LMFDB - Embedded newform 14.7.b.a.13.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [14,7,Mod(13,14)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("14.13"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	14.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.22075717068$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.211968.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 30x^{2} + 207 $ x^4 + 30*x^2 + 207
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.4
Root			$4.38664i$ of defining polynomial
Character	$\chi$	$=$	14.13
Dual form			14.7.b.a.13.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+5.65685 q^{2} +29.9539i q^{3} +32.0000 q^{4} +98.3767i q^{5} +169.445i q^{6} +(195.794 - 281.627i) q^{7} +181.019 q^{8} -168.235 q^{9} +556.502i q^{10} -1042.12 q^{11} +958.524i q^{12} -3661.70i q^{13} +(1107.58 - 1593.12i) q^{14} -2946.76 q^{15} +1024.00 q^{16} -1856.59i q^{17} -951.679 q^{18} +7493.18i q^{19} +3148.05i q^{20} +(8435.82 + 5864.79i) q^{21} -5895.11 q^{22} +11639.4 q^{23} +5422.23i q^{24} +5947.03 q^{25} -20713.7i q^{26} +16797.1i q^{27} +(6265.41 - 9012.06i) q^{28} -41697.6 q^{29} -16669.4 q^{30} -22040.5i q^{31} +5792.62 q^{32} -31215.5i q^{33} -10502.4i q^{34} +(27705.5 + 19261.6i) q^{35} -5383.51 q^{36} -49174.8 q^{37} +42387.8i q^{38} +109682. q^{39} +17808.1i q^{40} -18029.8i q^{41} +(47720.2 + 33176.2i) q^{42} -114355. q^{43} -33347.8 q^{44} -16550.4i q^{45} +65842.4 q^{46} +139635. i q^{47} +30672.8i q^{48} +(-40978.5 - 110282. i) q^{49} +33641.5 q^{50} +55612.0 q^{51} -117175. i q^{52} +124198. q^{53} +95018.7i q^{54} -102520. i q^{55} +(35442.5 - 50979.9i) q^{56} -224450. q^{57} -235877. q^{58} +271907. i q^{59} -94296.4 q^{60} -338552. i q^{61} -124680. i q^{62} +(-32939.3 + 47379.4i) q^{63} +32768.0 q^{64} +360226. q^{65} -176581. i q^{66} -106386. q^{67} -59410.8i q^{68} +348645. i q^{69} +(156726. + 108960. i) q^{70} +216021. q^{71} -30453.7 q^{72} +111927. i q^{73} -278174. q^{74} +178137. i q^{75} +239782. i q^{76} +(-204040. + 293488. i) q^{77} +620456. q^{78} +451441. q^{79} +100738. i q^{80} -625781. q^{81} -101992. i q^{82} -225775. i q^{83} +(269946. + 187673. i) q^{84} +182645. q^{85} -646890. q^{86} -1.24900e6i q^{87} -188643. q^{88} -411409. i q^{89} -93623.0i q^{90} +(-1.03123e6 - 716939. i) q^{91} +372461. q^{92} +660198. q^{93} +789893. i q^{94} -737154. q^{95} +173511. i q^{96} +117248. i q^{97} +(-231809. - 623847. i) q^{98} +175320. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 128 q^{4} + 308 q^{7} + 1092 q^{9} - 4440 q^{11} + 2688 q^{14} - 4320 q^{15} + 4096 q^{16} - 9984 q^{18} + 19488 q^{21} + 1536 q^{22} + 40584 q^{23} - 40700 q^{25} + 9856 q^{28} - 18264 q^{29} - 42240 q^{30}+ \cdots - 1331928 q^{99}+O(q^{100}) $ 4 * q + 128 * q^4 + 308 * q^7 + 1092 * q^9 - 4440 * q^11 + 2688 * q^14 - 4320 * q^15 + 4096 * q^16 - 9984 * q^18 + 19488 * q^21 + 1536 * q^22 + 40584 * q^23 - 40700 * q^25 + 9856 * q^28 - 18264 * q^29 - 42240 * q^30 - 84000 * q^35 + 34944 * q^36 - 23192 * q^37 + 208608 * q^39 + 80640 * q^42 - 44696 * q^43 - 142080 * q^44 + 33792 * q^46 - 310268 * q^49 + 364800 * q^50 + 157824 * q^51 + 248616 * q^53 + 86016 * q^56 - 472992 * q^57 - 840192 * q^58 - 138240 * q^60 - 125580 * q^63 + 131072 * q^64 + 1293600 * q^65 - 434776 * q^67 + 1102080 * q^70 - 451608 * q^71 - 319488 * q^72 - 981504 * q^74 - 309624 * q^77 + 1301760 * q^78 + 2092904 * q^79 - 252828 * q^81 + 623616 * q^84 - 2117760 * q^85 - 2334720 * q^86 + 49152 * q^88 - 1109472 * q^91 + 1298688 * q^92 + 995328 * q^93 - 190560 * q^95 + 827904 * q^98 - 1331928 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	5.65685			0.707107
$2$	5.65685			0.707107
$3$			29.9539i			1.10940i	0.832049	+	0.554701i	$0.187167\pi$
$3$			29.9539i			1.10940i	−0.832049	+	0.554701i	$0.812833\pi$
$4$	32.0000			0.500000
$5$			98.3767i			0.787013i	0.919322	+	0.393507i	$0.128738\pi$
$5$			98.3767i			0.787013i	−0.919322	+	0.393507i	$0.871262\pi$
$6$			169.445i			0.784466i
$7$	195.794	−	281.627i	0.570828	−	0.821070i
$7$	195.794	−	281.627i	0.570828	−	0.821070i
$8$	181.019			0.353553
$9$	−168.235			−0.230775
$10$			556.502i			0.556502i
$11$	−1042.12			−0.782958			−0.391479	−	0.920187i	$-0.628037\pi$
$11$	−1042.12			−0.782958			−0.391479	+	0.920187i	$0.628037\pi$
$12$			958.524i			0.554701i
$13$		−	3661.70i		−	1.66668i	−0.552758	−	0.833342i	$-0.686425\pi$
$13$		−	3661.70i		−	1.66668i	0.552758	−	0.833342i	$-0.313575\pi$
$14$	1107.58	−	1593.12i	0.403636	−	0.580584i
$15$	−2946.76			−0.873115
$16$	1024.00			0.250000
$17$		−	1856.59i		−	0.377893i	−0.981987	−	0.188946i	$-0.939493\pi$
$17$		−	1856.59i		−	0.377893i	0.981987	−	0.188946i	$-0.0605072\pi$
$18$	−951.679			−0.163182
$19$			7493.18i			1.09246i	0.837635	+	0.546230i	$0.183937\pi$
$19$			7493.18i			1.09246i	−0.837635	+	0.546230i	$0.816063\pi$
$20$			3148.05i			0.393507i
$21$	8435.82	+	5864.79i	0.910897	+	0.633278i
$22$	−5895.11			−0.553635
$23$	11639.4			0.956638			0.478319	−	0.878186i	$-0.341246\pi$
$23$	11639.4			0.956638			0.478319	+	0.878186i	$0.341246\pi$
$24$			5422.23i			0.392233i
$25$	5947.03			0.380610
$26$		−	20713.7i		−	1.17852i
$27$			16797.1i			0.853381i
$28$	6265.41	−	9012.06i	0.285414	−	0.410535i
$29$	−41697.6			−1.70969			−0.854844	−	0.518885i	$-0.826347\pi$
$29$	−41697.6			−1.70969			−0.854844	+	0.518885i	$0.826347\pi$
$30$	−16669.4			−0.617385
$31$		−	22040.5i		−	0.739838i	−0.929064	−	0.369919i	$-0.879386\pi$
$31$		−	22040.5i		−	0.739838i	0.929064	−	0.369919i	$-0.120614\pi$
$32$	5792.62			0.176777
$33$		−	31215.5i		−	0.868616i
$34$		−	10502.4i		−	0.267211i
$35$	27705.5	+	19261.6i	0.646193	+	0.449249i
$36$	−5383.51			−0.115387
$37$	−49174.8			−0.970816			−0.485408	−	0.874288i	$-0.661329\pi$
$37$	−49174.8			−0.970816			−0.485408	+	0.874288i	$0.661329\pi$
$38$			42387.8i			0.772486i
$39$	109682.			1.84902
$40$			17808.1i			0.278251i
$41$		−	18029.8i		−	0.261601i	−0.991409	−	0.130801i	$-0.958245\pi$
$41$		−	18029.8i		−	0.261601i	0.991409	−	0.130801i	$-0.0417548\pi$
$42$	47720.2	+	33176.2i	0.644102	+	0.447795i
$43$	−114355.			−1.43830			−0.719151	−	0.694854i	$-0.755469\pi$
$43$	−114355.			−1.43830			−0.719151	+	0.694854i	$0.755469\pi$
$44$	−33347.8			−0.391479
$45$		−	16550.4i		−	0.181623i
$46$	65842.4			0.676445
$47$			139635.i			1.34493i	0.740129	+	0.672465i	$0.234765\pi$
$47$			139635.i			1.34493i	−0.740129	+	0.672465i	$0.765235\pi$
$48$			30672.8i			0.277351i
$49$	−40978.5	−	110282.i	−0.348311	−	0.937379i
$50$	33641.5			0.269132
$51$	55612.0			0.419235
$52$		−	117175.i		−	0.833342i
$53$	124198.			0.834235			0.417117	−	0.908853i	$-0.363040\pi$
$53$	124198.			0.834235			0.417117	+	0.908853i	$0.363040\pi$
$54$			95018.7i			0.603431i
$55$		−	102520.i		−	0.616199i
$56$	35442.5	−	50979.9i	0.201818	−	0.290292i
$57$	−224450.			−1.21198
$58$	−235877.			−1.20893
$59$			271907.i			1.32393i	0.749537	+	0.661963i	$0.230276\pi$
$59$			271907.i			1.32393i	−0.749537	+	0.661963i	$0.769724\pi$
$60$	−94296.4			−0.436557
$61$		−	338552.i		−	1.49154i	−0.666202	−	0.745771i	$-0.732081\pi$
$61$		−	338552.i		−	1.49154i	0.666202	−	0.745771i	$-0.267919\pi$
$62$		−	124680.i		−	0.523144i
$63$	−32939.3	+	47379.4i	−0.131733	+	0.189482i
$64$	32768.0			0.125000
$65$	360226.			1.31170
$66$		−	176581.i		−	0.614204i
