LMFDB - Embedded newform 324.3.d.h.163.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(163,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(2))

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("324.163");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.389136420864.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 24x^{4} + 80x^{2} + 256 $ x^8 + 5x^6 + 24x^4 + 80*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.3
Root			$0.656712 - 1.88911i$ of defining polynomial
Character	$\chi$	$=$	324.163
Dual form			324.3.d.h.163.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.656712 - 1.88911i) q^{2} +(-3.13746 + 2.48120i) q^{4} +0.894797 q^{5} +1.58166i q^{7} +(6.74766 + 4.29756i) q^{8} +O(q^{10})$	\(q+(-0.656712 - 1.88911i) q^{2} +(-3.13746 + 2.48120i) q^{4} +0.894797 q^{5} +1.58166i q^{7} +(6.74766 + 4.29756i) q^{8} +(-0.587624 - 1.69037i) q^{10} -12.3733i q^{11} -11.5498 q^{13} +(2.98793 - 1.03870i) q^{14} +(3.68729 - 15.5693i) q^{16} +26.0958 q^{17} -21.4313i q^{19} +(-2.80739 + 2.22017i) q^{20} +(-23.3746 + 8.12572i) q^{22} -27.4862i q^{23} -24.1993 q^{25} +(7.58492 + 21.8189i) q^{26} +(-3.92442 - 4.96240i) q^{28} -9.49751 q^{29} -49.1892i q^{31} +(-31.8336 + 3.25887i) q^{32} +(-17.1375 - 49.2979i) q^{34} +1.41527i q^{35} -20.4502 q^{37} +(-40.4860 + 14.0742i) q^{38} +(6.03779 + 3.84545i) q^{40} -5.25370 q^{41} +80.1104i q^{43} +(30.7007 + 38.8209i) q^{44} +(-51.9244 + 18.0505i) q^{46} -60.4515i q^{47} +46.4983 q^{49} +(15.8920 + 45.7152i) q^{50} +(36.2371 - 28.6574i) q^{52} +12.4121 q^{53} -11.0716i q^{55} +(-6.79730 + 10.6725i) q^{56} +(6.23713 + 17.9418i) q^{58} -30.2257i q^{59} -56.8488 q^{61} +(-92.9237 + 32.3031i) q^{62} +(27.0619 + 57.9970i) q^{64} -10.3348 q^{65} -70.6204i q^{67} +(-81.8746 + 64.7490i) q^{68} +(2.67359 - 0.929423i) q^{70} -71.5006i q^{71} +31.9003 q^{73} +(13.4299 + 38.6326i) q^{74} +(53.1752 + 67.2397i) q^{76} +19.5705 q^{77} +96.7967i q^{79} +(3.29938 - 13.9314i) q^{80} +(3.45017 + 9.92480i) q^{82} +24.7467i q^{83} +23.3505 q^{85} +(151.337 - 52.6095i) q^{86} +(53.1752 - 83.4911i) q^{88} -68.1254 q^{89} -18.2679i q^{91} +(68.1988 + 86.2368i) q^{92} +(-114.199 + 39.6992i) q^{94} -19.1766i q^{95} +100.900 q^{97} +(-30.5360 - 87.8404i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 10 q^{4}+O(q^{10}) $ 8 * q - 10 * q^4	$ 8 q - 10 q^{4} - 50 q^{10} - 32 q^{13} - 46 q^{16} - 36 q^{22} + 48 q^{25} + 180 q^{28} - 122 q^{34} - 224 q^{37} + 154 q^{40} - 204 q^{46} - 232 q^{49} + 154 q^{52} - 86 q^{58} - 32 q^{61} - 10 q^{64} - 492 q^{70} + 376 q^{73} + 516 q^{76} + 88 q^{82} + 368 q^{85} + 516 q^{88} - 672 q^{94} + 928 q^{97}+O(q^{100}) $ 8 * q - 10 * q^4 - 50 * q^10 - 32 * q^13 - 46 * q^16 - 36 * q^22 + 48 * q^25 + 180 * q^28 - 122 * q^34 - 224 * q^37 + 154 * q^40 - 204 * q^46 - 232 * q^49 + 154 * q^52 - 86 * q^58 - 32 * q^61 - 10 * q^64 - 492 * q^70 + 376 * q^73 + 516 * q^76 + 88 * q^82 + 368 * q^85 + 516 * q^88 - 672 * q^94 + 928 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$1$

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 $

$2$	−0.656712	−	1.88911i	−0.328356	−	0.944554i
$2$	−0.656712	−	1.88911i	−0.328356	−	0.944554i
$3$		0			0
$3$		0			0
$4$	−3.13746	+	2.48120i	−0.784365	+	0.620300i
$5$	0.894797			0.178959			0.0894797	−	0.995989i	$-0.471480\pi$
$5$	0.894797			0.178959			0.0894797	+	0.995989i	$0.471480\pi$
$6$		0			0
$7$			1.58166i			0.225952i	0.993598	+	0.112976i	$0.0360383\pi$
$7$			1.58166i			0.225952i	−0.993598	+	0.112976i	$0.963962\pi$
$8$	6.74766	+	4.29756i	0.843458	+	0.537196i
$9$		0			0
$10$	−0.587624	−	1.69037i	−0.0587624	−	0.169037i
$11$		−	12.3733i		−	1.12485i	−0.826848	−	0.562425i	$-0.809869\pi$
$11$		−	12.3733i		−	1.12485i	0.826848	−	0.562425i	$-0.190131\pi$
$12$		0			0
$13$	−11.5498			−0.888449			−0.444224	−	0.895916i	$-0.646521\pi$
$13$	−11.5498			−0.888449			−0.444224	+	0.895916i	$0.646521\pi$
$14$	2.98793	−	1.03870i	0.213424	−	0.0741926i
$15$		0			0
$16$	3.68729	−	15.5693i	0.230456	−	0.973083i
$17$	26.0958			1.53505			0.767525	−	0.641019i	$-0.221488\pi$
$17$	26.0958			1.53505			0.767525	+	0.641019i	$0.221488\pi$
$18$		0			0
$19$		−	21.4313i		−	1.12796i	−0.825788	−	0.563981i	$-0.809269\pi$
$19$		−	21.4313i		−	1.12796i	0.825788	−	0.563981i	$-0.190731\pi$
$20$	−2.80739	+	2.22017i	−0.140369	+	0.111009i
$21$		0			0
$22$	−23.3746	+	8.12572i	−1.06248	+	0.369351i
$23$		−	27.4862i		−	1.19505i	−0.801849	−	0.597526i	$-0.796150\pi$
$23$		−	27.4862i		−	1.19505i	0.801849	−	0.597526i	$-0.203850\pi$
$24$		0			0
$25$	−24.1993			−0.967974
$26$	7.58492	+	21.8189i	0.291728	+	0.839188i
$27$		0			0
$28$	−3.92442	−	4.96240i	−0.140158	−	0.177229i
$29$	−9.49751			−0.327500			−0.163750	−	0.986502i	$-0.552359\pi$
$29$	−9.49751			−0.327500			−0.163750	+	0.986502i	$0.552359\pi$
$30$		0			0
$31$		−	49.1892i		−	1.58675i	−0.608735	−	0.793374i	$-0.708323\pi$
$31$		−	49.1892i		−	1.58675i	0.608735	−	0.793374i	$-0.291677\pi$
$32$	−31.8336	+	3.25887i	−0.994801	+	0.101840i
$33$		0			0
$34$	−17.1375	−	49.2979i	−0.504043	−	1.44994i
$35$			1.41527i			0.0404362i
$36$		0			0
$37$	−20.4502			−0.552707			−0.276354	−	0.961056i	$-0.589126\pi$
$37$	−20.4502			−0.552707			−0.276354	+	0.961056i	$0.589126\pi$
$38$	−40.4860	+	14.0742i	−1.06542	+	0.370373i
$39$		0			0
$40$	6.03779	+	3.84545i	0.150945	+	0.0961362i
$41$	−5.25370			−0.128139			−0.0640695	−	0.997945i	$-0.520408\pi$
$41$	−5.25370			−0.128139			−0.0640695	+	0.997945i	$0.520408\pi$
$42$		0			0
$43$			80.1104i			1.86303i	0.363699	+	0.931516i	$0.381514\pi$
$43$			80.1104i			1.86303i	−0.363699	+	0.931516i	$0.618486\pi$
$44$	30.7007	+	38.8209i	0.697744	+	0.882292i
$45$		0			0
$46$	−51.9244	+	18.0505i	−1.12879	+	0.392403i
$47$		−	60.4515i		−	1.28620i	−0.765782	−	0.643101i	$-0.777648\pi$
$47$		−	60.4515i		−	1.28620i	0.765782	−	0.643101i	$-0.222352\pi$
$48$		0			0
$49$	46.4983			0.948946
$50$	15.8920	+	45.7152i	0.317840	+	0.914303i
$51$		0			0
$52$	36.2371	−	28.6574i	0.696868	−	0.551105i
$53$	12.4121			0.234190			0.117095	−	0.993121i	$-0.462642\pi$
$53$	12.4121			0.234190			0.117095	+	0.993121i	$0.462642\pi$
$54$		0			0
$55$		−	11.0716i		−	0.201302i
$56$	−6.79730	+	10.6725i	−0.121380	+	0.190581i
$57$		0			0
$58$	6.23713	+	17.9418i	0.107537	+	0.309342i
$59$		−	30.2257i		−	0.512300i	−0.966637	−	0.256150i	$-0.917546\pi$
$59$		−	30.2257i		−	0.512300i	0.966637	−	0.256150i	$-0.0824542\pi$
$60$		0			0
$61$	−56.8488			−0.931948			−0.465974	−	0.884798i	$-0.654296\pi$
$61$	−56.8488			−0.931948			−0.465974	+	0.884798i	$0.654296\pi$
$62$	−92.9237	+	32.3031i	−1.49877	+	0.521018i
$63$		0			0
$64$	27.0619	+	57.9970i	0.422842	+	0.906203i
$65$	−10.3348			−0.158996
$66$		0			0
