LMFDB - Embedded newform 21.8.g.b.17.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [21,8,Mod(5,21)] 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("21.5"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(21, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	21.g (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.56008553517$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.10
Character	$\chi$	$=$	21.17
Dual form			21.8.g.b.5.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(6.40713 - 3.69916i) q^{2} +(-11.8808 - 45.2310i) q^{3} +(-36.6324 + 63.4492i) q^{4} +(-101.547 - 175.885i) q^{5} +(-243.439 - 245.852i) q^{6} +(-682.340 - 598.293i) q^{7} +1489.02i q^{8} +(-1904.69 + 1074.76i) q^{9} +(-1301.25 - 751.279i) q^{10} +(-1685.57 - 973.165i) q^{11} +(3305.10 + 903.097i) q^{12} -7873.88i q^{13} +(-6585.03 - 1309.26i) q^{14} +(-6749.00 + 6682.74i) q^{15} +(819.181 + 1418.86i) q^{16} +(4615.11 - 7993.61i) q^{17} +(-8227.93 + 13931.9i) q^{18} +(9012.39 - 5203.30i) q^{19} +14879.7 q^{20} +(-18954.7 + 37971.1i) q^{21} -14399.6 q^{22} +(70904.4 - 40936.7i) q^{23} +(67350.0 - 17690.7i) q^{24} +(18438.8 - 31937.0i) q^{25} +(-29126.8 - 50449.0i) q^{26} +(71241.7 + 73382.4i) q^{27} +(62957.0 - 21377.0i) q^{28} +195123. i q^{29} +(-18521.2 + 67782.8i) q^{30} +(-84434.3 - 48748.2i) q^{31} +(-154563. - 89236.8i) q^{32} +(-23991.4 + 87802.1i) q^{33} -68288.2i q^{34} +(-35941.0 + 180768. i) q^{35} +(1580.94 - 160222. i) q^{36} +(-285316. - 494181. i) q^{37} +(38495.7 - 66676.5i) q^{38} +(-356144. + 93547.8i) q^{39} +(261897. - 151206. i) q^{40} -339491. q^{41} +(19016.1 + 313403. i) q^{42} -356328. q^{43} +(123493. - 71298.8i) q^{44} +(382451. + 225868. i) q^{45} +(302863. - 524573. i) q^{46} +(383075. + 663506. i) q^{47} +(54444.1 - 53909.6i) q^{48} +(107634. + 816479. i) q^{49} -272832. i q^{50} +(-416391. - 113776. i) q^{51} +(499592. + 288439. i) q^{52} +(-137209. - 79217.5i) q^{53} +(727908. + 206636. i) q^{54} +395289. i q^{55} +(890872. - 1.01602e6i) q^{56} +(-342425. - 345820. i) q^{57} +(721792. + 1.25018e6i) q^{58} +(1.28115e6 - 2.21902e6i) q^{59} +(-176782. - 673024. i) q^{60} +(-1.49737e6 + 864504. i) q^{61} -721309. q^{62} +(1.94267e6 + 406214. i) q^{63} -1.53012e6 q^{64} +(-1.38490e6 + 799571. i) q^{65} +(171078. + 651308. i) q^{66} +(1.10259e6 - 1.90974e6i) q^{67} +(338126. + 585651. i) q^{68} +(-2.69401e6 - 2.72072e6i) q^{69} +(438413. + 1.29116e6i) q^{70} +5.29805e6i q^{71} +(-1.60034e6 - 2.83613e6i) q^{72} +(2.20247e6 + 1.27160e6i) q^{73} +(-3.65611e6 - 2.11086e6i) q^{74} +(-1.66361e6 - 454571. i) q^{75} +762439. i q^{76} +(567895. + 1.67249e6i) q^{77} +(-1.93581e6 + 1.91681e6i) q^{78} +(-372291. - 644826. i) q^{79} +(166371. - 288163. i) q^{80} +(2.47275e6 - 4.09418e6i) q^{81} +(-2.17516e6 + 1.25583e6i) q^{82} +5.20177e6 q^{83} +(-1.71488e6 - 2.59364e6i) q^{84} -1.87461e6 q^{85} +(-2.28304e6 + 1.31811e6i) q^{86} +(8.82563e6 - 2.31821e6i) q^{87} +(1.44906e6 - 2.50985e6i) q^{88} +(-5.08205e6 - 8.80237e6i) q^{89} +(3.28594e6 + 32422.8i) q^{90} +(-4.71089e6 + 5.37267e6i) q^{91} +5.99844e6i q^{92} +(-1.20179e6 + 4.39822e6i) q^{93} +(4.90883e6 + 2.83411e6i) q^{94} +(-1.83037e6 - 1.05676e6i) q^{95} +(-2.19995e6 + 8.05124e6i) q^{96} -3.36084e6i q^{97} +(3.70991e6 + 4.83314e6i) q^{98} +(4.25641e6 + 41998.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 84 q^{3} + 1150 q^{4} + 2464 q^{7} - 3516 q^{9} - 630 q^{10} - 3864 q^{12} + 27576 q^{15} - 19594 q^{16} + 33498 q^{18} - 47880 q^{19} + 151788 q^{21} + 105132 q^{22} - 211554 q^{24} - 331252 q^{25}+ \cdots + 35642232 q^{99}+O(q^{100}) $ 32 * q - 84 * q^3 + 1150 * q^4 + 2464 * q^7 - 3516 * q^9 - 630 * q^10 - 3864 * q^12 + 27576 * q^15 - 19594 * q^16 + 33498 * q^18 - 47880 * q^19 + 151788 * q^21 + 105132 * q^22 - 211554 * q^24 - 331252 * q^25 - 353122 * q^28 - 40662 * q^30 + 628152 * q^31 - 66024 * q^33 - 227244 * q^36 - 618748 * q^37 + 1996104 * q^39 + 1986138 * q^40 + 4274802 * q^42 - 1416064 * q^43 - 4757508 * q^45 - 3492840 * q^46 - 6640312 * q^49 + 677340 * q^51 + 11962272 * q^52 - 6743898 * q^54 - 6279408 * q^57 - 2064342 * q^58 + 7521282 * q^60 + 10948728 * q^61 + 13194636 * q^63 - 589508 * q^64 - 6977250 * q^66 - 1944728 * q^67 - 24852702 * q^70 - 1544472 * q^72 + 13351212 * q^73 - 23106048 * q^75 + 1917432 * q^78 + 7626328 * q^79 + 8703036 * q^81 + 14640192 * q^82 + 15191904 * q^84 + 3418848 * q^85 + 15346296 * q^87 + 12313398 * q^88 + 3988992 * q^91 - 24832104 * q^93 - 51594732 * q^94 - 57374730 * q^96 + 35642232 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	6.40713	−	3.69916i	0.566316	−	0.326963i	−0.189361	−	0.981908i	$-0.560642\pi$
$2$	6.40713	−	3.69916i	0.566316	−	0.326963i	0.755677	+	0.654945i	$0.227308\pi$
$3$	−11.8808	−	45.2310i	−0.254051	−	0.967191i
$3$	−11.8808	−	45.2310i	−0.254051	−	0.967191i
$4$	−36.6324	+	63.4492i	−0.286191	+	0.495697i
$5$	−101.547	−	175.885i	−0.363306	−	0.629265i	0.625196	−	0.780467i	$-0.285019\pi$
$5$	−101.547	−	175.885i	−0.363306	−	0.629265i	−0.988503	+	0.151202i	$0.951686\pi$
$6$	−243.439	−	245.852i	−0.460108	−	0.464671i
$7$	−682.340	−	598.293i	−0.751896	−	0.659281i
$7$	−682.340	−	598.293i	−0.751896	−	0.659281i
$8$			1489.02i			1.02822i
$9$	−1904.69	+	1074.76i	−0.870917	+	0.491431i
$10$	−1301.25	−	751.279i	−0.411493	−	0.237575i
$11$	−1685.57	−	973.165i	−0.381832	−	0.220451i	0.296783	−	0.954945i	$-0.404086\pi$
$11$	−1685.57	−	973.165i	−0.381832	−	0.220451i	−0.678615	+	0.734494i	$0.737420\pi$
$12$	3305.10	+	903.097i	0.552141	+	0.150869i
$13$		−	7873.88i		−	0.994002i	−0.867750	−	0.497001i	$-0.834435\pi$
$13$		−	7873.88i		−	0.994002i	0.867750	−	0.497001i	$-0.165565\pi$
$14$	−6585.03	−	1309.26i	−0.641371	−	0.127520i
$15$	−6749.00	+	6682.74i	−0.516321	+	0.511252i
$16$	819.181	+	1418.86i	0.0499988	+	0.0866005i
$17$	4615.11	−	7993.61i	0.227830	−	0.394613i	−0.729335	−	0.684157i	$-0.760170\pi$
$17$	4615.11	−	7993.61i	0.227830	−	0.394613i	0.957165	+	0.289544i	$0.0935036\pi$
$18$	−8227.93	+	13931.9i	−0.332534	+	0.563062i
$19$	9012.39	−	5203.30i	0.301441	−	0.174037i	−0.341649	−	0.939828i	$-0.610985\pi$
$19$	9012.39	−	5203.30i	0.301441	−	0.174037i	0.643090	+	0.765791i	$0.277652\pi$
$20$	14879.7			0.415900
$21$	−18954.7	+	37971.1i	−0.446631	+	0.894718i
$22$	−14399.6			−0.288317
$23$	70904.4	−	40936.7i	1.21514	−	0.701560i	0.251264	−	0.967919i	$-0.419154\pi$
$23$	70904.4	−	40936.7i	1.21514	−	0.701560i	0.963874	+	0.266358i	$0.0858204\pi$
$24$	67350.0	−	17690.7i	0.994485	−	0.261220i
$25$	18438.8	−	31937.0i	0.236017	−	0.408793i
$26$	−29126.8	−	50449.0i	−0.325002	−	0.562919i
$27$	71241.7	+	73382.4i	0.696564	+	0.717494i
$28$	62957.0	−	21377.0i	0.541990	−	0.184032i
$29$			195123.i			1.48565i	0.669487	+	0.742824i	$0.266514\pi$
$29$			195123.i			1.48565i	−0.669487	+	0.742824i	$0.733486\pi$
$30$	−18521.2	+	67782.8i	−0.125241	+	0.458348i
$31$	−84434.3	−	48748.2i	−0.509041	−	0.293895i	0.223398	−	0.974727i	$-0.428285\pi$
$31$	−84434.3	−	48748.2i	−0.509041	−	0.293895i	−0.732439	+	0.680832i	$0.761618\pi$
$32$	−154563.	−	89236.8i	−0.833835	−	0.481415i
$33$	−23991.4	+	87802.1i	−0.116213	+	0.425310i
$34$		−	68288.2i		−	0.297968i
$35$	−35941.0	+	180768.i	−0.141694	+	0.712663i
$36$	1580.94	−	160222.i	0.00564750	−	0.572354i
$37$	−285316.	−	494181.i	−0.926019	−	1.60391i	−0.789915	−	0.613217i	$-0.789875\pi$
$37$	−285316.	−	494181.i	−0.926019	−	1.60391i	−0.136104	−	0.990695i	$-0.543458\pi$
$38$	38495.7	−	66676.5i	0.113807	−	0.197120i
$39$	−356144.	+	93547.8i	−0.961390	+	0.252527i
$40$	261897.	−	151206.i	0.647023	−	0.373559i
$41$	−339491.			−0.769280			−0.384640	−	0.923067i	$-0.625674\pi$
$41$	−339491.			−0.769280			−0.384640	+	0.923067i	$0.625674\pi$
$42$	19016.1	+	313403.i	0.0396050	+	0.652725i
$43$	−356328.			−0.683455			−0.341727	−	0.939799i	$-0.611012\pi$
$43$	−356328.			−0.683455			−0.341727	+	0.939799i	$0.611012\pi$
$44$	123493.	−	71298.8i	0.218554	−	0.126182i
$45$	382451.	+	225868.i	0.625650	+	0.369498i
$46$	302863.	−	524573.i	0.458768	−	0.794610i
$47$	383075.	+	663506.i	0.538198	+	0.932185i	0.999001	+	0.0446833i	$0.0142279\pi$
$47$	383075.	+	663506.i	0.538198	+	0.932185i	−0.460804	+	0.887502i	$0.652439\pi$
$48$	54444.1	−	53909.6i	0.0710570	−	0.0703593i
$49$	107634.	+	816479.i	0.130696	+	0.991423i
$50$		−	272832.i		−	0.308675i
$51$	−416391.	−	113776.i	−0.439547	−	0.120103i
$52$	499592.	+	288439.i	0.492724	+	0.284474i
$53$	−137209.	−	79217.5i	−0.126595	−	0.0730896i	0.435365	−	0.900254i	$-0.356619\pi$
$53$	−137209.	−	79217.5i	−0.126595	−	0.0730896i	−0.561960	+	0.827164i	$0.689953\pi$
$54$	727908.	+	206636.i	0.629069	+	0.178578i
$55$			395289.i			0.320365i
$56$	890872.	−	1.01602e6i	0.677887	−	0.773115i
$57$	−342425.	−	345820.i	−0.244908	−	0.247337i
$58$	721792.	+	1.25018e6i	0.485751	+	0.841346i
$59$	1.28115e6	−	2.21902e6i	0.812117	−	1.40663i	−0.0992632	−	0.995061i	$-0.531649\pi$
$59$	1.28115e6	−	2.21902e6i	0.812117	−	1.40663i	0.911380	−	0.411566i	$-0.135018\pi$
$60$	−176782.	−	673024.i	−0.105660	−	0.402255i
$61$	−1.49737e6	+	864504.i	−0.844643	+	0.487655i	−0.858840	−	0.512244i	$-0.828814\pi$
$61$	−1.49737e6	+	864504.i	−0.844643	+	0.487655i	0.0141966	+	0.999899i	$0.495481\pi$
$62$	−721309.			−0.384371
$63$	1.94267e6	+	406214.i	0.978830	+	0.204674i
$64$	−1.53012e6			−0.729616
$65$	−1.38490e6	+	799571.i	−0.625491	+	0.361127i
$66$	171078.	+	651308.i	0.0732471	+	0.278857i
$67$	1.10259e6	−	1.90974e6i	0.447870	−	0.775734i	−0.550377	−	0.834916i	$-0.685516\pi$
$67$	1.10259e6	−	1.90974e6i	0.447870	−	0.775734i	0.998247	+	0.0591826i	$0.0188494\pi$
$68$	338126.	+	585651.i	0.130406	+	0.225869i
