.67928i
$782$	−59.9890	−	38.0653i	−0.0767123	−	0.0486769i
$783$		−	33.2841i		−	0.0425084i
$784$	−3.36251	+	7.36287i	−0.00428891	+	0.00939141i
$785$	−44.7998	+	16.4934i	−0.0570699	+	0.0210107i
$786$	545.232	+	629.231i	0.693679	+	0.800548i
$787$	−823.370	+	529.148i	−1.04621	+	0.672360i	−0.946516	−	0.322657i	$-0.895424\pi$
$787$	−823.370	+	529.148i	−1.04621	+	0.672360i	−0.0996974	+	0.995018i	$0.531787\pi$
$788$	83.2179	+	72.1087i	0.105606	+	0.0915085i
$789$	995.831	+	143.179i	1.26214	+	0.181469i
$790$	−488.830	+	647.261i	−0.618772	+	0.819318i
$791$	−351.580	−	225.947i	−0.444475	−	0.285647i
$792$	−145.636	−	1012.92i	−0.183884	−	1.27894i
$793$	−52.3809	−	114.698i	−0.0660540	−	0.144638i
$794$	−126.630	−	277.281i	−0.159484	−	0.349221i
$795$	−579.539	+	574.645i	−0.728980	+	0.722824i
$796$	−414.482	+	644.947i	−0.520706	+	0.810235i
$797$	1242.30	−	364.771i	1.55871	−	0.457680i	0.615023	−	0.788509i	$-0.289147\pi$
$797$	1242.30	−	364.771i	1.55871	−	0.457680i	0.943691	+	0.330829i	$0.107328\pi$
$798$	−250.673	−	36.0413i	−0.314127	−	0.0451646i
$799$	61.7103	+	53.4723i	0.0772344	+	0.0669240i
$800$	−772.088	+	219.611i	−0.965110	+	0.274514i
$801$	431.414	−	373.822i	0.538594	−	0.466694i
$802$	444.561	+	130.535i	0.554315	+	0.162762i
$803$	−585.872	+	1282.88i	−0.729605	+	1.59761i
$804$		−	334.133i		−	0.415589i
$805$	16.7115	+	228.740i	0.0207597	+	0.284149i
$806$	−291.744			−0.361965
$807$	−547.594	−	250.078i	−0.678555	−	0.309886i
$808$	15.3333	−	52.2204i	0.0189769	−	0.0646292i
$809$	−270.691	−	312.394i	−0.334599	−	0.386148i	0.563371	−	0.826204i	$-0.309504\pi$
$809$	−270.691	−	312.394i	−0.334599	−	0.386148i	−0.897970	+	0.440056i	$0.854959\pi$
$810$	543.116	+	205.199i	0.670513	+	0.253332i
$811$	−352.358	+	406.643i	−0.434473	+	0.501409i	−0.930192	−	0.367074i	$-0.880359\pi$
$811$	−352.358	+	406.643i	−0.434473	+	0.501409i	0.495718	+	0.868483i	$0.334905\pi$
$812$	3.06663	−	21.3289i	0.00377663	−	0.0262671i
$813$	−41.2426	−	140.459i	−0.0507289	−	0.172767i
$814$	22.0471	+	14.1688i	0.0270849	+	0.0174064i
$815$	−655.221	+	649.688i	−0.803952	+	0.797163i
$816$	1.64999	−	0.753526i	0.00202205	−	0.000923438i
$817$	916.309	−	418.464i	1.12155	−	0.512196i
$818$	−253.614	+	36.4641i	−0.310041	+	0.0445772i
$819$	−78.9018	+	122.774i	−0.0963392	+	0.149907i
$820$	559.755	−	741.174i	0.682628	−	0.903870i
$821$	21.3661	−	148.605i	0.0260245	−	0.181005i	−0.972663	−	0.232221i	$-0.925401\pi$
$821$	21.3661	−	148.605i	0.0260245	−	0.181005i	0.998688	+	0.0512164i	$0.0163098\pi$
$822$	−814.020	+	939.430i	−0.990292	+	1.14286i
$823$	460.680	+	716.833i	0.559757	+	0.870999i	0.999634	−	0.0270588i	$-0.00861415\pi$
