LMFDB - Embedded newform 216.3.h.f.53.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(53,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("216.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.h (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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.242095489024.11
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 2x^{4} - 32x^{2} + 256 $ x^8 - 2x^6 + 2x^4 - 32*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			53.5
Root			$0.926315 - 1.77255i$ of defining polynomial
Character	$\chi$	$=$	216.53
Dual form			216.3.h.f.53.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.926315 - 1.77255i) q^{2} +(-2.28388 - 3.28388i) q^{4} +5.39773 q^{5} +11.5678 q^{7} +(-7.93645 + 1.00639i) q^{8} +O(q^{10})$	\(q+(0.926315 - 1.77255i) q^{2} +(-2.28388 - 3.28388i) q^{4} +5.39773 q^{5} +11.5678 q^{7} +(-7.93645 + 1.00639i) q^{8} +(5.00000 - 9.56776i) q^{10} -1.69247 q^{11} +9.56776i q^{13} +(10.7154 - 20.5045i) q^{14} +(-5.56776 + 15.0000i) q^{16} -19.2578i q^{17} -1.86447i q^{19} +(-12.3278 - 17.7255i) q^{20} +(-1.56776 + 3.00000i) q^{22} -30.3736i q^{23} +4.13553 q^{25} +(16.9594 + 8.86276i) q^{26} +(-26.4194 - 37.9872i) q^{28} -49.3112 q^{29} +23.4066 q^{31} +(21.4308 + 23.7639i) q^{32} +(-34.1355 - 17.8388i) q^{34} +62.4397 q^{35} +24.9744i q^{37} +(-3.30487 - 1.72709i) q^{38} +(-42.8388 + 5.43224i) q^{40} +68.7984i q^{41} +83.6776i q^{43} +(3.86541 + 5.55789i) q^{44} +(-53.8388 - 28.1355i) q^{46} -28.2699i q^{47} +84.8132 q^{49} +(3.83080 - 7.33044i) q^{50} +(31.4194 - 21.8516i) q^{52} -61.3879 q^{53} -9.13553 q^{55} +(-91.8069 + 11.6417i) q^{56} +(-45.6776 + 87.4066i) q^{58} +75.3389 q^{59} +4.70329i q^{61} +(21.6819 - 41.4894i) q^{62} +(61.9744 - 15.9744i) q^{64} +51.6442i q^{65} -99.8132i q^{67} +(-63.2405 + 43.9826i) q^{68} +(57.8388 - 110.678i) q^{70} +73.0058i q^{71} +8.72894 q^{73} +(44.2683 + 23.1341i) q^{74} +(-6.12270 + 4.25823i) q^{76} -19.5782 q^{77} -3.83882 q^{79} +(-30.0533 + 80.9660i) q^{80} +(121.949 + 63.7289i) q^{82} -37.0526 q^{83} -103.949i q^{85} +(148.323 + 77.5118i) q^{86} +(13.4322 - 1.70329i) q^{88} +43.4112i q^{89} +110.678i q^{91} +(-99.7434 + 69.3698i) q^{92} +(-50.1099 - 26.1868i) q^{94} -10.0639i q^{95} -86.9487 q^{97} +(78.5637 - 150.336i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 48 q^{7}+O(q^{10}) $ 8 * q + 4 * q^4 + 48 * q^7	$ 8 q + 4 q^{4} + 48 q^{7} + 40 q^{10} + 32 q^{22} - 56 q^{25} - 100 q^{28} - 80 q^{31} - 184 q^{34} - 120 q^{40} - 208 q^{46} + 144 q^{49} + 140 q^{52} + 16 q^{55} + 80 q^{58} + 184 q^{64} + 240 q^{70} + 248 q^{73} + 196 q^{76} + 192 q^{79} + 352 q^{82} + 152 q^{88} - 72 q^{97}+O(q^{100}) $ 8 * q + 4 * q^4 + 48 * q^7 + 40 * q^10 + 32 * q^22 - 56 * q^25 - 100 * q^28 - 80 * q^31 - 184 * q^34 - 120 * q^40 - 208 * q^46 + 144 * q^49 + 140 * q^52 + 16 * q^55 + 80 * q^58 + 184 * q^64 + 240 * q^70 + 248 * q^73 + 196 * q^76 + 192 * q^79 + 352 * q^82 + 152 * q^88 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	0.926315	−	1.77255i	0.463157	−	0.886276i
$2$	0.926315	−	1.77255i	0.463157	−	0.886276i
$3$		0			0
$3$		0			0
$4$	−2.28388	−	3.28388i	−0.570971	−	0.820971i
$5$	5.39773			1.07955			0.539773	−	0.841810i	$-0.318510\pi$
$5$	5.39773			1.07955			0.539773	+	0.841810i	$0.318510\pi$
$6$		0			0
$7$	11.5678			1.65254			0.826269	−	0.563276i	$-0.190459\pi$
$7$	11.5678			1.65254			0.826269	+	0.563276i	$0.190459\pi$
$8$	−7.93645	+	1.00639i	−0.992056	+	0.125799i
$9$		0			0
$10$	5.00000	−	9.56776i	0.500000	−	0.956776i
$11$	−1.69247			−0.153861			−0.0769307	−	0.997036i	$-0.524512\pi$
$11$	−1.69247			−0.153861			−0.0769307	+	0.997036i	$0.524512\pi$
$12$		0			0
$13$			9.56776i			0.735982i	0.929829	+	0.367991i	$0.119954\pi$
$13$			9.56776i			0.735982i	−0.929829	+	0.367991i	$0.880046\pi$
$14$	10.7154	−	20.5045i	0.765385	−	1.46460i
$15$		0			0
$16$	−5.56776	+	15.0000i	−0.347985	+	0.937500i
$17$		−	19.2578i		−	1.13281i	−0.824126	−	0.566407i	$-0.808333\pi$
$17$		−	19.2578i		−	1.13281i	0.824126	−	0.566407i	$-0.191667\pi$
$18$		0			0
$19$		−	1.86447i		−	0.0981301i	−0.998796	−	0.0490650i	$-0.984376\pi$
$19$		−	1.86447i		−	0.0981301i	0.998796	−	0.0490650i	$-0.0156242\pi$
$20$	−12.3278	−	17.7255i	−0.616389	−	0.886276i
$21$		0			0
$22$	−1.56776	+	3.00000i	−0.0712620	+	0.136364i
$23$		−	30.3736i		−	1.32059i	−0.751005	−	0.660296i	$-0.770431\pi$
$23$		−	30.3736i		−	1.32059i	0.751005	−	0.660296i	$-0.229569\pi$
$24$		0			0
$25$	4.13553			0.165421
$26$	16.9594	+	8.86276i	0.652283	+	0.340875i
$27$		0			0
$28$	−26.4194	−	37.9872i	−0.943550	−	1.35668i
$29$	−49.3112			−1.70038			−0.850192	−	0.526472i	$-0.823514\pi$
$29$	−49.3112			−1.70038			−0.850192	+	0.526472i	$0.823514\pi$
$30$		0			0
$31$	23.4066			0.755051			0.377526	−	0.925999i	$-0.376775\pi$
$31$	23.4066			0.755051			0.377526	+	0.925999i	$0.376775\pi$
$32$	21.4308	+	23.7639i	0.669712	+	0.742621i
$33$		0			0
$34$	−34.1355	−	17.8388i	−1.00399	−	0.524671i
$35$	62.4397			1.78399
$36$		0			0
$37$			24.9744i			0.674982i	0.941329	+	0.337491i	$0.109578\pi$
$37$			24.9744i			0.674982i	−0.941329	+	0.337491i	$0.890422\pi$
$38$	−3.30487	−	1.72709i	−0.0869703	−	0.0454497i
$39$		0			0
$40$	−42.8388	+	5.43224i	−1.07097	+	0.135806i
$41$			68.7984i			1.67801i	0.544124	+	0.839005i	$0.316862\pi$
$41$			68.7984i			1.67801i	−0.544124	+	0.839005i	$0.683138\pi$
$42$		0			0
$43$			83.6776i			1.94599i	0.230823	+	0.972996i	$0.425858\pi$
$43$			83.6776i			1.94599i	−0.230823	+	0.972996i	$0.574142\pi$
$44$	3.86541	+	5.55789i	0.0878503	+	0.126316i
$45$		0			0
$46$	−53.8388	−	28.1355i	−1.17041	−	0.611642i
$47$		−	28.2699i		−	0.601487i	−0.953705	−	0.300744i	$-0.902765\pi$
$47$		−	28.2699i		−	0.601487i	0.953705	−	0.300744i	$-0.0972349\pi$
$48$		0			0
$49$	84.8132			1.73088
$50$	3.83080	−	7.33044i	0.0766160	−	0.146609i
$51$		0			0
$52$	31.4194	−	21.8516i	0.604219	−	0.420224i
$53$	−61.3879			−1.15826			−0.579131	−	0.815235i	$-0.696608\pi$
$53$	−61.3879			−1.15826			−0.579131	+	0.815235i	$0.696608\pi$
$54$		0			0
$55$	−9.13553			−0.166101
$56$	−91.8069	+	11.6417i	−1.63941	+	0.207888i
$57$		0			0
$58$	−45.6776	+	87.4066i	−0.787546	+	1.50701i
$59$	75.3389			1.27693			0.638465	−	0.769651i	$-0.279570\pi$
$59$	75.3389			1.27693			0.638465	+	0.769651i	$0.279570\pi$
$60$		0			0
$61$			4.70329i			0.0771032i	0.999257	+	0.0385516i	$0.0122744\pi$
$61$			4.70329i			0.0771032i	−0.999257	+	0.0385516i	$0.987726\pi$
$62$	21.6819	−	41.4894i	0.349707	−	0.669184i
$63$		0			0
$64$	61.9744	−	15.9744i	0.968349	−	0.249599i
$65$			51.6442i			0.794527i
$66$		0			0
$67$		−	99.8132i		−	1.48975i	−0.667205	−	0.744874i	$-0.732509\pi$