$67$	−106386.			−0.353720			−0.176860	−	0.984236i	$-0.556594\pi$
$67$	−106386.			−0.353720			−0.176860	+	0.984236i	$0.556594\pi$
$68$		−	59410.8i		−	0.188946i
$69$			348645.i			1.06130i
$70$	156726.	+	108960.i	0.456927	+	0.317667i
$71$	216021.			0.603562			0.301781	−	0.953377i	$-0.402419\pi$
$71$	216021.			0.603562			0.301781	+	0.953377i	$0.402419\pi$
$72$	−30453.7			−0.0815911
$73$			111927.i			0.287718i	0.989598	+	0.143859i	$0.0459512\pi$
$73$			111927.i			0.287718i	−0.989598	+	0.143859i	$0.954049\pi$
$74$	−278174.			−0.686471
$75$			178137.i			0.422250i
$76$			239782.i			0.546230i
$77$	−204040.	+	293488.i	−0.446934	+	0.642864i
$78$	620456.			1.30746
$79$	451441.			0.915628			0.457814	−	0.889048i	$-0.348632\pi$
$79$	451441.			0.915628			0.457814	+	0.889048i	$0.348632\pi$
$80$			100738.i			0.196753i
$81$	−625781.			−1.17752
$82$		−	101992.i		−	0.184980i
$83$		−	225775.i		−	0.394859i	−0.980317	−	0.197430i	$-0.936741\pi$
$83$		−	225775.i		−	0.394859i	0.980317	−	0.197430i	$-0.0632594\pi$
$84$	269946.	+	187673.i	0.455449	+	0.316639i
$85$	182645.			0.297407
$86$	−646890.			−1.01703
$87$		−	1.24900e6i		−	1.89673i
$88$	−188643.			−0.276818
$89$		−	411409.i		−	0.583585i	−0.956482	−	0.291792i	$-0.905748\pi$
$89$		−	411409.i		−	0.583585i	0.956482	−	0.291792i	$-0.0942516\pi$
$90$		−	93623.0i		−	0.128427i
$91$	−1.03123e6	−	716939.i	−1.36846	−	0.951389i
$92$	372461.			0.478319
$93$	660198.			0.820778
$94$			789893.i			0.951010i
$95$	−737154.			−0.859780
$96$			173511.i			0.196117i
$97$			117248.i			0.128467i	0.997935	+	0.0642333i	$0.0204602\pi$
$97$			117248.i			0.128467i	−0.997935	+	0.0642333i	$0.979540\pi$
$98$	−231809.	−	623847.i	−0.246293	−	0.662827i
$99$	175320.			0.180687
$100$	190305.			0.190305
$101$			706191.i			0.685422i	0.939441	+	0.342711i	$0.111345\pi$
$101$			706191.i			0.685422i	−0.939441	+	0.342711i	$0.888655\pi$
$102$	314589.			0.296444
$103$			1.61841e6i			1.48107i	0.672016	+	0.740536i	$0.265428\pi$
$103$			1.61841e6i			1.48107i	−0.672016	+	0.740536i	$0.734572\pi$
$104$		−	662839.i		−	0.589262i
$105$	−576958.	+	829888.i	−0.498398	+	0.716888i
$106$	702572.			0.589893
$107$	439211.			0.358527			0.179264	−	0.983801i	$-0.442629\pi$
$107$	439211.			0.358527			0.179264	+	0.983801i	$0.442629\pi$
$108$			537507.i			0.426690i
$109$	1.80395e6			1.39298			0.696490	−	0.717567i	$-0.254744\pi$
$109$	1.80395e6			1.39298			0.696490	+	0.717567i	$0.254744\pi$
$110$		−	579941.i		−	0.435718i
$111$		−	1.47297e6i		−	1.07703i
$112$	200493.	−	288386.i	0.142707	−	0.205267i
$113$	1.20195e6			0.833014			0.416507	−	0.909133i	$-0.363254\pi$
$113$	1.20195e6			0.833014			0.416507	+	0.909133i	$0.363254\pi$
$114$	−1.26968e6			−0.856998
$115$			1.14505e6i			0.752886i
$116$	−1.33432e6			−0.854844
$117$			616025.i			0.384628i
$118$			1.53814e6i			0.936157i
$119$	−522865.	−	363508.i	−0.310276	−	0.215712i
$120$	−533421.			−0.308693
$121$	−685552.			−0.386976
$122$		−	1.91514e6i		−	1.05468i
$123$	540063.			0.290221
$124$		−	705296.i		−	0.369919i
$125$			2.12218e6i			1.08656i
$126$	−186333.	+	268018.i	−0.0931490	+	0.133984i
$127$	−1.39321e6			−0.680150			−0.340075	−	0.940398i	$-0.610452\pi$
$127$	−1.39321e6			−0.680150			−0.340075	+	0.940398i	$0.610452\pi$
$128$	185364.			0.0883883
$129$		−	3.42538e6i		−	1.59566i
$130$	2.03775e6			0.927513
$131$		−	2.60277e6i		−	1.15777i	−0.815410	−	0.578884i	$-0.803489\pi$
$131$		−	2.60277e6i		−	1.15777i	0.815410	−	0.578884i	$-0.196511\pi$
$132$		−	998895.i		−	0.434308i
$133$	2.11028e6	+	1.46712e6i	0.896986	+	0.623606i
$134$	−601810.			−0.250118
$135$	−1.65244e6			−0.671622
$136$		−	336078.i		−	0.133605i
$137$	−692462.			−0.269299			−0.134649	−	0.990893i	$-0.542991\pi$
$137$	−692462.			−0.269299			−0.134649	+	0.990893i	$0.542991\pi$
$138$			1.97224e6i			0.750450i
$139$		−	481984.i		−	0.179469i	−0.995966	−	0.0897343i	$-0.971398\pi$
$139$		−	481984.i		−	0.179469i	0.995966	−	0.0897343i	$-0.0286018\pi$
$140$	886576.	+	616370.i	0.323096	+	0.224625i
$141$	−4.18260e6			−1.49207
$142$	1.22200e6			0.426783
$143$			3.81593e6i			1.30494i
$144$	−172272.			−0.0576936
$145$		−	4.10207e6i		−	1.34555i
$146$			633156.i			0.203447i
$147$	3.30336e6	−	1.22746e6i	1.03993	−	0.386417i
$148$	−1.57359e6			−0.485408
$149$	−655599.			−0.198189			−0.0990945	−	0.995078i	$-0.531595\pi$
$149$	−655599.			−0.198189			−0.0990945	+	0.995078i	$0.531595\pi$
$150$			1.00769e6i			0.298576i
$151$	47651.6			0.0138403			0.00692017	−	0.999976i	$-0.497797\pi$
$151$	47651.6			0.0138403			0.00692017	+	0.999976i	$0.497797\pi$
$152$			1.35641e6i			0.386243i
$153$			312342.i			0.0872080i
$154$	−1.15423e6	+	1.66022e6i	−0.316030	+	0.454573i
$155$	2.16827e6			0.582262
$156$	3.50983e6			0.924512
$157$			2.08512e6i			0.538806i	0.963027	+	0.269403i	$0.0868264\pi$
$157$			2.08512e6i			0.538806i	−0.963027	+	0.269403i	$0.913174\pi$
$158$	2.55373e6			0.647447
$159$			3.72022e6i			0.925502i
$160$			569858.i			0.139126i
$161$	2.27893e6	−	3.27797e6i	0.546075	−	0.785466i
$162$	−3.53995e6			−0.832631
$163$	1.59326e6			0.367894			0.183947	−	0.982936i	$-0.441112\pi$
$163$	1.59326e6			0.367894			0.183947	+	0.982936i	$0.441112\pi$
$164$		−	576955.i		−	0.130801i
$165$	3.07087e6			0.683613
$166$		−	1.27718e6i		−	0.279208i
$167$			1.21740e6i			0.261387i	0.991423	+	0.130693i	$0.0417203\pi$
$167$			1.21740e6i			0.261387i	−0.991423	+	0.130693i	$0.958280\pi$
$168$	1.52705e6	+	1.06164e6i	0.322051	+	0.223898i
$169$	−8.58126e6			−1.77783
$170$	1.03320e6			0.210298
$171$		−	1.26061e6i		−	0.252112i
$172$	−3.65936e6			−0.719151
$173$			4.61804e6i			0.891907i	0.895056	+	0.445953i	$0.147135\pi$
$173$			4.61804e6i			0.891907i	−0.895056	+	0.445953i	$0.852865\pi$
$174$		−	7.06544e6i		−	1.34119i
$175$	1.16439e6	−	1.67485e6i	0.217263	−	0.312508i
$176$	−1.06713e6			−0.195740
$177$	−8.14465e6			−1.46877
$178$		−	2.32728e6i		−	0.412657i
$179$	−2.87045e6			−0.500484			−0.250242	−	0.968183i	$-0.580510\pi$
$179$	−2.87045e6			−0.500484			−0.250242	+	0.968183i	$0.580510\pi$
$180$		−	529612.i		−	0.0908113i
$181$		−	6.81242e6i		−	1.14886i	−0.818555	−	0.574428i	$-0.805224\pi$
$181$		−	6.81242e6i		−	1.14886i	0.818555	−	0.574428i	$-0.194776\pi$
$182$	−5.83354e6	−	4.05562e6i	−0.967650	−	0.672734i
$183$	1.01409e7			1.65472
$184$	2.10696e6			0.338222
$185$		−	4.83765e6i		−	0.764045i
$186$	3.73465e6			0.580378
$187$			1.93478e6i			0.295874i
$188$			4.46831e6i			0.672465i
$189$	4.73051e6	+	3.28877e6i	0.700685	+	0.487134i
$190$	−4.16997e6			−0.607956
$191$	−5.00597e6			−0.718435			−0.359218	−	0.933254i	$-0.616956\pi$
$191$	−5.00597e6			−0.718435			−0.359218	+	0.933254i	$0.616956\pi$
$192$			981529.i			0.138675i
$193$	1.94995e6			0.271238			0.135619	−	0.990761i	$-0.456698\pi$
$193$	1.94995e6			0.271238			0.135619	+	0.990761i	$0.456698\pi$
$194$			663255.i			0.0908396i
$195$			1.07902e7i			1.45521i
$196$	−1.31131e6	−	3.52901e6i	−0.174156	−	0.468689i
$197$	1.16023e7			1.51756			0.758782	−	0.651345i	$-0.225795\pi$
$197$	1.16023e7			1.51756			0.758782	+	0.651345i	$0.225795\pi$
$198$	991761.			0.127765
$199$			727194.i			0.0922765i	0.998935	+	0.0461382i	$0.0146915\pi$
$199$			727194.i			0.0922765i	−0.998935	+	0.0461382i	$0.985309\pi$
$200$	1.07653e6			0.134566
$201$		−	3.18667e6i		−	0.392418i
$202$			3.99482e6i			0.484666i
$203$	−8.16414e6	+	1.17432e7i	−0.975938	+	1.40377i
$204$	1.77958e6			0.209618
