LMFDB - Embedded newform 16.9.f.a.3.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,9,Mod(3,16)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("16.3");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	16.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.51805776098$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.5
Character	$\chi$	$=$	16.3
Dual form			16.9.f.a.11.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.02121 - 13.8441i) q^{2} +(17.4297 - 17.4297i) q^{3} +(-127.320 + 222.093i) q^{4} +(-396.274 + 396.274i) q^{5} +(-381.106 - 101.492i) q^{6} +432.698 q^{7} +(4095.96 - 18.8169i) q^{8} +5953.41i q^{9} +O(q^{10})$	\(q+(-8.02121 - 13.8441i) q^{2} +(17.4297 - 17.4297i) q^{3} +(-127.320 + 222.093i) q^{4} +(-396.274 + 396.274i) q^{5} +(-381.106 - 101.492i) q^{6} +432.698 q^{7} +(4095.96 - 18.8169i) q^{8} +5953.41i q^{9} +(8664.66 + 2307.47i) q^{10} +(8018.41 + 8018.41i) q^{11} +(1651.87 + 6090.18i) q^{12} +(12722.0 + 12722.0i) q^{13} +(-3470.76 - 5990.33i) q^{14} +13813.9i q^{15} +(-33115.0 - 56554.1i) q^{16} -81068.2 q^{17} +(82419.9 - 47753.6i) q^{18} +(-129572. + 129572. i) q^{19} +(-37556.1 - 138464. i) q^{20} +(7541.79 - 7541.79i) q^{21} +(46690.7 - 175325. i) q^{22} +1311.99 q^{23} +(71063.3 - 71719.2i) q^{24} +76559.4i q^{25} +(74079.0 - 278170. i) q^{26} +(218122. + 218122. i) q^{27} +(-55091.3 + 96099.4i) q^{28} +(-447381. - 447381. i) q^{29} +(191241. - 110804. i) q^{30} +1.21901e6i q^{31} +(-517320. + 912081. i) q^{32} +279517. q^{33} +(650265. + 1.12232e6i) q^{34} +(-171467. + 171467. i) q^{35} +(-1.32221e6 - 757991. i) q^{36} +(1.65436e6 - 1.65436e6i) q^{37} +(2.83314e6 + 754490. i) q^{38} +443479. q^{39} +(-1.61566e6 + 1.63058e6i) q^{40} -3.85885e6i q^{41} +(-164904. - 43915.3i) q^{42} +(2.19140e6 + 2.19140e6i) q^{43} +(-2.80175e6 + 759930. i) q^{44} +(-2.35918e6 - 2.35918e6i) q^{45} +(-10523.7 - 18163.3i) q^{46} -3.58952e6i q^{47} +(-1.56290e6 - 408535. i) q^{48} -5.57757e6 q^{49} +(1.05990e6 - 614099. i) q^{50} +(-1.41299e6 + 1.41299e6i) q^{51} +(-4.44523e6 + 1.20570e6i) q^{52} +(6.45817e6 - 6.45817e6i) q^{53} +(1.27011e6 - 4.76932e6i) q^{54} -6.35497e6 q^{55} +(1.77231e6 - 8142.04i) q^{56} +4.51681e6i q^{57} +(-2.60507e6 + 9.78215e6i) q^{58} +(1.37598e7 + 1.37598e7i) q^{59} +(-3.06797e6 - 1.75879e6i) q^{60} +(7.47881e6 + 7.47881e6i) q^{61} +(1.68762e7 - 9.77796e6i) q^{62} +2.57603e6i q^{63} +(1.67765e7 - 154146. i) q^{64} -1.00827e7 q^{65} +(-2.24206e6 - 3.86967e6i) q^{66} +(-9.70997e6 + 9.70997e6i) q^{67} +(1.03216e7 - 1.80047e7i) q^{68} +(22867.5 - 22867.5i) q^{69} +(3.74918e6 + 998440. i) q^{70} -2.18411e7 q^{71} +(112025. + 2.43849e7i) q^{72} +4.21800e7i q^{73} +(-3.61731e7 - 9.63321e6i) q^{74} +(1.33441e6 + 1.33441e6i) q^{75} +(-1.22800e7 - 4.52743e7i) q^{76} +(3.46955e6 + 3.46955e6i) q^{77} +(-3.55724e6 - 6.13959e6i) q^{78} -7.15216e7i q^{79} +(3.55335e7 + 9.28827e6i) q^{80} -3.14567e7 q^{81} +(-5.34224e7 + 3.09526e7i) q^{82} +(4.46933e7 - 4.46933e7i) q^{83} +(714759. + 2.63521e6i) q^{84} +(3.21252e7 - 3.21252e7i) q^{85} +(1.27604e7 - 4.79157e7i) q^{86} -1.55954e7 q^{87} +(3.29940e7 + 3.26922e7i) q^{88} +6.27230e7i q^{89} +(-1.37373e7 + 5.15843e7i) q^{90} +(5.50477e6 + 5.50477e6i) q^{91} +(-167043. + 291384. i) q^{92} +(2.12470e7 + 2.12470e7i) q^{93} +(-4.96938e7 + 2.87923e7i) q^{94} -1.02692e8i q^{95} +(6.88057e6 + 2.49140e7i) q^{96} -3.58042e7 q^{97} +(4.47389e7 + 7.72167e7i) q^{98} +(-4.77369e7 + 4.77369e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8}+O(q^{10}) $ 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8	\( 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8} - 1860 q^{10} - 19778 q^{11} + 14068 q^{12} - 2 q^{13} - 58900 q^{14} + 245336 q^{16} - 4 q^{17} - 223730 q^{18} + 167550 q^{19} - 135380 q^{20} - 13124 q^{21} + 985700 q^{22} - 845572 q^{23} - 800592 q^{24} - 184760 q^{26} + 38656 q^{27} + 94136 q^{28} + 1066174 q^{29} + 1881700 q^{30} - 3395192 q^{32} - 4 q^{33} + 1634900 q^{34} + 426620 q^{35} + 1877324 q^{36} + 2360254 q^{37} - 3010352 q^{38} - 7650052 q^{39} + 3256936 q^{40} - 3731304 q^{42} + 6314814 q^{43} - 10360940 q^{44} + 794370 q^{45} + 1510780 q^{46} + 4591848 q^{48} + 14823770 q^{49} + 14752710 q^{50} - 28969860 q^{51} + 4335652 q^{52} + 2679358 q^{53} + 18667040 q^{54} + 46326780 q^{55} - 36346408 q^{56} - 1034696 q^{58} - 46004162 q^{59} - 20687200 q^{60} - 24476034 q^{61} - 64043472 q^{62} + 50827456 q^{64} - 14970820 q^{65} + 65035780 q^{66} + 59474558 q^{67} + 74339312 q^{68} + 8623420 q^{69} + 39082496 q^{70} - 79832068 q^{71} + 929812 q^{72} - 168043460 q^{74} + 88519490 q^{75} - 166219388 q^{76} + 35952572 q^{77} + 5059788 q^{78} - 12904856 q^{80} - 66961570 q^{81} + 261305296 q^{82} - 34471682 q^{83} + 456781480 q^{84} - 107741252 q^{85} + 9841444 q^{86} + 149712636 q^{87} - 173775752 q^{88} - 650366536 q^{90} - 76429060 q^{91} - 449169832 q^{92} + 138269056 q^{93} - 239278032 q^{94} + 378359728 q^{96} - 4 q^{97} + 630040554 q^{98} + 184838270 q^{99}+O(q^{100}) \) 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8 - 1860 * q^10 - 19778 * q^11 + 14068 * q^12 - 2 * q^13 - 58900 * q^14 + 245336 * q^16 - 4 * q^17 - 223730 * q^18 + 167550 * q^19 - 135380 * q^20 - 13124 * q^21 + 985700 * q^22 - 845572 * q^23 - 800592 * q^24 - 184760 * q^26 + 38656 * q^27 + 94136 * q^28 + 1066174 * q^29 + 1881700 * q^30 - 3395192 * q^32 - 4 * q^33 + 1634900 * q^34 + 426620 * q^35 + 1877324 * q^36 + 2360254 * q^37 - 3010352 * q^38 - 7650052 * q^39 + 3256936 * q^40 - 3731304 * q^42 + 6314814 * q^43 - 10360940 * q^44 + 794370 * q^45 + 1510780 * q^46 + 4591848 * q^48 + 14823770 * q^49 + 14752710 * q^50 - 28969860 * q^51 + 4335652 * q^52 + 2679358 * q^53 + 18667040 * q^54 + 46326780 * q^55 - 36346408 * q^56 - 1034696 * q^58 - 46004162 * q^59 - 20687200 * q^60 - 24476034 * q^61 - 64043472 * q^62 + 50827456 * q^64 - 14970820 * q^65 + 65035780 * q^66 + 59474558 * q^67 + 74339312 * q^68 + 8623420 * q^69 + 39082496 * q^70 - 79832068 * q^71 + 929812 * q^72 - 168043460 * q^74 + 88519490 * q^75 - 166219388 * q^76 + 35952572 * q^77 + 5059788 * q^78 - 12904856 * q^80 - 66961570 * q^81 + 261305296 * q^82 - 34471682 * q^83 + 456781480 * q^84 - 107741252 * q^85 + 9841444 * q^86 + 149712636 * q^87 - 173775752 * q^88 - 650366536 * q^90 - 76429060 * q^91 - 449169832 * q^92 + 138269056 * q^93 - 239278032 * q^94 + 378359728 * q^96 - 4 * q^97 + 630040554 * q^98 + 184838270 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−8.02121	−	13.8441i	−0.501326	−	0.865259i
$2$	−8.02121	−	13.8441i	−0.501326	−	0.865259i
$3$	17.4297	−	17.4297i	0.215181	−	0.215181i	−0.591283	−	0.806464i	$-0.701378\pi$
$3$	17.4297	−	17.4297i	0.215181	−	0.215181i	0.806464	+	0.591283i	$0.201378\pi$
$4$	−127.320	+	222.093i	−0.497345	+	0.867553i
$5$	−396.274	+	396.274i	−0.634038	+	0.634038i	−0.949078	−	0.315040i	$-0.897982\pi$
$5$	−396.274	+	396.274i	−0.634038	+	0.634038i	0.315040	+	0.949078i	$0.397982\pi$
$6$	−381.106	−	101.492i	−0.294063	−	0.0783116i
$7$	432.698			0.180216			0.0901079	−	0.995932i	$-0.471279\pi$
$7$	432.698			0.180216			0.0901079	+	0.995932i	$0.471279\pi$
$8$	4095.96	−	18.8169i	0.999989	−	0.00459397i
$9$			5953.41i			0.907394i
$10$	8664.66	+	2307.47i	0.866466	+	0.230747i
$11$	8018.41	+	8018.41i	0.547669	+	0.547669i	0.925766	−	0.378097i	$-0.123422\pi$
$11$	8018.41	+	8018.41i	0.547669	+	0.547669i	−0.378097	+	0.925766i	$0.623422\pi$
$12$	1651.87	+	6090.18i	0.0796617	+	0.293701i
$13$	12722.0	+	12722.0i	0.445431	+	0.445431i	0.893832	−	0.448401i	$-0.148006\pi$
$13$	12722.0	+	12722.0i	0.445431	+	0.445431i	−0.448401	+	0.893832i	$0.648006\pi$
$14$	−3470.76	−	5990.33i	−0.0903468	−	0.155933i
$15$			13813.9i			0.272866i
$16$	−33115.0	−	56554.1i	−0.505295	−	0.862947i
$17$	−81068.2			−0.970633			−0.485317	−	0.874339i	$-0.661296\pi$
$17$	−81068.2			−0.970633			−0.485317	+	0.874339i	$0.661296\pi$
$18$	82419.9	−	47753.6i	0.785131	−	0.454900i
$19$	−129572.	+	129572.i	−0.994254	+	0.994254i	−0.999984	−	0.00572915i	$-0.998176\pi$
$19$	−129572.	+	129572.i	−0.994254	+	0.994254i	0.00572915	+	0.999984i	$0.498176\pi$
$20$	−37556.1	−	138464.i	−0.234725	−	0.865397i
$21$	7541.79	−	7541.79i	0.0387791	−	0.0387791i
$22$	46690.7	−	175325.i	0.199315	−	0.748435i
$23$	1311.99			0.00468833			0.00234417	−	0.999997i	$-0.499254\pi$
$23$	1311.99			0.00468833			0.00234417	+	0.999997i	$0.499254\pi$
$24$	71063.3	−	71719.2i	0.214191	−	0.216168i
$25$			76559.4i			0.195992i
$26$	74079.0	−	278170.i	0.162107	−	0.608719i
$27$	218122.	+	218122.i	0.410436	+	0.410436i
$28$	−55091.3	+	96099.4i	−0.0896295	+	0.156347i
$29$	−447381.	−	447381.i	−0.632537	−	0.632537i	0.316167	−	0.948704i	$-0.397604\pi$
$29$	−447381.	−	447381.i	−0.632537	−	0.632537i	−0.948704	+	0.316167i	$0.897604\pi$
$30$	191241.	−	110804.i	0.236100	−	0.136795i
$31$			1.21901e6i			1.31996i	0.751282	+	0.659982i	$0.229436\pi$
$31$			1.21901e6i			1.31996i	−0.751282	+	0.659982i	$0.770564\pi$
$32$	−517320.	+	912081.i	−0.493355	+	0.869828i
$33$	279517.			0.235696
$34$	650265.	+	1.12232e6i	0.486603	+	0.839849i
$35$	−171467.	+	171467.i	−0.114264	+	0.114264i
$36$	−1.32221e6	−	757991.i	−0.787212	−	0.451288i
$37$	1.65436e6	−	1.65436e6i	0.882719	−	0.882719i	−0.111091	−	0.993810i	$-0.535434\pi$
$37$	1.65436e6	−	1.65436e6i	0.882719	−	0.882719i	0.993810	+	0.111091i	$0.0354345\pi$
$38$	2.83314e6	+	754490.i	1.35873	+	0.361842i
$39$	443479.			0.191697
$40$	−1.61566e6	+	1.63058e6i	−0.631118	+	0.636944i
$41$		−	3.85885e6i		−	1.36560i	−0.730607	−	0.682798i	$-0.760763\pi$
$41$		−	3.85885e6i		−	1.36560i	0.730607	−	0.682798i	$-0.239237\pi$
$42$	−164904.	−	43915.3i	−0.0529949	−	0.0141130i
$43$	2.19140e6	+	2.19140e6i	0.640984	+	0.640984i	0.950797	−	0.309813i	$-0.100266\pi$
$43$	2.19140e6	+	2.19140e6i	0.640984	+	0.640984i	−0.309813	+	0.950797i	$0.600266\pi$
$44$	−2.80175e6	+	759930.i	−0.747512	+	0.202751i
$45$	−2.35918e6	−	2.35918e6i	−0.575322	−	0.575322i
$46$	−10523.7	−	18163.3i	−0.00235038	−	0.00405662i
