LMFDB - Embedded newform 21.8.g.b.5.6

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			5.6
Character	$\chi$	$=$	21.5
Dual form			21.8.g.b.17.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.08214 - 4.66623i) q^{2} +(-31.7364 + 34.3482i) q^{3} +(-20.4526 - 35.4250i) q^{4} +(-123.341 + 213.633i) q^{5} +(416.775 - 129.518i) q^{6} +(658.195 - 624.758i) q^{7} +1576.30i q^{8} +(-172.602 - 2180.18i) q^{9} +(1993.72 - 1151.08i) q^{10} +(5786.68 - 3340.94i) q^{11} +(1865.88 + 421.750i) q^{12} -6161.99i q^{13} +(-8234.89 + 1978.09i) q^{14} +(-3423.52 - 11016.5i) q^{15} +(4737.44 - 8205.49i) q^{16} +(15876.7 + 27499.2i) q^{17} +(-8778.22 + 18425.9i) q^{18} +(5952.65 + 3436.76i) q^{19} +10090.6 q^{20} +(570.584 + 42435.4i) q^{21} -62358.4 q^{22} +(-48216.7 - 27837.9i) q^{23} +(-54143.1 - 50026.1i) q^{24} +(8636.42 + 14958.7i) q^{25} +(-28753.2 + 49802.1i) q^{26} +(80363.0 + 63262.4i) q^{27} +(-35593.9 - 10538.6i) q^{28} -167195. i q^{29} +(-23736.1 + 105012. i) q^{30} +(198606. - 114665. i) q^{31} +(98157.6 - 56671.3i) q^{32} +(-68893.0 + 304792. i) q^{33} -296336. i q^{34} +(52286.4 + 217671. i) q^{35} +(-73702.7 + 50704.8i) q^{36} +(140271. - 242956. i) q^{37} +(-32073.4 - 55552.8i) q^{38} +(211653. + 195559. i) q^{39} +(-336750. - 194423. i) q^{40} -78668.6 q^{41} +(193402. - 345631. i) q^{42} +118106. q^{43} +(-236706. - 136662. i) q^{44} +(487047. + 232032. i) q^{45} +(259796. + 449980. i) q^{46} +(4178.48 - 7237.34i) q^{47} +(131495. + 423135. i) q^{48} +(42898.4 - 822425. i) q^{49} -161198. i q^{50} +(-1.44842e6 - 327390. i) q^{51} +(-218288. + 126029. i) q^{52} +(153510. - 88629.0i) q^{53} +(-354309. - 886288. i) q^{54} +1.64830e6i q^{55} +(984806. + 1.03751e6i) q^{56} +(-306962. + 95392.4i) q^{57} +(-780169. + 1.35129e6i) q^{58} +(117304. + 203177. i) q^{59} +(-320240. + 346595. i) q^{60} +(-205451. - 118617. i) q^{61} -2.14022e6 q^{62} +(-1.47569e6 - 1.32715e6i) q^{63} -2.27055e6 q^{64} +(1.31640e6 + 760026. i) q^{65} +(1.97903e6 - 2.14190e6i) q^{66} +(1.68244e6 + 2.91407e6i) q^{67} +(649439. - 1.12486e6i) q^{68} +(2.48641e6 - 772682. i) q^{69} +(593114. - 2.00323e6i) q^{70} +711242. i q^{71} +(3.43662e6 - 272073. i) q^{72} +(4.65054e6 - 2.68499e6i) q^{73} +(-2.26738e6 + 1.30907e6i) q^{74} +(-787894. - 178090. i) q^{75} -281163. i q^{76} +(1.72149e6 - 5.81427e6i) q^{77} +(-798089. - 2.56816e6i) q^{78} +(-1.27598e6 + 2.21006e6i) q^{79} +(1.16864e6 + 2.02415e6i) q^{80} +(-4.72339e6 + 752606. i) q^{81} +(635811. + 367086. i) q^{82} -2.04843e6 q^{83} +(1.49160e6 - 888129. i) q^{84} -7.83298e6 q^{85} +(-954547. - 551108. i) q^{86} +(5.74284e6 + 5.30616e6i) q^{87} +(5.26633e6 + 9.12155e6i) q^{88} +(2.31881e6 - 4.01630e6i) q^{89} +(-2.85367e6 - 4.14799e6i) q^{90} +(-3.84975e6 - 4.05579e6i) q^{91} +2.27743e6i q^{92} +(-2.36450e6 + 1.04608e7i) q^{93} +(-67542.1 + 38995.5i) q^{94} +(-1.46841e6 + 847788. i) q^{95} +(-1.16861e6 + 5.17008e6i) q^{96} -217594. i q^{97} +(-4.18433e6 + 6.44678e6i) q^{98} +(-8.28264e6 - 1.20393e7i) 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 $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−8.08214	−	4.66623i	−0.714367	−	0.412440i	0.0983087	−	0.995156i	$-0.468657\pi$
$2$	−8.08214	−	4.66623i	−0.714367	−	0.412440i	−0.812676	+	0.582716i	$0.801990\pi$
$3$	−31.7364	+	34.3482i	−0.678630	+	0.734480i
$3$	−31.7364	+	34.3482i	−0.678630	+	0.734480i
$4$	−20.4526	−	35.4250i	−0.159786	−	0.276758i
$5$	−123.341	+	213.633i	−0.441279	+	0.764317i	−0.997785	−	0.0665264i	$-0.978808\pi$
$5$	−123.341	+	213.633i	−0.441279	+	0.764317i	0.556506	+	0.830844i	$0.312142\pi$
$6$	416.775	−	129.518i	0.787720	−	0.244794i
$7$	658.195	−	624.758i	0.725290	−	0.688444i
$7$	658.195	−	624.758i	0.725290	−	0.688444i
$8$			1576.30i			1.08849i
$9$	−172.602	−	2180.18i	−0.0789218	−	0.996881i
$10$	1993.72	−	1151.08i	0.630470	−	0.364002i
$11$	5786.68	−	3340.94i	1.31086	−	0.756824i	0.328619	−	0.944463i	$-0.393417\pi$
$11$	5786.68	−	3340.94i	1.31086	−	0.756824i	0.982238	+	0.187639i	$0.0600835\pi$
$12$	1865.88	+	421.750i	0.311709	+	0.0704565i
$13$		−	6161.99i		−	0.777891i	−0.921261	−	0.388946i	$-0.872839\pi$
$13$		−	6161.99i		−	0.777891i	0.921261	−	0.388946i	$-0.127161\pi$
$14$	−8234.89	+	1978.09i	−0.802065	+	0.192663i
$15$	−3423.52	−	11016.5i	−0.261911	−	0.842799i
$16$	4737.44	−	8205.49i	0.289151	−	0.500823i
$17$	15876.7	+	27499.2i	0.783769	+	1.35753i	0.929732	+	0.368237i	$0.120039\pi$
$17$	15876.7	+	27499.2i	0.783769	+	1.35753i	−0.145963	+	0.989290i	$0.546628\pi$
$18$	−8778.22	+	18425.9i	−0.354775	+	0.744690i
$19$	5952.65	+	3436.76i	0.199101	+	0.114951i	0.596236	−	0.802809i	$-0.296662\pi$
$19$	5952.65	+	3436.76i	0.199101	+	0.114951i	−0.397135	+	0.917760i	$0.629996\pi$
$20$	10090.6			0.282041
$21$	570.584	+	42435.4i	0.0134447	+	0.999910i
$22$	−62358.4			−1.24858
$23$	−48216.7	−	27837.9i	−0.826323	−	0.477078i	0.0262691	−	0.999655i	$-0.491637\pi$
$23$	−48216.7	−	27837.9i	−0.826323	−	0.477078i	−0.852592	+	0.522577i	$0.824971\pi$
$24$	−54143.1	−	50026.1i	−0.799474	−	0.738682i
$25$	8636.42	+	14958.7i	0.110546	+	0.191471i
$26$	−28753.2	+	49802.1i	−0.320834	+	0.555700i
$27$	80363.0	+	63262.4i	0.785748	+	0.618547i
$28$	−35593.9	−	10538.6i	−0.306424	−	0.0907258i
$29$		−	167195.i		−	1.27300i	−0.771275	−	0.636502i	$-0.780381\pi$
$29$		−	167195.i		−	1.27300i	0.771275	−	0.636502i	$-0.219619\pi$
$30$	−23736.1	+	105012.i	−0.160504	+	0.710091i
$31$	198606.	−	114665.i	1.19737	−	0.691300i	0.237399	−	0.971412i	$-0.423705\pi$
$31$	198606.	−	114665.i	1.19737	−	0.691300i	0.959967	+	0.280112i	$0.0903716\pi$
$32$	98157.6	−	56671.3i	0.529540	−	0.305730i
$33$	−68893.0	+	304792.i	−0.333715	+	1.47640i
$34$		−	296336.i		−	1.29303i
$35$	52286.4	+	217671.i	0.206135	+	0.858147i
$36$	−73702.7	+	50704.8i	−0.263284	+	0.181130i
$37$	140271.	−	242956.i	0.455262	−	0.788537i	−0.543441	−	0.839447i	$-0.682879\pi$
$37$	140271.	−	242956.i	0.455262	−	0.788537i	0.998703	+	0.0509105i	$0.0162123\pi$
$38$	−32073.4	−	55552.8i	−0.0948206	−	0.164234i
$39$	211653.	+	195559.i	0.571346	+	0.527901i
$40$	−336750.	−	194423.i	−0.831951	−	0.480327i
$41$	−78668.6			−0.178262			−0.0891309	−	0.996020i	$-0.528409\pi$
$41$	−78668.6			−0.178262			−0.0891309	+	0.996020i	$0.528409\pi$
$42$	193402.	−	345631.i	0.402798	−	0.719848i
$43$	118106.			0.226533			0.113266	−	0.993565i	$-0.463869\pi$
$43$	118106.			0.226533			0.113266	+	0.993565i	$0.463869\pi$
$44$	−236706.	−	136662.i	−0.418914	−	0.241860i
$45$	487047.	+	232032.i	0.796760	+	0.379581i
$46$	259796.	+	449980.i	0.393532	+	0.681617i
$47$	4178.48	−	7237.34i	0.00587051	−	0.0101680i	−0.863075	−	0.505075i	$-0.831465\pi$
$47$	4178.48	−	7237.34i	0.00587051	−	0.0101680i	0.868946	+	0.494907i	$0.164798\pi$
$48$	131495.	+	423135.i	0.171618	+	0.552249i
$49$	42898.4	−	822425.i	0.0520901	−	0.998642i
$50$		−	161198.i		−	0.182375i
$51$	−1.44842e6	−	327390.i	−1.52897	−	0.345597i
$52$	−218288.	+	126029.i	−0.215288	+	0.124296i
$53$	153510.	−	88629.0i	0.141635	−	0.0817731i	−0.427508	−	0.904012i	$-0.640608\pi$
$53$	153510.	−	88629.0i	0.141635	−	0.0817731i	0.569143	+	0.822239i	$0.307275\pi$
$54$	−354309.	−	886288.i	−0.306199	−	0.765944i
$55$			1.64830e6i			1.33588i
$56$	984806.	+	1.03751e6i	0.749364	+	0.789470i
$57$	−306962.	+	95392.4i	−0.219545	+	0.0682263i
$58$	−780169.	+	1.35129e6i	−0.525038	+	0.909392i
$59$	117304.	+	203177.i	0.0743586	+	0.128793i	0.900807	−	0.434219i	$-0.142976\pi$
$59$	117304.	+	203177.i	0.0743586	+	0.128793i	−0.826449	+	0.563012i	$0.809642\pi$
$60$	−320240.	+	346595.i	−0.191402	+	0.207154i
$61$	−205451.	−	118617.i	−0.115892	−	0.0669105i	0.440933	−	0.897540i	$-0.354648\pi$
$61$	−205451.	−	118617.i	−0.115892	−	0.0669105i	−0.556826	+	0.830629i	$0.687981\pi$
$62$	−2.14022e6			−1.14048
$63$	−1.47569e6	−	1.32715e6i	−0.743538	−	0.668694i
$64$	−2.27055e6			−1.08268
$65$	1.31640e6	+	760026.i	0.594556	+	0.343267i
$66$	1.97903e6	−	2.14190e6i	0.847323	−	0.917055i
$67$	1.68244e6	+	2.91407e6i	0.683403	+	1.18369i	0.973936	+	0.226824i	$0.0728343\pi$
$67$	1.68244e6	+	2.91407e6i	0.683403	+	1.18369i	−0.290532	+	0.956865i	$0.593832\pi$
$68$	649439.	−	1.12486e6i	0.250471	−	0.433828i
$69$	2.48641e6	−	772682.i	0.911172	−	0.283158i
$70$	593114.	−	2.00323e6i	0.206678	−	0.698050i
$71$			711242.i			0.235838i	0.993023	+	0.117919i	$0.0376223\pi$
$71$			711242.i			0.235838i	−0.993023	+	0.117919i	$0.962378\pi$
$72$	3.43662e6	−	272073.i	1.08509	−	0.0859055i
$73$	4.65054e6	−	2.68499e6i	1.39918	−	0.807816i	0.404871	−	0.914374i	$-0.367316\pi$
$73$	4.65054e6	−	2.68499e6i	1.39918	−	0.807816i	0.994307	+	0.106558i	$0.0339829\pi$
$74$	−2.26738e6	+	1.30907e6i	−0.650448	+	0.375536i
$75$	−787894.	−	178090.i	−0.215652	−	0.0487444i
$76$		−	281163.i		−	0.0734702i
$77$	1.72149e6	−	5.81427e6i	0.429720	−	1.45137i
$78$	−798089.	−	2.56816e6i	−0.190423	−	0.612761i
$79$	−1.27598e6	+	2.21006e6i	−0.291171	+	0.504324i	−0.974087	−	0.226174i	$-0.927378\pi$
$79$	−1.27598e6	+	2.21006e6i	−0.291171	+	0.504324i	0.682916	+	0.730497i	$0.260712\pi$
$80$	1.16864e6	+	2.02415e6i	0.255192	+	0.442005i
$81$	−4.72339e6	+	752606.i	−0.987543	+	0.157351i
$82$	635811.	+	367086.i	0.127344	+	0.0735223i
$83$	−2.04843e6			−0.393231			−0.196615	−	0.980481i	$-0.562995\pi$
$83$	−2.04843e6			−0.393231			−0.196615	+	0.980481i	$0.562995\pi$