$69$	−2.69401e6	−	2.72072e6i	−0.987249	−	0.997039i
$70$	438413.	+	1.29116e6i	0.152771	+	0.449921i
$71$			5.29805e6i			1.75676i	0.477965	+	0.878379i	$0.341375\pi$
$71$			5.29805e6i			1.75676i	−0.477965	+	0.878379i	$0.658625\pi$
$72$	−1.60034e6	−	2.83613e6i	−0.505299	−	0.895494i
$73$	2.20247e6	+	1.27160e6i	0.662644	+	0.382577i	0.793284	−	0.608852i	$-0.208370\pi$
$73$	2.20247e6	+	1.27160e6i	0.662644	+	0.382577i	−0.130640	+	0.991430i	$0.541703\pi$
$74$	−3.65611e6	−	2.11086e6i	−1.04884	−	0.605547i
$75$	−1.66361e6	−	454571.i	−0.455341	−	0.124419i
$76$			762439.i			0.199231i
$77$	567895.	+	1.67249e6i	0.141759	+	0.417491i
$78$	−1.93581e6	+	1.91681e6i	−0.461883	+	0.457348i
$79$	−372291.	−	644826.i	−0.0849547	−	0.147146i	0.820417	−	0.571765i	$-0.193741\pi$
$79$	−372291.	−	644826.i	−0.0849547	−	0.147146i	−0.905372	+	0.424619i	$0.860408\pi$
$80$	166371.	−	288163.i	0.0363298	−	0.0629251i
$81$	2.47275e6	−	4.09418e6i	0.516991	−	0.855991i
$82$	−2.17516e6	+	1.25583e6i	−0.435656	+	0.251526i
$83$	5.20177e6			0.998569			0.499284	−	0.866438i	$-0.333596\pi$
$83$	5.20177e6			0.998569			0.499284	+	0.866438i	$0.333596\pi$
$84$	−1.71488e6	−	2.59364e6i	−0.315687	−	0.477454i
$85$	−1.87461e6			−0.331089
$86$	−2.28304e6	+	1.31811e6i	−0.387051	+	0.223464i
$87$	8.82563e6	−	2.31821e6i	1.43691	−	0.377430i
$88$	1.44906e6	−	2.50985e6i	0.226672	−	0.392608i
$89$	−5.08205e6	−	8.80237e6i	−0.764142	−	1.32353i	−0.940699	−	0.339242i	$-0.889829\pi$
$89$	−5.08205e6	−	8.80237e6i	−0.764142	−	1.32353i	0.176557	−	0.984290i	$-0.443504\pi$
$90$	3.28594e6	+	32422.8i	0.475128	+	0.00468815i
$91$	−4.71089e6	+	5.37267e6i	−0.655327	+	0.747386i
$92$			5.99844e6i			0.803120i
$93$	−1.20179e6	+	4.39822e6i	−0.154930	+	0.567004i
$94$	4.90883e6	+	2.83411e6i	0.609580	+	0.351941i
$95$	−1.83037e6	−	1.05676e6i	−0.219031	−	0.126458i
$96$	−2.19995e6	+	8.05124e6i	−0.253784	+	0.928781i
$97$		−	3.36084e6i		−	0.373893i	−0.982370	−	0.186946i	$-0.940141\pi$
$97$		−	3.36084e6i		−	0.373893i	0.982370	−	0.186946i	$-0.0598591\pi$
$98$	3.70991e6	+	4.83314e6i	0.398173	+	0.518726i
$99$	4.25641e6	+	41998.7i	0.440880	+	0.00435023i
$100$	1.35092e6	+	2.33986e6i	0.135092	+	0.233986i
$101$	6.35468e6	−	1.10066e7i	0.613718	−	1.06299i	−0.376890	−	0.926258i	$-0.623007\pi$
$101$	6.35468e6	−	1.10066e7i	0.613718	−	1.06299i	0.990608	−	0.136732i	$-0.0436600\pi$
$102$	−3.08875e6	+	811316.i	−0.288192	+	0.0756989i
$103$	7.43275e6	−	4.29130e6i	0.670223	−	0.386954i	−0.125938	−	0.992038i	$-0.540194\pi$
$103$	7.43275e6	−	4.29130e6i	0.670223	−	0.386954i	0.796161	+	0.605085i	$0.206861\pi$
$104$	1.17244e7			1.02205
$105$	8.60335e6	−	522020.i	0.725279	−	0.0440073i
$106$	−1.17215e6			−0.0955903
$107$	−428036.	+	247127.i	−0.0337782	+	0.0195019i	−0.516794	−	0.856110i	$-0.672875\pi$
$107$	−428036.	+	247127.i	−0.0337782	+	0.0195019i	0.483016	+	0.875612i	$0.339541\pi$
$108$	−7.26581e6	+	1.83206e6i	−0.555010	+	0.139945i
$109$	5.23969e6	−	9.07541e6i	0.387537	−	0.671233i	−0.604581	−	0.796544i	$-0.706659\pi$
$109$	5.23969e6	−	9.07541e6i	0.387537	−	0.671233i	0.992118	+	0.125311i	$0.0399928\pi$
$110$	1.46224e6	+	2.53267e6i	0.104747	+	0.181428i
$111$	−1.89626e7	+	1.87764e7i	−1.31603	+	1.30311i
$112$	289936.	−	1.45826e6i	0.0195002	−	0.0980779i
$113$			63166.9i			0.00411827i	0.999998	+	0.00205914i	$0.000655444\pi$
$113$			63166.9i			0.00411827i	−0.999998	+	0.00205914i	$0.999345\pi$
$114$	−3.47321e6	−	949033.i	−0.219565	−	0.0599949i
$115$	−1.44003e7	−	8.31401e6i	−0.882935	−	0.509763i
$116$	−1.23804e7	−	7.14784e6i	−0.736431	−	0.425179i
$117$	8.46253e6	+	1.49973e7i	0.488483	+	0.865693i
$118$		−	1.89567e7i		−	1.06213i
$119$	−7.93160e6	+	2.69317e6i	−0.431466	+	0.146504i
$120$	−9.95074e6	−	1.00494e7i	−0.525680	−	0.530892i
$121$	−7.84949e6	−	1.35957e7i	−0.402803	−	0.697675i
$122$	−6.39588e6	+	1.10780e7i	−0.318890	+	0.552334i
$123$	4.03341e6	+	1.53555e7i	0.195436	+	0.744041i
$124$	6.18607e6	−	3.57153e6i	0.291366	−	0.168220i
$125$	−2.33564e7			−1.06960
$126$	1.39496e7	−	4.58358e6i	0.621248	−	0.204131i
$127$	−1.51366e7			−0.655716			−0.327858	−	0.944727i	$-0.606327\pi$
$127$	−1.51366e7			−0.655716			−0.327858	+	0.944727i	$0.606327\pi$
$128$	9.98037e6	−	5.76217e6i	0.420641	−	0.242857i
$129$	4.23345e6	+	1.61171e7i	0.173632	+	0.661031i
$130$	−5.91548e6	+	1.02459e7i	−0.236150	+	0.409024i
$131$	4.13717e6	+	7.16578e6i	0.160788	+	0.278493i	0.935151	−	0.354248i	$-0.115263\pi$
$131$	4.13717e6	+	7.16578e6i	0.160788	+	0.278493i	−0.774364	+	0.632741i	$0.781930\pi$
$132$	−4.69211e6	−	4.73864e6i	−0.177566	−	0.179327i
$133$	−9.26262e6	−	1.84162e6i	−0.341392	−	0.0678767i
$134$		−	1.63146e7i		−	0.585747i
$135$	5.67245e6	−	1.99821e7i	0.198428	−	0.698994i
$136$	1.19027e7	+	6.87201e6i	0.405749	+	0.234260i
$137$	3.06109e7	+	1.76732e7i	1.01708	+	0.587210i	0.913256	−	0.407386i	$-0.133560\pi$
$137$	3.06109e7	+	1.76732e7i	1.01708	+	0.587210i	0.103821	+	0.994596i	$0.466893\pi$
$138$	−2.73252e7	−	7.46645e6i	−0.885090	−	0.241845i
$139$			3.41607e6i			0.107888i	0.998544	+	0.0539442i	$0.0171793\pi$
$139$			3.41607e6i			0.107888i	−0.998544	+	0.0539442i	$0.982821\pi$
$140$	−1.01530e7	−	8.90241e6i	−0.312714	−	0.274195i
$141$	2.54598e7	−	2.52099e7i	0.764872	−	0.757362i
$142$	1.95983e7	+	3.39453e7i	0.574394	+	0.994880i
$143$	−7.66258e6	+	1.32720e7i	−0.219129	+	0.379542i
$144$	−3.08523e6	−	1.82208e6i	−0.0861030	−	0.0508509i
$145$	3.43192e7	−	1.98142e7i	0.934867	−	0.539746i
$146$	1.88154e7			0.500354
$147$	3.56514e7	−	1.45688e7i	0.925691	−	0.378279i
$148$	4.18072e7			1.06007
$149$	1.80764e7	−	1.04364e7i	0.447671	−	0.258463i	−0.259175	−	0.965830i	$-0.583451\pi$
$149$	1.80764e7	−	1.04364e7i	0.447671	−	0.258463i	0.706846	+	0.707367i	$0.250117\pi$
$150$	−1.23405e7	+	3.24146e6i	−0.298547	+	0.0784190i
$151$	−3.98707e7	+	6.90580e7i	−0.942398	+	1.63228i	−0.181518	+	0.983388i	$0.558101\pi$
$151$	−3.98707e7	+	6.90580e7i	−0.942398	+	1.63228i	−0.760880	+	0.648893i	$0.775232\pi$
$152$	7.74783e6	+	1.34196e7i	0.178948	+	0.309948i
$153$	−199174.	+	2.01855e7i	−0.00449585	+	0.455638i
$154$	9.82541e6	+	8.61516e6i	0.216784	+	0.190082i
$155$			1.98010e7i			0.427096i
$156$	7.11088e6	−	2.60239e7i	0.149964	−	0.548829i
$157$	−7.15232e7	−	4.12939e7i	−1.47502	−	0.851603i	−0.475417	−	0.879761i	$-0.657703\pi$
$157$	−7.15232e7	−	4.12939e7i	−1.47502	−	0.851603i	−0.999604	+	0.0281573i	$0.991036\pi$
$158$	−4.77063e6	−	2.75433e6i	−0.0962224	−	0.0555540i
$159$	−1.95295e6	+	7.14726e6i	−0.0385301	+	0.141010i
$160$			3.62470e7i			0.699604i
$161$	−7.28730e7	−	1.44889e7i	−1.37618	−	0.273617i
$162$	698248.	−	3.53791e7i	0.0129035	−	0.653798i
$163$	2.43298e7	+	4.21404e7i	0.440029	+	0.762153i	0.997691	−	0.0679149i	$-0.0216347\pi$
$163$	2.43298e7	+	4.21404e7i	0.440029	+	0.762153i	−0.557662	+	0.830068i	$0.688301\pi$
$164$	1.24364e7	−	2.15404e7i	0.220161	−	0.381330i
$165$	1.78793e7	−	4.69634e6i	0.309854	−	0.0813889i
$166$	3.33284e7	−	1.92422e7i	0.565505	−	0.326495i
$167$	5.93974e7			0.986869			0.493435	−	0.869783i	$-0.335741\pi$
$167$	5.93974e7			0.986869			0.493435	+	0.869783i	$0.335741\pi$
$168$	−5.65399e7	−	2.82240e7i	−0.919967	−	0.459235i
$169$	750490.			0.0119603
$170$	−1.20109e7	+	6.93448e6i	−0.187501	+	0.108254i
$171$	−1.15735e7	+	1.95969e7i	−0.177003	+	0.299709i
$172$	1.30531e7	−	2.26087e7i	0.195599	−	0.338787i
$173$	−5.09012e7	−	8.81635e7i	−0.747423	−	1.29458i	−0.949054	−	0.315114i	$-0.897957\pi$
$173$	−5.09012e7	−	8.81635e7i	−0.747423	−	1.29458i	0.201630	−	0.979462i	$-0.435376\pi$
$174$	4.79715e7	−	4.75005e7i	0.690337	−	0.683559i
$175$	−3.16892e7	+	1.07601e7i	−0.446970	+	0.151768i
$176$		−	3.18879e6i		−	0.0440892i
$177$	−1.15590e8	−	3.15842e7i	−1.56680	−	0.428117i
$178$	−6.51227e7	−	3.75986e7i	−0.865491	−	0.499692i
$179$	5.48559e7	+	3.16711e7i	0.714888	+	0.412741i	0.812868	−	0.582448i	$-0.197905\pi$
$179$	5.48559e7	+	3.16711e7i	0.714888	+	0.412741i	−0.0979805	+	0.995188i	$0.531238\pi$
$180$	−2.83413e7	+	1.59921e7i	−0.362214	+	0.204386i
$181$		−	2.79149e6i		−	0.0349913i	−0.999847	−	0.0174957i	$-0.994431\pi$
$181$		−	2.79149e6i		−	0.0349913i	0.999847	−	0.0174957i	$-0.00556933\pi$
$182$	−1.03089e7	+	5.18497e7i	−0.126755	+	0.637524i
$183$	5.68923e7	+	5.74564e7i	0.686238	+	0.693042i
$184$	6.09556e7	+	1.05578e8i	0.721358	+	1.24943i
$185$	−5.79461e7	+	1.00366e8i	−0.672857	+	1.16542i
$186$	8.56971e6	+	3.26256e7i	0.0976497	+	0.371760i
$187$	−1.55582e7	+	8.98253e6i	−0.173986	+	0.100451i
$188$	−5.61319e7			−0.616109
$189$	−4.70695e6	−	9.26952e7i	−0.0507134	−	0.998713i
$190$	−1.56365e7			−0.165388
$191$	3.62562e7	−	2.09325e7i	0.376500	−	0.217373i	−0.299794	−	0.954004i	$-0.596918\pi$
$191$	3.62562e7	−	2.09325e7i	0.376500	−	0.217373i	0.676295	+	0.736631i	$0.263585\pi$
$192$	1.81790e7	+	6.92087e7i	0.185359	+	0.705678i
$193$	4.02081e7	−	6.96425e7i	0.402590	−	0.697306i	−0.591448	−	0.806343i	$-0.701443\pi$
$193$	4.02081e7	−	6.96425e7i	0.402590	−	0.697306i	0.994038	+	0.109037i	$0.0347767\pi$
$194$	−1.24323e7	−	2.15334e7i	−0.122249	−	0.211741i
$195$	5.26191e7	+	5.31409e7i	0.508185	+	0.513225i
$196$	−5.57478e7	−	2.30803e7i	−0.528849	−	0.218950i
$197$		−	2.46045e7i		−	0.229289i	−0.993407	−	0.114645i	$-0.963427\pi$
$197$		−	2.46045e7i		−	0.229289i	0.993407	−	0.114645i	$-0.0365729\pi$
$198$	2.74268e7	−	1.54761e7i	0.251100	−	0.141688i
$199$	−2.62301e7	−	1.51439e7i	−0.235947	−	0.136224i	0.377366	−	0.926064i	$-0.376830\pi$
$199$	−2.62301e7	−	1.51439e7i	−0.235947	−	0.136224i	−0.613312	+	0.789840i	$0.710163\pi$
$200$	4.75548e7	+	2.74558e7i	0.420329	+	0.242677i
$201$	−9.94792e7	−	2.71821e7i	−0.864064	−	0.236100i
$202$		−	9.40279e7i		−	0.802651i
$203$	1.16741e8	−	1.33140e8i	0.979460	−	1.11705i
$204$	2.24724e7	−	2.22518e7i	0.185329	−	0.183510i
