LMFDB - Embedded newform 57.2.j.b.29.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,2,Mod(2,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("57.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	57.j (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.455147291521$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			29.2
Character	$\chi$	$=$	57.29
Dual form			57.2.j.b.2.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.336464 - 1.90818i) q^{2} +(1.43743 - 0.966337i) q^{3} +(-1.64856 + 0.600025i) q^{4} +(-1.09544 + 3.00968i) q^{5} +(-2.32759 - 2.41773i) q^{6} +(-1.23083 + 2.13186i) q^{7} +(-0.237981 - 0.412196i) q^{8} +(1.13238 - 2.77808i) q^{9} +O(q^{10})$	\(q+(-0.336464 - 1.90818i) q^{2} +(1.43743 - 0.966337i) q^{3} +(-1.64856 + 0.600025i) q^{4} +(-1.09544 + 3.00968i) q^{5} +(-2.32759 - 2.41773i) q^{6} +(-1.23083 + 2.13186i) q^{7} +(-0.237981 - 0.412196i) q^{8} +(1.13238 - 2.77808i) q^{9} +(6.11159 + 1.07764i) q^{10} +(-2.11115 + 1.21887i) q^{11} +(-1.78985 + 2.45555i) q^{12} +(1.65491 - 1.97225i) q^{13} +(4.48210 + 1.63135i) q^{14} +(1.33376 + 5.38476i) q^{15} +(-3.39430 + 2.84816i) q^{16} +(3.75838 - 0.662704i) q^{17} +(-5.68207 - 1.22607i) q^{18} +(-2.59177 - 3.50468i) q^{19} -5.61892i q^{20} +(0.290870 + 4.25378i) q^{21} +(3.03615 + 3.61834i) q^{22} +(0.817753 + 2.24676i) q^{23} +(-0.740401 - 0.362531i) q^{24} +(-4.02800 - 3.37989i) q^{25} +(-4.32022 - 2.49428i) q^{26} +(-1.05684 - 5.08754i) q^{27} +(0.749922 - 4.25302i) q^{28} +(0.705026 - 3.99840i) q^{29} +(9.82632 - 4.35683i) q^{30} +(-3.82192 - 2.20658i) q^{31} +(5.84764 + 4.90675i) q^{32} +(-1.85677 + 3.79212i) q^{33} +(-2.52912 - 6.94869i) q^{34} +(-5.06793 - 6.03972i) q^{35} +(-0.199882 + 5.25927i) q^{36} +9.08219i q^{37} +(-5.81552 + 6.12475i) q^{38} +(0.472956 - 4.43416i) q^{39} +(1.50127 - 0.264715i) q^{40} +(-4.39728 + 3.68975i) q^{41} +(8.01912 - 1.98628i) q^{42} +(3.86432 + 1.40650i) q^{43} +(2.74899 - 3.27612i) q^{44} +(7.12068 + 6.45132i) q^{45} +(4.01207 - 2.31637i) q^{46} +(3.04197 + 0.536381i) q^{47} +(-2.12677 + 7.37405i) q^{48} +(0.470118 + 0.814268i) q^{49} +(-5.09416 + 8.82335i) q^{50} +(4.76200 - 4.58445i) q^{51} +(-1.54482 + 4.24435i) q^{52} +(3.11998 - 1.13558i) q^{53} +(-9.35235 + 3.72842i) q^{54} +(-1.35579 - 7.68908i) q^{55} +1.17166 q^{56} +(-7.11217 - 2.53319i) q^{57} -7.86688 q^{58} +(-1.78173 - 10.1047i) q^{59} +(-5.42977 - 8.07678i) q^{60} +(0.932543 - 0.339418i) q^{61} +(-2.92462 + 8.03534i) q^{62} +(4.52870 + 5.83342i) q^{63} +(2.96450 - 5.13466i) q^{64} +(4.12299 + 7.14123i) q^{65} +(7.86077 + 2.26715i) q^{66} +(-6.74077 - 1.18858i) q^{67} +(-5.79826 + 3.34763i) q^{68} +(3.34659 + 2.43932i) q^{69} +(-9.81970 + 11.7027i) q^{70} +(-0.208227 - 0.0757884i) q^{71} +(-1.41460 + 0.194366i) q^{72} +(12.8811 - 10.8085i) q^{73} +(17.3304 - 3.05582i) q^{74} +(-9.05606 - 0.965937i) q^{75} +(6.37556 + 4.22253i) q^{76} -6.00089i q^{77} +(-8.62030 + 0.589448i) q^{78} +(2.67409 + 3.18686i) q^{79} +(-4.85382 - 13.3357i) q^{80} +(-6.43541 - 6.29170i) q^{81} +(8.52023 + 7.14932i) q^{82} +(-2.45843 - 1.41938i) q^{83} +(-3.03189 - 6.83807i) q^{84} +(-2.12253 + 12.0375i) q^{85} +(1.38365 - 7.84704i) q^{86} +(-2.85038 - 6.42870i) q^{87} +(1.00483 + 0.580137i) q^{88} +(6.53953 + 5.48732i) q^{89} +(9.91443 - 15.7582i) q^{90} +(2.16764 + 5.95553i) q^{91} +(-2.69622 - 3.21323i) q^{92} +(-7.62602 + 0.521460i) q^{93} -5.98510i q^{94} +(13.3871 - 3.96125i) q^{95} +(13.1471 + 1.40230i) q^{96} +(3.82196 - 0.673914i) q^{97} +(1.39559 - 1.17104i) q^{98} +(0.995488 + 7.24515i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9}+O(q^{10}) $ 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9	$ 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9} - 6 q^{10} + 9 q^{12} + 6 q^{13} - 9 q^{15} + 30 q^{16} - 12 q^{19} - 6 q^{21} + 24 q^{22} - 21 q^{24} + 12 q^{25} - 27 q^{27} - 48 q^{28} + 42 q^{30} - 18 q^{31} + 21 q^{33} - 42 q^{34} + 63 q^{36} + 30 q^{40} + 105 q^{42} + 54 q^{43} + 6 q^{45} - 54 q^{46} - 33 q^{48} + 6 q^{49} + 3 q^{51} - 48 q^{52} - 87 q^{54} - 90 q^{55} - 6 q^{57} + 24 q^{58} - 66 q^{60} - 6 q^{61} - 9 q^{63} + 18 q^{64} - 57 q^{66} - 36 q^{69} + 18 q^{70} + 24 q^{72} + 90 q^{73} + 12 q^{76} + 9 q^{78} + 30 q^{79} + 3 q^{81} + 126 q^{82} + 99 q^{84} - 6 q^{85} + 15 q^{87} + 54 q^{88} + 24 q^{90} + 66 q^{91} + 33 q^{93} - 18 q^{96} - 78 q^{97} + 12 q^{99}+O(q^{100}) $ 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9 - 6 * q^10 + 9 * q^12 + 6 * q^13 - 9 * q^15 + 30 * q^16 - 12 * q^19 - 6 * q^21 + 24 * q^22 - 21 * q^24 + 12 * q^25 - 27 * q^27 - 48 * q^28 + 42 * q^30 - 18 * q^31 + 21 * q^33 - 42 * q^34 + 63 * q^36 + 30 * q^40 + 105 * q^42 + 54 * q^43 + 6 * q^45 - 54 * q^46 - 33 * q^48 + 6 * q^49 + 3 * q^51 - 48 * q^52 - 87 * q^54 - 90 * q^55 - 6 * q^57 + 24 * q^58 - 66 * q^60 - 6 * q^61 - 9 * q^63 + 18 * q^64 - 57 * q^66 - 36 * q^69 + 18 * q^70 + 24 * q^72 + 90 * q^73 + 12 * q^76 + 9 * q^78 + 30 * q^79 + 3 * q^81 + 126 * q^82 + 99 * q^84 - 6 * q^85 + 15 * q^87 + 54 * q^88 + 24 * q^90 + 66 * q^91 + 33 * q^93 - 18 * q^96 - 78 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$-1$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	−0.336464	−	1.90818i	−0.237916	−	1.34929i	−0.836386	−	0.548141i	$-0.815336\pi$
$2$	−0.336464	−	1.90818i	−0.237916	−	1.34929i	0.598470	−	0.801145i	$-0.295776\pi$
$3$	1.43743	−	0.966337i	0.829898	−	0.557915i
$3$	1.43743	−	0.966337i	0.829898	−	0.557915i
$4$	−1.64856	+	0.600025i	−0.824278	+	0.300013i
$5$	−1.09544	+	3.00968i	−0.489894	+	1.34597i	0.410883	+	0.911688i	$0.365221\pi$
$5$	−1.09544	+	3.00968i	−0.489894	+	1.34597i	−0.900776	+	0.434283i	$0.857002\pi$
$6$	−2.32759	−	2.41773i	−0.950233	−	0.987033i
$7$	−1.23083	+	2.13186i	−0.465210	+	0.805767i	−0.999211	−	0.0397167i	$-0.987354\pi$
$7$	−1.23083	+	2.13186i	−0.465210	+	0.805767i	0.534001	+	0.845484i	$0.320688\pi$
$8$	−0.237981	−	0.412196i	−0.0841391	−	0.145733i
$9$	1.13238	−	2.77808i	0.377461	−	0.926025i
$10$	6.11159	+	1.07764i	1.93265	+	0.340779i
$11$	−2.11115	+	1.21887i	−0.636535	+	0.367503i	−0.783278	−	0.621671i	$-0.786454\pi$
$11$	−2.11115	+	1.21887i	−0.636535	+	0.367503i	0.146744	+	0.989175i	$0.453121\pi$
$12$	−1.78985	+	2.45555i	−0.516685	+	0.708857i
$13$	1.65491	−	1.97225i	0.458990	−	0.547003i	−0.486062	−	0.873924i	$-0.661567\pi$
$13$	1.65491	−	1.97225i	0.458990	−	0.547003i	0.945051	+	0.326922i	$0.106011\pi$
$14$	4.48210	+	1.63135i	1.19789	+	0.435997i
$15$	1.33376	+	5.38476i	0.344376	+	1.39034i
$16$	−3.39430	+	2.84816i	−0.848575	+	0.712039i
$17$	3.75838	−	0.662704i	0.911541	−	0.160729i	0.301838	−	0.953359i	$-0.402400\pi$
$17$	3.75838	−	0.662704i	0.911541	−	0.160729i	0.609703	+	0.792630i	$0.291289\pi$
$18$	−5.68207	−	1.22607i	−1.33928	−	0.288988i
$19$	−2.59177	−	3.50468i	−0.594592	−	0.804028i
$19$	−2.59177	−	3.50468i	−0.594592	−	0.804028i
$20$		−	5.61892i		−	1.25643i
$21$	0.290870	+	4.25378i	0.0634730	+	0.928252i
$22$	3.03615	+	3.61834i	0.647309	+	0.771433i
$23$	0.817753	+	2.24676i	0.170513	+	0.468481i	0.995286	−	0.0969829i	$-0.0309192\pi$
$23$	0.817753	+	2.24676i	0.170513	+	0.468481i	−0.824773	+	0.565464i	$0.808697\pi$
$24$	−0.740401	−	0.362531i	−0.151134	−	0.0740012i
$25$	−4.02800	−	3.37989i	−0.805599	−	0.675978i
$26$	−4.32022	−	2.49428i	−0.847264	−	0.489168i
$27$	−1.05684	−	5.08754i	−0.203389	−	0.979098i
$28$	0.749922	−	4.25302i	0.141722	−	0.803745i
$29$	0.705026	−	3.99840i	0.130920	−	0.742484i	−0.846694	−	0.532080i	$-0.821411\pi$
$29$	0.705026	−	3.99840i	0.130920	−	0.742484i	0.977614	−	0.210405i	$-0.0674782\pi$
$30$	9.82632	−	4.35683i	1.79403	−	0.795445i
$31$	−3.82192	−	2.20658i	−0.686436	−	0.396314i	0.115839	−	0.993268i	$-0.463044\pi$
$31$	−3.82192	−	2.20658i	−0.686436	−	0.396314i	−0.802276	+	0.596954i	$0.796378\pi$
$32$	5.84764	+	4.90675i	1.03373	+	0.867399i
$33$	−1.85677	+	3.79212i	−0.323223	+	0.660123i
$34$	−2.52912	−	6.94869i	−0.433740	−	1.19169i
$35$	−5.06793	−	6.03972i	−0.856636	−	1.02090i
$36$	−0.199882	+	5.25927i	−0.0333137	+	0.876545i
$37$			9.08219i			1.49310i	0.665328	+	0.746551i	$0.268292\pi$
$37$			9.08219i			1.49310i	−0.665328	+	0.746551i	$0.731708\pi$
$38$	−5.81552	+	6.12475i	−0.943401	+	0.993566i
$39$	0.472956	−	4.43416i	0.0757335	−	0.710034i
$40$	1.50127	−	0.264715i	0.237372	−	0.0418551i
$41$	−4.39728	+	3.68975i	−0.686739	+	0.576243i	−0.917967	−	0.396657i	$-0.870170\pi$
$41$	−4.39728	+	3.68975i	−0.686739	+	0.576243i	0.231228	+	0.972900i	$0.425726\pi$
$42$	8.01912	−	1.98628i	1.23738	−	0.306489i
$43$	3.86432	+	1.40650i	0.589303	+	0.214489i	0.619423	−	0.785058i	$-0.287367\pi$
$43$	3.86432	+	1.40650i	0.589303	+	0.214489i	−0.0301200	+	0.999546i	$0.509589\pi$
$44$	2.74899	−	3.27612i	0.414426	−	0.493893i
$45$	7.12068	+	6.45132i	1.06149	+	0.961706i
$46$	4.01207	−	2.31637i	0.591548	−	0.341530i
$47$	3.04197	+	0.536381i	0.443717	+	0.0782393i	0.391043	−	0.920372i	$-0.372114\pi$
$47$	3.04197	+	0.536381i	0.443717	+	0.0782393i	0.0526741	+	0.998612i	$0.483226\pi$
$48$	−2.12677	+	7.37405i	−0.306973	+	1.06435i
$49$	0.470118	+	0.814268i	0.0671597	+	0.116324i
$50$	−5.09416	+	8.82335i	−0.720423	+	1.24781i
$51$	4.76200	−	4.58445i	0.666813	−	0.641951i
$52$	−1.54482	+	4.24435i	−0.214227	+	0.588585i
$53$	3.11998	−	1.13558i	0.428562	−	0.155984i	−0.118728	−	0.992927i	$-0.537882\pi$
$53$	3.11998	−	1.13558i	0.428562	−	0.155984i	0.547290	+	0.836943i	$0.315659\pi$
$54$	−9.35235	+	3.72842i	−1.27269	+	0.507373i
$55$	−1.35579	−	7.68908i	−0.182815	−	1.03679i
$56$	1.17166			0.156569
$57$	−7.11217	−	2.53319i	−0.942030	−	0.335529i
$58$	−7.86688			−1.03297
$59$	−1.78173	−	10.1047i	−0.231961	−	1.31552i	−0.848920	−	0.528521i	$-0.822747\pi$