$823$	460.680	+	716.833i	0.559757	+	0.870999i	−0.439876	+	0.898058i	$0.644978\pi$
$824$	−422.027	+	365.688i	−0.512169	+	0.443797i
$825$	994.977	−	1519.72i	1.20603	−	1.84209i
$826$	128.225	+	58.5584i	0.155236	+	0.0708940i
$827$	1032.90			1.24897			0.624485	−	0.781037i	$-0.285309\pi$
$827$	1032.90			1.24897			0.624485	+	0.781037i	$0.285309\pi$
$828$	305.416	−	267.746i	0.368860	−	0.323364i
$829$	377.485			0.455350			0.227675	−	0.973737i	$-0.426888\pi$
$829$	377.485			0.455350			0.227675	+	0.973737i	$0.426888\pi$
$830$	−182.167	+	38.8198i	−0.219479	+	0.0467709i
$831$	−24.3125	−	7.13881i	−0.0292570	−	0.00859062i
$832$	−302.110	+	261.780i	−0.363114	+	0.314640i
$833$	−95.2798	+	61.2326i	−0.114382	+	0.0735086i
$834$	−296.833	+	342.563i	−0.355915	+	0.410747i
$835$	1157.08	−	625.460i	1.38573	−	0.749053i
$836$	−1116.98	+	327.974i	−1.33610	+	0.392313i
$837$	−95.4897	+	148.585i	−0.114086	+	0.177521i
$838$	21.5589	+	149.946i	0.0257266	+	0.178933i
$839$	452.668	−	206.726i	0.539533	−	0.246396i	−0.126960	−	0.991908i	$-0.540522\pi$
$839$	452.668	−	206.726i	0.539533	−	0.246396i	0.666493	+	0.745512i	$0.267795\pi$
$840$	279.178	+	153.983i	0.332355	+	0.183313i
$841$	117.012	+	813.835i	0.139134	+	0.967700i
$842$	−287.896	−	185.020i	−0.341920	−	0.219739i
$843$	1391.81	−	408.671i	1.65102	−	0.484782i
$844$	−92.3659	+	642.419i	−0.109438	+	0.761160i
$845$	−23.5568	+	310.839i	−0.0278778	+	0.367856i
$846$	237.588	−	152.689i	0.280837	−	0.180483i
$847$	−270.599	−	312.288i	−0.319479	−	0.368698i
$848$	−7.02046	−	2.06139i	−0.00827884	−	0.00243089i
$849$	−2048.14	−	935.355i	−2.41242	−	1.10171i
$850$	−73.9095	−	22.3843i	−0.0869523	−	0.0263345i
$851$	0.156341	+	27.0961i	0.000183715	+	0.0318404i
$852$			1154.53i			1.35509i
$853$	−482.903	−	220.534i	−0.566123	−	0.258540i	0.111728	−	0.993739i	$-0.464361\pi$
$853$	−482.903	−	220.534i	−0.566123	−	0.258540i	−0.677851	+	0.735199i	$0.737089\pi$
$854$	28.6891	+	8.42388i	0.0335938	+	0.00986403i
$855$	−197.964	+	891.806i	−0.231537	+	1.04305i
$856$	−415.261	−	646.159i	−0.485118	−	0.754859i
$857$	566.033	+	490.471i	0.660482	+	0.572311i	0.919272	−	0.393622i	$-0.128778\pi$
$857$	566.033	+	490.471i	0.660482	+	0.572311i	−0.258790	+	0.965934i	$0.583324\pi$
$858$	131.129	−	912.021i	0.152831	−	1.06296i
$859$	−116.241	+	34.1313i	−0.135321	+	0.0397337i	−0.348692	−	0.937238i	$-0.613374\pi$
$859$	−116.241	+	34.1313i	−0.135321	+	0.0397337i	0.213371	+	0.976971i	$0.431556\pi$
$860$	−485.726	+	32.6704i	−0.564798	+	0.0379888i
$861$	−590.131	+	84.8480i	−0.685401	+	0.0985458i
$862$	−109.290	−	239.312i	−0.126787	−	0.277624i
