LMFDB - Embedded newform 17.16.b.a.16.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,16,Mod(16,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("17.16");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	17.b (of order $2$, degree $1$, 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:	$24.2578958670$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			16.9
Character	$\chi$	$=$	17.16
Dual form			17.16.b.a.16.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-103.869 q^{2} +2983.33i q^{3} -21979.3 q^{4} +46006.2i q^{5} -309875. i q^{6} -1.62872e6i q^{7} +5.68653e6 q^{8} +5.44863e6 q^{9} +O(q^{10})$	\(q-103.869 q^{2} +2983.33i q^{3} -21979.3 q^{4} +46006.2i q^{5} -309875. i q^{6} -1.62872e6i q^{7} +5.68653e6 q^{8} +5.44863e6 q^{9} -4.77860e6i q^{10} -1.35916e6i q^{11} -6.55716e7i q^{12} +1.50953e8 q^{13} +1.69173e8i q^{14} -1.37252e8 q^{15} +1.29567e8 q^{16} +(-4.86244e7 - 1.69117e9i) q^{17} -5.65942e8 q^{18} -4.25135e9 q^{19} -1.01118e9i q^{20} +4.85903e9 q^{21} +1.41174e8i q^{22} +2.06255e10i q^{23} +1.69648e10i q^{24} +2.84010e10 q^{25} -1.56792e10 q^{26} +5.90626e10i q^{27} +3.57982e10i q^{28} +4.62927e10i q^{29} +1.42561e10 q^{30} +1.50996e11i q^{31} -1.99794e11 q^{32} +4.05482e9 q^{33} +(5.05055e9 + 1.75660e11i) q^{34} +7.49314e10 q^{35} -1.19757e11 q^{36} +5.41826e11i q^{37} +4.41582e11 q^{38} +4.50342e11i q^{39} +2.61615e11i q^{40} -8.28608e11i q^{41} -5.04700e11 q^{42} +1.26585e12 q^{43} +2.98734e10i q^{44} +2.50671e11i q^{45} -2.14234e12i q^{46} -2.50786e12 q^{47} +3.86541e11i q^{48} +2.09482e12 q^{49} -2.94997e12 q^{50} +(5.04533e12 - 1.45063e11i) q^{51} -3.31784e12 q^{52} -4.63505e12 q^{53} -6.13475e12i q^{54} +6.25297e10 q^{55} -9.26178e12i q^{56} -1.26832e13i q^{57} -4.80836e12i q^{58} +1.77228e13 q^{59} +3.01670e12 q^{60} -4.38647e12i q^{61} -1.56837e13i q^{62} -8.87432e12i q^{63} +1.65067e13 q^{64} +6.94476e12i q^{65} -4.21168e11 q^{66} -3.84782e13 q^{67} +(1.06873e12 + 3.71708e13i) q^{68} -6.15327e13 q^{69} -7.78302e12 q^{70} +6.45958e13i q^{71} +3.09838e13 q^{72} +1.84287e14i q^{73} -5.62787e13i q^{74} +8.47297e13i q^{75} +9.34418e13 q^{76} -2.21369e12 q^{77} -4.67764e13i q^{78} +6.09955e13i q^{79} +5.96087e12i q^{80} -9.80216e13 q^{81} +8.60664e13i q^{82} +2.68027e14 q^{83} -1.06798e14 q^{84} +(7.78043e13 - 2.23702e12i) q^{85} -1.31482e14 q^{86} -1.38107e14 q^{87} -7.72889e12i q^{88} +1.33880e14 q^{89} -2.60368e13i q^{90} -2.45860e14i q^{91} -4.53334e14i q^{92} -4.50471e14 q^{93} +2.60488e14 q^{94} -1.95588e14i q^{95} -5.96052e14i q^{96} -5.71138e14i q^{97} -2.17586e14 q^{98} -7.40555e12i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 258 q^{2} + 414386 q^{4} - 12648450 q^{8} - 78109330 q^{9}+O(q^{10}) $ 22 * q - 258 * q^2 + 414386 * q^4 - 12648450 * q^8 - 78109330 * q^9	$ 22 q - 258 q^{2} + 414386 q^{4} - 12648450 q^{8} - 78109330 q^{9} + 702506672 q^{13} - 1787378376 q^{15} + 3524081474 q^{16} - 2245058454 q^{17} + 6803778314 q^{18} + 9958891784 q^{19} - 4168893668 q^{21} - 238696683970 q^{25} - 33467295588 q^{26} - 62541989808 q^{30} - 43445086338 q^{32} + 213283309748 q^{33} + 521524562854 q^{34} - 467785613304 q^{35} - 2300588654186 q^{36} + 3162083165688 q^{38} - 3011205093968 q^{42} - 2215728209008 q^{43} - 7793870107128 q^{47} - 1555224751482 q^{49} + 30118817411766 q^{50} - 21451923375880 q^{51} + 51163160044372 q^{52} - 6062965973460 q^{53} - 11679154373592 q^{55} + 22772194849344 q^{59} - 86295684546192 q^{60} - 28567749560318 q^{64} + 251781147903680 q^{66} + 153875904272808 q^{67} - 48849686100870 q^{68} + 60664072036996 q^{69} - 150925771647648 q^{70} - 293782759569702 q^{72} - 388479948338264 q^{76} - 622427249887884 q^{77} + 983865215787034 q^{81} - 15\!\cdots\!44 q^{83}+ \cdots + 26\!\cdots\!90 q^{98}+O(q^{100}) $ 22 * q - 258 * q^2 + 414386 * q^4 - 12648450 * q^8 - 78109330 * q^9 + 702506672 * q^13 - 1787378376 * q^15 + 3524081474 * q^16 - 2245058454 * q^17 + 6803778314 * q^18 + 9958891784 * q^19 - 4168893668 * q^21 - 238696683970 * q^25 - 33467295588 * q^26 - 62541989808 * q^30 - 43445086338 * q^32 + 213283309748 * q^33 + 521524562854 * q^34 - 467785613304 * q^35 - 2300588654186 * q^36 + 3162083165688 * q^38 - 3011205093968 * q^42 - 2215728209008 * q^43 - 7793870107128 * q^47 - 1555224751482 * q^49 + 30118817411766 * q^50 - 21451923375880 * q^51 + 51163160044372 * q^52 - 6062965973460 * q^53 - 11679154373592 * q^55 + 22772194849344 * q^59 - 86295684546192 * q^60 - 28567749560318 * q^64 + 251781147903680 * q^66 + 153875904272808 * q^67 - 48849686100870 * q^68 + 60664072036996 * q^69 - 150925771647648 * q^70 - 293782759569702 * q^72 - 388479948338264 * q^76 - 622427249887884 * q^77 + 983865215787034 * q^81 - 1541046988482144 * q^83 + 1542636638603936 * q^84 + 94526232685248 * q^85 + 102594718370712 * q^86 - 428830075363560 * q^87 - 894061425316800 * q^89 + 2342465228549812 * q^93 + 2620489835637760 * q^94 + 2662999543720290 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$	−103.869			−0.573798			−0.286899	−	0.957961i	$-0.592624\pi$
$2$	−103.869			−0.573798			−0.286899	+	0.957961i	$0.592624\pi$
$3$			2983.33i			0.787576i	0.919201	+	0.393788i	$0.128836\pi$
$3$			2983.33i			0.787576i	−0.919201	+	0.393788i	$0.871164\pi$
$4$	−21979.3			−0.670756
$5$			46006.2i			0.263355i	0.991293	+	0.131677i	$0.0420363\pi$
$5$			46006.2i			0.263355i	−0.991293	+	0.131677i	$0.957964\pi$
$6$		−	309875.i		−	0.451910i
$7$		−	1.62872e6i		−	0.747502i	−0.927529	−	0.373751i	$-0.878072\pi$
$7$		−	1.62872e6i		−	0.747502i	0.927529	−	0.373751i	$-0.121928\pi$
$8$	5.68653e6			0.958677
$9$	5.44863e6			0.379725
$10$		−	4.77860e6i		−	0.151113i
$11$		−	1.35916e6i		−	0.0210293i	−0.999945	−	0.0105146i	$-0.996653\pi$
$11$		−	1.35916e6i		−	0.0210293i	0.999945	−	0.0105146i	$-0.00334698\pi$
$12$		−	6.55716e7i		−	0.528271i
$13$	1.50953e8			0.667215			0.333608	−	0.942712i	$-0.391734\pi$
$13$	1.50953e8			0.667215			0.333608	+	0.942712i	$0.391734\pi$
$14$			1.69173e8i			0.428915i
$15$	−1.37252e8			−0.207412
$16$	1.29567e8			0.120668
$17$	−4.86244e7	−	1.69117e9i	−0.0287400	−	0.999587i
$17$	−4.86244e7	−	1.69117e9i	−0.0287400	−	0.999587i
$18$	−5.65942e8			−0.217885
$19$	−4.25135e9			−1.09113			−0.545563	−	0.838070i	$-0.683684\pi$
$19$	−4.25135e9			−1.09113			−0.545563	+	0.838070i	$0.683684\pi$
$20$		−	1.01118e9i		−	0.176647i
$21$	4.85903e9			0.588714
$22$			1.41174e8i			0.0120666i
$23$			2.06255e10i			1.26312i	0.775326	+	0.631562i	$0.217586\pi$
$23$			2.06255e10i			1.26312i	−0.775326	+	0.631562i	$0.782414\pi$
$24$			1.69648e10i			0.755030i
$25$	2.84010e10			0.930644
$26$	−1.56792e10			−0.382847
$27$			5.90626e10i			1.08664i
$28$			3.57982e10i			0.501391i
$29$			4.62927e10i			0.498342i	0.968460	+	0.249171i	$0.0801581\pi$
$29$			4.62927e10i			0.498342i	−0.968460	+	0.249171i	$0.919842\pi$
$30$	1.42561e10			0.119013
$31$			1.50996e11i			0.985718i	0.870109	+	0.492859i	$0.164048\pi$
$31$			1.50996e11i			0.985718i	−0.870109	+	0.492859i	$0.835952\pi$
$32$	−1.99794e11			−1.02792
$33$	4.05482e9			0.0165622
$34$	5.05055e9	+	1.75660e11i	0.0164910	+	0.573561i
$35$	7.49314e10			0.196858
$36$	−1.19757e11			−0.254702
$37$			5.41826e11i			0.938311i	0.883116	+	0.469155i	$0.155442\pi$
$37$			5.41826e11i			0.938311i	−0.883116	+	0.469155i	$0.844558\pi$
$38$	4.41582e11			0.626086
$39$			4.50342e11i			0.525482i
$40$			2.61615e11i			0.252472i
$41$		−	8.28608e11i		−	0.664462i	−0.943198	−	0.332231i	$-0.892199\pi$
$41$		−	8.28608e11i		−	0.664462i	0.943198	−	0.332231i	$-0.107801\pi$
$42$	−5.04700e11			−0.337803
