LMFDB - Embedded newform 24.3.b.a.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [24,3,Mod(19,24)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(24, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("24.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	24.b (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:	$0.653952634465$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.4752.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} - 6x + 6 $ x^4 + 3x^2 - 6x + 6
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.4
Root			$-0.866025 - 1.99551i$ of defining polynomial
Character	$\chi$	$=$	24.19
Dual form			24.3.b.a.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 + 1.46081i) q^{2} -1.73205 q^{3} +(-0.267949 + 3.99102i) q^{4} -7.98203i q^{5} +(-2.36603 - 2.53020i) q^{6} +2.13878i q^{7} +(-6.19615 + 5.06040i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(1.36603 + 1.46081i) q^{2} -1.73205 q^{3} +(-0.267949 + 3.99102i) q^{4} -7.98203i q^{5} +(-2.36603 - 2.53020i) q^{6} +2.13878i q^{7} +(-6.19615 + 5.06040i) q^{8} +3.00000 q^{9} +(11.6603 - 10.9037i) q^{10} -8.00000 q^{11} +(0.464102 - 6.91264i) q^{12} +11.6865i q^{13} +(-3.12436 + 2.92163i) q^{14} +13.8253i q^{15} +(-15.8564 - 2.13878i) q^{16} +11.8564 q^{17} +(4.09808 + 4.38244i) q^{18} +14.9282 q^{19} +(31.8564 + 2.13878i) q^{20} -3.70447i q^{21} +(-10.9282 - 11.6865i) q^{22} -4.27756i q^{23} +(10.7321 - 8.76488i) q^{24} -38.7128 q^{25} +(-17.0718 + 15.9641i) q^{26} -5.19615 q^{27} +(-8.53590 - 0.573084i) q^{28} +0.573084i q^{29} +(-20.1962 + 18.8857i) q^{30} -57.4399i q^{31} +(-18.5359 - 26.0849i) q^{32} +13.8564 q^{33} +(16.1962 + 17.3200i) q^{34} +17.0718 q^{35} +(-0.803848 + 11.9730i) q^{36} +27.6506i q^{37} +(20.3923 + 21.8073i) q^{38} -20.2416i q^{39} +(40.3923 + 49.4579i) q^{40} -31.5692 q^{41} +(5.41154 - 5.06040i) q^{42} +28.7846 q^{43} +(2.14359 - 31.9281i) q^{44} -23.9461i q^{45} +(6.24871 - 5.84325i) q^{46} +59.5787i q^{47} +(27.4641 + 3.70447i) q^{48} +44.4256 q^{49} +(-52.8827 - 56.5522i) q^{50} -20.5359 q^{51} +(-46.6410 - 3.13139i) q^{52} +31.3550i q^{53} +(-7.09808 - 7.59061i) q^{54} +63.8562i q^{55} +(-10.8231 - 13.2522i) q^{56} -25.8564 q^{57} +(-0.837169 + 0.782847i) q^{58} -52.7846 q^{59} +(-55.1769 - 3.70447i) q^{60} -59.5787i q^{61} +(83.9090 - 78.4644i) q^{62} +6.41634i q^{63} +(12.7846 - 62.7101i) q^{64} +93.2820 q^{65} +(18.9282 + 20.2416i) q^{66} -84.7846 q^{67} +(-3.17691 + 47.3191i) q^{68} +7.40895i q^{69} +(23.3205 + 24.9387i) q^{70} -42.4685i q^{71} +(-18.5885 + 15.1812i) q^{72} -5.42563 q^{73} +(-40.3923 + 37.7714i) q^{74} +67.0526 q^{75} +(-4.00000 + 59.5787i) q^{76} -17.1102i q^{77} +(29.5692 - 27.6506i) q^{78} +44.6072i q^{79} +(-17.0718 + 126.566i) q^{80} +9.00000 q^{81} +(-43.1244 - 46.1167i) q^{82} +67.7128 q^{83} +(14.7846 + 0.992611i) q^{84} -94.6382i q^{85} +(39.3205 + 42.0489i) q^{86} -0.992611i q^{87} +(49.5692 - 40.4832i) q^{88} -133.138 q^{89} +(34.9808 - 32.7110i) q^{90} -24.9948 q^{91} +(17.0718 + 1.14617i) q^{92} +99.4888i q^{93} +(-87.0333 + 81.3860i) q^{94} -119.157i q^{95} +(32.1051 + 45.1803i) q^{96} +97.1384 q^{97} +(60.6865 + 64.8975i) q^{98} -24.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 8 q^{4} - 6 q^{6} - 4 q^{8} + 12 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 8 * q^4 - 6 * q^6 - 4 * q^8 + 12 * q^9	$ 4 q + 2 q^{2} - 8 q^{4} - 6 q^{6} - 4 q^{8} + 12 q^{9} + 12 q^{10} - 32 q^{11} - 12 q^{12} + 36 q^{14} - 8 q^{16} - 8 q^{17} + 6 q^{18} + 32 q^{19} + 72 q^{20} - 16 q^{22} + 36 q^{24} - 44 q^{25} - 96 q^{26} - 48 q^{28} - 60 q^{30} - 88 q^{32} + 44 q^{34} + 96 q^{35} - 24 q^{36} + 40 q^{38} + 120 q^{40} + 40 q^{41} + 84 q^{42} + 32 q^{43} + 64 q^{44} - 72 q^{46} + 96 q^{48} - 44 q^{49} - 118 q^{50} - 96 q^{51} - 48 q^{52} - 18 q^{54} - 168 q^{56} - 48 q^{57} + 156 q^{58} - 128 q^{59} - 96 q^{60} + 204 q^{62} - 32 q^{64} + 96 q^{65} + 48 q^{66} - 256 q^{67} + 112 q^{68} + 24 q^{70} - 12 q^{72} + 200 q^{73} - 120 q^{74} + 192 q^{75} - 16 q^{76} - 48 q^{78} - 96 q^{80} + 36 q^{81} - 124 q^{82} + 160 q^{83} - 24 q^{84} + 88 q^{86} + 32 q^{88} - 200 q^{89} + 36 q^{90} + 288 q^{91} + 96 q^{92} - 168 q^{94} - 24 q^{96} + 56 q^{97} + 170 q^{98} - 96 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 8 * q^4 - 6 * q^6 - 4 * q^8 + 12 * q^9 + 12 * q^10 - 32 * q^11 - 12 * q^12 + 36 * q^14 - 8 * q^16 - 8 * q^17 + 6 * q^18 + 32 * q^19 + 72 * q^20 - 16 * q^22 + 36 * q^24 - 44 * q^25 - 96 * q^26 - 48 * q^28 - 60 * q^30 - 88 * q^32 + 44 * q^34 + 96 * q^35 - 24 * q^36 + 40 * q^38 + 120 * q^40 + 40 * q^41 + 84 * q^42 + 32 * q^43 + 64 * q^44 - 72 * q^46 + 96 * q^48 - 44 * q^49 - 118 * q^50 - 96 * q^51 - 48 * q^52 - 18 * q^54 - 168 * q^56 - 48 * q^57 + 156 * q^58 - 128 * q^59 - 96 * q^60 + 204 * q^62 - 32 * q^64 + 96 * q^65 + 48 * q^66 - 256 * q^67 + 112 * q^68 + 24 * q^70 - 12 * q^72 + 200 * q^73 - 120 * q^74 + 192 * q^75 - 16 * q^76 - 48 * q^78 - 96 * q^80 + 36 * q^81 - 124 * q^82 + 160 * q^83 - 24 * q^84 + 88 * q^86 + 32 * q^88 - 200 * q^89 + 36 * q^90 + 288 * q^91 + 96 * q^92 - 168 * q^94 - 24 * q^96 + 56 * q^97 + 170 * q^98 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/24\mathbb{Z}\right)^\times$.

$n$	$7$	$13$	$17$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	1.36603	+	1.46081i	0.683013	+	0.730406i
$2$	1.36603	+	1.46081i	0.683013	+	0.730406i
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−0.267949	+	3.99102i	−0.0669873	+	0.997754i
$5$		−	7.98203i		−	1.59641i	−0.602388	−	0.798203i	$-0.705784\pi$
$5$		−	7.98203i		−	1.59641i	0.602388	−	0.798203i	$-0.294216\pi$
$6$	−2.36603	−	2.53020i	−0.394338	−	0.421700i
$7$			2.13878i			0.305540i	0.988262	+	0.152770i	$0.0488193\pi$
$7$			2.13878i			0.305540i	−0.988262	+	0.152770i	$0.951181\pi$
$8$	−6.19615	+	5.06040i	−0.774519	+	0.632551i
$9$	3.00000			0.333333
$10$	11.6603	−	10.9037i	1.16603	−	1.09037i
$11$	−8.00000			−0.727273			−0.363636	−	0.931541i	$-0.618465\pi$
$11$	−8.00000			−0.727273			−0.363636	+	0.931541i	$0.618465\pi$
$12$	0.464102	−	6.91264i	0.0386751	−	0.576053i
$13$			11.6865i			0.898962i	0.893290	+	0.449481i	$0.148391\pi$
$13$			11.6865i			0.898962i	−0.893290	+	0.449481i	$0.851609\pi$
$14$	−3.12436	+	2.92163i	−0.223168	+	0.208688i
$15$			13.8253i			0.921686i
$16$	−15.8564	−	2.13878i	−0.991025	−	0.133674i
$17$	11.8564			0.697436			0.348718	−	0.937228i	$-0.386617\pi$
$17$	11.8564			0.697436			0.348718	+	0.937228i	$0.386617\pi$
$18$	4.09808	+	4.38244i	0.227671	+	0.243469i
$19$	14.9282			0.785695			0.392847	−	0.919604i	$-0.371490\pi$
$19$	14.9282			0.785695			0.392847	+	0.919604i	$0.371490\pi$
$20$	31.8564	+	2.13878i	1.59282	+	0.106939i
$21$		−	3.70447i		−	0.176403i
$22$	−10.9282	−	11.6865i	−0.496737	−	0.531205i
$23$		−	4.27756i		−	0.185981i	−0.995667	−	0.0929904i	$-0.970357\pi$
$23$		−	4.27756i		−	0.185981i	0.995667	−	0.0929904i	$-0.0296426\pi$
$24$	10.7321	−	8.76488i	0.447169	−	0.365203i
$25$	−38.7128			−1.54851
$26$	−17.0718	+	15.9641i	−0.656608	+	0.614002i
$27$	−5.19615			−0.192450
$28$	−8.53590	−	0.573084i	−0.304854	−	0.0204673i
$29$			0.573084i			0.0197615i	0.999951	+	0.00988076i	$0.00314519\pi$
$29$			0.573084i			0.0197615i	−0.999951	+	0.00988076i	$0.996855\pi$
$30$	−20.1962	+	18.8857i	−0.673205	+	0.629523i
$31$		−	57.4399i		−	1.85290i	−0.376417	−	0.926450i	$-0.622844\pi$
$31$		−	57.4399i		−	1.85290i	0.376417	−	0.926450i	$-0.377156\pi$
$32$	−18.5359	−	26.0849i	−0.579247	−	0.815152i
$33$	13.8564			0.419891
$34$	16.1962	+	17.3200i	0.476357	+	0.509412i
$35$	17.0718			0.487766
$36$	−0.803848	+	11.9730i	−0.0223291	+	0.332585i
$37$			27.6506i			0.747313i	0.927567	+	0.373656i	$0.121896\pi$
$37$			27.6506i			0.747313i	−0.927567	+	0.373656i	$0.878104\pi$
$38$	20.3923	+	21.8073i	0.536640	+	0.573877i
$39$		−	20.2416i		−	0.519016i
$40$	40.3923	+	49.4579i	1.00981	+	1.23645i
$41$	−31.5692			−0.769981			−0.384990	−	0.922921i	$-0.625795\pi$
$41$	−31.5692			−0.769981			−0.384990	+	0.922921i	$0.625795\pi$
$42$	5.41154	−	5.06040i	0.128846	−	0.120486i
$43$	28.7846			0.669410			0.334705	−	0.942323i	$-0.391363\pi$
$43$	28.7846			0.669410			0.334705	+	0.942323i	$0.391363\pi$
$44$	2.14359	−	31.9281i	0.0487180	−	0.725639i
$45$		−	23.9461i		−	0.532135i
$46$	6.24871	−	5.84325i	0.135842	−	0.127027i
$47$			59.5787i			1.26763i	0.773484	+	0.633816i	$0.218512\pi$
$47$			59.5787i			1.26763i	−0.773484	+	0.633816i	$0.781488\pi$
