LMFDB - Embedded newform 18.21.d.a.5.2

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			5.2
Character	$\chi$	$=$	18.5
Dual form			18.21.d.a.11.2

$q$-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} +(57522.4 - 13339.9i) q^{3} +(262144. - 454047. i) q^{4} +(8.06063e6 + 4.65381e6i) q^{5} +(-3.12410e7 + 2.91904e7i) q^{6} +(-1.01532e8 - 1.75858e8i) q^{7} +3.79625e8i q^{8} +(3.13088e9 - 1.53468e9i) q^{9} -6.73943e9 q^{10} +(-1.53701e10 + 8.87390e9i) q^{11} +(9.02224e9 - 2.96148e10i) q^{12} +(1.33852e11 - 2.31839e11i) q^{13} +(1.27335e11 + 7.35167e10i) q^{14} +(5.25748e11 + 1.60171e11i) q^{15} +(-1.37439e11 - 2.38051e11i) q^{16} +6.42475e9i q^{17} +(-1.40766e12 + 2.09585e12i) q^{18} +5.82352e12 q^{19} +(4.22609e12 - 2.43994e12i) q^{20} +(-8.18626e12 - 8.76135e12i) q^{21} +(6.42539e12 - 1.11291e13i) q^{22} +(-5.23343e13 - 3.02152e13i) q^{23} +(5.06415e12 + 2.18370e13i) q^{24} +(-4.36787e12 - 7.56538e12i) q^{25} +1.93839e14i q^{26} +(1.59623e14 - 1.30044e14i) q^{27} -1.06464e14 q^{28} +(-6.25402e14 + 3.61076e14i) q^{29} +(-3.87669e14 + 8.99032e13i) q^{30} +(-1.97720e14 + 3.42460e14i) q^{31} +(1.72368e14 + 9.95164e13i) q^{32} +(-7.65746e14 + 7.15483e14i) q^{33} +(-2.32601e12 - 4.02877e12i) q^{34} -1.89003e15i q^{35} +(1.23923e14 - 1.82387e15i) q^{36} +6.51357e15 q^{37} +(-3.65175e15 + 2.10834e15i) q^{38} +(4.60681e15 - 1.51215e16i) q^{39} +(-1.76670e15 + 3.06002e15i) q^{40} +(7.50009e15 + 4.33018e15i) q^{41} +(8.30530e15 + 2.53023e15i) q^{42} +(-1.60054e16 - 2.77222e16i) q^{43} +9.30496e15i q^{44} +(3.23790e16 + 2.19998e15i) q^{45} +4.37563e16 q^{46} +(3.97355e16 - 2.29413e16i) q^{47} +(-1.10814e16 - 1.18599e16i) q^{48} +(1.92788e16 - 3.33919e16i) q^{49} +(5.47792e15 + 3.16268e15i) q^{50} +(8.57054e13 + 3.69568e14i) q^{51} +(-7.01771e16 - 1.21550e17i) q^{52} -1.92375e17i q^{53} +(-5.30138e16 + 1.39337e17i) q^{54} -1.65190e17 q^{55} +(6.67600e16 - 3.85439e16i) q^{56} +(3.34983e17 - 7.76851e16i) q^{57} +(2.61447e17 - 4.52840e17i) q^{58} +(1.73030e17 + 9.98989e16i) q^{59} +(2.10547e17 - 1.96727e17i) q^{60} +(1.72807e17 + 2.99311e17i) q^{61} -2.86328e17i q^{62} +(-5.87769e17 - 3.94771e17i) q^{63} -1.44115e17 q^{64} +(2.15787e18 - 1.24585e18i) q^{65} +(2.21143e17 - 7.25887e17i) q^{66} +(8.47875e17 - 1.46856e18i) q^{67} +(2.91714e15 + 1.68421e15i) q^{68} +(-3.41346e18 - 1.03992e18i) q^{69} +(6.84265e17 + 1.18518e18i) q^{70} +1.64941e18i q^{71} +(5.82605e17 + 1.18856e18i) q^{72} +2.42721e18 q^{73} +(-4.08446e18 + 2.35817e18i) q^{74} +(-3.52172e17 - 3.76912e17i) q^{75} +(1.52660e18 - 2.64415e18i) q^{76} +(3.12109e18 + 1.80196e18i) q^{77} +(2.58579e18 + 1.11501e19i) q^{78} +(-3.95134e18 - 6.84391e18i) q^{79} -2.55846e18i q^{80} +(7.44715e18 - 9.60983e18i) q^{81} -6.27077e18 q^{82} +(5.73077e18 - 3.30866e18i) q^{83} +(-6.12404e18 + 1.42021e18i) q^{84} +(-2.98996e16 + 5.17876e16i) q^{85} +(2.00730e19 + 1.15892e19i) q^{86} +(-3.11580e19 + 2.91128e19i) q^{87} +(-3.36876e18 - 5.83486e18i) q^{88} +2.07037e19i q^{89} +(-2.11004e19 + 1.03429e19i) q^{90} -5.43609e19 q^{91} +(-2.74382e19 + 1.58415e19i) q^{92} +(-6.80493e18 + 2.23367e19i) q^{93} +(-1.66113e19 + 2.87716e19i) q^{94} +(4.69412e19 + 2.71015e19i) q^{95} +(1.12425e19 + 3.42507e18i) q^{96} +(-3.43083e19 - 5.94238e19i) q^{97} +2.79187e19i q^{98} +(-3.45031e19 + 5.13713e19i) 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
$3$	57522.4	−	13339.9i	0.974148	−	0.225912i
$3$	57522.4	−	13339.9i	0.974148	−	0.225912i
$4$	262144.	−	454047.i	0.250000	−	0.433013i
$5$	8.06063e6	+	4.65381e6i	0.825409	+	0.476550i	0.852278	−	0.523089i	$-0.175221\pi$
$5$	8.06063e6	+	4.65381e6i	0.825409	+	0.476550i	−0.0268694	+	0.999639i	$0.508554\pi$
$6$	−3.12410e7	+	2.91904e7i	−0.516669	+	0.482756i
$7$	−1.01532e8	−	1.75858e8i	−0.359435	−	0.622560i	0.628431	−	0.777865i	$-0.283697\pi$
$7$	−1.01532e8	−	1.75858e8i	−0.359435	−	0.622560i	−0.987867	+	0.155305i	$0.950364\pi$
$8$			3.79625e8i			0.353553i
$9$	3.13088e9	−	1.53468e9i	0.897928	−	0.440143i
$10$	−6.73943e9			−0.673943
$11$	−1.53701e10	+	8.87390e9i	−0.592582	+	0.342127i	−0.766118	−	0.642700i	$-0.777814\pi$
$11$	−1.53701e10	+	8.87390e9i	−0.592582	+	0.342127i	0.173536	+	0.984828i	$0.444481\pi$
$12$	9.02224e9	−	2.96148e10i	0.145714	−	0.478296i
$13$	1.33852e11	−	2.31839e11i	0.970940	−	1.68172i	0.278209	−	0.960521i	$-0.410259\pi$
$13$	1.33852e11	−	2.31839e11i	0.970940	−	1.68172i	0.692731	−	0.721196i	$-0.256407\pi$
$14$	1.27335e11	+	7.35167e10i	0.440216	+	0.254159i
$15$	5.25748e11	+	1.60171e11i	0.911728	+	0.277760i
$16$	−1.37439e11	−	2.38051e11i	−0.125000	−	0.216506i
$17$			6.42475e9i			0.00318689i	0.999999	+	0.00159345i	$0.000507210\pi$
$17$			6.42475e9i			0.00318689i	−0.999999	+	0.00159345i	$0.999493\pi$
$18$	−1.40766e12	+	2.09585e12i	−0.394252	+	0.586997i
$19$	5.82352e12			0.949838			0.474919	−	0.880029i	$-0.342477\pi$
$19$	5.82352e12			0.949838			0.474919	+	0.880029i	$0.342477\pi$
$20$	4.22609e12	−	2.43994e12i	0.412704	−	0.238275i
$21$	−8.18626e12	−	8.76135e12i	−0.490787	−	0.525265i
$22$	6.42539e12	−	1.11291e13i	0.241921	−	0.419019i
$23$	−5.23343e13	−	3.02152e13i	−1.26330	−	0.729369i	−0.289592	−	0.957150i	$-0.593519\pi$
$23$	−5.23343e13	−	3.02152e13i	−1.26330	−	0.729369i	−0.973712	+	0.227781i	$0.926853\pi$
$24$	5.06415e12	+	2.18370e13i	0.0798720	+	0.344413i
$25$	−4.36787e12	−	7.56538e12i	−0.0458005	−	0.0793287i
$26$			1.93839e14i			1.37312i
$27$	1.59623e14	−	1.30044e14i	0.775280	−	0.631617i
$28$	−1.06464e14			−0.359435
$29$	−6.25402e14	+	3.61076e14i	−1.48655	+	0.858260i	−0.999883	−	0.0153276i	$-0.995121\pi$
$29$	−6.25402e14	+	3.61076e14i	−1.48655	+	0.858260i	−0.486667	+	0.873587i	$0.661788\pi$
$30$	−3.87669e14	+	8.99032e13i	−0.656520	+	0.152252i
$31$	−1.97720e14	+	3.42460e14i	−0.241231	+	0.417824i	−0.961065	−	0.276322i	$-0.910884\pi$
$31$	−1.97720e14	+	3.42460e14i	−0.241231	+	0.417824i	0.719834	+	0.694146i	$0.244218\pi$
$32$	1.72368e14	+	9.95164e13i	0.153093	+	0.0883883i
$33$	−7.65746e14	+	7.15483e14i	−0.499972	+	0.467154i
$34$	−2.32601e12	−	4.02877e12i	−0.00112674	−	0.00195156i
$35$		−	1.89003e15i		−	0.685155i
$36$	1.23923e14	−	1.82387e15i	0.0338942	−	0.498850i
$37$	6.51357e15			1.35457			0.677286	−	0.735720i	$-0.263156\pi$
$37$	6.51357e15			1.35457			0.677286	+	0.735720i	$0.263156\pi$
$38$	−3.65175e15	+	2.10834e15i	−0.581655	+	0.335818i
$39$	4.60681e15	−	1.51215e16i	0.565919	−	1.85759i
$40$	−1.76670e15	+	3.06002e15i	−0.168486	+	0.291826i
$41$	7.50009e15	+	4.33018e15i	0.558763	+	0.322602i	0.752649	−	0.658422i	$-0.228776\pi$
$41$	7.50009e15	+	4.33018e15i	0.558763	+	0.322602i	−0.193886	+	0.981024i	$0.562109\pi$
$42$	8.30530e15	+	2.53023e15i	0.486253	+	0.148138i
$43$	−1.60054e16	−	2.77222e16i	−0.740599	−	1.28275i	−0.952223	−	0.305404i	$-0.901209\pi$
$43$	−1.60054e16	−	2.77222e16i	−0.740599	−	1.28275i	0.211624	−	0.977351i	$-0.432125\pi$
$44$			9.30496e15i			0.342127i
$45$	3.23790e16	+	2.19998e15i	0.950907	+	0.0646092i
$46$	4.37563e16			1.03148
$47$	3.97355e16	−	2.29413e16i	0.755440	−	0.436153i	−0.0722164	−	0.997389i	$-0.523007\pi$
$47$	3.97355e16	−	2.29413e16i	0.755440	−	0.436153i	0.827656	+	0.561236i	$0.189674\pi$
$48$	−1.10814e16	−	1.18599e16i	−0.170680	−	0.182670i
$49$	1.92788e16	−	3.33919e16i	0.241613	−	0.418486i
$50$	5.47792e15	+	3.16268e15i	0.0560939	+	0.0323858i
$51$	8.57054e13	+	3.69568e14i	0.000719957	+	0.00310450i
$52$	−7.01771e16	−	1.21550e17i	−0.485470	−	0.840858i
$53$		−	1.92375e17i		−	1.10000i	−0.835166	−	0.549998i	$-0.814629\pi$
$53$		−	1.92375e17i		−	1.10000i	0.835166	−	0.549998i	$-0.185371\pi$
$54$	−5.30138e16	+	1.39337e17i	−0.251450	+	0.660888i
$55$	−1.65190e17			−0.652163
$56$	6.67600e16	−	3.85439e16i	0.220108	−	0.127079i
$57$	3.34983e17	−	7.76851e16i	0.925283	−	0.214580i
$58$	2.61447e17	−	4.52840e17i	0.606881	−	1.05115i
$59$	1.73030e17	+	9.98989e16i	0.338533	+	0.195452i	0.659623	−	0.751596i	$-0.270716\pi$
$59$	1.73030e17	+	9.98989e16i	0.338533	+	0.195452i	−0.321090	+	0.947049i	$0.604049\pi$
$60$	2.10547e17	−	1.96727e17i	0.348206	−	0.325350i
$61$	1.72807e17	+	2.99311e17i	0.242250	+	0.419589i	0.961355	−	0.275313i	$-0.0887814\pi$
$61$	1.72807e17	+	2.99311e17i	0.242250	+	0.419589i	−0.719105	+	0.694901i	$0.755448\pi$
$62$		−	2.86328e17i		−	0.341152i
$63$	−5.87769e17	−	3.94771e17i	−0.596762	−	0.400811i
$64$	−1.44115e17			−0.125000
$65$	2.15787e18	−	1.24585e18i	1.60284	−	0.925402i
$66$	2.21143e17	−	7.25887e17i	0.141005	−	0.462839i
$67$	8.47875e17	−	1.46856e18i	0.465140	−	0.805646i	−0.534068	−	0.845442i	$-0.679337\pi$
$67$	8.47875e17	−	1.46856e18i	0.465140	−	0.805646i	0.999208	+	0.0397955i	$0.0126706\pi$
$68$	2.91714e15	+	1.68421e15i	0.00137996	+	0.000796723i
$69$	−3.41346e18	−	1.03992e18i	−1.39542	−	0.425117i
$70$	6.84265e17	+	1.18518e18i	0.242239	+	0.419570i
$71$			1.64941e18i			0.506692i	0.967376	+	0.253346i	$0.0815312\pi$
$71$			1.64941e18i			0.506692i	−0.967376	+	0.253346i	$0.918469\pi$
$72$	5.82605e17	+	1.18856e18i	0.155614	+	0.317465i
$73$	2.42721e18			0.564779			0.282389	−	0.959300i	$-0.408873\pi$
$73$	2.42721e18			0.564779			0.282389	+	0.959300i	$0.408873\pi$
$74$	−4.08446e18	+	2.35817e18i	−0.829503	+	0.478914i
$75$	−3.52172e17	−	3.76912e17i	−0.0625377	−	0.0669310i
$76$	1.52660e18	−	2.64415e18i	0.237460	−	0.411292i
$77$	3.12109e18	+	1.80196e18i	0.425990	+	0.245945i
$78$	2.58579e18	+	1.11501e19i	0.310203	+	1.33762i
$79$	−3.95134e18	−	6.84391e18i	−0.417324	−	0.722826i	0.578346	−	0.815792i	$-0.303699\pi$
$79$	−3.95134e18	−	6.84391e18i	−0.417324	−	0.722826i	−0.995669	+	0.0929661i	$0.970365\pi$
