LMFDB - Embedded newform 234.8.l.c.199.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,8,Mod(127,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("234.127");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$N$	$=$	$234 = 2 \cdot 3^{2} \cdot 13$
Weight:	$k$	$=$	$8$
Character orbit:	$[\chi]$	$=$	234.l (of order $6$ , degree $2$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$73.0980959633$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} + 22180 x^{14} + 184473654 x^{12} + 707524481236 x^{10} + \cdots + 18\!\cdots\!76$ x^16 + 22180x^14 + 184473654x^12 + 707524481236x^10 + 1235305573179121x^8 + 834592841081820432x^6 + 142296444753813668448x^4 + 5907885179463590558976*x^2 + 18970385728293762437376
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$2^{34}\cdot 3^{2}\cdot 13^{2}$
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.3
Root			$79.3738i$ of defining polynomial
Character	$\chi$	$=$	234.199
Dual form			234.8.l.c.127.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.92820 - 4.00000i) q^{2} +(32.0000 + 55.4256i) q^{4} +12.5639i q^{5} +(-93.7198 + 54.1091i) q^{7} -512.000i q^{8} +(50.2557 - 87.0454i) q^{10} +(5776.62 + 3335.13i) q^{11} +(5200.37 + 5975.34i) q^{13} +865.746 q^{14} +(-2048.00 + 3547.24i) q^{16} +(-8266.62 - 14318.2i) q^{17} +(-30598.6 + 17666.1i) q^{19} +(-696.363 + 402.045i) q^{20} +(-26681.1 - 46212.9i) q^{22} +(13987.1 - 24226.4i) q^{23} +77967.1 q^{25} +(-12127.8 - 62199.8i) q^{26} +(-5998.07 - 3462.98i) q^{28} +(16627.8 - 28800.2i) q^{29} +220834. i q^{31} +(28377.9 - 16384.0i) q^{32} +132266. i q^{34} +(-679.823 - 1177.49i) q^{35} +(165533. + 95570.7i) q^{37} +282658. q^{38} +6432.73 q^{40} +(70555.0 + 40734.9i) q^{41} +(-484095. - 838477. i) q^{43} +426897. i q^{44} +(-193811. + 111897. i) q^{46} -1.10569e6i q^{47} +(-405916. + 703067. i) q^{49} +(-540172. - 311869. i) q^{50} +(-164775. + 479445. i) q^{52} -160288. q^{53} +(-41902.3 + 72577.0i) q^{55} +(27703.9 + 47984.5i) q^{56} +(-230402. + 133023. i) q^{58} +(-1.93517e6 + 1.11727e6i) q^{59} +(-934692. - 1.61893e6i) q^{61} +(883335. - 1.52998e6i) q^{62} -262144. q^{64} +(-75073.7 + 65337.0i) q^{65} +(3.10630e6 + 1.79343e6i) q^{67} +(529064. - 916365. i) q^{68} +10877.2i q^{70} +(-640083. + 369552. i) q^{71} +4.24974e6i q^{73} +(-764566. - 1.32427e6i) q^{74} +(-1.95831e6 - 1.13063e6i) q^{76} -721844. q^{77} +2.45055e6 q^{79} +(-44567.2 - 25730.9i) q^{80} +(-325879. - 564440. i) q^{82} +5.19912e6i q^{83} +(179893. - 103861. i) q^{85} +7.74552e6i q^{86} +(1.70759e6 - 2.95763e6i) q^{88} +(-3.73776e6 - 2.15800e6i) q^{89} +(-810698. - 278620. i) q^{91} +1.79035e6 q^{92} +(-4.42278e6 + 7.66047e6i) q^{94} +(-221956. - 384439. i) q^{95} +(7.39963e6 - 4.27218e6i) q^{97} +(5.62454e6 - 3.24733e6i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q + 512 q^{4} + 2520 q^{7} + 2432 q^{10} + 8496 q^{11} - 3620 q^{13} - 34560 q^{14} - 32768 q^{16} - 41520 q^{17} - 54432 q^{19} + 16128 q^{20} - 17280 q^{22} + 7560 q^{23} - 273960 q^{25} - 51072 q^{26}+ \cdots - 19031040 q^{98}+O(q^{100})$ 16 * q + 512 * q^4 + 2520 * q^7 + 2432 * q^10 + 8496 * q^11 - 3620 * q^13 - 34560 * q^14 - 32768 * q^16 - 41520 * q^17 - 54432 * q^19 + 16128 * q^20 - 17280 * q^22 + 7560 * q^23 - 273960 * q^25 - 51072 * q^26 + 161280 * q^28 + 346056 * q^29 + 283248 * q^35 - 68280 * q^37 + 1059840 * q^38 + 311296 * q^40 + 1288008 * q^41 + 285360 * q^43 - 188928 * q^46 - 2131660 * q^49 - 85248 * q^50 + 354560 * q^52 - 3666600 * q^53 - 1091472 * q^55 - 1105920 * q^56 + 3504000 * q^58 - 1799280 * q^59 - 4626000 * q^61 + 2770560 * q^62 - 4194304 * q^64 + 11518020 * q^65 - 7094400 * q^67 + 2657280 * q^68 - 25958520 * q^71 + 1142400 * q^74 - 3483648 * q^76 + 20577480 * q^77 + 34143488 * q^79 + 1032192 * q^80 + 12202240 * q^82 + 7123932 * q^85 + 1105920 * q^88 - 10609452 * q^89 - 38683952 * q^91 + 967680 * q^92 - 14303616 * q^94 - 33837504 * q^95 + 83706300 * q^97 - 19031040 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$ .

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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

)

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

$2$	−6.92820	−	4.00000i	−0.612372	−	0.353553i
$2$	−6.92820	−	4.00000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	32.0000	+	55.4256i	0.250000	+	0.433013i
$5$			12.5639i			0.0449500i	0.999747	+	0.0224750i	$0.00715462\pi$
$5$			12.5639i			0.0449500i	−0.999747	+	0.0224750i	$0.992845\pi$
$6$		0			0
$7$	−93.7198	+	54.1091i	−0.103273	+	0.0596249i	−0.550747	−	0.834672i	$-0.685657\pi$
$7$	−93.7198	+	54.1091i	−0.103273	+	0.0596249i	0.447474	+	0.894297i	$0.352324\pi$
$8$		−	512.000i		−	0.353553i
$9$		0			0
$10$	50.2557	−	87.0454i	0.0158922	−	0.0275262i
$11$	5776.62	+	3335.13i	1.30858	+	0.755507i	0.981859	−	0.189614i	$-0.0607238\pi$
$11$	5776.62	+	3335.13i	1.30858	+	0.755507i	0.326718	+	0.945122i	$0.394057\pi$
$12$		0			0
$13$	5200.37	+	5975.34i	0.656496	+	0.754329i
$13$	5200.37	+	5975.34i	0.656496	+	0.754329i
$14$	865.746			0.0843223
$15$		0			0
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	−8266.62	−	14318.2i	−0.408091	−	0.706834i	0.586585	−	0.809888i	$-0.300472\pi$
$17$	−8266.62	−	14318.2i	−0.408091	−	0.706834i	−0.994676	+	0.103054i	$0.967139\pi$
$18$		0			0
$19$	−30598.6	+	17666.1i	−1.02344	+	0.590886i	−0.915100	−	0.403227i	$-0.867888\pi$
$19$	−30598.6	+	17666.1i	−1.02344	+	0.590886i	−0.108345	+	0.994113i	$0.534555\pi$
$20$	−696.363	+	402.045i	−0.0194639	+	0.0112375i
$21$		0			0
$22$	−26681.1	−	46212.9i	−0.534224	−	0.925304i
$23$	13987.1	−	24226.4i	0.239707	−	0.415185i	−0.720923	−	0.693015i	$-0.756282\pi$
$23$	13987.1	−	24226.4i	0.239707	−	0.415185i	0.960630	+	0.277830i	$0.0896152\pi$
$24$		0			0
$25$	77967.1			0.997979
$26$	−12127.8	−	62199.8i	−0.135325	−	0.694037i
$27$		0			0
$28$	−5998.07	−	3462.98i	−0.0516367	−	0.0298124i
$29$	16627.8	−	28800.2i	0.126603	−	0.219282i	−0.795756	−	0.605618i	$-0.792926\pi$
$29$	16627.8	−	28800.2i	0.126603	−	0.219282i	0.922358	+	0.386336i	$0.126259\pi$
$30$		0			0
$31$			220834.i			1.33137i	0.746232	+	0.665686i	$0.231861\pi$
$31$			220834.i			1.33137i	−0.746232	+	0.665686i	$0.768139\pi$
$32$	28377.9	−	16384.0i	0.153093	−	0.0883883i
$33$		0			0
$34$			132266.i			0.577128i
$35$	−679.823	−	1177.49i	−0.00268014	−	0.00464214i
$36$		0			0
$37$	165533.	+	95570.7i	0.537254	+	0.310183i	0.743965	−	0.668218i	$-0.232943\pi$
$37$	165533.	+	95570.7i	0.537254	+	0.310183i	−0.206712	+	0.978402i	$0.566276\pi$
$38$	282658.			0.835639
$39$		0			0
$40$	6432.73			0.0158922
$41$	70555.0	+	40734.9i	0.159876	+	0.0923046i	0.577804	−	0.816176i	$-0.303910\pi$
$41$	70555.0	+	40734.9i	0.159876	+	0.0923046i	−0.417927	+	0.908480i	$0.637243\pi$
$42$		0			0
$43$	−484095.	−	838477.i	−0.928519	−	1.60824i	−0.785802	−	0.618478i	$-0.787749\pi$
$43$	−484095.	−	838477.i	−0.928519	−	1.60824i	−0.142717	−	0.989764i	$-0.545584\pi$
$44$			426897.i			0.755507i
$45$		0			0
$46$	−193811.	+	111897.i	−0.293580	+	0.169499i
$47$		−	1.10569e6i		−	1.55343i	−0.629851	−	0.776716i	$-0.716884\pi$
$47$		−	1.10569e6i		−	1.55343i	0.629851	−	0.776716i	$-0.283116\pi$
$48$		0			0
$49$	−405916.	+	703067.i	−0.492890	+	0.853710i
$50$	−540172.	−	311869.i	−0.611135	−	0.352839i
$51$		0			0
$52$	−164775.	+	479445.i	−0.162510	+	0.472854i
$53$	−160288.			−0.147889			−0.0739443	−	0.997262i	$-0.523559\pi$
$53$	−160288.			−0.147889			−0.0739443	+	0.997262i	$0.523559\pi$
$54$		0			0