$43$	1.26585e12			0.710181			0.355091	−	0.934832i	$-0.384450\pi$
$43$	1.26585e12			0.710181			0.355091	+	0.934832i	$0.384450\pi$
$44$			2.98734e10i			0.0141055i
$45$			2.50671e11i			0.100002i
$46$		−	2.14234e12i		−	0.724778i
$47$	−2.50786e12			−0.722054			−0.361027	−	0.932555i	$-0.617574\pi$
$47$	−2.50786e12			−0.722054			−0.361027	+	0.932555i	$0.617574\pi$
$48$			3.86541e11i			0.0950355i
$49$	2.09482e12			0.441241
$50$	−2.94997e12			−0.534002
$51$	5.04533e12	−	1.45063e11i	0.787250	−	0.0226350i
$52$	−3.31784e12			−0.447538
$53$	−4.63505e12			−0.541982			−0.270991	−	0.962582i	$-0.587351\pi$
$53$	−4.63505e12			−0.541982			−0.270991	+	0.962582i	$0.587351\pi$
$54$		−	6.13475e12i		−	0.623511i
$55$	6.25297e10			0.00553817
$56$		−	9.26178e12i		−	0.716612i
$57$		−	1.26832e13i		−	0.859345i
$58$		−	4.80836e12i		−	0.285948i
$59$	1.77228e13			0.927134			0.463567	−	0.886062i	$-0.346569\pi$
$59$	1.77228e13			0.927134			0.463567	+	0.886062i	$0.346569\pi$
$60$	3.01670e12			0.139123
$61$		−	4.38647e12i		−	0.178707i	−0.996000	−	0.0893535i	$-0.971520\pi$
$61$		−	4.38647e12i		−	0.178707i	0.996000	−	0.0893535i	$-0.0284801\pi$
$62$		−	1.56837e13i		−	0.565603i
$63$		−	8.87432e12i		−	0.283845i
$64$	1.65067e13			0.469148
$65$			6.94476e12i			0.175714i
$66$	−4.21168e11			−0.00950334
$67$	−3.84782e13			−0.775627			−0.387814	−	0.921738i	$-0.626770\pi$
$67$	−3.84782e13			−0.775627			−0.387814	+	0.921738i	$0.626770\pi$
$68$	1.06873e12	+	3.71708e13i	0.0192775	+	0.670478i
$69$	−6.15327e13			−0.994805
$70$	−7.78302e12			−0.112957
$71$			6.45958e13i			0.842882i	0.906856	+	0.421441i	$0.138476\pi$
$71$			6.45958e13i			0.842882i	−0.906856	+	0.421441i	$0.861524\pi$
$72$	3.09838e13			0.364033
$73$			1.84287e14i			1.95242i	0.216824	+	0.976211i	$0.430430\pi$
$73$			1.84287e14i			1.95242i	−0.216824	+	0.976211i	$0.569570\pi$
$74$		−	5.62787e13i		−	0.538401i
$75$			8.47297e13i			0.732953i
$76$	9.34418e13			0.731879
$77$	−2.21369e12			−0.0157194
$78$		−	4.67764e13i		−	0.301521i
$79$			6.09955e13i			0.357350i	0.983908	+	0.178675i	$0.0571811\pi$
$79$			6.09955e13i			0.357350i	−0.983908	+	0.178675i	$0.942819\pi$
$80$			5.96087e12i			0.0317786i
$81$	−9.80216e13			−0.476085
$82$			8.60664e13i			0.381267i
$83$	2.68027e14			1.08416			0.542080	−	0.840327i	$-0.317637\pi$
$83$	2.68027e14			1.08416			0.542080	+	0.840327i	$0.317637\pi$
$84$	−1.06798e14			−0.394883
$85$	7.78043e13	−	2.23702e12i	0.263246	−	0.00756882i
$86$	−1.31482e14			−0.407501
$87$	−1.38107e14			−0.392482
$88$		−	7.72889e12i		−	0.0201603i
$89$	1.33880e14			0.320841			0.160421	−	0.987049i	$-0.448715\pi$
$89$	1.33880e14			0.320841			0.160421	+	0.987049i	$0.448715\pi$
$90$		−	2.60368e13i		−	0.0573811i
$91$		−	2.45860e14i		−	0.498744i
$92$		−	4.53334e14i		−	0.847247i
$93$	−4.50471e14			−0.776328
$94$	2.60488e14			0.414314
$95$		−	1.95588e14i		−	0.287353i
$96$		−	5.96052e14i		−	0.809562i
$97$		−	5.71138e14i		−	0.717717i	−0.933392	−	0.358858i	$-0.883166\pi$
$97$		−	5.71138e14i		−	0.717717i	0.933392	−	0.358858i	$-0.116834\pi$
$98$	−2.17586e14			−0.253183
$99$		−	7.40555e12i		−	0.00798534i
$100$	−6.24235e14			−0.624235
$101$	3.42221e14			0.317612			0.158806	−	0.987310i	$-0.449236\pi$
$101$	3.42221e14			0.317612			0.158806	+	0.987310i	$0.449236\pi$
$102$	−5.24051e14	+	1.50675e13i	−0.451723	+	0.0129879i
$103$	1.45063e15			1.16219			0.581095	−	0.813836i	$-0.302624\pi$
$103$	1.45063e15			1.16219			0.581095	+	0.813836i	$0.302624\pi$
$104$	8.58397e14			0.639644
$105$			2.23545e14i			0.155041i
$106$	4.81436e14			0.310988
$107$			1.27536e15i			0.767812i	0.923372	+	0.383906i	$0.125421\pi$
$107$			1.27536e15i			0.767812i	−0.923372	+	0.383906i	$0.874579\pi$
$108$		−	1.29816e15i		−	0.728868i
$109$		−	1.00832e15i		−	0.528323i	−0.964478	−	0.264162i	$-0.914905\pi$
$109$		−	1.00832e15i		−	0.528323i	0.964478	−	0.264162i	$-0.0850953\pi$
$110$	−6.49487e12			−0.00317779
$111$	−1.61645e15			−0.738991
$112$		−	2.11029e14i		−	0.0901999i
$113$			3.89599e15i			1.55786i	0.627109	+	0.778931i	$0.284238\pi$
$113$			3.89599e15i			1.55786i	−0.627109	+	0.778931i	$0.715762\pi$
$114$			1.31739e15i			0.493090i
$115$	−9.48901e14			−0.332650
$116$		−	1.01748e15i		−	0.334266i
$117$	8.22486e14			0.253358
$118$	−1.84084e15			−0.531988
$119$	−2.75445e15	+	7.91957e13i	−0.747193	+	0.0214832i
$120$	−7.80486e14			−0.198841
$121$	4.17540e15			0.999558
$122$			4.55617e14i			0.102542i
$123$	2.47201e15			0.523314
$124$		−	3.31879e15i		−	0.661176i
$125$			2.71062e15i			0.508444i
$126$			9.21763e14i			0.162870i
$127$	−5.32510e15			−0.886747			−0.443374	−	0.896337i	$-0.646218\pi$
$127$	−5.32510e15			−0.886747			−0.443374	+	0.896337i	$0.646218\pi$
$128$	4.83232e15			0.758720
$129$			3.77645e15i			0.559321i
$130$		−	7.21342e14i		−	0.100825i
$131$			1.07235e16i			1.41514i	0.706641	+	0.707572i	$0.250210\pi$
$131$			1.07235e16i			1.41514i	−0.706641	+	0.707572i	$0.749790\pi$
$132$	−8.91222e13			−0.0111092
$133$			6.92428e15i			0.815619i
$134$	3.99667e15			0.445054
$135$	−2.71725e15			−0.286171
$136$	−2.76504e14	−	9.61689e15i	−0.0275524	−	0.958281i
$137$	−3.10047e15			−0.292430			−0.146215	−	0.989253i	$-0.546709\pi$
$137$	−3.10047e15			−0.292430			−0.146215	+	0.989253i	$0.546709\pi$
$138$	6.39132e15			0.570818
$139$			4.23105e15i			0.357962i	0.983852	+	0.178981i	$0.0572801\pi$
$139$			4.23105e15i			0.357962i	−0.983852	+	0.178981i	$0.942720\pi$
$140$	−1.64694e15			−0.132044
$141$		−	7.48179e15i		−	0.568672i
$142$		−	6.70948e15i		−	0.483644i
$143$		−	2.05169e14i		−	0.0140311i
$144$	7.05962e14			0.0458208
$145$	−2.12975e15			−0.131241
$146$		−	1.91416e16i		−	1.12030i
$147$			6.24954e15i			0.347511i
$148$		−	1.19090e16i		−	0.629377i
$149$	−6.07067e15			−0.305028			−0.152514	−	0.988301i	$-0.548737\pi$
$149$	−6.07067e15			−0.305028			−0.152514	+	0.988301i	$0.548737\pi$
$150$		−	8.80075e15i		−	0.420567i
$151$	−4.05067e15			−0.184162			−0.0920810	−	0.995752i	$-0.529352\pi$
$151$	−4.05067e15			−0.184162			−0.0920810	+	0.995752i	$0.529352\pi$
$152$	−2.41754e16			−1.04604
$153$	−2.64936e14	−	9.21457e15i	−0.0109133	−	0.379568i
$154$	2.29933e14			0.00901978
$155$	−6.94675e15			−0.259594
$156$		−	9.89821e15i		−	0.352470i
$157$	4.78109e16			1.62286			0.811428	−	0.584453i	$-0.198691\pi$
$157$	4.78109e16			1.62286			0.811428	+	0.584453i	$0.198691\pi$
$158$		−	6.33551e15i		−	0.205047i
$159$		−	1.38279e16i		−	0.426852i
$160$		−	9.19176e15i		−	0.270707i
$161$	3.35933e16			0.944187
$162$	1.01814e16			0.273177
$163$		−	1.56612e16i		−	0.401254i	−0.979668	−	0.200627i	$-0.935702\pi$
$163$		−	1.56612e16i		−	0.401254i	0.979668	−	0.200627i	$-0.0642979\pi$
$164$			1.82122e16i			0.445692i
$165$			1.86547e14i			0.00436172i
$166$	−2.78396e16			−0.622089
$167$			7.24968e16i			1.54862i	0.632806	+	0.774311i	$0.281903\pi$
$167$			7.24968e16i			1.54862i	−0.632806	+	0.774311i	$0.718097\pi$
$168$	2.76310e16			0.564386
$169$	−2.83992e16			−0.554824
$170$	−8.08142e15	+	2.32356e14i	−0.151050	+	0.00434298i
$171$	−2.31641e16			−0.414328
$172$	−2.78225e16			−0.476358
$173$			5.75828e16i			0.943946i	0.881613	+	0.471973i	$0.156458\pi$
$173$			5.75828e16i			0.943946i	−0.881613	+	0.471973i	$0.843542\pi$
$174$	1.43449e16			0.225206
$175$		−	4.62574e16i		−	0.695658i
$176$		−	1.76102e14i		−	0.00253757i
$177$			5.28730e16i			0.730188i
$178$	−1.39059e16			−0.184098
$179$	−3.25505e16			−0.413200			−0.206600	−	0.978426i	$-0.566240\pi$
$179$	−3.25505e16			−0.413200			−0.206600	+	0.978426i	$0.566240\pi$
$180$		−	5.50957e15i		−	0.0670771i
$181$			9.90706e16i			1.15706i	0.815662	+	0.578529i	$0.196373\pi$
