LMFDB - Embedded newform 216.3.b.b.163.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(163,216)]

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([1, 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("216.163");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} - 56x^{10} + 400x^{8} - 896x^{6} - 512x^{4} - 8192x^{2} + 65536 $ x^16 - 2x^14 - 2x^12 - 56x^10 + 400x^8 - 896x^6 - 512x^4 - 8192*x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.8
Root			$-0.808307 + 1.82938i$ of defining polynomial
Character	$\chi$	$=$	216.163
Dual form			216.3.b.b.163.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.808307 + 1.82938i) q^{2} +(-2.69328 - 2.95740i) q^{4} -5.51565i q^{5} +11.2126i q^{7} +(7.58722 - 2.53655i) q^{8} +O(q^{10})$	\(q+(-0.808307 + 1.82938i) q^{2} +(-2.69328 - 2.95740i) q^{4} -5.51565i q^{5} +11.2126i q^{7} +(7.58722 - 2.53655i) q^{8} +(10.0902 + 4.45834i) q^{10} -17.9286 q^{11} +5.65548i q^{13} +(-20.5121 - 9.06320i) q^{14} +(-1.49248 + 15.9302i) q^{16} -9.53773 q^{17} -33.1648 q^{19} +(-16.3120 + 14.8552i) q^{20} +(14.4918 - 32.7983i) q^{22} +19.3990i q^{23} -5.42237 q^{25} +(-10.3460 - 4.57136i) q^{26} +(33.1601 - 30.1986i) q^{28} -29.8204i q^{29} -6.52238i q^{31} +(-27.9361 - 15.6068i) q^{32} +(7.70941 - 17.4482i) q^{34} +61.8446 q^{35} +33.9065i q^{37} +(26.8073 - 60.6710i) q^{38} +(-13.9907 - 41.8484i) q^{40} -56.8489 q^{41} +19.1239 q^{43} +(48.2868 + 53.0222i) q^{44} +(-35.4883 - 15.6804i) q^{46} +30.9806i q^{47} -76.7218 q^{49} +(4.38294 - 9.91959i) q^{50} +(16.7255 - 15.2318i) q^{52} -11.2982i q^{53} +98.8879i q^{55} +(28.4412 + 85.0723i) q^{56} +(54.5529 + 24.1040i) q^{58} +10.2309 q^{59} +3.18731i q^{61} +(11.9319 + 5.27208i) q^{62} +(51.1318 - 38.4907i) q^{64} +31.1936 q^{65} +13.1962 q^{67} +(25.6878 + 28.2069i) q^{68} +(-49.9894 + 113.137i) q^{70} +103.766i q^{71} -21.3079 q^{73} +(-62.0280 - 27.4069i) q^{74} +(89.3220 + 98.0816i) q^{76} -201.026i q^{77} -134.797i q^{79} +(87.8656 + 8.23201i) q^{80} +(45.9514 - 103.998i) q^{82} +56.2011 q^{83} +52.6068i q^{85} +(-15.4580 + 34.9849i) q^{86} +(-136.028 + 45.4768i) q^{88} +114.816 q^{89} -63.4125 q^{91} +(57.3708 - 52.2471i) q^{92} +(-56.6754 - 25.0418i) q^{94} +182.925i q^{95} +126.760 q^{97} +(62.0148 - 140.354i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4}+O(q^{10}) $ 16 * q + 4 * q^4	$ 16 q + 4 q^{4} + 24 q^{10} + 16 q^{16} - 64 q^{19} + 80 q^{22} - 80 q^{25} - 12 q^{28} + 8 q^{34} - 72 q^{40} - 64 q^{43} - 192 q^{46} - 128 q^{49} + 84 q^{52} - 96 q^{58} + 376 q^{64} + 128 q^{67} + 192 q^{70} + 80 q^{73} + 308 q^{76} + 272 q^{82} - 136 q^{88} + 192 q^{91} + 336 q^{94} + 80 q^{97}+O(q^{100}) $ 16 * q + 4 * q^4 + 24 * q^10 + 16 * q^16 - 64 * q^19 + 80 * q^22 - 80 * q^25 - 12 * q^28 + 8 * q^34 - 72 * q^40 - 64 * q^43 - 192 * q^46 - 128 * q^49 + 84 * q^52 - 96 * q^58 + 376 * q^64 + 128 * q^67 + 192 * q^70 + 80 * q^73 + 308 * q^76 + 272 * q^82 - 136 * q^88 + 192 * q^91 + 336 * q^94 + 80 * 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 $

$2$	−0.808307	+	1.82938i	−0.404153	+	0.914691i
$2$	−0.808307	+	1.82938i	−0.404153	+	0.914691i
$3$		0			0
$3$		0			0
$4$	−2.69328	−	2.95740i	−0.673320	−	0.739351i
$5$		−	5.51565i		−	1.10313i	−0.834132	−	0.551565i	$-0.814031\pi$
$5$		−	5.51565i		−	1.10313i	0.834132	−	0.551565i	$-0.185969\pi$
$6$		0			0
$7$			11.2126i			1.60180i	0.598801	+	0.800898i	$0.295644\pi$
$7$			11.2126i			1.60180i	−0.598801	+	0.800898i	$0.704356\pi$
$8$	7.58722	−	2.53655i	0.948403	−	0.317069i
$9$		0			0
$10$	10.0902	+	4.45834i	1.00902	+	0.445834i
$11$	−17.9286			−1.62987			−0.814937	−	0.579549i	$-0.803229\pi$
$11$	−17.9286			−1.62987			−0.814937	+	0.579549i	$0.803229\pi$
$12$		0			0
$13$			5.65548i			0.435037i	0.976056	+	0.217519i	$0.0697962\pi$
$13$			5.65548i			0.435037i	−0.976056	+	0.217519i	$0.930204\pi$
$14$	−20.5121	−	9.06320i	−1.46515	−	0.647371i
$15$		0			0
$16$	−1.49248	+	15.9302i	−0.0932802	+	0.995640i
$17$	−9.53773			−0.561043			−0.280522	−	0.959848i	$-0.590507\pi$
$17$	−9.53773			−0.561043			−0.280522	+	0.959848i	$0.590507\pi$
$18$		0			0
$19$	−33.1648			−1.74551			−0.872757	−	0.488155i	$-0.837670\pi$
$19$	−33.1648			−1.74551			−0.872757	+	0.488155i	$0.837670\pi$
$20$	−16.3120	+	14.8552i	−0.815600	+	0.742759i
$21$		0			0
$22$	14.4918	−	32.7983i	0.658719	−	1.49083i
$23$			19.3990i			0.843437i	0.906727	+	0.421718i	$0.138573\pi$
$23$			19.3990i			0.843437i	−0.906727	+	0.421718i	$0.861427\pi$
$24$		0			0
$25$	−5.42237			−0.216895
$26$	−10.3460	−	4.57136i	−0.397925	−	0.175822i
$27$		0			0
$28$	33.1601	−	30.1986i	1.18429	−	1.07852i
$29$		−	29.8204i		−	1.02829i	−0.857704	−	0.514144i	$-0.828110\pi$
$29$		−	29.8204i		−	1.02829i	0.857704	−	0.514144i	$-0.171890\pi$
$30$		0			0
$31$		−	6.52238i		−	0.210399i	−0.994451	−	0.105200i	$-0.966452\pi$
$31$		−	6.52238i		−	0.210399i	0.994451	−	0.105200i	$-0.0335482\pi$
$32$	−27.9361	−	15.6068i	−0.873004	−	0.487714i
$33$		0			0
$34$	7.70941	−	17.4482i	0.226747	−	0.513181i
$35$	61.8446			1.76699
$36$		0			0
$37$			33.9065i			0.916393i	0.888851	+	0.458196i	$0.151504\pi$
$37$			33.9065i			0.916393i	−0.888851	+	0.458196i	$0.848496\pi$
$38$	26.8073	−	60.6710i	0.705455	−	1.59661i
$39$		0			0
$40$	−13.9907	−	41.8484i	−0.349768	−	1.04621i