$67$		−	70.6204i		−	1.05404i	−0.849854	−	0.527018i	$-0.823310\pi$
$67$		−	70.6204i		−	1.05404i	0.849854	−	0.527018i	$-0.176690\pi$
$68$	−81.8746	+	64.7490i	−1.20404	+	0.952192i
$69$		0			0
$70$	2.67359	−	0.929423i	0.0381942	−	0.0132775i
$71$		−	71.5006i		−	1.00705i	−0.863981	−	0.503525i	$-0.832036\pi$
$71$		−	71.5006i		−	1.00705i	0.863981	−	0.503525i	$-0.167964\pi$
$72$		0			0
$73$	31.9003			0.436991			0.218495	−	0.975838i	$-0.429885\pi$
$73$	31.9003			0.436991			0.218495	+	0.975838i	$0.429885\pi$
$74$	13.4299	+	38.6326i	0.181485	+	0.522062i
$75$		0			0
$76$	53.1752	+	67.2397i	0.699674	+	0.884733i
$77$	19.5705			0.254162
$78$		0			0
$79$			96.7967i			1.22527i	0.790364	+	0.612637i	$0.209891\pi$
$79$			96.7967i			1.22527i	−0.790364	+	0.612637i	$0.790109\pi$
$80$	3.29938	−	13.9314i	0.0412422	−	0.174142i
$81$		0			0
$82$	3.45017	+	9.92480i	0.0420752	+	0.121034i
$83$			24.7467i			0.298153i	0.988826	+	0.149076i	$0.0476301\pi$
$83$			24.7467i			0.298153i	−0.988826	+	0.149076i	$0.952370\pi$
$84$		0			0
$85$	23.3505			0.274712
$86$	151.337	−	52.6095i	1.75974	−	0.611738i
$87$		0			0
$88$	53.1752	−	83.4911i	0.604264	−	0.948763i
$89$	−68.1254			−0.765454			−0.382727	−	0.923861i	$-0.625015\pi$
$89$	−68.1254			−0.765454			−0.382727	+	0.923861i	$0.625015\pi$
$90$		0			0
$91$		−	18.2679i		−	0.200747i
$92$	68.1988	+	86.2368i	0.741291	+	0.937357i
$93$		0			0
$94$	−114.199	+	39.6992i	−1.21489	+	0.422332i
$95$		−	19.1766i		−	0.201859i
$96$		0			0
$97$	100.900			1.04021			0.520105	−	0.854102i	$-0.325893\pi$
$97$	100.900			1.04021			0.520105	+	0.854102i	$0.325893\pi$
$98$	−30.5360	−	87.8404i	−0.311592	−	0.896331i
$99$		0			0
$100$	75.9244	−	60.0434i	0.759244	−	0.600434i
$101$	198.259			1.96296			0.981482	−	0.191553i	$-0.0613525\pi$
$101$	198.259			1.96296			0.981482	+	0.191553i	$0.0613525\pi$
$102$		0			0
$103$			69.9084i			0.678723i	0.940656	+	0.339361i	$0.110211\pi$
$103$			69.9084i			0.678723i	−0.940656	+	0.339361i	$0.889789\pi$
$104$	−77.9344	−	49.6362i	−0.749369	−	0.477271i
$105$		0			0
$106$	−8.15116	−	23.4478i	−0.0768977	−	0.221205i
$107$		−	153.959i		−	1.43887i	−0.694559	−	0.719435i	$-0.744401\pi$
$107$		−	153.959i		−	1.43887i	0.694559	−	0.719435i	$-0.255599\pi$
$108$		0			0
$109$	103.447			0.949054			0.474527	−	0.880241i	$-0.342619\pi$
$109$	103.447			0.949054			0.474527	+	0.880241i	$0.342619\pi$
$110$	−20.9155	+	7.27088i	−0.190141	+	0.0660989i
$111$		0			0
$112$	24.6254	+	5.83205i	0.219870	+	0.0520719i
$113$	123.091			1.08930			0.544649	−	0.838664i	$-0.316663\pi$
$113$	123.091			1.08930			0.544649	+	0.838664i	$0.316663\pi$
$114$		0			0
$115$		−	24.5946i		−	0.213866i
$116$	29.7980	−	23.5652i	0.256880	−	0.203148i
$117$		0			0
$118$	−57.0997	+	19.8496i	−0.483895	+	0.168217i
$119$			41.2748i			0.346847i
$120$		0			0
$121$	−32.0997			−0.265287
$122$	37.3333	+	107.394i	0.306011	+	0.880275i
$123$		0			0
$124$	122.048	+	154.329i	0.984260	+	1.24459i
$125$	−44.0234			−0.352187
$126$		0			0
$127$			4.74499i			0.0373621i	0.999825	+	0.0186811i	$0.00594671\pi$
$127$			4.74499i			0.0373621i	−0.999825	+	0.0186811i	$0.994053\pi$
$128$	91.7908	−	89.2102i	0.717115	−	0.696954i
$129$		0			0
$130$	6.78696	+	19.5235i	0.0522074	+	0.150181i
$131$			28.8105i			0.219927i	0.993936	+	0.109964i	$0.0350734\pi$
$131$			28.8105i			0.219927i	−0.993936	+	0.109964i	$0.964927\pi$
$132$		0			0
$133$	33.8970			0.254865
$134$	−133.410	+	46.3773i	−0.995594	+	0.346099i
$135$		0			0
$136$	176.086	+	112.149i	1.29475	+	0.824622i
$137$	−137.407			−1.00297			−0.501487	−	0.865165i	$-0.667214\pi$
$137$	−137.407			−1.00297			−0.501487	+	0.865165i	$0.667214\pi$
$138$		0			0
$139$			141.241i			1.01612i	0.861321	+	0.508061i	$0.169637\pi$
$139$			141.241i			1.01612i	−0.861321	+	0.508061i	$0.830363\pi$
$140$	−3.51156	−	4.44034i	−0.0250826	−	0.0317167i
$141$		0			0
$142$	−135.072	+	46.9553i	−0.951213	+	0.330671i
$143$			142.910i			0.999371i
$144$		0			0
$145$	−8.49834			−0.0586093
$146$	−20.9493	−	60.2632i	−0.143489	−	0.412761i
$147$		0			0
$148$	64.1615	−	50.7410i	0.433524	−	0.342844i
$149$	−139.919			−0.939055			−0.469528	−	0.882918i	$-0.655576\pi$
$149$	−139.919			−0.939055			−0.469528	+	0.882918i	$0.655576\pi$
$150$		0			0
$151$		−	74.4958i		−	0.493349i	−0.969098	−	0.246675i	$-0.920662\pi$
$151$		−	74.4958i		−	0.493349i	0.969098	−	0.246675i	$-0.0793379\pi$
$152$	92.1022	−	144.611i	0.605936	−	0.951388i
$153$		0			0
$154$	−12.8522	−	36.9707i	−0.0834555	−	0.240069i
$155$		−	44.0143i		−	0.283963i
$156$		0			0
$157$	−53.5498			−0.341082			−0.170541	−	0.985351i	$-0.554551\pi$
$157$	−53.5498			−0.341082			−0.170541	+	0.985351i	$0.554551\pi$
$158$	182.859	−	63.5675i	1.15734	−	0.402326i
$159$		0			0
$160$	−28.4846	+	2.91603i	−0.178029	+	0.0182252i
$161$	43.4739			0.270024
$162$		0			0
$163$			204.823i			1.25658i	0.777979	+	0.628290i	$0.216245\pi$
$163$			204.823i			1.25658i	−0.777979	+	0.628290i	$0.783755\pi$
$164$	16.4833	−	13.0355i	0.100508	−	0.0794846i
$165$		0			0
$166$	46.7492	−	16.2514i	0.281622	−	0.0979003i
$167$			175.784i			1.05260i	0.850299	+	0.526300i	$0.176421\pi$
$167$			175.784i			1.05260i	−0.850299	+	0.526300i	$0.823579\pi$
$168$		0			0
$169$	−35.6013			−0.210659
$170$	−15.3346	−	44.1116i	−0.0902032	−	0.259480i
$171$		0			0
$172$	−198.770	−	251.343i	−1.15564	−	1.46130i
$173$	−30.9726			−0.179033			−0.0895163	−	0.995985i	$-0.528532\pi$
$173$	−30.9726			−0.179033			−0.0895163	+	0.995985i	$0.528532\pi$
$174$		0			0
$175$		−	38.2752i		−	0.218715i
$176$	−192.645	−	45.6241i	−1.09457	−	0.259228i
$177$		0			0
$178$	44.7388	+	128.696i	0.251341	+	0.723013i
$179$			250.115i			1.39729i	0.715467	+	0.698646i	$0.246214\pi$
$179$			250.115i			1.39729i	−0.715467	+	0.698646i	$0.753786\pi$
$180$		0			0
$181$	−263.196			−1.45412			−0.727061	−	0.686573i	$-0.759114\pi$
$181$	−263.196			−1.45412			−0.727061	+	0.686573i	$0.759114\pi$
$182$	−34.5101	+	11.9968i	−0.189616	+	0.0659163i
$183$		0			0
$184$	118.124	−	185.468i	0.641977	−	1.00798i
$185$	−18.2988			−0.0989122
$186$		0			0
$187$		−	322.893i		−	1.72670i
$188$	149.992	+	189.664i	0.797831	+	1.00885i
$189$		0			0
$190$	−36.2267	+	12.5935i	−0.190667	+	0.0662817i
$191$			310.476i			1.62553i	0.582593	+	0.812764i	$0.302038\pi$
$191$			310.476i			1.62553i	−0.582593	+	0.812764i	$0.697962\pi$
$192$		0			0
$193$	176.100			0.912434			0.456217	−	0.889869i	$-0.349204\pi$
$193$	176.100			0.912434			0.456217	+	0.889869i	$0.349204\pi$
$194$	−66.2625	−	190.612i	−0.341559	−	0.982534i
$195$		0			0
$196$	−145.887	+	115.372i	−0.744320	+	0.588631i
$197$	−117.920			−0.598581			−0.299290	−	0.954162i	$-0.596750\pi$
$197$	−117.920			−0.598581			−0.299290	+	0.954162i	$0.596750\pi$
$198$		0			0
