LMFDB - Embedded newform 17.12.c.a.13.3

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			13.3
Character	$\chi$	$=$	17.13
Dual form			17.12.c.a.4.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-66.7457i q^{2} +(-522.898 - 522.898i) q^{3} -2406.98 q^{4} +(7524.98 + 7524.98i) q^{5} +(-34901.2 + 34901.2i) q^{6} +(-23035.1 + 23035.1i) q^{7} +23960.6i q^{8} +369698. i q^{9} +O(q^{10})$	\(q-66.7457i q^{2} +(-522.898 - 522.898i) q^{3} -2406.98 q^{4} +(7524.98 + 7524.98i) q^{5} +(-34901.2 + 34901.2i) q^{6} +(-23035.1 + 23035.1i) q^{7} +23960.6i q^{8} +369698. i q^{9} +(502260. - 502260. i) q^{10} +(128154. - 128154. i) q^{11} +(1.25861e6 + 1.25861e6i) q^{12} -2.00393e6 q^{13} +(1.53749e6 + 1.53749e6i) q^{14} -7.86960e6i q^{15} -3.33024e6 q^{16} +(3.76445e6 + 4.48339e6i) q^{17} +2.46758e7 q^{18} +6.91595e6i q^{19} +(-1.81125e7 - 1.81125e7i) q^{20} +2.40900e7 q^{21} +(-8.55375e6 - 8.55375e6i) q^{22} +(3.18807e6 - 3.18807e6i) q^{23} +(1.25290e7 - 1.25290e7i) q^{24} +6.44226e7i q^{25} +1.33754e8i q^{26} +(1.00685e8 - 1.00685e8i) q^{27} +(5.54450e7 - 5.54450e7i) q^{28} +(1.17349e8 + 1.17349e8i) q^{29} -5.25262e8 q^{30} +(-1.60804e8 - 1.60804e8i) q^{31} +2.71350e8i q^{32} -1.34023e8 q^{33} +(2.99247e8 - 2.51261e8i) q^{34} -3.46677e8 q^{35} -8.89858e8i q^{36} +(-3.63135e8 - 3.63135e8i) q^{37} +4.61610e8 q^{38} +(1.04785e9 + 1.04785e9i) q^{39} +(-1.80303e8 + 1.80303e8i) q^{40} +(-4.12204e8 + 4.12204e8i) q^{41} -1.60790e9i q^{42} +7.21965e8i q^{43} +(-3.08465e8 + 3.08465e8i) q^{44} +(-2.78197e9 + 2.78197e9i) q^{45} +(-2.12790e8 - 2.12790e8i) q^{46} +7.23219e8 q^{47} +(1.74137e9 + 1.74137e9i) q^{48} +9.16099e8i q^{49} +4.29993e9 q^{50} +(3.75932e8 - 4.31278e9i) q^{51} +4.82342e9 q^{52} -2.18311e8i q^{53} +(-6.72027e9 - 6.72027e9i) q^{54} +1.92872e9 q^{55} +(-5.51934e8 - 5.51934e8i) q^{56} +(3.61634e9 - 3.61634e9i) q^{57} +(7.83254e9 - 7.83254e9i) q^{58} -4.16568e8i q^{59} +1.89420e10i q^{60} +(-6.64788e9 + 6.64788e9i) q^{61} +(-1.07330e10 + 1.07330e10i) q^{62} +(-8.51602e9 - 8.51602e9i) q^{63} +1.12911e10 q^{64} +(-1.50795e10 - 1.50795e10i) q^{65} +8.94548e9i q^{66} +3.24026e9 q^{67} +(-9.06098e9 - 1.07914e10i) q^{68} -3.33407e9 q^{69} +2.31392e10i q^{70} +(8.45955e9 + 8.45955e9i) q^{71} -8.85820e9 q^{72} +(5.17818e9 + 5.17818e9i) q^{73} +(-2.42377e10 + 2.42377e10i) q^{74} +(3.36865e10 - 3.36865e10i) q^{75} -1.66466e10i q^{76} +5.90408e9i q^{77} +(6.99395e10 - 6.99395e10i) q^{78} +(-3.77179e10 + 3.77179e10i) q^{79} +(-2.50600e10 - 2.50600e10i) q^{80} -3.98048e10 q^{81} +(2.75128e10 + 2.75128e10i) q^{82} -2.98294e10i q^{83} -5.79842e10 q^{84} +(-5.41000e9 + 6.20649e10i) q^{85} +4.81880e10 q^{86} -1.22723e11i q^{87} +(3.07066e9 + 3.07066e9i) q^{88} -5.62020e10 q^{89} +(1.85685e11 + 1.85685e11i) q^{90} +(4.61606e10 - 4.61606e10i) q^{91} +(-7.67364e9 + 7.67364e9i) q^{92} +1.68169e11i q^{93} -4.82717e10i q^{94} +(-5.20424e10 + 5.20424e10i) q^{95} +(1.41889e11 - 1.41889e11i) q^{96} +(-4.57775e10 - 4.57775e10i) q^{97} +6.11457e10 q^{98} +(4.73784e10 + 4.73784e10i) 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 $

$2$		−	66.7457i		−	1.47488i	−0.675410	−	0.737442i	$-0.736033\pi$
$2$		−	66.7457i		−	1.47488i	0.675410	−	0.737442i	$-0.263967\pi$
$3$	−522.898	−	522.898i	−1.24237	−	1.24237i	−0.959016	−	0.283352i	$-0.908553\pi$
$3$	−522.898	−	522.898i	−1.24237	−	1.24237i	−0.283352	−	0.959016i	$-0.591447\pi$
$4$	−2406.98			−1.17529
$5$	7524.98	+	7524.98i	1.07689	+	1.07689i	0.996787	+	0.0801013i	$0.0255244\pi$
$5$	7524.98	+	7524.98i	1.07689	+	1.07689i	0.0801013	+	0.996787i	$0.474476\pi$
$6$	−34901.2	+	34901.2i	−1.83235	+	1.83235i
$7$	−23035.1	+	23035.1i	−0.518024	+	0.518024i	−0.916973	−	0.398949i	$-0.869375\pi$
$7$	−23035.1	+	23035.1i	−0.518024	+	0.518024i	0.398949	+	0.916973i	$0.369375\pi$
$8$			23960.6i			0.258525i
$9$			369698.i			2.08696i
$10$	502260.	−	502260.i	1.58829	−	1.58829i
$11$	128154.	−	128154.i	0.239924	−	0.239924i	−0.576895	−	0.816819i	$-0.695736\pi$
$11$	128154.	−	128154.i	0.239924	−	0.239924i	0.816819	+	0.576895i	$0.195736\pi$
$12$	1.25861e6	+	1.25861e6i	1.46014	+	1.46014i
$13$	−2.00393e6			−1.49690			−0.748452	−	0.663189i	$-0.769202\pi$
$13$	−2.00393e6			−1.49690			−0.748452	+	0.663189i	$0.769202\pi$
$14$	1.53749e6	+	1.53749e6i	0.764026	+	0.764026i
$15$		−	7.86960e6i		−	2.67578i
$16$	−3.33024e6			−0.793990
$17$	3.76445e6	+	4.48339e6i	0.643032	+	0.765839i
$17$	3.76445e6	+	4.48339e6i	0.643032	+	0.765839i
$18$	2.46758e7			3.07802
$19$			6.91595e6i			0.640777i	0.947286	+	0.320389i	$0.103814\pi$
$19$			6.91595e6i			0.640777i	−0.947286	+	0.320389i	$0.896186\pi$
$20$	−1.81125e7	−	1.81125e7i	−1.26565	−	1.26565i
$21$	2.40900e7			1.28715
$22$	−8.55375e6	−	8.55375e6i	−0.353860	−	0.353860i
$23$	3.18807e6	−	3.18807e6i	0.103282	−	0.103282i	−0.653578	−	0.756860i	$-0.726733\pi$
$23$	3.18807e6	−	3.18807e6i	0.103282	−	0.103282i	0.756860	+	0.653578i	$0.226733\pi$
$24$	1.25290e7	−	1.25290e7i	0.321184	−	0.321184i
$25$			6.44226e7i			1.31938i
$26$			1.33754e8i			2.20776i
$27$	1.00685e8	−	1.00685e8i	1.35040	−	1.35040i
$28$	5.54450e7	−	5.54450e7i	0.608826	−	0.608826i
$29$	1.17349e8	+	1.17349e8i	1.06241	+	1.06241i	0.997918	+	0.0644882i	$0.0205415\pi$
$29$	1.17349e8	+	1.17349e8i	1.06241	+	1.06241i	0.0644882	+	0.997918i	$0.479459\pi$
$30$	−5.25262e8			−3.94647
$31$	−1.60804e8	−	1.60804e8i	−1.00881	−	1.00881i	−0.999961	−	0.00884649i	$-0.997184\pi$
$31$	−1.60804e8	−	1.60804e8i	−1.00881	−	1.00881i	−0.00884649	−	0.999961i	$-0.502816\pi$
$32$			2.71350e8i			1.42957i
$33$	−1.34023e8			−0.596148
$34$	2.99247e8	−	2.51261e8i	1.12952	−	0.948398i
$35$	−3.46677e8			−1.11571
$36$		−	8.89858e8i		−	2.45277i
$37$	−3.63135e8	−	3.63135e8i	−0.860913	−	0.860913i	0.130532	−	0.991444i	$-0.458332\pi$
$37$	−3.63135e8	−	3.63135e8i	−0.860913	−	0.860913i	−0.991444	+	0.130532i	$0.958332\pi$
$38$	4.61610e8			0.945073
$39$	1.04785e9	+	1.04785e9i	1.85971	+	1.85971i
$40$	−1.80303e8	+	1.80303e8i	−0.278403	+	0.278403i
$41$	−4.12204e8	+	4.12204e8i	−0.555650	+	0.555650i	−0.928066	−	0.372416i	$-0.878529\pi$
$41$	−4.12204e8	+	4.12204e8i	−0.555650	+	0.555650i	0.372416	+	0.928066i	$0.378529\pi$
$42$		−	1.60790e9i		−	1.89840i
$43$			7.21965e8i			0.748927i	0.927242	+	0.374464i	$0.122173\pi$
$43$			7.21965e8i			0.748927i	−0.927242	+	0.374464i	$0.877827\pi$
$44$	−3.08465e8	+	3.08465e8i	−0.281979	+	0.281979i
$45$	−2.78197e9	+	2.78197e9i	−2.24742	+	2.24742i
$46$	−2.12790e8	−	2.12790e8i	−0.152329	−	0.152329i
$47$	7.23219e8			0.459972			0.229986	−	0.973194i	$-0.426132\pi$
$47$	7.23219e8			0.459972			0.229986	+	0.973194i	$0.426132\pi$
$48$	1.74137e9	+	1.74137e9i	0.986428	+	0.986428i
$49$			9.16099e8i			0.463302i
$50$	4.29993e9			1.94593
$51$	3.75932e8	−	4.31278e9i	0.152571	−	1.75034i
$52$	4.82342e9			1.75929
$53$		−	2.18311e8i		−	0.0717065i	−0.999357	−	0.0358533i	$-0.988585\pi$
$53$		−	2.18311e8i		−	0.0717065i	0.999357	−	0.0358533i	$-0.0114149\pi$
$54$	−6.72027e9	−	6.72027e9i	−1.99169	−	1.99169i
$55$	1.92872e9			0.516742
$56$	−5.51934e8	−	5.51934e8i	−0.133922	−	0.133922i
$57$	3.61634e9	−	3.61634e9i	0.796081	−	0.796081i
$58$	7.83254e9	−	7.83254e9i	1.56693	−	1.56693i
$59$		−	4.16568e8i		−	0.0758577i	−0.999280	−	0.0379288i	$-0.987924\pi$
$59$		−	4.16568e8i		−	0.0758577i	0.999280	−	0.0379288i	$-0.0120760\pi$
$60$			1.89420e10i			3.14481i
$61$	−6.64788e9	+	6.64788e9i	−1.00779	+	1.00779i	−0.00781828	+	0.999969i	$0.502489\pi$
$61$	−6.64788e9	+	6.64788e9i	−1.00779	+	1.00779i	−0.999969	+	0.00781828i	$0.997511\pi$
$62$	−1.07330e10	+	1.07330e10i	−1.48787	+	1.48787i
$63$	−8.51602e9	−	8.51602e9i	−1.08109	−	1.08109i
$64$	1.12911e10			1.31446
$65$	−1.50795e10	−	1.50795e10i	−1.61200	−	1.61200i
$66$			8.94548e9i			0.879249i
$67$	3.24026e9			0.293203			0.146602	−	0.989196i	$-0.453166\pi$
$67$	3.24026e9			0.293203			0.146602	+	0.989196i	$0.453166\pi$
$68$	−9.06098e9	−	1.07914e10i	−0.755746	−	0.900079i
$69$	−3.33407e9			−0.256629
$70$			2.31392e10i			1.64554i
$71$	8.45955e9	+	8.45955e9i	0.556450	+	0.556450i	0.928295	−	0.371845i	$-0.121275\pi$
$71$	8.45955e9	+	8.45955e9i	0.556450	+	0.556450i	−0.371845	+	0.928295i	$0.621275\pi$
$72$	−8.85820e9			−0.539531
$73$	5.17818e9	+	5.17818e9i	0.292349	+	0.292349i	0.838007	−	0.545659i	$-0.183721\pi$
$73$	5.17818e9	+	5.17818e9i	0.292349	+	0.292349i	−0.545659	+	0.838007i	$0.683721\pi$
$74$	−2.42377e10	+	2.42377e10i	−1.26975	+	1.26975i
$75$	3.36865e10	−	3.36865e10i	1.63915	−	1.63915i
$76$		−	1.66466e10i		−	0.753096i
$77$			5.90408e9i			0.248573i
$78$	6.99395e10	−	6.99395e10i	2.74285	−	2.74285i