$67$		−	99.8132i		−	1.48975i	0.667205	−	0.744874i	$-0.267491\pi$
$68$	−63.2405	+	43.9826i	−0.930007	+	0.646804i
$69$		0			0
$70$	57.8388	−	110.678i	0.826269	−	1.58111i
$71$			73.0058i			1.02825i	0.857715	+	0.514125i	$0.171883\pi$
$71$			73.0058i			1.02825i	−0.857715	+	0.514125i	$0.828117\pi$
$72$		0			0
$73$	8.72894			0.119575			0.0597873	−	0.998211i	$-0.480958\pi$
$73$	8.72894			0.119575			0.0597873	+	0.998211i	$0.480958\pi$
$74$	44.2683	+	23.1341i	0.598221	+	0.312623i
$75$		0			0
$76$	−6.12270	+	4.25823i	−0.0805619	+	0.0560294i
$77$	−19.5782			−0.254262
$78$		0			0
$79$	−3.83882			−0.0485927			−0.0242963	−	0.999705i	$-0.507735\pi$
$79$	−3.83882			−0.0485927			−0.0242963	+	0.999705i	$0.507735\pi$
$80$	−30.0533	+	80.9660i	−0.375666	+	1.01208i
$81$		0			0
$82$	121.949	+	63.7289i	1.48718	+	0.777182i
$83$	−37.0526			−0.446417			−0.223208	−	0.974771i	$-0.571653\pi$
$83$	−37.0526			−0.446417			−0.223208	+	0.974771i	$0.571653\pi$
$84$		0			0
$85$		−	103.949i		−	1.22293i
$86$	148.323	+	77.5118i	1.72469	+	0.901300i
$87$		0			0
$88$	13.4322	−	1.70329i	0.152639	−	0.0193556i
$89$			43.4112i			0.487767i	0.969805	+	0.243883i	$0.0784214\pi$
$89$			43.4112i			0.487767i	−0.969805	+	0.243883i	$0.921579\pi$
$90$		0			0
$91$			110.678i			1.21624i
$92$	−99.7434	+	69.3698i	−1.08417	+	0.754019i
$93$		0			0
$94$	−50.1099	−	26.1868i	−0.533084	−	0.278583i
$95$		−	10.0639i		−	0.105936i
$96$		0			0
$97$	−86.9487			−0.896378			−0.448189	−	0.893939i	$-0.647931\pi$
$97$	−86.9487			−0.896378			−0.448189	+	0.893939i	$0.647931\pi$
$98$	78.5637	−	150.336i	0.801670	−	1.53404i
$99$		0			0
$100$	−9.44506	−	13.5806i	−0.0944506	−	0.135806i
$101$	−51.4149			−0.509058			−0.254529	−	0.967065i	$-0.581920\pi$
$101$	−51.4149			−0.509058			−0.254529	+	0.967065i	$0.581920\pi$
$102$		0			0
$103$	47.2454			0.458693			0.229347	−	0.973345i	$-0.426341\pi$
$103$	47.2454			0.458693			0.229347	+	0.973345i	$0.426341\pi$
$104$	−9.62892	−	75.9340i	−0.0925858	−	0.730135i
$105$		0			0
$106$	−56.8645	+	108.813i	−0.536457	+	1.02654i
$107$	75.1570			0.702402			0.351201	−	0.936300i	$-0.385773\pi$
$107$	75.1570			0.702402			0.351201	+	0.936300i	$0.385773\pi$
$108$		0			0
$109$			133.136i			1.22143i	0.791852	+	0.610713i	$0.209117\pi$
$109$			133.136i			1.22143i	−0.791852	+	0.610713i	$0.790883\pi$
$110$	−8.46237	+	16.1932i	−0.0769307	+	0.147211i
$111$		0			0
$112$	−64.4066	+	173.516i	−0.575059	+	1.54925i
$113$		−	90.1599i		−	0.797875i	−0.916978	−	0.398938i	$-0.869379\pi$
$113$		−	90.1599i		−	0.797875i	0.916978	−	0.398938i	$-0.130621\pi$
$114$		0			0
$115$		−	163.949i		−	1.42564i
$116$	112.621	+	161.932i	0.970869	+	1.39597i
$117$		0			0
$118$	69.7875	−	133.542i	0.591420	−	1.13171i
$119$		−	222.770i		−	1.87202i
$120$		0			0
$121$	−118.136			−0.976327
$122$	8.33683	+	4.35673i	0.0683347	+	0.0357109i
$123$		0			0
$124$	−53.4579	−	76.8645i	−0.431112	−	0.619875i
$125$	−112.621			−0.900967
$126$		0			0
$127$	−111.355			−0.876813			−0.438407	−	0.898777i	$-0.644457\pi$
$127$	−111.355			−0.876813			−0.438407	+	0.898777i	$0.644457\pi$
$128$	29.0924	−	124.650i	0.227284	−	0.973828i
$129$		0			0
$130$	91.5421	+	47.8388i	0.704170	+	0.367991i
$131$	92.4930			0.706054			0.353027	−	0.935613i	$-0.385152\pi$
$131$	92.4930			0.706054			0.353027	+	0.935613i	$0.385152\pi$
$132$		0			0
$133$		−	21.5678i		−	0.162164i
$134$	−176.924	−	92.4584i	−1.32033	−	0.689988i
$135$		0			0
$136$	19.3809	+	152.839i	0.142507	+	1.12381i
$137$			199.396i			1.45544i	0.685872	+	0.727722i	$0.259421\pi$
$137$			199.396i			1.45544i	−0.685872	+	0.727722i	$0.740579\pi$
$138$		0			0
$139$		−	99.4908i		−	0.715761i	−0.933767	−	0.357881i	$-0.883499\pi$
$139$		−	99.4908i		−	0.715761i	0.933767	−	0.357881i	$-0.116501\pi$
$140$	−142.605	−	205.045i	−1.01861	−	1.46460i
$141$		0			0
$142$	129.407	+	67.6263i	0.911314	+	0.476242i
$143$		−	16.1932i		−	0.113239i
$144$		0			0
$145$	−266.168			−1.83564
$146$	8.08575	−	15.4725i	0.0553818	−	0.105976i
$147$		0			0
$148$	82.0128	−	57.0385i	0.554141	−	0.385395i
$149$	−100.085			−0.671714			−0.335857	−	0.941913i	$-0.609026\pi$
$149$	−100.085			−0.671714			−0.335857	+	0.941913i	$0.609026\pi$
$150$		0			0
$151$	−185.788			−1.23038			−0.615190	−	0.788379i	$-0.710921\pi$
$151$	−185.788			−1.23038			−0.615190	+	0.788379i	$0.710921\pi$
$152$	1.87639	+	14.7973i	0.0123447	+	0.0973505i
$153$		0			0
$154$	−18.1355	+	34.7033i	−0.117763	+	0.225346i
$155$	126.343			0.815113
$156$		0			0
$157$		−	201.575i		−	1.28392i	−0.766739	−	0.641959i	$-0.778122\pi$
$157$		−	201.575i		−	1.28392i	0.766739	−	0.641959i	$-0.221878\pi$
$158$	−3.55596	+	6.80451i	−0.0225061	+	0.0430665i
$159$		0			0
$160$	115.678	+	128.271i	0.722985	+	0.801694i
$161$		−	351.355i		−	2.18233i
$162$		0			0
$163$			19.8645i			0.121868i	0.998142	+	0.0609340i	$0.0194079\pi$
$163$			19.8645i			0.121868i	−0.998142	+	0.0609340i	$0.980592\pi$
$164$	225.926	−	157.127i	1.37760	−	0.958094i
$165$		0			0
$166$	−34.3224	+	65.6776i	−0.206761	+	0.395648i
$167$		−	22.3225i		−	0.133668i	−0.997764	−	0.0668338i	$-0.978710\pi$
$167$		−	22.3225i		−	0.133668i	0.997764	−	0.0668338i	$-0.0212897\pi$
$168$		0			0
$169$	77.4579			0.458331
$170$	−184.254	−	96.2892i	−1.08385	−	0.566407i
$171$		0			0
$172$	274.788	−	191.110i	1.59760	−	1.11110i
$173$	262.476			1.51720			0.758602	−	0.651555i	$-0.225883\pi$
$173$	262.476			1.51720			0.758602	+	0.651555i	$0.225883\pi$
$174$		0			0
$175$	47.8388			0.273365
$176$	9.42330	−	25.3871i	0.0535415	−	0.144245i
$177$		0			0
$178$	76.9487	+	40.2125i	0.432296	+	0.225913i
$179$	88.1037			0.492200			0.246100	−	0.969244i	$-0.420851\pi$
$179$	88.1037			0.492200			0.246100	+	0.969244i	$0.420851\pi$
$180$		0			0
$181$		−	201.568i		−	1.11363i	−0.830635	−	0.556817i	$-0.812022\pi$
$181$		−	201.568i		−	1.11363i	0.830635	−	0.556817i	$-0.187978\pi$
$182$	196.182	+	102.522i	1.07792	+	0.563309i
$183$		0			0
$184$	30.5678	+	241.059i	0.166129	+	1.31010i
$185$			134.805i			0.728675i
$186$		0			0
$187$			32.5934i			0.174296i
$188$	−92.8350	+	64.5651i	−0.493803	+	0.343432i
$189$		0			0
$190$	−17.8388	−	9.32236i	−0.0938885	−	0.0490650i
$191$			28.0880i			0.147058i	0.997293	+	0.0735289i	$0.0234261\pi$
$191$			28.0880i			0.147058i	−0.997293	+	0.0735289i	$0.976574\pi$
$192$		0			0
$193$	265.762			1.37700			0.688502	−	0.725234i	$-0.258269\pi$
$193$	265.762			1.37700			0.688502	+	0.725234i	$0.258269\pi$
$194$	−80.5419	+	154.121i	−0.415164	+	0.794439i
$195$		0			0
$196$	−193.703	−	278.516i	−0.988282	−	1.42100i
$197$	27.9930			0.142096			0.0710482	−	0.997473i	$-0.477366\pi$
$197$	27.9930			0.142096			0.0710482	+	0.997473i	$0.477366\pi$
