LMFDB - Embedded newform 9.19.d.a.5.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9,19,Mod(2,9)] 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("9.2"); S:= CuspForms(chi, 19); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 19, names="a")

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 19 $
Character orbit:	$[\chi]$	$=$	9.d (of order $6$, degree $2$, 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:	$18.4847523939$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.16
Character	$\chi$	$=$	9.5
Dual form			9.19.d.a.2.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(709.707 - 409.750i) q^{2} +(13445.3 - 14375.1i) q^{3} +(204718. - 354581. i) q^{4} +(-432139. - 249496. i) q^{5} +(3.65207e6 - 1.57113e7i) q^{6} +(-1.14976e7 - 1.99144e7i) q^{7} -1.20705e8i q^{8} +(-2.58659e7 - 3.86556e8i) q^{9} -4.08923e8 q^{10} +(-8.30317e8 + 4.79384e8i) q^{11} +(-2.34464e9 - 7.71030e9i) q^{12} +(6.95909e9 - 1.20535e10i) q^{13} +(-1.63199e10 - 9.42227e9i) q^{14} +(-9.39678e9 + 2.85748e9i) q^{15} +(4.20662e9 + 7.28608e9i) q^{16} +1.64035e11i q^{17} +(-1.76748e11 - 2.63743e11i) q^{18} +3.16899e11 q^{19} +(-1.76933e11 + 1.02152e11i) q^{20} +(-4.40861e11 - 1.02477e11i) q^{21} +(-3.92855e11 + 6.80444e11i) q^{22} +(-8.72662e11 - 5.03832e11i) q^{23} +(-1.73515e12 - 1.62292e12i) q^{24} +(-1.78285e12 - 3.08799e12i) q^{25} -1.14059e13i q^{26} +(-5.90455e12 - 4.82555e12i) q^{27} -9.41504e12 q^{28} +(1.84179e13 - 1.06336e13i) q^{29} +(-5.49811e12 + 5.87831e12i) q^{30} +(-2.05722e13 + 3.56321e13i) q^{31} +(3.33738e13 + 1.92684e13i) q^{32} +(-4.27271e12 + 1.83814e13i) q^{33} +(6.72133e13 + 1.16417e14i) q^{34} +1.14744e13i q^{35} +(-1.42361e14 - 6.99633e13i) q^{36} +1.48344e14 q^{37} +(2.24906e14 - 1.29849e14i) q^{38} +(-7.97027e13 - 2.62101e14i) q^{39} +(-3.01154e13 + 5.21614e13i) q^{40} +(1.43068e14 + 8.26001e13i) q^{41} +(-3.54872e14 + 1.07914e14i) q^{42} +(2.67926e14 + 4.64062e14i) q^{43} +3.92553e14i q^{44} +(-8.52664e13 + 1.73499e14i) q^{45} -8.25779e14 q^{46} +(1.05914e15 - 6.11495e14i) q^{47} +(1.61297e14 + 3.74933e13i) q^{48} +(5.49817e14 - 9.52311e14i) q^{49} +(-2.53061e15 - 1.46105e15i) q^{50} +(2.35802e15 + 2.20551e15i) q^{51} +(-2.84930e15 - 4.93513e15i) q^{52} +4.85358e15i q^{53} +(-6.16777e15 - 1.00534e15i) q^{54} +4.78417e14 q^{55} +(-2.40377e15 + 1.38782e15i) q^{56} +(4.26082e15 - 4.55546e15i) q^{57} +(8.71421e15 - 1.50935e16i) q^{58} +(-2.12508e15 - 1.22691e15i) q^{59} +(-9.10477e14 + 3.91690e15i) q^{60} +(-2.85754e15 - 4.94941e15i) q^{61} +3.37178e16i q^{62} +(-7.40065e15 + 4.95957e15i) q^{63} +2.93754e16 q^{64} +(-6.01459e15 + 3.47253e15i) q^{65} +(4.49938e15 + 1.47961e16i) q^{66} +(1.46461e15 - 2.53677e15i) q^{67} +(5.81637e16 + 3.35809e16i) q^{68} +(-1.89759e16 + 5.77040e15i) q^{69} +(4.70163e15 + 8.14347e15i) q^{70} -2.65834e16i q^{71} +(-4.66593e16 + 3.12215e15i) q^{72} -9.27269e16 q^{73} +(1.05281e17 - 6.07837e16i) q^{74} +(-6.83612e16 - 1.58904e16i) q^{75} +(6.48749e16 - 1.12367e17i) q^{76} +(1.90933e16 + 1.10235e16i) q^{77} +(-1.63961e17 - 1.53357e17i) q^{78} +(4.00087e16 + 6.92972e16i) q^{79} -4.19813e15i q^{80} +(-1.48757e17 + 1.99973e16i) q^{81} +1.35381e17 q^{82} +(-1.79384e17 + 1.03568e17i) q^{83} +(-1.26589e17 + 1.35342e17i) q^{84} +(4.09260e16 - 7.08859e16i) q^{85} +(3.80298e17 + 2.19565e17i) q^{86} +(9.47763e16 - 4.07731e17i) q^{87} +(5.78641e16 + 1.00224e17i) q^{88} +1.84754e17i q^{89} +(1.05772e16 + 1.58072e17i) q^{90} -3.20051e17 q^{91} +(-3.57299e17 + 2.06286e17i) q^{92} +(2.35614e17 + 7.74813e17i) q^{93} +(5.01120e17 - 8.67965e17i) q^{94} +(-1.36945e17 - 7.90650e16i) q^{95} +(7.25707e17 - 2.20682e17i) q^{96} +(-1.10757e17 - 1.91837e17i) q^{97} -9.01150e17i q^{98} +(2.06786e17 + 3.08564e17i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 3 q^{2} + 3804 q^{3} + 2097151 q^{4} + 2192181 q^{5} + 3257181 q^{6} + 4302359 q^{7} + 397977264 q^{9} - 524292 q^{10} + 1022992575 q^{11} + 32417762010 q^{12} + 3839449319 q^{13} + 129938709678 q^{14}+ \cdots - 52\!\cdots\!15 q^{99}+O(q^{100}) $ 34 * q - 3 * q^2 + 3804 * q^3 + 2097151 * q^4 + 2192181 * q^5 + 3257181 * q^6 + 4302359 * q^7 + 397977264 * q^9 - 524292 * q^10 + 1022992575 * q^11 + 32417762010 * q^12 + 3839449319 * q^13 + 129938709678 * q^14 - 124119415395 * q^15 - 240517906433 * q^16 - 285581999484 * q^18 - 608222566264 * q^19 + 1471193748174 * q^20 - 1381493495229 * q^21 + 851254438911 * q^22 + 375441179325 * q^23 + 305135298351 * q^24 + 12156817117552 * q^25 + 11936276558406 * q^27 + 4648789868540 * q^28 - 31101186224271 * q^29 + 62775784981818 * q^30 - 20376334153801 * q^31 - 113411230023465 * q^32 - 20701744605945 * q^33 - 99737362554111 * q^34 - 472069890962721 * q^36 + 56970364072604 * q^37 + 1244853240655323 * q^38 + 277868300554299 * q^39 + 236076863983350 * q^40 - 1178988706876521 * q^41 + 1034549802657900 * q^42 - 230641688892691 * q^43 - 5286549794938479 * q^45 + 131852496280800 * q^46 + 3640523435126673 * q^47 + 11085451646520237 * q^48 - 4168576830678822 * q^49 - 18078797603969781 * q^50 + 7526452896180882 * q^51 + 1286623499256920 * q^52 - 26455557995217045 * q^54 - 1446925762710942 * q^55 + 59834487378592914 * q^56 + 23867830767470574 * q^57 + 8463343484826222 * q^58 - 29968086845368137 * q^59 + 17080074037610118 * q^60 - 6976259792083513 * q^61 - 73583064644919705 * q^63 - 120930519493421318 * q^64 + 47229492730318989 * q^65 + 58361174960027994 * q^66 - 20333770074023707 * q^67 - 116938167206248431 * q^68 + 99272218824151677 * q^69 - 18312927374667108 * q^70 + 186892024430477907 * q^72 + 209341663176867296 * q^73 - 88916838511745634 * q^74 - 103202922056583144 * q^75 - 180442619960522287 * q^76 + 384727796507616477 * q^77 - 113580855335113884 * q^78 + 126425698081194923 * q^79 + 749177961563573568 * q^81 - 856725985700547270 * q^82 - 819712186371296103 * q^83 - 1069135371708878382 * q^84 + 372804006624771096 * q^85 + 1989011602082127453 * q^86 - 689457779704913391 * q^87 - 648793548761104653 * q^88 + 2069849112225424614 * q^90 - 29982940436364482 * q^91 - 2013198581519506428 * q^92 - 2088815715502953 * q^93 - 769920889934866620 * q^94 + 167036756670646446 * q^95 + 338414304229215984 * q^96 + 1172101248161568089 * q^97 - 529477370297396415 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	709.707	−	409.750i	1.38615	−	0.800292i	0.393269	−	0.919424i	$-0.371344\pi$
$2$	709.707	−	409.750i	1.38615	−	0.800292i	0.992879	+	0.119131i	$0.0380109\pi$
$3$	13445.3	−	14375.1i	0.683094	−	0.730330i
$3$	13445.3	−	14375.1i	0.683094	−	0.730330i
$4$	204718.	−	354581.i	0.780936	−	1.35262i
$5$	−432139.	−	249496.i	−0.221255	−	0.127742i	0.385276	−	0.922801i	$-0.374106\pi$
$5$	−432139.	−	249496.i	−0.221255	−	0.127742i	−0.606531	+	0.795060i	$0.707440\pi$
$6$	3.65207e6	−	1.57113e7i	0.362391	−	1.55902i
$7$	−1.14976e7	−	1.99144e7i	−0.284921	−	0.493498i	0.687669	−	0.726024i	$-0.258634\pi$
$7$	−1.14976e7	−	1.99144e7i	−0.284921	−	0.493498i	−0.972590	+	0.232526i	$0.925301\pi$
$8$		−	1.20705e8i		−	0.899323i
$9$	−2.58659e7	−	3.86556e8i	−0.0667644	−	0.997769i
$10$	−4.08923e8			−0.408923
$11$	−8.30317e8	+	4.79384e8i	−0.352136	+	0.203306i	−0.665625	−	0.746286i	$-0.731835\pi$
$11$	−8.30317e8	+	4.79384e8i	−0.352136	+	0.203306i	0.313490	+	0.949592i	$0.398502\pi$
$12$	−2.34464e9	−	7.71030e9i	−0.454407	−	1.49431i
$13$	6.95909e9	−	1.20535e10i	0.656239	−	1.13664i	−0.325342	−	0.945596i	$-0.605480\pi$
$13$	6.95909e9	−	1.20535e10i	0.656239	−	1.13664i	0.981582	−	0.191043i	$-0.0611871\pi$
$14$	−1.63199e10	−	9.42227e9i	−0.789885	−	0.456041i
$15$	−9.39678e9	+	2.85748e9i	−0.244432	+	0.0743297i
$16$	4.20662e9	+	7.28608e9i	0.0612143	+	0.106026i
$17$			1.64035e11i			1.38324i	0.722264	+	0.691618i	$0.243102\pi$
$17$			1.64035e11i			1.38324i	−0.722264	+	0.691618i	$0.756898\pi$
$18$	−1.76748e11	−	2.63743e11i	−0.891052	−	1.32962i
$19$	3.16899e11			0.982062			0.491031	−	0.871142i	$-0.336620\pi$
$19$	3.16899e11			0.982062			0.491031	+	0.871142i	$0.336620\pi$
$20$	−1.76933e11	+	1.02152e11i	−0.345572	+	0.199516i
$21$	−4.40861e11	−	1.02477e11i	−0.555045	−	0.129019i
$22$	−3.92855e11	+	6.80444e11i	−0.325408	+	0.563623i
$23$	−8.72662e11	−	5.03832e11i	−0.484502	−	0.279727i	0.237789	−	0.971317i	$-0.423577\pi$
$23$	−8.72662e11	−	5.03832e11i	−0.484502	−	0.279727i	−0.722291	+	0.691590i	$0.756911\pi$
$24$	−1.73515e12	−	1.62292e12i	−0.656803	−	0.614322i
$25$	−1.78285e12	−	3.08799e12i	−0.467364	−	0.809498i
$26$		−	1.14059e13i		−	2.10073i
$27$	−5.90455e12	−	4.82555e12i	−0.774307	−	0.632810i
$28$	−9.41504e12			−0.890021
$29$	1.84179e13	−	1.06336e13i	1.26957	−	0.732989i	0.294666	−	0.955600i	$-0.404791\pi$
$29$	1.84179e13	−	1.06336e13i	1.26957	−	0.732989i	0.974907	+	0.222611i	$0.0714581\pi$
$30$	−5.49811e12	+	5.87831e12i	−0.279333	+	0.298649i
$31$	−2.05722e13	+	3.56321e13i	−0.778083	+	1.34768i	0.154963	+	0.987920i	$0.450474\pi$
$31$	−2.05722e13	+	3.56321e13i	−0.778083	+	1.34768i	−0.933045	+	0.359758i	$0.882859\pi$
$32$	3.33738e13	+	1.92684e13i	0.948541	+	0.547640i
$33$	−4.27271e12	+	1.83814e13i	−0.0920616	+	0.396052i
$34$	6.72133e13	+	1.16417e14i	1.10699	+	1.91737i
$35$			1.14744e13i			0.145585i
$36$	−1.42361e14	−	6.99633e13i	−1.40174	−	0.688886i
$37$	1.48344e14			1.14144			0.570720	−	0.821145i	$-0.306664\pi$
$37$	1.48344e14			1.14144			0.570720	+	0.821145i	$0.306664\pi$
$38$	2.24906e14	−	1.29849e14i	1.36128	−	0.785937i
$39$	−7.97027e13	−	2.62101e14i	−0.381849	−	1.25570i
$40$	−3.01154e13	+	5.21614e13i	−0.114881	+	0.198980i
$41$	1.43068e14	+	8.26001e13i	0.437005	+	0.252305i	0.702326	−	0.711855i	$-0.252145\pi$
$41$	1.43068e14	+	8.26001e13i	0.437005	+	0.252305i	−0.265321	+	0.964160i	$0.585478\pi$
$42$	−3.54872e14	+	1.07914e14i	−0.872626	+	0.265358i
$43$	2.67926e14	+	4.64062e14i	0.533088	+	0.923336i	0.999253	+	0.0386380i	$0.0123019\pi$
$43$	2.67926e14	+	4.64062e14i	0.533088	+	0.923336i	−0.466165	+	0.884698i	$0.654365\pi$
$44$			3.92553e14i			0.635074i
$45$	−8.52664e13	+	1.73499e14i	−0.112685	+	0.229290i
$46$	−8.25779e14			−0.895455
$47$	1.05914e15	−	6.11495e14i	0.946396	−	0.546402i	0.0544363	−	0.998517i	$-0.482664\pi$
$47$	1.05914e15	−	6.11495e14i	0.946396	−	0.546402i	0.891959	+	0.452115i	$0.149330\pi$