$79$	−3.77179e10	+	3.77179e10i	−1.37911	+	1.37911i	−0.532978	+	0.846129i	$0.678927\pi$
$79$	−3.77179e10	+	3.77179e10i	−1.37911	+	1.37911i	−0.846129	+	0.532978i	$0.821073\pi$
$80$	−2.50600e10	−	2.50600e10i	−0.855038	−	0.855038i
$81$	−3.98048e10			−1.26843
$82$	2.75128e10	+	2.75128e10i	0.819520	+	0.819520i
$83$		−	2.98294e10i		−	0.831217i	−0.909544	−	0.415609i	$-0.863569\pi$
$83$		−	2.98294e10i		−	0.831217i	0.909544	−	0.415609i	$-0.136431\pi$
$84$	−5.79842e10			−1.51277
$85$	−5.41000e9	+	6.20649e10i	−0.132249	+	1.51720i
$86$	4.81880e10			1.10458
$87$		−	1.22723e11i		−	2.63980i
$88$	3.07066e9	+	3.07066e9i	0.0620264	+	0.0620264i
$89$	−5.62020e10			−1.06686			−0.533429	−	0.845845i	$-0.679097\pi$
$89$	−5.62020e10			−1.06686			−0.533429	+	0.845845i	$0.679097\pi$
$90$	1.85685e11	+	1.85685e11i	3.31468	+	3.31468i
$91$	4.61606e10	−	4.61606e10i	0.775432	−	0.775432i
$92$	−7.67364e9	+	7.67364e9i	−0.121386	+	0.121386i
$93$			1.68169e11i			2.50662i
$94$		−	4.82717e10i		−	0.678406i
$95$	−5.20424e10	+	5.20424e10i	−0.690045	+	0.690045i
$96$	1.41889e11	−	1.41889e11i	1.77605	−	1.77605i
$97$	−4.57775e10	−	4.57775e10i	−0.541262	−	0.541262i	0.382637	−	0.923899i	$-0.375016\pi$
$97$	−4.57775e10	−	4.57775e10i	−0.541262	−	0.541262i	−0.923899	+	0.382637i	$0.875016\pi$
$98$	6.11457e10			0.683317
$99$	4.73784e10	+	4.73784e10i	0.500711	+	0.500711i
$100$		−	1.55064e11i		−	1.55064i
$101$	−1.63184e11			−1.54493			−0.772466	−	0.635056i	$-0.780977\pi$
$101$	−1.63184e11			−1.54493			−0.772466	+	0.635056i	$0.780977\pi$
$102$	−2.87860e11	−	2.50918e10i	−2.58155	−	0.225025i
$103$	7.39578e10			0.628607			0.314303	−	0.949323i	$-0.398229\pi$
$103$	7.39578e10			0.628607			0.314303	+	0.949323i	$0.398229\pi$
$104$		−	4.80154e10i		−	0.386987i
$105$	1.81277e11	+	1.81277e11i	1.38612	+	1.38612i
$106$	−1.45713e10			−0.105759
$107$	−7.11222e10	−	7.11222e10i	−0.490224	−	0.490224i	0.418153	−	0.908377i	$-0.362678\pi$
$107$	−7.11222e10	−	7.11222e10i	−0.490224	−	0.490224i	−0.908377	+	0.418153i	$0.862678\pi$
$108$	−2.42346e11	+	2.42346e11i	−1.58711	+	1.58711i
$109$	−8.96563e9	+	8.96563e9i	−0.0558130	+	0.0558130i	−0.734462	−	0.678649i	$-0.762566\pi$
$109$	−8.96563e9	+	8.96563e9i	−0.0558130	+	0.0558130i	0.678649	+	0.734462i	$0.262566\pi$
$110$		−	1.28734e11i		−	0.762136i
$111$			3.79766e11i			2.13914i
$112$	7.67122e10	−	7.67122e10i	0.411306	−	0.411306i
$113$	7.57341e10	−	7.57341e10i	0.386687	−	0.386687i	−0.486817	−	0.873504i	$-0.661842\pi$
$113$	7.57341e10	−	7.57341e10i	0.386687	−	0.386687i	0.873504	+	0.486817i	$0.161842\pi$
$114$	−2.41375e11	−	2.41375e11i	−1.17413	−	1.17413i
$115$	4.79804e10			0.222446
$116$	−2.82457e11	−	2.82457e11i	−1.24863	−	1.24863i
$117$		−	7.40849e11i		−	3.12397i
$118$	−2.78041e10			−0.111881
$119$	−1.89990e11	−	1.65608e10i	−0.729829	−	0.0636169i
$120$	1.88561e11			0.691758
$121$			2.52465e11i			0.884873i
$122$	4.43717e11	+	4.43717e11i	1.48637	+	1.48637i
$123$	4.31082e11			1.38064
$124$	3.87053e11	+	3.87053e11i	1.18564	+	1.18564i
$125$	−1.17348e11	+	1.17348e11i	−0.343932	+	0.343932i
$126$	−5.68407e11	+	5.68407e11i	−1.59449	+	1.59449i
$127$		−	2.51234e11i		−	0.674773i	−0.941366	−	0.337386i	$-0.890457\pi$
$127$		−	2.51234e11i		−	0.674773i	0.941366	−	0.337386i	$-0.109543\pi$
$128$		−	1.97908e11i		−	0.509108i
$129$	3.77514e11	−	3.77514e11i	0.930444	−	0.930444i
$130$	−1.00649e12	+	1.00649e12i	−2.37751	+	2.37751i
$131$	−5.10889e10	−	5.10889e10i	−0.115700	−	0.115700i	0.646886	−	0.762586i	$-0.276071\pi$
$131$	−5.10889e10	−	5.10889e10i	−0.115700	−	0.115700i	−0.762586	+	0.646886i	$0.776071\pi$
$132$	3.22592e11			0.700644
$133$	−1.59309e11	−	1.59309e11i	−0.331938	−	0.331938i
$134$		−	2.16273e11i		−	0.432441i
$135$	1.51530e12			2.90846
$136$	−1.07425e11	+	9.01986e10i	−0.197989	+	0.166240i
$137$	−1.97091e11			−0.348901			−0.174451	−	0.984666i	$-0.555815\pi$
$137$	−1.97091e11			−0.348901			−0.174451	+	0.984666i	$0.555815\pi$
$138$			2.22535e11i			0.378498i
$139$	−5.18813e11	−	5.18813e11i	−0.848066	−	0.848066i	0.141826	−	0.989892i	$-0.454703\pi$
$139$	−5.18813e11	−	5.18813e11i	−0.848066	−	0.848066i	−0.989892	+	0.141826i	$0.954703\pi$
$140$	8.34446e11			1.31128
$141$	−3.78170e11	−	3.78170e11i	−0.571455	−	0.571455i
$142$	5.64638e11	−	5.64638e11i	0.820700	−	0.820700i
$143$	−2.56812e11	+	2.56812e11i	−0.359143	+	0.359143i
$144$		−	1.23118e12i		−	1.65702i
$145$			1.76610e12i			2.28819i
$146$	3.45621e11	−	3.45621e11i	0.431181	−	0.431181i
$147$	4.79027e11	−	4.79027e11i	0.575592	−	0.575592i
$148$	8.74061e11	+	8.74061e11i	1.01182	+	1.01182i
$149$	9.65214e11			1.07671			0.538355	−	0.842718i	$-0.319046\pi$
$149$	9.65214e11			1.07671			0.538355	+	0.842718i	$0.319046\pi$
$150$	−2.24843e12	−	2.24843e12i	−2.41756	−	2.41756i
$151$			5.61597e11i			0.582172i	0.956697	+	0.291086i	$0.0940166\pi$
$151$			5.61597e11i			0.582172i	−0.956697	+	0.291086i	$0.905983\pi$
$152$	−1.65710e11			−0.165657
$153$	−1.65750e12	+	1.39171e12i	−1.59827	+	1.34198i
$154$	3.94072e11			0.366616
$155$		−	2.42010e12i		−	2.17275i
$156$	−2.52216e12	−	2.52216e12i	−2.18568	−	2.18568i
$157$	1.36698e12			1.14371			0.571853	−	0.820356i	$-0.306225\pi$
$157$	1.36698e12			1.14371			0.571853	+	0.820356i	$0.306225\pi$
$158$	2.51750e12	+	2.51750e12i	2.03402	+	2.03402i
$159$	−1.14155e11	+	1.14155e11i	−0.0890859	+	0.0890859i
$160$	−2.04191e12	+	2.04191e12i	−1.53949	+	1.53949i
$161$			1.46875e11i			0.107005i
$162$			2.65680e12i			1.87079i
$163$	−1.74672e12	+	1.74672e12i	−1.18903	+	1.18903i	−0.211692	+	0.977336i	$0.567897\pi$
$163$	−1.74672e12	+	1.74672e12i	−1.18903	+	1.18903i	−0.977336	+	0.211692i	$0.932103\pi$
$164$	9.92169e11	−	9.92169e11i	0.653047	−	0.653047i
$165$	−1.00852e12	−	1.00852e12i	−0.641984	−	0.641984i
$166$	−1.99098e12			−1.22595
$167$	1.75041e12	+	1.75041e12i	1.04279	+	1.04279i	0.999042	+	0.0437522i	$0.0139312\pi$
$167$	1.75041e12	+	1.75041e12i	1.04279	+	1.04279i	0.0437522	+	0.999042i	$0.486069\pi$
$168$			5.77211e11i			0.332762i
$169$	2.22357e12			1.24072
$170$	4.14256e12	+	3.61094e11i	2.23769	+	0.195052i
$171$	−2.55681e12			−1.33727
$172$		−	1.73776e12i		−	0.880203i
$173$	−1.13850e12	−	1.13850e12i	−0.558573	−	0.558573i	0.370328	−	0.928901i	$-0.379245\pi$
$173$	−1.13850e12	−	1.13850e12i	−0.558573	−	0.558573i	−0.928901	+	0.370328i	$0.879245\pi$
$174$	−8.19125e12			−3.89340
$175$	−1.48398e12	−	1.48398e12i	−0.683468	−	0.683468i
$176$	−4.26784e11	+	4.26784e11i	−0.190497	+	0.190497i
$177$	−2.17822e11	+	2.17822e11i	−0.0942431	+	0.0942431i
$178$			3.75124e12i			1.57349i
$179$		−	2.73248e11i		−	0.111139i	−0.998455	−	0.0555693i	$-0.982303\pi$
$179$		−	2.73248e11i		−	0.111139i	0.998455	−	0.0555693i	$-0.0176974\pi$
$180$	6.69616e12	−	6.69616e12i	2.64136	−	2.64136i
$181$	4.45699e11	−	4.45699e11i	0.170533	−	0.170533i	−0.616680	−	0.787214i	$-0.711523\pi$
$181$	4.45699e11	−	4.45699e11i	0.170533	−	0.170533i	0.787214	+	0.616680i	$0.211523\pi$
$182$	−3.08102e12	−	3.08102e12i	−1.14367	−	1.14367i
$183$	6.95233e12			2.50409
$184$	7.63882e10	+	7.63882e10i	0.0267010	+	0.0267010i
$185$		−	5.46518e12i		−	1.85421i
$186$	1.12245e13			3.69698
$187$	1.05700e12	+	9.21351e10i	0.338022	+	0.0294643i
$188$	−1.74078e12			−0.540599
$189$			4.63855e12i			1.39908i
$190$	3.47361e12	+	3.47361e12i	1.01774	+	1.01774i
$191$	−3.56536e11			−0.101489			−0.0507445	−	0.998712i	$-0.516159\pi$
$191$	−3.56536e11			−0.101489			−0.0507445	+	0.998712i	$0.516159\pi$
$192$	−5.90411e12	−	5.90411e12i	−1.63304	−	1.63304i
$193$	1.62356e12	−	1.62356e12i	0.436417	−	0.436417i	−0.454387	−	0.890804i	$-0.650142\pi$
$193$	1.62356e12	−	1.62356e12i	0.436417	−	0.436417i	0.890804	+	0.454387i	$0.150142\pi$
$194$	−3.05545e12	+	3.05545e12i	−0.798299	+	0.798299i
$195$			1.57701e13i			4.00539i
$196$		−	2.20504e12i		−	0.544512i
$197$	−4.31894e11	+	4.31894e11i	−0.103708	+	0.103708i	−0.757057	−	0.653349i	$-0.773363\pi$
$197$	−4.31894e11	+	4.31894e11i	−0.103708	+	0.103708i	0.653349	+	0.757057i	$0.273363\pi$
$198$	3.16230e12	−	3.16230e12i	0.738491	−	0.738491i
$199$	−5.27504e12	−	5.27504e12i	−1.19821	−	1.19821i	−0.974702	−	0.223510i	$-0.928248\pi$
$199$	−5.27504e12	−	5.27504e12i	−1.19821	−	1.19821i	−0.223510	−	0.974702i	$-0.571752\pi$
$200$	−1.54361e12			−0.341092
$201$	−1.69433e12	−	1.69433e12i	−0.364266	−	0.364266i
$202$			1.08918e13i			2.27860i
$203$	−5.40629e12			−1.10070
$204$	−9.04862e11	+	1.03808e13i	−0.179315	+	2.05714i
$205$	−6.20366e12			−1.19675
$206$		−	4.93636e12i		−	0.927123i
$207$	1.17862e12	+	1.17862e12i	0.215545	+	0.215545i
$208$	6.67355e12			1.18853
$209$	8.86309e11	+	8.86309e11i	0.153738	+	0.153738i
$210$	1.20994e13	−	1.20994e13i	2.04437	−	2.04437i