$55$	−41902.3	+	72577.0i	−0.0339601	+	0.0588206i
$56$	27703.9	+	47984.5i	0.0210806	+	0.0365126i
$57$		0			0
$58$	−230402.	+	133023.i	−0.155056	+	0.0895216i
$59$	−1.93517e6	+	1.11727e6i	−1.22670	+	0.708235i	−0.966338	−	0.257277i	$-0.917175\pi$
$59$	−1.93517e6	+	1.11727e6i	−1.22670	+	0.708235i	−0.260361	+	0.965511i	$0.583841\pi$
$60$		0			0
$61$	−934692.	−	1.61893e6i	−0.527247	−	0.913219i	−0.999496	−	0.0317533i	$-0.989891\pi$
$61$	−934692.	−	1.61893e6i	−0.527247	−	0.913219i	0.472249	−	0.881465i	$-0.343442\pi$
$62$	883335.	−	1.52998e6i	0.470711	−	0.815295i
$63$		0			0
$64$	−262144.			−0.125000
$65$	−75073.7	+	65337.0i	−0.0339071	+	0.0295095i
$66$		0			0
$67$	3.10630e6	+	1.79343e6i	1.26178	+	0.728486i	0.973418	−	0.229036i	$-0.0735574\pi$
$67$	3.10630e6	+	1.79343e6i	1.26178	+	0.728486i	0.288358	+	0.957523i	$0.406891\pi$
$68$	529064.	−	916365.i	0.204045	−	0.353417i
$69$		0			0
$70$			10877.2i			0.00379029i
$71$	−640083.	+	369552.i	−0.212242	+	0.122538i	−0.602353	−	0.798230i	$-0.705770\pi$
$71$	−640083.	+	369552.i	−0.212242	+	0.122538i	0.390111	+	0.920768i	$0.372437\pi$
$72$		0			0
$73$			4.24974e6i			1.27859i	0.768960	+	0.639297i	$0.220774\pi$
$73$			4.24974e6i			1.27859i	−0.768960	+	0.639297i	$0.779226\pi$
$74$	−764566.	−	1.32427e6i	−0.219333	−	0.379896i
$75$		0			0
$76$	−1.95831e6	−	1.13063e6i	−0.511722	−	0.295443i
$77$	−721844.			−0.180188
$78$		0			0
$79$	2.45055e6			0.559202			0.279601	−	0.960116i	$-0.409798\pi$
$79$	2.45055e6			0.559202			0.279601	+	0.960116i	$0.409798\pi$
$80$	−44567.2	−	25730.9i	−0.00973197	−	0.00561876i
$81$		0			0
$82$	−325879.	−	564440.i	−0.0652692	−	0.113050i
$83$			5.19912e6i			0.998060i	0.866585	+	0.499030i	$0.166310\pi$
$83$			5.19912e6i			0.998060i	−0.866585	+	0.499030i	$0.833690\pi$
$84$		0			0
$85$	179893.	−	103861.i	0.0317722	−	0.0183437i
$86$			7.74552e6i			1.31312i
$87$		0			0
$88$	1.70759e6	−	2.95763e6i	0.267112	−	0.462652i
$89$	−3.73776e6	−	2.15800e6i	−0.562013	−	0.324479i	0.191940	−	0.981407i	$-0.438522\pi$
$89$	−3.73776e6	−	2.15800e6i	−0.562013	−	0.324479i	−0.753953	+	0.656928i	$0.771855\pi$
$90$		0			0
$91$	−810698.	−	278620.i	−0.112775	−	0.0387586i
$92$	1.79035e6			0.239707
$93$		0			0
$94$	−4.42278e6	+	7.66047e6i	−0.549221	+	0.951279i
$95$	−221956.	−	384439.i	−0.0265603	−	0.0460039i
$96$		0			0
$97$	7.39963e6	−	4.27218e6i	0.823206	−	0.475278i	−0.0283145	−	0.999599i	$-0.509014\pi$
$97$	7.39963e6	−	4.27218e6i	0.823206	−	0.475278i	0.851521	+	0.524321i	$0.175681\pi$
$98$	5.62454e6	−	3.24733e6i	0.603664	−	0.348526i
$99$		0			0
$100$	2.49495e6	+	4.32138e6i	0.249495	+	0.432138i
$101$	−9.46833e6	+	1.63996e7i	−0.914426	+	1.58383i	−0.106687	+	0.994293i	$0.534024\pi$
$101$	−9.46833e6	+	1.63996e7i	−0.914426	+	1.58383i	−0.807739	+	0.589540i	$0.799309\pi$
$102$		0			0
$103$	1.11380e7			1.00433			0.502166	−	0.864771i	$-0.332537\pi$
$103$	1.11380e7			1.00433			0.502166	+	0.864771i	$0.332537\pi$
$104$	3.05937e6	−	2.66259e6i	0.266696	−	0.232106i
$105$		0			0
$106$	1.11051e6	+	641151.i	0.0905629	+	0.0522865i
$107$	1.83954e6	−	3.18618e6i	0.145166	−	0.251435i	−0.784269	−	0.620421i	$-0.786962\pi$
$107$	1.83954e6	−	3.18618e6i	0.145166	−	0.251435i	0.929435	+	0.368986i	$0.120295\pi$
$108$		0			0
$109$			1.55046e7i			1.14675i	0.819293	+	0.573375i	$0.194366\pi$
$109$			1.55046e7i			1.14675i	−0.819293	+	0.573375i	$0.805634\pi$
$110$	580616.	−	335219.i	0.0415924	−	0.0240134i
$111$		0			0
$112$		−	443262.i		−	0.0298124i
$113$	9.63829e6	+	1.66940e7i	0.628385	+	1.08839i	0.987876	+	0.155246i	$0.0496169\pi$
$113$	9.63829e6	+	1.66940e7i	0.628385	+	1.08839i	−0.359491	+	0.933148i	$0.617050\pi$
$114$		0			0
$115$	304379.	+	175733.i	0.0186626	+	0.0107749i
$116$	2.12836e6			0.126603
$117$		0			0
$118$	1.78764e7			1.00160
$119$	1.54949e6	+	894600.i	0.0842898	+	0.0486647i
$120$		0			0
$121$	1.25026e7	+	2.16552e7i	0.641582	+	1.11125i
$122$			1.49551e7i			0.745640i
$123$		0			0
$124$	−1.22398e7	+	7.06668e6i	−0.576501	+	0.332843i
$125$			1.96113e6i			0.0898093i
$126$		0			0
$127$	−1.93352e7	+	3.34895e7i	−0.837596	+	1.45076i	0.0543027	+	0.998525i	$0.482706\pi$
$127$	−1.93352e7	+	3.34895e7i	−0.837596	+	1.45076i	−0.891899	+	0.452235i	$0.850627\pi$
$128$	1.81619e6	+	1.04858e6i	0.0765466	+	0.0441942i
$129$		0			0
$130$	781474.	−	152373.i	0.0311970	−	0.00608284i
$131$	4.18957e7			1.62825			0.814123	−	0.580693i	$-0.197218\pi$
$131$	4.18957e7			1.62825			0.814123	+	0.580693i	$0.197218\pi$
$132$		0			0
$133$	1.91180e6	−	3.31133e6i	0.0704630	−	0.122045i
$134$	−1.43474e7	−	2.48504e7i	−0.515118	−	0.892210i
$135$		0			0
$136$	−7.33092e6	+	4.23251e6i	−0.249904	+	0.144282i
$137$	5.46930e6	−	3.15770e6i	0.181723	−	0.104918i	−0.406379	−	0.913705i	$-0.633209\pi$
$137$	5.46930e6	−	3.15770e6i	0.181723	−	0.104918i	0.588102	+	0.808787i	$0.299875\pi$
$138$		0			0
$139$	1.36659e7	+	2.36701e7i	0.431607	+	0.747564i	0.997012	−	0.0772488i	$-0.0246136\pi$
$139$	1.36659e7	+	2.36701e7i	0.431607	+	0.747564i	−0.565405	+	0.824813i	$0.691280\pi$
$140$	43508.7	−	75359.2i	0.00134007	−	0.00232107i
$141$		0			0
$142$	5.91283e6			0.173295
$143$	1.01120e7	+	5.18612e7i	0.289175	+	1.48309i
$144$		0			0
$145$	361844.	+	208911.i	0.00985674	+	0.00569079i
$146$	1.69990e7	−	2.94431e7i	0.452051	−	0.782975i
$147$		0			0
$148$			1.22330e7i			0.310183i
$149$	1.92420e7	−	1.11094e7i	0.476539	−	0.275130i	−0.242434	−	0.970168i	$-0.577946\pi$
$149$	1.92420e7	−	1.11094e7i	0.476539	−	0.275130i	0.718973	+	0.695038i	$0.244612\pi$
$150$		0			0
$151$			4.67506e7i			1.10501i	0.833508	+	0.552507i	$0.186329\pi$
$151$			4.67506e7i			1.10501i	−0.833508	+	0.552507i	$0.813671\pi$
$152$	9.04505e6	+	1.56665e7i	0.208910	+	0.361842i
$153$		0			0
$154$	5.00109e6	+	2.88738e6i	0.110342	+	0.0637061i
$155$	−2.77454e6			−0.0598452
$156$		0			0
$157$	−5.59114e7			−1.15306			−0.576530	−	0.817076i	$-0.695594\pi$
$157$	−5.59114e7			−1.15306			−0.576530	+	0.817076i	$0.695594\pi$
$158$	−1.69779e7	−	9.80220e6i	−0.342440	−	0.197708i
$159$		0			0
$160$	205847.	+	356538.i	0.00397306	+	0.00688154i
$161$			3.02733e6i			0.0571701i
$162$		0			0
$163$	−3.14275e7	+	1.81447e7i	−0.568399	+	0.328166i	−0.756510	−	0.653982i	$-0.773097\pi$
$163$	−3.14275e7	+	1.81447e7i	−0.568399	+	0.328166i	0.188110	+	0.982148i	$0.439764\pi$
$164$			5.21407e6i			0.0923046i
$165$		0			0
$166$	2.07965e7	−	3.60206e7i	0.352867	−	0.611184i
$167$	−6.06842e7	−	3.50360e7i	−1.00825	−	0.582113i	−0.0975708	−	0.995229i	$-0.531107\pi$
$167$	−6.06842e7	−	3.50360e7i	−1.00825	−	0.582113i	−0.910679	+	0.413116i	$0.864441\pi$
$168$		0			0
$169$	−8.66088e6	+	6.21479e7i	−0.138025	+	0.990429i
$170$	−1.66178e6			−0.0259419
$171$		0			0
$172$	3.09821e7	−	5.36625e7i	0.464259	−	0.804121i
$173$	3.16133e7	+	5.47559e7i	0.464204	+	0.804025i	0.999165	−	0.0408514i	$-0.0130070\pi$
$173$	3.16133e7	+	5.47559e7i	0.464204	+	0.804025i	−0.534961	+	0.844877i	$0.679674\pi$
$174$		0			0
$175$	−7.30706e6	+	4.21873e6i	−0.103065	+	0.0595044i
$176$	−2.36610e7	+	1.36607e7i	−0.327144	+	0.188877i
$177$		0			0
$178$	1.72640e7	+	2.99021e7i	0.229441	+	0.397404i
$179$	−2.80744e7	+	4.86262e7i	−0.365868	+	0.633702i	−0.988915	−	0.148483i	$-0.952561\pi$
$179$	−2.80744e7	+	4.86262e7i	−0.365868	+	0.633702i	0.623047	+	0.782184i	$0.285894\pi$
$180$		0			0
$181$	1.03528e8			1.29773			0.648864	−	0.760904i	$-0.275244\pi$
$181$	1.03528e8			1.29773			0.648864	+	0.760904i	$0.275244\pi$
$182$	4.50220e6	+	5.17313e6i	0.0553573	+	0.0636068i
$183$		0			0
$184$	−1.24039e7	−	7.16141e6i	−0.146790	−	0.0847493i