$59$	−1.78173	−	10.1047i	−0.231961	−	1.31552i	0.616959	−	0.786995i	$-0.288364\pi$
$60$	−5.42977	−	8.07678i	−0.700981	−	1.04271i
$61$	0.932543	−	0.339418i	0.119400	−	0.0434580i	−0.281629	−	0.959523i	$-0.590875\pi$
$61$	0.932543	−	0.339418i	0.119400	−	0.0434580i	0.401029	+	0.916065i	$0.368653\pi$
$62$	−2.92462	+	8.03534i	−0.371427	+	1.02049i
$63$	4.52870	+	5.83342i	0.570562	+	0.734942i
$64$	2.96450	−	5.13466i	0.370562	−	0.641832i
$65$	4.12299	+	7.14123i	0.511394	+	0.885760i
$66$	7.86077	+	2.26715i	0.967594	+	0.279067i
$67$	−6.74077	−	1.18858i	−0.823516	−	0.145208i	−0.254017	−	0.967200i	$-0.581752\pi$
$67$	−6.74077	−	1.18858i	−0.823516	−	0.145208i	−0.569499	+	0.821992i	$0.692863\pi$
$68$	−5.79826	+	3.34763i	−0.703142	+	0.405959i
$69$	3.34659	+	2.43932i	0.402882	+	0.293660i
$70$	−9.81970	+	11.7027i	−1.17368	+	1.39874i
$71$	−0.208227	−	0.0757884i	−0.0247120	−	0.00899443i	0.329635	−	0.944109i	$-0.393074\pi$
$71$	−0.208227	−	0.0757884i	−0.0247120	−	0.00899443i	−0.354347	+	0.935114i	$0.615297\pi$
$72$	−1.41460	+	0.194366i	−0.166712	+	0.0229063i
$73$	12.8811	−	10.8085i	1.50761	−	1.26504i	0.639373	−	0.768897i	$-0.279194\pi$
$73$	12.8811	−	10.8085i	1.50761	−	1.26504i	0.868241	−	0.496142i	$-0.165251\pi$
$74$	17.3304	−	3.05582i	2.01462	−	0.355232i
$75$	−9.05606	−	0.965937i	−1.04570	−	0.111537i
$76$	6.37556	+	4.22253i	0.731327	+	0.484357i
$77$		−	6.00089i		−	0.683865i
$78$	−8.62030	+	0.589448i	−0.976057	+	0.0667418i
$79$	2.67409	+	3.18686i	0.300859	+	0.358550i	0.895201	−	0.445663i	$-0.147032\pi$
$79$	2.67409	+	3.18686i	0.300859	+	0.358550i	−0.594342	+	0.804212i	$0.702587\pi$
$80$	−4.85382	−	13.3357i	−0.542673	−	1.49098i
$81$	−6.43541	−	6.29170i	−0.715046	−	0.699077i
$82$	8.52023	+	7.14932i	0.940902	+	0.789511i
$83$	−2.45843	−	1.41938i	−0.269848	−	0.155797i	0.358970	−	0.933349i	$-0.383128\pi$
$83$	−2.45843	−	1.41938i	−0.269848	−	0.155797i	−0.628819	+	0.777552i	$0.716461\pi$
$84$	−3.03189	−	6.83807i	−0.330807	−	0.746095i
$85$	−2.12253	+	12.0375i	−0.230221	+	1.30565i
$86$	1.38365	−	7.84704i	0.149202	−	0.846168i
$87$	−2.85038	−	6.42870i	−0.305593	−	0.689228i
$88$	1.00483	+	0.580137i	0.107115	+	0.0618428i
$89$	6.53953	+	5.48732i	0.693189	+	0.581654i	0.919827	−	0.392325i	$-0.128329\pi$
$89$	6.53953	+	5.48732i	0.693189	+	0.581654i	−0.226638	+	0.973979i	$0.572774\pi$
$90$	9.91443	−	15.7582i	1.04507	−	1.66106i
$91$	2.16764	+	5.95553i	0.227230	+	0.624310i
$92$	−2.69622	−	3.21323i	−0.281101	−	0.335003i
$93$	−7.62602	+	0.521460i	−0.790782	+	0.0540729i
$94$		−	5.98510i		−	0.617316i
$95$	13.3871	−	3.96125i	1.37349	−	0.406416i
$96$	13.1471	+	1.40230i	1.34182	+	0.143121i
$97$	3.82196	−	0.673914i	0.388061	−	0.0684256i	0.0237859	−	0.999717i	$-0.492428\pi$
$97$	3.82196	−	0.673914i	0.388061	−	0.0684256i	0.364275	+	0.931291i	$0.381317\pi$
$98$	1.39559	−	1.17104i	0.140976	−	0.118293i
$99$	0.995488	+	7.24515i	0.100050	+	0.728165i
$100$	8.66840	+	3.15504i	0.866840	+	0.315504i
$101$	−1.71188	+	2.04014i	−0.170338	+	0.203001i	−0.844459	−	0.535620i	$-0.820078\pi$
$101$	−1.71188	+	2.04014i	−0.170338	+	0.203001i	0.674121	+	0.738621i	$0.264523\pi$
$102$	−10.3502	−	7.54424i	−1.02482	−	0.746991i
$103$	−12.6300	+	7.29193i	−1.24447	+	0.718495i	−0.970001	−	0.243101i	$-0.921835\pi$
$103$	−12.6300	+	7.29193i	−1.24447	+	0.718495i	−0.274469	+	0.961596i	$0.588502\pi$
$104$	−1.20679	−	0.212790i	−0.118335	−	0.0208657i
$105$	−13.1212	−	3.78432i	−1.28050	−	0.369312i
$106$	−3.21665	−	5.57140i	−0.312428	−	0.541142i
$107$	−2.82927	+	4.90044i	−0.273516	+	0.473744i	−0.969760	−	0.244062i	$-0.921520\pi$
$107$	−2.82927	+	4.90044i	−0.273516	+	0.473744i	0.696244	+	0.717806i	$0.254853\pi$
$108$	4.79492	+	7.75297i	0.461391	+	0.746030i
$109$	2.04837	−	5.62784i	0.196198	−	0.539049i	−0.802111	−	0.597174i	$-0.796290\pi$
$109$	2.04837	−	5.62784i	0.196198	−	0.539049i	0.998309	+	0.0581251i	$0.0185122\pi$
$110$	−14.2160	+	5.17419i	−1.35544	+	0.493339i
$111$	8.77646	+	13.0550i	0.833025	+	1.23912i
$112$	−1.89406	−	10.7418i	−0.178972	−	1.01500i
$113$	−3.46411			−0.325876			−0.162938	−	0.986636i	$-0.552097\pi$
$113$	−3.46411			−0.325876			−0.162938	+	0.986636i	$0.552097\pi$
$114$	−2.44080	+	14.4236i	−0.228601	+	1.35090i
$115$	−7.65783			−0.714096
$116$	1.23687	+	7.01462i	0.114840	+	0.651291i
$117$	−3.60505	−	6.83081i	−0.333287	−	0.631508i
$118$	−18.6820	+	6.79971i	−1.71982	+	0.625964i
$119$	−3.21313	+	8.82801i	−0.294547	+	0.809262i
$120$	1.90216	−	1.83124i	0.173643	−	0.167169i
$121$	−2.52871	+	4.37985i	−0.229883	+	0.398168i
$122$	−0.961437	−	1.66526i	−0.0870444	−	0.150765i
$123$	−2.75521	+	9.55300i	−0.248429	+	0.861365i
$124$	7.62465	+	1.34443i	0.684714	+	0.120733i
$125$	0.716113	−	0.413448i	0.0640510	−	0.0369799i
$126$	9.60747	−	10.6043i	0.855902	−	0.944706i
$127$	3.39146	−	4.04178i	0.300943	−	0.358650i	−0.594288	−	0.804252i	$-0.702566\pi$
$127$	3.39146	−	4.04178i	0.300943	−	0.358650i	0.895231	+	0.445602i	$0.147010\pi$
$128$	3.55108	+	1.29249i	0.313874	+	0.114241i
$129$	6.91382	−	1.71250i	0.608728	−	0.150777i
$130$	12.2395	−	10.2702i	1.07348	−	0.900753i
$131$	−15.2563	+	2.69009i	−1.33295	+	0.235034i	−0.794314	−	0.607507i	$-0.792169\pi$
$131$	−15.2563	+	2.69009i	−1.33295	+	0.235034i	−0.538631	+	0.842542i	$0.681058\pi$
$132$	0.785632	−	7.36563i	0.0683805	−	0.641095i
$133$	10.6615	−	1.21162i	0.924469	−	0.105061i
$134$			13.2625i			1.14571i
$135$	16.4696	+	2.39231i	1.41748	+	0.205898i
$136$	−1.16759	−	1.39148i	−0.100120	−	0.119318i
$137$	3.42271	+	9.40381i	0.292422	+	0.803422i	0.995711	+	0.0925182i	$0.0294916\pi$
$137$	3.42271	+	9.40381i	0.292422	+	0.803422i	−0.703289	+	0.710904i	$0.748286\pi$
$138$	3.52866	−	7.20663i	0.300379	−	0.613469i
$139$	6.94034	+	5.82364i	0.588672	+	0.493954i	0.887782	−	0.460264i	$-0.152245\pi$
$139$	6.94034	+	5.82364i	0.588672	+	0.493954i	−0.299110	+	0.954219i	$0.596690\pi$
$140$	11.9787	+	6.91593i	1.01239	+	0.584503i
$141$	4.89093	−	2.16856i	0.411891	−	0.182626i
$142$	−0.0745571	+	0.422834i	−0.00625669	+	0.0354835i
$143$	−1.08985	+	6.18082i	−0.0911375	+	0.516866i
$144$	4.06875	+	12.6548i	0.339062	+	1.05457i
$145$	11.2616	+	6.50189i	0.935226	+	0.539953i
$146$	−24.9586	−	20.9427i	−2.06558	−	1.73323i
$147$	1.46262	+	0.716157i	0.120635	+	0.0590677i
$148$	−5.44954	−	14.9725i	−0.447950	−	1.23073i
$149$	−8.09355	−	9.64552i	−0.663049	−	0.790191i	0.324771	−	0.945793i	$-0.394713\pi$
$149$	−8.09355	−	9.64552i	−0.663049	−	0.790191i	−0.987820	+	0.155601i	$0.950268\pi$
$150$	1.20385	+	17.6056i	0.0982942	+	1.43749i
$151$		−	14.4103i		−	1.17269i	−0.810061	−	0.586345i	$-0.800566\pi$
$151$		−	14.4103i		−	1.17269i	0.810061	−	0.586345i	$-0.199434\pi$
$152$	−0.827821	+	1.90236i	−0.0671451	+	0.154302i
$153$	2.41489	−	11.1915i	0.195232	−	0.904779i
$154$	−11.4508	+	2.01908i	−0.922729	+	0.162702i
$155$	10.8278	−	9.08559i	0.869708	−	0.729772i
$156$	1.88091	+	7.59374i	0.150594	+	0.607986i
$157$	−16.4270	−	5.97895i	−1.31102	−	0.477172i	−0.410450	−	0.911883i	$-0.634628\pi$
$157$	−16.4270	−	5.97895i	−1.31102	−	0.477172i	−0.900570	+	0.434711i	$0.856851\pi$
$158$	5.18136	−	6.17491i	0.412207	−	0.491249i
$159$	3.38738	−	4.64726i	0.268637	−	0.368552i
$160$	−21.1735	+	12.2245i	−1.67391	+	0.966432i
$161$	−5.79629	−	1.02204i	−0.456811	−	0.0805482i
$162$	−9.84041	+	14.3969i	−0.773135	+	1.13112i
$163$	1.15756	+	2.00495i	0.0906671	+	0.157040i	0.907792	−	0.419421i	$-0.137767\pi$
$163$	1.15756	+	2.00495i	0.0906671	+	0.157040i	−0.817125	+	0.576461i	$0.804433\pi$
$164$	5.03521	−	8.72124i	0.393184	−	0.681014i
$165$	−9.37909	−	9.74232i	−0.730161	−	0.758439i
$166$	−1.88125	+	5.16870i	−0.146014	+	0.401169i
$167$	21.7247	−	7.90714i	1.68111	−	0.611873i	0.687646	−	0.726046i	$-0.258644\pi$
$167$	21.7247	−	7.90714i	1.68111	−	0.611873i	0.993461	+	0.114173i	$0.0364219\pi$
$168$	1.68417	−	1.13222i	0.129937	−	0.0873524i
$169$	1.10640	+	6.27472i	0.0851079	+	0.482671i
$170$	23.6838			1.81647
$171$	−12.6711	+	3.23148i	−0.968985	+	0.247118i
$172$	−7.21447			−0.550098
$173$	0.749063	+	4.24815i	0.0569502	+	0.322981i	0.999952	−	0.00980732i	$-0.00312182\pi$
$173$	0.749063	+	4.24815i	0.0569502	+	0.322981i	−0.943002	+	0.332788i	$0.892011\pi$
$174$	−11.3081	+	7.60206i	−0.857261	+	0.576311i
$175$	12.1632	−	4.42705i	0.919453	−	0.334654i
$176$	3.69433	−	10.1501i	0.278471	−	0.765092i
$177$	−12.3256	−	12.8030i	−0.926450	−	0.962330i
$178$	8.27047	−	14.3249i	0.619898	−	1.07369i
$179$	0.273237	+	0.473261i	0.0204227	+	0.0353732i	0.876056	−	0.482209i	$-0.160165\pi$
$179$	0.273237	+	0.473261i	0.0204227	+	0.0353732i	−0.855633	+	0.517582i	$0.826832\pi$
$180$	−15.6098	−	6.36278i	−1.16349	−	0.474253i
$181$	−1.89534	−	0.334200i	−0.140880	−	0.0248409i	0.102764	−	0.994706i	$-0.467231\pi$
$181$	−1.89534	−	0.334200i	−0.140880	−	0.0248409i	−0.243643	+	0.969865i	$0.578343\pi$
$182$	10.6349	−	6.14006i	0.788311	−	0.455132i
$183$	1.01247	−	1.38904i	0.0748439	−	0.102681i
$184$	0.731494	−	0.871761i	0.0539265	−	0.0642671i
$185$	−27.3345	−	9.94895i	−2.00967	−	0.731461i
$186$	3.56092	+	14.3764i	0.261099	+	1.05413i
$187$	−7.12674	+	5.98004i	−0.521159	+	0.437304i
$188$	−5.33670	+	0.941004i	−0.389219	+	0.0686298i
$189$	12.1467	+	4.00886i	0.883543	+	0.291602i
$190$	−12.0630	−	24.2121i	−0.875145	−	1.75653i
$191$			13.6405i			0.986988i	0.869749	+	0.493494i	$0.164281\pi$
$191$			13.6405i			0.986988i	−0.869749	+	0.493494i	$0.835719\pi$
$192$	−0.700570	−	10.2454i	−0.0505593	−	0.739398i
$193$	16.4792	+	19.6392i	1.18620	+	1.41366i	0.888423	+	0.459025i	$0.151801\pi$
$193$	16.4792	+	19.6392i	1.18620	+	1.41366i	0.297778	+	0.954635i	$0.403754\pi$
$194$	−2.57190	−	7.06623i	−0.184651	−	0.507326i
$195$	12.8273	+	6.28078i	0.918584	+	0.449776i
$196$	−1.26360	−	1.06028i	−0.0902570	−	0.0757346i
