LMFDB - Embedded newform 336.4.bj.f.95.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,4,Mod(95,336)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 3, 4])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("336.95"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,0,0,0,0,38] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			95.13
Character	$\chi$	$=$	336.95
Dual form			336.4.bj.f.191.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.74483 - 2.11816i) q^{3} +(7.60125 - 4.38858i) q^{5} +(3.39378 + 18.2067i) q^{7} +(18.0268 - 20.1006i) q^{9} +(12.1881 - 21.1105i) q^{11} +2.78841 q^{13} +(26.7709 - 36.9237i) q^{15} +(23.4934 + 13.5639i) q^{17} +(57.2288 - 33.0411i) q^{19} +(54.6675 + 79.1989i) q^{21} +(44.5496 + 77.1622i) q^{23} +(-23.9807 + 41.5357i) q^{25} +(42.9580 - 133.558i) q^{27} -77.3681i q^{29} +(76.0645 + 43.9159i) q^{31} +(13.1154 - 125.982i) q^{33} +(105.698 + 123.499i) q^{35} +(-107.685 - 186.516i) q^{37} +(13.2305 - 5.90629i) q^{39} -197.104i q^{41} -251.818i q^{43} +(48.8133 - 231.902i) q^{45} +(307.037 + 531.804i) q^{47} +(-319.964 + 123.579i) q^{49} +(140.203 + 14.5958i) q^{51} +(-254.789 - 147.102i) q^{53} -213.955i q^{55} +(201.555 - 277.994i) q^{57} +(78.1027 - 135.278i) q^{59} +(-215.445 - 373.162i) q^{61} +(427.144 + 259.991i) q^{63} +(21.1954 - 12.2372i) q^{65} +(414.998 + 239.599i) q^{67} +(374.822 + 271.759i) q^{69} +794.386 q^{71} +(-372.340 + 644.912i) q^{73} +(-25.8050 + 247.875i) q^{75} +(425.715 + 150.261i) q^{77} +(389.250 - 224.734i) q^{79} +(-79.0671 - 724.700i) q^{81} -1026.68 q^{83} +238.106 q^{85} +(-163.878 - 367.098i) q^{87} +(578.622 - 334.067i) q^{89} +(9.46326 + 50.7676i) q^{91} +(453.934 + 47.2568i) q^{93} +(290.007 - 502.307i) q^{95} -1674.05 q^{97} +(-204.619 - 625.543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 38 q^{7} - 70 q^{9} + 124 q^{13} - 462 q^{19} + 500 q^{21} + 566 q^{25} + 1266 q^{31} + 64 q^{33} + 338 q^{37} + 1254 q^{39} - 488 q^{45} - 206 q^{49} + 522 q^{51} + 2324 q^{57} - 340 q^{61} - 840 q^{63}+ \cdots - 3344 q^{97}+O(q^{100}) $ 28 * q + 38 * q^7 - 70 * q^9 + 124 * q^13 - 462 * q^19 + 500 * q^21 + 566 * q^25 + 1266 * q^31 + 64 * q^33 + 338 * q^37 + 1254 * q^39 - 488 * q^45 - 206 * q^49 + 522 * q^51 + 2324 * q^57 - 340 * q^61 - 840 * q^63 + 2934 * q^67 - 776 * q^69 + 2050 * q^73 - 1458 * q^75 + 2070 * q^79 + 910 * q^81 + 2400 * q^85 + 3132 * q^87 - 5170 * q^91 + 714 * q^93 - 3344 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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			0
$2$		0			0
$3$	4.74483	−	2.11816i	0.913143	−	0.407639i
$3$	4.74483	−	2.11816i	0.913143	−	0.407639i
$4$		0			0
$5$	7.60125	−	4.38858i	0.679877	−	0.392527i	−0.119932	−	0.992782i	$-0.538268\pi$
$5$	7.60125	−	4.38858i	0.679877	−	0.392527i	0.799809	+	0.600255i	$0.204934\pi$
$6$		0			0
$7$	3.39378	+	18.2067i	0.183247	+	0.983067i
$7$	3.39378	+	18.2067i	0.183247	+	0.983067i
$8$		0			0
$9$	18.0268	−	20.1006i	0.667660	−	0.744466i
$10$		0			0
$11$	12.1881	−	21.1105i	0.334078	−	0.578641i	−0.649229	−	0.760593i	$-0.724908\pi$
$11$	12.1881	−	21.1105i	0.334078	−	0.578641i	0.983307	+	0.181952i	$0.0582417\pi$
$12$		0			0
$13$	2.78841			0.0594897			0.0297449	−	0.999558i	$-0.490531\pi$
$13$	2.78841			0.0594897			0.0297449	+	0.999558i	$0.490531\pi$
$14$		0			0
$15$	26.7709	−	36.9237i	0.460815	−	0.635578i
$16$		0			0
$17$	23.4934	+	13.5639i	0.335176	+	0.193514i	0.658137	−	0.752898i	$-0.271345\pi$
$17$	23.4934	+	13.5639i	0.335176	+	0.193514i	−0.322961	+	0.946412i	$0.604678\pi$
$18$		0			0
$19$	57.2288	−	33.0411i	0.691010	−	0.398955i	−0.112980	−	0.993597i	$-0.536040\pi$
$19$	57.2288	−	33.0411i	0.691010	−	0.398955i	0.803990	+	0.594643i	$0.202706\pi$
$20$		0			0
$21$	54.6675	+	79.1989i	0.568068	+	0.822982i
$22$		0			0
$23$	44.5496	+	77.1622i	0.403880	+	0.699541i	0.994190	−	0.107636i	$-0.0343280\pi$
$23$	44.5496	+	77.1622i	0.403880	+	0.699541i	−0.590310	+	0.807176i	$0.700995\pi$
$24$		0			0
$25$	−23.9807	+	41.5357i	−0.191845	+	0.332286i
$26$		0			0
$27$	42.9580	−	133.558i	0.306196	−	0.951969i
$28$		0			0
$29$		−	77.3681i		−	0.495410i	−0.968835	−	0.247705i	$-0.920324\pi$
$29$		−	77.3681i		−	0.495410i	0.968835	−	0.247705i	$-0.0796764\pi$
$30$		0			0
$31$	76.0645	+	43.9159i	0.440696	+	0.254436i	0.703893	−	0.710306i	$-0.251443\pi$
$31$	76.0645	+	43.9159i	0.440696	+	0.254436i	−0.263197	+	0.964742i	$0.584777\pi$
$32$		0			0
$33$	13.1154	−	125.982i	0.0691845	−	0.664565i
$34$		0			0
$35$	105.698	+	123.499i	0.510466	+	0.596435i
$36$		0			0
$37$	−107.685	−	186.516i	−0.478468	−	0.828731i	0.521227	−	0.853418i	$-0.325474\pi$
$37$	−107.685	−	186.516i	−0.478468	−	0.828731i	−0.999695	+	0.0246870i	$0.992141\pi$
$38$		0			0
$39$	13.2305	−	5.90629i	0.0543226	−	0.0242504i
$40$		0			0
$41$		−	197.104i		−	0.750791i	−0.926865	−	0.375395i	$-0.877507\pi$
$41$		−	197.104i		−	0.750791i	0.926865	−	0.375395i	$-0.122493\pi$
$42$		0			0
$43$		−	251.818i		−	0.893067i	−0.894767	−	0.446533i	$-0.852658\pi$
$43$		−	251.818i		−	0.893067i	0.894767	−	0.446533i	$-0.147342\pi$
$44$		0			0
$45$	48.8133	−	231.902i	0.161704	−	0.768220i
$46$		0			0
$47$	307.037	+	531.804i	0.952893	+	1.65046i	0.739118	+	0.673576i	$0.235242\pi$
$47$	307.037	+	531.804i	0.952893	+	1.65046i	0.213775	+	0.976883i	$0.431424\pi$
$48$		0			0
$49$	−319.964	+	123.579i	−0.932841	+	0.360288i
$50$		0			0
$51$	140.203	+	14.5958i	0.384948	+	0.0400750i
$52$		0			0
$53$	−254.789	−	147.102i	−0.660339	−	0.381247i	0.132067	−	0.991241i	$-0.457839\pi$
$53$	−254.789	−	147.102i	−0.660339	−	0.381247i	−0.792406	+	0.609994i	$0.791172\pi$
$54$		0			0
$55$		−	213.955i		−	0.524539i
$56$		0			0
$57$	201.555	−	277.994i	0.468361	−	0.645986i
$58$		0			0
$59$	78.1027	−	135.278i	0.172341	−	0.298503i	−0.766897	−	0.641770i	$-0.778200\pi$
$59$	78.1027	−	135.278i	0.172341	−	0.298503i	0.939238	+	0.343267i	$0.111534\pi$
$60$		0			0
$61$	−215.445	−	373.162i	−0.452212	−	0.783254i	0.546311	−	0.837582i	$-0.316032\pi$
$61$	−215.445	−	373.162i	−0.452212	−	0.783254i	−0.998523	+	0.0543280i	$0.982698\pi$
$62$		0			0
$63$	427.144	+	259.991i	0.854207	+	0.519933i
$64$		0			0
$65$	21.1954	−	12.2372i	0.0404457	−	0.0233513i
$66$		0			0
$67$	414.998	+	239.599i	0.756718	+	0.436891i	0.828116	−	0.560557i	$-0.189413\pi$
$67$	414.998	+	239.599i	0.756718	+	0.436891i	−0.0713984	+	0.997448i	$0.522746\pi$
$68$		0			0
$69$	374.822	+	271.759i	0.653961	+	0.474143i
$70$		0			0
$71$	794.386			1.32783			0.663917	−	0.747806i	$-0.268893\pi$
$71$	794.386			1.32783			0.663917	+	0.747806i	$0.268893\pi$
$72$		0			0
$73$	−372.340	+	644.912i	−0.596974	+	1.03399i	0.396291	+	0.918125i	$0.370297\pi$