$198$		0			0
$199$	7.34801			0.0369247			0.0184623	−	0.999830i	$-0.494123\pi$
$199$	7.34801			0.0369247			0.0184623	+	0.999830i	$0.494123\pi$
$200$	−32.8214	+	4.16196i	−0.164107	+	0.0208098i
$201$		0			0
$202$	−47.6263	+	91.1355i	−0.235774	+	0.451166i
$203$	−570.420			−2.80995
$204$		0			0
$205$			371.355i			1.81149i
$206$	43.7641	−	83.7449i	0.212447	−	0.406529i
$207$		0			0
$208$	−143.516	−	53.2711i	−0.689983	−	0.256111i
$209$			3.15557i			0.0150984i
$210$		0			0
$211$			140.678i			0.666719i	0.942800	+	0.333359i	$0.108182\pi$
$211$			140.678i			0.666719i	−0.942800	+	0.333359i	$0.891818\pi$
$212$	140.203	+	201.590i	0.661333	+	0.950898i
$213$		0			0
$214$	69.6191	−	133.220i	0.325323	−	0.622522i
$215$			451.670i			2.10079i
$216$		0			0
$217$	270.762			1.24775
$218$	235.990	+	123.325i	1.08252	+	0.565713i
$219$		0			0
$220$	20.8645	+	30.0000i	0.0948385	+	0.136364i
$221$	184.254			0.833731
$222$		0			0
$223$	−0.593414			−0.00266105			−0.00133052	−	0.999999i	$-0.500424\pi$
$223$	−0.593414			−0.00266105			−0.00133052	+	0.999999i	$0.500424\pi$
$224$	247.906	+	274.895i	1.10672	+	1.22721i
$225$		0			0
$226$	−159.813	−	83.5165i	−0.707138	−	0.369542i
$227$	−381.044			−1.67861			−0.839305	−	0.543661i	$-0.817038\pi$
$227$	−381.044			−1.67861			−0.839305	+	0.543661i	$0.817038\pi$
$228$		0			0
$229$		−	127.458i		−	0.556585i	−0.960496	−	0.278292i	$-0.910232\pi$
$229$		−	127.458i		−	0.556585i	0.960496	−	0.278292i	$-0.0897684\pi$
$230$	−290.608	−	151.868i	−1.26351	−	0.660296i
$231$		0			0
$232$	391.355	−	49.6263i	1.68688	−	0.213907i
$233$		−	427.153i		−	1.83327i	−0.399722	−	0.916636i	$-0.630893\pi$
$233$		−	427.153i		−	1.83327i	0.399722	−	0.916636i	$-0.369107\pi$
$234$		0			0
$235$		−	152.593i		−	0.649334i
$236$	−172.065	−	247.404i	−0.729090	−	1.04832i
$237$		0			0
$238$	−394.872	−	206.355i	−1.65913	−	0.867039i
$239$		−	190.475i		−	0.796965i	−0.917176	−	0.398483i	$-0.869537\pi$
$239$		−	190.475i		−	0.796965i	0.917176	−	0.398483i	$-0.130463\pi$
$240$		0			0
$241$	−2.78024			−0.0115363			−0.00576814	−	0.999983i	$-0.501836\pi$
$241$	−2.78024			−0.0115363			−0.00576814	+	0.999983i	$0.501836\pi$
$242$	−109.431	+	209.401i	−0.452193	+	0.865295i
$243$		0			0
$244$	15.4451	−	10.7418i	0.0632994	−	0.0440236i
$245$	457.799			1.86857
$246$		0			0
$247$	17.8388			0.0722220
$248$	−185.765	+	23.5562i	−0.749053	+	0.0949847i
$249$		0			0
$250$	−104.322	+	199.626i	−0.417289	+	0.798505i
$251$	−100.085			−0.398747			−0.199373	−	0.979924i	$-0.563891\pi$
$251$	−100.085			−0.398747			−0.199373	+	0.979924i	$0.563891\pi$
$252$		0			0
$253$			51.4066i			0.203188i
$254$	−103.150	+	197.383i	−0.406103	+	0.777099i
$255$		0			0
$256$	−194.000	−	167.033i	−0.757812	−	0.652472i
$257$			344.719i			1.34132i	0.741765	+	0.670660i	$0.233989\pi$
$257$			344.719i			1.34132i	−0.741765	+	0.670660i	$0.766011\pi$
$258$		0			0
$259$			288.897i			1.11543i
$260$	169.594	−	117.949i	0.652283	−	0.453651i
$261$		0			0
$262$	85.6776	−	163.949i	0.327014	−	0.625758i
$263$			169.801i			0.645632i	0.946462	+	0.322816i	$0.104630\pi$
$263$			169.801i			0.645632i	−0.946462	+	0.322816i	$0.895370\pi$
$264$		0			0
$265$	−331.355			−1.25040
$266$	−38.2300	−	19.9785i	−0.143722	−	0.0751073i
$267$		0			0
$268$	−327.775	+	227.962i	−1.22304	+	0.850603i
$269$	−263.666			−0.980173			−0.490086	−	0.871674i	$-0.663035\pi$
$269$	−263.666			−0.980173			−0.490086	+	0.871674i	$0.663035\pi$
$270$		0			0
$271$	55.6849			0.205479			0.102740	−	0.994708i	$-0.467239\pi$
$271$	55.6849			0.205479			0.102740	+	0.994708i	$0.467239\pi$
$272$	288.868	+	107.223i	1.06201	+	0.394203i
$273$		0			0
$274$	353.440	+	184.703i	1.28993	+	0.674100i
$275$	−6.99928			−0.0254519
$276$		0			0
$277$		−	244.051i		−	0.881052i	−0.897740	−	0.440526i	$-0.854792\pi$
$277$		−	244.051i		−	0.881052i	0.897740	−	0.440526i	$-0.145208\pi$
$278$	−176.353	−	92.1598i	−0.634362	−	0.331510i
$279$		0			0
$280$	−495.549	+	62.8388i	−1.76982	+	0.224424i
$281$			123.780i			0.440498i	0.975444	+	0.220249i	$0.0706871\pi$
$281$			123.780i			0.440498i	−0.975444	+	0.220249i	$0.929313\pi$
$282$		0			0
$283$		−	41.5092i		−	0.146676i	−0.997307	−	0.0733378i	$-0.976635\pi$
$283$		−	41.5092i		−	0.146676i	0.997307	−	0.0733378i	$-0.0233651\pi$
$284$	239.742	−	166.737i	0.844164	−	0.587101i
$285$		0			0
$286$	−28.7033	−	15.0000i	−0.100361	−	0.0524476i
$287$			795.843i			2.77297i
$288$		0			0
$289$	−81.8645			−0.283268
$290$	−246.556	+	471.797i	−0.850192	+	1.62689i
$291$		0			0
$292$	−19.9359	−	28.6648i	−0.0682735	−	0.0981672i
$293$	371.985			1.26957			0.634786	−	0.772688i	$-0.281088\pi$
$293$	371.985			1.26957			0.634786	+	0.772688i	$0.281088\pi$
$294$		0			0
$295$	406.659			1.37851
$296$	−25.1340	−	198.208i	−0.0849121	−	0.669620i
$297$		0			0
$298$	−92.7106	+	177.407i	−0.311109	+	0.595324i
$299$	290.608			0.971932
$300$		0			0
$301$			967.963i			3.21582i
$302$	−172.098	+	329.318i	−0.569860	+	1.09046i
$303$		0			0
$304$	27.9671	+	10.3809i	0.0919969	+	0.0341478i
$305$			25.3871i			0.0832365i
$306$		0			0
$307$			215.033i			0.700433i	0.936669	+	0.350216i	$0.113892\pi$
$307$			215.033i			0.700433i	−0.936669	+	0.350216i	$0.886108\pi$
$308$	44.7142	+	64.2923i	0.145176	+	0.208741i
$309$		0			0
$310$	117.033	−	223.949i	0.377526	−	0.722415i
$311$		−	200.539i		−	0.644819i	−0.946600	−	0.322409i	$-0.895507\pi$
$311$		−	200.539i		−	0.644819i	0.946600	−	0.322409i	$-0.104493\pi$
$312$		0			0
$313$	142.033			0.453779			0.226890	−	0.973920i	$-0.427144\pi$
$313$	142.033			0.453779			0.226890	+	0.973920i	$0.427144\pi$
$314$	−357.302	−	186.722i	−1.13791	−	0.594656i
$315$		0			0
$316$	8.76742	+	12.6062i	0.0277450	+	0.0398932i
$317$	3.20309			0.0101044			0.00505219	−	0.999987i	$-0.498392\pi$
$317$	3.20309			0.0101044			0.00505219	+	0.999987i	$0.498392\pi$
$318$		0			0
$319$	83.4579			0.261623
$320$	334.521	−	86.2253i	1.04538	−	0.269454i
$321$		0			0
$322$	−622.795	−	325.465i	−1.93415	−	1.01076i
$323$	−35.9057			−0.111163
$324$		0			0
$325$			39.5678i			0.121747i
$326$	35.2108	+	18.4008i	0.108009	+	0.0564440i
$327$		0			0
$328$	−69.2381	−	546.015i	−0.211092	−	1.66468i
$329$		−	327.020i		−	0.993981i
$330$		0			0
$331$		−	328.136i		−	0.991346i	−0.868509	−	0.495673i	$-0.834921\pi$
$331$		−	328.136i		−	0.991346i	0.868509	−	0.495673i	$-0.165079\pi$
$332$	84.6237	+	121.676i	0.254891	+	0.366495i
$333$		0			0
$334$	−39.5678	−	20.6776i	−0.118466	−	0.0619091i
$335$		−	538.765i		−	1.60825i
$336$		0			0
$337$	430.678			1.27798			0.638988	−	0.769217i	$-0.279354\pi$
$337$	430.678			1.27798			0.638988	+	0.769217i	$0.279354\pi$
$338$	71.7504	−	137.298i	0.212279	−	0.406208i
$339$		0			0
