LMFDB - Embedded newform 17.16.b.a.16.6

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			16.6
Character	$\chi$	$=$	17.16
Dual form			17.16.b.a.16.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-252.822 q^{2} -1625.59i q^{3} +31151.0 q^{4} -14176.6i q^{5} +410984. i q^{6} -2.61491e6i q^{7} +408809. q^{8} +1.17064e7 q^{9} +O(q^{10})$	\(q-252.822 q^{2} -1625.59i q^{3} +31151.0 q^{4} -14176.6i q^{5} +410984. i q^{6} -2.61491e6i q^{7} +408809. q^{8} +1.17064e7 q^{9} +3.58415e6i q^{10} +9.06238e7i q^{11} -5.06386e7i q^{12} -3.07328e8 q^{13} +6.61106e8i q^{14} -2.30452e7 q^{15} -1.12411e9 q^{16} +(1.04424e9 + 1.33116e9i) q^{17} -2.95963e9 q^{18} +3.48752e9 q^{19} -4.41614e8i q^{20} -4.25076e9 q^{21} -2.29117e10i q^{22} +1.84334e10i q^{23} -6.64554e8i q^{24} +3.03166e10 q^{25} +7.76993e10 q^{26} -4.23551e10i q^{27} -8.14570e10i q^{28} -1.65191e11i q^{29} +5.82634e9 q^{30} -4.60451e10i q^{31} +2.70805e11 q^{32} +1.47317e11 q^{33} +(-2.64006e11 - 3.36547e11i) q^{34} -3.70704e10 q^{35} +3.64666e11 q^{36} +7.57959e11i q^{37} -8.81721e11 q^{38} +4.99588e11i q^{39} -5.79551e9i q^{40} -1.84594e12i q^{41} +1.07468e12 q^{42} -2.12614e11 q^{43} +2.82302e12i q^{44} -1.65956e11i q^{45} -4.66036e12i q^{46} +5.74469e12 q^{47} +1.82734e12i q^{48} -2.09018e12 q^{49} -7.66471e12 q^{50} +(2.16392e12 - 1.69750e12i) q^{51} -9.57358e12 q^{52} +2.93991e12 q^{53} +1.07083e13i q^{54} +1.28473e12 q^{55} -1.06900e12i q^{56} -5.66926e12i q^{57} +4.17639e13i q^{58} -1.35404e13 q^{59} -7.17882e11 q^{60} +6.99499e12i q^{61} +1.16412e13i q^{62} -3.06111e13i q^{63} -3.16305e13 q^{64} +4.35685e12i q^{65} -3.72449e13 q^{66} +2.93685e13 q^{67} +(3.25291e13 + 4.14670e13i) q^{68} +2.99650e13 q^{69} +9.37221e12 q^{70} -1.16827e14i q^{71} +4.78567e12 q^{72} +4.82393e13i q^{73} -1.91629e14i q^{74} -4.92822e13i q^{75} +1.08640e14 q^{76} +2.36973e14 q^{77} -1.26307e14i q^{78} -2.99848e14i q^{79} +1.59360e13i q^{80} +9.91219e13 q^{81} +4.66694e14i q^{82} -8.36166e13 q^{83} -1.32415e14 q^{84} +(1.88713e13 - 1.48037e13i) q^{85} +5.37534e13 q^{86} -2.68532e14 q^{87} +3.70478e13i q^{88} -2.13650e14 q^{89} +4.19574e13i q^{90} +8.03634e14i q^{91} +5.74218e14i q^{92} -7.48502e13 q^{93} -1.45238e15 q^{94} -4.94410e13i q^{95} -4.40216e14i q^{96} -8.90136e14i q^{97} +5.28443e14 q^{98} +1.06088e15i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−252.822			−1.39666			−0.698329	−	0.715777i	$-0.746073\pi$
$2$	−252.822			−1.39666			−0.698329	+	0.715777i	$0.746073\pi$
$3$		−	1625.59i		−	0.429141i	−0.976708	−	0.214571i	$-0.931165\pi$
$3$		−	1625.59i		−	0.429141i	0.976708	−	0.214571i	$-0.0688352\pi$
$4$	31151.0			0.950654
$5$		−	14176.6i		−	0.0811514i	−0.999176	−	0.0405757i	$-0.987081\pi$
$5$		−	14176.6i		−	0.0811514i	0.999176	−	0.0405757i	$-0.0129192\pi$
$6$			410984.i			0.599364i
$7$		−	2.61491e6i		−	1.20011i	−0.799959	−	0.600055i	$-0.795145\pi$
$7$		−	2.61491e6i		−	1.20011i	0.799959	−	0.600055i	$-0.204855\pi$
$8$	408809.			0.0689200
$9$	1.17064e7			0.815838
$10$			3.58415e6i			0.113341i
$11$			9.06238e7i			1.40216i	0.713084	+	0.701079i	$0.247298\pi$
$11$			9.06238e7i			1.40216i	−0.713084	+	0.701079i	$0.752702\pi$
$12$		−	5.06386e7i		−	0.407965i
$13$	−3.07328e8			−1.35840			−0.679199	−	0.733954i	$-0.737673\pi$
$13$	−3.07328e8			−1.35840			−0.679199	+	0.733954i	$0.737673\pi$
$14$			6.61106e8i			1.67614i
$15$	−2.30452e7			−0.0348254
$16$	−1.12411e9			−1.04691
$17$	1.04424e9	+	1.33116e9i	0.617209	+	0.786799i
$17$	1.04424e9	+	1.33116e9i	0.617209	+	0.786799i
$18$	−2.95963e9			−1.13945
$19$	3.48752e9			0.895085			0.447542	−	0.894263i	$-0.352299\pi$
$19$	3.48752e9			0.895085			0.447542	+	0.894263i	$0.352299\pi$
$20$		−	4.41614e8i		−	0.0771468i
$21$	−4.25076e9			−0.515017
$22$		−	2.29117e10i		−	1.95833i
$23$			1.84334e10i			1.12888i	0.825476	+	0.564438i	$0.190907\pi$
$23$			1.84334e10i			1.12888i	−0.825476	+	0.564438i	$0.809093\pi$
$24$		−	6.64554e8i		−	0.0295764i
$25$	3.03166e10			0.993414
$26$	7.76993e10			1.89722
$27$		−	4.23551e10i		−	0.779251i
$28$		−	8.14570e10i		−	1.14089i
$29$		−	1.65191e11i		−	1.77829i	−0.457630	−	0.889143i	$-0.651302\pi$
$29$		−	1.65191e11i		−	1.77829i	0.457630	−	0.889143i	$-0.348698\pi$
$30$	5.82634e9			0.0486392
$31$		−	4.60451e10i		−	0.300587i	−0.988641	−	0.150294i	$-0.951978\pi$
$31$		−	4.60451e10i		−	0.300587i	0.988641	−	0.150294i	$-0.0480219\pi$
$32$	2.70805e11			1.39326
$33$	1.47317e11			0.601724
$34$	−2.64006e11	−	3.36547e11i	−0.862030	−	1.09889i
$35$	−3.70704e10			−0.0973906
$36$	3.64666e11			0.775579
$37$			7.57959e11i			1.31260i	0.754499	+	0.656301i	$0.227880\pi$
$37$			7.57959e11i			1.31260i	−0.754499	+	0.656301i	$0.772120\pi$
$38$	−8.81721e11			−1.25013
$39$			4.99588e11i			0.582945i
$40$		−	5.79551e9i		−	0.00559296i
$41$		−	1.84594e12i		−	1.48026i	−0.672463	−	0.740131i	$-0.734764\pi$
$41$		−	1.84594e12i		−	1.48026i	0.672463	−	0.740131i	$-0.265236\pi$
$42$	1.07468e12			0.719302
$43$	−2.12614e11			−0.119283			−0.0596413	−	0.998220i	$-0.518996\pi$
$43$	−2.12614e11			−0.119283			−0.0596413	+	0.998220i	$0.518996\pi$
$44$			2.82302e12i			1.33297i
$45$		−	1.65956e11i		−	0.0662063i
$46$		−	4.66036e12i		−	1.57665i
$47$	5.74469e12			1.65399			0.826994	−	0.562211i	$-0.190049\pi$
$47$	5.74469e12			1.65399			0.826994	+	0.562211i	$0.190049\pi$
$48$			1.82734e12i			0.449273i
$49$	−2.09018e12			−0.440263
$50$	−7.66471e12			−1.38746
$51$	2.16392e12	−	1.69750e12i	0.337648	−	0.264870i
$52$	−9.57358e12			−1.29137
$53$	2.93991e12			0.343767			0.171884	−	0.985117i	$-0.445015\pi$
$53$	2.93991e12			0.343767			0.171884	+	0.985117i	$0.445015\pi$
$54$			1.07083e13i			1.08835i
$55$	1.28473e12			0.113787
$56$		−	1.06900e12i		−	0.0827116i
$57$		−	5.66926e12i		−	0.384118i
$58$			4.17639e13i			2.48366i
$59$	−1.35404e13			−0.708341			−0.354171	−	0.935181i	$-0.615237\pi$
$59$	−1.35404e13			−0.708341			−0.354171	+	0.935181i	$0.615237\pi$
$60$	−7.17882e11			−0.0331069
$61$			6.99499e12i			0.284979i	0.989796	+	0.142490i	$0.0455108\pi$
$61$			6.99499e12i			0.284979i	−0.989796	+	0.142490i	$0.954489\pi$
$62$			1.16412e13i			0.419817i
$63$		−	3.06111e13i		−	0.979095i
$64$	−3.16305e13			−0.898992
$65$			4.35685e12i			0.110236i
$66$	−3.72449e13			−0.840403
$67$	2.93685e13			0.592000			0.296000	−	0.955188i	$-0.404347\pi$
$67$	2.93685e13			0.592000			0.296000	+	0.955188i	$0.404347\pi$
$68$	3.25291e13	+	4.14670e13i	0.586752	+	0.747974i
$69$	2.99650e13			0.484447
$70$	9.37221e12			0.136021
$71$		−	1.16827e14i		−	1.52442i	−0.647330	−	0.762209i	$-0.724115\pi$
$71$		−	1.16827e14i		−	1.52442i	0.647330	−	0.762209i	$-0.275885\pi$
$72$	4.78567e12			0.0562276
$73$			4.82393e13i			0.511069i	0.966800	+	0.255535i	$0.0822515\pi$
$73$			4.82393e13i			0.511069i	−0.966800	+	0.255535i	$0.917748\pi$
$74$		−	1.91629e14i		−	1.83326i
$75$		−	4.92822e13i		−	0.426315i
$76$	1.08640e14			0.850916
$77$	2.36973e14			1.68274
$78$		−	1.26307e14i		−	0.814174i
$79$		−	2.99848e14i		−	1.75670i	−0.478015	−	0.878352i	$-0.658644\pi$
