LMFDB - Embedded newform 18.21.d.a.5.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [18,21,Mod(5,18)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(18, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 21, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("18.5"); S:= CuspForms(chi, 21); N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 21 $
Character orbit:	$[\chi]$	$=$	18.d (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$45.6324777185$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.15
Character	$\chi$	$=$	18.5
Dual form			18.21.d.a.11.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(627.069 - 362.039i) q^{2} +(-2376.61 + 59001.2i) q^{3} +(262144. - 454047. i) q^{4} +(-6.58251e6 - 3.80041e6i) q^{5} +(1.98704e7 + 3.78582e7i) q^{6} +(7.46524e7 + 1.29302e8i) q^{7} -3.79625e8i q^{8} +(-3.47549e9 - 2.80445e8i) q^{9} -5.50358e9 q^{10} +(3.07406e10 - 1.77481e10i) q^{11} +(2.61663e10 + 1.65459e10i) q^{12} +(-1.12062e11 + 1.94097e11i) q^{13} +(9.36245e10 + 5.40541e10i) q^{14} +(2.39873e11 - 3.79343e11i) q^{15} +(-1.37439e11 - 2.38051e11i) q^{16} -2.48192e12i q^{17} +(-2.28090e12 + 1.08240e12i) q^{18} -7.60316e12 q^{19} +(-3.45113e12 + 1.99251e12i) q^{20} +(-7.80637e12 + 4.09728e12i) q^{21} +(1.28510e13 - 2.22586e13i) q^{22} +(5.93735e12 + 3.42793e12i) q^{23} +(2.23983e13 + 9.02221e11i) q^{24} +(-1.87975e13 - 3.25581e13i) q^{25} +1.62283e14i q^{26} +(2.48065e13 - 2.04391e14i) q^{27} +7.82787e13 q^{28} +(6.25109e14 - 3.60907e14i) q^{29} +(1.30799e13 - 3.24718e14i) q^{30} +(4.26088e14 - 7.38006e14i) q^{31} +(-1.72368e14 - 9.95164e13i) q^{32} +(9.74099e14 + 1.85591e15i) q^{33} +(-8.98551e14 - 1.55634e15i) q^{34} -1.13484e15i q^{35} +(-1.03841e15 + 1.50452e15i) q^{36} +5.72383e15 q^{37} +(-4.76771e15 + 2.75264e15i) q^{38} +(-1.11856e16 - 7.07308e15i) q^{39} +(-1.44273e15 + 2.49888e15i) q^{40} +(3.48457e15 + 2.01182e15i) q^{41} +(-3.41176e15 + 5.39549e15i) q^{42} +(-1.52227e16 - 2.63664e16i) q^{43} -1.86102e16i q^{44} +(2.18116e16 + 1.50543e16i) q^{45} +4.96417e15 q^{46} +(-1.80696e16 + 1.04325e16i) q^{47} +(1.43719e16 - 7.54330e15i) q^{48} +(2.87502e16 - 4.97968e16i) q^{49} +(-2.35746e16 - 1.36108e16i) q^{50} +(1.46436e17 + 5.89855e15i) q^{51} +(5.87527e16 + 1.01763e17i) q^{52} -2.64537e17i q^{53} +(-5.84422e16 - 1.37148e17i) q^{54} -2.69800e17 q^{55} +(4.90862e16 - 2.83399e16i) q^{56} +(1.80697e16 - 4.48595e17i) q^{57} +(2.61325e17 - 4.52628e17i) q^{58} +(-1.59453e17 - 9.20605e16i) q^{59} +(-1.09358e17 - 2.08356e17i) q^{60} +(-1.11733e17 - 1.93528e17i) q^{61} -6.17041e17i q^{62} +(-2.23191e17 - 4.70323e17i) q^{63} -1.44115e17 q^{64} +(1.47530e18 - 8.51763e17i) q^{65} +(1.28274e18 + 8.11123e17i) q^{66} +(2.13397e17 - 3.69615e17i) q^{67} +(-1.12691e18 - 6.50620e17i) q^{68} +(-2.16363e17 + 3.42163e17i) q^{69} +(-4.10856e17 - 7.11623e17i) q^{70} +5.24061e17i q^{71} +(-1.06464e17 + 1.31938e18i) q^{72} -4.66174e18 q^{73} +(3.58924e18 - 2.07225e18i) q^{74} +(1.96564e18 - 1.03169e18i) q^{75} +(-1.99312e18 + 3.45219e18i) q^{76} +(4.58972e18 + 2.64987e18i) q^{77} +(-9.57489e18 - 3.85684e17i) q^{78} +(1.90733e18 + 3.30360e18i) q^{79} +2.08930e18i q^{80} +(1.20004e19 + 1.94937e18i) q^{81} +2.91343e18 q^{82} +(-1.63293e19 + 9.42772e18i) q^{83} +(-1.86038e17 + 4.61853e18i) q^{84} +(-9.43231e18 + 1.63372e19i) q^{85} +(-1.90913e19 - 1.10224e19i) q^{86} +(1.98083e19 + 3.77399e19i) q^{87} +(-6.73762e18 - 1.16699e19i) q^{88} -3.96851e19i q^{89} +(1.91276e19 + 1.54346e18i) q^{90} -3.34628e19 q^{91} +(3.11288e18 - 1.79722e18i) q^{92} +(4.25305e19 + 2.68936e19i) q^{93} +(-7.55392e18 + 1.30838e19i) q^{94} +(5.00478e19 + 2.88951e19i) q^{95} +(6.28123e18 - 9.93337e18i) q^{96} +(5.68257e19 + 9.84250e19i) q^{97} -4.16347e19i q^{98} +(-1.11816e20 + 5.30622e19i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 18846 q^{3} + 10485760 q^{4} + 29763918 q^{5} + 102690816 q^{6} + 133479866 q^{7} + 967310598 q^{9} - 35793208728 q^{11} + 26559381504 q^{12} + 39827158550 q^{13} + 187564400640 q^{14} - 965812538286 q^{15}+ \cdots + 52\!\cdots\!22 q^{99}+O(q^{100}) $ 40 * q - 18846 * q^3 + 10485760 * q^4 + 29763918 * q^5 + 102690816 * q^6 + 133479866 * q^7 + 967310598 * q^9 - 35793208728 * q^11 + 26559381504 * q^12 + 39827158550 * q^13 + 187564400640 * q^14 - 965812538286 * q^15 - 5497558138880 * q^16 - 481837940736 * q^18 - 10560819523540 * q^19 + 15604865040384 * q^20 - 64715095872294 * q^21 + 10829007458304 * q^22 - 95164852839678 * q^23 + 18380312543232 * q^24 + 485893942617694 * q^25 - 312810773554224 * q^27 + 139963783970816 * q^28 + 487337329131246 * q^29 - 1016412645851136 * q^30 - 386065992062842 * q^31 + 2417458230482544 * q^33 - 810410730184704 * q^34 + 440007640743936 * q^36 + 7650497672534432 * q^37 - 27431157167935488 * q^38 + 21847743729103830 * q^39 - 76546903885431012 * q^41 - 27408162766282752 * q^42 - 10868849409851092 * q^43 - 151711625857797018 * q^45 + 13732137981788160 * q^46 + 220882065588142506 * q^47 + 19105114044235776 * q^48 - 201918836583922386 * q^49 + 84434006357065728 * q^50 - 112944490440784866 * q^51 - 20880901301862400 * q^52 - 907744599291211776 * q^54 - 689556443803109316 * q^55 + 98337764482744320 * q^56 + 524175567253271298 * q^57 + 289875600503808000 * q^58 - 4671324023815652220 * q^59 + 999198431835586560 * q^60 - 608513692992272866 * q^61 - 6762387225153657666 * q^63 - 5764607523034234880 * q^64 + 4959300225343873626 * q^65 + 7794266473078972416 * q^66 - 2581864509390888904 * q^67 - 5171455594224156672 * q^68 - 715869785458553814 * q^69 - 584784912675889152 * q^70 - 3996696553325592576 * q^72 + 15022099327729072004 * q^73 + 7089371473773993984 * q^74 + 10151951406704814570 * q^75 - 2768455473178869760 * q^76 - 30865724759591472834 * q^77 + 14351578809049718784 * q^78 + 18532232803602736754 * q^79 - 14205809545514203338 * q^81 - 35601230743051272192 * q^82 + 54829678294093455594 * q^83 - 34962890419605602304 * q^84 + 43688870161052471388 * q^85 + 47393791396458614784 * q^86 + 23116374920781444150 * q^87 - 5677518662299287552 * q^88 + 122957322600559583232 * q^90 - 35182774173576758996 * q^91 - 49893790365609099264 * q^92 + 30021582829442833806 * q^93 + 19892618446780047360 * q^94 + 332020921293200455200 * q^95 - 18590859261785407488 * q^96 - 66463398176406835216 * q^97 + 525216922205664004722 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	627.069	−	362.039i	0.612372	−	0.353553i
$2$	627.069	−	362.039i	0.612372	−	0.353553i
$3$	−2376.61	+	59001.2i	−0.0402481	+	0.999190i
$3$	−2376.61	+	59001.2i	−0.0402481	+	0.999190i
$4$	262144.	−	454047.i	0.250000	−	0.433013i
$5$	−6.58251e6	−	3.80041e6i	−0.674049	−	0.389162i	0.123560	−	0.992337i	$-0.460569\pi$
$5$	−6.58251e6	−	3.80041e6i	−0.674049	−	0.389162i	−0.797609	+	0.603175i	$0.793902\pi$
$6$	1.98704e7	+	3.78582e7i	0.328620	+	0.626106i
$7$	7.46524e7	+	1.29302e8i	0.264279	+	0.457745i	0.967375	−	0.253350i	$-0.0815326\pi$
$7$	7.46524e7	+	1.29302e8i	0.264279	+	0.457745i	−0.703095	+	0.711096i	$0.748199\pi$
$8$		−	3.79625e8i		−	0.353553i
$9$	−3.47549e9	−	2.80445e8i	−0.996760	−	0.0804310i
$10$	−5.50358e9			−0.550358
$11$	3.07406e10	−	1.77481e10i	1.18518	−	0.684266i	0.227975	−	0.973667i	$-0.426790\pi$
$11$	3.07406e10	−	1.77481e10i	1.18518	−	0.684266i	0.957208	+	0.289401i	$0.0934563\pi$
$12$	2.61663e10	+	1.65459e10i	0.422600	+	0.267225i
$13$	−1.12062e11	+	1.94097e11i	−0.812877	+	1.40794i	0.0979657	+	0.995190i	$0.468766\pi$
$13$	−1.12062e11	+	1.94097e11i	−0.812877	+	1.40794i	−0.910842	+	0.412754i	$0.864567\pi$
$14$	9.36245e10	+	5.40541e10i	0.323675	+	0.186874i
$15$	2.39873e11	−	3.79343e11i	0.415976	−	0.657839i
$16$	−1.37439e11	−	2.38051e11i	−0.125000	−	0.216506i
$17$		−	2.48192e12i		−	1.23111i	−0.788092	−	0.615557i	$-0.788931\pi$
$17$		−	2.48192e12i		−	1.23111i	0.788092	−	0.615557i	$-0.211069\pi$
$18$	−2.28090e12	+	1.08240e12i	−0.638825	+	0.303154i
$19$	−7.60316e12			−1.24010			−0.620052	−	0.784561i	$-0.712888\pi$
$19$	−7.60316e12			−1.24010			−0.620052	+	0.784561i	$0.712888\pi$
$20$	−3.45113e12	+	1.99251e12i	−0.337024	+	0.194581i
$21$	−7.80637e12	+	4.09728e12i	−0.468011	+	0.245642i
$22$	1.28510e13	−	2.22586e13i	0.483849	−	0.838051i
$23$	5.93735e12	+	3.42793e12i	0.143322	+	0.0827472i	0.569946	−	0.821682i	$-0.306964\pi$
$23$	5.93735e12	+	3.42793e12i	0.143322	+	0.0827472i	−0.426624	+	0.904429i	$0.640297\pi$
$24$	2.23983e13	+	9.02221e11i	0.353267	+	0.0142299i
$25$	−1.87975e13	−	3.25581e13i	−0.197106	−	0.341397i
$26$			1.62283e14i			1.14958i
$27$	2.48065e13	−	2.04391e14i	0.120484	−	0.992715i
$28$	7.82787e13			0.264279
$29$	6.25109e14	−	3.60907e14i	1.48585	−	0.857858i	0.485984	−	0.873968i	$-0.338461\pi$
$29$	6.25109e14	−	3.60907e14i	1.48585	−	0.857858i	0.999870	+	0.0161097i	$0.00512810\pi$
$30$	1.30799e13	−	3.24718e14i	0.0221509	−	0.549913i
$31$	4.26088e14	−	7.38006e14i	0.519855	−	0.900415i	−0.479879	−	0.877335i	$-0.659319\pi$
$31$	4.26088e14	−	7.38006e14i	0.519855	−	0.900415i	0.999734	−	0.0230802i	$-0.00734730\pi$
$32$	−1.72368e14	−	9.95164e13i	−0.153093	−	0.0883883i
$33$	9.74099e14	+	1.85591e15i	0.636010	+	1.21176i
$34$	−8.98551e14	−	1.55634e15i	−0.435265	−	0.753900i
$35$		−	1.13484e15i		−	0.411390i
$36$	−1.03841e15	+	1.50452e15i	−0.284018	+	0.411502i
$37$	5.72383e15			1.19033			0.595167	−	0.803602i	$-0.297086\pi$
$37$	5.72383e15			1.19033			0.595167	+	0.803602i	$0.297086\pi$
$38$	−4.76771e15	+	2.75264e15i	−0.759405	+	0.438443i
$39$	−1.11856e16	−	7.07308e15i	−1.37409	−	0.868885i
$40$	−1.44273e15	+	2.49888e15i	−0.137590	+	0.238312i
$41$	3.48457e15	+	2.01182e15i	0.259604	+	0.149882i	0.624154	−	0.781301i	$-0.285444\pi$
$41$	3.48457e15	+	2.01182e15i	0.259604	+	0.149882i	−0.364550	+	0.931184i	$0.618777\pi$
$42$	−3.41176e15	+	5.39549e15i	−0.199750	+	0.315891i
$43$	−1.52227e16	−	2.63664e16i	−0.704379	−	1.22002i	−0.966915	−	0.255098i	$-0.917892\pi$
$43$	−1.52227e16	−	2.63664e16i	−0.704379	−	1.22002i	0.262537	−	0.964922i	$-0.415441\pi$
$44$		−	1.86102e16i		−	0.684266i
$45$	2.18116e16	+	1.50543e16i	0.640564	+	0.442116i
$46$	4.96417e15			0.117022
$47$	−1.80696e16	+	1.04325e16i	−0.343534	+	0.198339i	−0.661834	−	0.749651i	$-0.730221\pi$
$47$	−1.80696e16	+	1.04325e16i	−0.343534	+	0.198339i	0.318300	+	0.947990i	$0.396888\pi$