$340$	−341.355	+	237.407i	−1.00399	+	0.698255i
$341$	−39.6151			−0.116173
$342$		0			0
$343$	414.278			1.20781
$344$	−84.2125	−	664.103i	−0.244804	−	1.93053i
$345$		0			0
$346$	243.136	−	465.253i	0.702704	−	1.34466i
$347$	−152.418			−0.439244			−0.219622	−	0.975585i	$-0.570482\pi$
$347$	−152.418			−0.439244			−0.219622	+	0.975585i	$0.570482\pi$
$348$		0			0
$349$		−	370.718i		−	1.06223i	−0.847300	−	0.531114i	$-0.821773\pi$
$349$		−	370.718i		−	1.06223i	0.847300	−	0.531114i	$-0.178227\pi$
$350$	44.3138	−	84.7968i	0.126611	−	0.242277i
$351$		0			0
$352$	−36.2711	−	40.2198i	−0.103043	−	0.114261i
$353$		−	64.7728i		−	0.183492i	−0.995782	−	0.0917462i	$-0.970755\pi$
$353$		−	64.7728i		−	0.183492i	0.995782	−	0.0917462i	$-0.0292448\pi$
$354$		0			0
$355$			394.066i			1.11004i
$356$	142.557	−	99.1462i	0.400442	−	0.278500i
$357$		0			0
$358$	81.6118	−	156.168i	0.227966	−	0.436225i
$359$		−	375.093i		−	1.04483i	−0.852692	−	0.522414i	$-0.825032\pi$
$359$		−	375.093i		−	1.04483i	0.852692	−	0.522414i	$-0.174968\pi$
$360$		0			0
$361$	357.524			0.990370
$362$	−357.289	−	186.715i	−0.986987	−	0.515788i
$363$		0			0
$364$	363.452	−	252.775i	0.998495	−	0.694436i
$365$	47.1165			0.129086
$366$		0			0
$367$	367.839			1.00229			0.501143	−	0.865365i	$-0.332913\pi$
$367$	367.839			1.00229			0.501143	+	0.865365i	$0.332913\pi$
$368$	455.604	+	169.113i	1.23806	+	0.459547i
$369$		0			0
$370$	238.949	+	124.872i	0.645807	+	0.337491i
$371$	−710.120			−1.91407
$372$		0			0
$373$		−	247.128i		−	0.662542i	−0.943536	−	0.331271i	$-0.892523\pi$
$373$		−	247.128i		−	0.662542i	0.943536	−	0.331271i	$-0.107477\pi$
$374$	57.7735	+	30.1918i	0.154475	+	0.0807266i
$375$		0			0
$376$	28.4506	+	224.363i	0.0756665	+	0.596709i
$377$		−	471.797i		−	1.25145i
$378$		0			0
$379$		−	401.776i		−	1.06010i	−0.847968	−	0.530048i	$-0.822174\pi$
$379$		−	401.776i		−	1.06010i	0.847968	−	0.530048i	$-0.177826\pi$
$380$	−33.0487	+	22.9848i	−0.0869703	+	0.0604863i
$381$		0			0
$382$	49.7875	+	26.0184i	0.130334	+	0.0681109i
$383$			319.475i			0.834138i	0.908875	+	0.417069i	$0.136943\pi$
$383$			319.475i			0.834138i	−0.908875	+	0.417069i	$0.863057\pi$
$384$		0			0
$385$	−105.678			−0.274487
$386$	246.179	−	471.077i	0.637770	−	1.22041i
$387$		0			0
$388$	198.581	+	285.529i	0.511806	+	0.735900i
$389$	−213.802			−0.549618			−0.274809	−	0.961499i	$-0.588615\pi$
$389$	−213.802			−0.549618			−0.274809	+	0.961499i	$0.588615\pi$
$390$		0			0
$391$	−584.930			−1.49599
$392$	−673.115	+	85.3553i	−1.71713	+	0.217743i
$393$		0			0
$394$	25.9303	−	49.6191i	0.0658130	−	0.125937i
$395$	−20.7209			−0.0524581
$396$		0			0
$397$			421.136i			1.06079i	0.847749	+	0.530397i	$0.177957\pi$
$397$			421.136i			1.06079i	−0.847749	+	0.530397i	$0.822043\pi$
$398$	6.80657	−	13.0247i	0.0171019	−	0.0327254i
$399$		0			0
$400$	−23.0256	+	62.0329i	−0.0575641	+	0.155082i
$401$		−	203.097i		−	0.506476i	−0.967404	−	0.253238i	$-0.918504\pi$
$401$		−	203.097i		−	0.506476i	0.967404	−	0.253238i	$-0.0814956\pi$
$402$		0			0
$403$			223.949i			0.555704i
$404$	117.425	+	168.840i	0.290657	+	0.417922i
$405$		0			0
$406$	−528.388	+	1011.10i	−1.30145	+	2.49039i
$407$		−	42.2685i		−	0.103854i
$408$		0			0
$409$	−622.267			−1.52144			−0.760718	−	0.649083i	$-0.775153\pi$
$409$	−622.267			−1.52144			−0.760718	+	0.649083i	$0.775153\pi$
$410$	658.247	+	343.992i	1.60548	+	0.839005i
$411$		0			0
$412$	−107.903	−	155.148i	−0.261900	−	0.376574i
$413$	871.503			2.11018
$414$		0			0
$415$	−200.000			−0.481928
$416$	−227.367	+	205.045i	−0.546556	+	0.492896i
$417$		0			0
$418$	5.59341	+	2.92305i	0.0133814	+	0.00699295i
$419$	271.397			0.647726			0.323863	−	0.946104i	$-0.395018\pi$
$419$	271.397			0.647726			0.323863	+	0.946104i	$0.395018\pi$
$420$		0			0
$421$		−	610.381i		−	1.44984i	−0.688835	−	0.724918i	$-0.741878\pi$
$421$		−	610.381i		−	1.44984i	0.688835	−	0.724918i	$-0.258122\pi$
$422$	249.358	+	130.312i	0.590897	+	0.308796i
$423$		0			0
$424$	487.201	−	61.7802i	1.14906	−	0.145708i
$425$		−	79.6414i		−	0.187391i
$426$		0			0
$427$			54.4066i			0.127416i
$428$	−171.650	−	246.807i	−0.401051	−	0.576651i
$429$		0			0
$430$	800.608	+	418.388i	1.86188	+	0.972996i
$431$		−	303.282i		−	0.703669i	−0.936062	−	0.351835i	$-0.885558\pi$
$431$		−	303.282i		−	0.703669i	0.936062	−	0.351835i	$-0.114442\pi$
$432$		0			0
$433$	224.659			0.518844			0.259422	−	0.965764i	$-0.416468\pi$
$433$	224.659			0.518844			0.259422	+	0.965764i	$0.416468\pi$
$434$	250.811	−	479.940i	0.577905	−	1.10585i
$435$		0			0
$436$	437.201	−	304.066i	1.00276	−	0.697399i
$437$	−56.6307			−0.129590
$438$		0			0
$439$	−828.930			−1.88822			−0.944112	−	0.329625i	$-0.893078\pi$
$439$	−828.930			−1.88822			−0.944112	+	0.329625i	$0.893078\pi$
$440$	72.5036	−	9.19392i	0.164781	−	0.0208953i
$441$		0			0
$442$	170.678	−	326.601i	0.386149	−	0.738916i
$443$	−286.716			−0.647215			−0.323608	−	0.946191i	$-0.604896\pi$
$443$	−286.716			−0.647215			−0.323608	+	0.946191i	$0.604896\pi$
$444$		0			0
$445$			234.322i			0.526567i
$446$	−0.549688	+	1.05186i	−0.00123248	+	0.00235842i
$447$		0			0
$448$	716.905	−	184.788i	1.60023	−	0.412472i
$449$			196.928i			0.438593i	0.975658	+	0.219297i	$0.0703763\pi$
$449$			196.928i			0.438593i	−0.975658	+	0.219297i	$0.929624\pi$
$450$		0			0
$451$		−	116.440i		−	0.258181i
$452$	−296.075	+	205.915i	−0.655032	+	0.455563i
$453$		0			0
$454$	−352.967	+	675.421i	−0.777461	+	1.48771i
$455$			597.408i			1.31299i
$456$		0			0
$457$	7.03293			0.0153893			0.00769467	−	0.999970i	$-0.497551\pi$
$457$	7.03293			0.0153893			0.00769467	+	0.999970i	$0.497551\pi$
$458$	−225.926	−	118.066i	−0.493288	−	0.257786i
$459$		0			0
$460$	−538.388	+	374.440i	−1.17041	+	0.813999i
$461$	−217.282			−0.471326			−0.235663	−	0.971835i	$-0.575726\pi$
$461$	−217.282			−0.471326			−0.235663	+	0.971835i	$0.575726\pi$
$462$		0			0
$463$	−538.344			−1.16273			−0.581365	−	0.813643i	$-0.697481\pi$
$463$	−538.344			−1.16273			−0.581365	+	0.813643i	$0.697481\pi$
$464$	274.553	−	739.667i	0.591709	−	1.59411i
$465$		0			0
$466$	−757.150	−	395.678i	−1.62479	−	0.849094i
$467$	612.637			1.31186			0.655928	−	0.754824i	$-0.272278\pi$
$467$	612.637			1.31186			0.655928	+	0.754824i	$0.272278\pi$
$468$		0			0
$469$		−	1154.62i		−	2.46187i
$470$	−270.480	−	141.350i	−0.575489	−	0.300744i
$471$		0			0
$472$	−597.923	+	75.8205i	−1.26679	+	0.160637i
$473$		−	141.622i		−	0.299413i
$474$		0			0
$475$		−	7.71057i		−	0.0162328i
$476$	−731.551	+	508.781i	−1.53687	+	1.06887i
$477$		0			0
$478$	−337.626	−	176.440i	−0.706331	−	0.369120i
$479$			103.652i			0.216393i	0.994130	+	0.108196i	$0.0345076\pi$