$48$	27.4641	+	3.70447i	0.572169	+	0.0771765i
$49$	44.4256			0.906645
$50$	−52.8827	−	56.5522i	−1.05765	−	1.13104i
$51$	−20.5359			−0.402665
$52$	−46.6410	−	3.13139i	−0.896943	−	0.0602190i
$53$			31.3550i			0.591604i	0.955249	+	0.295802i	$0.0955869\pi$
$53$			31.3550i			0.591604i	−0.955249	+	0.295802i	$0.904413\pi$
$54$	−7.09808	−	7.59061i	−0.131446	−	0.140567i
$55$			63.8562i			1.16102i
$56$	−10.8231	−	13.2522i	−0.193269	−	0.236646i
$57$	−25.8564			−0.453621
$58$	−0.837169	+	0.782847i	−0.0144339	+	0.0134974i
$59$	−52.7846			−0.894654			−0.447327	−	0.894370i	$-0.647624\pi$
$59$	−52.7846			−0.894654			−0.447327	+	0.894370i	$0.647624\pi$
$60$	−55.1769	−	3.70447i	−0.919615	−	0.0617412i
$61$		−	59.5787i		−	0.976700i	−0.872648	−	0.488350i	$-0.837599\pi$
$61$		−	59.5787i		−	0.976700i	0.872648	−	0.488350i	$-0.162401\pi$
$62$	83.9090	−	78.4644i	1.35337	−	1.26555i
$63$			6.41634i			0.101847i
$64$	12.7846	−	62.7101i	0.199760	−	0.979845i
$65$	93.2820			1.43511
$66$	18.9282	+	20.2416i	0.286791	+	0.306691i
$67$	−84.7846			−1.26544			−0.632721	−	0.774380i	$-0.718062\pi$
$67$	−84.7846			−1.26544			−0.632721	+	0.774380i	$0.718062\pi$
$68$	−3.17691	+	47.3191i	−0.0467193	+	0.695869i
$69$			7.40895i			0.107376i
$70$	23.3205	+	24.9387i	0.333150	+	0.356267i
$71$		−	42.4685i		−	0.598147i	−0.954230	−	0.299074i	$-0.903322\pi$
$71$		−	42.4685i		−	0.598147i	0.954230	−	0.299074i	$-0.0966776\pi$
$72$	−18.5885	+	15.1812i	−0.258173	+	0.210850i
$73$	−5.42563			−0.0743236			−0.0371618	−	0.999309i	$-0.511832\pi$
$73$	−5.42563			−0.0743236			−0.0371618	+	0.999309i	$0.511832\pi$
$74$	−40.3923	+	37.7714i	−0.545842	+	0.510424i
$75$	67.0526			0.894034
$76$	−4.00000	+	59.5787i	−0.0526316	+	0.783930i
$77$		−	17.1102i		−	0.222211i
$78$	29.5692	−	27.6506i	0.379093	−	0.354494i
$79$			44.6072i			0.564649i	0.959319	+	0.282324i	$0.0911054\pi$
$79$			44.6072i			0.564649i	−0.959319	+	0.282324i	$0.908895\pi$
$80$	−17.0718	+	126.566i	−0.213397	+	1.58208i
$81$	9.00000			0.111111
$82$	−43.1244	−	46.1167i	−0.525907	−	0.562399i
$83$	67.7128			0.815817			0.407909	−	0.913023i	$-0.366258\pi$
$83$	67.7128			0.815817			0.407909	+	0.913023i	$0.366258\pi$
$84$	14.7846	+	0.992611i	0.176007	+	0.0118168i
$85$		−	94.6382i		−	1.11339i
$86$	39.3205	+	42.0489i	0.457215	+	0.488941i
$87$		−	0.992611i		−	0.0114093i
$88$	49.5692	−	40.4832i	0.563287	−	0.460037i
$89$	−133.138			−1.49594			−0.747969	−	0.663734i	$-0.768971\pi$
$89$	−133.138			−1.49594			−0.747969	+	0.663734i	$0.768971\pi$
$90$	34.9808	−	32.7110i	0.388675	−	0.363455i
$91$	−24.9948			−0.274669
$92$	17.0718	+	1.14617i	0.185563	+	0.0124583i
$93$			99.4888i			1.06977i
$94$	−87.0333	+	81.3860i	−0.925886	+	0.865809i
$95$		−	119.157i		−	1.25429i
$96$	32.1051	+	45.1803i	0.334428	+	0.470628i
$97$	97.1384			1.00143			0.500714	−	0.865613i	$-0.333071\pi$
$97$	97.1384			1.00143			0.500714	+	0.865613i	$0.333071\pi$
$98$	60.6865	+	64.8975i	0.619250	+	0.662220i
$99$	−24.0000			−0.242424
$100$	10.3731	−	154.503i	0.103731	−	1.54503i
$101$		−	62.1370i		−	0.615218i	−0.951513	−	0.307609i	$-0.900471\pi$
$101$		−	62.1370i		−	0.615218i	0.951513	−	0.307609i	$-0.0995288\pi$
$102$	−28.0526	−	29.9991i	−0.275025	−	0.294109i
$103$		−	27.8041i		−	0.269943i	−0.990849	−	0.134971i	$-0.956906\pi$
$103$		−	27.8041i		−	0.269943i	0.990849	−	0.134971i	$-0.0430943\pi$
$104$	−59.1384	−	72.4114i	−0.568639	−	0.696263i
$105$	−29.5692			−0.281612
$106$	−45.8038	+	42.8318i	−0.432112	+	0.404073i
$107$	37.7795			0.353079			0.176540	−	0.984294i	$-0.443510\pi$
$107$	37.7795			0.353079			0.176540	+	0.984294i	$0.443510\pi$
$108$	1.39230	−	20.7379i	0.0128917	−	0.192018i
$109$			141.691i			1.29992i	0.759968	+	0.649960i	$0.225214\pi$
$109$			141.691i			1.29992i	−0.759968	+	0.649960i	$0.774786\pi$
$110$	−93.2820	+	87.2293i	−0.848018	+	0.792993i
$111$		−	47.8922i		−	0.431461i
$112$	4.57437	−	33.9133i	0.0408426	−	0.302798i
$113$	−58.2872			−0.515816			−0.257908	−	0.966170i	$-0.583033\pi$
$113$	−58.2872			−0.515816			−0.257908	+	0.966170i	$0.583033\pi$
$114$	−35.3205	−	37.7714i	−0.309829	−	0.331328i
$115$	−34.1436			−0.296901
$116$	−2.28719	−	0.153557i	−0.0197171	−	0.00132377i
$117$			35.0595i			0.299654i
$118$	−72.1051	−	77.1084i	−0.611060	−	0.653461i
$119$			25.3582i			0.213094i
$120$	−69.9615	−	85.6636i	−0.583013	−	0.713863i
$121$	−57.0000			−0.471074
$122$	87.0333	−	81.3860i	0.713388	−	0.667098i
$123$	54.6795			0.444549
$124$	229.244	+	15.3910i	1.84874	+	0.124121i
$125$			109.456i			0.875649i
$126$	−9.37307	+	8.76488i	−0.0743894	+	0.0695625i
$127$			185.152i			1.45789i	0.684571	+	0.728946i	$0.259990\pi$
$127$			185.152i			1.45789i	−0.684571	+	0.728946i	$0.740010\pi$
$128$	109.072	−	66.9876i	0.852123	−	0.523341i
$129$	−49.8564			−0.386484
$130$	127.426	+	136.268i	0.980197	+	1.04821i
$131$	125.359			0.956939			0.478469	−	0.878104i	$-0.341192\pi$
$131$	125.359			0.956939			0.478469	+	0.878104i	$0.341192\pi$
$132$	−3.71281	+	55.3011i	−0.0281274	+	0.418948i
$133$			31.9281i			0.240061i
$134$	−115.818	−	123.854i	−0.864313	−	0.924287i
$135$			41.4758i			0.307229i
$136$	−73.4641	+	59.9982i	−0.540177	+	0.441163i
$137$	99.5692			0.726783			0.363391	−	0.931637i	$-0.381619\pi$
$137$	99.5692			0.726783			0.363391	+	0.931637i	$0.381619\pi$
$138$	−10.8231	+	10.1208i	−0.0784282	+	0.0733392i
$139$	177.492			1.27692			0.638461	−	0.769654i	$-0.279571\pi$
$139$	177.492			1.27692			0.638461	+	0.769654i	$0.279571\pi$
$140$	−4.57437	+	68.1338i	−0.0326741	+	0.486670i
$141$		−	103.193i		−	0.731867i
$142$	62.0385	−	58.0130i	0.436891	−	0.408542i
$143$		−	93.4920i		−	0.653790i
$144$	−47.5692	−	6.41634i	−0.330342	−	0.0445579i
$145$	4.57437			0.0315474
$146$	−7.41154	−	7.92582i	−0.0507640	−	0.0542865i
$147$	−76.9474			−0.523452
$148$	−110.354	−	7.40895i	−0.745634	−	0.0500605i
$149$			87.8023i			0.589277i	0.955609	+	0.294639i	$0.0951993\pi$
$149$			87.8023i			0.589277i	−0.955609	+	0.294639i	$0.904801\pi$
$150$	91.5955	+	97.9512i	0.610637	+	0.653008i
$151$		−	219.066i		−	1.45077i	−0.688345	−	0.725383i	$-0.741663\pi$
$151$		−	219.066i		−	1.45077i	0.688345	−	0.725383i	$-0.258337\pi$
$152$	−92.4974	+	75.5427i	−0.608536	+	0.496992i
$153$	35.5692			0.232479
$154$	24.9948	−	23.3730i	0.162304	−	0.151773i
$155$	−458.487			−2.95798
$156$	80.7846	+	5.42373i	0.517850	+	0.0347675i
$157$		−	253.440i		−	1.61427i	−0.590370	−	0.807133i	$-0.701018\pi$
$157$		−	253.440i		−	1.61427i	0.590370	−	0.807133i	$-0.298982\pi$
$158$	−65.1628	+	60.9346i	−0.412423	+	0.385662i
$159$		−	54.3085i		−	0.341563i
$160$	−208.210	+	147.954i	−1.30131	+	0.924713i
$161$	9.14875			0.0568245
$162$	12.2942	+	13.1473i	0.0758903	+	0.0811563i
$163$	−102.354			−0.627938			−0.313969	−	0.949433i	$-0.601659\pi$
$163$	−102.354			−0.627938			−0.313969	+	0.949433i	$0.601659\pi$
$164$	8.45895	−	125.993i	0.0515789	−	0.768251i
$165$		−	110.602i		−	0.670317i
$166$	92.4974	+	98.9158i	0.557213	+	0.595878i
$167$			281.090i			1.68318i	0.540120	+	0.841588i	$0.318379\pi$
$167$			281.090i			1.68318i	−0.540120	+	0.841588i	$0.681621\pi$
$168$	18.7461	+	22.9535i	0.111584	+	0.136628i
$169$	32.4256			0.191868
$170$	138.249	−	129.278i	0.813228	−	0.760460i
$171$	44.7846			0.261898
$172$	−7.71281	+	114.880i	−0.0448419	+	0.667906i
$173$		−	242.858i		−	1.40381i	−0.712273	−	0.701903i	$-0.752334\pi$
$173$		−	242.858i		−	1.40381i	0.712273	−	0.701903i	$-0.247666\pi$
$174$	1.45002	−	1.35593i	0.00833344	−	0.00779271i
$175$		−	82.7981i		−	0.473132i
$176$	126.851	+	17.1102i	0.720746	+	0.0972172i
$177$	91.4256			0.516529
$178$	−181.870	−	194.490i	−1.02174	−	1.09264i
$179$	318.354			1.77851			0.889257	−	0.457409i	$-0.151222\pi$
$179$	318.354			1.77851			0.889257	+	0.457409i	$0.151222\pi$
$180$	95.5692	+	6.41634i	0.530940	+	0.0356463i
$181$			79.5132i			0.439299i	0.975579	+	0.219650i	$0.0704914\pi$
$181$			79.5132i			0.439299i	−0.975579	+	0.219650i	$0.929509\pi$
$182$	−34.1436	−	36.5128i	−0.187602	−	0.200620i
$183$			103.193i			0.563898i
$184$	21.6462	+	26.5044i	0.117642	+	0.144046i
$185$	220.708			1.19301
$186$	−145.335	+	135.904i	−0.781369	+	0.730668i
$187$	−94.8513			−0.507226
$188$	−237.779	−	15.9641i	−1.26478	−	0.0849152i
$189$		−	11.1134i		−	0.0588012i
$190$	174.067	−	162.772i	0.916140	−	0.856695i
$191$			352.887i			1.84758i	0.382902	+	0.923789i	$0.374925\pi$
$191$			352.887i			1.84758i	−0.382902	+	0.923789i	$0.625075\pi$
$192$	−22.1436	+	108.617i	−0.115331	+	0.565714i