$205$	1.77371e6			0.205884
$206$			9.15510e6i			1.04728i
$207$	−1.95815e6			−0.220768
$208$		−	3.74958e6i		−	0.416671i
$209$		−	7.80878e6i		−	0.855350i
$210$	−3.26377e6	+	4.69455e6i	−0.352421	+	0.506916i
$211$	5.82550e6			0.620134			0.310067	−	0.950715i	$-0.399648\pi$
$211$	5.82550e6			0.620134			0.310067	+	0.950715i	$0.399648\pi$
$212$	3.97435e6			0.417117
$213$			6.47068e6i			0.669593i
$214$	2.48455e6			0.253517
$215$		−	1.12499e7i		−	1.13196i
$216$			3.04060e6i			0.301716i
$217$	−6.20720e6	−	4.31540e6i	−0.607458	−	0.422320i
$218$	1.02047e7			0.984985
$219$	−3.35265e6			−0.319195
$220$		−	3.28064e6i		−	0.308099i
$221$	−6.79827e6			−0.629828
$222$		−	8.33240e6i		−	0.761573i
$223$		−	6.05484e6i		−	0.545994i	−0.962015	−	0.272997i	$-0.911985\pi$
$223$		−	6.05484e6i		−	0.545994i	0.962015	−	0.272997i	$-0.0880150\pi$
$224$	1.13416e6	−	1.63136e6i	0.100909	−	0.145146i
$225$	−1.00050e6			−0.0878351
$226$	6.79927e6			0.589030
$227$		−	1.70220e7i		−	1.45524i	−0.685981	−	0.727619i	$-0.740627\pi$
$227$		−	1.70220e7i		−	1.45524i	0.685981	−	0.727619i	$-0.259373\pi$
$228$	−7.18239e6			−0.605989
$229$			8.49217e6i			0.707151i	0.935406	+	0.353576i	$0.115034\pi$
$229$			8.49217e6i			0.707151i	−0.935406	+	0.353576i	$0.884966\pi$
$230$			6.47736e6i			0.532371i
$231$	−8.79112e6	−	6.11180e6i	−0.713195	−	0.495830i
$232$	−7.54807e6			−0.604466
$233$	−4.76243e6			−0.376496			−0.188248	−	0.982122i	$-0.560281\pi$
$233$	−4.76243e6			−0.376496			−0.188248	+	0.982122i	$0.560281\pi$
$234$			3.48477e6i			0.271973i
$235$	−1.37368e7			−1.05848
$236$			8.70101e6i			0.661963i
$237$			1.35224e7i			1.01580i
$238$	−2.95777e6	−	2.05631e6i	−0.219398	−	0.152531i
$239$	1.58931e7			1.16416			0.582082	−	0.813130i	$-0.302238\pi$
$239$	1.58931e7			1.16416			0.582082	+	0.813130i	$0.302238\pi$
$240$	−3.01748e6			−0.218279
$241$			266157.i			0.0190146i	0.999955	+	0.00950730i	$0.00302631\pi$
$241$			266157.i			0.0190146i	−0.999955	+	0.00950730i	$0.996974\pi$
$242$	−3.87807e6			−0.273633
$243$		−	6.49949e6i		−	0.452960i
$244$		−	1.08337e7i		−	0.745771i
$245$	1.08491e7	−	4.03132e6i	0.737730	−	0.274126i
$246$	3.05506e6			0.205217
$247$	2.74378e7			1.82078
$248$		−	3.98976e6i		−	0.261572i
$249$	6.76285e6			0.438058
$250$			1.20049e7i			0.768313i
$251$		−	1.01995e7i		−	0.644999i	−0.946570	−	0.322499i	$-0.895477\pi$
$251$		−	1.01995e7i		−	0.644999i	0.946570	−	0.322499i	$-0.104523\pi$
$252$	−1.05406e6	+	1.51614e6i	−0.0658663	+	0.0947410i
$253$	−1.21296e7			−0.749008
$254$	−7.88117e6			−0.480939
$255$			5.47092e6i			0.329944i
$256$	1.04858e6			0.0625000
$257$			2.68033e7i			1.57902i	0.613735	+	0.789512i	$0.289667\pi$
$257$			2.68033e7i			1.57902i	−0.613735	+	0.789512i	$0.710333\pi$
$258$		−	1.93769e7i		−	1.12830i
$259$	−9.62812e6	+	1.38489e7i	−0.554169	+	0.797108i
$260$	1.15272e7			0.655851
$261$	7.01498e6			0.394553
$262$		−	1.47235e7i		−	0.818665i
$263$	−2.62513e7			−1.44306			−0.721529	−	0.692385i	$-0.756560\pi$
$263$	−2.62513e7			−1.44306			−0.721529	+	0.692385i	$0.756560\pi$
$264$		−	5.65060e6i		−	0.307102i
$265$			1.22182e7i			0.656554i
$266$	1.19376e7	+	8.29928e6i	0.634265	+	0.440956i
$267$	1.23233e7			0.647431
$268$	−3.40435e6			−0.176860
$269$			3.58901e7i			1.84382i	0.387408	+	0.921909i	$0.373371\pi$
$269$			3.58901e7i			1.84382i	−0.387408	+	0.921909i	$0.626629\pi$
$270$	−9.34762e6			−0.474908
$271$			1.64221e6i			0.0825127i	0.999149	+	0.0412563i	$0.0131360\pi$
$271$			1.64221e6i			0.0825127i	−0.999149	+	0.0412563i	$0.986864\pi$
$272$		−	1.90115e6i		−	0.0944732i
$273$	2.14751e7	−	3.08895e7i	1.05547	−	1.51818i
$274$	−3.91715e6			−0.190423
$275$	−6.19751e6			−0.298002
$276$			1.11567e7i			0.530648i
$277$	3.84263e7			1.80796			0.903980	−	0.427574i	$-0.140632\pi$
$277$	3.84263e7			1.80796			0.903980	+	0.427574i	$0.140632\pi$
$278$		−	2.72652e6i		−	0.126904i
$279$			3.70798e6i			0.170736i
$280$	5.01523e6	+	3.48671e6i	0.228464	+	0.158834i
$281$	−3.78655e7			−1.70657			−0.853286	−	0.521443i	$-0.825394\pi$
$281$	−3.78655e7			−1.70657			−0.853286	+	0.521443i	$0.825394\pi$
$282$	−2.36604e7			−1.05505
$283$		−	3.58026e6i		−	0.157963i	−0.996876	−	0.0789815i	$-0.974833\pi$
$283$		−	3.58026e6i		−	0.157963i	0.996876	−	0.0789815i	$-0.0251668\pi$
$284$	6.91269e6			0.301781
$285$		−	2.20806e7i		−	0.953842i
$286$			2.15861e7i			0.922735i
$287$	−5.07769e6	−	3.53013e6i	−0.214793	−	0.149329i
$288$	−974519.			−0.0407956
$289$	2.06907e7			0.857197
$290$		−	2.32048e7i		−	0.951446i
$291$	−3.51203e6			−0.142521
$292$			3.58167e6i			0.143859i
$293$		−	3.57198e7i		−	1.42006i	−0.704172	−	0.710030i	$-0.748682\pi$
$293$		−	3.57198e7i		−	1.42006i	0.704172	−	0.710030i	$-0.251318\pi$
$294$	1.86866e7	−	6.94358e6i	0.735342	−	0.273238i
$295$	−2.67493e7			−1.04195
$296$	−8.90158e6			−0.343235
$297$		−	1.75046e7i		−	0.668162i
$298$	−3.70863e6			−0.140141
$299$		−	4.26201e7i		−	1.59441i
$300$			5.70038e6i			0.211125i
$301$	−2.23900e7	+	3.22055e7i	−0.821022	+	1.18095i
$302$	269558.			0.00978660
$303$	−2.11531e7			−0.760409
$304$			7.67302e6i			0.273115i
$305$	3.33056e7			1.17386
$306$			1.76687e6i			0.0616654i
$307$			3.71810e7i			1.28501i	0.766282	+	0.642504i	$0.222105\pi$
$307$			3.71810e7i			1.28501i	−0.766282	+	0.642504i	$0.777895\pi$
$308$	−6.52929e6	+	9.39163e6i	−0.223467	+	0.321432i
$309$	−4.84776e7			−1.64311
$310$	1.22656e7			0.411721
$311$		−	1.37937e7i		−	0.458563i	−0.973360	−	0.229281i	$-0.926362\pi$
$311$		−	1.37937e7i		−	0.458563i	0.973360	−	0.229281i	$-0.0736376\pi$
$312$	1.98546e7			0.653728
$313$		−	9.13790e6i		−	0.297998i	−0.988837	−	0.148999i	$-0.952395\pi$
$313$		−	9.13790e6i		−	0.297998i	0.988837	−	0.148999i	$-0.0476051\pi$
$314$			1.17952e7i			0.380994i
$315$	−4.66103e6	−	3.24046e6i	−0.149125	−	0.103675i
$316$	1.44461e7			0.457814
$317$	−1.28223e7			−0.402520			−0.201260	−	0.979538i	$-0.564504\pi$
$317$	−1.28223e7			−0.402520			−0.201260	+	0.979538i	$0.564504\pi$
$318$			2.10448e7i			0.654429i
$319$	4.34538e7			1.33862
$320$			3.22361e6i			0.0983767i
$321$			1.31561e7i			0.397751i
$322$	1.28916e7	−	1.85430e7i	0.386134	−	0.555408i
$323$	1.39117e7			0.412833
$324$	−2.00250e7			−0.588759
$325$		−	2.17763e7i		−	0.634357i
$326$	9.01282e6			0.260141
$327$			5.40353e7i			1.54538i
$328$		−	3.26375e6i		−	0.0924901i
$329$	3.93249e7	+	2.73396e7i	1.10428	+	0.767724i
$330$	1.73715e7			0.483387
$331$	6.24496e7			1.72205			0.861025	−	0.508563i	$-0.169823\pi$
$331$	6.24496e7			1.72205			0.861025	+	0.508563i	$0.169823\pi$
$332$		−	7.22481e6i		−	0.197430i
$333$	8.27290e6			0.224040
$334$			6.88665e6i			0.184828i
$335$		−	1.04659e7i		−	0.278383i
$336$	8.63828e6	+	6.00554e6i	0.227724	+	0.158319i
$337$	−5.54168e7			−1.44794			−0.723972	−	0.689829i	$-0.757686\pi$
$337$	−5.54168e7			−1.44794			−0.723972	+	0.689829i	$0.757686\pi$
$338$	−4.85430e7			−1.25712
$339$			3.60031e7i			0.924148i
$340$	5.84463e6			0.148703
$341$			2.29688e7i			0.579262i
$342$		−	7.13110e6i		−	0.178270i
$343$	−3.90816e7	−	1.00518e7i	−0.968479	−	0.249094i
$344$	−2.07005e7			−0.508516
$345$	−3.42986e7			−0.835254
$346$			2.61236e7i			0.630673i
$347$	−1.00493e7			−0.240518			−0.120259	−	0.992743i	$-0.538372\pi$
$347$	−1.00493e7			−0.240518			−0.120259	+	0.992743i	$0.538372\pi$
$348$		−	3.99681e7i		−	0.948367i
$349$		−	7.23514e7i		−	1.70204i	−0.525130	−	0.851022i	$-0.675983\pi$
$349$		−	7.23514e7i		−	1.70204i	0.525130	−	0.851022i	$-0.324017\pi$
