LMFDB - Embedded newform 504.3.g.b.379.8

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:	$8$
Coefficient field:	8.0.292213762624.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} - 2x^{5} + 24x^{4} - 8x^{3} - 32x^{2} - 64x + 256 $ x^8 - x^7 - 2x^6 - 2x^5 + 24x^4 - 8x^3 - 32x^2 - 64x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.8
Root			$-1.67467 - 1.09337i$ of defining polynomial
Character	$\chi$	$=$	504.379
Dual form			504.3.g.b.379.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.67467 + 1.09337i) q^{2} +(1.60906 + 3.66209i) q^{4} -5.73252i q^{5} -2.64575i q^{7} +(-1.30939 + 7.89212i) q^{8} +O(q^{10})$	\(q+(1.67467 + 1.09337i) q^{2} +(1.60906 + 3.66209i) q^{4} -5.73252i q^{5} -2.64575i q^{7} +(-1.30939 + 7.89212i) q^{8} +(6.26779 - 9.60010i) q^{10} +1.40065 q^{11} -19.0821i q^{13} +(2.89280 - 4.43077i) q^{14} +(-10.8218 + 11.7851i) q^{16} +32.2699 q^{17} +12.5675 q^{19} +(20.9930 - 9.22398i) q^{20} +(2.34563 + 1.53143i) q^{22} -15.8893i q^{23} -7.86180 q^{25} +(20.8639 - 31.9563i) q^{26} +(9.68898 - 4.25718i) q^{28} +3.29194i q^{29} +22.6705i q^{31} +(-31.0085 + 7.90382i) q^{32} +(54.0415 + 35.2831i) q^{34} -15.1668 q^{35} -54.1537i q^{37} +(21.0464 + 13.7410i) q^{38} +(45.2417 + 7.50608i) q^{40} +7.59607 q^{41} -20.8478 q^{43} +(2.25373 + 5.12930i) q^{44} +(17.3729 - 26.6094i) q^{46} -21.6384i q^{47} -7.00000 q^{49} +(-13.1659 - 8.59589i) q^{50} +(69.8804 - 30.7043i) q^{52} -0.356667i q^{53} -8.02924i q^{55} +(20.8806 + 3.46431i) q^{56} +(-3.59933 + 5.51293i) q^{58} -26.8583 q^{59} +86.2287i q^{61} +(-24.7873 + 37.9656i) q^{62} +(-60.5710 - 20.6676i) q^{64} -109.389 q^{65} +114.523 q^{67} +(51.9243 + 118.175i) q^{68} +(-25.3995 - 16.5830i) q^{70} +104.792i q^{71} -24.3974 q^{73} +(59.2103 - 90.6898i) q^{74} +(20.2218 + 46.0232i) q^{76} -3.70576i q^{77} +117.128i q^{79} +(67.5582 + 62.0364i) q^{80} +(12.7209 + 8.30535i) q^{82} -79.2706 q^{83} -184.988i q^{85} +(-34.9133 - 22.7945i) q^{86} +(-1.83399 + 11.0541i) q^{88} -2.66078 q^{89} -50.4865 q^{91} +(58.1880 - 25.5669i) q^{92} +(23.6589 - 36.2373i) q^{94} -72.0433i q^{95} -52.0930 q^{97} +(-11.7227 - 7.65362i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 5 q^{4} - 13 q^{8}+O(q^{10}) $ 8 * q - q^2 + 5 * q^4 - 13 * q^8	$ 8 q - q^{2} + 5 q^{4} - 13 q^{8} + 16 q^{10} + 32 q^{11} - 7 q^{14} - 71 q^{16} + 80 q^{17} + 56 q^{19} + 108 q^{20} + 66 q^{22} - 16 q^{25} - 24 q^{26} + 7 q^{28} + 19 q^{32} + 74 q^{34} - 56 q^{35} + 14 q^{38} + 84 q^{40} - 128 q^{41} - 50 q^{44} - 152 q^{46} - 56 q^{49} - 33 q^{50} + 132 q^{52} + 49 q^{56} + 24 q^{58} - 104 q^{59} - 120 q^{62} - 55 q^{64} + 72 q^{65} + 304 q^{67} + 190 q^{68} + 56 q^{70} - 112 q^{73} - 8 q^{74} + 70 q^{76} - 124 q^{80} + 450 q^{82} - 72 q^{83} - 210 q^{86} - 486 q^{88} + 512 q^{89} - 56 q^{91} + 472 q^{92} + 472 q^{94} + 64 q^{97} + 7 q^{98}+O(q^{100}) $ 8 * q - q^2 + 5 * q^4 - 13 * q^8 + 16 * q^10 + 32 * q^11 - 7 * q^14 - 71 * q^16 + 80 * q^17 + 56 * q^19 + 108 * q^20 + 66 * q^22 - 16 * q^25 - 24 * q^26 + 7 * q^28 + 19 * q^32 + 74 * q^34 - 56 * q^35 + 14 * q^38 + 84 * q^40 - 128 * q^41 - 50 * q^44 - 152 * q^46 - 56 * q^49 - 33 * q^50 + 132 * q^52 + 49 * q^56 + 24 * q^58 - 104 * q^59 - 120 * q^62 - 55 * q^64 + 72 * q^65 + 304 * q^67 + 190 * q^68 + 56 * q^70 - 112 * q^73 - 8 * q^74 + 70 * q^76 - 124 * q^80 + 450 * q^82 - 72 * q^83 - 210 * q^86 - 486 * q^88 + 512 * q^89 - 56 * q^91 + 472 * q^92 + 472 * q^94 + 64 * q^97 + 7 * q^98

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 $

$2$	1.67467	+	1.09337i	0.837337	+	0.546687i
$2$	1.67467	+	1.09337i	0.837337	+	0.546687i
$3$		0			0
$3$		0			0
$4$	1.60906	+	3.66209i	0.402266	+	0.915523i
$5$		−	5.73252i		−	1.14650i	−0.819379	−	0.573252i	$-0.805682\pi$
$5$		−	5.73252i		−	1.14650i	0.819379	−	0.573252i	$-0.194318\pi$
$6$		0			0
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	−1.30939	+	7.89212i	−0.163673	+	0.986515i
$9$		0			0
$10$	6.26779	−	9.60010i	0.626779	−	0.960010i
$11$	1.40065			0.127332			0.0636658	−	0.997971i	$-0.479721\pi$
$11$	1.40065			0.127332			0.0636658	+	0.997971i	$0.479721\pi$
$12$		0			0
$13$		−	19.0821i		−	1.46785i	−0.679228	−	0.733927i	$-0.737685\pi$
$13$		−	19.0821i		−	1.46785i	0.679228	−	0.733927i	$-0.262315\pi$
$14$	2.89280	−	4.43077i	0.206628	−	0.316484i
$15$		0			0
$16$	−10.8218	+	11.7851i	−0.676365	+	0.736567i
$17$	32.2699			1.89823			0.949114	−	0.314932i	$-0.101982\pi$
$17$	32.2699			1.89823			0.949114	+	0.314932i	$0.101982\pi$
$18$		0			0
$19$	12.5675			0.661446			0.330723	−	0.943728i	$-0.392707\pi$
$19$	12.5675			0.661446			0.330723	+	0.943728i	$0.392707\pi$
$20$	20.9930	−	9.22398i	1.04965	−	0.461199i
$21$		0			0
$22$	2.34563	+	1.53143i	0.106619	+	0.0696105i
$23$		−	15.8893i		−	0.690839i	−0.938448	−	0.345419i	$-0.887737\pi$
$23$		−	15.8893i		−	0.690839i	0.938448	−	0.345419i	$-0.112263\pi$
$24$		0			0
$25$	−7.86180			−0.314472
$26$	20.8639	−	31.9563i	0.802457	−	1.22909i
$27$		0			0
$28$	9.68898	−	4.25718i	0.346035	−	0.152042i
$29$			3.29194i			0.113515i	0.998388	+	0.0567576i	$0.0180762\pi$
$29$			3.29194i			0.113515i	−0.998388	+	0.0567576i	$0.981924\pi$
$30$		0			0
$31$			22.6705i			0.731306i	0.930751	+	0.365653i	$0.119154\pi$
$31$			22.6705i			0.731306i	−0.930751	+	0.365653i	$0.880846\pi$
$32$	−31.0085	+	7.90382i	−0.969017	+	0.246994i
$33$		0			0
$34$	54.0415	+	35.2831i	1.58946	+	1.03774i
$35$	−15.1668			−0.433338
$36$		0			0
$37$		−	54.1537i		−	1.46361i	−0.681512	−	0.731807i	$-0.738677\pi$
$37$		−	54.1537i		−	1.46361i	0.681512	−	0.731807i	$-0.261323\pi$
$38$	21.0464	+	13.7410i	0.553853	+	0.361604i
$39$		0			0
$40$	45.2417	+	7.50608i	1.13104	+	0.187652i
$41$	7.59607			0.185270			0.0926350	−	0.995700i	$-0.470471\pi$
$41$	7.59607			0.185270			0.0926350	+	0.995700i	$0.470471\pi$
$42$		0			0
$43$	−20.8478			−0.484833			−0.242417	−	0.970172i	$-0.577940\pi$
$43$	−20.8478			−0.484833			−0.242417	+	0.970172i	$0.577940\pi$
$44$	2.25373	+	5.12930i	0.0512211	+	0.116575i
$45$		0			0
$46$	17.3729	−	26.6094i	0.377673	−	0.578465i
$47$		−	21.6384i		−	0.460392i	−0.973144	−	0.230196i	$-0.926063\pi$
$47$		−	21.6384i		−	0.460392i	0.973144	−	0.230196i	$-0.0739367\pi$
$48$		0			0
$49$	−7.00000			−0.142857
$50$	−13.1659	−	8.59589i	−0.263319	−	0.171918i
$51$		0			0
$52$	69.8804	−	30.7043i	1.34385	−	0.590467i
$53$		−	0.356667i		−	0.00672957i	−0.999994	−	0.00336479i	$-0.998929\pi$
$53$		−	0.356667i		−	0.00672957i	0.999994	−	0.00336479i	$-0.00107105\pi$
$54$		0			0
$55$		−	8.02924i		−	0.145986i
$56$	20.8806	+	3.46431i	0.372867	+	0.0618627i
$57$		0			0
$58$	−3.59933	+	5.51293i	−0.0620574	+	0.0950505i
$59$	−26.8583			−0.455226			−0.227613	−	0.973752i	$-0.573092\pi$
$59$	−26.8583			−0.455226			−0.227613	+	0.973752i	$0.573092\pi$
$60$		0			0
$61$			86.2287i			1.41359i	0.707420	+	0.706793i	$0.249859\pi$
$61$			86.2287i			1.41359i	−0.707420	+	0.706793i	$0.750141\pi$