$185$	−1.20074e6	+	2.07975e6i	−0.0139428	+	0.0241496i
$186$		0			0
$187$		−	1.10281e8i		−	1.23326i
$188$	6.12838e7	−	3.53822e7i	0.672656	−	0.388358i
$189$		0			0
$190$			3.55129e6i			0.0375620i
$191$	2.49874e7	+	4.32795e7i	0.259481	+	0.449434i	0.966103	−	0.258157i	$-0.0831153\pi$
$191$	2.49874e7	+	4.32795e7i	0.259481	+	0.449434i	−0.706622	+	0.707591i	$0.749782\pi$
$192$		0			0
$193$	4.14043e7	+	2.39048e7i	0.414567	+	0.239350i	0.692750	−	0.721178i	$-0.256399\pi$
$193$	4.14043e7	+	2.39048e7i	0.414567	+	0.239350i	−0.278183	+	0.960528i	$0.589732\pi$
$194$	−6.83548e7			−0.672145
$195$		0			0
$196$	−5.19572e7			−0.492890
$197$	2.06870e7	+	1.19437e7i	0.192782	+	0.111303i	0.593284	−	0.804993i	$-0.297831\pi$
$197$	2.06870e7	+	1.19437e7i	0.192782	+	0.111303i	−0.400502	+	0.916296i	$0.631164\pi$
$198$		0			0
$199$	−8.06424e7	−	1.39677e8i	−0.725400	−	1.25643i	−0.958809	−	0.284051i	$-0.908321\pi$
$199$	−8.06424e7	−	1.39677e8i	−0.725400	−	1.25643i	0.233409	−	0.972379i	$-0.425012\pi$
$200$		−	3.99192e7i		−	0.352839i
$201$		0			0
$202$	1.31197e8	−	7.57466e7i	1.11994	−	0.646597i
$203$			3.59887e6i			0.0301947i
$204$		0			0
$205$	−511790.	+	886447.i	−0.00414910	+	0.00718645i
$206$	−7.71664e7	−	4.45520e7i	−0.615025	−	0.355085i
$207$		0			0
$208$	−3.18463e7	+	6.20945e6i	−0.245379	+	0.0478445i
$209$	−2.35675e8			−1.78567
$210$		0			0
$211$	−3.89068e7	+	6.73886e7i	−0.285126	+	0.493853i	−0.972640	−	0.232318i	$-0.925369\pi$
$211$	−3.89068e7	+	6.73886e7i	−0.285126	+	0.493853i	0.687514	+	0.726172i	$0.258702\pi$
$212$	−5.12921e6	−	8.88404e6i	−0.0369721	−	0.0640376i
$213$		0			0
$214$	−2.54894e7	+	1.47163e7i	−0.177792	+	0.102648i
$215$	1.05346e7	−	6.08213e6i	0.0722905	−	0.0417370i
$216$		0			0
$217$	−1.19491e7	−	2.06965e7i	−0.0793829	−	0.137495i
$218$	6.20185e7	−	1.07419e8i	0.405437	−	0.702238i
$219$		0			0
$220$	−5.36350e6			−0.0339601
$221$	4.25667e7	−	1.23856e8i	0.265276	−	0.771869i
$222$		0			0
$223$	5.97190e7	+	3.44788e7i	0.360617	+	0.208202i	0.669351	−	0.742946i	$-0.266572\pi$
$223$	5.97190e7	+	3.44788e7i	0.360617	+	0.208202i	−0.308735	+	0.951148i	$0.599905\pi$
$224$	−1.77305e6	+	3.07101e6i	−0.0105403	+	0.0182563i
$225$		0			0
$226$		−	1.54213e8i		−	0.888670i
$227$	1.27607e7	−	7.36742e6i	0.0724079	−	0.0418047i	−0.463359	−	0.886171i	$-0.653356\pi$
$227$	1.27607e7	−	7.36742e6i	0.0724079	−	0.0418047i	0.535767	+	0.844366i	$0.320023\pi$
$228$		0			0
$229$		−	1.39239e8i		−	0.766188i	−0.923709	−	0.383094i	$-0.874859\pi$
$229$		−	1.39239e8i		−	0.766188i	0.923709	−	0.383094i	$-0.125141\pi$
$230$	−1.40587e6	−	2.43503e6i	−0.00761897	−	0.0131964i
$231$		0			0
$232$	−1.47457e7	−	8.51345e6i	−0.0775279	−	0.0447608i
$233$	6.42701e6			0.0332861			0.0166431	−	0.999861i	$-0.494702\pi$
$233$	6.42701e6			0.0332861			0.0166431	+	0.999861i	$0.494702\pi$
$234$		0			0
$235$	1.38918e7			0.0698269
$236$	−1.23851e8	−	7.15055e7i	−0.613349	−	0.354117i
$237$		0			0
$238$	−7.15680e6	−	1.23959e7i	−0.0344112	−	0.0596019i
$239$			2.32090e8i			1.09967i	0.835272	+	0.549837i	$0.185310\pi$
$239$			2.32090e8i			1.09967i	−0.835272	+	0.549837i	$0.814690\pi$
$240$		0			0
$241$	−1.64784e8	+	9.51384e7i	−0.758327	+	0.437820i	−0.828695	−	0.559701i	$-0.810916\pi$
$241$	−1.64784e8	+	9.51384e7i	−0.758327	+	0.437820i	0.0703677	+	0.997521i	$0.477583\pi$
$242$		−	2.00042e8i		−	0.907335i
$243$		0			0
$244$	5.98203e7	−	1.03612e8i	0.263624	−	0.456609i
$245$	−8.83328e6	−	5.09989e6i	−0.0383743	−	0.0221554i
$246$		0			0
$247$	−2.64685e8	−	9.09669e7i	−1.11761	−	0.384100i
$248$	1.13067e8			0.470711
$249$		0			0
$250$	7.84452e6	−	1.35871e7i	0.0317524	−	0.0549967i
$251$	−9.40925e7	−	1.62973e8i	−0.375575	−	0.650516i	0.614838	−	0.788654i	$-0.289222\pi$
$251$	−9.40925e7	−	1.62973e8i	−0.375575	−	0.650516i	−0.990413	+	0.138138i	$0.955888\pi$
$252$		0			0
$253$	1.61597e8	−	9.32978e7i	0.627351	−	0.362201i
$254$	2.67916e8	−	1.54681e8i	1.02584	−	0.592270i
$255$		0			0
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	−7.14981e7	+	1.23838e8i	−0.262741	+	0.455081i	−0.966969	−	0.254892i	$-0.917960\pi$
$257$	−7.14981e7	+	1.23838e8i	−0.262741	+	0.455081i	0.704228	+	0.709974i	$0.251293\pi$
$258$		0			0
$259$	−2.06850e7			−0.0739786
$260$	−6.02370e6	−	2.07022e6i	−0.0212548	−	0.00730484i
$261$		0			0
$262$	−2.90262e8	−	1.67583e8i	−0.997093	−	0.575672i
$263$	−1.87354e8	+	3.24506e8i	−0.635063	+	1.09996i	0.351438	+	0.936211i	$0.385693\pi$
$263$	−1.87354e8	+	3.24506e8i	−0.635063	+	1.09996i	−0.986502	+	0.163751i	$0.947641\pi$
$264$		0			0
$265$		−	2.01384e6i		−	0.00664760i
$266$	−2.64906e7	+	1.52944e7i	−0.0862992	+	0.0498249i
$267$		0			0
$268$			2.29558e8i			0.728486i
$269$	−3.12901e8	−	5.41961e8i	−0.980108	−	1.69760i	−0.661928	−	0.749567i	$-0.730262\pi$
$269$	−3.12901e8	−	5.41961e8i	−0.980108	−	1.69760i	−0.318180	−	0.948030i	$-0.603072\pi$
$270$		0			0
$271$	−1.80927e8	−	1.04458e8i	−0.552218	−	0.318823i	0.197798	−	0.980243i	$-0.436621\pi$
$271$	−1.80927e8	−	1.04458e8i	−0.552218	−	0.318823i	−0.750016	+	0.661419i	$0.769954\pi$
$272$	6.77202e7			0.204045
$273$		0			0
$274$	−5.05233e7			−0.148376
$275$	4.50386e8	+	2.60031e8i	1.30593	+	0.753981i
$276$		0			0
$277$	6.99093e7	+	1.21087e8i	0.197631	+	0.342308i	0.947760	−	0.318984i	$-0.103342\pi$
$277$	6.99093e7	+	1.21087e8i	0.197631	+	0.342308i	−0.750129	+	0.661292i	$0.770008\pi$
$278$		−	2.18655e8i		−	0.610384i
$279$		0			0
$280$	−602874.	+	348069.i	−0.00164124	+	0.000947573i
$281$			9.44593e7i			0.253964i	0.991905	+	0.126982i	$0.0405291\pi$
$281$			9.44593e7i			0.253964i	−0.991905	+	0.126982i	$0.959471\pi$
$282$		0			0
$283$	1.65237e8	−	2.86200e8i	0.433367	−	0.750614i	−0.563794	−	0.825916i	$-0.690659\pi$
$283$	1.65237e8	−	2.86200e8i	0.433367	−	0.750614i	0.997161	+	0.0753019i	$0.0239921\pi$
$284$	−4.09653e7	−	2.36513e7i	−0.106121	−	0.0612690i
$285$		0			0
$286$	1.37387e8	−	3.99753e8i	0.347267	−	1.01044i
$287$	−8.81653e6			−0.0220146
$288$		0			0
$289$	6.84952e7	−	1.18637e8i	0.166924	−	0.289120i
$290$	−1.67129e6	−	2.89475e6i	−0.00402400	−	0.00696977i
$291$		0			0
$292$	−2.35545e8	+	1.35992e8i	−0.553647	+	0.319648i
$293$	1.45881e8	−	8.42243e7i	0.338814	−	0.195614i	−0.320934	−	0.947102i	$-0.603997\pi$
$293$	1.45881e8	−	8.42243e7i	0.338814	−	0.195614i	0.659747	+	0.751487i	$0.270663\pi$
$294$		0			0
$295$	−1.40373e7	−	2.43134e7i	−0.0318352	−	0.0551401i
$296$	4.89322e7	−	8.47530e7i	0.109666	−	0.189948i
$297$		0			0
$298$	−1.77750e8			−0.389093
$299$	2.17499e8	−	4.24084e7i	0.470553	−	0.0917493i
$300$		0			0
$301$	9.07385e7	+	5.23879e7i	0.191782	+	0.110726i
$302$	1.87002e8	−	3.23898e8i	0.390682	−	0.676680i
$303$		0			0
$304$		−	1.44721e8i		−	0.295443i
$305$	2.03402e7	−	1.17434e7i	0.0410492	−	0.0236998i
$306$		0			0
$307$			1.35886e8i			0.268034i	0.990979	+	0.134017i	$0.0427877\pi$
$307$			1.35886e8i			0.268034i	−0.990979	+	0.134017i	$0.957212\pi$
$308$	−2.30990e7	−	4.00087e7i	−0.0450470	−	0.0780237i
$309$		0			0
$310$	1.92226e7	+	1.10981e7i	0.0366476	+	0.0211585i
$311$	−5.41703e8			−1.02117			−0.510587	−	0.859826i	$-0.670572\pi$
$311$	−5.41703e8			−1.02117			−0.510587	+	0.859826i	$0.670572\pi$
$312$		0			0
$313$	−7.16256e8			−1.32027			−0.660135	−	0.751147i	$-0.729501\pi$
$313$	−7.16256e8			−1.32027			−0.660135	+	0.751147i	$0.729501\pi$
$314$	3.87366e8	+	2.23646e8i	0.706102	+	0.407668i
$315$		0			0
$316$	7.84176e7	+	1.35823e8i	0.139801	+	0.242142i
$317$		−	5.13860e6i		−	0.00906020i	−0.999990	−	0.00453010i	$-0.998558\pi$
$317$		−	5.13860e6i		−	0.00906020i	0.999990	−	0.00453010i	$-0.00144198\pi$