$79$		−	2.99848e14i		−	1.75670i	0.478015	−	0.878352i	$-0.341356\pi$
$80$			1.59360e13i			0.0849583i
$81$	9.91219e13			0.481429
$82$			4.66694e14i			2.06742i
$83$	−8.36166e13			−0.338226			−0.169113	−	0.985597i	$-0.554090\pi$
$83$	−8.36166e13			−0.338226			−0.169113	+	0.985597i	$0.554090\pi$
$84$	−1.32415e14			−0.489603
$85$	1.88713e13	−	1.48037e13i	0.0638498	−	0.0500874i
$86$	5.37534e13			0.166597
$87$	−2.68532e14			−0.763136
$88$			3.70478e13i			0.0966368i
$89$	−2.13650e14			−0.512009			−0.256004	−	0.966676i	$-0.582406\pi$
$89$	−2.13650e14			−0.512009			−0.256004	+	0.966676i	$0.582406\pi$
$90$			4.19574e13i			0.0924676i
$91$			8.03634e14i			1.63023i
$92$			5.74218e14i			1.07317i
$93$	−7.48502e13			−0.128994
$94$	−1.45238e15			−2.31006
$95$		−	4.94410e13i		−	0.0726374i
$96$		−	4.40216e14i		−	0.597904i
$97$		−	8.90136e14i		−	1.11858i	−0.828971	−	0.559292i	$-0.811073\pi$
$97$		−	8.90136e14i		−	1.11858i	0.828971	−	0.559292i	$-0.188927\pi$
$98$	5.28443e14			0.614898
$99$			1.06088e15i			1.14393i
$100$	9.44393e14			0.944393
$101$	1.25424e15			1.16405			0.582024	−	0.813171i	$-0.302261\pi$
$101$	1.25424e15			1.16405			0.582024	+	0.813171i	$0.302261\pi$
$102$	−5.47086e14	+	4.29165e14i	−0.471579	+	0.369933i
$103$	−3.81543e14			−0.305678			−0.152839	−	0.988251i	$-0.548842\pi$
$103$	−3.81543e14			−0.305678			−0.152839	+	0.988251i	$0.548842\pi$
$104$	−1.25638e14			−0.0936208
$105$			6.02611e13i			0.0417943i
$106$	−7.43273e14			−0.480125
$107$		−	8.87823e14i		−	0.534500i	−0.963627	−	0.267250i	$-0.913885\pi$
$107$		−	8.87823e14i		−	0.534500i	0.963627	−	0.267250i	$-0.0861150\pi$
$108$		−	1.31940e15i		−	0.740798i
$109$		−	9.21872e14i		−	0.483028i	−0.970397	−	0.241514i	$-0.922356\pi$
$109$		−	9.21872e14i		−	0.483028i	0.970397	−	0.241514i	$-0.0776439\pi$
$110$	−3.24809e14			−0.158922
$111$	1.23213e15			0.563292
$112$			2.93945e15i			1.25641i
$113$			2.13896e15i			0.855292i	0.903946	+	0.427646i	$0.140657\pi$
$113$			2.13896e15i			0.855292i	−0.903946	+	0.427646i	$0.859343\pi$
$114$			1.43331e15i			0.536481i
$115$	2.61322e14			0.0916098
$116$		−	5.14587e15i		−	1.69053i
$117$	−3.59770e15			−1.10823
$118$	3.42332e15			0.989310
$119$	3.48086e15	−	2.73058e15i	0.944245	−	0.740719i
$120$	−9.42109e12			−0.00240017
$121$	−4.03542e15			−0.966047
$122$		−	1.76849e15i		−	0.398019i
$123$	−3.00073e15			−0.635242
$124$		−	1.43435e15i		−	0.285754i
$125$		−	8.62420e14i		−	0.161768i
$126$			7.73916e15i			1.36746i
$127$	9.73409e15			1.62094			0.810471	−	0.585779i	$-0.199211\pi$
$127$	9.73409e15			1.62094			0.810471	+	0.585779i	$0.199211\pi$
$128$	−8.76842e14			−0.137672
$129$			3.45621e14i			0.0511891i
$130$		−	1.10151e15i		−	0.153962i
$131$		−	1.38930e15i		−	0.183342i	−0.995789	−	0.0916711i	$-0.970779\pi$
$131$		−	1.38930e15i		−	0.183342i	0.995789	−	0.0916711i	$-0.0292208\pi$
$132$	4.58906e15			0.572031
$133$		−	9.11953e15i		−	1.07420i
$134$	−7.42502e15			−0.826821
$135$	−6.00450e14			−0.0632373
$136$	4.26894e14	+	5.44191e14i	0.0425381	+	0.0542262i
$137$	1.87525e16			1.76871			0.884353	−	0.466818i	$-0.154600\pi$
$137$	1.87525e16			1.76871			0.884353	+	0.466818i	$0.154600\pi$
$138$	−7.57582e15			−0.676607
$139$		−	2.40632e14i		−	0.0203584i	−0.999948	−	0.0101792i	$-0.996760\pi$
$139$		−	2.40632e14i		−	0.0203584i	0.999948	−	0.0101792i	$-0.00324019\pi$
$140$	−1.15478e15			−0.0925847
$141$		−	9.33848e15i		−	0.709795i
$142$			2.95364e16i			2.12909i
$143$		−	2.78512e16i		−	1.90469i
$144$	−1.31593e16			−0.854110
$145$	−2.34184e15			−0.144310
$146$		−	1.21960e16i		−	0.713789i
$147$			3.39776e15i			0.188935i
$148$			2.36112e16i			1.24783i
$149$	2.28747e16			1.14937			0.574683	−	0.818376i	$-0.305125\pi$
$149$	2.28747e16			1.14937			0.574683	+	0.818376i	$0.305125\pi$
$150$			1.24596e16i			0.595417i
$151$	−2.06204e16			−0.937496			−0.468748	−	0.883332i	$-0.655295\pi$
$151$	−2.06204e16			−0.937496			−0.468748	+	0.883332i	$0.655295\pi$
$152$	1.42573e15			0.0616893
$153$	1.22242e16	+	1.55831e16i	0.503542	+	0.641900i
$154$	−5.99119e16			−2.35022
$155$	−6.52761e14			−0.0243931
$156$			1.55627e16i			0.554179i
$157$	−4.24766e16			−1.44179			−0.720895	−	0.693044i	$-0.756269\pi$
$157$	−4.24766e16			−1.44179			−0.720895	+	0.693044i	$0.756269\pi$
$158$			7.58083e16i			2.45351i
$159$		−	4.77907e15i		−	0.147525i
$160$		−	3.83908e15i		−	0.113065i
$161$	4.82016e16			1.35477
$162$	−2.50602e16			−0.672391
$163$			2.93159e16i			0.751097i	0.926803	+	0.375548i	$0.122546\pi$
$163$			2.93159e16i			0.751097i	−0.926803	+	0.375548i	$0.877454\pi$
$164$		−	5.75029e16i		−	1.40722i
$165$		−	2.08844e15i		−	0.0488307i
$166$	2.11401e16			0.472386
$167$		−	3.49470e16i		−	0.746510i	−0.927729	−	0.373255i	$-0.878242\pi$
$167$		−	3.49470e16i		−	0.746510i	0.927729	−	0.373255i	$-0.121758\pi$
$168$	−1.73775e15			−0.0354950
$169$	4.32646e16			0.845245
$170$	−4.77108e15	+	3.74270e15i	−0.0891764	+	0.0699549i
$171$	4.08262e16			0.730244
$172$	−6.62313e15			−0.113397
$173$		−	6.85197e16i		−	1.12323i	−0.827398	−	0.561616i	$-0.810180\pi$
$173$		−	6.85197e16i		−	1.12323i	0.827398	−	0.561616i	$-0.189820\pi$
$174$	6.78909e16			1.06584
$175$		−	7.92751e16i		−	1.19221i
$176$		−	1.01871e17i		−	1.46793i
$177$			2.20111e16i			0.303978i
$178$	5.40154e16			0.715101
$179$	−3.69630e16			−0.469213			−0.234606	−	0.972090i	$-0.575380\pi$
$179$	−3.69630e16			−0.469213			−0.234606	+	0.972090i	$0.575380\pi$
$180$		−	5.16970e15i		−	0.0629393i
$181$			8.34399e16i			0.974506i	0.873261	+	0.487253i	$0.162001\pi$
$181$			8.34399e16i			0.974506i	−0.873261	+	0.487253i	$0.837999\pi$
$182$		−	2.03176e17i		−	2.27687i
$183$	1.13710e16			0.122296
$184$			7.53573e15i			0.0778021i
$185$	1.07453e16			0.106519
$186$	1.89238e16			0.180161
$187$	−1.20635e17	+	9.46327e16i	−1.10322	+	0.865424i
$188$	1.78953e17			1.57237
$189$	−1.10755e17			−0.935187
$190$			1.24998e16i			0.101450i
$191$	6.97699e16			0.544400			0.272200	−	0.962241i	$-0.412249\pi$
$191$	6.97699e16			0.544400			0.272200	+	0.962241i	$0.412249\pi$
$192$			5.14180e16i			0.385795i
$193$			7.23313e16i			0.521971i	0.965343	+	0.260985i	$0.0840475\pi$
$193$			7.23313e16i			0.521971i	−0.965343	+	0.260985i	$0.915953\pi$
$194$			2.25046e17i			1.56228i
$195$	7.08244e15			0.0473068
$196$	−6.51112e16			−0.418538
$197$			1.26989e17i			0.785721i	0.919598	+	0.392861i	$0.128515\pi$
$197$			1.26989e17i			0.785721i	−0.919598	+	0.392861i	$0.871485\pi$
$198$		−	2.68213e17i		−	1.59768i
$199$			1.09538e17i			0.628298i	0.949374	+	0.314149i	$0.101719\pi$
$199$			1.09538e17i			0.628298i	−0.949374	+	0.314149i	$0.898281\pi$
$200$	1.23937e16			0.0684662
$201$		−	4.77411e16i		−	0.254052i
$202$	−3.17100e17			−1.62578
$203$	−4.31959e17			−2.13414
$204$	6.74082e16	−	5.28788e16i	0.320986	−	0.251800i
$205$	−2.61691e16			−0.120125
$206$	9.64625e16			0.426928
$207$			2.15788e17i			0.920979i
$208$	3.45471e17			1.42212
$209$			3.16052e17i			1.25505i
$210$		−	1.52353e16i		−	0.0583724i
