LMFDB - Embedded newform 56.3.g.a.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,3,Mod(43,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, 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("56.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	56.g (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:	$1.52588948042$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 6x^{2} + 16 $ x^4 + 6*x^2 + 16
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			43.1
Root			$-0.707107 - 1.87083i$ of defining polynomial
Character	$\chi$	$=$	56.43
Dual form			56.3.g.a.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.87083i) q^{2} +0.585786 q^{3} +(-3.00000 + 2.64575i) q^{4} -9.03316i q^{5} +(-0.414214 - 1.09591i) q^{6} -2.64575i q^{7} +(7.07107 + 3.74166i) q^{8} -8.65685 q^{9} +O(q^{10})$	\(q+(-0.707107 - 1.87083i) q^{2} +0.585786 q^{3} +(-3.00000 + 2.64575i) q^{4} -9.03316i q^{5} +(-0.414214 - 1.09591i) q^{6} -2.64575i q^{7} +(7.07107 + 3.74166i) q^{8} -8.65685 q^{9} +(-16.8995 + 6.38741i) q^{10} +12.4853 q^{11} +(-1.75736 + 1.54985i) q^{12} +9.03316i q^{13} +(-4.94975 + 1.87083i) q^{14} -5.29150i q^{15} +(2.00000 - 15.8745i) q^{16} +12.3431 q^{17} +(6.12132 + 16.1955i) q^{18} +28.8701 q^{19} +(23.8995 + 27.0995i) q^{20} -1.54985i q^{21} +(-8.82843 - 23.3578i) q^{22} +24.6418i q^{23} +(4.14214 + 2.19181i) q^{24} -56.5980 q^{25} +(16.8995 - 6.38741i) q^{26} -10.3431 q^{27} +(7.00000 + 7.93725i) q^{28} -22.4499i q^{29} +(-9.89949 + 3.74166i) q^{30} +16.7824i q^{31} +(-31.1127 + 7.48331i) q^{32} +7.31371 q^{33} +(-8.72792 - 23.0919i) q^{34} -23.8995 q^{35} +(25.9706 - 22.9039i) q^{36} -16.2506i q^{37} +(-20.4142 - 54.0109i) q^{38} +5.29150i q^{39} +(33.7990 - 63.8741i) q^{40} +6.97056 q^{41} +(-2.89949 + 1.09591i) q^{42} -22.8284 q^{43} +(-37.4558 + 33.0329i) q^{44} +78.1987i q^{45} +(46.1005 - 17.4244i) q^{46} +6.19938i q^{47} +(1.17157 - 9.29907i) q^{48} -7.00000 q^{49} +(40.0208 + 105.885i) q^{50} +7.23045 q^{51} +(-23.8995 - 27.0995i) q^{52} -8.01514i q^{53} +(7.31371 + 19.3503i) q^{54} -112.782i q^{55} +(9.89949 - 18.7083i) q^{56} +16.9117 q^{57} +(-42.0000 + 15.8745i) q^{58} +30.4437 q^{59} +(14.0000 + 15.8745i) q^{60} +15.2325i q^{61} +(31.3970 - 11.8669i) q^{62} +22.9039i q^{63} +(36.0000 + 52.9150i) q^{64} +81.5980 q^{65} +(-5.17157 - 13.6827i) q^{66} -78.6274 q^{67} +(-37.0294 + 32.6569i) q^{68} +14.4348i q^{69} +(16.8995 + 44.7119i) q^{70} +17.5345i q^{71} +(-61.2132 - 32.3910i) q^{72} +46.6863 q^{73} +(-30.4020 + 11.4909i) q^{74} -33.1543 q^{75} +(-86.6102 + 76.3830i) q^{76} -33.0329i q^{77} +(9.89949 - 3.74166i) q^{78} +81.0325i q^{79} +(-143.397 - 18.0663i) q^{80} +71.8528 q^{81} +(-4.92893 - 13.0407i) q^{82} +40.3848 q^{83} +(4.10051 + 4.64954i) q^{84} -111.498i q^{85} +(16.1421 + 42.7081i) q^{86} -13.1509i q^{87} +(88.2843 + 46.7156i) q^{88} +111.941 q^{89} +(146.296 - 55.2949i) q^{90} +23.8995 q^{91} +(-65.1960 - 73.9253i) q^{92} +9.83089i q^{93} +(11.5980 - 4.38362i) q^{94} -260.788i q^{95} +(-18.2254 + 4.38362i) q^{96} -164.108 q^{97} +(4.94975 + 13.0958i) q^{98} -108.083 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{9}+O(q^{10}) $ 4 * q + 8 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^9	$ 4 q + 8 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{9} - 28 q^{10} + 16 q^{11} - 24 q^{12} + 8 q^{16} + 72 q^{17} + 16 q^{18} + 8 q^{19} + 56 q^{20} - 24 q^{22} - 40 q^{24} - 68 q^{25} + 28 q^{26} - 64 q^{27} + 28 q^{28} - 16 q^{33} + 16 q^{34} - 56 q^{35} + 36 q^{36} - 76 q^{38} + 56 q^{40} - 40 q^{41} + 28 q^{42} - 80 q^{43} - 48 q^{44} + 224 q^{46} + 16 q^{48} - 28 q^{49} + 112 q^{50} + 176 q^{51} - 56 q^{52} - 16 q^{54} - 136 q^{57} - 168 q^{58} + 184 q^{59} + 56 q^{60} - 112 q^{62} + 144 q^{64} + 168 q^{65} - 32 q^{66} - 224 q^{67} - 216 q^{68} + 28 q^{70} - 160 q^{72} + 232 q^{73} - 280 q^{74} + 88 q^{75} - 24 q^{76} - 336 q^{80} - 52 q^{81} - 48 q^{82} + 88 q^{83} + 56 q^{84} + 8 q^{86} + 240 q^{88} + 312 q^{89} + 308 q^{90} + 56 q^{91} + 56 q^{92} - 112 q^{94} + 176 q^{96} - 136 q^{97} - 240 q^{99}+O(q^{100}) $ 4 * q + 8 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^9 - 28 * q^10 + 16 * q^11 - 24 * q^12 + 8 * q^16 + 72 * q^17 + 16 * q^18 + 8 * q^19 + 56 * q^20 - 24 * q^22 - 40 * q^24 - 68 * q^25 + 28 * q^26 - 64 * q^27 + 28 * q^28 - 16 * q^33 + 16 * q^34 - 56 * q^35 + 36 * q^36 - 76 * q^38 + 56 * q^40 - 40 * q^41 + 28 * q^42 - 80 * q^43 - 48 * q^44 + 224 * q^46 + 16 * q^48 - 28 * q^49 + 112 * q^50 + 176 * q^51 - 56 * q^52 - 16 * q^54 - 136 * q^57 - 168 * q^58 + 184 * q^59 + 56 * q^60 - 112 * q^62 + 144 * q^64 + 168 * q^65 - 32 * q^66 - 224 * q^67 - 216 * q^68 + 28 * q^70 - 160 * q^72 + 232 * q^73 - 280 * q^74 + 88 * q^75 - 24 * q^76 - 336 * q^80 - 52 * q^81 - 48 * q^82 + 88 * q^83 + 56 * q^84 + 8 * q^86 + 240 * q^88 + 312 * q^89 + 308 * q^90 + 56 * q^91 + 56 * q^92 - 112 * q^94 + 176 * q^96 - 136 * q^97 - 240 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−0.707107	−	1.87083i	−0.353553	−	0.935414i
$2$	−0.707107	−	1.87083i	−0.353553	−	0.935414i
$3$	0.585786			0.195262			0.0976311	−	0.995223i	$-0.468873\pi$
$3$	0.585786			0.195262			0.0976311	+	0.995223i	$0.468873\pi$
$4$	−3.00000	+	2.64575i	−0.750000	+	0.661438i
$5$		−	9.03316i		−	1.80663i	−0.428976	−	0.903316i	$-0.641125\pi$
$5$		−	9.03316i		−	1.80663i	0.428976	−	0.903316i	$-0.358875\pi$
$6$	−0.414214	−	1.09591i	−0.0690356	−	0.182651i
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	7.07107	+	3.74166i	0.883883	+	0.467707i
$9$	−8.65685			−0.961873
$10$	−16.8995	+	6.38741i	−1.68995	+	0.638741i
$11$	12.4853			1.13503			0.567513	−	0.823365i	$-0.307906\pi$
$11$	12.4853			1.13503			0.567513	+	0.823365i	$0.307906\pi$
$12$	−1.75736	+	1.54985i	−0.146447	+	0.129154i
$13$			9.03316i			0.694858i	0.937706	+	0.347429i	$0.112945\pi$
$13$			9.03316i			0.694858i	−0.937706	+	0.347429i	$0.887055\pi$
$14$	−4.94975	+	1.87083i	−0.353553	+	0.133631i
$15$		−	5.29150i		−	0.352767i
$16$	2.00000	−	15.8745i	0.125000	−	0.992157i
$17$	12.3431			0.726067			0.363034	−	0.931776i	$-0.381741\pi$
$17$	12.3431			0.726067			0.363034	+	0.931776i	$0.381741\pi$
$18$	6.12132	+	16.1955i	0.340073	+	0.899750i
$19$	28.8701			1.51948			0.759738	−	0.650229i	$-0.225327\pi$
$19$	28.8701			1.51948			0.759738	+	0.650229i	$0.225327\pi$
$20$	23.8995	+	27.0995i	1.19497	+	1.35497i
$21$		−	1.54985i		−	0.0738022i
$22$	−8.82843	−	23.3578i	−0.401292	−	1.06172i
$23$			24.6418i			1.07138i	0.844414	+	0.535690i	$0.179949\pi$
$23$			24.6418i			1.07138i	−0.844414	+	0.535690i	$0.820051\pi$
$24$	4.14214	+	2.19181i	0.172589	+	0.0913255i
$25$	−56.5980			−2.26392
$26$	16.8995	−	6.38741i	0.649981	−	0.245670i
$27$	−10.3431			−0.383079
$28$	7.00000	+	7.93725i	0.250000	+	0.283473i
$29$		−	22.4499i		−	0.774136i	−0.922051	−	0.387068i	$-0.873488\pi$
$29$		−	22.4499i		−	0.774136i	0.922051	−	0.387068i	$-0.126512\pi$
$30$	−9.89949	+	3.74166i	−0.329983	+	0.124722i
$31$			16.7824i			0.541367i	0.962668	+	0.270684i	$0.0872497\pi$
$31$			16.7824i			0.541367i	−0.962668	+	0.270684i	$0.912750\pi$
$32$	−31.1127	+	7.48331i	−0.972272	+	0.233854i
$33$	7.31371			0.221628
$34$	−8.72792	−	23.0919i	−0.256704	−	0.679174i
$35$	−23.8995			−0.682843
$36$	25.9706	−	22.9039i	0.721405	−	0.636219i
$37$		−	16.2506i		−	0.439204i	−0.975589	−	0.219602i	$-0.929524\pi$
$37$		−	16.2506i		−	0.439204i	0.975589	−	0.219602i	$-0.0704759\pi$
$38$	−20.4142	−	54.0109i	−0.537216	−	1.42134i
$39$			5.29150i			0.135680i
$40$	33.7990	−	63.8741i	0.844975	−	1.59685i
$41$	6.97056			0.170014			0.0850069	−	0.996380i	$-0.472909\pi$
$41$	6.97056			0.170014			0.0850069	+	0.996380i	$0.472909\pi$
$42$	−2.89949	+	1.09591i	−0.0690356	+	0.0260930i
$43$	−22.8284			−0.530894			−0.265447	−	0.964126i	$-0.585519\pi$
$43$	−22.8284			−0.530894			−0.265447	+	0.964126i	$0.585519\pi$
$44$	−37.4558	+	33.0329i	−0.851269	+	0.750749i
$45$			78.1987i			1.73775i
$46$	46.1005	−	17.4244i	1.00218	−	0.378790i
$47$			6.19938i			0.131902i	0.997823	+	0.0659509i	$0.0210081\pi$
$47$			6.19938i			0.131902i	−0.997823	+	0.0659509i	$0.978992\pi$
$48$	1.17157	−	9.29907i	0.0244078	−	0.193731i
$49$	−7.00000			−0.142857
$50$	40.0208	+	105.885i	0.800416	+	2.11770i
$51$	7.23045			0.141773
$52$	−23.8995	−	27.0995i	−0.459606	−	0.521144i