$863$	−64.1110	+	29.2785i	−0.0742886	+	0.0339265i	−0.452213	−	0.891910i	$-0.649365\pi$
$863$	−64.1110	+	29.2785i	−0.0742886	+	0.0339265i	0.377924	+	0.925837i	$0.376638\pi$
$864$	35.0816	+	243.998i	0.0406037	+	0.282405i
$865$	−34.1041	−	507.042i	−0.0394267	−	0.586176i
$866$	−198.652	−	676.547i	−0.229390	−	0.781232i
$867$	−1122.17	−	161.344i	−1.29432	−	0.186095i
$868$	−74.8808	+	86.4171i	−0.0862682	+	0.0995588i
$869$	2013.40	−	1293.93i	2.31691	−	1.48899i
$870$	104.219	+	23.1348i	0.119792	+	0.0265917i
$871$	97.2619	−	331.244i	0.111667	−	0.380303i
$872$	−424.676	+	929.911i	−0.487014	+	1.06641i
$873$	307.628			0.352381
$874$	553.087	+	473.693i	0.632823	+	0.541983i
$875$	84.1409	+	234.664i	0.0961610	+	0.268188i
$876$	−323.252	+	707.822i	−0.369009	+	0.808016i
$877$	−303.765	+	1034.53i	−0.346369	+	1.17962i	0.583617	+	0.812029i	$0.301637\pi$
$877$	−303.765	+	1034.53i	−0.346369	+	1.17962i	−0.929986	+	0.367595i	$0.880181\pi$
$878$	−240.788	+	208.644i	−0.274246	+	0.237636i
$879$	−1198.44	−	1864.80i	−1.36341	−	2.12151i
$880$	16.2384	+	1.23062i	0.0184527	+	0.00139843i
$881$	−965.835	−	138.866i	−1.09629	−	0.157623i	−0.429647	−	0.902997i	$-0.641362\pi$
$881$	−965.835	−	138.866i	−1.09629	−	0.157623i	−0.666647	+	0.745373i	$0.732271\pi$
$882$	110.365	+	375.867i	0.125130	+	0.426153i
$883$	713.525	−	1110.27i	0.808070	−	1.25738i	−0.154943	−	0.987923i	$-0.549519\pi$
$883$	713.525	−	1110.27i	0.808070	−	1.25738i	0.963012	−	0.269457i	$-0.0868443\pi$
$884$	64.0871	−	9.21433i	0.0724967	−	0.0104235i
$885$	557.496	−	1010.77i	0.629939	−	1.14211i
$886$	132.357	+	289.822i	0.149388	+	0.327113i
$887$	−871.014	+	125.233i	−0.981978	+	0.141187i	−0.614561	−	0.788869i	$-0.710667\pi$
$887$	−871.014	+	125.233i	−0.981978	+	0.141187i	−0.367417	+	0.930056i	$0.619758\pi$
$888$	31.6883	+	20.3649i	0.0356851	+	0.0229334i
$889$	2.69614	+	9.18222i	0.00303278	+	0.0103287i
$890$	−235.202	−	435.117i	−0.264272	−	0.488895i
$891$	−1294.69	−	1121.86i	−1.45308	−	1.25910i
$892$	−452.726	−	704.456i	−0.507541	−	0.789749i
$893$	−548.076	−	632.514i	−0.613747	−	0.708302i
$894$	79.5102	−	270.787i	0.0889376	−	0.302894i
$895$	136.929	+	642.556i	0.152993	+	0.717940i
$896$			161.350i			0.180078i
$897$	864.272	−	400.743i	0.963514	−	0.446759i
$898$			594.277i			0.661779i
$899$	−41.4334	+	90.7266i	−0.0460884	+	0.100919i
$900$	241.823	−	369.359i	0.268692	−	0.410399i
$901$	−67.0448	−	77.3739i	−0.0744116	−	0.0858755i
$902$	1394.87	−	896.430i	1.54642	−	0.993825i
$903$	236.167	+	204.640i	0.261536	+	0.226623i
$904$	1653.55	+	237.745i	1.82915	+	0.262992i
$905$	626.986	+	473.517i	0.692802	+	0.523223i
$906$	294.293	+	189.131i	0.324827	+	0.208753i