$62$	−24.7873	+	37.9656i	−0.399796	+	0.612349i
$63$		0			0
$64$	−60.5710	−	20.6676i	−0.946422	−	0.322932i
$65$	−109.389			−1.68290
$66$		0			0
$67$	114.523			1.70929			0.854646	−	0.519211i	$-0.173774\pi$
$67$	114.523			1.70929			0.854646	+	0.519211i	$0.173774\pi$
$68$	51.9243	+	118.175i	0.763592	+	1.73787i
$69$		0			0
$70$	−25.3995	−	16.5830i	−0.362850	−	0.236900i
$71$			104.792i			1.47594i	0.674834	+	0.737969i	$0.264215\pi$
$71$			104.792i			1.47594i	−0.674834	+	0.737969i	$0.735785\pi$
$72$		0			0
$73$	−24.3974			−0.334211			−0.167106	−	0.985939i	$-0.553442\pi$
$73$	−24.3974			−0.334211			−0.167106	+	0.985939i	$0.553442\pi$
$74$	59.2103	−	90.6898i	0.800140	−	1.22554i
$75$		0			0
$76$	20.2218	+	46.0232i	0.266077	+	0.605569i
$77$		−	3.70576i		−	0.0481268i
$78$		0			0
$79$			117.128i			1.48263i	0.671157	+	0.741315i	$0.265798\pi$
$79$			117.128i			1.48263i	−0.671157	+	0.741315i	$0.734202\pi$
$80$	67.5582	+	62.0364i	0.844477	+	0.775455i
$81$		0			0
$82$	12.7209	+	8.30535i	0.155133	+	0.101285i
$83$	−79.2706			−0.955067			−0.477534	−	0.878614i	$-0.658469\pi$
$83$	−79.2706			−0.955067			−0.477534	+	0.878614i	$0.658469\pi$
$84$		0			0
$85$		−	184.988i		−	2.17633i
$86$	−34.9133	−	22.7945i	−0.405969	−	0.265052i
$87$		0			0
$88$	−1.83399	+	11.0541i	−0.0208408	+	0.125614i
$89$	−2.66078			−0.0298964			−0.0149482	−	0.999888i	$-0.504758\pi$
$89$	−2.66078			−0.0298964			−0.0149482	+	0.999888i	$0.504758\pi$
$90$		0			0
$91$	−50.4865			−0.554797
$92$	58.1880	−	25.5669i	0.632479	−	0.277901i
$93$		0			0
$94$	23.6589	−	36.2373i	0.251691	−	0.385503i
$95$		−	72.0433i		−	0.758350i
$96$		0			0
$97$	−52.0930			−0.537042			−0.268521	−	0.963274i	$-0.586535\pi$
$97$	−52.0930			−0.537042			−0.268521	+	0.963274i	$0.586535\pi$
$98$	−11.7227	−	7.65362i	−0.119620	−	0.0780982i
$99$		0			0
$100$	−12.6501	−	28.7906i	−0.126501	−	0.287906i
$101$		−	91.4742i		−	0.905685i	−0.891591	−	0.452842i	$-0.850410\pi$
$101$		−	91.4742i		−	0.905685i	0.891591	−	0.452842i	$-0.149590\pi$
$102$		0			0
$103$			39.7891i			0.386302i	0.981169	+	0.193151i	$0.0618708\pi$
$103$			39.7891i			0.386302i	−0.981169	+	0.193151i	$0.938129\pi$
$104$	150.598	+	24.9858i	1.44806	+	0.240248i
$105$		0			0
$106$	0.389971	−	0.597301i	0.00367897	−	0.00563492i
$107$	−82.6631			−0.772552			−0.386276	−	0.922383i	$-0.626239\pi$
$107$	−82.6631			−0.772552			−0.386276	+	0.922383i	$0.626239\pi$
$108$		0			0
$109$		−	29.4719i		−	0.270384i	−0.990819	−	0.135192i	$-0.956835\pi$
$109$		−	29.4719i		−	0.270384i	0.990819	−	0.135192i	$-0.0431652\pi$
$110$	8.77897	−	13.4463i	0.0798088	−	0.122240i
$111$		0			0
$112$	31.1804	+	28.6319i	0.278396	+	0.255642i
$113$	−159.133			−1.40826			−0.704130	−	0.710071i	$-0.748663\pi$
$113$	−159.133			−1.40826			−0.704130	+	0.710071i	$0.748663\pi$
$114$		0			0
$115$	−91.0857			−0.792049
$116$	−12.0554	+	5.29694i	−0.103926	+	0.0456633i
$117$		0			0
$118$	−44.9789	−	29.3662i	−0.381177	−	0.248866i
$119$		−	85.3781i		−	0.717463i
$120$		0			0
$121$	−119.038			−0.983787
$122$	−94.2803	+	144.405i	−0.772790	+	1.18365i
$123$		0			0
$124$	−83.0214	+	36.4782i	−0.669527	+	0.294179i
$125$		−	98.2451i		−	0.785961i
$126$		0			0
$127$			16.0834i			0.126641i	0.997993	+	0.0633205i	$0.0201690\pi$
$127$			16.0834i			0.126641i	−0.997993	+	0.0633205i	$0.979831\pi$
$128$	−78.8392	−	100.838i	−0.615931	−	0.787800i
$129$		0			0
$130$	−183.190	−	119.603i	−1.40915	−	0.920021i
$131$	118.136			0.901799			0.450899	−	0.892575i	$-0.351103\pi$
$131$	118.136			0.901799			0.450899	+	0.892575i	$0.351103\pi$
$132$		0			0
$133$		−	33.2504i		−	0.250003i
$134$	191.788	+	125.216i	1.43125	+	0.934448i
$135$		0			0
$136$	−42.2537	+	254.678i	−0.310689	+	1.87263i
$137$	19.1708			0.139933			0.0699664	−	0.997549i	$-0.477711\pi$
$137$	19.1708			0.139933			0.0699664	+	0.997549i	$0.477711\pi$
$138$		0			0
$139$	104.954			0.755062			0.377531	−	0.925997i	$-0.376773\pi$
$139$	104.954			0.755062			0.377531	+	0.925997i	$0.376773\pi$
$140$	−24.4044	−	55.5423i	−0.174317	−	0.396731i
$141$		0			0
$142$	−114.577	+	175.492i	−0.806877	+	1.23586i
$143$		−	26.7273i		−	0.186904i
$144$		0			0
$145$	18.8711			0.130146
$146$	−40.8577	−	26.6755i	−0.279847	−	0.182709i
$147$		0			0
$148$	198.316	−	87.1367i	1.33997	−	0.588762i
$149$			82.3906i			0.552957i	0.961020	+	0.276478i	$0.0891674\pi$
$149$			82.3906i			0.552957i	−0.961020	+	0.276478i	$0.910833\pi$
$150$		0			0
$151$		−	57.7395i		−	0.382381i	−0.981553	−	0.191190i	$-0.938765\pi$
$151$		−	57.7395i		−	0.382381i	0.981553	−	0.191190i	$-0.0612347\pi$
$152$	−16.4557	+	99.1840i	−0.108261	+	0.652526i
$153$		0			0
$154$	4.05179	−	6.20594i	0.0263103	−	0.0402983i
$155$	129.959			0.838445
$156$		0			0
$157$			3.72975i			0.0237564i	0.999929	+	0.0118782i	$0.00378104\pi$
$157$			3.72975i			0.0237564i	−0.999929	+	0.0118782i	$0.996219\pi$
$158$	−128.065	+	196.151i	−0.810536	+	1.24146i
$159$		0			0
$160$	45.3088	+	177.757i	0.283180	+	1.11098i
$161$	−42.0391			−0.261112
$162$		0			0
$163$	77.7069			0.476729			0.238365	−	0.971176i	$-0.423389\pi$
$163$	77.7069			0.476729			0.238365	+	0.971176i	$0.423389\pi$
$164$	12.2225	+	27.8175i	0.0745277	+	0.169619i
$165$		0			0
$166$	−132.752	−	86.6724i	−0.799713	−	0.522123i
$167$		−	62.0837i		−	0.371759i	−0.982573	−	0.185879i	$-0.940487\pi$
$167$		−	62.0837i		−	0.371759i	0.982573	−	0.185879i	$-0.0595133\pi$
$168$		0			0
$169$	−195.127			−1.15459
$170$	202.261	−	309.794i	1.18977	−	1.82232i
$171$		0			0
$172$	−33.5455	−	76.3467i	−0.195032	−	0.443876i
$173$			195.614i			1.13072i	0.824846	+	0.565358i	$0.191262\pi$
$173$			195.614i			1.13072i	−0.824846	+	0.565358i	$0.808738\pi$
$174$		0			0
$175$			20.8004i			0.118859i
$176$	−15.1576	+	16.5067i	−0.0861225	+	0.0937882i
$177$		0			0
$178$	−4.45594	−	2.90923i	−0.0250334	−	0.0163440i
$179$	−72.2099			−0.403407			−0.201704	−	0.979447i	$-0.564648\pi$
$179$	−72.2099			−0.403407			−0.201704	+	0.979447i	$0.564648\pi$
$180$		0			0
$181$		−	140.980i		−	0.778895i	−0.921049	−	0.389448i	$-0.872666\pi$
$181$		−	140.980i		−	0.778895i	0.921049	−	0.389448i	$-0.127334\pi$
$182$	−84.5484	−	55.2007i	−0.464552	−	0.303300i
$183$		0			0
$184$	125.400	+	20.8052i	0.681522	+	0.113072i
$185$	−310.437			−1.67804
$186$		0			0
$187$	45.1987			0.241704
$188$	79.2419	−	34.8176i	0.421499	−	0.185200i
$189$		0			0
$190$	78.7703	−	120.649i	0.414581	−	0.634995i
$191$			284.473i			1.48939i	0.667407	+	0.744693i	$0.267404\pi$
$191$			284.473i			1.48939i	−0.667407	+	0.744693i	$0.732596\pi$
$192$		0			0
$193$	−123.850			−0.641710			−0.320855	−	0.947128i	$-0.603970\pi$
$193$	−123.850			−0.641710			−0.320855	+	0.947128i	$0.603970\pi$
$194$	−87.2388	−	56.9572i	−0.449685	−	0.293594i
$195$		0			0
$196$	−11.2634	−	25.6346i	−0.0574665	−	0.130789i
$197$		−	108.098i		−	0.548721i	−0.961627	−	0.274361i	$-0.911534\pi$
$197$		−	108.098i		−	0.548721i	0.961627	−	0.274361i	$-0.0884662\pi$
$198$		0			0
$199$			331.854i			1.66761i	0.552060	+	0.833804i	$0.313842\pi$