$53$		−	8.01514i		−	0.151229i	−0.997137	−	0.0756145i	$-0.975908\pi$
$53$		−	8.01514i		−	0.151229i	0.997137	−	0.0756145i	$-0.0240918\pi$
$54$	7.31371	+	19.3503i	0.135439	+	0.358338i
$55$		−	112.782i		−	2.05057i
$56$	9.89949	−	18.7083i	0.176777	−	0.334077i
$57$	16.9117			0.296696
$58$	−42.0000	+	15.8745i	−0.724138	+	0.273698i
$59$	30.4437			0.515994			0.257997	−	0.966146i	$-0.416938\pi$
$59$	30.4437			0.515994			0.257997	+	0.966146i	$0.416938\pi$
$60$	14.0000	+	15.8745i	0.233333	+	0.264575i
$61$			15.2325i			0.249714i	0.992175	+	0.124857i	$0.0398472\pi$
$61$			15.2325i			0.249714i	−0.992175	+	0.124857i	$0.960153\pi$
$62$	31.3970	−	11.8669i	0.506403	−	0.191402i
$63$			22.9039i			0.363554i
$64$	36.0000	+	52.9150i	0.562500	+	0.826797i
$65$	81.5980			1.25535
$66$	−5.17157	−	13.6827i	−0.0783572	−	0.207314i
$67$	−78.6274			−1.17354			−0.586772	−	0.809752i	$-0.699601\pi$
$67$	−78.6274			−1.17354			−0.586772	+	0.809752i	$0.699601\pi$
$68$	−37.0294	+	32.6569i	−0.544551	+	0.480248i
$69$			14.4348i			0.209200i
$70$	16.8995	+	44.7119i	0.241421	+	0.638741i
$71$			17.5345i			0.246965i	0.992347	+	0.123482i	$0.0394062\pi$
$71$			17.5345i			0.246965i	−0.992347	+	0.123482i	$0.960594\pi$
$72$	−61.2132	−	32.3910i	−0.850183	−	0.449875i
$73$	46.6863			0.639538			0.319769	−	0.947495i	$-0.396395\pi$
$73$	46.6863			0.639538			0.319769	+	0.947495i	$0.396395\pi$
$74$	−30.4020	+	11.4909i	−0.410838	+	0.155282i
$75$	−33.1543			−0.442058
$76$	−86.6102	+	76.3830i	−1.13961	+	1.00504i
$77$		−	33.0329i		−	0.428999i
$78$	9.89949	−	3.74166i	0.126917	−	0.0479700i
$79$			81.0325i			1.02573i	0.858470	+	0.512864i	$0.171416\pi$
$79$			81.0325i			1.02573i	−0.858470	+	0.512864i	$0.828584\pi$
$80$	−143.397	−	18.0663i	−1.79246	−	0.225829i
$81$	71.8528			0.887072
$82$	−4.92893	−	13.0407i	−0.0601089	−	0.159033i
$83$	40.3848			0.486564			0.243282	−	0.969956i	$-0.421776\pi$
$83$	40.3848			0.486564			0.243282	+	0.969956i	$0.421776\pi$
$84$	4.10051	+	4.64954i	0.0488155	+	0.0553516i
$85$		−	111.498i		−	1.31174i
$86$	16.1421	+	42.7081i	0.187699	+	0.496606i
$87$		−	13.1509i		−	0.151159i
$88$	88.2843	+	46.7156i	1.00323	+	0.530860i
$89$	111.941			1.25777			0.628883	−	0.777500i	$-0.283513\pi$
$89$	111.941			1.25777			0.628883	+	0.777500i	$0.283513\pi$
$90$	146.296	−	55.2949i	1.62552	−	0.614387i
$91$	23.8995			0.262632
$92$	−65.1960	−	73.9253i	−0.708652	−	0.803536i
$93$			9.83089i			0.105709i
$94$	11.5980	−	4.38362i	0.123383	−	0.0466343i
$95$		−	260.788i		−	2.74514i
$96$	−18.2254	+	4.38362i	−0.189848	+	0.0456628i
$97$	−164.108			−1.69183			−0.845916	−	0.533317i	$-0.820945\pi$
$97$	−164.108			−1.69183			−0.845916	+	0.533317i	$0.820945\pi$
$98$	4.94975	+	13.0958i	0.0505076	+	0.133631i
$99$	−108.083			−1.09175
$100$	169.794	−	149.744i	1.69794	−	1.49744i
$101$		−	12.1329i		−	0.120127i	−0.998195	−	0.0600636i	$-0.980870\pi$
$101$		−	12.1329i		−	0.120127i	0.998195	−	0.0600636i	$-0.0191304\pi$
$102$	−5.11270	−	13.5269i	−0.0501245	−	0.132617i
$103$			106.582i			1.03478i	0.855750	+	0.517389i	$0.173096\pi$
$103$			106.582i			1.03478i	−0.855750	+	0.517389i	$0.826904\pi$
$104$	−33.7990	+	63.8741i	−0.324990	+	0.614174i
$105$	−14.0000			−0.133333
$106$	−14.9949	+	5.66756i	−0.141462	+	0.0534675i
$107$	−63.5980			−0.594374			−0.297187	−	0.954819i	$-0.596048\pi$
$107$	−63.5980			−0.594374			−0.297187	+	0.954819i	$0.596048\pi$
$108$	31.0294	−	27.3654i	0.287310	−	0.253383i
$109$			130.848i			1.20044i	0.799835	+	0.600220i	$0.204920\pi$
$109$			130.848i			1.20044i	−0.799835	+	0.600220i	$0.795080\pi$
$110$	−210.995	+	79.7486i	−1.91814	+	0.724987i
$111$		−	9.51936i		−	0.0857600i
$112$	−42.0000	−	5.29150i	−0.375000	−	0.0472456i
$113$	−138.225			−1.22323			−0.611617	−	0.791154i	$-0.709481\pi$
$113$	−138.225			−1.22323			−0.611617	+	0.791154i	$0.709481\pi$
$114$	−11.9584	−	31.6389i	−0.104898	−	0.277534i
$115$	222.593			1.93559
$116$	59.3970	+	67.3498i	0.512043	+	0.580602i
$117$		−	78.1987i		−	0.668365i
$118$	−21.5269	−	56.9549i	−0.182431	−	0.482668i
$119$		−	32.6569i		−	0.274428i
$120$	19.7990	−	37.4166i	0.164992	−	0.311805i
$121$	34.8823			0.288283
$122$	28.4975	−	10.7710i	0.233586	−	0.0882872i
$123$	4.08326			0.0331972
$124$	−44.4020	−	50.3472i	−0.358081	−	0.406025i
$125$			285.430i			2.28344i
$126$	42.8492	−	16.1955i	0.340073	−	0.128536i
$127$			114.442i			0.901114i	0.892748	+	0.450557i	$0.148775\pi$
$127$			114.442i			0.901114i	−0.892748	+	0.450557i	$0.851225\pi$
$128$	73.5391	−	104.766i	0.574524	−	0.818488i
$129$	−13.3726			−0.103663
$130$	−57.6985	−	152.656i	−0.443834	−	1.17428i
$131$	−168.350			−1.28512			−0.642558	−	0.766237i	$-0.722127\pi$
$131$	−168.350			−1.28512			−0.642558	+	0.766237i	$0.722127\pi$
$132$	−21.9411	+	19.3503i	−0.166221	+	0.146593i
$133$		−	76.3830i		−	0.574308i
$134$	55.5980	+	147.098i	0.414910	+	1.09775i
$135$			93.4313i			0.692084i
$136$	87.2792	+	46.1838i	0.641759	+	0.339587i
$137$	34.6863			0.253185			0.126592	−	0.991955i	$-0.459596\pi$
$137$	34.6863			0.253185			0.126592	+	0.991955i	$0.459596\pi$
$138$	27.0051	−	10.2069i	0.195689	−	0.0739634i
$139$	107.664			0.774561			0.387281	−	0.921962i	$-0.373414\pi$
$139$	107.664			0.774561			0.387281	+	0.921962i	$0.373414\pi$
$140$	71.6985	−	63.2321i	0.512132	−	0.451658i
$141$			3.63151i			0.0257554i
$142$	32.8040	−	12.3988i	0.231014	−	0.0873152i
$143$			112.782i			0.788682i
$144$	−17.3137	+	137.423i	−0.120234	+	0.954328i
$145$	−202.794			−1.39858
$146$	−33.0122	−	87.3421i	−0.226111	−	0.598233i
$147$	−4.10051			−0.0278946
$148$	42.9949	+	48.7517i	0.290506	+	0.329403i
$149$		−	252.176i		−	1.69246i	−0.532819	−	0.846229i	$-0.678867\pi$
$149$		−	252.176i		−	1.69246i	0.532819	−	0.846229i	$-0.321133\pi$
$150$	23.4437	+	62.0261i	0.156291	+	0.413507i
$151$			234.486i			1.55289i	0.630186	+	0.776444i	$0.282979\pi$
$151$			234.486i			1.55289i	−0.630186	+	0.776444i	$0.717021\pi$
$152$	204.142	+	108.022i	1.34304	+	0.710670i
$153$	−106.853			−0.698384
$154$	−61.7990	+	23.3578i	−0.401292	+	0.151674i
$155$	151.598			0.978051
$156$	−14.0000	−	15.8745i	−0.0897436	−	0.101760i
$157$			10.0968i			0.0643109i	0.999483	+	0.0321554i	$0.0102372\pi$
$157$			10.0968i			0.0643109i	−0.999483	+	0.0321554i	$0.989763\pi$
$158$	151.598	−	57.2987i	0.959481	−	0.362650i
$159$		−	4.69516i		−	0.0295293i
$160$	67.5980	+	281.046i	0.422487	+	1.75654i
$161$	65.1960			0.404944
$162$	−50.8076	−	134.424i	−0.313627	−	0.829780i
$163$	104.534			0.641313			0.320657	−	0.947196i	$-0.396096\pi$
$163$	104.534			0.641313			0.320657	+	0.947196i	$0.396096\pi$
$164$	−20.9117	+	18.4424i	−0.127510	+	0.112454i
$165$		−	66.0659i		−	0.400399i
$166$	−28.5563	−	75.5530i	−0.172026	−	0.455139i
$167$		−	296.765i		−	1.77703i	−0.458843	−	0.888517i	$-0.651736\pi$
$167$		−	296.765i		−	1.77703i	0.458843	−	0.888517i	$-0.348264\pi$
$168$	5.79899	−	10.9591i	0.0345178	−	0.0652325i
$169$	87.4020			0.517172
$170$	−208.593	+	78.8407i	−1.22702	+	0.463769i
$171$	−249.924			−1.46154
$172$	68.4853	−	60.3983i	0.398170	−	0.351153i
$173$			40.0301i			0.231388i	0.993285	+	0.115694i	$0.0369091\pi$
$173$			40.0301i			0.231388i	−0.993285	+	0.115694i	$0.963091\pi$
$174$	−24.6030	+	9.29907i	−0.141397	+	0.0534429i
$175$			149.744i			0.855681i
$176$	24.9706	−	198.198i	0.141878	−	1.12612i
$177$	17.8335			0.100754
$178$	−79.1543	−	209.423i	−0.444687	−	1.17653i
$179$	294.794			1.64689			0.823447	−	0.567394i	$-0.192048\pi$
$179$	294.794			1.64689			0.823447	+	0.567394i	$0.192048\pi$
$180$	−206.894	−	234.596i	−1.14941	−	1.30331i
$181$			40.4706i			0.223595i	0.993731	+	0.111797i	$0.0356608\pi$
$181$			40.4706i			0.223595i	−0.993731	+	0.111797i	$0.964339\pi$
$182$	−16.8995	−	44.7119i	−0.0928544	−	0.245670i
$183$			8.92302i			0.0487596i
$184$	−92.2010	+	174.244i	−0.501092	+	0.946976i
$185$	−146.794			−0.793481
$186$	18.3919	−	6.95149i	0.0988813	−	0.0373736i
$187$	154.108			0.824105
$188$	−16.4020	−	18.5981i	−0.0872448	−	0.0989263i
$189$			27.3654i			0.144790i
$190$	−487.889	+	184.405i	−2.56784	+	0.970552i
$191$		−	156.929i		−	0.821619i	−0.911721	−	0.410810i	$-0.865246\pi$
$191$		−	156.929i		−	0.821619i	0.911721	−	0.410810i	$-0.134754\pi$
$192$	21.0883	+	30.9969i	0.109835	+	0.161442i
$193$	−261.304			−1.35390			−0.676952	−	0.736027i	$-0.736700\pi$
$193$	−261.304			−1.35390			−0.676952	+	0.736027i	$0.736700\pi$
$194$	116.042	+	307.017i	0.598153	+	1.58256i