$73$	−372.340	+	644.912i	−0.596974	+	1.03399i	−0.993265	+	0.115865i	$0.963036\pi$
$74$		0			0
$75$	−25.8050	+	247.875i	−0.0397294	+	0.381628i
$76$		0			0
$77$	425.715	+	150.261i	0.630061	+	0.222387i
$78$		0			0
$79$	389.250	−	224.734i	0.554355	−	0.320057i	−0.196522	−	0.980499i	$-0.562965\pi$
$79$	389.250	−	224.734i	0.554355	−	0.320057i	0.750877	+	0.660442i	$0.229631\pi$
$80$		0			0
$81$	−79.0671	−	724.700i	−0.108460	−	0.994101i
$82$		0			0
$83$	−1026.68			−1.35775			−0.678875	−	0.734254i	$-0.737532\pi$
$83$	−1026.68			−1.35775			−0.678875	+	0.734254i	$0.737532\pi$
$84$		0			0
$85$	238.106			0.303838
$86$		0			0
$87$	−163.878	−	367.098i	−0.201949	−	0.452380i
$88$		0			0
$89$	578.622	−	334.067i	0.689144	−	0.397877i	−0.114148	−	0.993464i	$-0.536414\pi$
$89$	578.622	−	334.067i	0.689144	−	0.397877i	0.803291	+	0.595587i	$0.203080\pi$
$90$		0			0
$91$	9.46326	+	50.7676i	0.0109013	+	0.0584824i
$92$		0			0
$93$	453.934	+	47.2568i	0.506137	+	0.0526914i
$94$		0			0
$95$	290.007	−	502.307i	0.313201	−	0.542480i
$96$		0			0
$97$	−1674.05			−1.75231			−0.876156	−	0.482028i	$-0.839900\pi$
$97$	−1674.05			−1.75231			−0.876156	+	0.482028i	$0.839900\pi$
$98$		0			0
$99$	−204.619	−	625.543i	−0.207728	−	0.635045i
$100$		0			0
$101$	1218.79	+	703.669i	1.20073	+	0.693244i	0.960718	−	0.277525i	$-0.0895142\pi$
$101$	1218.79	+	703.669i	1.20073	+	0.693244i	0.240015	+	0.970769i	$0.422848\pi$
$102$		0			0
$103$	−1081.01	+	624.120i	−1.03412	+	0.597052i	−0.918164	−	0.396202i	$-0.870328\pi$
$103$	−1081.01	+	624.120i	−1.03412	+	0.597052i	−0.115961	+	0.993254i	$0.536995\pi$
$104$		0			0
$105$	763.112	+	362.098i	0.709258	+	0.336544i
$106$		0			0
$107$	−703.195	−	1217.97i	−0.635331	−	1.10043i	−0.986445	−	0.164093i	$-0.947530\pi$
$107$	−703.195	−	1217.97i	−0.635331	−	1.10043i	0.351114	−	0.936333i	$-0.385803\pi$
$108$		0			0
$109$	−400.519	+	693.719i	−0.351952	+	0.609599i	−0.986591	−	0.163210i	$-0.947815\pi$
$109$	−400.519	+	693.719i	−0.351952	+	0.609599i	0.634639	+	0.772808i	$0.281149\pi$
$110$		0			0
$111$	−906.018	−	656.893i	−0.774733	−	0.561707i
$112$		0			0
$113$		−	312.505i		−	0.260160i	−0.991504	−	0.130080i	$-0.958477\pi$
$113$		−	312.505i		−	0.260160i	0.991504	−	0.130080i	$-0.0415233\pi$
$114$		0			0
$115$	677.266	+	391.020i	0.549177	+	0.317068i
$116$		0			0
$117$	50.2662	−	56.0487i	0.0397189	−	0.0442881i
$118$		0			0
$119$	−167.222	+	473.770i	−0.128817	+	0.364962i
$120$		0			0
$121$	368.399	+	638.085i	0.276783	+	0.479403i
$122$		0			0
$123$	−417.496	−	935.223i	−0.306052	−	0.685579i
$124$		0			0
$125$			1518.11i			1.08627i
$126$		0			0
$127$			2205.83i			1.54122i	0.637305	+	0.770612i	$0.280049\pi$
$127$			2205.83i			1.54122i	−0.637305	+	0.770612i	$0.719951\pi$
$128$		0			0
$129$	−533.390	−	1194.83i	−0.364049	−	0.815498i
$130$		0			0
$131$	−188.937	−	327.249i	−0.126012	−	0.218258i	0.796116	−	0.605144i	$-0.206884\pi$
$131$	−188.937	−	327.249i	−0.126012	−	0.218258i	−0.922128	+	0.386885i	$0.873551\pi$
$132$		0			0
$133$	795.789	+	929.811i	0.518825	+	0.606202i
$134$		0			0
$135$	−259.594	−	1203.73i	−0.165498	−	0.767411i
$136$		0			0
$137$	−2751.92	−	1588.82i	−1.71615	−	0.990818i	−0.925675	−	0.378320i	$-0.876502\pi$
$137$	−2751.92	−	1588.82i	−1.71615	−	0.990818i	−0.790472	−	0.612498i	$-0.790165\pi$
$138$		0			0
$139$			2010.28i			1.22669i	0.789815	+	0.613345i	$0.210176\pi$
$139$			2010.28i			1.22669i	−0.789815	+	0.613345i	$0.789824\pi$
$140$		0			0
$141$	2583.28	+	1872.97i	1.54292	+	1.11867i
$142$		0			0
$143$	33.9855	−	58.8647i	0.0198742	−	0.0344232i
$144$		0			0
$145$	−339.536	−	588.094i	−0.194462	−	0.336818i
$146$		0			0
$147$	−1256.42	+	1264.10i	−0.704950	+	0.709257i
$148$		0			0
$149$	−2070.47	+	1195.39i	−1.13839	+	0.657249i	−0.946031	−	0.324076i	$-0.894947\pi$
$149$	−2070.47	+	1195.39i	−1.13839	+	0.657249i	−0.192357	+	0.981325i	$0.561613\pi$
$150$		0			0
$151$	1138.17	+	657.121i	0.613395	+	0.354144i	0.774293	−	0.632827i	$-0.218106\pi$
$151$	1138.17	+	657.121i	0.613395	+	0.354144i	−0.160898	+	0.986971i	$0.551439\pi$
$152$		0			0
$153$	696.156	−	227.717i	0.367849	−	0.120326i
$154$		0			0
$155$	770.914			0.399492
$156$		0			0
$157$	57.9218	−	100.323i	0.0294437	−	0.0509980i	−0.850928	−	0.525282i	$-0.823960\pi$
$157$	57.9218	−	100.323i	0.0294437	−	0.0509980i	0.880372	+	0.474284i	$0.157293\pi$
$158$		0			0
$159$	−1520.52	−	158.293i	−0.758395	−	0.0789527i
$160$		0			0
$161$	−1253.67	+	1072.97i	−0.613686	+	0.525230i
$162$		0			0
$163$	−1761.05	+	1016.74i	−0.846235	+	0.488574i	−0.859379	−	0.511340i	$-0.829149\pi$
$163$	−1761.05	+	1016.74i	−0.846235	+	0.488574i	0.0131437	+	0.999914i	$0.495816\pi$
$164$		0			0
$165$	−453.189	−	1015.18i	−0.213823	−	0.478979i
$166$		0			0
$167$	−4291.70			−1.98863			−0.994317	−	0.106457i	$-0.966049\pi$
$167$	−4291.70			−1.98863			−0.994317	+	0.106457i	$0.966049\pi$
$168$		0			0
$169$	−2189.22			−0.996461
$170$		0			0
$171$	367.509	−	1745.96i	0.164352	−	0.780800i
$172$		0			0
$173$	1813.17	−	1046.84i	0.796839	−	0.460055i	−0.0455258	−	0.998963i	$-0.514496\pi$
$173$	1813.17	−	1046.84i	0.796839	−	0.460055i	0.842365	+	0.538908i	$0.181163\pi$
$174$		0			0
$175$	−837.612	−	295.644i	−0.361814	−	0.127706i
$176$		0			0
$177$	84.0444	−	807.305i	0.0356902	−	0.342829i
$178$		0			0
$179$	−814.114	+	1410.09i	−0.339943	+	0.588798i	−0.984422	−	0.175824i	$-0.943741\pi$
$179$	−814.114	+	1410.09i	−0.339943	+	0.588798i	0.644479	+	0.764622i	$0.277074\pi$
$180$		0			0
$181$	−850.842			−0.349407			−0.174703	−	0.984621i	$-0.555897\pi$
$181$	−850.842			−0.349407			−0.174703	+	0.984621i	$0.555897\pi$
$182$		0			0
$183$	−1812.67	−	1314.24i	−0.732220	−	0.530884i
$184$		0			0
$185$	−1637.08	−	945.170i	−0.650598	−	0.375623i
$186$		0			0
$187$	572.683	−	330.639i	0.223950	−	0.129298i
$188$		0			0
$189$	2577.43	+	328.857i	0.991958	+	0.126565i
$190$		0			0
$191$	−944.455	−	1635.84i	−0.357792	−	0.619714i	0.629799	−	0.776758i	$-0.283137\pi$
$191$	−944.455	−	1635.84i	−0.357792	−	0.619714i	−0.987592	+	0.157043i	$0.949804\pi$
$192$		0			0
$193$	−2397.16	+	4152.00i	−0.894049	+	1.54854i	−0.0590708	+	0.998254i	$0.518814\pi$
$193$	−2397.16	+	4152.00i	−0.894049	+	1.54854i	−0.834978	+	0.550284i	$0.814520\pi$
$194$		0			0
$195$	74.6484	−	102.959i	0.0274138	−	0.0378103i
$196$		0			0
$197$			3853.03i			1.39349i	0.717321	+	0.696743i	$0.245368\pi$
$197$			3853.03i			1.39349i	−0.717321	+	0.696743i	$0.754632\pi$
$198$		0			0
$199$	−1716.62	−	991.091i	−0.611497	−	0.353048i	0.162054	−	0.986782i	$-0.448188\pi$
$199$	−1716.62	−	991.091i	−0.611497	−	0.353048i	−0.773551	+	0.633734i	$0.781521\pi$
$200$		0			0
$201$	2476.60	+	257.827i	0.869085	+	0.0904761i
