LMFDB - Embedded newform 29.9.c.a.12.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,9,Mod(12,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("29.12");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	29.c (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:	$11.8139796918$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.16
Character	$\chi$	$=$	29.12
Dual form			29.9.c.a.17.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(17.5030 + 17.5030i) q^{2} +(-100.063 - 100.063i) q^{3} +356.708i q^{4} +183.024i q^{5} -3502.79i q^{6} +3415.09 q^{7} +(-1762.69 + 1762.69i) q^{8} +13464.1i q^{9} +O(q^{10})$	\(q+(17.5030 + 17.5030i) q^{2} +(-100.063 - 100.063i) q^{3} +356.708i q^{4} +183.024i q^{5} -3502.79i q^{6} +3415.09 q^{7} +(-1762.69 + 1762.69i) q^{8} +13464.1i q^{9} +(-3203.47 + 3203.47i) q^{10} +(19251.1 + 19251.1i) q^{11} +(35693.1 - 35693.1i) q^{12} -39089.7i q^{13} +(59774.3 + 59774.3i) q^{14} +(18313.9 - 18313.9i) q^{15} +29612.7 q^{16} +(26206.1 + 26206.1i) q^{17} +(-235661. + 235661. i) q^{18} +(-36798.6 - 36798.6i) q^{19} -65286.2 q^{20} +(-341724. - 341724. i) q^{21} +673904. i q^{22} -42044.3 q^{23} +352758. q^{24} +357127. q^{25} +(684185. - 684185. i) q^{26} +(690741. - 690741. i) q^{27} +1.21819e6i q^{28} +(-588008. + 393056. i) q^{29} +641096. q^{30} +(-189937. - 189937. i) q^{31} +(969558. + 969558. i) q^{32} -3.85264e6i q^{33} +917371. i q^{34} +625045. i q^{35} -4.80274e6 q^{36} +(868404. - 868404. i) q^{37} -1.28817e6i q^{38} +(-3.91142e6 + 3.91142e6i) q^{39} +(-322615. - 322615. i) q^{40} +(-790709. + 790709. i) q^{41} -1.19624e7i q^{42} +(2.02106e6 + 2.02106e6i) q^{43} +(-6.86704e6 + 6.86704e6i) q^{44} -2.46426e6 q^{45} +(-735900. - 735900. i) q^{46} +(1.48070e6 - 1.48070e6i) q^{47} +(-2.96313e6 - 2.96313e6i) q^{48} +5.89807e6 q^{49} +(6.25078e6 + 6.25078e6i) q^{50} -5.24451e6i q^{51} +1.39436e7 q^{52} +3.55690e6 q^{53} +2.41800e7 q^{54} +(-3.52343e6 + 3.52343e6i) q^{55} +(-6.01974e6 + 6.01974e6i) q^{56} +7.36433e6i q^{57} +(-1.71715e7 - 3.41222e6i) q^{58} -2.31564e7 q^{59} +(6.53272e6 + 6.53272e6i) q^{60} +(-4.46842e6 - 4.46842e6i) q^{61} -6.64893e6i q^{62} +4.59811e7i q^{63} +2.63594e7i q^{64} +7.15436e6 q^{65} +(6.74327e7 - 6.74327e7i) q^{66} -3.52505e7i q^{67} +(-9.34794e6 + 9.34794e6i) q^{68} +(4.20707e6 + 4.20707e6i) q^{69} +(-1.09402e7 + 1.09402e7i) q^{70} +2.36943e7i q^{71} +(-2.37330e7 - 2.37330e7i) q^{72} +(-2.39041e7 + 2.39041e7i) q^{73} +3.03993e7 q^{74} +(-3.57351e7 - 3.57351e7i) q^{75} +(1.31263e7 - 1.31263e7i) q^{76} +(6.57445e7 + 6.57445e7i) q^{77} -1.36923e8 q^{78} +(-7.43977e6 - 7.43977e6i) q^{79} +5.41985e6i q^{80} -4.98969e7 q^{81} -2.76795e7 q^{82} -2.88404e7 q^{83} +(1.21895e8 - 1.21895e8i) q^{84} +(-4.79636e6 + 4.79636e6i) q^{85} +7.07492e7i q^{86} +(9.81679e7 + 1.95073e7i) q^{87} -6.78675e7 q^{88} +(-104009. - 104009. i) q^{89} +(-4.31318e7 - 4.31318e7i) q^{90} -1.33495e8i q^{91} -1.49975e7i q^{92} +3.80113e7i q^{93} +5.18333e7 q^{94} +(6.73504e6 - 6.73504e6i) q^{95} -1.94033e8i q^{96} +(8.70674e7 - 8.70674e7i) q^{97} +(1.03234e8 + 1.03234e8i) q^{98} +(-2.59199e8 + 2.59199e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8}+O(q^{10}) $ 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8} + 15870 q^{10} - 8390 q^{11} + 5022 q^{12} + 12728 q^{14} - 35530 q^{15} - 245912 q^{16} + 76234 q^{17} - 465022 q^{18} - 164488 q^{19} + 4092 q^{20} - 514620 q^{21} + 733568 q^{23} - 482376 q^{24} - 1528354 q^{25} + 1405470 q^{26} - 1279754 q^{27} + 1420996 q^{29} + 3659852 q^{30} + 291062 q^{31} + 1592134 q^{32} - 10223688 q^{36} + 7994574 q^{37} - 309930 q^{39} + 9093994 q^{40} + 9561658 q^{41} - 5181022 q^{43} - 11400526 q^{44} + 9526060 q^{45} - 32561820 q^{46} + 5445034 q^{47} - 17683542 q^{48} + 45106458 q^{49} + 3122002 q^{50} + 56198616 q^{52} - 25331452 q^{53} - 42307016 q^{54} + 3037606 q^{55} - 25661184 q^{56} - 33846328 q^{58} + 27333008 q^{59} + 30592014 q^{60} - 49572406 q^{61} - 121974972 q^{65} + 133443354 q^{66} + 21192980 q^{68} - 28739184 q^{69} - 17976124 q^{70} - 186114192 q^{72} + 45787870 q^{73} + 91919252 q^{74} - 159074460 q^{75} + 243795016 q^{76} + 59851916 q^{77} + 163580208 q^{78} - 99827470 q^{79} - 75138586 q^{81} - 18178416 q^{82} - 177270160 q^{83} - 9436684 q^{84} + 156307616 q^{85} - 20584526 q^{87} + 563433236 q^{88} - 388451858 q^{89} + 306402752 q^{90} + 81569204 q^{94} - 44386260 q^{95} - 121157834 q^{97} - 129908712 q^{98} - 216447384 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8 + 15870 * q^10 - 8390 * q^11 + 5022 * q^12 + 12728 * q^14 - 35530 * q^15 - 245912 * q^16 + 76234 * q^17 - 465022 * q^18 - 164488 * q^19 + 4092 * q^20 - 514620 * q^21 + 733568 * q^23 - 482376 * q^24 - 1528354 * q^25 + 1405470 * q^26 - 1279754 * q^27 + 1420996 * q^29 + 3659852 * q^30 + 291062 * q^31 + 1592134 * q^32 - 10223688 * q^36 + 7994574 * q^37 - 309930 * q^39 + 9093994 * q^40 + 9561658 * q^41 - 5181022 * q^43 - 11400526 * q^44 + 9526060 * q^45 - 32561820 * q^46 + 5445034 * q^47 - 17683542 * q^48 + 45106458 * q^49 + 3122002 * q^50 + 56198616 * q^52 - 25331452 * q^53 - 42307016 * q^54 + 3037606 * q^55 - 25661184 * q^56 - 33846328 * q^58 + 27333008 * q^59 + 30592014 * q^60 - 49572406 * q^61 - 121974972 * q^65 + 133443354 * q^66 + 21192980 * q^68 - 28739184 * q^69 - 17976124 * q^70 - 186114192 * q^72 + 45787870 * q^73 + 91919252 * q^74 - 159074460 * q^75 + 243795016 * q^76 + 59851916 * q^77 + 163580208 * q^78 - 99827470 * q^79 - 75138586 * q^81 - 18178416 * q^82 - 177270160 * q^83 - 9436684 * q^84 + 156307616 * q^85 - 20584526 * q^87 + 563433236 * q^88 - 388451858 * q^89 + 306402752 * q^90 + 81569204 * q^94 - 44386260 * q^95 - 121157834 * q^97 - 129908712 * q^98 - 216447384 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	17.5030	+	17.5030i	1.09394	+	1.09394i	0.995104	+	0.0988314i	$0.0315105\pi$
$2$	17.5030	+	17.5030i	1.09394	+	1.09394i	0.0988314	+	0.995104i	$0.468490\pi$
$3$	−100.063	−	100.063i	−1.23534	−	1.23534i	−0.961884	−	0.273458i	$-0.911833\pi$
$3$	−100.063	−	100.063i	−1.23534	−	1.23534i	−0.273458	−	0.961884i	$-0.588167\pi$
$4$			356.708i			1.39339i
$5$			183.024i			0.292839i	0.989223	+	0.146419i	$0.0467749\pi$
$5$			183.024i			0.292839i	−0.989223	+	0.146419i	$0.953225\pi$
$6$		−	3502.79i		−	2.70277i
$7$	3415.09			1.42236			0.711182	−	0.703008i	$-0.248160\pi$
$7$	3415.09			1.42236			0.711182	+	0.703008i	$0.248160\pi$
$8$	−1762.69	+	1762.69i	−0.430344	+	0.430344i
$9$			13464.1i			2.05214i
$10$	−3203.47	+	3203.47i	−0.320347	+	0.320347i
$11$	19251.1	+	19251.1i	1.31488	+	1.31488i	0.917772	+	0.397107i	$0.129986\pi$
$11$	19251.1	+	19251.1i	1.31488	+	1.31488i	0.397107	+	0.917772i	$0.370014\pi$
$12$	35693.1	−	35693.1i	1.72131	−	1.72131i
$13$		−	39089.7i		−	1.36864i	−0.729183	−	0.684319i	$-0.760100\pi$
$13$		−	39089.7i		−	1.36864i	0.729183	−	0.684319i	$-0.239900\pi$
$14$	59774.3	+	59774.3i	1.55597	+	1.55597i
$15$	18313.9	−	18313.9i	0.361756	−	0.361756i
$16$	29612.7			0.451854
$17$	26206.1	+	26206.1i	0.313767	+	0.313767i	0.846367	−	0.532600i	$-0.178785\pi$
$17$	26206.1	+	26206.1i	0.313767	+	0.313767i	−0.532600	+	0.846367i	$0.678785\pi$
$18$	−235661.	+	235661.i	−2.24491	+	2.24491i
$19$	−36798.6	−	36798.6i	−0.282369	−	0.282369i	0.551684	−	0.834053i	$-0.313985\pi$
$19$	−36798.6	−	36798.6i	−0.282369	−	0.282369i	−0.834053	+	0.551684i	$0.813985\pi$
$20$	−65286.2			−0.408039
$21$	−341724.	−	341724.i	−1.75710	−	1.75710i
$22$			673904.i			2.87679i
$23$	−42044.3			−0.150244			−0.0751218	−	0.997174i	$-0.523935\pi$
$23$	−42044.3			−0.150244			−0.0751218	+	0.997174i	$0.523935\pi$
$24$	352758.			1.06324
$25$	357127.			0.914245
$26$	684185.	−	684185.i	1.49720	−	1.49720i
$27$	690741.	−	690741.i	1.29975	−	1.29975i
$28$			1.21819e6i			1.98191i
$29$	−588008.	+	393056.i	−0.831364	+	0.555729i
$29$	−588008.	+	393056.i	−0.831364	+	0.555729i
$30$	641096.			0.791476
$31$	−189937.	−	189937.i	−0.205666	−	0.205666i	0.596756	−	0.802423i	$-0.296456\pi$
$31$	−189937.	−	189937.i	−0.205666	−	0.205666i	−0.802423	+	0.596756i	$0.796456\pi$
$32$	969558.	+	969558.i	0.924643	+	0.924643i
$33$		−	3.85264e6i		−	3.24865i
$34$			917371.i			0.686482i
$35$			625045.i			0.416523i
$36$	−4.80274e6			−2.85943
$37$	868404.	−	868404.i	0.463356	−	0.463356i	−0.436398	−	0.899754i	$-0.643746\pi$
$37$	868404.	−	868404.i	0.463356	−	0.463356i	0.899754	+	0.436398i	$0.143746\pi$
$38$		−	1.28817e6i		−	0.617786i
$39$	−3.91142e6	+	3.91142e6i	−1.69074	+	1.69074i
$40$	−322615.	−	322615.i	−0.126021	−	0.126021i
$41$	−790709.	+	790709.i	−0.279822	+	0.279822i	−0.833038	−	0.553216i	$-0.813400\pi$
$41$	−790709.	+	790709.i	−0.279822	+	0.279822i	0.553216	+	0.833038i	$0.313400\pi$
$42$		−	1.19624e7i		−	3.84432i
$43$	2.02106e6	+	2.02106e6i	0.591162	+	0.591162i	0.937945	−	0.346784i	$-0.112726\pi$
$43$	2.02106e6	+	2.02106e6i	0.591162	+	0.591162i	−0.346784	+	0.937945i	$0.612726\pi$
$44$	−6.86704e6	+	6.86704e6i	−1.83214	+	1.83214i
$45$	−2.46426e6			−0.600946
$46$	−735900.	−	735900.i	−0.164357	−	0.164357i
$47$	1.48070e6	−	1.48070e6i	0.303442	−	0.303442i	−0.538917	−	0.842359i	$-0.681166\pi$