$205$	3.44744e7	+	5.97113e7i	0.279484	+	0.484081i
$206$	3.17484e7	−	5.49899e7i	0.253039	−	0.438276i
$207$	−9.10541e7	+	1.54177e8i	−0.713516	+	1.20816i
$208$	1.11720e7	−	6.45013e6i	0.0860811	−	0.0496989i
$209$	−2.02547e7			−0.153466
$210$	5.31918e7	−	3.51698e7i	0.396348	−	0.262061i
$211$	6.47500e7			0.474517			0.237258	−	0.971447i	$-0.423751\pi$
$211$	6.47500e7			0.474517			0.237258	+	0.971447i	$0.423751\pi$
$212$	1.00526e7	−	5.80386e6i	0.0724606	−	0.0418352i
$213$	2.39636e8	−	6.29449e7i	1.69912	−	0.446305i
$214$	−1.82832e6	+	3.16675e6i	−0.0127528	+	0.0220884i
$215$	3.61841e7	+	6.26727e7i	0.248304	+	0.430074i
$216$	−1.09268e8	+	1.06080e8i	−0.737742	+	0.716222i
$217$	2.84472e7	+	8.37793e7i	0.188987	+	0.556580i
$218$		−	7.75298e7i		−	0.506840i
$219$	3.13486e7	−	1.14728e8i	0.201680	−	0.738097i
$220$	−2.50808e7	−	1.44804e7i	−0.158804	−	0.0916855i
$221$	−6.29408e7	−	3.63389e7i	−0.392246	−	0.226464i
$222$	−5.20389e7	+	1.90448e8i	−0.319222	+	1.16827i
$223$		−	6.67311e7i		−	0.402959i	−0.979493	−	0.201480i	$-0.935425\pi$
$223$		−	6.67311e7i		−	0.402959i	0.979493	−	0.201480i	$-0.0645750\pi$
$224$	5.20746e7	+	1.53364e8i	0.309569	+	0.911705i
$225$	−795760.	+	8.06474e7i	−0.00465740	+	0.472011i
$226$	233664.	+	404719.i	0.00134652	+	0.00233224i
$227$	−7.17280e7	+	1.24237e8i	−0.407004	+	0.704951i	−0.994552	−	0.104238i	$-0.966760\pi$
$227$	−7.17280e7	+	1.24237e8i	−0.407004	+	0.704951i	0.587549	+	0.809189i	$0.300093\pi$
$228$	3.44859e7	−	9.05836e6i	0.192695	−	0.0506148i
$229$	3.13577e8	−	1.81044e8i	1.72552	−	0.996230i	0.819382	−	0.573248i	$-0.194317\pi$
$229$	3.13577e8	−	1.81044e8i	1.72552	−	0.996230i	0.906138	−	0.422982i	$-0.139017\pi$
$230$	−1.23019e8			−0.666694
$231$	6.89017e7	−	4.55570e7i	0.367780	−	0.243172i
$232$	−2.90543e8			−1.52757
$233$	−1.70716e8	+	9.85632e7i	−0.884157	+	0.510469i	−0.872027	−	0.489458i	$-0.837195\pi$
$233$	−1.70716e8	+	9.85632e7i	−0.884157	+	0.510469i	−0.0121305	+	0.999926i	$0.503861\pi$
$234$	1.09698e8	+	6.47857e7i	0.559685	+	0.330540i
$235$	7.78005e7	−	1.34754e8i	0.391061	−	0.677338i
$236$	9.38634e7	+	1.62576e8i	0.464841	+	0.805128i
$237$	−2.47431e7	+	2.45001e7i	−0.120735	+	0.119550i
$238$	−4.08564e7	+	4.65958e7i	−0.196445	+	0.224041i
$239$		−	8.32422e7i		−	0.394413i	−0.980362	−	0.197206i	$-0.936813\pi$
$239$		−	8.32422e7i		−	0.394413i	0.980362	−	0.197206i	$-0.0631869\pi$
$240$	−1.50105e7	−	4.10154e6i	−0.0700902	−	0.0191517i
$241$	−1.89741e8	−	1.09547e8i	−0.873176	−	0.504128i	−0.00477351	−	0.999989i	$-0.501519\pi$
$241$	−1.89741e8	−	1.09547e8i	−0.873176	−	0.504128i	−0.868402	+	0.495860i	$0.834853\pi$
$242$	−1.00585e8	−	5.80730e7i	−0.456227	−	0.263403i
$243$	−2.14562e8	−	6.32033e7i	−0.959248	−	0.282564i
$244$		−	1.26676e8i		−	0.558250i
$245$	1.32677e8	−	1.01842e8i	0.576385	−	0.442433i
$246$	8.26451e7	+	8.34646e7i	0.353952	+	0.357462i
$247$	−4.09702e7	−	7.09625e7i	−0.172993	−	0.299633i
$248$	7.25871e7	−	1.25725e8i	0.302189	−	0.523406i
$249$	−6.18010e7	−	2.35282e8i	−0.253687	−	0.965806i
$250$	−1.49648e8	+	8.63991e7i	−0.605731	+	0.349719i
$251$	6.98425e6			0.0278780			0.0139390	−	0.999903i	$-0.495563\pi$
$251$	6.98425e6			0.0278780			0.0139390	+	0.999903i	$0.495563\pi$
$252$	−9.69387e7	+	1.08380e8i	−0.381589	+	0.426627i
$253$	−1.59352e8			−0.618638
$254$	−9.69823e7	+	5.59928e7i	−0.371342	+	0.214395i
$255$	2.22718e7	+	8.47905e7i	0.0841133	+	0.320226i
$256$	1.40558e8	−	2.43453e8i	0.523619	−	0.906934i
$257$	1.29051e8	+	2.23524e8i	0.474239	+	0.821406i	0.999565	−	0.0294953i	$-0.00939001\pi$
$257$	1.29051e8	+	2.23524e8i	0.474239	+	0.821406i	−0.525326	+	0.850901i	$0.676057\pi$
$258$	8.67439e7	+	8.76040e7i	0.314463	+	0.317581i
$259$	−1.00983e8	+	5.07902e8i	−0.361159	+	1.81648i
$260$		−	1.17161e8i		−	0.413405i
$261$	−2.09710e8	−	3.71650e8i	−0.730093	−	1.29388i
$262$	5.30148e7	+	3.06081e7i	0.182114	+	0.105143i
$263$	−1.14712e8	−	6.62289e7i	−0.388833	−	0.224493i	0.292821	−	0.956167i	$-0.405406\pi$
$263$	−1.14712e8	−	6.62289e7i	−0.388833	−	0.224493i	−0.681654	+	0.731674i	$0.738739\pi$
$264$	−1.30739e8	−	3.57237e7i	−0.437313	−	0.119493i
$265$			3.21773e7i			0.106216i
$266$	−6.61593e7	+	2.24644e7i	−0.215529	+	0.0731827i
$267$	−3.37762e8	+	3.34445e8i	−1.08598	+	1.07532i
$268$	8.07810e7	+	1.39917e8i	0.256353	+	0.444016i
$269$	2.27615e8	−	3.94240e8i	0.712964	−	1.23489i	−0.250776	−	0.968045i	$-0.580686\pi$
$269$	2.27615e8	−	3.94240e8i	0.712964	−	1.23489i	0.963740	−	0.266844i	$-0.0859809\pi$
$270$	−3.75729e7	−	1.49011e8i	−0.116172	−	0.460730i
$271$	4.78434e8	−	2.76224e8i	1.46026	−	0.843080i	0.461235	−	0.887278i	$-0.347407\pi$
$271$	4.78434e8	−	2.76224e8i	1.46026	−	0.843080i	0.999023	+	0.0441978i	$0.0140732\pi$
$272$	1.51225e7			0.0455650
$273$	2.98980e8	+	1.49247e8i	0.889351	+	0.443952i
$274$	2.61504e8			0.767983
$275$	−6.21598e7	+	3.58880e7i	−0.180238	+	0.104060i
$276$	2.71316e8	−	7.12661e7i	0.776771	−	0.204033i
$277$	−2.62828e8	+	4.55231e8i	−0.743006	+	1.28692i	0.208115	+	0.978104i	$0.433267\pi$
$277$	−2.62828e8	+	4.55231e8i	−0.743006	+	1.28692i	−0.951121	+	0.308819i	$0.900066\pi$
$278$	1.26366e7	+	2.18872e7i	0.0352755	+	0.0610990i
$279$	2.13214e8	+	2.10381e6i	0.587762	+	0.00579953i
$280$	−2.69168e8	−	5.35169e7i	−0.732775	−	0.145693i
$281$			3.06215e8i			0.823292i	0.911344	+	0.411646i	$0.135046\pi$
$281$			3.06215e8i			0.823292i	−0.911344	+	0.411646i	$0.864954\pi$
$282$	6.98693e7	−	2.55703e8i	0.185530	−	0.678991i
$283$	4.82049e8	+	2.78311e8i	1.26427	+	0.729924i	0.973897	−	0.226990i	$-0.0728886\pi$
$283$	4.82049e8	+	2.78311e8i	1.26427	+	0.729924i	0.290369	+	0.956915i	$0.406222\pi$
$284$	−3.36157e8	−	1.94080e8i	−0.870820	−	0.502768i
$285$	−2.60523e7	+	9.53445e7i	−0.0666637	+	0.243971i
$286$			1.13381e8i			0.286588i
$287$	2.31648e8	+	2.03115e8i	0.578419	+	0.507172i
$288$	3.90303e8	+	3.85118e6i	0.962782	+	0.00949991i
$289$	1.62571e8	+	2.81581e8i	0.396187	+	0.686216i
$290$	1.46592e8	−	2.53905e8i	0.352953	−	0.611333i
$291$	−1.52014e8	+	3.99294e7i	−0.361626	+	0.0949877i
$292$	−1.61364e8	+	9.31633e7i	−0.379285	+	0.218980i
$293$	1.60840e8			0.373557			0.186779	−	0.982402i	$-0.440195\pi$
$293$	1.60840e8			0.373557			0.186779	+	0.982402i	$0.440195\pi$
$294$	1.74531e8	−	2.25225e8i	0.400551	−	0.516892i
$295$	−5.20390e8			−1.18019
$296$	7.35847e8	−	4.24841e8i	1.64917	−	0.952151i
$297$	−4.86698e7	−	1.93021e8i	−0.107798	−	0.427521i
$298$	7.72118e7	−	1.33735e8i	0.169016	−	0.292744i
$299$	−3.22330e8	−	5.58293e8i	−0.697352	−	1.20785i
$300$	8.97842e7	−	8.89027e7i	0.191989	−	0.190104i
$301$	2.43137e8	+	2.13188e8i	0.513887	+	0.450589i
$302$			5.89952e8i			1.23252i
$303$	−5.73339e8	−	1.56661e8i	−1.18403	−	0.323529i
$304$	1.47656e7	+	8.52489e6i	0.0301434	+	0.0174033i
$305$	3.04107e8	+	1.75576e8i	0.613729	+	0.354336i
$306$	7.33934e7	+	1.30068e8i	0.146431	+	0.259505i
$307$		−	1.76458e8i		−	0.348063i	−0.984740	−	0.174032i	$-0.944321\pi$
$307$		−	1.76458e8i		−	0.348063i	0.984740	−	0.174032i	$-0.0556795\pi$
$308$	−1.26922e8	−	2.52350e7i	−0.247519	−	0.0492126i
$309$	−2.82407e8	−	2.85207e8i	−0.544529	−	0.549928i
$310$	7.32470e7	+	1.26867e8i	0.139644	+	0.241871i
$311$	−3.53583e8	+	6.12424e8i	−0.666546	+	1.15449i	0.312317	+	0.949978i	$0.398895\pi$
$311$	−3.53583e8	+	6.12424e8i	−0.666546	+	1.15449i	−0.978864	+	0.204514i	$0.934439\pi$
$312$	−1.39295e8	−	5.30306e8i	−0.259653	−	0.988520i
$313$	−4.45721e8	+	2.57337e8i	−0.821595	+	0.474348i	−0.850966	−	0.525221i	$-0.823983\pi$
$313$	−4.45721e8	+	2.57337e8i	−0.821595	+	0.474348i	0.0293714	+	0.999569i	$0.490649\pi$
$314$	−6.11011e8			−1.11377
$315$	−1.25826e8	−	3.82937e8i	−0.226821	−	0.690303i
$316$	5.45516e7			0.0972530
$317$	−7.02781e8	+	4.05751e8i	−1.23912	+	0.715405i	−0.968914	−	0.247398i	$-0.920425\pi$
$317$	−7.02781e8	+	4.05751e8i	−1.23912	+	0.715405i	−0.270204	+	0.962803i	$0.587091\pi$
$318$	1.39261e7	+	5.30177e7i	0.0242848	+	0.0924541i
$319$	1.89887e8	−	3.28894e8i	0.327512	−	0.567268i
$320$	1.55379e8	+	2.69124e8i	0.265074	+	0.459122i
$321$	1.62632e7	+	1.64244e7i	0.0274434	+	0.0277155i
$322$	−5.20504e8	+	1.76737e8i	−0.868817	+	0.295007i
$323$		−	9.60554e7i		−	0.158604i
$324$	1.69189e8	+	3.06874e8i	0.276354	+	0.501248i
$325$	−2.51468e8	−	1.45185e8i	−0.406341	−	0.234601i
$326$	3.11768e8	+	1.80000e8i	0.498391	+	0.287746i
$327$	−4.72742e8	−	1.29174e8i	−0.747664	−	0.204295i
$328$		−	5.05509e8i		−	0.790989i
$329$	1.35583e8	−	6.81928e8i	0.209904	−	1.05573i
$330$	9.71827e7	−	9.62285e7i	0.148864	−	0.147403i
$331$	−3.58708e7	−	6.21300e7i	−0.0543680	−	0.0941681i	0.837561	−	0.546345i	$-0.183981\pi$
$331$	−3.58708e7	−	6.21300e7i	−0.0543680	−	0.0941681i	−0.891929	+	0.452176i	$0.850648\pi$
$332$	−1.90553e8	+	3.30048e8i	−0.285781	+	0.494987i
$333$	1.07457e9	+	6.34619e8i	1.59470	+	0.941799i
$334$	3.80567e8	−	2.19720e8i	0.558880	−	0.322669i
$335$	−4.47860e8			−0.650856
$336$	−6.94032e7	+	4.21113e6i	−0.0998141	+	0.00605635i
$337$	8.22484e7			0.117064			0.0585320	−	0.998286i	$-0.481358\pi$
$337$	8.22484e7			0.117064			0.0585320	+	0.998286i	$0.481358\pi$
$338$	4.80849e6	−	2.77618e6i	0.00677330	−	0.00391056i
$339$	2.85710e6	−	750471.i	0.00398315	−	0.00104625i
$340$	6.86715e7	−	1.18942e8i	0.0947545	−	0.164120i
$341$	9.48800e7	+	1.64337e8i	0.129579	+	0.224437i
$342$	−1.66135e6	+	1.68372e8i	−0.00224580	+	0.227603i
$343$	4.15051e8	−	6.21513e8i	0.555357	−	0.831612i
$344$		−	5.30580e8i		−	0.702742i
$345$	−2.04965e8	+	7.50117e8i	−0.268728	+	0.983472i
$346$	−6.52262e8	−	3.76583e8i	−0.846556	−	0.488759i
$347$	7.69144e7	+	4.44065e7i	0.0988221	+	0.0570550i	0.548597	−	0.836087i	$-0.315162\pi$
$347$	7.69144e7	+	4.44065e7i	0.0988221	+	0.0570550i	−0.449774	+	0.893142i	$0.648496\pi$
$348$	−1.76215e8	+	6.44901e8i	−0.224138	+	0.820287i
