LMFDB - Embedded newform 17.12.c.a.13.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,12,Mod(4,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("17.4");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	17.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.0618340695$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.15
Character	$\chi$	$=$	17.13
Dual form			17.12.c.a.4.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+66.0051i q^{2} +(-572.909 - 572.909i) q^{3} -2308.67 q^{4} +(-7460.40 - 7460.40i) q^{5} +(37814.9 - 37814.9i) q^{6} +(-24652.1 + 24652.1i) q^{7} -17205.8i q^{8} +479304. i q^{9} +O(q^{10})$	\(q+66.0051i q^{2} +(-572.909 - 572.909i) q^{3} -2308.67 q^{4} +(-7460.40 - 7460.40i) q^{5} +(37814.9 - 37814.9i) q^{6} +(-24652.1 + 24652.1i) q^{7} -17205.8i q^{8} +479304. i q^{9} +(492425. - 492425. i) q^{10} +(398673. - 398673. i) q^{11} +(1.32266e6 + 1.32266e6i) q^{12} -226008. q^{13} +(-1.62716e6 - 1.62716e6i) q^{14} +8.54827e6i q^{15} -3.59249e6 q^{16} +(5.04395e6 - 2.97161e6i) q^{17} -3.16365e7 q^{18} -2.30062e6i q^{19} +(1.72236e7 + 1.72236e7i) q^{20} +2.82468e7 q^{21} +(2.63144e7 + 2.63144e7i) q^{22} +(-1.59051e7 + 1.59051e7i) q^{23} +(-9.85736e6 + 9.85736e6i) q^{24} +6.24870e7i q^{25} -1.49177e7i q^{26} +(1.73108e8 - 1.73108e8i) q^{27} +(5.69136e7 - 5.69136e7i) q^{28} +(2.98189e7 + 2.98189e7i) q^{29} -5.64229e8 q^{30} +(1.34369e8 + 1.34369e8i) q^{31} -2.72360e8i q^{32} -4.56807e8 q^{33} +(1.96141e8 + 3.32926e8i) q^{34} +3.67829e8 q^{35} -1.10656e9i q^{36} +(-8.02130e7 - 8.02130e7i) q^{37} +1.51853e8 q^{38} +(1.29482e8 + 1.29482e8i) q^{39} +(-1.28362e8 + 1.28362e8i) q^{40} +(-5.65151e8 + 5.65151e8i) q^{41} +1.86444e9i q^{42} -6.61760e8i q^{43} +(-9.20405e8 + 9.20405e8i) q^{44} +(3.57580e9 - 3.57580e9i) q^{45} +(-1.04982e9 - 1.04982e9i) q^{46} +1.01625e9 q^{47} +(2.05817e9 + 2.05817e9i) q^{48} +7.61875e8i q^{49} -4.12446e9 q^{50} +(-4.59219e9 - 1.18726e9i) q^{51} +5.21780e8 q^{52} +1.72604e9i q^{53} +(1.14260e10 + 1.14260e10i) q^{54} -5.94852e9 q^{55} +(4.24159e8 + 4.24159e8i) q^{56} +(-1.31805e9 + 1.31805e9i) q^{57} +(-1.96820e9 + 1.96820e9i) q^{58} +5.73219e9i q^{59} -1.97352e10i q^{60} +(5.29761e9 - 5.29761e9i) q^{61} +(-8.86905e9 + 8.86905e9i) q^{62} +(-1.18158e10 - 1.18158e10i) q^{63} +1.06197e10 q^{64} +(1.68611e9 + 1.68611e9i) q^{65} -3.01516e10i q^{66} -1.57842e9 q^{67} +(-1.16448e10 + 6.86047e9i) q^{68} +1.82244e10 q^{69} +2.42786e10i q^{70} +(1.57627e10 + 1.57627e10i) q^{71} +8.24680e9 q^{72} +(-1.72752e10 - 1.72752e10i) q^{73} +(5.29447e9 - 5.29447e9i) q^{74} +(3.57994e10 - 3.57994e10i) q^{75} +5.31138e9i q^{76} +1.96562e10i q^{77} +(-8.54650e9 + 8.54650e9i) q^{78} +(8.68421e9 - 8.68421e9i) q^{79} +(2.68014e10 + 2.68014e10i) q^{80} -1.13444e11 q^{81} +(-3.73029e10 - 3.73029e10i) q^{82} +3.00937e10i q^{83} -6.52127e10 q^{84} +(-5.97993e10 - 1.54605e10i) q^{85} +4.36795e10 q^{86} -3.41671e10i q^{87} +(-6.85948e9 - 6.85948e9i) q^{88} +5.49331e10 q^{89} +(2.36021e11 + 2.36021e11i) q^{90} +(5.57158e9 - 5.57158e9i) q^{91} +(3.67198e10 - 3.67198e10i) q^{92} -1.53963e11i q^{93} +6.70778e10i q^{94} +(-1.71635e10 + 1.71635e10i) q^{95} +(-1.56038e11 + 1.56038e11i) q^{96} +(-5.33230e9 - 5.33230e9i) q^{97} -5.02877e10 q^{98} +(1.91085e11 + 1.91085e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 528 q^{3} - 32772 q^{4} - 15496 q^{5} + 39058 q^{6} - 38368 q^{7}+O(q^{10}) $ 32 * q - 528 * q^3 - 32772 * q^4 - 15496 * q^5 + 39058 * q^6 - 38368 * q^7	\( 32 q - 528 q^{3} - 32772 q^{4} - 15496 q^{5} + 39058 q^{6} - 38368 q^{7} + 178138 q^{10} - 24816 q^{11} + 1322202 q^{12} - 1533752 q^{13} - 757692 q^{14} + 22082308 q^{16} + 17346416 q^{17} + 16775420 q^{18} + 11716134 q^{20} + 16504072 q^{21} + 55362010 q^{22} - 70945120 q^{23} - 7042078 q^{24} - 27445824 q^{27} + 339432756 q^{28} + 185239264 q^{29} - 1261021320 q^{30} + 415468304 q^{31} - 1075445880 q^{33} + 969384454 q^{34} - 1094449168 q^{35} - 49028824 q^{37} - 1340995872 q^{38} + 3217138400 q^{39} + 1182717098 q^{40} - 1419194816 q^{41} - 509236610 q^{44} + 1839923056 q^{45} - 3796371488 q^{46} - 8774740352 q^{47} + 4059548014 q^{48} + 4114666548 q^{50} - 9057963232 q^{51} + 18756164724 q^{52} + 25648728424 q^{54} - 17548144256 q^{55} + 966113388 q^{56} + 23148052104 q^{57} + 32800009486 q^{58} + 1217387240 q^{61} - 42857202380 q^{62} - 58090649872 q^{63} - 43481694148 q^{64} - 12772720712 q^{65} + 17181896368 q^{67} - 120669329406 q^{68} + 84389704104 q^{69} + 36350065824 q^{71} - 62012005860 q^{72} + 41295758480 q^{73} + 108372466886 q^{74} + 143581200752 q^{75} + 103160490932 q^{78} - 86305741264 q^{79} - 278909687742 q^{80} - 398139885080 q^{81} + 84221472400 q^{82} + 278009687832 q^{84} - 131899000528 q^{85} + 214354160644 q^{86} + 95628137594 q^{88} - 158760835496 q^{89} + 629605313178 q^{90} + 149211106624 q^{91} + 288480507416 q^{92} - 267919909216 q^{95} - 242746850002 q^{96} - 126853433800 q^{97} - 829249376752 q^{98} + 229465269792 q^{99}+O(q^{100}) \) 32 * q - 528 * q^3 - 32772 * q^4 - 15496 * q^5 + 39058 * q^6 - 38368 * q^7 + 178138 * q^10 - 24816 * q^11 + 1322202 * q^12 - 1533752 * q^13 - 757692 * q^14 + 22082308 * q^16 + 17346416 * q^17 + 16775420 * q^18 + 11716134 * q^20 + 16504072 * q^21 + 55362010 * q^22 - 70945120 * q^23 - 7042078 * q^24 - 27445824 * q^27 + 339432756 * q^28 + 185239264 * q^29 - 1261021320 * q^30 + 415468304 * q^31 - 1075445880 * q^33 + 969384454 * q^34 - 1094449168 * q^35 - 49028824 * q^37 - 1340995872 * q^38 + 3217138400 * q^39 + 1182717098 * q^40 - 1419194816 * q^41 - 509236610 * q^44 + 1839923056 * q^45 - 3796371488 * q^46 - 8774740352 * q^47 + 4059548014 * q^48 + 4114666548 * q^50 - 9057963232 * q^51 + 18756164724 * q^52 + 25648728424 * q^54 - 17548144256 * q^55 + 966113388 * q^56 + 23148052104 * q^57 + 32800009486 * q^58 + 1217387240 * q^61 - 42857202380 * q^62 - 58090649872 * q^63 - 43481694148 * q^64 - 12772720712 * q^65 + 17181896368 * q^67 - 120669329406 * q^68 + 84389704104 * q^69 + 36350065824 * q^71 - 62012005860 * q^72 + 41295758480 * q^73 + 108372466886 * q^74 + 143581200752 * q^75 + 103160490932 * q^78 - 86305741264 * q^79 - 278909687742 * q^80 - 398139885080 * q^81 + 84221472400 * q^82 + 278009687832 * q^84 - 131899000528 * q^85 + 214354160644 * q^86 + 95628137594 * q^88 - 158760835496 * q^89 + 629605313178 * q^90 + 149211106624 * q^91 + 288480507416 * q^92 - 267919909216 * q^95 - 242746850002 * q^96 - 126853433800 * q^97 - 829249376752 * q^98 + 229465269792 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			66.0051i			1.45852i	0.684236	+	0.729260i	$0.260136\pi$
$2$			66.0051i			1.45852i	−0.684236	+	0.729260i	$0.739864\pi$
$3$	−572.909	−	572.909i	−1.36119	−	1.36119i	−0.872402	−	0.488789i	$-0.837439\pi$
$3$	−572.909	−	572.909i	−1.36119	−	1.36119i	−0.488789	−	0.872402i	$-0.662561\pi$
$4$	−2308.67			−1.12728
$5$	−7460.40	−	7460.40i	−1.06765	−	1.06765i	−0.997540	−	0.0701061i	$-0.977666\pi$
$5$	−7460.40	−	7460.40i	−1.06765	−	1.06765i	−0.0701061	−	0.997540i	$-0.522334\pi$
$6$	37814.9	−	37814.9i	1.98533	−	1.98533i
$7$	−24652.1	+	24652.1i	−0.554389	+	0.554389i	−0.927704	−	0.373316i	$-0.878221\pi$
$7$	−24652.1	+	24652.1i	−0.554389	+	0.554389i	0.373316	+	0.927704i	$0.378221\pi$
$8$		−	17205.8i		−	0.185643i
$9$			479304.i			2.70568i
$10$	492425.	−	492425.i	1.55718	−	1.55718i
$11$	398673.	−	398673.i	0.746375	−	0.746375i	−0.227422	−	0.973796i	$-0.573030\pi$
$11$	398673.	−	398673.i	0.746375	−	0.746375i	0.973796	+	0.227422i	$0.0730296\pi$
$12$	1.32266e6	+	1.32266e6i	1.53445	+	1.53445i
$13$	−226008.			−0.168825			−0.0844124	−	0.996431i	$-0.526901\pi$
$13$	−226008.			−0.168825			−0.0844124	+	0.996431i	$0.526901\pi$
$14$	−1.62716e6	−	1.62716e6i	−0.808588	−	0.808588i
$15$			8.54827e6i			2.90654i
$16$	−3.59249e6			−0.856517
$17$	5.04395e6	−	2.97161e6i	0.861592	−	0.507601i
$17$	5.04395e6	−	2.97161e6i	0.861592	−	0.507601i
$18$	−3.16365e7			−3.94629
$19$		−	2.30062e6i		−	0.213157i	−0.994304	−	0.106579i	$-0.966010\pi$
$19$		−	2.30062e6i		−	0.213157i	0.994304	−	0.106579i	$-0.0339896\pi$
$20$	1.72236e7	+	1.72236e7i	1.20354	+	1.20354i
$21$	2.82468e7			1.50926
$22$	2.63144e7	+	2.63144e7i	1.08860	+	1.08860i
$23$	−1.59051e7	+	1.59051e7i	−0.515269	+	0.515269i	−0.916136	−	0.400867i	$-0.868709\pi$
$23$	−1.59051e7	+	1.59051e7i	−0.515269	+	0.515269i	0.400867	+	0.916136i	$0.368709\pi$
$24$	−9.85736e6	+	9.85736e6i	−0.252696	+	0.252696i
$25$			6.24870e7i			1.27973i
$26$		−	1.49177e7i		−	0.246234i
$27$	1.73108e8	−	1.73108e8i	2.32176	−	2.32176i
$28$	5.69136e7	−	5.69136e7i	0.624953	−	0.624953i
$29$	2.98189e7	+	2.98189e7i	0.269962	+	0.269962i	0.829085	−	0.559123i	$-0.188862\pi$
$29$	2.98189e7	+	2.98189e7i	0.269962	+	0.269962i	−0.559123	+	0.829085i	$0.688862\pi$
$30$	−5.64229e8			−4.23925
$31$	1.34369e8	+	1.34369e8i	0.842966	+	0.842966i	0.989244	−	0.146278i	$-0.0467293\pi$
$31$	1.34369e8	+	1.34369e8i	0.842966	+	0.842966i	−0.146278	+	0.989244i	$0.546729\pi$
$32$		−	2.72360e8i		−	1.43489i
$33$	−4.56807e8			−2.03192
$34$	1.96141e8	+	3.32926e8i	0.740347	+	1.25665i
$35$	3.67829e8			1.18378
$36$		−	1.10656e9i		−	3.05007i
$37$	−8.02130e7	−	8.02130e7i	−0.190167	−	0.190167i	0.605601	−	0.795768i	$-0.292933\pi$
$37$	−8.02130e7	−	8.02130e7i	−0.190167	−	0.190167i	−0.795768	+	0.605601i	$0.792933\pi$
$38$	1.51853e8			0.310894
$39$	1.29482e8	+	1.29482e8i	0.229803	+	0.229803i
