LMFDB - Embedded newform 21.18.e.b.4.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [21,18,Mod(4,21)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("21.4"); S:= CuspForms(chi, 18); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(21, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 18, names="a")

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	21.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$38.4766383424$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.12
Character	$\chi$	$=$	21.4
Dual form			21.18.e.b.16.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(311.865 + 540.166i) q^{2} +(-3280.50 + 5681.99i) q^{3} +(-128983. + 223406. i) q^{4} +(-103085. - 178549. i) q^{5} -4.09229e6 q^{6} +(-1.46500e7 + 4.24364e6i) q^{7} -7.91478e7 q^{8} +(-2.15234e7 - 3.72796e7i) q^{9} +(6.42974e7 - 1.11366e8i) q^{10} +(1.58732e8 - 2.74932e8i) q^{11} +(-8.46259e8 - 1.46576e9i) q^{12} -1.74666e9 q^{13} +(-6.86108e9 - 6.58997e9i) q^{14} +1.35269e9 q^{15} +(-7.77733e9 - 1.34707e10i) q^{16} +(6.80782e9 - 1.17915e10i) q^{17} +(1.34248e10 - 2.32524e10i) q^{18} +(1.53183e10 + 2.65322e10i) q^{19} +5.31851e10 q^{20} +(2.39469e10 - 9.71624e10i) q^{21} +1.98012e11 q^{22} +(-1.00381e11 - 1.73865e11i) q^{23} +(2.59645e11 - 4.49717e11i) q^{24} +(3.60217e11 - 6.23913e11i) q^{25} +(-5.44723e11 - 9.43488e11i) q^{26} +2.82430e11 q^{27} +(9.41549e11 - 3.82025e12i) q^{28} -2.23032e12 q^{29} +(4.21855e11 + 7.30674e11i) q^{30} +(1.37220e12 - 2.37673e12i) q^{31} +(-3.36082e11 + 5.82112e11i) q^{32} +(1.04144e12 + 1.80383e12i) q^{33} +8.49247e12 q^{34} +(2.26790e12 + 2.17828e12i) q^{35} +1.11046e13 q^{36} +(1.65244e13 + 2.86211e13i) q^{37} +(-9.55451e12 + 1.65489e13i) q^{38} +(5.72993e12 - 9.92453e12i) q^{39} +(8.15898e12 + 1.41318e13i) q^{40} -8.69504e13 q^{41} +(5.99520e13 - 1.73662e13i) q^{42} -2.01301e13 q^{43} +(4.09475e13 + 7.09232e13i) q^{44} +(-4.43749e12 + 7.68595e12i) q^{45} +(6.26106e13 - 1.08445e14i) q^{46} +(2.36558e13 + 4.09730e13i) q^{47} +1.02054e14 q^{48} +(1.96613e14 - 1.24339e14i) q^{49} +4.49355e14 q^{50} +(4.46661e13 + 7.73639e13i) q^{51} +(2.25290e14 - 3.90215e14i) q^{52} +(5.75801e13 - 9.97317e13i) q^{53} +(8.80798e13 + 1.52559e14i) q^{54} -6.54517e13 q^{55} +(1.15951e15 - 3.35875e14i) q^{56} -2.01007e14 q^{57} +(-6.95558e14 - 1.20474e15i) q^{58} +(9.36357e14 - 1.62182e15i) q^{59} +(-1.74474e14 + 3.02197e14i) q^{60} +(-1.03834e15 - 1.79845e15i) q^{61} +1.71177e15 q^{62} +(4.73518e14 + 4.54807e14i) q^{63} -2.45803e15 q^{64} +(1.80055e14 + 3.11865e14i) q^{65} +(-6.49577e14 + 1.12510e15i) q^{66} +(-2.65449e15 + 4.59771e15i) q^{67} +(1.75619e15 + 3.04181e15i) q^{68} +1.31720e15 q^{69} +(-4.69356e14 + 1.90437e15i) q^{70} +4.01181e15 q^{71} +(1.70353e15 + 2.95060e15i) q^{72} +(7.03575e14 - 1.21863e15i) q^{73} +(-1.03067e16 + 1.78518e16i) q^{74} +(2.36338e15 + 4.09350e15i) q^{75} -7.90324e15 q^{76} +(-1.15871e15 + 4.70135e15i) q^{77} +7.14786e15 q^{78} +(-1.28654e16 - 2.22836e16i) q^{79} +(-1.60346e15 + 2.77727e15i) q^{80} +(-9.26510e14 + 1.60476e15i) q^{81} +(-2.71168e16 - 4.69676e16i) q^{82} -2.65986e16 q^{83} +(1.86179e16 + 1.78822e16i) q^{84} -2.80714e15 q^{85} +(-6.27787e15 - 1.08736e16i) q^{86} +(7.31657e15 - 1.26727e16i) q^{87} +(-1.25633e16 + 2.17603e16i) q^{88} +(-2.87458e16 - 4.97892e16i) q^{89} -5.53558e15 q^{90} +(2.55886e16 - 7.41222e15i) q^{91} +5.17899e16 q^{92} +(9.00302e15 + 1.55937e16i) q^{93} +(-1.47548e16 + 2.55561e16i) q^{94} +(3.15819e15 - 5.47015e15i) q^{95} +(-2.20504e15 - 3.81923e15i) q^{96} -4.18174e16 q^{97} +(1.28480e17 + 6.74270e16i) q^{98} -1.36658e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 527 q^{2} - 78732 q^{3} - 824597 q^{4} - 802228 q^{5} + 6915294 q^{6} - 17244326 q^{7} + 280999302 q^{8} - 516560652 q^{9} - 81038239 q^{10} - 1091441542 q^{11} - 5410180917 q^{12} + 1377874148 q^{13}+ \cdots + 93\!\cdots\!64 q^{99}+O(q^{100}) $ 24 * q - 527 * q^2 - 78732 * q^3 - 824597 * q^4 - 802228 * q^5 + 6915294 * q^6 - 17244326 * q^7 + 280999302 * q^8 - 516560652 * q^9 - 81038239 * q^10 - 1091441542 * q^11 - 5410180917 * q^12 + 1377874148 * q^13 + 9596165342 * q^14 + 10526835816 * q^15 - 21305353865 * q^16 - 29762315004 * q^17 - 22685621967 * q^18 + 134684488214 * q^19 - 67717940690 * q^20 - 20050416 * q^21 + 256932532070 * q^22 - 51348084852 * q^23 - 921818210211 * q^24 - 2315181203426 * q^25 - 1335176827238 * q^26 + 6778308875544 * q^27 - 1318749761181 * q^28 + 7999387458656 * q^29 - 531691886079 * q^30 - 6090449057846 * q^31 - 20868024134839 * q^32 - 7160947957062 * q^33 + 26852630021136 * q^34 + 1735719535804 * q^35 + 70992393992874 * q^36 - 54733176744902 * q^37 + 7280793906586 * q^38 - 4520116142514 * q^39 + 73862463026835 * q^40 - 27548774664344 * q^41 - 80212376938581 * q^42 + 510786805993428 * q^43 - 321620688061823 * q^44 - 34533284894388 * q^45 + 77839362592056 * q^46 + 103809747879084 * q^47 + 279568853416530 * q^48 - 236440721256732 * q^49 + 1013098269255332 * q^50 - 195270548741244 * q^51 - 283701282686172 * q^52 - 1010218047002136 * q^53 - 148840365725487 * q^54 + 1972078098308176 * q^55 + 1233346210952391 * q^56 - 1767329854344108 * q^57 + 1528509468372767 * q^58 + 2328649228583166 * q^59 + 222148704433545 * q^60 - 3998785778824516 * q^61 + 1409261729849730 * q^62 + 742443240934422 * q^63 - 2683125102449406 * q^64 + 4887629102559224 * q^65 - 842867171455635 * q^66 - 9451977110365378 * q^67 - 23926389667119312 * q^68 + 673789569427944 * q^69 + 47817629546626777 * q^70 + 15905639914696920 * q^71 - 6048049277194371 * q^72 - 3172717130305346 * q^73 - 20195455410155766 * q^74 - 15189903875677986 * q^75 - 32127389607192264 * q^76 + 59990389152537784 * q^77 + 17520190327017036 * q^78 - 31353048526453194 * q^79 - 36639257137112195 * q^80 - 22236242266222092 * q^81 - 18361225205383004 * q^82 - 60978221772235572 * q^83 + 39272641366893516 * q^84 + 154577029948375320 * q^85 - 138998274620112904 * q^86 - 26241990558121008 * q^87 - 111950342432035965 * q^88 - 89425944181493704 * q^89 + 6976860929128638 * q^90 + 349190114341235694 * q^91 + 22890301604535456 * q^92 - 39959436268527606 * q^93 - 120621193755985614 * q^94 - 206240949632274064 * q^95 - 136915106348678679 * q^96 + 208230990106434268 * q^97 + 769866652642429915 * q^98 + 93965959092567564 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	311.865	+	540.166i	0.861413	+	1.49201i	0.870565	+	0.492053i	$0.163753\pi$
$2$	311.865	+	540.166i	0.861413	+	1.49201i	−0.00915260	+	0.999958i	$0.502913\pi$
$3$	−3280.50	+	5681.99i	−0.288675	+	0.500000i
$3$	−3280.50	+	5681.99i	−0.288675	+	0.500000i
$4$	−128983.	+	223406.i	−0.984064	+	1.70445i
$5$	−103085.	−	178549.i	−0.118019	−	0.204415i	0.800964	−	0.598713i	$-0.204321\pi$
$5$	−103085.	−	178549.i	−0.118019	−	0.204415i	−0.918983	+	0.394298i	$0.870988\pi$
$6$	−4.09229e6			−0.994674
$7$	−1.46500e7	+	4.24364e6i	−0.960514	+	0.278231i
$7$	−1.46500e7	+	4.24364e6i	−0.960514	+	0.278231i
$8$	−7.91478e7			−1.66792
$9$	−2.15234e7	−	3.72796e7i	−0.166667	−	0.288675i
$10$	6.42974e7	−	1.11366e8i	0.203326	−	0.352171i
$11$	1.58732e8	−	2.74932e8i	0.223268	−	0.386711i	−0.732530	−	0.680734i	$-0.761661\pi$
$11$	1.58732e8	−	2.74932e8i	0.223268	−	0.386711i	0.955798	+	0.294023i	$0.0949942\pi$
$12$	−8.46259e8	−	1.46576e9i	−0.568150	−	0.984064i
$13$	−1.74666e9			−0.593869			−0.296935	−	0.954898i	$-0.595964\pi$
$13$	−1.74666e9			−0.593869			−0.296935	+	0.954898i	$0.595964\pi$
$14$	−6.86108e9	−	6.58997e9i	−1.24252	−	1.19343i
$15$	1.35269e9			0.136277
$16$	−7.77733e9	−	1.34707e10i	−0.452700	−	0.784100i
$17$	6.80782e9	−	1.17915e10i	0.236697	−	0.409970i	−0.723068	−	0.690777i	$-0.757269\pi$
$17$	6.80782e9	−	1.17915e10i	0.236697	−	0.409970i	0.959764	+	0.280807i	$0.0906019\pi$
$18$	1.34248e10	−	2.32524e10i	0.287138	−	0.497337i
$19$	1.53183e10	+	2.65322e10i	0.206922	+	0.358399i	0.950743	−	0.309979i	$-0.100322\pi$
$19$	1.53183e10	+	2.65322e10i	0.206922	+	0.358399i	−0.743822	+	0.668378i	$0.766989\pi$
$20$	5.31851e10			0.464553
$21$	2.39469e10	−	9.71624e10i	0.138161	−	0.560575i
$22$	1.98012e11			0.769303
$23$	−1.00381e11	−	1.73865e11i	−0.267279	−	0.462941i	0.700879	−	0.713280i	$-0.252791\pi$
$23$	−1.00381e11	−	1.73865e11i	−0.267279	−	0.462941i	−0.968158	+	0.250339i	$0.919458\pi$
$24$	2.59645e11	−	4.49717e11i	0.481486	−	0.833958i
$25$	3.60217e11	−	6.23913e11i	0.472143	−	0.817776i
$26$	−5.44723e11	−	9.43488e11i	−0.511567	−	0.886060i
$27$	2.82430e11			0.192450
$28$	9.41549e11	−	3.82025e12i	0.470977	−	1.91094i
$29$	−2.23032e12			−0.827912			−0.413956	−	0.910297i	$-0.635853\pi$
$29$	−2.23032e12			−0.827912			−0.413956	+	0.910297i	$0.635853\pi$
$30$	4.21855e11	+	7.30674e11i	0.117390	+	0.203326i
$31$	1.37220e12	−	2.37673e12i	0.288964	−	0.500501i	−0.684599	−	0.728920i	$-0.740022\pi$
$31$	1.37220e12	−	2.37673e12i	0.288964	−	0.500501i	0.973563	+	0.228420i	$0.0733558\pi$
$32$	−3.36082e11	+	5.82112e11i	−0.0540345	+	0.0935904i
$33$	1.04144e12	+	1.80383e12i	0.128904	+	0.223268i
$34$	8.49247e12			0.815574
$35$	2.26790e12	+	2.17828e12i	0.170233	+	0.163507i
$36$	1.11046e13			0.656043
$37$	1.65244e13	+	2.86211e13i	0.773412	+	1.33959i	0.935683	+	0.352842i	$0.114785\pi$
$37$	1.65244e13	+	2.86211e13i	0.773412	+	1.33959i	−0.162271	+	0.986746i	$0.551882\pi$
$38$	−9.55451e12	+	1.65489e13i	−0.356490	+	0.617459i
$39$	5.72993e12	−	9.92453e12i	0.171435	−	0.296935i
$40$	8.15898e12	+	1.41318e13i	0.196846	+	0.340947i
$41$	−8.69504e13			−1.70063			−0.850313	−	0.526278i	$-0.823587\pi$
$41$	−8.69504e13			−1.70063			−0.850313	+	0.526278i	$0.823587\pi$
$42$	5.99520e13	−	1.73662e13i	0.955398	−	0.276749i
$43$	−2.01301e13			−0.262642			−0.131321	−	0.991340i	$-0.541922\pi$
$43$	−2.01301e13			−0.262642			−0.131321	+	0.991340i	$0.541922\pi$
$44$	4.09475e13	+	7.09232e13i	0.439420	+	0.761098i
$45$	−4.43749e12	+	7.68595e12i	−0.0393397	+	0.0681383i
$46$	6.26106e13	−	1.08445e14i	0.460475	−	0.797567i