$80$		−	2.55846e18i		−	0.238275i
$81$	7.44715e18	−	9.60983e18i	0.612548	−	0.790434i
$82$	−6.27077e18			−0.456228
$83$	5.73077e18	−	3.30866e18i	0.369345	−	0.213241i	−0.303827	−	0.952727i	$-0.598265\pi$
$83$	5.73077e18	−	3.30866e18i	0.369345	−	0.213241i	0.673172	+	0.739486i	$0.264931\pi$
$84$	−6.12404e18	+	1.42021e18i	−0.350143	+	0.0812007i
$85$	−2.98996e16	+	5.17876e16i	−0.00151871	+	0.00263049i
$86$	2.00730e19	+	1.15892e19i	0.907045	+	0.523682i
$87$	−3.11580e19	+	2.91128e19i	−1.25423	+	1.17190i
$88$	−3.36876e18	−	5.83486e18i	−0.120960	−	0.209509i
$89$			2.07037e19i			0.663969i	0.943285	+	0.331985i	$0.107718\pi$
$89$			2.07037e19i			0.663969i	−0.943285	+	0.331985i	$0.892282\pi$
$90$	−2.11004e19	+	1.03429e19i	−0.605152	+	0.296632i
$91$	−5.43609e19			−1.39596
$92$	−2.74382e19	+	1.58415e19i	−0.631652	+	0.364684i
$93$	−6.80493e18	+	2.23367e19i	−0.140603	+	0.461519i
$94$	−1.66113e19	+	2.87716e19i	−0.308407	+	0.534176i
$95$	4.69412e19	+	2.71015e19i	0.784005	+	0.452645i
$96$	1.12425e19	+	3.42507e18i	0.169103	+	0.0515177i
$97$	−3.43083e19	−	5.94238e19i	−0.465246	−	0.805829i	0.533967	−	0.845505i	$-0.320701\pi$
$97$	−3.43083e19	−	5.94238e19i	−0.465246	−	0.805829i	−0.999213	+	0.0396764i	$0.987367\pi$
$98$			2.79187e19i			0.341692i
$99$	−3.45031e19	+	5.13713e19i	−0.381511	+	0.568027i
$100$	−4.58005e18			−0.0458005
$101$	−7.90037e19	+	4.56128e19i	−0.715210	+	0.412927i	−0.812987	−	0.582282i	$-0.802160\pi$
$101$	−7.90037e19	+	4.56128e19i	−0.715210	+	0.412927i	0.0977771	+	0.995208i	$0.468827\pi$
$102$	−1.87541e17	−	2.00716e17i	−0.00153849	−	0.00164657i
$103$	3.50836e19	−	6.07666e19i	0.261055	−	0.452161i	−0.705468	−	0.708742i	$-0.749263\pi$
$103$	3.50836e19	−	6.07666e19i	0.261055	−	0.452161i	0.966523	+	0.256582i	$0.0825963\pi$
$104$	8.80119e19	+	5.08137e19i	0.594577	+	0.343279i
$105$	−2.52128e19	−	1.08719e20i	−0.154785	−	0.667442i
$106$	6.96473e19	+	1.20633e20i	0.388907	+	0.673607i
$107$		−	3.29090e20i		−	1.67293i	−0.548022	−	0.836464i	$-0.684619\pi$
$107$		−	3.29090e20i		−	1.67293i	0.548022	−	0.836464i	$-0.315381\pi$
$108$	−1.72019e19	−	1.06567e20i	−0.0796782	−	0.493611i
$109$	3.78299e20			1.59798			0.798988	−	0.601347i	$-0.205369\pi$
$109$	3.78299e20			1.59798			0.798988	+	0.601347i	$0.205369\pi$
$110$	1.03585e20	−	5.98051e19i	0.399367	−	0.230574i
$111$	3.74677e20	−	8.68903e19i	1.31955	−	0.306014i
$112$	−2.79088e19	+	4.83394e19i	−0.0898588	+	0.155640i
$113$	1.84937e20	+	1.06774e20i	0.544804	+	0.314543i	0.747024	−	0.664797i	$-0.231482\pi$
$113$	1.84937e20	+	1.06774e20i	0.544804	+	0.314543i	−0.202220	+	0.979340i	$0.564815\pi$
$114$	−1.81933e20	+	1.69991e20i	−0.490752	+	0.458540i
$115$	−2.81231e20	−	4.87107e20i	−0.695161	−	1.20405i
$116$			3.78616e20i			0.858260i
$117$	6.32757e19	−	9.31281e20i	0.131637	−	1.93741i
$118$	−1.44669e20			−0.276411
$119$	1.12984e18	−	6.52315e17i	0.00198403	−	0.00114548i
$120$	−6.08048e19	+	1.99587e20i	−0.0982031	+	0.322345i
$121$	−1.78883e20	+	3.09834e20i	−0.265898	+	0.460548i
$122$	−2.16724e20	−	1.25126e20i	−0.296694	−	0.171296i
$123$	4.89188e20	+	1.49032e20i	0.617198	+	0.188031i
$124$	1.03662e20	+	1.79548e20i	0.120615	+	0.208912i
$125$		−	9.68952e20i		−	1.04040i
$126$	5.11494e20	+	3.47534e19i	0.507149	+	0.0344581i
$127$	−1.86654e20			−0.171002			−0.0855009	−	0.996338i	$-0.527249\pi$
$127$	−1.86654e20			−0.171002			−0.0855009	+	0.996338i	$0.527249\pi$
$128$	9.03702e19	−	5.21753e19i	0.0765466	−	0.0441942i
$129$	−1.29048e21	−	1.38114e21i	−1.01124	−	1.08228i
$130$	−9.02088e20	+	1.56246e21i	−0.654358	+	1.13338i
$131$	7.27585e20	+	4.20071e20i	0.488844	+	0.282234i	0.724095	−	0.689700i	$-0.242258\pi$
$131$	7.27585e20	+	4.20071e20i	0.488844	+	0.282234i	−0.235250	+	0.971935i	$0.575591\pi$
$132$	1.24127e20	+	5.35244e20i	0.0772907	+	0.333283i
$133$	−5.91271e20	−	1.02411e21i	−0.341405	−	0.591331i
$134$			1.22785e21i			0.657807i
$135$	1.89187e21	−	3.05383e20i	0.940920	−	0.151883i
$136$	−2.43900e18			−0.00112674
$137$	−2.47525e20	+	1.42909e20i	−0.106271	+	0.0613554i	−0.552193	−	0.833716i	$-0.686209\pi$
$137$	−2.47525e20	+	1.42909e20i	−0.106271	+	0.0613554i	0.445923	+	0.895071i	$0.352876\pi$
$138$	2.51697e21	−	5.83704e20i	1.00482	−	0.233024i
$139$	−7.91307e20	+	1.37058e21i	−0.293898	+	0.509047i	−0.974728	−	0.223395i	$-0.928286\pi$
$139$	−7.91307e20	+	1.37058e21i	−0.293898	+	0.509047i	0.680830	+	0.732442i	$0.261619\pi$
$140$	−8.58163e20	−	4.95461e20i	−0.296681	−	0.171289i
$141$	1.97965e21	−	1.84970e21i	0.637377	−	0.595541i
$142$	−5.97149e20	−	1.03429e21i	−0.179143	−	0.310285i
$143$			4.75117e21i			1.32874i
$144$	−7.95638e20	−	5.34384e20i	−0.207535	−	0.139389i
$145$	−6.72151e21			−1.63601
$146$	−1.52203e21	+	8.78743e20i	−0.345855	+	0.199679i
$147$	6.63522e20	−	2.17796e21i	0.140826	−	0.462250i
$148$	1.70749e21	−	2.95747e21i	0.338643	−	0.586547i
$149$	1.38226e21	+	7.98048e20i	0.256287	+	0.147968i	0.622640	−	0.782509i	$-0.286060\pi$
$149$	1.38226e21	+	7.98048e20i	0.256287	+	0.147968i	−0.366352	+	0.930476i	$0.619394\pi$
$150$	3.57293e20	+	1.08850e20i	0.0619601	+	0.0188763i
$151$	5.34589e21	+	9.25935e21i	0.867462	+	1.50249i	0.864582	+	0.502492i	$0.167584\pi$
$151$	5.34589e21	+	9.25935e21i	0.867462	+	1.50249i	0.00288045	+	0.999996i	$0.499083\pi$
$152$			2.21075e21i			0.335818i
$153$	9.85997e18	+	2.01151e19i	0.00140269	+	0.00286160i
$154$	−2.60952e21			−0.347819
$155$	−3.18749e21	+	1.84030e21i	−0.398228	+	0.229917i
$156$	−5.65823e21	−	6.05572e21i	−0.662879	−	0.709447i
$157$	−7.77244e21	+	1.34623e22i	−0.854203	+	1.47952i	0.0231800	+	0.999731i	$0.492621\pi$
$157$	−7.77244e21	+	1.34623e22i	−0.854203	+	1.47952i	−0.877383	+	0.479791i	$0.840712\pi$
$158$	4.95552e21	+	2.86107e21i	0.511115	+	0.295092i
$159$	−2.56626e21	−	1.10659e22i	−0.248502	−	1.07156i
$160$	9.26261e20	+	1.60433e21i	0.0842429	+	0.145913i
$161$			1.22712e22i			1.04864i
$162$	−1.19075e21	+	8.72218e21i	−0.0956468	+	0.700608i
$163$	−9.90873e21			−0.748414			−0.374207	−	0.927345i	$-0.622085\pi$
$163$	−9.90873e21			−0.748414			−0.374207	+	0.927345i	$0.622085\pi$
$164$	3.93221e21	−	2.27026e21i	0.279382	−	0.161301i
$165$	−9.50212e21	+	2.20361e21i	−0.635303	+	0.147331i
$166$	−2.39573e21	+	4.14952e21i	−0.150784	+	0.261166i
$167$	2.06954e22	+	1.19485e22i	1.22662	+	0.708189i	0.966321	−	0.257340i	$-0.0828459\pi$
$167$	2.06954e22	+	1.19485e22i	1.22662	+	0.708189i	0.260298	+	0.965528i	$0.416179\pi$
$168$	3.32603e21	−	3.10771e21i	0.185709	−	0.173519i
$169$	−2.63304e22	−	4.56056e22i	−1.38545	−	2.39967i
$170$		−	4.32992e19i		−	0.00214778i
$171$	1.82327e22	−	8.93727e21i	0.852886	−	0.418065i
$172$	−1.67829e22			−0.740599
$173$	2.93179e22	−	1.69267e22i	1.22088	−	0.704874i	0.255773	−	0.966737i	$-0.417670\pi$
$173$	2.93179e22	−	1.69267e22i	1.22088	−	0.704874i	0.965105	+	0.261863i	$0.0843367\pi$
$174$	8.99825e21	−	2.95361e22i	0.353725	−	1.16108i
$175$	−8.86953e20	+	1.53625e21i	−0.0329246	+	0.0570270i
$176$	4.22489e21	+	2.43924e21i	0.148146	+	0.0855318i
$177$	1.12857e22	+	3.43823e21i	0.373936	+	0.113921i
$178$	−7.49554e21	−	1.29827e22i	−0.234749	−	0.406596i
$179$			3.68224e22i			1.09039i	0.838310	+	0.545194i	$0.183544\pi$
$179$			3.68224e22i			1.09039i	−0.838310	+	0.545194i	$0.816456\pi$
$180$	9.48685e21	−	1.41249e22i	0.265703	−	0.395603i
$181$	4.47850e21			0.118672			0.0593358	−	0.998238i	$-0.481102\pi$
$181$	4.47850e21			0.118672			0.0593358	+	0.998238i	$0.481102\pi$
$182$	3.40881e22	−	1.96807e22i	0.854847	−	0.493546i
$183$	1.39331e22	+	1.49119e22i	0.330777	+	0.354014i
$184$	1.14704e22	−	1.98674e22i	0.257871	−	0.446645i
$185$	5.25035e22	+	3.03129e22i	1.11808	+	0.645521i
$186$	−3.81959e21	−	1.64703e22i	−0.0770703	−	0.332332i
$187$	−5.70126e19	−	9.87488e19i	−0.00109032	−	0.00188849i
$188$		−	2.40557e22i		−	0.436153i
$189$	−3.90761e22	−	1.48674e22i	−0.671882	−	0.255633i
$190$	−3.92472e22			−0.640137
$191$	−7.01989e22	+	4.05293e22i	−1.08642	+	0.627243i	−0.932620	−	0.360860i	$-0.882483\pi$
$191$	−7.01989e22	+	4.05293e22i	−1.08642	+	0.627243i	−0.153796	+	0.988103i	$0.549150\pi$
$192$	−8.28986e21	+	1.92248e21i	−0.121768	+	0.0282390i
$193$	−1.00068e21	+	1.73323e21i	−0.0139547	+	0.0241703i	−0.872918	−	0.487866i	$-0.837775\pi$
$193$	−1.00068e21	+	1.73323e21i	−0.0139547	+	0.0241703i	0.858964	+	0.512036i	$0.171109\pi$
$194$	4.30274e22	+	2.48419e22i	0.569807	+	0.328978i
$195$	1.07506e23	−	1.00450e23i	1.35235	−	1.26358i
$196$	−1.01077e22	−	1.75070e22i	−0.120806	−	0.209243i
$197$			8.05945e22i			0.915468i	0.889089	+	0.457734i	$0.151339\pi$
$197$			8.05945e22i			0.915468i	−0.889089	+	0.457734i	$0.848661\pi$
$198$	3.03746e21	−	4.47048e22i	0.0327989	−	0.482728i
$199$	−1.38061e23			−1.41755			−0.708777	−	0.705432i	$-0.750753\pi$
$199$	−1.38061e23			−1.41755			−0.708777	+	0.705432i	$0.750753\pi$
$200$	2.87201e21	−	1.65815e21i	0.0280469	−	0.0161929i
$201$	2.91814e22	−	9.57858e22i	0.271110	−	0.889899i
$202$	3.30272e22	−	5.72048e22i	0.291983	−	0.505730i
$203$	1.26996e23	+	7.33212e22i	1.06864	+	0.616977i
$204$	1.90268e20	+	5.79657e19i	0.00152428	+	0.000464375i
$205$	4.03036e22	+	6.98079e22i	0.307472	+	0.532557i
$206$			5.08065e22i			0.369188i
$207$	−2.10223e23	−	1.42836e22i	−1.45538	−	0.0988856i
$208$	−7.35861e22			−0.485470
$209$	−8.95078e22	+	5.16774e22i	−0.562857	+	0.324966i
$210$	5.51708e22	+	5.90465e22i	0.330762	+	0.353998i
$211$	−1.49292e23	+	2.58582e23i	−0.853518	+	1.47834i	0.0244957	+	0.999700i	$0.492202\pi$
$211$	−1.49292e23	+	2.58582e23i	−0.853518	+	1.47834i	−0.878013	+	0.478636i	$0.841131\pi$
$212$	−8.73474e22	−	5.04300e22i	−0.476312	−	0.274999i