$48$	1.61297e14	+	3.74933e13i	0.119249	+	0.0277193i
$49$	5.49817e14	−	9.52311e14i	0.337640	−	0.584809i
$50$	−2.53061e15	−	1.46105e15i	−1.29567	−	0.748056i
$51$	2.35802e15	+	2.20551e15i	1.01022	+	0.944880i
$52$	−2.84930e15	−	4.93513e15i	−1.02496	−	1.77529i
$53$			4.85358e15i			1.47089i	0.677586	+	0.735443i	$0.263026\pi$
$53$			4.85358e15i			1.47089i	−0.677586	+	0.735443i	$0.736974\pi$
$54$	−6.16777e15	−	1.00534e15i	−1.57974	−	0.257496i
$55$	4.78417e14			0.103882
$56$	−2.40377e15	+	1.38782e15i	−0.443814	+	0.256236i
$57$	4.26082e15	−	4.55546e15i	0.670841	−	0.717230i
$58$	8.71421e15	−	1.50935e16i	1.17321	−	2.03206i
$59$	−2.12508e15	−	1.22691e15i	−0.245305	−	0.141627i	0.372308	−	0.928109i	$-0.378567\pi$
$59$	−2.12508e15	−	1.22691e15i	−0.245305	−	0.141627i	−0.617613	+	0.786483i	$0.711900\pi$
$60$	−9.10477e14	+	3.91690e15i	−0.0903457	+	0.388670i
$61$	−2.85754e15	−	4.94941e15i	−0.244357	−	0.423238i	0.717594	−	0.696462i	$-0.245243\pi$
$61$	−2.85754e15	−	4.94941e15i	−0.244357	−	0.423238i	−0.961951	+	0.273224i	$0.911910\pi$
$62$			3.37178e16i			2.49077i
$63$	−7.40065e15	+	4.95957e15i	−0.473374	+	0.317234i
$64$	2.93754e16			1.63066
$65$	−6.01459e15	+	3.47253e15i	−0.290393	+	0.167658i
$66$	4.49938e15	+	1.47961e16i	0.189347	+	0.622663i
$67$	1.46461e15	−	2.53677e15i	0.0538329	−	0.0932414i	−0.837853	−	0.545896i	$-0.816189\pi$
$67$	1.46461e15	−	2.53677e15i	0.0538329	−	0.0932414i	0.891686	+	0.452654i	$0.149523\pi$
$68$	5.81637e16	+	3.35809e16i	1.87099	+	1.08022i
$69$	−1.89759e16	+	5.77040e15i	−0.535254	+	0.162766i
$70$	4.70163e15	+	8.14347e15i	0.116511	+	0.201803i
$71$		−	2.65834e16i		−	0.579810i	−0.957055	−	0.289905i	$-0.906376\pi$
$71$		−	2.65834e16i		−	0.579810i	0.957055	−	0.289905i	$-0.0936238\pi$
$72$	−4.66593e16	+	3.12215e15i	−0.897317	+	0.0600428i
$73$	−9.27269e16			−1.57507			−0.787536	−	0.616269i	$-0.788643\pi$
$73$	−9.27269e16			−1.57507			−0.787536	+	0.616269i	$0.788643\pi$
$74$	1.05281e17	−	6.07837e16i	1.58220	−	0.913486i
$75$	−6.83612e16	−	1.58904e16i	−0.910455	−	0.211634i
$76$	6.48749e16	−	1.12367e17i	0.766928	−	1.32836i
$77$	1.90933e16	+	1.10235e16i	0.200662	+	0.115852i
$78$	−1.63961e17	−	1.53357e17i	−1.53423	−	1.43500i
$79$	4.00087e16	+	6.92972e16i	0.333819	+	0.578192i	0.983257	−	0.182223i	$-0.0583292\pi$
$79$	4.00087e16	+	6.92972e16i	0.333819	+	0.578192i	−0.649438	+	0.760414i	$0.724996\pi$
$80$		−	4.19813e15i		−	0.0312785i
$81$	−1.48757e17	+	1.99973e16i	−0.991085	+	0.133231i
$82$	1.35381e17			0.807671
$83$	−1.79384e17	+	1.03568e17i	−0.959582	+	0.554015i	−0.896044	−	0.443965i	$-0.853572\pi$
$83$	−1.79384e17	+	1.03568e17i	−0.959582	+	0.554015i	−0.0635374	+	0.997979i	$0.520238\pi$
$84$	−1.26589e17	+	1.35342e17i	−0.607968	+	0.650009i
$85$	4.09260e16	−	7.08859e16i	0.176697	−	0.306048i
$86$	3.80298e17	+	2.19565e17i	1.47788	+	0.853253i
$87$	9.47763e16	−	4.07731e17i	0.331915	−	1.42791i
$88$	5.78641e16	+	1.00224e17i	0.182837	+	0.316684i
$89$			1.84754e17i			0.527331i	0.964614	+	0.263665i	$0.0849314\pi$
$89$			1.84754e17i			0.527331i	−0.964614	+	0.263665i	$0.915069\pi$
$90$	1.05772e16	+	1.58072e17i	0.0273015	+	0.408011i
$91$	−3.20051e17			−0.747906
$92$	−3.57299e17	+	2.06286e17i	−0.756730	+	0.436898i
$93$	2.35614e17	+	7.74813e17i	0.452747	+	1.48885i
$94$	5.01120e17	−	8.67965e17i	0.874562	−	1.51479i
$95$	−1.36945e17	−	7.90650e16i	−0.217286	−	0.125450i
$96$	7.25707e17	−	2.20682e17i	1.04790	−	0.318658i
$97$	−1.10757e17	−	1.91837e17i	−0.145689	−	0.252341i	0.783941	−	0.620836i	$-0.213207\pi$
$97$	−1.10757e17	−	1.91837e17i	−0.145689	−	0.252341i	−0.929630	+	0.368495i	$0.879873\pi$
$98$		−	9.01150e17i		−	1.08084i
$99$	2.06786e17	+	3.08564e17i	0.226362	+	0.337776i
$100$	−1.45993e18			−1.45993
$101$	−1.63932e17	+	9.46461e16i	−0.149889	+	0.0865387i	−0.573069	−	0.819507i	$-0.694247\pi$
$101$	−1.63932e17	+	9.46461e16i	−0.149889	+	0.0865387i	0.423180	+	0.906046i	$0.360914\pi$
$102$	2.57721e18	+	5.99067e17i	2.15649	+	0.501273i
$103$	2.47961e17	−	4.29480e17i	0.190041	−	0.329161i	−0.755222	−	0.655469i	$-0.772471\pi$
$103$	2.47961e17	−	4.29480e17i	0.190041	−	0.329161i	0.945264	+	0.326308i	$0.105805\pi$
$104$	−1.45492e18	−	8.39998e17i	−1.02221	−	0.590171i
$105$	1.64946e17	+	1.54277e17i	0.106325	+	0.0994485i
$106$	1.98875e18	+	3.44462e18i	1.17714	+	2.03886i
$107$			2.48818e18i			1.35340i	0.736257	+	0.676702i	$0.236591\pi$
$107$			2.48818e18i			1.35340i	−0.736257	+	0.676702i	$0.763409\pi$
$108$	−2.91982e18	+	1.10577e18i	−1.46064	+	0.553160i
$109$	−2.53145e18			−1.16555			−0.582774	−	0.812634i	$-0.698033\pi$
$109$	−2.53145e18			−1.16555			−0.582774	+	0.812634i	$0.698033\pi$
$110$	3.39536e17	−	1.96031e17i	0.143996	−	0.0831363i
$111$	1.99453e18	−	2.13245e18i	0.779711	−	0.833628i
$112$	9.67320e16	−	1.67545e17i	0.0348825	−	0.0604183i
$113$	−2.10291e18	−	1.21412e18i	−0.700028	−	0.404161i	0.107330	−	0.994223i	$-0.465770\pi$
$113$	−2.10291e18	−	1.21412e18i	−0.700028	−	0.404161i	−0.807358	+	0.590062i	$0.799103\pi$
$114$	1.15734e18	−	4.97891e18i	0.355891	−	1.53105i
$115$	2.51408e17	+	4.35451e17i	0.0714657	+	0.123782i
$116$		−	8.70752e18i		−	2.28967i
$117$	−4.83936e18	−	2.37830e18i	−1.17792	−	0.578888i
$118$	−2.01091e18			−0.453372
$119$	3.26666e18	−	1.88601e18i	0.682624	−	0.394113i
$120$	3.44913e17	+	1.13424e18i	0.0668464	+	0.219823i
$121$	−2.32034e18	+	4.01895e18i	−0.417334	+	0.722843i
$122$	−4.05604e18	−	2.34176e18i	−0.677429	−	0.391114i
$123$	3.11098e18	−	9.46022e17i	0.482782	−	0.146810i
$124$	8.42299e18	+	1.45890e19i	1.21527	+	2.10490i
$125$			3.68276e18i			0.494291i
$126$	−3.22011e18	+	6.55226e18i	−0.402287	+	0.818570i
$127$	−1.15089e19			−1.33906			−0.669531	−	0.742784i	$-0.733505\pi$
$127$	−1.15089e19			−1.33906			−0.669531	+	0.742784i	$0.733505\pi$
$128$	1.20992e19	−	6.98546e18i	1.31179	−	0.757365i
$129$	1.02733e19	+	2.38801e18i	1.03849	+	0.241395i
$130$	−2.84573e18	+	4.92895e18i	−0.268351	+	0.464798i
$131$	9.57025e18	+	5.52539e18i	0.842329	+	0.486319i	0.858055	−	0.513558i	$-0.171673\pi$
$131$	9.57025e18	+	5.52539e18i	0.842329	+	0.486319i	−0.0157264	+	0.999876i	$0.505006\pi$
$132$	5.64299e18	+	5.27801e18i	0.463814	+	0.433816i
$133$	−3.64358e18	−	6.31087e18i	−0.279810	−	0.484646i
$134$		−	2.40049e18i		−	0.172328i
$135$	1.34763e18	+	3.55847e18i	0.0904832	+	0.238924i
$136$	1.97999e19			1.24398
$137$	−2.49762e19	+	1.44200e19i	−1.46907	+	0.848167i	−0.999399	−	0.0346752i	$-0.988960\pi$
$137$	−2.49762e19	+	1.44200e19i	−1.46907	+	0.848167i	−0.469670	+	0.882842i	$0.655627\pi$
$138$	−1.11029e19	+	1.18707e19i	−0.611680	+	0.653978i
$139$	1.51263e19	−	2.61996e19i	0.780908	−	1.35257i	−0.150505	−	0.988609i	$-0.548090\pi$
$139$	1.51263e19	−	2.61996e19i	0.780908	−	1.35257i	0.931413	−	0.363964i	$-0.118577\pi$
$140$	4.06861e18	+	2.34901e18i	0.196922	+	0.113693i
$141$	5.45021e18	−	2.34470e19i	0.247424	−	1.06443i
$142$	−1.08926e19	−	1.88665e19i	−0.464018	−	0.803703i
$143$			1.33443e19i			0.533668i
$144$	2.70767e18	−	1.81455e18i	0.101703	−	0.0681566i
$145$	−1.06121e19			−0.374533
$146$	−6.58090e19	+	3.79948e19i	−2.18328	+	1.26052i
$147$	−6.29708e18	−	2.07078e19i	−0.196464	−	0.646068i
$148$	3.03685e19	−	5.25999e19i	0.891392	−	1.54394i
$149$	3.48787e19	+	2.01372e19i	0.963570	+	0.556318i	0.897270	−	0.441482i	$-0.145547\pi$
$149$	3.48787e19	+	2.01372e19i	0.963570	+	0.556318i	0.0663003	+	0.997800i	$0.478880\pi$
$150$	−5.50276e19	+	1.67334e19i	−1.43139	+	0.435275i
$151$	−2.35514e19	−	4.07923e19i	−0.577065	−	0.999505i	−0.995814	−	0.0914035i	$-0.970865\pi$
$151$	−2.35514e19	−	4.07923e19i	−0.577065	−	0.999505i	0.418749	−	0.908102i	$-0.362469\pi$
$152$		−	3.82514e19i		−	0.883191i
$153$	6.34087e19	−	4.24291e18i	1.38015	−	0.0923510i
$154$	1.80675e19			0.370862
$155$	1.77801e19	−	1.02654e19i	0.344310	−	0.198787i
$156$	−1.09253e20	−	2.53956e19i	−1.99669	−	0.464127i
$157$	−2.38736e19	+	4.13503e19i	−0.411928	+	0.713480i	−0.995101	−	0.0988680i	$-0.968478\pi$
$157$	−2.38736e19	+	4.13503e19i	−0.411928	+	0.713480i	0.583172	+	0.812348i	$0.301811\pi$
$158$	5.67890e19	+	3.27871e19i	0.925445	+	0.534306i
$159$	6.97706e19	+	6.52580e19i	1.07423	+	1.00475i
$160$	−9.61476e18	−	1.66532e19i	−0.139913	−	0.242337i
$161$			2.31714e19i			0.318801i
$162$	−9.73797e19	+	7.51451e19i	−1.26717	+	0.977835i
$163$	7.83280e19			0.964336			0.482168	−	0.876079i	$-0.339849\pi$
$163$	7.83280e19			0.964336			0.482168	+	0.876079i	$0.339849\pi$
$164$	5.85769e19	−	3.38194e19i	0.682546	−	0.394068i
$165$	6.43248e18	−	6.87728e18i	0.0709615	−	0.0758685i
$166$	−8.48736e19	+	1.47005e20i	−0.886747	+	1.53589i
$167$	5.56562e19	+	3.21331e19i	0.550890	+	0.318057i	0.749481	−	0.662026i	$-0.230303\pi$
$167$	5.56562e19	+	3.21331e19i	0.550890	+	0.318057i	−0.198591	+	0.980082i	$0.563636\pi$
$168$	−1.23695e19	+	5.32141e19i	−0.116030	+	0.499164i
$169$	−4.06301e19	−	7.03735e19i	−0.361300	−	0.625790i
$170$		−	6.70777e19i		−	0.565637i
$171$	−8.19689e18	−	1.22499e20i	−0.0655668	−	0.979871i
$172$	2.19397e20			1.66523
$173$	1.20108e20	−	6.93446e19i	0.865284	−	0.499572i	−0.000494275	−	1.00000i	$-0.500157\pi$
$173$	1.20108e20	−	6.93446e19i	0.865284	−	0.499572i	0.865778	+	0.500428i	$0.166824\pi$
$174$	−9.98042e19	−	3.28204e20i	−0.682662	−	2.24492i
$175$	−4.09970e19	+	7.10090e19i	−0.266324	+	0.461286i
$176$	−6.98565e18	−	4.03317e18i	−0.0431115	−	0.0248904i
$177$	−4.62094e19	+	1.40519e19i	−0.271001	+	0.0824091i
$178$	7.57027e19	+	1.31121e20i	0.422019	+	0.730958i
$179$			1.73245e20i			0.918299i	0.888359	+	0.459149i	$0.151846\pi$
$179$			1.73245e20i			0.918299i	−0.888359	+	0.459149i	$0.848154\pi$
$180$	4.40641e19	+	6.57523e19i	0.222143	+	0.331481i
$181$	−2.04573e19			−0.0981163			−0.0490581	−	0.998796i	$-0.515622\pi$
$181$	−2.04573e19			−0.0981163			−0.0490581	+	0.998796i	$0.515622\pi$
$182$	−2.27143e20	+	1.31141e20i	−1.03671	+	0.598543i
$183$	−1.09569e20	−	2.54691e19i	−0.476022	−	0.110651i
$184$	−6.08150e19	+	1.05335e20i	−0.251565	+	0.435724i
$185$	−6.41051e19	−	3.70111e19i	−0.252550	−	0.145810i
$186$	4.84697e20	+	4.53348e20i	1.81909	+	1.70143i
$187$	−7.86357e19	−	1.36201e20i	−0.281219	−	0.487086i
$188$		−	5.00735e20i		−	1.70682i
$189$	−2.82099e19	+	1.73068e20i	−0.0916740	+	0.562420i
$190$	−1.29587e20			−0.401588