$202$		0			0
$203$	1408.61	−	262.570i	0.487021	−	0.0907824i
$204$		0			0
$205$	−865.006	−	1498.23i	−0.294706	−	0.510445i
$206$		0			0
$207$	2354.09	+	495.516i	0.790439	+	0.166381i
$208$		0			0
$209$		−	1610.84i		−	0.533128i
$210$		0			0
$211$		−	762.088i		−	0.248646i	−0.992242	−	0.124323i	$-0.960324\pi$
$211$		−	762.088i		−	0.248646i	0.992242	−	0.124323i	$-0.0396759\pi$
$212$		0			0
$213$	3769.23	−	1682.63i	1.21250	−	0.541278i
$214$		0			0
$215$	−1105.12	−	1914.13i	−0.350553	−	0.607175i
$216$		0			0
$217$	−541.414	+	1533.92i	−0.169371	+	0.479859i
$218$		0			0
$219$	−400.666	+	3848.67i	−0.123628	+	1.18753i
$220$		0			0
$221$	65.5094	+	37.8219i	0.0199395	+	0.0115121i
$222$		0			0
$223$		−	384.858i		−	0.115570i	−0.998329	−	0.0577848i	$-0.981596\pi$
$223$		−	384.858i		−	0.115570i	0.998329	−	0.0577848i	$-0.0184037\pi$
$224$		0			0
$225$	402.597	+	1230.78i	0.119288	+	0.364676i
$226$		0			0
$227$	−634.801	+	1099.51i	−0.185609	+	0.321484i	−0.943782	−	0.330570i	$-0.892759\pi$
$227$	−634.801	+	1099.51i	−0.185609	+	0.321484i	0.758173	+	0.652054i	$0.226092\pi$
$228$		0			0
$229$	−343.776	−	595.437i	−0.0992024	−	0.171824i	0.812152	−	0.583445i	$-0.198296\pi$
$229$	−343.776	−	595.437i	−0.0992024	−	0.171824i	−0.911355	+	0.411622i	$0.864962\pi$
$230$		0			0
$231$	2338.22	−	188.769i	0.665990	−	0.0537665i
$232$		0			0
$233$	3084.40	−	1780.78i	0.867234	−	0.500698i	0.000805994	−	1.00000i	$-0.499743\pi$
$233$	3084.40	−	1780.78i	0.867234	−	0.500698i	0.866428	+	0.499302i	$0.166410\pi$
$234$		0			0
$235$	4667.73	+	2694.92i	1.29570	+	0.748072i
$236$		0			0
$237$	1370.90	−	1890.82i	0.375738	−	0.518235i
$238$		0			0
$239$	6005.30			1.62532			0.812658	−	0.582741i	$-0.198020\pi$
$239$	6005.30			1.62532			0.812658	+	0.582741i	$0.198020\pi$
$240$		0			0
$241$	568.914	−	985.388i	0.152062	−	0.263379i	−0.779923	−	0.625875i	$-0.784742\pi$
$241$	568.914	−	985.388i	0.152062	−	0.263379i	0.931985	+	0.362496i	$0.118075\pi$
$242$		0			0
$243$	−1910.19	−	3271.10i	−0.504274	−	0.863544i
$244$		0			0
$245$	−1889.79	+	2343.54i	−0.492794	+	0.611117i
$246$		0			0
$247$	159.577	−	92.1321i	0.0411080	−	0.0237337i
$248$		0			0
$249$	−4871.44	+	2174.68i	−1.23982	+	0.553473i
$250$		0			0
$251$	4620.63			1.16196			0.580980	−	0.813918i	$-0.302670\pi$
$251$	4620.63			1.16196			0.580980	+	0.813918i	$0.302670\pi$
$252$		0			0
$253$	2171.91			0.539710
$254$		0			0
$255$	1129.77	−	504.346i	0.277448	−	0.123856i
$256$		0			0
$257$	6191.64	−	3574.75i	1.50282	−	0.867652i	0.502823	−	0.864389i	$-0.332295\pi$
$257$	6191.64	−	3574.75i	1.50282	−	0.867652i	0.999995	−	0.00326261i	$-0.00103852\pi$
$258$		0			0
$259$	3030.37	−	2593.58i	0.727020	−	0.622229i
$260$		0			0
$261$	−1555.14	−	1394.70i	−0.368816	−	0.330766i
$262$		0			0
$263$	−1809.48	+	3134.11i	−0.424248	+	0.734819i	−0.996350	−	0.0853634i	$-0.972795\pi$
$263$	−1809.48	+	3134.11i	−0.424248	+	0.734819i	0.572102	+	0.820183i	$0.306128\pi$
$264$		0			0
$265$	−2582.29			−0.598599
$266$		0			0
$267$	2037.85	−	2810.70i	0.467096	−	0.644241i
$268$		0			0
$269$	5220.52	+	3014.07i	1.18327	+	0.683164i	0.956770	−	0.290847i	$-0.0939369\pi$
$269$	5220.52	+	3014.07i	1.18327	+	0.683164i	0.226504	+	0.974010i	$0.427270\pi$
$270$		0			0
$271$	608.576	−	351.362i	0.136415	−	0.0787591i	−0.430239	−	0.902715i	$-0.641571\pi$
$271$	608.576	−	351.362i	0.136415	−	0.0787591i	0.566654	+	0.823956i	$0.308238\pi$
$272$		0			0
$273$	152.435	+	220.839i	0.0337942	+	0.0489590i
$274$		0			0
$275$	584.559	+	1012.49i	0.128183	+	0.222019i
$276$		0			0
$277$	−1253.40	+	2170.96i	−0.271876	+	0.470903i	−0.969342	−	0.245715i	$-0.920977\pi$
$277$	−1253.40	+	2170.96i	−0.271876	+	0.470903i	0.697466	+	0.716618i	$0.254311\pi$
$278$		0			0
$279$	2253.94	−	737.277i	0.483655	−	0.158207i
$280$		0			0
$281$		−	2033.41i		−	0.431684i	−0.976428	−	0.215842i	$-0.930750\pi$
$281$		−	2033.41i		−	0.431684i	0.976428	−	0.215842i	$-0.0692497\pi$
$282$		0			0
$283$	−1275.45	−	736.382i	−0.267907	−	0.154676i	0.360029	−	0.932941i	$-0.382767\pi$
$283$	−1275.45	−	736.382i	−0.267907	−	0.154676i	−0.627936	+	0.778265i	$0.716100\pi$
$284$		0			0
$285$	312.069	−	2997.64i	0.0648610	−	0.623035i
$286$		0			0
$287$	3588.60	−	668.927i	0.738077	−	0.137580i
$288$		0			0
$289$	−2088.54	−	3617.45i	−0.425105	−	0.736303i
$290$		0			0
$291$	−7943.09	+	3545.90i	−1.60011	+	0.714311i
$292$		0			0
$293$		−	7744.68i		−	1.54420i	−0.635504	−	0.772098i	$-0.719208\pi$
$293$		−	7744.68i		−	1.54420i	0.635504	−	0.772098i	$-0.280792\pi$
$294$		0			0
$295$		−	1371.04i		−	0.270594i
$296$		0			0
$297$	−2295.88	−	2534.68i	−0.448554	−	0.495209i
$298$		0			0
$299$	124.223	+	215.160i	0.0240267	+	0.0416155i
$300$		0			0
$301$	4584.76	−	854.615i	0.877945	−	0.163652i
$302$		0			0
$303$	7273.43	+	757.200i	1.37904	+	0.143564i
$304$		0			0
$305$	−3275.31	−	1891.00i	−0.614897	−	0.355011i
$306$		0			0
$307$			1959.84i			0.364344i	0.983267	+	0.182172i	$0.0583128\pi$
$307$			1959.84i			0.364344i	−0.983267	+	0.182172i	$0.941687\pi$
$308$		0			0
$309$	−3807.21	+	5251.09i	−0.700922	+	0.966744i
$310$		0			0
$311$	−1502.61	+	2602.60i	−0.273972	+	0.474533i	−0.969875	−	0.243602i	$-0.921671\pi$
$311$	−1502.61	+	2602.60i	−0.273972	+	0.474533i	0.695903	+	0.718135i	$0.255004\pi$
$312$		0			0
$313$	−4305.63	−	7457.56i	−0.777535	−	1.34673i	−0.933359	−	0.358945i	$-0.883137\pi$
$313$	−4305.63	−	7457.56i	−0.777535	−	1.34673i	0.155824	−	0.987785i	$-0.450197\pi$
$314$		0			0
$315$	4387.82	+	101.703i	0.784843	+	0.0181914i
$316$		0			0
$317$	2090.67	−	1207.05i	0.370422	−	0.213863i	−0.303221	−	0.952920i	$-0.598062\pi$
$317$	2090.67	−	1207.05i	0.370422	−	0.213863i	0.673643	+	0.739057i	$0.264729\pi$
$318$		0			0
$319$	−1633.28	−	942.973i	−0.286664	−	0.165506i
$320$		0			0
$321$	−5916.39	−	4289.58i	−1.02872	−	0.745860i
$322$		0			0
$323$	1792.67			0.308814
$324$		0			0
$325$	−66.8680	+	115.819i	−0.0114128	+	0.0197676i
$326$		0			0
$327$	−430.989	+	4139.94i	−0.0728860	+	0.700120i
$328$		0			0
$329$	−8640.35	+	7394.94i	−1.44790	+	1.23920i
$330$		0			0
$331$	1812.45	−	1046.42i	0.300970	−	0.173765i	−0.341909	−	0.939733i	$-0.611073\pi$
$331$	1812.45	−	1046.42i	0.300970	−	0.173765i	0.642879	+	0.765968i	$0.277740\pi$
$332$		0			0
$333$	−5690.30	−	1197.76i	−0.936416	−	0.197107i
$334$		0			0
$335$	4206.01			0.685966
$336$		0			0
$337$	11050.9			1.78629			0.893143	−	0.449773i	$-0.148495\pi$
$337$	11050.9			1.78629			0.893143	+	0.449773i	$0.148495\pi$
$338$		0			0
$339$	−661.935	−	1482.78i	−0.106051	−	0.237563i
$340$		0			0
$341$	1854.17	−	1070.50i	0.294454	−	0.170003i
$342$		0			0
$343$	−3335.85	−	5406.08i	−0.525128	−	0.851023i
$344$		0			0
