LMFDB - Embedded newform 504.3.g.a.379.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,3,Mod(379,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("504.379");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.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:	$13.7330053238$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.3
Root			$-0.707107 + 1.87083i$ of defining polynomial
Character	$\chi$	$=$	504.379
Dual form			504.3.g.a.379.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 1.87083i) q^{2} +(-3.00000 - 2.64575i) q^{4} -9.03316i q^{5} +2.64575i q^{7} +(-7.07107 + 3.74166i) q^{8} +O(q^{10})$	\(q+(0.707107 - 1.87083i) q^{2} +(-3.00000 - 2.64575i) q^{4} -9.03316i q^{5} +2.64575i q^{7} +(-7.07107 + 3.74166i) q^{8} +(-16.8995 - 6.38741i) q^{10} -12.4853 q^{11} -9.03316i q^{13} +(4.94975 + 1.87083i) q^{14} +(2.00000 + 15.8745i) q^{16} -12.3431 q^{17} +28.8701 q^{19} +(-23.8995 + 27.0995i) q^{20} +(-8.82843 + 23.3578i) q^{22} +24.6418i q^{23} -56.5980 q^{25} +(-16.8995 - 6.38741i) q^{26} +(7.00000 - 7.93725i) q^{28} -22.4499i q^{29} -16.7824i q^{31} +(31.1127 + 7.48331i) q^{32} +(-8.72792 + 23.0919i) q^{34} +23.8995 q^{35} +16.2506i q^{37} +(20.4142 - 54.0109i) q^{38} +(33.7990 + 63.8741i) q^{40} -6.97056 q^{41} -22.8284 q^{43} +(37.4558 + 33.0329i) q^{44} +(46.1005 + 17.4244i) q^{46} +6.19938i q^{47} -7.00000 q^{49} +(-40.0208 + 105.885i) q^{50} +(-23.8995 + 27.0995i) q^{52} -8.01514i q^{53} +112.782i q^{55} +(-9.89949 - 18.7083i) q^{56} +(-42.0000 - 15.8745i) q^{58} -30.4437 q^{59} -15.2325i q^{61} +(-31.3970 - 11.8669i) q^{62} +(36.0000 - 52.9150i) q^{64} -81.5980 q^{65} -78.6274 q^{67} +(37.0294 + 32.6569i) q^{68} +(16.8995 - 44.7119i) q^{70} +17.5345i q^{71} +46.6863 q^{73} +(30.4020 + 11.4909i) q^{74} +(-86.6102 - 76.3830i) q^{76} -33.0329i q^{77} -81.0325i q^{79} +(143.397 - 18.0663i) q^{80} +(-4.92893 + 13.0407i) q^{82} -40.3848 q^{83} +111.498i q^{85} +(-16.1421 + 42.7081i) q^{86} +(88.2843 - 46.7156i) q^{88} -111.941 q^{89} +23.8995 q^{91} +(65.1960 - 73.9253i) q^{92} +(11.5980 + 4.38362i) q^{94} -260.788i q^{95} -164.108 q^{97} +(-4.94975 + 13.0958i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 12 q^{4}+O(q^{10}) $ 4 * q - 12 * q^4	$ 4 q - 12 q^{4} - 28 q^{10} - 16 q^{11} + 8 q^{16} - 72 q^{17} + 8 q^{19} - 56 q^{20} - 24 q^{22} - 68 q^{25} - 28 q^{26} + 28 q^{28} + 16 q^{34} + 56 q^{35} + 76 q^{38} + 56 q^{40} + 40 q^{41} - 80 q^{43} + 48 q^{44} + 224 q^{46} - 28 q^{49} - 112 q^{50} - 56 q^{52} - 168 q^{58} - 184 q^{59} + 112 q^{62} + 144 q^{64} - 168 q^{65} - 224 q^{67} + 216 q^{68} + 28 q^{70} + 232 q^{73} + 280 q^{74} - 24 q^{76} + 336 q^{80} - 48 q^{82} - 88 q^{83} - 8 q^{86} + 240 q^{88} - 312 q^{89} + 56 q^{91} - 56 q^{92} - 112 q^{94} - 136 q^{97}+O(q^{100}) $ 4 * q - 12 * q^4 - 28 * q^10 - 16 * q^11 + 8 * q^16 - 72 * q^17 + 8 * q^19 - 56 * q^20 - 24 * q^22 - 68 * q^25 - 28 * q^26 + 28 * q^28 + 16 * q^34 + 56 * q^35 + 76 * q^38 + 56 * q^40 + 40 * q^41 - 80 * q^43 + 48 * q^44 + 224 * q^46 - 28 * q^49 - 112 * q^50 - 56 * q^52 - 168 * q^58 - 184 * q^59 + 112 * q^62 + 144 * q^64 - 168 * q^65 - 224 * q^67 + 216 * q^68 + 28 * q^70 + 232 * q^73 + 280 * q^74 - 24 * q^76 + 336 * q^80 - 48 * q^82 - 88 * q^83 - 8 * q^86 + 240 * q^88 - 312 * q^89 + 56 * q^91 - 56 * q^92 - 112 * q^94 - 136 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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			0
$3$		0			0
$4$	−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			0
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	−7.07107	+	3.74166i	−0.883883	+	0.467707i
$9$		0			0
$10$	−16.8995	−	6.38741i	−1.68995	−	0.638741i
$11$	−12.4853			−1.13503			−0.567513	−	0.823365i	$-0.692094\pi$
$11$	−12.4853			−1.13503			−0.567513	+	0.823365i	$0.692094\pi$
$12$		0			0
$13$		−	9.03316i		−	0.694858i	−0.937706	−	0.347429i	$-0.887055\pi$
$13$		−	9.03316i		−	0.694858i	0.937706	−	0.347429i	$-0.112945\pi$
$14$	4.94975	+	1.87083i	0.353553	+	0.133631i
$15$		0			0
$16$	2.00000	+	15.8745i	0.125000	+	0.992157i
$17$	−12.3431			−0.726067			−0.363034	−	0.931776i	$-0.618259\pi$
$17$	−12.3431			−0.726067			−0.363034	+	0.931776i	$0.618259\pi$
$18$		0			0
$19$	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
$21$		0			0
$22$	−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	$0.820051\pi$
$24$		0			0
$25$	−56.5980			−2.26392
$26$	−16.8995	−	6.38741i	−0.649981	−	0.245670i
$27$		0			0
$28$	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	$-0.126512\pi$
$30$		0			0
$31$		−	16.7824i		−	0.541367i	−0.962668	−	0.270684i	$-0.912750\pi$
$31$		−	16.7824i		−	0.541367i	0.962668	−	0.270684i	$-0.0872497\pi$
$32$	31.1127	+	7.48331i	0.972272	+	0.233854i
$33$		0			0
$34$	−8.72792	+	23.0919i	−0.256704	+	0.679174i
$35$	23.8995			0.682843
$36$		0			0
$37$			16.2506i			0.439204i	0.975589	+	0.219602i	$0.0704759\pi$
$37$			16.2506i			0.439204i	−0.975589	+	0.219602i	$0.929524\pi$
$38$	20.4142	−	54.0109i	0.537216	−	1.42134i
$39$		0			0
$40$	33.7990	+	63.8741i	0.844975	+	1.59685i
$41$	−6.97056			−0.170014			−0.0850069	−	0.996380i	$-0.527091\pi$
$41$	−6.97056			−0.170014			−0.0850069	+	0.996380i	$0.527091\pi$
$42$		0			0
$43$	−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
$45$		0			0
$46$	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	$0.978992\pi$
$48$		0			0
$49$	−7.00000			−0.142857
$50$	−40.0208	+	105.885i	−0.800416	+	2.11770i
$51$		0			0
$52$	−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	$-0.0240918\pi$
$54$		0			0
$55$			112.782i			2.05057i
$56$	−9.89949	−	18.7083i	−0.176777	−	0.334077i
$57$		0			0
$58$	−42.0000	−	15.8745i	−0.724138	−	0.273698i
$59$	−30.4437			−0.515994			−0.257997	−	0.966146i	$-0.583062\pi$