$907$	50.2876	+	349.758i	0.0554438	+	0.385620i	0.998583	+	0.0532215i	$0.0169489\pi$
$907$	50.2876	+	349.758i	0.0554438	+	0.385620i	−0.943139	+	0.332399i	$0.892142\pi$
$908$	231.244	+	506.353i	0.254674	+	0.557658i
$909$	20.0958	+	44.0037i	0.0221076	+	0.0484089i
$910$	89.0364	+	89.7947i	0.0978422	+	0.0986755i
$911$	433.096	−	673.911i	0.475407	−	0.739748i	−0.517876	−	0.855456i	$-0.673277\pi$
$911$	433.096	−	673.911i	0.475407	−	0.739748i	0.993283	+	0.115707i	$0.0369135\pi$
$912$	−17.8390	+	5.23800i	−0.0195603	+	0.00574342i
$913$	543.992	+	78.2143i	0.595829	+	0.0856673i
$914$	113.560	+	98.4004i	0.124245	+	0.107659i
$915$	86.5369	−	229.044i	0.0945758	−	0.250321i
$916$	279.951	−	242.579i	0.305623	−	0.264824i
$917$	323.504	+	94.9894i	0.352785	+	0.103587i
$918$	−9.85160	+	21.5720i	−0.0107316	+	0.0234989i
$919$		−	816.287i		−	0.888234i	−0.895969	−	0.444117i	$-0.853517\pi$
$919$		−	816.287i		−	0.888234i	0.895969	−	0.444117i	$-0.146483\pi$
$920$	−440.593	−	803.960i	−0.478906	−	0.873870i
$921$	2274.90			2.47003
$922$	424.258	+	193.752i	0.460149	+	0.210143i
$923$	−336.070	+	1144.55i	−0.364106	+	1.24003i
$924$	−236.492	−	272.927i	−0.255944	−	0.295375i
$925$	8.05787	+	28.3291i	0.00871122	+	0.0306261i
$926$	171.319	−	197.712i	0.185009	−	0.213512i
$927$	70.6378	−	491.297i	0.0762004	−	0.529986i
$928$	39.2181	+	133.565i	0.0422609	+	0.143927i
$929$	−1067.69	−	686.164i	−1.14929	−	0.738605i	−0.179793	−	0.983704i	$-0.557543\pi$
$929$	−1067.69	−	686.164i	−1.14929	−	0.738605i	−0.969498	+	0.245100i	$0.921179\pi$
$930$	−398.878	−	402.275i	−0.428901	−	0.432554i
$931$	1055.97	−	482.246i	1.13423	−	0.517987i
$932$	−223.533	+	102.084i	−0.239842	+	0.109532i
$933$	−1932.61	+	277.868i	−2.07140	+	0.297822i
$934$	−39.5151	+	61.4868i	−0.0423074	+	0.0658317i
$935$	181.835	+	137.327i	0.194476	+	0.146874i
$936$	83.0218	−	577.430i	0.0886985	−	0.616912i
$937$	441.665	−	509.708i	0.471361	−	0.543979i	−0.469429	−	0.882970i	$-0.655540\pi$
$937$	441.665	−	509.708i	0.471361	−	0.543979i	0.940790	+	0.338991i	$0.110086\pi$
$938$	44.2588	+	68.8680i	0.0471842	+	0.0734201i
$939$	−185.159	+	160.441i	−0.197187	+	0.170864i
$940$	139.740	+	379.565i	0.148660	+	0.403793i
$941$	1646.61	+	751.983i	1.74985	+	0.799131i	0.988579	+	0.150702i	$0.0481533\pi$
$941$	1646.61	+	751.983i	1.74985	+	0.799131i	0.761274	+	0.648430i	$0.224574\pi$
$942$	−47.0221			−0.0499173
$943$	1563.50	+	703.154i	1.65801	+	0.745656i
$944$	10.3487			0.0109626
$945$	74.8746	−	15.9558i	0.0792324	−	0.0168844i
$946$	−833.874	−	244.847i	−0.881473	−	0.258824i
$947$	501.578	−	434.620i	0.529649	−	0.458944i	−0.348515	−	0.937303i	$-0.613314\pi$
