LMFDB - Embedded newform 18.21.d.a.5.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			5.1
Character	$\chi$	$=$	18.5
Dual form			18.21.d.a.11.1

$q$-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} +(-29056.0 - 51405.6i) q^{3} +(262144. - 454047. i) q^{4} +(1.35661e7 + 7.83237e6i) q^{5} +(3.68309e7 + 2.17155e7i) q^{6} +(-1.44553e8 - 2.50374e8i) q^{7} +3.79625e8i q^{8} +(-1.79828e9 + 2.98728e9i) q^{9} -1.13425e10 q^{10} +(2.16289e8 - 1.24874e8i) q^{11} +(-3.09574e10 - 2.82884e8i) q^{12} +(-1.02318e11 + 1.77219e11i) q^{13} +(1.81290e11 + 1.04668e11i) q^{14} +(8.45203e9 - 9.24949e11i) q^{15} +(-1.37439e11 - 2.38051e11i) q^{16} -3.27084e12i q^{17} +(4.61368e10 - 2.52428e12i) q^{18} +6.83256e12 q^{19} +(7.11253e12 - 4.10642e12i) q^{20} +(-8.67046e12 + 1.47057e13i) q^{21} +(-9.04188e10 + 1.56610e11i) q^{22} +(-1.99240e13 - 1.15031e13i) q^{23} +(1.95148e13 - 1.10304e13i) q^{24} +(7.50084e13 + 1.29918e14i) q^{25} -1.48172e14i q^{26} +(2.05814e14 + 5.64334e12i) q^{27} -1.51575e14 q^{28} +(-4.37882e13 + 2.52811e13i) q^{29} +(3.29567e14 + 5.83067e14i) q^{30} +(-5.34721e13 + 9.26164e13i) q^{31} +(1.72368e14 + 9.95164e13i) q^{32} +(-1.27037e13 - 7.49011e12i) q^{33} +(1.18417e15 + 2.05104e15i) q^{34} -4.52878e15i q^{35} +(8.84956e14 + 1.59960e15i) q^{36} -6.08677e15 q^{37} +(-4.28449e15 + 2.47365e15i) q^{38} +(1.20830e16 + 1.10413e14i) q^{39} +(-2.97336e15 + 5.15002e15i) q^{40} +(-1.11337e16 - 6.42805e15i) q^{41} +(1.12949e14 - 1.23605e16i) q^{42} +(-1.04115e16 - 1.80333e16i) q^{43} -1.30940e14i q^{44} +(-4.77931e16 + 2.64408e16i) q^{45} +1.66583e16 q^{46} +(-3.71215e16 + 2.14321e16i) q^{47} +(-8.24374e15 + 1.39819e16i) q^{48} +(-1.89519e15 + 3.28256e15i) q^{49} +(-9.40709e16 - 5.43119e16i) q^{50} +(-1.68139e17 + 9.50375e16i) q^{51} +(5.36439e16 + 9.29140e16i) q^{52} +2.87385e17i q^{53} +(-1.31103e17 + 7.09738e16i) q^{54} +3.91225e15 q^{55} +(9.50481e16 - 5.48761e16i) q^{56} +(-1.98527e17 - 3.51232e17i) q^{57} +(1.83055e16 - 3.17061e16i) q^{58} +(3.86495e17 + 2.23143e17i) q^{59} +(-4.17754e17 - 2.46307e17i) q^{60} +(-4.61942e17 - 8.00108e17i) q^{61} -7.74359e16i q^{62} +(1.00788e18 + 1.84213e16i) q^{63} -1.44115e17 q^{64} +(-2.77610e18 + 1.60278e18i) q^{65} +(1.06778e16 + 9.75723e13i) q^{66} +(-1.15505e18 + 2.00061e18i) q^{67} +(-1.48511e18 - 8.57431e17i) q^{68} +(-1.24132e16 + 1.35844e18i) q^{69} +(1.63959e18 + 2.83986e18i) q^{70} +4.08371e17i q^{71} +(-1.13405e18 - 6.82673e17i) q^{72} -5.70990e18 q^{73} +(3.81683e18 - 2.20365e18i) q^{74} +(4.49908e18 - 7.63076e18i) q^{75} +(1.79111e18 - 3.10230e18i) q^{76} +(-6.25306e16 - 3.61020e16i) q^{77} +(-7.61685e18 + 4.30528e18i) q^{78} +(7.17413e18 + 1.24260e19i) q^{79} -4.30589e18i q^{80} +(-5.69003e18 - 1.07439e19i) q^{81} +9.30881e18 q^{82} +(-1.76947e19 + 1.02160e19i) q^{83} +(4.40417e18 + 7.79181e18i) q^{84} +(2.56184e19 - 4.43724e19i) q^{85} +(1.30575e19 + 7.53876e18i) q^{86} +(2.57190e18 + 1.51639e18i) q^{87} +(4.74055e16 + 8.21087e16i) q^{88} +8.44270e18i q^{89} +(2.03970e19 - 3.38832e19i) q^{90} +5.91614e19 q^{91} +(-1.04459e19 + 6.03096e18i) q^{92} +(6.31468e18 + 5.77026e16i) q^{93} +(1.55185e19 - 2.68788e19i) q^{94} +(9.26910e19 + 5.35152e19i) q^{95} +(1.07390e17 - 1.17522e19i) q^{96} +(9.95365e18 + 1.72402e19i) q^{97} -2.74453e18i q^{98} +(-1.59135e16 + 8.70675e17i) 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
$3$	−29056.0	−	51405.6i	−0.492066	−	0.870558i
$3$	−29056.0	−	51405.6i	−0.492066	−	0.870558i
$4$	262144.	−	454047.i	0.250000	−	0.433013i
$5$	1.35661e7	+	7.83237e6i	1.38917	+	0.802035i	0.993221	−	0.116240i	$-0.0370841\pi$
$5$	1.35661e7	+	7.83237e6i	1.38917	+	0.802035i	0.395944	+	0.918275i	$0.370417\pi$
$6$	3.68309e7	+	2.17155e7i	0.609116	+	0.359134i
$7$	−1.44553e8	−	2.50374e8i	−0.511738	−	0.886356i	−0.999907	−	0.0136073i	$-0.995669\pi$
$7$	−1.44553e8	−	2.50374e8i	−0.511738	−	0.886356i	0.488169	−	0.872749i	$-0.337665\pi$
$8$			3.79625e8i			0.353553i
$9$	−1.79828e9	+	2.98728e9i	−0.515742	+	0.856744i
$10$	−1.13425e10			−1.13425
$11$	2.16289e8	−	1.24874e8i	0.00833887	−	0.00481445i	−0.495825	−	0.868423i	$-0.665134\pi$
$11$	2.16289e8	−	1.24874e8i	0.00833887	−	0.00481445i	0.504164	+	0.863608i	$0.331801\pi$
$12$	−3.09574e10	−	2.82884e8i	−0.499979	−	0.00456873i
$13$	−1.02318e11	+	1.77219e11i	−0.742193	+	1.28552i	0.209302	+	0.977851i	$0.432881\pi$
$13$	−1.02318e11	+	1.77219e11i	−0.742193	+	1.28552i	−0.951495	+	0.307665i	$0.900452\pi$
$14$	1.81290e11	+	1.04668e11i	0.626748	+	0.361853i
$15$	8.45203e9	−	9.24949e11i	0.0146571	−	1.60400i
$16$	−1.37439e11	−	2.38051e11i	−0.125000	−	0.216506i
$17$		−	3.27084e12i		−	1.62245i	−0.584737	−	0.811223i	$-0.698802\pi$
$17$		−	3.27084e12i		−	1.62245i	0.584737	−	0.811223i	$-0.301198\pi$
$18$	4.61368e10	−	2.52428e12i	0.0129218	−	0.706989i
$19$	6.83256e12			1.11442			0.557208	−	0.830373i	$-0.311873\pi$
$19$	6.83256e12			1.11442			0.557208	+	0.830373i	$0.311873\pi$
$20$	7.11253e12	−	4.10642e12i	0.694583	−	0.401017i
$21$	−8.67046e12	+	1.47057e13i	−0.519816	+	0.881643i
$22$	−9.04188e10	+	1.56610e11i	−0.00340433	+	0.00589647i
$23$	−1.99240e13	−	1.15031e13i	−0.480948	−	0.277676i	0.239863	−	0.970807i	$-0.422897\pi$
$23$	−1.99240e13	−	1.15031e13i	−0.480948	−	0.277676i	−0.720812	+	0.693131i	$0.756231\pi$
$24$	1.95148e13	−	1.10304e13i	0.307789	−	0.173972i
$25$	7.50084e13	+	1.29918e14i	0.786520	+	1.36229i
$26$		−	1.48172e14i		−	1.04962i
$27$	2.05814e14	+	5.64334e12i	0.999624	+	0.0274093i
$28$	−1.51575e14			−0.511738
$29$	−4.37882e13	+	2.52811e13i	−0.104082	+	0.0600920i	−0.551138	−	0.834414i	$-0.685806\pi$
$29$	−4.37882e13	+	2.52811e13i	−0.104082	+	0.0600920i	0.447055	+	0.894506i	$0.352473\pi$
$30$	3.29567e14	+	5.83067e14i	0.558125	+	0.987429i
$31$	−5.34721e13	+	9.26164e13i	−0.0652394	+	0.112998i	−0.896800	−	0.442436i	$-0.854114\pi$
$31$	−5.34721e13	+	9.26164e13i	−0.0652394	+	0.112998i	0.831561	+	0.555434i	$0.187448\pi$
$32$	1.72368e14	+	9.95164e13i	0.153093	+	0.0883883i
$33$	−1.27037e13	−	7.49011e12i	−0.00829453	−	0.00489045i
$34$	1.18417e15	+	2.05104e15i	0.573621	+	0.993541i
$35$		−	4.52878e15i		−	1.64173i
$36$	8.84956e14	+	1.59960e15i	0.242045	+	0.437509i
$37$	−6.08677e15			−1.26581			−0.632906	−	0.774228i	$-0.718138\pi$
$37$	−6.08677e15			−1.26581			−0.632906	+	0.774228i	$0.718138\pi$
$38$	−4.28449e15	+	2.47365e15i	−0.682438	+	0.394006i
$39$	1.20830e16	+	1.10413e14i	1.48432	+	0.0135635i
$40$	−2.97336e15	+	5.15002e15i	−0.283562	+	0.491144i
$41$	−1.11337e16	−	6.42805e15i	−0.829471	−	0.478896i	0.0242002	−	0.999707i	$-0.492296\pi$
$41$	−1.11337e16	−	6.42805e15i	−0.829471	−	0.478896i	−0.853672	+	0.520812i	$0.825629\pi$
$42$	1.12949e14	−	1.23605e16i	0.00661284	−	0.723677i
$43$	−1.04115e16	−	1.80333e16i	−0.481760	−	0.834433i	0.518021	−	0.855368i	$-0.326669\pi$
$43$	−1.04115e16	−	1.80333e16i	−0.481760	−	0.834433i	−0.999781	+	0.0209353i	$0.993336\pi$
$44$		−	1.30940e14i		−	0.00481445i
$45$	−4.77931e16	+	2.64408e16i	−1.40359	+	0.776515i
$46$	1.66583e16			0.392693
$47$	−3.71215e16	+	2.14321e16i	−0.705744	+	0.407461i	−0.809483	−	0.587143i	$-0.800253\pi$
$47$	−3.71215e16	+	2.14321e16i	−0.705744	+	0.407461i	0.103740	+	0.994605i	$0.466919\pi$
$48$	−8.24374e15	+	1.39819e16i	−0.126973	+	0.215355i
$49$	−1.89519e15	+	3.28256e15i	−0.0237515	+	0.0411389i
$50$	−9.40709e16	−	5.43119e16i	−0.963286	−	0.556154i
$51$	−1.68139e17	+	9.50375e16i	−1.41243	+	0.798350i
$52$	5.36439e16	+	9.29140e16i	0.371097	+	0.642758i
$53$			2.87385e17i			1.64326i	0.570024	+	0.821628i	$0.306934\pi$
$53$			2.87385e17i			1.64326i	−0.570024	+	0.821628i	$0.693066\pi$
$54$	−1.31103e17	+	7.09738e16i	−0.621833	+	0.336636i
$55$	3.91225e15			0.0154454
$56$	9.50481e16	−	5.48761e16i	0.313374	−	0.180927i
$57$	−1.98527e17	−	3.51232e17i	−0.548366	−	0.970164i
$58$	1.83055e16	−	3.17061e16i	0.0424915	−	0.0735974i
$59$	3.86495e17	+	2.23143e17i	0.756177	+	0.436579i	0.827921	−	0.560844i	$-0.189523\pi$
$59$	3.86495e17	+	2.23143e17i	0.756177	+	0.436579i	−0.0717445	+	0.997423i	$0.522857\pi$
$60$	−4.17754e17	−	2.46307e17i	−0.690889	−	0.407347i
$61$	−4.61942e17	−	8.00108e17i	−0.647574	−	1.12163i	−0.983701	−	0.179814i	$-0.942450\pi$
$61$	−4.61942e17	−	8.00108e17i	−0.647574	−	1.12163i	0.336127	−	0.941817i	$-0.390883\pi$
$62$		−	7.74359e16i		−	0.0922625i
$63$	1.00788e18	+	1.84213e16i	1.02331	+	0.0187032i
$64$	−1.44115e17			−0.125000
$65$	−2.77610e18	+	1.60278e18i	−2.06206	+	1.19053i
$66$	1.06778e16	+	9.75723e13i	0.00680838	+	6.22139e-5i
$67$	−1.15505e18	+	2.00061e18i	−0.633655	+	1.09752i	0.353143	+	0.935569i	$0.385113\pi$
$67$	−1.15505e18	+	2.00061e18i	−0.633655	+	1.09752i	−0.986798	+	0.161954i	$0.948220\pi$
$68$	−1.48511e18	−	8.57431e17i	−0.702540	−	0.405611i
$69$	−1.24132e16	+	1.35844e18i	−0.00507450	+	0.555328i
$70$	1.63959e18	+	2.83986e18i	0.580438	+	1.00535i
$71$			4.08371e17i			0.125450i	0.998031	+	0.0627250i	$0.0199791\pi$
$71$			4.08371e17i			0.125450i	−0.998031	+	0.0627250i	$0.980021\pi$
$72$	−1.13405e18	−	6.82673e17i	−0.302905	−	0.182342i
$73$	−5.70990e18			−1.32862			−0.664309	−	0.747458i	$-0.731274\pi$
$73$	−5.70990e18			−1.32862			−0.664309	+	0.747458i	$0.731274\pi$
$74$	3.81683e18	−	2.20365e18i	0.775149	−	0.447532i
$75$	4.49908e18	−	7.63076e18i	0.798935	−	1.35505i
$76$	1.79111e18	−	3.10230e18i	0.278604	−	0.482556i
$77$	−6.25306e16	−	3.61020e16i	−0.00853464	−	0.00492748i
$78$	−7.61685e18	+	4.30528e18i	−0.913755	+	0.516482i
$79$	7.17413e18	+	1.24260e19i	0.757702	+	1.31238i	0.944020	+	0.329888i	$0.107011\pi$
$79$	7.17413e18	+	1.24260e19i	0.757702	+	1.31238i	−0.186319	+	0.982489i	$0.559656\pi$