$479$			103.652i			0.216393i	−0.994130	+	0.108196i	$0.965492\pi$
$480$		0			0
$481$	−238.949			−0.496775
$482$	−2.57538	+	4.92812i	−0.00534311	+	0.0102243i
$483$		0			0
$484$	269.808	+	387.943i	0.557454	+	0.801535i
$485$	−469.326			−0.967682
$486$		0			0
$487$	163.516			0.335763			0.167881	−	0.985807i	$-0.446307\pi$
$487$	163.516			0.335763			0.167881	+	0.985807i	$0.446307\pi$
$488$	−4.73336	−	37.3274i	−0.00969950	−	0.0764906i
$489$		0			0
$490$	424.066	−	811.472i	0.865441	−	1.65607i
$491$	770.543			1.56933			0.784667	−	0.619917i	$-0.212834\pi$
$491$	770.543			1.56933			0.784667	+	0.619917i	$0.212834\pi$
$492$		0			0
$493$			949.626i			1.92622i
$494$	16.5244	−	31.6202i	0.0334501	−	0.0640086i
$495$		0			0
$496$	−130.322	+	351.099i	−0.262747	+	0.707860i
$497$			844.514i			1.69922i
$498$		0			0
$499$		−	345.253i		−	0.691889i	−0.938255	−	0.345945i	$-0.887559\pi$
$499$		−	345.253i		−	0.691889i	0.938255	−	0.345945i	$-0.112441\pi$
$500$	257.213	+	369.834i	0.514426	+	0.739667i
$501$		0			0
$502$	−92.7106	+	177.407i	−0.184682	+	0.353400i
$503$		−	358.445i		−	0.712614i	−0.934369	−	0.356307i	$-0.884036\pi$
$503$		−	358.445i		−	0.712614i	0.934369	−	0.356307i	$-0.115964\pi$
$504$		0			0
$505$	−277.524			−0.549552
$506$	91.1209	+	47.6187i	0.180081	+	0.0941081i
$507$		0			0
$508$	254.322	+	365.678i	0.500635	+	0.719838i
$509$	−403.367			−0.792469			−0.396235	−	0.918149i	$-0.629683\pi$
$509$	−403.367			−0.792469			−0.396235	+	0.918149i	$0.629683\pi$
$510$		0			0
$511$	100.974			0.197601
$512$	−475.780	+	189.150i	−0.929257	+	0.369434i
$513$		0			0
$514$	611.033	+	319.319i	1.18878	+	0.621242i
$515$	255.018			0.495181
$516$		0			0
$517$			47.8461i			0.0925457i
$518$	512.086	+	267.610i	0.988582	+	0.516621i
$519$		0			0
$520$	−51.9744	−	409.872i	−0.0999507	−	0.788215i
$521$			835.047i			1.60278i	0.598144	+	0.801389i	$0.295905\pi$
$521$			835.047i			1.60278i	−0.598144	+	0.801389i	$0.704095\pi$
$522$		0			0
$523$		−	21.1539i		−	0.0404472i	−0.999795	−	0.0202236i	$-0.993562\pi$
$523$		−	21.1539i		−	0.0404472i	0.999795	−	0.0202236i	$-0.00643781\pi$
$524$	−211.243	−	303.736i	−0.403136	−	0.579649i
$525$		0			0
$526$	300.982	+	157.289i	0.572208	+	0.299029i
$527$		−	450.760i		−	0.855333i
$528$		0			0
$529$	−393.557			−0.743963
$530$	−306.939	+	587.345i	−0.579131	+	1.10820i
$531$		0			0
$532$	−70.8260	+	49.2582i	−0.133132	+	0.0925907i
$533$	−658.247			−1.23498
$534$		0			0
$535$	405.678			0.758276
$536$	100.451	+	792.162i	0.187409	+	1.47791i
$537$		0			0
$538$	−244.238	+	467.363i	−0.453974	+	0.868704i
$539$	−143.544			−0.266316
$540$		0			0
$541$		−	130.718i		−	0.241623i	−0.992675	−	0.120811i	$-0.961450\pi$
$541$		−	130.718i		−	0.241623i	0.992675	−	0.120811i	$-0.0385496\pi$
$542$	51.5818	−	98.7044i	0.0951693	−	0.182112i
$543$		0			0
$544$	457.641	−	412.711i	0.841252	−	0.758659i
$545$			718.630i			1.31859i
$546$		0			0
$547$		−	544.963i		−	0.996277i	−0.867098	−	0.498138i	$-0.834017\pi$
$547$		−	544.963i		−	0.996277i	0.867098	−	0.498138i	$-0.165983\pi$
$548$	654.792	−	455.397i	1.19488	−	0.831016i
$549$		0			0
$550$	−6.48353	+	12.4066i	−0.0117882	+	0.0225574i
$551$			91.9392i			0.166859i
$552$		0			0
$553$	−44.4066			−0.0803012
$554$	−432.594	−	226.068i	−0.780855	−	0.408066i
$555$		0			0
$556$	−326.716	+	227.225i	−0.587619	+	0.408679i
$557$	−796.393			−1.42979			−0.714895	−	0.699232i	$-0.753526\pi$
$557$	−796.393			−1.42979			−0.714895	+	0.699232i	$0.753526\pi$
$558$		0			0
$559$	−800.608			−1.43221
$560$	−347.650	+	936.596i	−0.620803	+	1.67249i
$561$		0			0
$562$	219.407	+	114.659i	0.390403	+	0.204020i
$563$	519.646			0.922994			0.461497	−	0.887142i	$-0.347313\pi$
$563$	519.646			0.922994			0.461497	+	0.887142i	$0.347313\pi$
$564$		0			0
$565$		−	486.659i		−	0.861344i
$566$	−73.5772	−	38.4506i	−0.129995	−	0.0679339i
$567$		0			0
$568$	−73.4724	−	579.407i	−0.129353	−	1.02008i
$569$		−	676.128i		−	1.18827i	−0.804364	−	0.594137i	$-0.797494\pi$
$569$		−	676.128i		−	1.18827i	0.804364	−	0.594137i	$-0.202506\pi$
$570$		0			0
$571$			1048.64i			1.83650i	0.396002	+	0.918249i	$0.370397\pi$
$571$			1048.64i			1.83650i	−0.396002	+	0.918249i	$0.629603\pi$
$572$	−53.1766	+	36.9834i	−0.0929660	+	0.0646562i
$573$		0			0
$574$	1410.67	+	737.201i	2.45762	+	1.28432i
$575$		−	125.611i		−	0.218454i
$576$		0			0
$577$	−494.150			−0.856413			−0.428206	−	0.903681i	$-0.640854\pi$
$577$	−494.150			−0.856413			−0.428206	+	0.903681i	$0.640854\pi$
$578$	−75.8323	+	145.109i	−0.131198	+	0.251054i
$579$		0			0
$580$	607.897	+	874.066i	1.04810	+	1.50701i
$581$	−428.616			−0.737720
$582$		0			0
$583$	103.897			0.178212
$584$	−69.2768	+	8.78474i	−0.118625	+	0.0150424i
$585$		0			0
$586$	344.575	−	659.363i	0.588012	−	1.12519i
$587$	737.611			1.25658			0.628289	−	0.777980i	$-0.283756\pi$
$587$	737.611			1.25658			0.628289	+	0.777980i	$0.283756\pi$
$588$		0			0
$589$		−	43.6409i		−	0.0740932i
$590$	376.694	−	720.825i	0.638465	−	1.22174i
$591$		0			0
$592$	−374.615	−	139.051i	−0.632796	−	0.234884i
$593$			528.883i			0.891877i	0.895064	+	0.445938i	$0.147130\pi$
$593$			528.883i			0.891877i	−0.895064	+	0.445938i	$0.852870\pi$
$594$		0			0
$595$		−	1202.45i		−	2.02093i
$596$	228.583	+	328.669i	0.383529	+	0.551457i
$597$		0			0
$598$	269.194	−	515.117i	0.450157	−	0.861400i
$599$		−	576.826i		−	0.962982i	−0.876451	−	0.481491i	$-0.840095\pi$
$599$		−	576.826i		−	0.962982i	0.876451	−	0.481491i	$-0.159905\pi$
$600$		0			0
$601$	353.407			0.588031			0.294015	−	0.955801i	$-0.405008\pi$
$601$	353.407			0.588031			0.294015	+	0.955801i	$0.405008\pi$
$602$	1715.77	+	896.639i	2.85011	+	1.48943i
$603$		0			0
$604$	424.317	+	610.104i	0.702511	+	1.01011i
$605$	−637.664			−1.05399
$606$		0			0
$607$	585.634			0.964800			0.482400	−	0.875951i	$-0.339765\pi$
$607$	585.634			0.964800			0.482400	+	0.875951i	$0.339765\pi$
$608$	44.3071	−	39.9571i	0.0728735	−	0.0657189i
$609$		0			0
$610$	45.0000	+	23.5165i	0.0737705	+	0.0385516i
$611$	270.480			0.442684
$612$		0			0
$613$		−	301.282i		−	0.491488i	−0.969335	−	0.245744i	$-0.920968\pi$
$613$		−	301.282i		−	0.491488i	0.969335	−	0.245744i	$-0.0790323\pi$
$614$	381.157	+	199.188i	0.620777	+	0.324411i
$615$		0			0
$616$	155.381	−	19.7033i	0.252242	−	0.0319859i
$617$			203.058i			0.329105i	0.986368	+	0.164552i	$0.0526180\pi$
$617$			203.058i			0.329105i	−0.986368	+	0.164552i	$0.947382\pi$
$618$		0			0
$619$		−	667.879i		−	1.07896i	−0.841997	−	0.539482i	$-0.818620\pi$
$619$		−	667.879i		−	1.07896i	0.841997	−	0.539482i	$-0.181380\pi$
$620$	−288.551	−	414.894i	−0.465406	−	0.669184i
$621$		0			0
$622$	−355.465	−	185.762i	−0.571487	−	0.298653i
