LMFDB - Embedded newform 17.12.c.a.13.4

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			13.4
Character	$\chi$	$=$	17.13
Dual form			17.12.c.a.4.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-63.2626i q^{2} +(72.6870 + 72.6870i) q^{3} -1954.16 q^{4} +(5432.90 + 5432.90i) q^{5} +(4598.37 - 4598.37i) q^{6} +(37054.9 - 37054.9i) q^{7} -5936.57i q^{8} -166580. i q^{9} +O(q^{10})$	\(q-63.2626i q^{2} +(72.6870 + 72.6870i) q^{3} -1954.16 q^{4} +(5432.90 + 5432.90i) q^{5} +(4598.37 - 4598.37i) q^{6} +(37054.9 - 37054.9i) q^{7} -5936.57i q^{8} -166580. i q^{9} +(343700. - 343700. i) q^{10} +(-338197. + 338197. i) q^{11} +(-142042. - 142042. i) q^{12} +2.30995e6 q^{13} +(-2.34419e6 - 2.34419e6i) q^{14} +789803. i q^{15} -4.37768e6 q^{16} +(-5.83642e6 + 456147. i) q^{17} -1.05383e7 q^{18} -1.38158e7i q^{19} +(-1.06168e7 - 1.06168e7i) q^{20} +5.38682e6 q^{21} +(2.13952e7 + 2.13952e7i) q^{22} +(1.13125e7 - 1.13125e7i) q^{23} +(431512. - 431512. i) q^{24} +1.02047e7i q^{25} -1.46134e8i q^{26} +(2.49845e7 - 2.49845e7i) q^{27} +(-7.24112e7 + 7.24112e7i) q^{28} +(9.40016e7 + 9.40016e7i) q^{29} +4.99650e7 q^{30} +(-9.85658e7 - 9.85658e7i) q^{31} +2.64786e8i q^{32} -4.91651e7 q^{33} +(2.88571e7 + 3.69227e8i) q^{34} +4.02631e8 q^{35} +3.25524e8i q^{36} +(-8.32805e7 - 8.32805e7i) q^{37} -8.74022e8 q^{38} +(1.67903e8 + 1.67903e8i) q^{39} +(3.22528e7 - 3.22528e7i) q^{40} +(7.82172e8 - 7.82172e8i) q^{41} -3.40784e8i q^{42} +1.31632e9i q^{43} +(6.60891e8 - 6.60891e8i) q^{44} +(9.05014e8 - 9.05014e8i) q^{45} +(-7.15656e8 - 7.15656e8i) q^{46} -3.01382e6 q^{47} +(-3.18201e8 - 3.18201e8i) q^{48} -7.68806e8i q^{49} +6.45578e8 q^{50} +(-4.57388e8 - 3.91076e8i) q^{51} -4.51401e9 q^{52} +1.47016e9i q^{53} +(-1.58059e9 - 1.58059e9i) q^{54} -3.67478e9 q^{55} +(-2.19979e8 - 2.19979e8i) q^{56} +(1.00423e9 - 1.00423e9i) q^{57} +(5.94679e9 - 5.94679e9i) q^{58} +7.91987e9i q^{59} -1.54340e9i q^{60} +(-1.86582e9 + 1.86582e9i) q^{61} +(-6.23553e9 + 6.23553e9i) q^{62} +(-6.17261e9 - 6.17261e9i) q^{63} +7.78554e9 q^{64} +(1.25497e10 + 1.25497e10i) q^{65} +3.11031e9i q^{66} +4.89004e9 q^{67} +(1.14053e10 - 8.91385e8i) q^{68} +1.64454e9 q^{69} -2.54715e10i q^{70} +(-4.84554e9 - 4.84554e9i) q^{71} -9.88916e8 q^{72} +(1.85061e10 + 1.85061e10i) q^{73} +(-5.26854e9 + 5.26854e9i) q^{74} +(-7.41751e8 + 7.41751e8i) q^{75} +2.69982e10i q^{76} +2.50637e10i q^{77} +(1.06220e10 - 1.06220e10i) q^{78} +(9.10604e8 - 9.10604e8i) q^{79} +(-2.37835e10 - 2.37835e10i) q^{80} -2.58771e10 q^{81} +(-4.94823e10 - 4.94823e10i) q^{82} +6.44546e10i q^{83} -1.05267e10 q^{84} +(-3.41869e10 - 2.92305e10i) q^{85} +8.32738e10 q^{86} +1.36654e10i q^{87} +(2.00773e9 + 2.00773e9i) q^{88} -3.59054e10 q^{89} +(-5.72536e10 - 5.72536e10i) q^{90} +(8.55950e10 - 8.55950e10i) q^{91} +(-2.21064e10 + 2.21064e10i) q^{92} -1.43289e10i q^{93} +1.90662e8i q^{94} +(7.50597e10 - 7.50597e10i) q^{95} +(-1.92465e10 + 1.92465e10i) q^{96} +(-6.08566e9 - 6.08566e9i) q^{97} -4.86367e10 q^{98} +(5.63369e10 + 5.63369e10i) 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 $

$2$		−	63.2626i		−	1.39792i	−0.715161	−	0.698960i	$-0.753647\pi$
$2$		−	63.2626i		−	1.39792i	0.715161	−	0.698960i	$-0.246353\pi$
$3$	72.6870	+	72.6870i	0.172699	+	0.172699i	0.788164	−	0.615465i	$-0.211032\pi$
$3$	72.6870	+	72.6870i	0.172699	+	0.172699i	−0.615465	+	0.788164i	$0.711032\pi$
$4$	−1954.16			−0.954180
$5$	5432.90	+	5432.90i	0.777494	+	0.777494i	0.979404	−	0.201910i	$-0.0647150\pi$
$5$	5432.90	+	5432.90i	0.777494	+	0.777494i	−0.201910	+	0.979404i	$0.564715\pi$
$6$	4598.37	−	4598.37i	0.241419	−	0.241419i
$7$	37054.9	−	37054.9i	0.833310	−	0.833310i	−0.154658	−	0.987968i	$-0.549428\pi$
$7$	37054.9	−	37054.9i	0.833310	−	0.833310i	0.987968	+	0.154658i	$0.0494276\pi$
$8$		−	5936.57i		−	0.0640532i
$9$		−	166580.i		−	0.940350i
$10$	343700.	−	343700.i	1.08687	−	1.08687i
$11$	−338197.	+	338197.i	−0.633155	+	0.633155i	−0.948858	−	0.315703i	$-0.897760\pi$
$11$	−338197.	+	338197.i	−0.633155	+	0.633155i	0.315703	+	0.948858i	$0.397760\pi$
$12$	−142042.	−	142042.i	−0.164786	−	0.164786i
$13$	2.30995e6			1.72550			0.862749	−	0.505633i	$-0.168741\pi$
$13$	2.30995e6			1.72550			0.862749	+	0.505633i	$0.168741\pi$
$14$	−2.34419e6	−	2.34419e6i	−1.16490	−	1.16490i
$15$			789803.i			0.268545i
$16$	−4.37768e6			−1.04372
$17$	−5.83642e6	+	456147.i	−0.996960	+	0.0779177i
$17$	−5.83642e6	+	456147.i	−0.996960	+	0.0779177i
$18$	−1.05383e7			−1.31453
$19$		−	1.38158e7i		−	1.28006i	−0.768350	−	0.640030i	$-0.778922\pi$
$19$		−	1.38158e7i		−	1.28006i	0.768350	−	0.640030i	$-0.221078\pi$
$20$	−1.06168e7	−	1.06168e7i	−0.741869	−	0.741869i
$21$	5.38682e6			0.287824
$22$	2.13952e7	+	2.13952e7i	0.885100	+	0.885100i
$23$	1.13125e7	−	1.13125e7i	0.366483	−	0.366483i	−0.499710	−	0.866193i	$-0.666560\pi$
$23$	1.13125e7	−	1.13125e7i	0.366483	−	0.366483i	0.866193	+	0.499710i	$0.166560\pi$
$24$	431512.	−	431512.i	0.0110619	−	0.0110619i
$25$			1.02047e7i			0.208993i
$26$		−	1.46134e8i		−	2.41211i
$27$	2.49845e7	−	2.49845e7i	0.335097	−	0.335097i
$28$	−7.24112e7	+	7.24112e7i	−0.795127	+	0.795127i
$29$	9.40016e7	+	9.40016e7i	0.851032	+	0.851032i	0.990260	−	0.139228i	$-0.0444621\pi$
$29$	9.40016e7	+	9.40016e7i	0.851032	+	0.851032i	−0.139228	+	0.990260i	$0.544462\pi$
$30$	4.99650e7			0.375404
$31$	−9.85658e7	−	9.85658e7i	−0.618353	−	0.618353i	0.326755	−	0.945109i	$-0.394045\pi$
$31$	−9.85658e7	−	9.85658e7i	−0.618353	−	0.618353i	−0.945109	+	0.326755i	$0.894045\pi$
$32$			2.64786e8i			1.39498i
$33$	−4.91651e7			−0.218691
$34$	2.88571e7	+	3.69227e8i	0.108923	+	1.39367i
$35$	4.02631e8			1.29579
$36$			3.25524e8i			0.897263i
$37$	−8.32805e7	−	8.32805e7i	−0.197439	−	0.197439i	0.601462	−	0.798901i	$-0.294585\pi$
$37$	−8.32805e7	−	8.32805e7i	−0.197439	−	0.197439i	−0.798901	+	0.601462i	$0.794585\pi$
$38$	−8.74022e8			−1.78942
$39$	1.67903e8	+	1.67903e8i	0.297992	+	0.297992i
$40$	3.22528e7	−	3.22528e7i	0.0498010	−	0.0498010i
$41$	7.82172e8	−	7.82172e8i	1.05437	−	1.05437i	0.0559311	−	0.998435i	$-0.482187\pi$
$41$	7.82172e8	−	7.82172e8i	1.05437	−	1.05437i	0.998435	−	0.0559311i	$-0.0178127\pi$
$42$		−	3.40784e8i		−	0.402354i
$43$			1.31632e9i			1.36548i	0.730663	+	0.682739i	$0.239211\pi$
$43$			1.31632e9i			1.36548i	−0.730663	+	0.682739i	$0.760789\pi$
$44$	6.60891e8	−	6.60891e8i	0.604144	−	0.604144i
$45$	9.05014e8	−	9.05014e8i	0.731116	−	0.731116i
$46$	−7.15656e8	−	7.15656e8i	−0.512314	−	0.512314i
$47$	−3.01382e6			−0.00191681			−0.000958406	−	1.00000i	$-0.500305\pi$
$47$	−3.01382e6			−0.00191681			−0.000958406		1.00000i	$0.500305\pi$
$48$	−3.18201e8	−	3.18201e8i	−0.180250	−	0.180250i
$49$		−	7.68806e8i		−	0.388811i
$50$	6.45578e8			0.292155
$51$	−4.57388e8	−	3.91076e8i	−0.185630	−	0.158718i
$52$	−4.51401e9			−1.64643
$53$			1.47016e9i			0.482890i	0.970415	+	0.241445i	$0.0776213\pi$
$53$			1.47016e9i			0.482890i	−0.970415	+	0.241445i	$0.922379\pi$
$54$	−1.58059e9	−	1.58059e9i	−0.468438	−	0.468438i
$55$	−3.67478e9			−0.984548
$56$	−2.19979e8	−	2.19979e8i	−0.0533762	−	0.0533762i
$57$	1.00423e9	−	1.00423e9i	0.221065	−	0.221065i
$58$	5.94679e9	−	5.94679e9i	1.18967	−	1.18967i
$59$			7.91987e9i			1.44222i	0.692820	+	0.721110i	$0.256368\pi$
$59$			7.91987e9i			1.44222i	−0.692820	+	0.721110i	$0.743632\pi$
$60$		−	1.54340e9i		−	0.256240i
$61$	−1.86582e9	+	1.86582e9i	−0.282850	+	0.282850i	−0.834244	−	0.551395i	$-0.814096\pi$
$61$	−1.86582e9	+	1.86582e9i	−0.282850	+	0.282850i	0.551395	+	0.834244i	$0.314096\pi$
$62$	−6.23553e9	+	6.23553e9i	−0.864409	+	0.864409i
$63$	−6.17261e9	−	6.17261e9i	−0.783603	−	0.783603i
$64$	7.78554e9			0.906356
$65$	1.25497e10	+	1.25497e10i	1.34156	+	1.34156i
$66$			3.11031e9i			0.305712i
$67$	4.89004e9			0.442488			0.221244	−	0.975219i	$-0.428988\pi$
$67$	4.89004e9			0.442488			0.221244	+	0.975219i	$0.428988\pi$
$68$	1.14053e10	−	8.91385e8i	0.951279	−	0.0743475i
$69$	1.64454e9			0.126583
$70$		−	2.54715e10i		−	1.81141i
$71$	−4.84554e9	−	4.84554e9i	−0.318729	−	0.318729i	0.529550	−	0.848279i	$-0.322361\pi$
$71$	−4.84554e9	−	4.84554e9i	−0.318729	−	0.318729i	−0.848279	+	0.529550i	$0.822361\pi$
$72$	−9.88916e8			−0.0602324
$73$	1.85061e10	+	1.85061e10i	1.04482	+	1.04482i	0.998947	+	0.0458684i	$0.0146055\pi$
$73$	1.85061e10	+	1.85061e10i	1.04482	+	1.04482i	0.0458684	+	0.998947i	$0.485395\pi$
$74$	−5.26854e9	+	5.26854e9i	−0.276004	+	0.276004i
$75$	−7.41751e8	+	7.41751e8i	−0.0360929	+	0.0360929i
$76$			2.69982e10i			1.22141i
$77$			2.50637e10i			1.05523i
$78$	1.06220e10	−	1.06220e10i	0.416568	−	0.416568i
$79$	9.10604e8	−	9.10604e8i	0.0332951	−	0.0332951i	−0.690263	−	0.723558i	$-0.742505\pi$
