LMFDB - Embedded newform 18.21.d.a.5.4

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)

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);

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")

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			5.4
Character	$\chi$	$=$	18.5
Dual form			18.21.d.a.11.4

$q$-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} +(-21083.2 - 55156.9i) q^{3} +(262144. - 454047. i) q^{4} +(-667393. - 385320. i) q^{5} +(3.31896e7 + 2.69543e7i) q^{6} +(2.18628e8 + 3.78675e8i) q^{7} +3.79625e8i q^{8} +(-2.59778e9 + 2.32577e9i) q^{9} +5.58002e8 q^{10} +(-5.02399e9 + 2.90060e9i) q^{11} +(-3.05706e10 - 4.88630e9i) q^{12} +(1.09387e11 - 1.89464e11i) q^{13} +(-2.74190e11 - 1.58304e11i) q^{14} +(-7.18226e9 + 4.49351e10i) q^{15} +(-1.37439e11 - 2.38051e11i) q^{16} +4.54755e11i q^{17} +(7.86972e11 - 2.39891e12i) q^{18} -5.45058e12 q^{19} +(-3.49906e11 + 2.02018e11i) q^{20} +(1.62771e13 - 2.00425e13i) q^{21} +(2.10026e12 - 3.63776e12i) q^{22} +(1.39965e13 + 8.08086e12i) q^{23} +(2.09389e13 - 8.00371e12i) q^{24} +(-4.73868e13 - 8.20763e13i) q^{25} +1.58409e14i q^{26} +(1.83052e14 + 9.42510e13i) q^{27} +2.29248e14 q^{28} +(4.33195e13 - 2.50105e13i) q^{29} +(-1.17645e13 - 3.07777e13i) q^{30} +(-1.93207e14 + 3.34644e14i) q^{31} +(1.72368e14 + 9.95164e13i) q^{32} +(2.65910e14 + 2.15954e14i) q^{33} +(-1.64639e14 - 2.85163e14i) q^{34} -3.36967e14i q^{35} +(3.75014e14 + 1.78920e15i) q^{36} +4.87938e15 q^{37} +(3.41789e15 - 1.97332e15i) q^{38} +(-1.27564e16 - 2.03894e15i) q^{39} +(1.46277e14 - 2.53359e14i) q^{40} +(-2.14231e16 - 1.23686e16i) q^{41} +(-2.95074e15 + 1.84610e16i) q^{42} +(-1.02039e15 - 1.76737e15i) q^{43} +3.04150e15i q^{44} +(2.62991e15 - 5.51224e14i) q^{45} -1.17023e16 q^{46} +(-7.64882e16 + 4.41605e16i) q^{47} +(-1.02325e16 + 1.25996e16i) q^{48} +(-5.57002e16 + 9.64756e16i) q^{49} +(5.94296e16 + 3.43117e16i) q^{50} +(2.50829e16 - 9.58769e15i) q^{51} +(-5.73502e16 - 9.93334e16i) q^{52} +1.73047e17i q^{53} +(-1.48909e17 + 7.16984e15i) q^{54} +4.47063e15 q^{55} +(-1.43754e17 + 8.29966e16i) q^{56} +(1.14916e17 + 3.00637e17i) q^{57} +(-1.81096e16 + 3.13667e16i) q^{58} +(-2.89091e17 - 1.66907e17i) q^{59} +(1.85199e16 + 1.50405e16i) q^{60} +(2.41445e17 + 4.18195e17i) q^{61} -2.79793e17i q^{62} +(-1.44866e18 - 4.75237e17i) q^{63} -1.44115e17 q^{64} +(-1.46008e17 + 8.42978e16i) q^{65} +(-2.44928e17 - 3.91483e16i) q^{66} +(-8.55016e17 + 1.48093e18i) q^{67} +(2.06480e17 + 1.19211e17i) q^{68} +(1.50625e17 - 9.42372e17i) q^{69} +(1.21995e17 + 2.11301e17i) q^{70} +5.73031e18i q^{71} +(-8.82919e17 - 9.86183e17i) q^{72} +3.36117e18 q^{73} +(-3.05971e18 + 1.76653e18i) q^{74} +(-3.52801e18 + 4.34414e18i) q^{75} +(-1.42884e18 + 2.47482e18i) q^{76} +(-2.19677e18 - 1.26830e18i) q^{77} +(8.73735e18 - 3.33977e18i) q^{78} +(-7.76808e18 - 1.34547e19i) q^{79} +2.11832e17i q^{80} +(1.33928e18 - 1.20837e19i) q^{81} +1.79117e19 q^{82} +(3.36181e18 - 1.94094e18i) q^{83} +(-4.83328e18 - 1.26446e19i) q^{84} +(1.75226e17 - 3.03500e17i) q^{85} +(1.27971e18 + 7.38843e17i) q^{86} +(-2.29282e18 - 1.86207e18i) q^{87} +(-1.10114e18 - 1.90723e18i) q^{88} +3.05235e18i q^{89} +(-1.44957e18 + 1.29778e18i) q^{90} +9.56600e19 q^{91} +(7.33818e18 - 4.23670e18i) q^{92} +(2.25313e19 + 3.60132e18i) q^{93} +(3.19756e19 - 5.53834e19i) q^{94} +(3.63768e18 + 2.10021e18i) q^{95} +(1.85496e18 - 1.16054e19i) q^{96} +(4.63693e19 + 8.03139e19i) q^{97} -8.06625e19i q^{98} +(6.30511e18 - 1.92198e19i) 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
$3$	−21083.2	−	55156.9i	−0.357046	−	0.934087i
$3$	−21083.2	−	55156.9i	−0.357046	−	0.934087i
$4$	262144.	−	454047.i	0.250000	−	0.433013i
$5$	−667393.	−	385320.i	−0.0683411	−	0.0394567i	0.465440	−	0.885079i	$-0.345896\pi$
$5$	−667393.	−	385320.i	−0.0683411	−	0.0394567i	−0.533781	+	0.845623i	$0.679229\pi$
$6$	3.31896e7	+	2.69543e7i	0.548895	+	0.445774i
$7$	2.18628e8	+	3.78675e8i	0.773972	+	1.34056i	0.935370	+	0.353669i	$0.115066\pi$
$7$	2.18628e8	+	3.78675e8i	0.773972	+	1.34056i	−0.161399	+	0.986889i	$0.551600\pi$
$8$			3.79625e8i			0.353553i
$9$	−2.59778e9	+	2.32577e9i	−0.745037	+	0.667023i
$10$	5.58002e8			0.0558002
$11$	−5.02399e9	+	2.90060e9i	−0.193697	+	0.111831i	−0.593712	−	0.804678i	$-0.702338\pi$
$11$	−5.02399e9	+	2.90060e9i	−0.193697	+	0.111831i	0.400015	+	0.916508i	$0.369005\pi$
$12$	−3.05706e10	−	4.88630e9i	−0.493733	−	0.0789164i
$13$	1.09387e11	−	1.89464e11i	0.793472	−	1.37433i	−0.130333	−	0.991470i	$-0.541605\pi$
$13$	1.09387e11	−	1.89464e11i	0.793472	−	1.37433i	0.923805	−	0.382863i	$-0.125062\pi$
$14$	−2.74190e11	−	1.58304e11i	−0.947918	−	0.547281i
$15$	−7.18226e9	+	4.49351e10i	−0.0124551	+	0.0779244i
$16$	−1.37439e11	−	2.38051e11i	−0.125000	−	0.216506i
$17$			4.54755e11i			0.225574i	0.993619	+	0.112787i	$0.0359777\pi$
$17$			4.54755e11i			0.225574i	−0.993619	+	0.112787i	$0.964022\pi$
$18$	7.86972e11	−	2.39891e12i	0.220412	−	0.671877i
$19$	−5.45058e12			−0.889010			−0.444505	−	0.895776i	$-0.646620\pi$
$19$	−5.45058e12			−0.889010			−0.444505	+	0.895776i	$0.646620\pi$
$20$	−3.49906e11	+	2.02018e11i	−0.0341705	+	0.0197284i
$21$	1.62771e13	−	2.00425e13i	0.975855	−	1.20160i
$22$	2.10026e12	−	3.63776e12i	0.0790763	−	0.136964i
$23$	1.39965e13	+	8.08086e12i	0.337862	+	0.195065i	0.659326	−	0.751857i	$-0.270842\pi$
$23$	1.39965e13	+	8.08086e12i	0.337862	+	0.195065i	−0.321464	+	0.946922i	$0.604175\pi$
$24$	2.09389e13	−	8.00371e12i	0.330250	−	0.126235i
$25$	−4.73868e13	−	8.20763e13i	−0.496886	−	0.860632i
$26$			1.58409e14i			1.12214i
$27$	1.83052e14	+	9.42510e13i	0.889070	+	0.457771i
$28$	2.29248e14			0.773972
$29$	4.33195e13	−	2.50105e13i	0.102968	−	0.0594488i	−0.447632	−	0.894218i	$-0.647732\pi$
$29$	4.33195e13	−	2.50105e13i	0.102968	−	0.0594488i	0.550600	+	0.834769i	$0.314399\pi$
$30$	−1.17645e13	−	3.07777e13i	−0.0199232	−	0.0521223i
$31$	−1.93207e14	+	3.34644e14i	−0.235725	+	0.408288i	−0.959483	−	0.281766i	$-0.909080\pi$
$31$	−1.93207e14	+	3.34644e14i	−0.235725	+	0.408288i	0.723758	+	0.690054i	$0.242413\pi$
$32$	1.72368e14	+	9.95164e13i	0.153093	+	0.0883883i
$33$	2.65910e14	+	2.15954e14i	0.173618	+	0.141001i
$34$	−1.64639e14	−	2.85163e14i	−0.0797523	−	0.138135i
$35$		−	3.36967e14i		−	0.122154i
$36$	3.75014e14	+	1.78920e15i	0.102570	+	0.489366i
$37$	4.87938e15			1.01472			0.507362	−	0.861733i	$-0.330621\pi$
$37$	4.87938e15			1.01472			0.507362	+	0.861733i	$0.330621\pi$
$38$	3.41789e15	−	1.97332e15i	0.544405	−	0.314312i
$39$	−1.27564e16	−	2.03894e15i	−1.56705	−	0.250472i
$40$	1.46277e14	−	2.53359e14i	0.0139501	−	0.0241622i
$41$	−2.14231e16	−	1.23686e16i	−1.59604	−	0.921473i	−0.992240	−	0.124336i	$-0.960320\pi$
$41$	−2.14231e16	−	1.23686e16i	−1.59604	−	0.921473i	−0.603798	−	0.797137i	$-0.706347\pi$
$42$	−2.95074e15	+	1.84610e16i	−0.172758	+	1.08084i
$43$	−1.02039e15	−	1.76737e15i	−0.0472153	−	0.0817793i	0.841452	−	0.540332i	$-0.181701\pi$
$43$	−1.02039e15	−	1.76737e15i	−0.0472153	−	0.0817793i	−0.888667	+	0.458553i	$0.848368\pi$
$44$			3.04150e15i			0.111831i
$45$	2.62991e15	−	5.51224e14i	0.0772352	−	0.0161884i
$46$	−1.17023e16			−0.275863
$47$	−7.64882e16	+	4.41605e16i	−1.45417	+	0.839567i	−0.998714	−	0.0506899i	$-0.983858\pi$
$47$	−7.64882e16	+	4.41605e16i	−1.45417	+	0.839567i	−0.455458	+	0.890257i	$0.650525\pi$
$48$	−1.02325e16	+	1.25996e16i	−0.157605	+	0.194064i
$49$	−5.57002e16	+	9.64756e16i	−0.698065	+	1.20908i
$50$	5.94296e16	+	3.43117e16i	0.608559	+	0.351352i
$51$	2.50829e16	−	9.58769e15i	0.210705	−	0.0805401i
$52$	−5.73502e16	−	9.93334e16i	−0.396736	−	0.687167i
$53$			1.73047e17i			0.989474i	0.869043	+	0.494737i	$0.164736\pi$
$53$			1.73047e17i			0.989474i	−0.869043	+	0.494737i	$0.835264\pi$
$54$	−1.48909e17	+	7.16984e15i	−0.706289	+	0.0340073i
$55$	4.47063e15			0.0176499
$56$	−1.43754e17	+	8.29966e16i	−0.473959	+	0.273640i
$57$	1.14916e17	+	3.00637e17i	0.317417	+	0.830412i
$58$	−1.81096e16	+	3.13667e16i	−0.0420366	+	0.0728096i
$59$	−2.89091e17	−	1.66907e17i	−0.565606	−	0.326553i	0.189787	−	0.981825i	$-0.439220\pi$
$59$	−2.89091e17	−	1.66907e17i	−0.565606	−	0.326553i	−0.755392	+	0.655273i	$0.772554\pi$
$60$	1.85199e16	+	1.50405e16i	0.0306285	+	0.0248743i
$61$	2.41445e17	+	4.18195e17i	0.338470	+	0.586247i	0.984145	−	0.177365i	$-0.0567573\pi$
$61$	2.41445e17	+	4.18195e17i	0.338470	+	0.586247i	−0.645675	+	0.763612i	$0.723424\pi$
$62$		−	2.79793e17i		−	0.333365i
$63$	−1.44866e18	−	4.75237e17i	−1.47082	−	0.482508i
$64$	−1.44115e17			−0.125000
$65$	−1.46008e17	+	8.42978e16i	−0.108453	+	0.0626156i
$66$	−2.44928e17	−	3.91483e16i	−0.156170	−	0.0249617i
$67$	−8.55016e17	+	1.48093e18i	−0.469058	+	0.812432i	−0.999374	−	0.0353678i	$-0.988740\pi$
$67$	−8.55016e17	+	1.48093e18i	−0.469058	+	0.812432i	0.530317	+	0.847800i	$0.322073\pi$
$68$	2.06480e17	+	1.19211e17i	0.0976763	+	0.0563934i
$69$	1.50625e17	−	9.42372e17i	0.0615753	−	0.385240i
$70$	1.21995e17	+	2.11301e17i	0.0431878	+	0.0748035i
$71$			5.73031e18i			1.76033i	0.474665	+	0.880167i	$0.342569\pi$
$71$			5.73031e18i			1.76033i	−0.474665	+	0.880167i	$0.657431\pi$
$72$	−8.82919e17	−	9.86183e17i	−0.235828	−	0.263410i
$73$	3.36117e18			0.782100			0.391050	−	0.920370i	$-0.372112\pi$
$73$	3.36117e18			0.782100			0.391050	+	0.920370i	$0.372112\pi$
$74$	−3.05971e18	+	1.76653e18i	−0.621389	+	0.358759i
$75$	−3.52801e18	+	4.34414e18i	−0.626494	+	0.771420i
$76$	−1.42884e18	+	2.47482e18i	−0.222252	+	0.384952i
$77$	−2.19677e18	−	1.26830e18i	−0.299831	−	0.173108i
$78$	8.73735e18	−	3.33977e18i	1.04817	−	0.400655i