$84$	1.49160e6	−	888129.i	0.274585	−	0.163493i
$85$	−7.83298e6			−1.38344
$86$	−954547.	−	551108.i	−0.161828	−	0.0934312i
$87$	5.74284e6	+	5.30616e6i	0.934996	+	0.863899i
$88$	5.26633e6	+	9.12155e6i	0.823794	+	1.42685i
$89$	2.31881e6	−	4.01630e6i	0.348658	−	0.603894i	−0.637353	−	0.770572i	$-0.719971\pi$
$89$	2.31881e6	−	4.01630e6i	0.348658	−	0.603894i	0.986011	+	0.166678i	$0.0533040\pi$
$90$	−2.85367e6	−	4.14799e6i	−0.412625	−	0.599776i
$91$	−3.84975e6	−	4.05579e6i	−0.535535	−	0.564197i
$92$			2.27743e6i			0.304922i
$93$	−2.36450e6	+	1.04608e7i	−0.304823	+	1.34858i
$94$	−67542.1	+	38995.5i	−0.00838740	+	0.00484247i
$95$	−1.46841e6	+	847788.i	−0.175718	+	0.101451i
$96$	−1.16861e6	+	5.17008e6i	−0.134809	+	0.596414i
$97$		−	217594.i		−	0.0242073i	−0.999927	−	0.0121036i	$-0.996147\pi$
$97$		−	217594.i		−	0.0242073i	0.999927	−	0.0121036i	$-0.00385280\pi$
$98$	−4.18433e6	+	6.44678e6i	−0.449092	+	0.691913i
$99$	−8.28264e6	−	1.20393e7i	−0.857918	−	1.24704i
$100$	353275.	−	611890.i	0.0353275	−	0.0611890i
$101$	−2.03096e6	−	3.51772e6i	−0.196144	−	0.339732i	0.751131	−	0.660154i	$-0.229509\pi$
$101$	−2.03096e6	−	3.51772e6i	−0.196144	−	0.339732i	−0.947275	+	0.320421i	$0.896175\pi$
$102$	1.01786e7	+	9.40465e6i	0.949705	+	0.877490i
$103$	3.44147e6	+	1.98693e6i	0.310323	+	0.179165i	0.647071	−	0.762430i	$-0.275994\pi$
$103$	3.44147e6	+	1.98693e6i	0.310323	+	0.179165i	−0.336748	+	0.941595i	$0.609327\pi$
$104$	9.71314e6			0.846726
$105$	−9.13598e6	−	5.11214e6i	−0.770181	−	0.430963i
$106$	−1.65425e6			−0.134906
$107$	−1.06757e7	−	6.16361e6i	−0.842466	−	0.486398i	0.0156354	−	0.999878i	$-0.495023\pi$
$107$	−1.06757e7	−	6.16361e6i	−0.842466	−	0.486398i	−0.858102	+	0.513480i	$0.828356\pi$
$108$	597436.	−	4.14074e6i	0.0456361	−	0.316297i
$109$	−7.16481e6	−	1.24098e7i	−0.529922	−	0.917852i	−0.999391	−	0.0349027i	$-0.988888\pi$
$109$	−7.16481e6	−	1.24098e7i	−0.529922	−	0.917852i	0.469469	−	0.882949i	$-0.344445\pi$
$110$	7.69136e6	−	1.33218e7i	0.550971	−	0.954309i
$111$	3.89342e6	+	1.25286e7i	0.270210	+	0.869505i
$112$	−2.00828e6	−	8.36057e6i	−0.135071	−	0.562306i
$113$			2.51834e7i			1.64187i	0.571019	+	0.820937i	$0.306548\pi$
$113$			2.51834e7i			1.64187i	−0.571019	+	0.820937i	$0.693452\pi$
$114$	2.92604e6	+	661380.i	0.184975	+	0.0418104i
$115$	1.18942e7	−	6.86712e6i	0.729277	−	0.421049i
$116$	−5.92287e6	+	3.41957e6i	−0.352314	+	0.203408i
$117$	−1.34342e7	+	1.06357e6i	−0.775465	+	0.0613926i
$118$		−	2.18947e6i		−	0.122674i
$119$	2.76303e7	+	8.18076e6i	1.50304	+	0.445020i
$120$	1.73653e7	−	5.39649e6i	0.917378	−	0.285087i
$121$	1.25802e7	−	2.17896e7i	0.645564	−	1.11815i
$122$	1.10699e6	+	1.91737e6i	0.0551931	+	0.0955973i
$123$	2.49666e6	−	2.70213e6i	0.120974	−	0.130930i
$124$	−8.12405e6	−	4.69042e6i	−0.382645	−	0.220920i
$125$	−2.35330e7			−1.07768
$126$	5.73396e6	+	1.76121e7i	0.255363	+	0.784358i
$127$	2.57045e7			1.11352			0.556758	−	0.830675i	$-0.312045\pi$
$127$	2.57045e7			1.11352			0.556758	+	0.830675i	$0.312045\pi$
$128$	5.78674e6	+	3.34098e6i	0.243893	+	0.140812i
$129$	−3.74825e6	+	4.05672e6i	−0.153732	+	0.166384i
$130$	−7.09291e6	−	1.22853e7i	−0.283154	−	0.490437i
$131$	−1.45564e7	+	2.52125e7i	−0.565724	+	0.979863i	0.431257	+	0.902229i	$0.358070\pi$
$131$	−1.45564e7	+	2.52125e7i	−0.565724	+	0.979863i	−0.996982	+	0.0776345i	$0.975263\pi$
$132$	1.22063e7	−	3.79326e6i	0.461929	−	0.143550i
$133$	6.06515e6	−	1.45690e6i	0.223543	−	0.0536970i
$134$		−	3.14025e7i		−	1.12745i
$135$	−2.34270e7	+	9.36535e6i	−0.819500	+	0.327609i
$136$	−4.33470e7	+	2.50264e7i	−1.47765	+	0.853124i
$137$	4.69427e7	−	2.71024e7i	1.55972	−	0.900504i	0.562436	−	0.826841i	$-0.309864\pi$
$137$	4.69427e7	−	2.71024e7i	1.55972	−	0.900504i	0.997283	−	0.0736637i	$-0.0234691\pi$
$138$	−2.37010e7	−	5.35721e6i	−0.767697	−	0.173525i
$139$			2.23460e7i			0.705745i	0.935671	+	0.352872i	$0.114795\pi$
$139$			2.23460e7i			0.705745i	−0.935671	+	0.352872i	$0.885205\pi$
$140$	6.64159e6	−	6.30419e6i	0.204561	−	0.194169i
$141$	115980.	+	373210.i	0.00348430	+	0.0112121i
$142$	3.31882e6	−	5.74836e6i	0.0972690	−	0.168475i
$143$	−2.05868e7	−	3.56575e7i	−0.588726	−	1.01970i
$144$	−1.87071e7	−	8.91218e6i	−0.522082	−	0.248723i
$145$	3.57183e7	+	2.06220e7i	0.972978	+	0.561749i
$146$	−5.01151e7			−1.33270
$147$	2.68874e7	+	2.75743e7i	0.698133	+	0.715968i
$148$	−1.14756e7			−0.290978
$149$	−1.56718e7	−	9.04810e6i	−0.388120	−	0.224081i	0.293225	−	0.956043i	$-0.405271\pi$
$149$	−1.56718e7	−	9.04810e6i	−0.388120	−	0.224081i	−0.681345	+	0.731962i	$0.738605\pi$
$150$	5.53686e6	+	5.11584e6i	0.133951	+	0.123765i
$151$	4.12037e6	+	7.13668e6i	0.0973905	+	0.168685i	0.910604	−	0.413281i	$-0.135617\pi$
$151$	4.12037e6	+	7.13668e6i	0.0973905	+	0.168685i	−0.813213	+	0.581966i	$0.802284\pi$
$152$	−5.41737e6	+	9.38316e6i	−0.125123	+	0.216719i
$153$	5.72128e7	−	3.93604e7i	1.29144	−	0.888462i
$154$	−4.10440e7	+	3.89589e7i	−0.905580	+	0.859576i
$155$			5.65719e7i			1.22022i
$156$	2.59882e6	−	1.14975e7i	0.0548075	−	0.242476i
$157$	−4.62768e7	+	2.67179e7i	−0.954366	+	0.551003i	−0.894434	−	0.447199i	$-0.852422\pi$
$157$	−4.62768e7	+	2.67179e7i	−0.954366	+	0.551003i	−0.0599313	+	0.998203i	$0.519088\pi$
$158$	2.06253e7	−	1.19080e7i	0.416007	−	0.240182i
$159$	−1.82760e6	+	8.08556e6i	−0.0360572	+	0.159522i
$160$			2.79596e7i			0.539649i
$161$	−4.91279e7	+	1.18010e7i	−0.927765	+	0.222857i
$162$	4.16869e7	+	1.59577e7i	0.770366	+	0.294896i
$163$	1.50570e7	−	2.60795e7i	0.272322	−	0.471675i	−0.697134	−	0.716941i	$-0.745542\pi$
$163$	1.50570e7	−	2.60795e7i	0.272322	−	0.471675i	0.969456	+	0.245266i	$0.0788752\pi$
$164$	1.60898e6	+	2.78684e6i	0.0284838	+	0.0493353i
$165$	−5.66163e7	−	5.23112e7i	−0.981178	−	0.906569i
$166$	1.65557e7	+	9.55844e6i	0.280911	+	0.162184i
$167$	6.70162e7			1.11345			0.556726	−	0.830696i	$-0.312057\pi$
$167$	6.70162e7			1.11345			0.556726	+	0.830696i	$0.312057\pi$
$168$	−6.68910e7	+	899412.i	−1.08839	+	0.0146344i
$169$	2.47784e7			0.394885
$170$	6.33073e7	+	3.65505e7i	0.988286	+	0.570587i
$171$	6.46531e6	−	1.35710e7i	0.0988788	−	0.207552i
$172$	−2.41557e6	−	4.18389e6i	−0.0361968	−	0.0626947i
$173$	3.64465e7	−	6.31273e7i	0.535174	−	0.926949i	−0.463981	−	0.885845i	$-0.653579\pi$
$173$	3.64465e7	−	6.31273e7i	0.535174	−	0.926949i	0.999155	−	0.0411034i	$-0.0130873\pi$
$174$	−2.16547e7	−	6.96825e7i	−0.311624	−	1.00277i
$175$	1.50300e7	+	4.45008e6i	0.211995	+	0.0627675i
$176$		−	6.33101e7i		−	0.875344i
$177$	−1.07016e7	−	2.41891e6i	−0.145058	−	0.0327878i
$178$	−3.74819e7	+	2.16402e7i	−0.498140	+	0.287602i
$179$	−9.08984e7	+	5.24802e7i	−1.18460	+	0.683927i	−0.957073	−	0.289846i	$-0.906396\pi$
$179$	−9.08984e7	+	5.24802e7i	−1.18460	+	0.683927i	−0.227523	+	0.973773i	$0.573063\pi$
$180$	−1.74166e6	−	2.19993e7i	−0.0222592	−	0.281161i
$181$		−	7.36629e7i		−	0.923366i	−0.887045	−	0.461683i	$-0.847246\pi$
$181$		−	7.36629e7i		−	0.923366i	0.887045	−	0.461683i	$-0.152754\pi$
$182$	1.21890e7	+	5.07433e7i	0.149871	+	0.623920i
$183$	1.05946e7	−	3.29240e6i	0.127792	−	0.0397131i
$184$	4.38809e7	−	7.60040e7i	0.519294	−	0.899444i
$185$	3.46023e7	+	5.99330e7i	0.401795	+	0.695929i
$186$	6.79229e7	−	7.35128e7i	0.773964	−	0.837659i
$187$	1.83746e8	+	1.06086e8i	2.05482	+	1.18635i
$188$	−341844.			−0.00375210
$189$	9.24183e7	−	8.56841e6i	0.995730	−	0.0923175i
$190$	1.58239e7			0.167369
$191$	5.07941e6	+	2.93260e6i	0.0527468	+	0.0304534i	0.526141	−	0.850397i	$-0.323638\pi$
$191$	5.07941e6	+	2.93260e6i	0.0527468	+	0.0304534i	−0.473395	+	0.880850i	$0.656972\pi$
$192$	7.20591e7	−	7.79894e7i	0.734741	−	0.795209i
$193$	−5.81619e7	−	1.00739e8i	−0.582355	−	1.00867i	−0.995199	−	0.0978673i	$-0.968798\pi$
$193$	−5.81619e7	−	1.00739e8i	−0.582355	−	1.00867i	0.412844	−	0.910802i	$-0.364535\pi$
$194$	−1.01534e6	+	1.75862e6i	−0.00998404	+	0.0172929i
$195$	−6.78835e7	+	2.10957e7i	−0.655606	+	0.203738i
$196$	−3.00118e7	+	1.53011e7i	−0.284705	+	0.145153i
$197$			2.35040e7i			0.219033i	0.993985	+	0.109516i	$0.0349302\pi$
$197$			2.35040e7i			0.219033i	−0.993985	+	0.109516i	$0.965070\pi$
$198$	1.07632e7	+	1.35952e8i	0.0985400	+	1.24468i
$199$	−1.70988e8	+	9.87198e7i	−1.53808	+	0.888011i	−0.539130	+	0.842223i	$0.681247\pi$
$199$	−1.70988e8	+	9.87198e7i	−1.53808	+	0.888011i	−0.998951	+	0.0457885i	$0.985420\pi$
$200$	−2.35794e7	+	1.36136e7i	−0.208415	+	0.120328i
$201$	−1.53488e8	−	3.46933e7i	−1.33317	−	0.301341i
$202$			3.79076e7i			0.323591i
$203$	−1.04456e8	−	1.10047e8i	−0.876391	−	0.923296i
$204$	1.80261e7	+	5.80061e7i	0.148661	+	0.478375i
$205$	9.70308e6	−	1.68062e7i	0.0786631	−	0.136249i
$206$	−1.85430e7	−	3.21174e7i	−0.147790	−	0.255979i
$207$	−5.23693e7	+	1.09926e8i	−0.410375	+	0.861397i
$208$	−5.05621e7	−	2.91921e7i	−0.389586	−	0.224928i
$209$	4.59281e7			0.347990
$210$	4.99840e7	+	8.39476e7i	0.372446	+	0.625519i
$211$	−1.62963e8			−1.19427			−0.597134	−	0.802142i	$-0.703694\pi$
$211$	−1.62963e8			−1.19427			−0.597134	+	0.802142i	$0.703694\pi$
$212$	−6.27937e6	−	3.62539e6i	−0.0452627	−	0.0261324i
$213$	−2.44299e7	−	2.25723e7i	−0.173218	−	0.160047i
$214$	5.75216e7	+	9.96304e7i	0.401220	+	0.694934i
$215$	−1.45673e7	+	2.52313e7i	−0.0999641	+	0.173143i
$216$	−9.97206e7	+	1.26676e8i	−0.673282	+	0.855278i
$217$	5.90836e7	−	1.99553e8i	0.392516	−	1.32571i
$218$			1.33731e8i			0.874245i
