LMFDB - Embedded newform 810.3.h.a.431.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,3,Mod(431,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("810.431");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	810.h (of order $6$, degree $2$, not 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:	$22.0709014132$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} + 7x^{4} + 36x^{2} + 81 $ x^8 + 4x^6 + 7x^4 + 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			431.3
Root			$-0.178197 + 1.72286i$ of defining polynomial
Character	$\chi$	$=$	810.431
Dual form			810.3.h.a.701.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(3.74342 - 6.48379i) q^{7} +2.82843i q^{8} +O(q^{10})$	\(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(3.74342 - 6.48379i) q^{7} +2.82843i q^{8} -3.16228 q^{10} +(-7.34847 - 4.24264i) q^{11} +(5.00000 + 8.66025i) q^{13} +(9.16946 - 5.29399i) q^{14} +(-2.00000 + 3.46410i) q^{16} -30.3870i q^{17} +26.9737 q^{19} +(-3.87298 - 2.23607i) q^{20} +(-6.00000 - 10.3923i) q^{22} +(7.94472 - 4.58688i) q^{23} +(2.50000 - 4.33013i) q^{25} +14.1421i q^{26} +14.9737 q^{28} +(23.2379 + 13.4164i) q^{29} +(-4.00000 - 6.92820i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(21.4868 - 37.2163i) q^{34} +16.7411i q^{35} +15.9473 q^{37} +(33.0359 + 19.0733i) q^{38} +(-3.16228 - 5.47723i) q^{40} +(41.0128 - 23.6788i) q^{41} +(7.23025 - 12.5232i) q^{43} -16.9706i q^{44} +12.9737 q^{46} +(-39.7236 - 22.9344i) q^{47} +(-3.52633 - 6.10779i) q^{49} +(6.12372 - 3.53553i) q^{50} +(-10.0000 + 17.3205i) q^{52} -30.3870i q^{53} +18.9737 q^{55} +(18.3389 + 10.5880i) q^{56} +(18.9737 + 32.8634i) q^{58} +(-20.8529 + 12.0394i) q^{59} +(26.9737 - 46.7198i) q^{61} -11.3137i q^{62} -8.00000 q^{64} +(-19.3649 - 11.1803i) q^{65} +(55.2302 + 95.6616i) q^{67} +(52.6318 - 30.3870i) q^{68} +(-11.8377 + 20.5035i) q^{70} +15.5936i q^{71} +87.9473 q^{73} +(19.5314 + 11.2765i) q^{74} +(26.9737 + 46.7198i) q^{76} +(-55.0168 + 31.7639i) q^{77} +(23.4868 - 40.6804i) q^{79} -8.94427i q^{80} +66.9737 q^{82} +(-22.6417 - 13.0722i) q^{83} +(33.9737 + 58.8441i) q^{85} +(17.7104 - 10.2251i) q^{86} +(12.0000 - 20.7846i) q^{88} +60.7739i q^{89} +74.8683 q^{91} +(15.8894 + 9.17377i) q^{92} +(-32.4342 - 56.1776i) q^{94} +(-52.2343 + 30.1575i) q^{95} +(-18.0263 + 31.2225i) q^{97} -9.97398i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} - 8 q^{7}+O(q^{10}) $ 8 * q + 8 * q^4 - 8 * q^7	$ 8 q + 8 q^{4} - 8 q^{7} + 40 q^{13} - 16 q^{16} + 64 q^{19} - 48 q^{22} + 20 q^{25} - 32 q^{28} - 32 q^{31} + 96 q^{34} - 176 q^{37} - 56 q^{43} - 48 q^{46} - 180 q^{49} - 80 q^{52} + 64 q^{61} - 64 q^{64} + 328 q^{67} - 120 q^{70} + 400 q^{73} + 64 q^{76} + 112 q^{79} + 384 q^{82} + 120 q^{85} + 96 q^{88} - 160 q^{91} + 120 q^{94} - 296 q^{97}+O(q^{100}) $ 8 * q + 8 * q^4 - 8 * q^7 + 40 * q^13 - 16 * q^16 + 64 * q^19 - 48 * q^22 + 20 * q^25 - 32 * q^28 - 32 * q^31 + 96 * q^34 - 176 * q^37 - 56 * q^43 - 48 * q^46 - 180 * q^49 - 80 * q^52 + 64 * q^61 - 64 * q^64 + 328 * q^67 - 120 * q^70 + 400 * q^73 + 64 * q^76 + 112 * q^79 + 384 * q^82 + 120 * q^85 + 96 * q^88 - 160 * q^91 + 120 * q^94 - 296 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$6$		0			0
$7$	3.74342	−	6.48379i	0.534774	−	0.926255i	−0.464400	−	0.885625i	$-0.653730\pi$
$7$	3.74342	−	6.48379i	0.534774	−	0.926255i	0.999174	−	0.0406300i	$-0.0129365\pi$
$8$			2.82843i			0.353553i
$9$		0			0
$10$	−3.16228			−0.316228
$11$	−7.34847	−	4.24264i	−0.668043	−	0.385695i	0.127292	−	0.991865i	$-0.459371\pi$
$11$	−7.34847	−	4.24264i	−0.668043	−	0.385695i	−0.795335	+	0.606171i	$0.792705\pi$
$12$		0			0
$13$	5.00000	+	8.66025i	0.384615	+	0.666173i	0.991716	−	0.128452i	$-0.0410008\pi$
$13$	5.00000	+	8.66025i	0.384615	+	0.666173i	−0.607100	+	0.794625i	$0.707667\pi$
$14$	9.16946	−	5.29399i	0.654961	−	0.378142i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$		−	30.3870i		−	1.78747i	−0.448596	−	0.893734i	$-0.648076\pi$
$17$		−	30.3870i		−	1.78747i	0.448596	−	0.893734i	$-0.351924\pi$
$18$		0			0
$19$	26.9737			1.41967			0.709833	−	0.704370i	$-0.248770\pi$
$19$	26.9737			1.41967			0.709833	+	0.704370i	$0.248770\pi$
$20$	−3.87298	−	2.23607i	−0.193649	−	0.111803i
$21$		0			0
$22$	−6.00000	−	10.3923i	−0.272727	−	0.472377i
$23$	7.94472	−	4.58688i	0.345422	−	0.199430i	−0.317245	−	0.948344i	$-0.602758\pi$
$23$	7.94472	−	4.58688i	0.345422	−	0.199430i	0.662667	+	0.748914i	$0.269424\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$			14.1421i			0.543928i
$27$		0			0
$28$	14.9737			0.534774
$29$	23.2379	+	13.4164i	0.801307	+	0.462635i	0.843928	−	0.536457i	$-0.180237\pi$
$29$	23.2379	+	13.4164i	0.801307	+	0.462635i	−0.0426210	+	0.999091i	$0.513571\pi$
$30$		0			0
$31$	−4.00000	−	6.92820i	−0.129032	−	0.223490i	0.794270	−	0.607565i	$-0.207854\pi$
$31$	−4.00000	−	6.92820i	−0.129032	−	0.223490i	−0.923302	+	0.384075i	$0.874520\pi$
$32$	−4.89898	+	2.82843i	−0.153093	+	0.0883883i
$33$		0			0
$34$	21.4868	−	37.2163i	0.631966	−	1.09460i
$35$			16.7411i			0.478316i
$36$		0			0
$37$	15.9473			0.431009			0.215504	−	0.976503i	$-0.430860\pi$
$37$	15.9473			0.431009			0.215504	+	0.976503i	$0.430860\pi$
$38$	33.0359	+	19.0733i	0.869365	+	0.501928i
$39$		0			0
$40$	−3.16228	−	5.47723i	−0.0790569	−	0.136931i
$41$	41.0128	−	23.6788i	1.00031	−	0.577531i	0.0919720	−	0.995762i	$-0.470683\pi$
$41$	41.0128	−	23.6788i	1.00031	−	0.577531i	0.908341	+	0.418231i	$0.137350\pi$
$42$		0			0
$43$	7.23025	−	12.5232i	0.168145	−	0.291236i	−0.769622	−	0.638499i	$-0.779556\pi$
$43$	7.23025	−	12.5232i	0.168145	−	0.291236i	0.937768	+	0.347263i	$0.112889\pi$
$44$		−	16.9706i		−	0.385695i
$45$		0			0
$46$	12.9737			0.282036
$47$	−39.7236	−	22.9344i	−0.845182	−	0.487966i	0.0138400	−	0.999904i	$-0.495594\pi$
$47$	−39.7236	−	22.9344i	−0.845182	−	0.487966i	−0.859022	+	0.511938i	$0.828928\pi$
$48$		0			0
$49$	−3.52633	−	6.10779i	−0.0719660	−	0.124649i
$50$	6.12372	−	3.53553i	0.122474	−	0.0707107i
$51$		0			0
$52$	−10.0000	+	17.3205i	−0.192308	+	0.333087i
$53$		−	30.3870i		−	0.573339i	−0.958030	−	0.286670i	$-0.907452\pi$
$53$		−	30.3870i		−	0.573339i	0.958030	−	0.286670i	$-0.0925482\pi$
$54$		0			0
$55$	18.9737			0.344976
$56$	18.3389	+	10.5880i	0.327481	+	0.189071i
$57$		0			0
$58$	18.9737	+	32.8634i	0.327132	+	0.566610i
$59$	−20.8529	+	12.0394i	−0.353439	+	0.204058i	−0.666199	−	0.745774i	$-0.732080\pi$
$59$	−20.8529	+	12.0394i	−0.353439	+	0.204058i	0.312760	+	0.949832i	$0.398747\pi$
$60$		0			0
$61$	26.9737	−	46.7198i	0.442191	−	0.765898i	−0.555661	−	0.831409i	$-0.687535\pi$
$61$	26.9737	−	46.7198i	0.442191	−	0.765898i	0.997852	+	0.0655115i	$0.0208679\pi$
$62$		−	11.3137i		−	0.182479i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−19.3649	−	11.1803i	−0.297922	−	0.172005i
$66$		0			0
$67$	55.2302	+	95.6616i	0.824332	+	1.42779i	0.902429	+	0.430839i	$0.141782\pi$
$67$	55.2302	+	95.6616i	0.824332	+	1.42779i	−0.0780966	+	0.996946i	$0.524884\pi$
$68$	52.6318	−	30.3870i	0.773997	−	0.446867i
$69$		0			0
$70$	−11.8377	+	20.5035i	−0.169110	+	0.292908i
$71$			15.5936i			0.219628i	0.993952	+	0.109814i	$0.0350255\pi$
$71$			15.5936i			0.219628i	−0.993952	+	0.109814i	$0.964974\pi$
$72$		0			0
$73$	87.9473			1.20476			0.602379	−	0.798210i	$-0.294220\pi$
$73$	87.9473			1.20476			0.602379	+	0.798210i	$0.294220\pi$
