LMFDB - Embedded newform 60.3.c.a.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,3,Mod(31,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("60.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	60.c (of order $2$, degree $1$, 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:	$1.63488158616$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.85100625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + x^{5} + 3x^{4} + 2x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + x^5 + 3x^4 + 2x^3 - 8x^2 - 8*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			31.3
Root			$1.40906 + 0.120653i$ of defining polynomial
Character	$\chi$	$=$	60.31
Dual form			60.3.c.a.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.438172 - 1.95141i) q^{2} -1.73205i q^{3} +(-3.61601 - 1.71011i) q^{4} +2.23607 q^{5} +(-3.37994 - 0.758935i) q^{6} -6.33166i q^{7} +(-4.92155 + 6.30701i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(0.438172 - 1.95141i) q^{2} -1.73205i q^{3} +(-3.61601 - 1.71011i) q^{4} +2.23607 q^{5} +(-3.37994 - 0.758935i) q^{6} -6.33166i q^{7} +(-4.92155 + 6.30701i) q^{8} -3.00000 q^{9} +(0.979781 - 4.36349i) q^{10} +9.27963i q^{11} +(-2.96199 + 6.26312i) q^{12} +18.5674 q^{13} +(-12.3557 - 2.77436i) q^{14} -3.87298i q^{15} +(10.1511 + 12.3675i) q^{16} +13.9110 q^{17} +(-1.31451 + 5.85423i) q^{18} -17.2468i q^{19} +(-8.08565 - 3.82391i) q^{20} -10.9668 q^{21} +(18.1084 + 4.06607i) q^{22} +33.7148i q^{23} +(10.9241 + 8.52438i) q^{24} +5.00000 q^{25} +(8.13571 - 36.2327i) q^{26} +5.19615i q^{27} +(-10.8278 + 22.8954i) q^{28} -28.6177 q^{29} +(-7.55778 - 1.69703i) q^{30} +23.4939i q^{31} +(28.5820 - 14.3898i) q^{32} +16.0728 q^{33} +(6.09542 - 27.1461i) q^{34} -14.1580i q^{35} +(10.8480 + 5.13032i) q^{36} -67.3338 q^{37} +(-33.6556 - 7.55706i) q^{38} -32.1597i q^{39} +(-11.0049 + 14.1029i) q^{40} -44.0791 q^{41} +(-4.80532 + 21.4007i) q^{42} -50.2937i q^{43} +(15.8691 - 33.5552i) q^{44} -6.70820 q^{45} +(65.7915 + 14.7729i) q^{46} +31.1594i q^{47} +(21.4212 - 17.5822i) q^{48} +8.91003 q^{49} +(2.19086 - 9.75706i) q^{50} -24.0946i q^{51} +(-67.1400 - 31.7522i) q^{52} +81.6070 q^{53} +(10.1398 + 2.27681i) q^{54} +20.7499i q^{55} +(39.9338 + 31.1616i) q^{56} -29.8724 q^{57} +(-12.5395 + 55.8449i) q^{58} +19.2751i q^{59} +(-6.62321 + 14.0048i) q^{60} -53.1563 q^{61} +(45.8462 + 10.2943i) q^{62} +18.9950i q^{63} +(-15.5566 - 62.0805i) q^{64} +41.5180 q^{65} +(7.04264 - 31.3646i) q^{66} +4.49911i q^{67} +(-50.3025 - 23.7893i) q^{68} +58.3958 q^{69} +(-27.6281 - 6.20365i) q^{70} +13.3360i q^{71} +(14.7647 - 18.9210i) q^{72} +40.8904 q^{73} +(-29.5037 + 131.396i) q^{74} -8.66025i q^{75} +(-29.4939 + 62.3647i) q^{76} +58.7555 q^{77} +(-62.7568 - 14.0915i) q^{78} +141.309i q^{79} +(22.6985 + 27.6546i) q^{80} +9.00000 q^{81} +(-19.3142 + 86.0164i) q^{82} -69.8503i q^{83} +(39.6559 + 18.7543i) q^{84} +31.1060 q^{85} +(-98.1438 - 22.0373i) q^{86} +49.5673i q^{87} +(-58.5266 - 45.6702i) q^{88} -46.3079 q^{89} +(-2.93934 + 13.0905i) q^{90} -117.563i q^{91} +(57.6559 - 121.913i) q^{92} +40.6926 q^{93} +(60.8049 + 13.6532i) q^{94} -38.5651i q^{95} +(-24.9239 - 49.5055i) q^{96} +68.5543 q^{97} +(3.90412 - 17.3871i) q^{98} -27.8389i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 10 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 + 10 * q^4 - 6 * q^6 - 20 * q^8 - 24 * q^9	$ 8 q + 4 q^{2} + 10 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9} + 10 q^{10} + 16 q^{13} - 20 q^{14} + 34 q^{16} - 12 q^{18} - 40 q^{20} - 48 q^{21} + 68 q^{22} + 18 q^{24} + 40 q^{25} - 36 q^{26} + 28 q^{28} + 64 q^{29} - 76 q^{32} - 92 q^{34} - 30 q^{36} - 112 q^{37} - 40 q^{38} - 10 q^{40} - 16 q^{41} + 108 q^{42} + 172 q^{44} + 152 q^{46} + 48 q^{48} - 56 q^{49} + 20 q^{50} - 128 q^{52} + 352 q^{53} + 18 q^{54} + 116 q^{56} + 144 q^{57} - 204 q^{58} + 30 q^{60} - 176 q^{61} - 56 q^{62} - 110 q^{64} - 80 q^{65} + 108 q^{66} - 184 q^{68} - 96 q^{69} - 60 q^{70} + 60 q^{72} - 240 q^{73} + 132 q^{74} - 24 q^{76} - 288 q^{77} - 240 q^{78} - 80 q^{80} + 72 q^{81} + 40 q^{82} - 36 q^{84} + 160 q^{85} - 200 q^{86} + 140 q^{88} + 80 q^{89} - 30 q^{90} + 144 q^{92} + 144 q^{93} - 96 q^{94} - 174 q^{96} + 432 q^{97} + 660 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 + 10 * q^4 - 6 * q^6 - 20 * q^8 - 24 * q^9 + 10 * q^10 + 16 * q^13 - 20 * q^14 + 34 * q^16 - 12 * q^18 - 40 * q^20 - 48 * q^21 + 68 * q^22 + 18 * q^24 + 40 * q^25 - 36 * q^26 + 28 * q^28 + 64 * q^29 - 76 * q^32 - 92 * q^34 - 30 * q^36 - 112 * q^37 - 40 * q^38 - 10 * q^40 - 16 * q^41 + 108 * q^42 + 172 * q^44 + 152 * q^46 + 48 * q^48 - 56 * q^49 + 20 * q^50 - 128 * q^52 + 352 * q^53 + 18 * q^54 + 116 * q^56 + 144 * q^57 - 204 * q^58 + 30 * q^60 - 176 * q^61 - 56 * q^62 - 110 * q^64 - 80 * q^65 + 108 * q^66 - 184 * q^68 - 96 * q^69 - 60 * q^70 + 60 * q^72 - 240 * q^73 + 132 * q^74 - 24 * q^76 - 288 * q^77 - 240 * q^78 - 80 * q^80 + 72 * q^81 + 40 * q^82 - 36 * q^84 + 160 * q^85 - 200 * q^86 + 140 * q^88 + 80 * q^89 - 30 * q^90 + 144 * q^92 + 144 * q^93 - 96 * q^94 - 174 * q^96 + 432 * q^97 + 660 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	0.438172	−	1.95141i	0.219086	−	0.975706i
$2$	0.438172	−	1.95141i	0.219086	−	0.975706i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−3.61601	−	1.71011i	−0.904003	−	0.427526i
$5$	2.23607			0.447214
$5$	2.23607			0.447214
$6$	−3.37994	−	0.758935i	−0.563324	−	0.126489i
$7$		−	6.33166i		−	0.904523i	−0.891885	−	0.452262i	$-0.850617\pi$
$7$		−	6.33166i		−	0.904523i	0.891885	−	0.452262i	$-0.149383\pi$
$8$	−4.92155	+	6.30701i	−0.615194	+	0.788376i
$9$	−3.00000			−0.333333
$10$	0.979781	−	4.36349i	0.0979781	−	0.436349i
$11$			9.27963i			0.843602i	0.906688	+	0.421801i	$0.138602\pi$
$11$			9.27963i			0.843602i	−0.906688	+	0.421801i	$0.861398\pi$
$12$	−2.96199	+	6.26312i	−0.246833	+	0.521926i
$13$	18.5674			1.42826			0.714131	−	0.700012i	$-0.246822\pi$
$13$	18.5674			1.42826			0.714131	+	0.700012i	$0.246822\pi$
$14$	−12.3557	−	2.77436i	−0.882549	−	0.198168i
$15$		−	3.87298i		−	0.258199i
$16$	10.1511	+	12.3675i	0.634442	+	0.772970i
$17$	13.9110			0.818296			0.409148	−	0.912468i	$-0.365826\pi$
$17$	13.9110			0.818296			0.409148	+	0.912468i	$0.365826\pi$
$18$	−1.31451	+	5.85423i	−0.0730286	+	0.325235i
$19$		−	17.2468i		−	0.907727i	−0.891071	−	0.453864i	$-0.850045\pi$
$19$		−	17.2468i		−	0.907727i	0.891071	−	0.453864i	$-0.149955\pi$
$20$	−8.08565	−	3.82391i	−0.404282	−	0.191196i
$21$	−10.9668			−0.522227
$22$	18.1084	+	4.06607i	0.823108	+	0.184821i
$23$			33.7148i			1.46586i	0.680303	+	0.732931i	$0.261848\pi$
$23$			33.7148i			1.46586i	−0.680303	+	0.732931i	$0.738152\pi$
$24$	10.9241	+	8.52438i	0.455169	+	0.355183i
$25$	5.00000			0.200000
$26$	8.13571	−	36.2327i	0.312912	−	1.39356i
$27$			5.19615i			0.192450i
$28$	−10.8278	+	22.8954i	−0.386708	+	0.817692i
$29$	−28.6177			−0.986817			−0.493409	−	0.869798i	$-0.664249\pi$
$29$	−28.6177			−0.986817			−0.493409	+	0.869798i	$0.664249\pi$
$30$	−7.55778	−	1.69703i	−0.251926	−	0.0565677i
$31$			23.4939i			0.757866i	0.925424	+	0.378933i	$0.123709\pi$
$31$			23.4939i			0.757866i	−0.925424	+	0.378933i	$0.876291\pi$
$32$	28.5820	−	14.3898i	0.893189	−	0.449682i
$33$	16.0728			0.487054
$34$	6.09542	−	27.1461i	0.179277	−	0.798416i
$35$		−	14.1580i		−	0.404515i
$36$	10.8480	+	5.13032i	0.301334	+	0.142509i
$37$	−67.3338			−1.81983			−0.909916	−	0.414793i	$-0.863854\pi$
$37$	−67.3338			−1.81983			−0.909916	+	0.414793i	$0.863854\pi$
$38$	−33.6556	−	7.55706i	−0.885674	−	0.198870i
$39$		−	32.1597i		−	0.824608i
$40$	−11.0049	+	14.1029i	−0.275123	+	0.352572i
$41$	−44.0791			−1.07510			−0.537550	−	0.843232i	$-0.680650\pi$
$41$	−44.0791			−1.07510			−0.537550	+	0.843232i	$0.680650\pi$
$42$	−4.80532	+	21.4007i	−0.114412	+	0.509540i
$43$		−	50.2937i		−	1.16962i	−0.811170	−	0.584811i	$-0.801169\pi$
$43$		−	50.2937i		−	1.16962i	0.811170	−	0.584811i	$-0.198831\pi$
$44$	15.8691	−	33.5552i	0.360662	−	0.762619i
$45$	−6.70820			−0.149071
$46$	65.7915	+	14.7729i	1.43025	+	0.321150i
$47$			31.1594i			0.662967i	0.943461	+	0.331483i	$0.107549\pi$
$47$			31.1594i			0.662967i	−0.943461	+	0.331483i	$0.892451\pi$
$48$	21.4212	−	17.5822i	0.446275	−	0.366295i
$49$	8.91003			0.181837