$947$	501.578	−	434.620i	0.529649	−	0.458944i	0.878164	+	0.478360i	$0.158768\pi$
$948$	1110.88	−	713.919i	1.17181	−	0.753079i
$949$	−526.494	+	607.606i	−0.554788	+	0.640260i
$950$	717.189	+	334.909i	0.754936	+	0.352535i
$951$	−1331.66	+	391.011i	−1.40028	+	0.411158i
$952$	−21.6231	+	33.6461i	−0.0227133	+	0.0353426i
$953$	42.9296	+	298.582i	0.0450468	+	0.313308i	0.999870	+	0.0161326i	$0.00513538\pi$
$953$	42.9296	+	298.582i	0.0450468	+	0.313308i	−0.954823	+	0.297175i	$0.903956\pi$
$954$	−322.107	+	147.102i	−0.337639	+	0.154194i
$955$	−364.338	+	660.561i	−0.381506	+	0.691687i
$956$	−95.8183	−	666.431i	−0.100228	−	0.697103i
$957$	−264.998	−	170.304i	−0.276905	−	0.177956i
$958$	181.357	−	53.2512i	0.189308	−	0.0555858i
$959$	−71.6378	+	498.252i	−0.0747005	+	0.519554i
$960$	−774.011	−	58.6581i	−0.806261	−	0.0611021i
$961$	−363.192	+	233.409i	−0.377931	+	0.242882i
$962$	9.78358	+	11.2908i	0.0101700	+	0.0117368i
$963$	655.057	+	192.342i	0.680226	+	0.199732i
$964$	−99.4524	−	45.4184i	−0.103166	−	0.0471145i
$965$	130.126	+	175.372i	0.134845	+	0.181733i
$966$	−62.3927	+	217.116i	−0.0645887	+	0.224758i
$967$		−	1596.45i		−	1.65093i	−0.564452	−	0.825466i	$-0.690912\pi$
$967$		−	1596.45i		−	1.65093i	0.564452	−	0.825466i	$-0.309088\pi$
$968$	1502.47	+	686.156i	1.55214	+	0.708839i
$969$	−249.610	−	73.2922i	−0.257596	−	0.0756370i
$970$	57.7633	−	260.217i	0.0595498	−	0.268265i
$971$	276.089	+	429.602i	0.284334	+	0.442433i	0.953814	−	0.300397i	$-0.0971193\pi$
$971$	276.089	+	429.602i	0.284334	+	0.442433i	−0.669480	+	0.742830i	$0.733483\pi$
$972$	−584.200	−	506.212i	−0.601029	−	0.520794i
$973$	−26.1228	+	181.688i	−0.0268476	+	0.186729i
$974$	−277.532	+	81.4907i	−0.284940	+	0.0836660i
$975$	788.301	−	671.447i	0.808514	−	0.688664i
$976$	2.17275	−	0.312394i	0.00222618	−	0.000320076i
$977$	−222.079	−	486.285i	−0.227307	−	0.497733i	0.761273	−	0.648432i	$-0.224575\pi$
$977$	−222.079	−	486.285i	−0.227307	−	0.497733i	−0.988580	+	0.150699i	$0.951848\pi$
$978$	−826.722	+	377.551i	−0.845319	+	0.386044i
$979$	207.703	+	1444.60i	0.212158	+	1.47559i
$980$	−559.760	+	37.6499i	−0.571183	+	0.0384183i
$981$	−255.999	−	871.851i	−0.260957	−	0.888737i
$982$	−14.6830	−	2.11110i	−0.0149522	−	0.00214980i
$983$	−377.052	+	435.141i	−0.383573	+	0.442667i	−0.914399	−	0.404814i	$-0.867336\pi$
$983$	−377.052	+	435.141i	−0.383573	+	0.442667i	0.530826	+	0.847481i	$0.321882\pi$
$984$	2004.85	−	1288.44i	2.03745	−	1.30939i
$985$	−47.8740	+	215.666i	−0.0486030	+	0.218951i
$986$	−3.77296	+	12.8495i	−0.00382654	+	0.0130320i
$987$	107.855	−	236.169i	0.109276	−	0.239280i
$988$	−663.630			−0.671690