$193$	−284.277			−1.47294			−0.736469	−	0.676472i	$-0.763508\pi$
$193$	−284.277			−1.47294			−0.736469	+	0.676472i	$0.763508\pi$
$194$	132.694	+	141.901i	0.683988	+	0.731449i
$195$	−161.569			−0.828560
$196$	−11.9038	+	177.303i	−0.0607337	+	0.904609i
$197$			75.8087i			0.384816i	0.981315	+	0.192408i	$0.0616297\pi$
$197$			75.8087i			0.384816i	−0.981315	+	0.192408i	$0.938370\pi$
$198$	−32.7846	−	35.0595i	−0.165579	−	0.177068i
$199$		−	104.186i		−	0.523547i	−0.965129	−	0.261774i	$-0.915693\pi$
$199$		−	104.186i		−	0.523547i	0.965129	−	0.261774i	$-0.0843074\pi$
$200$	239.870	−	195.902i	1.19935	−	0.979512i
$201$	146.851			0.730603
$202$	90.7705	−	84.8807i	0.449359	−	0.420202i
$203$	−1.22570			−0.00603793
$204$	5.50258	−	81.9591i	0.0269734	−	0.401760i
$205$			251.986i			1.22920i
$206$	40.6166	−	37.9811i	0.197168	−	0.184374i
$207$		−	12.8327i		−	0.0619936i
$208$	24.9948	−	185.306i	0.120168	−	0.890894i
$209$	−119.426			−0.571414
$210$	−40.3923	−	43.1951i	−0.192344	−	0.205691i
$211$	136.918			0.648900			0.324450	−	0.945903i	$-0.394821\pi$
$211$	136.918			0.648900			0.324450	+	0.945903i	$0.394821\pi$
$212$	−125.138	−	8.40156i	−0.590276	−	0.0396300i
$213$			73.5575i			0.345341i
$214$	51.6077	+	55.1887i	0.241157	+	0.257891i
$215$		−	229.760i		−	1.06865i
$216$	32.1962	−	26.2946i	0.149056	−	0.121734i
$217$	122.851			0.566135
$218$	−206.985	+	193.554i	−0.949470	+	0.887862i
$219$	9.39746			0.0429108
$220$	−254.851	−	17.1102i	−1.15841	−	0.0777738i
$221$			138.560i			0.626968i
$222$	69.9615	−	65.4219i	0.315142	−	0.294693i
$223$		−	53.1624i		−	0.238396i	−0.992870	−	0.119198i	$-0.961968\pi$
$223$		−	53.1624i		−	0.238396i	0.992870	−	0.119198i	$-0.0380324\pi$
$224$	55.7898	−	39.6442i	0.249061	−	0.176983i
$225$	−116.138			−0.516171
$226$	−79.6218	−	85.1467i	−0.352309	−	0.376755i
$227$	−119.846			−0.527956			−0.263978	−	0.964529i	$-0.585035\pi$
$227$	−119.846			−0.527956			−0.263978	+	0.964529i	$0.585035\pi$
$228$	6.92820	−	103.193i	0.0303869	−	0.452602i
$229$			214.103i			0.934946i	0.884007	+	0.467473i	$0.154836\pi$
$229$			214.103i			0.934946i	−0.884007	+	0.467473i	$0.845164\pi$
$230$	−46.6410	−	49.8774i	−0.202787	−	0.216858i
$231$			29.6358i			0.128293i
$232$	−2.90004	−	3.55092i	−0.0125002	−	0.0153057i
$233$	−127.436			−0.546935			−0.273468	−	0.961881i	$-0.588171\pi$
$233$	−127.436			−0.546935			−0.273468	+	0.961881i	$0.588171\pi$
$234$	−51.2154	+	47.8922i	−0.218869	+	0.204667i
$235$	475.559			2.02365
$236$	14.1436	−	210.664i	0.0599305	−	0.892645i
$237$		−	77.2620i		−	0.326000i
$238$	−37.0436	+	34.6400i	−0.155646	+	0.145546i
$239$		−	319.281i		−	1.33590i	−0.744204	−	0.667952i	$-0.767171\pi$
$239$		−	319.281i		−	1.33590i	0.744204	−	0.667952i	$-0.232829\pi$
$240$	29.5692	−	219.219i	0.123205	−	0.913414i
$241$	−247.415			−1.02662			−0.513310	−	0.858203i	$-0.671581\pi$
$241$	−247.415			−1.02662			−0.513310	+	0.858203i	$0.671581\pi$
$242$	−77.8634	−	83.2663i	−0.321750	−	0.344076i
$243$	−15.5885			−0.0641500
$244$	237.779	+	15.9641i	0.974506	+	0.0654265i
$245$		−	354.607i		−	1.44737i
$246$	74.6936	+	79.8765i	0.303632	+	0.324701i
$247$			174.459i			0.706310i
$248$	290.669	+	355.906i	1.17205	+	1.43511i
$249$	−117.282			−0.471012
$250$	−159.895	+	149.520i	−0.639580	+	0.598079i
$251$	−214.851			−0.855981			−0.427991	−	0.903783i	$-0.640778\pi$
$251$	−214.851			−0.855981			−0.427991	+	0.903783i	$0.640778\pi$
$252$	−25.6077	−	1.71925i	−0.101618	−	0.00682243i
$253$			34.2205i			0.135259i
$254$	−270.473	+	252.923i	−1.06485	+	0.995759i
$255$			163.918i			0.642816i
$256$	246.851	+	67.8267i	0.964263	+	0.264948i
$257$	−84.2769			−0.327926			−0.163963	−	0.986467i	$-0.552428\pi$
$257$	−84.2769			−0.327926			−0.163963	+	0.986467i	$0.552428\pi$
$258$	−68.1051	−	72.8309i	−0.263973	−	0.282290i
$259$	−59.1384			−0.228334
$260$	−24.9948	+	372.290i	−0.0961340	+	1.43188i
$261$			1.71925i			0.00658717i
$262$	171.244	+	183.126i	0.653601	+	0.698954i
$263$		−	277.120i		−	1.05369i	−0.849962	−	0.526844i	$-0.823375\pi$
$263$		−	277.120i		−	1.05369i	0.849962	−	0.526844i	$-0.176625\pi$
$264$	−85.8564	+	70.1190i	−0.325214	+	0.265602i
$265$	250.277			0.944441
$266$	−46.6410	+	43.6146i	−0.175342	+	0.163965i
$267$	230.603			0.863680
$268$	22.7180	−	338.377i	0.0847685	−	1.26260i
$269$			123.701i			0.459855i	0.973208	+	0.229927i	$0.0738489\pi$
$269$			123.701i			0.459855i	−0.973208	+	0.229927i	$0.926151\pi$
$270$	−60.5885	+	56.6571i	−0.224402	+	0.209841i
$271$		−	197.985i		−	0.730572i	−0.930895	−	0.365286i	$-0.880971\pi$
$271$		−	197.985i		−	0.730572i	0.930895	−	0.365286i	$-0.119029\pi$
$272$	−188.000	−	25.3582i	−0.691176	−	0.0932288i
$273$	43.2923			0.158580
$274$	136.014	+	145.452i	0.496402	+	0.530847i
$275$	309.703			1.12619
$276$	−29.5692	−	1.98522i	−0.107135	−	0.00719283i
$277$		−	247.709i		−	0.894256i	−0.894470	−	0.447128i	$-0.852447\pi$
$277$		−	247.709i		−	0.894256i	0.894470	−	0.447128i	$-0.147553\pi$
$278$	242.459	+	259.283i	0.872154	+	0.932673i
$279$		−	172.320i		−	0.617633i
$280$	−105.779	+	86.3902i	−0.377784	+	0.308536i
$281$	443.128			1.57697			0.788484	−	0.615055i	$-0.210866\pi$
$281$	443.128			1.57697			0.788484	+	0.615055i	$0.210866\pi$
$282$	150.746	−	140.965i	0.534561	−	0.499875i
$283$	−294.620			−1.04106			−0.520531	−	0.853843i	$-0.674266\pi$
$283$	−294.620			−1.04106			−0.520531	+	0.853843i	$0.674266\pi$
$284$	169.492	+	11.3794i	0.596804	+	0.0400683i
$285$			206.387i			0.724164i
$286$	136.574	−	127.712i	0.477533	−	0.446547i
$287$		−	67.5196i		−	0.235260i
$288$	−55.6077	−	78.2546i	−0.193082	−	0.271717i
$289$	−148.426			−0.513583
$290$	6.24871	+	6.68231i	0.0215473	+	0.0230424i
$291$	−168.249			−0.578174
$292$	1.45379	−	21.6538i	0.00497874	−	0.0741567i
$293$		−	66.7217i		−	0.227719i	−0.993497	−	0.113859i	$-0.963679\pi$
$293$		−	66.7217i		−	0.227719i	0.993497	−	0.113859i	$-0.0363214\pi$
$294$	−105.112	−	112.406i	−0.357524	−	0.382333i
$295$			421.328i			1.42823i
$296$	−139.923	−	171.327i	−0.472713	−	0.578808i
$297$	41.5692			0.139964
$298$	−128.263	+	119.940i	−0.430412	+	0.402484i
$299$	49.9897			0.167190
$300$	−17.9667	+	267.608i	−0.0598889	+	0.892026i
$301$			61.5639i			0.204531i
$302$	320.014	−	299.249i	1.05965	−	0.990892i
$303$			107.624i			0.355196i
$304$	−236.708	−	31.9281i	−0.778644	−	0.105027i
$305$	−475.559			−1.55921
$306$	48.5885	+	51.9600i	0.158786	+	0.169804i
$307$	−524.210			−1.70753			−0.853763	−	0.520662i	$-0.825685\pi$
$307$	−524.210			−1.70753			−0.853763	+	0.520662i	$0.825685\pi$
$308$	68.2872	+	4.58467i	0.221712	+	0.0148853i
$309$			48.1582i			0.155852i
$310$	−626.305	−	669.764i	−2.02034	−	2.16053i
$311$			362.057i			1.16417i	0.813128	+	0.582085i	$0.197763\pi$
$311$			362.057i			1.16417i	−0.813128	+	0.582085i	$0.802237\pi$
$312$	102.431	+	125.420i	0.328304	+	0.401988i
$313$	252.277			0.805996			0.402998	−	0.915201i	$-0.367968\pi$
$313$	252.277			0.805996			0.402998	+	0.915201i	$0.367968\pi$
$314$	370.228	−	346.205i	1.17907	−	1.10256i
$315$	51.2154			0.162589
$316$	−178.028	−	11.9525i	−0.563380	−	0.0378243i
$317$		−	80.3934i		−	0.253607i	−0.991928	−	0.126803i	$-0.959528\pi$
$317$		−	80.3934i		−	0.253607i	0.991928	−	0.126803i	$-0.0404717\pi$
$318$	79.3346	−	74.1868i	0.249480	−	0.233292i
$319$		−	4.58467i		−	0.0143720i
$320$	−500.554	−	102.047i	−1.56423	−	0.318897i
$321$	−65.4359			−0.203850
$322$	12.4974	+	13.3646i	0.0388119	+	0.0415050i
$323$	176.995			0.547972
$324$	−2.41154	+	35.9191i	−0.00744303	+	0.110862i
$325$		−	452.417i		−	1.39205i
$326$	−139.818	−	149.520i	−0.428889	−	0.458650i
$327$		−	245.417i		−	0.750509i
$328$	195.608	−	159.753i	0.596365	−	0.487052i
$329$	−127.426			−0.387312
$330$	161.569	−	151.085i	0.489604	−	0.457835i
$331$	172.056			0.519808			0.259904	−	0.965635i	$-0.416309\pi$
$331$	172.056			0.519808			0.259904	+	0.965635i	$0.416309\pi$
$332$	−18.1436	+	270.243i	−0.0546494	+	0.813985i
$333$			82.9517i			0.249104i
$334$	−410.620	+	383.977i	−1.22940	+	1.14963i
$335$			676.753i			2.02016i
$336$	−7.92305	+	58.7396i	−0.0235805	+	0.174820i
$337$	564.277			1.67441			0.837206	−	0.546888i	$-0.184187\pi$
$337$	564.277			1.67441			0.837206	+	0.546888i	$0.184187\pi$
$338$	44.2942	+	47.3678i	0.131048	+	0.140141i
$339$	100.956			0.297806
$340$	377.703	+	25.3582i	1.11089	+	0.0745830i
$341$			459.519i			1.34756i
$342$	61.1769	+	65.4219i	0.178880	+	0.191292i
$343$			199.817i			0.582556i
$344$	−178.354	+	145.662i	−0.518470	+	0.423435i