$197$	−3.20655	−	1.85131i	−0.228458	−	0.131900i	0.381403	−	0.924409i	$-0.375441\pi$
$197$	−3.20655	−	1.85131i	−0.228458	−	0.131900i	−0.609860	+	0.792509i	$0.708774\pi$
$198$	13.4901	−	4.33730i	0.958700	−	0.308238i
$199$	1.47970	−	8.39179i	0.104893	−	0.594878i	−0.886370	−	0.462978i	$-0.846781\pi$
$199$	1.47970	−	8.39179i	0.104893	−	0.594878i	0.991263	−	0.131900i	$-0.0421079\pi$
$200$	−0.434589	+	2.46467i	−0.0307301	+	0.174279i
$201$	−10.8379	+	4.80536i	−0.764448	+	0.338944i
$202$	4.46893	+	2.58014i	0.314433	+	0.181538i
$203$	7.65626	+	6.42436i	0.537364	+	0.450902i
$204$	−5.09963	+	10.4150i	−0.357045	+	0.729199i
$205$	−6.28806	−	17.2763i	−0.439177	−	1.20663i
$206$	18.1638	+	21.6468i	1.26553	+	1.50821i
$207$	7.16768	+	0.272412i	0.498188	+	0.0189340i
$208$			11.4078i			0.790992i
$209$	9.74334	+	4.23986i	0.673961	+	0.293277i
$210$	−2.80637	+	26.3108i	−0.193658	+	1.81562i
$211$	3.89977	−	0.687634i	0.268471	−	0.0473387i	−0.0377920	−	0.999286i	$-0.512032\pi$
$211$	3.89977	−	0.687634i	0.268471	−	0.0473387i	0.306263	+	0.951947i	$0.400921\pi$
$212$	−4.46208	+	3.74413i	−0.306457	+	0.257148i
$213$	−0.372548	+	0.0922773i	−0.0255266	+	0.00632273i
$214$	10.3029	+	3.74994i	0.704290	+	0.256341i
$215$	−8.46622	+	10.0896i	−0.577391	+	0.688108i
$216$	−1.84556	+	1.64637i	−0.125574	+	0.112021i
$217$	9.40825	−	5.43186i	0.638674	−	0.368738i
$218$	−11.4281	−	2.01509i	−0.774011	−	0.136479i
$219$	8.07091	−	27.9839i	0.545382	−	1.89097i
$220$	6.84874	+	11.8624i	0.461742	+	0.799760i
$221$	4.91277	−	8.50916i	0.330469	−	0.572388i
$222$	21.9583	−	21.1396i	1.47374	−	1.41880i
$223$	−4.89903	+	13.4600i	−0.328063	+	0.901347i	0.660538	+	0.750792i	$0.270328\pi$
$223$	−4.89903	+	13.4600i	−0.328063	+	0.901347i	−0.988602	+	0.150555i	$0.951894\pi$
$224$	−17.6579	+	6.42697i	−1.17982	+	0.429420i
$225$	−13.9508	+	7.36275i	−0.930055	+	0.490850i
$226$	1.16555	+	6.61015i	0.0775311	+	0.439701i
$227$	−14.0873			−0.935008			−0.467504	−	0.883991i	$-0.654847\pi$
$227$	−14.0873			−0.935008			−0.467504	+	0.883991i	$0.654847\pi$
$228$	13.2448	−	0.0913760i	0.877157	−	0.00605152i
$229$	−2.07159			−0.136894			−0.0684471	−	0.997655i	$-0.521804\pi$
$229$	−2.07159			−0.136894			−0.0684471	+	0.997655i	$0.521804\pi$
$230$	2.57658	+	14.6125i	0.169895	+	0.963520i
$231$	−5.79888	−	8.62583i	−0.381538	−	0.567538i
$232$	−1.81591	+	0.660936i	−0.119220	+	0.0433926i
$233$	9.11566	−	25.0451i	0.597187	−	1.64076i	−0.159665	−	0.987171i	$-0.551041\pi$
$233$	9.11566	−	25.0451i	0.597187	−	1.64076i	0.756852	−	0.653586i	$-0.226736\pi$
$234$	−11.8214	+	9.17741i	−0.772791	+	0.599946i
$235$	−4.94662	+	8.56780i	−0.322682	+	0.558901i
$236$	9.00033	+	15.5890i	0.585872	+	1.01476i
$237$	6.92339	+	1.99680i	0.449722	+	0.129706i
$238$	17.9265	+	3.16093i	1.16200	+	0.204893i
$239$	−15.2895	+	8.82739i	−0.988995	+	0.570996i	−0.904974	−	0.425468i	$-0.860110\pi$
$239$	−15.2895	+	8.82739i	−0.988995	+	0.570996i	−0.0840210	+	0.996464i	$0.526776\pi$
$240$	−19.8638	−	14.4787i	−1.28220	−	0.934597i
$241$	−4.98745	+	5.94381i	−0.321270	+	0.382874i	−0.902373	−	0.430955i	$-0.858177\pi$
$241$	−4.98745	+	5.94381i	−0.321270	+	0.382874i	0.581104	+	0.813830i	$0.302621\pi$
$242$	9.20836	+	3.35157i	0.591936	+	0.215447i
$243$	−15.3303	−	2.82506i	−0.983441	−	0.181228i
$244$	−1.33369	+	1.11910i	−0.0853808	+	0.0716430i
$245$	−2.96567	+	0.522928i	−0.189470	+	0.0334087i
$246$	19.1559	+	2.04320i	1.22133	+	0.130270i
$247$	−11.2012	−	0.688327i	−0.712717	−	0.0437972i
$248$			2.10050i			0.133382i
$249$	−4.90542	+	0.335428i	−0.310868	+	0.0212569i
$250$	−1.02988	−	1.22736i	−0.0651352	−	0.0776251i
$251$	−2.47858	−	6.80985i	−0.156447	−	0.429834i	0.836562	−	0.547872i	$-0.184562\pi$
$251$	−2.47858	−	6.80985i	−0.156447	−	0.429834i	−0.993009	+	0.118038i	$0.962340\pi$
$252$	−10.9660	−	6.89939i	−0.690793	−	0.434621i
$253$	−4.46490	−	3.74650i	−0.280706	−	0.235540i
$254$	−8.85355	−	5.11160i	−0.555521	−	0.320730i
$255$	8.58129	+	19.3541i	0.537381	+	1.21200i
$256$	3.33061	−	18.8888i	0.208163	−	1.18055i
$257$	1.96119	−	11.1224i	0.122336	−	0.693799i	−0.860519	−	0.509418i	$-0.829861\pi$
$257$	1.96119	−	11.1224i	0.122336	−	0.693799i	0.982855	−	0.184381i	$-0.0590281\pi$
$258$	−5.59400	−	12.6166i	−0.348267	−	0.785476i
$259$	−19.3619	−	11.1786i	−1.20309	−	0.694606i
$260$	−11.0819	−	9.29881i	−0.687270	−	0.576688i
$261$	−10.3095	−	6.48634i	−0.638142	−	0.401494i
$262$	10.2663	+	28.2066i	0.634257	+	1.74261i
$263$	14.1677	+	16.8844i	0.873618	+	1.04114i	0.998799	+	0.0490039i	$0.0156047\pi$
$263$	14.1677	+	16.8844i	0.873618	+	1.04114i	−0.125180	+	0.992134i	$0.539951\pi$
$264$	2.00497	−	0.137098i	0.123398	−	0.00843780i
$265$			10.6341i			0.653248i
$266$	−5.89919	−	19.9364i	−0.361703	−	1.22238i
$267$	14.7027	+	1.56822i	0.899789	+	0.0959733i
$268$	11.8257	−	2.08519i	0.722370	−	0.127373i
$269$	−8.97080	+	7.52740i	−0.546960	+	0.458954i	−0.873910	−	0.486088i	$-0.838423\pi$
$269$	−8.97080	+	7.52740i	−0.546960	+	0.458954i	0.326950	+	0.945042i	$0.393979\pi$
$270$	−0.976452	−	32.2319i	−0.0594250	−	1.96157i
$271$	−7.86382	−	2.86220i	−0.477693	−	0.173866i	0.0919411	−	0.995764i	$-0.470693\pi$
$271$	−7.86382	−	2.86220i	−0.477693	−	0.173866i	−0.569634	+	0.821898i	$0.692915\pi$
$272$	−10.8696	+	12.9539i	−0.659066	+	0.785444i
$273$	8.87087	+	6.46597i	0.536890	+	0.391338i
$274$	16.7925	−	9.69518i	1.01447	−	0.585707i
$275$	12.6233	+	2.22584i	0.761216	+	0.134223i
$276$	−6.98069	−	2.01332i	−0.420188	−	0.121188i
$277$	7.41703	+	12.8467i	0.445646	+	0.771881i	0.998097	−	0.0616640i	$-0.0196407\pi$
$277$	7.41703	+	12.8467i	0.445646	+	0.771881i	−0.552451	+	0.833545i	$0.686307\pi$
$278$	8.77737	−	15.2029i	0.526432	−	0.911806i
$279$	−10.4579	+	8.11887i	−0.626100	+	0.486064i
$280$	−1.28348	+	3.52632i	−0.0767023	+	0.210738i
$281$	5.55341	−	2.02128i	0.331289	−	0.120579i	−0.171020	−	0.985268i	$-0.554706\pi$
$281$	5.55341	−	2.02128i	0.331289	−	0.120579i	0.502309	+	0.864688i	$0.332484\pi$
$282$	−5.78362	−	8.60313i	−0.344410	−	0.512309i
$283$	−3.79608	−	21.5286i	−0.225653	−	1.27974i	−0.861432	−	0.507873i	$-0.830432\pi$
$283$	−3.79608	−	21.5286i	−0.225653	−	1.27974i	0.635779	−	0.771871i	$-0.280679\pi$
$284$	0.388749			0.0230680
$285$	15.4150	−	18.6304i	0.913107	−	1.10357i
$286$	12.1608			0.719084
$287$	−2.45374	−	13.9158i	−0.144839	−	0.821425i
$288$	20.2531	−	10.6889i	1.19343	−	0.629847i
$289$	−2.28853	+	0.832957i	−0.134620	+	0.0489975i
$290$	8.61766	−	23.6768i	0.506046	−	1.39035i
$291$	4.84255	−	4.66200i	0.283875	−	0.273291i
$292$	−14.7498	+	25.5474i	−0.863166	+	1.49505i
$293$	−10.2048	−	17.6752i	−0.596169	−	1.03260i	−0.993381	−	0.114869i	$-0.963355\pi$
$293$	−10.2048	−	17.6752i	−0.596169	−	1.03260i	0.397211	−	0.917727i	$-0.369978\pi$
$294$	0.874439	−	3.03190i	0.0509983	−	0.176824i
$295$	32.3636	+	5.70658i	1.88428	+	0.332250i
$296$	3.74364	−	2.16139i	0.217595	−	0.125628i
$297$	8.43220	+	9.45239i	0.489286	+	0.548483i
$298$	−15.6822	+	18.6893i	−0.908445	+	1.08264i
$299$	5.78447	+	2.10537i	0.334524	+	0.121757i
$300$	15.5090	−	3.84146i	0.895413	−	0.221787i
$301$	−7.75476	+	6.50702i	−0.446977	+	0.375058i
$302$	−27.4974	+	4.84853i	−1.58230	+	0.279001i
$303$	−0.489236	+	4.58680i	−0.0281059	+	0.263505i
$304$	18.7791	+	4.51417i	1.07706	+	0.258905i
$305$			3.17847i			0.181999i
$306$	−22.1679	−	0.842507i	−1.26726	−	0.0481629i
$307$	0.936090	+	1.11559i	0.0534255	+	0.0636700i	0.792095	−	0.610397i	$-0.208990\pi$
$307$	0.936090	+	1.11559i	0.0534255	+	0.0636700i	−0.738670	+	0.674067i	$0.764546\pi$
$308$	3.60068	+	9.89280i	0.205168	+	0.563695i
$309$	−11.1082	+	22.6864i	−0.631924	+	1.29059i
$310$	−20.9801	−	17.6044i	−1.19159	−	0.999862i
$311$	22.8208	+	13.1756i	1.29405	+	0.747118i	0.979369	−	0.202081i	$-0.0647704\pi$
$311$	22.8208	+	13.1756i	1.29405	+	0.747118i	0.314677	+	0.949199i	$0.398104\pi$
$312$	−1.94030	+	0.860297i	−0.109848	+	0.0487047i
$313$	3.97326	−	22.5335i	0.224582	−	1.27367i	−0.638901	−	0.769289i	$-0.720610\pi$
$313$	3.97326	−	22.5335i	0.224582	−	1.27367i	0.863483	−	0.504379i	$-0.168278\pi$
$314$	−5.88181	+	33.3574i	−0.331930	+	1.88247i
$315$	−22.5176	+	7.23981i	−1.26873	+	0.407917i
$316$	−6.32058	−	3.64919i	−0.355561	−	0.205283i
$317$	4.05314	+	3.40099i	0.227647	+	0.191019i	0.749476	−	0.662032i	$-0.230306\pi$
$317$	4.05314	+	3.40099i	0.227647	+	0.191019i	−0.521829	+	0.853050i	$0.674750\pi$
$318$	−10.0075	−	4.90010i	−0.561195	−	0.274784i
$319$	3.38512	+	9.30054i	0.189530	+	0.520730i
$320$	12.2063	+	14.5469i	0.682352	+	0.813196i
$321$	0.668614	+	9.77805i	0.0373184	+	0.545758i
$322$			11.4042i			0.635533i
$323$	−12.0634	−	11.4543i	−0.671226	−	0.637336i
$324$	14.3843	+	6.51080i	0.799129	+	0.361711i
$325$	−13.3319	+	2.35078i	−0.739523	+	0.130398i
$326$	3.43633	−	2.88343i	0.190321	−	0.159698i
$327$	−2.49402	−	10.0690i	−0.137920	−	0.556818i
$328$	2.56737	+	0.934447i	0.141759	+	0.0515962i
$329$	−4.88764	+	5.82486i	−0.269464	+	0.321135i
$330$	−15.4344	+	21.1749i	−0.849635	+	1.16564i
$331$	22.9821	−	13.2687i	1.26321	−	0.729313i	0.289514	−	0.957174i	$-0.406506\pi$
$331$	22.9821	−	13.2687i	1.26321	−	0.729313i	0.973694	+	0.227860i	$0.0731729\pi$
$332$	4.90453	+	0.864801i	0.269171	+	0.0474621i
$333$	25.2310	+	10.2845i	1.38265	+	0.563588i
$334$	−22.3978	−	38.7941i	−1.22555	−	2.12272i
$335$	10.9613	−	18.9856i	0.598881	−	1.03729i
$336$	−13.1027	−	13.6102i	−0.714814	−	0.742497i
$337$	5.20079	−	14.2890i	0.283305	−	0.778374i	−0.713658	−	0.700494i	$-0.752963\pi$
$337$	5.20079	−	14.2890i	0.283305	−	0.778374i	0.996963	−	0.0778793i	$-0.0248149\pi$
$338$	11.6010	−	4.22243i	0.631013	−	0.229670i
$339$	−4.97940	+	3.34750i	−0.270444	+	0.181811i
$340$	−3.72368	−	21.1180i	−0.201945	−	1.14529i
$341$	10.7582			0.582587
$342$	10.4296	+	23.0915i	0.563969	+	1.24865i