$350$	6.58680e6	−	9.47435e6i	0.153628	−	0.220976i
$351$	6.15060e7			1.42232
$352$	−6.03659e6			−0.138409
$353$		−	3.04434e7i		−	0.692099i	−0.938216	−	0.346050i	$-0.887523\pi$
$353$		−	3.04434e7i		−	0.692099i	0.938216	−	0.346050i	$-0.112477\pi$
$354$	−4.60731e7			−1.03858
$355$			2.12515e7i			0.475011i
$356$		−	1.31651e7i		−	0.291792i
$357$	1.08885e7	−	1.56618e7i	0.239311	−	0.344221i
$358$	−1.62377e7			−0.353896
$359$	7.98054e6			0.172484			0.0862420	−	0.996274i	$-0.472514\pi$
$359$	7.98054e6			0.172484			0.0862420	+	0.996274i	$0.472514\pi$
$360$		−	2.99594e6i		−	0.0642133i
$361$	−9.10187e6			−0.193468
$362$		−	3.85369e7i		−	0.812364i
$363$		−	2.05349e7i		−	0.429312i
$364$	−3.29995e7	−	2.29421e7i	−0.684232	−	0.475695i
$365$	−1.10110e7			−0.226438
$366$	5.73658e7			1.17006
$367$			2.06363e7i			0.417478i	0.977971	+	0.208739i	$0.0669360\pi$
$367$			2.06363e7i			0.417478i	−0.977971	+	0.208739i	$0.933064\pi$
$368$	1.19188e7			0.239159
$369$			3.03324e6i			0.0603709i
$370$		−	2.73659e7i		−	0.540262i
$371$	2.43173e7	−	3.49776e7i	0.476204	−	0.684965i
$372$	2.11264e7			0.410389
$373$	−9.06283e6			−0.174637			−0.0873187	−	0.996180i	$-0.527830\pi$
$373$	−9.06283e6			−0.174637			−0.0873187	+	0.996180i	$0.527830\pi$
$374$			1.09448e7i			0.209215i
$375$	−6.35676e7			−1.20543
$376$			2.52766e7i			0.475505i
$377$			1.52684e8i			2.84951i
$378$	2.67598e7	+	1.86041e7i	0.495459	+	0.344455i
$379$	3.92591e7			0.721146			0.360573	−	0.932731i	$-0.382581\pi$
$379$	3.92591e7			0.721146			0.360573	+	0.932731i	$0.382581\pi$
$380$	−2.35889e7			−0.429890
$381$		−	4.17320e7i		−	0.754560i
$382$	−2.83180e7			−0.508011
$383$			4.25901e7i			0.758075i	0.925381	+	0.379037i	$0.123745\pi$
$383$			4.25901e7i			0.758075i	−0.925381	+	0.379037i	$0.876255\pi$
$384$			5.55236e6i			0.0980583i
$385$	−2.88724e7	−	2.00728e7i	−0.505942	−	0.351743i
$386$	1.10306e7			0.191795
$387$	1.92385e7			0.331923
$388$			3.75194e6i			0.0642333i
$389$	−3.23230e7			−0.549114			−0.274557	−	0.961571i	$-0.588531\pi$
$389$	−3.23230e7			−0.549114			−0.274557	+	0.961571i	$0.588531\pi$
$390$			6.10384e7i			1.02899i
$391$		−	2.16096e7i		−	0.361506i
$392$	−7.41789e6	−	1.99631e7i	−0.123147	−	0.331414i
$393$	7.79629e7			1.28443
$394$	6.56327e7			1.07308
$395$			4.44112e7i			0.720612i
$396$	5.61025e6			0.0903434
$397$		−	1.21097e8i		−	1.93536i	−0.252186	−	0.967679i	$-0.581149\pi$
$397$		−	1.21097e8i		−	1.93536i	0.252186	−	0.967679i	$-0.418851\pi$
$398$			4.11363e6i			0.0652493i
$399$	−4.39459e7	+	6.32111e7i	−0.691831	+	0.995118i
$400$	6.08976e6			0.0951526
$401$	4.98925e7			0.773753			0.386876	−	0.922132i	$-0.373554\pi$
$401$	4.98925e7			0.773753			0.386876	+	0.922132i	$0.373554\pi$
$402$		−	1.80265e7i		−	0.277482i
$403$	−8.07058e7			−1.23308
$404$			2.25981e7i			0.342711i
$405$		−	6.15623e7i		−	0.926722i
$406$	−4.61833e7	+	6.64294e7i	−0.690092	+	0.992618i
$407$	5.12459e7			0.760109
$408$	1.00668e7			0.148222
$409$		−	1.08411e7i		−	0.158454i	−0.996857	−	0.0792269i	$-0.974755\pi$
$409$		−	1.08411e7i		−	0.158454i	0.996857	−	0.0792269i	$-0.0252452\pi$
$410$	1.00336e7			0.145582
$411$		−	2.07419e7i		−	0.298761i
$412$			5.17891e7i			0.740536i
$413$	7.65762e7	+	5.32377e7i	1.08704	+	0.755734i
$414$	−1.10770e7			−0.156106
$415$	2.22110e7			0.310759
$416$		−	2.12109e7i		−	0.294631i
$417$	1.44373e7			0.199103
$418$		−	4.41731e7i		−	0.604824i
$419$		−	3.85015e7i		−	0.523402i	−0.965149	−	0.261701i	$-0.915717\pi$
$419$		−	3.85015e7i		−	0.523402i	0.965149	−	0.261701i	$-0.0842834\pi$
$420$	−1.84627e7	+	2.65564e7i	−0.249199	+	0.358444i
$421$	−6.80531e7			−0.912014			−0.456007	−	0.889976i	$-0.650721\pi$
$421$	−6.80531e7			−0.912014			−0.456007	+	0.889976i	$0.650721\pi$
$422$	3.29540e7			0.438501
$423$		−	2.34914e7i		−	0.310376i
$424$	2.24823e7			0.294947
$425$		−	1.10412e7i		−	0.143830i
$426$			3.66037e7i			0.473474i
$427$	−9.53453e7	−	6.62864e7i	−1.22466	−	0.851414i
$428$	1.40548e7			0.179264
$429$	−1.14302e8			−1.44771
$430$		−	6.36388e7i		−	0.800418i
$431$	−5.94074e7			−0.742008			−0.371004	−	0.928631i	$-0.620986\pi$
$431$	−5.94074e7			−0.742008			−0.371004	+	0.928631i	$0.620986\pi$
$432$			1.72002e7i			0.213345i
$433$			6.40026e7i			0.788377i	0.919030	+	0.394189i	$0.128974\pi$
$433$			6.40026e7i			0.788377i	−0.919030	+	0.394189i	$0.871026\pi$
$434$	−3.51132e7	−	2.44116e7i	−0.429538	−	0.298625i
$435$	1.22873e8			1.49275
$436$	5.77264e7			0.696490
$437$			8.72162e7i			1.04509i
$438$	−1.89655e7			−0.225705
$439$		−	5.84728e7i		−	0.691131i	−0.938395	−	0.345565i	$-0.887687\pi$
$439$		−	5.84728e7i		−	0.691131i	0.938395	−	0.345565i	$-0.112313\pi$
$440$		−	1.85581e7i		−	0.217859i
$441$	6.89400e6	+	1.85532e7i	0.0803814	+	0.216323i
$442$	−3.84568e7			−0.445355
$443$	−1.54616e8			−1.77845			−0.889227	−	0.457467i	$-0.848757\pi$
$443$	−1.54616e8			−1.77845			−0.889227	+	0.457467i	$0.848757\pi$
$444$		−	4.71352e7i		−	0.538513i
$445$	4.04731e7			0.459289
$446$		−	3.42513e7i		−	0.386076i
$447$		−	1.96377e7i		−	0.219871i
$448$	6.41578e6	−	9.22835e6i	0.0713535	−	0.102634i
$449$	8.30902e7			0.917933			0.458966	−	0.888454i	$-0.348220\pi$
$449$	8.30902e7			0.917933			0.458966	+	0.888454i	$0.348220\pi$
$450$	−5.65967e6			−0.0621088
$451$			1.87892e7i			0.204823i
$452$	3.84625e7			0.416507
$453$			1.42735e6i			0.0153545i
$454$		−	9.62913e7i		−	1.02901i
$455$	7.05301e7	−	1.01449e8i	0.748756	−	1.07700i
$456$	−4.06298e7			−0.428499
$457$	3.71422e7			0.389152			0.194576	−	0.980887i	$-0.437667\pi$
$457$	3.71422e7			0.389152			0.194576	+	0.980887i	$0.437667\pi$
$458$			4.80390e7i			0.500031i
$459$	3.11853e7			0.322486
$460$			3.66415e7i			0.376443i
$461$		−	3.38118e6i		−	0.0345116i	−0.999851	−	0.0172558i	$-0.994507\pi$
$461$		−	3.38118e6i		−	0.0345116i	0.999851	−	0.0172558i	$-0.00549296\pi$
$462$	−4.97301e7	−	3.45736e7i	−0.504305	−	0.350605i
$463$	6.63410e7			0.668404			0.334202	−	0.942502i	$-0.391533\pi$
$463$	6.63410e7			0.668404			0.334202	+	0.942502i	$0.391533\pi$
$464$	−4.26983e7			−0.427422
$465$			6.49481e7i			0.645963i
$466$	−2.69404e7			−0.266223
$467$			9.97322e7i			0.979230i	0.871939	+	0.489615i	$0.162863\pi$
$467$			9.97322e7i			0.979230i	−0.871939	+	0.489615i	$0.837137\pi$
$468$			1.97128e7i			0.192314i
$469$	−2.08297e7	+	2.99612e7i	−0.201913	+	0.290429i
$470$	−7.77071e7			−0.748457
$471$	−6.24575e7			−0.597753
$472$			4.92203e7i			0.468078i
$473$	1.19171e8			1.12613
$474$			7.64942e7i			0.718280i
$475$			4.45622e7i			0.415801i
$476$	−1.67317e7	−	1.16323e7i	−0.155138	−	0.107856i
$477$	−2.08945e7			−0.192520
$478$	8.99048e7			0.823188
$479$		−	8.50867e7i		−	0.774203i	−0.922037	−	0.387102i	$-0.873476\pi$
$479$		−	8.50867e7i		−	0.774203i	0.922037	−	0.387102i	$-0.126524\pi$
$480$	−1.70695e7			−0.154346
$481$			1.80063e8i			1.61804i
$482$			1.50561e6i			0.0134453i
$483$	9.81879e7	+	6.82627e7i	0.871398	+	0.605818i
$484$	−2.19377e7			−0.193488
$485$	−1.15345e7			−0.101105
$486$		−	3.67667e7i		−	0.320291i
$487$	1.19789e8			1.03712			0.518560	−	0.855041i	$-0.326468\pi$
$487$	1.19789e8			1.03712			0.518560	+	0.855041i	$0.326468\pi$
$488$		−	6.12844e7i		−	0.527340i
$489$			4.77242e7i			0.408143i
$490$	6.13720e7	−	2.28046e7i	0.521654	−	0.193836i
$491$	−2.24857e8			−1.89960			−0.949800	−	0.312859i	$-0.898713\pi$
$491$	−2.24857e8			−1.89960			−0.949800	+	0.312859i	$0.898713\pi$