$349$			1.32408e8i			0.166735i	0.996519	+	0.0833673i	$0.0265675\pi$
$349$			1.32408e8i			0.166735i	−0.996519	+	0.0833673i	$0.973433\pi$
$350$	−1.63234e8	+	1.86165e8i	−0.203504	+	0.232091i
$351$	5.77804e8	−	5.60949e8i	0.713191	−	0.692386i
$352$	1.73684e8	+	3.00830e8i	0.212257	+	0.367639i
$353$	1.43729e8	−	2.48947e8i	0.173914	−	0.301228i	−0.765871	−	0.642994i	$-0.777692\pi$
$353$	1.43729e8	−	2.48947e8i	0.173914	−	0.301228i	0.939785	+	0.341767i	$0.111025\pi$
$354$	−8.57433e8	+	2.25221e8i	−1.02728	+	0.269834i
$355$	9.31848e8	−	5.38002e8i	1.10547	−	0.638241i
$356$	7.44671e8			0.874761
$357$	2.16049e8	+	3.26758e8i	0.251312	+	0.380090i
$358$	4.68626e8			0.539803
$359$	3.87962e8	−	2.23990e8i	0.442546	−	0.255504i	−0.262131	−	0.965032i	$-0.584425\pi$
$359$	3.87962e8	−	2.23990e8i	0.442546	−	0.255504i	0.704677	+	0.709528i	$0.251092\pi$
$360$	−3.36323e8	+	5.69477e8i	−0.379925	+	0.643306i
$361$	−3.92787e8	+	6.80327e8i	−0.439422	+	0.761102i
$362$	−1.03262e7	−	1.78854e7i	−0.0114409	−	0.0198161i
$363$	−5.21690e8	+	5.16568e8i	−0.572453	+	0.566832i
$364$	−1.68320e8	−	4.95716e8i	−0.182929	−	0.538739i
$365$		−	5.16509e8i		−	0.555972i
$366$	5.77057e8	+	1.57677e8i	0.615226	+	0.168107i
$367$	−5.98195e8	−	3.45368e8i	−0.631701	−	0.364713i	0.149710	−	0.988730i	$-0.452166\pi$
$367$	−5.98195e8	−	3.45368e8i	−0.631701	−	0.364713i	−0.781410	+	0.624017i	$0.785499\pi$
$368$	1.16167e8	+	6.70691e7i	0.121511	+	0.0701544i
$369$	6.46626e8	−	3.64871e8i	0.669979	−	0.378048i
$370$			8.57407e8i			0.879997i
$371$	4.62278e7	+	1.36144e8i	0.0469996	+	0.138418i
$372$	−2.35039e8	−	2.37370e8i	−0.236723	−	0.239070i
$373$	−1.81997e8	−	3.15228e8i	−0.181586	−	0.314517i	0.760835	−	0.648946i	$-0.224790\pi$
$373$	−1.81997e8	−	3.15228e8i	−0.181586	−	0.314517i	−0.942421	+	0.334429i	$0.891456\pi$
$374$	−6.64557e7	+	1.15105e8i	−0.0656873	+	0.113774i
$375$	2.77492e8	+	1.05643e9i	0.271732	+	1.03451i
$376$	−9.87975e8	+	5.70408e8i	−0.958492	+	0.553386i
$377$	1.53638e9			1.47674
$378$	−3.73052e8	−	5.76499e8i	−0.355262	−	0.549006i
$379$	1.08976e9			1.02823			0.514117	−	0.857720i	$-0.328120\pi$
$379$	1.08976e9			1.02823			0.514117	+	0.857720i	$0.328120\pi$
$380$	1.34102e8	−	7.74235e7i	0.125369	−	0.0723820i
$381$	1.79835e8	+	6.84645e8i	0.166585	+	0.634203i
$382$	1.54865e8	−	2.68235e8i	0.142145	−	0.246203i
$383$	−8.81103e8	−	1.52611e9i	−0.801366	−	1.38801i	−0.918717	−	0.394916i	$-0.870774\pi$
$383$	−8.81103e8	−	1.52611e9i	−0.801366	−	1.38801i	0.117351	−	0.993090i	$-0.462560\pi$
$384$	−3.79204e8	−	3.82964e8i	−0.341754	−	0.345142i
$385$	2.36499e8	−	2.69721e8i	0.211211	−	0.240881i
$386$		−	5.94945e8i		−	0.526528i
$387$	6.78695e8	−	3.82966e8i	0.595232	−	0.335871i
$388$	2.13243e8	+	1.23116e8i	0.185338	+	0.107005i
$389$	6.07063e8	+	3.50488e8i	0.522890	+	0.301890i	0.738116	−	0.674674i	$-0.235716\pi$
$389$	6.07063e8	+	3.50488e8i	0.522890	+	0.301890i	−0.215227	+	0.976564i	$0.569049\pi$
$390$	5.33714e8	+	1.45834e8i	0.455599	+	0.124490i
$391$		−	7.55709e8i		−	0.639346i
$392$	−1.21576e9	+	1.60269e8i	−1.01940	+	0.134384i
$393$	2.74963e8	−	2.72263e8i	0.228508	−	0.226264i
$394$	−9.10161e7	−	1.57645e8i	−0.0749690	−	0.129850i
$395$	−7.56102e7	+	1.30961e8i	−0.0617292	+	0.106918i
$396$	−1.58588e8	+	2.68528e8i	−0.128332	+	0.217298i
$397$	−3.58805e8	+	2.07156e8i	−0.287801	+	0.166162i	−0.636950	−	0.770905i	$-0.719804\pi$
$397$	−3.58805e8	+	2.07156e8i	−0.287801	+	0.166162i	0.349149	+	0.937067i	$0.386471\pi$
$398$	−2.24079e8			−0.178160
$399$	2.67484e7	+	4.40838e8i	0.0210811	+	0.347435i
$400$	6.04189e7			0.0472023
$401$	−5.40563e8	+	3.12094e8i	−0.418640	+	0.241702i	−0.694495	−	0.719497i	$-0.744372\pi$
$401$	−5.40563e8	+	3.12094e8i	−0.418640	+	0.241702i	0.275855	+	0.961199i	$0.411039\pi$
$402$	−7.37927e8	+	1.93830e8i	−0.566529	+	0.148809i
$403$	−3.83837e8	+	6.64826e8i	−0.292132	+	0.505988i
$404$	4.65574e8	+	8.06398e8i	0.351281	+	0.608436i
$405$	−9.71206e8	−	1.91679e7i	−0.726472	−	0.0143378i
$406$	2.55467e8	−	1.28489e9i	0.189449	−	0.952852i
$407$			1.11064e9i			0.816567i
$408$	1.69415e8	−	6.20015e8i	0.123493	−	0.451951i
$409$	−5.20958e8	−	3.00775e8i	−0.376505	−	0.217375i	0.299791	−	0.954005i	$-0.403083\pi$
$409$	−5.20958e8	−	3.00775e8i	−0.376505	−	0.217375i	−0.676297	+	0.736629i	$0.736416\pi$
$410$	4.41764e8	+	2.55052e8i	0.316553	+	0.182762i
$411$	4.35696e8	−	1.59453e9i	0.309555	−	1.13289i
$412$			6.28803e8i			0.442970i
$413$	−2.20181e9	+	7.47622e8i	−1.53799	+	0.522224i
$414$	−1.30706e7	+	1.32466e9i	−0.00905302	+	0.917491i
$415$	−5.28226e8	−	9.14914e8i	−0.362786	−	0.628365i
$416$	−7.02640e8	+	1.21701e9i	−0.478527	+	0.828833i
$417$	1.54512e8	−	4.05855e7i	0.104349	−	0.0274091i
$418$	−1.29774e8	+	7.49253e7i	−0.0869105	+	0.0501778i
$419$	8.13509e8			0.540273			0.270136	−	0.962822i	$-0.412931\pi$
$419$	8.13509e8			0.540273			0.270136	+	0.962822i	$0.412931\pi$
$420$	−2.82040e8	+	5.64999e8i	−0.185754	+	0.372113i
$421$	−5.73076e8			−0.374304			−0.187152	−	0.982331i	$-0.559926\pi$
$421$	−5.73076e8			−0.374304			−0.187152	+	0.982331i	$0.559926\pi$
$422$	4.14862e8	−	2.39521e8i	0.268726	−	0.155149i
$423$	−1.44275e9	−	8.52062e8i	−0.926830	−	0.547369i
$424$	1.17957e8	−	2.04307e8i	0.0751522	−	0.130168i
$425$	−1.70194e8	−	2.94785e8i	−0.107543	−	0.186271i
$426$	1.30254e9	−	1.28975e9i	0.816314	−	0.808299i
$427$	1.53894e9	+	3.05977e8i	0.956586	+	0.190192i
$428$		−	3.62114e7i		−	0.0223250i
$429$	6.91343e8	+	1.88905e8i	0.422759	+	0.115516i
$430$	4.63673e8	+	2.67702e8i	0.281237	+	0.162372i
$431$	−1.83415e9	−	1.05895e9i	−1.10348	−	0.637094i	−0.166346	−	0.986067i	$-0.553197\pi$
$431$	−1.83415e9	−	1.05895e9i	−1.10348	−	0.637094i	−0.937133	+	0.348973i	$0.886530\pi$
$432$	−4.57596e7	+	1.61196e8i	−0.0273080	+	0.0961967i
$433$			1.49662e9i			0.885938i	0.896537	+	0.442969i	$0.146075\pi$
$433$			1.49662e9i			0.885938i	−0.896537	+	0.442969i	$0.853925\pi$
$434$	4.92178e8	+	4.31554e8i	0.289007	+	0.253409i
$435$	−1.30396e9	−	1.31689e9i	−0.759540	−	0.767072i
$436$	3.83885e8	+	6.64908e8i	0.221819	+	0.384201i
$437$	4.26012e8	−	7.37874e8i	0.244195	−	0.422958i
$438$	−2.23541e8	−	8.51038e8i	−0.127115	−	0.483938i
$439$	−5.81492e8	+	3.35725e8i	−0.328033	+	0.189390i	−0.654968	−	0.755657i	$-0.727318\pi$
$439$	−5.81492e8	+	3.35725e8i	−0.328033	+	0.189390i	0.326934	+	0.945047i	$0.393984\pi$
$440$	−5.88594e8			−0.329406
$441$	−1.08253e9	−	1.43946e9i	−0.601041	−	0.799218i
$442$	−5.37693e8			−0.296181
$443$	1.41709e9	−	8.18157e8i	0.774434	−	0.447119i	−0.0600203	−	0.998197i	$-0.519117\pi$
$443$	1.41709e9	−	8.18157e8i	0.774434	−	0.447119i	0.834454	+	0.551078i	$0.185783\pi$
$444$	−4.96702e8	−	1.89098e9i	−0.269312	−	1.02529i
$445$	−1.03214e9	+	1.78771e9i	−0.555235	+	0.961696i
$446$	−2.46849e8	−	4.27555e8i	−0.131753	−	0.228202i
$447$	−6.86810e8	−	6.93621e8i	−0.363714	−	0.367321i
$448$	1.04406e9	+	9.15458e8i	0.548596	+	0.481022i
$449$			1.40788e9i			0.734011i	0.930219	+	0.367005i	$0.119617\pi$
$449$			1.40788e9i			0.734011i	−0.930219	+	0.367005i	$0.880383\pi$
$450$	2.93229e8	+	5.19663e8i	0.151692	+	0.268830i
$451$	5.72236e8	+	3.30380e8i	0.293736	+	0.169588i
$452$	−4.00789e6	−	2.31396e6i	−0.00204141	−	0.00117861i
$453$	3.59726e9	+	9.82929e8i	1.81814	+	0.496797i
$454$			1.06133e9i			0.532300i
$455$	1.42335e9	+	2.82995e8i	0.708389	+	0.140844i
$456$	5.14934e8	−	5.09878e8i	0.254317	−	0.251820i
$457$	−5.66627e8	−	9.81427e8i	−0.277710	−	0.481007i	0.693106	−	0.720836i	$-0.256242\pi$
$457$	−5.66627e8	−	9.81427e8i	−0.277710	−	0.481007i	−0.970815	+	0.239829i	$0.922909\pi$
$458$	1.33942e9	−	2.31994e9i	0.651460	−	1.12836i
$459$	9.15379e8	−	2.30811e8i	0.441831	−	0.111407i
$460$	1.05504e9	−	6.09125e8i	0.505376	−	0.291779i
$461$	1.36884e9			0.650726			0.325363	−	0.945589i	$-0.394514\pi$
$461$	1.36884e9			0.650726			0.325363	+	0.945589i	$0.394514\pi$
$462$	2.72939e8	−	5.46768e8i	0.128771	−	0.257962i
$463$	1.03418e9			0.484241			0.242121	−	0.970246i	$-0.422157\pi$
$463$	1.03418e9			0.484241			0.242121	+	0.970246i	$0.422157\pi$
$464$	−2.76853e8	+	1.59841e8i	−0.128658	+	0.0742807i
$465$	8.95618e8	−	2.35251e8i	0.413083	−	0.108504i
$466$	−7.29202e8	+	1.26302e9i	−0.333808	+	0.578173i
$467$	8.87927e8	+	1.53794e9i	0.403430	+	0.698761i	0.994137	−	0.108124i	$-0.0344845\pi$
$467$	8.87927e8	+	1.53794e9i	0.403430	+	0.698761i	−0.590707	+	0.806886i	$0.701151\pi$
$468$	−1.26157e9	−	1.24481e7i	−0.568921	−	0.00561362i
$469$	−1.89493e9	+	6.43421e8i	−0.848178	+	0.287999i
$470$		−	1.15119e9i		−	0.511450i
$471$	−1.01802e9	+	3.72567e9i	−0.448933	+	1.64298i
$472$	3.30417e9	+	1.90766e9i	1.44632	+	0.835035i
$473$	6.00615e8	+	3.46765e8i	0.260965	+	0.150668i
$474$	−6.79023e7	+	2.48504e8i	−0.0292860	+	0.107179i
$475$		−	3.83771e8i		−	0.164303i
$476$	1.19674e8	−	6.01911e8i	0.0508599	−	0.255805i
$477$	3.46481e8	+	3.41878e6i	0.146172	+	0.00144230i
$478$	−3.07926e8	−	5.33344e8i	−0.128958	−	0.223362i
$479$	−1.30103e9	+	2.25346e9i	−0.540896	+	0.936860i	0.457957	+	0.888975i	$0.348582\pi$
$479$	−1.30103e9	+	2.25346e9i	−0.540896	+	0.936860i	−0.998853	+	0.0478853i	$0.984752\pi$
$480$	1.63949e9	−	4.30643e8i	0.676651	−	0.177735i
$481$	−3.89113e9	+	2.24654e9i	−1.59429	+	0.920464i
$482$	−1.62093e9			−0.659325
$483$	2.10441e8	+	3.46826e9i	0.0849799	+	1.40054i
$484$	1.15018e9			0.461114
$485$	−5.91122e8	+	3.41284e8i	−0.235278	+	0.135838i
$486$	−1.60853e9	+	3.88748e8i	−0.635626	+	0.153618i
$487$	1.62989e9	−	2.82305e9i	0.639449	−	1.10756i	−0.346105	−	0.938196i	$-0.612496\pi$
$487$	1.62989e9	−	2.82305e9i	0.639449	−	1.10756i	0.985554	−	0.169362i	$-0.0541708\pi$
$488$	−1.28727e9	−	2.22961e9i	−0.501417	−	0.868479i
$489$	1.61700e9	−	1.60112e9i	0.625358	−	0.619218i
$490$	4.73345e8	−	1.14331e9i	0.181757	−	0.439013i