$191$	−3.07553e20	+	1.77566e20i	−0.909118	+	0.524880i	−0.880147	−	0.474701i	$-0.842556\pi$
$191$	−3.07553e20	+	1.77566e20i	−0.909118	+	0.524880i	−0.0289707	+	0.999580i	$0.509223\pi$
$192$	3.94962e20	−	4.22274e20i	1.11390	−	1.19092i
$193$	−8.57628e18	+	1.48545e19i	−0.0230825	+	0.0399801i	−0.877336	−	0.479877i	$-0.840681\pi$
$193$	−8.57628e18	+	1.48545e19i	−0.0230825	+	0.0399801i	0.854253	+	0.519857i	$0.174015\pi$
$194$	−1.57211e20	−	9.07655e19i	−0.403893	−	0.233188i
$195$	−3.09504e19	+	1.33150e20i	−0.0759197	+	0.326609i
$196$	−2.25115e20	−	3.89910e20i	−0.527350	−	0.913397i
$197$		−	5.29187e20i		−	1.18417i	−0.805876	−	0.592084i	$-0.798305\pi$
$197$		−	5.29187e20i		−	1.18417i	0.805876	−	0.592084i	$-0.201695\pi$
$198$	2.73191e20	+	1.34260e20i	0.584091	+	0.287052i
$199$	−6.12743e20			−1.25199			−0.625994	−	0.779828i	$-0.715307\pi$
$199$	−6.12743e20			−1.25199			−0.625994	+	0.779828i	$0.715307\pi$
$200$	−3.72736e20	+	2.15199e20i	−0.728001	+	0.420311i
$201$	−1.67742e19	−	5.51617e19i	−0.0313240	−	0.103008i
$202$	−7.75624e19	+	1.34342e20i	−0.138512	+	0.239911i
$203$	−4.23523e20	−	2.44521e20i	−0.723457	−	0.417688i
$204$	1.26476e21	−	3.84603e20i	2.06698	−	0.628552i
$205$	−4.12167e19	−	7.13895e19i	−0.0644598	−	0.111648i
$206$		−	4.06407e20i		−	0.608354i
$207$	−1.72187e20	+	3.50365e20i	−0.246756	+	0.502097i
$208$	1.17097e20			0.160685
$209$	−2.63127e20	+	1.51916e20i	−0.345819	+	0.199659i
$210$	1.80278e20	+	4.19053e19i	0.226971	+	0.0527589i
$211$	1.72075e20	−	2.98043e20i	0.207576	−	0.359531i	−0.743375	−	0.668875i	$-0.766776\pi$
$211$	1.72075e20	−	2.98043e20i	0.207576	−	0.359531i	0.950950	+	0.309344i	$0.100109\pi$
$212$	1.72099e21	+	9.93613e20i	1.98955	+	1.14867i
$213$	−3.82139e20	−	3.57423e20i	−0.423453	−	0.396065i
$214$	1.01953e21	+	1.76588e21i	1.08312	+	1.87602i
$215$		−	2.67386e20i		−	0.272391i
$216$	−5.82469e20	+	7.12710e20i	−0.569101	+	0.696352i
$217$	9.46124e20			0.886769
$218$	−1.79659e21	+	1.03726e21i	−1.61562	+	0.932780i
$219$	−1.24675e21	+	1.33296e21i	−1.07592	+	1.15032i
$220$	9.79404e19	−	1.69638e20i	0.0811255	−	0.140514i
$221$	1.97719e21	+	1.14153e21i	1.57224	+	0.907734i
$222$	5.41761e20	−	2.33068e21i	0.413648	−	1.77953i
$223$	1.05022e21	+	1.81904e21i	0.770084	+	1.33382i	0.937516	+	0.347941i	$0.113119\pi$
$223$	1.05022e21	+	1.81904e21i	0.770084	+	1.33382i	−0.167433	+	0.985884i	$0.553548\pi$
$224$		−	8.86160e20i		−	0.624137i
$225$	−1.14757e21	+	7.69046e20i	−0.776489	+	0.520367i
$226$	−1.98994e21			−1.29379
$227$	2.17037e21	−	1.25306e21i	1.35613	−	0.782961i	0.367028	−	0.930210i	$-0.380375\pi$
$227$	2.17037e21	−	1.25306e21i	1.35613	−	0.782961i	0.989099	+	0.147249i	$0.0470419\pi$
$228$	−7.43015e20	−	2.44339e21i	−0.446256	−	1.46750i
$229$	1.28124e20	−	2.21918e20i	0.0739797	−	0.128137i	−0.826662	−	0.562698i	$-0.809763\pi$
$229$	1.28124e20	−	2.21918e20i	0.0739797	−	0.128137i	0.900642	+	0.434562i	$0.143097\pi$
$230$	3.56852e20	+	2.06028e20i	0.198124	+	0.114387i
$231$	4.15180e20	−	1.26253e20i	0.221681	−	0.0674114i
$232$	−1.28353e21	−	2.22313e21i	−0.659194	−	1.14176i
$233$		−	3.67653e21i		−	1.81650i	−0.418431	−	0.908249i	$-0.637420\pi$
$233$		−	3.67653e21i		−	1.81650i	0.418431	−	0.908249i	$-0.362580\pi$
$234$	−4.40903e21	+	2.95025e20i	−2.09605	+	0.140254i
$235$	−6.10261e20			−0.279193
$236$	−8.70081e20	+	5.02341e20i	−0.383135	+	0.221203i
$237$	1.53408e21	+	3.56595e20i	0.650301	+	0.151161i
$238$	1.54558e21	−	2.67703e21i	0.630812	−	1.09260i
$239$	−4.20279e20	−	2.42648e20i	−0.165180	−	0.0953666i	0.415131	−	0.909762i	$-0.363736\pi$
$239$	−4.20279e20	−	2.42648e20i	−0.165180	−	0.0953666i	−0.580311	+	0.814395i	$0.697069\pi$
$240$	−6.03485e19	−	5.64453e19i	−0.0228436	−	0.0213662i
$241$	−4.78904e20	−	8.29486e20i	−0.174620	−	0.302451i	0.765409	−	0.643544i	$-0.222537\pi$
$241$	−4.78904e20	−	8.29486e20i	−0.174620	−	0.302451i	−0.940030	+	0.341092i	$0.889203\pi$
$242$			3.80304e21i			1.33596i
$243$	−1.71262e21	+	2.40726e21i	−0.579702	+	0.814829i
$244$	−2.33996e21			−0.763308
$245$	−4.75195e20	+	2.74354e20i	−0.149409	+	0.0862614i
$246$	1.82025e21	−	1.94612e21i	0.551716	−	0.589867i
$247$	2.20533e21	−	3.81975e21i	0.644468	−	1.11625i
$248$	4.30098e21	+	2.48317e21i	1.21200	+	0.699748i
$249$	−9.23091e20	+	3.97117e21i	−0.250871	+	1.07926i
$250$	1.50901e21	+	2.61368e21i	0.395578	+	0.685160i
$251$			3.06766e21i			0.775790i	0.921704	+	0.387895i	$0.126798\pi$
$251$			3.06766e21i			0.775790i	−0.921704	+	0.387895i	$0.873202\pi$
$252$	2.43529e20	+	3.63944e21i	0.0594217	+	0.888035i
$253$	9.66115e20			0.227480
$254$	−8.16795e21	+	4.71577e21i	−1.85614	+	1.07164i
$255$	−4.68727e20	−	1.54140e21i	−0.102816	−	0.338107i
$256$	1.87429e21	−	3.24637e21i	0.396897	−	0.687445i
$257$	−9.62753e20	−	5.55846e20i	−0.196842	−	0.113647i	0.398340	−	0.917238i	$-0.369586\pi$
$257$	−9.62753e20	−	5.55846e20i	−0.196842	−	0.113647i	−0.595181	+	0.803591i	$0.702920\pi$
$258$	8.26951e21	−	2.51469e21i	1.63269	−	0.496486i
$259$	−1.70559e21	−	2.95418e21i	−0.325221	−	0.563299i
$260$			2.84355e21i			0.523722i
$261$	−4.58687e21	−	6.84450e21i	−0.816116	−	1.21780i
$262$	9.05610e21			1.55679
$263$	4.53179e21	−	2.61643e21i	0.752780	−	0.434618i	−0.0739173	−	0.997264i	$-0.523550\pi$
$263$	4.53179e21	−	2.61643e21i	0.752780	−	0.434618i	0.826698	+	0.562646i	$0.190217\pi$
$264$	2.21872e21	+	5.15739e20i	0.356179	+	0.0827931i
$265$	1.21095e21	−	2.09742e21i	0.187894	−	0.325441i
$266$	−5.17175e21	−	2.98591e21i	−0.775717	−	0.447860i
$267$	2.65585e21	+	2.48408e21i	0.385125	+	0.360216i
$268$	−5.99662e20	−	1.03864e21i	−0.0840801	−	0.145631i
$269$			3.71642e21i			0.503911i	0.967739	+	0.251956i	$0.0810737\pi$
$269$			3.71642e21i			0.503911i	−0.967739	+	0.251956i	$0.918926\pi$
$270$	2.41451e21	+	1.97328e21i	0.316632	+	0.258771i
$271$	−5.71098e21			−0.724414			−0.362207	−	0.932098i	$-0.617977\pi$
$271$	−5.71098e21			−0.724414			−0.362207	+	0.932098i	$0.617977\pi$
$272$	−1.19517e21	+	6.90032e20i	−0.146659	+	0.0846739i
$273$	−4.30320e21	+	4.60077e21i	−0.510890	+	0.546218i
$274$	−1.18172e22	+	2.04680e22i	−1.35756	+	2.35137i
$275$	2.96067e21	+	1.70934e21i	0.329151	+	0.190035i
$276$	−1.83862e21	+	7.90979e21i	−0.197838	+	0.851105i
$277$	−2.64599e21	−	4.58300e21i	−0.275595	−	0.477344i	0.694690	−	0.719309i	$-0.255541\pi$
$277$	−2.64599e21	−	4.58300e21i	−0.275595	−	0.477344i	−0.970285	+	0.241965i	$0.922208\pi$
$278$		−	2.47920e22i		−	2.49982i
$279$	1.43059e22	+	7.03066e21i	1.39662	+	0.686370i
$280$	1.38502e21			0.130928
$281$	1.46566e22	−	8.46201e21i	1.34177	−	0.774670i	0.354701	−	0.934980i	$-0.384583\pi$
$281$	1.46566e22	−	8.46201e21i	1.34177	−	0.774670i	0.987067	+	0.160310i	$0.0512493\pi$
$282$	−5.73935e21	−	1.88737e22i	−0.508886	−	1.67346i
$283$	−1.96105e21	+	3.39664e21i	−0.168427	+	0.291724i	−0.937867	−	0.346995i	$-0.887202\pi$
$283$	−1.96105e21	+	3.39664e21i	−0.168427	+	0.291724i	0.769440	+	0.638719i	$0.220535\pi$
$284$	−9.42599e21	−	5.44210e21i	−0.784263	−	0.452795i
$285$	−2.97783e21	+	9.05535e20i	−0.240047	+	0.0729964i
$286$	5.46782e21	+	9.47055e21i	0.427091	+	0.739743i
$287$		−	3.79881e21i		−	0.287548i
$288$	6.58507e21	−	1.33992e22i	0.483090	−	0.982987i
$289$	−1.28444e22			−0.913341
$290$	−7.53150e21	+	4.34831e21i	−0.519158	+	0.299736i
$291$	−4.24685e21	−	9.87172e20i	−0.283811	−	0.0659714i
$292$	−1.89828e22	+	3.28792e22i	−1.23003	+	2.13047i
$293$	1.85544e22	+	1.07124e22i	1.16584	+	0.673096i	0.952696	−	0.303926i	$-0.0982974\pi$
$293$	1.85544e22	+	1.07124e22i	1.16584	+	0.673096i	0.213141	+	0.977022i	$0.431631\pi$
$294$	−1.29541e22	−	1.21163e22i	−0.789372	−	0.738317i
$295$	6.12219e20	+	1.06039e21i	0.0361833	+	0.0626714i
$296$		−	1.79058e22i		−	1.02652i
$297$	7.21595e21	+	1.17619e21i	0.401315	+	0.0654140i
$298$	3.30049e22			1.78087
$299$	−1.21459e22	+	7.01242e21i	−0.635898	+	0.367136i
$300$	−1.96292e22	+	2.09866e22i	−0.997267	+	1.06623i
$301$	6.16101e21	−	1.06712e22i	0.303776	−	0.526156i
$302$	−3.34292e22	−	1.93004e22i	−1.59979	−	0.923641i
$303$	−8.43574e20	+	3.62908e21i	−0.0391868	+	0.168583i
$304$	1.33307e21	+	2.30895e21i	0.0601163	+	0.104124i
$305$			2.85178e21i			0.124858i
$306$	4.32631e22	−	2.89929e22i	1.83918	−	1.23254i
$307$	−2.98790e21			−0.123345			−0.0616724	−	0.998096i	$-0.519643\pi$
$307$	−2.98790e21			−0.123345			−0.0616724	+	0.998096i	$0.519643\pi$
$308$	7.81747e21	−	4.51342e21i	0.313408	−	0.180946i
$309$	−2.83990e21	−	9.33897e21i	−0.110580	−	0.363641i
$310$	8.41245e21	−	1.45708e22i	0.318176	−	0.551097i
$311$	2.24633e22	+	1.29692e22i	0.825335	+	0.476507i	0.852253	−	0.523130i	$-0.175236\pi$
$311$	2.24633e22	+	1.29692e22i	0.825335	+	0.476507i	−0.0269177	+	0.999638i	$0.508569\pi$
$312$	−3.16369e22	+	9.62053e21i	−1.12928	+	0.343406i
$313$	−2.67696e22	−	4.63663e22i	−0.928416	−	1.60806i	−0.785973	−	0.618261i	$-0.787838\pi$
$313$	−2.67696e22	−	4.63663e22i	−0.928416	−	1.60806i	−0.142443	−	0.989803i	$-0.545496\pi$
$314$			3.91288e22i			1.31865i
$315$	4.43550e21	−	2.96796e20i	0.145261	−	0.00971993i
$316$	3.27620e22			1.04277
$317$	−1.43895e22	+	8.30777e21i	−0.445155	+	0.257011i	−0.705782	−	0.708429i	$-0.749404\pi$
$317$	−1.43895e22	+	8.30777e21i	−0.445155	+	0.257011i	0.260627	+	0.965440i	$0.416071\pi$
$318$	7.62562e22	+	1.77256e22i	2.29314	+	0.533037i
$319$	−1.01951e22	+	1.76585e22i	−0.298041	+	0.516223i
$320$	−1.26943e22	−	7.32903e21i	−0.360792	−	0.208304i
$321$	3.57678e22	+	3.34544e22i	0.988432	+	0.924502i
$322$	9.49448e21	+	1.64449e22i	0.255134	+	0.441905i
$323$			5.19826e22i			1.35842i
$324$	−2.33624e22	+	5.68401e22i	−0.593763	+	1.44461i
$325$	−4.96281e22			−1.22681
$326$	5.55900e22	−	3.20949e22i	1.33671	−	0.771751i
$327$	−3.40362e22	+	3.63898e22i	−0.796179	+	0.851235i
$328$	9.97025e21	−	1.72690e22i	0.226904	−	0.393009i
$329$	−2.43551e22	−	1.40614e22i	−0.539296	−	0.311363i
$330$	1.74721e21	−	7.51657e21i	0.0376461	−	0.161955i
$331$	−2.36968e22	−	4.10441e22i	−0.496865	−	0.860595i	0.503129	−	0.864211i	$-0.332182\pi$
$331$	−2.36968e22	−	4.10441e22i	−0.496865	−	0.860595i	−0.999993	+	0.00361663i	$0.998849\pi$
$332$			8.48085e22i			1.73060i
$333$	−3.83704e21	−	5.73431e22i	−0.0762076	−	1.13889i
$334$	5.26661e22			1.01815
$335$	−1.26583e21	+	7.30826e20i	−0.0238216	+	0.0137534i
$336$	−1.10788e21	−	3.64323e21i	−0.0202973	−	0.0667472i