$345$	4041.75	+	420.767i	0.630727	+	0.0656618i
$346$		0			0
$347$	−5378.34	+	9315.56i	−0.832059	+	1.44117i	0.0643444	+	0.997928i	$0.479504\pi$
$347$	−5378.34	+	9315.56i	−0.832059	+	1.44117i	−0.896403	+	0.443240i	$0.853829\pi$
$348$		0			0
$349$	−559.037			−0.0857438			−0.0428719	−	0.999081i	$-0.513651\pi$
$349$	−559.037			−0.0857438			−0.0428719	+	0.999081i	$0.513651\pi$
$350$		0			0
$351$	119.785	−	372.413i	0.0182155	−	0.0566323i
$352$		0			0
$353$	333.482	+	192.536i	0.0502818	+	0.0290302i	0.524930	−	0.851145i	$-0.324091\pi$
$353$	333.482	+	192.536i	0.0502818	+	0.0290302i	−0.474648	+	0.880176i	$0.657425\pi$
$354$		0			0
$355$	6038.32	−	3486.23i	0.902763	−	0.521211i
$356$		0			0
$357$	210.077	+	2602.16i	0.0311442	+	0.385773i
$358$		0			0
$359$	2671.75	+	4627.60i	0.392784	+	0.680322i	0.992816	−	0.119655i	$-0.0381787\pi$
$359$	2671.75	+	4627.60i	0.392784	+	0.680322i	−0.600032	+	0.799976i	$0.704845\pi$
$360$		0			0
$361$	−1246.08	+	2158.27i	−0.181670	+	0.314662i
$362$		0			0
$363$	3099.55	+	2247.28i	0.448166	+	0.324936i
$364$		0			0
$365$			6536.19i			0.937314i
$366$		0			0
$367$	−3484.74	−	2011.91i	−0.495645	−	0.286161i	0.231268	−	0.972890i	$-0.425713\pi$
$367$	−3484.74	−	2011.91i	−0.495645	−	0.286161i	−0.726914	+	0.686729i	$0.759046\pi$
$368$		0			0
$369$	−3961.90	−	3553.15i	−0.558938	−	0.501273i
$370$		0			0
$371$	1813.55	−	5138.09i	0.253786	−	0.719020i
$372$		0			0
$373$	3513.21	+	6085.05i	0.487686	+	0.844697i	0.999900	−	0.0141608i	$-0.00450767\pi$
$373$	3513.21	+	6085.05i	0.487686	+	0.844697i	−0.512213	+	0.858858i	$0.671174\pi$
$374$		0			0
$375$	3215.60	+	7203.18i	0.442807	+	0.991921i
$376$		0			0
$377$		−	215.734i		−	0.0294718i
$378$		0			0
$379$		−	3545.64i		−	0.480547i	−0.970705	−	0.240273i	$-0.922763\pi$
$379$		−	3545.64i		−	0.480547i	0.970705	−	0.240273i	$-0.0772371\pi$
$380$		0			0
$381$	4672.28	+	10466.3i	0.628263	+	1.40736i
$382$		0			0
$383$	−4402.09	−	7624.65i	−0.587301	−	1.01724i	−0.994584	−	0.103933i	$-0.966857\pi$
$383$	−4402.09	−	7624.65i	−0.587301	−	1.01724i	0.407283	−	0.913302i	$-0.366476\pi$
$384$		0			0
$385$	3895.40	−	726.116i	0.515657	−	0.0961202i
$386$		0			0
$387$	−5061.69	−	4539.48i	−0.664858	−	0.596265i
$388$		0			0
$389$	−9530.96	−	5502.70i	−1.24226	−	0.717219i	−0.272706	−	0.962098i	$-0.587918\pi$
$389$	−9530.96	−	5502.70i	−1.24226	−	0.717219i	−0.969554	+	0.244879i	$0.921252\pi$
$390$		0			0
$391$			2417.08i			0.312626i
$392$		0			0
$393$	−1589.64	−	1152.54i	−0.204037	−	0.147934i
$394$		0			0
$395$	1972.52	−	3416.51i	0.251262	−	0.435199i
$396$		0			0
$397$	−6019.91	−	10426.8i	−0.761035	−	1.31815i	−0.942318	−	0.334720i	$-0.891358\pi$
$397$	−6019.91	−	10426.8i	−0.761035	−	1.31815i	0.181283	−	0.983431i	$-0.441975\pi$
$398$		0			0
$399$	5745.37	+	2726.19i	0.720873	+	0.342055i
$400$		0			0
$401$	8573.68	−	4950.01i	1.06770	−	0.616439i	0.140150	−	0.990130i	$-0.455241\pi$
$401$	8573.68	−	4950.01i	1.06770	−	0.616439i	0.927553	+	0.373692i	$0.121908\pi$
$402$		0			0
$403$	212.099	+	122.455i	0.0262169	+	0.0151363i
$404$		0			0
$405$	−3781.41	−	5161.63i	−0.463951	−	0.633293i
$406$		0			0
$407$	−5249.92			−0.639383
$408$		0			0
$409$	925.425	−	1602.88i	0.111881	−	0.193784i	−0.804648	−	0.593753i	$-0.797646\pi$
$409$	925.425	−	1602.88i	0.111881	−	0.193784i	0.916529	+	0.399969i	$0.130979\pi$
$410$		0			0
$411$	−16422.7	−	1709.69i	−1.97098	−	0.205189i
$412$		0			0
$413$	2728.02	+	962.886i	0.325030	+	0.114723i
$414$		0			0
$415$	−7804.09	+	4505.69i	−0.923103	+	0.532954i
$416$		0			0
$417$	4258.09	+	9538.45i	0.500047	+	1.12014i
$418$		0			0
$419$	1239.28			0.144493			0.0722465	−	0.997387i	$-0.476983\pi$
$419$	1239.28			0.144493			0.0722465	+	0.997387i	$0.476983\pi$
$420$		0			0
$421$	10125.5			1.17217			0.586086	−	0.810249i	$-0.300668\pi$
$421$	10125.5			1.17217			0.586086	+	0.810249i	$0.300668\pi$
$422$		0			0
$423$	16224.5	+	3415.11i	1.86492	+	0.392549i
$424$		0			0
$425$	−1126.78	+	650.545i	−0.128604	+	0.0742496i
$426$		0			0
$427$	6062.86	−	5188.97i	0.687125	−	0.588084i
$428$		0			0
$429$	36.5710	−	351.290i	0.00411577	−	0.0395348i
$430$		0			0
$431$	−1419.73	+	2459.04i	−0.158668	+	0.274821i	−0.934389	−	0.356255i	$-0.884053\pi$
$431$	−1419.73	+	2459.04i	−0.158668	+	0.274821i	0.775720	+	0.631077i	$0.217387\pi$
$432$		0			0
$433$	7227.32			0.802131			0.401065	−	0.916049i	$-0.368640\pi$
$433$	7227.32			0.802131			0.401065	+	0.916049i	$0.368640\pi$
$434$		0			0
$435$	−2856.72	−	2071.22i	−0.314872	−	0.228292i
$436$		0			0
$437$	5099.04	+	2943.93i	0.558170	+	0.322260i
$438$		0			0
$439$	−9330.15	+	5386.77i	−1.01436	+	0.585641i	−0.912465	−	0.409154i	$-0.865824\pi$
$439$	−9330.15	+	5386.77i	−1.01436	+	0.585641i	−0.101895	+	0.994795i	$0.532490\pi$
$440$		0			0
$441$	−3283.94	+	8659.21i	−0.354598	+	0.935019i
$442$		0			0
$443$	−4647.03	−	8048.89i	−0.498391	−	0.863238i	0.501608	−	0.865095i	$-0.332742\pi$
$443$	−4647.03	−	8048.89i	−0.498391	−	0.863238i	−0.999998	+	0.00185721i	$0.999409\pi$
$444$		0			0
$445$	2932.17	−	5078.66i	0.312355	−	0.541015i
$446$		0			0
$447$	−7292.03	+	10057.5i	−0.771591	+	1.06421i
$448$		0			0
$449$			10672.5i			1.12176i	0.827899	+	0.560878i	$0.189536\pi$
$449$			10672.5i			1.12176i	−0.827899	+	0.560878i	$0.810464\pi$
$450$		0			0
$451$	−4160.95	−	2402.33i	−0.434438	−	0.250823i
$452$		0			0
$453$	6792.29	+	707.111i	0.704480	+	0.0733399i
$454$		0			0
$455$	294.731	+	344.367i	0.0303675	+	0.0354817i
$456$		0			0
$457$	5558.05	+	9626.82i	0.568916	+	0.985391i	0.996674	+	0.0814975i	$0.0259703\pi$
$457$	5558.05	+	9626.82i	0.568916	+	0.985391i	−0.427758	+	0.903893i	$0.640696\pi$
$458$		0			0
$459$	2820.80	−	2555.05i	0.286849	−	0.259824i
$460$		0			0
$461$		−	8828.83i		−	0.891973i	−0.895040	−	0.445987i	$-0.852853\pi$
$461$		−	8828.83i		−	0.891973i	0.895040	−	0.445987i	$-0.147147\pi$
$462$		0			0
$463$		−	5136.70i		−	0.515600i	−0.966198	−	0.257800i	$-0.917002\pi$
$463$		−	5136.70i		−	0.515600i	0.966198	−	0.257800i	$-0.0829975\pi$
$464$		0			0
$465$	3657.85	−	1632.92i	0.364793	−	0.162849i
$466$		0			0
$467$	−4743.26	−	8215.57i	−0.470004	−	0.814071i	0.529408	−	0.848368i	$-0.322414\pi$
$467$	−4743.26	−	8215.57i	−0.470004	−	0.814071i	−0.999412	+	0.0342966i	$0.989081\pi$
$468$		0			0
$469$	−2953.89	+	8368.87i	−0.290827	+	0.823963i
$470$		0			0
$471$	62.3282	−	598.705i	0.00609752	−	0.0585709i
$472$		0			0
$473$	−5316.00	−	3069.19i	−0.516765	−	0.298354i
$474$		0			0
$475$			3169.39i			0.306150i
$476$		0			0
$477$	−7549.88	+	2469.62i	−0.724707	+	0.237057i
$478$		0			0
$479$	2121.83	−	3675.12i	0.202399	−	0.350565i	−0.746902	−	0.664934i	$-0.768460\pi$
$479$	2121.83	−	3675.12i	0.202399	−	0.350565i	0.949301	+	0.314369i	$0.101793\pi$