$79$	−7.76808e18	−	1.34547e19i	−0.820432	−	1.42103i	−0.905361	−	0.424643i	$-0.860400\pi$
$79$	−7.76808e18	−	1.34547e19i	−0.820432	−	1.42103i	0.0849289	−	0.996387i	$-0.472934\pi$
$80$			2.11832e17i			0.0197284i
$81$	1.33928e18	−	1.20837e19i	0.110159	−	0.993914i
$82$	1.79117e19			1.30316
$83$	3.36181e18	−	1.94094e18i	0.216667	−	0.125093i	−0.387739	−	0.921769i	$-0.626744\pi$
$83$	3.36181e18	−	1.94094e18i	0.216667	−	0.125093i	0.604406	+	0.796677i	$0.293411\pi$
$84$	−4.83328e18	−	1.26446e19i	−0.276343	−	0.722957i
$85$	1.75226e17	−	3.03500e17i	0.00890040	−	0.0154159i
$86$	1.27971e18	+	7.38843e17i	0.0578267	+	0.0333863i
$87$	−2.29282e18	−	1.86207e18i	−0.0922947	−	0.0749554i
$88$	−1.10114e18	−	1.90723e18i	−0.0395381	−	0.0684821i
$89$			3.05235e18i			0.0978891i	0.998801	+	0.0489445i	$0.0155858\pi$
$89$			3.05235e18i			0.0978891i	−0.998801	+	0.0489445i	$0.984414\pi$
$90$	−1.44957e18	+	1.29778e18i	−0.0415732	+	0.0372201i
$91$	9.56600e19			2.45650
$92$	7.33818e18	−	4.23670e18i	0.168931	−	0.0975325i
$93$	2.25313e19	+	3.60132e18i	0.465541	+	0.0744102i
$94$	3.19756e19	−	5.53834e19i	0.593664	−	1.02826i
$95$	3.63768e18	+	2.10021e18i	0.0607559	+	0.0350774i
$96$	1.85496e18	−	1.16054e19i	0.0279012	−	0.174561i
$97$	4.63693e19	+	8.03139e19i	0.628801	+	1.08911i	0.987793	+	0.155774i	$0.0497871\pi$
$97$	4.63693e19	+	8.03139e19i	0.628801	+	1.08911i	−0.358992	+	0.933341i	$0.616880\pi$
$98$		−	8.06625e19i		−	0.987213i
$99$	6.30511e18	−	1.92198e19i	0.0697173	−	0.212518i
$100$	−4.96886e19			−0.496886
$101$	−1.19988e20	+	6.92752e19i	−1.08624	+	0.627140i	−0.932572	−	0.360983i	$-0.882441\pi$
$101$	−1.19988e20	+	6.92752e19i	−1.08624	+	0.627140i	−0.153665	+	0.988123i	$0.549108\pi$
$102$	−1.22576e19	+	1.50931e19i	−0.100555	+	0.123816i
$103$	1.19846e19	−	2.07579e19i	0.0891763	−	0.154458i	−0.817987	−	0.575237i	$-0.804910\pi$
$103$	1.19846e19	−	2.07579e19i	0.0891763	−	0.154458i	0.907163	+	0.420779i	$0.138243\pi$
$104$	7.19251e19	+	4.15260e19i	0.485900	+	0.280535i
$105$	−1.85860e19	+	7.10433e18i	−0.114102	+	0.0436144i
$106$	−6.26495e19	−	1.08512e20i	−0.349832	−	0.605926i
$107$			3.30918e20i			1.68222i	0.540866	+	0.841109i	$0.318097\pi$
$107$			3.30918e20i			1.68222i	−0.540866	+	0.841109i	$0.681903\pi$
$108$	9.07803e19	−	5.84067e19i	0.420488	−	0.270536i
$109$	−4.27188e20			−1.80449			−0.902245	−	0.431224i	$-0.858082\pi$
$109$	−4.27188e20			−1.80449			−0.902245	+	0.431224i	$0.858082\pi$
$110$	−2.80340e18	+	1.61854e18i	−0.0108083	+	0.00624018i
$111$	−1.02873e20	−	2.69132e20i	−0.362303	−	0.947840i
$112$	6.00960e19	−	1.04089e20i	0.193493	−	0.335140i
$113$	−2.00182e20	−	1.15575e20i	−0.589714	−	0.340471i	0.175271	−	0.984520i	$-0.443920\pi$
$113$	−2.00182e20	−	1.15575e20i	−0.589714	−	0.340471i	−0.764984	+	0.644049i	$0.777253\pi$
$114$	−1.80902e20	−	1.46916e20i	−0.487972	−	0.396298i
$115$	−6.22743e18	−	1.07862e19i	−0.0153933	−	0.0266619i
$116$		−	2.62254e19i		−	0.0594488i
$117$	1.56485e20	+	7.46593e20i	0.325547	+	1.55319i
$118$	2.41706e20			0.461815
$119$	−1.72204e20	+	9.94222e19i	−0.302395	+	0.174588i
$120$	−1.70585e19	−	2.72656e18i	−0.0275504	−	0.00440355i
$121$	−3.19548e20	+	5.53473e20i	−0.474988	+	0.822703i
$122$	−3.02806e20	−	1.74825e20i	−0.414539	−	0.239334i
$123$	−2.30548e20	+	1.44240e21i	−0.290877	+	1.81985i
$124$	1.01296e20	+	1.75450e20i	0.117862	+	0.204144i
$125$			1.46530e20i			0.157336i
$126$	1.08046e21	−	2.26463e20i	1.07128	−	0.224539i
$127$	−3.04486e19			−0.0278953			−0.0139476	−	0.999903i	$-0.504440\pi$
$127$	−3.04486e19			−0.0278953			−0.0139476	+	0.999903i	$0.504440\pi$
$128$	9.03702e19	−	5.21753e19i	0.0765466	−	0.0441942i
$129$	−7.59696e19	+	9.35435e19i	−0.0595309	+	0.0733021i
$130$	6.10381e19	−	1.05721e20i	0.0442759	−	0.0766881i
$131$	−1.37552e20	−	7.94159e19i	−0.0924177	−	0.0533574i	0.453079	−	0.891470i	$-0.350326\pi$
$131$	−1.37552e20	−	7.94159e19i	−0.0924177	−	0.0533574i	−0.545497	+	0.838113i	$0.683659\pi$
$132$	1.67760e20	−	6.41245e19i	0.104460	−	0.0399287i
$133$	−1.19165e21	−	2.06400e21i	−0.688068	−	1.19177i
$134$		−	1.23820e21i		−	0.663348i
$135$	−8.58506e19	−	1.33436e20i	−0.0426978	−	0.0663644i
$136$	−1.72636e20			−0.0797523
$137$	−7.37064e20	+	4.25544e20i	−0.316446	+	0.182700i	−0.649807	−	0.760099i	$-0.725150\pi$
$137$	−7.37064e20	+	4.25544e20i	−0.316446	+	0.182700i	0.333361	+	0.942799i	$0.391817\pi$
$138$	2.46723e20	+	6.45465e20i	0.0984959	+	0.257680i
$139$	9.05658e20	−	1.56865e21i	0.336369	−	0.582608i	−0.647378	−	0.762169i	$-0.724134\pi$
$139$	9.05658e20	−	1.56865e21i	0.336369	−	0.582608i	0.983747	+	0.179561i	$0.0574677\pi$
$140$	−1.52999e20	−	8.83338e19i	−0.0528941	−	0.0305384i
$141$	4.04837e21	+	3.28781e21i	1.30343	+	1.05856i
$142$	−2.07459e21	−	3.59330e21i	−0.622372	−	1.07798i
$143$			1.26915e21i			0.354938i
$144$	9.10688e20	+	2.98754e20i	0.237544	+	0.0779273i
$145$	−3.85482e19			−0.00938261
$146$	−2.10769e21	+	1.21687e21i	−0.478936	+	0.276514i
$147$	6.49563e21	+	1.03824e21i	1.37863	+	0.220355i
$148$	1.27910e21	−	2.21547e21i	0.253681	−	0.439388i
$149$	−3.77344e21	−	2.17860e21i	−0.699641	−	0.403938i	0.107573	−	0.994197i	$-0.465692\pi$
$149$	−3.77344e21	−	2.17860e21i	−0.699641	−	0.403938i	−0.807214	+	0.590259i	$0.799025\pi$
$150$	6.39561e20	−	4.00135e21i	0.110910	−	0.693896i
$151$	−2.28303e21	−	3.95433e21i	−0.370461	−	0.641657i	0.619176	−	0.785253i	$-0.287467\pi$
$151$	−2.28303e21	−	3.95433e21i	−0.370461	−	0.641657i	−0.989636	+	0.143596i	$0.954134\pi$
$152$		−	2.06918e21i		−	0.314312i
$153$	−1.05765e21	−	1.18135e21i	−0.150463	−	0.168061i
$154$	1.83670e21			0.244811
$155$	2.57890e20	−	1.48893e20i	0.0322194	−	0.0186019i
$156$	−4.26980e21	+	5.25752e21i	−0.500221	+	0.615936i
$157$	1.76923e21	−	3.06439e21i	0.194440	−	0.336781i	−0.752277	−	0.658848i	$-0.771044\pi$
$157$	1.76923e21	−	3.06439e21i	0.194440	−	0.336781i	0.946717	+	0.322067i	$0.104378\pi$
$158$	9.74225e21	+	5.62469e21i	1.00482	+	0.580133i
$159$	9.54471e21	−	3.64837e21i	0.924254	−	0.353287i
$160$	−7.66913e19	−	1.32833e20i	−0.00697503	−	0.0120811i
$161$			7.06681e21i			0.603899i
$162$	3.53493e21	+	8.06217e21i	0.283943	+	0.647593i
$163$	2.09901e22			1.58540			0.792698	−	0.609614i	$-0.208676\pi$
$163$	2.09901e22			1.58540			0.792698	+	0.609614i	$0.208676\pi$
$164$	−1.12319e22	+	6.48472e21i	−0.798019	+	0.460737i
$165$	−9.42553e19	−	2.46586e20i	−0.00630182	−	0.0164865i
$166$	−1.40539e21	+	2.43421e21i	−0.0884538	+	0.153206i
$167$	−2.04058e22	−	1.17813e22i	−1.20946	−	0.698280i	−0.246815	−	0.969063i	$-0.579384\pi$
$167$	−2.04058e22	−	1.17813e22i	−1.20946	−	0.698280i	−0.962640	+	0.270783i	$0.912717\pi$
$168$	7.60864e21	+	6.17921e21i	0.424829	+	0.345017i
$169$	−1.44285e22	−	2.49908e22i	−0.759195	−	1.31496i
$170$			2.53754e20i			0.0125871i
$171$	1.41594e22	−	1.26768e22i	0.662345	−	0.592990i
$172$	−1.06996e21			−0.0472153
$173$	−2.64993e22	+	1.52994e22i	−1.10350	+	0.637109i	−0.937139	−	0.348955i	$-0.886536\pi$
$173$	−2.64993e22	+	1.52994e22i	−1.10350	+	0.637109i	−0.166365	+	0.986064i	$0.553203\pi$
$174$	2.11190e21	+	3.37557e20i	0.0830195	+	0.0132695i
$175$	2.07201e22	−	3.58883e22i	0.769152	−	1.33221i
$176$	1.38098e21	+	7.97311e20i	0.0484241	+	0.0279577i
$177$	−3.11109e21	+	1.94643e22i	−0.103081	+	0.644919i
$178$	−1.10507e21	−	1.91403e21i	−0.0346090	−	0.0599446i
$179$			5.16173e22i			1.52850i	0.644920	+	0.764250i	$0.276891\pi$
$179$			5.16173e22i			1.52850i	−0.644920	+	0.764250i	$0.723109\pi$
$180$	4.39132e20	−	1.33860e21i	0.0122990	−	0.0374909i
$181$	−5.15823e22			−1.36683			−0.683416	−	0.730029i	$-0.739507\pi$
$181$	−5.15823e22			−1.36683			−0.683416	+	0.730029i	$0.739507\pi$
$182$	−5.99855e22	+	3.46326e22i	−1.50429	+	0.868504i
$183$	1.79759e22	−	2.21343e22i	0.426757	−	0.525477i
$184$	−3.06770e21	+	5.31341e21i	−0.0689659	+	0.119452i
$185$	−3.25647e21	−	1.88012e21i	−0.0693473	−	0.0400377i
$186$	−1.54325e22	+	5.89894e21i	−0.311392	+	0.119027i
$187$	−1.31906e21	−	2.28468e21i	−0.0252261	−	0.0436928i
$188$			4.63056e22i			0.839567i
$189$	4.32972e21	+	8.99229e22i	0.0744461	+	1.54615i
$190$	−3.04143e21			−0.0496069
$191$	−9.88107e22	+	5.70484e22i	−1.52922	+	0.882896i	−0.529827	+	0.848106i	$0.677743\pi$
$191$	−9.88107e22	+	5.70484e22i	−1.52922	+	0.882896i	−0.999395	+	0.0347903i	$0.988924\pi$
$192$	3.03841e21	+	7.94895e21i	0.0446307	+	0.116761i
$193$	5.62919e22	−	9.75004e22i	0.785005	−	1.35967i	−0.143991	−	0.989579i	$-0.545994\pi$
$193$	5.62919e22	−	9.75004e22i	0.785005	−	1.35967i	0.928996	−	0.370090i	$-0.120673\pi$
$194$	−5.81535e22	−	3.35749e22i	−0.770120	−	0.444629i
$195$	7.72792e21	+	6.27608e21i	0.0972112	+	0.0789483i
$196$	2.92029e22	+	5.05810e22i	0.349033	+	0.604542i
$197$		−	1.24155e23i		−	1.41027i	−0.709073	−	0.705135i	$-0.750887\pi$
$197$		−	1.24155e23i		−	1.41027i	0.709073	−	0.705135i	$-0.249113\pi$
$198$	3.00456e21	+	1.43348e22i	0.0324436	+	0.154789i
$199$	4.08553e22			0.419486			0.209743	−	0.977757i	$-0.432737\pi$
$199$	4.08553e22			0.419486			0.209743	+	0.977757i	$0.432737\pi$
$200$	3.11582e22	−	1.79892e22i	0.304279	−	0.175676i
$201$	9.97101e22	+	1.59373e22i	0.926357	+	0.148065i
$202$	5.01606e22	−	8.68808e22i	0.443455	−	0.768086i
$203$	1.89417e22	+	1.09360e22i	0.159389	+	0.0920233i
$204$	2.22207e21	−	1.39022e22i	0.0178015	−	0.111373i
$205$	9.53174e21	+	1.65095e22i	0.0727166	+	0.125949i
$206$			1.73555e22i			0.126114i
$207$	−5.51540e22	+	1.15602e22i	−0.381833	+	0.0800316i
$208$	−6.01360e22			−0.396736
$209$	2.73836e22	−	1.58099e22i	0.172198	−	0.0994186i
$210$	9.08269e21	−	1.11838e22i	0.0544529	−	0.0670495i
$211$	4.82829e22	−	8.36285e22i	0.276038	−	0.478112i	−0.694358	−	0.719629i	$-0.744312\pi$