$318$		0			0
$319$	1.92105e8	−	1.10912e8i	0.331338	−	0.191298i
$320$		−	3.29356e6i		−	0.00561876i
$321$		0			0
$322$	1.21093e7	−	2.09739e7i	0.0202127	−	0.0350094i
$323$	5.05894e8	+	2.92078e8i	0.835317	+	0.482270i
$324$		0			0
$325$	4.05458e8	+	4.65880e8i	0.655170	+	0.752805i
$326$	2.90315e8			0.464096
$327$		0			0
$328$	2.08563e7	−	3.61241e7i	0.0326346	−	0.0565248i
$329$	5.98281e7	+	1.03625e8i	0.0926232	+	0.160428i
$330$		0			0
$331$	3.08173e8	−	1.77924e8i	0.467085	−	0.269672i	−0.247934	−	0.968777i	$-0.579751\pi$
$331$	3.08173e8	−	1.77924e8i	0.467085	−	0.269672i	0.715019	+	0.699105i	$0.246418\pi$
$332$	−2.88164e8	+	1.66372e8i	−0.432172	+	0.249515i
$333$		0			0
$334$	2.80288e8	+	4.85474e8i	0.411616	+	0.712940i
$335$	−2.25325e7	+	3.90274e7i	−0.0327455	+	0.0567169i
$336$		0			0
$337$	−4.39540e8			−0.625596			−0.312798	−	0.949820i	$-0.601266\pi$
$337$	−4.39540e8			−0.625596			−0.312798	+	0.949820i	$0.601266\pi$
$338$	3.08596e8	−	3.95930e8i	0.434692	−	0.557712i
$339$		0			0
$340$	1.15131e7	+	6.64712e6i	0.0158861	+	0.00917185i
$341$	−7.36509e8	+	1.27567e9i	−1.00586	+	1.74220i
$342$		0			0
$343$		−	1.76977e8i		−	0.236804i
$344$	−4.29300e8	+	2.47857e8i	−0.568599	+	0.328281i
$345$		0			0
$346$		−	5.05814e8i		−	0.656484i
$347$	3.55843e8	+	6.16339e8i	0.457199	+	0.791893i	0.998812	−	0.0487358i	$-0.0155192\pi$
$347$	3.55843e8	+	6.16339e8i	0.457199	+	0.791893i	−0.541612	+	0.840628i	$0.682186\pi$
$348$		0			0
$349$	1.32703e9	+	7.66162e8i	1.67106	+	0.964787i	0.967046	+	0.254602i	$0.0819444\pi$
$349$	1.32703e9	+	7.66162e8i	1.67106	+	0.964787i	0.704015	+	0.710186i	$0.251389\pi$
$350$	6.74998e7			0.0841519
$351$		0			0
$352$	2.18571e8			0.267112
$353$	−5.75284e7	−	3.32140e7i	−0.0696099	−	0.0401893i	0.464791	−	0.885420i	$-0.346129\pi$
$353$	−5.75284e7	−	3.32140e7i	−0.0696099	−	0.0401893i	−0.534401	+	0.845231i	$0.679463\pi$
$354$		0			0
$355$	−4.64302e6	−	8.04195e6i	−0.00550809	−	0.00954030i
$356$		−	2.76224e8i		−	0.324479i
$357$		0			0
$358$	3.89010e8	−	2.24595e8i	0.448095	−	0.258708i
$359$		−	1.24265e9i		−	1.41748i	−0.705468	−	0.708742i	$-0.749263\pi$
$359$		−	1.24265e9i		−	1.41748i	0.705468	−	0.708742i	$-0.250737\pi$
$360$		0			0
$361$	1.77248e8	−	3.07002e8i	0.198292	−	0.343452i
$362$	−7.17265e8	−	4.14113e8i	−0.794693	−	0.458816i
$363$		0			0
$364$	−1.04996e7	−	5.38493e7i	−0.0114109	−	0.0585228i
$365$	−5.33934e7			−0.0574728
$366$		0			0
$367$	−1.15229e7	+	1.99583e7i	−0.0121684	+	0.0210762i	−0.872045	−	0.489425i	$-0.837207\pi$
$367$	−1.15229e7	+	1.99583e7i	−0.0121684	+	0.0210762i	0.859877	+	0.510501i	$0.170540\pi$
$368$	5.72913e7	+	9.92314e7i	0.0599268	+	0.103796i
$369$		0			0
$370$	1.66380e7	−	9.60594e6i	0.0170763	−	0.00985902i
$371$	1.50221e7	−	8.67303e6i	0.0152729	−	0.00881784i
$372$		0			0
$373$	3.56036e8	+	6.16672e8i	0.355232	+	0.615280i	0.987158	−	0.159749i	$-0.0510684\pi$
$373$	3.56036e8	+	6.16672e8i	0.355232	+	0.615280i	−0.631925	+	0.775029i	$0.717735\pi$
$374$	−4.41124e8	+	7.64050e8i	−0.436024	+	0.755216i
$375$		0			0
$376$	−5.66115e8			−0.549221
$377$	2.58562e8	−	5.04149e7i	0.248525	−	0.0484579i
$378$		0			0
$379$	−8.78626e8	−	5.07275e8i	−0.829023	−	0.478637i	0.0244948	−	0.999700i	$-0.492202\pi$
$379$	−8.78626e8	−	5.07275e8i	−0.829023	−	0.478637i	−0.853518	+	0.521063i	$0.825536\pi$
$380$	1.42052e7	−	2.46041e7i	0.0132802	−	0.0230019i
$381$		0			0
$382$		−	3.99799e8i		−	0.366961i
$383$	−9.35938e8	+	5.40364e8i	−0.851238	+	0.491463i	−0.861068	−	0.508489i	$-0.830204\pi$
$383$	−9.35938e8	+	5.40364e8i	−0.851238	+	0.491463i	0.00983015	+	0.999952i	$0.496871\pi$
$384$		0			0
$385$		−	9.06920e6i		−	0.00809946i
$386$	−1.91238e8	−	3.31234e8i	−0.169246	−	0.293143i
$387$		0			0
$388$	4.73576e8	+	2.73419e8i	0.411603	+	0.237639i
$389$	8.28300e8			0.713450			0.356725	−	0.934209i	$-0.383893\pi$
$389$	8.28300e8			0.713450			0.356725	+	0.934209i	$0.383893\pi$
$390$		0			0
$391$	−4.62505e8			−0.391289
$392$	3.59970e8	+	2.07829e8i	0.301832	+	0.174263i
$393$		0			0
$394$	−9.55492e7	−	1.65496e8i	−0.0787028	−	0.136317i
$395$			3.07885e7i			0.0251362i
$396$		0			0
$397$	−7.06056e6	+	4.07642e6i	−0.00566334	+	0.00326973i	−0.502829	−	0.864386i	$-0.667707\pi$
$397$	−7.06056e6	+	4.07642e6i	−0.00566334	+	0.00326973i	0.497166	+	0.867656i	$0.334374\pi$
$398$			1.29028e9i			1.02587i
$399$		0			0
$400$	−1.59677e8	+	2.76568e8i	−0.124747	+	0.216069i
$401$	−4.29147e8	−	2.47768e8i	−0.332354	−	0.191885i	0.324532	−	0.945875i	$-0.394793\pi$
$401$	−4.29147e8	−	2.47768e8i	−0.332354	−	0.191885i	−0.656886	+	0.753990i	$0.728127\pi$
$402$		0			0
$403$	−1.31956e9	+	1.14842e9i	−1.00429	+	0.874041i
$404$	−1.21195e9			−0.914426
$405$		0			0
$406$	1.43955e7	−	2.49337e7i	0.0106754	−	0.0184904i
$407$	6.37482e8	+	1.10415e9i	0.468692	+	0.811798i
$408$		0			0
$409$	3.33752e8	−	1.92692e8i	0.241208	−	0.139262i	−0.374524	−	0.927217i	$-0.622194\pi$
$409$	3.33752e8	−	1.92692e8i	0.241208	−	0.139262i	0.615732	+	0.787956i	$0.288860\pi$
$410$	7.09158e6	−	4.09432e6i	0.00508159	−	0.00293386i
$411$		0			0
$412$	3.56416e8	+	6.17331e8i	0.251083	+	0.434888i
$413$	1.20909e8	−	2.09421e8i	0.0844568	−	0.146283i
$414$		0			0
$415$	−6.53213e7			−0.0448628
$416$	2.45476e8	+	8.43649e7i	0.167179	+	0.0574560i
$417$		0			0
$418$	1.63281e9	+	9.42702e8i	1.09350	+	0.631331i
$419$	1.03381e9	−	1.79061e9i	0.686579	−	1.18919i	−0.286359	−	0.958122i	$-0.592445\pi$
$419$	1.03381e9	−	1.79061e9i	0.686579	−	1.18919i	0.972938	−	0.231067i	$-0.0742217\pi$
$420$		0			0
$421$			9.36163e8i			0.611454i	0.952119	+	0.305727i	$0.0988996\pi$
$421$			9.36163e8i			0.611454i	−0.952119	+	0.305727i	$0.901100\pi$
$422$	5.39109e8	−	3.11255e8i	0.349207	−	0.201615i
$423$		0			0
$424$			8.20673e7i			0.0522865i
$425$	−6.44525e8	−	1.11635e9i	−0.407266	−	0.705406i
$426$		0			0
$427$	1.75198e8	+	1.01151e8i	0.108901	+	0.0628741i
$428$	2.35461e8			0.145166
$429$		0			0
$430$	−9.73140e7			−0.0590250
$431$	4.32169e8	+	2.49513e8i	0.260006	+	0.150114i	0.624337	−	0.781155i	$-0.285369\pi$
$431$	4.32169e8	+	2.49513e8i	0.260006	+	0.150114i	−0.364331	+	0.931269i	$0.618702\pi$
$432$		0			0
$433$	−5.31056e8	−	9.19815e8i	−0.314364	−	0.544494i	0.664938	−	0.746898i	$-0.268458\pi$
$433$	−5.31056e8	−	9.19815e8i	−0.314364	−	0.544494i	−0.979302	+	0.202404i	$0.935124\pi$
$434$			1.91186e8i			0.112264i
$435$		0			0
$436$	−8.59353e8	+	4.96148e8i	−0.496557	+	0.286687i
$437$			9.88393e8i			0.566558i
$438$		0			0
$439$	−4.98585e8	+	8.63575e8i	−0.281264	+	0.487163i	−0.971696	−	0.236234i	$-0.924087\pi$
$439$	−4.98585e8	+	8.63575e8i	−0.281264	+	0.487163i	0.690433	+	0.723397i	$0.257420\pi$
$440$	3.71594e7	+	2.14540e7i	0.0207962	+	0.0120067i
$441$		0			0
$442$	−7.90334e8	+	6.87832e8i	−0.435344	+	0.378882i
$443$	−3.24508e8			−0.177342			−0.0886711	−	0.996061i	$-0.528262\pi$
$443$	−3.24508e8			−0.177342			−0.0886711	+	0.996061i	$0.528262\pi$
$444$		0			0
$445$	2.71129e7	−	4.69609e7i	0.0145853	−	0.0252625i
$446$	−2.75830e8	−	4.77752e8i	−0.147221	−	0.254994i
$447$		0			0
$448$	2.45681e7	−	1.41844e7i	0.0129092	−	0.00745311i
$449$	−7.38956e8	+	4.26636e8i	−0.385262	+	0.222431i	−0.680105	−	0.733115i	$-0.738066\pi$
$449$	−7.38956e8	+	4.26636e8i	−0.385262	+	0.222431i	0.294843	+	0.955546i	$0.404733\pi$
$450$		0			0
$451$	2.71713e8	+	4.70620e8i	0.139474	+	0.241575i
$452$	−6.16851e8	+	1.06842e9i	−0.314192	+	0.544197i
$453$		0			0
$454$	−1.17879e8			−0.0591208
$455$	3.50056e6	−	1.01855e7i	0.00174220	−	0.00506926i
$456$		0			0
$457$	1.20028e9	+	6.92980e8i	0.588267	+	0.339636i	0.764412	−	0.644728i	$-0.223029\pi$