$80$		−	4.30589e18i		−	0.401017i
$81$	−5.69003e18	−	1.07439e19i	−0.468020	−	0.883718i
$82$	9.30881e18			0.677261
$83$	−1.76947e19	+	1.02160e19i	−1.14041	+	0.658418i	−0.946533	−	0.322607i	$-0.895441\pi$
$83$	−1.76947e19	+	1.02160e19i	−1.14041	+	0.658418i	−0.193881	+	0.981025i	$0.562107\pi$
$84$	4.40417e18	+	7.79181e18i	0.251809	+	0.445498i
$85$	2.56184e19	−	4.43724e19i	1.30126	−	2.25385i
$86$	1.30575e19	+	7.53876e18i	0.590033	+	0.340656i
$87$	2.57190e18	+	1.51639e18i	0.103529	+	0.0610406i
$88$	4.74055e16	+	8.21087e16i	0.00170217	+	0.00294824i
$89$			8.44270e18i			0.270758i	0.990794	+	0.135379i	$0.0432252\pi$
$89$			8.44270e18i			0.270758i	−0.990794	+	0.135379i	$0.956775\pi$
$90$	2.03970e19	−	3.38832e19i	0.584980	−	0.971760i
$91$	5.91614e19			1.51923
$92$	−1.04459e19	+	6.03096e18i	−0.240474	+	0.138838i
$93$	6.31468e18	+	5.77026e16i	0.130473	+	0.00119225i
$94$	1.55185e19	−	2.68788e19i	0.288119	−	0.499036i
$95$	9.26910e19	+	5.35152e19i	1.54811	+	0.893801i
$96$	1.07390e17	−	1.17522e19i	0.00161529	−	0.176769i
$97$	9.95365e18	+	1.72402e19i	0.134979	+	0.233790i	0.925589	−	0.378529i	$-0.123570\pi$
$97$	9.95365e18	+	1.72402e19i	0.134979	+	0.233790i	−0.790611	+	0.612319i	$0.790237\pi$
$98$		−	2.74453e18i		−	0.0335897i
$99$	−1.59135e16	+	8.70675e17i	−0.000175960	+	0.00962729i
$100$	7.86520e19			0.786520
$101$	−1.55530e20	+	8.97954e19i	−1.40799	+	0.812906i	−0.995195	−	0.0979163i	$-0.968782\pi$
$101$	−1.55530e20	+	8.97954e19i	−1.40799	+	0.812906i	−0.412799	+	0.910822i	$0.635449\pi$
$102$	7.10278e19	−	1.20468e20i	0.582676	−	0.988258i
$103$	−1.27016e20	+	2.19998e20i	−0.945117	+	1.63699i	−0.189600	+	0.981861i	$0.560719\pi$
$103$	−1.27016e20	+	2.19998e20i	−0.945117	+	1.63699i	−0.755517	+	0.655129i	$0.772614\pi$
$104$	−6.72769e19	−	3.88423e19i	−0.454499	−	0.262405i
$105$	−2.32805e20	+	1.31588e20i	−1.42922	+	0.807838i
$106$	−1.04044e20	−	1.80210e20i	−0.580979	−	1.00628i
$107$		−	3.38566e20i		−	1.72110i	−0.509368	−	0.860549i	$-0.670121\pi$
$107$		−	3.38566e20i		−	1.72110i	0.509368	−	0.860549i	$-0.329879\pi$
$108$	5.65152e19	−	9.19697e19i	0.261775	−	0.425998i
$109$	5.36620e19			0.226674			0.113337	−	0.993557i	$-0.463846\pi$
$109$	5.36620e19			0.226674			0.113337	+	0.993557i	$0.463846\pi$
$110$	−2.45325e18	+	1.41639e18i	−0.00945836	+	0.00546078i
$111$	1.76857e20	+	3.12894e20i	0.622863	+	1.10196i
$112$	−3.97345e19	+	6.88222e19i	−0.127934	+	0.221589i
$113$	−9.91388e19	−	5.72378e19i	−0.292051	−	0.168616i	0.346815	−	0.937933i	$-0.387263\pi$
$113$	−9.91388e19	−	5.72378e19i	−0.292051	−	0.168616i	−0.638867	+	0.769318i	$0.720596\pi$
$114$	2.51650e20	+	1.48372e20i	0.678809	+	0.400225i
$115$	−1.80194e20	−	3.12105e20i	−0.445411	−	0.771475i
$116$			2.65092e19i			0.0600920i
$117$	−3.45408e20	−	6.24342e20i	−0.718578	−	1.29886i
$118$	−3.23145e20			−0.617416
$119$	−8.18932e20	+	4.72811e20i	−1.43806	+	0.830267i
$120$	3.51134e20	+	3.20860e18i	0.567101	+	0.00518207i
$121$	−3.36344e20	+	5.82565e20i	−0.499954	+	0.865945i
$122$	5.79340e20	+	3.34482e20i	0.793113	+	0.457904i
$123$	−6.93661e18	+	7.59108e20i	−0.00875178	+	0.957751i
$124$	2.80348e19	+	4.85577e19i	0.0326197	+	0.0564990i
$125$			8.56068e20i			0.919196i
$126$	−6.38683e20	+	3.53342e20i	−0.633256	+	0.350340i
$127$	−3.25700e20			−0.298387			−0.149194	−	0.988808i	$-0.547668\pi$
$127$	−3.25700e20			−0.298387			−0.149194	+	0.988808i	$0.547668\pi$
$128$	9.03702e19	−	5.21753e19i	0.0765466	−	0.0441942i
$129$	−6.24496e20	+	1.05919e21i	−0.489364	+	0.829996i
$130$	1.16054e21	−	2.01011e21i	0.841832	−	1.45810i
$131$	−1.16487e20	−	6.72538e19i	−0.0782644	−	0.0451860i	0.460357	−	0.887734i	$-0.347721\pi$
$131$	−1.16487e20	−	6.72538e19i	−0.0782644	−	0.0451860i	−0.538621	+	0.842548i	$0.681055\pi$
$132$	−6.73107e18	+	3.80460e18i	−0.00419126	+	0.00236903i
$133$	−9.87669e20	−	1.71069e21i	−0.570289	−	0.987770i
$134$		−	1.67269e21i		−	0.896124i
$135$	2.74788e21	+	1.68857e21i	1.36666	+	0.839810i
$136$	1.24169e21			0.573621
$137$	−6.80672e20	+	3.92986e20i	−0.292235	+	0.168722i	−0.638949	−	0.769249i	$-0.720631\pi$
$137$	−6.80672e20	+	3.92986e20i	−0.292235	+	0.168722i	0.346714	+	0.937971i	$0.387297\pi$
$138$	−4.84024e20	−	8.56331e20i	−0.193231	−	0.341862i
$139$	1.24417e21	−	2.15497e21i	0.462095	−	0.800373i	−0.536970	−	0.843601i	$-0.680431\pi$
$139$	1.24417e21	−	2.15497e21i	0.462095	−	0.800373i	0.999065	+	0.0432287i	$0.0137644\pi$
$140$	−2.05628e21	−	1.18719e21i	−0.710889	−	0.410432i
$141$	2.18033e21	+	1.28552e21i	0.701991	+	0.413893i
$142$	−1.47846e20	−	2.56077e20i	−0.0443533	−	0.0768222i
$143$			5.11074e19i			0.0142930i
$144$	9.58280e20	+	1.75147e19i	0.249958	+	0.00456854i
$145$	−7.92045e20			−0.192784
$146$	3.58050e21	−	2.06720e21i	0.813609	−	0.469737i
$147$	2.23809e20	+	2.04513e18i	0.0475011	+	0.000434057i
$148$	−1.59561e21	+	2.76368e21i	−0.316453	+	0.548113i
$149$	−3.88733e21	−	2.24435e21i	−0.720756	−	0.416129i	0.0942750	−	0.995546i	$-0.469947\pi$
$149$	−3.88733e21	−	2.24435e21i	−0.720756	−	0.416129i	−0.815031	+	0.579418i	$0.803280\pi$
$150$	−5.86088e19	+	6.41386e21i	−0.0101637	+	1.11226i
$151$	−3.02147e21	−	5.23334e21i	−0.490285	−	0.849199i	0.509652	−	0.860380i	$-0.329774\pi$
$151$	−3.02147e21	−	5.23334e21i	−0.490285	−	0.849199i	−0.999937	+	0.0111818i	$0.996441\pi$
$152$			2.59381e21i			0.394006i
$153$	9.77092e21	+	5.88190e21i	1.39002	+	0.836764i
$154$	5.22813e19			0.00696850
$155$	−1.45081e21	+	8.37627e20i	−0.181257	+	0.104649i
$156$	3.21762e21	−	5.45730e21i	0.376954	−	0.639340i
$157$	3.24291e21	−	5.61689e21i	0.356401	−	0.617305i	−0.630956	−	0.775819i	$-0.717337\pi$
$157$	3.24291e21	−	5.61689e21i	0.356401	−	0.617305i	0.987357	+	0.158514i	$0.0506704\pi$
$158$	−8.99735e21	−	5.19462e21i	−0.927991	−	0.535776i
$159$	1.47732e22	−	8.35025e21i	1.43055	−	0.808590i
$160$	1.55890e21	+	2.70009e21i	0.141781	+	0.245572i
$161$			6.65127e21i			0.568389i
$162$	7.45777e21	+	4.67719e21i	0.599044	+	0.375695i
$163$	1.02093e22			0.771116			0.385558	−	0.922684i	$-0.374009\pi$
$163$	1.02093e22			0.771116			0.385558	+	0.922684i	$0.374009\pi$
$164$	−5.83727e21	+	3.37015e21i	−0.414736	+	0.239448i
$165$	−1.13674e20	−	2.01112e20i	−0.00760017	−	0.0134461i
$166$	7.39720e21	−	1.28123e22i	0.465572	−	0.806394i
$167$	5.46994e21	+	3.15807e21i	0.324203	+	0.187179i	0.653265	−	0.757130i	$-0.273399\pi$
$167$	5.46994e21	+	3.15807e21i	0.324203	+	0.187179i	−0.329061	+	0.944309i	$0.606732\pi$
$168$	−5.58265e21	−	3.29153e21i	−0.311708	−	0.183783i
$169$	−1.14353e22	−	1.98065e22i	−0.601701	−	1.04218i
$170$			3.70995e22i			1.84026i
$171$	−1.22869e22	+	2.04108e22i	−0.574752	+	0.954769i
$172$	−1.09173e22			−0.481760
$173$	−3.93259e22	+	2.27048e22i	−1.63764	+	0.945490i	−0.655992	+	0.754768i	$0.727750\pi$
$173$	−3.93259e22	+	2.27048e22i	−1.63764	+	0.945490i	−0.981644	+	0.190722i	$0.938917\pi$
$174$	−2.16175e21	−	1.97538e19i	−0.0849794	−	0.000776528i
$175$	2.16854e22	−	3.75603e22i	0.804984	−	1.39427i
$176$	−5.94530e19	−	3.43252e19i	−0.00208472	−	0.00120361i
$177$	2.40797e20	−	2.63516e22i	0.00797844	−	0.873121i
$178$	−3.05658e21	−	5.29416e21i	−0.0957274	−	0.165805i
$179$		−	2.01936e22i		−	0.597975i	−0.954257	−	0.298987i	$-0.903351\pi$
$179$		−	2.01936e22i		−	0.597975i	0.954257	−	0.298987i	$-0.0966489\pi$
$180$	−5.23306e20	+	2.86316e22i	−0.0146565	+	0.801901i
$181$	6.08622e22			1.61273			0.806366	−	0.591417i	$-0.201431\pi$
$181$	6.08622e22			1.61273			0.806366	+	0.591417i	$0.201431\pi$
$182$	−3.70983e22	+	2.14187e22i	−0.930337	+	0.537130i
$183$	−2.77078e22	+	4.69943e22i	−0.657796	+	1.11567i
$184$	4.36688e21	−	7.56366e21i	0.0981732	−	0.170041i
$185$	−8.25735e22	−	4.76738e22i	−1.75842	−	1.01523i
$186$	−3.98064e21	+	2.24998e21i	−0.0803199	+	0.0453992i
$187$	−4.08444e20	−	7.07447e20i	−0.00781119	−	0.0135294i
$188$			2.24732e22i			0.407461i
$189$	−2.83381e22	−	5.23461e22i	−0.487251	−	0.900050i
$190$	−7.74982e22			−1.26403
$191$	−5.88269e22	+	3.39637e22i	−0.910420	+	0.525631i	−0.880566	−	0.473923i	$-0.842838\pi$
$191$	−5.88269e22	+	3.39637e22i	−0.910420	+	0.525631i	−0.0298540	+	0.999554i	$0.509504\pi$
$192$	4.18741e21	+	7.40832e21i	0.0615082	+	0.108820i
$193$	−2.20472e22	+	3.81868e22i	−0.307454	+	0.532525i	−0.977805	−	0.209519i	$-0.932810\pi$
$193$	−2.20472e22	+	3.81868e22i	−0.307454	+	0.532525i	0.670351	+	0.742044i	$0.266144\pi$
$194$	−1.24833e22	−	7.20721e21i	−0.165314	−	0.0954443i
$195$	1.63054e23	+	9.61364e22i	2.05109	+	1.20932i
$196$	9.93625e20	+	1.72101e21i	0.0118758	+	0.0205694i
$197$			6.40286e22i			0.727297i	0.931536	+	0.363648i	$0.118469\pi$
$197$			6.40286e22i			0.727297i	−0.931536	+	0.363648i	$0.881531\pi$
$198$	−3.05239e20	−	5.51735e20i	−0.00329601	−	0.00595770i
$199$	−1.08194e20			−0.00111090			−0.000555448	−	1.00000i	$-0.500177\pi$
$199$	−1.08194e20			−0.00111090			−0.000555448		1.00000i	$0.500177\pi$
$200$	−4.93203e22	+	2.84751e22i	−0.481643	+	0.278077i
$201$	1.36404e23	+	1.24643e21i	1.26726	+	0.0115800i
$202$	6.50188e22	−	1.12616e23i	0.574811	−	0.995602i
$203$	1.26595e22	+	7.30895e21i	0.106526	+	0.0615027i
$204$	−9.25267e20	+	1.01257e23i	−0.00741251	+	0.811189i
$205$	−1.00694e23	−	1.74407e23i	−0.768182	−	1.33053i
$206$		−	1.83939e23i		−	1.33660i
$207$	7.01921e22	−	3.88327e22i	0.485942	−	0.268840i
$208$	5.62497e22			0.371097
$209$	1.47781e21	−	8.53212e20i	0.00929298	−	0.00536530i
$210$	9.83446e22	−	1.66799e23i	0.589600	−	1.00000i
$211$	5.46452e22	−	9.46482e22i	0.312412	−	0.541113i	−0.666472	−	0.745530i	$-0.732196\pi$
$211$	5.46452e22	−	9.46482e22i	0.312412	−	0.541113i	0.978884	+	0.204417i	$0.0655298\pi$