$47$	2.36558e13	+	4.09730e13i	0.144912	+	0.250996i	0.929340	−	0.369224i	$-0.120377\pi$
$47$	2.36558e13	+	4.09730e13i	0.144912	+	0.250996i	−0.784428	+	0.620220i	$0.787043\pi$
$48$	1.02054e14			0.522733
$49$	1.96613e14	−	1.24339e14i	0.845175	−	0.534490i
$50$	4.49355e14			1.62684
$51$	4.46661e13	+	7.73639e13i	0.136657	+	0.236697i
$52$	2.25290e14	−	3.90215e14i	0.584406	−	1.01222i
$53$	5.75801e13	−	9.97317e13i	0.127036	−	0.220033i	−0.795491	−	0.605966i	$-0.792787\pi$
$53$	5.75801e13	−	9.97317e13i	0.127036	−	0.220033i	0.922527	+	0.385932i	$0.126120\pi$
$54$	8.80798e13	+	1.52559e14i	0.165779	+	0.287138i
$55$	−6.54517e13			−0.105399
$56$	1.15951e15	−	3.35875e14i	1.60206	−	0.464066i
$57$	−2.01007e14			−0.238933
$58$	−6.95558e14	−	1.20474e15i	−0.713174	−	1.23525i
$59$	9.36357e14	−	1.62182e15i	0.830232	−	1.43800i	−0.0676229	−	0.997711i	$-0.521541\pi$
$59$	9.36357e14	−	1.62182e15i	0.830232	−	1.43800i	0.897854	−	0.440292i	$-0.145125\pi$
$60$	−1.74474e14	+	3.02197e14i	−0.134105	+	0.232276i
$61$	−1.03834e15	−	1.79845e15i	−0.693482	−	1.20115i	−0.970690	−	0.240336i	$-0.922742\pi$
$61$	−1.03834e15	−	1.79845e15i	−0.693482	−	1.20115i	0.277208	−	0.960810i	$-0.410591\pi$
$62$	1.71177e15			0.995670
$63$	4.73518e14	+	4.54807e14i	0.240404	+	0.230905i
$64$	−2.45803e15			−1.09158
$65$	1.80055e14	+	3.11865e14i	0.0700879	+	0.121396i
$66$	−6.49577e14	+	1.12510e15i	−0.222079	+	0.384652i
$67$	−2.65449e15	+	4.59771e15i	−0.798630	+	1.38327i	0.121879	+	0.992545i	$0.461108\pi$
$67$	−2.65449e15	+	4.59771e15i	−0.798630	+	1.38327i	−0.920509	+	0.390722i	$0.872225\pi$
$68$	1.75619e15	+	3.04181e15i	0.465849	+	0.806875i
$69$	1.31720e15			0.308627
$70$	−4.69356e14	+	1.90437e15i	−0.0973127	+	0.394837i
$71$	4.01181e15			0.737300			0.368650	−	0.929568i	$-0.379820\pi$
$71$	4.01181e15			0.737300			0.368650	+	0.929568i	$0.379820\pi$
$72$	1.70353e15	+	2.95060e15i	0.277986	+	0.481486i
$73$	7.03575e14	−	1.21863e15i	0.102109	−	0.176859i	−0.810444	−	0.585816i	$-0.800774\pi$
$73$	7.03575e14	−	1.21863e15i	0.102109	−	0.176859i	0.912554	+	0.408957i	$0.134107\pi$
$74$	−1.03067e16	+	1.78518e16i	−1.33245	+	2.30788i
$75$	2.36338e15	+	4.09350e15i	0.272592	+	0.472143i
$76$	−7.90324e15			−0.814497
$77$	−1.15871e15	+	4.70135e15i	−0.106857	+	0.433562i
$78$	7.14786e15			0.590706
$79$	−1.28654e16	−	2.22836e16i	−0.954102	−	1.65255i	−0.736411	−	0.676535i	$-0.763481\pi$
$79$	−1.28654e16	−	2.22836e16i	−0.954102	−	1.65255i	−0.217691	−	0.976018i	$-0.569852\pi$
$80$	−1.60346e15	+	2.77727e15i	−0.106854	+	0.185077i
$81$	−9.26510e14	+	1.60476e15i	−0.0555556	+	0.0962250i
$82$	−2.71168e16	−	4.69676e16i	−1.46494	−	2.53735i
$83$	−2.65986e16			−1.29627			−0.648133	−	0.761527i	$-0.724450\pi$
$83$	−2.65986e16			−1.29627			−0.648133	+	0.761527i	$0.724450\pi$
$84$	1.86179e16	+	1.78822e16i	0.819513	+	0.787131i
$85$	−2.80714e15			−0.111739
$86$	−6.27787e15	−	1.08736e16i	−0.226243	−	0.391865i
$87$	7.31657e15	−	1.26727e16i	0.238998	−	0.413956i
$88$	−1.25633e16	+	2.17603e16i	−0.372392	+	0.645002i
$89$	−2.87458e16	−	4.97892e16i	−0.774033	−	1.34067i	−0.935336	−	0.353760i	$-0.884903\pi$
$89$	−2.87458e16	−	4.97892e16i	−0.774033	−	1.34067i	0.161303	−	0.986905i	$-0.448430\pi$
$90$	−5.53558e15			−0.135551
$91$	2.55886e16	−	7.41222e15i	0.570420	−	0.165233i
$92$	5.17899e16			1.05208
$93$	9.00302e15	+	1.55937e16i	0.166834	+	0.288964i
$94$	−1.47548e16	+	2.55561e16i	−0.249659	+	0.432422i
$95$	3.15819e15	−	5.47015e15i	0.0488414	−	0.0845958i
$96$	−2.20504e15	−	3.81923e15i	−0.0311968	−	0.0540345i
$97$	−4.18174e16			−0.541748			−0.270874	−	0.962615i	$-0.587313\pi$
$97$	−4.18174e16			−0.541748			−0.270874	+	0.962615i	$0.587313\pi$
$98$	1.28480e17	+	6.74270e16i	1.52551	+	0.800594i
$99$	−1.36658e16			−0.148845
$100$	9.29238e16	+	1.60949e17i	0.929238	+	1.60949i
$101$	−5.33267e14	+	9.23646e14i	−0.00490020	+	0.00848739i	−0.868465	−	0.495750i	$-0.834893\pi$
$101$	−5.33267e14	+	9.23646e14i	−0.00490020	+	0.00848739i	0.863565	+	0.504238i	$0.168226\pi$
$102$	−2.78596e16	+	4.82542e16i	−0.235436	+	0.407787i
$103$	−8.76843e16	−	1.51874e17i	−0.682033	−	1.18132i	−0.974359	−	0.224997i	$-0.927763\pi$
$103$	−8.76843e16	−	1.51874e17i	−0.682033	−	1.18132i	0.292327	−	0.956319i	$-0.405571\pi$
$104$	1.38245e17			0.990524
$105$	−1.98168e16	+	5.74032e15i	−0.130896	+	0.0379164i
$106$	7.18289e16			0.437723
$107$	−1.01172e17	−	1.75234e17i	−0.569241	−	0.985955i	−0.996641	−	0.0818923i	$-0.973904\pi$
$107$	−1.01172e17	−	1.75234e17i	−0.569241	−	0.985955i	0.427400	−	0.904063i	$-0.359430\pi$
$108$	−3.64287e16	+	6.30963e16i	−0.189383	+	0.328021i
$109$	−1.02663e17	+	1.77817e17i	−0.493501	+	0.854768i	−0.999972	−	0.00748867i	$-0.997616\pi$
$109$	−1.02663e17	+	1.77817e17i	−0.493501	+	0.854768i	0.506471	+	0.862257i	$0.330950\pi$
$110$	−2.04121e16	−	3.53548e16i	−0.0907924	−	0.157257i
$111$	−2.16833e17			−0.893059
$112$	1.71103e17	+	1.64342e17i	0.652986	+	0.627184i
$113$	−2.58019e16			−0.0913031			−0.0456515	−	0.998957i	$-0.514536\pi$
$113$	−2.58019e16			−0.0913031			−0.0456515	+	0.998957i	$0.514536\pi$
$114$	−6.26871e16	−	1.08577e17i	−0.205820	−	0.356490i
$115$	−2.06956e16	+	3.58459e16i	−0.0630880	+	0.109272i
$116$	2.87674e17	−	4.98266e17i	0.814719	−	1.41113i
$117$	3.75941e16	+	6.51149e16i	0.0989782	+	0.171435i
$118$	1.16807e18			2.86069
$119$	−4.96955e16	+	2.01635e17i	−0.113284	+	0.459639i
$120$	−1.07062e17			−0.227298
$121$	2.02332e17	+	3.50449e17i	0.400303	+	0.693345i
$122$	6.47642e17	−	1.12175e18i	1.19475	−	2.06937i
$123$	2.85241e17	−	4.94051e17i	0.490928	−	0.850313i
$124$	3.53982e17	+	6.13116e17i	0.568719	+	0.985049i
$125$	−3.05828e17			−0.458925
$126$	−9.79977e16	+	3.97617e17i	−0.137425	+	0.557590i
$127$	−7.45665e17			−0.977714			−0.488857	−	0.872364i	$-0.662586\pi$
$127$	−7.45665e17			−0.977714			−0.488857	+	0.872364i	$0.662586\pi$
$128$	−7.22522e17	−	1.25144e18i	−0.886270	−	1.53507i
$129$	6.60368e16	−	1.14379e17i	0.0758183	−	0.131321i
$130$	−1.12306e17	+	1.94520e17i	−0.120749	+	0.209144i
$131$	−1.21053e16	−	2.09670e16i	−0.0121947	−	0.0211218i	0.859864	−	0.510524i	$-0.170548\pi$
$131$	−1.21053e16	−	2.09670e16i	−0.0121947	−	0.0211218i	−0.872058	+	0.489402i	$0.837215\pi$
$132$	−5.37313e17			−0.507398
$133$	−3.37007e17	−	3.23690e17i	−0.298469	−	0.286675i
$134$	−3.31137e18			−2.75180
$135$	−2.91143e16	−	5.04275e16i	−0.0227128	−	0.0393397i
$136$	−5.38824e17	+	9.33271e17i	−0.394790	+	0.683796i
$137$	4.34528e17	−	7.52625e17i	0.299153	−	0.518148i	−0.676789	−	0.736177i	$-0.736629\pi$
$137$	4.34528e17	−	7.52625e17i	0.299153	−	0.518148i	0.975942	+	0.218028i	$0.0699626\pi$
$138$	4.10788e17	+	7.11506e17i	0.265856	+	0.460475i
$139$	2.29725e18			1.39824			0.699122	−	0.715003i	$-0.253575\pi$
$139$	2.29725e18			1.39824			0.699122	+	0.715003i	$0.253575\pi$
$140$	−7.79161e17	+	2.25699e17i	−0.446210	+	0.129253i
$141$	−3.10411e17			−0.167330
$142$	1.25114e18	+	2.16704e18i	0.635120	+	1.10006i
$143$	−2.77251e17	+	4.80213e17i	−0.132592	+	0.229656i
$144$	−3.34789e17	+	5.79871e17i	−0.150900	+	0.261367i
$145$	2.29913e17	+	3.98221e17i	0.0977093	+	0.169238i
$146$	8.77681e17			0.351834
$147$	6.15005e16	+	1.52505e18i	0.0232638	+	0.576881i
$148$	−8.52548e18			−3.04435
$149$	2.75224e18	+	4.76703e18i	0.928119	+	1.60755i	0.786466	+	0.617633i	$0.211908\pi$
$149$	2.75224e18	+	4.76703e18i	0.928119	+	1.60755i	0.141653	+	0.989916i	$0.454758\pi$
$150$	−1.47411e18	+	2.55323e18i	−0.469628	+	0.813420i
$151$	−3.50491e17	+	6.07069e17i	−0.105529	+	0.182782i	−0.913954	−	0.405817i	$-0.866987\pi$
$151$	−3.50491e17	+	6.07069e17i	−0.105529	+	0.182782i	0.808425	+	0.588599i	$0.200320\pi$
$152$	−1.21241e18	−	2.09996e18i	−0.345128	−	0.597780i
$153$	−5.86108e17			−0.157798
$154$	−2.90087e18	+	8.40290e17i	−0.738927	+	0.214044i
$155$	−5.65816e17			−0.136413
$156$	1.47813e18	+	2.56020e18i	0.337407	+	0.584406i
$157$	−7.31771e17	+	1.26746e18i	−0.158208	+	0.274024i	−0.934222	−	0.356691i	$-0.883905\pi$
$157$	−7.31771e17	+	1.26746e18i	−0.158208	+	0.274024i	0.776015	+	0.630715i	$0.217238\pi$
$158$	8.02456e18	−	1.38989e19i	1.64375	−	2.84706i
$159$	3.77783e17	+	6.54340e17i	0.0733444	+	0.127036i
$160$	1.38581e17			0.0255084
$161$	2.20840e18	+	2.12114e18i	0.385530	+	0.370296i
$162$	−1.15578e18			−0.191425
$163$	1.75164e18	+	3.03392e18i	0.275327	+	0.476881i	0.970218	−	0.242235i	$-0.0778804\pi$
$163$	1.75164e18	+	3.03392e18i	0.275327	+	0.476881i	−0.694890	+	0.719116i	$0.744547\pi$
$164$	1.12151e19	−	1.94252e19i	1.67352	−	2.89863i
$165$	2.14714e17	−	3.71896e17i	0.0304262	−	0.0526997i
$166$	−8.29515e18	−	1.43676e19i	−1.11662	−	1.93404i
$167$	8.72738e18			1.11633			0.558167	−	0.829729i	$-0.311505\pi$
$167$	8.72738e18			1.11633			0.558167	+	0.829729i	$0.311505\pi$
$168$	−1.89535e18	+	7.69019e18i	−0.230441	+	0.934993i
$169$	−5.59958e18			−0.647319
$170$	−8.75449e17	−	1.51632e18i	−0.0962532	−	0.166715i
$171$	6.59405e17	−	1.14212e18i	0.0689739	−	0.119466i
$172$	2.59645e18	−	4.49718e18i	0.258457	−	0.447660i
$173$	1.16878e18	+	2.02439e18i	0.110749	+	0.191824i	0.916073	−	0.401012i	$-0.131342\pi$
$173$	1.16878e18	+	2.02439e18i	0.110749	+	0.191824i	−0.805323	+	0.592836i	$0.798008\pi$
$174$	9.12712e18			0.823503
$175$	−2.62950e18	+	1.06690e19i	−0.225970	+	0.916850i
$176$	−4.93804e18			−0.404294
$177$	6.14344e18	+	1.06407e19i	0.479334	+	0.830232i
$178$	1.79296e19	−	3.10550e19i	1.33352	−	2.30973i
$179$	−1.23744e19	+	2.14330e19i	−0.877550	+	1.51996i	−0.0235280	+	0.999723i	$0.507490\pi$
$179$	−1.23744e19	+	2.14330e19i	−0.877550	+	1.51996i	−0.854022	+	0.520237i	$0.825843\pi$
$180$	−1.14472e18	−	1.98272e18i	−0.0774255	−	0.134105i
$181$	4.24857e18			0.274141			0.137071	−	0.990561i	$-0.456231\pi$
$181$	4.24857e18			0.274141			0.137071	+	0.990561i	$0.456231\pi$
$182$	1.19840e19	+	1.15105e19i	0.737896	+	0.708739i
$183$	1.36251e19			0.800764
$184$	7.94494e18	+	1.37610e19i	0.445799	+	0.772147i
$185$	3.40684e18	−	5.90083e18i	0.182554	−	0.316194i
$186$	−5.61545e18	+	9.72625e18i	−0.287425	+	0.497835i