$343$	−19.5462			−1.05539
$344$	−0.339883	−	1.92758i	−0.0183253	−	0.103928i
$345$	−11.0076	+	7.40005i	−0.592627	+	0.398405i
$346$	7.85419	−	2.85869i	0.422244	−	0.153684i
$347$	−4.51031	+	12.3920i	−0.242126	+	0.665236i	0.757793	+	0.652495i	$0.226278\pi$
$347$	−4.51031	+	12.3920i	−0.242126	+	0.665236i	−0.999919	+	0.0127407i	$0.995944\pi$
$348$	8.55639	+	8.88776i	0.458671	+	0.476434i
$349$	6.48287	−	11.2287i	0.347020	−	0.601056i	−0.638699	−	0.769457i	$-0.720527\pi$
$349$	6.48287	−	11.2287i	0.347020	−	0.601056i	0.985719	+	0.168401i	$0.0538603\pi$
$350$	−12.5401	−	21.7201i	−0.670296	−	1.16099i
$351$	−11.7829	−	6.33508i	−0.628923	−	0.338141i
$352$	−18.3259	−	3.23135i	−0.976774	−	0.172232i
$353$	31.2379	−	18.0352i	1.66262	−	0.959916i	0.691168	−	0.722694i	$-0.257096\pi$
$353$	31.2379	−	18.0352i	1.66262	−	0.959916i	0.971455	−	0.237222i	$-0.0762369\pi$
$354$	−20.2832	+	27.8272i	−1.07804	+	1.47900i
$355$	0.456198	−	0.543676i	0.0242125	−	0.0288553i
$356$	−14.0733	−	5.12226i	−0.745884	−	0.271479i
$357$	3.91220	+	15.7946i	0.207055	+	0.835938i
$358$	0.811132	−	0.680620i	0.0428696	−	0.0359719i
$359$	−9.61424	+	1.69525i	−0.507420	+	0.0894719i	−0.421497	−	0.906830i	$-0.638495\pi$
$359$	−9.61424	+	1.69525i	−0.507420	+	0.0894719i	−0.0859235	+	0.996302i	$0.527384\pi$
$360$	0.964619	−	4.47041i	0.0508399	−	0.235611i
$361$	−5.56550	+	18.1666i	−0.292921	+	0.956137i
$362$			3.72910i			0.195997i
$363$	0.597584	+	8.73929i	0.0313650	+	0.458694i
$364$	−7.14694	−	8.51739i	−0.374602	−	0.446433i
$365$	18.4198	+	50.6079i	0.964136	+	2.64894i
$366$	−2.99120	−	1.46461i	−0.156352	−	0.0765565i
$367$	10.0386	+	8.42341i	0.524012	+	0.439698i	0.866028	−	0.499996i	$-0.166665\pi$
$367$	10.0386	+	8.42341i	0.524012	+	0.439698i	−0.342016	+	0.939694i	$0.611110\pi$
$368$	−9.17482	−	5.29709i	−0.478271	−	0.276130i
$369$	5.27101	+	16.3942i	0.274398	+	0.853447i
$370$	−9.78731	+	55.5066i	−0.508818	+	2.88565i
$371$	−1.41927	+	8.04906i	−0.0736846	+	0.417886i
$372$	12.2590	−	5.43546i	0.635601	−	0.281816i
$373$	−27.0751	−	15.6318i	−1.40190	−	0.809385i	−0.407309	−	0.913290i	$-0.633533\pi$
$373$	−27.0751	−	15.6318i	−1.40190	−	0.809385i	−0.994587	+	0.103905i	$0.966866\pi$
$374$	13.8089	+	11.5870i	0.714040	+	0.599151i
$375$	0.629828	−	1.28631i	0.0325242	−	0.0664246i
$376$	−0.502838	−	1.38154i	−0.0259319	−	0.0712473i
$377$	−6.71907	−	8.00748i	−0.346050	−	0.412406i
$378$	3.56270	−	24.5269i	0.183245	−	1.26153i
$379$		−	8.43182i		−	0.433114i	−0.976270	−	0.216557i	$-0.930517\pi$
$379$		−	8.43182i		−	0.433114i	0.976270	−	0.216557i	$-0.0694827\pi$
$380$	−19.6925	+	14.5629i	−1.01020	+	0.747062i
$381$	0.969243	−	9.08706i	0.0496558	−	0.465544i
$382$	26.0284	−	4.58951i	1.33173	−	0.234820i
$383$	2.71999	−	2.28234i	0.138985	−	0.116622i	−0.570645	−	0.821197i	$-0.693307\pi$
$383$	2.71999	−	2.28234i	0.138985	−	0.116622i	0.709630	+	0.704575i	$0.248862\pi$
$384$	6.35340	−	1.57369i	0.324220	−	0.0803069i
$385$	18.0608	+	6.57359i	0.920462	+	0.335021i
$386$	31.9304	−	38.0532i	1.62522	−	1.93686i
$387$	8.28324	−	9.14267i	0.421061	−	0.464748i
$388$	−5.89634	+	3.40425i	−0.299341	+	0.172825i
$389$	−31.7209	−	5.59325i	−1.60831	−	0.283589i	−0.703917	−	0.710282i	$-0.748567\pi$
$389$	−31.7209	−	5.59325i	−1.60831	−	0.283589i	−0.904396	+	0.426693i	$0.859678\pi$
$390$	7.66893	−	26.5901i	0.388331	−	1.34644i
$391$	4.56236	+	7.90224i	0.230729	+	0.399634i
$392$	0.223759	−	0.387561i	0.0113015	−	0.0195748i
$393$	−19.3302	+	18.6095i	−0.975079	+	0.938725i
$394$	−2.45373	+	6.74158i	−0.123617	+	0.339636i
$395$	−12.5207	+	4.55717i	−0.629986	+	0.229296i
$396$	−5.98839	−	11.3467i	−0.300928	−	0.570194i
$397$	3.01861	+	17.1194i	0.151500	+	0.859197i	0.961917	+	0.273343i	$0.0881295\pi$
$397$	3.01861	+	17.1194i	0.151500	+	0.859197i	−0.810417	+	0.585854i	$0.800759\pi$
$398$	−16.5109			−0.827617
$399$	14.1543	−	12.0442i	0.708600	−	0.602965i
$400$	23.2987			1.16493
$401$	5.63502	+	31.9578i	0.281399	+	1.59589i	0.717871	+	0.696177i	$0.245117\pi$
$401$	5.63502	+	31.9578i	0.281399	+	1.59589i	−0.436471	+	0.899718i	$0.643772\pi$
$402$	12.8161	+	19.0639i	0.639207	+	0.950819i
$403$	−10.6769	+	3.88606i	−0.531852	+	0.193578i
$404$	1.59799	−	4.39045i	0.0795031	−	0.218433i
$405$	25.9856	−	12.4764i	1.29123	−	0.619958i
$406$	9.68279	−	16.7711i	0.480549	−	0.832335i
$407$	−11.0700	−	19.1738i	−0.548720	−	0.950411i
$408$	−3.02296	−	0.871861i	−0.149659	−	0.0431635i
$409$	−19.4539	−	3.43025i	−0.961933	−	0.169615i	−0.329436	−	0.944178i	$-0.606859\pi$
$409$	−19.4539	−	3.43025i	−0.961933	−	0.169615i	−0.632497	+	0.774563i	$0.717970\pi$
$410$	−30.8506	+	17.8116i	−1.52360	+	0.879652i
$411$	14.0071	+	10.2098i	0.690921	+	0.503612i
$412$	16.4459	−	19.5995i	0.810231	−	0.965596i
$413$	23.7347	+	8.63874i	1.16791	+	0.425084i
$414$	−1.89185	−	13.7689i	−0.0929793	−	0.676703i
$415$	6.96494	−	5.84428i	0.341895	−	0.286884i
$416$	19.3546	−	3.41274i	0.948939	−	0.167324i
$417$	15.6038	+	1.66433i	0.764122	+	0.0815027i
$418$	4.81213	−	20.0186i	0.235369	−	0.979142i
$419$		−	26.9961i		−	1.31884i	−0.751773	−	0.659422i	$-0.770801\pi$
$419$		−	26.9961i		−	1.31884i	0.751773	−	0.659422i	$-0.229199\pi$
$420$	23.9017	−	1.63437i	1.16628	−	0.0797493i
$421$	−18.8465	−	22.4604i	−0.918522	−	1.09465i	−0.995226	−	0.0975979i	$-0.968884\pi$
$421$	−18.8465	−	22.4604i	−0.918522	−	1.09465i	0.0767040	−	0.997054i	$-0.475560\pi$
$422$	−2.62426	−	7.21009i	−0.127747	−	0.350982i
$423$	4.93479	−	7.84343i	0.239938	−	0.381361i
$424$	−1.21058	−	1.01580i	−0.0587909	−	0.0493314i
$425$	−17.3786	−	10.0335i	−0.842986	−	0.486698i
$426$	0.301430	+	0.679840i	0.0146043	+	0.0329384i
$427$	−0.424210	+	2.40582i	−0.0205290	+	0.116426i
$428$	1.72382	−	9.77629i	0.0833242	−	0.472555i
$429$	4.40619	+	9.93763i	0.212733	+	0.479793i
$430$	22.1014	+	12.7603i	1.06583	+	0.615355i
$431$	−7.56785	−	6.35018i	−0.364530	−	0.305877i	0.442063	−	0.896984i	$-0.354247\pi$
$431$	−7.56785	−	6.35018i	−0.364530	−	0.305877i	−0.806593	+	0.591107i	$0.798691\pi$
$432$	18.0774	+	14.2586i	0.869747	+	0.686017i
$433$	−12.4605	−	34.2348i	−0.598811	−	1.64522i	−0.753646	−	0.657280i	$-0.771707\pi$
$433$	−12.4605	−	34.2348i	−0.598811	−	1.64522i	0.154835	−	0.987940i	$-0.450515\pi$
$434$	−13.5305	−	16.1250i	−0.649484	−	0.774025i
$435$	22.4707	−	1.53653i	1.07739	−	0.0736709i
$436$			10.5069i			0.503188i
$437$	5.75473	−	8.68903i	0.275286	−	0.415653i
$438$	−56.1138	−	5.98521i	−2.68122	−	0.285984i
$439$	−36.5493	+	6.44463i	−1.74440	+	0.307586i	−0.952834	−	0.303492i	$-0.901847\pi$
$439$	−36.5493	+	6.44463i	−1.74440	+	0.307586i	−0.791571	+	0.611078i	$0.790736\pi$
$440$	−2.84675	+	2.38871i	−0.135714	+	0.113877i
$441$	2.79445	−	0.383959i	0.133069	−	0.0182838i
$442$	−17.8900	−	6.51142i	−0.850940	−	0.309717i
$443$	−13.6540	+	16.2722i	−0.648719	+	0.773113i	−0.985720	−	0.168391i	$-0.946143\pi$
$443$	−13.6540	+	16.2722i	−0.648719	+	0.773113i	0.337001	+	0.941504i	$0.390587\pi$
$444$	−22.3018	−	16.2557i	−1.05840	−	0.771464i
$445$	−23.6787	+	13.6709i	−1.12248	+	0.648063i
$446$	27.3324	+	4.81944i	1.29423	+	0.228207i
$447$	−20.9547	−	6.04361i	−0.991123	−	0.285853i
$448$	7.29758	+	12.6398i	0.344778	+	0.597173i
$449$	−12.1746	+	21.0870i	−0.574553	+	0.995155i	0.421537	+	0.906811i	$0.361491\pi$
$449$	−12.1746	+	21.0870i	−0.574553	+	0.995155i	−0.996090	+	0.0883439i	$0.971843\pi$
$450$	18.7434	+	24.1434i	0.883572	+	1.13813i
$451$	4.78596	−	13.1493i	0.225362	−	0.619177i
$452$	5.71078	−	2.07855i	0.268613	−	0.0977670i
$453$	−13.9252	−	20.7137i	−0.654262	−	0.973214i
$454$	4.73987	+	26.8811i	0.222453	+	1.26159i
$455$	−20.2988			−0.951622
$456$	0.648394	+	3.53446i	0.0303638	+	0.165516i
$457$	22.9690			1.07444			0.537221	−	0.843441i	$-0.319474\pi$
$457$	22.9690			1.07444			0.537221	+	0.843441i	$0.319474\pi$
$458$	0.697013	+	3.95296i	0.0325693	+	0.184710i
$459$	−7.34355	−	18.4205i	−0.342767	−	0.859797i
$460$	12.6244	−	4.59489i	0.588614	−	0.214238i
$461$	−1.89821	+	5.21530i	−0.0884086	+	0.242901i	−0.976015	−	0.217701i	$-0.930144\pi$
$461$	−1.89821	+	5.21530i	−0.0884086	+	0.242901i	0.887607	+	0.460602i	$0.152366\pi$
$462$	−14.5085	+	13.9676i	−0.674997	+	0.649831i
$463$	−1.08672	+	1.88225i	−0.0505040	+	0.0874755i	−0.890172	−	0.455624i	$-0.849416\pi$
$463$	−1.08672	+	1.88225i	−0.0505040	+	0.0874755i	0.839668	+	0.543100i	$0.182749\pi$
$464$	8.99500	+	15.5798i	0.417583	+	0.723274i
$465$	6.78439	−	23.5231i	0.314618	−	1.09086i
$466$	−50.8576	−	8.96757i	−2.35593	−	0.415414i
$467$	20.8547	−	12.0405i	0.965040	−	0.557166i	0.0673192	−	0.997731i	$-0.478555\pi$
$467$	20.8547	−	12.0405i	0.965040	−	0.557166i	0.897720	+	0.440566i	$0.145222\pi$
$468$	10.0418	+	9.09784i	0.464182	+	0.420548i
$469$	10.8306	−	12.9074i	0.500111	−	0.596010i
$470$	18.0133	+	6.55629i	0.830889	+	0.302419i
$471$	−29.3903	+	7.27976i	−1.35423	+	0.335434i
$472$	−3.74109	+	3.13914i	−0.172197	+	0.144491i
$473$	−9.87247	+	1.74078i	−0.453937	+	0.0800413i
$474$	1.48078	−	13.8829i	0.0680144	−	0.637663i
$475$	−1.40580	+	22.8767i	−0.0645024	+	1.04966i
$476$		−	16.4814i		−	0.755425i
$477$	0.378288	−	9.95345i	0.0173206	−	0.455737i
$478$	21.9886	+	26.2050i	1.00574	+	1.19859i
$479$	−9.79379	−	26.9082i	−0.447490	−	1.22947i	−0.934466	−	0.356053i	$-0.884122\pi$
$479$	−9.79379	−	26.9082i	−0.447490	−	1.22947i	0.486976	−	0.873415i	$-0.338100\pi$
$480$	−18.6223	+	38.0325i	−0.849987	+	1.73594i
$481$	17.9123	+	15.0302i	0.816731	+	0.685319i
$482$	13.0199	+	7.51707i	0.593042	+	0.342393i
$483$	−9.31937	+	4.13206i	−0.424046	+	0.188015i
$484$	1.54070	−	8.73772i	0.0700316	−	0.397169i
$485$	−2.15844	+	12.2411i	−0.0980096	+	0.555840i
$486$	−0.232634	+	30.2036i	−0.0105525	+	1.37006i
$487$	23.5201	+	13.5793i	1.06580	+	0.615338i	0.927030	−	0.374987i	$-0.122353\pi$