$212$	1.30486e23	+	7.53362e22i	0.711550	+	0.410814i
$213$	2.09925e22	−	1.18656e22i	0.109212	−	0.0617297i
$214$	1.22574e23	+	2.12304e23i	0.608500	+	1.05395i
$215$		−	3.26188e23i		−	1.54555i
$216$	−2.14235e21	+	7.81321e22i	−0.00969066	+	0.353421i
$217$	3.09183e22			0.133542
$218$	−3.36498e22	+	1.94277e22i	−0.138809	+	0.0801414i
$219$	1.65907e23	+	2.93521e23i	0.653767	+	1.15664i
$220$	1.02557e21	−	1.77635e21i	0.00386136	−	0.00668807i
$221$	5.79656e23	+	3.34665e23i	2.08568	+	1.20417i
$222$	−2.24181e23	−	1.32177e23i	−0.771027	−	0.454597i
$223$	−1.14885e23	−	1.98987e23i	−0.377759	−	0.654299i	0.612976	−	0.790101i	$-0.289972\pi$
$223$	−1.14885e23	−	1.98987e23i	−0.377759	−	0.654299i	−0.990736	+	0.135803i	$0.956639\pi$
$224$		−	5.75417e22i		−	0.180927i
$225$	−5.22989e23	−	9.55877e21i	−1.57278	−	0.0287460i
$226$	8.28892e22			0.238459
$227$	−1.67461e23	+	9.66839e22i	−0.460952	+	0.266131i	−0.712445	−	0.701728i	$-0.752412\pi$
$227$	−1.67461e23	+	9.66839e22i	−0.460952	+	0.266131i	0.251492	+	0.967859i	$0.419079\pi$
$228$	−2.11518e23	−	1.93282e21i	−0.557185	−	0.00509147i
$229$	−1.06364e23	+	1.84228e23i	−0.268188	+	0.464515i	−0.968394	−	0.249426i	$-0.919758\pi$
$229$	−1.06364e23	+	1.84228e23i	−0.268188	+	0.464515i	0.700206	+	0.713941i	$0.253091\pi$
$230$	2.25988e23	+	1.30474e23i	0.545515	+	0.314953i
$231$	−3.89583e19	+	4.26340e21i	−9.00492e−5	+	0.00985454i
$232$	−9.59736e21	−	1.66231e22i	−0.0212457	−	0.0367987i
$233$			2.12636e23i			0.450897i	0.974255	+	0.225449i	$0.0723848\pi$
$233$			2.12636e23i			0.450897i	−0.974255	+	0.225449i	$0.927615\pi$
$234$	4.42631e23	+	2.66455e23i	0.899255	+	0.541333i
$235$	−6.71457e23			−1.30719
$236$	2.02635e23	−	1.16991e23i	0.378088	−	0.218289i
$237$	4.30312e23	−	7.29839e23i	0.769662	−	1.30540i
$238$	3.42352e23	−	5.92970e23i	0.587087	−	1.01687i
$239$	−8.24298e23	−	4.75909e23i	−1.35552	−	0.782609i	−0.366502	−	0.930417i	$-0.619445\pi$
$239$	−8.24298e23	−	4.75909e23i	−1.35552	−	0.782609i	−0.989016	+	0.147809i	$0.952778\pi$
$240$	−2.21347e23	+	1.25112e23i	−0.349109	+	0.197327i
$241$	4.02417e23	+	6.97006e23i	0.608843	+	1.05455i	0.991431	+	0.130628i	$0.0416995\pi$
$241$	4.02417e23	+	6.97006e23i	0.608843	+	1.05455i	−0.382588	+	0.923919i	$0.624967\pi$
$242$		−	4.87078e23i		−	0.707041i
$243$	−3.86970e23	+	6.04675e23i	−0.539031	+	0.842286i
$244$	−4.84382e23			−0.647574
$245$	−5.14205e22	+	2.96876e22i	−0.0659896	+	0.0380991i
$246$	−2.70477e23	−	4.78525e23i	−0.333257	−	0.589595i
$247$	−6.99091e23	+	1.21086e24i	−0.827112	+	1.43260i
$248$	−3.51595e22	−	2.02993e22i	−0.0399508	−	0.0230656i
$249$	1.03930e24	+	6.12769e23i	1.13435	+	0.668811i
$250$	−3.09930e23	−	5.36814e23i	−0.324985	−	0.562890i
$251$		−	1.16823e24i		−	1.17704i	−0.808483	−	0.588519i	$-0.799711\pi$
$251$		−	1.16823e24i		−	1.17704i	0.808483	−	0.588519i	$-0.200289\pi$
$252$	2.72575e23	−	4.52797e23i	0.263925	−	0.438428i
$253$	−5.74579e21			−0.00534742
$254$	2.04236e23	−	1.17916e23i	0.182724	−	0.105496i
$255$	−3.02536e24	−	2.76453e22i	−2.60241	−	0.0237804i
$256$	−3.77789e22	+	6.54350e22i	−0.0312500	+	0.0541266i
$257$	8.59422e23	+	4.96187e23i	0.683715	+	0.394743i	0.801253	−	0.598325i	$-0.204167\pi$
$257$	8.59422e23	+	4.96187e23i	0.683715	+	0.394743i	−0.117538	+	0.993068i	$0.537500\pi$
$258$	8.13520e21	−	8.90276e23i	0.00622545	−	0.681283i
$259$	8.79862e23	+	1.52397e24i	0.647764	+	1.12196i
$260$			1.68064e24i			1.19053i
$261$	3.22173e21	−	1.76270e23i	0.00219626	−	0.120164i
$262$	9.73938e22			0.0639026
$263$	6.48744e23	−	3.74553e23i	0.409747	−	0.236568i	−0.280934	−	0.959727i	$-0.590644\pi$
$263$	6.48744e23	−	3.74553e23i	0.409747	−	0.236568i	0.690681	+	0.723159i	$0.257311\pi$
$264$	2.84343e21	−	4.82266e21i	0.00172903	−	0.00293256i
$265$	−2.25090e24	+	3.89868e24i	−1.31795	+	2.28275i
$266$	1.23867e24	+	7.15149e23i	0.698459	+	0.403255i
$267$	4.34002e23	−	2.45311e23i	0.235710	−	0.133231i
$268$	6.05579e23	+	1.04889e24i	0.316828	+	0.548762i
$269$		−	2.06928e24i		−	1.04303i	−0.853242	−	0.521515i	$-0.825367\pi$
$269$		−	2.06928e24i		−	1.04303i	0.853242	−	0.521515i	$-0.174633\pi$
$270$	−2.33444e24	−	6.40095e22i	−1.13382	−	0.0310890i
$271$	3.76536e24			1.76244			0.881218	−	0.472710i	$-0.156724\pi$
$271$	3.76536e24			1.76244			0.881218	+	0.472710i	$0.156724\pi$
$272$	−7.78628e23	+	4.49541e23i	−0.351270	+	0.202806i
$273$	−1.71899e24	−	3.04123e24i	−0.747563	−	1.32258i
$274$	2.84552e23	−	4.92859e23i	0.119304	−	0.206641i
$275$	3.24470e22	+	1.87333e22i	0.0131174	+	0.00757332i
$276$	6.13541e23	+	3.61743e23i	0.239196	+	0.141029i
$277$	−1.02367e24	−	1.77305e24i	−0.384914	−	0.666690i	0.606843	−	0.794821i	$-0.292435\pi$
$277$	−1.02367e24	−	1.77305e24i	−0.384914	−	0.666690i	−0.991757	+	0.128131i	$0.959102\pi$
$278$			1.80175e24i			0.653502i
$279$	−1.80513e23	−	3.26287e23i	−0.0631636	−	0.114171i
$280$	1.71924e24			0.580438
$281$	2.63952e24	−	1.52393e24i	0.859927	−	0.496479i	−0.00406093	−	0.999992i	$-0.501293\pi$
$281$	2.63952e24	−	1.52393e24i	0.859927	−	0.496479i	0.863988	+	0.503513i	$0.167959\pi$
$282$	−1.83263e24	−	1.67463e22i	−0.576213	−	0.00526534i
$283$	2.82190e24	−	4.88768e24i	0.856402	−	1.48333i	−0.0189360	−	0.999821i	$-0.506028\pi$
$283$	2.82190e24	−	4.88768e24i	0.856402	−	1.48333i	0.875338	−	0.483511i	$-0.160639\pi$
$284$	1.85419e23	+	1.07052e23i	0.0543215	+	0.0313625i
$285$	5.77490e22	−	6.31977e24i	0.0163341	−	1.78753i
$286$	−1.85029e22	−	3.20479e22i	−0.00505334	−	0.00875265i
$287$			3.71678e24i			0.980276i
$288$	−6.07249e23	+	3.35951e23i	−0.154683	+	0.0855759i
$289$	−6.63417e24			−1.63233
$290$	4.96667e23	−	2.86751e23i	0.118055	−	0.0681593i
$291$	5.97031e23	−	1.01260e24i	0.137109	−	0.232547i
$292$	−1.49682e24	+	2.59256e24i	−0.332154	+	0.575308i
$293$	4.60556e24	+	2.65902e24i	0.987657	+	0.570224i	0.904573	−	0.426319i	$-0.140190\pi$
$293$	4.60556e24	+	2.65902e24i	0.987657	+	0.570224i	0.0830836	+	0.996543i	$0.473523\pi$
$294$	−1.41084e23	+	7.97449e22i	−0.0292418	+	0.0165284i
$295$	3.49548e24	+	6.05434e24i	0.700303	+	1.21296i
$296$		−	2.31069e24i		−	0.447532i
$297$	4.52199e22	−	2.44803e22i	0.00846770	−	0.00458408i
$298$	3.25016e24			0.588495
$299$	4.07716e24	−	2.35395e24i	0.713913	−	0.412178i
$300$	−2.28531e24	−	4.04315e24i	−0.387020	−	0.684711i
$301$	−3.01005e24	+	5.21355e24i	−0.493070	+	0.854022i
$302$	3.78934e24	+	2.18778e24i	0.600474	+	0.346684i
$303$	9.13507e24	+	5.38602e24i	1.40051	+	0.825737i
$304$	−9.39060e23	−	1.62650e24i	−0.139302	−	0.241278i
$305$		−	1.44724e25i		−	2.07751i
$306$	−8.25652e24	−	1.50906e23i	−1.14705	−	0.0209649i
$307$	7.43201e23			0.0999362			0.0499681	−	0.998751i	$-0.484088\pi$
$307$	7.43201e23			0.0999362			0.0499681	+	0.998751i	$0.484088\pi$
$308$	−3.27840e22	+	1.89279e22i	−0.00426732	+	0.00246374i
$309$	1.49997e25	+	1.37065e23i	1.89015	+	0.0172719i
$310$	6.06507e23	−	1.05050e24i	0.0739978	−	0.128168i
$311$	−7.81079e24	−	4.50956e24i	−0.922765	−	0.532759i	−0.0382488	−	0.999268i	$-0.512178\pi$
$311$	−7.81079e24	−	4.50956e24i	−0.922765	−	0.532759i	−0.884516	+	0.466510i	$0.845511\pi$
$312$	−4.19154e22	+	4.58701e24i	−0.00479543	+	0.524788i
$313$	−3.26100e23	−	5.64821e23i	−0.0361332	−	0.0625846i	0.847393	−	0.530966i	$-0.178171\pi$
$313$	−3.26100e23	−	5.64821e23i	−0.0361332	−	0.0625846i	−0.883526	+	0.468381i	$0.844837\pi$
$314$			4.69624e24i			0.504027i
$315$	1.35287e25	+	8.14403e24i	1.40654	+	0.846708i
$316$	7.52262e24			0.757702
$317$	−9.07358e24	+	5.23864e24i	−0.885495	+	0.511241i	−0.872466	−	0.488674i	$-0.837481\pi$
$317$	−9.07358e24	+	5.23864e24i	−0.885495	+	0.511241i	−0.0130290	+	0.999915i	$0.504147\pi$
$318$	−6.24070e24	+	1.05847e25i	−0.590149	+	1.00093i
$319$	−6.31394e21	+	1.09361e22i	−0.000578620	+	0.00100220i
$320$	−1.95508e24	−	1.12876e24i	−0.173646	−	0.100254i
$321$	−1.74042e25	+	9.83737e24i	−1.49832	+	0.846893i
$322$	−2.40802e24	−	4.17080e24i	−0.200956	−	0.348066i
$323$		−	2.23482e25i		−	1.80808i
$324$	−6.36986e24	−	2.32924e23i	−0.499666	−	0.0182711i
$325$	−3.06987e25			−2.33500
$326$	−6.40194e24	+	3.69616e24i	−0.472210	+	0.272631i
$327$	−1.55920e24	−	2.75853e24i	−0.111539	−	0.197333i
$328$	2.44025e24	−	4.22664e24i	0.169315	−	0.293262i
$329$	1.07321e25	+	6.19616e24i	0.722312	+	0.417027i
$330$	1.44092e23	+	8.49564e22i	0.00940806	+	0.00554698i
$331$	5.88449e24	+	1.01922e25i	0.372760	+	0.645639i	0.989989	−	0.141144i	$-0.0450782\pi$
$331$	5.88449e24	+	1.01922e25i	0.372760	+	0.645639i	−0.617229	+	0.786783i	$0.711745\pi$
$332$			1.07123e25i			0.658418i
$333$	1.09457e25	−	1.81829e25i	0.652833	−	1.08448i
$334$	−4.57337e24			−0.264711
$335$	−3.13390e25	+	1.80936e25i	−1.76050	+	1.01643i
$336$	4.69237e24	+	4.28781e22i	0.255858	+	0.00233799i
$337$	1.35298e25	−	2.34343e25i	0.716132	−	1.24038i	−0.246390	−	0.969171i	$-0.579244\pi$
$337$	1.35298e25	−	2.34343e25i	0.716132	−	1.24038i	0.962521	−	0.271206i	$-0.0874223\pi$
$338$	1.43415e25	+	8.28005e24i	0.736931	+	0.425467i
$339$	−6.17662e22	+	6.75939e24i	−0.00308144	+	0.337218i
$340$	−1.34314e25	−	2.32639e25i	−0.650629	−	1.12692i
$341$			2.67092e22i			0.00125637i
$342$	3.15232e23	−	1.72473e25i	0.0144002	−	0.787880i
$343$	−2.19727e25			−0.974858
$344$	6.84590e24	−	3.95248e24i	0.295016	−	0.170328i
$345$	−1.08082e25	+	1.83315e25i	−0.452442	+	0.767373i
$346$	1.64400e25	−	2.84750e25i	0.668562	−	1.15798i
$347$	−1.84040e25	−	1.06256e25i	−0.727139	−	0.419814i	0.0902356	−	0.995920i	$-0.471238\pi$
$347$	−1.84040e25	−	1.06256e25i	−0.727139	−	0.419814i	−0.817375	+	0.576107i	$0.804571\pi$
$348$	1.36272e24	−	7.70251e23i	0.0523136	−	0.0295692i
$349$	3.86177e24	+	6.68878e24i	0.144056	+	0.249513i	0.929020	−	0.370028i	$-0.120652\pi$