$199$		−	100.118i		−	0.503104i	−0.967844	−	0.251552i	$-0.919059\pi$
$199$		−	100.118i		−	0.503104i	0.967844	−	0.251552i	$-0.0809409\pi$
$200$	−163.289	−	103.998i	−0.816445	−	0.519991i
$201$		0			0
$202$	−130.199	−	374.533i	−0.644551	−	1.85413i
$203$		−	15.0218i		−	0.0739993i
$204$		0			0
$205$	−4.70099			−0.0229317
$206$	132.065	−	45.9097i	0.641090	−	0.222863i
$207$		0			0
$208$	−42.5876	+	179.823i	−0.204748	+	0.864534i
$209$	−265.176			−1.26879
$210$		0			0
$211$		−	8.77796i		−	0.0416017i	−0.999784	−	0.0208009i	$-0.993378\pi$
$211$		−	8.77796i		−	0.0416017i	0.999784	−	0.0208009i	$-0.00662160\pi$
$212$	−38.9424	+	30.7968i	−0.183690	+	0.145268i
$213$		0			0
$214$	−290.846	+	101.107i	−1.35909	+	0.472462i
$215$			71.6826i			0.333407i
$216$		0			0
$217$	77.8007			0.358528
$218$	−67.9348	−	195.422i	−0.311627	−	0.896433i
$219$		0			0
$220$	27.4709	+	34.7368i	0.124868	+	0.157895i
$221$	−301.403			−1.36381
$222$		0			0
$223$		−	350.809i		−	1.57313i	−0.617506	−	0.786566i	$-0.711857\pi$
$223$		−	350.809i		−	1.57313i	0.617506	−	0.786566i	$-0.288143\pi$
$224$	−5.15443	−	50.3500i	−0.0230108	−	0.224777i
$225$		0			0
$226$	−80.8351	−	232.532i	−0.357678	−	1.02890i
$227$		−	17.8524i		−	0.0786449i	−0.999227	−	0.0393224i	$-0.987480\pi$
$227$		−	17.8524i		−	0.0786449i	0.999227	−	0.0393224i	$-0.0125199\pi$
$228$		0			0
$229$	−415.344			−1.81373			−0.906864	−	0.421423i	$-0.861531\pi$
$229$	−415.344			−1.81373			−0.906864	+	0.421423i	$0.861531\pi$
$230$	−46.4618	+	16.1516i	−0.202008	+	0.0702242i
$231$		0			0
$232$	−64.0860	−	40.8162i	−0.276233	−	0.175932i
$233$	311.712			1.33782			0.668909	−	0.743344i	$-0.266762\pi$
$233$	311.712			1.33782			0.668909	+	0.743344i	$0.266762\pi$
$234$		0			0
$235$		−	54.0918i		−	0.230178i
$236$	74.9961	+	94.8320i	0.317780	+	0.401830i
$237$		0			0
$238$	77.9726	−	27.1057i	0.327616	−	0.113889i
$239$			44.0143i			0.184160i	0.995752	+	0.0920802i	$0.0293516\pi$
$239$			44.0143i			0.184160i	−0.995752	+	0.0920802i	$0.970648\pi$
$240$		0			0
$241$	118.801			0.492949			0.246474	−	0.969149i	$-0.420728\pi$
$241$	118.801			0.492949			0.246474	+	0.969149i	$0.420728\pi$
$242$	21.0802	+	60.6397i	0.0871084	+	0.250577i
$243$		0			0
$244$	178.361	−	141.053i	0.730987	−	0.578087i
$245$	41.6066			0.169823
$246$		0			0
$247$			247.528i			1.00214i
$248$	211.394	−	331.912i	0.852394	−	1.33835i
$249$		0			0
$250$	28.9107	+	83.1650i	0.115643	+	0.332660i
$251$			342.026i			1.36265i	0.731980	+	0.681326i	$0.238597\pi$
$251$			342.026i			1.36265i	−0.731980	+	0.681326i	$0.761403\pi$
$252$		0			0
$253$	−340.096			−1.34425
$254$	8.96379	−	3.11609i	0.0352905	−	0.0122681i
$255$		0			0
$256$	−228.808	−	114.817i	−0.893780	−	0.448505i
$257$	202.241			0.786932			0.393466	−	0.919339i	$-0.371276\pi$
$257$	202.241			0.786932			0.393466	+	0.919339i	$0.371276\pi$
$258$		0			0
$259$		−	32.3453i		−	0.124885i
$260$	32.4249	−	25.6426i	0.124711	−	0.0986254i
$261$		0			0
$262$	54.4261	−	18.9202i	0.207733	−	0.0722144i
$263$		−	346.454i		−	1.31731i	−0.752443	−	0.658657i	$-0.771125\pi$
$263$		−	346.454i		−	1.31731i	0.752443	−	0.658657i	$-0.228875\pi$
$264$		0			0
$265$	11.1063			0.0419105
$266$	−22.2606	−	64.0351i	−0.0836864	−	0.240734i
$267$		0			0
$268$	175.223	+	221.569i	0.653819	+	0.826749i
$269$	123.174			0.457896			0.228948	−	0.973439i	$-0.426471\pi$
$269$	123.174			0.457896			0.228948	+	0.973439i	$0.426471\pi$
$270$		0			0
$271$			247.528i			0.913386i	0.889624	+	0.456693i	$0.150966\pi$
$271$			247.528i			0.913386i	−0.889624	+	0.456693i	$0.849034\pi$
$272$	96.2230	−	406.295i	0.353761	−	1.49373i
$273$		0			0
$274$	90.2371	+	259.578i	0.329333	+	0.947363i
$275$			299.427i			1.08882i
$276$		0			0
$277$	−231.801			−0.836825			−0.418413	−	0.908257i	$-0.637413\pi$
$277$	−231.801			−0.836825			−0.418413	+	0.908257i	$0.637413\pi$
$278$	266.819	−	92.7546i	0.959782	−	0.333650i
$279$		0			0
$280$	−6.08220	+	9.54974i	−0.0217222	+	0.0341062i
$281$	−172.227			−0.612907			−0.306453	−	0.951886i	$-0.599142\pi$
$281$	−172.227			−0.612907			−0.306453	+	0.951886i	$0.599142\pi$
$282$		0			0
$283$			46.0258i			0.162636i	0.996688	+	0.0813178i	$0.0259129\pi$
$283$			46.0258i			0.162636i	−0.996688	+	0.0813178i	$0.974087\pi$
$284$	177.407	+	224.330i	0.624673	+	0.789894i
$285$		0			0
$286$	269.973	−	93.8508i	0.943960	−	0.328150i
$287$		−	8.30957i		−	0.0289532i
$288$		0			0
$289$	391.993			1.35638
$290$	5.58097	+	16.0543i	0.0192447	+	0.0553596i
$291$		0			0
$292$	−100.086	+	79.1511i	−0.342760	+	0.271065i
$293$	42.4640			0.144928			0.0724642	−	0.997371i	$-0.476914\pi$
$293$	42.4640			0.144928			0.0724642	+	0.997371i	$0.476914\pi$
$294$		0			0
$295$		−	27.0459i		−	0.0916810i
$296$	−137.991	−	87.8859i	−0.466185	−	0.296912i
$297$		0			0
$298$	91.8866	+	264.323i	0.308344	+	0.886988i
$299$			317.461i			1.06174i
$300$		0			0
$301$	−126.708			−0.420956
$302$	−140.731	+	48.9223i	−0.465995	+	0.161994i
$303$		0			0
$304$	−333.670	−	79.0233i	−1.09760	−	0.259945i
$305$	−50.8682			−0.166781
$306$		0			0
$307$		−	304.625i		−	0.992264i	−0.868247	−	0.496132i	$-0.834753\pi$
$307$		−	304.625i		−	0.992264i	0.868247	−	0.496132i	$-0.165247\pi$
$308$	−61.4015	+	48.5582i	−0.199355	+	0.157657i
$309$		0			0
$310$	−83.1478	+	28.9047i	−0.268219	+	0.0932411i
$311$		−	390.468i		−	1.25552i	−0.778405	−	0.627762i	$-0.783971\pi$
$311$		−	390.468i		−	1.25552i	0.778405	−	0.627762i	$-0.216029\pi$
$312$		0			0
$313$	548.389			1.75204			0.876020	−	0.482274i	$-0.160189\pi$
$313$	548.389			1.75204			0.876020	+	0.482274i	$0.160189\pi$
$314$	35.1668	+	101.161i	0.111996	+	0.322170i
$315$		0			0
$316$	−240.172	−	303.696i	−0.760038	−	0.961062i
$317$	569.865			1.79768			0.898841	−	0.438276i	$-0.144411\pi$
$317$	569.865			1.79768			0.898841	+	0.438276i	$0.144411\pi$
$318$		0			0
$319$			117.516i			0.368389i
$320$	24.2149	+	51.8956i	0.0756716	+	0.162174i
$321$		0			0
$322$	−28.5498	−	82.1269i	−0.0886641	−	0.255052i
$323$		−	559.267i		−	1.73148i
$324$		0			0
$325$	279.498			0.859995
$326$	386.932	−	134.509i	1.18691	−	0.412606i
$327$		0			0
$328$	−35.4502	−	22.5781i	−0.108080	−	0.0688357i
$329$	95.6138			0.290619
$330$		0			0
$331$			160.933i			0.486202i	0.970001	+	0.243101i	$0.0781646\pi$
$331$			160.933i			0.486202i	−0.970001	+	0.243101i	$0.921835\pi$
$332$	−61.4015	−	77.6417i	−0.184944	−	0.233861i
$333$		0			0
$334$	332.076	−	115.440i	0.994238	−	0.345628i
$335$		−	63.1910i		−	0.188630i
$336$		0			0
$337$	46.3023			0.137396			0.0686978	−	0.997638i	$-0.478116\pi$
$337$	46.3023			0.137396			0.0686978	+	0.997638i	$0.478116\pi$
$338$	23.3798	+	67.2547i	0.0691711	+	0.198979i
$339$		0			0
$340$	−73.2612	+	57.9373i	−0.215474	+	0.170404i
$341$	−608.635			−1.78485
$342$		0			0
$343$			151.046i			0.440368i