$74$	19.5314	+	11.2765i	0.263938	+	0.152385i
$75$		0			0
$76$	26.9737	+	46.7198i	0.354917	+	0.614734i
$77$	−55.0168	+	31.7639i	−0.714503	+	0.412519i
$78$		0			0
$79$	23.4868	−	40.6804i	0.297302	−	0.514942i	−0.678216	−	0.734863i	$-0.737247\pi$
$79$	23.4868	−	40.6804i	0.297302	−	0.514942i	0.975518	+	0.219921i	$0.0705800\pi$
$80$		−	8.94427i		−	0.111803i
$81$		0			0
$82$	66.9737			0.816752
$83$	−22.6417	−	13.0722i	−0.272791	−	0.157496i	0.357364	−	0.933965i	$-0.383675\pi$
$83$	−22.6417	−	13.0722i	−0.272791	−	0.157496i	−0.630155	+	0.776469i	$0.717009\pi$
$84$		0			0
$85$	33.9737	+	58.8441i	0.399690	+	0.692284i
$86$	17.7104	−	10.2251i	0.205935	−	0.118897i
$87$		0			0
$88$	12.0000	−	20.7846i	0.136364	−	0.236189i
$89$			60.7739i			0.682853i	0.939908	+	0.341427i	$0.110910\pi$
$89$			60.7739i			0.682853i	−0.939908	+	0.341427i	$0.889090\pi$
$90$		0			0
$91$	74.8683			0.822729
$92$	15.8894	+	9.17377i	0.172711	+	0.0997149i
$93$		0			0
$94$	−32.4342	−	56.1776i	−0.345044	−	0.597634i
$95$	−52.2343	+	30.1575i	−0.549835	+	0.317447i
$96$		0			0
$97$	−18.0263	+	31.2225i	−0.185838	+	0.321882i	−0.943859	−	0.330349i	$-0.892833\pi$
$97$	−18.0263	+	31.2225i	−0.185838	+	0.321882i	0.758020	+	0.652231i	$0.226167\pi$
$98$		−	9.97398i		−	0.101775i
$99$		0			0
$100$	10.0000			0.100000
$101$	41.7058	+	24.0789i	0.412929	+	0.238405i	0.692047	−	0.721852i	$-0.256709\pi$
$101$	41.7058	+	24.0789i	0.412929	+	0.238405i	−0.279118	+	0.960257i	$0.590042\pi$
$102$		0			0
$103$	−70.2039	−	121.597i	−0.681591	−	1.18055i	−0.974495	−	0.224409i	$-0.927955\pi$
$103$	−70.2039	−	121.597i	−0.681591	−	1.18055i	0.292904	−	0.956142i	$-0.405378\pi$
$104$	−24.4949	+	14.1421i	−0.235528	+	0.135982i
$105$		0			0
$106$	21.4868	−	37.2163i	0.202706	−	0.351097i
$107$		−	43.1149i		−	0.402943i	−0.979494	−	0.201471i	$-0.935428\pi$
$107$		−	43.1149i		−	0.402943i	0.979494	−	0.201471i	$-0.0645723\pi$
$108$		0			0
$109$	133.842			1.22791			0.613954	−	0.789342i	$-0.289578\pi$
$109$	133.842			1.22791			0.613954	+	0.789342i	$0.289578\pi$
$110$	23.2379	+	13.4164i	0.211254	+	0.121967i
$111$		0			0
$112$	14.9737	+	25.9352i	0.133693	+	0.231564i
$113$	6.84898	−	3.95426i	0.0606104	−	0.0349935i	−0.469389	−	0.882992i	$-0.655526\pi$
$113$	6.84898	−	3.95426i	0.0606104	−	0.0349935i	0.529999	+	0.847998i	$0.322192\pi$
$114$		0			0
$115$	−10.2566	+	17.7649i	−0.0891877	+	0.154478i
$116$			53.6656i			0.462635i
$117$		0			0
$118$	−34.0527			−0.288582
$119$	−197.023	−	113.751i	−1.65565	−	0.955891i
$120$		0			0
$121$	−24.5000	−	42.4352i	−0.202479	−	0.350705i
$122$	66.0717	−	38.1465i	0.541571	−	0.312676i
$123$		0			0
$124$	8.00000	−	13.8564i	0.0645161	−	0.111745i
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	−134.460			−1.05874			−0.529372	−	0.848390i	$-0.677572\pi$
$127$	−134.460			−1.05874			−0.529372	+	0.848390i	$0.677572\pi$
$128$	−9.79796	−	5.65685i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−15.8114	−	27.3861i	−0.121626	−	0.210663i
$131$	−190.867	+	110.197i	−1.45700	+	0.841198i	−0.998862	−	0.0476846i	$-0.984816\pi$
$131$	−190.867	+	110.197i	−1.45700	+	0.841198i	−0.458135	+	0.888883i	$0.651482\pi$
$132$		0			0
$133$	100.974	−	174.892i	0.759200	−	1.31497i
$134$			156.215i			1.16578i
$135$		0			0
$136$	85.9473			0.631966
$137$	−82.7187	−	47.7576i	−0.603786	−	0.348596i	0.166744	−	0.986000i	$-0.446675\pi$
$137$	−82.7187	−	47.7576i	−0.603786	−	0.348596i	−0.770529	+	0.637404i	$0.780008\pi$
$138$		0			0
$139$	38.4078	+	66.5243i	0.276315	+	0.478592i	0.970466	−	0.241237i	$-0.0775533\pi$
$139$	38.4078	+	66.5243i	0.276315	+	0.478592i	−0.694151	+	0.719830i	$0.744220\pi$
$140$	−28.9964	+	16.7411i	−0.207117	+	0.119579i
$141$		0			0
$142$	−11.0263	+	19.0982i	−0.0776502	+	0.134494i
$143$		−	84.8528i		−	0.593376i
$144$		0			0
$145$	−60.0000			−0.413793
$146$	107.713	+	62.1882i	0.737761	+	0.425946i
$147$		0			0
$148$	15.9473	+	27.6216i	0.107752	+	0.186632i
$149$	−239.228	+	138.118i	−1.60556	+	0.926969i	−0.615209	+	0.788364i	$0.710928\pi$
$149$	−239.228	+	138.118i	−1.60556	+	0.926969i	−0.990348	+	0.138605i	$0.955738\pi$
$150$		0			0
$151$	−9.02633	+	15.6341i	−0.0597770	+	0.103537i	−0.894365	−	0.447337i	$-0.852372\pi$
$151$	−9.02633	+	15.6341i	−0.0597770	+	0.103537i	0.834588	+	0.550874i	$0.185706\pi$
$152$			76.2930i			0.501928i
$153$		0			0
$154$	−89.8420			−0.583390
$155$	15.4919	+	8.94427i	0.0999480	+	0.0577050i
$156$		0			0
$157$	−51.9210	−	89.9298i	−0.330707	−	0.572801i	0.651944	−	0.758267i	$-0.273954\pi$
$157$	−51.9210	−	89.9298i	−0.330707	−	0.572801i	−0.982651	+	0.185466i	$0.940621\pi$
$158$	57.5308	−	33.2154i	0.364119	−	0.210224i
$159$		0			0
$160$	6.32456	−	10.9545i	0.0395285	−	0.0684653i
$161$		−	68.6825i		−	0.426599i
$162$		0			0
$163$	−11.3815			−0.0698251			−0.0349126	−	0.999390i	$-0.511115\pi$
$163$	−11.3815			−0.0698251			−0.0349126	+	0.999390i	$0.511115\pi$
$164$	82.0257	+	47.3575i	0.500156	+	0.288765i
$165$		0			0
$166$	−18.4868	−	32.0201i	−0.111366	−	0.192892i
$167$	218.472	−	126.135i	1.30821	−	0.755298i	0.326416	−	0.945226i	$-0.394159\pi$
$167$	218.472	−	126.135i	1.30821	−	0.755298i	0.981798	+	0.189928i	$0.0608255\pi$
$168$		0			0
$169$	34.5000	−	59.7558i	0.204142	−	0.353584i
$170$			96.0920i			0.565247i
$171$		0			0
$172$	28.9210			0.168145
$173$	−10.2329	−	5.90799i	−0.0591500	−	0.0341502i	0.470133	−	0.882595i	$-0.344206\pi$
$173$	−10.2329	−	5.90799i	−0.0591500	−	0.0341502i	−0.529283	+	0.848445i	$0.677539\pi$
$174$		0			0
$175$	−18.7171	−	32.4189i	−0.106955	−	0.185251i
$176$	29.3939	−	16.9706i	0.167011	−	0.0964237i
$177$		0			0
$178$	−42.9737	+	74.4326i	−0.241425	+	0.418161i
$179$		−	69.0358i		−	0.385675i	−0.981231	−	0.192837i	$-0.938231\pi$
$179$		−	69.0358i		−	0.385675i	0.981231	−	0.192837i	$-0.0617690\pi$
$180$		0			0
$181$	−189.684			−1.04798			−0.523989	−	0.851725i	$-0.675557\pi$
$181$	−189.684			−1.04798			−0.523989	+	0.851725i	$0.675557\pi$
$182$	91.6946	+	52.9399i	0.503816	+	0.290879i
$183$		0			0
$184$	12.9737	+	22.4710i	0.0705091	+	0.122125i
$185$	−30.8819	+	17.8297i	−0.166929	+	0.0963765i
$186$		0			0
$187$	−128.921	+	223.298i	−0.689417	+	1.19411i
$188$		−	91.7377i		−	0.487966i
$189$		0			0
$190$	−85.2982			−0.448938
$191$	−94.1441	−	54.3541i	−0.492901	−	0.284577i	0.232876	−	0.972506i	$-0.425186\pi$
$191$	−94.1441	−	54.3541i	−0.492901	−	0.284577i	−0.725777	+	0.687930i	$0.758520\pi$
$192$		0			0
$193$	83.9737	+	145.447i	0.435097	+	0.753610i	0.997304	−	0.0733871i	$-0.0233808\pi$
$193$	83.9737	+	145.447i	0.435097	+	0.753610i	−0.562207	+	0.826997i	$0.690048\pi$
$194$	−44.1553	+	25.4931i	−0.227605	+	0.131408i
$195$		0			0
$196$	7.05267	−	12.2156i	0.0359830	−	0.0623244i
$197$			171.659i			0.871367i	0.900100	+	0.435684i	$0.143493\pi$
$197$			171.659i			0.871367i	−0.900100	+	0.435684i	$0.856507\pi$
$198$		0			0
$199$	35.0790			0.176276			0.0881382	−	0.996108i	$-0.471908\pi$
$199$	35.0790			0.176276			0.0881382	+	0.996108i	$0.471908\pi$
$200$	12.2474	+	7.07107i	0.0612372	+	0.0353553i
$201$		0			0
$202$	34.0527	+	58.9810i	0.168578	+	0.291985i
$203$	173.978	−	100.446i	0.857036	−	0.494810i
$204$		0			0
$205$	−52.9473	+	91.7075i	−0.258280	+	0.447354i
$206$		−	198.567i		−	0.963916i
$207$		0			0
$208$	−40.0000			−0.192308
$209$	−198.215	−	114.440i	−0.948398	−	0.547558i
$210$		0			0