$59$	−30.4437			−0.515994			−0.257997	+	0.966146i	$0.583062\pi$
$60$		0			0
$61$		−	15.2325i		−	0.249714i	−0.992175	−	0.124857i	$-0.960153\pi$
$61$		−	15.2325i		−	0.249714i	0.992175	−	0.124857i	$-0.0398472\pi$
$62$	−31.3970	−	11.8669i	−0.506403	−	0.191402i
$63$		0			0
$64$	36.0000	−	52.9150i	0.562500	−	0.826797i
$65$	−81.5980			−1.25535
$66$		0			0
$67$	−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
$69$		0			0
$70$	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	$0.960594\pi$
$72$		0			0
$73$	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
$75$		0			0
$76$	−86.6102	−	76.3830i	−1.13961	−	1.00504i
$77$		−	33.0329i		−	0.428999i
$78$		0			0
$79$		−	81.0325i		−	1.02573i	−0.858470	−	0.512864i	$-0.828584\pi$
$79$		−	81.0325i		−	1.02573i	0.858470	−	0.512864i	$-0.171416\pi$
$80$	143.397	−	18.0663i	1.79246	−	0.225829i
$81$		0			0
$82$	−4.92893	+	13.0407i	−0.0601089	+	0.159033i
$83$	−40.3848			−0.486564			−0.243282	−	0.969956i	$-0.578224\pi$
$83$	−40.3848			−0.486564			−0.243282	+	0.969956i	$0.578224\pi$
$84$		0			0
$85$			111.498i			1.31174i
$86$	−16.1421	+	42.7081i	−0.187699	+	0.496606i
$87$		0			0
$88$	88.2843	−	46.7156i	1.00323	−	0.530860i
$89$	−111.941			−1.25777			−0.628883	−	0.777500i	$-0.716487\pi$
$89$	−111.941			−1.25777			−0.628883	+	0.777500i	$0.716487\pi$
$90$		0			0
$91$	23.8995			0.262632
$92$	65.1960	−	73.9253i	0.708652	−	0.803536i
$93$		0			0
$94$	11.5980	+	4.38362i	0.123383	+	0.0466343i
$95$		−	260.788i		−	2.74514i
$96$		0			0
$97$	−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
$99$		0			0
$100$	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	$-0.0191304\pi$
$102$		0			0
$103$		−	106.582i		−	1.03478i	−0.855750	−	0.517389i	$-0.826904\pi$
$103$		−	106.582i		−	1.03478i	0.855750	−	0.517389i	$-0.173096\pi$
$104$	33.7990	+	63.8741i	0.324990	+	0.614174i
$105$		0			0
$106$	−14.9949	−	5.66756i	−0.141462	−	0.0534675i
$107$	63.5980			0.594374			0.297187	−	0.954819i	$-0.403952\pi$
$107$	63.5980			0.594374			0.297187	+	0.954819i	$0.403952\pi$
$108$		0			0
$109$		−	130.848i		−	1.20044i	−0.799835	−	0.600220i	$-0.795080\pi$
$109$		−	130.848i		−	1.20044i	0.799835	−	0.600220i	$-0.204920\pi$
$110$	210.995	+	79.7486i	1.91814	+	0.724987i
$111$		0			0
$112$	−42.0000	+	5.29150i	−0.375000	+	0.0472456i
$113$	138.225			1.22323			0.611617	−	0.791154i	$-0.290519\pi$
$113$	138.225			1.22323			0.611617	+	0.791154i	$0.290519\pi$
$114$		0			0
$115$	222.593			1.93559
$116$	−59.3970	+	67.3498i	−0.512043	+	0.580602i
$117$		0			0
$118$	−21.5269	+	56.9549i	−0.182431	+	0.482668i
$119$		−	32.6569i		−	0.274428i
$120$		0			0
$121$	34.8823			0.288283
$122$	−28.4975	−	10.7710i	−0.233586	−	0.0882872i
$123$		0			0
$124$	−44.4020	+	50.3472i	−0.358081	+	0.406025i
$125$			285.430i			2.28344i
$126$		0			0
$127$		−	114.442i		−	0.901114i	−0.892748	−	0.450557i	$-0.851225\pi$
$127$		−	114.442i		−	0.901114i	0.892748	−	0.450557i	$-0.148775\pi$
$128$	−73.5391	−	104.766i	−0.574524	−	0.818488i
$129$		0			0
$130$	−57.6985	+	152.656i	−0.443834	+	1.17428i
$131$	168.350			1.28512			0.642558	−	0.766237i	$-0.277873\pi$
$131$	168.350			1.28512			0.642558	+	0.766237i	$0.277873\pi$
$132$		0			0
$133$			76.3830i			0.574308i
$134$	−55.5980	+	147.098i	−0.414910	+	1.09775i
$135$		0			0
$136$	87.2792	−	46.1838i	0.641759	−	0.339587i
$137$	−34.6863			−0.253185			−0.126592	−	0.991955i	$-0.540404\pi$
$137$	−34.6863			−0.253185			−0.126592	+	0.991955i	$0.540404\pi$
$138$		0			0
$139$	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
$141$		0			0
$142$	32.8040	+	12.3988i	0.231014	+	0.0873152i
$143$			112.782i			0.788682i
$144$		0			0
$145$	−202.794			−1.39858
$146$	33.0122	−	87.3421i	0.226111	−	0.598233i
$147$		0			0
$148$	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	$-0.321133\pi$
$150$		0			0
$151$		−	234.486i		−	1.55289i	−0.630186	−	0.776444i	$-0.717021\pi$
$151$		−	234.486i		−	1.55289i	0.630186	−	0.776444i	$-0.282979\pi$
$152$	−204.142	+	108.022i	−1.34304	+	0.710670i
$153$		0			0
$154$	−61.7990	−	23.3578i	−0.401292	−	0.151674i
$155$	−151.598			−0.978051
$156$		0			0
$157$		−	10.0968i		−	0.0643109i	−0.999483	−	0.0321554i	$-0.989763\pi$
$157$		−	10.0968i		−	0.0643109i	0.999483	−	0.0321554i	$-0.0102372\pi$
$158$	−151.598	−	57.2987i	−0.959481	−	0.362650i
$159$		0			0
$160$	67.5980	−	281.046i	0.422487	−	1.75654i
$161$	−65.1960			−0.404944
$162$		0			0
$163$	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
$165$		0			0
$166$	−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	$-0.348264\pi$
$168$		0			0
$169$	87.4020			0.517172
$170$	208.593	+	78.8407i	1.22702	+	0.463769i
$171$		0			0
$172$	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	$0.963091\pi$
$174$		0			0
$175$		−	149.744i		−	0.855681i
$176$	−24.9706	−	198.198i	−0.141878	−	1.12612i
$177$		0			0
$178$	−79.1543	+	209.423i	−0.444687	+	1.17653i
$179$	−294.794			−1.64689			−0.823447	−	0.567394i	$-0.807952\pi$
$179$	−294.794			−1.64689			−0.823447	+	0.567394i	$0.807952\pi$
$180$		0			0
$181$		−	40.4706i		−	0.223595i	−0.993731	−	0.111797i	$-0.964339\pi$
$181$		−	40.4706i		−	0.223595i	0.993731	−	0.111797i	$-0.0356608\pi$
$182$	16.8995	−	44.7119i	0.0928544	−	0.245670i
$183$		0			0
$184$	−92.2010	−	174.244i	−0.501092	−	0.946976i
$185$	146.794			0.793481
$186$		0			0
$187$	154.108			0.824105
$188$	16.4020	−	18.5981i	0.0872448	−	0.0989263i
$189$		0			0
$190$	−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	$-0.134754\pi$
$192$		0			0
$193$	−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
$195$		0			0
$196$	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	$-0.120210\pi$
$198$		0			0
$199$			390.508i			1.96235i	0.193122	+	0.981175i	$0.438139\pi$
$199$			390.508i			1.96235i	−0.193122	+	0.981175i	$0.561861\pi$