$344$	−344.280	+	540.558i	−1.00081	+	1.57139i
$345$		0			0
$346$	20.3401	+	58.5107i	0.0587864	+	0.169106i
$347$		−	207.334i		−	0.597505i	−0.954331	−	0.298753i	$-0.903429\pi$
$347$		−	207.334i		−	0.597505i	0.954331	−	0.298753i	$-0.0965705\pi$
$348$		0			0
$349$	−393.492			−1.12748			−0.563742	−	0.825951i	$-0.690639\pi$
$349$	−393.492			−1.12748			−0.563742	+	0.825951i	$0.690639\pi$
$350$	−72.3060	+	25.1358i	−0.206588	+	0.0718165i
$351$		0			0
$352$	40.3231	+	393.888i	0.114554	+	1.11900i
$353$	−259.002			−0.733717			−0.366858	−	0.930277i	$-0.619567\pi$
$353$	−259.002			−0.733717			−0.366858	+	0.930277i	$0.619567\pi$
$354$		0			0
$355$		−	63.9785i		−	0.180221i
$356$	213.741	−	169.033i	0.600395	−	0.474811i
$357$		0			0
$358$	472.495	−	164.254i	1.31982	−	0.458809i
$359$		−	219.981i		−	0.612760i	−0.951909	−	0.306380i	$-0.900882\pi$
$359$		−	219.981i		−	0.612760i	0.951909	−	0.306380i	$-0.0991177\pi$
$360$		0			0
$361$	−98.2990			−0.272296
$362$	172.844	+	497.206i	0.477470	+	1.37350i
$363$		0			0
$364$	45.3264	+	57.3149i	0.124523	+	0.157459i
$365$	28.5443			0.0782036
$366$		0			0
$367$			530.167i			1.44460i	0.691582	+	0.722298i	$0.256914\pi$
$367$			530.167i			1.44460i	−0.691582	+	0.722298i	$0.743086\pi$
$368$	−427.942	−	101.350i	−1.16289	−	0.275407i
$369$		0			0
$370$	12.0170	+	34.5683i	0.0324784	+	0.0934279i
$371$			19.6317i			0.0529157i
$372$		0			0
$373$	509.189			1.36512			0.682560	−	0.730830i	$-0.260867\pi$
$373$	509.189			1.36512			0.682560	+	0.730830i	$0.260867\pi$
$374$	−609.980	+	212.048i	−1.63096	+	0.566972i
$375$		0			0
$376$	259.794	−	407.906i	0.690942	−	1.08486i
$377$	109.695			0.290967
$378$		0			0
$379$		−	9.48997i		−	0.0250395i	−0.999922	−	0.0125198i	$-0.996015\pi$
$379$		−	9.48997i		−	0.0250395i	0.999922	−	0.0125198i	$-0.00398527\pi$
$380$	47.5811	+	60.1659i	0.125213	+	0.158331i
$381$		0			0
$382$	586.522	−	203.893i	1.53540	−	0.533752i
$383$			396.038i			1.03404i	0.855973	+	0.517021i	$0.172959\pi$
$383$			396.038i			1.03404i	−0.855973	+	0.517021i	$0.827041\pi$
$384$		0			0
$385$	17.5116			0.0454846
$386$	−115.647	−	332.671i	−0.299603	−	0.861843i
$387$		0			0
$388$	−316.571	+	250.354i	−0.815904	+	0.645242i
$389$	618.285			1.58942			0.794710	−	0.606989i	$-0.207623\pi$
$389$	618.285			1.58942			0.794710	+	0.606989i	$0.207623\pi$
$390$		0			0
$391$		−	717.276i		−	1.83447i
$392$	313.755	+	199.830i	0.800396	+	0.509769i
$393$		0			0
$394$	77.4398	+	222.764i	0.196548	+	0.565392i
$395$			86.6134i			0.219274i
$396$		0			0
$397$	−377.151			−0.950003			−0.475001	−	0.879985i	$-0.657552\pi$
$397$	−377.151			−0.950003			−0.475001	+	0.879985i	$0.657552\pi$
$398$	−189.133	+	65.7485i	−0.475209	+	0.165197i
$399$		0			0
$400$	−89.2300	+	376.767i	−0.223075	+	0.941918i
$401$	243.811			0.608007			0.304003	−	0.952671i	$-0.401677\pi$
$401$	243.811			0.608007			0.304003	+	0.952671i	$0.401677\pi$
$402$		0			0
$403$			568.127i			1.40974i
$404$	−622.031	+	491.921i	−1.53968	+	1.21763i
$405$		0			0
$406$	−28.3779	+	9.86503i	−0.0698963	+	0.0242981i
$407$			253.037i			0.621712i
$408$		0			0
$409$	512.698			1.25354			0.626770	−	0.779204i	$-0.284377\pi$
$409$	512.698			1.25354			0.626770	+	0.779204i	$0.284377\pi$
$410$	3.08720	+	8.88068i	0.00752975	+	0.0216602i
$411$		0			0
$412$	−173.457	−	219.335i	−0.421012	−	0.532366i
$413$	47.8069			0.115755
$414$		0			0
$415$			22.1433i			0.0533573i
$416$	367.673	−	37.6394i	0.883830	−	0.0904793i
$417$		0			0
$418$	174.145	+	500.947i	0.416614	+	1.19844i
$419$		−	420.330i		−	1.00317i	−0.865107	−	0.501587i	$-0.832750\pi$
$419$		−	420.330i		−	1.00317i	0.865107	−	0.501587i	$-0.167250\pi$
$420$		0			0
$421$	−110.849			−0.263299			−0.131649	−	0.991296i	$-0.542027\pi$
$421$	−110.849			−0.263299			−0.131649	+	0.991296i	$0.542027\pi$
$422$	−16.5825	+	5.76459i	−0.0392951	+	0.0136602i
$423$		0			0
$424$	83.7525	+	53.3417i	0.197529	+	0.125806i
$425$	−631.502			−1.48589
$426$		0			0
$427$		−	89.9157i		−	0.210575i
$428$	382.004	+	483.041i	0.892532	+	1.12860i
$429$		0			0
$430$	135.416	−	47.0748i	0.314921	−	0.109476i
$431$		−	621.316i		−	1.44157i	−0.693160	−	0.720784i	$-0.743782\pi$
$431$		−	621.316i		−	1.44157i	0.693160	−	0.720784i	$-0.256218\pi$
$432$		0			0
$433$	431.797			0.997223			0.498611	−	0.866826i	$-0.333844\pi$
$433$	431.797			0.997223			0.498611	+	0.866826i	$0.333844\pi$
$434$	−51.0926	−	146.974i	−0.117725	−	0.338649i
$435$		0			0
$436$	−324.560	+	256.672i	−0.744404	+	0.588698i
$437$	−589.064			−1.34797
$438$		0			0
$439$			301.462i			0.686701i	0.939207	+	0.343350i	$0.111562\pi$
$439$			301.462i			0.686701i	−0.939207	+	0.343350i	$0.888438\pi$
$440$	47.5811	−	74.7077i	0.108139	−	0.169790i
$441$		0			0
$442$	197.935	+	569.382i	0.447816	+	1.28820i
$443$		−	654.372i		−	1.47714i	−0.674178	−	0.738569i	$-0.735502\pi$
$443$		−	654.372i		−	1.47714i	0.674178	−	0.738569i	$-0.264498\pi$
$444$		0			0
$445$	−60.9584			−0.136985
$446$	−662.715	+	230.380i	−1.48591	+	0.516547i
$447$		0			0
$448$	−91.7317	+	42.8028i	−0.204758	+	0.0955419i
$449$	−384.567			−0.856497			−0.428248	−	0.903661i	$-0.640869\pi$
$449$	−384.567			−0.856497			−0.428248	+	0.903661i	$0.640869\pi$
$450$		0			0
$451$			65.0058i			0.144137i
$452$	−386.192	+	305.413i	−0.854407	+	0.675692i
$453$		0			0
$454$	−33.7251	+	11.7239i	−0.0742843	+	0.0258235i
$455$		−	16.3461i		−	0.0359255i
$456$		0			0
$457$	−28.4983			−0.0623596			−0.0311798	−	0.999514i	$-0.509926\pi$
$457$	−28.4983			−0.0623596			−0.0311798	+	0.999514i	$0.509926\pi$
$458$	272.761	+	784.629i	0.595549	+	1.71316i
$459$		0			0
$460$	61.0241	+	77.1645i	0.132661	+	0.167749i
$461$	452.008			0.980494			0.490247	−	0.871584i	$-0.336907\pi$
$461$	452.008			0.980494			0.490247	+	0.871584i	$0.336907\pi$
$462$		0			0
$463$		−	96.6390i		−	0.208724i	−0.994539	−	0.104362i	$-0.966720\pi$
$463$		−	96.6390i		−	0.208724i	0.994539	−	0.104362i	$-0.0332800\pi$
$464$	−35.0201	+	147.870i	−0.0754743	+	0.318685i
$465$		0			0
$466$	−204.705	−	588.857i	−0.439281	−	1.26364i
$467$		−	197.791i		−	0.423536i	−0.977320	−	0.211768i	$-0.932078\pi$
$467$		−	197.791i		−	0.423536i	0.977320	−	0.211768i	$-0.0679222\pi$
$468$		0			0
$469$	111.698			0.238161
$470$	−102.185	+	35.5227i	−0.217415	+	0.0755803i
$471$		0			0
$472$	129.897	−	203.953i	0.275206	−	0.432104i
$473$	991.234			2.09563
$474$		0			0
$475$			518.622i			1.09184i
$476$	−102.411	−	129.498i	−0.215149	−	0.272055i
$477$		0			0
$478$	83.1478	−	28.9047i	0.173949	−	0.0604702i
$479$		−	491.648i		−	1.02641i	−0.858267	−	0.513203i	$-0.828459\pi$
$479$		−	491.648i		−	1.02641i	0.858267	−	0.513203i	$-0.171541\pi$
$480$		0			0
$481$	236.196			0.491052
$482$	−78.0178	−	224.427i	−0.161863	−	0.465617i
$483$		0			0