$491$			9.35676e7i			0.0356730i	0.999841	+	0.0178365i	$0.00567784\pi$
$491$			9.35676e7i			0.0356730i	−0.999841	+	0.0178365i	$0.994322\pi$
$492$	−1.12205e9	−	3.06593e8i	−0.424751	−	0.116061i
$493$	1.55974e9	+	9.00516e8i	0.586257	+	0.338475i
$494$	−5.25003e8	−	3.03111e8i	−0.195938	−	0.113125i
$495$	−4.24840e8	−	7.52904e8i	−0.157437	−	0.279011i
$496$		−	1.59734e8i		−	0.0587776i
$497$	3.16979e9	−	3.61507e9i	1.15820	−	1.32090i
$498$	−1.26631e9	−	1.27887e9i	−0.459450	−	0.464005i
$499$	−1.78825e9	−	3.09734e9i	−0.644283	−	1.11593i	−0.984467	−	0.175571i	$-0.943823\pi$
$499$	−1.78825e9	−	3.09734e9i	−0.644283	−	1.11593i	0.340184	−	0.940359i	$-0.389511\pi$
$500$	8.55602e8	−	1.48195e9i	0.306109	−	0.530197i
$501$	−7.05686e8	−	2.68660e9i	−0.250715	−	0.954491i
$502$	4.47490e7	−	2.58359e7i	0.0157878	−	0.00911507i
$503$	−3.25287e9			−1.13967			−0.569835	−	0.821759i	$-0.692993\pi$
$503$	−3.25287e9			−1.13967			−0.569835	+	0.821759i	$0.692993\pi$
$504$	−6.04862e8	+	2.89268e9i	−0.210450	+	1.00645i
$505$	−2.58120e9			−0.891870
$506$	−1.02099e9	+	5.89470e8i	−0.350345	+	0.202272i
$507$	−8.91640e6	−	3.39454e7i	−0.00303852	−	0.0115679i
$508$	5.54491e8	−	9.60406e8i	0.187660	−	0.325036i
$509$	1.33800e9	+	2.31748e9i	0.449722	+	0.778941i	0.998368	−	0.0571140i	$-0.0181899\pi$
$509$	1.33800e9	+	2.31748e9i	0.449722	+	0.778941i	−0.548646	+	0.836055i	$0.684857\pi$
$510$	4.56352e8	+	4.60877e8i	0.152337	+	0.153847i
$511$	−7.42047e8	−	2.18538e9i	−0.246013	−	0.724527i
$512$		−	6.04668e8i		−	0.199100i
$513$	1.02389e9	+	2.90658e8i	0.334844	+	0.0950542i
$514$	1.65370e9	+	9.54764e8i	0.537138	+	0.310117i
$515$	−1.50955e9	−	8.71540e8i	−0.486993	−	0.281165i
$516$	−1.17770e9	−	3.21798e8i	−0.377363	−	0.103112i
$517$		−	1.49118e9i		−	0.474585i
$518$	1.23180e9	+	3.62775e9i	0.389392	+	1.14679i
$519$	−3.38298e9	+	3.34976e9i	−1.06222	+	1.05179i
$520$	−1.19058e9	−	2.06214e9i	−0.371318	−	0.643142i
$521$	−1.10364e9	+	1.91155e9i	−0.341896	+	0.592181i	−0.984785	−	0.173778i	$-0.944402\pi$
$521$	−1.10364e9	+	1.91155e9i	−0.341896	+	0.592181i	0.642889	+	0.765959i	$0.277736\pi$
$522$	−2.71844e9	−	1.60546e9i	−0.836512	−	0.494029i
$523$	−2.49597e9	+	1.44105e9i	−0.762929	+	0.440477i	−0.830346	−	0.557248i	$-0.811857\pi$
$523$	−2.49597e9	+	1.44105e9i	−0.762929	+	0.440477i	0.0674174	+	0.997725i	$0.478524\pi$
$524$	−6.06218e8			−0.184064
$525$	8.63181e8	+	1.30550e9i	0.260342	+	0.393748i
$526$	−9.79966e8			−0.293603
$527$	−7.79348e8	+	4.49957e8i	−0.231950	+	0.133916i
$528$	−1.44232e8	+	3.78853e7i	−0.0426426	+	0.0112009i
$529$	1.64921e9	−	2.85651e9i	0.484374	−	0.838960i
$530$	1.19029e8	+	2.06164e8i	0.0347286	+	0.0601517i
$531$	−5.52904e7	+	5.60348e9i	−0.0160258	+	1.62415i
$532$	4.56162e8	−	5.20243e8i	0.131349	−	0.149801i
$533$			2.67311e9i			0.764666i
$534$	−9.26917e8	+	3.39227e9i	−0.263419	+	0.964042i
$535$	8.69317e7	+	5.01900e7i	0.0245437	+	0.0141703i
$536$	2.84365e9	+	1.64178e9i	0.797625	+	0.460509i
$537$	7.80785e8	−	2.85747e9i	0.217581	−	0.796290i
$538$		−	3.36793e9i		−	0.932450i
$539$	6.13144e8	−	1.48098e9i	0.168656	−	0.407369i
$540$	1.06005e9	+	1.09191e9i	0.289701	+	0.298406i
$541$	−8.95243e8	−	1.55061e9i	−0.243081	−	0.421028i	0.718510	−	0.695517i	$-0.244825\pi$
$541$	−8.95243e8	−	1.55061e9i	−0.243081	−	0.421028i	−0.961590	+	0.274489i	$0.911491\pi$
$542$	2.04359e9	−	3.53961e9i	0.551312	−	0.954900i
$543$	−1.26262e8	+	3.31650e7i	−0.0338433	+	0.00888957i
$544$	−1.42665e9	+	8.23676e8i	−0.379945	+	0.219362i
$545$	−2.12830e9			−0.563178
$546$	2.46770e9	−	1.49731e8i	0.648810	−	0.0393674i
$547$	6.81952e9			1.78155			0.890776	−	0.454443i	$-0.150162\pi$
$547$	6.81952e9			1.78155			0.890776	+	0.454443i	$0.150162\pi$
$548$	−2.24270e9	+	1.29482e9i	−0.582156	+	0.336108i
$549$	1.92289e9	−	3.25592e9i	0.495965	−	0.839791i
$550$	−2.65511e8	+	4.59878e8i	−0.0680476	+	0.117862i
$551$	1.01529e9	+	1.75853e9i	0.258558	+	0.447835i
$552$	4.05121e9	−	4.01144e9i	1.02518	−	1.01511i
$553$	−1.31766e8	+	6.62730e8i	−0.0331334	+	0.166647i
$554$			3.88897e9i			0.971741i
$555$	5.22808e9	+	1.42854e9i	1.29813	+	0.354705i
$556$	−2.16747e8	−	1.25139e8i	−0.0534800	−	0.0308767i
$557$	−4.57836e9	−	2.64332e9i	−1.12258	−	0.648121i	−0.180521	−	0.983571i	$-0.557778\pi$
$557$	−4.57836e9	−	2.64332e9i	−1.12258	−	0.648121i	−0.942058	+	0.335450i	$0.891112\pi$
$558$	1.37387e9	−	7.75234e8i	0.334755	−	0.188892i
$559$			2.80568e9i			0.679355i
$560$	−2.85928e8	+	9.70867e7i	−0.0688016	+	0.0233616i
$561$	5.91133e8	+	5.96994e8i	0.141356	+	0.142758i
$562$	1.13274e9	+	1.96196e9i	0.269186	+	0.466243i
$563$	3.34695e9	−	5.79708e9i	0.790441	−	1.36908i	−0.135253	−	0.990811i	$-0.543185\pi$
$563$	3.34695e9	−	5.79708e9i	0.790441	−	1.36908i	0.925694	−	0.378273i	$-0.123482\pi$
$564$	6.66890e8	+	2.53890e9i	0.156523	+	0.595895i
$565$	1.11101e7	−	6.41442e6i	0.00259149	−	0.00149619i
$566$	4.11807e9			0.954632
$567$	−4.13678e9	+	1.31419e9i	−0.953063	+	0.302773i
$568$	−7.88891e9			−1.80633
$569$	1.43511e9	−	8.28559e8i	0.326581	−	0.188552i	−0.327741	−	0.944768i	$-0.606287\pi$
$569$	1.43511e9	−	8.28559e8i	0.326581	−	0.188552i	0.654322	+	0.756216i	$0.272954\pi$
$570$	1.85774e8	+	7.07257e8i	0.0420168	+	0.159961i
$571$	1.75946e7	−	3.04747e7i	0.00395506	−	0.00685036i	−0.864041	−	0.503421i	$-0.832074\pi$
$571$	1.75946e7	−	3.04747e7i	0.00395506	−	0.00685036i	0.867996	+	0.496571i	$0.165408\pi$
$572$	−5.61398e8	−	9.72370e8i	−0.125425	−	0.217243i
$573$	−1.37755e9	−	1.39121e9i	−0.305891	−	0.308924i
$574$	2.23556e9	+	4.44481e8i	0.493394	+	0.0980983i
$575$		−	3.01929e9i		−	0.662320i
$576$	2.91440e9	−	1.64451e9i	0.635435	−	0.358556i
$577$	5.92334e9	+	3.41984e9i	1.28366	+	0.741123i	0.977516	−	0.210861i	$-0.0676267\pi$
$577$	5.92334e9	+	3.41984e9i	1.28366	+	0.741123i	0.306147	+	0.951984i	$0.400960\pi$
$578$	2.08323e9	+	1.20275e9i	0.448734	+	0.259077i
$579$	−3.62771e9	−	9.91248e8i	−0.776707	−	0.212230i
$580$			2.90337e9i			0.617881i
$581$	−3.54938e9	−	3.11218e9i	−0.750820	−	0.658338i
$582$	−8.26272e8	+	8.18159e8i	−0.173737	+	0.172031i
$583$	1.54183e8	+	2.67054e8i	0.0322254	+	0.0558160i
$584$	−1.89344e9	+	3.27953e9i	−0.393374	+	0.681344i
$585$	1.77846e9	−	3.01137e9i	0.367281	−	0.621897i
$586$	1.03052e9	−	5.94973e8i	0.211552	−	0.122139i
$587$	3.21879e9			0.656839			0.328420	−	0.944532i	$-0.393484\pi$
$587$	3.21879e9			0.656839			0.328420	+	0.944532i	$0.393484\pi$
$588$	−3.81620e8	+	2.79575e9i	−0.0774124	+	0.567123i
$589$	−1.01461e9			−0.204594
$590$	−3.33421e9	+	1.92500e9i	−0.668360	+	0.385878i
$591$	−1.11289e9	+	2.92321e8i	−0.221766	+	0.0582510i
$592$	4.67450e8	−	8.09648e8i	0.0925997	−	0.160387i
$593$	7.68197e8	+	1.33056e9i	0.151280	+	0.262024i	0.931698	−	0.363233i	$-0.118327\pi$
$593$	7.68197e8	+	1.33056e9i	0.151280	+	0.262024i	−0.780418	+	0.625258i	$0.784994\pi$
$594$	−1.02585e9	−	1.05667e9i	−0.200831	−	0.206866i
$595$	1.27912e9	+	1.12157e9i	0.248944	+	0.218281i
$596$			1.52924e9i			0.295879i
$597$	−3.73343e8	+	1.36634e9i	−0.0718121	+	0.262813i
$598$	−4.13043e9	−	2.38470e9i	−0.789843	−	0.456016i
$599$	9.86828e8	+	5.69745e8i	0.187606	+	0.108315i	0.590862	−	0.806773i	$-0.298788\pi$
$599$	9.86828e8	+	5.69745e8i	0.187606	+	0.108315i	−0.403255	+	0.915088i	$0.632121\pi$
$600$	6.76866e8	−	2.47715e9i	0.127930	−	0.468191i
$601$		−	4.72513e9i		−	0.887878i	−0.896057	−	0.443939i	$-0.853581\pi$
$601$		−	4.72513e9i		−	0.887878i	0.896057	−	0.443939i	$-0.146419\pi$
$602$	2.34643e9	+	4.66525e8i	0.438348	+	0.0871539i
$603$	−4.75842e7	+	4.82249e9i	−0.00883797	+	0.895696i
$604$	−2.92112e9	−	5.05953e9i	−0.539411	−	0.934287i
$605$	−1.59419e9	+	2.76121e9i	−0.292682	+	0.506940i
$606$	−4.25298e9	+	1.11712e9i	−0.776317	+	0.203914i
$607$	−5.52426e8	+	3.18943e8i	−0.100257	+	0.0578832i	−0.549290	−	0.835632i	$-0.685102\pi$
$607$	−5.52426e8	+	3.18943e8i	−0.100257	+	0.0578832i	0.449033	+	0.893515i	$0.351768\pi$
$608$	−1.85731e9			−0.335136
$609$	−7.40905e9	−	3.69850e9i	−1.32924	−	0.663537i
$610$	2.59794e9			0.463419
$611$	5.22437e9	−	3.01629e9i	0.926594	−	0.534969i
$612$	−1.27346e9	−	7.52082e8i	−0.224572	−	0.132628i
$613$	−2.68130e9	+	4.64414e9i	−0.470147	+	0.814318i	−0.999417	−	0.0341354i	$-0.989132\pi$
$613$	−2.68130e9	+	4.64414e9i	−0.470147	+	0.814318i	0.529271	+	0.848453i	$0.322466\pi$
$614$	−6.52748e8	−	1.13059e9i	−0.113804	−	0.197114i
$615$	2.29122e9	−	2.26873e9i	0.397196	−	0.393296i
$616$	−2.49038e9	+	8.45608e8i	−0.429273	+	0.145759i
$617$		−	9.68182e9i		−	1.65943i	−0.558187	−	0.829715i	$-0.688503\pi$
$617$		−	9.68182e9i		−	1.65943i	0.558187	−	0.829715i	$-0.311497\pi$
$618$	−2.86445e9	−	7.82692e8i	−0.488181	−	0.133392i
$619$	−2.58436e8	−	1.49208e8i	−0.0437961	−	0.0252857i	0.477942	−	0.878391i	$-0.341383\pi$
$619$	−2.58436e8	−	1.49208e8i	−0.0437961	−	0.0252857i	−0.521738	+	0.853106i	$0.674716\pi$
$620$	−1.25636e9	−	7.25357e8i	−0.211710	−	0.122231i
$621$	8.05538e9	+	2.28673e9i	1.34979	+	0.383173i
$622$			5.23184e9i			0.871743i
$623$	−1.79871e9	+	9.04677e9i	−0.298025	+	1.49894i
$624$	−4.24478e8	−	4.28687e8i	−0.0699373	−	0.0706308i
$625$	9.31246e8	+	1.61297e9i	0.152575	+	0.264268i
$626$	−1.90386e9	+	3.29758e9i	−0.310188	+	0.537262i
$627$	2.40641e8	+	9.16141e8i	0.0389883	+	0.148431i
$628$	5.24013e9	−	3.02539e9i	0.844275	−	0.487442i
$629$	−5.26706e9			−0.843900
$630$	−2.22273e9	−	1.98808e9i	−0.354156	−	0.316768i
$631$	3.70007e9			0.586282			0.293141	−	0.956069i	$-0.405299\pi$
$631$	3.70007e9			0.586282			0.293141	+	0.956069i	$0.405299\pi$
$632$	9.60161e8	−	5.54349e8i	0.151298	−	0.0873521i
$633$	−7.69280e8	−	2.92871e9i	−0.120551	−	0.458948i
$634$	−3.00188e9	+	5.19940e9i	−0.467822	+	0.810291i
$635$	1.53708e9	+	2.66230e9i	0.238226	+	0.412619i
$636$	−3.81947e8	−	3.85734e8i	−0.0588713	−	0.0594550i