$337$	3.91591e22	−	6.78256e22i	0.698496	−	1.20983i	−0.270492	−	0.962722i	$-0.587186\pi$
$337$	3.91591e22	−	6.78256e22i	0.698496	−	1.20983i	0.968988	−	0.247108i	$-0.0794803\pi$
$338$	−5.76710e22	−	3.32964e22i	−1.00163	−	0.578291i
$339$	−4.57274e22	+	1.39053e22i	−0.773356	+	0.235171i
$340$	−1.67566e22	−	2.90232e22i	−0.275978	−	0.478008i
$341$		−	3.94479e22i		−	0.632754i
$342$	−5.60115e22	−	8.35800e22i	−0.875069	−	1.30577i
$343$	−6.27320e22			−0.954645
$344$	5.60146e22	−	3.23401e22i	0.830377	−	0.479419i
$345$	9.63991e21	+	2.24078e21i	0.139220	+	0.0323614i
$346$	5.68279e22	−	9.84288e22i	0.799607	−	1.38496i
$347$	−8.51873e21	−	4.91829e21i	−0.116791	−	0.0674293i	0.440467	−	0.897769i	$-0.354813\pi$
$347$	−8.51873e21	−	4.91829e21i	−0.116791	−	0.0674293i	−0.557258	+	0.830340i	$0.688146\pi$
$348$	−1.25171e23	−	1.17076e23i	−1.67221	−	1.56406i
$349$	5.88831e22	+	1.01988e23i	0.766587	+	1.32777i	0.939403	+	0.342814i	$0.111380\pi$
$349$	5.88831e22	+	1.01988e23i	0.766587	+	1.32777i	−0.172816	+	0.984954i	$0.555287\pi$
$350$			6.71941e22i			0.852548i
$351$	−9.92551e22	+	3.75891e22i	−1.22741	+	0.464833i
$352$	−3.69478e22			−0.445353
$353$	9.07311e22	−	5.23836e22i	1.06607	−	0.615493i	0.138962	−	0.990298i	$-0.455624\pi$
$353$	9.07311e22	−	5.23836e22i	1.06607	−	0.615493i	0.927104	+	0.374805i	$0.122290\pi$
$354$	−2.70374e22	+	2.89070e22i	−0.309696	+	0.331111i
$355$	−6.63245e21	+	1.14877e22i	−0.0740660	+	0.128286i
$356$	6.55102e22	+	3.78223e22i	0.713278	+	0.411811i
$357$	1.68099e22	−	7.23166e22i	0.178464	−	0.767757i
$358$	7.09872e22	+	1.22953e23i	0.734907	+	1.27290i
$359$			1.00413e23i			1.01377i	0.862014	+	0.506884i	$0.169203\pi$
$359$			1.00413e23i			1.01377i	−0.862014	+	0.506884i	$0.830797\pi$
$360$	2.09423e22	+	1.02921e22i	0.206206	+	0.101340i
$361$	−3.70213e21			−0.0355539
$362$	−1.45187e22	+	8.38237e21i	−0.136004	+	0.0785217i
$363$	2.65750e22	+	8.73913e22i	0.242836	+	0.798561i
$364$	−6.55201e22	+	1.13484e23i	−0.584067	+	1.01163i
$365$	4.00709e22	+	2.31350e22i	0.348493	+	0.201202i
$366$	−8.81978e22	+	2.68202e22i	−0.748390	+	0.227579i
$367$	8.98072e22	+	1.55551e23i	0.743561	+	1.28789i	0.950864	+	0.309609i	$0.100198\pi$
$367$	8.98072e22	+	1.55551e23i	0.743561	+	1.28789i	−0.207303	+	0.978277i	$0.566469\pi$
$368$		−	8.47771e21i		−	0.0684933i
$369$	2.82290e22	−	5.74402e22i	0.222566	−	0.452875i
$370$	−6.06611e22			−0.466761
$371$	9.66562e22	−	5.58045e22i	0.725879	−	0.419087i
$372$	3.22969e23	+	7.50735e22i	2.36741	+	0.550301i
$373$	9.62421e22	−	1.66696e23i	0.688630	−	1.19274i	−0.283652	−	0.958927i	$-0.591546\pi$
$373$	9.62421e22	−	1.66696e23i	0.688630	−	1.19274i	0.972281	−	0.233814i	$-0.0751207\pi$
$374$	−1.11617e23	−	6.44419e22i	−0.779623	−	0.450116i
$375$	5.29400e22	+	4.95159e22i	0.360996	+	0.337648i
$376$	−7.38106e22	−	1.27844e23i	−0.491392	−	0.851116i
$377$		−	2.96000e23i		−	1.92406i
$378$	5.08938e22	+	1.34387e23i	0.323027	+	0.852963i
$379$	−1.00347e23			−0.621944			−0.310972	−	0.950419i	$-0.600654\pi$
$379$	−1.00347e23			−0.621944			−0.310972	+	0.950419i	$0.600654\pi$
$380$	−5.60700e22	+	3.23720e22i	−0.339373	+	0.195937i
$381$	−1.54741e23	+	1.65442e23i	−0.914705	+	0.977957i
$382$	−1.45515e23	+	2.52040e23i	−0.840114	+	1.45512i
$383$	1.07974e22	+	6.23387e21i	0.0608876	+	0.0351535i	0.530135	−	0.847913i	$-0.322141\pi$
$383$	1.07974e22	+	6.23387e21i	0.0608876	+	0.0351535i	−0.469247	+	0.883067i	$0.655475\pi$
$384$	6.22609e22	−	2.67849e23i	0.342953	−	1.47540i
$385$	−5.50064e21	−	9.52739e21i	−0.0295983	−	0.0512658i
$386$			1.40565e22i			0.0738910i
$387$	1.72456e23	−	1.15572e23i	0.885684	−	0.593545i
$388$	−9.06959e22			−0.455095
$389$	−1.36081e23	+	7.85665e22i	−0.667193	+	0.385204i	−0.795012	−	0.606593i	$-0.792536\pi$
$389$	−1.36081e23	+	7.85665e22i	−0.667193	+	0.385204i	0.127819	+	0.991797i	$0.459202\pi$
$390$	3.25923e22	+	1.07179e23i	0.156147	+	0.513486i
$391$	8.26460e22	−	1.43147e23i	0.386929	−	0.670180i
$392$	−1.14949e23	−	6.63658e22i	−0.525933	−	0.303647i
$393$	2.08103e23	−	6.32825e22i	0.930563	−	0.282977i
$394$	−2.16834e23	−	3.75568e23i	−0.947680	−	1.64143i
$395$		−	3.99280e22i		−	0.170571i
$396$	1.51744e23	−	1.01538e22i	0.633657	−	0.0424004i
$397$	3.74061e23			1.52696			0.763480	−	0.645831i	$-0.223489\pi$
$397$	3.74061e23			1.52696			0.763480	+	0.645831i	$0.223489\pi$
$398$	−4.34868e23	+	2.51071e23i	−1.73544	+	1.00196i
$399$	−1.39709e23	−	3.24750e22i	−0.545088	−	0.126705i
$400$	1.49996e22	−	2.59800e22i	0.0572188	−	0.0991058i
$401$	−1.38328e23	−	7.98640e22i	−0.515956	−	0.297887i	0.219323	−	0.975652i	$-0.429615\pi$
$401$	−1.38328e23	−	7.98640e22i	−0.515956	−	0.297887i	−0.735278	+	0.677765i	$0.762949\pi$
$402$	−3.45073e22	−	3.22754e22i	−0.125857	−	0.117716i
$403$	2.86328e23	+	4.95934e23i	1.02122	+	1.76880i
$404$			7.75029e22i			0.270325i
$405$	6.92728e22	+	2.84725e22i	0.236302	+	0.0971249i
$406$	−4.00770e23			−1.33709
$407$	−1.23172e23	+	7.11135e22i	−0.401942	+	0.232061i
$408$	2.66216e23	−	2.84625e23i	0.849753	−	0.908513i
$409$	−7.74687e22	+	1.34180e23i	−0.241889	+	0.418964i	−0.961252	−	0.275670i	$-0.911100\pi$
$409$	−7.74687e22	+	1.34180e23i	−0.241889	+	0.418964i	0.719363	+	0.694634i	$0.244434\pi$
$410$	−5.85036e22	−	3.37771e22i	−0.178701	−	0.103173i
$411$	−1.28525e23	+	5.52918e23i	−0.384070	+	1.65228i
$412$	−1.01524e23	−	1.75844e23i	−0.296820	−	0.514107i
$413$			5.64262e22i			0.161410i
$414$	2.13595e22	+	3.19210e23i	0.0597845	+	0.893457i
$415$	1.03359e23			0.283083
$416$	4.64503e23	−	2.68181e23i	1.24494	−	0.718766i
$417$	−1.73242e23	−	5.69704e23i	−0.454391	−	1.49426i
$418$	−1.24495e23	+	2.15632e23i	−0.319571	+	0.553513i
$419$	−2.88090e23	−	1.66329e23i	−0.723772	−	0.417870i	0.0923671	−	0.995725i	$-0.470557\pi$
$419$	−2.88090e23	−	1.66329e23i	−0.723772	−	0.417870i	−0.816140	+	0.577855i	$0.803890\pi$
$420$	8.84711e22	−	2.69033e22i	0.217549	−	0.0661550i
$421$	−1.74263e23	−	3.01833e23i	−0.419437	−	0.726487i	0.576445	−	0.817136i	$-0.304439\pi$
$421$	−1.74263e23	−	3.01833e23i	−0.419437	−	0.726487i	−0.995883	+	0.0906486i	$0.971106\pi$
$422$		−	2.82031e23i		−	0.664485i
$423$	−2.63773e23	−	3.93600e23i	−0.608368	−	0.907804i
$424$	5.85852e23			1.32280
$425$	5.06539e23	−	2.92450e23i	1.11973	−	0.646475i
$426$	−4.17661e23	−	9.70846e22i	−0.903936	−	0.210118i
$427$	−6.57098e22	+	1.13813e23i	−0.139245	+	0.241179i
$428$	8.82261e23	+	5.09374e23i	1.83064	+	1.05692i
$429$	1.91826e23	+	1.79419e23i	0.389754	+	0.364546i
$430$	−1.09561e23	−	1.89766e23i	−0.217992	−	0.377573i
$431$		−	1.62293e22i		−	0.0316232i	−0.999875	−	0.0158116i	$-0.994967\pi$
$431$		−	1.62293e22i		−	0.0316232i	0.999875	−	0.0158116i	$-0.00503319\pi$
$432$	1.03212e22	−	6.33203e22i	0.0196958	−	0.120834i
$433$	−6.99806e23			−1.30794			−0.653969	−	0.756522i	$-0.726897\pi$
$433$	−6.99806e23			−1.30794			−0.653969	+	0.756522i	$0.726897\pi$
$434$	6.71471e23	−	3.87674e23i	1.22919	−	0.709674i
$435$	−1.42684e23	+	1.52550e23i	−0.255841	+	0.273533i
$436$	−5.18232e23	+	8.97604e23i	−0.910219	+	1.57654i
$437$	−2.76546e23	−	1.59664e23i	−0.475811	−	0.274710i
$438$	−3.38645e23	+	1.45686e24i	−0.570792	+	2.45557i
$439$	3.70551e23	+	6.41814e23i	0.611882	+	1.05981i	0.990923	+	0.134431i	$0.0429205\pi$
$439$	3.70551e23	+	6.41814e23i	0.611882	+	1.05981i	−0.379041	+	0.925380i	$0.623746\pi$
$440$		−	5.77474e22i		−	0.0934239i
$441$	−3.82343e23	−	1.87903e23i	−0.606047	−	0.297842i
$442$	1.87097e24			2.90581
$443$	−8.16308e23	+	4.71295e23i	−1.24228	+	0.717232i	−0.969558	−	0.244860i	$-0.921258\pi$
$443$	−8.16308e23	+	4.71295e23i	−1.24228	+	0.717232i	−0.272724	+	0.962092i	$0.587925\pi$
$444$	−3.47812e23	−	1.14377e24i	−0.518678	−	1.70566i
$445$	4.60952e22	−	7.98393e22i	0.0673621	−	0.116675i
$446$	1.49070e24	+	8.60658e23i	2.13490	+	1.23258i
$447$	7.58430e23	−	2.30632e23i	1.06450	−	0.323707i
$448$	−3.37746e23	−	5.84994e23i	−0.464610	−	0.804728i
$449$			4.56954e23i			0.616107i	0.951369	+	0.308053i	$0.0996775\pi$
$449$			4.56954e23i			0.616107i	−0.951369	+	0.308053i	$0.900322\pi$
$450$	−4.99320e23	+	1.01601e24i	−0.659882	+	1.34272i
$451$	−1.58389e23			−0.205180
$452$	−8.61007e23	+	4.97102e23i	−1.09335	+	0.631248i
$453$	−9.03049e23	−	2.09912e23i	−1.12416	−	0.261309i
$454$	1.02688e24	−	1.77861e24i	1.25319	−	2.17060i
$455$	1.38307e23	+	7.98514e22i	0.165478	+	0.0955388i
$456$	−5.49867e23	−	5.14303e23i	−0.645021	−	0.603303i
$457$	1.94626e23	+	3.37102e23i	0.223849	+	0.387718i	0.955974	−	0.293453i	$-0.0948044\pi$
$457$	1.94626e23	+	3.37102e23i	0.223849	+	0.387718i	−0.732124	+	0.681171i	$0.761471\pi$
$458$		−	2.09996e23i		−	0.236822i
$459$	7.91560e23	−	9.68553e23i	0.875325	−	1.07105i
$460$	2.05870e23			0.223241
$461$	−8.52130e23	+	4.91978e23i	−0.906145	+	0.523163i	−0.879189	−	0.476473i	$-0.841915\pi$
$461$	−8.52130e23	+	4.91978e23i	−0.906145	+	0.523163i	−0.0269563	+	0.999637i	$0.508581\pi$
$462$	2.42924e23	−	2.59723e23i	0.253334	−	0.270852i
$463$	−2.14837e23	+	3.72109e23i	−0.219726	+	0.380576i	−0.954724	−	0.297493i	$-0.903850\pi$
$463$	−2.14837e23	+	3.72109e23i	−0.219726	+	0.380576i	0.734998	+	0.678069i	$0.237183\pi$
$464$	1.54954e23	+	8.94628e22i	0.155432	+	0.0897388i
$465$	9.14944e22	−	3.93612e23i	0.0900156	−	0.387250i
$466$	−1.50646e24	−	2.60926e24i	−1.45373	−	2.51793i
$467$			4.67271e23i			0.442300i	0.975240	+	0.221150i	$0.0709810\pi$
$467$			4.67271e23i			0.442300i	−0.975240	+	0.221150i	$0.929019\pi$
$468$	−1.83400e24	+	1.22906e24i	−1.70289	+	1.14120i
$469$	−6.73579e22			−0.0613526
$470$	−4.33107e23	+	2.50054e23i	−0.387003	+	0.223436i
$471$	2.73426e23	+	8.99155e23i	0.239691	+	0.788218i
$472$	−1.48095e23	+	2.56507e23i	−0.127368	+	0.220608i
$473$	−4.44927e23	−	2.56879e23i	−0.375439	−	0.216760i
$474$	1.23487e24	−	3.75513e23i	1.02239	−	0.310899i
$475$	−5.64985e23	−	9.78582e23i	−0.458981	−	0.794978i
$476$		−	1.54440e24i		−	1.23111i
$477$	1.87618e24	−	1.25542e23i	1.46760	−	0.0982029i
$478$	−3.97700e23			−0.305285
$479$	−4.19719e23	+	2.42325e23i	−0.316184	+	0.182549i	−0.649690	−	0.760199i	$-0.725101\pi$
$479$	−4.19719e23	+	2.42325e23i	−0.316184	+	0.182549i	0.333507	+	0.942748i	$0.391768\pi$
$480$	−3.68666e23	−	8.56956e22i	−0.272560	−	0.0633560i
$481$	1.03234e24	−	1.78806e24i	0.749058	−	1.29741i
$482$	−6.79763e23	−	3.92462e23i	−0.484099	−	0.279495i