$484$	100.711	−	79.6457i	0.208081	−	0.164557i
$485$	90.2853			0.186155
$486$		0			0
$487$		−	566.388i		−	1.16301i	−0.813542	−	0.581507i	$-0.802463\pi$
$487$		−	566.388i		−	1.16301i	0.813542	−	0.581507i	$-0.197537\pi$
$488$	−383.597	−	244.312i	−0.786059	−	0.500638i
$489$		0			0
$490$	−27.3236	−	78.5994i	−0.0557623	−	0.160407i
$491$			333.716i			0.679667i	0.940486	+	0.339833i	$0.110371\pi$
$491$			333.716i			0.679667i	−0.940486	+	0.339833i	$0.889629\pi$
$492$		0			0
$493$	−247.846			−0.502729
$494$	467.606	−	162.554i	0.946571	−	0.329057i
$495$		0			0
$496$	−765.842	−	181.375i	−1.54404	−	0.365675i
$497$	113.090			0.227545
$498$		0			0
$499$		−	27.7579i		−	0.0556271i	−0.999613	−	0.0278135i	$-0.991146\pi$
$499$		−	27.7579i		−	0.0556271i	0.999613	−	0.0278135i	$-0.00885447\pi$
$500$	138.122	−	109.231i	0.276243	−	0.218462i
$501$		0			0
$502$	646.124	−	224.612i	1.28710	−	0.447435i
$503$			494.752i			0.983602i	0.870708	+	0.491801i	$0.163661\pi$
$503$			494.752i			0.983602i	−0.870708	+	0.491801i	$0.836339\pi$
$504$		0			0
$505$	177.402			0.351291
$506$	223.345	+	642.479i	0.441394	+	1.26972i
$507$		0			0
$508$	−11.7733	−	14.8872i	−0.0231757	−	0.0293055i
$509$	−565.748			−1.11149			−0.555744	−	0.831353i	$-0.687567\pi$
$509$	−565.748			−1.11149			−0.555744	+	0.831353i	$0.687567\pi$
$510$		0			0
$511$			50.4556i			0.0987388i
$512$	−66.6415	+	507.644i	−0.130159	+	0.991493i
$513$		0			0
$514$	−132.814	−	382.056i	−0.258394	−	0.743299i
$515$			62.5539i			0.121464i
$516$		0			0
$517$	−747.987			−1.44678
$518$	−61.1037	+	21.2415i	−0.117961	+	0.0410068i
$519$		0			0
$520$	−69.7355	−	44.4143i	−0.134107	−	0.0854121i
$521$	896.794			1.72129			0.860647	−	0.509203i	$-0.170060\pi$
$521$	896.794			1.72129			0.860647	+	0.509203i	$0.170060\pi$
$522$		0			0
$523$			216.764i			0.414463i	0.978292	+	0.207231i	$0.0664453\pi$
$523$			216.764i			0.414463i	−0.978292	+	0.207231i	$0.933555\pi$
$524$	−71.4845	−	90.3916i	−0.136421	−	0.172503i
$525$		0			0
$526$	−654.488	+	227.520i	−1.24427	+	0.432548i
$527$		−	1283.63i		−	2.43574i
$528$		0			0
$529$	−226.492			−0.428151
$530$	−7.29364	−	20.9810i	−0.0137616	−	0.0395868i
$531$		0			0
$532$	−106.350	+	84.1053i	−0.199907	+	0.158093i
$533$	60.6793			0.113845
$534$		0			0
$535$		−	137.762i		−	0.257500i
$536$	303.496	−	476.523i	0.566224	−	0.889035i
$537$		0			0
$538$	−80.8899	−	232.689i	−0.150353	−	0.432508i
$539$		−	575.340i		−	1.06742i
$540$		0			0
$541$	−639.646			−1.18234			−0.591170	−	0.806547i	$-0.701334\pi$
$541$	−639.646			−1.18234			−0.591170	+	0.806547i	$0.701334\pi$
$542$	467.606	−	162.554i	0.862742	−	0.299916i
$543$		0			0
$544$	−830.726	+	85.0429i	−1.52707	+	0.156329i
$545$	92.5640			0.169842
$546$		0			0
$547$		−	593.749i		−	1.08546i	−0.839906	−	0.542732i	$-0.817390\pi$
$547$		−	593.749i		−	1.08546i	0.839906	−	0.542732i	$-0.182610\pi$
$548$	431.110	−	340.935i	0.786697	−	0.622145i
$549$		0			0
$550$	565.650	−	196.637i	1.02845	−	0.357522i
$551$			203.544i			0.369408i
$552$		0			0
$553$	−153.100			−0.276853
$554$	152.226	+	437.897i	0.274777	+	0.790427i
$555$		0			0
$556$	−350.447	−	443.137i	−0.630300	−	0.797010i
$557$	426.623			0.765929			0.382965	−	0.923763i	$-0.374903\pi$
$557$	426.623			0.765929			0.382965	+	0.923763i	$0.374903\pi$
$558$		0			0
$559$		−	925.262i		−	1.65521i
$560$	22.0348	+	5.21850i	0.0393478	+	0.00931876i
$561$		0			0
$562$	113.103	+	325.355i	0.201252	+	0.578924i
$563$		−	330.199i		−	0.586498i	−0.956036	−	0.293249i	$-0.905263\pi$
$563$		−	330.199i		−	0.586498i	0.956036	−	0.293249i	$-0.0947366\pi$
$564$		0			0
$565$	110.141			0.194940
$566$	86.9478	−	30.2257i	0.153618	−	0.0534023i
$567$		0			0
$568$	307.278	−	482.462i	0.540983	−	0.849404i
$569$	−798.527			−1.40339			−0.701694	−	0.712479i	$-0.747572\pi$
$569$	−798.527			−1.40339			−0.701694	+	0.712479i	$0.747572\pi$
$570$		0			0
$571$		−	801.419i		−	1.40354i	−0.712405	−	0.701768i	$-0.752394\pi$
$571$		−	801.419i		−	1.40354i	0.712405	−	0.701768i	$-0.247606\pi$
$572$	−354.589	−	448.374i	−0.619910	−	0.783871i
$573$		0			0
$574$	−15.6977	+	5.45700i	−0.0273479	+	0.00950696i
$575$			665.148i			1.15678i
$576$		0			0
$577$	345.694			0.599124			0.299562	−	0.954077i	$-0.403160\pi$
$577$	345.694			0.599124			0.299562	+	0.954077i	$0.403160\pi$
$578$	−257.427	−	740.518i	−0.445375	−	1.28117i
$579$		0			0
$580$	26.6632	−	21.0861i	0.0459710	−	0.0363553i
$581$	−39.1409			−0.0673682
$582$		0			0
$583$		−	153.579i		−	0.263429i
$584$	215.253	+	137.094i	0.368583	+	0.234750i
$585$		0			0
$586$	−27.8866	−	80.2191i	−0.0475881	−	0.136893i
$587$		−	328.237i		−	0.559178i	−0.960120	−	0.279589i	$-0.909802\pi$
$587$		−	328.237i		−	0.559178i	0.960120	−	0.279589i	$-0.0901981\pi$
$588$		0			0
$589$	−1054.19			−1.78979
$590$	−51.0926	+	17.7614i	−0.0865977	+	0.0301040i
$591$		0			0
$592$	−75.4058	+	318.395i	−0.127375	+	0.537830i
$593$	529.415			0.892774			0.446387	−	0.894840i	$-0.352711\pi$
$593$	529.415			0.892774			0.446387	+	0.894840i	$0.352711\pi$
$594$		0			0
$595$			36.9326i			0.0620716i
$596$	438.991	−	347.168i	0.736562	−	0.582496i
$597$		0			0
$598$	599.718	−	208.481i	1.00287	−	0.348630i
$599$			805.319i			1.34444i	0.740352	+	0.672219i	$0.234659\pi$
$599$			805.319i			1.34444i	−0.740352	+	0.672219i	$0.765341\pi$
$600$		0			0
$601$	−111.900			−0.186190			−0.0930951	−	0.995657i	$-0.529676\pi$
$601$	−111.900			−0.186190			−0.0930951	+	0.995657i	$0.529676\pi$
$602$	83.2104	+	239.364i	0.138223	+	0.397615i
$603$		0			0
$604$	184.839	+	233.727i	0.306025	+	0.386966i
$605$	−28.7227			−0.0474755
$606$		0			0
$607$			874.333i			1.44042i	0.693757	+	0.720209i	$0.255954\pi$
$607$			874.333i			1.44042i	−0.693757	+	0.720209i	$0.744046\pi$
$608$	69.8417	+	682.235i	0.114871	+	1.12210i
$609$		0			0
$610$	33.4058	+	96.0955i	0.0547635	+	0.157534i
$611$			698.204i			1.14272i
$612$		0			0
$613$	−152.804			−0.249272			−0.124636	−	0.992203i	$-0.539776\pi$
$613$	−152.804			−0.249272			−0.124636	+	0.992203i	$0.539776\pi$
$614$	−575.470	+	200.051i	−0.937247	+	0.325816i
$615$		0			0
$616$	132.055	+	84.1053i	0.214375	+	0.136535i
$617$	−71.4112			−0.115739			−0.0578697	−	0.998324i	$-0.518431\pi$
$617$	−71.4112			−0.115739			−0.0578697	+	0.998324i	$0.518431\pi$
$618$		0			0
$619$		−	321.866i		−	0.519977i	−0.965612	−	0.259988i	$-0.916281\pi$
$619$		−	321.866i		−	0.519977i	0.965612	−	0.259988i	$-0.0837187\pi$
$620$	109.208	+	138.093i	0.176143	+	0.222731i
$621$		0			0
$622$	−737.636	+	256.425i	−1.18591	+	0.412259i
$623$		−	107.751i		−	0.172956i
$624$		0			0
$625$	565.591			0.904946
$626$	−360.133	−	1035.97i	−0.575293	−	1.65490i
$627$		0			0
$628$	168.010	−	132.868i	0.267532	−	0.211573i
$629$	−533.664			−0.848433
$630$		0			0