$213$	2.20029e22	+	9.48780e22i	0.114468	+	0.493593i
$214$	1.19143e23	+	2.06362e23i	0.591469	+	1.02445i
$215$		−	2.97945e23i		−	1.41173i
$216$	4.93681e22	+	6.05970e22i	0.223310	+	0.274103i
$217$	8.02990e22			0.346827
$218$	−2.37220e23	+	1.36959e23i	−0.978557	+	0.564970i
$219$	1.39619e23	−	3.23786e22i	0.550178	−	0.127590i
$220$	−4.33035e22	+	7.50039e22i	−0.163041	+	0.282395i
$221$	1.48951e21	+	8.59968e20i	0.00535945	+	0.00309428i
$222$	−2.03491e23	+	1.90134e23i	−0.699866	+	0.653927i
$223$	−1.05274e23	−	1.82340e23i	−0.346156	−	0.599560i	0.639407	−	0.768868i	$-0.279180\pi$
$223$	−1.05274e23	−	1.82340e23i	−0.346156	−	0.599560i	−0.985563	+	0.169308i	$0.945847\pi$
$224$		−	4.04162e22i		−	0.127079i
$225$	−2.52858e22	−	1.69830e22i	−0.0760415	−	0.0510727i
$226$	−1.54625e23			−0.444831
$227$	−1.98296e23	+	1.14486e23i	−0.545828	+	0.315134i	−0.747437	−	0.664332i	$-0.768716\pi$
$227$	−1.98296e23	+	1.14486e23i	−0.545828	+	0.315134i	0.201610	+	0.979466i	$0.435383\pi$
$228$	5.25412e22	−	1.72463e23i	0.138405	−	0.454304i
$229$	−4.16162e22	+	7.20814e22i	−0.104932	+	0.181748i	−0.913710	−	0.406366i	$-0.866796\pi$
$229$	−4.16162e22	+	7.20814e22i	−0.104932	+	0.181748i	0.808778	+	0.588113i	$0.200129\pi$
$230$	3.52703e23	+	2.03633e23i	0.851395	+	0.491553i
$231$	2.03571e23	+	6.20183e22i	0.470539	+	0.143351i
$232$	−1.37074e23	−	2.37418e23i	−0.303441	−	0.525575i
$233$		−	2.77285e23i		−	0.587987i	−0.955807	−	0.293993i	$-0.905016\pi$
$233$		−	2.77285e23i		−	0.587987i	0.955807	−	0.293993i	$-0.0949844\pi$
$234$	2.97481e23	+	6.06886e23i	0.604368	+	1.23296i
$235$	4.27057e23			0.831395
$236$	9.07175e22	−	5.23758e22i	0.169267	−	0.0977261i
$237$	−3.18587e23	−	3.40968e23i	−0.569830	−	0.609861i
$238$	−4.72326e20	+	8.18093e20i	−0.000809977	+	0.00140292i
$239$	−4.54167e23	−	2.62214e23i	−0.746856	−	0.431198i	0.0777008	−	0.996977i	$-0.475242\pi$
$239$	−4.54167e23	−	2.62214e23i	−0.746856	−	0.431198i	−0.824557	+	0.565779i	$0.808575\pi$
$240$	−3.41295e22	−	1.47169e23i	−0.0538292	−	0.232115i
$241$	3.99458e23	+	6.91882e23i	0.604367	+	1.04680i	0.992151	+	0.125045i	$0.0399074\pi$
$241$	3.99458e23	+	6.91882e23i	0.604367	+	1.04680i	−0.387784	+	0.921750i	$0.626759\pi$
$242$		−	2.59050e23i		−	0.376036i
$243$	3.00184e23	−	6.52125e23i	0.418143	−	0.908381i
$244$	1.81201e23			0.242250
$245$	3.10799e23	−	1.79440e23i	0.398859	−	0.230281i
$246$	−3.60710e23	+	8.36513e22i	−0.444434	+	0.103067i
$247$	7.79491e23	−	1.35012e24i	0.922235	−	1.59736i
$248$	−1.30006e23	−	7.50593e22i	−0.147723	−	0.0852879i
$249$	2.85511e23	−	2.66770e23i	0.311623	−	0.291168i
$250$	3.50798e23	+	6.07600e23i	0.367839	+	0.637115i
$251$		−	3.13007e23i		−	0.315367i	−0.987490	−	0.157684i	$-0.949597\pi$
$251$		−	3.13007e23i		−	0.315367i	0.987490	−	0.157684i	$-0.0504026\pi$
$252$	−3.33324e23	+	1.63388e23i	−0.322747	+	0.158203i
$253$	1.07251e24			0.998148
$254$	1.17045e23	−	6.75761e22i	0.104717	−	0.0604583i
$255$	−1.02906e21	+	3.37780e21i	−0.000885192	+	0.00290558i
$256$	−3.77789e22	+	6.54350e22i	−0.0312500	+	0.0541266i
$257$	−7.85091e23	−	4.53273e23i	−0.624581	−	0.360602i	0.154069	−	0.988060i	$-0.450762\pi$
$257$	−7.85091e23	−	4.53273e23i	−0.624581	−	0.360602i	−0.778650	+	0.627458i	$0.784095\pi$
$258$	1.30925e24	+	3.98866e23i	1.00190	+	0.305232i
$259$	−6.61333e23	−	1.14546e24i	−0.486881	−	0.843302i
$260$		−	1.30636e24i		−	0.925402i
$261$	−1.40392e24	+	2.09028e24i	−0.957057	+	1.42495i
$262$	−6.08328e23			−0.399140
$263$	−2.16759e24	+	1.25146e24i	−1.36905	+	0.790424i	−0.990807	−	0.135281i	$-0.956806\pi$
$263$	−2.16759e24	+	1.25146e24i	−1.36905	+	0.790424i	−0.378247	+	0.925705i	$0.623473\pi$
$264$	−2.71615e23	−	2.90696e23i	−0.165164	−	0.176767i
$265$	8.95278e23	−	1.55067e24i	0.524203	−	0.907945i
$266$	7.41536e23	+	4.28126e23i	0.418134	+	0.241410i
$267$	2.76185e23	+	1.19093e24i	0.149999	+	0.646804i
$268$	−4.44531e23	−	7.69950e23i	−0.232570	−	0.402823i
$269$		−	1.00011e24i		−	0.504111i	−0.967713	−	0.252055i	$-0.918894\pi$
$269$		−	1.00011e24i		−	0.504111i	0.967713	−	0.252055i	$-0.0811065\pi$
$270$	−1.07577e24	+	8.76425e23i	−0.522495	+	0.425674i
$271$	2.64771e24			1.23930			0.619652	−	0.784877i	$-0.287274\pi$
$271$	2.64771e24			1.23930			0.619652	+	0.784877i	$0.287274\pi$
$272$	1.52942e21	−	8.83011e20i	0.000689982	−	0.000398361i
$273$	−3.12697e24	+	7.25168e23i	−1.35987	+	0.315364i
$274$	1.03477e23	−	1.79227e23i	0.0433848	−	0.0751447i
$275$	1.34269e23	+	7.75201e22i	0.0542811	+	0.0313392i
$276$	−1.36699e24	+	1.27726e24i	−0.532936	+	0.497954i
$277$	1.13286e24	+	1.96217e24i	0.425969	+	0.737801i	0.996510	−	0.0834684i	$-0.0265998\pi$
$277$	1.13286e24	+	1.96217e24i	0.425969	+	0.737801i	−0.570541	+	0.821269i	$0.693266\pi$
$278$		−	1.14594e24i		−	0.415635i
$279$	−9.34674e22	+	1.37564e24i	−0.0327053	+	0.481352i
$280$	7.17504e23			0.242239
$281$	3.41626e24	−	1.97238e24i	1.11298	−	0.642580i	0.173381	−	0.984855i	$-0.444531\pi$
$281$	3.41626e24	−	1.97238e24i	1.11298	−	0.642580i	0.939600	+	0.342275i	$0.111197\pi$
$282$	−5.71712e23	+	1.87660e24i	−0.179757	+	0.590040i
$283$	−1.10356e24	+	1.91142e24i	−0.334911	+	0.580084i	−0.983468	−	0.181083i	$-0.942040\pi$
$283$	−1.10356e24	+	1.91142e24i	−0.334911	+	0.580084i	0.648556	+	0.761167i	$0.275373\pi$
$284$	7.48908e23	+	4.32382e23i	0.219404	+	0.126673i
$285$	3.06171e24	+	9.32757e23i	0.865994	+	0.263827i
$286$	−1.72011e24	−	2.97931e24i	−0.469781	−	0.813684i
$287$		−	1.75860e24i		−	0.463818i
$288$	6.92388e23	+	4.70442e22i	0.176370	+	0.0119834i
$289$	4.06419e24			0.999990
$290$	4.21486e24	−	2.43345e24i	1.00185	−	0.578418i
$291$	−2.76620e24	−	2.96053e24i	−0.635264	−	0.679892i
$292$	6.36278e23	−	1.10207e24i	0.141195	−	0.244556i
$293$	−2.90622e24	−	1.67791e24i	−0.623236	−	0.359825i	0.154892	−	0.987931i	$-0.450497\pi$
$293$	−2.90622e24	−	1.67791e24i	−0.623236	−	0.359825i	−0.778128	+	0.628106i	$0.783830\pi$
$294$	3.72433e23	+	1.60595e24i	0.0771924	+	0.332859i
$295$	9.29820e23	+	1.61050e24i	0.186285	+	0.322656i
$296$			2.47272e24i			0.478914i
$297$	−1.29942e24	+	3.41527e24i	−0.243324	+	0.639530i
$298$	−1.15570e24			−0.209258
$299$	−1.40101e25	+	8.08875e24i	−2.45318	+	1.41635i
$300$	−2.63455e23	+	6.10973e22i	−0.0446164	+	0.0103469i
$301$	−3.25011e24	+	5.62936e24i	−0.532394	+	0.922134i
$302$	−6.70449e24	−	3.87084e24i	−1.06242	−	0.613388i
$303$	−3.93602e24	+	3.67766e24i	−0.603435	+	0.563826i
$304$	−8.00379e23	−	1.38630e24i	−0.118730	−	0.205646i
$305$			3.21684e24i			0.461776i
$306$	−1.34653e22	−	9.04389e21i	−0.00187070	−	0.00125644i
$307$	−2.48095e24			−0.333606			−0.166803	−	0.985990i	$-0.553344\pi$
$307$	−2.48095e24			−0.333606			−0.166803	+	0.985990i	$0.553344\pi$
$308$	1.63635e24	−	9.44747e23i	0.212995	−	0.122973i
$309$	1.20748e24	−	3.96346e24i	0.152158	−	0.499447i
$310$	1.33252e24	−	2.30799e24i	0.162576	−	0.281590i
$311$	1.29608e25	+	7.48290e24i	1.53118	+	0.884028i	0.999308	+	0.0372043i	$0.0118452\pi$
$311$	1.29608e25	+	7.48290e24i	1.53118	+	0.884028i	0.531874	+	0.846824i	$0.321488\pi$
$312$	5.74051e24	+	1.74886e24i	0.656756	+	0.200082i
$313$	8.08425e24	+	1.40023e25i	0.895770	+	1.55152i	0.832849	+	0.553501i	$0.186708\pi$
$313$	8.08425e24	+	1.40023e25i	0.895770	+	1.55152i	0.0629215	+	0.998018i	$0.479958\pi$
$314$		−	1.12557e25i		−	1.20803i
$315$	−2.90060e24	−	5.91746e24i	−0.301566	−	0.615219i
$316$	−4.14328e24			−0.417324
$317$	−1.36062e25	+	7.85553e24i	−1.32783	+	0.766625i	−0.984964	−	0.172759i	$-0.944732\pi$
$317$	−1.36062e25	+	7.85553e24i	−1.32783	+	0.766625i	−0.342868	+	0.939383i	$0.611399\pi$
$318$	5.61551e24	+	6.01000e24i	0.531029	+	0.568334i
$319$	6.40831e24	−	1.10995e25i	0.587268	−	1.01718i
$320$	−1.16166e24	−	6.70684e23i	−0.103176	−	0.0595687i
$321$	−4.39002e24	−	1.89301e25i	−0.377934	−	1.62968i
$322$	−4.44264e24	−	7.69488e24i	−0.370751	−	0.642160i
$323$			3.74147e22i			0.00302703i
$324$	−2.41109e24	−	5.90051e24i	−0.189131	−	0.462849i
$325$	−2.33860e24			−0.177878
$326$	6.21346e24	−	3.58734e24i	0.458308	−	0.264604i
$327$	2.17607e25	−	5.04646e24i	1.55666	−	0.361002i
$328$	−1.64384e24	+	2.84722e24i	−0.114057	+	0.197553i
$329$	−8.06880e24	−	4.65853e24i	−0.543063	−	0.313538i
$330$	5.16070e24	−	4.82195e24i	0.336953	−	0.314835i
$331$	5.27671e24	+	9.13953e24i	0.334259	+	0.578954i	0.983342	−	0.181764i	$-0.0581806\pi$
$331$	5.27671e24	+	9.13953e24i	0.334259	+	0.578954i	−0.649083	+	0.760717i	$0.724847\pi$
$332$		−	3.46938e24i		−	0.213241i
$333$	2.03932e25	−	9.99628e24i	1.21631	−	0.596206i
$334$	−1.73033e25			−1.00153
$335$	1.36688e25	−	7.89169e24i	0.767861	−	0.443325i
$336$	−9.60539e23	+	3.15290e24i	−0.0523748	+	0.171916i
$337$	1.21766e25	−	2.10905e25i	0.644506	−	1.11632i	−0.339910	−	0.940458i	$-0.610397\pi$
$337$	1.21766e25	−	2.10905e25i	0.644506	−	1.11632i	0.984415	−	0.175858i	$-0.0562701\pi$
$338$	3.30219e25	+	1.90652e25i	1.69682	+	0.979659i
$339$	1.20624e25	+	3.67484e24i	0.601779	+	0.183333i
$340$	1.56760e22	+	2.71516e22i	0.000759356	+	0.00131524i
$341$		−	7.01818e24i		−	0.330127i
$342$	−8.19756e24	+	1.22052e25i	−0.374475	+	0.557552i
$343$	−2.40325e25			−1.06625
$344$	1.05241e25	−	6.07606e24i	0.453522	−	0.261841i
$345$	−2.26751e25	−	2.42680e25i	−0.949200	−	1.01588i
$346$	−1.22563e25	+	2.12285e25i	−0.498421	+	0.863291i
$347$	−1.69796e24	−	9.80315e23i	−0.0670859	−	0.0387321i	0.466082	−	0.884742i	$-0.345665\pi$
$347$	−1.69796e24	−	9.80315e23i	−0.0670859	−	0.0387321i	−0.533168	+	0.846010i	$0.678999\pi$
$348$	5.05069e24	+	2.17789e25i	0.193891	+	0.836072i
$349$	1.01008e25	+	1.74951e25i	0.376792	+	0.652623i	0.990594	−	0.136837i	$-0.0436937\pi$