$989$	−258.124	−	860.689i	−0.260995	−	0.870262i
$990$	632.927	−	469.629i	0.639320	−	0.474372i
$991$	−155.145	+	339.720i	−0.156554	+	0.342805i	−0.971614	−	0.236571i	$-0.923976\pi$
$991$	−155.145	+	339.720i	−0.156554	+	0.342805i	0.815060	+	0.579376i	$0.196704\pi$
$992$	208.112	−	708.765i	0.209791	−	0.714481i
$993$	−1331.39	+	1153.66i	−1.34078	+	1.16179i
$994$	−152.928	−	237.960i	−0.153851	−	0.239396i
$995$	−1533.71	−	116.231i	−1.54141	−	0.116815i
$996$	300.145	+	43.1543i	0.301350	+	0.0433276i
$997$	293.826	+	1000.68i	0.294710	+	1.00369i	0.965144	+	0.261721i	$0.0842901\pi$
$997$	293.826	+	1000.68i	0.294710	+	1.00369i	−0.670433	+	0.741970i	$0.733892\pi$
$998$	291.681	−	453.864i	0.292265	−	0.454773i
$999$	8.95265	−	1.28720i	0.00896161	−	0.00128849i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.3.i.a.109.8	yes	220
5.4	even	2	inner	115.3.i.a.109.15	yes	220
23.19	odd	22	inner	115.3.i.a.19.15	yes	220
115.19	odd	22	inner	115.3.i.a.19.8	✓	220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.3.i.a.19.8	✓	220	115.19	odd	22	inner
115.3.i.a.19.15	yes	220	23.19	odd	22	inner
115.3.i.a.109.8	yes	220	1.1	even	1	trivial
115.3.i.a.109.15	yes	220	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	115.i (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11696 - 0.510100i) q^{2} +(-1.12995 + 3.84825i) q^{3} +(-1.63204 - 1.88347i) q^{4} +(1.76717 - 4.67730i) q^{5} +(3.22510 - 3.72197i) q^{6} +(0.283825 - 1.97405i) q^{7} +(2.24596 + 7.64903i) q^{8} +(-5.96096 - 3.83087i) q^{9} +(-4.35975 + 4.32294i) q^{10} +(16.4790 - 7.52571i) q^{11} +(9.09219 - 4.15226i) q^{12} +(10.2222 - 1.46973i) q^{13} +(-1.32398 + 2.06016i) q^{14} +(16.0026 + 12.0856i) q^{15} +(-0.0255859 + 0.177954i) q^{16} +(-1.64738 + 1.90117i) q^{17} +(4.70404 + 7.31963i) q^{18} +(19.4865 - 16.8851i) q^{19} +(-11.6936 + 4.30511i) q^{20} +(7.27591 + 3.32280i) q^{21} -22.2453 q^{22} +(-12.5462 - 19.2768i) q^{23} -31.9732 q^{24} +(-18.7542 - 16.5312i) q^{25} +(-12.1676 - 3.57272i) q^{26} +(-5.80211 + 5.02756i) q^{27} +(-4.18127 + 2.68714i) q^{28} +(-2.83908 + 3.27647i) q^{29} +(-11.7094 - 21.6621i) q^{30} +(22.0740 - 6.48152i) q^{31} +(17.3592 - 27.0114i) q^{32} +(10.3404 + 71.9190i) q^{33} +(2.80985 - 1.28321i) q^{34} +(-8.73163 - 4.81601i) q^{35} +(2.51316 + 17.4794i) q^{36} +(-0.991092 - 0.636936i) q^{37} +(-30.3788 + 8.92002i) q^{38} +(-5.89468 + 40.9984i) q^{39} +(39.7458 + 3.01211i) q^{40} +(-62.7042 + 40.2975i) q^{41} +(-6.43197 - 7.42289i) q^{42} +(37.4854 + 11.0067i) q^{43} +(-41.0688 - 18.7555i) q^{44} +(-28.4522 + 21.1114i) q^{45} +(4.18053 + 27.9312i) q^{46} -32.4591i