$48$	1.43719e16	−	7.54330e15i	0.221362	−	0.116185i
$49$	2.87502e16	−	4.97968e16i	0.360313	−	0.624080i
$50$	−2.35746e16	−	1.36108e16i	−0.241404	−	0.139375i
$51$	1.46436e17	+	5.89855e15i	1.23012	+	0.0495500i
$52$	5.87527e16	+	1.01763e17i	0.406438	+	0.703972i
$53$		−	2.64537e17i		−	1.51261i	−0.654219	−	0.756305i	$-0.727002\pi$
$53$		−	2.64537e17i		−	1.51261i	0.654219	−	0.756305i	$-0.272998\pi$
$54$	−5.84422e16	−	1.37148e17i	−0.277197	−	0.650509i
$55$	−2.69800e17			−1.06516
$56$	4.90862e16	−	2.83399e16i	0.161837	−	0.0934369i
$57$	1.80697e16	−	4.48595e17i	0.0499118	−	1.23910i
$58$	2.61325e17	−	4.52628e17i	0.606597	−	1.05066i
$59$	−1.59453e17	−	9.20605e16i	−0.311971	−	0.180116i	0.335837	−	0.941920i	$-0.390981\pi$
$59$	−1.59453e17	−	9.20605e16i	−0.311971	−	0.180116i	−0.647808	+	0.761804i	$0.724314\pi$
$60$	−1.09358e17	−	2.08356e17i	−0.180859	−	0.344583i
$61$	−1.11733e17	−	1.93528e17i	−0.156633	−	0.271297i	0.777019	−	0.629477i	$-0.216731\pi$
$61$	−1.11733e17	−	1.93528e17i	−0.156633	−	0.271297i	−0.933653	+	0.358180i	$0.883397\pi$
$62$		−	6.17041e17i		−	0.735186i
$63$	−2.23191e17	−	4.70323e17i	−0.226606	−	0.477519i
$64$	−1.44115e17			−0.125000
$65$	1.47530e18	−	8.51763e17i	1.09584	−	0.632682i
$66$	1.28274e18	+	8.11123e17i	0.817898	+	0.517187i
$67$	2.13397e17	−	3.69615e17i	0.117069	−	0.202769i	−0.801536	−	0.597946i	$-0.795984\pi$
$67$	2.13397e17	−	3.69615e17i	0.117069	−	0.202769i	0.918605	+	0.395177i	$0.129317\pi$
$68$	−1.12691e18	−	6.50620e17i	−0.533088	−	0.307779i
$69$	−2.16363e17	+	3.42163e17i	−0.0884486	+	0.139876i
$70$	−4.10856e17	−	7.11623e17i	−0.145448	−	0.251924i
$71$			5.24061e17i			0.160990i	0.996755	+	0.0804950i	$0.0256501\pi$
$71$			5.24061e17i			0.160990i	−0.996755	+	0.0804950i	$0.974350\pi$
$72$	−1.06464e17	+	1.31938e18i	−0.0284366	+	0.352408i
$73$	−4.66174e18			−1.08472			−0.542362	−	0.840145i	$-0.682470\pi$
$73$	−4.66174e18			−1.08472			−0.542362	+	0.840145i	$0.682470\pi$
$74$	3.58924e18	−	2.07225e18i	0.728928	−	0.420847i
$75$	1.96564e18	−	1.03169e18i	0.349053	−	0.183205i
$76$	−1.99312e18	+	3.45219e18i	−0.310026	+	0.536981i
$77$	4.58972e18	+	2.64987e18i	0.626439	+	0.361675i
$78$	−9.57489e18	−	3.85684e17i	−1.14865	−	0.0462685i
$79$	1.90733e18	+	3.30360e18i	0.201444	+	0.348912i	0.948994	−	0.315294i	$-0.102103\pi$
$79$	1.90733e18	+	3.30360e18i	0.201444	+	0.348912i	−0.747550	+	0.664206i	$0.768770\pi$
$80$			2.08930e18i			0.194581i
$81$	1.20004e19	+	1.94937e18i	0.987062	+	0.160341i
$82$	2.91343e18			0.211966
$83$	−1.63293e19	+	9.42772e18i	−1.05241	+	0.607611i	−0.923324	−	0.384022i	$-0.874539\pi$
$83$	−1.63293e19	+	9.42772e18i	−1.05241	+	0.607611i	−0.129089	+	0.991633i	$0.541205\pi$
$84$	−1.86038e17	+	4.61853e18i	−0.0106367	+	0.264065i
$85$	−9.43231e18	+	1.63372e19i	−0.479103	+	0.829831i
$86$	−1.90913e19	−	1.10224e19i	−0.862684	−	0.498071i
$87$	1.98083e19	+	3.77399e19i	0.797360	+	1.51918i
$88$	−6.73762e18	−	1.16699e19i	−0.241924	−	0.419025i
$89$		−	3.96851e19i		−	1.27270i	−0.771399	−	0.636352i	$-0.780442\pi$
$89$		−	3.96851e19i		−	1.27270i	0.771399	−	0.636352i	$-0.219558\pi$
$90$	1.91276e19	+	1.54346e18i	0.548575	+	0.0442659i
$91$	−3.34628e19			−0.859306
$92$	3.11288e18	−	1.79722e18i	0.0716612	−	0.0413736i
$93$	4.25305e19	+	2.68936e19i	0.878762	+	0.555674i
$94$	−7.55392e18	+	1.30838e19i	−0.140247	+	0.242915i
$95$	5.00478e19	+	2.88951e19i	0.835890	+	0.482601i
$96$	6.28123e18	−	9.93337e18i	0.0944784	−	0.149412i
$97$	5.68257e19	+	9.84250e19i	0.770597	+	1.33471i	0.937236	+	0.348695i	$0.113375\pi$
$97$	5.68257e19	+	9.84250e19i	0.770597	+	1.33471i	−0.166639	+	0.986018i	$0.553292\pi$
$98$		−	4.16347e19i		−	0.509559i
$99$	−1.11816e20	+	5.30622e19i	−1.23638	+	0.586723i
$100$	−1.97106e19			−0.197106
$101$	−6.10749e19	+	3.52616e19i	−0.552903	+	0.319219i	−0.750292	−	0.661106i	$-0.770087\pi$
$101$	−6.10749e19	+	3.52616e19i	−0.552903	+	0.319219i	0.197389	+	0.980325i	$0.436754\pi$
$102$	9.39611e19	−	4.93167e19i	0.770808	−	0.404569i
$103$	3.14589e19	−	5.44884e19i	0.234084	−	0.405445i	−0.724922	−	0.688831i	$-0.758124\pi$
$103$	3.14589e19	−	5.44884e19i	0.234084	−	0.405445i	0.959006	+	0.283386i	$0.0914577\pi$
$104$	7.36841e19	+	4.25415e19i	0.497783	+	0.287395i
$105$	6.69568e19	+	2.69707e18i	0.411057	+	0.0165577i
$106$	−9.57725e19	−	1.65883e20i	−0.534789	−	0.926281i
$107$			3.83535e19i			0.194970i	0.995237	+	0.0974848i	$0.0310797\pi$
$107$			3.83535e19i			0.194970i	−0.995237	+	0.0974848i	$0.968920\pi$
$108$	−8.63003e19	−	6.48433e19i	−0.399737	−	0.300350i
$109$	−2.15650e20			−0.910928			−0.455464	−	0.890254i	$-0.650527\pi$
$109$	−2.15650e20			−0.910928			−0.455464	+	0.890254i	$0.650527\pi$
$110$	−1.69183e20	+	9.76781e19i	−0.652275	+	0.376591i
$111$	−1.36033e19	+	3.37712e20i	−0.0479087	+	1.18937i
$112$	2.05203e19	−	3.55422e19i	0.0660698	−	0.114436i
$113$	6.06526e19	+	3.50178e19i	0.178675	+	0.103158i	0.586670	−	0.809826i	$-0.300439\pi$
$113$	6.06526e19	+	3.50178e19i	0.178675	+	0.103158i	−0.407995	+	0.912984i	$0.633772\pi$
$114$	−1.51078e20	−	2.87842e20i	−0.407523	−	0.776436i
$115$	−2.60551e19	−	4.51287e19i	−0.0644042	−	0.111551i
$116$		−	3.78439e20i		−	0.857858i
$117$	4.43904e20	−	6.43155e20i	0.923486	−	1.33800i
$118$	−1.33318e20			−0.254723
$119$	3.20916e20	−	1.85281e20i	0.563537	−	0.325358i
$120$	−1.44008e20	−	9.10617e19i	−0.232581	−	0.147070i
$121$	2.93614e20	−	5.08555e20i	0.436439	−	0.755934i
$122$	−1.40129e20	−	8.09035e19i	−0.191836	−	0.110756i
$123$	−1.26981e20	+	2.00813e20i	−0.160209	+	0.253361i
$124$	−2.23393e20	−	3.86927e20i	−0.259927	−	0.450207i
$125$			1.01062e21i			1.08515i
$126$	−3.10231e20	−	2.14121e20i	−0.307596	−	0.212302i
$127$	1.83140e21			1.67782			0.838909	−	0.544271i	$-0.183194\pi$
$127$	1.83140e21			1.67782			0.838909	+	0.544271i	$0.183194\pi$
$128$	−9.03702e19	+	5.21753e19i	−0.0765466	+	0.0441942i
$129$	1.59183e21	−	8.35492e20i	1.24738	−	0.654704i
$130$	6.16743e20	−	1.06823e21i	0.447374	−	0.774874i
$131$	−7.80204e20	−	4.50451e20i	−0.524198	−	0.302646i	0.214452	−	0.976734i	$-0.431203\pi$
$131$	−7.80204e20	−	4.50451e20i	−0.524198	−	0.302646i	−0.738651	+	0.674089i	$0.764537\pi$
$132$	1.09802e21	+	4.42292e19i	0.683711	+	0.0275404i
$133$	−5.67594e20	−	9.83101e20i	−0.327734	−	0.567652i
$134$		−	3.09032e20i		−	0.165560i
$135$	−9.40060e20	+	1.25113e21i	−0.467539	+	0.622251i
$136$	−9.42199e20			−0.435265
$137$	−3.41822e21	+	1.97351e21i	−1.46756	+	0.847293i	−0.999340	−	0.0363210i	$-0.988436\pi$
$137$	−3.41822e21	+	1.97351e21i	−1.46756	+	0.847293i	−0.468215	+	0.883614i	$0.655103\pi$
$138$	−1.17979e19	+	2.92892e20i	−0.00470992	+	0.116927i
$139$	−1.81808e20	+	3.14901e20i	−0.0675252	+	0.116957i	−0.897811	−	0.440380i	$-0.854844\pi$
$139$	−1.81808e20	+	3.14901e20i	−0.0675252	+	0.116957i	0.830286	+	0.557337i	$0.188177\pi$
$140$	−5.15270e20	−	2.97491e20i	−0.178137	−	0.102848i
$141$	−5.72584e20	−	1.09092e21i	−0.184352	−	0.351238i
$142$	1.89731e20	+	3.28623e20i	0.0569185	+	0.0985858i
$143$			7.95554e21i			2.22489i
$144$	4.10907e20	+	8.65888e20i	0.107181	+	0.225859i
$145$	−5.48638e21			−1.33538
$146$	−2.92323e21	+	1.68773e21i	−0.664255	+	0.383508i
$147$	2.86974e21	+	1.81464e21i	0.609072	+	0.385139i
$148$	1.50047e21	−	2.59888e21i	0.297584	−	0.515430i
$149$	5.60568e21	+	3.23644e21i	1.03936	+	0.600074i	0.919652	−	0.392735i	$-0.128471\pi$
$149$	5.60568e21	+	3.23644e21i	1.03936	+	0.600074i	0.119707	+	0.992809i	$0.461804\pi$
$150$	8.59081e20	−	1.35858e21i	0.148978	−	0.235599i
$151$	2.43706e20	+	4.22110e20i	0.0395454	+	0.0684946i	0.885121	−	0.465362i	$-0.154076\pi$
$151$	2.43706e20	+	4.22110e20i	0.0395454	+	0.0684946i	−0.845575	+	0.533856i	$0.820742\pi$
$152$			2.88635e21i			0.438443i
$153$	−6.96043e20	+	8.62588e21i	−0.0990197	+	1.22713i
$154$	3.83743e21			0.511485
$155$	−5.60945e21	+	3.23862e21i	−0.700815	+	0.404616i
$156$	−6.14375e21	+	3.22463e21i	−0.719760	+	0.377776i
$157$	7.80176e21	−	1.35130e22i	0.857424	−	1.48510i	−0.0169529	−	0.999856i	$-0.505397\pi$
$157$	7.80176e21	−	1.35130e22i	0.857424	−	1.48510i	0.874377	−	0.485246i	$-0.161270\pi$
$158$	2.39206e21	+	1.38106e21i	0.246718	+	0.142443i
$159$	1.56080e22	+	6.28701e20i	1.51139	+	0.0608797i
$160$	7.56407e20	+	1.31014e21i	0.0687948	+	0.119156i
$161$			1.02361e21i			0.0874735i
$162$	8.23081e21	−	3.12221e21i	0.661138	−	0.250791i
$163$	−1.64606e22			−1.24328			−0.621642	−	0.783301i	$-0.713534\pi$
$163$	−1.64606e22			−1.24328			−0.621642	+	0.783301i	$0.713534\pi$
$164$	1.82692e21	−	1.05477e21i	0.129802	−	0.0749412i
$165$	6.41210e20	−	1.59185e22i	0.0428707	−	1.06430i
$166$	−6.82640e21	+	1.18237e22i	−0.429646	+	0.744169i
$167$	−1.96107e22	−	1.13222e22i	−1.16233	−	0.671069i	−0.210465	−	0.977601i	$-0.567498\pi$
$167$	−1.96107e22	−	1.13222e22i	−1.16233	−	0.671069i	−0.951860	+	0.306532i	$0.900831\pi$
$168$	1.55543e21	+	2.96349e21i	0.0868475	+	0.165467i
$169$	−1.56133e22	−	2.70430e22i	−0.821537	−	1.42294i
$170$			1.36595e22i			0.677554i
$171$	2.64247e22	+	2.13227e21i	1.23609	+	0.0997427i
$172$	−1.59621e22			−0.704379
$173$	−1.12442e19	+	6.49185e18i	−0.000468239	+	0.000270338i	−0.500234	−	0.865890i	$-0.666753\pi$
$173$	−1.12442e19	+	6.49185e18i	−0.000468239	+	0.000270338i	0.499766	+	0.866161i	$0.333419\pi$
$174$	2.60845e22	+	1.64942e22i	1.02539	+	0.648393i
$175$	2.80655e21	−	4.86109e21i	0.104182	−	0.180448i
$176$	−8.44991e21	−	4.87856e21i	−0.296296	−	0.171066i
$177$	5.81063e21	−	9.18914e21i	0.192527	−	0.304469i
$178$	−1.43675e22	−	2.48853e22i	−0.449969	−	0.779369i
$179$		−	7.50426e21i		−	0.222217i	−0.993808	−	0.111109i	$-0.964560\pi$
$179$		−	7.50426e21i		−	0.222217i	0.993808	−	0.111109i	$-0.0354402\pi$
$180$	1.25531e22	−	5.95709e21i	0.351583	−	0.166843i
$181$	1.29707e22			0.343698			0.171849	−	0.985123i	$-0.445026\pi$
$181$	1.29707e22			0.343698			0.171849	+	0.985123i	$0.445026\pi$
$182$	−2.09835e22	+	1.21148e22i	−0.526216	+	0.303811i
$183$	1.16839e22	−	6.13245e21i	0.277381	−	0.145587i
$184$	1.30133e21	−	2.25397e21i	0.0292556	−	0.0506721i
$185$	−3.76771e22	−	2.17529e22i	−0.802344	−	0.463233i
$186$	3.64061e22	+	1.46647e21i	0.734590	+	0.0295898i
$187$	−4.40493e22	−	7.62956e22i	−0.842409	−	1.45910i
$188$			1.09392e22i			0.198339i
$189$	2.82800e22	−	1.20508e22i	0.486252	−	0.207203i
$190$	4.18446e22			0.682501