$47$	1.48070e6	−	1.48070e6i	0.303442	−	0.303442i	0.842359	+	0.538917i	$0.181166\pi$
$48$	−2.96313e6	−	2.96313e6i	−0.558194	−	0.558194i
$49$	5.89807e6			1.02312
$50$	6.25078e6	+	6.25078e6i	1.00013	+	1.00013i
$51$		−	5.24451e6i		−	0.775219i
$52$	1.39436e7			1.90705
$53$	3.55690e6			0.450784			0.225392	−	0.974268i	$-0.427634\pi$
$53$	3.55690e6			0.450784			0.225392	+	0.974268i	$0.427634\pi$
$54$	2.41800e7			2.84369
$55$	−3.52343e6	+	3.52343e6i	−0.385048	+	0.385048i
$56$	−6.01974e6	+	6.01974e6i	−0.612105	+	0.612105i
$57$			7.36433e6i			0.697644i
$58$	−1.71715e7	−	3.41222e6i	−1.51739	−	0.301527i
$59$	−2.31564e7			−1.91101			−0.955505	−	0.294975i	$-0.904689\pi$
$59$	−2.31564e7			−1.91101			−0.955505	+	0.294975i	$0.904689\pi$
$60$	6.53272e6	+	6.53272e6i	0.504068	+	0.504068i
$61$	−4.46842e6	−	4.46842e6i	−0.322726	−	0.322726i	0.527086	−	0.849812i	$-0.323285\pi$
$61$	−4.46842e6	−	4.46842e6i	−0.322726	−	0.322726i	−0.849812	+	0.527086i	$0.823285\pi$
$62$		−	6.64893e6i		−	0.449972i
$63$			4.59811e7i			2.91889i
$64$			2.63594e7i			1.57115i
$65$	7.15436e6			0.400790
$66$	6.74327e7	−	6.74327e7i	3.55381	−	3.55381i
$67$		−	3.52505e7i		−	1.74931i	−0.484747	−	0.874654i	$-0.661088\pi$
$67$		−	3.52505e7i		−	1.74931i	0.484747	−	0.874654i	$-0.338912\pi$
$68$	−9.34794e6	+	9.34794e6i	−0.437200	+	0.437200i
$69$	4.20707e6	+	4.20707e6i	0.185602	+	0.185602i
$70$	−1.09402e7	+	1.09402e7i	−0.455650	+	0.455650i
$71$			2.36943e7i			0.932419i	0.884674	+	0.466209i	$0.154381\pi$
$71$			2.36943e7i			0.932419i	−0.884674	+	0.466209i	$0.845619\pi$
$72$	−2.37330e7	−	2.37330e7i	−0.883125	−	0.883125i
$73$	−2.39041e7	+	2.39041e7i	−0.841747	+	0.841747i	−0.989086	−	0.147339i	$-0.952929\pi$
$73$	−2.39041e7	+	2.39041e7i	−0.841747	+	0.841747i	0.147339	+	0.989086i	$0.452929\pi$
$74$	3.03993e7			1.01376
$75$	−3.57351e7	−	3.57351e7i	−1.12941	−	1.12941i
$76$	1.31263e7	−	1.31263e7i	0.393450	−	0.393450i
$77$	6.57445e7	+	6.57445e7i	1.87024	+	1.87024i
$78$	−1.36923e8			−3.69911
$79$	−7.43977e6	−	7.43977e6i	−0.191008	−	0.191008i	0.605124	−	0.796131i	$-0.293124\pi$
$79$	−7.43977e6	−	7.43977e6i	−0.191008	−	0.191008i	−0.796131	+	0.605124i	$0.793124\pi$
$80$			5.41985e6i			0.132320i
$81$	−4.98969e7			−1.15913
$82$	−2.76795e7			−0.612214
$83$	−2.88404e7			−0.607700			−0.303850	−	0.952720i	$-0.598272\pi$
$83$	−2.88404e7			−0.607700			−0.303850	+	0.952720i	$0.598272\pi$
$84$	1.21895e8	−	1.21895e8i	2.44833	−	2.44833i
$85$	−4.79636e6	+	4.79636e6i	−0.0918833	+	0.0918833i
$86$			7.07492e7i			1.29339i
$87$	9.81679e7	+	1.95073e7i	1.71353	+	0.340503i
$88$	−6.78675e7			−1.13170
$89$	−104009.	−	104009.i	−0.00165771	−	0.00165771i	0.706277	−	0.707935i	$-0.250373\pi$
$89$	−104009.	−	104009.i	−0.00165771	−	0.00165771i	−0.707935	+	0.706277i	$0.750373\pi$
$90$	−4.31318e7	−	4.31318e7i	−0.657396	−	0.657396i
$91$		−	1.33495e8i		−	1.94670i
$92$		−	1.49975e7i		−	0.209348i
$93$			3.80113e7i			0.508137i
$94$	5.18333e7			0.663892
$95$	6.73504e6	−	6.73504e6i	0.0826886	−	0.0826886i
$96$		−	1.94033e8i		−	2.28450i
$97$	8.70674e7	−	8.70674e7i	0.983487	−	0.983487i	−0.0163786	−	0.999866i	$-0.505214\pi$
$97$	8.70674e7	−	8.70674e7i	0.983487	−	0.983487i	0.999866	+	0.0163786i	$0.00521370\pi$
$98$	1.03234e8	+	1.03234e8i	1.11922	+	1.11922i
$99$	−2.59199e8	+	2.59199e8i	−2.69831	+	2.69831i
$100$			1.27390e8i			1.27390i
$101$	5.27024e7	+	5.27024e7i	0.506460	+	0.506460i	0.913438	−	0.406978i	$-0.133418\pi$
$101$	5.27024e7	+	5.27024e7i	0.506460	+	0.506460i	−0.406978	+	0.913438i	$0.633418\pi$
$102$	9.17946e7	−	9.17946e7i	0.848040	−	0.848040i
$103$	−9.83642e7			−0.873953			−0.436977	−	0.899473i	$-0.643951\pi$
$103$	−9.83642e7			−0.873953			−0.436977	+	0.899473i	$0.643951\pi$
$104$	6.89028e7	+	6.89028e7i	0.588984	+	0.588984i
$105$	6.25437e7	−	6.25437e7i	0.514549	−	0.514549i
$106$	6.22563e7	+	6.22563e7i	0.493128	+	0.493128i
$107$	−2.42970e8			−1.85361			−0.926805	−	0.375543i	$-0.877456\pi$
$107$	−2.42970e8			−1.85361			−0.926805	+	0.375543i	$0.877456\pi$
$108$	2.46393e8	+	2.46393e8i	1.81106	+	1.81106i
$109$		−	1.26703e8i		−	0.897599i	−0.893632	−	0.448799i	$-0.851852\pi$
$109$		−	1.26703e8i		−	0.897599i	0.893632	−	0.448799i	$-0.148148\pi$
$110$	−1.23341e8			−0.842435
$111$	−1.73790e8			−1.14481
$112$	1.01130e8			0.642701
$113$	1.44437e8	−	1.44437e8i	0.885862	−	0.885862i	−0.108261	−	0.994123i	$-0.534528\pi$
$113$	1.44437e8	−	1.44437e8i	0.885862	−	0.885862i	0.994123	+	0.108261i	$0.0345281\pi$
$114$	−1.28898e8	+	1.28898e8i	−0.763177	+	0.763177i
$115$		−	7.69513e6i		−	0.0439972i
$116$	−1.40206e8	−	2.09747e8i	−0.774347	−	1.15841i
$117$	5.26306e8			2.80863
$118$	−4.05306e8	−	4.05306e8i	−2.09052	−	2.09052i
$119$	8.94965e7	+	8.94965e7i	0.446291	+	0.446291i
$120$			6.45634e7i			0.311359i
$121$			5.26854e8i			2.45781i
$122$		−	1.56421e8i		−	0.706083i
$123$	1.58241e8			0.691351
$124$	6.77521e7	−	6.77521e7i	0.286574	−	0.286574i
$125$			1.36857e8i			0.560566i
$126$	−8.04806e8	+	8.04806e8i	−3.19307	+	3.19307i
$127$	−1.54963e8	−	1.54963e8i	−0.595681	−	0.595681i	0.343479	−	0.939160i	$-0.388394\pi$
$127$	−1.54963e8	−	1.54963e8i	−0.595681	−	0.595681i	−0.939160	+	0.343479i	$0.888394\pi$
$128$	−2.13162e8	+	2.13162e8i	−0.794089	+	0.794089i
$129$		−	4.04466e8i		−	1.46057i
$130$	1.25223e8	+	1.25223e8i	0.438439	+	0.438439i
$131$	1.90873e8	−	1.90873e8i	0.648126	−	0.648126i	−0.304414	−	0.952540i	$-0.598461\pi$
$131$	1.90873e8	−	1.90873e8i	0.648126	−	0.648126i	0.952540	+	0.304414i	$0.0984607\pi$
$132$	1.37427e9			4.52664
$133$	−1.25671e8	−	1.25671e8i	−0.401631	−	0.401631i
$134$	6.16989e8	−	6.16989e8i	1.91363	−	1.91363i
$135$	1.26422e8	+	1.26422e8i	0.380618	+	0.380618i
$136$	−9.23865e7			−0.270055
$137$	−2.06468e8	−	2.06468e8i	−0.586099	−	0.586099i	0.350474	−	0.936573i	$-0.386021\pi$
$137$	−2.06468e8	−	2.06468e8i	−0.586099	−	0.586099i	−0.936573	+	0.350474i	$0.886021\pi$
$138$			1.47272e8i			0.406074i
$139$	1.03078e8			0.276125			0.138063	−	0.990423i	$-0.455912\pi$
$139$	1.03078e8			0.276125			0.138063	+	0.990423i	$0.455912\pi$
$140$	−2.22959e8			−0.580380
$141$	−2.96326e8			−0.749709
$142$	−4.14721e8	+	4.14721e8i	−1.02001	+	1.02001i
$143$	7.52521e8	−	7.52521e8i	1.79959	−	1.79959i
$144$			3.98708e8i			0.927267i
$145$	−7.19389e7	−	1.07620e8i	−0.162739	−	0.243456i
$146$	−8.36787e8			−1.84163
$147$	−5.90177e8	−	5.90177e8i	−1.26390	−	1.26390i
$148$	3.09767e8	+	3.09767e8i	0.645636	+	0.645636i
$149$		−	2.38122e8i		−	0.483119i	−0.970386	−	0.241560i	$-0.922341\pi$
$149$		−	2.38122e8i		−	0.483119i	0.970386	−	0.241560i	$-0.0776589\pi$
$150$		−	1.25094e9i		−	2.47099i
$151$			5.59366e8i			1.07594i	0.842964	+	0.537970i	$0.180809\pi$
$151$			5.59366e8i			1.07594i	−0.842964	+	0.537970i	$0.819191\pi$
$152$	1.29729e8			0.243031
$153$	−3.52842e8	+	3.52842e8i	−0.643894	+	0.643894i
$154$			2.30145e9i			4.09184i
$155$	3.47631e7	−	3.47631e7i	0.0602271	−	0.0602271i
$156$	−1.39523e9	−	1.39523e9i	−2.35585	−	2.35585i
$157$	−5.25829e7	+	5.25829e7i	−0.0865457	+	0.0865457i	−0.749054	−	0.662509i	$-0.769492\pi$
$157$	−5.25829e7	+	5.25829e7i	−0.0865457	+	0.0865457i	0.662509	+	0.749054i	$0.269492\pi$
$158$		−	2.60436e8i		−	0.417900i
$159$	−3.55913e8	−	3.55913e8i	−0.556872	−	0.556872i
$160$	−1.77453e8	+	1.77453e8i	−0.270771	+	0.270771i
$161$	−1.43585e8			−0.213701
$162$	−8.73345e8	−	8.73345e8i	−1.26802	−	1.26802i
$163$	4.02789e8	−	4.02789e8i	0.570594	−	0.570594i	−0.361700	−	0.932294i	$-0.617804\pi$
$163$	4.02789e8	−	4.02789e8i	0.570594	−	0.570594i	0.932294	+	0.361700i	$0.117804\pi$
$164$	−2.82052e8	−	2.82052e8i	−0.389901	−	0.389901i
$165$	7.05127e8			0.951331
$166$	−5.04793e8	−	5.04793e8i	−0.664785	−	0.664785i
$167$			1.39613e9i			1.79498i	0.441033	+	0.897491i	$0.354612\pi$
$167$			1.39613e9i			1.79498i	−0.441033	+	0.897491i	$0.645388\pi$
$168$	1.20470e9			1.51232
$169$	−7.12271e8			−0.873169
$170$	−1.67901e8			−0.201029
$171$	4.95459e8	−	4.95459e8i	0.579460	−	0.579460i
$172$	−7.20929e8	+	7.20929e8i	−0.823719	+	0.823719i
$173$			2.31942e8i			0.258937i	0.991584	+	0.129469i	$0.0413272\pi$
$173$			2.31942e8i			0.258937i	−0.991584	+	0.129469i	$0.958673\pi$
$174$	1.37679e9	+	2.05967e9i	1.50201	+	2.24698i
$175$	1.21962e9			1.30039
$176$	5.70078e8	+	5.70078e8i	0.594133	+	0.594133i
$177$	2.31709e9	+	2.31709e9i	2.36075	+	2.36075i
$178$		−	3.64092e6i		−	0.00362686i
$179$		−	1.08210e9i		−	1.05404i	−0.849854	−	0.527019i	$-0.823310\pi$
$179$		−	1.08210e9i		−	1.05404i	0.849854	−	0.527019i	$-0.176690\pi$
$180$		−	8.79019e8i		−	0.837353i
$181$	−1.36536e9			−1.27213			−0.636065	−	0.771635i	$-0.719439\pi$
$181$	−1.36536e9			−1.27213			−0.636065	+	0.771635i	$0.719439\pi$
$182$	2.33656e9	−	2.33656e9i	2.12956	−	2.12956i
$183$			8.94243e8i			0.797354i
$184$	7.41109e7	−	7.41109e7i	0.0646563	−	0.0646563i
$185$	1.58939e8	+	1.58939e8i	0.135689	+	0.135689i
$186$	−6.65310e8	+	6.65310e8i	−0.555869	+	0.555869i
$187$			1.00900e9i			0.825132i
$188$	5.28178e8	+	5.28178e8i	0.422813	+	0.422813i
$189$	2.35895e9	−	2.35895e9i	1.84872	−	1.84872i
$190$	2.35766e8			0.180912
$191$	−5.10649e8	−	5.10649e8i	−0.383697	−	0.383697i	0.488735	−	0.872432i	$-0.337459\pi$