$200$	400.208	−	211.770i	2.00104	−	1.05885i
$201$		0			0
$202$	−22.6985	−	8.57922i	−0.112369	−	0.0424714i
$203$	59.3970			0.292596
$204$		0			0
$205$			62.9662i			0.307152i
$206$	−199.397	−	75.3650i	−0.967946	−	0.365849i
$207$		0			0
$208$	143.397	−	18.0663i	0.689409	−	0.0868573i
$209$	−360.451			−1.72464
$210$		0			0
$211$	−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
$213$		0			0
$214$	44.9706	−	118.981i	0.210143	−	0.555986i
$215$			206.213i			0.959129i
$216$		0			0
$217$	44.4020			0.204618
$218$	−244.794	−	92.5234i	−1.12291	−	0.424419i
$219$		0			0
$220$	298.392	−	338.345i	1.35633	−	1.53793i
$221$			111.498i			0.504514i
$222$		0			0
$223$			10.5830i			0.0474574i	0.999718	+	0.0237287i	$0.00755379\pi$
$223$			10.5830i			0.0474574i	−0.999718	+	0.0237287i	$0.992446\pi$
$224$	−19.7990	+	82.3165i	−0.0883883	+	0.367484i
$225$		0			0
$226$	97.7401	−	258.596i	0.432478	−	1.14423i
$227$	213.806			0.941877			0.470939	−	0.882166i	$-0.343915\pi$
$227$	213.806			0.941877			0.470939	+	0.882166i	$0.343915\pi$
$228$		0			0
$229$			232.028i			1.01322i	0.862174	+	0.506612i	$0.169102\pi$
$229$			232.028i			1.01322i	−0.862174	+	0.506612i	$0.830898\pi$
$230$	157.397	−	416.433i	0.684335	−	1.81058i
$231$		0			0
$232$	84.0000	+	158.745i	0.362069	+	0.684246i
$233$	192.863			0.827738			0.413869	−	0.910336i	$-0.364177\pi$
$233$	192.863			0.827738			0.413869	+	0.910336i	$0.364177\pi$
$234$		0			0
$235$	56.0000			0.238298
$236$	91.3310	+	80.5463i	0.386996	+	0.341298i
$237$		0			0
$238$	−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	$0.759356\pi$
$240$		0			0
$241$	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
$243$		0			0
$244$	−40.3015	+	45.6976i	−0.165170	+	0.187285i
$245$			63.2321i			0.258090i
$246$		0			0
$247$		−	260.788i		−	1.05582i
$248$	62.7939	+	118.669i	0.253201	+	0.478506i
$249$		0			0
$250$	533.990	+	201.829i	2.13596	+	0.807317i
$251$	256.919			1.02358			0.511790	−	0.859110i	$-0.328982\pi$
$251$	256.919			1.02358			0.511790	+	0.859110i	$0.328982\pi$
$252$		0			0
$253$		−	307.659i		−	1.21604i
$254$	−214.101	−	80.9224i	−0.842915	−	0.318592i
$255$		0			0
$256$	−248.000	+	63.4980i	−0.968750	+	0.248039i
$257$	−319.352			−1.24262			−0.621308	−	0.783566i	$-0.713398\pi$
$257$	−319.352			−1.24262			−0.621308	+	0.783566i	$0.713398\pi$
$258$		0			0
$259$	−42.9949			−0.166004
$260$	244.794	+	215.888i	0.941515	+	0.830338i
$261$		0			0
$262$	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	$0.745328\pi$
$264$		0			0
$265$	−72.4020			−0.273215
$266$	142.899	+	54.0109i	0.537216	+	0.203049i
$267$		0			0
$268$	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	$-0.0166704\pi$
$270$		0			0
$271$			399.715i			1.47496i	0.675367	+	0.737482i	$0.263985\pi$
$271$			399.715i			1.47496i	−0.675367	+	0.737482i	$0.736015\pi$
$272$	−24.6863	−	195.941i	−0.0907584	−	0.720373i
$273$		0			0
$274$	−24.5269	+	64.8921i	−0.0895143	+	0.236833i
$275$	706.642			2.56961
$276$		0			0
$277$		−	102.951i		−	0.371663i	−0.982582	−	0.185831i	$-0.940502\pi$
$277$		−	102.951i		−	0.371663i	0.982582	−	0.185831i	$-0.0594979\pi$
$278$	76.1299	−	201.421i	0.273849	−	0.724536i
$279$		0			0
$280$	−168.995	+	89.4237i	−0.603553	+	0.319370i
$281$	150.235			0.534646			0.267323	−	0.963607i	$-0.413861\pi$
$281$	150.235			0.534646			0.267323	+	0.963607i	$0.413861\pi$
$282$		0			0
$283$	−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
$285$		0			0
$286$	210.995	+	79.7486i	0.737745	+	0.278841i
$287$		−	18.4424i		−	0.0642591i
$288$		0			0
$289$	−136.647			−0.472826
$290$	−143.397	+	379.393i	−0.494472	+	1.30825i
$291$		0			0
$292$	−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	$0.877971\pi$
$294$		0			0
$295$			275.002i			0.932211i
$296$	−60.8040	−	114.909i	−0.205419	−	0.388206i
$297$		0			0
$298$	−471.779	−	178.316i	−1.58315	−	0.598375i
$299$	222.593			0.744458
$300$		0			0
$301$		−	60.3983i		−	0.200659i
$302$	−438.683	−	165.807i	−1.45259	−	0.549029i
$303$		0			0
$304$	57.7401	+	458.298i	0.189935	+	1.50756i
$305$	−137.598			−0.451141
$306$		0			0
$307$	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
$309$		0			0
$310$	−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	$-0.0370656\pi$
$312$		0			0
$313$	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
$315$		0			0
$316$	−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	$0.944925\pi$
$318$		0			0
$319$			280.294i			0.878664i
$320$	−477.990	−	325.194i	−1.49372	−	1.01623i
$321$		0			0
$322$	−46.1005	+	121.970i	−0.143169	+	0.378790i
$323$	−356.347			−1.10324
$324$		0			0
$325$			511.259i			1.57310i
$326$	73.9167	−	195.565i	0.226738	−	0.599894i
$327$		0			0
$328$	49.2893	−	26.0815i	0.150272	−	0.0795166i
$329$	−16.4020			−0.0498542
$330$		0			0
$331$	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
$333$		0			0
$334$	−555.196	−	209.844i	−1.66226	−	0.628276i
$335$			710.254i			2.12016i
$336$		0			0
$337$	−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
$339$		0			0
$340$	294.995	−	334.493i	0.867632	−	0.983802i
$341$			209.533i			0.614466i
$342$		0			0
$343$		−	18.5203i		−	0.0539949i
$344$	161.421	−	85.4162i	0.469248	−	0.248303i
$345$		0			0
$346$	74.8894	+	28.3055i	0.216443	+	0.0818079i
$347$	330.309			0.951898			0.475949	−	0.879473i	$-0.342105\pi$
$347$	330.309			0.951898			0.475949	+	0.879473i	$0.342105\pi$
$348$		0			0
$349$			262.402i			0.751869i	0.926646	+	0.375934i	$0.122678\pi$
$349$			262.402i			0.751869i	−0.926646	+	0.375934i	$0.877322\pi$
$350$	−280.146	−	105.885i	−0.800416	−	0.302529i
$351$		0			0
$352$	−388.451	−	93.4313i	−1.10355	−	0.265430i
$353$	578.098			1.63767			0.818835	−	0.574029i	$-0.194620\pi$
$353$	578.098			1.63767			0.818835	+	0.574029i	$0.194620\pi$