$349$	1.01008e25	+	1.74951e25i	0.376792	+	0.652623i	−0.613801	+	0.789461i	$0.710360\pi$
$350$		−	1.28445e24i		−	0.0465624i
$351$	−8.78340e24	−	5.44136e25i	−0.309451	−	1.91706i
$352$	−3.53240e24			−0.120960
$353$	−4.88442e24	+	2.82002e24i	−0.162580	+	0.0938654i	−0.579082	−	0.815269i	$-0.696589\pi$
$353$	−4.88442e24	+	2.82002e24i	−0.162580	+	0.0938654i	0.416503	+	0.909135i	$0.363256\pi$
$354$	−8.32172e24	+	1.92987e24i	−0.269265	+	0.0624446i
$355$	−7.67602e24	+	1.32953e25i	−0.241464	+	0.418228i
$356$	9.40045e24	+	5.42735e24i	0.287507	+	0.165992i
$357$	5.62895e22	−	5.25947e22i	0.00167396	−	0.00156408i
$358$	−1.33311e25	−	2.30902e25i	−0.385511	−	0.667724i
$359$			4.06417e25i			1.14295i	0.820619	+	0.571476i	$0.193629\pi$
$359$			4.06417e25i			1.14295i	−0.820619	+	0.571476i	$0.806371\pi$
$360$	−8.35169e23	+	1.22919e25i	−0.0228428	+	0.336197i
$361$	−3.67658e24			−0.0978075
$362$	−2.80833e24	+	1.62139e24i	−0.0726713	+	0.0419568i
$363$	−6.15662e24	+	2.02087e25i	−0.154980	+	0.508712i
$364$	−1.42504e25	+	2.46824e25i	−0.348990	+	0.604468i
$365$	1.95648e25	+	1.12958e25i	0.466173	+	0.269145i
$366$	−1.41357e25	−	4.30646e24i	−0.327722	−	0.0998412i
$367$	−2.64242e25	−	4.57680e25i	−0.596129	−	1.03253i	−0.993386	−	0.114819i	$-0.963371\pi$
$367$	−2.64242e25	−	4.57680e25i	−0.596129	−	1.03253i	0.397257	−	0.917707i	$-0.369962\pi$
$368$			1.66110e25i			0.364684i
$369$	3.01273e25	+	2.04699e24i	0.643720	+	0.0437374i
$370$	−4.38978e25			−0.912905
$371$	−3.38307e25	+	1.95322e25i	−0.684813	+	0.395377i
$372$	8.35804e24	+	8.94519e24i	0.164693	+	0.176263i
$373$	−9.66169e24	+	1.67345e25i	−0.185338	+	0.321015i	−0.943690	−	0.330830i	$-0.892671\pi$
$373$	−9.66169e24	+	1.67345e25i	−0.185338	+	0.321015i	0.758352	+	0.651845i	$0.226005\pi$
$374$	7.15018e22	+	4.12816e22i	0.00133537	+	0.000770975i
$375$	−1.29257e25	−	5.57365e25i	−0.235040	−	1.01351i
$376$	8.70909e24	+	1.50846e25i	0.154203	+	0.267088i
$377$			1.93323e26i			3.33327i
$378$	2.98860e25	−	4.82417e24i	0.501822	−	0.0810037i
$379$	1.30273e25			0.213040			0.106520	−	0.994311i	$-0.466029\pi$
$379$	1.30273e25			0.213040			0.106520	+	0.994311i	$0.466029\pi$
$380$	2.46107e25	−	1.42090e25i	0.392002	−	0.226323i
$381$	−1.07368e25	+	2.48995e24i	−0.166581	+	0.0386314i
$382$	2.93464e25	−	5.08294e25i	0.443528	−	0.768213i
$383$	−8.26639e25	−	4.77260e25i	−1.21711	−	0.702696i	−0.252808	−	0.967516i	$-0.581354\pi$
$383$	−8.26639e25	−	4.77260e25i	−1.21711	−	0.702696i	−0.964298	+	0.264820i	$0.914687\pi$
$384$	4.50230e24	−	4.20678e24i	0.0645837	−	0.0603444i
$385$	1.67720e25	+	2.90499e25i	0.234410	+	0.406010i
$386$		−	1.44914e24i		−	0.0197350i
$387$	−9.26560e25	−	6.22317e25i	−1.22960	−	0.825851i
$388$	−3.59749e25			−0.465246
$389$	1.21827e26	−	7.03370e25i	1.53549	−	0.886518i	0.536401	−	0.843964i	$-0.319784\pi$
$389$	1.21827e26	−	7.03370e25i	1.53549	−	0.886518i	0.999094	−	0.0425548i	$-0.0135497\pi$
$390$	−3.10473e25	+	1.01910e26i	−0.381397	+	1.25191i
$391$	1.94125e23	−	3.36235e23i	0.00232442	−	0.00402601i
$392$	1.26764e25	+	7.31873e24i	0.147957	+	0.0854230i
$393$	4.74562e25	+	1.44576e25i	0.539967	+	0.164502i
$394$	−2.91783e25	−	5.05384e25i	−0.323667	−	0.560608i
$395$		−	7.35550e25i		−	0.795502i
$396$	1.42802e25	+	2.91327e25i	0.150585	+	0.307206i
$397$	−4.67383e25			−0.480583			−0.240291	−	0.970701i	$-0.577243\pi$
$397$	−4.67383e25			−0.480583			−0.240291	+	0.970701i	$0.577243\pi$
$398$	8.65737e25	−	4.99834e25i	0.868072	−	0.501181i
$399$	−4.76729e25	−	5.10219e25i	−0.466168	−	0.498916i
$400$	−1.20063e24	+	2.07955e24i	−0.0114501	+	0.0198322i
$401$	9.15282e25	+	5.28438e25i	0.851356	+	0.491531i	0.861108	−	0.508422i	$-0.169771\pi$
$401$	9.15282e25	+	5.28438e25i	0.851356	+	0.491531i	−0.00975206	+	0.999952i	$0.503104\pi$
$402$	1.63794e25	+	7.06292e25i	0.148607	+	0.640802i
$403$	5.29304e25	+	9.16782e25i	0.468441	+	0.811363i
$404$			4.78285e25i			0.412927i
$405$	1.04751e26	−	4.28037e25i	0.882283	−	0.360521i
$406$	−1.06180e26			−0.872538
$407$	−1.00114e26	+	5.78008e25i	−0.802695	+	0.463436i
$408$	−1.40297e23	+	3.25359e22i	−0.00109761	+	0.000254543i
$409$	7.54698e25	−	1.30718e26i	0.576156	−	0.997932i	−0.419759	−	0.907636i	$-0.637885\pi$
$409$	7.54698e25	−	1.30718e26i	0.576156	−	0.997932i	0.995915	−	0.0902960i	$-0.0287813\pi$
$410$	−5.05463e25	−	2.91829e25i	−0.376575	−	0.217416i
$411$	−1.23319e25	+	1.15224e25i	−0.0896624	+	0.0837770i
$412$	−1.83939e25	−	3.18592e25i	−0.130528	−	0.226080i
$413$		−	4.05715e25i		−	0.281009i
$414$	1.36996e26	−	6.71521e25i	0.926197	−	0.454000i
$415$	6.15915e25			0.406481
$416$	4.61436e25	−	2.66410e25i	0.297288	−	0.171639i
$417$	−2.72345e25	+	8.93953e25i	−0.171301	+	0.562282i
$418$	3.74184e25	−	6.48106e25i	0.229785	−	0.398000i
$419$	−1.03425e26	−	5.97123e25i	−0.620132	−	0.358034i	0.156788	−	0.987632i	$-0.449886\pi$
$419$	−1.03425e26	−	5.97123e25i	−0.620132	−	0.358034i	−0.776921	+	0.629599i	$0.783219\pi$
$420$	−5.59730e25	−	1.70523e25i	−0.327707	−	0.0998368i
$421$	5.21835e25	+	9.03844e25i	0.298340	+	0.516741i	0.975756	−	0.218860i	$-0.0702336\pi$
$421$	5.21835e25	+	9.03844e25i	0.298340	+	0.516741i	−0.677416	+	0.735600i	$0.736900\pi$
$422$		−	2.16198e26i		−	1.20706i
$423$	8.91993e25	−	1.32808e26i	0.486360	−	0.724136i
$424$	7.30305e25			0.388907
$425$	4.86057e22	−	2.80625e22i	0.000252812	−	0.000145961i
$426$	−4.81468e25	−	5.15292e25i	−0.244609	−	0.261792i
$427$	3.50907e25	−	6.07789e25i	0.174146	−	0.301630i
$428$	−1.49422e26	−	8.62690e25i	−0.724399	−	0.418232i
$429$	6.33800e25	+	2.73299e26i	0.300178	+	1.29439i
$430$	1.07868e26	+	1.86832e26i	0.499122	+	0.864504i
$431$		−	1.99933e26i		−	0.903880i	−0.892048	−	0.451940i	$-0.850732\pi$
$431$		−	1.99933e26i		−	0.903880i	0.892048	−	0.451940i	$-0.149268\pi$
$432$	−5.28957e25	−	2.01254e25i	−0.233659	−	0.0889010i
$433$	3.57117e26			1.54146			0.770728	−	0.637164i	$-0.219893\pi$
$433$	3.57117e26			1.54146			0.770728	+	0.637164i	$0.219893\pi$
$434$	−5.03531e25	+	2.90714e25i	−0.212387	+	0.122622i
$435$	−3.86638e26	+	8.96642e25i	−1.59372	+	0.369595i
$436$	9.91688e25	−	1.71765e26i	0.399494	−	0.691944i
$437$	−3.04770e26	−	1.75959e26i	−1.19993	−	0.692782i
$438$	−7.58284e25	+	7.08511e25i	−0.291804	+	0.272650i
$439$	9.20050e25	+	1.59357e26i	0.346072	+	0.599414i	0.985548	−	0.169397i	$-0.0541820\pi$
$439$	9.20050e25	+	1.59357e26i	0.346072	+	0.599414i	−0.639476	+	0.768811i	$0.720849\pi$
$440$		−	6.27102e25i		−	0.230574i
$441$	9.11364e24	−	1.34133e26i	0.0327571	−	0.482114i
$442$	−1.24537e24			−0.00437597
$443$	−5.76151e25	+	3.32641e25i	−0.197924	+	0.114272i	−0.595687	−	0.803217i	$-0.703120\pi$
$443$	−5.76151e25	+	3.32641e25i	−0.197924	+	0.114272i	0.397763	+	0.917488i	$0.369787\pi$
$444$	5.87670e25	−	1.92899e26i	0.197380	−	0.647887i
$445$	−9.63510e25	+	1.66885e26i	−0.316414	+	0.548046i
$446$	1.32028e26	+	7.62264e25i	0.423953	+	0.244769i
$447$	9.01569e25	+	2.74665e25i	0.283089	+	0.0862439i
$448$	1.46322e25	+	2.53438e25i	0.0449294	+	0.0778200i
$449$			3.84470e26i			1.15451i	0.816562	+	0.577257i	$0.195877\pi$
$449$			3.84470e26i			1.15451i	−0.816562	+	0.577257i	$0.804123\pi$
$450$	2.20044e25	+	1.49508e24i	0.0646226	+	0.00439077i
$451$	−1.53702e26			−0.441484
$452$	9.69605e25	−	5.59802e25i	0.272402	−	0.157271i
$453$	4.31027e26	+	4.61307e26i	1.18447	+	1.26768i
$454$	8.28969e25	−	1.43582e26i	0.222833	−	0.385958i
$455$	−4.38183e26	−	2.52985e26i	−1.15224	−	0.665244i
$456$	2.94912e25	+	1.27168e26i	0.0758654	+	0.327137i
$457$	2.66193e26	+	4.61059e26i	0.669937	+	1.16036i	0.977921	+	0.208973i	$0.0670122\pi$
$457$	2.66193e26	+	4.61059e26i	0.669937	+	1.16036i	−0.307984	+	0.951391i	$0.599654\pi$
$458$		−	6.02668e25i		−	0.148396i
$459$	8.35503e23	+	1.02554e24i	0.00201290	+	0.00247073i
$460$	−2.94893e26			−0.695161
$461$	−5.28822e26	+	3.05315e26i	−1.21983	+	0.704270i	−0.964882	−	0.262684i	$-0.915392\pi$
$461$	−5.28822e26	+	3.05315e26i	−1.21983	+	0.704270i	−0.254950	+	0.966954i	$0.582059\pi$
$462$	−1.50106e26	+	3.48107e25i	−0.338827	+	0.0785765i
$463$	1.07592e26	−	1.86354e26i	0.237667	−	0.411652i	−0.722377	−	0.691499i	$-0.756951\pi$
$463$	1.07592e26	−	1.86354e26i	0.237667	−	0.411652i	0.960044	+	0.279847i	$0.0902839\pi$
$464$	1.71909e26	+	9.92519e25i	0.371637	+	0.214565i
$465$	−1.58803e26	+	1.48379e26i	−0.335992	+	0.313937i
$466$	1.00388e26	+	1.73877e26i	0.207885	+	0.360067i
$467$		−	5.22646e26i		−	1.05935i	−0.848201	−	0.529674i	$-0.822314\pi$
$467$		−	5.22646e26i		−	1.05935i	0.848201	−	0.529674i	$-0.177686\pi$
$468$	−4.06258e26	−	2.72860e26i	−0.806015	−	0.541354i
$469$	−3.44344e26			−0.668751
$470$	−2.67794e26	+	1.54611e26i	−0.509123	+	0.293943i
$471$	−2.67505e26	+	8.78066e26i	−0.497878	+	1.63425i
$472$	−3.79241e25	+	6.56865e25i	−0.0691028	+	0.119690i
$473$	4.92009e26	+	2.84061e26i	0.877731	+	0.506758i
$474$	3.23220e26	+	9.84698e25i	0.564566	+	0.171997i
$475$	−2.54364e25	−	4.40571e25i	−0.0435030	−	0.0753494i
$476$		−	6.84002e23i		−	0.00114548i
$477$	−2.95236e26	−	6.02304e26i	−0.484156	−	0.987716i
$478$	3.79726e26			0.609805
$479$	7.03249e26	−	4.06021e26i	1.10600	−	0.638548i	0.168207	−	0.985752i	$-0.446202\pi$
$479$	7.03249e26	−	4.06021e26i	1.10600	−	0.638548i	0.937790	+	0.347204i	$0.112869\pi$
$480$	7.46823e25	+	7.99288e25i	0.115029	+	0.123109i
$481$	8.71857e26	−	1.51010e27i	1.31521	−	2.27801i
$482$	−5.00976e26	−	2.89239e26i	−0.740196	−	0.427352i
$483$	1.63696e26	+	7.05868e26i	0.236901	+	1.02153i
$484$	9.37860e25	+	1.62442e26i	0.132949	+	0.230274i
$485$		−	6.38657e26i		−	0.886851i
$486$	4.78580e25	+	5.17606e26i	0.0651016	+	0.704104i