$211$	29.0790	+	50.3663i	0.137815	+	0.238703i	0.926669	−	0.375878i	$-0.122659\pi$
$211$	29.0790	+	50.3663i	0.137815	+	0.238703i	−0.788854	+	0.614580i	$0.789325\pi$
$212$	52.6318	−	30.3870i	0.248263	−	0.143335i
$213$		0			0
$214$	30.4868	−	52.8047i	0.142462	−	0.246751i
$215$			32.3347i			0.150394i
$216$		0			0
$217$	−59.8947			−0.276012
$218$	163.922	+	94.6406i	0.751937	+	0.434131i
$219$		0			0
$220$	18.9737	+	32.8634i	0.0862439	+	0.149379i
$221$	263.159	−	151.935i	1.19076	−	0.687488i
$222$		0			0
$223$	−49.6907	+	86.0669i	−0.222828	+	0.385950i	−0.955666	−	0.294454i	$-0.904862\pi$
$223$	−49.6907	+	86.0669i	−0.222828	+	0.385950i	0.732837	+	0.680404i	$0.238196\pi$
$224$			42.3519i			0.189071i
$225$		0			0
$226$	11.1843			0.0494882
$227$	187.885	+	108.476i	0.827689	+	0.477867i	0.853061	−	0.521811i	$-0.174744\pi$
$227$	187.885	+	108.476i	0.827689	+	0.477867i	−0.0253716	+	0.999678i	$0.508077\pi$
$228$		0			0
$229$	−162.842	−	282.051i	−0.711100	−	1.23166i	−0.964444	−	0.264286i	$-0.914864\pi$
$229$	−162.842	−	282.051i	−0.711100	−	1.23166i	0.253344	−	0.967376i	$-0.418470\pi$
$230$	−25.1234	+	14.5050i	−0.109232	+	0.0630652i
$231$		0			0
$232$	−37.9473	+	65.7267i	−0.163566	+	0.283305i
$233$		−	51.7119i		−	0.221939i	−0.993824	−	0.110970i	$-0.964604\pi$
$233$		−	51.7119i		−	0.221939i	0.993824	−	0.110970i	$-0.0353957\pi$
$234$		0			0
$235$	102.566			0.436450
$236$	−41.7058	−	24.0789i	−0.176720	−	0.102029i
$237$		0			0
$238$	−160.868	−	278.632i	−0.675917	−	1.17072i
$239$	−355.112	+	205.024i	−1.48582	+	0.857840i	−0.999870	−	0.0161453i	$-0.994861\pi$
$239$	−355.112	+	205.024i	−1.48582	+	0.857840i	−0.485953	+	0.873985i	$0.661527\pi$
$240$		0			0
$241$	−222.763	+	385.837i	−0.924328	+	1.60098i	−0.131689	+	0.991291i	$0.542040\pi$
$241$	−222.763	+	385.837i	−0.924328	+	1.60098i	−0.792639	+	0.609692i	$0.791293\pi$
$242$		−	69.2965i		−	0.286349i
$243$		0			0
$244$	107.895			0.442191
$245$	13.6574	+	7.88512i	0.0557446	+	0.0321842i
$246$		0			0
$247$	134.868	+	233.599i	0.546026	+	0.945744i
$248$	19.5959	−	11.3137i	0.0790158	−	0.0456198i
$249$		0			0
$250$	−7.90569	+	13.6931i	−0.0316228	+	0.0547723i
$251$		−	237.364i		−	0.945675i	−0.881150	−	0.472838i	$-0.843230\pi$
$251$		−	237.364i		−	0.945675i	0.881150	−	0.472838i	$-0.156770\pi$
$252$		0			0
$253$	−77.8420			−0.307676
$254$	−164.680	−	95.0779i	−0.648346	−	0.374323i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−276.164	+	159.443i	−1.07457	+	0.620402i	−0.929426	−	0.369009i	$-0.879697\pi$
$257$	−276.164	+	159.443i	−1.07457	+	0.620402i	−0.145142	+	0.989411i	$0.546364\pi$
$258$		0			0
$259$	59.6975	−	103.399i	0.230492	−	0.399224i
$260$		−	44.7214i		−	0.172005i
$261$		0			0
$262$	−311.684			−1.18963
$263$	31.3761	+	18.1150i	0.119301	+	0.0688784i	0.558463	−	0.829529i	$-0.311391\pi$
$263$	31.3761	+	18.1150i	0.119301	+	0.0688784i	−0.439162	+	0.898408i	$0.644725\pi$
$264$		0			0
$265$	33.9737	+	58.8441i	0.128203	+	0.222053i
$266$	247.334	−	142.798i	0.929827	−	0.536836i
$267$		0			0
$268$	−110.460	+	191.323i	−0.412166	+	0.713893i
$269$			528.041i			1.96298i	0.191518	+	0.981489i	$0.438659\pi$
$269$			528.041i			1.96298i	−0.191518	+	0.981489i	$0.561341\pi$
$270$		0			0
$271$	−475.895			−1.75607			−0.878034	−	0.478597i	$-0.841145\pi$
$271$	−475.895			−1.75607			−0.878034	+	0.478597i	$0.841145\pi$
$272$	105.264	+	60.7739i	0.386998	+	0.223434i
$273$		0			0
$274$	−67.5395	−	116.982i	−0.246495	−	0.426941i
$275$	−36.7423	+	21.2132i	−0.133609	+	0.0771389i
$276$		0			0
$277$	−94.0790	+	162.950i	−0.339635	+	0.588266i	−0.984364	−	0.176146i	$-0.943637\pi$
$277$	−94.0790	+	162.950i	−0.339635	+	0.588266i	0.644729	+	0.764411i	$0.276970\pi$
$278$			108.634i			0.390769i
$279$		0			0
$280$	−47.3509			−0.169110
$281$	21.1589	+	12.2161i	0.0752985	+	0.0434736i	0.537177	−	0.843470i	$-0.319491\pi$
$281$	21.1589	+	12.2161i	0.0752985	+	0.0434736i	−0.461878	+	0.886943i	$0.652824\pi$
$282$		0			0
$283$	−99.2302	−	171.872i	−0.350637	−	0.607321i	0.635724	−	0.771916i	$-0.280702\pi$
$283$	−99.2302	−	171.872i	−0.350637	−	0.607321i	−0.986361	+	0.164595i	$0.947368\pi$
$284$	−27.0089	+	15.5936i	−0.0951017	+	0.0549070i
$285$		0			0
$286$	60.0000	−	103.923i	0.209790	−	0.363367i
$287$		−	354.558i		−	1.23539i
$288$		0			0
$289$	−634.368			−2.19504
$290$	−73.4847	−	42.4264i	−0.253395	−	0.146298i
$291$		0			0
$292$	87.9473	+	152.329i	0.301189	+	0.521676i
$293$	444.985	−	256.912i	1.51872	−	0.876834i	0.518963	−	0.854796i	$-0.326318\pi$
$293$	444.985	−	256.912i	1.51872	−	0.876834i	0.999757	−	0.0220373i	$-0.00701524\pi$
$294$		0			0
$295$	26.9210	−	46.6285i	0.0912576	−	0.158063i
$296$			45.1059i			0.152385i
$297$		0			0
$298$	−390.658			−1.31093
$299$	79.4472	+	45.8688i	0.265710	+	0.153407i
$300$		0			0
$301$	−54.1317	−	93.7588i	−0.179839	−	0.311491i
$302$	−22.1099	+	12.7652i	−0.0732116	+	0.0422688i
$303$		0			0
$304$	−53.9473	+	93.4395i	−0.177458	+	0.307367i
$305$			120.630i			0.395508i
$306$		0			0
$307$	−11.3815			−0.0370733			−0.0185366	−	0.999828i	$-0.505901\pi$
$307$	−11.3815			−0.0370733			−0.0185366	+	0.999828i	$0.505901\pi$
$308$	−110.034	−	63.5279i	−0.357252	−	0.206259i
$309$		0			0
$310$	12.6491	+	21.9089i	0.0408036	+	0.0706739i
$311$	449.256	−	259.378i	1.44455	−	0.834012i	0.446403	−	0.894832i	$-0.352705\pi$
$311$	449.256	−	259.378i	1.44455	−	0.834012i	0.998149	+	0.0608197i	$0.0193715\pi$
$312$		0			0
$313$	23.1580	−	40.1108i	0.0739872	−	0.128150i	−0.826658	−	0.562704i	$-0.809761\pi$
$313$	23.1580	−	40.1108i	0.0739872	−	0.128150i	0.900645	+	0.434555i	$0.143094\pi$
$314$		−	146.855i		−	0.467690i
$315$		0			0
$316$	93.9473			0.297302
$317$	33.8579	+	19.5479i	0.106807	+	0.0616651i	0.552452	−	0.833545i	$-0.313692\pi$
$317$	33.8579	+	19.5479i	0.106807	+	0.0616651i	−0.445645	+	0.895210i	$0.647026\pi$
$318$		0			0
$319$	−113.842	−	197.180i	−0.356871	−	0.618120i
$320$	15.4919	−	8.94427i	0.0484123	−	0.0279508i
$321$		0			0
$322$	48.5658	−	84.1185i	0.150826	−	0.261238i
$323$		−	819.648i		−	2.53761i
$324$		0			0
$325$	50.0000			0.153846
$326$	−13.9394	−	8.04793i	−0.0427590	−	0.0246869i
$327$		0			0
$328$	66.9737	+	116.002i	0.204188	+	0.353664i
$329$	−297.404	+	171.706i	−0.903963	+	0.521903i
$330$		0			0
$331$	222.710	−	385.746i	0.672841	−	1.16539i	−0.304254	−	0.952591i	$-0.598407\pi$
$331$	222.710	−	385.746i	0.672841	−	1.16539i	0.977095	−	0.212804i	$-0.0682595\pi$
$332$		−	52.2887i		−	0.157496i
$333$		0			0
$334$	356.763			1.06815
$335$	−213.906	−	123.499i	−0.638525	−	0.368653i
$336$		0			0
$337$	−162.842	−	282.051i	−0.483211	−	0.836945i	0.516603	−	0.856225i	$-0.327196\pi$
$337$	−162.842	−	282.051i	−0.483211	−	0.836945i	−0.999814	+	0.0192793i	$0.993863\pi$
$338$	84.5074	−	48.7904i	0.250022	−	0.144350i
$339$		0			0
$340$	−67.9473	+	117.688i	−0.199845	+	0.346142i
$341$			67.8823i			0.199068i
$342$		0			0
$343$	314.053			0.915605
$344$	35.4208	+	20.4502i	0.102968	+	0.0594484i
$345$		0			0
$346$	−8.35516	−	14.4716i	−0.0241479	−	0.0418253i
$347$	44.8806	−	25.9118i	0.129339	−	0.0746738i	−0.433935	−	0.900944i	$-0.642875\pi$
$347$	44.8806	−	25.9118i	0.129339	−	0.0746738i	0.563273	+	0.826271i	$0.309542\pi$
$348$		0			0
$349$	48.7893	−	84.5056i	0.139798	−	0.242136i	−0.787622	−	0.616158i	$-0.788688\pi$
$349$	48.7893	−	84.5056i	0.139798	−	0.242136i	0.927420	+	0.374022i	$0.122022\pi$
$350$		−	52.9399i		−	0.151257i