$354$		0			0
$355$	158.392			0.446174
$356$	335.823	+	296.168i	0.943324	+	0.831934i
$357$		0			0
$358$	−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	$-0.169805\pi$
$360$		0			0
$361$	472.480			1.30881
$362$	−75.7136	−	28.6171i	−0.209154	−	0.0790527i
$363$		0			0
$364$	−71.6985	−	63.2321i	−0.196974	−	0.173715i
$365$		−	421.725i		−	1.15541i
$366$		0			0
$367$		−	520.071i		−	1.41709i	−0.705666	−	0.708544i	$-0.749352\pi$
$367$		−	520.071i		−	1.41709i	0.705666	−	0.708544i	$-0.250648\pi$
$368$	−391.176	+	49.2835i	−1.06298	+	0.133923i
$369$		0			0
$370$	103.799	−	274.626i	0.280538	−	0.742233i
$371$	21.2061			0.0571592
$372$		0			0
$373$			526.711i			1.41210i	0.708164	+	0.706048i	$0.249524\pi$
$373$			526.711i			1.41210i	−0.708164	+	0.706048i	$0.750476\pi$
$374$	108.971	−	288.309i	0.291365	−	0.770880i
$375$		0			0
$376$	−23.1960	−	43.8362i	−0.0616914	−	0.116586i
$377$	−202.794			−0.537915
$378$		0			0
$379$	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
$381$		0			0
$382$	−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	$-0.135550\pi$
$384$		0			0
$385$	−298.392			−0.775044
$386$	−184.770	+	488.854i	−0.478678	+	1.26646i
$387$		0			0
$388$	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	$0.962210\pi$
$390$		0			0
$391$		−	304.157i		−	0.777895i
$392$	49.4975	−	26.1916i	0.126269	−	0.0668153i
$393$		0			0
$394$	−271.799	−	102.730i	−0.689845	−	0.260737i
$395$	−731.980			−1.85311
$396$		0			0
$397$		−	562.267i		−	1.41629i	−0.706068	−	0.708144i	$-0.749533\pi$
$397$		−	562.267i		−	1.41629i	0.706068	−	0.708144i	$-0.250467\pi$
$398$	730.573	+	276.131i	1.83561	+	0.693795i
$399$		0			0
$400$	−113.196	−	898.465i	−0.282990	−	2.24616i
$401$	−81.2061			−0.202509			−0.101254	−	0.994861i	$-0.532286\pi$
$401$	−81.2061			−0.202509			−0.101254	+	0.994861i	$0.532286\pi$
$402$		0			0
$403$	−151.598			−0.376174
$404$	−32.1005	+	36.3986i	−0.0794567	+	0.0900954i
$405$		0			0
$406$	42.0000	−	111.122i	0.103448	−	0.273698i
$407$		−	202.893i		−	0.498508i
$408$		0			0
$409$	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
$411$		0			0
$412$	−281.990	+	319.746i	−0.684442	+	0.776084i
$413$		−	80.5463i		−	0.195027i
$414$		0			0
$415$			364.802i			0.879041i
$416$	67.5980	−	281.046i	0.162495	−	0.675591i
$417$		0			0
$418$	−254.877	+	674.342i	−0.609754	+	1.61326i
$419$	−624.988			−1.49162			−0.745809	−	0.666160i	$-0.767937\pi$
$419$	−624.988			−1.49162			−0.745809	+	0.666160i	$0.767937\pi$
$420$		0			0
$421$		−	566.476i		−	1.34555i	−0.739848	−	0.672774i	$-0.765103\pi$
$421$		−	566.476i		−	1.34555i	0.739848	−	0.672774i	$-0.234897\pi$
$422$	−116.000	+	306.907i	−0.274882	+	0.727268i
$423$		0			0
$424$	29.9899	+	56.6756i	0.0707309	+	0.133669i
$425$	698.597			1.64376
$426$		0			0
$427$	40.3015			0.0943829
$428$	−190.794	−	168.264i	−0.445780	−	0.393141i
$429$		0			0
$430$	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	$0.890966\pi$
$432$		0			0
$433$	−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
$435$		0			0
$436$	−346.191	+	392.544i	−0.794016	+	0.900329i
$437$			711.409i			1.62794i
$438$		0			0
$439$			38.3890i			0.0874464i	0.999044	+	0.0437232i	$0.0139220\pi$
$439$			38.3890i			0.0874464i	−0.999044	+	0.0437232i	$0.986078\pi$
$440$	−421.990	−	797.486i	−0.959068	−	1.81247i
$441$		0			0
$442$	208.593	+	78.8407i	0.471930	+	0.178373i
$443$	−599.058			−1.35228			−0.676138	−	0.736775i	$-0.736348\pi$
$443$	−599.058			−1.35228			−0.676138	+	0.736775i	$0.736348\pi$
$444$		0			0
$445$			1011.18i			2.27232i
$446$	19.7990	+	7.48331i	0.0443924	+	0.0167787i
$447$		0			0
$448$	140.000	+	95.2470i	0.312500	+	0.212605i
$449$	460.039			1.02459			0.512293	−	0.858811i	$-0.328796\pi$
$449$	460.039			1.02459			0.512293	+	0.858811i	$0.328796\pi$
$450$		0			0
$451$	87.0294			0.192970
$452$	−414.676	−	365.710i	−0.917425	−	0.809093i
$453$		0			0
$454$	151.184	−	399.995i	0.333004	−	0.881045i
$455$		−	215.888i		−	0.474479i
$456$		0			0
$457$	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
$459$		0			0
$460$	−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	$-0.310341\pi$
$462$		0			0
$463$		−	123.988i		−	0.267792i	−0.990995	−	0.133896i	$-0.957251\pi$
$463$		−	123.988i		−	0.267792i	0.990995	−	0.133896i	$-0.0427488\pi$
$464$	356.382	−	44.8999i	0.768064	−	0.0967670i
$465$		0			0
$466$	136.375	−	360.813i	0.292650	−	0.774278i
$467$	768.718			1.64608			0.823038	−	0.567986i	$-0.192277\pi$
$467$	768.718			1.64608			0.823038	+	0.567986i	$0.192277\pi$
$468$		0			0
$469$		−	208.029i		−	0.443558i
$470$	39.5980	−	104.766i	0.0842510	−	0.222907i
$471$		0			0
$472$	215.269	−	113.910i	0.456079	−	0.241334i
$473$	285.019			0.602578
$474$		0			0
$475$	−1633.99			−3.43997
$476$	−86.4020	+	97.9707i	−0.181517	+	0.205821i
$477$		0			0
$478$	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	$-0.0396355\pi$
$480$		0			0
$481$	146.794			0.305185
$482$	50.8213	−	134.460i	0.105438	−	0.278964i
$483$		0			0
$484$	−104.647	−	92.2898i	−0.216212	−	0.190681i
$485$			1482.41i			3.05652i
$486$		0			0
$487$			282.577i			0.580240i	0.956990	+	0.290120i	$0.0936952\pi$
$487$			282.577i			0.580240i	−0.956990	+	0.290120i	$0.906305\pi$
$488$	56.9949	+	107.710i	0.116793	+	0.220718i
$489$		0			0
$490$	118.296	+	44.7119i	0.241421	+	0.0912487i
$491$	388.049			0.790323			0.395162	−	0.918612i	$-0.370689\pi$
$491$	388.049			0.790323			0.395162	+	0.918612i	$0.370689\pi$
$492$		0			0
$493$			277.103i			0.562075i
$494$	−487.889	−	184.405i	−0.987630	−	0.373289i
$495$		0			0
$496$	266.412	−	33.5648i	0.537121	−	0.0676709i
$497$	−46.3919			−0.0933439
$498$		0			0
$499$	−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
$501$		0			0
$502$	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	$0.742699\pi$