$623$			502.171i			0.806053i
$624$		0			0
$625$	−711.286			−1.13806
$626$	131.567	−	251.761i	0.210171	−	0.402174i
$627$		0			0
$628$	−661.949	+	460.374i	−1.05406	+	0.733079i
$629$	480.952			0.764630
$630$		0			0
$631$	874.755			1.38630			0.693149	−	0.720794i	$-0.256223\pi$
$631$	874.755			1.38630			0.693149	+	0.720794i	$0.256223\pi$
$632$	30.4666	−	3.86336i	0.0482066	−	0.00611291i
$633$		0			0
$634$	2.96707	−	5.67764i	0.00467992	−	0.00895527i
$635$	−601.066			−0.946561
$636$		0			0
$637$			811.472i			1.27390i
$638$	77.3083	−	147.933i	0.121173	−	0.231871i
$639$		0			0
$640$	157.033	−	672.828i	0.245364	−	1.05129i
$641$		−	160.738i		−	0.250761i	−0.992109	−	0.125380i	$-0.959985\pi$
$641$		−	160.738i		−	0.250761i	0.992109	−	0.125380i	$-0.0400151\pi$
$642$		0			0
$643$		−	133.949i		−	0.208318i	−0.994561	−	0.104159i	$-0.966785\pi$
$643$		−	133.949i		−	0.208318i	0.994561	−	0.104159i	$-0.0332151\pi$
$644$	−1153.81	+	802.453i	−1.79163	+	1.24605i
$645$		0			0
$646$	−33.2600	+	63.6447i	−0.0514860	+	0.0985212i
$647$			383.417i			0.592607i	0.955094	+	0.296304i	$0.0957540\pi$
$647$			383.417i			0.592607i	−0.955094	+	0.296304i	$0.904246\pi$
$648$		0			0
$649$	−127.509			−0.196470
$650$	70.1359	+	36.6522i	0.107901	+	0.0563880i
$651$		0			0
$652$	65.2326	−	45.3681i	0.100050	−	0.0695830i
$653$	367.323			0.562516			0.281258	−	0.959632i	$-0.409248\pi$
$653$	367.323			0.562516			0.281258	+	0.959632i	$0.409248\pi$
$654$		0			0
$655$	499.253			0.762218
$656$	−1031.98	−	383.053i	−1.57313	−	0.583922i
$657$		0			0
$658$	−579.659	−	302.923i	−0.880941	−	0.460369i
$659$	584.418			0.886826			0.443413	−	0.896317i	$-0.353768\pi$
$659$	584.418			0.886826			0.443413	+	0.896317i	$0.353768\pi$
$660$		0			0
$661$		−	526.059i		−	0.795853i	−0.917417	−	0.397926i	$-0.869730\pi$
$661$		−	526.059i		−	0.795853i	0.917417	−	0.397926i	$-0.130270\pi$
$662$	−581.637	−	303.957i	−0.878606	−	0.459149i
$663$		0			0
$664$	294.066	−	37.2894i	0.442870	−	0.0561588i
$665$		−	116.417i		−	0.175063i
$666$		0			0
$667$			1497.76i			2.24551i
$668$	−73.3044	+	50.9819i	−0.109737	+	0.0763202i
$669$		0			0
$670$	−954.989	−	499.066i	−1.42536	−	0.744874i
$671$		−	7.96021i		−	0.0118632i
$672$		0			0
$673$	952.538			1.41536			0.707681	−	0.706532i	$-0.249742\pi$
$673$	952.538			1.41536			0.707681	+	0.706532i	$0.249742\pi$
$674$	398.943	−	763.399i	0.591904	−	1.13264i
$675$		0			0
$676$	−176.905	−	254.363i	−0.261693	−	0.376276i
$677$	425.772			0.628910			0.314455	−	0.949272i	$-0.398178\pi$
$677$	425.772			0.628910			0.314455	+	0.949272i	$0.398178\pi$
$678$		0			0
$679$	−1005.80			−1.48130
$680$	104.613	+	824.983i	0.153843	+	1.21321i
$681$		0			0
$682$	−36.6960	+	70.2198i	−0.0538065	+	0.102962i
$683$	−319.752			−0.468158			−0.234079	−	0.972218i	$-0.575207\pi$
$683$	−319.752			−0.468158			−0.234079	+	0.972218i	$0.575207\pi$
$684$		0			0
$685$			1076.29i			1.57122i
$686$	383.752	−	734.330i	0.559405	−	1.07045i
$687$		0			0
$688$	−1255.16	−	465.897i	−1.82437	−	0.677176i
$689$		−	587.345i		−	0.852459i
$690$		0			0
$691$			152.454i			0.220628i	0.993897	+	0.110314i	$0.0351857\pi$
$691$			152.454i			0.220628i	−0.993897	+	0.110314i	$0.964814\pi$
$692$	−599.465	−	861.941i	−0.866278	−	1.24558i
$693$		0			0
$694$	−141.187	+	270.168i	−0.203439	+	0.389292i
$695$		−	537.025i		−	0.772698i
$696$		0			0
$697$	1324.91			1.90087
$698$	−657.117	−	343.401i	−0.941428	−	0.491979i
$699$		0			0
$700$	−109.258	−	157.097i	−0.156083	−	0.224424i
$701$	−376.643			−0.537294			−0.268647	−	0.963239i	$-0.586576\pi$
$701$	−376.643			−0.537294			−0.268647	+	0.963239i	$0.586576\pi$
$702$		0			0
$703$	46.5640			0.0662361
$704$	−104.890	+	27.0362i	−0.148992	+	0.0384037i
$705$		0			0
$706$	−114.813	−	60.0000i	−0.162625	−	0.0849858i
$707$	−594.755			−0.841238
$708$		0			0
$709$			3.09151i			0.00436038i	0.999998	+	0.00218019i	$0.000693977\pi$
$709$			3.09151i			0.00436038i	−0.999998	+	0.00218019i	$0.999306\pi$
$710$	698.502	+	365.029i	0.983806	+	0.514125i
$711$		0			0
$712$	−43.6887	−	344.531i	−0.0613606	−	0.483892i
$713$		−	710.943i		−	0.997115i
$714$		0			0
$715$		−	87.4066i		−	0.122247i
$716$	−201.219	−	289.322i	−0.281031	−	0.404081i
$717$		0			0
$718$	−664.872	−	347.454i	−0.926005	−	0.483919i
$719$		−	1103.79i		−	1.53517i	−0.640947	−	0.767585i	$-0.721458\pi$
$719$		−	1103.79i		−	1.53517i	0.640947	−	0.767585i	$-0.278542\pi$
$720$		0			0
$721$	546.524			0.758008
$722$	331.179	−	633.729i	0.458697	−	0.877742i
$723$		0			0
$724$	−661.925	+	460.357i	−0.914261	+	0.635852i
$725$	−203.928			−0.281280
$726$		0			0
$727$	−788.051			−1.08398			−0.541989	−	0.840386i	$-0.682328\pi$
$727$	−788.051			−1.08398			−0.541989	+	0.840386i	$0.682328\pi$
$728$	−111.385	−	878.387i	−0.153001	−	1.20658i
$729$		0			0
$730$	43.6447	−	83.5165i	0.0597873	−	0.114406i
$731$	1611.45			2.20445
$732$		0			0
$733$			678.996i			0.926325i	0.886273	+	0.463162i	$0.153285\pi$
$733$			678.996i			0.926325i	−0.886273	+	0.463162i	$0.846715\pi$
$734$	340.735	−	652.013i	0.464216	−	0.888302i
$735$		0			0
$736$	721.795	−	650.930i	0.980699	−	0.884416i
$737$			168.931i			0.229215i
$738$		0			0
$739$			789.744i			1.06867i	0.845274	+	0.534333i	$0.179437\pi$
$739$			789.744i			1.06867i	−0.845274	+	0.534333i	$0.820563\pi$
$740$	442.683	−	307.878i	0.598221	−	0.416052i
$741$		0			0
$742$	−657.795	+	1258.73i	−0.886516	+	1.69640i
$743$		−	216.641i		−	0.291576i	−0.989316	−	0.145788i	$-0.953428\pi$
$743$		−	216.641i		−	0.291576i	0.989316	−	0.145788i	$-0.0465717\pi$
$744$		0			0
$745$	−540.234			−0.725147
$746$	−438.048	−	228.919i	−0.587195	−	0.306861i
$747$		0			0
$748$	107.033	−	74.4395i	0.143092	−	0.0995181i
$749$	869.399			1.16075
$750$		0			0
$751$	932.681			1.24192			0.620959	−	0.783843i	$-0.286743\pi$
$751$	932.681			1.24192			0.620959	+	0.783843i	$0.286743\pi$
$752$	424.049	+	157.400i	0.563894	+	0.209309i
$753$		0			0
$754$	−836.286	−	437.033i	−1.10913	−	0.579619i
$755$	−1002.83			−1.32825
$756$		0			0
$757$		−	361.451i		−	0.477478i	−0.971084	−	0.238739i	$-0.923266\pi$
$757$		−	361.451i		−	0.477478i	0.971084	−	0.238739i	$-0.0767340\pi$
$758$	−712.170	−	372.171i	−0.939538	−	0.490991i
$759$		0			0
$760$	10.1282	+	79.8718i	0.0133266	+	0.105094i
$761$			883.718i			1.16126i	0.814168	+	0.580629i	$0.197193\pi$
$761$			883.718i			1.16126i	−0.814168	+	0.580629i	$0.802807\pi$
$762$		0			0
$763$			1540.08i			2.01845i
$764$	92.2378	−	64.1498i	0.120730	−	0.0839657i
$765$		0			0
$766$	566.286	+	295.934i	0.739276	+	0.386337i
$767$			720.825i			0.939798i
$768$		0			0
$769$	−177.103			−0.230302			−0.115151	−	0.993348i	$-0.536735\pi$
$769$	−177.103			−0.230302			−0.115151	+	0.993348i	$0.536735\pi$