$187$	−2.16123e18	−	3.74337e18i	−0.105694	−	0.183067i
$188$	−1.22048e19			−0.570413
$189$	−4.13759e18	+	1.19853e18i	−0.184851	+	0.0535456i
$190$	3.93972e18			0.168290
$191$	−4.00005e18	−	6.92829e18i	−0.163411	−	0.283037i	0.772679	−	0.634797i	$-0.218916\pi$
$191$	−4.00005e18	−	6.92829e18i	−0.163411	−	0.283037i	−0.936090	+	0.351761i	$0.885583\pi$
$192$	8.06357e18	−	1.39665e19i	0.315113	−	0.545792i
$193$	−1.44383e19	+	2.50078e19i	−0.539856	+	0.935058i	0.459056	+	0.888408i	$0.348188\pi$
$193$	−1.44383e19	+	2.50078e19i	−0.539856	+	0.935058i	−0.998911	+	0.0466500i	$0.985145\pi$
$194$	−1.30414e19	−	2.25883e19i	−0.466669	−	0.808294i
$195$	−2.36269e18			−0.0809305
$196$	2.41809e18	+	5.99621e19i	0.0793040	+	1.96653i
$197$	−5.27108e19			−1.65553			−0.827764	−	0.561077i	$-0.810387\pi$
$197$	−5.27108e19			−1.65553			−0.827764	+	0.561077i	$0.810387\pi$
$198$	−4.26187e18	−	7.38178e18i	−0.128217	−	0.222079i
$199$	−1.32164e18	+	2.28915e18i	−0.0380945	+	0.0659817i	−0.884444	−	0.466646i	$-0.845462\pi$
$199$	−1.32164e18	+	2.28915e18i	−0.0380945	+	0.0659817i	0.846350	+	0.532628i	$0.178795\pi$
$200$	−2.85104e19	+	4.93814e19i	−0.787495	+	1.36398i
$201$	−1.74161e19	−	3.01656e19i	−0.461089	−	0.798630i
$202$	−6.65229e17			−0.0168844
$203$	3.26742e19	−	9.46468e18i	0.795221	−	0.230351i
$204$	−2.30447e19			−0.537916
$205$	8.96331e18	+	1.55249e19i	0.200706	+	0.347633i
$206$	5.46913e19	−	9.47280e19i	1.17502	−	2.03520i
$207$	−4.32107e18	+	7.48432e18i	−0.0890930	+	0.154314i
$208$	1.35844e19	+	2.35289e19i	0.268845	+	0.465653i
$209$	9.72604e18			0.184796
$210$	−9.28089e18	−	8.91416e18i	−0.169327	−	0.162636i
$211$	−3.04158e18			−0.0532964			−0.0266482	−	0.999645i	$-0.508483\pi$
$211$	−3.04158e18			−0.0532964			−0.0266482	+	0.999645i	$0.508483\pi$
$212$	1.48537e19	+	2.57274e19i	0.250024	+	0.433054i
$213$	−1.31607e19	+	2.27951e19i	−0.212840	+	0.368650i
$214$	6.31037e19	−	1.09299e20i	0.980704	−	1.69863i
$215$	2.07512e18	+	3.59421e18i	0.0309968	+	0.0536880i
$216$	−2.23537e19			−0.320991
$217$	−1.00168e19	+	4.06421e19i	−0.138299	+	0.561137i
$218$	−1.28068e20			−1.70043
$219$	4.61615e18	+	7.99541e18i	0.0589529	+	0.102109i
$220$	8.44217e18	−	1.46223e19i	0.103720	−	0.179648i
$221$	−1.18910e19	+	2.05958e19i	−0.140567	+	0.243469i
$222$	−6.76226e19	−	1.17126e20i	−0.769292	−	1.33245i
$223$	−1.16875e20			−1.27977			−0.639883	−	0.768472i	$-0.721017\pi$
$223$	−1.16875e20			−1.27977			−0.639883	+	0.768472i	$0.721017\pi$
$224$	2.45333e18	−	9.95414e18i	0.0258611	−	0.104929i
$225$	−3.10123e19			−0.314762
$226$	−8.04671e18	−	1.39373e19i	−0.0786496	−	0.136225i
$227$	1.33141e19	−	2.30607e19i	0.125341	−	0.217097i	−0.796525	−	0.604605i	$-0.793331\pi$
$227$	1.33141e19	−	2.30607e19i	0.125341	−	0.217097i	0.921866	+	0.387509i	$0.126664\pi$
$228$	2.59266e19	−	4.49062e19i	0.235125	−	0.407249i
$229$	−1.09866e19	−	1.90294e19i	−0.0959980	−	0.166273i	0.814027	−	0.580827i	$-0.197271\pi$
$229$	−1.09866e19	−	1.90294e19i	−0.0959980	−	0.166273i	−0.910025	+	0.414554i	$0.863938\pi$
$230$	−2.58169e19			−0.217379
$231$	−2.29119e19	−	2.20065e19i	−0.185934	−	0.178587i
$232$	1.76525e20			1.38089
$233$	8.97366e18	+	1.55428e19i	0.0676775	+	0.117221i	0.897879	−	0.440243i	$-0.145108\pi$
$233$	8.97366e18	+	1.55428e19i	0.0676775	+	0.117221i	−0.830201	+	0.557464i	$0.811774\pi$
$234$	−2.34485e19	+	4.06141e19i	−0.170522	+	0.295353i
$235$	4.87713e18	−	8.44744e18i	0.0342048	−	0.0592445i
$236$	2.41549e20	+	4.18375e20i	1.63400	+	2.83017i
$237$	1.68820e20			1.10170
$238$	−1.24415e20	+	3.60390e19i	−0.783370	+	0.226918i
$239$	−1.34685e20			−0.818346			−0.409173	−	0.912457i	$-0.634183\pi$
$239$	−1.34685e20			−0.818346			−0.409173	+	0.912457i	$0.634183\pi$
$240$	−1.05203e19	−	1.82217e19i	−0.0616924	−	0.106854i
$241$	−1.04393e20	+	1.80813e20i	−0.590915	+	1.02349i	0.403194	+	0.915114i	$0.367900\pi$
$241$	−1.04393e20	+	1.80813e20i	−0.590915	+	1.02349i	−0.994109	+	0.108381i	$0.965433\pi$
$242$	−1.26200e20	+	2.18585e20i	−0.689652	+	1.19451i
$243$	−6.07883e18	−	1.05288e19i	−0.0320750	−	0.0555556i
$244$	5.35713e20			2.72972
$245$	−4.24685e19	−	2.22877e19i	−0.209004	−	0.109686i
$246$	3.55826e20			1.69157
$247$	−2.67560e19	−	4.63428e19i	−0.122885	−	0.212842i
$248$	−1.08607e20	+	1.88113e20i	−0.481968	+	0.834793i
$249$	8.72566e19	−	1.51133e20i	0.374200	−	0.648133i
$250$	−9.53769e19	−	1.65198e20i	−0.395324	−	0.684721i
$251$	3.38813e20			1.35748			0.678741	−	0.734378i	$-0.262526\pi$
$251$	3.38813e20			1.35748			0.678741	+	0.734378i	$0.262526\pi$
$252$	−1.62682e20	+	4.71240e19i	−0.630138	+	0.182531i
$253$	−6.37347e19			−0.238699
$254$	−2.32546e20	−	4.02782e20i	−0.842215	−	1.45876i
$255$	9.20883e18	−	1.59502e19i	0.0322562	−	0.0558694i
$256$	2.89569e20	−	5.01548e20i	0.981097	−	1.69931i
$257$	2.31853e20	+	4.01581e20i	0.759943	+	1.31626i	0.942879	+	0.333135i	$0.108106\pi$
$257$	2.31853e20	+	4.01581e20i	0.759943	+	1.31626i	−0.182936	+	0.983125i	$0.558560\pi$
$258$	8.23783e19			0.261243
$259$	−3.63540e20	−	3.49175e20i	−1.11559	−	1.07151i
$260$	−9.28966e19			−0.275884
$261$	4.80040e19	+	8.31453e19i	0.137985	+	0.238998i
$262$	7.55045e18	−	1.30778e19i	0.0210093	−	0.0363892i
$263$	−6.94825e19	+	1.20347e20i	−0.187177	+	0.324199i	−0.944308	−	0.329064i	$-0.893267\pi$
$263$	−6.94825e19	+	1.20347e20i	−0.187177	+	0.324199i	0.757131	+	0.653263i	$0.226600\pi$
$264$	−8.24277e19	−	1.42769e20i	−0.215001	−	0.372392i
$265$	−2.37427e19			−0.0599708
$266$	6.97458e19	−	2.82987e20i	0.170618	−	0.692265i
$267$	3.77203e20			0.893777
$268$	−6.84770e20	−	1.18606e21i	−1.57181	−	2.72245i
$269$	7.65312e19	−	1.32556e20i	0.170194	−	0.294785i	−0.768294	−	0.640098i	$-0.778894\pi$
$269$	7.65312e19	−	1.32556e20i	0.170194	−	0.294785i	0.938488	+	0.345313i	$0.112227\pi$
$270$	1.81595e19	−	3.14531e19i	0.0391301	−	0.0677754i
$271$	−1.15123e20	−	1.99400e20i	−0.240394	−	0.416375i	0.720432	−	0.693525i	$-0.243943\pi$
$271$	−1.15123e20	−	1.99400e20i	−0.240394	−	0.416375i	−0.960827	+	0.277150i	$0.910610\pi$
$272$	−2.11787e20			−0.428610
$273$	−4.18272e19	+	1.69710e20i	−0.0820496	+	0.332909i
$274$	5.42056e20			1.03078
$275$	−1.14356e20	−	1.98070e20i	−0.210829	−	0.365166i
$276$	−1.69897e20	+	2.94270e20i	−0.303709	+	0.526040i
$277$	−1.91118e20	+	3.31026e20i	−0.331301	+	0.573831i	−0.982767	−	0.184847i	$-0.940821\pi$
$277$	−1.91118e20	+	3.31026e20i	−0.331301	+	0.573831i	0.651466	+	0.758678i	$0.274154\pi$
$278$	7.16432e20	+	1.24090e21i	1.20446	+	2.08619i
$279$	−1.18138e20			−0.192643
$280$	−1.79499e20	−	1.72406e20i	−0.283935	−	0.272716i
$281$	7.42707e20			1.13976			0.569880	−	0.821728i	$-0.306990\pi$
$281$	7.42707e20			1.13976			0.569880	+	0.821728i	$0.306990\pi$
$282$	−9.68064e19	−	1.67674e20i	−0.144141	−	0.249659i
$283$	−6.88831e20	+	1.19309e21i	−0.995240	+	1.72381i	−0.413220	+	0.910631i	$0.635596\pi$
$283$	−6.88831e20	+	1.19309e21i	−0.995240	+	1.72381i	−0.582020	+	0.813175i	$0.697737\pi$
$284$	−5.17456e20	+	8.96261e20i	−0.725551	+	1.25669i
$285$	2.07209e19	+	3.58897e19i	0.0281986	+	0.0488414i
$286$	−3.45860e20			−0.456866
$287$	1.27382e21	−	3.68986e20i	1.63348	−	0.473167i
$288$	2.89345e19			0.0360230
$289$	3.20927e20	+	5.55863e20i	0.387949	+	0.671948i
$290$	−1.43404e20	+	2.48382e20i	−0.168336	+	0.291567i
$291$	1.37182e20	−	2.37606e20i	0.156389	−	0.270874i
$292$	1.81499e20	+	3.14365e20i	0.200964	+	0.348081i
$293$	−1.22273e21			−1.31509			−0.657543	−	0.753417i	$-0.728404\pi$
$293$	−1.22273e21			−1.31509			−0.657543	+	0.753417i	$0.728404\pi$
$294$	−8.04599e20	+	5.08830e20i	−0.840673	+	0.531643i
$295$	−3.86099e20			−0.391932
$296$	−1.30787e21	−	2.26530e21i	−1.28999	−	2.23432i
$297$	4.48306e19	−	7.76488e19i	0.0429679	−	0.0744226i
$298$	−1.71666e21	+	2.97334e21i	−1.59899	+	2.76953i
$299$	1.75332e20	+	3.03684e20i	0.158729	+	0.274926i
$300$	−1.21935e21			−1.07299
$301$	2.94906e20	−	8.54250e19i	0.252272	−	0.0730752i
$302$	−4.37224e20			−0.363617
$303$	−3.49877e18	−	6.06004e18i	−0.00282913	−	0.00490020i
$304$	2.38272e20	−	4.12699e20i	0.187347	−	0.324495i
$305$	−2.14075e20	+	3.70788e20i	−0.163688	+	0.283516i
$306$	−1.82787e20	−	3.16596e20i	−0.135929	−	0.235436i
$307$	1.52933e21			1.10618			0.553090	−	0.833122i	$-0.313449\pi$
$307$	1.52933e21			1.10618			0.553090	+	0.833122i	$0.313449\pi$
$308$	−9.00853e20	−	8.65257e20i	−0.633830	−	0.608785i
$309$	1.15059e21			0.787544
$310$	−1.76458e20	−	3.05634e20i	−0.117508	−	0.203530i
$311$	1.28850e21	−	2.23174e21i	0.834873	−	1.44604i	−0.0592611	−	0.998243i	$-0.518874\pi$
$311$	1.28850e21	−	2.23174e21i	0.834873	−	1.44604i	0.894134	−	0.447800i	$-0.147792\pi$
$312$	−4.53512e20	+	7.85506e20i	−0.285940	+	0.495262i
$313$	−1.27999e21	−	2.21700e21i	−0.785377	−	1.36031i	−0.928774	−	0.370648i	$-0.879136\pi$
$313$	−1.27999e21	−	2.21700e21i	−0.785377	−	1.36031i	0.143397	−	0.989665i	$-0.454198\pi$
$314$	−9.12854e20			−0.545129
$315$	3.23927e19	−	1.31430e20i	0.0188281	−	0.0763933i
$316$	6.63771e21			3.75559
$317$	−6.64291e20	−	1.15059e21i	−0.365893	−	0.633746i	0.623026	−	0.782201i	$-0.285903\pi$
$317$	−6.64291e20	−	1.15059e21i	−0.365893	−	0.633746i	−0.988919	+	0.148455i	$0.952570\pi$
$318$	−2.35635e20	+	4.08131e20i	−0.126360	+	0.218861i
$319$	−3.54023e20	+	6.13186e20i	−0.184846	+	0.320163i
$320$	2.53387e20	+	4.38879e20i	0.128828	+	0.223136i
$321$	1.32757e21			0.657303
$322$	−4.57043e20	+	1.85441e21i	−0.220385	+	0.894193i
$323$	4.17138e20			0.195911
$324$	−2.39009e20	−	4.13975e20i	−0.109340	−	0.189383i
$325$	−6.29177e20	+	1.08977e21i	−0.280391	+	0.485652i
$326$	−1.09255e21	+	1.89235e21i	−0.474341	+	0.821583i
$327$	−6.73570e20	−	1.16666e21i	−0.284923	−	0.493501i
$328$	6.88194e21			2.83650
$329$	−5.20432e20	−	4.99868e20i	−0.209025	−	0.200766i
$330$	2.67847e20			0.104838
$331$	−2.04388e21	−	3.54010e21i	−0.779681	−	1.35045i	−0.932126	−	0.362135i	$-0.882048\pi$
$331$	−2.04388e21	−	3.54010e21i	−0.779681	−	1.35045i	0.152445	−	0.988312i	$-0.451285\pi$
$332$	3.43077e21	−	5.94227e21i	1.27561	−	2.20942i
$333$	7.11321e20	−	1.23204e21i	0.257804	−	0.446529i