$199$			331.854i			1.66761i	−0.552060	+	0.833804i	$0.686158\pi$
$200$	10.2941	−	62.0462i	0.0514706	−	0.310231i
$201$		0			0
$202$	100.016	−	153.189i	0.495127	−	0.758363i
$203$	8.70966			0.0429047
$204$		0			0
$205$		−	43.5446i		−	0.212413i
$206$	−43.5044	+	66.6338i	−0.211187	+	0.323465i
$207$		0			0
$208$	224.884	+	206.503i	1.08117	+	0.992805i
$209$	17.6026			0.0842229
$210$		0			0
$211$	26.3950			0.125095			0.0625475	−	0.998042i	$-0.480078\pi$
$211$	26.3950			0.125095			0.0625475	+	0.998042i	$0.480078\pi$
$212$	1.30615	−	0.573900i	0.00616108	−	0.00270708i
$213$		0			0
$214$	−138.434	−	90.3818i	−0.646887	−	0.422345i
$215$			119.511i			0.555864i
$216$		0			0
$217$	59.9804			0.276408
$218$	32.2238	−	49.3558i	0.147816	−	0.226403i
$219$		0			0
$220$	29.4038	−	12.9195i	0.133654	−	0.0587252i
$221$		−	615.777i		−	2.78632i
$222$		0			0
$223$		−	161.183i		−	0.722796i	−0.932412	−	0.361398i	$-0.882300\pi$
$223$		−	161.183i		−	0.722796i	0.932412	−	0.361398i	$-0.117700\pi$
$224$	20.9115	+	82.0409i	0.0933551	+	0.366254i
$225$		0			0
$226$	−266.497	−	173.993i	−1.17919	−	0.769879i
$227$	171.279			0.754533			0.377266	−	0.926105i	$-0.376864\pi$
$227$	171.279			0.754533			0.377266	+	0.926105i	$0.376864\pi$
$228$		0			0
$229$			229.251i			1.00110i	0.865709	+	0.500548i	$0.166868\pi$
$229$			229.251i			1.00110i	−0.865709	+	0.500548i	$0.833132\pi$
$230$	−152.539	−	99.5908i	−0.663212	−	0.433003i
$231$		0			0
$232$	−25.9804	−	4.31042i	−0.111984	−	0.0185794i
$233$	270.154			1.15946			0.579730	−	0.814808i	$-0.303158\pi$
$233$	270.154			1.15946			0.579730	+	0.814808i	$0.303158\pi$
$234$		0			0
$235$	−124.043			−0.527841
$236$	−43.2167	−	98.3576i	−0.183122	−	0.416770i
$237$		0			0
$238$	93.3503	−	142.980i	0.392228	−	0.600758i
$239$			157.155i			0.657551i	0.944408	+	0.328776i	$0.106636\pi$
$239$			157.155i			0.657551i	−0.944408	+	0.328776i	$0.893364\pi$
$240$		0			0
$241$	−97.7124			−0.405445			−0.202723	−	0.979236i	$-0.564979\pi$
$241$	−97.7124			−0.405445			−0.202723	+	0.979236i	$0.564979\pi$
$242$	−199.350	−	130.153i	−0.823761	−	0.537824i
$243$		0			0
$244$	−315.778	+	138.747i	−1.29417	+	0.568637i
$245$			40.1276i			0.163786i
$246$		0			0
$247$		−	239.814i		−	0.970906i
$248$	−178.918	−	29.6844i	−0.721444	−	0.119695i
$249$		0			0
$250$	107.419	−	164.528i	0.429675	−	0.658114i
$251$	313.145			1.24759			0.623796	−	0.781587i	$-0.285590\pi$
$251$	313.145			1.24759			0.623796	+	0.781587i	$0.285590\pi$
$252$		0			0
$253$		−	22.2553i		−	0.0879655i
$254$	−17.5852	+	26.9345i	−0.0692331	+	0.106041i
$255$		0			0
$256$	−21.7757	−	255.072i	−0.0850614	−	0.996376i
$257$	348.855			1.35741			0.678707	−	0.734409i	$-0.262541\pi$
$257$	348.855			1.35741			0.678707	+	0.734409i	$0.262541\pi$
$258$		0			0
$259$	−143.277			−0.553194
$260$	−176.013	−	400.591i	−0.676973	−	1.54073i
$261$		0			0
$262$	197.839	+	129.167i	0.755109	+	0.493002i
$263$			384.364i			1.46146i	0.682667	+	0.730729i	$0.260820\pi$
$263$			384.364i			1.46146i	−0.682667	+	0.730729i	$0.739180\pi$
$264$		0			0
$265$	−2.04460			−0.00771548
$266$	36.3552	−	55.6836i	0.136674	−	0.209337i
$267$		0			0
$268$	184.274	+	419.392i	0.687589	+	1.56490i
$269$			37.7613i			0.140376i	0.997534	+	0.0701882i	$0.0223600\pi$
$269$			37.7613i			0.140376i	−0.997534	+	0.0701882i	$0.977640\pi$
$270$		0			0
$271$			308.730i			1.13922i	0.821914	+	0.569612i	$0.192907\pi$
$271$			308.730i			1.13922i	−0.821914	+	0.569612i	$0.807093\pi$
$272$	−349.219	+	380.303i	−1.28389	+	1.39817i
$273$		0			0
$274$	32.1048	+	20.9609i	0.117171	+	0.0764995i
$275$	−11.0116			−0.0400422
$276$		0			0
$277$		−	244.210i		−	0.881623i	−0.897600	−	0.440812i	$-0.854691\pi$
$277$		−	244.210i		−	0.881623i	0.897600	−	0.440812i	$-0.145309\pi$
$278$	175.763	+	114.754i	0.632241	+	0.412783i
$279$		0			0
$280$	19.8592	−	119.698i	0.0709258	−	0.427494i
$281$	−266.569			−0.948646			−0.474323	−	0.880351i	$-0.657307\pi$
$281$	−266.569			−0.948646			−0.474323	+	0.880351i	$0.657307\pi$
$282$		0			0
$283$	165.605			0.585177			0.292589	−	0.956238i	$-0.405483\pi$
$283$	165.605			0.585177			0.292589	+	0.956238i	$0.405483\pi$
$284$	−383.757	+	168.616i	−1.35126	+	0.593719i
$285$		0			0
$286$	29.2229	−	44.7595i	0.102178	−	0.156502i
$287$		−	20.0973i		−	0.0700255i
$288$		0			0
$289$	752.346			2.60327
$290$	31.6030	+	20.6332i	0.108976	+	0.0711490i
$291$		0			0
$292$	−39.2570	−	89.3456i	−0.134442	−	0.305978i
$293$			34.3652i			0.117288i	0.998279	+	0.0586438i	$0.0186776\pi$
$293$			34.3652i			0.117288i	−0.998279	+	0.0586438i	$0.981322\pi$
$294$		0			0
$295$			153.966i			0.521918i
$296$	427.388	+	70.9081i	1.44388	+	0.239554i
$297$		0			0
$298$	−90.0838	+	137.977i	−0.302295	+	0.463011i
$299$	−303.201			−1.01405
$300$		0			0
$301$			55.1582i			0.183250i
$302$	63.1309	−	96.6947i	0.209043	−	0.320181i
$303$		0			0
$304$	−136.003	+	148.109i	−0.447379	+	0.487199i
$305$	494.308			1.62068
$306$		0			0
$307$	−222.934			−0.726170			−0.363085	−	0.931756i	$-0.618276\pi$
$307$	−222.934			−0.726170			−0.363085	+	0.931756i	$0.618276\pi$
$308$	13.5708	−	5.96280i	0.0440612	−	0.0193598i
$309$		0			0
$310$	217.639	+	142.094i	0.702061	+	0.458367i
$311$			419.934i			1.35027i	0.737694	+	0.675135i	$0.235915\pi$
$311$			419.934i			1.35027i	−0.737694	+	0.675135i	$0.764085\pi$
$312$		0			0
$313$	−293.869			−0.938878			−0.469439	−	0.882965i	$-0.655544\pi$
$313$	−293.869			−0.938878			−0.469439	+	0.882965i	$0.655544\pi$
$314$	−4.07802	+	6.24612i	−0.0129873	+	0.0198921i
$315$		0			0
$316$	−428.933	+	188.466i	−1.35738	+	0.596411i
$317$			423.461i			1.33584i	0.744234	+	0.667919i	$0.232815\pi$
$317$			423.461i			1.33584i	−0.744234	+	0.667919i	$0.767185\pi$
$318$		0			0
$319$			4.61085i			0.0144541i
$320$	−118.478	+	347.225i	−0.370243	+	1.08508i
$321$		0			0
$322$	−70.4018	−	45.9645i	−0.218639	−	0.142747i
$323$	405.551			1.25558
$324$		0			0
$325$			150.020i			0.461599i
$326$	130.134	+	84.9627i	0.399183	+	0.260622i
$327$		0			0
$328$	−9.94618	+	59.9491i	−0.0303237	+	0.182772i
$329$	−57.2499			−0.174012
$330$		0			0
$331$	−126.666			−0.382678			−0.191339	−	0.981524i	$-0.561283\pi$
$331$	−126.666			−0.382678			−0.191339	+	0.981524i	$0.561283\pi$
$332$	−127.551	−	290.296i	−0.384191	−	0.874386i
$333$		0			0
$334$	67.8807	−	103.970i	0.203236	−	0.311287i
$335$		−	656.503i		−	1.95971i
$336$		0			0
$337$	302.404			0.897341			0.448671	−	0.893697i	$-0.351898\pi$
$337$	302.404			0.897341			0.448671	+	0.893697i	$0.351898\pi$
$338$	−326.773	−	213.346i	−0.966785	−	0.631202i
$339$		0			0
$340$	677.442	−	297.657i	1.99248	−	0.875462i
$341$			31.7533i			0.0931183i
$342$		0			0
$343$			18.5203i			0.0539949i
$344$	27.2979	−	164.534i	0.0793542	−	0.478295i
$345$		0			0
$346$	−213.879	+	327.589i	−0.618148	+	0.946790i
$347$	−320.532			−0.923724			−0.461862	−	0.886952i	$-0.652818\pi$
$347$	−320.532			−0.923724			−0.461862	+	0.886952i	$0.652818\pi$
$348$		0			0