$504$		0			0
$505$	−109.598			−0.217026
$506$	−575.578	−	217.548i	−1.13751	−	0.429937i
$507$		0			0
$508$	−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	$-0.214074\pi$
$510$		0			0
$511$			123.520i			0.241723i
$512$	−56.5685	+	508.865i	−0.110485	+	0.993878i
$513$		0			0
$514$	−225.816	+	597.454i	−0.439331	+	1.16236i
$515$	−962.774			−1.86946
$516$		0			0
$517$		−	77.4010i		−	0.149712i
$518$	−30.4020	+	80.4362i	−0.0586912	+	0.155282i
$519$		0			0
$520$	576.985	−	305.312i	1.10959	−	0.587138i
$521$	−833.127			−1.59909			−0.799546	−	0.600605i	$-0.794927\pi$
$521$	−833.127			−1.59909			−0.799546	+	0.600605i	$0.794927\pi$
$522$		0			0
$523$	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
$525$		0			0
$526$	705.970	+	266.831i	1.34215	+	0.507284i
$527$			207.147i			0.393069i
$528$		0			0
$529$	−78.2162			−0.147857
$530$	−51.1960	+	135.452i	−0.0965961	+	0.255569i
$531$		0			0
$532$	202.090	−	229.149i	0.379869	−	0.430731i
$533$			62.9662i			0.118135i
$534$		0			0
$535$		−	574.491i		−	1.07381i
$536$	555.980	−	294.197i	1.03728	−	0.548875i
$537$		0			0
$538$	−52.6884	−	19.9143i	−0.0979338	−	0.0370155i
$539$	87.3970			0.162147
$540$		0			0
$541$		−	405.915i		−	0.750305i	−0.926963	−	0.375152i	$-0.877590\pi$
$541$		−	405.915i		−	0.750305i	0.926963	−	0.375152i	$-0.122410\pi$
$542$	747.799	+	282.641i	1.37970	+	0.521479i
$543$		0			0
$544$	−384.029	−	92.3676i	−0.705935	−	0.169793i
$545$	−1181.97			−2.16875
$546$		0			0
$547$	−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
$549$		0			0
$550$	499.671	−	1322.01i	0.908493	−	2.40365i
$551$		−	648.131i		−	1.17628i
$552$		0			0
$553$	214.392			0.387689
$554$	−192.603	−	72.7971i	−0.347659	−	0.131403i
$555$		0			0
$556$	−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	$-0.0104153\pi$
$558$		0			0
$559$			206.213i			0.368896i
$560$	47.7990	+	379.393i	0.0853553	+	0.677487i
$561$		0			0
$562$	106.233	−	281.065i	0.189026	−	0.500115i
$563$	186.389			0.331064			0.165532	−	0.986204i	$-0.447066\pi$
$563$	186.389			0.331064			0.165532	+	0.986204i	$0.447066\pi$
$564$		0			0
$565$		−	1248.61i		−	2.20993i
$566$	−126.262	+	334.058i	−0.223078	+	0.590208i
$567$		0			0
$568$	−65.6081	−	123.988i	−0.115507	−	0.218288i
$569$	670.891			1.17907			0.589536	−	0.807742i	$-0.299311\pi$
$569$	670.891			1.17907			0.589536	+	0.807742i	$0.299311\pi$
$570$		0			0
$571$	−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
$573$		0			0
$574$	−34.5025	−	13.0407i	−0.0601089	−	0.0227190i
$575$		−	1394.67i		−	2.42552i
$576$		0			0
$577$	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
$579$		0			0
$580$	608.382	+	536.542i	1.04893	+	0.925073i
$581$		−	106.848i		−	0.183904i
$582$		0			0
$583$			100.071i			0.171649i
$584$	−330.122	+	174.684i	−0.565277	+	0.299117i
$585$		0			0
$586$	410.065	+	154.990i	0.699770	+	0.264488i
$587$	321.120			0.547053			0.273526	−	0.961865i	$-0.411810\pi$
$587$	321.120			0.547053			0.273526	+	0.961865i	$0.411810\pi$
$588$		0			0
$589$		−	484.508i		−	0.822595i
$590$	514.482	+	194.456i	0.872004	+	0.329587i
$591$		0			0
$592$	−257.970	+	32.5011i	−0.435760	+	0.0549006i
$593$	219.255			0.369738			0.184869	−	0.982763i	$-0.440814\pi$
$593$	219.255			0.369738			0.184869	+	0.982763i	$0.440814\pi$
$594$		0			0
$595$	−294.995			−0.495790
$596$	−667.196	+	756.529i	−1.11946	+	1.26934i
$597$		0			0
$598$	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	$-0.0412464\pi$
$600$		0			0
$601$	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
$603$		0			0
$604$	−620.392	+	703.458i	−1.02714	+	1.16467i
$605$		−	315.097i		−	0.520821i
$606$		0			0
$607$			790.663i			1.30258i	0.758831	+	0.651288i	$0.225771\pi$
$607$			790.663i			1.30258i	−0.758831	+	0.651288i	$0.774229\pi$
$608$	898.225	+	216.044i	1.47734	+	0.355335i
$609$		0			0
$610$	−97.2965	+	257.422i	−0.159502	+	0.422004i
$611$	56.0000			0.0916530
$612$		0			0
$613$			741.471i			1.20958i	0.796386	+	0.604789i	$0.206743\pi$
$613$			741.471i			1.20958i	−0.796386	+	0.604789i	$0.793257\pi$
$614$	223.919	−	592.434i	0.364689	−	0.964875i
$615$		0			0
$616$	123.598	+	233.578i	0.200646	+	0.379185i
$617$	−171.578			−0.278084			−0.139042	−	0.990286i	$-0.544402\pi$
$617$	−171.578			−0.278084			−0.139042	+	0.990286i	$0.544402\pi$
$618$		0			0
$619$	−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
$621$		0			0
$622$	−135.196	−	51.0993i	−0.217357	−	0.0821532i
$623$		−	296.168i		−	0.475391i
$624$		0			0
$625$	1163.38			1.86141
$626$	57.9483	−	153.317i	0.0925691	−	0.244915i
$627$		0			0
$628$	−26.7136	+	30.2904i	−0.0425376	+	0.0482331i
$629$		−	200.583i		−	0.318892i
$630$		0			0
$631$			269.399i			0.426940i	0.976950	+	0.213470i	$0.0684766\pi$
$631$			269.399i			0.426940i	−0.976950	+	0.213470i	$0.931523\pi$
$632$	303.196	+	572.987i	0.479740	+	0.906624i
$633$		0			0
$634$	204.201	+	77.1807i	0.322084	+	0.121736i
$635$	−1033.77			−1.62798
$636$		0			0
$637$			63.2321i			0.0992655i
$638$	524.382	+	198.198i	0.821915	+	0.310655i
$639$		0			0
$640$	−946.372	+	664.291i	−1.47871	+	1.03795i
$641$	−36.1867			−0.0564535			−0.0282268	−	0.999602i	$-0.508986\pi$
$641$	−36.1867			−0.0564535			−0.0282268	+	0.999602i	$0.508986\pi$
$642$		0			0
$643$	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
$645$		0			0
$646$	−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	$0.682883\pi$
$648$		0			0
$649$	380.098			0.585666
$650$	956.477	+	361.514i	1.47150	+	0.556176i
$651$		0			0
$652$	−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	$-0.368026\pi$
$654$		0			0
$655$		−	1520.74i		−	2.32173i
$656$	−13.9411	−	110.654i	−0.0212517	−	0.168680i
$657$		0			0
$658$	−11.5980	+	30.6854i	−0.0176261	+	0.0466343i
$659$	685.220			1.03979			0.519894	−	0.854231i	$-0.325971\pi$