$41$	−56.8489			−1.38656			−0.693279	−	0.720669i	$-0.743835\pi$
$41$	−56.8489			−1.38656			−0.693279	+	0.720669i	$0.743835\pi$
$42$		0			0
$43$	19.1239			0.444741			0.222371	−	0.974962i	$-0.428621\pi$
$43$	19.1239			0.444741			0.222371	+	0.974962i	$0.428621\pi$
$44$	48.2868	+	53.0222i	1.09743	+	1.20505i
$45$		0			0
$46$	−35.4883	−	15.6804i	−0.771484	−	0.340878i
$47$			30.9806i			0.659162i	0.944127	+	0.329581i	$0.106907\pi$
$47$			30.9806i			0.659162i	−0.944127	+	0.329581i	$0.893093\pi$
$48$		0			0
$49$	−76.7218			−1.56575
$50$	4.38294	−	9.91959i	0.0876588	−	0.198392i
$51$		0			0
$52$	16.7255	−	15.2318i	0.321645	−	0.292919i
$53$		−	11.2982i		−	0.213173i	−0.994303	−	0.106587i	$-0.966008\pi$
$53$		−	11.2982i		−	0.213173i	0.994303	−	0.106587i	$-0.0339921\pi$
$54$		0			0
$55$			98.8879i			1.79796i
$56$	28.4412	+	85.0723i	0.507879	+	1.51915i
$57$		0			0
$58$	54.5529	+	24.1040i	0.940567	+	0.415586i
$59$	10.2309			0.173405			0.0867025	−	0.996234i	$-0.472367\pi$
$59$	10.2309			0.173405			0.0867025	+	0.996234i	$0.472367\pi$
$60$		0			0
$61$			3.18731i			0.0522509i	0.999659	+	0.0261255i	$0.00831694\pi$
$61$			3.18731i			0.0522509i	−0.999659	+	0.0261255i	$0.991683\pi$
$62$	11.9319	+	5.27208i	0.192450	+	0.0850336i
$63$		0			0
$64$	51.1318	−	38.4907i	0.798935	−	0.601417i
$65$	31.1936			0.479902
$66$		0			0
$67$	13.1962			0.196957			0.0984787	−	0.995139i	$-0.468602\pi$
$67$	13.1962			0.196957			0.0984787	+	0.995139i	$0.468602\pi$
$68$	25.6878	+	28.2069i	0.377762	+	0.414808i
$69$		0			0
$70$	−49.9894	+	113.137i	−0.714135	+	1.61625i
$71$			103.766i			1.46149i	0.682650	+	0.730746i	$0.260828\pi$
$71$			103.766i			1.46149i	−0.682650	+	0.730746i	$0.739172\pi$
$72$		0			0
$73$	−21.3079			−0.291889			−0.145944	−	0.989293i	$-0.546622\pi$
$73$	−21.3079			−0.291889			−0.145944	+	0.989293i	$0.546622\pi$
$74$	−62.0280	−	27.4069i	−0.838216	−	0.370363i
$75$		0			0
$76$	89.3220	+	98.0816i	1.17529	+	1.29055i
$77$		−	201.026i		−	2.61073i
$78$		0			0
$79$		−	134.797i		−	1.70629i	−0.521672	−	0.853146i	$-0.674692\pi$
$79$		−	134.797i		−	1.70629i	0.521672	−	0.853146i	$-0.325308\pi$
$80$	87.8656	+	8.23201i	1.09832	+	0.102900i
$81$		0			0
$82$	45.9514	−	103.998i	0.560382	−	1.26827i
$83$	56.2011			0.677122			0.338561	−	0.940944i	$-0.390060\pi$
$83$	56.2011			0.677122			0.338561	+	0.940944i	$0.390060\pi$
$84$		0			0
$85$			52.6068i			0.618903i
$86$	−15.4580	+	34.9849i	−0.179744	+	0.406801i
$87$		0			0
$88$	−136.028	+	45.4768i	−1.54578	+	0.516782i
$89$	114.816			1.29006			0.645032	−	0.764155i	$-0.276844\pi$
$89$	114.816			1.29006			0.645032	+	0.764155i	$0.276844\pi$
$90$		0			0
$91$	−63.4125			−0.696841
$92$	57.3708	−	52.2471i	0.623596	−	0.567903i
$93$		0			0
$94$	−56.6754	−	25.0418i	−0.602929	−	0.266402i
$95$			182.925i			1.92553i
$96$		0			0
$97$	126.760			1.30680			0.653402	−	0.757011i	$-0.273341\pi$
$97$	126.760			1.30680			0.653402	+	0.757011i	$0.273341\pi$
$98$	62.0148	−	140.354i	0.632804	−	1.43218i
$99$		0			0
$100$	14.6040	+	16.0361i	0.146040	+	0.160361i
$101$			102.509i			1.01494i	0.861670	+	0.507469i	$0.169419\pi$
$101$			102.509i			1.01494i	−0.861670	+	0.507469i	$0.830581\pi$
$102$		0			0
$103$			71.3790i			0.693000i	0.938050	+	0.346500i	$0.112630\pi$
$103$			71.3790i			0.693000i	−0.938050	+	0.346500i	$0.887370\pi$
$104$	14.3454	+	42.9094i	0.137937	+	0.412590i
$105$		0			0
$106$	20.6687	+	9.13239i	0.194988	+	0.0861546i
$107$	−9.86985			−0.0922416			−0.0461208	−	0.998936i	$-0.514686\pi$
$107$	−9.86985			−0.0922416			−0.0461208	+	0.998936i	$0.514686\pi$
$108$		0			0
$109$		−	34.6257i		−	0.317667i	−0.987305	−	0.158833i	$-0.949227\pi$
$109$		−	34.6257i		−	0.317667i	0.987305	−	0.158833i	$-0.0507732\pi$
$110$	−180.904	−	79.9318i	−1.64458	−	0.726653i
$111$		0			0
$112$	−178.619	−	16.7346i	−1.59481	−	0.149416i
$113$	−118.118			−1.04529			−0.522647	−	0.852549i	$-0.675056\pi$
$113$	−118.118			−1.04529			−0.522647	+	0.852549i	$0.675056\pi$
$114$		0			0
$115$	106.998			0.930420
$116$	−88.1909	+	80.3146i	−0.760266	+	0.692367i
$117$		0			0
$118$	−8.26970	+	18.7162i	−0.0700822	+	0.158612i
$119$		−	106.943i		−	0.898677i
$120$		0			0
$121$	200.435			1.65649
$122$	−5.83080	−	2.57632i	−0.0477935	−	0.0211174i
$123$		0			0
$124$	−19.2893	+	17.5666i	−0.155559	+	0.141666i
$125$		−	107.983i		−	0.863866i
$126$		0			0
$127$		−	100.868i		−	0.794232i	−0.917768	−	0.397116i	$-0.870011\pi$
$127$		−	100.868i		−	0.794232i	0.917768	−	0.397116i	$-0.129989\pi$
$128$	29.0840	+	124.652i	0.227219	+	0.973844i
$129$		0			0
$130$	−25.2140	+	57.0651i	−0.193954	+	0.438962i
$131$	47.5053			0.362636			0.181318	−	0.983425i	$-0.441964\pi$
$131$	47.5053			0.362636			0.181318	+	0.983425i	$0.441964\pi$
$132$		0			0
$133$		−	371.862i		−	2.79596i
$134$	−10.6665	+	24.1408i	−0.0796010	+	0.180155i
$135$		0			0
$136$	−72.3649	+	24.1929i	−0.532095	+	0.177889i
$137$	−223.008			−1.62780			−0.813898	−	0.581008i	$-0.802659\pi$
$137$	−223.008			−1.62780			−0.813898	+	0.581008i	$0.802659\pi$
$138$		0			0
$139$	−45.9277			−0.330415			−0.165208	−	0.986259i	$-0.552829\pi$
$139$	−45.9277			−0.330415			−0.165208	+	0.986259i	$0.552829\pi$
$140$	−166.565	−	182.900i	−1.18975	−	1.30643i
$141$		0			0
$142$	−189.828	−	83.8747i	−1.33681	−	0.590667i
$143$		−	101.395i		−	0.709056i
$144$		0			0