$487$	−1.06366e27			−1.41747			−0.708735	−	0.705474i	$-0.750734\pi$
$487$	−1.06366e27			−1.41747			−0.708735	+	0.705474i	$0.750734\pi$
$488$	−1.13626e26	+	6.56019e25i	−0.148347	+	0.0856482i
$489$	−5.69975e26	+	1.32181e26i	−0.729066	+	0.169076i
$490$	−1.29928e26	+	2.25043e26i	−0.162833	+	0.282036i
$491$	6.01006e26	+	3.46991e26i	0.738012	+	0.426092i	0.821346	−	0.570430i	$-0.193223\pi$
$491$	6.01006e26	+	3.46991e26i	0.738012	+	0.426092i	−0.0833339	+	0.996522i	$0.526557\pi$
$492$	1.95905e26	−	1.83046e26i	0.235719	−	0.220247i
$493$	−2.31983e24	−	4.01806e24i	−0.00273518	−	0.00473747i
$494$			1.12882e27i			1.30424i
$495$	−5.17189e26	+	2.53514e26i	−0.585595	+	0.287045i
$496$	1.08697e26			0.120615
$497$	2.90061e26	−	1.67467e26i	0.315446	−	0.182123i
$498$	−8.24540e25	+	2.70649e26i	−0.0878857	+	0.288479i
$499$	2.24828e26	−	3.89414e26i	0.234880	−	0.406824i	−0.724358	−	0.689424i	$-0.757864\pi$
$499$	2.24828e26	−	3.89414e26i	0.234880	−	0.406824i	0.959238	+	0.282600i	$0.0911971\pi$
$500$	−4.39950e26	−	2.54005e26i	−0.450508	−	0.260101i
$501$	1.34984e27	+	4.11233e26i	1.35490	+	0.412772i
$502$	1.13321e26	+	1.96277e26i	0.111499	+	0.193122i
$503$			3.04565e26i			0.293765i	0.989154	+	0.146882i	$0.0469239\pi$
$503$			3.04565e26i			0.293765i	−0.989154	+	0.146882i	$0.953076\pi$
$504$	1.49865e26	−	2.23132e26i	0.141708	−	0.210987i
$505$	−8.49093e26			−0.787121
$506$	−6.72536e26	+	3.88289e26i	−0.611238	+	0.352899i
$507$	−2.12296e27	−	2.27210e27i	−1.89174	−	2.02464i
$508$	−4.89303e25	+	8.47498e25i	−0.0427505	+	0.0740460i
$509$	8.90992e26	+	5.14414e26i	0.763301	+	0.440692i	0.830480	−	0.557049i	$-0.188066\pi$
$509$	8.90992e26	+	5.14414e26i	0.763301	+	0.440692i	−0.0671788	+	0.997741i	$0.521400\pi$
$510$	−5.77606e23	−	2.49068e24i	−0.000485210	−	0.00209226i
$511$	−2.46438e26	−	4.26843e26i	−0.203001	−	0.351608i
$512$		−	5.47097e25i		−	0.0441942i
$513$	9.29570e26	−	7.57316e26i	0.736391	−	0.599934i
$514$	6.56409e26			0.509968
$515$	5.65592e26	−	3.26545e26i	0.430954	−	0.248811i
$516$	−9.65394e26	+	2.23882e26i	−0.721453	+	0.167310i
$517$	−4.07157e26	+	7.05217e26i	−0.298440	+	0.516913i
$518$	8.29403e26	+	4.78856e26i	0.596305	+	0.344277i
$519$	1.46064e27	−	1.36476e27i	1.03008	−	0.962463i
$520$	4.72954e26	+	8.19181e26i	0.327179	+	0.566691i
$521$		−	1.95116e27i		−	1.32408i	−0.749467	−	0.662041i	$-0.769690\pi$
$521$		−	1.95116e27i		−	1.32408i	0.749467	−	0.662041i	$-0.230310\pi$
$522$	1.23593e26	−	1.81903e27i	0.0822791	−	1.21097i
$523$	−1.44148e27			−0.941437			−0.470719	−	0.882283i	$-0.656005\pi$
$523$	−1.44148e27			−0.941437			−0.470719	+	0.882283i	$0.656005\pi$
$524$	3.81464e26	−	2.20238e26i	0.244422	−	0.141117i
$525$	−3.05264e25	+	1.00201e26i	−0.0191903	+	0.0629908i
$526$	9.06155e26	−	1.56951e27i	0.558914	−	0.968067i
$527$	−2.20022e24	−	1.27030e24i	−0.00133156	−	0.000768776i
$528$	2.75565e26	+	8.39516e25i	0.163638	+	0.0498528i
$529$	9.67840e26	+	1.67635e27i	0.563958	+	0.976804i
$530$			1.29650e27i			0.741334i
$531$	6.95049e26	+	4.72249e25i	0.390005	+	0.0264988i
$532$	−6.19992e26			−0.341405
$533$	2.00781e27	−	1.15921e27i	1.08505	−	0.626454i
$534$	−6.04349e26	−	6.46805e26i	−0.320535	−	0.343052i
$535$	1.53152e27	−	2.65267e27i	0.797233	−	1.38085i
$536$	5.57503e26	+	3.21875e26i	0.284839	+	0.164452i
$537$	4.91206e26	+	2.11811e27i	0.246332	+	1.06220i
$538$	3.62079e26	+	6.27140e26i	0.178230	+	0.308703i
$539$			6.84314e26i			0.330650i
$540$	3.57283e26	−	9.39050e26i	0.169463	−	0.445401i
$541$	−3.35338e27			−1.56139			−0.780693	−	0.624914i	$-0.785134\pi$
$541$	−3.35338e27			−1.56139			−0.780693	+	0.624914i	$0.785134\pi$
$542$	−1.66030e27	+	9.58574e26i	−0.758915	+	0.438160i
$543$	2.57614e26	−	5.97427e25i	0.115604	−	0.0268094i
$544$	−6.39369e23	+	1.10742e24i	−0.000281684	+	0.000487891i
$545$	3.04933e27	+	1.76053e27i	1.31898	+	0.761515i
$546$	1.69829e27	−	1.58682e27i	0.721249	−	0.673907i
$547$	−7.57903e26	−	1.31273e27i	−0.316039	−	0.547395i	0.663619	−	0.748071i	$-0.269020\pi$
$547$	−7.57903e26	−	1.31273e27i	−0.316039	−	0.547395i	−0.979658	+	0.200676i	$0.935686\pi$
$548$			1.49851e26i			0.0613554i
$549$	1.00039e27	+	6.71901e26i	0.402202	+	0.270136i
$550$	−1.12261e26			−0.0443203
$551$	−3.64204e27	+	2.10273e27i	−1.41198	+	0.815208i
$552$	3.94780e26	−	1.29584e27i	0.150302	−	0.493355i
$553$	−8.02370e26	+	1.38975e27i	−0.300002	+	0.519618i
$554$	−1.42076e27	−	8.20278e26i	−0.521704	−	0.301206i
$555$	3.42450e27	+	1.04328e27i	1.23500	+	0.376246i
$556$	4.14873e26	+	7.18581e26i	0.146949	+	0.254523i
$557$			3.36862e27i			1.17192i	0.810338	+	0.585962i	$0.199283\pi$
$557$			3.36862e27i			1.17192i	−0.810338	+	0.585962i	$0.800717\pi$
$558$	−4.39424e26	−	8.96460e26i	−0.150156	−	0.306330i
$559$	−8.56946e27			−2.87631
$560$	−4.49925e26	+	2.59764e26i	−0.148340	+	0.0856444i
$561$	−4.59680e24	−	4.91973e24i	−0.00148877	−	0.00159336i
$562$	−1.42815e27	+	2.47364e27i	−0.454372	+	0.786996i
$563$	−1.83914e27	−	1.06183e27i	−0.574817	−	0.331871i	0.184254	−	0.982879i	$-0.441013\pi$
$563$	−1.83914e27	−	1.06183e27i	−0.574817	−	0.331871i	−0.759071	+	0.651008i	$0.774347\pi$
$564$	−3.20900e26	−	1.38374e27i	−0.0985323	−	0.424878i
$565$	9.93808e26	+	1.72133e27i	0.299791	+	0.519253i
$566$		−	1.59812e27i		−	0.473636i
$567$	−2.44608e27	−	3.33939e26i	−0.712263	−	0.0972380i
$568$	−6.26156e26			−0.179143
$569$	1.53087e27	−	8.83851e26i	0.430345	−	0.248460i	−0.269149	−	0.963099i	$-0.586742\pi$
$569$	1.53087e27	−	8.83851e26i	0.430345	−	0.248460i	0.699494	+	0.714639i	$0.253409\pi$
$570$	−2.25760e27	+	5.23553e26i	−0.623588	+	0.144615i
$571$	−8.43161e26	+	1.46040e27i	−0.228849	+	0.396379i	−0.957467	−	0.288542i	$-0.906830\pi$
$571$	−8.43161e26	+	1.46040e27i	−0.228849	+	0.396379i	0.728618	+	0.684920i	$0.240163\pi$
$572$	2.15725e27	+	1.24549e27i	0.575361	+	0.332185i
$573$	−3.49735e27	+	3.26779e27i	−0.916629	+	0.856462i
$574$	6.36681e26	+	1.10276e27i	0.163984	+	0.284029i
$575$			5.27905e26i			0.133622i
$576$	−4.51207e26	+	2.21171e26i	−0.112241	+	0.0550179i
$577$	1.65982e27			0.405793			0.202896	−	0.979200i	$-0.434965\pi$
$577$	1.65982e27			0.405793			0.202896	+	0.979200i	$0.434965\pi$
$578$	−2.54853e27	+	1.47139e27i	−0.612366	+	0.353550i
$579$	−3.44404e25	+	1.13048e26i	−0.00813360	+	0.0266980i
$580$	−1.76200e27	+	3.05188e27i	−0.409004	+	0.708415i
$581$	−1.16371e27	−	6.71867e26i	−0.265511	−	0.153293i
$582$	2.80643e27	+	8.54986e26i	0.629396	+	0.191747i
$583$	1.70712e27	+	2.95682e27i	0.376338	+	0.651837i
$584$			9.21429e26i			0.199679i
$585$	4.84404e27	−	7.21224e27i	1.03193	−	1.53643i
$586$	2.42987e27			0.508870
$587$	1.38848e26	−	8.01637e25i	0.0285863	−	0.0165043i	−0.485639	−	0.874160i	$-0.661413\pi$
$587$	1.38848e26	−	8.01637e25i	0.0285863	−	0.0165043i	0.514225	+	0.857655i	$0.328080\pi$
$588$	−8.14959e26	−	8.72210e26i	−0.164954	−	0.176542i
$589$	−1.15142e27	+	1.99432e27i	−0.229130	+	0.396865i
$590$	−1.16612e27	−	6.73262e26i	−0.228152	−	0.131724i
$591$	1.07512e27	+	4.63600e27i	0.206815	+	0.891801i
$592$	−8.95219e26	−	1.55056e27i	−0.169322	−	0.293273i
$593$			1.33432e26i			0.0248148i	0.999923	+	0.0124074i	$0.00394951\pi$
$593$			1.33432e26i			0.0248148i	−0.999923	+	0.0124074i	$0.996050\pi$
$594$	−4.21635e26	−	2.61205e27i	−0.0771032	−	0.477658i
$595$	1.21430e25			0.00218351
$596$	7.24702e26	−	4.18407e26i	0.128144	−	0.0739838i
$597$	−7.94160e27	+	1.84172e27i	−1.38091	+	0.320243i
$598$	5.85688e27	−	1.01444e28i	1.00151	−	1.73466i
$599$	8.47109e27	+	4.89078e27i	1.42453	+	0.822452i	0.996682	−	0.0814000i	$-0.0259391\pi$
$599$	8.47109e27	+	4.89078e27i	1.42453	+	0.822452i	0.427846	+	0.903851i	$0.359272\pi$
$600$	1.43085e26	−	1.33693e26i	0.0236637	−	0.0221104i
$601$	−6.03942e26	−	1.04606e27i	−0.0982315	−	0.170142i	0.812721	−	0.582653i	$-0.197985\pi$
$601$	−6.03942e26	−	1.04606e27i	−0.0982315	−	0.170142i	−0.910953	+	0.412511i	$0.864652\pi$
$602$		−	4.70667e27i		−	0.752919i
$603$	4.00814e26	−	5.89911e27i	0.0630623	−	0.928140i
$604$	5.60557e27			0.867462
$605$	−2.88381e27	+	1.66497e27i	−0.438948	+	0.253427i
$606$	1.13670e27	−	3.73114e27i	0.170184	−	0.558618i
$607$	3.59555e27	−	6.22767e27i	0.529515	−	0.917146i	−0.469893	−	0.882724i	$-0.655707\pi$
$607$	3.59555e27	−	6.22767e27i	0.529515	−	0.917146i	0.999407	−	0.0344227i	$-0.0109593\pi$
$608$	1.00379e27	+	5.79536e26i	0.145414	+	0.0839546i
$609$	8.28322e27	+	2.52350e27i	1.18039	+	0.359609i
$610$	−1.16462e27	−	2.01718e27i	−0.163262	−	0.282779i
$611$		−	1.22830e28i		−	1.69391i
$612$	1.17179e25	+	7.96173e23i	0.00158978	+	0.000108017i
$613$	9.50610e27			1.26881			0.634407	−	0.773000i	$-0.281245\pi$
$613$	9.50610e27			1.26881			0.634407	+	0.773000i	$0.281245\pi$
$614$	1.55573e27	−	8.98198e26i	0.204291	−	0.117947i
$615$	3.24959e27	+	3.47788e27i	0.419834	+	0.449328i
$616$	−6.84070e26	+	1.18484e27i	−0.0869547	+	0.150610i
$617$	−2.70034e27	−	1.55904e27i	−0.337728	−	0.194987i	0.321539	−	0.946896i	$-0.395800\pi$
$617$	−2.70034e27	−	1.55904e27i	−0.337728	−	0.194987i	−0.659267	+	0.751909i	$0.729133\pi$
$618$	6.77753e26	+	2.92251e27i	0.0834039	+	0.359643i
$619$	3.57439e27	+	6.19102e27i	0.432808	+	0.749645i	0.997114	−	0.0759204i	$-0.0241895\pi$
$619$	3.57439e27	+	6.19102e27i	0.432808	+	0.749645i	−0.564306	+	0.825566i	$0.690856\pi$
$620$			1.92969e27i			0.229917i
$621$	−1.22831e28	+	1.98273e27i	−1.44010	+	0.232459i
$622$	−1.08364e28			−1.25020
$623$	3.64091e27	−	2.10208e27i	0.413361	−	0.238654i
$624$	−4.23285e27	+	9.81629e26i	−0.472919	+	0.109673i
$625$	4.09276e27	−	7.08888e27i	0.450004	−	0.779430i
$626$	−1.01388e28	−	5.85363e27i	−1.09709	−	0.633405i