$457$	1.20028e9	+	6.92980e8i	0.588267	+	0.339636i	−0.176145	+	0.984364i	$0.556363\pi$
$458$	−5.56954e8	+	9.64673e8i	−0.270888	+	0.469192i
$459$		0			0
$460$			2.24938e7i			0.0107749i
$461$	2.17739e9	−	1.25712e9i	1.03510	−	0.597616i	0.116659	−	0.993172i	$-0.462781\pi$
$461$	2.17739e9	−	1.25712e9i	1.03510	−	0.597616i	0.918442	+	0.395556i	$0.129448\pi$
$462$		0			0
$463$			3.33173e9i			1.56004i	0.625753	+	0.780021i	$0.284792\pi$
$463$			3.33173e9i			1.56004i	−0.625753	+	0.780021i	$0.715208\pi$
$464$	6.81076e7	+	1.17966e8i	0.0316506	+	0.0548205i
$465$		0			0
$466$	−4.45276e7	−	2.57080e7i	−0.0203835	−	0.0117684i
$467$	1.46658e9			0.666342			0.333171	−	0.942866i	$-0.391881\pi$
$467$	1.46658e9			0.666342			0.333171	+	0.942866i	$0.391881\pi$
$468$		0			0
$469$	−3.88163e8			−0.173744
$470$	−9.62456e7	−	5.55674e7i	−0.0427600	−	0.0246875i
$471$		0			0
$472$	5.72044e8	+	9.90809e8i	0.250399	+	0.433703i
$473$		−	6.45808e9i		−	2.80601i
$474$		0			0
$475$	−2.38569e9	+	1.37738e9i	−1.02138	+	0.589692i
$476$			1.14509e8i			0.0486647i
$477$		0			0
$478$	9.28361e8	−	1.60797e9i	0.388794	−	0.673410i
$479$	−3.18752e9	−	1.84031e9i	−1.32519	−	0.765099i	−0.340639	−	0.940194i	$-0.610643\pi$
$479$	−3.18752e9	−	1.84031e9i	−1.32519	−	0.765099i	−0.984552	+	0.175095i	$0.943977\pi$
$480$		0			0
$481$	2.89766e8	+	1.48612e9i	0.118724	+	0.608900i
$482$	1.52221e9			0.619172
$483$		0			0
$484$	−8.00168e8	+	1.38593e9i	−0.320791	+	0.555627i
$485$	5.36753e7	+	9.29683e7i	0.0213638	+	0.0370032i
$486$		0			0
$487$	3.30378e9	−	1.90744e9i	1.29616	−	0.748340i	0.316424	−	0.948618i	$-0.397518\pi$
$487$	3.30378e9	−	1.90744e9i	1.29616	−	0.748340i	0.979739	+	0.200278i	$0.0641845\pi$
$488$	−8.28894e8	+	4.78562e8i	−0.322872	+	0.186410i
$489$		0			0
$490$	4.07992e7	+	7.06662e7i	0.0156662	+	0.0271347i
$491$	−2.14842e9	+	3.72118e9i	−0.819096	+	1.41872i	0.0872534	+	0.996186i	$0.472191\pi$
$491$	−2.14842e9	+	3.72118e9i	−0.819096	+	1.41872i	−0.906349	+	0.422529i	$0.861142\pi$
$492$		0			0
$493$	−5.49824e8			−0.206661
$494$	1.46993e9	+	1.68898e9i	0.548594	+	0.630347i
$495$		0			0
$496$	−7.83350e8	−	4.52267e8i	−0.288250	−	0.166421i
$497$	3.99923e7	−	6.92686e7i	0.0146126	−	0.0253098i
$498$		0			0
$499$		−	1.52473e9i		−	0.549341i	−0.961538	−	0.274670i	$-0.911431\pi$
$499$		−	1.52473e9i		−	0.549341i	0.961538	−	0.274670i	$-0.0885687\pi$
$500$	−1.08697e8	+	6.27561e7i	−0.0388886	+	0.0224523i
$501$		0			0
$502$			1.50548e9i			0.531144i
$503$	1.40843e9	+	2.43947e9i	0.493454	+	0.854687i	0.999972	−	0.00754273i	$-0.00240095\pi$
$503$	1.40843e9	+	2.43947e9i	0.493454	+	0.854687i	−0.506518	+	0.862229i	$0.669068\pi$
$504$		0			0
$505$	−2.06044e8	−	1.18959e8i	−0.0711933	−	0.0411035i
$506$	−1.49277e9			−0.512230
$507$		0			0
$508$	−2.47490e9			−0.837596
$509$	4.95616e9	+	2.86144e9i	1.66584	+	0.961772i	0.969844	+	0.243725i	$0.0783695\pi$
$509$	4.95616e9	+	2.86144e9i	1.66584	+	0.961772i	0.695994	+	0.718047i	$0.254964\pi$
$510$		0			0
$511$	−2.29950e8	−	3.98285e8i	−0.0762360	−	0.132045i
$512$			1.34218e8i			0.0441942i
$513$		0			0
$514$	9.90707e8	−	5.71985e8i	0.321791	−	0.185786i
$515$			1.39937e8i			0.0451448i
$516$		0			0
$517$	3.68764e9	−	6.38717e9i	1.17363	−	2.03279i
$518$	1.43310e8	+	8.27400e7i	0.0453025	+	0.0261554i
$519$		0			0
$520$	3.34525e7	+	3.84377e7i	0.0104332	+	0.0119880i
$521$	1.74794e9			0.541496			0.270748	−	0.962650i	$-0.412729\pi$
$521$	1.74794e9			0.541496			0.270748	+	0.962650i	$0.412729\pi$
$522$		0			0
$523$	8.72984e8	−	1.51205e9i	0.266840	−	0.462180i	−0.701204	−	0.712960i	$-0.747354\pi$
$523$	8.72984e8	−	1.51205e9i	0.266840	−	0.462180i	0.968044	+	0.250781i	$0.0806873\pi$
$524$	1.34066e9	+	2.32210e9i	0.407061	+	0.705051i
$525$		0			0
$526$	2.59605e9	−	1.49883e9i	0.777791	−	0.449058i
$527$	3.16194e9	−	1.82555e9i	0.941059	−	0.543321i
$528$		0			0
$529$	1.31113e9	+	2.27095e9i	0.385081	+	0.666980i
$530$	−8.05536e6	+	1.39523e7i	−0.00235028	+	0.00407081i
$531$		0			0
$532$	2.44710e8			0.0704630
$533$	1.23507e8	+	6.33427e8i	0.0353301	+	0.181197i
$534$		0			0
$535$	4.00309e7	+	2.31118e7i	0.0113020	+	0.00652523i
$536$	9.18234e8	−	1.59043e9i	0.257559	−	0.446105i
$537$		0			0
$538$			5.00642e9i			1.38608i
$539$	−4.68964e9	+	2.70757e9i	−1.28997	+	0.744764i
$540$		0			0
$541$			3.07314e8i			0.0834433i	0.999129	+	0.0417217i	$0.0132843\pi$
$541$			3.07314e8i			0.0834433i	−0.999129	+	0.0417217i	$0.986716\pi$
$542$	8.35666e8	+	1.44742e9i	0.225442	+	0.390477i
$543$		0			0
$544$	−4.69179e8	−	2.70881e8i	−0.124952	−	0.0721410i
$545$	−1.94799e8			−0.0515464
$546$		0			0
$547$	2.37307e9			0.619947			0.309973	−	0.950745i	$-0.399680\pi$
$547$	2.37307e9			0.619947			0.309973	+	0.950745i	$0.399680\pi$
$548$	3.50035e8	+	2.02093e8i	0.0908615	+	0.0524589i
$549$		0			0
$550$	−2.08025e9	−	3.60309e9i	−0.533145	−	0.923434i
$551$			1.17500e9i			0.299231i
$552$		0			0
$553$	−2.29665e8	+	1.32597e8i	−0.0577507	+	0.0333424i
$554$		−	1.11855e9i		−	0.279493i
$555$		0			0
$556$	−8.74621e8	+	1.51489e9i	−0.215803	+	0.373782i
$557$	−2.40567e9	−	1.38891e9i	−0.589851	−	0.340551i	0.175188	−	0.984535i	$-0.443947\pi$
$557$	−2.40567e9	−	1.38891e9i	−0.589851	−	0.340551i	−0.765039	+	0.643984i	$0.777280\pi$
$558$		0			0
$559$	2.49271e9	−	7.25302e9i	0.603575	−	1.75621i
$560$	5.56911e6			0.00134007
$561$		0			0
$562$	3.77837e8	−	6.54433e8i	0.0897899	−	0.155521i
$563$	−3.36862e9	−	5.83462e9i	−0.795559	−	1.37795i	−0.922484	−	0.386036i	$-0.873844\pi$
$563$	−3.36862e9	−	5.83462e9i	−0.795559	−	1.37795i	0.126924	−	0.991912i	$-0.459489\pi$
$564$		0			0
$565$	−2.09742e8	+	1.21095e8i	−0.0489234	+	0.0282459i
$566$	−2.28960e9	+	1.32190e9i	−0.530764	+	0.306437i
$567$		0			0
$568$	1.89211e8	+	3.27722e8i	0.0433238	+	0.0750390i
$569$	−2.30137e9	+	3.98610e9i	−0.523714	+	0.907100i	0.475905	+	0.879497i	$0.342121\pi$
$569$	−2.30137e9	+	3.98610e9i	−0.523714	+	0.907100i	−0.999619	+	0.0276028i	$0.991213\pi$
$570$		0			0
$571$	−5.31765e9			−1.19535			−0.597673	−	0.801740i	$-0.703908\pi$
$571$	−5.31765e9			−1.19535			−0.597673	+	0.801740i	$0.703908\pi$
$572$	−2.55085e9	+	2.22002e9i	−0.569901	+	0.495988i
$573$		0			0
$574$	6.10827e7	+	3.52661e7i	0.0134811	+	0.00778334i
$575$	1.09054e9	−	1.88886e9i	0.239223	−	0.414346i
$576$		0			0
$577$		−	2.20076e9i		−	0.476934i	−0.971151	−	0.238467i	$-0.923355\pi$
$577$		−	2.20076e9i		−	0.476934i	0.971151	−	0.238467i	$-0.0766449\pi$
$578$	−9.49098e8	+	5.47962e8i	−0.204439	+	0.118033i
$579$		0			0
$580$			2.67406e7i			0.00569079i
$581$	−2.81320e8	−	4.87260e8i	−0.0595092	−	0.103073i
$582$		0			0
$583$	−9.25921e8	−	5.34581e8i	−0.193524	−	0.111731i
$584$	2.17587e9			0.452051
$585$		0			0
$586$	−1.34759e9			−0.276640
$587$	−4.80872e9	−	2.77632e9i	−0.981287	−	0.566546i	−0.0786286	−	0.996904i	$-0.525054\pi$
$587$	−4.80872e9	−	2.77632e9i	−0.981287	−	0.566546i	−0.902658	+	0.430358i	$0.858387\pi$
$588$		0			0
$589$	−3.90127e9	−	6.75721e9i	−0.786689	−	1.36258i
$590$			2.24597e8i			0.0450217i
$591$		0			0
$592$	−6.78024e8	+	3.91458e8i	−0.134313	+	0.0775459i
$593$		−	5.70359e9i		−	1.12320i	−0.827409	−	0.561600i	$-0.810186\pi$
$593$		−	5.70359e9i		−	1.12320i	0.827409	−	0.561600i	$-0.189814\pi$
$594$		0			0
$595$	−1.12397e7	+	1.94677e7i	−0.00218748	+	0.00378883i
$596$	1.23149e9	+	7.11000e8i	0.238270	+	0.137565i
$597$		0			0
$598$	−1.67651e9	−	5.76183e8i	−0.320592	−	0.110181i
$599$	−3.84338e9			−0.730666			−0.365333	−	0.930877i	$-0.619045\pi$
$599$	−3.84338e9			−0.730666			−0.365333	+	0.930877i	$0.619045\pi$