$145$	−164.479			−1.13434
$146$	17.2233	−	38.9802i	0.117968	−	0.266988i
$147$		0			0
$148$	100.275	−	91.3198i	0.677536	−	0.617025i
$149$		−	83.0427i		−	0.557334i	−0.960388	−	0.278667i	$-0.910107\pi$
$149$		−	83.0427i		−	0.557334i	0.960388	−	0.278667i	$-0.0898925\pi$
$150$		0			0
$151$		−	86.2824i		−	0.571406i	−0.958318	−	0.285703i	$-0.907773\pi$
$151$		−	86.2824i		−	0.571406i	0.958318	−	0.285703i	$-0.0922272\pi$
$152$	−251.628	+	84.1241i	−1.65545	+	0.553448i
$153$		0			0
$154$	367.753	+	162.491i	2.38801	+	1.05513i
$155$	−35.9752			−0.232098
$156$		0			0
$157$		−	95.3824i		−	0.607531i	−0.952747	−	0.303766i	$-0.901756\pi$
$157$		−	95.3824i		−	0.607531i	0.952747	−	0.303766i	$-0.0982440\pi$
$158$	246.595	+	108.957i	1.56073	+	0.689604i
$159$		0			0
$160$	−86.0819	+	154.086i	−0.538012	+	0.963036i
$161$	−217.513			−1.35101
$162$		0			0
$163$	92.4235			0.567015			0.283508	−	0.958970i	$-0.408502\pi$
$163$	92.4235			0.567015			0.283508	+	0.958970i	$0.408502\pi$
$164$	153.110	+	168.125i	0.933598	+	1.02515i
$165$		0			0
$166$	−45.4277	+	102.813i	−0.273661	+	0.619357i
$167$			139.707i			0.836567i	0.908317	+	0.418283i	$0.137368\pi$
$167$			139.707i			0.836567i	−0.908317	+	0.418283i	$0.862632\pi$
$168$		0			0
$169$	137.016			0.810743
$170$	−96.2379	−	42.5224i	−0.566105	−	0.250132i
$171$		0			0
$172$	−51.5059	−	56.5570i	−0.299453	−	0.328820i
$173$			101.832i			0.588623i	0.955710	+	0.294312i	$0.0950903\pi$
$173$			101.832i			0.588623i	−0.955710	+	0.294312i	$0.904910\pi$
$174$		0			0
$175$		−	60.7987i		−	0.347421i
$176$	26.7582	−	285.607i	0.152035	−	1.62277i
$177$		0			0
$178$	−92.8063	+	210.042i	−0.521384	+	1.18001i
$179$	−306.808			−1.71401			−0.857005	−	0.515308i	$-0.827678\pi$
$179$	−306.808			−1.71401			−0.857005	+	0.515308i	$0.827678\pi$
$180$		0			0
$181$			350.293i			1.93532i	0.252261	+	0.967659i	$0.418826\pi$
$181$			350.293i			1.93532i	−0.252261	+	0.967659i	$0.581174\pi$
$182$	51.2568	−	116.006i	0.281631	−	0.637394i
$183$		0			0
$184$	49.2066	+	147.185i	0.267427	+	0.799918i
$185$	187.016			1.01090
$186$		0			0
$187$	170.998			0.914430
$188$	91.6222	−	83.4394i	0.487352	−	0.443827i
$189$		0			0
$190$	−334.640	−	147.860i	−1.76126	−	0.778209i
$191$		−	319.455i		−	1.67254i	−0.548318	−	0.836270i	$-0.684732\pi$
$191$		−	319.455i		−	1.67254i	0.548318	−	0.836270i	$-0.315268\pi$
$192$		0			0
$193$	−106.441			−0.551505			−0.275753	−	0.961229i	$-0.588927\pi$
$193$	−106.441			−0.551505			−0.275753	+	0.961229i	$0.588927\pi$
$194$	−102.461	+	231.892i	−0.528149	+	1.19532i
$195$		0			0
$196$	206.633	+	226.897i	1.05425	+	1.15764i
$197$			209.051i			1.06117i	0.847632	+	0.530585i	$0.178028\pi$
$197$			209.051i			1.06117i	−0.847632	+	0.530585i	$0.821972\pi$
$198$		0			0
$199$			0.832764i			0.00418475i	0.999998	+	0.00209237i	$0.000666023\pi$
$199$			0.832764i			0.00418475i	−0.999998	+	0.00209237i	$0.999334\pi$
$200$	−41.1407	+	13.7541i	−0.205704	+	0.0687705i
$201$		0			0
$202$	−187.528	−	82.8585i	−0.928355	−	0.410191i
$203$	334.363			1.64711
$204$		0			0
$205$			313.559i			1.52955i
$206$	−130.580	−	57.6962i	−0.633881	−	0.280078i
$207$		0			0
$208$	−90.0932	−	8.44071i	−0.433140	−	0.0405804i
$209$	594.598			2.84497
$210$		0			0
$211$	−49.8265			−0.236144			−0.118072	−	0.993005i	$-0.537671\pi$
$211$	−49.8265			−0.236144			−0.118072	+	0.993005i	$0.537671\pi$
$212$	−33.4133	+	30.4292i	−0.157610	+	0.143534i
$213$		0			0
$214$	7.97787	−	18.0557i	0.0372798	−	0.0843726i
$215$		−	105.481i		−	0.490607i
$216$		0			0
$217$	73.1327			0.337017
$218$	63.3436	+	27.9882i	0.290567	+	0.128386i
$219$		0			0
$220$	292.452	−	266.333i	1.32933	−	1.21060i
$221$		−	53.9405i		−	0.244074i
$222$		0			0
$223$			190.860i			0.855874i	0.903809	+	0.427937i	$0.140760\pi$
$223$			190.860i			0.855874i	−0.903809	+	0.427937i	$0.859240\pi$
$224$	174.993	−	313.236i	0.781218	−	1.39837i
$225$		0			0
$226$	95.4758	−	216.083i	0.422459	−	0.956122i
$227$	−363.127			−1.59968			−0.799839	−	0.600215i	$-0.795082\pi$
$227$	−363.127			−1.59968			−0.799839	+	0.600215i	$0.795082\pi$
$228$		0			0
$229$		−	133.771i		−	0.584154i	−0.956395	−	0.292077i	$-0.905654\pi$
$229$		−	133.771i		−	0.584154i	0.956395	−	0.292077i	$-0.0943463\pi$
$230$	−86.4875	+	195.741i	−0.376032	+	0.851047i
$231$		0			0
$232$	−75.6408	−	226.254i	−0.326038	−	0.975232i
$233$	25.7134			0.110358			0.0551790	−	0.998476i	$-0.482427\pi$
$233$	25.7134			0.110358			0.0551790	+	0.998476i	$0.482427\pi$
$234$		0			0
$235$	170.878			0.727141
$236$	−27.5547	−	30.2569i	−0.116757	−	0.128207i
$237$		0			0
$238$	195.639	+	86.4424i	0.822012	+	0.363203i
$239$			352.274i			1.47395i	0.675920	+	0.736975i	$0.263746\pi$
$239$			352.274i			1.47395i	−0.675920	+	0.736975i	$0.736254\pi$
$240$		0			0
$241$	−317.143			−1.31595			−0.657973	−	0.753042i	$-0.728586\pi$
$241$	−317.143			−1.31595			−0.657973	+	0.753042i	$0.728586\pi$
$242$	−162.013	+	366.673i	−0.669476	+	1.51518i
$243$		0			0
$244$	9.42616	−	8.58431i	0.0386318	−	0.0351816i
$245$			423.171i			1.72723i
$246$		0			0
$247$		−	187.563i		−	0.759363i
$248$	−16.5443	−	49.4867i	−0.0667110	−	0.199543i
$249$		0			0
$250$	197.543	+	87.2836i	0.790171	+	0.349135i
$251$	103.378			0.411865			0.205933	−	0.978566i	$-0.433977\pi$
$251$	103.378			0.411865			0.205933	+	0.978566i	$0.433977\pi$
$252$		0			0