$211$	4.05024e11	−	4.05024e11i	0.0666695	−	0.0666695i	−0.672986	−	0.739655i	$-0.734989\pi$
$211$	4.05024e11	−	4.05024e11i	0.0666695	−	0.0666695i	0.739655	+	0.672986i	$0.234989\pi$
$212$			5.25472e11i			0.0842756i
$213$		−	8.84696e12i		−	1.38263i
$214$	−4.74710e12	+	4.74710e12i	−0.723023	+	0.723023i
$215$	−5.43278e12	+	5.43278e12i	−0.806511	+	0.806511i
$216$	2.41247e12	+	2.41247e12i	0.349113	+	0.349113i
$217$	7.40827e12			1.04517
$218$	5.98417e11	+	5.98417e11i	0.0823177	+	0.0823177i
$219$		−	5.41532e12i		−	0.726409i
$220$	−4.64240e12			−0.607320
$221$	−7.54369e12	−	8.98440e12i	−0.962557	−	1.14639i
$222$	2.53477e13			3.15499
$223$		−	5.67786e12i		−	0.689458i	−0.938702	−	0.344729i	$-0.887971\pi$
$223$		−	5.67786e12i		−	0.689458i	0.938702	−	0.344729i	$-0.112029\pi$
$224$	−6.25056e12	−	6.25056e12i	−0.740551	−	0.740551i
$225$	−2.38169e13			−2.75348
$226$	−5.05492e12	−	5.05492e12i	−0.570319	−	0.570319i
$227$	−4.09120e12	+	4.09120e12i	−0.450514	+	0.450514i	−0.895525	−	0.445011i	$-0.853200\pi$
$227$	−4.09120e12	+	4.09120e12i	−0.450514	+	0.450514i	0.445011	+	0.895525i	$0.353200\pi$
$228$	−8.70447e12	+	8.70447e12i	−0.935623	+	0.935623i
$229$		−	1.00879e12i		−	0.105853i	−0.998598	−	0.0529267i	$-0.983145\pi$
$229$		−	1.00879e12i		−	0.105853i	0.998598	−	0.0529267i	$-0.0168550\pi$
$230$		−	3.20248e12i		−	0.328083i
$231$	3.08724e12	−	3.08724e12i	0.308819	−	0.308819i
$232$	−2.81176e12	+	2.81176e12i	−0.274659	+	0.274659i
$233$	−2.32215e12	−	2.32215e12i	−0.221530	−	0.221530i	0.587613	−	0.809142i	$-0.300068\pi$
$233$	−2.32215e12	−	2.32215e12i	−0.221530	−	0.221530i	−0.809142	+	0.587613i	$0.800068\pi$
$234$	−4.94484e13			−4.60750
$235$	5.44221e12	+	5.44221e12i	0.495339	+	0.495339i
$236$			1.00267e12i			0.0891544i
$237$	3.94452e13			3.42672
$238$	−1.10536e12	+	1.26810e13i	−0.0938277	+	1.07641i
$239$	9.85483e12			0.817449			0.408725	−	0.912658i	$-0.365974\pi$
$239$	9.85483e12			0.817449			0.408725	+	0.912658i	$0.365974\pi$
$240$			2.62076e13i			2.12454i
$241$	5.99965e12	+	5.99965e12i	0.475371	+	0.475371i	0.903648	−	0.428277i	$-0.140879\pi$
$241$	5.99965e12	+	5.99965e12i	0.475371	+	0.475371i	−0.428277	+	0.903648i	$0.640879\pi$
$242$	1.68509e13			1.30509
$243$	2.97785e12	+	2.97785e12i	0.225460	+	0.225460i
$244$	1.60013e13	−	1.60013e13i	1.18444	−	1.18444i
$245$	−6.89363e12	+	6.89363e12i	−0.498924	+	0.498924i
$246$		−	2.87728e13i		−	2.03629i
$247$		−	1.38591e13i		−	0.959182i
$248$	3.85297e12	−	3.85297e12i	0.260802	−	0.260802i
$249$	−1.55977e13	+	1.55977e13i	−1.03268	+	1.03268i
$250$	7.83250e12	+	7.83250e12i	0.507260	+	0.507260i
$251$	−5.32497e12			−0.337374			−0.168687	−	0.985670i	$-0.553953\pi$
$251$	−5.32497e12			−0.337374			−0.168687	+	0.985670i	$0.553953\pi$
$252$	2.04979e13	+	2.04979e13i	1.27059	+	1.27059i
$253$		−	8.17131e11i		−	0.0495597i
$254$	−1.67688e13			−0.995212
$255$	3.52825e13	−	2.96247e13i	2.04922	−	1.72061i
$256$	9.91469e12			0.563585
$257$		−	3.92318e12i		−	0.218276i	−0.994027	−	0.109138i	$-0.965191\pi$
$257$		−	3.92318e12i		−	0.218276i	0.994027	−	0.109138i	$-0.0348090\pi$
$258$	−2.51974e13	−	2.51974e13i	−1.37230	−	1.37230i
$259$	1.67297e13			0.891947
$260$	3.62962e13	+	3.62962e13i	1.89456	+	1.89456i
$261$	−4.33838e13	+	4.33838e13i	−2.21720	+	2.21720i
$262$	−3.40996e12	+	3.40996e12i	−0.170644	+	0.170644i
$263$		−	1.93194e13i		−	0.946756i	−0.880859	−	0.473378i	$-0.843035\pi$
$263$		−	1.93194e13i		−	0.946756i	0.880859	−	0.473378i	$-0.156965\pi$
$264$		−	3.21128e12i		−	0.154119i
$265$	1.64279e12	−	1.64279e12i	0.0772199	−	0.0772199i
$266$	−1.06332e13	+	1.06332e13i	−0.489570	+	0.489570i
$267$	2.93879e13	+	2.93879e13i	1.32543	+	1.32543i
$268$	−7.79926e12			−0.344597
$269$	2.19538e12	+	2.19538e12i	0.0950326	+	0.0950326i	0.753025	−	0.657992i	$-0.228594\pi$
$269$	2.19538e12	+	2.19538e12i	0.0950326	+	0.0950326i	−0.657992	+	0.753025i	$0.728594\pi$
$270$		−	1.01140e14i		−	4.28964i
$271$	5.00783e12			0.208122			0.104061	−	0.994571i	$-0.466816\pi$
$271$	5.00783e12			0.208122			0.104061	+	0.994571i	$0.466816\pi$
$272$	−1.25365e13	−	1.49307e13i	−0.510561	−	0.608069i
$273$	−4.82746e13			−1.92674
$274$			1.31549e13i			0.514589i
$275$	8.25604e12	+	8.25604e12i	0.316550	+	0.316550i
$276$	8.02506e12			0.301612
$277$	−3.22325e13	−	3.22325e13i	−1.18756	−	1.18756i	−0.977740	−	0.209819i	$-0.932713\pi$
$277$	−3.22325e13	−	3.22325e13i	−1.18756	−	1.18756i	−0.209819	−	0.977740i	$-0.567287\pi$
$278$	−3.46285e13	+	3.46285e13i	−1.25080	+	1.25080i
$279$	5.94490e13	−	5.94490e13i	2.10534	−	2.10534i
$280$		−	8.30659e12i		−	0.288439i
$281$			4.56081e13i			1.55295i	0.630149	+	0.776474i	$0.282994\pi$
$281$			4.56081e13i			1.55295i	−0.630149	+	0.776474i	$0.717006\pi$
$282$	−2.52412e13	+	2.52412e13i	−0.842830	+	0.842830i
$283$	−2.01780e13	+	2.01780e13i	−0.660772	+	0.660772i	−0.955562	−	0.294790i	$-0.904750\pi$
$283$	−2.01780e13	+	2.01780e13i	−0.660772	+	0.660772i	0.294790	+	0.955562i	$0.404750\pi$
$284$	−2.03620e13	−	2.03620e13i	−0.653987	−	0.653987i
$285$	5.44258e13			1.71458
$286$	1.71411e13	+	1.71411e13i	0.529694	+	0.529694i
$287$		−	1.89903e13i		−	0.575680i
$288$	−1.00318e14			−2.98345
$289$	−5.92969e12	+	3.37550e13i	−0.173019	+	0.984918i
$290$	1.17880e14			3.37481
$291$			4.78740e13i			1.34489i
$292$	−1.24638e13	−	1.24638e13i	−0.343593	−	0.343593i
$293$	−3.80425e12			−0.102919			−0.0514596	−	0.998675i	$-0.516387\pi$
$293$	−3.80425e12			−0.102919			−0.0514596	+	0.998675i	$0.516387\pi$
$294$	−3.19730e13	−	3.19730e13i	−0.848931	−	0.848931i
$295$	3.13466e12	−	3.13466e12i	0.0816902	−	0.0816902i
$296$	8.70095e12	−	8.70095e12i	0.222568	−	0.222568i
$297$		−	2.58064e13i		−	0.647987i
$298$		−	6.44238e13i		−	1.58802i
$299$	−6.38867e12	+	6.38867e12i	−0.154603	+	0.154603i
$300$	−8.10828e13	+	8.10828e13i	−1.92647	+	1.92647i
$301$	−1.66305e13	−	1.66305e13i	−0.387963	−	0.387963i
$302$	3.74841e13			0.858636
$303$	8.53285e13	+	8.53285e13i	1.91937	+	1.91937i
$304$		−	2.30317e13i		−	0.508771i
$305$	−1.00050e14			−2.17055
$306$	9.28907e13	+	1.10631e14i	1.97927	+	2.35727i
$307$	4.51385e13			0.944683			0.472342	−	0.881416i	$-0.343409\pi$
$307$	4.51385e13			0.944683			0.472342	+	0.881416i	$0.343409\pi$
$308$		−	1.42110e13i		−	0.292144i
$309$	−3.86724e13	−	3.86724e13i	−0.780961	−	0.780961i
$310$	−1.61531e14			−3.20455
$311$	4.89556e12	+	4.89556e12i	0.0954158	+	0.0954158i	0.753203	−	0.657788i	$-0.228508\pi$
$311$	4.89556e12	+	4.89556e12i	0.0954158	+	0.0954158i	−0.657788	+	0.753203i	$0.728508\pi$
$312$	−2.51072e13	+	2.51072e13i	−0.480781	+	0.480781i
$313$	−4.10030e13	+	4.10030e13i	−0.771475	+	0.771475i	−0.978364	−	0.206889i	$-0.933666\pi$
$313$	−4.10030e13	+	4.10030e13i	−0.771475	+	0.771475i	0.206889	+	0.978364i	$0.433666\pi$
$314$		−	9.12401e13i		−	1.68684i
$315$		−	1.28166e14i		−	2.32843i
$316$	9.07863e13	−	9.07863e13i	1.62084	−	1.62084i
$317$	7.36501e12	−	7.36501e12i	0.129225	−	0.129225i	−0.639536	−	0.768761i	$-0.720873\pi$
$317$	7.36501e12	−	7.36501e12i	0.129225	−	0.129225i	0.768761	+	0.639536i	$0.220873\pi$
$318$	7.61932e12	+	7.61932e12i	0.131391	+	0.131391i
$319$	3.00776e13			0.509794
$320$	8.49655e13	+	8.49655e13i	1.41553	+	1.41553i
$321$			7.43793e13i			1.21808i
$322$	9.80326e12			0.157820
$323$	−3.10069e13	+	2.60348e13i	−0.490732	+	0.412040i
$324$	9.58094e13			1.49077
$325$		−	1.29098e14i		−	1.97498i
$326$	1.16586e14	+	1.16586e14i	1.75368	+	1.75368i
$327$	9.37622e12			0.138680
$328$	−9.87667e12	−	9.87667e12i	−0.143650	−	0.143650i
$329$	−1.66594e13	+	1.66594e13i	−0.238277	+	0.238277i
$330$	−6.73146e13	+	6.73146e13i	−0.946853	+	0.946853i
$331$		−	7.37420e13i		−	1.02014i	−0.860132	−	0.510072i	$-0.829619\pi$
$331$		−	7.37420e13i		−	1.02014i	0.860132	−	0.510072i	$-0.170381\pi$
$332$			7.17988e13i			0.976917i
$333$	1.34250e14	−	1.34250e14i	1.79669	−	1.79669i
$334$	1.16832e14	−	1.16832e14i	1.53800	−	1.53800i
$335$	2.43829e13	+	2.43829e13i	0.315747	+	0.315747i
$336$	−8.02253e13			−1.02199
$337$	1.09987e13	+	1.09987e13i	0.137841	+	0.137841i	0.772661	−	0.634819i	$-0.218926\pi$
$337$	1.09987e13	+	1.09987e13i	0.137841	+	0.137841i	−0.634819	+	0.772661i	$0.718926\pi$
$338$		−	1.48414e14i		−	1.82992i
$339$	−7.92024e13			−0.960816
$340$	1.30218e13	−	1.49389e14i	0.155431	−	1.78314i
$341$	−4.12155e13			−0.484074
$342$			1.70656e14i			1.97233i
$343$	−6.66502e13	−	6.66502e13i	−0.758026	−	0.758026i
$344$	−1.72987e13			−0.193617
$345$	−2.50889e13	−	2.50889e13i	−0.276360	−	0.276360i
$346$	−7.59901e13	+	7.59901e13i	−0.823831	+	0.823831i
$347$	1.23311e14	−	1.23311e14i	1.31579	−	1.31579i	0.398723	−	0.917072i	$-0.369454\pi$
$347$	1.23311e14	−	1.23311e14i	1.31579	−	1.31579i	0.917072	−	0.398723i	$-0.130546\pi$