$770$	−97.8908	+	187.319i	−0.127131	+	0.243272i
$771$		0			0
$772$	−606.969	−	872.731i	−0.786229	−	1.13048i
$773$	327.067			0.423114			0.211557	−	0.977366i	$-0.432147\pi$
$773$	327.067			0.423114			0.211557	+	0.977366i	$0.432147\pi$
$774$		0			0
$775$	96.7986			0.124901
$776$	690.064	−	87.5045i	0.889257	−	0.112763i
$777$		0			0
$778$	−198.047	+	378.974i	−0.254560	+	0.487114i
$779$	128.273			0.164663
$780$		0			0
$781$		−	123.560i		−	0.158208i
$782$	−541.830	+	1036.82i	−0.692877	+	1.32586i
$783$		0			0
$784$	−472.220	+	1272.20i	−0.602321	+	1.62270i
$785$		−	1088.05i		−	1.38605i
$786$		0			0
$787$		−	884.033i		−	1.12329i	−0.827377	−	0.561647i	$-0.810168\pi$
$787$		−	884.033i		−	1.12329i	0.827377	−	0.561647i	$-0.189832\pi$
$788$	−63.9327	−	91.9257i	−0.0811329	−	0.116657i
$789$		0			0
$790$	−19.1941	+	36.7289i	−0.0242963	+	0.0464923i
$791$		−	1042.95i		−	1.31852i
$792$		0			0
$793$	−45.0000			−0.0567465
$794$	746.485	+	390.104i	0.940157	+	0.491315i
$795$		0			0
$796$	−16.7820	−	24.1300i	−0.0210829	−	0.0303141i
$797$	−1262.52			−1.58409			−0.792043	−	0.610466i	$-0.790982\pi$
$797$	−1262.52			−1.58409			−0.792043	+	0.610466i	$0.790982\pi$
$798$		0			0
$799$	−544.417			−0.681373
$800$	88.6276	+	98.2762i	0.110785	+	0.122845i
$801$		0			0
$802$	−360.000	−	188.132i	−0.448878	−	0.234578i
$803$	−14.7735			−0.0183979
$804$		0			0
$805$		−	1896.52i		−	2.35593i
$806$	396.961	+	207.447i	0.492507	+	0.257378i
$807$		0			0
$808$	408.051	−	51.7435i	0.505014	−	0.0640390i
$809$			1136.54i			1.40487i	0.711750	+	0.702433i	$0.247903\pi$
$809$			1136.54i			1.40487i	−0.711750	+	0.702433i	$0.752097\pi$
$810$		0			0
$811$		−	245.509i		−	0.302724i	−0.988478	−	0.151362i	$-0.951634\pi$
$811$		−	245.509i		−	0.302724i	0.988478	−	0.151362i	$-0.0483659\pi$
$812$	1302.77	+	1873.19i	1.60440	+	2.30689i
$813$		0			0
$814$	−74.9231	−	39.1539i	−0.0920431	−	0.0481006i
$815$			107.223i			0.131562i
$816$		0			0
$817$	156.015			0.190960
$818$	−576.415	+	1103.00i	−0.704664	+	1.34841i
$819$		0			0
$820$	1219.49	−	848.132i	1.48718	−	1.03431i
$821$	−733.724			−0.893695			−0.446848	−	0.894610i	$-0.647453\pi$
$821$	−733.724			−0.893695			−0.446848	+	0.894610i	$0.647453\pi$
$822$		0			0
$823$	1289.78			1.56717			0.783584	−	0.621285i	$-0.213389\pi$
$823$	1289.78			1.56717			0.783584	+	0.621285i	$0.213389\pi$
$824$	−374.961	+	47.5474i	−0.455049	+	0.0577032i
$825$		0			0
$826$	807.286	−	1544.78i	0.977343	−	1.87020i
$827$	468.729			0.566782			0.283391	−	0.959004i	$-0.408541\pi$
$827$	468.729			0.566782			0.283391	+	0.959004i	$0.408541\pi$
$828$		0			0
$829$			1356.65i			1.63649i	0.574868	+	0.818246i	$0.305053\pi$
$829$			1356.65i			1.63649i	−0.574868	+	0.818246i	$0.694947\pi$
$830$	−185.263	+	354.510i	−0.223208	+	0.427121i
$831$		0			0
$832$	152.839	+	592.956i	0.183701	+	0.712687i
$833$		−	1633.32i		−	1.96077i
$834$		0			0
$835$		−	120.491i		−	0.144300i
$836$	10.3625	−	7.20695i	0.0123954	−	0.00862076i
$837$		0			0
$838$	251.399	−	481.066i	0.299999	−	0.574064i
$839$			1196.01i			1.42552i	0.701408	+	0.712760i	$0.252555\pi$
$839$			1196.01i			1.42552i	−0.701408	+	0.712760i	$0.747445\pi$
$840$		0			0
$841$	1590.59			1.89131
$842$	−1081.93	−	565.405i	−1.28495	−	0.671502i
$843$		0			0
$844$	461.969	−	321.291i	0.547356	−	0.380677i
$845$	418.097			0.494789
$846$		0			0
$847$	−1366.56			−1.61342
$848$	341.793	−	920.818i	0.403058	−	1.08587i
$849$		0			0
$850$	−141.168	−	73.7730i	−0.166081	−	0.0867917i
$851$	758.561			0.891376
$852$		0			0
$853$			310.242i			0.363706i	0.983326	+	0.181853i	$0.0582096\pi$
$853$			310.242i			0.363706i	−0.983326	+	0.181853i	$0.941790\pi$
$854$	96.4385	+	50.3976i	0.112926	+	0.0590136i
$855$		0			0
$856$	−596.480	+	75.6374i	−0.696822	+	0.0883615i
$857$			1253.46i			1.46261i	0.682048	+	0.731307i	$0.261089\pi$
$857$			1253.46i			1.46261i	−0.682048	+	0.731307i	$0.738911\pi$
$858$		0			0
$859$		−	979.740i		−	1.14056i	−0.821451	−	0.570279i	$-0.806835\pi$
$859$		−	979.740i		−	1.14056i	0.821451	−	0.570279i	$-0.193165\pi$
$860$	1483.23	−	1031.56i	1.72469	−	1.19949i
$861$		0			0
$862$	−537.582	−	280.934i	−0.623645	−	0.325910i
$863$		−	1240.83i		−	1.43781i	−0.695111	−	0.718903i	$-0.744645\pi$
$863$		−	1240.83i		−	1.43781i	0.695111	−	0.718903i	$-0.255355\pi$
$864$		0			0
$865$	1416.78			1.63789
$866$	208.105	−	398.220i	0.240306	−	0.459839i
$867$		0			0
$868$	−618.388	−	889.150i	−0.712429	−	1.02437i
$869$	6.49711			0.00747654
$870$		0			0
$871$	954.989			1.09643
$872$	−133.987	−	1056.62i	−0.153654	−	1.21172i
$873$		0			0
$874$	−52.4579	+	100.381i	−0.0600205	+	0.114852i
$875$	−1302.77			−1.48888
$876$		0			0
$877$			320.586i			0.365549i	0.983155	+	0.182774i	$0.0585078\pi$
$877$			320.586i			0.365549i	−0.983155	+	0.182774i	$0.941492\pi$
$878$	−767.850	+	1469.32i	−0.874545	+	1.67349i
$879$		0			0
$880$	50.8645	−	137.033i	0.0578005	−	0.155719i
$881$			208.356i			0.236500i	0.992984	+	0.118250i	$0.0377284\pi$
$881$			208.356i			0.236500i	−0.992984	+	0.118250i	$0.962272\pi$
$882$		0			0
$883$			624.590i			0.707350i	0.935368	+	0.353675i	$0.115068\pi$
$883$			624.590i			0.707350i	−0.935368	+	0.353675i	$0.884932\pi$
$884$	−420.816	−	605.070i	−0.476036	−	0.684468i
$885$		0			0
$886$	−265.590	+	508.220i	−0.299763	+	0.573611i
$887$			1468.63i			1.65573i	0.560926	+	0.827866i	$0.310445\pi$
$887$			1468.63i			1.65573i	−0.560926	+	0.827866i	$0.689555\pi$
$888$		0			0
$889$	−1288.13			−1.44897
$890$	415.349	+	217.056i	0.466684	+	0.243883i
$891$		0			0
$892$	1.35529	+	1.94870i	0.00151938	+	0.00218464i
$893$	−52.7084			−0.0590240
$894$		0			0
$895$	475.560			0.531352
$896$	336.534	−	1441.92i	0.375596	−	1.60929i
$897$		0			0
$898$	349.066	+	182.418i	0.388715	+	0.203138i
$899$	−1154.21			−1.28388
$900$		0			0
$901$			1182.20i			1.31209i
$902$	−206.395	−	107.860i	−0.228819	−	0.119578i
$903$		0			0
$904$	90.7362	+	715.549i	0.100372	+	0.791537i
$905$		−	1088.01i		−	1.20222i
$906$		0			0
$907$			418.333i			0.461227i	0.973045	+	0.230614i	$0.0740733\pi$
$907$			418.333i			0.461227i	−0.973045	+	0.230614i	$0.925927\pi$
$908$	870.261	+	1251.31i	0.958437	+	1.37809i
$909$		0			0
$910$	1058.94	+	553.388i	1.16367	+	0.608119i
$911$		−	69.9928i		−	0.0768307i	−0.999262	−	0.0384154i	$-0.987769\pi$
$911$		−	69.9928i		−	0.0768307i	0.999262	−	0.0384154i	$-0.0122310\pi$
$912$		0			0
$913$	62.7106			0.0686863
$914$	6.51471	−	12.4662i	0.00712769	−	0.0136392i
$915$		0			0
$916$	−418.557	+	291.099i	−0.456940	+	0.317793i
$917$	1069.94			1.16678
$918$		0			0
$919$	1272.39			1.38454			0.692268	−	0.721641i	$-0.256612\pi$
$919$	1272.39			1.38454			0.692268	+	0.721641i	$0.256612\pi$