$637$	6.42886e9	−	8.47495e8i	0.985476	−	0.129912i
$638$		−	2.80969e9i		−	0.428337i
$639$	−5.69413e9	−	1.00912e10i	−0.863325	−	1.52999i
$640$	−2.02696e9	−	1.17027e9i	−0.305643	−	0.176463i
$641$	−9.30690e8	−	5.37334e8i	−0.139573	−	0.0805826i	0.428587	−	0.903500i	$-0.359011\pi$
$641$	−9.30690e8	−	5.37334e8i	−0.139573	−	0.0805826i	−0.568161	+	0.822918i	$0.692345\pi$
$642$	1.64957e8	+	4.50735e7i	0.0246036	+	0.00672278i
$643$			5.89391e9i			0.874309i	0.899386	+	0.437155i	$0.144014\pi$
$643$			5.89391e9i			0.874309i	−0.899386	+	0.437155i	$0.855986\pi$
$644$	3.58882e9	−	4.09298e9i	0.529482	−	0.603863i
$645$	2.40486e9	−	2.38124e9i	0.352882	−	0.349418i
$646$	−3.55324e8	−	6.15440e8i	−0.0518574	−	0.0898197i
$647$	−3.42510e9	+	5.93245e9i	−0.497174	+	0.861130i	−0.999995	−	0.00326023i	$-0.998962\pi$
$647$	−3.42510e9	+	5.93245e9i	−0.497174	+	0.861130i	0.502821	+	0.864391i	$0.332296\pi$
$648$	6.09632e9	+	3.68198e9i	0.880147	+	0.531581i
$649$	−4.31894e9	+	2.49354e9i	−0.620185	+	0.358064i
$650$	−2.14825e9			−0.306823
$651$	3.45145e9	−	2.28206e9i	0.490307	−	0.324186i
$652$	−3.56504e9			−0.503730
$653$	2.32858e9	−	1.34441e9i	0.327261	−	0.188944i	−0.327363	−	0.944899i	$-0.606160\pi$
$653$	2.32858e9	−	1.34441e9i	0.327261	−	0.188944i	0.654625	+	0.755954i	$0.272827\pi$
$654$	−3.50675e9	+	9.21114e8i	−0.490211	+	0.128763i
$655$	8.40236e8	−	1.45533e9i	0.116831	−	0.202357i
$656$	−2.78104e8	−	4.81691e8i	−0.0384631	−	0.0666200i
$657$	−5.56169e9	−	5.48780e7i	−0.765118	−	0.00754953i
$658$	−1.65386e9	−	4.87075e9i	−0.226313	−	0.666508i
$659$		−	7.57949e9i		−	1.03167i	−0.856688	−	0.515835i	$-0.827482\pi$
$659$		−	7.57949e9i		−	1.03167i	0.856688	−	0.515835i	$-0.172518\pi$
$660$	−3.56984e8	+	1.30647e9i	−0.0483332	+	0.176887i
$661$	−1.05293e10	−	6.07911e9i	−1.41806	−	0.818720i	−0.421935	−	0.906626i	$-0.638649\pi$
$661$	−1.05293e10	−	6.07911e9i	−1.41806	−	0.818720i	−0.996129	+	0.0879063i	$0.971982\pi$
$662$	−4.59658e8	−	2.65384e8i	−0.0615789	−	0.0355526i
$663$	−8.95860e8	+	3.27861e9i	−0.119383	+	0.436910i
$664$			7.74555e9i			1.02675i
$665$	6.16679e8	+	1.81617e9i	0.0813174	+	0.239486i
$666$	9.23244e9	+	9.10979e7i	1.21104	+	0.0119495i
$667$	7.98769e9	+	1.38351e10i	1.04227	+	1.80527i
$668$	−2.17587e9	+	3.76872e9i	−0.282433	+	0.489188i
$669$	−3.01832e9	+	7.92817e8i	−0.389738	+	0.102372i
$670$	−2.86950e9	+	1.65670e9i	−0.368590	+	0.212806i
$671$	3.36522e9			0.430016
$672$	6.31811e9	−	4.17747e9i	0.803147	−	0.531032i
$673$	1.01796e10			1.28729			0.643647	−	0.765323i	$-0.277421\pi$
$673$	1.01796e10			1.28729			0.643647	+	0.765323i	$0.277421\pi$
$674$	5.26977e8	−	3.04250e8i	0.0662952	−	0.0382755i
$675$	3.65722e9	−	9.22161e8i	0.457708	−	0.115410i
$676$	−2.74923e7	+	4.76180e7i	−0.00342292	+	0.00592867i
$677$	−2.54214e9	−	4.40311e9i	−0.314875	−	0.545380i	0.664536	−	0.747256i	$-0.268629\pi$
$677$	−2.54214e9	−	4.40311e9i	−0.314875	−	0.545380i	−0.979411	+	0.201877i	$0.935296\pi$
$678$	1.55297e7	−	1.53773e7i	0.00191364	−	0.00189485i
$679$	−2.01077e9	+	2.29324e9i	−0.246501	+	0.281129i
$680$		−	2.79133e9i		−	0.340432i
$681$	6.47154e9	+	1.76831e9i	0.785222	+	0.214557i
$682$	1.21582e9	+	7.01953e8i	0.146765	+	0.0847349i
$683$	1.13512e10	+	6.55362e9i	1.36323	+	0.787061i	0.990052	−	0.140699i	$-0.0449349\pi$
$683$	1.13512e10	+	6.55362e9i	1.36323	+	0.787061i	0.373178	+	0.927760i	$0.378268\pi$
$684$	−8.19438e8	−	1.45221e9i	−0.0979083	−	0.173514i
$685$		−	7.17866e9i		−	0.853348i
$686$	3.60210e8	−	5.51746e9i	0.0426012	−	0.652536i
$687$	−1.19143e10	−	1.20325e10i	−1.40191	−	1.41581i
$688$	−2.91897e8	−	5.05580e8i	−0.0341719	−	0.0591876i
$689$	−6.23750e8	+	1.08037e9i	−0.0726512	+	0.125836i
$690$	1.46157e9	+	5.56430e9i	0.169374	+	0.644820i
$691$	4.26203e9	−	2.46068e9i	0.491409	−	0.283715i	−0.233750	−	0.972297i	$-0.575100\pi$
$691$	4.26203e9	−	2.46068e9i	0.491409	−	0.283715i	0.725159	+	0.688582i	$0.241766\pi$
$692$	7.45854e9			0.855623
$693$	−2.87920e9	−	2.57524e9i	−0.328628	−	0.293935i
$694$	6.57067e8			0.0746194
$695$	6.00836e8	−	3.46893e8i	0.0678905	−	0.0391966i
$696$	3.45187e9	+	1.31415e10i	0.388081	+	1.47745i
$697$	−1.56679e9	+	2.71376e9i	−0.175265	+	0.303568i
$698$	4.89799e8	+	8.48357e8i	0.0545160	+	0.0944245i
$699$	6.48636e9	+	6.55068e9i	0.718341	+	0.725464i
$700$	4.78135e8	−	2.40482e9i	0.0526875	−	0.264996i
$701$			7.59763e9i			0.833039i	0.909127	+	0.416519i	$0.136750\pi$
$701$			7.59763e9i			0.833039i	−0.909127	+	0.416519i	$0.863250\pi$
$702$	1.62703e9	−	5.73147e9i	0.177507	−	0.625296i
$703$	−5.14275e9	−	2.96917e9i	−0.558280	−	0.322323i
$704$	2.57912e9	+	1.48905e9i	0.278591	+	0.160845i
$705$	−7.01941e9	−	1.91801e9i	−0.754465	−	0.206153i
$706$		−	2.12671e9i		−	0.227453i
$707$	−1.09212e10	+	3.70830e9i	−1.16226	+	0.394646i
$708$	6.23832e9	−	6.17707e9i	0.660619	−	0.654133i
$709$	3.94437e9	+	6.83184e9i	0.415638	+	0.719906i	0.995495	−	0.0948119i	$-0.0302250\pi$
$709$	3.94437e9	+	6.83184e9i	0.415638	+	0.719906i	−0.579857	+	0.814718i	$0.696892\pi$
$710$	3.98031e9	−	6.89411e9i	0.417362	−	0.722893i
$711$	1.40213e9	+	8.28074e8i	0.146300	+	0.0864024i
$712$	1.31069e10	−	7.56728e9i	1.36088	−	0.785706i
$713$	−7.98235e9			−0.824740
$714$	2.59298e9	+	1.29438e9i	0.266597	+	0.133082i
$715$	3.11246e9			0.318443
$716$	−4.01901e9	+	2.32038e9i	−0.409189	+	0.236245i
$717$	−3.76513e9	+	9.88981e8i	−0.381472	+	0.100201i
$718$	1.65715e9	−	2.87027e9i	0.167081	−	0.289392i
$719$	1.75089e9	+	3.03262e9i	0.175674	+	0.304276i	0.940394	−	0.340086i	$-0.110456\pi$
$719$	1.75089e9	+	3.03262e9i	0.175674	+	0.304276i	−0.764721	+	0.644362i	$0.777123\pi$
$720$	−7.18004e6	+	7.27672e8i	−0.000716908	+	0.0726561i
$721$	−7.63912e9	−	1.51884e9i	−0.759050	−	0.150917i
$722$			5.81193e9i			0.574699i
$723$	−2.70066e9	+	9.88369e9i	−0.265757	+	0.972602i
$724$	1.77118e8	+	1.02259e8i	0.0173451	+	0.0100142i
$725$	6.23164e9	+	3.59784e9i	0.607323	+	0.350638i
$726$	−1.43167e9	+	5.23954e9i	−0.138856	+	0.508177i
$727$		−	2.03022e10i		−	1.95962i	−0.199923	−	0.979812i	$-0.564069\pi$
$727$		−	2.03022e10i		−	1.95962i	0.199923	−	0.979812i	$-0.435931\pi$
$728$	−8.00002e9	−	7.01462e9i	−0.768478	−	0.673820i
$729$	−3.09586e8	+	1.04558e10i	−0.0295962	+	0.999562i
$730$	−1.91065e9	−	3.30934e9i	−0.181782	−	0.314856i
$731$	−1.64449e9	+	2.84834e9i	−0.155712	+	0.269700i
$732$	−5.72967e9	+	1.50500e9i	−0.539934	+	0.141824i
$733$	−3.06543e9	+	1.76982e9i	−0.287493	+	0.165984i	−0.636811	−	0.771020i	$-0.719747\pi$
$733$	−3.06543e9	+	1.76982e9i	−0.287493	+	0.165984i	0.349318	+	0.937004i	$0.386413\pi$
$734$	−5.11028e9			−0.476990
$735$	−6.18274e9	−	4.79113e9i	−0.574348	−	0.445074i
$736$	−1.46122e10			−1.35097
$737$	−3.71698e9	+	2.14600e9i	−0.342022	+	0.197467i
$738$	2.79330e9	−	4.72975e9i	0.255812	−	0.433153i
$739$	−6.63405e8	+	1.14905e9i	−0.0604677	+	0.104733i	−0.894675	−	0.446719i	$-0.852593\pi$
$739$	−6.63405e8	+	1.14905e9i	−0.0604677	+	0.104733i	0.834207	+	0.551452i	$0.185926\pi$
$740$	−4.24541e9	−	7.35327e9i	−0.385131	−	0.667067i
$741$	−2.72295e9	+	2.69621e9i	−0.245853	+	0.243439i
$742$	7.99808e8	+	7.01291e8i	0.0718740	+	0.0630209i
$743$			5.32031e9i			0.475857i	0.971283	+	0.237928i	$0.0764683\pi$
$743$			5.32031e9i			0.475857i	−0.971283	+	0.237928i	$0.923532\pi$
$744$	−6.54904e9	−	1.78949e9i	−0.583005	−	0.159303i
$745$	−3.67121e9	−	2.11958e9i	−0.325284	−	0.187803i
$746$	−2.33216e9	−	1.34647e9i	−0.205670	−	0.118744i
$747$	−9.90778e9	+	5.59065e9i	−0.869670	+	0.490727i
$748$		−	1.31621e9i		−	0.114992i
$749$	4.39920e8	+	8.74664e7i	0.0382549	+	0.00760598i
$750$	5.68585e9	+	5.74223e9i	0.492131	+	0.497011i
$751$	−3.08077e9	−	5.33605e9i	−0.265411	−	0.459706i	0.702260	−	0.711921i	$-0.252174\pi$
$751$	−3.08077e9	−	5.33605e9i	−0.265411	−	0.459706i	−0.967671	+	0.252215i	$0.918841\pi$
$752$	−6.27616e8	+	1.08706e9i	−0.0538185	+	0.0932164i
$753$	−8.29782e7	−	3.15905e8i	−0.00708242	−	0.0269633i
$754$	9.84377e9	−	5.68331e9i	0.836300	−	0.482838i
$755$	1.61950e10			1.36952
$756$	6.05386e9	+	3.09700e9i	0.509573	+	0.260684i
$757$	−4.11040e9			−0.344388			−0.172194	−	0.985063i	$-0.555086\pi$
$757$	−4.11040e9			−0.344388			−0.172194	+	0.985063i	$0.555086\pi$
$758$	6.98221e9	−	4.03118e9i	0.582305	−	0.336194i
$759$	1.89323e9	+	7.20768e9i	0.157165	+	0.598342i
$760$	1.57354e9	−	2.72546e9i	0.130026	−	0.225212i
$761$	−2.24277e9	−	3.88460e9i	−0.184476	−	0.319521i	0.758924	−	0.651179i	$-0.225725\pi$
$761$	−2.24277e9	−	3.88460e9i	−0.184476	−	0.319521i	−0.943400	+	0.331658i	$0.892392\pi$
$762$	3.68484e9	+	3.72137e9i	0.301700	+	0.304692i
$763$	−9.00500e9	+	3.05765e9i	−0.733919	+	0.249202i
$764$			3.06724e9i			0.248840i
$765$	3.57056e9	−	2.01475e9i	0.288351	−	0.162707i
$766$	−1.12907e10	−	6.51868e9i	−0.907653	−	0.524034i
$767$	−1.74723e10	−	1.00876e10i	−1.39819	−	0.807246i
$768$	−1.26816e10	−	3.46516e9i	−1.01020	−	0.276032i
$769$		−	1.62822e9i		−	0.129114i	−0.997914	−	0.0645568i	$-0.979437\pi$
$769$		−	1.62822e9i		−	0.129114i	0.997914	−	0.0645568i	$-0.0205634\pi$
$770$	5.17535e8	−	2.60299e9i	0.0408528	−	0.205473i
$771$	8.57698e9	−	8.49277e9i	0.673975	−	0.667358i
$772$	2.94584e9	+	5.10235e9i	0.230435	+	0.399125i
$773$	9.50104e9	−	1.64563e10i	0.739849	−	1.28146i	−0.212714	−	0.977115i	$-0.568230\pi$
$773$	9.50104e9	−	1.64563e10i	0.739849	−	1.28146i	0.952563	−	0.304342i	$-0.0984364\pi$
$774$	2.93184e9	−	4.96432e9i	0.227272	−	0.384828i
$775$	−3.11374e9	+	1.79772e9i	−0.240285	+	0.138728i
$776$	5.00437e9			0.384444
$777$	2.41727e10	−	1.46671e9i	1.84864	−	0.112169i
$778$	5.18604e9			0.394828
$779$	−3.05962e9	+	1.76647e9i	−0.231892	+	0.133883i
$780$	−5.29931e9	+	1.39196e9i	−0.399842	+	0.105026i
$781$	5.15588e9	−	8.93024e9i	0.387279	−	0.670787i