$40$	−1.28362e8	+	1.28362e8i	−0.198201	+	0.198201i
$41$	−5.65151e8	+	5.65151e8i	−0.761822	+	0.761822i	−0.976651	−	0.214830i	$-0.931080\pi$
$41$	−5.65151e8	+	5.65151e8i	−0.761822	+	0.761822i	0.214830	+	0.976651i	$0.431080\pi$
$42$			1.86444e9i			2.20128i
$43$		−	6.61760e8i		−	0.686474i	−0.939249	−	0.343237i	$-0.888477\pi$
$43$		−	6.61760e8i		−	0.686474i	0.939249	−	0.343237i	$-0.111523\pi$
$44$	−9.20405e8	+	9.20405e8i	−0.841375	+	0.841375i
$45$	3.57580e9	−	3.57580e9i	2.88871	−	2.88871i
$46$	−1.04982e9	−	1.04982e9i	−0.751531	−	0.751531i
$47$	1.01625e9			0.646343			0.323172	−	0.946340i	$-0.395251\pi$
$47$	1.01625e9			0.646343			0.323172	+	0.946340i	$0.395251\pi$
$48$	2.05817e9	+	2.05817e9i	1.16588	+	1.16588i
$49$			7.61875e8i			0.385306i
$50$	−4.12446e9			−1.86652
$51$	−4.59219e9	−	1.18726e9i	−1.86373	−	0.481850i
$52$	5.21780e8			0.190313
$53$			1.72604e9i			0.566937i	0.958982	+	0.283468i	$0.0914851\pi$
$53$			1.72604e9i			0.566937i	−0.958982	+	0.283468i	$0.908515\pi$
$54$	1.14260e10	+	1.14260e10i	3.38633	+	3.38633i
$55$	−5.94852e9			−1.59373
$56$	4.24159e8	+	4.24159e8i	0.102919	+	0.102919i
$57$	−1.31805e9	+	1.31805e9i	−0.290147	+	0.290147i
$58$	−1.96820e9	+	1.96820e9i	−0.393745	+	0.393745i
$59$			5.73219e9i			1.04384i	0.852994	+	0.521921i	$0.174784\pi$
$59$			5.73219e9i			1.04384i	−0.852994	+	0.521921i	$0.825216\pi$
$60$		−	1.97352e10i		−	3.27649i
$61$	5.29761e9	−	5.29761e9i	0.803092	−	0.803092i	−0.180485	−	0.983578i	$-0.557767\pi$
$61$	5.29761e9	−	5.29761e9i	0.803092	−	0.803092i	0.983578	+	0.180485i	$0.0577668\pi$
$62$	−8.86905e9	+	8.86905e9i	−1.22948	+	1.22948i
$63$	−1.18158e10	−	1.18158e10i	−1.50000	−	1.50000i
$64$	1.06197e10			1.23630
$65$	1.68611e9	+	1.68611e9i	0.180245	+	0.180245i
$66$		−	3.01516e10i		−	2.96359i
$67$	−1.57842e9			−0.142828			−0.0714138	−	0.997447i	$-0.522751\pi$
$67$	−1.57842e9			−0.142828			−0.0714138	+	0.997447i	$0.522751\pi$
$68$	−1.16448e10	+	6.86047e9i	−0.971257	+	0.572210i
$69$	1.82244e10			1.40276
$70$			2.42786e10i			1.72657i
$71$	1.57627e10	+	1.57627e10i	1.03683	+	1.03683i	0.999295	+	0.0375374i	$0.0119513\pi$
$71$	1.57627e10	+	1.57627e10i	1.03683	+	1.03683i	0.0375374	+	0.999295i	$0.488049\pi$
$72$	8.24680e9			0.502292
$73$	−1.72752e10	−	1.72752e10i	−0.975318	−	0.975318i	0.0243849	−	0.999703i	$-0.492237\pi$
$73$	−1.72752e10	−	1.72752e10i	−0.975318	−	0.975318i	−0.999703	+	0.0243849i	$0.992237\pi$
$74$	5.29447e9	−	5.29447e9i	0.277363	−	0.277363i
$75$	3.57994e10	−	3.57994e10i	1.74196	−	1.74196i
$76$			5.31138e9i			0.240288i
$77$			1.96562e10i			0.827564i
$78$	−8.54650e9	+	8.54650e9i	−0.335172	+	0.335172i
$79$	8.68421e9	−	8.68421e9i	0.317528	−	0.317528i	−0.530289	−	0.847817i	$-0.677917\pi$
$79$	8.68421e9	−	8.68421e9i	0.317528	−	0.317528i	0.847817	+	0.530289i	$0.177917\pi$
$80$	2.68014e10	+	2.68014e10i	0.914457	+	0.914457i
$81$	−1.13444e11			−3.61504
$82$	−3.73029e10	−	3.73029e10i	−1.11113	−	1.11113i
$83$			3.00937e10i			0.838584i	0.907851	+	0.419292i	$0.137722\pi$
$83$			3.00937e10i			0.838584i	−0.907851	+	0.419292i	$0.862278\pi$
$84$	−6.52127e10			−1.70136
$85$	−5.97993e10	−	1.54605e10i	−1.46181	−	0.377937i
$86$	4.36795e10			1.00124
$87$		−	3.41671e10i		−	0.734940i
$88$	−6.85948e9	−	6.85948e9i	−0.138560	−	0.138560i
$89$	5.49331e10			1.04277			0.521385	−	0.853321i	$-0.325415\pi$
$89$	5.49331e10			1.04277			0.521385	+	0.853321i	$0.325415\pi$
$90$	2.36021e11	+	2.36021e11i	4.21324	+	4.21324i
$91$	5.57158e9	−	5.57158e9i	0.0935946	−	0.0935946i
$92$	3.67198e10	−	3.67198e10i	0.580854	−	0.580854i
$93$		−	1.53963e11i		−	2.29488i
$94$			6.70778e10i			0.942705i
$95$	−1.71635e10	+	1.71635e10i	−0.227576	+	0.227576i
$96$	−1.56038e11	+	1.56038e11i	−1.95316	+	1.95316i
$97$	−5.33230e9	−	5.33230e9i	−0.0630478	−	0.0630478i	0.674880	−	0.737928i	$-0.264195\pi$
$97$	−5.33230e9	−	5.33230e9i	−0.0630478	−	0.0630478i	−0.737928	+	0.674880i	$0.764195\pi$
$98$	−5.02877e10			−0.561976
$99$	1.91085e11	+	1.91085e11i	2.01945	+	2.01945i
$100$		−	1.44262e11i		−	1.44262i
$101$	3.19060e10			0.302068			0.151034	−	0.988529i	$-0.451740\pi$
$101$	3.19060e10			0.302068			0.151034	+	0.988529i	$0.451740\pi$
$102$	7.83655e10	−	3.03108e11i	0.702788	−	2.71829i
$103$	1.03360e11			0.878515			0.439258	−	0.898361i	$-0.355242\pi$
$103$	1.03360e11			0.878515			0.439258	+	0.898361i	$0.355242\pi$
$104$			3.88865e9i			0.0313412i
$105$	−2.10733e11	−	2.10733e11i	−1.61135	−	1.61135i
$106$	−1.13928e11			−0.826889
$107$	4.41421e9	+	4.41421e9i	0.0304258	+	0.0304258i	0.722156	−	0.691730i	$-0.243151\pi$
$107$	4.41421e9	+	4.41421e9i	0.0304258	+	0.0304258i	−0.691730	+	0.722156i	$0.743151\pi$
$108$	−3.99651e11	+	3.99651e11i	−2.61728	+	2.61728i
$109$	1.34586e11	−	1.34586e11i	0.837828	−	0.837828i	−0.150745	−	0.988573i	$-0.548167\pi$
$109$	1.34586e11	−	1.34586e11i	0.837828	−	0.837828i	0.988573	+	0.150745i	$0.0481671\pi$
$110$		−	3.92633e11i		−	2.32448i
$111$			9.19096e10i			0.517708i
$112$	8.85625e10	−	8.85625e10i	0.474844	−	0.474844i
$113$	−2.24160e11	+	2.24160e11i	−1.14453	+	1.14453i	−0.156917	+	0.987612i	$0.550156\pi$
$113$	−2.24160e11	+	2.24160e11i	−1.14453	+	1.14453i	−0.987612	+	0.156917i	$0.949844\pi$
$114$	−8.69977e10	−	8.69977e10i	−0.423186	−	0.423186i
$115$	2.37317e11			1.10025
$116$	−6.88422e10	−	6.88422e10i	−0.304324	−	0.304324i
$117$		−	1.08327e11i		−	0.456786i
$118$	−3.78354e11			−1.52246
$119$	−5.10876e10	+	1.97600e11i	−0.196249	+	0.759066i
$120$	1.47080e11			0.539580
$121$		−	3.25684e10i		−	0.114150i
$122$	3.49669e11	+	3.49669e11i	1.17133	+	1.17133i
$123$	6.47561e11			2.07397
$124$	−3.10214e11	−	3.10214e11i	−0.950260	−	0.950260i
$125$	1.01901e11	−	1.01901e11i	0.298657	−	0.298657i
$126$	7.79905e11	−	7.79905e11i	2.18778	−	2.18778i
$127$			4.62563e11i			1.24237i	0.783665	+	0.621184i	$0.213348\pi$
$127$			4.62563e11i			1.24237i	−0.783665	+	0.621184i	$0.786652\pi$
$128$			1.43163e11i			0.368279i
$129$	−3.79128e11	+	3.79128e11i	−0.934422	+	0.934422i
$130$	−1.11292e11	+	1.11292e11i	−0.262891	+	0.262891i
$131$	1.76846e11	+	1.76846e11i	0.400501	+	0.400501i	0.878409	−	0.477909i	$-0.158605\pi$
$131$	1.76846e11	+	1.76846e11i	0.400501	+	0.400501i	−0.477909	+	0.878409i	$0.658605\pi$
$132$	1.05462e12			2.29054
$133$	5.67150e10	+	5.67150e10i	0.118172	+	0.118172i
$134$		−	1.04184e11i		−	0.208317i
$135$	−2.58292e12			−4.95763
$136$	−5.11289e10	−	8.67851e10i	−0.0942328	−	0.159949i
$137$	7.66134e11			1.35626			0.678128	−	0.734944i	$-0.262792\pi$
$137$	7.66134e11			1.35626			0.678128	+	0.734944i	$0.262792\pi$
$138$			1.20290e12i			2.04595i
$139$	6.13254e11	+	6.13254e11i	1.00244	+	1.00244i	0.999997	+	0.00244482i	$0.000778212\pi$
$139$	6.13254e11	+	6.13254e11i	1.00244	+	1.00244i	0.00244482	+	0.999997i	$0.499222\pi$
$140$	−8.49197e11			−1.33446
$141$	−5.82220e11	−	5.82220e11i	−0.879797	−	0.879797i
$142$	−1.04042e12	+	1.04042e12i	−1.51224	+	1.51224i
$143$	−9.01034e10	+	9.01034e10i	−0.126007	+	0.126007i
$144$		−	1.72189e12i		−	2.31746i
$145$		−	4.44922e11i		−	0.576448i
$146$	1.14025e12	−	1.14025e12i	1.42252	−	1.42252i
$147$	4.36486e11	−	4.36486e11i	0.524475	−	0.524475i
$148$	1.85186e11	+	1.85186e11i	0.214372	+	0.214372i
$149$	−1.04891e12			−1.17008			−0.585040	−	0.811004i	$-0.698921\pi$
$149$	−1.04891e12			−1.17008			−0.585040	+	0.811004i	$0.698921\pi$
$150$	2.36294e12	+	2.36294e12i	2.54069	+	2.54069i
$151$		−	2.66941e10i		−	0.0276721i	−0.999904	−	0.0138361i	$-0.995596\pi$
$151$		−	2.66941e10i		−	0.0276721i	0.999904	−	0.0138361i	$-0.00440429\pi$
$152$	−3.95839e10			−0.0395712
$153$	1.42430e12	+	2.41758e12i	1.37341	+	2.33120i
$154$	−1.29741e12			−1.20702
$155$		−	2.00489e12i		−	1.79998i
$156$	−2.98933e11	−	2.98933e11i	−0.259053	−	0.259053i
$157$	−1.70979e12			−1.43052			−0.715262	−	0.698856i	$-0.753693\pi$
$157$	−1.70979e12			−1.43052			−0.715262	+	0.698856i	$0.753693\pi$
$158$	5.73202e11	+	5.73202e11i	0.463120	+	0.463120i
$159$	9.88867e11	−	9.88867e11i	0.771709	−	0.771709i
$160$	−2.03192e12	+	2.03192e12i	−1.53196	+	1.53196i
$161$		−	7.84190e11i		−	0.571319i
$162$		−	7.48786e12i		−	5.27260i
$163$	−6.43236e11	+	6.43236e11i	−0.437863	+	0.437863i	−0.891292	−	0.453429i	$-0.850201\pi$
$163$	−6.43236e11	+	6.43236e11i	−0.437863	+	0.437863i	0.453429	+	0.891292i	$0.350201\pi$
$164$	1.30475e12	−	1.30475e12i	0.858788	−	0.858788i
$165$	3.40796e12	+	3.40796e12i	2.16937	+	2.16937i
$166$	−1.98634e12			−1.22309
$167$	3.03409e11	+	3.03409e11i	0.180754	+	0.180754i	0.791684	−	0.610930i	$-0.209204\pi$
$167$	3.03409e11	+	3.03409e11i	0.180754	+	0.180754i	−0.610930	+	0.791684i	$0.709204\pi$
$168$		−	4.86009e11i		−	0.280184i
$169$	−1.74108e12			−0.971498
$170$	1.02047e12	−	3.94706e12i	0.551229	−	2.13208i
$171$	1.10269e12			0.576735
$172$			1.52779e12i			0.773849i
$173$	−6.81916e11	−	6.81916e11i	−0.334562	−	0.334562i	0.519754	−	0.854316i	$-0.326024\pi$
$173$	−6.81916e11	−	6.81916e11i	−0.334562	−	0.334562i	−0.854316	+	0.519754i	$0.826024\pi$
$174$	2.25520e12			1.07193
$175$	−1.54044e12	−	1.54044e12i	−0.709471	−	0.709471i
$176$	−1.43223e12	+	1.43223e12i	−0.639283	+	0.639283i
$177$	3.28403e12	−	3.28403e12i	1.42087	−	1.42087i
$178$			3.62586e12i			1.52090i
$179$			3.70206e12i			1.50575i	0.658165	+	0.752874i	$0.271333\pi$
$179$			3.70206e12i			1.50575i	−0.658165	+	0.752874i	$0.728667\pi$
$180$	−8.25535e12	+	8.25535e12i	−3.25639	+	3.25639i
$181$	2.73751e12	−	2.73751e12i	1.04743	−	1.04743i	0.0486092	−	0.998818i	$-0.484521\pi$
$181$	2.73751e12	−	2.73751e12i	1.04743	−	1.04743i	0.998818	−	0.0486092i	$-0.0154789\pi$