$50$	2.19086	−	9.75706i	0.0438172	−	0.195141i
$51$		−	24.0946i		−	0.472444i
$52$	−67.1400	−	31.7522i	−1.29115	−	0.610620i
$53$	81.6070			1.53975			0.769877	−	0.638192i	$-0.220318\pi$
$53$	81.6070			1.53975			0.769877	+	0.638192i	$0.220318\pi$
$54$	10.1398	+	2.27681i	0.187775	+	0.0421631i
$55$			20.7499i			0.377270i
$56$	39.9338	+	31.1616i	0.713104	+	0.556457i
$57$	−29.8724			−0.524077
$58$	−12.5395	+	55.8449i	−0.216198	+	0.962843i
$59$			19.2751i			0.326697i	0.986568	+	0.163349i	$0.0522296\pi$
$59$			19.2751i			0.326697i	−0.986568	+	0.163349i	$0.947770\pi$
$60$	−6.62321	+	14.0048i	−0.110387	+	0.233413i
$61$	−53.1563			−0.871415			−0.435707	−	0.900088i	$-0.643502\pi$
$61$	−53.1563			−0.871415			−0.435707	+	0.900088i	$0.643502\pi$
$62$	45.8462	+	10.2943i	0.739455	+	0.166038i
$63$			18.9950i			0.301508i
$64$	−15.5566	−	62.0805i	−0.243072	−	0.970008i
$65$	41.5180			0.638738
$66$	7.04264	−	31.3646i	0.106707	−	0.475221i
$67$			4.49911i			0.0671509i	0.999436	+	0.0335754i	$0.0106894\pi$
$67$			4.49911i			0.0671509i	−0.999436	+	0.0335754i	$0.989311\pi$
$68$	−50.3025	−	23.7893i	−0.739742	−	0.349843i
$69$	58.3958			0.846316
$70$	−27.6281	−	6.20365i	−0.394688	−	0.0886235i
$71$			13.3360i			0.187832i	0.995580	+	0.0939158i	$0.0299385\pi$
$71$			13.3360i			0.187832i	−0.995580	+	0.0939158i	$0.970062\pi$
$72$	14.7647	−	18.9210i	0.205065	−	0.262792i
$73$	40.8904			0.560143			0.280071	−	0.959979i	$-0.409642\pi$
$73$	40.8904			0.560143			0.280071	+	0.959979i	$0.409642\pi$
$74$	−29.5037	+	131.396i	−0.398699	+	1.77562i
$75$		−	8.66025i		−	0.115470i
$76$	−29.4939	+	62.3647i	−0.388077	+	0.820588i
$77$	58.7555			0.763058
$78$	−62.7568	−	14.0915i	−0.804574	−	0.180660i
$79$			141.309i			1.78872i	0.447352	+	0.894358i	$0.352367\pi$
$79$			141.309i			1.78872i	−0.447352	+	0.894358i	$0.647633\pi$
$80$	22.6985	+	27.6546i	0.283731	+	0.345683i
$81$	9.00000			0.111111
$82$	−19.3142	+	86.0164i	−0.235539	+	1.04898i
$83$		−	69.8503i		−	0.841570i	−0.907160	−	0.420785i	$-0.861755\pi$
$83$		−	69.8503i		−	0.841570i	0.907160	−	0.420785i	$-0.138245\pi$
$84$	39.6559	+	18.7543i	0.472095	+	0.223266i
$85$	31.1060			0.365953
$86$	−98.1438	−	22.0373i	−1.14121	−	0.256248i
$87$			49.5673i			0.569739i
$88$	−58.5266	−	45.6702i	−0.665076	−	0.518979i
$89$	−46.3079			−0.520313			−0.260157	−	0.965566i	$-0.583774\pi$
$89$	−46.3079			−0.520313			−0.260157	+	0.965566i	$0.583774\pi$
$90$	−2.93934	+	13.0905i	−0.0326594	+	0.145450i
$91$		−	117.563i		−	1.29190i
$92$	57.6559	−	121.913i	0.626695	−	1.32514i
$93$	40.6926			0.437554
$94$	60.8049	+	13.6532i	0.646860	+	0.145247i
$95$		−	38.5651i		−	0.405948i
$96$	−24.9239	−	49.5055i	−0.259624	−	0.515683i
$97$	68.5543			0.706745			0.353373	−	0.935483i	$-0.385035\pi$
$97$	68.5543			0.706745			0.353373	+	0.935483i	$0.385035\pi$
$98$	3.90412	−	17.3871i	0.0398380	−	0.177420i
$99$		−	27.8389i		−	0.281201i
$100$	−18.0801	−	8.55053i	−0.180801	−	0.0855053i
$101$	−43.3949			−0.429653			−0.214826	−	0.976652i	$-0.568919\pi$
$101$	−43.3949			−0.429653			−0.214826	+	0.976652i	$0.568919\pi$
$102$	−47.0185	−	10.5576i	−0.460966	−	0.103506i
$103$		−	85.7919i		−	0.832931i	−0.909152	−	0.416465i	$-0.863269\pi$
$103$		−	85.7919i		−	0.832931i	0.909152	−	0.416465i	$-0.136731\pi$
$104$	−91.3805	+	117.105i	−0.878659	+	1.12601i
$105$	−24.5224			−0.233547
$106$	35.7579	−	159.249i	0.337338	−	1.50235i
$107$		−	183.075i		−	1.71098i	−0.517818	−	0.855491i	$-0.673255\pi$
$107$		−	183.075i		−	1.71098i	0.517818	−	0.855491i	$-0.326745\pi$
$108$	8.88597	−	18.7893i	0.0822775	−	0.173975i
$109$	81.4798			0.747521			0.373761	−	0.927525i	$-0.378068\pi$
$109$	81.4798			0.747521			0.373761	+	0.927525i	$0.378068\pi$
$110$	40.4915	+	9.09201i	0.368105	+	0.0826546i
$111$			116.625i			1.05068i
$112$	78.3070	−	64.2732i	0.699170	−	0.573868i
$113$	−172.814			−1.52933			−0.764664	−	0.644429i	$-0.777095\pi$
$113$	−172.814			−1.52933			−0.764664	+	0.644429i	$0.777095\pi$
$114$	−13.0892	+	58.2933i	−0.114818	+	0.511344i
$115$			75.3886i			0.655553i
$116$	103.482	+	48.9393i	0.892086	+	0.421891i
$117$	−55.7022			−0.476087
$118$	37.6137	+	8.44582i	0.318760	+	0.0715748i
$119$		−	88.0800i		−	0.740168i
$120$	24.4269	+	19.0611i	0.203558	+	0.158842i
$121$	34.8885			0.288335
$122$	−23.2916	+	103.730i	−0.190915	+	0.850244i
$123$			76.3472i			0.620709i
$124$	40.1770	−	84.9541i	0.324008	−	0.685113i
$125$	11.1803			0.0894427
$126$	37.0670	+	8.32307i	0.294183	+	0.0660561i
$127$			22.3785i			0.176208i	0.996111	+	0.0881041i	$0.0280808\pi$
$127$			22.3785i			0.176208i	−0.996111	+	0.0881041i	$0.971919\pi$
$128$	−127.961	+	3.15546i	−0.999696	+	0.0246520i
$129$	−87.1113			−0.675282
$130$	18.1920	−	81.0187i	0.139938	−	0.623221i
$131$		−	1.75315i		−	0.0133828i	−0.999978	−	0.00669141i	$-0.997870\pi$
$131$		−	1.75315i		−	0.0133828i	0.999978	−	0.00669141i	$-0.00212996\pi$
$132$	−58.1194	−	27.4862i	−0.440298	−	0.208228i
$133$	−109.201			−0.821060
$134$	8.77961	+	1.97138i	0.0655195	+	0.0147118i
$135$			11.6190i			0.0860663i
$136$	−68.4639	+	87.7370i	−0.503411	+	0.645125i
$137$	−19.5084			−0.142397			−0.0711987	−	0.997462i	$-0.522682\pi$
$137$	−19.5084			−0.142397			−0.0711987	+	0.997462i	$0.522682\pi$
$138$	25.5874	−	113.954i	0.185416	−	0.825755i
$139$			257.370i			1.85158i	0.378038	+	0.925790i	$0.376599\pi$
$139$			257.370i			1.85158i	−0.378038	+	0.925790i	$0.623401\pi$
$140$	−24.2117	+	51.1956i	−0.172941	+	0.365683i
$141$	53.9697			0.382764
$142$	26.0241	+	5.84348i	0.183268	+	0.0411512i
$143$			172.299i			1.20489i
$144$	−30.4532	−	37.1026i	−0.211481	−	0.257657i
$145$	−63.9911			−0.441318
$146$	17.9170	−	79.7940i	0.122719	−	0.546534i
$147$		−	15.4326i		−	0.104984i
$148$	243.480	+	115.148i	1.64513	+	0.778026i
$149$	−111.673			−0.749486			−0.374743	−	0.927129i	$-0.622269\pi$
$149$	−111.673			−0.749486			−0.374743	+	0.927129i	$0.622269\pi$
$150$	−16.8997	−	3.79468i	−0.112665	−	0.0252978i
$151$			6.45275i			0.0427335i	0.999772	+	0.0213667i	$0.00680176\pi$
$151$			6.45275i			0.0427335i	−0.999772	+	0.0213667i	$0.993198\pi$
$152$	108.776	+	84.8811i	0.715630	+	0.558428i
$153$	−41.7331			−0.272765
$154$	25.7450	−	114.656i	0.167175	−	0.744520i
$155$			52.5339i			0.338928i
$156$	−54.9965	+	116.290i	−0.352542	+	0.745448i
$157$	−75.9075			−0.483488			−0.241744	−	0.970340i	$-0.577719\pi$
$157$	−75.9075			−0.483488			−0.241744	+	0.970340i	$0.577719\pi$
$158$	275.751	+	61.9174i	1.74526	+	0.391882i
$159$		−	141.347i		−	0.888977i
$160$	63.9114	−	32.1766i	0.399446	−	0.201104i
$161$	213.471			1.32591
$162$	3.94354	−	17.5627i	0.0243429	−	0.108412i
$163$		−	249.298i		−	1.52944i	−0.644364	−	0.764719i	$-0.722878\pi$
$163$		−	249.298i		−	1.52944i	0.644364	−	0.764719i	$-0.277122\pi$
$164$	159.391	+	75.3799i	0.971893	+	0.459634i
$165$	35.9398			0.217817
$166$	−136.307	−	30.6064i	−0.821124	−	0.184376i
$167$			79.1883i			0.474182i	0.971487	+	0.237091i	$0.0761939\pi$
$167$			79.1883i			0.474182i	−0.971487	+	0.237091i	$0.923806\pi$
$168$	53.9735	−	69.1674i	0.321271	−	0.411711i
$169$	175.749			1.03993
$170$	13.6298	−	60.7006i	0.0801751	−	0.357063i
$171$			51.7404i			0.302576i
$172$	−86.0076	+	181.863i	−0.500044	+	1.05734i
$173$	−27.7204			−0.160234			−0.0801168	−	0.996785i	$-0.525529\pi$
$173$	−27.7204			−0.160234			−0.0801168	+	0.996785i	$0.525529\pi$
$174$	96.7262	+	21.7190i	0.555898	+	0.124822i
$175$		−	31.6583i		−	0.180905i
$176$	−114.766	+	94.1982i	−0.652080	+	0.535217i
$177$	33.3855			0.188619
$178$	−20.2908	+	90.3657i	−0.113993	+	0.507673i
$179$		−	204.324i		−	1.14147i	−0.821133	−	0.570737i	$-0.806658\pi$
$179$		−	204.324i		−	1.14147i	0.821133	−	0.570737i	$-0.193342\pi$
$180$	24.2569	+	11.4717i	0.134761	+	0.0637319i
$181$	−49.8262			−0.275283			−0.137641	−	0.990482i	$-0.543952\pi$
$181$	−49.8262			−0.275283			−0.137641	+	0.990482i	$0.543952\pi$
$182$	−229.413	−	51.5126i	−1.26051	−	0.283036i
$183$			92.0694i			0.503112i
$184$	−212.640	−	165.929i	−1.15565	−	0.901790i
$185$	−150.563			−0.813853
$186$	17.8303	−	79.4079i	0.0958620	−	0.426924i
$187$			129.089i			0.690317i
$188$	53.2859	−	112.673i	0.283436	−	0.599324i
$189$	32.9003			0.174076
$190$	−75.2563	−	16.8981i	−0.396086	−	0.0889374i
$191$			1.13703i			0.00595301i	0.999996	+	0.00297651i	$0.000947453\pi$
$191$			1.13703i			0.00595301i	−0.999996	+	0.00297651i	$0.999053\pi$