$782$	−2.79549e9	−	4.84193e9i	−0.209042	−	0.362072i
$783$	−1.43186e10	+	1.39009e10i	−1.06594	+	1.03485i
$784$	−1.07030e9	+	8.21562e8i	−0.0793231	+	0.0608883i
$785$			1.67731e10i			1.23757i
$786$	7.54579e8	−	2.76156e9i	0.0554276	−	0.202850i
$787$	5.57282e9	+	3.21747e9i	0.407534	+	0.235290i	0.689730	−	0.724067i	$-0.257729\pi$
$787$	5.57282e9	+	3.21747e9i	0.407534	+	0.235290i	−0.282196	+	0.959357i	$0.591063\pi$
$788$	1.56114e9	+	9.01324e8i	0.113658	+	0.0656204i
$789$	−1.63274e9	+	5.97539e9i	−0.118344	+	0.433109i
$790$			1.11878e9i			0.0807326i
$791$	3.77923e7	−	4.31013e7i	0.00271510	−	0.00309651i
$792$	−6.25369e7	+	6.33790e9i	−0.00447300	+	0.453322i
$793$	6.80700e9	+	1.17901e10i	0.484730	+	0.839577i
$794$	−1.53261e9	+	2.65456e9i	−0.108657	+	0.188200i
$795$	1.45541e9	−	3.82291e8i	0.102731	−	0.0269842i
$796$	1.92174e9	−	1.10952e9i	0.135052	−	0.0779720i
$797$	1.31128e10			0.917468			0.458734	−	0.888574i	$-0.348303\pi$
$797$	1.31128e10			0.917468			0.458734	+	0.888574i	$0.348303\pi$
$798$	1.80211e9	+	2.72556e9i	0.125537	+	0.189865i
$799$	7.07175e9			0.490470
$800$	−5.69991e9	+	3.29084e9i	−0.393598	+	0.227244i
$801$	1.91402e10	+	1.13038e10i	1.31593	+	0.777163i
$802$	−2.30897e9	+	3.99926e9i	−0.158055	+	0.273760i
$803$	−2.47495e9	−	4.28673e9i	−0.168679	−	0.292161i
$804$	5.36884e9	−	5.31613e9i	0.364321	−	0.360744i
$805$	4.85168e9	+	1.42886e10i	0.327798	+	0.965392i
$806$			5.67950e9i			0.382065i
$807$	−2.05361e10	−	5.61137e9i	−1.37550	−	0.375848i
$808$	1.63891e10	+	9.46225e9i	1.09299	+	0.631037i
$809$	1.00071e10	+	5.77760e9i	0.664490	+	0.383643i	0.793986	−	0.607937i	$-0.208003\pi$
$809$	1.00071e10	+	5.77760e9i	0.664490	+	0.383643i	−0.129496	+	0.991580i	$0.541336\pi$
$810$	−6.29355e9	+	3.46983e9i	−0.416100	+	0.229409i
$811$			1.69436e9i			0.111541i	0.998444	+	0.0557703i	$0.0177615\pi$
$811$			1.69436e9i			0.111541i	−0.998444	+	0.0557703i	$0.982239\pi$
$812$	4.17116e9	+	1.22844e10i	0.273407	+	0.805206i
$813$	−1.81781e10	−	1.83583e10i	−1.18640	−	1.19816i
$814$	4.10842e9	+	7.11600e9i	0.266987	+	0.462435i
$815$	4.94125e9	−	8.55849e9i	0.319731	−	0.553791i
$816$	−1.79666e8	−	6.84004e8i	−0.0115758	−	0.0440700i
$817$	−3.21136e9	+	1.85408e9i	−0.206021	+	0.118946i
$818$	−4.45046e9			−0.284295
$819$	3.19848e9	−	1.52964e10i	0.203446	−	0.972959i
$820$	−5.05152e9			−0.319943
$821$	2.08588e10	−	1.20428e10i	1.31549	−	0.759500i	0.332492	−	0.943106i	$-0.392110\pi$
$821$	2.08588e10	−	1.20428e10i	1.31549	−	0.759500i	0.983000	+	0.183606i	$0.0587771\pi$
$822$	−3.10687e9	−	1.18281e10i	−0.195106	−	0.742786i
$823$	9.37342e9	−	1.62352e10i	0.586136	−	1.01522i	−0.408597	−	0.912715i	$-0.633982\pi$
$823$	9.37342e9	−	1.62352e10i	0.586136	−	1.01522i	0.994733	−	0.102502i	$-0.0326849\pi$
$824$	6.38984e9	+	1.10675e10i	0.397873	+	0.689137i
$825$	2.36176e9	+	2.38518e9i	0.146436	+	0.147888i
$826$	−1.13417e10	+	1.29349e10i	−0.700241	+	0.798610i
$827$		−	1.55760e10i		−	0.957605i	−0.877923	−	0.478803i	$-0.841071\pi$
$827$		−	1.55760e10i		−	0.957605i	0.877923	−	0.478803i	$-0.158929\pi$
$828$	−6.44688e9	−	1.14252e10i	−0.394678	−	0.699451i
$829$	7.07215e9	+	4.08311e9i	0.431132	+	0.248914i	0.699829	−	0.714311i	$-0.253260\pi$
$829$	7.07215e9	+	4.08311e9i	0.431132	+	0.248914i	−0.268697	+	0.963225i	$0.586593\pi$
$830$	−6.76882e9	−	3.90798e9i	−0.410904	−	0.237235i
$831$	2.37132e10	+	6.47948e9i	1.43346	+	0.391685i
$832$			1.20480e10i			0.725240i
$833$	7.02336e9	+	2.90776e9i	0.421005	+	0.174302i
$834$	8.39849e8	−	8.31603e8i	0.0501326	−	0.0496404i
$835$	−6.03164e9	−	1.04471e10i	−0.358536	−	0.621002i
$836$	7.41978e8	−	1.28514e9i	0.0439207	−	0.0760729i
$837$	−2.43799e9	−	9.66889e9i	−0.143712	−	0.569951i
$838$	5.21226e9	−	3.00930e9i	0.305965	−	0.176649i
$839$	−1.89484e10			−1.10766			−0.553830	−	0.832630i	$-0.686834\pi$
$839$	−1.89484e10			−1.10766			−0.553830	+	0.832630i	$0.686834\pi$
$840$	7.77299e8	+	1.28106e10i	0.0452492	+	0.745747i
$841$	−2.08232e10			−1.20715
$842$	−3.67177e9	+	2.11990e9i	−0.211974	+	0.122384i
$843$	1.38504e10	−	3.63807e9i	0.796280	−	0.209158i
$844$	−2.37195e9	+	4.10834e9i	−0.135802	+	0.235216i
$845$	−7.62102e7	−	1.32000e8i	−0.00434525	−	0.00752619i
$846$	−1.23958e10	−	1.22311e8i	−0.703848	−	0.00694497i
$847$	−2.77820e9	+	1.39732e10i	−0.157098	+	0.790140i
$848$		−	2.59574e8i		−	0.0146176i
$849$	6.86119e9	−	2.51101e10i	0.384789	−	1.40822i
$850$	−2.18092e9	−	1.25915e9i	−0.121807	−	0.0703254i
$851$	−4.04603e10	−	2.33598e10i	−2.25048	−	1.29932i
$852$	−4.78465e9	+	1.75106e10i	−0.265040	+	0.969977i
$853$		−	9.10063e9i		−	0.502053i	−0.967980	−	0.251027i	$-0.919232\pi$
$853$		−	9.10063e9i		−	0.502053i	0.967980	−	0.251027i	$-0.0807682\pi$
$854$	1.09921e10	−	3.73235e9i	0.603915	−	0.205059i
$855$	4.62205e9	+	4.56065e7i	0.252903	+	0.00249543i
$856$	−3.67977e8	−	6.37355e8i	−0.0200522	−	0.0347315i
$857$	−6.53138e9	+	1.13127e10i	−0.354464	+	0.613950i	−0.987026	−	0.160560i	$-0.948670\pi$
$857$	−6.53138e9	+	1.13127e10i	−0.354464	+	0.613950i	0.632562	+	0.774510i	$0.282003\pi$
$858$	5.12832e9	−	1.34705e9i	0.277185	−	0.0728077i
$859$	1.67085e10	−	9.64667e9i	0.899419	−	0.519280i	0.0224075	−	0.999749i	$-0.492867\pi$
$859$	1.67085e10	−	9.64667e9i	0.899419	−	0.519280i	0.877012	+	0.480469i	$0.159534\pi$
$860$	−5.30204e9			−0.284249
$861$	6.43494e9	−	1.28909e10i	0.343585	−	0.688289i
$862$	−1.56688e10			−0.833224
$863$	−2.72330e10	+	1.57230e10i	−1.44231	+	0.832716i	−0.998003	−	0.0631611i	$-0.979882\pi$
$863$	−2.72330e10	+	1.57230e10i	−1.44231	+	0.832716i	−0.444303	+	0.895877i	$0.646548\pi$
$864$	−4.46291e9	−	1.76996e10i	−0.235407	−	0.933608i
$865$	−1.03378e10	+	1.79055e10i	−0.543088	+	0.940655i
$866$	5.53623e9	+	9.58903e9i	0.289669	+	0.501721i
$867$	1.08047e10	−	1.06986e10i	0.563050	−	0.557522i
$868$	−6.35782e9	−	1.26408e9i	−0.329981	−	0.0656080i
$869$			1.44920e9i			0.0749134i
$870$	−1.32260e10	−	3.61392e9i	−0.680944	−	0.186064i
$871$	−1.50371e10	−	8.68166e9i	−0.771081	−	0.445184i
$872$	1.35135e10	+	7.80201e9i	0.690175	+	0.398473i
$873$	3.61210e9	+	6.40138e9i	0.183742	+	0.325629i
$874$		−	6.30354e9i		−	0.319370i
$875$	1.59370e10	+	1.39740e10i	0.804227	+	0.705167i
$876$	6.13100e9	+	6.19179e9i	0.308153	+	0.311209i
$877$	9.22119e9	+	1.59716e10i	0.461624	+	0.799556i	0.999042	−	0.0437597i	$-0.0139336\pi$
$877$	9.22119e9	+	1.59716e10i	0.461624	+	0.799556i	−0.537418	+	0.843316i	$0.680600\pi$
$878$	−2.48380e9	+	4.30206e9i	−0.123847	+	0.214509i
$879$	−1.91090e9	−	7.27496e9i	−0.0949025	−	0.361301i
$880$	−5.60861e8	+	3.23813e8i	−0.0277438	+	0.0160179i
$881$	−2.28663e10			−1.12663			−0.563314	−	0.826243i	$-0.690474\pi$
$881$	−2.28663e10			−1.12663			−0.563314	+	0.826243i	$0.690474\pi$
$882$	−1.22607e10	−	5.21839e9i	−0.601694	−	0.256092i
$883$	9.87721e9			0.482805			0.241402	−	0.970425i	$-0.422393\pi$
$883$	9.87721e9			0.482805			0.241402	+	0.970425i	$0.422393\pi$
$884$	4.61135e9	−	2.66236e9i	0.224515	−	0.129624i
$885$	6.18263e9	+	2.35378e10i	0.299828	+	1.14147i
$886$	6.05299e9	−	1.04841e10i	0.292383	−	0.506422i
$887$	1.38028e10	+	2.39071e10i	0.664099	+	1.15025i	0.979529	+	0.201305i	$0.0645182\pi$
$887$	1.38028e10	+	2.39071e10i	0.664099	+	1.15025i	−0.315429	+	0.948949i	$0.602148\pi$
$888$	−2.79585e10	−	2.82357e10i	−1.33989	−	1.35317i
$889$	1.03283e10	+	9.05613e9i	0.493030	+	0.432301i
$890$			1.52722e10i			0.726165i
$891$	−8.15231e9	+	4.49463e9i	−0.386108	+	0.212874i
$892$	4.23403e9	+	2.44452e9i	0.199746	+	0.115323i
$893$	6.90485e9	+	3.98651e9i	0.324470	+	0.187333i
$894$	−6.96630e9	−	1.90350e9i	−0.326078	−	0.0890987i
$895$		−	1.28644e10i		−	0.599805i
$896$	−1.02575e10	−	2.03943e9i	−0.476390	−	0.0947175i
$897$	−2.14226e10	+	2.12123e10i	−0.991058	+	0.981328i
$898$	5.20796e9	+	9.02045e9i	0.239994	+	0.415682i
$899$	9.51190e9	−	1.64751e10i	0.436625	−	0.756256i
$900$	−5.08787e9	−	3.00480e9i	−0.232641	−	0.137394i
$901$	−1.26647e9	+	7.31196e8i	−0.0576843	+	0.0333040i
$902$	4.88852e9			0.221796
$903$	6.75408e9	−	1.35302e10i	0.305252	−	0.611499i
$904$	−9.40569e7			−0.00423449
$905$	−4.90981e8	+	2.83468e8i	−0.0220188	+	0.0127126i
$906$	2.66841e10	−	7.00908e9i	1.19208	−	0.313121i
$907$	−7.28171e9	+	1.26123e10i	−0.324047	+	0.561266i	−0.981319	−	0.192388i	$-0.938377\pi$
$907$	−7.28171e9	+	1.26123e10i	−0.324047	+	0.561266i	0.657272	+	0.753653i	$0.271710\pi$
$908$	−5.25514e9	−	9.10218e9i	−0.232961	−	0.403501i
$909$	−2.74247e8	+	2.77940e10i	−0.0121107	+	1.22738i
$910$	1.01664e10	−	3.45201e9i	0.447223	−	0.151854i
$911$		−	1.79017e10i		−	0.784478i	−0.919863	−	0.392239i	$-0.871701\pi$
$911$		−	1.79017e10i		−	0.784478i	0.919863	−	0.392239i	$-0.128299\pi$
$912$	2.10164e8	−	7.69144e8i	0.00917436	−	0.0335757i
$913$	−8.76795e9	−	5.06218e9i	−0.381286	−	0.220135i
$914$	−7.26091e9	−	4.19209e9i	−0.314543	−	0.181601i
$915$	4.32847e9	−	1.58410e10i	0.186793	−	0.683612i
$916$			2.65283e10i			1.14045i
$917$	1.46428e9	−	7.36474e9i	0.0627093	−	0.315402i
$918$	5.01115e9	−	4.86497e9i	0.213790	−	0.207554i
$919$	−9.87387e9	−	1.71021e10i	−0.419646	−	0.726849i	0.576258	−	0.817268i	$-0.304513\pi$
$919$	−9.87387e9	−	1.71021e10i	−0.419646	−	0.726849i	−0.995904	+	0.0904196i	$0.971179\pi$
$920$	1.23797e10	−	2.14423e10i	0.524148	−	0.907852i
$921$	−7.98140e9	+	2.09646e9i	−0.336644	+	0.0884257i
$922$	8.77031e9	−	5.06354e9i	0.368516	−	0.212763i
$923$	4.17162e10			1.74622
$924$	3.66523e8	+	6.04062e9i	0.0152844	+	0.251901i
$925$	−2.10435e10			−0.874224
$926$	6.62611e9	−	3.82559e9i	0.274233	−	0.158329i
$927$	−9.54501e9	+	1.61620e10i	−0.393548	+	0.666373i
$928$	1.74122e10	−	3.01588e10i	0.715213	−	1.23878i
$929$	−1.38621e10	−	2.40099e10i	−0.567249	−	0.982504i	−0.996837	−	0.0794792i	$-0.974674\pi$
$929$	−1.38621e10	−	2.40099e10i	−0.567249	−	0.982504i	0.429587	−	0.903025i	$-0.358659\pi$