$195$	47.7990			0.245123
$196$	21.0000	−	18.5203i	0.107143	−	0.0944911i
$197$		−	145.283i		−	0.737475i	−0.929533	−	0.368738i	$-0.879790\pi$
$197$		−	145.283i		−	0.737475i	0.929533	−	0.368738i	$-0.120210\pi$
$198$	76.4264	+	202.205i	0.385992	+	1.02124i
$199$		−	390.508i		−	1.96235i	−0.193122	−	0.981175i	$-0.561861\pi$
$199$		−	390.508i		−	1.96235i	0.193122	−	0.981175i	$-0.438139\pi$
$200$	−400.208	−	211.770i	−2.00104	−	1.05885i
$201$	−46.0589			−0.229149
$202$	−22.6985	+	8.57922i	−0.112369	+	0.0424714i
$203$	−59.3970			−0.292596
$204$	−21.6913	+	19.1300i	−0.106330	+	0.0937743i
$205$		−	62.9662i		−	0.307152i
$206$	199.397	−	75.3650i	0.967946	−	0.365849i
$207$		−	213.320i		−	1.03053i
$208$	143.397	+	18.0663i	0.689409	+	0.0868573i
$209$	360.451			1.72464
$210$	9.89949	+	26.1916i	0.0471405	+	0.124722i
$211$	−164.049			−0.777482			−0.388741	−	0.921347i	$-0.627090\pi$
$211$	−164.049			−0.777482			−0.388741	+	0.921347i	$0.627090\pi$
$212$	21.2061	+	24.0454i	0.100029	+	0.113422i
$213$			10.2715i			0.0482229i
$214$	44.9706	+	118.981i	0.210143	+	0.555986i
$215$			206.213i			0.959129i
$216$	−73.1371	−	38.7005i	−0.338598	−	0.179169i
$217$	44.4020			0.204618
$218$	244.794	−	92.5234i	1.12291	−	0.424419i
$219$	27.3482			0.124878
$220$	298.392	+	338.345i	1.35633	+	1.53793i
$221$			111.498i			0.504514i
$222$	−17.8091	+	6.73120i	−0.0802211	+	0.0303207i
$223$		−	10.5830i		−	0.0474574i	−0.999718	−	0.0237287i	$-0.992446\pi$
$223$		−	10.5830i		−	0.0474574i	0.999718	−	0.0237287i	$-0.00755379\pi$
$224$	19.7990	+	82.3165i	0.0883883	+	0.367484i
$225$	489.960			2.17760
$226$	97.7401	+	258.596i	0.432478	+	1.14423i
$227$	−213.806			−0.941877			−0.470939	−	0.882166i	$-0.656085\pi$
$227$	−213.806			−0.941877			−0.470939	+	0.882166i	$0.656085\pi$
$228$	−50.7351	+	44.7441i	−0.222522	+	0.196246i
$229$		−	232.028i		−	1.01322i	−0.862174	−	0.506612i	$-0.830898\pi$
$229$		−	232.028i		−	1.01322i	0.862174	−	0.506612i	$-0.169102\pi$
$230$	−157.397	−	416.433i	−0.684335	−	1.81058i
$231$		−	19.3503i		−	0.0837673i
$232$	84.0000	−	158.745i	0.362069	−	0.684246i
$233$	−192.863			−0.827738			−0.413869	−	0.910336i	$-0.635823\pi$
$233$	−192.863			−0.827738			−0.413869	+	0.910336i	$0.635823\pi$
$234$	−146.296	+	55.2949i	−0.625199	+	0.236303i
$235$	56.0000			0.238298
$236$	−91.3310	+	80.5463i	−0.386996	+	0.341298i
$237$			47.4678i			0.200286i
$238$	−61.0955	+	23.0919i	−0.256704	+	0.0970248i
$239$			327.917i			1.37204i	0.727583	+	0.686020i	$0.240644\pi$
$239$			327.917i			1.37204i	−0.727583	+	0.686020i	$0.759356\pi$
$240$	−84.0000	−	10.5830i	−0.350000	−	0.0440959i
$241$	71.8721			0.298225			0.149112	−	0.988820i	$-0.452358\pi$
$241$	71.8721			0.298225			0.149112	+	0.988820i	$0.452358\pi$
$242$	−24.6655	−	65.2587i	−0.101923	−	0.269664i
$243$	135.179			0.556291
$244$	−40.3015	−	45.6976i	−0.165170	−	0.187285i
$245$			63.2321i			0.258090i
$246$	−2.88730	−	7.63908i	−0.0117370	−	0.0310532i
$247$			260.788i			1.05582i
$248$	−62.7939	+	118.669i	−0.253201	+	0.478506i
$249$	23.6569			0.0950074
$250$	533.990	−	201.829i	2.13596	−	0.807317i
$251$	−256.919			−1.02358			−0.511790	−	0.859110i	$-0.671018\pi$
$251$	−256.919			−1.02358			−0.511790	+	0.859110i	$0.671018\pi$
$252$	−60.5980	−	68.7117i	−0.240468	−	0.272665i
$253$			307.659i			1.21604i
$254$	214.101	−	80.9224i	0.842915	−	0.318592i
$255$		−	65.3138i		−	0.256133i
$256$	−248.000	−	63.4980i	−0.968750	−	0.248039i
$257$	319.352			1.24262			0.621308	−	0.783566i	$-0.286602\pi$
$257$	319.352			1.24262			0.621308	+	0.783566i	$0.286602\pi$
$258$	9.45584	+	25.0178i	0.0366506	+	0.0969683i
$259$	−42.9949			−0.166004
$260$	−244.794	+	215.888i	−0.941515	+	0.830338i
$261$			194.346i			0.744620i
$262$	119.042	+	314.955i	0.454357	+	1.20212i
$263$			377.357i			1.43482i	0.696653	+	0.717408i	$0.254672\pi$
$263$			377.357i			1.43482i	−0.696653	+	0.717408i	$0.745328\pi$
$264$	51.7157	+	27.3654i	0.195893	+	0.103657i
$265$	−72.4020			−0.273215
$266$	−142.899	+	54.0109i	−0.537216	+	0.203049i
$267$	65.5736			0.245594
$268$	235.882	−	208.029i	0.880158	−	0.776226i
$269$		−	28.1631i		−	0.104696i	−0.998629	−	0.0523478i	$-0.983330\pi$
$269$		−	28.1631i		−	0.104696i	0.998629	−	0.0523478i	$-0.0166704\pi$
$270$	174.794	−	66.0659i	0.647385	−	0.244689i
$271$		−	399.715i		−	1.47496i	−0.675367	−	0.737482i	$-0.736015\pi$
$271$		−	399.715i		−	1.47496i	0.675367	−	0.737482i	$-0.263985\pi$
$272$	24.6863	−	195.941i	0.0907584	−	0.720373i
$273$	14.0000			0.0512821
$274$	−24.5269	−	64.8921i	−0.0895143	−	0.236833i
$275$	−706.642			−2.56961
$276$	−38.1909	−	43.3044i	−0.138373	−	0.156900i
$277$			102.951i			0.371663i	0.982582	+	0.185831i	$0.0594979\pi$
$277$			102.951i			0.371663i	−0.982582	+	0.185831i	$0.940502\pi$
$278$	−76.1299	−	201.421i	−0.273849	−	0.724536i
$279$		−	145.283i		−	0.520726i
$280$	−168.995	−	89.4237i	−0.603553	−	0.319370i
$281$	−150.235			−0.534646			−0.267323	−	0.963607i	$-0.586139\pi$
$281$	−150.235			−0.534646			−0.267323	+	0.963607i	$0.586139\pi$
$282$	6.79394	−	2.56787i	0.0240920	−	0.00910591i
$283$	−178.561			−0.630959			−0.315480	−	0.948932i	$-0.602165\pi$
$283$	−178.561			−0.630959			−0.315480	+	0.948932i	$0.602165\pi$
$284$	−46.3919	−	52.6035i	−0.163352	−	0.185224i
$285$		−	152.766i		−	0.536021i
$286$	210.995	−	79.7486i	0.737745	−	0.278841i
$287$		−	18.4424i		−	0.0642591i
$288$	269.338	−	64.7820i	0.935202	−	0.224937i
$289$	−136.647			−0.472826
$290$	143.397	+	379.393i	0.494472	+	1.30825i
$291$	−96.1320			−0.330351
$292$	−140.059	+	123.520i	−0.479654	+	0.423015i
$293$			219.189i			0.748085i	0.927411	+	0.374043i	$0.122029\pi$
$293$			219.189i			0.748085i	−0.927411	+	0.374043i	$0.877971\pi$
$294$	2.89949	+	7.67134i	0.00986223	+	0.0260930i
$295$		−	275.002i		−	0.932211i
$296$	60.8040	−	114.909i	0.205419	−	0.388206i
$297$	−129.137			−0.434805
$298$	−471.779	+	178.316i	−1.58315	+	0.598375i
$299$	−222.593			−0.744458
$300$	99.4630	−	87.7181i	0.331543	−	0.292394i
$301$			60.3983i			0.200659i
$302$	438.683	−	165.807i	1.45259	−	0.549029i
$303$		−	7.10726i		−	0.0234563i
$304$	57.7401	−	458.298i	0.189935	−	1.50756i
$305$	137.598			0.451141
$306$	75.5563	+	199.903i	0.246916	+	0.653279i
$307$	316.669			1.03150			0.515748	−	0.856741i	$-0.327514\pi$
$307$	316.669			1.03150			0.515748	+	0.856741i	$0.327514\pi$
$308$	87.3970	+	99.0988i	0.283756	+	0.321750i
$309$			62.4344i			0.202053i
$310$	−107.196	−	283.614i	−0.345793	−	0.914883i
$311$		−	72.2653i		−	0.232364i	−0.993228	−	0.116182i	$-0.962934\pi$
$311$		−	72.2653i		−	0.232364i	0.993228	−	0.116182i	$-0.0370656\pi$
$312$	−19.7990	+	37.4166i	−0.0634583	+	0.119925i
$313$	81.9512			0.261825			0.130913	−	0.991394i	$-0.458209\pi$
$313$	81.9512			0.261825			0.130913	+	0.991394i	$0.458209\pi$
$314$	18.8894	−	7.13952i	0.0601573	−	0.0227373i
$315$	206.894			0.656808
$316$	−214.392	−	243.098i	−0.678455	−	0.769296i
$317$			109.150i			0.344322i	0.985069	+	0.172161i	$0.0550749\pi$
$317$			109.150i			0.344322i	−0.985069	+	0.172161i	$0.944925\pi$
$318$	−8.78384	+	3.31998i	−0.0276221	+	0.0104402i
$319$		−	280.294i		−	0.878664i
$320$	477.990	−	325.194i	1.49372	−	1.01623i
$321$	−37.2548			−0.116059
$322$	−46.1005	−	121.970i	−0.143169	−	0.378790i
$323$	356.347			1.10324
$324$	−215.558	+	190.105i	−0.665304	+	0.586743i
$325$		−	511.259i		−	1.57310i
$326$	−73.9167	−	195.565i	−0.226738	−	0.599894i
$327$			76.6489i			0.234400i
$328$	49.2893	+	26.0815i	0.150272	+	0.0795166i
$329$	16.4020			0.0498542
$330$	−123.598	+	46.7156i	−0.374539	+	0.141563i
$331$	321.740			0.972025			0.486012	−	0.873952i	$-0.338451\pi$
$331$	321.740			0.972025			0.486012	+	0.873952i	$0.338451\pi$
$332$	−121.154	+	106.848i	−0.364923	+	0.321832i
$333$			140.679i			0.422459i
$334$	−555.196	+	209.844i	−1.66226	+	0.628276i
$335$			710.254i			2.12016i
$336$	−24.6030	−	3.09969i	−0.0732233	−	0.00922527i
$337$	−164.049			−0.486792			−0.243396	−	0.969927i	$-0.578261\pi$
$337$	−164.049			−0.486792			−0.243396	+	0.969927i	$0.578261\pi$
$338$	−61.8026	−	163.514i	−0.182848	−	0.483770i
$339$	−80.9706			−0.238851
$340$	294.995	+	334.493i	0.867632	+	0.983802i
$341$			209.533i			0.614466i
$342$	176.723	+	467.565i	0.516734	+	1.36715i
$343$			18.5203i			0.0539949i
$344$	−161.421	−	85.4162i	−0.469248	−	0.248303i
$345$	130.392			0.377948