$627$	−4.45934e27	+	4.16663e27i	−0.474892	+	0.443721i
$628$	4.07500e27	+	7.05810e27i	0.427101	+	0.739761i
$629$			4.18481e25i			0.00431687i
$630$	3.96123e27	+	2.66053e27i	0.402184	+	0.270124i
$631$	−1.16704e28			−1.16625			−0.583125	−	0.812383i	$-0.698170\pi$
$631$	−1.16704e28			−1.16625			−0.583125	+	0.812383i	$0.698170\pi$
$632$	2.59812e27	−	1.50003e27i	0.255558	−	0.147546i
$633$	−5.13820e27	+	1.68658e28i	−0.497478	+	1.63294i
$634$	5.68801e27	−	9.85192e27i	0.542085	−	0.938919i
$635$	−1.50455e27	−	8.68653e26i	−0.141146	−	0.0814909i
$636$	−5.69717e27	−	1.73566e27i	−0.526124	−	0.160285i
$637$	−5.16103e27	−	8.93917e27i	−0.469183	−	0.812649i
$638$			9.28022e27i			0.830523i
$639$	2.53132e27	+	5.16410e27i	0.223017	+	0.454973i
$640$	9.71255e26			0.0842429
$641$	1.17621e28	−	6.79083e27i	1.00439	−	0.579886i	0.0948471	−	0.995492i	$-0.469764\pi$
$641$	1.17621e28	−	6.79083e27i	1.00439	−	0.579886i	0.909545	+	0.415606i	$0.136430\pi$
$642$	9.60627e27	+	1.02811e28i	0.807615	+	0.864350i
$643$	6.24753e27	−	1.08210e28i	0.517129	−	0.895693i	−0.482674	−	0.875800i	$-0.660334\pi$
$643$	6.24753e27	−	1.08210e28i	0.517129	−	0.895693i	0.999802	−	0.0198927i	$-0.00633245\pi$
$644$	5.57169e27	+	3.21682e27i	0.454076	+	0.262161i
$645$	−3.97455e27	−	1.71385e28i	−0.318927	−	1.37523i
$646$	−1.35456e25	−	2.34616e25i	−0.00107022	−	0.00185367i
$647$		−	2.23044e27i		−	0.173519i	−0.996229	−	0.0867595i	$-0.972349\pi$
$647$		−	2.23044e27i		−	0.173519i	0.996229	−	0.0867595i	$-0.0276512\pi$
$648$	3.64813e27	+	2.82712e27i	0.279460	+	0.216568i
$649$	−3.54597e27			−0.267478
$650$	1.46646e27	−	8.46663e26i	0.108928	−	0.0628893i
$651$	4.61900e27	−	1.07118e27i	0.337861	−	0.0783524i
$652$	−2.59751e27	+	4.49903e27i	−0.187104	+	0.324073i
$653$	−1.48221e28	−	8.55756e27i	−1.05143	−	0.607041i	−0.128377	−	0.991725i	$-0.540977\pi$
$653$	−1.48221e28	−	8.55756e27i	−1.05143	−	0.607041i	−0.923048	+	0.384685i	$0.874310\pi$
$654$	−1.18184e28	+	1.10427e28i	−0.825625	+	0.771432i
$655$	3.90986e27	+	6.77208e27i	0.268998	+	0.465918i
$656$		−	2.38054e27i		−	0.161301i
$657$	7.59929e27	−	3.72500e27i	0.507130	−	0.248583i
$658$	6.74627e27			0.443409
$659$	−1.39307e28	+	8.04292e27i	−0.901821	+	0.520667i	−0.877791	−	0.479045i	$-0.840983\pi$
$659$	−1.39307e28	+	8.04292e27i	−0.901821	+	0.520667i	−0.0240304	+	0.999711i	$0.507650\pi$
$660$	−1.49038e27	+	4.89207e27i	−0.0950294	+	0.311927i
$661$	4.46868e27	−	7.73997e27i	0.280650	−	0.486099i	−0.690895	−	0.722955i	$-0.742783\pi$
$661$	4.46868e27	−	7.73997e27i	0.280650	−	0.486099i	0.971545	+	0.236856i	$0.0761168\pi$
$662$	−6.61773e27	−	3.82075e27i	−0.409382	−	0.236357i
$663$	9.71520e25	+	2.95976e25i	0.00591993	+	0.00180352i
$664$	1.25605e27	+	2.17554e27i	0.0753922	+	0.130583i
$665$		−	1.10066e28i		−	0.650786i
$666$	−9.16892e27	+	1.36515e28i	−0.534043	+	0.795130i
$667$	4.36400e28			2.50395
$668$	1.08504e28	−	6.26446e27i	0.613309	−	0.354094i
$669$	−8.48800e27	−	9.08429e27i	−0.472655	−	0.505859i
$670$	−5.71420e27	+	9.89728e27i	−0.313478	+	0.542960i
$671$	−5.31211e27	−	3.06695e27i	−0.287106	−	0.165760i
$672$	−5.39147e26	−	2.32484e27i	−0.0287088	−	0.123794i
$673$	6.18390e27	+	1.07108e28i	0.324423	+	0.561917i	0.981395	−	0.191997i	$-0.0614965\pi$
$673$	6.18390e27	+	1.07108e28i	0.324423	+	0.561917i	−0.656972	+	0.753915i	$0.728163\pi$
$674$			1.76336e28i			0.911468i
$675$	−1.68105e27	−	6.39594e26i	−0.0856136	−	0.0325736i
$676$	−2.76094e28			−1.38545
$677$	−1.29681e28	+	7.48712e27i	−0.641193	+	0.370193i	−0.785074	−	0.619402i	$-0.787375\pi$
$677$	−1.29681e28	+	7.48712e27i	−0.641193	+	0.370193i	0.143881	+	0.989595i	$0.454042\pi$
$678$	−8.89440e27	+	2.06268e27i	−0.433331	+	0.100493i
$679$	−6.96675e27	+	1.20668e28i	−0.334451	+	0.579286i
$680$	−1.96599e25	−	1.13506e25i	−0.000930018	−	0.000536946i
$681$	−9.87924e27	+	9.23078e27i	−0.460524	+	0.430296i
$682$	2.54085e27	+	4.40088e27i	0.116717	+	0.202160i
$683$			2.17993e28i			0.986813i	0.869799	+	0.493406i	$0.164248\pi$
$683$			2.17993e28i			0.986813i	−0.869799	+	0.493406i	$0.835752\pi$
$684$	7.21666e26	−	1.06214e28i	0.0321940	−	0.473827i
$685$	−2.66028e27			−0.116956
$686$	1.50700e28	−	8.70069e27i	0.652940	−	0.376975i
$687$	−1.43231e27	+	4.70146e27i	−0.0611603	+	0.200754i
$688$	−4.39954e27	+	7.62023e27i	−0.185150	+	0.320689i
$689$	−4.46001e28	−	2.57499e28i	−1.84988	−	1.06803i
$690$	2.30048e28	+	7.00847e27i	0.940432	+	0.286505i
$691$	1.47473e28	+	2.55431e28i	0.594199	+	1.02918i	0.993659	+	0.112433i	$0.0358643\pi$
$691$	1.47473e28	+	2.55431e28i	0.594199	+	1.02918i	−0.399460	+	0.916751i	$0.630802\pi$
$692$		−	1.77489e28i		−	0.704874i
$693$	1.25372e28	+	8.51837e26i	0.490759	+	0.0333445i
$694$	1.41965e27			0.0547754
$695$	−1.27569e28	+	7.36518e27i	−0.485173	+	0.280114i
$696$	−1.10519e28	−	1.18283e28i	−0.414330	−	0.443436i
$697$	−2.78203e25	+	4.81862e25i	−0.00102810	+	0.00178072i
$698$	−1.26678e28	−	7.31377e27i	−0.461474	−	0.266432i
$699$	−3.69895e27	−	1.59501e28i	−0.132833	−	0.572786i
$700$	4.65019e26	+	8.05436e26i	0.0164623	+	0.0285135i
$701$			4.78290e28i			1.66921i	0.550849	+	0.834605i	$0.314304\pi$
$701$			4.78290e28i			1.66921i	−0.550849	+	0.834605i	$0.685696\pi$
$702$	2.52076e28	+	3.09412e28i	0.867284	+	1.06455i
$703$	3.79319e28			1.28662
$704$	2.21506e27	−	1.27886e27i	0.0740728	−	0.0427659i
$705$	2.45654e28	−	5.69689e27i	0.809902	−	0.187822i
$706$	2.04191e27	−	3.53670e27i	0.0663729	−	0.114961i
$707$	1.60427e28	+	9.26227e27i	0.514143	+	0.296841i
$708$	4.51961e27	−	4.22294e27i	0.142813	−	0.133439i
$709$	−3.03443e28	−	5.25579e28i	−0.945398	−	1.63748i	−0.754952	−	0.655780i	$-0.772340\pi$
$709$	−3.03443e28	−	5.25579e28i	−0.945398	−	1.63748i	−0.190445	−	0.981698i	$-0.560993\pi$
$710$		−	1.11161e28i		−	0.341482i
$711$	−2.28744e28	−	1.53634e28i	−0.692873	−	0.465363i
$712$	−7.85964e27			−0.234749
$713$	2.06950e28	−	1.19483e28i	0.609495	−	0.351892i
$714$	−1.62561e25	+	5.33595e25i	−0.000472101	+	0.00154964i
$715$	−2.21110e28	+	3.82974e28i	−0.633211	+	1.09675i
$716$	1.67191e28	+	9.65276e27i	0.472152	+	0.272597i
$717$	−2.96227e28	−	9.02463e27i	−0.824961	−	0.251326i
$718$	−1.47139e28	−	2.54852e28i	−0.404094	−	0.699912i
$719$		−	5.76968e28i		−	1.56265i	−0.624122	−	0.781327i	$-0.714543\pi$
$719$		−	5.76968e28i		−	1.56265i	0.624122	−	0.781327i	$-0.285457\pi$
$720$	−3.92643e27	−	8.01022e27i	−0.104875	−	0.213954i
$721$	−1.42484e28			−0.375329
$722$	2.30547e27	−	1.33106e27i	0.0598946	−	0.0345802i
$723$	3.22074e28	+	3.44700e28i	0.825227	+	0.883199i
$724$	1.17401e27	−	2.03345e27i	0.0296679	−	0.0513863i
$725$	5.46335e27	+	3.15427e27i	0.136169	+	0.0786174i
$726$	−3.45569e27	−	1.49012e28i	−0.0849511	−	0.366315i
$727$	1.26142e28	+	2.18484e28i	0.305855	+	0.529756i	0.977451	−	0.211161i	$-0.0677245\pi$
$727$	1.26142e28	+	2.18484e28i	0.305855	+	0.529756i	−0.671597	+	0.740917i	$0.734391\pi$
$728$		−	2.06368e28i		−	0.493546i
$729$	8.56807e27	−	4.15162e28i	0.202119	−	0.979361i
$730$	−1.63580e28			−0.380629
$731$	1.78109e26	−	1.02831e26i	0.00408800	−	0.00236021i
$732$	1.04231e28	−	2.41720e27i	0.235987	−	0.0547271i
$733$	−2.25801e28	+	3.91099e28i	−0.504296	+	0.873467i	0.495691	+	0.868499i	$0.334915\pi$
$733$	−2.25801e28	+	3.91099e28i	−0.504296	+	0.873467i	−0.999988	+	0.00496813i	$0.998419\pi$
$734$	3.31396e28	+	1.91331e28i	0.730106	+	0.421527i
$735$	1.54842e28	−	1.44679e28i	0.336524	−	0.314435i
$736$	−6.01382e27	−	1.04162e28i	−0.128935	−	0.223323i
$737$			3.00958e28i			0.636549i
$738$	−1.96330e28	+	9.62365e27i	−0.409660	+	0.200806i
$739$	−2.81917e28			−0.580332			−0.290166	−	0.956976i	$-0.593711\pi$
$739$	−2.81917e28			−0.580332			−0.290166	+	0.956976i	$0.593711\pi$
$740$	2.75270e28	−	1.58927e28i	0.559038	−	0.322761i
$741$	2.68278e28	−	8.80605e28i	0.537531	−	1.76441i
$742$	1.41428e28	−	2.44960e28i	0.279574	−	0.484236i
$743$	7.25975e28	+	4.19142e28i	1.41590	+	0.817472i	0.995936	−	0.0900671i	$-0.0287081\pi$
$743$	7.25975e28	+	4.19142e28i	1.41590	+	0.817472i	0.419967	+	0.907539i	$0.362041\pi$
$744$	−8.47957e27	−	2.58332e27i	−0.163172	−	0.0497106i
$745$	7.42793e27	+	1.28655e28i	0.141028	+	0.244267i
$746$		−	1.39916e28i		−	0.262108i
$747$	1.28646e28	−	1.91539e28i	0.237788	−	0.354040i
$748$	−5.97821e25			−0.00109032
$749$	−5.78730e28	+	3.34130e28i	−1.04150	+	0.601309i
$750$	2.82841e28	+	3.02711e28i	0.502261	+	0.537545i
$751$	1.51318e28	−	2.62091e28i	0.265150	−	0.459253i	−0.702453	−	0.711730i	$-0.747912\pi$
$751$	1.51318e28	−	2.62091e28i	0.265150	−	0.459253i	0.967603	+	0.252477i	$0.0812452\pi$
$752$	−1.09224e28	−	6.30605e27i	−0.188860	−	0.109038i
$753$	−4.17548e27	−	1.80049e28i	−0.0712453	−	0.307214i
$754$	−6.99906e28	−	1.21227e29i	−1.17849	−	2.04121i
$755$			9.95150e28i			1.65356i
$756$	−1.69941e28	+	1.38450e28i	−0.278663	+	0.227025i
$757$	2.36706e28			0.383045			0.191523	−	0.981488i	$-0.438657\pi$
$757$	2.36706e28			0.383045			0.191523	+	0.981488i	$0.438657\pi$
$758$	−8.16902e27	+	4.71638e27i	−0.130460	+	0.0753212i
$759$	6.16932e28	−	1.43071e28i	0.972344	−	0.225494i
$760$	−1.02884e28	+	1.78201e28i	−0.160034	+	0.277187i
$761$	3.66505e28	+	2.11602e28i	0.562643	+	0.324842i	0.754206	−	0.656638i	$-0.228022\pi$
$761$	3.66505e28	+	2.11602e28i	0.562643	+	0.324842i	−0.191563	+	0.981480i	$0.561356\pi$
$762$	5.83127e27	−	5.44851e27i	0.0883514	−	0.0825521i
$763$	−3.84093e28	−	6.65268e28i	−0.574369	−	0.994836i
$764$			4.24981e28i			0.627243i
$765$	−1.41343e25	+	2.08027e26i	−0.000205902	+	0.00303044i
$766$	6.91147e28			0.993763
$767$	4.63209e28	−	2.67434e28i	0.657390	−	0.379544i
$768$	−1.30024e27	+	4.26795e27i	−0.0182143	+	0.0597870i