$211$	4.82829e22	−	8.36285e22i	0.276038	−	0.478112i	0.970397	+	0.241517i	$0.0776450\pi$
$212$	7.85712e22	+	4.53631e22i	0.428455	+	0.247368i
$213$	3.16066e23	−	1.20813e23i	1.64430	−	0.628519i
$214$	−1.19805e23	−	2.07508e23i	−0.594754	−	1.03014i
$215$			1.57271e21i			0.00745184i
$216$	−3.57801e22	+	6.94910e22i	−0.161847	+	0.314334i
$217$	−1.68962e23			−0.729778
$218$	2.67877e23	−	1.54659e23i	1.10502	−	0.637983i
$219$	−7.08642e22	−	1.85392e23i	−0.279245	−	0.730549i
$220$	1.17195e21	−	2.02988e21i	0.00441248	−	0.00764263i
$221$	8.61595e22	+	4.97442e22i	0.310013	+	0.178986i
$222$	1.61945e23	+	1.31520e23i	0.556976	+	0.452338i
$223$	−4.89356e22	−	8.47590e22i	−0.160908	−	0.278700i	0.774287	−	0.632835i	$-0.218109\pi$
$223$	−4.89356e22	−	8.47590e22i	−0.160908	−	0.278700i	−0.935194	+	0.354135i	$0.884775\pi$
$224$			8.70283e22i			0.273640i
$225$	3.13991e23	+	1.03006e23i	0.944261	+	0.309768i
$226$	1.67371e23			0.481499
$227$	−2.52178e23	+	1.45595e23i	−0.694142	+	0.400763i	−0.805162	−	0.593055i	$-0.797922\pi$
$227$	−2.52178e23	+	1.45595e23i	−0.694142	+	0.400763i	0.111020	+	0.993818i	$0.464588\pi$
$228$	1.66628e23	+	2.66331e22i	0.438933	+	0.0701574i
$229$	−3.44190e23	+	5.96155e23i	−0.867848	+	1.50316i	−0.00365671	+	0.999993i	$0.501164\pi$
$229$	−3.44190e23	+	5.96155e23i	−0.867848	+	1.50316i	−0.864191	+	0.503163i	$0.832169\pi$
$230$	7.81006e21	+	4.50914e21i	0.0188528	+	0.0108847i
$231$	−2.36409e22	+	1.47907e23i	−0.0546441	+	0.341876i
$232$	9.49462e21	+	1.64452e22i	0.0210183	+	0.0364048i
$233$		−	7.59350e23i		−	1.61021i	−0.593132	−	0.805105i	$-0.702109\pi$
$233$		−	7.59350e23i		−	1.61021i	0.593132	−	0.805105i	$-0.297891\pi$
$234$	−3.68422e23	−	4.11512e23i	−0.748493	−	0.836034i
$235$	6.80636e22			0.132506
$236$	−1.51567e23	+	8.75071e22i	−0.282803	+	0.163276i
$237$	−5.78344e23	+	7.12131e23i	−1.03443	+	1.27373i
$238$	7.19893e22	−	1.24689e23i	0.123452	−	0.213825i
$239$	4.45435e23	+	2.57172e23i	0.732496	+	0.422907i	0.819335	−	0.573316i	$-0.194343\pi$
$239$	4.45435e23	+	2.57172e23i	0.732496	+	0.422907i	−0.0868385	+	0.996222i	$0.527676\pi$
$240$	1.16840e22	−	4.46609e21i	0.0184280	−	0.00704393i
$241$	1.39839e22	+	2.42207e22i	0.0211571	+	0.0366452i	0.876410	−	0.481565i	$-0.159932\pi$
$241$	1.39839e22	+	2.42207e22i	0.0211571	+	0.0366452i	−0.855253	+	0.518211i	$0.826598\pi$
$242$		−	4.62755e23i		−	0.671734i
$243$	−6.94734e23	+	1.80892e23i	−0.967734	+	0.251974i
$244$	2.53174e23			0.338470
$245$	7.43479e22	−	4.29248e22i	0.0954130	−	0.0550867i
$246$	−3.77635e23	−	9.87952e23i	−0.465288	−	1.21726i
$247$	−5.96221e23	+	1.03269e24i	−0.705404	+	1.22180i
$248$	−1.27039e23	−	7.33461e22i	−0.144351	−	0.0833413i
$249$	−1.77934e23	−	1.44506e23i	−0.194207	−	0.157722i
$250$	−5.30496e22	−	9.18845e22i	−0.0556265	−	0.0963479i
$251$		−	3.56718e23i		−	0.359408i	−0.983721	−	0.179704i	$-0.942486\pi$
$251$		−	3.56718e23i		−	0.359408i	0.983721	−	0.179704i	$-0.0575140\pi$
$252$	−5.95536e23	+	5.33177e23i	−0.576638	+	0.516257i
$253$	−9.37574e22			−0.0872570
$254$	1.90934e22	−	1.10236e22i	0.0170823	−	0.00986246i
$255$	−2.04345e22	−	3.26617e21i	−0.0175777	−	0.00280955i
$256$	−3.77789e22	+	6.54350e22i	−0.0312500	+	0.0541266i
$257$	5.35943e23	+	3.09427e23i	0.426371	+	0.246165i	0.697799	−	0.716293i	$-0.254163\pi$
$257$	5.35943e23	+	3.09427e23i	0.426371	+	0.246165i	−0.271429	+	0.962459i	$0.587496\pi$
$258$	1.37718e22	−	8.61622e22i	0.0105389	−	0.0659356i
$259$	1.06677e24	+	1.84770e24i	0.785368	+	1.36030i
$260$			8.83926e22i			0.0626156i
$261$	−5.43660e22	+	1.65723e23i	−0.0370614	+	0.112974i
$262$	1.15007e23			0.0754588
$263$	−3.65251e23	+	2.10878e23i	−0.230693	+	0.133191i	−0.610892	−	0.791714i	$-0.709189\pi$
$263$	−3.65251e23	+	2.10878e23i	−0.230693	+	0.133191i	0.380199	+	0.924905i	$0.375856\pi$
$264$	−8.19814e22	+	1.00946e23i	−0.0498513	+	0.0613833i
$265$	6.66782e22	−	1.15490e23i	0.0390414	−	0.0676217i
$266$	1.49449e24	+	8.62845e23i	0.842708	+	0.486538i
$267$	1.68358e23	−	6.43533e22i	0.0914369	−	0.0349509i
$268$	4.48275e23	+	7.76435e23i	0.234529	+	0.406216i
$269$			9.49994e23i			0.478849i	0.970915	+	0.239424i	$0.0769587\pi$
$269$			9.49994e23i			0.478849i	−0.970915	+	0.239424i	$0.923041\pi$
$270$	1.02143e23	+	5.25923e22i	0.0496103	+	0.0255437i
$271$	−1.60313e24			−0.750372			−0.375186	−	0.926949i	$-0.622421\pi$
$271$	−1.60313e24			−0.750372			−0.375186	+	0.926949i	$0.622421\pi$
$272$	1.08255e23	−	6.25011e22i	0.0488381	−	0.0281967i
$273$	−2.01682e24	−	5.27631e24i	−0.877082	−	2.29458i
$274$	3.08127e23	−	5.33692e23i	0.129189	−	0.223761i
$275$	4.76141e23	+	2.74900e23i	0.192490	+	0.111134i
$276$	−3.88395e23	−	3.15428e23i	−0.151420	−	0.122973i
$277$	1.47458e24	+	2.55405e24i	0.554460	+	0.960354i	0.997945	+	0.0640718i	$0.0204087\pi$
$277$	1.47458e24	+	2.55405e24i	0.554460	+	0.960354i	−0.443485	+	0.896282i	$0.646258\pi$
$278$			1.31153e24i			0.475698i
$279$	−2.76395e23	−	1.31869e24i	−0.0967136	−	0.461423i
$280$	1.27921e23			0.0431878
$281$	2.03369e24	−	1.17415e24i	0.662554	−	0.382526i	−0.130695	−	0.991423i	$-0.541721\pi$
$281$	2.03369e24	−	1.17415e24i	0.662554	−	0.382526i	0.793250	+	0.608897i	$0.208388\pi$
$282$	−3.72892e24	−	5.96017e23i	−1.17245	−	0.187399i
$283$	−1.81786e24	+	3.14863e24i	−0.551693	+	0.955560i	0.446460	+	0.894804i	$0.352684\pi$
$283$	−1.81786e24	+	3.14863e24i	−0.551693	+	0.955560i	−0.998153	+	0.0607560i	$0.980649\pi$
$284$	2.60183e24	+	1.50217e24i	0.762247	+	0.440083i
$285$	3.91474e22	−	2.44922e23i	0.0110727	−	0.0692755i
$286$	−4.59481e23	−	7.95845e23i	−0.125490	−	0.217354i
$287$		−	1.08165e25i		−	2.85278i
$288$	−6.79225e23	+	1.42365e23i	−0.173017	+	0.0362641i
$289$	3.85743e24			0.949117
$290$	2.41724e22	−	1.39559e22i	0.00574565	−	0.00331726i
$291$	3.45225e24	−	4.25086e24i	0.792817	−	0.976218i
$292$	8.81111e23	−	1.52613e24i	0.195525	−	0.338659i
$293$	−2.15359e24	−	1.24337e24i	−0.461834	−	0.266640i	0.250981	−	0.967992i	$-0.419247\pi$
$293$	−2.15359e24	−	1.24337e24i	−0.461834	−	0.266640i	−0.712815	+	0.701352i	$0.752580\pi$
$294$	−4.44909e24	+	1.70062e24i	−0.922143	+	0.352480i
$295$	1.28625e23	+	2.22785e23i	0.0257694	+	0.0446339i
$296$			1.85234e24i			0.358759i
$297$	−1.19303e24	+	5.74437e22i	−0.223403	+	0.0107567i
$298$	3.15495e24			0.571254
$299$	3.06206e24	−	1.76788e24i	0.536168	−	0.309557i
$300$	1.04760e24	+	2.74067e24i	0.177411	+	0.464135i
$301$	4.46173e23	−	7.72794e23i	0.0730866	−	0.126590i
$302$	2.86324e24	+	1.65309e24i	0.453720	+	0.261955i
$303$	6.35074e24	+	5.15764e24i	0.973639	+	0.790723i
$304$	7.49121e23	+	1.29752e24i	0.111126	+	0.192476i
$305$		−	3.72134e23i		−	0.0534197i
$306$	1.09092e24	+	3.57880e23i	0.151558	+	0.0497190i
$307$	−1.22221e24			−0.164347			−0.0821733	−	0.996618i	$-0.526186\pi$
$307$	−1.22221e24			−0.164347			−0.0821733	+	0.996618i	$0.526186\pi$
$308$	−1.15174e24	+	6.64957e23i	−0.149916	+	0.0865539i
$309$	−1.39761e24	−	2.23389e23i	−0.176117	−	0.0281499i
$310$	−1.07810e23	+	1.86732e23i	−0.0131535	+	0.0227825i
$311$	7.97019e24	+	4.60159e24i	0.941596	+	0.543631i	0.890460	−	0.455061i	$-0.150383\pi$
$311$	7.97019e24	+	4.60159e24i	0.941596	+	0.543631i	0.0511356	+	0.998692i	$0.483716\pi$
$312$	7.74033e23	−	4.84267e24i	0.0885551	−	0.554037i
$313$	−1.65535e23	−	2.86716e23i	−0.0183420	−	0.0317693i	0.856709	−	0.515801i	$-0.172505\pi$
$313$	−1.65535e23	−	2.86716e23i	−0.0183420	−	0.0317693i	−0.875051	+	0.484031i	$0.839172\pi$
$314$			2.56211e24i			0.274980i
$315$	7.83706e23	+	8.75366e23i	0.0814793	+	0.0910089i
$316$	−8.14542e24			−0.820432
$317$	−1.76002e24	+	1.01615e24i	−0.171761	+	0.0991663i	−0.583416	−	0.812174i	$-0.698284\pi$
$317$	−1.76002e24	+	1.01615e24i	−0.171761	+	0.0991663i	0.411655	+	0.911340i	$0.364951\pi$
$318$	−4.66434e24	+	5.74334e24i	−0.441082	+	0.543117i
$319$	−1.45091e23	+	2.51305e23i	−0.0132964	+	0.0230300i
$320$	9.61815e22	+	5.55304e22i	0.00854263	+	0.00493209i
$321$	1.82524e25	−	6.97680e24i	1.57134	−	0.600629i
$322$	−2.55846e24	−	4.43138e24i	−0.213511	−	0.369811i
$323$		−	2.47868e24i		−	0.200537i
$324$	−5.13547e24	−	3.77576e24i	−0.402837	−	0.296179i
$325$	−2.07340e25			−1.57706
$326$	−1.31622e25	+	7.59922e24i	−0.970853	+	0.560522i
$327$	9.00649e24	+	2.35624e25i	0.644285	+	1.68555i
$328$	4.69544e24	−	8.13274e24i	0.325790	−	0.564285i
$329$	−3.34449e25	−	1.93094e25i	−2.25098	−	1.29960i
$330$	1.48378e23	+	1.20503e23i	0.00968793	+	0.00786787i
$331$	−4.03921e24	−	6.99612e24i	−0.255868	−	0.443177i	0.709263	−	0.704944i	$-0.249028\pi$
$331$	−4.03921e24	−	6.99612e24i	−0.255868	−	0.443177i	−0.965131	+	0.261767i	$0.915695\pi$
$332$		−	2.03522e24i		−	0.125093i
$333$	−1.26756e25	+	1.13483e25i	−0.756006	+	0.676844i
$334$	1.70612e25			0.987516
$335$	1.14126e24	−	6.58909e23i	0.0641118	−	0.0370150i
$336$	−7.00826e24	−	1.12017e24i	−0.382135	−	0.0610791i
$337$	−9.56011e24	+	1.65586e25i	−0.506016	+	0.876445i	0.493960	+	0.869485i	$0.335549\pi$
$337$	−9.56011e24	+	1.65586e25i	−0.506016	+	0.876445i	−0.999976	+	0.00696047i	$0.997784\pi$
$338$	1.80953e25	+	1.04473e25i	0.929820	+	0.536832i
$339$	−2.15429e24	+	1.34781e25i	−0.107475	+	0.672408i
$340$	−9.18689e22	−	1.59122e23i	−0.00445020	−	0.00770797i
$341$		−	2.24166e24i		−	0.105445i
$342$	−4.28945e24	+	1.30755e25i	−0.195948	+	0.597305i
$343$	−1.38208e25			−0.613187
$344$	6.70939e23	−	3.87367e23i	0.0289133	−	0.0166931i
$345$	−4.63640e23	+	5.70894e23i	−0.0194084	+	0.0238981i
$346$	1.10780e25	−	1.91876e25i	0.450504	−	0.780296i
$347$	−1.03748e25	−	5.98988e24i	−0.409906	−	0.236659i	0.280843	−	0.959754i	$-0.409386\pi$
$347$	−1.03748e25	−	5.98988e24i	−0.409906	−	0.236659i	−0.690749	+	0.723094i	$0.742719\pi$