$253$		−	347.798i		−	1.37470i
$254$	184.525	+	81.5319i	0.726477	+	0.320992i
$255$		0			0
$256$	−251.545	−	47.5512i	−0.982598	−	0.185747i
$257$	−57.2700			−0.222841			−0.111420	−	0.993773i	$-0.535540\pi$
$257$	−57.2700			−0.222841			−0.111420	+	0.993773i	$0.535540\pi$
$258$		0			0
$259$	−380.179			−1.46787
$260$	−84.0132	−	92.2522i	−0.323128	−	0.354816i
$261$		0			0
$262$	−38.3989	+	86.9054i	−0.146561	+	0.331700i
$263$		−	209.524i		−	0.796671i	−0.917240	−	0.398335i	$-0.869588\pi$
$263$		−	209.524i		−	0.796671i	0.917240	−	0.398335i	$-0.130412\pi$
$264$		0			0
$265$	−62.3168			−0.235158
$266$	680.279	+	300.579i	2.55744	+	1.13000i
$267$		0			0
$268$	−35.5409	−	39.0264i	−0.132615	−	0.145621i
$269$			247.352i			0.919525i	0.888042	+	0.459762i	$0.152065\pi$
$269$			247.352i			0.919525i	−0.888042	+	0.459762i	$0.847935\pi$
$270$		0			0
$271$			351.648i			1.29759i	0.760962	+	0.648797i	$0.224727\pi$
$271$			351.648i			1.29759i	−0.760962	+	0.648797i	$0.775273\pi$
$272$	14.2349	−	151.938i	0.0523342	−	0.558597i
$273$		0			0
$274$	180.259	−	407.967i	0.657879	−	1.48893i
$275$	97.2156			0.353511
$276$		0			0
$277$			110.191i			0.397803i	0.980019	+	0.198902i	$0.0637374\pi$
$277$			110.191i			0.397803i	−0.980019	+	0.198902i	$0.936263\pi$
$278$	37.1237	−	84.0194i	0.133538	−	0.302228i
$279$		0			0
$280$	469.229	−	156.872i	1.67582	−	0.560257i
$281$	258.226			0.918955			0.459477	−	0.888189i	$-0.348037\pi$
$281$	258.226			0.918955			0.459477	+	0.888189i	$0.348037\pi$
$282$		0			0
$283$	−168.135			−0.594116			−0.297058	−	0.954859i	$-0.596005\pi$
$283$	−168.135			−0.594116			−0.297058	+	0.954859i	$0.596005\pi$
$284$	306.878	−	279.471i	1.08056	−	0.984052i
$285$		0			0
$286$	185.490	+	81.9582i	0.648567	+	0.286567i
$287$		−	637.423i		−	2.22098i
$288$		0			0
$289$	−198.032			−0.685231
$290$	132.949	−	300.894i	0.458446	−	1.03757i
$291$		0			0
$292$	57.3881	+	63.0160i	0.196534	+	0.215808i
$293$		−	176.983i		−	0.604037i	−0.953302	−	0.302018i	$-0.902340\pi$
$293$		−	176.983i		−	0.604037i	0.953302	−	0.302018i	$-0.0976604\pi$
$294$		0			0
$295$		−	56.4300i		−	0.191288i
$296$	86.0056	+	257.256i	0.290559	+	0.869109i
$297$		0			0
$298$	151.917	+	67.1240i	0.509788	+	0.225248i
$299$	−109.711			−0.366926
$300$		0			0
$301$			214.428i			0.712385i
$302$	157.843	+	69.7426i	0.522661	+	0.230936i
$303$		0			0
$304$	49.4979	−	528.323i	0.162822	−	1.73790i
$305$	17.5801			0.0576396
$306$		0			0
$307$	−458.839			−1.49459			−0.747295	−	0.664492i	$-0.768648\pi$
$307$	−458.839			−1.49459			−0.747295	+	0.664492i	$0.768648\pi$
$308$	−594.515	+	541.419i	−1.93024	+	1.75785i
$309$		0			0
$310$	29.0790	−	65.8123i	0.0938031	−	0.212298i
$311$		−	499.431i		−	1.60589i	−0.596056	−	0.802943i	$-0.703266\pi$
$311$		−	499.431i		−	1.60589i	0.596056	−	0.802943i	$-0.296734\pi$
$312$		0			0
$313$	351.252			1.12221			0.561105	−	0.827745i	$-0.310376\pi$
$313$	351.252			1.12221			0.561105	+	0.827745i	$0.310376\pi$
$314$	174.491	+	77.0983i	0.555704	+	0.245536i
$315$		0			0
$316$	−398.649	+	363.046i	−1.26155	+	1.14888i
$317$			504.828i			1.59252i	0.604957	+	0.796258i	$0.293190\pi$
$317$			504.828i			1.59252i	−0.604957	+	0.796258i	$0.706810\pi$
$318$		0			0
$319$			534.638i			1.67598i
$320$	−212.301	−	282.025i	−0.663441	−	0.881329i
$321$		0			0
$322$	175.817	−	397.915i	0.546017	−	1.23576i
$323$	316.317			0.979308
$324$		0			0
$325$		−	30.6661i		−	0.0943573i
$326$	−74.7065	+	169.078i	−0.229161	+	0.518644i
$327$		0			0
$328$	−431.325	+	144.200i	−1.31502	+	0.439634i
$329$	−347.372			−1.05584
$330$		0			0
$331$	−184.420			−0.557160			−0.278580	−	0.960413i	$-0.589864\pi$
$331$	−184.420			−0.557160			−0.278580	+	0.960413i	$0.589864\pi$
$332$	−151.365	−	166.209i	−0.455920	−	0.500631i
$333$		0			0
$334$	−255.577	−	112.926i	−0.765200	−	0.338101i
$335$		−	72.7853i		−	0.217270i
$336$		0			0
$337$	−54.1599			−0.160712			−0.0803559	−	0.996766i	$-0.525606\pi$
$337$	−54.1599			−0.160712			−0.0803559	+	0.996766i	$0.525606\pi$
$338$	−110.751	+	250.654i	−0.327664	+	0.741579i
$339$		0			0
$340$	155.579	−	141.685i	0.457587	−	0.416720i
$341$			116.937i			0.342924i
$342$		0			0
$343$		−	310.833i		−	0.906219i
$344$	145.097	−	48.5086i	0.421794	−	0.141013i
$345$		0			0
$346$	−186.289	−	82.3113i	−0.538408	−	0.237894i
$347$	−459.688			−1.32475			−0.662374	−	0.749173i	$-0.730451\pi$
$347$	−459.688			−1.32475			−0.662374	+	0.749173i	$0.730451\pi$
$348$		0			0
$349$			441.208i			1.26421i	0.774884	+	0.632103i	$0.217808\pi$
$349$			441.208i			1.26421i	−0.774884	+	0.632103i	$0.782192\pi$
$350$	111.224	+	49.1440i	0.317783	+	0.140412i
$351$		0			0
$352$	500.856	+	279.809i	1.42289	+	0.794912i
$353$	−316.168			−0.895660			−0.447830	−	0.894119i	$-0.647803\pi$
$353$	−316.168			−0.895660			−0.447830	+	0.894119i	$0.647803\pi$
$354$		0			0
$355$	572.336			1.61221
$356$	−309.231	−	339.557i	−0.868626	−	0.953811i
$357$		0			0
$358$	247.995	−	561.269i	0.692723	−	1.56779i
$359$			459.684i			1.28046i	0.768184	+	0.640229i	$0.221161\pi$
$359$			459.684i			1.28046i	−0.768184	+	0.640229i	$0.778839\pi$
$360$		0			0
$361$	738.902			2.04682
$362$	−640.819	−	283.144i	−1.77022	−	0.782165i
$363$		0			0
$364$	170.788	+	187.536i	0.469197	+	0.515210i
$365$			117.527i			0.321991i
$366$		0			0