$191$	−5.31082e22	+	3.06621e22i	−0.821917	+	0.474534i	−0.851077	−	0.525041i	$-0.824050\pi$
$191$	−5.31082e22	+	3.06621e22i	−0.821917	+	0.474534i	0.0291598	+	0.999575i	$0.490717\pi$
$192$	3.42506e20	−	8.50296e21i	0.00503101	−	0.124899i
$193$	3.02115e22	−	5.23278e22i	0.421307	−	0.729725i	−0.574760	−	0.818322i	$-0.694905\pi$
$193$	3.02115e22	−	5.23278e22i	0.421307	−	0.729725i	0.996068	+	0.0885963i	$0.0282381\pi$
$194$	7.12673e22	+	4.11462e22i	0.943785	+	0.544894i
$195$	4.67488e22	+	8.90686e22i	0.588064	+	1.12041i
$196$	−1.50734e22	−	2.61078e22i	−0.180156	−	0.312040i
$197$		−	1.14453e22i		−	0.130007i	−0.997885	−	0.0650033i	$-0.979294\pi$
$197$		−	1.14453e22i		−	0.130007i	0.997885	−	0.0650033i	$-0.0207058\pi$
$198$	−5.09058e22	+	7.37554e22i	−0.549686	+	0.796419i
$199$	−1.31665e23			−1.35189			−0.675944	−	0.736953i	$-0.736264\pi$
$199$	−1.31665e23			−1.35189			−0.675944	+	0.736953i	$0.736264\pi$
$200$	−1.23599e22	+	7.13598e21i	−0.120702	+	0.0696873i
$201$	2.13005e22	+	1.34691e22i	0.197893	+	0.125135i
$202$	−2.55321e22	+	4.42230e22i	−0.225722	+	0.390962i
$203$	9.33318e22	+	5.38852e22i	0.785361	+	0.453428i
$204$	4.10656e22	−	6.49426e22i	0.328985	−	0.520269i
$205$	−1.52915e22	−	2.64856e22i	−0.116657	−	0.202056i
$206$		−	4.55573e22i		−	0.331044i
$207$	−1.96738e22	−	1.35788e22i	−0.136203	−	0.0940067i
$208$	6.16067e22			0.406438
$209$	−2.33726e23	+	1.34941e23i	−1.46975	+	0.848560i
$210$	4.29630e22	−	2.25497e22i	0.257574	−	0.135191i
$211$	9.04919e22	−	1.56737e23i	0.517351	−	0.896078i	−0.482446	−	0.875926i	$-0.660252\pi$
$211$	9.04919e22	−	1.56737e23i	0.517351	−	0.896078i	0.999797	−	0.0201520i	$-0.00641503\pi$
$212$	−1.20112e23	−	6.93467e22i	−0.654980	−	0.378153i
$213$	−3.09202e22	−	1.24549e21i	−0.160859	−	0.00647954i
$214$	1.38854e22	+	2.40503e22i	0.0689322	+	0.119394i
$215$			2.31410e23i			1.09647i
$216$	−7.75921e22	−	9.41716e21i	−0.350978	−	0.0425974i
$217$	1.27234e23			0.549548
$218$	−1.35227e23	+	7.80736e22i	−0.557827	+	0.322062i
$219$	1.10791e22	−	2.75048e23i	0.0436581	−	1.08384i
$220$	−7.07265e22	+	1.22502e23i	−0.266290	+	0.461228i
$221$	4.81733e23	+	2.78129e23i	1.73334	+	1.00074i
$222$	1.13735e23	+	2.16694e23i	0.391168	+	0.745276i
$223$	1.43694e23	+	2.48886e23i	0.472489	+	0.818375i	0.999504	−	0.0314811i	$-0.0100224\pi$
$223$	1.43694e23	+	2.48886e23i	0.472489	+	0.818375i	−0.527016	+	0.849856i	$0.676689\pi$
$224$		−	2.97166e22i		−	0.0934369i
$225$	5.61995e22	+	1.18427e23i	0.169008	+	0.356144i
$226$	5.07112e22			0.145888
$227$	1.30573e23	−	7.53864e22i	0.359414	−	0.207508i	−0.309410	−	0.950929i	$-0.600131\pi$
$227$	1.30573e23	−	7.53864e22i	0.359414	−	0.207508i	0.668824	+	0.743421i	$0.266798\pi$
$228$	−1.98946e23	−	1.25801e23i	−0.524068	−	0.331387i
$229$	−3.18946e23	+	5.52431e23i	−0.804197	+	1.39291i	0.112635	+	0.993636i	$0.464071\pi$
$229$	−3.18946e23	+	5.52431e23i	−0.804197	+	1.39291i	−0.916832	+	0.399274i	$0.869262\pi$
$230$	−3.26767e22	−	1.88659e22i	−0.0788787	−	0.0455406i
$231$	−1.67254e23	+	2.64501e23i	−0.386594	+	0.611374i
$232$	−1.37009e23	−	2.37307e23i	−0.303299	−	0.525329i
$233$		−	6.25874e22i		−	0.132717i	−0.997796	−	0.0663587i	$-0.978862\pi$
$233$		−	6.25874e22i		−	0.132717i	0.997796	−	0.0663587i	$-0.0211382\pi$
$234$	4.55116e22	−	5.64013e23i	0.0924620	−	1.14586i
$235$	1.58591e23			0.308745
$236$	−8.35995e22	+	4.82662e22i	−0.155985	+	0.0900582i
$237$	−1.99449e23	+	1.04683e23i	−0.356737	+	0.187238i
$238$	1.34158e23	−	2.32368e23i	0.230063	−	0.398481i
$239$	−2.82126e23	−	1.62886e23i	−0.463943	−	0.267857i	0.249758	−	0.968308i	$-0.419649\pi$
$239$	−2.82126e23	−	1.62886e23i	−0.463943	−	0.267857i	−0.713701	+	0.700451i	$0.752982\pi$
$240$	−1.23271e23	−	4.96545e21i	−0.194423	−	0.00783152i
$241$	7.38294e22	+	1.27876e23i	0.111701	+	0.193473i	0.916456	−	0.400135i	$-0.131037\pi$
$241$	7.38294e22	+	1.27876e23i	0.111701	+	0.193473i	−0.804755	+	0.593607i	$0.797703\pi$
$242$		−	4.25199e23i		−	0.617217i
$243$	−1.43535e23	+	7.03403e23i	−0.199938	+	0.979809i
$244$	−1.17161e23			−0.156633
$245$	−3.78496e23	+	2.18525e23i	−0.485737	+	0.280440i
$246$	−6.92408e21	+	1.71895e23i	−0.00853121	+	0.211794i
$247$	8.52025e23	−	1.47575e24i	1.00805	−	1.74600i
$248$	−2.80165e23	−	1.61754e23i	−0.318345	−	0.183796i
$249$	−5.17438e23	−	9.85853e23i	−0.564761	−	1.07602i
$250$	3.65885e23	+	6.33731e23i	0.383658	+	0.664515i
$251$		−	1.48369e24i		−	1.49488i	−0.664331	−	0.747439i	$-0.731283\pi$
$251$		−	1.48369e24i		−	1.49488i	0.664331	−	0.747439i	$-0.268717\pi$
$252$	−2.72057e23	−	2.19529e22i	−0.263423	−	0.0212562i
$253$	2.43357e23			0.226484
$254$	1.14841e24	−	6.63036e23i	1.02745	−	0.593199i
$255$	−9.41500e23	−	5.95345e23i	−0.809876	−	0.512114i
$256$	−3.77789e22	+	6.54350e22i	−0.0312500	+	0.0541266i
$257$	2.06910e24	+	1.19460e24i	1.64608	+	0.950363i	0.978610	+	0.205723i	$0.0659547\pi$
$257$	2.06910e24	+	1.19460e24i	1.64608	+	0.950363i	0.667467	+	0.744640i	$0.267379\pi$
$258$	6.95706e23	−	1.10021e24i	0.532389	−	0.841939i
$259$	4.27297e23	+	7.40101e23i	0.314581	+	0.544870i
$260$		−	8.93139e23i		−	0.632682i
$261$	−2.27378e24	+	1.07902e24i	−1.55004	+	0.735570i
$262$	−6.52323e23			−0.428006
$263$	1.37083e24	−	7.91449e23i	0.865816	−	0.499879i	−0.000139273	−	1.00000i	$-0.500044\pi$
$263$	1.37083e24	−	7.91449e23i	0.865816	−	0.499879i	0.865956	+	0.500121i	$0.166711\pi$
$264$	7.04550e23	−	3.69792e23i	0.428423	−	0.224863i
$265$	−1.00535e24	+	1.74131e24i	−0.588651	+	1.01957i
$266$	−7.11841e23	−	4.10982e23i	−0.401390	−	0.231743i
$267$	2.34147e24	+	9.43160e22i	1.27167	+	0.0512239i
$268$	−1.11882e23	−	1.93785e23i	−0.0585343	−	0.101384i
$269$		−	2.82543e24i		−	1.42417i	−0.702093	−	0.712085i	$-0.747751\pi$
$269$		−	2.82543e24i		−	1.42417i	0.702093	−	0.712085i	$-0.252249\pi$
$270$	−1.36525e23	+	1.12488e24i	−0.0663091	+	0.546349i
$271$	9.79278e23			0.458367			0.229183	−	0.973383i	$-0.426394\pi$
$271$	9.79278e23			0.458367			0.229183	+	0.973383i	$0.426394\pi$
$272$	−5.90824e23	+	3.41112e23i	−0.266544	+	0.153889i
$273$	7.95280e22	−	1.97434e24i	0.0345854	−	0.858610i
$274$	−1.42897e24	+	2.47506e24i	−0.599127	+	1.03772i
$275$	−1.15569e24	−	6.67238e23i	−0.467212	−	0.269745i
$276$	9.86401e22	+	1.87935e23i	0.0384559	+	0.0732683i
$277$	1.42582e23	+	2.46958e23i	0.0536124	+	0.0928595i	0.891586	−	0.452851i	$-0.149593\pi$
$277$	1.42582e23	+	2.46958e23i	0.0536124	+	0.0928595i	−0.837974	+	0.545711i	$0.816260\pi$
$278$			2.63287e23i			0.0954950i
$279$	−1.68783e24	+	2.44543e24i	−0.590592	+	0.855685i
$280$	−4.30813e23			−0.145448
$281$	3.45341e24	−	1.99383e24i	1.12508	−	0.649568i	0.182391	−	0.983226i	$-0.441616\pi$
$281$	3.45341e24	−	1.99383e24i	1.12508	−	0.649568i	0.942694	+	0.333658i	$0.108283\pi$
$282$	−7.54005e23	−	4.76785e23i	−0.237074	−	0.149910i
$283$	−1.81450e24	+	3.14281e24i	−0.550672	+	0.953792i	0.447554	+	0.894257i	$0.352295\pi$
$283$	−1.81450e24	+	3.14281e24i	−0.550672	+	0.953792i	−0.998226	+	0.0595353i	$0.981038\pi$
$284$	2.37948e23	+	1.37380e23i	0.0697107	+	0.0402475i
$285$	−1.82379e24	+	2.88421e24i	−0.515853	+	0.815789i
$286$	2.88021e24	+	4.98868e24i	0.786619	+	1.36246i
$287$			6.00749e23i			0.158443i
$288$	5.71152e23	+	3.94208e23i	0.145488	+	0.100415i
$289$	−2.09569e24			−0.515642
$290$	−3.44034e24	+	1.98628e24i	−0.817752	+	0.472129i
$291$	−5.94224e24	+	3.11886e24i	−1.36465	+	0.716253i
$292$	−1.22205e24	+	2.11665e24i	−0.271181	+	0.469699i
$293$	3.58144e24	+	2.06774e24i	0.768036	+	0.443426i	0.832173	−	0.554516i	$-0.187096\pi$
$293$	3.58144e24	+	2.06774e24i	0.768036	+	0.443426i	−0.0641378	+	0.997941i	$0.520430\pi$
$294$	2.45650e24	+	9.89494e22i	0.509146	+	0.0205088i
$295$	6.99735e23	+	1.21198e24i	0.140189	+	0.242814i
$296$		−	2.17291e24i		−	0.420847i
$297$	−2.86499e24	−	6.72338e24i	−0.536486	−	1.25899i
$298$	4.68686e24			0.848633
$299$	−1.33070e24	+	7.68281e23i	−0.233007	+	0.134527i
$300$	4.68443e22	−	1.16295e24i	0.00793312	−	0.196946i
$301$	2.27282e24	−	3.93663e24i	0.372306	−	0.644852i
$302$	3.05641e23	+	1.76462e23i	0.0484330	+	0.0279628i
$303$	−1.93532e24	−	3.68729e24i	−0.296707	−	0.565303i
$304$	1.04497e24	+	1.80994e24i	0.155013	+	0.268490i
$305$			1.69853e24i			0.243823i
$306$	2.68643e24	+	5.66102e24i	0.373218	+	0.786467i
$307$	8.10863e23			0.109034			0.0545172	−	0.998513i	$-0.482638\pi$
$307$	8.10863e23			0.109034			0.0545172	+	0.998513i	$0.482638\pi$
$308$	2.40633e24	−	1.38930e24i	0.313219	−	0.180837i
$309$	3.14011e24	+	1.98561e24i	0.395695	+	0.250212i
$310$	−2.34501e24	+	4.06168e24i	−0.286106	+	0.495551i
$311$	4.54701e24	+	2.62521e24i	0.537182	+	0.310142i	0.743936	−	0.668251i	$-0.232957\pi$
$311$	4.54701e24	+	2.62521e24i	0.537182	+	0.310142i	−0.206754	+	0.978393i	$0.566290\pi$
$312$	−2.68512e24	+	4.24634e24i	−0.307197	+	0.485813i
$313$	−6.63668e24	−	1.14951e25i	−0.735373	−	1.27370i	−0.954560	−	0.298020i	$-0.903674\pi$
$313$	−6.63668e24	−	1.14951e25i	−0.735373	−	1.27370i	0.219187	−	0.975683i	$-0.429660\pi$
$314$		−	1.12982e25i		−	1.21258i
$315$	−3.18261e23	+	3.94412e24i	−0.0330885	+	0.410057i
$316$	1.99998e24			0.201444
$317$	−3.58125e24	+	2.06763e24i	−0.349496	+	0.201781i	−0.664463	−	0.747321i	$-0.731340\pi$
$317$	−3.58125e24	+	2.06763e24i	−0.349496	+	0.201781i	0.314968	+	0.949102i	$0.398006\pi$
$318$	1.00149e25	−	5.25645e24i	0.947055	−	0.497074i
$319$	1.28108e25	−	2.21890e25i	1.17401	−	2.03344i
$320$	9.48639e23	+	5.47697e23i	0.0842561	+	0.0486453i
$321$	−2.26290e24	−	9.11513e22i	−0.194812	−	0.00784716i
$322$	3.70587e23	+	6.41876e23i	0.0309266	+	0.0535664i
$323$			1.88704e25i			1.52671i
$324$	4.03093e24	−	4.93771e24i	0.316195	−	0.387325i
$325$	8.42592e24			0.640890
$326$	−1.03220e25	+	5.95939e24i	−0.761353	+	0.439568i
$327$	5.12515e23	−	1.27236e25i	0.0366631	−	0.910190i
$328$	7.63737e23	−	1.32283e24i	0.0529914	−	0.0917838i
$329$	−2.69788e24	−	1.55762e24i	−0.181578	−	0.104834i
$330$	−5.36104e24	−	1.02142e25i	−0.350033	−	0.666904i
$331$	−7.88493e24	−	1.36571e25i	−0.499480	−	0.865125i	0.500520	−	0.865725i	$-0.333142\pi$
$331$	−7.88493e24	−	1.36571e25i	−0.499480	−	0.865125i	−1.00000		0.000600484i	$0.999809\pi$
$332$			9.88568e24i			0.607611i
$333$	−1.98931e25	−	1.60522e24i	−1.18648	−	0.0957398i
$334$	−1.63963e25			−0.949035
$335$	−2.80938e24	+	1.62199e24i	−0.157820	+	0.0911174i
$336$	2.04826e24	+	1.29519e24i	0.111684	+	0.0706222i