$47$		−	3.58952e6i		−	0.735605i	−0.929904	−	0.367803i	$-0.880110\pi$
$47$		−	3.58952e6i		−	0.735605i	0.929904	−	0.367803i	$-0.119890\pi$
$48$	−1.56290e6	−	408535.i	−0.294420	−	0.0769599i
$49$	−5.57757e6			−0.967522
$50$	1.05990e6	−	614099.i	0.169584	−	0.0982558i
$51$	−1.41299e6	+	1.41299e6i	−0.208862	+	0.208862i
$52$	−4.44523e6	+	1.20570e6i	−0.607968	+	0.164902i
$53$	6.45817e6	−	6.45817e6i	0.818476	−	0.818476i	−0.167411	−	0.985887i	$-0.553541\pi$
$53$	6.45817e6	−	6.45817e6i	0.818476	−	0.818476i	0.985887	+	0.167411i	$0.0535406\pi$
$54$	1.27011e6	−	4.76932e6i	0.149371	−	0.560895i
$55$	−6.35497e6			−0.694485
$56$	1.77231e6	−	8142.04i	0.180214	−	0.000827906i
$57$			4.51681e6i			0.427890i
$58$	−2.60507e6	+	9.78215e6i	−0.230201	+	0.864415i
$59$	1.37598e7	+	1.37598e7i	1.13554	+	1.13554i	0.989240	+	0.146303i	$0.0467376\pi$
$59$	1.37598e7	+	1.37598e7i	1.13554	+	1.13554i	0.146303	+	0.989240i	$0.453262\pi$
$60$	−3.06797e6	−	1.75879e6i	−0.236726	−	0.135709i
$61$	7.47881e6	+	7.47881e6i	0.540149	+	0.540149i	0.923572	−	0.383424i	$-0.125255\pi$
$61$	7.47881e6	+	7.47881e6i	0.540149	+	0.540149i	−0.383424	+	0.923572i	$0.625255\pi$
$62$	1.68762e7	−	9.77796e6i	1.14211	−	0.661731i
$63$			2.57603e6i			0.163527i
$64$	1.67765e7	−	154146.i	0.999958	−	0.00918785i
$65$	−1.00827e7			−0.564840
$66$	−2.24206e6	−	3.86967e6i	−0.118160	−	0.203938i
$67$	−9.70997e6	+	9.70997e6i	−0.481857	+	0.481857i	−0.905724	−	0.423867i	$-0.860672\pi$
$67$	−9.70997e6	+	9.70997e6i	−0.481857	+	0.481857i	0.423867	+	0.905724i	$0.360672\pi$
$68$	1.03216e7	−	1.80047e7i	0.482740	−	0.842075i
$69$	22867.5	−	22867.5i	0.00100884	−	0.00100884i
$70$	3.74918e6	+	998440.i	0.156151	+	0.0415843i
$71$	−2.18411e7			−0.859492			−0.429746	−	0.902950i	$-0.641397\pi$
$71$	−2.18411e7			−0.859492			−0.429746	+	0.902950i	$0.641397\pi$
$72$	112025.	+	2.43849e7i	0.00416854	+	0.907384i
$73$			4.21800e7i			1.48530i	0.669678	+	0.742652i	$0.266432\pi$
$73$			4.21800e7i			1.48530i	−0.669678	+	0.742652i	$0.733568\pi$
$74$	−3.61731e7	−	9.63321e6i	−1.20631	−	0.321251i
$75$	1.33441e6	+	1.33441e6i	0.0421738	+	0.0421738i
$76$	−1.22800e7	−	4.52743e7i	−0.368080	−	1.35706i
$77$	3.46955e6	+	3.46955e6i	0.0986985	+	0.0986985i
$78$	−3.55724e6	−	6.13959e6i	−0.0961025	−	0.165867i
$79$		−	7.15216e7i		−	1.83624i	−0.396304	−	0.918119i	$-0.629707\pi$
$79$		−	7.15216e7i		−	1.83624i	0.396304	−	0.918119i	$-0.370293\pi$
$80$	3.55335e7	+	9.28827e6i	0.867517	+	0.226764i
$81$	−3.14567e7			−0.730758
$82$	−5.34224e7	+	3.09526e7i	−1.18159	+	0.684608i
$83$	4.46933e7	−	4.46933e7i	0.941737	−	0.941737i	−0.0566565	−	0.998394i	$-0.518044\pi$
$83$	4.46933e7	−	4.46933e7i	0.941737	−	0.941737i	0.998394	+	0.0566565i	$0.0180440\pi$
$84$	714759.	+	2.63521e6i	0.0143563	+	0.0529295i
$85$	3.21252e7	−	3.21252e7i	0.615418	−	0.615418i
$86$	1.27604e7	−	4.79157e7i	0.233275	−	0.875959i
$87$	−1.55954e7			−0.272220
$88$	3.29940e7	+	3.26922e7i	0.550179	+	0.545147i
$89$			6.27230e7i			0.999693i	0.866114	+	0.499847i	$0.166610\pi$
$89$			6.27230e7i			0.999693i	−0.866114	+	0.499847i	$0.833390\pi$
$90$	−1.37373e7	+	5.15843e7i	−0.209379	+	0.786226i
$91$	5.50477e6	+	5.50477e6i	0.0802737	+	0.0802737i
$92$	−167043.	+	291384.i	−0.00233172	+	0.00406738i
$93$	2.12470e7	+	2.12470e7i	0.284031	+	0.284031i
$94$	−4.96938e7	+	2.87923e7i	−0.636489	+	0.368778i
$95$		−	1.02692e8i		−	1.26079i
$96$	6.88057e6	+	2.49140e7i	0.0810101	+	0.293332i
$97$	−3.58042e7			−0.404433			−0.202217	−	0.979341i	$-0.564815\pi$
$97$	−3.58042e7			−0.404433			−0.202217	+	0.979341i	$0.564815\pi$
$98$	4.47389e7	+	7.72167e7i	0.485044	+	0.837157i
$99$	−4.77369e7	+	4.77369e7i	−0.496951	+	0.496951i
$100$	−1.70033e7	−	9.74757e6i	−0.170033	−	0.0974757i
$101$	1.03261e8	−	1.03261e8i	0.992315	−	0.992315i	−0.00765596	−	0.999971i	$-0.502437\pi$
$101$	1.03261e8	−	1.03261e8i	0.992315	−	0.992315i	0.999971	+	0.00765596i	$0.00243699\pi$
$102$	3.08956e7	+	8.22777e6i	0.285428	+	0.0760119i
$103$	−2.68686e7			−0.238724			−0.119362	−	0.992851i	$-0.538085\pi$
$103$	−2.68686e7			−0.238724			−0.119362	+	0.992851i	$0.538085\pi$
$104$	5.23480e7	+	5.18692e7i	0.447473	+	0.443380i
$105$			5.97723e6i			0.0491748i
$106$	−1.41210e8	−	3.76055e7i	−1.11852	−	0.297871i
$107$	1.19926e8	+	1.19926e8i	0.914913	+	0.914913i	0.996654	−	0.0817411i	$-0.0260481\pi$
$107$	1.19926e8	+	1.19926e8i	0.914913	+	0.914913i	−0.0817411	+	0.996654i	$0.526048\pi$
$108$	−7.62150e7	+	2.06721e7i	−0.560203	+	0.151946i
$109$	4.88291e7	+	4.88291e7i	0.345917	+	0.345917i	0.858586	−	0.512669i	$-0.171343\pi$
$109$	4.88291e7	+	4.88291e7i	0.345917	+	0.345917i	−0.512669	+	0.858586i	$0.671343\pi$
$110$	5.09746e7	+	8.79791e7i	0.348163	+	0.600909i
$111$		−	5.76699e7i		−	0.379889i
$112$	−1.43288e7	−	2.44708e7i	−0.0910622	−	0.155517i
$113$	−9.33670e7			−0.572637			−0.286319	−	0.958134i	$-0.592432\pi$
$113$	−9.33670e7			−0.572637			−0.286319	+	0.958134i	$0.592432\pi$
$114$	6.25313e7	−	3.62303e7i	0.370236	−	0.214512i
$115$	−519906.	+	519906.i	−0.00297258	+	0.00297258i
$116$	1.56321e8	−	4.23997e7i	0.863348	−	0.234170i
$117$	−7.57390e7	+	7.57390e7i	−0.404181	+	0.404181i
$118$	8.01223e7	−	3.00863e8i	0.413262	−	1.55182i
$119$	−3.50781e7			−0.174923
$120$	259934.	+	5.65809e7i	0.00125354	+	0.272863i
$121$		−	8.57689e7i		−	0.400118i
$122$	4.35486e7	−	1.63527e8i	0.196578	−	0.738159i
$123$	−6.72585e7	−	6.72585e7i	−0.293851	−	0.293851i
$124$	−2.70735e8	−	1.55205e8i	−1.14514	−	0.656477i
$125$	−1.85133e8	−	1.85133e8i	−0.758304	−	0.758304i
$126$	3.56629e7	−	2.06629e7i	0.141493	−	0.0819801i
$127$			5.08338e8i			1.95406i	0.213102	+	0.977030i	$0.431643\pi$
$127$			5.08338e8i			1.95406i	−0.213102	+	0.977030i	$0.568357\pi$
$128$	−1.36702e8	−	2.31020e8i	−0.509254	−	0.860616i
$129$	7.63908e7			0.275856
$130$	8.08758e7	+	1.39587e8i	0.283169	+	0.488733i
$131$	−5.84521e7	+	5.84521e7i	−0.198479	+	0.198479i	−0.799348	−	0.600869i	$-0.794821\pi$
$131$	−5.84521e7	+	5.84521e7i	−0.198479	+	0.198479i	0.600869	+	0.799348i	$0.294821\pi$
$132$	−3.55882e7	+	6.20789e7i	−0.117222	+	0.204479i
$133$	−5.60657e7	+	5.60657e7i	−0.179180	+	0.179180i
$134$	2.12312e8	+	5.65405e7i	0.658499	+	0.175364i
$135$	−1.72872e8			−0.520463
$136$	−3.32052e8	+	1.52545e6i	−0.970623	+	0.00445906i
$137$		−	1.39981e8i		−	0.397362i	−0.980064	−	0.198681i	$-0.936334\pi$
$137$		−	1.39981e8i		−	0.397362i	0.980064	−	0.198681i	$-0.0636657\pi$
$138$	−500007.	−	133156.i	−0.00137867	−	0.000367151i
$139$	2.10219e8	+	2.10219e8i	0.563136	+	0.563136i	0.930197	−	0.367061i	$-0.119636\pi$
$139$	2.10219e8	+	2.10219e8i	0.563136	+	0.563136i	−0.367061	+	0.930197i	$0.619636\pi$
$140$	−1.62504e7	−	5.99129e7i	−0.0423012	−	0.155958i
$141$	−6.25642e7	−	6.25642e7i	−0.158289	−	0.158289i
$142$	1.75192e8	+	3.02372e8i	0.430886	+	0.743683i
$143$			2.04020e8i			0.487897i
$144$	3.36690e8	−	1.97147e8i	0.783032	−	0.458502i
$145$	3.54571e8			0.802105
$146$	5.83946e8	−	3.38335e8i	1.28517	−	0.744621i
$147$	−9.72154e7	+	9.72154e7i	−0.208193	+	0.208193i
$148$	1.56789e8	+	5.78056e8i	0.326789	+	1.20482i
$149$	−6.81341e7	+	6.81341e7i	−0.138235	+	0.138235i	−0.772838	−	0.634603i	$-0.781164\pi$
$149$	−6.81341e7	+	6.81341e7i	−0.138235	+	0.138235i	0.634603	+	0.772838i	$0.281164\pi$
$150$	7.77016e6	−	2.91773e7i	0.0153485	−	0.0576341i
$151$	9.51262e8			1.82975			0.914877	−	0.403733i	$-0.132288\pi$
$151$	9.51262e8			1.82975			0.914877	+	0.403733i	$0.132288\pi$
$152$	−5.28284e8	+	5.33160e8i	−0.989676	+	0.998812i
$153$		−	4.82633e8i		−	0.880747i
$154$	2.02030e7	−	7.58630e7i	0.0359197	−	0.134880i
$155$	−4.83063e8	−	4.83063e8i	−0.836907	−	0.836907i
$156$	−5.64640e7	+	9.84939e7i	−0.0953395	+	0.166307i
$157$	1.55929e8	+	1.55929e8i	0.256643	+	0.256643i	0.823687	−	0.567044i	$-0.191913\pi$
$157$	1.55929e8	+	1.55929e8i	0.256643	+	0.256643i	−0.567044	+	0.823687i	$0.691913\pi$
$158$	−9.90156e8	+	5.73690e8i	−1.58882	+	0.920553i
$159$		−	2.25128e8i		−	0.352242i
$160$	−1.56434e8	−	5.66434e8i	−0.238699	−	0.864310i
$161$	567695.			0.000844912
$162$	2.52321e8	+	4.35491e8i	0.366348	+	0.632295i
$163$	2.04851e8	−	2.04851e8i	0.290193	−	0.290193i	−0.546963	−	0.837156i	$-0.684216\pi$
$163$	2.04851e8	−	2.04851e8i	0.290193	−	0.290193i	0.837156	+	0.546963i	$0.184216\pi$
$164$	8.57025e8	+	4.91310e8i	1.18473	+	0.679173i
$165$	−1.10765e8	+	1.10765e8i	−0.149440	+	0.149440i
$166$	−9.77234e8	−	2.60246e8i	−1.28696	−	0.342729i
$167$	−2.21144e8			−0.284321			−0.142161	−	0.989844i	$-0.545405\pi$
$167$	−2.21144e8			−0.284321			−0.142161	+	0.989844i	$0.545405\pi$
$168$	3.07490e7	−	3.10328e7i	0.0386005	−	0.0389568i
$169$		−	4.92035e8i		−	0.603183i
$170$	−7.02429e8	−	1.87063e8i	−0.841021	−	0.223971i
$171$	−7.71397e8	−	7.71397e8i	−0.902180	−	0.902180i
$172$	−7.65705e8	+	2.07686e8i	−0.874878	+	0.237297i
$173$	−2.13113e8	−	2.13113e8i	−0.237917	−	0.237917i	0.578070	−	0.815987i	$-0.303806\pi$
$173$	−2.13113e8	−	2.13113e8i	−0.237917	−	0.237917i	−0.815987	+	0.578070i	$0.803806\pi$
$174$	1.25094e8	+	2.15905e8i	0.136471	+	0.235541i
$175$			3.31271e7i			0.0353209i
$176$	1.87944e8	−	7.19004e8i	0.195874	−	0.749343i
$177$	4.79658e8			0.488695
$178$	8.68346e8	−	5.03114e8i	0.864993	−	0.501172i
$179$	4.82168e8	−	4.82168e8i	0.469663	−	0.469663i	−0.432142	−	0.901805i	$-0.642242\pi$
$179$	4.82168e8	−	4.82168e8i	0.469663	−	0.469663i	0.901805	+	0.432142i	$0.142242\pi$
$180$	8.24330e8	−	2.23587e8i	0.785256	−	0.212988i
$181$	−5.82329e8	+	5.82329e8i	−0.542568	+	0.542568i	−0.924281	−	0.381713i	$-0.875334\pi$
$181$	−5.82329e8	+	5.82329e8i	−0.542568	+	0.542568i	0.381713	+	0.924281i	$0.375334\pi$
$182$	3.20539e7	−	1.20364e8i	0.0292143	−	0.109701i
$183$	2.60707e8			0.232460
$184$	5.37385e6	−	24687.5i	0.00468828	−	2.15381e-5i
$185$			1.31116e9i			1.11935i
$186$	1.23720e8	−	4.64574e8i	0.103368	−	0.388153i
$187$	−6.50039e8	−	6.50039e8i	−0.531585	−	0.531585i
$188$	7.97209e8	+	4.57019e8i	0.638176	+	0.365850i
$189$	9.43811e7	+	9.43811e7i	0.0739670	+	0.0739670i
$190$	−1.42168e9	+	8.23715e8i	−1.09091	+	0.632066i
$191$			7.57653e8i			0.569294i	0.958632	+	0.284647i	$0.0918764\pi$
$191$			7.57653e8i			0.569294i	−0.958632	+	0.284647i	$0.908124\pi$
