LMFDB - Embedded newform 32.8.g.a.13.27

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			13.27
Character	$\chi$	$=$	32.13
Dual form			32.8.g.a.5.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.3081 + 0.356189i) q^{2} +(27.3562 - 66.0437i) q^{3} +(127.746 + 8.05564i) q^{4} +(250.611 - 103.807i) q^{5} +(332.870 - 737.084i) q^{6} +(-662.282 + 662.282i) q^{7} +(1441.70 + 136.596i) q^{8} +(-2066.96 - 2066.96i) q^{9} +O(q^{10})$	\(q+(11.3081 + 0.356189i) q^{2} +(27.3562 - 66.0437i) q^{3} +(127.746 + 8.05564i) q^{4} +(250.611 - 103.807i) q^{5} +(332.870 - 737.084i) q^{6} +(-662.282 + 662.282i) q^{7} +(1441.70 + 136.596i) q^{8} +(-2066.96 - 2066.96i) q^{9} +(2870.91 - 1084.59i) q^{10} +(12.1423 + 29.3140i) q^{11} +(4026.67 - 8216.46i) q^{12} +(-7276.98 - 3014.22i) q^{13} +(-7725.05 + 7253.26i) q^{14} -19391.0i q^{15} +(16254.2 + 2058.16i) q^{16} +14716.0i q^{17} +(-22637.2 - 24109.7i) q^{18} +(46419.5 + 19227.6i) q^{19} +(32850.9 - 11242.1i) q^{20} +(25622.0 + 61857.1i) q^{21} +(126.865 + 335.811i) q^{22} +(-67886.2 - 67886.2i) q^{23} +(48460.6 - 91478.3i) q^{24} +(-3212.55 + 3212.55i) q^{25} +(-81215.2 - 36677.1i) q^{26} +(-48616.6 + 20137.6i) q^{27} +(-89939.2 + 79269.0i) q^{28} +(-57554.3 + 138948. i) q^{29} +(6906.87 - 219276. i) q^{30} +199317. q^{31} +(183071. + 29063.4i) q^{32} +2268.17 q^{33} +(-5241.69 + 166410. i) q^{34} +(-97226.1 + 234725. i) q^{35} +(-247396. - 280698. i) q^{36} +(-366691. + 151889. i) q^{37} +(518068. + 233962. i) q^{38} +(-398141. + 398141. i) q^{39} +(375485. - 115425. i) q^{40} +(-166094. - 166094. i) q^{41} +(267704. + 708612. i) q^{42} +(315714. + 762200. i) q^{43} +(1314.99 + 3842.57i) q^{44} +(-732568. - 303440. i) q^{45} +(-743483. - 791844. i) q^{46} -119202. i q^{47} +(580581. - 1.01718e6i) q^{48} -53692.4i q^{49} +(-37472.1 + 35183.6i) q^{50} +(971901. + 402575. i) q^{51} +(-905326. - 443677. i) q^{52} +(-208229. - 502710. i) q^{53} +(-556934. + 210402. i) q^{54} +(6085.98 + 6085.98i) q^{55} +(-1.04528e6 + 864346. i) q^{56} +(2.53972e6 - 2.53972e6i) q^{57} +(-700321. + 1.55074e6i) q^{58} +(1.20574e6 - 499433. i) q^{59} +(156207. - 2.47713e6i) q^{60} +(531358. - 1.28281e6i) q^{61} +(2.25390e6 + 70994.6i) q^{62} +2.73783e6 q^{63} +(2.05984e6 + 393860. i) q^{64} -2.13659e6 q^{65} +(25648.7 + 807.898i) q^{66} +(1.29282e6 - 3.12115e6i) q^{67} +(-118547. + 1.87992e6i) q^{68} +(-6.34056e6 + 2.62635e6i) q^{69} +(-1.18305e6 + 2.61966e6i) q^{70} +(-1.40872e6 + 1.40872e6i) q^{71} +(-2.69760e6 - 3.26228e6i) q^{72} +(944098. + 944098. i) q^{73} +(-4.20068e6 + 1.58696e6i) q^{74} +(124286. + 300052. i) q^{75} +(5.77503e6 + 2.83019e6i) q^{76} +(-27455.8 - 11372.6i) q^{77} +(-4.64403e6 + 4.36040e6i) q^{78} -2.52254e6i q^{79} +(4.28714e6 - 1.17150e6i) q^{80} -2.63117e6i q^{81} +(-1.81904e6 - 1.93737e6i) q^{82} +(-8.11459e6 - 3.36117e6i) q^{83} +(2.77482e6 + 8.10841e6i) q^{84} +(1.52762e6 + 3.68800e6i) q^{85} +(3.29863e6 + 8.73149e6i) q^{86} +(7.60219e6 + 7.60219e6i) q^{87} +(13501.3 + 43920.6i) q^{88} +(-4.96152e6 + 4.96152e6i) q^{89} +(-8.17588e6 - 3.69226e6i) q^{90} +(6.81568e6 - 2.82315e6i) q^{91} +(-8.12534e6 - 9.21907e6i) q^{92} +(5.45256e6 - 1.31636e7i) q^{93} +(42458.6 - 1.34795e6i) q^{94} +1.36292e7 q^{95} +(6.92758e6 - 1.12956e7i) q^{96} -1.10016e7 q^{97} +(19124.6 - 607159. i) q^{98} +(35493.4 - 85688.7i) 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 $

$2$	11.3081	+	0.356189i	0.999504	+	0.0314829i
$2$	11.3081	+	0.356189i	0.999504	+	0.0314829i
$3$	27.3562	−	66.0437i	0.584967	−	1.41223i	−0.303295	−	0.952897i	$-0.598087\pi$
$3$	27.3562	−	66.0437i	0.584967	−	1.41223i	0.888262	−	0.459338i	$-0.151913\pi$
$4$	127.746	+	8.05564i	0.998018	+	0.0629347i
$5$	250.611	−	103.807i	0.896614	−	0.371390i	0.113697	−	0.993516i	$-0.463731\pi$
$5$	250.611	−	103.807i	0.896614	−	0.371390i	0.782917	+	0.622126i	$0.213731\pi$
$6$	332.870	−	737.084i	0.629138	−	1.39312i
$7$	−662.282	+	662.282i	−0.729793	+	0.729793i	−0.970578	−	0.240785i	$-0.922595\pi$
$7$	−662.282	+	662.282i	−0.729793	+	0.729793i	0.240785	+	0.970578i	$0.422595\pi$
$8$	1441.70	+	136.596i	0.995542	+	0.0943240i
$9$	−2066.96	−	2066.96i	−0.945114	−	0.945114i
$10$	2870.91	−	1084.59i	0.907862	−	0.342977i
$11$	12.1423	+	29.3140i	0.00275059	+	0.00664051i	0.925249	−	0.379361i	$-0.123856\pi$
$11$	12.1423	+	29.3140i	0.00275059	+	0.00664051i	−0.922498	+	0.386001i	$0.873856\pi$
$12$	4026.67	−	8216.46i	0.672686	−	1.37262i
$13$	−7276.98	−	3014.22i	−0.918649	−	0.380517i	−0.127288	−	0.991866i	$-0.540627\pi$
$13$	−7276.98	−	3014.22i	−0.918649	−	0.380517i	−0.791361	+	0.611349i	$0.790627\pi$
$14$	−7725.05	+	7253.26i	−0.752408	+	0.706456i
$15$		−	19391.0i		−	1.48348i
$16$	16254.2	+	2058.16i	0.992078	+	0.125620i
$17$			14716.0i			0.726473i	0.931697	+	0.363237i	$0.118328\pi$
$17$			14716.0i			0.726473i	−0.931697	+	0.363237i	$0.881672\pi$
$18$	−22637.2	−	24109.7i	−0.914890	−	0.974400i
$19$	46419.5	+	19227.6i	1.55261	+	0.643113i	0.983786	−	0.179346i	$-0.0573981\pi$
$19$	46419.5	+	19227.6i	1.55261	+	0.643113i	0.568825	+	0.822458i	$0.307398\pi$
$20$	32850.9	−	11242.1i	0.918210	−	0.314225i
$21$	25622.0	+	61857.1i	0.603735	+	1.45754i
$22$	126.865	+	335.811i	0.00254016	+	0.00672381i
$23$	−67886.2	−	67886.2i	−1.16341	−	1.16341i	−0.983723	−	0.179690i	$-0.942491\pi$
$23$	−67886.2	−	67886.2i	−1.16341	−	1.16341i	−0.179690	−	0.983723i	$-0.557509\pi$
$24$	48460.6	−	91478.3i	0.715566	−	1.35076i
$25$	−3212.55	+	3212.55i	−0.0411207	+	0.0411207i
$26$	−81215.2	−	36677.1i	−0.906214	−	0.409250i
$27$	−48616.6	+	20137.6i	−0.475347	+	0.196895i
$28$	−89939.2	+	79269.0i	−0.774276	+	0.682417i
$29$	−57554.3	+	138948.i	−0.438212	+	1.05794i	0.538354	+	0.842719i	$0.319046\pi$
$29$	−57554.3	+	138948.i	−0.438212	+	1.05794i	−0.976566	+	0.215219i	$0.930954\pi$
$30$	6906.87	−	219276.i	0.0467043	−	1.48274i
$31$	199317.			1.20165			0.600826	−	0.799380i	$-0.294838\pi$
$31$	199317.			1.20165			0.600826	+	0.799380i	$0.294838\pi$
$32$	183071.	+	29063.4i	0.987632	+	0.156791i
$33$	2268.17			0.0109870
$34$	−5241.69	+	166410.i	−0.0228715	+	0.726113i
$35$	−97226.1	+	234725.i	−0.383305	+	0.925381i
$36$	−247396.	−	280698.i	−0.883760	−	1.00272i
$37$	−366691.	+	151889.i	−1.19013	+	0.492968i	−0.887798	−	0.460234i	$-0.847766\pi$
$37$	−366691.	+	151889.i	−1.19013	+	0.492968i	−0.302333	+	0.953202i	$0.597766\pi$
$38$	518068.	+	233962.i	1.53159	+	0.691675i
$39$	−398141.	+	398141.i	−1.07476	+	1.07476i
$40$	375485.	−	115425.i	0.927647	−	0.285162i
$41$	−166094.	−	166094.i	−0.376365	−	0.376365i	0.493424	−	0.869789i	$-0.335745\pi$
$41$	−166094.	−	166094.i	−0.376365	−	0.376365i	−0.869789	+	0.493424i	$0.835745\pi$
$42$	267704.	+	708612.i	0.557548	+	1.47583i
$43$	315714.	+	762200.i	0.605555	+	1.46194i	0.867788	+	0.496935i	$0.165541\pi$
$43$	315714.	+	762200.i	0.605555	+	1.46194i	−0.262232	+	0.965005i	$0.584459\pi$
$44$	1314.99	+	3842.57i	0.00232722	+	0.00680045i
$45$	−732568.	−	303440.i	−1.19841	−	0.496397i
$46$	−743483.	−	791844.i	−1.12621	−	1.19946i
$47$		−	119202.i		−	0.167472i	−0.996488	−	0.0837361i	$-0.973315\pi$
$47$		−	119202.i		−	0.167472i	0.996488	−	0.0837361i	$-0.0266853\pi$
$48$	580581.	−	1.01718e6i	0.757738	−	1.32756i
$49$		−	53692.4i		−	0.0651968i
$50$	−37472.1	+	35183.6i	−0.0423949	+	0.0398057i
$51$	971901.	+	402575.i	1.02595	+	0.424963i
$52$	−905326.	−	443677.i	−0.892880	−	0.437577i
$53$	−208229.	−	502710.i	−0.192122	−	0.463823i	0.798238	−	0.602342i	$-0.205766\pi$
$53$	−208229.	−	502710.i	−0.192122	−	0.463823i	−0.990360	+	0.138519i	$0.955766\pi$
$54$	−556934.	+	210402.i	−0.481311	+	0.181832i
$55$	6085.98	+	6085.98i	0.00493243	+	0.00493243i
$56$	−1.04528e6	+	864346.i	−0.795377	+	0.657703i
$57$	2.53972e6	−	2.53972e6i	1.81645	−	1.81645i
$58$	−700321.	+	1.55074e6i	−0.471302	+	1.04362i
$59$	1.20574e6	−	499433.i	0.764312	−	0.316589i	0.0337462	−	0.999430i	$-0.489256\pi$
$59$	1.20574e6	−	499433.i	0.764312	−	0.316589i	0.730566	+	0.682842i	$0.239256\pi$
$60$	156207.	−	2.47713e6i	0.0933623	−	1.48054i
$61$	531358.	−	1.28281e6i	0.299732	−	0.723616i	−0.700222	−	0.713926i	$-0.746915\pi$
$61$	531358.	−	1.28281e6i	0.299732	−	0.723616i	0.999953	−	0.00969031i	$-0.00308457\pi$
$62$	2.25390e6	+	70994.6i	1.20106	+	0.0378316i
$63$	2.73783e6			1.37948
$64$	2.05984e6	+	393860.i	0.982206	+	0.187807i
$65$	−2.13659e6			−0.964993
$66$	25648.7	+	807.898i	0.0109815	+	0.000345902i
$67$	1.29282e6	−	3.12115e6i	0.525142	−	1.26781i	−0.409530	−	0.912297i	$-0.634307\pi$
$67$	1.29282e6	−	3.12115e6i	0.525142	−	1.26781i	0.934673	−	0.355509i	$-0.115693\pi$
$68$	−118547.	+	1.87992e6i	−0.0457204	+	0.725033i
$69$	−6.34056e6	+	2.62635e6i	−2.32357	+	0.962454i
$70$	−1.18305e6	+	2.61966e6i	−0.412249	+	0.912854i
$71$	−1.40872e6	+	1.40872e6i	−0.467110	+	0.467110i	−0.900977	−	0.433867i	$-0.857149\pi$
$71$	−1.40872e6	+	1.40872e6i	−0.467110	+	0.467110i	0.433867	+	0.900977i	$0.357149\pi$
$72$	−2.69760e6	−	3.26228e6i	−0.851753	−	1.03005i
$73$	944098.	+	944098.i	0.284045	+	0.284045i	0.834720	−	0.550675i	$-0.185630\pi$
$73$	944098.	+	944098.i	0.284045	+	0.284045i	−0.550675	+	0.834720i	$0.685630\pi$
$74$	−4.20068e6	+	1.58696e6i	−1.20506	+	0.455255i
$75$	124286.	+	300052.i	0.0340178	+	0.0821262i
$76$	5.77503e6	+	2.83019e6i	1.50906	+	0.739551i
$77$	−27455.8	−	11372.6i	−0.00685356	−	0.00283884i
$78$	−4.64403e6	+	4.36040e6i	−1.10806	+	1.04039i
$79$		−	2.52254e6i		−	0.575631i	−0.957686	−	0.287815i	$-0.907071\pi$
$79$		−	2.52254e6i		−	0.575631i	0.957686	−	0.287815i	$-0.0929290\pi$
$80$	4.28714e6	−	1.17150e6i	0.936165	−	0.255815i