$334$	2.72176e21	+	4.71423e21i	0.961624	+	1.66558i
$335$	1.09456e21			0.377014
$336$	−1.49509e21	+	4.33081e20i	−0.502093	+	0.145441i
$337$	6.50916e20			0.213143			0.106571	−	0.994305i	$-0.466013\pi$
$337$	6.50916e20			0.213143			0.106571	+	0.994305i	$0.466013\pi$
$338$	−1.74631e21	−	3.02470e21i	−0.557609	−	0.965807i
$339$	8.46432e19	−	1.46606e20i	0.0263569	−	0.0456515i
$340$	3.62075e20	−	6.27131e20i	0.109958	−	0.190453i
$341$	−4.35625e20	−	7.54524e20i	−0.129033	−	0.223491i
$342$	8.22580e20			0.237660
$343$	−2.35274e21	+	2.65592e21i	−0.663091	+	0.748539i
$344$	1.59326e21			0.438065
$345$	−1.35784e20	−	2.35185e20i	−0.0364239	−	0.0630880i
$346$	−7.29004e20	+	1.26267e21i	−0.190802	+	0.330479i
$347$	1.77647e21	−	3.07693e21i	0.453687	−	0.785809i	−0.544924	−	0.838485i	$-0.683442\pi$
$347$	1.77647e21	−	3.07693e21i	0.453687	−	0.785809i	0.998612	+	0.0526757i	$0.0167750\pi$
$348$	1.88743e21	+	3.26912e21i	0.470378	+	0.814719i
$349$	−6.33203e21			−1.54002			−0.770010	−	0.638031i	$-0.779749\pi$
$349$	−6.33203e21			−1.54002			−0.770010	+	0.638031i	$0.779749\pi$
$350$	−6.58305e21	+	1.90690e21i	−1.56260	+	0.452637i
$351$	−4.93310e20			−0.114290
$352$	1.06694e20	+	1.84799e20i	0.0241283	+	0.0417915i
$353$	2.03523e20	−	3.52512e20i	0.0449292	−	0.0778196i	−0.842686	−	0.538405i	$-0.819027\pi$
$353$	2.03523e20	−	3.52512e20i	0.0449292	−	0.0778196i	0.887615	+	0.460585i	$0.152360\pi$
$354$	−3.83184e21	+	6.63695e21i	−0.825810	+	1.43034i
$355$	−4.13559e20	−	7.16305e20i	−0.0870154	−	0.150715i
$356$	1.48309e22			3.04679
$357$	−9.82662e20	−	9.43833e20i	−0.197117	−	0.189328i
$358$	−1.54365e22			−3.02373
$359$	2.91046e21	+	5.04107e21i	0.556749	+	0.964318i	0.997765	+	0.0668185i	$0.0212848\pi$
$359$	2.91046e21	+	5.04107e21i	0.556749	+	0.964318i	−0.441016	+	0.897499i	$0.645382\pi$
$360$	3.51217e20	−	6.08326e20i	0.0656152	−	0.113649i
$361$	2.27089e21	−	3.93330e21i	0.414367	−	0.717704i
$362$	1.32498e21	+	2.29493e21i	0.236149	+	0.409022i
$363$	−2.65500e21			−0.462230
$364$	−1.64457e21	+	6.67269e21i	−0.279699	+	1.13485i
$365$	−2.90113e20			−0.0482034
$366$	4.24918e21	+	7.35980e21i	0.689788	+	1.19475i
$367$	1.77137e21	−	3.06810e21i	0.280962	−	0.486640i	−0.690660	−	0.723180i	$-0.742680\pi$
$367$	1.77137e21	−	3.06810e21i	0.280962	−	0.486640i	0.971622	+	0.236539i	$0.0760132\pi$
$368$	−1.56139e21	+	2.70441e21i	−0.241995	+	0.419147i
$369$	1.87146e21	+	3.24147e21i	0.283438	+	0.490928i
$370$	4.24990e21			0.629019
$371$	−4.20322e20	+	1.70542e21i	−0.0608001	+	0.246691i
$372$	−4.64496e21			−0.656700
$373$	−2.31739e21	−	4.01384e21i	−0.320239	−	0.554671i	0.660298	−	0.751004i	$-0.270430\pi$
$373$	−2.31739e21	−	4.01384e21i	−0.320239	−	0.554671i	−0.980537	+	0.196333i	$0.937097\pi$
$374$	1.34803e21	−	2.33485e21i	0.182091	−	0.315392i
$375$	1.00327e21	−	1.73771e21i	0.132480	−	0.229463i
$376$	−1.87231e21	−	3.24293e21i	−0.241702	−	0.418640i
$377$	3.89562e21			0.491672
$378$	−1.93777e21	−	1.86120e21i	−0.239124	−	0.229675i
$379$	−9.79459e21			−1.18182			−0.590912	−	0.806736i	$-0.701232\pi$
$379$	−9.79459e21			−1.18182			−0.590912	+	0.806736i	$0.701232\pi$
$380$	8.14708e20	+	1.41112e21i	0.0961261	+	0.166495i
$381$	2.44615e21	−	4.23686e21i	0.282242	−	0.488857i
$382$	2.49495e21	−	4.32138e21i	0.281529	−	0.487623i
$383$	−4.14039e21	−	7.17136e21i	−0.456932	−	0.791429i	0.541865	−	0.840465i	$-0.317718\pi$
$383$	−4.14039e21	−	7.17136e21i	−0.456932	−	0.791429i	−0.998797	+	0.0490364i	$0.984385\pi$
$384$	9.48093e21			1.02338
$385$	9.58866e20	−	2.77754e20i	0.101238	−	0.0293254i
$386$	−1.80111e22			−1.86015
$387$	4.33268e20	+	7.50442e20i	0.0437737	+	0.0758183i
$388$	5.39374e21	−	9.34224e21i	0.533115	−	0.923382i
$389$	6.94456e20	−	1.20283e21i	0.0671542	−	0.116314i	−0.830493	−	0.557029i	$-0.811941\pi$
$389$	6.94456e20	−	1.20283e21i	0.0671542	−	0.116314i	0.897648	+	0.440714i	$0.145275\pi$
$390$	−7.36839e20	−	1.27624e21i	−0.0697146	−	0.120749i
$391$	−2.73350e21			−0.253056
$392$	−1.55615e22	+	9.84113e21i	−1.40968	+	0.891484i
$393$	1.58846e20			0.0140812
$394$	−1.64386e22	−	2.84725e22i	−1.42609	−	2.47007i
$395$	−2.65248e21	+	4.59423e21i	−0.225204	+	0.390065i
$396$	1.76266e21	−	3.05301e21i	0.146473	−	0.253699i
$397$	6.76857e21	+	1.17235e22i	0.550526	+	0.953539i	0.998237	+	0.0593603i	$0.0189061\pi$
$397$	6.76857e21	+	1.17235e22i	0.550526	+	0.953539i	−0.447711	+	0.894178i	$0.647761\pi$
$398$	−1.64869e21			−0.131260
$399$	2.94475e21	−	8.53003e20i	0.229498	−	0.0664785i
$400$	−1.12061e22			−0.854957
$401$	2.62559e21	+	4.54765e21i	0.196110	+	0.339672i	0.947264	−	0.320455i	$-0.103836\pi$
$401$	2.62559e21	+	4.54765e21i	0.196110	+	0.339672i	−0.751154	+	0.660127i	$0.770502\pi$
$402$	1.08629e22	−	1.88152e22i	0.794376	−	1.37590i
$403$	−2.39678e21	+	4.15134e21i	−0.171607	+	0.297232i
$404$	−1.37565e20	−	2.38270e20i	−0.00964421	−	0.0167043i
$405$	3.82038e20			0.0262264
$406$	1.53024e22	+	1.46978e22i	1.02870	+	0.988052i
$407$	1.04918e22			0.690712
$408$	−3.53522e21	−	6.12319e21i	−0.227932	−	0.394790i
$409$	−2.55515e20	+	4.42564e20i	−0.0161349	+	0.0279465i	−0.873980	−	0.485962i	$-0.838469\pi$
$409$	−2.55515e20	+	4.42564e20i	−0.0161349	+	0.0279465i	0.857845	+	0.513908i	$0.171803\pi$
$410$	−5.59068e21	+	9.68334e21i	−0.345782	+	0.598911i
$411$	2.85094e21	+	4.93797e21i	0.172716	+	0.299153i
$412$	4.52392e22			2.68466
$413$	−6.83520e21	+	2.77332e22i	−0.397352	+	1.61222i
$414$	−5.39036e21			−0.306984
$415$	2.74192e21	+	4.74915e21i	0.152984	+	0.264976i
$416$	5.87023e20	−	1.01675e21i	0.0320894	−	0.0555805i
$417$	−7.53613e21	+	1.30530e22i	−0.403638	+	0.699122i
$418$	3.03321e21	+	5.25367e21i	0.159186	+	0.275718i
$419$	1.59995e21			0.0822789			0.0411394	−	0.999153i	$-0.486901\pi$
$419$	1.59995e21			0.0822789			0.0411394	+	0.999153i	$0.486901\pi$
$420$	1.27362e21	−	5.16759e21i	0.0641831	−	0.260417i
$421$	−7.29515e20			−0.0360277			−0.0180138	−	0.999838i	$-0.505734\pi$
$421$	−7.29515e20			−0.0360277			−0.0180138	+	0.999838i	$0.505734\pi$
$422$	−9.48560e20	−	1.64295e21i	−0.0459102	−	0.0795188i
$423$	1.01830e21	−	1.76375e21i	0.0483042	−	0.0836652i
$424$	−4.55734e21	+	7.89355e21i	−0.211886	+	0.366997i
$425$	−4.90458e21	−	8.49497e21i	−0.223509	−	0.387129i
$426$	−1.64175e22			−0.733373
$427$	2.28436e22	+	2.19410e22i	1.00030	+	0.960770i
$428$	5.21978e22			2.24068
$429$	−1.81905e21	−	3.15068e21i	−0.0765520	−	0.132592i
$430$	−1.29431e21	+	2.24182e21i	−0.0534020	+	0.0924950i
$431$	−7.81303e21	+	1.35326e22i	−0.316055	+	0.547424i	−0.979661	−	0.200659i	$-0.935692\pi$
$431$	−7.81303e21	+	1.35326e22i	−0.316055	+	0.547424i	0.663606	+	0.748082i	$0.269025\pi$
$432$	−2.19655e21	−	3.80453e21i	−0.0871222	−	0.150900i
$433$	3.53068e22			1.37313			0.686564	−	0.727069i	$-0.259118\pi$
$433$	3.53068e22			1.37313			0.686564	+	0.727069i	$0.259118\pi$
$434$	−2.50774e22	+	7.26413e21i	−0.956355	+	0.277026i
$435$	−3.01692e21			−0.112825
$436$	−2.64836e22	−	4.58709e22i	−0.971272	−	1.68229i
$437$	3.07534e21	−	5.32665e21i	0.110612	−	0.191585i
$438$	−2.87923e21	+	4.98697e21i	−0.101566	+	0.175917i
$439$	−8.73577e21	−	1.51308e22i	−0.302240	−	0.523496i	0.674403	−	0.738364i	$-0.264401\pi$
$439$	−8.73577e21	−	1.51308e22i	−0.302240	−	0.523496i	−0.976643	+	0.214868i	$0.931068\pi$
$440$	5.18036e21			0.175797
$441$	−8.86707e21	−	4.65348e21i	−0.295156	−	0.154899i
$442$	−1.48335e22			−0.484344
$443$	1.57746e22	+	2.73223e22i	0.505272	+	0.875158i	0.999981	+	0.00609885i	$0.00194134\pi$
$443$	1.57746e22	+	2.73223e22i	0.505272	+	0.875158i	−0.494709	+	0.869059i	$0.664725\pi$
$444$	2.79678e22	−	4.84417e22i	0.878827	−	1.52217i
$445$	−5.92654e21	+	1.02651e22i	−0.182701	+	0.316448i
$446$	−3.64492e22	−	6.31319e22i	−1.10241	−	1.90942i
$447$	−3.61150e22			−1.07170
$448$	3.60101e22	−	1.04310e22i	1.04848	−	0.303713i
$449$	5.90523e22			1.68711			0.843554	−	0.537044i	$-0.180459\pi$
$449$	5.90523e22			1.68711			0.843554	+	0.537044i	$0.180459\pi$
$450$	−9.67164e21	−	1.67518e22i	−0.271140	−	0.469628i
$451$	−1.38018e22	+	2.39054e22i	−0.379695	+	0.657651i
$452$	3.32802e21	−	5.76429e21i	0.0898481	−	0.155621i
$453$	−2.29957e21	−	3.98298e21i	−0.0609274	−	0.105529i
$454$	1.66088e22			0.431881
$455$	−3.96125e21	−	3.80473e21i	−0.101096	−	0.0971017i
$456$	1.59093e22			0.398520
$457$	1.50282e22	+	2.60296e22i	0.369504	+	0.639999i	0.989488	−	0.144615i	$-0.0461944\pi$
$457$	1.50282e22	+	2.60296e22i	0.369504	+	0.639999i	−0.619984	+	0.784614i	$0.712861\pi$
$458$	6.85267e21	−	1.18692e22i	0.165388	−	0.286460i
$459$	1.92273e21	−	3.33026e21i	0.0455523	−	0.0788989i
$460$	−5.33878e21	−	9.24703e21i	−0.124165	−	0.215061i
$461$	−5.83009e22			−1.33112			−0.665561	−	0.746344i	$-0.731807\pi$
$461$	−5.83009e22			−1.33112			−0.665561	+	0.746344i	$0.731807\pi$
$462$	4.74177e21	−	1.92393e22i	0.106288	−	0.431253i
$463$	3.22883e22			0.710569			0.355285	−	0.934758i	$-0.384384\pi$
$463$	3.22883e22			0.710569			0.355285	+	0.934758i	$0.384384\pi$
$464$	1.73459e22	+	3.00440e22i	0.374796	+	0.649166i
$465$	1.85616e21	−	3.21496e21i	0.0393790	−	0.0682065i
$466$	−5.59714e21	+	9.69452e21i	−0.116597	+	0.201951i
$467$	−4.59564e21	−	7.95988e21i	−0.0940053	−	0.162822i	0.815188	−	0.579197i	$-0.196634\pi$
$467$	−4.59564e21	−	7.95988e21i	−0.0940053	−	0.162822i	−0.909193	+	0.416375i	$0.863300\pi$
$468$	−1.93960e22			−0.389604
$469$	1.93772e22	−	7.86211e22i	0.382227	−	1.55085i
$470$	6.08402e21			0.117858
$471$	−4.80115e21	−	8.31583e21i	−0.0913413	−	0.158208i
$472$	−7.41106e22	+	1.28363e23i	−1.38476	+	2.39847i
$473$	−3.19529e21	+	5.53441e21i	−0.0586396	+	0.101567i
$474$	5.26491e22	+	9.11910e22i	0.949020	+	1.64375i
$475$	2.20717e22			0.390787
$476$	−3.86365e22	−	3.71098e22i	−0.671952	−	0.645401i
$477$	−4.95727e21			−0.0846908
$478$	−4.20035e22	−	7.27522e22i	−0.704934	−	1.22098i
$479$	−4.31178e22	+	7.46822e22i	−0.710893	+	1.23130i	0.253629	+	0.967302i	$0.418376\pi$
$479$	−4.31178e22	+	7.46822e22i	−0.710893	+	1.23130i	−0.964522	+	0.264002i	$0.914958\pi$
$480$	−4.54614e20	+	7.87414e20i	−0.00736363	+	0.0127542i