$631$			642.307i			1.01792i	0.860790	+	0.508960i	$0.169970\pi$
$631$			642.307i			1.01792i	−0.860790	+	0.508960i	$0.830030\pi$
$632$	−415.990	+	653.151i	−0.658212	+	1.03347i
$633$		0			0
$634$	−374.237	−	1076.54i	−0.590279	−	1.69801i
$635$			4.24580i			0.00668630i
$636$		0			0
$637$	−537.048			−0.843090
$638$	222.000	−	77.1741i	0.347963	−	0.120963i
$639$		0			0
$640$	82.1341	−	79.8250i	0.128335	−	0.124727i
$641$	99.1987			0.154756			0.0773781	−	0.997002i	$-0.475345\pi$
$641$	99.1987			0.154756			0.0773781	+	0.997002i	$0.475345\pi$
$642$		0			0
$643$			512.296i			0.796727i	0.917228	+	0.398364i	$0.130422\pi$
$643$			512.296i			0.796727i	−0.917228	+	0.398364i	$0.869578\pi$
$644$	−136.398	+	107.867i	−0.211797	+	0.167496i
$645$		0			0
$646$	−1056.52	+	367.277i	−1.63547	+	0.568541i
$647$		−	142.728i		−	0.220600i	−0.993898	−	0.110300i	$-0.964819\pi$
$647$		−	142.728i		−	0.220600i	0.993898	−	0.110300i	$-0.0351811\pi$
$648$		0			0
$649$	−373.993			−0.576261
$650$	−183.550	−	528.003i	−0.282385	−	0.812312i
$651$		0			0
$652$	−508.206	−	642.623i	−0.779457	−	0.985617i
$653$	−221.766			−0.339611			−0.169805	−	0.985478i	$-0.554314\pi$
$653$	−221.766			−0.339611			−0.169805	+	0.985478i	$0.554314\pi$
$654$		0			0
$655$			25.7795i			0.0393581i
$656$	−19.3719	+	81.7965i	−0.0295304	+	0.124690i
$657$		0			0
$658$	−62.7907	−	180.625i	−0.0954266	−	0.274506i
$659$		−	130.446i		−	0.197945i	−0.995090	−	0.0989725i	$-0.968444\pi$
$659$		−	130.446i		−	0.197945i	0.995090	−	0.0989725i	$-0.0315556\pi$
$660$		0			0
$661$	717.749			1.08585			0.542927	−	0.839780i	$-0.317316\pi$
$661$	717.749			1.08585			0.542927	+	0.839780i	$0.317316\pi$
$662$	304.020	−	105.687i	0.459244	−	0.159647i
$663$		0			0
$664$	−106.350	+	166.982i	−0.160166	+	0.251479i
$665$	30.3310			0.0456105
$666$		0			0
$667$			261.050i			0.391380i
$668$	−436.156	−	551.516i	−0.652928	−	0.825623i
$669$		0			0
$670$	−119.375	+	41.4983i	−0.178171	+	0.0619377i
$671$			703.410i			1.04830i
$672$		0			0
$673$	1059.89			1.57488			0.787440	−	0.616392i	$-0.211406\pi$
$673$	1059.89			1.57488			0.787440	+	0.616392i	$0.211406\pi$
$674$	−30.4073	−	87.4701i	−0.0451147	−	0.129778i
$675$		0			0
$676$	111.698	−	88.3340i	0.165233	−	0.130672i
$677$	429.152			0.633902			0.316951	−	0.948442i	$-0.397341\pi$
$677$	429.152			0.633902			0.316951	+	0.948442i	$0.397341\pi$
$678$		0			0
$679$			159.590i			0.235037i
$680$	157.561	+	100.350i	0.231708	+	0.147574i
$681$		0			0
$682$	399.698	+	1149.78i	0.586067	+	1.68589i
$683$			565.979i			0.828667i	0.910125	+	0.414333i	$0.135985\pi$
$683$			565.979i			0.828667i	−0.910125	+	0.414333i	$0.864015\pi$
$684$		0			0
$685$	−122.952			−0.179492
$686$	285.342	−	99.1938i	0.415951	−	0.144597i
$687$		0			0
$688$	1247.26	+	295.391i	1.81289	+	0.429347i
$689$	−143.357			−0.208066
$690$		0			0
$691$		−	867.768i		−	1.25581i	−0.778288	−	0.627907i	$-0.783912\pi$
$691$		−	867.768i		−	1.25581i	0.778288	−	0.627907i	$-0.216088\pi$
$692$	97.1754	−	76.8493i	0.140427	−	0.111054i
$693$		0			0
$694$	−391.677	+	136.159i	−0.564376	+	0.196194i
$695$			126.382i			0.181845i
$696$		0			0
$697$	−137.100			−0.196700
$698$	258.411	+	743.348i	0.370216	+	1.06497i
$699$		0			0
$700$	94.9684	+	120.087i	0.135669	+	0.171553i
$701$	−405.608			−0.578613			−0.289307	−	0.957237i	$-0.593425\pi$
$701$	−405.608			−0.578613			−0.289307	+	0.957237i	$0.593425\pi$
$702$		0			0
$703$			438.273i			0.623432i
$704$	717.617	−	334.846i	1.01934	−	0.475633i
$705$		0			0
$706$	170.090	+	489.283i	0.240920	+	0.693035i
$707$			313.579i			0.443535i
$708$		0			0
$709$	370.636			0.522759			0.261380	−	0.965236i	$-0.415823\pi$
$709$	370.636			0.522759			0.261380	+	0.965236i	$0.415823\pi$
$710$	−120.862	+	42.0155i	−0.170229	+	0.0591767i
$711$		0			0
$712$	−459.687	−	292.773i	−0.645628	−	0.411199i
$713$	−1352.02			−1.89625
$714$		0			0
$715$			127.876i			0.178847i
$716$	−620.586	−	784.727i	−0.866741	−	1.09599i
$717$		0			0
$718$	−415.567	+	144.464i	−0.578785	+	0.201203i
$719$			24.6557i			0.0342916i	0.999853	+	0.0171458i	$0.00545795\pi$
$719$			24.6557i			0.0342916i	−0.999853	+	0.0171458i	$0.994542\pi$
$720$		0			0
$721$	−110.572			−0.153359
$722$	64.5541	+	185.697i	0.0894102	+	0.257199i
$723$		0			0
$724$	825.767	−	653.042i	1.14056	−	0.901992i
$725$	229.833			0.317012
$726$		0			0
$727$		−	574.611i		−	0.790387i	−0.918598	−	0.395193i	$-0.870678\pi$
$727$		−	574.611i		−	0.790387i	0.918598	−	0.395193i	$-0.129322\pi$
$728$	78.5076	−	123.266i	0.107840	−	0.169321i
$729$		0			0
$730$	−18.7454	−	53.9233i	−0.0256786	−	0.0738676i
$731$			2090.55i			2.85985i
$732$		0			0
$733$	−210.193			−0.286757			−0.143378	−	0.989668i	$-0.545797\pi$
$733$	−210.193			−0.286757			−0.143378	+	0.989668i	$0.545797\pi$
$734$	1001.54	−	348.167i	1.36450	−	0.474342i
$735$		0			0
$736$	89.5739	+	874.986i	0.121704	+	1.18884i
$737$	−873.811			−1.18563
$738$		0			0
$739$		−	270.937i		−	0.366627i	−0.983055	−	0.183313i	$-0.941318\pi$
$739$		−	270.937i		−	0.366627i	0.983055	−	0.183313i	$-0.0586823\pi$
$740$	57.4116	−	45.4029i	0.0775832	−	0.0613552i
$741$		0			0
$742$	37.0864	−	12.8924i	0.0499817	−	0.0173752i
$743$			465.072i			0.625938i	0.949763	+	0.312969i	$0.101324\pi$
$743$			465.072i			0.625938i	−0.949763	+	0.312969i	$0.898676\pi$
$744$		0			0
$745$	−125.199			−0.168053
$746$	−334.391	−	961.914i	−0.448245	−	1.28943i
$747$		0			0
$748$	801.162	+	1013.06i	1.07107	+	1.35436i
$749$	243.511			0.325115
$750$		0			0
$751$		−	905.967i		−	1.20635i	−0.797610	−	0.603174i	$-0.793903\pi$
$751$		−	905.967i		−	1.20635i	0.797610	−	0.603174i	$-0.206097\pi$
$752$	−941.188	−	222.902i	−1.25158	−	0.296413i
$753$		0			0
$754$	−72.0378	−	207.225i	−0.0955408	−	0.274834i
$755$		−	66.6586i		−	0.0882896i
$756$		0			0
$757$	−263.196			−0.347683			−0.173841	−	0.984774i	$-0.555618\pi$
$757$	−263.196			−0.347683			−0.173841	+	0.984774i	$0.555618\pi$
$758$	−17.9276	+	6.23218i	−0.0236512	+	0.00822187i
$759$		0			0
$760$	82.4128	−	129.397i	0.108438	−	0.170260i
$761$	−1080.31			−1.41959			−0.709797	−	0.704407i	$-0.751213\pi$
$761$	−1080.31			−1.41959			−0.709797	+	0.704407i	$0.751213\pi$
$762$		0			0
$763$			163.618i			0.214440i
$764$	−770.353	−	974.105i	−1.00832	−	1.27501i
$765$		0			0
$766$	748.159	−	260.083i	0.976708	−	0.339534i
$767$			349.102i			0.455153i
$768$		0			0
$769$	512.100			0.665929			0.332965	−	0.942939i	$-0.391951\pi$
$769$	512.100			0.665929			0.332965	+	0.942939i	$0.391951\pi$
$770$	−11.5001	−	33.0813i	−0.0149352	−	0.0429627i
$771$		0			0
$772$	−552.505	+	436.938i	−0.715681	+	0.565983i
$773$	−546.612			−0.707130			−0.353565	−	0.935410i	$-0.615031\pi$
$773$	−546.612			−0.707130			−0.353565	+	0.935410i	$0.615031\pi$
$774$		0			0
$775$			1190.35i			1.53593i