$81$		−	2.63117e6i		−	0.550113i
$82$	−1.81904e6	−	1.93737e6i	−0.364330	−	0.388028i
$83$	−8.11459e6	−	3.36117e6i	−1.55773	−	0.645234i	−0.573039	−	0.819528i	$-0.694236\pi$
$83$	−8.11459e6	−	3.36117e6i	−1.55773	−	0.645234i	−0.984694	+	0.174294i	$0.944236\pi$
$84$	2.77482e6	+	8.10841e6i	0.510808	+	1.49265i
$85$	1.52762e6	+	3.68800e6i	0.269805	+	0.651366i
$86$	3.29863e6	+	8.73149e6i	0.559229	+	1.48028i
$87$	7.60219e6	+	7.60219e6i	1.23772	+	1.23772i
$88$	13501.3	+	43920.6i	0.00211197	+	0.00687035i
$89$	−4.96152e6	+	4.96152e6i	−0.746019	+	0.746019i	−0.973729	−	0.227710i	$-0.926876\pi$
$89$	−4.96152e6	+	4.96152e6i	−0.746019	+	0.746019i	0.227710	+	0.973729i	$0.426876\pi$
$90$	−8.17588e6	−	3.69226e6i	−1.18219	−	0.533880i
$91$	6.81568e6	−	2.82315e6i	0.948123	−	0.392725i
$92$	−8.12534e6	−	9.21907e6i	−1.08789	−	1.23433i
$93$	5.45256e6	−	1.31636e7i	0.702927	−	1.69702i
$94$	42458.6	−	1.34795e6i	0.00527252	−	0.167389i
$95$	1.36292e7			1.63094
$96$	6.92758e6	−	1.12956e7i	0.799158	−	1.30305i
$97$	−1.10016e7			−1.22392			−0.611962	−	0.790887i	$-0.709620\pi$
$97$	−1.10016e7			−1.22392			−0.611962	+	0.790887i	$0.709620\pi$
$98$	19124.6	−	607159.i	0.00205259	−	0.0651645i
$99$	35493.4	−	85688.7i	0.00367641	−	0.00887565i
$100$	−436271.	+	384512.i	−0.0436271	+	0.0384512i
$101$	8.18837e6	−	3.39173e6i	0.790810	−	0.327564i	0.0495411	−	0.998772i	$-0.484224\pi$
$101$	8.18837e6	−	3.39173e6i	0.790810	−	0.327564i	0.741269	+	0.671208i	$0.234224\pi$
$102$	1.08470e7	+	4.89853e6i	1.01206	+	0.457052i
$103$	−1.14142e7	+	1.14142e7i	−1.02923	+	1.02923i	−0.0296745	+	0.999560i	$0.509447\pi$
$103$	−1.14142e7	+	1.14142e7i	−1.02923	+	1.02923i	−0.999560	+	0.0296745i	$0.990553\pi$
$104$	−1.00795e7	−	5.33961e6i	−0.878661	−	0.465471i
$105$	1.28423e7	+	1.28423e7i	1.08263	+	1.08263i
$106$	−2.17562e6	−	5.75887e6i	−0.177424	−	0.469642i
$107$	−604339.	−	1.45900e6i	−0.0476911	−	0.115136i	0.898239	−	0.439508i	$-0.144847\pi$
$107$	−604339.	−	1.45900e6i	−0.0476911	−	0.115136i	−0.945930	+	0.324372i	$0.894847\pi$
$108$	−6.37281e6	+	2.18087e6i	−0.486797	+	0.166589i
$109$	−2.32637e7	−	9.63615e6i	−1.72063	−	0.712707i	−0.999808	−	0.0195817i	$-0.993767\pi$
$109$	−2.32637e7	−	9.63615e6i	−1.72063	−	0.712707i	−0.720818	−	0.693125i	$-0.756233\pi$
$110$	66653.1	+	70988.6i	0.00477470	+	0.00508527i
$111$			2.83727e7i			1.96911i
$112$	−1.21280e7	+	9.40180e6i	−0.815689	+	0.632336i
$113$		−	1.33154e7i		−	0.868121i	−0.900884	−	0.434061i	$-0.857080\pi$
$113$		−	1.33154e7i		−	0.868121i	0.900884	−	0.434061i	$-0.142920\pi$
$114$	2.96240e7	−	2.78148e7i	1.87274	−	1.75836i
$115$	−2.40601e7	−	9.96601e6i	−1.47521	−	0.611053i
$116$	−8.47166e6	+	1.72865e7i	−0.503925	+	1.02826i
$117$	8.81096e6	+	2.12715e7i	0.508596	+	1.22786i
$118$	1.38125e7	−	5.21817e6i	0.773901	−	0.292369i
$119$	−9.74617e6	−	9.74617e6i	−0.530175	−	0.530175i
$120$	2.64873e6	−	2.79560e7i	0.139928	−	1.47687i
$121$	1.37788e7	−	1.37788e7i	0.707070	−	0.707070i
$122$	6.46557e6	−	1.43169e7i	0.322365	−	0.713821i
$123$	−1.55131e7	+	6.42575e6i	−0.751677	+	0.311355i
$124$	2.54620e7	+	1.60563e6i	1.19927	+	0.0756256i
$125$	−8.58150e6	+	2.07176e7i	−0.392987	+	0.948755i
$126$	3.09596e7	+	975183.i	1.37879	+	0.0434299i
$127$	−3.03886e6			−0.131643			−0.0658214	−	0.997831i	$-0.520967\pi$
$127$	−3.03886e6			−0.131643			−0.0658214	+	0.997831i	$0.520967\pi$
$128$	2.31525e7	+	5.18750e6i	0.975806	+	0.218637i
$129$	5.89752e7			2.41883
$130$	−2.41608e7	−	761029.i	−0.964515	−	0.0303808i
$131$	1.54401e7	−	3.72756e7i	0.600066	−	1.44869i	−0.273447	−	0.961887i	$-0.588164\pi$
$131$	1.54401e7	−	3.72756e7i	0.600066	−	1.44869i	0.873513	−	0.486801i	$-0.161836\pi$
$132$	289751.	+	18271.6i	0.0109652	+	0.000691460i
$133$	−4.34769e7	+	1.80087e7i	−1.60242	+	0.663746i
$134$	1.57311e7	−	3.48338e7i	0.564796	−	1.25064i
$135$	−1.00934e7	+	1.00934e7i	−0.353078	+	0.353078i
$136$	−2.01015e6	+	2.12161e7i	−0.0685239	+	0.723234i
$137$	309029.	+	309029.i	0.0102678	+	0.0102678i	0.712222	−	0.701954i	$-0.247689\pi$
$137$	309029.	+	309029.i	0.0102678	+	0.0102678i	−0.701954	+	0.712222i	$0.747689\pi$
$138$	−7.26352e7	+	2.74405e7i	−2.35272	+	0.888824i
$139$	−5.15073e6	−	1.24350e7i	−0.162674	−	0.392729i	0.821434	−	0.570304i	$-0.193175\pi$
$139$	−5.15073e6	−	1.24350e7i	−0.162674	−	0.392729i	−0.984107	+	0.177575i	$0.943175\pi$
$140$	−1.43111e7	+	2.92020e7i	−0.440784	+	0.899423i
$141$	−7.87256e6	−	3.26092e6i	−0.236510	−	0.0979656i
$142$	−1.64317e7	+	1.54281e7i	−0.481585	+	0.452173i
$143$		−	249917.i		−	0.00714694i
$144$	−2.93427e7	−	3.78510e7i	−0.818902	−	1.05635i
$145$			4.07965e7i			1.11131i
$146$	1.03397e7	+	1.10122e7i	0.274961	+	0.292847i
$147$	−3.54604e6	−	1.46882e6i	−0.0920732	−	0.0381380i
$148$	−4.80670e7	+	1.64493e7i	−1.21880	+	0.417091i
$149$	5.63062e6	+	1.35935e7i	0.139446	+	0.336651i	0.978139	−	0.207953i	$-0.0666800\pi$
$149$	5.63062e6	+	1.35935e7i	0.139446	+	0.336651i	−0.838693	+	0.544604i	$0.816680\pi$
$150$	1.29856e6	+	3.43729e6i	0.0314154	+	0.0831565i
$151$	−6.29794e6	−	6.29794e6i	−0.148860	−	0.148860i	0.628748	−	0.777609i	$-0.283568\pi$
$151$	−6.29794e6	−	6.29794e6i	−0.148860	−	0.148860i	−0.777609	+	0.628748i	$0.783568\pi$
$152$	6.42965e7	+	3.40611e7i	1.48503	+	0.786694i
$153$	3.04175e7	−	3.04175e7i	0.686600	−	0.686600i
$154$	−306422.	−	138381.i	−0.00676079	−	0.00305320i
$155$	4.99511e7	−	2.06904e7i	1.07742	−	0.446281i
$156$	−5.40683e7	+	4.76537e7i	−1.14027	+	1.00499i
$157$	−1.36738e7	+	3.30114e7i	−0.281994	+	0.680793i	−0.999882	−	0.0153654i	$-0.995109\pi$
$157$	−1.36738e7	+	3.30114e7i	−0.281994	+	0.680793i	0.717888	+	0.696158i	$0.245109\pi$
$158$	898502.	−	2.85252e7i	0.0181226	−	0.575345i
$159$	−3.88972e7			−0.767412
$160$	4.88967e7	−	1.17204e7i	0.943755	−	0.226215i
$161$	8.99196e7			1.69810
$162$	937195.	−	2.97536e7i	0.0173192	−	0.549841i
$163$	−2.55510e7	+	6.16856e7i	−0.462117	+	1.11565i	0.505410	+	0.862879i	$0.331341\pi$
$163$	−2.55510e7	+	6.16856e7i	−0.462117	+	1.11565i	−0.967527	+	0.252769i	$0.918659\pi$
$164$	−1.98799e7	−	2.25558e7i	−0.351933	−	0.399306i
$165$	568429.	−	235451.i	0.00985106	−	0.00408044i
$166$	−9.05633e7	−	4.08988e7i	−1.53665	−	0.693956i
$167$	4.24479e7	−	4.24479e7i	0.705259	−	0.705259i	−0.260275	−	0.965534i	$-0.583813\pi$
$167$	4.24479e7	−	4.24479e7i	0.705259	−	0.705259i	0.965534	+	0.260275i	$0.0838133\pi$
$168$	2.84898e7	+	9.26791e7i	0.463561	+	1.50799i
$169$	−500975.	−	500975.i	−0.00798385	−	0.00798385i
$170$	1.59609e7	+	4.22484e7i	0.249164	+	0.659537i
$171$	−5.62047e7	−	1.35690e8i	−0.859579	−	2.07521i
$172$	3.41912e7	+	9.99115e7i	0.512348	+	1.49715i
$173$	2.08387e7	+	8.63169e6i	0.305992	+	0.126746i	0.530396	−	0.847750i	$-0.322043\pi$
$173$	2.08387e7	+	8.63169e6i	0.305992	+	0.126746i	−0.224404	+	0.974496i	$0.572043\pi$
$174$	8.32585e7	+	8.86741e7i	1.19814	+	1.27607i
$175$		−	4.25523e6i		−	0.0600192i
$176$	137030.	+	501467.i	0.00189462	+	0.00693343i
$177$		−	9.32939e7i		−	1.26458i
$178$	−5.78726e7	+	5.43381e7i	−0.769136	+	0.722162i
$179$	3.38279e7	+	1.40120e7i	0.440848	+	0.182605i	0.592056	−	0.805897i	$-0.298316\pi$
$179$	3.38279e7	+	1.40120e7i	0.440848	+	0.182605i	−0.151208	+	0.988502i	$0.548316\pi$
$180$	−9.11385e7	−	4.46646e7i	−1.16479	−	0.570834i
$181$	−2.98272e7	−	7.20093e7i	−0.373885	−	0.902638i	−0.993084	−	0.117404i	$-0.962543\pi$
$181$	−2.98272e7	−	7.20093e7i	−0.373885	−	0.902638i	0.619199	−	0.785234i	$-0.287457\pi$
$182$	7.80780e7	−	2.94968e7i	0.960017	−	0.362681i
$183$	−7.01856e7	−	7.01856e7i	−0.846582	−	0.846582i
$184$	−8.85984e7	−	1.07144e8i	−1.04849	−	1.26796i
$185$	−7.61300e7	+	7.61300e7i	−0.884005	+	0.884005i
$186$	6.63468e7	−	1.46914e8i	0.756005	−	1.67404i
$187$	−431386.	+	178686.i	−0.00482415	+	0.00199823i
$188$	960252.	−	1.52277e7i	0.0105398	−	0.167140i
$189$	1.88611e7	−	4.55347e7i	0.203212	−	0.490598i
$190$	1.54120e8	+	4.85457e6i	1.63013	+	0.0513467i
$191$	1.22355e8			1.27059			0.635295	−	0.772269i	$-0.280878\pi$
$191$	1.22355e8			1.27059			0.635295	+	0.772269i	$0.280878\pi$
$192$	8.23612e7	−	1.25265e8i	0.839785	−	1.27724i
$193$	1.16910e8			1.17058			0.585290	−	0.810824i	$-0.300981\pi$
$193$	1.16910e8			1.17058			0.585290	+	0.810824i	$0.300981\pi$
$194$	−1.24407e8	−	3.91865e6i	−1.22332	−	0.0385327i
$195$	−5.84489e7	+	1.41108e8i	−0.564489	+	1.36280i
$196$	432526.	−	6.85900e6i	0.00410314	−	0.0650676i
$197$	2.60897e7	−	1.08067e7i	0.243129	−	0.100707i	−0.257792	−	0.966201i	$-0.582995\pi$
$197$	2.60897e7	−	1.08067e7i	0.243129	−	0.100707i	0.500921	+	0.865493i	$0.332995\pi$
$198$	431884.	−	956334.i	0.00395402	−	0.00875551i
$199$	−3.25196e7	+	3.25196e7i	−0.292523	+	0.292523i	−0.838076	−	0.545553i	$-0.816320\pi$
$199$	−3.25196e7	+	3.25196e7i	−0.292523	+	0.292523i	0.545553	+	0.838076i	$0.316320\pi$
$200$	−5.07035e6	+	4.19271e6i	−0.0448160	+	0.0370587i
$201$	−1.70765e8	−	1.70765e8i	−1.48325	−	1.48325i
$202$	9.38029e7	−	3.54374e7i	0.800731	−	0.302505i
$203$	−5.39058e7	−	1.30140e8i	−0.452272	−	1.09188i
$204$	1.20914e8	+	5.92567e7i	0.997172	+	0.488688i
$205$	−5.88666e7	−	2.43833e7i	−0.477233	−	0.197676i
$206$	−1.33138e8	+	1.25007e8i	−1.06113	+	0.996321i
$207$			2.80637e8i			2.19912i
$208$	−1.12078e8	−	6.39710e7i	−0.863571	−	0.492903i
$209$			1.59421e6i			0.0120791i
$210$	1.40648e8	+	1.49797e8i	1.04801	+	1.11618i
$211$	1.95713e8	+	8.10668e7i	1.43427	+	0.594093i	0.958401	−	0.285425i	$-0.0921346\pi$
$211$	1.95713e8	+	8.10668e7i	1.43427	+	0.594093i	0.475866	+	0.879518i	$0.342135\pi$
$212$	−2.25509e7	−	6.58968e7i	−0.162550	−	0.474995i
$213$	5.44997e7	+	1.31574e8i	0.386425	+	0.932914i
$214$	−6.31424e6	−	1.67138e7i	−0.0440426	−	0.116581i