$192$	−107.527	+	26.9449i	−0.560034	+	0.140338i
$193$	−76.6452			−0.397126			−0.198563	−	0.980088i	$-0.563627\pi$
$193$	−76.6452			−0.397126			−0.198563	+	0.980088i	$0.563627\pi$
$194$	30.0385	−	133.778i	0.154838	−	0.689575i
$195$		−	71.9113i		−	0.368776i
$196$	−32.2188	−	15.2371i	−0.164382	−	0.0777403i
$197$	134.496			0.682719			0.341359	−	0.939933i	$-0.389113\pi$
$197$	134.496			0.682719			0.341359	+	0.939933i	$0.389113\pi$
$198$	−54.3251	−	12.1982i	−0.274369	−	0.0616071i
$199$		−	176.014i		−	0.884491i	−0.896894	−	0.442245i	$-0.854182\pi$
$199$		−	176.014i		−	0.884491i	0.896894	−	0.442245i	$-0.145818\pi$
$200$	−24.6078	+	31.5350i	−0.123039	+	0.157675i
$201$	7.79269			0.0387696
$202$	−19.0144	+	84.6813i	−0.0941308	+	0.419214i
$203$			181.198i			0.892599i
$204$	−41.2044	+	87.1264i	−0.201982	+	0.427090i
$205$	−98.5638			−0.480799
$206$	−167.415	−	37.5916i	−0.812695	−	0.182483i
$207$		−	101.144i		−	0.488621i
$208$	188.479	+	229.633i	0.906150	+	1.10400i
$209$	160.044			0.765761
$210$	−10.7450	+	47.8533i	−0.0511668	+	0.227873i
$211$		−	218.087i		−	1.03359i	−0.856110	−	0.516793i	$-0.827126\pi$
$211$		−	218.087i		−	1.03359i	0.856110	−	0.516793i	$-0.172874\pi$
$212$	−295.092	−	139.557i	−1.39194	−	0.658286i
$213$	23.0987			0.108445
$214$	−357.255	−	80.2183i	−1.66941	−	0.374852i
$215$		−	112.460i		−	0.523071i
$216$	−32.7722	−	25.5731i	−0.151723	−	0.118394i
$217$	148.755			0.685508
$218$	35.7021	−	159.001i	0.163771	−	0.729361i
$219$		−	70.8243i		−	0.323399i
$220$	35.4845	−	75.0318i	0.161293	−	0.341054i
$221$	258.292			1.16874
$222$	227.584	+	51.1020i	1.02515	+	0.230189i
$223$			328.579i			1.47345i	0.676193	+	0.736724i	$0.263628\pi$
$223$			328.579i			1.47345i	−0.676193	+	0.736724i	$0.736372\pi$
$224$	−91.1115	−	180.972i	−0.406748	−	0.807910i
$225$	−15.0000			−0.0666667
$226$	−75.7222	+	337.231i	−0.335054	+	1.49217i
$227$			157.649i			0.694491i	0.937774	+	0.347245i	$0.112883\pi$
$227$			157.649i			0.694491i	−0.937774	+	0.347245i	$0.887117\pi$
$228$	108.019	+	51.0849i	0.473767	+	0.224057i
$229$	−273.148			−1.19279			−0.596393	−	0.802692i	$-0.703400\pi$
$229$	−273.148			−1.19279			−0.596393	+	0.802692i	$0.703400\pi$
$230$	147.114	+	33.0332i	0.639627	+	0.143622i
$231$		−	101.767i		−	0.440552i
$232$	140.844	−	180.492i	0.607084	−	0.777983i
$233$	108.746			0.466720			0.233360	−	0.972390i	$-0.425028\pi$
$233$	108.746			0.466720			0.233360	+	0.972390i	$0.425028\pi$
$234$	−24.4071	+	108.698i	−0.104304	+	0.464521i
$235$			69.6746i			0.296488i
$236$	32.9625	−	69.6992i	0.139672	−	0.295335i
$237$	244.754			1.03272
$238$	−171.880	−	38.5942i	−0.722186	−	0.162160i
$239$		−	178.994i		−	0.748927i	−0.927242	−	0.374464i	$-0.877827\pi$
$239$		−	178.994i		−	0.748927i	0.927242	−	0.374464i	$-0.122173\pi$
$240$	47.8992	−	39.3149i	0.199580	−	0.163812i
$241$	358.623			1.48806			0.744032	−	0.668144i	$-0.232911\pi$
$241$	358.623			1.48806			0.744032	+	0.668144i	$0.232911\pi$
$242$	15.2872	−	68.0819i	0.0631701	−	0.281330i
$243$		−	15.5885i		−	0.0641500i
$244$	192.214	+	90.9029i	0.787762	+	0.372553i
$245$	19.9234			0.0813202
$246$	148.985	+	33.4532i	0.605629	+	0.135989i
$247$		−	320.229i		−	1.29647i
$248$	−148.176	−	115.626i	−0.597483	−	0.466235i
$249$	−120.984			−0.485881
$250$	4.89891	−	21.8174i	0.0195956	−	0.0872698i
$251$			306.220i			1.22000i	0.792401	+	0.610000i	$0.208831\pi$
$251$			306.220i			1.22000i	−0.792401	+	0.610000i	$0.791169\pi$
$252$	32.4834	−	68.6861i	0.128903	−	0.272564i
$253$	−312.861			−1.23660
$254$	43.6696	+	9.80560i	0.171927	+	0.0386047i
$255$		−	53.8772i		−	0.211283i
$256$	−49.9113	+	251.087i	−0.194966	+	0.980810i
$257$	−251.062			−0.976895			−0.488447	−	0.872593i	$-0.662437\pi$
$257$	−251.062			−0.976895			−0.488447	+	0.872593i	$0.662437\pi$
$258$	−38.1697	+	169.990i	−0.147945	+	0.658876i
$259$			426.335i			1.64608i
$260$	−150.130	−	71.0002i	−0.577421	−	0.273078i
$261$	85.8531			0.328939
$262$	−3.42112	−	0.768181i	−0.0130577	−	0.00293199i
$263$			48.7645i			0.185416i	0.995693	+	0.0927082i	$0.0295524\pi$
$263$			48.7645i			0.185416i	−0.995693	+	0.0927082i	$0.970448\pi$
$264$	−79.1031	+	101.371i	−0.299633	+	0.383982i
$265$	182.479			0.688599
$266$	−47.8488	+	213.096i	−0.179883	+	0.801113i
$267$			80.2076i			0.300403i
$268$	7.69395	−	16.2688i	0.0287088	−	0.0607046i
$269$	148.696			0.552772			0.276386	−	0.961047i	$-0.410863\pi$
$269$	148.696			0.552772			0.276386	+	0.961047i	$0.410863\pi$
$270$	22.6733	+	5.09109i	0.0839754	+	0.0188559i
$271$		−	83.3415i		−	0.307533i	−0.988107	−	0.153767i	$-0.950860\pi$
$271$		−	83.3415i		−	0.307533i	0.988107	−	0.153767i	$-0.0491404\pi$
$272$	141.212	+	172.045i	0.519162	+	0.632519i
$273$	−203.624			−0.745877
$274$	−8.54805	+	38.0690i	−0.0311972	+	0.138938i
$275$			46.3981i			0.168720i
$276$	−211.160	−	99.8630i	−0.765072	−	0.361822i
$277$	144.080			0.520146			0.260073	−	0.965589i	$-0.416253\pi$
$277$	144.080			0.520146			0.260073	+	0.965589i	$0.416253\pi$
$278$	502.234	+	112.772i	1.80660	+	0.405655i
$279$		−	70.4816i		−	0.252622i
$280$	89.2948	+	69.6795i	0.318910	+	0.248855i
$281$	−343.671			−1.22303			−0.611514	−	0.791233i	$-0.709439\pi$
$281$	−343.671			−1.22303			−0.611514	+	0.791233i	$0.709439\pi$
$282$	23.6480	−	105.317i	0.0838581	−	0.373465i
$283$		−	314.955i		−	1.11292i	−0.830876	−	0.556458i	$-0.812160\pi$
$283$		−	314.955i		−	1.11292i	0.830876	−	0.556458i	$-0.187840\pi$
$284$	22.8061	−	48.2233i	0.0803030	−	0.169800i
$285$	−66.7966			−0.234374
$286$	336.225	+	75.4964i	1.17561	+	0.263973i
$287$			279.094i			0.972453i
$288$	−85.7461	+	43.1695i	−0.297730	+	0.149894i
$289$	−95.4831			−0.330391
$290$	−28.0391	+	124.873i	−0.0966865	+	0.430597i
$291$		−	118.740i		−	0.408040i
$292$	−147.860	−	69.9269i	−0.506371	−	0.239476i
$293$	−6.55421			−0.0223693			−0.0111847	−	0.999937i	$-0.503560\pi$
$293$	−6.55421			−0.0223693			−0.0111847	+	0.999937i	$0.503560\pi$
$294$	−30.1154	−	6.76214i	−0.102433	−	0.0230005i
$295$			43.1005i			0.146104i
$296$	331.387	−	424.674i	1.11955	−	1.43471i
$297$	−48.2184			−0.162351
$298$	−48.9321	+	217.921i	−0.164202	+	0.731278i
$299$			625.997i			2.09364i
$300$	−14.8100	+	31.3156i	−0.0493665	+	0.104385i
$301$	−318.443			−1.05795
$302$	12.5920	+	2.82741i	0.0416953	+	0.00936229i
$303$			75.1622i			0.248060i
$304$	213.300	−	175.074i	0.701646	−	0.575900i
$305$	−118.861			−0.389709
$306$	−18.2863	+	81.4384i	−0.0597590	+	0.266139i
$307$		−	354.559i		−	1.15492i	−0.816420	−	0.577458i	$-0.804045\pi$
$307$		−	354.559i		−	1.15492i	0.816420	−	0.577458i	$-0.195955\pi$
$308$	−212.460	−	100.478i	−0.689807	−	0.326228i
$309$	−148.596			−0.480893
$310$	102.515	+	23.0188i	0.330694	+	0.0742543i
$311$		−	193.387i		−	0.621823i	−0.950439	−	0.310912i	$-0.899366\pi$
$311$		−	193.387i		−	0.621823i	0.950439	−	0.310912i	$-0.100634\pi$
$312$	202.831	+	158.276i	0.650101	+	0.507294i
$313$	−23.5224			−0.0751514			−0.0375757	−	0.999294i	$-0.511964\pi$
$313$	−23.5224			−0.0751514			−0.0375757	+	0.999294i	$0.511964\pi$
$314$	−33.2605	+	148.127i	−0.105925	+	0.471742i
$315$			42.4741i			0.134838i
$316$	241.653	−	510.973i	0.764724	−	1.61700i
$317$	−214.004			−0.675092			−0.337546	−	0.941309i	$-0.609597\pi$
$317$	−214.004			−0.675092			−0.337546	+	0.941309i	$0.609597\pi$
$318$	−275.827	−	61.9344i	−0.867380	−	0.194762i
$319$		−	265.562i		−	0.832481i
$320$	−34.7857	−	138.816i	−0.108705	−	0.433801i
$321$	−317.095			−0.987836
$322$	93.5369	−	416.570i	0.290487	−	1.29369i
$323$		−	239.921i		−	0.742790i
$324$	−32.5441	−	15.3910i	−0.100445	−	0.0475029i
$325$	92.8371			0.285652
$326$	−486.483	−	109.235i	−1.49228	−	0.335078i
$327$		−	141.127i		−	0.431582i
$328$	216.938	−	278.007i	0.661395	−	0.847583i
$329$	197.291			0.599669
$330$	15.7478	−	70.1334i	0.0477207	−	0.212525i
$331$			412.454i			1.24609i	0.782188	+	0.623043i	$0.214104\pi$
$331$			412.454i			1.24609i	−0.782188	+	0.623043i	$0.785896\pi$
$332$	−119.451	+	252.579i	−0.359793	+	0.760782i
$333$	202.001			0.606610
$334$	154.529	+	34.6981i	0.462662	+	0.103886i
$335$			10.0603i			0.0300308i
$336$	−111.324	−	135.632i	−0.331323	−	0.403666i
$337$	103.268			0.306433			0.153216	−	0.988193i	$-0.451037\pi$
$337$	103.268			0.306433			0.153216	+	0.988193i	$0.451037\pi$
$338$	77.0081	−	342.958i	0.227835	−	1.01467i
$339$			299.323i			0.882958i
$340$	−112.480	−	53.1946i	−0.330823	−	0.156455i