$191$	−5.10649e8	−	5.10649e8i	−0.383697	−	0.383697i	−0.872432	+	0.488735i	$0.837459\pi$
$192$	2.63760e9	−	2.63760e9i	1.94090	−	1.94090i
$193$	3.36245e8	+	3.36245e8i	0.242341	+	0.242341i	0.817818	−	0.575477i	$-0.195184\pi$
$193$	3.36245e8	+	3.36245e8i	0.242341	+	0.242341i	−0.575477	+	0.817818i	$0.695184\pi$
$194$	3.04788e9			2.15174
$195$	−7.15885e8	−	7.15885e8i	−0.495113	−	0.495113i
$196$			2.10389e9i			1.42560i
$197$	−1.12935e9			−0.749834			−0.374917	−	0.927058i	$-0.622329\pi$
$197$	−1.12935e9			−0.749834			−0.374917	+	0.927058i	$0.622329\pi$
$198$	−9.07350e9			−5.90356
$199$	−2.48297e8			−0.158328			−0.0791641	−	0.996862i	$-0.525225\pi$
$199$	−2.48297e8			−0.158328			−0.0791641	+	0.996862i	$0.525225\pi$
$200$	−6.29503e8	+	6.29503e8i	−0.393440	+	0.393440i
$201$	−3.52726e9	+	3.52726e9i	−2.16099	+	2.16099i
$202$			1.84490e9i			1.10807i
$203$	−2.00810e9	+	1.34233e9i	−1.18250	+	0.790448i
$204$	1.87076e9			1.08018
$205$	−1.44719e8	−	1.44719e8i	−0.0819427	−	0.0819427i
$206$	−1.72167e9	−	1.72167e9i	−0.956048	−	0.956048i
$207$		−	5.66088e8i		−	0.308321i
$208$		−	1.15755e9i		−	0.618424i
$209$		−	1.41683e9i		−	0.742561i
$210$	2.18940e9			1.12577
$211$	−1.88592e9	+	1.88592e9i	−0.951469	+	0.951469i	−0.998876	−	0.0474071i	$-0.984904\pi$
$211$	−1.88592e9	+	1.88592e9i	−0.951469	+	0.951469i	0.0474071	+	0.998876i	$0.484904\pi$
$212$			1.26877e9i			0.628118i
$213$	2.37092e9	−	2.37092e9i	1.15186	−	1.15186i
$214$	−4.25270e9	−	4.25270e9i	−2.02773	−	2.02773i
$215$	−3.69904e8	+	3.69904e8i	−0.173115	+	0.173115i
$216$			2.43512e9i			1.11868i
$217$	−6.48654e8	−	6.48654e8i	−0.292532	−	0.292532i
$218$	2.21769e9	−	2.21769e9i	0.981915	−	0.981915i
$219$	4.78383e9			2.07969
$220$	−1.25683e9	−	1.25683e9i	−0.536522	−	0.536522i
$221$	1.02439e9	−	1.02439e9i	0.429433	−	0.429433i
$222$	−3.04184e9	−	3.04184e9i	−1.25234	−	1.25234i
$223$	−3.95002e9			−1.59727			−0.798637	−	0.601813i	$-0.794445\pi$
$223$	−3.95002e9			−1.59727			−0.798637	+	0.601813i	$0.794445\pi$
$224$	3.31113e9	+	3.31113e9i	1.31518	+	1.31518i
$225$			4.80839e9i			1.87616i
$226$	5.05617e9			1.93815
$227$	2.61946e9			0.986527			0.493263	−	0.869880i	$-0.335804\pi$
$227$	2.61946e9			0.986527			0.493263	+	0.869880i	$0.335804\pi$
$228$	−2.62691e9			−0.972090
$229$	1.27720e9	−	1.27720e9i	0.464425	−	0.464425i	−0.435678	−	0.900103i	$-0.643491\pi$
$229$	1.27720e9	−	1.27720e9i	0.464425	−	0.464425i	0.900103	+	0.435678i	$0.143491\pi$
$230$	1.34688e8	−	1.34688e8i	0.0481301	−	0.0481301i
$231$		−	1.31571e10i		−	4.62076i
$232$	3.43638e8	−	1.72931e9i	0.118618	−	0.596926i
$233$	−4.19073e9			−1.42189			−0.710945	−	0.703248i	$-0.751732\pi$
$233$	−4.19073e9			−1.42189			−0.710945	+	0.703248i	$0.751732\pi$
$234$	9.21192e9	+	9.21192e9i	3.07247	+	3.07247i
$235$	2.71004e8	+	2.71004e8i	0.0888597	+	0.0888597i
$236$		−	8.26007e9i		−	2.66278i
$237$			1.48889e9i			0.471920i
$238$			3.13291e9i			0.976427i
$239$	−2.32017e9			−0.711095			−0.355548	−	0.934658i	$-0.615706\pi$
$239$	−2.32017e9			−0.711095			−0.355548	+	0.934658i	$0.615706\pi$
$240$	5.42324e8	−	5.42324e8i	0.163461	−	0.163461i
$241$			1.93706e9i			0.574215i	0.957898	+	0.287107i	$0.0926936\pi$
$241$			1.93706e9i			0.574215i	−0.957898	+	0.287107i	$0.907306\pi$
$242$	−9.22151e9	+	9.22151e9i	−2.68869	+	2.68869i
$243$	4.60871e8	+	4.60871e8i	0.132177	+	0.132177i
$244$	1.59392e9	−	1.59392e9i	0.449684	−	0.449684i
$245$			1.07949e9i			0.299609i
$246$	2.76969e9	+	2.76969e9i	0.756293	+	0.756293i
$247$	−1.43844e9	+	1.43844e9i	−0.386460	+	0.386460i
$248$	6.69600e8			0.177014
$249$	2.88585e9	+	2.88585e9i	0.750718	+	0.750718i
$250$	−2.39540e9	+	2.39540e9i	−0.613223	+	0.613223i
$251$	−2.29297e8	−	2.29297e8i	−0.0577702	−	0.0577702i	0.677631	−	0.735402i	$-0.263006\pi$
$251$	−2.29297e8	−	2.29297e8i	−0.0577702	−	0.0577702i	−0.735402	+	0.677631i	$0.763006\pi$
$252$	−1.64018e10			−4.06715
$253$	−8.09401e8	−	8.09401e8i	−0.197552	−	0.197552i
$254$		−	5.42463e9i		−	1.30327i
$255$	9.59874e8			0.227014
$256$	−7.13905e8			−0.166219
$257$	5.08549e9			1.16574			0.582868	−	0.812567i	$-0.301931\pi$
$257$	5.08549e9			1.16574			0.582868	+	0.812567i	$0.301931\pi$
$258$	7.07936e9	−	7.07936e9i	1.59777	−	1.59777i
$259$	2.96568e9	−	2.96568e9i	0.659061	−	0.659061i
$260$			2.55202e9i			0.558457i
$261$	−5.29214e9	−	7.91698e9i	−1.14043	−	1.70607i
$262$	6.68169e9			1.41802
$263$	1.29878e9	+	1.29878e9i	0.271464	+	0.271464i	0.829689	−	0.558225i	$-0.188518\pi$
$263$	1.29878e9	+	1.29878e9i	0.271464	+	0.271464i	−0.558225	+	0.829689i	$0.688518\pi$
$264$	6.79100e9	+	6.79100e9i	1.39804	+	1.39804i
$265$			6.50999e8i			0.132007i
$266$		−	4.39922e9i		−	0.878717i
$267$			2.08148e7i			0.00409568i
$268$	1.25741e10			2.43747
$269$	7.10945e7	−	7.10945e7i	0.0135777	−	0.0135777i	−0.700285	−	0.713863i	$-0.746944\pi$
$269$	7.10945e7	−	7.10945e7i	0.0135777	−	0.0135777i	0.713863	+	0.700285i	$0.246944\pi$
$270$			4.42554e9i			0.832743i
$271$	−4.42920e9	+	4.42920e9i	−0.821199	+	0.821199i	−0.986280	−	0.165081i	$-0.947211\pi$
$271$	−4.42920e9	+	4.42920e9i	−0.821199	+	0.821199i	0.165081	+	0.986280i	$0.447211\pi$
$272$	7.76035e8	+	7.76035e8i	0.141777	+	0.141777i
$273$	−1.33579e10	+	1.33579e10i	−2.40484	+	2.40484i
$274$		−	7.22761e9i		−	1.28231i
$275$	6.87511e9	+	6.87511e9i	1.20212	+	1.20212i
$276$	−1.50069e9	+	1.50069e9i	−0.258616	+	0.258616i
$277$	−8.58576e9			−1.45834			−0.729171	−	0.684331i	$-0.760094\pi$
$277$	−8.58576e9			−1.45834			−0.729171	+	0.684331i	$0.760094\pi$
$278$	1.80417e9	+	1.80417e9i	0.302064	+	0.302064i
$279$	2.55733e9	−	2.55733e9i	0.422056	−	0.422056i
$280$	−1.10176e9	−	1.10176e9i	−0.179248	−	0.179248i
$281$	2.69310e9			0.431943			0.215972	−	0.976400i	$-0.430708\pi$
$281$	2.69310e9			0.431943			0.215972	+	0.976400i	$0.430708\pi$
$282$	−5.18658e9	−	5.18658e9i	−0.820134	−	0.820134i
$283$			1.65174e9i			0.257512i	0.991676	+	0.128756i	$0.0410984\pi$
$283$			1.65174e9i			0.257512i	−0.991676	+	0.128756i	$0.958902\pi$
$284$	−8.45195e9			−1.29922
$285$	−1.34785e9			−0.204297
$286$	2.63427e10			3.93728
$287$	−2.70035e9	+	2.70035e9i	−0.398008	+	0.398008i
$288$	−1.30542e10	+	1.30542e10i	−1.89750	+	1.89750i
$289$		−	5.60223e9i		−	0.803100i
$290$	6.24520e8	−	3.14281e9i	0.0882987	−	0.444351i
$291$	−1.74244e10			−2.42989
$292$	−8.52680e9	−	8.52680e9i	−1.17288	−	1.17288i
$293$	8.71324e9	+	8.71324e9i	1.18225	+	1.18225i	0.979160	+	0.203090i	$0.0650983\pi$
$293$	8.71324e9	+	8.71324e9i	1.18225	+	1.18225i	0.203090	+	0.979160i	$0.434902\pi$
$294$		−	2.06597e10i		−	2.76525i
$295$		−	4.23819e9i		−	0.559618i
$296$			3.06145e9i			0.398805i
$297$	2.65951e10			3.41803
$298$	4.16784e9	−	4.16784e9i	0.528501	−	0.528501i
$299$			1.64350e9i			0.205629i
$300$	1.27470e10	−	1.27470e10i	1.57370	−	1.57370i
$301$	6.90212e9	+	6.90212e9i	0.840847	+	0.840847i
$302$	−9.79056e9	+	9.79056e9i	−1.17701	+	1.17701i
$303$		−	1.05471e10i		−	1.25130i
$304$	−1.08971e9	−	1.08971e9i	−0.127589	−	0.127589i
$305$	8.17829e8	−	8.17829e8i	0.0945068	−	0.0945068i
$306$	−1.23516e10			−1.40876
$307$	−7.93911e9	−	7.93911e9i	−0.893755	−	0.893755i	0.101120	−	0.994874i	$-0.467758\pi$
$307$	−7.93911e9	−	7.93911e9i	−0.893755	−	0.893755i	−0.994874	+	0.101120i	$0.967758\pi$
$308$	−2.34516e10	+	2.34516e10i	−2.60597	+	2.60597i
$309$	9.84258e9	+	9.84258e9i	1.07963	+	1.07963i
$310$	1.21692e9			0.131769
$311$	3.49015e9	+	3.49015e9i	0.373080	+	0.373080i	0.868598	−	0.495518i	$-0.165022\pi$
$311$	3.49015e9	+	3.49015e9i	0.373080	+	0.373080i	−0.495518	+	0.868598i	$0.665022\pi$
$312$		−	1.37892e10i		−	1.45519i
$313$	−3.35972e9			−0.350046			−0.175023	−	0.984564i	$-0.556000\pi$
$313$	−3.35972e9			−0.350046			−0.175023	+	0.984564i	$0.556000\pi$
$314$	−1.84071e9			−0.189351
$315$	−8.41566e9			−0.854764
$316$	2.65382e9	−	2.65382e9i	0.266148	−	0.266148i
$317$	6.33684e9	−	6.33684e9i	0.627532	−	0.627532i	−0.319914	−	0.947446i	$-0.603654\pi$
$317$	6.33684e9	−	6.33684e9i	0.627532	−	0.627532i	0.947446	+	0.319914i	$0.103654\pi$
$318$		−	1.24591e10i		−	1.21836i
$319$	−1.88866e10	−	3.75303e9i	−1.82386	−	0.362426i
$320$	−4.82442e9			−0.460093
$321$	2.43123e10	+	2.43123e10i	2.28984	+	2.28984i
$322$	−2.51317e9	−	2.51317e9i	−0.233775	−	0.233775i
$323$		−	1.92870e9i		−	0.177196i
$324$		−	1.77986e10i		−	1.61513i
$325$		−	1.39600e10i		−	1.25127i
$326$	1.41000e10			1.24839
$327$	−1.26783e10	+	1.26783e10i	−1.10884	+	1.10884i
$328$		−	2.78755e9i		−	0.240839i
$329$	5.05673e9	−	5.05673e9i	0.431605	−	0.431605i
$330$	1.23418e10	+	1.23418e10i	1.04070	+	1.04070i
$331$	2.95500e9	−	2.95500e9i	0.246176	−	0.246176i	−0.573223	−	0.819399i	$-0.694307\pi$
$331$	2.95500e9	−	2.95500e9i	0.246176	−	0.246176i	0.819399	+	0.573223i	$0.194307\pi$
$332$		−	1.02876e10i		−	0.846764i
$333$	1.16923e10	+	1.16923e10i	0.950871	+	0.950871i
$334$	−2.44364e10	+	2.44364e10i	−1.96359	+	1.96359i
$335$	6.45171e9			0.512266
$336$	−1.01194e10	−	1.01194e10i	−0.793955	−	0.793955i
$337$	1.11297e10	−	1.11297e10i	0.862908	−	0.862908i	−0.128766	−	0.991675i	$-0.541102\pi$
$337$	1.11297e10	−	1.11297e10i	0.862908	−	0.862908i	0.991675	+	0.128766i	$0.0411018\pi$
$338$	−1.24669e10	−	1.24669e10i	−0.955191	−	0.955191i
$339$	−2.89056e10			−2.18868