$215$	1.58243e8	+	1.58243e8i	1.08590	+	1.08590i
$216$	−7.28411e7	+	2.23916e7i	−0.491800	+	0.151181i
$217$	−1.32004e8	+	1.32004e8i	−0.876958	+	0.876958i
$218$	−2.59636e8	−	1.17253e8i	−1.69733	−	0.766524i
$219$	8.81786e7	−	3.65248e7i	0.567295	−	0.234981i
$220$	728434.	+	826487.i	0.00461223	+	0.00523307i
$221$	4.43574e7	−	1.07088e8i	0.276435	−	0.667374i
$222$	−1.01061e7	+	3.20842e8i	−0.0619935	+	1.96814i
$223$	3.37401e7			0.203741			0.101871	−	0.994798i	$-0.467517\pi$
$223$	3.37401e7			0.203741			0.101871	+	0.994798i	$0.467517\pi$
$224$	−1.40493e8	+	1.01997e8i	−0.835192	+	0.606342i
$225$	1.32805e7			0.0777274
$226$	4.74281e6	−	1.50572e8i	0.0273310	−	0.867691i
$227$	−1.04051e8	+	2.51202e8i	−0.590413	+	1.42538i	0.292691	+	0.956207i	$0.405449\pi$
$227$	−1.04051e8	+	2.51202e8i	−0.590413	+	1.42538i	−0.883104	+	0.469177i	$0.844551\pi$
$228$	3.44899e8	−	3.03981e8i	1.92717	−	1.69853i
$229$	−9.16409e7	+	3.79589e7i	−0.504273	+	0.208877i	−0.620293	−	0.784370i	$-0.712986\pi$
$229$	−9.16409e7	+	3.79589e7i	−0.504273	+	0.208877i	0.116020	+	0.993247i	$0.462986\pi$
$230$	−2.68524e8	−	1.21267e8i	−1.45524	−	0.657194i
$231$	−1.50217e6	+	1.50217e6i	−0.00801821	+	0.00801821i
$232$	−1.01956e8	+	1.92460e8i	−0.536047	+	1.01189i
$233$	−3.90091e7	−	3.90091e7i	−0.202032	−	0.202032i	0.598838	−	0.800870i	$-0.295629\pi$
$233$	−3.90091e7	−	3.90091e7i	−0.202032	−	0.202032i	−0.800870	+	0.598838i	$0.795629\pi$
$234$	9.20586e7	+	2.43679e8i	0.469687	+	1.24326i
$235$	−1.23740e7	−	2.98735e7i	−0.0621974	−	0.150158i
$236$	1.58052e8	−	5.40877e7i	0.782722	−	0.267859i
$237$	−1.66598e8	−	6.90072e7i	−0.812926	−	0.336725i
$238$	−1.06739e8	−	1.13682e8i	−0.513221	−	0.546604i
$239$		−	4.24581e7i		−	0.201172i	−0.994928	−	0.100586i	$-0.967928\pi$
$239$		−	4.24581e7i		−	0.201172i	0.994928	−	0.100586i	$-0.0320718\pi$
$240$	3.99098e7	−	3.15186e8i	0.186354	−	1.47173i
$241$			3.08991e8i			1.42196i	0.703215	+	0.710978i	$0.251747\pi$
$241$			3.08991e8i			1.42196i	−0.703215	+	0.710978i	$0.748253\pi$
$242$	1.60720e8	−	1.50904e8i	0.728980	−	0.684459i
$243$	−2.80097e8	−	1.16020e8i	−1.25224	−	0.518693i
$244$	7.82128e7	−	1.59594e8i	0.344678	−	0.703318i
$245$	−5.57362e6	−	1.34559e7i	−0.0242134	−	0.0584564i
$246$	−1.77713e8	+	6.71374e7i	−0.761107	+	0.287536i
$247$	−2.79838e8	−	2.79838e8i	−1.18159	−	1.18159i
$248$	2.87355e8	+	2.72259e7i	1.19630	+	0.113345i
$249$	−4.43968e8	+	4.43968e8i	−1.82244	+	1.82244i
$250$	−1.04420e8	+	2.31220e8i	−0.422662	+	0.935912i
$251$	2.41396e8	−	9.99894e7i	0.963544	−	0.399113i	0.155239	−	0.987877i	$-0.450385\pi$
$251$	2.41396e8	−	9.99894e7i	0.963544	−	0.399113i	0.808305	+	0.588764i	$0.200385\pi$
$252$	3.49747e8	+	2.20549e7i	1.37674	+	0.0868168i
$253$	1.16573e6	−	2.81431e6i	0.00452558	−	0.0109257i
$254$	−3.43637e7	−	1.08241e6i	−0.131578	−	0.00414450i
$255$	2.85359e8			1.07771
$256$	2.59963e8	+	6.69074e7i	0.968439	+	0.249249i
$257$	−1.60101e8			−0.588340			−0.294170	−	0.955753i	$-0.595043\pi$
$257$	−1.60101e8			−0.588340			−0.294170	+	0.955753i	$0.595043\pi$
$258$	6.66898e8	+	2.10063e7i	2.41763	+	0.0761519i
$259$	1.42260e8	−	3.43446e8i	0.508785	−	1.22831i
$260$	−2.72941e8	−	1.72116e7i	−0.963080	−	0.0607315i
$261$	4.06164e8	−	1.68238e8i	1.41403	−	0.585711i
$262$	1.87875e8	−	4.16016e8i	0.645378	−	1.42908i
$263$	9.98596e7	−	9.98596e7i	0.338489	−	0.338489i	−0.517309	−	0.855798i	$-0.673066\pi$
$263$	9.98596e7	−	9.98596e7i	0.338489	−	0.338489i	0.855798	+	0.517309i	$0.173066\pi$
$264$	3.27002e6	+	309823.i	0.0109380	+	0.00103633i
$265$	−1.04369e8	−	1.04369e8i	−0.344518	−	0.344518i
$266$	−4.98055e8	+	1.88158e8i	−1.62253	+	0.612968i
$267$	1.91949e8	+	4.63405e8i	0.617158	+	1.48995i
$268$	1.90296e8	−	3.88301e8i	0.603890	−	1.23224i
$269$	1.11942e8	+	4.63679e7i	0.350639	+	0.145239i	0.551049	−	0.834473i	$-0.314228\pi$
$269$	1.11942e8	+	4.63679e7i	0.350639	+	0.145239i	−0.200410	+	0.979712i	$0.564228\pi$
$270$	−1.17733e8	+	1.10542e8i	−0.364019	+	0.341787i
$271$			5.77302e7i			0.176202i	0.996112	+	0.0881010i	$0.0280798\pi$
$271$			5.77302e7i			0.176202i	−0.996112	+	0.0881010i	$0.971920\pi$
$272$	−3.02879e7	+	2.39198e8i	−0.0912594	+	0.720718i
$273$		−	5.27363e8i		−	1.56870i
$274$	3.38446e6	+	3.60460e6i	0.00993945	+	0.0105860i
$275$	−133181.	−	55165.2i	−0.000386168	−	0.000159956i
$276$	−8.31140e8	+	2.84429e8i	−2.37954	+	0.814313i
$277$	2.02875e8	+	4.89784e8i	0.573521	+	1.38460i	0.898539	+	0.438895i	$0.144630\pi$
$277$	2.02875e8	+	4.89784e8i	0.573521	+	1.38460i	−0.325017	+	0.945708i	$0.605370\pi$
$278$	−5.38158e7	−	1.42451e8i	−0.150229	−	0.397656i
$279$	−4.11981e8	−	4.11981e8i	−1.13570	−	1.13570i
$280$	−1.72233e8	+	3.25121e8i	−0.468882	+	0.885100i
$281$	3.61532e8	−	3.61532e8i	0.972019	−	0.972019i	−0.0276001	−	0.999619i	$-0.508786\pi$
$281$	3.61532e8	−	3.61532e8i	0.972019	−	0.972019i	0.999619	+	0.0276001i	$0.00878649\pi$
$282$	−8.78622e7	−	3.96790e7i	−0.233308	−	0.105363i
$283$	−5.28270e7	+	2.18816e7i	−0.138549	+	0.0573888i	−0.450881	−	0.892584i	$-0.648890\pi$
$283$	−5.28270e7	+	2.18816e7i	−0.138549	+	0.0573888i	0.312332	+	0.949973i	$0.398890\pi$
$284$	−1.91306e8	+	1.68610e8i	−0.495582	+	0.436787i
$285$	3.72843e8	−	9.00122e8i	0.954044	−	2.30327i
$286$	89017.8	−	2.82609e6i	0.000225007	−	0.00714340i
$287$	2.20002e8			0.549338
$288$	−3.18328e8	−	4.38474e8i	−0.785239	−	1.08161i
$289$	1.93777e8			0.472237
$290$	−1.45313e7	+	4.61331e8i	−0.0349873	+	1.11076i
$291$	−3.00962e8	+	7.26586e8i	−0.715955	+	1.72847i
$292$	1.13000e8	+	1.28210e8i	0.265605	+	0.301358i
$293$	−1.86436e8	+	7.72245e7i	−0.433006	+	0.179357i	−0.588530	−	0.808475i	$-0.700293\pi$
$293$	−1.86436e8	+	7.72245e7i	−0.433006	+	0.179357i	0.155524	+	0.987832i	$0.450293\pi$
$294$	−3.95758e7	−	1.78726e7i	−0.0908269	−	0.0410178i
$295$	2.50327e8	−	2.50327e8i	0.567715	−	0.567715i
$296$	−5.49406e8	+	1.68889e8i	−1.23132	+	0.378513i
$297$	−1.18063e6	−	1.18063e6i	−0.00261497	−	0.00261497i
$298$	5.88298e7	+	1.55723e8i	0.128778	+	0.340875i
$299$	2.89382e8	+	6.98631e8i	0.626070	+	1.51147i
$300$	1.34599e7	+	3.93317e7i	0.0287818	+	0.0841043i
$301$	−7.13883e8	−	2.95700e8i	−1.50884	−	0.624984i
$302$	−6.89745e7	−	7.34610e7i	−0.144100	−	0.153473i
$303$		−	6.33575e8i		−	1.30842i
$304$	7.14939e8	+	4.08068e8i	1.45952	+	0.833057i
$305$		−	3.76645e8i		−	0.760121i
$306$	3.54799e8	−	3.33130e8i	0.707875	−	0.664643i
$307$	2.53280e8	+	1.04912e8i	0.499593	+	0.206938i	0.618227	−	0.786000i	$-0.287851\pi$
$307$	2.53280e8	+	1.04912e8i	0.499593	+	0.206938i	−0.118634	+	0.992938i	$0.537851\pi$
$308$	−3.41576e6	−	1.67398e6i	−0.00666131	−	0.00326454i
$309$	4.41586e8	+	1.06608e9i	0.851452	+	2.05559i
$310$	5.72222e8	−	2.16177e8i	1.09093	−	0.412140i
$311$	−6.44120e8	−	6.44120e8i	−1.21424	−	1.21424i	−0.969618	−	0.244624i	$-0.921335\pi$
$311$	−6.44120e8	−	6.44120e8i	−1.21424	−	1.21424i	−0.244624	−	0.969618i	$-0.578665\pi$
$312$	−6.28383e8	+	5.19615e8i	−1.17134	+	0.968591i
$313$	9.64215e7	−	9.64215e7i	0.177733	−	0.177733i	−0.612634	−	0.790367i	$-0.709890\pi$
$313$	9.64215e7	−	9.64215e7i	0.177733	−	0.177733i	0.790367	+	0.612634i	$0.209890\pi$
$314$	−1.66383e8	+	3.68426e8i	−0.303287	+	0.671577i
$315$	6.86130e8	−	2.84204e8i	1.23686	−	0.512323i
$316$	2.03207e7	−	3.22246e8i	0.0362271	−	0.574490i
$317$	8.57833e7	−	2.07099e8i	0.151250	−	0.365150i	−0.830035	−	0.557711i	$-0.811680\pi$
$317$	8.57833e7	−	2.07099e8i	0.151250	−	0.365150i	0.981285	+	0.192562i	$0.0616796\pi$
$318$	−4.39854e8	−	1.38548e7i	−0.767031	−	0.0241604i
$319$	−4.77197e6			−0.00823059
$320$	5.57103e8	−	1.15119e8i	0.950409	−	0.196391i
$321$	−1.12890e8			−0.190497
$322$	1.01682e9	+	3.20284e7i	1.69726	+	0.0534613i
$323$	−2.82954e8	+	6.83111e8i	−0.467204	+	1.12793i
$324$	2.11958e7	−	3.36123e8i	0.0346212	−	0.549023i
$325$	3.30610e7	−	1.36943e7i	0.0534226	−	0.0221284i
$326$	−3.10905e8	+	6.88446e8i	−0.497012	+	1.10055i
$327$	−1.27281e9	+	1.27281e9i	−2.01302	+	2.01302i
$328$	−2.16769e8	−	2.62145e8i	−0.339187	−	0.410188i
$329$	7.89456e7	+	7.89456e7i	0.122220	+	0.122220i
$330$	6.51172e6	−	2.46004e6i	0.00997464	−	0.00376828i
$331$	−2.53108e8	−	6.11056e8i	−0.383626	−	0.926154i	−0.991258	−	0.131936i	$-0.957881\pi$
$331$	−2.53108e8	−	6.11056e8i	−0.383626	−	0.926154i	0.607633	−	0.794218i	$-0.292119\pi$
$332$	−1.00953e9	−	4.94745e8i	−1.51404	−	0.741990i
$333$	1.07189e9	+	4.43990e8i	1.59072	+	0.658898i
$334$	4.95125e8	−	4.64886e8i	0.727113	−	0.682706i
$335$		−	9.16398e8i		−	1.33176i
$336$	2.89155e8	+	1.05817e9i	0.415856	+	1.52184i
$337$			3.08652e8i			0.439303i	0.975578	+	0.219652i	$0.0704921\pi$
$337$			3.08652e8i			0.439303i	−0.975578	+	0.219652i	$0.929508\pi$
$338$	−5.48663e6	−	5.84352e6i	−0.00772854	−	0.00823125i
$339$	−8.79400e8	−	3.64259e8i	−1.22599	−	0.507822i
$340$	1.65439e8	+	4.83435e8i	0.228276	+	0.667055i
$341$	2.42016e6	+	5.84279e6i	0.00330525	+	0.00797958i
$342$	−5.87237e8	−	1.55442e9i	−0.793820	−	2.10124i
$343$	−5.09858e8	−	5.09858e8i	−0.682213	−	0.682213i
$344$	3.51051e8	+	1.14199e9i	0.464959	+	1.51254i
$345$	−1.31638e9	+	1.31638e9i	−1.72590	+	1.72590i
$346$	2.32572e8	+	1.05031e8i	0.301850	+	0.136317i
$347$	1.07682e8	−	4.46034e7i	0.138354	−	0.0573080i	−0.312432	−	0.949940i	$-0.601144\pi$
$347$	1.07682e8	−	4.46034e7i	0.138354	−	0.0573080i	0.450786	+	0.892632i	$0.351144\pi$
$348$	9.09911e8	+	1.03239e9i	1.15737	+	1.31316i
$349$	2.73737e8	−	6.60860e8i	0.344703	−	0.832187i	−0.652524	−	0.757768i	$-0.726290\pi$
$349$	2.73737e8	−	6.60860e8i	0.344703	−	0.832187i	0.997227	−	0.0744187i	$-0.0237101\pi$
$350$	1.51567e6	−	4.81186e7i	0.00188958	−	0.0599894i
$351$	4.14481e8			0.511599
$352$	1.37093e6	+	5.71945e6i	0.00167540	+	0.00698964i