$349$		−	380.678i		−	1.09077i	−0.838186	−	0.545385i	$-0.816384\pi$
$349$		−	380.678i		−	1.09077i	0.838186	−	0.545385i	$-0.183616\pi$
$350$	−22.7426	+	34.8338i	−0.0649788	+	0.0995252i
$351$		0			0
$352$	−43.4320	+	11.0705i	−0.123386	+	0.0314502i
$353$	364.369			1.03221			0.516104	−	0.856526i	$-0.327382\pi$
$353$	364.369			1.03221			0.516104	+	0.856526i	$0.327382\pi$
$354$		0			0
$355$	600.720			1.69217
$356$	−4.28137	−	9.74403i	−0.0120263	−	0.0273709i
$357$		0			0
$358$	−120.928	−	78.9525i	−0.337788	−	0.220538i
$359$			111.995i			0.311965i	0.987760	+	0.155982i	$0.0498543\pi$
$359$			111.995i			0.311965i	−0.987760	+	0.155982i	$0.950146\pi$
$360$		0			0
$361$	−203.059			−0.562489
$362$	154.144	−	236.096i	0.425812	−	0.652198i
$363$		0			0
$364$	−81.2359	−	184.886i	−0.223176	−	0.507929i
$365$			139.859i			0.383174i
$366$		0			0
$367$			439.042i			1.19630i	0.801384	+	0.598150i	$0.204097\pi$
$367$			439.042i			1.19630i	−0.801384	+	0.598150i	$0.795903\pi$
$368$	187.256	+	171.951i	0.508849	+	0.467259i
$369$		0			0
$370$	−519.881	−	339.424i	−1.40508	−	0.917363i
$371$	−0.943653			−0.00254354
$372$		0			0
$373$			254.996i			0.683637i	0.939766	+	0.341818i	$0.111043\pi$
$373$			254.996i			0.683637i	−0.939766	+	0.341818i	$0.888957\pi$
$374$	75.6931	+	49.4191i	0.202388	+	0.132137i
$375$		0			0
$376$	170.773	+	28.3330i	0.454183	+	0.0753538i
$377$	62.8172			0.166624
$378$		0			0
$379$	603.048			1.59116			0.795578	−	0.605852i	$-0.207167\pi$
$379$	603.048			1.59116			0.795578	+	0.605852i	$0.207167\pi$
$380$	263.829	−	115.922i	0.694287	−	0.305058i
$381$		0			0
$382$	−311.035	+	476.399i	−0.814229	+	1.24712i
$383$		−	73.3855i		−	0.191607i	−0.995400	−	0.0958035i	$-0.969458\pi$
$383$		−	73.3855i		−	0.191607i	0.995400	−	0.0958035i	$-0.0305420\pi$
$384$		0			0
$385$	−21.2434			−0.0551776
$386$	−207.408	−	135.415i	−0.537328	−	0.350815i
$387$		0			0
$388$	−83.8209	−	190.769i	−0.216033	−	0.491674i
$389$		−	340.800i		−	0.876092i	−0.898953	−	0.438046i	$-0.855671\pi$
$389$		−	340.800i		−	0.876092i	0.898953	−	0.438046i	$-0.144329\pi$
$390$		0			0
$391$		−	512.745i		−	1.31137i
$392$	9.16570	−	55.2448i	0.0233819	−	0.140931i
$393$		0			0
$394$	118.192	−	181.029i	0.299979	−	0.459465i
$395$	671.438			1.69984
$396$		0			0
$397$		−	111.540i		−	0.280957i	−0.990084	−	0.140478i	$-0.955136\pi$
$397$		−	111.540i		−	0.280957i	0.990084	−	0.140478i	$-0.0448640\pi$
$398$	−362.841	+	555.747i	−0.911661	+	1.39635i
$399$		0			0
$400$	85.0791	−	92.6518i	0.212698	−	0.231630i
$401$	−340.535			−0.849215			−0.424607	−	0.905378i	$-0.639588\pi$
$401$	−340.535			−0.849215			−0.424607	+	0.905378i	$0.639588\pi$
$402$		0			0
$403$	432.600			1.07345
$404$	334.987	−	147.188i	0.829175	−	0.364326i
$405$		0			0
$406$	14.5858	+	9.52293i	0.0359257	+	0.0234555i
$407$		−	75.8502i		−	0.186364i
$408$		0			0
$409$	666.959			1.63071			0.815354	−	0.578963i	$-0.196543\pi$
$409$	666.959			1.63071			0.815354	+	0.578963i	$0.196543\pi$
$410$	47.6106	−	72.9230i	0.116123	−	0.177861i
$411$		0			0
$412$	−145.711	+	64.0232i	−0.353669	+	0.155396i
$413$			71.0604i			0.172059i
$414$		0			0
$415$			454.420i			1.09499i
$416$	150.821	+	591.708i	0.362552	+	1.42238i
$417$		0			0
$418$	29.4786	+	19.2462i	0.0705229	+	0.0460436i
$419$	200.191			0.477783			0.238891	−	0.971046i	$-0.423216\pi$
$419$	200.191			0.477783			0.238891	+	0.971046i	$0.423216\pi$
$420$		0			0
$421$		−	15.9136i		−	0.0377996i	−0.999821	−	0.0188998i	$-0.993984\pi$
$421$		−	15.9136i		−	0.0377996i	0.999821	−	0.0188998i	$-0.00601636\pi$
$422$	44.2031	+	28.8597i	0.104747	+	0.0683878i
$423$		0			0
$424$	2.81486	+	0.467015i	0.00663882	+	0.00110145i
$425$	−253.699			−0.596940
$426$		0			0
$427$	228.140			0.534285
$428$	−133.010	−	302.720i	−0.310771	−	0.707290i
$429$		0			0
$430$	−130.670	+	200.141i	−0.303884	+	0.465445i
$431$		−	628.013i		−	1.45711i	−0.684989	−	0.728553i	$-0.740193\pi$
$431$		−	628.013i		−	1.45711i	0.684989	−	0.728553i	$-0.259807\pi$
$432$		0			0
$433$	789.232			1.82271			0.911353	−	0.411625i	$-0.135039\pi$
$433$	789.232			1.82271			0.911353	+	0.411625i	$0.135039\pi$
$434$	100.448	+	65.5811i	0.231446	+	0.151109i
$435$		0			0
$436$	107.929	−	47.4221i	0.247543	−	0.108766i
$437$		−	199.688i		−	0.456952i
$438$		0			0
$439$		−	665.570i		−	1.51610i	−0.652194	−	0.758052i	$-0.726151\pi$
$439$		−	665.570i		−	1.51610i	0.652194	−	0.758052i	$-0.273849\pi$
$440$	63.3677	+	10.5134i	0.144017	+	0.0238940i
$441$		0			0
$442$	673.275	−	1031.23i	1.52325	−	2.33309i
$443$	−507.152			−1.14481			−0.572406	−	0.819970i	$-0.693990\pi$
$443$	−507.152			−1.14481			−0.572406	+	0.819970i	$0.693990\pi$
$444$		0			0
$445$			15.2530i			0.0342764i
$446$	176.234	−	269.930i	0.395143	−	0.605224i
$447$		0			0
$448$	−54.6815	+	160.256i	−0.122057	+	0.357714i
$449$	279.029			0.621446			0.310723	−	0.950501i	$-0.399429\pi$
$449$	279.029			0.621446			0.310723	+	0.950501i	$0.399429\pi$
$450$		0			0
$451$	10.6394			0.0235907
$452$	−256.056	−	582.761i	−0.566495	−	1.28930i
$453$		0			0
$454$	286.836	+	187.272i	0.631798	+	0.412494i
$455$			289.415i			0.636077i
$456$		0			0
$457$	−720.881			−1.57742			−0.788710	−	0.614765i	$-0.789251\pi$
$457$	−720.881			−1.57742			−0.788710	+	0.614765i	$0.789251\pi$
$458$	−250.657	+	383.921i	−0.547287	+	0.838255i
$459$		0			0
$460$	−146.563	−	333.564i	−0.318614	−	0.725139i
$461$			483.262i			1.04829i	0.851629	+	0.524145i	$0.175615\pi$
$461$			483.262i			1.04829i	−0.851629	+	0.524145i	$0.824385\pi$
$462$		0			0
$463$			39.6326i			0.0855995i	0.999084	+	0.0427997i	$0.0136277\pi$
$463$			39.6326i			0.0855995i	−0.999084	+	0.0427997i	$0.986372\pi$
$464$	−38.7958	−	35.6249i	−0.0836116	−	0.0767777i
$465$		0			0
$466$	452.420	+	295.380i	0.970859	+	0.633863i
$467$	−17.7868			−0.0380874			−0.0190437	−	0.999819i	$-0.506062\pi$
$467$	−17.7868			−0.0380874			−0.0190437	+	0.999819i	$0.506062\pi$
$468$		0			0
$469$		−	302.998i		−	0.646052i
$470$	−207.731	−	135.625i	−0.441981	−	0.288564i
$471$		0			0
$472$	35.1679	−	211.969i	0.0745083	−	0.449087i
$473$	−29.2005			−0.0617346
$474$		0			0
$475$	−98.8029			−0.208006
$476$	312.662	−	137.379i	0.656854	−	0.288611i
$477$		0			0
$478$	−171.829	+	263.183i	−0.359475	+	0.550592i
$479$		−	668.616i		−	1.39586i	−0.716166	−	0.697930i	$-0.754105\pi$
$479$		−	668.616i		−	1.39586i	0.716166	−	0.697930i	$-0.245895\pi$
$480$		0			0
$481$	−1033.37			−2.14837
$482$	−163.636	−	106.836i	−0.339494	−	0.221652i
$483$		0			0
$484$	−191.540	−	435.929i	−0.395744	−	0.900679i
$485$			298.624i			0.615720i
$486$		0			0
$487$		−	418.484i		−	0.859311i	−0.902993	−	0.429656i	$-0.858635\pi$
$487$		−	418.484i		−	0.859311i	0.902993	−	0.429656i	$-0.141365\pi$
$488$	−680.527	−	112.907i	−1.39452	−	0.231366i
$489$		0			0
$490$	−43.8746	+	67.2007i	−0.0895399	+	0.137144i
$491$	−381.031			−0.776030			−0.388015	−	0.921653i	$-0.626839\pi$
$491$	−381.031			−0.776030			−0.388015	+	0.921653i	$0.626839\pi$
$492$		0			0