$341$	−218.014			−0.639338
$342$	100.967	+	22.6712i	0.295225	+	0.0662900i
$343$		−	366.667i		−	1.06900i
$344$	317.203	+	247.523i	0.922102	+	0.719545i
$345$	130.577			0.378484
$346$	−12.1463	+	54.0939i	−0.0351049	+	0.156341i
$347$			153.211i			0.441531i	0.975327	+	0.220766i	$0.0708556\pi$
$347$			153.211i			0.441531i	−0.975327	+	0.220766i	$0.929144\pi$
$348$	84.7654	−	179.236i	0.243579	−	0.515046i
$349$	−84.7317			−0.242784			−0.121392	−	0.992605i	$-0.538736\pi$
$349$	−84.7317			−0.242784			−0.121392	+	0.992605i	$0.538736\pi$
$350$	−61.7784	−	13.8718i	−0.176510	−	0.0396336i
$351$			96.4791i			0.274869i
$352$	133.532	+	265.231i	0.379353	+	0.753496i
$353$	256.065			0.725396			0.362698	−	0.931907i	$-0.381856\pi$
$353$	256.065			0.725396			0.362698	+	0.931907i	$0.381856\pi$
$354$	14.6286	−	65.1489i	0.0413237	−	0.184036i
$355$			29.8203i			0.0840009i
$356$	167.450	+	79.1914i	0.470365	+	0.222448i
$357$	−152.559			−0.427336
$358$	−398.720	−	89.5289i	−1.11374	−	0.250081i
$359$		−	667.258i		−	1.85866i	−0.369253	−	0.929329i	$-0.620386\pi$
$359$		−	667.258i		−	1.85866i	0.369253	−	0.929329i	$-0.379614\pi$
$360$	33.0148	−	42.3087i	0.0917077	−	0.117524i
$361$	63.5473			0.176031
$362$	−21.8324	+	97.2314i	−0.0603106	+	0.268595i
$363$		−	60.4287i		−	0.166470i
$364$	−201.044	+	425.108i	−0.552320	+	1.16788i
$365$	91.4338			0.250503
$366$	179.665	+	40.3422i	0.490889	+	0.110225i
$367$			245.301i			0.668396i	0.942503	+	0.334198i	$0.108465\pi$
$367$			245.301i			0.668396i	−0.942503	+	0.334198i	$0.891535\pi$
$368$	−416.969	+	342.242i	−1.13307	+	0.930005i
$369$	132.237			0.358367
$370$	−65.9724	+	293.810i	−0.178304	+	0.794081i
$371$		−	516.708i		−	1.39274i
$372$	−147.145	−	69.5886i	−0.395550	−	0.187066i
$373$	698.787			1.87342			0.936712	−	0.350101i	$-0.113853\pi$
$373$	698.787			1.87342			0.936712	+	0.350101i	$0.113853\pi$
$374$	251.906	+	56.5632i	0.673546	+	0.151239i
$375$		−	19.3649i		−	0.0516398i
$376$	−196.523	−	153.353i	−0.522667	−	0.407853i
$377$	−531.357			−1.40943
$378$	14.4160	−	64.2020i	0.0381375	−	0.169847i
$379$			208.691i			0.550636i	0.961353	+	0.275318i	$0.0887831\pi$
$379$			208.691i			0.550636i	−0.961353	+	0.275318i	$0.911217\pi$
$380$	−65.9503	+	139.452i	−0.173553	+	0.366978i
$381$	38.7606			0.101734
$382$	2.21880	+	0.498212i	0.00580839	+	0.00130422i
$383$		−	156.524i		−	0.408680i	−0.978900	−	0.204340i	$-0.934495\pi$
$383$		−	156.524i		−	0.408680i	0.978900	−	0.204340i	$-0.0655048\pi$
$384$	5.46541	+	221.635i	0.0142328	+	0.577175i
$385$	131.381			0.341250
$386$	−33.5838	+	149.566i	−0.0870046	+	0.387478i
$387$			150.881i			0.389874i
$388$	−247.893	−	117.235i	−0.638900	−	0.302152i
$389$	386.588			0.993801			0.496900	−	0.867808i	$-0.334471\pi$
$389$	386.588			0.993801			0.496900	+	0.867808i	$0.334471\pi$
$390$	−140.328	−	31.5095i	−0.359817	−	0.0807935i
$391$			469.008i			1.19951i
$392$	−43.8512	+	56.1956i	−0.111865	+	0.143356i
$393$	−3.03655			−0.00772658
$394$	58.9322	−	262.456i	0.149574	−	0.666133i
$395$			315.976i			0.799938i
$396$	−47.6074	+	100.666i	−0.120221	+	0.254206i
$397$	−561.155			−1.41349			−0.706744	−	0.707470i	$-0.749837\pi$
$397$	−561.155			−1.41349			−0.706744	+	0.707470i	$0.749837\pi$
$398$	−343.475	−	77.1242i	−0.863002	−	0.193779i
$399$			189.142i			0.474039i
$400$	50.7554	+	61.8376i	0.126888	+	0.154594i
$401$	16.9333			0.0422276			0.0211138	−	0.999777i	$-0.493279\pi$
$401$	16.9333			0.0422276			0.0211138	+	0.999777i	$0.493279\pi$
$402$	3.41453	−	15.2067i	0.00849387	−	0.0378277i
$403$			436.220i			1.08243i
$404$	156.917	+	74.2099i	0.388407	+	0.183688i
$405$	20.1246			0.0496904
$406$	353.591	+	79.3957i	0.870914	+	0.195556i
$407$		−	624.832i		−	1.53521i
$408$	151.965	+	118.583i	0.372463	+	0.290644i
$409$	258.490			0.632006			0.316003	−	0.948758i	$-0.397659\pi$
$409$	258.490			0.632006			0.316003	+	0.948758i	$0.397659\pi$
$410$	−43.1879	+	192.339i	−0.105336	+	0.469119i
$411$			33.7896i			0.0822132i
$412$	−146.713	+	310.224i	−0.356100	+	0.752972i
$413$	122.044			0.295505
$414$	−197.374	−	44.3186i	−0.476750	−	0.107050i
$415$		−	156.190i		−	0.376362i
$416$	530.694	−	267.182i	1.27571	−	0.642264i
$417$	445.777			1.06901
$418$	70.1267	−	312.312i	0.167767	−	0.747157i
$419$			258.917i			0.617941i	0.951072	+	0.308970i	$0.0999844\pi$
$419$			258.917i			0.617941i	−0.951072	+	0.308970i	$0.900016\pi$
$420$	88.6734	+	41.9359i	0.211127	+	0.0998475i
$421$	97.4654			0.231509			0.115755	−	0.993278i	$-0.463071\pi$
$421$	97.4654			0.231509			0.115755	+	0.993278i	$0.463071\pi$
$422$	−425.577	−	95.5594i	−1.00848	−	0.226444i
$423$		−	93.4783i		−	0.220989i
$424$	−401.633	+	514.696i	−0.947248	+	1.21390i
$425$	69.5552			0.163659
$426$	10.1212	−	45.0751i	0.0237587	−	0.105810i
$427$			336.568i			0.788215i
$428$	−313.078	+	662.002i	−0.731490	+	1.54673i
$429$	298.430			0.695641
$430$	−219.456	−	49.2769i	−0.510363	−	0.114597i
$431$			389.968i			0.904799i	0.891815	+	0.452399i	$0.149432\pi$
$431$			389.968i			0.904799i	−0.891815	+	0.452399i	$0.850568\pi$
$432$	−64.2635	+	52.7465i	−0.148758	+	0.122098i
$433$	275.893			0.637166			0.318583	−	0.947895i	$-0.396793\pi$
$433$	275.893			0.637166			0.318583	+	0.947895i	$0.396793\pi$
$434$	65.1803	−	290.283i	0.150185	−	0.668854i
$435$			110.836i			0.254795i
$436$	−294.632	−	139.339i	−0.675761	−	0.319585i
$437$	581.473			1.33060
$438$	−138.207	−	31.0332i	−0.315542	−	0.0708520i
$439$		−	446.143i		−	1.01627i	−0.861277	−	0.508136i	$-0.830335\pi$
$439$		−	446.143i		−	1.01627i	0.861277	−	0.508136i	$-0.169665\pi$
$440$	−130.870	−	102.122i	−0.297431	−	0.232095i
$441$	−26.7301			−0.0606125
$442$	113.176	−	504.034i	0.256055	−	1.14035i
$443$		−	794.679i		−	1.79386i	−0.442174	−	0.896929i	$-0.645793\pi$
$443$		−	794.679i		−	1.79386i	0.442174	−	0.896929i	$-0.354207\pi$
$444$	199.442	−	421.719i	0.449194	−	0.949818i
$445$	−103.548			−0.232691
$446$	641.193	+	143.974i	1.43765	+	0.322812i
$447$			193.424i			0.432716i
$448$	−393.073	+	98.4993i	−0.877395	+	0.219865i
$449$	−750.226			−1.67088			−0.835441	−	0.549581i	$-0.814788\pi$
$449$	−750.226			−1.67088			−0.835441	+	0.549581i	$0.814788\pi$
$450$	−6.57257	+	29.2712i	−0.0146057	+	0.0650470i
$451$		−	409.037i		−	0.906957i
$452$	624.898	+	295.530i	1.38252	+	0.653828i
$453$	11.1765			0.0246722
$454$	307.639	+	69.0775i	0.677619	+	0.152153i
$455$		−	262.878i		−	0.577754i
$456$	147.018	−	188.405i	0.322409	−	0.413169i
$457$	101.092			0.221209			0.110604	−	0.993865i	$-0.464721\pi$
$457$	101.092			0.221209			0.110604	+	0.993865i	$0.464721\pi$
$458$	−119.686	+	533.024i	−0.261323	+	1.16381i
$459$			72.2839i			0.157481i
$460$	128.923	−	272.606i	0.280266	−	0.592622i
$461$	−4.48690			−0.00973297			−0.00486648	−	0.999988i	$-0.501549\pi$
$461$	−4.48690			−0.00973297			−0.00486648	+	0.999988i	$0.501549\pi$
$462$	−198.590	−	44.5916i	−0.429849	−	0.0965186i
$463$			515.108i			1.11254i	0.831000	+	0.556272i	$0.187769\pi$
$463$			515.108i			1.11254i	−0.831000	+	0.556272i	$0.812231\pi$
$464$	−290.500	−	353.930i	−0.626079	−	0.762780i
$465$	90.9913			0.195680
$466$	47.6493	−	212.208i	0.102252	−	0.455382i
$467$		−	295.498i		−	0.632758i	−0.948633	−	0.316379i	$-0.897533\pi$
$467$		−	295.498i		−	0.632758i	0.948633	−	0.316379i	$-0.102467\pi$
$468$	201.420	+	95.2567i	0.430384	+	0.203540i
$469$	28.4869			0.0607396
$470$	135.964	+	30.5294i	0.289285	+	0.0649562i
$471$			131.476i			0.279142i
$472$	−121.568	−	94.8637i	−0.257560	−	0.200982i
$473$	466.707			0.986696
$474$	107.244	−	477.615i	0.226253	−	1.00763i
$475$		−	86.2341i		−	0.181545i
$476$	−150.626	+	318.498i	−0.316441	+	0.669114i
$477$	−244.821			−0.513251
$478$	−349.290	−	78.4299i	−0.730732	−	0.164079i
$479$			273.155i			0.570260i	0.958489	+	0.285130i	$0.0920368\pi$
$479$			273.155i			0.570260i	−0.958489	+	0.285130i	$0.907963\pi$
$480$	−55.7316	−	110.698i	−0.116107	−	0.230620i
$481$	−1250.21			−2.59920
$482$	157.139	−	699.822i	0.326014	−	1.45191i
$483$		−	369.743i		−	0.765512i
$484$	−126.157	−	59.6631i	−0.260656	−	0.123271i
$485$	153.292			0.316066
$486$	−30.4195	−	6.83042i	−0.0625915	−	0.0140544i
$487$			357.751i			0.734601i	0.930102	+	0.367301i	$0.119718\pi$
$487$			357.751i			0.734601i	−0.930102	+	0.367301i	$0.880282\pi$
$488$	261.612	−	335.257i	0.536089	−	0.687002i
$489$	−431.797			−0.883021
$490$	8.72989	−	38.8788i	0.0178161	−	0.0793446i