$79$	9.10604e8	−	9.10604e8i	0.0332951	−	0.0332951i	0.723558	+	0.690263i	$0.242505\pi$
$80$	−2.37835e10	−	2.37835e10i	−0.811486	−	0.811486i
$81$	−2.58771e10			−0.824608
$82$	−4.94823e10	−	4.94823e10i	−1.47392	−	1.47392i
$83$			6.44546e10i			1.79607i	0.439919	+	0.898037i	$0.355007\pi$
$83$			6.44546e10i			1.79607i	−0.439919	+	0.898037i	$0.644993\pi$
$84$	−1.05267e10			−0.274635
$85$	−3.41869e10	−	2.92305e10i	−0.835710	−	0.714549i
$86$	8.32738e10			1.90883
$87$			1.36654e10i			0.293945i
$88$	2.00773e9	+	2.00773e9i	0.0405556	+	0.0405556i
$89$	−3.59054e10			−0.681577			−0.340788	−	0.940140i	$-0.610694\pi$
$89$	−3.59054e10			−0.681577			−0.340788	+	0.940140i	$0.610694\pi$
$90$	−5.72536e10	−	5.72536e10i	−1.02204	−	1.02204i
$91$	8.55950e10	−	8.55950e10i	1.43787	−	1.43787i
$92$	−2.21064e10	+	2.21064e10i	−0.349691	+	0.349691i
$93$		−	1.43289e10i		−	0.213578i
$94$			1.90662e8i			0.00267955i
$95$	7.50597e10	−	7.50597e10i	0.995239	−	0.995239i
$96$	−1.92465e10	+	1.92465e10i	−0.240913	+	0.240913i
$97$	−6.08566e9	−	6.08566e9i	−0.0719554	−	0.0719554i	0.670213	−	0.742169i	$-0.266203\pi$
$97$	−6.08566e9	−	6.08566e9i	−0.0719554	−	0.0719554i	−0.742169	+	0.670213i	$0.766203\pi$
$98$	−4.86367e10			−0.543526
$99$	5.63369e10	+	5.63369e10i	0.595387	+	0.595387i
$100$		−	1.99417e10i		−	0.199417i
$101$	1.35653e11			1.28429			0.642144	−	0.766584i	$-0.278045\pi$
$101$	1.35653e11			1.28429			0.642144	+	0.766584i	$0.278045\pi$
$102$	−2.47405e10	+	2.89356e10i	−0.221875	+	0.259496i
$103$	−1.69086e11			−1.43715			−0.718577	−	0.695447i	$-0.755206\pi$
$103$	−1.69086e11			−1.43715			−0.718577	+	0.695447i	$0.755206\pi$
$104$		−	1.37132e10i		−	0.110524i
$105$	2.92661e10	+	2.92661e10i	0.223781	+	0.223781i
$106$	9.30063e10			0.675041
$107$	9.80144e10	+	9.80144e10i	0.675584	+	0.675584i	0.958998	−	0.283414i	$-0.0914670\pi$
$107$	9.80144e10	+	9.80144e10i	0.675584	+	0.675584i	−0.283414	+	0.958998i	$0.591467\pi$
$108$	−4.88237e10	+	4.88237e10i	−0.319742	+	0.319742i
$109$	−4.28387e10	+	4.28387e10i	−0.266680	+	0.266680i	−0.827761	−	0.561081i	$-0.810386\pi$
$109$	−4.28387e10	+	4.28387e10i	−0.266680	+	0.266680i	0.561081	+	0.827761i	$0.310386\pi$
$110$			2.32476e11i			1.37632i
$111$		−	1.21068e10i		−	0.0681952i
$112$	−1.62215e11	+	1.62215e11i	−0.869743	+	0.869743i
$113$	−9.43580e10	+	9.43580e10i	−0.481778	+	0.481778i	−0.905699	−	0.423921i	$-0.860653\pi$
$113$	−9.43580e10	+	9.43580e10i	−0.481778	+	0.481778i	0.423921	+	0.905699i	$0.360653\pi$
$114$	−6.35300e10	−	6.35300e10i	−0.309031	−	0.309031i
$115$	1.22919e11			0.569877
$116$	−1.83694e11	−	1.83694e11i	−0.812038	−	0.812038i
$117$		−	3.84792e11i		−	1.62257i
$118$	5.01032e11			2.01611
$119$	−1.99366e11	+	2.33171e11i	−0.765847	+	0.895706i
$120$	4.68872e9			0.0172012
$121$			5.65571e10i			0.198229i
$122$	1.18037e11	+	1.18037e11i	0.395401	+	0.395401i
$123$	1.13708e11			0.364176
$124$	1.92613e11	+	1.92613e11i	0.590020	+	0.590020i
$125$	2.09837e11	−	2.09837e11i	0.615003	−	0.615003i
$126$	−3.90496e11	+	3.90496e11i	−1.09541	+	1.09541i
$127$		−	2.50343e11i		−	0.672381i	−0.941794	−	0.336191i	$-0.890861\pi$
$127$		−	2.50343e11i		−	0.672381i	0.941794	−	0.336191i	$-0.109139\pi$
$128$			4.97473e10i			0.127972i
$129$	−9.56793e10	+	9.56793e10i	−0.235817	+	0.235817i
$130$	7.93929e11	−	7.93929e11i	1.87540	−	1.87540i
$131$	−1.52408e11	−	1.52408e11i	−0.345157	−	0.345157i	0.513145	−	0.858302i	$-0.328480\pi$
$131$	−1.52408e11	−	1.52408e11i	−0.345157	−	0.345157i	−0.858302	+	0.513145i	$0.828480\pi$
$132$	9.60764e10			0.208670
$133$	−5.11942e11	−	5.11942e11i	−1.06669	−	1.06669i
$134$		−	3.09357e11i		−	0.618562i
$135$	2.71477e11			0.521071
$136$	2.70795e9	+	3.46483e10i	0.00499088	+	0.0638585i
$137$	−6.38331e11			−1.13001			−0.565006	−	0.825087i	$-0.691126\pi$
$137$	−6.38331e11			−1.13001			−0.565006	+	0.825087i	$0.691126\pi$
$138$		−	1.04038e11i		−	0.176952i
$139$	−5.24259e11	−	5.24259e11i	−0.856967	−	0.856967i	0.134012	−	0.990980i	$-0.457214\pi$
$139$	−5.24259e11	−	5.24259e11i	−0.856967	−	0.856967i	−0.990980	+	0.134012i	$0.957214\pi$
$140$	−7.86806e11			−1.23641
$141$	−2.19066e8	−	2.19066e8i	−0.000331031	−	0.000331031i
$142$	−3.06542e11	+	3.06542e11i	−0.445557	+	0.445557i
$143$	−7.81219e11	+	7.81219e11i	−1.09251	+	1.09251i
$144$			7.29235e11i			0.981463i
$145$			1.02140e12i			1.32334i
$146$	1.17075e12	−	1.17075e12i	1.46057	−	1.46057i
$147$	5.58822e10	−	5.58822e10i	0.0671472	−	0.0671472i
$148$	1.62743e11	+	1.62743e11i	0.188393	+	0.188393i
$149$	−1.38897e10			−0.0154941			−0.00774707	−	0.999970i	$-0.502466\pi$
$149$	−1.38897e10			−0.0154941			−0.00774707	+	0.999970i	$0.502466\pi$
$150$	4.69251e10	+	4.69251e10i	0.0504549	+	0.0504549i
$151$		−	2.27493e10i		−	0.0235827i	−0.999930	−	0.0117914i	$-0.996247\pi$
$151$		−	2.27493e10i		−	0.0235827i	0.999930	−	0.0117914i	$-0.00375339\pi$
$152$	−8.20183e10			−0.0819920
$153$	7.59851e10	+	9.72232e11i	0.0732699	+	0.937491i
$154$	1.58560e12			1.47513
$155$		−	1.07100e12i		−	0.961532i
$156$	−3.28110e11	−	3.28110e11i	−0.284338	−	0.284338i
$157$	9.69222e11			0.810915			0.405457	−	0.914114i	$-0.367112\pi$
$157$	9.69222e11			0.810915			0.405457	+	0.914114i	$0.367112\pi$
$158$	−5.76072e10	−	5.76072e10i	−0.0465439	−	0.0465439i
$159$	−1.06862e11	+	1.06862e11i	−0.0833946	+	0.0833946i
$160$	−1.43855e12	+	1.43855e12i	−1.08459	+	1.08459i
$161$		−	8.38365e11i		−	0.610788i
$162$			1.63705e12i			1.15274i
$163$	1.74847e12	−	1.74847e12i	1.19022	−	1.19022i	0.213215	−	0.977005i	$-0.431606\pi$
$163$	1.74847e12	−	1.74847e12i	1.19022	−	1.19022i	0.977005	−	0.213215i	$-0.0683936\pi$
$164$	−1.52849e12	+	1.52849e12i	−1.00605	+	1.00605i
$165$	−2.67109e11	−	2.67109e11i	−0.170031	−	0.170031i
$166$	4.07757e12			2.51077
$167$	−1.59344e12	−	1.59344e12i	−0.949284	−	0.949284i	0.0494904	−	0.998775i	$-0.484240\pi$
$167$	−1.59344e12	−	1.59344e12i	−0.949284	−	0.949284i	−0.998775	+	0.0494904i	$0.984240\pi$
$168$		−	3.19793e10i		−	0.0184360i
$169$	3.54371e12			1.97734
$170$	−1.84920e12	+	2.16275e12i	−0.998883	+	1.16826i
$171$	−2.30143e12			−1.20370
$172$		−	2.57230e12i		−	1.30291i
$173$	1.51591e12	+	1.51591e12i	0.743737	+	0.743737i	0.973295	−	0.229558i	$-0.0737281\pi$
$173$	1.51591e12	+	1.51591e12i	0.743737	+	0.743737i	−0.229558	+	0.973295i	$0.573728\pi$
$174$	8.64508e11			0.410911
$175$	3.78135e11	+	3.78135e11i	0.174156	+	0.174156i
$176$	1.48052e12	−	1.48052e12i	0.660837	−	0.660837i
$177$	−5.75671e11	+	5.75671e11i	−0.249070	+	0.249070i
$178$			2.27147e12i			0.952790i
$179$			2.78141e12i			1.13129i	0.824649	+	0.565644i	$0.191372\pi$
$179$			2.78141e12i			1.13129i	−0.824649	+	0.565644i	$0.808628\pi$
$180$	−1.76854e12	+	1.76854e12i	−0.697616	+	0.697616i
$181$	−1.53631e12	+	1.53631e12i	−0.587824	+	0.587824i	−0.937042	−	0.349217i	$-0.886447\pi$
$181$	−1.53631e12	+	1.53631e12i	−0.587824	+	0.587824i	0.349217	+	0.937042i	$0.386447\pi$
$182$	−5.41496e12	−	5.41496e12i	−2.01003	−	2.01003i
$183$	−2.71242e11			−0.0976957
$184$	−6.71573e10	−	6.71573e10i	−0.0234744	−	0.0234744i
$185$		−	9.04910e11i		−	0.307016i
$186$	−9.06484e11			−0.298565
$187$	1.81959e12	−	2.12813e12i	0.581896	−	0.680564i
$188$	5.88949e9			0.00182898
$189$		−	1.85160e12i		−	0.558479i
$190$	−4.74848e12	−	4.74848e12i	−1.39126	−	1.39126i
$191$	−6.15764e11			−0.175279			−0.0876397	−	0.996152i	$-0.527932\pi$
$191$	−6.15764e11			−0.175279			−0.0876397	+	0.996152i	$0.527932\pi$
$192$	5.65907e11	+	5.65907e11i	0.156527	+	0.156527i
$193$	−1.54247e12	+	1.54247e12i	−0.414621	+	0.414621i	−0.883345	−	0.468724i	$-0.844714\pi$
$193$	−1.54247e12	+	1.54247e12i	−0.414621	+	0.414621i	0.468724	+	0.883345i	$0.344714\pi$
$194$	−3.84995e11	+	3.84995e11i	−0.100588	+	0.100588i
$195$			1.82441e12i			0.463373i
$196$			1.50237e12i			0.370995i
$197$	1.74717e12	−	1.74717e12i	0.419539	−	0.419539i	−0.465506	−	0.885045i	$-0.654128\pi$
$197$	1.74717e12	−	1.74717e12i	0.419539	−	0.419539i	0.885045	+	0.465506i	$0.154128\pi$
$198$	3.56402e12	−	3.56402e12i	0.832304	−	0.832304i
$199$	−4.81791e11	−	4.81791e11i	−0.109438	−	0.109438i	0.650268	−	0.759705i	$-0.274657\pi$
$199$	−4.81791e11	−	4.81791e11i	−0.109438	−	0.109438i	−0.759705	+	0.650268i	$0.774657\pi$
$200$	6.05811e10			0.0133867
$201$	3.55443e11	+	3.55443e11i	0.0764172	+	0.0764172i
$202$		−	8.58178e12i		−	1.79533i
$203$	6.96644e12			1.41835
$204$	8.93809e11	+	7.64225e11i	0.177125	+	0.151445i
$205$	8.49893e12			1.63953
$206$			1.06968e13i			2.00903i
$207$	−1.88443e12	−	1.88443e12i	−0.344623	−	0.344623i
$208$	−1.01122e13			−1.80094
$209$	4.67245e12	+	4.67245e12i	0.810477	+	0.810477i
$210$	1.85145e12	−	1.85145e12i	0.312828	−	0.312828i
$211$	−1.68041e12	+	1.68041e12i	−0.276606	+	0.276606i	−0.831752	−	0.555147i	$-0.812662\pi$