$776$	680.841	+	433.626i	0.877373	+	0.558796i
$777$		0			0
$778$	−406.035	−	1168.01i	−0.521896	−	1.50129i
$779$			112.593i			0.144536i
$780$		0			0
$781$	−884.701			−1.13278
$782$	−1355.01	+	471.044i	−1.73275	+	0.602358i
$783$		0			0
$784$	171.453	−	723.948i	0.218690	−	0.923403i
$785$	−47.9162			−0.0610398
$786$		0			0
$787$			1304.94i			1.65812i	0.559163	+	0.829058i	$0.311123\pi$
$787$			1304.94i			1.65812i	−0.559163	+	0.829058i	$0.688877\pi$
$788$	369.971	−	292.584i	0.469506	−	0.371300i
$789$		0			0
$790$	163.622	−	56.8801i	0.207117	−	0.0720001i
$791$			194.688i			0.246129i
$792$		0			0
$793$	656.595			0.827988
$794$	247.680	+	712.479i	0.311939	+	0.897329i
$795$		0			0
$796$	248.412	+	314.115i	0.312075	+	0.394617i
$797$	−161.394			−0.202502			−0.101251	−	0.994861i	$-0.532285\pi$
$797$	−161.394			−0.202502			−0.101251	+	0.994861i	$0.532285\pi$
$798$		0			0
$799$		−	1577.53i		−	1.97438i
$800$	770.353	−	78.8624i	0.962941	−	0.0985781i
$801$		0			0
$802$	−160.113	−	460.585i	−0.199643	−	0.574295i
$803$		−	394.714i		−	0.491549i
$804$		0			0
$805$	38.9003			0.0483234
$806$	1073.25	−	373.096i	1.33158	−	0.462898i
$807$		0			0
$808$	1337.79	+	852.033i	1.65568	+	1.05450i
$809$	144.054			0.178064			0.0890319	−	0.996029i	$-0.471623\pi$
$809$	144.054			0.178064			0.0890319	+	0.996029i	$0.471623\pi$
$810$		0			0
$811$		−	219.215i		−	0.270302i	−0.990825	−	0.135151i	$-0.956848\pi$
$811$		−	219.215i		−	0.270302i	0.990825	−	0.135151i	$-0.0431520\pi$
$812$	37.2722	+	47.1304i	0.0459017	+	0.0580424i
$813$		0			0
$814$	478.014	−	166.172i	0.587241	−	0.204143i
$815$			183.275i			0.224877i
$816$		0			0
$817$	1716.87			2.10143
$818$	−336.695	−	968.541i	−0.411607	−	1.18404i
$819$		0			0
$820$	14.7492	−	11.6641i	0.0179868	−	0.0142245i
$821$	1442.82			1.75739			0.878696	−	0.477382i	$-0.158414\pi$
$821$	1442.82			1.75739			0.878696	+	0.477382i	$0.158414\pi$
$822$		0			0
$823$			1255.35i			1.52534i	0.646790	+	0.762668i	$0.276111\pi$
$823$			1255.35i			1.52534i	−0.646790	+	0.762668i	$0.723889\pi$
$824$	−300.436	+	471.718i	−0.364607	+	0.572474i
$825$		0			0
$826$	−31.3954	−	90.3124i	−0.0380089	−	0.109337i
$827$		−	518.447i		−	0.626901i	−0.949605	−	0.313451i	$-0.898515\pi$
$827$		−	518.447i		−	0.626901i	0.949605	−	0.313451i	$-0.101485\pi$
$828$		0			0
$829$	481.382			0.580678			0.290339	−	0.956924i	$-0.406232\pi$
$829$	481.382			0.580678			0.290339	+	0.956924i	$0.406232\pi$
$830$	41.8310	−	14.5418i	0.0503988	−	0.0175202i
$831$		0			0
$832$	−312.560	−	669.856i	−0.375673	−	0.805115i
$833$	1213.41			1.45668
$834$		0			0
$835$			157.291i			0.188373i
$836$	831.980	−	657.956i	0.995191	−	0.787028i
$837$		0			0
$838$	−794.048	+	276.036i	−0.947552	+	0.329398i
$839$			629.352i			0.750122i	0.927000	+	0.375061i	$0.122378\pi$
$839$			629.352i			0.750122i	−0.927000	+	0.375061i	$0.877622\pi$
$840$		0			0
$841$	−750.797			−0.892744
$842$	72.7958	+	209.405i	0.0864558	+	0.248700i
$843$		0			0
$844$	21.7799	+	27.5405i	0.0258055	+	0.0326309i
$845$	−31.8560			−0.0376994
$846$		0			0
$847$		−	50.7708i		−	0.0599420i
$848$	45.7670	−	193.248i	0.0539705	−	0.227886i
$849$		0			0
$850$	414.715	+	1192.98i	0.487900	+	1.40350i
$851$			562.098i			0.660514i
$852$		0			0
$853$	799.003			0.936698			0.468349	−	0.883544i	$-0.344849\pi$
$853$	799.003			0.936698			0.468349	+	0.883544i	$0.344849\pi$
$854$	−169.860	+	59.0487i	−0.198900	+	0.0691437i
$855$		0			0
$856$	661.650	−	1038.86i	0.772955	−	1.21363i
$857$	829.923			0.968405			0.484202	−	0.874956i	$-0.339110\pi$
$857$	829.923			0.968405			0.484202	+	0.874956i	$0.339110\pi$
$858$		0			0
$859$			898.689i			1.04620i	0.852270	+	0.523102i	$0.175225\pi$
$859$			898.689i			1.04620i	−0.852270	+	0.523102i	$0.824775\pi$
$860$	−177.859	−	224.901i	−0.206813	−	0.261513i
$861$		0			0
$862$	−1173.73	+	408.026i	−1.36164	+	0.473347i
$863$		−	604.060i		−	0.699953i	−0.936758	−	0.349977i	$-0.886190\pi$
$863$		−	604.060i		−	0.699953i	0.936758	−	0.349977i	$-0.113810\pi$
$864$		0			0
$865$	−27.7142			−0.0320396
$866$	−283.567	−	815.712i	−0.327444	−	0.941931i
$867$		0			0
$868$	−244.096	+	193.039i	−0.281217	+	0.222395i
$869$	1197.70			1.37825
$870$		0			0
$871$			815.654i			0.936457i
$872$	698.024	+	444.570i	0.800487	+	0.509827i
$873$		0			0
$874$	386.846	+	1112.81i	0.442615	+	1.27323i
$875$		−	69.6302i		−	0.0795774i
$876$		0			0
$877$	−110.540			−0.126043			−0.0630216	−	0.998012i	$-0.520074\pi$
$877$	−110.540			−0.126043			−0.0630216	+	0.998012i	$0.520074\pi$
$878$	569.494	−	197.974i	0.648626	−	0.225482i
$879$		0			0
$880$	−172.378	−	40.8244i	−0.195884	−	0.0463913i
$881$	−1020.91			−1.15881			−0.579407	−	0.815039i	$-0.696716\pi$
$881$	−1020.91			−1.15881			−0.579407	+	0.815039i	$0.696716\pi$
$882$		0			0
$883$			194.702i			0.220501i	0.993904	+	0.110250i	$0.0351653\pi$
$883$			194.702i			0.220501i	−0.993904	+	0.110250i	$0.964835\pi$
$884$	945.639	−	747.840i	1.06973	−	0.845973i
$885$		0			0
$886$	−1236.18	+	429.734i	−1.39524	+	0.485027i
$887$		−	959.187i		−	1.08138i	−0.841221	−	0.540692i	$-0.818163\pi$
$887$		−	959.187i		−	1.08138i	0.841221	−	0.540692i	$-0.181837\pi$
$888$		0			0
$889$	−7.50497			−0.00844203
$890$	40.0321	+	115.157i	0.0449799	+	0.129390i
$891$		0			0
$892$	870.426	+	1100.65i	0.975814	+	1.23391i
$893$	−1295.55			−1.45079
$894$		0			0
$895$			223.803i			0.250059i
$896$	141.100	+	145.182i	0.157478	+	0.162034i
$897$		0			0
$898$	252.550	+	726.489i	0.281236	+	0.809008i
$899$			467.175i			0.519660i
$900$		0			0
$901$	323.904			0.359493
$902$	122.803	−	42.6901i	0.136145	−	0.0473283i
$903$		0			0
$904$	830.574	+	528.990i	0.918777	+	0.585166i
$905$	−235.507			−0.260229
$906$		0			0
$907$		−	465.161i		−	0.512857i	−0.966563	−	0.256428i	$-0.917454\pi$
$907$		−	465.161i		−	0.512857i	0.966563	−	0.256428i	$-0.0825458\pi$
$908$	44.2953	+	56.0111i	0.0487834	+	0.0616863i
$909$		0			0
$910$	−30.8796	+	10.7347i	−0.0339336	+	0.0117964i
$911$			134.601i			0.147750i	0.997267	+	0.0738751i	$0.0235366\pi$
$911$			134.601i			0.147750i	−0.997267	+	0.0738751i	$0.976463\pi$
$912$		0			0
$913$	306.199			0.335377
$914$	18.7152	+	53.8365i	0.0204762	+	0.0589020i
$915$		0			0
$916$	1303.12	−	1030.55i	1.42262	−	1.12506i
$917$	−45.5684			−0.0496929
$918$		0			0
$919$		−	105.178i		−	0.114448i	−0.998361	−	0.0572241i	$-0.981775\pi$
$919$		−	105.178i		−	0.114448i	0.998361	−	0.0572241i	$-0.0182250\pi$
$920$	105.697	−	165.956i	0.114888	−	0.180387i
$921$		0			0
$922$	−296.839	−	853.891i	−0.321951	−	0.926130i
$923$			825.820i			0.894712i
$924$		0			0
$925$	494.880			0.535006
$926$	−182.562	+	63.4640i	−0.197151	+	0.0685357i
$927$		0			0
$928$	302.340	−	30.9511i	0.325798	−	0.0333525i
$929$	517.308			0.556844			0.278422	−	0.960459i	$-0.410189\pi$