$491$		−	422.379i		−	0.860242i	−0.902771	−	0.430121i	$-0.858471\pi$
$491$		−	422.379i		−	0.860242i	0.902771	−	0.430121i	$-0.141529\pi$
$492$	130.562	−	276.072i	0.265370	−	0.561123i
$493$	−398.102			−0.807509
$494$	−624.898	−	140.315i	−1.26498	−	0.284039i
$495$		−	62.2496i		−	0.125757i
$496$	−290.561	+	238.488i	−0.585808	+	0.480822i
$497$	84.4394			0.169898
$498$	−53.0119	+	236.090i	−0.106450	+	0.474076i
$499$		−	207.096i		−	0.415021i	−0.978233	−	0.207511i	$-0.933464\pi$
$499$		−	207.096i		−	0.415021i	0.978233	−	0.207511i	$-0.0665362\pi$
$500$	−40.4282	−	19.1196i	−0.0808565	−	0.0382391i
$501$	137.158			0.273769
$502$	597.562	+	134.177i	1.19036	+	0.267285i
$503$			702.853i			1.39732i	0.715452	+	0.698661i	$0.246221\pi$
$503$			702.853i			1.39732i	−0.715452	+	0.698661i	$0.753779\pi$
$504$	−119.802	−	93.4849i	−0.237701	−	0.185486i
$505$	−97.0340			−0.192147
$506$	−137.087	+	610.520i	−0.270923	+	1.20656i
$507$		−	304.406i		−	0.600406i
$508$	38.2695	−	80.9207i	0.0753337	−	0.159293i
$509$	−389.029			−0.764300			−0.382150	−	0.924100i	$-0.624816\pi$
$509$	−389.029			−0.764300			−0.382150	+	0.924100i	$0.624816\pi$
$510$	−105.137	−	23.6075i	−0.206150	−	0.0462891i
$511$		−	258.904i		−	0.506662i
$512$	468.105	+	207.417i	0.914267	+	0.405111i
$513$	89.6171			0.174692
$514$	−110.008	+	489.925i	−0.214024	+	0.953162i
$515$		−	191.836i		−	0.372498i
$516$	314.996	+	148.970i	0.610457	+	0.288701i
$517$	−289.148			−0.559280
$518$	831.954	+	186.808i	1.60609	+	0.360633i
$519$			48.0132i			0.0925109i
$520$	−204.333	+	261.854i	−0.392948	+	0.503566i
$521$	−151.753			−0.291273			−0.145637	−	0.989338i	$-0.546523\pi$
$521$	−151.753			−0.291273			−0.145637	+	0.989338i	$0.546523\pi$
$522$	37.6184	−	167.535i	0.0720659	−	0.320948i
$523$			557.762i			1.06647i	0.845968	+	0.533234i	$0.179023\pi$
$523$			557.762i			1.06647i	−0.845968	+	0.533234i	$0.820977\pi$
$524$	−2.99807	+	6.33941i	−0.00572151	+	0.0120981i
$525$	−54.8338			−0.104445
$526$	95.1596	+	21.3672i	0.180912	+	0.0406221i
$527$			326.824i			0.620159i
$528$	163.156	+	198.781i	0.309008	+	0.376478i
$529$	−607.689			−1.14875
$530$	79.9570	−	356.091i	0.150862	−	0.671870i
$531$		−	57.8254i		−	0.108899i
$532$	394.872	+	186.745i	0.742241	+	0.351025i
$533$	−818.435			−1.53552
$534$	156.518	+	35.1447i	0.293105	+	0.0658141i
$535$		−	409.368i		−	0.765174i
$536$	−28.3759	−	22.1426i	−0.0529401	−	0.0413108i
$537$	−353.899			−0.659030
$538$	65.1542	−	290.166i	0.121104	−	0.539342i
$539$			82.6818i			0.153398i
$540$	19.8696	−	42.0143i	0.0367956	−	0.0778042i
$541$	340.979			0.630275			0.315137	−	0.949046i	$-0.397949\pi$
$541$	340.979			0.630275			0.315137	+	0.949046i	$0.397949\pi$
$542$	−162.633	−	36.5179i	−0.300062	−	0.0673761i
$543$			86.3015i			0.158935i
$544$	397.606	−	200.177i	0.730893	−	0.367973i
$545$	182.194			0.334302
$546$	−89.2224	+	397.355i	−0.163411	+	0.727756i
$547$		−	113.651i		−	0.207771i	−0.994589	−	0.103885i	$-0.966872\pi$
$547$		−	113.651i		−	0.207771i	0.994589	−	0.103885i	$-0.0331275\pi$
$548$	70.5428	+	33.3615i	0.128728	+	0.0608787i
$549$	159.469			0.290472
$550$	90.5418	+	20.3303i	0.164622	+	0.0369643i
$551$			493.564i			0.895761i
$552$	−287.398	+	368.303i	−0.520649	+	0.667215i
$553$	894.718			1.61794
$554$	63.1319	−	281.160i	0.113957	−	0.507509i
$555$			260.783i			0.469878i
$556$	440.129	−	930.651i	0.791599	−	1.67383i
$557$	233.232			0.418728			0.209364	−	0.977838i	$-0.432861\pi$
$557$	233.232			0.418728			0.209364	+	0.977838i	$0.432861\pi$
$558$	−137.539	−	30.8830i	−0.246485	−	0.0553459i
$559$		−	933.825i		−	1.67053i
$560$	175.100	−	143.719i	0.312678	−	0.256641i
$561$	223.589			0.398554
$562$	−150.587	+	670.644i	−0.267948	+	1.19332i
$563$		−	167.786i		−	0.298021i	−0.988836	−	0.149011i	$-0.952391\pi$
$563$		−	167.786i		−	0.298021i	0.988836	−	0.149011i	$-0.0476088\pi$
$564$	−195.155	−	92.2939i	−0.346020	−	0.163642i
$565$	−386.424			−0.683936
$566$	−614.607	−	138.004i	−1.08588	−	0.243824i
$567$		−	56.9850i		−	0.100503i
$568$	−84.1105	−	65.6341i	−0.148082	−	0.115553i
$569$	381.089			0.669752			0.334876	−	0.942262i	$-0.391306\pi$
$569$	381.089			0.669752			0.334876	+	0.942262i	$0.391306\pi$
$570$	−29.2684	+	130.348i	−0.0513480	+	0.228680i
$571$			453.871i			0.794870i	0.917630	+	0.397435i	$0.130100\pi$
$571$			453.871i			0.794870i	−0.917630	+	0.397435i	$0.869900\pi$
$572$	294.649	−	623.034i	0.515120	−	1.08922i
$573$	1.96939			0.00343697
$574$	544.627	+	122.291i	0.948828	+	0.213051i
$575$			168.574i			0.293172i
$576$	46.6699	+	186.242i	0.0810241	+	0.323336i
$577$	688.294			1.19288			0.596442	−	0.802656i	$-0.296581\pi$
$577$	688.294			1.19288			0.596442	+	0.802656i	$0.296581\pi$
$578$	−41.8380	+	186.327i	−0.0723841	+	0.322365i
$579$			132.753i			0.229281i
$580$	231.393	+	109.432i	0.398953	+	0.188675i
$581$	−442.269			−0.761220
$582$	−231.710	−	52.0283i	−0.398127	−	0.0893957i
$583$			757.282i			1.29894i
$584$	−201.244	+	257.896i	−0.344597	+	0.441603i
$585$	−124.554			−0.212913
$586$	−2.87187	+	12.7900i	−0.00490080	+	0.0218259i
$587$			249.163i			0.424468i	0.977219	+	0.212234i	$0.0680739\pi$
$587$			249.163i			0.424468i	−0.977219	+	0.212234i	$0.931926\pi$
$588$	−26.3914	+	55.8046i	−0.0448834	+	0.0949057i
$589$	405.194			0.687936
$590$	84.1069	+	18.8854i	0.142554	+	0.0320092i
$591$		−	232.953i		−	0.394168i
$592$	−683.510	−	832.752i	−1.15458	−	1.40668i
$593$	−163.937			−0.276454			−0.138227	−	0.990401i	$-0.544140\pi$
$593$	−163.937			−0.276454			−0.138227	+	0.990401i	$0.544140\pi$
$594$	−21.1279	+	94.0938i	−0.0355689	+	0.158407i
$595$		−	196.953i		−	0.331013i
$596$	403.812	+	190.973i	0.677538	+	0.320425i
$597$	−304.865			−0.510661
$598$	1221.58	+	274.294i	2.04277	+	0.458686i
$599$			170.412i			0.284494i	0.989831	+	0.142247i	$0.0454327\pi$
$599$			170.412i			0.284494i	−0.989831	+	0.142247i	$0.954567\pi$
$600$	54.6203	+	42.6219i	0.0910338	+	0.0710365i
$601$	1119.87			1.86335			0.931674	−	0.363295i	$-0.118348\pi$
$601$	1119.87			1.86335			0.931674	+	0.363295i	$0.118348\pi$
$602$	−139.533	+	621.413i	−0.231782	+	1.03225i
$603$		−	13.4973i		−	0.0223836i
$604$	11.0349	−	23.3332i	0.0182697	−	0.0386312i
$605$	78.0132			0.128947
$606$	146.672	+	32.9339i	0.242034	+	0.0543464i
$607$			660.957i			1.08889i	0.838796	+	0.544445i	$0.183260\pi$
$607$			660.957i			1.08889i	−0.838796	+	0.544445i	$0.816740\pi$
$608$	−248.179	−	492.949i	−0.408189	−	0.810772i
$609$	313.844			0.515342
$610$	−52.0816	+	231.947i	−0.0853796	+	0.380241i
$611$			578.550i			0.946890i
$612$	150.907	+	71.3680i	0.246581	+	0.116614i
$613$	−179.315			−0.292520			−0.146260	−	0.989246i	$-0.546724\pi$
$613$	−179.315			−0.292520			−0.146260	+	0.989246i	$0.546724\pi$
$614$	−691.891	−	155.358i	−1.12686	−	0.253026i
$615$			170.718i			0.277590i
$616$	−289.168	+	370.571i	−0.469429	+	0.601576i
$617$	−63.6752			−0.103201			−0.0516007	−	0.998668i	$-0.516432\pi$
$617$	−63.6752			−0.103201			−0.0516007	+	0.998668i	$0.516432\pi$
$618$	−65.1105	+	289.972i	−0.105357	+	0.469210i
$619$		−	872.350i		−	1.40929i	−0.709561	−	0.704644i	$-0.751107\pi$
$619$		−	872.350i		−	1.40929i	0.709561	−	0.704644i	$-0.248893\pi$
$620$	89.8385	−	189.963i	0.144901	−	0.306392i
$621$	−175.187			−0.282105
$622$	−377.378	−	84.7367i	−0.606716	−	0.136233i
$623$			293.206i			0.470636i
$624$	397.736	−	326.456i	0.637397	−	0.523166i
$625$	25.0000			0.0400000
$626$	−10.3068	+	45.9019i	−0.0164646	+	0.0733257i
$627$		−	277.204i		−	0.442112i
$628$	274.483	+	129.810i	0.437074	+	0.206704i
$629$	−936.682			−1.48916
$630$	82.8844	+	18.6109i	0.131563	+	0.0295412i
$631$			340.783i			0.540068i	0.962851	+	0.270034i	$0.0870349\pi$
$631$			340.783i			0.540068i	−0.962851	+	0.270034i	$0.912965\pi$
$632$	−891.234	−	695.458i	−1.41018	−	1.10041i
$633$	−377.737			−0.596742
$634$	−93.7705	+	417.610i	−0.147903	+	0.658691i
$635$			50.0397i			0.0788027i
$636$	−241.719	+	511.114i	−0.380061	+	0.803638i
$637$	165.436			0.259712
$638$	−518.220	−	116.362i	−0.812257	−	0.182385i
$639$		−	40.0081i		−	0.0626105i
$640$	−286.130	+	7.05582i	−0.447078	+	0.0110247i
$641$	766.210			1.19534			0.597668	−	0.801744i	$-0.296094\pi$
$641$	766.210			1.19534			0.597668	+	0.801744i	$0.296094\pi$
$642$	−138.942	+	618.783i	−0.216421	+	0.963837i
$643$		−	1163.47i		−	1.80943i	−0.426014	−	0.904717i	$-0.640083\pi$