$483$	3.33091e23	+	3.11548e23i	0.232830	+	0.217771i
$484$	9.50029e23	+	1.64550e24i	0.651822	+	1.12899i
$485$			1.10534e23i			0.0744423i
$486$	−2.29086e23	+	2.41019e24i	−0.151451	+	1.59340i
$487$	−2.62024e24			−1.70052			−0.850259	−	0.526365i	$-0.823555\pi$
$487$	−2.62024e24			−1.70052			−0.850259	+	0.526365i	$0.823555\pi$
$488$	−5.97419e23	+	3.44920e23i	−0.380628	+	0.219756i
$489$	1.05315e24	−	1.12597e24i	0.658733	−	0.704284i
$490$	−2.24833e23	+	3.89422e23i	−0.138069	+	0.239142i
$491$	1.61324e24	+	9.31407e23i	0.972672	+	0.561573i	0.900050	−	0.435787i	$-0.143530\pi$
$491$	1.61324e24	+	9.31407e23i	0.972672	+	0.561573i	0.0726224	+	0.997360i	$0.476863\pi$
$492$	3.01430e23	−	1.29676e24i	0.178443	−	0.767670i
$493$	1.74428e24	+	3.02118e24i	1.01390	+	1.75612i
$494$		−	3.61453e24i		−	2.06305i
$495$	−1.23747e22	−	1.84935e23i	−0.00693565	−	0.103651i
$496$	−3.46158e23			−0.190519
$497$	−5.29394e23	+	3.05646e23i	−0.286135	+	0.165200i
$498$	9.72061e23	+	3.19660e24i	0.515976	+	1.69678i
$499$	4.84377e23	−	8.38965e23i	0.252510	−	0.437360i	−0.711706	−	0.702477i	$-0.752077\pi$
$499$	4.84377e23	−	8.38965e23i	0.252510	−	0.437360i	0.964216	+	0.265117i	$0.0854106\pi$
$500$	1.30584e24	+	7.53925e23i	0.668588	+	0.386010i
$501$	1.21023e24	−	3.68022e23i	0.608596	−	0.185069i
$502$	1.25697e24	+	2.17714e24i	0.620859	+	1.07536i
$503$			9.85615e23i			0.478184i	0.970997	+	0.239092i	$0.0768498\pi$
$503$			9.85615e23i			0.478184i	−0.970997	+	0.239092i	$0.923150\pi$
$504$	5.98646e23	+	8.93296e23i	0.285296	+	0.425716i
$505$	9.44551e22			0.0442184
$506$	6.85659e23	−	3.95865e23i	0.315321	−	0.182051i
$507$	−1.55791e24	−	3.62134e23i	−0.703835	−	0.163605i
$508$	−2.35608e24	+	4.08084e24i	−1.04572	+	1.81124i
$509$	1.29061e24	+	7.45132e23i	0.562774	+	0.324918i	0.754258	−	0.656578i	$-0.227997\pi$
$509$	1.29061e24	+	7.45132e23i	0.562774	+	0.324918i	−0.191484	+	0.981496i	$0.561330\pi$
$510$	−9.64248e23	−	9.01883e23i	−0.413102	−	0.386383i
$511$	1.06614e24	+	1.84660e24i	0.448771	+	0.777294i
$512$			5.90431e23i			0.244197i
$513$	−1.87115e24	−	1.52922e24i	−0.760418	−	0.621459i
$514$	−9.11031e23			−0.363802
$515$	−2.14307e23	+	1.23730e23i	−0.0840952	+	0.0485524i
$516$	2.94987e24	−	3.15385e24i	1.13751	−	1.21617i
$517$	−5.86282e23	+	1.01547e24i	−0.222173	+	0.384815i
$518$	−2.42095e24	−	1.39773e24i	−0.901607	−	0.520543i
$519$	6.18064e23	−	2.65893e24i	0.226218	−	0.973198i
$520$	4.19152e23	+	7.25992e23i	0.150779	+	0.261157i
$521$		−	2.42672e24i		−	0.857986i	−0.903308	−	0.428993i	$-0.858869\pi$
$521$		−	2.42672e24i		−	0.857986i	0.903308	−	0.428993i	$-0.141131\pi$
$522$	−6.05987e24	−	2.97812e24i	−2.10586	−	1.03492i
$523$	1.40090e24			0.478510			0.239255	−	0.970957i	$-0.423097\pi$
$523$	1.40090e24			0.478510			0.239255	+	0.970957i	$0.423097\pi$
$524$	3.91840e24	−	2.26229e24i	1.31561	−	0.759567i
$525$	4.69541e23	+	1.54408e24i	0.154967	+	0.509606i
$526$	2.14416e24	−	3.71380e24i	0.695643	−	1.20489i
$527$	−5.84491e24	−	3.37456e24i	−1.86416	−	1.07627i
$528$	−1.51902e23	+	4.61921e22i	−0.0476274	+	0.0144831i
$529$	−1.11438e24	−	1.93017e24i	−0.343505	−	0.594969i
$530$		−	1.98474e24i		−	0.601479i
$531$	−4.19304e23	+	8.53196e23i	−0.124933	+	0.254213i
$532$	−2.98362e24			−0.874056
$533$	1.99124e24	−	1.14964e24i	0.573560	−	0.331145i
$534$	2.90273e24	+	6.74733e23i	0.822119	+	0.191100i
$535$	6.20790e23	−	1.07524e24i	0.172886	−	0.299448i
$536$	−3.06202e23	−	1.76786e23i	−0.0838541	−	0.0484132i
$537$	2.49042e24	+	2.32934e24i	0.670661	+	0.627285i
$538$	1.52280e24	+	2.63757e24i	0.403276	+	0.698495i
$539$			1.05429e24i			0.274576i
$540$	1.53765e24	+	2.50636e23i	0.393835	+	0.0641948i
$541$	−5.90827e24			−1.48828			−0.744141	−	0.668023i	$-0.767141\pi$
$541$	−5.90827e24			−1.48828			−0.744141	+	0.668023i	$0.767141\pi$
$542$	−4.05312e24	+	2.34007e24i	−1.00414	+	0.579743i
$543$	−2.75055e23	+	2.94076e23i	−0.0670227	+	0.0716573i
$544$	−3.16069e24	+	5.47447e24i	−0.757516	+	1.31206i
$545$	1.09394e24	+	6.31585e23i	0.257884	+	0.148889i
$546$	−1.16885e24	+	5.02843e24i	−0.271035	+	1.16600i
$547$	−3.44329e23	−	5.96395e23i	−0.0785394	−	0.136034i	0.824081	−	0.566473i	$-0.191692\pi$
$547$	−3.44329e23	−	5.96395e23i	−0.0785394	−	0.136034i	−0.902620	+	0.430438i	$0.858359\pi$
$548$			1.18081e25i			2.64946i
$549$	−1.83931e24	+	1.23262e24i	−0.405980	+	0.272069i
$550$	2.80161e24			0.608336
$551$	5.83662e24	−	3.36977e24i	1.24680	−	0.719840i
$552$	6.96517e23	+	2.29048e24i	0.146379	+	0.481366i
$553$	9.20009e23	−	1.59350e24i	0.190224	−	0.329478i
$554$	−3.75576e24	−	2.16839e24i	−0.764030	−	0.441113i
$555$	−1.39395e24	+	4.23889e23i	−0.279004	+	0.0848429i
$556$	−6.19325e24	−	1.07270e25i	−1.21968	−	2.11255i
$557$			3.61436e22i			0.00700381i	0.999994	+	0.00350191i	$0.00111469\pi$
$557$			3.61436e22i			0.00700381i	−0.999994	+	0.00350191i	$0.998885\pi$
$558$	1.30338e25	−	8.72143e23i	2.48522	−	0.166295i
$559$	7.45809e24			1.39933
$560$	−8.36034e22	+	4.82684e22i	−0.0154359	+	0.00891191i
$561$	−3.01519e24	−	7.00875e23i	−0.547833	−	0.127343i
$562$	6.93461e24	−	1.20111e25i	1.23992	−	2.14761i
$563$	1.82133e23	+	1.05155e23i	0.0320490	+	0.0185035i	0.515939	−	0.856625i	$-0.327443\pi$
$563$	1.82133e23	+	1.05155e23i	0.0320490	+	0.0185035i	−0.483890	+	0.875129i	$0.660776\pi$
$564$	−7.19811e24	−	6.73256e24i	−1.24654	−	1.16592i
$565$	6.05834e23	+	1.04934e24i	0.103257	+	0.178846i
$566$			3.21416e24i			0.539163i
$567$	2.10858e24	+	2.73248e24i	0.348130	+	0.451138i
$568$	−3.20876e24			−0.521437
$569$	−4.53913e24	+	2.62067e24i	−0.726043	+	0.419181i	−0.816973	−	0.576676i	$-0.804349\pi$
$569$	−4.53913e24	+	2.62067e24i	−0.726043	+	0.419181i	0.0909297	+	0.995857i	$0.471016\pi$
$570$	−1.74235e24	+	1.86283e24i	−0.274322	+	0.293292i
$571$	1.25128e24	−	2.16728e24i	0.193923	−	0.335885i	−0.752624	−	0.658451i	$-0.771212\pi$
$571$	1.25128e24	−	2.16728e24i	0.193923	−	0.335885i	0.946547	+	0.322566i	$0.104545\pi$
$572$	4.73164e24	+	2.73181e24i	0.721851	+	0.416761i
$573$	−1.58263e24	+	6.80854e24i	−0.237678	+	1.02250i
$574$	−1.55656e24	−	2.69604e24i	−0.230123	−	0.398584i
$575$			3.59303e24i			0.522938i
$576$	−7.59821e23	−	1.13552e25i	−0.108870	−	1.62702i
$577$	1.12947e25			1.59328			0.796638	−	0.604457i	$-0.206610\pi$
$577$	1.12947e25			1.59328			0.796638	+	0.604457i	$0.206610\pi$
$578$	−9.11576e24	+	5.26298e24i	−1.26602	+	0.730940i
$579$	9.82244e22	+	3.23009e23i	0.0134311	+	0.0441680i
$580$	−2.17249e24	+	3.76286e24i	−0.292486	+	0.506601i
$581$	4.12498e24	+	2.38156e24i	0.546810	+	0.315701i
$582$	−3.41851e24	+	1.03954e24i	−0.446201	+	0.135686i
$583$	−2.32673e24	−	4.03001e24i	−0.299039	−	0.517951i
$584$			1.11926e25i			1.41650i
$585$	1.49790e24	+	2.23516e24i	0.186672	+	0.278551i
$586$	1.75576e25			2.15469
$587$	9.61410e24	−	5.55071e24i	1.16189	−	0.670819i	0.210136	−	0.977672i	$-0.432609\pi$
$587$	9.61410e24	−	5.55071e24i	1.16189	−	0.670819i	0.951757	+	0.306853i	$0.0992761\pi$
$588$	−8.63173e24	−	2.00643e24i	−1.02731	−	0.238797i
$589$	−6.51932e24	+	1.12918e25i	−0.764126	+	1.32350i
$590$	8.68992e23	+	5.01713e23i	0.100311	+	0.0579145i
$591$	−7.60711e24	−	7.11510e24i	−0.864833	−	0.808898i
$592$	6.24025e23	+	1.08084e24i	0.0698725	+	0.121023i
$593$		−	3.18046e24i		−	0.350750i	−0.984502	−	0.175375i	$-0.943886\pi$
$593$		−	3.18046e24i		−	0.350750i	0.984502	−	0.175375i	$-0.0561137\pi$
$594$	5.60315e24	−	2.12198e24i	0.608632	−	0.230496i
$595$	−1.88220e24			−0.201379
$596$	1.42806e25	−	8.24488e24i	1.50497	−	0.868897i
$597$	−8.23853e24	+	8.80823e24i	−0.855226	+	0.914365i
$598$	−5.74667e24	+	9.95353e24i	−0.587632	+	1.01781i
$599$	−3.18898e24	−	1.84116e24i	−0.321226	−	0.185460i	0.330713	−	0.943731i	$-0.392711\pi$
$599$	−3.18898e24	−	1.84116e24i	−0.321226	−	0.185460i	−0.651939	+	0.758272i	$0.726044\pi$
$600$	−1.91806e24	+	8.25155e24i	−0.190327	+	0.818793i
$601$	4.55585e23	+	7.89097e23i	0.0445348	+	0.0771365i	0.887434	−	0.460936i	$-0.152486\pi$
$601$	4.55585e23	+	7.89097e23i	0.0445348	+	0.0771365i	−0.842899	+	0.538072i	$0.819153\pi$
$602$		−	1.00979e25i		−	0.972439i
$603$	−1.01849e24	−	5.00537e23i	−0.0966274	−	0.0474876i
$604$	−1.92856e25			−1.80260
$605$	2.00542e24	−	1.15783e24i	0.184675	−	0.106622i
$606$	8.88325e23	+	2.92124e24i	0.0805969	+	0.265041i
$607$	1.38694e24	−	2.40226e24i	0.123982	−	0.214744i	−0.797352	−	0.603514i	$-0.793767\pi$
$607$	1.38694e24	−	2.40226e24i	0.123982	−	0.214744i	0.921335	+	0.388770i	$0.127100\pi$
$608$	1.05761e25	+	6.10614e24i	0.931526	+	0.537817i
$609$	−9.20943e24	+	2.80051e24i	−0.799239	+	0.243042i
$610$	1.16852e24	+	2.02393e24i	0.0999231	+	0.173072i
$611$		−	1.70218e25i		−	1.43428i
$612$	1.14764e25	−	2.33521e25i	0.952892	−	1.93894i
$613$	−9.89291e24			−0.809431			−0.404715	−	0.914443i	$-0.632629\pi$
$613$	−9.89291e24			−0.809431			−0.404715	+	0.914443i	$0.632629\pi$
$614$	−2.12054e24	+	1.22429e24i	−0.170974	+	0.0987120i
$615$	−1.58040e24	−	3.67362e23i	−0.125572	−	0.0291889i
$616$	1.33060e24	−	2.30466e24i	0.104188	−	0.180460i
$617$	−7.18642e24	−	4.14908e24i	−0.554557	−	0.320174i	0.196401	−	0.980524i	$-0.437075\pi$
$617$	−7.18642e24	−	4.14908e24i	−0.554557	−	0.320174i	−0.750958	+	0.660350i	$0.770408\pi$
$618$	−5.84214e24	−	5.46429e24i	−0.444299	−	0.415563i
$619$	−8.13425e24	−	1.40889e25i	−0.609680	−	1.05600i	−0.991293	−	0.131674i	$-0.957965\pi$
$619$	−8.13425e24	−	1.40889e25i	−0.609680	−	1.05600i	0.381614	−	0.924322i	$-0.375369\pi$
$620$		−	8.40600e24i		−	0.620961i
$621$	2.72141e24	+	7.18598e24i	0.198139	+	0.523193i
$622$	2.12565e25			1.52538
$623$	3.67926e24	−	2.12422e24i	0.260237	−	0.150248i
$624$	1.57441e24	−	1.68328e24i	0.109763	−	0.117353i
$625$	−5.88221e24	+	1.01883e25i	−0.404222	+	0.700134i
$626$	−3.79971e25	−	2.19377e25i	−2.57384	−	1.48601i
$627$	−1.35402e24	+	5.82504e24i	−0.0904102	+	0.388948i
$628$	9.77470e24	+	1.69303e25i	0.643379	+	1.11436i
$629$			2.43335e25i			1.57888i
$630$	3.02629e24	−	2.02808e24i	0.193574	−	0.129724i
$631$	−3.36744e23			−0.0212342			−0.0106171	−	0.999944i	$-0.503380\pi$
$631$	−3.36744e23			−0.0212342			−0.0106171	+	0.999944i	$0.503380\pi$
$632$	8.36452e24	−	4.82926e24i	0.519981	−	0.300211i
$633$	−1.97078e24	−	6.48089e24i	−0.120783	−	0.397193i
$634$	−6.80821e24	+	1.17922e25i	−0.411367	+	0.712509i
$635$	4.97345e24	+	2.87142e24i	0.296274	+	0.171054i