$493$			106.231i			0.215478i
$494$	262.206	−	401.610i	0.530782	−	0.812975i
$495$		0			0
$496$	−267.173	−	245.336i	−0.538656	−	0.494629i
$497$	277.253			0.557852
$498$		0			0
$499$	−438.392			−0.878541			−0.439271	−	0.898355i	$-0.644763\pi$
$499$	−438.392			−0.878541			−0.439271	+	0.898355i	$0.644763\pi$
$500$	359.783	−	158.083i	0.719565	−	0.316165i
$501$		0			0
$502$	524.416	+	342.385i	1.04465	+	0.682043i
$503$		−	754.754i		−	1.50050i	−0.661151	−	0.750252i	$-0.729932\pi$
$503$		−	754.754i		−	1.50050i	0.661151	−	0.750252i	$-0.270068\pi$
$504$		0			0
$505$	−524.378			−1.03837
$506$	24.3334	−	37.2703i	0.0480896	−	0.0736568i
$507$		0			0
$508$	−58.8989	+	25.8792i	−0.115943	+	0.0509433i
$509$			494.029i			0.970588i	0.874351	+	0.485294i	$0.161287\pi$
$509$			494.029i			0.970588i	−0.874351	+	0.485294i	$0.838713\pi$
$510$		0			0
$511$			64.5495i			0.126320i
$512$	242.422	−	450.972i	0.473481	−	0.880804i
$513$		0			0
$514$	584.219	+	381.430i	1.13661	+	0.742081i
$515$	228.092			0.442897
$516$		0			0
$517$		−	30.3078i		−	0.0586224i
$518$	−239.943	−	156.656i	−0.463210	−	0.302424i
$519$		0			0
$520$	143.232	−	863.307i	0.275446	−	1.66021i
$521$	32.8747			0.0630993			0.0315496	−	0.999502i	$-0.489956\pi$
$521$	32.8747			0.0630993			0.0315496	+	0.999502i	$0.489956\pi$
$522$		0			0
$523$	−28.2755			−0.0540640			−0.0270320	−	0.999635i	$-0.508606\pi$
$523$	−28.2755			−0.0540640			−0.0270320	+	0.999635i	$0.508606\pi$
$524$	190.088	+	432.624i	0.362763	+	0.825617i
$525$		0			0
$526$	−420.254	+	643.684i	−0.798961	+	1.22373i
$527$			731.574i			1.38819i
$528$		0			0
$529$	276.531			0.522742
$530$	−3.42404	−	2.23552i	−0.00646046	−	0.00421796i
$531$		0			0
$532$	121.766	−	53.5020i	0.228884	−	0.100568i
$533$		−	144.949i		−	0.271949i
$534$		0			0
$535$			473.868i			0.885735i
$536$	−149.954	+	903.825i	−0.279765	+	1.68624i
$537$		0			0
$538$	−41.2872	+	63.2378i	−0.0767420	+	0.117542i
$539$	−9.80453			−0.0181902
$540$		0			0
$541$			1071.59i			1.98077i	0.138352	+	0.990383i	$0.455820\pi$
$541$			1071.59i			1.98077i	−0.138352	+	0.990383i	$0.544180\pi$
$542$	−337.558	+	517.022i	−0.622800	+	0.953915i
$543$		0			0
$544$	−1000.64	+	255.055i	−1.83942	+	0.468852i
$545$	−168.948			−0.309997
$546$		0			0
$547$	−986.888			−1.80418			−0.902091	−	0.431545i	$-0.857968\pi$
$547$	−986.888			−1.80418			−0.902091	+	0.431545i	$0.857968\pi$
$548$	30.8470	+	70.2052i	0.0562901	+	0.128112i
$549$		0			0
$550$	−18.4408	−	12.0398i	−0.0335288	−	0.0218906i
$551$			41.3714i			0.0750842i
$552$		0			0
$553$	309.891			0.560382
$554$	267.013	−	408.971i	0.481972	−	0.738215i
$555$		0			0
$556$	168.877	+	384.350i	0.303736	+	0.691277i
$557$			483.550i			0.868133i	0.900881	+	0.434067i	$0.142922\pi$
$557$			483.550i			0.868133i	−0.900881	+	0.434067i	$0.857078\pi$
$558$		0			0
$559$			397.821i			0.711665i
$560$	164.133	−	178.742i	0.293094	−	0.319182i
$561$		0			0
$562$	−446.417	−	291.460i	−0.794336	−	0.518613i
$563$	−520.893			−0.925210			−0.462605	−	0.886564i	$-0.653085\pi$
$563$	−520.893			−0.925210			−0.462605	+	0.886564i	$0.653085\pi$
$564$		0			0
$565$			912.236i			1.61458i
$566$	277.334	+	181.068i	0.489990	+	0.319909i
$567$		0			0
$568$	−827.028	−	137.213i	−1.45603	−	0.241572i
$569$	732.959			1.28815			0.644077	−	0.764961i	$-0.277242\pi$
$569$	732.959			1.28815			0.644077	+	0.764961i	$0.277242\pi$
$570$		0			0
$571$	−999.584			−1.75058			−0.875292	−	0.483595i	$-0.839331\pi$
$571$	−999.584			−1.75058			−0.875292	+	0.483595i	$0.839331\pi$
$572$	97.8777	−	43.0059i	0.171115	−	0.0751851i
$573$		0			0
$574$	21.9739	−	33.6564i	0.0382820	−	0.0586349i
$575$			124.918i			0.217249i
$576$		0			0
$577$	465.859			0.807381			0.403690	−	0.914896i	$-0.367727\pi$
$577$	465.859			0.807381			0.403690	+	0.914896i	$0.367727\pi$
$578$	1259.93	+	822.596i	2.17982	+	1.42318i
$579$		0			0
$580$	30.3648	+	69.1078i	0.0523531	+	0.119151i
$581$			209.730i			0.360981i
$582$		0			0
$583$		−	0.499565i		−	0.000856887i
$584$	31.9456	−	192.547i	0.0547014	−	0.329704i
$585$		0			0
$586$	−37.5741	+	57.5506i	−0.0641196	+	0.0982092i
$587$	574.851			0.979303			0.489651	−	0.871918i	$-0.337124\pi$
$587$	574.851			0.979303			0.489651	+	0.871918i	$0.337124\pi$
$588$		0			0
$589$			284.911i			0.483719i
$590$	−168.342	+	257.843i	−0.285326	+	0.437021i
$591$		0			0
$592$	638.205	+	586.043i	1.07805	+	0.989937i
$593$	−943.055			−1.59031			−0.795156	−	0.606405i	$-0.792611\pi$
$593$	−943.055			−1.59031			−0.795156	+	0.606405i	$0.792611\pi$
$594$		0			0
$595$	−489.432			−0.822574
$596$	−301.722	+	132.572i	−0.506245	+	0.222436i
$597$		0			0
$598$	−507.763	−	331.512i	−0.849101	−	0.554368i
$599$		−	9.26699i		−	0.0154708i	−0.999970	−	0.00773538i	$-0.997538\pi$
$599$		−	9.26699i		−	0.0154708i	0.999970	−	0.00773538i	$-0.00246227\pi$
$600$		0			0
$601$	57.7003			0.0960072			0.0480036	−	0.998847i	$-0.484714\pi$
$601$	57.7003			0.0960072			0.0480036	+	0.998847i	$0.484714\pi$
$602$	−60.3086	+	92.3720i	−0.100180	+	0.153442i
$603$		0			0
$604$	211.447	−	92.9064i	0.350078	−	0.153819i
$605$			682.389i			1.12792i
$606$		0			0
$607$		−	1024.68i		−	1.68810i	−0.536264	−	0.844050i	$-0.680165\pi$
$607$		−	1024.68i		−	1.68810i	0.536264	−	0.844050i	$-0.319835\pi$
$608$	−389.699	+	99.3310i	−0.640952	+	0.163373i
$609$		0			0
$610$	827.805	+	540.464i	1.35706	+	0.886007i
$611$	−412.906			−0.675788
$612$		0			0
$613$		−	404.818i		−	0.660389i	−0.943913	−	0.330195i	$-0.892886\pi$
$613$		−	404.818i		−	0.660389i	0.943913	−	0.330195i	$-0.107114\pi$
$614$	−373.342	−	243.750i	−0.608048	−	0.396988i
$615$		0			0
$616$	29.2463	+	4.85227i	0.0474778	+	0.00787707i
$617$	−894.209			−1.44928			−0.724642	−	0.689125i	$-0.757995\pi$
$617$	−894.209			−1.44928			−0.724642	+	0.689125i	$0.757995\pi$
$618$		0			0
$619$	−779.388			−1.25911			−0.629554	−	0.776957i	$-0.716762\pi$
$619$	−779.388			−1.25911			−0.629554	+	0.776957i	$0.716762\pi$
$620$	209.112	+	475.922i	0.337278	+	0.767616i
$621$		0			0
$622$	−459.145	+	703.252i	−0.738176	+	1.13063i
$623$			7.03977i			0.0112998i
$624$		0			0
$625$	−759.737			−1.21558
$626$	−492.134	−	321.309i	−0.786157	−	0.513273i
$627$		0			0
$628$	−13.6587	+	6.00140i	−0.0217495	+	0.00955638i
$629$		−	1747.53i		−	2.77827i
$630$		0			0
$631$		−	780.191i		−	1.23644i	−0.786007	−	0.618218i	$-0.787855\pi$
$631$		−	780.191i		−	1.23644i	0.786007	−	0.618218i	$-0.212145\pi$
$632$	−924.387	−	153.366i	−1.46264	−	0.242667i
$633$		0			0
$634$	−463.001	+	709.158i	−0.730286	+	1.11855i
$635$	92.1985			0.145194
$636$		0			0
$637$			133.575i			0.209693i
$638$	−5.04139	+	7.72166i	−0.00790186	+	0.0121029i
$639$		0			0
$640$	−578.058	+	451.947i	−0.903216	+	0.706168i
$641$	23.3139			0.0363712			0.0181856	−	0.999835i	$-0.494211\pi$
$641$	23.3139			0.0363712			0.0181856	+	0.999835i	$0.494211\pi$
$642$		0			0
$643$	530.706			0.825360			0.412680	−	0.910876i	$-0.364593\pi$
$643$	530.706			0.825360			0.412680	+	0.910876i	$0.364593\pi$