$192$	2.89723e8	−	2.95096e8i	0.213195	−	0.217149i
$193$	1.96232e9			1.41430			0.707150	−	0.707063i	$-0.249980\pi$
$193$	1.96232e9			1.41430			0.707150	+	0.707063i	$0.249980\pi$
$194$	2.87193e8	+	4.95678e8i	0.202753	+	0.349940i
$195$	−1.75739e8	+	1.75739e8i	−0.121543	+	0.121543i
$196$	7.10139e8	−	1.23874e9i	0.481193	−	0.839377i
$197$	−1.79043e9	+	1.79043e9i	−1.18876	+	1.18876i	−0.211344	+	0.977412i	$0.567784\pi$
$197$	−1.79043e9	+	1.79043e9i	−1.18876	+	1.18876i	−0.977412	+	0.211344i	$0.932216\pi$
$198$	1.04378e9	+	2.77969e8i	0.679126	+	0.180857i
$199$	8.44356e8			0.538410			0.269205	−	0.963083i	$-0.413239\pi$
$199$	8.44356e8			0.538410			0.269205	+	0.963083i	$0.413239\pi$
$200$	1.44061e6	+	3.13584e8i	0.000900382	+	0.195990i
$201$			3.38483e8i			0.207373i
$202$	−2.25783e9	−	6.01280e8i	−1.35608	−	0.361136i
$203$	−1.93581e8	−	1.93581e8i	−0.113993	−	0.113993i
$204$	−1.33914e8	−	4.93720e8i	−0.0773223	−	0.285076i
$205$	1.52916e9	+	1.52916e9i	0.865840	+	0.865840i
$206$	2.15518e8	+	3.71972e8i	0.119678	+	0.206558i
$207$			7.81080e6i			0.00425416i
$208$	2.98190e8	−	1.14077e9i	0.159309	−	0.609457i
$209$	−2.07793e9			−1.08904
$210$	8.27496e7	−	4.79446e7i	0.0425489	−	0.0246526i
$211$	1.16153e8	−	1.16153e8i	0.0586002	−	0.0586002i	−0.677199	−	0.735800i	$-0.736807\pi$
$211$	1.16153e8	−	1.16153e8i	0.0586002	−	0.0586002i	0.735800	+	0.677199i	$0.236807\pi$
$212$	6.12061e8	+	2.25658e9i	0.303006	+	1.11714i
$213$	−3.80684e8	+	3.80684e8i	−0.184947	+	0.184947i
$214$	6.98323e8	−	2.62223e9i	0.332967	−	1.25031i
$215$	−1.73679e9			−0.812817
$216$	8.97524e8	+	8.89315e8i	0.412317	+	0.408546i
$217$			5.27465e8i			0.237878i
$218$	2.84328e8	−	1.06766e9i	0.125891	−	0.472725i
$219$	7.35184e8	+	7.35184e8i	0.319610	+	0.319610i
$220$	8.09118e8	−	1.41140e9i	0.345399	−	0.602502i
$221$	−1.03135e9	−	1.03135e9i	−0.432350	−	0.432350i
$222$	−7.98390e8	+	4.62582e8i	−0.328703	+	0.190448i
$223$		−	3.76615e8i		−	0.152292i	−0.997097	−	0.0761461i	$-0.975738\pi$
$223$		−	3.76615e8i		−	0.152292i	0.997097	−	0.0761461i	$-0.0242616\pi$
$224$	−2.23843e8	+	3.94656e8i	−0.0889103	+	0.156757i
$225$	−4.55790e8			−0.177842
$226$	7.48916e8	+	1.29259e9i	0.287078	+	0.495479i
$227$	1.46377e8	−	1.46377e8i	0.0551277	−	0.0551277i	−0.679005	−	0.734133i	$-0.737589\pi$
$227$	1.46377e8	−	1.46377e8i	0.0551277	−	0.0551277i	0.734133	+	0.679005i	$0.237589\pi$
$228$	−1.00315e9	−	5.75082e8i	−0.371217	−	0.212809i
$229$	3.63359e9	−	3.63359e9i	1.32128	−	1.32128i	0.408531	−	0.912744i	$-0.366041\pi$
$229$	3.63359e9	−	3.63359e9i	1.32128	−	1.32128i	0.912744	−	0.408531i	$-0.133959\pi$
$230$	1.13679e7	+	3.02738e6i	0.00406228	+	0.00108182i
$231$	1.20946e8			0.0424762
$232$	−1.84087e9	−	1.82404e9i	−0.635436	−	0.629624i
$233$		−	3.12507e9i		−	1.06032i	−0.847898	−	0.530160i	$-0.822132\pi$
$233$		−	3.12507e9i		−	1.06032i	0.847898	−	0.530160i	$-0.177868\pi$
$234$	1.65606e9	+	4.41023e8i	0.552348	+	0.147095i
$235$	1.42243e9	+	1.42243e9i	0.466402	+	0.466402i
$236$	−4.80786e9	+	1.30406e9i	−1.54990	+	0.420386i
$237$	−1.24660e9	−	1.24660e9i	−0.395124	−	0.395124i
$238$	2.81369e8	+	4.85626e8i	0.0876936	+	0.151354i
$239$		−	2.22692e9i		−	0.682515i	−0.939970	−	0.341258i	$-0.889147\pi$
$239$		−	2.22692e9i		−	0.682515i	0.939970	−	0.341258i	$-0.110853\pi$
$240$	7.81230e8	−	4.57446e8i	0.235469	−	0.137878i
$241$	7.25899e7			0.0215183			0.0107592	−	0.999942i	$-0.496575\pi$
$241$	7.25899e7			0.0215183			0.0107592	+	0.999942i	$0.496575\pi$
$242$	−1.18740e9	+	6.87971e8i	−0.346206	+	0.200590i
$243$	−1.97938e9	+	1.97938e9i	−0.567681	+	0.567681i
$244$	−2.61320e9	+	7.08790e8i	−0.737248	+	0.199967i
$245$	2.21025e9	−	2.21025e9i	0.613446	−	0.613446i
$246$	−3.91642e8	+	1.47063e9i	−0.106942	+	0.401572i
$247$	−3.29682e9			−0.885743
$248$	2.29381e7	+	4.99303e9i	0.00606387	+	1.31995i
$249$		−	1.55798e9i		−	0.405289i
$250$	−1.07802e9	+	4.04799e9i	−0.275972	+	1.03629i
$251$	3.52679e9	+	3.52679e9i	0.888556	+	0.888556i	0.994384	−	0.105829i	$-0.0337496\pi$
$251$	3.52679e9	+	3.52679e9i	0.888556	+	0.888556i	−0.105829	+	0.994384i	$0.533750\pi$
$252$	−5.72120e8	−	3.27981e8i	−0.141868	−	0.0813293i
$253$	1.05201e7	+	1.05201e7i	0.00256765	+	0.00256765i
$254$	7.03751e9	−	4.07749e9i	1.69077	−	0.979620i
$255$		−	1.11986e9i		−	0.264853i
$256$	−2.10176e9	+	3.74558e9i	−0.489353	+	0.872086i
$257$	−5.06381e9			−1.16077			−0.580384	−	0.814343i	$-0.697097\pi$
$257$	−5.06381e9			−1.16077			−0.580384	+	0.814343i	$0.697097\pi$
$258$	−6.12746e8	−	1.05756e9i	−0.138294	−	0.238687i
$259$	7.15838e8	−	7.15838e8i	0.159080	−	0.159080i
$260$	1.28374e9	−	2.23931e9i	0.280921	−	0.490029i
$261$	2.66345e9	−	2.66345e9i	0.573960	−	0.573960i
$262$	1.27808e9	+	3.40362e8i	0.271238	+	0.0722331i
$263$	7.32397e9			1.53082			0.765409	−	0.643544i	$-0.222537\pi$
$263$	7.32397e9			1.53082			0.765409	+	0.643544i	$0.222537\pi$
$264$	1.14489e9	−	5.25964e6i	0.235694	−	0.00108278i
$265$			5.11841e9i			1.03789i
$266$	1.22590e9	+	3.26466e8i	0.244865	+	0.0652097i
$267$	1.09324e9	+	1.09324e9i	0.215115	+	0.215115i
$268$	−9.20244e8	−	3.39280e9i	−0.178387	−	0.657686i
$269$	−1.52871e8	−	1.52871e8i	−0.0291955	−	0.0291955i	0.692358	−	0.721554i	$-0.256572\pi$
$269$	−1.52871e8	−	1.52871e8i	−0.0291955	−	0.0291955i	−0.721554	+	0.692358i	$0.756572\pi$
$270$	1.38664e9	+	2.39327e9i	0.260922	+	0.450336i
$271$			3.16717e9i			0.587211i	0.955927	+	0.293606i	$0.0948552\pi$
$271$			3.16717e9i			0.587211i	−0.955927	+	0.293606i	$0.905145\pi$
$272$	2.68458e9	+	4.58474e9i	0.490456	+	0.837604i
$273$	1.91893e8			0.0345468
$274$	−1.93791e9	+	1.12281e9i	−0.343821	+	0.199208i
$275$	−6.13885e8	+	6.13885e8i	−0.107339	+	0.107339i
$276$	2.16723e6	+	7.99024e6i	0.000373481	+	0.00137697i
$277$	7.27183e8	−	7.27183e8i	0.123516	−	0.123516i	−0.642646	−	0.766163i	$-0.722164\pi$
$277$	7.27183e8	−	7.27183e8i	0.123516	−	0.123516i	0.766163	+	0.642646i	$0.222164\pi$
$278$	1.22409e9	−	4.59652e9i	0.204944	−	0.769573i
$279$	−7.25729e9			−1.19773
$280$	−6.99094e8	+	7.05547e8i	−0.113738	+	0.114787i
$281$			2.09010e9i			0.335230i	0.985853	+	0.167615i	$0.0536065\pi$
$281$			2.09010e9i			0.335230i	−0.985853	+	0.167615i	$0.946393\pi$
$282$	−3.64307e8	+	1.36799e9i	−0.0576065	+	0.216315i
$283$	1.76522e9	+	1.76522e9i	0.275203	+	0.275203i	0.831191	−	0.555987i	$-0.187660\pi$
$283$	1.76522e9	+	1.76522e9i	0.275203	+	0.275203i	−0.555987	+	0.831191i	$0.687660\pi$
$284$	2.78082e9	−	4.85078e9i	0.427465	−	0.745655i
$285$	−1.78989e9	−	1.78989e9i	−0.271298	−	0.271298i
$286$	2.82448e9	−	1.63649e9i	0.422157	−	0.244595i
$287$		−	1.66972e9i		−	0.246102i
$288$	−5.42999e9	−	3.07982e9i	−0.789277	−	0.447667i
$289$	−4.03697e8			−0.0578714
$290$	−2.84409e9	−	4.90873e9i	−0.402116	−	0.694028i
$291$	−6.24056e8	+	6.24056e8i	−0.0870265	+	0.0870265i
$292$	−9.36790e9	−	5.37037e9i	−1.28858	−	0.738709i
$293$	−9.94428e8	+	9.94428e8i	−0.134928	+	0.134928i	−0.771345	−	0.636417i	$-0.780416\pi$
$293$	−9.94428e8	+	9.94428e8i	−0.134928	+	0.134928i	0.636417	+	0.771345i	$0.280416\pi$
$294$	2.12565e9	+	5.66078e8i	0.284513	+	0.0757682i
$295$	−1.09053e10			−1.43995
$296$	6.74505e9	−	6.80731e9i	0.878655	−	0.886765i
$297$			3.49799e9i			0.449565i
$298$	1.48978e9	+	3.96740e8i	0.188910	+	0.0503085i
$299$	1.66910e7	+	1.66910e7i	0.00208833	+	0.00208833i
$300$	−4.66260e8	+	1.26466e8i	−0.0575630	+	0.0156131i
$301$	9.48214e8	+	9.48214e8i	0.115516	+	0.115516i
$302$	−7.63028e9	−	1.31694e10i	−0.917302	−	1.58321i
$303$		−	3.59960e9i		−	0.427055i
$304$	1.16186e10	+	3.03705e9i	1.36038	+	0.355596i
$305$	−5.92731e9			−0.684949
$306$	−6.68163e9	+	3.87130e9i	−0.762074	+	0.441541i
$307$	−4.41901e9	+	4.41901e9i	−0.497475	+	0.497475i	−0.910651	−	0.413176i	$-0.864419\pi$
$307$	−4.41901e9	+	4.41901e9i	−0.497475	+	0.497475i	0.413176	+	0.910651i	$0.364419\pi$
$308$	−1.21231e9	+	3.28820e8i	−0.134713	+	0.0365389i
$309$	−4.68311e8	+	4.68311e8i	−0.0513689	+	0.0513689i
$310$	−2.81284e9	+	1.05623e10i	−0.304578	+	1.14370i
$311$	1.03964e10			1.11132			0.555661	−	0.831409i	$-0.312465\pi$
$311$	1.03964e10			1.11132			0.555661	+	0.831409i	$0.312465\pi$
$312$	1.81647e9	−	8.34491e6i	0.191695	−	0.000880650i
$313$			3.34903e9i			0.348933i	0.984663	+	0.174466i	$0.0558200\pi$
$313$			3.34903e9i			0.348933i	−0.984663	+	0.174466i	$0.944180\pi$
$314$	9.07965e8	−	3.40945e9i	0.0934008	−	0.350724i
$315$	−1.02081e9	−	1.02081e9i	−0.103682	−	0.103682i
$316$	1.58845e10	+	9.10616e9i	1.59303	+	0.913245i
$317$	7.77841e9	+	7.77841e9i	0.770289	+	0.770289i	0.978157	−	0.207868i	$-0.0666525\pi$
$317$	7.77841e9	+	7.77841e9i	0.770289	+	0.770289i	−0.207868	+	0.978157i	$0.566652\pi$
$318$	−3.11670e9	+	1.80580e9i	−0.304780	+	0.176588i
$319$		−	7.17458e9i		−	0.692841i
$320$	−6.58700e9	+	6.70917e9i	−0.628186	+	0.639837i
$321$	4.18056e9			0.393744
$322$	−4.55360e6	−	7.85924e6i	−0.000423576	−	0.000731067i
$323$	1.05042e10	−	1.05042e10i	0.965056	−	0.965056i
$324$	4.00508e9	−	6.98633e9i	0.363439	−	0.633971i
$325$	−9.73985e8	+	9.73985e8i	−0.0873009	+	0.0873009i
$326$	−4.47913e9	−	1.19283e9i	−0.396573	−	0.105611i
$327$	1.70215e9			0.148870
$328$	−7.26116e7	−	1.58057e10i	−0.00627351	−	1.36558i
$329$		−	1.55318e9i		−	0.132568i
$330$	2.42192e9	+	6.44978e8i	0.204223	+	0.0543863i
$331$	−3.22345e9	−	3.22345e9i	−0.268540	−	0.268540i	0.559972	−	0.828512i	$-0.310812\pi$
$331$	−3.22345e9	−	3.22345e9i	−0.268540	−	0.268540i	−0.828512	+	0.559972i	$0.810812\pi$
$332$	4.23572e9	+	1.56164e10i	0.348638	+	1.28538i
$333$	9.84907e9	+	9.84907e9i	0.800974	+	0.800974i
$334$	1.77384e9	+	3.06155e9i	0.142538	+	0.246012i
$335$		−	7.69561e9i		−	0.611032i
$336$	−6.76266e8	−	1.76772e8i	−0.0530592	−	0.0138694i
$337$	3.75960e8			0.0291489			0.0145744	−	0.999894i	$-0.495361\pi$
$337$	3.75960e8			0.0291489			0.0145744	+	0.999894i	$0.495361\pi$
$338$	−6.81180e9	+	3.94671e9i	−0.521909	+	0.302391i
$339$	−1.62736e9	+	1.62736e9i	−0.123221	+	0.123221i
$340$	3.04461e9	+	1.12250e10i	0.227832	+	0.839983i
$341$	−9.77456e9	+	9.77456e9i	−0.722902	+	0.722902i
$342$	−4.49179e9	+	1.68669e10i	−0.328333	+	1.23291i
$343$	−4.90782e9			−0.354579
$344$	9.01711e9	+	8.93464e9i	0.643922	+	0.638033i