$636$	3.74226e25	−	1.13799e25i	2.19796	−	0.668381i
$637$	−7.65245e24	−	1.32544e25i	−0.443145	−	0.767550i
$638$			1.67098e25i			0.954081i
$639$	−1.02760e25	+	6.87605e23i	−0.578517	+	0.0387107i
$640$	−6.97137e24			−0.386989
$641$	−2.58915e24	+	1.49485e24i	−0.141721	+	0.0818229i	−0.569184	−	0.822210i	$-0.692741\pi$
$641$	−2.58915e24	+	1.49485e24i	−0.141721	+	0.0818229i	0.427463	+	0.904033i	$0.359408\pi$
$642$	3.90926e25	+	9.08700e24i	2.10998	+	0.490462i
$643$	4.99218e24	−	8.64670e24i	0.265700	−	0.460206i	−0.702047	−	0.712131i	$-0.747730\pi$
$643$	4.99218e24	−	8.64670e24i	0.265700	−	0.460206i	0.967747	+	0.251925i	$0.0810637\pi$
$644$	8.21615e24	+	4.74360e24i	0.431217	+	0.248963i
$645$	−3.84369e24	−	3.59509e24i	−0.198935	−	0.186068i
$646$	2.12998e25	+	3.68924e25i	1.08714	+	1.88297i
$647$			1.28363e25i			0.646105i	0.946381	+	0.323052i	$0.104709\pi$
$647$			1.28363e25i			0.646105i	−0.946381	+	0.323052i	$0.895291\pi$
$648$	2.41377e24	+	1.79557e25i	0.119818	+	0.891306i
$649$	2.35265e24			0.115174
$650$	−3.52214e25	+	2.03351e25i	−1.70054	+	0.981807i
$651$	1.27210e25	−	1.36006e25i	0.605747	−	0.647634i
$652$	1.60351e25	−	2.77736e25i	0.753085	−	1.30438i
$653$	−7.19234e24	−	4.15250e24i	−0.333159	−	0.192350i	0.324084	−	0.946028i	$-0.394944\pi$
$653$	−7.19234e24	−	4.15250e24i	−0.333159	−	0.192350i	−0.657243	+	0.753679i	$0.728277\pi$
$654$	−9.24502e24	+	3.97724e25i	−0.422385	+	1.81711i
$655$	−2.75712e24	−	4.77547e24i	−0.124246	−	0.215201i
$656$			1.38987e24i			0.0617787i
$657$	2.39847e24	+	3.58442e25i	0.105159	+	1.57156i
$658$	−2.30467e25			−0.996726
$659$	1.06753e25	−	6.16339e24i	0.455420	−	0.262937i	−0.254697	−	0.967021i	$-0.581976\pi$
$659$	1.06753e25	−	6.16339e24i	0.455420	−	0.262937i	0.710116	+	0.704084i	$0.248642\pi$
$660$	−1.12171e24	−	3.68874e24i	−0.0472049	−	0.155232i
$661$	5.87782e24	−	1.01807e25i	0.244008	−	0.422634i	−0.717844	−	0.696203i	$-0.754871\pi$
$661$	5.87782e24	−	1.01807e25i	0.244008	−	0.422634i	0.961852	+	0.273570i	$0.0882045\pi$
$662$	−3.36356e25	−	1.94195e25i	−1.37745	−	0.795274i
$663$	4.29937e25	−	1.30740e25i	1.73693	−	0.528187i
$664$	1.25011e25	+	2.16526e25i	0.498238	+	0.862974i
$665$			3.63623e24i			0.142974i
$666$	−2.62195e25	−	3.91246e25i	−1.01708	−	1.51769i
$667$	−2.14301e25			−0.820148
$668$	2.27876e25	−	1.31564e25i	0.860420	−	0.496763i
$669$	4.02695e25	+	9.36057e24i	1.50017	+	0.348712i
$670$	−5.98912e23	+	1.03735e24i	−0.0220135	+	0.0381285i
$671$	4.74534e24	+	2.73972e24i	0.172093	+	0.0993582i
$672$	−1.27386e25	−	1.19147e25i	−0.455826	−	0.426345i
$673$	−1.59958e25	−	2.77055e25i	−0.564767	−	0.978205i	−0.997071	−	0.0764770i	$-0.975633\pi$
$673$	−1.59958e25	−	2.77055e25i	−0.564767	−	0.978205i	0.432305	−	0.901728i	$-0.357701\pi$
$674$		−	6.41818e25i		−	2.23600i
$675$	−4.37432e24	+	2.68365e25i	−0.150375	+	0.922553i
$676$	−3.32708e25			−1.12861
$677$	1.38572e25	−	8.00043e24i	0.463849	−	0.267803i	−0.249813	−	0.968294i	$-0.580369\pi$
$677$	1.38572e25	−	8.00043e24i	0.463849	−	0.267803i	0.713661	+	0.700491i	$0.247036\pi$
$678$	−2.67554e25	+	2.86055e25i	−0.883780	+	0.944893i
$679$	−2.54689e24	+	4.41134e24i	−0.0830198	+	0.143794i
$680$	−8.55630e24	−	4.93998e24i	−0.275236	−	0.158908i
$681$	1.11685e25	−	4.80471e25i	0.354543	−	1.52526i
$682$	−1.61638e25	−	2.79965e25i	−0.506388	−	0.877090i
$683$			8.71847e24i			0.269559i	0.990876	+	0.134779i	$0.0430326\pi$
$683$			8.71847e24i			0.269559i	−0.990876	+	0.134779i	$0.956967\pi$
$684$	−4.51140e25	−	2.21713e25i	−1.37660	−	0.676529i
$685$	1.43910e25			0.433385
$686$	−4.45214e25	+	2.57044e25i	−1.32328	+	0.763995i
$687$	−1.46741e24	−	4.82557e24i	−0.0430469	−	0.141559i
$688$	−2.25413e24	+	3.90426e24i	−0.0652653	+	0.113043i
$689$	5.85026e25	+	3.37765e25i	1.67187	+	0.965253i
$690$	7.75967e24	−	2.35965e24i	0.218878	−	0.0665589i
$691$	2.18258e25	+	3.78033e25i	0.607669	+	1.05251i	0.991624	+	0.129161i	$0.0412284\pi$
$691$	2.18258e25	+	3.78033e25i	0.607669	+	1.05251i	−0.383955	+	0.923352i	$0.625438\pi$
$692$		−	5.67843e25i		−	1.56053i
$693$	3.76734e24	−	7.66577e24i	0.102197	−	0.207949i
$694$	−8.06107e24			−0.215853
$695$	−1.30733e25	+	7.54790e24i	−0.345560	+	0.199509i
$696$	−4.92152e25	−	1.14400e25i	−1.28415	−	0.298499i
$697$	−1.35493e25	+	2.34681e25i	−0.348997	+	0.604481i
$698$	8.35795e25	+	4.82546e25i	2.12521	+	1.22699i
$699$	−5.28504e25	−	4.94322e25i	−1.32664	−	1.24084i
$700$	1.67856e25	+	2.90736e25i	0.415964	+	0.720470i
$701$			1.44979e25i			0.354684i	0.984149	+	0.177342i	$0.0567499\pi$
$701$			1.44979e25i			0.354684i	−0.984149	+	0.177342i	$0.943250\pi$
$702$	−5.50400e25	+	6.73470e25i	−1.32937	+	1.62661i
$703$	4.70100e25			1.12097
$704$	−2.43909e25	+	1.40821e25i	−0.574214	+	0.331522i
$705$	−8.20517e24	+	8.77256e24i	−0.190715	+	0.203903i
$706$	4.29284e25	−	7.43541e25i	0.985149	−	1.70633i
$707$	3.76964e24	+	2.17640e24i	0.0854133	+	0.0493134i
$708$	−4.47733e24	+	1.92616e25i	−0.100166	+	0.430917i
$709$	−2.66754e24	−	4.62032e24i	−0.0589244	−	0.102060i	0.835058	−	0.550161i	$-0.185434\pi$
$709$	−2.66754e24	−	4.62032e24i	−0.0589244	−	0.102060i	−0.893983	+	0.448101i	$0.852100\pi$
$710$			1.08706e25i			0.237098i
$711$	2.57524e25	−	1.72581e25i	0.554614	−	0.371677i
$712$	2.23007e25			0.474241
$713$	3.59052e25	−	2.07299e25i	0.753965	−	0.435302i
$714$	−1.77016e25	−	5.82114e25i	−0.367053	−	1.20705i
$715$	3.32935e24	−	5.76659e24i	0.0681718	−	0.118077i
$716$	6.14295e25	+	3.54664e25i	1.24211	+	0.717132i
$717$	−9.13889e24	+	2.77906e24i	−0.182482	+	0.0554914i
$718$	4.11441e25	+	7.12636e25i	0.811311	+	1.40523i
$719$			6.72316e24i			0.130922i	0.997855	+	0.0654612i	$0.0208518\pi$
$719$			6.72316e24i			0.130922i	−0.997855	+	0.0654612i	$0.979148\pi$
$720$	−1.62281e24	+	1.08589e23i	−0.0312087	+	0.00208829i
$721$	−1.14038e25			−0.216587
$722$	−2.62743e24	+	1.51695e24i	−0.0492829	+	0.0284535i
$723$	−1.83630e25	−	4.26844e24i	−0.340172	−	0.0790723i
$724$	−4.18797e24	+	7.25378e24i	−0.0766225	+	0.132714i
$725$	−6.56728e25	−	3.79162e25i	−1.18671	−	0.685145i
$726$	5.46690e25	+	5.11331e25i	0.975689	+	0.912584i
$727$	−3.59616e25	−	6.22873e25i	−0.633912	−	1.09797i	−0.986745	−	0.162281i	$-0.948115\pi$
$727$	−3.59616e25	−	6.22873e25i	−0.633912	−	1.09797i	0.352833	−	0.935686i	$-0.385219\pi$
$728$			3.86318e25i			0.672609i
$729$	1.15778e25	+	5.69855e25i	0.199103	+	0.979979i
$730$	3.79182e25			0.644083
$731$	−7.61224e25	+	4.39493e25i	−1.27719	+	0.737387i
$732$	−3.14615e25	+	3.36371e25i	−0.521411	+	0.557467i
$733$	2.02999e24	−	3.51605e24i	0.0332322	−	0.0575598i	−0.848931	−	0.528504i	$-0.822753\pi$
$733$	2.02999e24	−	3.51605e24i	0.0332322	−	0.0575598i	0.882163	+	0.470944i	$0.156087\pi$
$734$	1.27474e26	+	7.35970e25i	2.06137	+	1.19013i
$735$	−2.44530e24	+	1.05198e25i	−0.0390612	+	0.168043i
$736$	−1.94160e25	−	3.36296e25i	−0.306380	−	0.530666i
$737$			2.80844e24i			0.0437781i
$738$	−3.50177e24	−	5.23325e25i	−0.0539237	−	0.805869i
$739$	−4.65947e25			−0.708821			−0.354410	−	0.935090i	$-0.615318\pi$
$739$	−4.65947e25			−0.708821			−0.354410	+	0.935090i	$0.615318\pi$
$740$	−2.62469e25	+	1.51536e25i	−0.394450	+	0.227736i
$741$	−2.52577e25	−	8.30596e25i	−0.375000	−	1.23318i
$742$	4.57317e25	−	7.92097e25i	0.670784	−	1.16183i
$743$	−5.37474e25	−	3.10311e25i	−0.778857	−	0.449673i	0.0571679	−	0.998365i	$-0.481793\pi$
$743$	−5.37474e25	−	3.10311e25i	−0.778857	−	0.449673i	−0.836025	+	0.548691i	$0.815126\pi$
$744$	9.35239e25	−	2.84399e25i	1.33896	−	0.407166i
$745$	−1.00483e25	−	1.74042e25i	−0.142130	−	0.246176i
$746$		−	1.57741e26i		−	2.20442i
$747$	4.46746e25	+	6.66633e25i	0.616844	+	0.920452i
$748$	−6.43925e25			−0.878457
$749$	4.95506e25	−	2.86081e25i	0.667902	−	0.385613i
$750$	5.78610e25	+	1.34497e25i	0.770610	+	0.179127i
$751$	−4.54770e25	+	7.87684e25i	−0.598456	+	1.03656i	0.394593	+	0.918856i	$0.370885\pi$
$751$	−4.54770e25	+	7.87684e25i	−0.598456	+	1.03656i	−0.993049	+	0.117700i	$0.962448\pi$
$752$	8.91080e24	+	5.14465e24i	0.115866	+	0.0668953i
$753$	4.40979e25	+	4.12458e25i	0.566583	+	0.529938i
$754$	−1.21286e26	−	2.10073e26i	−1.53981	−	2.66704i
$755$			2.35039e25i			0.294861i
$756$	5.55916e25	+	4.54328e25i	0.689149	+	0.563214i
$757$	1.15016e26			1.40895			0.704474	−	0.709730i	$-0.251183\pi$
$757$	1.15016e26			1.40895			0.704474	+	0.709730i	$0.251183\pi$
$758$	−7.12169e25	+	4.11171e25i	−0.862105	+	0.497737i
$759$	1.29897e25	−	1.38880e25i	0.155391	−	0.166136i
$760$	−9.54355e24	+	1.65299e25i	−0.112820	+	0.195411i
$761$	−1.45962e26	−	8.42712e25i	−1.70521	−	0.984504i	−0.940287	−	0.340383i	$-0.889443\pi$
$761$	−1.45962e26	−	8.42712e25i	−1.70521	−	0.984504i	−0.764924	−	0.644121i	$-0.777223\pi$
$762$	−4.20313e25	+	1.80820e26i	−0.485264	+	2.08762i
$763$	2.91056e25	+	5.04123e25i	0.332089	+	0.575196i
$764$			1.45404e26i			1.63959i
$765$	−2.84600e25	−	1.39867e25i	−0.317162	−	0.155870i
$766$	1.02173e25			0.112532
$767$	−2.95772e25	+	1.70764e25i	−0.321957	+	0.185882i
$768$	−2.14663e25	−	7.05916e25i	−0.230944	−	0.759455i
$769$	−7.68056e25	+	1.33031e26i	−0.816687	+	1.41454i	0.0914229	+	0.995812i	$0.470858\pi$
$769$	−7.68056e25	+	1.33031e26i	−0.816687	+	1.41454i	−0.908110	+	0.418731i	$0.862475\pi$
$770$	−7.80769e24	−	4.50777e24i	−0.0820552	−	0.0473746i
$771$	−2.09349e25	+	6.36613e24i	−0.217461	+	0.0661281i
$772$	3.51143e24	+	6.08198e24i	0.0360519	+	0.0624437i
$773$			8.13790e24i			0.0825842i	0.999147	+	0.0412921i	$0.0131474\pi$
$773$			8.13790e24i			0.0825842i	−0.999147	+	0.0412921i	$0.986853\pi$
$774$	7.50375e25	−	1.52686e26i	0.752679	−	1.53155i
$775$	1.46709e26			1.45459
$776$	−2.31557e25	+	1.33690e25i	−0.226936	+	0.131021i
$777$	−6.53989e25	−	1.52018e25i	−0.633550	−	0.147268i
$778$	−6.43852e25	+	1.11518e26i	−0.616552	+	1.06790i
$779$	4.53380e25	+	2.61759e25i	0.429166	+	0.247779i
$780$	4.08763e25	+	3.82325e25i	0.382490	+	0.357751i
$781$	1.27437e25	+	2.20727e25i	0.117879	+	0.204172i
$782$		−	1.35457e26i		−	1.23862i
$783$	−1.60062e26	−	2.60900e25i	−1.44688	−	0.235841i
$784$	9.25148e24			0.0826736
$785$	2.06335e25	−	1.19127e25i	0.182283	−	0.105241i
$786$	1.21762e26	−	1.30182e26i	1.06343	−	1.13697i
$787$	7.21061e25	−	1.24891e26i	0.622586	−	1.07835i	−0.366416	−	0.930451i	$-0.619415\pi$
$787$	7.21061e25	−	1.24891e26i	0.622586	−	1.07835i	0.989002	−	0.147900i	$-0.0472514\pi$