$337$	−9.06706e24	+	1.57046e25i	−0.479918	+	0.831243i	−0.999735	−	0.0230352i	$-0.992667\pi$
$337$	−9.06706e24	+	1.57046e25i	−0.479918	+	0.831243i	0.519816	+	0.854278i	$0.326000\pi$
$338$	−1.95812e25	−	1.13052e25i	−1.00617	−	0.580915i
$339$	−2.21024e24	+	3.49535e24i	−0.110266	+	0.174379i
$340$	4.94525e24	+	8.56542e24i	0.239552	+	0.414915i
$341$		−	3.02490e25i		−	1.42287i
$342$	1.73421e25	−	8.22967e24i	0.792209	−	0.375943i
$343$	2.04984e25			0.909452
$344$	−1.00094e25	+	5.77891e24i	−0.431342	+	0.249035i
$345$	2.72457e24	−	1.43003e24i	0.114053	−	0.0598623i
$346$	−4.70060e21	+	8.14168e21i	−0.000191158	+	0.000331095i
$347$	3.70313e25	+	2.13800e25i	1.46310	+	0.844722i	0.999153	−	0.0411410i	$-0.0130993\pi$
$347$	3.70313e25	+	2.13800e25i	1.46310	+	0.844722i	0.463947	+	0.885863i	$0.346433\pi$
$348$	2.23283e25	+	8.99401e23i	0.857163	+	0.0345272i
$349$	−2.08032e25	−	3.60322e25i	−0.776026	−	1.34412i	−0.934216	−	0.356708i	$-0.883899\pi$
$349$	−2.08032e25	−	3.60322e25i	−0.776026	−	1.34412i	0.158190	−	0.987409i	$-0.449434\pi$
$350$		−	4.06432e24i		−	0.147335i
$351$	3.68919e25	+	2.77194e25i	1.29975	+	0.976589i
$352$	−7.06490e24			−0.241924
$353$	−3.51532e25	+	2.02957e25i	−1.17009	+	0.675550i	−0.953701	−	0.300757i	$-0.902761\pi$
$353$	−3.51532e25	+	2.02957e25i	−1.17009	+	0.675550i	−0.216387	+	0.976308i	$0.569427\pi$
$354$	3.16844e23	−	7.86590e24i	0.0102521	−	0.254517i
$355$	1.99165e24	−	3.44964e24i	0.0626512	−	0.108515i
$356$	−1.80189e25	−	1.04032e25i	−0.551097	−	0.318176i
$357$	1.01691e25	+	1.93748e25i	0.302413	+	0.576175i
$358$	−2.71683e24	−	4.70569e24i	−0.0785657	−	0.136080i
$359$			4.95875e25i			1.39453i	0.716813	+	0.697265i	$0.245600\pi$
$359$			4.95875e25i			1.39453i	−0.716813	+	0.697265i	$0.754400\pi$
$360$	5.71500e24	−	8.28024e24i	0.156312	−	0.226474i
$361$	2.02180e25			0.537857
$362$	8.13351e24	−	4.69588e24i	0.210471	−	0.121515i
$363$	2.93075e25	+	1.85322e25i	0.737756	+	0.466510i
$364$	−8.77207e24	+	1.51937e25i	−0.214827	+	0.372091i
$365$	3.06859e25	+	1.77165e25i	0.731157	+	0.422133i
$366$	5.10643e24	−	8.07549e24i	0.118388	−	0.187223i
$367$	−3.21235e25	−	5.56395e25i	−0.724706	−	1.25523i	−0.959095	−	0.283084i	$-0.908642\pi$
$367$	−3.21235e25	−	5.56395e25i	−0.724706	−	1.25523i	0.234389	−	0.972143i	$-0.424691\pi$
$368$		−	1.88452e24i		−	0.0413736i
$369$	−1.15464e25	−	7.96929e24i	−0.246708	−	0.170277i
$370$	−3.15016e25			−0.655111
$371$	3.42051e25	−	1.97483e25i	0.692391	−	0.399752i
$372$	2.33601e25	−	1.22608e25i	0.460304	−	0.241597i
$373$	−2.95448e23	+	5.11730e23i	−0.00566751	+	0.00981642i	−0.868845	−	0.495084i	$-0.835137\pi$
$373$	−2.95448e23	+	5.11730e23i	−0.00566751	+	0.00981642i	0.863178	+	0.504900i	$0.168471\pi$
$374$	−5.52439e25	−	3.18951e25i	−1.03174	−	0.595673i
$375$	−5.96279e25	−	2.40186e24i	−1.08427	−	0.0436752i
$376$	3.96043e24	+	6.85967e24i	0.0701236	+	0.121458i
$377$			1.61776e26i			2.78933i
$378$	1.33707e25	−	1.77951e25i	0.224510	−	0.298802i
$379$	−2.73780e25			−0.447724			−0.223862	−	0.974621i	$-0.571866\pi$
$379$	−2.73780e25			−0.447724			−0.223862	+	0.974621i	$0.571866\pi$
$380$	2.62395e25	−	1.51494e25i	0.417945	−	0.241301i
$381$	−4.35251e24	+	1.08054e26i	−0.0675290	+	1.67646i
$382$	−2.22017e25	+	3.84545e25i	−0.335546	+	0.581183i
$383$	−8.05273e25	−	4.64925e25i	−1.18565	−	0.684534i	−0.228333	−	0.973583i	$-0.573328\pi$
$383$	−8.05273e25	−	4.64925e25i	−1.18565	−	0.684534i	−0.957314	+	0.289049i	$0.906661\pi$
$384$	−2.86363e24	−	5.45595e24i	−0.0410775	−	0.0782633i
$385$	−2.01412e25	−	3.48856e25i	−0.281500	−	0.487573i
$386$		−	4.37509e25i		−	0.595818i
$387$	4.55118e25	+	9.59053e25i	0.603969	+	1.27272i
$388$	5.95860e25			0.770597
$389$	1.85413e25	−	1.07048e25i	0.233692	−	0.134922i	−0.378582	−	0.925568i	$-0.623588\pi$
$389$	1.85413e25	−	1.07048e25i	0.233692	−	0.134922i	0.612274	+	0.790645i	$0.290255\pi$
$390$	6.15610e25	+	3.89273e25i	0.756240	+	0.478198i
$391$	8.50784e24	−	1.47360e25i	0.101871	−	0.176446i
$392$	−1.89041e25	−	1.09143e25i	−0.220646	−	0.127390i
$393$	2.84314e25	−	4.49624e25i	0.323499	−	0.511592i
$394$	−4.14364e24	−	7.17700e24i	−0.0459643	−	0.0796124i
$395$		−	2.89946e25i		−	0.313578i
$396$	−5.21915e24	+	6.46796e25i	−0.0550361	+	0.682049i
$397$	−1.11602e26			−1.14754			−0.573768	−	0.819018i	$-0.694519\pi$
$397$	−1.11602e26			−1.14754			−0.573768	+	0.819018i	$0.694519\pi$
$398$	−8.25633e25	+	4.76679e25i	−0.827859	+	0.477964i
$399$	5.93531e25	−	3.11522e25i	0.580382	−	0.304621i
$400$	−5.16700e24	+	8.94951e24i	−0.0492764	+	0.0853492i
$401$	−4.79054e25	−	2.76582e25i	−0.445596	−	0.257265i	0.260373	−	0.965508i	$-0.416155\pi$
$401$	−4.79054e25	−	2.76582e25i	−0.445596	−	0.257265i	−0.705968	+	0.708243i	$0.749488\pi$
$402$	1.82333e25	+	7.34449e23i	0.165426	+	0.00666348i
$403$	9.54965e25	+	1.65405e26i	0.845156	+	1.46385i
$404$			3.69745e25i			0.319219i
$405$	−7.15841e25	−	5.84381e25i	−0.602929	−	0.492205i
$406$	7.80340e25			0.641245
$407$	1.75954e26	−	1.01587e26i	1.41076	−	0.814505i
$408$	2.23924e24	−	5.55908e25i	0.0175186	−	0.434912i
$409$	4.79100e25	−	8.29825e25i	0.365757	−	0.633510i	−0.623140	−	0.782110i	$-0.714143\pi$
$409$	4.79100e25	−	8.29825e25i	0.365757	−	0.633510i	0.988897	+	0.148600i	$0.0474767\pi$
$410$	−1.91776e25	−	1.10722e25i	−0.142875	−	0.0824890i
$411$	−1.08316e26	−	2.06369e26i	−0.787541	−	1.50047i
$412$	−1.64935e25	−	2.85676e25i	−0.117042	−	0.202722i
$413$		−	2.74901e25i		−	0.190404i
$414$	−1.72529e25	−	1.39218e24i	−0.116643	−	0.00941221i
$415$	1.43317e26			0.945837
$416$	3.86317e25	−	2.23040e25i	0.248892	−	0.143698i
$417$	−1.81474e25	−	1.14753e25i	−0.114145	−	0.0721778i
$418$	−9.77081e25	+	1.69235e26i	−0.600023	+	1.03927i
$419$	1.42182e26	+	8.20890e25i	0.852521	+	0.492203i	0.861501	−	0.507756i	$-0.169525\pi$
$419$	1.42182e26	+	8.20890e25i	0.852521	+	0.492203i	−0.00897958	+	0.999960i	$0.502858\pi$
$420$	1.87769e25	−	2.96945e25i	0.109934	−	0.173853i
$421$	−1.67320e26	−	2.89806e26i	−0.956590	−	1.65686i	−0.730687	−	0.682712i	$-0.760800\pi$
$421$	−1.67320e26	−	2.89806e26i	−0.956590	−	1.65686i	−0.225902	−	0.974150i	$-0.572533\pi$
$422$		−	1.31046e26i		−	0.731644i
$423$	6.57264e25	−	3.11904e25i	0.358374	−	0.170066i
$424$	−1.00425e26			−0.534789
$425$	−8.08067e25	+	4.66538e25i	−0.420299	+	0.242659i
$426$	−1.98400e25	+	1.04133e25i	−0.100797	+	0.0529045i
$427$	1.66823e25	−	2.88946e25i	0.0827899	−	0.143396i
$428$	1.74143e25	+	1.00541e25i	0.0844243	+	0.0487424i
$429$	−4.69386e26	−	1.89072e25i	−2.22309	−	0.0895478i
$430$	8.37792e25	+	1.45110e26i	0.387661	+	0.671448i
$431$		−	1.33586e26i		−	0.603933i	−0.953318	−	0.301967i	$-0.902357\pi$
$431$		−	1.33586e26i		−	0.603933i	0.953318	−	0.301967i	$-0.0976431\pi$
$432$	−5.20650e25	+	2.21861e25i	−0.229990	+	0.0980040i
$433$	3.10651e26			1.34089			0.670446	−	0.741958i	$-0.266103\pi$
$433$	3.10651e26			1.34089			0.670446	+	0.741958i	$0.266103\pi$
$434$	7.97845e25	−	4.60636e25i	0.336528	−	0.194294i
$435$	1.30390e25	−	3.23703e26i	0.0537467	−	1.33430i
$436$	−5.65313e25	+	9.79151e25i	−0.227732	+	0.394443i
$437$	−4.51426e25	−	2.60631e25i	−0.177735	−	0.102615i
$438$	−9.26306e25	−	1.76485e26i	−0.356462	−	0.679152i
$439$	−5.58564e25	−	9.67461e25i	−0.210101	−	0.363905i	0.741645	−	0.670793i	$-0.234046\pi$
$439$	−5.58564e25	−	9.67461e25i	−0.210101	−	0.363905i	−0.951746	+	0.306887i	$0.900713\pi$
$440$			1.02423e26i			0.376591i
$441$	−1.13886e26	+	1.65005e26i	−0.409341	+	0.593078i
$442$	4.02773e26			1.41527
$443$	2.50501e26	−	1.44627e26i	0.860542	−	0.496834i	−0.00365183	−	0.999993i	$-0.501162\pi$
$443$	2.50501e26	−	1.44627e26i	0.860542	−	0.496834i	0.864194	+	0.503159i	$0.167829\pi$
$444$	1.49771e26	+	9.47058e25i	0.503035	+	0.318088i
$445$	−1.50820e26	+	2.61228e26i	−0.495288	+	0.857865i
$446$	1.80213e26	+	1.04046e26i	0.578678	+	0.334100i
$447$	−2.04276e26	+	3.23050e26i	−0.641420	+	1.01436i
$448$	−1.07585e25	−	1.86343e25i	−0.0330349	−	0.0572182i
$449$		−	3.29826e26i		−	0.990426i	−0.868772	−	0.495213i	$-0.835090\pi$
$449$		−	3.29826e26i		−	0.990426i	0.868772	−	0.495213i	$-0.164910\pi$
$450$	7.81162e25	+	5.39156e25i	0.229412	+	0.158339i
$451$	1.42824e26			0.410237
$452$	3.17994e25	−	1.83594e25i	0.0893377	−	0.0515791i
$453$	−2.54842e25	+	1.33757e25i	−0.0700308	+	0.0367566i
$454$	5.45856e25	−	9.45450e25i	0.146730	−	0.254144i
$455$	2.20269e26	+	1.27172e26i	0.579214	+	0.334410i
$456$	−1.70298e26	−	6.85973e24i	−0.438088	−	0.0176465i
$457$	3.15710e26	+	5.46825e26i	0.794559	+	1.37622i	0.923119	+	0.384515i	$0.125631\pi$
$457$	3.15710e26	+	5.46825e26i	0.794559	+	1.37622i	−0.128560	+	0.991702i	$0.541035\pi$
$458$			4.61883e26i			1.13731i
$459$	−5.07283e26	−	6.15677e25i	−1.22215	−	0.148329i
$460$	−2.73207e25			−0.0644042
$461$	−1.34579e26	+	7.76995e25i	−0.310434	+	0.179229i	−0.647121	−	0.762388i	$-0.724027\pi$
$461$	−1.34579e26	+	7.76995e25i	−0.310434	+	0.179229i	0.336687	+	0.941617i	$0.390694\pi$
$462$	−9.12007e24	+	2.26413e26i	−0.0205863	+	0.511071i
$463$	−1.94143e26	+	3.36266e26i	−0.428857	+	0.742803i	−0.996772	−	0.0802848i	$-0.974417\pi$
$463$	−1.94143e26	+	3.36266e26i	−0.428857	+	0.742803i	0.567915	+	0.823087i	$0.307750\pi$
$464$	−1.71829e26	−	9.92054e25i	−0.371463	−	0.214465i
$465$	−1.77751e26	−	3.38661e26i	−0.376081	−	0.716532i
$466$	−2.26591e25	−	3.92466e25i	−0.0469227	−	0.0812725i
$467$			4.39240e26i			0.890293i	0.895458	+	0.445147i	$0.146848\pi$
$467$			4.39240e26i			0.890293i	−0.895458	+	0.445147i	$0.853152\pi$
$468$	−1.75656e26	−	3.70152e26i	−0.348500	−	0.734381i
$469$	6.37224e25			0.123755
$470$	9.94475e25	−	5.74160e25i	0.189067	−	0.109158i
$471$	7.78743e26	+	4.92428e26i	1.44939	+	0.916502i
$472$	−3.49485e25	+	6.05325e25i	−0.0636807	+	0.110298i
$473$	−9.35907e26	−	5.40346e26i	−1.66963	−	0.963964i
$474$	−8.71689e25	+	1.37852e26i	−0.152257	+	0.240785i
$475$	1.42920e26	+	2.47545e26i	0.244431	+	0.423367i
$476$		−	1.94281e26i		−	0.325358i
$477$	−7.41881e25	+	9.19394e26i	−0.121661	+	1.50771i
$478$	−2.35883e26			−0.378807
$479$	1.71483e26	−	9.90056e25i	0.269690	−	0.155706i	−0.359057	−	0.933316i	$-0.616902\pi$
$479$	1.71483e26	−	9.90056e25i	0.269690	−	0.155706i	0.628747	+	0.777610i	$0.283568\pi$
$480$	−7.90972e25	+	4.15152e25i	−0.121828	+	0.0639433i
$481$	−6.41423e26	+	1.11098e27i	−0.967596	+	1.67592i
