LMFDB - Embedded newform 32.8.g.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [32,8,Mod(5,32)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(32, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("32.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 32 = 2^{5} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	32.g (of order $8$, degree $4$, 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:	$9.99632081549$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$27$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			13.2
Character	$\chi$	$=$	32.13
Dual form			32.8.g.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.1568 - 1.87795i) q^{2} +(26.2524 - 63.3790i) q^{3} +(120.947 + 41.9036i) q^{4} +(-452.646 + 187.492i) q^{5} +(-411.914 + 657.803i) q^{6} +(210.637 - 210.637i) q^{7} +(-1270.68 - 694.640i) q^{8} +(-1781.26 - 1781.26i) q^{9} +O(q^{10})$	\(q+(-11.1568 - 1.87795i) q^{2} +(26.2524 - 63.3790i) q^{3} +(120.947 + 41.9036i) q^{4} +(-452.646 + 187.492i) q^{5} +(-411.914 + 657.803i) q^{6} +(210.637 - 210.637i) q^{7} +(-1270.68 - 694.640i) q^{8} +(-1781.26 - 1781.26i) q^{9} +(5402.17 - 1241.76i) q^{10} +(1854.88 + 4478.07i) q^{11} +(5830.95 - 6565.40i) q^{12} +(-6549.58 - 2712.92i) q^{13} +(-2745.60 + 1954.47i) q^{14} +33610.4i q^{15} +(12872.2 + 10136.2i) q^{16} +25881.2i q^{17} +(16528.0 + 23218.2i) q^{18} +(20631.9 + 8546.02i) q^{19} +(-62602.7 + 3709.03i) q^{20} +(-7820.24 - 18879.7i) q^{21} +(-12284.8 - 53444.1i) q^{22} +(24469.2 + 24469.2i) q^{23} +(-77384.0 + 62298.4i) q^{24} +(114493. - 114493. i) q^{25} +(67977.4 + 42567.2i) q^{26} +(-21047.0 + 8717.96i) q^{27} +(34302.4 - 16649.4i) q^{28} +(-80161.3 + 193526. i) q^{29} +(63118.5 - 374983. i) q^{30} -139502. q^{31} +(-124576. - 137260. i) q^{32} +332510. q^{33} +(48603.5 - 288750. i) q^{34} +(-55851.4 + 134837. i) q^{35} +(-140796. - 290079. i) q^{36} +(-489572. + 202788. i) q^{37} +(-214136. - 134092. i) q^{38} +(-343885. + 343885. i) q^{39} +(705408. + 76183.7i) q^{40} +(-176068. - 176068. i) q^{41} +(51793.4 + 225323. i) q^{42} +(-127834. - 308618. i) q^{43} +(36693.8 + 619333. i) q^{44} +(1.14025e6 + 472308. i) q^{45} +(-227045. - 318948. i) q^{46} -819080. i q^{47} +(980348. - 549725. i) q^{48} +734807. i q^{49} +(-1.49238e6 + 1.06236e6i) q^{50} +(1.64032e6 + 679443. i) q^{51} +(-678468. - 602570. i) q^{52} +(68507.7 + 165392. i) q^{53} +(251188. - 57739.0i) q^{54} +(-1.67921e6 - 1.67921e6i) q^{55} +(-413970. + 121336. i) q^{56} +(1.08328e6 - 1.08328e6i) q^{57} +(1.25777e6 - 2.00859e6i) q^{58} +(-2.11876e6 + 877618. i) q^{59} +(-1.40840e6 + 4.06506e6i) q^{60} +(-262763. + 634365. i) q^{61} +(1.55639e6 + 261977. i) q^{62} -750400. q^{63} +(1.13210e6 + 1.76533e6i) q^{64} +3.47330e6 q^{65} +(-3.70974e6 - 624437. i) q^{66} +(-976529. + 2.35755e6i) q^{67} +(-1.08451e6 + 3.13024e6i) q^{68} +(2.19320e6 - 908455. i) q^{69} +(876338. - 1.39946e6i) q^{70} +(266616. - 266616. i) q^{71} +(1.02608e6 + 3.50075e6i) q^{72} +(-1.90706e6 - 1.90706e6i) q^{73} +(5.84287e6 - 1.34306e6i) q^{74} +(-4.25072e6 - 1.02621e7i) q^{75} +(2.13725e6 + 1.89816e6i) q^{76} +(1.33396e6 + 552542. i) q^{77} +(4.48244e6 - 3.19084e6i) q^{78} +5.03765e6i q^{79} +(-7.72700e6 - 2.17468e6i) q^{80} -3.94643e6i q^{81} +(1.63370e6 + 2.29499e6i) q^{82} +(-3.53046e6 - 1.46236e6i) q^{83} +(-154703. - 2.61114e6i) q^{84} +(-4.85252e6 - 1.17150e7i) q^{85} +(846643. + 3.68324e6i) q^{86} +(1.01611e7 + 1.01611e7i) q^{87} +(753692. - 6.97866e6i) q^{88} +(-2.09666e6 + 2.09666e6i) q^{89} +(-1.18346e7 - 7.41077e6i) q^{90} +(-1.95103e6 + 808143. i) q^{91} +(1.93412e6 + 3.98481e6i) q^{92} +(-3.66226e6 + 8.84147e6i) q^{93} +(-1.53819e6 + 9.13828e6i) q^{94} -1.09413e7 q^{95} +(-1.19699e7 + 4.29211e6i) q^{96} +1.58577e7 q^{97} +(1.37993e6 - 8.19806e6i) q^{98} +(4.67259e6 - 1.12806e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 108 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 13004 q^{10} - 4 q^{11} + 30668 q^{12} - 4 q^{13} - 26196 q^{14} - 52784 q^{16} + 102056 q^{18} - 4 q^{19} + 81996 q^{20} - 4 q^{21} - 374240 q^{22} - 143420 q^{23} + 380880 q^{24} - 4 q^{25} - 363984 q^{26} + 476084 q^{27} - 195464 q^{28} - 4 q^{29} + 870468 q^{30} - 714992 q^{31} + 535656 q^{32} - 8 q^{33} - 201072 q^{34} + 816500 q^{35} - 1669712 q^{36} - 4 q^{37} - 2533100 q^{38} - 283948 q^{39} + 2746344 q^{40} - 4 q^{41} + 4924936 q^{42} + 366180 q^{43} - 1585404 q^{44} + 8744 q^{45} - 2715812 q^{46} - 5044368 q^{48} - 1653804 q^{50} + 3002072 q^{51} + 8882212 q^{52} - 1815636 q^{53} + 6815776 q^{54} - 4191012 q^{55} - 3655000 q^{56} - 4 q^{57} - 12448736 q^{58} - 1835940 q^{59} - 6364808 q^{60} - 4559780 q^{61} + 12948600 q^{62} + 10001872 q^{63} + 16915544 q^{64} - 8 q^{65} - 11246068 q^{66} - 1940684 q^{67} - 8895536 q^{68} + 9580892 q^{69} - 8149480 q^{70} - 12348708 q^{71} + 12884564 q^{72} - 4 q^{73} + 10931436 q^{74} + 11573008 q^{75} + 14443516 q^{76} - 11914452 q^{77} - 38252364 q^{78} - 11333192 q^{80} + 15827196 q^{82} - 9565884 q^{83} + 8101984 q^{84} + 312496 q^{85} - 14812992 q^{86} + 40789108 q^{87} + 5716448 q^{88} - 4 q^{89} + 5335400 q^{90} - 3406996 q^{91} + 27562664 q^{92} - 8752 q^{93} - 14227032 q^{94} - 54872008 q^{95} - 25080448 q^{96} - 8 q^{97} + 57598104 q^{98} - 9738480 q^{99}+O(q^{100}) \) 108 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 13004 * q^10 - 4 * q^11 + 30668 * q^12 - 4 * q^13 - 26196 * q^14 - 52784 * q^16 + 102056 * q^18 - 4 * q^19 + 81996 * q^20 - 4 * q^21 - 374240 * q^22 - 143420 * q^23 + 380880 * q^24 - 4 * q^25 - 363984 * q^26 + 476084 * q^27 - 195464 * q^28 - 4 * q^29 + 870468 * q^30 - 714992 * q^31 + 535656 * q^32 - 8 * q^33 - 201072 * q^34 + 816500 * q^35 - 1669712 * q^36 - 4 * q^37 - 2533100 * q^38 - 283948 * q^39 + 2746344 * q^40 - 4 * q^41 + 4924936 * q^42 + 366180 * q^43 - 1585404 * q^44 + 8744 * q^45 - 2715812 * q^46 - 5044368 * q^48 - 1653804 * q^50 + 3002072 * q^51 + 8882212 * q^52 - 1815636 * q^53 + 6815776 * q^54 - 4191012 * q^55 - 3655000 * q^56 - 4 * q^57 - 12448736 * q^58 - 1835940 * q^59 - 6364808 * q^60 - 4559780 * q^61 + 12948600 * q^62 + 10001872 * q^63 + 16915544 * q^64 - 8 * q^65 - 11246068 * q^66 - 1940684 * q^67 - 8895536 * q^68 + 9580892 * q^69 - 8149480 * q^70 - 12348708 * q^71 + 12884564 * q^72 - 4 * q^73 + 10931436 * q^74 + 11573008 * q^75 + 14443516 * q^76 - 11914452 * q^77 - 38252364 * q^78 - 11333192 * q^80 + 15827196 * q^82 - 9565884 * q^83 + 8101984 * q^84 + 312496 * q^85 - 14812992 * q^86 + 40789108 * q^87 + 5716448 * q^88 - 4 * q^89 + 5335400 * q^90 - 3406996 * q^91 + 27562664 * q^92 - 8752 * q^93 - 14227032 * q^94 - 54872008 * q^95 - 25080448 * q^96 - 8 * q^97 + 57598104 * q^98 - 9738480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

$n$	$5$	$31$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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 $

$2$	−11.1568	−	1.87795i	−0.986128	−	0.165989i
$2$	−11.1568	−	1.87795i	−0.986128	−	0.165989i
$3$	26.2524	−	63.3790i	0.561365	−	1.35525i	−0.347311	−	0.937750i	$-0.612905\pi$
$3$	26.2524	−	63.3790i	0.561365	−	1.35525i	0.908675	−	0.417504i	$-0.137095\pi$
$4$	120.947	+	41.9036i	0.944896	+	0.327372i
$5$	−452.646	+	187.492i	−1.61944	+	0.670793i	−0.993990	−	0.109474i	$-0.965084\pi$
$5$	−452.646	+	187.492i	−1.61944	+	0.670793i	−0.625447	+	0.780266i	$0.715084\pi$
$6$	−411.914	+	657.803i	−0.778534	+	1.24327i
$7$	210.637	−	210.637i	0.232109	−	0.232109i	−0.581463	−	0.813573i	$-0.697520\pi$
$7$	210.637	−	210.637i	0.232109	−	0.232109i	0.813573	+	0.581463i	$0.197520\pi$
$8$	−1270.68	−	694.640i	−0.877448	−	0.479673i
$9$	−1781.26	−	1781.26i	−0.814476	−	0.814476i
$10$	5402.17	−	1241.76i	1.70832	−	0.392679i
$11$	1854.88	+	4478.07i	0.420185	+	1.01442i	0.982293	+	0.187352i	$0.0599906\pi$
$11$	1854.88	+	4478.07i	0.420185	+	1.01442i	−0.562108	+	0.827064i	$0.690009\pi$
$12$	5830.95	−	6565.40i	0.974103	−	1.09680i
$13$	−6549.58	−	2712.92i	−0.826821	−	0.342481i	−0.0711777	−	0.997464i	$-0.522676\pi$
$13$	−6549.58	−	2712.92i	−0.826821	−	0.342481i	−0.755644	+	0.654983i	$0.772676\pi$
$14$	−2745.60	+	1954.47i	−0.267417	+	0.190362i
$15$			33610.4i			2.57131i
$16$	12872.2	+	10136.2i	0.785655	+	0.618665i
$17$			25881.2i			1.27765i	0.769351	+	0.638826i	$0.220580\pi$
$17$			25881.2i			1.27765i	−0.769351	+	0.638826i	$0.779420\pi$
$18$	16528.0	+	23218.2i	0.667984	+	0.938372i
$19$	20631.9	+	8546.02i	0.690084	+	0.285842i	0.700035	−	0.714108i	$-0.253168\pi$
$19$	20631.9	+	8546.02i	0.690084	+	0.285842i	−0.00995111	+	0.999950i	$0.503168\pi$
$20$	−62602.7	+	3709.03i	−1.74980	+	0.103671i
$21$	−7820.24	−	18879.7i	−0.184269	−	0.444865i
$22$	−12284.8	−	53444.1i	−0.245974	−	1.07009i
$23$	24469.2	+	24469.2i	0.419345	+	0.419345i	0.884978	−	0.465633i	$-0.154173\pi$
$23$	24469.2	+	24469.2i	0.419345	+	0.419345i	−0.465633	+	0.884978i	$0.654173\pi$
$24$	−77384.0	+	62298.4i	−1.14265	+	0.919893i
$25$	114493.	−	114493.i	1.46551	−	1.46551i
$26$	67977.4	+	42567.2i	0.758503	+	0.474973i
$27$	−21047.0	+	8717.96i	−0.205787	+	0.0852397i
$28$	34302.4	−	16649.4i	0.295305	−	0.143333i
$29$	−80161.3	+	193526.i	−0.610340	+	1.47349i	0.252288	+	0.967652i	$0.418817\pi$
$29$	−80161.3	+	193526.i	−0.610340	+	1.47349i	−0.862628	+	0.505839i	$0.831183\pi$
$30$	63118.5	−	374983.i	0.426808	−	2.53564i
$31$	−139502.			−0.841034			−0.420517	−	0.907285i	$-0.638151\pi$
$31$	−139502.			−0.841034			−0.420517	+	0.907285i	$0.638151\pi$
$32$	−124576.	−	137260.i	−0.672065	−	0.740492i
$33$	332510.			1.61067
$34$	48603.5	−	288750.i	0.212076	−	1.25993i
$35$	−55851.4	+	134837.i	−0.220189	+	0.531584i
$36$	−140796.	−	290079.i	−0.502958	−	1.03623i
$37$	−489572.	+	202788.i	−1.58895	+	0.658166i	−0.989799	−	0.142469i	$-0.954496\pi$
$37$	−489572.	+	202788.i	−1.58895	+	0.658166i	−0.599153	+	0.800634i	$0.704496\pi$
$38$	−214136.	−	134092.i	−0.633065	−	0.396423i
$39$	−343885.	+	343885.i	−0.928296	+	0.928296i
$40$	705408.	+	76183.7i	1.74273	+	0.188214i
$41$	−176068.	−	176068.i	−0.398966	−	0.398966i	0.478902	−	0.877868i	$-0.341035\pi$
$41$	−176068.	−	176068.i	−0.398966	−	0.398966i	−0.877868	+	0.478902i	$0.841035\pi$
$42$	51793.4	+	225323.i	0.107870	+	0.469280i
$43$	−127834.	−	308618.i	−0.245192	−	0.591946i	0.752592	−	0.658487i	$-0.228803\pi$