$182$	3.67753e11	+	3.67753e11i	0.136510	+	0.136510i
$183$	−6.07010e12			−2.18632
$184$	2.73660e11	+	2.73660e11i	0.0956564	+	0.0956564i
$185$			1.19684e12i			0.406062i
$186$	1.01623e13			3.34712
$187$	8.26187e11	−	3.19559e12i	0.264210	−	1.02193i
$188$	−2.34619e12			−0.728611
$189$			8.53497e12i			2.57432i
$190$	−1.13288e12	−	1.13288e12i	−0.331925	−	0.331925i
$191$	3.44468e12			0.980541			0.490270	−	0.871570i	$-0.336898\pi$
$191$	3.44468e12			0.980541			0.490270	+	0.871570i	$0.336898\pi$
$192$	−6.08415e12	−	6.08415e12i	−1.68284	−	1.68284i
$193$	1.59830e12	−	1.59830e12i	0.429627	−	0.429627i	−0.458874	−	0.888501i	$-0.651747\pi$
$193$	1.59830e12	−	1.59830e12i	0.429627	−	0.429627i	0.888501	+	0.458874i	$0.151747\pi$
$194$	3.51959e11	−	3.51959e11i	0.0919565	−	0.0919565i
$195$		−	1.93198e12i		−	0.490696i
$196$		−	1.75892e12i		−	0.434348i
$197$	4.69061e12	−	4.69061e12i	1.12633	−	1.12633i	0.135560	−	0.990769i	$-0.456717\pi$
$197$	4.69061e12	−	4.69061e12i	1.12633	−	1.12633i	0.990769	−	0.135560i	$-0.0432835\pi$
$198$	−1.26126e13	+	1.26126e13i	−2.94541	+	2.94541i
$199$	2.05379e11	+	2.05379e11i	0.0466514	+	0.0466514i	0.730048	−	0.683396i	$-0.239498\pi$
$199$	2.05379e11	+	2.05379e11i	0.0466514	+	0.0466514i	−0.683396	+	0.730048i	$0.739498\pi$
$200$	1.07514e12			0.237574
$201$	9.04293e11	+	9.04293e11i	0.194416	+	0.194416i
$202$			2.10596e12i			0.440573i
$203$	−1.47020e12			−0.299328
$204$	1.06019e13	+	2.74101e12i	2.10095	+	0.543180i
$205$	8.43251e12			1.62671
$206$			6.82231e12i			1.28133i
$207$	−7.62339e12	−	7.62339e12i	−1.39416	−	1.39416i
$208$	8.11934e11			0.144601
$209$	−9.17194e11	−	9.17194e11i	−0.159095	−	0.159095i
$210$	1.39094e13	−	1.39094e13i	2.35019	−	2.35019i
$211$	−5.05324e12	+	5.05324e12i	−0.831795	+	0.831795i	−0.987762	−	0.155968i	$-0.950150\pi$
$211$	−5.05324e12	+	5.05324e12i	−0.831795	+	0.831795i	0.155968	+	0.987762i	$0.450150\pi$
$212$		−	3.98487e12i		−	0.639098i
$213$		−	1.80612e13i		−	2.82265i
$214$	−2.91361e11	+	2.91361e11i	−0.0443767	+	0.0443767i
$215$	−4.93699e12	+	4.93699e12i	−0.732911	+	0.732911i
$216$	−2.97847e12	−	2.97847e12i	−0.431020	−	0.431020i
$217$	−6.62496e12			−0.934662
$218$	8.88338e12	+	8.88338e12i	1.22199	+	1.22199i
$219$			1.97942e13i			2.65519i
$220$	1.37332e13			1.79658
$221$	−1.13998e12	+	6.71609e11i	−0.145458	+	0.0856957i
$222$	−6.06650e12			−0.755087
$223$		−	9.28232e12i		−	1.12714i	−0.826067	−	0.563572i	$-0.809427\pi$
$223$		−	9.28232e12i		−	1.12714i	0.826067	−	0.563572i	$-0.190573\pi$
$224$	6.71425e12	+	6.71425e12i	0.795488	+	0.795488i
$225$	−2.99503e13			−3.46256
$226$	−1.47957e13	−	1.47957e13i	−1.66932	−	1.66932i
$227$	−1.07022e12	+	1.07022e12i	−0.117851	+	0.117851i	−0.763573	−	0.645722i	$-0.776557\pi$
$227$	−1.07022e12	+	1.07022e12i	−0.117851	+	0.117851i	0.645722	+	0.763573i	$0.276557\pi$
$228$	3.04294e12	−	3.04294e12i	0.327078	−	0.327078i
$229$			4.10251e11i			0.0430481i	0.999768	+	0.0215241i	$0.00685185\pi$
$229$			4.10251e11i			0.0430481i	−0.999768	+	0.0215241i	$0.993148\pi$
$230$			1.56642e13i			1.60474i
$231$	1.12612e13	−	1.12612e13i	1.12647	−	1.12647i
$232$	5.13058e11	−	5.13058e11i	0.0501167	−	0.0501167i
$233$	−8.07362e12	−	8.07362e12i	−0.770213	−	0.770213i	0.207931	−	0.978143i	$-0.433327\pi$
$233$	−8.07362e12	−	8.07362e12i	−0.770213	−	0.770213i	−0.978143	+	0.207931i	$0.933327\pi$
$234$	7.15011e12			0.666232
$235$	−7.58165e12	−	7.58165e12i	−0.690065	−	0.690065i
$236$		−	1.32338e13i		−	1.17670i
$237$	−9.95053e12			−0.864431
$238$	−1.30426e13	−	3.37204e12i	−1.10711	−	0.286233i
$239$	1.59966e13			1.32690			0.663451	−	0.748219i	$-0.269091\pi$
$239$	1.59966e13			1.32690			0.663451	+	0.748219i	$0.269091\pi$
$240$		−	3.07096e13i		−	2.48950i
$241$	−4.30977e12	−	4.30977e12i	−0.341476	−	0.341476i	0.515446	−	0.856922i	$-0.327626\pi$
$241$	−4.30977e12	−	4.30977e12i	−0.341476	−	0.341476i	−0.856922	+	0.515446i	$0.827626\pi$
$242$	2.14968e12			0.166491
$243$	3.43273e13	+	3.43273e13i	2.59899	+	2.59899i
$244$	−1.22304e13	+	1.22304e13i	−0.905312	+	0.905312i
$245$	5.68390e12	−	5.68390e12i	0.411370	−	0.411370i
$246$			4.27423e13i			3.02493i
$247$			5.19959e11i			0.0359862i
$248$	2.31193e12	−	2.31193e12i	0.156491	−	0.156491i
$249$	1.72410e13	−	1.72410e13i	1.14147	−	1.14147i
$250$	6.72598e12	+	6.72598e12i	0.435598	+	0.435598i
$251$	8.74153e12			0.553837			0.276919	−	0.960893i	$-0.410687\pi$
$251$	8.74153e12			0.553837			0.276919	+	0.960893i	$0.410687\pi$
$252$	2.72789e13	+	2.72789e13i	1.69092	+	1.69092i
$253$			1.26819e13i			0.769168i
$254$	−3.05315e13			−1.81202
$255$	2.54021e13	+	4.31170e13i	1.47536	+	2.50425i
$256$	1.22997e13			0.699158
$257$		−	3.15244e12i		−	0.175394i	−0.996147	−	0.0876971i	$-0.972049\pi$
$257$		−	3.15244e12i		−	0.175394i	0.996147	−	0.0876971i	$-0.0279507\pi$
$258$	−2.50244e13	−	2.50244e13i	−1.36287	−	1.36287i
$259$	3.95484e12			0.210853
$260$	−3.89269e12	−	3.89269e12i	−0.203187	−	0.203187i
$261$	−1.42923e13	+	1.42923e13i	−0.730432	+	0.730432i
$262$	−1.16727e13	+	1.16727e13i	−0.584138	+	0.584138i
$263$			8.74867e12i			0.428732i	0.976753	+	0.214366i	$0.0687685\pi$
$263$			8.74867e12i			0.428732i	−0.976753	+	0.214366i	$0.931232\pi$
$264$			7.85972e12i			0.377212i
$265$	1.28770e13	−	1.28770e13i	0.605288	−	0.605288i
$266$	−3.74348e12	+	3.74348e12i	−0.172356	+	0.172356i
$267$	−3.14717e13	−	3.14717e13i	−1.41941	−	1.41941i
$268$	3.64406e12			0.161007
$269$	−7.30926e12	−	7.30926e12i	−0.316400	−	0.316400i	0.530983	−	0.847383i	$-0.321823\pi$
$269$	−7.30926e12	−	7.30926e12i	−0.316400	−	0.316400i	−0.847383	+	0.530983i	$0.821823\pi$
$270$		−	1.70486e14i		−	7.23081i
$271$	1.17788e13			0.489518			0.244759	−	0.969584i	$-0.421291\pi$
$271$	1.17788e13			0.489518			0.244759	+	0.969584i	$0.421291\pi$
$272$	−1.81204e13	+	1.06755e13i	−0.737969	+	0.434769i
$273$	−6.38402e12			−0.254800
$274$			5.05687e13i			1.97813i
$275$	2.49119e13	+	2.49119e13i	0.955161	+	0.955161i
$276$	−4.20742e13			−1.58131
$277$	1.04187e12	+	1.04187e12i	0.0383862	+	0.0383862i	0.726039	−	0.687653i	$-0.241359\pi$
$277$	1.04187e12	+	1.04187e12i	0.0383862	+	0.0383862i	−0.687653	+	0.726039i	$0.741359\pi$
$278$	−4.04779e13	+	4.04779e13i	−1.46208	+	1.46208i
$279$	−6.44036e13	+	6.44036e13i	−2.28080	+	2.28080i
$280$		−	6.32879e12i		−	0.219761i
$281$			3.72319e13i			1.26774i	0.773439	+	0.633871i	$0.218535\pi$
$281$			3.72319e13i			1.26774i	−0.773439	+	0.633871i	$0.781465\pi$
$282$	3.84295e13	−	3.84295e13i	1.28320	−	1.28320i
$283$	−1.28000e13	+	1.28000e13i	−0.419165	+	0.419165i	−0.884916	−	0.465751i	$-0.845784\pi$
$283$	−1.28000e13	+	1.28000e13i	−0.419165	+	0.419165i	0.465751	+	0.884916i	$0.345784\pi$
$284$	−3.63908e13	−	3.63908e13i	−1.16880	−	1.16880i
$285$	1.96663e13			0.619549
$286$	−5.94729e12	−	5.94729e12i	−0.183783	−	0.183783i
$287$		−	2.78643e13i		−	0.844691i
$288$	1.30543e14			3.88236
$289$	1.66110e13	−	2.99773e13i	0.484682	−	0.874690i
$290$	2.93671e13			0.840761
$291$			6.10985e12i			0.171640i
$292$	3.98827e13	+	3.98827e13i	1.09946	+	1.09946i
$293$	5.14559e13			1.39208			0.696039	−	0.718004i	$-0.254944\pi$
$293$	5.14559e13			1.39208			0.696039	+	0.718004i	$0.254944\pi$
$294$	2.88103e13	+	2.88103e13i	0.764957	+	0.764957i
$295$	4.27644e13	−	4.27644e13i	1.11445	−	1.11445i
$296$	−1.38013e12	+	1.38013e12i	−0.0353033	+	0.0353033i
$297$		−	1.38027e14i		−	3.46581i
$298$		−	6.92337e13i		−	1.70659i
$299$	3.59469e12	−	3.59469e12i	0.0869902	−	0.0869902i
$300$	−8.26492e13	+	8.26492e13i	−1.96368	+	1.96368i
$301$	1.63138e13	+	1.63138e13i	0.380573	+	0.380573i
$302$	1.76195e12			0.0403603
$303$	−1.82793e13	−	1.82793e13i	−0.411173	−	0.411173i
$304$			8.26495e12i			0.182573i
$305$	−7.90445e13			−1.71484
$306$	−1.59573e14	+	9.40112e13i	−3.40010	+	2.00314i
$307$	−3.10593e13			−0.650025			−0.325013	−	0.945710i	$-0.605369\pi$
$307$	−3.10593e13			−0.650025			−0.325013	+	0.945710i	$0.605369\pi$
$308$		−	4.53798e13i		−	0.932898i
$309$	−5.92161e13	−	5.92161e13i	−1.19583	−	1.19583i
$310$	1.32333e14			2.62530
$311$	3.67924e13	+	3.67924e13i	0.717095	+	0.717095i	0.968009	−	0.250915i	$-0.0807314\pi$
$311$	3.67924e13	+	3.67924e13i	0.717095	+	0.717095i	−0.250915	+	0.968009i	$0.580731\pi$
$312$	2.22785e12	−	2.22785e12i	0.0426614	−	0.0426614i
$313$	6.85331e12	−	6.85331e12i	0.128946	−	0.128946i	−0.639689	−	0.768634i	$-0.720937\pi$
$313$	6.85331e12	−	6.85331e12i	0.128946	−	0.128946i	0.768634	+	0.639689i	$0.220937\pi$
$314$		−	1.12855e14i		−	2.08645i
$315$			1.76302e14i			3.20294i
$316$	−2.00490e13	+	2.00490e13i	−0.357943	+	0.357943i
$317$	−5.38067e13	+	5.38067e13i	−0.944084	+	0.944084i	−0.998517	−	0.0544333i	$-0.982665\pi$
$317$	−5.38067e13	+	5.38067e13i	−0.944084	+	0.944084i	0.0544333	+	0.998517i	$0.482665\pi$
$318$	6.52703e13	+	6.52703e13i	1.12555	+	1.12555i
$319$	2.37760e13			0.402986
$320$	−7.92276e13	−	7.92276e13i	−1.31993	−	1.31993i
$321$		−	5.05789e12i		−	0.0828307i
$322$	5.17605e13			0.833281
$323$	−6.83654e12	−	1.16042e13i	−0.108199	−	0.183654i
$324$	2.61904e14			4.07516
$325$		−	1.41226e13i		−	0.216051i
$326$	−4.24569e13	−	4.24569e13i	−0.638633	−	0.638633i
$327$	−1.54211e14			−2.28089
$328$	9.72387e12	+	9.72387e12i	0.141427	+	0.141427i
$329$	−2.50527e13	+	2.50527e13i	−0.358325	+	0.358325i
$330$	−2.24943e14	+	2.24943e14i	−3.16407	+	3.16407i
$331$			1.24816e14i			1.72670i	0.504609	+	0.863348i	$0.331637\pi$
$331$			1.24816e14i			1.72670i	−0.504609	+	0.863348i	$0.668363\pi$
$332$		−	6.94766e13i		−	0.945320i