$351$		0			0
$352$	48.0000			0.136364
$353$	493.459	+	284.899i	1.39790	+	0.807078i	0.994173	−	0.107801i	$-0.0343809\pi$
$353$	493.459	+	284.899i	1.39790	+	0.807078i	0.403728	+	0.914879i	$0.367714\pi$
$354$		0			0
$355$	−17.4342	−	30.1969i	−0.0491103	−	0.0850616i
$356$	−105.264	+	60.7739i	−0.295684	+	0.170713i
$357$		0			0
$358$	48.8157	−	84.5512i	0.136357	−	0.236177i
$359$			274.283i			0.764019i	0.924158	+	0.382010i	$0.124768\pi$
$359$			274.283i			0.764019i	−0.924158	+	0.382010i	$0.875232\pi$
$360$		0			0
$361$	366.579			1.01545
$362$	−232.314	−	134.127i	−0.641753	−	0.370516i
$363$		0			0
$364$	74.8683	+	129.676i	0.205682	+	0.356252i
$365$	−170.309	+	98.3281i	−0.466601	+	0.269392i
$366$		0			0
$367$	−230.914	+	399.955i	−0.629194	+	1.08980i	0.358520	+	0.933522i	$0.383282\pi$
$367$	−230.914	+	399.955i	−0.629194	+	1.08980i	−0.987714	+	0.156274i	$0.950052\pi$
$368$			36.6951i			0.0997149i
$369$		0			0
$370$	−50.4299			−0.136297
$371$	−197.023	−	113.751i	−0.531058	−	0.306607i
$372$		0			0
$373$	245.974	+	426.039i	0.659447	+	1.14220i	0.980759	+	0.195222i	$0.0625428\pi$
$373$	245.974	+	426.039i	0.659447	+	1.14220i	−0.321312	+	0.946973i	$0.604124\pi$
$374$	−315.791	+	182.322i	−0.844360	+	0.487492i
$375$		0			0
$376$	64.8683	−	112.355i	0.172522	−	0.298817i
$377$			268.328i			0.711746i
$378$		0			0
$379$	−258.763			−0.682752			−0.341376	−	0.939927i	$-0.610893\pi$
$379$	−258.763			−0.682752			−0.341376	+	0.939927i	$0.610893\pi$
$380$	−104.469	−	60.3150i	−0.274917	−	0.158724i
$381$		0			0
$382$	−76.8683	−	133.140i	−0.201226	−	0.348534i
$383$	452.430	−	261.211i	1.18128	−	0.682012i	0.224970	−	0.974366i	$-0.427772\pi$
$383$	452.430	−	261.211i	1.18128	−	0.682012i	0.956310	+	0.292353i	$0.0944383\pi$
$384$		0			0
$385$	71.0263	−	123.021i	0.184484	−	0.319536i
$386$			237.513i			0.615320i
$387$		0			0
$388$	−72.1053			−0.185838
$389$	529.009	+	305.423i	1.35992	+	0.785150i	0.989613	−	0.143759i	$-0.0459192\pi$
$389$	529.009	+	305.423i	1.35992	+	0.785150i	0.370307	+	0.928909i	$0.379253\pi$
$390$		0			0
$391$	−139.381	−	241.416i	−0.356474	−	0.617432i
$392$	17.2754	−	9.97398i	0.0440700	−	0.0254438i
$393$		0			0
$394$	−121.381	+	210.239i	−0.308075	+	0.533601i
$395$			105.036i			0.265915i
$396$		0			0
$397$	−214.000			−0.539043			−0.269521	−	0.962994i	$-0.586865\pi$
$397$	−214.000			−0.539043			−0.269521	+	0.962994i	$0.586865\pi$
$398$	42.9628	+	24.8046i	0.107947	+	0.0623231i
$399$		0			0
$400$	10.0000	+	17.3205i	0.0250000	+	0.0433013i
$401$	−393.658	+	227.279i	−0.981692	+	0.566780i	−0.902780	−	0.430102i	$-0.858478\pi$
$401$	−393.658	+	227.279i	−0.981692	+	0.566780i	−0.0789111	+	0.996882i	$0.525144\pi$
$402$		0			0
$403$	40.0000	−	69.2820i	0.0992556	−	0.171916i
$404$			96.3155i			0.238405i
$405$		0			0
$406$	284.105			0.699767
$407$	−117.188	−	67.6588i	−0.287932	−	0.166238i
$408$		0			0
$409$	286.921	+	496.962i	0.701518	+	1.21507i	0.967933	+	0.251207i	$0.0808275\pi$
$409$	286.921	+	496.962i	0.701518	+	1.21507i	−0.266415	+	0.963858i	$0.585839\pi$
$410$	−129.694	+	74.8788i	−0.316327	+	0.182631i
$411$		0			0
$412$	140.408	−	243.193i	0.340796	−	0.590275i
$413$			180.274i			0.436500i
$414$		0			0
$415$	58.4605			0.140869
$416$	−48.9898	−	28.2843i	−0.117764	−	0.0679910i
$417$		0			0
$418$	−161.842	−	280.319i	−0.387182	−	0.670619i
$419$	−84.7977	+	48.9580i	−0.202381	+	0.116845i	−0.597766	−	0.801671i	$-0.703945\pi$
$419$	−84.7977	+	48.9580i	−0.202381	+	0.116845i	0.395385	+	0.918516i	$0.370611\pi$
$420$		0			0
$421$	−358.658	+	621.213i	−0.851918	+	1.47557i	0.0275562	+	0.999620i	$0.491227\pi$
$421$	−358.658	+	621.213i	−0.851918	+	1.47557i	−0.879475	+	0.475946i	$0.842106\pi$
$422$			82.2478i			0.194900i
$423$		0			0
$424$	85.9473			0.202706
$425$	−131.579	−	75.9674i	−0.309599	−	0.178747i
$426$		0			0
$427$	−201.947	−	349.783i	−0.472945	−	0.819164i
$428$	74.6772	−	43.1149i	0.174479	−	0.100736i
$429$		0			0
$430$	−22.8641	+	39.6017i	−0.0531722	+	0.0920970i
$431$		−	293.077i		−	0.679994i	−0.940427	−	0.339997i	$-0.889574\pi$
$431$		−	293.077i		−	0.679994i	0.940427	−	0.339997i	$-0.110426\pi$
$432$		0			0
$433$	487.526			1.12593			0.562963	−	0.826482i	$-0.309661\pi$
$433$	487.526			1.12593			0.562963	+	0.826482i	$0.309661\pi$
$434$	−73.3557	−	42.3519i	−0.169022	−	0.0975851i
$435$		0			0
$436$	133.842	+	231.821i	0.306977	+	0.531700i
$437$	214.298	−	123.725i	0.490385	−	0.283124i
$438$		0			0
$439$	−128.619	+	222.774i	−0.292981	+	0.507457i	−0.974513	−	0.224331i	$-0.927980\pi$
$439$	−128.619	+	222.774i	−0.292981	+	0.507457i	0.681532	+	0.731788i	$0.261314\pi$
$440$			53.6656i			0.121967i
$441$		0			0
$442$	429.737			0.972255
$443$	−253.828	−	146.548i	−0.572976	−	0.330808i	0.185361	−	0.982670i	$-0.440654\pi$
$443$	−253.828	−	146.548i	−0.572976	−	0.330808i	−0.758337	+	0.651863i	$0.773988\pi$
$444$		0			0
$445$	−67.9473	−	117.688i	−0.152691	−	0.264468i
$446$	−121.717	+	70.2733i	−0.272908	+	0.157564i
$447$		0			0
$448$	−29.9473	+	51.8703i	−0.0668467	+	0.115782i
$449$			585.614i			1.30426i	0.758106	+	0.652132i	$0.226125\pi$
$449$			585.614i			1.30426i	−0.758106	+	0.652132i	$0.773875\pi$
$450$		0			0
$451$	−401.842			−0.891002
$452$	13.6980	+	7.90852i	0.0303052	+	0.0174967i
$453$		0			0
$454$	153.408	+	265.710i	0.337903	+	0.585265i
$455$	−144.982	+	83.7053i	−0.318642	+	0.183968i
$456$		0			0
$457$	406.526	−	704.124i	0.889554	−	1.54075i	0.0491497	−	0.998791i	$-0.484349\pi$
$457$	406.526	−	704.124i	0.889554	−	1.54075i	0.840404	−	0.541961i	$-0.182318\pi$
$458$		−	460.587i		−	1.00565i
$459$		0			0
$460$	−41.0263			−0.0891877
$461$	479.842	+	277.037i	1.04087	+	0.600948i	0.920080	−	0.391730i	$-0.128123\pi$
$461$	479.842	+	277.037i	1.04087	+	0.600948i	0.120792	+	0.992678i	$0.461457\pi$
$462$		0			0
$463$	224.862	+	389.472i	0.485662	+	0.841192i	0.999864	−	0.0164775i	$-0.00524520\pi$
$463$	224.862	+	389.472i	0.485662	+	0.841192i	−0.514202	+	0.857669i	$0.671912\pi$
$464$	−92.9516	+	53.6656i	−0.200327	+	0.115659i
$465$		0			0
$466$	36.5658	−	63.3339i	0.0784675	−	0.135910i
$467$			30.7221i			0.0657862i	0.999459	+	0.0328931i	$0.0104721\pi$
$467$			30.7221i			0.0657862i	−0.999459	+	0.0328931i	$0.989528\pi$
$468$		0			0
$469$	826.999			1.76332
$470$	125.617	+	72.5250i	0.267270	+	0.154309i
$471$		0			0
$472$	−34.0527	−	58.9810i	−0.0721455	−	0.124960i
$473$	−106.263	+	61.3507i	−0.224657	+	0.129705i
$474$		0			0
$475$	67.4342	−	116.799i	0.141967	−	0.245893i
$476$		−	455.004i		−	0.955891i
$477$		0			0
$478$	−579.895			−1.21317
$479$	−636.738	−	367.621i	−1.32931	−	0.767476i	−0.344115	−	0.938928i	$-0.611821\pi$
$479$	−636.738	−	367.621i	−1.32931	−	0.767476i	−0.985193	+	0.171451i	$0.945154\pi$
$480$		0			0
$481$	79.7367	+	138.108i	0.165773	+	0.287127i
$482$	−545.656	+	315.034i	−1.13207	+	0.653598i
$483$		0			0
$484$	49.0000	−	84.8705i	0.101240	−	0.175352i
$485$		−	80.6162i		−	0.166219i
$486$		0			0
$487$	−92.6185			−0.190182			−0.0950909	−	0.995469i	$-0.530314\pi$
$487$	−92.6185			−0.190182			−0.0950909	+	0.995469i	$0.530314\pi$
$488$	132.143	+	76.2930i	0.270786	+	0.156338i
$489$		0			0
$490$	11.1512	+	19.3145i	0.0227576	+	0.0394174i
$491$	777.970	−	449.161i	1.58446	−	0.914789i	0.590264	−	0.807210i	$-0.299024\pi$
$491$	777.970	−	449.161i	1.58446	−	0.914789i	0.994197	−	0.107579i	$-0.0343097\pi$
$492$		0			0
$493$	407.684	−	706.129i	0.826945	−	1.43231i