$492$	1.72820e7			0.145111
$493$			7.74152e7i			0.646079i
$494$	1.55212e8			1.28749
$495$			1.72474e7i			0.142203i
$496$		−	2.25695e7i		−	0.184959i
$497$	4.22957e7	−	6.08375e7i	0.344530	−	0.495566i
$498$	3.82564e7			0.309754
$499$	5.80019e7			0.466810			0.233405	−	0.972380i	$-0.425013\pi$
$499$	5.80019e7			0.466810			0.233405	+	0.972380i	$0.425013\pi$
$500$			6.79099e7i			0.543279i
$501$	−3.64658e7			−0.289983
$502$		−	5.76972e7i		−	0.456083i
$503$		−	9.94846e7i		−	0.781721i	−0.920450	−	0.390860i	$-0.872177\pi$
$503$		−	9.94846e7i		−	0.781721i	0.920450	−	0.390860i	$-0.127823\pi$
$504$	−5.96265e6	+	8.57659e6i	−0.0465745	+	0.0669920i
$505$	−6.94727e7			−0.539436
$506$	−6.86156e7			−0.529628
$507$		−	2.57042e8i		−	1.97233i
$508$	−4.45826e7			−0.340075
$509$		−	1.51579e8i		−	1.14944i	−0.818350	−	0.574721i	$-0.805111\pi$
$509$		−	1.51579e8i		−	1.14944i	0.818350	−	0.574721i	$-0.194889\pi$
$510$			3.09482e7i			0.233305i
$511$	3.15217e7	+	2.19147e7i	0.236237	+	0.164237i
$512$	5.93164e6			0.0441942
$513$	−1.25864e8			−0.932284
$514$			1.51622e8i			1.11654i
$515$	−1.59214e8			−1.16562
$516$		−	1.09612e8i		−	0.797828i
$517$		−	1.45516e8i		−	1.05302i
$518$	−5.44649e7	+	7.83414e7i	−0.391857	+	0.563640i
$519$	−1.38328e8			−0.989484
$520$	6.52079e7			0.463757
$521$		−	1.36113e8i		−	0.962469i	−0.876592	−	0.481234i	$-0.840189\pi$
$521$		−	1.36113e8i		−	0.962469i	0.876592	−	0.481234i	$-0.159811\pi$
$522$	3.96827e7			0.278991
$523$			1.02678e8i			0.717749i	0.933386	+	0.358874i	$0.116839\pi$
$523$			1.02678e8i			0.717749i	−0.933386	+	0.358874i	$0.883161\pi$
$524$		−	8.32885e7i		−	0.578884i
$525$	5.01681e7	+	3.48781e7i	0.346697	+	0.241032i
$526$	−1.48500e8			−1.02040
$527$	−4.09201e7			−0.279579
$528$		−	3.19646e7i		−	0.217154i
$529$	−1.25600e7			−0.0848445
$530$			6.91167e7i			0.464254i
$531$		−	4.57441e7i		−	0.305528i
$532$	6.75290e7	+	4.69478e7i	0.448493	+	0.311803i
$533$	−6.60199e7			−0.436007
$534$	6.97111e7			0.457803
$535$			4.32081e7i			0.282166i
$536$	−1.92579e7			−0.125059
$537$		−	8.59810e7i		−	0.555239i
$538$			2.03025e8i			1.30378i
$539$	4.27044e7	+	1.14927e8i	0.272713	+	0.733929i
$540$	−5.28781e7			−0.335811
$541$	1.71991e8			1.08621			0.543104	−	0.839665i	$-0.317249\pi$
$541$	1.71991e8			1.08621			0.543104	+	0.839665i	$0.317249\pi$
$542$			9.28974e6i			0.0583453i
$543$	2.04058e8			1.27454
$544$		−	1.07545e7i		−	0.0668026i
$545$			1.77466e8i			1.09629i
$546$	1.21482e8	−	1.74737e8i	0.746333	−	1.07351i
$547$	−3.57048e7			−0.218154			−0.109077	−	0.994033i	$-0.534790\pi$
$547$	−3.57048e7			−0.218154			−0.109077	+	0.994033i	$0.534790\pi$
$548$	−2.21588e7			−0.134649
$549$			5.69561e7i			0.344210i
$550$	−3.50584e7			−0.210719
$551$		−	3.12448e8i		−	1.86777i
$552$			6.31116e7i			0.375225i
$553$	8.83893e7	−	1.27138e8i	0.522666	−	0.751795i
$554$	2.17372e8			1.27842
$555$	1.44906e8			0.847634
$556$		−	1.54235e7i		−	0.0897343i
$557$	−7.51706e7			−0.434993			−0.217497	−	0.976061i	$-0.569789\pi$
$557$	−7.51706e7			−0.434993			−0.217497	+	0.976061i	$0.569789\pi$
$558$			2.09755e7i			0.120728i
$559$			4.18734e8i			2.39719i
$560$	2.83704e7	+	1.97238e7i	0.161548	+	0.112312i
$561$	−5.79542e7			−0.328244
$562$	−2.14200e8			−1.20673
$563$			2.09618e8i			1.17464i	0.809356	+	0.587318i	$0.199816\pi$
$563$			2.09618e8i			1.17464i	−0.809356	+	0.587318i	$0.800184\pi$
$564$	−1.33843e8			−0.746035
$565$			1.18244e8i			0.655593i
$566$		−	2.02530e7i		−	0.111697i
$567$	−1.22524e8	+	1.76237e8i	−0.672160	+	0.966824i
$568$	3.91041e7			0.213391
$569$	3.85572e7			0.209300			0.104650	−	0.994509i	$-0.466628\pi$
$569$	3.85572e7			0.209300			0.104650	+	0.994509i	$0.466628\pi$
$570$		−	1.24907e8i		−	0.674468i
$571$	6.50282e7			0.349296			0.174648	−	0.984631i	$-0.444121\pi$
$571$	6.50282e7			0.349296			0.174648	+	0.984631i	$0.444121\pi$
$572$			1.22110e8i			0.652472i
$573$		−	1.49948e8i		−	0.797034i
$574$	−2.87237e7	−	1.99694e7i	−0.151882	−	0.105592i
$575$	6.92200e7			0.364106
$576$	−5.51271e6			−0.0288468
$577$		−	1.17548e8i		−	0.611909i	−0.952046	−	0.305954i	$-0.901025\pi$
$577$		−	1.17548e8i		−	0.611909i	0.952046	−	0.305954i	$-0.0989755\pi$
$578$	1.17044e8			0.606130
$579$			5.84085e7i			0.300913i
$580$		−	1.31266e8i		−	0.672774i
$581$	−6.35844e7	−	4.42055e7i	−0.324207	−	0.225397i
$582$	−1.98671e7			−0.100778
$583$	−1.29429e8			−0.653171
$584$			2.02610e7i			0.101724i
$585$	−6.06025e7			−0.302707
$586$		−	2.02062e8i		−	1.00413i
$587$		−	2.41814e8i		−	1.19555i	−0.801664	−	0.597775i	$-0.796052\pi$
$587$		−	2.41814e8i		−	1.19555i	0.801664	−	0.597775i	$-0.203948\pi$
$588$	1.05708e8	−	3.92788e7i	0.519965	−	0.193209i
$589$	1.65153e8			0.808243
$590$	−1.51317e8			−0.736768
$591$			3.47535e8i			1.68359i
$592$	−5.03550e7			−0.242704
$593$			2.31180e8i			1.10863i	0.832307	+	0.554314i	$0.187019\pi$
$593$			2.31180e8i			1.10863i	−0.832307	+	0.554314i	$0.812981\pi$
$594$		−	9.90207e7i		−	0.472462i
$595$	3.57607e7	−	5.14377e7i	0.169768	−	0.244192i
$596$	−2.09792e7			−0.0990945
$597$	−2.17823e7			−0.102372
$598$		−	2.41096e8i		−	1.12742i
$599$	−3.84910e7			−0.179093			−0.0895464	−	0.995983i	$-0.528542\pi$
$599$	−3.84910e7			−0.179093			−0.0895464	+	0.995983i	$0.528542\pi$
$600$			3.22462e7i			0.149288i
$601$		−	3.32931e8i		−	1.53367i	−0.641847	−	0.766833i	$-0.721832\pi$
$601$		−	3.32931e8i		−	1.53367i	0.641847	−	0.766833i	$-0.278168\pi$
$602$	−1.26657e8	+	1.82182e8i	−0.580550	+	0.835055i
$603$	1.78978e7			0.0816297
$604$	1.52485e6			0.00692017
$605$		−	6.74423e7i		−	0.304555i
$606$	−1.19660e8			−0.537690
$607$		−	5.87633e7i		−	0.262749i	−0.991333	−	0.131374i	$-0.958061\pi$
$607$		−	5.87633e7i		−	0.262749i	0.991333	−	0.131374i	$-0.0419390\pi$
$608$			4.34051e7i			0.193121i
$609$	−3.51753e8	−	2.44547e8i	−1.55735	−	1.08271i
$610$	1.88405e8			0.830047
$611$	5.11301e8			2.24157
$612$			9.99495e6i			0.0436040i
$613$	−1.11411e7			−0.0483665			−0.0241833	−	0.999708i	$-0.507699\pi$
$613$	−1.11411e7			−0.0483665			−0.0241833	+	0.999708i	$0.507699\pi$
$614$			2.10328e8i			0.908639i
$615$			5.31296e7i			0.228408i
$616$	−3.69352e7	+	5.31271e7i	−0.158015	+	0.227287i
$617$	6.61360e7			0.281567			0.140784	−	0.990040i	$-0.455038\pi$
$617$	6.61360e7			0.281567			0.140784	+	0.990040i	$0.455038\pi$
$618$	−2.74231e8			−1.16185
$619$		−	1.81247e8i		−	0.764185i	−0.924124	−	0.382093i	$-0.875204\pi$
$619$		−	1.81247e8i		−	0.764185i	0.924124	−	0.382093i	$-0.124796\pi$
$620$	6.93847e7			0.291131
$621$			1.95508e8i			0.816376i
$622$		−	7.80288e7i		−	0.324253i
$623$	−1.15864e8	−	8.05514e7i	−0.479164	−	0.333126i
$624$	1.12315e8			0.462256
$625$	−1.15851e8			−0.474526
$626$		−	5.16918e7i		−	0.210716i
$627$	2.33903e8			0.948928
$628$			6.67239e7i			0.269403i
$629$			9.12972e7i			0.366864i
$630$	−2.63668e7	−	1.83308e7i	−0.105447	−	0.0733095i
$631$	−1.25706e8			−0.500344			−0.250172	−	0.968201i	$-0.580487\pi$
$631$	−1.25706e8			−0.500344			−0.250172	+	0.968201i	$0.580487\pi$
$632$	8.17195e7			0.323724
$633$			1.74496e8i			0.687979i
$634$	−7.25338e7			−0.284625
$635$		−	1.37059e8i		−	0.535287i
$636$			1.19047e8i			0.462751i
$637$	−4.03819e8	+	1.50051e8i	−1.56231	+	0.580525i
$638$	2.45812e8			0.946544
$639$	−3.63423e7			−0.139287
$640$			1.82355e7i			0.0695628i
$641$	−5.14744e8			−1.95442			−0.977209	−	0.212281i	$-0.931911\pi$
$641$	−5.14744e8			−1.95442			−0.977209	+	0.212281i	$0.931911\pi$