$43$	−127834.	−	308618.i	−0.245192	−	0.591946i	−0.997784	+	0.0665417i	$0.978803\pi$
$44$	36693.8	+	619333.i	0.0649394	+	1.09607i
$45$	1.14025e6	+	472308.i	1.86534	+	0.772648i
$46$	−227045.	−	318948.i	−0.343921	−	0.483134i
$47$		−	819080.i		−	1.15076i	−0.817887	−	0.575378i	$-0.804855\pi$
$47$		−	819080.i		−	1.15076i	0.817887	−	0.575378i	$-0.195145\pi$
$48$	980348.	−	549725.i	1.27949	−	0.717466i
$49$			734807.i			0.892251i
$50$	−1.49238e6	+	1.06236e6i	−1.68843	+	1.20192i
$51$	1.64032e6	+	679443.i	1.73154	+	0.717229i
$52$	−678468.	−	602570.i	−0.669141	−	0.594287i
$53$	68507.7	+	165392.i	0.0632082	+	0.152598i	0.952328	−	0.305077i	$-0.0986822\pi$
$53$	68507.7	+	165392.i	0.0632082	+	0.152598i	−0.889119	+	0.457675i	$0.848682\pi$
$54$	251188.	−	57739.0i	0.217081	−	0.0498989i
$55$	−1.67921e6	−	1.67921e6i	−1.36093	−	1.36093i
$56$	−413970.	+	121336.i	−0.315000	+	0.0923272i
$57$	1.08328e6	−	1.08328e6i	0.774778	−	0.774778i
$58$	1.25777e6	−	2.00859e6i	0.846456	−	1.35174i
$59$	−2.11876e6	+	877618.i	−1.34307	+	0.556318i	−0.934355	−	0.356343i	$-0.884023\pi$
$59$	−2.11876e6	+	877618.i	−1.34307	+	0.556318i	−0.408716	+	0.912662i	$0.634023\pi$
$60$	−1.40840e6	+	4.06506e6i	−0.841774	+	2.42962i
$61$	−262763.	+	634365.i	−0.148221	+	0.357837i	−0.980500	−	0.196520i	$-0.937036\pi$
$61$	−262763.	+	634365.i	−0.148221	+	0.357837i	0.832279	+	0.554357i	$0.187036\pi$
$62$	1.55639e6	+	261977.i	0.829367	+	0.139602i
$63$	−750400.			−0.378095
$64$	1.13210e6	+	1.76533e6i	0.539828	+	0.841775i
$65$	3.47330e6			1.56872
$66$	−3.70974e6	−	624437.i	−1.58833	−	0.267353i
$67$	−976529.	+	2.35755e6i	−0.396665	+	0.957633i	0.591787	+	0.806095i	$0.298423\pi$
$67$	−976529.	+	2.35755e6i	−0.396665	+	0.957633i	−0.988451	+	0.151538i	$0.951577\pi$
$68$	−1.08451e6	+	3.13024e6i	−0.418268	+	1.20725i
$69$	2.19320e6	−	908455.i	0.803725	−	0.332914i
$70$	876338.	−	1.39946e6i	0.305371	−	0.487660i
$71$	266616.	−	266616.i	0.0884061	−	0.0884061i	−0.661521	−	0.749927i	$-0.730089\pi$
$71$	266616.	−	266616.i	0.0884061	−	0.0884061i	0.749927	+	0.661521i	$0.230089\pi$
$72$	1.02608e6	+	3.50075e6i	0.323978	+	1.10534i
$73$	−1.90706e6	−	1.90706e6i	−0.573764	−	0.573764i	0.359414	−	0.933178i	$-0.382977\pi$
$73$	−1.90706e6	−	1.90706e6i	−0.573764	−	0.573764i	−0.933178	+	0.359414i	$0.882977\pi$
$74$	5.84287e6	−	1.34306e6i	1.67616	−	0.385287i
$75$	−4.25072e6	−	1.02621e7i	−1.16345	−	2.80882i
$76$	2.13725e6	+	1.89816e6i	0.558481	+	0.496005i
$77$	1.33396e6	+	552542.i	0.332984	+	0.137927i
$78$	4.48244e6	−	3.19084e6i	1.06951	−	0.761332i
$79$			5.03765e6i			1.14956i	0.818307	+	0.574782i	$0.194913\pi$
$79$			5.03765e6i			1.14956i	−0.818307	+	0.574782i	$0.805087\pi$
$80$	−7.72700e6	−	2.17468e6i	−1.68731	−	0.474877i
$81$		−	3.94643e6i		−	0.825100i
$82$	1.63370e6	+	2.29499e6i	0.327208	+	0.459655i
$83$	−3.53046e6	−	1.46236e6i	−0.677731	−	0.280726i	0.0171468	−	0.999853i	$-0.494542\pi$
$83$	−3.53046e6	−	1.46236e6i	−0.677731	−	0.280726i	−0.694878	+	0.719127i	$0.744542\pi$
$84$	−154703.	−	2.61114e6i	−0.0284787	−	0.480675i
$85$	−4.85252e6	−	1.17150e7i	−0.857040	−	2.06908i
$86$	846643.	+	3.68324e6i	0.143534	+	0.624433i
$87$	1.01611e7	+	1.01611e7i	1.65433	+	1.65433i
$88$	753692.	−	6.97866e6i	0.117897	−	1.09165i
$89$	−2.09666e6	+	2.09666e6i	−0.315256	+	0.315256i	−0.846942	−	0.531686i	$-0.821559\pi$
$89$	−2.09666e6	+	2.09666e6i	−0.315256	+	0.315256i	0.531686	+	0.846942i	$0.321559\pi$
$90$	−1.18346e7	−	7.41077e6i	−1.71121	−	1.07156i
$91$	−1.95103e6	+	808143.i	−0.271406	+	0.112420i
$92$	1.93412e6	+	3.98481e6i	0.258955	+	0.533519i
$93$	−3.66226e6	+	8.84147e6i	−0.472127	+	1.13981i
$94$	−1.53819e6	+	9.13828e6i	−0.191013	+	1.13479i
$95$	−1.09413e7			−1.30929
$96$	−1.19699e7	+	4.29211e6i	−1.38083	+	0.495132i
$97$	1.58577e7			1.76416			0.882081	−	0.471097i	$-0.156142\pi$
$97$	1.58577e7			1.76416			0.882081	+	0.471097i	$0.156142\pi$
$98$	1.37993e6	−	8.19806e6i	0.148104	−	0.879873i
$99$	4.67259e6	−	1.12806e7i	0.483987	−	1.16845i
$100$	1.86452e7	−	9.04985e6i	1.86452	−	0.904985i
$101$	−2.67794e6	+	1.10924e6i	−0.258628	+	0.107127i	−0.508230	−	0.861221i	$-0.669700\pi$
$101$	−2.67794e6	+	1.10924e6i	−0.258628	+	0.107127i	0.249602	+	0.968348i	$0.419700\pi$
$102$	−1.70247e7	−	1.06608e7i	−1.58847	−	0.994695i
$103$	1.39677e7	−	1.39677e7i	1.25949	−	1.25949i	0.308147	−	0.951339i	$-0.400291\pi$
$103$	1.39677e7	−	1.39677e7i	1.25949	−	1.25949i	0.951339	−	0.308147i	$-0.0997089\pi$
$104$	6.43791e6	+	7.99686e6i	0.561214	+	0.697112i
$105$	7.07961e6	+	7.07961e6i	0.596824	+	0.596824i
$106$	−453726.	−	1.97389e6i	−0.0370018	−	0.160973i
$107$	−1.07929e6	−	2.60564e6i	−0.0851716	−	0.205622i	0.875555	−	0.483118i	$-0.160496\pi$
$107$	−1.07929e6	−	2.60564e6i	−0.0851716	−	0.205622i	−0.960727	+	0.277495i	$0.910496\pi$
$108$	−2.91088e6	+	172462.i	−0.222352	+	0.0131737i
$109$	−1.61709e6	−	669821.i	−0.119603	−	0.0495411i	0.322079	−	0.946713i	$-0.395618\pi$
$109$	−1.61709e6	−	669821.i	−0.119603	−	0.0495411i	−0.441682	+	0.897172i	$0.645618\pi$
$110$	1.55810e7	+	2.18880e7i	1.11615	+	1.56795i
$111$			3.63523e7i			2.52291i
$112$	4.84643e6	−	576297.i	0.325956	−	0.0387600i
$113$			1.39642e7i			0.910418i	0.890385	+	0.455209i	$0.150436\pi$
$113$			1.39642e7i			0.910418i	−0.890385	+	0.455209i	$0.849564\pi$
$114$	−1.41202e7	+	1.00515e7i	−0.892634	+	0.635425i
$115$	−1.56637e7	−	6.48810e6i	−0.960397	−	0.397809i
$116$	−1.78047e7	+	2.00473e7i	−1.05909	+	1.19249i
$117$	6.83408e6	+	1.64989e7i	0.394484	+	0.952369i
$118$	2.52866e7	−	5.81246e6i	1.41678	−	0.325666i
$119$	5.45154e6	+	5.45154e6i	0.296555	+	0.296555i
$120$	2.33471e7	−	4.27080e7i	1.23339	−	2.25619i
$121$	−2.83302e6	+	2.83302e6i	−0.145378	+	0.145378i
$122$	4.12288e6	−	6.58401e6i	0.205561	−	0.328270i
$123$	−1.57812e7	+	6.53678e6i	−0.764666	+	0.316735i
$124$	−1.68723e7	−	5.84563e6i	−0.794689	−	0.275331i
$125$	−1.57104e7	+	3.79282e7i	−0.719452	+	1.73691i
$126$	8.37204e6	+	1.40921e6i	0.372850	+	0.0627595i
$127$	1.25179e7			0.542276			0.271138	−	0.962541i	$-0.412600\pi$
$127$	1.25179e7			0.542276			0.271138	+	0.962541i	$0.412600\pi$
$128$	−9.31539e6	−	2.18214e7i	−0.392615	−	0.919703i
$129$	−2.29158e7			−0.939879
$130$	−3.87507e7	−	6.52267e6i	−1.54696	−	0.260390i
$131$	6.78301e6	−	1.63756e7i	0.263617	−	0.636427i	−0.735540	−	0.677481i	$-0.763072\pi$
$131$	6.78301e6	−	1.63756e7i	0.263617	−	0.636427i	0.999157	+	0.0410541i	$0.0130716\pi$
$132$	4.02160e7	+	1.39334e7i	1.52191	+	0.527288i
$133$	6.14597e6	−	2.54574e6i	0.226522	−	0.0938283i
$134$	1.53223e7	−	2.44688e7i	0.550118	−	0.878507i
$135$	7.89231e6	−	7.89231e6i	0.276081	−	0.276081i
$136$	1.79781e7	−	3.28867e7i	0.612855	−	1.12107i
$137$	−4.01464e6	−	4.01464e6i	−0.133390	−	0.133390i	0.637259	−	0.770650i	$-0.280068\pi$
$137$	−4.01464e6	−	4.01464e6i	−0.133390	−	0.133390i	−0.770650	+	0.637259i	$0.780068\pi$
$138$	−2.61751e7	+	6.01669e6i	−0.847835	+	0.194886i
$139$	1.33507e7	+	3.22314e7i	0.421649	+	1.01795i	0.981861	+	0.189602i	$0.0607197\pi$
$139$	1.33507e7	+	3.22314e7i	0.421649	+	1.01795i	−0.560212	+	0.828349i	$0.689280\pi$
$140$	−1.24052e7	+	1.39677e7i	−0.382081	+	0.430207i
$141$	−5.19124e7	−	2.15028e7i	−1.55957	−	0.645994i
$142$	−3.47526e6	+	2.47388e6i	−0.101854	+	0.0725053i
$143$		−	3.43616e7i		−	0.982646i
$144$	−4.87347e6	−	4.09839e7i	−0.136010	−	1.14379i
$145$		−	1.02629e8i		−	2.79564i
$146$	1.76952e7	+	2.48579e7i	0.470566	+	0.661043i
$147$	4.65713e7	+	1.92905e7i	1.20923	+	0.500878i
$148$	−6.77097e7	+	4.01161e6i	−1.71686	+	0.101719i
$149$	−2.05746e7	−	4.96716e7i	−0.509542	−	1.23014i	−0.944148	−	0.329523i	$-0.893112\pi$
$149$	−2.05746e7	−	4.96716e7i	−0.509542	−	1.23014i	0.434605	−	0.900621i	$-0.356888\pi$
$150$	2.81525e7	+	1.22475e8i	0.681079	+	2.96297i
$151$	3.48226e7	+	3.48226e7i	0.823079	+	0.823079i	0.986548	−	0.163470i	$-0.0522686\pi$
$151$	3.48226e7	+	3.48226e7i	0.823079	+	0.823079i	−0.163470	+	0.986548i	$0.552269\pi$
$152$	−2.02802e7	−	2.51910e7i	−0.468402	−	0.581826i
$153$	4.61011e7	−	4.61011e7i	1.04062	−	1.04062i
$154$	−1.38450e7	−	8.66968e6i	−0.305471	−	0.191285i
$155$	6.31450e7	−	2.61555e7i	1.36200	−	0.564160i
$156$	−5.60017e7	+	2.71817e7i	−1.18104	+	0.573245i
$157$	−2.39558e6	+	5.78345e6i	−0.0494040	+	0.119272i	−0.946655	−	0.322249i	$-0.895561\pi$
$157$	−2.39558e6	+	5.78345e6i	−0.0494040	+	0.119272i	0.897251	+	0.441521i	$0.145561\pi$
$158$	9.46044e6	−	5.62038e7i	0.190814	−	1.13362i
$159$	1.22809e7			0.242292
$160$	8.21244e7	+	3.87733e7i	1.58508	+	0.748364i
$161$	1.03082e7			0.194668
$162$	−7.41118e6	+	4.40293e7i	−0.136957	+	0.813654i
$163$	6.17444e6	−	1.49064e7i	0.111671	−	0.269598i	−0.858157	−	0.513387i	$-0.828391\pi$
$163$	6.17444e6	−	1.49064e7i	0.111671	−	0.269598i	0.969828	+	0.243789i	$0.0783905\pi$
$164$	−1.39169e7	−	2.86726e7i	−0.246371	−	0.507591i
$165$	−1.50510e8	+	6.23431e7i	−2.60838	+	1.08043i
$166$	3.66422e7	+	2.29452e7i	0.621732	+	0.389327i
$167$	−5.72199e7	+	5.72199e7i	−0.950690	+	0.950690i	−0.998840	−	0.0481497i	$-0.984668\pi$
$167$	−5.72199e7	+	5.72199e7i	−0.950690	+	0.950690i	0.0481497	+	0.998840i	$0.484668\pi$
$168$	−3.17760e6	+	2.94223e7i	−0.0517031	+	0.478735i
$169$	−8.83288e6	−	8.83288e6i	−0.140766	−	0.140766i
$170$	3.21382e7	+	1.39814e8i	0.501707	+	2.18263i
$171$	−2.15281e7	−	5.19735e7i	−0.329246	−	0.794869i
$172$	−2.52885e6	−	4.26830e7i	−0.0378943	−	0.639596i
$173$	4.76694e7	+	1.97453e7i	0.699969	+	0.289936i	0.704146	−	0.710055i	$-0.251330\pi$
$173$	4.76694e7	+	1.97453e7i	0.699969	+	0.289936i	−0.00417783	+	0.999991i	$0.501330\pi$
$174$	−9.42827e7	−	1.32447e8i	−1.35678	−	1.90598i
$175$		−	4.82329e7i		−	0.680315i
$176$	−2.15143e7	+	7.64439e7i	−0.297463	+	1.05694i
$177$			1.57324e8i			2.13250i
$178$	2.73293e7	−	1.94545e7i	0.363211	−	0.258553i
$179$	−9.52496e7	−	3.94537e7i	−1.24130	−	0.514164i	−0.337181	−	0.941440i	$-0.609473\pi$
$179$	−9.52496e7	−	3.94537e7i	−1.24130	−	0.514164i	−0.904121	+	0.427276i	$0.859473\pi$
$180$	1.18118e8	+	1.04905e8i	1.50961	+	1.34073i
$181$	1.24762e7	+	3.01201e7i	0.156389	+	0.377556i	0.982582	−	0.185831i	$-0.0594978\pi$
$181$	1.24762e7	+	3.01201e7i	0.156389	+	0.377556i	−0.826193	+	0.563388i	$0.809498\pi$
$182$	2.32848e7	−	5.35233e6i	0.286301	−	0.0658101i
$183$	3.33072e7	+	3.33072e7i	0.401754	+	0.401754i
$184$	−1.40952e7	−	4.80897e7i	−0.166805	−	0.569102i
$185$	1.83582e8	−	1.83582e8i	2.13172	−	2.13172i
$186$	5.74628e7	−	9.17647e7i	0.654774	−	1.04564i