$181$			9.90706e16i			1.15706i	−0.815662	+	0.578529i	$0.803627\pi$
$182$			2.55372e16i			0.286179i
$183$	1.30863e16			0.140745
$184$			1.17287e17i			1.21093i
$185$	−2.49273e16			−0.247109
$186$	4.67898e16			0.445455
$187$	−2.29857e15	+	6.60882e13i	−0.0210206	+	0.000604383i
$188$	5.51211e16			0.484322
$189$	9.61967e16			0.812263
$190$			2.03155e16i			0.164883i
$191$	−7.39248e16			−0.576820			−0.288410	−	0.957507i	$-0.593127\pi$
$191$	−7.39248e16			−0.576820			−0.288410	+	0.957507i	$0.593127\pi$
$192$			4.92449e16i			0.369490i
$193$		−	1.83227e17i		−	1.32223i	−0.750282	−	0.661117i	$-0.770082\pi$
$193$		−	1.83227e17i		−	1.32223i	0.750282	−	0.661117i	$-0.229918\pi$
$194$			5.93233e16i			0.411825i
$195$	−2.07185e16			−0.138388
$196$	−4.60427e16			−0.295965
$197$		−	2.65678e17i		−	1.64384i	−0.569604	−	0.821919i	$-0.692904\pi$
$197$		−	2.65678e17i		−	1.64384i	0.569604	−	0.821919i	$-0.307096\pi$
$198$			7.69204e14i			0.00458198i
$199$		−	1.74592e17i		−	1.00144i	−0.865609	−	0.500721i	$-0.833068\pi$
$199$		−	1.74592e17i		−	1.00144i	0.865609	−	0.500721i	$-0.166932\pi$
$200$	1.61503e17			0.892187
$201$		−	1.14793e17i		−	0.610865i
$202$	−3.55461e16			−0.182245
$203$	7.53980e16			0.372511
$204$	−1.10893e17	+	3.18838e15i	−0.528052	+	0.0151825i
$205$	3.81211e16			0.174989
$206$	−1.50675e17			−0.666863
$207$			1.12381e17i			0.479639i
$208$	1.95585e16			0.0805118
$209$			5.77826e15i			0.0229456i
$210$		−	2.32193e16i		−	0.0889621i
$211$		−	3.97495e17i		−	1.46965i	−0.678259	−	0.734823i	$-0.737265\pi$
$211$		−	3.97495e17i		−	1.46965i	0.678259	−	0.734823i	$-0.262735\pi$
$212$	1.01875e17			0.363538
$213$	−1.92711e17			−0.663833
$214$		−	1.32470e17i		−	0.440569i
$215$			5.82370e16i			0.187030i
$216$			3.35861e17i			1.04173i
$217$	2.45931e17			0.736826
$218$			1.04733e17i			0.303151i
$219$	−5.49790e17			−1.53768
$220$	−1.37436e15			−0.00371475
$221$	−7.33998e15	−	2.55287e17i	−0.0191758	−	0.666939i
$222$	1.67898e17			0.424032
$223$	7.25829e16			0.177234			0.0886171	−	0.996066i	$-0.471755\pi$
$223$	7.25829e16			0.177234			0.0886171	+	0.996066i	$0.471755\pi$
$224$			3.25409e17i			0.768369i
$225$	1.54747e17			0.353389
$226$		−	4.04671e17i		−	0.893899i
$227$			6.30600e16i			0.134760i	0.997727	+	0.0673799i	$0.0214639\pi$
$227$			6.30600e16i			0.134760i	−0.997727	+	0.0673799i	$0.978536\pi$
$228$			2.78768e17i			0.576410i
$229$	4.56053e17			0.912534			0.456267	−	0.889843i	$-0.349186\pi$
$229$	4.56053e17			0.912534			0.456267	+	0.889843i	$0.349186\pi$
$230$	9.85610e16			0.190874
$231$		−	6.60418e15i		−	0.0123802i
$232$			2.63245e17i			0.477749i
$233$			2.98704e17i			0.524894i	0.964946	+	0.262447i	$0.0845295\pi$
$233$			2.98704e17i			0.524894i	−0.964946	+	0.262447i	$0.915471\pi$
$234$	−8.54305e16			−0.145376
$235$		−	1.15377e17i		−	0.190156i
$236$	−3.89535e17			−0.621880
$237$	−1.81970e17			−0.281441
$238$	2.86101e17	−	8.22595e15i	0.428738	−	0.0123270i
$239$	3.63049e17			0.527206			0.263603	−	0.964631i	$-0.415089\pi$
$239$	3.63049e17			0.527206			0.263603	+	0.964631i	$0.415089\pi$
$240$	−1.77833e16			−0.0250281
$241$		−	3.82184e17i		−	0.521368i	−0.965424	−	0.260684i	$-0.916052\pi$
$241$		−	3.82184e17i		−	0.521368i	0.965424	−	0.260684i	$-0.0839481\pi$
$242$	−4.33693e17			−0.573545
$243$			5.55053e17i			0.711685i
$244$			9.64117e16i			0.119869i
$245$			9.63747e16i			0.116203i
$246$	−2.56765e17			−0.300277
$247$	−6.41753e17			−0.728016
$248$			8.58643e17i			0.944985i
$249$			7.99614e17i			0.853857i
$250$		−	2.81548e17i		−	0.291745i
$251$	7.80205e17			0.784613			0.392307	−	0.919835i	$-0.371677\pi$
$251$	7.80205e17			0.784613			0.392307	+	0.919835i	$0.371677\pi$
$252$			1.95051e17i			0.190390i
$253$	2.80333e16			0.0265626
$254$	5.53111e17			0.508814
$255$	6.67378e15	+	2.32116e17i	0.00596102	+	0.207326i
$256$	−1.04282e18			−0.904500
$257$	−1.83365e18			−1.54460			−0.772302	−	0.635255i	$-0.780895\pi$
$257$	−1.83365e18			−1.54460			−0.772302	+	0.635255i	$0.780895\pi$
$258$		−	3.92255e17i		−	0.320938i
$259$	8.82484e17			0.701389
$260$		−	1.52641e17i		−	0.117861i
$261$			2.52232e17i			0.189233i
$262$		−	1.11383e18i		−	0.812007i
$263$	2.37881e18			1.68535			0.842677	−	0.538419i	$-0.180978\pi$
$263$	2.37881e18			1.68535			0.842677	+	0.538419i	$0.180978\pi$
$264$	2.30578e16			0.0158778
$265$		−	2.13241e17i		−	0.142734i
$266$		−	7.19215e17i		−	0.468001i
$267$			3.99408e17i			0.252687i
$268$	8.45723e17			0.520256
$269$		−	8.38413e17i		−	0.501552i	−0.968045	−	0.250776i	$-0.919314\pi$
$269$		−	8.38413e17i		−	0.501552i	0.968045	−	0.250776i	$-0.0806858\pi$
$270$	2.82237e17			0.164205
$271$	−2.18446e18			−1.23616			−0.618079	−	0.786116i	$-0.712089\pi$
$271$	−2.18446e18			−1.23616			−0.618079	+	0.786116i	$0.712089\pi$
$272$	−6.30011e15	−	2.19120e17i	−0.00346802	−	0.120619i
$273$	7.33483e17			0.392799
$274$	3.22041e17			0.167796
$275$		−	3.86015e16i		−	0.0195708i
$276$	1.35245e18			0.667271
$277$		−	3.79753e17i		−	0.182349i	−0.995835	−	0.0911744i	$-0.970938\pi$
$277$		−	3.79753e17i		−	0.182349i	0.995835	−	0.0911744i	$-0.0290621\pi$
$278$		−	4.39473e17i		−	0.205398i
$279$			8.22722e17i			0.374301i
$280$	4.26099e17			0.188723
$281$	−3.19899e18			−1.37948			−0.689740	−	0.724057i	$-0.742275\pi$
$281$	−3.19899e18			−1.37948			−0.689740	+	0.724057i	$0.742275\pi$
$282$			7.77123e17i			0.326303i
$283$		−	4.02290e18i		−	1.64491i	−0.568833	−	0.822453i	$-0.692605\pi$
$283$		−	4.02290e18i		−	1.64491i	0.568833	−	0.822453i	$-0.307395\pi$
$284$		−	1.41977e18i		−	0.565368i
$285$	5.83506e17			0.226312
$286$			2.13106e16i			0.00805100i
$287$	−1.34957e18			−0.496687
$288$	−1.08860e18			−0.390325
$289$	−2.85769e18	+	1.64464e17i	−0.998348	+	0.0574563i
$290$	2.21214e17			0.0753057
$291$	1.70389e18			0.565256
$292$		−	4.05051e18i		−	1.30960i
$293$	2.29839e18			0.724297			0.362149	−	0.932120i	$-0.382043\pi$
$293$	2.29839e18			0.724297			0.362149	+	0.932120i	$0.382043\pi$
$294$		−	6.49131e17i		−	0.199401i
$295$			8.15359e17i			0.244165i
$296$			3.08111e18i			0.899536i
$297$	8.02755e16			0.0228512
$298$	6.30552e17			0.175025
$299$			3.11348e18i			0.842775i
$300$		−	1.86230e18i		−	0.491632i
$301$		−	2.06172e18i		−	0.530862i
$302$	4.20738e17			0.105672
$303$			1.02096e18i			0.250143i
$304$	−5.50834e17			−0.131665
$305$	2.01805e17			0.0470634
$306$	2.75186e16	+	9.57104e17i	0.00626203	+	0.217795i
$307$	4.56228e18			1.01308			0.506540	−	0.862216i	$-0.330924\pi$
$307$	4.56228e18			1.01308			0.506540	+	0.862216i	$0.330924\pi$
$308$	4.86555e16			0.0105439
$309$			4.32771e18i			0.915313i
$310$	7.21549e17			0.148954
$311$			9.09210e18i			1.83215i	0.401005	+	0.916076i	$0.368661\pi$
$311$			9.09210e18i			1.83215i	−0.401005	+	0.916076i	$0.631339\pi$
$312$			2.56088e18i			0.503768i
$313$		−	3.74348e17i		−	0.0718941i	−0.999354	−	0.0359470i	$-0.988555\pi$
$313$		−	3.74348e17i		−	0.0718941i	0.999354	−	0.0359470i	$-0.0114448\pi$
$314$	−4.96606e18			−0.931192
$315$	4.08274e17			0.0747519
$316$		−	1.34064e18i		−	0.239695i
$317$			2.21829e18i			0.387323i	0.981068	+	0.193662i	$0.0620364\pi$
$317$			2.21829e18i			0.387323i	−0.981068	+	0.193662i	$0.937964\pi$
$318$			1.43628e18i			0.244927i
$319$	6.29191e16			0.0104798
$320$			7.59409e17i			0.123552i
$321$	−3.80483e18			−0.604710
$322$	−3.48928e18			−0.541773
$323$	2.06719e17	+	7.18976e18i	0.0313590	+	1.09068i
$324$	2.15445e18			0.319336
$325$	4.28721e18			0.620940
$326$			1.62671e18i			0.230239i
$327$	3.00816e18			0.416095
$328$		−	4.71190e18i		−	0.637005i
$329$			4.08462e18i			0.539737i
$330$		−	1.93764e16i		−	0.00250275i
$331$	−2.55801e17			−0.0322993			−0.0161496	−	0.999870i	$-0.505141\pi$