$642$			7.44220e7i			0.281252i
$643$			2.77852e8i			1.04515i	0.852592	+	0.522577i	$0.175029\pi$
$643$			2.77852e8i			1.04515i	−0.852592	+	0.522577i	$0.824971\pi$
$644$	7.29256e7	−	1.04895e8i	0.273038	−	0.392733i
$645$	3.36977e8			1.25580
$646$	7.86967e7			0.291917
$647$		−	1.33880e8i		−	0.494315i	−0.968975	−	0.247157i	$-0.920504\pi$
$647$		−	1.33880e8i		−	0.494315i	0.968975	−	0.247157i	$-0.0794965\pi$
$648$	−1.13278e8			−0.416315
$649$		−	2.83359e8i		−	1.03658i
$650$		−	1.23185e8i		−	0.448558i
$651$	1.29263e8	−	1.85930e8i	0.468523	−	0.673916i
$652$	5.09842e7			0.183947
$653$	3.72064e8			1.33622			0.668110	−	0.744062i	$-0.267103\pi$
$653$	3.72064e8			1.33622			0.668110	+	0.744062i	$0.267103\pi$
$654$			3.05670e8i			1.09275i
$655$	2.56051e8			0.911178
$656$		−	1.84625e7i		−	0.0654003i
$657$		−	1.88300e7i		−	0.0663980i
$658$	2.22455e8	+	1.54656e8i	0.780845	+	0.542863i
$659$	−4.95336e7			−0.173079			−0.0865394	−	0.996248i	$-0.527581\pi$
$659$	−4.95336e7			−0.173079			−0.0865394	+	0.996248i	$0.527581\pi$
$660$	9.82679e7			0.341806
$661$			6.94997e7i			0.240646i	0.992735	+	0.120323i	$0.0383930\pi$
$661$			6.94997e7i			0.240646i	−0.992735	+	0.120323i	$0.961607\pi$
$662$	3.53268e8			1.21767
$663$		−	2.03635e8i		−	0.698732i
$664$		−	4.08697e7i		−	0.139604i
$665$	−1.44330e8	+	2.07602e8i	−0.490786	+	0.705939i
$666$	4.67986e7			0.158420
$667$	−4.85335e8			−1.63555
$668$			3.89568e7i			0.130693i
$669$	1.81366e8			0.605728
$670$		−	5.92041e7i		−	0.196846i
$671$			3.52811e8i			1.16782i
$672$	4.88655e7	+	3.39725e7i	0.161025	+	0.111949i
$673$	1.80776e8			0.593056			0.296528	−	0.955024i	$-0.404171\pi$
$673$	1.80776e8			0.593056			0.296528	+	0.955024i	$0.404171\pi$
$674$	−3.13485e8			−1.02385
$675$			9.98929e7i			0.324805i
$676$	−2.74600e8			−0.888917
$677$			2.40792e8i			0.776024i	0.921654	+	0.388012i	$0.126838\pi$
$677$			2.40792e8i			0.776024i	−0.921654	+	0.388012i	$0.873162\pi$
$678$			2.03665e8i			0.653471i
$679$	3.30202e7	+	2.29564e7i	0.105480	+	0.0733323i
$680$	3.30622e7			0.105149
$681$	5.09876e8			1.61445
$682$			1.29931e8i			0.409600i
$683$	−5.06433e8			−1.58950			−0.794749	−	0.606939i	$-0.792397\pi$
$683$	−5.06433e8			−1.58950			−0.794749	+	0.606939i	$0.792397\pi$
$684$		−	4.03396e7i		−	0.126056i
$685$		−	6.81221e7i		−	0.211942i
$686$	−2.21079e8	−	5.68618e7i	−0.684818	−	0.176136i
$687$	−2.54373e8			−0.784515
$688$	−1.17100e8			−0.359575
$689$		−	4.54778e8i		−	1.39041i
$690$	−1.94022e8			−0.590614
$691$		−	3.85108e7i		−	0.116721i	−0.998296	−	0.0583604i	$-0.981413\pi$
$691$		−	3.85108e7i		−	0.116721i	0.998296	−	0.0583604i	$-0.0185873\pi$
$692$			1.47777e8i			0.445953i
$693$	3.43267e7	−	4.93749e7i	0.103141	−	0.148357i
$694$	−5.68474e7			−0.170072
$695$	4.74160e7			0.141244
$696$		−	2.26094e8i		−	0.670596i
$697$	−3.34739e7			−0.0988573
$698$		−	4.09281e8i		−	1.20353i
$699$		−	1.42653e8i		−	0.417686i
$700$	3.72606e7	−	5.35950e7i	0.108631	−	0.156254i
$701$	3.57882e8			1.03893			0.519464	−	0.854492i	$-0.326132\pi$
$701$	3.57882e8			1.03893			0.519464	+	0.854492i	$0.326132\pi$
$702$	3.47930e8			1.00573
$703$		−	3.68475e8i		−	1.06058i
$704$	−3.41481e7			−0.0978698
$705$		−	4.11470e8i		−	1.17428i
$706$		−	1.72214e8i		−	0.489388i
$707$	1.98882e8	+	1.38268e8i	0.562779	+	0.391258i
$708$	−2.60629e8			−0.734383
$709$	−2.84537e8			−0.798361			−0.399181	−	0.916872i	$-0.630705\pi$
$709$	−2.84537e8			−0.798361			−0.399181	+	0.916872i	$0.630705\pi$
$710$			1.20216e8i			0.335884i
$711$	−7.59479e7			−0.211304
$712$		−	7.44730e7i		−	0.206328i
$713$		−	2.56538e8i		−	0.707756i
$714$	6.15946e7	−	8.85967e7i	0.169219	−	0.243401i
$715$	−3.75398e8			−1.02701
$716$	−9.18543e7			−0.250242
$717$			4.76059e8i			1.29153i
$718$	4.51447e7			0.121965
$719$			3.52700e8i			0.948896i	0.880283	+	0.474448i	$0.157352\pi$
$719$			3.52700e8i			0.948896i	−0.880283	+	0.474448i	$0.842648\pi$
$720$		−	1.69476e7i		−	0.0454057i
$721$	4.55787e8	+	3.16874e8i	1.21606	+	0.845437i
$722$	−5.14879e7			−0.136802
$723$	−7.97244e6			−0.0210948
$724$		−	2.17997e8i		−	0.574428i
$725$	−2.47977e8			−0.650725
$726$		−	1.16163e8i		−	0.303570i
$727$		−	7.48885e8i		−	1.94900i	−0.224387	−	0.974500i	$-0.572038\pi$
$727$		−	7.48885e8i		−	1.94900i	0.224387	−	0.974500i	$-0.427962\pi$
$728$	−1.86673e8	−	1.29780e8i	−0.483825	−	0.336367i
$729$	−2.61510e8			−0.675002
$730$	−6.22877e7			−0.160116
$731$			2.12310e8i			0.543524i
$732$	3.24510e8			0.827361
$733$			6.35196e8i			1.61286i	0.591331	+	0.806429i	$0.298602\pi$
$733$			6.35196e8i			1.61286i	−0.591331	+	0.806429i	$0.701398\pi$
$734$			1.16737e8i			0.295202i
$735$	1.20754e8	+	3.24974e8i	0.304116	+	0.818439i
$736$	6.74227e7			0.169111
$737$	1.10867e8			0.276948
$738$			1.71586e7i			0.0426887i
$739$	3.65308e8			0.905161			0.452580	−	0.891724i	$-0.350504\pi$
$739$	3.65308e8			0.905161			0.452580	+	0.891724i	$0.350504\pi$
$740$		−	1.54805e8i		−	0.382023i
$741$			8.21869e8i			2.01998i
$742$	1.37559e8	−	1.97863e8i	0.336727	−	0.484343i
$743$	−2.84817e8			−0.694384			−0.347192	−	0.937794i	$-0.612865\pi$
$743$	−2.84817e8			−0.694384			−0.347192	+	0.937794i	$0.612865\pi$
$744$	1.19509e8			0.290189
$745$		−	6.44956e7i		−	0.155977i
$746$	−5.12671e7			−0.123487
$747$			3.79832e7i			0.0911235i
$748$			6.19130e7i			0.147937i
$749$	8.59949e7	−	1.23694e8i	0.204657	−	0.294376i
$750$	−3.59593e8			−0.852368
$751$	−1.41864e8			−0.334929			−0.167465	−	0.985878i	$-0.553558\pi$
$751$	−1.41864e8			−0.334929			−0.167465	+	0.985878i	$0.553558\pi$
$752$			1.42986e8i			0.336233i
$753$	3.05515e8			0.715563
$754$			8.63712e8i			2.01491i
$755$			4.68781e6i			0.0108925i
$756$	1.51376e8	+	1.05241e8i	0.350343	+	0.243567i
$757$	4.81270e8			1.10943			0.554716	−	0.832040i	$-0.312827\pi$
$757$	4.81270e8			1.10943			0.554716	+	0.832040i	$0.312827\pi$
$758$	2.22083e8			0.509927
$759$		−	3.63330e8i		−	0.830951i
$760$	−1.33439e8			−0.303978
$761$			4.55601e8i			1.03379i	0.856050	+	0.516893i	$0.172912\pi$
$761$			4.55601e8i			1.03379i	−0.856050	+	0.516893i	$0.827088\pi$
$762$		−	2.36072e8i		−	0.533555i
$763$	3.53202e8	−	5.08041e8i	0.795151	−	1.14373i
$764$	−1.60191e8			−0.359218
$765$	−3.07272e7			−0.0686339
$766$			2.40926e8i			0.536040i
$767$	9.95641e8			2.20657
$768$			3.14089e7i			0.0693377i
$769$			3.23170e8i			0.710643i	0.934744	+	0.355322i	$0.115629\pi$
$769$			3.23170e8i			0.710643i	−0.934744	+	0.355322i	$0.884371\pi$
$770$	−1.63327e8	−	1.13549e8i	−0.357755	−	0.248720i
$771$	−8.02863e8			−1.75177
$772$	6.23984e7			0.135619
$773$		−	2.14005e8i		−	0.463324i	−0.972796	−	0.231662i	$-0.925584\pi$
$773$		−	2.14005e8i		−	0.463324i	0.972796	−	0.231662i	$-0.0744164\pi$
$774$	1.08829e8			0.234705
$775$		−	1.31076e8i		−	0.281590i
$776$			2.12242e7i			0.0454198i
$777$	−4.14829e8	−	2.88399e8i	−0.884314	−	0.614797i
$778$	−1.82846e8			−0.388282
$779$	1.35101e8			0.285789
$780$			3.45285e8i			0.727603i
$781$	−2.25120e8			−0.472564
$782$		−	1.22242e8i		−	0.255624i
$783$		−	7.00398e8i		−	1.45902i
$784$	−4.19619e7	−	1.12928e8i	−0.0870778	−	0.234345i
$785$	−2.05127e8			−0.424048
$786$	4.41025e8			0.908229
$787$			6.93076e8i			1.42186i	0.703263	+	0.710930i	$0.251726\pi$
$787$			6.93076e8i			1.42186i	−0.703263	+	0.710930i	$0.748274\pi$
$788$	3.71275e8			0.758782
$789$		−	7.86328e8i		−	1.60093i
$790$			2.51228e8i			0.509549i