$333$	3.84464e13	−	3.84464e13i	0.514532	−	0.514532i
$334$	−2.00265e13	+	2.00265e13i	−0.263633	+	0.263633i
$335$	1.17757e13	+	1.17757e13i	0.152489	+	0.152489i
$336$	−1.01477e14			−1.29271
$337$	5.67293e13	+	5.67293e13i	0.710956	+	0.710956i	0.966735	−	0.255779i	$-0.0823320\pi$
$337$	5.67293e13	+	5.67293e13i	0.710956	+	0.710956i	−0.255779	+	0.966735i	$0.582332\pi$
$338$		−	1.14920e14i		−	1.41695i
$339$	2.56847e14			3.11585
$340$	1.38057e14	+	3.56933e13i	1.64788	+	0.426042i
$341$	1.07139e14			1.25834
$342$			7.27834e13i			0.841180i
$343$	−6.75271e13	−	6.75271e13i	−0.767998	−	0.767998i
$344$	−1.13861e13			−0.127439
$345$	−1.35961e14	−	1.35961e14i	−1.49765	−	1.49765i
$346$	4.50099e13	−	4.50099e13i	0.487966	−	0.487966i
$347$	4.88012e13	−	4.88012e13i	0.520737	−	0.520737i	−0.397057	−	0.917794i	$-0.629969\pi$
$347$	4.88012e13	−	4.88012e13i	0.520737	−	0.520737i	0.917794	+	0.397057i	$0.129969\pi$
$348$			7.88807e13i			0.828485i
$349$			4.20380e13i			0.434612i	0.976104	+	0.217306i	$0.0697270\pi$
$349$			4.20380e13i			0.434612i	−0.976104	+	0.217306i	$0.930273\pi$
$350$	1.01677e14	−	1.01677e14i	1.03478	−	1.03478i
$351$	−3.91240e13	+	3.91240e13i	−0.391971	+	0.391971i
$352$	−1.08583e14	−	1.08583e14i	−1.07097	−	1.07097i
$353$	−1.12451e14			−1.09195			−0.545973	−	0.837803i	$-0.683840\pi$
$353$	−1.12451e14			−1.09195			−0.545973	+	0.837803i	$0.683840\pi$
$354$	2.16763e14	+	2.16763e14i	2.07236	+	2.07236i
$355$		−	2.35192e14i		−	2.21394i
$356$	−1.26823e14			−1.17550
$357$	1.42476e14	−	8.39385e13i	1.30037	−	0.766101i
$358$	−2.44355e14			−2.19616
$359$		−	5.23536e13i		−	0.463369i	−0.972791	−	0.231685i	$-0.925576\pi$
$359$		−	5.23536e13i		−	0.463369i	0.972791	−	0.231685i	$-0.0744237\pi$
$360$	−6.15244e13	−	6.15244e13i	−0.536270	−	0.536270i
$361$	1.11197e14			0.954564
$362$	1.80690e14	+	1.80690e14i	1.52769	+	1.52769i
$363$	−1.86588e13	+	1.86588e13i	−0.155380	+	0.155380i
$364$	−1.28630e13	+	1.28630e13i	−0.105508	+	0.105508i
$365$			2.57759e14i			2.08259i
$366$		−	4.00657e14i		−	3.18880i
$367$	−5.42816e12	+	5.42816e12i	−0.0425588	+	0.0425588i	−0.728066	−	0.685507i	$-0.759581\pi$
$367$	−5.42816e12	+	5.42816e12i	−0.0425588	+	0.0425588i	0.685507	+	0.728066i	$0.259581\pi$
$368$	5.71391e13	−	5.71391e13i	0.441337	−	0.441337i
$369$	−2.70879e14	−	2.70879e14i	−2.06125	−	2.06125i
$370$	−7.89977e13			−0.592250
$371$	−4.25506e13	−	4.25506e13i	−0.314304	−	0.314304i
$372$			3.55449e14i			2.58697i
$373$	−2.83706e13			−0.203456			−0.101728	−	0.994812i	$-0.532437\pi$
$373$	−2.83706e13			−0.203456			−0.101728	+	0.994812i	$0.532437\pi$
$374$	2.10925e14	+	5.45325e13i	1.49051	+	0.385356i
$375$	−1.16760e14			−0.813059
$376$		−	1.74854e13i		−	0.119989i
$377$	−6.73933e12	−	6.73933e12i	−0.0455763	−	0.0455763i
$378$	−5.63351e14			−3.75469
$379$	−8.04941e13	−	8.04941e13i	−0.528747	−	0.528747i	0.391451	−	0.920199i	$-0.371973\pi$
$379$	−8.04941e13	−	8.04941e13i	−0.528747	−	0.528747i	−0.920199	+	0.391451i	$0.871973\pi$
$380$	3.96250e13	−	3.96250e13i	0.256543	−	0.256543i
$381$	2.65007e14	−	2.65007e14i	1.69110	−	1.69110i
$382$			2.27367e14i			1.43014i
$383$			2.72444e14i			1.68921i	0.535390	+	0.844605i	$0.320165\pi$
$383$			2.72444e14i			1.68921i	−0.535390	+	0.844605i	$0.679835\pi$
$384$	8.20197e13	−	8.20197e13i	0.501299	−	0.501299i
$385$	1.46643e14	−	1.46643e14i	0.883545	−	0.883545i
$386$	1.05496e14	+	1.05496e14i	0.626620	+	0.626620i
$387$	3.17184e14			1.85738
$388$	1.23105e13	+	1.23105e13i	0.0710727	+	0.0710727i
$389$			7.51145e13i			0.427564i	0.976881	+	0.213782i	$0.0685782\pi$
$389$			7.51145e13i			0.427564i	−0.976881	+	0.213782i	$0.931422\pi$
$390$	1.27521e14			0.715690
$391$	−3.29609e13	+	1.27489e14i	−0.182401	+	0.705503i
$392$	1.31087e13			0.0715295
$393$		−	2.02634e14i		−	1.09032i
$394$	3.09604e14	+	3.09604e14i	1.64277	+	1.64277i
$395$	−1.29575e14			−0.678014
$396$	−4.41154e14	−	4.41154e14i	−2.27649	−	2.27649i
$397$	−1.48745e14	+	1.48745e14i	−0.756998	+	0.756998i	−0.975775	−	0.218777i	$-0.929793\pi$
$397$	−1.48745e14	+	1.48745e14i	−0.756998	+	0.756998i	0.218777	+	0.975775i	$0.429793\pi$
$398$	−1.35561e13	+	1.35561e13i	−0.0680421	+	0.0680421i
$399$		−	6.49852e13i		−	0.321709i
$400$		−	2.24484e14i		−	1.09611i
$401$	−2.78174e14	+	2.78174e14i	−1.33974	+	1.33974i	−0.443439	+	0.896304i	$0.646242\pi$
$401$	−2.78174e14	+	2.78174e14i	−1.33974	+	1.33974i	−0.896304	+	0.443439i	$0.853758\pi$
$402$	−5.96880e13	+	5.96880e13i	−0.283559	+	0.283559i
$403$	−3.03686e13	−	3.03686e13i	−0.142314	−	0.142314i
$404$	−7.36606e13			−0.340516
$405$	8.46335e14	+	8.46335e14i	3.85958	+	3.85958i
$406$		−	9.70406e13i		−	0.436576i
$407$	−6.39575e13			−0.283872
$408$	−2.04278e13	+	7.90122e13i	−0.0894522	+	0.345990i
$409$	−1.55798e14			−0.673106			−0.336553	−	0.941665i	$-0.609261\pi$
$409$	−1.55798e14			−0.673106			−0.336553	+	0.941665i	$0.609261\pi$
$410$			5.56588e14i			2.37259i
$411$	−4.38925e14	−	4.38925e14i	−1.84612	−	1.84612i
$412$	−2.38625e14			−0.990334
$413$	−1.41310e14	−	1.41310e14i	−0.578694	−	0.578694i
$414$	5.03182e14	−	5.03182e14i	2.03340	−	2.03340i
$415$	2.24511e14	−	2.24511e14i	0.895310	−	0.895310i
$416$			6.15557e13i			0.242245i
$417$		−	7.02678e14i		−	2.72903i
$418$	6.05395e13	−	6.05395e13i	0.232043	−	0.232043i
$419$	−2.33178e14	+	2.33178e14i	−0.882086	+	0.882086i	−0.993746	−	0.111660i	$-0.964383\pi$
$419$	−2.33178e14	+	2.33178e14i	−0.882086	+	0.882086i	0.111660	+	0.993746i	$0.464383\pi$
$420$	4.86513e14	+	4.86513e14i	1.81645	+	1.81645i
$421$	2.74640e14			1.01208			0.506038	−	0.862511i	$-0.331110\pi$
$421$	2.74640e14			1.01208			0.506038	+	0.862511i	$0.331110\pi$
$422$	−3.33539e14	−	3.33539e14i	−1.21319	−	1.21319i
$423$			4.87093e14i			1.74880i
$424$	2.96980e13			0.105248
$425$	1.85687e14	+	3.15182e14i	0.649595	+	1.10261i
$426$	1.19213e15			4.11690
$427$			2.61194e14i			0.890451i
$428$	−1.01910e13	−	1.01910e13i	−0.0342985	−	0.0342985i
$429$	1.03242e14			0.343038
$430$	−3.25867e14	−	3.25867e14i	−1.06897	−	1.06897i
$431$	2.44218e14	−	2.44218e14i	0.790955	−	0.790955i	−0.190694	−	0.981649i	$-0.561074\pi$
$431$	2.44218e14	−	2.44218e14i	0.790955	−	0.790955i	0.981649	+	0.190694i	$0.0610739\pi$
$432$	−6.21891e14	+	6.21891e14i	−1.98863	+	1.98863i
$433$			1.44356e14i			0.455777i	0.973687	+	0.227888i	$0.0731822\pi$
$433$			1.44356e14i			0.455777i	−0.973687	+	0.227888i	$0.926818\pi$
$434$		−	4.37281e14i		−	1.36322i
$435$	−2.54900e14	+	2.54900e14i	−0.784656	+	0.784656i
$436$	−3.10716e14	+	3.10716e14i	−0.944469	+	0.944469i
$437$	3.65916e13	+	3.65916e13i	0.109833	+	0.109833i
$438$	−1.30652e15			−3.87265
$439$	−3.38317e14	−	3.38317e14i	−0.990306	−	0.990306i	0.00964794	−	0.999953i	$-0.496929\pi$
$439$	−3.38317e14	−	3.38317e14i	−0.990306	−	0.990306i	−0.999953	+	0.00964794i	$0.996929\pi$
$440$			1.02349e14i			0.295865i
$441$	−3.65170e14			−1.04252
$442$	−4.43296e13	−	7.52442e13i	−0.124989	−	0.212154i
$443$	−4.00118e13			−0.111421			−0.0557106	−	0.998447i	$-0.517742\pi$
$443$	−4.00118e13			−0.111421			−0.0557106	+	0.998447i	$0.517742\pi$
$444$		−	2.12189e14i		−	0.583603i
$445$	−4.09823e14	−	4.09823e14i	−1.11331	−	1.11331i
$446$	6.12680e14			1.64396
$447$	6.00933e14	+	6.00933e14i	1.59270	+	1.59270i
$448$	−2.61799e14	+	2.61799e14i	−0.685392	+	0.685392i
$449$	1.97846e14	−	1.97846e14i	0.511650	−	0.511650i	−0.403382	−	0.915032i	$-0.632165\pi$
$449$	1.97846e14	−	1.97846e14i	0.511650	−	0.511650i	0.915032	+	0.403382i	$0.132165\pi$
$450$		−	1.97687e15i		−	5.05021i
$451$			4.50621e14i			1.13721i
$452$	5.17512e14	−	5.17512e14i	1.29021	−	1.29021i
$453$	−1.52933e13	+	1.52933e13i	−0.0376670	+	0.0376670i
$454$	−7.06401e13	−	7.06401e13i	−0.171888	−	0.171888i
$455$	−8.31325e13			−0.199852
$456$	2.26780e13	+	2.26780e13i	0.0538640	+	0.0538640i
$457$		−	1.66674e14i		−	0.391138i	−0.980690	−	0.195569i	$-0.937345\pi$
$457$		−	1.66674e14i		−	0.391138i	0.980690	−	0.195569i	$-0.0626554\pi$
$458$	−2.70786e13			−0.0627866
$459$	3.58740e14	−	1.38756e15i	0.821882	−	3.17894i
$460$	−5.47888e14			−1.24029
$461$			3.33407e14i			0.745796i	0.927872	+	0.372898i	$0.121636\pi$
$461$			3.33407e14i			0.745796i	−0.927872	+	0.372898i	$0.878364\pi$
$462$	7.43300e14	+	7.43300e14i	1.64298	+	1.64298i
$463$	5.65838e13			0.123594			0.0617969	−	0.998089i	$-0.480317\pi$
$463$	5.65838e13			0.123594			0.0617969	+	0.998089i	$0.480317\pi$
$464$	−1.07124e14	−	1.07124e14i	−0.231227	−	0.231227i
$465$	−1.14862e15	+	1.14862e15i	−2.45011	+	2.45011i
$466$	5.32900e14	−	5.32900e14i	1.12337	−	1.12337i
$467$			1.51959e14i			0.316579i	0.987393	+	0.158290i	$0.0505980\pi$
$467$			1.51959e14i			0.316579i	−0.987393	+	0.158290i	$0.949402\pi$
$468$			2.50091e14i			0.514927i
$469$	3.89114e13	−	3.89114e13i	0.0791820	−	0.0791820i
$470$	5.00427e14	−	5.00427e14i	1.00647	−	1.00647i
$471$	9.79556e14	+	9.79556e14i	1.94722	+	1.94722i
$472$	9.86269e13			0.193782
$473$	−2.63826e14	−	2.63826e14i	−0.512367	−	0.512367i
$474$		−	6.56786e14i		−	1.26079i
$475$	1.43759e14			0.272784
$476$	1.17945e14	−	4.56195e14i	0.221228	−	0.855681i
$477$	−8.27299e14			−1.53395
$478$			1.05586e15i			1.93531i
$479$	5.21754e14	+	5.21754e14i	0.945410	+	0.945410i	0.998585	−	0.0531751i	$-0.0169342\pi$
$479$	5.21754e14	+	5.21754e14i	0.945410	+	0.945410i	−0.0531751	+	0.998585i	$0.516934\pi$
$480$	2.32821e15			4.17057
$481$	1.81288e13	+	1.81288e13i	0.0321049	+	0.0321049i
$482$	2.84467e14	−	2.84467e14i	0.498050	−	0.498050i
$483$	−4.49270e14	+	4.49270e14i	−0.777675	+	0.777675i