$487$	23.5201	+	13.5793i	1.06580	+	0.615338i	0.138766	+	0.990325i	$0.455686\pi$
$488$	−0.361835	−	0.303615i	−0.0163795	−	0.0137440i
$489$	3.60137	+	1.76338i	0.162859	+	0.0797426i
$490$	1.99568	+	5.48309i	0.0901558	+	0.247701i
$491$	8.78555	+	10.4702i	0.396486	+	0.472514i	0.926945	−	0.375197i	$-0.122425\pi$
$491$	8.78555	+	10.4702i	0.396486	+	0.472514i	−0.530459	+	0.847711i	$0.677980\pi$
$492$	−1.18992	−	17.4018i	−0.0536458	−	0.784536i
$493$		−	15.4947i		−	0.697848i
$494$	2.45535	+	21.6055i	0.110472	+	0.972079i
$495$	−22.8961	−	4.94049i	−1.02910	−	0.222059i
$496$	19.2574	−	3.39561i	0.864684	−	0.152467i
$497$	0.417862	−	0.350628i	0.0187437	−	0.0157278i
$498$	2.29055	+	9.24755i	0.102642	+	0.414393i
$499$	27.5375	+	10.0228i	1.23275	+	0.448684i	0.874538	−	0.484956i	$-0.161164\pi$
$499$	27.5375	+	10.0228i	1.23275	+	0.448684i	0.358211	+	0.933640i	$0.383387\pi$
$500$	−0.932472	+	1.11128i	−0.0417014	+	0.0496978i
$501$	23.5867	−	32.3593i	1.05377	−	1.44571i
$502$	−12.1605	+	7.02084i	−0.542748	+	0.313356i
$503$	28.9203	+	5.09943i	1.28949	+	0.227372i	0.776006	−	0.630726i	$-0.217243\pi$
$503$	28.9203	+	5.09943i	1.28949	+	0.227372i	0.513486	+	0.858098i	$0.328354\pi$
$504$	1.32677	−	3.25496i	0.0590989	−	0.144987i
$505$	−4.26492	−	7.38705i	−0.189786	−	0.328719i
$506$	−5.64672	+	9.78040i	−0.251027	+	0.434792i
$507$	7.65387	+	7.95028i	0.339920	+	0.353085i
$508$	−3.16584	+	8.69807i	−0.140461	+	0.385914i
$509$	26.4535	−	9.62828i	1.17253	−	0.426766i	0.318972	−	0.947764i	$-0.396662\pi$
$509$	26.4535	−	9.62828i	1.17253	−	0.426766i	0.853558	+	0.520998i	$0.174440\pi$
$510$	34.0437	−	22.8866i	1.50748	−	1.01343i
$511$	7.18780	+	40.7640i	0.317969	+	1.80329i
$512$	−29.6059			−1.30841
$513$	−15.0911	+	16.8896i	−0.666288	+	0.745694i
$514$	−21.8835			−0.965240
$515$	−8.11106	−	46.0001i	−0.357416	−	2.02701i
$516$	−10.3703	+	6.97162i	−0.456526	+	0.306908i
$517$	−7.07582	+	2.57539i	−0.311194	+	0.113265i
$518$	−14.8162	+	40.7073i	−0.650988	+	1.78857i
$519$	5.18186	+	5.38254i	0.227459	+	0.236268i
$520$	1.96239	−	3.39896i	0.0860565	−	0.149054i
$521$	−0.605033	−	1.04795i	−0.0265070	−	0.0459115i	0.852468	−	0.522780i	$-0.175105\pi$
$521$	−0.605033	−	1.04795i	−0.0265070	−	0.0459115i	−0.878975	+	0.476869i	$0.841772\pi$
$522$	−8.90833	+	21.8548i	−0.389907	+	0.956558i
$523$	14.2503	+	2.51272i	0.623124	+	0.109873i	0.476291	−	0.879288i	$-0.341981\pi$
$523$	14.2503	+	2.51272i	0.623124	+	0.109873i	0.146833	+	0.989161i	$0.453092\pi$
$524$	23.5367	−	13.5889i	1.02820	−	0.593634i
$525$	13.2057	−	18.1173i	0.576344	−	0.790705i
$526$	27.4516	−	32.7155i	1.19695	−	1.42646i
$527$	−15.8265	−	5.76038i	−0.689414	−	0.250926i
$528$	−4.49809	−	18.1600i	−0.195754	−	0.790311i
$529$	13.2398	−	11.1095i	0.575644	−	0.483023i
$530$	20.2918	−	3.57799i	0.881418	−	0.155418i
$531$	−30.0891	−	6.49260i	−1.30576	−	0.281755i
$532$	−16.8491	+	8.39459i	−0.730500	+	0.363952i
$533$			14.7787i			0.640137i
$534$	−1.95448	−	28.5830i	−0.0845785	−	1.23691i
$535$	−11.6495	−	13.8833i	−0.503652	−	0.600229i
$536$	1.11425	+	3.06138i	0.0481283	+	0.132231i
$537$	0.850087	+	0.416238i	0.0366840	+	0.0179620i
$538$	17.3820	+	14.5852i	0.749390	+	0.628813i
$539$	−1.98498	−	1.14603i	−0.0854990	−	0.0493629i
$540$	−28.5865	+	5.93831i	−1.23017	+	0.255544i
$541$	−7.38884	+	41.9042i	−0.317671	+	1.80160i	0.239164	+	0.970979i	$0.423127\pi$
$541$	−7.38884	+	41.9042i	−0.317671	+	1.80160i	−0.556835	+	0.830623i	$0.687984\pi$
$542$	−2.81570	+	15.9686i	−0.120944	+	0.685910i
$543$	−3.04736	+	1.35115i	−0.130775	+	0.0579835i
$544$	25.2294	+	14.5662i	1.08170	+	0.624520i
$545$	14.6942	+	12.3299i	0.629429	+	0.528154i
$546$	9.35350	−	19.1028i	0.400293	−	0.817523i
$547$	−3.75150	−	10.3072i	−0.160403	−	0.440703i	0.833291	−	0.552835i	$-0.186454\pi$
$547$	−3.75150	−	10.3072i	−0.160403	−	0.440703i	−0.993693	+	0.112132i	$0.964232\pi$
$548$	−11.2851	−	13.4490i	−0.482073	−	0.574513i
$549$	0.113068	−	2.97503i	0.00482562	−	0.126971i
$550$		−	24.8365i		−	1.05903i
$551$	−15.8404	+	7.89203i	−0.674822	+	0.336212i
$552$	0.209053	−	1.95996i	0.00889790	−	0.0834215i
$553$	−10.0853	+	1.77831i	−0.428870	+	0.0756213i
$554$	22.0182	−	18.4755i	0.935463	−	0.784947i
$555$	−48.9054	+	12.1135i	−2.07592	+	0.514189i
$556$	−14.9359	−	5.43621i	−0.633422	−	0.230547i
$557$	0.363563	−	0.433278i	0.0154047	−	0.0183586i	−0.758287	−	0.651921i	$-0.773963\pi$
$557$	0.363563	−	0.433278i	0.0154047	−	0.0183586i	0.773692	+	0.633562i	$0.218408\pi$
$558$	19.0110	+	17.2239i	0.804799	+	0.729146i
$559$	9.16905	−	5.29376i	0.387810	−	0.223902i
$560$	34.4042	+	6.06638i	1.45384	+	0.256351i
$561$	−4.46542	+	15.4827i	−0.188530	+	0.653680i
$562$	−5.72548	−	9.91682i	−0.241515	−	0.418316i
$563$	−15.0497	+	26.0669i	−0.634271	+	1.09859i	0.352398	+	0.935850i	$0.385366\pi$
$563$	−15.0497	+	26.0669i	−0.634271	+	1.09859i	−0.986669	+	0.162739i	$0.947967\pi$
$564$	−6.76178	+	6.50968i	−0.284722	+	0.274107i
$565$	3.79471	−	10.4259i	0.159645	−	0.438620i
$566$	−39.8032	+	14.4872i	−1.67306	+	0.608942i
$567$	21.3339	−	5.97539i	0.895940	−	0.250943i
$568$	0.0183145	+	0.103866i	0.000768458	+	0.00435814i
$569$	−1.55575			−0.0652205			−0.0326103	−	0.999468i	$-0.510382\pi$
$569$	−1.55575			−0.0652205			−0.0326103	+	0.999468i	$0.510382\pi$
$570$	−40.7368	−	23.1462i	−1.70628	−	0.969486i
$571$	11.9752			0.501147			0.250574	−	0.968098i	$-0.419381\pi$
$571$	11.9752			0.501147			0.250574	+	0.968098i	$0.419381\pi$
$572$	−1.91198	−	10.8434i	−0.0799438	−	0.453384i
$573$	13.1813	+	19.6071i	0.550656	+	0.819100i
$574$	−25.7283	+	9.36434i	−1.07388	+	0.390860i
$575$	4.29989	−	11.8138i	0.179318	−	0.492672i
$576$	−10.9075	−	14.0500i	−0.454480	−	0.585417i
$577$	1.38649	−	2.40147i	0.0577204	−	0.0999746i	−0.835721	−	0.549154i	$-0.814950\pi$
$577$	1.38649	−	2.40147i	0.0577204	−	0.0999746i	0.893442	+	0.449179i	$0.148283\pi$
$578$	2.35944	+	4.08667i	0.0981398	+	0.169983i
$579$	42.6658	+	12.3054i	1.77313	+	0.511394i
$580$	−22.4667	−	3.96148i	−0.932879	−	0.164492i
$581$	6.05183	−	3.49402i	0.251072	−	0.144957i
$582$	−10.5253	−	7.67186i	−0.436287	−	0.318009i
$583$	−5.20261	+	6.20022i	−0.215470	+	0.256787i
$584$	−7.52067	−	2.73730i	−0.311208	−	0.113270i
$585$	24.5077	−	3.36737i	1.01327	−	0.139223i
$586$	−30.2939	+	25.4196i	−1.25143	+	1.05007i
$587$	12.2045	−	2.15199i	0.503735	−	0.0888221i	0.0839947	−	0.996466i	$-0.473232\pi$
$587$	12.2045	−	2.15199i	0.503735	−	0.0888221i	0.419741	+	0.907644i	$0.362121\pi$
$588$	−2.84092	−	0.303018i	−0.117158	−	0.0124962i
$589$	2.17215	+	19.1135i	0.0895018	+	0.787559i
$590$		−	63.6757i		−	2.62149i
$591$	−6.39817	+	0.437501i	−0.263186	+	0.0179964i
$592$	−25.8675	−	30.8277i	−1.06315	−	1.26701i
$593$	−9.59916	−	26.3735i	−0.394190	−	1.08303i	−0.965069	−	0.261994i	$-0.915620\pi$
$593$	−9.59916	−	26.3735i	−0.394190	−	1.08303i	0.570879	−	0.821034i	$-0.306602\pi$
$594$	15.1997	−	19.2705i	0.623653	−	0.790680i
$595$	−23.0497	−	19.3410i	−0.944947	−	0.792905i
$596$	19.1302	+	11.0448i	0.783604	+	0.452414i
$597$	−5.98234	−	13.4925i	−0.244841	−	0.552210i
$598$	2.07117	−	11.7462i	0.0846964	−	0.480337i
$599$	4.69683	−	26.6371i	0.191907	−	1.08836i	−0.724847	−	0.688910i	$-0.758090\pi$
$599$	4.69683	−	26.6371i	0.191907	−	1.08836i	0.916754	−	0.399451i	$-0.130799\pi$
$600$	1.75702	+	3.96275i	0.0717300	+	0.161778i
$601$	−6.54900	−	3.78107i	−0.267139	−	0.154233i	0.360448	−	0.932779i	$-0.382624\pi$
$601$	−6.54900	−	3.78107i	−0.267139	−	0.154233i	−0.627587	+	0.778547i	$0.715957\pi$
$602$	15.0258	+	12.6081i	0.612404	+	0.513868i
$603$	−10.9351	+	17.3804i	−0.445312	+	0.707786i
$604$	8.64652	+	23.7561i	0.351822	+	0.966623i
$605$	−10.4119	−	12.4085i	−0.423305	−	0.504475i
$606$	8.91704	−	0.609739i	0.362230	−	0.0247689i
$607$		−	14.7418i		−	0.598352i	−0.954198	−	0.299176i	$-0.903288\pi$
$607$		−	14.7418i		−	0.598352i	0.954198	−	0.299176i	$-0.0967117\pi$
$608$	2.04086	−	33.2112i	0.0827679	−	1.34689i
$609$	17.2134	+	1.83601i	0.697522	+	0.0743991i
$610$	6.06509	−	1.06944i	0.245568	−	0.0433003i
$611$	6.09206	−	5.11185i	0.246459	−	0.206803i
$612$	2.73411	+	19.8988i	0.110520	+	0.804362i
$613$	3.20258	+	1.16564i	0.129351	+	0.0470799i	0.405885	−	0.913924i	$-0.366963\pi$
$613$	3.20258	+	1.16564i	0.129351	+	0.0470799i	−0.276534	+	0.961004i	$0.589186\pi$
$614$	1.81378	−	2.16158i	0.0731983	−	0.0872343i
$615$	−25.7333	−	18.7570i	−1.03767	−	0.756355i
$616$	−2.47354	+	1.42810i	−0.0996618	+	0.0575398i
$617$	−31.0226	−	5.47012i	−1.24892	−	0.220219i	−0.490187	−	0.871617i	$-0.663071\pi$
$617$	−31.0226	−	5.47012i	−1.24892	−	0.220219i	−0.758736	+	0.651399i	$0.774182\pi$
$618$	47.0273	+	13.5633i	1.89172	+	0.545596i
$619$	9.59361	+	16.6166i	0.385600	+	0.667878i	0.991852	−	0.127394i	$-0.0406612\pi$
$619$	9.59361	+	16.6166i	0.385600	+	0.667878i	−0.606253	+	0.795272i	$0.707328\pi$
$620$	−12.3986	+	21.4750i	−0.497941	+	0.862458i
$621$	10.5662	−	6.53482i	0.424009	−	0.262233i
$622$	17.4630	−	47.9792i	0.700202	−	1.92379i
$623$	−19.7472	+	7.18740i	−0.791156	+	0.287957i
$624$	11.0238	+	16.3979i	0.441306	+	0.656442i
$625$	−4.10547	−	23.2833i	−0.164219	−	0.931331i
$626$	−44.3348			−1.77197
$627$	18.1025	−	3.32088i	0.722943	−	0.132623i
$628$	30.6684			1.22380
$629$	6.01880	+	34.1343i	0.239985	+	1.36102i
$630$	21.3912	+	40.5318i	0.852246	+	1.61482i
$631$	33.0297	−	12.0218i	1.31489	−	0.478581i	0.413074	−	0.910698i	$-0.364455\pi$
$631$	33.0297	−	12.0218i	1.31489	−	0.478581i	0.901818	+	0.432116i	$0.142233\pi$
$632$	0.677226	−	1.86066i	0.0269386	−	0.0740132i
$633$	4.94114	−	4.75691i	0.196393	−	0.189070i
$634$	5.12596	−	8.87843i	0.203578	−	0.352608i
$635$	8.44937	+	14.6347i	0.335303	+	0.580762i
$636$	−2.79582	+	9.69379i	−0.110861	+	0.384384i
$637$	2.38394	+	0.420353i	0.0944552	+	0.0166550i