$353$	5.91432e8			0.715638			0.357819	−	0.933791i	$-0.383520\pi$
$353$	5.91432e8			0.715638			0.357819	+	0.933791i	$0.383520\pi$
$354$	3.32303e7	−	1.05498e9i	0.0398128	−	1.26396i
$355$	−2.06806e8	+	4.99274e8i	−0.245338	+	0.592298i
$356$	−6.73784e8	+	5.93848e8i	−0.791491	+	0.697590i
$357$	−9.10291e8	+	3.77055e8i	−1.05887	+	0.438597i
$358$	3.77538e8	+	1.70498e8i	0.434881	+	0.196394i
$359$	−6.35514e7	+	6.35514e7i	−0.0724927	+	0.0724927i	−0.742424	−	0.669931i	$-0.766324\pi$
$359$	−6.35514e7	+	6.35514e7i	−0.0724927	+	0.0724927i	0.669931	+	0.742424i	$0.266324\pi$
$360$	−1.01469e9	−	5.37534e8i	−1.14624	−	0.607222i
$361$	1.15301e9	+	1.15301e9i	1.28990	+	1.28990i
$362$	−3.11641e8	−	8.24913e8i	−0.345282	−	0.913962i
$363$	−5.33067e8	−	1.28694e9i	−0.584936	−	1.41216i
$364$	8.93420e8	−	3.05742e8i	0.970959	−	0.332277i
$365$	3.34605e8	+	1.38598e8i	0.360170	+	0.149187i
$366$	−7.68667e8	−	8.18665e8i	−0.819510	−	0.872816i
$367$			4.50169e8i			0.475383i	0.971341	+	0.237692i	$0.0763908\pi$
$367$			4.50169e8i			0.475383i	−0.971341	+	0.237692i	$0.923609\pi$
$368$	−9.63716e8	−	1.24316e9i	−1.00805	−	1.30034i
$369$			6.86619e8i			0.711416i
$370$	−8.88002e8	+	8.33768e8i	−0.911397	+	0.855735i
$371$	4.70843e8	+	1.95029e8i	0.478704	+	0.198286i
$372$	8.02586e8	−	1.63768e9i	0.808334	−	1.64941i
$373$	1.51770e8	+	3.66406e8i	0.151428	+	0.365580i	0.981331	−	0.192329i	$-0.0616040\pi$
$373$	1.51770e8	+	3.66406e8i	0.151428	+	0.365580i	−0.829902	+	0.557908i	$0.811604\pi$
$374$	−4.94181e6	+	1.86695e6i	−0.00488467	+	0.00184536i
$375$	1.13351e9	+	1.13351e9i	1.10998	+	1.10998i
$376$	1.62825e7	−	1.71854e8i	0.0157966	−	0.166725i
$377$	8.37643e8	−	8.37643e8i	0.805126	−	0.805126i
$378$	2.29502e8	−	5.08193e8i	0.218557	−	0.483957i
$379$	−8.24078e8	+	3.41344e8i	−0.777555	+	0.322074i	−0.735928	−	0.677059i	$-0.763254\pi$
$379$	−8.24078e8	+	3.41344e8i	−0.777555	+	0.322074i	−0.0416266	+	0.999133i	$0.513254\pi$
$380$	1.74108e9	+	1.09792e8i	1.62771	+	0.102643i
$381$	−8.31315e7	+	2.00697e8i	−0.0770067	+	0.185911i
$382$	1.38360e9	+	4.35816e7i	1.26996	+	0.0400019i
$383$	1.26685e9			1.15220			0.576101	−	0.817378i	$-0.304573\pi$
$383$	1.26685e9			1.15220			0.576101	+	0.817378i	$0.304573\pi$
$384$	9.75966e8	−	1.38717e9i	0.879580	−	1.25017i
$385$	−8.06127e6			−0.00719931
$386$	1.32203e9	+	4.16421e7i	1.17000	+	0.0368533i
$387$	9.22871e8	−	2.22801e9i	0.809381	−	1.95402i
$388$	−1.40541e9	−	8.86249e7i	−1.22150	−	0.0770273i
$389$	5.44067e8	−	2.25360e8i	0.468629	−	0.194112i	−0.135857	−	0.990728i	$-0.543379\pi$
$389$	5.44067e8	−	2.25360e8i	0.468629	−	0.194112i	0.604486	+	0.796616i	$0.293379\pi$
$390$	−7.11208e8	+	1.57485e9i	−0.607114	+	1.34435i
$391$	9.99015e8	−	9.99015e8i	0.845188	−	0.845188i
$392$	7.33415e6	−	7.74082e7i	0.00614963	−	0.0649061i
$393$	−2.03944e9	−	2.03944e9i	−1.69487	−	1.69487i
$394$	2.98874e8	−	1.12910e8i	0.246179	−	0.0930031i
$395$	−2.61857e8	−	6.32178e8i	−0.213783	−	0.516119i
$396$	5.22443e6	−	1.06605e7i	0.00422771	−	0.00862668i
$397$	−9.91343e8	−	4.10628e8i	−0.795165	−	0.329368i	−0.0521469	−	0.998639i	$-0.516606\pi$
$397$	−9.91343e8	−	4.10628e8i	−0.795165	−	0.329368i	−0.743018	+	0.669271i	$0.766606\pi$
$398$	−3.79318e8	+	3.56152e8i	−0.301587	+	0.283168i
$399$			3.36402e9i			2.65127i
$400$	−5.88294e7	+	4.56056e7i	−0.0459605	+	0.0356294i
$401$			1.22788e9i			0.950931i	0.879734	+	0.475466i	$0.157720\pi$
$401$			1.22788e9i			0.950931i	−0.879734	+	0.475466i	$0.842280\pi$
$402$	−1.87021e9	−	1.99186e9i	−1.43582	−	1.52921i
$403$	−1.45043e9	−	6.00787e8i	−1.10390	−	0.457249i
$404$	1.07336e9	−	3.67319e8i	0.809858	−	0.277146i
$405$	−2.73133e8	−	6.59402e8i	−0.204306	−	0.493239i
$406$	−5.63218e8	−	1.49084e9i	−0.417672	−	1.10558i
$407$	−8.90493e6	−	8.90493e6i	−0.00654712	−	0.00654712i
$408$	1.34620e9	+	7.13149e8i	0.981292	+	0.519840i
$409$	2.25817e8	−	2.25817e8i	0.163202	−	0.163202i	−0.620782	−	0.783983i	$-0.713185\pi$
$409$	2.25817e8	−	2.25817e8i	0.163202	−	0.163202i	0.783983	+	0.620782i	$0.213185\pi$
$410$	−6.56984e8	−	2.96697e8i	−0.470773	−	0.212603i
$411$	2.88633e7	−	1.19556e7i	0.0205069	−	0.00849422i
$412$	−1.55007e9	+	1.36617e9i	−1.09197	+	0.962419i
$413$	−4.67773e8	+	1.12930e9i	−0.326746	+	0.788834i
$414$	−9.99596e7	+	3.17347e9i	−0.0692346	+	2.19802i
$415$	−2.38252e9			−1.63632
$416$	−1.24460e9	−	7.63312e8i	−0.847625	−	0.519847i
$417$	−9.62156e8			−0.649784
$418$	−567840.	+	1.80275e7i	−0.000380284	+	0.0120731i
$419$	−7.05628e8	+	1.70354e9i	−0.468627	+	1.13136i	0.496136	+	0.868245i	$0.334752\pi$
$419$	−7.05628e8	+	1.70354e9i	−0.468627	+	1.13136i	−0.964763	+	0.263120i	$0.915248\pi$
$420$	1.53711e9	+	1.74401e9i	1.01235	+	1.14862i
$421$	1.40304e9	−	5.81158e8i	0.916395	−	0.379583i	0.125894	−	0.992044i	$-0.459820\pi$
$421$	1.40304e9	−	5.81158e8i	0.916395	−	0.379583i	0.790501	+	0.612461i	$0.209820\pi$
$422$	2.18426e9	+	9.86422e8i	1.41485	+	0.638953i
$423$	−2.46387e8	+	2.46387e8i	−0.158280	+	0.158280i
$424$	−2.31536e8	−	7.53200e8i	−0.147516	−	0.479877i
$425$	−4.72760e7	−	4.72760e7i	−0.0298731	−	0.0298731i
$426$	5.69423e8	+	1.50726e9i	0.356863	+	0.944617i
$427$	4.97674e8	+	1.20149e9i	0.309348	+	0.746832i
$428$	−6.54488e7	−	1.91250e8i	−0.0403505	−	0.117910i
$429$	−1.65055e7	−	6.83678e6i	−0.0100932	−	0.00418072i
$430$	1.73306e9	+	1.84579e9i	1.05117	+	1.11955i
$431$			1.23014e8i			0.0740087i	0.999315	+	0.0370044i	$0.0117815\pi$
$431$			1.23014e8i			0.0740087i	−0.999315	+	0.0370044i	$0.988218\pi$
$432$	−8.31670e8	+	2.27261e8i	−0.496316	+	0.135623i
$433$		−	6.94424e8i		−	0.411071i	−0.978650	−	0.205536i	$-0.934106\pi$
$433$		−	6.94424e8i		−	0.411071i	0.978650	−	0.205536i	$-0.0658936\pi$
$434$	−1.53974e9	+	1.44570e9i	−0.904133	+	0.848914i
$435$	2.69435e9	+	1.11604e9i	1.56943	+	0.650079i
$436$	−2.89423e9	−	1.41839e9i	−1.67236	−	0.819581i
$437$	−1.84595e9	−	4.45653e9i	−1.05812	−	2.55453i
$438$	1.01014e9	−	3.81617e8i	0.574411	−	0.217005i
$439$	7.61337e8	+	7.61337e8i	0.429488	+	0.429488i	0.888454	−	0.458966i	$-0.151780\pi$
$439$	7.61337e8	+	7.61337e8i	0.429488	+	0.429488i	−0.458966	+	0.888454i	$0.651780\pi$
$440$	7.94282e6	+	9.60546e6i	0.00444519	+	0.00537569i
$441$	−1.10980e8	+	1.10980e8i	−0.0616184	+	0.0616184i
$442$	5.39742e8	−	1.19517e9i	0.297309	−	0.658340i
$443$	2.87420e8	−	1.19053e8i	0.157074	−	0.0650621i	−0.302761	−	0.953066i	$-0.597909\pi$
$443$	2.87420e8	−	1.19053e8i	0.157074	−	0.0650621i	0.459835	+	0.888004i	$0.347909\pi$
$444$	−2.28561e8	+	3.62451e9i	−0.123926	+	1.96521i
$445$	−7.28374e8	+	1.75845e9i	−0.391827	+	0.945955i
$446$	3.81536e8	+	1.20178e7i	0.203640	+	0.00641438i
$447$	1.05180e9			0.557002
$448$	−1.62504e9	+	1.10335e9i	−0.853868	+	0.579747i
$449$	3.11611e9			1.62462			0.812309	−	0.583228i	$-0.198210\pi$
$449$	3.11611e9			1.62462			0.812309	+	0.583228i	$0.198210\pi$
$450$	1.50177e8	+	4.73035e6i	0.0776889	+	0.00244709i
$451$	2.85212e6	−	6.88563e6i	0.00146403	−	0.00353448i
$452$	1.07264e8	−	1.70100e9i	0.0546349	−	0.866401i
$453$	−5.88227e8	+	2.43652e8i	−0.297304	+	0.123147i
$454$	−1.26610e9	+	2.80355e9i	−0.634996	+	1.40609i
$455$	1.41503e9	−	1.41503e9i	0.704246	−	0.704246i
$456$	4.00842e9	−	3.31459e9i	1.97969	−	1.63702i
$457$	−1.52962e9	−	1.52962e9i	−0.749681	−	0.749681i	0.224738	−	0.974419i	$-0.427847\pi$
$457$	−1.52962e9	−	1.52962e9i	−0.749681	−	0.749681i	−0.974419	+	0.224738i	$0.927847\pi$
$458$	−1.04981e9	+	3.96602e8i	−0.510599	+	0.192897i
$459$	−2.96346e8	−	7.15443e8i	−0.143039	−	0.345327i
$460$	−2.99330e9	−	1.46694e9i	−1.43383	−	0.702683i
$461$	−1.45783e9	−	6.03855e8i	−0.693035	−	0.287064i	0.00822930	−	0.999966i	$-0.497381\pi$
$461$	−1.45783e9	−	6.03855e8i	−0.693035	−	0.287064i	−0.701264	+	0.712902i	$0.747381\pi$
$462$	−1.75218e7	+	1.64516e7i	−0.00826667	+	0.00776180i
$463$		−	9.88040e8i		−	0.462638i	−0.972878	−	0.231319i	$-0.925696\pi$
$463$		−	9.88040e8i		−	0.462638i	0.972878	−	0.231319i	$-0.0743041\pi$
$464$	−1.22148e9	+	2.14004e9i	−0.567639	+	0.994509i
$465$		−	3.86497e9i		−	1.78263i
$466$	−4.27224e8	−	4.55014e8i	−0.195571	−	0.208293i
$467$	1.40598e9	+	5.82376e8i	0.638807	+	0.264603i	0.678490	−	0.734610i	$-0.262635\pi$
$467$	1.40598e9	+	5.82376e8i	0.638807	+	0.264603i	−0.0396827	+	0.999212i	$0.512635\pi$
$468$	9.54212e8	+	2.78834e9i	0.430313	+	1.25743i
$469$	1.21087e9	+	2.92329e9i	0.541991	+	1.30848i
$470$	−1.29286e8	−	3.42220e8i	−0.0574392	−	0.152042i
$471$	1.80613e9	+	1.80613e9i	0.796482	+	0.796482i
$472$	1.80653e9	−	5.55333e8i	0.790767	−	0.243084i
$473$	−1.85097e7	+	1.85097e7i	−0.00804239	+	0.00804239i
$474$	−1.85933e9	−	8.39681e8i	−0.801922	−	0.362151i
$475$	−2.10895e8	+	8.73554e7i	−0.0902896	+	0.0373992i
$476$	−1.16652e9	−	1.32355e9i	−0.495758	−	0.562491i
$477$	−6.08681e8	+	1.46949e9i	−0.256789	+	0.619942i
$478$	1.51231e7	−	4.80121e8i	0.00633350	−	0.201073i
$479$	−1.71809e9			−0.714283			−0.357142	−	0.934050i	$-0.616249\pi$
$479$	−1.71809e9			−0.714283			−0.357142	+	0.934050i	$0.616249\pi$
$480$	5.63569e8	−	3.54994e9i	0.232596	−	1.46513i
$481$	3.12623e9			1.28090
$482$	−1.10059e8	+	3.49410e9i	−0.0447673	+	1.42125i
$483$	2.45986e9	−	5.93862e9i	0.993333	−	2.39812i
$484$	1.87119e9	−	1.64919e9i	0.750168	−	0.661169i
$485$	−2.75712e9	+	1.14204e9i	−1.09739	+	0.454553i
$486$	−3.12604e9	−	1.41173e9i	−1.23529	−	0.557860i
$487$	8.69077e8	−	8.69077e8i	0.340963	−	0.340963i	−0.515766	−	0.856729i	$-0.672493\pi$
$487$	8.69077e8	−	8.69077e8i	0.340963	−	0.340963i	0.856729	+	0.515766i	$0.172493\pi$
$488$	9.41284e8	−	1.77684e9i	0.366650	−	0.692118i
$489$	3.37497e9	+	3.37497e9i	1.30523	+	1.30523i
$490$	−5.82342e7	−	1.54146e8i	−0.0223610	−	0.0591897i