$367$			348.283i			0.948999i	0.880256	+	0.474499i	$0.157371\pi$
$367$			348.283i			0.948999i	−0.880256	+	0.474499i	$0.842629\pi$
$368$	−309.031	−	28.9528i	−0.839759	−	0.0786760i
$369$		0			0
$370$	−151.167	+	342.125i	−0.408559	+	0.924661i
$371$	126.682			0.341460
$372$		0			0
$373$			570.551i			1.52963i	0.644252	+	0.764813i	$0.277169\pi$
$373$			570.551i			1.52963i	−0.644252	+	0.764813i	$0.722831\pi$
$374$	−138.219	+	312.821i	−0.369570	+	0.836421i
$375$		0			0
$376$	78.5838	+	235.057i	0.208999	+	0.625151i
$377$	168.649			0.447344
$378$		0			0
$379$	−211.672			−0.558502			−0.279251	−	0.960218i	$-0.590086\pi$
$379$	−211.672			−0.558502			−0.279251	+	0.960218i	$0.590086\pi$
$380$	540.984	−	492.669i	1.42364	−	1.29650i
$381$		0			0
$382$	584.406	+	258.218i	1.52986	+	0.675963i
$383$			338.893i			0.884839i	0.896808	+	0.442420i	$0.145880\pi$
$383$			338.893i			0.884839i	−0.896808	+	0.442420i	$0.854120\pi$
$384$		0			0
$385$	−1108.79			−2.87997
$386$	86.0366	−	194.720i	0.222893	−	0.504457i
$387$		0			0
$388$	−341.400	−	374.880i	−0.879897	−	0.966187i
$389$		−	359.148i		−	0.923259i	−0.887073	−	0.461629i	$-0.847265\pi$
$389$		−	359.148i		−	0.923259i	0.887073	−	0.461629i	$-0.152735\pi$
$390$		0			0
$391$		−	185.023i		−	0.473204i
$392$	−582.105	+	194.609i	−1.48496	+	0.496451i
$393$		0			0
$394$	−382.434	−	168.977i	−0.970643	−	0.428876i
$395$	−743.493			−1.88226
$396$		0			0
$397$		−	387.084i		−	0.975022i	−0.873117	−	0.487511i	$-0.837905\pi$
$397$		−	387.084i		−	0.975022i	0.873117	−	0.487511i	$-0.162095\pi$
$398$	−1.52344	−	0.673129i	−0.00382775	−	0.00169128i
$399$		0			0
$400$	8.09280	−	86.3796i	0.0202320	−	0.215949i
$401$	172.739			0.430770			0.215385	−	0.976529i	$-0.430899\pi$
$401$	172.739			0.430770			0.215385	+	0.976529i	$0.430899\pi$
$402$		0			0
$403$	36.8872			0.0915315
$404$	303.160	−	276.085i	0.750396	−	0.683378i
$405$		0			0
$406$	−270.268	+	611.678i	−0.665685	+	1.50660i
$407$		−	607.897i		−	1.49360i
$408$		0			0
$409$	−137.938			−0.337257			−0.168629	−	0.985680i	$-0.553934\pi$
$409$	−137.938			−0.337257			−0.168629	+	0.985680i	$0.553934\pi$
$410$	−573.618	−	253.452i	−1.39907	−	0.618174i
$411$		0			0
$412$	211.097	−	192.244i	0.512371	−	0.466611i
$413$			114.715i			0.277760i
$414$		0			0
$415$		−	309.985i		−	0.746953i
$416$	88.2642	−	157.992i	0.212174	−	0.379789i
$417$		0			0
$418$	−480.618	+	1087.75i	−1.14980	+	2.60227i
$419$	−64.3179			−0.153503			−0.0767517	−	0.997050i	$-0.524455\pi$
$419$	−64.3179			−0.153503			−0.0767517	+	0.997050i	$0.524455\pi$
$420$		0			0
$421$		−	575.683i		−	1.36742i	−0.729755	−	0.683709i	$-0.760366\pi$
$421$		−	575.683i		−	1.36742i	0.729755	−	0.683709i	$-0.239634\pi$
$422$	40.2751	−	91.1517i	0.0954386	−	0.215999i
$423$		0			0
$424$	−28.6584	−	85.7218i	−0.0675905	−	0.202174i
$425$	51.7171			0.121687
$426$		0			0
$427$	−35.7379			−0.0836954
$428$	26.5823	+	29.1891i	0.0621081	+	0.0681989i
$429$		0			0
$430$	192.964	+	85.2606i	0.448754	+	0.198281i
$431$			32.6745i			0.0758109i	0.999281	+	0.0379055i	$0.0120686\pi$
$431$			32.6745i			0.0758109i	−0.999281	+	0.0379055i	$0.987931\pi$
$432$		0			0
$433$	82.5217			0.190581			0.0952906	−	0.995449i	$-0.469622\pi$
$433$	82.5217			0.190581			0.0952906	+	0.995449i	$0.469622\pi$
$434$	−59.1136	+	133.788i	−0.136207	+	0.308266i
$435$		0			0
$436$	−102.402	+	93.2566i	−0.234867	+	0.213891i
$437$		−	643.365i		−	1.47223i
$438$		0			0
$439$			282.325i			0.643109i	0.946891	+	0.321554i	$0.104205\pi$
$439$			282.325i			0.643109i	−0.946891	+	0.321554i	$0.895795\pi$
$440$	250.834	+	750.285i	0.570077	+	1.70519i
$441$		0			0
$442$	98.6777	+	43.6004i	0.223253	+	0.0986435i
$443$	−34.2623			−0.0773414			−0.0386707	−	0.999252i	$-0.512312\pi$
$443$	−34.2623			−0.0773414			−0.0386707	+	0.999252i	$0.512312\pi$
$444$		0			0
$445$		−	633.283i		−	1.42311i
$446$	−349.156	−	154.273i	−0.782861	−	0.345904i
$447$		0			0
$448$	431.580	+	573.320i	0.963348	+	1.27973i
$449$	678.253			1.51059			0.755293	−	0.655387i	$-0.227494\pi$
$449$	678.253			1.51059			0.755293	+	0.655387i	$0.227494\pi$
$450$		0			0
$451$	1019.22			2.25992
$452$	318.126	+	349.324i	0.703818	+	0.772840i
$453$		0			0
$454$	293.518	−	664.298i	0.646515	−	1.46321i
$455$			349.761i			0.768706i
$456$		0			0
$457$	284.464			0.622459			0.311230	−	0.950335i	$-0.399259\pi$
$457$	284.464			0.622459			0.311230	+	0.950335i	$0.399259\pi$
$458$	244.719	+	108.128i	0.534320	+	0.236088i
$459$		0			0
$460$	−288.176	−	316.437i	−0.626471	−	0.687907i
$461$			172.339i			0.373837i	0.982375	+	0.186919i	$0.0598501\pi$
$461$			172.339i			0.373837i	−0.982375	+	0.186919i	$0.940150\pi$
$462$		0			0
$463$		−	647.213i		−	1.39787i	−0.715186	−	0.698934i	$-0.753658\pi$
$463$		−	647.213i		−	1.39787i	0.715186	−	0.698934i	$-0.246342\pi$
$464$	475.046	+	44.5064i	1.02381	+	0.0959190i
$465$		0			0
$466$	−20.7843	+	47.0397i	−0.0446016	+	0.100944i
$467$	188.854			0.404399			0.202200	−	0.979344i	$-0.435191\pi$
$467$	188.854			0.404399			0.202200	+	0.979344i	$0.435191\pi$
$468$		0			0
$469$			147.963i			0.315486i
$470$	−138.122	+	312.601i	−0.293876	+	0.665109i
$471$		0			0
$472$	77.6241	−	25.9512i	0.164458	−	0.0549813i
$473$	−342.865			−0.724872
$474$		0			0
$475$	179.832			0.378593
$476$	−316.272	+	288.026i	−0.664438	+	0.605097i
$477$		0			0
$478$	−644.444	−	284.745i	−1.34821	−	0.595702i