$348$	−1.44651e24	+	5.52916e23i	−0.0555303	+	0.0212259i
$349$	4.64785e23	+	8.05031e23i	0.0173379	+	0.0300302i	0.874564	−	0.484910i	$-0.161148\pi$
$349$	4.64785e23	+	8.05031e23i	0.0173379	+	0.0300302i	−0.857226	+	0.514940i	$0.827814\pi$
$350$			3.00060e25i			1.08775i
$351$	3.78806e25	−	2.43718e25i	1.33458	−	0.858650i
$352$	−1.15463e24			−0.0395381
$353$	−3.29479e25	+	1.90225e25i	−1.09668	+	0.633169i	−0.935347	−	0.353731i	$-0.884913\pi$
$353$	−3.29479e25	+	1.90225e25i	−1.09668	+	0.633169i	−0.161334	+	0.986900i	$0.551580\pi$
$354$	−5.09594e24	−	1.33318e25i	−0.164889	−	0.431375i
$355$	2.20800e24	−	3.82437e24i	0.0694570	−	0.120303i
$356$	1.38591e24	+	8.00155e23i	0.0423872	+	0.0244723i
$357$	9.11443e24	+	7.40211e24i	0.271049	+	0.220127i
$358$	−1.86875e25	−	3.23677e25i	−0.540406	−	0.936011i
$359$			2.36096e25i			0.663965i	0.943286	+	0.331982i	$0.107717\pi$
$359$			2.36096e25i			0.663965i	−0.943286	+	0.331982i	$0.892283\pi$
$360$	2.09259e23	+	9.98378e23i	0.00572346	+	0.0273068i
$361$	−7.88119e24			−0.209662
$362$	3.23457e25	−	1.86748e25i	0.837011	−	0.483248i
$363$	3.72650e25	+	5.95629e24i	0.938068	+	0.149937i
$364$	2.50767e25	−	4.34341e25i	0.614125	−	1.06370i
$365$	−2.24322e24	−	1.29513e24i	−0.0534495	−	0.0308591i
$366$	−3.25869e24	+	2.03877e25i	−0.0755496	+	0.472669i
$367$	2.99205e25	+	5.18238e25i	0.675007	+	1.16915i	0.976467	+	0.215667i	$0.0691927\pi$
$367$	2.99205e25	+	5.18238e25i	0.675007	+	1.16915i	−0.301460	+	0.953479i	$0.597474\pi$
$368$		−	4.44250e24i		−	0.0975325i
$369$	8.44190e25	−	1.76941e25i	1.80375	−	0.378064i
$370$	2.72271e24			0.0566218
$371$	−6.55283e25	+	3.78328e25i	−1.32645	+	0.765825i
$372$	7.54163e24	−	9.28622e24i	0.148606	−	0.182982i
$373$	4.78517e25	−	8.28816e25i	0.917929	−	1.58990i	0.115373	−	0.993322i	$-0.463194\pi$
$373$	4.78517e25	−	8.28816e25i	0.917929	−	1.58990i	0.802556	−	0.596577i	$-0.203473\pi$
$374$	1.65429e24	+	9.55104e23i	0.0308955	+	0.0178375i
$375$	8.08215e24	−	3.08932e24i	0.146965	−	0.0561760i
$376$	−1.67644e25	−	2.90369e25i	−0.296832	−	0.514128i
$377$		−	1.09433e25i		−	0.188684i
$378$	−3.52706e25	−	5.48204e25i	−0.592236	−	0.920501i
$379$	1.19404e25			0.195266			0.0976328	−	0.995223i	$-0.468873\pi$
$379$	1.19404e25			0.195266			0.0976328	+	0.995223i	$0.468873\pi$
$380$	1.90719e24	−	1.10112e24i	0.0303779	−	0.0175387i
$381$	6.41954e23	+	1.67945e24i	0.00995988	+	0.0260566i
$382$	4.13074e25	−	7.15466e25i	0.624302	−	1.08132i
$383$	−5.03304e25	−	2.90583e25i	−0.741041	−	0.427840i	0.0814066	−	0.996681i	$-0.474059\pi$
$383$	−5.03304e25	−	2.90583e25i	−0.741041	−	0.427840i	−0.822448	+	0.568841i	$0.807392\pi$
$384$	−4.78312e24	−	3.88452e24i	−0.0686118	−	0.0557218i
$385$	9.77406e23	+	1.69292e24i	0.0136605	+	0.0236607i
$386$			8.15193e25i			1.11017i
$387$	6.76125e24	+	2.21805e24i	0.0897258	+	0.0294349i
$388$	4.86217e25			0.628801
$389$	9.10939e25	−	5.25931e25i	1.14814	−	0.662877i	0.199704	−	0.979856i	$-0.436002\pi$
$389$	9.10939e25	−	5.25931e25i	1.14814	−	0.662877i	0.948432	+	0.316979i	$0.102669\pi$
$390$	−7.11813e24	−	1.13773e24i	−0.0874419	−	0.0139764i
$391$	−3.67481e24	+	6.36496e24i	−0.0440015	+	0.0762129i
$392$	−3.66245e25	−	2.11452e25i	−0.427476	−	0.246803i
$393$	−1.48029e24	+	9.26131e24i	−0.0168431	+	0.105377i
$394$	4.49489e25	+	7.78538e25i	0.498606	+	0.863610i
$395$			1.19728e25i			0.129486i
$396$	−7.07382e24	−	7.90116e24i	−0.0745937	−	0.0833180i
$397$	−1.03451e26			−1.06373			−0.531865	−	0.846829i	$-0.678509\pi$
$397$	−1.03451e26			−1.06373			−0.531865	+	0.846829i	$0.678509\pi$
$398$	−2.56191e25	+	1.47912e25i	−0.256882	+	0.148311i
$399$	−8.87198e25	+	1.09243e26i	−0.867544	+	1.06823i
$400$	−1.30256e25	+	2.25610e25i	−0.124222	+	0.215158i
$401$	−6.53392e25	−	3.77236e25i	−0.607757	−	0.350889i	0.164330	−	0.986405i	$-0.447454\pi$
$401$	−6.53392e25	−	3.77236e25i	−0.607757	−	0.350889i	−0.772087	+	0.635517i	$0.780787\pi$
$402$	−6.82950e25	+	2.61051e25i	−0.619625	+	0.236846i
$403$	4.22686e25	+	7.32113e25i	0.374082	+	0.647929i
$404$			7.26403e25i			0.627140i
$405$	−5.54990e24	+	7.54851e24i	−0.0467450	+	0.0635786i
$406$	−1.58370e25			−0.130141
$407$	−2.45140e25	+	1.41531e25i	−0.196548	+	0.113477i
$408$	3.63973e24	+	9.52209e24i	0.0284752	+	0.0744956i
$409$	−5.69746e25	+	9.86828e25i	−0.434959	+	0.753370i	−0.997292	−	0.0735400i	$-0.976570\pi$
$409$	−5.69746e25	+	9.86828e25i	−0.434959	+	0.753370i	0.562334	+	0.826910i	$0.309904\pi$
$410$	−1.19541e25	−	6.90172e24i	−0.0890593	−	0.0514184i
$411$	3.90114e25	+	3.16824e25i	0.283644	+	0.230356i
$412$	−6.28336e24	−	1.08831e25i	−0.0445882	−	0.0772290i
$413$		−	1.45962e26i		−	1.01097i
$414$	3.04001e25	−	2.72169e25i	0.205528	−	0.184007i
$415$	−2.99153e24			−0.0197430
$416$	3.77095e25	−	2.17716e25i	0.242950	−	0.140267i
$417$	−1.05616e26	−	1.68812e25i	−0.664306	−	0.106180i
$418$	−1.14476e25	+	1.98279e25i	−0.0702996	+	0.121762i
$419$	1.07570e26	+	6.21053e25i	0.644984	+	0.372382i	0.786532	−	0.617550i	$-0.211875\pi$
$419$	1.07570e26	+	6.21053e25i	0.644984	+	0.372382i	−0.141548	+	0.989931i	$0.545208\pi$
$420$	−1.64652e24	+	1.03013e25i	−0.00963992	+	0.0603113i
$421$	−9.16950e25	−	1.58820e26i	−0.524234	−	0.907999i	−0.999602	−	0.0282123i	$-0.991019\pi$
$421$	−9.16950e25	−	1.58820e26i	−0.524234	−	0.907999i	0.475368	−	0.879787i	$-0.342315\pi$
$422$			6.99212e25i			0.390377i
$423$	9.59928e25	−	2.92613e26i	0.523401	−	1.59548i
$424$	−6.56928e25			−0.349832
$425$	3.73246e25	−	2.15494e25i	0.194136	−	0.112084i
$426$	−1.54456e26	+	1.90187e26i	−0.784711	+	0.966237i
$427$	−1.05573e26	+	1.82858e26i	−0.523932	+	0.907478i
$428$	1.50252e26	+	8.67481e25i	0.728422	+	0.420554i
$429$	7.00024e25	−	2.67577e25i	0.331543	−	0.126729i
$430$	−5.69381e23	−	9.86198e23i	−0.00263462	−	0.00456330i
$431$			6.52842e25i			0.295145i	0.989051	+	0.147573i	$0.0471460\pi$
$431$			6.52842e25i			0.295145i	−0.989051	+	0.147573i	$0.952854\pi$
$432$	−2.72185e24	−	5.65294e25i	−0.0120234	−	0.249711i
$433$	−1.97881e26			−0.854133			−0.427066	−	0.904220i	$-0.640453\pi$
$433$	−1.97881e26			−0.854133			−0.427066	+	0.904220i	$0.640453\pi$
$434$	1.05951e26	−	6.11706e25i	0.446896	−	0.258015i
$435$	8.12719e23	+	2.12620e24i	0.00335002	+	0.00876418i
$436$	−1.11985e26	+	1.93963e26i	−0.451122	+	0.781367i
$437$	−7.62888e25	−	4.40453e25i	−0.300363	−	0.173415i
$438$	1.11556e26	+	9.05979e25i	0.429290	+	0.348640i
$439$	1.86217e26	+	3.22538e26i	0.700446	+	1.21321i	0.968310	+	0.249751i	$0.0803489\pi$
$439$	1.86217e26	+	3.22538e26i	0.700446	+	1.21321i	−0.267864	+	0.963457i	$0.586318\pi$
$440$			1.69716e24i			0.00624018i
$441$	−7.96827e25	−	3.80168e26i	−0.286403	−	1.36644i
$442$	−7.20373e25			−0.253125
$443$	5.03331e26	−	2.90598e26i	1.72908	−	0.998287i	0.835291	−	0.549808i	$-0.185299\pi$
$443$	5.03331e26	−	2.90598e26i	1.72908	−	0.998287i	0.893793	−	0.448479i	$-0.148034\pi$
$444$	−1.49166e26	−	2.38421e25i	−0.501002	−	0.0800783i
$445$	1.17613e24	−	2.03712e24i	0.00386238	−	0.00668984i
$446$	6.13720e25	+	3.54332e25i	0.197071	+	0.113779i
$447$	−4.06085e25	+	2.54063e26i	−0.127509	+	0.797750i
$448$	−3.15076e25	−	5.45728e25i	−0.0967465	−	0.167570i
$449$		−	4.99291e26i		−	1.49931i	−0.661831	−	0.749653i	$-0.730220\pi$
$449$		−	4.99291e26i		−	1.49931i	0.661831	−	0.749653i	$-0.269780\pi$
$450$	−2.34186e26	+	4.90851e25i	−0.687759	+	0.144153i
$451$	1.43506e26			0.412196
$452$	−1.04953e26	+	6.05947e25i	−0.294857	+	0.170236i
$453$	−1.69975e26	+	2.09295e26i	−0.467092	+	0.575143i
$454$	1.05422e26	−	1.82596e26i	0.283382	−	0.490832i
$455$	−6.38429e25	−	3.68597e25i	−0.167880	−	0.0969254i
$456$	−1.14129e26	+	4.36248e25i	−0.293595	+	0.112224i
$457$	3.25342e26	+	5.63508e26i	0.818799	+	1.41820i	0.906567	+	0.422061i	$0.138693\pi$
$457$	3.25342e26	+	5.63508e26i	0.818799	+	1.41820i	−0.0877678	+	0.996141i	$0.527973\pi$
$458$		−	4.98441e26i		−	1.22732i
$459$	−4.28611e25	+	8.32437e25i	−0.103261	+	0.200551i
$460$	−6.52993e24			−0.0153933
$461$	3.56979e26	−	2.06102e26i	0.823443	−	0.475415i	−0.0281593	−	0.999603i	$-0.508965\pi$
$461$	3.56979e26	−	2.06102e26i	0.823443	−	0.475415i	0.851602	+	0.524188i	$0.175631\pi$
$462$	−3.87235e25	−	1.01307e26i	−0.0874088	−	0.228675i
$463$	3.05087e26	−	5.28426e26i	0.673929	−	1.16728i	−0.302852	−	0.953038i	$-0.597939\pi$
$463$	3.05087e26	−	5.28426e26i	0.673929	−	1.16728i	0.976781	−	0.214241i	$-0.0687279\pi$
$464$	−1.19076e25	−	6.87484e24i	−0.0257421	−	0.0148622i
$465$	−1.36496e25	−	1.10853e25i	−0.0288796	−	0.0234540i
$466$	2.74914e26	+	4.76165e26i	0.569296	+	0.986049i
$467$			7.35178e26i			1.49013i	0.666993	+	0.745064i	$0.267581\pi$
$467$			7.35178e26i			1.49013i	−0.666993	+	0.745064i	$0.732419\pi$
$468$	3.80010e26	+	1.24663e26i	0.753939	+	0.247332i
$469$	−7.47722e26			−1.45215
$470$	−4.26806e25	+	2.46417e25i	−0.0811432	+	0.0468481i
$471$	−2.06323e26	−	3.29779e25i	−0.384007	−	0.0613782i
$472$	6.33619e25	−	1.09746e26i	0.115454	−	0.199972i
$473$	1.02529e25	+	5.91950e24i	0.0182909	+	0.0105602i
$474$	1.04843e26	−	6.55938e26i	0.183128	−	1.14572i
$475$	2.58285e26	+	4.47363e26i	0.441737	+	0.765110i
$476$			1.04252e26i			0.174588i
$477$	−4.02466e26	−	4.49537e26i	−0.660002	−	0.737194i
$478$	−3.72425e26			−0.598081
$479$	7.10812e26	−	4.10387e26i	1.11789	−	0.645415i	0.177029	−	0.984206i	$-0.443351\pi$
$479$	7.10812e26	−	4.10387e26i	1.11789	−	0.645415i	0.940862	+	0.338791i	$0.110018\pi$
$480$	−5.70977e24	+	7.03060e24i	−0.00879440	+	0.0108288i
$481$	5.33740e26	−	9.24465e26i	0.805154	−	1.39457i
$482$	−1.75377e25	−	1.01254e25i	−0.0259121	−	0.0149603i
$483$	3.89783e26	−	1.48991e26i	0.564094	−	0.215620i
$484$	1.67535e26	+	2.90179e26i	0.237494	+	0.411351i