$484$			7.51898e13i			0.128680i
$485$			7.95622e13i			0.134625i
$486$	−2.26578e15	+	2.26578e15i	−3.79069	+	3.79069i
$487$	−3.08122e14	+	3.08122e14i	−0.509698	+	0.509698i	−0.914434	−	0.404736i	$-0.867364\pi$
$487$	−3.08122e14	+	3.08122e14i	−0.509698	+	0.509698i	0.404736	+	0.914434i	$0.367364\pi$
$488$	−9.11495e13	−	9.11495e13i	−0.149089	−	0.149089i
$489$	7.37032e14			1.19203
$490$	3.75166e14	+	3.75166e14i	0.599992	+	0.599992i
$491$		−	1.04047e15i		−	1.64543i	−0.568452	−	0.822716i	$-0.692457\pi$
$491$		−	1.04047e15i		−	1.64543i	0.568452	−	0.822716i	$-0.307543\pi$
$492$	−1.49501e15			−2.33795
$493$	2.39015e14	+	6.17950e13i	0.369630	+	0.0955642i
$494$	−3.43200e13			−0.0524866
$495$		−	2.85115e15i		−	4.31212i
$496$	−4.82720e14	−	4.82720e14i	−0.722015	−	0.722015i
$497$	−7.77165e14			−1.14962
$498$	1.13799e15	+	1.13799e15i	1.66486	+	1.66486i
$499$	−9.57924e14	+	9.57924e14i	−1.38605	+	1.38605i	−0.552604	+	0.833444i	$0.686366\pi$
$499$	−9.57924e14	+	9.57924e14i	−1.38605	+	1.38605i	−0.833444	+	0.552604i	$0.813634\pi$
$500$	−2.35256e14	+	2.35256e14i	−0.336671	+	0.336671i
$501$		−	3.47652e14i		−	0.492081i
$502$			5.76986e14i			0.807783i
$503$	9.66554e14	−	9.66554e14i	1.33845	−	1.33845i	0.440887	−	0.897563i	$-0.354664\pi$
$503$	9.66554e14	−	9.66554e14i	1.33845	−	1.33845i	0.897563	−	0.440887i	$-0.145336\pi$
$504$	−2.03301e14	+	2.03301e14i	−0.278465	+	0.278465i
$505$	−2.38032e14	−	2.38032e14i	−0.322502	−	0.322502i
$506$	−8.37069e14			−1.12185
$507$	9.97482e14	+	9.97482e14i	1.32239	+	1.32239i
$508$		−	1.06791e15i		−	1.40050i
$509$	8.39095e14			1.08859			0.544294	−	0.838895i	$-0.316798\pi$
$509$	8.39095e14			1.08859			0.544294	+	0.838895i	$0.316798\pi$
$510$	−2.84595e15	+	1.67667e15i	−3.65250	+	2.15185i
$511$	8.51737e14			1.08141
$512$			1.10504e15i			1.38802i
$513$	−3.98256e14	−	3.98256e14i	−0.494899	−	0.494899i
$514$	2.08077e14			0.255816
$515$	−7.71110e14	−	7.71110e14i	−0.937943	−	0.937943i
$516$	8.75284e14	−	8.75284e14i	1.05336	−	1.05336i
$517$	4.05152e14	−	4.05152e14i	0.482414	−	0.482414i
$518$			2.61040e14i			0.307534i
$519$			7.81352e14i			0.910807i
$520$	2.90109e13	−	2.90109e13i	0.0334613	−	0.0334613i
$521$	7.99935e14	−	7.99935e14i	0.912950	−	0.912950i	−0.0835530	−	0.996503i	$-0.526627\pi$
$521$	7.99935e14	−	7.99935e14i	0.912950	−	0.912950i	0.996503	+	0.0835530i	$0.0266268\pi$
$522$	−9.43366e14	−	9.43366e14i	−1.06535	−	1.06535i
$523$	1.69892e14			0.189851			0.0949255	−	0.995484i	$-0.469739\pi$
$523$	1.69892e14			0.189851			0.0949255	+	0.995484i	$0.469739\pi$
$524$	−4.08280e14	−	4.08280e14i	−0.451477	−	0.451477i
$525$			1.76506e15i			1.93145i
$526$	−5.77457e14			−0.625314
$527$	1.07704e15	+	2.78459e14i	1.15418	+	0.298403i
$528$	1.64108e15			1.74037
$529$			4.46863e14i			0.468995i
$530$	8.49947e14	+	8.49947e14i	0.882824	+	0.882824i
$531$	−2.74746e15			−2.82430
$532$	−1.30937e14	−	1.30937e14i	−0.133213	−	0.133213i
$533$	1.27729e14	−	1.27729e14i	0.128614	−	0.128614i
$534$	2.07729e15	−	2.07729e15i	2.07024	−	2.07024i
$535$		−	6.58636e13i		−	0.0649680i
$536$			2.71580e13i			0.0265150i
$537$	2.12095e15	−	2.12095e15i	2.04961	−	2.04961i
$538$	4.82449e14	−	4.82449e14i	0.461475	−	0.461475i
$539$	3.03739e14	+	3.03739e14i	0.287582	+	0.287582i
$540$	5.96311e15			5.58865
$541$	−4.28529e14	−	4.28529e14i	−0.397554	−	0.397554i	0.479816	−	0.877369i	$-0.340704\pi$
$541$	−4.28529e14	−	4.28529e14i	−0.397554	−	0.397554i	−0.877369	+	0.479816i	$0.840704\pi$
$542$			7.77459e14i			0.713973i
$543$	−3.13669e15			−2.85150
$544$	−8.09348e14	−	1.37377e15i	−0.728352	−	1.23629i
$545$	−2.00813e15			−1.78901
$546$		−	4.21378e14i		−	0.371631i
$547$	1.07108e15	+	1.07108e15i	0.935168	+	0.935168i	0.998023	−	0.0628545i	$-0.0200204\pi$
$547$	1.07108e15	+	1.07108e15i	0.935168	+	0.935168i	−0.0628545	+	0.998023i	$0.520020\pi$
$548$	−1.76875e15			−1.52888
$549$	2.53916e15	+	2.53916e15i	2.17291	+	2.17291i
$550$	−1.64431e15	+	1.64431e15i	−1.39312	+	1.39312i
$551$	6.86019e13	−	6.86019e13i	0.0575443	−	0.0575443i
$552$		−	3.13565e14i		−	0.260413i
$553$			4.28168e14i			0.352068i
$554$	−6.87688e13	+	6.87688e13i	−0.0559871	+	0.0559871i
$555$	6.85683e14	−	6.85683e14i	0.552728	−	0.552728i
$556$	−1.41580e15	−	1.41580e15i	−1.13003	−	1.13003i
$557$	−1.84170e15			−1.45551			−0.727755	−	0.685837i	$-0.759436\pi$
$557$	−1.84170e15			−1.45551			−0.727755	+	0.685837i	$0.759436\pi$
$558$	−4.25096e15	−	4.25096e15i	−3.32659	−	3.32659i
$559$			1.49563e14i			0.115894i
$560$	−1.32142e15			−1.01393
$561$	−2.30411e15	+	1.35745e15i	−1.75068	+	1.03140i
$562$	−2.45750e15			−1.84903
$563$		−	2.48406e15i		−	1.85083i	−0.378959	−	0.925413i	$-0.623718\pi$
$563$		−	2.48406e15i		−	1.85083i	0.378959	−	0.925413i	$-0.376282\pi$
$564$	1.34416e15	+	1.34416e15i	0.991779	+	0.991779i
$565$	3.34465e15			2.44390
$566$	−8.44866e14	−	8.44866e14i	−0.611360	−	0.611360i
$567$	2.79662e15	−	2.79662e15i	2.00414	−	2.00414i
$568$	2.71209e14	−	2.71209e14i	0.192481	−	0.192481i
$569$			2.62629e15i			1.84597i	0.384833	+	0.922986i	$0.374259\pi$
$569$			2.62629e15i			1.84597i	−0.384833	+	0.922986i	$0.625741\pi$
$570$			1.29808e15i			0.903625i
$571$	1.23370e15	−	1.23370e15i	0.850574	−	0.850574i	−0.139629	−	0.990204i	$-0.544591\pi$
$571$	1.23370e15	−	1.23370e15i	0.850574	−	0.850574i	0.990204	+	0.139629i	$0.0445911\pi$
$572$	2.08019e14	−	2.08019e14i	0.142045	−	0.142045i
$573$	−1.97349e15	−	1.97349e15i	−1.33470	−	1.33470i
$574$	1.83919e15			1.23200
$575$	−9.93865e14	−	9.93865e14i	−0.659408	−	0.659408i
$576$			5.09008e15i			3.34504i
$577$	8.20188e14			0.533883			0.266942	−	0.963713i	$-0.413987\pi$
$577$	8.20188e14			0.533883			0.266942	+	0.963713i	$0.413987\pi$
$578$	1.97865e15	+	1.09641e15i	1.27575	+	0.706919i
$579$	−1.83136e15			−1.16961
$580$			1.02718e15i			0.649819i
$581$	−7.41873e14	−	7.41873e14i	−0.464902	−	0.464902i
$582$	−4.03281e14			−0.250341
$583$	6.88127e14	+	6.88127e14i	0.423147	+	0.423147i
$584$	−2.97233e14	+	2.97233e14i	−0.181061	+	0.181061i
$585$	−8.08160e14	+	8.08160e14i	−0.487686	+	0.487686i
$586$			3.39635e15i			2.03037i
$587$			3.08301e14i			0.182585i	0.995824	+	0.0912927i	$0.0290999\pi$
$587$			3.08301e14i			0.182585i	−0.995824	+	0.0912927i	$0.970900\pi$
$588$	−1.00770e15	+	1.00770e15i	−0.591231	+	0.591231i
$589$	3.09132e14	−	3.09132e14i	0.179684	−	0.179684i
$590$	2.82267e15	+	2.82267e15i	1.62545	+	1.62545i
$591$	−5.37459e15			−3.06630
$592$	2.88165e14	+	2.88165e14i	0.162881	+	0.162881i
$593$			1.88138e15i			1.05360i	0.849989	+	0.526800i	$0.176608\pi$
$593$			1.88138e15i			1.05360i	−0.849989	+	0.526800i	$0.823392\pi$
$594$	9.11050e15			5.05495
$595$	1.85531e15	−	1.09304e15i	1.01994	−	0.600889i
$596$	2.42160e15			1.31901
$597$		−	2.35328e14i		−	0.127003i
$598$	2.37268e14	+	2.37268e14i	0.126877	+	0.126877i
$599$	3.86622e14			0.204851			0.102426	−	0.994741i	$-0.467340\pi$
$599$	3.86622e14			0.204851			0.102426	+	0.994741i	$0.467340\pi$
$600$	−6.15957e14	−	6.15957e14i	−0.323384	−	0.323384i
$601$	−1.43541e15	+	1.43541e15i	−0.746736	+	0.746736i	−0.973865	−	0.227129i	$-0.927066\pi$
$601$	−1.43541e15	+	1.43541e15i	−0.746736	+	0.746736i	0.227129	+	0.973865i	$0.427066\pi$
$602$	−1.07679e15	+	1.07679e15i	−0.555074	+	0.555074i
$603$		−	7.56544e14i		−	0.386446i
$604$			6.16280e13i			0.0311943i
$605$	−2.42973e14	+	2.42973e14i	−0.121872	+	0.121872i
$606$	1.20652e15	−	1.20652e15i	0.599704	−	0.599704i
$607$	−3.37922e14	−	3.37922e14i	−0.166448	−	0.166448i	0.618968	−	0.785416i	$-0.287551\pi$
$607$	−3.37922e14	−	3.37922e14i	−0.166448	−	0.166448i	−0.785416	+	0.618968i	$0.787551\pi$
$608$	−6.26597e14			−0.305857
$609$	8.42290e14	+	8.42290e14i	0.407443	+	0.407443i
$610$		−	5.21734e15i		−	2.50112i
$611$	−2.29682e14			−0.109119
$612$	−3.28825e15	−	5.58141e15i	−1.54822	−	2.62791i
$613$	1.77359e15			0.827600			0.413800	−	0.910368i	$-0.364201\pi$
$613$	1.77359e15			0.827600			0.413800	+	0.910368i	$0.364201\pi$
$614$		−	2.05007e15i		−	0.948075i
$615$	−4.83106e15	−	4.83106e15i	−2.21426	−	2.21426i
$616$	3.38201e14			0.153632
$617$	6.43780e14	+	6.43780e14i	0.289847	+	0.289847i	0.837020	−	0.547173i	$-0.184296\pi$
$617$	6.43780e14	+	6.43780e14i	0.289847	+	0.289847i	−0.547173	+	0.837020i	$0.684296\pi$
$618$	3.90857e15	−	3.90857e15i	1.74414	−	1.74414i
$619$	−1.47541e14	+	1.47541e14i	−0.0652550	+	0.0652550i	−0.738981	−	0.673726i	$-0.764693\pi$
$619$	−1.47541e14	+	1.47541e14i	−0.0652550	+	0.0652550i	0.673726	+	0.738981i	$0.264693\pi$
$620$			4.62865e15i			2.02908i
$621$			5.50662e15i			2.39266i
$622$	−2.42849e15	+	2.42849e15i	−1.04590	+	1.04590i
$623$	−1.35422e15	+	1.35422e15i	−0.578101	+	0.578101i
$624$	−4.65165e14	−	4.65165e14i	−0.196830	−	0.196830i
$625$	1.53068e15			0.642014
$626$	4.52353e14	+	4.52353e14i	0.188070	+	0.188070i
$627$			1.05094e15i			0.433117i
$628$	3.94735e15			1.61260
$629$	−6.42952e14	−	1.66229e14i	−0.260376	−	0.0673175i
$630$	−1.16368e16			−4.67155
$631$		−	2.32603e15i		−	0.925667i	−0.886445	−	0.462833i	$-0.846833\pi$
$631$		−	2.32603e15i		−	0.925667i	0.886445	−	0.462833i	$-0.153167\pi$
$632$	−1.49419e14	−	1.49419e14i	−0.0589469	−	0.0589469i
$633$	5.79009e15			2.26446
$634$	−3.55152e15	−	3.55152e15i	−1.37697	−	1.37697i
$635$	3.45090e15	−	3.45090e15i	1.32641	−	1.32641i
$636$	−2.28297e15	+	2.28297e15i	−0.869934	+	0.869934i
$637$		−	1.72190e14i		−	0.0650492i
$638$			1.56934e15i			0.587763i
$639$	−7.55510e15	+	7.55510e15i	−2.80534	+	2.80534i
$640$	1.06806e15	−	1.06806e15i	0.393192	−	0.393192i