$219$	−5.53667e7	+	2.44950e8i	−0.356200	+	1.57588i
$220$	5.83911e7	−	3.37121e7i	0.369715	−	0.213455i
$221$	1.69450e8	−	9.78318e7i	1.05601	−	0.609687i
$222$	2.69941e7	−	1.19426e8i	0.165590	−	0.732592i
$223$			1.23475e8i			0.745609i	0.927910	+	0.372804i	$0.121604\pi$
$223$			1.23475e8i			0.745609i	−0.927910	+	0.372804i	$0.878396\pi$
$224$	2.92010e7	−	9.86255e7i	0.173592	−	0.586301i
$225$	3.11220e7	−	2.14108e7i	0.182150	−	0.125313i
$226$	1.17512e8	−	2.03536e8i	0.677175	−	1.17290i
$227$	−6.50316e7	−	1.12638e8i	−0.369007	−	0.639138i	0.620404	−	0.784282i	$-0.286969\pi$
$227$	−6.50316e7	−	1.12638e8i	−0.369007	−	0.639138i	−0.989410	+	0.145144i	$0.953635\pi$
$228$	9.65746e6	+	8.92311e6i	0.0539624	+	0.0498591i
$229$	−1.10742e8	−	6.39370e7i	−0.609381	−	0.351826i	0.163342	−	0.986569i	$-0.447773\pi$
$229$	−1.10742e8	−	6.39370e7i	−0.609381	−	0.351826i	−0.772723	+	0.634743i	$0.781106\pi$
$230$	−1.28174e8			−0.694629
$231$	1.45076e8	+	2.43654e8i	0.774379	+	1.30056i
$232$	2.63549e8			1.38565
$233$	−5.11658e7	−	2.95406e7i	−0.264993	−	0.152994i	0.361617	−	0.932327i	$-0.382225\pi$
$233$	−5.11658e7	−	2.95406e7i	−0.264993	−	0.152994i	−0.626610	+	0.779333i	$0.715558\pi$
$234$	1.13540e8	+	5.40912e7i	0.579288	+	0.275976i
$235$	1.03076e6	+	1.78532e6i	0.00518106	+	0.00897386i
$236$	4.79836e6	−	8.31100e6i	0.0237630	−	0.0411586i
$237$	−3.54167e7	−	1.13967e8i	−0.172818	−	0.556109i
$238$	−1.85139e8	−	1.95047e8i	−0.890179	−	0.937822i
$239$		−	2.73993e8i		−	1.29822i	−0.760696	−	0.649109i	$-0.775142\pi$
$239$		−	2.73993e8i		−	1.29822i	0.760696	−	0.649109i	$-0.224858\pi$
$240$	−1.06614e8	−	2.40984e7i	−0.497825	−	0.112525i
$241$	7.49303e7	−	4.32610e7i	0.344824	−	0.199084i	−0.317579	−	0.948232i	$-0.602870\pi$
$241$	7.49303e7	−	4.32610e7i	0.344824	−	0.199084i	0.662403	+	0.749148i	$0.269537\pi$
$242$	−2.03350e8	+	1.17404e8i	−0.922339	+	0.532513i
$243$	1.24053e8	−	1.86125e8i	0.554605	−	0.832114i
$244$			9.70416e6i			0.0427655i
$245$	1.70406e8	+	1.10603e8i	0.740293	+	0.480493i
$246$	−3.27871e7	+	1.01890e7i	−0.140420	+	0.0436374i
$247$	2.11773e7	−	3.66801e7i	0.0894192	−	0.154879i
$248$	1.80747e8	+	3.13063e8i	0.752473	+	1.30332i
$249$	6.50098e7	−	7.03599e7i	0.266858	−	0.288820i
$250$	1.90197e8	+	1.09810e8i	0.769862	+	0.444480i
$251$	3.83930e8			1.53248			0.766238	−	0.642557i	$-0.222126\pi$
$251$	3.83930e8			1.53248			0.766238	+	0.642557i	$0.222126\pi$
$252$	−1.68325e7	+	7.94200e7i	−0.0662593	+	0.312628i
$253$	−3.72019e8			−1.44425
$254$	−2.07747e8	−	1.19943e8i	−0.795459	−	0.459258i
$255$	2.48591e8	−	2.69049e8i	0.938846	−	1.01611i
$256$	1.14136e8	+	1.97689e8i	0.425188	+	0.736448i
$257$	−2.58949e8	+	4.48512e8i	−0.951585	+	1.64819i	−0.209590	+	0.977789i	$0.567213\pi$
$257$	−2.58949e8	+	4.48512e8i	−0.951585	+	1.64819i	−0.741995	+	0.670405i	$0.766120\pi$
$258$	4.92235e7	−	1.52968e7i	0.178445	−	0.0554539i
$259$	−5.94632e7	−	2.47548e8i	−0.212666	−	0.885340i
$260$		−	6.21782e7i		−	0.219397i
$261$	−3.64514e8	+	2.88581e7i	−1.26903	+	0.100468i
$262$	2.35294e8	−	1.35847e8i	0.808270	−	0.466655i
$263$	−6.77099e7	+	3.90924e7i	−0.229513	+	0.132509i	−0.610347	−	0.792134i	$-0.708970\pi$
$263$	−6.77099e7	+	3.90924e7i	−0.229513	+	0.132509i	0.380834	+	0.924643i	$0.375637\pi$
$264$	−4.80444e8	−	1.08596e8i	−1.60705	−	0.363246i
$265$			4.37264e7i			0.144339i
$266$	−5.58176e7	−	1.65265e7i	−0.181838	−	0.0538386i
$267$	6.43620e7	+	2.07110e8i	0.206938	+	0.665904i
$268$	6.88206e7	−	1.19201e8i	0.218397	−	0.378275i
$269$	2.96624e7	+	5.13768e7i	0.0929123	+	0.160929i	0.908735	−	0.417373i	$-0.137049\pi$
$269$	2.96624e7	+	5.13768e7i	0.0929123	+	0.160929i	−0.815823	+	0.578302i	$0.803716\pi$
$270$	2.33041e8	+	3.36238e7i	0.720543	+	0.103962i
$271$	2.71742e8	+	1.56890e8i	0.829401	+	0.478855i	0.853648	−	0.520851i	$-0.174385\pi$
$271$	2.71742e8	+	1.56890e8i	0.829401	+	0.478855i	−0.0242466	+	0.999706i	$0.507719\pi$
$272$	3.00859e8			0.906509
$273$	2.61486e8	−	3.51593e6i	0.777821	−	0.0104585i
$274$	−5.05864e8			−1.48562
$275$	9.99524e7	+	5.77075e7i	0.289820	+	0.167328i
$276$	−7.82258e7	−	7.22776e7i	−0.223959	−	0.206929i
$277$	3.31928e8	+	5.74916e8i	0.938349	+	1.62527i	0.768550	+	0.639790i	$0.220979\pi$
$277$	3.31928e8	+	5.74916e8i	0.938349	+	1.62527i	0.169799	+	0.985479i	$0.445688\pi$
$278$	1.04271e8	−	1.80603e8i	0.291077	−	0.504161i
$279$	−2.84271e8	−	4.13206e8i	−0.783642	−	1.13907i
$280$	−3.43114e8	+	8.24192e7i	−0.934084	+	0.224375i
$281$		−	4.05619e8i		−	1.09055i	−0.838257	−	0.545275i	$-0.816425\pi$
$281$		−	4.05619e8i		−	1.09055i	0.838257	−	0.545275i	$-0.183575\pi$
$282$	804119.	−	3.55753e6i	0.00213525	−	0.00944662i
$283$	−2.57463e8	+	1.48646e8i	−0.675246	+	0.389853i	−0.798061	−	0.602576i	$-0.794141\pi$
$283$	−2.57463e8	+	1.48646e8i	−0.675246	+	0.389853i	0.122815	+	0.992430i	$0.460808\pi$
$284$	2.51958e7	−	1.45468e7i	0.0652700	−	0.0376836i
$285$	1.74821e7	−	7.73431e7i	0.0447339	−	0.197909i
$286$			3.84252e8i			0.971258i
$287$	−5.17793e7	+	4.91488e7i	−0.129291	+	0.122723i
$288$	−1.40496e8	−	2.04219e8i	−0.346569	−	0.503760i
$289$	−2.98967e8	+	5.17827e8i	−0.728587	+	1.26195i
$290$	−1.92454e8	−	3.33340e8i	−0.463376	−	0.802591i
$291$	7.47396e6	+	6.90565e6i	0.0177797	+	0.0164278i
$292$	−1.90231e8	−	1.09830e8i	−0.447139	−	0.258156i
$293$	−6.28561e8			−1.45986			−0.729929	−	0.683522i	$-0.760447\pi$
$293$	−6.28561e8			−1.45986			−0.729929	+	0.683522i	$0.760447\pi$
$294$	−8.86399e7	−	3.48322e8i	−0.203429	−	0.799402i
$295$	−5.78737e7			−0.131251
$296$	3.82972e8	+	2.21109e8i	0.858314	+	0.495548i
$297$	6.76392e8	+	9.75913e7i	1.49813	+	0.216154i
$298$	8.44410e7	+	1.46256e8i	0.184840	+	0.320153i
$299$	−1.71537e8	+	2.97110e8i	−0.371115	+	0.642789i
$300$	9.80567e6	+	3.15536e7i	0.0209678	+	0.0674720i
$301$	7.77366e7	−	7.37874e7i	0.164302	−	0.155955i
$302$		−	7.69063e7i		−	0.160671i
$303$	1.85283e8	+	4.18800e7i	0.382636	+	0.0864884i
$304$	5.64006e7	−	3.25629e7i	0.115140	−	0.0664761i
$305$	5.06812e7	−	2.92608e7i	0.102282	−	0.0590524i
$306$	−6.46066e8	+	5.11483e7i	−1.28900	+	0.102048i
$307$		−	1.40498e7i		−	0.0277132i	−0.999904	−	0.0138566i	$-0.995589\pi$
$307$		−	1.40498e7i		−	0.0277132i	0.999904	−	0.0138566i	$-0.00441083\pi$
$308$	−2.41179e8	+	5.79334e7i	−0.470341	+	0.112980i
$309$	−1.77468e8	+	5.51503e7i	−0.342188	+	0.106339i
$310$	2.63977e8	−	4.57222e8i	0.503269	−	0.871688i
$311$	1.79268e8	+	3.10501e8i	0.337941	+	0.585330i	0.984045	−	0.177918i	$-0.0569363\pi$
$311$	1.79268e8	+	3.10501e8i	0.337941	+	0.585330i	−0.646105	+	0.763249i	$0.723603\pi$
$312$	−3.08260e8	+	3.33629e8i	−0.574614	+	0.621904i
$313$	7.45237e8	+	4.30263e8i	1.37369	+	0.793101i	0.991391	−	0.130937i	$-0.0417987\pi$
$313$	7.45237e8	+	4.30263e8i	1.37369	+	0.793101i	0.382300	+	0.924038i	$0.375132\pi$
$314$	4.98688e8			0.909024
$315$	4.65536e8	−	1.51564e8i	0.839202	−	0.273218i
$316$	1.04389e8			0.186101
$317$	−2.67116e8	−	1.54219e8i	−0.470969	−	0.271914i	0.245676	−	0.969352i	$-0.420990\pi$
$317$	−2.67116e8	−	1.54219e8i	−0.470969	−	0.271914i	−0.716645	+	0.697438i	$0.754323\pi$
$318$	5.25000e7	−	5.68207e7i	0.0915513	−	0.0990858i
$319$	−5.58588e8	−	9.67503e8i	−0.963439	−	1.66873i
$320$	2.80052e8	−	4.85065e8i	0.477765	−	0.827513i
$321$	5.50517e8	−	1.71080e8i	0.928973	−	0.288690i
$322$	4.52125e8	+	1.33865e8i	0.754680	+	0.223445i
$323$			2.18257e8i			0.360379i
$324$	1.23267e8	+	1.51933e8i	0.201344	+	0.248168i
$325$	9.21754e7	−	5.32175e7i	0.148944	−	0.0859929i
$326$	−2.43386e8	+	1.40519e8i	−0.389075	+	0.224633i
$327$	6.53641e8	+	1.47744e8i	1.03377	+	0.233665i
$328$		−	1.24005e8i		−	0.194036i
$329$	−1.77133e6	−	7.37412e6i	−0.00274229	−	0.0114163i
$330$	2.13485e8	+	6.86971e8i	0.327016	+	1.05230i
$331$	7.52682e7	−	1.30368e8i	0.114081	−	0.197594i	−0.803331	−	0.595533i	$-0.796941\pi$
$331$	7.52682e7	−	1.30368e8i	0.114081	−	0.197594i	0.917412	+	0.397939i	$0.130274\pi$
$332$	4.18958e7	+	7.25656e7i	0.0628329	+	0.108830i
$333$	−5.53899e8	−	2.63881e8i	−0.822007	−	0.391609i
$334$	−5.41634e8	−	3.12713e8i	−0.795414	−	0.459233i
$335$	−8.30055e8			−1.20629
$336$	3.50906e8	+	1.96353e8i	0.504666	+	0.282391i
$337$	4.66726e8			0.664289			0.332145	−	0.943228i	$-0.392228\pi$
$337$	4.66726e8			0.664289			0.332145	+	0.943228i	$0.392228\pi$
$338$	−2.00263e8	−	1.15622e8i	−0.282093	−	0.162866i
$339$	−8.65005e8	−	7.99231e8i	−1.20592	−	1.11423i
$340$	1.60205e8	+	2.77483e8i	0.221055	+	0.382878i
$341$	7.66181e8	−	1.32706e9i	1.04638	−	1.81239i
$342$	−1.15579e8	+	7.95143e7i	−0.156238	+	0.107486i
$343$	−4.85581e8	−	5.68117e8i	−0.649729	−	0.760166i
$344$			1.86170e8i			0.246579i
$345$	−1.41606e8	+	6.26482e8i	−0.185658	+	0.821376i
$346$	−5.89132e8	+	3.40136e8i	−0.764622	+	0.441455i
$347$	5.79493e8	−	3.34570e8i	0.744552	−	0.429867i	−0.0791701	−	0.996861i	$-0.525227\pi$
$347$	5.79493e8	−	3.34570e8i	0.744552	−	0.429867i	0.823722	+	0.566994i	$0.191894\pi$
$348$	7.05144e7	−	3.11965e8i	0.0896913	−	0.396806i
$349$			4.41794e8i			0.556327i	0.960534	+	0.278164i	$0.0897258\pi$
$349$			4.41794e8i			0.556327i	−0.960534	+	0.278164i	$0.910274\pi$
$350$	−1.00710e8	−	1.06100e8i	−0.125555	−	0.132274i
$351$	3.89822e8	−	4.95196e8i	0.481162	−	0.611226i
$352$	3.78671e8	−	6.55878e8i	0.462767	−	0.801537i
$353$	4.41373e8	+	7.64481e8i	0.534065	+	0.925028i	0.999208	+	0.0397926i	$0.0126697\pi$
$353$	4.41373e8	+	7.64481e8i	0.534065	+	0.925028i	−0.465143	+	0.885236i	$0.653997\pi$