$187$	−1.15898e8	+	4.80064e7i	−1.29607	+	0.536850i
$188$	3.43224e7	−	9.90649e7i	0.376726	−	1.08735i
$189$	−2.59696e6	+	6.26962e6i	−0.0279801	+	0.0675499i
$190$	1.22069e8	+	2.05471e7i	1.29113	+	0.217327i
$191$	−1.73246e6			−0.0179906			−0.00899532	−	0.999960i	$-0.502863\pi$
$191$	−1.73246e6			−0.0179906			−0.00899532	+	0.999960i	$0.502863\pi$
$192$	1.41605e8	−	2.54073e7i	1.44386	−	0.259062i
$193$	−1.15043e8			−1.15188			−0.575942	−	0.817491i	$-0.695365\pi$
$193$	−1.15043e8			−1.15188			−0.575942	+	0.817491i	$0.695365\pi$
$194$	−1.76920e8	−	2.97799e7i	−1.73969	−	0.292831i
$195$	9.11824e7	−	2.20134e8i	0.880623	−	2.12601i
$196$	−3.07911e7	+	8.88724e7i	−0.292098	+	0.843084i
$197$	−1.85849e7	+	7.69811e6i	−0.173192	+	0.0717385i	−0.467595	−	0.883943i	$-0.654879\pi$
$197$	−1.85849e7	+	7.69811e6i	−0.173192	+	0.0717385i	0.294403	+	0.955681i	$0.404879\pi$
$198$	−7.33153e7	+	1.17080e8i	−0.671223	+	1.07190i
$199$	−6.59866e7	+	6.59866e7i	−0.593568	+	0.593568i	−0.938593	−	0.345026i	$-0.887870\pi$
$199$	−6.59866e7	+	6.59866e7i	−0.593568	+	0.593568i	0.345026	+	0.938593i	$0.387870\pi$
$200$	−2.25015e8	+	6.59523e7i	−1.98887	+	0.582942i
$201$	1.23783e8	+	1.23783e8i	1.07516	+	1.07516i
$202$	3.19602e7	−	7.34648e6i	0.272822	−	0.0627118i
$203$	2.38790e7	+	5.76489e7i	0.200345	+	0.483676i
$204$	1.69920e8	+	1.50912e8i	1.40133	+	1.24456i
$205$	1.12708e8	+	4.66850e7i	0.913724	+	0.378477i
$206$	−1.82064e8	+	1.29603e8i	−1.45107	+	1.03295i
$207$		−	8.71719e7i		−	0.683093i
$208$	−5.68086e7	−	1.01309e8i	−0.437716	−	0.780597i
$209$			1.08243e8i			0.820139i
$210$	−6.56904e7	−	9.22806e7i	−0.489479	−	0.687611i
$211$	−2.54792e7	−	1.05538e7i	−0.186723	−	0.0773430i	0.287363	−	0.957822i	$-0.407221\pi$
$211$	−2.54792e7	−	1.05538e7i	−0.186723	−	0.0773430i	−0.474086	+	0.880479i	$0.657221\pi$
$212$	1.35524e6	+	2.28743e7i	0.00976880	+	0.164882i
$213$	−9.89853e6	−	2.38972e7i	−0.0701846	−	0.169441i
$214$	7.14813e6	+	3.10973e7i	0.0498591	+	0.216907i
$215$	1.15727e8	+	1.15727e8i	0.794146	+	0.794146i
$216$	3.27999e7	+	3.54237e6i	0.221454	+	0.0239169i
$217$	−2.93843e7	+	2.93843e7i	−0.195212	+	0.195212i
$218$	1.67836e7	+	1.05098e7i	0.109720	+	0.0687066i
$219$	−1.70932e8	+	7.08024e7i	−1.09969	+	0.455505i
$220$	−1.32730e8	−	2.73459e8i	−0.840404	−	1.73146i
$221$	7.02136e7	−	1.69511e8i	0.437571	−	1.05639i
$222$	6.82676e7	−	4.05573e8i	0.418774	−	2.48791i
$223$	4.86472e7			0.293759			0.146879	−	0.989154i	$-0.453077\pi$
$223$	4.86472e7			0.293759			0.146879	+	0.989154i	$0.453077\pi$
$224$	−5.51527e7	−	2.67172e6i	−0.327868	−	0.0158827i
$225$	−4.07883e8			−2.38724
$226$	2.62240e7	−	1.55795e8i	0.151119	−	0.897789i
$227$	−3.00989e7	+	7.26653e7i	−0.170789	+	0.412322i	−0.985978	−	0.166873i	$-0.946633\pi$
$227$	−3.00989e7	+	7.26653e7i	−0.170789	+	0.412322i	0.815189	+	0.579195i	$0.196633\pi$
$228$	1.76412e8	−	8.56254e7i	0.985724	−	0.478443i
$229$	2.42721e8	−	1.00538e8i	1.33562	−	0.553233i	0.403368	−	0.915038i	$-0.367839\pi$
$229$	2.42721e8	−	1.00538e8i	1.33562	−	0.553233i	0.932254	+	0.361805i	$0.117839\pi$
$230$	1.62571e8	+	1.01802e8i	0.881042	+	0.551706i
$231$	7.00391e7	−	7.00391e7i	0.373851	−	0.373851i
$232$	2.36291e8	−	1.90227e8i	1.24233	−	1.00015i
$233$	1.07669e8	+	1.07669e8i	0.557629	+	0.557629i	0.928632	−	0.371002i	$-0.120986\pi$
$233$	1.07669e8	+	1.07669e8i	0.557629	+	0.557629i	−0.371002	+	0.928632i	$0.620986\pi$
$234$	−4.52621e7	−	1.96909e8i	−0.230929	−	1.00464i
$235$	1.53571e8	+	3.70753e8i	0.771919	+	1.86358i
$236$	−2.93032e8	+	1.73613e7i	−1.45118	+	0.0859787i
$237$	3.19281e8	+	1.32250e8i	1.55795	+	0.645324i
$238$	−5.05838e7	−	7.10593e7i	−0.243216	−	0.341666i
$239$		−	2.33458e7i		−	0.110615i	−0.998469	−	0.0553077i	$-0.982386\pi$
$239$		−	2.33458e7i		−	0.110615i	0.998469	−	0.0553077i	$-0.0176140\pi$
$240$	−3.40682e8	+	4.32639e8i	−1.59078	+	2.02016i
$241$		−	8.56484e7i		−	0.394148i	−0.980389	−	0.197074i	$-0.936856\pi$
$241$		−	8.56484e7i		−	0.394148i	0.980389	−	0.197074i	$-0.0631440\pi$
$242$	3.69275e7	−	2.62870e7i	0.167493	−	0.119231i
$243$	−2.96150e8	−	1.22669e8i	−1.32401	−	0.548421i
$244$	−5.83624e7	+	6.57136e7i	−0.257199	+	0.289595i
$245$	−1.37771e8	−	3.32608e8i	−0.598515	−	1.44494i
$246$	1.88343e8	−	4.32930e7i	0.806632	−	0.185415i
$247$	−1.11946e8	−	1.11946e8i	−0.472681	−	0.472681i
$248$	1.77262e8	+	9.69035e7i	0.737963	+	0.403421i
$249$	−1.85366e8	+	1.85366e8i	−0.760909	+	0.760909i
$250$	2.46504e8	−	3.93653e8i	0.997779	−	1.59339i
$251$	6.81454e7	−	2.82267e7i	0.272006	−	0.112669i	−0.242511	−	0.970149i	$-0.577971\pi$
$251$	6.81454e7	−	2.82267e7i	0.272006	−	0.112669i	0.514517	+	0.857480i	$0.327971\pi$
$252$	−9.07584e7	−	3.14445e7i	−0.357260	−	0.123778i
$253$	−6.41873e7	+	1.54962e8i	−0.249188	+	0.601593i
$254$	−1.39660e8	−	2.35081e7i	−0.534753	−	0.0900116i
$255$	−8.69876e8			−3.28524
$256$	6.29502e7	+	2.60950e8i	0.234508	+	0.972114i
$257$	2.31924e8			0.852276			0.426138	−	0.904658i	$-0.359874\pi$
$257$	2.31924e8			0.852276			0.426138	+	0.904658i	$0.359874\pi$
$258$	2.55667e8	+	4.30348e7i	0.926841	+	0.156009i
$259$	−6.04076e7	+	1.45837e8i	−0.216044	+	0.521577i
$260$	4.20083e8	+	1.45544e8i	1.48228	+	0.513555i
$261$	4.87509e8	−	2.01933e8i	1.69723	−	0.703016i
$262$	−1.06429e8	+	1.69961e8i	−0.365599	+	0.583841i
$263$	9.64373e7	−	9.64373e7i	0.326889	−	0.326889i	−0.524513	−	0.851402i	$-0.675753\pi$
$263$	9.64373e7	−	9.64373e7i	0.326889	−	0.326889i	0.851402	+	0.524513i	$0.175753\pi$
$264$	−4.22514e8	−	2.30975e8i	−1.41328	−	0.772594i
$265$	−6.20195e7	−	6.20195e7i	−0.204724	−	0.204724i
$266$	−7.33499e7	+	1.68604e7i	−0.238954	+	0.0549267i
$267$	7.78417e7	+	1.87926e8i	0.250278	+	0.604225i
$268$	−2.16898e8	+	2.44218e8i	−0.688309	+	0.775006i
$269$	−2.06373e8	−	8.54824e7i	−0.646427	−	0.267759i	0.0352875	−	0.999377i	$-0.488765\pi$
$269$	−2.06373e8	−	8.54824e7i	−0.646427	−	0.267759i	−0.681714	+	0.731618i	$0.738765\pi$
$270$	−1.02874e8	+	7.32312e7i	−0.318077	+	0.226424i
$271$		−	1.67633e8i		−	0.511643i	−0.966724	−	0.255822i	$-0.917654\pi$
$271$		−	1.67633e8i		−	0.511643i	0.966724	−	0.255822i	$-0.0823460\pi$
$272$	−2.62337e8	+	3.33147e8i	−0.790438	+	1.00379i
$273$			1.44870e8i			0.430932i
$274$	3.72511e7	+	5.23297e7i	0.109399	+	0.153681i
$275$	7.25076e8	+	3.00336e8i	2.10242	+	0.870850i
$276$	3.03328e8	−	1.79714e7i	0.868422	−	0.0514516i
$277$	8.53814e7	+	2.06129e8i	0.241371	+	0.582720i	0.997419	−	0.0717952i	$-0.0228728\pi$
$277$	8.53814e7	+	2.06129e8i	0.241371	+	0.582720i	−0.756049	+	0.654515i	$0.772873\pi$
$278$	−8.84214e7	−	3.84669e8i	−0.246832	−	1.07382i
$279$	2.48489e8	+	2.48489e8i	0.685003	+	0.685003i
$280$	1.64633e8	−	1.32538e8i	0.448191	−	0.360818i
$281$	1.90591e8	−	1.90591e8i	0.512424	−	0.512424i	−0.402845	−	0.915268i	$-0.631978\pi$
$281$	1.90591e8	−	1.90591e8i	0.512424	−	0.512424i	0.915268	+	0.402845i	$0.131978\pi$
$282$	5.38793e8	+	3.37391e8i	1.43071	+	0.895903i
$283$	−4.66311e8	+	1.93152e8i	−1.22299	+	0.506579i	−0.898359	−	0.439262i	$-0.855240\pi$
$283$	−4.66311e8	+	1.93152e8i	−1.22299	+	0.506579i	−0.324631	+	0.945841i	$0.605240\pi$
$284$	4.34185e7	−	2.10741e7i	0.112476	−	0.0545928i
$285$	−2.87235e8	+	6.93447e8i	−0.734988	+	1.77442i
$286$	−6.45293e7	+	3.83364e8i	−0.163108	+	0.969015i
$287$	−7.41729e7			−0.185207
$288$	−2.25935e7	+	4.66400e8i	−0.0557326	+	1.15049i
$289$	−2.59496e8			−0.632394
$290$	−1.92731e8	+	1.14500e9i	−0.464044	+	2.75686i
$291$	4.16303e8	−	1.00504e9i	0.990339	−	2.39089i
$292$	−1.50739e8	−	3.10565e8i	−0.354313	−	0.729982i
$293$	1.56285e8	−	6.47354e7i	0.362978	−	0.150350i	−0.193738	−	0.981053i	$-0.562061\pi$
$293$	1.56285e8	−	6.47354e7i	0.362978	−	0.150350i	0.556716	+	0.830703i	$0.312061\pi$
$294$	−4.83358e8	−	3.02677e8i	−1.10931	−	0.694647i
$295$	7.94501e8	−	7.94501e8i	1.80184	−	1.80184i
$296$	7.62954e8	+	8.23986e7i	1.70993	+	0.184671i
$297$	−7.80792e7	−	7.80792e7i	−0.172937	−	0.172937i
$298$	1.36266e8	+	5.92812e8i	0.298284	+	1.29766i
$299$	−9.38797e7	−	2.26646e8i	−0.203106	−	0.490341i
$300$	−8.40891e7	−	1.41929e9i	−0.179811	−	3.03492i
$301$	−9.19332e7	−	3.80800e7i	−0.194307	−	0.0804848i
$302$	−3.23112e8	−	4.53902e8i	−0.675039	−	0.948282i
$303$			1.98845e8i			0.410644i
$304$	1.78953e8	+	3.19135e8i	0.365328	+	0.651504i
$305$		−	3.36409e8i		−	0.678919i
$306$	−6.00914e8	+	4.27763e8i	−1.19891	+	0.853451i
$307$	1.80162e8	+	7.46256e7i	0.355369	+	0.147198i	0.553224	−	0.833033i	$-0.313398\pi$
$307$	1.80162e8	+	7.46256e7i	0.355369	+	0.147198i	−0.197855	+	0.980231i	$0.563398\pi$
$308$	1.38184e8	+	1.22726e8i	0.269482	+	0.239336i
$309$	−5.18571e8	−	1.25194e9i	−0.999892	−	2.41395i
$310$	−7.53612e8	+	1.73228e8i	−1.43675	+	0.330257i
$311$	−4.27839e8	−	4.27839e8i	−0.806527	−	0.806527i	0.177580	−	0.984106i	$-0.443173\pi$
$311$	−4.27839e8	−	4.27839e8i	−0.806527	−	0.806527i	−0.984106	+	0.177580i	$0.943173\pi$
$312$	6.75843e8	−	1.98091e8i	1.25981	−	0.369253i
$313$	2.37604e8	−	2.37604e8i	0.437975	−	0.437975i	−0.453355	−	0.891330i	$-0.649773\pi$
$313$	2.37604e8	−	2.37604e8i	0.437975	−	0.437975i	0.891330	+	0.453355i	$0.149773\pi$
$314$	3.75879e7	−	6.00257e7i	0.0685164	−	0.109417i
$315$	3.39666e8	−	1.40694e8i	0.612301	−	0.253623i
$316$	−2.11096e8	+	6.09286e8i	−0.376335	+	1.08622i
$317$	−7.51454e7	+	1.81417e8i	−0.132494	+	0.319868i	−0.976178	−	0.216972i	$-0.930382\pi$
$317$	−7.51454e7	+	1.81417e8i	−0.132494	+	0.319868i	0.843684	+	0.536840i	$0.180382\pi$
$318$	−1.37015e8	−	2.30628e7i	−0.238931	−	0.0402178i
$319$	−1.01531e9			−1.75119
$320$	−8.43428e8	−	5.86810e8i	−1.43887	−	1.00109i
$321$	−1.93476e8			−0.326483
$322$	−1.15007e8	−	1.93583e7i	−0.191967	−	0.0323126i
$323$	−2.21181e8	+	5.33978e8i	−0.365207	+	0.881687i
$324$	1.65370e8	−	4.77307e8i	0.270115	−	0.779633i
$325$	−1.06049e9	+	4.39269e8i	−1.71362	+	0.709805i
$326$	−9.68802e7	+	1.54712e8i	−0.154872	+	0.247322i
$327$	−8.49051e7	+	8.49051e7i	−0.134282	+	0.134282i
$328$	1.01422e8	+	3.46029e8i	0.158699	+	0.541445i
$329$	−1.72529e8	−	1.72529e8i	−0.267101	−	0.267101i
$330$	1.79628e9	−	4.12898e8i	2.75153	−	0.632476i
$331$	3.66209e8	+	8.84106e8i	0.555048	+	1.34001i	0.913645	+	0.406513i	$0.133255\pi$
$331$	3.66209e8	+	8.84106e8i	0.555048	+	1.34001i	−0.358597	+	0.933493i	$0.616745\pi$
$332$	−3.65719e8	−	3.24807e8i	−0.548484	−	0.487127i
$333$	1.23327e9	+	5.10838e8i	1.83022	+	0.758104i
$334$	7.45844e8	−	5.30932e8i	1.09531	−	0.779698i
$335$		−	1.25023e9i		−	1.81691i