$211$	−1.68041e12	+	1.68041e12i	−0.276606	+	0.276606i	0.555147	+	0.831752i	$0.312662\pi$
$212$		−	2.87293e12i		−	0.460763i
$213$		−	7.04416e11i		−	0.110088i
$214$	6.20065e12	−	6.20065e12i	0.944412	−	0.944412i
$215$	−7.15143e12	+	7.15143e12i	−1.06165	+	1.06165i
$216$	−1.48322e11	−	1.48322e11i	−0.0214640	−	0.0214640i
$217$	−7.30469e12			−1.03056
$218$	2.71009e12	+	2.71009e12i	0.372797	+	0.372797i
$219$			2.69031e12i			0.360877i
$220$	7.18112e12			0.939436
$221$	−1.34818e13	+	1.05368e12i	−1.72025	+	0.134447i
$222$	−7.65909e11			−0.0953314
$223$		−	5.77981e12i		−	0.701838i	−0.936406	−	0.350919i	$-0.885869\pi$
$223$		−	5.77981e12i		−	0.701838i	0.936406	−	0.350919i	$-0.114131\pi$
$224$	9.81161e12	+	9.81161e12i	1.16245	+	1.16245i
$225$	1.69991e12			0.196526
$226$	5.96933e12	+	5.96933e12i	0.673487	+	0.673487i
$227$	−1.76103e12	+	1.76103e12i	−0.193921	+	0.193921i	−0.797388	−	0.603467i	$-0.793785\pi$
$227$	−1.76103e12	+	1.76103e12i	−0.193921	+	0.193921i	0.603467	+	0.797388i	$0.293785\pi$
$228$	−1.96242e12	+	1.96242e12i	−0.210936	+	0.210936i
$229$			1.43762e13i			1.50852i	0.656577	+	0.754259i	$0.272004\pi$
$229$			1.43762e13i			1.50852i	−0.656577	+	0.754259i	$0.727996\pi$
$230$		−	7.77618e12i		−	0.796642i
$231$	−1.82181e12	+	1.82181e12i	−0.182237	+	0.182237i
$232$	5.58047e11	−	5.58047e11i	0.0545114	−	0.0545114i
$233$	9.99003e12	+	9.99003e12i	0.953035	+	0.953035i	0.998946	−	0.0459102i	$-0.0146188\pi$
$233$	9.99003e12	+	9.99003e12i	0.953035	+	0.953035i	−0.0459102	+	0.998946i	$0.514619\pi$
$234$	−2.43430e13			−2.26822
$235$	−1.63738e10	−	1.63738e10i	−0.00149031	−	0.00149031i
$236$		−	1.54767e13i		−	1.37614i
$237$	1.32378e11			0.0115001
$238$	1.47510e13	+	1.26124e13i	1.25213	+	1.07059i
$239$	4.77380e12			0.395983			0.197991	−	0.980204i	$-0.436558\pi$
$239$	4.77380e12			0.395983			0.197991	+	0.980204i	$0.436558\pi$
$240$		−	3.45751e12i		−	0.280286i
$241$	−9.69509e12	−	9.69509e12i	−0.768171	−	0.768171i	0.209613	−	0.977784i	$-0.432780\pi$
$241$	−9.69509e12	−	9.69509e12i	−0.768171	−	0.768171i	−0.977784	+	0.209613i	$0.932780\pi$
$242$	3.57795e12			0.277108
$243$	−6.30686e12	−	6.30686e12i	−0.477506	−	0.477506i
$244$	3.64611e12	−	3.64611e12i	0.269889	−	0.269889i
$245$	4.17685e12	−	4.17685e12i	0.302298	−	0.302298i
$246$		−	7.19344e12i		−	0.509089i
$247$		−	3.19138e13i		−	2.20874i
$248$	−5.85143e11	+	5.85143e11i	−0.0396075	+	0.0396075i
$249$	−4.68501e12	+	4.68501e12i	−0.310180	+	0.310180i
$250$	−1.32748e13	−	1.32748e13i	−0.859725	−	0.859725i
$251$	1.90437e13			1.20655			0.603277	−	0.797532i	$-0.293861\pi$
$251$	1.90437e13			1.20655			0.603277	+	0.797532i	$0.293861\pi$
$252$	1.20623e13	+	1.20623e13i	0.747698	+	0.747698i
$253$			7.65169e12i			0.464082i
$254$	−1.58374e13			−0.939935
$255$	−3.60267e11	−	4.60962e12i	−0.0209244	−	0.267728i
$256$	1.90919e13			1.08525
$257$			1.16195e13i			0.646481i	0.946317	+	0.323241i	$0.104772\pi$
$257$			1.16195e13i			0.646481i	−0.946317	+	0.323241i	$0.895228\pi$
$258$	6.05292e12	+	6.05292e12i	0.329653	+	0.329653i
$259$	−6.17190e12			−0.329056
$260$	−2.45242e13	−	2.45242e13i	−1.28009	−	1.28009i
$261$	1.56588e13	−	1.56588e13i	0.800268	−	0.800268i
$262$	−9.64176e12	+	9.64176e12i	−0.482502	+	0.482502i
$263$		−	2.98998e13i		−	1.46525i	−0.680634	−	0.732624i	$-0.738295\pi$
$263$		−	2.98998e13i		−	1.46525i	0.680634	−	0.732624i	$-0.261705\pi$
$264$			2.91872e11i			0.0140078i
$265$	−7.98725e12	+	7.98725e12i	−0.375444	+	0.375444i
$266$	−3.23868e13	+	3.23868e13i	−1.49114	+	1.49114i
$267$	−2.60986e12	−	2.60986e12i	−0.117708	−	0.117708i
$268$	−9.55593e12			−0.422213
$269$	2.88979e13	+	2.88979e13i	1.25092	+	1.25092i	0.955309	+	0.295608i	$0.0955222\pi$
$269$	2.88979e13	+	2.88979e13i	1.25092	+	1.25092i	0.295608	+	0.955309i	$0.404478\pi$
$270$		−	1.71743e13i		−	0.728415i
$271$	−2.97474e13			−1.23628			−0.618142	−	0.786066i	$-0.712114\pi$
$271$	−2.97474e13			−1.23628			−0.618142	+	0.786066i	$0.712114\pi$
$272$	2.55500e13	−	1.99687e12i	1.04055	−	0.0813243i
$273$	1.24433e13			0.496639
$274$			4.03825e13i			1.57967i
$275$	−3.45121e12	−	3.45121e12i	−0.132325	−	0.132325i
$276$	−3.21369e12			−0.120783
$277$	−2.27062e13	−	2.27062e13i	−0.836576	−	0.836576i	0.151830	−	0.988407i	$-0.451483\pi$
$277$	−2.27062e13	−	2.27062e13i	−0.836576	−	0.836576i	−0.988407	+	0.151830i	$0.951483\pi$
$278$	−3.31660e13	+	3.31660e13i	−1.19797	+	1.19797i
$279$	−1.64191e13	+	1.64191e13i	−0.581469	+	0.581469i
$280$		−	2.39025e12i		−	0.0829993i
$281$		−	1.05065e13i		−	0.357744i	−0.983872	−	0.178872i	$-0.942755\pi$
$281$		−	1.05065e13i		−	0.357744i	0.983872	−	0.178872i	$-0.0572448\pi$
$282$	−1.38587e10	+	1.38587e10i	−0.000462755	+	0.000462755i
$283$	6.69421e12	−	6.69421e12i	0.219217	−	0.219217i	−0.588951	−	0.808168i	$-0.700459\pi$
$283$	6.69421e12	−	6.69421e12i	0.219217	−	0.219217i	0.808168	+	0.588951i	$0.200459\pi$
$284$	9.46896e12	+	9.46896e12i	0.304125	+	0.304125i
$285$	1.09117e13			0.343753
$286$	4.94219e13	+	4.94219e13i	1.52724	+	1.52724i
$287$		−	5.79667e13i		−	1.75723i
$288$	4.41080e13			1.31177
$289$	3.38558e13	−	5.32454e12i	0.987858	−	0.155362i
$290$	6.46166e13			1.84993
$291$		−	8.84697e11i		−	0.0248533i
$292$	−3.61639e13	−	3.61639e13i	−0.996942	−	0.996942i
$293$	−3.80314e12			−0.102889			−0.0514447	−	0.998676i	$-0.516383\pi$
$293$	−3.80314e12			−0.102889			−0.0514447	+	0.998676i	$0.516383\pi$
$294$	−3.53525e12	−	3.53525e12i	−0.0938664	−	0.0938664i
$295$	−4.30279e13	+	4.30279e13i	−1.12132	+	1.12132i
$296$	−4.94401e11	+	4.94401e11i	−0.0126466	+	0.0126466i
$297$			1.68994e13i			0.424336i
$298$			8.78697e11i			0.0216596i
$299$	2.61312e13	−	2.61312e13i	0.632366	−	0.632366i
$300$	1.44950e12	−	1.44950e12i	0.0344391	−	0.0344391i
$301$	4.87761e13	+	4.87761e13i	1.13787	+	1.13787i
$302$	−1.43918e12			−0.0329668
$303$	9.86023e12	+	9.86023e12i	0.221795	+	0.221795i
$304$			6.04811e13i			1.33603i
$305$	−2.02736e13			−0.439827
$306$	6.15060e13	−	4.80702e12i	1.31054	−	0.102425i
$307$	−6.46075e13			−1.35214			−0.676071	−	0.736837i	$-0.736319\pi$
$307$	−6.46075e13			−1.35214			−0.676071	+	0.736837i	$0.736319\pi$
$308$		−	4.89785e13i		−	1.00688i
$309$	−1.22904e13	−	1.22904e13i	−0.248195	−	0.248195i
$310$	−6.77540e13			−1.34414
$311$	−1.70664e13	−	1.70664e13i	−0.332629	−	0.332629i	0.520955	−	0.853584i	$-0.325576\pi$
$311$	−1.70664e13	−	1.70664e13i	−0.332629	−	0.332629i	−0.853584	+	0.520955i	$0.825576\pi$
$312$	9.96771e11	−	9.96771e11i	0.0190873	−	0.0190873i
$313$	5.09880e13	−	5.09880e13i	0.959343	−	0.959343i	−0.0398622	−	0.999205i	$-0.512692\pi$
$313$	5.09880e13	−	5.09880e13i	0.959343	−	0.959343i	0.999205	+	0.0398622i	$0.0126919\pi$
$314$		−	6.13155e13i		−	1.13359i
$315$		−	6.70704e13i		−	1.21849i
$316$	−1.77947e12	+	1.77947e12i	−0.0317695	+	0.0317695i
$317$	−6.32666e13	+	6.32666e13i	−1.11007	+	1.11007i	−0.116924	+	0.993141i	$0.537304\pi$
$317$	−6.32666e13	+	6.32666e13i	−1.11007	+	1.11007i	−0.993141	+	0.116924i	$0.962696\pi$
$318$	6.76035e12	+	6.76035e12i	0.116579	+	0.116579i
$319$	−6.35821e13			−1.07767
$320$	4.22981e13	+	4.22981e13i	0.704686	+	0.704686i
$321$			1.42488e13i			0.233345i
$322$	−5.30372e13			−0.853833
$323$	6.30203e12	+	8.06347e13i	0.0997393	+	1.27617i
$324$	5.05680e13			0.786825
$325$			2.35724e13i			0.360617i
$326$	−1.10613e14	−	1.10613e14i	−1.66383	−	1.66383i
$327$	−6.22763e12			−0.0921108
$328$	−4.64342e12	−	4.64342e12i	−0.0675355	−	0.0675355i
$329$	−1.11677e11	+	1.11677e11i	−0.00159730	+	0.00159730i
$330$	−1.68980e13	+	1.68980e13i	−0.237689	+	0.237689i
$331$		−	5.87024e13i		−	0.812086i	−0.913854	−	0.406043i	$-0.866908\pi$
$331$		−	5.87024e13i		−	0.812086i	0.913854	−	0.406043i	$-0.133092\pi$
$332$		−	1.25955e14i		−	1.71378i
$333$	−1.38729e13	+	1.38729e13i	−0.185662	+	0.185662i
$334$	−1.00805e14	+	1.00805e14i	−1.32702	+	1.32702i
$335$	2.65671e13	+	2.65671e13i	0.344031	+	0.344031i
$336$	−2.35818e13			−0.300408
$337$	5.28218e13	+	5.28218e13i	0.661986	+	0.661986i	0.955848	−	0.293862i	$-0.0949406\pi$
$337$	5.28218e13	+	5.28218e13i	0.661986	+	0.661986i	−0.293862	+	0.955848i	$0.594941\pi$
$338$		−	2.24185e14i		−	2.76416i
$339$	−1.37172e13			−0.166405
$340$	6.68067e13	+	5.71211e13i	0.797418	+	0.681808i
$341$	6.66693e13			0.783027
$342$			1.45595e14i			1.68268i
$343$	4.47816e13	+	4.47816e13i	0.509310	+	0.509310i
$344$	7.81442e12			0.0874632
$345$	8.93462e12	+	8.93462e12i	0.0984172	+	0.0984172i
$346$	9.59003e13	−	9.59003e13i	1.03968	−	1.03968i
$347$	1.69599e13	−	1.69599e13i	0.180972	−	0.180972i	−0.610807	−	0.791779i	$-0.709155\pi$
$347$	1.69599e13	−	1.69599e13i	0.180972	−	0.180972i	0.791779	+	0.610807i	$0.209155\pi$
$348$		−	2.67043e13i		−	0.280476i