q^{47} +(-0.655900 - 0.299540i) q^{48} +(43.1989 + 12.6843i) q^{49} +(12.5152 + 28.0312i) q^{50} +(-5.45474 - 8.48774i) q^{51} +(-19.4513 - 16.8546i) q^{52} +(-5.79193 + 40.2837i) q^{53} +(9.04530 - 2.65594i) q^{54} +(-6.07880 - 90.3764i) q^{55} +(15.7370 - 2.26264i) q^{56} +(42.9595 + 94.0682i) q^{57} +(4.84248 - 2.21149i) q^{58} +(-8.19189 - 56.9758i) q^{59} +(-3.35394 - 49.8646i) q^{60} +(-3.43984 - 11.7150i) q^{61} +(-27.9621 - 4.02034i) q^{62} +(-9.25419 + 10.6799i) q^{63} +(-32.5631 + 20.9271i) q^{64} +(11.1900 - 50.4097i) q^{65} +(25.1360 - 85.6054i) q^{66} +(13.8867 - 30.4077i) q^{67} +6.26939 q^{68} +(88.3583 - 26.4990i) q^{69} +(7.29627 + 9.83331i) q^{70} +(-47.9828 + 105.068i) q^{71} +(15.9144 - 54.1995i) q^{72} +(-58.8347 + 50.9806i) q^{73} +(0.782112 + 1.21699i) q^{74} +(84.8073 - 53.4916i) q^{75} +(-63.6054 - 9.14508i) q^{76} +(-10.1789 - 34.6663i) q^{77} +(27.4974 - 42.7868i) q^{78} +(130.766 - 18.8013i) q^{79} +(0.787129 + 0.434148i) q^{80} +(-39.2831 - 86.0181i) q^{81} +(90.5940 - 13.0255i) q^{82} +(25.5210 + 16.4014i) q^{83} +(-5.61617 - 19.1269i) q^{84} +(5.98116 + 11.0650i) q^{85} +(-36.2553 - 31.4154i) q^{86} +(-9.40068 - 14.6277i) q^{87} +(94.5755 + 109.146i) q^{88} +(-22.6968 + 77.2981i) q^{89} +(42.5489 - 9.06717i) q^{90} -20.5963i q^{91} +(-15.8314 + 55.0908i) q^{92} +92.2702i q^{93} +(-16.5574 + 36.2556i) q^{94} +(-44.5409 - 120.983i) q^{95} +(84.3317 + 97.3240i) q^{96} +(-36.5228 + 23.4718i) q^{97} +(-41.7813 - 36.2037i) q^{98} +(-127.061 - 18.2686i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q + 26 q^{4} - 11 q^{5} - 14 q^{6} + 32 q^{9} - 11 q^{10} - 22 q^{11} - 22 q^{14} - 88 q^{15} - 142 q^{16} - 22 q^{19} - 99 q^{20} - 22 q^{21} - 88 q^{24} + 17 q^{25} + 34 q^{26} + 92 q^{29} + 341 q^{30}+ \cdots + 1628 q^{99}+O(q^{100}) \) 220 * q + 26 * q^4 - 11 * q^5 - 14 * q^6 + 32 * q^9 - 11 * q^10 - 22 * q^11 - 22 * q^14 - 88 * q^15 - 142 * q^16 - 22 * q^19 - 99 * q^20 - 22 * q^21 - 88 * q^24 + 17 * q^25 + 34 * q^26 + 92 * q^29 + 341 * q^30 - 152 * q^31 - 264 * q^34 - 13 * q^35 - 62 * q^36 - 118 * q^39 - 11 * q^40 - 80 * q^41 - 242 * q^44 + 226 * q^46 + 90 * q^49 - 211 * q^50 - 22 * q^51 + 658 * q^54 - 565 * q^55 + 770 * q^56 - 172 * q^59 - 891 * q^60 + 286 * q^61 - 474 * q^64 - 242 * q^65 - 44 * q^66 - 288 * q^69 + 790 * q^70 - 210 * q^71 + 506 * q^74 + 804 * q^75 - 2376 * q^76 + 462 * q^79 + 2398 * q^80 - 2408 * q^81 + 1034 * q^84 + 1197 * q^85 - 1518 * q^86 - 22 * q^89 + 154 * q^90 - 210 * q^94 - 338 * q^95 + 2772 * q^96 + 1628 * q^99

Introduction

L-functions

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