$340$	−1.71090e9	−	1.71090e9i	−0.128029	−	0.128029i
$341$		−	7.31302e9i		−	0.540853i
$342$	1.73440e10			1.26778
$343$	4.55121e8			0.0328814
$344$	−7.12501e9			−0.508805
$345$	−7.69996e8	+	7.69996e8i	−0.0543515	+	0.0543515i
$346$	−4.05967e9	+	4.05967e9i	−0.283261	+	0.283261i
$347$		−	6.47755e9i		−	0.446779i	−0.974729	−	0.223390i	$-0.928288\pi$
$347$		−	6.47755e9i		−	0.446779i	0.974729	−	0.223390i	$-0.0717122\pi$
$348$	−6.95842e9	+	3.50173e10i	−0.474454	+	2.38762i
$349$	−3.80330e9			−0.256365			−0.128182	−	0.991751i	$-0.540914\pi$
$349$	−3.80330e9			−0.256365			−0.128182	+	0.991751i	$0.540914\pi$
$350$	2.13470e10	+	2.13470e10i	1.42254	+	1.42254i
$351$	−2.70008e10	−	2.70008e10i	−1.77889	−	1.77889i
$352$			3.73302e10i			2.43159i
$353$		−	1.40563e9i		−	0.0905259i	−0.998975	−	0.0452629i	$-0.985587\pi$
$353$		−	1.40563e9i		−	0.0905259i	0.998975	−	0.0452629i	$-0.0144126\pi$
$354$			8.11120e10i			5.16502i
$355$	−4.33664e9			−0.273049
$356$	3.71007e7	−	3.71007e7i	0.00230984	−	0.00230984i
$357$		−	1.79105e10i		−	1.10264i
$358$	1.89400e10	−	1.89400e10i	1.15305	−	1.15305i
$359$	−1.21785e10	−	1.21785e10i	−0.733192	−	0.733192i	0.238059	−	0.971251i	$-0.423489\pi$
$359$	−1.21785e10	−	1.21785e10i	−0.733192	−	0.733192i	−0.971251	+	0.238059i	$0.923489\pi$
$360$	4.34371e9	−	4.34371e9i	0.258613	−	0.258613i
$361$		−	1.42753e10i		−	0.840536i
$362$	−2.38978e10	−	2.38978e10i	−1.39163	−	1.39163i
$363$	5.27185e10	−	5.27185e10i	3.03624	−	3.03624i
$364$	4.76187e10			2.71251
$365$	−4.37504e9	−	4.37504e9i	−0.246496	−	0.246496i
$366$	−1.56519e10	+	1.56519e10i	−0.872254	+	0.872254i
$367$	1.53652e10	+	1.53652e10i	0.846979	+	0.846979i	0.989755	−	0.142776i	$-0.0456029\pi$
$367$	1.53652e10	+	1.53652e10i	0.846979	+	0.846979i	−0.142776	+	0.989755i	$0.545603\pi$
$368$	−1.24505e9			−0.0678881
$369$	−1.06462e10	−	1.06462e10i	−0.574233	−	0.574233i
$370$			5.56381e9i			0.296870i
$371$	1.21471e10			0.641178
$372$	−1.35589e10			−0.708032
$373$	2.27502e8			0.0117530			0.00587650	−	0.999983i	$-0.498129\pi$
$373$	2.27502e8			0.0117530			0.00587650	+	0.999983i	$0.498129\pi$
$374$	−1.76604e10	+	1.76604e10i	−0.902641	+	0.902641i
$375$	1.36943e10	−	1.36943e10i	0.692490	−	0.692490i
$376$			5.22002e9i			0.261169i
$377$	1.53644e10	+	2.29850e10i	0.760591	+	1.13784i
$378$	8.25771e10			4.04476
$379$	−3.40008e9	−	3.40008e9i	−0.164791	−	0.164791i	0.619894	−	0.784685i	$-0.287175\pi$
$379$	−3.40008e9	−	3.40008e9i	−0.164791	−	0.164791i	−0.784685	+	0.619894i	$0.787175\pi$
$380$	2.40244e9	+	2.40244e9i	0.115217	+	0.115217i
$381$			3.10121e10i			1.47174i
$382$		−	1.78757e10i		−	0.839481i
$383$			7.50328e9i			0.348703i	0.984683	+	0.174352i	$0.0557829\pi$
$383$			7.50328e9i			0.348703i	−0.984683	+	0.174352i	$0.944217\pi$
$384$	4.26590e10			1.96194
$385$	−1.20328e10	+	1.20328e10i	−0.547678	+	0.547678i
$386$			1.17706e10i			0.530210i
$387$	−2.72118e10	+	2.72118e10i	−1.21315	+	1.21315i
$388$	3.10576e10	+	3.10576e10i	1.37038	+	1.37038i
$389$	1.99931e10	−	1.99931e10i	0.873136	−	0.873136i	−0.119677	−	0.992813i	$-0.538186\pi$
$389$	1.99931e10	−	1.99931e10i	0.873136	−	0.873136i	0.992813	+	0.119677i	$0.0381859\pi$
$390$		−	2.50602e10i		−	1.08324i
$391$	−1.10182e9	−	1.10182e9i	−0.0471415	−	0.0471415i
$392$	−1.03964e10	+	1.03964e10i	−0.440292	+	0.440292i
$393$	−3.81985e10			−1.60131
$394$	−1.97670e10	−	1.97670e10i	−0.820270	−	0.820270i
$395$	1.36166e9	−	1.36166e9i	0.0559345	−	0.0559345i
$396$	−9.24583e10	−	9.24583e10i	−3.75980	−	3.75980i
$397$	4.01105e10			1.61472			0.807358	−	0.590061i	$-0.200896\pi$
$397$	4.01105e10			1.61472			0.807358	+	0.590061i	$0.200896\pi$
$398$	−4.34593e9	−	4.34593e9i	−0.173201	−	0.173201i
$399$			2.51499e10i			0.992303i
$400$	1.05755e10			0.413105
$401$	1.43250e10			0.554011			0.277006	−	0.960868i	$-0.410658\pi$
$401$	1.43250e10			0.554011			0.277006	+	0.960868i	$0.410658\pi$
$402$	−1.23475e11			−4.72798
$403$	−7.42458e9	+	7.42458e9i	−0.281483	+	0.281483i
$404$	−1.87994e10	+	1.87994e10i	−0.705696	+	0.705696i
$405$		−	9.13236e9i		−	0.339440i
$406$	−5.86424e10	−	1.16531e10i	−2.15828	−	0.428880i
$407$	3.34355e10			1.21851
$408$	9.24444e9	+	9.24444e9i	0.333611	+	0.333611i
$409$	3.69988e10	+	3.69988e10i	1.32219	+	1.32219i	0.911998	+	0.410195i	$0.134539\pi$
$409$	3.69988e10	+	3.69988e10i	1.32219	+	1.32219i	0.410195	+	0.911998i	$0.365461\pi$
$410$		−	5.06603e9i		−	0.179280i
$411$			4.13195e10i			1.44807i
$412$		−	3.50873e10i		−	1.21776i
$413$	−7.90813e10			−2.71815
$414$	9.90822e9	−	9.90822e9i	0.337283	−	0.337283i
$415$		−	5.27850e9i		−	0.177958i
$416$	3.78997e10	−	3.78997e10i	1.26550	−	1.26550i
$417$	−1.03143e10	−	1.03143e10i	−0.341109	−	0.341109i
$418$	2.47987e10	−	2.47987e10i	0.812314	−	0.812314i
$419$		−	4.39655e10i		−	1.42645i	−0.700937	−	0.713223i	$-0.747234\pi$
$419$		−	4.39655e10i		−	1.42645i	0.700937	−	0.713223i	$-0.252766\pi$
$420$	2.23098e10	+	2.23098e10i	0.716967	+	0.716967i
$421$	5.82019e9	−	5.82019e9i	0.185272	−	0.185272i	−0.608377	−	0.793648i	$-0.708179\pi$
$421$	5.82019e9	−	5.82019e9i	0.185272	−	0.185272i	0.793648	+	0.608377i	$0.208179\pi$
$422$	−6.60186e10			−2.08169
$423$	1.99363e10	+	1.99363e10i	0.622705	+	0.622705i
$424$	−6.26970e9	+	6.26970e9i	−0.193992	+	0.193992i
$425$	9.35892e9	+	9.35892e9i	0.286860	+	0.286860i
$426$	8.29962e10			2.52011
$427$	−1.52601e10	−	1.52601e10i	−0.459034	−	0.459034i
$428$		−	8.66695e10i		−	2.58280i
$429$	−1.50598e11			−4.44622
$430$	−1.29488e10			−0.378754
$431$	2.30280e10			0.667340			0.333670	−	0.942690i	$-0.391713\pi$
$431$	2.30280e10			0.667340			0.333670	+	0.942690i	$0.391713\pi$
$432$	2.04547e10	−	2.04547e10i	0.587298	−	0.587298i
$433$	−1.65844e10	+	1.65844e10i	−0.471789	+	0.471789i	−0.902493	−	0.430704i	$-0.858265\pi$
$433$	−1.65844e10	+	1.65844e10i	−0.471789	+	0.471789i	0.430704	+	0.902493i	$0.358265\pi$
$434$		−	2.27067e10i		−	0.640023i
$435$	−3.57032e9	+	1.79671e10i	−0.0997126	+	0.501789i
$436$	4.51961e10			1.25071
$437$	1.54717e9	+	1.54717e9i	0.0424241	+	0.0424241i
$438$	8.37312e10	+	8.37312e10i	2.27505	+	2.27505i
$439$			1.14176e10i			0.307410i	0.988117	+	0.153705i	$0.0491206\pi$
$439$			1.14176e10i			0.307410i	−0.988117	+	0.153705i	$0.950879\pi$
$440$		−	1.24214e10i		−	0.331406i
$441$			7.94121e10i			2.09958i
$442$	3.58597e10			0.939545
$443$	1.48525e10	−	1.48525e10i	0.385643	−	0.385643i	−0.487487	−	0.873130i	$-0.662086\pi$
$443$	1.48525e10	−	1.48525e10i	0.385643	−	0.385643i	0.873130	+	0.487487i	$0.162086\pi$
$444$		−	6.19922e10i		−	1.59516i
$445$	1.90361e7	−	1.90361e7i	0.000485443	−	0.000485443i
$446$	−6.91370e10	−	6.91370e10i	−1.74732	−	1.74732i
$447$	−2.38271e10	+	2.38271e10i	−0.596817	+	0.596817i
$448$			9.00200e10i			2.23474i
$449$	2.35842e10	+	2.35842e10i	0.580277	+	0.580277i	0.934979	−	0.354702i	$-0.115418\pi$
$449$	2.35842e10	+	2.35842e10i	0.580277	+	0.580277i	−0.354702	+	0.934979i	$0.615418\pi$
$450$	−8.41611e10	+	8.41611e10i	−2.05240	+	2.05240i
$451$	−3.04441e10			−0.735863
$452$	5.15220e10	+	5.15220e10i	1.23435	+	1.23435i
$453$	5.59716e10	−	5.59716e10i	1.32915	−	1.32915i
$454$	4.58484e10	+	4.58484e10i	1.07920	+	1.07920i
$455$	2.44328e10			0.570070
$456$	−1.29810e10	−	1.29810e10i	−0.300226	−	0.300226i
$457$		−	8.38130e9i		−	0.192153i	−0.995374	−	0.0960764i	$-0.969371\pi$
$457$		−	8.38130e9i		−	0.192153i	0.995374	−	0.0960764i	$-0.0306293\pi$
$458$	4.47094e10			1.01610
$459$	3.62033e10			0.815638
$460$	2.74491e9			0.0613052
$461$	5.67464e9	−	5.67464e9i	0.125642	−	0.125642i	−0.641490	−	0.767132i	$-0.721683\pi$
$461$	5.67464e9	−	5.67464e9i	0.125642	−	0.125642i	0.767132	+	0.641490i	$0.221683\pi$
$462$	2.30289e11	−	2.30289e11i	5.05481	−	5.05481i
$463$			5.34891e10i			1.16397i	0.813200	+	0.581984i	$0.197723\pi$
$463$			5.34891e10i			1.16397i	−0.813200	+	0.581984i	$0.802277\pi$
$464$	−1.74125e10	+	1.16395e10i	−0.375655	+	0.251108i
$465$	−6.95699e9			−0.148802
$466$	−7.33502e10	−	7.33502e10i	−1.55546	−	1.55546i
$467$	3.70717e9	+	3.70717e9i	0.0779427	+	0.0779427i	0.745003	−	0.667061i	$-0.232448\pi$
$467$	3.70717e9	+	3.70717e9i	0.0779427	+	0.0779427i	−0.667061	+	0.745003i	$0.732448\pi$
$468$			1.87738e11i			3.91352i
$469$		−	1.20384e11i		−	2.48815i
$470$			9.48676e9i			0.194414i
$471$	1.05232e10			0.213827
$472$	4.08175e10	−	4.08175e10i	0.822391	−	0.822391i
$473$			7.78156e10i			1.55461i
$474$	−2.60599e10	+	2.60599e10i	−0.516250	+	0.516250i
$475$	−1.31418e10	−	1.31418e10i	−0.258154	−	0.258154i
$476$	−3.19241e10	+	3.19241e10i	−0.621857	+	0.621857i
$477$			4.78904e10i			0.925071i
$478$	−4.06098e10	−	4.06098e10i	−0.777892	−	0.777892i
$479$	4.21342e10	−	4.21342e10i	0.800374	−	0.800374i	−0.182780	−	0.983154i	$-0.558510\pi$
$479$	4.21342e10	−	4.21342e10i	0.800374	−	0.800374i	0.983154	+	0.182780i	$0.0585095\pi$
$480$	3.55128e10			0.668991
$481$	−3.39456e10	−	3.39456e10i	−0.634167	−	0.634167i
$482$	−3.39043e10	+	3.39043e10i	−0.628154	+	0.628154i
$483$	1.43675e10	+	1.43675e10i	0.263994	+	0.263994i
$484$	−1.87933e11			−3.42469
$485$	1.59355e10	+	1.59355e10i	0.288003	+	0.288003i
$486$			1.61332e10i			0.289185i
$487$	−2.04421e10			−0.363420			−0.181710	−	0.983352i	$-0.558163\pi$