$346$	74.8894	−	28.3055i	0.216443	−	0.0818079i
$347$	−330.309			−0.951898			−0.475949	−	0.879473i	$-0.657895\pi$
$347$	−330.309			−0.951898			−0.475949	+	0.879473i	$0.657895\pi$
$348$	34.7939	+	39.4526i	0.0999826	+	0.113370i
$349$		−	262.402i		−	0.751869i	−0.926646	−	0.375934i	$-0.877322\pi$
$349$		−	262.402i		−	0.751869i	0.926646	−	0.375934i	$-0.122678\pi$
$350$	280.146	−	105.885i	0.800416	−	0.302529i
$351$		−	93.4313i		−	0.266186i
$352$	−388.451	+	93.4313i	−1.10355	+	0.265430i
$353$	−578.098			−1.63767			−0.818835	−	0.574029i	$-0.805380\pi$
$353$	−578.098			−1.63767			−0.818835	+	0.574029i	$0.805380\pi$
$354$	−12.6102	−	33.3634i	−0.0356220	−	0.0942468i
$355$	158.392			0.446174
$356$	−335.823	+	296.168i	−0.943324	+	0.831934i
$357$		−	19.1300i		−	0.0535853i
$358$	−208.451	−	551.509i	−0.582265	−	1.54053i
$359$		−	365.114i		−	1.01703i	−0.861053	−	0.508515i	$-0.830195\pi$
$359$		−	365.114i		−	1.01703i	0.861053	−	0.508515i	$-0.169805\pi$
$360$	−292.593	+	552.949i	−0.812758	+	1.53597i
$361$	472.480			1.30881
$362$	75.7136	−	28.6171i	0.209154	−	0.0790527i
$363$	20.4335			0.0562908
$364$	−71.6985	+	63.2321i	−0.196974	+	0.173715i
$365$		−	421.725i		−	1.15541i
$366$	16.6934	−	6.30953i	0.0456105	−	0.0172391i
$367$			520.071i			1.41709i	0.705666	+	0.708544i	$0.250648\pi$
$367$			520.071i			1.41709i	−0.705666	+	0.708544i	$0.749352\pi$
$368$	391.176	+	49.2835i	1.06298	+	0.133923i
$369$	−60.3431			−0.163532
$370$	103.799	+	274.626i	0.280538	+	0.742233i
$371$	−21.2061			−0.0571592
$372$	−26.0101	−	29.4927i	−0.0699196	−	0.0792814i
$373$		−	526.711i		−	1.41210i	−0.708164	−	0.706048i	$-0.750476\pi$
$373$		−	526.711i		−	1.41210i	0.708164	−	0.706048i	$-0.249524\pi$
$374$	−108.971	−	288.309i	−0.291365	−	0.770880i
$375$			167.201i			0.445869i
$376$	−23.1960	+	43.8362i	−0.0616914	+	0.116586i
$377$	202.794			0.537915
$378$	51.1960	−	19.3503i	0.135439	−	0.0511911i
$379$	121.976			0.321835			0.160918	−	0.986968i	$-0.448555\pi$
$379$	121.976			0.321835			0.160918	+	0.986968i	$0.448555\pi$
$380$	689.980	+	782.364i	1.81574	+	2.05885i
$381$			67.0383i			0.175954i
$382$	−293.588	+	110.966i	−0.768555	+	0.290486i
$383$		−	316.427i		−	0.826179i	−0.910690	−	0.413089i	$-0.864450\pi$
$383$		−	316.427i		−	0.826179i	0.910690	−	0.413089i	$-0.135550\pi$
$384$	43.0782	−	61.3707i	0.112183	−	0.159820i
$385$	−298.392			−0.775044
$386$	184.770	+	488.854i	0.478678	+	1.26646i
$387$	197.622			0.510652
$388$	492.323	−	434.188i	1.26887	−	1.11904i
$389$			92.1474i			0.236883i	0.992961	+	0.118441i	$0.0377898\pi$
$389$			92.1474i			0.236883i	−0.992961	+	0.118441i	$0.962210\pi$
$390$	−33.7990	−	89.4237i	−0.0866641	−	0.229292i
$391$			304.157i			0.777895i
$392$	−49.4975	−	26.1916i	−0.126269	−	0.0668153i
$393$	−98.6173			−0.250935
$394$	−271.799	+	102.730i	−0.689845	+	0.260737i
$395$	731.980			1.85311
$396$	324.250	−	285.961i	0.818813	−	0.722125i
$397$			562.267i			1.41629i	0.706068	+	0.708144i	$0.250467\pi$
$397$			562.267i			1.41629i	−0.706068	+	0.708144i	$0.749533\pi$
$398$	−730.573	+	276.131i	−1.83561	+	0.693795i
$399$		−	44.7441i		−	0.112141i
$400$	−113.196	+	898.465i	−0.282990	+	2.24616i
$401$	81.2061			0.202509			0.101254	−	0.994861i	$-0.467714\pi$
$401$	81.2061			0.202509			0.101254	+	0.994861i	$0.467714\pi$
$402$	32.5685	+	86.1683i	0.0810163	+	0.214349i
$403$	−151.598			−0.376174
$404$	32.1005	+	36.3986i	0.0794567	+	0.0900954i
$405$		−	649.058i		−	1.60261i
$406$	42.0000	+	111.122i	0.103448	+	0.273698i
$407$		−	202.893i		−	0.498508i
$408$	51.1270	+	27.0539i	0.125311	+	0.0663085i
$409$	450.735			1.10204			0.551021	−	0.834491i	$-0.314238\pi$
$409$	450.735			1.10204			0.551021	+	0.834491i	$0.314238\pi$
$410$	−117.799	+	44.5238i	−0.287315	+	0.108595i
$411$	20.3188			0.0494374
$412$	−281.990	−	319.746i	−0.684442	−	0.776084i
$413$		−	80.5463i		−	0.195027i
$414$	−399.085	+	150.840i	−0.963974	+	0.364348i
$415$		−	364.802i		−	0.879041i
$416$	−67.5980	−	281.046i	−0.162495	−	0.675591i
$417$	63.0681			0.151242
$418$	−254.877	−	674.342i	−0.609754	−	1.61326i
$419$	624.988			1.49162			0.745809	−	0.666160i	$-0.232063\pi$
$419$	624.988			1.49162			0.745809	+	0.666160i	$0.232063\pi$
$420$	42.0000	−	37.0405i	0.100000	−	0.0881917i
$421$			566.476i			1.34555i	0.739848	+	0.672774i	$0.234897\pi$
$421$			566.476i			1.34555i	−0.739848	+	0.672774i	$0.765103\pi$
$422$	116.000	+	306.907i	0.274882	+	0.727268i
$423$		−	53.6671i		−	0.126873i
$424$	29.9899	−	56.6756i	0.0707309	−	0.133669i
$425$	−698.597			−1.64376
$426$	19.2162	−	7.26303i	0.0451084	−	0.0170494i
$427$	40.3015			0.0943829
$428$	190.794	−	168.264i	0.445780	−	0.393141i
$429$			66.0659i			0.154000i
$430$	385.789	−	145.814i	0.897183	−	0.339103i
$431$			289.528i			0.671760i	0.941905	+	0.335880i	$0.109034\pi$
$431$			289.528i			0.671760i	−0.941905	+	0.335880i	$0.890966\pi$
$432$	−20.6863	+	164.192i	−0.0478849	+	0.380075i
$433$	−597.696			−1.38036			−0.690180	−	0.723638i	$-0.742468\pi$
$433$	−597.696			−1.38036			−0.690180	+	0.723638i	$0.742468\pi$
$434$	−31.3970	−	83.0686i	−0.0723432	−	0.191402i
$435$	−118.794			−0.273090
$436$	−346.191	−	392.544i	−0.794016	−	0.900329i
$437$			711.409i			1.62794i
$438$	−19.3381	−	51.1638i	−0.0441509	−	0.116812i
$439$		−	38.3890i		−	0.0874464i	−0.999044	−	0.0437232i	$-0.986078\pi$
$439$		−	38.3890i		−	0.0874464i	0.999044	−	0.0437232i	$-0.0139220\pi$
$440$	421.990	−	797.486i	0.959068	−	1.81247i
$441$	60.5980			0.137410
$442$	208.593	−	78.8407i	0.471930	−	0.178373i
$443$	599.058			1.35228			0.676138	−	0.736775i	$-0.263652\pi$
$443$	599.058			1.35228			0.676138	+	0.736775i	$0.263652\pi$
$444$	25.1859	+	28.5581i	0.0567249	+	0.0643200i
$445$		−	1011.18i		−	2.27232i
$446$	−19.7990	+	7.48331i	−0.0443924	+	0.0167787i
$447$		−	147.721i		−	0.330473i
$448$	140.000	−	95.2470i	0.312500	−	0.212605i
$449$	−460.039			−1.02459			−0.512293	−	0.858811i	$-0.671204\pi$
$449$	−460.039			−1.02459			−0.512293	+	0.858811i	$0.671204\pi$
$450$	−346.454	−	916.632i	−0.769899	−	2.03696i
$451$	87.0294			0.192970
$452$	414.676	−	365.710i	0.917425	−	0.809093i
$453$			137.359i			0.303220i
$454$	151.184	+	399.995i	0.333004	+	0.881045i
$455$		−	215.888i		−	0.474479i
$456$	119.584	+	63.2777i	0.262245	+	0.138767i
$457$	266.323			0.582764			0.291382	−	0.956607i	$-0.405885\pi$
$457$	266.323			0.582764			0.291382	+	0.956607i	$0.405885\pi$
$458$	−434.085	+	164.069i	−0.947785	+	0.358229i
$459$	−127.667			−0.278142
$460$	−667.779	+	588.926i	−1.45169	+	1.28027i
$461$		−	763.123i		−	1.65537i	−0.561196	−	0.827683i	$-0.689659\pi$
$461$		−	763.123i		−	1.65537i	0.561196	−	0.827683i	$-0.310341\pi$
$462$	−36.2010	+	13.6827i	−0.0783572	+	0.0296162i
$463$			123.988i			0.267792i	0.990995	+	0.133896i	$0.0427488\pi$
$463$			123.988i			0.267792i	−0.990995	+	0.133896i	$0.957251\pi$
$464$	−356.382	−	44.8999i	−0.768064	−	0.0967670i
$465$	88.8040			0.190976
$466$	136.375	+	360.813i	0.292650	+	0.774278i
$467$	−768.718			−1.64608			−0.823038	−	0.567986i	$-0.807723\pi$
$467$	−768.718			−1.64608			−0.823038	+	0.567986i	$0.807723\pi$
$468$	206.894	+	234.596i	0.442082	+	0.501274i
$469$			208.029i			0.443558i
$470$	−39.5980	−	104.766i	−0.0842510	−	0.222907i
$471$			5.91457i			0.0125575i
$472$	215.269	+	113.910i	0.456079	+	0.241334i
$473$	−285.019			−0.602578
$474$	88.8040	−	33.5648i	0.187350	−	0.0708118i
$475$	−1633.99			−3.43997
$476$	86.4020	+	97.9707i	0.181517	+	0.205821i
$477$			69.3859i			0.145463i
$478$	613.477	−	231.873i	1.28343	−	0.485089i
$479$		−	118.981i		−	0.248394i	−0.992258	−	0.124197i	$-0.960364\pi$
$479$		−	118.981i		−	0.248394i	0.992258	−	0.124197i	$-0.0396355\pi$
$480$	39.5980	+	164.633i	0.0824958	+	0.342985i
$481$	146.794			0.305185
$482$	−50.8213	−	134.460i	−0.105438	−	0.278964i
$483$	38.1909			0.0790702
$484$	−104.647	+	92.2898i	−0.216212	+	0.190681i
$485$			1482.41i			3.05652i
$486$	−95.5858	−	252.896i	−0.196679	−	0.520363i
$487$		−	282.577i		−	0.580240i	−0.956990	−	0.290120i	$-0.906305\pi$
$487$		−	282.577i		−	0.580240i	0.956990	−	0.290120i	$-0.0936952\pi$
$488$	−56.9949	+	107.710i	−0.116793	+	0.220718i
$489$	61.2346			0.125224
$490$	118.296	−	44.7119i	0.241421	−	0.0912487i
$491$	−388.049			−0.790323			−0.395162	−	0.918612i	$-0.629311\pi$
$491$	−388.049			−0.790323			−0.395162	+	0.918612i	$0.629311\pi$
$492$	−12.2498	+	10.8033i	−0.0248979	+	0.0219579i