$481$	−2.88626e22	−	4.99914e22i	−0.459306	−	0.795541i
$482$	−1.30226e23			−2.03609
$483$	−1.92970e22	+	5.58973e21i	−0.296441	+	0.0858697i
$484$	−1.04390e23			−1.57569
$485$	4.31076e21	+	7.46646e21i	0.0639365	+	0.110741i
$486$	3.79155e21	−	6.56715e21i	0.0552597	−	0.0957125i
$487$	−1.54567e21	+	2.67718e21i	−0.0221371	+	0.0383426i	−0.876882	−	0.480706i	$-0.840380\pi$
$487$	−1.54567e21	+	2.67718e21i	−0.0221371	+	0.0383426i	0.854745	+	0.519049i	$0.173714\pi$
$488$	8.21822e22	+	1.42344e23i	1.15667	+	2.00341i
$489$	−2.29850e22			−0.317921
$490$	−1.20540e21	−	2.98908e22i	−0.0163857	−	0.406322i
$491$	−4.52895e22			−0.605069			−0.302534	−	0.953139i	$-0.597833\pi$
$491$	−4.52895e22			−0.605069			−0.302534	+	0.953139i	$0.597833\pi$
$492$	7.35826e22	+	1.27449e23i	0.966210	+	1.67352i
$493$	−1.51836e22	+	2.62988e22i	−0.195964	+	0.339420i
$494$	1.66885e22	−	2.89054e22i	0.211709	−	0.366690i
$495$	1.40874e21	+	2.44001e21i	0.0175666	+	0.0304262i
$496$	−4.26883e22			−0.523257
$497$	−5.87730e22	+	1.70247e22i	−0.708187	+	0.205140i
$498$	1.08849e23			1.28936
$499$	−5.93096e22	−	1.02727e23i	−0.690669	−	1.19627i	−0.971619	−	0.236552i	$-0.923983\pi$
$499$	−5.93096e22	−	1.02727e23i	−0.690669	−	1.19627i	0.280949	−	0.959723i	$-0.409351\pi$
$500$	3.94467e22	−	6.83236e22i	0.451612	−	0.782215i
$501$	−2.86302e22	+	4.95889e22i	−0.322258	+	0.558167i
$502$	1.05664e23	+	1.83015e23i	1.16935	+	2.02538i
$503$	6.51602e22			0.709013			0.354507	−	0.935054i	$-0.384649\pi$
$503$	6.51602e22			0.709013			0.354507	+	0.935054i	$0.384649\pi$
$504$	−3.74779e22	−	3.59970e22i	−0.400974	−	0.385130i
$505$	2.19888e20			0.00231326
$506$	−1.98766e22	−	3.44273e22i	−0.205619	−	0.356142i
$507$	1.83694e22	−	3.18168e22i	0.186865	−	0.323660i
$508$	9.61782e22	−	1.66586e23i	0.962133	−	1.66646i
$509$	4.20043e22	+	7.27535e22i	0.413230	+	0.715736i	0.995241	−	0.0974454i	$-0.0310671\pi$
$509$	4.20043e22	+	7.27535e22i	0.413230	+	0.715736i	−0.582011	+	0.813181i	$0.697734\pi$
$510$	1.14876e22			0.111144
$511$	−5.13594e21	+	2.08386e22i	−0.0488700	+	0.198285i
$512$	1.71820e23			1.60798
$513$	4.32635e21	+	7.49346e21i	0.0398221	+	0.0689739i
$514$	−1.44613e23	+	2.50478e23i	−1.30925	+	2.26769i
$515$	−1.80779e22	+	3.13119e22i	−0.160986	+	0.278835i
$516$	1.70353e22	+	2.95060e22i	0.149220	+	0.258457i
$517$	1.50197e22			0.129417
$518$	7.52370e22	−	3.05267e23i	0.637718	−	2.58748i
$519$	−1.53368e22			−0.127882
$520$	−1.42510e22	−	2.46835e22i	−0.116901	−	0.202478i
$521$	5.22294e22	−	9.04640e22i	0.421497	−	0.730055i	−0.574589	−	0.818442i	$-0.694838\pi$
$521$	5.22294e22	−	9.04640e22i	0.421497	−	0.730055i	0.996086	+	0.0883876i	$0.0281714\pi$
$522$	−2.99415e22	+	5.18602e22i	−0.237725	+	0.411751i
$523$	−8.57014e22	−	1.48439e23i	−0.669459	−	1.15954i	−0.978056	−	0.208344i	$-0.933193\pi$
$523$	−8.57014e22	−	1.48439e23i	−0.669459	−	1.15954i	0.308597	−	0.951193i	$-0.400141\pi$
$524$	6.24554e21			0.0480014
$525$	−5.19948e22	−	4.99403e22i	−0.393193	−	0.377657i
$526$	−8.66765e22			−0.644945
$527$	−1.86834e22	−	3.23606e22i	−0.136794	−	0.236934i
$528$	1.61992e22	−	2.80579e22i	0.116710	−	0.202147i
$529$	5.03723e22	−	8.72474e22i	0.357124	−	0.618557i
$530$	−7.40450e21	−	1.28250e22i	−0.0516596	−	0.0894770i
$531$	−8.06142e22			−0.553488
$532$	1.15782e23	−	3.35385e22i	0.782336	−	0.226618i
$533$	1.51873e23			1.00995
$534$	1.17636e23	+	2.03752e23i	0.769911	+	1.33352i
$535$	−2.08586e22	+	3.61282e22i	−0.134363	+	0.232723i
$536$	2.10097e23	−	3.63899e23i	1.33205	−	2.30717i
$537$	−8.11881e22	−	1.40622e23i	−0.506654	−	0.877550i
$538$	9.54696e22			0.586429
$539$	−2.97579e21	−	7.37918e22i	−0.0179928	−	0.446173i
$540$	1.50210e22			0.0894032
$541$	−1.04033e23	−	1.80190e23i	−0.609528	−	1.05573i	−0.991318	−	0.131484i	$-0.958026\pi$
$541$	−1.04033e23	−	1.80190e23i	−0.609528	−	1.05573i	0.381790	−	0.924249i	$-0.375308\pi$
$542$	7.18058e22	−	1.24371e23i	0.414158	−	0.717342i
$543$	−1.39374e22	+	2.41403e22i	−0.0791378	+	0.137071i
$544$	4.57597e21	+	7.92582e21i	0.0255795	+	0.0443051i
$545$	4.23321e22			0.232970
$546$	−1.04716e23	+	3.03330e22i	−0.567382	+	0.164353i
$547$	2.66667e23			1.42258			0.711291	−	0.702897i	$-0.248111\pi$
$547$	2.66667e23			1.42258			0.711291	+	0.702897i	$0.248111\pi$
$548$	1.12094e23	+	1.94152e23i	0.588771	+	1.01978i
$549$	−4.46970e22	+	7.74176e22i	−0.231161	+	0.400382i
$550$	7.13270e22	−	1.23542e23i	0.363221	−	0.629118i
$551$	−3.41648e22	−	5.91752e22i	−0.171313	−	0.296723i
$552$	−1.04254e23			−0.514764
$553$	2.83042e23	+	2.71858e23i	1.37622	+	1.32184i
$554$	−2.38412e23			−1.14155
$555$	2.23523e22	+	3.87153e22i	0.105398	+	0.182554i
$556$	−2.96307e23	+	5.13219e23i	−1.37596	+	2.38323i
$557$	−1.84427e23	+	3.19437e23i	−0.843442	+	1.46088i	0.0435251	+	0.999052i	$0.486141\pi$
$557$	−1.84427e23	+	3.19437e23i	−0.843442	+	1.46088i	−0.886967	+	0.461832i	$0.847192\pi$
$558$	−3.68430e22	−	6.38139e22i	−0.165945	−	0.287425i
$559$	3.51606e22			0.155975
$560$	1.17049e22	−	4.74915e22i	0.0511410	−	0.207500i
$561$	2.83597e22			0.122044
$562$	2.31624e23	+	4.01185e23i	0.981805	+	1.70054i
$563$	1.79066e23	−	3.10151e23i	0.747638	−	1.29495i	−0.201314	−	0.979527i	$-0.564521\pi$
$563$	1.79066e23	−	3.10151e23i	0.747638	−	1.29495i	0.948952	−	0.315420i	$-0.102145\pi$
$564$	4.00379e22	−	6.93476e22i	0.164664	−	0.285206i
$565$	2.65980e21	+	4.60691e21i	0.0107755	+	0.0186637i
$566$	−8.59288e23			−3.42925
$567$	6.76332e21	−	2.74415e22i	0.0265891	−	0.107883i
$568$	−3.17526e23			−1.22976
$569$	2.33952e23	+	4.05217e23i	0.892633	+	1.54609i	0.836707	+	0.547650i	$0.184478\pi$
$569$	2.33952e23	+	4.05217e23i	0.892633	+	1.54609i	0.0559256	+	0.998435i	$0.482189\pi$
$570$	−1.29242e22	+	2.23854e22i	−0.0485813	+	0.0841452i
$571$	3.82617e22	−	6.62712e22i	0.141696	−	0.245424i	−0.786439	−	0.617667i	$-0.788078\pi$
$571$	3.82617e22	−	6.62712e22i	0.141696	−	0.245424i	0.928135	+	0.372243i	$0.121411\pi$
$572$	−7.15216e22	−	1.23879e23i	−0.260958	−	0.451993i
$573$	5.24887e22			0.188691
$574$	5.96574e23	+	5.73001e23i	2.11307	+	2.02957i
$575$	−1.44636e23			−0.504776
$576$	5.29051e22	+	9.16342e22i	0.181931	+	0.315113i
$577$	−6.92863e22	+	1.20007e23i	−0.234776	+	0.406643i	−0.959207	−	0.282703i	$-0.908769\pi$
$577$	−6.92863e22	+	1.20007e23i	−0.234776	+	0.406643i	0.724432	+	0.689346i	$0.242102\pi$
$578$	−2.00172e23	+	3.46708e23i	−0.668369	+	1.15765i
$579$	−9.47294e22	−	1.64076e23i	−0.311686	−	0.539856i
$580$	−1.18620e23			−0.384609
$581$	3.89668e23	−	1.12875e23i	1.24508	−	0.360662i
$582$	1.71129e23			0.538863
$583$	−1.82796e22	−	3.16612e22i	−0.0567263	−	0.0982528i
$584$	−5.56864e22	+	9.64517e22i	−0.170310	+	0.294986i
$585$	7.75080e21	−	1.34248e22i	0.0233626	−	0.0404652i
$586$	−3.81325e23	−	6.60474e23i	−1.13283	−	1.96212i
$587$	−1.51709e23			−0.444210			−0.222105	−	0.975023i	$-0.571293\pi$
$587$	−1.51709e23			−0.444210			−0.222105	+	0.975023i	$0.571293\pi$
$588$	−3.48637e23	−	1.82966e23i	−1.00616	−	0.528036i
$589$	8.40795e22			0.239172
$590$	−1.20411e23	−	2.08557e23i	−0.337615	−	0.584767i
$591$	1.72918e23	−	2.99502e23i	0.477910	−	0.827764i
$592$	2.57031e23	−	4.45191e23i	0.700247	−	1.21286i
$593$	−1.84121e22	−	3.18906e22i	−0.0494467	−	0.0856442i	0.840243	−	0.542211i	$-0.182412\pi$
$593$	−1.84121e22	−	3.18906e22i	−0.0494467	−	0.0856442i	−0.889689	+	0.456566i	$0.849079\pi$
$594$	5.59243e22			0.148053
$595$	4.11246e22	−	1.19125e22i	0.107327	−	0.0310892i
$596$	−1.41997e24			−3.65332
$597$	−8.67129e21	−	1.50191e22i	−0.0219939	−	0.0380945i
$598$	−1.09360e23	+	1.89417e23i	−0.273462	+	0.473650i
$599$	6.55225e21	−	1.13488e22i	0.0161534	−	0.0279784i	−0.857836	−	0.513924i	$-0.828191\pi$
$599$	6.55225e21	−	1.13488e22i	0.0161534	−	0.0279784i	0.873989	+	0.485946i	$0.161525\pi$
$600$	−1.87057e23	−	3.23991e23i	−0.454660	−	0.787495i
$601$	−3.58718e22			−0.0859647			−0.0429823	−	0.999076i	$-0.513686\pi$
$601$	−3.58718e22			−0.0859647			−0.0429823	+	0.999076i	$0.513686\pi$
$602$	1.38114e23	+	1.32657e23i	0.326339	+	0.313444i
$603$	2.28534e23			0.532420
$604$	−9.04150e22	−	1.56603e23i	−0.207695	−	0.359739i
$605$	4.17149e22	−	7.22523e22i	0.0944867	−	0.163656i
$606$	2.18228e21	−	3.77983e21i	0.00487410	−	0.00844218i
$607$	−2.89636e23	−	5.01664e23i	−0.637894	−	1.10486i	−0.985894	−	0.167370i	$-0.946473\pi$
$607$	−2.89636e23	−	5.01664e23i	−0.637894	−	1.10486i	0.348001	−	0.937494i	$-0.386861\pi$
$608$	−2.05929e22			−0.0447236
$609$	−5.34093e22	+	2.16703e23i	−0.114385	+	0.464107i
$610$	−2.67050e23			−0.564012
$611$	−4.13187e22	−	7.15661e22i	−0.0860591	−	0.149059i
$612$	7.55982e22	−	1.30940e23i	0.155283	−	0.268958i
$613$	−2.93917e23	+	5.09079e23i	−0.595402	+	1.03127i	0.398088	+	0.917347i	$0.369674\pi$
$613$	−2.93917e23	+	5.09079e23i	−0.595402	+	1.03127i	−0.993490	+	0.113919i	$0.963660\pi$
$614$	4.76945e23	+	8.26093e23i	0.952877	+	1.65043i
$615$	−1.17617e23			−0.231755
$616$	9.17092e22	−	3.72101e23i	0.178228	−	0.723145i
$617$	7.52957e23			1.44327			0.721633	−	0.692276i	$-0.243392\pi$
$617$	7.52957e23			1.44327			0.721633	+	0.692276i	$0.243392\pi$
$618$	3.58829e23	+	6.21511e23i	0.678400	+	1.17502i
$619$	8.84993e22	−	1.53285e23i	0.165033	−	0.285845i	−0.771634	−	0.636066i	$-0.780560\pi$
$619$	8.84993e22	−	1.53285e23i	0.165033	−	0.285845i	0.936667	+	0.350222i	$0.113894\pi$
$620$	7.29808e22	−	1.26406e23i	0.134239	−	0.232509i
$621$	−2.83506e22	−	4.91046e22i	−0.0514379	−	0.0890930i
$622$	1.60735e24			2.87668
$623$	6.32414e23	+	6.07424e23i	1.11648	+	1.07237i
$624$	−1.78254e23			−0.310435
$625$	−2.43297e23	−	4.21403e23i	−0.417981	−	0.723965i
$626$	7.98365e23	−	1.38281e24i	1.35307	−	2.34358i
$627$	−3.19063e22	+	5.52633e22i	−0.0533460	+	0.0923980i
$628$	−1.88772e23	−	3.26963e23i	−0.311373	−	0.539314i
$629$	4.49980e23			0.732256
$630$	8.10962e22	−	2.34910e22i	0.130198	−	0.0377144i
$631$	−1.01969e24			−1.61517			−0.807586	−	0.589750i	$-0.799226\pi$
$631$	−1.01969e24			−1.61517			−0.807586	+	0.589750i	$0.799226\pi$
$632$	1.01827e24	+	1.76370e24i	1.59136	+	2.75632i