$336$	9.07053e7	−	3.22291e8i	0.130450	−	0.463511i
$337$			7.66781e8i			1.09136i	0.837995	+	0.545678i	$0.183728\pi$
$337$			7.66781e8i			1.09136i	−0.837995	+	0.545678i	$0.816272\pi$
$338$	8.19586e7	+	1.15134e8i	0.115448	+	0.162179i
$339$	8.85035e8	+	3.66594e8i	1.23385	+	0.511077i
$340$	−9.59941e7	−	1.62023e9i	−0.132455	−	2.23563i
$341$	−2.58758e8	−	6.24698e8i	−0.353390	−	0.853159i
$342$	1.42581e8	+	6.20285e8i	0.192739	+	0.838493i
$343$	3.28247e8	+	3.28247e8i	0.439209	+	0.439209i
$344$	−5.19427e7	+	4.80953e8i	−0.0687971	+	0.637013i
$345$	−8.22418e8	+	8.22418e8i	−1.07827	+	1.07827i
$346$	−4.94756e8	−	3.09815e8i	−0.642132	−	0.402101i
$347$	8.24369e7	−	3.41465e7i	0.105918	−	0.0438726i	−0.329095	−	0.944297i	$-0.606744\pi$
$347$	8.24369e7	−	3.41465e7i	0.105918	−	0.0438726i	0.435013	+	0.900424i	$0.356744\pi$
$348$	8.03162e8	+	1.65473e9i	1.02159	+	2.10475i
$349$	−2.66751e7	+	6.43993e7i	−0.0335905	+	0.0810947i	−0.939785	−	0.341767i	$-0.888975\pi$
$349$	−2.66751e7	+	6.43993e7i	−0.0335905	+	0.0810947i	0.906194	+	0.422862i	$0.138975\pi$
$350$	−9.05789e7	+	5.38123e8i	−0.112925	+	0.670878i
$351$	1.61500e8			0.199342
$352$	3.83588e8	−	8.12463e8i	0.468776	−	0.992897i
$353$	−1.04450e9			−1.26385			−0.631924	−	0.775030i	$-0.717735\pi$
$353$	−1.04450e9			−1.26385			−0.631924	+	0.775030i	$0.717735\pi$
$354$	2.95447e8	−	1.75523e9i	0.353971	−	2.10292i
$355$	−7.06943e7	+	1.70671e8i	−0.0838659	+	0.202470i
$356$	−3.41441e8	+	1.65726e8i	−0.401089	+	0.194678i
$357$	4.88629e8	−	2.02397e8i	0.568383	−	0.235432i
$358$	9.88585e8	+	6.19049e8i	1.13874	+	0.713074i
$359$	1.99602e6	−	1.99602e6i	0.00227685	−	0.00227685i	−0.705967	−	0.708244i	$-0.749488\pi$
$359$	1.99602e6	−	1.99602e6i	0.00227685	−	0.00227685i	0.708244	+	0.705967i	$0.249488\pi$
$360$	−1.12081e9	−	1.39222e9i	−1.26612	−	1.57271i
$361$	−2.79421e8	−	2.79421e8i	−0.312596	−	0.312596i
$362$	−8.26296e7	−	3.59473e8i	−0.0915494	−	0.398278i
$363$	1.05180e8	+	2.53927e8i	0.115414	+	0.278635i
$364$	−2.69835e8	+	1.59870e7i	−0.293253	+	0.0173744i
$365$	1.22078e9	+	5.05664e8i	1.31405	+	0.544298i
$366$	−3.09052e8	−	4.34150e8i	−0.329494	−	0.462867i
$367$			1.09994e9i			1.16155i	0.814064	+	0.580775i	$0.197250\pi$
$367$			1.09994e9i			1.16155i	−0.814064	+	0.580775i	$0.802750\pi$
$368$	6.69468e7	+	5.62996e8i	0.0700265	+	0.588895i
$369$			6.27244e8i			0.649897i
$370$	−2.39294e9	+	1.70342e9i	−2.45598	+	1.74830i
$371$	4.92681e7	+	2.04075e7i	0.0500907	+	0.0207482i
$372$	−8.13428e8	+	9.15885e8i	−0.819254	+	0.922445i
$373$	−9.32698e7	−	2.25173e8i	−0.0930594	−	0.224665i	0.870495	−	0.492177i	$-0.163799\pi$
$373$	−9.32698e7	−	2.25173e8i	−0.0930594	−	0.224665i	−0.963555	+	0.267512i	$0.913799\pi$
$374$	1.38320e9	−	3.17946e8i	1.36720	−	0.314270i
$375$	1.99142e9	+	1.99142e9i	1.95008	+	1.95008i
$376$	−5.68966e8	+	1.04079e9i	−0.551987	+	1.00973i
$377$	1.05005e9	−	1.05005e9i	1.00928	−	1.00928i
$378$	4.07477e7	−	6.50717e7i	0.0388045	−	0.0619685i
$379$	−1.31752e9	+	5.45735e8i	−1.24314	+	0.514926i	−0.904695	−	0.426060i	$-0.859901\pi$
$379$	−1.31752e9	+	5.45735e8i	−1.24314	+	0.514926i	−0.338446	+	0.940986i	$0.609901\pi$
$380$	−1.32331e9	−	4.58479e8i	−1.23714	−	0.428625i
$381$	3.28626e8	−	7.93374e8i	0.304414	−	0.734921i
$382$	1.93286e7	+	3.25347e6i	0.0177411	+	0.00298624i
$383$	1.66926e9			1.51820			0.759100	−	0.650974i	$-0.225639\pi$
$383$	1.66926e9			1.51820			0.759100	+	0.650974i	$0.225639\pi$
$384$	−1.62757e9	+	1.75354e7i	−1.46683	+	0.0158036i
$385$	−7.07408e8			−0.631767
$386$	1.28350e9	+	2.16044e8i	1.13590	+	0.191200i
$387$	−3.22024e8	+	7.77435e8i	−0.282423	+	0.681829i
$388$	1.91793e9	+	6.64494e8i	1.66695	+	0.577538i
$389$	3.83280e8	−	1.58760e8i	0.330136	−	0.136747i	−0.211458	−	0.977387i	$-0.567821\pi$
$389$	3.83280e8	−	1.58760e8i	0.330136	−	0.136747i	0.541594	+	0.840640i	$0.317821\pi$
$390$	−1.43070e9	+	2.28475e9i	−1.22130	+	1.95035i
$391$	−6.33290e8	+	6.33290e8i	−0.535777	+	0.535777i
$392$	5.10426e8	−	9.33704e8i	0.427988	−	0.782903i
$393$	−8.59800e8	−	8.59800e8i	−0.714535	−	0.714535i
$394$	2.21804e8	−	5.09845e7i	0.182697	−	0.0419954i
$395$	−9.44520e8	−	2.28027e9i	−0.771119	−	1.86165i
$396$	1.03783e9	−	1.16855e9i	0.839835	−	0.945618i
$397$	−1.98516e9	−	8.22281e8i	−1.59232	−	0.659559i	−0.602013	−	0.798486i	$-0.705634\pi$
$397$	−1.98516e9	−	8.22281e8i	−1.59232	−	0.659559i	−0.990303	+	0.138928i	$0.955634\pi$
$398$	8.60117e8	−	6.12278e8i	0.683859	−	0.486808i
$399$		−	4.56357e8i		−	0.359666i
$400$	2.63429e9	−	3.13248e8i	2.05804	−	0.244725i
$401$			1.40484e9i			1.08798i	0.839092	+	0.543990i	$0.183087\pi$
$401$			1.40484e9i			1.08798i	−0.839092	+	0.543990i	$0.816913\pi$
$402$	−1.14856e9	−	1.61347e9i	−0.881783	−	1.23871i
$403$	9.13678e8	+	3.78458e8i	0.695385	+	0.288038i
$404$	−3.70369e8	+	2.19433e7i	−0.279447	+	0.0165565i
$405$	7.39925e8	+	1.78634e9i	0.553471	+	1.33620i
$406$	−1.58150e8	−	6.88018e8i	−0.117281	−	0.510222i
$407$	−1.81619e9	−	1.81619e9i	−1.33531	−	1.33531i
$408$	−1.61235e9	−	2.00279e9i	−1.17530	−	1.45990i
$409$	−2.42974e8	+	2.42974e8i	−0.175601	+	0.175601i	−0.789435	−	0.613834i	$-0.789626\pi$
$409$	−2.42974e8	+	2.42974e8i	−0.175601	+	0.175601i	0.613834	+	0.789435i	$0.289626\pi$
$410$	−1.16978e9	−	7.32513e8i	−0.838225	−	0.524894i
$411$	−3.59838e8	+	1.49050e8i	−0.255659	+	0.105897i
$412$	2.27464e9	−	1.10405e9i	1.60240	−	0.777762i
$413$	−2.61430e8	+	6.31149e8i	−0.182613	+	0.440866i
$414$	−1.63704e8	+	9.72556e8i	−0.113386	+	0.673617i
$415$	1.87223e9			1.28585
$416$	4.43546e8	+	1.23696e9i	0.302073	+	0.842424i
$417$	2.39328e9			1.61628
$418$	2.03275e8	−	1.20764e9i	0.136134	−	0.808762i
$419$	1.08285e9	−	2.61424e9i	0.719152	−	1.73619i	0.0433996	−	0.999058i	$-0.486181\pi$
$419$	1.08285e9	−	2.61424e9i	0.719152	−	1.73619i	0.675752	−	0.737129i	$-0.263819\pi$
$420$	5.59593e8	+	1.15292e9i	0.368553	+	0.759320i
$421$	−1.68846e9	+	6.99383e8i	−1.10282	+	0.456802i	−0.858458	−	0.512883i	$-0.828577\pi$
$421$	−1.68846e9	+	6.99383e8i	−1.10282	+	0.456802i	−0.244358	+	0.969685i	$0.578577\pi$
$422$	2.64446e8	+	1.65595e8i	0.171294	+	0.107264i
$423$	−1.45899e9	+	1.45899e9i	−0.937264	+	0.937264i
$424$	2.78367e7	−	2.57749e8i	0.0177353	−	0.164216i
$425$	2.96320e9	+	2.96320e9i	1.87241	+	1.87241i
$426$	6.55579e7	+	2.85204e8i	0.0410858	+	0.178740i
$427$	7.82734e7	+	1.88969e8i	0.0486538	+	0.117461i
$428$	−2.13509e7	−	3.60369e8i	−0.0131632	−	0.222174i
$429$	−2.17780e9	−	9.02075e8i	−1.33174	−	0.551623i
$430$	−1.07381e9	−	1.50847e9i	−0.651310	−	0.914949i
$431$			8.52969e8i			0.513172i	0.966521	+	0.256586i	$0.0825976\pi$
$431$			8.52969e8i			0.513172i	−0.966521	+	0.256586i	$0.917402\pi$
$432$	−3.59288e8	−	1.01118e8i	−0.214412	−	0.0603440i
$433$		−	2.13924e9i		−	1.26634i	−0.774011	−	0.633172i	$-0.781752\pi$
$433$		−	2.13924e9i		−	1.26634i	0.774011	−	0.633172i	$-0.218248\pi$
$434$	3.83016e8	−	2.72651e8i	0.224907	−	0.160101i
$435$	−6.50450e9	−	2.69425e9i	−3.78880	−	1.56937i
$436$	−1.67514e8	−	1.48774e8i	−0.0967938	−	0.0859658i
$437$	2.95732e8	+	7.13960e8i	0.169517	+	0.409250i
$438$	2.04001e9	−	4.68924e8i	1.16004	−	0.266651i
$439$	4.36725e8	+	4.36725e8i	0.246367	+	0.246367i	0.819478	−	0.573111i	$-0.194264\pi$
$439$	4.36725e8	+	4.36725e8i	0.246367	+	0.246367i	−0.573111	+	0.819478i	$0.694264\pi$
$440$	9.67289e8	+	3.30018e9i	0.541342	+	1.84694i
$441$	1.30888e9	−	1.30888e9i	0.726717	−	0.726717i
$442$	−1.10169e9	+	1.75933e9i	−0.606850	+	0.969103i
$443$	1.20244e9	−	4.98067e8i	0.657128	−	0.272191i	−0.0291014	−	0.999576i	$-0.509265\pi$
$443$	1.20244e9	−	4.98067e8i	0.657128	−	0.272191i	0.686229	+	0.727385i	$0.259265\pi$
$444$	−1.52329e9	+	4.39668e9i	−0.825929	+	2.38388i
$445$	5.55938e8	−	1.34215e9i	0.299065	−	0.722008i
$446$	−5.42746e8	−	9.13570e7i	−0.289684	−	0.0487607i
$447$	−3.68827e9			−1.95320
$448$	6.10308e8	+	1.33382e8i	0.320683	+	0.0700846i
$449$	−9.17839e8			−0.478524			−0.239262	−	0.970955i	$-0.576906\pi$
$449$	−9.17839e8			−0.478524			−0.239262	+	0.970955i	$0.576906\pi$
$450$	4.55065e9	+	7.65982e8i	2.35412	+	0.396255i
$451$	4.61859e8	−	1.11503e9i	0.237078	−	0.572357i
$452$	−5.85150e8	+	1.68892e9i	−0.298046	+	0.860250i
$453$	3.12119e9	−	1.29284e9i	1.57753	−	0.653433i
$454$	4.72268e8	−	7.54185e8i	0.236861	−	0.378253i
$455$	7.31606e8	−	7.31606e8i	0.364114	−	0.364114i
$456$	−2.12898e9	+	6.24010e8i	−1.05147	+	0.308187i
$457$	1.38061e9	+	1.38061e9i	0.676651	+	0.676651i	0.959241	−	0.282590i	$-0.0911935\pi$
$457$	1.38061e9	+	1.38061e9i	0.676651	+	0.676651i	−0.282590	+	0.959241i	$0.591193\pi$
$458$	−2.89679e9	+	6.65866e8i	−1.40892	+	0.323860i
$459$	−2.25631e8	−	5.44721e8i	−0.108907	−	0.262924i
$460$	−1.62259e9	−	1.44108e9i	−0.777243	−	0.690295i
$461$	2.83602e9	+	1.17472e9i	1.34821	+	0.558445i	0.935793	−	0.352551i	$-0.114686\pi$
$461$	2.83602e9	+	1.17472e9i	1.34821	+	0.558445i	0.412414	+	0.910997i	$0.364686\pi$
$462$	−9.12940e8	+	6.49880e8i	−0.430720	+	0.306610i
$463$		−	1.65368e9i		−	0.774317i	−0.922013	−	0.387158i	$-0.873457\pi$
$463$		−	1.65368e9i		−	0.774317i	0.922013	−	0.387158i	$-0.126543\pi$
$464$	−2.99347e9	+	1.67857e9i	−1.39111	+	0.780060i
$465$		−	4.68871e9i		−	2.16256i
$466$	−9.99042e8	−	1.40344e9i	−0.457334	−	0.642454i
$467$	−3.17244e9	−	1.31407e9i	−1.44140	−	0.597046i	−0.481261	−	0.876577i	$-0.659821\pi$
$467$	−3.17244e9	−	1.31407e9i	−1.44140	−	0.597046i	−0.960137	+	0.279531i	$0.909821\pi$
$468$	1.35194e8	+	2.28186e9i	0.0609673	+	1.02903i
$469$	2.90895e8	+	7.02282e8i	0.130206	+	0.314345i
$470$	−1.01710e9	−	4.42481e9i	−0.451878	−	1.96586i
$471$	3.03659e8	+	3.03659e8i	0.133910	+	0.133910i
$472$	3.30189e9	+	3.56602e8i	1.44532	+	0.156094i
$473$	1.14490e9	−	1.14490e9i	0.497454	−	0.497454i
$474$	−3.31378e9	−	2.07508e9i	−1.42922	−	0.894974i
$475$	3.34066e9	−	1.38375e9i	1.43023	−	0.592419i
$476$	4.30906e8	+	8.87785e8i	0.183130	+	0.377297i
$477$	1.72576e8	−	4.16636e8i	0.0728060	−	0.175769i
$478$	−4.38421e7	+	2.60463e8i	−0.0183609	+	0.109081i
$479$	3.11349e9			1.29442			0.647208	−	0.762314i	$-0.275937\pi$
$479$	3.11349e9			1.29442			0.647208	+	0.762314i	$0.275937\pi$
$480$	4.61338e9	−	4.18706e9i	1.90403	−	1.72809i
$481$	3.75664e9			1.53919
$482$	−1.60843e8	+	9.55559e8i	−0.0654241	+	0.388680i
$483$	2.70616e8	−	6.53326e8i	0.109280	−	0.263824i
$484$	−4.61357e8	+	2.23930e8i	−0.184960	+	0.0897746i
$485$	−7.17792e9	+	2.97319e9i	−2.85695	+	1.18339i
$486$	3.07371e9	+	1.92475e9i	1.21461	+	0.760584i