$349$			5.35264e13i			0.553386i	0.960958	+	0.276693i	$0.0892386\pi$
$349$			5.35264e13i			0.553386i	−0.960958	+	0.276693i	$0.910761\pi$
$350$	2.39218e13	−	2.39218e13i	0.243456	−	0.243456i
$351$	5.77130e13	−	5.77130e13i	0.578208	−	0.578208i
$352$	−8.95497e13	−	8.95497e13i	−0.883242	−	0.883242i
$353$	−6.51138e13			−0.632284			−0.316142	−	0.948712i	$-0.602388\pi$
$353$	−6.51138e13			−0.632284			−0.316142	+	0.948712i	$0.602388\pi$
$354$	3.64185e13	+	3.64185e13i	0.348180	+	0.348180i
$355$		−	5.26507e13i		−	0.495619i
$356$	7.01649e13			0.650347
$357$	−3.14398e13	+	2.45718e12i	−0.286949	+	0.0224266i
$358$	1.75959e14			1.58145
$359$			4.34677e13i			0.384722i	0.981324	+	0.192361i	$0.0616144\pi$
$359$			4.34677e13i			0.384722i	−0.981324	+	0.192361i	$0.938386\pi$
$360$	−5.37268e12	−	5.37268e12i	−0.0468303	−	0.0468303i
$361$	−7.43853e13			−0.638554
$362$	9.71912e13	+	9.71912e13i	0.821731	+	0.821731i
$363$	−4.11097e12	+	4.11097e12i	−0.0342340	+	0.0342340i
$364$	−1.67266e14	+	1.67266e14i	−1.37199	+	1.37199i
$365$			2.01084e14i			1.62468i
$366$			1.71595e13i			0.136571i
$367$	6.03423e13	−	6.03423e13i	0.473106	−	0.473106i	−0.429812	−	0.902918i	$-0.641420\pi$
$367$	6.03423e13	−	6.03423e13i	0.473106	−	0.473106i	0.902918	+	0.429812i	$0.141420\pi$
$368$	−4.95224e13	+	4.95224e13i	−0.382506	+	0.382506i
$369$	−1.30294e14	−	1.30294e14i	−0.991473	−	0.991473i
$370$	−5.72470e13			−0.429183
$371$	5.44767e13	+	5.44767e13i	0.402397	+	0.402397i
$372$			2.80010e13i			0.203792i
$373$	2.27085e14			1.62851			0.814255	−	0.580507i	$-0.197146\pi$
$373$	2.27085e14			1.62851			0.814255	+	0.580507i	$0.197146\pi$
$374$	−1.34631e14	−	1.15112e14i	−0.951374	−	0.813444i
$375$	3.05049e13			0.212421
$376$			1.78918e10i			0.000122778i
$377$	2.17139e14	+	2.17139e14i	1.46845	+	1.46845i
$378$	−1.17137e14			−0.780708
$379$	−1.79475e14	−	1.79475e14i	−1.17893	−	1.17893i	−0.980017	−	0.198915i	$-0.936258\pi$
$379$	−1.79475e14	−	1.79475e14i	−1.17893	−	1.17893i	−0.198915	−	0.980017i	$-0.563742\pi$
$380$	−1.46679e14	+	1.46679e14i	−0.949636	+	0.949636i
$381$	1.81967e13	−	1.81967e13i	0.116120	−	0.116120i
$382$			3.89549e13i			0.245027i
$383$		−	5.79638e13i		−	0.359388i	−0.983723	−	0.179694i	$-0.942489\pi$
$383$		−	5.79638e13i		−	0.359388i	0.983723	−	0.179694i	$-0.0575107\pi$
$384$	−3.61598e12	+	3.61598e12i	−0.0221006	+	0.0221006i
$385$	−1.36169e14	+	1.36169e14i	−0.820434	+	0.820434i
$386$	9.75806e13	+	9.75806e13i	0.579607	+	0.579607i
$387$	2.19273e14			1.28403
$388$	1.18924e13	+	1.18924e13i	0.0686584	+	0.0686584i
$389$		−	4.24554e13i		−	0.241663i	−0.992673	−	0.120832i	$-0.961444\pi$
$389$		−	4.24554e13i		−	0.241663i	0.992673	−	0.120832i	$-0.0385561\pi$
$390$	1.15417e14			0.647759
$391$	−6.08642e13	+	7.11845e13i	−0.336814	+	0.393925i
$392$	−4.56407e12			−0.0249046
$393$		−	2.21562e13i		−	0.119217i
$394$	−1.10531e14	−	1.10531e14i	−0.586482	−	0.586482i
$395$	9.89445e12			0.0517735
$396$	−1.10091e14	−	1.10091e14i	−0.568107	−	0.568107i
$397$	1.58155e14	−	1.58155e14i	0.804888	−	0.804888i	−0.178967	−	0.983855i	$-0.557276\pi$
$397$	1.58155e14	−	1.58155e14i	0.804888	−	0.804888i	0.983855	+	0.178967i	$0.0572756\pi$
$398$	−3.04793e13	+	3.04793e13i	−0.152985	+	0.152985i
$399$		−	7.44231e13i		−	0.368431i
$400$		−	4.46731e13i		−	0.218130i
$401$	3.99498e13	−	3.99498e13i	0.192407	−	0.192407i	−0.604329	−	0.796735i	$-0.706559\pi$
$401$	3.99498e13	−	3.99498e13i	0.192407	−	0.192407i	0.796735	+	0.604329i	$0.206559\pi$
$402$	2.24862e13	−	2.24862e13i	0.106825	−	0.106825i
$403$	−2.27682e14	−	2.27682e14i	−1.06697	−	1.06697i
$404$	−2.65088e14			−1.22544
$405$	−1.40588e14	−	1.40588e14i	−0.641128	−	0.641128i
$406$		−	4.40715e14i		−	1.98274i
$407$	5.63304e13			0.250020
$408$	−2.32165e12	+	2.71532e12i	−0.0101664	+	0.0118902i
$409$	2.82384e14			1.22000			0.610002	−	0.792400i	$-0.291169\pi$
$409$	2.82384e14			1.22000			0.610002	+	0.792400i	$0.291169\pi$
$410$		−	5.37665e14i		−	2.29192i
$411$	−4.63984e13	−	4.63984e13i	−0.195152	−	0.195152i
$412$	3.30421e14			1.37130
$413$	2.93470e14	+	2.93470e14i	1.20182	+	1.20182i
$414$	−1.19214e14	+	1.19214e14i	−0.481755	+	0.481755i
$415$	−3.50176e14	+	3.50176e14i	−1.39644	+	1.39644i
$416$			6.11642e14i			2.40704i
$417$		−	7.62136e13i		−	0.295995i
$418$	2.95592e14	−	2.95592e14i	1.13298	−	1.13298i
$419$	−4.42804e13	+	4.42804e13i	−0.167508	+	0.167508i	−0.785883	−	0.618375i	$-0.787791\pi$
$419$	−4.42804e13	+	4.42804e13i	−0.167508	+	0.167508i	0.618375	+	0.785883i	$0.287791\pi$
$420$	−5.71906e13	−	5.71906e13i	−0.213527	−	0.213527i
$421$	−2.13605e14			−0.787155			−0.393577	−	0.919291i	$-0.628763\pi$
$421$	−2.13605e14			−0.787155			−0.393577	+	0.919291i	$0.628763\pi$
$422$	1.06307e14	+	1.06307e14i	0.386673	+	0.386673i
$423$			5.02043e11i			0.00180247i
$424$	8.72772e12			0.0309306
$425$	−4.65486e12	−	5.95591e13i	−0.0162842	−	0.208357i
$426$	−4.45632e13			−0.153895
$427$			1.38276e14i			0.471403i
$428$	−1.91536e14	−	1.91536e14i	−0.644628	−	0.644628i
$429$	−1.13569e14			−0.377350
$430$	4.52418e14	+	4.52418e14i	1.48410	+	1.48410i
$431$	1.07303e14	−	1.07303e14i	0.347525	−	0.347525i	−0.511662	−	0.859187i	$-0.670970\pi$
$431$	1.07303e14	−	1.07303e14i	0.347525	−	0.347525i	0.859187	+	0.511662i	$0.170970\pi$
$432$	−1.09374e14	+	1.09374e14i	−0.349747	+	0.349747i
$433$		−	4.35184e14i		−	1.37401i	−0.726654	−	0.687004i	$-0.758926\pi$
$433$		−	4.35184e14i		−	1.37401i	0.726654	−	0.687004i	$-0.241074\pi$
$434$			4.62114e14i			1.44064i
$435$	−7.42427e13	+	7.42427e13i	−0.228540	+	0.228540i
$436$	8.37137e13	−	8.37137e13i	0.254461	−	0.254461i
$437$	−1.56290e14	−	1.56290e14i	−0.469121	−	0.469121i
$438$	1.70196e14			0.504478
$439$	−3.16492e14	−	3.16492e14i	−0.926421	−	0.926421i	0.0710519	−	0.997473i	$-0.477364\pi$
$439$	−3.16492e14	−	3.16492e14i	−0.926421	−	0.926421i	−0.997473	+	0.0710519i	$0.977364\pi$
$440$			2.18156e13i			0.0630635i
$441$	−1.28068e14			−0.365618
$442$	6.66584e13	+	8.52897e14i	0.187946	+	2.40477i
$443$	−3.29733e14			−0.918210			−0.459105	−	0.888382i	$-0.651830\pi$
$443$	−3.29733e14			−0.918210			−0.459105	+	0.888382i	$0.651830\pi$
$444$			2.36587e13i			0.0650705i
$445$	−1.95071e14	−	1.95071e14i	−0.529922	−	0.529922i
$446$	−3.65646e14			−0.981113
$447$	−1.00960e12	−	1.00960e12i	−0.00267582	−	0.00267582i
$448$	2.88492e14	−	2.88492e14i	0.755275	−	0.755275i
$449$	−2.83046e14	+	2.83046e14i	−0.731985	+	0.731985i	−0.971013	−	0.239028i	$-0.923171\pi$
$449$	−2.83046e14	+	2.83046e14i	−0.731985	+	0.731985i	0.239028	+	0.971013i	$0.423171\pi$
$450$		−	1.07540e14i		−	0.274728i
$451$			5.29057e14i			1.33515i
$452$	1.84391e14	−	1.84391e14i	0.459703	−	0.459703i
$453$	1.65358e12	−	1.65358e12i	0.00407271	−	0.00407271i
$454$	1.11407e14	+	1.11407e14i	0.271086	+	0.271086i
$455$	9.30059e14			2.23588
$456$	−5.96167e12	−	5.96167e12i	−0.0141599	−	0.0141599i
$457$			4.41292e14i			1.03559i	0.855505	+	0.517794i	$0.173247\pi$
$457$			4.41292e14i			1.03559i	−0.855505	+	0.517794i	$0.826753\pi$
$458$	9.09479e14			2.10879
$459$	−1.34423e14	+	1.57217e14i	−0.307968	+	0.360188i
$460$	−2.40203e14			−0.543765
$461$			1.22295e14i			0.273560i	0.990601	+	0.136780i	$0.0436753\pi$
$461$			1.22295e14i			0.273560i	−0.990601	+	0.136780i	$0.956325\pi$
$462$	1.15252e14	+	1.15252e14i	0.254753	+	0.254753i
$463$	1.78067e14			0.388945			0.194472	−	0.980908i	$-0.437701\pi$
$463$	1.78067e14			0.388945			0.194472	+	0.980908i	$0.437701\pi$
$464$	−4.11509e14	−	4.11509e14i	−0.888240	−	0.888240i
$465$	7.78475e13	−	7.78475e13i	0.166056	−	0.166056i
$466$	6.31995e14	−	6.31995e14i	1.33227	−	1.33227i
$467$		−	3.18299e13i		−	0.0663120i	−0.999450	−	0.0331560i	$-0.989444\pi$
$467$		−	3.18299e13i		−	0.0663120i	0.999450	−	0.0331560i	$-0.0105558\pi$
$468$			7.51945e14i			1.54822i
$469$	1.81200e14	−	1.81200e14i	0.368729	−	0.368729i
$470$	−1.03585e12	+	1.03585e12i	−0.00208333	+	0.00208333i
$471$	7.04498e13	+	7.04498e13i	0.140044	+	0.140044i
$472$	4.70169e13			0.0923789
$473$	−4.45175e14	−	4.45175e14i	−0.864559	−	0.864559i
$474$		−	8.37459e12i		−	0.0160762i
$475$	1.40986e14			0.267523
$476$	3.89592e14	−	4.55653e14i	0.730755	−	0.854664i
$477$	2.44900e14			0.454085
$478$		−	3.02003e14i		−	0.553552i
$479$	−2.88562e14	−	2.88562e14i	−0.522871	−	0.522871i	0.395566	−	0.918437i	$-0.370548\pi$
$479$	−2.88562e14	−	2.88562e14i	−0.522871	−	0.522871i	−0.918437	+	0.395566i	$0.870548\pi$
$480$	−2.09128e14			−0.374616
$481$	−1.92374e14	−	1.92374e14i	−0.340681	−	0.340681i
$482$	−6.13337e14	+	6.13337e14i	−1.07384	+	1.07384i
$483$	6.09382e13	−	6.09382e13i	0.105483	−	0.105483i
$484$		−	1.10522e14i		−	0.189146i
$485$		−	6.61256e13i		−	0.111890i
$486$	−3.98988e14	+	3.98988e14i	−0.667515	+	0.667515i