$211$		−	2.25782e17i		−	0.834779i	−0.908728	−	0.417389i	$-0.862945\pi$
$211$		−	2.25782e17i		−	0.834779i	0.908728	−	0.417389i	$-0.137055\pi$
$212$	9.15811e16			0.326804
$213$	−1.89912e17			−0.654191
$214$			2.24461e17i			0.746514i
$215$			3.01413e15i			0.00967995i
$216$		−	1.73151e16i		−	0.0537060i
$217$	−1.20404e17			−0.360738
$218$			2.33070e17i			0.674624i
$219$	7.84172e16			0.219321
$220$	4.00207e16			0.108172
$221$	−3.20923e17	−	4.09103e17i	−0.838415	−	1.06879i
$222$	−3.11509e17			−0.786726
$223$	4.39584e17			1.07339			0.536693	−	0.843778i	$-0.319674\pi$
$223$	4.39584e17			1.07339			0.536693	+	0.843778i	$0.319674\pi$
$224$		−	7.08129e17i		−	1.67206i
$225$	3.54898e17			0.810465
$226$		−	5.40776e17i		−	1.19455i
$227$			7.84825e17i			1.67718i	0.544765	+	0.838589i	$0.316619\pi$
$227$			7.84825e17i			1.67718i	−0.544765	+	0.838589i	$0.683381\pi$
$228$		−	1.76603e17i		−	0.365163i
$229$	5.48895e17			1.09830			0.549152	−	0.835722i	$-0.314951\pi$
$229$	5.48895e17			1.09830			0.549152	+	0.835722i	$0.314951\pi$
$230$	−6.60679e16			−0.127948
$231$		−	3.85219e17i		−	0.722135i
$232$		−	6.75316e16i		−	0.122560i
$233$			5.07193e17i			0.891259i	0.895217	+	0.445630i	$0.147020\pi$
$233$			5.07193e17i			0.891259i	−0.895217	+	0.445630i	$0.852980\pi$
$234$	9.09578e17			1.54782
$235$		−	8.14399e16i		−	0.134223i
$236$	−4.21798e17			−0.673387
$237$	−4.87429e17			−0.753874
$238$	−8.80039e17	+	6.90352e17i	−1.31879	+	1.03453i
$239$	9.33234e16			0.135521			0.0677605	−	0.997702i	$-0.478415\pi$
$239$	9.33234e16			0.135521			0.0677605	+	0.997702i	$0.478415\pi$
$240$	2.59054e16			0.0364591
$241$		−	7.08439e16i		−	0.0966439i	−0.998832	−	0.0483220i	$-0.984613\pi$
$241$		−	7.08439e16i		−	0.0966439i	0.998832	−	0.0483220i	$-0.0153874\pi$
$242$	1.02024e18			1.34924
$243$		−	7.68880e17i		−	0.985852i
$244$			2.17901e17i			0.270917i
$245$			2.96315e16i			0.0357280i
$246$	7.58651e17			0.887215
$247$	−1.07181e18			−1.21588
$248$		−	1.88236e16i		−	0.0207165i
$249$			1.35926e17i			0.145147i
$250$			2.18039e17i			0.225935i
$251$	2.42932e17			0.244305			0.122153	−	0.992511i	$-0.461020\pi$
$251$	2.42932e17			0.244305			0.122153	+	0.992511i	$0.461020\pi$
$252$		−	9.53567e17i		−	0.930780i
$253$	−1.67050e18			−1.58286
$254$	−2.46099e18			−2.26390
$255$	−2.40647e16	−	3.06769e16i	−0.0214946	−	0.0274006i
$256$	1.25815e18			1.09127
$257$	1.52996e18			1.28879			0.644394	−	0.764694i	$-0.277110\pi$
$257$	1.52996e18			1.28879			0.644394	+	0.764694i	$0.277110\pi$
$258$		−	8.73807e16i		−	0.0714937i
$259$	1.98199e18			1.57527
$260$			1.35720e17i			0.104796i
$261$		−	1.93379e18i		−	1.45079i
$262$			3.51247e17i			0.256066i
$263$	1.91880e18			1.35944			0.679721	−	0.733471i	$-0.262101\pi$
$263$	1.91880e18			1.35944			0.679721	+	0.733471i	$0.262101\pi$
$264$	6.02244e16			0.0414708
$265$		−	4.16778e16i		−	0.0278972i
$266$			2.30562e18i			1.50029i
$267$			3.47306e17i			0.219724i
$268$	9.14860e17			0.562787
$269$		−	2.24920e18i		−	1.34551i	−0.739867	−	0.672753i	$-0.765112\pi$
$269$		−	2.24920e18i		−	1.34551i	0.739867	−	0.672753i	$-0.234888\pi$
$270$	1.51807e17			0.0883209
$271$	−6.88632e17			−0.389688			−0.194844	−	0.980834i	$-0.562420\pi$
$271$	−6.88632e17			−0.389688			−0.194844	+	0.980834i	$0.562420\pi$
$272$	−1.17384e18	−	1.49638e18i	−0.646163	−	0.823709i
$273$	1.30638e18			0.699598
$274$	−4.74106e18			−2.47028
$275$			2.74740e18i			1.39292i
$276$	9.33441e17			0.460541
$277$			2.94259e18i			1.41296i	0.707731	+	0.706482i	$0.249719\pi$
$277$			2.94259e18i			1.41296i	−0.707731	+	0.706482i	$0.750281\pi$
$278$			6.08372e16i			0.0284337i
$279$		−	5.39021e17i		−	0.245230i
$280$	−1.51547e16			−0.00671216
$281$	−4.07658e18			−1.75792			−0.878958	−	0.476899i	$-0.841761\pi$
$281$	−4.07658e18			−1.75792			−0.878958	+	0.476899i	$0.841761\pi$
$282$			2.36097e18i			0.991341i
$283$		−	1.52576e18i		−	0.623863i	−0.950105	−	0.311931i	$-0.899024\pi$
$283$		−	1.52576e18i		−	0.623863i	0.950105	−	0.311931i	$-0.100976\pi$
$284$		−	3.63927e18i		−	1.44919i
$285$	−8.03706e16			−0.0311717
$286$			7.04140e18i			2.66020i
$287$	−4.82696e18			−1.77648
$288$	3.17014e18			1.13667
$289$	−6.81560e17	+	2.78010e18i	−0.238106	+	0.971239i
$290$	5.92069e17			0.201552
$291$	−1.44699e18			−0.480030
$292$			1.50270e18i			0.485850i
$293$	3.63048e18			1.14408			0.572041	−	0.820225i	$-0.306152\pi$
$293$	3.63048e18			1.14408			0.572041	+	0.820225i	$0.306152\pi$
$294$		−	8.59030e17i		−	0.263878i
$295$			1.91957e17i			0.0574829i
$296$			3.09861e17i			0.0904646i
$297$	3.83838e18			1.09263
$298$	−5.78323e18			−1.60527
$299$		−	5.66509e18i		−	1.53346i
$300$		−	1.53519e18i		−	0.405278i
$301$			5.55965e17i			0.143152i
$302$	5.21329e18			1.30936
$303$		−	2.03888e18i		−	0.499542i
$304$	−3.92036e18			−0.937075
$305$	9.91649e16			0.0231265
$306$	−3.09056e18	−	3.93975e18i	−0.703277	−	0.896515i
$307$	1.53509e17			0.0340877			0.0170438	−	0.999855i	$-0.494575\pi$
$307$	1.53509e17			0.0340877			0.0170438	+	0.999855i	$0.494575\pi$
$308$	7.38194e18			1.59971
$309$			6.20231e17i			0.131179i
$310$	1.65032e17			0.0340688
$311$		−	1.07356e17i		−	0.0216334i	−0.999941	−	0.0108167i	$-0.996557\pi$
$311$		−	1.07356e17i		−	0.0216334i	0.999941	−	0.0108167i	$-0.00344312\pi$
$312$			2.04236e17i			0.0401766i
$313$		−	2.94846e17i		−	0.0566255i	−0.999599	−	0.0283128i	$-0.990987\pi$
$313$		−	2.94846e17i		−	0.0566255i	0.999599	−	0.0283128i	$-0.00901343\pi$
$314$	1.07390e19			2.01369
$315$	−4.33960e17			−0.0794549
$316$		−	9.34058e18i		−	1.67002i
$317$		−	2.24754e18i		−	0.392431i	−0.980561	−	0.196216i	$-0.937135\pi$
$317$		−	2.24754e18i		−	0.392431i	0.980561	−	0.196216i	$-0.0628652\pi$
$318$			1.20825e18i			0.206042i
$319$	1.49702e19			2.49344
$320$			4.48411e17i			0.0729545i
$321$	−1.44323e18			−0.229376
$322$	−1.21864e19			−1.89216
$323$	3.64179e18	+	4.64245e18i	0.552454	+	0.704252i
$324$	3.08775e18			0.457672
$325$	−9.31714e18			−1.34945
$326$		−	7.41170e18i		−	1.04903i
$327$	−1.49858e18			−0.207287
$328$		−	7.54637e17i		−	0.102020i
$329$		−	1.50218e19i		−	1.98497i
$330$			5.28005e17i			0.0681998i
$331$	1.51928e18			0.191835			0.0959176	−	0.995389i	$-0.469421\pi$
$331$	1.51928e18			0.191835			0.0959176	+	0.995389i	$0.469421\pi$
$332$	−2.60474e18			−0.321536
$333$			8.87296e18i			1.07087i
$334$			8.83536e18i			1.04262i
$335$		−	4.16345e17i		−	0.0480416i
$336$	4.77833e18			0.539177
$337$			9.76836e18i			1.07795i	0.842323	+	0.538973i	$0.181188\pi$
$337$			9.76836e18i			1.07795i	−0.842323	+	0.538973i	$0.818812\pi$
$338$	−1.09382e19			−1.18052
$339$	3.47706e18			0.367041
$340$	5.87860e17	−	4.61150e17i	0.0606991	−	0.0476157i
$341$	4.17278e18			0.421471
$342$	−1.03218e19			−1.01990
$343$		−	6.94881e18i		−	0.671745i
$344$	−8.69183e16			−0.00822097
$345$		−	4.24801e17i		−	0.0393136i
$346$			1.73233e19i			1.56877i
$347$		−	6.92732e18i		−	0.613895i	−0.951726	−	0.306947i	$-0.900692\pi$
$347$		−	6.92732e18i		−	0.613895i	0.951726	−	0.306947i	$-0.0993076\pi$