$349$	3.86177e24	+	6.68878e24i	0.144056	+	0.249513i	−0.784964	+	0.619541i	$0.787319\pi$
$350$			3.14038e25i			1.13842i
$351$	−2.20585e25	+	3.58968e25i	−0.777149	+	1.26469i
$352$	4.97082e22			0.00170217
$353$	−6.97163e23	+	4.02507e23i	−0.0232053	+	0.0133976i	−0.511558	−	0.859249i	$-0.670931\pi$
$353$	−6.97163e23	+	4.02507e23i	−0.0232053	+	0.0133976i	0.488352	+	0.872646i	$0.337598\pi$
$354$	9.38931e24	+	1.66115e25i	0.303809	+	0.537496i
$355$	−3.19851e24	+	5.53998e24i	−0.100615	+	0.174271i
$356$	3.83338e24	+	2.21320e24i	0.117242	+	0.0676895i
$357$	4.81000e25	+	2.83597e25i	1.43042	+	0.843373i
$358$	7.31086e24	+	1.26628e25i	0.211416	+	0.366183i
$359$			2.40384e25i			0.676021i	0.941142	+	0.338010i	$0.109754\pi$
$359$			2.40384e25i			0.676021i	−0.941142	+	0.338010i	$0.890246\pi$
$360$	−1.00376e25	−	1.81435e25i	−0.274540	−	0.496244i
$361$	9.09391e24			0.241924
$362$	−3.81648e25	+	2.20345e25i	−0.987593	+	0.570187i
$363$	3.97199e25	+	3.62954e23i	0.999866	+	0.00913661i
$364$	1.55088e25	−	2.68620e25i	0.379808	−	0.657848i
$365$	−7.74609e25	−	4.47221e25i	−1.84567	−	1.06560i
$366$	3.60945e23	−	3.95000e25i	0.00836816	−	0.915770i
$367$	−1.21188e24	−	2.09903e24i	−0.0273399	−	0.0473541i	0.852032	−	0.523490i	$-0.175370\pi$
$367$	−1.21188e24	−	2.09903e24i	−0.0273399	−	0.0473541i	−0.879372	+	0.476136i	$0.842037\pi$
$368$			6.32392e24i			0.138838i
$369$	3.92240e25	−	2.17001e25i	0.838084	−	0.463658i
$370$	6.90391e25			1.43575
$371$	7.19536e25	−	4.15424e25i	1.45651	−	0.840916i
$372$	1.68156e24	−	2.85204e24i	0.0331346	−	0.0561986i
$373$	−1.39422e24	+	2.41485e24i	−0.0267449	+	0.0463236i	−0.879088	−	0.476659i	$-0.841848\pi$
$373$	−1.39422e24	+	2.41485e24i	−0.0267449	+	0.0463236i	0.852343	+	0.522983i	$0.175181\pi$
$374$	5.12246e23	+	2.95745e23i	0.00956671	+	0.00552334i
$375$	4.40067e25	−	2.48739e25i	0.800214	−	0.452305i
$376$	−8.13616e24	−	1.40923e25i	−0.144059	−	0.249518i
$377$		−	1.03468e25i		−	0.178400i
$378$	3.67213e25	+	2.25652e25i	0.616595	+	0.378896i
$379$	4.34516e25			0.710582			0.355291	−	0.934756i	$-0.384382\pi$
$379$	4.34516e25			0.710582			0.355291	+	0.934756i	$0.384382\pi$
$380$	4.85968e25	−	2.80574e25i	0.774054	−	0.446900i
$381$	9.46353e24	+	1.67428e25i	0.146826	+	0.259763i
$382$	2.45923e25	−	4.25952e25i	0.371678	−	0.643764i
$383$	−4.18050e25	−	2.41361e25i	−0.615518	−	0.355370i	0.159604	−	0.987181i	$-0.448978\pi$
$383$	−4.18050e25	−	2.41361e25i	−0.615518	−	0.355370i	−0.775122	+	0.631812i	$0.782312\pi$
$384$	−5.30790e24	−	3.12953e24i	−0.0761395	−	0.0448918i
$385$	−5.65529e23	−	9.79525e23i	−0.00790401	−	0.0136902i
$386$		−	3.19277e25i		−	0.434805i
$387$	7.25935e25	+	1.32681e24i	0.963359	+	0.0176075i
$388$	1.04372e25			0.134979
$389$	−7.59402e25	+	4.38441e25i	−0.957141	+	0.552605i	−0.895292	−	0.445480i	$-0.853033\pi$
$389$	−7.59402e25	+	4.38441e25i	−0.957141	+	0.552605i	−0.0618489	+	0.998086i	$0.519700\pi$
$390$	−1.37051e26	−	1.25235e24i	−1.68359	−	0.0153844i
$391$	−3.76249e25	+	6.51683e25i	−0.450514	+	0.780313i
$392$	−1.24614e24	−	7.19461e23i	−0.0145448	−	0.00839743i
$393$	−7.25746e22	+	7.94220e24i	−0.000825770	+	0.0903682i
$394$	−2.31808e25	−	4.01504e25i	−0.257138	−	0.445376i
$395$			2.24762e26i			2.43081i
$396$	3.91156e23	+	2.35468e23i	0.00412475	+	0.00248302i
$397$	−8.53397e24			−0.0877498			−0.0438749	−	0.999037i	$-0.513970\pi$
$397$	−8.53397e24			−0.0877498			−0.0438749	+	0.999037i	$0.513970\pi$
$398$	6.78453e22	−	3.91705e22i	0.000680282	−	0.000392761i
$399$	−5.92415e25	+	1.00478e26i	−0.579291	+	0.982518i
$400$	2.06181e25	−	3.57117e25i	0.196630	−	0.340573i
$401$	−1.27396e26	−	7.35523e25i	−1.18499	−	0.684152i	−0.227823	−	0.973703i	$-0.573161\pi$
$401$	−1.27396e26	−	7.35523e25i	−1.18499	−	0.684152i	−0.957163	+	0.289551i	$0.906494\pi$
$402$	−8.59857e25	+	4.86017e25i	−0.780128	+	0.440952i
$403$	−1.09423e25	−	1.89526e25i	−0.0968405	−	0.167733i
$404$			9.41573e25i			0.812906i
$405$	6.95934e24	−	1.90320e26i	0.0586162	−	1.60300i
$406$	−1.05845e25			−0.0869780
$407$	−1.31650e24	+	7.60082e23i	−0.0105555	+	0.00609419i
$408$	−3.60786e25	−	6.38299e25i	−0.282259	−	0.499370i
$409$	9.09184e25	−	1.57475e26i	0.694095	−	1.20221i	−0.276390	−	0.961046i	$-0.589138\pi$
$409$	9.09184e25	−	1.57475e26i	0.694095	−	1.20221i	0.970485	−	0.241162i	$-0.0775285\pi$
$410$	1.26284e26	+	7.29101e25i	0.940827	+	0.543187i
$411$	3.99793e25	+	2.35717e25i	0.290681	+	0.171385i
$412$	6.65929e25	+	1.15342e26i	0.472558	+	0.818495i
$413$		−	1.29024e26i		−	0.893656i
$414$	−2.99564e25	+	4.97631e25i	−0.202528	+	0.336437i
$415$	−3.20063e26			−2.11230
$416$	−3.52725e25	+	2.03646e25i	−0.227249	+	0.131202i
$417$	−1.46928e26	−	1.34260e24i	−0.924152	−	0.00844475i
$418$	−6.17792e23	+	1.07005e24i	−0.00379384	+	0.00657113i
$419$	1.20430e26	+	6.95301e25i	0.722093	+	0.416901i	0.815523	−	0.578725i	$-0.196450\pi$
$419$	1.20430e26	+	6.95301e25i	0.722093	+	0.416901i	−0.0934295	+	0.995626i	$0.529783\pi$
$420$	−1.28112e24	+	1.40199e26i	−0.00750060	+	0.820829i
$421$	6.94255e25	+	1.20249e26i	0.396916	+	0.687478i	0.993344	−	0.115189i	$-0.0367472\pi$
$421$	6.94255e25	+	1.20249e26i	0.396916	+	0.687478i	−0.596428	+	0.802667i	$0.703414\pi$
$422$			7.91347e25i			0.441817i
$423$	2.73122e24	−	1.49433e26i	0.0148920	−	0.814786i
$424$	−1.09098e26			−0.580979
$425$	4.24942e26	−	2.45340e26i	2.21025	−	1.27609i
$426$	−8.86796e24	+	1.50407e25i	−0.0450534	+	0.0764137i
$427$	−1.33551e26	+	2.31316e26i	−0.662776	+	1.14796i
$428$	−1.53725e26	−	8.87530e25i	−0.745257	−	0.430274i
$429$	2.62721e24	−	1.48498e24i	0.0124429	−	0.00703310i
$430$	1.18093e26	+	2.04543e26i	0.546435	+	0.946454i
$431$		−	2.59226e26i		−	1.17194i	−0.810332	−	0.585971i	$-0.800713\pi$
$431$		−	2.59226e26i		−	1.17194i	0.810332	−	0.585971i	$-0.199287\pi$
$432$	−2.69434e25	−	4.97698e25i	−0.119019	−	0.219851i
$433$	−6.00398e25			−0.259155			−0.129578	−	0.991569i	$-0.541362\pi$
$433$	−6.00398e25			−0.259155			−0.129578	+	0.991569i	$0.541362\pi$
$434$	−1.93879e25	+	1.11936e25i	−0.0817774	+	0.0472142i
$435$	2.30137e25	+	4.07156e25i	0.0948622	+	0.167829i
$436$	1.40672e25	−	2.43651e25i	0.0566686	−	0.0981528i
$437$	−1.36132e26	−	7.85959e25i	−0.535977	−	0.309446i
$438$	−2.10301e26	−	1.23993e26i	−0.809282	−	0.477152i
$439$	1.70308e26	+	2.94982e26i	0.640603	+	1.10956i	0.985298	+	0.170843i	$0.0546490\pi$
$439$	1.70308e26	+	2.94982e26i	0.640603	+	1.10956i	−0.344695	+	0.938715i	$0.612018\pi$
$440$			1.48519e24i			0.00546078i
$441$	−6.39785e24	−	1.15644e25i	−0.0229958	−	0.0415660i
$442$	−4.84646e26			−1.70295
$443$	2.21589e26	−	1.27935e26i	0.761222	−	0.439492i	−0.0685123	−	0.997650i	$-0.521825\pi$
$443$	2.21589e26	−	1.27935e26i	0.761222	−	0.439492i	0.829734	+	0.558159i	$0.188492\pi$
$444$	1.88430e26	+	1.72185e24i	0.632880	+	0.00578315i
$445$	−6.61263e25	+	1.14534e26i	−0.217157	+	0.376127i
$446$	1.44082e26	+	8.31857e25i	0.462659	+	0.267116i
$447$	−2.42191e24	+	2.65042e26i	−0.00760471	+	0.832222i
$448$	2.08323e25	+	3.60827e25i	0.0639672	+	0.110795i
$449$		−	3.39399e26i		−	1.01917i	−0.860420	−	0.509586i	$-0.829799\pi$
$449$		−	3.39399e26i		−	1.01917i	0.860420	−	0.509586i	$-0.170201\pi$
$450$	3.31411e26	−	1.83348e26i	0.973289	−	0.538458i
$451$	−3.21080e24			−0.00922248
$452$	−5.19773e25	+	3.00091e25i	−0.146026	+	0.0843080i
$453$	−1.81231e26	+	3.07380e26i	−0.498024	+	0.844683i
$454$	7.00066e25	−	1.21255e26i	0.188183	−	0.325943i
$455$	8.02588e26	+	4.63374e26i	2.11047	+	1.21848i
$456$	1.33336e26	−	7.53658e25i	0.343005	−	0.193877i
$457$	−1.29708e26	−	2.24661e26i	−0.326441	−	0.565413i	0.655362	−	0.755315i	$-0.272516\pi$
$457$	−1.29708e26	−	2.24661e26i	−0.326441	−	0.565413i	−0.981803	+	0.189902i	$0.939183\pi$
$458$		−	1.54031e26i		−	0.379275i
$459$	1.84585e25	−	6.73184e26i	0.0444701	−	1.62184i
$460$	−1.88947e26			−0.445411
$461$	−3.02090e26	+	1.74412e26i	−0.696830	+	0.402315i	−0.806166	−	0.591690i	$-0.798461\pi$
$461$	−3.02090e26	+	1.74412e26i	−0.696830	+	0.402315i	0.109336	+	0.994005i	$0.465128\pi$
$462$	−1.51909e24	−	2.68755e24i	−0.00342896	−	0.00606649i
$463$	−4.60365e25	+	7.97376e25i	−0.101693	+	0.176138i	−0.912382	−	0.409339i	$-0.865759\pi$
$463$	−4.60365e25	+	7.97376e25i	−0.101693	+	0.176138i	0.810689	+	0.585477i	$0.199093\pi$
$464$	1.20364e25	+	6.94923e24i	0.0260206	+	0.0150230i
$465$	8.52135e25	+	5.02418e25i	0.180293	+	0.106300i
$466$	−7.69825e25	−	1.33338e26i	−0.159416	−	0.276117i
$467$		−	3.75500e26i		−	0.761100i	−0.924760	−	0.380550i	$-0.875735\pi$
$467$		−	3.75500e26i		−	0.761100i	0.924760	−	0.380550i	$-0.124265\pi$
$468$	−3.74027e26	−	6.83617e24i	−0.742069	−	0.0135630i
$469$	6.67866e26			1.29706
$470$	4.21050e26	−	2.43093e26i	0.800489	−	0.462162i
$471$	−3.82966e26	−	3.49948e24i	−0.712772	−	0.00651320i
$472$	−8.47106e25	+	1.46723e26i	−0.154354	+	0.267349i
$473$	−4.50380e24	−	2.60027e24i	−0.00803467	−	0.00463882i
$474$	−5.60560e24	+	6.13449e26i	−0.00979126	+	1.07151i
$475$	5.12499e26	+	8.87675e26i	0.876511	+	1.51816i
$476$			4.95778e26i			0.830267i
$477$	−8.58499e26	−	5.16799e26i	−1.40785	−	0.847497i
$478$	6.89189e26			1.10678
$479$	−1.81412e26	+	1.04738e26i	−0.285306	+	0.164722i	−0.635823	−	0.771835i	$-0.719339\pi$
$479$	−1.81412e26	+	1.04738e26i	−0.285306	+	0.164722i	0.350517	+	0.936556i	$0.386006\pi$
$480$	9.35045e25	−	1.58590e26i	0.144019	−	0.244266i
$481$	6.22784e26	−	1.07869e27i	0.939478	−	1.62722i
$482$	−5.04686e26	−	2.91381e26i	−0.745678	−	0.430517i
$483$	3.41912e26	−	1.93259e26i	0.494815	−	0.279685i
$484$	1.76341e26	+	3.05432e26i	0.249977	+	0.432973i
$485$			3.11843e26i			0.433030i