$487$	5.70816e14	−	5.70816e14i	0.944250	−	0.944250i	−0.0542760	−	0.998526i	$-0.517285\pi$
$487$	5.70816e14	−	5.70816e14i	0.944250	−	0.944250i	0.998526	+	0.0542760i	$0.0172851\pi$
$488$	1.10766e13	+	1.10766e13i	0.0181174	+	0.0181174i
$489$	2.54183e14			0.411100
$490$	−2.64238e14	−	2.64238e14i	−0.422588	−	0.422588i
$491$		−	6.45941e14i		−	1.02151i	−0.859725	−	0.510757i	$-0.829365\pi$
$491$		−	6.45941e14i		−	1.02151i	0.859725	−	0.510757i	$-0.170635\pi$
$492$	−2.22203e14			−0.347489
$493$	−5.91511e14	−	5.05754e14i	−0.914755	−	0.782134i
$494$	−2.01895e15			−3.08764
$495$			6.12146e14i			0.925820i
$496$	4.31490e14	+	4.31490e14i	0.645388	+	0.645388i
$497$	−3.59102e14			−0.531200
$498$	2.96386e14	+	2.96386e14i	0.433607	+	0.433607i
$499$	−5.78324e14	+	5.78324e14i	−0.836794	+	0.836794i	−0.988436	−	0.151642i	$-0.951544\pi$
$499$	−5.78324e14	+	5.78324e14i	−0.836794	+	0.836794i	0.151642	+	0.988436i	$0.451544\pi$
$500$	−4.10055e14	+	4.10055e14i	−0.586823	+	0.586823i
$501$		−	2.31645e14i		−	0.327881i
$502$		−	1.20476e15i		−	1.68666i
$503$	−2.26615e14	+	2.26615e14i	−0.313808	+	0.313808i	−0.846383	−	0.532575i	$-0.821224\pi$
$503$	−2.26615e14	+	2.26615e14i	−0.313808	+	0.313808i	0.532575	+	0.846383i	$0.321224\pi$
$504$	−3.66442e13	+	3.66442e13i	−0.0501923	+	0.0501923i
$505$	7.36991e14	+	7.36991e14i	0.998526	+	0.998526i
$506$	4.84066e14			0.648749
$507$	2.57582e14	+	2.57582e14i	0.341485	+	0.341485i
$508$			4.89211e14i			0.641572i
$509$	3.43626e14			0.445799			0.222899	−	0.974841i	$-0.428448\pi$
$509$	3.43626e14			0.445799			0.222899	+	0.974841i	$0.428448\pi$
$510$	−2.91617e14	+	2.27914e13i	−0.374263	+	0.0292506i
$511$	1.37149e15			1.74131
$512$		−	1.10592e15i		−	1.38912i
$513$	−3.45180e14	−	3.45180e14i	−0.428944	−	0.428944i
$514$	7.35081e14			0.903729
$515$	−9.18629e14	−	9.18629e14i	−1.11738	−	1.11738i
$516$	1.86973e14	−	1.86973e14i	0.225011	−	0.225011i
$517$	1.01927e12	−	1.01927e12i	0.00121364	−	0.00121364i
$518$			3.90451e14i			0.459994i
$519$			2.20374e14i			0.256885i
$520$	7.45024e13	−	7.45024e13i	0.0859314	−	0.0859314i
$521$	−7.82285e14	+	7.82285e14i	−0.892807	+	0.892807i	−0.994787	−	0.101979i	$-0.967482\pi$
$521$	−7.82285e14	+	7.82285e14i	−0.892807	+	0.892807i	0.101979	+	0.994787i	$0.467482\pi$
$522$	−9.90617e14	−	9.90617e14i	−1.11871	−	1.11871i
$523$	−7.31419e13			−0.0817348			−0.0408674	−	0.999165i	$-0.513012\pi$
$523$	−7.31419e13			−0.0817348			−0.0408674	+	0.999165i	$0.513012\pi$
$524$	2.97830e14	+	2.97830e14i	0.329342	+	0.329342i
$525$			5.49710e13i			0.0601531i
$526$	−1.89154e15			−2.04830
$527$	6.20232e14	+	5.30311e14i	0.664654	+	0.568293i
$528$	2.15229e14			0.228252
$529$			6.96866e14i			0.731380i
$530$	5.05294e14	+	5.05294e14i	0.524840	+	0.524840i
$531$	1.31929e15			1.35619
$532$	1.00042e15	+	1.00042e15i	1.01781	+	1.01781i
$533$	1.80678e15	−	1.80678e15i	1.81931	−	1.81931i
$534$	−1.65106e14	+	1.65106e14i	−0.164546	+	0.164546i
$535$			1.06501e15i			1.05052i
$536$		−	2.90301e13i		−	0.0283428i
$537$	−2.02172e14	+	2.02172e14i	−0.195372	+	0.195372i
$538$	1.82816e15	−	1.82816e15i	1.74868	−	1.74868i
$539$	2.60008e14	+	2.60008e14i	0.246177	+	0.246177i
$540$	−5.30509e14			−0.497195
$541$	−1.23830e15	−	1.23830e15i	−1.14879	−	1.14879i	−0.986791	−	0.161998i	$-0.948206\pi$
$541$	−1.23830e15	−	1.23830e15i	−1.14879	−	1.14879i	−0.161998	−	0.986791i	$-0.551794\pi$
$542$			1.88190e15i			1.72823i
$543$	−2.23340e14			−0.203033
$544$	−1.20781e14	−	1.54540e15i	−0.108694	−	1.39074i
$545$	−4.65477e14			−0.414684
$546$		−	7.87195e14i		−	0.694261i
$547$	1.26979e15	+	1.26979e15i	1.10867	+	1.10867i	0.993326	+	0.115339i	$0.0367955\pi$
$547$	1.26979e15	+	1.26979e15i	1.10867	+	1.10867i	0.115339	+	0.993326i	$0.463204\pi$
$548$	1.24740e15			1.07823
$549$	3.10809e14	+	3.10809e14i	0.265978	+	0.265978i
$550$	−2.18333e14	+	2.18333e14i	−0.184980	+	0.184980i
$551$	1.29870e15	−	1.29870e15i	1.08937	−	1.08937i
$552$		−	9.76292e12i		−	0.00810802i
$553$		−	6.74847e13i		−	0.0554903i
$554$	−1.43645e15	+	1.43645e15i	−1.16947	+	1.16947i
$555$	6.57752e13	−	6.57752e13i	0.0530213	−	0.0530213i
$556$	1.02449e15	+	1.02449e15i	0.817701	+	0.817701i
$557$	−1.55543e15			−1.22927			−0.614635	−	0.788812i	$-0.710697\pi$
$557$	−1.55543e15			−1.22927			−0.614635	+	0.788812i	$0.710697\pi$
$558$	1.03872e15	+	1.03872e15i	0.812847	+	0.812847i
$559$			3.04063e15i			2.35613i
$560$	−1.76259e15			−1.35244
$561$	2.86948e14	−	2.24265e13i	0.218026	−	0.0170399i
$562$	−6.64667e14			−0.500097
$563$			1.76447e15i			1.31467i	0.753598	+	0.657335i	$0.228317\pi$
$563$			1.76447e15i			1.31467i	−0.753598	+	0.657335i	$0.771683\pi$
$564$	4.28089e11	+	4.28089e11i	0.000315863	+	0.000315863i
$565$	−1.02528e15			−0.749159
$566$	−4.23493e14	−	4.23493e14i	−0.306448	−	0.306448i
$567$	−9.58873e14	+	9.58873e14i	−0.687154	+	0.687154i
$568$	−2.87659e13	+	2.87659e13i	−0.0204156	+	0.0204156i
$569$		−	2.22370e15i		−	1.56300i	−0.623906	−	0.781499i	$-0.714455\pi$
$569$		−	2.22370e15i		−	1.56300i	0.623906	−	0.781499i	$-0.285545\pi$
$570$		−	6.90305e14i		−	0.480540i
$571$	−2.46396e14	+	2.46396e14i	−0.169877	+	0.169877i	−0.786925	−	0.617048i	$-0.788328\pi$
$571$	−2.46396e14	+	2.46396e14i	−0.169877	+	0.169877i	0.617048	+	0.786925i	$0.288328\pi$
$572$	1.52663e15	−	1.52663e15i	1.04245	−	1.04245i
$573$	−4.47580e13	−	4.47580e13i	−0.0302706	−	0.0302706i
$574$	−3.66712e15			−2.45646
$575$	1.15441e14	+	1.15441e14i	0.0765924	+	0.0765924i
$576$		−	1.29692e15i		−	0.852292i
$577$	−1.99017e15			−1.29546			−0.647728	−	0.761872i	$-0.724281\pi$
$577$	−1.99017e15			−1.29546			−0.647728	+	0.761872i	$0.724281\pi$
$578$	−3.36844e14	−	2.14180e15i	−0.217183	−	1.38095i
$579$	−2.24235e14			−0.143209
$580$		−	1.99598e15i		−	1.26271i
$581$	2.38836e15	+	2.38836e15i	1.49669	+	1.49669i
$582$	−5.59683e13			−0.0347429
$583$	−4.97205e14	−	4.97205e14i	−0.305744	−	0.305744i
$584$	1.09863e14	−	1.09863e14i	0.0669238	−	0.0669238i
$585$	2.09054e15	−	2.09054e15i	1.26154	−	1.26154i
$586$			2.40597e14i			0.143831i
$587$		−	1.78010e15i		−	1.05423i	−0.849795	−	0.527114i	$-0.823274\pi$
$587$		−	1.78010e15i		−	1.05423i	0.849795	−	0.527114i	$-0.176726\pi$
$588$	−1.09203e14	+	1.09203e14i	−0.0640705	+	0.0640705i
$589$	−1.36176e15	+	1.36176e15i	−0.791530	+	0.791530i
$590$	2.72206e15	+	2.72206e15i	1.56751	+	1.56751i
$591$	2.53994e14			0.144908
$592$	3.64576e14	+	3.64576e14i	0.206072	+	0.206072i
$593$			1.25634e14i			0.0703570i	0.999381	+	0.0351785i	$0.0112000\pi$
$593$			1.25634e14i			0.0703570i	−0.999381	+	0.0351785i	$0.988800\pi$
$594$	1.06910e15			0.593188
$595$	−2.34993e15	+	1.83659e14i	−1.29185	+	0.100965i
$596$	2.71426e13			0.0147842
$597$		−	7.00398e13i		−	0.0377995i
$598$	−1.65313e15	−	1.65313e15i	−0.883997	−	0.883997i
$599$	−9.73731e14			−0.515931			−0.257965	−	0.966154i	$-0.583052\pi$
$599$	−9.73731e14			−0.515931			−0.257965	+	0.966154i	$0.583052\pi$
$600$	4.40346e12	+	4.40346e12i	0.00231186	+	0.00231186i
$601$	1.86105e14	−	1.86105e14i	0.0968162	−	0.0968162i	−0.657040	−	0.753856i	$-0.728192\pi$
$601$	1.86105e14	−	1.86105e14i	0.0968162	−	0.0968162i	0.753856	+	0.657040i	$0.228192\pi$
$602$	3.08570e15	−	3.08570e15i	1.59064	−	1.59064i
$603$		−	8.14584e14i		−	0.416093i
$604$			4.44557e13i			0.0225022i
$605$	−3.07269e14	+	3.07269e14i	−0.154122	+	0.154122i
$606$	6.23784e14	−	6.23784e14i	0.310052	−	0.310052i
$607$	−1.71551e15	−	1.71551e15i	−0.844999	−	0.844999i	0.144505	−	0.989504i	$-0.453841\pi$
$607$	−1.71551e15	−	1.71551e15i	−0.844999	−	0.844999i	−0.989504	+	0.144505i	$0.953841\pi$
$608$	3.65822e15			1.78566
$609$	5.06370e14	+	5.06370e14i	0.244947	+	0.244947i
$610$			1.28256e15i			0.614843i
$611$	−6.96178e12			−0.00330745
$612$	−1.48487e14	−	1.89990e15i	−0.0699127	−	0.894535i
$613$	−1.11345e14			−0.0519563			−0.0259781	−	0.999663i	$-0.508270\pi$
$613$	−1.11345e14			−0.0519563			−0.0259781	+	0.999663i	$0.508270\pi$
$614$			4.08724e15i			1.89019i
$615$	6.17762e14	+	6.17762e14i	0.283144	+	0.283144i
$616$	1.48793e14			0.0675908
$617$	−2.20765e15	−	2.20765e15i	−0.993945	−	0.993945i	0.00603688	−	0.999982i	$-0.498078\pi$
$617$	−2.20765e15	−	2.20765e15i	−0.993945	−	0.993945i	−0.999982	+	0.00603688i	$0.998078\pi$
$618$	−7.77521e14	+	7.77521e14i	−0.346957	+	0.346957i
$619$	2.24222e15	−	2.24222e15i	0.991698	−	0.991698i	−0.00826826	−	0.999966i	$-0.502632\pi$
$619$	2.24222e15	−	2.24222e15i	0.991698	−	0.991698i	0.999966	+	0.00826826i	$0.00263190\pi$
$620$			2.09290e15i			0.917474i
$621$		−	5.65273e14i		−	0.245615i
$622$	−1.07967e15	+	1.07967e15i	−0.464989	+	0.464989i
$623$	−1.33047e15	+	1.33047e15i	−0.567965	+	0.567965i
$624$	−7.35028e14	−	7.35028e14i	−0.311020	−	0.311020i