$348$	−8.36505e18			−0.725478
$349$	−1.00159e19			−0.850161			−0.425080	−	0.905156i	$-0.639754\pi$
$349$	−1.00159e19			−0.850161			−0.425080	+	0.905156i	$0.639754\pi$
$350$			2.00425e19i			1.66510i
$351$			1.30169e19i			1.05853i
$352$			2.45413e19i			1.95357i
$353$	−2.07450e18			−0.161660			−0.0808302	−	0.996728i	$-0.525757\pi$
$353$	−2.07450e18			−0.161660			−0.0808302	+	0.996728i	$0.525757\pi$
$354$		−	5.56490e18i		−	0.424554i
$355$	−1.65620e18			−0.123709
$356$	−6.65541e18			−0.486743
$357$	−4.43880e18	−	5.65844e18i	−0.317873	−	0.405215i
$358$	9.34507e18			0.655330
$359$	6.07138e18			0.416945			0.208473	−	0.978028i	$-0.433151\pi$
$359$	6.07138e18			0.416945			0.208473	+	0.978028i	$0.433151\pi$
$360$		−	6.78444e16i		−	0.00456294i
$361$	−3.01836e18			−0.198823
$362$		−	2.10954e19i		−	1.36105i
$363$			6.55991e18i			0.414571i
$364$			2.50340e19i			1.54978i
$365$	6.83868e17			0.0414740
$366$	−2.87483e18			−0.170806
$367$		−	2.03535e19i		−	1.18480i	−0.805645	−	0.592399i	$-0.798181\pi$
$367$		−	2.03535e19i		−	1.18480i	0.805645	−	0.592399i	$-0.201819\pi$
$368$		−	2.07212e19i		−	1.18183i
$369$		−	2.16093e19i		−	1.20765i
$370$	−2.71664e18			−0.148771
$371$		−	7.68758e18i		−	0.412559i
$372$	−2.33166e18			−0.122629
$373$	4.29198e17			0.0221229			0.0110614	−	0.999939i	$-0.496479\pi$
$373$	4.29198e17			0.0221229			0.0110614	+	0.999939i	$0.496479\pi$
$374$	3.04992e19	−	2.39252e19i	1.54082	−	1.20870i
$375$	−1.40194e18			−0.0694215
$376$	2.34848e18			0.113993
$377$			5.07678e19i			2.41562i
$378$	2.80012e19			1.30614
$379$		−	6.89973e18i		−	0.315528i	−0.987477	−	0.157764i	$-0.949571\pi$
$379$		−	6.89973e18i		−	0.315528i	0.987477	−	0.157764i	$-0.0504285\pi$
$380$		−	1.54014e18i		−	0.0690530i
$381$		−	1.58236e19i		−	0.695613i
$382$	−1.76394e19			−0.760340
$383$	1.77704e19			0.751113			0.375557	−	0.926799i	$-0.377452\pi$
$383$	1.77704e19			0.751113			0.375557	+	0.926799i	$0.377452\pi$
$384$			1.42538e18i			0.0590809i
$385$		−	3.35946e18i		−	0.136557i
$386$		−	1.82869e19i		−	0.729015i
$387$	−2.48893e18			−0.0973153
$388$		−	2.77286e19i		−	1.06338i
$389$	1.50257e19			0.565212			0.282606	−	0.959236i	$-0.408801\pi$
$389$	1.50257e19			0.565212			0.282606	+	0.959236i	$0.408801\pi$
$390$	−1.79060e18			−0.0660714
$391$	−2.45378e19	+	1.92488e19i	−0.888198	+	0.696752i
$392$	−8.54484e17			−0.0303430
$393$	−2.25843e18			−0.0786797
$394$		−	3.21056e19i		−	1.09738i
$395$	−4.25082e18			−0.142559
$396$			3.30474e19i			1.08748i
$397$			3.06167e19i			0.988620i	0.869286	+	0.494310i	$0.164579\pi$
$397$			3.06167e19i			0.988620i	−0.869286	+	0.494310i	$0.835421\pi$
$398$		−	2.76936e19i		−	0.877518i
$399$	−1.48246e19			−0.460984
$400$	−3.40793e19			−1.04002
$401$			4.84183e19i			1.45020i	0.688645	+	0.725098i	$0.258206\pi$
$401$			4.84183e19i			1.45020i	−0.688645	+	0.725098i	$0.741794\pi$
$402$			1.20700e19i			0.354823i
$403$			1.41509e19i			0.408317i
$404$	3.90709e19			1.10661
$405$		−	1.40521e18i		−	0.0390686i
$406$	1.09209e20			2.98066
$407$	−6.86891e19			−1.84047
$408$	8.84629e17	−	6.93952e17i	0.0232707	−	0.0182548i
$409$	2.11629e19			0.546576			0.273288	−	0.961932i	$-0.411889\pi$
$409$	2.11629e19			0.546576			0.273288	+	0.961932i	$0.411889\pi$
$410$	6.61612e18			0.167774
$411$		−	3.04839e19i		−	0.759025i
$412$	−1.18855e19			−0.290594
$413$			3.54070e19i			0.850087i
$414$		−	5.45560e19i		−	1.28629i
$415$			1.18540e18i			0.0274475i
$416$	−8.32258e19			−1.89260
$417$	−3.91168e17			−0.00873662
$418$		−	7.99049e19i		−	1.75288i
$419$		−	2.91834e19i		−	0.628827i	−0.949286	−	0.314413i	$-0.898192\pi$
$419$		−	2.91834e19i		−	0.628827i	0.949286	−	0.314413i	$-0.101808\pi$
$420$			1.87719e18i			0.0397319i
$421$	−3.53064e19			−0.734071			−0.367035	−	0.930207i	$-0.619627\pi$
$421$	−3.53064e19			−0.734071			−0.367035	+	0.930207i	$0.619627\pi$
$422$			5.70827e19i			1.16590i
$423$	6.72495e19			1.34939
$424$	1.20186e18			0.0236925
$425$	3.16577e19	+	4.03563e19i	0.613144	+	0.781618i
$426$	4.80139e19			0.913681
$427$	1.82912e19			0.342006
$428$		−	2.76566e19i		−	0.508125i
$429$	−4.52745e19			−0.817381
$430$		−	7.62038e17i		−	0.0135196i
$431$		−	3.52853e19i		−	0.615197i	−0.951516	−	0.307598i	$-0.900475\pi$
$431$		−	3.52853e19i		−	0.615197i	0.951516	−	0.307598i	$-0.0995253\pi$
$432$			4.76119e19i			0.815807i
$433$	−1.03780e20			−1.74765			−0.873823	−	0.486245i	$-0.838366\pi$
$433$	−1.03780e20			−1.74765			−0.873823	+	0.486245i	$0.838366\pi$
$434$	3.04407e19			0.503827
$435$			3.80686e18i			0.0619295i
$436$		−	2.87172e19i		−	0.459192i
$437$			6.42867e19i			1.01044i
$438$	−1.98256e19			−0.306316
$439$		−	3.42990e19i		−	0.520951i	−0.965480	−	0.260476i	$-0.916121\pi$
$439$		−	3.42990e19i		−	0.520951i	0.965480	−	0.260476i	$-0.0838794\pi$
$440$	5.25210e17			0.00784221
$441$	−2.44684e19			−0.359184
$442$	8.11365e19	+	1.03430e20i	1.17098	+	1.49273i
$443$	−5.55934e19			−0.788852			−0.394426	−	0.918928i	$-0.629056\pi$
$443$	−5.55934e19			−0.788852			−0.394426	+	0.918928i	$0.629056\pi$
$444$	3.83820e19			0.535495
$445$			3.02882e18i			0.0415502i
$446$	−1.11137e20			−1.49915
$447$		−	3.71848e19i		−	0.493241i
$448$			8.27108e19i			1.07889i
$449$			6.66678e19i			0.855202i	0.903967	+	0.427601i	$0.140641\pi$
$449$			6.66678e19i			0.855202i	−0.903967	+	0.427601i	$0.859359\pi$
$450$	−8.97260e19			−1.13194
$451$	1.67286e20			2.07556
$452$			6.66308e19i			0.813086i
$453$			3.35202e19i			0.402318i
$454$		−	1.98421e20i		−	2.34244i
$455$	1.13928e19			0.132295
$456$		−	2.31764e18i		−	0.0264734i
$457$	7.51441e18			0.0844351			0.0422176	−	0.999108i	$-0.486558\pi$
$457$	7.51441e18			0.0844351			0.0422176	+	0.999108i	$0.486558\pi$
$458$	−1.38773e20			−1.53396
$459$	5.63815e19	−	4.42288e19i	0.613114	−	0.480961i
$460$	8.14044e18			0.0870892
$461$	−5.07427e19			−0.534093			−0.267047	−	0.963684i	$-0.586048\pi$
$461$	−5.07427e19			−0.534093			−0.267047	+	0.963684i	$0.586048\pi$
$462$			9.73920e19i			1.00858i
$463$	1.32118e20			1.34618			0.673090	−	0.739561i	$-0.264967\pi$
$463$	1.32118e20			1.34618			0.673090	+	0.739561i	$0.264967\pi$
$464$			1.85693e20i			1.86171i
$465$			1.06112e18i			0.0104681i
$466$		−	1.28230e20i		−	1.24478i
$467$	−1.73640e20			−1.65873			−0.829363	−	0.558711i	$-0.811296\pi$
$467$	−1.73640e20			−1.65873			−0.829363	+	0.558711i	$0.811296\pi$
$468$	−1.12072e20			−1.05354
$469$		−	7.67960e19i		−	0.710465i
$470$			2.05898e19i			0.187464i
$471$			6.90493e19i			0.618732i
$472$	−5.53545e18			−0.0488189
$473$		−	1.92678e19i		−	0.167253i
$474$	1.23233e20			1.05290
$475$	1.05730e20			0.889190
$476$	1.08432e20	−	8.50605e19i	0.897650	−	0.704167i
$477$	3.44157e19			0.280458
$478$	−2.35942e19			−0.189276
$479$		−	3.51051e19i		−	0.277239i	−0.990346	−	0.138619i	$-0.955734\pi$
$479$		−	3.51051e19i		−	0.277239i	0.990346	−	0.138619i	$-0.0442664\pi$
$480$	−6.24075e18			−0.0485208
$481$		−	2.32942e20i		−	1.78304i
$482$			1.79109e19i			0.134979i
$483$		−	7.83557e19i		−	0.581390i
$484$	−1.25707e20			−0.918376