$487$	−2.04421e10			−0.363420			−0.181710	+	0.983352i	$0.558163\pi$
$488$	1.57528e10			0.277766
$489$	−8.06083e10			−1.40976
$490$	−1.88943e10	+	1.88943e10i	−0.327753	+	0.327753i
$491$	−4.87134e10	+	4.87134e10i	−0.838151	+	0.838151i	−0.988615	−	0.150464i	$-0.951923\pi$
$491$	−4.87134e10	+	4.87134e10i	−0.838151	+	0.838151i	0.150464	+	0.988615i	$0.451923\pi$
$492$			5.64458e10i			0.963322i
$493$	−2.57099e10	−	5.10892e9i	−0.435224	−	0.0864851i
$494$	−5.03541e10			−0.845526
$495$	−4.74397e10	−	4.74397e10i	−0.790172	−	0.790172i
$496$	−5.62455e9	−	5.62455e9i	−0.0929312	−	0.0929312i
$497$			8.09184e10i			1.32624i
$498$			1.01022e11i			1.64247i
$499$		−	1.86262e10i		−	0.300415i	−0.988655	−	0.150207i	$-0.952006\pi$
$499$		−	1.86262e10i		−	0.300415i	0.988655	−	0.150207i	$-0.0479941\pi$
$500$	−4.88179e10			−0.781087
$501$	1.39701e11	−	1.39701e11i	2.21742	−	2.21742i
$502$		−	8.02677e9i		−	0.126394i
$503$	4.54877e9	−	4.54877e9i	0.0710596	−	0.0710596i	−0.670684	−	0.741743i	$-0.733999\pi$
$503$	4.54877e9	−	4.54877e9i	0.0710596	−	0.0710596i	0.741743	+	0.670684i	$0.233999\pi$
$504$	−8.10503e10	−	8.10503e10i	−1.25612	−	1.25612i
$505$	−9.64582e9	+	9.64582e9i	−0.148311	+	0.148311i
$506$		−	2.83338e10i		−	0.432219i
$507$	7.12717e10	+	7.12717e10i	1.07866	+	1.07866i
$508$	5.52766e10	−	5.52766e10i	0.830016	−	0.830016i
$509$	2.50031e10			0.372497			0.186248	−	0.982503i	$-0.440367\pi$
$509$	2.50031e10			0.372497			0.186248	+	0.982503i	$0.440367\pi$
$510$	1.68006e10	+	1.68006e10i	0.248339	+	0.248339i
$511$	−8.16349e10	+	8.16349e10i	−1.19727	+	1.19727i
$512$	4.20739e10	+	4.20739e10i	0.612256	+	0.612256i
$513$	−5.08366e10			−0.734018
$514$	8.90111e10	+	8.90111e10i	1.27524	+	1.27524i
$515$		−	1.80030e10i		−	0.255928i
$516$	1.44276e11			2.03515
$517$	5.70104e10			0.797979
$518$	1.03816e11			1.44194
$519$	2.32087e10	−	2.32087e10i	0.319876	−	0.319876i
$520$	−1.26109e10	+	1.26109e10i	−0.172478	+	0.172478i
$521$		−	4.30572e9i		−	0.0584380i	−0.999573	−	0.0292190i	$-0.990698\pi$
$521$		−	4.30572e9i		−	0.0584380i	0.999573	−	0.0292190i	$-0.00930202\pi$
$522$	4.59425e10	−	2.31199e11i	0.618774	−	3.11389i
$523$	1.80967e10			0.241876			0.120938	−	0.992660i	$-0.461410\pi$
$523$	1.80967e10			0.241876			0.120938	+	0.992660i	$0.461410\pi$
$524$	6.80859e10	+	6.80859e10i	0.903092	+	0.903092i
$525$	−1.22039e11	−	1.22039e11i	−1.60642	−	1.60642i
$526$			4.54650e10i			0.593929i
$527$		−	9.95504e9i		−	0.129063i
$528$		−	1.14087e11i		−	1.46792i
$529$	−7.65433e10			−0.977427
$530$	−1.13944e10	+	1.13944e10i	−0.144407	+	0.144407i
$531$		−	3.11780e11i		−	3.92166i
$532$	4.48277e10	−	4.48277e10i	0.559629	−	0.559629i
$533$	3.09086e10	+	3.09086e10i	0.382974	+	0.382974i
$534$	−3.64320e8	+	3.64320e8i	−0.00448042	+	0.00448042i
$535$		−	4.44695e10i		−	0.542809i
$536$	6.21356e10	+	6.21356e10i	0.752804	+	0.752804i
$537$	−1.08278e11	+	1.08278e11i	−1.30210	+	1.30210i
$538$	2.48873e9			0.0297063
$539$	1.13545e11	+	1.13545e11i	1.34528	+	1.34528i
$540$	−4.50959e10	+	4.50959e10i	−0.530349	+	0.530349i
$541$	−1.48786e10	−	1.48786e10i	−0.173689	−	0.173689i	0.614909	−	0.788598i	$-0.289193\pi$
$541$	−1.48786e10	−	1.48786e10i	−0.173689	−	0.173689i	−0.788598	+	0.614909i	$0.789193\pi$
$542$	−1.55048e11			−1.79668
$543$	1.36621e11	+	1.36621e11i	1.57152	+	1.57152i
$544$			5.08168e10i			0.580245i
$545$	2.31898e10			0.262852
$546$	−4.67604e11			−5.26148
$547$	−2.59563e10			−0.289931			−0.144965	−	0.989437i	$-0.546307\pi$
$547$	−2.59563e10			−0.289931			−0.144965	+	0.989437i	$0.546307\pi$
$548$	7.36488e10	−	7.36488e10i	0.816665	−	0.816665i
$549$	6.01631e10	−	6.01631e10i	0.662279	−	0.662279i
$550$			2.40670e11i			2.63009i
$551$	3.61018e10	+	7.17392e9i	0.391672	+	0.0778306i
$552$	−1.48315e10			−0.159745
$553$	−2.54075e10	−	2.54075e10i	−0.271682	−	0.271682i
$554$	−1.50276e11	−	1.50276e11i	−1.59533	−	1.59533i
$555$		−	3.18077e10i		−	0.335244i
$556$			3.67687e10i			0.384751i
$557$		−	1.04691e11i		−	1.08764i	−0.839200	−	0.543822i	$-0.816977\pi$
$557$		−	1.04691e11i		−	1.08764i	0.839200	−	0.543822i	$-0.183023\pi$
$558$	8.95218e10			0.923404
$559$	7.90027e10	−	7.90027e10i	0.809086	−	0.809086i
$560$			1.85093e10i			0.188208i
$561$	1.00963e11	−	1.00963e11i	1.01932	−	1.01932i
$562$	4.71372e10	+	4.71372e10i	0.472518	+	0.472518i
$563$	−9.72051e10	+	9.72051e10i	−0.967510	+	0.967510i	−0.999489	−	0.0319788i	$-0.989819\pi$
$563$	−9.72051e10	+	9.72051e10i	−0.967510	+	0.967510i	0.0319788	+	0.999489i	$0.489819\pi$
$564$		−	1.05702e11i		−	1.04464i
$565$	2.64356e10	+	2.64356e10i	0.259415	+	0.259415i
$566$	−2.89104e10	+	2.89104e10i	−0.281701	+	0.281701i
$567$	−1.70403e11			−1.64871
$568$	−4.17657e10	−	4.17657e10i	−0.401260	−	0.401260i
$569$	−5.93666e10	+	5.93666e10i	−0.566361	+	0.566361i	−0.931107	−	0.364746i	$-0.881156\pi$
$569$	−5.93666e10	+	5.93666e10i	−0.566361	+	0.566361i	0.364746	+	0.931107i	$0.381156\pi$
$570$	−2.35914e10	−	2.35914e10i	−0.223488	−	0.223488i
$571$	1.09281e11			1.02802			0.514008	−	0.857785i	$-0.328160\pi$
$571$	1.09281e11			1.02802			0.514008	+	0.857785i	$0.328160\pi$
$572$	2.68430e11	+	2.68430e11i	2.50754	+	2.50754i
$573$			1.02194e11i			0.947995i
$574$	−9.45282e10			−0.870790
$575$	−1.50152e10			−0.137359
$576$	−3.54906e11			−3.22421
$577$	1.54956e10	−	1.54956e10i	0.139799	−	0.139799i	−0.633744	−	0.773543i	$-0.718483\pi$
$577$	1.54956e10	−	1.54956e10i	0.139799	−	0.139799i	0.773543	+	0.633744i	$0.218483\pi$
$578$	9.80557e10	−	9.80557e10i	0.878540	−	0.878540i
$579$		−	6.72911e10i		−	0.598747i
$580$	3.83888e10	−	2.56612e10i	0.339229	−	0.226759i
$581$	−9.84928e10			−0.864371
$582$	−3.04979e11	−	3.04979e11i	−2.65814	−	2.65814i
$583$	6.84744e10	+	6.84744e10i	0.592726	+	0.592726i
$584$		−	8.42711e10i		−	0.724481i
$585$			9.63269e10i			0.822478i
$586$			3.05015e11i			2.58661i
$587$	−1.66491e11			−1.40229			−0.701146	−	0.713018i	$-0.747328\pi$
$587$	−1.66491e11			−1.40229			−0.701146	+	0.713018i	$0.747328\pi$
$588$	2.10521e11	−	2.10521e11i	1.76111	−	1.76111i
$589$			1.39788e10i			0.116148i
$590$	7.41808e10	−	7.41808e10i	0.612186	−	0.612186i
$591$	1.13006e11	+	1.13006e11i	0.926301	+	0.926301i
$592$	2.57158e10	−	2.57158e10i	0.209369	−	0.209369i
$593$		−	8.08753e10i		−	0.654030i	−0.945019	−	0.327015i	$-0.893957\pi$
$593$		−	8.08753e10i		−	0.654030i	0.945019	−	0.327015i	$-0.106043\pi$
$594$	4.65493e11	+	4.65493e11i	3.73911	+	3.73911i
$595$	−1.63800e10	+	1.63800e10i	−0.130691	+	0.130691i
$596$	8.49400e10			0.673174
$597$	2.48452e10	+	2.48452e10i	0.195589	+	0.195589i
$598$	−2.87661e10	+	2.87661e10i	−0.224945	+	0.224945i
$599$	−8.74885e10	−	8.74885e10i	−0.679585	−	0.679585i	0.280321	−	0.959906i	$-0.409559\pi$
$599$	−8.74885e10	−	8.74885e10i	−0.679585	−	0.679585i	−0.959906	+	0.280321i	$0.909559\pi$
$600$	1.25980e11			0.972065
$601$	−8.47563e8	−	8.47563e8i	−0.00649642	−	0.00649642i	0.703851	−	0.710348i	$-0.251462\pi$
$601$	−8.47563e8	−	8.47563e8i	−0.00649642	−	0.00649642i	−0.710348	+	0.703851i	$0.751462\pi$
$602$			2.41615e11i			1.83966i
$603$	4.74616e11			3.58982
$604$	−1.99530e11			−1.49920
$605$	−9.64272e10			−0.719744
$606$	1.84605e11	−	1.84605e11i	1.36884	−	1.36884i
$607$	−1.07472e11	+	1.07472e11i	−0.791663	+	0.791663i	−0.981764	−	0.190102i	$-0.939118\pi$
$607$	−1.07472e11	+	1.07472e11i	−0.791663	+	0.791663i	0.190102	+	0.981764i	$0.439118\pi$
$608$		−	7.13567e10i		−	0.522180i
$609$	3.35253e11	+	6.66194e10i	2.43727	+	0.484319i
$610$	2.86289e10			0.206769
$611$	−5.78801e10	−	5.78801e10i	−0.415302	−	0.415302i
$612$	−1.25861e11	−	1.25861e11i	−0.897195	−	0.897195i
$613$		−	2.02870e11i		−	1.43673i	−0.695664	−	0.718367i	$-0.744890\pi$
$613$		−	2.02870e11i		−	1.43673i	0.695664	−	0.718367i	$-0.255110\pi$
$614$		−	2.77916e11i		−	1.95542i
$615$			2.89620e10i			0.202454i
$616$	−2.31774e11			−1.60969
$617$	6.28386e10	−	6.28386e10i	0.433597	−	0.433597i	−0.456253	−	0.889850i	$-0.650809\pi$
$617$	6.28386e10	−	6.28386e10i	0.433597	−	0.433597i	0.889850	+	0.456253i	$0.150809\pi$
$618$			3.44549e11i			2.36209i
$619$	−1.31339e11	+	1.31339e11i	−0.894604	+	0.894604i	−0.994952	−	0.100348i	$-0.968004\pi$
$619$	−1.31339e11	+	1.31339e11i	−0.894604	+	0.894604i	0.100348	+	0.994952i	$0.468004\pi$
$620$	1.24003e10	+	1.24003e10i	0.0839199	+	0.0839199i
$621$	−2.90417e10	+	2.90417e10i	−0.195279	+	0.195279i
$622$			1.22176e11i			0.816252i
$623$	−3.55199e8	−	3.55199e8i	−0.00235787	−	0.00235787i
$624$	−1.15828e11	+	1.15828e11i	−0.763965	+	0.763965i
$625$	1.14455e11			0.750090
$626$	−5.88050e10	−	5.88050e10i	−0.382928	−	0.382928i
$627$	−1.41772e11	+	1.41772e11i	−0.917317	+	0.917317i
$628$	−1.87567e10	−	1.87567e10i	−0.120592	−	0.120592i
$629$	4.55150e10			0.290772
$630$	−1.47299e11	−	1.47299e11i	−0.935057	−	0.935057i
$631$			2.52043e10i			0.158985i	0.996835	+	0.0794926i	$0.0253300\pi$
$631$			2.52043e10i			0.158985i	−0.996835	+	0.0794926i	$0.974670\pi$
$632$	2.62280e10			0.164398
$633$	3.77421e11			2.35078
$634$	2.21827e11			1.37296
$635$	2.83620e10	−	2.83620e10i	0.174439	−	0.174439i
$636$	1.26957e11	−	1.26957e11i	0.775940	−	0.775940i
$637$		−	2.30553e11i		−	1.40028i
$638$	−2.64883e11	−	3.96261e11i	−1.59871	−	2.39166i