$494$			381.465i			0.772197i
$495$		0			0
$496$	32.0000			0.0645161
$497$	101.106	+	58.3733i	0.203432	+	0.117451i
$498$		0			0
$499$	−68.4605	−	118.577i	−0.137195	−	0.237629i	0.789239	−	0.614087i	$-0.210475\pi$
$499$	−68.4605	−	118.577i	−0.137195	−	0.237629i	−0.926434	+	0.376457i	$0.877142\pi$
$500$	−19.3649	+	11.1803i	−0.0387298	+	0.0223607i
$501$		0			0
$502$	167.842	−	290.711i	0.334347	−	0.579105i
$503$			443.077i			0.880868i	0.897785	+	0.440434i	$0.145175\pi$
$503$			443.077i			0.880868i	−0.897785	+	0.440434i	$0.854825\pi$
$504$		0			0
$505$	−107.684			−0.213236
$506$	−95.3366	−	55.0426i	−0.188412	−	0.108780i
$507$		0			0
$508$	−134.460	−	232.892i	−0.264686	−	0.458450i
$509$	−184.517	+	106.531i	−0.362509	+	0.209295i	−0.670181	−	0.742198i	$-0.733783\pi$
$509$	−184.517	+	106.531i	−0.362509	+	0.209295i	0.307672	+	0.951493i	$0.400450\pi$
$510$		0			0
$511$	329.223	−	570.232i	0.644273	−	1.11591i
$512$		−	22.6274i		−	0.0441942i
$513$		0			0
$514$	−450.974			−0.877381
$515$	271.899	+	156.981i	0.527958	+	0.304817i
$516$		0			0
$517$	194.605	+	337.066i	0.376412	+	0.651965i
$518$	146.228	−	84.4250i	0.282294	−	0.162983i
$519$		0			0
$520$	31.6228	−	54.7723i	0.0608130	−	0.105331i
$521$		−	3.20085i		−	0.00614366i	−0.999995	−	0.00307183i	$-0.999022\pi$
$521$		−	3.20085i		−	0.00614366i	0.999995	−	0.00307183i	$-0.000977795\pi$
$522$		0			0
$523$	966.644			1.84827			0.924134	−	0.382069i	$-0.124788\pi$
$523$	966.644			1.84827			0.924134	+	0.382069i	$0.124788\pi$
$524$	−381.733	−	220.394i	−0.728499	−	0.420599i
$525$		0			0
$526$	25.6185	+	44.3725i	0.0487044	+	0.0843585i
$527$	−210.527	+	121.548i	−0.399482	+	0.230641i
$528$		0			0
$529$	−222.421	+	385.244i	−0.420456	+	0.728250i
$530$			96.0920i			0.181306i
$531$		0			0
$532$	403.895			0.759200
$533$	410.128	+	236.788i	0.769471	+	0.444255i
$534$		0			0
$535$	48.2039	+	83.4916i	0.0901008	+	0.156059i
$536$	−270.572	+	156.215i	−0.504798	+	0.291445i
$537$		0			0
$538$	−373.381	+	646.716i	−0.694018	+	1.20207i
$539$			59.8439i			0.111028i
$540$		0			0
$541$	−186.105			−0.344002			−0.172001	−	0.985097i	$-0.555023\pi$
$541$	−186.105			−0.344002			−0.172001	+	0.985097i	$0.555023\pi$
$542$	−582.850	−	336.508i	−1.07537	−	0.620864i
$543$		0			0
$544$	85.9473	+	148.865i	0.157991	+	0.273649i
$545$	−259.184	+	149.640i	−0.475567	+	0.274569i
$546$		0			0
$547$	154.717	−	267.978i	0.282847	−	0.489905i	−0.689238	−	0.724535i	$-0.742055\pi$
$547$	154.717	−	267.978i	0.282847	−	0.489905i	0.972085	+	0.234630i	$0.0753879\pi$
$548$		−	191.031i		−	0.348596i
$549$		0			0
$550$	−60.0000			−0.109091
$551$	626.811	+	361.890i	1.13759	+	0.656787i
$552$		0			0
$553$	−175.842	−	304.567i	−0.317978	−	0.550755i
$554$	−230.446	+	133.048i	−0.415967	+	0.240158i
$555$		0			0
$556$	−76.8157	+	133.049i	−0.138158	+	0.239296i
$557$		−	4.00106i		−	0.00718323i	−0.999994	−	0.00359161i	$-0.998857\pi$
$557$		−	4.00106i		−	0.00718323i	0.999994	−	0.00359161i	$-0.00114325\pi$
$558$		0			0
$559$	144.605			0.258685
$560$	−57.9928	−	33.4821i	−0.103558	−	0.0597895i
$561$		0			0
$562$	17.2762	+	29.9232i	0.0307405	+	0.0532441i
$563$	144.600	−	83.4849i	0.256839	−	0.148286i	−0.366053	−	0.930594i	$-0.619291\pi$
$563$	144.600	−	83.4849i	0.256839	−	0.148286i	0.622892	+	0.782308i	$0.285958\pi$
$564$		0			0
$565$	−8.84200	+	15.3148i	−0.0156496	+	0.0271058i
$566$		−	280.666i		−	0.495875i
$567$		0			0
$568$	−44.1053			−0.0776502
$569$	−135.350	−	78.1446i	−0.237874	−	0.137337i	0.376325	−	0.926488i	$-0.377188\pi$
$569$	−135.350	−	78.1446i	−0.237874	−	0.137337i	−0.614199	+	0.789151i	$0.710521\pi$
$570$		0			0
$571$	72.0527	+	124.799i	0.126187	+	0.218562i	0.922196	−	0.386722i	$-0.126393\pi$
$571$	72.0527	+	124.799i	0.126187	+	0.218562i	−0.796009	+	0.605284i	$0.793059\pi$
$572$	146.969	−	84.8528i	0.256939	−	0.148344i
$573$		0			0
$574$	250.710	−	434.243i	0.436778	−	0.756521i
$575$		−	45.8688i		−	0.0797719i
$576$		0			0
$577$	532.947			0.923651			0.461826	−	0.886971i	$-0.347195\pi$
$577$	532.947			0.923651			0.461826	+	0.886971i	$0.347195\pi$
$578$	−776.939	−	448.566i	−1.34419	−	0.776066i
$579$		0			0
$580$	−60.0000	−	103.923i	−0.103448	−	0.179178i
$581$	−169.514	+	97.8691i	−0.291763	+	0.168449i
$582$		0			0
$583$	−128.921	+	223.298i	−0.221134	+	0.383015i
$584$			248.753i			0.425946i
$585$		0			0
$586$	726.658			1.24003
$587$	−164.841	−	95.1710i	−0.280820	−	0.162131i	0.352975	−	0.935633i	$-0.385170\pi$
$587$	−164.841	−	95.1710i	−0.280820	−	0.162131i	−0.633794	+	0.773502i	$0.718503\pi$
$588$		0			0
$589$	−107.895	−	186.879i	−0.183183	−	0.317282i
$590$	65.9427	−	38.0720i	0.111767	−	0.0645289i
$591$		0			0
$592$	−31.8947	+	55.2432i	−0.0538761	+	0.0933162i
$593$			345.719i			0.583001i	0.956571	+	0.291500i	$0.0941544\pi$
$593$			345.719i			0.583001i	−0.956571	+	0.291500i	$0.905846\pi$
$594$		0			0
$595$	508.710			0.854975
$596$	−478.456	−	276.237i	−0.802778	−	0.463484i
$597$		0			0
$598$	64.8683	+	112.355i	0.108475	+	0.187885i
$599$	−609.729	+	352.027i	−1.01791	+	0.587692i	−0.913499	−	0.406842i	$-0.866630\pi$
$599$	−609.729	+	352.027i	−1.01791	+	0.587692i	−0.104414	+	0.994534i	$0.533297\pi$
$600$		0			0
$601$	−169.237	+	293.127i	−0.281592	+	0.487732i	−0.971777	−	0.235901i	$-0.924196\pi$
$601$	−169.237	+	293.127i	−0.281592	+	0.487732i	0.690185	+	0.723633i	$0.257529\pi$
$602$		−	153.107i		−	0.254331i
$603$		0			0
$604$	−36.1053			−0.0597770
$605$	94.8881	+	54.7837i	0.156840	+	0.0905515i
$606$		0			0
$607$	408.257	+	707.121i	0.672581	+	1.16494i	0.977170	+	0.212460i	$0.0681476\pi$
$607$	408.257	+	707.121i	0.672581	+	1.16494i	−0.304589	+	0.952484i	$0.598519\pi$
$608$	−132.143	+	76.2930i	−0.217341	+	0.125482i
$609$		0			0
$610$	−85.2982	+	147.741i	−0.139833	+	0.242198i
$611$		−	458.688i		−	0.750717i
$612$		0			0
$613$	−229.263			−0.374001			−0.187001	−	0.982360i	$-0.559877\pi$
$613$	−229.263			−0.374001			−0.187001	+	0.982360i	$0.559877\pi$
$614$	−13.9394	−	8.04793i	−0.0227027	−	0.0131074i
$615$		0			0
$616$	−89.8420	−	155.611i	−0.145847	−	0.252615i
$617$	928.598	−	536.126i	1.50502	−	0.868924i	0.505038	−	0.863097i	$-0.331478\pi$
$617$	928.598	−	536.126i	1.50502	−	0.868924i	0.999983	−	0.00582739i	$-0.00185493\pi$
$618$		0			0
$619$	40.3552	−	69.8972i	0.0651941	−	0.112920i	−0.831586	−	0.555396i	$-0.812567\pi$
$619$	40.3552	−	69.8972i	0.0651941	−	0.112920i	0.896780	+	0.442477i	$0.145900\pi$
$620$			35.7771i			0.0577050i
$621$		0			0
$622$	733.631			1.17947
$623$	394.045	+	227.502i	0.632497	+	0.365172i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	56.7253	−	32.7504i	0.0906155	−	0.0523169i
$627$		0			0
$628$	103.842	−	179.860i	0.165353	−	0.286401i
$629$		−	484.591i		−	0.770415i
$630$		0			0
$631$	492.894			0.781131			0.390566	−	0.920575i	$-0.372279\pi$
$631$	492.894			0.781131			0.390566	+	0.920575i	$0.372279\pi$
$632$	115.062	+	66.4308i	0.182059	+	0.105112i
$633$		0			0
$634$	27.6448	+	47.8823i	0.0436038	+	0.0755241i
$635$	260.382	−	150.331i	0.410050	−	0.236742i
$636$		0			0
$637$	35.2633	−	61.0779i	0.0553585	−	0.0958837i
$638$		−	321.994i		−	0.504692i
$639$		0			0
$640$	25.2982			0.0395285
$641$	56.7087	+	32.7408i	0.0884692	+	0.0510777i	0.543582	−	0.839356i	$-0.317068\pi$
$641$	56.7087	+	32.7408i	0.0884692	+	0.0510777i	−0.455113	+	0.890434i	$0.650401\pi$
$642$		0			0