$348$			2.95393e14i			3.10252i
$349$			5.86378e13i			0.606231i	0.952954	+	0.303116i	$0.0980268\pi$
$349$			5.86378e13i			0.606231i	−0.952954	+	0.303116i	$0.901973\pi$
$350$	−9.90492e13	+	9.90492e13i	−1.00804	+	1.00804i
$351$	−2.01765e14	+	2.01765e14i	−2.02142	+	2.02142i
$352$	3.47747e13	+	3.47747e13i	0.342988	+	0.342988i
$353$	−6.74183e13			−0.654662			−0.327331	−	0.944910i	$-0.606149\pi$
$353$	−6.74183e13			−0.654662			−0.327331	+	0.944910i	$0.606149\pi$
$354$	1.45387e13	+	1.45387e13i	0.138998	+	0.138998i
$355$			1.27316e14i			1.19847i
$356$	1.35277e14			1.25386
$357$	9.06856e13	+	1.08005e14i	0.827681	+	0.985752i
$358$	−1.82381e13			−0.163916
$359$			2.74607e12i			0.0243048i	0.999926	+	0.0121524i	$0.00386832\pi$
$359$			2.74607e12i			0.0243048i	−0.999926	+	0.0121524i	$0.996132\pi$
$360$	−6.66578e13	−	6.66578e13i	−0.581015	−	0.581015i
$361$	6.86599e13			0.589404
$362$	−2.97484e13	−	2.97484e13i	−0.251517	−	0.251517i
$363$	1.32013e14	−	1.32013e14i	1.09934	−	1.09934i
$364$	−1.11108e14	+	1.11108e14i	−0.911354	+	0.911354i
$365$			7.79314e13i			0.629654i
$366$		−	4.64038e14i		−	3.69324i
$367$	−1.39085e14	+	1.39085e14i	−1.09048	+	1.09048i	−0.0949987	+	0.995477i	$0.530285\pi$
$367$	−1.39085e14	+	1.39085e14i	−1.09048	+	1.09048i	−0.995477	+	0.0949987i	$0.969715\pi$
$368$	−1.06170e13	+	1.06170e13i	−0.0820049	+	0.0820049i
$369$	−1.52391e14	−	1.52391e14i	−1.15962	−	1.15962i
$370$	−3.64777e14			−2.73475
$371$	5.02881e12	+	5.02881e12i	0.0371457	+	0.0371457i
$372$		−	4.04779e14i		−	2.94599i
$373$	2.46763e14			1.76963			0.884813	−	0.465945i	$-0.154286\pi$
$373$	2.46763e14			1.76963			0.884813	+	0.465945i	$0.154286\pi$
$374$	6.14962e12	−	7.05500e13i	0.0434565	−	0.498543i
$375$	1.22723e14			0.854580
$376$			1.73288e13i			0.118915i
$377$	−2.35159e14	−	2.35159e14i	−1.59032	−	1.59032i
$378$	3.09603e14			2.06348
$379$	4.18147e13	+	4.18147e13i	0.274671	+	0.274671i	0.830977	−	0.556306i	$-0.187782\pi$
$379$	4.18147e13	+	4.18147e13i	0.274671	+	0.274671i	−0.556306	+	0.830977i	$0.687782\pi$
$380$	1.25265e14	−	1.25265e14i	0.811000	−	0.811000i
$381$	−1.31370e14	+	1.31370e14i	−0.838316	+	0.838316i
$382$			2.37972e13i			0.149685i
$383$			2.97263e14i			1.84310i	0.388265	+	0.921548i	$0.373075\pi$
$383$			2.97263e14i			1.84310i	−0.388265	+	0.921548i	$0.626925\pi$
$384$	−1.03486e14	+	1.03486e14i	−0.632499	+	0.632499i
$385$	−4.44281e13	+	4.44281e13i	−0.267685	+	0.267685i
$386$	−1.08365e14	−	1.08365e14i	−0.643665	−	0.643665i
$387$	−2.66909e14			−1.56298
$388$	1.10186e14	+	1.10186e14i	0.636137	+	0.636137i
$389$		−	4.39705e13i		−	0.250287i	−0.992139	−	0.125143i	$-0.960061\pi$
$389$		−	4.39705e13i		−	0.250287i	0.992139	−	0.125143i	$-0.0399391\pi$
$390$	1.05259e15			5.90749
$391$	2.62947e13	+	2.29203e12i	0.145511	+	0.0126838i
$392$	−2.19503e13			−0.119775
$393$			5.34286e13i			0.287484i
$394$	2.88270e13	+	2.88270e13i	0.152957	+	0.152957i
$395$	−5.67653e14			−2.97029
$396$	−1.14039e14	−	1.14039e14i	−0.588478	−	0.588478i
$397$	2.46656e14	−	2.46656e14i	1.25529	−	1.25529i	0.301970	−	0.953318i	$-0.402356\pi$
$397$	2.46656e14	−	2.46656e14i	1.25529	−	1.25529i	0.953318	−	0.301970i	$-0.0976442\pi$
$398$	−3.52086e14	+	3.52086e14i	−1.76722	+	1.76722i
$399$			1.66605e14i			0.824779i
$400$		−	2.14543e14i		−	1.04757i
$401$	5.99607e13	−	5.99607e13i	0.288784	−	0.288784i	−0.547816	−	0.836599i	$-0.684540\pi$
$401$	5.99607e13	−	5.99607e13i	0.288784	−	0.288784i	0.836599	+	0.547816i	$0.184540\pi$
$402$	−1.13089e14	+	1.13089e14i	−0.537251	+	0.537251i
$403$	3.22240e14	+	3.22240e14i	1.51009	+	1.51009i
$404$	3.92781e14			1.81574
$405$	−2.99530e14	−	2.99530e14i	−1.36596	−	1.36596i
$406$			3.60846e14i			1.62341i
$407$	−9.30747e13			−0.413107
$408$	1.03337e14	+	9.00756e12i	0.452506	+	0.0394436i
$409$	2.01734e14			0.871566			0.435783	−	0.900052i	$-0.356471\pi$
$409$	2.01734e14			0.871566			0.435783	+	0.900052i	$0.356471\pi$
$410$			4.14067e14i			1.76506i
$411$	1.03058e14	+	1.03058e14i	0.433464	+	0.433464i
$412$	−1.78015e14			−0.738792
$413$	9.59566e12	+	9.59566e12i	0.0392961	+	0.0392961i
$414$	7.86681e13	−	7.86681e13i	0.317904	−	0.317904i
$415$	2.24466e14	−	2.24466e14i	0.895128	−	0.895128i
$416$		−	5.43766e14i		−	2.13993i
$417$			5.42573e14i			2.10722i
$418$	5.91573e13	−	5.91573e13i	0.226746	−	0.226746i
$419$	5.92756e13	−	5.92756e13i	0.224233	−	0.224233i	−0.586045	−	0.810278i	$-0.699316\pi$
$419$	5.92756e13	−	5.92756e13i	0.224233	−	0.224233i	0.810278	+	0.586045i	$0.199316\pi$
$420$	−4.36330e14	−	4.36330e14i	−1.62909	−	1.62909i
$421$	3.83479e14			1.41315			0.706577	−	0.707636i	$-0.250238\pi$
$421$	3.83479e14			1.41315			0.706577	+	0.707636i	$0.250238\pi$
$422$	−2.70336e13	−	2.70336e13i	−0.0983299	−	0.0983299i
$423$			2.67373e14i			0.959943i
$424$	5.23087e12			0.0185380
$425$	−2.88832e14	+	2.42516e14i	−1.01043	+	0.848401i
$426$	−5.90496e14			−2.03922
$427$		−	3.06269e14i		−	1.04412i
$428$	1.71190e14	+	1.71190e14i	0.576152	+	0.576152i
$429$	2.68573e14			0.892376
$430$	3.62614e14	+	3.62614e14i	1.18951	+	1.18951i
$431$	3.10787e14	−	3.10787e14i	1.00655	−	1.00655i	0.00657657	−	0.999978i	$-0.497907\pi$
$431$	3.10787e14	−	3.10787e14i	1.00655	−	1.00655i	0.999978	−	0.00657657i	$-0.00209340\pi$
$432$	−3.35304e14	+	3.35304e14i	−1.07220	+	1.07220i
$433$		−	4.56138e13i		−	0.144017i	−0.997404	−	0.0720083i	$-0.977059\pi$
$433$		−	4.56138e13i		−	0.144017i	0.997404	−	0.0720083i	$-0.0229408\pi$
$434$		−	4.94470e14i		−	1.54151i
$435$	9.23491e14	−	9.23491e14i	2.84277	−	2.84277i
$436$	2.15801e13	−	2.15801e13i	0.0655961	−	0.0655961i
$437$	2.20486e13	+	2.20486e13i	0.0661808	+	0.0661808i
$438$	−3.61449e14			−1.07137
$439$	−2.77482e14	−	2.77482e14i	−0.812233	−	0.812233i	0.172736	−	0.984968i	$-0.444739\pi$
$439$	−2.77482e14	−	2.77482e14i	−0.812233	−	0.812233i	−0.984968	+	0.172736i	$0.944739\pi$
$440$			4.62133e13i			0.133591i
$441$	−3.38680e14			−0.966891
$442$	−5.99669e14	+	5.03509e14i	−1.69079	+	1.41966i
$443$	4.25682e14			1.18540			0.592700	−	0.805423i	$-0.298062\pi$
$443$	4.25682e14			1.18540			0.592700	+	0.805423i	$0.298062\pi$
$444$		−	9.14090e14i		−	2.51410i
$445$	−4.22919e14	−	4.22919e14i	−1.14889	−	1.14889i
$446$	−3.78973e14			−1.01687
$447$	−5.04709e14	−	5.04709e14i	−1.33767	−	1.33767i
$448$	−2.60092e14	+	2.60092e14i	−0.680922	+	0.680922i
$449$	−7.52186e13	+	7.52186e13i	−0.194523	+	0.194523i	−0.797647	−	0.603124i	$-0.793922\pi$
$449$	−7.52186e13	+	7.52186e13i	−0.194523	+	0.194523i	0.603124	+	0.797647i	$0.293922\pi$
$450$			1.58968e15i			4.06107i
$451$			1.05652e14i			0.266627i
$452$	−1.82291e14	+	1.82291e14i	−0.454468	+	0.454468i
$453$	2.93658e14	−	2.93658e14i	0.723272	−	0.723272i
$454$	2.73070e14	+	2.73070e14i	0.664456	+	0.664456i
$455$	6.94716e14			1.67011
$456$	8.66497e13	+	8.66497e13i	0.205807	+	0.205807i
$457$			2.71682e14i			0.637562i	0.947828	+	0.318781i	$0.103273\pi$
$457$			2.71682e14i			0.637562i	−0.947828	+	0.318781i	$0.896727\pi$
$458$	−6.73323e13			−0.156122
$459$	8.30431e14	+	7.23861e13i	1.90254	+	0.165839i
$460$	−1.15488e14			−0.261438
$461$			4.16252e13i			0.0931111i	0.998916	+	0.0465555i	$0.0148244\pi$
$461$			4.16252e13i			0.0931111i	−0.998916	+	0.0465555i	$0.985176\pi$
$462$	−2.06060e14	−	2.06060e14i	−0.455472	−	0.455472i
$463$	−6.21736e14			−1.35803			−0.679017	−	0.734123i	$-0.737594\pi$
$463$	−6.21736e14			−1.35803			−0.679017	+	0.734123i	$0.737594\pi$
$464$	−3.90800e14	−	3.90800e14i	−0.843540	−	0.843540i
$465$	−1.26547e15	+	1.26547e15i	−2.69935	+	2.69935i
$466$	−1.54993e14	+	1.54993e14i	−0.326731	+	0.326731i
$467$			4.08408e14i			0.850846i	0.904995	+	0.425423i	$0.139875\pi$
$467$			4.08408e14i			0.850846i	−0.904995	+	0.425423i	$0.860125\pi$
$468$			1.78321e15i			3.67156i
$469$	−7.46396e13	+	7.46396e13i	−0.151886	+	0.151886i
$470$	3.63244e14	−	3.63244e14i	0.730568	−	0.730568i
$471$	−7.14792e14	−	7.14792e14i	−1.42090	−	1.42090i
$472$	9.98122e12			0.0196111
$473$	9.25230e13	+	9.25230e13i	0.179686	+	0.179686i
$474$		−	2.63280e15i		−	5.05401i
$475$	−4.45544e14			−0.845426
$476$	4.57302e14	+	3.98616e13i	0.857758	+	0.0747680i
$477$	8.07093e13			0.149648
$478$		−	6.57767e14i		−	1.20564i
$479$	2.45514e14	+	2.45514e14i	0.444868	+	0.444868i	0.893644	−	0.448776i	$-0.148140\pi$
$479$	2.45514e14	+	2.45514e14i	0.444868	+	0.444868i	−0.448776	+	0.893644i	$0.648140\pi$
$480$	2.13542e15			3.82522
$481$	7.27697e14	+	7.27697e14i	1.28870	+	1.28870i
$482$	4.00451e14	−	4.00451e14i	0.701117	−	0.701117i
$483$	7.68006e13	−	7.68006e13i	0.132940	−	0.132940i
$484$		−	6.07678e14i		−	1.03998i
$485$		−	6.88950e14i		−	1.16576i