$930$	4.86812e9	−	4.82032e9i	0.198459	−	0.196510i
$931$	5.21843e9	+	6.79837e9i	0.211941	+	0.276109i
$932$		−	1.44424e10i		−	0.584366i
$933$	3.19014e10	+	8.71687e9i	1.28595	+	0.351378i
$934$	1.13781e10	+	6.56917e9i	0.456938	+	0.263813i
$935$	3.15979e9	+	1.82430e9i	0.126420	+	0.0729888i
$936$	−2.23314e10	+	1.26009e10i	−0.890123	+	0.502268i
$937$		−	2.09195e10i		−	0.830736i	−0.909654	−	0.415368i	$-0.863653\pi$
$937$		−	2.09195e10i		−	0.830736i	0.909654	−	0.415368i	$-0.136347\pi$
$938$	−9.76092e9	+	1.11321e10i	−0.386172	+	0.440421i
$939$	1.69351e10	+	1.71031e10i	0.667512	+	0.674131i
$940$	5.70004e9	+	9.87276e9i	0.223836	+	0.387696i
$941$	1.79927e9	−	3.11642e9i	0.0703934	−	0.121925i	−0.828680	−	0.559722i	$-0.810908\pi$
$941$	1.79927e9	−	3.11642e9i	0.0703934	−	0.121925i	0.899074	+	0.437797i	$0.144241\pi$
$942$	7.25929e9	+	2.76367e10i	0.282954	+	1.07723i
$943$	−2.40714e10	+	1.38976e10i	−0.934781	+	0.539696i
$944$	4.19798e9			0.162420
$945$	−1.58257e10	+	1.02408e10i	−0.610031	+	0.394751i
$946$	5.13096e9			0.197052
$947$	5.48175e9	−	3.16489e9i	0.209746	−	0.121097i	−0.391447	−	0.920201i	$-0.628025\pi$
$947$	5.48175e9	−	3.16489e9i	0.209746	−	0.121097i	0.601194	+	0.799103i	$0.294692\pi$
$948$	−6.48116e8	−	2.46743e9i	−0.0247072	−	0.0940622i
$949$	1.00124e10	−	1.73420e10i	0.380283	−	0.658669i
$950$	−1.41963e9	−	2.45887e9i	−0.0537208	−	0.0930472i
$951$	2.67021e10	+	2.69669e10i	1.00673	+	1.01671i
$952$	−4.01019e9	−	1.18103e10i	−0.150639	−	0.443642i
$953$			2.82104e10i			1.05581i	0.849304	+	0.527904i	$0.177022\pi$
$953$			2.82104e10i			1.05581i	−0.849304	+	0.527904i	$0.822978\pi$
$954$	2.23259e9	−	1.25978e9i	0.0832512	−	0.0469760i
$955$	−7.36343e9	−	4.25128e9i	−0.273570	−	0.157946i
$956$	5.28165e9	+	3.04936e9i	0.195509	+	0.112877i
$957$	−1.71322e10	−	4.68127e9i	−0.631861	−	0.172652i
$958$			1.92509e10i			0.707412i
$959$	−1.03133e10	−	3.03734e10i	−0.377600	−	1.11206i
$960$	1.03268e10	−	1.02254e10i	0.376716	−	0.373018i
$961$	−9.00354e9	−	1.55946e10i	−0.327251	−	0.566816i
$962$	−1.66206e10	+	2.87878e10i	−0.601915	+	1.04255i
$963$	5.49676e8	−	9.30736e8i	0.0198342	−	0.0335842i
$964$	1.39014e10	−	8.02595e9i	0.499790	−	0.288554i
$965$	−1.63321e10			−0.585054
$966$	1.41780e10	+	2.14432e10i	0.506051	+	0.765366i
$967$	2.10247e10			0.747718			0.373859	−	0.927486i	$-0.378034\pi$
$967$	2.10247e10			0.747718			0.373859	+	0.927486i	$0.378034\pi$
$968$	2.02443e10	−	1.16881e10i	0.717363	−	0.414170i
$969$	−4.34468e9	+	1.14121e9i	−0.153400	+	0.0402933i
$970$	−2.52493e9	+	4.37331e9i	−0.0888277	+	0.153854i
$971$	−5.42124e9	−	9.38986e9i	−0.190034	−	0.329148i	0.755227	−	0.655463i	$-0.227526\pi$
$971$	−5.42124e9	−	9.38986e9i	−0.190034	−	0.329148i	−0.945261	+	0.326315i	$0.894193\pi$
$972$	1.18701e10	−	1.12985e10i	0.414594	−	0.394629i
$973$	2.04381e9	−	2.33092e9i	0.0711289	−	0.0811209i
$974$		−	2.41168e10i		−	0.836304i
$975$	−3.57924e9	+	1.30991e10i	−0.123673	+	0.452610i
$976$	−2.45323e9	−	1.41637e9i	−0.0844624	−	0.0487644i
$977$	2.12950e10	+	1.22947e10i	0.730546	+	0.421781i	0.818622	−	0.574333i	$-0.194739\pi$
$977$	2.12950e10	+	1.22947e10i	0.730546	+	0.421781i	−0.0880760	+	0.996114i	$0.528072\pi$
$978$	4.43752e9	−	1.62401e10i	0.151689	−	0.555142i
$979$			1.97827e10i			0.673823i
$980$	1.60156e9	+	1.21490e10i	0.0543564	+	0.412333i
$981$	−2.26128e8	+	2.29173e10i	−0.00764739	+	0.775035i
$982$	3.46122e8	+	5.99500e8i	0.0116638	+	0.0202022i
$983$	−1.03177e10	+	1.78707e10i	−0.346452	+	0.600073i	−0.985617	−	0.168997i	$-0.945947\pi$
$983$	−1.03177e10	+	1.78707e10i	−0.346452	+	0.600073i	0.639164	+	0.769070i	$0.279280\pi$
$984$	−2.28647e10	+	6.00584e9i	−0.765038	+	0.200951i
$985$	−4.32757e9	+	2.49852e9i	−0.144284	+	0.0833022i
$986$	1.33246e10			0.442675
$987$	−3.24552e10	+	1.96926e9i	−1.07442	+	0.0651918i
$988$	6.00335e9			0.198036
$989$	−2.52652e10	+	1.45869e10i	−0.830492	+	0.479485i
$990$	−5.50712e9	−	3.25241e9i	−0.180385	−	0.106532i
$991$	−4.21196e9	+	7.29534e9i	−0.137476	+	0.238115i	−0.926541	−	0.376195i	$-0.877232\pi$
$991$	−4.21196e9	+	7.29534e9i	−0.137476	+	0.238115i	0.789065	+	0.614310i	$0.210566\pi$
$992$	8.70026e9	+	1.50693e10i	0.282971	+	0.490120i
$993$	−2.38403e9	+	2.36063e9i	−0.0772663	+	0.0765077i
$994$	6.93651e9	−	3.48878e10i	0.224021	−	1.12673i
$995$			6.15130e9i			0.197964i
$996$	1.71924e10	+	4.69770e9i	0.551350	+	0.150653i
$997$	−3.03176e10	−	1.75039e10i	−0.968863	−	0.559373i	−0.0699736	−	0.997549i	$-0.522291\pi$
$997$	−3.03176e10	−	1.75039e10i	−0.968863	−	0.559373i	−0.898889	+	0.438176i	$0.855625\pi$
$998$	−2.29151e10	−	1.32300e10i	−0.729735	−	0.421313i
$999$	1.59378e10	−	5.61435e10i	0.505766	−	1.78164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.8.g.b.17.10	yes	32
3.2	odd	2	inner	21.8.g.b.17.7	yes	32
7.3	odd	6		147.8.c.b.146.14		32
7.4	even	3		147.8.c.b.146.20		32
7.5	odd	6	inner	21.8.g.b.5.7	✓	32
21.5	even	6	inner	21.8.g.b.5.10	yes	32
21.11	odd	6		147.8.c.b.146.13		32
21.17	even	6		147.8.c.b.146.19		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.8.g.b.5.7	✓	32	7.5	odd	6	inner
21.8.g.b.5.10	yes	32	21.5	even	6	inner
21.8.g.b.17.7	yes	32	3.2	odd	2	inner
21.8.g.b.17.10	yes	32	1.1	even	1	trivial
147.8.c.b.146.13		32	21.11	odd	6
147.8.c.b.146.14		32	7.3	odd	6
147.8.c.b.146.19		32	21.17	even	6
147.8.c.b.146.20		32	7.4	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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	21.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(6.40713 - 3.69916i) q^{2} +(-11.8808 - 45.2310i) q^{3} +(-36.6324 + 63.4492i) q^{4} +(-101.547 - 175.885i) q^{5} +(-243.439 - 245.852i) q^{6} +(-682.340 - 598.293i) q^{7} +1489.02i q^{8} +(-1904.69 + 1074.76i) q^{9} +(-1301.25 - 751.279i) q^{10} +(-1685.57 - 973.165i) q^{11} +(3305.10 + 903.097i) q^{12} -7873.88i q^{13} +(-6585.03 - 1309.26i) q^{14} +(-6749.00 + 6682.74i) q^{15} +(819.181 + 1418.86i) q^{16} +(4615.11 - 7993.61i) q^{17} +(-8227.93 + 13931.9i) q^{18} +(9012.39 - 5203.30i) q^{19} +14879.7 q^{20} +(-18954.7 + 37971.1i) q^{21} -14399.6 q^{22} +(70904.4 - 40936.7i) q^{23} +(67350.0 - 17690.7i) q^{24} +(18438.8 - 31937.0i) q^{25} +(-29126.8 - 50449.0i) q^{26} +(71241.7 + 73382.4i) q^{27} +(62957.0 - 21377.0i) q^{28} +195123. i q^{29} +(-18521.2 + 67782.8i) q^{30} +(-84434.3 - 48748.2i) q^{31} +(-154563. - 89236.8i) q^{32} +(-23991.4 + 87802.1i) q^{33} -68288.2i q^{34} +(-35941.0 + 180768. i) q^{35} +(1580.94 - 160222. i) q^{36} +(-285316. - 494181. i) q^{37} +(38495.7 - 66676.5i) q^{38} +(-356144. + 93547.8i) q^{39} +(261897. - 151206. i) q^{40} -339491. q^{41} +(19016.1 + 313403. i) q^{42} -356328. q^{43} +(123493. - 71298.8i) q^{44} +(382451. + 225868. i) q^{45} +(302863. - 524573. i) q^{46} +(383075. + 663506. i) q^{47} +(54444.1 - 53909.6i) q^{48} +(107634. + 816479. i) q^{49} -272832. i q^{50} +(-416391. - 113776. i) q^{51} +(499592. + 288439. i) q^{52} +(-137209. - 79217.5i) q^{53} +(727908. + 206636. i) q^{54} +395289. i q^{55} +(890872. - 1.01602e6i) q^{56} +(-342425. - 345820. i) q^{57} +(721792. + 1.25018e6i) q^{58} +(1.28115e6 - 2.21902e6i) q^{59} +(-176782. - 673024. i) q^{60} +(-1.49737e6 + 864504. i) q^{61} -721309. q^{62} +(1.94267e6 + 406214. i) q^{63} -1.53012e6 q^{64} +(-1.38490e6 + 799571. i) q^{65} +(171078. + 651308. i) q^{66} +(1.10259e6 - 1.90974e6i) q^{67} +(338126. + 585651. i) q^{68} +(-2.69401e6 - 2.72072e6i) q^{69} +(438413. + 1.29116e6i) q^{70} +5.29805e6i q^{71} +(-1.60034e6 - 2.83613e6i) q^{72} +(2.20247e6 + 1.27160e6i) q^{73} +(-3.65611e6 - 2.11086e6i) q^{74} +(-1.66361e6 - 454571. i) q^{75} +762439. i q^{76} +(567895. + 1.67249e6i) q^{77} +(-1.93581e6 + 1.91681e6i) q^{78} +(-372291. - 644826. i) q^{79} +(166371. - 288163. i) q^{80} +(2.47275e6 - 4.09418e6i) q^{81} +(-2.17516e6 + 1.25583e6i) q^{82} +5.20177e6 q^{83} +(-1.71488e6 - 2.59364e6i) q^{84} -1.87461e6 q^{85} +(-2.28304e6 + 1.31811e6i) q^{86} +(8.82563e6 - 2.31821e6i) q^{87} +(1.44906e6 - 2.50985e6i) q^{88} +(-5.08205e6 - 8.80237e6i) q^{89} +(3.28594e6 + 32422.8i) q^{90} +(-4.71089e6 + 5.37267e6i) q^{91} +5.99844e6i q^{92} +(-1.20179e6 + 4.39822e6i) q^{93} +(4.90883e6 + 2.83411e6i) q^{94} +(-1.83037e6 - 1.05676e6i) q^{95} +(-2.19995e6 + 8.05124e6i) q^{96} -3.36084e6i q^{97} +(3.70991e6 + 4.83314e6i) q^{98} +(4.25641e6 + 41998.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 84 q^{3} + 1150 q^{4} + 2464 q^{7} - 3516 q^{9} - 630 q^{10} - 3864 q^{12} + 27576 q^{15} - 19594 q^{16} + 33498 q^{18} - 47880 q^{19} + 151788 q^{21} + 105132 q^{22} - 211554 q^{24} - 331252 q^{25}+ \cdots + 35642232 q^{99}+O(q^{100}) \) 32 * q - 84 * q^3 + 1150 * q^4 + 2464 * q^7 - 3516 * q^9 - 630 * q^10 - 3864 * q^12 + 27576 * q^15 - 19594 * q^16 + 33498 * q^18 - 47880 * q^19 + 151788 * q^21 + 105132 * q^22 - 211554 * q^24 - 331252 * q^25 - 353122 * q^28 - 40662 * q^30 + 628152 * q^31 - 66024 * q^33 - 227244 * q^36 - 618748 * q^37 + 1996104 * q^39 + 1986138 * q^40 + 4274802 * q^42 - 1416064 * q^43 - 4757508 * q^45 - 3492840 * q^46 - 6640312 * q^49 + 677340 * q^51 + 11962272 * q^52 - 6743898 * q^54 - 6279408 * q^57 - 2064342 * q^58 + 7521282 * q^60 + 10948728 * q^61 + 13194636 * q^63 - 589508 * q^64 - 6977250 * q^66 - 1944728 * q^67 - 24852702 * q^70 - 1544472 * q^72 + 13351212 * q^73 - 23106048 * q^75 + 1917432 * q^78 + 7626328 * q^79 + 8703036 * q^81 + 14640192 * q^82 + 15191904 * q^84 + 3418848 * q^85 + 15346296 * q^87 + 12313398 * q^88 + 3988992 * q^91 - 24832104 * q^93 - 51594732 * q^94 - 57374730 * q^96 + 35642232 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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