$643$	214.309	+	371.195i	0.333296	+	0.577285i	0.983156	−	0.182768i	$-0.0585059\pi$
$643$	214.309	+	371.195i	0.333296	+	0.577285i	−0.649860	+	0.760054i	$0.725173\pi$
$644$	118.962	−	68.6825i	0.184723	−	0.106650i
$645$		0			0
$646$	579.579	−	1003.86i	0.897181	−	1.55396i
$647$			462.801i			0.715303i	0.933855	+	0.357652i	$0.116422\pi$
$647$			462.801i			0.715303i	−0.933855	+	0.357652i	$0.883578\pi$
$648$		0			0
$649$	204.316			0.314817
$650$	61.2372	+	35.3553i	0.0942111	+	0.0543928i
$651$		0			0
$652$	−11.3815	−	19.7133i	−0.0174563	−	0.0302352i
$653$	368.116	−	212.532i	0.563731	−	0.325470i	−0.190911	−	0.981607i	$-0.561144\pi$
$653$	368.116	−	212.532i	0.563731	−	0.325470i	0.754642	+	0.656137i	$0.227811\pi$
$654$		0			0
$655$	246.408	−	426.791i	0.376195	−	0.651589i
$656$			189.430i			0.288765i
$657$		0			0
$658$	−485.658			−0.738083
$659$	158.282	+	91.3844i	0.240186	+	0.138671i	0.615262	−	0.788323i	$-0.289050\pi$
$659$	158.282	+	91.3844i	0.240186	+	0.138671i	−0.375076	+	0.926994i	$0.622384\pi$
$660$		0			0
$661$	241.026	+	417.470i	0.364639	+	0.631573i	0.988718	−	0.149788i	$-0.0478591\pi$
$661$	241.026	+	417.470i	0.364639	+	0.631573i	−0.624079	+	0.781361i	$0.714526\pi$
$662$	545.527	−	314.960i	0.824058	−	0.475770i
$663$		0			0
$664$	36.9737	−	64.0403i	0.0556832	−	0.0964462i
$665$			451.568i			0.679050i
$666$		0			0
$667$	246.158			0.369052
$668$	436.944	+	252.270i	0.654107	+	0.377649i
$669$		0			0
$670$	−174.653	−	302.509i	−0.260677	−	0.451505i
$671$	−396.430	+	228.879i	−0.590805	+	0.341102i
$672$		0			0
$673$	−92.2897	+	159.850i	−0.137132	+	0.237519i	−0.926410	−	0.376517i	$-0.877122\pi$
$673$	−92.2897	+	159.850i	−0.137132	+	0.237519i	0.789278	+	0.614036i	$0.210455\pi$
$674$		−	460.587i		−	0.683363i
$675$		0			0
$676$	138.000			0.204142
$677$	923.054	+	532.926i	1.36345	+	0.787187i	0.990081	−	0.140497i	$-0.0448700\pi$
$677$	923.054	+	532.926i	1.36345	+	0.787187i	0.373367	+	0.927684i	$0.378203\pi$
$678$		0			0
$679$	134.960	+	233.758i	0.198763	+	0.344268i
$680$	−166.436	+	96.0920i	−0.244759	+	0.141312i
$681$		0			0
$682$	−48.0000	+	83.1384i	−0.0703812	+	0.121904i
$683$		−	788.926i		−	1.15509i	−0.816359	−	0.577545i	$-0.804011\pi$
$683$		−	788.926i		−	1.15509i	0.816359	−	0.577545i	$-0.195989\pi$
$684$		0			0
$685$	213.579			0.311794
$686$	384.634	+	222.069i	0.560692	+	0.323715i
$687$		0			0
$688$	28.9210	+	50.0926i	0.0420363	+	0.0728091i
$689$	263.159	−	151.935i	0.381943	−	0.220515i
$690$		0			0
$691$	−466.000	+	807.136i	−0.674385	+	1.16807i	0.302263	+	0.953224i	$0.402258\pi$
$691$	−466.000	+	807.136i	−0.674385	+	1.16807i	−0.976648	+	0.214845i	$0.931076\pi$
$692$		−	23.6320i		−	0.0341502i
$693$		0			0
$694$	73.2897			0.105605
$695$	−148.753	−	85.8825i	−0.214033	−	0.123572i
$696$		0			0
$697$	−719.526	−	1246.26i	−1.03232	−	1.78803i
$698$	119.509	−	68.9985i	0.171216	−	0.0988518i
$699$		0			0
$700$	37.4342	−	64.8379i	0.0534774	−	0.0926255i
$701$			1352.75i			1.92974i	0.262721	+	0.964872i	$0.415380\pi$
$701$			1352.75i			1.92974i	−0.262721	+	0.964872i	$0.584620\pi$
$702$		0			0
$703$	430.158			0.611889
$704$	58.7878	+	33.9411i	0.0835053	+	0.0482118i
$705$		0			0
$706$	402.907	+	697.856i	0.570690	+	0.988465i
$707$	312.245	−	180.274i	0.441647	−	0.254985i
$708$		0			0
$709$	134.737	−	233.371i	0.190038	−	0.329155i	−0.755225	−	0.655466i	$-0.772472\pi$
$709$	134.737	−	233.371i	0.190038	−	0.329155i	0.945262	+	0.326311i	$0.105806\pi$
$710$		−	49.3113i		−	0.0694525i
$711$		0			0
$712$	−171.895			−0.241425
$713$	−63.5577	−	36.6951i	−0.0891413	−	0.0514657i
$714$		0			0
$715$	94.8683	+	164.317i	0.132683	+	0.229814i
$716$	119.573	−	69.0358i	0.167002	−	0.0964187i
$717$		0			0
$718$	−193.947	+	335.927i	−0.270122	+	0.467864i
$719$		−	537.103i		−	0.747014i	−0.927627	−	0.373507i	$-0.878155\pi$
$719$		−	537.103i		−	0.747014i	0.927627	−	0.373507i	$-0.121845\pi$
$720$		0			0
$721$	−1051.21			−1.45799
$722$	448.965	+	259.210i	0.621836	+	0.359017i
$723$		0			0
$724$	−189.684	−	328.542i	−0.261994	−	0.453788i
$725$	116.190	−	67.0820i	0.160261	−	0.0925270i
$726$		0			0
$727$	558.914	−	968.068i	0.768795	−	1.33159i	−0.169421	−	0.985544i	$-0.554190\pi$
$727$	558.914	−	968.068i	0.768795	−	1.33159i	0.938216	−	0.346049i	$-0.112477\pi$
$728$			211.760i			0.290879i
$729$		0			0
$730$	−278.114			−0.380978
$731$	−380.541	−	219.705i	−0.520576	−	0.300555i
$732$		0			0
$733$	−3.76299	−	6.51770i	−0.00513369	−	0.00889181i	0.863447	−	0.504439i	$-0.168301\pi$
$733$	−3.76299	−	6.51770i	−0.00513369	−	0.00889181i	−0.868581	+	0.495548i	$0.834967\pi$
$734$	−565.622	+	326.562i	−0.770602	+	0.444907i
$735$		0			0
$736$	−25.9473	+	44.9421i	−0.0352545	+	0.0610626i
$737$		−	937.288i		−	1.27176i
$738$		0			0
$739$	−823.079			−1.11377			−0.556887	−	0.830588i	$-0.688004\pi$
$739$	−823.079			−1.11377			−0.556887	+	0.830588i	$0.688004\pi$
$740$	−61.7638	−	35.6593i	−0.0834645	−	0.0481883i
$741$		0			0
$742$	−160.868	−	278.632i	−0.216804	−	0.375515i
$743$	−2.78772	+	1.60949i	−0.00375197	+	0.00216620i	−0.501875	−	0.864940i	$-0.667356\pi$
$743$	−2.78772	+	1.60949i	−0.00375197	+	0.00216620i	0.498123	+	0.867106i	$0.334023\pi$
$744$		0			0
$745$	308.842	−	534.930i	0.414553	−	0.718027i
$746$			695.719i			0.932599i
$747$		0			0
$748$	−515.684			−0.689417
$749$	−279.548	−	161.397i	−0.373228	−	0.215483i
$750$		0			0
$751$	−592.816	−	1026.79i	−0.789368	−	1.36723i	−0.926354	−	0.376653i	$-0.877075\pi$
$751$	−592.816	−	1026.79i	−0.789368	−	1.36723i	0.136986	−	0.990573i	$-0.456258\pi$
$752$	158.894	−	91.7377i	0.211296	−	0.121992i
$753$		0			0
$754$	−189.737	+	328.634i	−0.251640	+	0.435853i
$755$		−	40.3670i		−	0.0534662i
$756$		0			0
$757$	−863.315			−1.14044			−0.570221	−	0.821491i	$-0.693143\pi$
$757$	−863.315			−1.14044			−0.570221	+	0.821491i	$0.693143\pi$
$758$	−316.919	−	182.973i	−0.418098	−	0.241389i
$759$		0			0
$760$	−85.2982	−	147.741i	−0.112235	−	0.194396i
$761$	494.152	−	285.299i	0.649345	−	0.374900i	−0.138860	−	0.990312i	$-0.544344\pi$
$761$	494.152	−	285.299i	0.649345	−	0.374900i	0.788205	+	0.615412i	$0.211010\pi$
$762$		0			0
$763$	501.026	−	867.803i	0.656653	−	1.13736i
$764$		−	217.416i		−	0.284577i
$765$		0			0
$766$	738.816			0.964511
$767$	−208.529	−	120.394i	−0.271876	−	0.156968i
$768$		0			0
$769$	370.842	+	642.317i	0.482239	+	0.835263i	0.999792	−	0.0203883i	$-0.00649025\pi$
$769$	370.842	+	642.317i	0.482239	+	0.835263i	−0.517553	+	0.855651i	$0.673157\pi$
$770$	173.978	−	100.446i	0.225946	−	0.130450i
$771$		0			0
$772$	−167.947	+	290.893i	−0.217548	+	0.376805i
$773$		−	623.203i		−	0.806214i	−0.915153	−	0.403107i	$-0.867930\pi$
$773$		−	623.203i		−	0.806214i	0.915153	−	0.403107i	$-0.132070\pi$
$774$		0			0
$775$	−40.0000			−0.0516129
$776$	−88.3106	−	50.9862i	−0.113802	−	0.0657038i
$777$		0			0
$778$	431.934	+	748.131i	0.555185	+	0.961608i
$779$	1106.27	−	638.703i	1.42011	−	0.819901i
$780$		0			0
$781$	66.1580	−	114.589i	0.0847094	−	0.146721i
$782$		−	394.230i		−	0.504131i
$783$		0			0
$784$	28.2107			0.0359830
$785$	201.089	+	116.099i	0.256165	+	0.147897i
$786$		0			0
$787$	−167.652	−	290.381i	−0.213026	−	0.368972i	0.739634	−	0.673009i	$-0.234999\pi$
$787$	−167.652	−	290.381i	−0.213026	−	0.368972i	−0.952660	+	0.304037i	$0.901665\pi$
$788$	−297.323	+	171.659i	−0.377313	+	0.217842i
$789$		0			0
$790$	−74.2719	+	128.643i	−0.0940150	+	0.162839i