$493$		−	277.103i		−	0.562075i
$494$	487.889	−	184.405i	0.987630	−	0.373289i
$495$			976.333i			1.97239i
$496$	266.412	+	33.5648i	0.537121	+	0.0676709i
$497$	46.3919			0.0933439
$498$	−16.7279	−	44.2579i	−0.0335902	−	0.0888713i
$499$	−27.7157			−0.0555425			−0.0277713	−	0.999614i	$-0.508841\pi$
$499$	−27.7157			−0.0555425			−0.0277713	+	0.999614i	$0.508841\pi$
$500$	−755.176	−	856.289i	−1.51035	−	1.71258i
$501$		−	173.841i		−	0.346988i
$502$	181.669	+	480.651i	0.361891	+	0.957472i
$503$			727.477i			1.44628i	0.690703	+	0.723138i	$0.257301\pi$
$503$			727.477i			1.44628i	−0.690703	+	0.723138i	$0.742699\pi$
$504$	−85.6985	+	161.955i	−0.170037	+	0.321339i
$505$	−109.598			−0.217026
$506$	575.578	−	217.548i	1.13751	−	0.429937i
$507$	51.1989			0.100984
$508$	−302.784	−	343.325i	−0.596031	−	0.675836i
$509$		−	634.183i		−	1.24594i	−0.782246	−	0.622969i	$-0.785926\pi$
$509$		−	634.183i		−	1.24594i	0.782246	−	0.622969i	$-0.214074\pi$
$510$	−122.191	+	46.1838i	−0.239590	+	0.0905565i
$511$		−	123.520i		−	0.241723i
$512$	56.5685	+	508.865i	0.110485	+	0.993878i
$513$	−298.607			−0.582080
$514$	−225.816	−	597.454i	−0.439331	−	1.16236i
$515$	962.774			1.86946
$516$	40.1177	−	35.3805i	0.0777476	−	0.0685669i
$517$			77.4010i			0.149712i
$518$	30.4020	+	80.4362i	0.0586912	+	0.155282i
$519$			23.4491i			0.0451813i
$520$	576.985	+	305.312i	1.10959	+	0.587138i
$521$	833.127			1.59909			0.799546	−	0.600605i	$-0.205073\pi$
$521$	833.127			1.59909			0.799546	+	0.600605i	$0.205073\pi$
$522$	363.588	−	137.423i	0.696529	−	0.263263i
$523$	876.434			1.67578			0.837891	−	0.545838i	$-0.183789\pi$
$523$	876.434			1.67578			0.837891	+	0.545838i	$0.183789\pi$
$524$	505.051	−	445.413i	0.963838	−	0.850025i
$525$			87.7181i			0.167082i
$526$	705.970	−	266.831i	1.34215	−	0.507284i
$527$			207.147i			0.393069i
$528$	14.6274	−	116.102i	0.0277034	−	0.219889i
$529$	−78.2162			−0.147857
$530$	51.1960	+	135.452i	0.0965961	+	0.255569i
$531$	−263.546			−0.496321
$532$	202.090	+	229.149i	0.379869	+	0.430731i
$533$			62.9662i			0.118135i
$534$	−46.3675	−	122.677i	−0.0868306	−	0.229732i
$535$			574.491i			1.07381i
$536$	−555.980	−	294.197i	−1.03728	−	0.548875i
$537$	172.686			0.321576
$538$	−52.6884	+	19.9143i	−0.0979338	+	0.0370155i
$539$	−87.3970			−0.162147
$540$	−247.196	−	280.294i	−0.457770	−	0.519063i
$541$			405.915i			0.750305i	0.926963	+	0.375152i	$0.122410\pi$
$541$			405.915i			0.750305i	−0.926963	+	0.375152i	$0.877590\pi$
$542$	−747.799	+	282.641i	−1.37970	+	0.521479i
$543$			23.7072i			0.0436596i
$544$	−384.029	+	92.3676i	−0.705935	+	0.169793i
$545$	1181.97			2.16875
$546$	−9.89949	−	26.1916i	−0.0181309	−	0.0479700i
$547$	−606.024			−1.10791			−0.553953	−	0.832548i	$-0.686881\pi$
$547$	−606.024			−1.10791			−0.553953	+	0.832548i	$0.686881\pi$
$548$	−104.059	+	91.7713i	−0.189888	+	0.167466i
$549$		−	131.866i		−	0.240193i
$550$	499.671	+	1322.01i	0.908493	+	2.40365i
$551$		−	648.131i		−	1.17628i
$552$	−54.0101	+	102.069i	−0.0978444	+	0.184909i
$553$	214.392			0.387689
$554$	192.603	−	72.7971i	0.347659	−	0.131403i
$555$	−85.9899			−0.154937
$556$	−322.992	+	284.852i	−0.580921	+	0.512324i
$557$		−	36.4442i		−	0.0654294i	−0.999465	−	0.0327147i	$-0.989585\pi$
$557$		−	36.4442i		−	0.0654294i	0.999465	−	0.0327147i	$-0.0104153\pi$
$558$	−271.799	+	102.730i	−0.487095	+	0.184105i
$559$		−	206.213i		−	0.368896i
$560$	−47.7990	+	379.393i	−0.0853553	+	0.677487i
$561$	90.2742			0.160917
$562$	106.233	+	281.065i	0.189026	+	0.500115i
$563$	−186.389			−0.331064			−0.165532	−	0.986204i	$-0.552934\pi$
$563$	−186.389			−0.331064			−0.165532	+	0.986204i	$0.552934\pi$
$564$	−9.60808	−	10.8945i	−0.0170356	−	0.0193166i
$565$			1248.61i			2.20993i
$566$	126.262	+	334.058i	0.223078	+	0.590208i
$567$		−	190.105i		−	0.335282i
$568$	−65.6081	+	123.988i	−0.115507	+	0.218288i
$569$	−670.891			−1.17907			−0.589536	−	0.807742i	$-0.700689\pi$
$569$	−670.891			−1.17907			−0.589536	+	0.807742i	$0.700689\pi$
$570$	−285.799	+	108.022i	−0.501402	+	0.189512i
$571$	−677.082			−1.18578			−0.592892	−	0.805282i	$-0.702014\pi$
$571$	−677.082			−1.18578			−0.592892	+	0.805282i	$0.702014\pi$
$572$	−298.392	−	338.345i	−0.521664	−	0.591512i
$573$		−	91.9271i		−	0.160431i
$574$	−34.5025	+	13.0407i	−0.0601089	+	0.0227190i
$575$		−	1394.67i		−	2.42552i
$576$	−311.647	−	458.078i	−0.541053	−	0.795274i
$577$	927.901			1.60815			0.804073	−	0.594530i	$-0.202662\pi$
$577$	927.901			1.60815			0.804073	+	0.594530i	$0.202662\pi$
$578$	96.6238	+	255.643i	0.167169	+	0.442288i
$579$	−153.068			−0.264366
$580$	608.382	−	536.542i	1.04893	−	0.925073i
$581$		−	106.848i		−	0.183904i
$582$	67.9756	+	179.847i	0.116797	+	0.309015i
$583$		−	100.071i		−	0.171649i
$584$	330.122	+	174.684i	0.565277	+	0.299117i
$585$	−706.382			−1.20749
$586$	410.065	−	154.990i	0.699770	−	0.264488i
$587$	−321.120			−0.547053			−0.273526	−	0.961865i	$-0.588190\pi$
$587$	−321.120			−0.547053			−0.273526	+	0.961865i	$0.588190\pi$
$588$	12.3015	−	10.8489i	0.0209209	−	0.0184505i
$589$			484.508i			0.822595i
$590$	−514.482	+	194.456i	−0.872004	+	0.329587i
$591$		−	85.1046i		−	0.144001i
$592$	−257.970	−	32.5011i	−0.435760	−	0.0549006i
$593$	−219.255			−0.369738			−0.184869	−	0.982763i	$-0.559186\pi$
$593$	−219.255			−0.369738			−0.184869	+	0.982763i	$0.559186\pi$
$594$	91.3137	+	241.593i	0.153727	+	0.406723i
$595$	−294.995			−0.495790
$596$	667.196	+	756.529i	1.11946	+	1.26934i
$597$		−	228.754i		−	0.383173i
$598$	157.397	+	416.433i	0.263206	+	0.696377i
$599$		−	154.802i		−	0.258434i	−0.991616	−	0.129217i	$-0.958754\pi$
$599$		−	154.802i		−	0.258434i	0.991616	−	0.129217i	$-0.0412464\pi$
$600$	−234.437	−	124.052i	−0.390728	−	0.206754i
$601$	205.862			0.342533			0.171266	−	0.985225i	$-0.445214\pi$
$601$	205.862			0.342533			0.171266	+	0.985225i	$0.445214\pi$
$602$	112.995	−	42.7081i	0.187699	−	0.0709436i
$603$	680.666			1.12880
$604$	−620.392	−	703.458i	−1.02714	−	1.16467i
$605$		−	315.097i		−	0.520821i
$606$	−13.2965	+	5.02559i	−0.0219414	+	0.00829305i
$607$		−	790.663i		−	1.30258i	−0.758831	−	0.651288i	$-0.774229\pi$
$607$		−	790.663i		−	1.30258i	0.758831	−	0.651288i	$-0.225771\pi$
$608$	−898.225	+	216.044i	−1.47734	+	0.355335i
$609$	−34.7939			−0.0571329
$610$	−97.2965	−	257.422i	−0.159502	−	0.422004i
$611$	−56.0000			−0.0916530
$612$	320.558	−	282.706i	0.523788	−	0.461938i
$613$		−	741.471i		−	1.20958i	−0.796386	−	0.604789i	$-0.793257\pi$
$613$		−	741.471i		−	1.20958i	0.796386	−	0.604789i	$-0.206743\pi$
$614$	−223.919	−	592.434i	−0.364689	−	0.964875i
$615$		−	36.8848i		−	0.0599752i
$616$	123.598	−	233.578i	0.200646	−	0.379185i
$617$	171.578			0.278084			0.139042	−	0.990286i	$-0.455598\pi$
$617$	171.578			0.278084			0.139042	+	0.990286i	$0.455598\pi$
$618$	116.804	−	44.1478i	0.189003	−	0.0714365i
$619$	−540.198			−0.872695			−0.436347	−	0.899778i	$-0.643728\pi$
$619$	−540.198			−0.872695			−0.436347	+	0.899778i	$0.643728\pi$
$620$	−454.794	+	401.091i	−0.733539	+	0.646920i
$621$		−	254.873i		−	0.410424i
$622$	−135.196	+	51.0993i	−0.217357	+	0.0821532i
$623$		−	296.168i		−	0.475391i
$624$	84.0000	+	10.5830i	0.134615	+	0.0169599i
$625$	1163.38			1.86141
$626$	−57.9483	−	153.317i	−0.0925691	−	0.244915i
$627$	211.147			0.336758
$628$	−26.7136	−	30.2904i	−0.0425376	−	0.0482331i
$629$		−	200.583i		−	0.318892i
$630$	−146.296	−	387.064i	−0.232217	−	0.614387i
$631$		−	269.399i		−	0.426940i	−0.976950	−	0.213470i	$-0.931523\pi$
$631$		−	269.399i		−	0.426940i	0.976950	−	0.213470i	$-0.0684766\pi$
$632$	−303.196	+	572.987i	−0.479740	+	0.906624i
$633$	−96.0975			−0.151813
$634$	204.201	−	77.1807i	0.322084	−	0.121736i
$635$	1033.77			1.62798
$636$	12.4222	+	14.0855i	0.0195318	+	0.0221470i
$637$		−	63.2321i		−	0.0992655i
$638$	−524.382	+	198.198i	−0.821915	+	0.310655i
$639$		−	151.794i		−	0.237549i
$640$	−946.372	−	664.291i	−1.47871	−	1.03795i
$641$	36.1867			0.0564535			0.0282268	−	0.999602i	$-0.491014\pi$
$641$	36.1867			0.0564535			0.0282268	+	0.999602i	$0.491014\pi$
$642$	26.3431	+	69.6974i	0.0410329	+	0.108563i
$643$	266.297			0.414148			0.207074	−	0.978325i	$-0.433606\pi$
$643$	266.297			0.414148			0.207074	+	0.978325i	$0.433606\pi$
$644$	−195.588	+	172.492i	−0.303708	+	0.267845i
$645$			120.797i			0.187282i
$646$	−251.976	−	666.665i	−0.390055	−	1.03199i