$331$	−2.55801e17			−0.0322993			−0.0161496	+	0.999870i	$0.505141\pi$
$332$	−5.89105e18			−0.727206
$333$			2.95221e18i			0.356300i
$334$		−	7.53014e18i		−	0.888596i
$335$		−	1.77023e18i		−	0.204265i
$336$	6.29568e17			0.0710392
$337$		−	1.49326e19i		−	1.64783i	−0.566717	−	0.823913i	$-0.691787\pi$
$337$		−	1.49326e19i		−	1.64783i	0.566717	−	0.823913i	$-0.308213\pi$
$338$	2.94978e18			0.318357
$339$	−1.16230e19			−1.22693
$340$	−1.71009e18	+	4.91682e16i	−0.176574	+	0.00507683i
$341$	2.05227e17			0.0207290
$342$	2.40602e18			0.237740
$343$		−	1.11444e19i		−	1.07733i
$344$	7.19830e18			0.680834
$345$		−	2.83089e18i		−	0.261987i
$346$		−	5.98105e18i		−	0.541635i
$347$		−	7.71727e18i		−	0.683900i	−0.939718	−	0.341950i	$-0.888913\pi$
$347$		−	7.71727e18i		−	0.683900i	0.939718	−	0.341950i	$-0.111087\pi$
$348$	3.03549e18			0.263259
$349$	2.24641e17			0.0190677			0.00953386	−	0.999955i	$-0.496965\pi$
$349$	2.24641e17			0.0190677			0.00953386	+	0.999955i	$0.496965\pi$
$350$			4.80469e18i			0.399167i
$351$			8.91567e18i			0.725021i
$352$			2.71552e17i			0.0216164i
$353$	1.43886e19			1.12126			0.560631	−	0.828066i	$-0.310558\pi$
$353$	1.43886e19			1.12126			0.560631	+	0.828066i	$0.310558\pi$
$354$		−	5.49185e18i		−	0.418981i
$355$	−2.97181e18			−0.221977
$356$	−2.94259e18			−0.215206
$357$	−2.36267e17	−	8.21744e18i	−0.0169197	−	0.588471i
$358$	3.38097e18			0.237093
$359$	−7.90159e17			−0.0542633			−0.0271316	−	0.999632i	$-0.508637\pi$
$359$	−7.90159e17			−0.0542633			−0.0271316	+	0.999632i	$0.508637\pi$
$360$			1.42545e18i			0.0958699i
$361$	2.89287e18			0.190557
$362$		−	1.02903e19i		−	0.663918i
$363$			1.24566e19i			0.787227i
$364$			5.40384e18i			0.334536i
$365$	−8.47835e18			−0.514179
$366$	−1.35926e18			−0.0807594
$367$		−	1.89005e19i		−	1.10022i	−0.835093	−	0.550109i	$-0.814586\pi$
$367$		−	1.89005e19i		−	1.10022i	0.835093	−	0.550109i	$-0.185414\pi$
$368$			2.67238e18i			0.152419i
$369$		−	4.51478e18i		−	0.252313i
$370$	2.58917e18			0.141790
$371$			7.54921e18i			0.405133i
$372$	9.90105e18			0.520726
$373$	−1.18655e19			−0.611605			−0.305802	−	0.952095i	$-0.598925\pi$
$373$	−1.18655e19			−0.611605			−0.305802	+	0.952095i	$0.598925\pi$
$374$	2.38749e17	−	6.86449e15i	0.0120616	−	0.000346794i
$375$	−8.08668e18			−0.400438
$376$	−1.42610e19			−0.692217
$377$			6.98801e18i			0.332501i
$378$	−9.99182e18			−0.466075
$379$			2.02421e19i			0.925680i	0.886442	+	0.462840i	$0.153170\pi$
$379$			2.02421e19i			0.925680i	−0.886442	+	0.462840i	$0.846830\pi$
$380$			4.29890e18i			0.192744i
$381$		−	1.58865e19i		−	0.698380i
$382$	7.67847e18			0.330978
$383$	−1.74686e19			−0.738359			−0.369180	−	0.929358i	$-0.620361\pi$
$383$	−1.74686e19			−0.738359			−0.369180	+	0.929358i	$0.620361\pi$
$384$			1.44164e19i			0.597549i
$385$		−	1.01844e17i		−	0.00413979i
$386$			1.90315e19i			0.758696i
$387$	6.89716e18			0.269673
$388$			1.25532e19i			0.481412i
$389$	3.64147e19			1.36979			0.684897	−	0.728640i	$-0.259847\pi$
$389$	3.64147e19			1.36979			0.684897	+	0.728640i	$0.259847\pi$
$390$	2.15200e18			0.0794070
$391$	3.48812e19	−	1.00290e18i	1.26260	−	0.0363022i
$392$	1.19122e19			0.423008
$393$	−3.19917e19			−1.11453
$394$			2.75956e19i			0.943231i
$395$	−2.80617e18			−0.0941099
$396$			1.62769e17i			0.00535621i
$397$		−	2.20829e19i		−	0.713062i	−0.934283	−	0.356531i	$-0.883959\pi$
$397$		−	2.20829e19i		−	0.713062i	0.934283	−	0.356531i	$-0.116041\pi$
$398$			1.81346e19i			0.574625i
$399$	−2.06574e19			−0.642362
$400$	3.67983e18			0.112299
$401$		−	1.55412e19i		−	0.465479i	−0.972539	−	0.232740i	$-0.925231\pi$
$401$		−	1.55412e19i		−	0.465479i	0.972539	−	0.232740i	$-0.0747690\pi$
$402$			1.19234e19i			0.350513i
$403$			2.27933e19i			0.657686i
$404$	−7.52179e18			−0.213040
$405$		−	4.50960e18i		−	0.125379i
$406$	−7.83149e18			−0.213746
$407$	7.36427e17			0.0197320
$408$	2.86904e19	−	8.24903e17i	0.754719	−	0.0216996i
$409$	3.07772e19			0.794885			0.397442	−	0.917627i	$-0.369898\pi$
$409$	3.07772e19			0.794885			0.397442	+	0.917627i	$0.369898\pi$
$410$	−3.95959e18			−0.100409
$411$		−	9.24972e18i		−	0.230311i
$412$	−3.18838e19			−0.779546
$413$		−	2.88656e19i		−	0.693034i
$414$		−	1.16728e19i		−	0.275216i
$415$			1.23309e19i			0.285518i
$416$	−3.01595e19			−0.685841
$417$	−1.26226e19			−0.281922
$418$		−	6.00180e17i		−	0.0131662i
$419$			6.44452e18i			0.138863i	0.997587	+	0.0694313i	$0.0221185\pi$
$419$			6.44452e18i			0.138863i	−0.997587	+	0.0694313i	$0.977882\pi$
$420$		−	4.91337e18i		−	0.103994i
$421$	6.32762e19			1.31560			0.657801	−	0.753192i	$-0.271487\pi$
$421$	6.32762e19			1.31560			0.657801	+	0.753192i	$0.271487\pi$
$422$			4.12872e19i			0.843281i
$423$	−1.36644e19			−0.274182
$424$	−2.63573e19			−0.519586
$425$	−1.38098e18	−	4.80310e19i	−0.0267467	−	0.930260i
$426$	2.00166e19			0.380906
$427$	−7.14435e18			−0.133584
$428$		−	2.80316e19i		−	0.515014i
$429$	6.12086e17			0.0110505
$430$		−	6.04899e18i		−	0.107317i
$431$		−	5.66879e19i		−	0.988350i	−0.869363	−	0.494175i	$-0.835470\pi$
$431$		−	5.66879e19i		−	0.988350i	0.869363	−	0.494175i	$-0.164530\pi$
$432$			7.65256e18i			0.131123i
$433$	−9.58417e19			−1.61397			−0.806985	−	0.590572i	$-0.798902\pi$
$433$	−9.58417e19			−1.61397			−0.806985	+	0.590572i	$0.798902\pi$
$434$	−2.55445e19			−0.422789
$435$		−	6.35375e18i		−	0.103362i
$436$			2.21622e19i			0.354376i
$437$		−	8.76863e19i		−	1.37823i
$438$	5.71059e19			0.882318
$439$			1.15200e20i			1.74971i	0.484381	+	0.874857i	$0.339045\pi$
$439$			1.15200e20i			1.74971i	−0.484381	+	0.874857i	$0.660955\pi$
$440$	3.55577e17			0.00530931
$441$	1.14139e19			0.167550
$442$	7.62394e17	+	2.65163e19i	0.0110030	+	0.382689i
$443$	6.80470e19			0.965564			0.482782	−	0.875741i	$-0.339626\pi$
$443$	6.80470e19			0.965564			0.482782	+	0.875741i	$0.339626\pi$
$444$	3.55284e19			0.495682
$445$			6.15931e18i			0.0844951i
$446$	−7.53908e18			−0.101697
$447$		−	1.81108e19i		−	0.240233i
$448$		−	2.68848e19i		−	0.350689i
$449$		−	4.06027e19i		−	0.520843i	−0.965495	−	0.260422i	$-0.916138\pi$
$449$		−	4.06027e19i		−	0.520843i	0.965495	−	0.260422i	$-0.0838616\pi$
$450$	−1.60733e19			−0.202774
$451$	−1.12621e18			−0.0139732
$452$		−	8.56311e19i		−	1.04495i
$453$		−	1.20845e19i		−	0.145042i
$454$		−	6.54995e18i		−	0.0773249i
$455$	1.13111e19			0.131347
$456$		−	7.21233e19i		−	0.823834i
$457$	1.13930e20			1.28017			0.640086	−	0.768304i	$-0.278899\pi$
$457$	1.13930e20			1.28017			0.640086	+	0.768304i	$0.278899\pi$
$458$	−4.73696e19			−0.523610
$459$	9.98850e19	−	2.87189e18i	1.08619	−	0.0312300i
$460$	2.08562e19			0.223127
$461$	−1.54322e19			−0.162431			−0.0812157	−	0.996697i	$-0.525880\pi$
$461$	−1.54322e19			−0.162431			−0.0812157	+	0.996697i	$0.525880\pi$
$462$			6.85967e17i			0.00710376i
$463$	−1.64731e20			−1.67849			−0.839244	−	0.543756i	$-0.817002\pi$
$463$	−1.64731e20			−1.67849			−0.839244	+	0.543756i	$0.817002\pi$
$464$			5.99800e18i			0.0601342i
$465$		−	2.07245e19i		−	0.204450i
$466$		−	3.10260e19i		−	0.301183i
$467$	−1.59760e20			−1.52613			−0.763065	−	0.646321i	$-0.776307\pi$
$467$	−1.59760e20			−1.52613			−0.763065	+	0.646321i	$0.776307\pi$
$468$	−1.80777e19			−0.169941
$469$			6.26703e19i			0.579783i
$470$			1.19841e19i			0.109111i
$471$			1.42636e20i			1.27812i
$472$	1.00781e20			0.888821
$473$		−	1.72049e18i		−	0.0149346i
$474$	1.89009e19			0.161490
$475$	−1.20743e20			−1.01545
$476$	6.05409e19	−	1.74067e18i	0.501184	−	0.0144100i
$477$	−2.52547e19			−0.205804
$478$	−3.77093e19			−0.302510
$479$			1.51839e20i			1.19913i	0.800326	+	0.599565i	$0.204660\pi$