$345$	59.1384			0.171416
$346$	354.771	−	331.751i	1.02535	−	0.958817i
$347$	−286.123			−0.824562			−0.412281	−	0.911057i	$-0.635268\pi$
$347$	−286.123			−0.824562			−0.412281	+	0.911057i	$0.635268\pi$
$348$	3.96152	+	0.265969i	0.0113837	+	0.000764279i
$349$		−	421.021i		−	1.20636i	−0.797603	−	0.603182i	$-0.793899\pi$
$349$		−	421.021i		−	1.20636i	0.797603	−	0.603182i	$-0.206101\pi$
$350$	120.953	−	113.104i	0.345579	−	0.323155i
$351$		−	60.7249i		−	0.173005i
$352$	148.287	+	208.679i	0.421270	+	0.592838i
$353$	429.138			1.21569			0.607845	−	0.794056i	$-0.292034\pi$
$353$	429.138			1.21569			0.607845	+	0.794056i	$0.292034\pi$
$354$	124.890	+	133.556i	0.352796	+	0.377276i
$355$	−338.985			−0.954886
$356$	35.6743	−	531.358i	0.100209	−	1.49258i
$357$		−	43.9217i		−	0.123030i
$358$	434.879	+	465.055i	1.21475	+	1.29904i
$359$		−	263.673i		−	0.734465i	−0.930129	−	0.367233i	$-0.880305\pi$
$359$		−	263.673i		−	0.734465i	0.930129	−	0.367233i	$-0.119695\pi$
$360$	121.177	+	148.374i	0.336603	+	0.412149i
$361$	−138.149			−0.382684
$362$	−116.154	+	108.617i	−0.320867	+	0.300047i
$363$	98.7269			0.271975
$364$	6.69735	−	99.7548i	0.0183993	−	0.274052i
$365$			43.3075i			0.118651i
$366$	−150.746	+	140.965i	−0.411875	+	0.385149i
$367$			129.544i			0.352981i	0.984302	+	0.176491i	$0.0564745\pi$
$367$			129.544i			0.352981i	−0.984302	+	0.176491i	$0.943525\pi$
$368$	−9.14875	+	67.8267i	−0.0248607	+	0.184312i
$369$	−94.7077			−0.256660
$370$	301.492	+	322.413i	0.814844	+	0.871385i
$371$	−67.0615			−0.180759
$372$	−397.061	−	26.6580i	−1.06737	−	0.0716612i
$373$			302.478i			0.810933i	0.914110	+	0.405467i	$0.132891\pi$
$373$			302.478i			0.810933i	−0.914110	+	0.405467i	$0.867109\pi$
$374$	−129.569	−	138.560i	−0.346442	−	0.370481i
$375$		−	189.584i		−	0.505556i
$376$	−301.492	−	369.159i	−0.801841	−	0.981805i
$377$	−6.69735			−0.0177649
$378$	16.2346	−	15.1812i	0.0429488	−	0.0401619i
$379$	−116.210			−0.306623			−0.153312	−	0.988178i	$-0.548994\pi$
$379$	−116.210			−0.306623			−0.153312	+	0.988178i	$0.548994\pi$
$380$	475.559	+	31.9281i	1.25147	+	0.0840214i
$381$		−	320.693i		−	0.841715i
$382$	−515.503	+	482.053i	−1.34948	+	1.26192i
$383$		−	566.151i		−	1.47820i	−0.673595	−	0.739101i	$-0.735251\pi$
$383$		−	566.151i		−	1.47820i	0.673595	−	0.739101i	$-0.264749\pi$
$384$	−188.918	+	116.026i	−0.491974	+	0.302151i
$385$	−136.574			−0.354739
$386$	−388.329	−	415.275i	−1.00603	−	1.07584i
$387$	86.3538			0.223137
$388$	−26.0282	+	387.681i	−0.0670829	+	0.999178i
$389$			350.104i			0.900011i	0.893026	+	0.450006i	$0.148578\pi$
$389$			350.104i			0.900011i	−0.893026	+	0.450006i	$0.851422\pi$
$390$	−220.708	−	236.022i	−0.565917	−	0.605186i
$391$		−	50.7165i		−	0.129710i
$392$	−275.268	+	224.812i	−0.702214	+	0.573499i
$393$	−217.128			−0.552489
$394$	−110.742	+	103.557i	−0.281072	+	0.262834i
$395$	356.056			0.901408
$396$	6.43078	−	95.7844i	0.0162393	−	0.241880i
$397$		−	544.149i		−	1.37065i	−0.728236	−	0.685326i	$-0.759660\pi$
$397$		−	544.149i		−	1.37065i	0.728236	−	0.685326i	$-0.240340\pi$
$398$	152.196	−	142.321i	0.382402	−	0.357589i
$399$		−	55.3011i		−	0.138599i
$400$	613.846	+	82.7981i	1.53462	+	0.206995i
$401$	−296.431			−0.739229			−0.369614	−	0.929185i	$-0.620510\pi$
$401$	−296.431			−0.739229			−0.369614	+	0.929185i	$0.620510\pi$
$402$	200.603	+	214.522i	0.499011	+	0.533637i
$403$	671.272			1.66569
$404$	247.990	+	16.6496i	0.613836	+	0.0412118i
$405$		−	71.8383i		−	0.177378i
$406$	−1.67434	−	1.79052i	−0.00412398	−	0.00441014i
$407$		−	221.205i		−	0.543500i
$408$	127.244	−	103.920i	0.311871	−	0.254706i
$409$	−247.415			−0.604927			−0.302464	−	0.953161i	$-0.597809\pi$
$409$	−247.415			−0.604927			−0.302464	+	0.953161i	$0.597809\pi$
$410$	−368.105	+	344.220i	−0.897817	+	0.839561i
$411$	−172.459			−0.419608
$412$	110.967	+	7.45009i	0.269337	+	0.0180827i
$413$		−	112.895i		−	0.273353i
$414$	18.7461	−	17.5298i	0.0452805	−	0.0423424i
$415$		−	540.486i		−	1.30238i
$416$	304.841	−	216.620i	0.732791	−	0.520721i
$417$	−307.426			−0.737232
$418$	−163.138	−	174.459i	−0.390283	−	0.417365i
$419$	−92.1333			−0.219889			−0.109944	−	0.993938i	$-0.535067\pi$
$419$	−92.1333			−0.219889			−0.109944	+	0.993938i	$0.535067\pi$
$420$	7.92305	−	118.011i	0.0188644	−	0.280979i
$421$			445.540i			1.05829i	0.848531	+	0.529145i	$0.177487\pi$
$421$			445.540i			1.05829i	−0.848531	+	0.529145i	$0.822513\pi$
$422$	187.033	+	200.011i	0.443207	+	0.473961i
$423$			178.736i			0.422544i
$424$	−158.669	−	194.281i	−0.374220	−	0.458209i
$425$	−458.995			−1.07999
$426$	−107.454	+	100.481i	−0.252239	+	0.235872i
$427$	127.426			0.298421
$428$	−10.1230	+	150.778i	−0.0236518	+	0.352286i
$429$			161.933i			0.377466i
$430$	335.636	−	313.857i	0.780549	−	0.729901i
$431$			186.677i			0.433125i	0.976269	+	0.216563i	$0.0694845\pi$
$431$			186.677i			0.433125i	−0.976269	+	0.216563i	$0.930515\pi$
$432$	82.3923	+	11.1134i	0.190723	+	0.0257255i
$433$	291.128			0.672351			0.336176	−	0.941799i	$-0.390866\pi$
$433$	291.128			0.672351			0.336176	+	0.941799i	$0.390866\pi$
$434$	167.818	+	179.463i	0.386677	+	0.413509i
$435$	−7.92305			−0.0182139
$436$	−565.492	−	37.9661i	−1.29700	−	0.0870782i
$437$		−	63.8562i		−	0.146124i
$438$	12.8372	+	13.7279i	0.0293086	+	0.0313423i
$439$		−	87.6899i		−	0.199749i	−0.995000	−	0.0998746i	$-0.968156\pi$
$439$		−	87.6899i		−	0.199749i	0.995000	−	0.0998746i	$-0.0318442\pi$
$440$	−323.138	−	395.663i	−0.734406	−	0.899234i
$441$	133.277			0.302215
$442$	−202.410	+	189.276i	−0.457942	+	0.428227i
$443$	20.7077			0.0467441			0.0233721	−	0.999727i	$-0.492560\pi$
$443$	20.7077			0.0467441			0.0233721	+	0.999727i	$0.492560\pi$
$444$	191.138	+	12.8327i	0.430492	+	0.0289024i
$445$			1062.72i			2.38812i
$446$	77.6603	−	72.6211i	0.174126	−	0.162828i
$447$		−	152.078i		−	0.340219i
$448$	134.123	+	27.3435i	0.299382	+	0.0610345i
$449$	584.410			1.30158			0.650791	−	0.759257i	$-0.274437\pi$
$449$	584.410			1.30158			0.650791	+	0.759257i	$0.274437\pi$
$450$	−158.648	−	169.657i	−0.352551	−	0.377015i
$451$	252.554			0.559986
$452$	15.6180	−	232.625i	0.0345531	−	0.514657i
$453$			379.433i			0.837600i
$454$	−163.713	−	175.073i	−0.360601	−	0.385623i
$455$			199.510i			0.438483i
$456$	160.210	−	130.844i	0.351338	−	0.286938i
$457$	−269.692			−0.590136			−0.295068	−	0.955476i	$-0.595342\pi$
$457$	−269.692			−0.590136			−0.295068	+	0.955476i	$0.595342\pi$
$458$	−312.764	+	292.470i	−0.682891	+	0.638580i
$459$	−61.6077			−0.134222
$460$	9.14875	−	136.268i	0.0198886	−	0.296234i
$461$			44.4948i			0.0965181i	0.998835	+	0.0482590i	$0.0153673\pi$
$461$			44.4948i			0.0965181i	−0.998835	+	0.0482590i	$0.984633\pi$
$462$	−43.2923	+	40.4832i	−0.0937064	+	0.0876261i
$463$			611.065i			1.31980i	0.751355	+	0.659898i	$0.229400\pi$
$463$			611.065i			1.31980i	−0.751355	+	0.659898i	$0.770600\pi$
$464$	1.22570	−	9.08705i	0.00264159	−	0.0195842i
$465$	794.123			1.70779
$466$	−174.081	−	186.160i	−0.373564	−	0.399485i
$467$	146.410			0.313512			0.156756	−	0.987637i	$-0.449896\pi$
$467$	146.410			0.313512			0.156756	+	0.987637i	$0.449896\pi$
$468$	−139.923	−	9.39417i	−0.298981	−	0.0200730i
$469$		−	181.336i		−	0.386643i
$470$	649.626	+	694.703i	1.38218	+	1.47809i
$471$			438.971i			0.931997i
$472$	327.061	−	267.111i	0.692927	−	0.565914i
$473$	−230.277			−0.486843
$474$	112.865	−	105.542i	0.238113	−	0.222662i
$475$	−577.913			−1.21666
$476$	−101.205	−	6.79472i	−0.212616	−	0.0142746i
$477$			94.0651i			0.197201i
$478$	466.410	−	436.146i	0.975753	−	0.912440i
$479$			191.876i			0.400576i	0.979737	+	0.200288i	$0.0641878\pi$
$479$			191.876i			0.400576i	−0.979737	+	0.200288i	$0.935812\pi$
$480$	360.631	−	256.264i	0.751314	−	0.533883i
$481$	−323.138			−0.671805
$482$	−337.976	−	361.428i	−0.701194	−	0.749850i
$483$	−15.8461			−0.0328077
$484$	15.2731	−	227.488i	0.0315560	−	0.470016i
$485$		−	775.362i		−	1.59868i
$486$	−21.2942	−	22.7718i	−0.0438153	−	0.0468556i
$487$		−	610.758i		−	1.25412i	−0.778969	−	0.627062i	$-0.784257\pi$
$487$		−	610.758i		−	1.25412i	0.778969	−	0.627062i	$-0.215743\pi$
$488$	301.492	+	369.159i	0.617812	+	0.756473i
$489$	177.282			0.362540
$490$	518.014	−	484.402i	1.05717	−	0.988575i
$491$	−142.354			−0.289926			−0.144963	−	0.989437i	$-0.546306\pi$
$491$	−142.354			−0.289926			−0.144963	+	0.989437i	$0.546306\pi$
$492$	−14.6513	+	218.227i	−0.0297791	+	0.443550i
$493$			6.79472i			0.0137824i