$644$	−67.6435	−	153.951i	−0.105037	−	0.239054i
$645$		0			0
$646$	679.165	+	443.419i	1.05134	+	0.686407i
$647$			213.435i			0.329883i	0.986303	+	0.164942i	$0.0527436\pi$
$647$			213.435i			0.329883i	−0.986303	+	0.164942i	$0.947256\pi$
$648$		0			0
$649$	−37.6190			−0.0579646
$650$	−164.028	+	251.234i	−0.252350	+	0.386514i
$651$		0			0
$652$	125.035	+	284.570i	0.191772	+	0.436457i
$653$		−	274.874i		−	0.420941i	−0.977600	−	0.210470i	$-0.932500\pi$
$653$		−	274.874i		−	0.420941i	0.977600	−	0.210470i	$-0.0674995\pi$
$654$		0			0
$655$		−	677.215i		−	1.03392i
$656$	−82.2034	+	89.5202i	−0.125310	+	0.136464i
$657$		0			0
$658$	−95.8749	−	62.5956i	−0.145706	−	0.0951301i
$659$	−1234.48			−1.87327			−0.936633	−	0.350313i	$-0.886075\pi$
$659$	−1234.48			−1.87327			−0.936633	+	0.350313i	$0.886075\pi$
$660$		0			0
$661$		−	582.733i		−	0.881593i	−0.897607	−	0.440797i	$-0.854696\pi$
$661$		−	582.733i		−	0.881593i	0.897607	−	0.440797i	$-0.145304\pi$
$662$	−212.125	−	138.494i	−0.320430	−	0.209205i
$663$		0			0
$664$	103.796	−	625.613i	0.156319	−	0.942188i
$665$	−190.609			−0.286630
$666$		0			0
$667$	52.3066			0.0784207
$668$	227.356	−	99.8965i	0.340353	−	0.149546i
$669$		0			0
$670$	717.804	−	1099.43i	1.07135	−	1.64094i
$671$			120.776i			0.179994i
$672$		0			0
$673$	−399.145			−0.593083			−0.296542	−	0.955020i	$-0.595833\pi$
$673$	−399.145			−0.593083			−0.296542	+	0.955020i	$0.595833\pi$
$674$	506.428	+	330.641i	0.751377	+	0.490565i
$675$		0			0
$676$	−313.971	−	714.571i	−0.464454	−	1.05706i
$677$		−	754.467i		−	1.11443i	−0.830369	−	0.557214i	$-0.811870\pi$
$677$		−	754.467i		−	1.11443i	0.830369	−	0.557214i	$-0.188130\pi$
$678$		0			0
$679$			137.825i			0.202983i
$680$	1459.95	+	242.220i	2.14698	+	0.356206i
$681$		0			0
$682$	−34.7183	+	53.1765i	−0.0509066	+	0.0779713i
$683$	−288.264			−0.422055			−0.211028	−	0.977480i	$-0.567681\pi$
$683$	−288.264			−0.422055			−0.211028	+	0.977480i	$0.567681\pi$
$684$		0			0
$685$		−	109.897i		−	0.160433i
$686$	−20.2496	+	31.0154i	−0.0295183	+	0.0452119i
$687$		0			0
$688$	225.612	−	245.693i	0.327924	−	0.357112i
$689$	−6.80596			−0.00987803
$690$		0			0
$691$	−156.692			−0.226761			−0.113380	−	0.993552i	$-0.536168\pi$
$691$	−156.692			−0.226761			−0.113380	+	0.993552i	$0.536168\pi$
$692$	−716.356	+	314.755i	−1.03520	+	0.454848i
$693$		0			0
$694$	−536.787	−	350.462i	−0.773468	−	0.504988i
$695$		−	601.649i		−	0.865682i
$696$		0			0
$697$	245.124			0.351685
$698$	416.224	−	637.512i	0.596310	−	0.913341i
$699$		0			0
$700$	−76.1728	+	33.4691i	−0.108818	+	0.0478130i
$701$			1126.50i			1.60700i	0.595307	+	0.803498i	$0.297030\pi$
$701$			1126.50i			1.60700i	−0.595307	+	0.803498i	$0.702970\pi$
$702$		0			0
$703$		−	680.575i		−	0.968102i
$704$	−84.8386	−	28.9481i	−0.120509	−	0.0411194i
$705$		0			0
$706$	610.200	+	398.392i	0.864306	+	0.564295i
$707$	−242.018			−0.342317
$708$		0			0
$709$		−	1096.17i		−	1.54608i	−0.634356	−	0.773041i	$-0.718734\pi$
$709$		−	1096.17i		−	1.54608i	0.634356	−	0.773041i	$-0.281266\pi$
$710$	1006.01	+	656.812i	1.41692	+	0.925088i
$711$		0			0
$712$	3.48399	−	20.9992i	0.00489325	−	0.0294933i
$713$	360.218			0.505214
$714$		0			0
$715$	−153.215			−0.214286
$716$	−116.190	−	264.439i	−0.162277	−	0.369328i
$717$		0			0
$718$	−122.453	+	187.556i	−0.170547	+	0.261220i
$719$		−	605.362i		−	0.841949i	−0.907072	−	0.420975i	$-0.861688\pi$
$719$		−	605.362i		−	0.841949i	0.907072	−	0.420975i	$-0.138312\pi$
$720$		0			0
$721$	105.272			0.146009
$722$	−340.057	−	222.019i	−0.470993	−	0.307506i
$723$		0			0
$724$	516.282	−	226.846i	0.713097	−	0.313323i
$725$		−	25.8806i		−	0.0356974i
$726$		0			0
$727$		−	443.659i		−	0.610260i	−0.952311	−	0.305130i	$-0.901300\pi$
$727$		−	443.659i		−	0.610260i	0.952311	−	0.305130i	$-0.0986999\pi$
$728$	66.1063	−	398.445i	0.0908053	−	0.547315i
$729$		0			0
$730$	−152.918	+	234.218i	−0.209477	+	0.320846i
$731$	−672.757			−0.920325
$732$		0			0
$733$			750.026i			1.02323i	0.859216	+	0.511614i	$0.170952\pi$
$733$			750.026i			1.02323i	−0.859216	+	0.511614i	$0.829048\pi$
$734$	−480.038	+	735.252i	−0.654002	+	1.00171i
$735$		0			0
$736$	125.586	+	492.704i	0.170633	+	0.669434i
$737$	160.406			0.217647
$738$		0			0
$739$	619.293			0.838015			0.419007	−	0.907983i	$-0.362378\pi$
$739$	619.293			0.838015			0.419007	+	0.907983i	$0.362378\pi$
$740$	−499.513	−	1136.85i	−0.675018	−	1.53628i
$741$		0			0
$742$	−1.58031	−	1.03177i	−0.00212980	−	0.00139052i
$743$			30.5255i			0.0410842i	0.999789	+	0.0205421i	$0.00653921\pi$
$743$			30.5255i			0.0410842i	−0.999789	+	0.0205421i	$0.993461\pi$
$744$		0			0
$745$	472.306			0.633967
$746$	−278.807	+	427.036i	−0.373736	+	0.572434i
$747$		0			0
$748$	72.7275	+	165.522i	0.0972293	+	0.221286i
$749$			218.706i			0.291997i
$750$		0			0
$751$			968.214i			1.28923i	0.764506	+	0.644616i	$0.222983\pi$
$751$			968.214i			1.28923i	−0.764506	+	0.644616i	$0.777017\pi$
$752$	255.010	+	234.167i	0.339109	+	0.311393i
$753$		0			0
$754$	105.198	+	68.6827i	0.139520	+	0.0910911i
$755$	−330.993			−0.438401
$756$		0			0
$757$			1171.15i			1.54710i	0.633736	+	0.773550i	$0.281521\pi$
$757$			1171.15i			1.54710i	−0.633736	+	0.773550i	$0.718479\pi$
$758$	1009.91	+	659.357i	1.33233	+	0.869865i
$759$		0			0
$760$	568.574	+	94.3325i	0.748124	+	0.124122i
$761$	−235.996			−0.310113			−0.155057	−	0.987906i	$-0.549556\pi$
$761$	−235.996			−0.310113			−0.155057	+	0.987906i	$0.549556\pi$
$762$		0			0
$763$	−77.9753			−0.102196
$764$	−1041.77	+	457.734i	−1.36357	+	0.599129i
$765$		0			0
$766$	80.2379	−	122.897i	0.104749	−	0.160440i
$767$			512.513i			0.668205i
$768$		0			0
$769$	−124.257			−0.161582			−0.0807912	−	0.996731i	$-0.525745\pi$
$769$	−124.257			−0.161582			−0.0807912	+	0.996731i	$0.525745\pi$
$770$	−35.5757	−	23.2270i	−0.0462022	−	0.0301649i
$771$		0			0
$772$	−199.283	−	453.550i	−0.258138	−	0.587501i
$773$			178.223i			0.230560i	0.993333	+	0.115280i	$0.0367765\pi$
$773$			178.223i			0.230560i	−0.993333	+	0.115280i	$0.963224\pi$
$774$		0			0
$775$		−	178.231i		−	0.229975i
$776$	68.2099	−	411.124i	0.0878993	−	0.529799i
$777$		0			0
$778$	372.622	−	570.728i	0.478948	−	0.733584i
$779$	95.4634			0.122546
$780$		0			0
$781$			146.776i			0.187933i
$782$	560.623	−	858.681i	0.716909	−	1.09806i
$783$		0			0
$784$	75.7529	−	82.4955i	0.0966235	−	0.105224i
$785$	21.3809			0.0272368
$786$		0			0
$787$	−1107.90			−1.40775			−0.703873	−	0.710326i	$-0.748547\pi$
$787$	−1107.90			−1.40775			−0.703873	+	0.710326i	$0.748547\pi$
$788$	395.865	−	173.937i	0.502367	−	0.220732i
$789$		0			0
$790$	1124.44	+	734.133i	1.42334	+	0.929283i
$791$			421.028i			0.532273i
$792$		0			0
$793$	1645.43			2.07494
$794$	121.955	−	186.793i	0.153595	−	0.235255i
$795$		0			0
$796$	−1215.28	+	533.974i	−1.52673	+	0.670821i
$797$		−	1094.69i		−	1.37351i	−0.726889	−	0.686755i	$-0.759034\pi$
$797$		−	1094.69i		−	1.37351i	0.726889	−	0.686755i	$-0.240966\pi$