$479$			1.51839e20i			1.19913i	−0.800326	+	0.599565i	$0.795340\pi$
$480$	2.74221e19			0.213202
$481$			8.17901e19i			0.626055i
$482$			3.96969e19i			0.299160i
$483$			1.00220e20i			0.743619i
$484$	−9.17725e19			−0.670459
$485$	2.62759e19			0.189014
$486$		−	5.76526e19i		−	0.408364i
$487$			1.54186e20i			1.07542i	0.843131	+	0.537709i	$0.180710\pi$
$487$			1.54186e20i			1.07542i	−0.843131	+	0.537709i	$0.819290\pi$
$488$		−	2.49438e19i		−	0.171322i
$489$	4.67227e19			0.316018
$490$		−	1.00103e19i		−	0.0666771i
$491$	2.09856e20			1.37661			0.688304	−	0.725422i	$-0.258355\pi$
$491$	2.09856e20			1.37661			0.688304	+	0.725422i	$0.258355\pi$
$492$	−5.43332e19			−0.351016
$493$	7.82889e19	−	2.25095e18i	0.498136	−	0.0143224i
$494$	6.66580e19			0.417734
$495$	3.40701e17			0.00210298
$496$			1.95641e19i			0.118945i
$497$	1.05209e20			0.630056
$498$		−	8.30548e19i		−	0.489942i
$499$			2.83960e20i			1.65007i	0.565079	+	0.825037i	$0.308846\pi$
$499$			2.83960e20i			1.65007i	−0.565079	+	0.825037i	$0.691154\pi$
$500$		−	5.95776e19i		−	0.341042i
$501$	−2.16282e20			−1.21966
$502$	−8.10388e19			−0.450210
$503$			5.30065e19i			0.290114i	0.989423	+	0.145057i	$0.0463366\pi$
$503$			5.30065e19i			0.290114i	−0.989423	+	0.145057i	$0.953663\pi$
$504$		−	5.04641e19i		−	0.272115i
$505$			1.57443e19i			0.0836446i
$506$	−2.91178e18			−0.0152416
$507$		−	8.47242e19i		−	0.436966i
$508$	1.17042e20			0.594791
$509$	−3.69092e20			−1.84821			−0.924105	−	0.382140i	$-0.875187\pi$
$509$	−3.69092e20			−1.84821			−0.924105	+	0.382140i	$0.875187\pi$
$510$	−6.93196e17	−	2.41096e19i	−0.00342042	−	0.118963i
$511$	3.00153e20			1.45944
$512$	−5.00296e19			−0.239719
$513$		−	2.51096e20i		−	1.18566i
$514$	1.90458e20			0.886292
$515$			6.67379e19i			0.306068i
$516$		−	8.30039e19i		−	0.375168i
$517$			3.40858e18i			0.0151843i
$518$	−9.16624e19			−0.402456
$519$	−1.71789e20			−0.743429
$520$			3.94916e19i			0.168453i
$521$		−	3.10002e20i		−	1.30341i	−0.758471	−	0.651706i	$-0.774053\pi$
$521$		−	3.10002e20i		−	1.30341i	0.758471	−	0.651706i	$-0.225947\pi$
$522$		−	2.61990e19i		−	0.108581i
$523$	7.75037e19			0.316636			0.158318	−	0.987388i	$-0.449393\pi$
$523$	7.75037e19			0.316636			0.158318	+	0.987388i	$0.449393\pi$
$524$		−	2.35695e20i		−	0.949216i
$525$	1.38001e20			0.547883
$526$	−2.47083e20			−0.967053
$527$	2.55360e20	−	7.34209e18i	0.985311	−	0.0283296i
$528$	5.25370e17			0.00199853
$529$	−1.58776e20			−0.595481
$530$			2.21490e19i			0.0819003i
$531$	9.65651e19			0.352056
$532$		−	1.52191e20i		−	0.547081i
$533$		−	1.25081e20i		−	0.443339i
$534$		−	4.14860e19i		−	0.144991i
$535$	−5.86745e19			−0.202207
$536$	−2.18807e20			−0.743576
$537$		−	9.71090e19i		−	0.325426i
$538$			8.70848e19i			0.287790i
$539$		−	2.84719e18i		−	0.00927899i
$540$	5.97232e19			0.191951
$541$		−	2.10789e20i		−	0.668142i	−0.942548	−	0.334071i	$-0.891578\pi$
$541$		−	2.10789e20i		−	0.668142i	0.942548	−	0.334071i	$-0.108422\pi$
$542$	2.26897e20			0.709306
$543$	−2.95560e20			−0.911271
$544$	9.71486e18	+	3.37886e20i	0.0295423	+	1.02749i
$545$	4.63890e19			0.139137
$546$	−7.61859e19			−0.225387
$547$		−	3.66267e19i		−	0.106879i	−0.998571	−	0.0534395i	$-0.982982\pi$
$547$		−	3.66267e19i		−	0.106879i	0.998571	−	0.0534395i	$-0.0170184\pi$
$548$	6.81461e19			0.196149
$549$		−	2.39003e19i		−	0.0678595i
$550$			4.00948e18i			0.0112297i
$551$		−	1.96807e20i		−	0.543754i
$552$	−3.49908e20			−0.953697
$553$	9.93448e19			0.267120
$554$			3.94444e19i			0.104631i
$555$		−	7.43665e19i		−	0.194617i
$556$		−	9.29957e19i		−	0.240105i
$557$	7.39350e20			1.88337			0.941686	−	0.336494i	$-0.109241\pi$
$557$	7.39350e20			1.88337			0.941686	+	0.336494i	$0.109241\pi$
$558$		−	8.54549e19i		−	0.214774i
$559$	1.91084e20			0.473844
$560$	9.70862e18			0.0237546
$561$	−1.97163e17	−	6.85739e18i	−0.000475997	−	0.0165553i
$562$	3.32275e20			0.791544
$563$	8.51567e19			0.200173			0.100087	−	0.994979i	$-0.468088\pi$
$563$	8.51567e19			0.200173			0.100087	+	0.994979i	$0.468088\pi$
$564$			1.64445e20i			0.381440i
$565$	−1.79240e20			−0.410271
$566$			4.17853e20i			0.943844i
$567$			1.59650e20i			0.355874i
$568$			3.67326e20i			0.808051i
$569$	−6.26381e20			−1.35987			−0.679933	−	0.733274i	$-0.737991\pi$
$569$	−6.26381e20			−1.35987			−0.679933	+	0.733274i	$0.737991\pi$
$570$	−6.06079e19			−0.129858
$571$			9.31795e20i			1.97038i	0.171472	+	0.985189i	$0.445148\pi$
$571$			9.31795e20i			1.97038i	−0.171472	+	0.985189i	$0.554852\pi$
$572$			4.50947e18i			0.00941141i
$573$		−	2.20542e20i		−	0.454289i
$574$	1.40178e20			0.284998
$575$			5.85785e20i			1.17552i
$576$	8.99388e19			0.178147
$577$	−9.16819e20			−1.79252			−0.896262	−	0.443524i	$-0.853728\pi$
$577$	−9.16819e20			−1.79252			−0.896262	+	0.443524i	$0.853728\pi$
$578$	2.96825e20	−	1.70827e19i	0.572850	−	0.0329683i
$579$	5.46626e20			1.04136
$580$	4.68105e19			0.0880304
$581$		−	4.36542e20i		−	0.810411i
$582$	−1.76981e20			−0.324343
$583$			6.29976e18i			0.0113975i
$584$			1.04795e21i			1.87174i
$585$			3.78394e19i			0.0667230i
$586$	−2.38731e20			−0.415601
$587$	−1.07845e21			−1.85359			−0.926794	−	0.375571i	$-0.877447\pi$
$587$	−1.07845e21			−1.85359			−0.926794	+	0.375571i	$0.877447\pi$
$588$		−	1.37361e20i		−	0.233095i
$589$		−	6.41937e20i		−	1.07554i
$590$		−	8.46902e19i		−	0.140102i
$591$	7.92606e20			1.29465
$592$			7.02026e19i			0.113224i
$593$	−6.61741e20			−1.05385			−0.526924	−	0.849913i	$-0.676655\pi$
$593$	−6.61741e20			−1.05385			−0.526924	+	0.849913i	$0.676655\pi$
$594$	−8.33810e18			−0.0131120
$595$	−3.64349e18	−	1.26722e20i	−0.00565771	−	0.196777i
$596$	1.33429e20			0.204599
$597$	5.20865e20			0.788711
$598$		−	3.23392e20i		−	0.483583i
$599$	2.48300e20			0.366670			0.183335	−	0.983051i	$-0.441311\pi$
$599$	2.48300e20			0.366670			0.183335	+	0.983051i	$0.441311\pi$
$600$			4.81817e20i			0.702665i
$601$		−	1.07376e21i		−	1.54649i	−0.634105	−	0.773247i	$-0.718631\pi$
$601$		−	1.07376e21i		−	1.54649i	0.634105	−	0.773247i	$-0.281369\pi$
$602$			2.14148e20i			0.304608i
$603$	−2.09653e20			−0.294525
$604$	8.90310e19			0.123528
$605$			1.92094e20i			0.263238i
$606$		−	1.06046e20i		−	0.143532i
$607$		−	7.39252e19i		−	0.0988273i	−0.998778	−	0.0494137i	$-0.984265\pi$
$607$		−	7.39252e19i		−	0.0988273i	0.998778	−	0.0494137i	$-0.0157353\pi$
$608$	8.49395e20			1.12159
$609$			2.24937e20i			0.293381i
$610$	−2.09612e19			−0.0270049
$611$	−3.78569e20			−0.481766
$612$	5.82312e18	+	2.02530e20i	0.00732015	+	0.254597i
$613$	1.43718e21			1.78466			0.892331	−	0.451381i	$-0.149068\pi$
$613$	1.43718e21			1.78466			0.892331	+	0.451381i	$0.149068\pi$
$614$	−4.73877e20			−0.581304
$615$			1.13728e20i			0.137817i
$616$	−1.25882e19			−0.0150699
$617$		−	5.20343e20i		−	0.615391i	−0.951485	−	0.307695i	$-0.900442\pi$
$617$		−	5.20343e20i		−	0.615391i	0.951485	−	0.307695i	$-0.0995578\pi$
$618$		−	4.49513e20i		−	0.525205i
$619$			5.89325e19i			0.0680260i	0.999421	+	0.0340130i	$0.0108288\pi$
$619$			5.89325e19i			0.0680260i	−0.999421	+	0.0340130i	$0.989171\pi$
$620$	1.52685e20			0.174124
$621$	−1.21820e21			−1.37256
$622$		−	9.44384e20i		−	1.05129i
$623$		−	2.18053e20i		−	0.239830i
$624$			5.83494e19i			0.0634091i
$625$	7.42025e20			0.796743
$626$			3.88830e19i			0.0412527i
$627$	−1.72385e19			−0.0180714
$628$	−1.05085e21			−1.08854
$629$	9.16320e20	−	2.63459e19i	0.937923	−	0.0269671i
$630$	−4.24068e19			−0.0428925
$631$	−1.66850e21			−1.66765			−0.833826	−	0.552027i	$-0.813855\pi$
$631$	−1.66850e21			−1.66765			−0.833826	+	0.552027i	$0.813855\pi$
$632$			3.46852e20i			0.342584i
$633$	1.18586e21			1.15746