$788$	−1.87640e26	−	1.08334e26i	−1.60173	−	0.924759i
$789$	2.33201e25	−	1.00324e26i	0.196805	−	0.846663i
$790$	−1.63605e25	−	2.83372e25i	−0.136506	−	0.236436i
$791$			5.58377e25i			0.460616i
$792$	3.72453e25	−	2.49601e25i	0.303770	−	0.203573i
$793$	−7.95436e25			−0.641426
$794$	2.65474e26	−	1.53271e26i	2.11659	−	1.22202i
$795$	−1.38690e25	−	4.56080e25i	−0.109331	−	0.359532i
$796$	−1.25439e26	+	2.17267e26i	−0.977723	+	1.69347i
$797$	−1.57138e26	−	9.07238e25i	−1.21104	−	0.699192i	−0.248050	−	0.968747i	$-0.579790\pi$
$797$	−1.57138e26	−	9.07238e25i	−1.21104	−	0.699192i	−0.962985	+	0.269556i	$0.913123\pi$
$798$	−1.12459e26	+	3.41978e25i	−0.856973	+	0.260599i
$799$	1.00307e26	+	1.73736e26i	0.755803	+	1.30909i
$800$		−	1.37411e26i		−	1.02379i
$801$	7.14176e25	−	4.77882e24i	0.526154	−	0.0352069i
$802$	−1.30897e26			−0.953587
$803$	7.69928e25	−	4.44518e25i	0.554639	−	0.320221i
$804$	−2.29933e25	−	5.34474e24i	−0.163793	−	0.0380735i
$805$	5.78117e24	−	1.00133e25i	0.0407242	−	0.0705364i
$806$	4.06418e26	+	2.34645e26i	2.83111	+	1.63454i
$807$	5.34238e25	+	4.99685e25i	0.368022	+	0.344219i
$808$	1.14243e25	+	1.97874e25i	0.0778262	+	0.134799i
$809$		−	1.65628e26i		−	1.11583i	−0.829899	−	0.557913i	$-0.811602\pi$
$809$		−	1.65628e26i		−	1.11583i	0.829899	−	0.557913i	$-0.188398\pi$
$810$	6.08300e25	−	8.17734e24i	0.405278	−	0.0544812i
$811$	1.32911e26			0.875734			0.437867	−	0.899040i	$-0.355734\pi$
$811$	1.32911e26			0.875734			0.437867	+	0.899040i	$0.355734\pi$
$812$	−1.73405e26	+	1.00116e26i	−1.12995	+	0.652375i
$813$	−7.67861e25	+	8.20958e25i	−0.494843	+	0.529062i
$814$	−5.82775e25	+	1.00940e26i	−0.371434	+	0.643342i
$815$	−3.38486e25	−	1.95425e25i	−0.213365	−	0.123186i
$816$	−6.15021e24	+	2.64584e25i	−0.0383423	+	0.164950i
$817$	8.49056e25	+	1.47061e26i	0.523526	+	0.906773i
$818$			1.26971e26i			0.774328i
$819$	8.27842e24	+	1.23718e26i	0.0499335	+	0.746237i
$820$	−3.37512e25			−0.201356
$821$	1.19327e26	−	6.88932e25i	0.704123	−	0.406526i	−0.104758	−	0.994498i	$-0.533407\pi$
$821$	1.19327e26	−	6.88932e25i	0.704123	−	0.406526i	0.808881	+	0.587972i	$0.200073\pi$
$822$	1.35343e26	+	4.45073e26i	0.789932	+	2.59768i
$823$	−9.89806e25	+	1.71439e26i	−0.571415	+	0.989719i	0.425006	+	0.905190i	$0.360272\pi$
$823$	−9.89806e25	+	1.71439e26i	−0.571415	+	0.989719i	−0.996421	+	0.0845289i	$0.973061\pi$
$824$	−5.18405e25	−	2.99301e25i	−0.296022	−	0.170908i
$825$	6.43791e25	−	1.95772e25i	0.363630	−	0.110577i
$826$	2.31206e25	+	4.00461e25i	0.129175	+	0.223738i
$827$			5.92459e25i			0.327423i	0.986508	+	0.163711i	$0.0523466\pi$
$827$			5.92459e25i			0.327423i	−0.986508	+	0.163711i	$0.947653\pi$
$828$	8.89831e25	+	1.32780e26i	0.486446	+	0.725872i
$829$	−1.15502e26			−0.624596			−0.312298	−	0.949984i	$-0.601099\pi$
$829$	−1.15502e26			−0.624596			−0.312298	+	0.949984i	$0.601099\pi$
$830$	7.33544e25	−	4.23512e25i	0.392395	−	0.226549i
$831$	−1.01457e26	−	2.35836e25i	−0.536876	−	0.124796i
$832$	2.04426e26	−	3.54076e26i	1.07010	−	1.85347i
$833$	1.56212e26	+	9.01893e25i	0.808929	+	0.467035i
$834$	−3.56387e26	−	3.33337e26i	−1.82569	−	1.70761i
$835$	−1.60341e25	−	2.77719e25i	−0.0812582	−	0.140743i
$836$			1.24400e26i			0.623683i
$837$	2.93414e26	−	1.11119e26i	1.45530	−	0.551139i
$838$	−2.72613e26			−1.33767
$839$	−1.49988e26	+	8.65955e25i	−0.728112	+	0.420376i	−0.817731	−	0.575600i	$-0.804768\pi$
$839$	−1.49988e26	+	8.65955e25i	−0.728112	+	0.420376i	0.0896190	+	0.995976i	$0.471435\pi$
$840$	1.86221e25	−	1.99098e25i	0.0894364	−	0.0956209i
$841$	1.20917e26	−	2.09435e26i	0.574545	−	0.995141i
$842$	−2.47352e26	−	1.42809e26i	−1.16280	−	0.671345i
$843$	7.54213e25	−	3.24465e26i	0.350789	−	1.50911i
$844$	−7.04537e25	−	1.22029e26i	−0.324206	−	0.561542i
$845$			4.05482e25i			0.184612i
$846$	−3.48479e26	−	1.71260e26i	−1.56980	−	0.771477i
$847$	1.06713e26			0.475629
$848$	−3.53635e25	+	2.04171e25i	−0.155953	+	0.0900393i
$849$	2.24600e25	+	7.38594e25i	0.0980034	+	0.322282i
$850$	2.39663e26	−	4.15108e26i	1.03474	−	1.79222i
$851$	−1.29454e26	−	7.47402e25i	−0.553030	−	0.319292i
$852$	−2.04966e26	+	6.23286e25i	−0.866416	+	0.263470i
$853$	−1.38597e26	−	2.40057e26i	−0.579711	−	1.00409i	−0.995512	−	0.0946336i	$-0.969832\pi$
$853$	−1.38597e26	−	2.40057e26i	−0.579711	−	1.00409i	0.415801	−	0.909456i	$-0.363501\pi$
$854$			1.07698e26i			0.445746i
$855$	−2.70209e25	+	5.49819e25i	−0.110663	+	0.225177i
$856$	3.00336e26			1.21715
$857$	1.78907e24	−	1.03292e24i	0.00717465	−	0.00414229i	−0.496408	−	0.868089i	$-0.665348\pi$
$857$	1.78907e24	−	1.03292e24i	0.00717465	−	0.00414229i	0.503583	+	0.863947i	$0.332015\pi$
$858$	2.09657e26	+	4.87343e25i	0.832000	+	0.193397i
$859$	6.37972e24	−	1.10500e25i	0.0250532	−	0.0433934i	−0.853227	−	0.521540i	$-0.825358\pi$
$859$	6.37972e24	−	1.10500e25i	0.0250532	−	0.0433934i	0.878280	+	0.478146i	$0.158691\pi$
$860$	−9.48100e25	−	5.47386e25i	−0.368441	−	0.212720i
$861$	−5.46083e25	−	5.10763e25i	−0.210005	−	0.196423i
$862$	−6.64997e24	−	1.15181e25i	−0.0253078	−	0.0438344i
$863$			3.65603e26i			1.37693i	0.725268	+	0.688467i	$0.241716\pi$
$863$			3.65603e26i			1.37693i	−0.725268	+	0.688467i	$0.758284\pi$
$864$	−1.04077e26	−	2.74818e26i	−0.387910	−	1.02429i
$865$	−6.92048e25			−0.255265
$866$	−4.96658e26	+	2.86745e26i	−1.81299	+	1.04673i
$867$	−1.72697e26	+	1.84639e26i	−0.623898	+	0.667040i
$868$	1.93688e26	−	3.35478e26i	0.692510	−	1.19946i
$869$	−6.64399e25	−	3.83591e25i	−0.235099	−	0.135735i
$870$	−3.87562e25	+	1.66731e26i	−0.135728	+	0.583905i
$871$	−2.03847e25	−	3.53073e25i	−0.0706546	−	0.122377i
$872$			3.05559e26i			1.04820i
$873$	−7.12910e25	+	4.77760e25i	−0.242051	+	0.162211i
$874$	−2.61689e26			−0.879392
$875$	7.33400e25	−	4.23429e25i	0.243932	−	0.140834i
$876$	2.17411e26	+	7.14953e26i	0.715723	+	2.35364i
$877$	2.17938e26	−	3.77479e26i	0.710127	−	1.22998i	−0.254682	−	0.967025i	$-0.581971\pi$
$877$	2.17938e26	−	3.77479e26i	0.710127	−	1.22998i	0.964809	−	0.262951i	$-0.0846958\pi$
$878$	5.25966e26	+	3.03667e26i	1.69632	+	0.979369i
$879$	4.03461e26	−	1.22689e26i	1.28796	−	0.391658i
$880$	2.01252e24	+	3.48578e24i	0.00635910	+	0.0110143i
$881$		−	6.06233e25i		−	0.189608i	−0.995496	−	0.0948039i	$-0.969778\pi$
$881$		−	6.06233e25i		−	0.189608i	0.995496	−	0.0948039i	$-0.0302224\pi$
$882$	−3.48345e26	+	2.33091e25i	−1.07843	+	0.0721618i
$883$	−4.02894e26			−1.23465			−0.617326	−	0.786707i	$-0.711784\pi$
$883$	−4.02894e26			−1.23465			−0.617326	+	0.786707i	$0.711784\pi$
$884$	8.09533e26	−	4.67384e26i	2.45564	−	1.41776i
$885$	2.34748e25	+	5.45666e24i	0.0704874	+	0.0163847i
$886$	−3.86226e26	+	6.68964e26i	−1.14799	+	1.98838i
$887$	−1.14706e26	−	6.62257e25i	−0.337501	−	0.194856i	0.321666	−	0.946853i	$-0.395757\pi$
$887$	−1.14706e26	−	6.62257e25i	−0.337501	−	0.194856i	−0.659166	+	0.751997i	$0.729091\pi$
$888$	−2.57398e26	−	2.40750e26i	−0.749701	−	0.701212i
$889$	1.32325e26	+	2.29193e26i	0.381527	+	0.660824i
$890$		−	7.55500e25i		−	0.215638i
$891$	1.13929e26	−	8.79156e25i	0.321910	−	0.248408i
$892$	8.59997e26			2.40554
$893$	3.35641e26	−	1.93782e26i	0.929419	−	0.536601i
$894$	4.43762e26	−	4.74448e26i	1.21650	−	1.30062i
$895$	4.32239e25	−	7.48660e25i	0.117305	−	0.203178i
$896$	−2.78223e26	−	1.60632e26i	−0.747516	−	0.431579i
$897$	−6.25012e25	+	2.68882e26i	−0.166248	+	0.715204i
$898$	1.87237e26	+	3.24304e26i	0.493065	+	0.854014i
$899$			8.75025e26i			2.28130i
$900$	3.77623e25	+	5.64343e26i	0.0974711	+	1.45667i
$901$	−7.96156e26			−2.03458
$902$	−1.12410e26	+	6.48997e25i	−0.284410	+	0.164204i
$903$	−7.05624e25	−	2.32043e26i	−0.176760	−	0.581271i
$904$	−1.46550e26	+	2.53832e26i	−0.363472	+	0.629551i
$905$	8.84040e24	+	5.10401e24i	0.0217087	+	0.0125336i
$906$	−7.26912e26	+	2.21048e26i	−1.76737	+	0.537443i
$907$	2.83256e26	+	4.90614e26i	0.681890	+	1.18107i	0.974403	+	0.224806i	$0.0721749\pi$
$907$	2.83256e26	+	4.90614e26i	0.681890	+	1.18107i	−0.292514	+	0.956261i	$0.594492\pi$
$908$		−	1.02610e27i		−	2.44577i
$909$	4.08263e25	+	6.09207e25i	0.0963528	+	0.143777i
$910$	1.30876e26			0.305836
$911$	3.92997e26	−	2.26897e26i	0.909334	−	0.525004i	0.0291171	−	0.999576i	$-0.490730\pi$
$911$	3.92997e26	−	2.26897e26i	0.909334	−	0.525004i	0.880217	+	0.474572i	$0.157397\pi$
$912$	5.11151e25	+	1.18816e25i	0.117110	+	0.0272221i
$913$	9.92973e25	−	1.71988e26i	0.225269	−	0.390177i
$914$	2.76255e26	+	1.59496e26i	0.620575	+	0.358289i
$915$	4.09946e25	+	3.83432e25i	0.0911878	+	0.0852900i
$916$	−5.24587e25	−	9.08611e25i	−0.115547	−	0.200133i
$917$		−	2.54115e26i		−	0.554250i
$918$	1.64911e26	−	1.01173e27i	0.356177	−	2.18515i
$919$	−2.34222e26			−0.500944			−0.250472	−	0.968124i	$-0.580586\pi$
$919$	−2.34222e26			−0.500944			−0.250472	+	0.968124i	$0.580586\pi$
$920$	5.25611e25	−	3.03462e25i	0.111320	−	0.0642708i
$921$	−4.01734e25	+	4.29514e25i	−0.0842562	+	0.0900825i
$922$	−4.03175e26	+	6.98320e26i	−0.837367	+	1.45036i
$923$	−3.20423e26	−	1.84997e26i	−0.659036	−	0.380494i
$924$	4.02278e25	−	1.73061e26i	0.0819367	−	0.352495i
$925$	−2.64475e26	−	4.58084e26i	−0.533468	−	0.923994i
$926$			3.52118e26i			0.703379i
$927$	−1.72432e26	−	8.47418e25i	−0.341115	−	0.167641i
$928$	8.19567e26			1.60566
$929$	3.85486e26	−	2.22561e26i	0.747941	−	0.431824i	−0.0770083	−	0.997030i	$-0.524537\pi$
$929$	3.85486e26	−	2.22561e26i	0.747941	−	0.431824i	0.824950	+	0.565206i	$0.191203\pi$
$930$	−9.63482e25	−	3.16839e26i	−0.185139	−	0.608825i
$931$	1.74237e26	−	3.01787e26i	0.331583	−	0.574319i
$932$	−1.30363e27	−	7.52651e26i	−2.45703	−	1.41857i
$933$	4.88460e26	−	1.48537e26i	0.911789	−	0.277268i
$934$	1.91464e26	+	3.31626e26i	0.353969	+	0.613093i
$935$			7.84771e25i			0.143694i
$936$	−2.87073e26	+	5.84135e26i	−0.520607	+	1.05933i
$937$	3.46115e26			0.621676			0.310838	−	0.950463i	$-0.399390\pi$
$937$	3.46115e26			0.621676			0.310838	+	0.950463i	$0.399390\pi$
$938$	−4.78044e25	+	2.75999e25i	−0.0850437	+	0.0491000i
$939$	−1.02645e27	−	2.38595e26i	−1.80861	−	0.420409i
$940$	−1.24931e26	+	2.16387e26i	−0.218032	+	0.377643i
$941$	8.14463e26	+	4.70230e26i	1.40788	+	0.812838i	0.995183	−	0.0980323i	$-0.0312548\pi$
$941$	8.14463e26	+	4.70230e26i	1.40788	+	0.812838i	0.412693	+	0.910870i	$0.364588\pi$