$486$	1.98759e14	−	1.98759e14i	0.332527	−	0.332527i
$487$	−1.31356e14	+	1.31356e14i	−0.217290	+	0.217290i	−0.807355	−	0.590066i	$-0.799102\pi$
$487$	−1.31356e14	+	1.31356e14i	−0.217290	+	0.217290i	0.590066	+	0.807355i	$0.299102\pi$
$488$	−1.59287e14	−	1.59287e14i	−0.260539	−	0.260539i
$489$	1.82672e15			2.95442
$490$	4.60120e14	+	4.60120e14i	0.735856	+	0.735856i
$491$			4.88776e14i			0.772969i	0.922296	+	0.386484i	$0.126311\pi$
$491$			4.88776e14i			0.772969i	−0.922296	+	0.386484i	$0.873689\pi$
$492$	−1.03761e15			−1.62265
$493$	−8.43668e13	+	9.67877e14i	−0.130471	+	1.49679i
$494$	−9.25033e14			−1.41468
$495$			7.13044e14i			1.07842i
$496$	5.35516e14	+	5.35516e14i	0.800983	+	0.800983i
$497$	−3.89732e14			−0.576509
$498$	1.04108e15	+	1.04108e15i	1.52308	+	1.52308i
$499$	−1.54737e14	+	1.54737e14i	−0.223893	+	0.223893i	−0.810136	−	0.586242i	$-0.800607\pi$
$499$	−1.54737e14	+	1.54737e14i	−0.223893	+	0.223893i	0.586242	+	0.810136i	$0.300607\pi$
$500$	2.82456e14	−	2.82456e14i	0.404218	−	0.404218i
$501$		−	1.83057e15i		−	2.59107i
$502$			3.55419e14i			0.497588i
$503$	−8.55184e14	+	8.55184e14i	−1.18423	+	1.18423i	−0.205590	+	0.978638i	$0.565911\pi$
$503$	−8.55184e14	+	8.55184e14i	−1.18423	+	1.18423i	−0.978638	+	0.205590i	$0.934089\pi$
$504$	2.04049e14	−	2.04049e14i	0.279490	−	0.279490i
$505$	−1.22796e15	−	1.22796e15i	−1.66372	−	1.66372i
$506$	−5.45399e13			−0.0730948
$507$	−1.16270e15	−	1.16270e15i	−1.54143	−	1.54143i
$508$			6.04716e14i			0.793051i
$509$	1.09653e15			1.42257			0.711284	−	0.702905i	$-0.248114\pi$
$509$	1.09653e15			1.42257			0.711284	+	0.702905i	$0.248114\pi$
$510$	−1.97732e15	−	2.35495e15i	−2.53771	−	3.02236i
$511$	−2.38559e14			−0.302887
$512$		−	1.06708e15i		−	1.34033i
$513$	6.96330e14	+	6.96330e14i	0.865306	+	0.865306i
$514$	−2.61855e14			−0.321932
$515$	5.56531e14	+	5.56531e14i	0.676939	+	0.676939i
$516$	−9.08671e14	+	9.08671e14i	−1.09354	+	1.09354i
$517$	9.26837e13	−	9.26837e13i	0.110358	−	0.110358i
$518$		−	1.11663e15i		−	1.31552i
$519$			1.19064e15i			1.38791i
$520$	3.61315e14	−	3.61315e14i	0.416742	−	0.416742i
$521$	3.29114e13	−	3.29114e13i	0.0375612	−	0.0375612i	−0.688077	−	0.725638i	$-0.741545\pi$
$521$	3.29114e13	−	3.29114e13i	0.0375612	−	0.0375612i	0.725638	+	0.688077i	$0.241545\pi$
$522$	2.89568e15	+	2.89568e15i	3.27011	+	3.27011i
$523$	−2.64851e14			−0.295966			−0.147983	−	0.988990i	$-0.547278\pi$
$523$	−2.64851e14			−0.295966			−0.147983	+	0.988990i	$0.547278\pi$
$524$	1.22970e14	+	1.22970e14i	0.135981	+	0.135981i
$525$			1.55194e15i			1.69824i
$526$	−1.28949e15			−1.39636
$527$	1.15608e14	−	1.32629e15i	0.123889	−	1.42128i
$528$	4.46329e14			0.473335
$529$			9.32482e14i			0.978666i
$530$	−1.09649e14	−	1.09649e14i	−0.113890	−	0.113890i
$531$	1.54004e14			0.158312
$532$	3.83455e14	+	3.83455e14i	0.390122	+	0.390122i
$533$	8.26028e14	−	8.26028e14i	0.831754	−	0.831754i
$534$	1.96152e15	−	1.96152e15i	1.95486	−	1.95486i
$535$		−	1.07039e15i		−	1.05583i
$536$			7.76387e13i			0.0758005i
$537$	−1.42881e14	+	1.42881e14i	−0.138075	+	0.138075i
$538$	1.46532e14	−	1.46532e14i	0.140162	−	0.140162i
$539$	1.17402e14	+	1.17402e14i	0.111157	+	0.111157i
$540$	−3.64731e15			−3.41827
$541$	1.24573e15	+	1.24573e15i	1.15568	+	1.15568i	0.985394	+	0.170288i	$0.0544697\pi$
$541$	1.24573e15	+	1.24573e15i	1.15568	+	1.15568i	0.170288	+	0.985394i	$0.445530\pi$
$542$		−	3.34251e14i		−	0.306956i
$543$	−4.66110e14			−0.423730
$544$	−1.21657e15	+	1.02148e15i	−1.09482	+	0.919259i
$545$	−1.34932e14			−0.120209
$546$			3.22212e15i			2.84173i
$547$	−7.86402e14	−	7.86402e14i	−0.686617	−	0.686617i	0.274866	−	0.961483i	$-0.411367\pi$
$547$	−7.86402e14	−	7.86402e14i	−0.686617	−	0.686617i	−0.961483	+	0.274866i	$0.911367\pi$
$548$	4.74394e14			0.410059
$549$	−2.45771e15	−	2.45771e15i	−2.10321	−	2.10321i
$550$	5.51055e14	−	5.51055e14i	0.466875	−	0.466875i
$551$	−8.11581e14	+	8.11581e14i	−0.680766	+	0.680766i
$552$		−	7.98865e13i		−	0.0663450i
$553$		−	1.73767e15i		−	1.42882i
$554$	−2.15138e15	+	2.15138e15i	−1.75151	+	1.75151i
$555$	−2.85773e15	+	2.85773e15i	−2.30362	+	2.30362i
$556$	1.24877e15	+	1.24877e15i	0.996719	+	0.996719i
$557$	5.59521e14			0.442194			0.221097	−	0.975252i	$-0.429036\pi$
$557$	5.59521e14			0.442194			0.221097	+	0.975252i	$0.429036\pi$
$558$	−3.96797e15	−	3.96797e15i	−3.10513	−	3.10513i
$559$		−	1.44677e15i		−	1.12107i
$560$	1.15452e15			0.885861
$561$	−5.04525e14	−	6.00879e14i	−0.383342	−	0.456553i
$562$	3.04414e15			2.29042
$563$		−	7.94518e13i		−	0.0591981i	−0.999562	−	0.0295990i	$-0.990577\pi$
$563$		−	7.94518e13i		−	0.0591981i	0.999562	−	0.0295990i	$-0.00942304\pi$
$564$	9.10249e14	+	9.10249e14i	0.671622	+	0.671622i
$565$	1.13980e15			0.832838
$566$	1.34679e15	+	1.34679e15i	0.974563	+	0.974563i
$567$	9.16905e14	−	9.16905e14i	0.657079	−	0.657079i
$568$	−2.02696e14	+	2.02696e14i	−0.143856	+	0.143856i
$569$			1.23663e15i			0.869204i	0.900623	+	0.434602i	$0.143111\pi$
$569$			1.23663e15i			0.869204i	−0.900623	+	0.434602i	$0.856889\pi$
$570$		−	3.63269e15i		−	2.52881i
$571$	1.21327e15	−	1.21327e15i	0.836485	−	0.836485i	−0.151909	−	0.988394i	$-0.548542\pi$
$571$	1.21327e15	−	1.21327e15i	0.836485	−	0.836485i	0.988394	+	0.151909i	$0.0485422\pi$
$572$	6.18143e14	−	6.18143e14i	0.422095	−	0.422095i
$573$	1.86432e14	+	1.86432e14i	0.126087	+	0.126087i
$574$	−1.26752e15			−0.849062
$575$	2.05384e14	+	2.05384e14i	0.136268	+	0.136268i
$576$			4.17431e15i			2.74322i
$577$	−2.12427e15			−1.38275			−0.691373	−	0.722498i	$-0.742994\pi$
$577$	−2.12427e15			−1.38275			−0.691373	+	0.722498i	$0.742994\pi$
$578$	2.25300e15	+	3.95781e14i	1.45264	+	0.255183i
$579$	−1.69791e15			−1.08438
$580$		−	4.25097e15i		−	2.68927i
$581$	6.87121e14	+	6.87121e14i	0.430591	+	0.430591i
$582$	3.19538e15			1.98356
$583$	−2.79775e13	−	2.79775e13i	−0.0172041	−	0.0172041i
$584$	−1.24072e14	+	1.24072e14i	−0.0755795	+	0.0755795i
$585$	5.57487e15	−	5.57487e15i	3.36417	−	3.36417i
$586$			2.53917e14i			0.151794i
$587$			2.35581e15i			1.39518i	0.716497	+	0.697590i	$0.245744\pi$
$587$			2.35581e15i			1.39518i	−0.716497	+	0.697590i	$0.754256\pi$
$588$	−1.15301e15	+	1.15301e15i	−0.676484	+	0.676484i
$589$	1.11211e15	−	1.11211e15i	0.646421	−	0.646421i
$590$	−2.09225e14	−	2.09225e14i	−0.120484	−	0.120484i
$591$	4.51673e14			0.257687
$592$	1.20933e15	+	1.20933e15i	0.683556	+	0.683556i
$593$			2.91794e14i			0.163409i	0.996657	+	0.0817043i	$0.0260363\pi$
$593$			2.91794e14i			0.163409i	−0.996657	+	0.0817043i	$0.973964\pi$
$594$	−1.72246e15			−0.955706
$595$	−1.30505e15	−	1.55429e15i	−0.717436	−	0.854453i
$596$	−2.32325e15			−1.26544
$597$			5.51662e15i			2.97724i
$598$	4.26416e14	+	4.26416e14i	0.228022	+	0.228022i
$599$	−2.97010e15			−1.57370			−0.786852	−	0.617141i	$-0.788291\pi$
$599$	−2.97010e15			−1.57370			−0.786852	+	0.617141i	$0.788291\pi$
$600$	8.07149e14	+	8.07149e14i	0.423762	+	0.423762i
$601$	2.52397e14	−	2.52397e14i	0.131303	−	0.131303i	−0.638401	−	0.769704i	$-0.720404\pi$
$601$	2.52397e14	−	2.52397e14i	0.131303	−	0.131303i	0.769704	+	0.638401i	$0.220404\pi$
$602$	−1.11001e15	+	1.11001e15i	−0.572200	+	0.572200i
$603$			1.19792e15i			0.611903i
$604$		−	1.35175e15i		−	0.684218i
$605$	−1.89979e15	+	1.89979e15i	−0.952909	+	0.952909i
$606$	5.69531e15	−	5.69531e15i	2.83086	−	2.83086i
$607$	−2.37979e14	−	2.37979e14i	−0.117220	−	0.117220i	0.646064	−	0.763283i	$-0.276414\pi$
$607$	−2.37979e14	−	2.37979e14i	−0.117220	−	0.117220i	−0.763283	+	0.646064i	$0.776414\pi$
$608$	−1.87664e15			−0.916035
$609$	2.82694e15	+	2.82694e15i	1.36748	+	1.36748i
$610$			6.67793e15i			3.20131i
$611$	−1.44928e15			−0.688534
$612$	3.98958e15	−	3.34983e15i	1.87843	−	1.57721i
$613$	−7.33735e14			−0.342379			−0.171189	−	0.985238i	$-0.554761\pi$
$613$	−7.33735e14			−0.342379			−0.171189	+	0.985238i	$0.554761\pi$
$614$		−	3.01280e15i		−	1.39330i
$615$	3.24388e15	+	3.24388e15i	1.48680	+	1.48680i
$616$	−1.41466e14			−0.0642624
$617$	−2.78895e15	−	2.78895e15i	−1.25566	−	1.25566i	−0.953144	−	0.302517i	$-0.902173\pi$
$617$	−2.78895e15	−	2.78895e15i	−1.25566	−	1.25566i	−0.302517	−	0.953144i	$-0.597827\pi$
$618$	−2.58121e15	+	2.58121e15i	−1.15183	+	1.15183i
$619$	−4.02604e14	+	4.02604e14i	−0.178065	+	0.178065i	−0.790512	−	0.612447i	$-0.790185\pi$
$619$	−4.02604e14	+	4.02604e14i	−0.178065	+	0.178065i	0.612447	+	0.790512i	$0.290185\pi$
$620$			5.82514e15i			2.55360i
$621$		−	6.41980e14i		−	0.278944i
$622$	3.26758e14	−	3.26758e14i	0.140727	−	0.140727i
$623$	1.29462e15	−	1.29462e15i	0.552658	−	0.552658i
$624$	−3.48959e15	−	3.48959e15i	−1.47659	−	1.47659i
$625$	1.37955e15			0.578623