$482$	9.25923e25	+	5.34582e25i	0.136806	+	0.0789849i
$483$	−6.03943e25	−	2.43273e24i	−0.0874027	−	0.00352064i
$484$	−1.53938e26	−	2.66629e26i	−0.218219	−	0.377967i
$485$		−	8.63844e26i		−	1.19955i
$486$	1.64652e26	+	4.93048e26i	0.223978	+	0.670697i
$487$	1.08075e27			1.44025			0.720123	−	0.693847i	$-0.244086\pi$
$487$	1.08075e27			1.44025			0.720123	+	0.693847i	$0.244086\pi$
$488$	−7.34679e25	+	4.24167e25i	−0.0959179	+	0.0553782i
$489$	3.91205e25	−	9.71197e26i	0.0500398	−	1.24228i
$490$	−1.58229e26	+	2.74061e26i	−0.198301	+	0.343468i
$491$	1.14696e27	+	6.62200e26i	1.40843	+	0.813157i	0.995237	−	0.0974864i	$-0.0310802\pi$
$491$	1.14696e27	+	6.62200e26i	1.40843	+	0.813157i	0.413193	+	0.910644i	$0.364414\pi$
$492$	5.78909e25	+	1.10297e26i	0.0696562	+	0.132713i
$493$	−8.95742e26	−	1.55147e27i	−1.05612	−	1.82926i
$494$		−	1.23386e27i		−	1.42560i
$495$	9.37687e26	+	7.56642e25i	1.06171	+	0.0856719i
$496$	−2.34244e26			−0.259927
$497$	−6.77621e25	+	3.91224e25i	−0.0736924	+	0.0425463i
$498$	−6.81386e26	−	4.30866e26i	−0.726273	−	0.459249i
$499$	−6.50855e26	+	1.12731e27i	−0.679953	+	1.17771i	0.295041	+	0.955484i	$0.404667\pi$
$499$	−6.50855e26	+	1.12731e27i	−0.679953	+	1.17771i	−0.974995	+	0.222229i	$0.928667\pi$
$500$	4.58870e26	+	2.64929e26i	0.469883	+	0.271287i
$501$	7.14631e26	−	1.13014e27i	0.717307	−	1.13437i
$502$	−5.37153e26	−	9.30376e26i	−0.528519	−	0.915421i
$503$		−	1.23825e26i		−	0.119434i	−0.998215	−	0.0597170i	$-0.980980\pi$
$503$		−	1.23825e26i		−	0.119434i	0.998215	−	0.0597170i	$-0.0190198\pi$
$504$	−1.78546e26	+	8.47290e25i	−0.168828	+	0.0801174i
$505$	5.36035e26			0.496912
$506$	1.52602e26	−	8.81045e25i	0.138693	−	0.0800743i
$507$	1.63268e27	−	8.56931e26i	1.45486	−	0.763601i
$508$	4.80089e26	−	8.31539e26i	0.419455	−	0.726517i
$509$	−3.75697e26	−	2.16909e26i	−0.321855	−	0.185823i	0.330364	−	0.943854i	$-0.392828\pi$
$509$	−3.75697e26	−	2.16909e26i	−0.321855	−	0.185823i	−0.652219	+	0.758030i	$0.726162\pi$
$510$	−8.05923e26	−	3.24632e25i	−0.677005	−	0.0272703i
$511$	−3.48010e26	−	6.02771e26i	−0.286670	−	0.496527i
$512$			5.47097e25i			0.0441942i
$513$	−1.88608e26	+	1.55402e27i	−0.149412	+	1.23107i
$514$	1.72996e27			1.34402
$515$	−4.14156e26	+	2.39113e26i	−0.315567	+	0.182193i
$516$	3.79357e25	−	9.41784e26i	0.0283499	−	0.703808i
$517$	−3.70313e26	+	6.41401e26i	−0.271434	+	0.470137i
$518$	5.35890e26	+	3.09396e26i	0.385281	+	0.222442i
$519$	−3.56303e23	−	6.78850e23i	−0.000251273	−	0.000478740i
$520$	−3.23351e26	−	5.60060e26i	−0.223687	−	0.387437i
$521$			1.03233e27i			0.700556i	0.936646	+	0.350278i	$0.113913\pi$
$521$			1.03233e27i			0.700556i	−0.936646	+	0.350278i	$0.886087\pi$
$522$	−1.03517e27	+	1.49981e27i	−0.689137	+	0.998464i
$523$	2.32816e26			0.152053			0.0760267	−	0.997106i	$-0.475777\pi$
$523$	2.32816e26			0.152053			0.0760267	+	0.997106i	$0.475777\pi$
$524$	−4.09052e26	+	2.36166e26i	−0.262099	+	0.151323i
$525$	2.80140e26	+	1.77143e26i	0.176109	+	0.111360i
$526$	5.73070e26	−	9.92586e26i	0.353468	−	0.612225i
$527$	−1.83167e27	−	1.05752e27i	−1.10851	−	0.640001i
$528$	3.07923e26	−	4.86960e26i	0.182853	−	0.289170i
$529$	−8.34577e26	−	1.44553e27i	−0.486306	−	0.842306i
$530$			1.45590e27i			0.832478i
$531$	5.28360e26	+	3.64673e26i	0.296473	+	0.204625i
$532$	−5.95165e26			−0.327734
$533$	−7.80976e26	+	4.50897e26i	−0.422052	+	0.243672i
$534$	1.50241e27	−	7.88559e26i	0.796848	−	0.418236i
$535$	1.45759e26	−	2.52462e26i	0.0758748	−	0.131419i
$536$	−1.40315e26	−	8.10109e25i	−0.0716896	−	0.0413900i
$537$	4.42760e26	+	1.78347e25i	0.222037	+	0.00894382i
$538$	−1.02291e27	−	1.77174e27i	−0.503520	−	0.872122i
$539$		−	2.04104e27i		−	0.986199i
$540$	3.21641e26	+	7.54808e26i	0.152558	+	0.358013i
$541$	−2.89168e27			−1.34641			−0.673206	−	0.739455i	$-0.735083\pi$
$541$	−2.89168e27			−1.34641			−0.673206	+	0.739455i	$0.735083\pi$
$542$	6.14075e26	−	3.54537e26i	0.280691	−	0.162057i
$543$	−3.08262e25	+	7.65284e26i	−0.0138332	+	0.343419i
$544$	−2.46992e26	+	4.27802e26i	−0.108816	+	0.188475i
$545$	1.41952e27	+	8.19558e26i	0.614010	+	0.354499i
$546$	−6.64919e26	−	1.26684e27i	−0.282385	−	0.538017i
$547$	5.87270e26	+	1.01718e27i	0.244887	+	0.424156i	0.962100	−	0.272698i	$-0.0879160\pi$
$547$	5.87270e26	+	1.01718e27i	0.244887	+	0.424156i	−0.717213	+	0.696854i	$0.754583\pi$
$548$			2.06938e27i			0.847293i
$549$	3.34053e26	+	7.03938e26i	0.134305	+	0.283016i
$550$	−9.66263e26			−0.381477
$551$	−4.75281e27	+	2.74403e27i	−1.84261	+	1.06383i
$552$	1.29894e26	+	8.21366e25i	0.0494536	+	0.0312713i
$553$	−2.84774e26	+	4.93243e26i	−0.106475	+	0.184421i
$554$	1.78817e26	+	1.03240e26i	0.0656615	+	0.0379097i
$555$	1.37299e27	−	2.17130e27i	0.495151	−	0.783049i
$556$	9.53199e25	+	1.65099e26i	0.0337626	+	0.0584785i
$557$			2.65590e27i			0.923975i	0.886887	+	0.461987i	$0.152863\pi$
$557$			2.65590e27i			0.923975i	−0.886887	+	0.461987i	$0.847137\pi$
$558$	−1.73046e26	+	2.14452e27i	−0.0591317	+	0.732804i
$559$	6.82353e27			2.29029
$560$	−2.70150e26	+	1.55971e26i	−0.0890686	+	0.0514238i
$561$	4.60622e27	−	2.41764e27i	1.49182	−	0.783001i
$562$	1.44369e27	−	2.50054e27i	0.459314	−	0.795555i
$563$	−9.29295e26	−	5.36529e26i	−0.290449	−	0.167691i	0.347695	−	0.937608i	$-0.386964\pi$
$563$	−9.29295e26	−	5.36529e26i	−0.290449	−	0.167691i	−0.638144	+	0.769917i	$0.720298\pi$
$564$	−6.45428e26	−	2.59983e25i	−0.198179	−	0.00798278i
$565$	−2.66164e26	−	4.61010e26i	−0.0802906	−	0.139067i
$566$			2.62768e27i			0.778768i
$567$	6.43799e26	+	1.69719e27i	0.187465	+	0.494198i
$568$	1.98947e26			0.0569185
$569$	−2.86879e27	+	1.65630e27i	−0.806447	+	0.465602i	−0.845720	−	0.533626i	$-0.820829\pi$
$569$	−2.86879e27	+	1.65630e27i	−0.806447	+	0.465602i	0.0392736	+	0.999228i	$0.487496\pi$
$570$	−9.94483e25	+	2.46888e27i	−0.0274694	+	0.681948i
$571$	2.67320e26	−	4.63013e26i	0.0725556	−	0.125670i	−0.827465	−	0.561517i	$-0.810218\pi$
$571$	2.67320e26	−	4.63013e26i	0.0725556	−	0.125670i	0.900021	+	0.435847i	$0.143551\pi$
$572$	3.61219e27	+	2.08550e27i	0.963407	+	0.556224i
$573$	−1.68288e27	−	3.20632e27i	−0.441069	−	0.840351i
$574$	2.17494e26	+	3.76711e26i	0.0560182	+	0.0970263i
$575$		−	2.57745e26i		−	0.0652398i
$576$	5.00871e26	+	4.04165e25i	0.124595	+	0.0100539i
$577$	1.90115e27			0.464791			0.232395	−	0.972621i	$-0.425344\pi$
$577$	1.90115e27			0.464791			0.232395	+	0.972621i	$0.425344\pi$
$578$	−1.31414e27	+	7.58721e26i	−0.315765	+	0.182307i
$579$	3.01560e27	+	1.90687e27i	0.712177	+	0.450336i
$580$	−1.43822e27	+	2.49107e27i	−0.333846	+	0.578238i
$581$	−2.43804e27	−	1.40760e27i	−0.556262	−	0.321158i
$582$	−2.59705e27	+	4.10706e27i	−0.582438	+	0.921089i
$583$	−4.69502e27	−	8.13201e27i	−1.03503	−	1.79272i
$584$			1.76971e27i			0.383508i
$585$	−5.36625e27	+	2.54655e27i	−1.14317	+	0.542493i
$586$	2.99441e27			0.627098
$587$	3.13416e27	−	1.80951e27i	0.645269	−	0.372546i	−0.141373	−	0.989956i	$-0.545152\pi$
$587$	3.13416e27	−	1.80951e27i	0.645269	−	0.372546i	0.786641	+	0.617410i	$0.211818\pi$
$588$	1.57622e27	−	8.27298e26i	0.319038	−	0.167451i
$589$	−3.23961e27	+	5.61117e27i	−0.644674	+	1.11661i
$590$	8.77565e26	+	5.06663e26i	0.171696	+	0.0991285i
$591$	6.75286e26	+	2.72010e25i	0.129901	+	0.00523252i
$592$	−7.86677e26	−	1.36256e27i	−0.148792	−	0.257715i
$593$		−	5.02313e27i		−	0.934174i	−0.884211	−	0.467087i	$-0.845304\pi$
$593$		−	5.02313e27i		−	0.934174i	0.884211	−	0.467087i	$-0.154696\pi$
$594$	−4.23067e27	−	3.17879e27i	−0.773650	−	0.581295i
$595$	−2.81658e27			−0.506468
$596$	2.93899e27	−	1.69683e27i	0.519679	−	0.300037i
$597$	3.12917e26	−	7.76840e27i	0.0544109	−	1.35079i
$598$	−5.56295e26	+	9.63531e26i	−0.0951247	+	0.164761i
$599$	3.45144e27	+	1.99269e27i	0.580406	+	0.335098i	0.761295	−	0.648406i	$-0.224564\pi$
$599$	3.45144e27	+	1.99269e27i	0.580406	+	0.335098i	−0.180889	+	0.983504i	$0.557897\pi$
$600$	−3.91657e26	−	7.46207e26i	−0.0647728	−	0.123409i
$601$	2.97714e27	+	5.15656e27i	0.484233	+	0.838716i	0.999836	−	0.0181115i	$-0.00576538\pi$
$601$	2.97714e27	+	5.15656e27i	0.484233	+	0.838716i	−0.515603	+	0.856828i	$0.672432\pi$
$602$		−	3.29139e27i		−	0.526520i
$603$	−8.45316e26	+	1.22475e27i	−0.132998	+	0.192696i
$604$	2.55544e26			0.0395454
$605$	−3.86543e27	+	2.23171e27i	−0.588362	+	0.339691i
$606$	−2.54853e27	−	1.61153e27i	−0.381560	−	0.241274i
$607$	−3.31580e27	+	5.74313e27i	−0.488316	+	0.845788i	−0.999910	−	0.0134392i	$-0.995722\pi$
$607$	−3.31580e27	+	5.74313e27i	−0.488316	+	0.845788i	0.511594	+	0.859228i	$0.329055\pi$
$608$	1.31054e27	+	7.56639e26i	0.189851	+	0.109611i
$609$	−3.40110e27	+	5.37862e27i	−0.484670	+	0.766475i
$610$	6.14933e26	+	1.06510e27i	0.0862044	+	0.149310i
$611$		−	4.67634e27i		−	0.644902i
$612$	3.73409e27	+	2.57726e27i	0.506606	+	0.349658i
$613$	−4.20248e26			−0.0560920			−0.0280460	−	0.999607i	$-0.508928\pi$
$613$	−4.20248e26			−0.0560920			−0.0280460	+	0.999607i	$0.508928\pi$
$614$	5.08467e26	−	2.93564e26i	0.0667697	−	0.0385495i
$615$	1.59902e27	−	8.39269e26i	0.206587	−	0.108430i
$616$	1.00596e27	−	1.74237e27i	0.127871	−	0.221480i
$617$	6.17174e27	+	3.56326e27i	0.771891	+	0.445652i	0.833549	−	0.552446i	$-0.186305\pi$
$617$	6.17174e27	+	3.56326e27i	0.771891	+	0.445652i	−0.0616577	+	0.998097i	$0.519639\pi$
$618$	2.68793e27	+	1.08272e26i	0.330776	+	0.0133239i
$619$	−5.18300e27	−	8.97721e27i	−0.627588	−	1.08701i	−0.988034	−	0.154234i	$-0.950709\pi$
$619$	−5.18300e27	−	8.97721e27i	−0.627588	−	1.08701i	0.360447	−	0.932780i	$-0.382624\pi$
$620$			3.39594e27i			0.404616i
$621$	8.47923e26	−	1.12851e27i	0.0994124	−	0.132309i
$622$	3.80172e27			0.438607
$623$	5.13135e27	−	2.96259e27i	0.582575	−	0.336350i
$624$	−1.46415e26	+	3.63487e27i	−0.0163584	+	0.406109i
$625$	2.04812e27	−	3.54745e27i	0.225193	−	0.390046i
$626$	−8.32332e27	−	4.80547e27i	−0.900644	−	0.519987i
$627$	−7.40623e27	−	1.41108e28i	−0.788718	−	1.50271i
$628$	−4.09037e27	−	7.08472e27i	−0.428712	−	0.742551i
$629$		−	1.42061e28i		−	1.46544i
$630$	1.22835e27	+	2.58846e27i	0.124715	+	0.262806i
$631$	1.08984e28			1.08910			0.544550	−	0.838728i	$-0.316700\pi$
$631$	1.08984e28			1.08910			0.544550	+	0.838728i	$0.316700\pi$
$632$	1.25413e27	−	7.24071e26i	0.123359	−	0.0712214i
$633$	9.03257e27	+	5.71163e27i	0.874529	+	0.552997i
$634$	−1.49713e27	+	2.59310e27i	−0.142681	+	0.247131i