$479$			135.970i			0.283861i	0.989877	+	0.141931i	$0.0453310\pi$
$479$			135.970i			0.283861i	−0.989877	+	0.141931i	$0.954669\pi$
$480$		0			0
$481$	−191.758			−0.398665
$482$	256.349	−	580.176i	0.531844	−	1.20368i
$483$		0			0
$484$	−539.828	−	592.768i	−1.11535	−	1.22473i
$485$		−	699.163i		−	1.44157i
$486$		0			0
$487$		−	561.056i		−	1.15207i	−0.817426	−	0.576033i	$-0.804600\pi$
$487$		−	561.056i		−	1.15207i	0.817426	−	0.576033i	$-0.195400\pi$
$488$	8.08476	+	24.1828i	0.0165671	+	0.0495549i
$489$		0			0
$490$	−774.141	−	342.052i	−1.57988	−	0.698065i
$491$	22.6668			0.0461645			0.0230823	−	0.999734i	$-0.492652\pi$
$491$	22.6668			0.0461645			0.0230823	+	0.999734i	$0.492652\pi$
$492$		0			0
$493$			284.419i			0.576914i
$494$	343.124	+	151.608i	0.694583	+	0.306899i
$495$		0			0
$496$	103.903	+	9.73455i	0.209482	+	0.0196261i
$497$	−1163.48			−2.34101
$498$		0			0
$499$	51.2632			0.102732			0.0513659	−	0.998680i	$-0.483643\pi$
$499$	51.2632			0.102732			0.0513659	+	0.998680i	$0.483643\pi$
$500$	−319.350	+	290.829i	−0.638701	+	0.581659i
$501$		0			0
$502$	−83.5613	+	189.118i	−0.166457	+	0.376730i
$503$			533.528i			1.06069i	0.847781	+	0.530346i	$0.177938\pi$
$503$			533.528i			1.06069i	−0.847781	+	0.530346i	$0.822062\pi$
$504$		0			0
$505$	565.402			1.11961
$506$	636.256	+	281.128i	1.25742	+	0.555588i
$507$		0			0
$508$	−298.306	+	271.664i	−0.587217	+	0.534773i
$509$			195.207i			0.383511i	0.981443	+	0.191756i	$0.0614181\pi$
$509$			195.207i			0.383511i	−0.981443	+	0.191756i	$0.938582\pi$
$510$		0			0
$511$		−	238.916i		−	0.467546i
$512$	290.315	−	421.736i	0.567021	−	0.823703i
$513$		0			0
$514$	46.2917	−	104.769i	0.0900618	−	0.203830i
$515$	393.702			0.764469
$516$		0			0
$517$		−	555.439i		−	1.07435i
$518$	307.302	−	695.494i	0.593246	−	1.34265i
$519$		0			0
$520$	236.673	−	79.1242i	0.455140	−	0.152162i
$521$	−9.53773			−0.0183066			−0.00915329	−	0.999958i	$-0.502914\pi$
$521$	−9.53773			−0.0183066			−0.00915329	+	0.999958i	$0.502914\pi$
$522$		0			0
$523$	468.442			0.895683			0.447841	−	0.894113i	$-0.352193\pi$
$523$	468.442			0.895683			0.447841	+	0.894113i	$0.352193\pi$
$524$	−127.945	−	140.492i	−0.244170	−	0.268115i
$525$		0			0
$526$	383.300	+	169.360i	0.728708	+	0.321977i
$527$			62.2087i			0.118043i
$528$		0			0
$529$	152.677			0.288614
$530$	50.3711	−	114.001i	0.0950397	−	0.215097i
$531$		0			0
$532$	−1099.75	+	1001.53i	−2.06719	+	1.88257i
$533$		−	321.508i		−	0.603204i
$534$		0			0
$535$			54.4386i			0.101754i
$536$	100.122	−	33.4727i	0.186795	−	0.0624490i
$537$		0			0
$538$	−452.502	−	199.936i	−0.841081	−	0.371629i
$539$	1375.52			2.55198
$540$		0			0
$541$		−	163.597i		−	0.302397i	−0.988503	−	0.151199i	$-0.951687\pi$
$541$		−	163.597i		−	0.302397i	0.988503	−	0.151199i	$-0.0483133\pi$
$542$	−643.298	−	284.239i	−1.18690	−	0.524427i
$543$		0			0
$544$	266.447	+	148.854i	0.489793	+	0.273628i
$545$	−190.983			−0.350427
$546$		0			0
$547$	−728.850			−1.33245			−0.666224	−	0.745751i	$-0.732091\pi$
$547$	−728.850			−1.33245			−0.666224	+	0.745751i	$0.732091\pi$
$548$	600.623	+	659.525i	1.09603	+	1.20351i
$549$		0			0
$550$	−78.5800	+	177.844i	−0.142873	+	0.323354i
$551$			988.986i			1.79489i
$552$		0			0
$553$	1511.42			2.73313
$554$	−201.582	−	89.0685i	−0.363867	−	0.160774i
$555$		0			0
$556$	123.696	+	135.827i	0.222475	+	0.244293i
$557$			66.1825i			0.118820i	0.998234	+	0.0594098i	$0.0189219\pi$
$557$			66.1825i			0.118820i	−0.998234	+	0.0594098i	$0.981078\pi$
$558$		0			0
$559$			108.155i			0.193479i
$560$	−92.3021	+	985.199i	−0.164825	+	1.75928i
$561$		0			0
$562$	−208.726	+	472.395i	−0.371399	+	0.840560i
$563$	702.807			1.24832			0.624162	−	0.781295i	$-0.285440\pi$
$563$	702.807			1.24832			0.624162	+	0.781295i	$0.285440\pi$
$564$		0			0
$565$			651.499i			1.15310i
$566$	135.905	−	307.583i	0.240114	−	0.543433i
$567$		0			0
$568$	263.207	+	787.295i	0.463393	+	1.38608i
$569$	591.739			1.03996			0.519982	−	0.854178i	$-0.325939\pi$
$569$	591.739			1.03996			0.519982	+	0.854178i	$0.325939\pi$
$570$		0			0
$571$	−535.959			−0.938633			−0.469316	−	0.883030i	$-0.655500\pi$
$571$	−535.959			−0.938633			−0.469316	+	0.883030i	$0.655500\pi$
$572$	−299.866	+	273.085i	−0.524241	+	0.477421i
$573$		0			0
$574$	1166.09	+	515.233i	2.03152	+	0.897619i
$575$		−	105.189i		−	0.182937i
$576$		0			0
$577$	−941.827			−1.63228			−0.816141	−	0.577853i	$-0.803891\pi$
$577$	−941.827			−1.63228			−0.816141	+	0.577853i	$0.803891\pi$
$578$	160.070	−	362.276i	0.276938	−	0.626775i
$579$		0			0
$580$	442.987	+	486.430i	0.763771	+	0.838672i
$581$			630.159i			1.08461i
$582$		0			0
$583$			202.561i			0.347445i
$584$	−161.668	+	54.0485i	−0.276828	+	0.0925487i
$585$		0			0
$586$	323.769	+	143.056i	0.552507	+	0.244124i
$587$	377.072			0.642372			0.321186	−	0.947016i	$-0.395919\pi$
$587$	377.072			0.642372			0.321186	+	0.947016i	$0.395919\pi$
$588$		0			0
$589$			216.313i			0.367255i
$590$	103.232	+	45.6128i	0.174970	+	0.0773098i
$591$		0			0
$592$	−540.139	−	50.6049i	−0.912397	−	0.0854813i
$593$	−59.0152			−0.0995197			−0.0497599	−	0.998761i	$-0.515846\pi$
$593$	−59.0152			−0.0995197			−0.0497599	+	0.998761i	$0.515846\pi$
$594$		0			0
$595$	−589.857			−0.991357
$596$	−245.591	+	223.657i	−0.412065	+	0.375264i