$929$	517.308			0.556844			0.278422	+	0.960459i	$0.410189\pi$
$930$		0			0
$931$		−	996.518i		−	1.07037i
$932$	−977.982	+	773.419i	−1.04934	+	0.829849i
$933$		0			0
$934$	−373.650	+	129.892i	−0.400053	+	0.139071i
$935$		−	288.924i		−	0.309009i
$936$		0			0
$937$	367.880			0.392615			0.196308	−	0.980542i	$-0.437105\pi$
$937$	367.880			0.392615			0.196308	+	0.980542i	$0.437105\pi$
$938$	−73.3532	−	211.009i	−0.0782017	−	0.224956i
$939$		0			0
$940$	134.213	+	169.711i	0.142779	+	0.180543i
$941$	−1274.91			−1.35484			−0.677422	−	0.735595i	$-0.736903\pi$
$941$	−1274.91			−1.35484			−0.677422	+	0.735595i	$0.736903\pi$
$942$		0			0
$943$			144.404i			0.153133i
$944$	−470.594	−	111.451i	−0.498511	−	0.118063i
$945$		0			0
$946$	−650.955	−	1872.55i	−0.688113	−	1.97944i
$947$		−	720.808i		−	0.761149i	−0.924750	−	0.380574i	$-0.875726\pi$
$947$		−	720.808i		−	0.761149i	0.924750	−	0.380574i	$-0.124274\pi$
$948$		0			0
$949$	−368.444			−0.388244
$950$	979.734	−	340.586i	1.03130	−	0.358511i
$951$		0			0
$952$	−177.381	+	278.509i	−0.186325	+	0.292551i
$953$	513.654			0.538986			0.269493	−	0.963002i	$-0.413144\pi$
$953$	513.654			0.538986			0.269493	+	0.963002i	$0.413144\pi$
$954$		0			0
$955$			277.813i			0.290904i
$956$	−109.208	−	138.093i	−0.114235	−	0.144449i
$957$		0			0
$958$	−928.777	+	322.871i	−0.969495	+	0.337026i
$959$		−	217.332i		−	0.226624i
$960$		0			0
$961$	−1458.57			−1.51777
$962$	−155.113	−	446.200i	−0.161240	−	0.463825i
$963$		0			0
$964$	−372.732	+	294.768i	−0.386652	+	0.305776i
$965$	157.574			0.163289
$966$		0			0
$967$		−	11.7022i		−	0.0121016i	−0.999982	−	0.00605078i	$-0.998074\pi$
$967$		−	11.7022i		−	0.0121016i	0.999982	−	0.00605078i	$-0.00192603\pi$
$968$	−216.598	−	137.950i	−0.223758	−	0.142511i
$969$		0			0
$970$	−59.2915	−	170.559i	−0.0611252	−	0.175834i
$971$			743.634i			0.765843i	0.923781	+	0.382922i	$0.125082\pi$
$971$			743.634i			0.765843i	−0.923781	+	0.382922i	$0.874918\pi$
$972$		0			0
$973$	−223.395			−0.229594
$974$	−1069.97	+	371.953i	−1.09853	+	0.381882i
$975$		0			0
$976$	−209.618	+	885.098i	−0.214773	+	0.906863i
$977$	957.744			0.980290			0.490145	−	0.871641i	$-0.336944\pi$
$977$	957.744			0.980290			0.490145	+	0.871641i	$0.336944\pi$
$978$		0			0
$979$			842.939i			0.861021i
$980$	−130.539	+	103.234i	−0.133203	+	0.105341i
$981$		0			0
$982$	630.426	−	219.155i	0.641982	−	0.223173i
$983$		−	539.312i		−	0.548639i	−0.961639	−	0.274320i	$-0.911547\pi$
$983$		−	539.312i		−	0.548639i	0.961639	−	0.274320i	$-0.0884526\pi$
$984$		0			0
$985$	−105.515			−0.107122
$986$	162.763	+	468.207i	0.165074	+	0.474855i
$987$		0			0
$988$	−614.165	−	776.607i	−0.621625	−	0.786040i
$989$	2201.93			2.22642
$990$		0			0
$991$		−	114.353i		−	0.115391i	−0.998334	−	0.0576956i	$-0.981625\pi$
$991$		−	114.353i		−	0.115391i	0.998334	−	0.0576956i	$-0.0183753\pi$
$992$	160.301	+	1565.87i	0.161594	+	1.57850i
$993$		0			0
$994$	−74.2674	−	213.639i	−0.0747157	−	0.214928i
$995$		−	89.5850i		−	0.0900352i
$996$		0			0
$997$	−3.73593			−0.00374717			−0.00187358	−	0.999998i	$-0.500596\pi$
$997$	−3.73593			−0.00374717			−0.00187358	+	0.999998i	$0.500596\pi$
$998$	−52.4377	+	18.2290i	−0.0525428	+	0.0182655i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.d.h.163.3	✓	8
3.2	odd	2	inner	324.3.d.h.163.6	yes	8
4.3	odd	2	inner	324.3.d.h.163.4	yes	8
9.2	odd	6		324.3.f.s.271.6		16
9.4	even	3		324.3.f.s.55.8		16
9.5	odd	6		324.3.f.s.55.1		16
9.7	even	3		324.3.f.s.271.3		16
12.11	even	2	inner	324.3.d.h.163.5	yes	8
36.7	odd	6		324.3.f.s.271.8		16
36.11	even	6		324.3.f.s.271.1		16
36.23	even	6		324.3.f.s.55.6		16
36.31	odd	6		324.3.f.s.55.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.d.h.163.3	✓	8	1.1	even	1	trivial
324.3.d.h.163.4	yes	8	4.3	odd	2	inner
324.3.d.h.163.5	yes	8	12.11	even	2	inner
324.3.d.h.163.6	yes	8	3.2	odd	2	inner
324.3.f.s.55.1		16	9.5	odd	6
324.3.f.s.55.3		16	36.31	odd	6
324.3.f.s.55.6		16	36.23	even	6
324.3.f.s.55.8		16	9.4	even	3
324.3.f.s.271.1		16	36.11	even	6
324.3.f.s.271.3		16	9.7	even	3
324.3.f.s.271.6		16	9.2	odd	6
324.3.f.s.271.8		16	36.7	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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.656712 - 1.88911i) q^{2} +(-3.13746 + 2.48120i) q^{4} +0.894797 q^{5} +1.58166i q^{7} +(6.74766 + 4.29756i) q^{8} +O(q^{10})\)	\(q+(-0.656712 - 1.88911i) q^{2} +(-3.13746 + 2.48120i) q^{4} +0.894797 q^{5} +1.58166i q^{7} +(6.74766 + 4.29756i) q^{8} +(-0.587624 - 1.69037i) q^{10} -12.3733i q^{11} -11.5498 q^{13} +(2.98793 - 1.03870i) q^{14} +(3.68729 - 15.5693i) q^{16} +26.0958 q^{17} -21.4313i q^{19} +(-2.80739 + 2.22017i) q^{20} +(-23.3746 + 8.12572i) q^{22} -27.4862i q^{23} -24.1993 q^{25} +(7.58492 + 21.8189i) q^{26} +(-3.92442 - 4.96240i) q^{28} -9.49751 q^{29} -49.1892i q^{31} +(-31.8336 + 3.25887i) q^{32} +(-17.1375 - 49.2979i) q^{34} +1.41527i q^{35} -20.4502 q^{37} +(-40.4860 + 14.0742i) q^{38} +(6.03779 + 3.84545i) q^{40} -5.25370 q^{41} +80.1104i q^{43} +(30.7007 + 38.8209i) q^{44} +(-51.9244 + 18.0505i) q^{46} -60.4515i q^{47} +46.4983 q^{49} +(15.8920 + 45.7152i) q^{50} +(36.2371 - 28.6574i) q^{52} +12.4121 q^{53} -11.0716i q^{55} +(-6.79730 + 10.6725i) q^{56} +(6.23713 + 17.9418i) q^{58} -30.2257i q^{59} -56.8488 q^{61} +(-92.9237 + 32.3031i) q^{62} +(27.0619 + 57.9970i) q^{64} -10.3348 q^{65} -70.6204i q^{67} +(-81.8746 + 64.7490i) q^{68} +(2.67359 - 0.929423i) q^{70} -71.5006i q^{71} +31.9003 q^{73} +(13.4299 + 38.6326i) q^{74} +(53.1752 + 67.2397i) q^{76} +19.5705 q^{77} +96.7967i q^{79} +(3.29938 - 13.9314i) q^{80} +(3.45017 + 9.92480i) q^{82} +24.7467i q^{83} +23.3505 q^{85} +(151.337 - 52.6095i) q^{86} +(53.1752 - 83.4911i) q^{88} -68.1254 q^{89} -18.2679i q^{91} +(68.1988 + 86.2368i) q^{92} +(-114.199 + 39.6992i) q^{94} -19.1766i q^{95} +100.900 q^{97} +(-30.5360 - 87.8404i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 10 q^{4}+O(q^{10}) \) 8 * q - 10 * q^4	\( 8 q - 10 q^{4} - 50 q^{10} - 32 q^{13} - 46 q^{16} - 36 q^{22} + 48 q^{25} + 180 q^{28} - 122 q^{34} - 224 q^{37} + 154 q^{40} - 204 q^{46} - 232 q^{49} + 154 q^{52} - 86 q^{58} - 32 q^{61} - 10 q^{64} - 492 q^{70} + 376 q^{73} + 516 q^{76} + 88 q^{82} + 368 q^{85} + 516 q^{88} - 672 q^{94} + 928 q^{97}+O(q^{100}) \) 8 * q - 10 * q^4 - 50 * q^10 - 32 * q^13 - 46 * q^16 - 36 * q^22 + 48 * q^25 + 180 * q^28 - 122 * q^34 - 224 * q^37 + 154 * q^40 - 204 * q^46 - 232 * q^49 + 154 * q^52 - 86 * q^58 - 32 * q^61 - 10 * q^64 - 492 * q^70 + 376 * q^73 + 516 * q^76 + 88 * q^82 + 368 * q^85 + 516 * q^88 - 672 * q^94 + 928 * q^97

Introduction

L-functions

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