$487$	−1.45530e9	+	1.45530e9i	−0.570952	+	0.570952i	−0.932394	−	0.361442i	$-0.882284\pi$
$487$	−1.45530e9	+	1.45530e9i	−0.570952	+	0.570952i	0.361442	+	0.932394i	$0.382284\pi$
$488$	7.74543e8	−	6.23549e8i	0.301700	−	0.242885i
$489$	−7.82659e8	−	7.82659e8i	−0.302685	−	0.302685i
$490$	9.12454e8	+	3.96955e9i	0.350368	+	1.52425i
$491$	1.89981e9	+	4.58655e9i	0.724311	+	1.74864i	0.660678	+	0.750669i	$0.270269\pi$
$491$	1.89981e9	+	4.58655e9i	0.724311	+	1.74864i	0.0636333	+	0.997973i	$0.479731\pi$
$492$	−2.18260e9	+	1.29313e8i	−0.826219	+	0.0489512i
$493$	−5.00869e9	−	2.07467e9i	−1.88261	−	0.779802i
$494$	1.03872e9	+	1.45918e9i	0.387664	+	0.544583i
$495$			5.98221e9i			2.21689i
$496$	−1.79569e9	−	1.41402e9i	−0.660763	−	0.520318i
$497$		−	1.12319e8i		−	0.0410397i
$498$	2.41619e9	−	1.71998e9i	0.876655	−	0.624051i
$499$	2.25411e9	+	9.33684e8i	0.812126	+	0.336394i	0.749802	−	0.661662i	$-0.230149\pi$
$499$	2.25411e9	+	9.33684e8i	0.812126	+	0.336394i	0.0623242	+	0.998056i	$0.480149\pi$
$500$	−3.48945e9	+	3.92897e9i	−1.24842	+	1.40567i
$501$	2.12437e9	+	5.12869e9i	0.754743	+	1.82211i
$502$	−8.13290e8	+	1.86946e8i	−0.286934	+	0.0659557i
$503$	−2.99074e9	−	2.99074e9i	−1.04783	−	1.04783i	−0.998797	−	0.0490320i	$-0.984386\pi$
$503$	−2.99074e9	−	2.99074e9i	−1.04783	−	1.04783i	−0.0490320	−	0.998797i	$-0.515614\pi$
$504$	9.53518e8	+	5.21258e8i	0.331759	+	0.181362i
$505$	1.00419e9	−	1.00419e9i	0.346972	−	0.346972i
$506$	1.00713e9	−	1.60833e9i	0.345589	−	0.551885i
$507$	−7.91703e8	+	3.27934e8i	−0.269795	+	0.111753i
$508$	1.51400e9	+	5.24547e8i	0.512394	+	0.177526i
$509$	−7.91043e8	+	1.90975e9i	−0.265881	+	0.641894i	−0.999281	−	0.0379031i	$-0.987932\pi$
$509$	−7.91043e8	+	1.90975e9i	−0.265881	+	0.641894i	0.733400	+	0.679797i	$0.237932\pi$
$510$	9.70500e9	+	1.63358e9i	3.23966	+	0.545312i
$511$	−8.03395e8			−0.266352
$512$	−2.12270e8	−	3.02957e9i	−0.0698946	−	0.997554i
$513$	−5.08744e8			−0.166375
$514$	−2.58752e9	−	4.35542e8i	−0.840453	−	0.141468i
$515$	−3.70358e9	+	8.94124e9i	−1.19480	+	2.88451i
$516$	−2.77159e9	−	9.60257e8i	−0.888087	−	0.307690i
$517$	3.66789e9	−	1.51929e9i	1.16735	−	0.483531i
$518$	9.47828e8	−	1.51363e9i	0.299623	−	0.478481i
$519$	2.50288e9	−	2.50288e9i	0.785875	−	0.785875i
$520$	−4.41345e9	−	2.41269e9i	−1.37647	−	0.752471i
$521$	−2.75335e9	−	2.75335e9i	−0.852963	−	0.852963i	0.137534	−	0.990497i	$-0.456082\pi$
$521$	−2.75335e9	−	2.75335e9i	−0.852963	−	0.852963i	−0.990497	+	0.137534i	$0.956082\pi$
$522$	−5.81824e9	+	1.33740e9i	−1.79038	+	0.411542i
$523$	1.07232e9	+	2.58881e9i	0.327769	+	0.791305i	0.998757	+	0.0498368i	$0.0158701\pi$
$523$	1.07232e9	+	2.58881e9i	0.327769	+	0.791305i	−0.670988	+	0.741468i	$0.734130\pi$
$524$	1.50658e9	−	1.69634e9i	0.457439	−	0.515056i
$525$	−3.05695e9	−	1.26623e9i	−0.922000	−	0.381905i
$526$	−1.25703e9	+	8.94824e8i	−0.376614	+	0.268094i
$527$		−	3.61047e9i		−	1.07455i
$528$	4.28013e9	+	3.37039e9i	1.26543	+	0.996464i
$529$		−	2.20735e9i		−	0.648299i
$530$	5.75467e8	+	8.08406e8i	0.167902	+	0.235865i
$531$	5.33732e9	+	2.21079e9i	1.54701	+	0.640792i
$532$	8.50010e8	−	5.03607e7i	0.244756	−	0.0145011i
$533$	6.75510e8	+	1.63083e9i	0.193235	+	0.466512i
$534$	−5.15545e8	−	2.24283e9i	−0.146512	−	0.637386i
$535$	9.77073e8	+	9.77073e8i	0.275860	+	0.275860i
$536$	2.87850e9	−	2.31735e9i	0.807403	−	0.650004i
$537$	−5.00107e9	+	5.00107e9i	−1.39365	+	1.39365i
$538$	2.14192e9	+	1.34126e9i	0.593014	+	0.371344i
$539$	−3.29051e9	+	1.36298e9i	−0.905114	+	0.374910i
$540$	1.28526e9	−	6.23832e8i	0.351248	−	0.170486i
$541$	7.28031e8	−	1.75762e9i	0.197679	−	0.477238i	−0.793693	−	0.608318i	$-0.791844\pi$
$541$	7.28031e8	−	1.75762e9i	0.197679	−	0.477238i	0.991372	+	0.131080i	$0.0418444\pi$
$542$	−3.14806e8	+	1.87024e9i	−0.0849270	+	0.504546i
$543$	2.23651e9			0.599476
$544$	3.55246e9	−	3.22418e9i	0.946091	−	0.858665i
$545$	8.57556e8			0.226921
$546$	2.72058e8	−	1.61628e9i	0.0715299	−	0.424954i
$547$	1.99308e9	−	4.81172e9i	0.520678	−	1.25703i	−0.416805	−	0.908996i	$-0.636850\pi$
$547$	1.99308e9	−	4.81172e9i	0.520678	−	1.25703i	0.937483	−	0.348032i	$-0.113150\pi$
$548$	−3.17329e8	−	6.53785e8i	−0.0823717	−	0.169708i
$549$	1.59802e9	−	6.61921e8i	0.412172	−	0.170727i
$550$	−7.52548e9	−	4.71244e9i	−1.92870	−	1.20775i
$551$	−3.30776e9	+	3.30776e9i	−0.842372	+	0.842372i
$552$	−3.41791e9	−	3.69132e8i	−0.864916	−	0.0934104i
$553$	1.06112e9	+	1.06112e9i	0.266824	+	0.266824i
$554$	−5.65481e8	−	2.46007e9i	−0.141297	−	0.614701i
$555$	−6.81577e9	−	1.64547e10i	−1.69235	−	4.08569i
$556$	2.64107e8	+	4.45772e9i	0.0651656	+	1.09989i
$557$	5.74180e9	+	2.37833e9i	1.40785	+	0.583149i	0.951776	−	0.306795i	$-0.0992567\pi$
$557$	5.74180e9	+	2.37833e9i	1.40785	+	0.583149i	0.456070	+	0.889944i	$0.349257\pi$
$558$	−2.30568e9	−	3.23898e9i	−0.561797	−	0.789203i
$559$			2.36812e9i			0.573407i
$560$	−2.08567e9	+	1.16953e9i	−0.501865	+	0.281418i
$561$			8.60575e9i			2.05787i
$562$	−2.48429e9	+	1.76845e9i	−0.590372	+	0.420259i
$563$	3.03262e9	+	1.25615e9i	0.716208	+	0.296663i	0.710871	−	0.703323i	$-0.248301\pi$
$563$	3.03262e9	+	1.25615e9i	0.716208	+	0.296663i	0.00533722	+	0.999986i	$0.498301\pi$
$564$	−5.37758e9	−	4.77601e9i	−1.26215	−	1.12096i
$565$	−2.61818e9	−	6.32084e9i	−0.610702	−	1.47437i
$566$	5.56525e9	−	1.27925e9i	1.29011	−	0.296549i
$567$	−8.31265e8	−	8.31265e8i	−0.191513	−	0.191513i
$568$	−5.23986e8	+	1.53581e8i	−0.119978	+	0.0351657i
$569$	−2.25533e9	+	2.25533e9i	−0.513235	+	0.513235i	−0.915516	−	0.402281i	$-0.868217\pi$
$569$	−2.25533e9	+	2.25533e9i	−0.513235	+	0.513235i	0.402281	+	0.915516i	$0.368217\pi$
$570$	4.50687e9	−	7.19721e9i	1.01933	−	1.62780i
$571$	5.96963e9	−	2.47270e9i	1.34190	−	0.555835i	0.407876	−	0.913037i	$-0.366269\pi$
$571$	5.96963e9	−	2.47270e9i	1.34190	−	0.555835i	0.934027	+	0.357203i	$0.116269\pi$
$572$	1.43988e9	−	4.15592e9i	0.321691	−	0.928498i
$573$	−4.54813e7	+	1.09802e8i	−0.0100993	+	0.0243819i
$574$	8.27529e8	+	1.39293e8i	0.182638	+	0.0307423i
$575$	5.60308e9			1.22911
$576$	1.12794e9	−	5.16108e9i	0.245929	−	1.12528i
$577$	7.20293e9			1.56097			0.780484	−	0.625176i	$-0.214973\pi$
$577$	7.20293e9			1.56097			0.780484	+	0.625176i	$0.214973\pi$
$578$	2.89513e9	+	4.87320e8i	0.623622	+	0.104970i
$579$	−3.02015e9	+	7.29129e9i	−0.646627	+	1.56110i
$580$	4.30051e9	−	1.24126e10i	0.915214	−	2.64158i
$581$	−1.05168e9	+	4.35618e8i	−0.222467	+	0.0921487i
$582$	−6.53201e9	+	1.04312e10i	−1.37346	+	2.19334i
$583$	−6.13564e8	+	6.13564e8i	−0.128239	+	0.128239i
$584$	1.09854e9	+	3.74798e9i	0.228229	+	0.778667i
$585$	−6.18684e9	−	6.18684e9i	−1.27768	−	1.27768i
$586$	−1.86520e9	+	4.28742e8i	−0.382899	+	0.0880145i
$587$	−1.86856e9	−	4.51110e9i	−0.381306	−	0.920554i	−0.991714	−	0.128467i	$-0.958994\pi$
$587$	−1.86856e9	−	4.51110e9i	−0.381306	−	0.920554i	0.610408	−	0.792087i	$-0.291006\pi$
$588$	4.82430e9	+	4.28462e9i	0.978619	+	0.869144i
$589$	−2.87819e9	−	1.19218e9i	−0.580384	−	0.240403i
$590$	−1.03561e10	+	7.37203e9i	−2.07593	+	1.47776i
$591$			1.37998e9i			0.274991i
$592$	−8.35736e9	−	2.35209e9i	−1.65555	−	0.465938i
$593$			1.39828e9i			0.275362i	0.990477	+	0.137681i	$0.0439648\pi$
$593$			1.39828e9i			0.275362i	−0.990477	+	0.137681i	$0.956035\pi$
$594$	7.24483e8	+	1.01774e9i	0.141832	+	0.199244i
$595$	−3.48974e9	−	1.44550e9i	−0.679179	−	0.281325i
$596$	−4.07014e8	−	6.86976e9i	−0.0787494	−	1.32917i
$597$	2.44986e9	+	5.91447e9i	0.471227	+	1.13764i
$598$	6.21765e8	+	2.70493e9i	0.118897	+	0.517252i
$599$	−1.18298e9	−	1.18298e9i	−0.224898	−	0.224898i	0.585659	−	0.810557i	$-0.300836\pi$
$599$	−1.18298e9	−	1.18298e9i	−0.224898	−	0.224898i	−0.810557	+	0.585659i	$0.800836\pi$
$600$	−1.72719e9	+	1.59926e10i	−0.326446	+	3.02267i
$601$	−6.54202e9	+	6.54202e9i	−1.22928	+	1.22928i	−0.265045	+	0.964236i	$0.585387\pi$
$601$	−6.54202e9	+	6.54202e9i	−1.22928	+	1.22928i	−0.964236	+	0.265045i	$0.914613\pi$
$602$	9.54164e8	+	5.97495e8i	0.178252	+	0.111621i
$603$	5.93886e9	−	2.45996e9i	1.10304	−	0.456896i
$604$	2.75248e9	+	5.67086e9i	0.508270	+	1.04718i
$605$	7.51186e8	−	1.81352e9i	0.137912	−	0.332950i
$606$	3.73421e8	−	2.21847e9i	0.0681623	−	0.404948i
$607$	6.57484e9			1.19323			0.596616	−	0.802527i	$-0.296512\pi$
$607$	6.57484e9			1.19323			0.596616	+	0.802527i	$0.296512\pi$
$608$	−1.39722e9	−	3.89658e9i	−0.252117	−	0.703107i
$609$	4.28061e9			0.767971
$610$	−6.31759e8	+	3.75324e9i	−0.112693	+	0.669501i
$611$	−2.22210e9	+	5.36463e9i	−0.394112	+	0.951470i
$612$	7.50757e9	−	3.64397e9i	1.32394	−	0.642606i
$613$	−9.15187e9	+	3.79083e9i	−1.60472	+	0.664695i	−0.992073	−	0.125665i	$-0.959893\pi$
$613$	−9.15187e9	+	3.79083e9i	−1.60472	+	0.664695i	−0.612643	+	0.790360i	$0.709893\pi$
$614$	−1.86988e9	−	1.17091e9i	−0.326005	−	0.204144i
$615$	5.91770e9	−	5.91770e9i	1.02586	−	1.02586i
$616$	−1.31121e9	−	1.62872e9i	−0.226017	−	0.280747i
$617$	2.81523e8	+	2.81523e8i	0.0482520	+	0.0482520i	0.730821	−	0.682569i	$-0.239137\pi$
$617$	2.81523e8	+	2.81523e8i	0.0482520	+	0.0482520i	−0.682569	+	0.730821i	$0.739137\pi$
$618$	3.43449e9	+	1.49414e10i	0.585333	+	2.54644i
$619$	6.22210e8	+	1.50215e9i	0.105443	+	0.254563i	0.967792	−	0.251753i	$-0.0810070\pi$
$619$	6.22210e8	+	1.50215e9i	0.105443	+	0.254563i	−0.862348	+	0.506316i	$0.831007\pi$
$620$	8.73318e9	−	5.17417e8i	1.47164	−	0.0871905i
$621$	−7.28324e8	−	3.01682e8i	−0.122040	−	0.0505508i
$622$	3.96984e9	+	5.57675e9i	0.661464	+	0.929212i
$623$			8.83270e8i			0.146347i
$624$	−7.91223e9	+	9.40857e8i	−1.30362	+	0.155016i
$625$		−	7.46387e9i		−	1.22288i
$626$	−3.09710e9	+	2.20469e9i	−0.504598	+	0.359200i
$627$	6.86033e9	+	2.84164e9i	1.11150	+	0.460397i
$628$	−5.32085e8	+	5.99105e8i	−0.0857279	+	0.0965259i
$629$	−5.24838e9	−	1.26707e10i	−0.840907	−	2.03013i
$630$	−4.05379e9	+	9.31817e8i	−0.645906	+	0.148470i
$631$	2.28535e9	+	2.28535e9i	0.362118	+	0.362118i	0.864592	−	0.502474i	$-0.167577\pi$
$631$	2.28535e9	+	2.28535e9i	0.362118	+	0.362118i	−0.502474	+	0.864592i	$0.667577\pi$
$632$	3.49935e9	−	6.40123e9i	0.551414	−	1.00868i
$633$	−1.33778e9	+	1.33778e9i	−0.209639	+	0.209639i
$634$	1.17907e9	−	1.88291e9i	0.183750	−	0.293438i
$635$	−5.66620e9	+	2.34702e9i	−0.878181	+	0.363755i
$636$	1.48533e9	+	5.14613e8i	0.228941	+	0.0793197i
$637$	1.99347e9	−	4.81267e9i	0.305578	−	0.737732i
$638$	1.13276e10	+	1.90671e9i	1.72690	+	0.290678i