$485$		−	7.14680e25i		−	0.0992417i
$486$	3.70157e26	−	3.64952e26i	0.503527	−	0.496448i
$487$	−4.40325e26			−0.586791			−0.293396	−	0.955991i	$-0.594785\pi$
$487$	−4.40325e26			−0.586791			−0.293396	+	0.955991i	$0.594785\pi$
$488$	−1.58757e26	+	9.16586e25i	−0.207270	+	0.119667i
$489$	−4.42538e26	−	1.15775e27i	−0.566059	−	1.48090i
$490$	−3.10808e25	+	5.38336e25i	−0.0389522	+	0.0674672i
$491$	1.76669e26	+	1.02000e26i	0.216943	+	0.125252i	0.604534	−	0.796579i	$-0.293359\pi$
$491$	1.76669e26	+	1.02000e26i	0.216943	+	0.125252i	−0.387591	+	0.921831i	$0.626693\pi$
$492$	5.94481e26	+	4.82796e26i	0.715297	+	0.580915i
$493$	1.13737e25	+	1.96998e25i	0.0134101	+	0.0232269i
$494$		−	8.63420e26i		−	0.997592i
$495$	−1.16137e25	+	1.03977e25i	−0.0131498	+	0.0117729i
$496$	1.06217e26			0.117862
$497$	−2.16992e27	+	1.25281e27i	−2.35983	+	1.36245i
$498$	1.63894e26	+	2.61961e25i	0.174690	+	0.0279218i
$499$	2.89309e26	−	5.01098e26i	0.302243	−	0.523501i	−0.674400	−	0.738366i	$-0.735598\pi$
$499$	2.89309e26	−	5.01098e26i	0.302243	−	0.523501i	0.976644	+	0.214865i	$0.0689311\pi$
$500$	6.65315e25	+	3.84120e25i	0.0681283	+	0.0393339i
$501$	−2.19601e26	+	1.37391e27i	−0.220423	+	1.37905i
$502$	1.29146e26	+	2.23687e26i	0.127070	+	0.220091i
$503$			1.71761e27i			1.65670i	0.560211	+	0.828350i	$0.310720\pi$
$503$			1.71761e27i			1.65670i	−0.560211	+	0.828350i	$0.689280\pi$
$504$	1.80412e26	−	5.49946e26i	0.170592	−	0.520014i
$505$	1.06772e26			0.0989795
$506$	5.87924e25	−	3.39438e25i	0.0534338	−	0.0308500i
$507$	−1.07422e27	+	1.32272e27i	−0.957223	+	1.17866i
$508$	−7.98192e24	+	1.38251e25i	−0.00697381	+	0.0120790i
$509$	1.60304e27	+	9.25514e26i	1.37330	+	0.792875i	0.991342	−	0.131304i	$-0.0419164\pi$
$509$	1.60304e27	+	9.25514e26i	1.37330	+	0.792875i	0.381958	+	0.924180i	$0.375250\pi$
$510$	1.39963e25	−	5.34995e24i	0.0117574	−	0.00449416i
$511$	7.34846e26	+	1.27279e27i	0.605323	+	1.04845i
$512$		−	5.47097e25i		−	0.0441942i
$513$	−9.97737e26	−	5.13722e26i	−0.790392	−	0.406963i
$514$	−4.48098e26			−0.348130
$515$	−1.59968e25	+	9.23577e24i	−0.0121888	+	0.00703721i
$516$	2.25582e25	+	5.90156e25i	0.0168580	+	0.0441032i
$517$	2.56184e26	−	4.43724e26i	0.187779	−	0.325242i
$518$	−1.33788e27	−	7.72424e26i	−0.961875	−	0.555339i
$519$	1.40256e27	+	1.13906e27i	0.989116	+	0.803292i
$520$	−3.20015e25	−	5.54283e25i	−0.0221380	−	0.0383441i
$521$		−	1.14745e27i		−	0.778673i	−0.921096	−	0.389336i	$-0.872704\pi$
$521$		−	1.14745e27i		−	0.778673i	0.921096	−	0.389336i	$-0.127296\pi$
$522$	−2.59069e25	−	1.23602e26i	−0.0172469	−	0.0822852i
$523$	−1.03264e27			−0.674422			−0.337211	−	0.941429i	$-0.609484\pi$
$523$	−1.03264e27			−0.674422			−0.337211	+	0.941429i	$0.609484\pi$
$524$	−7.21171e25	+	4.16368e25i	−0.0462089	+	0.0266787i
$525$	−2.41634e27	−	3.86218e26i	−1.51902	−	0.242795i
$526$	1.52692e26	−	2.64470e26i	0.0941799	−	0.163124i
$527$	−1.52181e26	−	8.78618e25i	−0.0920989	−	0.0531733i
$528$	1.48617e25	−	9.29806e25i	0.00882528	−	0.0552145i
$529$	−7.27477e26	−	1.26003e27i	−0.423899	−	0.734215i
$530$			9.65604e25i			0.0552129i
$531$	1.13918e27	−	2.38770e26i	0.639215	−	0.133979i
$532$	−1.24953e27			−0.688068
$533$	−4.68680e27	+	2.70593e27i	−2.53282	+	1.46233i
$534$	−8.22738e25	+	1.01306e26i	−0.0436364	+	0.0537308i
$535$	1.27509e26	−	2.20852e26i	0.0663748	−	0.114965i
$536$	−5.62199e26	−	3.24586e26i	−0.287238	−	0.165837i
$537$	2.84705e27	−	1.08826e27i	1.42775	−	0.545744i
$538$	−3.43935e26	−	5.95712e26i	−0.169299	−	0.293234i
$539$		−	6.46256e26i		−	0.312261i
$540$	−8.30914e25	+	4.00079e24i	−0.0394111	+	0.00189761i
$541$	6.46554e26			0.301045			0.150523	−	0.988607i	$-0.451904\pi$
$541$	6.46554e26			0.301045			0.150523	+	0.988607i	$0.451904\pi$
$542$	1.00528e27	−	5.80396e26i	0.459507	−	0.265297i
$543$	1.08752e27	+	2.84512e27i	0.488022	+	1.27674i
$544$	−4.52556e25	+	7.83850e25i	−0.0199381	+	0.0345338i
$545$	2.85103e26	+	1.64604e26i	0.123321	+	0.0711993i
$546$	3.17491e27	+	2.57845e27i	1.34836	+	1.09504i
$547$	−9.96886e26	−	1.72666e27i	−0.415692	−	0.720000i	0.579808	−	0.814753i	$-0.303127\pi$
$547$	−9.96886e26	−	1.72666e27i	−0.415692	−	0.720000i	−0.995501	+	0.0947524i	$0.969794\pi$
$548$			4.46216e26i			0.182700i
$549$	−1.59985e27	−	5.24835e26i	−0.643213	−	0.211008i
$550$	−3.98098e26			−0.157168
$551$	−2.36116e26	+	1.36322e26i	−0.0915398	+	0.0528505i
$552$	3.57748e26	+	5.71811e25i	0.136203	+	0.0217702i
$553$	3.39664e27	−	5.88315e27i	1.26998	−	2.19967i
$554$	−1.84933e27	−	1.06771e27i	−0.679073	−	0.392063i
$555$	−3.50450e25	+	2.19256e26i	−0.0126385	+	0.0790717i
$556$	−4.74825e26	−	8.22422e26i	−0.168185	−	0.291304i
$557$			2.03853e27i			0.709195i	0.935019	+	0.354597i	$0.115382\pi$
$557$			2.03853e27i			0.709195i	−0.935019	+	0.354597i	$0.884618\pi$
$558$	6.50734e26	+	7.26842e26i	0.222363	+	0.248369i
$559$	−4.46470e26			−0.149856
$560$	−8.02153e25	+	4.63123e25i	−0.0264470	+	0.0152692i
$561$	−9.82061e25	+	1.20924e26i	−0.0318060	+	0.0391637i
$562$	−8.50177e26	+	1.47255e27i	−0.270487	+	0.468497i
$563$	1.76578e27	+	1.01947e27i	0.551889	+	0.318633i	0.749884	−	0.661570i	$-0.230109\pi$
$563$	1.76578e27	+	1.01947e27i	0.551889	+	0.318633i	−0.197994	+	0.980203i	$0.563443\pi$
$564$	2.55408e27	−	9.76271e26i	0.784229	−	0.299764i
$565$	8.90669e25	+	1.54268e26i	0.0268678	+	0.0465364i
$566$		−	2.63255e27i		−	0.780211i
$567$	4.86859e27	−	2.13468e27i	1.41766	−	0.621586i
$568$	−2.17537e27			−0.622372
$569$	5.90624e27	−	3.40997e27i	1.66031	−	0.958578i	0.687738	−	0.725959i	$-0.258604\pi$
$569$	5.90624e27	−	3.40997e27i	1.66031	−	0.958578i	0.972568	−	0.232619i	$-0.0747295\pi$
$570$	6.41232e25	+	1.67756e26i	0.0177119	+	0.0463372i
$571$	2.79064e27	−	4.83353e27i	0.757431	−	1.31191i	−0.186726	−	0.982412i	$-0.559788\pi$
$571$	2.79064e27	−	4.83353e27i	0.757431	−	1.31191i	0.944157	−	0.329497i	$-0.106879\pi$
$572$	5.76253e26	+	3.32700e26i	0.153693	+	0.0887345i
$573$	5.22986e27	+	4.24733e27i	1.37070	+	1.11319i
$574$	3.91599e27	+	6.78270e27i	1.00861	+	1.74696i
$575$		−	1.53170e27i		−	0.387700i
$576$	3.74380e26	−	3.35178e26i	0.0931296	−	0.0833779i
$577$	−3.09153e27			−0.755816			−0.377908	−	0.925843i	$-0.623356\pi$
$577$	−3.09153e27			−0.755816			−0.377908	+	0.925843i	$0.623356\pi$
$578$	−2.41888e27	+	1.39654e27i	−0.581213	+	0.335563i
$579$	−6.56463e27	−	1.04927e27i	−1.55033	−	0.247799i
$580$	−1.01052e25	+	1.75027e25i	−0.00234565	+	0.00406279i
$581$	1.46997e27	+	8.48688e26i	0.335388	+	0.193636i
$582$	−6.25828e26	+	3.91543e27i	−0.140354	+	0.878112i
$583$	−5.01939e26	−	8.69384e26i	−0.110654	−	0.191658i
$584$			1.27598e27i			0.276514i
$585$	1.83240e26	−	5.58568e26i	0.0390357	−	0.118992i
$586$	1.80060e27			0.377086
$587$	−2.11799e27	+	1.22282e27i	−0.436056	+	0.251757i	−0.701923	−	0.712253i	$-0.747675\pi$
$587$	−2.11799e27	+	1.22282e27i	−0.436056	+	0.251757i	0.265867	+	0.964010i	$0.414342\pi$
$588$	2.17420e27	−	2.67715e27i	0.440074	−	0.541876i
$589$	1.05309e27	−	1.82400e27i	0.209562	−	0.362972i
$590$	−1.61313e26	−	9.31342e25i	−0.0315609	−	0.0182217i
$591$	−6.84801e27	+	2.61758e27i	−1.31731	+	0.503531i
$592$	−6.70617e26	−	1.16154e27i	−0.126840	−	0.219694i
$593$		−	9.51930e27i		−	1.77035i	−0.465263	−	0.885173i	$-0.654040\pi$
$593$		−	9.51930e27i		−	1.77035i	0.465263	−	0.885173i	$-0.345960\pi$
$594$	7.27318e26	−	4.67946e26i	0.133003	−	0.0855719i
$595$	1.53237e26			0.0275546
$596$	−1.97837e27	+	1.14221e27i	−0.349820	+	0.201969i
$597$	−8.61360e26	−	2.25345e27i	−0.149776	−	0.391836i
$598$	−1.28008e27	+	2.21717e27i	−0.218890	+	0.379128i
$599$	−2.93605e27	−	1.69513e27i	−0.493736	−	0.285059i	0.232387	−	0.972623i	$-0.425346\pi$
$599$	−2.93605e27	−	1.69513e27i	−0.493736	−	0.285059i	−0.726123	+	0.687565i	$0.758680\pi$
$600$	−1.64914e27	−	1.33932e27i	−0.272738	−	0.221499i
$601$	−3.90929e26	−	6.77109e26i	−0.0635848	−	0.110132i	0.832481	−	0.554054i	$-0.186920\pi$
$601$	−3.90929e26	−	6.77109e26i	−0.0635848	−	0.110132i	−0.896065	+	0.443922i	$0.853587\pi$
$602$			6.46127e26i			0.103360i
$603$	−1.22316e27	−	5.83571e27i	−0.192446	−	0.918164i
$604$	−2.39393e27			−0.370461
$605$	4.26528e26	−	2.46256e26i	0.0649223	−	0.0374829i
$606$	−5.84962e27	−	9.34981e26i	−0.875793	−	0.139983i
$607$	−7.40834e26	+	1.28316e27i	−0.109102	+	0.188971i	−0.915407	−	0.402530i	$-0.868131\pi$
$607$	−7.40834e26	+	1.28316e27i	−0.109102	+	0.188971i	0.806305	+	0.591501i	$0.201464\pi$
$608$	−9.39502e26	−	5.42422e26i	−0.136101	−	0.0785781i
$609$	2.03844e26	−	1.27533e27i	0.0290486	−	0.181740i
$610$	1.34727e26	+	2.33354e26i	0.0188867	+	0.0327127i
$611$			1.93223e28i			2.66469i
$612$	−8.13648e26	+	1.70539e26i	−0.110388	+	0.0231372i
$613$	−5.54135e27			−0.739623			−0.369812	−	0.929107i	$-0.620578\pi$
$613$	−5.54135e27			−0.739623			−0.369812	+	0.929107i	$0.620578\pi$
$614$	7.66408e26	−	4.42486e26i	0.100641	−	0.0581053i
$615$	7.09651e26	−	8.73814e26i	0.0916841	−	0.112893i
$616$	4.81480e26	−	8.33948e26i	0.0612028	−	0.106006i
$617$	4.76630e27	+	2.75182e27i	0.596114	+	0.344167i	0.767511	−	0.641035i	$-0.221495\pi$
$617$	4.76630e27	+	2.75182e27i	0.596114	+	0.344167i	−0.171397	+	0.985202i	$0.554828\pi$
$618$	9.57275e26	−	3.65909e26i	0.117802	−	0.0450286i
$619$	7.73455e27	+	1.33966e28i	0.936545	+	1.62214i	0.771855	+	0.635798i	$0.219329\pi$
$619$	7.73455e27	+	1.33966e28i	0.936545	+	1.62214i	0.164690	+	0.986345i	$0.447338\pi$
$620$		−	1.56125e26i		−	0.0186019i
$621$	1.80045e27	+	2.79840e27i	0.211088	+	0.328090i
$622$	−6.66381e27			−0.768810
$623$	−1.15585e27	+	6.67329e26i	−0.131226	+	0.0757634i
$624$	1.26786e27	+	3.31692e27i	0.141653	+	0.370586i
$625$	−4.46269e27	+	7.72961e27i	−0.490678	+	0.849880i