$634$		−	2.30410e20i		−	0.222245i
$635$		−	2.44987e20i		−	0.233529i
$636$			3.03927e20i			0.286313i
$637$	3.16219e20			0.294403
$638$	−6.53532e18			−0.00601328
$639$			3.51959e20i			0.320063i
$640$			2.22317e20i			0.199812i
$641$			6.32967e20i			0.562271i	0.959668	+	0.281136i	$0.0907111\pi$
$641$			6.32967e20i			0.562271i	−0.959668	+	0.281136i	$0.909289\pi$
$642$	3.95202e20			0.346982
$643$		−	1.53351e21i		−	1.33078i	−0.746498	−	0.665388i	$-0.768266\pi$
$643$		−	1.53351e21i		−	1.33078i	0.746498	−	0.665388i	$-0.231734\pi$
$644$	−7.38357e20			−0.633319
$645$	−1.73740e20			−0.147300
$646$	−2.14717e19	−	7.46791e20i	−0.0179937	−	0.625828i
$647$	−3.96202e20			−0.328197			−0.164098	−	0.986444i	$-0.552471\pi$
$647$	−3.96202e20			−0.328197			−0.164098	+	0.986444i	$0.552471\pi$
$648$	−5.57402e20			−0.456411
$649$		−	2.40881e19i		−	0.0194970i
$650$	−4.45306e20			−0.356294
$651$			7.33693e20i			0.580306i
$652$			3.44223e20i			0.269143i
$653$		−	1.94686e21i		−	1.50482i	−0.658694	−	0.752411i	$-0.728891\pi$
$653$		−	1.94686e21i		−	1.50482i	0.658694	−	0.752411i	$-0.271109\pi$
$654$	−3.12453e20			−0.238754
$655$	−4.93346e20			−0.372685
$656$		−	1.07360e20i		−	0.0801797i
$657$			1.00411e21i			0.741382i
$658$		−	4.24263e20i		−	0.309700i
$659$	1.31409e21			0.948382			0.474191	−	0.880422i	$-0.342741\pi$
$659$	1.31409e21			0.948382			0.474191	+	0.880422i	$0.342741\pi$
$660$		−	4.10017e18i		−	0.00292565i
$661$	8.51821e20			0.600949			0.300474	−	0.953790i	$-0.402855\pi$
$661$	8.51821e20			0.600949			0.300474	+	0.953790i	$0.402855\pi$
$662$	2.65697e19			0.0185333
$663$	7.61606e20	−	2.18976e19i	0.525265	−	0.0151024i
$664$	1.52414e21			1.03936
$665$	−3.18560e20			−0.214797
$666$		−	3.06642e20i		−	0.204444i
$667$	−9.54810e20			−0.629467
$668$		−	1.59343e21i		−	1.03875i
$669$			2.16539e20i			0.139585i
$670$			1.83872e20i			0.117207i
$671$	−5.96191e18			−0.00375808
$672$	−9.70804e20			−0.605149
$673$		−	9.19408e20i		−	0.566755i	−0.959008	−	0.283377i	$-0.908545\pi$
$673$		−	9.19408e20i		−	0.566755i	0.959008	−	0.283377i	$-0.0914549\pi$
$674$			1.55103e21i			0.945519i
$675$			1.67744e21i			1.01127i
$676$	6.24194e20			0.372151
$677$			1.73788e21i			1.02472i	0.858771	+	0.512359i	$0.171228\pi$
$677$			1.73788e21i			1.02472i	−0.858771	+	0.512359i	$0.828772\pi$
$678$	1.20727e21			0.704013
$679$	−9.30226e20			−0.536494
$680$	4.42436e20	−	1.27209e19i	0.252368	−	0.00725606i
$681$	−1.88129e20			−0.106133
$682$	−2.13167e19			−0.0118942
$683$			1.41787e21i			0.782492i	0.920286	+	0.391246i	$0.127956\pi$
$683$			1.41787e21i			0.782492i	−0.920286	+	0.391246i	$0.872044\pi$
$684$	5.09130e20			0.277912
$685$		−	1.42641e20i		−	0.0770130i
$686$			1.15755e21i			0.618170i
$687$			1.36056e21i			0.718689i
$688$	1.64012e20			0.0856965
$689$	−6.99673e20			−0.361619
$690$			2.94040e20i			0.150328i
$691$			1.51291e21i			0.765117i	0.923931	+	0.382559i	$0.124957\pi$
$691$			1.51291e21i			0.765117i	−0.923931	+	0.382559i	$0.875043\pi$
$692$		−	1.26563e21i		−	0.633157i
$693$	−1.20616e19			−0.00596906
$694$			8.01582e20i			0.392421i
$695$	−1.94655e20			−0.0942711
$696$	−7.85346e20			−0.376263
$697$	−1.40132e21	+	4.02906e19i	−0.664188	+	0.0190967i
$698$	−2.33332e19			−0.0109410
$699$	−8.91133e20			−0.413394
$700$			1.01671e21i			0.466617i
$701$	2.44897e21			1.11199			0.555993	−	0.831187i	$-0.312338\pi$
$701$	2.44897e21			1.11199			0.555993	+	0.831187i	$0.312338\pi$
$702$		−	9.26058e20i		−	0.416016i
$703$		−	2.30349e21i		−	1.02382i
$704$		−	2.24352e19i		−	0.00986585i
$705$	3.44209e20			0.149763
$706$	−1.49452e21			−0.643379
$707$		−	5.57384e20i		−	0.237415i
$708$		−	1.16211e21i		−	0.489778i
$709$			2.30975e21i			0.963206i	0.876390	+	0.481603i	$0.159945\pi$
$709$			2.30975e21i			0.963206i	−0.876390	+	0.481603i	$0.840055\pi$
$710$	3.08677e20			0.127370
$711$			3.32342e20i			0.135695i
$712$	7.61312e20			0.307583
$713$	−3.11437e21			−1.24508
$714$	2.45407e19	+	8.53534e20i	0.00970847	+	0.337664i
$715$	9.43902e18			0.00369515
$716$	7.15438e20			0.277156
$717$			1.08309e21i			0.415215i
$718$	8.20727e19			0.0311362
$719$			3.05892e21i			1.14842i	0.818708	+	0.574211i	$0.194691\pi$
$719$			3.05892e21i			1.14842i	−0.818708	+	0.574211i	$0.805309\pi$
$720$			3.24786e19i			0.0120671i
$721$		−	2.36267e21i		−	0.868739i
$722$	−3.00478e20			−0.109341
$723$	1.14018e21			0.410617
$724$		−	2.17750e21i		−	0.776103i
$725$			1.31476e21i			0.463779i
$726$		−	1.29385e21i		−	0.451710i
$727$	2.75273e21			0.951163			0.475582	−	0.879672i	$-0.342238\pi$
$727$	2.75273e21			0.951163			0.475582	+	0.879672i	$0.342238\pi$
$728$		−	1.39809e21i		−	0.478135i
$729$	−3.06241e21			−1.03659
$730$	8.80634e20			0.295035
$731$	−6.15512e19	−	2.14077e21i	−0.0204106	−	0.709888i
$732$	−2.87628e20			−0.0944057
$733$	3.11428e21			1.01176			0.505881	−	0.862603i	$-0.331168\pi$
$733$	3.11428e21			1.01176			0.505881	+	0.862603i	$0.331168\pi$
$734$			1.96317e21i			0.631303i
$735$	−2.87518e20			−0.0915186
$736$		−	4.12085e21i		−	1.29838i
$737$			5.22979e19i			0.0163109i
$738$			4.68944e20i			0.144777i
$739$	−1.19046e21			−0.363817			−0.181909	−	0.983315i	$-0.558227\pi$
$739$	−1.19046e21			−0.363817			−0.181909	+	0.983315i	$0.558227\pi$
$740$	5.47886e20			0.165749
$741$		−	1.91456e21i		−	0.573368i
$742$		−	7.84126e20i		−	0.232464i
$743$		−	3.04122e21i		−	0.892549i	−0.894896	−	0.446274i	$-0.852751\pi$
$743$		−	3.04122e21i		−	0.892549i	0.894896	−	0.446274i	$-0.147249\pi$
$744$	−2.56162e21			−0.744247
$745$		−	2.79288e20i		−	0.0803306i
$746$	1.23246e21			0.350938
$747$	1.46038e21			0.411682
$748$	5.05210e19	−	1.45257e18i	0.0140997	−	0.000405393i
$749$	2.07721e21			0.573941
$750$	8.39952e20			0.229771
$751$		−	4.41107e21i		−	1.19466i	−0.801995	−	0.597330i	$-0.796228\pi$
$751$		−	4.41107e21i		−	1.19466i	0.801995	−	0.597330i	$-0.203772\pi$
$752$	−3.24936e20			−0.0871292
$753$			2.32761e21i			0.617942i
$754$		−	7.25835e20i		−	0.190789i
$755$		−	1.86356e20i		−	0.0485000i
$756$	−2.11434e21			−0.544830
$757$	2.92307e21			0.745796			0.372898	−	0.927872i	$-0.378364\pi$
$757$	2.92307e21			0.745796			0.372898	+	0.927872i	$0.378364\pi$
$758$		−	2.10252e21i		−	0.531154i
$759$			8.36327e19i			0.0209201i
$760$		−	1.11222e21i		−	0.275479i
$761$	−4.36735e21			−1.07111			−0.535554	−	0.844501i	$-0.679897\pi$
$761$	−4.36735e21			−1.07111			−0.535554	+	0.844501i	$0.679897\pi$
$762$			1.65011e21i			0.400730i
$763$	−1.64228e21			−0.394923
$764$	1.62482e21			0.386905
$765$	4.23927e20	−	1.21887e19i	0.0999610	−	0.00287407i
$766$	1.81444e21			0.423669
$767$	2.67531e21			0.618598
$768$		−	3.11107e21i		−	0.712362i
$769$	−2.89584e21			−0.656639			−0.328319	−	0.944567i	$-0.606482\pi$
$769$	−2.89584e21			−0.656639			−0.328319	+	0.944567i	$0.606482\pi$
$770$			1.05783e19i			0.00237540i
$771$		−	5.47038e21i		−	1.21649i
$772$			4.02719e21i			0.886896i
$773$	−3.89791e21			−0.850131			−0.425066	−	0.905163i	$-0.639749\pi$
$773$	−3.89791e21			−0.850131			−0.425066	+	0.905163i	$0.639749\pi$
$774$	−7.16398e20			−0.154738
$775$			4.28844e21i			0.917353i
$776$		−	3.24779e21i		−	0.688058i
$777$			2.63274e21i			0.552397i
$778$	−3.78235e21			−0.785985
$779$			3.52271e21i			0.725013i
$780$	4.55379e20			0.0928247
$781$	8.77959e19			0.0177252
$782$	−3.62307e21	+	1.04170e20i	−0.724479	+	0.0208301i
$783$	−2.73417e21			−0.541517
$784$	2.71419e20			0.0532439
$785$			2.19960e21i			0.427387i
$786$	3.32293e21			0.639517
$787$		−	1.02248e21i		−	0.194914i	−0.995240	−	0.0974569i	$-0.968929\pi$
$787$		−	1.02248e21i		−	0.194914i	0.995240	−	0.0974569i	$-0.0310708\pi$
$788$			5.83942e21i			1.10261i