$494$	−254.851	+	238.315i	−0.515893	+	0.482419i
$495$			191.569i			0.387008i
$496$	−122.851	+	910.791i	−0.247684	+	1.83627i
$497$	90.8306			0.182758
$498$	−160.210	−	171.327i	−0.321707	−	0.344030i
$499$	91.3693			0.183105			0.0915524	−	0.995800i	$-0.470817\pi$
$499$	91.3693			0.183105			0.0915524	+	0.995800i	$0.470817\pi$
$500$	−436.841	−	29.3287i	−0.873682	−	0.0586573i
$501$		−	486.863i		−	0.971782i
$502$	−293.492	−	313.857i	−0.584646	−	0.625214i
$503$			230.067i			0.457389i	0.973498	+	0.228695i	$0.0734457\pi$
$503$			230.067i			0.457389i	−0.973498	+	0.228695i	$0.926554\pi$
$504$	−32.4693	−	39.7566i	−0.0644231	−	0.0788821i
$505$	−495.979			−0.982137
$506$	−49.9897	+	46.7460i	−0.0987939	+	0.0923834i
$507$	−56.1628			−0.110775
$508$	−738.946	−	49.6114i	−1.45462	−	0.0976603i
$509$		−	527.387i		−	1.03612i	−0.855343	−	0.518062i	$-0.826654\pi$
$509$		−	527.387i		−	1.03612i	0.855343	−	0.518062i	$-0.173346\pi$
$510$	−239.454	+	223.916i	−0.469517	+	0.439052i
$511$		−	11.6042i		−	0.0227088i
$512$	238.123	+	453.256i	0.465084	+	0.885267i
$513$	−77.5692			−0.151207
$514$	−115.124	−	123.113i	−0.223977	−	0.239519i
$515$	−221.933			−0.430939
$516$	13.3590	−	198.978i	0.0258895	−	0.385616i
$517$		−	476.630i		−	0.921914i
$518$	−80.7846	−	86.3902i	−0.155955	−	0.166776i
$519$			420.643i			0.810487i
$520$	−577.990	+	472.045i	−1.11152	+	0.907779i
$521$	191.856			0.368246			0.184123	−	0.982903i	$-0.441055\pi$
$521$	191.856			0.368246			0.184123	+	0.982903i	$0.441055\pi$
$522$	−2.51151	+	2.34854i	−0.00481131	+	0.00449912i
$523$	105.492			0.201706			0.100853	−	0.994901i	$-0.467843\pi$
$523$	105.492			0.201706			0.100853	+	0.994901i	$0.467843\pi$
$524$	−33.5898	+	500.310i	−0.0641027	+	0.954789i
$525$			143.411i			0.273163i
$526$	404.820	−	378.553i	0.769620	−	0.719682i
$527$		−	681.031i		−	1.29228i
$528$	−219.713	−	29.6358i	−0.416123	−	0.0561284i
$529$	510.703			0.965411
$530$	341.885	+	365.608i	0.645065	+	0.689826i
$531$	−158.354			−0.298218
$532$	−127.426	−	8.55511i	−0.239522	−	0.0160810i
$533$		−	368.934i		−	0.692184i
$534$	315.009	+	336.867i	0.589904	+	0.630837i
$535$		−	301.557i		−	0.563658i
$536$	525.338	−	429.044i	0.980109	−	0.800456i
$537$	−551.405			−1.02682
$538$	−180.704	+	168.979i	−0.335881	+	0.314087i
$539$	−355.405			−0.659378
$540$	−165.531	−	11.1134i	−0.306538	−	0.0205804i
$541$			459.744i			0.849804i	0.905239	+	0.424902i	$0.139691\pi$
$541$			459.744i			0.849804i	−0.905239	+	0.424902i	$0.860309\pi$
$542$	289.219	−	270.453i	0.533615	−	0.498990i
$543$		−	137.721i		−	0.253630i
$544$	−219.769	−	309.273i	−0.403987	−	0.568516i
$545$	1130.98			2.07520
$546$	59.1384	+	63.2420i	0.108312	+	0.115828i
$547$	67.3693			0.123161			0.0615807	−	0.998102i	$-0.480386\pi$
$547$	67.3693			0.123161			0.0615807	+	0.998102i	$0.480386\pi$
$548$	−26.6795	+	397.382i	−0.0486852	+	0.725150i
$549$		−	178.736i		−	0.325567i
$550$	423.061	+	452.417i	0.769203	+	0.822577i
$551$			8.55511i			0.0155265i
$552$	−37.4923	−	45.9070i	−0.0679208	−	0.0831648i
$553$	−95.4050			−0.172523
$554$	361.856	−	338.377i	0.653170	−	0.610788i
$555$	−382.277			−0.688787
$556$	−47.5589	+	708.374i	−0.0855376	+	1.27405i
$557$			476.671i			0.855782i	0.903830	+	0.427891i	$0.140743\pi$
$557$			476.671i			0.855782i	−0.903830	+	0.427891i	$0.859257\pi$
$558$	251.727	−	235.393i	0.451123	−	0.421851i
$559$			336.391i			0.601774i
$560$	−270.697	−	36.5128i	−0.483388	−	0.0652014i
$561$	164.287			0.292847
$562$	605.324	+	647.327i	1.07709	+	1.15183i
$563$	−910.123			−1.61656			−0.808280	−	0.588799i	$-0.799601\pi$
$563$	−910.123			−1.61656			−0.808280	+	0.588799i	$0.799601\pi$
$564$	411.846	+	27.6506i	0.730224	+	0.0490258i
$565$			465.250i			0.823452i
$566$	−402.459	−	430.385i	−0.711058	−	0.760398i
$567$			19.2490i			0.0339489i
$568$	214.908	+	263.141i	0.378358	+	0.463276i
$569$	−124.123			−0.218142			−0.109071	−	0.994034i	$-0.534788\pi$
$569$	−124.123			−0.218142			−0.109071	+	0.994034i	$0.534788\pi$
$570$	−301.492	+	281.929i	−0.528934	+	0.494613i
$571$	945.031			1.65504			0.827522	−	0.561433i	$-0.189750\pi$
$571$	945.031			1.65504			0.827522	+	0.561433i	$0.189750\pi$
$572$	373.128	+	25.0511i	0.652322	+	0.0437957i
$573$		−	611.219i		−	1.06670i
$574$	98.6335	−	92.2335i	0.171835	−	0.160685i
$575$			165.596i			0.287994i
$576$	38.3538	−	188.130i	0.0665865	−	0.326615i
$577$	215.682			0.373799			0.186899	−	0.982379i	$-0.440156\pi$
$577$	215.682			0.373799			0.186899	+	0.982379i	$0.440156\pi$
$578$	−202.753	−	216.822i	−0.350784	−	0.375125i
$579$	492.382			0.850401
$580$	−1.22570	+	18.2564i	−0.00211328	+	0.0314765i
$581$			144.823i			0.249265i
$582$	−229.832	−	245.780i	−0.394900	−	0.422302i
$583$		−	250.840i		−	0.430258i
$584$	33.6180	−	27.4559i	0.0575651	−	0.0470135i
$585$	279.846			0.478369
$586$	97.4679	−	91.1435i	0.166327	−	0.155535i
$587$	900.785			1.53456			0.767278	−	0.641314i	$-0.221611\pi$
$587$	900.785			1.53456			0.767278	+	0.641314i	$0.221611\pi$
$588$	20.6180	−	307.098i	0.0350646	−	0.522276i
$589$		−	857.475i		−	1.45581i
$590$	−615.482	+	575.545i	−1.04319	+	0.975500i
$591$		−	131.305i		−	0.222174i
$592$	59.1384	−	438.439i	0.0998960	−	0.740606i
$593$	−508.585			−0.857647			−0.428824	−	0.903388i	$-0.641072\pi$
$593$	−508.585			−0.857647			−0.428824	+	0.903388i	$0.641072\pi$
$594$	56.7846	+	60.7249i	0.0955970	+	0.102230i
$595$	202.410			0.340185
$596$	−350.420	−	23.5266i	−0.587954	−	0.0394741i
$597$			180.455i			0.302270i
$598$	68.2872	+	73.0256i	0.114193	+	0.122116i
$599$			846.934i			1.41391i	0.707257	+	0.706957i	$0.249933\pi$
$599$			846.934i			1.41391i	−0.707257	+	0.706957i	$0.750067\pi$
$600$	−415.468	+	339.313i	−0.692446	+	0.565522i
$601$	−406.000			−0.675541			−0.337770	−	0.941229i	$-0.609673\pi$
$601$	−406.000			−0.675541			−0.337770	+	0.941229i	$0.609673\pi$
$602$	−89.9334	+	84.0979i	−0.149391	+	0.139697i
$603$	−254.354			−0.421814
$604$	874.295	+	58.6985i	1.44751	+	0.0971829i
$605$			454.976i			0.752026i
$606$	−157.219	+	147.018i	−0.259438	+	0.242603i
$607$			771.156i			1.27044i	0.772332	+	0.635219i	$0.219090\pi$
$607$			771.156i			1.27044i	−0.772332	+	0.635219i	$0.780910\pi$
$608$	−276.708	−	389.400i	−0.455111	−	0.640461i
$609$	2.12297			0.00348600
$610$	−649.626	−	694.703i	−1.06496	−	1.13886i
$611$	−696.267			−1.13955
$612$	−9.53074	+	141.957i	−0.0155731	+	0.231956i
$613$			336.699i			0.549264i	0.961549	+	0.274632i	$0.0885560\pi$
$613$			336.699i			0.549264i	−0.961549	+	0.274632i	$0.911444\pi$
$614$	−716.084	−	765.773i	−1.16626	−	1.24719i
$615$		−	436.453i		−	0.709680i
$616$	86.5847	+	106.018i	0.140560	+	0.172106i
$617$	−908.831			−1.47298			−0.736492	−	0.676447i	$-0.763519\pi$
$617$	−908.831			−1.47298			−0.736492	+	0.676447i	$0.763519\pi$
$618$	−70.3501	+	65.7853i	−0.113835	+	0.106449i
$619$	−1047.77			−1.69268			−0.846340	−	0.532643i	$-0.821199\pi$
$619$	−1047.77			−1.69268			−0.846340	+	0.532643i	$0.821199\pi$
$620$	122.851	−	1829.83i	0.198147	−	2.95134i
$621$			22.2268i			0.0357920i
$622$	−528.897	+	494.579i	−0.850317	+	0.795143i
$623$		−	284.754i		−	0.457068i
$624$	−43.2923	+	320.959i	−0.0693788	+	0.514358i
$625$	−94.1384			−0.150622
$626$	344.617	+	368.529i	0.550506	+	0.588705i
$627$	206.851			0.329906
$628$	1011.48	+	67.9090i	1.61064	+	0.108135i
$629$			327.836i			0.521202i
$630$	69.9615	+	74.8161i	0.111050	+	0.118756i
$631$		−	610.758i		−	0.967921i	−0.875090	−	0.483961i	$-0.839198\pi$
$631$		−	610.758i		−	0.967921i	0.875090	−	0.483961i	$-0.160802\pi$
$632$	−225.731	−	276.393i	−0.357169	−	0.437331i
$633$	−237.149			−0.374643
$634$	117.440	−	109.819i	0.185236	−	0.173217i
$635$	1477.89			2.32739
$636$	216.746	+	14.5519i	0.340796	+	0.0228804i
$637$			519.180i			0.815040i
$638$	6.69735	−	6.26278i	0.0104974	−	0.00981627i
$639$		−	127.405i		−	0.199382i
$640$	−534.697	−	870.614i	−0.835465	−	1.36034i
$641$	9.60015			0.0149768			0.00748842	−	0.999972i	$-0.497616\pi$
$641$	9.60015			0.0149768			0.00748842	+	0.999972i	$0.497616\pi$
$642$	−89.3872	−	95.5897i	−0.139232	−	0.148894i
$643$	86.1999			0.134059			0.0670295	−	0.997751i	$-0.478648\pi$
$643$	86.1999			0.134059			0.0670295	+	0.997751i	$0.478648\pi$
$644$	−2.45140	+	36.5128i	−0.00380652	+	0.0566969i
$645$			397.955i			0.616985i
$646$	241.779	+	258.556i	0.374272	+	0.400242i
$647$			352.580i			0.544946i	0.962163	+	0.272473i	$0.0878416\pi$
$647$			352.580i			0.544946i	−0.962163	+	0.272473i	$0.912158\pi$
$648$	−55.7654	+	45.5436i	−0.0860577	+	0.0702834i