$345$			1.81236e7i			0.00127929i
$346$	−1.24094e9	+	4.65978e9i	−0.0865858	+	0.325133i
$347$	−1.04389e10	−	1.04389e10i	−0.720009	−	0.720009i	0.248598	−	0.968607i	$-0.420030\pi$
$347$	−1.04389e10	−	1.04389e10i	−0.720009	−	0.720009i	−0.968607	+	0.248598i	$0.920030\pi$
$348$	1.98562e9	−	3.46364e9i	0.135387	−	0.236165i
$349$	−1.11312e10	−	1.11312e10i	−0.750308	−	0.750308i	0.224229	−	0.974537i	$-0.428014\pi$
$349$	−1.11312e10	−	1.11312e10i	−0.750308	−	0.750308i	−0.974537	+	0.224229i	$0.928014\pi$
$350$	4.58616e8	−	2.65719e8i	0.0305617	−	0.0177073i
$351$			5.54988e9i			0.365641i
$352$	−1.14615e10	+	3.16536e9i	−0.746572	+	0.206183i
$353$	1.36730e10			0.880569			0.440285	−	0.897858i	$-0.354878\pi$
$353$	1.36730e10			0.880569			0.440285	+	0.897858i	$0.354878\pi$
$354$	−3.84743e9	−	6.64045e9i	−0.244996	−	0.422848i
$355$	8.65507e9	−	8.65507e9i	0.544951	−	0.544951i
$356$	−1.39304e10	−	7.98591e9i	−0.867286	−	0.497193i
$357$	−6.11400e8	+	6.11400e8i	−0.0376403	+	0.0376403i
$358$	−1.05428e10	−	2.80763e9i	−0.641834	−	0.170926i
$359$	2.09381e10			1.26055			0.630274	−	0.776373i	$-0.282943\pi$
$359$	2.09381e10			1.26055			0.630274	+	0.776373i	$0.282943\pi$
$360$	−9.70749e9	−	9.61871e9i	−0.577959	−	0.572673i
$361$		−	1.65944e10i		−	0.977084i
$362$	1.27328e10	+	3.39086e9i	0.741465	+	0.197459i
$363$	−1.49493e9	−	1.49493e9i	−0.0860980	−	0.0860980i
$364$	−1.92344e9	+	5.21704e8i	−0.109565	+	0.0297179i
$365$	−1.67148e10	−	1.67148e10i	−0.941739	−	0.941739i
$366$	−2.09118e9	−	3.60926e9i	−0.116538	−	0.201138i
$367$			1.47279e10i			0.811850i	0.913906	+	0.405925i	$0.133051\pi$
$367$			1.47279e10i			0.811850i	−0.913906	+	0.405925i	$0.866949\pi$
$368$	−4.34465e7	−	7.41982e7i	−0.00236899	−	0.00404578i
$369$	2.29733e10			1.23913
$370$	1.81518e10	−	1.05171e10i	0.968532	−	0.561161i
$371$	2.79444e9	−	2.79444e9i	0.147502	−	0.147502i
$372$	−7.42401e9	+	2.01365e9i	−0.387674	+	0.105151i
$373$	8.31890e8	−	8.31890e8i	0.0429765	−	0.0429765i	−0.685292	−	0.728268i	$-0.740325\pi$
$373$	8.31890e8	−	8.31890e8i	0.0429765	−	0.0429765i	0.728268	+	0.685292i	$0.240325\pi$
$374$	−3.78513e9	+	1.42133e10i	−0.193461	+	0.726456i
$375$	−6.45362e9			−0.326346
$376$	−6.75436e7	−	1.47025e10i	−0.00337935	−	0.735598i
$377$		−	1.13831e10i		−	0.563503i
$378$	5.49575e8	−	2.06368e9i	0.0269190	−	0.101082i
$379$	−2.66004e10	−	2.66004e10i	−1.28923	−	1.28923i	−0.935254	−	0.353978i	$-0.884829\pi$
$379$	−2.66004e10	−	2.66004e10i	−1.28923	−	1.28923i	−0.353978	−	0.935254i	$-0.615171\pi$
$380$	2.28073e10	+	1.30748e10i	1.09380	+	0.627048i
$381$	8.86018e9	+	8.86018e9i	0.420477	+	0.420477i
$382$	1.04891e10	−	6.07729e9i	0.492587	−	0.285402i
$383$			3.78625e10i			1.75960i	0.475344	+	0.879800i	$0.342324\pi$
$383$			3.78625e10i			1.75960i	−0.475344	+	0.879800i	$0.657676\pi$
$384$	−6.40928e9	−	1.64393e9i	−0.294771	−	0.0756065i
$385$	−2.74978e9			−0.125157
$386$	−1.57402e10	−	2.71667e10i	−0.709025	−	1.22374i
$387$	−1.30463e10	+	1.30463e10i	−0.581625	+	0.581625i
$388$	4.55861e9	−	7.95188e9i	0.201143	−	0.350867i
$389$	−2.54342e10	+	2.54342e10i	−1.11076	+	1.11076i	−0.117710	+	0.993048i	$0.537555\pi$
$389$	−2.54342e10	+	2.54342e10i	−1.11076	+	1.11076i	−0.993048	+	0.117710i	$0.962445\pi$
$390$	3.84260e9	+	1.02332e9i	0.166099	+	0.0442335i
$391$	−1.06361e8			−0.00455065
$392$	−2.28455e10	+	1.04953e8i	−0.967512	+	0.00444477i
$393$			2.03760e9i			0.0854180i
$394$	3.91484e10	+	1.04256e10i	1.62454	+	0.432628i
$395$	2.83421e10	+	2.83421e10i	1.16424	+	1.16424i
$396$	−4.52418e9	−	1.66799e10i	−0.183975	−	0.678288i
$397$	−7.72747e9	−	7.72747e9i	−0.311082	−	0.311082i	0.534247	−	0.845329i	$-0.320595\pi$
$397$	−7.72747e9	−	7.72747e9i	−0.311082	−	0.311082i	−0.845329	+	0.534247i	$0.820595\pi$
$398$	−6.77276e9	−	1.16894e10i	−0.269919	−	0.465864i
$399$			1.95441e9i			0.0771125i
$400$	4.32974e9	−	2.53527e9i	0.169131	−	0.0990339i
$401$	−2.48924e10			−0.962697			−0.481349	−	0.876529i	$-0.659853\pi$
$401$	−2.48924e10			−0.962697			−0.481349	+	0.876529i	$0.659853\pi$
$402$	4.68601e9	−	2.71505e9i	0.179432	−	0.103962i
$403$	−1.55082e10	+	1.55082e10i	−0.587952	+	0.587952i
$404$	9.78633e9	+	3.60807e10i	0.367362	+	1.35441i
$405$	1.24655e10	−	1.24655e10i	0.463328	−	0.463328i
$406$	−1.12721e9	+	4.23272e9i	−0.0414859	+	0.155781i
$407$	2.65307e10			0.966875
$408$	−5.76098e9	+	5.81415e9i	−0.207900	+	0.209819i
$409$		−	6.24940e9i		−	0.223329i	−0.993746	−	0.111665i	$-0.964382\pi$
$409$		−	6.24940e9i		−	0.223329i	0.993746	−	0.111665i	$-0.0356182\pi$
$410$	8.90419e9	−	3.34356e10i	0.315108	−	1.18324i
$411$	−2.43982e9	−	2.43982e9i	−0.0855048	−	0.0855048i
$412$	3.42091e9	−	5.96733e9i	0.118728	−	0.207105i
$413$	5.95383e9	+	5.95383e9i	0.204643	+	0.204643i
$414$	1.08134e8	−	6.26521e7i	0.00368095	−	0.00213272i
$415$			3.54215e10i			1.19419i
$416$	−1.81848e10	+	5.02213e9i	−0.607204	+	0.167693i
$417$	7.32811e9			0.242353
$418$	1.66675e10	+	2.87671e10i	0.545965	+	0.942305i
$419$	−1.40913e10	+	1.40913e10i	−0.457187	+	0.457187i	−0.897731	−	0.440544i	$-0.854786\pi$
$419$	−1.40913e10	+	1.40913e10i	−0.457187	+	0.457187i	0.440544	+	0.897731i	$0.354786\pi$
$420$	−1.32750e9	−	7.61023e8i	−0.0426617	−	0.0244569i
$421$	3.83758e9	−	3.83758e9i	0.122160	−	0.122160i	−0.643384	−	0.765544i	$-0.722470\pi$
$421$	3.83758e9	−	3.83758e9i	0.122160	−	0.122160i	0.765544	+	0.643384i	$0.222470\pi$
$422$	−2.53972e9	−	6.76349e8i	−0.0800821	−	0.0213266i
$423$	2.13699e10			0.667484
$424$	2.63309e10	−	2.65739e10i	0.814708	−	0.822228i
$425$		−	6.20654e9i		−	0.190236i
$426$	8.32380e9	+	2.21670e9i	0.252745	+	0.0673083i
$427$	3.23607e9	+	3.23607e9i	0.0973433	+	0.0973433i
$428$	−4.19039e10	+	1.13658e10i	−1.24876	+	0.338707i
$429$	3.55600e9	+	3.55600e9i	0.104986	+	0.104986i
$430$	1.39311e10	+	2.40443e10i	0.407486	+	0.703297i
$431$		−	3.56390e10i		−	1.03280i	−0.856347	−	0.516400i	$-0.827272\pi$
$431$		−	3.56390e10i		−	1.03280i	0.856347	−	0.516400i	$-0.172728\pi$
$432$	5.11258e9	−	1.95588e10i	0.146793	−	0.561575i
$433$	5.00093e10			1.42265			0.711326	−	0.702862i	$-0.248095\pi$
$433$	5.00093e10			1.42265			0.711326	+	0.702862i	$0.248095\pi$
$434$	7.30230e9	−	4.23091e9i	0.205826	−	0.119254i
$435$	6.18006e9	−	6.18006e9i	0.172598	−	0.172598i
$436$	−1.70615e10	+	4.62768e9i	−0.472142	+	0.128061i
$437$	−1.69997e8	+	1.69997e8i	−0.00466140	+	0.00466140i
$438$	4.28093e9	−	1.60751e10i	0.116317	−	0.436773i
$439$	−5.56469e10			−1.49824			−0.749122	−	0.662432i	$-0.769524\pi$
$439$	−5.56469e10			−1.49824			−0.749122	+	0.662432i	$0.769524\pi$
$440$	−2.60297e10	+	1.19581e8i	−0.694478	+	0.00319044i
$441$		−	3.32056e10i		−	0.877924i
$442$	−6.00546e9	+	2.25507e10i	−0.157346	+	0.590843i
$443$	7.97933e9	+	7.97933e9i	0.207182	+	0.207182i	0.803068	−	0.595887i	$-0.203199\pi$
$443$	7.97933e9	+	7.97933e9i	0.207182	+	0.207182i	−0.595887	+	0.803068i	$0.703199\pi$
$444$	1.28081e10	+	7.34255e9i	0.329574	+	0.188936i
$445$	−2.48555e10	−	2.48555e10i	−0.633843	−	0.633843i
$446$	−5.21391e9	+	3.02091e9i	−0.131772	+	0.0763480i
$447$			2.37511e9i			0.0594914i
$448$	7.25916e9	−	6.66989e7i	0.180208	−	0.00165579i
$449$	−6.34957e10			−1.56228			−0.781140	−	0.624356i	$-0.785361\pi$
$449$	−6.34957e10			−1.56228			−0.781140	+	0.624356i	$0.785361\pi$
$450$	3.65598e9	+	6.31001e9i	0.0891567	+	0.153879i
$451$	3.09418e10	−	3.09418e10i	0.747894	−	0.747894i
$452$	1.18875e10	−	2.07362e10i	0.284798	−	0.496793i
$453$	1.65802e10	−	1.65802e10i	0.393729	−	0.393729i
$454$	−3.20059e9	−	8.52344e8i	−0.0753367	−	0.0200628i
$455$	−4.36279e9			−0.101793
$456$	8.49923e7	+	1.85006e10i	0.00196571	+	0.427886i
$457$			3.41652e10i			0.783284i	0.920118	+	0.391642i	$0.128093\pi$
$457$			3.41652e10i			0.783284i	−0.920118	+	0.391642i	$0.871907\pi$
$458$	−7.94496e10	−	2.11581e10i	−1.80563	−	0.480856i
$459$	−1.76828e10	−	1.76828e10i	−0.398382	−	0.398382i
$460$	−4.92731e7	−	1.81662e8i	−0.00110047	−	0.00405727i
$461$	3.35800e7	+	3.35800e7i	0.000743494	+	0.000743494i	0.707478	−	0.706735i	$-0.249833\pi$
$461$	3.35800e7	+	3.35800e7i	0.000743494	+	0.000743494i	−0.706735	+	0.707478i	$0.749833\pi$
$462$	−9.70137e8	−	1.67440e9i	−0.0212944	−	0.0367529i
$463$		−	7.09349e10i		−	1.54360i	−0.635863	−	0.771802i	$-0.719356\pi$
$463$		−	7.09349e10i		−	1.54360i	0.635863	−	0.771802i	$-0.280644\pi$
$464$	−1.04862e10	+	4.01163e10i	−0.226228	+	0.865463i
$465$	−1.68393e10			−0.360173
$466$	−4.32640e10	+	2.50669e10i	−0.917450	+	0.531565i
$467$	3.23128e10	−	3.23128e10i	0.679371	−	0.679371i	−0.280487	−	0.959858i	$-0.590496\pi$
$467$	3.23128e10	−	3.23128e10i	0.679371	−	0.679371i	0.959858	+	0.280487i	$0.0904960\pi$
$468$	−7.17802e9	−	2.64643e10i	−0.149631	−	0.551666i
$469$	−4.20148e9	+	4.20148e9i	−0.0868383	+	0.0868383i
$470$	8.28272e9	−	3.11020e10i	0.169739	−	0.637377i
$471$	5.43560e9			0.110449
$472$	5.66184e10	+	5.61006e10i	1.14075	+	1.13031i
$473$			3.51431e10i			0.702094i
$474$	−7.25887e9	+	2.72573e10i	−0.143799	+	0.539971i
$475$	−9.91997e9	−	9.91997e9i	−0.194866	−	0.194866i
$476$	4.46616e9	−	7.79061e9i	0.0869973	−	0.151755i
$477$	3.84482e10	+	3.84482e10i	0.742681	+	0.742681i
$478$	−3.08297e10	+	1.78626e10i	−0.590552	+	0.342162i
$479$		−	1.08691e10i		−	0.206467i	−0.994657	−	0.103234i	$-0.967081\pi$
$479$		−	1.08691e10i		−	0.206467i	0.994657	−	0.103234i	$-0.0329189\pi$
$480$	−1.25994e10	−	7.14618e9i	−0.237347	−	0.134620i
$481$	4.20933e10			0.786381
$482$	−5.82259e8	−	1.00494e9i	−0.0107877	−	0.0186189i
$483$	9.89474e6	−	9.89474e6i	0.000181809	−	0.000181809i
$484$	1.90487e10	+	1.09201e10i	0.347124	+	0.198997i
$485$	1.41883e10	−	1.41883e10i	0.256426	−	0.256426i
$486$	4.32799e10	+	1.15258e10i	0.775784	+	0.206598i
$487$	−4.47957e9			−0.0796381			−0.0398190	−	0.999207i	$-0.512678\pi$
$487$	−4.47957e9			−0.0796381			−0.0398190	+	0.999207i	$0.512678\pi$
$488$	3.07736e10	+	3.04922e10i	0.542624	+	0.537661i
$489$		−	7.14097e9i		−	0.124888i
$490$	−4.83278e10	−	1.28701e10i	−0.838325	−	0.223253i
$491$	5.02372e10	+	5.02372e10i	0.864370	+	0.864370i	0.991842	−	0.127472i	$-0.0406865\pi$
$491$	5.02372e10	+	5.02372e10i	0.864370	+	0.864370i	−0.127472	+	0.991842i	$0.540686\pi$