$626$	2.73677e15	+	2.73677e15i	1.13784	+	1.13784i
$627$		−	9.26899e14i		−	0.381998i
$628$	−3.29030e15			−1.34418
$629$	2.61072e14	−	2.99508e15i	0.105726	−	1.21292i
$630$	−8.55451e15			−3.43417
$631$		−	2.01985e15i		−	0.803819i	−0.915680	−	0.401909i	$-0.868347\pi$
$631$		−	2.01985e15i		−	0.803819i	0.915680	−	0.401909i	$-0.131653\pi$
$632$	−9.03743e14	−	9.03743e14i	−0.356534	−	0.356534i
$633$	−4.23573e14			−0.165656
$634$	−4.91583e14	−	4.91583e14i	−0.190592	−	0.190592i
$635$	1.89053e15	−	1.89053e15i	0.726655	−	0.726655i
$636$	2.74768e14	−	2.74768e14i	0.104701	−	0.104701i
$637$		−	1.83580e15i		−	0.693518i
$638$		−	2.00755e15i		−	0.751887i
$639$	−3.12748e15	+	3.12748e15i	−1.16129	+	1.16129i
$640$	1.48926e15	−	1.48926e15i	0.548252	−	0.548252i
$641$	1.36409e15	+	1.36409e15i	0.497881	+	0.497881i	0.910778	−	0.412897i	$-0.135483\pi$
$641$	1.36409e15	+	1.36409e15i	0.497881	+	0.497881i	−0.412897	+	0.910778i	$0.635483\pi$
$642$	4.96450e15			1.79652
$643$	−2.29626e15	−	2.29626e15i	−0.823874	−	0.823874i	0.162787	−	0.986661i	$-0.447952\pi$
$643$	−2.29626e15	−	2.29626e15i	−0.823874	−	0.823874i	−0.986661	+	0.162787i	$0.947952\pi$
$644$		−	3.53525e14i		−	0.125762i
$645$	5.68158e15			2.00397
$646$	1.73771e15	+	2.06958e15i	0.607712	+	0.723774i
$647$	4.07163e14			0.141187			0.0705935	−	0.997505i	$-0.477511\pi$
$647$	4.07163e14			0.141187			0.0705935	+	0.997505i	$0.477511\pi$
$648$		−	9.53747e14i		−	0.327922i
$649$	−5.33849e13	−	5.33849e13i	−0.0182001	−	0.0182001i
$650$	−8.61676e15			−2.91287
$651$	−3.87377e15	−	3.87377e15i	−1.29849	−	1.29849i
$652$	4.20433e15	−	4.20433e15i	1.39745	−	1.39745i
$653$	−8.59695e14	+	8.59695e14i	−0.283349	+	0.283349i	−0.834443	−	0.551094i	$-0.814211\pi$
$653$	−8.59695e14	+	8.59695e14i	−0.283349	+	0.283349i	0.551094	+	0.834443i	$0.314211\pi$
$654$		−	6.25822e14i		−	0.204538i
$655$		−	7.68886e14i		−	0.249192i
$656$	1.37274e15	−	1.37274e15i	0.441180	−	0.441180i
$657$	−1.91436e15	+	1.91436e15i	−0.610119	+	0.610119i
$658$	1.11194e15	+	1.11194e15i	0.351431	+	0.351431i
$659$	5.95837e15			1.86749			0.933744	−	0.357941i	$-0.116521\pi$
$659$	5.95837e15			1.86749			0.933744	+	0.357941i	$0.116521\pi$
$660$	2.42750e15	+	2.42750e15i	0.754515	+	0.754515i
$661$			5.95831e15i			1.83660i	0.395882	+	0.918301i	$0.370439\pi$
$661$			5.95831e15i			1.83660i	−0.395882	+	0.918301i	$0.629561\pi$
$662$	−4.92196e15			−1.50459
$663$	−7.53340e14	+	8.64251e15i	−0.228385	+	2.62009i
$664$	7.14730e14			0.214891
$665$		−	2.39760e15i		−	0.714920i
$666$	−8.96064e15	−	8.96064e15i	−2.64991	−	2.64991i
$667$	7.48235e14			0.219455
$668$	−4.21320e15	−	4.21320e15i	−1.22558	−	1.22558i
$669$	−2.96894e15	+	2.96894e15i	−0.856561	+	0.856561i
$670$	1.62745e15	−	1.62745e15i	0.465691	−	0.465691i
$671$			1.70391e15i			0.483585i
$672$			6.53682e15i			1.84007i
$673$	3.60940e15	−	3.60940e15i	1.00775	−	1.00775i	0.00777956	−	0.999970i	$-0.497524\pi$
$673$	3.60940e15	−	3.60940e15i	1.00775	−	1.00775i	0.999970	−	0.00777956i	$-0.00247634\pi$
$674$	7.34119e14	−	7.34119e14i	0.203300	−	0.203300i
$675$	6.48637e15	+	6.48637e15i	1.78169	+	1.78169i
$676$	−5.35210e15			−1.45820
$677$	−1.39998e15	−	1.39998e15i	−0.378341	−	0.378341i	0.492162	−	0.870504i	$-0.336207\pi$
$677$	−1.39998e15	−	1.39998e15i	−0.378341	−	0.378341i	−0.870504	+	0.492162i	$0.836207\pi$
$678$			5.28642e15i			1.41709i
$679$	2.10898e15			0.560774
$680$	−1.48711e15	−	1.29627e14i	−0.392234	−	0.0341898i
$681$	4.27856e15			1.11941
$682$			2.75096e15i			0.713953i
$683$	3.25314e15	+	3.25314e15i	0.837509	+	0.837509i	0.988530	−	0.151022i	$-0.0482564\pi$
$683$	3.25314e15	+	3.25314e15i	0.837509	+	0.837509i	−0.151022	+	0.988530i	$0.548256\pi$
$684$	6.15421e15			1.57168
$685$	−1.48310e15	−	1.48310e15i	−0.375728	−	0.375728i
$686$	−4.44861e15	+	4.44861e15i	−1.11800	+	1.11800i
$687$	−5.27494e14	+	5.27494e14i	−0.131509	+	0.131509i
$688$		−	2.40431e15i		−	0.594641i
$689$			4.37480e14i			0.107338i
$690$	−1.67457e15	+	1.67457e15i	−0.407600	+	0.407600i
$691$	−7.54973e14	+	7.54973e14i	−0.182306	+	0.182306i	−0.792360	−	0.610054i	$-0.791148\pi$
$691$	−7.54973e14	+	7.54973e14i	−0.182306	+	0.182306i	0.610054	+	0.792360i	$0.291148\pi$
$692$	2.74036e15	+	2.74036e15i	0.656483	+	0.656483i
$693$	−2.18273e15			−0.518761
$694$	−8.23044e15	−	8.23044e15i	−1.94064	−	1.94064i
$695$		−	7.80812e15i		−	1.82654i
$696$	2.94053e15			0.682455
$697$	−3.39980e15	−	2.96350e14i	−0.782839	−	0.0682376i
$698$	3.91382e15			0.894121
$699$			2.42849e15i			0.550443i
$700$	3.57191e15	+	3.57191e15i	0.803270	+	0.803270i
$701$	8.43605e15			1.88230			0.941152	−	0.337983i	$-0.109745\pi$
$701$	8.43605e15			1.88230			0.941152	+	0.337983i	$0.109745\pi$
$702$	1.34669e16	+	1.34669e16i	2.98136	+	2.98136i
$703$	2.51143e15	−	2.51143e15i	0.551653	−	0.551653i
$704$	1.44701e15	−	1.44701e15i	0.315370	−	0.315370i
$705$		−	5.69145e15i		−	1.23079i
$706$			4.49988e15i			0.965551i
$707$	3.75895e15	−	3.75895e15i	0.800312	−	0.800312i
$708$	5.24295e14	−	5.24295e14i	0.110763	−	0.110763i
$709$	−2.68360e15	−	2.68360e15i	−0.562552	−	0.562552i	0.367479	−	0.930032i	$-0.380221\pi$
$709$	−2.68360e15	−	2.68360e15i	−0.562552	−	0.562552i	−0.930032	+	0.367479i	$0.880221\pi$
$710$	8.49778e15			1.76760
$711$	−1.39442e16	−	1.39442e16i	−2.87814	−	2.87814i
$712$		−	1.34663e15i		−	0.275810i
$713$	−1.02531e15			−0.208383
$714$	7.20885e15	−	6.05287e15i	1.45387	−	1.22073i
$715$	−3.86501e15			−0.773514
$716$			6.57702e14i			0.130619i
$717$	−5.15307e15	−	5.15307e15i	−1.01557	−	1.01557i
$718$	1.83288e14			0.0358468
$719$	1.42240e15	+	1.42240e15i	0.276066	+	0.276066i	0.831536	−	0.555470i	$-0.187462\pi$
$719$	1.42240e15	+	1.42240e15i	0.276066	+	0.276066i	−0.555470	+	0.831536i	$0.687462\pi$
$720$	9.26463e15	−	9.26463e15i	1.78443	−	1.78443i
$721$	−1.70362e15	+	1.70362e15i	−0.325634	+	0.325634i
$722$		−	4.58275e15i		−	0.869304i
$723$		−	6.27442e15i		−	1.18117i
$724$	−1.07279e15	+	1.07279e15i	−0.200425	+	0.200425i
$725$	−7.55994e15	+	7.55994e15i	−1.40171	+	1.40171i
$726$	−8.81132e15	−	8.81132e15i	−1.62140	−	1.62140i
$727$	−3.91636e15			−0.715226			−0.357613	−	0.933870i	$-0.616409\pi$
$727$	−3.91636e15			−0.715226			−0.357613	+	0.933870i	$0.616409\pi$
$728$	1.10604e15	+	1.10604e15i	0.200469	+	0.200469i
$729$			3.93707e15i			0.708225i
$730$	5.20158e15			0.928666
$731$	−3.23685e15	+	2.71780e15i	−0.573558	+	0.481584i
$732$	−1.67341e16			−2.94302
$733$			6.49057e15i			1.13295i	0.824079	+	0.566475i	$0.191693\pi$
$733$			6.49057e15i			1.13295i	−0.824079	+	0.566475i	$0.808307\pi$
$734$	9.28330e15	+	9.28330e15i	1.60833	+	1.60833i
$735$	7.20934e15			1.23970
$736$	8.65084e14	+	8.65084e14i	0.147649	+	0.147649i
$737$	4.15254e14	−	4.15254e14i	0.0703465	−	0.0703465i
$738$	−1.01714e16	+	1.01714e16i	−1.71030	+	1.71030i
$739$		−	2.64754e14i		−	0.0441874i	−0.999756	−	0.0220937i	$-0.992967\pi$
$739$		−	2.64754e14i		−	0.0441874i	0.999756	−	0.0220937i	$-0.00703322\pi$
$740$			1.31546e16i			2.17923i
$741$	−7.24688e15	+	7.24688e15i	−1.19166	+	1.19166i
$742$	3.35651e14	−	3.35651e14i	0.0547857	−	0.0547857i
$743$	6.98834e15	+	6.98834e15i	1.13223	+	1.13223i	0.989805	+	0.142428i	$0.0454909\pi$
$743$	6.98834e15	+	6.98834e15i	1.13223	+	1.13223i	0.142428	+	0.989805i	$0.454509\pi$
$744$	−4.02942e15			−0.648025
$745$	7.26322e15	+	7.26322e15i	1.15950	+	1.15950i
$746$		−	1.64704e16i		−	2.61000i
$747$	1.10279e16			1.73471
$748$	−2.54417e15	−	2.21768e14i	−0.397272	−	0.0346290i
$749$	3.27661e15			0.507895
$750$		−	8.19121e15i		−	1.26041i
$751$	−6.60216e15	−	6.60216e15i	−1.00848	−	1.00848i	−0.999964	−	0.00851432i	$-0.997290\pi$
$751$	−6.60216e15	−	6.60216e15i	−1.00848	−	1.00848i	−0.00851432	−	0.999964i	$-0.502710\pi$
$752$	−2.40849e15			−0.365213
$753$	2.78442e15	+	2.78442e15i	0.419143	+	0.419143i
$754$	−1.56959e16	+	1.56959e16i	−2.34554	+	2.34554i
$755$	−4.22601e15	+	4.22601e15i	−0.626934	+	0.626934i
$756$		−	1.11649e16i		−	1.64432i
$757$		−	8.75170e15i		−	1.27957i	−0.768553	−	0.639787i	$-0.779023\pi$
$757$		−	8.75170e15i		−	1.27957i	0.768553	−	0.639787i	$-0.220977\pi$
$758$	2.79095e15	−	2.79095e15i	0.405109	−	0.405109i
$759$	−4.27276e14	+	4.27276e14i	−0.0615714	+	0.0615714i
$760$	−1.24697e15	−	1.24697e15i	−0.178394	−	0.178394i
$761$	−2.46547e15			−0.350174			−0.175087	−	0.984553i	$-0.556021\pi$
$761$	−2.46547e15			−0.350174			−0.175087	+	0.984553i	$0.556021\pi$
$762$	8.76836e15	+	8.76836e15i	1.23642	+	1.23642i
$763$		−	4.13047e14i		−	0.0578249i
$764$	8.58175e14			0.119279
$765$	−2.29453e16	−	2.00007e15i	−3.16632	−	0.275999i
$766$	1.98410e16			2.71835
$767$			8.34772e14i			0.113552i