$649$	422.277			0.650658
$650$	660.897	−	618.014i	1.01677	−	0.950790i
$651$	−212.785			−0.326858
$652$	27.4256	−	408.496i	0.0420638	−	0.626527i
$653$			319.322i			0.489008i	0.969648	+	0.244504i	$0.0786252\pi$
$653$			319.322i			0.489008i	−0.969648	+	0.244504i	$0.921375\pi$
$654$	358.508	−	335.245i	0.548177	−	0.512607i
$655$		−	1000.62i		−	1.52766i
$656$	500.574	+	67.5196i	0.763071	+	0.102926i
$657$	−16.2769			−0.0247745
$658$	−174.067	−	186.145i	−0.264539	−	0.282895i
$659$	275.328			0.417797			0.208898	−	0.977937i	$-0.433012\pi$
$659$	275.328			0.417797			0.208898	+	0.977937i	$0.433012\pi$
$660$	441.415	+	29.6358i	0.668811	+	0.0449027i
$661$			133.668i			0.202221i	0.994875	+	0.101111i	$0.0322396\pi$
$661$			133.668i			0.202221i	−0.994875	+	0.101111i	$0.967760\pi$
$662$	235.033	+	251.342i	0.355035	+	0.379671i
$663$		−	239.993i		−	0.361980i
$664$	−419.559	+	342.654i	−0.631866	+	0.516046i
$665$	254.851			0.383235
$666$	−121.177	+	113.314i	−0.181947	+	0.170141i
$667$	2.45140			0.00367526
$668$	−1121.84	−	75.3179i	−1.67939	−	0.112751i
$669$			92.0799i			0.137638i
$670$	−988.610	+	924.462i	−1.47554	+	1.37979i
$671$			476.630i			0.710327i
$672$	−96.6307	+	68.6657i	−0.143796	+	0.102181i
$673$	187.703			0.278904			0.139452	−	0.990229i	$-0.455466\pi$
$673$	187.703			0.278904			0.139452	+	0.990229i	$0.455466\pi$
$674$	770.817	+	824.303i	1.14364	+	1.22300i
$675$	201.158			0.298011
$676$	−8.68842	+	129.411i	−0.0128527	+	0.191437i
$677$			1169.84i			1.72797i	0.503515	+	0.863986i	$0.332040\pi$
$677$			1169.84i			1.72797i	−0.503515	+	0.863986i	$0.667960\pi$
$678$	137.909	+	147.478i	0.203406	+	0.217520i
$679$			207.758i			0.305976i
$680$	478.908	+	586.393i	0.704276	+	0.862342i
$681$	207.580			0.304816
$682$	−671.272	+	627.715i	−0.984269	+	0.920403i
$683$	89.4566			0.130976			0.0654880	−	0.997853i	$-0.479140\pi$
$683$	89.4566			0.130976			0.0654880	+	0.997853i	$0.479140\pi$
$684$	−12.0000	+	178.736i	−0.0175439	+	0.261310i
$685$		−	794.765i		−	1.16024i
$686$	−291.895	+	272.955i	−0.425503	+	0.397893i
$687$		−	370.837i		−	0.539791i
$688$	−456.420	−	61.5639i	−0.663402	−	0.0894824i
$689$	−366.431			−0.531830
$690$	80.7846	+	86.3902i	0.117079	+	0.125203i
$691$	139.103			0.201306			0.100653	−	0.994922i	$-0.467907\pi$
$691$	139.103			0.201306			0.100653	+	0.994922i	$0.467907\pi$
$692$	969.251	+	65.0737i	1.40065	+	0.0940371i
$693$		−	51.3307i		−	0.0740703i
$694$	−390.851	−	417.972i	−0.563186	−	0.602265i
$695$		−	1416.75i		−	2.03849i
$696$	5.02301	+	6.15037i	0.00721697	+	0.00883673i
$697$	−374.297			−0.537012
$698$	615.033	−	575.126i	0.881137	−	0.823962i
$699$	220.726			0.315773
$700$	330.449	+	22.1857i	0.472069	+	0.0316938i
$701$		−	1218.34i		−	1.73801i	−0.494804	−	0.869004i	$-0.664760\pi$
$701$		−	1218.34i		−	1.73801i	0.494804	−	0.869004i	$-0.335240\pi$
$702$	88.7077	−	82.9517i	0.126364	−	0.118165i
$703$			412.773i			0.587160i
$704$	−102.277	+	501.681i	−0.145280	+	0.712615i
$705$	−823.692			−1.16836
$706$	586.214	+	626.891i	0.830331	+	0.887948i
$707$	132.897			0.187974
$708$	−24.4974	+	364.881i	−0.0346009	+	0.515369i
$709$		−	1080.13i		−	1.52346i	−0.647895	−	0.761730i	$-0.724351\pi$
$709$		−	1080.13i		−	1.52346i	0.647895	−	0.761730i	$-0.275649\pi$
$710$	−463.061	−	495.193i	−0.652199	−	0.697455i
$711$			133.822i			0.188216i
$712$	824.946	−	673.734i	1.15863	−	0.946256i
$713$	−245.703			−0.344604
$714$	64.1615	−	59.9982i	0.0898620	−	0.0840311i
$715$	−746.256			−1.04372
$716$	−85.3027	+	1270.56i	−0.119138	+	1.77452i
$717$			553.011i			0.771285i
$718$	385.177	−	360.184i	0.536458	−	0.501649i
$719$		−	20.7736i		−	0.0288923i	−0.999896	−	0.0144461i	$-0.995401\pi$
$719$		−	20.7736i		−	0.0288923i	0.999896	−	0.0144461i	$-0.00459851\pi$
$720$	−51.2154	+	379.699i	−0.0711325	+	0.527360i
$721$	59.4669			0.0824783
$722$	−188.715	−	201.809i	−0.261378	−	0.279515i
$723$	428.536			0.592719
$724$	−317.338	−	21.3055i	−0.438313	−	0.0294275i
$725$		−	22.1857i		−	0.0306010i
$726$	134.863	+	144.222i	0.185762	+	0.198652i
$727$			1031.17i			1.41838i	0.705015	+	0.709192i	$0.250940\pi$
$727$			1031.17i			1.41838i	−0.705015	+	0.709192i	$0.749060\pi$
$728$	154.872	−	126.484i	0.212736	−	0.173742i
$729$	27.0000			0.0370370
$730$	−63.2642	+	59.1592i	−0.0866633	+	0.0810399i
$731$	341.282			0.466870
$732$	−411.846	−	27.6506i	−0.562631	−	0.0377740i
$733$		−	881.072i		−	1.20201i	−0.799246	−	0.601004i	$-0.794767\pi$
$733$		−	881.072i		−	1.20201i	0.799246	−	0.601004i	$-0.205233\pi$
$734$	−189.240	+	176.961i	−0.257820	+	0.241091i
$735$			614.197i			0.835642i
$736$	−111.580	+	79.2884i	−0.151603	+	0.107729i
$737$	678.277			0.920321
$738$	−129.373	−	138.350i	−0.175302	−	0.187466i
$739$	−671.195			−0.908247			−0.454124	−	0.890939i	$-0.650048\pi$
$739$	−671.195			−0.908247			−0.454124	+	0.890939i	$0.650048\pi$
$740$	−59.1384	+	880.848i	−0.0799168	+	1.19033i
$741$		−	302.171i		−	0.407788i
$742$	−91.6077	−	97.9643i	−0.123461	−	0.132027i
$743$		−	254.197i		−	0.342122i	−0.985260	−	0.171061i	$-0.945281\pi$
$743$		−	254.197i		−	0.342122i	0.985260	−	0.171061i	$-0.0547195\pi$
$744$	−503.454	−	616.448i	−0.676685	−	0.828559i
$745$	700.841			0.940726
$746$	−441.864	+	413.193i	−0.592311	+	0.553878i
$747$	203.138			0.271939
$748$	25.4153	−	378.553i	0.0339777	−	0.506087i
$749$			80.8019i			0.107880i
$750$	276.946	−	258.976i	0.369261	−	0.345301i
$751$		−	728.994i		−	0.970698i	−0.874320	−	0.485349i	$-0.838693\pi$
$751$		−	728.994i		−	0.970698i	0.874320	−	0.485349i	$-0.161307\pi$
$752$	127.426	−	944.704i	0.169449	−	1.25626i
$753$	372.133			0.494201
$754$	−9.14875	−	9.78357i	−0.0121336	−	0.0129756i
$755$	−1748.59			−2.31601
$756$	44.3538	+	2.97783i	0.0586691	+	0.00393893i
$757$			372.679i			0.492311i	0.969230	+	0.246155i	$0.0791674\pi$
$757$			372.679i			0.492311i	−0.969230	+	0.246155i	$0.920833\pi$
$758$	−158.746	−	169.761i	−0.209428	−	0.223960i
$759$		−	59.2716i		−	0.0780917i
$760$	602.985	+	738.317i	0.793401	+	0.971470i
$761$	1257.80			1.65283			0.826416	−	0.563060i	$-0.190376\pi$
$761$	1257.80			1.65283			0.826416	+	0.563060i	$0.190376\pi$
$762$	468.473	−	438.075i	0.614794	−	0.574902i
$763$	−303.046			−0.397177
$764$	−1408.38	−	94.5559i	−1.84343	−	0.123764i
$765$		−	283.915i		−	0.371130i
$766$	827.041	−	773.377i	1.07969	−	1.00963i
$767$		−	616.868i		−	0.804260i
$768$	−427.559	−	117.479i	−0.556717	−	0.152968i
$769$	247.703			0.322110			0.161055	−	0.986945i	$-0.448510\pi$
$769$	247.703			0.322110			0.161055	+	0.986945i	$0.448510\pi$
$770$	−186.564	−	199.510i	−0.242291	−	0.259103i
$771$	145.972			0.189328
$772$	76.1718	−	1134.55i	0.0986681	−	1.46963i
$773$		−	587.805i		−	0.760420i	−0.924900	−	0.380210i	$-0.875852\pi$
$773$		−	587.805i		−	0.760420i	0.924900	−	0.380210i	$-0.124148\pi$
$774$	117.962	+	126.147i	0.152405	+	0.162980i
$775$			2223.66i			2.86924i
$776$	−601.885	+	491.560i	−0.775624	+	0.633453i
$777$	102.431			0.131829
$778$	−511.437	+	478.251i	−0.657374	+	0.614719i
$779$	−471.272			−0.604970
$780$	43.2923	−	644.825i	0.0555030	−	0.826699i
$781$			339.748i			0.435016i
$782$	74.0873	−	69.2800i	0.0947407	−	0.0885933i
$783$		−	2.97783i		−	0.00380311i
$784$	−704.431	−	95.0166i	−0.898509	−	0.121195i
$785$	−2022.96			−2.57702
$786$	−296.603	−	317.184i	−0.377357	−	0.403541i
$787$	−31.0821			−0.0394944			−0.0197472	−	0.999805i	$-0.506286\pi$
$787$	−31.0821			−0.0394944			−0.0197472	+	0.999805i	$0.506286\pi$
$788$	−302.554	−	20.3129i	−0.383951	−	0.0257778i
$789$			479.986i			0.608347i
$790$	486.382	+	520.132i	0.615673	+	0.658395i
$791$		−	124.663i		−	0.157602i
$792$	148.708	−	121.450i	0.187762	−	0.153346i
$793$	696.267			0.878016
$794$	794.900	−	743.321i	1.00113	−	0.936173i
$795$	−433.492			−0.545273
$796$	415.808	+	27.9165i	0.522371	+	0.0350710i
$797$			490.260i			0.615132i	0.951527	+	0.307566i	$0.0995145\pi$
$797$			490.260i			0.615132i	−0.951527	+	0.307566i	$0.900486\pi$
$798$	80.7846	−	75.5427i	0.101234	−	0.0946651i
$799$			706.389i			0.884092i
$800$	717.577	+	1009.82i	0.896971	+	1.26227i
$801$	−399.415			−0.498646
$802$	−404.932	−	433.030i	−0.504903	−	0.539938i
$803$	43.4050			0.0540536
$804$	−39.3487	+	586.086i	−0.0489411	+	0.728962i
$805$		−	73.0256i		−	0.0907150i
$806$	916.974	+	980.602i	1.13769	+	1.21663i
$807$		−	214.256i		−	0.265497i
$808$	314.438	+	385.010i	0.389156	+	0.476498i
$809$	676.102			0.835726			0.417863	−	0.908510i	$-0.362779\pi$