$638$	16.6081	−	9.58871i	0.657522	−	0.379621i
$639$	−0.446339	+	0.492649i	−0.0176569	+	0.0194889i
$640$	−7.77996	+	9.27180i	−0.307530	+	0.366500i
$641$	13.3925	+	4.87448i	0.528972	+	0.192530i	0.592679	−	0.805438i	$-0.298070\pi$
$641$	13.3925	+	4.87448i	0.528972	+	0.192530i	−0.0637070	+	0.997969i	$0.520292\pi$
$642$	18.4333	−	4.56579i	0.727505	−	0.180198i
$643$	10.2448	−	8.59638i	0.404014	−	0.339008i	−0.418029	−	0.908434i	$-0.637279\pi$
$643$	10.2448	−	8.59638i	0.404014	−	0.339008i	0.822043	+	0.569426i	$0.192834\pi$
$644$	10.1688	−	1.79303i	0.400705	−	0.0706551i
$645$	−2.41955	+	22.6843i	−0.0952699	+	0.893195i
$646$	−17.7980	+	26.8731i	−0.700254	+	1.05731i
$647$			44.1193i			1.73451i	0.497867	+	0.867254i	$0.334117\pi$
$647$			44.1193i			1.73451i	−0.497867	+	0.867254i	$0.665883\pi$
$648$	−1.06190	+	4.14996i	−0.0417155	+	0.163026i
$649$	16.0778	+	19.1607i	0.631108	+	0.752125i
$650$	8.97143	+	24.6488i	0.351888	+	0.966805i
$651$	8.27465	−	16.8994i	0.324309	−	0.662341i
$652$	−3.11132	−	2.61071i	−0.121849	−	0.102243i
$653$	0.0130791	+	0.00755119i	0.000511823	+	0.000295501i	0.500256	−	0.865878i	$-0.333239\pi$
$653$	0.0130791	+	0.00755119i	0.000511823	+	0.000295501i	−0.499744	+	0.866173i	$0.666573\pi$
$654$	−18.3743	+	8.14689i	−0.718494	+	0.318569i
$655$	8.61592	−	48.8633i	0.336652	−	1.90925i
$656$	4.41669	−	25.0483i	0.172443	−	0.977971i
$657$	−15.4405	−	48.0239i	−0.602392	−	1.87359i
$658$	12.7594	+	7.36663i	0.497413	+	0.287181i
$659$	12.3679	+	10.3779i	0.481784	+	0.404264i	0.851071	−	0.525051i	$-0.175954\pi$
$659$	12.3679	+	10.3779i	0.481784	+	0.404264i	−0.369287	+	0.929315i	$0.620398\pi$
$660$	21.3076	+	10.4331i	0.829397	+	0.406107i
$661$	16.1067	+	44.2528i	0.626477	+	1.72123i	0.690547	+	0.723287i	$0.257370\pi$
$661$	16.1067	+	44.2528i	0.626477	+	1.72123i	−0.0640698	+	0.997945i	$0.520408\pi$
$662$	−33.0517	−	39.3895i	−1.28459	−	1.53091i
$663$	−1.16099	−	16.9787i	−0.0450890	−	0.659397i
$664$			1.35114i			0.0524345i
$665$	−8.03238	+	33.4150i	−0.311482	+	1.29578i
$666$	11.1354	−	51.6057i	0.431488	−	1.99968i
$667$	9.55997	−	1.68568i	0.370164	−	0.0652698i
$668$	−31.0699	+	26.0707i	−1.20213	+	1.00871i
$669$	5.96489	+	24.0818i	0.230616	+	0.931058i
$670$	−39.9160	−	14.5282i	−1.54209	−	0.561274i
$671$	−1.55503	+	1.85321i	−0.0600312	+	0.0715424i
$672$	−19.1714	+	26.3018i	−0.739551	+	1.01461i
$673$	−24.0985	+	13.9133i	−0.928928	+	0.536317i	−0.886472	−	0.462782i	$-0.846851\pi$
$673$	−24.0985	+	13.9133i	−0.928928	+	0.536317i	−0.0424553	+	0.999098i	$0.513518\pi$
$674$	−29.0159	−	5.11629i	−1.11765	−	0.197072i
$675$	−12.9384	+	24.0646i	−0.497999	+	0.926247i
$676$	−5.58896	−	9.68036i	−0.214960	−	0.372321i
$677$	−11.1265	+	19.2717i	−0.427626	+	0.740670i	−0.996662	−	0.0816430i	$-0.973983\pi$
$677$	−11.1265	+	19.2717i	−0.427626	+	0.740670i	0.569036	+	0.822313i	$0.307317\pi$
$678$	8.06302	+	8.37528i	0.309658	+	0.321651i
$679$	−3.26749	+	8.97734i	−0.125395	+	0.344519i
$680$	5.46692	−	1.98980i	0.209647	−	0.0763053i
$681$	−20.2495	+	13.6131i	−0.775961	+	0.521655i
$682$	−3.61973	−	20.5285i	−0.138607	−	0.786077i
$683$	27.9609			1.06989			0.534947	−	0.844886i	$-0.320332\pi$
$683$	27.9609			1.06989			0.534947	+	0.844886i	$0.320332\pi$
$684$	18.9501	−	12.9303i	0.724575	−	0.494402i
$685$	−32.0519			−1.22464
$686$	6.57657	+	37.2976i	0.251094	+	1.42403i
$687$	−2.97775	+	2.00185i	−0.113608	+	0.0763754i
$688$	−17.1226	+	6.23211i	−0.652792	+	0.237597i
$689$	2.92364	−	8.03264i	0.111382	−	0.306019i
$690$	17.8243	+	18.5145i	0.678558	+	0.704837i
$691$	−21.6169	+	37.4416i	−0.822346	+	1.42435i	0.0815844	+	0.996666i	$0.474002\pi$
$691$	−21.6169	+	37.4416i	−0.822346	+	1.42435i	−0.903931	+	0.427679i	$0.859331\pi$
$692$	−3.78387	−	6.55385i	−0.143841	−	0.249140i
$693$	−16.6709	−	6.79531i	−0.633276	−	0.258132i
$694$	25.1637	+	4.43703i	0.955200	+	0.168427i
$695$	−25.1300	+	14.5088i	−0.953235	+	0.550350i
$696$	−1.97154	+	2.70483i	−0.0747312	+	0.102526i
$697$	−14.0814	+	16.7816i	−0.533372	+	0.635648i
$698$	−23.6075	−	8.59244i	−0.893559	−	0.325229i
$699$	−11.0989	−	44.8092i	−0.419799	−	1.69484i
$700$	−17.3954	+	14.5965i	−0.657485	+	0.551695i
$701$	43.7303	−	7.71084i	1.65167	−	0.291234i	0.731235	−	0.682125i	$-0.238944\pi$
$701$	43.7303	−	7.71084i	1.65167	−	0.291234i	0.920437	+	0.390891i	$0.127833\pi$
$702$	−8.12396	+	24.6153i	−0.306619	+	0.929046i
$703$	31.8301	−	23.5389i	1.20050	−	0.887786i
$704$			14.4534i			0.544731i
$705$	1.16899	+	17.0957i	0.0440265	+	0.643860i
$706$	−44.9248	−	53.5393i	−1.69077	−	2.01498i
$707$	−2.24225	−	6.16054i	−0.0843286	−	0.231691i
$708$	28.0016	+	13.7107i	1.05236	+	0.515280i
$709$	−20.8623	−	17.5055i	−0.783500	−	0.657434i	0.160628	−	0.987015i	$-0.448648\pi$
$709$	−20.8623	−	17.5055i	−0.783500	−	0.657434i	−0.944127	+	0.329581i	$0.893093\pi$
$710$	−1.19093	−	0.687581i	−0.0446946	−	0.0258045i
$711$	11.8814	−	3.82008i	0.445589	−	0.143264i
$712$	0.705563	−	4.00145i	0.0264421	−	0.149961i
$713$	1.83228	−	10.3914i	0.0686193	−	0.389160i
$714$	28.8226	−	12.7795i	1.07866	−	0.478260i
$715$	−17.4085	−	10.0508i	−0.651040	−	0.375878i
$716$	−0.734415	−	0.616247i	−0.0274464	−	0.0230302i
$717$	−13.4473	+	27.4635i	−0.502197	+	1.02564i
$718$	6.46968	+	17.7753i	0.241446	+	0.663369i
$719$	−3.69216	−	4.40015i	−0.137694	−	0.164098i	0.692791	−	0.721139i	$-0.256381\pi$
$719$	−3.69216	−	4.40015i	−0.137694	−	0.164098i	−0.830485	+	0.557041i	$0.811937\pi$
$720$	−42.5441	−	1.61692i	−1.58553	−	0.0602590i
$721$		−	35.9005i		−	1.33700i
$722$	36.5377	+	4.50758i	1.35979	+	0.167755i
$723$	−1.42536	+	13.3633i	−0.0530097	+	0.496988i
$724$	3.32510	−	0.586305i	0.123576	−	0.0217899i
$725$	−16.3540	+	13.7226i	−0.607372	+	0.509646i
$726$	16.4751	−	4.08075i	0.611447	−	0.151451i
$727$	−22.9240	−	8.34367i	−0.850206	−	0.309450i	−0.120081	−	0.992764i	$-0.538316\pi$
$727$	−22.9240	−	8.34367i	−0.850206	−	0.309450i	−0.730124	+	0.683314i	$0.760538\pi$
$728$	1.93899	−	2.31080i	0.0718637	−	0.0856439i
$729$	−24.7662	+	10.7535i	−0.917266	+	0.398276i
$730$	90.3714	−	52.1760i	3.34480	−	1.93112i
$731$	15.4557	+	2.72525i	0.571648	+	0.100797i
$732$	−0.835653	+	2.89742i	−0.0308866	+	0.107092i
$733$	5.91692	+	10.2484i	0.218546	+	0.378533i	0.954364	−	0.298647i	$-0.0965352\pi$
$733$	5.91692	+	10.2484i	0.218546	+	0.378533i	−0.735817	+	0.677180i	$0.763202\pi$
$734$	12.6957	−	21.9897i	0.468609	−	0.811654i
$735$	−3.75761	+	3.61751i	−0.138602	+	0.133434i
$736$	−6.24236	+	17.1507i	−0.230096	+	0.632184i
$737$	15.6795	−	5.70686i	0.577561	−	0.210215i
$738$	29.5095	−	15.5741i	1.08626	−	0.573290i
$739$	6.52457	+	37.0027i	0.240010	+	1.36117i	0.831801	+	0.555074i	$0.187310\pi$
$739$	6.52457	+	37.0027i	0.240010	+	1.36117i	−0.591791	+	0.806092i	$0.701579\pi$
$740$	51.0321			1.87598
$741$	−16.7661	+	9.83474i	−0.615917	+	0.361288i
$742$	15.8366			0.581379
$743$	−4.39621	−	24.9322i	−0.161281	−	0.914672i	−0.952816	−	0.303548i	$-0.901829\pi$
$743$	−4.39621	−	24.9322i	−0.161281	−	0.914672i	0.791535	−	0.611124i	$-0.209282\pi$
$744$	2.02980	+	3.01932i	0.0744159	+	0.110694i
$745$	37.8959	−	13.7930i	1.38840	−	0.505336i
$746$	−20.7185	+	56.9237i	−0.758559	+	2.08413i
$747$	−6.72703	+	5.22244i	−0.246129	+	0.191079i
$748$	8.16065	−	14.1347i	0.298383	−	0.516814i
$749$	−6.96470	−	12.0632i	−0.254485	−	0.440780i
$750$	−2.66642	−	0.769030i	−0.0973638	−	0.0280810i
$751$	−2.04271	−	0.360186i	−0.0745397	−	0.0131434i	0.136254	−	0.990674i	$-0.456494\pi$
$751$	−2.04271	−	0.360186i	−0.0745397	−	0.0131434i	−0.210794	+	0.977531i	$0.567605\pi$
$752$	−11.8531	+	6.84337i	−0.432237	+	0.249552i
$753$	−10.1434	−	7.39350i	−0.369646	−	0.269434i
$754$	−13.0190	+	15.5154i	−0.474123	+	0.565038i
$755$	43.3703	+	15.7855i	1.57841	+	0.574494i
$756$	−22.4300	+	0.679507i	−0.815770	+	0.0247134i
$757$	−25.7099	+	21.5732i	−0.934443	+	0.784091i	−0.976610	−	0.215020i	$-0.931018\pi$
$757$	−25.7099	+	21.5732i	−0.934443	+	0.784091i	0.0421666	+	0.999111i	$0.486574\pi$
$758$	−16.0894	+	2.83700i	−0.584395	+	0.103045i
$759$	−10.0383	−	1.07071i	−0.364369	−	0.0388643i
$760$	−4.81869	−	4.57539i	−0.174792	−	0.165967i
$761$		−	46.4063i		−	1.68223i	−0.540859	−	0.841113i	$-0.681901\pi$
$761$		−	46.4063i		−	1.68223i	0.540859	−	0.841113i	$-0.318099\pi$
$762$	−17.6658	+	1.20797i	−0.639966	+	0.0437603i
$763$	9.47657	+	11.2937i	0.343075	+	0.408861i
$764$	−8.18462	−	22.4870i	−0.296109	−	0.813553i
$765$	31.0375	+	19.5276i	1.12216	+	0.706022i
$766$	−5.27030	−	4.42231i	−0.190424	−	0.159784i
$767$	−22.8775	−	13.2083i	−0.826058	−	0.476925i
$768$	−13.4655	−	30.3698i	−0.485893	−	1.09587i
$769$	−2.30707	+	13.0840i	−0.0831950	+	0.471822i	0.914537	+	0.404503i	$0.132556\pi$
$769$	−2.30707	+	13.0840i	−0.0831950	+	0.471822i	−0.997732	+	0.0673188i	$0.978556\pi$
$770$	6.46679	−	36.6750i	0.233047	−	1.32167i
$771$	−7.92898	−	17.8829i	−0.285555	−	0.644035i
$772$	−38.9510	−	22.4883i	−1.40188	−	0.809373i
$773$	−31.9821	−	26.8362i	−1.15032	−	0.965230i	−0.150590	−	0.988596i	$-0.548117\pi$
$773$	−31.9821	−	26.8362i	−1.15032	−	0.965230i	−0.999727	+	0.0233660i	$0.992562\pi$
$774$	−20.2329	−	12.7297i	−0.727255	−	0.457561i
$775$	7.93665	+	21.8058i	0.285093	+	0.783286i
$776$	−1.18734	−	1.41502i	−0.0426230	−	0.0507961i
$777$	−38.6337	+	2.64173i	−1.38598	+	0.0947717i
$778$			62.4111i			2.23755i
$779$	24.3281	+	5.84805i	0.871644	+	0.209528i
$780$	−24.9152	−	2.65750i	−0.892107	−	0.0951538i
$781$	0.531974	−	0.0938013i	0.0190355	−	0.00335647i
$782$	13.5438	−	11.3646i	0.484326	−	0.406398i
$783$	−21.0871	+	0.638826i	−0.753593	+	0.0228298i
$784$	−3.91489	−	1.42490i	−0.139817	−	0.0508894i
$785$	35.9895	−	42.8906i	1.28452	−	1.53083i
$786$	42.0142	+	30.6241i	1.49860	+	1.09232i