$626$	2.07604e26	+	1.19860e26i	0.0224643	+	0.0129698i
$627$	−1.44936e27	−	1.17707e27i	−0.154348	−	0.125351i
$628$	−9.27583e26	−	1.60662e27i	−0.0972202	−	0.168390i
$629$			2.21892e27i			0.228895i
$630$	−8.08354e26	−	2.65183e26i	−0.0820722	−	0.0269241i
$631$	−1.68612e27			−0.168498			−0.0842490	−	0.996445i	$-0.526849\pi$
$631$	−1.68612e27			−0.168498			−0.0842490	+	0.996445i	$0.526849\pi$
$632$	5.10774e27	−	2.94896e27i	0.502410	−	0.290067i
$633$	−5.63065e27	−	8.99981e26i	−0.545157	−	0.0871358i
$634$	7.35769e26	−	1.27439e27i	0.0701212	−	0.121453i
$635$	2.03212e25	+	1.17324e25i	0.00190639	+	0.00110066i
$636$	8.45557e26	−	5.29014e27i	0.0780857	−	0.488536i
$637$	1.21857e28	+	2.11063e28i	1.10779	+	1.91875i
$638$		−	2.10114e26i		−	0.0188039i
$639$	−1.33274e28	−	1.48861e28i	−1.17418	−	1.31151i
$640$	−8.04166e25			−0.00697503
$641$	−5.64951e27	+	3.26174e27i	−0.482425	+	0.278528i	−0.721427	−	0.692491i	$-0.756513\pi$
$641$	−5.64951e27	+	3.26174e27i	−0.482425	+	0.278528i	0.239001	+	0.971019i	$0.423180\pi$
$642$	−8.91964e27	+	1.09830e28i	−0.749889	+	0.923360i
$643$	7.75132e27	−	1.34257e28i	0.641602	−	1.11129i	−0.343473	−	0.939162i	$-0.611603\pi$
$643$	7.75132e27	−	1.34257e28i	0.641602	−	1.11129i	0.985075	−	0.172125i	$-0.0550632\pi$
$644$	3.20866e27	+	1.85252e27i	0.261496	+	0.150975i
$645$	8.67458e25	−	3.31577e25i	0.00696067	−	0.00266065i
$646$	8.97377e26	+	1.55430e27i	0.0709006	+	0.122803i
$647$		−	2.04082e28i		−	1.58768i	−0.608129	−	0.793838i	$-0.708080\pi$
$647$		−	2.04082e28i		−	1.58768i	0.608129	−	0.793838i	$-0.291920\pi$
$648$	4.58727e27	+	5.08425e26i	0.351402	+	0.0389472i
$649$	1.93652e27			0.146074
$650$	1.30016e28	−	7.50649e27i	0.965749	−	0.557575i
$651$	3.56225e27	+	9.31940e27i	0.260564	+	0.681676i
$652$	5.50242e27	−	9.53048e27i	0.396349	−	0.686497i
$653$	−1.36550e28	−	7.88373e27i	−0.968635	−	0.559242i	−0.0698154	−	0.997560i	$-0.522241\pi$
$653$	−1.36550e28	−	7.88373e27i	−0.968635	−	0.559242i	−0.898820	+	0.438318i	$0.855574\pi$
$654$	−1.41782e28	−	1.15145e28i	−0.990474	−	0.804395i
$655$	6.12010e25	+	1.06003e26i	0.00421062	+	0.00729300i
$656$			6.79972e27i			0.460737i
$657$	−8.73159e27	+	7.81730e27i	−0.582693	+	0.521679i
$658$	2.79631e28			1.83792
$659$	2.50877e28	−	1.44844e28i	1.62408	−	0.937662i	0.638265	−	0.769817i	$-0.279652\pi$
$659$	2.50877e28	−	1.44844e28i	1.62408	−	0.937662i	0.985813	−	0.167845i	$-0.0536810\pi$
$660$	−1.36670e26	−	2.18448e25i	−0.00871434	−	0.00139287i
$661$	−1.25934e28	+	2.18123e28i	−0.790909	+	1.36990i	0.134495	+	0.990914i	$0.457059\pi$
$661$	−1.25934e28	+	2.18123e28i	−0.790909	+	1.36990i	−0.925404	+	0.378981i	$0.876275\pi$
$662$	5.06573e27	+	2.92470e27i	0.313373	+	0.180926i
$663$	9.27219e26	−	5.80106e27i	0.0564998	−	0.353486i
$664$	7.36830e26	+	1.27623e27i	0.0442269	+	0.0766032i
$665$			1.83666e27i			0.108596i
$666$	3.83994e27	−	1.17052e28i	0.223657	−	0.681769i
$667$	8.08426e26			0.0463855
$668$	−1.06985e28	+	6.17681e27i	−0.604728	+	0.349140i
$669$	−3.64332e27	+	4.48613e27i	−0.202879	+	0.249810i
$670$	−4.77101e26	+	8.26363e26i	−0.0261735	+	0.0453339i
$671$	−2.42604e27	−	1.40067e27i	−0.131121	−	0.0757027i
$672$	4.80021e27	−	1.83483e27i	0.255604	−	0.0977021i
$673$	−8.89683e27	−	1.54098e28i	−0.466750	−	0.808435i	0.532528	−	0.846412i	$-0.321242\pi$
$673$	−8.89683e27	−	1.54098e28i	−0.466750	−	0.808435i	−0.999279	+	0.0379771i	$0.987909\pi$
$674$		−	1.38445e28i		−	0.715614i
$675$	−9.38451e26	−	1.94905e28i	−0.0477940	−	0.992623i
$676$	−1.51293e28			−0.759195
$677$	1.87026e28	−	1.07980e28i	0.924731	−	0.533894i	0.0395898	−	0.999216i	$-0.487395\pi$
$677$	1.87026e28	−	1.07980e28i	0.924731	−	0.533894i	0.885141	+	0.465322i	$0.154062\pi$
$678$	−3.52871e27	−	9.23166e27i	−0.171917	−	0.449762i
$679$	−2.02752e28	+	3.51177e28i	−0.973348	+	1.68589i
$680$	1.15216e26	+	6.65202e25i	0.00545036	+	0.00314677i
$681$	1.33473e28	+	1.08397e28i	0.622188	+	0.505298i
$682$	8.11569e26	+	1.40568e27i	0.0372805	+	0.0645717i
$683$			2.44828e27i			0.110829i	0.998463	+	0.0554145i	$0.0176480\pi$
$683$			2.44828e27i			0.110829i	−0.998463	+	0.0554145i	$0.982352\pi$
$684$	−2.04404e27	−	9.75217e27i	−0.0911861	−	0.435051i
$685$	6.55882e26			0.0288350
$686$	8.66662e27	−	5.00368e27i	0.375499	−	0.216794i
$687$	4.01387e28	+	6.41561e27i	1.71394	+	0.273950i
$688$	−2.80483e26	+	4.85811e26i	−0.0118038	+	0.0204448i
$689$	3.27860e28	+	1.89290e28i	1.35987	+	0.785119i
$690$	8.40492e25	−	5.25846e26i	0.00343592	−	0.0214965i
$691$	−9.68206e27	−	1.67698e28i	−0.390110	−	0.675690i	0.602354	−	0.798229i	$-0.294230\pi$
$691$	−9.68206e27	−	1.67698e28i	−0.390110	−	0.675690i	−0.992464	+	0.122539i	$0.960896\pi$
$692$			1.60426e28i			0.637109i
$693$	8.65651e27	−	1.81439e27i	0.338852	−	0.0710229i
$694$	8.67428e27			0.334687
$695$	−1.20886e27	+	6.97935e26i	−0.0459756	+	0.0265440i
$696$	7.06887e26	−	8.70410e26i	0.0265007	−	0.0326311i
$697$	5.62469e27	−	9.74225e27i	0.207860	−	0.360024i
$698$	−5.82904e26	−	3.36540e26i	−0.0212346	−	0.0122598i
$699$	−4.18834e28	+	1.60095e28i	−1.50408	+	0.574919i
$700$	−1.08633e28	−	1.88158e28i	−0.384576	−	0.666105i
$701$			8.63502e27i			0.301358i	0.988583	+	0.150679i	$0.0481461\pi$
$701$			8.63502e27i			0.301358i	−0.988583	+	0.150679i	$0.951854\pi$
$702$	−1.49302e28	+	2.89970e28i	−0.513683	+	0.997660i
$703$	−2.65955e28			−0.902099
$704$	7.24033e26	−	4.18021e26i	0.0242121	−	0.0139788i
$705$	−1.43500e27	−	3.75418e27i	−0.0473108	−	0.123772i
$706$	1.37737e28	−	2.38568e28i	0.447718	−	0.775470i
$707$	−5.24656e28	−	3.02910e28i	−1.68144	−	0.970777i
$708$	8.02213e27	+	6.51502e27i	0.253488	+	0.205865i
$709$	1.44098e28	+	2.49585e28i	0.448948	+	0.777601i	0.998318	−	0.0579785i	$-0.0184655\pi$
$709$	1.44098e28	+	2.49585e28i	0.448948	+	0.777601i	−0.549370	+	0.835579i	$0.685132\pi$
$710$			3.19753e27i			0.0982270i
$711$	5.14723e28	+	1.68857e28i	1.55911	+	0.511472i
$712$	−1.15875e27			−0.0346090
$713$	−5.40842e27	+	3.12255e27i	−0.159285	+	0.0919633i
$714$	−8.39523e27	−	1.34186e27i	−0.243810	−	0.0389696i
$715$	4.89028e26	−	8.47022e26i	0.0140047	−	0.0242568i
$716$	2.34367e28	+	1.35312e28i	0.661860	+	0.382125i
$717$	4.79362e27	−	2.99908e28i	0.133497	−	0.835212i
$718$	−8.54761e27	−	1.48049e28i	−0.234747	−	0.406594i
$719$		−	4.70032e28i		−	1.27303i	−0.771265	−	0.636514i	$-0.780376\pi$
$719$		−	4.70032e28i		−	1.27303i	0.771265	−	0.636514i	$-0.219624\pi$
$720$	−4.92671e26	−	5.50293e26i	−0.0131593	−	0.0146984i
$721$	1.04806e28			0.276080
$722$	4.94205e27	−	2.85330e27i	0.128391	−	0.0741267i
$723$	1.04112e27	−	1.28196e27i	0.0266757	−	0.0328466i
$724$	−1.35220e28	+	2.34208e28i	−0.341708	+	0.591856i
$725$	−4.10554e27	−	2.37034e27i	−0.102327	−	0.0590785i
$726$	−2.55241e28	+	9.75635e27i	−0.627458	+	0.239840i
$727$	−1.80730e27	−	3.13034e27i	−0.0438214	−	0.0759009i	0.843283	−	0.537470i	$-0.180620\pi$
$727$	−1.80730e27	−	3.13034e27i	−0.0438214	−	0.0759009i	−0.887104	+	0.461569i	$0.847287\pi$
$728$			3.63149e28i			0.868504i
$729$	2.46246e28	+	3.45056e28i	0.580891	+	0.813981i
$730$	1.87554e27			0.0436413
$731$	8.03721e26	−	4.64029e26i	0.0184473	−	0.0106505i
$732$	−5.33771e27	−	1.39643e28i	−0.120849	−	0.316160i
$733$	−3.22762e27	+	5.59040e27i	−0.0720846	+	0.124854i	−0.899815	−	0.436272i	$-0.856298\pi$
$733$	−3.22762e27	+	5.59040e27i	−0.0720846	+	0.124854i	0.827730	+	0.561126i	$0.189632\pi$
$734$	−3.75245e28	−	2.16648e28i	−0.826711	−	0.477302i
$735$	−3.93509e27	−	3.19581e27i	−0.0855226	−	0.0694556i
$736$	1.60836e27	+	2.78576e27i	0.0344829	+	0.0597262i
$737$		−	9.92025e27i		−	0.209820i
$738$	−4.65306e28	+	4.16584e28i	−0.970902	+	0.869238i
$739$	−1.79901e28			−0.370330			−0.185165	−	0.982707i	$-0.559282\pi$
$739$	−1.79901e28			−0.370330			−0.185165	+	0.982707i	$0.559282\pi$
$740$	−1.70733e27	+	9.85726e26i	−0.0346736	+	0.0200188i
$741$	6.95300e28	+	1.11134e28i	1.39312	+	0.222672i
$742$	2.73939e28	−	4.74476e28i	0.541520	−	0.937940i
$743$	−4.16976e28	−	2.40741e28i	−0.813249	−	0.469529i	0.0348342	−	0.999393i	$-0.488910\pi$
$743$	−4.16976e28	−	2.40741e28i	−0.813249	−	0.469529i	−0.848083	+	0.529864i	$0.822243\pi$
$744$	−1.36715e27	+	8.55346e27i	−0.0263080	+	0.164593i
$745$	1.67891e27	+	2.90796e27i	0.0318761	+	0.0552111i
$746$			6.92967e28i			1.29815i
$747$	−4.21907e27	+	1.28609e28i	−0.0779849	+	0.237720i
$748$	−1.38314e27			−0.0252261
$749$	−1.25310e29	+	7.23478e28i	−2.25511	+	1.30199i
$750$	−3.94961e27	+	4.86327e27i	−0.0701361	+	0.0863606i
$751$	1.29559e27	−	2.24403e27i	0.0227022	−	0.0393213i	−0.854451	−	0.519532i	$-0.826106\pi$
$751$	1.29559e27	−	2.24403e27i	0.0227022	−	0.0393213i	0.877153	+	0.480210i	$0.159440\pi$
$752$	2.10249e28	+	1.21387e28i	0.363543	+	0.209892i
$753$	−1.96754e28	+	7.52075e27i	−0.335718	+	0.128325i
$754$	3.96189e27	+	6.86220e27i	0.0667097	+	0.115545i
$755$			3.51879e27i			0.0584687i
$756$	4.19642e28	+	2.16069e28i	0.688115	+	0.354302i
$757$	7.60867e28			1.23126			0.615630	−	0.788035i	$-0.288902\pi$
$757$	7.60867e28			1.23126			0.615630	+	0.788035i	$0.288902\pi$
$758$	−7.48744e27	+	4.32287e27i	−0.119575	+	0.0690368i
$759$	1.97671e27	+	5.17137e27i	0.0311547	+	0.0815056i
$760$	−7.97294e26	+	1.38095e27i	−0.0124017	+	0.0214804i
$761$	−2.23946e28	−	1.29295e28i	−0.343792	−	0.198489i	0.318155	−	0.948039i	$-0.396937\pi$
$761$	−2.23946e28	−	1.29295e28i	−0.343792	−	0.198489i	−0.661948	+	0.749550i	$0.730270\pi$
$762$	−1.01058e27	−	8.20720e26i	−0.0153116	−	0.0124350i
$763$	−9.33953e28	−	1.61765e29i	−1.39662	−	2.41902i
$764$			5.98196e28i			0.882896i
$765$	2.50672e26	+	1.19596e27i	0.00365167	+	0.0174222i
$766$	4.20808e28			0.605058