$354$	7.52044e7	+	6.94859e7i	0.0901015	+	0.0832502i
$355$	−1.51945e8	−	8.77255e7i	−0.180255	−	0.104070i
$356$	−1.89703e8			−0.222843
$357$	−1.15788e9	+	6.89423e8i	−1.34687	+	0.801949i
$358$	9.79538e8			1.12832
$359$	8.22004e8	+	4.74584e8i	0.937655	+	0.541356i	0.889225	−	0.457471i	$-0.151245\pi$
$359$	8.22004e8	+	4.74584e8i	0.937655	+	0.541356i	0.0484309	+	0.998827i	$0.484578\pi$
$360$	−3.65753e8	+	7.67733e8i	−0.413170	+	0.867264i
$361$	−4.23313e8	−	7.33200e8i	−0.473573	−	0.820252i
$362$	−3.43728e8	+	5.95354e8i	−0.380833	+	0.659622i
$363$	3.49182e8	+	1.12363e9i	0.383159	+	1.23296i
$364$	−6.49388e7	+	2.19329e8i	−0.0705748	+	0.238364i
$365$			1.32468e9i			1.42589i
$366$	−1.00990e8	−	2.28271e7i	−0.107670	−	0.0243370i
$367$	−6.86384e8	+	3.96284e8i	−0.724829	+	0.418480i	−0.816528	−	0.577307i	$-0.804104\pi$
$367$	−6.86384e8	+	3.96284e8i	−0.724829	+	0.418480i	0.0916984	+	0.995787i	$0.470770\pi$
$368$	−4.56847e8	+	2.63761e8i	−0.477863	+	0.275895i
$369$	1.35784e7	+	1.71512e8i	0.0140687	+	0.177706i
$370$		−	6.45849e8i		−	0.662865i
$371$	4.56678e7	−	1.54242e8i	0.0464303	−	0.156817i
$372$	4.18936e8	−	1.30190e8i	0.421936	−	0.131122i
$373$	−4.12311e8	+	7.14144e8i	−0.411381	+	0.712533i	−0.995041	−	0.0994651i	$-0.968287\pi$
$373$	−4.12311e8	+	7.14144e8i	−0.411381	+	0.712533i	0.583660	+	0.811998i	$0.301620\pi$
$374$	−9.90043e8	−	1.71480e9i	−0.978596	−	1.69498i
$375$	7.46851e8	−	8.08316e8i	0.731349	−	0.791537i
$376$	1.14082e7	+	6.58654e6i	0.0110678	+	0.00638999i
$377$	−1.03025e9			−0.990258
$378$	−7.86920e8	−	3.61994e8i	−0.749392	−	0.344730i
$379$	−4.65185e8			−0.438923			−0.219461	−	0.975621i	$-0.570430\pi$
$379$	−4.65185e8			−0.438923			−0.219461	+	0.975621i	$0.570430\pi$
$380$	6.00658e7	+	3.46790e7i	0.0561545	+	0.0324208i
$381$	−8.15768e8	+	8.82904e8i	−0.755665	+	0.817855i
$382$	−2.73683e7	−	4.74033e7i	−0.0251204	−	0.0435098i
$383$	−5.00552e8	+	8.66981e8i	−0.455254	+	0.788522i	−0.998703	−	0.0509196i	$-0.983785\pi$
$383$	−5.00552e8	+	8.66981e8i	−0.455254	+	0.788522i	0.543449	+	0.839442i	$0.317118\pi$
$384$	−2.98407e8	+	9.27338e7i	−0.268937	+	0.0835754i
$385$	1.02979e9	+	1.08490e9i	0.919679	+	0.968900i
$386$			1.08559e9i			0.960747i
$387$	−2.03853e7	−	2.57491e8i	−0.0178784	−	0.225826i
$388$	−7.70826e6	+	4.45037e6i	−0.00669955	+	0.00386799i
$389$	7.88764e8	−	4.55393e8i	0.679397	−	0.392250i	−0.120231	−	0.992746i	$-0.538363\pi$
$389$	7.88764e8	−	4.55393e8i	0.679397	−	0.392250i	0.799628	+	0.600496i	$0.205030\pi$
$390$	6.47081e8	+	1.46262e8i	0.552373	+	0.124855i
$391$		−	1.76789e9i		−	1.49567i
$392$	1.29639e9	+	6.76208e7i	1.08701	+	0.0566995i
$393$	−4.04035e8	−	1.30014e9i	−0.335772	−	1.08048i
$394$	1.09675e8	−	1.89962e8i	0.0903380	−	0.156470i
$395$	−3.14762e8	−	5.45183e8i	−0.256976	−	0.445095i
$396$	−2.57092e8	+	5.39649e8i	−0.208044	+	0.436695i
$397$	2.62646e8	+	1.51639e8i	0.210671	+	0.121631i	0.601623	−	0.798780i	$-0.294521\pi$
$397$	2.62646e8	+	1.51639e8i	0.210671	+	0.121631i	−0.390952	+	0.920411i	$0.627854\pi$
$398$	1.84260e9			1.46501
$399$	−1.42444e8	+	2.54564e8i	−0.112264	+	0.200628i
$400$	1.63658e8			0.127858
$401$	−1.18574e9	−	6.84586e8i	−0.918297	−	0.530179i	−0.0352055	−	0.999380i	$-0.511209\pi$
$401$	−1.18574e9	−	6.84586e8i	−0.918297	−	0.530179i	−0.883091	+	0.469201i	$0.844542\pi$
$402$	1.07862e9	+	9.96604e8i	0.828091	+	0.765123i
$403$	−7.06567e8	−	1.22381e9i	−0.537756	−	0.931421i
$404$	−8.30769e7	+	1.43893e8i	−0.0626824	+	0.108569i
$405$	4.21806e8	−	1.10190e9i	0.315515	−	0.824232i
$406$	3.30727e8	+	1.37683e9i	0.245261	+	1.02103i
$407$		−	1.87455e9i		−	1.37821i
$408$	5.16065e8	−	2.28314e9i	0.376178	−	1.66426i
$409$	4.11207e8	−	2.37410e8i	0.297186	−	0.171580i	−0.343992	−	0.938973i	$-0.611779\pi$
$409$	4.11207e8	−	2.37410e8i	0.297186	−	0.171580i	0.641178	+	0.767392i	$0.278446\pi$
$410$	−1.56843e8	+	9.05536e7i	−0.112389	+	0.0648877i
$411$	−5.58874e8	+	2.47253e9i	−0.397070	+	1.75669i
$412$		−	1.62552e8i		−	0.114512i
$413$	2.04145e8	+	6.04432e7i	0.142598	+	0.0422204i
$414$	9.36195e8	−	6.44069e8i	0.648433	−	0.446099i
$415$	2.52656e8	−	4.37612e8i	0.173524	−	0.300553i
$416$	−3.49208e8	−	6.04845e8i	−0.237825	−	0.411925i
$417$	−7.67545e8	−	7.09181e8i	−0.518355	−	0.478940i
$418$	−3.71197e8	−	2.14311e8i	−0.248592	−	0.143525i
$419$	1.13110e9			0.751197			0.375598	−	0.926783i	$-0.377437\pi$
$419$	1.13110e9			0.751197			0.375598	+	0.926783i	$0.377437\pi$
$420$	5.75754e6	+	4.28199e8i	0.00379197	+	0.282016i
$421$	1.77782e9			1.16118			0.580592	−	0.814195i	$-0.302821\pi$
$421$	1.77782e9			1.16118			0.580592	+	0.814195i	$0.302821\pi$
$422$	1.31709e9	+	7.60425e8i	0.853146	+	0.492564i
$423$	−1.64999e7	−	7.86065e6i	−0.0105996	−	0.00504972i
$424$	1.39706e8	+	2.41978e8i	0.0890092	+	0.154168i
$425$	−2.74235e8	+	4.74989e8i	−0.173285	+	0.300139i
$426$	9.21187e7	+	2.96428e8i	0.0577317	+	0.185774i
$427$	−2.09334e8	+	5.02840e7i	−0.130120	+	0.0312559i
$428$			5.04248e8i			0.310879i
$429$	1.87812e9	+	4.24518e8i	1.14848	+	0.259594i
$430$	2.35470e8	−	1.35949e8i	0.142822	−	0.0824584i
$431$	−1.64904e8	+	9.52075e7i	−0.0992113	+	0.0572797i	−0.548785	−	0.835964i	$-0.684909\pi$
$431$	−1.64904e8	+	9.52075e7i	−0.0992113	+	0.0572797i	0.449573	+	0.893243i	$0.351576\pi$
$432$	8.99815e8	−	3.59716e8i	0.536982	−	0.214668i
$433$			1.11786e9i			0.661729i	0.943678	+	0.330864i	$0.107340\pi$
$433$			1.11786e9i			0.661729i	−0.943678	+	0.330864i	$0.892660\pi$
$434$	−1.40868e9	+	1.33712e9i	−0.827178	+	0.785156i
$435$	−1.84190e9	+	5.72394e8i	−1.07289	+	0.333413i
$436$	−2.93079e8	+	5.07627e8i	−0.169348	+	0.293320i
$437$	−1.91344e8	−	3.31418e8i	−0.109681	−	0.189973i
$438$	1.59047e9	−	1.72136e9i	0.904412	−	0.978843i
$439$	−5.35334e8	−	3.09075e8i	−0.301994	−	0.174357i	0.341344	−	0.939938i	$-0.389118\pi$
$439$	−5.35334e8	−	3.09075e8i	−0.301994	−	0.174357i	−0.643338	+	0.765582i	$0.722451\pi$
$440$	−2.59822e9			−1.45409
$441$	−1.80044e9	+	4.84259e7i	−0.999638	+	0.0268870i
$442$	−1.82602e9			−1.00584
$443$	−2.26395e9	−	1.30709e9i	−1.23724	−	0.714322i	−0.268712	−	0.963221i	$-0.586598\pi$
$443$	−2.26395e9	−	1.30709e9i	−1.23724	−	0.714322i	−0.968529	+	0.248899i	$0.919931\pi$
$444$	3.64195e8	−	3.94168e8i	0.197467	−	0.213718i
$445$	5.72010e8	+	9.90750e8i	0.307711	+	0.532971i
$446$	5.76161e8	−	9.97941e8i	0.307519	−	0.532639i
$447$	8.08152e8	−	2.51144e8i	0.427973	−	0.132998i
$448$	−1.49446e9	+	1.41854e9i	−0.785258	+	0.745366i
$449$			8.76314e8i			0.456875i	0.973559	+	0.228438i	$0.0733617\pi$
$449$			8.76314e8i			0.456875i	−0.973559	+	0.228438i	$0.926638\pi$
$450$	−3.51440e8	+	2.78231e7i	−0.181806	+	0.0143933i
$451$	−4.55230e8	+	2.62827e8i	−0.233676	+	0.134913i
$452$	8.92122e8	−	5.15067e8i	0.454402	−	0.262349i
$453$	−3.75898e8	−	8.49653e7i	−0.189988	−	0.0429436i
$454$			1.21381e9i			0.608773i
$455$	1.34128e9	−	3.22188e8i	0.667545	−	0.160350i
$456$	−1.50367e8	−	4.83865e8i	−0.0742636	−	0.238972i
$457$	−1.15080e9	+	1.99324e9i	−0.564017	+	0.976906i	0.433123	+	0.901335i	$0.357411\pi$
$457$	−1.15080e9	+	1.99324e9i	−0.564017	+	0.976906i	−0.997140	+	0.0755715i	$0.975922\pi$
$458$	5.96689e8	+	1.03350e9i	0.290214	+	0.502666i
$459$	−4.63769e8	+	3.21431e9i	−0.223850	+	1.55147i
$460$	−4.86535e8	−	2.80901e8i	−0.233057	−	0.134555i
$461$	1.26292e9			0.600376			0.300188	−	0.953880i	$-0.402951\pi$
$461$	1.26292e9			0.600376			0.300188	+	0.953880i	$0.402951\pi$
$462$	−3.55807e7	−	2.64620e9i	−0.0167868	−	1.24846i
$463$	1.16895e9			0.547346			0.273673	−	0.961823i	$-0.411761\pi$
$463$	1.16895e9			0.547346			0.273673	+	0.961823i	$0.411761\pi$
$464$	−1.37191e9	−	7.92075e8i	−0.637550	−	0.368090i
$465$	−1.94314e9	−	1.79539e9i	−0.896230	−	0.828081i
$466$	2.75686e8	+	4.77503e8i	0.126202	+	0.218587i
$467$	4.98495e8	−	8.63419e8i	0.226492	−	0.392295i	−0.730274	−	0.683154i	$-0.760608\pi$
$467$	4.98495e8	−	8.63419e8i	0.226492	−	0.392295i	0.956766	+	0.290859i	$0.0939411\pi$
$468$	3.12442e8	+	4.54155e8i	0.140899	+	0.204806i
$469$	2.92796e9	+	8.66909e8i	1.31057	+	0.388033i
$470$		−	1.92390e7i		−	0.00854751i
$471$	5.50946e8	−	2.43746e9i	0.242961	−	1.07489i
$472$	−3.20268e8	+	1.84907e8i	−0.140190	+	0.0809385i
$473$	6.83440e8	−	3.94584e8i	0.296952	−	0.171445i
$474$	−2.45553e8	+	1.08636e9i	−0.105906	+	0.468543i
$475$			1.18725e8i			0.0508294i
$476$	−2.75308e8	−	1.14612e9i	−0.117002	−	0.487086i
$477$	−2.19723e8	−	3.19382e8i	−0.0926961	−	0.134740i
$478$	−1.27852e9	+	2.21445e9i	−0.535437	+	0.927404i
$479$	1.86276e9	+	3.22640e9i	0.774432	+	1.34136i	0.935113	+	0.354350i	$0.115298\pi$
$479$	1.86276e9	+	3.22640e9i	0.774432	+	1.34136i	−0.160680	+	0.987006i	$0.551369\pi$
$480$	−9.60363e8	−	8.87337e8i	−0.396361	−	0.366222i
$481$	−1.49709e9	−	8.64347e8i	−0.613396	−	0.354144i
$482$	−8.07463e8			−0.328441
$483$	1.15380e9	−	2.06198e9i	0.465925	−	0.832662i
$484$	−1.02919e9			−0.412609
$485$	4.64853e7	+	2.68383e7i	0.0185020	+	0.0106821i
$486$	−1.87111e9	+	9.25431e8i	−0.739389	+	0.365693i
$487$	6.77016e8	+	1.17263e9i	0.265612	+	0.460053i	0.967724	−	0.252013i	$-0.0810927\pi$
$487$	6.77016e8	+	1.17263e9i	0.265612	+	0.460053i	−0.702112	+	0.712067i	$0.747759\pi$
$488$	1.86977e8	−	3.23853e8i	0.0728314	−	0.126148i
$489$	4.17930e8	+	1.34485e9i	0.161630	+	0.520108i
$490$	−8.61146e8	−	1.68907e9i	−0.330667	−	0.648575i
$491$			1.16862e9i			0.445540i	0.974871	+	0.222770i	$0.0715099\pi$