$791$	2.35335e8	−	3.38502e8i	0.475507	−	0.683962i
$792$	3.17364e7			0.0638825
$793$	−1.23968e9			−2.48593
$794$		−	6.85027e8i		−	1.36850i
$795$	−3.65983e8			−0.728383
$796$			2.32702e7i			0.0461382i
$797$		−	1.42327e8i		−	0.281134i	−0.990071	−	0.140567i	$-0.955107\pi$
$797$		−	1.42327e8i		−	0.281134i	0.990071	−	0.140567i	$-0.0448926\pi$
$798$	−2.48596e8	+	3.57576e8i	−0.489198	+	0.703655i
$799$	2.59244e8			0.508240
$800$	3.44489e7			0.0672830
$801$			6.92133e7i			0.134676i
$802$	2.82235e8			0.547126
$803$		−	1.16641e8i		−	0.225271i
$804$		−	1.01974e8i		−	0.196209i
$805$	3.22476e8	+	2.24193e8i	0.618172	+	0.429769i
$806$	−4.56541e8			−0.871916
$807$	−1.07505e9			−2.04554
$808$			1.27834e8i			0.242333i
$809$	−2.01624e8			−0.380800			−0.190400	−	0.981707i	$-0.560979\pi$
$809$	−2.01624e8			−0.380800			−0.190400	+	0.981707i	$0.560979\pi$
$810$		−	3.48249e8i		−	0.655291i
$811$		−	1.69349e7i		−	0.0317483i	−0.999874	−	0.0158741i	$-0.994947\pi$
$811$		−	1.69349e7i		−	0.0317483i	0.999874	−	0.0158741i	$-0.00505311\pi$
$812$	−2.61252e8	+	3.75781e8i	−0.487969	+	0.701887i
$813$	−4.91905e7			−0.0915398
$814$	2.89891e8			0.537478
$815$			1.56739e8i			0.289538i
$816$	5.69467e7			0.104809
$817$		−	8.56883e8i		−	1.57129i
$818$		−	6.13264e7i		−	0.112044i
$819$	1.73489e8	+	1.20614e8i	0.315806	+	0.219556i
$820$	5.67589e7			0.102942
$821$	3.77973e8			0.683018			0.341509	−	0.939879i	$-0.389062\pi$
$821$	3.77973e8			0.683018			0.341509	+	0.939879i	$0.389062\pi$
$822$		−	1.17334e8i		−	0.211256i
$823$	5.19539e8			0.932006			0.466003	−	0.884783i	$-0.345694\pi$
$823$	5.19539e8			0.932006			0.466003	+	0.884783i	$0.345694\pi$
$824$			2.92963e8i			0.523638i
$825$		−	1.85639e8i		−	0.330604i
$826$	4.33180e8	+	3.01158e8i	0.768650	+	0.534384i
$827$	5.17270e7			0.0914536			0.0457268	−	0.998954i	$-0.485440\pi$
$827$	5.17270e7			0.0914536			0.0457268	+	0.998954i	$0.485440\pi$
$828$	−6.26609e7			−0.110384
$829$		−	7.51588e7i		−	0.131922i	−0.997822	−	0.0659609i	$-0.978989\pi$
$829$		−	7.51588e7i		−	0.131922i	0.997822	−	0.0659609i	$-0.0210113\pi$
$830$	1.25645e8			0.219740
$831$			1.15102e9i			2.00576i
$832$		−	1.19987e8i		−	0.208335i
$833$	−2.04748e8	+	7.60801e7i	−0.354229	+	0.131624i
$834$	8.16697e7			0.140787
$835$	−1.19764e8			−0.205715
$836$		−	2.49881e8i		−	0.427675i
$837$	3.70216e8			0.631363
$838$		−	2.17797e8i		−	0.370101i
$839$			8.14179e8i			1.37859i	0.724483	+	0.689293i	$0.242079\pi$
$839$			8.14179e8i			1.37859i	−0.724483	+	0.689293i	$0.757921\pi$
$840$	−1.04441e8	+	1.50226e8i	−0.176210	+	0.253458i
$841$	1.14387e9			1.92303
$842$	−3.84966e8			−0.644891
$843$		−	1.13422e9i		−	1.89328i
$844$	1.86416e8			0.310067
$845$		−	8.44196e8i		−	1.39918i
$846$		−	1.32887e8i		−	0.219469i
$847$	−1.34227e8	+	1.93070e8i	−0.220897	+	0.317734i
$848$	1.27179e8			0.208559
$849$	1.07243e8			0.175245
$850$		−	6.24584e7i		−	0.101703i
$851$	−5.72365e8			−0.928719
$852$			2.07062e8i			0.334797i
$853$			9.81909e8i			1.58206i	0.611774	+	0.791032i	$0.290456\pi$
$853$			9.81909e8i			1.58206i	−0.611774	+	0.791032i	$0.709544\pi$
$854$	−5.39354e8	−	3.74972e8i	−0.865966	−	0.602040i
$855$	1.24015e8			0.198415
$856$	7.95057e7			0.126759
$857$			1.05751e9i			1.68013i	0.542487	+	0.840064i	$0.317483\pi$
$857$			1.05751e9i			1.68013i	−0.542487	+	0.840064i	$0.682517\pi$
$858$	−6.46588e8			−1.02368
$859$			1.43809e8i			0.226886i	0.993545	+	0.113443i	$0.0361879\pi$
$859$			1.43809e8i			0.226886i	−0.993545	+	0.113443i	$0.963812\pi$
$860$		−	3.59996e8i		−	0.565981i
$861$	1.05741e8	−	1.52096e8i	0.165666	−	0.238292i
$862$	−3.36059e8			−0.524679
$863$	3.42007e8			0.532111			0.266056	−	0.963958i	$-0.414280\pi$
$863$	3.42007e8			0.532111			0.266056	+	0.963958i	$0.414280\pi$
$864$			9.72992e7i			0.150858i
$865$	−4.54307e8			−0.701942
$866$			3.62054e8i			0.557467i
$867$			6.19765e8i			0.950977i
$868$	−1.98630e8	−	1.38093e8i	−0.303729	−	0.211160i
$869$	−4.70454e8			−0.716899
$870$	6.95074e8			1.05554
$871$			3.89554e8i			0.589540i
$872$	3.26550e8			0.492493
$873$		−	1.97252e7i		−	0.0296468i
$874$			4.93369e8i			0.738989i
$875$	5.97664e8	+	4.15511e8i	0.892140	+	0.620238i
$876$	−1.07285e8			−0.159598
$877$	−2.00898e8			−0.297836			−0.148918	−	0.988850i	$-0.547579\pi$
$877$	−2.00898e8			−0.297836			−0.148918	+	0.988850i	$0.547579\pi$
$878$		−	3.30772e8i		−	0.488703i
$879$	1.06995e9			1.57542
$880$		−	1.04981e8i		−	0.154050i
$881$		−	1.00494e9i		−	1.46964i	−0.678262	−	0.734820i	$-0.737267\pi$
$881$		−	1.00494e9i		−	1.46964i	0.678262	−	0.734820i	$-0.262733\pi$
$882$	3.89983e7	+	1.04953e8i	0.0568382	+	0.152964i
$883$	5.37005e8			0.780003			0.390001	−	0.920814i	$-0.372475\pi$
$883$	5.37005e8			0.780003			0.390001	+	0.920814i	$0.372475\pi$
$884$	−2.17545e8			−0.314914
$885$		−	8.01244e8i		−	1.15594i
$886$	−8.74639e8			−1.25756
$887$			1.31599e8i			0.188574i	0.995545	+	0.0942871i	$0.0300572\pi$
$887$			1.31599e8i			0.188574i	−0.995545	+	0.0942871i	$0.969943\pi$
$888$		−	2.66637e8i		−	0.380786i
$889$	−2.72782e8	+	3.92365e8i	−0.388249	+	0.558451i
$890$	2.28950e8			0.324766
$891$	6.52138e8			0.921947
$892$		−	1.93755e8i		−	0.272997i
$893$	−1.04631e9			−1.46928
$894$		−	1.11088e8i		−	0.155473i
$895$		−	2.82385e8i		−	0.393888i
$896$	3.62931e7	−	5.22034e7i	0.0504545	−	0.0725730i
$897$	1.27664e9			1.76885
$898$	4.70029e8			0.649076
$899$			9.19036e8i			1.26489i
$900$	−3.20159e7			−0.0439176
$901$		−	2.30585e8i		−	0.315251i
$902$			1.06288e8i			0.144832i
$903$	−9.64678e8	−	6.70668e8i	−1.31014	−	0.910845i
$904$	2.17577e8			0.294515
$905$	6.70183e8			0.904165
$906$			8.07432e6i			0.0108573i
$907$	−1.20778e9			−1.61870			−0.809349	−	0.587328i	$-0.800180\pi$
$907$	−1.20778e9			−1.61870			−0.809349	+	0.587328i	$0.800180\pi$
$908$		−	5.44706e8i		−	0.727619i
$909$		−	1.18806e8i		−	0.158178i
$910$	3.98978e8	−	5.73884e8i	0.529450	−	0.761553i
$911$	−1.08236e8			−0.143158			−0.0715792	−	0.997435i	$-0.522804\pi$
$911$	−1.08236e8			−0.143158			−0.0715792	+	0.997435i	$0.522804\pi$
$912$	−2.29837e8			−0.302994
$913$			2.35285e8i			0.309158i
$914$	2.10108e8			0.275172
$915$			9.97631e8i			1.30229i
$916$			2.71749e8i			0.353576i
$917$	−7.33009e8	−	5.09606e8i	−0.950608	−	0.660886i
$918$	1.76411e8			0.228032
$919$	−8.87506e8			−1.14347			−0.571735	−	0.820438i	$-0.693729\pi$
$919$	−8.87506e8			−1.14347			−0.571735	+	0.820438i	$0.693729\pi$
$920$			2.07275e8i			0.266186i
$921$	−1.11372e9			−1.42559
$922$		−	1.91268e7i		−	0.0244034i
$923$		−	7.91006e8i		−	1.00595i
$924$	−2.81316e8	−	1.95578e8i	−0.356597	−	0.247915i
$925$	−2.92444e8			−0.369503
$926$	3.75281e8			0.472633
$927$		−	2.72272e8i		−	0.341794i
$928$	−2.41538e8			−0.302233
$929$			5.79061e7i			0.0722233i	0.999348	+	0.0361116i	$0.0114972\pi$
$929$			5.79061e7i			0.0722233i	−0.999348	+	0.0361116i	$0.988503\pi$
$930$			3.67402e8i			0.456765i
$931$	8.26361e8	−	3.07059e8i	1.02405	−	0.380516i
$932$	−1.52398e8			−0.188248
$933$	4.13174e8			0.508731
$934$			5.64171e8i			0.692420i
$935$	−1.90337e8			−0.232857
$936$			1.11512e8i			0.135987i
$937$		−	1.01207e9i		−	1.23024i	−0.788432	−	0.615122i	$-0.789107\pi$
$937$		−	1.01207e9i		−	1.23024i	0.788432	−	0.615122i	$-0.210893\pi$
$938$	−1.17831e8	+	1.69486e8i	−0.142774	+	0.205364i
$939$	2.73715e8			0.330600
$940$	−4.39578e8			−0.529239
$941$		−	9.96415e8i		−	1.19584i	−0.801557	−	0.597918i	$-0.795995\pi$