$633$	9.97789e21	−	1.72822e22i	0.0153853	−	0.0266482i
$634$	4.14338e23	−	7.17654e23i	0.630371	−	1.09183i
$635$	7.68671e22	+	1.33138e23i	0.115389	+	0.199859i
$636$	−1.94911e23			−0.288702
$637$	−3.43418e23	+	2.17178e23i	−0.501924	+	0.317417i
$638$	−4.41629e23			−0.636916
$639$	−8.63476e22	−	1.49559e23i	−0.122883	−	0.212840i
$640$	−1.48963e23	+	2.58011e23i	−0.209193	+	0.362334i
$641$	−2.18233e23	+	3.77991e23i	−0.302432	+	0.523827i	−0.976686	−	0.214672i	$-0.931132\pi$
$641$	−2.18233e23	+	3.77991e23i	−0.302432	+	0.523827i	0.674255	+	0.738499i	$0.264465\pi$
$642$	4.14023e23	+	7.17110e23i	0.566210	+	0.980704i
$643$	−1.14695e24			−1.54793			−0.773964	−	0.633230i	$-0.781729\pi$
$643$	−1.14695e24			−1.54793			−0.773964	+	0.633230i	$0.781729\pi$
$644$	−7.58721e23	+	2.19778e23i	−1.01054	+	0.292721i
$645$	−2.72297e22			−0.0357920
$646$	1.30091e23	+	2.25324e23i	0.168760	+	0.292301i
$647$	4.24487e22	−	7.35233e22i	0.0543473	−	0.0941322i	−0.837572	−	0.546327i	$-0.816026\pi$
$647$	4.24487e22	−	7.35233e22i	0.0543473	−	0.0941322i	0.891919	+	0.452195i	$0.149359\pi$
$648$	7.33313e22	−	1.27014e23i	0.0926620	−	0.160495i
$649$	−2.97259e23	−	5.14868e23i	−0.370728	−	0.642120i
$650$	−7.84873e23			−0.966131
$651$	−1.98068e23	−	1.90242e23i	−0.240645	−	0.231136i
$652$	−9.03727e23			−1.08376
$653$	−6.48370e22	−	1.12301e23i	−0.0767469	−	0.132930i	0.825098	−	0.564990i	$-0.191120\pi$
$653$	−6.48370e22	−	1.12301e23i	−0.0767469	−	0.132930i	−0.901845	+	0.432060i	$0.857787\pi$
$654$	4.20126e23	−	7.27679e23i	0.490872	−	0.850215i
$655$	−2.49576e21	+	4.32279e21i	−0.00287841	+	0.00498555i
$656$	6.76242e23	+	1.17129e24i	0.769874	+	1.33346i
$657$	−6.05732e22			−0.0680730
$658$	1.07707e23	−	4.37011e23i	0.119488	−	0.484810i
$659$	−9.23421e22			−0.101129			−0.0505643	−	0.998721i	$-0.516102\pi$
$659$	−9.23421e22			−0.101129			−0.0505643	+	0.998721i	$0.516102\pi$
$660$	5.53891e22	+	9.59367e22i	0.0598826	+	0.103720i
$661$	−4.81122e22	+	8.33327e22i	−0.0513502	+	0.0889412i	−0.890558	−	0.454870i	$-0.849686\pi$
$661$	−4.81122e22	+	8.33327e22i	−0.0513502	+	0.0889412i	0.839208	+	0.543811i	$0.183019\pi$
$662$	1.27483e24	−	2.20806e24i	1.34325	−	2.32658i
$663$	−7.80167e22	−	1.35129e23i	−0.0811563	−	0.140567i
$664$	2.10522e24			2.16206
$665$	−2.30541e22	+	9.35399e22i	−0.0233757	+	0.0948446i
$666$	8.87343e23			0.888302
$667$	2.23882e23	+	3.87775e23i	0.221284	+	0.383274i
$668$	−1.12569e24	+	1.94975e24i	−1.09854	+	1.90273i
$669$	3.83409e23	−	6.64083e23i	0.369437	−	0.639883i
$670$	3.41353e23	+	5.91242e23i	0.324764	+	0.562509i
$671$	−6.59269e23			−0.619329
$672$	4.85112e22	+	4.65943e22i	0.0449990	+	0.0432209i
$673$	−3.95982e23			−0.362700			−0.181350	−	0.983419i	$-0.558047\pi$
$673$	−3.95982e23			−0.362700			−0.181350	+	0.983419i	$0.558047\pi$
$674$	2.02998e23	+	3.51602e23i	0.183604	+	0.318011i
$675$	1.01736e23	−	1.76212e23i	0.0908640	−	0.157381i
$676$	7.22252e23	−	1.25098e24i	0.637003	−	1.10332i
$677$	6.16433e23	+	1.06769e24i	0.536886	+	0.929914i	0.999069	+	0.0431294i	$0.0137328\pi$
$677$	6.16433e23	+	1.06769e24i	0.536886	+	0.929914i	−0.462184	+	0.886784i	$0.652934\pi$
$678$	1.05589e23			0.0908168
$679$	6.12624e23	−	1.77458e23i	0.520357	−	0.150731i
$680$	2.22179e23			0.186371
$681$	8.73539e22	+	1.51301e23i	0.0723656	+	0.125341i
$682$	2.71712e23	−	4.70619e23i	0.222301	−	0.385037i
$683$	−1.79369e23	+	3.10676e23i	−0.144934	+	0.251033i	−0.929348	−	0.369204i	$-0.879630\pi$
$683$	−1.79369e23	+	3.10676e23i	−0.144934	+	0.251033i	0.784414	+	0.620237i	$0.212964\pi$
$684$	1.70104e23	+	2.94629e23i	0.135750	+	0.235125i
$685$	−1.79174e23			−0.141223
$686$	−2.16837e24	−	4.42580e23i	−1.68802	−	0.344538i
$687$	1.44166e23			0.110849
$688$	1.56559e23	+	2.71167e23i	0.118898	+	0.205938i
$689$	−1.00573e23	+	1.74198e23i	−0.0754430	+	0.130671i
$690$	8.46925e22	−	1.46692e23i	0.0627520	−	0.108690i
$691$	−8.11013e23	−	1.40472e24i	−0.593560	−	1.02808i	−0.993748	−	0.111643i	$-0.964389\pi$
$691$	−8.11013e23	−	1.40472e24i	−0.593560	−	1.02808i	0.400189	−	0.916433i	$-0.368945\pi$
$692$	−6.03013e23			−0.435938
$693$	2.00203e23	−	5.79927e22i	0.142968	−	0.0414134i
$694$	2.21607e24			1.56325
$695$	−2.36813e23	−	4.10172e23i	−0.165019	−	0.285822i
$696$	−5.79090e23	+	1.00301e24i	−0.398628	+	0.690444i
$697$	−5.91942e23	+	1.02527e24i	−0.402532	+	0.697206i
$698$	−1.97474e24	−	3.42034e24i	−1.32659	−	2.29773i
$699$	−1.17752e23			−0.0781472
$700$	−2.04434e24	−	1.96356e24i	−1.34036	−	1.28739i
$701$	2.40203e24			1.55588			0.777939	−	0.628340i	$-0.216265\pi$
$701$	2.40203e24			1.55588			0.777939	+	0.628340i	$0.216265\pi$
$702$	−1.53846e23	−	2.66469e23i	−0.0984511	−	0.170522i
$703$	−5.06253e23	+	8.76855e23i	−0.320072	+	0.554380i
$704$	−3.90168e23	+	6.75790e23i	−0.243716	+	0.422128i
$705$	3.19989e22	+	5.54236e22i	0.0197482	+	0.0342048i
$706$	2.53887e23			0.154810
$707$	3.89273e21	−	1.57944e22i	0.00234525	−	0.00951564i
$708$	−3.16960e24			−1.88678
$709$	−4.16089e23	−	7.20687e23i	−0.244733	−	0.423891i	0.717323	−	0.696740i	$-0.245367\pi$
$709$	−4.16089e23	−	7.20687e23i	−0.244733	−	0.423891i	−0.962057	+	0.272850i	$0.912034\pi$
$710$	2.57949e23	−	4.46780e23i	0.149912	−	0.259656i
$711$	−5.53815e23	+	9.59236e23i	−0.318034	+	0.550851i
$712$	2.27517e24	+	3.94071e24i	1.29102	+	2.23612i
$713$	−5.50973e23			−0.308936
$714$	2.03369e23	−	8.25149e23i	0.112681	−	0.457191i
$715$	1.14322e23			0.0625935
$716$	−3.19217e24	−	5.52900e24i	−1.72713	−	2.99148i
$717$	4.41834e23	−	7.65279e23i	0.236236	−	0.409173i
$718$	−1.81534e24	+	3.14427e24i	−0.959182	+	1.66135i
$719$	−7.17296e23	−	1.24239e24i	−0.374544	−	0.648729i	0.615715	−	0.787969i	$-0.288867\pi$
$719$	−7.17296e23	−	1.24239e24i	−0.374544	−	0.648729i	−0.990259	+	0.139240i	$0.955534\pi$
$720$	1.38047e23			0.0712363
$721$	1.92907e24	+	1.85284e24i	0.983781	+	0.944908i
$722$	2.83284e24			1.42776
$723$	−6.84920e23	−	1.18632e24i	−0.341165	−	0.590915i
$724$	−5.47994e23	+	9.49153e23i	−0.269773	+	0.467260i
$725$	−8.03398e23	+	1.39153e24i	−0.390893	+	0.677046i
$726$	−8.28001e23	−	1.43414e24i	−0.398171	−	0.689652i
$727$	−2.58645e24			−1.22931			−0.614655	−	0.788796i	$-0.710705\pi$
$727$	−2.58645e24			−1.22931			−0.614655	+	0.788796i	$0.710705\pi$
$728$	−2.02528e24	+	5.86661e23i	−0.951413	+	0.275595i
$729$	7.97664e22			0.0370370
$730$	−9.04760e22	−	1.56709e23i	−0.0415230	−	0.0719200i
$731$	−1.37042e23	+	2.37364e23i	−0.0621665	+	0.107676i
$732$	−1.75741e24	+	3.04392e24i	−0.788003	+	1.36486i
$733$	2.03537e24	+	3.52537e24i	0.902112	+	1.56250i	0.824748	+	0.565500i	$0.191317\pi$
$733$	2.03537e24	+	3.52537e24i	0.902112	+	1.56250i	0.0773635	+	0.997003i	$0.475350\pi$
$734$	2.20971e24			0.968097
$735$	2.65956e23	−	1.68191e23i	0.115178	−	0.0728384i
$736$	1.34945e23			0.0577691
$737$	8.42705e23	+	1.45961e24i	0.356617	+	0.617678i
$738$	−1.16729e24	+	2.02180e24i	−0.488314	+	0.845784i
$739$	−2.24715e24	+	3.89218e24i	−0.929298	+	1.60959i	−0.144798	+	0.989461i	$0.546253\pi$
$739$	−2.24715e24	+	3.89218e24i	−0.929298	+	1.60959i	−0.784499	+	0.620130i	$0.787080\pi$
$740$	8.78852e23	+	1.52222e24i	0.359291	+	0.622310i
$741$	3.51092e23			0.141895
$742$	−1.05229e24	+	3.04816e23i	−0.420439	+	0.121788i
$743$	4.72950e24			1.86814			0.934072	−	0.357084i	$-0.116229\pi$
$743$	4.72950e24			1.86814			0.934072	+	0.357084i	$0.116229\pi$
$744$	−7.12570e23	−	1.23421e24i	−0.278264	−	0.481968i
$745$	5.67432e23	−	9.82821e23i	0.219071	−	0.379443i
$746$	1.44543e24	−	2.50355e24i	0.551716	−	0.955601i
$747$	5.72490e23	+	9.91582e23i	0.216044	+	0.374200i
$748$	1.11505e24			0.416037
$749$	2.22579e24	+	2.13784e24i	0.821088	+	0.788643i
$750$	1.25154e24			0.456481
$751$	−8.88420e23	−	1.53879e24i	−0.320390	−	0.554932i	0.660179	−	0.751109i	$-0.270481\pi$
$751$	−8.88420e23	−	1.53879e24i	−0.320390	−	0.554932i	−0.980568	+	0.196177i	$0.937147\pi$
$752$	3.67958e23	−	6.37322e23i	0.131204	−	0.227252i
$753$	−1.11148e24	+	1.92514e24i	−0.391871	+	0.678741i
$754$	1.21491e24	+	2.10428e24i	0.423532	+	0.733580i
$755$	1.44522e23			0.0498179
$756$	2.65921e23	−	1.07895e24i	0.0906396	−	0.367761i
$757$	4.53730e24			1.52926			0.764632	−	0.644467i	$-0.222921\pi$
$757$	4.53730e24			1.52926			0.764632	+	0.644467i	$0.222921\pi$
$758$	−3.05459e24	−	5.29070e24i	−1.01804	−	1.76329i
$759$	2.09082e23	−	3.62140e23i	0.0689066	−	0.119350i
$760$	−2.49964e23	+	4.32951e23i	−0.0814634	+	0.141099i
$761$	−2.38533e24	−	4.13152e24i	−0.768741	−	1.33150i	−0.938246	−	0.345968i	$-0.887550\pi$
$761$	−2.38533e24	−	4.13152e24i	−0.768741	−	1.33150i	0.169506	−	0.985529i	$-0.445783\pi$
$762$	3.05147e24			0.972507
$763$	7.49415e23	−	3.04068e24i	0.236191	−	0.958324i
$764$	2.06376e24			0.643229
$765$	6.04192e22	+	1.04649e23i	0.0186231	+	0.0322562i
$766$	2.58248e24	−	4.47299e24i	0.787214	−	1.36349i
$767$	−1.63550e24	+	2.83277e24i	−0.493049	+	0.853986i
$768$	1.89986e24	+	3.29066e24i	0.566437	+	0.981097i
$769$	−1.14528e24			−0.337705			−0.168853	−	0.985641i	$-0.554006\pi$
$769$	−1.14528e24			−0.337705			−0.168853	+	0.985641i	$0.554006\pi$
$770$	4.49070e23	+	4.31325e23i	0.130961	+	0.125786i
$771$	−3.04237e24			−0.877506
$772$	−3.72459e24	−	6.45117e24i	−1.06251	−	1.84031i
$773$	−1.22056e24	+	2.11408e24i	−0.344378	+	0.596480i	−0.985241	−	0.171176i	$-0.945243\pi$
$773$	−1.22056e24	+	2.11408e24i	−0.344378	+	0.596480i	0.640863	+	0.767655i	$0.278577\pi$
$774$	−2.70242e23	+	4.68073e23i	−0.0754144	+	0.130622i
$775$	−9.88581e23	−	1.71227e24i	−0.272865	−	0.472616i
$776$	3.30976e24			0.903590
$777$	3.17660e24	−	9.20162e23i	0.857796	−	0.248477i
$778$	8.66306e23			0.231390
$779$	−1.33194e24	−	2.30698e24i	−0.351897	−	0.609503i
$780$	3.04747e23	−	5.27838e23i	0.0796408	−	0.137942i
$781$	6.36802e23	−	1.10297e24i	0.164616	−	0.285122i
$782$	−8.52483e23	−	1.47654e24i	−0.217986	−	0.377563i
$783$	−6.29908e23			−0.159332
$784$	−3.20406e24	−	1.68151e24i	−0.801704	−	0.420738i
$785$	3.01739e23			0.0746861
$786$	4.95385e22	+	8.58032e22i	0.0121297	+	0.0210093i
$787$	2.62249e24	−	4.54228e24i	0.635226	−	1.10024i	−0.351241	−	0.936285i	$-0.614240\pi$