$787$	19.3803	−	11.1892i	0.690834	−	0.398853i	−0.113090	−	0.993585i	$-0.536075\pi$
$787$	19.3803	−	11.1892i	0.690834	−	0.398853i	0.803924	+	0.594731i	$0.202742\pi$
$788$	6.39701	+	1.12797i	0.227884	+	0.0401821i
$789$	36.6811	+	10.5793i	1.30588	+	0.376633i
$790$	12.9087	+	22.3585i	0.459270	+	0.795479i
$791$	4.26373	−	7.38500i	0.151601	−	0.262580i
$792$	2.74952	−	2.13455i	0.0976998	−	0.0758479i
$793$	0.873860	−	2.40091i	0.0310317	−	0.0852589i
$794$	31.6512	−	11.5201i	1.12326	−	0.408833i
$795$	10.2761	+	15.2857i	0.364457	+	0.542129i
$796$	2.59592	+	14.7222i	0.0920099	+	0.521814i
$797$	43.7593			1.55003			0.775016	−	0.631941i	$-0.217742\pi$
$797$	43.7593			1.55003			0.775016	+	0.631941i	$0.217742\pi$
$798$	−27.7449	−	22.9564i	−0.982160	−	0.812649i
$799$	11.7883			0.417042
$800$	−6.96998	−	39.5287i	−0.246426	−	1.39755i
$801$	22.6494	−	11.9536i	0.800278	−	0.422358i
$802$	59.0852	−	21.5052i	2.08637	−	0.759377i
$803$	−14.0196	+	38.5187i	−0.494743	+	1.35929i
$804$	14.9836	−	14.4249i	0.528430	−	0.508728i
$805$	9.42548	−	16.3254i	0.332204	−	0.575395i
$806$	11.0077	+	19.0658i	0.387729	+	0.671565i
$807$	−5.62085	+	19.4889i	−0.197863	+	0.686042i
$808$	1.24833	+	0.220114i	0.0439161	+	0.00774360i
$809$	−27.8324	+	16.0690i	−0.978534	+	0.564957i	−0.901827	−	0.432097i	$-0.857774\pi$
$809$	−27.8324	+	16.0690i	−0.978534	+	0.564957i	−0.0767067	+	0.997054i	$0.524441\pi$
$810$	−32.5504	−	45.3873i	−1.14371	−	1.59475i
$811$	18.1542	−	21.6354i	0.637481	−	0.759720i	−0.346489	−	0.938054i	$-0.612626\pi$
$811$	18.1542	−	21.6354i	0.637481	−	0.759720i	0.983970	+	0.178334i	$0.0570706\pi$
$812$	−16.4766	−	5.99697i	−0.578214	−	0.210453i
$813$	−14.0695	+	3.48491i	−0.493439	+	0.122221i
$814$	−32.8624	+	27.5749i	−1.15183	+	0.966499i
$815$	−7.30231	+	1.28759i	−0.255789	+	0.0451024i
$816$	−3.10641	+	29.1239i	−0.108746	+	1.01954i
$817$	−5.08609	−	17.1885i	−0.177940	−	0.601349i
$818$			38.2757i			1.33828i
$819$	18.9995	+	0.722090i	0.663897	+	0.0252319i
$820$	20.7324	+	24.7079i	0.724008	+	0.862839i
$821$	−15.2947	−	42.0220i	−0.533790	−	1.46658i	−0.854526	−	0.519408i	$-0.826153\pi$
$821$	−15.2947	−	42.0220i	−0.533790	−	1.46658i	0.320736	−	0.947169i	$-0.396070\pi$
$822$	14.7692	−	30.1634i	0.515136	−	1.05207i
$823$	−12.7225	−	10.6754i	−0.443478	−	0.372122i	0.393531	−	0.919311i	$-0.371253\pi$
$823$	−12.7225	−	10.6754i	−0.443478	−	0.372122i	−0.837009	+	0.547189i	$0.815698\pi$
$824$	6.01140	+	3.47069i	0.209417	+	0.120907i
$825$	20.2960	−	8.99893i	0.706617	−	0.313303i
$826$	8.49839	−	48.1967i	0.295697	−	1.67698i
$827$	−7.61025	+	43.1599i	−0.264634	+	1.50082i	0.505441	+	0.862861i	$0.331330\pi$
$827$	−7.61025	+	43.1599i	−0.264634	+	1.50082i	−0.770075	+	0.637954i	$0.779781\pi$
$828$	−11.9798	+	3.85170i	−0.416326	+	0.133856i
$829$	−13.7220	−	7.92240i	−0.476585	−	0.275156i	0.242407	−	0.970175i	$-0.422063\pi$
$829$	−13.7220	−	7.92240i	−0.476585	−	0.275156i	−0.718992	+	0.695018i	$0.755396\pi$
$830$	−13.4954	−	11.3240i	−0.468431	−	0.393060i
$831$	23.0756	+	11.2988i	0.800485	+	0.391950i
$832$	−5.22083	−	14.3441i	−0.181000	−	0.497293i
$833$	2.30650	+	2.74878i	0.0799155	+	0.0952396i
$834$	−2.07427	−	30.3349i	−0.0718261	−	1.05041i
$835$			74.0462i			2.56247i
$836$	−18.6065	−	1.14339i	−0.643518	−	0.0395448i
$837$	−7.18693	+	21.7762i	−0.248417	+	0.752694i
$838$	−51.5134	+	9.08319i	−1.77950	+	0.313774i
$839$	35.1972	−	29.5340i	1.21514	−	1.01963i	0.216079	−	0.976376i	$-0.430673\pi$
$839$	35.1972	−	29.5340i	1.21514	−	1.01963i	0.999064	−	0.0432501i	$-0.0137712\pi$
$840$	1.56271	+	6.30909i	0.0539188	+	0.217684i
$841$	11.7609	+	4.28063i	0.405550	+	0.147608i
$842$	−36.5173	+	43.5196i	−1.25847	+	1.49978i
$843$	6.02938	−	8.27191i	0.207663	−	0.284900i
$844$	−6.01639	+	3.47356i	−0.207093	+	0.119565i
$845$	−20.0969	−	3.54363i	−0.691355	−	0.121905i
$846$	−16.6271	−	6.77743i	−0.571650	−	0.233013i
$847$	−6.22482	−	10.7817i	−0.213887	−	0.370463i
$848$	−7.35584	+	12.7407i	−0.252601	+	0.437517i
$849$	−26.2605	−	27.2775i	−0.901258	−	0.936162i
$850$	−13.2985	+	36.5374i	−0.456136	+	1.25322i
$851$	−20.4055	+	7.42699i	−0.699491	+	0.254594i
$852$	0.558797	−	0.375662i	0.0191441	−	0.0128700i
$853$	−4.05515	−	22.9979i	−0.138846	−	0.787434i	−0.972104	−	0.234550i	$-0.924638\pi$
$853$	−4.05515	−	22.9979i	−0.138846	−	0.787434i	0.833258	−	0.552884i	$-0.186473\pi$
$854$	4.73346			0.161976
$855$	4.15466	−	41.6760i	0.142086	−	1.42529i
$856$	2.69326			0.0920536
$857$	−1.22427	−	6.94316i	−0.0418201	−	0.237174i	0.956732	−	0.290972i	$-0.0939785\pi$
$857$	−1.22427	−	6.94316i	−0.0418201	−	0.237174i	−0.998552	+	0.0537977i	$0.982867\pi$
$858$	17.4803	−	11.7514i	0.596766	−	0.401188i
$859$	35.1960	−	12.8103i	1.20087	−	0.437081i	0.337343	−	0.941382i	$-0.390472\pi$
$859$	35.1960	−	12.8103i	1.20087	−	0.437081i	0.863528	+	0.504301i	$0.168250\pi$
$860$	7.90299	−	21.7133i	0.269490	−	0.740417i
$861$	−16.9744	−	17.6318i	−0.578488	−	0.600891i
$862$	−9.57098	+	16.5774i	−0.325989	+	0.564629i
$863$	13.0428	+	22.5907i	0.443981	+	0.768998i	0.997981	−	0.0635192i	$-0.0202324\pi$
$863$	13.0428	+	22.5907i	0.443981	+	0.768998i	−0.554000	+	0.832517i	$0.686899\pi$
$864$	18.7833	−	34.9358i	0.639020	−	1.18854i
$865$	−13.6061	−	2.39913i	−0.462622	−	0.0815728i
$866$	−61.1337	+	35.2956i	−2.07741	+	1.19939i
$867$	−2.48468	+	3.40881i	−0.0843840	+	0.115769i
$868$	−12.2508	+	14.5999i	−0.415818	+	0.495553i
$869$	−9.52977	−	3.46855i	−0.323275	−	0.117663i
$870$	−10.4926	−	42.3612i	−0.355731	−	1.43618i
$871$	−13.4995	+	11.3275i	−0.457414	+	0.383816i
$872$	−2.80725	+	0.494993i	−0.0950653	+	0.0167626i
$873$	2.45574	−	11.3808i	0.0831141	−	0.385182i
$874$	−18.5165	−	8.05752i	−0.626329	−	0.272550i
$875$			2.03553i			0.0688136i
$876$	3.48567	+	50.9757i	0.117770	+	1.72231i
$877$	−11.0745	−	13.1981i	−0.373959	−	0.445667i	0.545939	−	0.837825i	$-0.316173\pi$
$877$	−11.0745	−	13.1981i	−0.373959	−	0.445667i	−0.919898	+	0.392158i	$0.871729\pi$
$878$	24.5950	+	67.5743i	0.830042	+	2.28052i
$879$	−31.7488	−	15.5455i	−1.07086	−	0.524337i
$880$	26.5017	+	22.2375i	0.893371	+	0.749627i
$881$	−17.2569	−	9.96325i	−0.581398	−	0.335670i	0.180291	−	0.983613i	$-0.442296\pi$
$881$	−17.2569	−	9.96325i	−0.581398	−	0.335670i	−0.761689	+	0.647943i	$0.775630\pi$
$882$	−1.67290	−	5.20313i	−0.0563293	−	0.175199i
$883$	−1.89794	+	10.7637i	−0.0638707	+	0.362229i	0.936075	+	0.351801i	$0.114431\pi$
$883$	−1.89794	+	10.7637i	−0.0638707	+	0.362229i	−0.999946	+	0.0104281i	$0.996681\pi$
$884$	−2.99326	+	16.9756i	−0.100674	+	0.570952i
$885$	52.0348	−	23.0714i	1.74913	−	0.775537i
$886$	35.6442	+	20.5792i	1.19749	+	0.691372i
$887$	−4.00496	−	3.36056i	−0.134473	−	0.112837i	0.573070	−	0.819506i	$-0.305752\pi$
$887$	−4.00496	−	3.36056i	−0.134473	−	0.112837i	−0.707544	+	0.706670i	$0.750197\pi$
$888$	3.29257	−	6.72446i	0.110491	−	0.225658i
$889$	4.44220	+	12.2049i	0.148987	+	0.409338i
$890$	34.0536	+	40.5835i	1.14148	+	1.36036i
$891$	21.2549	+	5.43876i	0.712065	+	0.182205i
$892$		−	25.1291i		−	0.841384i
$893$	−6.00423	−	12.0513i	−0.200924	−	0.403281i
$894$	−4.48180	+	42.0188i	−0.149894	+	1.40532i
$895$	−1.72368	+	0.303931i	−0.0576162	+	0.0101593i
$896$	−7.12618	+	5.97957i	−0.238069	+	0.199764i
$897$	10.3492	−	2.56343i	0.345551	−	0.0855904i
$898$	44.3340	+	16.1363i	1.47944	+	0.538474i
$899$	−11.5174	+	13.7258i	−0.384125	+	0.457783i
$900$	18.5809	−	20.5088i	0.619363	−	0.683625i
$901$	10.9735	−	6.33556i	0.365581	−	0.211068i
$902$	−26.7016	−	4.70821i	−0.889065	−	0.156766i
$903$	−4.85892	+	16.8471i	−0.161695	+	0.560636i
$904$	0.824394	+	1.42789i	0.0274189	+	0.0474910i
$905$	3.08206	−	5.33828i	0.102451	−	0.177450i
$906$	−34.8401	+	33.5411i	−1.15749	+	1.11433i
$907$	−4.16304	+	11.4378i	−0.138231	+	0.379788i	−0.989421	−	0.145070i	$-0.953659\pi$
$907$	−4.16304	+	11.4378i	−0.138231	+	0.379788i	0.851190	+	0.524858i	$0.175881\pi$
$908$	23.2237	−	8.45275i	0.770706	−	0.280514i
$909$	3.72915	+	7.06595i	0.123688	+	0.234363i
$910$	6.82980	+	38.7337i	0.226406	+	1.28401i
$911$	4.05874			0.134472			0.0672360	−	0.997737i	$-0.478582\pi$
$911$	4.05874			0.134472			0.0672360	+	0.997737i	$0.478582\pi$
$912$	31.3558	−	11.6582i	1.03829	−	0.386040i
$913$	6.92015			0.229024
$914$	−7.72822	−	43.8289i	−0.255627	−	1.44973i
$915$	3.07148	+	4.56882i	0.101540	+	0.151040i
$916$	3.41513	−	1.24300i	0.112839	−	0.0410700i
$917$	13.0430	−	35.8352i	0.430716	−	1.18338i
$918$	−32.6789	+	20.2106i	−1.07856	+	0.667051i
$919$	−14.3647	+	24.8804i	−0.473848	+	0.820729i	−0.999552	−	0.0299386i	$-0.990469\pi$
$919$	−14.3647	+	24.8804i	−0.473848	+	0.820729i	0.525703	+	0.850668i	$0.323802\pi$
$920$	1.82242	+	3.15652i	0.0600834	+	0.104068i
$921$	2.42359	+	0.698996i	0.0798601	+	0.0230327i
$922$	10.5904	+	1.86737i	0.348776	+	0.0614987i
$923$	−0.494070	+	0.285252i	−0.0162625	+	0.00938917i
$924$	14.7355	+	10.7407i	0.484762	+	0.353343i
$925$	30.6968	−	36.5830i	1.00930	−	1.20284i
$926$	3.95731	+	1.44034i	0.130045	+	0.0473326i
$927$	5.95553	+	43.3443i	0.195605	+	1.42361i
$928$	23.7419	−	19.9218i	0.779366	−	0.653965i
$929$	−10.5318	+	1.85704i	−0.345537	+	0.0609274i	−0.343723	−	0.939071i	$-0.611688\pi$
$929$	−10.5318	+	1.85704i	−0.345537	+	0.0609274i	−0.00181316	+	0.999998i	$0.500577\pi$
$930$	−47.1691	−	5.03114i	−1.54674	−	0.164978i
$931$	1.63531	−	3.75800i	0.0535951	−	0.123164i
$932$			46.7578i			1.53160i
$933$	45.5352	−	3.11365i	1.49075	−	0.101936i
$934$	−29.9922	−	35.7433i	−0.981374	−	1.16956i
$935$	−10.1912	−	28.0000i	−0.333287	−	0.915697i
$936$	−1.95769	+	3.11159i	−0.0639892	+	0.101706i
$937$	11.7918	+	9.89450i	0.385221	+	0.323239i	0.814748	−	0.579815i	$-0.196875\pi$
$937$	11.7918	+	9.89450i	0.385221	+	0.323239i	−0.429527	+	0.903054i	$0.641320\pi$
$938$	−28.2738	−	16.3239i	−0.923172	−	0.532994i