$791$		−	59.2098i		−	0.0748543i
$792$		0			0
$793$	539.473			0.680294
$794$	−262.095	−	151.321i	−0.330095	−	0.190580i
$795$		0			0
$796$	35.0790	+	60.7586i	0.0440691	+	0.0763299i
$797$	−476.764	+	275.260i	−0.598198	+	0.345370i	−0.768332	−	0.640051i	$-0.778913\pi$
$797$	−476.764	+	275.260i	−0.598198	+	0.345370i	0.170134	+	0.985421i	$0.445580\pi$
$798$		0			0
$799$	−696.907	+	1207.08i	−0.872225	+	1.51074i
$800$			28.2843i			0.0353553i
$801$		0			0
$802$	−642.841			−0.801548
$803$	−646.278	−	373.129i	−0.804830	−	0.464669i
$804$		0			0
$805$	76.7893	+	133.003i	0.0953905	+	0.165221i
$806$	97.9796	−	56.5685i	0.121563	−	0.0701843i
$807$		0			0
$808$	−68.1053	+	117.962i	−0.0842888	+	0.145992i
$809$			560.288i			0.692569i	0.938130	+	0.346284i	$0.112557\pi$
$809$			560.288i			0.692569i	−0.938130	+	0.346284i	$0.887443\pi$
$810$		0			0
$811$	−237.842			−0.293270			−0.146635	−	0.989191i	$-0.546844\pi$
$811$	−237.842			−0.293270			−0.146635	+	0.989191i	$0.546844\pi$
$812$	347.957	+	200.893i	0.428518	+	0.247405i
$813$		0			0
$814$	−95.6840	−	165.730i	−0.117548	−	0.203599i
$815$	22.0402	−	12.7249i	0.0270432	−	0.0156134i
$816$		0			0
$817$	195.026	−	337.796i	0.238710	−	0.413458i
$818$			811.535i			0.992097i
$819$		0			0
$820$	−211.789			−0.258280
$821$	56.7087	+	32.7408i	0.0690728	+	0.0398792i	0.534139	−	0.845397i	$-0.320636\pi$
$821$	56.7087	+	32.7408i	0.0690728	+	0.0398792i	−0.465066	+	0.885276i	$0.653969\pi$
$822$		0			0
$823$	−260.756	−	451.643i	−0.316836	−	0.548776i	0.662990	−	0.748628i	$-0.269287\pi$
$823$	−260.756	−	451.643i	−0.316836	−	0.548776i	−0.979826	+	0.199852i	$0.935954\pi$
$824$	343.928	−	198.567i	0.417388	−	0.240979i
$825$		0			0
$826$	−127.473	+	220.790i	−0.154326	+	0.267301i
$827$		−	987.512i		−	1.19409i	−0.802208	−	0.597045i	$-0.796342\pi$
$827$		−	987.512i		−	1.19409i	0.802208	−	0.597045i	$-0.203658\pi$
$828$		0			0
$829$	333.631			0.402450			0.201225	−	0.979545i	$-0.435508\pi$
$829$	333.631			0.402450			0.201225	+	0.979545i	$0.435508\pi$
$830$	71.5992	+	41.3378i	0.0862641	+	0.0498046i
$831$		0			0
$832$	−40.0000	−	69.2820i	−0.0480769	−	0.0832717i
$833$	−185.597	+	107.155i	−0.222806	+	0.128637i
$834$		0			0
$835$	−282.046	+	488.518i	−0.337780	+	0.585051i
$836$		−	457.758i		−	0.547558i
$837$		0			0
$838$	−138.474			−0.165243
$839$	−112.031	−	64.6814i	−0.133530	−	0.0770934i	0.431747	−	0.901995i	$-0.357897\pi$
$839$	−112.031	−	64.6814i	−0.133530	−	0.0770934i	−0.565277	+	0.824901i	$0.691231\pi$
$840$		0			0
$841$	−60.5000	−	104.789i	−0.0719382	−	0.124601i
$842$	−878.528	+	507.219i	−1.04338	+	0.602397i
$843$		0			0
$844$	−58.1580	+	100.733i	−0.0689076	+	0.119351i
$845$			154.289i			0.182590i
$846$		0			0
$847$	−366.855			−0.433123
$848$	105.264	+	60.7739i	0.124132	+	0.0716674i
$849$		0			0
$850$	−107.434	−	186.081i	−0.126393	−	0.218919i
$851$	126.697	−	73.1486i	0.148880	−	0.0859560i
$852$		0			0
$853$	−540.210	+	935.671i	−0.633306	+	1.09692i	0.353565	+	0.935410i	$0.384969\pi$
$853$	−540.210	+	935.671i	−0.633306	+	1.09692i	−0.986871	+	0.161508i	$0.948364\pi$
$854$		−	571.193i		−	0.668845i
$855$		0			0
$856$	121.947			0.142462
$857$	608.424	+	351.274i	0.709947	+	0.409888i	0.811041	−	0.584989i	$-0.198901\pi$
$857$	608.424	+	351.274i	0.709947	+	0.409888i	−0.101094	+	0.994877i	$0.532234\pi$
$858$		0			0
$859$	140.566	+	243.467i	0.163639	+	0.283431i	0.936171	−	0.351545i	$-0.114343\pi$
$859$	140.566	+	243.467i	0.163639	+	0.283431i	−0.772532	+	0.634976i	$0.781010\pi$
$860$	−56.0053	+	32.3347i	−0.0651224	+	0.0375984i
$861$		0			0
$862$	207.237	−	358.945i	0.240414	−	0.416410i
$863$		−	419.221i		−	0.485772i	−0.970055	−	0.242886i	$-0.921906\pi$
$863$		−	419.221i		−	0.485772i	0.970055	−	0.242886i	$-0.0780941\pi$
$864$		0			0
$865$	26.4213			0.0305449
$866$	597.095	+	344.733i	0.689486	+	0.398075i
$867$		0			0
$868$	−59.8947	−	103.741i	−0.0690031	−	0.119517i
$869$	−345.185	+	199.292i	−0.397220	+	0.229335i
$870$		0			0
$871$	−552.302	+	956.616i	−0.634102	+	1.09830i
$872$			378.562i			0.434131i
$873$		0			0
$874$	349.947			0.400397
$875$	72.4909	+	41.8527i	0.0828468	+	0.0478316i
$876$		0			0
$877$	−539.710	−	934.806i	−0.615405	−	1.06591i	−0.990313	−	0.138851i	$-0.955659\pi$
$877$	−539.710	−	934.806i	−0.615405	−	1.06591i	0.374908	−	0.927062i	$-0.377674\pi$
$878$	−315.050	+	181.894i	−0.358827	+	0.207169i
$879$		0			0
$880$	−37.9473	+	65.7267i	−0.0431220	+	0.0746894i
$881$			748.212i			0.849275i	0.905363	+	0.424638i	$0.139599\pi$
$881$			748.212i			0.849275i	−0.905363	+	0.424638i	$0.860401\pi$
$882$		0			0
$883$	−875.749			−0.991788			−0.495894	−	0.868383i	$-0.665160\pi$
$883$	−875.749			−0.991788			−0.495894	+	0.868383i	$0.665160\pi$
$884$	526.318	+	303.870i	0.595382	+	0.343744i
$885$		0			0
$886$	−207.250	−	358.967i	−0.233916	−	0.405155i
$887$	−879.060	+	507.526i	−0.991048	+	0.572182i	−0.905588	−	0.424159i	$-0.860570\pi$
$887$	−879.060	+	507.526i	−0.991048	+	0.572182i	−0.0854609	+	0.996342i	$0.527236\pi$
$888$		0			0
$889$	−503.342	+	871.813i	−0.566189	+	0.980667i
$890$		−	192.184i		−	0.215937i
$891$		0			0
$892$	−198.763			−0.222828
$893$	−1071.49	−	618.625i	−1.19988	−	0.692750i
$894$		0			0
$895$	77.1843	+	133.687i	0.0862395	+	0.149371i
$896$	−73.3557	+	42.3519i	−0.0818702	+	0.0472678i
$897$		0			0
$898$	−414.092	+	717.228i	−0.461127	+	0.798695i
$899$		−	214.663i		−	0.238779i
$900$		0			0
$901$	−923.368			−1.02483
$902$	−492.154	−	284.145i	−0.545625	−	0.315017i
$903$		0			0
$904$	11.1843	+	19.3718i	0.0123721	+	0.0214290i
$905$	367.321	−	212.073i	0.405880	−	0.234335i
$906$		0			0
$907$	−752.348	+	1303.11i	−0.829491	+	1.43672i	0.0689469	+	0.997620i	$0.478036\pi$
$907$	−752.348	+	1303.11i	−0.829491	+	1.43672i	−0.898438	+	0.439100i	$0.855297\pi$
$908$			433.903i			0.477867i
$909$		0			0
$910$	−236.754			−0.260170
$911$	−867.925	−	501.097i	−0.952717	−	0.550051i	−0.0587928	−	0.998270i	$-0.518725\pi$
$911$	−867.925	−	501.097i	−0.952717	−	0.550051i	−0.893924	+	0.448219i	$0.852058\pi$
$912$		0			0
$913$	110.921	+	192.121i	0.121491	+	0.210428i
$914$	995.781	−	574.915i	1.08948	−	0.629009i
$915$		0			0
$916$	325.684	−	564.101i	0.355550	−	0.615831i
$917$			1650.05i			1.79940i
$918$		0			0
$919$	−780.289			−0.849063			−0.424532	−	0.905413i	$-0.639561\pi$
$919$	−780.289			−0.849063			−0.424532	+	0.905413i	$0.639561\pi$
$920$	−50.2468	−	29.0100i	−0.0546161	−	0.0315326i
$921$		0			0
$922$	391.789	+	678.599i	0.424934	+	0.736008i
$923$	−135.044	+	77.9680i	−0.146310	+	0.0844723i
$924$		0			0
$925$	39.8683	−	69.0540i	0.0431009	−	0.0746529i
$926$			636.005i			0.686830i
$927$		0			0
$928$	−151.789			−0.163566
$929$	947.291	+	546.919i	1.01969	+	0.588718i	0.914014	−	0.405683i	$-0.132966\pi$
$929$	947.291	+	546.919i	1.01969	+	0.588718i	0.105675	+	0.994401i	$0.466300\pi$
$930$		0			0
$931$	−95.1182	−	164.749i	−0.102168	−	0.176960i
$932$	89.5676	−	51.7119i	0.0961026	−	0.0554849i
$933$		0			0
$934$	−21.7238	+	37.6268i	−0.0232589	+	0.0402856i
$935$		−	576.552i		−	0.616633i
$936$		0			0
$937$	−407.947			−0.435376			−0.217688	−	0.976018i	$-0.569852\pi$
$937$	−407.947			−0.435376			−0.217688	+	0.976018i	$0.569852\pi$
$938$	1012.86	+	584.777i	1.07981	+	0.623429i
$939$		0			0
$940$	102.566	+	177.649i	0.109113	+	0.188989i
$941$	−581.110	+	335.504i	−0.617545	+	0.356540i	−0.775912	−	0.630841i	$-0.782710\pi$