$659$	685.220			1.03979			0.519894	+	0.854231i	$0.325971\pi$
$660$		0			0
$661$		−	993.382i		−	1.50285i	−0.659820	−	0.751423i	$-0.729368\pi$
$661$		−	993.382i		−	1.50285i	0.659820	−	0.751423i	$-0.270632\pi$
$662$	227.505	−	601.921i	0.343663	−	0.909246i
$663$		0			0
$664$	285.563	−	151.106i	0.430065	−	0.227569i
$665$	689.980			1.03756
$666$		0			0
$667$	553.206			0.829394
$668$	−785.166	+	890.294i	−1.17540	+	1.33278i
$669$		0			0
$670$	1328.76	+	502.225i	1.98323	+	0.749590i
$671$			190.183i			0.283432i
$672$		0			0
$673$	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
$675$		0			0
$676$	−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	$-0.265953\pi$
$678$		0			0
$679$		−	434.188i		−	0.639452i
$680$	−417.186	−	788.407i	−0.613509	−	1.15942i
$681$		0			0
$682$	392.000	+	148.162i	0.574780	+	0.217246i
$683$	678.225			0.993009			0.496505	−	0.868034i	$-0.334617\pi$
$683$	678.225			0.993009			0.496505	+	0.868034i	$0.334617\pi$
$684$		0			0
$685$			313.327i			0.457411i
$686$	−34.6482	−	13.0958i	−0.0505076	−	0.0190901i
$687$		0			0
$688$	−45.6569	−	362.390i	−0.0663617	−	0.526730i
$689$	−72.4020			−0.105083
$690$		0			0
$691$	−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
$693$		0			0
$694$	233.563	−	617.951i	0.336547	−	0.890419i
$695$		−	972.546i		−	1.39935i
$696$		0			0
$697$	86.0387			0.123441
$698$	490.910	+	185.546i	0.703309	+	0.265826i
$699$		0			0
$700$	−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	$-0.233997\pi$
$702$		0			0
$703$			469.155i			0.667361i
$704$	−449.470	+	660.659i	−0.638452	+	0.938436i
$705$		0			0
$706$	408.777	−	1081.52i	0.579004	−	1.53190i
$707$	32.1005			0.0454038
$708$		0			0
$709$		−	1057.46i		−	1.49148i	−0.666239	−	0.745738i	$-0.732097\pi$
$709$		−	1057.46i		−	1.49148i	0.666239	−	0.745738i	$-0.267903\pi$
$710$	112.000	−	296.324i	0.157746	−	0.417358i
$711$		0			0
$712$	791.543	−	418.845i	1.11172	−	0.588266i
$713$	413.547			0.580010
$714$		0			0
$715$	1018.77			1.42486
$716$	884.382	+	779.951i	1.23517	+	1.08932i
$717$		0			0
$718$	−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	$0.744312\pi$
$720$		0			0
$721$	281.990			0.391109
$722$	334.094	−	883.930i	0.462734	−	1.22428i
$723$		0			0
$724$	−107.075	+	121.412i	−0.147894	+	0.167696i
$725$			1270.62i			1.75258i
$726$		0			0
$727$		−	495.145i		−	0.681080i	−0.940230	−	0.340540i	$-0.889390\pi$
$727$		−	495.145i		−	0.681080i	0.940230	−	0.340540i	$-0.110610\pi$
$728$	−168.995	+	89.4237i	−0.232136	+	0.122835i
$729$		0			0
$730$	−788.975	−	298.204i	−1.08079	−	0.408499i
$731$	281.775			0.385465
$732$		0			0
$733$		−	567.494i		−	0.774207i	−0.922036	−	0.387103i	$-0.873476\pi$
$733$		−	567.494i		−	0.774207i	0.922036	−	0.387103i	$-0.126524\pi$
$734$	−972.965	−	367.746i	−1.32556	−	0.501016i
$735$		0			0
$736$	−184.402	+	766.672i	−0.250546	+	1.04167i
$737$	981.685			1.33200
$738$		0			0
$739$	−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
$741$		0			0
$742$	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	$0.836229\pi$
$744$		0			0
$745$	−2277.95			−3.05765
$746$	985.387	+	372.441i	1.32089	+	0.499251i
$747$		0			0
$748$	−462.323	−	407.731i	−0.618079	−	0.545094i
$749$			168.264i			0.224652i
$750$		0			0
$751$		−	666.262i		−	0.887166i	−0.896233	−	0.443583i	$-0.853707\pi$
$751$		−	666.262i		−	0.887166i	0.896233	−	0.443583i	$-0.146293\pi$
$752$	−98.4121	+	12.3988i	−0.130867	+	0.0164877i
$753$		0			0
$754$	−143.397	+	379.393i	−0.190182	+	0.503173i
$755$	−2118.15			−2.80550
$756$		0			0
$757$			238.623i			0.315222i	0.987501	+	0.157611i	$0.0503791\pi$
$757$			238.623i			0.315222i	−0.987501	+	0.157611i	$0.949621\pi$
$758$	86.2498	−	228.195i	0.113786	−	0.301049i
$759$		0			0
$760$	975.779	+	1844.05i	1.28392	+	2.42638i
$761$	−614.930			−0.808055			−0.404028	−	0.914747i	$-0.632390\pi$
$761$	−614.930			−0.808055			−0.404028	+	0.914747i	$0.632390\pi$
$762$		0			0
$763$	346.191			0.453723
$764$	−415.196	+	470.788i	−0.543450	+	0.616215i
$765$		0			0
$766$	−591.980	−	223.747i	−0.772820	−	0.292098i
$767$			275.002i			0.358543i
$768$		0			0
$769$	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
$771$		0			0
$772$	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	$-0.133965\pi$
$774$		0			0
$775$			949.849i			1.22561i
$776$	1160.42	−	614.035i	1.49538	−	0.791282i
$777$		0			0
$778$	172.392	+	65.1580i	0.221583	+	0.0837507i
$779$	−201.241			−0.258332
$780$		0			0
$781$		−	218.923i		−	0.280311i
$782$	−569.025	−	215.071i	−0.727654	−	0.275027i
$783$		0			0
$784$	−14.0000	−	111.122i	−0.0178571	−	0.141737i
$785$	−91.2061			−0.116186
$786$		0			0
$787$	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
$789$		0			0
$790$	−517.588	+	1369.41i	−0.655175	+	1.73343i
$791$			365.710i			0.462339i
$792$		0			0
$793$	−137.598			−0.173516
$794$	−1051.90	−	397.583i	−1.32482	−	0.500734i
$795$		0			0
$796$	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	$0.956216\pi$
$798$		0			0
$799$		−	76.5199i		−	0.0957695i
$800$	−1760.92	−	423.540i	−2.20114	−	0.529426i
$801$		0			0
$802$	−57.4214	+	151.923i	−0.0715977	+	0.189430i
$803$	−582.891			−0.725892
$804$		0			0
$805$			588.926i			0.731585i
$806$	−107.196	+	283.614i	−0.132997	+	0.351878i
$807$		0			0
$808$	45.3970	+	85.7922i	0.0561844	+	0.106178i
$809$	−1347.46			−1.66559			−0.832794	−	0.553584i	$-0.813260\pi$
$809$	−1347.46			−1.66559			−0.832794	+	0.553584i	$0.813260\pi$
$810$		0			0
$811$	−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
$813$		0			0
$814$	−379.578	−	143.467i	−0.466312	−	0.176249i
$815$		−	944.273i		−	1.15862i
$816$		0			0
$817$	−659.058			−0.806681
$818$	318.718	−	843.248i	0.389631	−	1.03087i
$819$		0			0
$820$	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	$-0.250412\pi$