$647$			1086.24i			1.67888i	0.543452	+	0.839440i	$0.317117\pi$
$647$			1086.24i			1.67888i	−0.543452	+	0.839440i	$0.682883\pi$
$648$	508.076	+	268.849i	0.784068	+	0.414890i
$649$	380.098			0.585666
$650$	−956.477	+	361.514i	−1.47150	+	0.556176i
$651$	26.0101			0.0399541
$652$	−313.602	+	276.571i	−0.480985	+	0.424189i
$653$		−	1195.35i		−	1.83055i	−0.402832	−	0.915274i	$-0.631974\pi$
$653$		−	1195.35i		−	1.83055i	0.402832	−	0.915274i	$-0.368026\pi$
$654$	143.397	−	54.1990i	0.219261	−	0.0828730i
$655$			1520.74i			2.32173i
$656$	13.9411	−	110.654i	0.0212517	−	0.168680i
$657$	−404.156			−0.615154
$658$	−11.5980	−	30.6854i	−0.0176261	−	0.0466343i
$659$	−685.220			−1.03979			−0.519894	−	0.854231i	$-0.674029\pi$
$659$	−685.220			−1.03979			−0.519894	+	0.854231i	$0.674029\pi$
$660$	174.794	+	198.198i	0.264839	+	0.300300i
$661$			993.382i			1.50285i	0.659820	+	0.751423i	$0.270632\pi$
$661$			993.382i			1.50285i	−0.659820	+	0.751423i	$0.729368\pi$
$662$	−227.505	−	601.921i	−0.343663	−	0.909246i
$663$			65.3138i			0.0985125i
$664$	285.563	+	151.106i	0.430065	+	0.227569i
$665$	−689.980			−1.03756
$666$	263.186	−	99.4749i	0.395174	−	0.149362i
$667$	553.206			0.829394
$668$	785.166	+	890.294i	1.17540	+	1.33278i
$669$		−	6.19938i		−	0.00926664i
$670$	1328.76	−	502.225i	1.98323	−	0.749590i
$671$			190.183i			0.283432i
$672$	11.5980	+	48.2199i	0.0172589	+	0.0717558i
$673$	106.569			0.158349			0.0791743	−	0.996861i	$-0.474772\pi$
$673$	106.569			0.158349			0.0791743	+	0.996861i	$0.474772\pi$
$674$	116.000	+	306.907i	0.172107	+	0.455352i
$675$	585.401			0.867261
$676$	−262.206	+	231.244i	−0.387879	+	0.342077i
$677$		−	1004.18i		−	1.48329i	−0.670795	−	0.741643i	$-0.734047\pi$
$677$		−	1004.18i		−	1.48329i	0.670795	−	0.741643i	$-0.265953\pi$
$678$	57.2548	+	151.482i	0.0844467	+	0.223425i
$679$			434.188i			0.639452i
$680$	417.186	−	788.407i	0.613509	−	1.15942i
$681$	−125.245			−0.183913
$682$	392.000	−	148.162i	0.574780	−	0.217246i
$683$	−678.225			−0.993009			−0.496505	−	0.868034i	$-0.665383\pi$
$683$	−678.225			−0.993009			−0.496505	+	0.868034i	$0.665383\pi$
$684$	749.772	−	661.236i	1.09616	−	0.966720i
$685$		−	313.327i		−	0.457411i
$686$	34.6482	−	13.0958i	0.0505076	−	0.0190901i
$687$		−	135.919i		−	0.197844i
$688$	−45.6569	+	362.390i	−0.0663617	+	0.526730i
$689$	72.4020			0.105083
$690$	−92.2010	−	243.941i	−0.133625	−	0.353538i
$691$	−365.175			−0.528473			−0.264236	−	0.964458i	$-0.585120\pi$
$691$	−365.175			−0.528473			−0.264236	+	0.964458i	$0.585120\pi$
$692$	−105.910	−	120.090i	−0.153049	−	0.173541i
$693$			285.961i			0.412643i
$694$	233.563	+	617.951i	0.336547	+	0.890419i
$695$		−	972.546i		−	1.39935i
$696$	49.2061	−	92.9907i	0.0706984	−	0.133607i
$697$	86.0387			0.123441
$698$	−490.910	+	185.546i	−0.703309	+	0.265826i
$699$	−112.976			−0.161626
$700$	−396.186	−	449.233i	−0.565980	−	0.641761i
$701$		−	940.292i		−	1.34136i	−0.741748	−	0.670679i	$-0.766003\pi$
$701$		−	940.292i		−	1.34136i	0.741748	−	0.670679i	$-0.233997\pi$
$702$	−174.794	+	66.0659i	−0.248994	+	0.0941110i
$703$		−	469.155i		−	0.667361i
$704$	449.470	+	660.659i	0.638452	+	0.938436i
$705$	32.8040			0.0465306
$706$	408.777	+	1081.52i	0.579004	+	1.53190i
$707$	−32.1005			−0.0454038
$708$	−53.5004	+	47.1829i	−0.0755656	+	0.0666426i
$709$			1057.46i			1.49148i	0.666239	+	0.745738i	$0.267903\pi$
$709$			1057.46i			1.49148i	−0.666239	+	0.745738i	$0.732097\pi$
$710$	−112.000	−	296.324i	−0.157746	−	0.417358i
$711$		−	701.487i		−	0.986620i
$712$	791.543	+	418.845i	1.11172	+	0.588266i
$713$	−413.547			−0.580010
$714$	−35.7889	+	13.5269i	−0.0501245	+	0.0189453i
$715$	1018.77			1.42486
$716$	−884.382	+	779.951i	−1.23517	+	1.08932i
$717$			192.090i			0.267907i
$718$	−683.065	+	258.174i	−0.951344	+	0.359574i
$719$			1034.82i			1.43926i	0.694360	+	0.719628i	$0.255688\pi$
$719$			1034.82i			1.43926i	−0.694360	+	0.719628i	$0.744312\pi$
$720$	1241.37	+	156.397i	1.72412	+	0.217219i
$721$	281.990			0.391109
$722$	−334.094	−	883.930i	−0.462734	−	1.22428i
$723$	42.1017			0.0582320
$724$	−107.075	−	121.412i	−0.147894	−	0.167696i
$725$			1270.62i			1.75258i
$726$	−14.4487	−	38.2277i	−0.0199018	−	0.0526552i
$727$			495.145i			0.681080i	0.940230	+	0.340540i	$0.110610\pi$
$727$			495.145i			0.681080i	−0.940230	+	0.340540i	$0.889390\pi$
$728$	168.995	+	89.4237i	0.232136	+	0.122835i
$729$	−567.489			−0.778449
$730$	−788.975	+	298.204i	−1.08079	+	0.408499i
$731$	−281.775			−0.385465
$732$	−23.6081	−	26.7690i	−0.0322515	−	0.0365697i
$733$			567.494i			0.774207i	0.922036	+	0.387103i	$0.126524\pi$
$733$			567.494i			0.774207i	−0.922036	+	0.387103i	$0.873476\pi$
$734$	972.965	−	367.746i	1.32556	−	0.501016i
$735$			37.0405i			0.0503953i
$736$	−184.402	−	766.672i	−0.250546	−	1.04167i
$737$	−981.685			−1.33200
$738$	42.6690	+	112.892i	0.0578171	+	0.152970i
$739$	−544.701			−0.737078			−0.368539	−	0.929612i	$-0.620142\pi$
$739$	−544.701			−0.737078			−0.368539	+	0.929612i	$0.620142\pi$
$740$	440.382	−	388.380i	0.595111	−	0.524838i
$741$			152.766i			0.206162i
$742$	14.9949	+	39.6729i	0.0202088	+	0.0534675i
$743$			731.264i			0.984205i	0.870537	+	0.492102i	$0.163771\pi$
$743$			731.264i			0.984205i	−0.870537	+	0.492102i	$0.836229\pi$
$744$	−36.7838	+	69.5149i	−0.0494406	+	0.0934340i
$745$	−2277.95			−3.05765
$746$	−985.387	+	372.441i	−1.32089	+	0.499251i
$747$	−349.605			−0.468012
$748$	−462.323	+	407.731i	−0.618079	+	0.545094i
$749$			168.264i			0.224652i
$750$	312.804	−	118.229i	0.417072	−	0.157638i
$751$			666.262i			0.887166i	0.896233	+	0.443583i	$0.146293\pi$
$751$			666.262i			0.887166i	−0.896233	+	0.443583i	$0.853707\pi$
$752$	98.4121	+	12.3988i	0.130867	+	0.0164877i
$753$	−150.500			−0.199867
$754$	−143.397	−	379.393i	−0.190182	−	0.503173i
$755$	2118.15			2.80550
$756$	−72.4020	−	82.0962i	−0.0957699	−	0.108593i
$757$		−	238.623i		−	0.315222i	−0.987501	−	0.157611i	$-0.949621\pi$
$757$		−	238.623i		−	0.315222i	0.987501	−	0.157611i	$-0.0503791\pi$
$758$	−86.2498	−	228.195i	−0.113786	−	0.301049i
$759$			180.223i			0.237447i
$760$	975.779	−	1844.05i	1.28392	−	2.42638i
$761$	614.930			0.808055			0.404028	−	0.914747i	$-0.367610\pi$
$761$	614.930			0.808055			0.404028	+	0.914747i	$0.367610\pi$
$762$	125.417	−	47.4032i	0.164589	−	0.0622090i
$763$	346.191			0.453723
$764$	415.196	+	470.788i	0.543450	+	0.616215i
$765$			965.219i			1.26172i
$766$	−591.980	+	223.747i	−0.772820	+	0.292098i
$767$			275.002i			0.358543i
$768$	−145.275	−	37.1963i	−0.189160	−	0.0484327i
$769$	178.950			0.232705			0.116353	−	0.993208i	$-0.462880\pi$
$769$	178.950			0.232705			0.116353	+	0.993208i	$0.462880\pi$
$770$	210.995	+	558.240i	0.274019	+	0.724987i
$771$	187.072			0.242636
$772$	783.911	−	691.344i	1.01543	−	0.895524i
$773$		−	631.615i		−	0.817095i	−0.912737	−	0.408548i	$-0.866035\pi$
$773$		−	631.615i		−	0.817095i	0.912737	−	0.408548i	$-0.133965\pi$
$774$	−139.740	−	369.718i	−0.180543	−	0.477671i
$775$		−	949.849i		−	1.22561i
$776$	−1160.42	−	614.035i	−1.49538	−	0.791282i
$777$	−25.1859			−0.0324142
$778$	172.392	−	65.1580i	0.221583	−	0.0837507i
$779$	201.241			0.258332
$780$	−143.397	+	126.464i	−0.183842	+	0.162134i
$781$			218.923i			0.280311i
$782$	569.025	−	215.071i	0.727654	−	0.275027i
$783$			232.203i			0.296556i
$784$	−14.0000	+	111.122i	−0.0178571	+	0.141737i
$785$	91.2061			0.116186
$786$	69.7330	+	184.496i	0.0887188	+	0.234728i
$787$	456.655			0.580247			0.290124	−	0.956989i	$-0.406304\pi$
$787$	456.655			0.580247			0.290124	+	0.956989i	$0.406304\pi$
$788$	384.382	+	435.848i	0.487794	+	0.553107i
$789$			221.050i			0.280165i
$790$	−517.588	−	1369.41i	−0.655175	−	1.73343i
$791$			365.710i			0.462339i
$792$	−764.264	−	404.411i	−0.964980	−	0.510619i
$793$	−137.598			−0.173516
$794$	1051.90	−	397.583i	1.32482	−	0.500734i
$795$	−42.4121			−0.0533486
$796$	1033.19	+	1171.52i	1.29797	+	1.47176i
$797$			218.566i			0.274236i	0.990555	+	0.137118i	$0.0437839\pi$
$797$			218.566i			0.274236i	−0.990555	+	0.137118i	$0.956216\pi$
$798$	−83.7086	+	31.6389i	−0.104898	+	0.0396477i
$799$			76.5199i			0.0957695i
$800$	1760.92	−	423.540i	2.20114	−	0.529426i
$801$	−969.058			−1.20981
$802$	−57.4214	−	151.923i	−0.0715977	−	0.189430i
$803$	582.891			0.725892
$804$	138.177	−	121.860i	0.171861	−	0.151568i