$639$	−9.49825e8			−0.144009
$640$	8.30792e9	+	8.13081e9i	1.25274	+	1.22604i
$641$	−6.17759e9			−0.926437			−0.463219	−	0.886244i	$-0.653306\pi$
$641$	−6.17759e9			−0.926437			−0.463219	+	0.886244i	$0.653306\pi$
$642$	2.15857e9	+	3.63339e8i	0.321954	+	0.0541925i
$643$	1.58742e9	−	3.83238e9i	0.235480	−	0.568500i	−0.761325	−	0.648371i	$-0.775451\pi$
$643$	1.58742e9	−	3.83238e9i	0.235480	−	0.568500i	0.996805	+	0.0798708i	$0.0254508\pi$
$644$	1.24675e9	+	4.31953e8i	0.183941	+	0.0637288i
$645$	1.03728e10	−	4.29654e9i	1.52207	−	0.630464i
$646$	3.47045e9	−	5.54210e9i	0.506491	−	0.808836i
$647$	−4.05328e9	+	4.05328e9i	−0.588357	+	0.588357i	−0.937186	−	0.348829i	$-0.886579\pi$
$647$	−4.05328e9	+	4.05328e9i	−0.588357	+	0.588357i	0.348829	+	0.937186i	$0.386579\pi$
$648$	−2.74135e9	+	5.01464e9i	−0.395778	+	0.723982i
$649$	−7.86006e9	−	7.86006e9i	−1.12868	−	1.12868i
$650$	1.26565e10	−	2.90928e9i	1.80767	−	0.415516i
$651$	1.09094e9	+	2.63375e9i	0.154977	+	0.374147i
$652$	1.37141e9	−	1.54415e9i	0.193776	−	0.218184i
$653$	1.29304e9	+	5.35595e8i	0.181725	+	0.0752731i	0.471691	−	0.881764i	$-0.343644\pi$
$653$	1.29304e9	+	5.35595e8i	0.181725	+	0.0752731i	−0.289965	+	0.957037i	$0.593644\pi$
$654$	1.10671e9	−	7.87818e8i	0.154708	−	0.110130i
$655$			8.68413e9i			1.20749i
$656$	−4.81715e8	−	4.05103e9i	−0.0666234	−	0.560276i
$657$			6.79393e9i			0.934635i
$658$	1.60086e9	+	2.24886e9i	0.219060	+	0.307732i
$659$	8.00436e9	+	3.31551e9i	1.08950	+	0.451286i	0.853833	−	0.520548i	$-0.174272\pi$
$659$	8.00436e9	+	3.31551e9i	1.08950	+	0.451286i	0.235668	+	0.971834i	$0.424272\pi$
$660$	−2.08160e10	+	1.23329e9i	−2.81834	+	0.166979i
$661$	2.37101e9	+	5.72413e9i	0.319322	+	0.770911i	0.999290	+	0.0376694i	$0.0119934\pi$
$661$	2.37101e9	+	5.72413e9i	0.319322	+	0.770911i	−0.679969	+	0.733241i	$0.738007\pi$
$662$	−2.42540e9	−	1.05515e10i	−0.324923	−	1.41355i
$663$	−8.90013e9	−	8.90013e9i	−1.18604	−	1.18604i
$664$	3.47026e9	+	4.31059e9i	0.460017	+	0.571411i
$665$	−2.30464e9	+	2.30464e9i	−0.303898	+	0.303898i
$666$	−1.28000e10	−	8.01532e9i	−1.67900	−	1.05138i
$667$	−6.69691e9	+	2.77395e9i	−0.873844	+	0.361958i
$668$	−9.31827e9	+	4.52283e9i	−1.20953	+	0.587074i
$669$	1.27711e9	−	3.08321e9i	0.164906	−	0.398118i
$670$	−2.34786e9	+	1.39485e10i	−0.301586	+	1.79170i
$671$	−3.32812e9			−0.425276
$672$	−1.61722e9	+	3.42538e9i	−0.205578	+	0.435428i
$673$	−1.45369e10			−1.83832			−0.919159	−	0.393888i	$-0.871130\pi$
$673$	−1.45369e10			−1.83832			−0.919159	+	0.393888i	$0.871130\pi$
$674$	1.43997e9	−	8.55479e9i	0.181153	−	1.07622i
$675$	−1.41159e9	+	3.40787e9i	−0.176663	+	0.426501i
$676$	−6.98177e8	−	1.43844e9i	−0.0869265	−	0.179092i
$677$	1.44992e10	−	6.00577e9i	1.79591	−	0.743889i	0.807933	−	0.589275i	$-0.200587\pi$
$677$	1.44992e10	−	6.00577e9i	1.79591	−	0.743889i	0.987975	−	0.154614i	$-0.0494135\pi$
$678$	−9.18568e9	−	5.75205e9i	−1.13190	−	0.708792i
$679$	3.34022e9	−	3.34022e9i	0.409479	−	0.409479i
$680$	−1.97172e9	+	1.82568e10i	−0.240472	+	2.22660i
$681$	3.81528e9	+	3.81528e9i	0.462926	+	0.462926i
$682$	1.71376e9	+	7.45554e9i	0.206873	+	0.899982i
$683$	1.59779e9	+	3.85742e9i	0.191888	+	0.463259i	0.990316	−	0.138831i	$-0.0443346\pi$
$683$	1.59779e9	+	3.85742e9i	0.191888	+	0.463259i	−0.798428	+	0.602091i	$0.794335\pi$
$684$	−4.25876e8	−	7.18813e9i	−0.0508847	−	0.858854i
$685$	2.56993e9	+	1.06450e9i	0.305495	+	0.126540i
$686$	−3.04574e9	−	4.27860e9i	−0.360212	−	0.506020i
$687$		−	1.80228e10i		−	2.12067i
$688$	1.48272e9	−	5.26834e9i	0.173580	−	0.616757i
$689$		−	1.26911e9i		−	0.147819i
$690$	1.07200e10	−	7.63106e9i	1.24229	−	0.884327i
$691$	−2.36124e9	−	9.78060e8i	−0.272250	−	0.112770i	0.242382	−	0.970181i	$-0.422071\pi$
$691$	−2.36124e9	−	9.78060e8i	−0.272250	−	0.112770i	−0.514632	+	0.857411i	$0.672071\pi$
$692$	4.93806e9	+	4.38565e9i	0.566480	+	0.503110i
$693$	−1.39190e9	−	3.36034e9i	−0.158870	−	0.383546i
$694$	−9.83854e8	+	2.26152e8i	−0.111731	+	0.0256828i
$695$	−1.20863e10	−	1.20863e10i	−1.36567	−	1.36567i
$696$	−5.85318e9	−	1.99698e10i	−0.658051	−	2.24513i
$697$	4.55683e9	−	4.55683e9i	0.509740	−	0.509740i
$698$	4.18546e8	−	6.68393e8i	0.0465853	−	0.0743940i
$699$	9.65054e9	−	3.99738e9i	1.06876	−	0.442696i
$700$	2.02113e9	−	5.83361e9i	0.222716	−	0.642827i
$701$	9.01954e8	−	2.17751e9i	0.0988943	−	0.238752i	−0.866688	−	0.498851i	$-0.833755\pi$
$701$	9.01954e8	−	2.17751e9i	0.0988943	−	0.238752i	0.965582	+	0.260099i	$0.0837553\pi$
$702$	−1.80182e9	−	3.03289e8i	−0.196576	−	0.0330885i
$703$	−1.18338e10			−1.28464
$704$	−5.80536e9	+	8.34410e9i	−0.627083	+	0.901312i
$705$	2.75296e10			2.95895
$706$	1.16532e10	+	1.96151e9i	1.24632	+	0.209785i
$707$	−3.30427e8	+	7.97721e8i	−0.0351648	+	0.0848952i
$708$	−6.59245e9	+	1.90278e10i	−0.698121	+	2.01499i
$709$	3.67994e9	−	1.52428e9i	0.387774	−	0.160621i	−0.180274	−	0.983616i	$-0.557699\pi$
$709$	3.67994e9	−	1.52428e9i	0.387774	−	0.160621i	0.568049	+	0.822995i	$0.307699\pi$
$710$	1.10923e9	−	1.77138e9i	0.116310	−	0.185741i
$711$	8.97336e9	−	8.97336e9i	0.936292	−	0.936292i
$712$	4.12061e9	−	1.20776e9i	0.427840	−	0.125401i
$713$	−3.41349e9	−	3.41349e9i	−0.352684	−	0.352684i
$714$	−5.83161e9	+	1.34047e9i	−0.599577	+	0.137821i
$715$	6.44253e9	+	1.55537e10i	0.659152	+	1.59133i
$716$	−9.86687e9	−	8.76309e9i	−1.00458	−	0.892199i
$717$	−1.47963e9	−	6.12883e8i	−0.149912	−	0.0620956i
$718$	−2.60175e7	+	1.85207e7i	−0.00262319	+	0.00186733i
$719$		−	3.25455e9i		−	0.326542i	−0.986581	−	0.163271i	$-0.947795\pi$
$719$		−	3.25455e9i		−	0.326542i	0.986581	−	0.163271i	$-0.0522045\pi$
$720$	9.89012e9	+	1.76375e10i	0.987502	+	1.76105i
$721$		−	5.88422e9i		−	0.584677i
$722$	2.59270e9	+	3.64217e9i	0.256372	+	0.360147i
$723$	−5.42831e9	−	2.24848e9i	−0.534171	−	0.221261i
$724$	2.46808e8	+	4.16572e9i	0.0241698	+	0.407949i
$725$	1.29795e10	+	3.13353e10i	1.26495	+	3.05387i
$726$	−6.96607e8	−	3.03053e9i	−0.0675631	−	0.293927i
$727$	1.40510e9	+	1.40510e9i	0.135624	+	0.135624i	0.771660	−	0.636036i	$-0.219427\pi$
$727$	1.40510e9	+	1.40510e9i	0.135624	+	0.135624i	−0.636036	+	0.771660i	$0.719427\pi$
$728$	3.04050e9	+	3.28373e8i	0.292069	+	0.0315433i
$729$	−9.44640e9	+	9.44640e9i	−0.903067	+	0.903067i
$730$	−1.26703e10	−	7.93413e9i	−1.20548	−	0.754865i
$731$	7.98740e9	−	3.30849e9i	0.756301	−	0.313270i
$732$	2.63270e9	+	5.42409e9i	0.248092	+	0.511138i
$733$	3.40155e9	−	8.21206e9i	0.319016	−	0.770173i	−0.680291	−	0.732942i	$-0.738146\pi$
$733$	3.40155e9	−	8.21206e9i	0.319016	−	0.770173i	0.999307	−	0.0372303i	$-0.0118535\pi$
$734$	2.06563e9	−	1.22718e10i	0.192804	−	1.14544i
$735$	−2.46971e10			−2.29425
$736$	3.10366e8	−	6.40693e9i	0.0286947	−	0.592349i
$737$	−1.23686e10			−1.13811
$738$	1.17793e9	−	6.99801e9i	0.107876	−	0.640881i
$739$	−7.16743e9	+	1.73037e10i	−0.653293	+	1.57719i	0.154676	+	0.987965i	$0.450566\pi$
$739$	−7.16743e9	+	1.73037e10i	−0.653293	+	1.57719i	−0.807970	+	0.589224i	$0.799434\pi$
$740$	2.98964e10	−	1.45109e10i	2.71211	−	1.31638i
$741$	−1.00338e10	+	4.15616e9i	−0.905949	+	0.375256i
$742$	−5.11348e8	−	3.20205e8i	−0.0459518	−	0.0287749i
$743$	−5.46402e9	+	5.46402e9i	−0.488710	+	0.488710i	−0.907899	−	0.419189i	$-0.862315\pi$
$743$	−5.46402e9	+	5.46402e9i	−0.488710	+	0.488710i	0.419189	+	0.907899i	$0.362315\pi$
$744$	1.07952e10	−	8.69073e9i	0.961005	−	0.773662i
$745$	1.86261e10	+	1.86261e10i	1.65034	+	1.65034i
$746$	6.17725e8	+	2.68736e9i	0.0544766	+	0.236995i
$747$	3.68381e9	+	8.89351e9i	0.323352	+	0.780641i
$748$	−1.60291e10	+	9.49677e8i	−1.40040	+	0.0829699i
$749$	−7.76183e8	−	3.21506e8i	−0.0674960	−	0.0279578i
$750$	−1.84780e10	−	2.59575e10i	−1.59934	−	2.24672i
$751$			2.49434e9i			0.214890i	0.994211	+	0.107445i	$0.0342669\pi$
$751$			2.49434e9i			0.214890i	−0.994211	+	0.107445i	$0.965733\pi$
$752$	8.30236e9	−	1.05433e10i	0.711933	−	0.904098i
$753$		−	5.06000e9i		−	0.431885i
$754$	−1.36870e10	+	9.74318e9i	−1.16281	+	0.827753i
$755$	−2.22913e10	−	9.23334e9i	−1.88504	−	0.780809i
$756$	−5.76813e8	+	6.49467e8i	−0.0485522	+	0.0546677i
$757$	−2.02279e9	−	4.88344e9i	−0.169478	−	0.409157i	0.816205	−	0.577762i	$-0.196074\pi$
$757$	−2.02279e9	−	4.88344e9i	−0.169478	−	0.409157i	−0.985684	+	0.168605i	$0.946074\pi$
$758$	1.57241e10	−	3.61440e9i	1.31137	−	0.301435i
$759$	8.13625e9	+	8.13625e9i	0.675426	+	0.675426i
$760$	1.39029e10	+	7.60025e9i	1.14883	+	0.628030i
$761$	3.93315e9	−	3.93315e9i	0.323515	−	0.323515i	−0.526599	−	0.850114i	$-0.676533\pi$
$761$	3.93315e9	−	3.93315e9i	0.323515	−	0.323515i	0.850114	+	0.526599i	$0.176533\pi$
$762$	−5.15632e9	+	8.23435e9i	−0.422180	+	0.674197i
$763$	−4.81709e8	+	1.99530e8i	−0.0392599	+	0.0162620i
$764$	−2.09535e8	−	7.25964e7i	−0.0169993	−	0.00588963i
$765$	−1.22239e10	+	2.95111e10i	−0.987176	+	2.38325i
$766$	−1.86236e10	−	3.13479e9i	−1.49714	−	0.252004i
$767$	1.62579e10			1.30101
$768$	1.81913e10	+	2.86085e9i	1.44911	+	0.227893i
$769$	−1.07971e10			−0.856178			−0.428089	−	0.903737i	$-0.640813\pi$
$769$	−1.07971e10			−0.856178			−0.428089	+	0.903737i	$0.640813\pi$
$770$	7.89238e9	+	1.32847e9i	0.623003	+	0.104866i
$771$	6.08858e9	−	1.46991e10i	0.478438	−	1.15505i
$772$	−1.39140e10	−	4.82071e9i	−1.08841	−	0.377095i
$773$	−8.09960e8	+	3.35497e8i	−0.0630718	+	0.0261252i	−0.413996	−	0.910279i	$-0.635867\pi$
$773$	−8.09960e8	+	3.35497e8i	−0.0630718	+	0.0261252i	0.350925	+	0.936404i	$0.385867\pi$
$774$	5.05273e9	−	8.06891e9i	0.391681	−	0.625491i
$775$	−1.59719e10	+	1.59719e10i	−1.23254	+	1.23254i
$776$	−2.01500e10	−	1.10154e10i	−1.54796	−	0.846221i
$777$	7.65715e9	+	7.65715e9i	0.585590	+	0.585590i
$778$	−4.57430e9	+	1.05146e9i	−0.348254	+	0.0800509i
$779$	−2.12793e9	−	5.13729e9i	−0.161279	−	0.389361i
$780$	2.02526e10	−	2.28036e10i	1.52809	−	1.72057i
$781$	1.68846e9	+	6.99385e8i	0.126827	+	0.0525337i
$782$	8.25475e9	−	5.87618e9i	0.617278	−	0.439412i
$783$		−	4.77200e9i		−	0.355250i
$784$	−7.44815e9	+	9.45856e9i	−0.552004	+	0.701001i
$785$		−	3.06701e9i		−	0.226293i
$786$	7.97792e9	+	1.12072e10i	0.586018	+	0.823227i
$787$	3.42388e9	+	1.41822e9i	0.250385	+	0.103713i	0.504346	−	0.863502i	$-0.331734\pi$
$787$	3.42388e9	+	1.41822e9i	0.250385	+	0.103713i	−0.253961	+	0.967214i	$0.581734\pi$
$788$	−2.57036e9	+	1.52286e8i	−0.187133	+	0.0110871i
$789$	−3.58038e9	−	8.64381e9i	−0.259514	−	0.626521i
$790$	6.25555e9	+	2.72142e10i	0.451409	+	1.96382i