$767$	−6.32454e28	+	3.65147e28i	−0.897584	+	0.518221i
$768$	4.40569e27	+	7.04189e26i	0.0617166	+	0.00986455i
$769$	−1.33210e28	+	2.30726e28i	−0.184193	+	0.319031i	−0.943304	−	0.331930i	$-0.892300\pi$
$769$	−1.33210e28	+	2.30726e28i	−0.184193	+	0.319031i	0.759111	+	0.650961i	$0.225634\pi$
$770$	−1.22580e27	−	7.07717e26i	−0.0167307	−	0.00965945i
$771$	5.76763e27	−	3.60847e28i	0.0777059	−	0.486159i
$772$	−2.95131e28	−	5.11183e28i	−0.392503	−	0.679834i
$773$		−	6.57201e27i		−	0.0862786i	−0.999069	−	0.0431393i	$-0.986264\pi$
$773$		−	6.57201e27i		−	0.0862786i	0.999069	−	0.0431393i	$-0.0137359\pi$
$774$	−5.04279e27	+	1.05696e27i	−0.0653524	+	0.0136978i
$775$	3.66218e28			0.468514
$776$	−3.04892e28	+	1.76029e28i	−0.385060	+	0.222315i
$777$	7.94224e28	−	9.77951e28i	0.990223	−	1.21929i
$778$	−3.80815e28	+	6.59591e28i	−0.468725	+	0.811855i
$779$	1.16768e29	+	6.74161e28i	1.41889	+	0.819198i
$780$	4.87546e27	−	1.86360e27i	0.0584884	−	0.0223566i
$781$	−1.66214e28	−	2.87890e28i	−0.196859	−	0.340970i
$782$		−	5.32170e27i		−	0.0622275i
$783$	1.02870e28	−	4.95310e26i	0.118760	−	0.00571820i
$784$	3.06215e28			0.349033
$785$	−2.36154e27	+	1.36343e27i	−0.0265765	+	0.0153440i
$786$	−2.42471e27	−	6.34340e27i	−0.0269422	−	0.0704850i
$787$	3.89178e27	−	6.74076e27i	0.0426973	−	0.0739539i	−0.843887	−	0.536521i	$-0.819738\pi$
$787$	3.89178e27	−	6.74076e27i	0.0426973	−	0.0739539i	0.886584	+	0.462567i	$0.153072\pi$
$788$	−5.63722e28	−	3.25465e28i	−0.610665	−	0.352567i
$789$	1.93320e28	+	1.57001e28i	0.206779	+	0.167932i
$790$	−4.33461e27	−	7.50776e27i	−0.0457803	−	0.0792938i
$791$		−	1.01072e29i		−	1.05406i
$792$	7.29630e27	+	2.39358e27i	0.0751365	+	0.0246488i
$793$	1.05644e29			1.07427
$794$	6.48712e28	−	3.74534e28i	0.651399	−	0.376085i
$795$	−7.77586e27	−	1.24286e27i	−0.0771041	−	0.0123240i
$796$	1.07100e28	−	1.85502e28i	0.104871	−	0.181643i
$797$	1.10363e29	+	6.37180e28i	1.06718	+	0.616139i	0.927411	−	0.374045i	$-0.122029\pi$
$797$	1.10363e29	+	6.37180e28i	1.06718	+	0.616139i	0.139773	+	0.990184i	$0.455363\pi$
$798$	1.60832e28	−	1.00623e29i	0.153583	−	0.960879i
$799$	−2.00822e28	−	3.47834e28i	−0.189384	−	0.328023i
$800$		−	1.88631e28i		−	0.175676i
$801$	−7.09905e27	−	7.92934e27i	−0.0652943	−	0.0729309i
$802$	5.46296e28			0.496232
$803$	−1.68865e28	+	9.74942e27i	−0.151490	+	0.0874628i
$804$	3.33747e28	−	4.10952e28i	0.295703	−	0.364108i
$805$	2.72298e27	−	4.71634e27i	0.0238279	−	0.0412711i
$806$	−5.30106e28	−	3.06057e28i	−0.458155	−	0.264516i
$807$	5.23987e28	−	2.00289e28i	0.447286	−	0.170971i
$808$	−2.62986e28	−	4.55505e28i	−0.221727	−	0.384043i
$809$		−	6.78302e28i		−	0.564856i	−0.959289	−	0.282428i	$-0.908860\pi$
$809$		−	6.78302e28i		−	0.564856i	0.959289	−	0.282428i	$-0.0911398\pi$
$810$	7.47322e26	−	6.74272e27i	0.00614692	−	0.0554606i
$811$	1.96370e29			1.59539			0.797695	−	0.603061i	$-0.206052\pi$
$811$	1.96370e29			1.59539			0.797695	+	0.603061i	$0.206052\pi$
$812$	9.93091e27	−	5.73361e27i	0.0796945	−	0.0460117i
$813$	3.37992e28	+	8.84239e28i	0.267917	+	0.700913i
$814$	1.02480e28	−	1.77500e28i	0.0802406	−	0.138981i
$815$	−1.40086e28	−	8.08789e27i	−0.108348	−	0.0625546i
$816$	−5.72973e27	−	4.65329e27i	−0.0437756	−	0.0355515i
$817$	5.56173e27	+	9.63319e27i	0.0419748	+	0.0727026i
$818$		−	8.25080e28i		−	0.615124i
$819$	−2.48504e29	+	2.22483e29i	−1.83018	+	1.63854i
$820$	9.99476e27			0.0727166
$821$	1.09037e29	−	6.29527e28i	0.783688	−	0.452463i	−0.0540474	−	0.998538i	$-0.517212\pi$
$821$	1.09037e29	−	6.29527e28i	0.783688	−	0.452463i	0.837736	+	0.546076i	$0.183879\pi$
$822$	−3.59331e28	−	5.74341e27i	−0.255139	−	0.0407804i
$823$	−9.36247e28	+	1.62163e29i	−0.656738	+	1.13750i	0.324717	+	0.945811i	$0.394731\pi$
$823$	−9.36247e28	+	1.62163e29i	−0.656738	+	1.13750i	−0.981455	+	0.191692i	$0.938602\pi$
$824$	7.88020e27	+	4.54964e27i	0.0546091	+	0.0315286i
$825$	5.12407e27	−	3.20582e28i	0.0350813	−	0.219483i
$826$	5.28438e28	+	9.15281e28i	0.357432	+	0.619090i
$827$			1.58430e29i			1.05872i	0.848396	+	0.529362i	$0.177569\pi$
$827$			1.58430e29i			1.05872i	−0.848396	+	0.529362i	$0.822431\pi$
$828$	−9.20941e27	+	2.80729e28i	−0.0608035	+	0.185346i
$829$	−1.24644e29			−0.813066			−0.406533	−	0.913636i	$-0.633262\pi$
$829$	−1.24644e29			−0.813066			−0.406533	+	0.913636i	$0.633262\pi$
$830$	1.87590e27	−	1.08305e27i	0.0120901	−	0.00698019i
$831$	1.09784e29	−	1.35181e29i	0.699086	−	0.860804i
$832$	−1.57643e28	+	2.73046e28i	−0.0991840	+	0.171792i
$833$	−4.38728e28	−	2.53299e28i	−0.272738	−	0.157465i
$834$	7.23401e28	−	2.76513e28i	0.444343	−	0.169846i
$835$	9.07915e27	+	1.57255e28i	0.0551037	+	0.0954423i
$836$		−	1.65779e28i		−	0.0994186i
$837$	−6.69074e28	+	4.30472e28i	−0.396478	+	0.255088i
$838$	−8.99381e28			−0.526627
$839$	−5.34411e28	+	3.08542e28i	−0.309212	+	0.178523i	−0.646574	−	0.762852i	$-0.723799\pi$
$839$	−5.34411e28	+	3.08542e28i	−0.309212	+	0.178523i	0.337362	+	0.941375i	$0.390465\pi$
$840$	−2.69698e27	−	7.05572e27i	−0.0154200	−	0.0403412i
$841$	−8.72462e28	+	1.51115e29i	−0.492932	+	0.853783i
$842$	1.14998e29	+	6.63943e28i	0.642052	+	0.370689i
$843$	−1.07639e29	−	8.74172e28i	−0.593875	−	0.482304i
$844$	−2.53142e28	−	4.38454e28i	−0.138019	−	0.239056i
$845$			2.22383e28i			0.119821i
$846$	4.57432e28	+	2.18242e29i	0.243569	+	1.16208i
$847$	−2.79448e29			−1.47051
$848$	4.11939e28	−	2.37833e28i	0.214227	−	0.123684i
$849$	2.11995e29	+	3.38845e28i	1.08956	+	0.174150i
$850$	−1.56034e28	+	2.70259e28i	−0.0792557	+	0.137275i
$851$	6.82941e28	+	3.94296e28i	0.342837	+	0.197937i
$852$	2.80000e28	−	1.75179e29i	0.138919	−	0.869134i
$853$	−5.00348e28	−	8.66629e28i	−0.245348	−	0.424955i	0.716882	−	0.697195i	$-0.245569\pi$
$853$	−5.00348e28	−	8.66629e28i	−0.245348	−	0.424955i	−0.962229	+	0.272240i	$0.912235\pi$
$854$		−	1.52886e29i		−	0.740952i
$855$	−1.43345e28	+	3.00449e27i	−0.0686628	+	0.0143916i
$856$	−1.25625e29			−0.594754
$857$	−8.53016e28	+	4.92489e28i	−0.399162	+	0.230456i	−0.686122	−	0.727486i	$-0.740688\pi$
$857$	−8.53016e28	+	4.92489e28i	−0.399162	+	0.230456i	0.286960	+	0.957942i	$0.407355\pi$
$858$	−3.42090e28	+	4.21225e28i	−0.158222	+	0.194824i
$859$	4.84420e27	−	8.39041e27i	0.0221458	−	0.0383576i	−0.854740	−	0.519056i	$-0.826284\pi$
$859$	4.84420e27	−	8.39041e27i	0.0221458	−	0.0383576i	0.876886	+	0.480699i	$0.159617\pi$
$860$	7.14083e26	+	4.12276e26i	0.00322674	+	0.00186296i
$861$	−5.96605e29	+	2.28046e29i	−2.66474	+	1.01857i
$862$	−2.36354e28	−	4.09377e28i	−0.104350	−	0.180739i
$863$		−	1.82176e29i		−	0.795028i	−0.917596	−	0.397514i	$-0.869873\pi$
$863$		−	1.82176e29i		−	0.795028i	0.917596	−	0.397514i	$-0.130127\pi$
$864$	2.21726e28	+	3.44625e28i	0.0956489	+	0.148665i
$865$	2.35806e28			0.100553
$866$	1.24085e29	−	7.16406e28i	0.523047	−	0.301981i
$867$	−8.13269e28	−	2.12764e29i	−0.338878	−	0.886557i
$868$	−4.42923e28	+	7.67165e28i	−0.182444	+	0.316003i
$869$	7.80535e28	+	4.50642e28i	0.317830	+	0.183499i
$870$	−1.27940e27	−	1.03904e27i	−0.00515007	−	0.00418253i
$871$	1.87055e29	+	3.23989e29i	0.744368	+	1.28928i
$872$		−	1.62171e29i		−	0.637983i
$873$	−3.07249e29	−	1.00794e29i	−1.19494	−	0.392006i
$874$	6.37845e28			0.245245
$875$	−5.54872e28	+	3.20356e28i	−0.210917	+	0.121773i
$876$	−1.02753e29	−	1.64237e28i	−0.386148	−	0.0617205i
$877$	−4.60091e28	+	7.96901e28i	−0.170942	+	0.296080i	−0.938749	−	0.344601i	$-0.888014\pi$
$877$	−4.60091e28	+	7.96901e28i	−0.170942	+	0.296080i	0.767808	+	0.640680i	$0.221348\pi$
$878$	−2.33542e29	−	1.34836e29i	−0.857868	−	0.495290i
$879$	−2.31762e28	+	1.44999e29i	−0.0841691	+	0.526596i
$880$	−6.14439e26	−	1.06424e27i	−0.00220624	−	0.00382132i
$881$		−	2.83861e28i		−	0.100773i	−0.998730	−	0.0503867i	$-0.983955\pi$
$881$		−	2.83861e28i		−	0.100773i	0.998730	−	0.0503867i	$-0.0160454\pi$
$882$	1.87602e29	+	2.09544e29i	0.658494	+	0.735510i
$883$	4.44553e29			1.54283			0.771413	−	0.636335i	$-0.219550\pi$
$883$	4.44553e29			1.54283			0.771413	+	0.636335i	$0.219550\pi$
$884$	4.51724e28	−	2.60803e28i	0.155007	−	0.0894932i
$885$	9.57629e27	−	1.17916e28i	0.0324911	−	0.0400072i
$886$	−2.10416e29	+	3.64450e29i	−0.705896	+	1.22265i
$887$	3.30645e29	+	1.90898e29i	1.09679	+	0.633234i	0.935377	−	0.353652i	$-0.115060\pi$
$887$	3.30645e29	+	1.90898e29i	1.09679	+	0.633234i	0.161417	+	0.986886i	$0.448394\pi$
$888$	1.02169e29	−	3.90532e28i	0.335112	−	0.128093i
$889$	−6.65692e27	−	1.15301e28i	−0.0215901	−	0.0373952i
$890$			1.70322e27i			0.00546223i
$891$	2.83214e28	+	6.45930e28i	0.0898126	+	0.204837i
$892$	−5.13127e28			−0.160908
$893$	4.16905e29	−	2.40700e29i	1.29277	−	0.746383i
$894$	−6.65164e28	−	1.74017e29i	−0.203964	−	0.533601i
$895$	1.98892e28	−	3.44491e28i	0.0603096	−	0.104459i
$896$	3.95149e28	+	2.28139e28i	0.118490	+	0.0684101i
$897$	−1.62069e29	−	1.31621e29i	−0.480590	−	0.390302i
$898$	1.80763e29	+	3.13090e29i	0.530085	+	0.918134i
$899$			1.93288e28i			0.0560542i
$900$	1.29080e29	−	1.15564e29i	0.370199	−	0.331435i
$901$	−7.86938e28			−0.223199
$902$	−8.99881e28	+	5.19546e28i	−0.252418	+	0.145733i
$903$	−5.20316e28	−	8.31654e27i	−0.144341	−	0.0230709i
$904$	4.38753e28	−	7.59942e28i	0.120375	−	0.208495i
$905$	3.44257e28	+	1.98757e28i	0.0934108	+	0.0539307i
$906$	3.08132e28	−	1.92780e29i	0.0826903	−	0.517344i
$907$	−1.15121e29	−	1.99395e29i	−0.305548	−	0.529225i	0.671835	−	0.740701i	$-0.265506\pi$
$907$	−1.15121e29	−	1.99395e29i	−0.305548	−	0.529225i	−0.977383	+	0.211476i	$0.932173\pi$
$908$			1.52667e29i			0.400763i
$909$	1.50585e29	−	4.59027e29i	0.390970	−	1.19179i
$910$	5.33785e28			0.137073