$641$	−3.92894e14	−	3.92894e14i	−0.143402	−	0.143402i	0.631761	−	0.775163i	$-0.282332\pi$
$641$	−3.92894e14	−	3.92894e14i	−0.143402	−	0.143402i	−0.775163	+	0.631761i	$0.782332\pi$
$642$	3.33846e14			0.120810
$643$	−4.93898e14	−	4.93898e14i	−0.177205	−	0.177205i	0.612931	−	0.790136i	$-0.289990\pi$
$643$	−4.93898e14	−	4.93898e14i	−0.177205	−	0.177205i	−0.790136	+	0.612931i	$0.789990\pi$
$644$			1.81044e15i			0.644038i
$645$	5.65690e15			1.99526
$646$	7.65937e14	−	4.51246e14i	0.267864	−	0.157810i
$647$	8.08319e14			0.280291			0.140146	−	0.990131i	$-0.455243\pi$
$647$	8.08319e14			0.280291			0.140146	+	0.990131i	$0.455243\pi$
$648$			1.95189e15i			0.671108i
$649$	2.28527e15	+	2.28527e15i	0.779097	+	0.779097i
$650$	9.32164e14			0.315115
$651$	3.79550e15	+	3.79550e15i	1.27225	+	1.27225i
$652$	1.48502e15	−	1.48502e15i	0.493596	−	0.493596i
$653$	−1.82112e15	+	1.82112e15i	−0.600227	+	0.600227i	−0.940373	−	0.340146i	$-0.889524\pi$
$653$	−1.82112e15	+	1.82112e15i	−0.600227	+	0.600227i	0.340146	+	0.940373i	$0.389524\pi$
$654$		−	1.01787e16i		−	3.32672i
$655$		−	2.63868e15i		−	0.855186i
$656$	2.03030e15	−	2.03030e15i	0.652513	−	0.652513i
$657$	8.28004e15	−	8.28004e15i	2.63890	−	2.63890i
$658$	−1.65361e15	−	1.65361e15i	−0.522625	−	0.522625i
$659$	−2.34325e15			−0.734427			−0.367213	−	0.930137i	$-0.619688\pi$
$659$	−2.34325e15			−0.734427			−0.367213	+	0.930137i	$0.619688\pi$
$660$	−7.86787e15	−	7.86787e15i	−2.44549	−	2.44549i
$661$			2.15849e15i			0.665337i	0.943044	+	0.332669i	$0.107949\pi$
$661$			2.15849e15i			0.665337i	−0.943044	+	0.332669i	$0.892051\pi$
$662$	−8.23849e15			−2.51842
$663$	1.03787e15	+	2.68332e14i	0.314644	+	0.0813482i
$664$	5.17786e14			0.155678
$665$		−	8.46234e14i		−	0.252331i
$666$	2.53766e15	+	2.53766e15i	0.750455	+	0.750455i
$667$	−9.48548e14			−0.278206
$668$	−7.00472e14	−	7.00472e14i	−0.203761	−	0.203761i
$669$	−5.31793e15	+	5.31793e15i	−1.53426	+	1.53426i
$670$	−7.77254e14	+	7.77254e14i	−0.222409	+	0.222409i
$671$		−	4.22402e15i		−	1.19882i
$672$		−	7.69332e15i		−	2.16562i
$673$	1.35032e15	−	1.35032e15i	0.377010	−	0.377010i	−0.493012	−	0.870022i	$-0.664104\pi$
$673$	1.35032e15	−	1.35032e15i	0.377010	−	0.377010i	0.870022	+	0.493012i	$0.164104\pi$
$674$	−3.74442e15	+	3.74442e15i	−1.03694	+	1.03694i
$675$	1.08170e16	+	1.08170e16i	2.97124	+	2.97124i
$676$	4.01959e15			1.09515
$677$	−2.41456e15	−	2.41456e15i	−0.652530	−	0.652530i	0.301072	−	0.953601i	$-0.402656\pi$
$677$	−2.41456e15	−	2.41456e15i	−0.652530	−	0.652530i	−0.953601	+	0.301072i	$0.902656\pi$
$678$			1.69532e16i			4.54452i
$679$	2.62905e14			0.0699060
$680$	−2.66010e14	+	1.02889e15i	−0.0701616	+	0.271376i
$681$	1.22628e15			0.320834
$682$			7.07170e15i			1.83531i
$683$	3.08693e15	+	3.08693e15i	0.794717	+	0.794717i	0.982257	−	0.187540i	$-0.0600513\pi$
$683$	3.08693e15	+	3.08693e15i	0.794717	+	0.794717i	−0.187540	+	0.982257i	$0.560051\pi$
$684$	−2.54576e15			−0.650143
$685$	−5.71566e15	−	5.71566e15i	−1.44800	−	1.44800i
$686$	4.45713e15	−	4.45713e15i	1.12014	−	1.12014i
$687$	2.35037e14	−	2.35037e14i	0.0585967	−	0.0585967i
$688$			2.37737e15i			0.587977i
$689$		−	3.90101e14i		−	0.0957130i
$690$	8.97414e15	−	8.97414e15i	2.18435	−	2.18435i
$691$	4.22697e15	−	4.22697e15i	1.02070	−	1.02070i	0.0209237	−	0.999781i	$-0.493339\pi$
$691$	4.22697e15	−	4.22697e15i	1.02070	−	1.02070i	0.999781	−	0.0209237i	$-0.00666072\pi$
$692$	1.57432e15	+	1.57432e15i	0.377146	+	0.377146i
$693$	−9.42131e15			−2.23912
$694$	3.22113e15	+	3.22113e15i	0.759505	+	0.759505i
$695$		−	9.15025e15i		−	2.14051i
$696$	−5.87872e14			−0.136437
$697$	−1.17119e15	+	4.53000e15i	−0.269678	+	1.04308i
$698$	−2.77472e15			−0.633891
$699$			9.25090e15i			2.09681i
$700$	3.55636e15	+	3.55636e15i	0.799774	+	0.799774i
$701$	−3.74331e15			−0.835232			−0.417616	−	0.908624i	$-0.637134\pi$
$701$	−3.74331e15			−0.835232			−0.417616	+	0.908624i	$0.637134\pi$
$702$	−2.58238e15	−	2.58238e15i	−0.571697	−	0.571697i
$703$	−1.84540e14	+	1.84540e14i	−0.0405355	+	0.0405355i
$704$	4.23380e15	−	4.23380e15i	0.922744	−	0.922744i
$705$			8.68719e15i			1.87862i
$706$		−	7.42232e15i		−	1.59263i
$707$	−7.86550e14	+	7.86550e14i	−0.167463	+	0.167463i
$708$	−7.58175e15	+	7.58175e15i	−1.60172	+	1.60172i
$709$	−5.95658e15	−	5.95658e15i	−1.24866	−	1.24866i	−0.956314	−	0.292343i	$-0.905565\pi$
$709$	−5.95658e15	−	5.95658e15i	−1.24866	−	1.24866i	−0.292343	−	0.956314i	$-0.594435\pi$
$710$	1.55238e16			3.22908
$711$	4.16237e15	+	4.16237e15i	0.859129	+	0.859129i
$712$		−	9.45167e14i		−	0.193584i
$713$	−4.27432e15			−0.868709
$714$	5.54037e15	+	9.40412e15i	1.11737	+	1.89661i
$715$	1.34442e15			0.269061
$716$		−	8.54686e15i		−	1.69740i
$717$	−9.16460e15	−	9.16460e15i	−1.80617	−	1.80617i
$718$	3.45561e15			0.675834
$719$	8.18936e14	+	8.18936e14i	0.158943	+	0.158943i	0.782098	−	0.623155i	$-0.214150\pi$
$719$	8.18936e14	+	8.18936e14i	0.158943	+	0.158943i	−0.623155	+	0.782098i	$0.714150\pi$
$720$	−1.28460e16	+	1.28460e16i	−2.47423	+	2.47423i
$721$	−2.54805e15	+	2.54805e15i	−0.487039	+	0.487039i
$722$			7.33960e15i			1.39225i
$723$			4.93822e15i			0.929630i
$724$	−6.32002e15	+	6.32002e15i	−1.18075	+	1.18075i
$725$	−1.86330e15	+	1.86330e15i	−0.345480	+	0.345480i
$726$	−1.23157e15	−	1.23157e15i	−0.226625	−	0.226625i
$727$	5.93011e15			1.08299			0.541494	−	0.840705i	$-0.317859\pi$
$727$	5.93011e15			1.08299			0.541494	+	0.840705i	$0.317859\pi$
$728$	−9.58635e13	−	9.58635e13i	−0.0173752	−	0.0173752i
$729$		−	1.92367e16i		−	3.46042i
$730$	−1.70134e16			−3.03750
$731$	−1.96649e15	−	3.33788e15i	−0.348455	−	0.591460i
$732$	1.40139e16			2.46460
$733$		−	2.97348e15i		−	0.519031i	−0.965739	−	0.259516i	$-0.916437\pi$
$733$		−	2.97348e15i		−	0.519031i	0.965739	−	0.259516i	$-0.0835629\pi$
$734$	−3.58286e14	−	3.58286e14i	−0.0620728	−	0.0620728i
$735$	−6.51272e15			−1.11991
$736$	4.33193e15	+	4.33193e15i	0.739355	+	0.739355i
$737$	−6.29274e14	+	6.29274e14i	−0.106603	+	0.106603i
$738$	1.78794e16	−	1.78794e16i	3.00637	−	3.00637i
$739$		−	3.01358e15i		−	0.502965i	−0.967862	−	0.251483i	$-0.919082\pi$
$739$		−	3.01358e15i		−	0.502965i	0.967862	−	0.251483i	$-0.0809182\pi$
$740$		−	2.76312e15i		−	0.457747i
$741$	2.97889e14	−	2.97889e14i	0.0489841	−	0.0489841i
$742$	2.80856e15	−	2.80856e15i	0.458418	−	0.458418i
$743$	2.80386e15	+	2.80386e15i	0.454275	+	0.454275i	0.896771	−	0.442496i	$-0.145907\pi$
$743$	2.80386e15	+	2.80386e15i	0.454275	+	0.454275i	−0.442496	+	0.896771i	$0.645907\pi$
$744$	−2.64905e15			−0.426029
$745$	7.82532e15	+	7.82532e15i	1.24923	+	1.24923i
$746$		−	1.87260e15i		−	0.296744i
$747$	−1.44240e16			−2.26894
$748$	−1.90740e15	+	7.37756e15i	−0.297839	+	1.15200i
$749$	−2.17639e14			−0.0337355
$750$		−	7.70676e15i		−	1.18586i
$751$	7.64573e15	+	7.64573e15i	1.16788	+	1.16788i	0.982705	+	0.185179i	$0.0592864\pi$
$751$	7.64573e15	+	7.64573e15i	1.16788	+	1.16788i	0.185179	+	0.982705i	$0.440714\pi$
$752$	−3.65088e15			−0.553604
$753$	−5.00811e15	−	5.00811e15i	−0.753878	−	0.753878i
$754$	4.44830e14	−	4.44830e14i	0.0664740	−	0.0664740i
$755$	−1.99149e14	+	1.99149e14i	−0.0295440	+	0.0295440i
$756$		−	1.97045e16i		−	2.90198i
$757$			1.59222e15i			0.232796i	0.993203	+	0.116398i	$0.0371347\pi$
$757$			1.59222e15i			0.232796i	−0.993203	+	0.116398i	$0.962865\pi$
$758$	5.31302e15	−	5.31302e15i	0.771189	−	0.771189i
$759$	7.26558e15	−	7.26558e15i	1.04698	−	1.04698i
$760$	2.95312e14	+	2.95312e14i	0.0422480	+	0.0422480i
$761$	−2.56520e15			−0.364339			−0.182169	−	0.983267i	$-0.558312\pi$
$761$	−2.56520e15			−0.364339			−0.182169	+	0.983267i	$0.558312\pi$
$762$	1.74918e16	+	1.74918e16i	2.46650	+	2.46650i
$763$			6.63567e15i			0.928965i
$764$	−7.95264e15			−1.10535
$765$	7.41027e15	−	2.86620e16i	1.02258	−	3.95520i
$766$	−1.79827e16			−2.46375
$767$		−	1.29552e15i		−	0.176226i
$768$	−7.04663e15	−	7.04663e15i	−0.951688	−	0.951688i
$769$	3.93910e15			0.528205			0.264102	−	0.964495i	$-0.414924\pi$
$769$	3.93910e15			0.528205			0.264102	+	0.964495i	$0.414924\pi$
$770$	9.67921e15	+	9.67921e15i	1.28867	+	1.28867i
$771$	−1.80606e15	+	1.80606e15i	−0.238745	+	0.238745i
$772$	−3.68994e15	+	3.68994e15i	−0.484311	+	0.484311i
$773$		−	4.32017e15i		−	0.563007i	−0.959560	−	0.281504i	$-0.909167\pi$
$773$		−	4.32017e15i		−	0.563007i	0.959560	−	0.281504i	$-0.0908331\pi$
$774$			2.09358e16i			2.70903i
$775$	−8.39633e15	+	8.39633e15i	−1.07877	+	1.07877i
$776$	−9.17464e13	+	9.17464e13i	−0.0117044	+	0.0117044i
$777$	−2.26576e15	−	2.26576e15i	−0.287011	−	0.287011i
$778$	−4.95794e15			−0.623611
$779$	1.30020e15	+	1.30020e15i	0.162388	+	0.162388i
$780$			4.46031e15i			0.553153i
$781$	1.25683e16			1.54773
$782$	−8.41489e15	−	2.17559e15i	−1.02899	−	0.266035i
$783$	1.03238e16			1.25357
$784$		−	2.73703e15i		−	0.330021i
$785$	1.27557e16	+	1.27557e16i	1.52729	+	1.52729i
$786$	1.33748e16			1.59025
$787$	7.44817e15	+	7.44817e15i	0.879404	+	0.879404i	0.993473	−	0.114069i	$-0.0363885\pi$
$787$	7.44817e15	+	7.44817e15i	0.879404	+	0.879404i	−0.114069	+	0.993473i	$0.536388\pi$
$788$	−1.08291e16	+	1.08291e16i	−1.26969	+	1.26969i
$789$	5.01220e15	−	5.01220e15i	0.583586	−	0.583586i
$790$		−	8.55264e15i		−	0.988897i
$791$		−	1.10520e16i		−	1.26903i
$792$	3.28777e15	−	3.28777e15i	0.374898	−	0.374898i
$793$	−1.19730e15	+	1.19730e15i	−0.135582	+	0.135582i
$794$	−9.81793e15	−	9.81793e15i	−1.10410	−	1.10410i
$795$	−1.47547e16			−1.64782
$796$	−4.74154e14	−	4.74154e14i	−0.0525893	−	0.0525893i