$789$			7.09677e21i			1.32734i
$790$	2.91473e20			0.0540001
$791$	6.34549e21			1.16451
$792$		−	4.21119e19i		−	0.00765536i
$793$		−	6.62150e20i		−	0.119236i
$794$			2.29372e21i			0.409154i
$795$	6.36168e20			0.112414
$796$			3.83741e21i			0.671722i
$797$	7.11412e21			1.23363			0.616814	−	0.787109i	$-0.288423\pi$
$797$	7.11412e21			1.23363			0.616814	+	0.787109i	$0.288423\pi$
$798$	2.14566e21			0.368586
$799$	1.21943e20	+	4.24123e21i	0.0207519	+	0.721756i
$800$	−5.67435e21			−0.956624
$801$	7.29463e20			0.121831
$802$			1.61424e21i			0.267091i
$803$	2.50475e20			0.0410580
$804$			2.52307e21i			0.409741i
$805$			1.54550e21i			0.248656i
$806$		−	2.36750e21i		−	0.377379i
$807$	2.50127e21			0.395010
$808$	1.94605e21			0.304487
$809$			1.20187e22i			1.86313i	0.363574	+	0.931565i	$0.381556\pi$
$809$			1.20187e22i			1.86313i	−0.363574	+	0.931565i	$0.618444\pi$
$810$			4.68406e20i			0.0719423i
$811$		−	2.48013e21i		−	0.377414i	−0.982033	−	0.188707i	$-0.939570\pi$
$811$		−	2.48013e21i		−	0.377414i	0.982033	−	0.188707i	$-0.0604297\pi$
$812$	−1.65720e21			−0.249864
$813$		−	6.51697e21i		−	0.973568i
$814$	−7.64916e19			−0.0113222
$815$	7.20514e20			0.105672
$816$	6.53706e20	−	1.87953e19i	0.0949963	−	0.00273132i
$817$	−5.38158e21			−0.774897
$818$	−3.19678e21			−0.456104
$819$		−	1.33960e21i		−	0.189386i
$820$	−8.37876e20			−0.117375
$821$			2.35765e21i			0.327270i	0.986521	+	0.163635i	$0.0523220\pi$
$821$			2.35765e21i			0.327270i	−0.986521	+	0.163635i	$0.947678\pi$
$822$			9.60755e20i			0.132152i
$823$		−	1.25453e22i		−	1.70995i	−0.518672	−	0.854973i	$-0.673573\pi$
$823$		−	1.25453e22i		−	1.70995i	0.518672	−	0.854973i	$-0.326427\pi$
$824$	8.24904e21			1.11416
$825$	1.15161e20			0.0154135
$826$			2.99822e21i			0.397662i
$827$		−	6.56197e21i		−	0.862468i	−0.902240	−	0.431234i	$-0.858078\pi$
$827$		−	6.56197e21i		−	0.862468i	0.902240	−	0.431234i	$-0.141922\pi$
$828$		−	2.47005e21i		−	0.321721i
$829$	−9.37218e21			−1.20971			−0.604856	−	0.796335i	$-0.706769\pi$
$829$	−9.37218e21			−1.20971			−0.604856	+	0.796335i	$0.706769\pi$
$830$		−	1.28079e21i		−	0.163830i
$831$	1.13293e21			0.143613
$832$	2.49173e21			0.313023
$833$	−1.01859e20	−	3.54270e21i	−0.0126813	−	0.441059i
$834$	1.31110e21			0.161767
$835$	−3.33530e21			−0.407837
$836$		−	1.27002e20i		−	0.0153909i
$837$	−8.91822e21			−1.07112
$838$		−	6.69383e20i		−	0.0796791i
$839$			2.22787e21i			0.262830i	0.991327	+	0.131415i	$0.0419520\pi$
$839$			2.22787e21i			0.262830i	−0.991327	+	0.131415i	$0.958048\pi$
$840$			1.27120e21i			0.148634i
$841$	6.48618e21			0.751655
$842$	−6.57241e21			−0.754890
$843$		−	9.54365e21i		−	1.08645i
$844$			8.73666e21i			0.985773i
$845$		−	1.30654e21i		−	0.146116i
$846$	1.41930e21			0.157325
$847$		−	6.80058e21i		−	0.747171i
$848$	−6.00548e20			−0.0654002
$849$	1.20017e22			1.29549
$850$	1.43441e20	+	4.98891e21i	0.0153472	+	0.533782i
$851$	−1.11754e22			−1.18520
$852$	4.23565e21			0.445270
$853$		−	7.16203e21i		−	0.746308i	−0.927769	−	0.373154i	$-0.878276\pi$
$853$		−	7.16203e21i		−	0.746308i	0.927769	−	0.373154i	$-0.121724\pi$
$854$	7.42074e20			0.0766502
$855$		−	1.06569e21i		−	0.109115i
$856$			7.25238e21i			0.736084i
$857$		−	5.97953e21i		−	0.601605i	−0.953687	−	0.300802i	$-0.902746\pi$
$857$		−	5.97953e21i		−	0.601605i	0.953687	−	0.300802i	$-0.0972544\pi$
$858$	−6.35765e19			−0.00634077
$859$	1.21777e22			1.20397			0.601987	−	0.798506i	$-0.294376\pi$
$859$	1.21777e22			1.20397			0.601987	+	0.798506i	$0.294376\pi$
$860$		−	1.28001e21i		−	0.125451i
$861$		−	4.02623e21i		−	0.391178i
$862$			5.88809e21i			0.567113i
$863$	−1.34735e22			−1.28647			−0.643236	−	0.765668i	$-0.722408\pi$
$863$	−1.34735e22			−1.28647			−0.643236	+	0.765668i	$0.722408\pi$
$864$		−	1.18004e22i		−	1.11697i
$865$	−2.64917e21			−0.248593
$866$	9.95494e21			0.926093
$867$	−4.90652e20	−	8.52545e21i	−0.0452512	−	0.786275i
$868$	−5.40539e21			−0.494230
$869$	8.29025e19			0.00751483
$870$			6.59955e20i			0.0593089i
$871$	−5.80838e21			−0.517510
$872$		−	5.73384e21i		−	0.506491i
$873$		−	3.11192e21i		−	0.272535i
$874$			9.10785e21i			0.790825i
$875$	4.41485e21			0.380063
$876$	1.20840e22			1.03141
$877$			1.55016e22i			1.31184i	0.754832	+	0.655919i	$0.227719\pi$
$877$			1.55016e22i			1.31184i	−0.754832	+	0.655919i	$0.772281\pi$
$878$		−	1.19656e22i		−	1.00398i
$879$			6.85687e21i			0.570439i
$880$	8.10177e18			0.000668282
$881$		−	2.86229e21i		−	0.234096i	−0.993126	−	0.117048i	$-0.962657\pi$
$881$		−	2.86229e21i		−	0.234096i	0.993126	−	0.117048i	$-0.0373432\pi$
$882$	−1.18555e21			−0.0961400
$883$	1.99033e22			1.60037			0.800184	−	0.599754i	$-0.204735\pi$
$883$	1.99033e22			1.60037			0.800184	+	0.599754i	$0.204735\pi$
$884$	1.61328e20	+	5.61103e21i	0.0128623	+	0.447353i
$885$	−2.43249e21			−0.192298
$886$	−7.06795e21			−0.554039
$887$		−	1.77935e22i		−	1.38304i	−0.722359	−	0.691519i	$-0.756942\pi$
$887$		−	1.77935e22i		−	1.38304i	0.722359	−	0.691519i	$-0.243058\pi$
$888$	−9.19196e21			−0.708453
$889$			8.67312e21i			0.662845i
$890$		−	6.39758e20i		−	0.0484832i
$891$			1.33227e20i			0.0100117i
$892$	−1.59532e21			−0.118881
$893$	1.06618e22			0.787853
$894$			1.88115e21i			0.137845i
$895$		−	1.49752e21i		−	0.108818i
$896$		−	7.87052e21i		−	0.567144i
$897$	−9.28854e21			−0.663749
$898$			4.21734e21i			0.298859i
$899$	−6.99001e21			−0.491225
$900$	−3.40123e21			−0.237037
$901$	2.25376e20	+	7.83865e21i	0.0155766	+	0.541758i
$902$	1.16978e20			0.00801779
$903$	6.15080e21			0.418094
$904$			2.21546e22i			1.49349i
$905$	−4.55786e21			−0.304717
$906$			1.25520e21i			0.0832246i
$907$			3.61348e21i			0.237613i	0.992917	+	0.118807i	$0.0379068\pi$
$907$			3.61348e21i			0.237613i	−0.992917	+	0.118807i	$0.962093\pi$
$908$		−	1.38602e21i		−	0.0903908i
$909$	1.86464e21			0.120605
$910$	−1.17487e21			−0.0753665
$911$		−	1.10115e22i		−	0.700579i	−0.936642	−	0.350289i	$-0.886083\pi$
$911$		−	1.10115e22i		−	0.700579i	0.936642	−	0.350289i	$-0.113917\pi$
$912$		−	1.64332e21i		−	0.103696i
$913$		−	3.64291e20i		−	0.0227991i
$914$	−1.18338e22			−0.734560
$915$			6.02051e20i			0.0370660i
$916$	−1.00237e22			−0.612087
$917$	1.74656e22			1.05782
$918$	−1.03749e22	+	2.98299e20i	−0.623253	+	0.0179197i
$919$	−1.32669e22			−0.790500			−0.395250	−	0.918574i	$-0.629342\pi$
$919$	−1.32669e22			−0.790500			−0.395250	+	0.918574i	$0.629342\pi$
$920$	−5.39595e21			−0.318903
$921$			1.36108e22i			0.797877i
$922$	1.60292e21			0.0932029
$923$			9.75092e21i			0.562384i
$924$			1.45155e20i			0.00830412i
$925$			1.53884e22i			0.873233i
$926$	1.71104e22			0.963113
$927$	7.90395e21			0.441312
$928$		−	9.24900e21i		−	0.512254i
$929$			2.12188e22i			1.16574i	0.812564	+	0.582872i	$0.198071\pi$
$929$			2.12188e22i			1.16574i	−0.812564	+	0.582872i	$0.801929\pi$
$930$			2.15262e21i			0.117313i
$931$	−8.90582e21			−0.481450
$932$		−	6.56531e21i		−	0.352076i
$933$	−2.71248e22			−1.44296
$934$	1.65941e22			0.875691
$935$	−3.04047e18	−	1.05748e20i	−0.000159167	−	0.00553588i
$936$	4.67709e21			0.242888
$937$	3.26893e22			1.68407			0.842033	−	0.539426i	$-0.181359\pi$
$937$	3.26893e22			1.68407			0.842033	+	0.539426i	$0.181359\pi$
$938$		−	6.50947e21i		−	0.332678i
$939$	1.11680e21			0.0566220
$940$			2.53591e21i			0.127548i
$941$			2.56794e21i			0.128133i	0.997946	+	0.0640667i	$0.0204070\pi$
$941$			2.56794e21i			0.128133i	−0.997946	+	0.0640667i	$0.979593\pi$
$942$		−	1.48154e22i		−	0.733384i
$943$	1.70905e22			0.839298
$944$	2.29629e21			0.111876
$945$			4.42565e21i			0.213913i
$946$			1.78705e20i			0.00856945i