$485$	−1.26191e19			−0.0907745
$486$			1.94390e20i			1.37690i
$487$		−	1.51276e20i		−	1.05512i	−0.849518	−	0.527560i	$-0.823107\pi$
$487$		−	1.51276e20i		−	1.05512i	0.849518	−	0.527560i	$-0.176893\pi$
$488$			2.85961e18i			0.0196408i
$489$	4.76555e19			0.322327
$490$		−	7.49151e18i		−	0.0498998i
$491$	2.15664e20			1.41470			0.707352	−	0.706862i	$-0.249890\pi$
$491$	2.15664e20			1.41470			0.707352	+	0.706862i	$0.249890\pi$
$492$	−9.34759e19			−0.603895
$493$	2.19896e20	−	1.72499e20i	1.39915	−	1.09757i
$494$	2.70978e20			1.69817
$495$	1.50396e19			0.0928318
$496$			5.17598e19i			0.314688i
$497$	−3.05491e20			−1.82947
$498$		−	3.43651e19i		−	0.202720i
$499$		−	8.17041e19i		−	0.474777i	−0.971415	−	0.237388i	$-0.923709\pi$
$499$		−	8.17041e19i		−	0.474777i	0.971415	−	0.237388i	$-0.0762914\pi$
$500$		−	2.68652e19i		−	0.153786i
$501$	−5.68093e19			−0.320358
$502$	−6.14187e19			−0.341211
$503$		−	2.96789e19i		−	0.162438i	−0.996696	−	0.0812192i	$-0.974119\pi$
$503$		−	2.96789e19i		−	0.162438i	0.996696	−	0.0812192i	$-0.0258814\pi$
$504$		−	1.25141e19i		−	0.0674793i
$505$		−	1.77808e19i		−	0.0944642i
$506$	4.22340e20			2.21072
$507$		−	7.03303e19i		−	0.362730i
$508$	3.03227e20			1.54095
$509$	9.53171e19			0.477296			0.238648	−	0.971106i	$-0.423296\pi$
$509$	9.53171e19			0.477296			0.238648	+	0.971106i	$0.423296\pi$
$510$	6.08408e18	+	7.75580e18i	0.0300205	+	0.0382693i
$511$	1.26141e20			0.613339
$512$	−2.89356e20			−1.38646
$513$		−	1.47714e20i		−	0.697496i
$514$	−3.86807e20			−1.80000
$515$			5.40897e18i			0.0248062i
$516$			1.07665e19i			0.0486631i
$517$			5.20605e20i			2.31915i
$518$	−5.01092e20			−2.20011
$519$	−1.11385e20			−0.482026
$520$			1.78112e18i			0.00759746i
$521$			1.68375e20i			0.707936i	0.935258	+	0.353968i	$0.115168\pi$
$521$			1.68375e20i			0.707936i	−0.935258	+	0.353968i	$0.884832\pi$
$522$			4.88905e20i			2.02626i
$523$	2.26469e20			0.925224			0.462612	−	0.886561i	$-0.346912\pi$
$523$	2.26469e20			0.925224			0.462612	+	0.886561i	$0.346912\pi$
$524$		−	4.32782e19i		−	0.174295i
$525$	−1.28868e20			−0.511625
$526$	−4.85114e20			−1.89868
$527$	6.12934e19	−	4.80820e19i	0.236502	−	0.185525i
$528$	−1.65600e20			−0.629952
$529$	−7.31540e19			−0.274360
$530$			1.05371e19i			0.0389628i
$531$	−1.58509e20			−0.577891
$532$		−	2.84083e20i		−	1.02119i
$533$			5.67309e20i			2.01078i
$534$		−	8.78067e19i		−	0.306880i
$535$	−1.25863e19			−0.0433754
$536$	1.20061e19			0.0408006
$537$			6.00866e19i			0.201359i
$538$			5.68647e20i			1.87921i
$539$		−	1.89420e20i		−	0.617319i
$540$	−1.87046e19			−0.0601168
$541$			2.37031e20i			0.751320i	0.926758	+	0.375660i	$0.122584\pi$
$541$			2.37031e20i			0.751320i	−0.926758	+	0.375660i	$0.877416\pi$
$542$	1.74101e20			0.544261
$543$	1.35639e20			0.418201
$544$	2.82784e20	+	3.60485e20i	0.859931	+	1.09621i
$545$	−1.30690e19			−0.0391983
$546$	−3.30281e20			−0.977099
$547$		−	3.38496e19i		−	0.0987752i	−0.998780	−	0.0493876i	$-0.984273\pi$
$547$		−	3.38496e19i		−	0.0987752i	0.998780	−	0.0493876i	$-0.0157270\pi$
$548$	5.84161e20			1.68143
$549$			8.18860e19i			0.232497i
$550$		−	6.94605e20i		−	1.94544i
$551$		−	5.76106e20i		−	1.59172i
$552$	1.22500e19			0.0333881
$553$	−7.84076e20			−2.10824
$554$		−	7.43951e20i		−	1.97343i
$555$		−	1.74673e19i		−	0.0457119i
$556$		−	7.49594e18i		−	0.0193538i
$557$	2.05296e18			0.00522957			0.00261478	−	0.999997i	$-0.499168\pi$
$557$	2.05296e18			0.00522957			0.00261478	+	0.999997i	$0.499168\pi$
$558$			1.36276e20i			0.342503i
$559$	6.53421e19			0.162033
$560$	4.16713e19			0.101959
$561$	1.53834e20	+	1.96102e20i	0.371389	+	0.473436i
$562$	1.03065e21			2.45521
$563$	9.31213e19			0.218895			0.109448	−	0.993993i	$-0.465092\pi$
$563$	9.31213e19			0.218895			0.109448	+	0.993993i	$0.465092\pi$
$564$		−	2.90903e20i		−	0.674769i
$565$	3.03231e19			0.0694081
$566$			3.85747e20i			0.871323i
$567$		−	2.59195e20i		−	0.577767i
$568$		−	4.77598e19i		−	0.105063i
$569$	5.37321e19			0.116652			0.0583260	−	0.998298i	$-0.481424\pi$
$569$	5.37321e19			0.116652			0.0583260	+	0.998298i	$0.481424\pi$
$570$	2.03195e19			0.0435362
$571$			1.70561e20i			0.360669i	0.983605	+	0.180334i	$0.0577179\pi$
$571$			1.70561e20i			0.360669i	−0.983605	+	0.180334i	$0.942282\pi$
$572$		−	8.67594e20i		−	1.81070i
$573$		−	1.13417e20i		−	0.233624i
$574$	1.22036e21			2.48113
$575$			5.58837e20i			1.12144i
$576$	−3.70278e20			−0.733432
$577$	−8.04238e20			−1.57241			−0.786205	−	0.617965i	$-0.787957\pi$
$577$	−8.04238e20			−1.57241			−0.786205	+	0.617965i	$0.787957\pi$
$578$	1.72313e20	−	7.02870e20i	0.332553	−	1.35649i
$579$	1.17581e20			0.223999
$580$	−7.29507e19			−0.137189
$581$			2.18650e20i			0.405908i
$582$	3.65831e20			0.670438
$583$			2.66425e20i			0.482016i
$584$			1.97207e19i			0.0352229i
$585$			5.10030e19i			0.0899346i
$586$	−9.17866e20			−1.59789
$587$	−2.28834e20			−0.393311			−0.196655	−	0.980473i	$-0.563008\pi$
$587$	−2.28834e20			−0.393311			−0.196655	+	0.980473i	$0.563008\pi$
$588$			1.05844e20i			0.179612i
$589$		−	1.60583e20i		−	0.269051i
$590$		−	4.85309e19i		−	0.0802839i
$591$	2.06431e20			0.337186
$592$		−	8.52032e20i		−	1.37418i
$593$	−5.40232e20			−0.860340			−0.430170	−	0.902748i	$-0.641546\pi$
$593$	−5.40232e20			−0.860340			−0.430170	+	0.902748i	$0.641546\pi$
$594$	−9.70427e20			−1.52603
$595$	−3.87103e19	−	4.93467e19i	−0.0601103	−	0.0766268i
$596$	7.12570e20			1.09265
$597$	1.78063e20			0.269629
$598$			1.43226e21i			2.14172i
$599$	8.93597e20			1.31959			0.659797	−	0.751444i	$-0.270642\pi$
$599$	8.93597e20			1.31959			0.659797	+	0.751444i	$0.270642\pi$
$600$		−	2.01470e19i		−	0.0293817i
$601$		−	4.12923e19i		−	0.0594717i	−0.999558	−	0.0297359i	$-0.990533\pi$
$601$		−	4.12923e19i		−	0.0594717i	0.999558	−	0.0297359i	$-0.00946662\pi$
$602$		−	1.40560e20i		−	0.199935i
$603$	3.43799e20			0.482976
$604$	−6.42346e20			−0.891234
$605$			5.72083e19i			0.0783960i
$606$			5.15474e20i			0.697689i
$607$		−	1.19497e21i		−	1.59750i	−0.601660	−	0.798752i	$-0.705494\pi$
$607$		−	1.19497e21i		−	1.59750i	0.601660	−	0.798752i	$-0.294506\pi$
$608$	9.44436e20			1.24708
$609$			7.02187e20i			0.915847i
$610$	−2.50711e19			−0.0322997
$611$	−1.76550e21			−2.24677
$612$	3.80797e20	+	4.85429e20i	0.478694	+	0.610225i
$613$	−4.53779e19			−0.0563496			−0.0281748	−	0.999603i	$-0.508970\pi$
$613$	−4.53779e19			−0.0563496			−0.0281748	+	0.999603i	$0.508970\pi$
$614$	−3.88106e19			−0.0476088
$615$			4.25401e19i			0.0515507i
$616$	9.68766e19			0.115975
$617$		−	4.67773e20i		−	0.553218i	−0.960983	−	0.276609i	$-0.910789\pi$
$617$		−	4.67773e20i		−	0.553218i	0.960983	−	0.276609i	$-0.0892107\pi$
$618$		−	1.56808e20i		−	0.183212i
$619$			1.17859e21i			1.36046i	0.733000	+	0.680228i	$0.238119\pi$
$619$			1.17859e21i			1.36046i	−0.733000	+	0.680228i	$0.761881\pi$
$620$	−2.03342e19			−0.0231893
$621$	7.80747e20			0.879677
$622$			2.71420e19i			0.0302144i
$623$			5.58675e20i			0.614467i