$797$		−	1.27276e16i		−	1.40193i	−0.713196	−	0.700964i	$-0.752753\pi$
$797$		−	1.27276e16i		−	1.40193i	0.713196	−	0.700964i	$-0.247247\pi$
$798$	4.28935e15			0.469219
$799$	5.12592e15	−	3.01990e15i	0.556884	−	0.328084i
$800$	1.70190e16			1.83628
$801$			2.63296e16i			2.82141i
$802$	−1.83609e16	−	1.83609e16i	−1.95404	−	1.95404i
$803$	−1.37743e16			−1.45590
$804$	−2.08772e15	−	2.08772e15i	−0.219161	−	0.219161i
$805$	−5.85037e15	+	5.85037e15i	−0.609966	+	0.609966i
$806$	2.00448e15	−	2.00448e15i	0.207567	−	0.207567i
$807$			8.37509e15i			0.861361i
$808$		−	5.48968e14i		−	0.0560770i
$809$	−1.21254e16	+	1.21254e16i	−1.23021	+	1.23021i	−0.266329	+	0.963882i	$0.585811\pi$
$809$	−1.21254e16	+	1.21254e16i	−1.23021	+	1.23021i	−0.963882	+	0.266329i	$0.914189\pi$
$810$	−5.58624e16	+	5.58624e16i	−5.62927	+	5.62927i
$811$	−9.31721e15	−	9.31721e15i	−0.932548	−	0.932548i	0.0653164	−	0.997865i	$-0.479194\pi$
$811$	−9.31721e15	−	9.31721e15i	−0.932548	−	0.932548i	−0.997865	+	0.0653164i	$0.979194\pi$
$812$	3.39421e15			0.337427
$813$	−6.74817e15	−	6.74817e15i	−0.666328	−	0.666328i
$814$		−	4.22152e15i		−	0.414033i
$815$	9.59760e15			0.934966
$816$	1.64974e16	+	4.26524e15i	1.59632	+	0.412713i
$817$	−1.52246e15			−0.146327
$818$		−	1.02835e16i		−	0.981739i
$819$	2.67048e15	+	2.67048e15i	0.253237	+	0.253237i
$820$	−1.94679e16			−1.83376
$821$	1.08860e16	+	1.08860e16i	1.01855	+	1.01855i	0.999825	+	0.0187256i	$0.00596091\pi$
$821$	1.08860e16	+	1.08860e16i	1.01855	+	1.01855i	0.0187256	+	0.999825i	$0.494039\pi$
$822$	2.89713e16	−	2.89713e16i	2.69261	−	2.69261i
$823$	−4.86163e15	+	4.86163e15i	−0.448831	+	0.448831i	−0.894966	−	0.446135i	$-0.852800\pi$
$823$	−4.86163e15	+	4.86163e15i	−0.448831	+	0.448831i	0.446135	+	0.894966i	$0.352800\pi$
$824$		−	1.77840e15i		−	0.163091i
$825$		−	2.85445e16i		−	2.60031i
$826$	9.32721e15	−	9.32721e15i	0.844037	−	0.844037i
$827$	−3.19438e15	+	3.19438e15i	−0.287148	+	0.287148i	−0.835952	−	0.548803i	$-0.815084\pi$
$827$	−3.19438e15	+	3.19438e15i	−0.287148	+	0.287148i	0.548803	+	0.835952i	$0.315084\pi$
$828$	1.75999e16	+	1.75999e16i	1.57161	+	1.57161i
$829$	−1.23889e16			−1.09897			−0.549483	−	0.835505i	$-0.685175\pi$
$829$	−1.23889e16			−1.09897			−0.549483	+	0.835505i	$0.685175\pi$
$830$	1.48189e16	+	1.48189e16i	1.30583	+	1.30583i
$831$		−	1.19380e15i		−	0.104502i
$832$	−2.40015e15			−0.208718
$833$	2.26400e15	+	3.84286e15i	0.195582	+	0.331976i
$834$	4.63804e16			3.98035
$835$		−	4.52711e15i		−	0.385962i
$836$	2.11750e15	+	2.11750e15i	0.179345	+	0.179345i
$837$	4.65208e16			3.91433
$838$	−1.53910e16	−	1.53910e16i	−1.28654	−	1.28654i
$839$	−1.20910e16	+	1.20910e16i	−1.00409	+	1.00409i	−0.00409345	+	0.999992i	$0.501303\pi$
$839$	−1.20910e16	+	1.20910e16i	−1.00409	+	1.00409i	−0.999992	+	0.00409345i	$0.998697\pi$
$840$	−3.62582e15	+	3.62582e15i	−0.299137	+	0.299137i
$841$		−	1.04222e16i		−	0.854241i
$842$			1.81277e16i			1.47613i
$843$	2.13305e16	−	2.13305e16i	1.72564	−	1.72564i
$844$	1.16663e16	−	1.16663e16i	0.937667	−	0.937667i
$845$	1.29892e16	+	1.29892e16i	1.03722	+	1.03722i
$846$	−3.21506e16			−2.55066
$847$	8.02880e14	+	8.02880e14i	0.0632837	+	0.0632837i
$848$		−	6.20080e15i		−	0.485591i
$849$	1.46665e16			1.14113
$850$	−2.08036e16	+	1.22563e16i	−1.60818	+	0.947447i
$851$	2.55160e15			0.195975
$852$			4.16973e16i			3.18193i
$853$	−7.50089e15	−	7.50089e15i	−0.568713	−	0.568713i	0.363055	−	0.931768i	$-0.381734\pi$
$853$	−7.50089e15	−	7.50089e15i	−0.568713	−	0.568713i	−0.931768	+	0.363055i	$0.881734\pi$
$854$	−1.72401e16			−1.29874
$855$	−8.22654e15	−	8.22654e15i	−0.615749	−	0.615749i
$856$	7.59500e13	−	7.59500e13i	0.00564836	−	0.00564836i
$857$	3.17721e15	−	3.17721e15i	0.234774	−	0.234774i	−0.579908	−	0.814682i	$-0.696911\pi$
$857$	3.17721e15	−	3.17721e15i	0.234774	−	0.234774i	0.814682	+	0.579908i	$0.196911\pi$
$858$			6.81451e15i			0.500328i
$859$			6.10364e14i			0.0445273i	0.999752	+	0.0222637i	$0.00708733\pi$
$859$			6.10364e14i			0.0445273i	−0.999752	+	0.0222637i	$0.992913\pi$
$860$	1.13979e16	−	1.13979e16i	0.826197	−	0.826197i
$861$	−1.59637e16	+	1.59637e16i	−1.14979	+	1.14979i
$862$	1.61196e16	+	1.61196e16i	1.15362	+	1.15362i
$863$	1.37112e16			0.975023			0.487511	−	0.873117i	$-0.337905\pi$
$863$	1.37112e16			0.975023			0.487511	+	0.873117i	$0.337905\pi$
$864$	−4.71479e16	−	4.71479e16i	−3.33147	−	3.33147i
$865$			1.01747e16i			0.714388i
$866$	−9.52825e15			−0.664760
$867$	−2.66909e16	+	7.65769e15i	−1.85037	+	0.530875i
$868$	1.52949e16			1.05363
$869$		−	6.92432e15i		−	0.473989i
$870$	−1.68247e16	−	1.68247e16i	−1.14444	−	1.14444i
$871$	3.56737e14			0.0241128
$872$	−2.31566e15	−	2.31566e15i	−0.155537	−	0.155537i
$873$	2.55579e15	−	2.55579e15i	0.170587	−	0.170587i
$874$	−2.41523e15	+	2.41523e15i	−0.160194	+	0.160194i
$875$			5.02414e15i			0.331145i
$876$		−	4.56983e16i		−	2.99315i
$877$	−4.09231e15	+	4.09231e15i	−0.266361	+	0.266361i	−0.827632	−	0.561271i	$-0.810313\pi$
$877$	−4.09231e15	+	4.09231e15i	−0.266361	+	0.266361i	0.561271	+	0.827632i	$0.310313\pi$
$878$	2.23307e16	−	2.23307e16i	1.44438	−	1.44438i
$879$	−2.94796e16	−	2.94796e16i	−1.89488	−	1.89488i
$880$	2.13700e16			1.36505
$881$	7.74246e15	+	7.74246e15i	0.491486	+	0.491486i	0.908774	−	0.417288i	$-0.137019\pi$
$881$	7.74246e15	+	7.74246e15i	0.491486	+	0.491486i	−0.417288	+	0.908774i	$0.637019\pi$
$882$		−	2.41031e16i		−	1.52053i
$883$	8.09133e15			0.507266			0.253633	−	0.967300i	$-0.418374\pi$
$883$	8.09133e15			0.507266			0.253633	+	0.967300i	$0.418374\pi$
$884$	2.63183e15	−	1.55053e15i	0.163972	−	0.0966032i
$885$	−4.90003e16			−3.03397
$886$		−	2.64098e15i		−	0.162510i
$887$	1.45740e16	+	1.45740e16i	0.891246	+	0.891246i	0.994640	−	0.103395i	$-0.0329704\pi$
$887$	1.45740e16	+	1.45740e16i	0.891246	+	0.891246i	−0.103395	+	0.994640i	$0.532970\pi$
$888$	1.58138e15			0.0961090
$889$	−1.14031e16	−	1.14031e16i	−0.688755	−	0.688755i
$890$	2.70504e16	−	2.70504e16i	1.62379	−	1.62379i
$891$	−4.52269e16	+	4.52269e16i	−2.69817	+	2.69817i
$892$			2.14298e16i			1.27061i
$893$		−	2.33801e15i		−	0.137773i
$894$	−3.96646e16	+	3.96646e16i	−2.32299	+	2.32299i
$895$	2.76189e16	−	2.76189e16i	1.60761	−	1.60761i
$896$	−3.52928e15	−	3.52928e15i	−0.204170	−	0.204170i
$897$	−4.11887e15			−0.236821
$898$	1.30589e16	+	1.30589e16i	0.746252	+	0.746252i
$899$			8.01348e15i			0.455138i
$900$	6.91454e16			3.90328
$901$	5.12913e15	+	8.70608e15i	0.287778	+	0.488468i
$902$	−2.97433e16			−1.65864
$903$		−	1.86926e16i		−	1.03607i
$904$	3.85685e15	+	3.85685e15i	0.212474	+	0.212474i
$905$	−4.08459e16			−2.23656
$906$	−1.00944e15	−	1.00944e15i	−0.0549381	−	0.0549381i
$907$	1.34516e16	−	1.34516e16i	0.727667	−	0.727667i	−0.242488	−	0.970154i	$-0.577963\pi$
$907$	1.34516e16	−	1.34516e16i	0.727667	−	0.727667i	0.970154	+	0.242488i	$0.0779634\pi$
$908$	2.47079e15	−	2.47079e15i	0.132851	−	0.132851i
$909$			1.52927e16i			0.817301i
$910$		−	5.48717e15i		−	0.291488i
$911$	−4.40432e15	+	4.40432e15i	−0.232556	+	0.232556i	−0.813759	−	0.581203i	$-0.802582\pi$
$911$	−4.40432e15	+	4.40432e15i	−0.232556	+	0.232556i	0.581203	+	0.813759i	$0.302582\pi$
$912$	4.73507e15	−	4.73507e15i	0.248516	−	0.248516i
$913$	1.19976e16	+	1.19976e16i	0.625898	+	0.625898i
$914$	1.10014e16			0.570483
$915$	4.52854e16	+	4.52854e16i	2.33422	+	2.33422i
$916$		−	9.47135e14i		−	0.0485274i
$917$	−8.71925e15			−0.444066
$918$	9.15861e16	+	2.36787e16i	4.63655	+	1.19873i
$919$	−2.95989e14			−0.0148950			−0.00744751	−	0.999972i	$-0.502371\pi$
$919$	−2.95989e14			−0.0148950			−0.00744751	+	0.999972i	$0.502371\pi$
$920$		−	4.08323e15i		−	0.204254i
$921$	1.77941e16	+	1.77941e16i	0.884808	+	0.884808i
$922$	−2.20066e16			−1.08776
$923$	−3.56250e15	−	3.56250e15i	−0.175043	−	0.175043i
$924$	−2.59985e16	+	2.59985e16i	−1.26985	+	1.26985i
$925$	5.01228e15	−	5.01228e15i	0.243363	−	0.243363i
$926$			3.73482e15i			0.180264i
$927$			4.95410e16i			2.37698i
$928$	8.12149e15	−	8.12149e15i	0.387366	−	0.387366i
$929$	9.15264e15	−	9.15264e15i	0.433970	−	0.433970i	−0.456006	−	0.889977i	$-0.650721\pi$
$929$	9.15264e15	−	9.15264e15i	0.433970	−	0.433970i	0.889977	+	0.456006i	$0.150721\pi$
$930$	−7.58150e16	−	7.58150e16i	−3.57354	−	3.57354i
$931$	1.75278e15			0.0821306
$932$	1.86393e16	+	1.86393e16i	0.868247	+	0.868247i
$933$		−	4.21575e16i		−	1.95221i
$934$	−1.00300e16			−0.461737
$935$	−3.00040e16	+	1.76767e16i	−1.37314	+	0.808978i
$936$	−1.86385e15			−0.0847994
$937$			9.38089e15i			0.424303i	0.977237	+	0.212152i	$0.0680471\pi$
$937$			9.38089e15i			0.424303i	−0.977237	+	0.212152i	$0.931953\pi$
$938$	2.56835e15	+	2.56835e15i	0.115489	+	0.115489i
$939$	−7.85265e15			−0.351039
$940$	1.75035e16	+	1.75035e16i	0.777898	+	0.777898i
$941$	1.23958e16	−	1.23958e16i	0.547686	−	0.547686i	−0.378085	−	0.925771i	$-0.623417\pi$
$941$	1.23958e16	−	1.23958e16i	0.547686	−	0.547686i	0.925771	+	0.378085i	$0.123417\pi$
$942$	−6.46557e16	+	6.46557e16i	−2.84005	+	2.84005i
$943$		−	1.79776e16i		−	0.785087i
$944$		−	2.05929e16i		−	0.894068i
$945$	6.36743e16	−	6.36743e16i	2.74846	−	2.74846i
$946$	1.74138e16	−	1.74138e16i	0.747297	−	0.747297i
$947$	1.90225e16	+	1.90225e16i	0.811600	+	0.811600i	0.984874	−	0.173274i	$-0.0554346\pi$
$947$	1.90225e16	+	1.90225e16i	0.811600	+	0.811600i	−0.173274	+	0.984874i	$0.555435\pi$
$948$	2.29725e16			0.974458
$949$	3.90433e15	+	3.90433e15i	0.164658	+	0.164658i
$950$			9.48881e15i			0.397862i
$951$	6.16528e16			2.57016