$491$			1.16862e9i			0.445540i	−0.974871	+	0.222770i	$0.928490\pi$
$492$	−1.46786e8	−	3.31785e7i	−0.0555658	−	0.0125597i
$493$	4.59772e9	−	2.65449e9i	1.72814	−	0.997740i
$494$	−3.42316e8	+	1.97636e8i	−0.127756	+	0.0737601i
$495$	3.59359e9	−	2.84500e8i	1.33171	−	0.105430i
$496$		−	2.17288e9i		−	0.799559i
$497$	4.44354e8	+	4.68136e8i	0.162361	+	0.171051i
$498$	−8.53734e8	+	2.65309e8i	−0.309756	+	0.0962606i
$499$	−6.44700e8	+	1.11665e9i	−0.232277	+	0.402315i	−0.958478	−	0.285167i	$-0.907951\pi$
$499$	−6.44700e8	+	1.11665e9i	−0.232277	+	0.402315i	0.726201	+	0.687483i	$0.241284\pi$
$500$	4.81311e8	+	8.33655e8i	0.172199	+	0.298258i
$501$	−2.12685e9	+	2.30189e9i	−0.755623	+	0.817809i
$502$	−3.10298e9	−	1.79150e9i	−1.09475	−	0.632055i
$503$	−3.67733e9			−1.28838			−0.644191	−	0.764864i	$-0.722806\pi$
$503$	−3.67733e9			−1.28838			−0.644191	+	0.764864i	$0.722806\pi$
$504$	2.09198e9	−	2.32613e9i	0.727866	−	0.809333i
$505$	1.00200e9			0.346218
$506$	3.00671e9	+	1.73593e9i	1.03173	+	0.595669i
$507$	−7.86379e8	+	8.51096e8i	−0.267981	+	0.290035i
$508$	−5.25725e8	−	9.10582e8i	−0.177924	−	0.308174i
$509$	−8.68881e7	+	1.50495e8i	−0.0292044	+	0.0505835i	−0.880258	−	0.474495i	$-0.842631\pi$
$509$	−8.68881e7	+	1.50495e8i	−0.0292044	+	0.0505835i	0.851054	+	0.525078i	$0.175964\pi$
$510$	−3.26459e9	+	1.01451e9i	−1.08977	+	0.338658i
$511$	1.38349e9	−	4.67270e9i	0.458673	−	1.54916i
$512$		−	2.98562e9i		−	0.983083i
$513$	2.60955e8	+	6.52767e8i	0.0853404	+	0.213475i
$514$	4.18572e9	−	2.41663e9i	1.35956	−	0.784944i
$515$	−8.48950e8	+	4.90141e8i	−0.273878	+	0.158123i
$516$	2.20371e8	+	4.98111e7i	0.0706123	+	0.0159607i
$517$		−	5.58402e7i		−	0.0177718i
$518$	−6.74524e8	+	2.27819e9i	−0.213228	+	0.720170i
$519$	1.01163e9	+	3.25531e9i	0.317640	+	1.02213i
$520$	−1.19803e9	+	2.07505e9i	−0.373642	+	0.647168i
$521$	−1.35635e9	−	2.34927e9i	−0.420185	−	0.727782i	0.575772	−	0.817610i	$-0.304701\pi$
$521$	−1.35635e9	−	2.34927e9i	−0.420185	−	0.727782i	−0.995957	+	0.0898283i	$0.971368\pi$
$522$	3.08072e9	+	1.46767e9i	0.947992	+	0.451629i
$523$	−1.52842e9	−	8.82433e8i	−0.467182	−	0.269728i	0.247877	−	0.968791i	$-0.420267\pi$
$523$	−1.52842e9	−	8.82433e8i	−0.467182	−	0.269728i	−0.715059	+	0.699064i	$0.753600\pi$
$524$	1.19087e9			0.361580
$525$	−6.29851e8	+	3.75025e8i	−0.189968	+	0.113110i
$526$	7.29655e8			0.218609
$527$	6.30641e9	+	3.64101e9i	1.87692	+	1.08364i
$528$	2.17459e9	+	2.00923e9i	0.642922	+	0.594035i
$529$	−1.52515e8	−	2.64163e8i	−0.0447937	−	0.0775850i
$530$	2.04038e8	−	3.53403e8i	0.0595312	−	0.103111i
$531$	4.22714e8	−	2.90813e8i	0.122523	−	0.0842912i
$532$	−1.75659e8	−	1.85060e8i	−0.0505801	−	0.0532872i
$533$			4.84755e8i			0.138668i
$534$	4.46239e8	−	1.97422e9i	0.126816	−	0.561049i
$535$	2.63350e9	−	1.52045e9i	0.743525	−	0.429274i
$536$	−4.59345e9	+	2.65203e9i	−1.28843	+	0.743877i
$537$	1.08218e9	−	4.78773e9i	0.301572	−	1.33420i
$538$		−	5.53646e8i		−	0.153283i
$539$	−2.49944e9	−	4.90243e9i	−0.687513	−	1.34850i
$540$	8.10912e8	+	6.38356e8i	0.221613	+	0.174456i
$541$	7.33347e8	−	1.27019e9i	0.199122	−	0.344889i	−0.749122	−	0.662432i	$-0.769524\pi$
$541$	7.33347e8	−	1.27019e9i	0.199122	−	0.344889i	0.948244	+	0.317543i	$0.102858\pi$
$542$	−1.46417e9	−	2.53602e9i	−0.394998	−	0.684157i
$543$	2.53019e9	+	2.33779e9i	0.678194	+	0.626624i
$544$	3.11683e9	+	1.79950e9i	0.830074	+	0.479243i
$545$	3.53486e9			0.935373
$546$	−2.12978e9	−	1.19174e9i	−0.559963	−	0.313333i
$547$	−6.14008e9			−1.60405			−0.802026	−	0.597290i	$-0.796244\pi$
$547$	−6.14008e9			−1.60405			−0.802026	+	0.597290i	$0.796244\pi$
$548$	−1.92021e9	−	1.10863e9i	−0.498443	−	0.287776i
$549$	−2.23146e8	+	4.68394e8i	−0.0575553	+	0.120812i
$550$	−5.38553e8	−	9.32801e8i	−0.138025	−	0.239067i
$551$	5.74608e8	−	9.95251e8i	0.146333	−	0.253456i
$552$	1.21798e9	+	3.91932e9i	0.308215	+	0.991801i
$553$	5.40909e8	+	2.25183e9i	0.136015	+	0.566236i
$554$		−	6.19540e9i		−	1.54805i
$555$	−3.15675e9	−	7.13528e8i	−0.783816	−	0.177168i
$556$	7.91607e8	−	4.57034e8i	0.195320	−	0.112768i
$557$	−3.05784e9	+	1.76545e9i	−0.749759	+	0.432874i	−0.825607	−	0.564246i	$-0.809167\pi$
$557$	−3.05784e9	+	1.76545e9i	−0.749759	+	0.432874i	0.0758478	+	0.997119i	$0.475834\pi$
$558$	3.69406e8	+	4.66606e9i	0.0900087	+	1.13692i
$559$		−	7.27765e8i		−	0.176218i
$560$	2.03380e9	+	6.02166e8i	0.489384	+	0.144897i
$561$	−9.47532e9	+	2.94457e9i	−2.26581	+	0.704130i
$562$	−1.89271e9	+	3.27827e9i	−0.449787	+	0.779054i
$563$	−3.97961e8	−	6.89288e8i	−0.0939855	−	0.162788i	0.815199	−	0.579181i	$-0.196627\pi$
$563$	−3.97961e8	−	6.89288e8i	−0.0939855	−	0.162788i	−0.909185	+	0.416393i	$0.863294\pi$
$564$	1.08489e7	−	1.17417e7i	0.00254629	−	0.00275585i
$565$	−5.38001e9	−	3.10615e9i	−1.25491	−	0.724524i
$566$	2.77447e9			0.643165
$567$	−2.63871e9	+	3.44633e9i	−0.607927	+	0.793993i
$568$	−1.12113e9			−0.256707
$569$	−5.57057e9	−	3.21617e9i	−1.26767	−	0.731891i	−0.293125	−	0.956074i	$-0.594695\pi$
$569$	−5.57057e9	−	3.21617e9i	−1.26767	−	0.731891i	−0.974547	+	0.224183i	$0.928029\pi$
$570$	−5.02193e8	+	5.43523e8i	−0.113582	+	0.122929i
$571$	3.06434e9	+	5.30759e9i	0.688827	+	1.19308i	0.972218	+	0.234078i	$0.0752073\pi$
$571$	3.06434e9	+	5.30759e9i	0.688827	+	1.19308i	−0.283391	+	0.959004i	$0.591459\pi$
$572$	−8.42110e8	+	1.45858e9i	−0.188141	+	0.325869i
$573$	−2.61932e8	+	8.13986e7i	−0.0581630	+	0.0180749i
$574$	6.47827e8	−	1.55614e8i	0.142978	−	0.0343445i
$575$		−	9.61679e8i		−	0.210956i
$576$	3.91901e8	+	4.95020e9i	0.0854472	+	1.07931i
$577$	−1.63361e9	+	9.43165e8i	−0.354024	+	0.204396i	−0.666456	−	0.745544i	$-0.732190\pi$
$577$	−1.63361e9	+	9.43165e8i	−0.354024	+	0.204396i	0.312432	+	0.949940i	$0.398856\pi$
$578$	4.83259e9	−	2.79010e9i	1.04096	−	0.600997i
$579$	5.30607e9	+	1.19935e9i	1.13605	+	0.256785i
$580$		−	1.68710e9i		−	0.359039i
$581$	−1.34827e9	+	1.27977e9i	−0.285206	+	0.270717i
$582$	−2.81823e7	−	9.06876e7i	−0.00592579	−	0.0190685i
$583$	5.92209e8	−	1.02574e9i	0.123776	−	0.214386i
$584$	4.23235e9	+	7.33064e9i	0.879299	+	1.52299i
$585$	1.42978e9	−	3.00118e9i	0.295273	−	0.619792i
$586$	5.08012e9	+	2.93301e9i	1.04288	+	0.602104i
$587$	−1.57758e9			−0.321927			−0.160964	−	0.986960i	$-0.551460\pi$
$587$	−1.57758e9			−0.321927			−0.160964	+	0.986960i	$0.551460\pi$
$588$	4.26901e8	−	1.51645e9i	0.0865978	−	0.307616i
$589$	1.57631e9			0.317862
$590$	4.67744e8	+	2.70052e8i	0.0937618	+	0.0541334i
$591$	−8.07320e8	−	7.45931e8i	−0.160875	−	0.148642i
$592$	−1.32905e9	−	2.30198e9i	−0.263278	−	0.456011i
$593$	−3.31281e9	+	5.73796e9i	−0.652387	+	1.12997i	0.330155	+	0.943927i	$0.392899\pi$
$593$	−3.31281e9	+	5.73796e9i	−0.652387	+	1.12997i	−0.982542	+	0.186041i	$0.940434\pi$
$594$	−5.01131e9	−	3.94494e9i	−0.981067	−	0.772304i
$595$	−5.15563e9	+	4.89372e9i	−1.00340	+	0.952422i
$596$			7.40230e8i			0.143220i
$597$	2.03568e9	−	9.00614e9i	0.391562	−	1.73232i
$598$	2.77277e9	−	1.60086e9i	0.530224	−	0.306125i
$599$	−2.71147e8	+	1.56547e8i	−0.0515480	+	0.0297612i	−0.525552	−	0.850761i	$-0.676141\pi$
$599$	−2.71147e8	+	1.56547e8i	−0.0515480	+	0.0297612i	0.474005	+	0.880522i	$0.342808\pi$
$600$	2.80723e8	−	1.24196e9i	0.0530578	−	0.234735i
$601$		−	3.12363e7i		−	0.00586947i	−0.999996	−	0.00293474i	$-0.999066\pi$
$601$		−	3.12363e7i		−	0.00586947i	0.999996	−	0.00293474i	$-0.000934157\pi$
$602$	−9.72587e8	+	2.33624e8i	−0.181694	+	0.0436445i
$603$	6.06279e9	−	4.17099e9i	1.12606	−	0.774691i
$604$	1.68545e8	−	2.91928e8i	0.0311233	−	0.0539071i
$605$	3.10332e9	+	5.37510e9i	0.569747	+	0.986831i
$606$	−1.30206e9	−	1.20305e9i	−0.237671	−	0.219599i
$607$	−5.00161e9	−	2.88768e9i	−0.907715	−	0.524069i	−0.0280196	−	0.999607i	$-0.508920\pi$
$607$	−5.00161e9	−	2.88768e9i	−0.907715	−	0.524069i	−0.879695	+	0.475538i	$0.842253\pi$
$608$	7.79063e8			0.140576
$609$	7.09497e9	−	9.53986e7i	1.27289	−	0.0171152i
$610$	−5.46151e8			−0.0974222
$611$	−4.45964e7	−	2.57477e7i	−0.00790961	−	0.00456662i
$612$	−2.56449e9	−	1.22174e9i	−0.452243	−	0.215451i
$613$	−5.43330e8	−	9.41075e8i	−0.0952691	−	0.165011i	0.814452	−	0.580231i	$-0.197038\pi$
$613$	−5.43330e8	−	9.41075e8i	−0.0952691	−	0.165011i	−0.909721	+	0.415220i	$0.863704\pi$
$614$	−6.55597e7	+	1.13553e8i	−0.0114300	+	0.0197974i
$615$	2.69323e8	+	8.66653e8i	0.0466886	+	0.150239i
$616$	9.16503e9	+	2.71358e9i	1.57980	+	0.467746i
$617$		−	4.36859e9i		−	0.748761i	−0.927275	−	0.374381i	$-0.877855\pi$
$617$		−	4.36859e9i		−	0.748761i	0.927275	−	0.374381i	$-0.122145\pi$
$618$	1.69166e9	+	3.82371e8i	0.288306	+	0.0651667i
$619$	−7.76831e9	+	4.48504e9i	−1.31646	+	0.760061i	−0.983158	−	0.182757i	$-0.941498\pi$
$619$	−7.76831e9	+	4.48504e9i	−1.31646	+	0.760061i	−0.333307	+	0.942818i	$0.608164\pi$
$620$	2.00406e9	−	1.15704e9i	0.337707	−	0.194975i
$621$	−2.11374e9	−	5.28744e9i	−0.354186	−	0.885982i
$622$		−	3.34601e9i		−	0.557521i
$623$	−9.82984e8	−	4.09220e9i	−0.162869	−	0.678030i
$624$	2.60735e9	−	8.10269e8i	0.429590	−	0.133501i
$625$	2.22786e9	−	3.85877e9i	0.365013	−	0.632221i
$626$	−4.01541e9	−	6.95489e9i	−0.654213	−	1.13313i
$627$	−1.45759e9	+	1.57755e9i	−0.236156	+	0.255591i
$628$	1.89297e9	+	1.09290e9i	0.304989	+	0.176085i
$629$	8.90813e9			1.42728
$630$	−4.46976e9	−	9.47334e8i	−0.712184	−	0.150942i
$631$	1.18971e10			1.88512			0.942558	−	0.334043i	$-0.108413\pi$