$635$	−1.20552e28	−	6.96006e27i	−1.13093	−	0.652944i
$636$	4.37700e27	−	6.92194e27i	0.404208	−	0.639229i
$637$	6.44360e27	+	1.11606e28i	0.585780	+	1.01460i
$638$		−	1.85521e28i		−	1.66029i
$639$	1.46971e26	−	1.82137e27i	0.0129486	−	0.160468i
$640$	7.93150e26			0.0687948
$641$	1.93720e28	−	1.11844e28i	1.65423	−	0.955068i	0.678919	−	0.734213i	$-0.262449\pi$
$641$	1.93720e28	−	1.11844e28i	1.65423	−	0.955068i	0.975307	−	0.220855i	$-0.0708847\pi$
$642$	−1.45200e27	+	7.62099e26i	−0.122072	+	0.0640709i
$643$	−1.08420e28	+	1.87789e28i	−0.897430	+	1.55439i	−0.0666624	+	0.997776i	$0.521235\pi$
$643$	−1.08420e28	+	1.87789e28i	−0.897430	+	1.55439i	−0.830768	+	0.556619i	$0.812098\pi$
$644$	4.64768e26	+	2.68334e26i	0.0378772	+	0.0218684i
$645$	−1.36534e28	−	5.49970e26i	−1.09558	−	0.0441308i
$646$	6.83182e27	+	1.18331e28i	0.539773	+	0.934915i
$647$			1.59598e28i			1.24161i	0.783966	+	0.620804i	$0.213194\pi$
$647$			1.59598e28i			1.24161i	−0.783966	+	0.620804i	$0.786806\pi$
$648$	7.40030e26	−	4.55564e27i	0.0566890	−	0.348979i
$649$	−6.53559e27			−0.492990
$650$	5.28364e27	−	3.05051e27i	0.392463	−	0.226589i
$651$	−3.02385e26	+	7.50694e27i	−0.0221182	+	0.549102i
$652$	−4.31506e27	+	7.47390e27i	−0.310821	+	0.538358i
$653$	−2.49877e27	−	1.44266e27i	−0.177253	−	0.102337i	0.408748	−	0.912647i	$-0.365965\pi$
$653$	−2.49877e27	−	1.44266e27i	−0.177253	−	0.102337i	−0.586001	+	0.810310i	$0.699299\pi$
$654$	−4.28505e27	−	8.16412e27i	−0.299349	−	0.570338i
$655$	3.42380e27	+	5.93020e27i	0.235557	+	0.407996i
$656$		−	1.10601e27i		−	0.0749412i
$657$	1.62018e28	+	1.30736e27i	1.08121	+	0.0872454i
$658$	−2.25567e27			−0.148258
$659$	1.70060e28	−	9.81842e27i	1.10090	−	0.635605i	0.164443	−	0.986387i	$-0.447417\pi$
$659$	1.70060e28	−	9.81842e27i	1.10090	−	0.635605i	0.936457	+	0.350781i	$0.114084\pi$
$660$	−7.05966e27	−	4.46408e27i	−0.450137	−	0.284638i
$661$	1.29251e28	−	2.23869e28i	0.811743	−	1.40598i	−0.0999008	−	0.994997i	$-0.531853\pi$
$661$	1.29251e28	−	2.23869e28i	0.811743	−	1.40598i	0.911643	−	0.410982i	$-0.134814\pi$
$662$	−9.88880e27	−	5.70930e27i	−0.611735	−	0.353186i
$663$	−1.75548e28	+	2.77618e28i	−1.06970	+	1.69166i
$664$	3.57900e27	+	6.19901e27i	0.214823	+	0.372084i
$665$			8.62836e27i			0.510166i
$666$	−1.30555e28	+	6.19548e27i	−0.760416	+	0.360855i
$667$	4.94866e27			0.283942
$668$	−1.02816e28	+	5.93611e27i	−0.581163	+	0.335534i
$669$	−1.50261e28	+	7.88663e27i	−0.836728	+	0.439168i
$670$	−1.17445e27	+	2.03421e27i	−0.0644297	+	0.111596i
$671$	−6.86949e27	−	3.96610e27i	−0.371278	−	0.214357i
$672$	1.75331e27	+	7.06247e25i	0.0933612	+	0.00376066i
$673$	2.02522e27	+	3.50778e27i	0.106248	+	0.184027i	0.914247	−	0.405156i	$-0.132783\pi$
$673$	2.02522e27	+	3.50778e27i	0.106248	+	0.184027i	−0.807999	+	0.589183i	$0.799450\pi$
$674$			1.31305e28i			0.678707i
$675$	−7.12090e27	+	3.03438e27i	−0.362658	+	0.154537i
$676$	−1.63717e28			−0.821537
$677$	−1.06064e28	+	6.12359e27i	−0.524421	+	0.302775i	−0.738742	−	0.673989i	$-0.764580\pi$
$677$	−1.06064e28	+	6.12359e27i	−0.524421	+	0.302775i	0.214321	+	0.976763i	$0.431246\pi$
$678$	−1.20521e26	+	2.99202e27i	−0.00587171	+	0.145770i
$679$	−8.48434e27	+	1.46953e28i	−0.407306	+	0.705474i
$680$	6.20203e27	+	3.58074e27i	0.293390	+	0.169389i
$681$	4.13756e27	+	7.88312e27i	0.192874	+	0.367475i
$682$	−1.09513e28	−	1.89682e28i	−0.503062	−	0.871329i
$683$			3.28560e28i			1.48733i	0.668552	+	0.743665i	$0.266914\pi$
$683$			3.28560e28i			1.48733i	−0.668552	+	0.743665i	$0.733086\pi$
$684$	7.89522e27	−	1.14391e28i	0.352211	−	0.510305i
$685$	3.00006e28			1.31894
$686$	1.28539e28	−	7.42123e27i	0.556923	−	0.321540i
$687$	−3.18360e28	−	2.01311e28i	−1.35941	−	0.859607i
$688$	−4.18437e27	+	7.24755e27i	−0.176095	+	0.305005i
$689$	5.13458e28	+	2.96445e28i	2.12967	+	1.22957i
$690$	1.19077e27	−	1.88313e27i	0.0486785	−	0.0769819i
$691$	1.76374e28	+	3.05489e28i	0.710647	+	1.23088i	0.964615	+	0.263664i	$0.0849311\pi$
$691$	1.76374e28	+	3.05489e28i	0.710647	+	1.23088i	−0.253967	+	0.967213i	$0.581736\pi$
$692$			6.80719e24i			0.000270338i
$693$	−1.52084e28	−	1.04968e28i	−0.595319	−	0.410888i
$694$	3.09616e28			1.19462
$695$	2.39351e27	−	1.38189e27i	0.0910305	−	0.0525565i
$696$	1.43270e28	−	7.51973e27i	0.537110	−	0.281909i
$697$	4.99317e27	−	8.64843e27i	0.184522	−	0.319602i
$698$	−2.60901e28	−	1.50631e28i	−0.950434	−	0.548733i
$699$	3.69273e27	+	1.48746e26i	0.132610	+	0.00534162i
$700$	−1.47144e27	−	2.54861e27i	−0.0520909	−	0.0902242i
$701$			7.70743e27i			0.268986i	0.990915	+	0.134493i	$0.0429406\pi$
$701$			7.70743e27i			0.268986i	−0.990915	+	0.134493i	$0.957059\pi$
$702$	3.31692e28	+	4.02567e27i	1.14121	+	0.138506i
$703$	−4.35191e28			−1.47614
$704$	−4.43019e27	+	2.55777e27i	−0.148148	+	0.0855332i
$705$	−3.76909e26	+	9.35705e27i	−0.0124264	+	0.308495i
$706$	−1.46957e28	+	2.54537e28i	−0.477686	+	0.827377i
$707$	−9.11877e27	−	5.26473e27i	−0.292242	−	0.168726i
$708$	−2.64908e27	−	5.04718e27i	−0.0837071	−	0.159484i
$709$	−9.62818e27	−	1.66765e28i	−0.299973	−	0.519568i	0.676157	−	0.736758i	$-0.263644\pi$
$709$	−9.62818e27	−	1.66765e28i	−0.299973	−	0.519568i	−0.976129	+	0.217190i	$0.930311\pi$
$710$		−	2.88422e27i		−	0.0886022i
$711$	−5.70243e27	−	1.20165e28i	−0.172728	−	0.363984i
$712$	−1.50655e28			−0.449969
$713$	5.05966e27	−	2.92120e27i	0.149014	−	0.0860331i
$714$	1.33912e28	+	8.46772e27i	0.388898	+	0.245915i
$715$	3.02343e28	−	5.23674e28i	0.865845	−	1.49969i
$716$	−3.40729e27	−	1.96720e27i	−0.0962229	−	0.0555543i
$717$	1.02809e28	−	1.62586e28i	0.286313	−	0.452786i
$718$	1.79526e28	+	3.10948e28i	0.493041	+	0.853972i
$719$		−	2.73891e28i		−	0.741804i	−0.928672	−	0.370902i	$-0.879049\pi$
$719$		−	2.73891e28i		−	0.741804i	0.928672	−	0.370902i	$-0.120951\pi$
$720$	5.85934e26	−	7.26133e27i	0.0156503	−	0.193951i
$721$	9.39392e27			0.247454
$722$	1.26781e28	−	7.31971e27i	0.329369	−	0.190161i
$723$	−7.72031e27	+	4.05211e27i	−0.197812	+	0.103824i
$724$	3.40018e27	−	5.88929e27i	0.0859244	−	0.148825i
$725$	−2.35009e28	−	1.35683e28i	−0.585740	−	0.338177i
$726$	2.50872e28	+	1.01053e27i	0.616717	+	0.0248418i
$727$	−3.18180e28	−	5.51104e28i	−0.771488	−	1.33626i	−0.936748	−	0.350006i	$-0.886180\pi$
$727$	−3.18180e28	−	5.51104e28i	−0.771488	−	1.33626i	0.165260	−	0.986250i	$-0.447154\pi$
$728$			1.27033e28i			0.303811i
$729$	−4.11604e28	−	1.01405e28i	−0.970967	−	0.239212i
$730$	2.56563e28			0.596987
$731$	−6.54393e28	+	3.77814e28i	−1.50198	+	0.867171i
$732$	2.78445e26	−	6.91262e27i	0.00630419	−	0.156506i
$733$	2.90889e28	−	5.03834e28i	0.649661	−	1.12525i	−0.333543	−	0.942735i	$-0.608244\pi$
$733$	2.90889e28	−	5.03834e28i	0.649661	−	1.12525i	0.983204	−	0.182511i	$-0.0584226\pi$
$734$	−4.02873e28	−	2.32599e28i	−0.887580	−	0.512444i
$735$	−1.19937e28	−	2.28511e28i	−0.260663	−	0.496630i
$736$	−6.82270e26	−	1.18173e27i	−0.0146278	−	0.0253361i
$737$		−	1.51496e28i		−	0.320424i
$738$	−1.01256e28	−	8.17057e26i	−0.211279	−	0.0170486i
$739$	−2.99816e28			−0.617178			−0.308589	−	0.951195i	$-0.599857\pi$
$739$	−2.99816e28			−0.617178			−0.308589	+	0.951195i	$0.599857\pi$
$740$	−1.97537e28	+	1.14048e28i	−0.401172	+	0.231617i
$741$	8.50460e28	+	5.37777e28i	1.70401	+	1.07751i
$742$	1.42993e28	−	2.47671e28i	0.282667	−	0.489594i
$743$	4.07816e28	+	2.35453e28i	0.795383	+	0.459215i	0.841854	−	0.539705i	$-0.181464\pi$
$743$	4.07816e28	+	2.35453e28i	0.795383	+	0.459215i	−0.0464709	+	0.998920i	$0.514797\pi$
$744$	1.02095e28	−	1.61457e28i	0.196460	−	0.310689i
$745$	−2.45996e28	−	4.26078e28i	−0.467052	−	0.808958i
$746$			4.27854e26i			0.00801507i
$747$	5.93962e28	−	2.81864e28i	1.09787	−	0.520996i
$748$	−4.61890e28			−0.842409
$749$	−4.95917e27	+	2.86318e27i	−0.0892464	+	0.0515265i
$750$	−3.82604e28	+	2.00815e28i	−0.679418	+	0.356602i
$751$	3.74640e28	−	6.48896e28i	0.656470	−	1.13704i	−0.325053	−	0.945696i	$-0.605382\pi$
$751$	3.74640e28	−	6.48896e28i	0.656470	−	1.13704i	0.981523	−	0.191344i	$-0.0612846\pi$
$752$	4.96693e27	+	2.86766e27i	0.0858835	+	0.0495849i
$753$	8.75393e28	+	3.52615e27i	1.49367	+	0.0601660i
$754$	5.85691e28	+	1.01445e29i	0.986178	+	1.70811i
$755$		−	3.70473e27i		−	0.0615583i
$756$	1.94182e27	−	1.59995e28i	0.0318413	−	0.262354i
$757$	−8.81836e28			−1.42702			−0.713508	−	0.700647i	$-0.752895\pi$
$757$	−8.81836e28			−1.42702			−0.713508	+	0.700647i	$0.752895\pi$
$758$	−1.71679e28	+	9.91190e27i	−0.274174	+	0.158294i
$759$	−5.78364e26	+	1.43583e28i	−0.00911556	+	0.226301i
$760$	1.09693e28	−	1.89994e28i	0.170625	−	0.295532i
$761$	4.68643e28	+	2.70571e28i	0.719441	+	0.415370i	0.814547	−	0.580098i	$-0.196986\pi$
$761$	4.68643e28	+	2.70571e28i	0.719441	+	0.415370i	−0.0951057	+	0.995467i	$0.530319\pi$
$762$	3.63906e28	+	6.93334e28i	0.551365	+	1.05049i
$763$	−1.60988e28	−	2.78839e28i	−0.240739	−	0.416973i
$764$			3.21515e28i			0.474534i
$765$	3.73636e28	−	5.41347e28i	0.544295	−	0.788608i
$766$	−6.73283e28			−0.968077
$767$	3.57373e28	−	2.06330e28i	0.507187	−	0.292825i
$768$	−3.77096e27	−	2.38451e27i	−0.0528250	−	0.0334032i
$769$	−2.50794e28	+	4.34388e28i	−0.346779	+	0.600640i	−0.985675	−	0.168654i	$-0.946058\pi$
$769$	−2.50794e28	+	4.34388e28i	−0.346779	+	0.600640i	0.638896	+	0.769293i	$0.279391\pi$
$770$	−2.52599e28	−	1.45838e28i	−0.344766	−	0.199051i
$771$	−7.53999e28	+	1.19240e29i	−1.01584	+	1.60649i
$772$	−1.58395e28	−	2.74348e28i	−0.210654	−	0.364863i
$773$			3.86083e28i			0.506857i	0.967354	+	0.253429i	$0.0815583\pi$
$773$			3.86083e28i			0.506857i	−0.967354	+	0.253429i	$0.918442\pi$
$774$	6.32605e28	+	4.36623e28i	0.819829	+	0.565844i
$775$	−3.20375e28			−0.409865
$776$	3.73646e28	−	2.15724e28i	0.471892	−	0.272447i
$777$	−4.46823e28	+	2.34521e28i	−0.557090	+	0.292396i
$778$	7.75113e27	−	1.34253e28i	0.0954045	−	0.165245i
$779$	−2.64938e28	−	1.52962e28i	−0.321936	−	0.185870i
$780$	5.26962e28	+	2.12264e27i	0.632169	+	0.0254642i
$781$	9.30109e27	+	1.61100e28i	0.110160	+	0.190802i
$782$		−	1.23207e28i		−	0.144068i
$783$	−5.82595e28	−	1.36720e29i	−0.672588	−	1.57839i
$784$	−1.58056e28			−0.180156
$785$	−1.02710e29	+	5.92998e28i	−1.15589	+	0.667354i
$786$	1.55032e27	−	3.84878e28i	0.0172264	−	0.427659i
$787$	1.73290e28	−	3.00147e28i	0.190119	−	0.329296i	−0.755171	−	0.655528i	$-0.772446\pi$