$643$		−	1163.47i		−	1.80943i	0.426014	−	0.904717i	$-0.359917\pi$
$644$	−771.913	−	365.058i	−1.19862	−	0.566860i
$645$	−194.787			−0.301995
$646$	−468.185	−	105.127i	−0.724744	−	0.162735i
$647$		−	740.530i		−	1.14456i	−0.820059	−	0.572279i	$-0.806059\pi$
$647$		−	740.530i		−	1.14456i	0.820059	−	0.572279i	$-0.193941\pi$
$648$	−44.2940	+	56.7630i	−0.0683549	+	0.0875973i
$649$	−178.866			−0.275603
$650$	40.6786	−	181.163i	0.0625824	−	0.278713i
$651$		−	257.652i		−	0.395778i
$652$	−426.326	+	901.465i	−0.653875	+	1.38262i
$653$	109.569			0.167793			0.0838967	−	0.996474i	$-0.473263\pi$
$653$	109.569			0.167793			0.0838967	+	0.996474i	$0.473263\pi$
$654$	−275.397	−	61.8379i	−0.421097	−	0.0945534i
$655$		−	3.92016i		−	0.00598498i
$656$	−447.450	−	545.149i	−0.682089	−	0.831020i
$657$	−122.671			−0.186714
$658$	86.4473	−	384.996i	0.131379	−	0.585100i
$659$			723.214i			1.09744i	0.836006	+	0.548721i	$0.184885\pi$
$659$			723.214i			1.09744i	−0.836006	+	0.548721i	$0.815115\pi$
$660$	−129.959	−	61.4609i	−0.196907	−	0.0931226i
$661$	700.333			1.05951			0.529753	−	0.848152i	$-0.322285\pi$
$661$	700.333			1.05951			0.529753	+	0.848152i	$0.322285\pi$
$662$	804.868	+	180.726i	1.21581	+	0.273000i
$663$		−	447.375i		−	0.674773i
$664$	440.546	+	343.772i	0.663473	+	0.517729i
$665$	−244.181			−0.367189
$666$	88.5112	−	394.188i	0.132900	−	0.591873i
$667$		−	964.841i		−	1.44654i
$668$	135.420	−	286.346i	0.202725	−	0.428662i
$669$	569.116			0.850696
$670$	19.6318	+	4.40814i	0.0293012	+	0.00657932i
$671$		−	493.271i		−	0.735128i
$672$	−313.452	+	157.810i	−0.466447	+	0.234836i
$673$	−1221.18			−1.81454			−0.907269	−	0.420552i	$-0.861837\pi$
$673$	−1221.18			−1.81454			−0.907269	+	0.420552i	$0.861837\pi$
$674$	45.2490	−	201.518i	0.0671350	−	0.298988i
$675$			25.9808i			0.0384900i
$676$	−635.509	−	300.549i	−0.940103	−	0.444599i
$677$	989.373			1.46141			0.730704	−	0.682695i	$-0.239192\pi$
$677$	989.373			1.46141			0.730704	+	0.682695i	$0.239192\pi$
$678$	584.102	+	131.155i	0.861507	+	0.193444i
$679$		−	434.063i		−	0.639268i
$680$	−153.090	+	196.186i	−0.225132	+	0.288509i
$681$	273.057			0.400965
$682$	−95.5276	+	425.435i	−0.140070	+	0.623806i
$683$		−	307.312i		−	0.449945i	−0.974365	−	0.224972i	$-0.927771\pi$
$683$		−	307.312i		−	0.449945i	0.974365	−	0.224972i	$-0.0722292\pi$
$684$	88.4816	−	187.094i	0.129359	−	0.273529i
$685$	−43.6222			−0.0636821
$686$	−715.518	−	160.663i	−1.04303	−	0.234203i
$687$			473.107i			0.688656i
$688$	622.009	−	510.536i	0.904083	−	0.742058i
$689$	1515.23			2.19917
$690$	57.2151	−	254.809i	0.0829205	−	0.369289i
$691$		−	893.378i		−	1.29288i	−0.762966	−	0.646438i	$-0.776258\pi$
$691$		−	893.378i		−	1.29288i	0.762966	−	0.646438i	$-0.223742\pi$
$692$	100.237	+	47.4048i	0.144852	+	0.0685041i
$693$	−176.266			−0.254353
$694$	298.978	+	67.1329i	0.430805	+	0.0967332i
$695$			575.496i			0.828052i
$696$	−312.621	−	243.948i	−0.449169	−	0.350500i
$697$	−613.186			−0.879750
$698$	−37.1270	+	165.346i	−0.0531906	+	0.236886i
$699$		−	188.353i		−	0.269461i
$700$	−54.1391	+	114.477i	−0.0773415	+	0.163538i
$701$	1127.42			1.60830			0.804149	−	0.594428i	$-0.202622\pi$
$701$	1127.42			1.60830			0.804149	+	0.594428i	$0.202622\pi$
$702$	188.270	+	42.2744i	0.268191	+	0.0602199i
$703$			1161.29i			1.65191i
$704$	576.084	−	144.360i	0.818301	−	0.205056i
$705$	120.680			0.171177
$706$	112.200	−	499.688i	0.158924	−	0.707773i
$707$			274.762i			0.388631i
$708$	−120.722	−	57.0928i	−0.170512	−	0.0806395i
$709$	1093.27			1.54199			0.770997	−	0.636839i	$-0.219758\pi$
$709$	1093.27			1.54199			0.770997	+	0.636839i	$0.219758\pi$
$710$	58.1917	+	13.0664i	0.0819601	+	0.0184034i
$711$		−	423.926i		−	0.596239i
$712$	227.907	−	292.064i	0.320094	−	0.410202i
$713$	−792.091			−1.11093
$714$	−66.8470	+	297.705i	−0.0936233	+	0.416954i
$715$			385.271i			0.538841i
$716$	−349.415	+	738.837i	−0.488010	+	1.03190i
$717$	−310.026			−0.432393
$718$	−1302.10	−	292.374i	−1.81350	−	0.407206i
$719$			769.690i			1.07050i	0.844693	+	0.535251i	$0.179783\pi$
$719$			769.690i			1.07050i	−0.844693	+	0.535251i	$0.820217\pi$
$720$	−68.0955	−	82.9639i	−0.0945771	−	0.115228i
$721$	−543.205			−0.753405
$722$	27.8446	−	124.007i	0.0385660	−	0.171755i
$723$		−	621.154i		−	0.859134i
$724$	180.172	+	85.2081i	0.248857	+	0.117691i
$725$	−143.089			−0.197363
$726$	−117.921	−	26.4782i	−0.162426	−	0.0364713i
$727$		−	295.050i		−	0.405846i	−0.979195	−	0.202923i	$-0.934956\pi$
$727$		−	295.050i		−	0.405846i	0.979195	−	0.202923i	$-0.0650441\pi$
$728$	741.468	+	578.591i	1.01850	+	0.794767i
$729$	−27.0000			−0.0370370
$730$	40.0637	−	178.425i	0.0548817	−	0.244418i
$731$		−	699.638i		−	0.957097i
$732$	157.448	−	332.924i	0.215094	−	0.454814i
$733$	261.200			0.356344			0.178172	−	0.983999i	$-0.442982\pi$
$733$	261.200			0.356344			0.178172	+	0.983999i	$0.442982\pi$
$734$	478.684	+	107.484i	0.652158	+	0.146436i
$735$		−	34.5084i		−	0.0469502i
$736$	485.150	+	963.638i	0.659172	+	1.30929i
$737$	−41.7501			−0.0566487
$738$	57.9426	−	258.049i	0.0785130	−	0.349660i
$739$			482.679i			0.653151i	0.945171	+	0.326576i	$0.105895\pi$
$739$			482.679i			0.653151i	−0.945171	+	0.326576i	$0.894105\pi$
$740$	544.437	+	257.478i	0.735726	+	0.347944i
$741$	−554.652			−0.748519
$742$	−1008.31	−	226.407i	−1.35891	−	0.305130i
$743$			23.7067i			0.0319067i	0.999873	+	0.0159534i	$0.00507833\pi$
$743$			23.7067i			0.0319067i	−0.999873	+	0.0159534i	$0.994922\pi$
$744$	−200.271	+	256.648i	−0.269181	+	0.344957i
$745$	−249.709			−0.335180
$746$	306.189	−	1363.62i	0.410441	−	1.82791i
$747$			209.551i			0.280523i
$748$	220.756	−	466.788i	0.295129	−	0.624048i
$749$	−1159.17			−1.54762
$750$	−37.7889	−	8.48516i	−0.0503852	−	0.0113135i
$751$			395.508i			0.526642i	0.964708	+	0.263321i	$0.0848179\pi$
$751$			395.508i			0.526642i	−0.964708	+	0.263321i	$0.915182\pi$
$752$	−385.365	+	316.302i	−0.512453	+	0.420614i
$753$	530.389			0.704368
$754$	−232.825	+	1036.90i	−0.308787	+	1.37519i
$755$			14.4288i			0.0191110i
$756$	−118.968	−	56.2630i	−0.157365	−	0.0744219i
$757$	393.940			0.520396			0.260198	−	0.965555i	$-0.416212\pi$
$757$	393.940			0.520396			0.260198	+	0.965555i	$0.416212\pi$
$758$	407.242	+	91.4425i	0.537259	+	0.120637i
$759$			541.891i			0.713954i
$760$	243.230	+	189.800i	0.320039	+	0.249737i
$761$	−369.354			−0.485354			−0.242677	−	0.970107i	$-0.578025\pi$
$761$	−369.354			−0.485354			−0.242677	+	0.970107i	$0.578025\pi$
$762$	16.9838	−	75.6379i	0.0222885	−	0.0992623i
$763$		−	515.903i		−	0.676150i
$764$	1.94443	−	4.11150i	0.00254507	−	0.00538154i
$765$	−93.3181			−0.121984
$766$	−305.444	−	68.5846i	−0.398751	−	0.0895360i
$767$			357.890i			0.466610i
$768$	434.896	+	86.4490i	0.566271	+	0.112564i
$769$	−873.491			−1.13588			−0.567940	−	0.823070i	$-0.692259\pi$
$769$	−873.491			−1.13588			−0.567940	+	0.823070i	$0.692259\pi$
$770$	57.5675	−	256.379i	0.0747630	−	0.332959i
$771$			434.852i			0.564010i
$772$	277.150	+	131.071i	0.359003	+	0.169782i
$773$	−1176.93			−1.52254			−0.761272	−	0.648432i	$-0.775425\pi$
$773$	−1176.93			−1.52254			−0.761272	+	0.648432i	$0.775425\pi$
$774$	294.431	+	66.1119i	0.380402	+	0.0854159i
$775$			117.469i			0.151573i
$776$	−337.394	+	432.372i	−0.434786	+	0.557181i
$777$	738.433			0.950365
$778$	169.392	−	754.393i	0.217728	−	0.969657i
$779$			760.224i			0.975897i
$780$	−122.976	+	260.032i	−0.157661	+	0.333374i
$781$	−123.754			−0.158455
$782$	915.228	+	205.506i	1.17037	+	0.262795i
$783$		−	148.702i		−	0.189913i
$784$	90.4464	+	110.195i	0.115365	+	0.140555i
$785$	−169.734			−0.216222
$786$	−1.33053	+	5.92555i	−0.00169278	+	0.00753887i
$787$			603.482i			0.766814i	0.923580	+	0.383407i	$0.125249\pi$
$787$			603.482i			0.766814i	−0.923580	+	0.383407i	$0.874751\pi$
$788$	−486.338	−	230.002i	−0.617180	−	0.291880i
$789$	84.4626			0.107050
$790$	616.598	+	138.452i	0.780504	+	0.175255i
$791$			1094.20i			1.38331i
$792$	175.580	+	137.011i	0.221692	+	0.172993i
$793$	−986.975			−1.24461
$794$	−245.882	+	1095.04i	−0.309675	+	1.37915i
$795$		−	316.062i		−	0.397563i
$796$	−301.002	+	636.467i	−0.378143	+	0.799582i
$797$	860.121			1.07920			0.539599	−	0.841922i	$-0.318576\pi$
$797$	860.121			1.07920			0.539599	+	0.841922i	$0.318576\pi$
$798$	369.093	+	82.8765i	0.462523	+	0.103855i
$799$			433.460i			0.542503i