$624$		−	5.61593e20i		−	0.610291i
$625$	9.12963e20			0.980287
$626$			7.45435e19i			0.0790865i
$627$	5.13769e20			0.538594
$628$	−1.32319e21			−1.37064
$629$	−1.00897e21	+	7.91489e20i	−1.03275	+	0.810150i
$630$	1.09715e20			0.110971
$631$	1.50342e20			0.150266			0.0751331	−	0.997174i	$-0.476062\pi$
$631$	1.50342e20			0.150266			0.0751331	+	0.997174i	$0.476062\pi$
$632$		−	1.22581e20i		−	0.121072i
$633$	−3.67028e20			−0.358238
$634$			5.68228e20i			0.548092i
$635$		−	1.37996e20i		−	0.131542i
$636$		−	1.48873e20i		−	0.140245i
$637$	6.42370e20			0.598053
$638$	−3.78481e21			−3.48248
$639$		−	1.36762e21i		−	1.24368i
$640$			1.24306e19i			0.0111723i
$641$			1.19171e21i			1.05861i	0.848432	+	0.529305i	$0.177547\pi$
$641$			1.19171e21i			1.05861i	−0.848432	+	0.529305i	$0.822453\pi$
$642$	3.64881e20			0.320360
$643$		−	2.11736e21i		−	1.83744i	−0.394909	−	0.918720i	$-0.629224\pi$
$643$		−	2.11736e21i		−	1.83744i	0.394909	−	0.918720i	$-0.370776\pi$
$644$	1.50153e21			1.28792
$645$	4.89972e18			0.00415407
$646$	−9.20726e20	−	1.17371e21i	−0.771590	−	0.983599i
$647$	1.21743e21			1.00847			0.504233	−	0.863568i	$-0.331775\pi$
$647$	1.21743e21			1.00847			0.504233	+	0.863568i	$0.331775\pi$
$648$	4.05219e19			0.0331801
$649$		−	1.22708e21i		−	0.993206i
$650$	2.35558e21			1.88472
$651$			1.95726e20i			0.154807i
$652$			9.13220e20i			0.714033i
$653$		−	2.78832e20i		−	0.215523i	−0.994177	−	0.107762i	$-0.965632\pi$
$653$		−	2.78832e20i		−	0.215523i	0.994177	−	0.107762i	$-0.0343683\pi$
$654$	3.78875e20			0.289509
$655$	−1.96955e19			−0.0148785
$656$			2.07504e21i			1.54970i
$657$			5.64708e20i			0.416950i
$658$			3.79785e21i			2.77232i
$659$	−3.05793e20			−0.220692			−0.110346	−	0.993893i	$-0.535196\pi$
$659$	−3.05793e20			−0.220692			−0.110346	+	0.993893i	$0.535196\pi$
$660$		−	6.50571e19i		−	0.0464211i
$661$	−2.46932e21			−1.74207			−0.871037	−	0.491218i	$-0.836552\pi$
$661$	−2.46932e21			−1.74207			−0.871037	+	0.491218i	$0.836552\pi$
$662$	−3.84108e20			−0.267928
$663$	−6.65032e20	+	5.21688e20i	−0.458660	+	0.359799i
$664$	−3.41832e19			−0.0233105
$665$	−1.29284e20			−0.0871728
$666$		−	2.24328e21i		−	1.49564i
$667$	3.04503e21			2.00746
$668$		−	1.08863e21i		−	0.709673i
$669$		−	7.14582e20i		−	0.460634i
$670$			1.05261e20i			0.0670977i
$671$	−6.33912e20			−0.399586
$672$	−1.15112e21			−0.717551
$673$			1.19965e21i			0.739504i	0.929130	+	0.369752i	$0.120557\pi$
$673$			1.19965e21i			0.739504i	−0.929130	+	0.369752i	$0.879443\pi$
$674$		−	2.46966e21i		−	1.50552i
$675$		−	1.28406e21i		−	0.774119i
$676$	1.34774e21			0.803535
$677$			1.55107e21i			0.914571i	0.889320	+	0.457286i	$0.151178\pi$
$677$			1.55107e21i			0.914571i	−0.889320	+	0.457286i	$0.848822\pi$
$678$	−8.79078e20			−0.512631
$679$	−2.32762e21			−1.34242
$680$	7.71476e18	−	6.05188e18i	0.00440053	−	0.00345202i
$681$	1.27580e21			0.719746
$682$	−1.05497e21			−0.588650
$683$			1.64329e21i			0.906897i	0.891282	+	0.453449i	$0.149806\pi$
$683$			1.64329e21i			0.906897i	−0.891282	+	0.453449i	$0.850194\pi$
$684$	1.27178e21			0.694209
$685$		−	2.65847e20i		−	0.143533i
$686$			1.75681e21i			0.938198i
$687$		−	8.92275e20i		−	0.471328i
$688$	2.39001e20			0.124878
$689$	−9.03516e20			−0.466973
$690$			1.07399e20i			0.0549076i
$691$			1.06053e21i			0.536337i	0.963372	+	0.268169i	$0.0864185\pi$
$691$			1.06053e21i			0.536337i	−0.963372	+	0.268169i	$0.913582\pi$
$692$		−	2.13446e21i		−	1.06780i
$693$	2.77409e21			1.37285
$694$			1.75138e21i			0.857401i
$695$	−3.41134e18			−0.00165211
$696$	−1.09778e20			−0.0525954
$697$	2.45724e21	−	1.92760e21i	1.16467	−	0.913631i
$698$	2.53225e21			1.18738
$699$	8.24486e20			0.382476
$700$		−	2.46950e21i		−	1.13338i
$701$	−1.58812e21			−0.721106			−0.360553	−	0.932739i	$-0.617412\pi$
$701$	−1.58812e21			−0.721106			−0.360553	+	0.932739i	$0.617412\pi$
$702$		−	3.29096e21i		−	1.47841i
$703$			2.64340e21i			1.17489i
$704$		−	2.86647e21i		−	1.26053i
$705$	−1.32388e20			−0.0576008
$706$	5.24480e20			0.225784
$707$		−	3.27973e21i		−	1.39699i
$708$			6.85669e20i			0.288978i
$709$		−	1.77097e19i		−	0.00738524i	−0.999993	−	0.00369262i	$-0.998825\pi$
$709$		−	1.77097e19i		−	0.00738524i	0.999993	−	0.00369262i	$-0.00117540\pi$
$710$	4.18724e20			0.172779
$711$		−	3.51014e21i		−	1.43318i
$712$	−8.73420e19			−0.0352877
$713$	8.48766e20			0.339325
$714$	1.12223e21	+	1.43058e21i	0.443960	+	0.565946i
$715$	−3.94834e20			−0.154568
$716$	−1.15144e21			−0.446059
$717$		−	1.51705e20i		−	0.0581576i
$718$	−1.53498e21			−0.582330
$719$			2.19877e21i			0.825491i	0.910846	+	0.412745i	$0.135430\pi$
$719$			2.19877e21i			0.825491i	−0.910846	+	0.412745i	$0.864570\pi$
$720$			1.86553e20i			0.0693122i
$721$			9.97700e20i			0.366847i
$722$	7.63107e20			0.277688
$723$	−1.15163e20			−0.0414739
$724$			2.59924e21i			0.926417i
$725$		−	5.00803e21i		−	1.76657i
$726$		−	1.65849e21i		−	0.579013i
$727$	−2.82053e21			−0.974593			−0.487296	−	0.873237i	$-0.662017\pi$
$727$	−2.82053e21			−0.974593			−0.487296	+	0.873237i	$0.662017\pi$
$728$			3.28533e20i			0.112355i
$729$	1.72410e20			0.0583589
$730$	−1.72897e20			−0.0579250
$731$	−2.22019e20	−	2.83023e20i	−0.0736224	−	0.0938515i
$732$	3.54217e20			0.116261
$733$	−3.17780e21			−1.03240			−0.516198	−	0.856469i	$-0.672653\pi$
$733$	−3.17780e21			−1.03240			−0.516198	+	0.856469i	$0.672653\pi$
$734$			5.14583e21i			1.65476i
$735$	4.81686e19			0.0153324
$736$			4.99184e21i			1.57281i
$737$			2.66149e21i			0.830077i
$738$			5.46330e21i			1.68668i
$739$	2.09467e21			0.640150			0.320075	−	0.947392i	$-0.396292\pi$
$739$	2.09467e21			0.640150			0.320075	+	0.947392i	$0.396292\pi$
$740$	3.34726e20			0.101263
$741$			1.74232e21i			0.521785i
$742$			1.94359e21i			0.576203i
$743$			2.21322e21i			0.649545i	0.945792	+	0.324773i	$0.105288\pi$
$743$			2.21322e21i			0.649545i	−0.945792	+	0.324773i	$0.894712\pi$
$744$	−3.05994e19			−0.00889030
$745$		−	3.24285e20i		−	0.0932727i
$746$	−1.08511e20			−0.0308981
$747$	−9.78848e20			−0.275937
$748$	−3.75790e21	+	2.94790e21i	−1.04878	+	0.822719i
$749$	−2.32157e21			−0.641459
$750$	3.54441e20			0.0969581
$751$			1.59851e21i			0.432927i	0.976291	+	0.216464i	$0.0694523\pi$
$751$			1.59851e21i			0.432927i	−0.976291	+	0.216464i	$0.930548\pi$
$752$	−6.45767e21			−1.73158
$753$		−	3.94907e20i		−	0.104841i
$754$		−	1.28352e22i		−	3.37379i
$755$			2.92326e20i			0.0760791i
$756$	−3.45012e21			−0.889039
$757$	1.35273e21			0.345137			0.172568	−	0.984998i	$-0.444793\pi$
$757$	1.35273e21			0.345137			0.172568	+	0.984998i	$0.444793\pi$
$758$			1.74440e21i			0.440685i
$759$			2.71554e21i			0.679271i
$760$		−	2.02119e19i		−	0.00500617i
$761$	6.73855e21			1.65265			0.826326	−	0.563192i	$-0.190427\pi$
$761$	6.73855e21			1.65265			0.826326	+	0.563192i	$0.190427\pi$
$762$			4.00055e21i			0.971533i
$763$	−2.41061e21			−0.579686
$764$	2.17340e21			0.517535
$765$	2.20915e20	−	1.73298e20i	0.0520911	−	0.0408632i
$766$	−4.49274e21			−1.04905
$767$	4.16135e21			0.962209