$480$		0			0
$481$	−300.270	−	520.084i	−0.0284639	−	0.0493010i
$482$		0			0
$483$	−3675.75	+	7746.55i	−0.346278	+	0.729772i
$484$		0			0
$485$	−12724.9	+	7346.72i	−1.19136	+	0.687829i
$486$		0			0
$487$	−29.4912	−	17.0267i	−0.00274409	−	0.00158430i	0.498627	−	0.866816i	$-0.333838\pi$
$487$	−29.4912	−	17.0267i	−0.00274409	−	0.00158430i	−0.501371	+	0.865232i	$0.667171\pi$
$488$		0			0
$489$	−6202.27	+	8554.47i	−0.573572	+	0.791097i
$490$		0			0
$491$	−5234.29			−0.481101			−0.240550	−	0.970637i	$-0.577328\pi$
$491$	−5234.29			−0.481101			−0.240550	+	0.970637i	$0.577328\pi$
$492$		0			0
$493$	1049.42	−	1817.64i	0.0958689	−	0.166050i
$494$		0			0
$495$	−4300.61	−	3856.92i	−0.390501	−	0.350214i
$496$		0			0
$497$	2695.97	+	14463.1i	0.243322	+	1.30535i
$498$		0			0
$499$	−1292.50	+	746.223i	−0.115952	+	0.0669450i	−0.556854	−	0.830610i	$-0.687992\pi$
$499$	−1292.50	+	746.223i	−0.115952	+	0.0669450i	0.440902	+	0.897555i	$0.354659\pi$
$500$		0			0
$501$	−20363.4	+	9090.50i	−1.81591	+	0.810646i
$502$		0			0
$503$	−10823.7			−0.959457			−0.479728	−	0.877417i	$-0.659265\pi$
$503$	−10823.7			−0.959457			−0.479728	+	0.877417i	$0.659265\pi$
$504$		0			0
$505$	12352.4			1.08847
$506$		0			0
$507$	−10387.5	+	4637.12i	−0.909911	+	0.406197i
$508$		0			0
$509$	−3420.40	+	1974.77i	−0.297852	+	0.171965i	−0.641478	−	0.767142i	$-0.721678\pi$
$509$	−3420.40	+	1974.77i	−0.297852	+	0.171965i	0.343625	+	0.939107i	$0.388345\pi$
$510$		0			0
$511$	−13005.3	−	4590.38i	−1.12588	−	0.397390i
$512$		0			0
$513$	−1954.44	−	9062.71i	−0.168208	−	0.779978i
$514$		0			0
$515$	−5478.01	+	9488.19i	−0.468718	+	0.811844i
$516$		0			0
$517$	14968.8			1.27336
$518$		0			0
$519$	6385.84	−	8807.65i	0.540091	−	0.744919i
$520$		0			0
$521$	−4057.40	−	2342.54i	−0.341186	−	0.196984i	0.319610	−	0.947549i	$-0.396448\pi$
$521$	−4057.40	−	2342.54i	−0.341186	−	0.196984i	−0.660796	+	0.750565i	$0.729781\pi$
$522$		0			0
$523$	5888.28	−	3399.60i	0.492307	−	0.284234i	−0.233224	−	0.972423i	$-0.574928\pi$
$523$	5888.28	−	3399.60i	0.492307	−	0.284234i	0.725531	+	0.688190i	$0.241594\pi$
$524$		0			0
$525$	−4600.55	+	371.410i	−0.382446	+	0.0308756i
$526$		0			0
$527$	1191.34	+	2063.47i	0.0984740	+	0.170562i
$528$		0			0
$529$	2114.16	−	3661.83i	0.173762	−	0.300964i
$530$		0			0
$531$	−1311.22	−	4008.54i	−0.107160	−	0.327601i
$532$		0			0
$533$		−	549.606i		−	0.0446643i
$534$		0			0
$535$	−10690.3	−	6172.06i	−0.863893	−	0.498769i
$536$		0			0
$537$	−876.048	+	8415.04i	−0.0703990	+	0.676231i
$538$		0			0
$539$	−1290.96	+	8260.80i	−0.103165	+	0.660144i
$540$		0			0
$541$	−9233.09	−	15992.2i	−0.733755	−	1.27090i	−0.955268	−	0.295743i	$-0.904433\pi$
$541$	−9233.09	−	15992.2i	−0.733755	−	1.27090i	0.221513	−	0.975157i	$-0.428901\pi$
$542$		0			0
$543$	−4037.10	+	1802.22i	−0.319058	+	0.142432i
$544$		0			0
$545$			7030.84i			0.552602i
$546$		0			0
$547$			21227.5i			1.65927i	0.558304	+	0.829637i	$0.311452\pi$
$547$			21227.5i			1.65927i	−0.558304	+	0.829637i	$0.688548\pi$
$548$		0			0
$549$	−11384.6	−	2396.35i	−0.885030	−	0.186291i
$550$		0			0
$551$	−2556.32	−	4427.68i	−0.197646	−	0.342333i
$552$		0			0
$553$	5412.68	+	6324.24i	0.416221	+	0.486319i
$554$		0			0
$555$	−9769.70	−	1017.07i	−0.747208	−	0.0777881i
$556$		0			0
$557$	−6535.13	−	3773.06i	−0.497132	−	0.287019i	0.230396	−	0.973097i	$-0.425998\pi$
$557$	−6535.13	−	3773.06i	−0.497132	−	0.287019i	−0.727528	+	0.686078i	$0.759331\pi$
$558$		0			0
$559$		−	702.172i		−	0.0531283i
$560$		0			0
$561$	2016.94	−	2781.86i	0.151792	−	0.209358i
$562$		0			0
$563$	7465.27	−	12930.2i	0.558834	−	0.967929i	−0.438760	−	0.898604i	$-0.644582\pi$
$563$	7465.27	−	12930.2i	0.558834	−	0.967929i	0.997594	−	0.0693250i	$-0.0220846\pi$
$564$		0			0
$565$	−1371.46	−	2375.43i	−0.102120	−	0.176876i
$566$		0			0
$567$	12926.0	−	3899.02i	0.957393	−	0.288789i
$568$		0			0
$569$	−3316.48	+	1914.77i	−0.244348	+	0.141074i	−0.617173	−	0.786827i	$-0.711722\pi$
$569$	−3316.48	+	1914.77i	−0.244348	+	0.141074i	0.372826	+	0.927901i	$0.378389\pi$
$570$		0			0
$571$	16305.8	+	9414.18i	1.19506	+	0.689967i	0.959449	−	0.281881i	$-0.0909583\pi$
$571$	16305.8	+	9414.18i	1.19506	+	0.689967i	0.235609	+	0.971848i	$0.424292\pi$
$572$		0			0
$573$	−7946.25	−	5761.30i	−0.579336	−	0.420038i
$574$		0			0
$575$	−4273.32			−0.309930
$576$		0			0
$577$	9133.01	−	15818.8i	0.658946	−	1.14133i	−0.321942	−	0.946759i	$-0.604336\pi$
$577$	9133.01	−	15818.8i	0.658946	−	1.14133i	0.980889	−	0.194569i	$-0.0623310\pi$
$578$		0			0
$579$	−2579.53	+	24778.1i	−0.185149	+	1.77849i
$580$		0			0
$581$	−3484.34	−	18692.5i	−0.248804	−	1.33476i
$582$		0			0
$583$	−6210.81	+	3585.81i	−0.441210	+	0.254733i
$584$		0			0
$585$	136.112	−	646.638i	0.00961970	−	0.0457012i
$586$		0			0
$587$	−6151.55			−0.432541			−0.216271	−	0.976333i	$-0.569389\pi$
$587$	−6151.55			−0.432541			−0.216271	+	0.976333i	$0.569389\pi$
$588$		0			0
$589$	5804.11			0.406034
$590$		0			0
$591$	8161.31	+	18282.0i	0.568040	+	1.27245i
$592$		0			0
$593$	19560.5	−	11293.3i	1.35456	−	0.782056i	0.365677	−	0.930742i	$-0.380838\pi$
$593$	19560.5	−	11293.3i	1.35456	−	0.782056i	0.988884	+	0.148686i	$0.0475043\pi$
$594$		0			0
$595$	808.080	+	4335.12i	0.0556774	+	0.298693i
$596$		0			0
$597$	−10244.4	−	1066.49i	−0.702301	−	0.0731130i
$598$		0			0
$599$	12117.8	−	20988.7i	0.826581	−	1.43168i	−0.0741247	−	0.997249i	$-0.523616\pi$
$599$	12117.8	−	20988.7i	0.826581	−	1.43168i	0.900705	−	0.434431i	$-0.143050\pi$
$600$		0			0
$601$	−4304.93			−0.292183			−0.146091	−	0.989271i	$-0.546669\pi$
$601$	−4304.93			−0.292183			−0.146091	+	0.989271i	$0.546669\pi$
$602$		0			0
$603$	12297.2	−	4022.49i	0.830481	−	0.271656i
$604$		0			0
$605$	5600.58	+	3233.50i	0.376357	+	0.217290i
$606$		0			0
$607$	15112.9	−	8725.46i	1.01057	−	0.583452i	0.0992104	−	0.995066i	$-0.468368\pi$
$607$	15112.9	−	8725.46i	1.01057	−	0.583452i	0.911358	+	0.411615i	$0.135035\pi$
$608$		0			0
$609$	6127.47	−	4229.52i	0.407714	−	0.281426i
$610$		0			0
$611$	856.146	+	1482.89i	0.0566873	+	0.0981853i
$612$		0			0
$613$	−5236.19	+	9069.34i	−0.345004	+	0.597565i	−0.985355	−	0.170518i	$-0.945456\pi$
$613$	−5236.19	+	9069.34i	−0.345004	+	0.597565i	0.640350	+	0.768083i	$0.278789\pi$
$614$		0			0
$615$	−7277.80	−	5276.65i	−0.477186	−	0.345976i
$616$		0			0
$617$			12748.9i			0.831847i	0.909400	+	0.415923i	$0.136542\pi$
$617$			12748.9i			0.831847i	−0.909400	+	0.415923i	$0.863458\pi$
$618$		0			0
$619$	−8761.41	−	5058.40i	−0.568903	−	0.328456i	0.187808	−	0.982206i	$-0.439862\pi$
$619$	−8761.41	−	5058.40i	−0.568903	−	0.328456i	−0.756711	+	0.653749i	$0.773195\pi$