$941$	−581.110	+	335.504i	−0.617545	+	0.356540i	0.158368	+	0.987380i	$0.449377\pi$
$942$		0			0
$943$	217.223	−	376.242i	0.230354	−	0.398984i
$944$		−	96.3155i		−	0.102029i
$945$		0			0
$946$	−173.526			−0.183431
$947$	−1392.68	−	804.063i	−1.47062	−	0.849064i	−0.471166	−	0.882045i	$-0.656167\pi$
$947$	−1392.68	−	804.063i	−1.47062	−	0.849064i	−0.999456	+	0.0329808i	$0.989500\pi$
$948$		0			0
$949$	439.737	+	761.646i	0.463368	+	0.802578i
$950$	165.179	−	95.3663i	0.173873	−	0.100386i
$951$		0			0
$952$	321.737	−	557.264i	0.337959	−	0.585362i
$953$			695.440i			0.729737i	0.931059	+	0.364869i	$0.118886\pi$
$953$			695.440i			0.729737i	−0.931059	+	0.364869i	$0.881114\pi$
$954$		0			0
$955$	243.079			0.254533
$956$	−710.223	−	410.047i	−0.742911	−	0.428920i
$957$		0			0
$958$	−519.895	−	900.484i	−0.542688	−	0.939962i
$959$	−619.301	+	357.553i	−0.645778	+	0.372840i
$960$		0			0
$961$	448.500	−	776.825i	0.466701	−	0.808350i
$962$			225.529i			0.234438i
$963$		0			0
$964$	−891.052			−0.924328
$965$	−325.229	−	187.771i	−0.337024	−	0.194581i
$966$		0			0
$967$	515.033	+	892.063i	0.532609	+	0.922506i	0.999275	+	0.0380724i	$0.0121218\pi$
$967$	515.033	+	892.063i	0.532609	+	0.922506i	−0.466666	+	0.884434i	$0.654545\pi$
$968$	120.025	−	69.2965i	0.123993	−	0.0715873i
$969$		0			0
$970$	57.0043	−	98.7343i	0.0587673	−	0.101788i
$971$		−	1165.24i		−	1.20004i	−0.799986	−	0.600019i	$-0.795160\pi$
$971$		−	1165.24i		−	1.20004i	0.799986	−	0.600019i	$-0.204840\pi$
$972$		0			0
$973$	575.106			0.591065
$974$	−113.434	−	65.4912i	−0.116462	−	0.0672394i
$975$		0			0
$976$	107.895	+	186.879i	0.110548	+	0.191474i
$977$	−629.115	+	363.220i	−0.643926	+	0.371771i	−0.786125	−	0.618067i	$-0.787916\pi$
$977$	−629.115	+	363.220i	−0.643926	+	0.371771i	0.142200	+	0.989838i	$0.454583\pi$
$978$		0			0
$979$	257.842	−	446.595i	0.263373	−	0.456175i
$980$			31.5405i			0.0321842i
$981$		0			0
$982$	1270.42			1.29371
$983$	886.989	+	512.103i	0.902329	+	0.520960i	0.877955	−	0.478743i	$-0.158908\pi$
$983$	886.989	+	512.103i	0.902329	+	0.520960i	0.0243736	+	0.999703i	$0.492241\pi$
$984$		0			0
$985$	−191.921	−	332.417i	−0.194844	−	0.337479i
$986$	998.618	−	576.552i	1.01280	−	0.584739i
$987$		0			0
$988$	−269.737	+	467.198i	−0.273013	+	0.472872i
$989$		−	132.657i		−	0.134133i
$990$		0			0
$991$	−1797.89			−1.81422			−0.907111	−	0.420892i	$-0.861717\pi$
$991$	−1797.89			−1.81422			−0.907111	+	0.420892i	$0.861717\pi$
$992$	39.1918	+	22.6274i	0.0395079	+	0.0228099i
$993$		0			0
$994$	82.5523	+	142.985i	0.0830506	+	0.143848i
$995$	−67.9302	+	39.2195i	−0.0682716	+	0.0394166i
$996$		0			0
$997$	−450.684	+	780.608i	−0.452040	+	0.782956i	−0.998513	−	0.0545206i	$-0.982637\pi$
$997$	−450.684	+	780.608i	−0.452040	+	0.782956i	0.546473	+	0.837477i	$0.315970\pi$
$998$		−	193.636i		−	0.194024i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.3.h.a.431.3		8
3.2	odd	2	inner	810.3.h.a.431.2		8
9.2	odd	6		30.3.d.a.11.4	yes	4
9.4	even	3	inner	810.3.h.a.701.2		8
9.5	odd	6	inner	810.3.h.a.701.3		8
9.7	even	3		30.3.d.a.11.2	✓	4
36.7	odd	6		240.3.l.c.161.1		4
36.11	even	6		240.3.l.c.161.2		4
45.2	even	12		150.3.b.b.149.1		8
45.7	odd	12		150.3.b.b.149.7		8
45.29	odd	6		150.3.d.c.101.1		4
45.34	even	6		150.3.d.c.101.3		4
45.38	even	12		150.3.b.b.149.8		8
45.43	odd	12		150.3.b.b.149.2		8
72.11	even	6		960.3.l.f.641.3		4
72.29	odd	6		960.3.l.e.641.2		4
72.43	odd	6		960.3.l.f.641.4		4
72.61	even	6		960.3.l.e.641.1		4
180.7	even	12		1200.3.c.k.449.4		8
180.43	even	12		1200.3.c.k.449.5		8
180.47	odd	12		1200.3.c.k.449.6		8
180.79	odd	6		1200.3.l.u.401.4		4
180.83	odd	12		1200.3.c.k.449.3		8
180.119	even	6		1200.3.l.u.401.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.d.a.11.2	✓	4	9.7	even	3
30.3.d.a.11.4	yes	4	9.2	odd	6
150.3.b.b.149.1		8	45.2	even	12
150.3.b.b.149.2		8	45.43	odd	12
150.3.b.b.149.7		8	45.7	odd	12
150.3.b.b.149.8		8	45.38	even	12
150.3.d.c.101.1		4	45.29	odd	6
150.3.d.c.101.3		4	45.34	even	6
240.3.l.c.161.1		4	36.7	odd	6
240.3.l.c.161.2		4	36.11	even	6
810.3.h.a.431.2		8	3.2	odd	2	inner
810.3.h.a.431.3		8	1.1	even	1	trivial
810.3.h.a.701.2		8	9.4	even	3	inner
810.3.h.a.701.3		8	9.5	odd	6	inner
960.3.l.e.641.1		4	72.61	even	6
960.3.l.e.641.2		4	72.29	odd	6
960.3.l.f.641.3		4	72.11	even	6
960.3.l.f.641.4		4	72.43	odd	6
1200.3.c.k.449.3		8	180.83	odd	12
1200.3.c.k.449.4		8	180.7	even	12
1200.3.c.k.449.5		8	180.43	even	12
1200.3.c.k.449.6		8	180.47	odd	12
1200.3.l.u.401.3		4	180.119	even	6
1200.3.l.u.401.4		4	180.79	odd	6

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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	810.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(3.74342 - 6.48379i) q^{7} +2.82843i q^{8} +O(q^{10})\)	\(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(3.74342 - 6.48379i) q^{7} +2.82843i q^{8} -3.16228 q^{10} +(-7.34847 - 4.24264i) q^{11} +(5.00000 + 8.66025i) q^{13} +(9.16946 - 5.29399i) q^{14} +(-2.00000 + 3.46410i) q^{16} -30.3870i q^{17} +26.9737 q^{19} +(-3.87298 - 2.23607i) q^{20} +(-6.00000 - 10.3923i) q^{22} +(7.94472 - 4.58688i) q^{23} +(2.50000 - 4.33013i) q^{25} +14.1421i q^{26} +14.9737 q^{28} +(23.2379 + 13.4164i) q^{29} +(-4.00000 - 6.92820i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(21.4868 - 37.2163i) q^{34} +16.7411i q^{35} +15.9473 q^{37} +(33.0359 + 19.0733i) q^{38} +(-3.16228 - 5.47723i) q^{40} +(41.0128 - 23.6788i) q^{41} +(7.23025 - 12.5232i) q^{43} -16.9706i q^{44} +12.9737 q^{46} +(-39.7236 - 22.9344i) q^{47} +(-3.52633 - 6.10779i) q^{49} +(6.12372 - 3.53553i) q^{50} +(-10.0000 + 17.3205i) q^{52} -30.3870i q^{53} +18.9737 q^{55} +(18.3389 + 10.5880i) q^{56} +(18.9737 + 32.8634i) q^{58} +(-20.8529 + 12.0394i) q^{59} +(26.9737 - 46.7198i) q^{61} -11.3137i q^{62} -8.00000 q^{64} +(-19.3649 - 11.1803i) q^{65} +(55.2302 + 95.6616i) q^{67} +(52.6318 - 30.3870i) q^{68} +(-11.8377 + 20.5035i) q^{70} +15.5936i q^{71} +87.9473 q^{73} +(19.5314 + 11.2765i) q^{74} +(26.9737 + 46.7198i) q^{76} +(-55.0168 + 31.7639i) q^{77} +(23.4868 - 40.6804i) q^{79} -8.94427i q^{80} +66.9737 q^{82} +(-22.6417 - 13.0722i) q^{83} +(33.9737 + 58.8441i) q^{85} +(17.7104 - 10.2251i) q^{86} +(12.0000 - 20.7846i) q^{88} +60.7739i q^{89} +74.8683 q^{91} +(15.8894 + 9.17377i) q^{92} +(-32.4342 - 56.1776i) q^{94} +(-52.2343 + 30.1575i) q^{95} +(-18.0263 + 31.2225i) q^{97} -9.97398i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} - 8 q^{7}+O(q^{10}) \) 8 * q + 8 * q^4 - 8 * q^7	\( 8 q + 8 q^{4} - 8 q^{7} + 40 q^{13} - 16 q^{16} + 64 q^{19} - 48 q^{22} + 20 q^{25} - 32 q^{28} - 32 q^{31} + 96 q^{34} - 176 q^{37} - 56 q^{43} - 48 q^{46} - 180 q^{49} - 80 q^{52} + 64 q^{61} - 64 q^{64} + 328 q^{67} - 120 q^{70} + 400 q^{73} + 64 q^{76} + 112 q^{79} + 384 q^{82} + 120 q^{85} + 96 q^{88} - 160 q^{91} + 120 q^{94} - 296 q^{97}+O(q^{100}) \) 8 * q + 8 * q^4 - 8 * q^7 + 40 * q^13 - 16 * q^16 + 64 * q^19 - 48 * q^22 + 20 * q^25 - 32 * q^28 - 32 * q^31 + 96 * q^34 - 176 * q^37 - 56 * q^43 - 48 * q^46 - 180 * q^49 - 80 * q^52 + 64 * q^61 - 64 * q^64 + 328 * q^67 - 120 * q^70 + 400 * q^73 + 64 * q^76 + 112 * q^79 + 384 * q^82 + 120 * q^85 + 96 * q^88 - 160 * q^91 + 120 * q^94 - 296 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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