$600$		0			0
$601$	5.56311e8	−	9.63559e8i	0.104534	−	0.181058i	−0.809014	−	0.587790i	$-0.799998\pi$
$601$	5.56311e8	−	9.63559e8i	0.104534	−	0.181058i	0.913548	+	0.406732i	$0.133332\pi$
$602$	−4.19103e8	−	7.25908e8i	−0.0782949	−	0.135611i
$603$		0			0
$604$	−2.59118e9	+	1.49602e9i	−0.478485	+	0.276254i
$605$	−2.72074e8	+	1.57082e8i	−0.0499509	+	0.0288392i
$606$		0			0
$607$	−1.02746e8	−	1.77961e8i	−0.0186468	−	0.0322972i	0.856551	−	0.516062i	$-0.172602\pi$
$607$	−1.02746e8	−	1.77961e8i	−0.0186468	−	0.0322972i	−0.875198	+	0.483764i	$0.839269\pi$
$608$	−5.78883e8	+	1.00266e9i	−0.104455	+	0.180921i
$609$		0			0
$610$	−1.87894e8			−0.0335165
$611$	6.60690e9	−	5.75001e9i	1.17180	−	1.01982i
$612$		0			0
$613$	2.52066e9	+	1.45530e9i	0.441979	+	0.255177i	0.704437	−	0.709767i	$-0.251200\pi$
$613$	2.52066e9	+	1.45530e9i	0.441979	+	0.255177i	−0.262458	+	0.964944i	$0.584533\pi$
$614$	5.43543e8	−	9.41444e8i	0.0947643	−	0.164137i
$615$		0			0
$616$			3.69584e8i			0.0637061i
$617$	6.36384e9	−	3.67416e9i	1.09074	−	0.629739i	0.156966	−	0.987604i	$-0.449829\pi$
$617$	6.36384e9	−	3.67416e9i	1.09074	−	0.629739i	0.933773	+	0.357865i	$0.116495\pi$
$618$		0			0
$619$		−	1.10538e9i		−	0.187324i	−0.995604	−	0.0936619i	$-0.970143\pi$
$619$		−	1.10538e9i		−	0.187324i	0.995604	−	0.0936619i	$-0.0298573\pi$
$620$	−8.87852e7	−	1.53780e8i	−0.0149613	−	0.0259137i
$621$		0			0
$622$	3.75303e9	+	2.16681e9i	0.625339	+	0.361040i
$623$	4.67070e8			0.0773880
$624$		0			0
$625$	6.06654e9			0.993943
$626$	4.96237e9	+	2.86502e9i	0.808497	+	0.466786i
$627$		0			0
$628$	−1.78917e9	−	3.09893e9i	−0.288265	−	0.499289i
$629$		−	3.16019e9i		−	0.506332i
$630$		0			0
$631$	3.96548e9	−	2.28947e9i	0.628337	−	0.362771i	−0.151771	−	0.988416i	$-0.548498\pi$
$631$	3.96548e9	−	2.28947e9i	0.628337	−	0.362771i	0.780108	+	0.625645i	$0.215164\pi$
$632$		−	1.25468e9i		−	0.197708i
$633$		0			0
$634$	−2.05544e7	+	3.56013e7i	−0.00320326	+	0.00554822i
$635$	−4.20759e8	−	2.42925e8i	−0.0652117	−	0.0376500i
$636$		0			0
$637$	−6.31198e9	+	1.23072e9i	−0.967559	+	0.188656i
$638$	−1.77459e9			−0.270537
$639$		0			0
$640$	−1.31742e7	+	2.28184e7i	−0.00198653	+	0.00344077i
$641$	4.74954e9	+	8.22645e9i	0.712277	+	1.23370i	0.964001	+	0.265900i	$0.0856692\pi$
$641$	4.74954e9	+	8.22645e9i	0.712277	+	1.23370i	−0.251724	+	0.967799i	$0.580997\pi$
$642$		0			0
$643$	−2.50812e9	+	1.44807e9i	−0.372058	+	0.214808i	−0.674357	−	0.738405i	$-0.735579\pi$
$643$	−2.50812e9	+	1.44807e9i	−0.372058	+	0.214808i	0.302299	+	0.953213i	$0.402246\pi$
$644$	−1.67791e8	+	9.68744e7i	−0.0247554	+	0.0142925i
$645$		0			0
$646$	−2.33663e9	−	4.04716e9i	−0.341017	−	0.590658i
$647$	−6.01700e9	+	1.04217e10i	−0.873403	+	1.51278i	−0.0149496	+	0.999888i	$0.504759\pi$
$647$	−6.01700e9	+	1.04217e10i	−0.873403	+	1.51278i	−0.858454	+	0.512891i	$0.828575\pi$
$648$		0			0
$649$	−1.49050e10			−2.14031
$650$	−9.45573e8	−	4.84954e9i	−0.135051	−	0.692635i
$651$		0			0
$652$	−2.01136e9	−	1.16126e9i	−0.284200	−	0.164083i
$653$	3.16905e9	−	5.48896e9i	0.445383	−	0.771426i	−0.552696	−	0.833383i	$-0.686401\pi$
$653$	3.16905e9	−	5.48896e9i	0.445383	−	0.771426i	0.998079	+	0.0619574i	$0.0197343\pi$
$654$		0			0
$655$			5.26374e8i			0.0731897i
$656$	−2.88993e8	+	1.66850e8i	−0.0399691	+	0.0230762i
$657$		0			0
$658$		−	9.57250e8i		−	0.130989i
$659$	−4.10410e9	−	7.10851e9i	−0.558623	−	0.967564i	−0.997612	−	0.0690711i	$-0.977996\pi$
$659$	−4.10410e9	−	7.10851e9i	−0.558623	−	0.967564i	0.438989	−	0.898493i	$-0.355337\pi$
$660$		0			0
$661$	7.68984e8	+	4.43973e8i	0.103565	+	0.0597931i	0.550888	−	0.834579i	$-0.314289\pi$
$661$	7.68984e8	+	4.43973e8i	0.103565	+	0.0597931i	−0.447323	+	0.894372i	$0.647623\pi$
$662$	−2.84678e9			−0.381373
$663$		0			0
$664$	2.66195e9			0.352867
$665$	4.16033e7	+	2.40197e7i	0.00548595	+	0.00316731i
$666$		0			0
$667$	−4.65151e8	−	8.05666e8i	−0.0606951	−	0.105127i
$668$		−	4.48461e9i		−	0.582113i
$669$		0			0
$670$	3.12219e8	−	1.80260e8i	0.0401049	−	0.0231546i
$671$		−	1.24693e10i		−	1.59336i
$672$		0			0
$673$	1.94451e9	−	3.36798e9i	0.245899	−	0.425909i	−0.716485	−	0.697602i	$-0.754250\pi$
$673$	1.94451e9	−	3.36798e9i	0.245899	−	0.425909i	0.962384	+	0.271693i	$0.0875836\pi$
$674$	3.04523e9	+	1.75816e9i	0.383098	+	0.221182i
$675$		0			0
$676$	−3.72174e9	+	1.50870e9i	−0.463375	+	0.187840i
$677$	−2.22163e9			−0.275176			−0.137588	−	0.990490i	$-0.543935\pi$
$677$	−2.22163e9			−0.275176			−0.137588	+	0.990490i	$0.543935\pi$
$678$		0			0
$679$	−4.62328e8	+	8.00775e8i	−0.0566768	+	0.0981672i
$680$	−5.31769e7	−	9.21051e7i	−0.00648548	−	0.0112332i
$681$		0			0
$682$	1.02054e10	−	5.89208e9i	1.23192	−	0.711251i
$683$	−4.37929e8	+	2.52838e8i	−0.0525934	+	0.0303648i	−0.526066	−	0.850444i	$-0.676334\pi$
$683$	−4.37929e8	+	2.52838e8i	−0.0525934	+	0.0303648i	0.473473	+	0.880808i	$0.343000\pi$
$684$		0			0
$685$	3.96731e7	+	6.87159e7i	0.00471606	+	0.00816846i
$686$	−7.07910e8	+	1.22614e9i	−0.0837227	+	0.145012i
$687$		0			0
$688$	3.96570e9			0.464259
$689$	−8.33555e8	−	9.57773e8i	−0.0970883	−	0.111557i
$690$		0			0
$691$	−2.74012e8	−	1.58201e8i	−0.0315934	−	0.0182405i	0.484120	−	0.875002i	$-0.339140\pi$
$691$	−2.74012e8	−	1.58201e8i	−0.0315934	−	0.0182405i	−0.515714	+	0.856761i	$0.672473\pi$
$692$	−2.02325e9	+	3.50438e9i	−0.232102	+	0.402013i
$693$		0			0
$694$		−	5.69349e9i		−	0.646578i
$695$	−2.97389e8	+	1.71698e8i	−0.0336031	+	0.0194007i
$696$		0			0
$697$		−	1.34696e9i		−	0.150675i
$698$	−6.12930e9	−	1.06163e10i	−0.682208	−	1.18162i
$699$		0			0
$700$	−4.67652e8	−	2.69999e8i	−0.0515323	−	0.0297522i
$701$	−1.61152e9			−0.176695			−0.0883474	−	0.996090i	$-0.528159\pi$
$701$	−1.61152e9			−0.176695			−0.0883474	+	0.996090i	$0.528159\pi$
$702$		0			0
$703$	−6.75345e9			−0.733132
$704$	−1.51431e9	−	8.74285e8i	−0.163572	−	0.0944384i
$705$		0			0
$706$	2.65712e8	+	4.60227e8i	0.0284181	+	0.0492216i
$707$		−	2.04929e9i		−	0.218090i
$708$		0			0
$709$	−3.75698e9	+	2.16909e9i	−0.395892	+	0.228568i	−0.684710	−	0.728816i	$-0.740071\pi$
$709$	−3.75698e9	+	2.16909e9i	−0.395892	+	0.228568i	0.288818	+	0.957384i	$0.406738\pi$
$710$			7.42883e7i			0.00778962i
$711$		0			0
$712$	−1.10490e9	+	1.91373e9i	−0.114721	+	0.198702i
$713$	5.35001e9	+	3.08883e9i	0.552766	+	0.319139i
$714$		0			0
$715$	−6.51580e8	+	1.27046e8i	−0.0666648	+	0.0129984i
$716$	−3.59352e9			−0.365868
$717$		0			0
$718$	−4.97060e9	+	8.60932e9i	−0.501156	+	0.868028i
$719$	−3.85660e9	−	6.67982e9i	−0.386949	−	0.670215i	0.605089	−	0.796158i	$-0.293138\pi$
$719$	−3.85660e9	−	6.67982e9i	−0.386949	−	0.670215i	−0.992037	+	0.125943i	$0.959804\pi$
$720$		0			0
$721$	−1.04385e9	+	6.02668e8i	−0.103721	+	0.0598832i
$722$	−2.45602e9	+	1.41798e9i	−0.242857	+	0.140214i
$723$		0			0
$724$	3.31290e9	+	5.73812e9i	0.324432	+	0.561933i
$725$	1.29642e9	−	2.24547e9i	0.126347	−	0.218839i
$726$		0			0
$727$	5.18765e9			0.500726			0.250363	−	0.968152i	$-0.419450\pi$
$727$	5.18765e9			0.500726			0.250363	+	0.968152i	$0.419450\pi$
$728$	−1.42654e8	+	4.15077e8i	−0.0137032	+	0.0398721i
$729$		0			0
$730$	3.69920e8	+	2.13574e8i	0.0351948	+	0.0203197i
$731$	−8.00366e9	+	1.38627e10i	−0.757840	+	1.31262i
$732$		0			0
$733$		−	8.08992e9i		−	0.758718i	−0.925250	−	0.379359i	$-0.876145\pi$
$733$		−	8.08992e9i		−	0.758718i	0.925250	−	0.379359i	$-0.123855\pi$
$734$	1.59667e8	−	9.21836e7i	0.0149031	−	0.00860434i
$735$		0			0
$736$		−	9.16660e8i		−	0.0847493i
$737$	1.19626e10	+	2.07199e10i	1.10075	+	1.90656i