$620$		0			0
$621$	12219.4	−	2635.20i	0.789607	−	0.170285i
$622$		0			0
$623$	8045.97	+	9401.01i	0.517423	+	0.604564i
$624$		0			0
$625$	3664.77	+	6347.57i	0.234546	+	0.406245i
$626$		0			0
$627$	−3412.00	−	7643.14i	−0.217324	−	0.486823i
$628$		0			0
$629$		−	5842.54i		−	0.370361i
$630$		0			0
$631$			11836.9i			0.746785i	0.927673	+	0.373393i	$0.121806\pi$
$631$			11836.9i			0.746785i	−0.927673	+	0.373393i	$0.878194\pi$
$632$		0			0
$633$	−1614.22	−	3615.98i	−0.101358	−	0.227049i
$634$		0			0
$635$	9680.45	+	16767.0i	0.604972	+	1.04784i
$636$		0			0
$637$	−892.193	+	344.589i	−0.0554944	+	0.0214334i
$638$		0			0
$639$	14320.3	−	15967.6i	0.886542	−	0.988528i
$640$		0			0
$641$	9540.73	+	5508.34i	0.587888	+	0.339417i	0.764262	−	0.644906i	$-0.223103\pi$
$641$	9540.73	+	5508.34i	0.587888	+	0.339417i	−0.176374	+	0.984323i	$0.556437\pi$
$642$		0			0
$643$		−	23348.8i		−	1.43201i	−0.698093	−	0.716007i	$-0.745968\pi$
$643$		−	23348.8i		−	1.43201i	0.698093	−	0.716007i	$-0.254032\pi$
$644$		0			0
$645$	−9298.06	−	6741.40i	−0.567613	−	0.411539i
$646$		0			0
$647$	−2201.38	+	3812.90i	−0.133764	+	0.231685i	−0.925124	−	0.379664i	$-0.876040\pi$
$647$	−2201.38	+	3812.90i	−0.133764	+	0.231685i	0.791361	+	0.611349i	$0.209373\pi$
$648$		0			0
$649$	−1903.85	−	3297.57i	−0.115151	−	0.199447i
$650$		0			0
$651$	680.165	+	8424.99i	0.0409489	+	0.507222i
$652$		0			0
$653$	10836.9	−	6256.70i	0.649435	−	0.374952i	−0.138804	−	0.990320i	$-0.544326\pi$
$653$	10836.9	−	6256.70i	0.649435	−	0.374952i	0.788240	+	0.615368i	$0.210993\pi$
$654$		0			0
$655$	−2872.32	−	1658.33i	−0.171345	−	0.0989258i
$656$		0			0
$657$	6251.00	+	19110.0i	0.371194	+	1.13478i
$658$		0			0
$659$	23795.0			1.40656			0.703279	−	0.710914i	$-0.251718\pi$
$659$	23795.0			1.40656			0.703279	+	0.710914i	$0.251718\pi$
$660$		0			0
$661$	−9965.48	+	17260.7i	−0.586403	+	1.01568i	0.408296	+	0.912849i	$0.366123\pi$
$661$	−9965.48	+	17260.7i	−0.586403	+	1.01568i	−0.994699	+	0.102830i	$0.967210\pi$
$662$		0			0
$663$	390.944	+	40.6992i	0.0229004	+	0.00238405i
$664$		0			0
$665$	10129.5	+	3575.34i	0.590687	+	0.208490i
$666$		0			0
$667$	5969.89	−	3446.72i	0.346560	−	0.200086i
$668$		0			0
$669$	−815.190	−	1826.09i	−0.0471107	−	0.105532i
$670$		0			0
$671$	−10503.5			−0.604297
$672$		0			0
$673$	−7281.03			−0.417033			−0.208516	−	0.978019i	$-0.566863\pi$
$673$	−7281.03			−0.417033			−0.208516	+	0.978019i	$0.566863\pi$
$674$		0			0
$675$	4517.24	+	4987.09i	0.257583	+	0.284375i
$676$		0			0
$677$	459.878	−	265.511i	0.0261071	−	0.0150730i	−0.486890	−	0.873464i	$-0.661869\pi$
$677$	459.878	−	265.511i	0.0261071	−	0.0150730i	0.512997	+	0.858391i	$0.328535\pi$
$678$		0			0
$679$	−5681.37	−	30478.9i	−0.321106	−	1.72264i
$680$		0			0
$681$	−683.094	+	6561.58i	−0.0384379	+	0.369222i
$682$		0			0
$683$	6673.07	−	11558.1i	0.373847	−	0.647523i	−0.616306	−	0.787506i	$-0.711372\pi$
$683$	6673.07	−	11558.1i	0.373847	−	0.647523i	0.990154	+	0.139984i	$0.0447050\pi$
$684$		0			0
$685$	−27890.7			−1.55569
$686$		0			0
$687$	−2892.39	−	2097.08i	−0.160628	−	0.116461i
$688$		0			0
$689$	−710.457	−	410.182i	−0.0392834	−	0.0226803i
$690$		0			0
$691$	26766.6	−	15453.7i	1.47359	−	0.850775i	0.474028	−	0.880510i	$-0.342799\pi$
$691$	26766.6	−	15453.7i	1.47359	−	0.850775i	0.999558	+	0.0297344i	$0.00946615\pi$
$692$		0			0
$693$	10694.6	−	5848.39i	0.586227	−	0.320580i
$694$		0			0
$695$	8822.29	+	15280.7i	0.481509	+	0.833998i
$696$		0			0
$697$	2673.50	−	4630.64i	0.145289	−	0.251647i
$698$		0			0
$699$	10863.0	−	14982.7i	0.587805	−	0.810728i
$700$		0			0
$701$		−	17128.9i		−	0.922898i	−0.887167	−	0.461449i	$-0.847330\pi$
$701$		−	17128.9i		−	0.922898i	0.887167	−	0.461449i	$-0.152670\pi$
$702$		0			0
$703$	−12325.4	−	7116.06i	−0.661252	−	0.381774i
$704$		0			0
$705$	27855.8	+	2899.93i	1.48810	+	0.154919i
$706$		0			0
$707$	−8675.14	+	24578.2i	−0.461474	+	1.30744i
$708$		0			0
$709$	−1208.87	−	2093.82i	−0.0640339	−	0.110910i	0.832231	−	0.554429i	$-0.187063\pi$
$709$	−1208.87	−	2093.82i	−0.0640339	−	0.110910i	−0.896265	+	0.443519i	$0.853730\pi$
$710$		0			0
$711$	2499.67	−	11875.4i	0.131849	−	0.626388i
$712$		0			0
$713$			7825.74i			0.411047i
$714$		0			0
$715$		−	596.594i		−	0.0312047i
$716$		0			0
$717$	28494.1	−	12720.2i	1.48415	−	0.662543i
$718$		0			0
$719$	3706.88	+	6420.51i	0.192272	+	0.333024i	0.946003	−	0.324159i	$-0.105081\pi$
$719$	3706.88	+	6420.51i	0.192272	+	0.333024i	−0.753731	+	0.657183i	$0.771748\pi$
$720$		0			0
$721$	−15031.8	−	17563.4i	−0.776443	−	0.907206i
$722$		0			0
$723$	612.194	−	5880.54i	0.0314907	−	0.302489i
$724$		0			0
$725$	3213.54	+	1855.34i	0.164618	+	0.0950421i
$726$		0			0
$727$			25603.2i			1.30615i	0.757293	+	0.653075i	$0.226521\pi$
$727$			25603.2i			1.30615i	−0.757293	+	0.653075i	$0.773479\pi$
$728$		0			0
$729$	−15992.2	−	11474.7i	−0.812489	−	0.582977i
$730$		0			0
$731$	3415.65	−	5916.07i	0.172821	−	0.299335i
$732$		0			0
$733$	2400.38	+	4157.59i	0.120955	+	0.209501i	0.920145	−	0.391579i	$-0.128071\pi$
$733$	2400.38	+	4157.59i	0.120955	+	0.209501i	−0.799189	+	0.601079i	$0.794738\pi$
$734$		0			0
$735$	−4002.76	+	15122.6i	−0.200876	+	0.758919i
$736$		0			0
$737$	10116.1	−	5840.54i	0.505606	−	0.291912i
$738$		0			0
$739$	20403.3	+	11779.8i	1.01562	+	0.586371i	0.912833	−	0.408332i	$-0.133889\pi$
$739$	20403.3	+	11779.8i	1.01562	+	0.586371i	0.102791	+	0.994703i	$0.467223\pi$
$740$		0			0
$741$	562.018	−	775.161i	0.0278627	−	0.0384295i
$742$		0			0
$743$	9070.46			0.447864			0.223932	−	0.974605i	$-0.428111\pi$
$743$	9070.46			0.447864			0.223932	+	0.974605i	$0.428111\pi$
$744$		0			0
$745$	−10492.1	+	18172.9i	−0.515976	+	0.893696i
$746$		0			0
$747$	−18507.9	+	20637.0i	−0.906516	+	1.01080i
$748$		0			0
$749$	19788.7	−	16936.3i	0.965369	−	0.826223i
$750$		0			0
$751$	15453.0	−	8921.78i	0.750848	−	0.433502i	−0.0751522	−	0.997172i	$-0.523944\pi$
$751$	15453.0	−	8921.78i	0.750848	−	0.433502i	0.826000	+	0.563670i	$0.190611\pi$
$752$		0			0
$753$	21924.1	−	9787.22i	1.06103	−	0.473660i
$754$		0			0
$755$	11535.3			0.556044
$756$		0			0
$757$	−29075.4			−1.39599			−0.697995	−	0.716103i	$-0.745924\pi$
$757$	−29075.4			−1.39599			−0.697995	+	0.716103i	$0.745924\pi$
$758$		0			0
$759$	10305.3	−	4600.44i	0.492833	−	0.220007i
$760$		0			0
$761$	−13557.9	+	7827.66i	−0.645826	+	0.372868i	−0.786855	−	0.617138i	$-0.788292\pi$
$761$	−13557.9	+	7827.66i	−0.645826	+	0.372868i	0.141029	+	0.990005i	$0.454959\pi$
$762$		0			0
$763$	−13989.6	−	4937.78i	−0.663770	−	0.234285i
$764$		0			0
$765$	4292.30	−	4786.07i	0.202861	−	0.226197i
$766$		0			0
$767$	217.783	−	377.211i	0.0102525	−	0.0177579i