$486$	2.37409e25	−	5.19271e26i	0.0322950	−	0.706369i
$487$	−5.41217e26			−0.721243			−0.360622	−	0.932712i	$-0.617435\pi$
$487$	−5.41217e26			−0.721243			−0.360622	+	0.932712i	$0.617435\pi$
$488$	3.03741e26	−	1.75365e26i	0.396556	−	0.228952i
$489$	−2.96641e26	−	5.24815e26i	−0.379440	−	0.671301i
$490$	2.14962e25	−	3.72324e25i	0.0269401	−	0.0466617i
$491$	9.29002e26	+	5.36359e26i	1.14078	+	0.658629i	0.946623	−	0.322342i	$-0.104470\pi$
$491$	9.29002e26	+	5.36359e26i	1.14078	+	0.658629i	0.194156	+	0.980971i	$0.437803\pi$
$492$	3.42852e26	+	2.02145e26i	0.412530	+	0.243227i
$493$	8.26906e25	+	1.43224e26i	0.0974960	+	0.168868i
$494$		−	1.01239e27i		−	1.16971i
$495$	−7.03534e24	+	1.16870e25i	−0.00796586	+	0.0132328i
$496$	2.93966e25			0.0326197
$497$	1.02245e26	−	5.90313e25i	0.111193	−	0.0641976i
$498$	−8.73559e26	−	7.98244e24i	−0.931105	−	0.00850829i
$499$	5.42966e26	−	9.40444e26i	0.567240	−	0.982488i	−0.429598	−	0.903020i	$-0.641345\pi$
$499$	5.42966e26	−	9.40444e26i	0.567240	−	0.982488i	0.996837	−	0.0794679i	$-0.0253221\pi$
$500$	3.88695e26	+	2.24413e26i	0.398024	+	0.229799i
$501$	3.40792e24	−	3.72946e26i	0.00342068	−	0.374342i
$502$	4.22944e26	+	7.32561e26i	0.416146	+	0.720786i
$503$			1.85221e27i			1.78653i	0.449534	+	0.893263i	$0.351590\pi$
$503$			1.85221e27i			1.78653i	−0.449534	+	0.893263i	$0.648410\pi$
$504$	−6.99319e24	+	3.82618e26i	−0.00661256	+	0.361793i
$505$	−2.81324e27			−2.60792
$506$	3.60301e24	−	2.08020e24i	0.00327462	−	0.00189060i
$507$	−6.85902e26	+	1.16334e27i	−0.611199	+	1.03664i
$508$	−8.53802e25	+	1.47883e26i	−0.0745968	+	0.129205i
$509$	−1.90313e27	−	1.09877e27i	−1.63039	−	0.941306i	−0.983972	−	0.178322i	$-0.942933\pi$
$509$	−1.90313e27	−	1.09877e27i	−1.63039	−	0.941306i	−0.646418	−	0.762984i	$-0.723734\pi$
$510$	1.90712e27	−	1.07796e27i	1.60205	−	0.905528i
$511$	8.25385e26	+	1.42961e27i	0.679904	+	1.17763i
$512$		−	5.47097e25i		−	0.0441942i
$513$	1.40624e27	+	3.85584e25i	1.11400	+	0.0305454i
$514$	−7.18556e26			−0.558251
$515$	−3.44621e27	+	1.98967e27i	−2.62585	+	1.51603i
$516$	3.17213e26	+	5.61210e26i	0.237058	+	0.419400i
$517$	−5.35265e24	+	9.27105e24i	−0.00392340	+	0.00679554i
$518$	−1.10347e27	−	6.37088e26i	−0.793346	−	0.458039i
$519$	2.30981e27	+	1.36186e27i	1.62893	+	0.960414i
$520$	−6.08455e26	−	1.05388e27i	−0.420916	−	0.729048i
$521$			1.95978e27i			1.32993i	0.746873	+	0.664966i	$0.231554\pi$
$521$			1.95978e27i			1.32993i	−0.746873	+	0.664966i	$0.768446\pi$
$522$	6.17964e25	+	1.11700e26i	0.0411395	+	0.0743616i
$523$	−1.44938e26			−0.0946599			−0.0473299	−	0.998879i	$-0.515071\pi$
$523$	−1.44938e26			−0.0946599			−0.0473299	+	0.998879i	$0.515071\pi$
$524$	−6.10727e25	+	3.52603e25i	−0.0391322	+	0.0225930i
$525$	−2.56090e27	−	2.34011e25i	−1.60990	−	0.0147110i
$526$	−2.71205e26	+	4.69741e26i	−0.167279	+	0.289735i
$527$	3.02933e26	+	1.74899e26i	0.183333	+	0.105847i
$528$	−3.70409e22	+	4.05357e24i	−2.19959e−5	+	0.00240713i
$529$	−5.93434e26	−	1.02786e27i	−0.345792	−	0.598930i
$530$		−	3.25966e27i		−	1.86386i
$531$	−1.36162e27	+	7.53294e26i	−0.764029	+	0.422688i
$532$	−1.03565e27			−0.570289
$533$	2.27835e27	−	1.31541e27i	1.23126	−	0.710866i
$534$	−1.83337e26	+	3.10952e26i	−0.0972384	+	0.164923i
$535$	2.65177e27	−	4.59301e27i	1.38038	−	2.39089i
$536$	−7.59480e26	−	4.38486e26i	−0.388033	−	0.224031i
$537$	−1.03806e27	+	5.86745e26i	−0.520572	+	0.294243i
$538$	7.49160e26	+	1.29758e27i	0.368767	+	0.638723i
$539$			9.46643e23i			0.000457402i
$540$	1.48703e27	−	8.05019e26i	0.705313	−	0.381829i
$541$	−1.84462e27			−0.858884			−0.429442	−	0.903095i	$-0.641290\pi$
$541$	−1.84462e27			−0.858884			−0.429442	+	0.903095i	$0.641290\pi$
$542$	−2.36114e27	+	1.36321e27i	−1.07927	+	0.623115i
$543$	−1.76841e27	−	3.12866e27i	−0.793570	−	1.40398i
$544$	3.25502e26	−	5.63787e26i	0.143405	−	0.248385i
$545$	7.27983e26	+	4.20301e26i	0.314888	+	0.181801i
$546$	2.17897e27	+	1.28472e27i	0.925390	+	0.545609i
$547$	5.95431e26	+	1.03132e27i	0.248289	+	0.430050i	0.963051	−	0.269318i	$-0.0867983\pi$
$547$	5.95431e26	+	1.03132e27i	0.248289	+	0.430050i	−0.714762	+	0.699368i	$0.753465\pi$
$548$			4.12076e26i			0.168722i
$549$	3.22085e27	+	5.88681e25i	1.29493	+	0.0236677i
$550$	−2.71287e25			−0.0107103
$551$	−2.99186e26	+	1.72735e26i	−0.115991	+	0.0669675i
$552$	−5.15698e26	−	4.71237e24i	−0.196338	−	0.00179411i
$553$	2.07409e27	−	3.59243e27i	0.775489	−	1.34319i
$554$	1.28383e27	+	7.41218e26i	0.471421	+	0.272175i
$555$	−5.14456e25	+	5.62995e27i	−0.0185532	+	2.03037i
$556$	−6.52303e26	−	1.12982e27i	−0.231048	−	0.400186i
$557$		−	1.47553e27i		−	0.513331i	−0.966500	−	0.256665i	$-0.917376\pi$
$557$		−	1.47553e27i		−	0.513331i	0.966500	−	0.256665i	$-0.0826238\pi$
$558$	2.31323e26	+	1.39252e26i	0.0790453	+	0.0475837i
$559$	4.26114e27			1.43024
$560$	−1.07808e27	+	6.22431e26i	−0.355444	+	0.205216i
$561$	−2.44989e25	+	4.15519e25i	−0.00793448	+	0.0134574i
$562$	−1.10344e27	+	1.91122e27i	−0.351064	+	0.608060i
$563$	−5.58880e26	−	3.22670e26i	−0.174677	−	0.100850i	0.410113	−	0.912035i	$-0.365489\pi$
$563$	−5.58880e26	−	3.22670e26i	−0.174677	−	0.100850i	−0.584789	+	0.811185i	$0.698823\pi$
$564$	1.15525e27	−	6.52981e26i	0.354719	−	0.200498i
$565$	−8.96616e26	−	1.55298e27i	−0.270472	−	0.468471i
$566$			4.08655e27i			1.21114i
$567$	−1.86749e27	+	2.97771e27i	−0.543786	+	0.867064i
$568$	−1.55028e26			−0.0443533
$569$	−4.20172e26	+	2.42586e26i	−0.118115	+	0.0681936i	−0.557893	−	0.829913i	$-0.688390\pi$
$569$	−4.20172e26	+	2.42586e26i	−0.118115	+	0.0681936i	0.439779	+	0.898106i	$0.355057\pi$
$570$	2.25179e27	+	3.98384e27i	0.621984	+	1.10041i
$571$	2.03620e27	−	3.52680e27i	0.552662	−	0.957239i	−0.445419	−	0.895322i	$-0.646945\pi$
$571$	2.03620e27	−	3.52680e27i	0.552662	−	0.957239i	0.998081	−	0.0619166i	$-0.0197213\pi$
$572$	2.32052e25	+	1.33975e25i	0.00618906	+	0.00357325i
$573$	3.45520e27	+	2.03718e27i	0.905579	+	0.533928i
$574$	−1.34562e27	−	2.33068e27i	−0.346580	−	0.600294i
$575$		−	3.45133e27i		−	0.873590i
$576$	2.59160e26	−	4.30513e26i	0.0644678	−	0.107093i
$577$	3.75159e27			0.917186			0.458593	−	0.888647i	$-0.348354\pi$
$577$	3.75159e27			0.917186			0.458593	+	0.888647i	$0.348354\pi$
$578$	4.16008e27	−	2.40182e27i	0.999594	−	0.577116i
$579$	2.60362e27	+	2.37914e25i	0.614882	+	0.00561869i
$580$	−2.07630e26	+	3.59626e26i	−0.0481959	+	0.0834777i
$581$	5.11566e27	+	2.95353e27i	1.16719	+	0.673875i
$582$	−7.77741e24	+	8.51122e26i	−0.00174424	+	0.190881i
$583$	3.58870e25	+	6.21581e25i	0.00791137	+	0.0137029i
$584$		−	2.16762e27i		−	0.469737i
$585$	2.04252e26	−	1.11752e28i	0.0435118	−	2.38066i
$586$	−3.85067e27			−0.806418
$587$	−7.02910e25	+	4.05825e25i	−0.0144717	+	0.00835522i	−0.507218	−	0.861818i	$-0.669326\pi$
$587$	−7.02910e25	+	4.05825e25i	−0.0144717	+	0.00835522i	0.492747	+	0.870173i	$0.335993\pi$
$588$	5.95987e25	−	1.01083e26i	0.0120632	−	0.0204601i
$589$	−3.65351e26	+	6.32807e26i	−0.0727039	+	0.125927i
$590$	−4.38381e27	−	2.53099e27i	−0.857693	−	0.495189i
$591$	3.29143e27	−	1.86041e27i	0.633154	−	0.357878i
$592$	8.36559e26	+	1.44896e27i	0.158227	+	0.274056i
$593$			3.25998e26i			0.0606273i	0.999540	+	0.0303137i	$0.00965061\pi$
$593$			3.25998e26i			0.0606273i	−0.999540	+	0.0303137i	$0.990349\pi$
$594$	−1.94932e25	+	3.17222e25i	−0.00356467	+	0.00580095i
$595$	−1.48129e28			−2.66361
$596$	−2.03808e27	+	1.17668e27i	−0.360378	+	0.208064i
$597$	3.14369e24	+	5.56179e24i	0.000546634	+	0.000967100i
$598$	−1.70444e27	+	2.95218e27i	−0.291454	+	0.504813i
$599$	1.41711e26	+	8.18170e25i	0.0238307	+	0.0137586i	0.511868	−	0.859064i	$-0.328954\pi$
$599$	1.41711e26	+	8.18170e25i	0.0238307	+	0.0137586i	−0.488037	+	0.872823i	$0.662287\pi$
$600$	2.89683e27	+	1.70797e27i	0.479082	+	0.282466i
$601$	3.58359e27	+	6.20696e27i	0.582872	+	1.00956i	0.995137	+	0.0985002i	$0.0314045\pi$
$601$	3.58359e27	+	6.20696e27i	0.582872	+	1.00956i	−0.412265	+	0.911064i	$0.635262\pi$
$602$		−	4.35901e27i		−	0.697306i
$603$	−3.89927e27	−	7.04812e27i	−0.613493	−	1.10892i
$604$	−3.16824e27			−0.490285
$605$	−9.12572e27	+	5.26874e27i	−1.38904	+	0.801961i
$606$	−7.67827e27	−	7.01628e25i	−1.14957	−	0.0105046i
$607$	4.96623e26	−	8.60177e26i	0.0731375	−	0.126678i	−0.827137	−	0.562000i	$-0.810032\pi$
$607$	4.96623e26	−	8.60177e26i	0.0731375	−	0.126678i	0.900275	+	0.435322i	$0.143365\pi$
$608$	1.17771e27	+	6.79952e26i	0.170609	+	0.0985014i
$609$	7.88720e24	−	8.63136e26i	0.00112396	−	0.123000i
$610$	5.23957e27	+	9.07521e27i	0.734510	+	1.27221i
$611$		−	8.77153e27i		−	1.20966i
$612$	5.23204e27	−	2.89455e27i	0.709834	−	0.392705i
$613$	−1.25966e27			−0.168131			−0.0840657	−	0.996460i	$-0.526791\pi$
$613$	−1.25966e27			−0.168131			−0.0840657	+	0.996460i	$0.526791\pi$
$614$	−4.66039e26	+	2.69068e26i	−0.0611982	+	0.0353328i
$615$	−6.03972e27	+	1.02438e28i	−0.780307	+	1.32346i
$616$	1.37052e25	−	2.37382e25i	0.00174213	−	0.00301745i
$617$	5.41799e27	+	3.12808e27i	0.677620	+	0.391224i	0.798958	−	0.601387i	$-0.205385\pi$
$617$	5.41799e27	+	3.12808e27i	0.677620	+	0.391224i	−0.121338	+	0.992611i	$0.538718\pi$
$618$	−9.45547e27	+	5.34452e27i	−1.16359	+	0.657694i
$619$	1.54446e27	+	2.67508e27i	0.187012	+	0.323914i	0.944253	−	0.329222i	$-0.106786\pi$
$619$	1.54446e27	+	2.67508e27i	0.187012	+	0.323914i	−0.757241	+	0.653136i	$0.773453\pi$
$620$			8.78315e26i			0.104649i
$621$	−4.03572e27	−	2.47994e27i	−0.473157	−	0.290754i
$622$	6.53054e27			0.753434
$623$	2.11383e27	−	1.22042e27i	0.239988	−	0.138557i
$624$	−1.63439e27	−	2.89155e27i	−0.182604	−	0.323061i
$625$	4.48314e26	−	7.76502e26i	0.0492926	−	0.0853773i