$738$		0			0
$739$	1.33487e10	+	7.70687e9i	1.21670	+	0.702461i	0.964210	−	0.265139i	$-0.0854177\pi$
$739$	1.33487e10	+	7.70687e9i	1.21670	+	0.702461i	0.252488	+	0.967600i	$0.418751\pi$
$740$	−1.53695e8			−0.0139428
$741$		0			0
$742$	−1.38768e8			−0.0124703
$743$	1.46083e10	+	8.43411e9i	1.30659	+	0.754360i	0.981525	−	0.191332i	$-0.0612807\pi$
$743$	1.46083e10	+	8.43411e9i	1.30659	+	0.754360i	0.325064	+	0.945692i	$0.394614\pi$
$744$		0			0
$745$	1.39577e8	+	2.41755e8i	0.0123671	+	0.0214205i
$746$		−	5.69657e9i		−	0.502374i
$747$		0			0
$748$	6.11240e9	−	3.52900e9i	0.534018	−	0.308316i
$749$			3.98144e8i			0.0346221i
$750$		0			0
$751$	−8.99510e9	+	1.55800e10i	−0.774937	+	1.34223i	0.159894	+	0.987134i	$0.448885\pi$
$751$	−8.99510e9	+	1.55800e10i	−0.774937	+	1.34223i	−0.934830	+	0.355095i	$0.884448\pi$
$752$	3.92216e9	+	2.26446e9i	0.336328	+	0.194179i
$753$		0			0
$754$	−1.99303e9	−	6.84964e8i	−0.169322	−	0.0581926i
$755$	−5.87371e8			−0.0496705
$756$		0			0
$757$	5.08895e9	−	8.81431e9i	0.426375	−	0.738504i	−0.570172	−	0.821525i	$-0.693124\pi$
$757$	5.08895e9	−	8.81431e9i	0.426375	−	0.738504i	0.996548	+	0.0830211i	$0.0264569\pi$
$758$	4.05820e9	+	7.02901e9i	0.338447	+	0.586208i
$759$		0			0
$760$	−1.96833e8	+	1.13641e8i	−0.0162648	+	0.00939050i
$761$	1.78234e10	−	1.02904e10i	1.46604	−	0.846417i	0.466757	−	0.884385i	$-0.345422\pi$
$761$	1.78234e10	−	1.02904e10i	1.46604	−	0.846417i	0.999279	+	0.0379689i	$0.0120888\pi$
$762$		0			0
$763$	−8.38942e8	−	1.45309e9i	−0.0683748	−	0.118429i
$764$	−1.59920e9	+	2.76989e9i	−0.129740	+	0.224717i
$765$		0			0
$766$	8.64582e9			0.695033
$767$	−1.67397e10	−	5.75309e9i	−1.33957	−	0.460381i
$768$		0			0
$769$	7.04864e9	+	4.06953e9i	0.558937	+	0.322702i	0.752719	−	0.658342i	$-0.228742\pi$
$769$	7.04864e9	+	4.06953e9i	0.558937	+	0.322702i	−0.193782	+	0.981045i	$0.562075\pi$
$770$	−3.62768e7	+	6.28332e7i	−0.00286359	+	0.00495989i
$771$		0			0
$772$			3.05981e9i			0.239350i
$773$	−1.14818e10	+	6.62903e9i	−0.894093	+	0.516205i	−0.875279	−	0.483618i	$-0.839322\pi$
$773$	−1.14818e10	+	6.62903e9i	−0.894093	+	0.516205i	−0.0188138	+	0.999823i	$0.505989\pi$
$774$		0			0
$775$			1.72178e10i			1.32868i
$776$	−2.18735e9	−	3.78861e9i	−0.168036	−	0.291047i
$777$		0			0
$778$	−5.73863e9	−	3.31320e9i	−0.436897	−	0.252243i
$779$	−2.87851e9			−0.218166
$780$		0			0
$781$	−4.93002e9			−0.370314
$782$	3.20433e9	+	1.85002e9i	0.239615	+	0.138342i
$783$		0			0
$784$	−1.66263e9	−	2.87976e9i	−0.123222	−	0.213428i
$785$		−	7.02467e8i		−	0.0518301i
$786$		0			0
$787$	−6.09232e9	+	3.51740e9i	−0.445524	+	0.257223i	−0.705938	−	0.708274i	$-0.749474\pi$
$787$	−6.09232e9	+	3.51740e9i	−0.445524	+	0.257223i	0.260414	+	0.965497i	$0.416141\pi$
$788$			1.52879e9i			0.111303i
$789$		0			0
$790$	1.23154e8	−	2.13309e8i	0.00888698	−	0.0153927i
$791$	−1.80660e9	−	1.04304e9i	−0.129791	−	0.0749347i
$792$		0			0
$793$	4.81294e9	−	1.40042e10i	0.342732	−	0.997242i
$794$	6.52227e7			0.00462410
$795$		0			0
$796$	5.16111e9	−	8.93931e9i	0.362700	−	0.628215i
$797$	−2.43301e9	−	4.21410e9i	−0.170232	−	0.294850i	0.768269	−	0.640127i	$-0.221118\pi$
$797$	−2.43301e9	−	4.21410e9i	−0.170232	−	0.294850i	−0.938501	+	0.345277i	$0.887785\pi$
$798$		0			0
$799$	−1.58316e10	+	9.14035e9i	−1.09802	+	0.633942i
$800$	2.21255e9	−	1.27741e9i	0.152784	−	0.0882098i
$801$		0			0
$802$	1.98215e9	+	3.43318e9i	0.135683	+	0.235010i
$803$	−1.41734e10	+	2.45491e10i	−0.965987	+	1.67314i
$804$		0			0
$805$	−3.80351e7			−0.00256980
$806$	1.37358e10	−	2.67823e9i	0.924021	−	0.180167i
$807$		0			0
$808$	8.39661e9	+	4.84779e9i	0.559969	+	0.323298i
$809$	6.03124e8	−	1.04464e9i	0.0400485	−	0.0693661i	−0.845306	−	0.534282i	$-0.820582\pi$
$809$	6.03124e8	−	1.04464e9i	0.0400485	−	0.0693661i	0.885355	+	0.464916i	$0.153915\pi$
$810$		0			0
$811$			8.41139e9i			0.553726i	0.960909	+	0.276863i	$0.0892948\pi$
$811$			8.41139e9i			0.553726i	−0.960909	+	0.276863i	$0.910705\pi$
$812$	−1.99470e8	+	1.15164e8i	−0.0130747	+	0.00754866i
$813$		0			0
$814$		−	1.01997e10i		−	0.662830i
$815$	−2.27968e8	−	3.94853e8i	−0.0147511	−	0.0255496i
$816$		0			0
$817$	2.96253e10	+	1.71042e10i	1.90057	+	1.09730i
$818$	−3.08307e9			−0.196946
$819$		0			0
$820$	−6.55092e7			−0.00414910
$821$	2.23410e10	+	1.28986e10i	1.40897	+	0.813469i	0.995289	−	0.0969528i	$-0.0309096\pi$
$821$	2.23410e10	+	1.28986e10i	1.40897	+	0.813469i	0.413681	+	0.910422i	$0.364243\pi$
$822$		0			0
$823$	−9.10197e7	−	1.57651e8i	−0.00569162	−	0.00985818i	0.863166	−	0.504921i	$-0.168478\pi$
$823$	−9.10197e7	−	1.57651e8i	−0.00569162	−	0.00985818i	−0.868857	+	0.495063i	$0.835145\pi$
$824$		−	5.70266e9i		−	0.355085i
$825$		0			0
$826$	−1.67537e9	+	9.67275e8i	−0.103438	+	0.0597200i
$827$			2.35099e10i			1.44538i	0.691175	+	0.722688i	$0.257094\pi$
$827$			2.35099e10i			1.44538i	−0.691175	+	0.722688i	$0.742906\pi$
$828$		0			0
$829$	2.15503e9	−	3.73263e9i	0.131375	−	0.227548i	−0.792832	−	0.609441i	$-0.791394\pi$
$829$	2.15503e9	−	3.73263e9i	0.131375	−	0.227548i	0.924207	+	0.381892i	$0.124727\pi$
$830$	4.52559e8	+	2.61285e8i	0.0274728	+	0.0158614i
$831$		0			0
$832$	−1.36324e9	−	1.56640e9i	−0.0820620	−	0.0942912i
$833$	1.34222e10			0.804575
$834$		0			0
$835$	4.40190e8	−	7.62431e8i	0.0261660	−	0.0453209i
$836$	−7.54161e9	−	1.30625e10i	−0.446419	−	0.773220i
$837$		0			0
$838$	−1.43249e10	+	8.27046e9i	−0.840884	+	0.485485i
$839$	−2.63154e10	+	1.51932e10i	−1.53831	+	0.888142i	−0.539368	+	0.842070i	$0.681337\pi$
$839$	−2.63154e10	+	1.51932e10i	−1.53831	+	0.888142i	−0.998938	+	0.0460715i	$0.985330\pi$
$840$		0			0
$841$	8.07197e9	+	1.39811e10i	0.467944	+	0.810502i
$842$	3.74465e9	−	6.48593e9i	0.216182	−	0.374438i
$843$		0			0
$844$	−4.98007e9			−0.285126
$845$	−7.80822e8	−	1.08815e8i	−0.0445198	−	0.00620424i
$846$		0			0
$847$	−2.34349e9	−	1.35301e9i	−0.132517	−	0.0765085i
$848$	3.28269e8	−	5.68579e8i	0.0184861	−	0.0320188i
$849$		0			0
$850$			1.03124e10i			0.575962i
$851$	4.63067e9	−	2.67352e9i	0.257567	−	0.148706i
$852$		0			0
$853$			5.71921e9i			0.315511i	0.987478	+	0.157756i	$0.0504258\pi$
$853$			5.71921e9i			0.315511i	−0.987478	+	0.157756i	$0.949574\pi$
$854$	−8.09206e8	−	1.40159e9i	−0.0444587	−	0.0770047i
$855$		0			0
$856$	−1.63132e9	−	9.41844e8i	−0.0888958	−	0.0513240i
$857$	−1.49325e10			−0.810401			−0.405201	−	0.914228i	$-0.632798\pi$
$857$	−1.49325e10			−0.810401			−0.405201	+	0.914228i	$0.632798\pi$
$858$		0			0
$859$	1.66438e10			0.895932			0.447966	−	0.894051i	$-0.352149\pi$
$859$	1.66438e10			0.895932			0.447966	+	0.894051i	$0.352149\pi$
$860$	6.74211e8	+	3.89256e8i	0.0361453	+	0.0208685i
$861$		0			0
$862$	−1.99610e9	−	3.45735e9i	−0.106147	−	0.183852i
$863$			1.42938e10i			0.757023i	0.925597	+	0.378512i	$0.123564\pi$
$863$			1.42938e10i			0.757023i	−0.925597	+	0.378512i	$0.876436\pi$
$864$		0			0
$865$	−6.87949e8	+	3.97188e8i	−0.0361410	+	0.0208660i
$866$			8.49689e9i			0.444577i
$867$		0			0
$868$	7.64744e8	−	1.32457e9i	0.0396914	−	0.0687476i
$869$	1.41559e10	+	8.17291e9i	0.731759	+	0.422481i
$870$		0			0
$871$	5.43759e9	+	2.78877e10i	0.278832	+	1.43004i
$872$	7.93837e9			0.405437
$873$		0			0
$874$	3.95357e9	−	6.84779e9i	0.200309	−	0.346945i
$875$	−1.06115e8	−	1.83797e8i	−0.00535487	−	0.00927490i
$876$		0			0
$877$	1.08404e10	−	6.25868e9i	0.542681	−	0.313317i	−0.203484	−	0.979078i	$-0.565226\pi$
$877$	1.08404e10	−	6.25868e9i	0.542681	−	0.313317i	0.746165	+	0.665761i	$0.231893\pi$
$878$	6.90860e9	−	3.98868e9i	0.344476	−	0.198883i