$631$	1.18971e10			1.88512			0.942558	+	0.334043i	$0.108413\pi$
$632$	−3.48372e9	−	2.01133e9i	−0.548951	−	0.316937i
$633$	5.17187e9	−	5.59751e9i	0.810466	−	0.877166i
$634$	1.43925e9	+	2.49285e9i	0.224296	+	0.388493i
$635$	−3.17042e9	+	5.49133e9i	−0.491371	+	0.851079i
$636$	3.23810e8	−	1.00628e8i	0.0499104	−	0.0155103i
$637$	−5.06777e9	−	2.64340e8i	−0.776835	−	0.0405204i
$638$			1.04260e10i			1.58944i
$639$	1.55064e9	−	1.22762e8i	0.235102	−	0.0186127i
$640$	−1.42749e9	+	8.24160e8i	−0.215250	+	0.124274i
$641$	5.80892e9	−	3.35378e9i	0.871148	−	0.502958i	0.00341864	−	0.999994i	$-0.498912\pi$
$641$	5.80892e9	−	3.35378e9i	0.871148	−	0.502958i	0.867730	+	0.497036i	$0.165578\pi$
$642$	−5.24766e9	−	1.18614e9i	−0.782695	−	0.176915i
$643$			9.24553e9i			1.37149i	0.727840	+	0.685747i	$0.240524\pi$
$643$			9.24553e9i			1.37149i	−0.727840	+	0.685747i	$0.759476\pi$
$644$	1.42284e9	+	1.49900e9i	0.209922	+	0.221157i
$645$	−4.04337e8	−	1.30111e9i	−0.0593313	−	0.190922i
$646$	1.01844e9	−	1.76399e9i	0.148635	−	0.257443i
$647$	−2.88538e9	−	4.99762e9i	−0.418830	−	0.725434i	0.576992	−	0.816750i	$-0.304226\pi$
$647$	−2.88538e9	−	4.99762e9i	−0.418830	−	0.725434i	−0.995822	+	0.0913152i	$0.970893\pi$
$648$	−1.18633e9	−	7.44548e9i	−0.171275	−	1.07493i
$649$	1.35760e9	+	7.83813e8i	0.194947	+	0.112553i
$650$	−9.93299e8			−0.141868
$651$	4.97919e9	+	8.36251e9i	0.707336	+	1.18796i
$652$	−1.23182e9			−0.174053
$653$	3.27258e9	+	1.88943e9i	0.459933	+	0.265542i	0.712016	−	0.702163i	$-0.247782\pi$
$653$	3.27258e9	+	1.88943e9i	0.459933	+	0.265542i	−0.252083	+	0.967706i	$0.581116\pi$
$654$	−4.59341e9	−	4.24413e9i	−0.642115	−	0.593289i
$655$	−3.59081e9	−	6.21947e9i	−0.499284	−	0.864786i
$656$	−3.72688e8	+	6.45515e8i	−0.0515445	+	0.0892776i
$657$	−6.65644e9	−	9.67556e9i	−0.915722	−	1.33106i
$658$	−2.00932e7	+	6.78641e7i	−0.00274953	+	0.00928644i
$659$			1.25248e10i			1.70479i	0.522897	+	0.852396i	$0.324851\pi$
$659$			1.25248e10i			1.70479i	−0.522897	+	0.852396i	$0.675149\pi$
$660$	−6.95172e8	+	3.07553e9i	−0.0941214	+	0.416406i
$661$	−4.37639e9	+	2.52671e9i	−0.589401	+	0.340291i	−0.764861	−	0.644196i	$-0.777192\pi$
$661$	−4.37639e9	+	2.52671e9i	−0.589401	+	0.340291i	0.175459	+	0.984487i	$0.443859\pi$
$662$	−1.21666e9	+	7.02437e8i	−0.162992	+	0.0941032i
$663$	−2.01737e9	+	8.92512e9i	−0.268837	+	1.18937i
$664$		−	3.22894e9i		−	0.428028i
$665$	−4.36839e8	+	1.47541e9i	−0.0576031	+	0.194553i
$666$	3.24536e9	+	4.71734e9i	0.425700	+	0.618781i
$667$	−4.65435e9	+	8.06157e9i	−0.607322	+	1.05191i
$668$	−1.37066e9	−	2.37405e9i	−0.177914	−	0.308157i
$669$	−4.24114e9	−	3.91864e9i	−0.547635	−	0.505993i
$670$	6.70863e9	+	3.87323e9i	0.861731	+	0.497521i
$671$	−1.58518e9			−0.202558
$672$	2.46088e9	+	4.13302e9i	0.312822	+	0.525382i
$673$	4.68666e9			0.592667			0.296333	−	0.955085i	$-0.404236\pi$
$673$	4.68666e9			0.592667			0.296333	+	0.955085i	$0.404236\pi$
$674$	−3.77215e9	−	2.17785e9i	−0.474546	−	0.273980i
$675$	−2.52276e8	+	1.74849e9i	−0.0315728	+	0.218826i
$676$	−5.06785e8	−	8.77777e8i	−0.0630972	−	0.109288i
$677$	4.99863e9	−	8.65788e9i	0.619143	−	1.07239i	−0.370500	−	0.928833i	$-0.620814\pi$
$677$	4.99863e9	−	8.65788e9i	0.619143	−	1.07239i	0.989642	−	0.143554i	$-0.0458531\pi$
$678$	3.26171e9	+	1.04958e10i	0.401921	+	1.29334i
$679$	−1.35943e8	−	1.43219e8i	−0.0166653	−	0.0175573i
$680$		−	1.23471e10i		−	1.50586i
$681$	5.93279e9	+	1.34101e9i	0.719853	+	0.162711i
$682$	−1.23848e10	+	7.15035e9i	−1.49501	+	0.863142i
$683$	2.37698e9	−	1.37235e9i	0.285465	−	0.164813i	−0.350430	−	0.936589i	$-0.613965\pi$
$683$	2.37698e9	−	1.37235e9i	0.285465	−	0.164813i	0.635895	+	0.771776i	$0.280631\pi$
$684$	−6.12986e8	+	4.85293e7i	−0.0732410	+	0.00579840i
$685$			1.33714e10i			1.58949i
$686$	1.27357e9	+	6.85744e9i	0.150622	+	0.811012i
$687$	5.71068e9	−	1.77467e9i	0.671954	−	0.208818i
$688$	5.59519e8	−	9.69115e8i	0.0655021	−	0.113453i
$689$	−5.46131e8	−	9.45926e8i	−0.0636106	−	0.110177i
$690$	4.06779e9	−	4.40256e9i	0.471396	−	0.510191i
$691$	−6.64389e9	−	3.83585e9i	−0.766036	−	0.442271i	0.0654228	−	0.997858i	$-0.479160\pi$
$691$	−6.64389e9	−	3.83585e9i	−0.766036	−	0.442271i	−0.831459	+	0.555587i	$0.812494\pi$
$692$	−2.98171e9			−0.342054
$693$	−1.29733e10	−	2.74959e9i	−1.48075	−	0.313835i
$694$	−6.24473e9			−0.709178
$695$	−4.77384e9	−	2.75618e9i	−0.539413	−	0.311430i
$696$	−8.36410e9	+	9.05245e9i	−0.940345	+	1.01773i
$697$	−1.24900e9	−	2.16332e9i	−0.139716	−	0.241995i
$698$	2.06151e9	−	3.57064e9i	0.229452	−	0.397422i
$699$	2.63849e9	−	8.19943e8i	0.292203	−	0.0908058i
$700$	−1.49759e8	−	6.23454e8i	−0.0165025	−	0.0687007i
$701$		−	1.08816e10i		−	1.19311i	−0.802571	−	0.596556i	$-0.796535\pi$
$701$		−	1.08816e10i		−	1.19311i	0.802571	−	0.596556i	$-0.203465\pi$
$702$	−5.46130e9	+	2.18324e9i	−0.595821	+	0.238189i
$703$	1.66996e9	−	9.64154e8i	0.181286	−	0.104665i
$704$	−1.31390e10	+	7.58578e9i	−1.41924	+	0.819400i
$705$	−9.40352e7	−	2.12551e7i	−0.0101071	−	0.00228455i
$706$		−	8.23819e9i		−	0.881080i
$707$	−3.53449e9	−	1.04649e9i	−0.376148	−	0.111370i
$708$	1.33185e8	+	4.28576e8i	0.0141039	+	0.0453849i
$709$	6.43595e9	−	1.11474e10i	0.678189	−	1.17466i	−0.297336	−	0.954773i	$-0.596098\pi$
$709$	6.43595e9	−	1.11474e10i	0.678189	−	1.17466i	0.975526	−	0.219886i	$-0.0705684\pi$
$710$	8.18694e8	+	1.41802e9i	0.0858455	+	0.148689i
$711$	5.03856e9	+	2.40040e9i	0.525730	+	0.250461i
$712$	6.33089e9	+	3.65514e9i	0.657332	+	0.379511i
$713$	−1.27682e10			−1.31922
$714$	1.25752e10	−	1.69085e8i	1.29291	−	0.0173845i
$715$	1.01568e10			1.03917
$716$	3.71822e9	+	2.14672e9i	0.378564	+	0.218564i
$717$	9.41119e9	+	8.69556e9i	0.953515	+	0.881010i
$718$	−4.42904e9	−	7.67131e9i	−0.446554	−	0.773454i
$719$	3.95961e9	−	6.85825e9i	0.397285	−	0.688117i	−0.596105	−	0.802906i	$-0.703286\pi$
$719$	3.95961e9	−	6.85825e9i	0.397285	−	0.688117i	0.993390	+	0.114789i	$0.0366192\pi$
$720$	4.21130e9	−	2.89722e9i	0.420487	−	0.289280i
$721$	3.50651e9	−	8.42295e8i	0.348419	−	0.0836933i
$722$			7.90110e9i			0.781282i
$723$	−8.92077e8	+	3.94667e9i	−0.0877846	+	0.388371i
$724$	−2.60951e9	+	1.50660e9i	−0.255549	+	0.147541i
$725$	2.50102e9	−	1.44396e9i	0.243744	−	0.140726i
$726$	2.42097e9	−	1.07107e10i	0.234807	−	1.03882i
$727$		−	1.17473e10i		−	1.13389i	−0.823757	−	0.566943i	$-0.808126\pi$
$727$		−	1.17473e10i		−	1.13389i	0.823757	−	0.566943i	$-0.191874\pi$
$728$	6.39314e9	−	6.06836e9i	0.614122	−	0.582924i
$729$	2.45608e9	+	1.01679e10i	0.234799	+	0.972044i
$730$	6.18125e9	−	1.07062e10i	0.588093	−	1.01861i
$731$	1.87512e9	+	3.24781e9i	0.177549	+	0.307524i
$732$	−3.33321e8	−	3.07975e8i	−0.0314104	−	0.0290220i
$733$	5.52135e9	+	3.18775e9i	0.517823	+	0.298965i	0.736044	−	0.676934i	$-0.236692\pi$
$733$	5.52135e9	+	3.18775e9i	0.517823	+	0.298965i	−0.218220	+	0.975899i	$0.570025\pi$
$734$	7.39660e9			0.690392
$735$	−9.20711e9	+	2.34300e9i	−0.855298	+	0.217654i
$736$	−6.31044e9			−0.583428
$737$	1.94715e10	+	1.12419e10i	1.79169	+	1.03443i
$738$	6.90570e8	−	1.44954e9i	0.0632427	−	0.132750i
$739$	3.01332e8	+	5.21922e8i	0.0274656	+	0.0475719i	0.879432	−	0.476025i	$-0.157923\pi$
$739$	3.01332e8	+	5.21922e8i	0.0274656	+	0.0475719i	−0.851966	+	0.523597i	$0.824590\pi$
$740$	1.41542e9	−	2.45157e9i	0.128403	−	0.222400i
$741$	5.87807e8	+	1.89150e9i	0.0530727	+	0.170782i
$742$	−1.08882e9	+	1.03351e9i	−0.0978460	+	0.0928752i
$743$			1.48198e10i			1.32550i	0.748839	+	0.662752i	$0.230612\pi$
$743$			1.48198e10i			1.32550i	−0.748839	+	0.662752i	$0.769388\pi$
$744$	−1.64894e10	−	3.72716e9i	−1.46791	−	0.331797i
$745$	3.86595e9	−	2.23201e9i	0.342538	−	0.197765i
$746$	6.66472e9	−	3.84788e9i	0.587755	−	0.339340i
$747$	3.53563e8	+	4.46594e9i	0.0310345	+	0.392004i
$748$		−	8.67895e9i		−	0.758249i
$749$	−1.08774e10	+	2.61286e9i	−0.945890	+	0.227211i
$750$	−9.80794e9	+	3.04794e9i	−0.848914	+	0.263811i
$751$	8.87480e9	−	1.53716e10i	0.764573	−	1.32428i	−0.175899	−	0.984408i	$-0.556283\pi$
$751$	8.87480e9	−	1.53716e10i	0.764573	−	1.32428i	0.940472	−	0.339871i	$-0.110383\pi$
$752$	−3.95906e7	−	6.85729e7i	−0.00339492	−	0.00588018i
$753$	−1.21845e10	+	1.31873e10i	−1.03998	+	1.12557i
$754$	8.32664e9	+	4.80739e9i	0.707408	+	0.408422i
$755$	−2.03284e9			−0.171905
$756$	−2.19373e9	−	3.09867e9i	−0.184653	−	0.260825i
$757$	−8.54076e9			−0.715585			−0.357792	−	0.933801i	$-0.616470\pi$
$757$	−8.54076e9			−0.715585			−0.357792	+	0.933801i	$0.616470\pi$
$758$	3.75969e9	+	2.17066e9i	0.313552	+	0.181029i
$759$	1.18066e10	−	1.27782e10i	0.980115	−	1.06078i
$760$	−1.33637e9	−	2.31466e9i	−0.110428	−	0.191267i
$761$	−6.04495e9	+	1.04702e10i	−0.497217	+	0.861206i	−0.999995	−	0.00321005i	$-0.998978\pi$
$761$	−6.04495e9	+	1.04702e10i	−0.497217	+	0.861206i	0.502777	+	0.864416i	$0.332312\pi$
$762$	1.07130e10	−	3.32920e9i	0.877139	−	0.272582i
$763$	−1.24690e10	−	3.69181e9i	−1.01624	−	0.300887i
$764$		−	2.39917e8i		−	0.0194641i
$765$	1.35199e9	+	1.70773e10i	0.109184	+	1.37913i
$766$	8.09107e9	−	4.67138e9i	0.650437	−	0.375530i
$767$	1.25197e9	−	7.22826e8i	0.100187	−	0.0578429i
$768$	−1.04125e10	−	2.35357e9i	−0.829452	−	0.187484i
$769$			1.19507e10i			0.947656i	0.880617	+	0.473828i	$0.157128\pi$
$769$			1.19507e10i			0.947656i	−0.880617	+	0.473828i	$0.842872\pi$
$770$	−3.26050e9	−	1.35736e10i	−0.257375	−	1.07146i
$771$	−7.18751e9	−	2.31286e10i	−0.564791	−	1.81744i