$491$	−1.16210e9	−	2.80556e9i	−0.443056	−	1.06963i	−0.974871	−	0.222771i	$-0.928490\pi$
$491$	−1.16210e9	−	2.80556e9i	−0.443056	−	1.06963i	0.531815	−	0.846861i	$-0.321510\pi$
$492$	−2.03351e9	+	6.95897e8i	−0.769782	+	0.263431i
$493$	−2.04477e9	−	8.46971e8i	−0.768564	−	0.318349i
$494$	−3.06476e9	−	3.26411e9i	−1.14380	−	1.21820i
$495$		−	2.51590e7i		−	0.00932341i
$496$	3.23974e9	+	4.10226e8i	1.19213	+	0.150951i
$497$		−	1.86594e9i		−	0.681788i
$498$	−5.17857e9	+	4.86230e9i	−1.87892	+	1.76416i
$499$	−4.35130e7	−	1.80237e7i	−0.0156772	−	0.00649369i	0.374831	−	0.927093i	$-0.377701\pi$
$499$	−4.35130e7	−	1.80237e7i	−0.0156772	−	0.00649369i	−0.390508	+	0.920599i	$0.627701\pi$
$500$	−1.26315e9	+	2.57746e9i	−0.451918	+	0.922142i
$501$	−1.64220e9	−	3.96463e9i	−0.583438	−	1.40854i
$502$	2.76534e9	−	1.04471e9i	0.975632	−	0.368580i
$503$	1.46618e9	+	1.46618e9i	0.513687	+	0.513687i	0.915654	−	0.401967i	$-0.131673\pi$
$503$	1.46618e9	+	1.46618e9i	0.513687	+	0.513687i	−0.401967	+	0.915654i	$0.631673\pi$
$504$	3.94712e9	+	3.73975e8i	1.37332	+	0.130118i
$505$	1.70001e9	−	1.70001e9i	0.587398	−	0.587398i
$506$	1.41846e7	−	3.14093e7i	0.00486731	−	0.0107778i
$507$	−4.67910e7	+	1.93815e7i	−0.0159454	+	0.00660478i
$508$	−3.88203e8	−	2.44799e7i	−0.131382	−	0.00828490i
$509$	−1.05332e9	+	2.54293e9i	−0.354036	+	0.854717i	0.642078	+	0.766639i	$0.278073\pi$
$509$	−1.05332e9	+	2.54293e9i	−0.354036	+	0.854717i	−0.996114	+	0.0880781i	$0.971927\pi$
$510$	3.22687e9	+	1.01642e8i	1.07717	+	0.0339294i
$511$	−1.25052e9			−0.414588
$512$	2.91586e9	+	8.49192e8i	0.960112	+	0.279615i
$513$	−2.64395e9			−0.864656
$514$	−1.81044e9	−	5.70262e7i	−0.588048	−	0.0185227i
$515$	−1.67565e9	+	4.04539e9i	−0.540579	+	1.30507i
$516$	7.53386e9	+	4.75083e8i	2.41404	+	0.152228i
$517$	3.49430e6	−	1.44739e6i	0.00111210	−	0.000460647i
$518$	1.73102e9	−	3.83305e9i	0.547203	−	1.21169i
$519$	1.14014e9	−	1.14014e9i	0.357990	−	0.357990i
$520$	−3.08032e9	−	2.91849e8i	−0.960691	−	0.0910221i
$521$	9.82287e8	+	9.82287e8i	0.304303	+	0.304303i	0.842695	−	0.538392i	$-0.180968\pi$
$521$	9.82287e8	+	9.82287e8i	0.304303	+	0.304303i	−0.538392	+	0.842695i	$0.680968\pi$
$522$	4.65286e9	−	1.75779e9i	1.43177	−	0.540903i
$523$	2.74961e8	+	6.63814e8i	0.0840455	+	0.202904i	0.960315	−	0.278917i	$-0.0899755\pi$
$523$	2.74961e8	+	6.63814e8i	0.0840455	+	0.202904i	−0.876270	+	0.481821i	$0.839976\pi$
$524$	2.27269e9	−	4.63744e9i	0.690049	−	1.40805i
$525$	−2.81031e8	−	1.16407e8i	−0.0847612	−	0.0351092i
$526$	1.16479e9	−	1.09365e9i	0.348978	−	0.327665i
$527$			2.93316e9i			0.872968i
$528$	3.68674e7	+	4.66825e6i	0.0108999	+	0.00138018i
$529$			5.81224e9i			1.70706i
$530$	−1.14304e9	−	1.21739e9i	−0.333501	−	0.355194i
$531$	−3.52453e9	−	1.45991e9i	−1.02157	−	0.423150i
$532$	−5.69908e9	+	1.95031e9i	−1.64102	+	0.561582i
$533$	7.08017e8	+	1.70930e9i	0.202534	+	0.488961i
$534$	2.00552e9	+	5.30861e9i	0.569944	+	1.50864i
$535$	−3.02908e8	−	3.02908e8i	−0.0855210	−	0.0855210i
$536$	2.29020e9	−	4.32316e9i	0.642386	−	1.21262i
$537$	1.85080e9	−	1.85080e9i	0.515763	−	0.515763i
$538$	1.24934e9	+	5.64205e8i	0.345893	+	0.156207i
$539$	1.57394e6	−	651948.i	0.000432940	−	0.000179330i
$540$	−1.37071e9	+	1.20809e9i	−0.374599	+	0.330157i
$541$	−2.24078e9	+	5.40973e9i	−0.608428	+	1.46888i	0.256280	+	0.966602i	$0.417503\pi$
$541$	−2.24078e9	+	5.40973e9i	−0.608428	+	1.46888i	−0.864709	+	0.502274i	$0.832497\pi$
$542$	−2.05629e7	+	6.52819e8i	−0.00554736	+	0.176115i
$543$	−5.57172e9			−1.49345
$544$	−4.27698e8	+	2.69408e9i	−0.113905	+	0.717488i
$545$	−6.83044e9			−1.80743
$546$	1.87841e8	−	5.96348e9i	0.0493874	−	1.56793i
$547$	6.34071e8	−	1.53078e9i	0.165646	−	0.399906i	−0.819159	−	0.573566i	$-0.805560\pi$
$547$	6.34071e8	−	1.53078e9i	0.165646	−	0.399906i	0.984806	+	0.173660i	$0.0555595\pi$
$548$	3.69879e7	+	4.19667e7i	0.00960124	+	0.0108936i
$549$	−3.74982e9	+	1.55323e9i	−0.967180	+	0.400619i
$550$	−1.48637e6	−	671251.i	−0.000380941	−	0.000172034i
$551$	−5.34328e9	+	5.34328e9i	−1.36075	+	1.36075i
$552$	−9.49992e9	+	2.92030e9i	−2.40399	+	0.738995i
$553$	1.67064e9	+	1.67064e9i	0.420092	+	0.420092i
$554$	2.11968e9	+	5.61079e9i	0.529646	+	1.40197i
$555$	2.94528e9	+	7.11053e9i	0.731309	+	1.76554i
$556$	−5.57815e8	−	1.63001e9i	−0.137635	−	0.402188i
$557$	5.74995e9	+	2.38171e9i	1.40984	+	0.583976i	0.952287	−	0.305204i	$-0.0987246\pi$
$557$	5.74995e9	+	2.38171e9i	1.40984	+	0.583976i	0.457557	+	0.889180i	$0.348725\pi$
$558$	−4.51198e9	−	4.80547e9i	−1.09938	−	1.17089i
$559$		−	6.49815e9i		−	1.57343i
$560$	−2.06343e9	+	3.61516e9i	−0.496515	+	0.869899i
$561$			3.33785e7i			0.00798173i
$562$	4.21701e9	−	3.95947e9i	1.00214	−	0.940935i
$563$	6.72630e8	+	2.78612e8i	0.158854	+	0.0657993i	0.460693	−	0.887559i	$-0.347601\pi$
$563$	6.72630e8	+	2.78612e8i	0.158854	+	0.0657993i	−0.301840	+	0.953359i	$0.597601\pi$
$564$	−9.79422e8	−	4.79989e8i	−0.229876	−	0.112656i
$565$	−1.38223e9	−	3.33699e9i	−0.322411	−	0.778370i
$566$	−6.05167e8	+	2.28623e8i	−0.140287	+	0.0529985i
$567$	1.74258e9	+	1.74258e9i	0.401469	+	0.401469i
$568$	−2.22337e9	+	1.83852e9i	−0.509088	+	0.420968i
$569$	5.42420e9	−	5.42420e9i	1.23436	−	1.23436i	0.272090	−	0.962272i	$-0.412285\pi$
$569$	5.42420e9	−	5.42420e9i	1.23436	−	1.23436i	0.962272	−	0.272090i	$-0.0877149\pi$
$570$	4.53676e9	−	1.00459e10i	1.02609	−	2.27209i
$571$	−4.74912e9	+	1.96715e9i	−1.06755	+	0.442193i	−0.846125	−	0.532985i	$-0.821070\pi$
$571$	−4.74912e9	+	1.96715e9i	−1.06755	+	0.442193i	−0.221423	+	0.975178i	$0.571070\pi$
$572$	2.01324e6	−	3.19260e7i	0.000449790	−	0.00713277i
$573$	3.34717e9	−	8.08079e9i	0.743253	−	1.79437i
$574$	2.48780e9	+	7.83622e7i	0.549066	+	0.0172948i
$575$	4.36176e8			0.0956806
$576$	−3.44351e9	−	5.07170e9i	−0.750797	−	1.10580i
$577$	−2.03138e8			−0.0440226			−0.0220113	−	0.999758i	$-0.507007\pi$
$577$	−2.03138e8			−0.0440226			−0.0220113	+	0.999758i	$0.507007\pi$
$578$	2.19125e9	+	6.90212e7i	0.472003	+	0.0148674i
$579$	3.19821e9	−	7.72117e9i	0.684751	−	1.65313i
$580$	−3.28642e8	+	5.21160e9i	−0.0699399	+	1.10911i
$581$	7.60019e9	−	3.14810e9i	1.60771	−	0.665936i
$582$	−3.66211e9	+	8.10911e9i	−0.770017	+	1.70507i
$583$	1.22081e7	−	1.22081e7i	0.00255157	−	0.00255157i
$584$	1.23214e9	+	1.49006e9i	0.255986	+	0.309571i
$585$	4.41625e9	+	4.41625e9i	0.912028	+	0.912028i
$586$	−2.13575e9	+	8.06856e8i	−0.438438	+	0.165636i
$587$	2.02034e9	+	4.87753e9i	0.412279	+	0.995329i	0.984525	+	0.175247i	$0.0560723\pi$
$587$	2.02034e9	+	4.87753e9i	0.412279	+	0.995329i	−0.572246	+	0.820082i	$0.693928\pi$
$588$	−4.41161e8	−	2.16202e8i	−0.0894905	−	0.0438570i
$589$	9.25220e9	+	3.83239e9i	1.86570	+	0.772798i
$590$	2.91989e9	−	2.74156e9i	0.585307	−	0.549561i
$591$		−	2.01869e9i		−	0.402266i
$592$	−6.27289e9	+	1.71412e9i	−1.24263	+	0.339559i
$593$			3.05583e9i			0.601780i	0.953659	+	0.300890i	$0.0972837\pi$
$593$			3.05583e9i			0.601780i	−0.953659	+	0.300890i	$0.902716\pi$
$594$	−1.29302e7	−	1.37712e7i	−0.00253135	−	0.00269600i
$595$	−3.45421e9	−	1.43078e9i	−0.672264	−	0.278461i
$596$	6.09787e8	+	1.78188e9i	0.117982	+	0.344760i
$597$	1.25810e9	+	3.03733e9i	0.241995	+	0.584227i
$598$	3.02352e9	+	8.00326e9i	0.578174	+	1.53043i
$599$	1.62032e9	+	1.62032e9i	0.308041	+	0.308041i	0.844149	−	0.536108i	$-0.180106\pi$
$599$	1.62032e9	+	1.62032e9i	0.308041	+	0.308041i	−0.536108	+	0.844149i	$0.680106\pi$
$600$	1.38196e8	+	4.49561e8i	0.0261197	+	0.0849688i
$601$	−5.96416e9	+	5.96416e9i	−1.12070	+	1.12070i	−0.129062	+	0.991637i	$0.541197\pi$
$601$	−5.96416e9	+	5.96416e9i	−1.12070	+	1.12070i	−0.991637	+	0.129062i	$0.958803\pi$
$602$	−7.96734e9	−	3.59808e9i	−1.48842	−	0.672177i
$603$	−9.12352e9	+	3.77908e9i	−1.69454	+	0.701901i
$604$	−7.53805e8	−	8.55272e8i	−0.139197	−	0.157934i
$605$	2.02279e9	−	4.88345e9i	0.371370	−	0.896568i
$606$	2.25672e8	−	7.16452e9i	0.0411930	−	1.30778i
$607$	4.24578e9			0.770544			0.385272	−	0.922803i	$-0.374108\pi$
$607$	4.24578e9			0.770544			0.385272	+	0.922803i	$0.374108\pi$
$608$	7.93925e9	+	4.86912e9i	1.43257	+	0.878594i
$609$	−1.00696e10			−1.80656
$610$	1.34157e8	−	4.25914e9i	0.0239309	−	0.759744i
$611$	−3.59303e8	+	8.67434e8i	−0.0637260	+	0.153848i
$612$	4.13075e9	−	3.64069e9i	0.728449	−	0.642028i
$613$	−4.54963e9	+	1.88452e9i	−0.797745	+	0.330437i	−0.744053	−	0.668121i	$-0.767099\pi$
$613$	−4.54963e9	+	1.88452e9i	−0.797745	+	0.330437i	−0.0536920	+	0.998558i	$0.517099\pi$
$614$	2.82675e9	+	1.27657e9i	0.492830	+	0.222564i
$615$	−3.22073e9	+	3.22073e9i	−0.558330	+	0.558330i
$616$	−3.80295e7	−	2.01461e7i	−0.00655523	−	0.00347264i
$617$	−6.02040e9	−	6.02040e9i	−1.03188	−	1.03188i	−0.999475	−	0.0324005i	$-0.989685\pi$
$617$	−6.02040e9	−	6.02040e9i	−1.03188	−	1.03188i	−0.0324005	−	0.999475i	$-0.510315\pi$
$618$	4.61377e9	+	1.22127e10i	0.786314	+	2.08137i
$619$	−4.32867e9	−	1.04503e10i	−0.733562	−	1.77098i	−0.630342	−	0.776318i	$-0.717085\pi$
$619$	−4.32867e9	−	1.04503e10i	−0.733562	−	1.77098i	−0.103221	−	0.994658i	$-0.532915\pi$
$620$	6.54774e9	−	2.24074e9i	1.10337	−	0.377590i
$621$	4.66746e9	+	1.93333e9i	0.782096	+	0.323955i
$622$	−7.05434e9	−	7.51320e9i	−1.17541	−	1.25187i
$623$		−	6.57186e9i		−	1.08888i
$624$	−7.29090e9	+	5.65203e9i	−1.20126	+	0.931233i
$625$			5.72793e9i			0.938465i
$626$	1.12469e9	−	1.05600e9i	0.183241	−	0.172050i
$627$	1.05287e8	+	4.36115e7i	0.0170585	+	0.00706585i
$628$	−2.01270e9	+	4.10693e9i	−0.324280	+	0.661696i
$629$	−2.23520e9	−	5.39624e9i	−0.358128	−	0.864598i
$630$	7.86005e9	−	2.96942e9i	1.25237	−	0.473129i
$631$	−9.33920e8	−	9.33920e8i	−0.147981	−	0.147981i	0.629234	−	0.777216i	$-0.283369\pi$