$625$	2.77833e15			1.16531
$626$	−3.22563e15	−	3.22563e15i	−1.34108	−	1.34108i
$627$			6.79253e14i			0.279937i
$628$	−1.89401e15			−0.773758
$629$	5.24048e14	+	4.48072e14i	0.212223	+	0.181455i
$630$	−4.24305e15			−1.70336
$631$			1.91335e15i			0.761433i	0.924692	+	0.380717i	$0.124323\pi$
$631$			1.91335e15i			0.761433i	−0.924692	+	0.380717i	$0.875677\pi$
$632$	−5.40587e12	−	5.40587e12i	−0.00213266	−	0.00213266i
$633$	−2.44288e14			−0.0955391
$634$	4.00241e15	+	4.00241e15i	1.55178	+	1.55178i
$635$	1.36009e15	−	1.36009e15i	0.522772	−	0.522772i
$636$	2.08825e14	−	2.08825e14i	0.0795734	−	0.0795734i
$637$		−	1.77590e15i		−	0.670892i
$638$			4.02237e15i			1.50650i
$639$	−8.07171e14	+	8.07171e14i	−0.299717	+	0.299717i
$640$	−2.70272e14	+	2.70272e14i	−0.0994974	+	0.0994974i
$641$	2.43403e15	+	2.43403e15i	0.888396	+	0.888396i	0.994369	−	0.105973i	$-0.0337957\pi$
$641$	2.43403e15	+	2.43403e15i	0.888396	+	0.888396i	−0.105973	+	0.994369i	$0.533796\pi$
$642$	9.01414e14			0.326198
$643$	8.44784e14	+	8.44784e14i	0.303099	+	0.303099i	0.842225	−	0.539126i	$-0.181245\pi$
$643$	8.44784e14	+	8.44784e14i	0.303099	+	0.303099i	−0.539126	+	0.842225i	$0.681245\pi$
$644$			1.63830e15i			0.582802i
$645$	−1.03963e15			−0.366692
$646$	5.10116e15	−	3.98683e14i	1.78398	−	0.139428i
$647$	−1.44940e14			−0.0502590			−0.0251295	−	0.999684i	$-0.508000\pi$
$647$	−1.44940e14			−0.0502590			−0.0251295	+	0.999684i	$0.508000\pi$
$648$			1.53621e14i			0.0528188i
$649$	−2.67848e15	−	2.67848e15i	−0.913150	−	0.913150i
$650$	1.49125e15			0.504113
$651$	−5.30956e14	−	5.30956e14i	−0.177977	−	0.177977i
$652$	−3.41680e15	+	3.41680e15i	−1.13568	+	1.13568i
$653$	−1.76074e15	+	1.76074e15i	−0.580326	+	0.580326i	−0.934993	−	0.354667i	$-0.884594\pi$
$653$	−1.76074e15	+	1.76074e15i	−0.580326	+	0.580326i	0.354667	+	0.934993i	$0.384594\pi$
$654$			3.93976e14i			0.128763i
$655$		−	1.65604e15i		−	0.536715i
$656$	−3.42410e15	+	3.42410e15i	−1.10046	+	1.10046i
$657$	3.08275e15	−	3.08275e15i	0.982493	−	0.982493i
$658$	7.06497e12	+	7.06497e12i	0.00223289	+	0.00223289i
$659$	2.80072e15			0.877809			0.438905	−	0.898534i	$-0.355367\pi$
$659$	2.80072e15			0.877809			0.438905	+	0.898534i	$0.355367\pi$
$660$	5.21974e14	+	5.21974e14i	0.162240	+	0.162240i
$661$			4.33193e15i			1.33528i	0.744483	+	0.667642i	$0.232696\pi$
$661$			4.33193e15i			1.33528i	−0.744483	+	0.667642i	$0.767304\pi$
$662$	−3.71367e15			−1.13523
$663$	−1.05654e15	−	9.03366e14i	−0.320305	−	0.273867i
$664$	3.82639e14			0.115044
$665$		−	5.56266e15i		−	1.65868i
$666$	8.77635e14	+	8.77635e14i	0.259541	+	0.259541i
$667$	2.12678e15			0.623778
$668$	3.11384e15	+	3.11384e15i	0.905788	+	0.905788i
$669$	4.20117e14	−	4.20117e14i	0.121207	−	0.121207i
$670$	1.68071e15	−	1.68071e15i	0.480928	−	0.480928i
$671$		−	1.26203e15i		−	0.358175i
$672$			1.42635e15i			0.401510i
$673$	2.83866e15	−	2.83866e15i	0.792558	−	0.792558i	−0.189352	−	0.981909i	$-0.560639\pi$
$673$	2.83866e15	−	2.83866e15i	0.792558	−	0.792558i	0.981909	+	0.189352i	$0.0606387\pi$
$674$	3.34165e15	−	3.34165e15i	0.925403	−	0.925403i
$675$	2.54960e14	+	2.54960e14i	0.0700328	+	0.0700328i
$676$	−6.92498e15			−1.88674
$677$	−1.72629e15	−	1.72629e15i	−0.466526	−	0.466526i	0.434261	−	0.900787i	$-0.357010\pi$
$677$	−1.72629e15	−	1.72629e15i	−0.466526	−	0.466526i	−0.900787	+	0.434261i	$0.857010\pi$
$678$			8.67786e14i			0.232621i
$679$	−4.51007e14			−0.119922
$680$	−1.73529e14	+	2.02953e14i	−0.0457692	+	0.0535299i
$681$	−2.56008e14			−0.0669799
$682$		−	4.21768e15i		−	1.09461i
$683$	2.73365e15	+	2.73365e15i	0.703767	+	0.703767i	0.965217	−	0.261450i	$-0.0842007\pi$
$683$	2.73365e15	+	2.73365e15i	0.703767	+	0.703767i	−0.261450	+	0.965217i	$0.584201\pi$
$684$	4.49737e15			1.14855
$685$	−3.46799e15	−	3.46799e15i	−0.878577	−	0.878577i
$686$	2.83300e15	−	2.83300e15i	0.711975	−	0.711975i
$687$	−1.04497e15	+	1.04497e15i	−0.260520	+	0.260520i
$688$		−	5.76242e15i		−	1.42518i
$689$			3.39600e15i			0.833225i
$690$	5.65227e14	−	5.65227e14i	0.137579	−	0.137579i
$691$	−2.68152e15	+	2.68152e15i	−0.647517	+	0.647517i	−0.952392	−	0.304875i	$-0.901385\pi$
$691$	−2.68152e15	+	2.68152e15i	−0.647517	+	0.647517i	0.304875	+	0.952392i	$0.401385\pi$
$692$	−2.96233e15	−	2.96233e15i	−0.709658	−	0.709658i
$693$	4.17512e15			0.992285
$694$	−1.07293e15	−	1.07293e15i	−0.252985	−	0.252985i
$695$		−	5.69649e15i		−	1.33257i
$696$	8.11256e13			0.0188281
$697$	−4.20830e15	+	4.92187e15i	−0.969006	+	1.13331i
$698$	3.38622e15			0.773590
$699$			1.45229e15i			0.329177i
$700$	−7.38937e14	−	7.38937e14i	−0.166176	−	0.166176i
$701$	−6.26372e15			−1.39760			−0.698800	−	0.715317i	$-0.746282\pi$
$701$	−6.26372e15			−1.39760			−0.698800	+	0.715317i	$0.746282\pi$
$702$	−3.65107e15	−	3.65107e15i	−0.808289	−	0.808289i
$703$	−1.15058e15	+	1.15058e15i	−0.252734	+	0.252734i
$704$	−2.63305e15	+	2.63305e15i	−0.573864	+	0.573864i
$705$		−	2.38033e12i		−	0.000514750i
$706$			4.11927e15i			0.883882i
$707$	5.02662e15	−	5.02662e15i	1.07021	−	1.07021i
$708$	1.12495e15	−	1.12495e15i	0.237658	−	0.237658i
$709$	4.29357e15	+	4.29357e15i	0.900046	+	0.900046i	0.995440	−	0.0953940i	$-0.0304111\pi$
$709$	4.29357e15	+	4.29357e15i	0.900046	+	0.900046i	−0.0953940	+	0.995440i	$0.530411\pi$
$710$	−3.33082e15			−0.692836
$711$	−1.51689e14	−	1.51689e14i	−0.0313091	−	0.0313091i
$712$			2.13155e14i			0.0436572i
$713$	−2.23004e15			−0.453232
$714$	1.55448e14	+	1.98896e15i	0.0313505	+	0.401131i
$715$	−8.48857e15			−1.69884
$716$		−	5.43532e15i		−	1.07945i
$717$	3.46993e14	+	3.46993e14i	0.0683858	+	0.0683858i
$718$	2.74988e15			0.537810
$719$	−6.93288e14	−	6.93288e14i	−0.134556	−	0.134556i	0.636621	−	0.771177i	$-0.280332\pi$
$719$	−6.93288e14	−	6.93288e14i	−0.134556	−	0.134556i	−0.771177	+	0.636621i	$0.780332\pi$
$720$	−3.96186e15	+	3.96186e15i	−0.763081	+	0.763081i
$721$	−6.26547e15	+	6.26547e15i	−1.19759	+	1.19759i
$722$			4.70581e15i			0.892647i
$723$		−	1.40941e15i		−	0.265325i
$724$	3.00220e15	−	3.00220e15i	0.560890	−	0.560890i
$725$	−9.59260e14	+	9.59260e14i	−0.177860	+	0.177860i
$726$	2.60070e14	+	2.60070e14i	0.0478564	+	0.0478564i
$727$	4.28650e15			0.782823			0.391411	−	0.920216i	$-0.371987\pi$
$727$	4.28650e15			0.782823			0.391411	+	0.920216i	$0.371987\pi$
$728$	−5.08141e14	−	5.08141e14i	−0.0921004	−	0.0921004i
$729$			3.66719e15i			0.659679i
$730$	1.27211e16			2.27117
$731$	−6.00435e14	−	7.68259e15i	−0.106395	−	1.36133i
$732$	5.30050e14			0.0932192
$733$		−	1.17298e15i		−	0.204747i	−0.994746	−	0.102374i	$-0.967356\pi$
$733$		−	1.17298e15i		−	0.204747i	0.994746	−	0.102374i	$-0.0326438\pi$
$734$	−3.81741e15	−	3.81741e15i	−0.661364	−	0.661364i
$735$	6.07205e14			0.104413
$736$	2.99538e15	+	2.99538e15i	0.511239	+	0.511239i
$737$	−1.65380e15	+	1.65380e15i	−0.280163	+	0.280163i
$738$	−8.24277e15	+	8.24277e15i	−1.38600	+	1.38600i
$739$			1.04404e16i			1.74250i	0.490843	+	0.871248i	$0.336689\pi$
$739$			1.04404e16i			1.74250i	−0.490843	+	0.871248i	$0.663311\pi$
$740$			1.76834e15i			0.292948i
$741$	2.31972e15	−	2.31972e15i	0.381447	−	0.381447i
$742$	3.44634e15	−	3.44634e15i	0.562518	−	0.562518i
$743$	−6.05787e15	−	6.05787e15i	−0.981480	−	0.981480i	0.0183519	−	0.999832i	$-0.494158\pi$
$743$	−6.05787e15	−	6.05787e15i	−0.981480	−	0.981480i	−0.999832	+	0.0183519i	$0.994158\pi$
$744$	−8.50646e13			−0.0136804
$745$	−7.54613e13	−	7.54613e13i	−0.0120466	−	0.0120466i
$746$		−	1.43660e16i		−	2.27653i
$747$	1.07369e16			1.68894
$748$	−3.55578e15	+	4.15870e15i	−0.555234	+	0.649381i
$749$	7.26383e15			1.12594
$750$		−	1.92982e15i		−	0.296947i
$751$	3.28929e15	+	3.28929e15i	0.502438	+	0.502438i	0.912195	−	0.409757i	$-0.134386\pi$
$751$	3.28929e15	+	3.28929e15i	0.502438	+	0.502438i	−0.409757	+	0.912195i	$0.634386\pi$
$752$	1.31936e13			0.00200062
$753$	1.38423e15	+	1.38423e15i	0.208371	+	0.208371i
$754$	1.37368e16	−	1.37368e16i	2.05278	−	2.05278i
$755$	1.23594e14	−	1.23594e14i	0.0183354	−	0.0183354i
$756$			3.61832e15i			0.532889i
$757$			7.02369e14i			0.102692i	0.998681	+	0.0513462i	$0.0163512\pi$
$757$			7.02369e14i			0.102692i	−0.998681	+	0.0513462i	$0.983649\pi$
$758$	−1.13541e16	+	1.13541e16i	−1.64805	+	1.64805i
$759$	−5.56178e14	+	5.56178e14i	−0.0801464	+	0.0801464i
$760$	−4.45598e14	−	4.45598e14i	−0.0637482	−	0.0637482i
$761$	8.74564e15			1.24216			0.621078	−	0.783749i	$-0.286695\pi$
$761$	8.74564e15			1.24216			0.621078	+	0.783749i	$0.286695\pi$
$762$	−1.15117e15	−	1.15117e15i	−0.162326	−	0.162326i
$763$			3.17477e15i			0.444454i
$764$	1.20330e15			0.167248
$765$	−4.86922e15	+	5.69486e15i	−0.671927	+	0.785860i
$766$	−3.66694e15			−0.502395
$767$			1.82945e16i			2.48855i