$947$		−	1.27636e22i		−	0.607223i	−0.952796	−	0.303611i	$-0.901808\pi$
$947$		−	1.27636e22i		−	0.607223i	0.952796	−	0.303611i	$-0.0981924\pi$
$948$	3.99957e21			0.188778
$949$			2.78186e22i			1.30268i
$950$	1.25414e22			0.582664
$951$	−6.61789e21			−0.305046
$952$	−1.56633e22	+	4.50349e20i	−0.716316	+	0.0205955i
$953$	−1.14426e22			−0.519191			−0.259596	−	0.965717i	$-0.583589\pi$
$953$	−1.14426e22			−0.519191			−0.259596	+	0.965717i	$0.583589\pi$
$954$	2.62317e21			0.118090
$955$		−	3.40100e21i		−	0.151908i
$956$	−7.97956e21			−0.353626
$957$			1.87709e20i			0.00825362i
$958$		−	1.57713e22i		−	0.688059i
$959$			5.04980e21i			0.218592i
$960$	−2.26557e21			−0.0973068
$961$	6.65473e20			0.0283599
$962$		−	8.49542e21i		−	0.359229i
$963$			6.94898e21i			0.291557i
$964$			8.40014e21i			0.349711i
$965$	8.42955e21			0.348217
$966$		−	1.04097e22i		−	0.426687i
$967$	−3.00912e22			−1.22388			−0.611942	−	0.790903i	$-0.709611\pi$
$967$	−3.00912e22			−1.22388			−0.611942	+	0.790903i	$0.709611\pi$
$968$	2.37435e22			0.958253
$969$	−2.14495e22	+	6.16713e20i	−0.858990	+	0.0246976i
$970$	−2.72924e21			−0.108456
$971$	−1.17913e22			−0.464960			−0.232480	−	0.972601i	$-0.574684\pi$
$971$	−1.17913e22			−0.464960			−0.232480	+	0.972601i	$0.574684\pi$
$972$		−	1.21997e22i		−	0.477367i
$973$	6.89122e21			0.267578
$974$		−	1.60151e22i		−	0.617072i
$975$			1.27902e22i			0.489037i
$976$		−	5.68341e20i		−	0.0215643i
$977$	2.52864e22			0.952090			0.476045	−	0.879421i	$-0.342070\pi$
$977$	2.52864e22			0.952090			0.476045	+	0.879421i	$0.342070\pi$
$978$	−4.85302e21			−0.181330
$979$		−	1.81964e20i		−	0.00674707i
$980$		−	2.11825e21i		−	0.0779438i
$981$		−	5.49397e21i		−	0.200617i
$982$	−2.17975e22			−0.789895
$983$			2.65619e22i			0.955229i	0.878569	+	0.477615i	$0.158498\pi$
$983$			2.65619e22i			0.955229i	−0.878569	+	0.477615i	$0.841502\pi$
$984$	1.40572e22			0.501689
$985$	1.22228e22			0.432913
$986$	−8.13175e21	+	2.33803e20i	−0.285830	+	0.00821815i
$987$	−1.21858e22			−0.425084
$988$	1.41053e22			0.488321
$989$			2.61088e22i			0.897046i
$990$	−3.53882e19			−0.00120669
$991$		−	3.33152e22i		−	1.12743i	−0.825969	−	0.563715i	$-0.809371\pi$
$991$		−	3.33152e22i		−	1.12743i	0.825969	−	0.563715i	$-0.190629\pi$
$992$		−	3.01681e22i		−	1.01324i
$993$		−	7.63141e20i		−	0.0254381i
$994$	−1.09279e22			−0.361525
$995$	8.03230e21			0.263734
$996$		−	1.75750e22i		−	0.572730i
$997$		−	3.80572e22i		−	1.23090i	−0.788175	−	0.615451i	$-0.788974\pi$
$997$		−	3.80572e22i		−	1.23090i	0.788175	−	0.615451i	$-0.211026\pi$
$998$		−	2.94945e22i		−	0.946810i
$999$	−3.20017e22			−1.01960

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.16.b.a.16.9	✓	22
17.16	even	2	inner	17.16.b.a.16.10	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.16.b.a.16.9	✓	22	1.1	even	1	trivial
17.16.b.a.16.10	yes	22	17.16	even	2	inner

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:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	17.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-103.869 q^{2} +2983.33i q^{3} -21979.3 q^{4} +46006.2i q^{5} -309875. i q^{6} -1.62872e6i q^{7} +5.68653e6 q^{8} +5.44863e6 q^{9} +O(q^{10})\)	\(q-103.869 q^{2} +2983.33i q^{3} -21979.3 q^{4} +46006.2i q^{5} -309875. i q^{6} -1.62872e6i q^{7} +5.68653e6 q^{8} +5.44863e6 q^{9} -4.77860e6i q^{10} -1.35916e6i q^{11} -6.55716e7i q^{12} +1.50953e8 q^{13} +1.69173e8i q^{14} -1.37252e8 q^{15} +1.29567e8 q^{16} +(-4.86244e7 - 1.69117e9i) q^{17} -5.65942e8 q^{18} -4.25135e9 q^{19} -1.01118e9i q^{20} +4.85903e9 q^{21} +1.41174e8i q^{22} +2.06255e10i q^{23} +1.69648e10i q^{24} +2.84010e10 q^{25} -1.56792e10 q^{26} +5.90626e10i q^{27} +3.57982e10i q^{28} +4.62927e10i q^{29} +1.42561e10 q^{30} +1.50996e11i q^{31} -1.99794e11 q^{32} +4.05482e9 q^{33} +(5.05055e9 + 1.75660e11i) q^{34} +7.49314e10 q^{35} -1.19757e11 q^{36} +5.41826e11i q^{37} +4.41582e11 q^{38} +4.50342e11i q^{39} +2.61615e11i q^{40} -8.28608e11i q^{41} -5.04700e11 q^{42} +1.26585e12 q^{43} +2.98734e10i q^{44} +2.50671e11i q^{45} -2.14234e12i q^{46} -2.50786e12 q^{47} +3.86541e11i q^{48} +2.09482e12 q^{49} -2.94997e12 q^{50} +(5.04533e12 - 1.45063e11i) q^{51} -3.31784e12 q^{52} -4.63505e12 q^{53} -6.13475e12i q^{54} +6.25297e10 q^{55} -9.26178e12i q^{56} -1.26832e13i q^{57} -4.80836e12i q^{58} +1.77228e13 q^{59} +3.01670e12 q^{60} -4.38647e12i q^{61} -1.56837e13i q^{62} -8.87432e12i q^{63} +1.65067e13 q^{64} +6.94476e12i q^{65} -4.21168e11 q^{66} -3.84782e13 q^{67} +(1.06873e12 + 3.71708e13i) q^{68} -6.15327e13 q^{69} -7.78302e12 q^{70} +6.45958e13i q^{71} +3.09838e13 q^{72} +1.84287e14i q^{73} -5.62787e13i q^{74} +8.47297e13i q^{75} +9.34418e13 q^{76} -2.21369e12 q^{77} -4.67764e13i q^{78} +6.09955e13i q^{79} +5.96087e12i q^{80} -9.80216e13 q^{81} +8.60664e13i q^{82} +2.68027e14 q^{83} -1.06798e14 q^{84} +(7.78043e13 - 2.23702e12i) q^{85} -1.31482e14 q^{86} -1.38107e14 q^{87} -7.72889e12i q^{88} +1.33880e14 q^{89} -2.60368e13i q^{90} -2.45860e14i q^{91} -4.53334e14i q^{92} -4.50471e14 q^{93} +2.60488e14 q^{94} -1.95588e14i q^{95} -5.96052e14i q^{96} -5.71138e14i q^{97} -2.17586e14 q^{98} -7.40555e12i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 258 q^{2} + 414386 q^{4} - 12648450 q^{8} - 78109330 q^{9}+O(q^{10}) \) 22 * q - 258 * q^2 + 414386 * q^4 - 12648450 * q^8 - 78109330 * q^9	\( 22 q - 258 q^{2} + 414386 q^{4} - 12648450 q^{8} - 78109330 q^{9} + 702506672 q^{13} - 1787378376 q^{15} + 3524081474 q^{16} - 2245058454 q^{17} + 6803778314 q^{18} + 9958891784 q^{19} - 4168893668 q^{21} - 238696683970 q^{25} - 33467295588 q^{26} - 62541989808 q^{30} - 43445086338 q^{32} + 213283309748 q^{33} + 521524562854 q^{34} - 467785613304 q^{35} - 2300588654186 q^{36} + 3162083165688 q^{38} - 3011205093968 q^{42} - 2215728209008 q^{43} - 7793870107128 q^{47} - 1555224751482 q^{49} + 30118817411766 q^{50} - 21451923375880 q^{51} + 51163160044372 q^{52} - 6062965973460 q^{53} - 11679154373592 q^{55} + 22772194849344 q^{59} - 86295684546192 q^{60} - 28567749560318 q^{64} + 251781147903680 q^{66} + 153875904272808 q^{67} - 48849686100870 q^{68} + 60664072036996 q^{69} - 150925771647648 q^{70} - 293782759569702 q^{72} - 388479948338264 q^{76} - 622427249887884 q^{77} + 983865215787034 q^{81} - 15\!\cdots\!44 q^{83}+ \cdots + 26\!\cdots\!90 q^{98}+O(q^{100}) \) 22 * q - 258 * q^2 + 414386 * q^4 - 12648450 * q^8 - 78109330 * q^9 + 702506672 * q^13 - 1787378376 * q^15 + 3524081474 * q^16 - 2245058454 * q^17 + 6803778314 * q^18 + 9958891784 * q^19 - 4168893668 * q^21 - 238696683970 * q^25 - 33467295588 * q^26 - 62541989808 * q^30 - 43445086338 * q^32 + 213283309748 * q^33 + 521524562854 * q^34 - 467785613304 * q^35 - 2300588654186 * q^36 + 3162083165688 * q^38 - 3011205093968 * q^42 - 2215728209008 * q^43 - 7793870107128 * q^47 - 1555224751482 * q^49 + 30118817411766 * q^50 - 21451923375880 * q^51 + 51163160044372 * q^52 - 6062965973460 * q^53 - 11679154373592 * q^55 + 22772194849344 * q^59 - 86295684546192 * q^60 - 28567749560318 * q^64 + 251781147903680 * q^66 + 153875904272808 * q^67 - 48849686100870 * q^68 + 60664072036996 * q^69 - 150925771647648 * q^70 - 293782759569702 * q^72 - 388479948338264 * q^76 - 622427249887884 * q^77 + 983865215787034 * q^81 - 1541046988482144 * q^83 + 1542636638603936 * q^84 + 94526232685248 * q^85 + 102594718370712 * q^86 - 428830075363560 * q^87 - 894061425316800 * q^89 + 2342465228549812 * q^93 + 2620489835637760 * q^94 + 2662999543720290 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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