$631$	−9.33920e8	−	9.33920e8i	−0.147981	−	0.147981i	−0.777216	+	0.629234i	$0.783369\pi$
$632$	3.44569e8	−	3.63675e9i	0.0542958	−	0.573064i
$633$	1.07079e10	−	1.07079e10i	1.67800	−	1.67800i
$634$	1.04381e9	−	2.31134e9i	0.162671	−	0.360207i
$635$	−7.61571e8	+	3.15453e8i	−0.118033	+	0.0488908i
$636$	−4.96897e9	−	3.13342e8i	−0.765891	−	0.0482968i
$637$	−1.61841e8	+	3.90719e8i	−0.0248085	+	0.0598930i
$638$	−5.39620e7	−	1.69972e6i	−0.00822651	−	0.000259123i
$639$	5.82353e9			0.882945
$640$	6.34078e9	−	1.10334e9i	0.956121	−	0.166372i
$641$	−1.24301e10			−1.86411			−0.932055	−	0.362316i	$-0.881986\pi$
$641$	−1.24301e10			−1.86411			−0.932055	+	0.362316i	$0.881986\pi$
$642$	−1.27657e9	−	4.02103e7i	−0.190403	−	0.00599742i
$643$	2.76542e9	−	6.67632e9i	0.410226	−	0.990373i	−0.574851	−	0.818258i	$-0.694940\pi$
$643$	2.76542e9	−	6.67632e9i	0.410226	−	0.990373i	0.985077	−	0.172115i	$-0.0550601\pi$
$644$	1.14869e10	+	7.24360e8i	1.69474	+	0.106870i
$645$	1.47799e10	−	6.12202e9i	2.16876	−	0.898329i
$646$	−3.44299e9	+	7.62390e9i	−0.502483	+	1.11266i
$647$	2.35367e9	−	2.35367e9i	0.341650	−	0.341650i	−0.515338	−	0.856987i	$-0.672333\pi$
$647$	2.35367e9	−	2.35367e9i	0.341650	−	0.341650i	0.856987	+	0.515338i	$0.172333\pi$
$648$	3.59407e8	−	3.79336e9i	0.0518889	−	0.547661i
$649$	2.92808e7	+	2.92808e7i	0.00420462	+	0.00420462i
$650$	3.78735e8	−	1.43081e8i	0.0540927	−	0.0204355i
$651$	5.10691e9	+	1.23292e10i	0.725479	+	1.75146i
$652$	−3.76097e9	+	7.67428e9i	−0.531414	+	1.08435i
$653$	−8.96659e9	−	3.71408e9i	−1.26018	−	0.521982i	−0.350212	−	0.936670i	$-0.613891\pi$
$653$	−8.96659e9	−	3.71408e9i	−1.26018	−	0.521982i	−0.909963	+	0.414689i	$0.863891\pi$
$654$	−1.48465e10	+	1.39397e10i	−2.07540	+	1.94864i
$655$		−	1.09445e10i		−	1.52177i
$656$	−2.35788e9	−	3.04157e9i	−0.326105	−	0.420663i
$657$		−	3.90283e9i		−	0.536909i
$658$	8.64606e8	+	9.20845e8i	0.118312	+	0.126007i
$659$	−4.53207e9	−	1.87725e9i	−0.616876	−	0.255518i	0.0522894	−	0.998632i	$-0.483348\pi$
$659$	−4.53207e9	−	1.87725e9i	−0.616876	−	0.255518i	−0.669165	+	0.743114i	$0.733348\pi$
$660$	7.45115e7	−	2.54989e7i	0.0100883	−	0.00345238i
$661$	2.53378e9	+	6.11709e9i	0.341243	+	0.823834i	0.997591	+	0.0693754i	$0.0221006\pi$
$661$	2.53378e9	+	6.11709e9i	0.341243	+	0.823834i	−0.656347	+	0.754459i	$0.727899\pi$
$662$	−2.64452e9	−	7.00004e9i	−0.354277	−	0.937773i
$663$	−5.85906e9	−	5.85906e9i	−0.780783	−	0.780783i
$664$	−1.12397e10	−	5.95421e9i	−1.48993	−	0.789289i
$665$	−9.02637e9	+	9.02637e9i	−1.19025	+	1.19025i
$666$	1.19628e10	+	5.40247e9i	1.56919	+	0.708652i
$667$	1.33398e10	−	5.52553e9i	1.74064	−	0.720997i
$668$	5.76451e9	−	5.08062e9i	0.748246	−	0.659476i
$669$	9.23000e8	−	2.22832e9i	0.119182	−	0.287731i
$670$	3.26411e8	−	1.03627e10i	0.0419279	−	1.33110i
$671$	4.40562e7			0.00562961
$672$	2.89288e9	+	1.20689e10i	0.367737	+	1.53418i
$673$	8.79411e9			1.11209			0.556044	−	0.831153i	$-0.312319\pi$
$673$	8.79411e9			1.11209			0.556044	+	0.831153i	$0.312319\pi$
$674$	−1.09938e8	+	3.49027e9i	−0.0138306	+	0.439085i
$675$	9.14900e7	−	2.20876e8i	0.0114501	−	0.0276431i
$676$	−5.99620e7	−	6.80333e7i	−0.00746557	−	0.00847049i
$677$	−1.16045e8	+	4.80673e7i	−0.0143736	+	0.00595373i	−0.389859	−	0.920875i	$-0.627476\pi$
$677$	−1.16045e8	+	4.80673e7i	−0.0143736	+	0.00595373i	0.375485	+	0.926828i	$0.377476\pi$
$678$	−9.81459e9	−	4.43231e9i	−1.20940	−	0.546168i
$679$	7.28616e9	−	7.28616e9i	0.893212	−	0.893212i
$680$	1.69860e9	+	5.52565e9i	0.207162	+	0.673911i
$681$	1.37438e10	+	1.37438e10i	1.66760	+	1.66760i
$682$	2.52863e7	+	6.69329e7i	0.00305239	+	0.00807969i
$683$	1.52232e9	+	3.67521e9i	0.182824	+	0.441377i	0.988546	−	0.150917i	$-0.0482225\pi$
$683$	1.52232e9	+	3.67521e9i	0.182824	+	0.441377i	−0.805722	+	0.592294i	$0.798222\pi$
$684$	−6.08687e9	−	1.77867e10i	−0.727273	−	2.12519i
$685$	1.09525e8	+	4.53669e7i	0.0130196	+	0.00539290i
$686$	−5.58392e9	−	5.94714e9i	−0.660397	−	0.703353i
$687$			7.09072e9i			0.834337i
$688$	3.56295e9	+	1.30388e10i	0.417110	+	1.52643i
$689$			4.28587e9i			0.499196i
$690$	−1.53547e10	+	1.44169e10i	−1.77938	+	1.67071i
$691$	7.84654e9	+	3.25014e9i	0.904701	+	0.374739i	0.786026	−	0.618194i	$-0.212135\pi$
$691$	7.84654e9	+	3.25014e9i	0.904701	+	0.374739i	0.118675	+	0.992933i	$0.462135\pi$
$692$	2.59254e9	+	1.27054e9i	0.297409	+	0.145752i
$693$	3.32434e7	+	8.02567e7i	0.00379437	+	0.00916041i
$694$	1.23357e9	−	4.66025e8i	0.140089	−	0.0529238i
$695$	−2.58166e9	−	2.58166e9i	−0.291711	−	0.291711i
$696$	9.92164e9	+	1.19985e10i	1.11545	+	1.34894i
$697$	2.44424e9	−	2.44424e9i	0.273419	−	0.273419i
$698$	3.33084e9	−	7.37557e9i	0.370732	−	0.820922i
$699$	−3.64345e9	+	1.50917e9i	−0.403499	+	0.167135i
$700$	3.42786e7	−	5.43590e8i	0.00377729	−	0.0599002i
$701$	−4.43261e9	+	1.07013e10i	−0.486011	+	1.17334i	0.470699	+	0.882294i	$0.344002\pi$
$701$	−4.43261e9	+	1.07013e10i	−0.486011	+	1.17334i	−0.956710	+	0.291042i	$0.905998\pi$
$702$	4.68700e9	+	1.47634e8i	0.511346	+	0.0161067i
$703$	−1.99421e10			−2.16485
$704$	1.34655e7	+	6.51644e7i	0.00145451	+	0.00703892i
$705$	−2.31146e9			−0.248441
$706$	6.68797e9	+	2.10661e8i	0.715283	+	0.0225304i
$707$	−3.17672e9	+	7.66929e9i	−0.338074	+	0.816183i
$708$	7.51542e8	−	1.19180e10i	0.0795861	−	1.26208i
$709$	2.99893e8	−	1.24220e8i	0.0316012	−	0.0130897i	−0.366827	−	0.930289i	$-0.619556\pi$
$709$	2.99893e8	−	1.24220e8i	0.0316012	−	0.0130897i	0.398428	+	0.917200i	$0.369556\pi$
$710$	−2.51642e9	+	5.57218e9i	−0.263863	+	0.584280i
$711$	−5.21401e9	+	5.21401e9i	−0.544036	+	0.544036i
$712$	−7.83074e9	+	6.47529e9i	−0.813060	+	0.672325i
$713$	−1.35309e10	−	1.35309e10i	−1.39802	−	1.39802i
$714$	−1.04280e10	+	3.93954e9i	−1.07215	+	0.405043i
$715$	−2.59431e7	−	6.26321e7i	−0.00265430	−	0.00640805i
$716$	4.20851e9	+	2.06248e9i	0.428482	+	0.209988i
$717$	−2.80409e9	−	1.16149e9i	−0.284103	−	0.117679i
$718$	−7.41282e8	+	6.96009e8i	−0.0747391	+	0.0701745i
$719$			3.00955e8i			0.0301961i	0.999886	+	0.0150980i	$0.00480604\pi$
$719$			3.00955e8i			0.0301961i	−0.999886	+	0.0150980i	$0.995194\pi$
$720$	−1.12828e10	−	6.43991e9i	−1.12656	−	0.643008i
$721$		−	1.51188e10i		−	1.50226i
$722$	1.26276e10	+	1.34490e10i	1.24865	+	1.32987i
$723$	2.04069e10	+	8.45281e9i	2.00813	+	0.831796i
$724$	−3.23024e9	−	9.43920e9i	−0.316337	−	0.924379i
$725$	−2.61483e8	−	6.31275e8i	−0.0254835	−	0.0615227i
$726$	−5.56958e9	−	1.47427e10i	−0.540188	−	1.42988i
$727$	8.71841e9	+	8.71841e9i	0.841525	+	0.841525i	0.989057	−	0.147532i	$-0.0471330\pi$
$727$	8.71841e9	+	8.71841e9i	0.841525	+	0.841525i	−0.147532	+	0.989057i	$0.547133\pi$
$728$	1.02118e10	−	3.13913e9i	0.980939	−	0.301544i
$729$	−1.12558e10	+	1.12558e10i	−1.07604	+	1.07604i
$730$	3.73438e9	+	1.68646e9i	0.355294	+	0.160452i
$731$	−1.12166e10	+	4.64605e9i	−1.06206	+	0.439920i
$732$	−8.40056e9	−	9.53134e9i	−0.791625	−	0.898184i
$733$	−2.57733e9	+	6.22222e9i	−0.241716	+	0.583554i	−0.997453	−	0.0713206i	$-0.977279\pi$
$733$	−2.57733e9	+	6.22222e9i	−0.241716	+	0.583554i	0.755737	+	0.654875i	$0.227279\pi$
$734$	−1.60345e8	+	5.09055e9i	−0.0149665	+	0.475148i
$735$	−1.04115e9			−0.0967182
$736$	−1.04550e10	−	1.44010e10i	−0.966611	−	1.33144i
$737$	1.07191e8			0.00986332
$738$	−2.44566e8	+	7.76436e9i	−0.0223975	+	0.711063i
$739$	−5.67594e9	+	1.37029e10i	−0.517347	+	1.24899i	0.422180	+	0.906512i	$0.361265\pi$
$739$	−5.67594e9	+	1.37029e10i	−0.517347	+	1.24899i	−0.939527	+	0.342474i	$0.888735\pi$
$740$	−1.03386e10	+	9.11204e9i	−0.937887	+	0.826618i
$741$	−2.61368e10	+	1.08262e10i	−2.35987	+	0.977491i
$742$	5.25487e9	+	2.37312e9i	0.472224	+	0.213259i
$743$	1.29791e10	−	1.29791e10i	1.16087	−	1.16087i	0.176585	−	0.984285i	$-0.443495\pi$
$743$	1.29791e10	−	1.29791e10i	1.16087	−	1.16087i	0.984285	−	0.176585i	$-0.0565052\pi$
$744$	9.65904e9	−	1.82332e10i	0.859862	−	1.62315i
$745$	2.82219e9	+	2.82219e9i	0.250058	+	0.250058i
$746$	1.58573e9	+	4.19742e9i	0.139843	+	0.370166i
$747$	9.82513e9	+	2.37200e10i	0.862415	+	2.08205i
$748$	−5.65474e7	+	1.93514e7i	−0.00494034	+	0.00169066i
$749$	1.36651e9	+	5.66029e8i	0.118830	+	0.0492212i
$750$	1.24141e10	+	1.32216e10i	1.07448	+	1.14438i
$751$			8.97080e9i			0.772843i	0.922322	+	0.386422i	$0.126289\pi$
$751$			8.97080e9i			0.772843i	−0.922322	+	0.386422i	$0.873711\pi$
$752$	2.45337e8	−	1.93754e9i	0.0210378	−	0.166145i
$753$		−	1.86780e10i		−	1.59422i
$754$	9.77051e9	−	9.17379e9i	0.830075	−	0.779380i
$755$	−2.23210e9	−	9.24567e8i	−0.188756	−	0.0781851i
$756$	2.77624e9	−	5.66495e9i	0.233685	−	0.476837i
$757$	−7.40459e9	−	1.78763e10i	−0.620391	−	1.49776i	−0.851245	−	0.524768i	$-0.824152\pi$
$757$	−7.40459e9	−	1.78763e10i	−0.620391	−	1.49776i	0.230854	−	0.972988i	$-0.425848\pi$
$758$	−9.44034e9	+	3.56643e9i	−0.787309	+	0.297434i
$759$	−1.53978e8	−	1.53978e8i	−0.0127824	−	0.0127824i
$760$	1.96492e10	+	1.86169e9i	1.62367	+	0.153837i
$761$	5.05047e9	−	5.05047e9i	0.415418	−	0.415418i	−0.468203	−	0.883621i	$-0.655098\pi$
$761$	5.05047e9	−	5.05047e9i	0.415418	−	0.415418i	0.883621	+	0.468203i	$0.155098\pi$
$762$	−1.01155e9	+	2.23989e9i	−0.0828215	+	0.183394i
$763$	2.17890e10	−	9.02530e9i	1.77583	−	0.735573i
$764$	1.56304e10	+	9.85649e8i	1.26807	+	0.0799642i
$765$	4.46543e9	−	1.07805e10i	0.360619	−	0.870611i
$766$	1.43256e10	+	4.51237e8i	1.15163	+	0.0362747i
$767$	−1.02795e10			−0.822602
$768$	1.15304e10	−	1.53386e10i	0.918503	−	1.22186i
$769$	3.89008e9			0.308472			0.154236	−	0.988034i	$-0.450708\pi$
$769$	3.89008e9			0.308472			0.154236	+	0.988034i	$0.450708\pi$