$639$	−3.19022e11			−1.91345
$640$	−3.90138e10	−	3.90138e10i	−0.232540	−	0.232540i
$641$	−6.61360e9	−	6.61360e9i	−0.0391747	−	0.0391747i	0.687248	−	0.726423i	$-0.258819\pi$
$641$	−6.61360e9	−	6.61360e9i	−0.0391747	−	0.0391747i	−0.726423	+	0.687248i	$0.758819\pi$
$642$			8.51074e11i			5.00988i
$643$			2.03135e11i			1.18834i	0.804339	+	0.594171i	$0.202520\pi$
$643$			2.03135e11i			1.18834i	−0.804339	+	0.594171i	$0.797480\pi$
$644$		−	5.12180e10i		−	0.297769i
$645$	7.40272e10			0.427713
$646$	3.37579e10	−	3.37579e10i	0.193841	−	0.193841i
$647$			2.18441e11i			1.24657i	0.781994	+	0.623285i	$0.214202\pi$
$647$			2.18441e11i			1.24657i	−0.781994	+	0.623285i	$0.785798\pi$
$648$	8.79527e10	−	8.79527e10i	0.498826	−	0.498826i
$649$	−4.45787e11	−	4.45787e11i	−2.51275	−	2.51275i
$650$	2.44341e11	−	2.44341e11i	1.36881	−	1.36881i
$651$			1.29812e11i			0.722755i
$652$	1.43678e11	+	1.43678e11i	0.795060	+	0.795060i
$653$	1.35088e11	−	1.35088e11i	0.742958	−	0.742958i	−0.230188	−	0.973146i	$-0.573934\pi$
$653$	1.35088e11	−	1.35088e11i	0.742958	−	0.742958i	0.973146	+	0.230188i	$0.0739342\pi$
$654$	−4.43815e11			−2.42600
$655$	3.49344e10	+	3.49344e10i	0.189796	+	0.189796i
$656$	−2.34150e10	+	2.34150e10i	−0.126439	+	0.126439i
$657$	−3.21847e11	−	3.21847e11i	−1.72738	−	1.72738i
$658$	1.77016e11			0.944296
$659$	−4.96423e10	−	4.96423e10i	−0.263215	−	0.263215i	0.563144	−	0.826359i	$-0.309592\pi$
$659$	−4.96423e10	−	4.96423e10i	−0.263215	−	0.263215i	−0.826359	+	0.563144i	$0.809592\pi$
$660$			2.51525e11i			1.32558i
$661$	−1.16358e11			−0.609523			−0.304761	−	0.952429i	$-0.598577\pi$
$661$	−1.16358e11			−0.609523			−0.304761	+	0.952429i	$0.598577\pi$
$662$	1.03443e11			0.538602
$663$	−2.05006e11			−1.06099
$664$	5.08367e10	−	5.08367e10i	0.261520	−	0.261520i
$665$	2.30008e10	−	2.30008e10i	0.117613	−	0.117613i
$666$			4.09299e11i			2.08038i
$667$	2.47224e10	−	1.65258e10i	0.124907	−	0.0834947i
$668$	−4.98011e11			−2.50111
$669$	3.95249e11	+	3.95249e11i	1.97318	+	1.97318i
$670$	1.12924e11	+	1.12924e11i	0.560386	+	0.560386i
$671$		−	1.72044e11i		−	0.848692i
$672$		−	6.62642e11i		−	3.24939i
$673$			2.76399e11i			1.34734i	0.739033	+	0.673669i	$0.235283\pi$
$673$			2.76399e11i			1.34734i	−0.739033	+	0.673669i	$0.764717\pi$
$674$	3.89606e11			1.88793
$675$	2.46682e11	−	2.46682e11i	1.18829	−	1.18829i
$676$		−	2.54073e11i		−	1.21666i
$677$	1.25276e11	−	1.25276e11i	0.596364	−	0.596364i	−0.342979	−	0.939343i	$-0.611436\pi$
$677$	1.25276e11	−	1.25276e11i	0.596364	−	0.596364i	0.939343	+	0.342979i	$0.111436\pi$
$678$	−5.05934e11	−	5.05934e11i	−2.39428	−	2.39428i
$679$	2.97343e11	−	2.97343e11i	1.39888	−	1.39888i
$680$		−	1.69090e10i		−	0.0790827i
$681$	−2.62111e11	−	2.62111e11i	−1.21870	−	1.21870i
$682$	1.28000e11	−	1.28000e11i	0.591658	−	0.591658i
$683$	−1.44880e10			−0.0665774			−0.0332887	−	0.999446i	$-0.510598\pi$
$683$	−1.44880e10			−0.0665774			−0.0332887	+	0.999446i	$0.510598\pi$
$684$	1.76734e11	+	1.76734e11i	0.807414	+	0.807414i
$685$	3.77887e10	−	3.77887e10i	0.171633	−	0.171633i
$686$	7.96596e9	+	7.96596e9i	0.0359701	+	0.0359701i
$687$	−2.55599e11			−1.14745
$688$	5.98492e10	+	5.98492e10i	0.267119	+	0.267119i
$689$		−	1.39038e11i		−	0.616959i
$690$	−2.69544e10			−0.118914
$691$	−5.44063e10			−0.238637			−0.119318	−	0.992856i	$-0.538071\pi$
$691$	−5.44063e10			−0.238637			−0.119318	+	0.992856i	$0.538071\pi$
$692$	−8.27355e10			−0.360801
$693$	−8.85189e11	+	8.85189e11i	−3.83798	+	3.83798i
$694$	1.13376e11	−	1.13376e11i	0.488748	−	0.488748i
$695$			1.88658e10i			0.0808603i
$696$	−2.07425e11	+	1.38654e11i	−0.883941	+	0.590875i
$697$	−4.14429e10			−0.175598
$698$	−6.65690e10	−	6.65690e10i	−0.280447	−	0.280447i
$699$	4.19335e11	+	4.19335e11i	1.75652	+	1.75652i
$700$			4.35049e11i			1.81195i
$701$			3.02289e11i			1.25184i	0.779886	+	0.625922i	$0.215277\pi$
$701$			3.02289e11i			1.25184i	−0.779886	+	0.625922i	$0.784723\pi$
$702$		−	9.45189e11i		−	3.89198i
$703$	−6.39121e10			−0.261675
$704$	−5.07449e11	+	5.07449e11i	−2.06587	+	2.06587i
$705$		−	5.42348e10i		−	0.219544i
$706$	2.46027e10	−	2.46027e10i	0.0990295	−	0.0990295i
$707$	1.79984e11	+	1.79984e11i	0.720370	+	0.720370i
$708$	−8.26525e11	+	8.26525e11i	−3.28945	+	3.28945i
$709$		−	2.27747e10i		−	0.0901297i	−0.998984	−	0.0450649i	$-0.985651\pi$
$709$		−	2.27747e10i		−	0.0901297i	0.998984	−	0.0450649i	$-0.0143495\pi$
$710$	−7.59041e10	−	7.59041e10i	−0.298698	−	0.298698i
$711$	1.00170e11	−	1.00170e11i	0.391974	−	0.391974i
$712$	3.66669e8			0.00142677
$713$	7.98578e9	+	7.98578e9i	0.0309000	+	0.0309000i
$714$	3.13487e11	−	3.13487e11i	1.20622	−	1.20622i
$715$	1.37730e11	+	1.37730e11i	0.526991	+	0.526991i
$716$	3.85994e11			1.46869
$717$	2.32162e11	+	2.32162e11i	0.878446	+	0.878446i
$718$		−	4.26321e11i		−	1.60413i
$719$	6.75119e10			0.252618			0.126309	−	0.991991i	$-0.459687\pi$
$719$	6.75119e10			0.252618			0.126309	+	0.991991i	$0.459687\pi$
$720$	−7.29733e10			−0.271540
$721$	−3.35923e11			−1.24308
$722$	2.49860e11	−	2.49860e11i	0.919492	−	0.919492i
$723$	1.93827e11	−	1.93827e11i	0.709351	−	0.709351i
$724$		−	4.87033e11i		−	1.77257i
$725$	−2.09993e11	+	1.40371e11i	−0.760070	+	0.508073i
$726$	1.84546e12			6.64290
$727$	−3.19368e11	−	3.19368e11i	−1.14328	−	1.14328i	−0.987846	−	0.155436i	$-0.950322\pi$
$727$	−3.19368e11	−	3.19368e11i	−1.14328	−	1.14328i	−0.155436	−	0.987846i	$-0.549678\pi$
$728$	2.35310e11	+	2.35310e11i	0.837750	+	0.837750i
$729$			2.35142e11i			0.832568i
$730$		−	1.53152e11i		−	0.539303i
$731$			1.05929e11i			0.370974i
$732$	−3.18984e11			−1.11103
$733$	−2.04987e10	+	2.04987e10i	−0.0710084	+	0.0710084i	−0.741719	−	0.670711i	$-0.765989\pi$
$733$	−2.04987e10	+	2.04987e10i	−0.0710084	+	0.0710084i	0.670711	+	0.741719i	$0.265989\pi$
$734$			5.37872e11i			1.85308i
$735$	1.08017e11	−	1.08017e11i	0.370119	−	0.370119i
$736$	−4.07644e10	−	4.07644e10i	−0.138922	−	0.138922i
$737$	6.78613e11	−	6.78613e11i	2.30013	−	2.30013i
$738$		−	3.72679e11i		−	1.25635i
$739$	2.36226e11	+	2.36226e11i	0.792046	+	0.792046i	0.981827	−	0.189780i	$-0.0607776\pi$
$739$	2.36226e11	+	2.36226e11i	0.792046	+	0.792046i	−0.189780	+	0.981827i	$0.560778\pi$
$740$	−5.66948e10	+	5.66948e10i	−0.189067	+	0.189067i
$741$	2.87869e11			0.954821
$742$	2.12611e11	+	2.12611e11i	0.701408	+	0.701408i
$743$	−2.88316e11	+	2.88316e11i	−0.946049	+	0.946049i	−0.998617	−	0.0525687i	$-0.983259\pi$
$743$	−2.88316e11	+	2.88316e11i	−0.946049	+	0.946049i	0.0525687	+	0.998617i	$0.483259\pi$
$744$	−6.70020e10	−	6.70020e10i	−0.218673	−	0.218673i
$745$	4.35821e10			0.141476
$746$	3.98195e9	+	3.98195e9i	0.0128570	+	0.0128570i
$747$		−	3.88310e11i		−	1.24709i
$748$	−3.59917e11			−1.14973
$749$	−8.29767e11			−2.63651
$750$	4.79381e11			1.51508
$751$	3.85870e11	−	3.85870e11i	1.21306	−	1.21306i	0.243042	−	0.970016i	$-0.421855\pi$
$751$	3.85870e11	−	3.85870e11i	1.21306	−	1.21306i	0.970016	−	0.243042i	$-0.0781453\pi$
$752$	4.38476e10	−	4.38476e10i	0.137112	−	0.137112i
$753$			4.58882e10i			0.142732i
$754$	−1.33383e11	+	6.71229e11i	−0.412681	+	2.07676i
$755$	−1.02378e11			−0.315077
$756$	8.41454e11	+	8.41454e11i	2.57599	+	2.57599i
$757$	3.66705e11	+	3.66705e11i	1.11669	+	1.11669i	0.992224	+	0.124467i	$0.0397220\pi$
$757$	3.66705e11	+	3.66705e11i	1.11669	+	1.11669i	0.124467	+	0.992224i	$0.460278\pi$
$758$		−	1.19023e11i		−	0.360541i
$759$			1.61982e11i			0.488089i
$760$			2.37435e10i			0.0711690i
$761$	−1.11777e11			−0.333284			−0.166642	−	0.986017i	$-0.553292\pi$
$761$	−1.11777e11			−0.333284			−0.166642	+	0.986017i	$0.553292\pi$
$762$	−5.42803e11	+	5.42803e11i	−1.60999	+	1.60999i
$763$		−	4.32704e11i		−	1.27671i
$764$	1.82152e11	−	1.82152e11i	0.534640	−	0.534640i
$765$	−6.45786e10	−	6.45786e10i	−0.188557	−	0.188557i
$766$	−1.31330e11	+	1.31330e11i	−0.381459	+	0.381459i
$767$			9.05176e11i			2.61548i
$768$	7.14353e10	+	7.14353e10i	0.205337	+	0.205337i
$769$	2.54673e11	−	2.54673e11i	0.728244	−	0.728244i	−0.242026	−	0.970270i	$-0.577812\pi$
$769$	2.54673e11	−	2.54673e11i	0.728244	−	0.728244i	0.970270	+	0.242026i	$0.0778120\pi$
$770$	−4.21221e11			−1.19825
$771$	−5.08867e11	−	5.08867e11i	−1.44008	−	1.44008i
$772$	−1.19941e11	+	1.19941e11i	−0.337675	+	0.337675i
$773$	−4.18706e11	−	4.18706e11i	−1.17271	−	1.17271i	−0.981560	−	0.191153i	$-0.938777\pi$
$773$	−4.18706e11	−	4.18706e11i	−1.17271	−	1.17271i	−0.191153	−	0.981560i	$-0.561223\pi$
$774$	−9.52574e11			−2.65421
$775$	−6.78317e10	−	6.78317e10i	−0.188030	−	0.188030i
$776$			3.06945e11i			0.846475i
$777$	−5.93508e11			−1.62833
$778$	6.99877e11			1.91031
$779$	5.81939e10			0.158026
$780$	2.55362e11	−	2.55362e11i	0.689886	−	0.689886i
$781$	−4.56143e11	+	4.56143e11i	−1.22602	+	1.22602i
$782$		−	3.85702e10i		−	0.103140i
$783$	−1.34661e11	+	6.77661e11i	−0.358256	+	1.80287i
$784$	1.74658e11			0.462300
$785$	−9.62394e9	−	9.62394e9i	−0.0253440	−	0.0253440i
$786$	−6.68588e11	−	6.68588e11i	−1.75173	−	1.75173i
$787$		−	4.65739e11i		−	1.21407i	−0.794675	−	0.607035i	$-0.792359\pi$
$787$		−	4.65739e11i		−	1.21407i	0.794675	−	0.607035i	$-0.207641\pi$
$788$		−	4.02849e11i		−	1.04481i