$492$	2.35011e10	−	6.37430e9i	0.401076	−	0.108786i
$493$	3.62684e10	+	3.62684e10i	0.613961	+	0.613961i
$494$	2.64445e10	+	4.56417e10i	0.444046	+	0.766397i
$495$		−	3.78338e10i		−	0.630172i
$496$	6.89402e10	−	4.03677e10i	1.13906	−	0.666971i
$497$	−9.45062e9			−0.154894
$498$	−2.15689e10	+	1.24969e10i	−0.350679	+	0.203182i
$499$	−4.04909e10	+	4.04909e10i	−0.653064	+	0.653064i	−0.953730	−	0.300666i	$-0.902791\pi$
$499$	−4.04909e10	+	4.04909e10i	−0.653064	+	0.653064i	0.300666	+	0.953730i	$0.402791\pi$
$500$	6.46880e10	−	1.75456e10i	1.03501	−	0.280730i
$501$	−3.85447e9	+	3.85447e9i	−0.0611807	+	0.0611807i
$502$	2.05362e10	−	7.71145e10i	0.323375	−	1.21429i
$503$	−4.60074e10			−0.718713			−0.359356	−	0.933200i	$-0.617004\pi$
$503$	−4.60074e10			−0.718713			−0.359356	+	0.933200i	$0.617004\pi$
$504$	4.84729e7	+	1.05513e10i	0.000751237	+	0.163525i
$505$			8.18390e10i			1.25833i
$506$	6.12576e7	−	2.30025e8i	0.000934454	−	0.00350891i
$507$	−8.57601e9	−	8.57601e9i	−0.129794	−	0.129794i
$508$	−1.12899e11	−	6.47218e10i	−1.69525	−	0.971843i
$509$	−1.66104e10	−	1.66104e10i	−0.247462	−	0.247462i	0.572466	−	0.819928i	$-0.305987\pi$
$509$	−1.66104e10	−	1.66104e10i	−0.247462	−	0.247462i	−0.819928	+	0.572466i	$0.805987\pi$
$510$	−1.55036e10	+	8.98267e9i	−0.229166	+	0.132778i
$511$			1.82512e10i			0.267675i
$512$	6.87130e10	−	9.47059e8i	0.999905	−	0.0137815i
$513$	−5.65252e10			−0.816155
$514$	4.06179e10	+	7.01041e10i	0.581922	+	1.00436i
$515$	1.06473e10	−	1.06473e10i	0.151360	−	0.151360i
$516$	−9.72610e9	+	1.69659e10i	−0.137196	+	0.239319i
$517$	2.87823e10	−	2.87823e10i	0.402868	−	0.402868i
$518$	−1.56520e10	−	4.16827e9i	−0.217396	−	0.0578945i
$519$	−7.42898e9			−0.102390
$520$	−4.12985e10	+	1.89726e8i	−0.564834	+	0.00259486i
$521$			1.05300e11i			1.42914i	0.699563	+	0.714571i	$0.253378\pi$
$521$			1.05300e11i			1.42914i	−0.699563	+	0.714571i	$0.746622\pi$
$522$	−5.82372e10	−	1.55091e10i	−0.784365	−	0.208883i
$523$	7.09010e10	+	7.09010e10i	0.947644	+	0.947644i	0.998696	−	0.0510516i	$-0.0162573\pi$
$523$	7.09010e10	+	7.09010e10i	0.947644	+	0.947644i	−0.0510516	+	0.998696i	$0.516257\pi$
$524$	−5.53968e9	−	2.04240e10i	−0.0734784	−	0.270904i
$525$	5.77395e8	+	5.77395e8i	0.00760039	+	0.00760039i
$526$	−5.87471e10	−	1.01394e11i	−0.767438	−	1.32455i
$527$		−	9.88233e10i		−	1.28120i
$528$	−9.25621e9	−	1.58078e10i	−0.119096	−	0.203393i
$529$	−7.83093e10			−0.999978
$530$	7.08599e10	−	4.10558e10i	0.898043	−	0.520321i
$531$	−8.19177e10	+	8.19177e10i	−1.03039	+	1.03039i
$532$	−5.31352e9	−	1.95901e10i	−0.0663339	−	0.244563i
$533$	4.90921e10	−	4.90921e10i	0.608279	−	0.608279i
$534$	6.36587e9	−	2.39041e10i	0.0782876	−	0.293973i
$535$	−9.50473e10			−1.16018
$536$	−3.95889e10	+	3.99543e10i	−0.479639	+	0.484066i
$537$		−	1.68081e10i		−	0.202126i
$538$	−8.90158e8	+	3.34258e9i	−0.0106252	+	0.0398981i
$539$	−4.47233e10	−	4.47233e10i	−0.529881	−	0.529881i
$540$	2.20102e10	−	3.83938e10i	0.258850	−	0.451529i
$541$	2.02697e9	+	2.02697e9i	0.0236623	+	0.0236623i	0.718839	−	0.695177i	$-0.244674\pi$
$541$	2.02697e9	+	2.02697e9i	0.0236623	+	0.0236623i	−0.695177	+	0.718839i	$0.744674\pi$
$542$	4.38467e10	−	2.54045e10i	0.508089	−	0.294384i
$543$			2.02996e10i			0.233501i
$544$	4.19382e10	−	7.39408e10i	0.478866	−	0.844284i
$545$	−3.86993e10			−0.438649
$546$	−1.53921e9	−	2.65659e9i	−0.0173192	−	0.0298919i
$547$	1.09781e11	−	1.09781e11i	1.22624	−	1.22624i	0.260867	−	0.965375i	$-0.415992\pi$
$547$	1.09781e11	−	1.09781e11i	1.22624	−	1.22624i	0.965375	−	0.260867i	$-0.0840083\pi$
$548$	3.10888e10	+	1.78224e10i	0.344732	+	0.197626i
$549$	−4.45244e10	+	4.45244e10i	−0.490128	+	0.490128i
$550$	1.34228e10	+	3.57461e9i	0.146687	+	0.0390641i
$551$	1.15936e11			1.25781
$552$	9.32342e7	−	9.40948e7i	0.00100420	−	0.00101347i
$553$		−	3.09473e10i		−	0.330919i
$554$	−1.59001e10	−	4.23433e9i	−0.168796	−	0.0449517i
$555$	2.28531e10	+	2.28531e10i	0.240864	+	0.240864i
$556$	−7.34535e10	+	1.99231e10i	−0.768623	+	0.208477i
$557$	−3.58458e9	−	3.58458e9i	−0.0372407	−	0.0372407i	0.688241	−	0.725482i	$-0.258383\pi$
$557$	−3.58458e9	−	3.58458e9i	−0.0372407	−	0.0372407i	−0.725482	+	0.688241i	$0.758383\pi$
$558$	5.82122e10	+	1.00471e11i	0.600451	+	1.03634i
$559$			5.57577e10i			0.571029i
$560$	1.53753e10	+	4.01902e9i	0.156340	+	0.0408665i
$561$	−2.26600e10			−0.228774
$562$	2.89357e10	−	1.67652e10i	0.290060	−	0.168059i
$563$	−1.03312e11	+	1.03312e11i	−1.02829	+	1.02829i	−0.0287012	+	0.999588i	$0.509137\pi$
$563$	−1.03312e11	+	1.03312e11i	−1.02829	+	1.02829i	−0.999588	+	0.0287012i	$0.990863\pi$
$564$	2.18608e10	−	5.92940e9i	0.216048	−	0.0585996i
$565$	3.69989e10	−	3.69989e10i	0.363074	−	0.363074i
$566$	1.02788e10	−	3.85972e10i	0.100156	−	0.376089i
$567$	−1.36113e10			−0.131694
$568$	−8.94604e10	+	4.10983e8i	−0.859483	+	0.00394848i
$569$		−	1.39680e11i		−	1.33256i	−0.745702	−	0.666280i	$-0.767886\pi$
$569$		−	1.39680e11i		−	1.33256i	0.745702	−	0.666280i	$-0.232114\pi$
$570$	−1.04224e10	+	3.91366e10i	−0.0987345	+	0.370752i
$571$	2.21750e10	+	2.21750e10i	0.208602	+	0.208602i	0.803673	−	0.595071i	$-0.202876\pi$
$571$	2.21750e10	+	2.21750e10i	0.208602	+	0.208602i	−0.595071	+	0.803673i	$0.702876\pi$
$572$	−4.53115e10	−	2.59759e10i	−0.423276	−	0.242653i
$573$	1.32057e10	+	1.32057e10i	0.122502	+	0.122502i
$574$	−2.31158e10	+	1.33931e10i	−0.212942	+	0.123377i
$575$			1.00445e8i			0.000918876i
$576$	9.17697e8	+	9.98775e10i	0.00833700	+	0.907356i
$577$	1.23169e11			1.11122			0.555609	−	0.831444i	$-0.312485\pi$
$577$	1.23169e11			1.11122			0.555609	+	0.831444i	$0.312485\pi$
$578$	3.23813e9	+	5.58883e9i	0.0290124	+	0.0500737i
$579$	3.42027e10	−	3.42027e10i	0.304331	−	0.304331i
$580$	−4.51441e10	+	7.87479e10i	−0.398923	+	0.695868i
$581$	1.93387e10	−	1.93387e10i	0.169716	−	0.169716i
$582$	1.36452e10	+	3.63384e9i	0.118929	+	0.0316718i
$583$	1.03569e11			0.896508
$584$	7.93697e8	+	1.72767e11i	0.00682344	+	1.48529i
$585$		−	6.00268e10i		−	0.512533i
$586$	2.17435e10	+	5.79049e9i	0.184391	+	0.0491049i
$587$	2.49488e10	+	2.49488e10i	0.210134	+	0.210134i	0.804325	−	0.594190i	$-0.202527\pi$
$587$	2.49488e10	+	2.49488e10i	0.210134	+	0.210134i	−0.594190	+	0.804325i	$0.702527\pi$
$588$	−9.21340e9	−	3.39684e10i	−0.0770745	−	0.284162i
$589$	−1.57950e11	−	1.57950e11i	−1.31238	−	1.31238i
$590$	8.74735e10	+	1.50974e11i	0.721886	+	1.24593i
$591$			6.24133e10i			0.511596i
$592$	−1.48345e11	−	3.87766e10i	−1.20777	−	0.315706i
$593$	1.19075e11			0.962944			0.481472	−	0.876461i	$-0.340102\pi$
$593$	1.19075e11			0.962944			0.481472	+	0.876461i	$0.340102\pi$
$594$	4.84267e10	−	2.80581e10i	0.388990	−	0.225379i
$595$	1.39005e10	−	1.39005e10i	0.110908	−	0.110908i
$596$	−6.45728e9	−	2.38070e10i	−0.0511758	−	0.188677i
$597$	1.47169e10	−	1.47169e10i	0.115856	−	0.115856i
$598$	9.71908e7	−	3.64956e8i	0.000760012	−	0.00285388i
$599$	−1.09711e11			−0.852206			−0.426103	−	0.904675i	$-0.640114\pi$
$599$	−1.09711e11			−0.852206			−0.426103	+	0.904675i	$0.640114\pi$
$600$	5.49078e9	+	5.44056e9i	0.0423671	+	0.0419796i
$601$			3.92417e10i			0.300781i	0.988627	+	0.150390i	$0.0480530\pi$
$601$			3.92417e10i			0.300781i	−0.988627	+	0.150390i	$0.951947\pi$
$602$	5.52138e9	−	2.07330e10i	0.0420399	−	0.157862i
$603$	−5.78074e10	−	5.78074e10i	−0.437235	−	0.437235i
$604$	−1.21115e11	+	2.11269e11i	−0.910019	+	1.58741i
$605$	3.39880e10	+	3.39880e10i	0.253690	+	0.253690i
$606$	−4.98334e10	+	2.88732e10i	−0.369513	+	0.214094i
$607$			2.28310e11i			1.68179i	0.541202	+	0.840893i	$0.317969\pi$
$607$			2.28310e11i			1.68179i	−0.541202	+	0.840893i	$0.682031\pi$
$608$	−5.11501e10	−	1.85211e11i	−0.374311	−	1.35535i
$609$	−6.74812e9			−0.0490584
$610$	4.75442e10	+	8.20585e10i	0.343383	+	0.592658i
$611$	4.56657e10	−	4.56657e10i	0.327661	−	0.327661i
$612$	1.07190e11	+	6.14490e10i	0.764094	+	0.438035i
$613$	−2.18428e10	+	2.18428e10i	−0.154691	+	0.154691i	−0.780209	−	0.625518i	$-0.784888\pi$
$613$	−2.18428e10	+	2.18428e10i	−0.154691	+	0.154691i	0.625518	+	0.780209i	$0.284888\pi$
$614$	9.66232e10	+	2.57316e10i	0.679842	+	0.181048i
$615$	5.33056e10			0.372625
$616$	1.42764e10	+	1.41459e10i	0.0991509	+	0.0982441i
$617$		−	2.67553e11i		−	1.84616i	−0.384605	−	0.923081i	$-0.625662\pi$
$617$		−	2.67553e11i		−	1.84616i	0.384605	−	0.923081i	$-0.374338\pi$
$618$	1.02398e10	+	2.72694e9i	0.0701999	+	0.0186948i
$619$	2.58311e10	+	2.58311e10i	0.175947	+	0.175947i	0.789586	−	0.613640i	$-0.210295\pi$
$619$	2.58311e10	+	2.58311e10i	0.175947	+	0.175947i	−0.613640	+	0.789586i	$0.710295\pi$
$620$	1.68789e11	−	4.57814e10i	1.14229	−	0.309829i
$621$	2.86174e8	+	2.86174e8i	0.00192426	+	0.00192426i
$622$	−8.33915e10	−	1.43929e11i	−0.557134	−	0.961582i
$623$			2.71401e10i			0.180160i
$624$	−1.46858e10	−	2.50806e10i	−0.0968635	−	0.165424i
$625$	1.16821e11			0.765595
$626$	4.63645e10	−	2.68633e10i	0.301917	−	0.174929i
$627$	−3.62176e10	+	3.62176e10i	−0.234342	+	0.234342i
$628$	−5.44838e10	+	1.47779e10i	−0.350291	+	0.0950110i
$629$	−1.34116e11	+	1.34116e11i	−0.856797	+	0.856797i
$630$	−5.94412e9	+	2.23204e10i	−0.0377334	+	0.141690i
$631$	−2.78827e10			−0.175880			−0.0879402	−	0.996126i	$-0.528028\pi$
$631$	−2.78827e10			−0.175880			−0.0879402	+	0.996126i	$0.528028\pi$
$632$	−1.34582e9	−	2.92950e11i	−0.00843563	−	1.83622i
$633$		−	4.04901e9i		−	0.0252193i
$634$	4.52931e10	−	1.70078e11i	0.280334	−	1.05266i
$635$	−2.01441e11	−	2.01441e11i	−1.23895	−	1.23895i
$636$	4.99994e10	+	2.86634e10i	0.305588	+	0.175186i
$637$	−7.09576e10	−	7.09576e10i	−0.430964	−	0.430964i
$638$	−9.93259e10	+	5.75488e10i	−0.599487	+	0.347339i
$639$		−	1.30029e11i		−	0.779898i
$640$	1.45718e11	+	3.73757e10i	0.868550	+	0.222777i
$641$	−5.16668e10			−0.306041			−0.153020	−	0.988223i	$-0.548900\pi$
$641$	−5.16668e10			−0.306041			−0.153020	+	0.988223i	$0.548900\pi$
$642$	−3.35331e10	−	5.78762e10i	−0.197394	−	0.340691i
$643$	1.22964e11	−	1.22964e11i	0.719339	−	0.719339i	−0.249131	−	0.968470i	$-0.580145\pi$
$643$	1.22964e11	−	1.22964e11i	0.719339	−	0.719339i	0.968470	+	0.249131i	$0.0801449\pi$