$798$		0			0
$799$		−	698.269i		−	0.873929i
$800$	243.783	−	62.1382i	0.304729	−	0.0776728i
$801$		0			0
$802$	−570.285	−	372.332i	−0.711079	−	0.464255i
$803$	−34.1722			−0.0425556
$804$		0			0
$805$			240.990i			0.299367i
$806$	724.464	+	472.994i	0.898839	+	0.586842i
$807$		0			0
$808$	721.925	+	119.775i	0.893471	+	0.148236i
$809$	1386.75			1.71416			0.857079	−	0.515185i	$-0.172277\pi$
$809$	1386.75			1.71416			0.857079	+	0.515185i	$0.172277\pi$
$810$		0			0
$811$	−312.204			−0.384962			−0.192481	−	0.981301i	$-0.561653\pi$
$811$	−312.204			−0.384962			−0.192481	+	0.981301i	$0.561653\pi$
$812$	14.0144	+	31.8956i	0.0172591	+	0.0392803i
$813$		0			0
$814$	82.9328	−	127.024i	0.101883	−	0.156050i
$815$		−	445.456i		−	0.546572i
$816$		0			0
$817$	−262.005			−0.320691
$818$	1116.94	+	729.237i	1.36545	+	0.891487i
$819$		0			0
$820$	159.464	−	70.0660i	0.194469	−	0.0854464i
$821$		−	1092.89i		−	1.33117i	−0.746324	−	0.665583i	$-0.768183\pi$
$821$		−	1092.89i		−	1.33117i	0.746324	−	0.665583i	$-0.231817\pi$
$822$		0			0
$823$			907.162i			1.10226i	0.834419	+	0.551131i	$0.185804\pi$
$823$			907.162i			1.10226i	−0.834419	+	0.551131i	$0.814196\pi$
$824$	−314.020	−	52.0993i	−0.381093	−	0.0632273i
$825$		0			0
$826$	−77.6957	+	119.003i	−0.0940626	+	0.144071i
$827$	607.144			0.734152			0.367076	−	0.930191i	$-0.380359\pi$
$827$	607.144			0.734152			0.367076	+	0.930191i	$0.380359\pi$
$828$		0			0
$829$			427.969i			0.516247i	0.966112	+	0.258124i	$0.0831042\pi$
$829$			427.969i			0.516247i	−0.966112	+	0.258124i	$0.916896\pi$
$830$	−496.852	+	761.005i	−0.598616	+	0.916874i
$831$		0			0
$832$	−394.382	+	1155.82i	−0.474017	+	1.38921i
$833$	−225.889			−0.271176
$834$		0			0
$835$	−355.896			−0.426223
$836$	28.3237	+	64.4623i	0.0338800	+	0.0771080i
$837$		0			0
$838$	335.255	+	218.884i	0.400065	+	0.261198i
$839$		−	1133.09i		−	1.35053i	−0.737575	−	0.675265i	$-0.764029\pi$
$839$		−	1133.09i		−	1.35053i	0.737575	−	0.675265i	$-0.235971\pi$
$840$		0			0
$841$	830.163			0.987114
$842$	17.3996	−	26.6502i	0.0206646	−	0.0316510i
$843$		0			0
$844$	42.4712	+	96.6610i	0.0503214	+	0.114527i
$845$			1118.57i			1.32375i
$846$		0			0
$847$			314.945i			0.371836i
$848$	4.20335	+	3.85980i	0.00495678	+	0.00455165i
$849$		0			0
$850$	−424.864	−	277.388i	−0.499839	−	0.326339i
$851$	−860.464			−1.01112
$852$		0			0
$853$			169.502i			0.198712i	0.995052	+	0.0993562i	$0.0316783\pi$
$853$			169.502i			0.198712i	−0.995052	+	0.0993562i	$0.968322\pi$
$854$	382.060	+	249.442i	0.447377	+	0.292087i
$855$		0			0
$856$	108.238	−	652.387i	0.126446	−	0.762134i
$857$	234.079			0.273138			0.136569	−	0.990631i	$-0.456393\pi$
$857$	234.079			0.273138			0.136569	+	0.990631i	$0.456393\pi$
$858$		0			0
$859$	894.342			1.04114			0.520571	−	0.853818i	$-0.325719\pi$
$859$	894.342			1.04114			0.520571	+	0.853818i	$0.325719\pi$
$860$	−437.659	+	192.300i	−0.508906	+	0.223605i
$861$		0			0
$862$	686.654	−	1051.72i	0.796582	−	1.22009i
$863$			778.580i			0.902178i	0.892479	+	0.451089i	$0.148964\pi$
$863$			778.580i			0.902178i	−0.892479	+	0.451089i	$0.851036\pi$
$864$		0			0
$865$	1121.36			1.29637
$866$	1321.71	+	862.927i	1.52622	+	0.996451i
$867$		0			0
$868$	96.5123	+	219.654i	0.111189	+	0.253058i
$869$			164.055i			0.188786i
$870$		0			0
$871$		−	2185.33i		−	2.50899i
$872$	232.596	+	38.5901i	0.266738	+	0.0442547i
$873$		0			0
$874$	218.334	−	334.412i	0.249810	−	0.382623i
$875$	−259.932			−0.297065
$876$		0			0
$877$		−	17.2780i		−	0.0197013i	−0.999951	−	0.00985064i	$-0.996864\pi$
$877$		−	17.2780i		−	0.0197013i	0.999951	−	0.00985064i	$-0.00313561\pi$
$878$	727.717	−	1114.61i	0.828835	−	1.26949i
$879$		0			0
$880$	94.6251	+	86.8911i	0.107529	+	0.0987399i
$881$	−770.918			−0.875049			−0.437524	−	0.899207i	$-0.644145\pi$
$881$	−770.918			−0.875049			−0.437524	+	0.899207i	$0.644145\pi$
$882$		0			0
$883$	776.362			0.879232			0.439616	−	0.898186i	$-0.355114\pi$
$883$	776.362			0.879232			0.439616	+	0.898186i	$0.355114\pi$
$884$	2255.03	−	990.824i	2.55094	−	1.12084i
$885$		0			0
$886$	−849.313	−	554.507i	−0.958593	−	0.625854i
$887$			1630.80i			1.83856i	0.393603	+	0.919280i	$0.371228\pi$
$887$			1630.80i			1.83856i	−0.393603	+	0.919280i	$0.628772\pi$
$888$		0			0
$889$	42.5527			0.0478658
$890$	−16.6772	+	25.5438i	−0.0187385	+	0.0287009i
$891$		0			0
$892$	590.269	−	259.354i	0.661736	−	0.290756i
$893$		−	271.940i		−	0.304524i
$894$		0			0
$895$			413.945i			0.462508i
$896$	−266.793	+	208.589i	−0.297760	+	0.232800i
$897$		0			0
$898$	467.283	+	305.084i	0.520360	+	0.339737i
$899$	−74.6299			−0.0830144
$900$		0			0
$901$		−	11.5096i		−	0.0127743i
$902$	17.8175	+	11.6329i	0.0197534	+	0.0128967i
$903$		0			0
$904$	208.367	−	1255.90i	0.230495	−	1.38927i
$905$	−808.171			−0.893007
$906$		0			0
$907$	−953.863			−1.05167			−0.525834	−	0.850587i	$-0.676247\pi$
$907$	−953.863			−1.05167			−0.525834	+	0.850587i	$0.676247\pi$
$908$	275.598	+	627.239i	0.303523	+	0.690792i
$909$		0			0
$910$	−316.439	+	484.675i	−0.347735	+	0.532610i
$911$		−	1681.15i		−	1.84539i	−0.385534	−	0.922694i	$-0.625983\pi$
$911$		−	1681.15i		−	1.84539i	0.385534	−	0.922694i	$-0.374017\pi$
$912$		0			0
$913$	−111.030			−0.121610
$914$	−1207.24	−	788.194i	−1.32083	−	0.862356i
$915$		0			0
$916$	−839.538	+	368.879i	−0.916527	+	0.402707i
$917$		−	312.557i		−	0.340848i
$918$		0			0
$919$			504.991i			0.549500i	0.961516	+	0.274750i	$0.0885952\pi$
$919$			504.991i			0.549500i	−0.961516	+	0.274750i	$0.911405\pi$
$920$	119.266	−	718.859i	0.129637	−	0.781368i
$921$		0			0
$922$	−528.387	+	809.306i	−0.573088	+	0.877773i
$923$	1999.64			2.16646
$924$		0			0
$925$			425.746i			0.460266i
$926$	−43.3333	+	66.3716i	−0.0467962	+	0.0716756i
$927$		0			0
$928$	−26.0189	−	102.078i	−0.0280376	−	0.109998i
$929$	−983.851			−1.05904			−0.529521	−	0.848297i	$-0.677628\pi$
$929$	−983.851			−1.05904			−0.529521	+	0.848297i	$0.677628\pi$
$930$		0			0
$931$	−87.9723			−0.0944923
$932$	434.695	+	989.330i	0.466411	+	1.06151i
$933$		0			0
$934$	−29.7871	−	19.4476i	−0.0318919	−	0.0208219i
$935$		−	259.103i		−	0.277115i
$936$		0			0
$937$	−389.648			−0.415846			−0.207923	−	0.978145i	$-0.566670\pi$
$937$	−389.648			−0.415846			−0.207923	+	0.978145i	$0.566670\pi$
$938$	331.291	−	507.423i	0.353188	−	0.540963i
$939$		0			0
$940$	−199.592	−	454.256i	−0.212332	−	0.483251i
$941$		−	875.465i		−	0.930356i	−0.885217	−	0.465178i	$-0.845990\pi$
$941$		−	875.465i		−	0.930356i	0.885217	−	0.465178i	$-0.154010\pi$
$942$		0			0
$943$		−	120.696i		−	0.127992i
$944$	290.656	−	316.527i	0.307899	−	0.335304i
$945$		0			0
$946$	−48.9012	−	31.9270i	−0.0516926	−	0.0337495i
$947$	1251.29			1.32132			0.660661	−	0.750685i	$-0.270276\pi$
$947$	1251.29			1.32132			0.660661	+	0.750685i	$0.270276\pi$
$948$		0			0
$949$			465.554i			0.490573i
$950$	−165.463	−	108.029i	−0.174171	−	0.113714i
$951$		0			0
$952$	673.814	+	111.793i	0.707788	+	0.117429i