$772$	−2.37913e9	+	4.12077e9i	−0.186105	+	0.322343i
$773$	−2.16386e9	−	3.74792e9i	−0.168501	−	0.291852i	0.769392	−	0.638777i	$-0.220559\pi$
$773$	−2.16386e9	−	3.74792e9i	−0.168501	−	0.291852i	−0.937893	+	0.346925i	$0.887226\pi$
$774$	−1.03676e9	+	2.17621e9i	−0.0803681	+	0.168697i
$775$	3.43049e9	+	1.98060e9i	0.264728	+	0.152841i
$776$	3.42993e8			0.0263493
$777$	1.03900e10	+	5.81382e9i	0.794586	+	0.444619i
$778$	−8.49987e9			−0.647119
$779$	−4.68286e8	−	2.70365e8i	−0.0354920	−	0.0204913i
$780$	2.13571e9	+	1.97331e9i	0.161143	+	0.148890i
$781$	2.37622e9	+	4.11573e9i	0.178488	+	0.309150i
$782$	−8.24939e9	+	1.42884e10i	−0.616876	+	1.06846i
$783$	1.05771e10	−	1.34363e10i	0.787412	−	1.00026i
$784$	−6.54517e9	−	4.24819e9i	−0.485082	−	0.314846i
$785$		−	1.31817e10i		−	0.972584i
$786$	−2.80128e9	+	1.23932e10i	−0.205768	+	0.910344i
$787$	−1.01407e10	+	5.85473e9i	−0.741576	+	0.428149i	−0.822642	−	0.568559i	$-0.807501\pi$
$787$	−1.01407e10	+	5.85473e9i	−0.741576	+	0.428149i	0.0810658	+	0.996709i	$0.474168\pi$
$788$	8.32628e8	−	4.80718e8i	0.0606191	−	0.0349984i
$789$	8.06117e8	−	3.56637e9i	0.0584290	−	0.258498i
$790$			5.87500e9i			0.423948i
$791$	1.57335e10	+	1.65756e10i	1.13034	+	1.19083i
$792$	1.89776e10	−	1.30559e10i	1.35739	−	0.933835i
$793$	−7.30919e8	+	1.26599e9i	−0.0520491	+	0.0901517i
$794$	−1.41516e9	−	2.45114e9i	−0.100331	−	0.173778i
$795$	−1.50193e9	−	1.38772e9i	−0.106014	−	0.0979528i
$796$	6.99430e9	+	4.03816e9i	0.491528	+	0.283784i
$797$	−2.83668e10			−1.98475			−0.992377	−	0.123238i	$-0.960672\pi$
$797$	−2.83668e10			−1.98475			−0.992377	+	0.123238i	$0.960672\pi$
$798$	2.33910e9	−	1.39275e9i	0.162944	−	0.0970201i
$799$	2.65361e8			0.0184045
$800$	1.69546e9	+	9.78874e8i	0.117077	+	0.0675945i
$801$	−9.15648e9	−	4.36220e9i	−0.629527	−	0.299911i
$802$	6.38887e9	+	1.10658e10i	0.437334	+	0.757485i
$803$	1.79408e10	−	3.10743e10i	1.22275	−	2.11786i
$804$	1.91022e9	+	6.14687e9i	0.129624	+	0.417117i
$805$	3.53842e9	−	1.19509e10i	0.239069	−	0.807449i
$806$			1.31880e10i			0.887169i
$807$	−2.70608e9	−	6.11663e8i	−0.181252	−	0.0409690i
$808$	5.54499e9	−	3.20140e9i	0.369795	−	0.213501i
$809$	1.01574e9	−	5.86436e8i	0.0674468	−	0.0389404i	−0.465897	−	0.884839i	$-0.654268\pi$
$809$	1.01574e9	−	5.86436e8i	0.0674468	−	0.0389404i	0.533344	+	0.845898i	$0.320935\pi$
$810$	−8.55081e9	+	6.93746e9i	−0.565340	+	0.458673i
$811$			1.21163e8i			0.00797623i	0.999992	+	0.00398811i	$0.00126946\pi$
$811$			1.21163e8i			0.00797623i	−0.999992	+	0.00398811i	$0.998731\pi$
$812$	−1.76200e9	+	5.95111e9i	−0.115494	+	0.390078i
$813$	−1.40130e10	+	4.35473e9i	−0.914566	+	0.284213i
$814$	−8.74706e9	+	1.51504e10i	−0.568430	+	0.984549i
$815$	3.71430e9	+	6.43335e9i	0.240339	+	0.416280i
$816$	−9.54818e9	+	1.03340e10i	−0.615184	+	0.665812i
$817$	7.03041e8	+	4.05901e8i	0.0451028	+	0.0260401i
$818$	−4.43124e9			−0.283067
$819$	−8.17787e9	+	9.09318e9i	−0.520171	+	0.578392i
$820$	−7.93814e8			−0.0502771
$821$	−1.82013e10	−	1.05085e10i	−1.14789	−	0.662736i	−0.199519	−	0.979894i	$-0.563938\pi$
$821$	−1.82013e10	−	1.05085e10i	−1.14789	−	0.662736i	−0.948373	+	0.317158i	$0.897271\pi$
$822$	1.60543e10	−	1.73755e10i	1.00818	−	1.09116i
$823$	3.99491e9	+	6.91938e9i	0.249808	+	0.432681i	0.963473	−	0.267807i	$-0.0862990\pi$
$823$	3.99491e9	+	6.91938e9i	0.249808	+	0.432681i	−0.713664	+	0.700488i	$0.752966\pi$
$824$	−3.13201e9	+	5.42479e9i	−0.195019	+	0.337783i
$825$	−5.15428e9	+	1.60176e9i	−0.319580	+	0.0993135i
$826$	−1.36789e9	−	1.44110e9i	−0.0844541	−	0.0889741i
$827$		−	8.63581e9i		−	0.530926i	−0.964121	−	0.265463i	$-0.914475\pi$
$827$		−	8.63581e9i		−	0.530926i	0.964121	−	0.265463i	$-0.0855247\pi$
$828$	4.96521e9	−	3.93090e8i	0.303971	−	0.0240650i
$829$	−1.09399e10	+	6.31616e9i	−0.666919	+	0.385046i	−0.794908	−	0.606730i	$-0.792481\pi$
$829$	−1.09399e10	+	6.31616e9i	−0.666919	+	0.385046i	0.127989	+	0.991776i	$0.459148\pi$
$830$	−4.08400e9	+	2.35790e9i	−0.247920	+	0.143137i
$831$	−3.02815e10	−	6.84463e9i	−1.83052	−	0.413758i
$832$			1.39911e10i			0.842209i
$833$	2.32971e10	−	1.18777e10i	1.39651	−	0.711991i
$834$	2.89421e9	+	9.31324e9i	0.172762	+	0.555930i
$835$	−8.26585e9	+	1.43169e10i	−0.491343	+	0.851031i
$836$	−9.39351e8	−	1.62700e9i	−0.0556040	−	0.0963089i
$837$	2.32146e10	+	3.34946e9i	1.36843	+	0.197440i
$838$	−9.14175e9	−	5.27799e9i	−0.536631	−	0.309824i
$839$	2.36975e10			1.38527			0.692637	−	0.721287i	$-0.256449\pi$
$839$	2.36975e10			1.38527			0.692637	+	0.721287i	$0.256449\pi$
$840$	8.05826e9	−	1.44011e10i	0.469098	−	0.838334i
$841$	−1.07042e10			−0.620538
$842$	−1.43686e10	−	8.29573e9i	−0.829512	−	0.478919i
$843$	1.39323e10	+	1.28729e10i	0.800988	+	0.740081i
$844$	3.33303e9	+	5.77298e9i	0.190827	+	0.330523i
$845$	−3.05620e9	+	5.29350e9i	−0.174254	+	0.301817i
$846$	9.66750e7	+	1.40523e8i	0.00548931	+	0.00797906i
$847$	−5.33297e9	−	2.22014e10i	−0.301562	−	1.25542i
$848$		−	1.67950e9i		−	0.0945789i
$849$	3.06521e9	−	1.35609e10i	0.171903	−	0.760521i
$850$	4.43281e9	−	2.55928e9i	0.247579	−	0.142940i
$851$	−1.35268e10	+	7.80969e9i	−0.752386	+	0.434390i
$852$	−2.99967e8	+	1.32709e9i	−0.0166163	+	0.0735127i
$853$			3.02762e10i			1.67024i	0.550065	+	0.835122i	$0.314603\pi$
$853$			3.02762e10i			1.67024i	−0.550065	+	0.835122i	$0.685397\pi$
$854$	1.92651e9	+	5.70399e8i	0.105844	+	0.0313384i
$855$	2.10178e9	+	3.05507e9i	0.115002	+	0.167163i
$856$	9.71571e9	−	1.68281e10i	0.529439	−	0.917016i
$857$	6.52454e9	+	1.13008e10i	0.354093	+	0.613306i	0.986962	−	0.160952i	$-0.0514564\pi$
$857$	6.52454e9	+	1.13008e10i	0.354093	+	0.613306i	−0.632870	+	0.774258i	$0.718123\pi$
$858$	−1.31984e10	−	1.21948e10i	−0.713369	−	0.659125i
$859$	−7.42726e9	−	4.28813e9i	−0.399809	−	0.230830i	0.286593	−	0.958053i	$-0.407477\pi$
$859$	−7.42726e9	−	4.28813e9i	−0.399809	−	0.230830i	−0.686401	+	0.727223i	$0.740811\pi$
$860$	1.19176e9			0.0638916
$861$	−4.48871e7	−	3.33833e9i	−0.00239668	−	0.178246i
$862$	1.77704e9			0.0944978
$863$	−1.76968e10	−	1.02173e10i	−0.937255	−	0.541124i	−0.0481561	−	0.998840i	$-0.515334\pi$
$863$	−1.76968e10	−	1.02173e10i	−0.937255	−	0.541124i	−0.889099	+	0.457716i	$0.848668\pi$
$864$	1.14734e10	+	1.65541e9i	0.605193	+	0.0873187i
$865$	8.99072e9	+	1.55724e10i	0.472322	+	0.818085i
$866$	5.21619e9	−	9.03471e9i	0.272923	−	0.472717i
$867$	−8.29828e9	−	2.67029e10i	−0.432435	−	1.39153i
$868$	−8.27758e9	+	1.98835e9i	−0.429620	+	0.103199i
$869$			1.70519e10i			0.881462i
$870$	1.75574e10	+	3.96856e9i	0.903948	+	0.204322i
$871$	1.79564e10	−	1.03672e10i	0.920782	−	0.531614i
$872$	1.95616e10	−	1.12939e10i	0.999072	−	0.576814i
$873$	−4.74393e8	+	3.75571e7i	−0.0241317	+	0.00191048i
$874$			3.57143e9i			0.180947i
$875$	−1.54893e10	+	1.47024e10i	−0.781633	+	0.741925i
$876$	9.80973e9	−	3.04850e9i	0.493052	−	0.153222i
$877$	1.23661e10	−	2.14187e10i	0.619061	−	1.07224i	−0.370597	−	0.928794i	$-0.620847\pi$
$877$	1.23661e10	−	2.14187e10i	0.619061	−	1.07224i	0.989657	−	0.143451i	$-0.0458198\pi$
$878$	2.88443e9	+	4.99598e9i	0.143823	+	0.249109i
$879$	1.99483e10	−	2.15900e10i	0.990705	−	1.07224i
$880$	1.35251e10	+	7.80874e9i	0.669040	+	0.386271i
$881$	6.10025e9			0.300560			0.150280	−	0.988643i	$-0.451982\pi$
$881$	6.10025e9			0.300560			0.150280	+	0.988643i	$0.451982\pi$
$882$	1.47774e10	+	8.00987e9i	0.725198	+	0.393084i
$883$	7.46738e9			0.365011			0.182505	−	0.983205i	$-0.441579\pi$
$883$	7.46738e9			0.365011			0.182505	+	0.983205i	$0.441579\pi$
$884$	−6.93138e9	−	4.00183e9i	−0.337471	−	0.194839i
$885$	1.83670e9	−	1.98786e9i	0.0890712	−	0.0964016i
$886$	1.21984e10	+	2.11282e10i	0.589230	+	1.02058i
$887$	3.69957e9	−	6.40785e9i	0.178000	−	0.308304i	−0.763196	−	0.646167i	$-0.776371\pi$
$887$	3.69957e9	−	6.40785e9i	0.178000	−	0.308304i	0.941195	+	0.337863i	$0.109704\pi$
$888$	−1.97489e10	+	6.13721e9i	−0.946447	+	0.294121i
$889$	1.69186e10	−	1.60591e10i	0.807621	−	0.766593i
$890$		−	1.06765e10i		−	0.507650i
$891$	−2.48183e10	+	2.01357e10i	−1.17544	+	0.953661i
$892$	4.37409e9	−	2.52538e9i	0.206353	−	0.119138i
$893$	4.97460e7	−	2.87209e7i	0.00233764	−	0.00134964i
$894$	−7.70349e9	−	1.74124e9i	−0.360584	−	0.0815039i
$895$		−	2.58919e10i		−	1.20721i
$896$	5.89611e9	−	1.41630e9i	0.273834	−	0.0657774i
$897$	−4.76126e9	−	1.53212e10i	−0.220266	−	0.708793i
$898$	4.08908e9	−	7.08250e9i	0.188434	−	0.326377i
$899$	−1.91715e10	−	3.32059e10i	−0.880027	−	1.52425i
$900$	−1.39501e9	−	6.64589e8i	−0.0637863	−	0.0303882i
$901$	4.87445e9	+	2.81427e9i	0.222018	+	0.128182i
$902$	4.90565e9			0.222574
$903$	6.73892e7	+	5.01186e9i	0.00304567	+	0.226512i
$904$	−3.96966e10			−1.78716
$905$	1.57368e10	+	9.08567e9i	0.705744	+	0.407462i
$906$	2.64159e9	+	2.44073e9i	0.118010	+	0.109036i
$907$	5.70402e9	+	9.87965e9i	0.253837	+	0.439659i	0.964579	−	0.263794i	$-0.0849739\pi$
$907$	5.70402e9	+	9.87965e9i	0.253837	+	0.439659i	−0.710742	+	0.703453i	$0.751641\pi$
$908$	−2.66014e9	+	4.60749e9i	−0.117924	+	0.204251i
$909$	−7.31871e9	+	5.03502e9i	−0.323192	+	0.222345i
$910$	−1.23438e10	−	3.65476e9i	−0.543007	−	0.160773i
$911$			9.95158e9i			0.436091i	0.975939	+	0.218046i	$0.0699682\pi$
$911$			9.95158e9i			0.436091i	−0.975939	+	0.218046i	$0.930032\pi$
$912$	−6.71474e8	+	2.97069e9i	−0.0293121	+	0.129681i
$913$	−1.18536e10	+	6.84368e9i	−0.515469	+	0.297606i