$809$	676.102			0.835726			0.417863	+	0.908510i	$0.362779\pi$
$810$	104.942	−	98.1329i	0.129558	−	0.121152i
$811$	−74.1793			−0.0914665			−0.0457332	−	0.998954i	$-0.514562\pi$
$811$	−74.1793			−0.0914665			−0.0457332	+	0.998954i	$0.514562\pi$
$812$	0.328425	−	4.89179i	0.000404465	−	0.00602437i
$813$			342.920i			0.421796i
$814$	323.138	−	302.171i	0.396976	−	0.371217i
$815$			816.991i			1.00244i
$816$	325.626	+	43.9217i	0.399051	+	0.0538257i
$817$	429.703			0.525952
$818$	−337.976	−	361.428i	−0.413173	−	0.441843i
$819$	−74.9845			−0.0915562
$820$	−1005.68	−	67.5196i	−1.22644	−	0.0823409i
$821$		−	1130.58i		−	1.37708i	−0.725198	−	0.688540i	$-0.758252\pi$
$821$		−	1130.58i		−	1.37708i	0.725198	−	0.688540i	$-0.241748\pi$
$822$	−235.583	−	251.930i	−0.286598	−	0.306485i
$823$		−	82.1839i		−	0.0998589i	−0.998753	−	0.0499295i	$-0.984100\pi$
$823$		−	82.1839i		−	0.0998589i	0.998753	−	0.0499295i	$-0.0158997\pi$
$824$	140.700	+	172.279i	0.170753	+	0.209076i
$825$	−536.420			−0.650207
$826$	164.918	−	154.217i	0.199658	−	0.186703i
$827$	1504.57			1.81931			0.909655	−	0.415365i	$-0.136346\pi$
$827$	1504.57			1.81931			0.909655	+	0.415365i	$0.136346\pi$
$828$	51.2154	+	3.43850i	0.0618543	+	0.00415278i
$829$			1409.65i			1.70042i	0.526445	+	0.850209i	$0.323525\pi$
$829$			1409.65i			1.70042i	−0.526445	+	0.850209i	$0.676475\pi$
$830$	789.549	−	738.317i	0.951263	−	0.889539i
$831$			429.044i			0.516299i
$832$	732.862	+	149.407i	0.880843	+	0.179576i
$833$	526.728			0.632327
$834$	−419.951	−	449.091i	−0.503539	−	0.538479i
$835$	2243.67			2.68703
$836$	32.0000	−	476.630i	0.0382775	−	0.570131i
$837$			298.467i			0.356591i
$838$	−125.856	−	134.589i	−0.150187	−	0.160608i
$839$		−	288.110i		−	0.343397i	−0.985150	−	0.171698i	$-0.945075\pi$
$839$		−	288.110i		−	0.343397i	0.985150	−	0.171698i	$-0.0549254\pi$
$840$	183.215	−	149.632i	0.218114	−	0.178134i
$841$	840.672			0.999609
$842$	−650.851	+	608.620i	−0.772982	+	0.722826i
$843$	−767.520			−0.910463
$844$	−36.6870	+	546.441i	−0.0434681	+	0.647442i
$845$		−	258.822i		−	0.306299i
$846$	−261.100	+	244.158i	−0.308629	+	0.288603i
$847$		−	121.910i		−	0.143932i
$848$	67.0615	−	497.178i	0.0790819	−	0.586295i
$849$	510.297			0.601057
$850$	−626.999	−	670.506i	−0.737645	−	0.788830i
$851$	118.277			0.138986
$852$	−293.569	−	19.7097i	−0.344565	−	0.0231334i
$853$		−	645.132i		−	0.756310i	−0.925742	−	0.378155i	$-0.876559\pi$
$853$		−	645.132i		−	0.756310i	0.925742	−	0.378155i	$-0.123441\pi$
$854$	174.067	+	186.145i	0.203825	+	0.217968i
$855$		−	357.472i		−	0.418096i
$856$	−234.087	+	191.179i	−0.273466	+	0.223340i
$857$	−995.549			−1.16167			−0.580833	−	0.814022i	$-0.697273\pi$
$857$	−995.549			−1.16167			−0.580833	+	0.814022i	$0.697273\pi$
$858$	−236.554	+	221.205i	−0.275704	+	0.257814i
$859$	−774.354			−0.901460			−0.450730	−	0.892660i	$-0.648836\pi$
$859$	−774.354			−0.901460			−0.450730	+	0.892660i	$0.648836\pi$
$860$	916.974	+	61.5639i	1.06625	+	0.0715859i
$861$			116.947i			0.135827i
$862$	−272.700	+	255.005i	−0.316357	+	0.295830i
$863$			1007.33i			1.16724i	0.812025	+	0.583622i	$0.198365\pi$
$863$			1007.33i			1.16724i	−0.812025	+	0.583622i	$0.801635\pi$
$864$	96.3154	+	135.541i	0.111476	+	0.156876i
$865$	−1938.50			−2.24104
$866$	397.688	+	425.284i	0.459225	+	0.491090i
$867$	257.081			0.296518
$868$	−32.9179	+	490.301i	−0.0379238	+	0.564863i
$869$		−	356.858i		−	0.410654i
$870$	−10.8231	−	11.5741i	−0.0124403	−	0.0133036i
$871$		−	990.836i		−	1.13758i
$872$	−717.015	−	877.941i	−0.822265	−	1.00681i
$873$	291.415			0.333809
$874$	93.2820	−	87.2293i	0.106730	−	0.0998046i
$875$	−234.102			−0.267546
$876$	−2.51804	+	37.5054i	−0.00287448	+	0.0428144i
$877$			681.645i			0.777246i	0.921397	+	0.388623i	$0.127049\pi$
$877$			681.645i			0.777246i	−0.921397	+	0.388623i	$0.872951\pi$
$878$	128.099	−	119.787i	0.145898	−	0.136431i
$879$			115.565i			0.131474i
$880$	136.574	−	1012.53i	0.155198	−	1.15060i
$881$	−679.108			−0.770837			−0.385419	−	0.922742i	$-0.625943\pi$
$881$	−679.108			−0.770837			−0.385419	+	0.922742i	$0.625943\pi$
$882$	182.060	+	194.693i	0.206417	+	0.220740i
$883$	−1059.44			−1.19982			−0.599910	−	0.800068i	$-0.704797\pi$
$883$	−1059.44			−1.19982			−0.599910	+	0.800068i	$0.704797\pi$
$884$	−552.995	−	37.1270i	−0.625560	−	0.0419989i
$885$		−	729.762i		−	0.824590i
$886$	28.2872	+	30.2500i	0.0319268	+	0.0341422i
$887$		−	856.411i		−	0.965514i	−0.875754	−	0.482757i	$-0.839635\pi$
$887$		−	856.411i		−	0.965514i	0.875754	−	0.482757i	$-0.160365\pi$
$888$	242.354	+	296.747i	0.272921	+	0.334175i
$889$	−396.000			−0.445444
$890$	−1552.43	+	1451.70i	−1.74430	+	1.63112i
$891$	−72.0000			−0.0808081
$892$	212.172	+	14.2448i	0.237861	+	0.0159695i
$893$			889.403i			0.995972i
$894$	222.158	−	207.743i	0.248499	−	0.232374i
$895$		−	2541.11i		−	2.83923i
$896$	143.272	+	233.280i	0.159901	+	0.260358i
$897$	−86.5847			−0.0965270
$898$	798.319	+	853.714i	0.888997	+	0.950684i
$899$	32.9179			0.0366161
$900$	31.1192	−	463.510i	0.0345769	−	0.515011i
$901$			371.758i			0.412606i
$902$	344.995	+	368.934i	0.382478	+	0.409018i
$903$		−	106.632i		−	0.118086i
$904$	361.156	−	294.957i	0.399509	−	0.326280i
$905$	634.677			0.701300
$906$	−554.281	+	518.315i	−0.611789	+	0.572092i
$907$	−761.492			−0.839573			−0.419786	−	0.907623i	$-0.637895\pi$
$907$	−761.492			−0.839573			−0.419786	+	0.907623i	$0.637895\pi$
$908$	32.1127	−	478.308i	0.0353664	−	0.526770i
$909$		−	186.411i		−	0.205073i
$910$	−291.446	+	272.535i	−0.320271	+	0.299489i
$911$		−	897.344i		−	0.985009i	−0.870310	−	0.492505i	$-0.836081\pi$
$911$		−	897.344i		−	0.985009i	0.870310	−	0.492505i	$-0.163919\pi$
$912$	409.990	+	55.3011i	0.449550	+	0.0606372i
$913$	−541.703			−0.593321
$914$	−368.406	−	393.970i	−0.403070	−	0.431039i
$915$	823.692			0.900210
$916$	−854.487	−	57.3686i	−0.932846	−	0.0626295i
$917$			268.115i			0.292383i
$918$	−84.1577	−	89.9973i	−0.0916750	−	0.0980363i
$919$			62.6388i			0.0681598i	0.999419	+	0.0340799i	$0.0108501\pi$
$919$			62.6388i			0.0681598i	−0.999419	+	0.0340799i	$0.989150\pi$
$920$	211.559	−	172.780i	0.229955	−	0.187805i
$921$	907.959			0.985840
$922$	−64.9986	+	60.7811i	−0.0704974	+	0.0659231i
$923$	496.308			0.537712
$924$	−118.277	−	7.94089i	−0.128005	−	0.00859403i
$925$		−	1070.43i		−	1.15722i
$926$	−892.652	+	834.731i	−0.963987	+	0.901437i
$927$		−	83.4124i		−	0.0899810i
$928$	14.9488	−	10.6226i	0.0161086	−	0.0114468i
$929$	253.313			0.272673			0.136336	−	0.990663i	$-0.456467\pi$
$929$	253.313			0.272673			0.136336	+	0.990663i	$0.456467\pi$
$930$	1084.79	+	1160.07i	1.16644	+	1.24738i
$931$	663.195			0.712347
$932$	34.1464	−	508.599i	0.0366377	−	0.545707i
$933$		−	627.101i		−	0.672134i
$934$	200.000	+	213.878i	0.214133	+	0.228991i
$935$			757.106i			0.809739i
$936$	−177.415	−	217.234i	−0.189546	−	0.232088i
$937$	−30.5538			−0.0326081			−0.0163040	−	0.999867i	$-0.505190\pi$
$937$	−30.5538			−0.0326081			−0.0163040	+	0.999867i	$0.505190\pi$
$938$	264.897	−	247.709i	0.282406	−	0.264082i
$939$	−436.956			−0.465342
$940$	−127.426	+	1897.96i	−0.135559	+	2.01911i
$941$		−	388.745i		−	0.413119i	−0.978434	−	0.206559i	$-0.933773\pi$
$941$		−	388.745i		−	0.413119i	0.978434	−	0.206559i	$-0.0662267\pi$
$942$	−641.254	+	599.645i	−0.680737	+	0.636566i
$943$			135.039i			0.143202i
$944$	836.974	+	112.895i	0.886625	+	0.119592i
$945$	−88.7077			−0.0938705
$946$	−314.564	−	336.391i	−0.332520	−	0.355594i
$947$	−263.615			−0.278369			−0.139184	−	0.990266i	$-0.544448\pi$
$947$	−263.615			−0.278369			−0.139184	+	0.990266i	$0.544448\pi$
$948$	308.354	+	20.7023i	0.325268	+	0.0218379i
$949$		−	63.4066i		−	0.0668141i
$950$	−789.443	−	844.222i	−0.830993	−	0.888655i
$951$			139.245i			0.146420i
$952$	−128.323	−	157.123i	−0.134793	−	0.165046i
$953$	1292.41			1.35615			0.678075	−	0.734993i	$-0.262815\pi$
$953$	1292.41			1.35615			0.678075	+	0.734993i	$0.262815\pi$
$954$	−137.412	+	128.495i	−0.144037	+	0.134691i
$955$	2816.76			2.94949
$956$	1274.26	+	85.5511i	1.33290	+	0.0894886i
$957$			7.94089i			0.00829769i
$958$	−280.295	+	262.107i	−0.292583	+	0.273598i
$959$			212.957i			0.222061i
$960$	866.985	+	176.751i	0.903109	+	0.184115i
$961$	−2338.34			−2.43324
$962$	−441.415	−	472.045i	−0.458852	−	0.490691i
$963$	113.338			0.117693
$964$	66.2947	−	987.438i	0.0687705	−	1.02431i
$965$			2269.11i			2.35141i
$966$	−21.6462	−	23.1482i	−0.0224080	−	0.0239629i
$967$		−	1110.00i		−	1.14788i	−0.818896	−	0.573942i	$-0.805413\pi$