$789$		−	2.59919e11i		−	0.670702i
$790$	4.76662e10			0.122378
$791$	4.93267e11	−	4.93267e11i	1.26002	−	1.26002i
$792$		−	9.13773e11i		−	2.32240i
$793$	−1.74669e11	+	1.74669e11i	−0.441695	+	0.441695i
$794$	7.02053e11	+	7.02053e11i	1.76640	+	1.76640i
$795$	6.51407e10	−	6.51407e10i	0.163074	−	0.163074i
$796$		−	8.85693e10i		−	0.220613i
$797$	−9.87078e10	−	9.87078e10i	−0.244635	−	0.244635i	0.574130	−	0.818764i	$-0.305341\pi$
$797$	−9.87078e10	−	9.87078e10i	−0.244635	−	0.244635i	−0.818764	+	0.574130i	$0.805341\pi$
$798$	−4.40198e11	+	4.40198e11i	−1.08552	+	1.08552i
$799$	7.76069e10			0.190420
$800$	3.46255e11	+	3.46255e11i	0.845350	+	0.845350i
$801$	1.40038e9	−	1.40038e9i	0.00340186	−	0.00340186i
$802$	2.50731e11	+	2.50731e11i	0.606053	+	0.606053i
$803$	−9.20364e11			−2.21359
$804$	−1.25820e12	−	1.25820e12i	−3.01111	−	3.01111i
$805$		−	2.62796e10i		−	0.0625800i
$806$	−2.59904e11			−0.615848
$807$	−1.42278e10			−0.0335463
$808$	−1.85796e11			−0.435903
$809$	−2.38060e11	+	2.38060e11i	−0.555767	+	0.555767i	−0.928099	−	0.372332i	$-0.878558\pi$
$809$	−2.38060e11	+	2.38060e11i	−0.555767	+	0.555767i	0.372332	+	0.928099i	$0.378558\pi$
$810$	1.59843e11	−	1.59843e11i	0.371325	−	0.371325i
$811$		−	4.59632e11i		−	1.06250i	−0.847217	−	0.531248i	$-0.821723\pi$
$811$		−	4.59632e11i		−	1.06250i	0.847217	−	0.531248i	$-0.178277\pi$
$812$	−4.78818e11	−	7.16306e11i	−1.10140	−	1.64769i
$813$	8.86396e11			2.02892
$814$	5.85221e11	+	5.85221e11i	1.33298	+	1.33298i
$815$	7.37202e10	+	7.37202e10i	0.167092	+	0.167092i
$816$		−	1.55304e11i		−	0.350286i
$817$		−	1.48745e11i		−	0.333851i
$818$			1.29518e12i			2.89279i
$819$	1.79739e12			3.99490
$820$	5.16224e10	−	5.16224e10i	0.114178	−	0.114178i
$821$			5.08415e11i			1.11904i	0.828817	+	0.559520i	$0.189015\pi$
$821$			5.08415e11i			1.11904i	−0.828817	+	0.559520i	$0.810985\pi$
$822$	−7.23214e11	+	7.23214e11i	−1.58409	+	1.58409i
$823$	2.40249e11	+	2.40249e11i	0.523676	+	0.523676i	0.918679	−	0.395004i	$-0.129257\pi$
$823$	2.40249e11	+	2.40249e11i	0.523676	+	0.523676i	−0.395004	+	0.918679i	$0.629257\pi$
$824$	1.73385e11	−	1.73385e11i	0.376100	−	0.376100i
$825$		−	1.37588e12i		−	2.97006i
$826$	−1.38416e12	−	1.38416e12i	−2.97348	−	2.97348i
$827$	−3.08856e11	+	3.08856e11i	−0.660288	+	0.660288i	−0.955448	−	0.295160i	$-0.904627\pi$
$827$	−3.08856e11	+	3.08856e11i	−0.660288	+	0.660288i	0.295160	+	0.955448i	$0.404627\pi$
$828$	2.01928e11			0.429611
$829$	1.84995e11	+	1.84995e11i	0.391690	+	0.391690i	0.875289	−	0.483599i	$-0.160671\pi$
$829$	1.84995e11	+	1.84995e11i	0.391690	+	0.391690i	−0.483599	+	0.875289i	$0.660671\pi$
$830$	9.23895e10	−	9.23895e10i	0.194675	−	0.194675i
$831$	8.59114e11	+	8.59114e11i	1.80155	+	1.80155i
$832$	1.03038e12			2.15033
$833$	1.54566e11	+	1.54566e11i	0.321021	+	0.321021i
$834$		−	3.61060e11i		−	0.746303i
$835$	−2.55526e11			−0.525641
$836$	5.05394e11			1.03468
$837$	−2.62395e11			−0.534630
$838$	7.69526e11	−	7.69526e11i	1.56044	−	1.56044i
$839$	−6.06892e11	+	6.06892e11i	−1.22480	+	1.22480i	−0.258889	+	0.965907i	$0.583356\pi$
$839$	−6.06892e11	+	6.06892e11i	−1.22480	+	1.22480i	−0.965907	+	0.258889i	$0.916644\pi$
$840$			2.20490e11i			0.442865i
$841$	1.91260e11	−	4.62240e11i	0.382331	−	0.924026i
$842$	2.03741e11			0.405351
$843$	−2.69479e11	−	2.69479e11i	−0.533598	−	0.533598i
$844$	−6.72724e11	−	6.72724e11i	−1.32577	−	1.32577i
$845$		−	1.30363e11i		−	0.255698i
$846$			6.97888e11i			1.36240i
$847$			1.79926e12i			3.49590i
$848$	1.05329e11			0.203688
$849$	1.65278e11	−	1.65278e11i	0.318115	−	0.318115i
$850$			3.27618e11i			0.627613i
$851$	−3.65114e10	+	3.65114e10i	−0.0696163	+	0.0696163i
$852$	8.45725e11	+	8.45725e11i	1.60498	+	1.60498i
$853$	−4.76536e11	+	4.76536e11i	−0.900118	+	0.900118i	−0.995446	−	0.0953283i	$-0.969610\pi$
$853$	−4.76536e11	+	4.76536e11i	−0.900118	+	0.900118i	0.0953283	+	0.995446i	$0.469610\pi$
$854$		−	5.34193e11i		−	1.00431i
$855$	9.06811e10	+	9.06811e10i	0.169688	+	0.169688i
$856$	4.28281e11	−	4.28281e11i	0.797689	−	0.797689i
$857$	2.42541e11			0.449638			0.224819	−	0.974401i	$-0.427821\pi$
$857$	2.42541e11			0.449638			0.224819	+	0.974401i	$0.427821\pi$
$858$	−2.63592e12	−	2.63592e12i	−4.86388	−	4.86388i
$859$	5.76546e11	−	5.76546e11i	1.05892	−	1.05892i	0.0607637	−	0.998152i	$-0.480646\pi$
$859$	5.76546e11	−	5.76546e11i	1.05892	−	1.05892i	0.998152	−	0.0607637i	$-0.0193536\pi$
$860$	−1.31948e11	−	1.31948e11i	−0.241217	−	0.241217i
$861$	5.40408e11			0.983352
$862$	4.03058e11	+	4.03058e11i	0.730027	+	0.730027i
$863$		−	5.99688e11i		−	1.08114i	−0.841299	−	0.540570i	$-0.818209\pi$
$863$		−	5.99688e11i		−	1.08114i	0.841299	−	0.540570i	$-0.181791\pi$
$864$	1.33943e12			2.40361
$865$	−4.24510e10			−0.0758269
$866$	−5.80552e11			−1.03221
$867$	−5.60575e11	+	5.60575e11i	−0.992103	+	0.992103i
$868$	2.31380e11	−	2.31380e11i	0.407612	−	0.407612i
$869$		−	2.86448e11i		−	0.502304i
$870$	−3.76969e11	+	2.51987e11i	−0.658004	+	0.439846i
$871$	−1.37793e12			−2.39417
$872$	2.23338e11	+	2.23338e11i	0.386276	+	0.386276i
$873$	1.17228e12	+	1.17228e12i	2.01825	+	2.01825i
$874$			5.41602e10i			0.0928184i
$875$			4.67379e11i			0.797328i
$876$			1.70643e12i			2.89782i
$877$	9.04467e10			0.152895			0.0764477	−	0.997074i	$-0.475642\pi$
$877$	9.04467e10			0.152895			0.0764477	+	0.997074i	$0.475642\pi$
$878$	−1.99843e11	+	1.99843e11i	−0.336287	+	0.336287i
$879$		−	1.74374e12i		−	2.92097i
$880$	−1.04338e11	+	1.04338e11i	−0.173985	+	0.173985i
$881$	3.51102e11	+	3.51102e11i	0.582814	+	0.582814i	0.935676	−	0.352862i	$-0.114791\pi$
$881$	3.51102e11	+	3.51102e11i	0.582814	+	0.582814i	−0.352862	+	0.935676i	$0.614791\pi$
$882$	−1.38995e12	+	1.38995e12i	−2.29680	+	2.29680i
$883$		−	4.22347e11i		−	0.694746i	−0.937727	−	0.347373i	$-0.887074\pi$
$883$		−	4.22347e11i		−	0.694746i	0.937727	−	0.347373i	$-0.112926\pi$
$884$	3.65408e11	+	3.65408e11i	0.598368	+	0.598368i
$885$	−4.24084e11	+	4.24084e11i	−0.691320	+	0.691320i
$886$	5.19927e11			0.843738
$887$	7.30771e11	+	7.30771e11i	1.18056	+	1.18056i	0.979600	+	0.200957i	$0.0644051\pi$
$887$	7.30771e11	+	7.30771e11i	1.18056	+	1.18056i	0.200957	+	0.979600i	$0.435595\pi$
$888$	3.06337e11	−	3.06337e11i	0.492660	−	0.492660i
$889$	−5.29214e11	−	5.29214e11i	−0.847275	−	0.847275i
$890$	6.66377e8			0.00106209
$891$	−9.60573e11	−	9.60573e11i	−1.52412	−	1.52412i
$892$		−	1.40900e12i		−	2.22563i
$893$	−1.08975e11			−0.171365
$894$	−8.34091e11			−1.30576
$895$	1.98051e11			0.308663
$896$	−7.27967e11	+	7.27967e11i	−1.12948	+	1.12948i
$897$	1.64453e11	−	1.64453e11i	0.254022	−	0.254022i
$898$			8.25586e11i			1.26957i
$899$	1.86341e11	+	3.70285e10i	0.285278	+	0.0566888i
$900$	−1.71519e12			−2.61422
$901$	9.32126e10	+	9.32126e10i	0.141441	+	0.141441i
$902$	−5.32862e11	−	5.32862e11i	−0.804987	−	0.804987i
$903$		−	1.38129e12i		−	2.07747i
$904$			5.09196e11i			0.762450i
$905$		−	2.49893e11i		−	0.372529i
$906$	1.95934e12			2.90802
$907$	2.10714e11	−	2.10714e11i	0.311362	−	0.311362i	−0.534075	−	0.845437i	$-0.679340\pi$
$907$	2.10714e11	−	2.10714e11i	0.311362	−	0.311362i	0.845437	+	0.534075i	$0.179340\pi$
$908$			9.34383e11i			1.37462i
$909$	−7.09589e11	+	7.09589e11i	−1.03933	+	1.03933i
$910$	4.27647e11	+	4.27647e11i	0.623619	+	0.623619i
$911$	−2.41137e11	+	2.41137e11i	−0.350098	+	0.350098i	−0.860146	−	0.510048i	$-0.829628\pi$
$911$	−2.41137e11	+	2.41137e11i	−0.350098	+	0.350098i	0.510048	+	0.860146i	$0.329628\pi$
$912$			2.18078e11i			0.315233i
$913$	−5.55212e11	−	5.55212e11i	−0.799053	−	0.799053i
$914$	1.46698e11	−	1.46698e11i	0.210203	−	0.210203i
$915$	−1.63668e11			−0.233496
$916$	4.55586e11	+	4.55586e11i	0.647125	+	0.647125i
$917$	6.51849e11	−	6.51849e11i	0.921870	−	0.921870i
$918$	6.33666e11	+	6.33666e11i	0.892256	+	0.892256i
$919$	−4.43483e11			−0.621748			−0.310874	−	0.950451i	$-0.600622\pi$
$919$	−4.43483e11			−0.621748			−0.310874	+	0.950451i	$0.600622\pi$
$920$	1.35641e10	+	1.35641e10i	0.0189339	+	0.0189339i
$921$			1.58882e12i			2.20819i
$922$	1.98646e11			0.274888
$923$	9.26203e11			1.27614
$924$	4.69325e12			6.43852
$925$	3.10131e11	−	3.10131e11i	0.423621	−	0.423621i
$926$	−9.36217e11	+	9.36217e11i	−1.27331	+	1.27331i
$927$		−	1.32438e12i		−	1.79347i
$928$	−9.51199e11	−	1.89016e11i	−1.28256	−	0.254864i
$929$	5.32289e11			0.714635			0.357318	−	0.933983i	$-0.383691\pi$
$929$	5.32289e11			0.714635			0.357318	+	0.933983i	$0.383691\pi$
$930$	−1.21768e11	−	1.21768e11i	−0.162780	−	0.162780i
$931$	−2.17041e11	−	2.17041e11i	−0.288896	−	0.288896i
$932$		−	1.49487e12i		−	1.98125i
$933$		−	6.98467e11i		−	0.921763i
$934$			1.29773e11i			0.170529i
$935$	−1.84671e11			−0.241631
$936$	−9.27713e11	+	9.27713e11i	−1.20868	+	1.20868i
$937$			2.28097e11i			0.295912i	0.988994	+	0.147956i	$0.0472694\pi$
$937$			2.28097e11i			0.295912i	−0.988994	+	0.147956i	$0.952731\pi$
$938$	2.10708e12	−	2.10708e12i	2.72188	−	2.72188i
$939$	3.36182e11	+	3.36182e11i	0.432427	+	0.432427i
$940$	−9.66694e10	+	9.66694e10i	−0.123816	+	0.123816i
$941$		−	3.72471e11i		−	0.475044i	−0.971382	−	0.237522i	$-0.923665\pi$
$941$		−	3.72471e11i		−	0.475044i	0.971382	−	0.237522i	$-0.0763351\pi$