$953$	882.129			0.925633			0.462817	−	0.886454i	$-0.346839\pi$
$953$	882.129			0.925633			0.462817	+	0.886454i	$0.346839\pi$
$954$		0			0
$955$	1630.75			1.70759
$956$	−575.515	+	252.872i	−0.602003	+	0.264510i
$957$		0			0
$958$	731.049	−	1119.71i	0.763099	−	1.16880i
$959$		−	50.7211i		−	0.0528896i
$960$		0			0
$961$	447.049			0.465192
$962$	−1730.55	−	1129.86i	−1.79891	−	1.17449i
$963$		0			0
$964$	−157.225	−	357.832i	−0.163097	−	0.371195i
$965$			709.973i			0.735724i
$966$		0			0
$967$			1410.24i			1.45836i	0.684320	+	0.729182i	$0.260099\pi$
$967$			1410.24i			1.45836i	−0.684320	+	0.729182i	$0.739901\pi$
$968$	155.867	−	939.463i	0.161020	−	0.970520i
$969$		0			0
$970$	−326.508	+	500.098i	−0.336607	+	0.515565i
$971$	−678.550			−0.698815			−0.349408	−	0.936971i	$-0.613617\pi$
$971$	−678.550			−0.698815			−0.349408	+	0.936971i	$0.613617\pi$
$972$		0			0
$973$		−	277.681i		−	0.285387i
$974$	457.560	−	700.825i	0.469775	−	0.719533i
$975$		0			0
$976$	−1016.21	−	933.153i	−1.04120	−	0.956100i
$977$	−111.815			−0.114447			−0.0572235	−	0.998361i	$-0.518225\pi$
$977$	−111.815			−0.114447			−0.0572235	+	0.998361i	$0.518225\pi$
$978$		0			0
$979$	−3.72682			−0.00380676
$980$	−146.951	+	64.5679i	−0.149950	+	0.0658856i
$981$		0			0
$982$	−638.102	−	416.609i	−0.649798	−	0.424246i
$983$			202.226i			0.205723i	0.994696	+	0.102862i	$0.0327999\pi$
$983$			202.226i			0.205723i	−0.994696	+	0.102862i	$0.967200\pi$
$984$		0			0
$985$	−619.675			−0.629111
$986$	−116.150	+	177.902i	−0.117799	+	0.180428i
$987$		0			0
$988$	878.220	−	385.875i	0.888887	−	0.390562i
$989$			331.257i			0.334942i
$990$		0			0
$991$			189.064i			0.190781i	0.995440	+	0.0953907i	$0.0304100\pi$
$991$			189.064i			0.190781i	−0.995440	+	0.0953907i	$0.969590\pi$
$992$	−179.183	−	702.978i	−0.180628	−	0.708648i
$993$		0			0
$994$	464.308	+	303.141i	0.467110	+	0.304971i
$995$	1902.36			1.91192
$996$		0			0
$997$		−	1632.91i		−	1.63783i	−0.573917	−	0.818914i	$-0.694577\pi$
$997$		−	1632.91i		−	1.63783i	0.573917	−	0.818914i	$-0.305423\pi$
$998$	−734.164	−	479.327i	−0.735635	−	0.480288i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.g.b.379.8		8
3.2	odd	2		56.3.g.b.43.1	✓	8
4.3	odd	2		2016.3.g.b.1135.2		8
8.3	odd	2	inner	504.3.g.b.379.7		8
8.5	even	2		2016.3.g.b.1135.7		8
12.11	even	2		224.3.g.b.15.2		8
21.2	odd	6		392.3.k.o.67.5		16
21.5	even	6		392.3.k.n.67.5		16
21.11	odd	6		392.3.k.o.275.7		16
21.17	even	6		392.3.k.n.275.7		16
21.20	even	2		392.3.g.m.99.1		8
24.5	odd	2		224.3.g.b.15.1		8
24.11	even	2		56.3.g.b.43.2	yes	8
48.5	odd	4		1792.3.d.j.1023.3		16
48.11	even	4		1792.3.d.j.1023.13		16
48.29	odd	4		1792.3.d.j.1023.14		16
48.35	even	4		1792.3.d.j.1023.4		16
84.83	odd	2		1568.3.g.m.687.7		8
168.11	even	6		392.3.k.o.275.5		16
168.59	odd	6		392.3.k.n.275.5		16
168.83	odd	2		392.3.g.m.99.2		8
168.107	even	6		392.3.k.o.67.7		16
168.125	even	2		1568.3.g.m.687.8		8
168.131	odd	6		392.3.k.n.67.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.1	✓	8	3.2	odd	2
56.3.g.b.43.2	yes	8	24.11	even	2
224.3.g.b.15.1		8	24.5	odd	2
224.3.g.b.15.2		8	12.11	even	2
392.3.g.m.99.1		8	21.20	even	2
392.3.g.m.99.2		8	168.83	odd	2
392.3.k.n.67.5		16	21.5	even	6
392.3.k.n.67.7		16	168.131	odd	6
392.3.k.n.275.5		16	168.59	odd	6
392.3.k.n.275.7		16	21.17	even	6
392.3.k.o.67.5		16	21.2	odd	6
392.3.k.o.67.7		16	168.107	even	6
392.3.k.o.275.5		16	168.11	even	6
392.3.k.o.275.7		16	21.11	odd	6
504.3.g.b.379.7		8	8.3	odd	2	inner
504.3.g.b.379.8		8	1.1	even	1	trivial
1568.3.g.m.687.7		8	84.83	odd	2
1568.3.g.m.687.8		8	168.125	even	2
1792.3.d.j.1023.3		16	48.5	odd	4
1792.3.d.j.1023.4		16	48.35	even	4
1792.3.d.j.1023.13		16	48.11	even	4
1792.3.d.j.1023.14		16	48.29	odd	4
2016.3.g.b.1135.2		8	4.3	odd	2
2016.3.g.b.1135.7		8	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)

\(f(q)\)	\(=\)	\(q+(1.67467 + 1.09337i) q^{2} +(1.60906 + 3.66209i) q^{4} -5.73252i q^{5} -2.64575i q^{7} +(-1.30939 + 7.89212i) q^{8} +O(q^{10})\)	\(q+(1.67467 + 1.09337i) q^{2} +(1.60906 + 3.66209i) q^{4} -5.73252i q^{5} -2.64575i q^{7} +(-1.30939 + 7.89212i) q^{8} +(6.26779 - 9.60010i) q^{10} +1.40065 q^{11} -19.0821i q^{13} +(2.89280 - 4.43077i) q^{14} +(-10.8218 + 11.7851i) q^{16} +32.2699 q^{17} +12.5675 q^{19} +(20.9930 - 9.22398i) q^{20} +(2.34563 + 1.53143i) q^{22} -15.8893i q^{23} -7.86180 q^{25} +(20.8639 - 31.9563i) q^{26} +(9.68898 - 4.25718i) q^{28} +3.29194i q^{29} +22.6705i q^{31} +(-31.0085 + 7.90382i) q^{32} +(54.0415 + 35.2831i) q^{34} -15.1668 q^{35} -54.1537i q^{37} +(21.0464 + 13.7410i) q^{38} +(45.2417 + 7.50608i) q^{40} +7.59607 q^{41} -20.8478 q^{43} +(2.25373 + 5.12930i) q^{44} +(17.3729 - 26.6094i) q^{46} -21.6384i q^{47} -7.00000 q^{49} +(-13.1659 - 8.59589i) q^{50} +(69.8804 - 30.7043i) q^{52} -0.356667i q^{53} -8.02924i q^{55} +(20.8806 + 3.46431i) q^{56} +(-3.59933 + 5.51293i) q^{58} -26.8583 q^{59} +86.2287i q^{61} +(-24.7873 + 37.9656i) q^{62} +(-60.5710 - 20.6676i) q^{64} -109.389 q^{65} +114.523 q^{67} +(51.9243 + 118.175i) q^{68} +(-25.3995 - 16.5830i) q^{70} +104.792i q^{71} -24.3974 q^{73} +(59.2103 - 90.6898i) q^{74} +(20.2218 + 46.0232i) q^{76} -3.70576i q^{77} +117.128i q^{79} +(67.5582 + 62.0364i) q^{80} +(12.7209 + 8.30535i) q^{82} -79.2706 q^{83} -184.988i q^{85} +(-34.9133 - 22.7945i) q^{86} +(-1.83399 + 11.0541i) q^{88} -2.66078 q^{89} -50.4865 q^{91} +(58.1880 - 25.5669i) q^{92} +(23.6589 - 36.2373i) q^{94} -72.0433i q^{95} -52.0930 q^{97} +(-11.7227 - 7.65362i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 5 q^{4} - 13 q^{8}+O(q^{10}) \) 8 * q - q^2 + 5 * q^4 - 13 * q^8	\( 8 q - q^{2} + 5 q^{4} - 13 q^{8} + 16 q^{10} + 32 q^{11} - 7 q^{14} - 71 q^{16} + 80 q^{17} + 56 q^{19} + 108 q^{20} + 66 q^{22} - 16 q^{25} - 24 q^{26} + 7 q^{28} + 19 q^{32} + 74 q^{34} - 56 q^{35} + 14 q^{38} + 84 q^{40} - 128 q^{41} - 50 q^{44} - 152 q^{46} - 56 q^{49} - 33 q^{50} + 132 q^{52} + 49 q^{56} + 24 q^{58} - 104 q^{59} - 120 q^{62} - 55 q^{64} + 72 q^{65} + 304 q^{67} + 190 q^{68} + 56 q^{70} - 112 q^{73} - 8 q^{74} + 70 q^{76} - 124 q^{80} + 450 q^{82} - 72 q^{83} - 210 q^{86} - 486 q^{88} + 512 q^{89} - 56 q^{91} + 472 q^{92} + 472 q^{94} + 64 q^{97} + 7 q^{98}+O(q^{100}) \) 8 * q - q^2 + 5 * q^4 - 13 * q^8 + 16 * q^10 + 32 * q^11 - 7 * q^14 - 71 * q^16 + 80 * q^17 + 56 * q^19 + 108 * q^20 + 66 * q^22 - 16 * q^25 - 24 * q^26 + 7 * q^28 + 19 * q^32 + 74 * q^34 - 56 * q^35 + 14 * q^38 + 84 * q^40 - 128 * q^41 - 50 * q^44 - 152 * q^46 - 56 * q^49 - 33 * q^50 + 132 * q^52 + 49 * q^56 + 24 * q^58 - 104 * q^59 - 120 * q^62 - 55 * q^64 + 72 * q^65 + 304 * q^67 + 190 * q^68 + 56 * q^70 - 112 * q^73 - 8 * q^74 + 70 * q^76 - 124 * q^80 + 450 * q^82 - 72 * q^83 - 210 * q^86 - 486 * q^88 + 512 * q^89 - 56 * q^91 + 472 * q^92 + 472 * q^94 + 64 * q^97 + 7 * q^98

Introduction

L-functions

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