$769$	−3.64018e28	+	6.30497e28i	−0.503337	+	0.871805i	0.496655	+	0.867948i	$0.334561\pi$
$769$	−3.64018e28	+	6.30497e28i	−0.503337	+	0.871805i	−0.999993	+	0.00385768i	$0.998772\pi$
$770$	−2.10344e28	−	1.21442e28i	−0.287093	−	0.165753i
$771$	−5.12070e28	−	1.56003e28i	−0.689899	−	0.210179i
$772$	5.24644e26	+	9.08709e26i	0.00697736	+	0.0120851i
$773$		−	3.31683e28i		−	0.435440i	−0.976011	−	0.217720i	$-0.930138\pi$
$773$		−	3.31683e28i		−	0.435440i	0.976011	−	0.217720i	$-0.0698620\pi$
$774$	8.06320e28	+	5.47852e27i	1.04496	+	0.0709992i
$775$	3.45445e27			0.0441939
$776$	2.25588e28	−	1.30243e28i	0.284904	−	0.164489i
$777$	−5.33218e28	−	5.70677e28i	−0.664806	−	0.711509i
$778$	−5.09294e28	+	8.82123e28i	−0.626863	+	1.08576i
$779$	4.36769e28	+	2.52169e28i	0.530735	+	0.306420i
$780$	−1.74267e28	−	7.51452e28i	−0.209059	−	0.901479i
$781$	−1.46367e28	−	2.53515e28i	−0.173353	−	0.300257i
$782$			2.81123e26i			0.00328723i
$783$	−5.28729e28	+	1.38966e29i	−0.610401	+	1.60432i
$784$	−1.05987e28			−0.120806
$785$	−1.25302e29	+	7.23429e28i	−1.41013	+	0.814140i
$786$	−3.49925e28	+	8.11502e27i	−0.388821	+	0.0901705i
$787$	5.86816e27	−	1.01639e28i	0.0643805	−	0.111510i	−0.832039	−	0.554718i	$-0.812826\pi$
$787$	5.86816e27	−	1.01639e28i	0.0643805	−	0.111510i	0.896419	+	0.443208i	$0.146160\pi$
$788$	3.65937e28	+	2.11274e28i	0.396409	+	0.228867i
$789$	−1.07991e29	+	1.00903e29i	−1.15509	+	1.07928i
$790$	2.66298e28	+	4.61241e28i	0.281252	+	0.487144i
$791$		−	4.33636e28i		−	0.452231i
$792$	−1.95018e28	−	1.30983e28i	−0.200828	−	0.134884i
$793$	9.25225e28			0.940839
$794$	2.93082e28	−	1.69211e28i	0.294296	−	0.169912i
$795$	3.08129e28	−	1.01141e29i	0.305535	−	1.00290i
$796$	−3.61918e28	+	6.26861e28i	−0.354389	+	0.613819i
$797$	1.46162e29	+	8.43866e28i	1.41335	+	0.816000i	0.995703	−	0.0926073i	$-0.0295201\pi$
$797$	1.46162e29	+	8.43866e28i	1.41335	+	0.816000i	0.417651	+	0.908608i	$0.362853\pi$
$798$	4.83661e28	+	1.47348e28i	0.461862	+	0.140707i
$799$	1.47392e26	+	2.55291e26i	0.00138997	+	0.00240750i
$800$		−	1.73870e27i		−	0.0161929i
$801$	3.17737e28	+	6.48208e28i	0.292242	+	0.596196i
$802$	−7.65261e28			−0.695129
$803$	−3.73063e28	+	2.15388e28i	−0.334678	+	0.193226i
$804$	−3.58415e28	−	3.83594e28i	−0.317560	−	0.339869i
$805$	−5.71077e28	+	9.89135e28i	−0.499731	+	0.865559i
$806$	−6.63821e28	−	3.83257e28i	−0.573721	−	0.331238i
$807$	−1.33414e28	−	5.75289e28i	−0.113885	−	0.491078i
$808$	−1.73158e28	−	2.99918e28i	−0.145992	−	0.252865i
$809$		−	6.38396e28i		−	0.531624i	−0.964025	−	0.265812i	$-0.914360\pi$
$809$		−	6.38396e28i		−	0.531624i	0.964025	−	0.265812i	$-0.0856401\pi$
$810$	−5.01896e28	+	6.47648e28i	−0.412822	+	0.532707i
$811$	−1.39379e29			−1.13237			−0.566184	−	0.824279i	$-0.691581\pi$
$811$	−1.39379e29			−1.13237			−0.566184	+	0.824279i	$0.691581\pi$
$812$	6.65825e28	−	3.84414e28i	0.534318	−	0.308489i
$813$	1.52303e29	−	3.53202e28i	1.20726	−	0.279974i
$814$	4.18523e28	−	7.24903e28i	0.327699	−	0.567591i
$815$	−7.98706e28	−	4.61133e28i	−0.617748	−	0.356657i
$816$	7.61968e25	−	7.11953e25i	0.000582150	−	0.000543938i
$817$	−9.32080e28	−	1.61441e29i	−0.703449	−	1.21841i
$818$			1.09292e29i			0.814808i
$819$	−1.70197e29	+	8.34268e28i	−1.25347	+	0.614422i
$820$	4.22614e28			0.307472
$821$	−1.02020e29	+	5.89014e28i	−0.733254	+	0.423345i	−0.819612	−	0.572920i	$-0.805811\pi$
$821$	−1.02020e29	+	5.89014e28i	−0.733254	+	0.423345i	0.0863572	+	0.996264i	$0.472477\pi$
$822$	3.56137e27	−	1.16900e28i	0.0252871	−	0.0830032i
$823$	−5.41616e28	+	9.38106e28i	−0.379921	+	0.658042i	−0.991050	−	0.133489i	$-0.957382\pi$
$823$	−5.41616e28	+	9.38106e28i	−0.379921	+	0.658042i	0.611130	+	0.791530i	$0.290715\pi$
$824$	2.30685e28	+	1.33186e28i	0.159863	+	0.0922969i
$825$	8.75758e27	+	2.66802e27i	0.0599577	+	0.0182663i
$826$	1.46885e28	+	2.54412e28i	0.0993518	+	0.172082i
$827$			1.40174e28i			0.0936723i	0.998903	+	0.0468361i	$0.0149139\pi$
$827$			1.40174e28i			0.0936723i	−0.998903	+	0.0468361i	$0.985086\pi$
$828$	−6.15941e28	+	9.17068e28i	−0.406664	+	0.605478i
$829$	8.81082e28			0.574739			0.287370	−	0.957820i	$-0.407219\pi$
$829$	8.81082e28			0.574739			0.287370	+	0.957820i	$0.407219\pi$
$830$	−3.86221e28	+	2.22985e28i	−0.248918	+	0.143713i
$831$	9.13400e28	+	9.77567e28i	0.581635	+	0.622495i
$832$	−1.92901e28	+	3.34115e28i	−0.121367	+	0.210215i
$833$	2.14535e26	+	1.23862e26i	0.00133367	+	0.000769994i
$834$	−1.52866e28	−	6.59170e28i	−0.0938970	−	0.404890i
$835$	1.11212e29	+	1.92625e29i	0.674974	+	1.16909i
$836$			5.41876e28i			0.324966i
$837$	1.29744e28	+	8.03770e28i	0.0768833	+	0.476296i
$838$	8.64727e28			0.506336
$839$	1.25928e29	−	7.27046e28i	0.728624	−	0.420671i	−0.0892949	−	0.996005i	$-0.528461\pi$
$839$	1.25928e29	−	7.27046e28i	0.728624	−	0.420671i	0.817918	+	0.575334i	$0.195128\pi$
$840$	4.12726e28	−	9.57141e27i	0.235976	−	0.0547247i
$841$	1.72255e29	−	2.98354e29i	0.973220	−	1.68567i
$842$	−6.54453e28	−	3.77849e28i	−0.365391	−	0.210958i
$843$	1.70200e29	−	1.59029e29i	0.939041	−	0.877403i
$844$	7.82721e28	+	1.35571e29i	0.426759	+	0.739168i
$845$		−	4.90146e29i		−	2.64094i
$846$	−7.85260e27	+	1.15573e29i	−0.0418129	+	0.615395i
$847$	7.26489e28			0.382292
$848$	−4.57952e28	+	2.64399e28i	−0.238156	+	0.137499i
$849$	−3.79812e28	+	1.24671e29i	−0.195205	+	0.640748i
$850$	−2.03194e25	+	3.51943e25i	−0.000103210	+	0.000178765i
$851$	−3.40883e29	−	1.96809e29i	−1.71124	−	0.987983i
$852$	4.88470e28	+	1.48813e28i	0.242349	+	0.0738323i
$853$	−5.64400e28	−	9.77570e28i	−0.276756	−	0.479355i	0.693821	−	0.720148i	$-0.255926\pi$
$853$	−5.64400e28	−	9.77570e28i	−0.276756	−	0.479355i	−0.970577	+	0.240793i	$0.922593\pi$
$854$			5.08168e28i			0.246280i
$855$	1.88560e29	+	1.28116e28i	0.903208	+	0.0613682i
$856$	1.24931e29			0.591469
$857$	2.13884e29	−	1.23486e29i	1.00085	−	0.577843i	0.0923526	−	0.995726i	$-0.470561\pi$
$857$	2.13884e29	−	1.23486e29i	1.00085	−	0.577843i	0.908501	+	0.417884i	$0.137228\pi$
$858$	−1.38688e29	−	1.48431e29i	−0.641457	−	0.686519i
$859$	8.70646e28	−	1.50800e29i	0.398024	−	0.689399i	−0.595458	−	0.803387i	$-0.703029\pi$
$859$	8.70646e28	−	1.50800e29i	0.398024	−	0.689399i	0.993482	+	0.113988i	$0.0363626\pi$
$860$	−1.35281e29	−	7.81045e28i	−0.611297	−	0.352932i
$861$	−2.34595e28	−	1.01159e29i	−0.104782	−	0.451827i
$862$	7.23833e28	+	1.25372e29i	0.319570	+	0.553511i
$863$		−	1.18441e29i		−	0.516884i	−0.966027	−	0.258442i	$-0.916791\pi$
$863$		−	1.18441e29i		−	0.516884i	0.966027	−	0.258442i	$-0.0832090\pi$
$864$	4.04554e28	−	6.53028e27i	0.174518	−	0.0281705i
$865$	3.15095e29			1.34363
$866$	−2.23937e29	+	1.29290e29i	−0.943946	+	0.544987i
$867$	2.33782e29	−	5.42158e28i	0.974138	−	0.225910i
$868$	2.10499e28	−	3.64595e28i	0.0867068	−	0.150181i
$869$	1.21464e29	+	7.01275e28i	0.494597	+	0.285556i
$870$	2.09987e29	−	1.96204e29i	0.845278	−	0.789795i
$871$	−2.26980e29	−	3.93141e29i	−0.903246	−	1.56447i
$872$			1.43612e29i			0.564970i
$873$	−1.98612e29	−	1.33396e29i	−0.772437	−	0.518801i
$874$	2.54816e29			0.979742
$875$	−1.70398e29	+	9.83792e28i	−0.647714	+	0.373958i
$876$	2.18988e28	−	7.18814e28i	0.0822962	−	0.270131i
$877$	−2.57456e29	+	4.45927e29i	−0.956548	+	1.65679i	−0.225764	+	0.974182i	$0.572488\pi$
$877$	−2.57456e29	+	4.45927e29i	−0.956548	+	1.65679i	−0.730784	+	0.682608i	$0.760846\pi$
$878$	−1.15387e29	−	6.66188e28i	−0.423850	−	0.244710i
$879$	−1.89556e29	−	5.77487e28i	−0.688413	−	0.209727i
$880$	2.27035e28	+	3.93236e28i	0.0815204	+	0.141197i
$881$			2.52743e28i			0.0897263i	0.998993	+	0.0448631i	$0.0142852\pi$
$881$			2.52743e28i			0.0897263i	−0.998993	+	0.0448631i	$0.985715\pi$
$882$	4.28465e28	+	8.74102e28i	0.150394	+	0.306815i
$883$	3.87163e29			1.34365			0.671826	−	0.740709i	$-0.265510\pi$
$883$	3.87163e29			1.34365			0.671826	+	0.740709i	$0.265510\pi$
$884$	7.80931e26	−	4.50871e26i	0.00267972	−	0.00154714i
$885$	7.49694e28	+	8.02360e28i	0.254361	+	0.272230i
$886$	2.40858e28	−	4.17178e28i	0.0808022	−	0.139954i
$887$	9.53611e28	+	5.50568e28i	0.316326	+	0.182631i	0.649754	−	0.760145i	$-0.274872\pi$
$887$	9.53611e28	+	5.50568e28i	0.316326	+	0.182631i	−0.333428	+	0.942776i	$0.608205\pi$
$888$	3.29857e28	+	1.42237e29i	0.108192	+	0.466533i
$889$	1.89513e28	+	3.28246e28i	0.0614641	+	0.106459i
$890$		−	1.39531e29i		−	0.447478i
$891$	−2.91864e28	+	2.13789e29i	−0.0925558	+	0.677966i
$892$	−1.10388e29			−0.346156
$893$	2.31400e29	−	1.33599e29i	0.717545	−	0.414275i
$894$	−6.64785e28	+	1.54169e28i	−0.203848	+	0.0472738i
$895$	−1.71364e29	+	2.96811e29i	−0.519624	+	0.900016i
$896$	−1.83508e28	−	1.05949e28i	−0.0550270	−	0.0317699i
$897$	−6.97994e29	+	6.52178e29i	−2.06979	+	1.93393i
$898$	−1.39193e29	−	2.41090e29i	−0.408183	−	0.706993i
$899$		−	2.85567e29i		−	0.828155i
$900$	−1.43396e28	+	7.02893e27i	−0.0411255	+	0.0201588i
$901$	1.23596e27			0.00350557
$902$	9.63820e28	−	5.56462e28i	0.270353	−	0.156088i
$903$	−1.11859e29	+	3.67171e29i	−0.310310	+	1.01857i
$904$	−4.05340e28	+	7.02069e28i	−0.111208	+	0.192617i
$905$	3.60996e28	+	2.08421e28i	0.0979526	+	0.0565530i
$906$	−4.37295e29	−	1.33223e29i	−1.17353	−	0.357517i
$907$	4.61468e28	+	7.99287e28i	0.122481	+	0.212144i	0.920746	−	0.390164i	$-0.127582\pi$
$907$	4.61468e28	+	7.99287e28i	0.122481	+	0.212144i	−0.798264	+	0.602307i	$0.794248\pi$
$908$			1.20048e29i			0.315134i
$909$	−1.77350e29	+	2.64054e29i	−0.460460	+	0.685573i
$910$	3.66362e29			0.940797
$911$	−2.48290e29	+	1.43350e29i	−0.630632	+	0.364095i	−0.780997	−	0.624535i	$-0.785288\pi$