$644$	−7.22791e7	+	1.26081e8i	−0.000420213	+	0.000733005i
$645$	−3.02717e10	+	3.02717e10i	−0.174903	+	0.174903i
$646$	−2.29678e11	−	6.11652e10i	−1.31883	−	0.351216i
$647$	2.35439e11			1.34357			0.671787	−	0.740745i	$-0.265527\pi$
$647$	2.35439e11			1.34357			0.671787	+	0.740745i	$0.265527\pi$
$648$	−1.28845e11	+	5.91918e8i	−0.730750	+	0.00335708i
$649$			2.20663e11i			1.24380i
$650$	2.12965e10	+	5.67145e9i	0.119304	+	0.0317717i
$651$	9.19355e9	+	9.19355e9i	0.0511870	+	0.0511870i
$652$	1.94143e10	+	7.15777e10i	0.107432	+	0.396084i
$653$	2.11080e11	+	2.11080e11i	1.16090	+	1.16090i	0.984279	+	0.176622i	$0.0565171\pi$
$653$	2.11080e11	+	2.11080e11i	1.16090	+	1.16090i	0.176622	+	0.984279i	$0.443483\pi$
$654$	−1.36533e10	−	2.35648e10i	−0.0746323	−	0.128811i
$655$		−	4.63260e10i		−	0.251687i
$656$	−2.18234e11	+	1.27786e11i	−1.17844	+	0.690029i
$657$	−2.51115e11			−1.34776
$658$	−2.15024e10	+	1.24584e10i	−0.114705	+	0.0664596i
$659$	−2.36757e11	+	2.36757e11i	−1.25534	+	1.25534i	−0.302048	+	0.953293i	$0.597670\pi$
$659$	−2.36757e11	+	2.36757e11i	−1.25534	+	1.25534i	−0.953293	+	0.302048i	$0.902330\pi$
$660$	−1.04976e10	−	3.87029e10i	−0.0553239	−	0.203971i
$661$	−1.58103e11	+	1.58103e11i	−0.828197	+	0.828197i	−0.987267	−	0.159070i	$-0.949150\pi$
$661$	−1.58103e11	+	1.58103e11i	−0.828197	+	0.828197i	0.159070	+	0.987267i	$0.449150\pi$
$662$	−1.87699e10	+	7.04818e10i	−0.0977305	+	0.366982i
$663$	−3.59521e10			−0.186067
$664$	1.82221e11	−	1.83903e11i	0.937401	−	0.946054i
$665$		−	4.44347e10i		−	0.227214i
$666$	5.73505e10	−	2.15353e11i	0.291501	−	1.09460i
$667$	−5.86959e8	−	5.86959e8i	−0.00296554	−	0.00296554i
$668$	2.81562e10	−	4.91147e10i	0.141406	−	0.246664i
$669$	−6.56428e9	−	6.56428e9i	−0.0327705	−	0.0327705i
$670$	−1.06539e11	+	6.17281e10i	−0.528700	+	0.306326i
$671$			1.19936e11i			0.591645i
$672$	2.97721e9	+	1.07802e10i	0.0145993	+	0.0528630i
$673$	2.86085e11			1.39455			0.697277	−	0.716801i	$-0.254395\pi$
$673$	2.86085e11			1.39455			0.697277	+	0.716801i	$0.254395\pi$
$674$	−3.01565e9	−	5.20484e9i	−0.0146131	−	0.0252213i
$675$	−1.66993e10	+	1.66993e10i	−0.0804421	+	0.0804421i
$676$	1.09278e11	+	6.26460e10i	0.523293	+	0.299990i
$677$	−1.08560e11	+	1.08560e11i	−0.516792	+	0.516792i	−0.916599	−	0.399807i	$-0.869077\pi$
$677$	−1.08560e11	+	1.08560e11i	−0.516792	+	0.516792i	0.399807	+	0.916599i	$0.369077\pi$
$678$	3.55827e10	+	9.47599e9i	0.168392	+	0.0448442i
$679$	−1.54924e10			−0.0728853
$680$	1.30979e11	−	1.32188e11i	0.612584	−	0.618239i
$681$		−	5.10262e9i		−	0.0237249i
$682$	2.13724e11	+	5.69166e10i	0.987907	+	0.263088i
$683$	−1.08099e11	−	1.08099e11i	−0.496752	−	0.496752i	0.413673	−	0.910426i	$-0.364246\pi$
$683$	−1.08099e11	−	1.08099e11i	−0.496752	−	0.496752i	−0.910426	+	0.413673i	$0.864246\pi$
$684$	2.69537e11	−	7.31077e10i	1.23138	−	0.333994i
$685$	5.54707e10	+	5.54707e10i	0.251942	+	0.251942i
$686$	3.93667e10	+	6.79446e10i	0.177759	+	0.306802i
$687$		−	1.26665e11i		−	0.568628i
$688$	5.13642e10	−	1.96501e11i	0.229249	−	0.877022i
$689$	1.64321e11			0.729149
$690$	2.50906e8	−	1.45373e8i	0.00110691	−	0.000641340i
$691$	1.91879e11	−	1.91879e11i	0.841618	−	0.841618i	−0.147451	−	0.989069i	$-0.547107\pi$
$691$	1.91879e11	−	1.91879e11i	0.841618	−	0.841618i	0.989069	+	0.147451i	$0.0471070\pi$
$692$	7.44646e10	−	2.01974e10i	0.324732	−	0.0880785i
$693$	−2.06557e10	+	2.06557e10i	−0.0895584	+	0.0895584i
$694$	−6.07851e10	+	2.28251e11i	−0.262035	+	0.983952i
$695$	−1.66609e11			−0.714099
$696$	−6.38782e10	+	2.93458e8i	−0.272217	+	0.00125057i
$697$			3.12830e11i			1.32549i
$698$	−6.48161e10	+	2.43387e11i	−0.273062	+	1.02536i
$699$	−5.44691e10	−	5.44691e10i	−0.228161	−	0.228161i
$700$	−7.35731e9	−	4.21776e9i	−0.0306427	−	0.0175667i
$701$	4.12696e10	+	4.12696e10i	0.170906	+	0.170906i	0.787377	−	0.616471i	$-0.211438\pi$
$701$	4.12696e10	+	4.12696e10i	0.170906	+	0.170906i	−0.616471	+	0.787377i	$0.711438\pi$
$702$	7.68334e10	−	4.45168e10i	0.316374	−	0.183305i
$703$			4.28718e11i			1.75530i
$704$	1.35757e11	+	1.33285e11i	0.552677	+	0.542614i
$705$	4.95851e10			0.200722
$706$	−1.09674e11	−	1.89290e11i	−0.441452	−	0.761920i
$707$	4.46807e10	−	4.46807e10i	0.178831	−	0.178831i
$708$	−6.10702e10	+	1.06529e11i	−0.243050	+	0.423969i
$709$	1.18846e11	−	1.18846e11i	0.470327	−	0.470327i	−0.431693	−	0.902020i	$-0.642084\pi$
$709$	1.18846e11	−	1.18846e11i	0.470327	−	0.470327i	0.902020	+	0.431693i	$0.142084\pi$
$710$	−1.89246e11	−	5.03979e10i	−0.744721	−	0.198326i
$711$	4.25798e11			1.66619
$712$	1.18025e9	+	2.56911e11i	0.00459256	+	0.999682i
$713$			1.59933e9i			0.00618843i
$714$	1.33685e10	+	3.56014e9i	0.0514386	+	0.0136985i
$715$	−8.08477e10	−	8.08477e10i	−0.309345	−	0.309345i
$716$	4.56966e10	+	1.68476e11i	0.173873	+	0.641042i
$717$	−3.88145e10	−	3.88145e10i	−0.146865	−	0.146865i
$718$	−1.67949e11	−	2.89870e11i	−0.631945	−	1.09070i
$719$		−	3.55119e11i		−	1.32880i	−0.747379	−	0.664398i	$-0.768688\pi$
$719$		−	3.55119e11i		−	1.32880i	0.747379	−	0.664398i	$-0.231312\pi$
$720$	−5.52969e10	+	2.11546e11i	−0.205765	+	0.787180i
$721$	−1.16260e10			−0.0430218
$722$	−2.29735e11	+	1.33107e11i	−0.845430	+	0.489837i
$723$	1.26522e9	−	1.26522e9i	0.00463034	−	0.00463034i
$724$	−5.51891e10	−	2.03474e11i	−0.200863	−	0.740550i
$725$	3.42512e10	−	3.42512e10i	0.123972	−	0.123972i
$726$	−8.70485e9	+	3.26871e10i	−0.0313339	+	0.117660i
$727$	−2.25791e11			−0.808294			−0.404147	−	0.914694i	$-0.632432\pi$
$727$	−2.25791e11			−0.808294			−0.404147	+	0.914694i	$0.632432\pi$
$728$	2.26509e10	+	2.24437e10i	0.0806416	+	0.0799041i
$729$		−	1.37388e11i		−	0.486449i
$730$	−9.73293e10	+	3.65475e11i	−0.342730	+	1.28697i
$731$	−1.77653e11	−	1.77653e11i	−0.622161	−	0.622161i
$732$	−3.31933e10	+	5.79013e10i	−0.115613	+	0.201671i
$733$	−2.83874e11	−	2.83874e11i	−0.983354	−	0.983354i	0.0165096	−	0.999864i	$-0.494745\pi$
$733$	−2.83874e11	−	2.83874e11i	−0.983354	−	0.983354i	−0.999864	+	0.0165096i	$0.994745\pi$
$734$	2.03895e11	−	1.18135e11i	0.702461	−	0.407001i
$735$		−	7.70478e10i		−	0.264004i
$736$	−6.78717e8	+	1.19664e9i	−0.00231301	+	0.00407804i
$737$	−1.55717e11			−0.527796
$738$	−1.84274e11	−	3.18046e11i	−0.621209	−	1.07217i
$739$	3.51743e11	−	3.51743e11i	1.17936	−	1.17936i	0.199458	−	0.979906i	$-0.436082\pi$
$739$	3.51743e11	−	3.51743e11i	1.17936	−	1.17936i	0.979906	−	0.199458i	$-0.0639180\pi$
$740$	−2.91199e11	−	1.66937e11i	−0.971099	−	0.556706i
$741$	−5.74626e10	+	5.74626e10i	−0.190595	+	0.190595i
$742$	−6.11014e10	−	1.62718e10i	−0.201574	−	0.0536810i
$743$	−1.24601e11			−0.408852			−0.204426	−	0.978882i	$-0.565533\pi$
$743$	−1.24601e11			−0.408852			−0.204426	+	0.978882i	$0.565533\pi$
$744$	8.74267e10	+	8.66271e10i	0.285333	+	0.282724i
$745$		−	5.39995e10i		−	0.175293i
$746$	−1.81896e10	−	4.84404e9i	−0.0587310	−	0.0156406i
$747$	2.66077e11	+	2.66077e11i	0.854527	+	0.854527i
$748$	2.27133e11	−	6.16062e10i	0.725560	−	0.196797i
$749$	5.18919e10	+	5.18919e10i	0.164882	+	0.164882i
$750$	5.17658e10	+	8.93448e10i	0.163606	+	0.282374i
$751$		−	5.24482e11i		−	1.64881i	−0.565999	−	0.824406i	$-0.691509\pi$
$751$		−	5.24482e11i		−	1.64881i	0.565999	−	0.824406i	$-0.308491\pi$
$752$	−2.03002e11	+	1.18867e11i	−0.634788	+	0.371698i
$753$	1.22942e11			0.382401
$754$	−1.57590e11	+	9.13064e10i	−0.487576	+	0.282498i
$755$	−3.76960e11	+	3.76960e11i	−1.16013	+	1.16013i
$756$	−3.29781e10	+	8.94479e9i	−0.100957	+	0.0273831i
$757$	1.46134e11	−	1.46134e11i	0.445009	−	0.445009i	−0.448682	−	0.893691i	$-0.648106\pi$
$757$	1.46134e11	−	1.46134e11i	0.445009	−	0.445009i	0.893691	+	0.448682i	$0.148106\pi$
$758$	−1.54892e11	+	5.81627e11i	−0.469194	+	1.76184i
$759$	3.66723e8			0.00110502
$760$	−1.93235e9	−	4.20622e11i	−0.00579203	−	1.26078i
$761$		−	2.39090e11i		−	0.712889i	−0.934316	−	0.356445i	$-0.883989\pi$
$761$		−	2.39090e11i		−	0.712889i	0.934316	−	0.356445i	$-0.116011\pi$
$762$	5.15922e10	−	1.93731e11i	0.153026	−	0.574618i
$763$	2.11282e10	+	2.11282e10i	0.0623398	+	0.0623398i
$764$	−1.68270e11	−	9.64647e10i	−0.493893	−	0.283136i
$765$	1.91255e11	+	1.91255e11i	0.558427	+	0.558427i
$766$	5.24174e11	−	3.03703e11i	1.52251	−	0.882133i
$767$			3.50103e11i			1.01161i
$768$	2.86513e10	+	1.01917e11i	0.0823568	+	0.292956i
$769$	−3.11063e11			−0.889494			−0.444747	−	0.895656i	$-0.646706\pi$
$769$	−3.11063e11			−0.889494			−0.444747	+	0.895656i	$0.646706\pi$
$770$	2.20566e10	+	3.80684e10i	0.0627445	+	0.108293i
$771$	−8.82607e10	+	8.82607e10i	−0.249775	+	0.249775i
$772$	−2.49844e11	+	4.35820e11i	−0.703396	+	1.22698i
$773$	3.58977e11	−	3.58977e11i	1.00542	−	1.00542i	0.00543843	−	0.999985i	$-0.498269\pi$
$773$	3.58977e11	−	3.58977e11i	1.00542	−	1.00542i	0.999985	−	0.00543843i	$-0.00173111\pi$
$774$	2.85262e11	+	7.59677e10i	0.794840	+	0.211673i
$775$	−9.33269e10			−0.258702
$776$	−1.46652e11	+	6.73724e8i	−0.404429	+	0.00185796i
$777$		−	2.49537e10i		−	0.0684621i
$778$	5.56127e11	+	1.48102e11i	1.51794	+	0.404242i
$779$	5.00000e11	+	5.00000e11i	1.35775	+	1.35775i
$780$	−1.66553e10	−	6.14057e10i	−0.0449961	−	0.165894i
$781$	−1.75131e11	−	1.75131e11i	−0.470717	−	0.470717i
$782$	8.53140e8	+	1.47247e9i	0.00228136	+	0.00393749i
$783$		−	1.95168e11i		−	0.519231i
$784$	1.84702e11	+	3.15434e11i	0.488884	+	0.834920i
$785$	−1.23581e11			−0.325442
$786$	2.82089e10	−	1.63440e10i	0.0739087	−	0.0428222i
$787$	3.10851e10	−	3.10851e10i	0.0810314	−	0.0810314i	−0.665429	−	0.746461i	$-0.731752\pi$
$787$	3.10851e10	−	3.10851e10i	0.0810314	−	0.0810314i	0.746461	+	0.665429i	$0.231752\pi$
$788$	−1.69685e11	−	6.25602e11i	−0.440086	−	1.62253i
$789$	1.27655e11	−	1.27655e11i	0.329404	−	0.329404i
$790$	1.65034e11	−	6.19711e11i	0.423707	−	1.59104i
$791$	−4.03997e10			−0.103198
$792$	−1.94630e11	+	1.96427e11i	−0.494663	+	0.499229i
$793$			1.90290e11i			0.481198i
$794$	−4.49965e10	+	1.68964e11i	−0.113213	+	0.425120i
$795$	8.92123e10	+	8.92123e10i	0.223335	+	0.223335i
$796$	−1.07504e11	+	1.87526e11i	−0.267776	+	0.467099i
$797$	2.43680e11	+	2.43680e11i	0.603929	+	0.603929i	0.941353	−	0.337424i	$-0.109556\pi$