$805$		−	588.926i		−	0.731585i
$806$	107.196	+	283.614i	0.132997	+	0.351878i
$807$		−	16.4976i		−	0.0204431i
$808$	45.3970	−	85.7922i	0.0561844	−	0.106178i
$809$	1347.46			1.66559			0.832794	−	0.553584i	$-0.186740\pi$
$809$	1347.46			1.66559			0.832794	+	0.553584i	$0.186740\pi$
$810$	−1214.28	+	458.953i	−1.49911	+	0.566609i
$811$	−672.620			−0.829371			−0.414686	−	0.909965i	$-0.636108\pi$
$811$	−672.620			−0.829371			−0.414686	+	0.909965i	$0.636108\pi$
$812$	178.191	−	157.150i	0.219447	−	0.193534i
$813$		−	234.148i		−	0.288005i
$814$	−379.578	+	143.467i	−0.466312	+	0.176249i
$815$		−	944.273i		−	1.15862i
$816$	14.4609	−	114.780i	0.0177217	−	0.140662i
$817$	−659.058			−0.806681
$818$	−318.718	−	843.248i	−0.389631	−	1.03087i
$819$	−206.894			−0.252618
$820$	166.593	+	188.899i	0.203162	+	0.230364i
$821$		−	1162.57i		−	1.41604i	−0.706190	−	0.708022i	$-0.749588\pi$
$821$		−	1162.57i		−	1.41604i	0.706190	−	0.708022i	$-0.250412\pi$
$822$	−14.3675	−	38.0129i	−0.0174787	−	0.0462444i
$823$		−	1041.65i		−	1.26567i	−0.774286	−	0.632835i	$-0.781891\pi$
$823$		−	1041.65i		−	1.26567i	0.774286	−	0.632835i	$-0.218109\pi$
$824$	−398.794	+	753.650i	−0.483973	+	0.914623i
$825$	−413.941			−0.501747
$826$	−150.688	+	56.9549i	−0.182431	+	0.0689526i
$827$	278.432			0.336678			0.168339	−	0.985729i	$-0.446160\pi$
$827$	278.432			0.336678			0.168339	+	0.985729i	$0.446160\pi$
$828$	564.392	+	639.960i	0.681633	+	0.772899i
$829$		−	1065.74i		−	1.28557i	−0.766046	−	0.642785i	$-0.777779\pi$
$829$		−	1065.74i		−	1.28557i	0.766046	−	0.642785i	$-0.222221\pi$
$830$	−682.482	+	257.954i	−0.822268	+	0.310788i
$831$			60.3071i			0.0725717i
$832$	−477.990	+	325.194i	−0.574507	+	0.390858i
$833$	−86.4020			−0.103724
$834$	−44.5959	−	117.990i	−0.0534723	−	0.141474i
$835$	−2680.72			−3.21045
$836$	−1081.35	+	953.663i	−1.29348	+	1.14075i
$837$		−	173.583i		−	0.207387i
$838$	−441.933	−	1169.25i	−0.527366	−	1.39528i
$839$			305.844i			0.364533i	0.983249	+	0.182267i	$0.0583434\pi$
$839$			305.844i			0.364533i	−0.983249	+	0.182267i	$0.941657\pi$
$840$	−98.9949	−	52.3832i	−0.117851	−	0.0623610i
$841$	337.000			0.400713
$842$	1059.78	−	400.559i	1.25864	−	0.475723i
$843$	−88.0059			−0.104396
$844$	492.146	−	434.032i	0.583112	−	0.514256i
$845$		−	789.516i		−	0.934339i
$846$	−100.402	+	37.9484i	−0.118679	+	0.0448563i
$847$		−	92.2898i		−	0.108961i
$848$	−127.236	−	16.0303i	−0.150043	−	0.0189036i
$849$	−104.599			−0.123202
$850$	493.983	+	1306.96i	0.581156	+	1.53759i
$851$	400.442			0.470555
$852$	−27.1758	−	30.8144i	−0.0318964	−	0.0361672i
$853$		−	164.018i		−	0.192283i	−0.995368	−	0.0961417i	$-0.969350\pi$
$853$		−	164.018i		−	0.192283i	0.995368	−	0.0961417i	$-0.0306502\pi$
$854$	−28.4975	−	75.3972i	−0.0333694	−	0.0882872i
$855$			2257.60i			2.64047i
$856$	−449.706	−	237.962i	−0.525357	−	0.277993i
$857$	851.068			0.993078			0.496539	−	0.868014i	$-0.334604\pi$
$857$	851.068			0.993078			0.496539	+	0.868014i	$0.334604\pi$
$858$	123.598	−	46.7156i	0.144054	−	0.0544471i
$859$	−1179.69			−1.37333			−0.686666	−	0.726973i	$-0.740927\pi$
$859$	−1179.69			−1.37333			−0.686666	+	0.726973i	$0.740927\pi$
$860$	−545.588	−	618.639i	−0.634405	−	0.719347i
$861$		−	10.8033i		−	0.0125474i
$862$	541.658	−	204.728i	0.628374	−	0.237503i
$863$			279.048i			0.323346i	0.986844	+	0.161673i	$0.0516890\pi$
$863$			279.048i			0.323346i	−0.986844	+	0.161673i	$0.948311\pi$
$864$	321.803	−	77.4010i	0.372457	−	0.0895845i
$865$	361.598			0.418032
$866$	422.635	+	1118.19i	0.488031	+	1.29121i
$867$	−80.0458			−0.0923250
$868$	−133.206	+	117.477i	−0.153463	+	0.135342i
$869$			1011.71i			1.16423i
$870$	84.0000	+	222.243i	0.0965517	+	0.255452i
$871$		−	710.254i		−	0.815447i
$872$	−489.588	+	925.234i	−0.561454	+	1.06105i
$873$	1420.66			1.62733
$874$	1330.92	−	503.042i	1.52280	−	0.575563i
$875$	755.176			0.863058
$876$	−82.0446	+	72.3565i	−0.0936582	+	0.0825988i
$877$		−	674.159i		−	0.768711i	−0.923185	−	0.384355i	$-0.874424\pi$
$877$		−	674.159i		−	0.768711i	0.923185	−	0.384355i	$-0.125576\pi$
$878$	−71.8192	+	27.1451i	−0.0817986	+	0.0309170i
$879$			128.398i			0.146073i
$880$	−1790.35	−	225.563i	−2.03449	−	0.256322i
$881$	−1001.29			−1.13654			−0.568271	−	0.822841i	$-0.692387\pi$
$881$	−1001.29			−1.13654			−0.568271	+	0.822841i	$0.692387\pi$
$882$	−42.8492	−	113.368i	−0.0485819	−	0.128536i
$883$	882.010			0.998879			0.499439	−	0.866349i	$-0.333539\pi$
$883$	882.010			0.998879			0.499439	+	0.866349i	$0.333539\pi$
$884$	−294.995	−	334.493i	−0.333705	−	0.378386i
$885$		−	161.093i		−	0.182026i
$886$	−423.598	−	1120.73i	−0.478102	−	1.26494i
$887$			7.08053i			0.00798256i	0.999992	+	0.00399128i	$0.00127047\pi$
$887$			7.08053i			0.00798256i	−0.999992	+	0.00399128i	$0.998730\pi$
$888$	35.6182	−	67.3120i	0.0401106	−	0.0758018i
$889$	302.784			0.340589
$890$	−1891.75	+	715.014i	−2.12556	+	0.803386i
$891$	897.103			1.00685
$892$	28.0000	+	31.7490i	0.0313901	+	0.0355931i
$893$			178.976i			0.200422i
$894$	−276.362	+	104.455i	−0.309129	+	0.116840i
$895$		−	2662.92i		−	2.97533i
$896$	−277.186	−	194.566i	−0.309359	−	0.217150i
$897$	−130.392			−0.145364
$898$	325.296	+	860.654i	0.362246	+	0.958412i
$899$	376.764			0.419092
$900$	−1469.88	+	1296.31i	−1.63320	+	1.44035i
$901$		−	98.9320i		−	0.109802i
$902$	−61.5391	−	162.817i	−0.0682252	−	0.180507i
$903$			35.3805i			0.0391811i
$904$	−977.401	−	517.192i	−1.08120	−	0.572115i
$905$	365.578			0.403953
$906$	256.975	−	97.1273i	0.283637	−	0.107205i
$907$	450.372			0.496551			0.248275	−	0.968689i	$-0.420136\pi$
$907$	450.372			0.496551			0.248275	+	0.968689i	$0.420136\pi$
$908$	641.418	−	565.678i	0.706408	−	0.622993i
$909$			105.032i			0.115547i
$910$	−403.889	+	152.656i	−0.443834	+	0.167754i
$911$			202.426i			0.222201i	0.993809	+	0.111101i	$0.0354376\pi$
$911$			202.426i			0.222201i	−0.993809	+	0.111101i	$0.964562\pi$
$912$	33.8234	−	268.465i	0.0370870	−	0.294369i
$913$	504.215			0.552262
$914$	−188.319	−	498.245i	−0.206038	−	0.545125i
$915$	80.6030			0.0880907
$916$	613.889	+	696.085i	0.670185	+	0.759918i
$917$			445.413i			0.485728i
$918$	90.2742	+	238.843i	0.0983379	+	0.260178i
$919$			1593.73i			1.73420i	0.498138	+	0.867098i	$0.334017\pi$
$919$			1593.73i			1.73420i	−0.498138	+	0.867098i	$0.665983\pi$
$920$	1573.97	+	832.866i	1.71084	+	0.905290i
$921$	185.500			0.201412
$922$	−1427.67	+	539.610i	−1.54845	+	0.585260i
$923$	−158.392			−0.171606
$924$	51.1960	+	58.0508i	0.0554069	+	0.0628255i
$925$			919.749i			0.994323i
$926$	231.960	−	87.6725i	0.250496	−	0.0946787i
$927$		−	922.666i		−	0.995325i
$928$	168.000	+	698.478i	0.181034	+	0.752671i
$929$	−1039.40			−1.11884			−0.559419	−	0.828885i	$-0.688976\pi$
$929$	−1039.40			−1.11884			−0.559419	+	0.828885i	$0.688976\pi$
$930$	−62.7939	−	166.137i	−0.0675204	−	0.178642i
$931$	−202.090			−0.217068
$932$	578.589	−	510.267i	0.620803	−	0.547497i
$933$		−	42.3320i		−	0.0453719i
$934$	543.566	+	1438.14i	0.581976	+	1.53976i
$935$		−	1392.08i		−	1.48885i
$936$	292.593	−	552.949i	0.312599	−	0.590757i
$937$	881.765			0.941051			0.470525	−	0.882386i	$-0.344064\pi$
$937$	881.765			0.941051			0.470525	+	0.882386i	$0.344064\pi$
$938$	389.186	−	147.098i	0.414910	−	0.156821i
$939$	48.0059			0.0511245
$940$	−168.000	+	148.162i	−0.178723	+	0.157619i
$941$			953.344i			1.01312i	0.862205	+	0.506559i	$0.169083\pi$
$941$			953.344i			1.01312i	−0.862205	+	0.506559i	$0.830917\pi$
$942$	11.0652	−	4.18223i	0.0117464	−	0.00443974i
$943$			171.767i			0.182149i
$944$	60.8873	−	483.278i	0.0644993	−	0.511947i
$945$	247.196			0.261583
$946$	201.539	+	533.222i	0.213043	+	0.563660i
$947$	16.8957			0.0178413			0.00892063	−	0.999960i	$-0.497160\pi$
$947$	16.8957			0.0178413			0.00892063	+	0.999960i	$0.497160\pi$
$948$	−125.588	−	142.403i	−0.132477	−	0.150214i
$949$			421.725i			0.444389i
$950$	1155.40	+	3056.91i	1.21621	+	3.21780i
$951$			63.9386i			0.0672330i
$952$	122.191	−	230.919i	0.128352	−	0.242562i
$953$	1526.31			1.60159			0.800794	−	0.598940i	$-0.204411\pi$
$953$	1526.31			1.60159			0.800794	+	0.598940i	$0.204411\pi$
$954$	129.809	−	49.0632i	0.136068	−	0.0514290i
$955$	−1417.57			−1.48436
$956$	−867.588	−	983.752i	−0.907519	−	1.02903i
$957$		−	164.192i		−	0.171570i
$958$	−222.593	+	84.1322i	−0.232352	+	0.0878207i
$959$		−	91.7713i		−	0.0956948i