$787$	2.62249e24	−	4.54228e24i	0.635226	−	1.10024i	0.986467	−	0.163959i	$-0.0524264\pi$
$788$	6.79881e24	−	1.17759e25i	1.62915	−	2.82176i
$789$	−4.55874e23	−	7.89598e23i	−0.108066	−	0.187177i
$790$	−3.30886e24			−0.775975
$791$	3.77998e23	−	1.09494e23i	0.0876979	−	0.0254033i
$792$	1.08162e24			0.248261
$793$	1.81363e24	+	3.14130e24i	0.411838	+	0.713324i
$794$	−4.22176e24	+	7.31230e24i	−0.948460	+	1.64278i
$795$	7.78878e22	−	1.34906e23i	0.0173121	−	0.0299854i
$796$	−3.40939e23	−	5.90524e23i	−0.0749749	−	0.129860i
$797$	2.92906e24			0.637284			0.318642	−	0.947875i	$-0.396773\pi$
$797$	2.92906e24			0.637284			0.318642	+	0.947875i	$0.396773\pi$
$798$	1.37913e24	+	1.32463e24i	0.296879	+	0.285148i
$799$	6.44177e23			0.137201
$800$	2.42125e23	+	4.19372e23i	0.0510240	+	0.0883761i
$801$	−1.23741e24	+	2.14326e24i	−0.258011	+	0.446888i
$802$	−1.63766e24	+	2.83651e24i	−0.337863	+	0.585196i
$803$	−2.23359e23	−	3.86870e23i	−0.0455955	−	0.0789738i
$804$	8.98555e24			1.81496
$805$	1.51073e23	−	6.12966e23i	0.0301942	−	0.122510i
$806$	−2.98988e24			−0.591298
$807$	5.02121e23	+	8.69700e23i	0.0982616	+	0.170194i
$808$	4.22070e22	−	7.31046e22i	0.00817312	−	0.0141563i
$809$	−2.58222e24	+	4.47254e24i	−0.494801	+	0.857021i	−0.999982	−	0.00599267i	$-0.998092\pi$
$809$	−2.58222e24	+	4.47254e24i	−0.494801	+	0.857021i	0.505181	+	0.863014i	$0.331426\pi$
$810$	1.19144e23	+	2.06364e23i	0.0225918	+	0.0391301i
$811$	−1.41204e24			−0.264953			−0.132477	−	0.991186i	$-0.542293\pi$
$811$	−1.41204e24			−0.264953			−0.132477	+	0.991186i	$0.542293\pi$
$812$	−2.09996e24	+	8.52037e24i	−0.389928	+	1.58209i
$813$	1.51065e24			0.277584
$814$	3.27202e24	+	5.66730e24i	0.594988	+	1.03055i
$815$	3.61136e23	−	6.25506e23i	0.0649877	−	0.112562i
$816$	6.94766e23	−	1.20337e24i	0.123729	−	0.214305i
$817$	−3.08360e23	−	5.34095e23i	−0.0543464	−	0.0941307i
$818$	−3.18744e23			−0.0555954
$819$	−8.27077e23	−	7.94396e23i	−0.142769	−	0.137127i
$820$	−4.62447e24			−0.790031
$821$	7.13878e23	+	1.23647e24i	0.120700	+	0.209058i	0.920044	−	0.391815i	$-0.128153\pi$
$821$	7.13878e23	+	1.23647e24i	0.120700	+	0.209058i	−0.799344	+	0.600874i	$0.794819\pi$
$822$	−1.77822e24	+	3.07996e24i	−0.297560	+	0.515388i
$823$	−8.40748e23	+	1.45622e24i	−0.139241	+	0.241173i	−0.927210	−	0.374543i	$-0.877800\pi$
$823$	−8.40748e23	+	1.45622e24i	−0.139241	+	0.241173i	0.787969	+	0.615716i	$0.211133\pi$
$824$	6.94002e24	+	1.20205e25i	1.13757	+	1.97034i
$825$	1.50058e24			0.243444
$826$	−1.71122e25	+	4.95686e24i	−2.74773	+	0.795932i
$827$	−4.75640e24			−0.755929			−0.377965	−	0.925820i	$-0.623376\pi$
$827$	−4.75640e24			−0.755929			−0.377965	+	0.925820i	$0.623376\pi$
$828$	−1.11469e24	−	1.93070e24i	−0.175347	−	0.303709i
$829$	2.66203e24	−	4.61077e24i	0.414476	−	0.717893i	−0.580898	−	0.813977i	$-0.697298\pi$
$829$	2.66203e24	−	4.61077e24i	0.414476	−	0.717893i	0.995373	+	0.0960839i	$0.0306317\pi$
$830$	−1.71022e24	+	2.96218e24i	−0.263565	+	0.456508i
$831$	−1.25392e24	−	2.17186e24i	−0.191277	−	0.331301i
$832$	4.29335e24			0.648259
$833$	−1.27628e23	−	3.16484e24i	−0.0190750	−	0.473009i
$834$	−9.40102e24			−1.39080
$835$	−8.99665e23	−	1.55827e24i	−0.131749	−	0.228195i
$836$	−1.25450e24	+	2.17285e24i	−0.181851	+	0.314975i
$837$	3.87551e23	−	6.71257e23i	0.0556112	−	0.0963214i
$838$	4.98969e23	+	8.64240e23i	0.0708761	+	0.122761i
$839$	−5.65066e24			−0.794552			−0.397276	−	0.917699i	$-0.630044\pi$
$839$	−5.65066e24			−0.794552			−0.397276	+	0.917699i	$0.630044\pi$
$840$	1.56846e24	−	4.54334e23i	0.218323	−	0.0632413i
$841$	−2.28282e24			−0.314561
$842$	−2.27510e23	−	3.94059e23i	−0.0310347	−	0.0537537i
$843$	−2.43645e24	+	4.22005e24i	−0.329021	+	0.569880i
$844$	3.92312e23	−	6.79505e23i	0.0524471	−	0.0908410i
$845$	5.77234e23	+	9.99799e23i	0.0763959	+	0.132322i
$846$	1.27029e24			0.166439
$847$	−4.45134e24	−	4.27545e24i	−0.577407	−	0.554591i
$848$	−1.79128e24			−0.230037
$849$	−4.51942e24	−	7.82786e24i	−0.574602	−	0.995240i
$850$	3.05913e24	−	5.29857e24i	0.385068	−	0.666957i
$851$	3.31747e24	−	5.74603e24i	0.413434	−	0.716088i
$852$	−3.39503e24	−	5.88037e24i	−0.418897	−	0.725551i
$853$	9.57197e24			1.16932			0.584661	−	0.811277i	$-0.301227\pi$
$853$	9.57197e24			1.16932			0.584661	+	0.811277i	$0.301227\pi$
$854$	−4.72764e24	+	1.91820e25i	−0.571811	+	2.32007i
$855$	−2.71900e23			−0.0325609
$856$	8.00751e24	+	1.38694e25i	0.949447	+	1.64449i
$857$	5.88362e24	−	1.01907e25i	0.690729	−	1.19638i	−0.280870	−	0.959746i	$-0.590623\pi$
$857$	5.88362e24	−	1.01907e25i	0.690729	−	1.19638i	0.971599	−	0.236632i	$-0.0760437\pi$
$858$	1.13459e24	−	1.96517e24i	0.131886	−	0.228433i
$859$	−5.13101e24	−	8.88718e24i	−0.590556	−	1.02287i	−0.994158	−	0.107939i	$-0.965575\pi$
$859$	−5.13101e24	−	8.88718e24i	−0.590556	−	1.02287i	0.403601	−	0.914935i	$-0.367758\pi$
$860$	−1.07062e24			−0.122011
$861$	−2.08219e24	+	8.44831e24i	−0.234960	+	0.953329i
$862$	−9.74644e24			−1.08902
$863$	−6.18128e24	−	1.07063e25i	−0.683891	−	1.18453i	−0.973784	−	0.227475i	$-0.926953\pi$
$863$	−6.18128e24	−	1.07063e25i	−0.683891	−	1.18453i	0.289893	−	0.957059i	$-0.406380\pi$
$864$	−9.49196e22	+	1.64405e23i	−0.0103989	+	0.0180115i
$865$	2.40968e23	−	4.17370e23i	0.0261411	−	0.0452776i
$866$	1.10109e25	+	1.90715e25i	1.18283	+	2.04872i
$867$	−4.21121e24			−0.447965
$868$	−7.78768e24	−	7.47996e24i	−0.820333	−	0.787919i
$869$	−8.16863e24			−0.852081
$870$	−9.40872e23	−	1.62964e24i	−0.0971889	−	0.168336i
$871$	4.63650e24	−	8.03066e24i	0.474282	−	0.821480i
$872$	8.12554e24	−	1.40738e25i	0.823118	−	1.42568i
$873$	9.00051e23	+	1.55893e24i	0.0902913	+	0.156389i
$874$	3.83636e24			0.381130
$875$	4.48037e24	−	1.29782e24i	0.440804	−	0.127687i
$876$	−2.38163e24			−0.232054
$877$	7.37652e24	+	1.27765e25i	0.711795	+	1.23286i	0.964183	+	0.265238i	$0.0854507\pi$
$877$	7.37652e24	+	1.27765e25i	0.711795	+	1.23286i	−0.252388	+	0.967626i	$0.581216\pi$
$878$	5.44876e24	−	9.43752e24i	0.520708	−	0.901892i
$879$	4.01115e24	−	6.94751e24i	0.379633	−	0.657543i
$880$	5.09040e23	+	8.81683e23i	0.0477143	+	0.0826437i
$881$	−3.33250e24			−0.309368			−0.154684	−	0.987964i	$-0.549436\pi$
$881$	−3.33250e24			−0.309368			−0.154684	+	0.987964i	$0.549436\pi$
$882$	−2.51678e23	−	6.24094e24i	−0.0231399	−	0.573809i
$883$	1.36231e25			1.24053			0.620267	−	0.784391i	$-0.287024\pi$
$883$	1.36231e25			1.24053			0.620267	+	0.784391i	$0.287024\pi$
$884$	−3.06747e24	−	5.31302e24i	−0.276654	−	0.479178i
$885$	1.26660e24	−	2.19381e24i	0.113141	−	0.195966i
$886$	−9.83906e24	+	1.70418e25i	−0.870496	+	1.50774i
$887$	−5.28795e24	−	9.15899e24i	−0.463379	−	0.802596i	0.535748	−	0.844378i	$-0.320030\pi$
$887$	−5.28795e24	−	9.15899e24i	−0.463379	−	0.802596i	−0.999127	+	0.0417823i	$0.986696\pi$
$888$	1.71619e25			1.48955
$889$	1.09240e25	−	3.16433e24i	0.939108	−	0.272030i
$890$	−7.39312e24			−0.629525
$891$	2.94133e23	+	5.09454e23i	0.0248075	+	0.0429679i
$892$	1.50749e25	−	2.61105e25i	1.25937	−	2.18130i
$893$	−7.24735e23	+	1.25528e24i	−0.0599711	+	0.103873i
$894$	−1.12630e25	−	1.95081e25i	−0.923176	−	1.59899i
$895$	5.10246e24			0.414270
$896$	1.58956e25	+	1.52675e25i	1.27838	+	1.22786i
$897$	−2.30071e24			−0.183284
$898$	1.84163e25	+	3.18980e25i	1.45330	+	2.51718i
$899$	−3.06045e24	+	5.30086e24i	−0.239237	+	0.414371i
$900$	4.00007e24	−	6.92832e24i	0.309746	−	0.536496i
$901$	−7.83990e23	−	1.35791e24i	−0.0601381	−	0.104162i
$902$	−1.72172e25			−1.30830
$903$	−4.82054e23	+	1.95589e24i	−0.0362869	+	0.147231i
$904$	2.04217e24			0.152286
$905$	−4.37965e23	−	7.58577e23i	−0.0323539	−	0.0560386i
$906$	1.43431e24	−	2.48430e24i	0.104967	−	0.181809i
$907$	−3.44273e24	+	5.96298e24i	−0.249598	+	0.432316i	−0.963414	−	0.268017i	$-0.913632\pi$
$907$	−3.44273e24	+	5.96298e24i	−0.249598	+	0.432316i	0.713816	+	0.700333i	$0.246965\pi$
$908$	3.43460e24	+	5.94890e24i	0.246687	+	0.427274i
$909$	4.59108e22			0.00326680
$910$	8.19808e23	−	3.32629e24i	0.0577910	−	0.234482i
$911$	−2.71963e25			−1.89935			−0.949673	−	0.313242i	$-0.898585\pi$
$911$	−2.71963e25			−1.89935			−0.949673	+	0.313242i	$0.898585\pi$
$912$	1.56330e24	+	2.70772e24i	0.108165	+	0.187347i
$913$	−4.22204e24	+	7.31279e24i	−0.289415	+	0.501281i
$914$	−9.37352e24	+	1.62354e25i	−0.636590	+	1.10261i
$915$	−1.40454e24	−	2.43274e24i	−0.0945053	−	0.163688i
$916$	5.66835e24			0.377873
$917$	2.66319e23	+	2.55796e23i	0.0175899	+	0.0168949i
$918$	2.39852e24			0.156957
$919$	−7.97548e23	−	1.38139e24i	−0.0517100	−	0.0895644i	0.839012	−	0.544113i	$-0.183134\pi$
$919$	−7.97548e23	−	1.38139e24i	−0.0517100	−	0.0895644i	−0.890722	+	0.454549i	$0.849800\pi$
$920$	1.63801e24	−	2.83712e24i	0.105225	−	0.182256i
$921$	−5.01697e24	+	8.68965e24i	−0.319327	+	0.553090i
$922$	−1.81820e25	−	3.14922e25i	−1.14664	−	1.98605i
$923$	−7.00729e24			−0.437860
$924$	7.87163e24	−	2.28017e24i	0.487363	−	0.141174i
$925$	2.38094e25			1.46064
$926$	1.00696e25	+	1.74410e25i	0.612093	+	1.06018i
$927$	−3.77452e24	+	6.53766e24i	−0.227344	+	0.393772i
$928$	7.49571e23	−	1.29830e24i	0.0447358	−	0.0774846i
$929$	9.79188e24	+	1.69600e25i	0.579072	+	1.00298i	0.995586	+	0.0938525i	$0.0299182\pi$
$929$	9.79188e24	+	1.69600e25i	0.579072	+	1.00298i	−0.416514	+	0.909129i	$0.636748\pi$
$930$	2.31548e24			0.135686
$931$	6.31076e24	+	3.31192e24i	0.366446	+	0.192312i
$932$	−4.62981e24			−0.266396
$933$	8.45383e24	+	1.46425e25i	0.482014	+	0.834873i
$934$	2.86644e24	−	4.96481e24i	0.161955	−	0.280514i
$935$	−4.45583e23	+	7.71773e23i	−0.0249477	+	0.0432106i
$936$	−2.97549e24	−	5.15370e24i	−0.165087	−	0.285940i
$937$	−2.07873e25			−1.14291			−0.571455	−	0.820634i	$-0.693621\pi$
$937$	−2.07873e25			−1.14291			−0.571455	+	0.820634i	$0.693621\pi$
$938$	4.85115e25	−	1.40523e25i	2.64314	−	0.765636i
$939$	1.67960e25			0.906875
$940$	1.25814e24	+	2.17916e24i	0.0673195	+	0.116601i
$941$	−8.12383e24	+	1.40709e25i	−0.430773	+	0.746122i	−0.996940	−	0.0781693i	$-0.975093\pi$