$768$	1.38774e15	+	1.38774e15i	0.187422	+	0.187422i
$769$	2.99644e15			0.401801			0.200900	−	0.979612i	$-0.435613\pi$
$769$	2.99644e15			0.401801			0.200900	+	0.979612i	$0.435613\pi$
$770$	8.61439e15	+	8.61439e15i	1.14690	+	1.14690i
$771$	−8.44588e14	+	8.44588e14i	−0.111647	+	0.111647i
$772$	3.01423e15	−	3.01423e15i	0.395623	−	0.395623i
$773$		−	4.84063e15i		−	0.630833i	−0.948953	−	0.315417i	$-0.897856\pi$
$773$		−	4.84063e15i		−	0.630833i	0.948953	−	0.315417i	$-0.102144\pi$
$774$		−	1.38718e16i		−	1.79497i
$775$	1.00584e15	−	1.00584e15i	0.129231	−	0.129231i
$776$	−3.61280e13	+	3.61280e13i	−0.00460897	+	0.00460897i
$777$	−4.48617e14	−	4.48617e14i	−0.0568277	−	0.0568277i
$778$	−2.68584e15			−0.337826
$779$	−1.08063e16	−	1.08063e16i	−1.34965	−	1.34965i
$780$		−	3.56518e15i		−	0.442141i
$781$	3.27750e15			0.403610
$782$	4.50332e15	+	3.85043e15i	0.550675	+	0.470838i
$783$	4.69716e15			0.570356
$784$			3.36559e15i			0.405810i
$785$	5.26569e15	+	5.26569e15i	0.630481	+	0.630481i
$786$	−1.40166e15			−0.166655
$787$	−6.08262e15	−	6.08262e15i	−0.718174	−	0.718174i	0.250057	−	0.968231i	$-0.419551\pi$
$787$	−6.08262e15	−	6.08262e15i	−0.718174	−	0.718174i	−0.968231	+	0.250057i	$0.919551\pi$
$788$	−3.41426e15	+	3.41426e15i	−0.400315	+	0.400315i
$789$	2.17332e15	−	2.17332e15i	0.253047	−	0.253047i
$790$		−	6.25949e14i		−	0.0723752i
$791$			6.99285e15i			0.802941i
$792$	3.34448e14	−	3.34448e14i	0.0381365	−	0.0381365i
$793$	−4.30995e15	+	4.30995e15i	−0.488056	+	0.488056i
$794$	−1.00053e16	−	1.00053e16i	−1.12517	−	1.12517i
$795$	−1.16114e15			−0.129678
$796$	9.41496e14	+	9.41496e14i	0.104423	+	0.104423i
$797$		−	8.18719e15i		−	0.901808i	−0.892572	−	0.450904i	$-0.851102\pi$
$797$		−	8.18719e15i		−	0.901808i	0.892572	−	0.450904i	$-0.148898\pi$
$798$	−4.70820e15			−0.515038
$799$	1.75899e13	−	1.37475e12i	0.00191098	−	0.000149354i
$800$	−2.70207e15			−0.291542
$801$			5.98113e15i			0.640921i
$802$	−2.52733e15	−	2.52733e15i	−0.268969	−	0.268969i
$803$	−1.25174e16			−1.32306
$804$	−6.94592e14	−	6.94592e14i	−0.0729158	−	0.0729158i
$805$	4.55475e15	−	4.55475e15i	0.474884	−	0.474884i
$806$	−1.44038e16	+	1.44038e16i	−1.49153	+	1.49153i
$807$			4.20100e15i			0.432064i
$808$		−	8.05315e14i		−	0.0822628i
$809$	3.35059e15	−	3.35059e15i	0.339941	−	0.339941i	−0.516404	−	0.856345i	$-0.672730\pi$
$809$	3.35059e15	−	3.35059e15i	0.339941	−	0.339941i	0.856345	+	0.516404i	$0.172730\pi$
$810$	−8.89395e15	+	8.89395e15i	−0.896245	+	0.896245i
$811$	−1.18183e16	−	1.18183e16i	−1.18288	−	1.18288i	−0.978995	−	0.203887i	$-0.934643\pi$
$811$	−1.18183e16	−	1.18183e16i	−1.18288	−	1.18288i	−0.203887	−	0.978995i	$-0.565357\pi$
$812$	−1.36135e16			−1.35336
$813$	−2.16225e15	−	2.16225e15i	−0.213505	−	0.213505i
$814$		−	3.56361e15i		−	0.349507i
$815$	1.89986e16			1.85078
$816$	2.00230e15	+	1.71201e15i	0.193746	+	0.165657i
$817$	1.81860e16			1.74789
$818$		−	1.78643e16i		−	1.70547i
$819$	−1.42584e16	−	1.42584e16i	−1.35210	−	1.35210i
$820$	−1.66083e16			−1.56440
$821$	9.99926e15	+	9.99926e15i	0.935579	+	0.935579i	0.998047	−	0.0624676i	$-0.0198970\pi$
$821$	9.99926e15	+	9.99926e15i	0.935579	+	0.935579i	−0.0624676	+	0.998047i	$0.519897\pi$
$822$	−2.93528e15	+	2.93528e15i	−0.272807	+	0.272807i
$823$	1.24228e16	−	1.24228e16i	1.14689	−	1.14689i	0.159729	−	0.987161i	$-0.448938\pi$
$823$	1.24228e16	−	1.24228e16i	1.14689	−	1.14689i	0.987161	−	0.159729i	$-0.0510621\pi$
$824$			1.00379e15i			0.0920543i
$825$		−	5.01716e14i		−	0.0457048i
$826$	1.85657e16	−	1.85657e16i	1.68004	−	1.68004i
$827$	−6.61458e15	+	6.61458e15i	−0.594596	+	0.594596i	−0.938870	−	0.344273i	$-0.888125\pi$
$827$	−6.61458e15	+	6.61458e15i	−0.594596	+	0.594596i	0.344273	+	0.938870i	$0.388125\pi$
$828$	3.68248e15	+	3.68248e15i	0.328832	+	0.328832i
$829$	−8.59046e15			−0.762021			−0.381010	−	0.924571i	$-0.624424\pi$
$829$	−8.59046e15			−0.762021			−0.381010	+	0.924571i	$0.624424\pi$
$830$	2.21530e16	+	2.21530e16i	1.95211	+	1.95211i
$831$		−	3.30089e15i		−	0.288952i
$832$	1.79842e16			1.56391
$833$	3.50689e14	+	4.48707e15i	0.0302952	+	0.387629i
$834$	−4.82147e15			−0.413777
$835$		−	1.73141e16i		−	1.47612i
$836$	−9.13072e15	−	9.13072e15i	−0.773340	−	0.773340i
$837$	−4.92523e15			−0.414416
$838$	2.80129e15	+	2.80129e15i	0.234162	+	0.234162i
$839$	4.43746e15	−	4.43746e15i	0.368505	−	0.368505i	−0.498427	−	0.866932i	$-0.666089\pi$
$839$	4.43746e15	−	4.43746e15i	0.368505	−	0.368505i	0.866932	+	0.498427i	$0.166089\pi$
$840$	1.73740e14	−	1.73740e14i	0.0143339	−	0.0143339i
$841$			5.47207e15i			0.448512i
$842$			1.35132e16i			1.10038i
$843$	7.63685e14	−	7.63685e14i	0.0617821	−	0.0617821i
$844$	3.28378e15	−	3.28378e15i	0.263931	−	0.263931i
$845$	1.92526e16	+	1.92526e16i	1.53737	+	1.53737i
$846$	3.17606e13			0.00251971
$847$	2.09572e15	+	2.09572e15i	0.165186	+	0.165186i
$848$		−	6.43590e15i		−	0.504002i
$849$	9.73165e14			0.0757171
$850$	−3.76787e15	+	2.94479e14i	−0.291267	+	0.0227641i
$851$	−1.88422e15			−0.144716
$852$			1.37654e15i			0.105044i
$853$	−6.94188e15	−	6.94188e15i	−0.526329	−	0.526329i	0.393146	−	0.919476i	$-0.371387\pi$
$853$	−6.94188e15	−	6.94188e15i	−0.526329	−	0.526329i	−0.919476	+	0.393146i	$0.871387\pi$
$854$	8.74767e15			0.658983
$855$	−1.25035e16	−	1.25035e16i	−0.935873	−	0.935873i
$856$	5.81870e14	−	5.81870e14i	0.0432733	−	0.0432733i
$857$	−6.95452e15	+	6.95452e15i	−0.513893	+	0.513893i	−0.915717	−	0.401824i	$-0.868376\pi$
$857$	−6.95452e15	+	6.95452e15i	−0.513893	+	0.513893i	0.401824	+	0.915717i	$0.368376\pi$
$858$			7.18467e15i			0.527505i
$859$			2.83271e15i			0.206652i	0.994648	+	0.103326i	$0.0329485\pi$
$859$			2.83271e15i			0.206652i	−0.994648	+	0.103326i	$0.967051\pi$
$860$	1.39750e16	−	1.39750e16i	1.01300	−	1.01300i
$861$	4.21342e15	−	4.21342e15i	0.303471	−	0.303471i
$862$	−6.78826e15	−	6.78826e15i	−0.485812	−	0.485812i
$863$	−1.36976e16			−0.974056			−0.487028	−	0.873386i	$-0.661919\pi$
$863$	−1.36976e16			−0.974056			−0.487028	+	0.873386i	$0.661919\pi$
$864$	6.61554e15	+	6.61554e15i	0.467455	+	0.467455i
$865$			1.64716e16i			1.15650i
$866$	−2.75309e16			−1.92075
$867$	2.84790e15	+	2.07385e15i	0.197433	+	0.143771i
$868$	1.42745e16			0.983339
$869$			6.15928e14i			0.0421620i
$870$	4.69679e15	+	4.69679e15i	0.319481	+	0.319481i
$871$	1.12958e16			0.763512
$872$	2.54315e14	+	2.54315e14i	0.0170817	+	0.0170817i
$873$	−1.01375e15	+	1.01375e15i	−0.0676633	+	0.0676633i
$874$	−9.88734e15	+	9.88734e15i	−0.655793	+	0.655793i
$875$		−	1.55510e16i		−	1.02498i
$876$		−	5.25730e15i		−	0.344342i
$877$	−1.27050e16	+	1.27050e16i	−0.826944	+	0.826944i	−0.987093	−	0.160149i	$-0.948802\pi$
$877$	−1.27050e16	+	1.27050e16i	−0.826944	+	0.826944i	0.160149	+	0.987093i	$0.448802\pi$
$878$	−2.00221e16	+	2.00221e16i	−1.29506	+	1.29506i
$879$	−2.76439e14	−	2.76439e14i	−0.0177689	−	0.0177689i
$880$	1.60870e16			1.02759
$881$	9.14601e15	+	9.14601e15i	0.580583	+	0.580583i	0.935063	−	0.354480i	$-0.115342\pi$
$881$	9.14601e15	+	9.14601e15i	0.580583	+	0.580583i	−0.354480	+	0.935063i	$0.615342\pi$
$882$			8.10190e15i			0.511105i
$883$	−1.45304e16			−0.910949			−0.455474	−	0.890249i	$-0.650530\pi$
$883$	−1.45304e16			−0.910949			−0.455474	+	0.890249i	$0.650530\pi$
$884$	2.63457e16	−	2.05906e15i	1.64143	−	0.128286i
$885$	−6.25513e15			−0.387301
$886$			2.08598e16i			1.28358i
$887$	7.91913e15	+	7.91913e15i	0.484281	+	0.484281i	0.906496	−	0.422215i	$-0.138747\pi$
$887$	7.91913e15	+	7.91913e15i	0.484281	+	0.484281i	−0.422215	+	0.906496i	$0.638747\pi$
$888$	−7.18730e13			−0.00436812
$889$	−9.27645e15	−	9.27645e15i	−0.560302	−	0.560302i
$890$	−1.23407e16	+	1.23407e16i	−0.740788	+	0.740788i
$891$	8.75156e15	−	8.75156e15i	0.522105	−	0.522105i
$892$			1.12947e16i			0.669679i
$893$			4.16383e13i			0.00245363i
$894$	−6.38699e13	+	6.38699e13i	−0.00374059	+	0.00374059i
$895$	−1.51111e16	+	1.51111e16i	−0.879570	+	0.879570i
$896$	1.84338e15	+	1.84338e15i	0.106640	+	0.106640i
$897$	3.79880e15			0.218418
$898$	1.79062e16	+	1.79062e16i	1.02326	+	1.02326i
$899$		−	1.85307e16i		−	1.05248i
$900$	−3.32189e15			−0.187522
$901$	−6.70611e14	−	8.58049e15i	−0.0376257	−	0.481422i
$902$	3.34695e16			1.86644
$903$			7.09077e15i			0.393017i
$904$	5.60163e14	+	5.60163e14i	0.0308594	+	0.0308594i
$905$	−1.66933e16			−0.914060
$906$	−1.04610e14	−	1.04610e14i	−0.00569333	−	0.00569333i
$907$	−1.56364e16	+	1.56364e16i	−0.845855	+	0.845855i	−0.989613	−	0.143758i	$-0.954081\pi$
$907$	−1.56364e16	+	1.56364e16i	−0.845855	+	0.845855i	0.143758	+	0.989613i	$0.454081\pi$
$908$	3.44133e15	−	3.44133e15i	0.185035	−	0.185035i
$909$		−	2.25971e16i		−	1.20768i
$910$		−	5.88380e16i		−	3.12557i