$768$		−	2.04523e21i		−	0.468311i
$769$	−3.17695e21			−0.720383			−0.360191	−	0.932878i	$-0.617289\pi$
$769$	−3.17695e21			−0.720383			−0.360191	+	0.932878i	$0.617289\pi$
$770$			8.49345e20i			0.190723i
$771$		−	2.48708e21i		−	0.553072i
$772$			2.25319e21i			0.496213i
$773$	9.83173e20			0.214429			0.107215	−	0.994236i	$-0.465807\pi$
$773$	9.83173e20			0.214429			0.107215	+	0.994236i	$0.465807\pi$
$774$	6.29258e20			0.135916
$775$		−	1.39593e21i		−	0.298608i
$776$		−	3.63895e20i		−	0.0770928i
$777$		−	3.22190e21i		−	0.676012i
$778$	−3.79882e21			−0.789408
$779$		−	6.43774e21i		−	1.32496i
$780$	2.20625e20			0.0449723
$781$	1.05873e22			2.13748
$782$	6.20370e21	−	4.86653e21i	1.24051	−	0.973124i
$783$	−6.99668e21			−1.38573
$784$	2.34960e21			0.460917
$785$			6.02172e20i			0.117003i
$786$	5.70981e20			0.109889
$787$			1.09264e21i			0.208290i	0.994562	+	0.104145i	$0.0332105\pi$
$787$			1.09264e21i			0.208290i	−0.994562	+	0.104145i	$0.966789\pi$
$788$			3.95583e21i			0.746949i
$789$		−	3.11917e21i		−	0.583393i
$790$	1.07470e21			0.199106
$791$	5.59318e21			1.02644
$792$			4.33696e20i			0.0788399i
$793$		−	2.14976e21i		−	0.387115i
$794$		−	7.74058e21i		−	1.38076i
$795$	−6.77508e19			−0.0119718
$796$			3.41221e21i			0.597294i
$797$	−1.40801e21			−0.244157			−0.122078	−	0.992520i	$-0.538956\pi$
$797$	−1.40801e21			−0.244157			−0.122078	+	0.992520i	$0.538956\pi$
$798$	3.74798e21			0.643837
$799$	5.99882e21	+	7.64711e21i	1.02086	+	1.30136i
$800$	8.20988e21			1.38408
$801$	−2.50107e21			−0.417716
$802$		−	1.22412e22i		−	2.02543i
$803$	−4.37163e21			−0.716600
$804$		−	1.48718e21i		−	0.241515i
$805$		−	6.83332e20i		−	0.109942i
$806$		−	3.57767e21i		−	0.570279i
$807$	−3.65626e21			−0.577412
$808$	5.12746e20			0.0802263
$809$		−	1.08076e22i		−	1.67539i	−0.546137	−	0.837696i	$-0.683902\pi$
$809$		−	1.08076e22i		−	1.67539i	0.546137	−	0.837696i	$-0.316098\pi$
$810$			3.55268e20i			0.0545655i
$811$			8.50397e21i			1.29409i	0.762451	+	0.647047i	$0.223996\pi$
$811$			8.50397e21i			1.29409i	−0.762451	+	0.647047i	$0.776004\pi$
$812$	−1.34560e22			−2.02883
$813$			1.11943e21i			0.167231i
$814$	1.73661e22			2.57051
$815$	4.15598e20			0.0609525
$816$	−2.43249e21	+	1.90818e21i	−0.353488	+	0.277295i
$817$	−7.41493e20			−0.106768
$818$	−5.35045e21			−0.763380
$819$			9.40765e21i			1.33000i
$820$	−8.15193e20			−0.114198
$821$		−	8.17537e21i		−	1.13484i	−0.823429	−	0.567419i	$-0.807942\pi$
$821$		−	8.17537e21i		−	1.13484i	0.823429	−	0.567419i	$-0.192058\pi$
$822$			7.70699e21i			1.06010i
$823$		−	8.97744e21i		−	1.22364i	−0.790997	−	0.611820i	$-0.790438\pi$
$823$		−	8.97744e21i		−	1.22364i	0.790997	−	0.611820i	$-0.209562\pi$
$824$	−1.55978e20			−0.0210673
$825$	4.46614e21			0.597761
$826$		−	8.95167e21i		−	1.18728i
$827$			6.91369e21i			0.908696i	0.890824	+	0.454348i	$0.150128\pi$
$827$			6.91369e21i			0.908696i	−0.890824	+	0.454348i	$0.849872\pi$
$828$			6.72202e21i			0.875532i
$829$	−5.44180e21			−0.702399			−0.351200	−	0.936301i	$-0.614226\pi$
$829$	−5.44180e21			−0.702399			−0.351200	+	0.936301i	$0.614226\pi$
$830$		−	2.99694e20i		−	0.0383348i
$831$	4.78342e21			0.606361
$832$	9.72093e21			1.22119
$833$	−2.18264e21	−	2.78237e21i	−0.271735	−	0.346399i
$834$	9.88960e19			0.0122021
$835$	−4.95428e20			−0.0605803
$836$			9.84534e21i			1.19312i
$837$	−1.95024e21			−0.234233
$838$			7.37821e21i			0.878256i
$839$			7.51639e21i			0.886737i	0.896339	+	0.443369i	$0.146217\pi$
$839$			7.51639e21i			0.886737i	−0.896339	+	0.443369i	$0.853783\pi$
$840$			2.46353e19i			0.00288047i
$841$	−1.86589e22			−2.16230
$842$	8.92624e21			1.02525
$843$			6.62682e21i			0.754395i
$844$		−	7.03335e21i		−	0.793585i
$845$		−	6.13343e20i		−	0.0685928i
$846$	−1.70022e22			−1.88463
$847$			1.05522e22i			1.15936i
$848$	−3.30479e21			−0.359894
$849$	−2.48026e21			−0.267725
$850$	−8.00377e21	−	1.02030e22i	−0.856353	−	1.09165i
$851$	−1.39717e22			−1.48176
$852$	−5.91594e21			−0.621909
$853$		−	1.95415e21i		−	0.203629i	−0.994803	−	0.101815i	$-0.967535\pi$
$853$		−	1.95415e21i		−	0.203629i	0.994803	−	0.101815i	$-0.0324649\pi$
$854$	−4.62443e21			−0.477666
$855$		−	5.78775e20i		−	0.0592603i
$856$		−	3.62950e20i		−	0.0368378i
$857$			1.21847e22i			1.22591i	0.790117	+	0.612956i	$0.210020\pi$
$857$			1.21847e22i			1.22591i	−0.790117	+	0.612956i	$0.789980\pi$
$858$	1.14464e22			1.14160
$859$	1.41730e22			1.40124			0.700620	−	0.713534i	$-0.252907\pi$
$859$	1.41730e22			1.40124			0.700620	+	0.713534i	$0.252907\pi$
$860$			9.38932e19i			0.00920228i
$861$			7.84664e21i			0.762360i
$862$			8.92090e21i			0.859219i
$863$	−1.53003e22			−1.46089			−0.730446	−	0.682970i	$-0.760688\pi$
$863$	−1.53003e22			−1.46089			−0.730446	+	0.682970i	$0.760688\pi$
$864$		−	1.14700e22i		−	1.08570i
$865$	−9.71374e20			−0.0911519
$866$	2.62378e22			2.44086
$867$	4.51929e21	+	1.10793e21i	0.416799	+	0.102181i
$868$	−3.75069e21			−0.342936
$869$	2.71734e22			2.46318
$870$		−	9.62459e20i		−	0.0864944i
$871$	−9.02578e21			−0.804171
$872$		−	3.76870e20i		−	0.0332903i
$873$		−	1.04203e22i		−	0.912582i
$874$		−	1.62531e22i		−	1.41124i
$875$	−2.25515e21			−0.194140
$876$	2.44277e21			0.208498
$877$			2.14574e22i			1.81585i	0.419128	+	0.907927i	$0.362336\pi$
$877$			2.14574e22i			1.81585i	−0.419128	+	0.907927i	$0.637664\pi$
$878$			8.67154e21i			0.727591i
$879$		−	5.90166e21i		−	0.490973i
$880$	−1.44418e21			−0.119125
$881$			9.45935e21i			0.773646i	0.922154	+	0.386823i	$0.126428\pi$
$881$			9.45935e21i			0.773646i	−0.922154	+	0.386823i	$0.873572\pi$
$882$	6.18616e21			0.501657
$883$	−2.28521e22			−1.83747			−0.918737	−	0.394870i	$-0.870790\pi$
$883$	−2.28521e22			−1.83747			−0.918737	+	0.394870i	$0.870790\pi$
$884$	−9.99709e21	−	1.27440e22i	−0.797043	−	1.01605i
$885$	3.12042e20			0.0246683
$886$	1.40552e22			1.10176
$887$		−	1.14008e22i		−	0.886148i	−0.896485	−	0.443074i	$-0.853888\pi$
$887$		−	1.14008e22i		−	0.886148i	0.896485	−	0.443074i	$-0.146112\pi$
$888$	5.03705e20			0.0388221
$889$		−	2.54537e22i		−	1.94531i
$890$		−	7.65753e20i		−	0.0580315i
$891$			8.98280e21i			0.675039i
$892$	1.36935e22			1.02042
$893$	2.00347e22			1.48046
$894$			9.40114e21i			0.688889i
$895$			5.24009e20i			0.0380773i
$896$			2.29286e21i			0.165222i
$897$	−9.20909e21			−0.658072
$898$		−	1.68551e22i		−	1.19443i
$899$	−7.60623e21			−0.534530
$900$	1.10554e22			0.770471
$901$	3.06996e21	+	3.91349e21i	0.212176	+	0.270476i
$902$	−4.22936e22			−2.89885
$903$	9.03768e20			0.0614326
$904$			8.74426e20i			0.0589468i
$905$	1.18289e21			0.0790825
$906$		−	8.47464e21i		−	0.561901i
$907$		−	1.35018e20i		−	0.00887843i	−0.999990	−	0.00443922i	$-0.998587\pi$
$907$		−	1.35018e20i		−	0.00887843i	0.999990	−	0.00443922i	$-0.00141305\pi$
$908$			2.44481e22i			1.59441i
$909$	1.46826e22			0.949675
$910$	−2.88034e21			−0.184771
$911$		−	9.58578e21i		−	0.609873i	−0.952373	−	0.304937i	$-0.901365\pi$
$911$		−	9.58578e21i		−	0.609873i	0.952373	−	0.304937i	$-0.0986353\pi$