$597$		0			0
$598$	88.6801	−	200.703i	0.148295	−	0.335624i
$599$		−	656.225i		−	1.09553i	−0.836631	−	0.547767i	$-0.815478\pi$
$599$		−	656.225i		−	1.09553i	0.836631	−	0.547767i	$-0.184522\pi$
$600$		0			0
$601$	488.573			0.812933			0.406466	−	0.913666i	$-0.366761\pi$
$601$	488.573			0.812933			0.406466	+	0.913666i	$0.366761\pi$
$602$	−392.271	−	173.323i	−0.651612	−	0.287913i
$603$		0			0
$604$	−255.172	+	232.383i	−0.422470	+	0.384739i
$605$		−	1105.53i		−	1.82732i
$606$		0			0
$607$		−	169.537i		−	0.279303i	−0.990201	−	0.139652i	$-0.955402\pi$
$607$		−	169.537i		−	0.279303i	0.990201	−	0.139652i	$-0.0445983\pi$
$608$	926.495	+	517.597i	1.52384	+	0.851311i
$609$		0			0
$610$	−14.2101	+	32.1607i	−0.0232952	+	0.0527224i
$611$	−175.210			−0.286760
$612$		0			0
$613$		−	918.527i		−	1.49841i	−0.662336	−	0.749206i	$-0.730435\pi$
$613$		−	918.527i		−	1.49841i	0.662336	−	0.749206i	$-0.269565\pi$
$614$	370.883	−	839.392i	0.604044	−	1.36709i
$615$		0			0
$616$	−509.912	−	1525.23i	−0.827780	−	2.47602i
$617$	606.281			0.982627			0.491313	−	0.870983i	$-0.336517\pi$
$617$	606.281			0.982627			0.491313	+	0.870983i	$0.336517\pi$
$618$		0			0
$619$	589.003			0.951540			0.475770	−	0.879570i	$-0.342169\pi$
$619$	589.003			0.951540			0.475770	+	0.879570i	$0.342169\pi$
$620$	96.8912	+	106.393i	0.156276	+	0.171602i
$621$		0			0
$622$	913.650	+	403.693i	1.46889	+	0.649024i
$623$			1287.38i			2.06642i
$624$		0			0
$625$	−731.157			−1.16985
$626$	−283.919	+	642.574i	−0.453545	+	1.02648i
$627$		0			0
$628$	−282.084	+	256.892i	−0.449179	+	0.409063i
$629$		−	323.391i		−	0.514136i
$630$		0			0
$631$			965.210i			1.52965i	0.644237	+	0.764826i	$0.277175\pi$
$631$			965.210i			1.52965i	−0.644237	+	0.764826i	$0.722825\pi$
$632$	−341.919	−	1022.73i	−0.541012	−	1.61825i
$633$		0			0
$634$	−923.523	−	408.056i	−1.45666	−	0.643621i
$635$	−556.350			−0.876141
$636$		0			0
$637$		−	433.899i		−	0.681160i
$638$	−978.057	−	432.152i	−1.53301	−	0.677353i
$639$		0			0
$640$	687.536	−	160.417i	1.07428	−	0.250652i
$641$	579.061			0.903372			0.451686	−	0.892177i	$-0.350823\pi$
$641$	579.061			0.903372			0.451686	+	0.892177i	$0.350823\pi$
$642$		0			0
$643$	317.494			0.493770			0.246885	−	0.969045i	$-0.420593\pi$
$643$	317.494			0.493770			0.246885	+	0.969045i	$0.420593\pi$
$644$	585.824	+	643.275i	0.909665	+	0.998874i
$645$		0			0
$646$	−255.681	+	578.664i	−0.395791	+	0.895765i
$647$			823.258i			1.27242i	0.771514	+	0.636212i	$0.219500\pi$
$647$			823.258i			1.27242i	−0.771514	+	0.636212i	$0.780500\pi$
$648$		0			0
$649$	−183.426			−0.282628
$650$	56.1000	+	24.7876i	0.0863078	+	0.0381348i
$651$		0			0
$652$	−248.922	−	273.334i	−0.381783	−	0.419223i
$653$		−	561.283i		−	0.859545i	−0.902937	−	0.429772i	$-0.858594\pi$
$653$		−	561.283i		−	0.859545i	0.902937	−	0.429772i	$-0.141406\pi$
$654$		0			0
$655$		−	262.022i		−	0.400034i
$656$	84.8461	−	905.617i	0.129339	−	1.38051i
$657$		0			0
$658$	280.783	−	635.477i	0.426722	−	0.965770i
$659$	−406.847			−0.617370			−0.308685	−	0.951164i	$-0.599889\pi$
$659$	−406.847			−0.617370			−0.308685	+	0.951164i	$0.599889\pi$
$660$		0			0
$661$		−	634.563i		−	0.960004i	−0.877267	−	0.480002i	$-0.840636\pi$
$661$		−	634.563i		−	0.960004i	0.877267	−	0.480002i	$-0.159364\pi$
$662$	149.068	−	337.374i	0.225178	−	0.509629i
$663$		0			0
$664$	426.410	−	142.557i	0.642184	−	0.214694i
$665$	−2051.06			−3.08430
$666$		0			0
$667$	578.487			0.867297
$668$	413.169	−	376.269i	0.618517	−	0.563277i
$669$		0			0
$670$	133.152	+	58.8329i	0.198735	+	0.0878103i
$671$		−	57.1440i		−	0.0851624i
$672$		0			0
$673$	79.9926			0.118860			0.0594299	−	0.998232i	$-0.481072\pi$
$673$	79.9926			0.118860			0.0594299	+	0.998232i	$0.481072\pi$
$674$	43.7778	−	99.0791i	0.0649522	−	0.147002i
$675$		0			0
$676$	−369.021	−	405.210i	−0.545889	−	0.599424i
$677$		−	930.841i		−	1.37495i	−0.726208	−	0.687475i	$-0.758719\pi$
$677$		−	930.841i		−	1.37495i	0.726208	−	0.687475i	$-0.241281\pi$
$678$		0			0
$679$			1421.31i			2.09323i
$680$	133.440	+	399.139i	0.196235	+	0.586969i
$681$		0			0
$682$	−213.923	−	94.5212i	−0.313670	−	0.138594i
$683$	−484.164			−0.708878			−0.354439	−	0.935079i	$-0.615328\pi$
$683$	−484.164			−0.708878			−0.354439	+	0.935079i	$0.615328\pi$
$684$		0			0
$685$			1230.03i			1.79567i
$686$	568.633	+	251.249i	0.828911	+	0.366252i
$687$		0			0
$688$	−28.5421	+	304.648i	−0.0414856	+	0.442802i
$689$	63.8966			0.0927382
$690$		0			0
$691$	−493.460			−0.714125			−0.357063	−	0.934080i	$-0.616222\pi$
$691$	−493.460			−0.714125			−0.357063	+	0.934080i	$0.616222\pi$
$692$	301.158	−	274.262i	0.435199	−	0.396332i
$693$		0			0
$694$	371.569	−	840.944i	0.535401	−	1.21174i
$695$			253.321i			0.364491i
$696$		0			0
$697$	542.210			0.777919
$698$	−807.138	−	356.631i	−1.15636	−	0.510933i
$699$		0			0
$700$	−179.806	+	163.748i	−0.256866	+	0.233926i
$701$		−	221.082i		−	0.315381i	−0.987489	−	0.157691i	$-0.949595\pi$
$701$		−	221.082i		−	0.315381i	0.987489	−	0.157691i	$-0.0504048\pi$
$702$		0			0
$703$		−	1124.50i		−	1.59958i
$704$	−916.723	+	690.085i	−1.30216	+	0.980235i
$705$		0			0
$706$	255.561	−	578.392i	0.361984	−	0.819252i
$707$	−1149.39			−1.62572
$708$		0			0
$709$			916.562i			1.29275i	0.763019	+	0.646376i	$0.223716\pi$