$768$		0			0
$769$	9369.72			0.439377			0.219688	−	0.975570i	$-0.429496\pi$
$769$	9369.72			0.439377			0.219688	+	0.975570i	$0.429496\pi$
$770$		0			0
$771$	21806.4	−	30076.4i	1.01860	−	1.40490i
$772$		0			0
$773$	−32342.1	−	18672.7i	−1.50487	−	0.868838i	−0.999984	−	0.00565196i	$-0.998201\pi$
$773$	−32342.1	−	18672.7i	−1.50487	−	0.868838i	−0.504887	−	0.863186i	$-0.668466\pi$
$774$		0			0
$775$	−3648.15	+	2106.26i	−0.169091	+	0.0976247i
$776$		0			0
$777$	8885.00	−	18724.9i	0.410228	−	0.864546i
$778$		0			0
$779$	−6512.51	−	11280.0i	−0.299531	−	0.518804i
$780$		0			0
$781$	9682.08	−	16769.9i	0.443601	−	0.768339i
$782$		0			0
$783$	−10333.1	−	3323.58i	−0.471615	−	0.151692i
$784$		0			0
$785$		−	1016.78i		−	0.0462298i
$786$		0			0
$787$	22693.0	+	13101.8i	1.02785	+	0.593430i	0.916368	−	0.400337i	$-0.131107\pi$
$787$	22693.0	+	13101.8i	1.02785	+	0.593430i	0.111482	+	0.993766i	$0.464440\pi$
$788$		0			0
$789$	−1947.14	+	18703.6i	−0.0878579	+	0.843935i
$790$		0			0
$791$	5689.68	−	1060.58i	0.255754	−	0.0476735i
$792$		0			0
$793$	−600.750	−	1040.53i	−0.0269020	−	0.0465956i
$794$		0			0
$795$	−12252.5	+	5469.69i	−0.546606	+	0.244012i
$796$		0			0
$797$			10114.2i			0.449513i	0.974415	+	0.224756i	$0.0721586\pi$
$797$			10114.2i			0.449513i	−0.974415	+	0.224756i	$0.927841\pi$
$798$		0			0
$799$			16658.5i			0.737593i
$800$		0			0
$801$	3715.76	−	17652.8i	0.163908	−	0.778691i
$802$		0			0
$803$	9076.27	+	15720.6i	0.398872	+	0.690867i
$804$		0			0
$805$	−4820.67	+	13657.8i	−0.211064	+	0.597980i
$806$		0			0
$807$	31154.8	+	3243.37i	1.35898	+	0.141477i
$808$		0			0
$809$	−17343.4	−	10013.2i	−0.753720	−	0.435161i	0.0733162	−	0.997309i	$-0.476642\pi$
$809$	−17343.4	−	10013.2i	−0.753720	−	0.435161i	−0.827037	+	0.562148i	$0.809975\pi$
$810$		0			0
$811$			3159.94i			0.136819i	0.997657	+	0.0684097i	$0.0217925\pi$
$811$			3159.94i			0.136819i	−0.997657	+	0.0684097i	$0.978207\pi$
$812$		0			0
$813$	2143.35	−	2956.21i	0.0924608	−	0.127526i
$814$		0			0
$815$	−8924.14	+	15457.1i	−0.383557	+	0.664340i
$816$		0			0
$817$	−8320.33	−	14411.2i	−0.356293	−	0.617118i
$818$		0			0
$819$	1191.05	+	724.962i	0.0508165	+	0.0309307i
$820$		0			0
$821$	−21797.5	+	12584.8i	−0.926599	+	0.534972i	−0.885734	−	0.464193i	$-0.846344\pi$
$821$	−21797.5	+	12584.8i	−0.926599	+	0.534972i	−0.0408643	+	0.999165i	$0.513011\pi$
$822$		0			0
$823$	−12732.5	−	7351.13i	−0.539281	−	0.311354i	0.205507	−	0.978656i	$-0.434116\pi$
$823$	−12732.5	−	7351.13i	−0.539281	−	0.311354i	−0.744787	+	0.667302i	$0.767449\pi$
$824$		0			0
$825$	4918.24	+	3565.89i	0.207553	+	0.150483i
$826$		0			0
$827$	−34523.2			−1.45162			−0.725810	−	0.687895i	$-0.758535\pi$
$827$	−34523.2			−1.45162			−0.725810	+	0.687895i	$0.758535\pi$
$828$		0			0
$829$	−10290.3	+	17823.4i	−0.431120	+	0.746722i	−0.996970	−	0.0777863i	$-0.975215\pi$
$829$	−10290.3	+	17823.4i	−0.431120	+	0.746722i	0.565850	+	0.824508i	$0.308548\pi$
$830$		0			0
$831$	−1348.75	+	12955.7i	−0.0563030	+	0.540829i
$832$		0			0
$833$	−9193.29	−	1436.69i	−0.382387	−	0.0597579i
$834$		0			0
$835$	−32622.3	+	18834.5i	−1.35203	+	0.780593i
$836$		0			0
$837$	9132.87	−	8272.44i	0.377154	−	0.341622i
$838$		0			0
$839$	13818.8			0.568626			0.284313	−	0.958731i	$-0.408234\pi$
$839$	13818.8			0.568626			0.284313	+	0.958731i	$0.408234\pi$
$840$		0			0
$841$	18403.2			0.754569
$842$		0			0
$843$	−4307.09	−	9648.20i	−0.175972	−	0.394189i
$844$		0			0
$845$	−16640.8	+	9607.60i	−0.677470	+	0.391138i
$846$		0			0
$847$	−10367.1	+	8872.83i	−0.420565	+	0.359946i
$848$		0			0
$849$	−7611.57	−	792.403i	−0.307690	−	0.0320320i
$850$		0			0
$851$	9594.66	−	16618.4i	0.386487	−	0.669416i
$852$		0			0
$853$	−22275.8			−0.894148			−0.447074	−	0.894497i	$-0.647534\pi$
$853$	−22275.8			−0.894148			−0.447074	+	0.894497i	$0.647534\pi$
$854$		0			0
$855$	−4868.76	−	14884.3i	−0.194746	−	0.595360i
$856$		0			0
$857$	−5704.00	−	3293.21i	−0.227357	−	0.131265i	0.381995	−	0.924164i	$-0.375237\pi$
$857$	−5704.00	−	3293.21i	−0.227357	−	0.131265i	−0.609352	+	0.792900i	$0.708570\pi$
$858$		0			0
$859$	34673.6	−	20018.8i	1.37724	−	0.795150i	0.385413	−	0.922744i	$-0.374059\pi$
$859$	34673.6	−	20018.8i	1.37724	−	0.795150i	0.991826	+	0.127595i	$0.0407257\pi$
$860$		0			0
$861$	15610.4	−	10775.2i	0.617887	−	0.426500i
$862$		0			0
$863$	10566.0	+	18300.9i	0.416769	+	0.721865i	0.995612	−	0.0935740i	$-0.0298292\pi$
$863$	10566.0	+	18300.9i	0.416769	+	0.721865i	−0.578844	+	0.815439i	$0.696496\pi$
$864$		0			0
$865$	9188.26	−	15914.5i	0.361168	−	0.625561i
$866$		0			0
$867$	−17572.1	−	12740.4i	−0.688327	−	0.499060i
$868$		0			0
$869$		−	10956.3i		−	0.427696i
$870$		0			0
$871$	1157.19	+	668.101i	0.0450169	+	0.0259905i
$872$		0			0
$873$	−30177.8	+	33649.4i	−1.16995	+	1.30454i
$874$		0			0
$875$	−27639.7	+	5152.14i	−1.06788	+	0.199056i
$876$		0			0
$877$	21605.4	+	37421.6i	0.831883	+	1.44086i	0.896544	+	0.442956i	$0.146070\pi$
$877$	21605.4	+	37421.6i	0.831883	+	1.44086i	−0.0646610	+	0.997907i	$0.520597\pi$
$878$		0			0
$879$	−16404.5	−	36747.2i	−0.629475	−	1.41007i
$880$		0			0
$881$			17875.4i			0.683584i	0.939776	+	0.341792i	$0.111034\pi$
$881$			17875.4i			0.683584i	−0.939776	+	0.341792i	$0.888966\pi$
$882$		0			0
$883$			39508.8i			1.50575i	0.658163	+	0.752875i	$0.271334\pi$
$883$			39508.8i			1.50575i	−0.658163	+	0.752875i	$0.728666\pi$
$884$		0			0
$885$	−2904.08	−	6505.36i	−0.110305	−	0.247091i
$886$		0			0
$887$	−1461.85	−	2532.00i	−0.0553372	−	0.0958469i	0.837030	−	0.547157i	$-0.184290\pi$
$887$	−1461.85	−	2532.00i	−0.0553372	−	0.0958469i	−0.892367	+	0.451310i	$0.850957\pi$
$888$		0			0
$889$	−40160.7	+	7486.09i	−1.51513	+	0.282425i
$890$		0			0
$891$	−16262.4	−	7163.59i	−0.611461	−	0.269348i
$892$		0			0
$893$	35142.7	+	20289.7i	1.31692	+	0.760322i
$894$		0			0
$895$			14291.2i			0.533747i
$896$		0			0
$897$	1045.16	+	757.775i	0.0389039	+	0.0282067i
$898$		0			0
$899$	3397.69	−	5884.96i	0.126050	−	0.218325i
$900$		0			0
$901$	−3990.58	−	6911.89i	−0.147553	−	0.255570i
$902$		0			0
$903$	19943.7	−	13766.3i	0.734978	−	0.507322i
$904$		0			0
$905$	−6467.46	+	3733.99i	−0.237553	+	0.137151i
$906$		0			0
$907$	27482.3	+	15866.9i	1.00610	+	0.580874i	0.910049	−	0.414502i	$-0.136044\pi$
$907$	27482.3	+	15866.9i	1.00610	+	0.580874i	0.0960553	+	0.995376i	$0.469377\pi$
$908$		0			0
$909$	36115.1	−	11813.5i	1.31778	−	0.431054i
$910$		0			0
$911$	−34819.5			−1.26633			−0.633163	−	0.774019i	$-0.718244\pi$
$911$	−34819.5			−1.26633			−0.633163	+	0.774019i	$0.718244\pi$
$912$		0			0
$913$	−12513.4	+	21673.8i	−0.453595	+	0.785650i
$914$		0			0