$912$			6.37288e21i			0.402137i
$913$		−	7.57765e21i		−	0.474246i
$914$	−1.89981e21			−0.117927
$915$		−	1.61201e20i		−	0.00992452i
$916$	1.70986e22			1.04411
$917$	−3.63290e21			−0.220031
$918$	−1.42545e22	+	1.11820e22i	−0.856311	+	0.671738i
$919$	−3.34622e21			−0.199383			−0.0996914	−	0.995018i	$-0.531786\pi$
$919$	−3.34622e21			−0.199383			−0.0996914	+	0.995018i	$0.531786\pi$
$920$	1.06831e20			0.00631375
$921$		−	2.49543e20i		−	0.0146284i
$922$	1.28289e22			0.745945
$923$			3.59041e22i			2.07077i
$924$		−	1.20000e22i		−	0.686500i
$925$			2.29788e22i			1.30396i
$926$	−3.34022e22			−1.88015
$927$	−4.46649e21			−0.249384
$928$		−	4.47345e22i		−	2.47761i
$929$		−	2.91872e22i		−	1.60352i	−0.597647	−	0.801760i	$-0.703897\pi$
$929$		−	2.91872e22i		−	1.60352i	0.597647	−	0.801760i	$-0.296103\pi$
$930$		−	2.68274e20i		−	0.0146203i
$931$	−7.28953e21			−0.394073
$932$			1.57996e22i			0.847279i
$933$	−1.74517e20			−0.00928377
$934$	4.39002e22			2.31667
$935$	1.34157e21	+	1.71019e21i	0.0702304	+	0.0895275i
$936$	−1.47077e21			−0.0763794
$937$	8.38797e21			0.432126			0.216063	−	0.976379i	$-0.430678\pi$
$937$	8.38797e21			0.432126			0.216063	+	0.976379i	$0.430678\pi$
$938$			1.94157e22i			0.992276i
$939$	−4.79297e20			−0.0243004
$940$		−	2.53694e21i		−	0.127600i
$941$		−	6.46184e21i		−	0.322429i	−0.986919	−	0.161215i	$-0.948459\pi$
$941$		−	6.46184e21i		−	0.322429i	0.986919	−	0.161215i	$-0.0515411\pi$
$942$		−	1.74572e22i		−	0.864157i
$943$	3.40269e22			1.67103
$944$	1.52210e22			0.741570
$945$			1.57012e21i			0.0758917i
$946$			4.87133e21i			0.233595i
$947$		−	1.49582e22i		−	0.711629i	−0.934557	−	0.355814i	$-0.884204\pi$
$947$		−	1.49582e22i		−	0.711629i	0.934557	−	0.355814i	$-0.115796\pi$
$948$	−1.51839e22			−0.716673
$949$		−	1.48253e22i		−	0.694236i
$950$	−2.67308e22			−1.24189
$951$	−3.65357e21			−0.168408
$952$	1.42301e21	−	1.11629e21i	0.0650774	−	0.0510504i
$953$	2.27588e22			1.03265			0.516324	−	0.856393i	$-0.327300\pi$
$953$	2.27588e22			1.03265			0.516324	+	0.856393i	$0.327300\pi$
$954$	−8.70104e21			−0.391704
$955$		−	9.89097e20i		−	0.0441788i
$956$	2.90712e21			0.128833
$957$		−	2.43354e22i		−	1.07004i
$958$			8.87534e21i			0.387208i
$959$		−	4.90361e22i		−	2.12264i
$960$	7.28931e20			0.0313078
$961$	2.13451e22			0.909647
$962$			5.88929e22i			2.49029i
$963$		−	1.03932e22i		−	0.436065i
$964$		−	2.20686e21i		−	0.0918749i
$965$	1.02541e21			0.0423586
$966$			1.98101e22i			0.812003i
$967$	−2.75197e22			−1.11930			−0.559649	−	0.828730i	$-0.689064\pi$
$967$	−2.75197e22			−1.11930			−0.559649	+	0.828730i	$0.689064\pi$
$968$	−1.64971e21			−0.0665800
$969$	7.54670e21	−	5.92005e21i	0.302224	−	0.237081i
$970$	3.19038e21			0.126781
$971$	2.01200e22			0.793386			0.396693	−	0.917951i	$-0.370158\pi$
$971$	2.01200e22			0.793386			0.396693	+	0.917951i	$0.370158\pi$
$972$		−	2.39514e22i		−	0.937204i
$973$	−6.29231e20			−0.0244323
$974$			3.82459e22i			1.47364i
$975$			1.51458e22i			0.579106i
$976$		−	7.86315e21i		−	0.298348i
$977$	2.52432e22			0.950463			0.475232	−	0.879861i	$-0.342364\pi$
$977$	2.52432e22			0.950463			0.475232	+	0.879861i	$0.342364\pi$
$978$	−1.20484e22			−0.450180
$979$		−	1.93618e22i		−	0.717917i
$980$			9.23053e20i			0.0339649i
$981$		−	1.07918e22i		−	0.394072i
$982$	−5.45245e22			−1.97586
$983$			3.27076e22i			1.17624i	0.808773	+	0.588121i	$0.200132\pi$
$983$			3.27076e22i			1.17624i	−0.808773	+	0.588121i	$0.799868\pi$
$984$	−1.22673e21			−0.0437809
$985$	1.80026e21			0.0637624
$986$	−5.55946e22	+	4.36115e22i	−1.95414	+	1.53294i
$987$	−2.44193e22			−0.851832
$988$	−3.33880e22			−1.15588
$989$		−	3.91918e21i		−	0.134655i
$990$	−3.80234e21			−0.129654
$991$			3.37244e22i			1.14128i	0.821201	+	0.570640i	$0.193305\pi$
$991$			3.37244e22i			1.14128i	−0.821201	+	0.570640i	$0.806695\pi$
$992$		−	1.24692e22i		−	0.418795i
$993$		−	2.46972e21i		−	0.0823245i
$994$	7.72348e22			2.55514
$995$	1.55287e21			0.0509873
$996$			4.23423e21i			0.137984i
$997$		−	2.46048e22i		−	0.795805i	−0.917428	−	0.397903i	$-0.869738\pi$
$997$		−	2.46048e22i		−	0.795805i	0.917428	−	0.397903i	$-0.130262\pi$
$998$			2.06566e22i			0.663101i
$999$	3.21034e22			1.02285

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.16.b.a.16.6	yes	22
17.16	even	2	inner	17.16.b.a.16.5	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.16.b.a.16.5	✓	22	17.16	even	2	inner
17.16.b.a.16.6	yes	22	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:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	17.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-252.822 q^{2} -1625.59i q^{3} +31151.0 q^{4} -14176.6i q^{5} +410984. i q^{6} -2.61491e6i q^{7} +408809. q^{8} +1.17064e7 q^{9} +O(q^{10})\)	\(q-252.822 q^{2} -1625.59i q^{3} +31151.0 q^{4} -14176.6i q^{5} +410984. i q^{6} -2.61491e6i q^{7} +408809. q^{8} +1.17064e7 q^{9} +3.58415e6i q^{10} +9.06238e7i q^{11} -5.06386e7i q^{12} -3.07328e8 q^{13} +6.61106e8i q^{14} -2.30452e7 q^{15} -1.12411e9 q^{16} +(1.04424e9 + 1.33116e9i) q^{17} -2.95963e9 q^{18} +3.48752e9 q^{19} -4.41614e8i q^{20} -4.25076e9 q^{21} -2.29117e10i q^{22} +1.84334e10i q^{23} -6.64554e8i q^{24} +3.03166e10 q^{25} +7.76993e10 q^{26} -4.23551e10i q^{27} -8.14570e10i q^{28} -1.65191e11i q^{29} +5.82634e9 q^{30} -4.60451e10i q^{31} +2.70805e11 q^{32} +1.47317e11 q^{33} +(-2.64006e11 - 3.36547e11i) q^{34} -3.70704e10 q^{35} +3.64666e11 q^{36} +7.57959e11i q^{37} -8.81721e11 q^{38} +4.99588e11i q^{39} -5.79551e9i q^{40} -1.84594e12i q^{41} +1.07468e12 q^{42} -2.12614e11 q^{43} +2.82302e12i q^{44} -1.65956e11i q^{45} -4.66036e12i q^{46} +5.74469e12 q^{47} +1.82734e12i q^{48} -2.09018e12 q^{49} -7.66471e12 q^{50} +(2.16392e12 - 1.69750e12i) q^{51} -9.57358e12 q^{52} +2.93991e12 q^{53} +1.07083e13i q^{54} +1.28473e12 q^{55} -1.06900e12i q^{56} -5.66926e12i q^{57} +4.17639e13i q^{58} -1.35404e13 q^{59} -7.17882e11 q^{60} +6.99499e12i q^{61} +1.16412e13i q^{62} -3.06111e13i q^{63} -3.16305e13 q^{64} +4.35685e12i q^{65} -3.72449e13 q^{66} +2.93685e13 q^{67} +(3.25291e13 + 4.14670e13i) q^{68} +2.99650e13 q^{69} +9.37221e12 q^{70} -1.16827e14i q^{71} +4.78567e12 q^{72} +4.82393e13i q^{73} -1.91629e14i q^{74} -4.92822e13i q^{75} +1.08640e14 q^{76} +2.36973e14 q^{77} -1.26307e14i q^{78} -2.99848e14i q^{79} +1.59360e13i q^{80} +9.91219e13 q^{81} +4.66694e14i q^{82} -8.36166e13 q^{83} -1.32415e14 q^{84} +(1.88713e13 - 1.48037e13i) q^{85} +5.37534e13 q^{86} -2.68532e14 q^{87} +3.70478e13i q^{88} -2.13650e14 q^{89} +4.19574e13i q^{90} +8.03634e14i q^{91} +5.74218e14i q^{92} -7.48502e13 q^{93} -1.45238e15 q^{94} -4.94410e13i q^{95} -4.40216e14i q^{96} -8.90136e14i q^{97} +5.28443e14 q^{98} +1.06088e15i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 258 q^{2} + 414386 q^{4} - 12648450 q^{8} - 78109330 q^{9}+O(q^{10}) \) 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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