$791$	2.94138e9	+	2.94138e9i	0.211317	+	0.211317i
$792$	−1.37733e10	+	1.10883e10i	−0.985147	+	0.793097i
$793$	3.44197e9	−	3.44197e9i	0.245104	−	0.245104i
$794$	2.06038e10	+	1.29020e10i	1.46075	+	0.914715i
$795$	−5.55889e9	+	2.30257e9i	−0.392377	+	0.162528i
$796$	−1.07459e10	+	5.21578e9i	−0.755177	+	0.366542i
$797$	3.61045e9	−	8.71640e9i	0.252614	−	0.609864i	−0.745800	−	0.666170i	$-0.767932\pi$
$797$	3.61045e9	−	8.71640e9i	0.252614	−	0.609864i	0.998414	+	0.0563062i	$0.0179323\pi$
$798$	−8.57015e8	+	5.09147e9i	−0.0597005	+	0.354677i
$799$	2.11987e10			1.47027
$800$	−2.99784e10	−	1.45222e9i	−2.07011	−	0.100281i
$801$	7.46939e9			0.513536
$802$	2.63821e9	−	1.56734e10i	0.180592	−	1.07289i
$803$	5.00257e9	−	1.20773e10i	0.340949	−	0.823123i
$804$	9.78416e9	+	2.01581e10i	0.663938	+	1.36789i
$805$	−4.66599e9	+	1.93272e9i	−0.315252	+	0.130582i
$806$	−9.48296e9	−	5.93820e9i	−0.637927	−	0.399468i
$807$	−1.08356e10	+	1.08356e10i	−0.725762	+	0.725762i
$808$	4.17332e9	+	4.50717e8i	0.278319	+	0.0300583i
$809$	1.77774e10	+	1.77774e10i	1.18045	+	1.18045i	0.979627	+	0.200827i	$0.0643629\pi$
$809$	1.77774e10	+	1.77774e10i	1.18045	+	1.18045i	0.200827	+	0.979627i	$0.435637\pi$
$810$	−4.90052e9	−	2.13193e10i	−0.323999	−	1.40953i
$811$	1.91587e9	+	4.62531e9i	0.126122	+	0.304486i	0.974311	−	0.225209i	$-0.0723064\pi$
$811$	1.91587e9	+	4.62531e9i	0.126122	+	0.304486i	−0.848188	+	0.529695i	$0.822306\pi$
$812$	4.72381e8	+	7.97306e9i	0.0309633	+	0.522611i
$813$	−1.06244e10	−	4.40078e9i	−0.693407	−	0.287219i
$814$	1.68521e10	+	2.36735e10i	1.09514	+	1.53843i
$815$			7.90499e9i			0.511505i
$816$	1.42275e10	+	2.53725e10i	0.916671	+	1.63474i
$817$		−	7.45986e9i		−	0.478579i
$818$	3.16709e9	−	2.25451e9i	0.202313	−	0.144017i
$819$	4.91481e9	+	2.03578e9i	0.312617	+	0.129490i
$820$	1.16753e10	+	1.03693e10i	0.739471	+	0.656749i
$821$	5.29374e9	+	1.27802e10i	0.333858	+	0.806004i	0.998279	+	0.0586458i	$0.0186783\pi$
$821$	5.29374e9	+	1.27802e10i	0.333858	+	0.806004i	−0.664421	+	0.747359i	$0.731322\pi$
$822$	4.29453e9	−	9.87155e8i	0.269690	−	0.0619918i
$823$	−1.94667e9	−	1.94667e9i	−0.121729	−	0.121729i	0.643618	−	0.765347i	$-0.277433\pi$
$823$	−1.94667e9	−	1.94667e9i	−0.121729	−	0.121729i	−0.765347	+	0.643618i	$0.777433\pi$
$824$	−2.74509e10	+	8.04592e9i	−1.70927	+	0.500992i
$825$	3.80700e10	−	3.80700e10i	2.36045	−	2.36045i
$826$	4.10198e9	−	6.55062e9i	0.253258	−	0.404438i
$827$	−1.18185e10	+	4.89540e9i	−0.726598	+	0.300967i	−0.715153	−	0.698968i	$-0.753643\pi$
$827$	−1.18185e10	+	4.89540e9i	−0.726598	+	0.300967i	−0.0114451	+	0.999935i	$0.503643\pi$
$828$	3.65282e9	−	1.05431e10i	0.223626	−	0.645452i
$829$	1.15343e10	−	2.78464e10i	0.703157	−	1.69757i	−0.0132743	−	0.999912i	$-0.504225\pi$
$829$	1.15343e10	−	2.78464e10i	0.703157	−	1.69757i	0.716431	−	0.697658i	$-0.245775\pi$
$830$	−2.08880e10	−	3.51595e9i	−1.26801	−	0.213437i
$831$	1.53057e10			0.925231
$832$	−2.62558e9	−	1.46335e10i	−0.158050	−	0.880878i
$833$	−1.90177e10			−1.13999
$834$	−2.67012e10	−	4.49445e9i	−1.59386	−	0.268284i
$835$	1.51721e10	−	3.66286e10i	0.901867	−	2.17730i
$836$	−4.53577e9	+	1.30916e10i	−0.268491	+	0.774946i
$837$	2.93610e9	−	1.21617e9i	0.173074	−	0.0716895i
$838$	−1.69905e10	+	2.71329e10i	−0.997363	+	1.59273i
$839$	3.26283e9	−	3.26283e9i	0.190734	−	0.190734i	−0.605279	−	0.796013i	$-0.706939\pi$
$839$	3.26283e9	−	3.26283e9i	0.190734	−	0.190734i	0.796013	+	0.605279i	$0.206939\pi$
$840$	−4.07813e9	−	1.39137e10i	−0.237402	−	0.809962i
$841$	−1.88292e10	−	1.88292e10i	−1.09155	−	1.09155i
$842$	2.01511e10	−	4.63201e9i	1.16334	−	0.267410i
$843$	−7.07597e9	−	1.70829e10i	−0.406808	−	0.982121i
$844$	−2.63938e9	−	2.34412e9i	−0.151113	−	0.134209i
$845$	5.65427e9	+	2.34207e9i	0.322387	+	0.133537i
$846$	1.90176e10	−	1.35377e10i	1.07984	−	0.768687i
$847$			1.19348e9i			0.0674874i
$848$	−7.94606e8	+	2.82336e9i	−0.0447473	+	0.158994i
$849$			3.46250e10i			1.94184i
$850$	−2.74950e10	−	3.86245e10i	−1.53563	−	2.15723i
$851$	−1.69415e10	−	7.01738e9i	−0.942318	−	0.390321i
$852$	−1.95816e8	−	3.30507e9i	−0.0108470	−	0.183080i
$853$	−4.53398e9	−	1.09460e10i	−0.250126	−	0.603857i	0.748088	−	0.663599i	$-0.230972\pi$
$853$	−4.53398e9	−	1.09460e10i	−0.250126	−	0.603857i	−0.998214	+	0.0597427i	$0.980972\pi$
$854$	−5.18404e8	−	2.25527e9i	−0.0284817	−	0.123907i
$855$	1.94893e10	+	1.94893e10i	1.06638	+	1.06638i
$856$	−4.38548e8	+	4.06065e9i	−0.0238978	+	0.221277i
$857$	−5.83389e9	+	5.83389e9i	−0.316611	+	0.316611i	−0.847464	−	0.530853i	$-0.821872\pi$
$857$	−5.83389e9	+	5.83389e9i	−0.316611	+	0.316611i	0.530853	+	0.847464i	$0.321872\pi$
$858$	2.26032e10	+	1.41540e10i	1.22170	+	0.765024i
$859$	−2.70511e10	+	1.12049e10i	−1.45616	+	0.603161i	−0.963655	−	0.267149i	$-0.913918\pi$
$859$	−2.70511e10	+	1.12049e10i	−1.45616	+	0.603161i	−0.492504	+	0.870310i	$0.663918\pi$
$860$	9.14741e9	+	1.88462e10i	0.490404	+	1.01037i
$861$	−1.94722e9	+	4.70100e9i	−0.103969	+	0.251003i
$862$	1.60183e9	−	9.51637e9i	0.0851807	−	0.506053i
$863$	−3.49043e10			−1.84859			−0.924297	−	0.381675i	$-0.875348\pi$
$863$	−3.49043e10			−1.84859			−0.924297	+	0.381675i	$0.875348\pi$
$864$	3.81859e9	+	1.80287e9i	0.201421	+	0.0950969i
$865$	−2.52795e10			−1.32804
$866$	−4.01738e9	+	2.38670e10i	−0.210199	+	1.24878i
$867$	−6.81240e9	+	1.64466e10i	−0.355004	+	0.857055i
$868$	−4.78524e9	+	2.32262e9i	−0.248362	+	0.120548i
$869$	−2.25589e10	+	9.34421e9i	−1.16614	+	0.483029i
$870$	6.75095e10	+	4.22742e10i	3.47574	+	2.17650i
$871$	1.27917e10	−	1.27917e10i	0.655941	−	0.655941i
$872$	1.58952e9	+	1.97442e9i	0.0811817	+	0.100840i
$873$	−2.82467e10	−	2.82467e10i	−1.43687	−	1.43687i
$874$	−1.95863e9	−	8.52085e9i	−0.0992344	−	0.431711i
$875$	4.67991e9	+	1.12983e10i	0.236162	+	0.570144i
$876$	−2.36405e10	+	1.40064e9i	−1.18821	+	0.0703981i
$877$	1.78916e10	+	7.41096e9i	0.895677	+	0.371002i	0.782556	−	0.622580i	$-0.213915\pi$
$877$	1.78916e10	+	7.41096e9i	0.895677	+	0.371002i	0.113121	+	0.993581i	$0.463915\pi$
$878$	−4.05229e9	−	5.69258e9i	−0.202055	−	0.283843i
$879$		−	1.16046e10i		−	0.576329i
$880$	−4.59426e9	−	3.86358e10i	−0.227261	−	1.91118i
$881$			3.00057e10i			1.47839i	0.673493	+	0.739194i	$0.264793\pi$
$881$			3.00057e10i			1.47839i	−0.673493	+	0.739194i	$0.735207\pi$
$882$	−1.70609e10	+	1.21449e10i	−0.837263	+	0.596009i
$883$	2.45412e10	+	1.01653e10i	1.19959	+	0.496887i	0.890867	−	0.454265i	$-0.150098\pi$
$883$	2.45412e10	+	1.01653e10i	1.19959	+	0.496887i	0.308724	+	0.951152i	$0.400098\pi$
$884$	1.55952e10	−	1.75595e10i	0.759291	−	0.854929i
$885$	−2.94971e10	−	7.12122e10i	−1.43047	−	3.45345i
$886$	−1.43507e10	+	3.29869e9i	−0.693193	+	0.159340i
$887$	1.93144e10	+	1.93144e10i	0.929284	+	0.929284i	0.997660	−	0.0683754i	$-0.0217816\pi$
$887$	1.93144e10	+	1.93144e10i	0.929284	+	0.929284i	−0.0683754	+	0.997660i	$0.521782\pi$
$888$	2.52517e10	−	4.61921e10i	1.21017	−	2.21372i
$889$	2.63675e9	−	2.63675e9i	0.125867	−	0.125867i
$890$	−8.72296e9	+	1.39301e10i	−0.414762	+	0.662350i
$891$	1.76724e10	−	7.32013e9i	0.836995	−	0.346695i
$892$	5.88372e9	+	2.03850e9i	0.277572	+	0.0961685i
$893$	6.99987e9	−	1.68992e10i	0.328935	−	0.794119i
$894$	4.11491e10	+	6.92637e9i	1.92610	+	0.324208i
$895$	5.05117e10			2.35511
$896$	−6.55858e9	−	2.63423e9i	−0.304601	−	0.122342i
$897$	−1.68291e10			−0.778553
$898$	1.02401e10	+	1.72365e9i	0.471886	+	0.0794297i
$899$	1.11826e10	−	2.69973e10i	0.513317	−	1.23926i
$900$	−4.93320e10	−	1.70918e10i	−2.25569	−	0.781516i
$901$	−4.28054e9	+	1.77306e9i	−0.194967	+	0.0807581i
$902$	−7.24681e9	+	1.15727e10i	−0.328794	+	0.525065i
$903$	−4.82694e9	+	4.82694e9i	−0.218155	+	0.218155i
$904$	9.70008e9	−	1.77440e10i	0.436703	−	0.798844i
$905$	−1.12946e10	−	1.12946e10i	−0.506524	−	0.506524i
$906$	−3.72503e10	+	8.56248e9i	−1.66411	+	0.382517i
$907$	−7.34626e9	−	1.77354e10i	−0.326919	−	0.789253i	−0.998818	−	0.0486100i	$-0.984521\pi$
$907$	−7.34626e9	−	1.77354e10i	−0.326919	−	0.789253i	0.671898	−	0.740643i	$-0.265479\pi$
$908$	−6.68530e9	+	7.52736e9i	−0.296361	+	0.333689i
$909$	6.74595e9	+	2.79426e9i	0.297899	+	0.123394i
$910$	−9.53627e9	+	6.78844e9i	−0.419502	+	0.298624i
$911$		−	1.69766e10i		−	0.743939i	−0.928245	−	0.371970i	$-0.878683\pi$
$911$		−	1.69766e10i		−	0.743939i	0.928245	−	0.371970i	$-0.121317\pi$
$912$	2.49244e10	−	2.96381e9i	1.08804	−	0.129380i
$913$		−	1.85221e10i		−	0.805459i
$914$	−1.28104e10	−	1.79959e10i	−0.554948	−	0.779581i
$915$	−2.13213e10	−	8.83155e9i	−0.920108	−	0.381121i
$916$	3.35692e10	−	1.98888e9i	1.44314	−	0.0855018i
$917$	−2.02057e9	−	4.87808e9i	−0.0865327	−	0.208908i
$918$	1.49435e9	+	6.50105e9i	0.0637534	+	0.277354i
$919$	2.14443e10	+	2.14443e10i	0.911397	+	0.911397i	0.996382	−	0.0849855i	$-0.0270844\pi$
$919$	2.14443e10	+	2.14443e10i	0.911397	+	0.911397i	−0.0849855	+	0.996382i	$0.527084\pi$
$920$	1.53966e10	+	1.91249e10i	0.651879	+	0.809733i
$921$	9.45938e9	−	9.45938e9i	0.398983	−	0.398983i
$922$	−2.94348e10	−	1.84320e10i	−1.23681	−	0.774485i
$923$	−2.46953e9	+	1.02291e9i	−0.103373	+	0.0428186i
$924$	1.14059e10	−	5.53610e9i	0.475639	−	0.230862i
$925$	−3.28348e10	+	7.92702e10i	−1.36407	+	3.29317i
$926$	−3.10553e9	+	1.84497e10i	−0.128528	+	0.763575i
$927$	−4.97601e10			−2.05164
$928$	3.65497e10	−	1.31059e10i	1.50130	−	0.538329i
$929$	3.51926e10			1.44011			0.720056	−	0.693916i	$-0.244116\pi$
$929$	3.51926e10			1.44011			0.720056	+	0.693916i	$0.244116\pi$
$930$	−8.80515e9	+	5.23108e10i	−0.358960	+	2.13256i
$931$	−6.27967e9	+	1.51605e10i	−0.255043	+	0.615728i
$932$	8.51050e9	+	1.75340e10i	0.344349	+	0.709454i
$933$	−3.83478e10	+	1.58842e10i	−1.54580	+	0.640293i
$934$	3.29264e10	+	2.06184e10i	1.32230	+	0.828020i
$935$	4.34598e10	−	4.34598e10i	1.73879	−	1.73879i
$936$	2.77689e9	−	2.57121e10i	0.110686	−	1.02488i
$937$	2.55450e10	+	2.55450e10i	1.01442	+	1.01442i	0.999894	+	0.0145255i	$0.00462376\pi$
$937$	2.55450e10	+	2.55450e10i	1.01442	+	1.01442i	0.0145255	+	0.999894i	$0.495376\pi$
$938$	−1.92659e9	−	8.38148e9i	−0.0762220	−	0.331597i
$939$	−8.82142e9	−	2.12968e10i	−0.347704	−	0.839431i
$940$	3.03799e9	+	5.12766e10i	0.119300	+	2.01359i
$941$	1.98510e10	+	8.22256e9i	0.776639	+	0.321694i	0.735558	−	0.677461i	$-0.236920\pi$
$941$	1.98510e10	+	8.22256e9i	0.776639	+	0.321694i	0.0410806	+	0.999156i	$0.486920\pi$
$942$	−2.81759e9	−	3.95811e9i	−0.109825	−	0.154280i