$952$	3.39987e15	+	8.79002e14i	0.140916	+	0.0364323i
$953$	−4.96683e14			−0.0204676			−0.0102338	−	0.999948i	$-0.503258\pi$
$953$	−4.96683e14			−0.0204676			−0.0102338	+	0.999948i	$0.503258\pi$
$954$		−	5.46060e16i		−	2.23730i
$955$	−2.56987e16	−	2.56987e16i	−1.04687	−	1.04687i
$956$	−3.69309e16			−1.49579
$957$	−1.36215e16	−	1.36215e16i	−0.548541	−	0.548541i
$958$	−3.44384e16	+	3.44384e16i	−1.37890	+	1.37890i
$959$	−1.88868e16	+	1.88868e16i	−0.751893	+	0.751893i
$960$			9.07805e16i			3.59336i
$961$			1.07016e16i			0.421183i
$962$	−1.19660e15	+	1.19660e15i	−0.0468257	+	0.0468257i
$963$	−2.11575e15	+	2.11575e15i	−0.0823226	+	0.0823226i
$964$	9.94986e15	+	9.94986e15i	0.384940	+	0.384940i
$965$	−2.38478e16			−0.917379
$966$	−2.96541e16	−	2.96541e16i	−1.13425	−	1.13425i
$967$			2.54965e15i			0.0969695i	0.998824	+	0.0484848i	$0.0154392\pi$
$967$			2.54965e15i			0.0969695i	−0.998824	+	0.0484848i	$0.984561\pi$
$968$	−5.60365e14			−0.0211913
$969$	−2.73144e15	+	1.05649e16i	−0.102710	+	0.397268i
$970$	−5.25151e15			−0.196354
$971$		−	1.08008e16i		−	0.401560i	−0.979636	−	0.200780i	$-0.935652\pi$
$971$		−	1.08008e16i		−	0.401560i	0.979636	−	0.200780i	$-0.0643476\pi$
$972$	−7.92506e16	−	7.92506e16i	−2.92980	−	2.92980i
$973$	−3.02360e16			−1.11149
$974$	−2.03376e16	−	2.03376e16i	−0.743405	−	0.743405i
$975$	−8.09097e15	+	8.09097e15i	−0.294087	+	0.294087i
$976$	−1.90316e16	+	1.90316e16i	−0.687862	+	0.687862i
$977$			3.28881e16i			1.18200i	0.806670	+	0.591002i	$0.201268\pi$
$977$			3.28881e16i			1.18200i	−0.806670	+	0.591002i	$0.798732\pi$
$978$			4.86479e16i			1.73860i
$979$	2.19003e16	−	2.19003e16i	0.778298	−	0.778298i
$980$	−1.31223e16	+	1.31223e16i	−0.463730	+	0.463730i
$981$	6.45077e16	+	6.45077e16i	2.26690	+	2.26690i
$982$	6.86761e16			2.39990
$983$	−3.61957e16	−	3.61957e16i	−1.25780	−	1.25780i	−0.952140	−	0.305663i	$-0.901122\pi$
$983$	−3.61957e16	−	3.61957e16i	−1.25780	−	1.25780i	−0.305663	−	0.952140i	$-0.598878\pi$
$984$		−	1.11418e16i		−	0.385019i
$985$	−6.99877e16			−2.40504
$986$	−4.07879e15	+	1.57762e16i	−0.139382	+	0.539114i
$987$	2.87059e16			0.975499
$988$		−	1.20042e15i		−	0.0405666i
$989$	1.05254e16	+	1.05254e16i	0.353719	+	0.353719i
$990$	1.88190e17			6.28932
$991$	−1.86850e16	−	1.86850e16i	−0.620994	−	0.620994i	0.324791	−	0.945786i	$-0.394706\pi$
$991$	−1.86850e16	−	1.86850e16i	−0.620994	−	0.620994i	−0.945786	+	0.324791i	$0.894706\pi$
$992$	3.65968e16	−	3.65968e16i	1.20956	−	1.20956i
$993$	7.15082e16	−	7.15082e16i	2.35036	−	2.35036i
$994$		−	5.12969e16i		−	1.67674i
$995$		−	3.06443e15i		−	0.0996144i
$996$	−3.98038e16	+	3.98038e16i	−1.28676	+	1.28676i
$997$	−1.51159e16	+	1.51159e16i	−0.485970	+	0.485970i	−0.907032	−	0.421062i	$-0.861658\pi$
$997$	−1.51159e16	+	1.51159e16i	−0.485970	+	0.485970i	0.421062	+	0.907032i	$0.361658\pi$
$998$	−6.32279e16	−	6.32279e16i	−2.02158	−	2.02158i
$999$	−2.77711e16			−0.883045

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.12.c.a.13.15	yes	32
17.4	even	4	inner	17.12.c.a.4.2	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.12.c.a.4.2	✓	32	17.4	even	4	inner
17.12.c.a.13.15	yes	32	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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	17.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+66.0051i q^{2} +(-572.909 - 572.909i) q^{3} -2308.67 q^{4} +(-7460.40 - 7460.40i) q^{5} +(37814.9 - 37814.9i) q^{6} +(-24652.1 + 24652.1i) q^{7} -17205.8i q^{8} +479304. i q^{9} +O(q^{10})\)	\(q+66.0051i q^{2} +(-572.909 - 572.909i) q^{3} -2308.67 q^{4} +(-7460.40 - 7460.40i) q^{5} +(37814.9 - 37814.9i) q^{6} +(-24652.1 + 24652.1i) q^{7} -17205.8i q^{8} +479304. i q^{9} +(492425. - 492425. i) q^{10} +(398673. - 398673. i) q^{11} +(1.32266e6 + 1.32266e6i) q^{12} -226008. q^{13} +(-1.62716e6 - 1.62716e6i) q^{14} +8.54827e6i q^{15} -3.59249e6 q^{16} +(5.04395e6 - 2.97161e6i) q^{17} -3.16365e7 q^{18} -2.30062e6i q^{19} +(1.72236e7 + 1.72236e7i) q^{20} +2.82468e7 q^{21} +(2.63144e7 + 2.63144e7i) q^{22} +(-1.59051e7 + 1.59051e7i) q^{23} +(-9.85736e6 + 9.85736e6i) q^{24} +6.24870e7i q^{25} -1.49177e7i q^{26} +(1.73108e8 - 1.73108e8i) q^{27} +(5.69136e7 - 5.69136e7i) q^{28} +(2.98189e7 + 2.98189e7i) q^{29} -5.64229e8 q^{30} +(1.34369e8 + 1.34369e8i) q^{31} -2.72360e8i q^{32} -4.56807e8 q^{33} +(1.96141e8 + 3.32926e8i) q^{34} +3.67829e8 q^{35} -1.10656e9i q^{36} +(-8.02130e7 - 8.02130e7i) q^{37} +1.51853e8 q^{38} +(1.29482e8 + 1.29482e8i) q^{39} +(-1.28362e8 + 1.28362e8i) q^{40} +(-5.65151e8 + 5.65151e8i) q^{41} +1.86444e9i q^{42} -6.61760e8i q^{43} +(-9.20405e8 + 9.20405e8i) q^{44} +(3.57580e9 - 3.57580e9i) q^{45} +(-1.04982e9 - 1.04982e9i) q^{46} +1.01625e9 q^{47} +(2.05817e9 + 2.05817e9i) q^{48} +7.61875e8i q^{49} -4.12446e9 q^{50} +(-4.59219e9 - 1.18726e9i) q^{51} +5.21780e8 q^{52} +1.72604e9i q^{53} +(1.14260e10 + 1.14260e10i) q^{54} -5.94852e9 q^{55} +(4.24159e8 + 4.24159e8i) q^{56} +(-1.31805e9 + 1.31805e9i) q^{57} +(-1.96820e9 + 1.96820e9i) q^{58} +5.73219e9i q^{59} -1.97352e10i q^{60} +(5.29761e9 - 5.29761e9i) q^{61} +(-8.86905e9 + 8.86905e9i) q^{62} +(-1.18158e10 - 1.18158e10i) q^{63} +1.06197e10 q^{64} +(1.68611e9 + 1.68611e9i) q^{65} -3.01516e10i q^{66} -1.57842e9 q^{67} +(-1.16448e10 + 6.86047e9i) q^{68} +1.82244e10 q^{69} +2.42786e10i q^{70} +(1.57627e10 + 1.57627e10i) q^{71} +8.24680e9 q^{72} +(-1.72752e10 - 1.72752e10i) q^{73} +(5.29447e9 - 5.29447e9i) q^{74} +(3.57994e10 - 3.57994e10i) q^{75} +5.31138e9i q^{76} +1.96562e10i q^{77} +(-8.54650e9 + 8.54650e9i) q^{78} +(8.68421e9 - 8.68421e9i) q^{79} +(2.68014e10 + 2.68014e10i) q^{80} -1.13444e11 q^{81} +(-3.73029e10 - 3.73029e10i) q^{82} +3.00937e10i q^{83} -6.52127e10 q^{84} +(-5.97993e10 - 1.54605e10i) q^{85} +4.36795e10 q^{86} -3.41671e10i q^{87} +(-6.85948e9 - 6.85948e9i) q^{88} +5.49331e10 q^{89} +(2.36021e11 + 2.36021e11i) q^{90} +(5.57158e9 - 5.57158e9i) q^{91} +(3.67198e10 - 3.67198e10i) q^{92} -1.53963e11i q^{93} +6.70778e10i q^{94} +(-1.71635e10 + 1.71635e10i) q^{95} +(-1.56038e11 + 1.56038e11i) q^{96} +(-5.33230e9 - 5.33230e9i) q^{97} -5.02877e10 q^{98} +(1.91085e11 + 1.91085e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 528 q^{3} - 32772 q^{4} - 15496 q^{5} + 39058 q^{6} - 38368 q^{7}+O(q^{10}) \) 32 * q - 528 * q^3 - 32772 * q^4 - 15496 * q^5 + 39058 * q^6 - 38368 * q^7	\( 32 q - 528 q^{3} - 32772 q^{4} - 15496 q^{5} + 39058 q^{6} - 38368 q^{7} + 178138 q^{10} - 24816 q^{11} + 1322202 q^{12} - 1533752 q^{13} - 757692 q^{14} + 22082308 q^{16} + 17346416 q^{17} + 16775420 q^{18} + 11716134 q^{20} + 16504072 q^{21} + 55362010 q^{22} - 70945120 q^{23} - 7042078 q^{24} - 27445824 q^{27} + 339432756 q^{28} + 185239264 q^{29} - 1261021320 q^{30} + 415468304 q^{31} - 1075445880 q^{33} + 969384454 q^{34} - 1094449168 q^{35} - 49028824 q^{37} - 1340995872 q^{38} + 3217138400 q^{39} + 1182717098 q^{40} - 1419194816 q^{41} - 509236610 q^{44} + 1839923056 q^{45} - 3796371488 q^{46} - 8774740352 q^{47} + 4059548014 q^{48} + 4114666548 q^{50} - 9057963232 q^{51} + 18756164724 q^{52} + 25648728424 q^{54} - 17548144256 q^{55} + 966113388 q^{56} + 23148052104 q^{57} + 32800009486 q^{58} + 1217387240 q^{61} - 42857202380 q^{62} - 58090649872 q^{63} - 43481694148 q^{64} - 12772720712 q^{65} + 17181896368 q^{67} - 120669329406 q^{68} + 84389704104 q^{69} + 36350065824 q^{71} - 62012005860 q^{72} + 41295758480 q^{73} + 108372466886 q^{74} + 143581200752 q^{75} + 103160490932 q^{78} - 86305741264 q^{79} - 278909687742 q^{80} - 398139885080 q^{81} + 84221472400 q^{82} + 278009687832 q^{84} - 131899000528 q^{85} + 214354160644 q^{86} + 95628137594 q^{88} - 158760835496 q^{89} + 629605313178 q^{90} + 149211106624 q^{91} + 288480507416 q^{92} - 267919909216 q^{95} - 242746850002 q^{96} - 126853433800 q^{97} - 829249376752 q^{98} + 229465269792 q^{99}+O(q^{100}) \) 32 * q - 528 * q^3 - 32772 * q^4 - 15496 * q^5 + 39058 * q^6 - 38368 * q^7 + 178138 * q^10 - 24816 * q^11 + 1322202 * q^12 - 1533752 * q^13 - 757692 * q^14 + 22082308 * q^16 + 17346416 * q^17 + 16775420 * q^18 + 11716134 * q^20 + 16504072 * q^21 + 55362010 * q^22 - 70945120 * q^23 - 7042078 * q^24 - 27445824 * q^27 + 339432756 * q^28 + 185239264 * q^29 - 1261021320 * q^30 + 415468304 * q^31 - 1075445880 * q^33 + 969384454 * q^34 - 1094449168 * q^35 - 49028824 * q^37 - 1340995872 * q^38 + 3217138400 * q^39 + 1182717098 * q^40 - 1419194816 * q^41 - 509236610 * q^44 + 1839923056 * q^45 - 3796371488 * q^46 - 8774740352 * q^47 + 4059548014 * q^48 + 4114666548 * q^50 - 9057963232 * q^51 + 18756164724 * q^52 + 25648728424 * q^54 - 17548144256 * q^55 + 966113388 * q^56 + 23148052104 * q^57 + 32800009486 * q^58 + 1217387240 * q^61 - 42857202380 * q^62 - 58090649872 * q^63 - 43481694148 * q^64 - 12772720712 * q^65 + 17181896368 * q^67 - 120669329406 * q^68 + 84389704104 * q^69 + 36350065824 * q^71 - 62012005860 * q^72 + 41295758480 * q^73 + 108372466886 * q^74 + 143581200752 * q^75 + 103160490932 * q^78 - 86305741264 * q^79 - 278909687742 * q^80 - 398139885080 * q^81 + 84221472400 * q^82 + 278009687832 * q^84 - 131899000528 * q^85 + 214354160644 * q^86 + 95628137594 * q^88 - 158760835496 * q^89 + 629605313178 * q^90 + 149211106624 * q^91 + 288480507416 * q^92 - 267919909216 * q^95 - 242746850002 * q^96 - 126853433800 * q^97 - 829249376752 * q^98 + 229465269792 * q^99

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