$800$	142.910	−	71.9491i	0.178638	−	0.0899364i
$801$	138.924			0.173438
$802$	7.41967	−	33.0437i	0.00925146	−	0.0412017i
$803$			379.448i			0.472538i
$804$	−28.1784	−	13.3263i	−0.0350478	−	0.0165750i
$805$	477.336			0.592963
$806$	851.245	+	191.139i	1.05614	+	0.237145i
$807$		−	257.548i		−	0.319143i
$808$	213.570	−	273.692i	0.264320	−	0.338728i
$809$	941.012			1.16318			0.581589	−	0.813483i	$-0.302431\pi$
$809$	941.012			1.16318			0.581589	+	0.813483i	$0.302431\pi$
$810$	8.81803	−	39.2714i	0.0108865	−	0.0484832i
$811$			1105.29i			1.36287i	0.731878	+	0.681436i	$0.238644\pi$
$811$			1105.29i			1.36287i	−0.731878	+	0.681436i	$0.761356\pi$
$812$	309.867	−	655.213i	0.381610	−	0.806912i
$813$	−144.352			−0.177554
$814$	−1219.30	−	273.784i	−1.49792	−	0.336344i
$815$		−	557.448i		−	0.683985i
$816$	297.991	−	244.586i	0.365185	−	0.299738i
$817$	−867.407			−1.06170
$818$	113.263	−	504.421i	0.138463	−	0.616652i
$819$			352.688i			0.430632i
$820$	356.408	+	168.555i	0.434644	+	0.205554i
$821$	−193.170			−0.235286			−0.117643	−	0.993056i	$-0.537534\pi$
$821$	−193.170			−0.235286			−0.117643	+	0.993056i	$0.537534\pi$
$822$	65.9374	+	14.8057i	0.0802159	+	0.0180117i
$823$			178.778i			0.217227i	0.994084	+	0.108614i	$0.0346411\pi$
$823$			178.778i			0.217227i	−0.994084	+	0.108614i	$0.965359\pi$
$824$	541.090	+	422.229i	0.656662	+	0.512414i
$825$	80.3639			0.0974108
$826$	53.4761	−	238.158i	0.0647410	−	0.288326i
$827$		−	1558.61i		−	1.88465i	−0.334697	−	0.942326i	$-0.608634\pi$
$827$		−	1558.61i		−	1.88465i	0.334697	−	0.942326i	$-0.391366\pi$
$828$	−172.968	+	365.740i	−0.208898	+	0.441714i
$829$	−565.477			−0.682119			−0.341059	−	0.940042i	$-0.610786\pi$
$829$	−565.477			−0.682119			−0.341059	+	0.940042i	$0.610786\pi$
$830$	−304.791	−	68.4380i	−0.367218	−	0.0824555i
$831$		−	249.554i		−	0.300306i
$832$	−288.846	−	1152.67i	−0.347171	−	1.38543i
$833$	123.948			0.148797
$834$	195.327	−	869.895i	0.234205	−	1.04304i
$835$			177.071i			0.212061i
$836$	−578.721	−	273.692i	−0.692250	−	0.327383i
$837$	−122.078			−0.145851
$838$	505.254	+	113.450i	0.602928	+	0.135382i
$839$		−	1280.25i		−	1.52592i	−0.646443	−	0.762962i	$-0.723744\pi$
$839$		−	1280.25i		−	1.52592i	0.646443	−	0.762962i	$-0.276256\pi$
$840$	120.688	−	154.663i	0.143677	−	0.184123i
$841$	−22.0271			−0.0261915
$842$	42.7066	−	190.195i	0.0507204	−	0.225885i
$843$			595.256i			0.706116i
$844$	−372.952	+	788.604i	−0.441886	+	0.934365i
$845$	392.986			0.465072
$846$	−182.415	−	40.9595i	−0.215620	−	0.0484155i
$847$		−	220.903i		−	0.260806i
$848$	828.398	+	1009.28i	0.976885	+	1.19018i
$849$	−545.518			−0.642542
$850$	30.4771	−	135.731i	0.0358554	−	0.159683i
$851$		−	2270.15i		−	2.66762i
$852$	−83.5252	−	39.5012i	−0.0980343	−	0.0463630i
$853$	120.366			0.141109			0.0705546	−	0.997508i	$-0.477523\pi$
$853$	120.366			0.141109			0.0705546	+	0.997508i	$0.477523\pi$
$854$	656.782	+	147.474i	0.769066	+	0.172687i
$855$			115.695i			0.135316i
$856$	1154.66	+	901.014i	1.34890	+	1.05259i
$857$	−717.784			−0.837554			−0.418777	−	0.908089i	$-0.637541\pi$
$857$	−717.784			−0.837554			−0.418777	+	0.908089i	$0.637541\pi$
$858$	130.764	−	582.360i	0.152405	−	0.678741i
$859$		−	252.894i		−	0.294405i	−0.989106	−	0.147203i	$-0.952973\pi$
$859$		−	252.894i		−	0.294405i	0.989106	−	0.147203i	$-0.0470269\pi$
$860$	−192.319	+	406.658i	−0.223627	+	0.472858i
$861$	483.405			0.561446
$862$	760.989	+	170.873i	0.882817	+	0.198229i
$863$		−	1234.73i		−	1.43075i	−0.698743	−	0.715373i	$-0.746257\pi$
$863$		−	1234.73i		−	1.43075i	0.698743	−	0.715373i	$-0.253743\pi$
$864$	74.7717	+	148.517i	0.0865413	+	0.171894i
$865$	−61.9847			−0.0716586
$866$	120.888	−	538.381i	0.139594	−	0.621687i
$867$			165.382i			0.190752i
$868$	−537.901	−	254.387i	−0.619701	−	0.293073i
$869$	−1311.29			−1.50897
$870$	216.286	+	48.5651i	0.248605	+	0.0558220i
$871$			83.5368i			0.0959091i
$872$	−401.007	+	513.894i	−0.459871	+	0.589327i
$873$	−205.663			−0.235582
$874$	254.785	−	1134.69i	0.291516	−	1.29828i
$875$		−	70.7902i		−	0.0809030i
$876$	−121.117	+	256.101i	−0.138261	+	0.292353i
$877$	−685.723			−0.781896			−0.390948	−	0.920413i	$-0.627853\pi$
$877$	−685.723			−0.781896			−0.390948	+	0.920413i	$0.627853\pi$
$878$	−870.609	−	195.487i	−0.991582	−	0.222651i
$879$			11.3522i			0.0129149i
$880$	−256.625	+	210.634i	−0.291619	+	0.239356i
$881$	−458.454			−0.520379			−0.260189	−	0.965558i	$-0.583785\pi$
$881$	−458.454			−0.520379			−0.260189	+	0.965558i	$0.583785\pi$
$882$	−11.7124	+	52.1614i	−0.0132793	+	0.0591399i
$883$			771.505i			0.873732i	0.899527	+	0.436866i	$0.143912\pi$
$883$			771.505i			0.873732i	−0.899527	+	0.436866i	$0.856088\pi$
$884$	−933.986	−	441.707i	−1.05655	−	0.499668i
$885$	74.6523			0.0843529
$886$	−1550.75	−	348.206i	−1.75028	−	0.393009i
$887$			1161.05i			1.30896i	0.756080	+	0.654480i	$0.227112\pi$
$887$			1161.05i			1.30896i	−0.756080	+	0.654480i	$0.772888\pi$
$888$	−735.558	−	573.979i	−0.828331	−	0.646372i
$889$	141.693			0.159385
$890$	−45.3716	+	202.064i	−0.0509793	+	0.227038i
$891$			83.5166i			0.0937336i
$892$	561.905	−	1188.15i	0.629938	−	1.33200i
$893$	537.401			0.601793
$894$	377.450	+	84.7529i	0.422203	+	0.0948019i
$895$		−	456.882i		−	0.510482i
$896$	19.9793	+	810.207i	0.0222983	+	0.904248i
$897$	1084.26			1.20876
$898$	−328.728	+	1464.00i	−0.366066	+	1.63029i
$899$		−	672.340i		−	0.747876i
$900$	54.2402	+	25.6516i	0.0602669	+	0.0285018i
$901$	1135.24			1.25997
$902$	−798.200	−	179.229i	−0.884923	−	0.198701i
$903$			551.560i			0.610808i
$904$	850.514	−	1089.94i	0.940834	−	1.20569i
$905$	−111.415			−0.123110
$906$	4.89722	−	21.8099i	0.00540532	−	0.0240728i
$907$		−	392.544i		−	0.432793i	−0.976306	−	0.216397i	$-0.930570\pi$
$907$		−	392.544i		−	0.432793i	0.976306	−	0.216397i	$-0.0694304\pi$
$908$	269.597	−	570.062i	0.296913	−	0.627822i
$909$	130.185			0.143218
$910$	−512.983	−	115.186i	−0.563718	−	0.126578i
$911$		−	1013.40i		−	1.11240i	−0.831048	−	0.556201i	$-0.812259\pi$
$911$		−	1013.40i		−	1.11240i	0.831048	−	0.556201i	$-0.187741\pi$
$912$	−303.237	−	369.447i	−0.332496	−	0.405096i
$913$	648.185			0.709950
$914$	44.2958	−	197.273i	0.0484637	−	0.215835i
$915$			205.874i			0.224998i
$916$	987.707	+	467.112i	1.07828	+	0.509948i
$917$	−11.1004			−0.0121051
$918$	141.056	+	31.6727i	0.153655	+	0.0345019i
$919$			970.018i			1.05551i	0.849395	+	0.527757i	$0.176967\pi$
$919$			970.018i			1.05551i	−0.849395	+	0.527757i	$0.823033\pi$
$920$	−475.477	−	371.029i	−0.516822	−	0.403293i
$921$	−614.115			−0.666791
$922$	−1.96603	+	8.75578i	−0.00213236	+	0.00949651i
$923$			247.616i			0.268273i
$924$	−174.033	+	367.992i	−0.188348	+	0.398260i
$925$	−336.669			−0.363966
$926$	1005.19	+	225.706i	1.08552	+	0.243743i
$927$			257.376i			0.277644i
$928$	−817.952	+	411.804i	−0.881414	+	0.443754i
$929$	980.857			1.05582			0.527910	−	0.849300i	$-0.322976\pi$
$929$	980.857			1.05582			0.527910	+	0.849300i	$0.322976\pi$
$930$	39.8698	−	177.561i	0.0428708	−	0.190926i
$931$		−	153.670i		−	0.165059i
$932$	−393.226	−	185.967i	−0.421917	−	0.199535i
$933$	−334.956			−0.359010
$934$	−576.638	−	129.479i	−0.617386	−	0.138628i
$935$			288.652i			0.308719i
$936$	274.141	−	351.314i	0.292886	−	0.375336i
$937$	964.666			1.02953			0.514763	−	0.857333i	$-0.327880\pi$
$937$	964.666			1.02953			0.514763	+	0.857333i	$0.327880\pi$
$938$	12.4821	−	55.5896i	0.0133072	−	0.0592639i
$939$			40.7420i			0.0433887i
$940$	119.151	−	251.944i	0.126756	−	0.268026i
$941$	−1581.10			−1.68023			−0.840117	−	0.542405i	$-0.817514\pi$
$941$	−1581.10			−1.68023			−0.840117	+	0.542405i	$0.817514\pi$
$942$	256.563	+	57.6089i	0.272360	+	0.0611560i
$943$		−	1486.12i		−	1.57595i
$944$	−238.386	+	195.663i	−0.252527	+	0.207271i
$945$	73.5673			0.0778490
$946$	204.498	−	910.738i	0.216171	−	0.962725i
$947$			1245.27i			1.31497i	0.753469	+	0.657483i	$0.228379\pi$
$947$			1245.27i			1.31497i	−0.753469	+	0.657483i	$0.771621\pi$
$948$	−885.032	−	418.555i	−0.933578	−	0.441513i
$949$	759.229			0.800031
$950$	−168.278	−	37.7853i	−0.177135	−	0.0397740i
$951$			370.666i			0.389765i
$952$	555.521	+	433.490i	0.583530	+	0.455347i
$953$	1106.52			1.16109			0.580546	−	0.814228i	$-0.302839\pi$
$953$	1106.52			1.16109			0.580546	+	0.814228i	$0.302839\pi$
$954$	−107.274	+	477.746i	−0.112446	+	0.500782i