$822$		0			0
$823$			1041.65i			1.26567i	0.774286	+	0.632835i	$0.218109\pi$
$823$			1041.65i			1.26567i	−0.774286	+	0.632835i	$0.781891\pi$
$824$	398.794	+	753.650i	0.483973	+	0.914623i
$825$		0			0
$826$	−150.688	−	56.9549i	−0.182431	−	0.0689526i
$827$	−278.432			−0.336678			−0.168339	−	0.985729i	$-0.553840\pi$
$827$	−278.432			−0.336678			−0.168339	+	0.985729i	$0.553840\pi$
$828$		0			0
$829$			1065.74i			1.28557i	0.766046	+	0.642785i	$0.222221\pi$
$829$			1065.74i			1.28557i	−0.766046	+	0.642785i	$0.777779\pi$
$830$	682.482	+	257.954i	0.822268	+	0.310788i
$831$		0			0
$832$	−477.990	−	325.194i	−0.574507	−	0.390858i
$833$	86.4020			0.103724
$834$		0			0
$835$	−2680.72			−3.21045
$836$	1081.35	+	953.663i	1.29348	+	1.14075i
$837$		0			0
$838$	−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	$0.941657\pi$
$840$		0			0
$841$	337.000			0.400713
$842$	−1059.78	−	400.559i	−1.25864	−	0.475723i
$843$		0			0
$844$	492.146	+	434.032i	0.583112	+	0.514256i
$845$		−	789.516i		−	0.934339i
$846$		0			0
$847$			92.2898i			0.108961i
$848$	127.236	−	16.0303i	0.150043	−	0.0189036i
$849$		0			0
$850$	493.983	−	1306.96i	0.581156	−	1.53759i
$851$	−400.442			−0.470555
$852$		0			0
$853$			164.018i			0.192283i	0.995368	+	0.0961417i	$0.0306502\pi$
$853$			164.018i			0.192283i	−0.995368	+	0.0961417i	$0.969350\pi$
$854$	28.4975	−	75.3972i	0.0333694	−	0.0882872i
$855$		0			0
$856$	−449.706	+	237.962i	−0.525357	+	0.277993i
$857$	−851.068			−0.993078			−0.496539	−	0.868014i	$-0.665396\pi$
$857$	−851.068			−0.993078			−0.496539	+	0.868014i	$0.665396\pi$
$858$		0			0
$859$	−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
$861$		0			0
$862$	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	$0.948311\pi$
$864$		0			0
$865$	361.598			0.418032
$866$	−422.635	+	1118.19i	−0.488031	+	1.29121i
$867$		0			0
$868$	−133.206	−	117.477i	−0.153463	−	0.135342i
$869$			1011.71i			1.16423i
$870$		0			0
$871$			710.254i			0.815447i
$872$	489.588	+	925.234i	0.561454	+	1.06105i
$873$		0			0
$874$	1330.92	+	503.042i	1.52280	+	0.575563i
$875$	−755.176			−0.863058
$876$		0			0
$877$			674.159i			0.768711i	0.923185	+	0.384355i	$0.125576\pi$
$877$			674.159i			0.768711i	−0.923185	+	0.384355i	$0.874424\pi$
$878$	71.8192	+	27.1451i	0.0817986	+	0.0309170i
$879$		0			0
$880$	−1790.35	+	225.563i	−2.03449	+	0.256322i
$881$	1001.29			1.13654			0.568271	−	0.822841i	$-0.307613\pi$
$881$	1001.29			1.13654			0.568271	+	0.822841i	$0.307613\pi$
$882$		0			0
$883$	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
$885$		0			0
$886$	−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	$0.998730\pi$
$888$		0			0
$889$	302.784			0.340589
$890$	1891.75	+	715.014i	2.12556	+	0.803386i
$891$		0			0
$892$	28.0000	−	31.7490i	0.0313901	−	0.0355931i
$893$			178.976i			0.200422i
$894$		0			0
$895$			2662.92i			2.97533i
$896$	277.186	−	194.566i	0.309359	−	0.217150i
$897$		0			0
$898$	325.296	−	860.654i	0.362246	−	0.958412i
$899$	−376.764			−0.419092
$900$		0			0
$901$			98.9320i			0.109802i
$902$	61.5391	−	162.817i	0.0682252	−	0.180507i
$903$		0			0
$904$	−977.401	+	517.192i	−1.08120	+	0.572115i
$905$	−365.578			−0.403953
$906$		0			0
$907$	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
$909$		0			0
$910$	−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	$0.964562\pi$
$912$		0			0
$913$	504.215			0.552262
$914$	188.319	−	498.245i	0.206038	−	0.545125i
$915$		0			0
$916$	613.889	−	696.085i	0.670185	−	0.759918i
$917$			445.413i			0.485728i
$918$		0			0
$919$		−	1593.73i		−	1.73420i	−0.498138	−	0.867098i	$-0.665983\pi$
$919$		−	1593.73i		−	1.73420i	0.498138	−	0.867098i	$-0.334017\pi$
$920$	−1573.97	+	832.866i	−1.71084	+	0.905290i
$921$		0			0
$922$	−1427.67	−	539.610i	−1.54845	−	0.585260i
$923$	158.392			0.171606
$924$		0			0
$925$		−	919.749i		−	0.994323i
$926$	−231.960	−	87.6725i	−0.250496	−	0.0946787i
$927$		0			0
$928$	168.000	−	698.478i	0.181034	−	0.752671i
$929$	1039.40			1.11884			0.559419	−	0.828885i	$-0.311024\pi$
$929$	1039.40			1.11884			0.559419	+	0.828885i	$0.311024\pi$
$930$		0			0
$931$	−202.090			−0.217068
$932$	−578.589	−	510.267i	−0.620803	−	0.547497i
$933$		0			0
$934$	543.566	−	1438.14i	0.581976	−	1.53976i
$935$		−	1392.08i		−	1.48885i
$936$		0			0
$937$	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
$939$		0			0
$940$	−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	$0.830917\pi$
$942$		0			0
$943$		−	171.767i		−	0.182149i
$944$	−60.8873	−	483.278i	−0.0644993	−	0.511947i
$945$		0			0
$946$	201.539	−	533.222i	0.213043	−	0.563660i
$947$	−16.8957			−0.0178413			−0.00892063	−	0.999960i	$-0.502840\pi$
$947$	−16.8957			−0.0178413			−0.00892063	+	0.999960i	$0.502840\pi$
$948$		0			0
$949$		−	421.725i		−	0.444389i
$950$	−1155.40	+	3056.91i	−1.21621	+	3.21780i
$951$		0			0
$952$	122.191	+	230.919i	0.128352	+	0.242562i
$953$	−1526.31			−1.60159			−0.800794	−	0.598940i	$-0.795589\pi$
$953$	−1526.31			−1.60159			−0.800794	+	0.598940i	$0.795589\pi$
$954$		0			0
$955$	−1417.57			−1.48436
$956$	867.588	−	983.752i	0.907519	−	1.02903i
$957$		0			0
$958$	−222.593	−	84.1322i	−0.232352	−	0.0878207i
$959$		−	91.7713i		−	0.0956948i
$960$		0			0
$961$	679.352			0.706921
$962$	103.799	−	274.626i	0.107899	−	0.285474i
$963$		0			0
$964$	−215.616	−	190.156i	−0.223669	−	0.197257i
$965$			2360.40i			2.44601i
$966$		0			0
$967$			1410.39i			1.45852i	0.684235	+	0.729262i	$0.260136\pi$
$967$			1410.39i			1.45852i	−0.684235	+	0.729262i	$0.739864\pi$
$968$	−246.655	+	130.517i	−0.254809	+	0.134832i
$969$		0			0
$970$	2773.34	+	1048.22i	2.85911	+	1.08064i
$971$	596.497			0.614312			0.307156	−	0.951659i	$-0.400623\pi$
$971$	596.497			0.614312			0.307156	+	0.951659i	$0.400623\pi$