$797$	2.43680e11	+	2.43680e11i	0.603929	+	0.603929i	−0.337424	+	0.941353i	$0.609556\pi$
$798$	2.70572e10	−	1.56768e10i	0.0667223	−	0.0386585i
$799$			2.90996e11i			0.714003i
$800$	−6.98284e10	−	3.96057e10i	−0.170479	−	0.0966936i
$801$	−3.73416e11			−0.907115
$802$	1.99667e11	+	3.44614e11i	0.482625	+	0.832982i
$803$	−3.38217e11	+	3.38217e11i	−0.813454	+	0.813454i
$804$	−7.51750e10	−	4.30958e10i	−0.179907	−	0.103136i
$805$	−2.24962e8	+	2.24962e8i	−0.000535706	+	0.000535706i
$806$	3.39093e11	+	9.03034e10i	0.803486	+	0.213975i
$807$	−5.32899e9			−0.0125647
$808$	4.21008e11	−	4.24894e11i	0.987746	−	0.996863i
$809$			2.53549e11i			0.591928i	0.955199	+	0.295964i	$0.0956408\pi$
$809$			2.53549e11i			0.591928i	−0.955199	+	0.295964i	$0.904359\pi$
$810$	−2.72562e11	−	7.25856e10i	−0.633177	−	0.168620i
$811$	5.92925e11	+	5.92925e11i	1.37062	+	1.37062i	0.859526	+	0.511093i	$0.170759\pi$
$811$	5.92925e11	+	5.92925e11i	1.37062	+	1.37062i	0.511093	+	0.859526i	$0.329241\pi$
$812$	6.76399e10	−	1.83463e10i	0.155589	−	0.0422011i
$813$	5.52028e10	+	5.52028e10i	0.126357	+	0.126357i
$814$	−2.12808e11	−	3.67294e11i	−0.484719	−	0.836597i
$815$			1.62354e11i			0.367987i
$816$	1.26702e11	+	3.31192e10i	0.285774	+	0.0746998i
$817$	−5.67889e11			−1.27460
$818$	−8.65176e10	+	5.01278e10i	−0.193237	+	0.111961i
$819$	−3.27721e10	+	3.27721e10i	−0.0728399	+	0.0728399i
$820$	−5.34310e11	+	1.44923e11i	−1.18178	+	0.320540i
$821$	1.91503e11	−	1.91503e11i	0.421506	−	0.421506i	−0.464216	−	0.885722i	$-0.653664\pi$
$821$	1.91503e11	−	1.91503e11i	0.421506	−	0.421506i	0.885722	+	0.464216i	$0.153664\pi$
$822$	−1.42069e10	+	5.33475e10i	−0.0311180	+	0.116850i
$823$	−7.47989e11			−1.63041			−0.815203	−	0.579175i	$-0.803375\pi$
$823$	−7.47989e11			−1.63041			−0.815203	+	0.579175i	$0.803375\pi$
$824$	−1.10052e11	+	5.05583e8i	−0.238721	+	0.00109669i
$825$			2.13996e10i			0.0461946i
$826$	3.46688e10	−	1.30183e11i	0.0744763	−	0.279662i
$827$	−1.05211e11	−	1.05211e11i	−0.224926	−	0.224926i	0.585643	−	0.810569i	$-0.300842\pi$
$827$	−1.05211e11	−	1.05211e11i	−0.224926	−	0.224926i	−0.810569	+	0.585643i	$0.800842\pi$
$828$	−1.73473e9	−	9.94475e8i	−0.00369071	−	0.00211579i
$829$	−4.02073e11	−	4.02073e11i	−0.851307	−	0.851307i	0.138987	−	0.990294i	$-0.455615\pi$
$829$	−4.02073e11	−	4.02073e11i	−0.851307	−	0.851307i	−0.990294	+	0.138987i	$0.955615\pi$
$830$	4.90381e11	−	2.84123e11i	1.03329	−	0.598680i
$831$		−	2.53491e10i		−	0.0531568i
$832$	2.15391e11	+	2.11469e11i	0.449505	+	0.441320i
$833$	4.52164e11			0.939109
$834$	−5.87803e10	−	1.01451e11i	−0.121498	−	0.209698i
$835$	8.76336e10	−	8.76336e10i	0.180271	−	0.180271i
$836$	2.64563e11	−	4.61494e11i	0.541631	−	0.944803i
$837$	−2.65894e11	+	2.65894e11i	−0.541760	+	0.541760i
$838$	3.08111e11	+	8.20525e10i	0.624785	+	0.166386i
$839$	5.61152e10			0.113249			0.0566243	−	0.998396i	$-0.481966\pi$
$839$	5.61152e10			0.113249			0.0566243	+	0.998396i	$0.481966\pi$
$840$	1.12473e8	+	2.44825e10i	0.000225908	+	0.0491743i
$841$		−	9.99464e10i		−	0.199794i
$842$	−8.39100e10	−	2.23460e10i	−0.166942	−	0.0444581i
$843$	3.64299e10	+	3.64299e10i	0.0721352	+	0.0721352i
$844$	1.10081e10	+	4.05853e10i	0.0216942	+	0.0799833i
$845$	1.94980e11	+	1.94980e11i	0.382441	+	0.382441i
$846$	−1.71412e11	−	2.95848e11i	−0.334627	−	0.577546i
$847$		−	3.71121e10i		−	0.0721077i
$848$	−5.79098e11	−	1.51373e11i	−1.11987	−	0.292729i
$849$	6.15346e10			0.118437
$850$	−8.59241e10	+	4.97839e10i	−0.164604	+	0.0953704i
$851$	2.17050e9	−	2.17050e9i	0.00413848	−	0.00413848i
$852$	−3.60786e10	−	1.33016e11i	−0.0684686	−	0.252433i
$853$	8.83084e10	−	8.83084e10i	0.166804	−	0.166804i	−0.618769	−	0.785573i	$-0.712368\pi$
$853$	8.83084e10	−	8.83084e10i	0.166804	−	0.166804i	0.785573	+	0.618769i	$0.212368\pi$
$854$	1.88434e10	−	7.07577e10i	0.0354265	−	0.133028i
$855$	6.11368e11			1.14403
$856$	4.93470e11	+	4.88957e11i	0.919106	+	0.910700i
$857$			3.49188e11i			0.647345i	0.946169	+	0.323672i	$0.104918\pi$
$857$			3.49188e11i			0.647345i	−0.946169	+	0.323672i	$0.895082\pi$
$858$	2.07063e10	−	7.77532e10i	0.0382080	−	0.143473i
$859$	−2.35998e11	−	2.35998e11i	−0.433447	−	0.433447i	0.456352	−	0.889799i	$-0.349156\pi$
$859$	−2.35998e11	−	2.35998e11i	−0.433447	−	0.433447i	−0.889799	+	0.456352i	$0.849156\pi$
$860$	2.21128e11	−	3.85729e11i	0.404251	−	0.705161i
$861$	−2.91026e10	−	2.91026e10i	−0.0529566	−	0.0529566i
$862$	−4.93391e11	+	2.85868e11i	−0.893640	+	0.517769i
$863$		−	6.33136e11i		−	1.14144i	−0.821144	−	0.570721i	$-0.806664\pi$
$863$		−	6.33136e11i		−	1.14144i	0.821144	−	0.570721i	$-0.193336\pi$
$864$	−3.11784e11	+	8.61063e10i	−0.559499	+	0.154518i
$865$	1.68902e11			0.301696
$866$	−4.01135e11	−	6.92335e11i	−0.713212	−	1.23096i
$867$	−7.03631e9	+	7.03631e9i	−0.0124528	+	0.0124528i
$868$	−1.17147e11	−	6.71570e10i	−0.206372	−	0.118308i
$869$	5.73490e11	−	5.73490e11i	1.00565	−	1.00565i
$870$	−1.35129e11	−	3.59861e10i	−0.235870	−	0.0628141i
$871$	−2.47059e11			−0.429268
$872$	2.00920e11	+	1.99083e11i	0.347503	+	0.344325i
$873$		−	2.13157e11i		−	0.366980i
$874$	3.71705e9	+	9.89882e8i	0.00637019	+	0.00169644i
$875$	−8.01066e10	−	8.01066e10i	−0.136658	−	0.136658i
$876$	−2.56884e11	+	6.96757e10i	−0.436235	+	0.118322i
$877$	−6.28602e11	−	6.28602e11i	−1.06262	−	1.06262i	−0.997904	−	0.0647149i	$-0.979386\pi$
$877$	−6.28602e11	−	6.28602e11i	−1.06262	−	1.06262i	−0.0647149	−	0.997904i	$-0.520614\pi$
$878$	4.46355e11	+	7.70383e11i	0.751108	+	1.29637i
$879$			3.46651e10i			0.0580681i
$880$	2.10445e11	+	3.59400e11i	0.350920	+	0.599304i
$881$	−3.33700e11			−0.553927			−0.276964	−	0.960880i	$-0.589328\pi$
$881$	−3.33700e11			−0.553927			−0.276964	+	0.960880i	$0.589328\pi$
$882$	−4.59703e11	+	2.66349e11i	−0.759631	+	0.440126i
$883$	−8.20284e10	+	8.20284e10i	−0.134934	+	0.134934i	−0.771348	−	0.636414i	$-0.780417\pi$
$883$	−8.20284e10	+	8.20284e10i	−0.134934	+	0.134934i	0.636414	+	0.771348i	$0.280417\pi$
$884$	3.60367e11	−	9.77439e10i	0.590114	−	0.160059i
$885$	−1.90076e11	+	1.90076e11i	−0.309851	+	0.309851i
$886$	4.64631e10	−	1.74471e11i	0.0754003	−	0.283131i
$887$	−9.30554e10			−0.150331			−0.0751653	−	0.997171i	$-0.523948\pi$
$887$	−9.30554e10			−0.150331			−0.0751653	+	0.997171i	$0.523948\pi$
$888$	−1.08517e9	−	2.36213e11i	−0.00174520	−	0.379885i
$889$			2.19957e11i			0.352152i
$890$	−1.44732e11	+	5.43473e11i	−0.230677	+	0.866200i
$891$	−2.52233e11	−	2.52233e11i	−0.400213	−	0.400213i
$892$	8.36437e10	+	4.79507e10i	0.132122	+	0.0757418i
$893$	4.65102e11	+	4.65102e11i	0.731379	+	0.731379i
$894$	3.28814e10	−	1.90513e10i	0.0514754	−	0.0298246i
$895$			3.82141e11i			0.595569i
$896$	−5.91507e10	−	9.99619e10i	−0.0917757	−	0.155097i
$897$	5.81840e8			0.000898739
$898$	5.09312e11	+	8.79043e11i	0.783211	+	1.35178i
$899$	5.45364e11	−	5.45364e11i	0.834925	−	0.834925i
$900$	5.80313e10	−	1.01228e11i	0.0884489	−	0.154287i
$901$	−5.23553e11	+	5.23553e11i	−0.794440	+	0.794440i
$902$	−6.76554e11	−	1.80172e11i	−1.02206	−	0.272183i
$903$	3.30541e10			0.0497136
$904$	−3.82427e11	+	1.75688e9i	−0.572631	+	0.00263068i
$905$		−	4.61523e11i		−	0.688017i
$906$	−3.62532e11	−	9.65454e10i	−0.538064	−	0.143291i
$907$	−3.20736e11	−	3.20736e11i	−0.473934	−	0.473934i	0.429251	−	0.903185i	$-0.358778\pi$
$907$	−3.20736e11	−	3.20736e11i	−0.473934	−	0.473934i	−0.903185	+	0.429251i	$0.858778\pi$
$908$	1.38726e10	+	5.11462e10i	0.0204087	+	0.0752437i
$909$	6.14753e11	+	6.14753e11i	0.900420	+	0.900420i
$910$	3.49948e10	+	6.03990e10i	0.0510315	+	0.0880774i
$911$		−	6.32265e11i		−	0.917963i	−0.888446	−	0.458982i	$-0.848214\pi$
$911$		−	6.32265e11i		−	0.917963i	0.888446	−	0.458982i	$-0.151786\pi$
$912$	2.55444e11	−	1.49574e11i	0.369246	−	0.216211i
$913$	7.16738e11			1.03152
$914$	4.72988e11	−	2.74046e11i	0.677744	−	0.392680i
$915$	−1.03311e11	+	1.03311e11i	−0.147388	+	0.147388i
$916$	3.44366e11	+	1.26963e12i	0.489146	+	1.80341i
$917$	−2.52921e10	+	2.52921e10i	−0.0357691	+	0.0357691i
$918$	−1.02966e11	+	3.86640e11i	−0.144985	+	0.544423i
$919$	3.80170e11			0.532986			0.266493	−	0.963837i	$-0.414135\pi$
$919$	3.80170e11			0.532986			0.266493	+	0.963837i	$0.414135\pi$
$920$	−2.11973e9	+	2.13930e9i	−0.00295889	+	0.00298620i
$921$			1.54044e11i			0.214095i
$922$	1.95534e8	−	7.34239e8i	0.000270582	−	0.00101605i
$923$	−2.77862e11	−	2.77862e11i	−0.382844	−	0.382844i
$924$	−1.53990e10	+	2.68614e10i	−0.0211253	+	0.0368503i
$925$	1.26657e11	+	1.26657e11i	0.173006	+	0.173006i
$926$	−9.82033e11	+	5.68984e11i	−1.33562	+	0.773848i
$927$		−	1.59960e11i		−	0.216616i
$928$	6.39487e11	−	1.76609e11i	0.862263	−	0.238134i
$929$	4.64783e11			0.624003			0.312002	−	0.950082i	$-0.399001\pi$
$929$	4.64783e11			0.624003			0.312002	+	0.950082i	$0.399001\pi$
$930$	1.35071e11	+	2.33125e11i	0.180564	+	0.311643i
$931$	7.22699e11	−	7.22699e11i	0.961963	−	0.961963i
$932$	6.94058e11	+	3.97886e11i	0.919883	+	0.527345i
$933$	1.81206e11	−	1.81206e11i	0.239136	−	0.239136i
$934$	−7.06530e11	−	1.88155e11i	−0.928417	−	0.247245i
$935$	5.15187e11			0.674090
$936$	−3.08799e11	+	3.11649e11i	−0.402320	+	0.406034i
$937$			1.25511e12i			1.62826i	0.580684	+	0.814129i	$0.302785\pi$
$937$			1.25511e12i			1.62826i	−0.580684	+	0.814129i	$0.697215\pi$
$938$	9.18669e10	+	2.44650e10i	0.118672	+	0.0316033i
$939$	5.83726e10	+	5.83726e10i	0.0750838	+	0.0750838i
$940$	−4.97017e11	+	1.34808e11i	−0.636591	+	0.172665i
$941$	−1.49937e11	−	1.49937e11i	−0.191228	−	0.191228i	0.604999	−	0.796226i	$-0.293174\pi$
$941$	−1.49937e11	−	1.49937e11i	−0.191228	−	0.191228i	−0.796226	+	0.604999i	$0.793174\pi$
$942$	−4.36000e10	−	7.52511e10i	−0.0553711	−	0.0955673i
$943$		−	5.06276e9i		−	0.00640237i
$944$	3.22516e11	−	1.23383e12i	0.406128	−	1.55370i
$945$	−7.48015e10			−0.0937957
$946$	4.86526e11	−	2.81890e11i	0.607493	−	0.351978i
$947$	1.85742e11	−	1.85742e11i	0.230946	−	0.230946i	−0.582141	−	0.813088i	$-0.697785\pi$
$947$	1.85742e11	−	1.85742e11i	0.230946	−	0.230946i	0.813088	+	0.582141i	$0.197785\pi$
$948$	4.35579e11	−	1.18144e11i	0.539304	−	0.146278i