$911$	−2.48290e29	+	1.43350e29i	−0.630632	+	0.364095i	0.150365	+	0.988631i	$0.451955\pi$
$912$	−6.45328e28	−	6.90662e28i	−0.162118	−	0.173507i
$913$	−5.87215e28	+	1.01709e29i	−0.145911	+	0.252726i
$914$	−3.33842e29	−	1.92744e29i	−0.820502	−	0.473717i
$915$	4.29123e28	+	1.85041e29i	0.104321	+	0.449838i
$916$	2.18189e28	+	3.77914e28i	0.0524660	+	0.0908738i
$917$		−	1.70602e29i		−	0.405780i
$918$	−8.95204e26	−	3.40601e26i	−0.00210618	−	0.000801344i
$919$	−6.67760e29			−1.55405			−0.777026	−	0.629469i	$-0.783273\pi$
$919$	−6.67760e29			−1.55405			−0.777026	+	0.629469i	$0.783273\pi$
$920$	1.84918e29	−	1.06763e29i	0.425698	−	0.245777i
$921$	−1.42710e29	+	3.30955e28i	−0.324981	+	0.0753655i
$922$	2.21072e29	−	3.82908e29i	0.497994	−	0.862552i
$923$	3.82397e29	+	2.20777e29i	0.852113	+	0.491968i
$924$	8.15240e28	−	7.61729e28i	0.179707	−	0.167912i
$925$	−2.84505e28	−	4.92776e28i	−0.0620400	−	0.107456i
$926$			1.55810e29i			0.336112i
$927$	1.65850e28	−	2.44095e29i	0.0353930	−	0.520909i
$928$	−1.43732e29			−0.303441
$929$	−5.95626e29	+	3.43885e29i	−1.24399	+	0.718217i	−0.969904	−	0.243488i	$-0.921708\pi$
$929$	−5.95626e29	+	3.43885e29i	−1.24399	+	0.718217i	−0.274085	+	0.961706i	$0.588375\pi$
$930$	4.58614e28	−	1.50537e29i	0.0947584	−	0.311038i
$931$	1.12271e29	−	1.94459e29i	0.229493	−	0.397494i
$932$	−1.25900e29	−	7.26887e28i	−0.254606	−	0.146997i
$933$	8.45356e29	+	2.57540e29i	1.69131	+	0.515262i
$934$	1.89218e29	+	3.27735e29i	0.374536	+	0.648716i
$935$		−	1.06130e27i		−	0.00207837i
$936$	3.53538e29	+	2.40210e28i	0.684979	+	0.0465407i
$937$	−4.51320e27			−0.00865144			−0.00432572	−	0.999991i	$-0.501377\pi$
$937$	−4.51320e27			−0.00865144			−0.00432572	+	0.999991i	$0.501377\pi$
$938$	2.15928e29	−	1.24666e29i	0.409524	−	0.236439i
$939$	6.51816e29	+	6.97606e29i	1.22312	+	1.30904i
$940$	1.11950e29	−	1.93904e29i	0.207849	−	0.360005i
$941$	8.65040e29	+	4.99431e29i	1.58906	+	0.917443i	0.993463	+	0.114159i	$0.0364172\pi$
$941$	8.65040e29	+	4.99431e29i	1.58906	+	0.917443i	0.595595	+	0.803285i	$0.296916\pi$
$942$	−1.50150e29	−	6.47455e29i	−0.272907	−	1.17679i
$943$	−2.61674e29	−	4.53233e29i	−0.470592	−	0.815089i
$944$		−	5.49200e28i		−	0.0977261i
$945$	−2.45788e29	−	3.01693e29i	−0.432756	−	0.531187i
$946$	−4.11365e29			−0.716664
$947$	4.09863e29	−	2.36634e29i	0.706543	−	0.407923i	−0.103237	−	0.994657i	$-0.532920\pi$
$947$	4.09863e29	−	2.36634e29i	0.706543	−	0.407923i	0.809780	+	0.586734i	$0.199587\pi$
$948$	−2.38331e29	+	5.52708e28i	−0.406535	+	0.0942784i
$949$	3.24887e29	−	5.62721e29i	0.548366	−	0.949797i
$950$	3.19008e28	+	1.84179e28i	0.0532801	+	0.0307613i
$951$	−6.77869e29	+	6.33374e29i	−1.12032	+	1.04678i
$952$	2.47635e26	+	4.28917e26i	0.000404989	+	0.000701461i
$953$			4.82446e29i			0.780764i	0.920653	+	0.390382i	$0.127657\pi$
$953$			4.82446e29i			0.780764i	−0.920653	+	0.390382i	$0.872343\pi$
$954$	4.03191e29	+	2.70800e29i	0.645694	+	0.433675i
$955$	−7.54463e29			−1.19565
$956$	−2.38114e29	+	1.37475e29i	−0.373428	+	0.215599i
$957$	2.20555e29	−	7.23957e29i	0.342293	−	1.12355i
$958$	−2.93991e29	+	5.09207e29i	−0.451521	+	0.782058i
$959$	5.02632e28	+	2.90194e28i	0.0763948	+	0.0441065i
$960$	−7.57683e28	−	2.30830e28i	−0.113966	−	0.0347200i
$961$	2.57709e29	+	4.46366e29i	0.383615	+	0.664442i
$962$			1.26258e30i			1.85998i
$963$	−5.05050e29	−	1.03034e30i	−0.736328	−	1.50217i
$964$	4.18862e29			0.604367
$965$	−1.61322e28	+	9.31393e27i	−0.0230367	+	0.0133002i
$966$	−3.58200e29	−	3.83364e29i	−0.506238	−	0.541802i
$967$	−1.54092e28	+	2.66896e28i	−0.0215534	+	0.0373317i	−0.876601	−	0.481218i	$-0.840195\pi$
$967$	−1.54092e28	+	2.66896e28i	−0.0215534	+	0.0373317i	0.855048	+	0.518550i	$0.173528\pi$
$968$	−1.17621e29	−	6.79083e28i	−0.162828	−	0.0940090i
$969$	4.99107e26	+	2.15218e27i	0.000683843	+	0.00294878i
$970$	2.31219e29	+	4.00482e29i	0.313549	+	0.543083i
$971$		−	5.02387e29i		−	0.674289i	−0.941453	−	0.337145i	$-0.890539\pi$
$971$		−	5.02387e29i		−	0.674289i	0.941453	−	0.337145i	$-0.109461\pi$
$972$	−2.17404e29	−	3.07248e29i	−0.288805	−	0.408157i
$973$	3.21371e29			0.422550
$974$	6.66990e29	−	3.85087e29i	0.868020	−	0.501152i
$975$	−1.34522e29	+	3.11966e28i	−0.173279	+	0.0401848i
$976$	4.75008e28	−	8.22739e28i	0.0605624	−	0.104897i
$977$	−2.97200e29	−	1.71588e29i	−0.375062	−	0.216542i	0.300606	−	0.953749i	$-0.402811\pi$
$977$	−2.97200e29	−	1.71588e29i	−0.375062	−	0.216542i	−0.675668	+	0.737206i	$0.736145\pi$
$978$	3.09559e29	−	2.89240e29i	0.386683	−	0.361301i
$979$	−1.83723e29	−	3.18217e29i	−0.227162	−	0.393456i
$980$		−	1.88156e29i		−	0.230281i
$981$	1.18441e30	−	5.80570e29i	1.43487	−	0.703339i
$982$	−5.02496e29			−0.602584
$983$	3.56920e28	−	2.06068e28i	0.0423677	−	0.0244610i	−0.478667	−	0.877997i	$-0.658880\pi$
$983$	3.56920e28	−	2.06068e28i	0.0423677	−	0.0244610i	0.521034	+	0.853536i	$0.325546\pi$
$984$	−5.65764e28	+	1.85708e29i	−0.0664789	+	0.218212i
$985$	−3.75071e29	+	6.49643e29i	−0.436266	+	0.755635i
$986$	2.90938e27	+	1.67973e27i	0.00334990	+	0.00193407i
$987$	−5.26282e29	−	1.60333e29i	−0.599855	−	0.182747i
$988$	−4.08678e29	−	7.07851e29i	−0.461118	−	0.798679i
$989$			1.93443e30i			2.16068i
$990$	2.32532e29	−	3.46213e29i	0.257117	−	0.382818i
$991$	−1.34309e30			−1.47017			−0.735084	−	0.677976i	$-0.762858\pi$
$991$	−1.34309e30			−1.47017			−0.735084	+	0.677976i	$0.762858\pi$
$992$	−6.81608e28	+	3.93527e28i	−0.0738615	+	0.0426440i
$993$	4.25449e29	+	4.55337e29i	0.456410	+	0.488473i
$994$	−1.21259e29	+	2.10027e29i	−0.128780	+	0.223054i
$995$	−1.11286e30	−	6.42509e29i	−1.17006	−	0.675536i
$996$	−4.62812e28	−	1.99567e29i	−0.0481738	−	0.207729i
$997$	−1.56426e29	−	2.70937e29i	−0.161197	−	0.279201i	0.774101	−	0.633062i	$-0.218202\pi$
$997$	−1.56426e29	−	2.70937e29i	−0.161197	−	0.279201i	−0.935298	+	0.353861i	$0.884869\pi$
$998$			3.25586e29i			0.332170i
$999$	1.03972e30	−	8.47054e29i	1.05017	−	0.855571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.21.d.a.5.2	✓	40
3.2	odd	2		54.21.d.a.17.19		40
9.2	odd	6	inner	18.21.d.a.11.2	yes	40
9.7	even	3		54.21.d.a.35.19		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.21.d.a.5.2	✓	40	1.1	even	1	trivial
18.21.d.a.11.2	yes	40	9.2	odd	6	inner
54.21.d.a.17.19		40	3.2	odd	2
54.21.d.a.35.19		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} +(57522.4 - 13339.9i) q^{3} +(262144. - 454047. i) q^{4} +(8.06063e6 + 4.65381e6i) q^{5} +(-3.12410e7 + 2.91904e7i) q^{6} +(-1.01532e8 - 1.75858e8i) q^{7} +3.79625e8i q^{8} +(3.13088e9 - 1.53468e9i) q^{9} -6.73943e9 q^{10} +(-1.53701e10 + 8.87390e9i) q^{11} +(9.02224e9 - 2.96148e10i) q^{12} +(1.33852e11 - 2.31839e11i) q^{13} +(1.27335e11 + 7.35167e10i) q^{14} +(5.25748e11 + 1.60171e11i) q^{15} +(-1.37439e11 - 2.38051e11i) q^{16} +6.42475e9i q^{17} +(-1.40766e12 + 2.09585e12i) q^{18} +5.82352e12 q^{19} +(4.22609e12 - 2.43994e12i) q^{20} +(-8.18626e12 - 8.76135e12i) q^{21} +(6.42539e12 - 1.11291e13i) q^{22} +(-5.23343e13 - 3.02152e13i) q^{23} +(5.06415e12 + 2.18370e13i) q^{24} +(-4.36787e12 - 7.56538e12i) q^{25} +1.93839e14i q^{26} +(1.59623e14 - 1.30044e14i) q^{27} -1.06464e14 q^{28} +(-6.25402e14 + 3.61076e14i) q^{29} +(-3.87669e14 + 8.99032e13i) q^{30} +(-1.97720e14 + 3.42460e14i) q^{31} +(1.72368e14 + 9.95164e13i) q^{32} +(-7.65746e14 + 7.15483e14i) q^{33} +(-2.32601e12 - 4.02877e12i) q^{34} -1.89003e15i q^{35} +(1.23923e14 - 1.82387e15i) q^{36} +6.51357e15 q^{37} +(-3.65175e15 + 2.10834e15i) q^{38} +(4.60681e15 - 1.51215e16i) q^{39} +(-1.76670e15 + 3.06002e15i) q^{40} +(7.50009e15 + 4.33018e15i) q^{41} +(8.30530e15 + 2.53023e15i) q^{42} +(-1.60054e16 - 2.77222e16i) q^{43} +9.30496e15i q^{44} +(3.23790e16 + 2.19998e15i) q^{45} +4.37563e16 q^{46} +(3.97355e16 - 2.29413e16i) q^{47} +(-1.10814e16 - 1.18599e16i) q^{48} +(1.92788e16 - 3.33919e16i) q^{49} +(5.47792e15 + 3.16268e15i) q^{50} +(8.57054e13 + 3.69568e14i) q^{51} +(-7.01771e16 - 1.21550e17i) q^{52} -1.92375e17i q^{53} +(-5.30138e16 + 1.39337e17i) q^{54} -1.65190e17 q^{55} +(6.67600e16 - 3.85439e16i) q^{56} +(3.34983e17 - 7.76851e16i) q^{57} +(2.61447e17 - 4.52840e17i) q^{58} +(1.73030e17 + 9.98989e16i) q^{59} +(2.10547e17 - 1.96727e17i) q^{60} +(1.72807e17 + 2.99311e17i) q^{61} -2.86328e17i q^{62} +(-5.87769e17 - 3.94771e17i) q^{63} -1.44115e17 q^{64} +(2.15787e18 - 1.24585e18i) q^{65} +(2.21143e17 - 7.25887e17i) q^{66} +(8.47875e17 - 1.46856e18i) q^{67} +(2.91714e15 + 1.68421e15i) q^{68} +(-3.41346e18 - 1.03992e18i) q^{69} +(6.84265e17 + 1.18518e18i) q^{70} +1.64941e18i q^{71} +(5.82605e17 + 1.18856e18i) q^{72} +2.42721e18 q^{73} +(-4.08446e18 + 2.35817e18i) q^{74} +(-3.52172e17 - 3.76912e17i) q^{75} +(1.52660e18 - 2.64415e18i) q^{76} +(3.12109e18 + 1.80196e18i) q^{77} +(2.58579e18 + 1.11501e19i) q^{78} +(-3.95134e18 - 6.84391e18i) q^{79} -2.55846e18i q^{80} +(7.44715e18 - 9.60983e18i) q^{81} -6.27077e18 q^{82} +(5.73077e18 - 3.30866e18i) q^{83} +(-6.12404e18 + 1.42021e18i) q^{84} +(-2.98996e16 + 5.17876e16i) q^{85} +(2.00730e19 + 1.15892e19i) q^{86} +(-3.11580e19 + 2.91128e19i) q^{87} +(-3.36876e18 - 5.83486e18i) q^{88} +2.07037e19i q^{89} +(-2.11004e19 + 1.03429e19i) q^{90} -5.43609e19 q^{91} +(-2.74382e19 + 1.58415e19i) q^{92} +(-6.80493e18 + 2.23367e19i) q^{93} +(-1.66113e19 + 2.87716e19i) q^{94} +(4.69412e19 + 2.71015e19i) q^{95} +(1.12425e19 + 3.42507e18i) q^{96} +(-3.43083e19 - 5.94238e19i) q^{97} +2.79187e19i q^{98} +(-3.45031e19 + 5.13713e19i) 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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