$915$	−19546.2	−	2034.86i	−0.706205	−	0.0735195i
$916$		0			0
$917$	5316.89	−	4550.52i	0.191471	−	0.163873i
$918$		0			0
$919$	−19143.4	+	11052.4i	−0.687140	+	0.396720i	−0.802540	−	0.596599i	$-0.796518\pi$
$919$	−19143.4	+	11052.4i	−0.687140	+	0.396720i	0.115400	+	0.993319i	$0.463185\pi$
$920$		0			0
$921$	4151.24	+	9299.09i	0.148521	+	0.332699i
$922$		0			0
$923$	2215.07			0.0789925
$924$		0			0
$925$	10329.4			0.367167
$926$		0			0
$927$	−6941.96	+	32979.8i	−0.245959	+	1.16850i
$928$		0			0
$929$	6330.81	−	3655.09i	0.223581	−	0.129085i	−0.384026	−	0.923322i	$-0.625463\pi$
$929$	6330.81	−	3655.09i	0.223581	−	0.129085i	0.607607	+	0.794237i	$0.292129\pi$
$930$		0			0
$931$	−14228.0	+	17644.2i	−0.500864	+	0.621124i
$932$		0			0
$933$	−1616.92	+	15531.7i	−0.0567371	+	0.544998i
$934$		0			0
$935$	2902.07	−	5026.53i	0.101506	−	0.175813i
$936$		0			0
$937$	13072.7			0.455782			0.227891	−	0.973687i	$-0.426817\pi$
$937$	13072.7			0.455782			0.227891	+	0.973687i	$0.426817\pi$
$938$		0			0
$939$	−36225.8	−	26264.9i	−1.25898	−	0.912803i
$940$		0			0
$941$	16652.8	+	9614.49i	0.576903	+	0.333075i	0.759902	−	0.650038i	$-0.225247\pi$
$941$	16652.8	+	9614.49i	0.576903	+	0.333075i	−0.182999	+	0.983113i	$0.558580\pi$
$942$		0			0
$943$	15209.0	−	8780.90i	0.525209	−	0.303229i
$944$		0			0
$945$	21034.9	−	8811.52i	0.724089	−	0.303322i
$946$		0			0
$947$	−26029.8	−	45085.0i	−0.893195	−	1.54706i	−0.836022	−	0.548695i	$-0.815125\pi$
$947$	−26029.8	−	45085.0i	−0.893195	−	1.54706i	−0.0571727	−	0.998364i	$-0.518209\pi$
$948$		0			0
$949$	−1038.24	+	1798.28i	−0.0355138	+	0.0615118i
$950$		0			0
$951$	7363.15	−	10155.6i	0.251069	−	0.346286i
$952$		0			0
$953$		−	34655.9i		−	1.17798i	−0.808141	−	0.588989i	$-0.799526\pi$
$953$		−	34655.9i		−	1.17798i	0.808141	−	0.588989i	$-0.200474\pi$
$954$		0			0
$955$	−14358.1	−	8289.64i	−0.486509	−	0.280886i
$956$		0			0
$957$	−9746.99	−	1014.71i	−0.329232	−	0.0342747i
$958$		0			0
$959$	19587.7	−	55495.3i	0.659561	−	1.86865i
$960$		0			0
$961$	−11038.3	−	19118.9i	−0.370524	−	0.641767i
$962$		0			0
$963$	−37158.3	−	7821.49i	−1.24341	−	0.261728i
$964$		0			0
$965$			42080.6i			1.40375i
$966$		0			0
$967$			57897.5i			1.92540i	0.270580	+	0.962698i	$0.412785\pi$
$967$			57897.5i			1.92540i	−0.270580	+	0.962698i	$0.587215\pi$
$968$		0			0
$969$	8505.91	−	3797.15i	0.281991	−	0.125885i
$970$		0			0
$971$	−5475.45	−	9483.76i	−0.180964	−	0.313438i	0.761245	−	0.648464i	$-0.224588\pi$
$971$	−5475.45	−	9483.76i	−0.180964	−	0.313438i	−0.942209	+	0.335026i	$0.891255\pi$
$972$		0			0
$973$	−36600.5	+	6822.46i	−1.20592	+	0.224787i
$974$		0			0
$975$	−71.9550	+	691.177i	−0.00236349	+	0.0227029i
$976$		0			0
$977$	39504.6	+	22808.0i	1.29362	+	0.746870i	0.979293	−	0.202447i	$-0.0648892\pi$
$977$	39504.6	+	22808.0i	1.29362	+	0.746870i	0.314323	+	0.949316i	$0.398223\pi$
$978$		0			0
$979$		−	16286.6i		−	0.531689i
$980$		0			0
$981$	6724.08	+	20556.2i	0.218841	+	0.669021i
$982$		0			0
$983$	4240.94	−	7345.52i	0.137604	−	0.238337i	−0.788985	−	0.614412i	$-0.789393\pi$
$983$	4240.94	−	7345.52i	0.137604	−	0.238337i	0.926589	+	0.376075i	$0.122726\pi$
$984$		0			0
$985$	16909.3	+	29287.8i	0.546981	+	0.947399i
$986$		0			0
$987$	−25333.3	+	53389.4i	−0.816990	+	1.72179i
$988$		0			0
$989$	19430.8	−	11218.4i	0.624737	−	0.360692i
$990$		0			0
$991$	−25611.9	−	14787.0i	−0.820977	−	0.473991i	0.0297762	−	0.999557i	$-0.490521\pi$
$991$	−25611.9	−	14787.0i	−0.820977	−	0.473991i	−0.850753	+	0.525565i	$0.823854\pi$
$992$		0			0
$993$	6383.28	−	8804.11i	0.203995	−	0.281360i
$994$		0			0
$995$	−17397.9			−0.554323
$996$		0			0
$997$	−4906.99	+	8499.15i	−0.155873	+	0.269981i	−0.933377	−	0.358898i	$-0.883153\pi$
$997$	−4906.99	+	8499.15i	−0.155873	+	0.269981i	0.777503	+	0.628879i	$0.216486\pi$
$998$		0			0
$999$	−29536.6	+	6369.79i	−0.935431	+	0.201733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bj.f.95.13	yes	28
3.2	odd	2	inner	336.4.bj.f.95.8	yes	28
4.3	odd	2		336.4.bj.e.95.2	✓	28
7.2	even	3		336.4.bj.e.191.7	yes	28
12.11	even	2		336.4.bj.e.95.7	yes	28
21.2	odd	6		336.4.bj.e.191.2	yes	28
28.23	odd	6	inner	336.4.bj.f.191.8	yes	28
84.23	even	6	inner	336.4.bj.f.191.13	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.4.bj.e.95.2	✓	28	4.3	odd	2
336.4.bj.e.95.7	yes	28	12.11	even	2
336.4.bj.e.191.2	yes	28	21.2	odd	6
336.4.bj.e.191.7	yes	28	7.2	even	3
336.4.bj.f.95.8	yes	28	3.2	odd	2	inner
336.4.bj.f.95.13	yes	28	1.1	even	1	trivial
336.4.bj.f.191.8	yes	28	28.23	odd	6	inner
336.4.bj.f.191.13	yes	28	84.23	even	6	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.74483 - 2.11816i) q^{3} +(7.60125 - 4.38858i) q^{5} +(3.39378 + 18.2067i) q^{7} +(18.0268 - 20.1006i) q^{9} +(12.1881 - 21.1105i) q^{11} +2.78841 q^{13} +(26.7709 - 36.9237i) q^{15} +(23.4934 + 13.5639i) q^{17} +(57.2288 - 33.0411i) q^{19} +(54.6675 + 79.1989i) q^{21} +(44.5496 + 77.1622i) q^{23} +(-23.9807 + 41.5357i) q^{25} +(42.9580 - 133.558i) q^{27} -77.3681i q^{29} +(76.0645 + 43.9159i) q^{31} +(13.1154 - 125.982i) q^{33} +(105.698 + 123.499i) q^{35} +(-107.685 - 186.516i) q^{37} +(13.2305 - 5.90629i) q^{39} -197.104i q^{41} -251.818i q^{43} +(48.8133 - 231.902i) q^{45} +(307.037 + 531.804i) q^{47} +(-319.964 + 123.579i) q^{49} +(140.203 + 14.5958i) q^{51} +(-254.789 - 147.102i) q^{53} -213.955i q^{55} +(201.555 - 277.994i) q^{57} +(78.1027 - 135.278i) q^{59} +(-215.445 - 373.162i) q^{61} +(427.144 + 259.991i) q^{63} +(21.1954 - 12.2372i) q^{65} +(414.998 + 239.599i) q^{67} +(374.822 + 271.759i) q^{69} +794.386 q^{71} +(-372.340 + 644.912i) q^{73} +(-25.8050 + 247.875i) q^{75} +(425.715 + 150.261i) q^{77} +(389.250 - 224.734i) q^{79} +(-79.0671 - 724.700i) q^{81} -1026.68 q^{83} +238.106 q^{85} +(-163.878 - 367.098i) q^{87} +(578.622 - 334.067i) q^{89} +(9.46326 + 50.7676i) q^{91} +(453.934 + 47.2568i) q^{93} +(290.007 - 502.307i) q^{95} -1674.05 q^{97} +(-204.619 - 625.543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 38 q^{7} - 70 q^{9} + 124 q^{13} - 462 q^{19} + 500 q^{21} + 566 q^{25} + 1266 q^{31} + 64 q^{33} + 338 q^{37} + 1254 q^{39} - 488 q^{45} - 206 q^{49} + 522 q^{51} + 2324 q^{57} - 340 q^{61} - 840 q^{63}+ \cdots - 3344 q^{97}+O(q^{100}) \) 28 * q + 38 * q^7 - 70 * q^9 + 124 * q^13 - 462 * q^19 + 500 * q^21 + 566 * q^25 + 1266 * q^31 + 64 * q^33 + 338 * q^37 + 1254 * q^39 - 488 * q^45 - 206 * q^49 + 522 * q^51 + 2324 * q^57 - 340 * q^61 - 840 * q^63 + 2934 * q^67 - 776 * q^69 + 2050 * q^73 - 1458 * q^75 + 2070 * q^79 + 910 * q^81 + 2400 * q^85 + 3132 * q^87 - 5170 * q^91 + 714 * q^93 - 3344 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more