$967$		−	1110.00i		−	1.14788i	0.818896	−	0.573942i	$-0.194587\pi$
$968$	353.181	−	288.443i	0.364856	−	0.297978i
$969$	−306.564			−0.316372
$970$	1132.66	−	1059.16i	1.16769	−	1.09192i
$971$	−1341.66			−1.38173			−0.690866	−	0.722983i	$-0.742770\pi$
$971$	−1341.66			−1.38173			−0.690866	+	0.722983i	$0.742770\pi$
$972$	4.17691	−	62.2138i	0.00429724	−	0.0640059i
$973$			379.617i			0.390151i
$974$	892.204	−	834.311i	0.916020	−	0.856583i
$975$			783.610i			0.803703i
$976$	−127.426	+	944.704i	−0.130559	+	0.967934i
$977$	−920.431			−0.942099			−0.471050	−	0.882107i	$-0.656125\pi$
$977$	−920.431			−0.942099			−0.471050	+	0.882107i	$0.656125\pi$
$978$	242.172	+	258.976i	0.247619	+	0.264802i
$979$	1065.11			1.08795
$980$	1415.24	+	95.0166i	1.44412	+	0.0969557i
$981$			425.074i			0.433307i
$982$	−194.459	−	207.952i	−0.198023	−	0.211764i
$983$			1697.84i			1.72720i	0.504176	+	0.863601i	$0.331796\pi$
$983$			1697.84i			1.72720i	−0.504176	+	0.863601i	$0.668204\pi$
$984$	−338.802	+	276.700i	−0.344311	+	0.281200i
$985$	605.108			0.614322
$986$	−9.92581	+	9.28176i	−0.0100667	+	0.00941355i
$987$	220.708			0.223615
$988$	−696.267	−	46.7460i	−0.704723	−	0.0473138i
$989$		−	123.128i		−	0.124497i
$990$	−279.846	+	261.688i	−0.282673	+	0.264331i
$991$			284.765i			0.287351i	0.989625	+	0.143675i	$0.0458921\pi$
$991$			284.765i			0.287351i	−0.989625	+	0.143675i	$0.954108\pi$
$992$	−1498.31	+	1064.70i	−1.51040	+	1.07329i
$993$	−298.010			−0.300111
$994$	124.077	+	132.687i	0.124826	+	0.133487i
$995$	−831.615			−0.835794
$996$	31.4256	−	468.074i	0.0315518	−	0.469954i
$997$			1093.80i			1.09710i	0.836119	+	0.548548i	$0.184819\pi$
$997$			1093.80i			1.09710i	−0.836119	+	0.548548i	$0.815181\pi$
$998$	124.813	+	133.473i	0.125063	+	0.133741i
$999$		−	143.677i		−	0.143820i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.3.b.a.19.4	yes	4
3.2	odd	2		72.3.b.b.19.1		4
4.3	odd	2		96.3.b.a.79.3		4
5.2	odd	4		600.3.p.a.499.4		8
5.3	odd	4		600.3.p.a.499.5		8
5.4	even	2		600.3.g.a.451.1		4
8.3	odd	2	inner	24.3.b.a.19.3	✓	4
8.5	even	2		96.3.b.a.79.4		4
12.11	even	2		288.3.b.b.271.4		4
16.3	odd	4		768.3.g.h.511.5		8
16.5	even	4		768.3.g.h.511.8		8
16.11	odd	4		768.3.g.h.511.4		8
16.13	even	4		768.3.g.h.511.1		8
20.3	even	4		2400.3.p.a.1999.6		8
20.7	even	4		2400.3.p.a.1999.3		8
20.19	odd	2		2400.3.g.a.751.2		4
24.5	odd	2		288.3.b.b.271.1		4
24.11	even	2		72.3.b.b.19.2		4
40.3	even	4		600.3.p.a.499.3		8
40.13	odd	4		2400.3.p.a.1999.7		8
40.19	odd	2		600.3.g.a.451.2		4
40.27	even	4		600.3.p.a.499.6		8
40.29	even	2		2400.3.g.a.751.1		4
40.37	odd	4		2400.3.p.a.1999.2		8
48.5	odd	4		2304.3.g.z.1279.1		8
48.11	even	4		2304.3.g.z.1279.2		8
48.29	odd	4		2304.3.g.z.1279.7		8
48.35	even	4		2304.3.g.z.1279.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.3.b.a.19.3	✓	4	8.3	odd	2	inner
24.3.b.a.19.4	yes	4	1.1	even	1	trivial
72.3.b.b.19.1		4	3.2	odd	2
72.3.b.b.19.2		4	24.11	even	2
96.3.b.a.79.3		4	4.3	odd	2
96.3.b.a.79.4		4	8.5	even	2
288.3.b.b.271.1		4	24.5	odd	2
288.3.b.b.271.4		4	12.11	even	2
600.3.g.a.451.1		4	5.4	even	2
600.3.g.a.451.2		4	40.19	odd	2
600.3.p.a.499.3		8	40.3	even	4
600.3.p.a.499.4		8	5.2	odd	4
600.3.p.a.499.5		8	5.3	odd	4
600.3.p.a.499.6		8	40.27	even	4
768.3.g.h.511.1		8	16.13	even	4
768.3.g.h.511.4		8	16.11	odd	4
768.3.g.h.511.5		8	16.3	odd	4
768.3.g.h.511.8		8	16.5	even	4
2304.3.g.z.1279.1		8	48.5	odd	4
2304.3.g.z.1279.2		8	48.11	even	4
2304.3.g.z.1279.7		8	48.29	odd	4
2304.3.g.z.1279.8		8	48.35	even	4
2400.3.g.a.751.1		4	40.29	even	2
2400.3.g.a.751.2		4	20.19	odd	2
2400.3.p.a.1999.2		8	40.37	odd	4
2400.3.p.a.1999.3		8	20.7	even	4
2400.3.p.a.1999.6		8	20.3	even	4
2400.3.p.a.1999.7		8	40.13	odd	4

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:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	24.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 + 1.46081i) q^{2} -1.73205 q^{3} +(-0.267949 + 3.99102i) q^{4} -7.98203i q^{5} +(-2.36603 - 2.53020i) q^{6} +2.13878i q^{7} +(-6.19615 + 5.06040i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(1.36603 + 1.46081i) q^{2} -1.73205 q^{3} +(-0.267949 + 3.99102i) q^{4} -7.98203i q^{5} +(-2.36603 - 2.53020i) q^{6} +2.13878i q^{7} +(-6.19615 + 5.06040i) q^{8} +3.00000 q^{9} +(11.6603 - 10.9037i) q^{10} -8.00000 q^{11} +(0.464102 - 6.91264i) q^{12} +11.6865i q^{13} +(-3.12436 + 2.92163i) q^{14} +13.8253i q^{15} +(-15.8564 - 2.13878i) q^{16} +11.8564 q^{17} +(4.09808 + 4.38244i) q^{18} +14.9282 q^{19} +(31.8564 + 2.13878i) q^{20} -3.70447i q^{21} +(-10.9282 - 11.6865i) q^{22} -4.27756i q^{23} +(10.7321 - 8.76488i) q^{24} -38.7128 q^{25} +(-17.0718 + 15.9641i) q^{26} -5.19615 q^{27} +(-8.53590 - 0.573084i) q^{28} +0.573084i q^{29} +(-20.1962 + 18.8857i) q^{30} -57.4399i q^{31} +(-18.5359 - 26.0849i) q^{32} +13.8564 q^{33} +(16.1962 + 17.3200i) q^{34} +17.0718 q^{35} +(-0.803848 + 11.9730i) q^{36} +27.6506i q^{37} +(20.3923 + 21.8073i) q^{38} -20.2416i q^{39} +(40.3923 + 49.4579i) q^{40} -31.5692 q^{41} +(5.41154 - 5.06040i) q^{42} +28.7846 q^{43} +(2.14359 - 31.9281i) q^{44} -23.9461i q^{45} +(6.24871 - 5.84325i) q^{46} +59.5787i q^{47} +(27.4641 + 3.70447i) q^{48} +44.4256 q^{49} +(-52.8827 - 56.5522i) q^{50} -20.5359 q^{51} +(-46.6410 - 3.13139i) q^{52} +31.3550i q^{53} +(-7.09808 - 7.59061i) q^{54} +63.8562i q^{55} +(-10.8231 - 13.2522i) q^{56} -25.8564 q^{57} +(-0.837169 + 0.782847i) q^{58} -52.7846 q^{59} +(-55.1769 - 3.70447i) q^{60} -59.5787i q^{61} +(83.9090 - 78.4644i) q^{62} +6.41634i q^{63} +(12.7846 - 62.7101i) q^{64} +93.2820 q^{65} +(18.9282 + 20.2416i) q^{66} -84.7846 q^{67} +(-3.17691 + 47.3191i) q^{68} +7.40895i q^{69} +(23.3205 + 24.9387i) q^{70} -42.4685i q^{71} +(-18.5885 + 15.1812i) q^{72} -5.42563 q^{73} +(-40.3923 + 37.7714i) q^{74} +67.0526 q^{75} +(-4.00000 + 59.5787i) q^{76} -17.1102i q^{77} +(29.5692 - 27.6506i) q^{78} +44.6072i q^{79} +(-17.0718 + 126.566i) q^{80} +9.00000 q^{81} +(-43.1244 - 46.1167i) q^{82} +67.7128 q^{83} +(14.7846 + 0.992611i) q^{84} -94.6382i q^{85} +(39.3205 + 42.0489i) q^{86} -0.992611i q^{87} +(49.5692 - 40.4832i) q^{88} -133.138 q^{89} +(34.9808 - 32.7110i) q^{90} -24.9948 q^{91} +(17.0718 + 1.14617i) q^{92} +99.4888i q^{93} +(-87.0333 + 81.3860i) q^{94} -119.157i q^{95} +(32.1051 + 45.1803i) q^{96} +97.1384 q^{97} +(60.6865 + 64.8975i) q^{98} -24.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 8 q^{4} - 6 q^{6} - 4 q^{8} + 12 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 8 * q^4 - 6 * q^6 - 4 * q^8 + 12 * q^9	\( 4 q + 2 q^{2} - 8 q^{4} - 6 q^{6} - 4 q^{8} + 12 q^{9} + 12 q^{10} - 32 q^{11} - 12 q^{12} + 36 q^{14} - 8 q^{16} - 8 q^{17} + 6 q^{18} + 32 q^{19} + 72 q^{20} - 16 q^{22} + 36 q^{24} - 44 q^{25} - 96 q^{26} - 48 q^{28} - 60 q^{30} - 88 q^{32} + 44 q^{34} + 96 q^{35} - 24 q^{36} + 40 q^{38} + 120 q^{40} + 40 q^{41} + 84 q^{42} + 32 q^{43} + 64 q^{44} - 72 q^{46} + 96 q^{48} - 44 q^{49} - 118 q^{50} - 96 q^{51} - 48 q^{52} - 18 q^{54} - 168 q^{56} - 48 q^{57} + 156 q^{58} - 128 q^{59} - 96 q^{60} + 204 q^{62} - 32 q^{64} + 96 q^{65} + 48 q^{66} - 256 q^{67} + 112 q^{68} + 24 q^{70} - 12 q^{72} + 200 q^{73} - 120 q^{74} + 192 q^{75} - 16 q^{76} - 48 q^{78} - 96 q^{80} + 36 q^{81} - 124 q^{82} + 160 q^{83} - 24 q^{84} + 88 q^{86} + 32 q^{88} - 200 q^{89} + 36 q^{90} + 288 q^{91} + 96 q^{92} - 168 q^{94} - 24 q^{96} + 56 q^{97} + 170 q^{98} - 96 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 8 * q^4 - 6 * q^6 - 4 * q^8 + 12 * q^9 + 12 * q^10 - 32 * q^11 - 12 * q^12 + 36 * q^14 - 8 * q^16 - 8 * q^17 + 6 * q^18 + 32 * q^19 + 72 * q^20 - 16 * q^22 + 36 * q^24 - 44 * q^25 - 96 * q^26 - 48 * q^28 - 60 * q^30 - 88 * q^32 + 44 * q^34 + 96 * q^35 - 24 * q^36 + 40 * q^38 + 120 * q^40 + 40 * q^41 + 84 * q^42 + 32 * q^43 + 64 * q^44 - 72 * q^46 + 96 * q^48 - 44 * q^49 - 118 * q^50 - 96 * q^51 - 48 * q^52 - 18 * q^54 - 168 * q^56 - 48 * q^57 + 156 * q^58 - 128 * q^59 - 96 * q^60 + 204 * q^62 - 32 * q^64 + 96 * q^65 + 48 * q^66 - 256 * q^67 + 112 * q^68 + 24 * q^70 - 12 * q^72 + 200 * q^73 - 120 * q^74 + 192 * q^75 - 16 * q^76 - 48 * q^78 - 96 * q^80 + 36 * q^81 - 124 * q^82 + 160 * q^83 - 24 * q^84 + 88 * q^86 + 32 * q^88 - 200 * q^89 + 36 * q^90 + 288 * q^91 + 96 * q^92 - 168 * q^94 - 24 * q^96 + 56 * q^97 + 170 * q^98 - 96 * q^99

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