$972$		0			0
$973$			284.852i			0.292757i
$974$	528.653	+	199.812i	0.542765	+	0.205146i
$975$		0			0
$976$	241.809	−	30.4651i	0.247755	−	0.0312142i
$977$	−146.686			−0.150140			−0.0750698	−	0.997178i	$-0.523918\pi$
$977$	−146.686			−0.150140			−0.0750698	+	0.997178i	$0.523918\pi$
$978$		0			0
$979$	1397.62			1.42760
$980$	167.296	−	189.696i	0.170711	−	0.193568i
$981$		0			0
$982$	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	$-0.0274704\pi$
$984$		0			0
$985$	−1312.36			−1.33235
$986$	518.412	+	195.941i	0.525773	+	0.198723i
$987$		0			0
$988$	−689.980	+	782.364i	−0.698360	+	0.791866i
$989$		−	562.533i		−	0.568789i
$990$		0			0
$991$		−	1686.90i		−	1.70222i	−0.524988	−	0.851109i	$-0.675930\pi$
$991$		−	1686.90i		−	1.70222i	0.524988	−	0.851109i	$-0.324070\pi$
$992$	125.588	−	522.145i	0.126601	−	0.526356i
$993$		0			0
$994$	−32.8040	+	86.7913i	−0.0330021	+	0.0873152i
$995$	3527.52			3.54524
$996$		0			0
$997$			1736.14i			1.74136i	0.491849	+	0.870680i	$0.336321\pi$
$997$			1736.14i			1.74136i	−0.491849	+	0.870680i	$0.663679\pi$
$998$	−19.5980	+	51.8514i	−0.0196373	+	0.0519553i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.g.a.379.3		4
3.2	odd	2		56.3.g.a.43.2	yes	4
4.3	odd	2		2016.3.g.a.1135.1		4
8.3	odd	2	inner	504.3.g.a.379.4		4
8.5	even	2		2016.3.g.a.1135.4		4
12.11	even	2		224.3.g.a.15.4		4
21.2	odd	6		392.3.k.i.67.4		8
21.5	even	6		392.3.k.j.67.4		8
21.11	odd	6		392.3.k.i.275.2		8
21.17	even	6		392.3.k.j.275.2		8
21.20	even	2		392.3.g.h.99.2		4
24.5	odd	2		224.3.g.a.15.3		4
24.11	even	2		56.3.g.a.43.1	✓	4
48.5	odd	4		1792.3.d.g.1023.3		8
48.11	even	4		1792.3.d.g.1023.5		8
48.29	odd	4		1792.3.d.g.1023.6		8
48.35	even	4		1792.3.d.g.1023.4		8
84.83	odd	2		1568.3.g.h.687.1		4
168.11	even	6		392.3.k.i.275.4		8
168.59	odd	6		392.3.k.j.275.4		8
168.83	odd	2		392.3.g.h.99.1		4
168.107	even	6		392.3.k.i.67.2		8
168.125	even	2		1568.3.g.h.687.2		4
168.131	odd	6		392.3.k.j.67.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.a.43.1	✓	4	24.11	even	2
56.3.g.a.43.2	yes	4	3.2	odd	2
224.3.g.a.15.3		4	24.5	odd	2
224.3.g.a.15.4		4	12.11	even	2
392.3.g.h.99.1		4	168.83	odd	2
392.3.g.h.99.2		4	21.20	even	2
392.3.k.i.67.2		8	168.107	even	6
392.3.k.i.67.4		8	21.2	odd	6
392.3.k.i.275.2		8	21.11	odd	6
392.3.k.i.275.4		8	168.11	even	6
392.3.k.j.67.2		8	168.131	odd	6
392.3.k.j.67.4		8	21.5	even	6
392.3.k.j.275.2		8	21.17	even	6
392.3.k.j.275.4		8	168.59	odd	6
504.3.g.a.379.3		4	1.1	even	1	trivial
504.3.g.a.379.4		4	8.3	odd	2	inner
1568.3.g.h.687.1		4	84.83	odd	2
1568.3.g.h.687.2		4	168.125	even	2
1792.3.d.g.1023.3		8	48.5	odd	4
1792.3.d.g.1023.4		8	48.35	even	4
1792.3.d.g.1023.5		8	48.11	even	4
1792.3.d.g.1023.6		8	48.29	odd	4
2016.3.g.a.1135.1		4	4.3	odd	2
2016.3.g.a.1135.4		4	8.5	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.87083i) q^{2} +(-3.00000 - 2.64575i) q^{4} -9.03316i q^{5} +2.64575i q^{7} +(-7.07107 + 3.74166i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 1.87083i) q^{2} +(-3.00000 - 2.64575i) q^{4} -9.03316i q^{5} +2.64575i q^{7} +(-7.07107 + 3.74166i) q^{8} +(-16.8995 - 6.38741i) q^{10} -12.4853 q^{11} -9.03316i q^{13} +(4.94975 + 1.87083i) q^{14} +(2.00000 + 15.8745i) q^{16} -12.3431 q^{17} +28.8701 q^{19} +(-23.8995 + 27.0995i) q^{20} +(-8.82843 + 23.3578i) q^{22} +24.6418i q^{23} -56.5980 q^{25} +(-16.8995 - 6.38741i) q^{26} +(7.00000 - 7.93725i) q^{28} -22.4499i q^{29} -16.7824i q^{31} +(31.1127 + 7.48331i) q^{32} +(-8.72792 + 23.0919i) q^{34} +23.8995 q^{35} +16.2506i q^{37} +(20.4142 - 54.0109i) q^{38} +(33.7990 + 63.8741i) q^{40} -6.97056 q^{41} -22.8284 q^{43} +(37.4558 + 33.0329i) q^{44} +(46.1005 + 17.4244i) q^{46} +6.19938i q^{47} -7.00000 q^{49} +(-40.0208 + 105.885i) q^{50} +(-23.8995 + 27.0995i) q^{52} -8.01514i q^{53} +112.782i q^{55} +(-9.89949 - 18.7083i) q^{56} +(-42.0000 - 15.8745i) q^{58} -30.4437 q^{59} -15.2325i q^{61} +(-31.3970 - 11.8669i) q^{62} +(36.0000 - 52.9150i) q^{64} -81.5980 q^{65} -78.6274 q^{67} +(37.0294 + 32.6569i) q^{68} +(16.8995 - 44.7119i) q^{70} +17.5345i q^{71} +46.6863 q^{73} +(30.4020 + 11.4909i) q^{74} +(-86.6102 - 76.3830i) q^{76} -33.0329i q^{77} -81.0325i q^{79} +(143.397 - 18.0663i) q^{80} +(-4.92893 + 13.0407i) q^{82} -40.3848 q^{83} +111.498i q^{85} +(-16.1421 + 42.7081i) q^{86} +(88.2843 - 46.7156i) q^{88} -111.941 q^{89} +23.8995 q^{91} +(65.1960 - 73.9253i) q^{92} +(11.5980 + 4.38362i) q^{94} -260.788i q^{95} -164.108 q^{97} +(-4.94975 + 13.0958i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 12 q^{4}+O(q^{10}) \) 4 * q - 12 * q^4	\( 4 q - 12 q^{4} - 28 q^{10} - 16 q^{11} + 8 q^{16} - 72 q^{17} + 8 q^{19} - 56 q^{20} - 24 q^{22} - 68 q^{25} - 28 q^{26} + 28 q^{28} + 16 q^{34} + 56 q^{35} + 76 q^{38} + 56 q^{40} + 40 q^{41} - 80 q^{43} + 48 q^{44} + 224 q^{46} - 28 q^{49} - 112 q^{50} - 56 q^{52} - 168 q^{58} - 184 q^{59} + 112 q^{62} + 144 q^{64} - 168 q^{65} - 224 q^{67} + 216 q^{68} + 28 q^{70} + 232 q^{73} + 280 q^{74} - 24 q^{76} + 336 q^{80} - 48 q^{82} - 88 q^{83} - 8 q^{86} + 240 q^{88} - 312 q^{89} + 56 q^{91} - 56 q^{92} - 112 q^{94} - 136 q^{97}+O(q^{100}) \) 4 * q - 12 * q^4 - 28 * q^10 - 16 * q^11 + 8 * q^16 - 72 * q^17 + 8 * q^19 - 56 * q^20 - 24 * q^22 - 68 * q^25 - 28 * q^26 + 28 * q^28 + 16 * q^34 + 56 * q^35 + 76 * q^38 + 56 * q^40 + 40 * q^41 - 80 * q^43 + 48 * q^44 + 224 * q^46 - 28 * q^49 - 112 * q^50 - 56 * q^52 - 168 * q^58 - 184 * q^59 + 112 * q^62 + 144 * q^64 - 168 * q^65 - 224 * q^67 + 216 * q^68 + 28 * q^70 + 232 * q^73 + 280 * q^74 - 24 * q^76 + 336 * q^80 - 48 * q^82 - 88 * q^83 - 8 * q^86 + 240 * q^88 - 312 * q^89 + 56 * q^91 - 56 * q^92 - 112 * q^94 - 136 * q^97

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