$941$		−	9.96415e8i		−	1.19584i	0.801557	−	0.597918i	$-0.204005\pi$
$942$	−3.53313e8			−0.422675
$943$		−	2.09857e8i		−	0.250258i
$944$			2.78432e8i			0.330981i
$945$	−3.23538e8	+	4.65372e8i	−0.383381	+	0.551449i
$946$	6.74135e8			0.796294
$947$	8.94254e8			1.05296			0.526479	−	0.850188i	$-0.323512\pi$
$947$	8.94254e8			1.05296			0.526479	+	0.850188i	$0.323512\pi$
$948$			4.32717e8i			0.507900i
$949$	4.09844e8			0.479535
$950$			2.52082e8i			0.294016i
$951$		−	3.84077e8i		−	0.446557i
$952$	−9.46487e7	−	6.58021e7i	−0.109699	−	0.0762656i
$953$	−7.60395e8			−0.878538			−0.439269	−	0.898355i	$-0.644763\pi$
$953$	−7.60395e8			−0.878538			−0.439269	+	0.898355i	$0.644763\pi$
$954$	−1.18197e8			−0.136132
$955$		−	4.92470e8i		−	0.565418i
$956$	5.08578e8			0.582082
$957$			1.30161e9i			1.48506i
$958$		−	4.81323e8i		−	0.547444i
$959$	−1.35580e8	+	1.95016e8i	−0.153723	+	0.221113i
$960$	−9.65595e7			−0.109139
$961$	4.01720e8			0.452640
$962$			1.01859e9i			1.14413i
$963$	−7.38905e7			−0.0827389
$964$			8.51703e6i			0.00950730i
$965$			1.91829e8i			0.213468i
$966$	5.55435e8	+	3.86152e8i	0.616172	+	0.428378i
$967$	9.71735e8			1.07465			0.537327	−	0.843374i	$-0.319434\pi$
$967$	9.71735e8			1.07465			0.537327	+	0.843374i	$0.319434\pi$
$968$	−1.24098e8			−0.136817
$969$			4.16711e8i			0.457998i
$970$	−6.52488e7			−0.0714920
$971$		−	1.27689e9i		−	1.39475i	−0.716708	−	0.697374i	$-0.754352\pi$
$971$		−	1.27689e9i		−	1.39475i	0.716708	−	0.697374i	$-0.245648\pi$
$972$		−	2.07984e8i		−	0.226480i
$973$	−1.35740e8	−	9.43696e7i	−0.147356	−	0.102446i
$974$	6.77628e8			0.733355
$975$	6.52284e8			0.703757
$976$		−	3.46677e8i		−	0.372886i
$977$	1.53509e9			1.64608			0.823040	−	0.567984i	$-0.192276\pi$
$977$	1.53509e9			1.64608			0.823040	+	0.567984i	$0.192276\pi$
$978$			2.69969e8i			0.288601i
$979$			4.28737e8i			0.456923i
$980$	3.47173e8	−	1.29002e8i	0.368865	−	0.137063i
$981$	−3.03487e8			−0.321464
$982$	−1.27198e9			−1.34322
$983$			9.46892e8i			0.996873i	0.866926	+	0.498436i	$0.166092\pi$
$983$			9.46892e8i			0.996873i	−0.866926	+	0.498436i	$0.833908\pi$
$984$	9.77619e7			0.102609
$985$			1.14140e9i			1.19434i
$986$			4.37927e8i			0.456847i
$987$	−8.18928e8	+	1.17793e9i	−0.851715	+	1.22509i
$988$	8.78010e8			0.910392
$989$	−1.33102e9			−1.37593
$990$			9.75662e7i			0.100553i
$991$	−1.27731e9			−1.31242			−0.656211	−	0.754577i	$-0.727842\pi$
$991$	−1.27731e9			−1.31242			−0.656211	+	0.754577i	$0.727842\pi$
$992$		−	1.27672e8i		−	0.130786i
$993$			1.87061e9i			1.91045i
$994$	2.39261e8	−	3.44149e8i	0.243619	−	0.350418i
$995$	−7.15389e7			−0.0726228
$996$	2.16411e8			0.219029
$997$		−	1.51510e9i		−	1.52882i	−0.644731	−	0.764409i	$-0.723031\pi$
$997$		−	1.51510e9i		−	1.52882i	0.644731	−	0.764409i	$-0.276969\pi$
$998$	3.28108e8			0.330085
$999$		−	8.25993e8i		−	0.828476i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.7.b.a.13.4	yes	4
3.2	odd	2		126.7.c.a.55.1		4
4.3	odd	2		112.7.c.c.97.1		4
5.2	odd	4		350.7.d.a.349.8		8
5.3	odd	4		350.7.d.a.349.1		8
5.4	even	2		350.7.b.a.251.1		4
7.2	even	3		98.7.d.b.31.1		8
7.3	odd	6		98.7.d.b.19.1		8
7.4	even	3		98.7.d.b.19.2		8
7.5	odd	6		98.7.d.b.31.2		8
7.6	odd	2	inner	14.7.b.a.13.3	✓	4
8.3	odd	2		448.7.c.e.321.4		4
8.5	even	2		448.7.c.h.321.1		4
21.20	even	2		126.7.c.a.55.2		4
28.27	even	2		112.7.c.c.97.4		4
35.13	even	4		350.7.d.a.349.4		8
35.27	even	4		350.7.d.a.349.5		8
35.34	odd	2		350.7.b.a.251.2		4
56.13	odd	2		448.7.c.h.321.4		4
56.27	even	2		448.7.c.e.321.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.7.b.a.13.3	✓	4	7.6	odd	2	inner
14.7.b.a.13.4	yes	4	1.1	even	1	trivial
98.7.d.b.19.1		8	7.3	odd	6
98.7.d.b.19.2		8	7.4	even	3
98.7.d.b.31.1		8	7.2	even	3
98.7.d.b.31.2		8	7.5	odd	6
112.7.c.c.97.1		4	4.3	odd	2
112.7.c.c.97.4		4	28.27	even	2
126.7.c.a.55.1		4	3.2	odd	2
126.7.c.a.55.2		4	21.20	even	2
350.7.b.a.251.1		4	5.4	even	2
350.7.b.a.251.2		4	35.34	odd	2
350.7.d.a.349.1		8	5.3	odd	4
350.7.d.a.349.4		8	35.13	even	4
350.7.d.a.349.5		8	35.27	even	4
350.7.d.a.349.8		8	5.2	odd	4
448.7.c.e.321.1		4	56.27	even	2
448.7.c.e.321.4		4	8.3	odd	2
448.7.c.h.321.1		4	8.5	even	2
448.7.c.h.321.4		4	56.13	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	14.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+5.65685 q^{2} +29.9539i q^{3} +32.0000 q^{4} +98.3767i q^{5} +169.445i q^{6} +(195.794 - 281.627i) q^{7} +181.019 q^{8} -168.235 q^{9} +556.502i q^{10} -1042.12 q^{11} +958.524i q^{12} -3661.70i q^{13} +(1107.58 - 1593.12i) q^{14} -2946.76 q^{15} +1024.00 q^{16} -1856.59i q^{17} -951.679 q^{18} +7493.18i q^{19} +3148.05i q^{20} +(8435.82 + 5864.79i) q^{21} -5895.11 q^{22} +11639.4 q^{23} +5422.23i q^{24} +5947.03 q^{25} -20713.7i q^{26} +16797.1i q^{27} +(6265.41 - 9012.06i) q^{28} -41697.6 q^{29} -16669.4 q^{30} -22040.5i q^{31} +5792.62 q^{32} -31215.5i q^{33} -10502.4i q^{34} +(27705.5 + 19261.6i) q^{35} -5383.51 q^{36} -49174.8 q^{37} +42387.8i q^{38} +109682. q^{39} +17808.1i q^{40} -18029.8i q^{41} +(47720.2 + 33176.2i) q^{42} -114355. q^{43} -33347.8 q^{44} -16550.4i q^{45} +65842.4 q^{46} +139635. i q^{47} +30672.8i q^{48} +(-40978.5 - 110282. i) q^{49} +33641.5 q^{50} +55612.0 q^{51} -117175. i q^{52} +124198. q^{53} +95018.7i q^{54} -102520. i q^{55} +(35442.5 - 50979.9i) q^{56} -224450. q^{57} -235877. q^{58} +271907. i q^{59} -94296.4 q^{60} -338552. i q^{61} -124680. i q^{62} +(-32939.3 + 47379.4i) q^{63} +32768.0 q^{64} +360226. q^{65} -176581. i q^{66} -106386. q^{67} -59410.8i q^{68} +348645. i q^{69} +(156726. + 108960. i) q^{70} +216021. q^{71} -30453.7 q^{72} +111927. i q^{73} -278174. q^{74} +178137. i q^{75} +239782. i q^{76} +(-204040. + 293488. i) q^{77} +620456. q^{78} +451441. q^{79} +100738. i q^{80} -625781. q^{81} -101992. i q^{82} -225775. i q^{83} +(269946. + 187673. i) q^{84} +182645. q^{85} -646890. q^{86} -1.24900e6i q^{87} -188643. q^{88} -411409. i q^{89} -93623.0i q^{90} +(-1.03123e6 - 716939. i) q^{91} +372461. q^{92} +660198. q^{93} +789893. i q^{94} -737154. q^{95} +173511. i q^{96} +117248. i q^{97} +(-231809. - 623847. i) q^{98} +175320. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 128 q^{4} + 308 q^{7} + 1092 q^{9} - 4440 q^{11} + 2688 q^{14} - 4320 q^{15} + 4096 q^{16} - 9984 q^{18} + 19488 q^{21} + 1536 q^{22} + 40584 q^{23} - 40700 q^{25} + 9856 q^{28} - 18264 q^{29} - 42240 q^{30}+ \cdots - 1331928 q^{99}+O(q^{100}) \) 4 * q + 128 * q^4 + 308 * q^7 + 1092 * q^9 - 4440 * q^11 + 2688 * q^14 - 4320 * q^15 + 4096 * q^16 - 9984 * q^18 + 19488 * q^21 + 1536 * q^22 + 40584 * q^23 - 40700 * q^25 + 9856 * q^28 - 18264 * q^29 - 42240 * q^30 - 84000 * q^35 + 34944 * q^36 - 23192 * q^37 + 208608 * q^39 + 80640 * q^42 - 44696 * q^43 - 142080 * q^44 + 33792 * q^46 - 310268 * q^49 + 364800 * q^50 + 157824 * q^51 + 248616 * q^53 + 86016 * q^56 - 472992 * q^57 - 840192 * q^58 - 138240 * q^60 - 125580 * q^63 + 131072 * q^64 + 1293600 * q^65 - 434776 * q^67 + 1102080 * q^70 - 451608 * q^71 - 319488 * q^72 - 981504 * q^74 - 309624 * q^77 + 1301760 * q^78 + 2092904 * q^79 - 252828 * q^81 + 623616 * q^84 - 2117760 * q^85 - 2334720 * q^86 + 49152 * q^88 - 1109472 * q^91 + 1298688 * q^92 + 995328 * q^93 - 190560 * q^95 + 827904 * q^98 - 1331928 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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