$911$	−2.94806e15	+	2.94806e15i	−0.155663	+	0.155663i	−0.780642	−	0.624979i	$-0.785108\pi$
$911$	−2.94806e15	+	2.94806e15i	−0.155663	+	0.155663i	0.624979	+	0.780642i	$0.285108\pi$
$912$	−4.39619e15	+	4.39619e15i	−0.230730	+	0.230730i
$913$	−2.17984e16	−	2.17984e16i	−1.13719	−	1.13719i
$914$	2.79173e16			1.44767
$915$	−1.47363e15	−	1.47363e15i	−0.0759578	−	0.0759578i
$916$		−	2.80935e16i		−	1.43940i
$917$	−1.12950e16			−0.575246
$918$	9.94594e15	+	8.50398e15i	0.503514	+	0.430514i
$919$	1.66374e16			0.837243			0.418621	−	0.908161i	$-0.362513\pi$
$919$	1.66374e16			0.837243			0.418621	+	0.908161i	$0.362513\pi$
$920$		−	7.29718e14i		−	0.0365024i
$921$	−4.69613e15	−	4.69613e15i	−0.233514	−	0.233514i
$922$	7.73668e15			0.382415
$923$	−1.11930e16	−	1.11930e16i	−0.549966	−	0.549966i
$924$	3.56010e15	−	3.56010e15i	0.173887	−	0.173887i
$925$	8.49855e14	−	8.49855e14i	0.0412634	−	0.0412634i
$926$		−	1.12650e16i		−	0.543714i
$927$			2.81664e16i			1.35143i
$928$	−2.48903e16	+	2.48903e16i	−1.18718	+	1.18718i
$929$	2.21306e16	−	2.21306e16i	1.04932	−	1.04932i	0.0505995	−	0.998719i	$-0.483887\pi$
$929$	2.21306e16	−	2.21306e16i	1.04932	−	1.04932i	0.998719	−	0.0505995i	$-0.0161132\pi$
$930$	−4.92484e15	−	4.92484e15i	−0.232132	−	0.232132i
$931$	−1.06216e16			−0.497701
$932$	−1.95221e16	−	1.95221e16i	−0.909367	−	0.909367i
$933$		−	2.48101e15i		−	0.114889i
$934$	−2.01364e15			−0.0926988
$935$	2.14476e16	−	1.67624e15i	0.981555	−	0.0767137i
$936$	−2.28435e15			−0.103931
$937$			5.37141e15i			0.242952i	0.992594	+	0.121476i	$0.0387627\pi$
$937$			5.37141e15i			0.242952i	−0.992594	+	0.121476i	$0.961237\pi$
$938$	−1.14632e16	−	1.14632e16i	−0.515454	−	0.515454i
$939$	7.41233e15			0.331355
$940$	3.19970e13	+	3.19970e13i	0.00142202	+	0.00142202i
$941$	1.01732e15	−	1.01732e15i	0.0449483	−	0.0449483i	−0.684275	−	0.729224i	$-0.739881\pi$
$941$	1.01732e15	−	1.01732e15i	0.0449483	−	0.0449483i	0.729224	+	0.684275i	$0.239881\pi$
$942$	4.45684e15	−	4.45684e15i	0.195770	−	0.195770i
$943$		−	1.76966e16i		−	0.772815i
$944$		−	3.46707e16i		−	1.50528i
$945$	1.00595e16	−	1.00595e16i	0.434214	−	0.434214i
$946$	−2.81629e16	+	2.81629e16i	−1.20858	+	1.20858i
$947$	2.82844e16	+	2.82844e16i	1.20676	+	1.20676i	0.972069	+	0.234694i	$0.0754089\pi$
$947$	2.82844e16	+	2.82844e16i	1.20676	+	1.20676i	0.234694	+	0.972069i	$0.424591\pi$
$948$	−2.58688e14			−0.0109731
$949$	4.27482e16	+	4.27482e16i	1.80283	+	1.80283i
$950$		−	8.91916e15i		−	0.373976i
$951$	−9.19732e15			−0.383414
$952$	1.38423e15	+	1.18355e15i	0.0573728	+	0.0490549i
$953$	−8.58955e15			−0.353964			−0.176982	−	0.984214i	$-0.556633\pi$
$953$	−8.58955e15			−0.353964			−0.176982	+	0.984214i	$0.556633\pi$
$954$		−	1.54930e16i		−	0.634775i
$955$	−3.34539e15	−	3.34539e15i	−0.136279	−	0.136279i
$956$	−9.32877e15			−0.377838
$957$	−4.62159e15	−	4.62159e15i	−0.186113	−	0.186113i
$958$	−1.82552e16	+	1.82552e16i	−0.730932	+	0.730932i
$959$	−2.36533e16	+	2.36533e16i	−0.941650	+	0.941650i
$960$			6.14904e15i			0.243397i
$961$		−	5.97805e15i		−	0.235278i
$962$	−1.21701e16	+	1.21701e16i	−0.476245	+	0.476245i
$963$	1.63273e16	−	1.63273e16i	0.635285	−	0.635285i
$964$	1.89458e16	+	1.89458e16i	0.732973	+	0.732973i
$965$	−1.67602e16			−0.644730
$966$	−3.85511e15	−	3.85511e15i	−0.147456	−	0.147456i
$967$		−	2.85688e16i		−	1.08654i	−0.839558	−	0.543270i	$-0.817186\pi$
$967$		−	2.85688e16i		−	1.08654i	0.839558	−	0.543270i	$-0.182814\pi$
$968$	3.35755e14			0.0126972
$969$	−5.40302e15	+	6.31917e15i	−0.203168	+	0.237618i
$970$	−4.18328e15			−0.156413
$971$			4.26067e16i			1.58406i	0.610480	+	0.792032i	$0.290977\pi$
$971$			4.26067e16i			1.58406i	−0.610480	+	0.792032i	$0.709023\pi$
$972$	1.23246e16	+	1.23246e16i	0.455626	+	0.455626i
$973$	−3.88527e16			−1.42824
$974$	−3.61113e16	−	3.61113e16i	−1.31999	−	1.31999i
$975$	−1.71341e15	+	1.71341e15i	−0.0622781	+	0.0622781i
$976$	8.16796e15	−	8.16796e15i	0.295216	−	0.295216i
$977$		−	4.62781e16i		−	1.66324i	−0.555343	−	0.831621i	$-0.687413\pi$
$977$		−	4.62781e16i		−	1.66324i	0.555343	−	0.831621i	$-0.312587\pi$
$978$		−	1.60803e16i		−	0.574685i
$979$	1.21431e16	−	1.21431e16i	0.431544	−	0.431544i
$980$	−8.16222e15	+	8.16222e15i	−0.288446	+	0.288446i
$981$	7.13608e15	+	7.13608e15i	0.250773	+	0.250773i
$982$	−4.08639e16			−1.42799
$983$	1.29847e16	+	1.29847e16i	0.451218	+	0.451218i	0.895759	−	0.444541i	$-0.146633\pi$
$983$	1.29847e16	+	1.29847e16i	0.451218	+	0.451218i	−0.444541	+	0.895759i	$0.646633\pi$
$984$		−	6.75033e14i		−	0.0233266i
$985$	1.89845e16			0.652377
$986$	−3.19953e16	+	3.74206e16i	−1.09336	+	1.27875i
$987$	−1.62349e13			−0.000551704
$988$			6.23646e16i			2.10753i
$989$	1.48908e16	+	1.48908e16i	0.500425	+	0.500425i
$990$	3.87260e16			1.29422
$991$	6.43866e15	+	6.43866e15i	0.213988	+	0.213988i	0.805959	−	0.591971i	$-0.201650\pi$
$991$	6.43866e15	+	6.43866e15i	0.213988	+	0.213988i	−0.591971	+	0.805959i	$0.701650\pi$
$992$	2.60988e16	−	2.60988e16i	0.862594	−	0.862594i
$993$	4.26690e15	−	4.26690e15i	0.140246	−	0.140246i
$994$			2.27178e16i			0.742575i
$995$		−	5.23504e15i		−	0.170174i
$996$	9.15526e15	−	9.15526e15i	0.295968	−	0.295968i
$997$	2.44294e15	−	2.44294e15i	0.0785398	−	0.0785398i	−0.666746	−	0.745285i	$-0.732313\pi$
$997$	2.44294e15	−	2.44294e15i	0.0785398	−	0.0785398i	0.745285	+	0.666746i	$0.232313\pi$
$998$	3.65863e16	+	3.65863e16i	1.16977	+	1.16977i
$999$	−4.16144e15			−0.132323

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.12.c.a.13.4	yes	32
17.4	even	4	inner	17.12.c.a.4.13	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.12.c.a.4.13	✓	32	17.4	even	4	inner
17.12.c.a.13.4	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)

\(f(q)\)	\(=\)	\(q-63.2626i q^{2} +(72.6870 + 72.6870i) q^{3} -1954.16 q^{4} +(5432.90 + 5432.90i) q^{5} +(4598.37 - 4598.37i) q^{6} +(37054.9 - 37054.9i) q^{7} -5936.57i q^{8} -166580. i q^{9} +O(q^{10})\)	\(q-63.2626i q^{2} +(72.6870 + 72.6870i) q^{3} -1954.16 q^{4} +(5432.90 + 5432.90i) q^{5} +(4598.37 - 4598.37i) q^{6} +(37054.9 - 37054.9i) q^{7} -5936.57i q^{8} -166580. i q^{9} +(343700. - 343700. i) q^{10} +(-338197. + 338197. i) q^{11} +(-142042. - 142042. i) q^{12} +2.30995e6 q^{13} +(-2.34419e6 - 2.34419e6i) q^{14} +789803. i q^{15} -4.37768e6 q^{16} +(-5.83642e6 + 456147. i) q^{17} -1.05383e7 q^{18} -1.38158e7i q^{19} +(-1.06168e7 - 1.06168e7i) q^{20} +5.38682e6 q^{21} +(2.13952e7 + 2.13952e7i) q^{22} +(1.13125e7 - 1.13125e7i) q^{23} +(431512. - 431512. i) q^{24} +1.02047e7i q^{25} -1.46134e8i q^{26} +(2.49845e7 - 2.49845e7i) q^{27} +(-7.24112e7 + 7.24112e7i) q^{28} +(9.40016e7 + 9.40016e7i) q^{29} +4.99650e7 q^{30} +(-9.85658e7 - 9.85658e7i) q^{31} +2.64786e8i q^{32} -4.91651e7 q^{33} +(2.88571e7 + 3.69227e8i) q^{34} +4.02631e8 q^{35} +3.25524e8i q^{36} +(-8.32805e7 - 8.32805e7i) q^{37} -8.74022e8 q^{38} +(1.67903e8 + 1.67903e8i) q^{39} +(3.22528e7 - 3.22528e7i) q^{40} +(7.82172e8 - 7.82172e8i) q^{41} -3.40784e8i q^{42} +1.31632e9i q^{43} +(6.60891e8 - 6.60891e8i) q^{44} +(9.05014e8 - 9.05014e8i) q^{45} +(-7.15656e8 - 7.15656e8i) q^{46} -3.01382e6 q^{47} +(-3.18201e8 - 3.18201e8i) q^{48} -7.68806e8i q^{49} +6.45578e8 q^{50} +(-4.57388e8 - 3.91076e8i) q^{51} -4.51401e9 q^{52} +1.47016e9i q^{53} +(-1.58059e9 - 1.58059e9i) q^{54} -3.67478e9 q^{55} +(-2.19979e8 - 2.19979e8i) q^{56} +(1.00423e9 - 1.00423e9i) q^{57} +(5.94679e9 - 5.94679e9i) q^{58} +7.91987e9i q^{59} -1.54340e9i q^{60} +(-1.86582e9 + 1.86582e9i) q^{61} +(-6.23553e9 + 6.23553e9i) q^{62} +(-6.17261e9 - 6.17261e9i) q^{63} +7.78554e9 q^{64} +(1.25497e10 + 1.25497e10i) q^{65} +3.11031e9i q^{66} +4.89004e9 q^{67} +(1.14053e10 - 8.91385e8i) q^{68} +1.64454e9 q^{69} -2.54715e10i q^{70} +(-4.84554e9 - 4.84554e9i) q^{71} -9.88916e8 q^{72} +(1.85061e10 + 1.85061e10i) q^{73} +(-5.26854e9 + 5.26854e9i) q^{74} +(-7.41751e8 + 7.41751e8i) q^{75} +2.69982e10i q^{76} +2.50637e10i q^{77} +(1.06220e10 - 1.06220e10i) q^{78} +(9.10604e8 - 9.10604e8i) q^{79} +(-2.37835e10 - 2.37835e10i) q^{80} -2.58771e10 q^{81} +(-4.94823e10 - 4.94823e10i) q^{82} +6.44546e10i q^{83} -1.05267e10 q^{84} +(-3.41869e10 - 2.92305e10i) q^{85} +8.32738e10 q^{86} +1.36654e10i q^{87} +(2.00773e9 + 2.00773e9i) q^{88} -3.59054e10 q^{89} +(-5.72536e10 - 5.72536e10i) q^{90} +(8.55950e10 - 8.55950e10i) q^{91} +(-2.21064e10 + 2.21064e10i) q^{92} -1.43289e10i q^{93} +1.90662e8i q^{94} +(7.50597e10 - 7.50597e10i) q^{95} +(-1.92465e10 + 1.92465e10i) q^{96} +(-6.08566e9 - 6.08566e9i) q^{97} -4.86367e10 q^{98} +(5.63369e10 + 5.63369e10i) 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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