$941$	−8.12383e24	+	1.40709e25i	−0.430773	+	0.746122i	0.566167	+	0.824291i	$0.308426\pi$
$942$	2.99462e24	−	5.18683e24i	0.157365	−	0.272565i
$943$	8.72817e24	+	1.51176e25i	0.454542	+	0.787289i
$944$	−2.91294e25			−1.50338
$945$	6.40521e23	+	6.15211e23i	0.0327614	+	0.0314669i
$946$	−3.98600e24			−0.202052
$947$	−1.05861e25	−	1.83356e25i	−0.531814	−	0.921129i	−0.999310	−	0.0371340i	$-0.988177\pi$
$947$	−1.05861e25	−	1.83356e25i	−0.531814	−	0.921129i	0.467496	−	0.883995i	$-0.345156\pi$
$948$	−2.17750e25	+	3.77154e25i	−1.08415	+	1.87779i
$949$	−1.22891e24	+	2.12853e24i	−0.0606397	+	0.105031i
$950$	6.88338e24	+	1.19224e25i	0.336629	+	0.583058i
$951$	8.71683e24			0.422497
$952$	3.93329e24	−	1.59590e25i	0.188948	−	0.766639i
$953$	3.96811e25			1.88927			0.944635	−	0.328122i	$-0.106416\pi$
$953$	3.96811e25			1.88927			0.944635	+	0.328122i	$0.106416\pi$
$954$	−1.54600e24	−	2.67775e24i	−0.0729538	−	0.126360i
$955$	−8.24693e23	+	1.42841e24i	−0.0385713	+	0.0668074i
$956$	1.73721e25	−	3.00894e25i	0.805305	−	1.39483i
$957$	−2.32274e24	−	4.02311e24i	−0.106721	−	0.184846i
$958$	−5.37877e25			−2.44949
$959$	−3.17196e24	+	1.28699e25i	−0.143176	+	0.580922i
$960$	−3.32494e24			−0.148757
$961$	7.50918e24	+	1.30063e25i	0.332999	+	0.576772i
$962$	1.80024e25	−	3.11811e25i	0.791303	−	1.37058i
$963$	−4.35511e24	+	7.54326e24i	−0.189747	+	0.328652i
$964$	−2.69298e25	−	4.66438e25i	−1.16300	−	2.01437i
$965$	5.95349e24			0.254853
$966$	−9.03742e24	−	8.68031e24i	−0.383477	−	0.368324i
$967$	−9.76655e24			−0.410786			−0.205393	−	0.978680i	$-0.565847\pi$
$967$	−9.76655e24			−0.410786			−0.205393	+	0.978680i	$0.565847\pi$
$968$	−1.60141e25	−	2.77373e25i	−0.667672	−	1.15644i
$969$	−1.36842e24	+	2.37017e24i	−0.0565546	+	0.0979554i
$970$	−2.68875e24	+	4.65705e24i	−0.110151	+	0.190788i
$971$	−6.50127e24	−	1.12605e25i	−0.264019	−	0.457294i	0.703287	−	0.710906i	$-0.251715\pi$
$971$	−6.50127e24	−	1.12605e25i	−0.264019	−	0.457294i	−0.967306	+	0.253612i	$0.918381\pi$
$972$	3.13627e24			0.126255
$973$	−3.36547e25	+	9.74872e24i	−1.34303	+	0.389035i
$974$	−1.92816e24			−0.0762768
$975$	−4.12803e24	−	7.14996e24i	−0.161884	−	0.280391i
$976$	−1.61510e25	+	2.79743e25i	−0.627879	+	1.08752i
$977$	5.61708e24	−	9.72907e24i	0.216475	−	0.374945i	−0.737253	−	0.675617i	$-0.763877\pi$
$977$	5.61708e24	−	9.72907e24i	0.216475	−	0.374945i	0.953728	+	0.300672i	$0.0972108\pi$
$978$	−7.16821e24	−	1.24157e25i	−0.273861	−	0.474341i
$979$	−1.82515e25			−0.691267
$980$	1.04569e25	−	6.61296e24i	0.392629	−	0.248299i
$981$	8.83859e24			0.329000
$982$	−1.41242e25	−	2.44638e25i	−0.521214	−	0.902769i
$983$	1.06560e25	−	1.84568e25i	0.389843	−	0.675228i	−0.602585	−	0.798055i	$-0.705863\pi$
$983$	1.06560e25	−	1.84568e25i	0.389843	−	0.675228i	0.992428	+	0.122826i	$0.0391959\pi$
$984$	−2.25762e25	+	3.91031e25i	−0.818827	+	1.41825i
$985$	5.43371e24	+	9.41146e24i	0.195384	+	0.338414i
$986$	−1.89409e25			−0.675223
$987$	4.54752e24	−	1.31727e24i	0.160723	−	0.0465565i
$988$	1.38043e25			0.483705
$989$	2.02068e24	+	3.49992e24i	0.0701988	+	0.121588i
$990$	−8.78673e23	+	1.52191e24i	−0.0302641	+	0.0524190i
$991$	1.03677e25	−	1.79574e25i	0.354043	−	0.613221i	−0.632910	−	0.774225i	$-0.718140\pi$
$991$	1.03677e25	−	1.79574e25i	0.354043	−	0.613221i	0.986954	+	0.161004i	$0.0514732\pi$
$992$	9.22346e23	+	1.59755e24i	0.0312280	+	0.0540886i
$993$	2.68198e25			0.900298
$994$	−2.75254e25	−	2.64377e25i	−0.916113	−	0.879913i
$995$	5.44967e23			0.0179835
$996$	2.25093e25	+	3.89872e25i	0.736473	+	1.27561i
$997$	−1.93450e25	+	3.35066e25i	−0.627568	+	1.08698i	0.360470	+	0.932771i	$0.382616\pi$
$997$	−1.93450e25	+	3.35066e25i	−0.627568	+	1.08698i	−0.988038	+	0.154209i	$0.950717\pi$
$998$	3.69931e25	−	6.40740e25i	1.18990	−	2.06097i
$999$	4.66698e24	+	8.08344e24i	0.148843	+	0.257804i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.18.e.b.4.12	✓	24
7.2	even	3	inner	21.18.e.b.16.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.18.e.b.4.12	✓	24	1.1	even	1	trivial
21.18.e.b.16.12	yes	24	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	21.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(311.865 + 540.166i) q^{2} +(-3280.50 + 5681.99i) q^{3} +(-128983. + 223406. i) q^{4} +(-103085. - 178549. i) q^{5} -4.09229e6 q^{6} +(-1.46500e7 + 4.24364e6i) q^{7} -7.91478e7 q^{8} +(-2.15234e7 - 3.72796e7i) q^{9} +(6.42974e7 - 1.11366e8i) q^{10} +(1.58732e8 - 2.74932e8i) q^{11} +(-8.46259e8 - 1.46576e9i) q^{12} -1.74666e9 q^{13} +(-6.86108e9 - 6.58997e9i) q^{14} +1.35269e9 q^{15} +(-7.77733e9 - 1.34707e10i) q^{16} +(6.80782e9 - 1.17915e10i) q^{17} +(1.34248e10 - 2.32524e10i) q^{18} +(1.53183e10 + 2.65322e10i) q^{19} +5.31851e10 q^{20} +(2.39469e10 - 9.71624e10i) q^{21} +1.98012e11 q^{22} +(-1.00381e11 - 1.73865e11i) q^{23} +(2.59645e11 - 4.49717e11i) q^{24} +(3.60217e11 - 6.23913e11i) q^{25} +(-5.44723e11 - 9.43488e11i) q^{26} +2.82430e11 q^{27} +(9.41549e11 - 3.82025e12i) q^{28} -2.23032e12 q^{29} +(4.21855e11 + 7.30674e11i) q^{30} +(1.37220e12 - 2.37673e12i) q^{31} +(-3.36082e11 + 5.82112e11i) q^{32} +(1.04144e12 + 1.80383e12i) q^{33} +8.49247e12 q^{34} +(2.26790e12 + 2.17828e12i) q^{35} +1.11046e13 q^{36} +(1.65244e13 + 2.86211e13i) q^{37} +(-9.55451e12 + 1.65489e13i) q^{38} +(5.72993e12 - 9.92453e12i) q^{39} +(8.15898e12 + 1.41318e13i) q^{40} -8.69504e13 q^{41} +(5.99520e13 - 1.73662e13i) q^{42} -2.01301e13 q^{43} +(4.09475e13 + 7.09232e13i) q^{44} +(-4.43749e12 + 7.68595e12i) q^{45} +(6.26106e13 - 1.08445e14i) q^{46} +(2.36558e13 + 4.09730e13i) q^{47} +1.02054e14 q^{48} +(1.96613e14 - 1.24339e14i) q^{49} +4.49355e14 q^{50} +(4.46661e13 + 7.73639e13i) q^{51} +(2.25290e14 - 3.90215e14i) q^{52} +(5.75801e13 - 9.97317e13i) q^{53} +(8.80798e13 + 1.52559e14i) q^{54} -6.54517e13 q^{55} +(1.15951e15 - 3.35875e14i) q^{56} -2.01007e14 q^{57} +(-6.95558e14 - 1.20474e15i) q^{58} +(9.36357e14 - 1.62182e15i) q^{59} +(-1.74474e14 + 3.02197e14i) q^{60} +(-1.03834e15 - 1.79845e15i) q^{61} +1.71177e15 q^{62} +(4.73518e14 + 4.54807e14i) q^{63} -2.45803e15 q^{64} +(1.80055e14 + 3.11865e14i) q^{65} +(-6.49577e14 + 1.12510e15i) q^{66} +(-2.65449e15 + 4.59771e15i) q^{67} +(1.75619e15 + 3.04181e15i) q^{68} +1.31720e15 q^{69} +(-4.69356e14 + 1.90437e15i) q^{70} +4.01181e15 q^{71} +(1.70353e15 + 2.95060e15i) q^{72} +(7.03575e14 - 1.21863e15i) q^{73} +(-1.03067e16 + 1.78518e16i) q^{74} +(2.36338e15 + 4.09350e15i) q^{75} -7.90324e15 q^{76} +(-1.15871e15 + 4.70135e15i) q^{77} +7.14786e15 q^{78} +(-1.28654e16 - 2.22836e16i) q^{79} +(-1.60346e15 + 2.77727e15i) q^{80} +(-9.26510e14 + 1.60476e15i) q^{81} +(-2.71168e16 - 4.69676e16i) q^{82} -2.65986e16 q^{83} +(1.86179e16 + 1.78822e16i) q^{84} -2.80714e15 q^{85} +(-6.27787e15 - 1.08736e16i) q^{86} +(7.31657e15 - 1.26727e16i) q^{87} +(-1.25633e16 + 2.17603e16i) q^{88} +(-2.87458e16 - 4.97892e16i) q^{89} -5.53558e15 q^{90} +(2.55886e16 - 7.41222e15i) q^{91} +5.17899e16 q^{92} +(9.00302e15 + 1.55937e16i) q^{93} +(-1.47548e16 + 2.55561e16i) q^{94} +(3.15819e15 - 5.47015e15i) q^{95} +(-2.20504e15 - 3.81923e15i) q^{96} -4.18174e16 q^{97} +(1.28480e17 + 6.74270e16i) q^{98} -1.36658e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 527 q^{2} - 78732 q^{3} - 824597 q^{4} - 802228 q^{5} + 6915294 q^{6} - 17244326 q^{7} + 280999302 q^{8} - 516560652 q^{9} - 81038239 q^{10} - 1091441542 q^{11} - 5410180917 q^{12} + 1377874148 q^{13}+ \cdots + 93\!\cdots\!64 q^{99}+O(q^{100}) \) 24 * q - 527 * q^2 - 78732 * q^3 - 824597 * q^4 - 802228 * q^5 + 6915294 * q^6 - 17244326 * q^7 + 280999302 * q^8 - 516560652 * q^9 - 81038239 * q^10 - 1091441542 * q^11 - 5410180917 * q^12 + 1377874148 * q^13 + 9596165342 * q^14 + 10526835816 * q^15 - 21305353865 * q^16 - 29762315004 * q^17 - 22685621967 * q^18 + 134684488214 * q^19 - 67717940690 * q^20 - 20050416 * q^21 + 256932532070 * q^22 - 51348084852 * q^23 - 921818210211 * q^24 - 2315181203426 * q^25 - 1335176827238 * q^26 + 6778308875544 * q^27 - 1318749761181 * q^28 + 7999387458656 * q^29 - 531691886079 * q^30 - 6090449057846 * q^31 - 20868024134839 * q^32 - 7160947957062 * q^33 + 26852630021136 * q^34 + 1735719535804 * q^35 + 70992393992874 * q^36 - 54733176744902 * q^37 + 7280793906586 * q^38 - 4520116142514 * q^39 + 73862463026835 * q^40 - 27548774664344 * q^41 - 80212376938581 * q^42 + 510786805993428 * q^43 - 321620688061823 * q^44 - 34533284894388 * q^45 + 77839362592056 * q^46 + 103809747879084 * q^47 + 279568853416530 * q^48 - 236440721256732 * q^49 + 1013098269255332 * q^50 - 195270548741244 * q^51 - 283701282686172 * q^52 - 1010218047002136 * q^53 - 148840365725487 * q^54 + 1972078098308176 * q^55 + 1233346210952391 * q^56 - 1767329854344108 * q^57 + 1528509468372767 * q^58 + 2328649228583166 * q^59 + 222148704433545 * q^60 - 3998785778824516 * q^61 + 1409261729849730 * q^62 + 742443240934422 * q^63 - 2683125102449406 * q^64 + 4887629102559224 * q^65 - 842867171455635 * q^66 - 9451977110365378 * q^67 - 23926389667119312 * q^68 + 673789569427944 * q^69 + 47817629546626777 * q^70 + 15905639914696920 * q^71 - 6048049277194371 * q^72 - 3172717130305346 * q^73 - 20195455410155766 * q^74 - 15189903875677986 * q^75 - 32127389607192264 * q^76 + 59990389152537784 * q^77 + 17520190327017036 * q^78 - 31353048526453194 * q^79 - 36639257137112195 * q^80 - 22236242266222092 * q^81 - 18361225205383004 * q^82 - 60978221772235572 * q^83 + 39272641366893516 * q^84 + 154577029948375320 * q^85 - 138998274620112904 * q^86 - 26241990558121008 * q^87 - 111950342432035965 * q^88 - 89425944181493704 * q^89 + 6976860929128638 * q^90 + 349190114341235694 * q^91 + 22890301604535456 * q^92 - 39959436268527606 * q^93 - 120621193755985614 * q^94 - 206240949632274064 * q^95 - 136915106348678679 * q^96 + 208230990106434268 * q^97 + 769866652642429915 * q^98 + 93965959092567564 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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