$879$		0			0
$880$	−1.71632e8	−	2.97275e8i	−0.00849002	−	0.0147051i
$881$	7.73880e9	−	1.34040e10i	0.381292	−	0.660417i	−0.609955	−	0.792436i	$-0.708813\pi$
$881$	7.73880e9	−	1.34040e10i	0.381292	−	0.660417i	0.991247	+	0.132019i	$0.0421459\pi$
$882$		0			0
$883$	1.77069e9			0.0865525			0.0432762	−	0.999063i	$-0.486220\pi$
$883$	1.77069e9			0.0865525			0.0432762	+	0.999063i	$0.486220\pi$
$884$	8.22692e9	−	1.60410e9i	0.400548	−	0.0780995i
$885$		0			0
$886$	2.24826e9	+	1.29803e9i	0.108600	+	0.0627000i
$887$	1.35468e9	−	2.34638e9i	0.0651787	−	0.112893i	−0.831595	−	0.555383i	$-0.812572\pi$
$887$	1.35468e9	−	2.34638e9i	0.0651787	−	0.112893i	0.896773	+	0.442490i	$0.145905\pi$
$888$		0			0
$889$		−	4.18483e9i		−	0.199766i
$890$	−3.75688e8	+	2.16903e8i	−0.0178633	+	0.0103134i
$891$		0			0
$892$			4.41329e9i			0.208202i
$893$	1.95333e10	+	3.38327e10i	0.917901	+	1.58985i
$894$		0			0
$895$	−6.10936e8	−	3.52724e8i	−0.0284849	−	0.0164458i
$896$	−2.26950e8			−0.0105403
$897$		0			0
$898$	6.82618e9			0.314565
$899$	6.36006e9	+	3.67198e9i	0.291946	+	0.168555i
$900$		0			0
$901$	1.32504e9	+	2.29503e9i	0.0603520	+	0.104533i
$902$		−	4.34740e9i		−	0.197246i
$903$		0			0
$904$	8.54733e9	−	4.93481e9i	0.384805	−	0.222167i
$905$			1.30072e9i			0.0583330i
$906$		0			0
$907$	−1.75120e10	+	3.03316e10i	−0.779308	+	1.34980i	0.153033	+	0.988221i	$0.451096\pi$
$907$	−1.75120e10	+	3.03316e10i	−0.779308	+	1.34980i	−0.932341	+	0.361580i	$0.882237\pi$
$908$	8.16688e8	+	4.71515e8i	0.0362039	+	0.0209023i
$909$		0			0
$910$	−6.49948e7	+	5.65652e7i	−0.00285913	+	0.00248831i
$911$	−6.59923e9			−0.289187			−0.144594	−	0.989491i	$-0.546187\pi$
$911$	−6.59923e9			−0.289187			−0.144594	+	0.989491i	$0.546187\pi$
$912$		0			0
$913$	−1.73398e10	+	3.00333e10i	−0.754041	+	1.30604i
$914$	−5.54384e9	−	9.60221e9i	−0.240159	−	0.415968i
$915$		0			0
$916$	7.71738e9	−	4.45563e9i	0.331769	−	0.191547i
$917$	−3.92646e9	+	2.26694e9i	−0.168154	+	0.0970839i
$918$		0			0
$919$	−1.24901e10	−	2.16334e10i	−0.530836	−	0.919435i	−0.999352	−	0.0359803i	$-0.988545\pi$
$919$	−1.24901e10	−	2.16334e10i	−0.530836	−	0.919435i	0.468516	−	0.883455i	$-0.344789\pi$
$920$	8.99754e7	−	1.55842e8i	0.00380948	−	0.00659822i
$921$		0			0
$922$	−2.01139e10			−0.845157
$923$	−5.53686e9	−	1.90291e9i	−0.231770	−	0.0796547i
$924$		0			0
$925$	1.29062e10	+	7.45137e9i	0.536168	+	0.309557i
$926$	1.33269e10	−	2.30829e10i	0.551558	−	0.955327i
$927$		0			0
$928$		−	1.08972e9i		−	0.0447608i
$929$	3.42370e10	−	1.97667e10i	1.40101	−	0.808872i	0.406512	−	0.913645i	$-0.366745\pi$
$929$	3.42370e10	−	1.97667e10i	1.40101	−	0.808872i	0.994496	+	0.104773i	$0.0334116\pi$
$930$		0			0
$931$		−	2.86838e10i		−	1.16497i
$932$	2.05664e8	+	3.56221e8i	0.00832153	+	0.0144133i
$933$		0			0
$934$	−1.01608e10	−	5.86633e9i	−0.408050	−	0.235588i
$935$	1.38556e9			0.0554352
$936$		0			0
$937$	2.31754e10			0.920319			0.460159	−	0.887836i	$-0.347792\pi$
$937$	2.31754e10			0.920319			0.460159	+	0.887836i	$0.347792\pi$
$938$	2.68927e9	+	1.55265e9i	0.106396	+	0.0614277i
$939$		0			0
$940$	4.44539e8	+	7.69964e8i	0.0174567	+	0.0302359i
$941$			8.48646e9i			0.332019i	0.986124	+	0.166009i	$0.0530882\pi$
$941$			8.48646e9i			0.332019i	−0.986124	+	0.166009i	$0.946912\pi$
$942$		0			0
$943$	1.97372e9	−	1.13953e9i	0.0766470	−	0.0442522i
$944$		−	9.15270e9i		−	0.354117i
$945$		0			0
$946$	−2.58323e10	+	4.47429e10i	−0.992075	+	1.71832i
$947$	−3.26354e10	−	1.88420e10i	−1.24872	−	0.720946i	−0.277863	−	0.960621i	$-0.589626\pi$
$947$	−3.26354e10	−	1.88420e10i	−1.24872	−	0.720946i	−0.970853	+	0.239674i	$0.922959\pi$
$948$		0			0
$949$	−2.53937e10	+	2.21002e10i	−0.964481	+	0.839392i
$950$	2.20380e10			0.833950
$951$		0			0
$952$	4.58035e8	−	7.93340e8i	0.0172056	−	0.0298009i
$953$	−2.21260e10	−	3.83234e10i	−0.828091	−	1.43429i	−0.899534	−	0.436850i	$-0.856094\pi$
$953$	−2.21260e10	−	3.83234e10i	−0.828091	−	1.43429i	0.0714438	−	0.997445i	$-0.477239\pi$
$954$		0			0
$955$	−5.43760e8	+	3.13940e8i	−0.0202021	+	0.0116637i
$956$	−1.28637e10	+	7.42689e9i	−0.476173	+	0.274919i
$957$		0			0
$958$	1.47225e10	+	2.55001e10i	0.541007	+	0.937051i
$959$	−3.41721e8	+	5.91878e8i	−0.0125114	+	0.0216704i
$960$		0			0
$961$	−2.12549e10			−0.772551
$962$	3.93692e9	−	1.14552e10i	0.142575	−	0.414849i
$963$		0			0
$964$	−1.05462e10	−	6.08885e9i	−0.379164	−	0.218910i
$965$	−3.00338e8	+	5.20200e8i	−0.0107588	+	0.0186348i
$966$		0			0
$967$		−	4.11792e10i		−	1.46449i	−0.681044	−	0.732243i	$-0.738474\pi$
$967$		−	4.11792e10i		−	1.46449i	0.681044	−	0.732243i	$-0.261526\pi$
$968$	1.10875e10	−	6.40135e9i	0.392887	−	0.226834i
$969$		0			0
$970$		−	8.58805e8i		−	0.0302130i
$971$	−1.49333e10	−	2.58652e10i	−0.523466	−	0.906669i	−0.999627	−	0.0273114i	$-0.991305\pi$
$971$	−1.49333e10	−	2.58652e10i	−0.523466	−	0.906669i	0.476161	−	0.879358i	$-0.342028\pi$
$972$		0			0
$973$	−2.56154e9	−	1.47891e9i	−0.0891469	−	0.0514690i
$974$	−3.05190e10			−1.05831
$975$		0			0
$976$	7.65700e9			0.263624
$977$	−2.70722e10	−	1.56301e10i	−0.928735	−	0.536205i	−0.0423237	−	0.999104i	$-0.513476\pi$
$977$	−2.70722e10	−	1.56301e10i	−0.928735	−	0.536205i	−0.886411	+	0.462899i	$0.846809\pi$
$978$		0			0
$979$	−1.43944e10	−	2.49319e10i	−0.490292	−	0.849210i
$980$		−	6.52787e8i		−	0.0221554i
$981$		0			0
$982$	2.97694e10	−	1.71874e10i	1.00318	−	0.579188i
$983$			2.53290e10i			0.850514i	0.905073	+	0.425257i	$0.139816\pi$
$983$			2.53290e10i			0.850514i	−0.905073	+	0.425257i	$0.860184\pi$
$984$		0			0
$985$	−1.50059e8	+	2.59910e8i	−0.00500306	+	0.00866555i
$986$	3.80929e9	+	2.19930e9i	0.126554	+	0.0730659i
$987$		0			0
$988$	−3.42803e9	−	1.75813e10i	−0.113082	−	0.579964i
$989$	−2.70844e10			−0.890291
$990$		0			0
$991$	1.59473e10	−	2.76216e10i	0.520512	−	0.901553i	−0.479204	−	0.877704i	$-0.659075\pi$
$991$	1.59473e10	−	2.76216e10i	0.520512	−	0.901553i	0.999716	−	0.0238492i	$-0.00759214\pi$
$992$	3.61814e9	+	6.26680e9i	0.117678	+	0.203824i
$993$		0			0
$994$	−5.54149e8	+	3.19938e8i	−0.0178968	+	0.0103327i
$995$	1.75489e9	−	1.01318e9i	0.0564766	−	0.0326068i
$996$		0			0
$997$	−2.74162e10	−	4.74863e10i	−0.876143	−	1.51752i	−0.855540	−	0.517736i	$-0.826775\pi$
$997$	−2.74162e10	−	4.74863e10i	−0.876143	−	1.51752i	−0.0206024	−	0.999788i	$-0.506558\pi$
$998$	−6.09893e9	+	1.05637e10i	−0.194221	+	0.336401i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.8.l.c.199.3		16
3.2	odd	2		26.8.e.a.17.5	✓	16
12.11	even	2		208.8.w.b.17.8		16
13.10	even	6	inner	234.8.l.c.127.2		16
39.17	odd	6		338.8.b.i.337.16		16
39.20	even	12		338.8.a.n.1.8		8
39.23	odd	6		26.8.e.a.23.5	yes	16
39.32	even	12		338.8.a.m.1.8		8
39.35	odd	6		338.8.b.i.337.8		16
156.23	even	6		208.8.w.b.49.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.8.e.a.17.5	✓	16	3.2	odd	2
26.8.e.a.23.5	yes	16	39.23	odd	6
208.8.w.b.17.8		16	12.11	even	2
208.8.w.b.49.8		16	156.23	even	6
234.8.l.c.127.2		16	13.10	even	6	inner
234.8.l.c.199.3		16	1.1	even	1	trivial
338.8.a.m.1.8		8	39.32	even	12
338.8.a.n.1.8		8	39.20	even	12
338.8.b.i.337.8		16	39.35	odd	6
338.8.b.i.337.16		16	39.17	odd	6

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Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

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Modular forms

Varieties

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	234.8.l.c.199.3

Level	$234$
Weight	$8$
Character	234.199
Analytic conductor	$73.098$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$