$787$	1.73290e28	−	3.00147e28i	0.190119	−	0.329296i	0.945290	+	0.326233i	$0.105779\pi$
$788$	−5.19670e27	−	3.00032e27i	−0.0562945	−	0.0325016i
$789$	4.34385e28	+	8.27615e28i	0.464627	+	0.885234i
$790$	−1.04972e28	−	1.81816e28i	−0.110867	−	0.192027i
$791$			1.04566e28i			0.109050i
$792$	2.01437e28	+	4.24481e28i	0.207438	+	0.437126i
$793$	5.00842e28			0.509294
$794$	−6.99821e28	+	4.04042e28i	−0.702720	+	0.405715i
$795$	−1.00350e29	−	6.34551e28i	−0.995055	−	0.629210i
$796$	−3.45153e28	+	5.97822e28i	−0.337972	+	0.585384i
$797$	3.24969e28	+	1.87621e28i	0.314238	+	0.181426i	0.648821	−	0.760941i	$-0.275262\pi$
$797$	3.24969e28	+	1.87621e28i	0.314238	+	0.181426i	−0.334583	+	0.942366i	$0.608596\pi$
$798$	2.59402e28	−	4.10227e28i	0.247710	−	0.391738i
$799$	2.58926e28	+	4.48473e28i	0.244178	+	0.422930i
$800$			7.48262e27i			0.0696873i
$801$	−1.11295e28	+	1.37925e29i	−0.102365	+	1.26858i
$802$	−4.00534e28			−0.363827
$803$	−1.43304e29	+	8.27369e28i	−1.28560	+	0.742239i
$804$	1.16994e28	−	6.14059e27i	0.103658	−	0.0544064i
$805$	3.89015e27	−	6.73793e27i	0.0340414	−	0.0589614i
$806$	1.19766e29	+	6.91468e28i	1.03510	+	0.597615i
$807$	1.66704e29	+	6.71494e27i	1.42302	+	0.0573201i
$808$	1.33862e28	+	2.31856e28i	0.112861	+	0.195481i
$809$		−	1.20471e29i		−	1.00322i	−0.865093	−	0.501611i	$-0.832741\pi$
$809$		−	1.20471e29i		−	1.00322i	0.865093	−	0.501611i	$-0.167259\pi$
$810$	−6.60450e28	−	1.07285e28i	−0.543238	−	0.0882449i
$811$	−9.11156e28			−0.740260			−0.370130	−	0.928980i	$-0.620687\pi$
$811$	−9.11156e28			−0.740260			−0.370130	+	0.928980i	$0.620687\pi$
$812$	4.89328e28	−	2.82513e28i	0.392681	−	0.226714i
$813$	−2.32736e27	+	5.77785e28i	−0.0184484	+	0.457995i
$814$	7.35568e28	−	1.27404e29i	0.575942	−	0.997561i
$815$	1.08352e29	+	6.25572e28i	0.838034	+	0.483839i
$816$	−1.87219e28	−	3.56700e28i	−0.143037	−	0.272522i
$817$	1.15740e29	+	2.00468e29i	0.873502	+	1.51295i
$818$		−	6.93811e28i		−	0.517259i
$819$	1.16299e29	+	9.38448e27i	0.856522	+	0.0691148i
$820$	−1.60343e28			−0.116657
$821$	1.66645e29	−	9.62123e28i	1.19773	−	0.691511i	0.237683	−	0.971343i	$-0.423612\pi$
$821$	1.66645e29	−	9.62123e28i	1.19773	−	0.691511i	0.960049	+	0.279832i	$0.0902786\pi$
$822$	−1.42635e29	−	9.01934e28i	−1.01276	−	0.640408i
$823$	−7.38735e28	+	1.27953e29i	−0.518191	+	0.897534i	0.481585	+	0.876399i	$0.340061\pi$
$823$	−7.38735e28	+	1.27953e29i	−0.518191	+	0.897534i	−0.999777	+	0.0211346i	$0.993272\pi$
$824$	−2.06851e28	−	1.19426e28i	−0.143346	−	0.0827610i
$825$	4.21144e28	−	6.66012e28i	0.288331	−	0.455977i
$826$	−9.95249e27	−	1.72382e28i	−0.0673180	−	0.116598i
$827$		−	1.21783e29i		−	0.813829i	−0.913466	−	0.406915i	$-0.866605\pi$
$827$		−	1.21783e29i		−	0.813829i	0.913466	−	0.406915i	$-0.133395\pi$
$828$	−1.13228e28	+	5.37323e27i	−0.0747567	+	0.0354758i
$829$	−6.95492e28			−0.453677			−0.226839	−	0.973932i	$-0.572839\pi$
$829$	−6.95492e28			−0.453677			−0.226839	+	0.973932i	$0.572839\pi$
$830$	8.98696e28	−	5.18863e28i	0.579205	−	0.334404i
$831$	−1.49097e28	+	7.82555e27i	−0.0949420	+	0.0498316i
$832$	1.61498e28	−	2.79723e28i	0.101610	−	0.175993i
$833$	−1.23592e29	−	7.13556e28i	−0.768314	−	0.443586i
$834$	−1.55342e28	−	6.25730e26i	−0.0954176	−	0.00384349i
$835$	8.60583e28	+	1.49057e29i	0.522309	+	0.904666i
$836$			1.41496e29i			0.848560i
$837$	−1.40272e29	−	1.05396e29i	−0.831222	−	0.624553i
$838$	1.18878e29			0.696081
$839$	−9.81035e28	+	5.66401e28i	−0.567629	+	0.327721i	−0.756202	−	0.654338i	$-0.772947\pi$
$839$	−9.81035e28	+	5.66401e28i	−0.567629	+	0.327721i	0.188573	+	0.982059i	$0.439614\pi$
$840$	1.02388e27	−	2.54185e28i	0.00585402	−	0.145331i
$841$	1.72011e29	−	2.97931e29i	0.971841	−	1.68328i
$842$	−2.09842e29	−	1.21152e29i	−1.17158	−	0.676411i
$843$	1.09431e29	+	2.08494e29i	0.603759	+	1.15032i
$844$	−4.74438e28	−	8.21751e28i	−0.258675	−	0.448039i
$845$			2.37348e29i			1.27885i
$846$	2.99229e28	−	4.33541e28i	0.159331	−	0.230848i
$847$	8.76760e28			0.461367
$848$	−6.29733e28	+	3.63576e28i	−0.327490	+	0.189076i
$849$	−1.81117e29	−	1.14527e29i	−0.930856	−	0.588614i
$850$	−3.37809e28	+	5.85103e28i	−0.171586	+	0.297196i
$851$	3.39843e28	+	1.96209e28i	0.170602	+	0.0984969i
$852$	−8.67106e27	+	1.37127e28i	−0.0430206	+	0.0680343i
$853$	4.37710e28	+	7.58137e28i	0.214633	+	0.371755i	0.953159	−	0.302470i	$-0.0978111\pi$
$853$	4.37710e28	+	7.58137e28i	0.214633	+	0.371755i	−0.738526	+	0.674225i	$0.764478\pi$
$854$		−	2.41586e28i		−	0.117083i
$855$	−1.65837e29	−	1.14460e29i	−0.794366	−	0.548269i
$856$	1.45599e28			0.0689322
$857$	1.45693e29	−	8.41156e28i	0.681756	−	0.393612i	−0.118760	−	0.992923i	$-0.537892\pi$
$857$	1.45693e29	−	8.41156e28i	0.681756	−	0.393612i	0.800516	+	0.599311i	$0.204559\pi$
$858$	−3.01183e29	+	1.58080e29i	−1.39302	+	0.731145i
$859$	−1.11663e27	+	1.93406e27i	−0.00510479	+	0.00884176i	−0.868567	−	0.495573i	$-0.834958\pi$
$859$	−1.11663e27	+	1.93406e27i	−0.00510479	+	0.00884176i	0.863462	+	0.504414i	$0.168292\pi$
$860$	1.05071e29	+	6.06626e28i	0.474786	+	0.274118i
$861$	−3.54449e28	−	1.42775e27i	−0.158315	−	0.00637704i
$862$	−4.83634e28	−	8.37678e28i	−0.213523	−	0.369832i
$863$		−	2.63875e29i		−	1.15157i	−0.817602	−	0.575784i	$-0.804697\pi$
$863$		−	2.63875e29i		−	1.15157i	0.817602	−	0.575784i	$-0.195303\pi$
$864$	−2.46161e28	+	3.27618e28i	−0.106190	+	0.141329i
$865$	9.86868e25			0.000420821
$866$	1.94800e29	−	1.12468e29i	0.821126	−	0.474077i
$867$	4.98064e27	−	1.23648e29i	0.0207536	−	0.515225i
$868$	3.33536e28	−	5.77701e28i	0.137387	−	0.237961i
$869$	1.17265e29	+	6.77030e28i	0.477497	+	0.275683i
$870$	−1.09017e29	−	2.07705e29i	−0.438834	−	0.836092i
$871$	4.78274e28	+	8.28395e28i	0.190325	+	0.329652i
$872$			8.18661e28i			0.322062i
$873$	−1.69894e29	−	3.58011e29i	−0.660748	−	1.39237i
$874$	−3.77434e28			−0.145120
$875$	−1.30675e29	+	7.54454e28i	−0.496722	+	0.286782i
$876$	−1.21980e29	−	7.71326e28i	−0.458404	−	0.289866i
$877$	−9.34026e28	+	1.61778e29i	−0.347027	+	0.601068i	−0.985720	−	0.168393i	$-0.946142\pi$
$877$	−9.34026e28	+	1.61778e29i	−0.347027	+	0.601068i	0.638693	+	0.769462i	$0.279475\pi$
$878$	−7.00517e28	−	4.04444e28i	−0.257320	−	0.148564i
$879$	−1.30511e29	+	2.06395e29i	−0.473978	+	0.749566i
$880$	3.70811e28	+	6.42263e28i	0.133145	+	0.230614i
$881$		−	3.16713e29i		−	1.12436i	−0.827013	−	0.562182i	$-0.809962\pi$
$881$		−	3.16713e29i		−	1.12436i	0.827013	−	0.562182i	$-0.190038\pi$
$882$	−1.16763e28	+	1.44701e29i	−0.0409843	+	0.507908i
$883$	2.71760e29			0.943146			0.471573	−	0.881827i	$-0.343686\pi$
$883$	2.71760e29			0.943146			0.471573	+	0.881827i	$0.343686\pi$
$884$	2.52567e29	−	1.45820e29i	0.866670	−	0.500372i
$885$	−7.31711e28	+	3.84048e28i	−0.248260	+	0.130303i
$886$	1.04721e29	−	1.81382e29i	0.351315	−	0.608495i
$887$	1.06647e29	+	6.15726e28i	0.353762	+	0.204245i	0.666341	−	0.745647i	$-0.267859\pi$
$887$	1.06647e29	+	6.15726e28i	0.353762	+	0.204245i	−0.312579	+	0.949892i	$0.601193\pi$
$888$	1.28204e29	+	5.16415e27i	0.420506	+	0.0169383i
$889$	1.36718e29	+	2.36803e29i	0.443413	+	0.768014i
$890$			2.18410e29i			0.700444i
$891$	4.03496e29	−	1.53059e29i	1.27956	−	0.485379i
$892$	1.50675e29			0.472489
$893$	1.37386e29	−	7.93198e28i	0.426018	−	0.245961i
$894$	−1.11388e28	+	2.76530e29i	−0.0341559	+	0.847945i
$895$	−2.85193e28	+	4.93969e28i	−0.0864786	+	0.149785i
$896$	−1.34927e28	−	7.79002e27i	−0.0404594	−	0.0233592i
$897$	−4.21669e28	−	8.03388e28i	−0.125040	−	0.238233i
$898$	−1.19410e29	−	2.06824e29i	−0.350169	−	0.606510i
$899$		−	6.15112e29i		−	1.78385i
$900$	6.85038e28	+	5.52774e27i	0.196467	+	0.0158534i
$901$	−6.56559e29			−1.86220
$902$	8.95604e28	−	5.17077e28i	0.251218	−	0.145041i
$903$	2.26864e29	+	1.43455e29i	0.629345	+	0.397958i
$904$	1.32936e28	−	2.30252e28i	0.0364720	−	0.0631713i
$905$	−8.53795e28	−	4.92939e28i	−0.231669	−	0.133754i
$906$	−1.11378e28	+	1.76138e28i	−0.0298895	+	0.0472683i
$907$	2.34821e29	+	4.06721e29i	0.623252	+	1.07950i	0.988876	+	0.148741i	$0.0475221\pi$
$907$	2.34821e29	+	4.06721e29i	0.623252	+	1.07950i	−0.365624	+	0.930762i	$0.619145\pi$
$908$		−	7.90484e28i		−	0.207508i
$909$	2.22154e29	−	1.05423e29i	0.576787	−	0.273714i
$910$	1.84165e29			0.472927
$911$	−1.59507e29	+	9.20916e28i	−0.405132	+	0.233903i	−0.688696	−	0.725050i	$-0.741817\pi$
$911$	−1.59507e29	+	9.20916e28i	−0.405132	+	0.233903i	0.283564	+	0.958953i	$0.408483\pi$
$912$	−1.09272e29	+	5.73529e28i	−0.274512	+	0.144081i
$913$	−3.34648e29	+	5.79627e29i	−0.831535	+	1.44026i
$914$	3.95944e29	+	2.28598e29i	0.973132	+	0.561838i
$915$	−1.00215e29	−	4.03674e27i	−0.243625	−	0.00981341i
$916$	1.67220e29	+	2.89633e29i	0.402099	+	0.696455i
$917$		−	1.34509e29i		−	0.319932i
$918$	−3.40391e29	+	1.45049e29i	−0.800851	+	0.341261i
$919$	2.44861e29			0.569855			0.284928	−	0.958549i	$-0.408030\pi$
$919$	2.44861e29			0.569855			0.284928	+	0.958549i	$0.408030\pi$
$920$	−1.71320e28	+	9.89116e27i	−0.0394393	+	0.0227703i
$921$	−1.92710e27	+	4.78418e28i	−0.00438843	+	0.108946i
$922$	−5.62604e28	+	9.74459e28i	−0.126734	+	0.219510i
$923$	−1.01719e29	−	5.87274e28i	−0.226665	−	0.130865i
$924$	7.62512e28	+	1.45278e29i	0.168084	+	0.320244i
$925$	−1.07593e29	−	1.86357e29i	−0.234622	−	0.406377i
$926$			2.81150e29i			0.606496i
$927$	−1.24616e29	+	1.80551e29i	−0.265935	+	0.385303i
$928$	−1.43665e29			−0.303299
$929$	−5.42304e29	+	3.13099e29i	−1.13262	+	0.653921i	−0.944594	−	0.328242i	$-0.893544\pi$
$929$	−5.42304e29	+	3.13099e29i	−1.13262	+	0.653921i	−0.188031	+	0.982163i	$0.560210\pi$
$930$	−2.34070e29	−	1.48011e29i	−0.483634	−	0.305820i
$931$	−2.18592e29	+	3.78613e29i	−0.446825	+	0.773924i
$932$	−2.84176e28	−	1.64069e28i	−0.0574683	−	0.0331793i
$933$	−1.65697e29	+	2.62039e29i	−0.331512	+	0.524264i
$934$	1.59022e29	+	2.75434e29i	0.314766	+	0.545191i
$935$			6.69622e29i			1.31134i
$936$	−2.44158e29	−	1.68517e29i	−0.473055	−	0.326501i
$937$	−9.05889e29			−1.73652			−0.868258	−	0.496112i	$-0.834760\pi$
$937$	−9.05889e29			−1.73652			−0.868258	+	0.496112i	$0.834760\pi$
$938$	3.99584e28	−	2.30700e28i	0.0757844	−	0.0437541i
$939$	6.93995e29	−	3.64252e29i	1.30227	−	0.683513i
$940$	4.15737e28	−	7.20077e28i	0.0771862	−	0.133690i
$941$	−2.45478e29	−	1.41727e29i	−0.450938	−	0.260349i	0.257288	−	0.966335i	$-0.417171\pi$