$960$	280.000	−	190.494i	0.291667	−	0.198431i
$961$	679.352			0.706921
$962$	−103.799	−	274.626i	−0.107899	−	0.285474i
$963$	550.558			0.571712
$964$	−215.616	+	190.156i	−0.223669	+	0.197257i
$965$			2360.40i			2.44601i
$966$	−27.0051	−	71.4486i	−0.0279555	−	0.0739634i
$967$		−	1410.39i		−	1.45852i	−0.684235	−	0.729262i	$-0.739864\pi$
$967$		−	1410.39i		−	1.45852i	0.684235	−	0.729262i	$-0.260136\pi$
$968$	246.655	+	130.517i	0.254809	+	0.134832i
$969$	208.743			0.215421
$970$	2773.34	−	1048.22i	2.85911	−	1.08064i
$971$	−596.497			−0.614312			−0.307156	−	0.951659i	$-0.599377\pi$
$971$	−596.497			−0.614312			−0.307156	+	0.951659i	$0.599377\pi$
$972$	−405.536	+	357.649i	−0.417218	+	0.367952i
$973$		−	284.852i		−	0.292757i
$974$	−528.653	+	199.812i	−0.542765	+	0.205146i
$975$		−	299.488i		−	0.307168i
$976$	241.809	+	30.4651i	0.247755	+	0.0312142i
$977$	146.686			0.150140			0.0750698	−	0.997178i	$-0.476082\pi$
$977$	146.686			0.150140			0.0750698	+	0.997178i	$0.476082\pi$
$978$	−43.2994	−	114.560i	−0.0442734	−	0.117137i
$979$	1397.62			1.42760
$980$	−167.296	−	189.696i	−0.170711	−	0.193568i
$981$		−	1132.73i		−	1.15467i
$982$	274.392	+	725.973i	0.279422	+	0.739280i
$983$		−	169.457i		−	0.172388i	−0.996278	−	0.0861939i	$-0.972530\pi$
$983$		−	169.457i		−	0.172388i	0.996278	−	0.0861939i	$-0.0274704\pi$
$984$	28.8730	+	15.2782i	0.0293425	+	0.0155266i
$985$	−1312.36			−1.33235
$986$	−518.412	+	195.941i	−0.525773	+	0.198723i
$987$	9.60808			0.00973463
$988$	−689.980	−	782.364i	−0.698360	−	0.791866i
$989$		−	562.533i		−	0.568789i
$990$	1826.55	−	690.372i	1.84500	−	0.697345i
$991$			1686.90i			1.70222i	0.524988	+	0.851109i	$0.324070\pi$
$991$			1686.90i			1.70222i	−0.524988	+	0.851109i	$0.675930\pi$
$992$	−125.588	−	522.145i	−0.126601	−	0.526356i
$993$	188.471			0.189800
$994$	−32.8040	−	86.7913i	−0.0330021	−	0.0873152i
$995$	−3527.52			−3.54524
$996$	−70.9706	+	62.5902i	−0.0712556	+	0.0628415i
$997$		−	1736.14i		−	1.74136i	−0.491849	−	0.870680i	$-0.663679\pi$
$997$		−	1736.14i		−	1.74136i	0.491849	−	0.870680i	$-0.336321\pi$
$998$	19.5980	+	51.8514i	0.0196373	+	0.0519553i
$999$			168.082i			0.168250i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.3.g.a.43.1	✓	4
3.2	odd	2		504.3.g.a.379.4		4
4.3	odd	2		224.3.g.a.15.3		4
7.2	even	3		392.3.k.i.67.2		8
7.3	odd	6		392.3.k.j.275.4		8
7.4	even	3		392.3.k.i.275.4		8
7.5	odd	6		392.3.k.j.67.2		8
7.6	odd	2		392.3.g.h.99.1		4
8.3	odd	2	inner	56.3.g.a.43.2	yes	4
8.5	even	2		224.3.g.a.15.4		4
12.11	even	2		2016.3.g.a.1135.4		4
16.3	odd	4		1792.3.d.g.1023.3		8
16.5	even	4		1792.3.d.g.1023.4		8
16.11	odd	4		1792.3.d.g.1023.6		8
16.13	even	4		1792.3.d.g.1023.5		8
24.5	odd	2		2016.3.g.a.1135.1		4
24.11	even	2		504.3.g.a.379.3		4
28.27	even	2		1568.3.g.h.687.2		4
56.3	even	6		392.3.k.j.275.2		8
56.11	odd	6		392.3.k.i.275.2		8
56.13	odd	2		1568.3.g.h.687.1		4
56.19	even	6		392.3.k.j.67.4		8
56.27	even	2		392.3.g.h.99.2		4
56.51	odd	6		392.3.k.i.67.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.a.43.1	✓	4	1.1	even	1	trivial
56.3.g.a.43.2	yes	4	8.3	odd	2	inner
224.3.g.a.15.3		4	4.3	odd	2
224.3.g.a.15.4		4	8.5	even	2
392.3.g.h.99.1		4	7.6	odd	2
392.3.g.h.99.2		4	56.27	even	2
392.3.k.i.67.2		8	7.2	even	3
392.3.k.i.67.4		8	56.51	odd	6
392.3.k.i.275.2		8	56.11	odd	6
392.3.k.i.275.4		8	7.4	even	3
392.3.k.j.67.2		8	7.5	odd	6
392.3.k.j.67.4		8	56.19	even	6
392.3.k.j.275.2		8	56.3	even	6
392.3.k.j.275.4		8	7.3	odd	6
504.3.g.a.379.3		4	24.11	even	2
504.3.g.a.379.4		4	3.2	odd	2
1568.3.g.h.687.1		4	56.13	odd	2
1568.3.g.h.687.2		4	28.27	even	2
1792.3.d.g.1023.3		8	16.3	odd	4
1792.3.d.g.1023.4		8	16.5	even	4
1792.3.d.g.1023.5		8	16.13	even	4
1792.3.d.g.1023.6		8	16.11	odd	4
2016.3.g.a.1135.1		4	24.5	odd	2
2016.3.g.a.1135.4		4	12.11	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:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	56.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.87083i) q^{2} +0.585786 q^{3} +(-3.00000 + 2.64575i) q^{4} -9.03316i q^{5} +(-0.414214 - 1.09591i) q^{6} -2.64575i q^{7} +(7.07107 + 3.74166i) q^{8} -8.65685 q^{9} +O(q^{10})\)	\(q+(-0.707107 - 1.87083i) q^{2} +0.585786 q^{3} +(-3.00000 + 2.64575i) q^{4} -9.03316i q^{5} +(-0.414214 - 1.09591i) q^{6} -2.64575i q^{7} +(7.07107 + 3.74166i) q^{8} -8.65685 q^{9} +(-16.8995 + 6.38741i) q^{10} +12.4853 q^{11} +(-1.75736 + 1.54985i) q^{12} +9.03316i q^{13} +(-4.94975 + 1.87083i) q^{14} -5.29150i q^{15} +(2.00000 - 15.8745i) q^{16} +12.3431 q^{17} +(6.12132 + 16.1955i) q^{18} +28.8701 q^{19} +(23.8995 + 27.0995i) q^{20} -1.54985i q^{21} +(-8.82843 - 23.3578i) q^{22} +24.6418i q^{23} +(4.14214 + 2.19181i) q^{24} -56.5980 q^{25} +(16.8995 - 6.38741i) q^{26} -10.3431 q^{27} +(7.00000 + 7.93725i) q^{28} -22.4499i q^{29} +(-9.89949 + 3.74166i) q^{30} +16.7824i q^{31} +(-31.1127 + 7.48331i) q^{32} +7.31371 q^{33} +(-8.72792 - 23.0919i) q^{34} -23.8995 q^{35} +(25.9706 - 22.9039i) q^{36} -16.2506i q^{37} +(-20.4142 - 54.0109i) q^{38} +5.29150i q^{39} +(33.7990 - 63.8741i) q^{40} +6.97056 q^{41} +(-2.89949 + 1.09591i) q^{42} -22.8284 q^{43} +(-37.4558 + 33.0329i) q^{44} +78.1987i q^{45} +(46.1005 - 17.4244i) q^{46} +6.19938i q^{47} +(1.17157 - 9.29907i) q^{48} -7.00000 q^{49} +(40.0208 + 105.885i) q^{50} +7.23045 q^{51} +(-23.8995 - 27.0995i) q^{52} -8.01514i q^{53} +(7.31371 + 19.3503i) q^{54} -112.782i q^{55} +(9.89949 - 18.7083i) q^{56} +16.9117 q^{57} +(-42.0000 + 15.8745i) q^{58} +30.4437 q^{59} +(14.0000 + 15.8745i) q^{60} +15.2325i q^{61} +(31.3970 - 11.8669i) q^{62} +22.9039i q^{63} +(36.0000 + 52.9150i) q^{64} +81.5980 q^{65} +(-5.17157 - 13.6827i) q^{66} -78.6274 q^{67} +(-37.0294 + 32.6569i) q^{68} +14.4348i q^{69} +(16.8995 + 44.7119i) q^{70} +17.5345i q^{71} +(-61.2132 - 32.3910i) q^{72} +46.6863 q^{73} +(-30.4020 + 11.4909i) q^{74} -33.1543 q^{75} +(-86.6102 + 76.3830i) q^{76} -33.0329i q^{77} +(9.89949 - 3.74166i) q^{78} +81.0325i q^{79} +(-143.397 - 18.0663i) q^{80} +71.8528 q^{81} +(-4.92893 - 13.0407i) q^{82} +40.3848 q^{83} +(4.10051 + 4.64954i) q^{84} -111.498i q^{85} +(16.1421 + 42.7081i) q^{86} -13.1509i q^{87} +(88.2843 + 46.7156i) q^{88} +111.941 q^{89} +(146.296 - 55.2949i) q^{90} +23.8995 q^{91} +(-65.1960 - 73.9253i) q^{92} +9.83089i q^{93} +(11.5980 - 4.38362i) q^{94} -260.788i q^{95} +(-18.2254 + 4.38362i) q^{96} -164.108 q^{97} +(4.94975 + 13.0958i) q^{98} -108.083 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{9}+O(q^{10}) \) 4 * q + 8 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^9	\( 4 q + 8 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{9} - 28 q^{10} + 16 q^{11} - 24 q^{12} + 8 q^{16} + 72 q^{17} + 16 q^{18} + 8 q^{19} + 56 q^{20} - 24 q^{22} - 40 q^{24} - 68 q^{25} + 28 q^{26} - 64 q^{27} + 28 q^{28} - 16 q^{33} + 16 q^{34} - 56 q^{35} + 36 q^{36} - 76 q^{38} + 56 q^{40} - 40 q^{41} + 28 q^{42} - 80 q^{43} - 48 q^{44} + 224 q^{46} + 16 q^{48} - 28 q^{49} + 112 q^{50} + 176 q^{51} - 56 q^{52} - 16 q^{54} - 136 q^{57} - 168 q^{58} + 184 q^{59} + 56 q^{60} - 112 q^{62} + 144 q^{64} + 168 q^{65} - 32 q^{66} - 224 q^{67} - 216 q^{68} + 28 q^{70} - 160 q^{72} + 232 q^{73} - 280 q^{74} + 88 q^{75} - 24 q^{76} - 336 q^{80} - 52 q^{81} - 48 q^{82} + 88 q^{83} + 56 q^{84} + 8 q^{86} + 240 q^{88} + 312 q^{89} + 308 q^{90} + 56 q^{91} + 56 q^{92} - 112 q^{94} + 176 q^{96} - 136 q^{97} - 240 q^{99}+O(q^{100}) \) 4 * q + 8 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^9 - 28 * q^10 + 16 * q^11 - 24 * q^12 + 8 * q^16 + 72 * q^17 + 16 * q^18 + 8 * q^19 + 56 * q^20 - 24 * q^22 - 40 * q^24 - 68 * q^25 + 28 * q^26 - 64 * q^27 + 28 * q^28 - 16 * q^33 + 16 * q^34 - 56 * q^35 + 36 * q^36 - 76 * q^38 + 56 * q^40 - 40 * q^41 + 28 * q^42 - 80 * q^43 - 48 * q^44 + 224 * q^46 + 16 * q^48 - 28 * q^49 + 112 * q^50 + 176 * q^51 - 56 * q^52 - 16 * q^54 - 136 * q^57 - 168 * q^58 + 184 * q^59 + 56 * q^60 - 112 * q^62 + 144 * q^64 + 168 * q^65 - 32 * q^66 - 224 * q^67 - 216 * q^68 + 28 * q^70 - 160 * q^72 + 232 * q^73 - 280 * q^74 + 88 * q^75 - 24 * q^76 - 336 * q^80 - 52 * q^81 - 48 * q^82 + 88 * q^83 + 56 * q^84 + 8 * q^86 + 240 * q^88 + 312 * q^89 + 308 * q^90 + 56 * q^91 + 56 * q^92 - 112 * q^94 + 176 * q^96 - 136 * q^97 - 240 * q^99

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