$770$	−9.11576e7	−	2.87133e6i	−0.00719574	−	0.000226655i
$771$	−4.37975e9	+	1.05737e10i	−0.344159	+	0.830874i
$772$	1.49348e10	+	9.41785e8i	1.16826	+	0.0736701i
$773$	1.20207e10	−	4.97912e9i	0.936052	−	0.387725i	0.138081	−	0.990421i	$-0.455907\pi$
$773$	1.20207e10	−	4.97912e9i	0.936052	−	0.387725i	0.797971	+	0.602696i	$0.205907\pi$
$774$	1.12295e10	−	2.48658e10i	0.870498	−	1.92757i
$775$	−6.40317e8	+	6.40317e8i	−0.0494128	+	0.0494128i
$776$	−1.58610e10	−	1.50277e9i	−1.21847	−	0.115445i
$777$	−1.87908e10	−	1.87908e10i	−1.43705	−	1.43705i
$778$	6.23264e9	−	2.35460e9i	0.474508	−	0.179262i
$779$	−4.51640e9	−	1.09036e10i	−0.342304	−	0.826395i
$780$	−8.60335e9	+	1.75552e10i	−0.649137	+	1.32457i
$781$	−5.84002e7	−	2.41902e7i	−0.00438668	−	0.00181702i
$782$	1.16528e10	−	1.09411e10i	0.871379	−	0.818160i
$783$		−	7.91419e9i		−	0.589170i
$784$	1.10507e8	−	8.72728e8i	0.00819001	−	0.0646804i
$785$			9.69245e9i			0.715138i
$786$	−2.23357e10	−	2.37886e10i	−1.64067	−	1.74739i
$787$	−5.40045e8	−	2.23694e8i	−0.0394928	−	0.0163585i	0.362850	−	0.931848i	$-0.381804\pi$
$787$	−5.40045e8	−	2.23694e8i	−0.0394928	−	0.0163585i	−0.402342	+	0.915489i	$0.631804\pi$
$788$	3.41992e9	−	1.17035e9i	0.248985	−	0.0852065i
$789$	−3.86332e9	−	9.32687e9i	−0.280021	−	0.676031i
$790$	−2.73593e9	−	7.24200e9i	−0.197428	−	0.522593i
$791$	8.81857e9	+	8.81857e9i	0.633549	+	0.633549i
$792$	6.28755e7	−	1.18689e8i	0.00449721	−	0.00848930i
$793$	−7.73336e9	+	7.73336e9i	−0.550696	+	0.550696i
$794$	−1.10639e10	−	4.99653e9i	−0.784401	−	0.354239i
$795$	−9.74807e9	+	4.03778e9i	−0.688072	+	0.285009i
$796$	−4.41623e9	+	3.89229e9i	−0.310353	+	0.273533i
$797$	−8.21690e9	+	1.98374e10i	−0.574916	+	1.38797i	0.322410	+	0.946600i	$0.395507\pi$
$797$	−8.21690e9	+	1.98374e10i	−0.574916	+	1.38797i	−0.897326	+	0.441369i	$0.854493\pi$
$798$	−1.19823e9	+	3.80407e10i	−0.0834698	+	2.64995i
$799$	1.75419e9			0.121664
$800$	−6.81493e8	+	4.94758e8i	−0.0470594	+	0.0341647i
$801$	2.05106e10			1.41015
$802$	−4.37356e8	+	1.38849e10i	−0.0299381	+	0.950460i
$803$	−1.62118e7	+	3.91388e7i	−0.00110491	+	0.00266749i
$804$	−2.04390e10	−	2.31903e10i	−1.38696	−	1.57366i
$805$	2.25349e10	−	9.33425e9i	1.52254	−	0.630658i
$806$	−1.61876e10	−	7.31039e9i	−1.08895	−	0.491776i
$807$	6.12461e9	−	6.12461e9i	0.410224	−	0.410224i
$808$	1.22684e10	−	3.77136e9i	0.818182	−	0.251512i
$809$	−2.64105e9	−	2.64105e9i	−0.175370	−	0.175370i	0.613964	−	0.789334i	$-0.289574\pi$
$809$	−2.64105e9	−	2.64105e9i	−0.175370	−	0.175370i	−0.789334	+	0.613964i	$0.789574\pi$
$810$	−2.85375e9	−	7.55387e9i	−0.188676	−	0.499427i
$811$	−1.13520e10	−	2.74061e10i	−0.747305	−	1.80415i	−0.573176	−	0.819432i	$-0.694289\pi$
$811$	−1.13520e10	−	2.74061e10i	−0.747305	−	1.80415i	−0.174129	−	0.984723i	$-0.555711\pi$
$812$	−5.83790e9	−	1.70592e10i	−0.382658	−	1.11818i
$813$	3.81272e9	+	1.57928e9i	0.248839	+	0.103072i
$814$	−9.75261e7	−	1.03870e8i	−0.00633775	−	0.00675000i
$815$			1.81115e10i			1.17193i
$816$	1.49689e10	+	8.54386e9i	0.964440	+	0.550476i
$817$			4.14514e10i			2.65926i
$818$	2.63399e9	−	2.47312e9i	0.168259	−	0.157983i
$819$	−1.99231e10	−	8.25242e9i	−1.26725	−	0.524914i
$820$	−7.32356e9	−	3.58909e9i	−0.463846	−	0.227319i
$821$	8.11041e9	+	1.95803e10i	0.511495	+	1.23486i	0.943013	+	0.332755i	$0.107978\pi$
$821$	8.11041e9	+	1.95803e10i	0.511495	+	1.23486i	−0.431518	+	0.902104i	$0.642022\pi$
$822$	3.30647e8	−	1.24914e8i	0.0207641	−	0.00784439i
$823$	−4.70804e9	−	4.70804e9i	−0.294402	−	0.294402i	0.544415	−	0.838816i	$-0.316752\pi$
$823$	−4.70804e9	−	4.70804e9i	−0.294402	−	0.294402i	−0.838816	+	0.544415i	$0.816752\pi$
$824$	−1.80149e10	+	1.48967e10i	−1.12173	+	0.927564i
$825$	−7.28662e6	+	7.28662e6i	−0.000451791	+	0.000451791i
$826$	−5.69187e9	+	1.26037e10i	−0.351419	+	0.778156i
$827$	−8.68389e8	+	3.59699e8i	−0.0533882	+	0.0221141i	−0.409218	−	0.912437i	$-0.634198\pi$
$827$	−8.68389e8	+	3.59699e8i	−0.0533882	+	0.0221141i	0.355830	+	0.934551i	$0.384198\pi$
$828$	−2.26071e9	+	3.58503e10i	−0.138401	+	2.19476i
$829$	4.27134e9	−	1.03119e10i	0.260390	−	0.628636i	−0.738573	−	0.674173i	$-0.764500\pi$
$829$	4.27134e9	−	1.03119e10i	0.260390	−	0.628636i	0.998963	+	0.0455374i	$0.0145000\pi$
$830$	−2.69417e10	−	8.48626e8i	−1.63551	−	0.0515161i
$831$	3.78970e10			2.29087
$832$	−1.38022e10	−	9.07492e9i	−0.830839	−	0.546275i
$833$	7.90139e8			0.0473637
$834$	−1.08802e10	−	3.42709e8i	−0.649462	−	0.0204571i
$835$	6.23155e9	−	1.50443e10i	0.370419	−	0.894271i
$836$	−1.28424e7	+	2.03654e8i	−0.000760192	+	0.0120551i
$837$	−9.69012e9	+	4.01378e9i	−0.571202	+	0.236600i
$838$	−8.58610e9	+	1.90124e10i	−0.504013	+	1.11605i
$839$	7.67766e9	−	7.67766e9i	0.448809	−	0.448809i	−0.446149	−	0.894959i	$-0.647205\pi$
$839$	7.67766e9	−	7.67766e9i	0.448809	−	0.448809i	0.894959	+	0.446149i	$0.147205\pi$
$840$	1.67606e10	+	2.02690e10i	0.975688	+	1.17993i
$841$	−3.79663e9	−	3.79663e9i	−0.220096	−	0.220096i
$842$	1.60727e10	−	6.07205e9i	0.927891	−	0.350544i
$843$	−1.39868e10	−	3.37670e10i	−0.804120	−	1.94132i
$844$	2.43485e10	+	1.19326e10i	1.39404	+	0.683180i
$845$	−1.77554e8	−	7.35454e7i	−0.0101236	−	0.00419331i
$846$	−2.87393e9	+	2.69841e9i	−0.163185	+	0.153219i
$847$			1.82509e10i			1.03203i
$848$	−2.34995e9	−	8.59973e9i	−0.132335	−	0.484283i
$849$			4.08749e9i			0.229234i
$850$	−5.17763e8	−	5.51441e8i	−0.0289178	−	0.0307987i
$851$	3.52044e10	+	1.45821e10i	1.95814	+	0.811088i
$852$	5.90222e9	+	1.72471e10i	0.326947	+	0.955384i
$853$	9.97677e9	+	2.40861e10i	0.550387	+	1.32875i	0.917189	+	0.398453i	$0.130453\pi$
$853$	9.97677e9	+	2.40861e10i	0.550387	+	1.32875i	−0.366801	+	0.930299i	$0.619547\pi$
$854$	5.19979e9	+	1.37639e10i	0.285682	+	0.756201i
$855$	−2.81710e10	−	2.81710e10i	−1.54142	−	1.54142i
$856$	−6.71980e8	−	2.18599e9i	−0.0366183	−	0.119122i
$857$	−1.10484e10	+	1.10484e10i	−0.599607	+	0.599607i	−0.940208	−	0.340601i	$-0.889369\pi$
$857$	−1.10484e10	+	1.10484e10i	−0.599607	+	0.599607i	0.340601	+	0.940208i	$0.389369\pi$
$858$	−1.84210e8	−	8.31901e7i	−0.00995653	−	0.00449641i
$859$	5.33895e9	−	2.21147e9i	0.287396	−	0.119043i	−0.234328	−	0.972158i	$-0.575289\pi$
$859$	5.33895e9	−	2.21147e9i	0.287396	−	0.119043i	0.521724	+	0.853114i	$0.325289\pi$
$860$	1.89402e10	+	2.14897e10i	1.01541	+	1.15209i
$861$	6.01841e9	−	1.45297e10i	0.321344	−	0.775794i
$862$	−4.38161e7	+	1.39105e9i	−0.00233001	+	0.0739721i
$863$	−3.53608e9			−0.187277			−0.0936386	−	0.995606i	$-0.529850\pi$
$863$	−3.53608e9			−0.187277			−0.0936386	+	0.995606i	$0.529850\pi$
$864$	−9.48556e9	+	2.27366e9i	−0.500340	+	0.119930i
$865$	6.11845e9			0.321429
$866$	2.47346e8	−	7.85261e9i	0.0129417	−	0.410867i
$867$	5.30100e9	−	1.27977e10i	0.276243	−	0.666909i
$868$	−1.79264e10	+	1.57997e10i	−0.930411	+	0.820029i
$869$	7.39460e7	−	3.06294e7i	0.00382248	−	0.00158332i
$870$	3.00705e10	+	1.35800e10i	1.54818	+	0.699167i
$871$	−1.88157e10	+	1.88157e10i	−0.964843	+	0.964843i
$872$	−3.22230e10	−	1.70701e10i	−1.64573	−	0.871825i
$873$	2.27399e10	+	2.27399e10i	1.15675	+	1.15675i
$874$	−1.92869e10	−	5.10524e10i	−0.977174	−	2.58658i
$875$	−8.03751e9	−	1.94043e10i	−0.405596	−	0.979195i
$876$	1.15587e10	−	3.95557e9i	0.580959	−	0.198813i
$877$	−2.00295e10	−	8.29648e9i	−1.00270	−	0.415332i	−0.179913	−	0.983682i	$-0.557582\pi$
$877$	−2.00295e10	−	8.29648e9i	−1.00270	−	0.415332i	−0.822787	+	0.568351i	$0.807582\pi$
$878$	8.33809e9	+	8.88045e9i	0.415753	+	0.442796i
$879$			1.44255e10i			0.716424i
$880$	8.63969e7	+	1.11449e8i	0.00427375	+	0.00551297i
$881$		−	3.78681e10i		−	1.86577i	−0.360176	−	0.932885i	$-0.617283\pi$
$881$		−	3.78681e10i		−	1.86577i	0.360176	−	0.932885i	$-0.382717\pi$
$882$	−1.29451e9	+	1.21545e9i	−0.0635278	+	0.0596479i
$883$	−2.97692e10	−	1.23308e10i	−1.45514	−	0.602739i	−0.491725	−	0.870750i	$-0.663634\pi$
$883$	−2.97692e10	−	1.23308e10i	−1.45514	−	0.602739i	−0.963416	+	0.268011i	$0.913634\pi$
$884$	6.52916e9	−	1.33228e10i	0.317888	−	0.648654i
$885$	−9.68452e9	−	2.33805e10i	−0.469653	−	1.13384i
$886$	3.29258e9	−	1.24389e9i	0.159044	−	0.0600847i
$887$	−2.72272e9	−	2.72272e9i	−0.131000	−	0.131000i	0.638567	−	0.769567i	$-0.279528\pi$
$887$	−2.72272e9	−	2.72272e9i	−0.131000	−	0.131000i	−0.769567	+	0.638567i	$0.779528\pi$
$888$	−3.87560e9	+	4.09049e10i	−0.185735	+	1.96033i
$889$	2.01258e9	−	2.01258e9i	0.0960721	−	0.0960721i
$890$	−8.86287e9	+	1.96253e10i	−0.421414	+	0.933150i
$891$	7.71303e7	−	3.19484e7i	0.00365303	−	0.00151313i
$892$	4.31017e9	+	2.71798e8i	0.203338	+	0.0128224i
$893$	2.29197e9	−	5.53331e9i	0.107703	−	0.260019i
$894$	1.18938e10	+	3.74639e8i	0.556725	+	0.0175360i
$895$	9.93218e9			0.463089
$896$	−1.87691e10	+	1.18979e10i	−0.871697	+	0.552578i
$897$	5.40565e10			2.50078
$898$	3.52373e10	+	1.10993e9i	1.62381	+	0.0511477i
$899$	−1.14716e10	+	2.76948e10i	−0.526579	+	1.27127i
$900$	1.69653e9	+	1.06983e8i	0.0775733	+	0.00489175i
$901$	7.39790e9	−	3.06431e9i	0.336955	−	0.139571i
$902$	3.47047e7	−	7.68475e7i	0.00157458	−	0.00348664i
$903$	−3.90582e10	+	3.90582e10i	−1.76525	+	1.76525i
$904$	1.81883e9	−	1.91968e10i	0.0818847	−	0.864251i
$905$	−1.49501e10	−	1.49501e10i	−0.670461	−	0.670461i
$906$	−6.73851e9	+	2.54572e9i	−0.301034	+	0.113726i
$907$	−3.56599e9	−	8.60905e9i	−0.158692	−	0.383116i	0.824457	−	0.565925i	$-0.191481\pi$
$907$	−3.56599e9	−	8.60905e9i	−0.158692	−	0.383116i	−0.983148	+	0.182809i	$0.941481\pi$
$908$	−1.53157e10	+	3.12519e10i	−0.678949	+	1.38540i
$909$	−2.39356e10	−	9.91446e9i	−1.05699	−	0.437820i
$910$	1.65053e10	−	1.54972e10i	0.726068	−	0.681725i
$911$		−	2.01865e10i		−	0.884598i	−0.896868	−	0.442299i	$-0.854163\pi$