$942$	5.62480e26	+	5.26101e26i	0.963051	+	0.900763i
$943$	−8.32331e25	−	1.44164e26i	−0.141153	−	0.244485i
$944$		−	2.06446e25i		−	0.0346784i
$945$	5.53704e25	−	6.77512e25i	0.0921279	−	0.112728i
$946$	−4.21024e26			−0.693884
$947$	−1.05000e27	+	6.06215e26i	−1.71411	+	0.989640i	−0.785266	+	0.619159i	$0.787474\pi$
$947$	−1.05000e27	+	6.06215e26i	−1.71411	+	0.989640i	−0.928840	+	0.370481i	$0.879193\pi$
$948$	4.40496e26	−	4.70956e26i	0.712307	−	0.761563i
$949$	−6.45295e26	+	1.11768e27i	−1.03362	+	1.79029i
$950$	−8.01948e26	−	4.63005e26i	−1.27243	−	0.734637i
$951$	−7.40466e25	+	3.18551e26i	−0.116381	+	0.500673i
$952$	−2.27651e26	−	3.94303e26i	−0.354435	−	0.613900i
$953$			6.53133e26i			1.00732i	0.863903	+	0.503658i	$0.168013\pi$
$953$			6.53133e26i			1.00732i	−0.863903	+	0.503658i	$0.831987\pi$
$954$	1.28010e27	−	8.57862e26i	1.95572	−	1.31064i
$955$	1.77208e26			0.268196
$956$	−1.72077e26	+	9.93488e25i	−0.257990	+	0.148950i
$957$	1.16765e26	+	3.83980e26i	0.173423	+	0.570297i
$958$	−1.98585e26	+	3.43960e26i	−0.292185	+	0.506079i
$959$	5.74334e26	+	3.31592e26i	0.837137	+	0.483322i
$960$	−2.76034e26	+	8.39397e25i	−0.398585	+	0.121207i
$961$	−4.96905e26	−	8.60665e26i	−0.710825	−	1.23119i
$962$		−	1.69200e27i		−	2.39786i
$963$	9.61820e26	−	6.43590e25i	1.35038	−	0.0903592i
$964$	−3.92160e26			−0.545469
$965$	7.41229e24	−	4.27949e24i	0.0102143	−	0.00589720i
$966$	3.64054e26	+	8.46236e25i	0.497017	+	0.115531i
$967$	4.96215e26	−	8.59469e26i	0.671168	−	1.16250i	−0.306405	−	0.951901i	$-0.599126\pi$
$967$	4.96215e26	−	8.59469e26i	0.671168	−	1.16250i	0.977573	−	0.210596i	$-0.0675405\pi$
$968$	4.85108e26	+	2.80077e26i	0.650070	+	0.375318i
$969$	7.47254e26	+	6.98924e26i	0.992098	+	0.927931i
$970$	4.52912e25	+	7.84467e25i	0.0595756	+	0.103188i
$971$		−	1.12810e27i		−	1.47020i	−0.677961	−	0.735098i	$-0.737136\pi$
$971$		−	1.12810e27i		−	1.47020i	0.677961	−	0.735098i	$-0.262864\pi$
$972$	5.02965e26	+	1.10007e27i	0.649444	+	1.42045i
$973$	−6.95665e26			−0.889989
$974$	−1.85961e27	+	1.07364e27i	−2.35717	+	1.36091i
$975$	−6.67267e26	+	7.13409e26i	−0.838027	+	0.895977i
$976$	2.40412e25	−	4.16406e25i	0.0299163	−	0.0518165i
$977$	−1.37257e27	−	7.92456e26i	−1.69233	−	0.977066i	−0.952632	−	0.304124i	$-0.901636\pi$
$977$	−1.37257e27	−	7.92456e26i	−1.69233	−	0.977066i	−0.739695	−	0.672942i	$-0.765030\pi$
$978$	2.86059e26	−	1.23064e27i	0.349467	−	1.50342i
$979$	−8.85679e25	−	1.53404e26i	−0.107209	−	0.185692i
$980$			2.24660e26i			0.269459i
$981$	6.54782e25	+	9.78546e26i	0.0778172	+	1.16295i
$982$	1.52657e27			1.79769
$983$	9.81652e26	−	5.66757e26i	1.14545	−	0.661326i	0.197676	−	0.980268i	$-0.436661\pi$
$983$	9.81652e26	−	5.66757e26i	1.14545	−	0.661326i	0.947774	+	0.318942i	$0.103327\pi$
$984$	−1.14190e26	−	3.75511e26i	−0.132030	−	0.434177i
$985$	−1.32030e26	+	2.28682e26i	−0.151268	+	0.262003i
$986$	2.47585e27	+	1.42943e27i	2.81082	+	1.62283i
$987$	−5.29598e26	+	1.61046e26i	−0.595788	+	0.181174i
$988$	−9.02940e26	−	1.56394e27i	−1.00658	−	1.74344i
$989$		−	5.39959e26i		−	0.596477i
$990$	−8.45594e25	−	1.26179e26i	−0.0925647	−	0.138125i
$991$	4.73558e26			0.513700			0.256850	−	0.966451i	$-0.417315\pi$
$991$	4.73558e26			0.513700			0.256850	+	0.966451i	$0.417315\pi$
$992$	−1.37315e27	+	7.92786e26i	−1.47609	+	0.852219i
$993$	−9.08624e26	−	2.11208e26i	−0.967924	−	0.224992i
$994$	−2.50476e26	+	4.33838e26i	−0.264417	+	0.457984i
$995$	2.64790e26	+	1.52877e26i	0.277009	+	0.159931i
$996$	1.21913e27	+	1.14028e27i	1.26391	+	1.18216i
$997$	5.72469e26	+	9.91546e26i	0.588160	+	1.01872i	0.994473	+	0.104989i	$0.0334809\pi$
$997$	5.72469e26	+	9.91546e26i	0.588160	+	1.01872i	−0.406313	+	0.913734i	$0.633186\pi$
$998$		−	7.93893e26i		−	0.808327i
$999$	−8.75903e26	−	7.15840e26i	−0.883825	−	0.722315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.19.d.a.5.16	yes	34
3.2	odd	2		27.19.d.a.17.2		34
9.2	odd	6	inner	9.19.d.a.2.16	✓	34
9.4	even	3		81.19.b.a.80.31		34
9.5	odd	6		81.19.b.a.80.4		34
9.7	even	3		27.19.d.a.8.2		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.19.d.a.2.16	✓	34	9.2	odd	6	inner
9.19.d.a.5.16	yes	34	1.1	even	1	trivial
27.19.d.a.8.2		34	9.7	even	3
27.19.d.a.17.2		34	3.2	odd	2
81.19.b.a.80.4		34	9.5	odd	6
81.19.b.a.80.31		34	9.4	even	3

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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	9.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(709.707 - 409.750i) q^{2} +(13445.3 - 14375.1i) q^{3} +(204718. - 354581. i) q^{4} +(-432139. - 249496. i) q^{5} +(3.65207e6 - 1.57113e7i) q^{6} +(-1.14976e7 - 1.99144e7i) q^{7} -1.20705e8i q^{8} +(-2.58659e7 - 3.86556e8i) q^{9} -4.08923e8 q^{10} +(-8.30317e8 + 4.79384e8i) q^{11} +(-2.34464e9 - 7.71030e9i) q^{12} +(6.95909e9 - 1.20535e10i) q^{13} +(-1.63199e10 - 9.42227e9i) q^{14} +(-9.39678e9 + 2.85748e9i) q^{15} +(4.20662e9 + 7.28608e9i) q^{16} +1.64035e11i q^{17} +(-1.76748e11 - 2.63743e11i) q^{18} +3.16899e11 q^{19} +(-1.76933e11 + 1.02152e11i) q^{20} +(-4.40861e11 - 1.02477e11i) q^{21} +(-3.92855e11 + 6.80444e11i) q^{22} +(-8.72662e11 - 5.03832e11i) q^{23} +(-1.73515e12 - 1.62292e12i) q^{24} +(-1.78285e12 - 3.08799e12i) q^{25} -1.14059e13i q^{26} +(-5.90455e12 - 4.82555e12i) q^{27} -9.41504e12 q^{28} +(1.84179e13 - 1.06336e13i) q^{29} +(-5.49811e12 + 5.87831e12i) q^{30} +(-2.05722e13 + 3.56321e13i) q^{31} +(3.33738e13 + 1.92684e13i) q^{32} +(-4.27271e12 + 1.83814e13i) q^{33} +(6.72133e13 + 1.16417e14i) q^{34} +1.14744e13i q^{35} +(-1.42361e14 - 6.99633e13i) q^{36} +1.48344e14 q^{37} +(2.24906e14 - 1.29849e14i) q^{38} +(-7.97027e13 - 2.62101e14i) q^{39} +(-3.01154e13 + 5.21614e13i) q^{40} +(1.43068e14 + 8.26001e13i) q^{41} +(-3.54872e14 + 1.07914e14i) q^{42} +(2.67926e14 + 4.64062e14i) q^{43} +3.92553e14i q^{44} +(-8.52664e13 + 1.73499e14i) q^{45} -8.25779e14 q^{46} +(1.05914e15 - 6.11495e14i) q^{47} +(1.61297e14 + 3.74933e13i) q^{48} +(5.49817e14 - 9.52311e14i) q^{49} +(-2.53061e15 - 1.46105e15i) q^{50} +(2.35802e15 + 2.20551e15i) q^{51} +(-2.84930e15 - 4.93513e15i) q^{52} +4.85358e15i q^{53} +(-6.16777e15 - 1.00534e15i) q^{54} +4.78417e14 q^{55} +(-2.40377e15 + 1.38782e15i) q^{56} +(4.26082e15 - 4.55546e15i) q^{57} +(8.71421e15 - 1.50935e16i) q^{58} +(-2.12508e15 - 1.22691e15i) q^{59} +(-9.10477e14 + 3.91690e15i) q^{60} +(-2.85754e15 - 4.94941e15i) q^{61} +3.37178e16i q^{62} +(-7.40065e15 + 4.95957e15i) q^{63} +2.93754e16 q^{64} +(-6.01459e15 + 3.47253e15i) q^{65} +(4.49938e15 + 1.47961e16i) q^{66} +(1.46461e15 - 2.53677e15i) q^{67} +(5.81637e16 + 3.35809e16i) q^{68} +(-1.89759e16 + 5.77040e15i) q^{69} +(4.70163e15 + 8.14347e15i) q^{70} -2.65834e16i q^{71} +(-4.66593e16 + 3.12215e15i) q^{72} -9.27269e16 q^{73} +(1.05281e17 - 6.07837e16i) q^{74} +(-6.83612e16 - 1.58904e16i) q^{75} +(6.48749e16 - 1.12367e17i) q^{76} +(1.90933e16 + 1.10235e16i) q^{77} +(-1.63961e17 - 1.53357e17i) q^{78} +(4.00087e16 + 6.92972e16i) q^{79} -4.19813e15i q^{80} +(-1.48757e17 + 1.99973e16i) q^{81} +1.35381e17 q^{82} +(-1.79384e17 + 1.03568e17i) q^{83} +(-1.26589e17 + 1.35342e17i) q^{84} +(4.09260e16 - 7.08859e16i) q^{85} +(3.80298e17 + 2.19565e17i) q^{86} +(9.47763e16 - 4.07731e17i) q^{87} +(5.78641e16 + 1.00224e17i) q^{88} +1.84754e17i q^{89} +(1.05772e16 + 1.58072e17i) q^{90} -3.20051e17 q^{91} +(-3.57299e17 + 2.06286e17i) q^{92} +(2.35614e17 + 7.74813e17i) q^{93} +(5.01120e17 - 8.67965e17i) q^{94} +(-1.36945e17 - 7.90650e16i) q^{95} +(7.25707e17 - 2.20682e17i) q^{96} +(-1.10757e17 - 1.91837e17i) q^{97} -9.01150e17i q^{98} +(2.06786e17 + 3.08564e17i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 3 q^{2} + 3804 q^{3} + 2097151 q^{4} + 2192181 q^{5} + 3257181 q^{6} + 4302359 q^{7} + 397977264 q^{9} - 524292 q^{10} + 1022992575 q^{11} + 32417762010 q^{12} + 3839449319 q^{13} + 129938709678 q^{14}+ \cdots - 52\!\cdots\!15 q^{99}+O(q^{100}) \) 34 * q - 3 * q^2 + 3804 * q^3 + 2097151 * q^4 + 2192181 * q^5 + 3257181 * q^6 + 4302359 * q^7 + 397977264 * q^9 - 524292 * q^10 + 1022992575 * q^11 + 32417762010 * q^12 + 3839449319 * q^13 + 129938709678 * q^14 - 124119415395 * q^15 - 240517906433 * q^16 - 285581999484 * q^18 - 608222566264 * q^19 + 1471193748174 * q^20 - 1381493495229 * q^21 + 851254438911 * q^22 + 375441179325 * q^23 + 305135298351 * q^24 + 12156817117552 * q^25 + 11936276558406 * q^27 + 4648789868540 * q^28 - 31101186224271 * q^29 + 62775784981818 * q^30 - 20376334153801 * q^31 - 113411230023465 * q^32 - 20701744605945 * q^33 - 99737362554111 * q^34 - 472069890962721 * q^36 + 56970364072604 * q^37 + 1244853240655323 * q^38 + 277868300554299 * q^39 + 236076863983350 * q^40 - 1178988706876521 * q^41 + 1034549802657900 * q^42 - 230641688892691 * q^43 - 5286549794938479 * q^45 + 131852496280800 * q^46 + 3640523435126673 * q^47 + 11085451646520237 * q^48 - 4168576830678822 * q^49 - 18078797603969781 * q^50 + 7526452896180882 * q^51 + 1286623499256920 * q^52 - 26455557995217045 * q^54 - 1446925762710942 * q^55 + 59834487378592914 * q^56 + 23867830767470574 * q^57 + 8463343484826222 * q^58 - 29968086845368137 * q^59 + 17080074037610118 * q^60 - 6976259792083513 * q^61 - 73583064644919705 * q^63 - 120930519493421318 * q^64 + 47229492730318989 * q^65 + 58361174960027994 * q^66 - 20333770074023707 * q^67 - 116938167206248431 * q^68 + 99272218824151677 * q^69 - 18312927374667108 * q^70 + 186892024430477907 * q^72 + 209341663176867296 * q^73 - 88916838511745634 * q^74 - 103202922056583144 * q^75 - 180442619960522287 * q^76 + 384727796507616477 * q^77 - 113580855335113884 * q^78 + 126425698081194923 * q^79 + 749177961563573568 * q^81 - 856725985700547270 * q^82 - 819712186371296103 * q^83 - 1069135371708878382 * q^84 + 372804006624771096 * q^85 + 1989011602082127453 * q^86 - 689457779704913391 * q^87 - 648793548761104653 * q^88 + 2069849112225424614 * q^90 - 29982940436364482 * q^91 - 2013198581519506428 * q^92 - 2088815715502953 * q^93 - 769920889934866620 * q^94 + 167036756670646446 * q^95 + 338414304229215984 * q^96 + 1172101248161568089 * q^97 - 529477370297396415 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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