$941$	−2.45478e29	−	1.41727e29i	−0.450938	−	0.260349i	−0.708226	+	0.705985i	$0.750504\pi$
$942$	6.66604e29	+	2.68513e28i	1.21160	+	0.0488041i
$943$	1.37927e28	+	2.38897e28i	0.0248047	+	0.0429630i
$944$			5.06108e28i			0.0900582i
$945$	−2.31951e29	−	2.81514e28i	−0.408393	−	0.0495657i
$946$	−7.82505e29			−1.36325
$947$	2.77884e29	−	1.60437e29i	0.479032	−	0.276569i	−0.240981	−	0.970530i	$-0.577469\pi$
$947$	2.77884e29	−	1.60437e29i	0.479032	−	0.276569i	0.720013	+	0.693961i	$0.244136\pi$
$948$	−4.75318e27	+	1.18001e29i	−0.00810776	+	0.201281i
$949$	5.22403e29	−	9.04829e29i	0.881747	−	1.52723i
$950$	1.79241e29	+	1.03485e29i	0.299366	+	0.172839i
$951$	−1.13482e29	−	2.16212e29i	−0.187551	−	0.357334i
$952$	−7.03374e28	−	1.21828e29i	−0.115031	−	0.199240i
$953$		−	5.97459e29i		−	0.966895i	−0.875373	−	0.483447i	$-0.839384\pi$
$953$		−	5.97459e29i		−	0.966895i	0.875373	−	0.483447i	$-0.160616\pi$
$954$	2.86335e29	+	6.03383e29i	0.458554	+	0.966294i
$955$	4.66114e29			0.738683
$956$	−1.47915e29	+	8.53989e28i	−0.231971	+	0.133929i
$957$	1.27873e30	+	8.08588e29i	1.98454	+	1.25490i
$958$	7.16877e28	−	1.24167e29i	0.110101	−	0.190700i
$959$	−5.10357e29	−	2.94655e29i	−0.775689	−	0.447844i
$960$	−3.45693e28	+	5.46691e28i	−0.0519970	+	0.0822299i
$961$	−2.72062e28	−	4.71225e28i	−0.0404981	−	0.0701447i
$962$			9.28880e29i			1.36839i
$963$	1.07561e28	−	1.33297e29i	0.0156816	−	0.194338i
$964$	7.74157e28			0.111701
$965$	−3.97734e29	+	2.29632e29i	−0.567963	+	0.327914i
$966$	−3.87522e28	+	2.03396e28i	−0.0547677	+	0.0287456i
$967$	3.60948e29	−	6.25180e29i	0.504870	−	0.874461i	−0.495114	−	0.868828i	$-0.664874\pi$
$967$	3.60948e29	−	6.25180e29i	0.504870	−	0.874461i	0.999984	−	0.00563284i	$-0.00179300\pi$
$968$	−1.93060e29	−	1.11463e29i	−0.267263	−	0.154304i
$969$	−1.11338e30	−	4.48476e28i	−1.52547	−	0.0614471i
$970$	−3.12745e29	−	5.41690e29i	−0.424105	−	0.734571i
$971$		−	1.69506e29i		−	0.227505i	−0.993509	−	0.113753i	$-0.963713\pi$
$971$		−	1.69506e29i		−	0.227505i	0.993509	−	0.113753i	$-0.0362872\pi$
$972$	2.81751e29	+	2.49564e29i	0.374285	+	0.331528i
$973$	−5.42897e28			−0.0713821
$974$	6.77706e29	−	3.91274e29i	0.881966	−	0.509204i
$975$	−2.00251e28	+	4.97139e29i	−0.0257946	+	0.640371i
$976$	−3.07130e28	+	5.31965e28i	−0.0391583	+	0.0678242i
$977$	1.87816e29	+	1.08436e29i	0.237021	+	0.136844i	0.613807	−	0.789456i	$-0.289637\pi$
$977$	1.87816e29	+	1.08436e29i	0.237021	+	0.136844i	−0.376786	+	0.926300i	$0.622971\pi$
$978$	−3.27079e29	−	6.23171e29i	−0.408568	−	0.778428i
$979$	−7.04335e29	−	1.21994e30i	−0.870868	−	1.50839i
$980$			2.29140e29i			0.280440i
$981$	7.49488e29	+	6.04780e28i	0.907977	+	0.0732668i
$982$	9.58969e29			1.14998
$983$	7.33174e29	−	4.23298e29i	0.870305	−	0.502471i	0.00285568	−	0.999996i	$-0.499091\pi$
$983$	7.33174e29	−	4.23298e29i	0.870305	−	0.502471i	0.867450	+	0.497525i	$0.165758\pi$
$984$	7.62335e28	+	4.82052e28i	0.0895766	+	0.0566426i
$985$	−4.34969e28	+	7.53388e28i	−0.0505936	+	0.0876307i
$986$	−1.12339e30	−	6.48587e29i	−1.29348	−	0.746791i
$987$	9.83131e28	−	1.55476e29i	0.112057	−	0.177211i
$988$	−4.46706e29	−	7.73718e29i	−0.504026	−	0.872998i
$989$		−	2.08729e29i		−	0.233142i
$990$	6.15388e29	−	2.92032e29i	0.680452	−	0.322908i
$991$	1.23295e30			1.34961			0.674805	−	0.737996i	$-0.264228\pi$
$991$	1.23295e30			1.34961			0.674805	+	0.737996i	$0.264228\pi$
$992$	−1.46887e29	+	8.48055e28i	−0.159172	+	0.0918982i
$993$	8.24524e29	−	4.32762e29i	0.884527	−	0.464256i
$994$	−2.83277e28	+	4.90650e28i	−0.0300848	+	0.0521084i
$995$	8.66688e29	+	5.00382e29i	0.911238	+	0.526103i
$996$	−5.83267e29	−	2.34944e28i	−0.607119	−	0.0244552i
$997$	−2.36157e29	−	4.09036e29i	−0.243360	−	0.421512i	0.718309	−	0.695724i	$-0.244916\pi$
$997$	−2.36157e29	−	4.09036e29i	−0.243360	−	0.421512i	−0.961669	+	0.274212i	$0.911583\pi$
$998$			9.42539e29i			0.961599i
$999$	1.41988e29	−	1.16990e30i	0.143416	−	1.18166i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.21.d.a.5.15	✓	40
3.2	odd	2		54.21.d.a.17.6		40
9.2	odd	6	inner	18.21.d.a.11.15	yes	40
9.7	even	3		54.21.d.a.35.6		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.21.d.a.5.15	✓	40	1.1	even	1	trivial
18.21.d.a.11.15	yes	40	9.2	odd	6	inner
54.21.d.a.17.6		40	3.2	odd	2
54.21.d.a.35.6		40	9.7	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:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	18.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(627.069 - 362.039i) q^{2} +(-2376.61 + 59001.2i) q^{3} +(262144. - 454047. i) q^{4} +(-6.58251e6 - 3.80041e6i) q^{5} +(1.98704e7 + 3.78582e7i) q^{6} +(7.46524e7 + 1.29302e8i) q^{7} -3.79625e8i q^{8} +(-3.47549e9 - 2.80445e8i) q^{9} -5.50358e9 q^{10} +(3.07406e10 - 1.77481e10i) q^{11} +(2.61663e10 + 1.65459e10i) q^{12} +(-1.12062e11 + 1.94097e11i) q^{13} +(9.36245e10 + 5.40541e10i) q^{14} +(2.39873e11 - 3.79343e11i) q^{15} +(-1.37439e11 - 2.38051e11i) q^{16} -2.48192e12i q^{17} +(-2.28090e12 + 1.08240e12i) q^{18} -7.60316e12 q^{19} +(-3.45113e12 + 1.99251e12i) q^{20} +(-7.80637e12 + 4.09728e12i) q^{21} +(1.28510e13 - 2.22586e13i) q^{22} +(5.93735e12 + 3.42793e12i) q^{23} +(2.23983e13 + 9.02221e11i) q^{24} +(-1.87975e13 - 3.25581e13i) q^{25} +1.62283e14i q^{26} +(2.48065e13 - 2.04391e14i) q^{27} +7.82787e13 q^{28} +(6.25109e14 - 3.60907e14i) q^{29} +(1.30799e13 - 3.24718e14i) q^{30} +(4.26088e14 - 7.38006e14i) q^{31} +(-1.72368e14 - 9.95164e13i) q^{32} +(9.74099e14 + 1.85591e15i) q^{33} +(-8.98551e14 - 1.55634e15i) q^{34} -1.13484e15i q^{35} +(-1.03841e15 + 1.50452e15i) q^{36} +5.72383e15 q^{37} +(-4.76771e15 + 2.75264e15i) q^{38} +(-1.11856e16 - 7.07308e15i) q^{39} +(-1.44273e15 + 2.49888e15i) q^{40} +(3.48457e15 + 2.01182e15i) q^{41} +(-3.41176e15 + 5.39549e15i) q^{42} +(-1.52227e16 - 2.63664e16i) q^{43} -1.86102e16i q^{44} +(2.18116e16 + 1.50543e16i) q^{45} +4.96417e15 q^{46} +(-1.80696e16 + 1.04325e16i) q^{47} +(1.43719e16 - 7.54330e15i) q^{48} +(2.87502e16 - 4.97968e16i) q^{49} +(-2.35746e16 - 1.36108e16i) q^{50} +(1.46436e17 + 5.89855e15i) q^{51} +(5.87527e16 + 1.01763e17i) q^{52} -2.64537e17i q^{53} +(-5.84422e16 - 1.37148e17i) q^{54} -2.69800e17 q^{55} +(4.90862e16 - 2.83399e16i) q^{56} +(1.80697e16 - 4.48595e17i) q^{57} +(2.61325e17 - 4.52628e17i) q^{58} +(-1.59453e17 - 9.20605e16i) q^{59} +(-1.09358e17 - 2.08356e17i) q^{60} +(-1.11733e17 - 1.93528e17i) q^{61} -6.17041e17i q^{62} +(-2.23191e17 - 4.70323e17i) q^{63} -1.44115e17 q^{64} +(1.47530e18 - 8.51763e17i) q^{65} +(1.28274e18 + 8.11123e17i) q^{66} +(2.13397e17 - 3.69615e17i) q^{67} +(-1.12691e18 - 6.50620e17i) q^{68} +(-2.16363e17 + 3.42163e17i) q^{69} +(-4.10856e17 - 7.11623e17i) q^{70} +5.24061e17i q^{71} +(-1.06464e17 + 1.31938e18i) q^{72} -4.66174e18 q^{73} +(3.58924e18 - 2.07225e18i) q^{74} +(1.96564e18 - 1.03169e18i) q^{75} +(-1.99312e18 + 3.45219e18i) q^{76} +(4.58972e18 + 2.64987e18i) q^{77} +(-9.57489e18 - 3.85684e17i) q^{78} +(1.90733e18 + 3.30360e18i) q^{79} +2.08930e18i q^{80} +(1.20004e19 + 1.94937e18i) q^{81} +2.91343e18 q^{82} +(-1.63293e19 + 9.42772e18i) q^{83} +(-1.86038e17 + 4.61853e18i) q^{84} +(-9.43231e18 + 1.63372e19i) q^{85} +(-1.90913e19 - 1.10224e19i) q^{86} +(1.98083e19 + 3.77399e19i) q^{87} +(-6.73762e18 - 1.16699e19i) q^{88} -3.96851e19i q^{89} +(1.91276e19 + 1.54346e18i) q^{90} -3.34628e19 q^{91} +(3.11288e18 - 1.79722e18i) q^{92} +(4.25305e19 + 2.68936e19i) q^{93} +(-7.55392e18 + 1.30838e19i) q^{94} +(5.00478e19 + 2.88951e19i) q^{95} +(6.28123e18 - 9.93337e18i) q^{96} +(5.68257e19 + 9.84250e19i) q^{97} -4.16347e19i q^{98} +(-1.11816e20 + 5.30622e19i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 18846 q^{3} + 10485760 q^{4} + 29763918 q^{5} + 102690816 q^{6} + 133479866 q^{7} + 967310598 q^{9} - 35793208728 q^{11} + 26559381504 q^{12} + 39827158550 q^{13} + 187564400640 q^{14} - 965812538286 q^{15}+ \cdots + 52\!\cdots\!22 q^{99}+O(q^{100}) \) 40 * q - 18846 * q^3 + 10485760 * q^4 + 29763918 * q^5 + 102690816 * q^6 + 133479866 * q^7 + 967310598 * q^9 - 35793208728 * q^11 + 26559381504 * q^12 + 39827158550 * q^13 + 187564400640 * q^14 - 965812538286 * q^15 - 5497558138880 * q^16 - 481837940736 * q^18 - 10560819523540 * q^19 + 15604865040384 * q^20 - 64715095872294 * q^21 + 10829007458304 * q^22 - 95164852839678 * q^23 + 18380312543232 * q^24 + 485893942617694 * q^25 - 312810773554224 * q^27 + 139963783970816 * q^28 + 487337329131246 * q^29 - 1016412645851136 * q^30 - 386065992062842 * q^31 + 2417458230482544 * q^33 - 810410730184704 * q^34 + 440007640743936 * q^36 + 7650497672534432 * q^37 - 27431157167935488 * q^38 + 21847743729103830 * q^39 - 76546903885431012 * q^41 - 27408162766282752 * q^42 - 10868849409851092 * q^43 - 151711625857797018 * q^45 + 13732137981788160 * q^46 + 220882065588142506 * q^47 + 19105114044235776 * q^48 - 201918836583922386 * q^49 + 84434006357065728 * q^50 - 112944490440784866 * q^51 - 20880901301862400 * q^52 - 907744599291211776 * q^54 - 689556443803109316 * q^55 + 98337764482744320 * q^56 + 524175567253271298 * q^57 + 289875600503808000 * q^58 - 4671324023815652220 * q^59 + 999198431835586560 * q^60 - 608513692992272866 * q^61 - 6762387225153657666 * q^63 - 5764607523034234880 * q^64 + 4959300225343873626 * q^65 + 7794266473078972416 * q^66 - 2581864509390888904 * q^67 - 5171455594224156672 * q^68 - 715869785458553814 * q^69 - 584784912675889152 * q^70 - 3996696553325592576 * q^72 + 15022099327729072004 * q^73 + 7089371473773993984 * q^74 + 10151951406704814570 * q^75 - 2768455473178869760 * q^76 - 30865724759591472834 * q^77 + 14351578809049718784 * q^78 + 18532232803602736754 * q^79 - 14205809545514203338 * q^81 - 35601230743051272192 * q^82 + 54829678294093455594 * q^83 - 34962890419605602304 * q^84 + 43688870161052471388 * q^85 + 47393791396458614784 * q^86 + 23116374920781444150 * q^87 - 5677518662299287552 * q^88 + 122957322600559583232 * q^90 - 35182774173576758996 * q^91 - 49893790365609099264 * q^92 + 30021582829442833806 * q^93 + 19892618446780047360 * q^94 + 332020921293200455200 * q^95 - 18590859261785407488 * q^96 - 66463398176406835216 * q^97 + 525216922205664004722 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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