$942$	1.84187e11	+	1.84187e11i	0.233913	+	0.233913i
$943$	3.32448e10	−	3.32448e10i	0.0420414	−	0.0420414i
$944$	−6.85724e11			−0.863498
$945$	4.31745e11	+	4.31745e11i	0.541377	+	0.541377i
$946$	−1.36200e12	+	1.36200e12i	−1.70065	+	1.70065i
$947$	4.77832e11	+	4.77832e11i	0.594121	+	0.594121i	0.938742	−	0.344621i	$-0.111993\pi$
$947$	4.77832e11	+	4.77832e11i	0.594121	+	0.594121i	−0.344621	+	0.938742i	$0.611993\pi$
$948$	−5.31098e11			−0.657568
$949$	9.34405e11	+	9.34405e11i	1.15205	+	1.15205i
$950$		−	4.60040e11i		−	0.564808i
$951$	−1.26816e12			−1.55043
$952$	−3.15508e11			−0.384117
$953$	6.56298e11			0.795664			0.397832	−	0.917458i	$-0.369763\pi$
$953$	6.56298e11			0.795664			0.397832	+	0.917458i	$0.369763\pi$
$954$	−8.38224e11	+	8.38224e11i	−1.01197	+	1.01197i
$955$	9.34612e10	−	9.34612e10i	0.112362	−	0.112362i
$956$		−	8.27622e11i		−	0.990833i
$957$	1.51431e12	+	2.26538e12i	1.80537	+	2.70081i
$958$	1.47495e12			1.75112
$959$	−7.05108e11	−	7.05108e11i	−0.833646	−	0.833646i
$960$	4.82744e11	+	4.82744e11i	0.568372	+	0.568372i
$961$		−	7.80739e11i		−	0.915403i
$962$		−	1.18830e12i		−	1.38748i
$963$		−	3.27137e12i		−	3.80386i
$964$	−6.90964e11			−0.800105
$965$	−6.15409e10	+	6.15409e10i	−0.0709667	+	0.0709667i
$966$			5.02949e11i			0.577584i
$967$	−7.37125e11	+	7.37125e11i	−0.843015	+	0.843015i	−0.989250	−	0.146235i	$-0.953284\pi$
$967$	−7.37125e11	+	7.37125e11i	−0.843015	+	0.843015i	0.146235	+	0.989250i	$0.453284\pi$
$968$	−9.28679e11	−	9.28679e11i	−1.05770	−	1.05770i
$969$	−1.92991e11	+	1.92991e11i	−0.218898	+	0.218898i
$970$			5.57836e11i			0.630114i
$971$	5.41917e11	+	5.41917e11i	0.609615	+	0.609615i	0.942845	−	0.333231i	$-0.108139\pi$
$971$	5.41917e11	+	5.41917e11i	0.609615	+	0.609615i	−0.333231	+	0.942845i	$0.608139\pi$
$972$	−1.64396e11	+	1.64396e11i	−0.184174	+	0.184174i
$973$	3.52021e11			0.392751
$974$	−3.57797e11	−	3.57797e11i	−0.397558	−	0.397558i
$975$	−1.39687e12	+	1.39687e12i	−1.54575	+	1.54575i
$976$	−1.32322e11	−	1.32322e11i	−0.145825	−	0.145825i
$977$	−1.07026e12			−1.17466			−0.587331	−	0.809347i	$-0.699821\pi$
$977$	−1.07026e12			−1.17466			−0.587331	+	0.809347i	$0.699821\pi$
$978$	−1.41088e12	−	1.41088e12i	−1.54218	−	1.54218i
$979$		−	4.00457e9i		−	0.00435938i
$980$	−3.85063e11			−0.417472
$981$	1.70595e12			1.84200
$982$	−1.70526e12			−1.83377
$983$	4.26579e11	−	4.26579e11i	0.456862	−	0.456862i	−0.440762	−	0.897624i	$-0.645292\pi$
$983$	4.26579e11	−	4.26579e11i	0.456862	−	0.456862i	0.897624	+	0.440762i	$0.145292\pi$
$984$	−2.78929e11	+	2.78929e11i	−0.297518	+	0.297518i
$985$		−	2.06699e11i		−	0.219581i
$986$	−3.60579e11	−	5.39421e11i	−0.381498	−	0.570716i
$987$	−1.01198e12			−1.06636
$988$	−5.13104e11	−	5.13104e11i	−0.538490	−	0.538490i
$989$	−8.49742e10	−	8.49742e10i	−0.0888182	−	0.0888182i
$990$		−	1.66067e12i		−	1.72879i
$991$		−	1.31382e11i		−	0.136220i	−0.997678	−	0.0681102i	$-0.978303\pi$
$991$		−	1.31382e11i		−	0.136220i	0.997678	−	0.0681102i	$-0.0216970\pi$
$992$		−	3.68310e11i		−	0.380336i
$993$	−5.91371e11			−0.608223
$994$	−1.41631e12	+	1.41631e12i	−1.45082	+	1.45082i
$995$		−	4.54443e10i		−	0.0463647i
$996$	−1.02941e12	+	1.02941e12i	−1.04604	+	1.04604i
$997$	−1.85137e11	−	1.85137e11i	−0.187376	−	0.187376i	0.607185	−	0.794561i	$-0.292299\pi$
$997$	−1.85137e11	−	1.85137e11i	−0.187376	−	0.187376i	−0.794561	+	0.607185i	$0.792299\pi$
$998$	3.26013e11	−	3.26013e11i	0.328634	−	0.328634i
$999$		−	1.19968e12i		−	1.20450i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.9.c.a.12.16	✓	38
29.17	odd	4	inner	29.9.c.a.17.16	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.9.c.a.12.16	✓	38	1.1	even	1	trivial
29.9.c.a.17.16	yes	38	29.17	odd	4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(17.5030 + 17.5030i) q^{2} +(-100.063 - 100.063i) q^{3} +356.708i q^{4} +183.024i q^{5} -3502.79i q^{6} +3415.09 q^{7} +(-1762.69 + 1762.69i) q^{8} +13464.1i q^{9} +O(q^{10})\)	\(q+(17.5030 + 17.5030i) q^{2} +(-100.063 - 100.063i) q^{3} +356.708i q^{4} +183.024i q^{5} -3502.79i q^{6} +3415.09 q^{7} +(-1762.69 + 1762.69i) q^{8} +13464.1i q^{9} +(-3203.47 + 3203.47i) q^{10} +(19251.1 + 19251.1i) q^{11} +(35693.1 - 35693.1i) q^{12} -39089.7i q^{13} +(59774.3 + 59774.3i) q^{14} +(18313.9 - 18313.9i) q^{15} +29612.7 q^{16} +(26206.1 + 26206.1i) q^{17} +(-235661. + 235661. i) q^{18} +(-36798.6 - 36798.6i) q^{19} -65286.2 q^{20} +(-341724. - 341724. i) q^{21} +673904. i q^{22} -42044.3 q^{23} +352758. q^{24} +357127. q^{25} +(684185. - 684185. i) q^{26} +(690741. - 690741. i) q^{27} +1.21819e6i q^{28} +(-588008. + 393056. i) q^{29} +641096. q^{30} +(-189937. - 189937. i) q^{31} +(969558. + 969558. i) q^{32} -3.85264e6i q^{33} +917371. i q^{34} +625045. i q^{35} -4.80274e6 q^{36} +(868404. - 868404. i) q^{37} -1.28817e6i q^{38} +(-3.91142e6 + 3.91142e6i) q^{39} +(-322615. - 322615. i) q^{40} +(-790709. + 790709. i) q^{41} -1.19624e7i q^{42} +(2.02106e6 + 2.02106e6i) q^{43} +(-6.86704e6 + 6.86704e6i) q^{44} -2.46426e6 q^{45} +(-735900. - 735900. i) q^{46} +(1.48070e6 - 1.48070e6i) q^{47} +(-2.96313e6 - 2.96313e6i) q^{48} +5.89807e6 q^{49} +(6.25078e6 + 6.25078e6i) q^{50} -5.24451e6i q^{51} +1.39436e7 q^{52} +3.55690e6 q^{53} +2.41800e7 q^{54} +(-3.52343e6 + 3.52343e6i) q^{55} +(-6.01974e6 + 6.01974e6i) q^{56} +7.36433e6i q^{57} +(-1.71715e7 - 3.41222e6i) q^{58} -2.31564e7 q^{59} +(6.53272e6 + 6.53272e6i) q^{60} +(-4.46842e6 - 4.46842e6i) q^{61} -6.64893e6i q^{62} +4.59811e7i q^{63} +2.63594e7i q^{64} +7.15436e6 q^{65} +(6.74327e7 - 6.74327e7i) q^{66} -3.52505e7i q^{67} +(-9.34794e6 + 9.34794e6i) q^{68} +(4.20707e6 + 4.20707e6i) q^{69} +(-1.09402e7 + 1.09402e7i) q^{70} +2.36943e7i q^{71} +(-2.37330e7 - 2.37330e7i) q^{72} +(-2.39041e7 + 2.39041e7i) q^{73} +3.03993e7 q^{74} +(-3.57351e7 - 3.57351e7i) q^{75} +(1.31263e7 - 1.31263e7i) q^{76} +(6.57445e7 + 6.57445e7i) q^{77} -1.36923e8 q^{78} +(-7.43977e6 - 7.43977e6i) q^{79} +5.41985e6i q^{80} -4.98969e7 q^{81} -2.76795e7 q^{82} -2.88404e7 q^{83} +(1.21895e8 - 1.21895e8i) q^{84} +(-4.79636e6 + 4.79636e6i) q^{85} +7.07492e7i q^{86} +(9.81679e7 + 1.95073e7i) q^{87} -6.78675e7 q^{88} +(-104009. - 104009. i) q^{89} +(-4.31318e7 - 4.31318e7i) q^{90} -1.33495e8i q^{91} -1.49975e7i q^{92} +3.80113e7i q^{93} +5.18333e7 q^{94} +(6.73504e6 - 6.73504e6i) q^{95} -1.94033e8i q^{96} +(8.70674e7 - 8.70674e7i) q^{97} +(1.03234e8 + 1.03234e8i) q^{98} +(-2.59199e8 + 2.59199e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8}+O(q^{10}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8} + 15870 q^{10} - 8390 q^{11} + 5022 q^{12} + 12728 q^{14} - 35530 q^{15} - 245912 q^{16} + 76234 q^{17} - 465022 q^{18} - 164488 q^{19} + 4092 q^{20} - 514620 q^{21} + 733568 q^{23} - 482376 q^{24} - 1528354 q^{25} + 1405470 q^{26} - 1279754 q^{27} + 1420996 q^{29} + 3659852 q^{30} + 291062 q^{31} + 1592134 q^{32} - 10223688 q^{36} + 7994574 q^{37} - 309930 q^{39} + 9093994 q^{40} + 9561658 q^{41} - 5181022 q^{43} - 11400526 q^{44} + 9526060 q^{45} - 32561820 q^{46} + 5445034 q^{47} - 17683542 q^{48} + 45106458 q^{49} + 3122002 q^{50} + 56198616 q^{52} - 25331452 q^{53} - 42307016 q^{54} + 3037606 q^{55} - 25661184 q^{56} - 33846328 q^{58} + 27333008 q^{59} + 30592014 q^{60} - 49572406 q^{61} - 121974972 q^{65} + 133443354 q^{66} + 21192980 q^{68} - 28739184 q^{69} - 17976124 q^{70} - 186114192 q^{72} + 45787870 q^{73} + 91919252 q^{74} - 159074460 q^{75} + 243795016 q^{76} + 59851916 q^{77} + 163580208 q^{78} - 99827470 q^{79} - 75138586 q^{81} - 18178416 q^{82} - 177270160 q^{83} - 9436684 q^{84} + 156307616 q^{85} - 20584526 q^{87} + 563433236 q^{88} - 388451858 q^{89} + 306402752 q^{90} + 81569204 q^{94} - 44386260 q^{95} - 121157834 q^{97} - 129908712 q^{98} - 216447384 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8 + 15870 * q^10 - 8390 * q^11 + 5022 * q^12 + 12728 * q^14 - 35530 * q^15 - 245912 * q^16 + 76234 * q^17 - 465022 * q^18 - 164488 * q^19 + 4092 * q^20 - 514620 * q^21 + 733568 * q^23 - 482376 * q^24 - 1528354 * q^25 + 1405470 * q^26 - 1279754 * q^27 + 1420996 * q^29 + 3659852 * q^30 + 291062 * q^31 + 1592134 * q^32 - 10223688 * q^36 + 7994574 * q^37 - 309930 * q^39 + 9093994 * q^40 + 9561658 * q^41 - 5181022 * q^43 - 11400526 * q^44 + 9526060 * q^45 - 32561820 * q^46 + 5445034 * q^47 - 17683542 * q^48 + 45106458 * q^49 + 3122002 * q^50 + 56198616 * q^52 - 25331452 * q^53 - 42307016 * q^54 + 3037606 * q^55 - 25661184 * q^56 - 33846328 * q^58 + 27333008 * q^59 + 30592014 * q^60 - 49572406 * q^61 - 121974972 * q^65 + 133443354 * q^66 + 21192980 * q^68 - 28739184 * q^69 - 17976124 * q^70 - 186114192 * q^72 + 45787870 * q^73 + 91919252 * q^74 - 159074460 * q^75 + 243795016 * q^76 + 59851916 * q^77 + 163580208 * q^78 - 99827470 * q^79 - 75138586 * q^81 - 18178416 * q^82 - 177270160 * q^83 - 9436684 * q^84 + 156307616 * q^85 - 20584526 * q^87 + 563433236 * q^88 - 388451858 * q^89 + 306402752 * q^90 + 81569204 * q^94 - 44386260 * q^95 - 121157834 * q^97 - 129908712 * q^98 - 216447384 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more