$949$	−5.36612e11	+	5.36612e11i	−0.661600	+	0.661600i
$950$	−5.77633e10	+	2.16904e11i	−0.0709182	+	0.266301i
$951$	2.71150e11			0.331504
$952$	−1.43678e11	+	6.60061e8i	−0.174922	+	0.000803593i
$953$		−	5.05408e11i		−	0.612731i	−0.951914	−	0.306366i	$-0.900887\pi$
$953$		−	5.05408e11i		−	0.612731i	0.951914	−	0.306366i	$-0.0991130\pi$
$954$	2.23881e11	−	8.40682e11i	0.270286	−	1.01494i
$955$	−3.00238e11	−	3.00238e11i	−0.360954	−	0.360954i
$956$	4.94584e11	+	2.83532e11i	0.592118	+	0.339446i
$957$	−1.25051e11	−	1.25051e11i	−0.149086	−	0.149086i
$958$	−1.50473e11	+	8.71833e10i	−0.178648	+	0.103507i
$959$		−	6.05694e10i		−	0.0716108i
$960$	2.12936e9	+	2.31748e11i	0.00250705	+	0.272855i
$961$	−6.33103e11			−0.742303
$962$	−3.37639e11	−	5.82746e11i	−0.394233	−	0.680423i
$963$	−7.13971e11	+	7.13971e11i	−0.830186	+	0.830186i
$964$	−9.24218e9	+	1.61217e10i	−0.0107020	+	0.0186683i
$965$	−7.77618e11	+	7.77618e11i	−0.896720	+	0.896720i
$966$	−2.16352e8	−	5.76164e7i	−0.000248458	−	6.61664e-5i
$967$	1.26110e10			0.0144226			0.00721131	−	0.999974i	$-0.497705\pi$
$967$	1.26110e10			0.0144226			0.00721131	+	0.999974i	$0.497705\pi$
$968$	−1.61391e9	−	3.51306e11i	−0.00183813	−	0.400114i
$969$		−	3.66170e11i		−	0.415324i
$970$	−3.10231e11	−	8.26173e10i	−0.350428	−	0.0933220i
$971$	−1.00158e11	−	1.00158e11i	−0.112670	−	0.112670i	0.648524	−	0.761194i	$-0.275387\pi$
$971$	−1.00158e11	−	1.00158e11i	−0.112670	−	0.112670i	−0.761194	+	0.648524i	$0.775387\pi$
$972$	−1.87592e11	−	6.91623e11i	−0.210160	−	0.774827i
$973$	9.09615e10	+	9.09615e10i	0.101486	+	0.101486i
$974$	3.59316e10	+	6.20158e10i	0.0399246	+	0.0689076i
$975$			3.39525e10i			0.0375711i
$976$	1.75296e11	−	6.70618e11i	0.193185	−	0.739054i
$977$	5.25120e11			0.576342			0.288171	−	0.957579i	$-0.406953\pi$
$977$	5.25120e11			0.576342			0.288171	+	0.957579i	$0.406953\pi$
$978$	−9.88606e10	+	5.72792e10i	−0.108061	+	0.0626097i
$979$	−5.02939e11	+	5.02939e11i	−0.547500	+	0.547500i
$980$	2.09472e11	+	7.72290e11i	0.227102	+	0.837291i
$981$	−2.90699e11	+	2.90699e11i	−0.313883	+	0.313883i
$982$	2.92528e11	−	1.09845e12i	0.314573	−	1.18123i
$983$	−1.37083e12			−1.46815			−0.734073	−	0.679071i	$-0.762383\pi$
$983$	−1.37083e12			−1.46815			−0.734073	+	0.679071i	$0.762383\pi$
$984$	−2.76754e11	−	2.74222e11i	−0.295198	−	0.292498i
$985$		−	1.41900e12i		−	1.50743i
$986$	2.11188e11	−	7.93022e11i	0.223441	−	0.839030i
$987$	−2.70714e10	−	2.70714e10i	−0.0285261	−	0.0285261i
$988$	4.19753e11	−	7.32203e11i	0.440520	−	0.768429i
$989$	2.87509e9	+	2.87509e9i	0.00300515	+	0.00300515i
$990$	−5.23776e11	+	3.03473e11i	−0.545261	+	0.315921i
$991$			1.45882e12i			1.51254i	0.654262	+	0.756268i	$0.272979\pi$
$991$			1.45882e12i			1.51254i	−0.654262	+	0.756268i	$0.727021\pi$
$992$	−1.11184e12	−	6.30620e11i	−1.14814	−	0.651210i
$993$	−1.12367e11			−0.115569
$994$	7.58054e10	+	1.30836e11i	0.0776524	+	0.134023i
$995$	−3.34596e11	+	3.34596e11i	−0.341372	+	0.341372i
$996$	3.46017e11	+	1.98363e11i	0.351609	+	0.201568i
$997$	−1.92677e11	+	1.92677e11i	−0.195007	+	0.195007i	−0.797856	−	0.602849i	$-0.794032\pi$
$997$	−1.92677e11	+	1.92677e11i	−0.195007	+	0.195007i	0.602849	+	0.797856i	$0.294032\pi$
$998$	8.85348e11	+	2.35776e11i	0.892467	+	0.237672i
$999$	7.21705e11			0.724599

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.9.f.a.3.5	✓	30
4.3	odd	2		64.9.f.a.47.7		30
8.3	odd	2		128.9.f.a.95.9		30
8.5	even	2		128.9.f.b.95.7		30
16.3	odd	4		128.9.f.b.31.7		30
16.5	even	4		64.9.f.a.15.7		30
16.11	odd	4	inner	16.9.f.a.11.5	yes	30
16.13	even	4		128.9.f.a.31.9		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.9.f.a.3.5	✓	30	1.1	even	1	trivial
16.9.f.a.11.5	yes	30	16.11	odd	4	inner
64.9.f.a.15.7		30	16.5	even	4
64.9.f.a.47.7		30	4.3	odd	2
128.9.f.a.31.9		30	16.13	even	4
128.9.f.a.95.9		30	8.3	odd	2
128.9.f.b.31.7		30	16.3	odd	4
128.9.f.b.95.7		30	8.5	even	2

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.02121 - 13.8441i) q^{2} +(17.4297 - 17.4297i) q^{3} +(-127.320 + 222.093i) q^{4} +(-396.274 + 396.274i) q^{5} +(-381.106 - 101.492i) q^{6} +432.698 q^{7} +(4095.96 - 18.8169i) q^{8} +5953.41i q^{9} +O(q^{10})\)	\(q+(-8.02121 - 13.8441i) q^{2} +(17.4297 - 17.4297i) q^{3} +(-127.320 + 222.093i) q^{4} +(-396.274 + 396.274i) q^{5} +(-381.106 - 101.492i) q^{6} +432.698 q^{7} +(4095.96 - 18.8169i) q^{8} +5953.41i q^{9} +(8664.66 + 2307.47i) q^{10} +(8018.41 + 8018.41i) q^{11} +(1651.87 + 6090.18i) q^{12} +(12722.0 + 12722.0i) q^{13} +(-3470.76 - 5990.33i) q^{14} +13813.9i q^{15} +(-33115.0 - 56554.1i) q^{16} -81068.2 q^{17} +(82419.9 - 47753.6i) q^{18} +(-129572. + 129572. i) q^{19} +(-37556.1 - 138464. i) q^{20} +(7541.79 - 7541.79i) q^{21} +(46690.7 - 175325. i) q^{22} +1311.99 q^{23} +(71063.3 - 71719.2i) q^{24} +76559.4i q^{25} +(74079.0 - 278170. i) q^{26} +(218122. + 218122. i) q^{27} +(-55091.3 + 96099.4i) q^{28} +(-447381. - 447381. i) q^{29} +(191241. - 110804. i) q^{30} +1.21901e6i q^{31} +(-517320. + 912081. i) q^{32} +279517. q^{33} +(650265. + 1.12232e6i) q^{34} +(-171467. + 171467. i) q^{35} +(-1.32221e6 - 757991. i) q^{36} +(1.65436e6 - 1.65436e6i) q^{37} +(2.83314e6 + 754490. i) q^{38} +443479. q^{39} +(-1.61566e6 + 1.63058e6i) q^{40} -3.85885e6i q^{41} +(-164904. - 43915.3i) q^{42} +(2.19140e6 + 2.19140e6i) q^{43} +(-2.80175e6 + 759930. i) q^{44} +(-2.35918e6 - 2.35918e6i) q^{45} +(-10523.7 - 18163.3i) q^{46} -3.58952e6i q^{47} +(-1.56290e6 - 408535. i) q^{48} -5.57757e6 q^{49} +(1.05990e6 - 614099. i) q^{50} +(-1.41299e6 + 1.41299e6i) q^{51} +(-4.44523e6 + 1.20570e6i) q^{52} +(6.45817e6 - 6.45817e6i) q^{53} +(1.27011e6 - 4.76932e6i) q^{54} -6.35497e6 q^{55} +(1.77231e6 - 8142.04i) q^{56} +4.51681e6i q^{57} +(-2.60507e6 + 9.78215e6i) q^{58} +(1.37598e7 + 1.37598e7i) q^{59} +(-3.06797e6 - 1.75879e6i) q^{60} +(7.47881e6 + 7.47881e6i) q^{61} +(1.68762e7 - 9.77796e6i) q^{62} +2.57603e6i q^{63} +(1.67765e7 - 154146. i) q^{64} -1.00827e7 q^{65} +(-2.24206e6 - 3.86967e6i) q^{66} +(-9.70997e6 + 9.70997e6i) q^{67} +(1.03216e7 - 1.80047e7i) q^{68} +(22867.5 - 22867.5i) q^{69} +(3.74918e6 + 998440. i) q^{70} -2.18411e7 q^{71} +(112025. + 2.43849e7i) q^{72} +4.21800e7i q^{73} +(-3.61731e7 - 9.63321e6i) q^{74} +(1.33441e6 + 1.33441e6i) q^{75} +(-1.22800e7 - 4.52743e7i) q^{76} +(3.46955e6 + 3.46955e6i) q^{77} +(-3.55724e6 - 6.13959e6i) q^{78} -7.15216e7i q^{79} +(3.55335e7 + 9.28827e6i) q^{80} -3.14567e7 q^{81} +(-5.34224e7 + 3.09526e7i) q^{82} +(4.46933e7 - 4.46933e7i) q^{83} +(714759. + 2.63521e6i) q^{84} +(3.21252e7 - 3.21252e7i) q^{85} +(1.27604e7 - 4.79157e7i) q^{86} -1.55954e7 q^{87} +(3.29940e7 + 3.26922e7i) q^{88} +6.27230e7i q^{89} +(-1.37373e7 + 5.15843e7i) q^{90} +(5.50477e6 + 5.50477e6i) q^{91} +(-167043. + 291384. i) q^{92} +(2.12470e7 + 2.12470e7i) q^{93} +(-4.96938e7 + 2.87923e7i) q^{94} -1.02692e8i q^{95} +(6.88057e6 + 2.49140e7i) q^{96} -3.58042e7 q^{97} +(4.47389e7 + 7.72167e7i) q^{98} +(-4.77369e7 + 4.77369e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8}+O(q^{10}) \) 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8	\( 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8} - 1860 q^{10} - 19778 q^{11} + 14068 q^{12} - 2 q^{13} - 58900 q^{14} + 245336 q^{16} - 4 q^{17} - 223730 q^{18} + 167550 q^{19} - 135380 q^{20} - 13124 q^{21} + 985700 q^{22} - 845572 q^{23} - 800592 q^{24} - 184760 q^{26} + 38656 q^{27} + 94136 q^{28} + 1066174 q^{29} + 1881700 q^{30} - 3395192 q^{32} - 4 q^{33} + 1634900 q^{34} + 426620 q^{35} + 1877324 q^{36} + 2360254 q^{37} - 3010352 q^{38} - 7650052 q^{39} + 3256936 q^{40} - 3731304 q^{42} + 6314814 q^{43} - 10360940 q^{44} + 794370 q^{45} + 1510780 q^{46} + 4591848 q^{48} + 14823770 q^{49} + 14752710 q^{50} - 28969860 q^{51} + 4335652 q^{52} + 2679358 q^{53} + 18667040 q^{54} + 46326780 q^{55} - 36346408 q^{56} - 1034696 q^{58} - 46004162 q^{59} - 20687200 q^{60} - 24476034 q^{61} - 64043472 q^{62} + 50827456 q^{64} - 14970820 q^{65} + 65035780 q^{66} + 59474558 q^{67} + 74339312 q^{68} + 8623420 q^{69} + 39082496 q^{70} - 79832068 q^{71} + 929812 q^{72} - 168043460 q^{74} + 88519490 q^{75} - 166219388 q^{76} + 35952572 q^{77} + 5059788 q^{78} - 12904856 q^{80} - 66961570 q^{81} + 261305296 q^{82} - 34471682 q^{83} + 456781480 q^{84} - 107741252 q^{85} + 9841444 q^{86} + 149712636 q^{87} - 173775752 q^{88} - 650366536 q^{90} - 76429060 q^{91} - 449169832 q^{92} + 138269056 q^{93} - 239278032 q^{94} + 378359728 q^{96} - 4 q^{97} + 630040554 q^{98} + 184838270 q^{99}+O(q^{100}) \) 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8 - 1860 * q^10 - 19778 * q^11 + 14068 * q^12 - 2 * q^13 - 58900 * q^14 + 245336 * q^16 - 4 * q^17 - 223730 * q^18 + 167550 * q^19 - 135380 * q^20 - 13124 * q^21 + 985700 * q^22 - 845572 * q^23 - 800592 * q^24 - 184760 * q^26 + 38656 * q^27 + 94136 * q^28 + 1066174 * q^29 + 1881700 * q^30 - 3395192 * q^32 - 4 * q^33 + 1634900 * q^34 + 426620 * q^35 + 1877324 * q^36 + 2360254 * q^37 - 3010352 * q^38 - 7650052 * q^39 + 3256936 * q^40 - 3731304 * q^42 + 6314814 * q^43 - 10360940 * q^44 + 794370 * q^45 + 1510780 * q^46 + 4591848 * q^48 + 14823770 * q^49 + 14752710 * q^50 - 28969860 * q^51 + 4335652 * q^52 + 2679358 * q^53 + 18667040 * q^54 + 46326780 * q^55 - 36346408 * q^56 - 1034696 * q^58 - 46004162 * q^59 - 20687200 * q^60 - 24476034 * q^61 - 64043472 * q^62 + 50827456 * q^64 - 14970820 * q^65 + 65035780 * q^66 + 59474558 * q^67 + 74339312 * q^68 + 8623420 * q^69 + 39082496 * q^70 - 79832068 * q^71 + 929812 * q^72 - 168043460 * q^74 + 88519490 * q^75 - 166219388 * q^76 + 35952572 * q^77 + 5059788 * q^78 - 12904856 * q^80 - 66961570 * q^81 + 261305296 * q^82 - 34471682 * q^83 + 456781480 * q^84 - 107741252 * q^85 + 9841444 * q^86 + 149712636 * q^87 - 173775752 * q^88 - 650366536 * q^90 - 76429060 * q^91 - 449169832 * q^92 + 138269056 * q^93 - 239278032 * q^94 + 378359728 * q^96 - 4 * q^97 + 630040554 * q^98 + 184838270 * q^99

Introduction

L-functions

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