$626$	4.08974e26	+	2.36121e26i	0.0442540	+	0.0255501i
$627$	−8.67990e25	−	5.11766e25i	−0.00924357	−	0.00544999i
$628$	−1.70022e27	−	2.94487e27i	−0.178200	−	0.308652i
$629$			1.99088e28i			2.05371i
$630$	−1.14319e28	−	2.08943e26i	−1.16068	−	0.0212140i
$631$	7.63696e27			0.763180			0.381590	−	0.924332i	$-0.375377\pi$
$631$	7.63696e27			0.763180			0.381590	+	0.924332i	$0.375377\pi$
$632$	−4.71720e27	+	2.72348e27i	−0.463996	+	0.267888i
$633$	−6.45322e27	−	5.89685e25i	−0.624797	−	0.00570930i
$634$	3.79318e27	−	6.56998e27i	0.361502	−	0.626140i
$635$	−4.41846e27	−	2.55100e27i	−0.414509	−	0.239317i
$636$	8.12965e25	−	8.89668e27i	0.00750759	−	0.821593i
$637$	−3.87822e26	−	6.71728e26i	−0.0352565	−	0.0610660i
$638$		−	9.14356e24i		−	0.000818293i
$639$	−1.21992e27	−	7.34366e26i	−0.107479	−	0.0646999i
$640$	1.63462e27			0.141781
$641$	1.33512e28	−	7.70830e27i	1.14009	−	0.658231i	0.193636	−	0.981073i	$-0.437972\pi$
$641$	1.33512e28	−	7.70830e27i	1.14009	−	0.658231i	0.946453	+	0.322843i	$0.104639\pi$
$642$	7.35212e27	−	1.24697e28i	0.618105	−	1.04835i
$643$	−7.08614e27	+	1.22736e28i	−0.586543	+	1.01592i	0.408138	+	0.912920i	$0.366178\pi$
$643$	−7.08614e27	+	1.22736e28i	−0.586543	+	1.01592i	−0.994681	+	0.103002i	$0.967155\pi$
$644$	3.01999e27	+	1.74359e27i	0.246120	+	0.142097i
$645$	−1.67679e28	+	9.47773e27i	−1.34549	+	0.760514i
$646$	8.09092e27	+	1.40139e28i	0.639253	+	1.10722i
$647$			1.51132e28i			1.17574i	0.808954	+	0.587871i	$0.200034\pi$
$647$			1.51132e28i			1.17574i	−0.808954	+	0.587871i	$0.799966\pi$
$648$	4.07867e27	−	2.16008e27i	0.312442	−	0.165470i
$649$	1.11459e26			0.00840755
$650$	1.92502e28	−	1.11141e28i	1.42989	−	0.825547i
$651$	−8.98361e26	−	1.58937e27i	−0.0657115	−	0.116256i
$652$	2.67631e27	−	4.63550e27i	0.192779	−	0.333903i
$653$	6.05384e25	+	3.49519e25i	0.00429437	+	0.00247935i	0.502146	−	0.864783i	$-0.332544\pi$
$653$	6.05384e25	+	3.49519e25i	0.00429437	+	0.00247935i	−0.497851	+	0.867262i	$0.665877\pi$
$654$	1.97642e27	+	1.16530e27i	0.138071	+	0.0814065i
$655$	−1.05351e27	−	1.82474e27i	−0.0724814	−	0.125542i
$656$			3.53386e27i			0.239448i
$657$	1.02680e28	−	1.70571e28i	0.685224	−	1.13828i
$658$	−8.97300e27			−0.589765
$659$	6.74915e27	−	3.89662e27i	0.436913	−	0.252252i	−0.265374	−	0.964145i	$-0.585496\pi$
$659$	6.74915e27	−	3.89662e27i	0.436913	−	0.252252i	0.702287	+	0.711894i	$0.252162\pi$
$660$	−1.21113e26	−	1.10671e24i	−0.00772239	−	7.05660e-5i
$661$	−1.12419e28	+	1.94715e28i	−0.706033	+	1.22288i	0.260285	+	0.965532i	$0.416184\pi$
$661$	−1.12419e28	+	1.94715e28i	−0.706033	+	1.22288i	−0.966318	+	0.257353i	$0.917150\pi$
$662$	−7.37997e27	−	4.26083e27i	−0.456536	−	0.263581i
$663$	3.61142e26	−	3.95216e28i	0.0220061	−	2.40824i
$664$	−3.87827e27	−	6.71735e27i	−0.232786	−	0.403197i
$665$		−	3.09432e28i		−	1.82957i
$666$	−2.80824e26	+	1.53647e28i	−0.0163565	+	0.894915i
$667$	1.16325e27			0.0667444
$668$	2.86782e27	−	1.65574e27i	0.162102	−	0.0935895i
$669$	−6.89094e27	+	1.16875e28i	−0.383722	+	0.650819i
$670$	1.31011e28	−	2.26919e28i	0.718723	−	1.24486i
$671$	−1.99826e26	−	1.15370e26i	−0.0108001	−	0.00623543i
$672$	−2.95797e27	+	1.67193e27i	−0.157507	+	0.0890279i
$673$	1.42705e28	+	2.47173e28i	0.748669	+	1.29673i	0.948461	+	0.316894i	$0.102640\pi$
$673$	1.42705e28	+	2.47173e28i	0.748669	+	1.29673i	−0.199792	+	0.979838i	$0.564027\pi$
$674$			1.95933e28i			1.01276i
$675$	1.47046e28	+	2.71623e28i	0.748885	+	1.38334i
$676$	−1.19908e28			−0.601701
$677$	8.68082e27	−	5.01188e27i	0.429214	−	0.247807i	−0.269798	−	0.962917i	$-0.586957\pi$
$677$	8.68082e27	−	5.01188e27i	0.429214	−	0.247807i	0.699012	+	0.715110i	$0.253623\pi$
$678$	−2.40843e27	−	4.26097e27i	−0.117338	−	0.207592i
$679$	2.87767e27	−	4.98426e27i	0.138147	−	0.239278i
$680$	1.68449e28	+	9.72540e27i	0.796855	+	0.460064i
$681$	9.83585e27	+	5.79920e27i	0.458501	+	0.270332i
$682$	−9.66976e24	−	1.67485e25i	−0.000444193	−	0.000769365i
$683$		−	3.20778e28i		−	1.45210i	−0.687639	−	0.726052i	$-0.741353\pi$
$683$		−	3.20778e28i		−	1.45210i	0.687639	−	0.726052i	$-0.258647\pi$
$684$	6.04652e27	+	1.09294e28i	0.269739	+	0.487567i
$685$	−1.23121e28			−0.541283
$686$	1.37784e28	−	7.95495e27i	0.596976	−	0.344664i
$687$	1.25608e28	+	1.14779e26i	0.536353	+	0.00490111i
$688$	−2.86190e27	+	4.95696e27i	−0.120440	+	0.208608i
$689$	−5.09301e28	−	2.94045e28i	−2.11243	−	1.21961i
$690$	1.40797e26	−	1.54081e28i	0.00575574	−	0.629880i
$691$	1.03068e28	+	1.78519e28i	0.415283	+	0.719291i	0.995458	−	0.0952006i	$-0.0303492\pi$
$691$	1.03068e28	+	1.78519e28i	0.415283	+	0.719291i	−0.580175	+	0.814492i	$0.697016\pi$
$692$			2.38077e28i			0.945490i
$693$	2.20295e26	−	1.21875e26i	0.00862326	−	0.00477069i
$694$	1.53874e28			0.593706
$695$	3.37570e28	−	1.94896e28i	1.28385	−	0.741233i
$696$	−5.75660e26	+	9.76359e26i	−0.0215811	+	0.0366030i
$697$	−2.10251e28	+	3.64166e28i	−0.776982	+	1.34577i
$698$	−4.84320e27	−	2.79622e27i	−0.176432	−	0.101863i
$699$	1.09307e28	−	6.17835e27i	0.392532	−	0.221871i
$700$	−1.13694e28	−	1.96924e28i	−0.402492	−	0.697137i
$701$			1.65456e28i			0.577433i	0.957415	+	0.288717i	$0.0932286\pi$
$701$			1.65456e28i			0.577433i	−0.957415	+	0.288717i	$0.906771\pi$
$702$	8.36183e26	−	3.04958e28i	0.0287694	−	1.04923i
$703$	−4.15882e28			−1.41064
$704$	−3.11705e25	+	1.79963e25i	−0.00104236	+	0.000601806i
$705$	1.95098e28	+	3.45166e28i	0.643225	+	1.13799i
$706$	2.91446e26	−	5.04800e26i	0.00947353	−	0.0164086i
$707$	4.49648e28	+	2.59604e28i	1.44105	+	0.831989i
$708$	−1.19017e28	−	7.01725e27i	−0.376078	−	0.221735i
$709$	−1.52468e28	−	2.64082e28i	−0.475024	−	0.822766i	0.524567	−	0.851369i	$-0.324227\pi$
$709$	−1.52468e28	−	2.64082e28i	−0.475024	−	0.822766i	−0.999591	+	0.0286034i	$0.990894\pi$
$710$		−	4.63194e27i		−	0.142292i
$711$	−5.00209e28	−	9.14242e26i	−1.51515	−	0.0276927i
$712$	−3.20506e27			−0.0957274
$713$	2.13076e27	−	1.23019e27i	0.0627536	−	0.0362308i
$714$	−4.04294e28	−	3.69437e26i	−1.17413	−	0.0107290i
$715$	−4.00292e26	+	6.93327e26i	−0.0114635	+	0.0198554i
$716$	−9.16883e27	−	5.29363e27i	−0.258931	−	0.149494i
$717$	−5.13560e26	+	5.62015e28i	−0.0143021	+	1.56515i
$718$	−8.70281e27	−	1.50737e28i	−0.239010	−	0.413977i
$719$			2.10680e28i			0.570604i	0.958438	+	0.285302i	$0.0920939\pi$
$719$			2.10680e28i			0.570604i	−0.958438	+	0.285302i	$0.907906\pi$
$720$	1.28629e28	+	7.74321e27i	0.343569	+	0.206822i
$721$	7.34422e28			1.93461
$722$	−5.70252e27	+	3.29235e27i	−0.148148	+	0.0855330i
$723$	2.41374e28	−	4.09387e28i	0.618454	−	1.04894i
$724$	1.59547e28	−	2.76343e28i	0.403183	−	0.698333i
$725$	−6.56897e27	−	3.79260e27i	−0.163726	−	0.0945272i
$726$	−2.50385e28	+	1.41525e28i	−0.615520	+	0.347911i
$727$	−3.48941e28	−	6.04384e28i	−0.846074	−	1.46544i	−0.884685	−	0.466189i	$-0.845627\pi$
$727$	−3.48941e28	−	6.04384e28i	−0.846074	−	1.46544i	0.0386109	−	0.999254i	$-0.487707\pi$
$728$			2.24592e28i			0.537130i
$729$	4.23275e28	+	2.32295e27i	0.998497	+	0.0547980i
$730$	6.47645e28			1.50698
$731$	−5.89841e28	+	3.40545e28i	−1.35382	+	0.781629i
$732$	1.40742e28	+	2.48999e28i	0.318649	+	0.563751i
$733$	1.90109e28	−	3.29278e28i	0.424583	−	0.735400i	−0.571798	−	0.820394i	$-0.693754\pi$
$733$	1.90109e28	−	3.29278e28i	0.424583	−	0.735400i	0.996381	+	0.0849946i	$0.0270873\pi$
$734$	1.51986e27	+	8.77491e26i	0.0334844	+	0.0193322i
$735$	3.02018e27	+	1.78070e27i	0.0656387	+	0.0387005i
$736$	−2.28950e27	−	3.96553e27i	−0.0490866	−	0.0850205i
$737$			5.76945e26i			0.0122028i
$738$	−1.67399e28	+	2.78080e28i	−0.349292	+	0.580239i
$739$	−3.19618e28			−0.657941			−0.328971	−	0.944340i	$-0.606702\pi$
$739$	−3.19618e28			−0.657941			−0.328971	+	0.944340i	$0.606702\pi$
$740$	−4.32923e28	+	2.49948e28i	−0.879212	+	0.507613i
$741$	8.25579e28	+	7.54400e26i	1.65416	+	0.0151154i
$742$	−3.00799e28	+	5.21000e28i	−0.594618	+	1.02991i
$743$	−5.55891e28	−	3.20944e28i	−1.08418	−	0.625952i	−0.152159	−	0.988356i	$-0.548623\pi$
$743$	−5.55891e28	−	3.20944e28i	−1.08418	−	0.625952i	−0.932021	+	0.362404i	$0.881956\pi$
$744$	−2.19053e25	+	2.39721e27i	−0.000421522	+	0.0461293i
$745$	−3.51571e28	−	6.08940e28i	−0.667499	−	1.15614i
$746$		−	2.01904e27i		−	0.0378231i
$747$	1.30189e27	−	7.12304e28i	0.0240641	−	1.31662i
$748$	−4.28285e26			−0.00781119
$749$	−8.47680e28	+	4.89408e28i	−1.52551	+	0.880751i
$750$	−1.85899e28	+	3.15298e28i	−0.330115	+	0.559897i
$751$	−2.13021e27	+	3.68964e27i	−0.0373270	+	0.0646523i	−0.884085	−	0.467325i	$-0.845218\pi$
$751$	−2.13021e27	+	3.68964e27i	−0.0373270	+	0.0646523i	0.846758	+	0.531978i	$0.178551\pi$
$752$	1.02039e28	+	5.89121e27i	0.176436	+	0.101865i
$753$	−6.00535e28	+	3.39441e28i	−1.02468	+	0.579181i
$754$	3.74595e27	+	6.48818e27i	0.0630738	+	0.109247i
$755$		−	9.46611e28i		−	1.57290i
$756$	−3.11963e28	−	8.55389e26i	−0.511546	−	0.0140264i
$757$	5.13713e28			0.831308			0.415654	−	0.909523i	$-0.363553\pi$
$757$	5.13713e28			0.831308			0.415654	+	0.909523i	$0.363553\pi$
$758$	−2.72472e28	+	1.57312e28i	−0.435141	+	0.251229i
$759$	1.66950e26	+	2.95366e26i	0.00263129	+	0.00465524i
$760$	−2.03157e28	+	3.51878e28i	−0.316006	+	0.547339i
$761$	5.22370e28	+	3.01591e28i	0.801922	+	0.462990i	0.844143	−	0.536119i	$-0.180110\pi$
$761$	5.22370e28	+	3.01591e28i	0.801922	+	0.462990i	−0.0422209	+	0.999108i	$0.513443\pi$
$762$	−1.19958e28	−	7.07272e27i	−0.181753	−	0.107161i
$763$	−7.75703e27	−	1.34356e28i	−0.115998	−	0.200914i
$764$			3.56135e28i			0.525631i
$765$	8.64837e28	+	1.56324e29i	1.25985	+	2.27725i
$766$	3.49529e28			0.502568
$767$	−7.90904e28	+	4.56629e28i	−1.12246	+	0.648052i