$911$	4.18506e29	−	2.41624e29i	1.06296	−	0.613701i	0.136712	−	0.990611i	$-0.456347\pi$
$911$	4.18506e29	−	2.41624e29i	1.06296	−	0.613701i	0.926250	+	0.376909i	$0.123013\pi$
$912$	5.57731e28	−	6.86750e28i	0.140112	−	0.172524i
$913$	−1.12598e28	+	1.95025e28i	−0.0279784	+	0.0484600i
$914$	−4.08023e29	−	2.35572e29i	−1.00282	−	0.578979i
$915$	−2.05258e28	+	7.84578e27i	−0.0498986	+	0.0190733i
$916$	1.80455e29	+	3.12557e29i	0.433924	+	0.751578i
$917$		−	6.94502e28i		−	0.165189i
$918$	−3.26052e27	−	6.77169e28i	−0.00767114	−	0.159320i
$919$	4.47274e29			1.04092			0.520462	−	0.853885i	$-0.325760\pi$
$919$	4.47274e29			1.04092			0.520462	+	0.853885i	$0.325760\pi$
$920$	4.09472e27	−	2.36409e27i	0.00942640	−	0.00544234i
$921$	2.57680e28	+	6.74131e28i	0.0586793	+	0.153514i
$922$	−1.49234e29	+	2.58480e29i	−0.336169	+	0.582262i
$923$	1.08569e30	+	6.26821e29i	2.41928	+	1.39677i
$924$	6.09593e28	+	4.95070e28i	0.134376	+	0.109131i
$925$	−2.31218e29	−	4.00482e29i	−0.504202	−	0.873304i
$926$			4.41813e29i			0.953079i
$927$	1.71447e28	+	8.17977e28i	0.0365874	+	0.174560i
$928$	9.95583e27			0.0210183
$929$	−7.08073e29	+	4.08806e29i	−1.47884	+	0.853809i	−0.999713	−	0.0239373i	$-0.992380\pi$
$929$	−7.08073e29	+	4.08806e29i	−1.47884	+	0.853809i	−0.479126	+	0.877746i	$0.659046\pi$
$930$	1.25725e28	+	2.00955e27i	0.0259773	+	0.00415211i
$931$	3.03598e29	−	5.25847e29i	0.620587	−	1.07489i
$932$	−3.44780e29	−	1.99059e29i	−0.697242	−	0.402553i
$933$	8.57724e28	−	5.36627e29i	0.171605	−	1.07363i
$934$	−2.66163e29	−	4.61008e29i	−0.526840	−	0.912514i
$935$			2.03304e27i			0.00398135i
$936$	−2.83425e29	+	5.94056e28i	−0.549137	+	0.115098i
$937$	1.17938e29			0.226078			0.113039	−	0.993591i	$-0.463942\pi$
$937$	1.17938e29			0.226078			0.113039	+	0.993591i	$0.463942\pi$
$938$	4.68873e29	−	2.70704e29i	0.889257	−	0.513413i
$939$	−1.23243e28	+	1.51753e28i	−0.0231264	+	0.0284761i
$940$	1.78425e28	−	3.09041e28i	0.0331266	−	0.0573769i
$941$	−7.80586e29	−	4.50671e29i	−1.43392	−	0.827873i	−0.436501	−	0.899704i	$-0.643782\pi$
$941$	−7.80586e29	−	4.50671e29i	−1.43392	−	0.827873i	−0.997417	+	0.0718309i	$0.977116\pi$
$942$	1.41318e29	−	5.40175e28i	0.256855	−	0.0981805i
$943$	−1.99898e29	−	3.46234e29i	−0.359494	−	0.622662i
$944$			9.17578e28i			0.163276i
$945$	3.17594e28	−	6.16823e28i	0.0559184	−	0.108603i
$946$	−8.57236e27			−0.0149344
$947$	−4.81622e29	+	2.78065e29i	−0.830246	+	0.479343i	−0.853937	−	0.520377i	$-0.825792\pi$
$947$	−4.81622e29	+	2.78065e29i	−0.830246	+	0.479343i	0.0236909	+	0.999719i	$0.492458\pi$
$948$	1.71731e29	+	4.49276e29i	0.292932	+	0.766355i
$949$	3.67668e29	−	6.36819e29i	0.620574	−	1.07487i
$950$	−3.23926e29	−	1.87018e29i	−0.541015	−	0.312355i
$951$	9.31544e28	+	7.56536e28i	0.153956	+	0.125033i
$952$	−3.77431e28	−	6.53730e28i	−0.0617261	−	0.106913i
$953$		−	1.67231e29i		−	0.270637i	−0.990802	−	0.135319i	$-0.956794\pi$
$953$		−	1.67231e29i		−	0.270637i	0.990802	−	0.135319i	$-0.0432058\pi$
$954$	4.15124e29	+	1.36183e29i	0.664805	+	0.218091i
$955$	8.79275e28			0.139345
$956$	2.33536e29	−	1.34832e29i	0.366248	−	0.211453i
$957$	1.69202e28	+	2.70446e27i	0.0262595	+	0.00419722i
$958$	−2.97152e29	+	5.14683e29i	−0.456377	+	0.790468i
$959$	−3.22286e29	−	1.86072e29i	−0.489841	−	0.282810i
$960$	1.03507e27	−	6.47583e27i	0.00155689	−	0.00974054i
$961$	2.61238e29	+	4.52477e29i	0.388868	+	0.673538i
$962$			7.72938e29i			1.13866i
$963$	−7.69637e29	−	8.59652e29i	−1.12208	−	1.25331i
$964$	1.46631e28			0.0211571
$965$	−7.51376e28	+	4.33807e28i	−0.107296	+	0.0619475i
$966$	−1.90481e29	+	2.34544e29i	−0.269203	+	0.331477i
$967$	−1.28699e29	+	2.22914e29i	−0.180016	+	0.311797i	−0.941886	−	0.335933i	$-0.890948\pi$
$967$	−1.28699e29	+	2.22914e29i	−0.180016	+	0.311797i	0.761870	+	0.647730i	$0.224282\pi$
$968$	−2.10112e29	−	1.21308e29i	−0.290869	−	0.167934i
$969$	−1.36716e29	+	5.22584e28i	−0.187319	+	0.0716009i
$970$	2.58742e28	+	4.48154e28i	0.0350872	+	0.0607729i
$971$			3.73254e29i			0.500971i	0.968120	+	0.250485i	$0.0805902\pi$
$971$			3.73254e29i			0.500971i	−0.968120	+	0.250485i	$0.919410\pi$
$972$	−9.99871e28	+	3.62862e29i	−0.132825	+	0.482035i
$973$	7.92008e29			1.04136
$974$	2.76114e29	−	1.59415e29i	0.359335	−	0.207462i
$975$	4.37138e29	+	1.14362e30i	0.563083	+	1.47311i
$976$	6.63679e28	−	1.14953e29i	0.0846175	−	0.146562i
$977$	1.37986e29	+	7.96664e28i	0.174137	+	0.100538i	0.584535	−	0.811369i	$-0.301277\pi$
$977$	1.37986e29	+	7.96664e28i	0.174137	+	0.100538i	−0.410398	+	0.911906i	$0.634610\pi$
$978$	6.96651e29	+	5.65772e29i	0.870216	+	0.706729i
$979$	−8.85365e27	−	1.53350e28i	−0.0109470	−	0.0189608i
$980$		−	4.50099e28i		−	0.0550867i
$981$	1.10974e30	−	9.93540e29i	1.34441	−	1.20364i
$982$	−1.47712e29			−0.177133
$983$	−9.71196e29	+	5.60720e29i	−1.15285	+	0.665596i	−0.949579	−	0.313527i	$-0.898489\pi$
$983$	−9.71196e29	+	5.60720e29i	−1.15285	+	0.665596i	−0.203267	+	0.979123i	$0.565156\pi$
$984$	−5.47571e29	−	8.75217e28i	−0.643413	−	0.102841i
$985$	−4.78394e28	+	8.28602e28i	−0.0556446	+	0.0963793i
$986$	−1.42642e28	−	8.23541e27i	−0.0164239	−	0.00948235i
$987$	−3.59923e29	+	2.25182e30i	−0.410240	+	2.56663i
$988$	3.12592e29	+	5.41424e29i	0.352702	+	0.610898i
$989$		−	3.29826e28i		−	0.0368402i
$990$	3.51827e27	−	1.07247e28i	0.00389024	−	0.0118586i
$991$	−1.19128e30			−1.30400			−0.652000	−	0.758219i	$-0.726070\pi$
$991$	−1.19128e30			−1.30400			−0.652000	+	0.758219i	$0.726070\pi$
$992$	−6.66052e28	+	3.84545e28i	−0.0721757	+	0.0416707i
$993$	−3.00725e29	+	3.70291e29i	−0.322609	+	0.397238i
$994$	9.07129e29	−	1.57119e30i	0.963397	−	1.66865i
$995$	−2.72665e28	−	1.57423e28i	−0.0286681	−	0.0165515i
$996$	−1.12257e29	+	4.29090e28i	−0.116847	+	0.0446638i
$997$	−3.42228e29	−	5.92756e29i	−0.352666	−	0.610836i	0.634049	−	0.773293i	$-0.281392\pi$
$997$	−3.42228e29	−	5.92756e29i	−0.352666	−	0.610836i	−0.986716	+	0.162457i	$0.948058\pi$
$998$			4.18965e29i			0.427437i
$999$	8.93179e29	+	4.59887e29i	0.902160	+	0.464511i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.21.d.a.5.4	✓	40
3.2	odd	2		54.21.d.a.17.17		40
9.2	odd	6	inner	18.21.d.a.11.4	yes	40
9.7	even	3		54.21.d.a.35.17		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.21.d.a.5.4	✓	40	1.1	even	1	trivial
18.21.d.a.11.4	yes	40	9.2	odd	6	inner
54.21.d.a.17.17		40	3.2	odd	2
54.21.d.a.35.17		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} +(-21083.2 - 55156.9i) q^{3} +(262144. - 454047. i) q^{4} +(-667393. - 385320. i) q^{5} +(3.31896e7 + 2.69543e7i) q^{6} +(2.18628e8 + 3.78675e8i) q^{7} +3.79625e8i q^{8} +(-2.59778e9 + 2.32577e9i) q^{9} +5.58002e8 q^{10} +(-5.02399e9 + 2.90060e9i) q^{11} +(-3.05706e10 - 4.88630e9i) q^{12} +(1.09387e11 - 1.89464e11i) q^{13} +(-2.74190e11 - 1.58304e11i) q^{14} +(-7.18226e9 + 4.49351e10i) q^{15} +(-1.37439e11 - 2.38051e11i) q^{16} +4.54755e11i q^{17} +(7.86972e11 - 2.39891e12i) q^{18} -5.45058e12 q^{19} +(-3.49906e11 + 2.02018e11i) q^{20} +(1.62771e13 - 2.00425e13i) q^{21} +(2.10026e12 - 3.63776e12i) q^{22} +(1.39965e13 + 8.08086e12i) q^{23} +(2.09389e13 - 8.00371e12i) q^{24} +(-4.73868e13 - 8.20763e13i) q^{25} +1.58409e14i q^{26} +(1.83052e14 + 9.42510e13i) q^{27} +2.29248e14 q^{28} +(4.33195e13 - 2.50105e13i) q^{29} +(-1.17645e13 - 3.07777e13i) q^{30} +(-1.93207e14 + 3.34644e14i) q^{31} +(1.72368e14 + 9.95164e13i) q^{32} +(2.65910e14 + 2.15954e14i) q^{33} +(-1.64639e14 - 2.85163e14i) q^{34} -3.36967e14i q^{35} +(3.75014e14 + 1.78920e15i) q^{36} +4.87938e15 q^{37} +(3.41789e15 - 1.97332e15i) q^{38} +(-1.27564e16 - 2.03894e15i) q^{39} +(1.46277e14 - 2.53359e14i) q^{40} +(-2.14231e16 - 1.23686e16i) q^{41} +(-2.95074e15 + 1.84610e16i) q^{42} +(-1.02039e15 - 1.76737e15i) q^{43} +3.04150e15i q^{44} +(2.62991e15 - 5.51224e14i) q^{45} -1.17023e16 q^{46} +(-7.64882e16 + 4.41605e16i) q^{47} +(-1.02325e16 + 1.25996e16i) q^{48} +(-5.57002e16 + 9.64756e16i) q^{49} +(5.94296e16 + 3.43117e16i) q^{50} +(2.50829e16 - 9.58769e15i) q^{51} +(-5.73502e16 - 9.93334e16i) q^{52} +1.73047e17i q^{53} +(-1.48909e17 + 7.16984e15i) q^{54} +4.47063e15 q^{55} +(-1.43754e17 + 8.29966e16i) q^{56} +(1.14916e17 + 3.00637e17i) q^{57} +(-1.81096e16 + 3.13667e16i) q^{58} +(-2.89091e17 - 1.66907e17i) q^{59} +(1.85199e16 + 1.50405e16i) q^{60} +(2.41445e17 + 4.18195e17i) q^{61} -2.79793e17i q^{62} +(-1.44866e18 - 4.75237e17i) q^{63} -1.44115e17 q^{64} +(-1.46008e17 + 8.42978e16i) q^{65} +(-2.44928e17 - 3.91483e16i) q^{66} +(-8.55016e17 + 1.48093e18i) q^{67} +(2.06480e17 + 1.19211e17i) q^{68} +(1.50625e17 - 9.42372e17i) q^{69} +(1.21995e17 + 2.11301e17i) q^{70} +5.73031e18i q^{71} +(-8.82919e17 - 9.86183e17i) q^{72} +3.36117e18 q^{73} +(-3.05971e18 + 1.76653e18i) q^{74} +(-3.52801e18 + 4.34414e18i) q^{75} +(-1.42884e18 + 2.47482e18i) q^{76} +(-2.19677e18 - 1.26830e18i) q^{77} +(8.73735e18 - 3.33977e18i) q^{78} +(-7.76808e18 - 1.34547e19i) q^{79} +2.11832e17i q^{80} +(1.33928e18 - 1.20837e19i) q^{81} +1.79117e19 q^{82} +(3.36181e18 - 1.94094e18i) q^{83} +(-4.83328e18 - 1.26446e19i) q^{84} +(1.75226e17 - 3.03500e17i) q^{85} +(1.27971e18 + 7.38843e17i) q^{86} +(-2.29282e18 - 1.86207e18i) q^{87} +(-1.10114e18 - 1.90723e18i) q^{88} +3.05235e18i q^{89} +(-1.44957e18 + 1.29778e18i) q^{90} +9.56600e19 q^{91} +(7.33818e18 - 4.23670e18i) q^{92} +(2.25313e19 + 3.60132e18i) q^{93} +(3.19756e19 - 5.53834e19i) q^{94} +(3.63768e18 + 2.10021e18i) q^{95} +(1.85496e18 - 1.16054e19i) q^{96} +(4.63693e19 + 8.03139e19i) q^{97} -8.06625e19i q^{98} +(6.30511e18 - 1.92198e19i) 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

Related objects

Downloads

Learn more