$939$	−16.0637	−	36.2297i	−0.524219	−	1.18231i
$940$	3.01388	−	17.0926i	0.0983021	−	0.557499i
$941$	4.24400	−	24.0689i	0.138351	−	0.784625i	−0.834117	−	0.551587i	$-0.814022\pi$
$941$	4.24400	−	24.0689i	0.138351	−	0.784625i	0.972468	−	0.233038i	$-0.0748665\pi$
$942$	23.7799	+	53.6326i	0.774790	+	1.74745i
$943$	−11.8859	−	6.86231i	−0.387057	−	0.223468i
$944$	34.8274	+	29.2237i	1.13354	+	0.951149i
$945$	−25.3713	+	32.1663i	−0.825330	+	1.04637i
$946$	6.64345	+	18.2527i	0.215997	+	0.593448i
$947$	35.5983	+	42.4244i	1.15679	+	1.37861i	0.912587	+	0.408883i	$0.134082\pi$
$947$	35.5983	+	42.4244i	1.15679	+	1.37861i	0.244202	+	0.969724i	$0.421474\pi$
$948$	−12.6117	+	0.862377i	−0.409610	+	0.0280087i
$949$		−	43.2917i		−	1.40531i
$950$	44.1259	−	5.01466i	1.43163	−	0.162697i
$951$	9.11259	+	0.971967i	0.295496	+	0.0315182i
$952$	4.40354	−	0.776462i	0.142719	−	0.0251653i
$953$	−31.1019	+	26.0976i	−1.00749	+	0.845384i	−0.988004	−	0.154426i	$-0.950647\pi$
$953$	−31.1019	+	26.0976i	−1.00749	+	0.845384i	−0.0194854	+	0.999810i	$0.506203\pi$
$954$	−19.1202	+	2.62713i	−0.619041	+	0.0850565i
$955$	−41.0534	−	14.9422i	−1.32846	−	0.483519i
$956$	19.9089	−	23.7265i	0.643900	−	0.767371i
$957$	13.8533	+	10.0977i	0.447814	+	0.326411i
$958$	−48.0505	+	27.7419i	−1.55244	+	0.896301i
$959$	−24.2604	−	4.27776i	−0.783408	−	0.138136i
$960$	31.6028	+	9.11467i	1.01998	+	0.294175i
$961$	−5.76197	−	9.98003i	−0.185870	−	0.321937i
$962$	22.6535	−	39.2370i	0.730378	−	1.26505i
$963$	10.4100	+	13.4091i	0.335457	+	0.432103i
$964$	4.65565	−	12.7913i	0.149948	−	0.411980i
$965$	−77.1597	+	28.0838i	−2.48386	+	0.904051i
$966$	11.0203	+	16.3927i	0.354574	+	0.527428i
$967$	−0.448828	−	2.54543i	−0.0144333	−	0.0818556i	0.976740	−	0.214426i	$-0.0687881\pi$
$967$	−0.448828	−	2.54543i	−0.0144333	−	0.0818556i	−0.991174	+	0.132570i	$0.957677\pi$
$968$	2.40714			0.0773685
$969$	−28.4090	−	4.80743i	−0.912628	−	0.154437i
$970$	24.0845			0.773306
$971$	0.137845	+	0.781759i	0.00442366	+	0.0250878i	0.986940	−	0.161090i	$-0.0515010\pi$
$971$	0.137845	+	0.781759i	0.00442366	+	0.0250878i	−0.982516	+	0.186178i	$0.940390\pi$
$972$	26.9680	−	4.54131i	0.864999	−	0.145663i
$973$	−20.9575	+	7.62792i	−0.671868	+	0.244540i
$974$	17.9981	−	49.4495i	0.576698	−	1.58446i
$975$	−16.8920	+	16.2622i	−0.540978	+	0.520808i
$976$	−2.19862	+	3.80812i	−0.0703760	+	0.121895i
$977$	18.5513	+	32.1317i	0.593508	+	1.02799i	0.993756	+	0.111578i	$0.0355906\pi$
$977$	18.5513	+	32.1317i	0.593508	+	1.02799i	−0.400248	+	0.916407i	$0.631076\pi$
$978$	2.15311	−	7.46537i	0.0688489	−	0.238716i
$979$	−20.4942	−	3.61369i	−0.654998	−	0.115494i
$980$	4.57531	−	2.64156i	0.146153	−	0.0843814i
$981$	−13.3150	−	12.0634i	−0.425116	−	0.385155i
$982$	17.0230	−	20.2873i	0.543227	−	0.647392i
$983$	3.33834	+	1.21506i	0.106476	+	0.0387542i	0.394709	−	0.918806i	$-0.370845\pi$
$983$	3.33834	+	1.21506i	0.106476	+	0.0387542i	−0.288233	+	0.957560i	$0.593068\pi$
$984$	4.59339	−	1.13775i	0.146432	−	0.0362701i
$985$	9.08442	−	7.62273i	0.289454	−	0.242880i
$986$	−29.5667	+	5.21341i	−0.941596	+	0.166029i
$987$	−1.39683	+	13.0959i	−0.0444617	+	0.416847i
$988$	18.8789	−	5.58627i	0.600616	−	0.177723i
$989$			9.83235i			0.312651i
$990$	−1.72364	+	45.3522i	−0.0547809	+	1.44139i
$991$	16.2156	+	19.3250i	0.515104	+	0.613877i	0.959416	−	0.281995i	$-0.0909962\pi$
$991$	16.2156	+	19.3250i	0.515104	+	0.613877i	−0.444312	+	0.895872i	$0.646552\pi$
$992$	−11.5220	−	31.6565i	−0.365824	−	1.00509i
$993$	20.2130	−	41.2812i	0.641439	−	1.31002i
$994$	−0.809656	−	0.679382i	−0.0256807	−	0.0215487i
$995$	23.6357	+	13.6461i	0.749303	+	0.432610i
$996$	7.88559	−	3.49634i	0.249864	−	0.110786i
$997$	−4.50827	+	25.5677i	−0.142778	+	0.809737i	0.826346	+	0.563163i	$0.190416\pi$
$997$	−4.50827	+	25.5677i	−0.142778	+	0.809737i	−0.969124	+	0.246574i	$0.920695\pi$
$998$	9.86001	−	55.9189i	0.312113	−	1.77008i
$999$	46.2060	−	9.59843i	1.46189	−	0.303681i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.2.j.b.29.2	yes	24
3.2	odd	2	inner	57.2.j.b.29.3	yes	24
4.3	odd	2		912.2.cc.e.257.1		24
12.11	even	2		912.2.cc.e.257.3		24
19.2	odd	18	inner	57.2.j.b.2.3	yes	24
19.6	even	9		1083.2.d.d.1082.7		24
19.13	odd	18		1083.2.d.d.1082.17		24
57.2	even	18	inner	57.2.j.b.2.2	✓	24
57.32	even	18		1083.2.d.d.1082.8		24
57.44	odd	18		1083.2.d.d.1082.18		24
76.59	even	18		912.2.cc.e.401.3		24
228.59	odd	18		912.2.cc.e.401.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.j.b.2.2	✓	24	57.2	even	18	inner
57.2.j.b.2.3	yes	24	19.2	odd	18	inner
57.2.j.b.29.2	yes	24	1.1	even	1	trivial
57.2.j.b.29.3	yes	24	3.2	odd	2	inner
912.2.cc.e.257.1		24	4.3	odd	2
912.2.cc.e.257.3		24	12.11	even	2
912.2.cc.e.401.1		24	228.59	odd	18
912.2.cc.e.401.3		24	76.59	even	18
1083.2.d.d.1082.7		24	19.6	even	9
1083.2.d.d.1082.8		24	57.32	even	18
1083.2.d.d.1082.17		24	19.13	odd	18
1083.2.d.d.1082.18		24	57.44	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.336464 - 1.90818i) q^{2} +(1.43743 - 0.966337i) q^{3} +(-1.64856 + 0.600025i) q^{4} +(-1.09544 + 3.00968i) q^{5} +(-2.32759 - 2.41773i) q^{6} +(-1.23083 + 2.13186i) q^{7} +(-0.237981 - 0.412196i) q^{8} +(1.13238 - 2.77808i) q^{9} +O(q^{10})\)	\(q+(-0.336464 - 1.90818i) q^{2} +(1.43743 - 0.966337i) q^{3} +(-1.64856 + 0.600025i) q^{4} +(-1.09544 + 3.00968i) q^{5} +(-2.32759 - 2.41773i) q^{6} +(-1.23083 + 2.13186i) q^{7} +(-0.237981 - 0.412196i) q^{8} +(1.13238 - 2.77808i) q^{9} +(6.11159 + 1.07764i) q^{10} +(-2.11115 + 1.21887i) q^{11} +(-1.78985 + 2.45555i) q^{12} +(1.65491 - 1.97225i) q^{13} +(4.48210 + 1.63135i) q^{14} +(1.33376 + 5.38476i) q^{15} +(-3.39430 + 2.84816i) q^{16} +(3.75838 - 0.662704i) q^{17} +(-5.68207 - 1.22607i) q^{18} +(-2.59177 - 3.50468i) q^{19} -5.61892i q^{20} +(0.290870 + 4.25378i) q^{21} +(3.03615 + 3.61834i) q^{22} +(0.817753 + 2.24676i) q^{23} +(-0.740401 - 0.362531i) q^{24} +(-4.02800 - 3.37989i) q^{25} +(-4.32022 - 2.49428i) q^{26} +(-1.05684 - 5.08754i) q^{27} +(0.749922 - 4.25302i) q^{28} +(0.705026 - 3.99840i) q^{29} +(9.82632 - 4.35683i) q^{30} +(-3.82192 - 2.20658i) q^{31} +(5.84764 + 4.90675i) q^{32} +(-1.85677 + 3.79212i) q^{33} +(-2.52912 - 6.94869i) q^{34} +(-5.06793 - 6.03972i) q^{35} +(-0.199882 + 5.25927i) q^{36} +9.08219i q^{37} +(-5.81552 + 6.12475i) q^{38} +(0.472956 - 4.43416i) q^{39} +(1.50127 - 0.264715i) q^{40} +(-4.39728 + 3.68975i) q^{41} +(8.01912 - 1.98628i) q^{42} +(3.86432 + 1.40650i) q^{43} +(2.74899 - 3.27612i) q^{44} +(7.12068 + 6.45132i) q^{45} +(4.01207 - 2.31637i) q^{46} +(3.04197 + 0.536381i) q^{47} +(-2.12677 + 7.37405i) q^{48} +(0.470118 + 0.814268i) q^{49} +(-5.09416 + 8.82335i) q^{50} +(4.76200 - 4.58445i) q^{51} +(-1.54482 + 4.24435i) q^{52} +(3.11998 - 1.13558i) q^{53} +(-9.35235 + 3.72842i) q^{54} +(-1.35579 - 7.68908i) q^{55} +1.17166 q^{56} +(-7.11217 - 2.53319i) q^{57} -7.86688 q^{58} +(-1.78173 - 10.1047i) q^{59} +(-5.42977 - 8.07678i) q^{60} +(0.932543 - 0.339418i) q^{61} +(-2.92462 + 8.03534i) q^{62} +(4.52870 + 5.83342i) q^{63} +(2.96450 - 5.13466i) q^{64} +(4.12299 + 7.14123i) q^{65} +(7.86077 + 2.26715i) q^{66} +(-6.74077 - 1.18858i) q^{67} +(-5.79826 + 3.34763i) q^{68} +(3.34659 + 2.43932i) q^{69} +(-9.81970 + 11.7027i) q^{70} +(-0.208227 - 0.0757884i) q^{71} +(-1.41460 + 0.194366i) q^{72} +(12.8811 - 10.8085i) q^{73} +(17.3304 - 3.05582i) q^{74} +(-9.05606 - 0.965937i) q^{75} +(6.37556 + 4.22253i) q^{76} -6.00089i q^{77} +(-8.62030 + 0.589448i) q^{78} +(2.67409 + 3.18686i) q^{79} +(-4.85382 - 13.3357i) q^{80} +(-6.43541 - 6.29170i) q^{81} +(8.52023 + 7.14932i) q^{82} +(-2.45843 - 1.41938i) q^{83} +(-3.03189 - 6.83807i) q^{84} +(-2.12253 + 12.0375i) q^{85} +(1.38365 - 7.84704i) q^{86} +(-2.85038 - 6.42870i) q^{87} +(1.00483 + 0.580137i) q^{88} +(6.53953 + 5.48732i) q^{89} +(9.91443 - 15.7582i) q^{90} +(2.16764 + 5.95553i) q^{91} +(-2.69622 - 3.21323i) q^{92} +(-7.62602 + 0.521460i) q^{93} -5.98510i q^{94} +(13.3871 - 3.96125i) q^{95} +(13.1471 + 1.40230i) q^{96} +(3.82196 - 0.673914i) q^{97} +(1.39559 - 1.17104i) q^{98} +(0.995488 + 7.24515i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9}+O(q^{10}) \) 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9	\( 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9} - 6 q^{10} + 9 q^{12} + 6 q^{13} - 9 q^{15} + 30 q^{16} - 12 q^{19} - 6 q^{21} + 24 q^{22} - 21 q^{24} + 12 q^{25} - 27 q^{27} - 48 q^{28} + 42 q^{30} - 18 q^{31} + 21 q^{33} - 42 q^{34} + 63 q^{36} + 30 q^{40} + 105 q^{42} + 54 q^{43} + 6 q^{45} - 54 q^{46} - 33 q^{48} + 6 q^{49} + 3 q^{51} - 48 q^{52} - 87 q^{54} - 90 q^{55} - 6 q^{57} + 24 q^{58} - 66 q^{60} - 6 q^{61} - 9 q^{63} + 18 q^{64} - 57 q^{66} - 36 q^{69} + 18 q^{70} + 24 q^{72} + 90 q^{73} + 12 q^{76} + 9 q^{78} + 30 q^{79} + 3 q^{81} + 126 q^{82} + 99 q^{84} - 6 q^{85} + 15 q^{87} + 54 q^{88} + 24 q^{90} + 66 q^{91} + 33 q^{93} - 18 q^{96} - 78 q^{97} + 12 q^{99}+O(q^{100}) \) 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9 - 6 * q^10 + 9 * q^12 + 6 * q^13 - 9 * q^15 + 30 * q^16 - 12 * q^19 - 6 * q^21 + 24 * q^22 - 21 * q^24 + 12 * q^25 - 27 * q^27 - 48 * q^28 + 42 * q^30 - 18 * q^31 + 21 * q^33 - 42 * q^34 + 63 * q^36 + 30 * q^40 + 105 * q^42 + 54 * q^43 + 6 * q^45 - 54 * q^46 - 33 * q^48 + 6 * q^49 + 3 * q^51 - 48 * q^52 - 87 * q^54 - 90 * q^55 - 6 * q^57 + 24 * q^58 - 66 * q^60 - 6 * q^61 - 9 * q^63 + 18 * q^64 - 57 * q^66 - 36 * q^69 + 18 * q^70 + 24 * q^72 + 90 * q^73 + 12 * q^76 + 9 * q^78 + 30 * q^79 + 3 * q^81 + 126 * q^82 + 99 * q^84 - 6 * q^85 + 15 * q^87 + 54 * q^88 + 24 * q^90 + 66 * q^91 + 33 * q^93 - 18 * q^96 - 78 * q^97 + 12 * q^99

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