$768$	4.46143e27	+	4.07678e25i	0.0624974	+	0.000571091i
$769$	−5.11668e28	+	8.86235e28i	−0.707498	+	1.22542i	0.258285	+	0.966069i	$0.416843\pi$
$769$	−5.11668e28	+	8.86235e28i	−0.707498	+	1.22542i	−0.965783	+	0.259353i	$0.916491\pi$
$770$	7.09252e26	+	4.09487e26i	0.00968040	+	0.00558898i
$771$	5.35443e26	−	5.85963e28i	0.00721390	−	0.789453i
$772$	1.15591e28	+	2.00209e28i	0.153727	+	0.266263i
$773$		−	5.76585e28i		−	0.756953i	−0.925611	−	0.378476i	$-0.876448\pi$
$773$		−	5.76585e28i		−	0.756953i	0.925611	−	0.378476i	$-0.123552\pi$
$774$	−4.60015e28	+	2.54497e28i	−0.596160	+	0.329816i
$775$	−1.60434e28			−0.205249
$776$	−6.54482e27	+	3.77865e27i	−0.0826572	+	0.0477221i
$777$	5.27751e28	−	8.95102e28i	0.657989	−	1.11600i
$778$	3.17465e28	−	5.49866e28i	0.390751	−	0.676801i
$779$	−7.60718e28	−	4.39201e28i	−0.924377	−	0.533689i
$780$	8.63941e28	−	4.88326e28i	1.03643	−	0.585819i
$781$	5.09951e25	+	8.83260e25i	0.000603973	+	0.00104611i
$782$		−	5.44867e28i		−	0.637123i
$783$	−9.15489e27	+	4.95610e27i	−0.105690	+	0.0572166i
$784$	1.04189e27			0.0118758
$785$	8.79872e28	−	5.07994e28i	0.990200	−	0.571692i
$786$	−2.82988e27	−	5.00659e27i	−0.0314443	−	0.0556309i
$787$	8.81592e28	−	1.52696e29i	0.967209	−	1.67526i	0.263650	−	0.964618i	$-0.415074\pi$
$787$	8.81592e28	−	1.52696e29i	0.967209	−	1.67526i	0.703559	−	0.710637i	$-0.251593\pi$
$788$	2.90720e28	+	1.67847e28i	0.314929	+	0.181824i
$789$	−3.81040e28	−	2.24661e28i	−0.407568	−	0.240302i
$790$	−8.13724e28	−	1.40941e29i	−0.859422	−	1.48856i
$791$			3.30957e28i			0.345149i
$792$	−3.30530e26	−	6.04117e24i	−0.00340376	−	6.22113e-5i
$793$	1.89059e29			1.92250
$794$	5.35139e27	−	3.08963e27i	0.0537356	−	0.0310242i
$795$	2.65816e29	+	2.42899e27i	2.63579	+	0.0240854i
$796$	−2.83625e25	+	4.91253e25i	−0.000277724	+	0.000481032i
$797$	5.65241e28	+	3.26342e28i	0.546576	+	0.315566i	0.747740	−	0.663992i	$-0.231139\pi$
$797$	5.65241e28	+	3.26342e28i	0.546576	+	0.315566i	−0.201164	+	0.979558i	$0.564472\pi$
$798$	7.71728e26	−	8.44541e28i	0.00736946	−	0.806477i
$799$	7.01010e28	+	1.21418e29i	0.661084	+	1.14503i
$800$			2.98583e28i			0.278077i
$801$	−2.52207e28	−	1.51824e28i	−0.231970	−	0.139641i
$802$	1.06515e29			0.967537
$803$	−1.23499e27	+	7.13021e26i	−0.0110792	+	0.00639656i
$804$	3.63233e28	−	6.16068e28i	0.321829	−	0.545844i
$805$	−5.20952e28	+	9.02315e28i	−0.455868	+	0.789586i
$806$	1.37231e28	+	7.92305e27i	0.118605	+	0.0684766i
$807$	−1.06373e29	+	6.01251e28i	−0.908019	+	0.513240i
$808$	−3.40886e28	−	5.90431e28i	−0.287406	−	0.497801i
$809$			1.62400e29i			1.35239i	0.736724	+	0.676194i	$0.236372\pi$
$809$			1.62400e29i			1.35239i	−0.736724	+	0.676194i	$0.763628\pi$
$810$	6.45390e28	+	1.21863e29i	0.530851	+	1.00236i
$811$	−1.45773e29			−1.18432			−0.592158	−	0.805822i	$-0.701724\pi$
$811$	−1.45773e29			−1.18432			−0.592158	+	0.805822i	$0.701724\pi$
$812$	6.63721e27	−	3.83199e27i	0.0532629	−	0.0307514i
$813$	−1.09406e29	−	1.93560e29i	−0.867235	−	1.53430i
$814$	5.50358e26	−	9.53248e26i	0.00430925	−	0.00746383i
$815$	1.38500e29	+	7.99630e28i	1.07121	+	0.618462i
$816$	4.57327e28	+	2.69639e28i	0.349402	+	0.206007i
$817$	−7.11375e28	−	1.23214e29i	−0.536881	−	0.929905i
$818$			1.31664e29i			0.981598i
$819$	−1.06389e29	+	1.76732e29i	−0.783533	+	1.30159i
$820$	−1.05585e29			−0.768182
$821$	−1.00485e29	+	5.80151e28i	−0.722221	+	0.416974i	−0.815569	−	0.578659i	$-0.803576\pi$
$821$	−1.00485e29	+	5.80151e28i	−0.722221	+	0.416974i	0.0933488	+	0.995633i	$0.470243\pi$
$822$	−3.36037e28	−	3.07065e26i	−0.238599	−	0.00218028i
$823$	2.91619e28	−	5.05099e28i	0.204559	−	0.354306i	−0.745433	−	0.666580i	$-0.767757\pi$
$823$	2.91619e28	−	5.05099e28i	0.204559	−	0.354306i	0.949992	+	0.312274i	$0.101091\pi$
$824$	−8.35167e28	−	4.82184e28i	−0.578764	−	0.334149i
$825$	2.02154e25	−	2.21227e27i	0.000138402	−	0.0151460i
$826$	4.67117e28	+	8.09071e28i	0.315955	+	0.547250i
$827$		−	1.07464e29i		−	0.718138i	−0.933311	−	0.359069i	$-0.883094\pi$
$827$		−	1.07464e29i		−	0.718138i	0.933311	−	0.359069i	$-0.116906\pi$
$828$	7.68561e26	−	4.20503e28i	0.00507429	−	0.277629i
$829$	1.36212e29			0.888526			0.444263	−	0.895896i	$-0.353466\pi$
$829$	1.36212e29			0.888526			0.444263	+	0.895896i	$0.353466\pi$
$830$	2.00702e29	−	1.15875e29i	1.29351	−	0.746810i
$831$	−6.14010e28	+	1.04140e29i	−0.390990	+	0.663145i
$832$	1.47455e28	−	2.55400e28i	0.0927741	−	0.160690i
$833$	1.07367e28	+	6.19886e27i	0.0667456	+	0.0385356i
$834$	9.26200e28	−	5.23517e28i	0.568911	−	0.321566i
$835$	4.94703e28	+	8.56852e28i	0.300248	+	0.520045i
$836$		−	8.94658e26i		−	0.00536530i
$837$	−1.15280e28	+	1.87600e28i	−0.0683121	+	0.111167i
$838$	−1.00690e29			−0.589587
$839$	8.80015e28	−	5.08077e28i	0.509179	−	0.293975i	−0.223317	−	0.974746i	$-0.571689\pi$
$839$	8.80015e28	−	5.08077e28i	0.509179	−	0.293975i	0.732496	+	0.680771i	$0.238355\pi$
$840$	−4.99542e28	−	8.83785e28i	−0.285614	−	0.505305i
$841$	−8.72190e28	+	1.51068e29i	−0.492778	+	0.853516i
$842$	−8.70692e28	−	5.02694e28i	−0.486120	−	0.280662i
$843$	−1.55032e29	−	9.14068e28i	−0.855354	−	0.504316i
$844$	−2.86498e28	−	4.96229e28i	−0.156206	−	0.270556i
$845$		−	3.58263e29i		−	1.93034i
$846$	5.23880e28	+	9.46939e28i	0.278951	+	0.504218i
$847$	1.94478e29			1.02338
$848$	6.84123e28	−	3.94979e28i	0.355775	−	0.205407i
$849$	−3.33247e29	−	3.04516e27i	−1.71273	−	0.0156507i
$850$	−1.77645e29	+	3.07691e29i	−0.902329	+	1.56288i
$851$	1.21273e29	+	7.00169e28i	0.608791	+	0.351485i
$852$	1.15521e26	−	1.26421e28i	0.000573147	−	0.0627224i
$853$	−2.70088e28	−	4.67807e28i	−0.132439	−	0.229391i	0.792177	−	0.610291i	$-0.208948\pi$
$853$	−2.70088e28	−	4.67807e28i	−0.132439	−	0.229391i	−0.924616	+	0.380900i	$0.875614\pi$
$854$		−	1.93402e29i		−	0.937307i
$855$	−3.26549e29	+	1.80659e29i	−1.56418	+	0.865361i
$856$	1.28528e29			0.608500
$857$	−1.13643e29	+	6.56120e28i	−0.531784	+	0.307026i	−0.741743	−	0.670685i	$-0.766000\pi$
$857$	−1.13643e29	+	6.56120e28i	−0.531784	+	0.307026i	0.209959	+	0.977710i	$0.432667\pi$
$858$	−1.10982e27	+	1.88233e27i	−0.00513311	+	0.00870611i
$859$	−1.52143e29	+	2.63519e29i	−0.695536	+	1.20470i	0.274464	+	0.961597i	$0.411500\pi$
$859$	−1.52143e29	+	2.63519e29i	−0.695536	+	1.20470i	−0.970000	+	0.243106i	$0.921834\pi$
$860$	−1.48105e29	−	8.55083e28i	−0.669244	−	0.386388i
$861$	1.91063e29	−	1.07995e29i	0.853387	−	0.482360i
$862$	9.38499e28	+	1.62553e29i	0.414344	+	0.717665i
$863$			7.66633e28i			0.334564i	0.985909	+	0.167282i	$0.0534991\pi$
$863$			7.66633e28i			0.334564i	−0.985909	+	0.167282i	$0.946501\pi$
$864$	3.49140e28	+	2.14546e28i	0.150613	+	0.0925513i
$865$	−7.11330e29			−3.03326
$866$	3.76491e28	−	2.17367e28i	0.158700	−	0.0916252i
$867$	1.92762e29	+	3.41033e29i	0.803214	+	1.42104i
$868$	8.10504e27	−	1.40383e28i	0.0333855	−	0.0578254i
$869$	3.10337e27	+	1.79173e27i	0.0126368	+	0.00729583i
$870$	−2.91718e28	−	1.71996e28i	−0.117428	−	0.0692352i
$871$	−2.36364e29	−	4.09395e29i	−0.940589	−	1.62915i
$872$			2.03715e28i			0.0801414i
$873$	−6.94009e28	−	1.26845e27i	−0.269912	−	0.00493324i
$874$	1.13819e29			0.437623
$875$	2.14337e29	−	1.23747e29i	0.814735	−	0.470388i
$876$	1.76764e29	+	1.61524e27i	0.664281	+	0.00607009i
$877$	−2.05590e29	+	3.56093e29i	−0.763848	+	1.32302i	0.177006	+	0.984210i	$0.443359\pi$
$877$	−2.05590e29	+	3.56093e29i	−0.763848	+	1.32302i	−0.940854	+	0.338813i	$0.889974\pi$
$878$	−2.13589e29	−	1.23316e29i	−0.784575	−	0.452975i
$879$	2.86939e27	−	3.14012e29i	0.0104208	−	1.14040i
$880$	−5.37696e26	−	9.31317e26i	−0.00193068	−	0.00334403i
$881$			2.10665e29i			0.747882i	0.927452	+	0.373941i	$0.121994\pi$
$881$			2.10665e29i			0.747882i	−0.927452	+	0.373941i	$0.878006\pi$
$882$	8.19867e27	+	4.93543e27i	0.0287778	+	0.0173237i
$883$	1.99293e29			0.691648			0.345824	−	0.938299i	$-0.387599\pi$
$883$	1.99293e29			0.691648			0.345824	+	0.938299i	$0.387599\pi$
$884$	3.03907e29	−	1.75461e29i	1.04284	−	0.602084i
$885$	2.09662e29	−	3.55602e29i	0.711357	−	1.20651i
$886$	−9.26345e28	+	1.60448e29i	−0.310768	+	0.538265i
$887$	2.34665e29	+	1.35484e29i	0.778415	+	0.449418i	0.835868	−	0.548930i	$-0.184965\pi$
$887$	2.34665e29	+	1.35484e29i	0.778415	+	0.449418i	−0.0574532	+	0.998348i	$0.518298\pi$
$888$	−1.18782e29	+	6.71394e28i	−0.389603	+	0.220215i
$889$	4.70810e28	+	8.15466e28i	0.152696	+	0.264477i
$890$		−	9.57612e28i		−	0.307107i
$891$	−2.57233e27	−	1.61326e27i	−0.00815737	−	0.00511596i
$892$	−1.20466e29			−0.377759
$893$	−2.53635e29	+	1.46436e29i	−0.786492	+	0.454081i
$894$	−9.44367e28	−	1.67077e29i	−0.289578	−	0.512319i
$895$	1.58164e29	−	2.73947e29i	0.479597	−	0.830686i
$896$	−2.61266e28	−	1.50842e28i	−0.0783436	−	0.0452317i
$897$	−2.39472e29	−	1.41192e29i	−0.710117	−	0.418684i
$898$	1.22876e29	+	2.12827e29i	0.360332	+	0.624113i
$899$		−	5.40734e27i		−	0.0156815i
$900$	−1.41439e29	+	2.34956e29i	−0.405642	+	0.673846i
$901$	9.39990e29			2.66609
$902$	2.01339e27	−	1.16243e27i	0.00564759	−	0.00326064i
$903$	3.55466e29	+	3.24819e27i	0.986098	+	0.00901081i
$904$	2.17289e28	−	3.76356e28i	0.0596147	−	0.103256i
$905$	8.25661e29	+	4.76696e29i	2.24035	+	1.29347i
$906$	2.36086e27	−	2.58361e29i	0.00633562	−	0.693339i
$907$	1.86159e29	+	3.22436e29i	0.494094	+	0.855797i	0.999977	−	0.00680574i	$-0.00216635\pi$
$907$	1.86159e29	+	3.22436e29i	0.494094	+	0.855797i	−0.505882	+	0.862602i	$0.668833\pi$
$908$			1.01380e29i			0.266131i
$909$	1.14432e28	−	6.26090e29i	0.0297103	−	1.62554i
$910$	−6.71038e29			−1.72319
$911$	−1.73791e29	+	1.00338e29i	−0.441412	+	0.254849i	−0.704196	−	0.710005i	$-0.748693\pi$