$768$	−5.18437e15	−	5.18437e15i	−0.700180	−	0.700180i
$769$	−1.38640e16			−1.85906			−0.929531	−	0.368743i	$-0.879788\pi$
$769$	−1.38640e16			−1.85906			−0.929531	+	0.368743i	$0.879788\pi$
$770$	2.96539e15	+	2.96539e15i	0.394805	+	0.394805i
$771$	−2.05142e15	+	2.05142e15i	−0.271179	+	0.271179i
$772$	−3.90787e15	+	3.90787e15i	−0.512915	+	0.512915i
$773$			3.97357e14i			0.0517838i	0.999665	+	0.0258919i	$0.00824257\pi$
$773$			3.97357e14i			0.0517838i	−0.999665	+	0.0258919i	$0.991757\pi$
$774$			1.78150e16i			2.30521i
$775$	1.03594e16	−	1.03594e16i	1.33100	−	1.33100i
$776$	1.09686e15	−	1.09686e15i	0.139930	−	0.139930i
$777$	−8.74792e15	−	8.74792e15i	−1.10813	−	1.10813i
$778$	−2.93484e15			−0.369144
$779$	−2.85078e15	−	2.85078e15i	−0.356048	−	0.356048i
$780$		−	3.79584e16i		−	4.70747i
$781$	2.16826e15			0.267011
$782$	1.52983e14	−	1.75506e15i	0.0187071	−	0.214612i
$783$	2.36305e16			2.86935
$784$		−	3.05083e15i		−	0.367857i
$785$	1.02865e16	+	1.02865e16i	1.23164	+	1.23164i
$786$	3.56612e15			0.424006
$787$	3.41657e15	+	3.41657e15i	0.403394	+	0.403394i	0.879427	−	0.476033i	$-0.157926\pi$
$787$	3.41657e15	+	3.41657e15i	0.403394	+	0.403394i	−0.476033	+	0.879427i	$0.657926\pi$
$788$	1.03956e15	−	1.03956e15i	0.121887	−	0.121887i
$789$	−1.01021e16	+	1.01021e16i	−1.17622	+	1.17622i
$790$			3.78883e16i			4.38083i
$791$			3.48908e15i			0.400627i
$792$	−1.13522e15	+	1.13522e15i	−0.129446	+	0.129446i
$793$	1.33219e16	−	1.33219e16i	1.50856	−	1.50856i
$794$	−1.64632e16	−	1.64632e16i	−1.85140	−	1.85140i
$795$	−1.71802e15			−0.191871
$796$	1.26969e16	+	1.26969e16i	1.40824	+	1.40824i
$797$		−	6.13618e15i		−	0.675892i	−0.941166	−	0.337946i	$-0.890268\pi$
$797$		−	6.13618e15i		−	0.675892i	0.941166	−	0.337946i	$-0.109732\pi$
$798$	1.11202e16			1.21645
$799$	2.72252e15	+	3.24247e15i	0.295777	+	0.352265i
$800$	−1.74811e16			−1.88614
$801$		−	2.07778e16i		−	2.22649i
$802$	−4.00212e15	−	4.00212e15i	−0.425922	−	0.425922i
$803$	1.32721e15			0.140283
$804$	4.07822e15	+	4.07822e15i	0.428117	+	0.428117i
$805$	−1.10523e15	+	1.10523e15i	−0.115233	+	0.115233i
$806$	2.15081e16	−	2.15081e16i	2.22720	−	2.22720i
$807$		−	2.29592e15i		−	0.236131i
$808$		−	3.90998e15i		−	0.399404i
$809$	2.89142e15	−	2.89142e15i	0.293356	−	0.293356i	−0.545049	−	0.838404i	$-0.683489\pi$
$809$	2.89142e15	−	2.89142e15i	0.293356	−	0.293356i	0.838404	+	0.545049i	$0.183489\pi$
$810$	−1.99923e16	+	1.99923e16i	−2.01463	+	2.01463i
$811$	−1.93039e15	−	1.93039e15i	−0.193211	−	0.193211i	0.603871	−	0.797082i	$-0.293624\pi$
$811$	−1.93039e15	−	1.93039e15i	−0.193211	−	0.193211i	−0.797082	+	0.603871i	$0.793624\pi$
$812$	1.30128e16			1.29364
$813$	−2.61859e15	−	2.61859e15i	−0.258565	−	0.258565i
$814$			6.21234e15i			0.609285i
$815$	−2.62881e16			−2.56090
$816$	−1.25194e15	+	1.43626e16i	−0.121140	+	1.38975i
$817$	−4.99308e15			−0.479896
$818$		−	1.34649e16i		−	1.28546i
$819$	1.70655e16	+	1.70655e16i	1.61829	+	1.61829i
$820$	1.49321e16			1.40652
$821$	4.91462e15	+	4.91462e15i	0.459835	+	0.459835i	0.898601	−	0.438766i	$-0.144584\pi$
$821$	4.91462e15	+	4.91462e15i	0.459835	+	0.459835i	−0.438766	+	0.898601i	$0.644584\pi$
$822$	6.87870e15	−	6.87870e15i	0.639309	−	0.639309i
$823$	5.50740e15	−	5.50740e15i	0.508449	−	0.508449i	−0.405601	−	0.914050i	$-0.632938\pi$
$823$	5.50740e15	−	5.50740e15i	0.508449	−	0.508449i	0.914050	+	0.405601i	$0.132938\pi$
$824$			1.77207e15i			0.162511i
$825$		−	8.63414e15i		−	0.786543i
$826$	6.40469e14	−	6.40469e14i	0.0579572	−	0.0579572i
$827$	9.30844e14	−	9.30844e14i	0.0836752	−	0.0836752i	−0.664030	−	0.747706i	$-0.731155\pi$
$827$	9.30844e14	−	9.30844e14i	0.0836752	−	0.0836752i	0.747706	+	0.664030i	$0.231155\pi$
$828$	−2.83693e15	−	2.83693e15i	−0.253327	−	0.253327i
$829$	−2.17487e15			−0.192923			−0.0964613	−	0.995337i	$-0.530752\pi$
$829$	−2.17487e15			−0.192923			−0.0964613	+	0.995337i	$0.530752\pi$
$830$	−1.49821e16	−	1.49821e16i	−1.32021	−	1.32021i
$831$			3.37086e16i			2.95077i
$832$	−2.26266e16			−1.96762
$833$	−4.10723e15	+	3.44861e15i	−0.354815	+	0.297918i
$834$	3.62144e16			3.10791
$835$			2.63436e16i			2.24595i
$836$	−2.13333e15	−	2.13333e15i	−0.180686	−	0.180686i
$837$	−3.23811e16			−2.72459
$838$	−3.95639e15	−	3.95639e15i	−0.330717	−	0.330717i
$839$	2.51490e15	−	2.51490e15i	0.208848	−	0.208848i	−0.594930	−	0.803778i	$-0.702820\pi$
$839$	2.51490e15	−	2.51490e15i	0.208848	−	0.208848i	0.803778	+	0.594930i	$0.202820\pi$
$840$	−4.34350e15	+	4.34350e15i	−0.358347	+	0.358347i
$841$			1.53411e16i			1.25742i
$842$		−	2.55955e16i		−	2.08424i
$843$	2.38484e16	−	2.38484e16i	1.92933	−	1.92933i
$844$	−9.74887e14	+	9.74887e14i	−0.0783557	+	0.0783557i
$845$	1.67323e16	+	1.67323e16i	1.33612	+	1.33612i
$846$	1.78460e16			1.41580
$847$	−5.81554e15	−	5.81554e15i	−0.458386	−	0.458386i
$848$			7.27028e14i			0.0569343i
$849$	2.11020e16			1.64184
$850$	1.61869e16	+	1.92783e16i	1.25129	+	1.49027i
$851$	−2.31540e15			−0.177834
$852$			2.12945e16i			1.62499i
$853$	1.68074e16	+	1.68074e16i	1.27433	+	1.27433i	0.943793	+	0.330537i	$0.107230\pi$
$853$	1.68074e16	+	1.68074e16i	1.27433	+	1.27433i	0.330537	+	0.943793i	$0.392770\pi$
$854$	−2.04421e16			−1.53995
$855$	−1.92400e16	−	1.92400e16i	−1.44010	−	1.44010i
$856$	1.70413e15	−	1.70413e15i	0.126735	−	0.126735i
$857$	−1.44824e16	+	1.44824e16i	−1.07015	+	1.07015i	−0.0728077	+	0.997346i	$0.523196\pi$
$857$	−1.44824e16	+	1.44824e16i	−1.07015	+	1.07015i	−0.997346	+	0.0728077i	$0.976804\pi$
$858$		−	1.79261e16i		−	1.31615i
$859$		−	4.91841e14i		−	0.0358808i	−0.999839	−	0.0179404i	$-0.994289\pi$
$859$		−	4.91841e14i		−	0.0358808i	0.999839	−	0.0179404i	$-0.00571092\pi$
$860$	1.30766e16	−	1.30766e16i	0.947880	−	0.947880i
$861$	−9.92999e15	+	9.92999e15i	−0.715207	+	0.715207i
$862$	−2.07437e16	−	2.07437e16i	−1.48455	−	1.48455i
$863$	−2.59939e16			−1.84847			−0.924233	−	0.381830i	$-0.875294\pi$
$863$	−2.59939e16			−1.84847			−0.924233	+	0.381830i	$0.875294\pi$
$864$	2.73208e16	+	2.73208e16i	1.93049	+	1.93049i
$865$		−	1.71344e16i		−	1.20304i
$866$	−3.04452e15			−0.212408
$867$	2.07511e16	−	1.45498e16i	1.43858	−	1.00868i
$868$	−1.78316e16			−1.22838
$869$			9.66741e15i			0.661762i
$870$	−6.16390e16	−	6.16390e16i	−4.19276	−	4.19276i
$871$	−6.49325e15			−0.438897
$872$	−2.14822e14	−	2.14822e14i	−0.0144291	−	0.0144291i
$873$	1.69239e16	−	1.69239e16i	1.12959	−	1.12959i
$874$	1.47165e15	−	1.47165e15i	0.0976091	−	0.0976091i
$875$		−	5.40626e15i		−	0.356330i
$876$			1.30346e16i			0.853738i
$877$	9.74991e15	−	9.74991e15i	0.634604	−	0.634604i	−0.314615	−	0.949219i	$-0.601876\pi$
$877$	9.74991e15	−	9.74991e15i	0.634604	−	0.634604i	0.949219	+	0.314615i	$0.101876\pi$
$878$	−1.85207e16	+	1.85207e16i	−1.19795	+	1.19795i
$879$	1.98923e15	+	1.98923e15i	0.127864	+	0.127864i
$880$	−6.42309e15			−0.410288
$881$	−3.97994e15	−	3.97994e15i	−0.252644	−	0.252644i	0.569410	−	0.822054i	$-0.307172\pi$
$881$	−3.97994e15	−	3.97994e15i	−0.252644	−	0.252644i	−0.822054	+	0.569410i	$0.807172\pi$
$882$			2.26054e16i			1.42605i
$883$	−3.06327e15			−0.192044			−0.0960220	−	0.995379i	$-0.530612\pi$
$883$	−3.06327e15			−0.192044			−0.0960220	+	0.995379i	$0.530612\pi$
$884$	1.81575e16	+	2.16253e16i	1.13128	+	1.34733i
$885$	−3.27822e15			−0.202979
$886$		−	2.84125e16i		−	1.74833i
$887$	−3.79436e15	−	3.79436e15i	−0.232038	−	0.232038i	0.581505	−	0.813543i	$-0.302464\pi$
$887$	−3.79436e15	−	3.79436e15i	−0.232038	−	0.232038i	−0.813543	+	0.581505i	$0.802464\pi$
$888$	−9.09942e15			−0.553022
$889$	5.78718e15	+	5.78718e15i	0.349549	+	0.349549i
$890$	−2.82280e16	+	2.82280e16i	−1.69447	+	1.69447i
$891$	−5.10115e15	+	5.10115e15i	−0.304327	+	0.304327i
$892$			1.36665e16i			0.810310i
$893$			5.00175e15i			0.294740i
$894$	−3.36871e16	+	3.36871e16i	−1.97291	+	1.97291i
$895$	2.05618e15	−	2.05618e15i	0.119684	−	0.119684i
$896$	4.55883e15	+	4.55883e15i	0.263730	+	0.263730i
$897$	6.68125e15			0.384148
$898$	5.02051e15	+	5.02051e15i	0.286899	+	0.286899i
$899$		−	3.77405e16i		−	2.14353i
$900$	5.73270e16			3.23612
$901$	9.78775e14	−	8.21822e14i	0.0549157	−	0.0461096i
$902$	7.05178e15			0.393245
$903$			1.73921e16i			0.963984i
$904$	1.81463e15	+	1.81463e15i	0.0999684	+	0.0999684i
$905$	6.70775e15			0.367290
$906$	−1.96004e16	−	1.96004e16i	−1.06674	−	1.06674i
$907$	8.95163e15	−	8.95163e15i	0.484241	−	0.484241i	−0.422242	−	0.906483i	$-0.638757\pi$
$907$	8.95163e15	−	8.95163e15i	0.484241	−	0.484241i	0.906483	+	0.422242i	$0.138757\pi$
$908$	9.84744e15	−	9.84744e15i	0.529482	−	0.529482i
$909$		−	6.03287e16i		−	3.22421i
$910$		−	4.63693e16i		−	2.46322i