$943$		−	8.61645e9i		−	0.334609i
$944$	−3.61687e10	−	1.01793e10i	−1.39937	−	0.393837i
$945$		−	3.32483e9i		−	0.128162i
$946$	−1.49234e10	+	1.06233e10i	−0.573124	+	0.407981i
$947$	3.44456e10	+	1.42678e10i	1.31798	+	0.545925i	0.927203	−	0.374560i	$-0.122206\pi$
$947$	3.44456e10	+	1.42678e10i	1.31798	+	0.545925i	0.390778	+	0.920485i	$0.372206\pi$
$948$	3.30742e10	+	2.93743e10i	1.26084	+	1.11979i
$949$	7.31671e9	+	1.76641e10i	0.277897	+	0.670903i
$950$	−3.98696e10	+	9.16455e9i	−1.50872	+	0.346800i
$951$	9.52527e9	+	9.52527e9i	0.359125	+	0.359125i
$952$	−3.14030e9	−	1.07140e10i	−0.117962	−	0.402461i
$953$	−1.15741e10	+	1.15741e10i	−0.433175	+	0.433175i	−0.889707	−	0.456532i	$-0.849091\pi$
$953$	−1.15741e10	+	1.15741e10i	−0.433175	+	0.433175i	0.456532	+	0.889707i	$0.349091\pi$
$954$	−2.70782e9	+	4.32422e9i	−0.100972	+	0.161246i
$955$	7.84192e8	−	3.24823e8i	0.0291347	−	0.0120680i
$956$	9.78273e8	−	2.82359e9i	0.0362124	−	0.104520i
$957$	−2.66545e10	+	6.43495e10i	−0.983055	+	2.37331i
$958$	−3.47365e10	−	5.84698e9i	−1.27646	−	0.214858i
$959$	−1.69127e9			−0.0619223
$960$	−5.93334e10	+	3.80504e10i	−2.16446	+	1.38806i
$961$	−8.05188e9			−0.292661
$962$	−4.19119e10	−	7.05477e9i	−1.51784	−	0.255488i
$963$	−2.71882e9	+	6.56381e9i	−0.0981043	+	0.236845i
$964$	3.58898e9	−	1.03589e10i	0.129033	−	0.372429i
$965$	5.20737e10	−	2.15696e10i	1.86540	−	0.772675i
$966$	−4.24611e9	+	6.78080e9i	−0.151555	+	0.242025i
$967$	−2.32194e10	+	2.32194e10i	−0.825768	+	0.825768i	−0.986928	−	0.161161i	$-0.948476\pi$
$967$	−2.32194e10	+	2.32194e10i	−0.825768	+	0.825768i	0.161161	+	0.986928i	$0.448476\pi$
$968$	5.56778e9	−	1.63193e9i	0.197296	−	0.0578279i
$969$	2.80364e10	+	2.80364e10i	0.989896	+	0.989896i
$970$	8.56659e10	−	1.96914e10i	3.01375	−	0.692750i
$971$	1.90326e10	+	4.59486e10i	0.667160	+	1.61067i	0.786341	+	0.617793i	$0.211973\pi$
$971$	1.90326e10	+	4.59486e10i	0.667160	+	1.61067i	−0.119181	+	0.992873i	$0.538027\pi$
$972$	−3.06781e10	−	2.72462e10i	−1.07151	−	0.951644i
$973$	9.60128e9	+	3.97698e9i	0.334145	+	0.138407i
$974$	1.89693e10	−	1.35034e10i	0.657803	−	0.468260i
$975$			7.87446e10i			2.72085i
$976$	−9.81238e9	+	5.50224e9i	−0.337831	+	0.189437i
$977$		−	5.17999e10i		−	1.77704i	−0.458835	−	0.888522i	$-0.651733\pi$
$977$		−	5.17999e10i		−	1.77704i	0.458835	−	0.888522i	$-0.348267\pi$
$978$	7.26215e9	+	1.02017e10i	0.248244	+	0.348729i
$979$	−1.32780e10	−	5.49994e9i	−0.452266	−	0.187335i
$980$	−2.72542e9	−	4.60009e10i	−0.0925002	−	1.56126i
$981$	1.68733e9	+	4.07358e9i	0.0570636	+	0.137764i
$982$	−1.25824e10	−	5.47388e10i	−0.424009	−	1.84461i
$983$	−3.47215e9	−	3.47215e9i	−0.116590	−	0.116590i	0.646405	−	0.762995i	$-0.276272\pi$
$983$	−3.47215e9	−	3.47215e9i	−0.116590	−	0.116590i	−0.762995	+	0.646405i	$0.776272\pi$
$984$	2.45935e10	+	2.65609e9i	0.822883	+	0.0888709i
$985$	6.96904e9	−	6.96904e9i	0.232352	−	0.232352i
$986$	5.19846e10	+	3.25526e10i	1.72705	+	1.08148i
$987$	−1.54640e10	+	6.40540e9i	−0.511931	+	0.212049i
$988$	−8.84852e9	−	1.82304e10i	−0.291891	−	0.601377i
$989$	4.42364e9	−	1.06796e10i	0.145410	−	0.351050i
$990$	1.12343e10	−	6.67420e10i	0.367978	−	2.18613i
$991$	−4.09824e10			−1.33764			−0.668820	−	0.743424i	$-0.733200\pi$
$991$	−4.09824e10			−1.33764			−0.668820	+	0.743424i	$0.733200\pi$
$992$	1.73786e10	+	1.91481e10i	0.565229	+	0.622779i
$993$	6.56476e10			2.12763
$994$	−2.10929e8	+	1.25311e9i	−0.00681213	+	0.0404704i
$995$	1.74966e10	−	4.22406e10i	0.563085	−	1.35941i
$996$	−3.01869e10	+	1.46519e10i	−0.968080	+	0.469879i
$997$	−2.72166e10	+	1.12735e10i	−0.869762	+	0.360267i	−0.772517	−	0.634993i	$-0.781003\pi$
$997$	−2.72166e10	+	1.12735e10i	−0.869762	+	0.360267i	−0.0972442	+	0.995261i	$0.531003\pi$
$998$	−2.33952e10	−	1.46500e10i	−0.745023	−	0.466531i
$999$	8.53614e9	−	8.53614e9i	0.270884	−	0.270884i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.8.g.a.13.2	yes	108
32.5	even	8	inner	32.8.g.a.5.2	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.8.g.a.5.2	✓	108	32.5	even	8	inner
32.8.g.a.13.2	yes	108	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	32.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-11.1568 - 1.87795i) q^{2} +(26.2524 - 63.3790i) q^{3} +(120.947 + 41.9036i) q^{4} +(-452.646 + 187.492i) q^{5} +(-411.914 + 657.803i) q^{6} +(210.637 - 210.637i) q^{7} +(-1270.68 - 694.640i) q^{8} +(-1781.26 - 1781.26i) q^{9} +O(q^{10})\)	\(q+(-11.1568 - 1.87795i) q^{2} +(26.2524 - 63.3790i) q^{3} +(120.947 + 41.9036i) q^{4} +(-452.646 + 187.492i) q^{5} +(-411.914 + 657.803i) q^{6} +(210.637 - 210.637i) q^{7} +(-1270.68 - 694.640i) q^{8} +(-1781.26 - 1781.26i) q^{9} +(5402.17 - 1241.76i) q^{10} +(1854.88 + 4478.07i) q^{11} +(5830.95 - 6565.40i) q^{12} +(-6549.58 - 2712.92i) q^{13} +(-2745.60 + 1954.47i) q^{14} +33610.4i q^{15} +(12872.2 + 10136.2i) q^{16} +25881.2i q^{17} +(16528.0 + 23218.2i) q^{18} +(20631.9 + 8546.02i) q^{19} +(-62602.7 + 3709.03i) q^{20} +(-7820.24 - 18879.7i) q^{21} +(-12284.8 - 53444.1i) q^{22} +(24469.2 + 24469.2i) q^{23} +(-77384.0 + 62298.4i) q^{24} +(114493. - 114493. i) q^{25} +(67977.4 + 42567.2i) q^{26} +(-21047.0 + 8717.96i) q^{27} +(34302.4 - 16649.4i) q^{28} +(-80161.3 + 193526. i) q^{29} +(63118.5 - 374983. i) q^{30} -139502. q^{31} +(-124576. - 137260. i) q^{32} +332510. q^{33} +(48603.5 - 288750. i) q^{34} +(-55851.4 + 134837. i) q^{35} +(-140796. - 290079. i) q^{36} +(-489572. + 202788. i) q^{37} +(-214136. - 134092. i) q^{38} +(-343885. + 343885. i) q^{39} +(705408. + 76183.7i) q^{40} +(-176068. - 176068. i) q^{41} +(51793.4 + 225323. i) q^{42} +(-127834. - 308618. i) q^{43} +(36693.8 + 619333. i) q^{44} +(1.14025e6 + 472308. i) q^{45} +(-227045. - 318948. i) q^{46} -819080. i q^{47} +(980348. - 549725. i) q^{48} +734807. i q^{49} +(-1.49238e6 + 1.06236e6i) q^{50} +(1.64032e6 + 679443. i) q^{51} +(-678468. - 602570. i) q^{52} +(68507.7 + 165392. i) q^{53} +(251188. - 57739.0i) q^{54} +(-1.67921e6 - 1.67921e6i) q^{55} +(-413970. + 121336. i) q^{56} +(1.08328e6 - 1.08328e6i) q^{57} +(1.25777e6 - 2.00859e6i) q^{58} +(-2.11876e6 + 877618. i) q^{59} +(-1.40840e6 + 4.06506e6i) q^{60} +(-262763. + 634365. i) q^{61} +(1.55639e6 + 261977. i) q^{62} -750400. q^{63} +(1.13210e6 + 1.76533e6i) q^{64} +3.47330e6 q^{65} +(-3.70974e6 - 624437. i) q^{66} +(-976529. + 2.35755e6i) q^{67} +(-1.08451e6 + 3.13024e6i) q^{68} +(2.19320e6 - 908455. i) q^{69} +(876338. - 1.39946e6i) q^{70} +(266616. - 266616. i) q^{71} +(1.02608e6 + 3.50075e6i) q^{72} +(-1.90706e6 - 1.90706e6i) q^{73} +(5.84287e6 - 1.34306e6i) q^{74} +(-4.25072e6 - 1.02621e7i) q^{75} +(2.13725e6 + 1.89816e6i) q^{76} +(1.33396e6 + 552542. i) q^{77} +(4.48244e6 - 3.19084e6i) q^{78} +5.03765e6i q^{79} +(-7.72700e6 - 2.17468e6i) q^{80} -3.94643e6i q^{81} +(1.63370e6 + 2.29499e6i) q^{82} +(-3.53046e6 - 1.46236e6i) q^{83} +(-154703. - 2.61114e6i) q^{84} +(-4.85252e6 - 1.17150e7i) q^{85} +(846643. + 3.68324e6i) q^{86} +(1.01611e7 + 1.01611e7i) q^{87} +(753692. - 6.97866e6i) q^{88} +(-2.09666e6 + 2.09666e6i) q^{89} +(-1.18346e7 - 7.41077e6i) q^{90} +(-1.95103e6 + 808143. i) q^{91} +(1.93412e6 + 3.98481e6i) q^{92} +(-3.66226e6 + 8.84147e6i) q^{93} +(-1.53819e6 + 9.13828e6i) q^{94} -1.09413e7 q^{95} +(-1.19699e7 + 4.29211e6i) q^{96} +1.58577e7 q^{97} +(1.37993e6 - 8.19806e6i) q^{98} +(4.67259e6 - 1.12806e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 108 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 13004 q^{10} - 4 q^{11} + 30668 q^{12} - 4 q^{13} - 26196 q^{14} - 52784 q^{16} + 102056 q^{18} - 4 q^{19} + 81996 q^{20} - 4 q^{21} - 374240 q^{22} - 143420 q^{23} + 380880 q^{24} - 4 q^{25} - 363984 q^{26} + 476084 q^{27} - 195464 q^{28} - 4 q^{29} + 870468 q^{30} - 714992 q^{31} + 535656 q^{32} - 8 q^{33} - 201072 q^{34} + 816500 q^{35} - 1669712 q^{36} - 4 q^{37} - 2533100 q^{38} - 283948 q^{39} + 2746344 q^{40} - 4 q^{41} + 4924936 q^{42} + 366180 q^{43} - 1585404 q^{44} + 8744 q^{45} - 2715812 q^{46} - 5044368 q^{48} - 1653804 q^{50} + 3002072 q^{51} + 8882212 q^{52} - 1815636 q^{53} + 6815776 q^{54} - 4191012 q^{55} - 3655000 q^{56} - 4 q^{57} - 12448736 q^{58} - 1835940 q^{59} - 6364808 q^{60} - 4559780 q^{61} + 12948600 q^{62} + 10001872 q^{63} + 16915544 q^{64} - 8 q^{65} - 11246068 q^{66} - 1940684 q^{67} - 8895536 q^{68} + 9580892 q^{69} - 8149480 q^{70} - 12348708 q^{71} + 12884564 q^{72} - 4 q^{73} + 10931436 q^{74} + 11573008 q^{75} + 14443516 q^{76} - 11914452 q^{77} - 38252364 q^{78} - 11333192 q^{80} + 15827196 q^{82} - 9565884 q^{83} + 8101984 q^{84} + 312496 q^{85} - 14812992 q^{86} + 40789108 q^{87} + 5716448 q^{88} - 4 q^{89} + 5335400 q^{90} - 3406996 q^{91} + 27562664 q^{92} - 8752 q^{93} - 14227032 q^{94} - 54872008 q^{95} - 25080448 q^{96} - 8 q^{97} + 57598104 q^{98} - 9738480 q^{99}+O(q^{100}) \) 108 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 13004 * q^10 - 4 * q^11 + 30668 * q^12 - 4 * q^13 - 26196 * q^14 - 52784 * q^16 + 102056 * q^18 - 4 * q^19 + 81996 * q^20 - 4 * q^21 - 374240 * q^22 - 143420 * q^23 + 380880 * q^24 - 4 * q^25 - 363984 * q^26 + 476084 * q^27 - 195464 * q^28 - 4 * q^29 + 870468 * q^30 - 714992 * q^31 + 535656 * q^32 - 8 * q^33 - 201072 * q^34 + 816500 * q^35 - 1669712 * q^36 - 4 * q^37 - 2533100 * q^38 - 283948 * q^39 + 2746344 * q^40 - 4 * q^41 + 4924936 * q^42 + 366180 * q^43 - 1585404 * q^44 + 8744 * q^45 - 2715812 * q^46 - 5044368 * q^48 - 1653804 * q^50 + 3002072 * q^51 + 8882212 * q^52 - 1815636 * q^53 + 6815776 * q^54 - 4191012 * q^55 - 3655000 * q^56 - 4 * q^57 - 12448736 * q^58 - 1835940 * q^59 - 6364808 * q^60 - 4559780 * q^61 + 12948600 * q^62 + 10001872 * q^63 + 16915544 * q^64 - 8 * q^65 - 11246068 * q^66 - 1940684 * q^67 - 8895536 * q^68 + 9580892 * q^69 - 8149480 * q^70 - 12348708 * q^71 + 12884564 * q^72 - 4 * q^73 + 10931436 * q^74 + 11573008 * q^75 + 14443516 * q^76 - 11914452 * q^77 - 38252364 * q^78 - 11333192 * q^80 + 15827196 * q^82 - 9565884 * q^83 + 8101984 * q^84 + 312496 * q^85 - 14812992 * q^86 + 40789108 * q^87 + 5716448 * q^88 - 4 * q^89 + 5335400 * q^90 - 3406996 * q^91 + 27562664 * q^92 - 8752 * q^93 - 14227032 * q^94 - 54872008 * q^95 - 25080448 * q^96 - 8 * q^97 + 57598104 * q^98 - 9738480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more