$911$		−	2.01865e10i		−	0.884598i	0.896868	−	0.442299i	$-0.145837\pi$
$912$	4.65083e10	−	3.60540e10i	2.03025	−	1.57388i
$913$		−	2.78684e8i		−	0.0121189i
$914$	−1.67522e10	−	1.78419e10i	−0.725707	−	0.772911i
$915$	−2.48750e10	−	1.03036e10i	−1.07347	−	0.444646i
$916$	−1.20126e10	+	4.11088e9i	−0.516419	+	0.176726i
$917$	1.44613e10	+	3.49126e10i	0.619319	+	1.49517i
$918$	−3.09628e9	−	8.19586e9i	−0.132096	−	0.349659i
$919$	2.00495e10	+	2.00495e10i	0.852116	+	0.852116i	0.990393	−	0.138278i	$-0.0441567\pi$
$919$	2.00495e10	+	2.00495e10i	0.852116	+	0.852116i	−0.138278	+	0.990393i	$0.544157\pi$
$920$	−3.33260e10	−	1.76545e10i	−1.41100	−	0.747476i
$921$	1.38575e10	−	1.38575e10i	0.584490	−	0.584490i
$922$	−1.62702e10	−	7.34771e9i	−0.683653	−	0.308741i
$923$	1.44974e10	−	6.00502e9i	0.606854	−	0.251367i
$924$	−2.03998e8	+	1.79796e8i	−0.00850694	+	0.00749769i
$925$	6.90065e8	−	1.66597e9i	0.0286678	−	0.0692102i
$926$	3.51929e8	−	1.11729e10i	0.0145652	−	0.462409i
$927$	4.71854e10			1.94549
$928$	−1.45748e10	+	2.37647e10i	−0.598668	+	0.976145i
$929$	6.39631e9			0.261743			0.130871	−	0.991399i	$-0.458223\pi$
$929$	6.39631e9			0.261743			0.130871	+	0.991399i	$0.458223\pi$
$930$	1.37666e9	−	4.37054e10i	0.0561223	−	1.78174i
$931$	1.03237e9	−	2.49237e9i	0.0419289	−	0.101225i
$932$	−4.66903e9	−	5.29751e9i	−0.188917	−	0.214346i
$933$	−6.01607e10	+	2.49194e10i	−2.42509	+	1.00450i
$934$	1.56915e10	+	7.08636e9i	0.630160	+	0.284583i
$935$	−8.95615e7	+	8.95615e7i	−0.00358328	+	0.00358328i
$936$	9.79715e9	+	3.18707e10i	0.390512	+	1.27036i
$937$	−1.53562e9	−	1.53562e9i	−0.0609809	−	0.0609809i	0.675959	−	0.736940i	$-0.263730\pi$
$937$	−1.53562e9	−	1.53562e9i	−0.0609809	−	0.0609809i	−0.736940	+	0.675959i	$0.763730\pi$
$938$	1.26514e10	+	3.34882e10i	0.500527	+	1.32490i
$939$	−3.73031e9	−	9.00575e9i	−0.147033	−	0.354969i
$940$	−1.34008e9	−	3.91590e9i	−0.0526240	−	0.153775i
$941$	2.08397e10	+	8.63208e9i	0.815319	+	0.337716i	0.751074	−	0.660218i	$-0.229536\pi$
$941$	2.08397e10	+	8.63208e9i	0.815319	+	0.337716i	0.0642450	+	0.997934i	$0.479536\pi$
$942$	1.97806e10	+	2.10672e10i	0.771012	+	0.821163i
$943$			2.25509e10i			0.875737i
$944$	2.06262e10	−	5.63629e9i	0.798028	−	0.218068i
$945$		−	1.33694e10i		−	0.515348i
$946$	−2.15902e8	+	2.02716e8i	−0.00829160	+	0.00778520i
$947$	−2.97232e10	−	1.23118e10i	−1.13729	−	0.471080i	−0.267036	−	0.963687i	$-0.586044\pi$
$947$	−2.97232e10	−	1.23118e10i	−1.13729	−	0.471080i	−0.870252	+	0.492606i	$0.836044\pi$
$948$	−2.07264e10	−	1.01575e10i	−0.790123	−	0.387219i
$949$	−4.02446e9	−	9.71590e9i	−0.152854	−	0.369021i
$950$	−2.41593e9	+	9.12705e8i	−0.0914223	+	0.0345381i
$951$	−1.13309e10	−	1.13309e10i	−0.427201	−	0.427201i
$952$	−1.27197e10	−	1.53823e10i	−0.477803	−	0.577820i
$953$	1.67100e10	−	1.67100e10i	0.625389	−	0.625389i	−0.321515	−	0.946904i	$-0.604192\pi$
$953$	1.67100e10	−	1.67100e10i	0.625389	−	0.625389i	0.946904	+	0.321515i	$0.104192\pi$
$954$	−7.40644e9	+	1.64003e10i	−0.276179	+	0.611551i
$955$	3.06636e10	−	1.27013e10i	1.13923	−	0.471884i
$956$	3.42027e8	−	5.42387e9i	0.0126607	−	0.200774i
$957$	−1.30543e8	+	3.15159e8i	−0.00481462	+	0.0116235i
$958$	−1.94283e10	−	6.11963e8i	−0.713929	−	0.0224877i
$959$	−4.09329e8			−0.0149867
$960$	7.63735e9	−	3.99423e10i	0.278608	−	1.45708i
$961$	1.22147e10			0.443969
$962$	3.53518e10	+	1.11353e9i	1.28026	+	0.0403264i
$963$	−1.76656e9	+	4.26485e9i	−0.0637435	+	0.153891i
$964$	−2.48912e9	+	3.94724e10i	−0.0894903	+	1.41914i
$965$	2.92990e10	−	1.21360e10i	1.04956	−	0.434742i
$966$	2.99316e10	−	6.62784e10i	1.06834	−	2.36566i
$967$	−9.83478e9	+	9.83478e9i	−0.349761	+	0.349761i	−0.860021	−	0.510259i	$-0.829549\pi$
$967$	−9.83478e9	+	9.83478e9i	−0.349761	+	0.349761i	0.510259	+	0.860021i	$0.329549\pi$
$968$	2.17470e10	−	1.79827e10i	0.770612	−	0.637224i
$969$	3.73746e10	+	3.73746e10i	1.31960	+	1.31960i
$970$	−3.15846e10	+	1.19322e10i	−1.11115	+	0.419779i
$971$	1.37567e10	+	3.32117e10i	0.482223	+	1.16419i	0.958551	+	0.284921i	$0.0919674\pi$
$971$	1.37567e10	+	3.32117e10i	0.482223	+	1.16419i	−0.476328	+	0.879268i	$0.658033\pi$
$972$	−3.48467e10	−	1.70775e10i	−1.21711	−	0.596474i
$973$	1.16467e10	+	4.82422e9i	0.405329	+	0.167893i
$974$	1.01372e10	−	9.51806e9i	0.351528	−	0.330059i
$975$		−	2.55810e9i		−	0.0883895i
$976$	1.12770e10	−	1.97575e10i	0.388258	−	0.680232i
$977$			1.05872e10i			0.363203i	0.983372	+	0.181602i	$0.0581281\pi$
$977$			1.05872e10i			0.363203i	−0.983372	+	0.181602i	$0.941872\pi$
$978$	3.69623e10	+	3.93666e10i	1.26350	+	1.34568i
$979$	−2.05686e8	−	8.51981e7i	−0.00700594	−	0.00290195i
$980$	−6.03613e8	−	1.76384e9i	−0.0204865	−	0.0598644i
$981$	2.81677e10	+	6.80028e10i	0.952598	+	2.29978i
$982$	−1.21418e10	−	3.21395e10i	−0.409161	−	1.08305i
$983$	1.54561e9	+	1.54561e9i	0.0518993	+	0.0518993i	0.732580	−	0.680681i	$-0.238316\pi$
$983$	1.54561e9	+	1.54561e9i	0.0518993	+	0.0518993i	−0.680681	+	0.732580i	$0.738316\pi$
$984$	−2.32430e10	+	7.14496e9i	−0.777694	+	0.239066i
$985$	5.41656e9	−	5.41656e9i	0.180591	−	0.180591i
$986$	−2.28208e10	−	1.03060e10i	−0.758160	−	0.342388i
$987$	7.37351e9	−	3.05421e9i	0.244098	−	0.101109i
$988$	−3.34939e10	−	3.80025e10i	−1.10488	−	1.25361i
$989$	3.03103e10	−	7.31755e10i	0.996329	−	2.40535i
$990$	8.96135e6	−	2.84500e8i	0.000293529	−	0.00931879i
$991$	−5.51642e10			−1.80053			−0.900263	−	0.435346i	$-0.856626\pi$
$991$	−5.51642e10			−1.80053			−0.900263	+	0.435346i	$0.856626\pi$
$992$	3.64892e10	+	5.79284e9i	1.18679	+	0.188408i
$993$	−4.72805e10			−1.53235
$994$	6.64626e8	−	2.11002e10i	0.0214647	−	0.681450i
$995$	−4.77403e9	+	1.15255e10i	−0.153640	+	0.370920i
$996$	−6.02917e10	+	5.31388e10i	−1.93353	+	1.70414i
$997$	−5.13420e10	+	2.12665e10i	−1.64074	+	0.679616i	−0.996372	−	0.0851007i	$-0.972879\pi$
$997$	−5.13420e10	+	2.12665e10i	−1.64074	+	0.679616i	−0.644366	+	0.764717i	$0.722879\pi$
$998$	−4.85630e8	−	2.19313e8i	−0.0154650	−	0.00698404i
$999$	1.47686e10	−	1.47686e10i	0.468662	−	0.468662i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.8.g.a.13.27	yes	108
32.5	even	8	inner	32.8.g.a.5.27	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.8.g.a.5.27	✓	108	32.5	even	8	inner
32.8.g.a.13.27	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)

\(f(q)\)	\(=\)	\(q+(11.3081 + 0.356189i) q^{2} +(27.3562 - 66.0437i) q^{3} +(127.746 + 8.05564i) q^{4} +(250.611 - 103.807i) q^{5} +(332.870 - 737.084i) q^{6} +(-662.282 + 662.282i) q^{7} +(1441.70 + 136.596i) q^{8} +(-2066.96 - 2066.96i) q^{9} +O(q^{10})\)	\(q+(11.3081 + 0.356189i) q^{2} +(27.3562 - 66.0437i) q^{3} +(127.746 + 8.05564i) q^{4} +(250.611 - 103.807i) q^{5} +(332.870 - 737.084i) q^{6} +(-662.282 + 662.282i) q^{7} +(1441.70 + 136.596i) q^{8} +(-2066.96 - 2066.96i) q^{9} +(2870.91 - 1084.59i) q^{10} +(12.1423 + 29.3140i) q^{11} +(4026.67 - 8216.46i) q^{12} +(-7276.98 - 3014.22i) q^{13} +(-7725.05 + 7253.26i) q^{14} -19391.0i q^{15} +(16254.2 + 2058.16i) q^{16} +14716.0i q^{17} +(-22637.2 - 24109.7i) q^{18} +(46419.5 + 19227.6i) q^{19} +(32850.9 - 11242.1i) q^{20} +(25622.0 + 61857.1i) q^{21} +(126.865 + 335.811i) q^{22} +(-67886.2 - 67886.2i) q^{23} +(48460.6 - 91478.3i) q^{24} +(-3212.55 + 3212.55i) q^{25} +(-81215.2 - 36677.1i) q^{26} +(-48616.6 + 20137.6i) q^{27} +(-89939.2 + 79269.0i) q^{28} +(-57554.3 + 138948. i) q^{29} +(6906.87 - 219276. i) q^{30} +199317. q^{31} +(183071. + 29063.4i) q^{32} +2268.17 q^{33} +(-5241.69 + 166410. i) q^{34} +(-97226.1 + 234725. i) q^{35} +(-247396. - 280698. i) q^{36} +(-366691. + 151889. i) q^{37} +(518068. + 233962. i) q^{38} +(-398141. + 398141. i) q^{39} +(375485. - 115425. i) q^{40} +(-166094. - 166094. i) q^{41} +(267704. + 708612. i) q^{42} +(315714. + 762200. i) q^{43} +(1314.99 + 3842.57i) q^{44} +(-732568. - 303440. i) q^{45} +(-743483. - 791844. i) q^{46} -119202. i q^{47} +(580581. - 1.01718e6i) q^{48} -53692.4i q^{49} +(-37472.1 + 35183.6i) q^{50} +(971901. + 402575. i) q^{51} +(-905326. - 443677. i) q^{52} +(-208229. - 502710. i) q^{53} +(-556934. + 210402. i) q^{54} +(6085.98 + 6085.98i) q^{55} +(-1.04528e6 + 864346. i) q^{56} +(2.53972e6 - 2.53972e6i) q^{57} +(-700321. + 1.55074e6i) q^{58} +(1.20574e6 - 499433. i) q^{59} +(156207. - 2.47713e6i) q^{60} +(531358. - 1.28281e6i) q^{61} +(2.25390e6 + 70994.6i) q^{62} +2.73783e6 q^{63} +(2.05984e6 + 393860. i) q^{64} -2.13659e6 q^{65} +(25648.7 + 807.898i) q^{66} +(1.29282e6 - 3.12115e6i) q^{67} +(-118547. + 1.87992e6i) q^{68} +(-6.34056e6 + 2.62635e6i) q^{69} +(-1.18305e6 + 2.61966e6i) q^{70} +(-1.40872e6 + 1.40872e6i) q^{71} +(-2.69760e6 - 3.26228e6i) q^{72} +(944098. + 944098. i) q^{73} +(-4.20068e6 + 1.58696e6i) q^{74} +(124286. + 300052. i) q^{75} +(5.77503e6 + 2.83019e6i) q^{76} +(-27455.8 - 11372.6i) q^{77} +(-4.64403e6 + 4.36040e6i) q^{78} -2.52254e6i q^{79} +(4.28714e6 - 1.17150e6i) q^{80} -2.63117e6i q^{81} +(-1.81904e6 - 1.93737e6i) q^{82} +(-8.11459e6 - 3.36117e6i) q^{83} +(2.77482e6 + 8.10841e6i) q^{84} +(1.52762e6 + 3.68800e6i) q^{85} +(3.29863e6 + 8.73149e6i) q^{86} +(7.60219e6 + 7.60219e6i) q^{87} +(13501.3 + 43920.6i) q^{88} +(-4.96152e6 + 4.96152e6i) q^{89} +(-8.17588e6 - 3.69226e6i) q^{90} +(6.81568e6 - 2.82315e6i) q^{91} +(-8.12534e6 - 9.21907e6i) q^{92} +(5.45256e6 - 1.31636e7i) q^{93} +(42458.6 - 1.34795e6i) q^{94} +1.36292e7 q^{95} +(6.92758e6 - 1.12956e7i) q^{96} -1.10016e7 q^{97} +(19124.6 - 607159. i) q^{98} +(35493.4 - 85688.7i) 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

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