$920$	164.997	+	1301.17i	0.179344	+	1.41432i
$921$		0			0
$922$	−201.271	+	385.143i	−0.218298	+	0.417725i
$923$	−698.502			−0.756774
$924$		0			0
$925$			103.282i			0.111656i
$926$	−498.676	+	954.243i	−0.538527	+	1.03050i
$927$		0			0
$928$	−1056.78	−	1171.82i	−1.13877	−	1.26274i
$929$		−	675.361i		−	0.726977i	−0.931599	−	0.363488i	$-0.881586\pi$
$929$		−	675.361i		−	0.726977i	0.931599	−	0.363488i	$-0.118414\pi$
$930$		0			0
$931$		−	158.132i		−	0.169851i
$932$	−1402.72	+	975.566i	−1.50506	+	1.04674i
$933$		0			0
$934$	567.494	−	1085.93i	0.607596	−	1.16267i
$935$			175.931i			0.188161i
$936$		0			0
$937$	−1790.67			−1.91107			−0.955534	−	0.294882i	$-0.904720\pi$
$937$	−1790.67			−1.91107			−0.955534	+	0.294882i	$0.904720\pi$
$938$	−2046.62	−	1069.54i	−2.18189	−	1.14023i
$939$		0			0
$940$	−501.099	+	348.505i	−0.533084	+	0.370750i
$941$	399.697			0.424758			0.212379	−	0.977187i	$-0.431879\pi$
$941$	399.697			0.424758			0.212379	+	0.977187i	$0.431879\pi$
$942$		0			0
$943$	2089.66			2.21597
$944$	−419.469	+	1130.08i	−0.444353	+	1.19712i
$945$		0			0
$946$	−251.033	−	131.187i	−0.265363	−	0.138675i
$947$	88.0644			0.0929931			0.0464965	−	0.998918i	$-0.485194\pi$
$947$	88.0644			0.0929931			0.0464965	+	0.998918i	$0.485194\pi$
$948$		0			0
$949$			83.5165i			0.0880047i
$950$	−13.6674	−	7.14242i	−0.0143867	−	0.00751834i
$951$		0			0
$952$	224.194	+	1768.00i	0.235498	+	1.85715i
$953$			1455.87i			1.52767i	0.645412	+	0.763835i	$0.276686\pi$
$953$			1455.87i			1.52767i	−0.645412	+	0.763835i	$0.723314\pi$
$954$		0			0
$955$			151.612i			0.158756i
$956$	−625.496	+	435.022i	−0.654285	+	0.455044i
$957$		0			0
$958$	183.729	+	96.0146i	0.191784	+	0.100224i
$959$			2306.56i			2.40518i
$960$		0			0
$961$	−413.132			−0.429898
$962$	−221.342	+	423.549i	−0.230085	+	0.440280i
$963$		0			0
$964$	6.34974	+	9.12999i	0.00658687	+	0.00947094i
$965$	1434.51			1.48654
$966$		0			0
$967$	−1118.86			−1.15704			−0.578520	−	0.815668i	$-0.696369\pi$
$967$	−1118.86			−1.15704			−0.578520	+	0.815668i	$0.696369\pi$
$968$	937.576	−	118.891i	0.968571	−	0.122821i
$969$		0			0
$970$	−434.744	+	831.905i	−0.448189	+	0.857634i
$971$	−1097.06			−1.12983			−0.564915	−	0.825149i	$-0.691091\pi$
$971$	−1097.06			−1.12983			−0.564915	+	0.825149i	$0.691091\pi$
$972$		0			0
$973$		−	1150.89i		−	1.18282i
$974$	151.468	−	289.841i	0.155511	−	0.297579i
$975$		0			0
$976$	−70.5494	−	26.1868i	−0.0722842	−	0.0268308i
$977$			590.176i			0.604069i	0.953297	+	0.302035i	$0.0976658\pi$
$977$			590.176i			0.604069i	−0.953297	+	0.302035i	$0.902334\pi$
$978$		0			0
$979$		−	73.4724i		−	0.0750485i
$980$	−1045.56	−	1503.36i	−1.06690	−	1.53404i
$981$		0			0
$982$	713.765	−	1365.83i	0.726849	−	1.39086i
$983$			1408.99i			1.43336i	0.697403	+	0.716679i	$0.254339\pi$
$983$			1408.99i			1.43336i	−0.697403	+	0.716679i	$0.745661\pi$
$984$		0			0
$985$	151.099			0.153400
$986$	1683.26	+	879.653i	1.70716	+	0.892143i
$987$		0			0
$988$	−40.7418	−	58.5806i	−0.0412366	−	0.0592921i
$989$	2541.59			2.56986
$990$		0			0
$991$	−939.516			−0.948049			−0.474024	−	0.880512i	$-0.657199\pi$
$991$	−939.516			−0.948049			−0.474024	+	0.880512i	$0.657199\pi$
$992$	501.621	+	556.231i	0.505667	+	0.560717i
$993$		0			0
$994$	1496.94	+	782.286i	1.50598	+	0.787008i
$995$	39.6626			0.0398619
$996$		0			0
$997$		−	1927.67i		−	1.93347i	−0.255779	−	0.966735i	$-0.582332\pi$
$997$		−	1927.67i		−	1.93347i	0.255779	−	0.966735i	$-0.417668\pi$
$998$	−611.978	−	319.813i	−0.613205	−	0.320454i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.h.f.53.5	yes	8
3.2	odd	2	inner	216.3.h.f.53.4	yes	8
4.3	odd	2		864.3.h.e.593.8		8
8.3	odd	2		864.3.h.e.593.1		8
8.5	even	2	inner	216.3.h.f.53.3	✓	8
12.11	even	2		864.3.h.e.593.2		8
24.5	odd	2	inner	216.3.h.f.53.6	yes	8
24.11	even	2		864.3.h.e.593.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.h.f.53.3	✓	8	8.5	even	2	inner
216.3.h.f.53.4	yes	8	3.2	odd	2	inner
216.3.h.f.53.5	yes	8	1.1	even	1	trivial
216.3.h.f.53.6	yes	8	24.5	odd	2	inner
864.3.h.e.593.1		8	8.3	odd	2
864.3.h.e.593.2		8	12.11	even	2
864.3.h.e.593.7		8	24.11	even	2
864.3.h.e.593.8		8	4.3	odd	2

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.926315 - 1.77255i) q^{2} +(-2.28388 - 3.28388i) q^{4} +5.39773 q^{5} +11.5678 q^{7} +(-7.93645 + 1.00639i) q^{8} +O(q^{10})\)	\(q+(0.926315 - 1.77255i) q^{2} +(-2.28388 - 3.28388i) q^{4} +5.39773 q^{5} +11.5678 q^{7} +(-7.93645 + 1.00639i) q^{8} +(5.00000 - 9.56776i) q^{10} -1.69247 q^{11} +9.56776i q^{13} +(10.7154 - 20.5045i) q^{14} +(-5.56776 + 15.0000i) q^{16} -19.2578i q^{17} -1.86447i q^{19} +(-12.3278 - 17.7255i) q^{20} +(-1.56776 + 3.00000i) q^{22} -30.3736i q^{23} +4.13553 q^{25} +(16.9594 + 8.86276i) q^{26} +(-26.4194 - 37.9872i) q^{28} -49.3112 q^{29} +23.4066 q^{31} +(21.4308 + 23.7639i) q^{32} +(-34.1355 - 17.8388i) q^{34} +62.4397 q^{35} +24.9744i q^{37} +(-3.30487 - 1.72709i) q^{38} +(-42.8388 + 5.43224i) q^{40} +68.7984i q^{41} +83.6776i q^{43} +(3.86541 + 5.55789i) q^{44} +(-53.8388 - 28.1355i) q^{46} -28.2699i q^{47} +84.8132 q^{49} +(3.83080 - 7.33044i) q^{50} +(31.4194 - 21.8516i) q^{52} -61.3879 q^{53} -9.13553 q^{55} +(-91.8069 + 11.6417i) q^{56} +(-45.6776 + 87.4066i) q^{58} +75.3389 q^{59} +4.70329i q^{61} +(21.6819 - 41.4894i) q^{62} +(61.9744 - 15.9744i) q^{64} +51.6442i q^{65} -99.8132i q^{67} +(-63.2405 + 43.9826i) q^{68} +(57.8388 - 110.678i) q^{70} +73.0058i q^{71} +8.72894 q^{73} +(44.2683 + 23.1341i) q^{74} +(-6.12270 + 4.25823i) q^{76} -19.5782 q^{77} -3.83882 q^{79} +(-30.0533 + 80.9660i) q^{80} +(121.949 + 63.7289i) q^{82} -37.0526 q^{83} -103.949i q^{85} +(148.323 + 77.5118i) q^{86} +(13.4322 - 1.70329i) q^{88} +43.4112i q^{89} +110.678i q^{91} +(-99.7434 + 69.3698i) q^{92} +(-50.1099 - 26.1868i) q^{94} -10.0639i q^{95} -86.9487 q^{97} +(78.5637 - 150.336i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 48 q^{7}+O(q^{10}) \) 8 * q + 4 * q^4 + 48 * q^7	\( 8 q + 4 q^{4} + 48 q^{7} + 40 q^{10} + 32 q^{22} - 56 q^{25} - 100 q^{28} - 80 q^{31} - 184 q^{34} - 120 q^{40} - 208 q^{46} + 144 q^{49} + 140 q^{52} + 16 q^{55} + 80 q^{58} + 184 q^{64} + 240 q^{70} + 248 q^{73} + 196 q^{76} + 192 q^{79} + 352 q^{82} + 152 q^{88} - 72 q^{97}+O(q^{100}) \) 8 * q + 4 * q^4 + 48 * q^7 + 40 * q^10 + 32 * q^22 - 56 * q^25 - 100 * q^28 - 80 * q^31 - 184 * q^34 - 120 * q^40 - 208 * q^46 + 144 * q^49 + 140 * q^52 + 16 * q^55 + 80 * q^58 + 184 * q^64 + 240 * q^70 + 248 * q^73 + 196 * q^76 + 192 * q^79 + 352 * q^82 + 152 * q^88 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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