$914$	1.86018e10	−	1.07398e10i	0.805831	−	0.465247i
$915$	−6.03382e8	+	2.66944e9i	−0.0260387	+	0.115199i
$916$			5.23072e9i			0.224868i
$917$	6.17071e9	+	2.56889e10i	0.264267	+	1.10015i
$918$	1.87470e10	−	2.38145e10i	0.799800	−	1.01600i
$919$	−1.59140e10	+	2.75639e10i	−0.676357	+	1.17149i	0.299713	+	0.954030i	$0.403109\pi$
$919$	−1.59140e10	+	2.75639e10i	−0.676357	+	1.17149i	−0.976070	+	0.217456i	$0.930224\pi$
$920$	1.08246e10	+	1.87488e10i	0.458307	+	0.793811i
$921$	4.82587e8	+	4.45891e8i	0.0203548	+	0.0188070i
$922$	−1.02071e10	−	5.89308e9i	−0.428889	−	0.247619i
$923$	4.38267e9			0.183456
$924$	5.66425e9	−	1.01227e10i	0.236206	−	0.422128i
$925$	4.84575e9			0.201310
$926$	−9.44761e9	−	5.45458e9i	−0.391006	−	0.225748i
$927$	3.73787e9	−	7.84597e9i	0.154115	−	0.323495i
$928$	−9.47514e9	−	1.64114e10i	−0.389195	−	0.674106i
$929$	−1.67195e10	+	2.89591e10i	−0.684177	+	1.18503i	0.289517	+	0.957173i	$0.406505\pi$
$929$	−1.67195e10	+	2.89591e10i	−0.684177	+	1.18503i	−0.973695	+	0.227857i	$0.926828\pi$
$930$	7.32708e9	+	2.35777e10i	0.298704	+	0.961195i
$931$	3.08184e9	−	4.74817e9i	0.125166	−	0.192842i
$932$			2.41673e9i			0.0977852i
$933$	−1.63545e10	−	3.69665e9i	−0.659250	−	0.149012i
$934$	−8.05782e9	+	4.65219e9i	−0.323596	+	0.186828i
$935$	−4.53270e10	+	2.61695e10i	−1.81349	+	1.04702i
$936$	−1.67651e9	−	2.11764e10i	−0.0668252	−	0.844085i
$937$			2.48503e10i			0.986832i	0.869793	+	0.493416i	$0.164252\pi$
$937$			2.48503e10i			0.986832i	−0.869793	+	0.493416i	$0.835748\pi$
$938$	−1.96190e10	−	2.06690e10i	−0.776187	−	0.817729i
$939$	−3.84299e10	+	1.19426e10i	−1.51475	+	0.470726i
$940$	4.21634e7	−	7.30291e7i	0.00165572	−	0.00286780i
$941$	−9.82751e9	−	1.70218e10i	−0.384485	−	0.665948i	0.607212	−	0.794540i	$-0.292288\pi$
$941$	−9.82751e9	−	1.70218e10i	−0.384485	−	0.665948i	−0.991698	+	0.128591i	$0.958954\pi$
$942$	−1.58266e10	+	1.71291e10i	−0.616891	+	0.667660i
$943$	3.79314e9	+	2.18997e9i	0.147302	+	0.0850447i
$944$	2.22289e9			0.0860033
$945$	−9.56848e9	+	2.08004e10i	−0.368835	+	0.801791i
$946$	−7.36488e9			−0.282844
$947$	3.15957e10	+	1.82418e10i	1.20893	+	0.697979i	0.962526	−	0.271188i	$-0.0874164\pi$
$947$	3.15957e10	+	1.82418e10i	1.20893	+	0.697979i	0.246408	+	0.969166i	$0.420750\pi$
$948$	−3.31292e9	+	3.58556e9i	−0.126294	+	0.136687i
$949$	−1.65449e10	−	2.86565e10i	−0.628393	−	1.08841i
$950$	5.53999e8	−	9.59554e8i	0.0209641	−	0.0363109i
$951$	1.37745e10	−	4.28059e9i	0.519329	−	0.161388i
$952$	−1.28953e10	+	4.35536e10i	−0.484399	+	1.63604i
$953$		−	1.60579e10i		−	0.600984i	−0.953784	−	0.300492i	$-0.902849\pi$
$953$		−	1.60579e10i		−	0.600984i	0.953784	−	0.300492i	$-0.0971508\pi$
$954$	2.85527e8	+	3.60657e9i	0.0106470	+	0.134485i
$955$	−1.25300e9	+	7.23420e8i	−0.0465521	+	0.0268769i
$956$	−9.70621e9	+	5.60389e9i	−0.359292	+	0.207437i
$957$	5.09596e10	+	1.15185e10i	1.87946	+	0.424821i
$958$		−	3.47683e10i		−	1.27763i
$959$	1.39650e10	−	4.71665e10i	0.511302	−	1.72691i
$960$	7.77327e9	+	2.50135e10i	0.283566	+	0.912484i
$961$	1.25400e10	−	2.17199e10i	0.455791	−	0.789454i
$962$	8.06648e9	+	1.39715e10i	0.292127	+	0.505978i
$963$	−1.15951e10	+	2.43388e10i	−0.418392	+	0.878226i
$964$	−3.06504e9	−	1.76960e9i	−0.110196	−	0.0636218i
$965$	2.86950e10			1.02792
$966$	−1.89468e10	+	1.12813e10i	−0.676265	+	0.402661i
$967$	5.02193e10			1.78599			0.892993	−	0.450071i	$-0.148601\pi$
$967$	5.02193e10			1.78599			0.892993	+	0.450071i	$0.148601\pi$
$968$	3.43469e10	+	1.98302e10i	1.21709	+	0.702689i
$969$	−7.49675e9	−	6.92670e9i	−0.264691	−	0.244564i
$970$	−2.50467e8	−	4.33822e8i	−0.00881149	−	0.0152620i
$971$	−1.22782e10	+	2.12665e10i	−0.430396	+	0.745467i	−0.996907	−	0.0785866i	$-0.974959\pi$
$971$	−1.22782e10	+	2.12665e10i	−0.430396	+	0.745467i	0.566512	+	0.824054i	$0.308293\pi$
$972$	−9.13068e9	−	5.87817e8i	−0.318912	−	0.0205310i
$973$	1.39608e10	+	1.47080e10i	0.485866	+	0.511869i
$974$		−	1.26364e10i		−	0.438196i
$975$	−1.09739e9	+	4.85499e9i	−0.0379179	+	0.167754i
$976$	−1.94663e9	+	1.12389e9i	−0.0670207	+	0.0386944i
$977$	5.35074e9	−	3.08925e9i	0.183562	−	0.105980i	−0.405403	−	0.914138i	$-0.632869\pi$
$977$	5.35074e9	−	3.08925e9i	0.183562	−	0.105980i	0.588965	+	0.808158i	$0.299535\pi$
$978$	2.89761e9	−	1.28194e10i	0.0990500	−	0.438211i
$979$		−	3.09881e10i		−	1.05549i
$980$	4.32871e8	−	8.29877e9i	0.0146915	−	0.281658i
$981$	−2.58190e10	+	1.77625e10i	−0.873167	+	0.600708i
$982$	5.45303e9	−	9.44492e9i	0.183759	−	0.318279i
$983$	1.69490e10	+	2.93565e10i	0.569122	+	0.985749i	0.996653	+	0.0817480i	$0.0260503\pi$
$983$	1.69490e10	+	2.93565e10i	0.569122	+	0.985749i	−0.427531	+	0.904001i	$0.640616\pi$
$984$	4.25937e9	+	3.93549e9i	0.142516	+	0.131679i
$985$	−5.02123e9	−	2.89901e9i	−0.167411	−	0.0966546i
$986$	−4.95459e10			−1.64603
$987$	3.09503e8	+	1.73186e8i	0.0102460	+	0.00573327i
$988$	−1.73252e9			−0.0571518
$989$	−5.69466e9	−	3.28781e9i	−0.187189	−	0.108074i
$990$	−3.03715e10	−	1.44692e10i	−0.994816	−	0.473936i
$991$	−1.85480e10	−	3.21261e10i	−0.605395	−	1.04858i	−0.991989	−	0.126325i	$-0.959682\pi$
$991$	−1.85480e10	−	3.21261e10i	−0.605395	−	1.04858i	0.386594	−	0.922250i	$-0.373652\pi$
$992$	1.29965e10	−	2.25106e10i	0.422702	−	0.732142i
$993$	2.08918e9	+	6.72275e9i	0.0677101	+	0.217884i
$994$	−1.40690e9	−	5.85700e9i	−0.0454373	−	0.189157i
$995$		−	4.87049e10i		−	1.56744i
$996$	−3.82212e9	−	8.63925e8i	−0.122574	−	0.0277057i
$997$	5.96722e9	−	3.44518e9i	0.190695	−	0.110098i	−0.401613	−	0.915810i	$-0.631550\pi$
$997$	5.96722e9	−	3.44518e9i	0.190695	−	0.110098i	0.592308	+	0.805712i	$0.298217\pi$
$998$	1.04211e10	−	6.01664e9i	0.331862	−	0.191601i
$999$	2.66426e10	−	1.06508e10i	0.845468	−	0.337990i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.8.g.b.5.6	✓	32
3.2	odd	2	inner	21.8.g.b.5.11	yes	32
7.2	even	3		147.8.c.b.146.10		32
7.3	odd	6	inner	21.8.g.b.17.11	yes	32
7.5	odd	6		147.8.c.b.146.24		32
21.2	odd	6		147.8.c.b.146.23		32
21.5	even	6		147.8.c.b.146.9		32
21.17	even	6	inner	21.8.g.b.17.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.8.g.b.5.6	✓	32	1.1	even	1	trivial
21.8.g.b.5.11	yes	32	3.2	odd	2	inner
21.8.g.b.17.6	yes	32	21.17	even	6	inner
21.8.g.b.17.11	yes	32	7.3	odd	6	inner
147.8.c.b.146.9		32	21.5	even	6
147.8.c.b.146.10		32	7.2	even	3
147.8.c.b.146.23		32	21.2	odd	6
147.8.c.b.146.24		32	7.5	odd	6

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+(-8.08214 - 4.66623i) q^{2} +(-31.7364 + 34.3482i) q^{3} +(-20.4526 - 35.4250i) q^{4} +(-123.341 + 213.633i) q^{5} +(416.775 - 129.518i) q^{6} +(658.195 - 624.758i) q^{7} +1576.30i q^{8} +(-172.602 - 2180.18i) q^{9} +(1993.72 - 1151.08i) q^{10} +(5786.68 - 3340.94i) q^{11} +(1865.88 + 421.750i) q^{12} -6161.99i q^{13} +(-8234.89 + 1978.09i) q^{14} +(-3423.52 - 11016.5i) q^{15} +(4737.44 - 8205.49i) q^{16} +(15876.7 + 27499.2i) q^{17} +(-8778.22 + 18425.9i) q^{18} +(5952.65 + 3436.76i) q^{19} +10090.6 q^{20} +(570.584 + 42435.4i) q^{21} -62358.4 q^{22} +(-48216.7 - 27837.9i) q^{23} +(-54143.1 - 50026.1i) q^{24} +(8636.42 + 14958.7i) q^{25} +(-28753.2 + 49802.1i) q^{26} +(80363.0 + 63262.4i) q^{27} +(-35593.9 - 10538.6i) q^{28} -167195. i q^{29} +(-23736.1 + 105012. i) q^{30} +(198606. - 114665. i) q^{31} +(98157.6 - 56671.3i) q^{32} +(-68893.0 + 304792. i) q^{33} -296336. i q^{34} +(52286.4 + 217671. i) q^{35} +(-73702.7 + 50704.8i) q^{36} +(140271. - 242956. i) q^{37} +(-32073.4 - 55552.8i) q^{38} +(211653. + 195559. i) q^{39} +(-336750. - 194423. i) q^{40} -78668.6 q^{41} +(193402. - 345631. i) q^{42} +118106. q^{43} +(-236706. - 136662. i) q^{44} +(487047. + 232032. i) q^{45} +(259796. + 449980. i) q^{46} +(4178.48 - 7237.34i) q^{47} +(131495. + 423135. i) q^{48} +(42898.4 - 822425. i) q^{49} -161198. i q^{50} +(-1.44842e6 - 327390. i) q^{51} +(-218288. + 126029. i) q^{52} +(153510. - 88629.0i) q^{53} +(-354309. - 886288. i) q^{54} +1.64830e6i q^{55} +(984806. + 1.03751e6i) q^{56} +(-306962. + 95392.4i) q^{57} +(-780169. + 1.35129e6i) q^{58} +(117304. + 203177. i) q^{59} +(-320240. + 346595. i) q^{60} +(-205451. - 118617. i) q^{61} -2.14022e6 q^{62} +(-1.47569e6 - 1.32715e6i) q^{63} -2.27055e6 q^{64} +(1.31640e6 + 760026. i) q^{65} +(1.97903e6 - 2.14190e6i) q^{66} +(1.68244e6 + 2.91407e6i) q^{67} +(649439. - 1.12486e6i) q^{68} +(2.48641e6 - 772682. i) q^{69} +(593114. - 2.00323e6i) q^{70} +711242. i q^{71} +(3.43662e6 - 272073. i) q^{72} +(4.65054e6 - 2.68499e6i) q^{73} +(-2.26738e6 + 1.30907e6i) q^{74} +(-787894. - 178090. i) q^{75} -281163. i q^{76} +(1.72149e6 - 5.81427e6i) q^{77} +(-798089. - 2.56816e6i) q^{78} +(-1.27598e6 + 2.21006e6i) q^{79} +(1.16864e6 + 2.02415e6i) q^{80} +(-4.72339e6 + 752606. i) q^{81} +(635811. + 367086. i) q^{82} -2.04843e6 q^{83} +(1.49160e6 - 888129. i) q^{84} -7.83298e6 q^{85} +(-954547. - 551108. i) q^{86} +(5.74284e6 + 5.30616e6i) q^{87} +(5.26633e6 + 9.12155e6i) q^{88} +(2.31881e6 - 4.01630e6i) q^{89} +(-2.85367e6 - 4.14799e6i) q^{90} +(-3.84975e6 - 4.05579e6i) q^{91} +2.27743e6i q^{92} +(-2.36450e6 + 1.04608e7i) q^{93} +(-67542.1 + 38995.5i) q^{94} +(-1.46841e6 + 847788. i) q^{95} +(-1.16861e6 + 5.17008e6i) q^{96} -217594. i q^{97} +(-4.18433e6 + 6.44678e6i) q^{98} +(-8.28264e6 - 1.20393e7i) 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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