$955$			2.54247i			0.00266227i
$956$	−306.098	+	647.243i	−0.320186	+	0.677032i
$957$	−459.966			−0.480633
$958$	533.037	+	119.689i	0.556406	+	0.124936i
$959$			123.521i			0.128802i
$960$	−240.437	+	60.2506i	−0.250455	+	0.0627610i
$961$	409.039			0.425638
$962$	−547.808	+	2439.68i	−0.569447	+	2.53605i
$963$			549.225i			0.570327i
$964$	−1296.79	−	613.284i	−1.34521	−	0.636187i
$965$	−171.384			−0.177600
$966$	−721.520	−	162.011i	−0.746915	−	0.167713i
$967$		−	406.453i		−	0.420324i	−0.977667	−	0.210162i	$-0.932601\pi$
$967$		−	406.453i		−	0.420324i	0.977667	−	0.210162i	$-0.0673992\pi$
$968$	−171.706	+	220.042i	−0.177382	+	0.227316i
$969$	−415.555			−0.428850
$970$	67.1682	−	299.136i	0.0692456	−	0.308388i
$971$			1815.22i			1.86943i	0.355393	+	0.934717i	$0.384347\pi$
$971$			1815.22i			1.86943i	−0.355393	+	0.934717i	$0.615653\pi$
$972$	−26.6579	+	56.3680i	−0.0274258	+	0.0579918i
$973$	1629.58			1.67480
$974$	698.119	+	156.756i	0.716754	+	0.160941i
$975$		−	160.798i		−	0.164922i
$976$	−539.594	−	657.412i	−0.552862	−	0.673578i
$977$	−1457.74			−1.49205			−0.746027	−	0.665916i	$-0.768041\pi$
$977$	−1457.74			−1.49205			−0.746027	+	0.665916i	$0.768041\pi$
$978$	−189.201	+	842.614i	−0.193457	+	0.861568i
$979$		−	429.720i		−	0.438938i
$980$	−72.0434	−	34.0712i	−0.0735137	−	0.0347665i
$981$	−244.439			−0.249174
$982$	−824.235	−	185.074i	−0.839343	−	0.188467i
$983$		−	19.9496i		−	0.0202946i	−0.999949	−	0.0101473i	$-0.996770\pi$
$983$		−	19.9496i		−	0.0202946i	0.999949	−	0.0101473i	$-0.00323004\pi$
$984$	−481.522	−	375.747i	−0.489352	−	0.381857i
$985$	300.741			0.305321
$986$	−174.437	+	776.860i	−0.176914	+	0.787891i
$987$		−	341.718i		−	0.346219i
$988$	−547.625	+	1157.95i	−0.554276	+	1.17201i
$989$	1695.65			1.71450
$990$	−121.475	−	27.2760i	−0.122702	−	0.0275515i
$991$		−	605.720i		−	0.611221i	−0.952157	−	0.305611i	$-0.901139\pi$
$991$		−	605.720i		−	0.611221i	0.952157	−	0.305611i	$-0.0988605\pi$
$992$	338.073	+	671.502i	0.340799	+	0.676918i
$993$	714.392			0.719428
$994$	36.9989	−	164.776i	0.0372223	−	0.165771i
$995$		−	393.578i		−	0.395556i
$996$	437.481	+	206.896i	0.439237	+	0.207727i
$997$	1238.47			1.24220			0.621099	−	0.783732i	$-0.286686\pi$
$997$	1238.47			1.24220			0.621099	+	0.783732i	$0.286686\pi$
$998$	−404.129	−	90.7434i	−0.404939	−	0.0909253i
$999$		−	349.876i		−	0.350227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.3.c.a.31.3	✓	8
3.2	odd	2		180.3.c.b.91.6		8
4.3	odd	2	inner	60.3.c.a.31.4	yes	8
5.2	odd	4		300.3.f.b.199.16		16
5.3	odd	4		300.3.f.b.199.1		16
5.4	even	2		300.3.c.d.151.6		8
8.3	odd	2		960.3.e.c.511.2		8
8.5	even	2		960.3.e.c.511.5		8
12.11	even	2		180.3.c.b.91.5		8
15.2	even	4		900.3.f.f.199.1		16
15.8	even	4		900.3.f.f.199.16		16
15.14	odd	2		900.3.c.u.451.3		8
20.3	even	4		300.3.f.b.199.15		16
20.7	even	4		300.3.f.b.199.2		16
20.19	odd	2		300.3.c.d.151.5		8
24.5	odd	2		2880.3.e.j.2431.5		8
24.11	even	2		2880.3.e.j.2431.8		8
60.23	odd	4		900.3.f.f.199.2		16
60.47	odd	4		900.3.f.f.199.15		16
60.59	even	2		900.3.c.u.451.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.c.a.31.3	✓	8	1.1	even	1	trivial
60.3.c.a.31.4	yes	8	4.3	odd	2	inner
180.3.c.b.91.5		8	12.11	even	2
180.3.c.b.91.6		8	3.2	odd	2
300.3.c.d.151.5		8	20.19	odd	2
300.3.c.d.151.6		8	5.4	even	2
300.3.f.b.199.1		16	5.3	odd	4
300.3.f.b.199.2		16	20.7	even	4
300.3.f.b.199.15		16	20.3	even	4
300.3.f.b.199.16		16	5.2	odd	4
900.3.c.u.451.3		8	15.14	odd	2
900.3.c.u.451.4		8	60.59	even	2
900.3.f.f.199.1		16	15.2	even	4
900.3.f.f.199.2		16	60.23	odd	4
900.3.f.f.199.15		16	60.47	odd	4
900.3.f.f.199.16		16	15.8	even	4
960.3.e.c.511.2		8	8.3	odd	2
960.3.e.c.511.5		8	8.5	even	2
2880.3.e.j.2431.5		8	24.5	odd	2
2880.3.e.j.2431.8		8	24.11	even	2

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	60.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.438172 - 1.95141i) q^{2} -1.73205i q^{3} +(-3.61601 - 1.71011i) q^{4} +2.23607 q^{5} +(-3.37994 - 0.758935i) q^{6} -6.33166i q^{7} +(-4.92155 + 6.30701i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(0.438172 - 1.95141i) q^{2} -1.73205i q^{3} +(-3.61601 - 1.71011i) q^{4} +2.23607 q^{5} +(-3.37994 - 0.758935i) q^{6} -6.33166i q^{7} +(-4.92155 + 6.30701i) q^{8} -3.00000 q^{9} +(0.979781 - 4.36349i) q^{10} +9.27963i q^{11} +(-2.96199 + 6.26312i) q^{12} +18.5674 q^{13} +(-12.3557 - 2.77436i) q^{14} -3.87298i q^{15} +(10.1511 + 12.3675i) q^{16} +13.9110 q^{17} +(-1.31451 + 5.85423i) q^{18} -17.2468i q^{19} +(-8.08565 - 3.82391i) q^{20} -10.9668 q^{21} +(18.1084 + 4.06607i) q^{22} +33.7148i q^{23} +(10.9241 + 8.52438i) q^{24} +5.00000 q^{25} +(8.13571 - 36.2327i) q^{26} +5.19615i q^{27} +(-10.8278 + 22.8954i) q^{28} -28.6177 q^{29} +(-7.55778 - 1.69703i) q^{30} +23.4939i q^{31} +(28.5820 - 14.3898i) q^{32} +16.0728 q^{33} +(6.09542 - 27.1461i) q^{34} -14.1580i q^{35} +(10.8480 + 5.13032i) q^{36} -67.3338 q^{37} +(-33.6556 - 7.55706i) q^{38} -32.1597i q^{39} +(-11.0049 + 14.1029i) q^{40} -44.0791 q^{41} +(-4.80532 + 21.4007i) q^{42} -50.2937i q^{43} +(15.8691 - 33.5552i) q^{44} -6.70820 q^{45} +(65.7915 + 14.7729i) q^{46} +31.1594i q^{47} +(21.4212 - 17.5822i) q^{48} +8.91003 q^{49} +(2.19086 - 9.75706i) q^{50} -24.0946i q^{51} +(-67.1400 - 31.7522i) q^{52} +81.6070 q^{53} +(10.1398 + 2.27681i) q^{54} +20.7499i q^{55} +(39.9338 + 31.1616i) q^{56} -29.8724 q^{57} +(-12.5395 + 55.8449i) q^{58} +19.2751i q^{59} +(-6.62321 + 14.0048i) q^{60} -53.1563 q^{61} +(45.8462 + 10.2943i) q^{62} +18.9950i q^{63} +(-15.5566 - 62.0805i) q^{64} +41.5180 q^{65} +(7.04264 - 31.3646i) q^{66} +4.49911i q^{67} +(-50.3025 - 23.7893i) q^{68} +58.3958 q^{69} +(-27.6281 - 6.20365i) q^{70} +13.3360i q^{71} +(14.7647 - 18.9210i) q^{72} +40.8904 q^{73} +(-29.5037 + 131.396i) q^{74} -8.66025i q^{75} +(-29.4939 + 62.3647i) q^{76} +58.7555 q^{77} +(-62.7568 - 14.0915i) q^{78} +141.309i q^{79} +(22.6985 + 27.6546i) q^{80} +9.00000 q^{81} +(-19.3142 + 86.0164i) q^{82} -69.8503i q^{83} +(39.6559 + 18.7543i) q^{84} +31.1060 q^{85} +(-98.1438 - 22.0373i) q^{86} +49.5673i q^{87} +(-58.5266 - 45.6702i) q^{88} -46.3079 q^{89} +(-2.93934 + 13.0905i) q^{90} -117.563i q^{91} +(57.6559 - 121.913i) q^{92} +40.6926 q^{93} +(60.8049 + 13.6532i) q^{94} -38.5651i q^{95} +(-24.9239 - 49.5055i) q^{96} +68.5543 q^{97} +(3.90412 - 17.3871i) q^{98} -27.8389i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 10 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 + 10 * q^4 - 6 * q^6 - 20 * q^8 - 24 * q^9	\( 8 q + 4 q^{2} + 10 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9} + 10 q^{10} + 16 q^{13} - 20 q^{14} + 34 q^{16} - 12 q^{18} - 40 q^{20} - 48 q^{21} + 68 q^{22} + 18 q^{24} + 40 q^{25} - 36 q^{26} + 28 q^{28} + 64 q^{29} - 76 q^{32} - 92 q^{34} - 30 q^{36} - 112 q^{37} - 40 q^{38} - 10 q^{40} - 16 q^{41} + 108 q^{42} + 172 q^{44} + 152 q^{46} + 48 q^{48} - 56 q^{49} + 20 q^{50} - 128 q^{52} + 352 q^{53} + 18 q^{54} + 116 q^{56} + 144 q^{57} - 204 q^{58} + 30 q^{60} - 176 q^{61} - 56 q^{62} - 110 q^{64} - 80 q^{65} + 108 q^{66} - 184 q^{68} - 96 q^{69} - 60 q^{70} + 60 q^{72} - 240 q^{73} + 132 q^{74} - 24 q^{76} - 288 q^{77} - 240 q^{78} - 80 q^{80} + 72 q^{81} + 40 q^{82} - 36 q^{84} + 160 q^{85} - 200 q^{86} + 140 q^{88} + 80 q^{89} - 30 q^{90} + 144 q^{92} + 144 q^{93} - 96 q^{94} - 174 q^{96} + 432 q^{97} + 660 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 + 10 * q^4 - 6 * q^6 - 20 * q^8 - 24 * q^9 + 10 * q^10 + 16 * q^13 - 20 * q^14 + 34 * q^16 - 12 * q^18 - 40 * q^20 - 48 * q^21 + 68 * q^22 + 18 * q^24 + 40 * q^25 - 36 * q^26 + 28 * q^28 + 64 * q^29 - 76 * q^32 - 92 * q^34 - 30 * q^36 - 112 * q^37 - 40 * q^38 - 10 * q^40 - 16 * q^41 + 108 * q^42 + 172 * q^44 + 152 * q^46 + 48 * q^48 - 56 * q^49 + 20 * q^50 - 128 * q^52 + 352 * q^53 + 18 * q^54 + 116 * q^56 + 144 * q^57 - 204 * q^58 + 30 * q^60 - 176 * q^61 - 56 * q^62 - 110 * q^64 - 80 * q^65 + 108 * q^66 - 184 * q^68 - 96 * q^69 - 60 * q^70 + 60 * q^72 - 240 * q^73 + 132 * q^74 - 24 * q^76 - 288 * q^77 - 240 * q^78 - 80 * q^80 + 72 * q^81 + 40 * q^82 - 36 * q^84 + 160 * q^85 - 200 * q^86 + 140 * q^88 + 80 * q^89 - 30 * q^90 + 144 * q^92 + 144 * q^93 - 96 * q^94 - 174 * q^96 + 432 * q^97 + 660 * q^98

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