$911$	−1.73791e29	+	1.00338e29i	−0.441412	+	0.254849i	0.262784	+	0.964855i	$0.415359\pi$
$912$	−5.63258e28	+	9.55325e28i	−0.141501	+	0.239995i
$913$	−2.55145e27	+	4.41923e27i	−0.00633984	+	0.0109809i
$914$	1.62672e29	+	9.39187e28i	0.399807	+	0.230829i
$915$	−7.43963e29	+	4.20511e29i	−1.80859	+	1.02227i
$916$	5.57653e28	+	9.65883e28i	0.134094	+	0.232258i
$917$			3.88870e28i			0.0924935i
$918$	2.32144e29	+	4.28816e29i	0.546173	+	1.00889i
$919$	6.33863e29			1.47516			0.737582	−	0.675258i	$-0.235968\pi$
$919$	6.33863e29			1.47516			0.737582	+	0.675258i	$0.235968\pi$
$920$	1.18483e29	−	6.84060e28i	0.272758	−	0.157477i
$921$	−2.15945e28	−	3.82047e28i	−0.0491752	−	0.0870002i
$922$	1.26287e29	−	2.18736e29i	0.284480	−	0.492733i
$923$	−7.23712e28	−	4.17835e28i	−0.161268	−	0.0931082i
$924$	1.92557e27	+	1.13531e27i	0.00424463	+	0.00250263i
$925$	−4.56559e29	−	7.90783e29i	−0.995587	−	1.72441i
$926$		−	6.66680e28i		−	0.143816i
$927$	−4.28785e29	−	7.75050e29i	−0.915044	−	1.65399i
$928$	−1.00636e28			−0.0212457
$929$	3.99049e29	−	2.30391e29i	0.833429	−	0.481180i	−0.0215963	−	0.999767i	$-0.506875\pi$
$929$	3.99049e29	−	2.30391e29i	0.833429	−	0.481180i	0.855025	+	0.518586i	$0.173542\pi$
$930$	−7.16242e28	−	6.54491e26i	−0.147989	−	0.00135230i
$931$	−1.29490e28	+	2.24283e28i	−0.0264691	+	0.0458458i
$932$	9.65467e28	+	5.57413e28i	0.195244	+	0.112724i
$933$	−4.86634e27	+	5.32548e29i	−0.00973612	+	1.06547i
$934$	1.35946e29	+	2.35465e29i	0.269089	+	0.466076i
$935$		−	1.27964e28i		−	0.0250594i
$936$	2.37016e29	−	1.31125e29i	0.459218	−	0.254056i
$937$	6.28798e29			1.20536			0.602678	−	0.797984i	$-0.294100\pi$
$937$	6.28798e29			1.20536			0.602678	+	0.797984i	$0.294100\pi$
$938$	−4.18798e29	+	2.41793e29i	−0.794285	+	0.458581i
$939$	−1.95598e28	+	3.31748e28i	−0.0367036	+	0.0622518i
$940$	−1.76018e29	+	3.04873e29i	−0.326798	+	0.566031i
$941$	−2.77198e29	−	1.60040e29i	−0.509206	−	0.293990i	0.223302	−	0.974749i	$-0.428317\pi$
$941$	−2.77198e29	−	1.60040e29i	−0.509206	−	0.293990i	−0.732507	+	0.680759i	$0.761650\pi$
$942$	2.41413e29	−	1.36454e29i	0.438785	−	0.248015i
$943$	1.47885e29	+	2.56145e29i	0.265955	+	0.460648i
$944$		−	1.22674e29i		−	0.218289i
$945$	2.55574e28	−	9.32086e29i	0.0449986	−	1.64111i
$946$	3.76560e27			0.00656028
$947$	−2.94641e29	+	1.70111e29i	−0.507918	+	0.293247i	−0.731977	−	0.681329i	$-0.761402\pi$
$947$	−2.94641e29	+	1.70111e29i	−0.507918	+	0.293247i	0.224059	+	0.974575i	$0.428069\pi$
$948$	−2.18577e29	−	3.86705e29i	−0.372839	−	0.659623i
$949$	5.84223e29	−	1.01190e30i	0.986091	−	1.70796i
$950$	−6.42745e29	−	3.71089e29i	−1.07350	−	0.619787i
$951$	5.32937e29	+	3.14219e29i	0.880787	+	0.519311i
$952$	−1.79491e29	−	3.10887e29i	−0.293544	−	0.508433i
$953$		−	8.83613e29i		−	1.42999i	−0.699130	−	0.714995i	$-0.746429\pi$
$953$		−	8.83613e29i		−	1.42999i	0.699130	−	0.714995i	$-0.253571\pi$
$954$	7.25440e29	+	1.32590e28i	1.16176	+	0.0212338i
$955$	−1.06407e30			−1.68630
$956$	−4.32170e29	+	2.49513e29i	−0.677759	+	0.391304i
$957$	7.45633e26	+	6.81347e24i	0.00115719	+	1.05742e-5i
$958$	7.58386e28	−	1.31356e29i	0.116476	−	0.201742i
$959$	1.96787e29	+	1.13615e29i	0.299095	+	0.172683i
$960$	−1.21807e27	+	1.33299e29i	−0.00183214	+	0.200500i
$961$	3.30177e29	+	5.71883e29i	0.491488	+	0.851282i
$962$			9.01887e29i			1.32862i
$963$	1.01139e30	+	6.08837e29i	1.47454	+	0.887643i
$964$	4.21964e29			0.608843
$965$	−5.98187e29	+	3.45363e29i	−0.854208	+	0.493177i
$966$	−1.44435e29	+	2.44972e29i	−0.204128	+	0.346215i
$967$	2.93257e29	−	5.07936e29i	0.410188	−	0.710467i	−0.584722	−	0.811234i	$-0.698796\pi$
$967$	2.93257e29	−	5.07936e29i	0.410188	−	0.710467i	0.994910	+	0.100767i	$0.0321296\pi$
$968$	−2.21156e29	−	1.27685e29i	−0.306158	−	0.176760i
$969$	−1.14882e30	+	6.49350e29i	−1.57404	+	0.889694i
$970$	−1.12899e29	−	1.95547e29i	−0.153099	−	0.265176i
$971$			3.69674e29i			0.496166i	0.968739	+	0.248083i	$0.0798005\pi$
$971$			3.69674e29i			0.496166i	−0.968739	+	0.248083i	$0.920199\pi$
$972$	1.73109e29	+	3.34214e29i	0.229963	+	0.443979i
$973$	−7.19395e29			−0.945887
$974$	3.39381e29	−	1.95941e29i	0.441670	−	0.254998i
$975$	8.91982e29	+	1.57809e30i	1.14897	+	2.03275i
$976$	−1.26978e29	+	2.19932e29i	−0.161894	+	0.280408i
$977$	−1.27081e30	−	7.33700e29i	−1.60374	−	0.925919i	−0.990731	−	0.135841i	$-0.956626\pi$
$977$	−1.27081e30	−	7.33700e29i	−1.60374	−	0.925919i	−0.613007	−	0.790077i	$-0.710040\pi$
$978$	3.76018e29	+	2.21700e29i	0.469699	+	0.276934i
$979$	1.05428e27	+	1.82606e27i	0.00130355	+	0.00225782i
$980$			3.11298e28i			0.0380991i
$981$	−9.64995e28	+	1.60304e29i	−0.116906	+	0.194202i
$982$	−7.76731e29			−0.931442
$983$	1.76471e29	−	1.01886e29i	0.209478	−	0.120942i	−0.391591	−	0.920139i	$-0.628075\pi$
$983$	1.76471e29	−	1.01886e29i	0.209478	−	0.120942i	0.601069	+	0.799197i	$0.294742\pi$
$984$	−2.88177e29	−	2.63331e27i	−0.338616	−	0.00309422i
$985$	−5.01496e29	+	8.68616e29i	−0.583317	+	1.01034i
$986$	−1.03705e29	−	5.98744e28i	−0.119408	−	0.0689401i
$987$	6.68638e27	−	7.31724e29i	0.00762113	−	0.834019i
$988$	3.66525e29	+	6.34840e29i	0.413556	+	0.716300i
$989$			4.79062e29i			0.535092i
$990$	1.80499e26	−	9.87562e27i	0.000199582	−	0.0109197i
$991$	2.62344e29			0.287166			0.143583	−	0.989638i	$-0.454138\pi$
$991$	2.62344e29			0.287166			0.143583	+	0.989638i	$0.454138\pi$
$992$	−1.84337e28	+	1.06427e28i	−0.0199754	+	0.0115328i
$993$	3.52958e29	−	5.98641e29i	0.378644	−	0.642206i
$994$	−4.27432e28	+	7.40335e28i	−0.0453945	+	0.0786257i
$995$	−1.46777e27	−	8.47418e26i	−0.00154322	−	0.000890978i
$996$	5.50672e29	−	3.11256e29i	0.573191	−	0.323985i
$997$	−5.55867e29	−	9.62790e29i	−0.572822	−	0.992156i	−0.996275	−	0.0862380i	$-0.972515\pi$
$997$	−5.55867e29	−	9.62790e29i	−0.572822	−	0.992156i	0.423453	−	0.905918i	$-0.360818\pi$
$998$			7.86298e29i			0.802198i
$999$	−1.25274e30	−	3.43497e28i	−1.26534	−	0.0346951i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.21.d.a.5.1	✓	40
3.2	odd	2		54.21.d.a.17.20		40
9.2	odd	6	inner	18.21.d.a.11.1	yes	40
9.7	even	3		54.21.d.a.35.20		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.21.d.a.5.1	✓	40	1.1	even	1	trivial
18.21.d.a.11.1	yes	40	9.2	odd	6	inner
54.21.d.a.17.20		40	3.2	odd	2
54.21.d.a.35.20		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} +(-29056.0 - 51405.6i) q^{3} +(262144. - 454047. i) q^{4} +(1.35661e7 + 7.83237e6i) q^{5} +(3.68309e7 + 2.17155e7i) q^{6} +(-1.44553e8 - 2.50374e8i) q^{7} +3.79625e8i q^{8} +(-1.79828e9 + 2.98728e9i) q^{9} -1.13425e10 q^{10} +(2.16289e8 - 1.24874e8i) q^{11} +(-3.09574e10 - 2.82884e8i) q^{12} +(-1.02318e11 + 1.77219e11i) q^{13} +(1.81290e11 + 1.04668e11i) q^{14} +(8.45203e9 - 9.24949e11i) q^{15} +(-1.37439e11 - 2.38051e11i) q^{16} -3.27084e12i q^{17} +(4.61368e10 - 2.52428e12i) q^{18} +6.83256e12 q^{19} +(7.11253e12 - 4.10642e12i) q^{20} +(-8.67046e12 + 1.47057e13i) q^{21} +(-9.04188e10 + 1.56610e11i) q^{22} +(-1.99240e13 - 1.15031e13i) q^{23} +(1.95148e13 - 1.10304e13i) q^{24} +(7.50084e13 + 1.29918e14i) q^{25} -1.48172e14i q^{26} +(2.05814e14 + 5.64334e12i) q^{27} -1.51575e14 q^{28} +(-4.37882e13 + 2.52811e13i) q^{29} +(3.29567e14 + 5.83067e14i) q^{30} +(-5.34721e13 + 9.26164e13i) q^{31} +(1.72368e14 + 9.95164e13i) q^{32} +(-1.27037e13 - 7.49011e12i) q^{33} +(1.18417e15 + 2.05104e15i) q^{34} -4.52878e15i q^{35} +(8.84956e14 + 1.59960e15i) q^{36} -6.08677e15 q^{37} +(-4.28449e15 + 2.47365e15i) q^{38} +(1.20830e16 + 1.10413e14i) q^{39} +(-2.97336e15 + 5.15002e15i) q^{40} +(-1.11337e16 - 6.42805e15i) q^{41} +(1.12949e14 - 1.23605e16i) q^{42} +(-1.04115e16 - 1.80333e16i) q^{43} -1.30940e14i q^{44} +(-4.77931e16 + 2.64408e16i) q^{45} +1.66583e16 q^{46} +(-3.71215e16 + 2.14321e16i) q^{47} +(-8.24374e15 + 1.39819e16i) q^{48} +(-1.89519e15 + 3.28256e15i) q^{49} +(-9.40709e16 - 5.43119e16i) q^{50} +(-1.68139e17 + 9.50375e16i) q^{51} +(5.36439e16 + 9.29140e16i) q^{52} +2.87385e17i q^{53} +(-1.31103e17 + 7.09738e16i) q^{54} +3.91225e15 q^{55} +(9.50481e16 - 5.48761e16i) q^{56} +(-1.98527e17 - 3.51232e17i) q^{57} +(1.83055e16 - 3.17061e16i) q^{58} +(3.86495e17 + 2.23143e17i) q^{59} +(-4.17754e17 - 2.46307e17i) q^{60} +(-4.61942e17 - 8.00108e17i) q^{61} -7.74359e16i q^{62} +(1.00788e18 + 1.84213e16i) q^{63} -1.44115e17 q^{64} +(-2.77610e18 + 1.60278e18i) q^{65} +(1.06778e16 + 9.75723e13i) q^{66} +(-1.15505e18 + 2.00061e18i) q^{67} +(-1.48511e18 - 8.57431e17i) q^{68} +(-1.24132e16 + 1.35844e18i) q^{69} +(1.63959e18 + 2.83986e18i) q^{70} +4.08371e17i q^{71} +(-1.13405e18 - 6.82673e17i) q^{72} -5.70990e18 q^{73} +(3.81683e18 - 2.20365e18i) q^{74} +(4.49908e18 - 7.63076e18i) q^{75} +(1.79111e18 - 3.10230e18i) q^{76} +(-6.25306e16 - 3.61020e16i) q^{77} +(-7.61685e18 + 4.30528e18i) q^{78} +(7.17413e18 + 1.24260e19i) q^{79} -4.30589e18i q^{80} +(-5.69003e18 - 1.07439e19i) q^{81} +9.30881e18 q^{82} +(-1.76947e19 + 1.02160e19i) q^{83} +(4.40417e18 + 7.79181e18i) q^{84} +(2.56184e19 - 4.43724e19i) q^{85} +(1.30575e19 + 7.53876e18i) q^{86} +(2.57190e18 + 1.51639e18i) q^{87} +(4.74055e16 + 8.21087e16i) q^{88} +8.44270e18i q^{89} +(2.03970e19 - 3.38832e19i) q^{90} +5.91614e19 q^{91} +(-1.04459e19 + 6.03096e18i) q^{92} +(6.31468e18 + 5.77026e16i) q^{93} +(1.55185e19 - 2.68788e19i) q^{94} +(9.26910e19 + 5.35152e19i) q^{95} +(1.07390e17 - 1.17522e19i) q^{96} +(9.95365e18 + 1.72402e19i) q^{97} -2.74453e18i q^{98} +(-1.59135e16 + 8.70675e17i) 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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