$911$	−1.79699e16	+	1.79699e16i	−0.948842	+	0.948842i	−0.998754	−	0.0499115i	$-0.984106\pi$
$911$	−1.79699e16	+	1.79699e16i	−0.948842	+	0.948842i	0.0499115	+	0.998754i	$0.484106\pi$
$912$	−1.20433e16	+	1.20433e16i	−0.632081	+	0.632081i
$913$	−3.82276e15	−	3.82276e15i	−0.199429	−	0.199429i
$914$	1.81336e16			0.940330
$915$	5.23162e16	+	5.23162e16i	2.69662	+	2.69662i
$916$			2.42814e15i			0.124408i
$917$	2.35367e15			0.119871
$918$	4.83146e15	−	5.54277e16i	0.244593	−	2.80603i
$919$	3.65413e15			0.183886			0.0919431	−	0.995764i	$-0.470692\pi$
$919$	3.65413e15			0.183886			0.0919431	+	0.995764i	$0.470692\pi$
$920$			1.14964e15i			0.0575081i
$921$	−2.36029e16	−	2.36029e16i	−1.17364	−	1.17364i
$922$	2.77830e15			0.137328
$923$	−1.69523e16	−	1.69523e16i	−0.832952	−	0.832952i
$924$	−7.43093e15	+	7.43093e15i	−0.362950	+	0.362950i
$925$	2.33941e16	−	2.33941e16i	1.13587	−	1.13587i
$926$			4.14982e16i			2.00294i
$927$			2.73421e16i			1.31188i
$928$	−3.18427e16	+	3.18427e16i	−1.51878	+	1.51878i
$929$	8.53577e15	−	8.53577e15i	0.404722	−	0.404722i	−0.475171	−	0.879893i	$-0.657614\pi$
$929$	8.53577e15	−	8.53577e15i	0.404722	−	0.404722i	0.879893	+	0.475171i	$0.157614\pi$
$930$	8.44643e16	+	8.44643e16i	3.98123	+	3.98123i
$931$	−6.33570e15			−0.296873
$932$	5.58937e15	+	5.58937e15i	0.260361	+	0.260361i
$933$		−	5.11976e15i		−	0.237083i
$934$	2.72594e16			1.25490
$935$	7.26057e15	+	8.64720e15i	0.332282	+	0.395742i
$936$	1.77512e16			0.807626
$937$			9.67662e15i			0.437679i	0.975761	+	0.218840i	$0.0702271\pi$
$937$			9.67662e15i			0.437679i	−0.975761	+	0.218840i	$0.929773\pi$
$938$	4.98187e15	+	4.98187e15i	0.224015	+	0.224015i
$939$	4.28808e16			1.91691
$940$	−1.30993e16	−	1.30993e16i	−0.582164	−	0.582164i
$941$	2.12964e16	−	2.12964e16i	0.940942	−	0.940942i	−0.0574088	−	0.998351i	$-0.518284\pi$
$941$	2.12964e16	−	2.12964e16i	0.940942	−	0.940942i	0.998351	+	0.0574088i	$0.0182838\pi$
$942$	−4.77093e16	+	4.77093e16i	−2.09567	+	2.09567i
$943$			2.62827e15i			0.114777i
$944$			1.38727e15i			0.0602302i
$945$	−3.49050e16	+	3.49050e16i	−1.50665	+	1.50665i
$946$	6.17551e15	−	6.17551e15i	0.265016	−	0.265016i
$947$	−5.99001e15	−	5.99001e15i	−0.255566	−	0.255566i	0.567682	−	0.823248i	$-0.307840\pi$
$947$	−5.99001e15	−	5.99001e15i	−0.255566	−	0.255566i	−0.823248	+	0.567682i	$0.807840\pi$
$948$	−9.49440e16			−4.02737
$949$	−1.03767e16	−	1.03767e16i	−0.437618	−	0.437618i
$950$			2.97381e16i			1.24691i
$951$	−7.70230e15			−0.321091
$952$	3.96807e14	−	4.55227e15i	0.0164466	−	0.188679i
$953$	−1.01378e16			−0.417764			−0.208882	−	0.977941i	$-0.566983\pi$
$953$	−1.01378e16			−0.417764			−0.208882	+	0.977941i	$0.566983\pi$
$954$		−	5.38699e15i		−	0.220714i
$955$	−2.68292e15	−	2.68292e15i	−0.109292	−	0.109292i
$956$	−2.37204e16			−0.960736
$957$	−1.57275e16	−	1.57275e16i	−0.633351	−	0.633351i
$958$	1.63870e16	−	1.63870e16i	0.656129	−	0.656129i
$959$	4.53999e15	−	4.53999e15i	0.180739	−	0.180739i
$960$		−	8.88566e16i		−	3.51721i
$961$			2.63075e16i			1.03538i
$962$	4.85706e16	−	4.85706e16i	1.90069	−	1.90069i
$963$	2.62937e16	−	2.62937e16i	1.02308	−	1.02308i
$964$	−1.44411e16	−	1.44411e16i	−0.558696	−	0.558696i
$965$	2.44345e16			0.939945
$966$	−5.12611e15	−	5.12611e15i	−0.196071	−	0.196071i
$967$			6.24449e15i			0.237493i	0.992925	+	0.118747i	$0.0378876\pi$
$967$			6.24449e15i			0.237493i	−0.992925	+	0.118747i	$0.962112\pi$
$968$	−6.04921e15			−0.228762
$969$	2.98270e16	+	2.59993e15i	1.12158	+	0.0977643i
$970$	−4.59844e16			−1.71936
$971$			3.54169e16i			1.31676i	0.752687	+	0.658378i	$0.228757\pi$
$971$			3.54169e16i			1.31676i	−0.752687	+	0.658378i	$0.771243\pi$
$972$	−7.16765e15	−	7.16765e15i	−0.264979	−	0.264979i
$973$	2.39018e16			0.878637
$974$	8.76742e15	+	8.76742e15i	0.320477	+	0.320477i
$975$	−6.75053e16	+	6.75053e16i	−2.45365	+	2.45365i
$976$	2.21390e16	−	2.21390e16i	0.800173	−	0.800173i
$977$			3.71453e16i			1.33501i	0.744606	+	0.667504i	$0.232637\pi$
$977$			3.71453e16i			1.33501i	−0.744606	+	0.667504i	$0.767363\pi$
$978$		−	1.21925e17i		−	4.35743i
$979$	−7.20253e15	+	7.20253e15i	−0.255965	+	0.255965i
$980$	1.65929e16	−	1.65929e16i	0.586378	−	0.586378i
$981$	−3.31458e15	−	3.31458e15i	−0.116479	−	0.116479i
$982$	3.26237e16			1.14004
$983$	−7.46175e15	−	7.46175e15i	−0.259296	−	0.259296i	0.565472	−	0.824768i	$-0.308694\pi$
$983$	−7.46175e15	−	7.46175e15i	−0.259296	−	0.259296i	−0.824768	+	0.565472i	$0.808694\pi$
$984$			1.03290e16i			0.356931i
$985$	−6.49999e15			−0.223364
$986$	6.46016e16	+	5.63112e15i	2.20760	+	0.192430i
$987$	1.74223e16			0.592055
$988$			3.33586e16i			1.12731i
$989$	2.30168e15	+	2.30168e15i	0.0773508	+	0.0773508i
$990$	4.75926e16			1.59054
$991$	−1.18779e16	−	1.18779e16i	−0.394760	−	0.394760i	0.481620	−	0.876380i	$-0.340049\pi$
$991$	−1.18779e16	−	1.18779e16i	−0.394760	−	0.394760i	−0.876380	+	0.481620i	$0.840049\pi$
$992$	4.36343e16	−	4.36343e16i	1.44216	−	1.44216i
$993$	−3.85596e16	+	3.85596e16i	−1.26739	+	1.26739i
$994$			2.60129e16i			0.850284i
$995$		−	7.93891e16i		−	2.58068i
$996$	3.75435e16	−	3.75435e16i	1.21369	−	1.21369i
$997$	−3.09072e16	+	3.09072e16i	−0.993657	+	0.993657i	−0.999980	−	0.00632293i	$-0.997987\pi$
$997$	−3.09072e16	+	3.09072e16i	−0.993657	+	0.993657i	0.00632293	+	0.999980i	$0.497987\pi$
$998$	1.03280e16	+	1.03280e16i	0.330217	+	0.330217i
$999$	−7.31243e16			−2.32515

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.12.c.a.13.3	yes	32
17.4	even	4	inner	17.12.c.a.4.14	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.12.c.a.4.14	✓	32	17.4	even	4	inner
17.12.c.a.13.3	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)

\(f(q)\)	\(=\)	\(q-66.7457i q^{2} +(-522.898 - 522.898i) q^{3} -2406.98 q^{4} +(7524.98 + 7524.98i) q^{5} +(-34901.2 + 34901.2i) q^{6} +(-23035.1 + 23035.1i) q^{7} +23960.6i q^{8} +369698. i q^{9} +O(q^{10})\)	\(q-66.7457i q^{2} +(-522.898 - 522.898i) q^{3} -2406.98 q^{4} +(7524.98 + 7524.98i) q^{5} +(-34901.2 + 34901.2i) q^{6} +(-23035.1 + 23035.1i) q^{7} +23960.6i q^{8} +369698. i q^{9} +(502260. - 502260. i) q^{10} +(128154. - 128154. i) q^{11} +(1.25861e6 + 1.25861e6i) q^{12} -2.00393e6 q^{13} +(1.53749e6 + 1.53749e6i) q^{14} -7.86960e6i q^{15} -3.33024e6 q^{16} +(3.76445e6 + 4.48339e6i) q^{17} +2.46758e7 q^{18} +6.91595e6i q^{19} +(-1.81125e7 - 1.81125e7i) q^{20} +2.40900e7 q^{21} +(-8.55375e6 - 8.55375e6i) q^{22} +(3.18807e6 - 3.18807e6i) q^{23} +(1.25290e7 - 1.25290e7i) q^{24} +6.44226e7i q^{25} +1.33754e8i q^{26} +(1.00685e8 - 1.00685e8i) q^{27} +(5.54450e7 - 5.54450e7i) q^{28} +(1.17349e8 + 1.17349e8i) q^{29} -5.25262e8 q^{30} +(-1.60804e8 - 1.60804e8i) q^{31} +2.71350e8i q^{32} -1.34023e8 q^{33} +(2.99247e8 - 2.51261e8i) q^{34} -3.46677e8 q^{35} -8.89858e8i q^{36} +(-3.63135e8 - 3.63135e8i) q^{37} +4.61610e8 q^{38} +(1.04785e9 + 1.04785e9i) q^{39} +(-1.80303e8 + 1.80303e8i) q^{40} +(-4.12204e8 + 4.12204e8i) q^{41} -1.60790e9i q^{42} +7.21965e8i q^{43} +(-3.08465e8 + 3.08465e8i) q^{44} +(-2.78197e9 + 2.78197e9i) q^{45} +(-2.12790e8 - 2.12790e8i) q^{46} +7.23219e8 q^{47} +(1.74137e9 + 1.74137e9i) q^{48} +9.16099e8i q^{49} +4.29993e9 q^{50} +(3.75932e8 - 4.31278e9i) q^{51} +4.82342e9 q^{52} -2.18311e8i q^{53} +(-6.72027e9 - 6.72027e9i) q^{54} +1.92872e9 q^{55} +(-5.51934e8 - 5.51934e8i) q^{56} +(3.61634e9 - 3.61634e9i) q^{57} +(7.83254e9 - 7.83254e9i) q^{58} -4.16568e8i q^{59} +1.89420e10i q^{60} +(-6.64788e9 + 6.64788e9i) q^{61} +(-1.07330e10 + 1.07330e10i) q^{62} +(-8.51602e9 - 8.51602e9i) q^{63} +1.12911e10 q^{64} +(-1.50795e10 - 1.50795e10i) q^{65} +8.94548e9i q^{66} +3.24026e9 q^{67} +(-9.06098e9 - 1.07914e10i) q^{68} -3.33407e9 q^{69} +2.31392e10i q^{70} +(8.45955e9 + 8.45955e9i) q^{71} -8.85820e9 q^{72} +(5.17818e9 + 5.17818e9i) q^{73} +(-2.42377e10 + 2.42377e10i) q^{74} +(3.36865e10 - 3.36865e10i) q^{75} -1.66466e10i q^{76} +5.90408e9i q^{77} +(6.99395e10 - 6.99395e10i) q^{78} +(-3.77179e10 + 3.77179e10i) q^{79} +(-2.50600e10 - 2.50600e10i) q^{80} -3.98048e10 q^{81} +(2.75128e10 + 2.75128e10i) q^{82} -2.98294e10i q^{83} -5.79842e10 q^{84} +(-5.41000e9 + 6.20649e10i) q^{85} +4.81880e10 q^{86} -1.22723e11i q^{87} +(3.07066e9 + 3.07066e9i) q^{88} -5.62020e10 q^{89} +(1.85685e11 + 1.85685e11i) q^{90} +(4.61606e10 - 4.61606e10i) q^{91} +(-7.67364e9 + 7.67364e9i) q^{92} +1.68169e11i q^{93} -4.82717e10i q^{94} +(-5.20424e10 + 5.20424e10i) q^{95} +(1.41889e11 - 1.41889e11i) q^{96} +(-4.57775e10 - 4.57775e10i) q^{97} +6.11457e10 q^{98} +(4.73784e10 + 4.73784e10i) 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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