$709$			916.562i			1.29275i	−0.763019	+	0.646376i	$0.776284\pi$
$710$	−462.623	+	1047.02i	−0.651582	+	1.47468i
$711$		0			0
$712$	871.132	−	291.236i	1.22350	−	0.409039i
$713$	126.528			0.177459
$714$		0			0
$715$	−559.259			−0.782180
$716$	826.319	+	907.355i	1.15408	+	1.26726i
$717$		0			0
$718$	−840.939	−	371.566i	−1.17122	−	0.517501i
$719$		−	268.184i		−	0.372996i	−0.982455	−	0.186498i	$-0.940286\pi$
$719$		−	268.184i		−	0.372996i	0.982455	−	0.186498i	$-0.0597138\pi$
$720$		0			0
$721$	−800.343			−1.11005
$722$	−597.259	+	1351.73i	−0.827229	+	1.87221i
$723$		0			0
$724$	1035.96	−	943.436i	1.43088	−	1.30309i
$725$			161.697i			0.223030i
$726$		0			0
$727$			69.5498i			0.0956669i	0.998855	+	0.0478334i	$0.0152317\pi$
$727$			69.5498i			0.0956669i	−0.998855	+	0.0478334i	$0.984768\pi$
$728$	−481.125	+	160.849i	−0.660886	+	0.220946i
$729$		0			0
$730$	−215.001	−	94.9977i	−0.294522	−	0.130134i
$731$	−182.398			−0.249519
$732$		0			0
$733$			838.094i			1.14337i	0.820472	+	0.571687i	$0.193711\pi$
$733$			838.094i			1.14337i	−0.820472	+	0.571687i	$0.806289\pi$
$734$	−637.142	−	281.519i	−0.868041	−	0.383541i
$735$		0			0
$736$	302.758	−	541.934i	0.411356	−	0.736323i
$737$	−236.589			−0.321016
$738$		0			0
$739$	−560.618			−0.758616			−0.379308	−	0.925270i	$-0.623838\pi$
$739$	−560.618			−0.758616			−0.379308	+	0.925270i	$0.623838\pi$
$740$	−503.688	−	553.083i	−0.680659	−	0.747410i
$741$		0			0
$742$	−102.398	+	231.749i	−0.138002	+	0.312330i
$743$		−	472.098i		−	0.635394i	−0.948192	−	0.317697i	$-0.897090\pi$
$743$		−	472.098i		−	0.635394i	0.948192	−	0.317697i	$-0.102910\pi$
$744$		0			0
$745$	−458.034			−0.614811
$746$	−1043.76	−	461.180i	−1.39914	−	0.618204i
$747$		0			0
$748$	−460.546	−	505.711i	−0.615704	−	0.676085i
$749$		−	110.666i		−	0.147752i
$750$		0			0
$751$		−	781.019i		−	1.03997i	−0.854175	−	0.519986i	$-0.825937\pi$
$751$		−	781.019i		−	1.03997i	0.854175	−	0.519986i	$-0.174063\pi$
$752$	−493.528	−	46.2380i	−0.656288	−	0.0614867i
$753$		0			0
$754$	−136.320	+	308.523i	−0.180795	+	0.409181i
$755$	−475.903			−0.630335
$756$		0			0
$757$			695.377i			0.918596i	0.888282	+	0.459298i	$0.151899\pi$
$757$			695.377i			0.918596i	−0.888282	+	0.459298i	$0.848101\pi$
$758$	171.096	−	387.230i	0.225721	−	0.510857i
$759$		0			0
$760$	463.999	+	1387.89i	0.610525	+	1.82618i
$761$	−116.663			−0.153303			−0.0766513	−	0.997058i	$-0.524423\pi$
$761$	−116.663			−0.153303			−0.0766513	+	0.997058i	$0.524423\pi$
$762$		0			0
$763$	388.243			0.508837
$764$	−944.758	+	860.382i	−1.23659	+	1.12615i
$765$		0			0
$766$	−619.966	−	273.930i	−0.809354	−	0.357611i
$767$			57.8606i			0.0754376i
$768$		0			0
$769$	−1362.04			−1.77119			−0.885593	−	0.464462i	$-0.846248\pi$
$769$	−1362.04			−1.77119			−0.885593	+	0.464462i	$0.846248\pi$
$770$	896.241	−	2028.40i	1.16395	−	2.63428i
$771$		0			0
$772$	286.674	+	314.788i	0.371340	+	0.407756i
$773$			30.8774i			0.0399448i	0.999801	+	0.0199724i	$0.00635784\pi$
$773$			30.8774i			0.0399448i	−0.999801	+	0.0199724i	$0.993642\pi$
$774$		0			0
$775$			35.3668i			0.0456345i
$776$	961.756	−	321.533i	1.23938	−	0.414346i
$777$		0			0
$778$	657.019	+	290.302i	0.844497	+	0.373138i
$779$	1885.38			2.42026
$780$		0			0
$781$		−	1860.38i		−	2.38205i
$782$	338.478	+	149.555i	0.432836	+	0.191247i
$783$		0			0
$784$	114.506	−	1222.20i	0.146054	−	1.55892i
$785$	−526.096			−0.670186
$786$		0			0
$787$	355.581			0.451818			0.225909	−	0.974148i	$-0.427465\pi$
$787$	355.581			0.451818			0.225909	+	0.974148i	$0.427465\pi$
$788$	618.247	−	563.032i	0.784578	−	0.714507i
$789$		0			0
$790$	600.970	−	1360.13i	0.760722	−	1.72169i
$791$		−	1324.41i		−	1.67435i
$792$		0			0
$793$	−18.0258			−0.0227311
$794$	708.125	+	312.883i	0.891844	+	0.394059i
$795$		0			0
$796$	2.46282	−	2.24287i	0.00309400	−	0.00281767i
$797$			1249.99i			1.56837i	0.620528	+	0.784184i	$0.286918\pi$
$797$			1249.99i			1.56837i	−0.620528	+	0.784184i	$0.713082\pi$
$798$		0			0
$799$		−	295.485i		−	0.369818i
$800$	151.480	+	84.6261i	0.189350	+	0.105783i
$801$		0			0
$802$	−139.626	+	316.006i	−0.174097	+	0.394022i
$803$	382.021			0.475742
$804$		0			0
$805$			1199.73i			1.49034i
$806$	−29.8162	+	67.4808i	−0.0369928	+	0.0837231i
$807$		0			0
$808$	260.019	+	777.757i	0.321805	+	0.962570i
$809$	201.995			0.249684			0.124842	−	0.992177i	$-0.460158\pi$
$809$	201.995			0.249684			0.124842	+	0.992177i	$0.460158\pi$
$810$		0			0
$811$	−536.647			−0.661710			−0.330855	−	0.943682i	$-0.607337\pi$
$811$	−536.647			−0.661710			−0.330855	+	0.943682i	$0.607337\pi$
$812$	−900.534	−	988.847i	−1.10903	−	1.21779i
$813$		0			0
$814$	1112.08	+	491.367i	1.36619	+	0.603645i
$815$		−	509.775i		−	0.625491i
$816$		0			0
$817$	−634.239			−0.776302
$818$	111.496	−	252.342i	0.136304	−	0.308486i
$819$		0			0
$820$	927.319	−	844.501i	1.13088	−	1.02988i
$821$			462.493i			0.563329i	0.959513	+	0.281664i	$0.0908864\pi$
$821$			462.493i			0.563329i	−0.959513	+	0.281664i	$0.909114\pi$
$822$		0			0
$823$		−	278.012i		−	0.337803i	−0.985633	−	0.168902i	$-0.945978\pi$
$823$		−	278.012i		−	0.337803i	0.985633	−	0.168902i	$-0.0540220\pi$
$824$	181.056	+	541.568i	0.219729	+	0.657243i
$825$		0			0
$826$	−209.857	−	92.7247i	−0.254064	−	0.112257i
$827$	71.7532			0.0867632			0.0433816	−	0.999059i	$-0.486187\pi$
$827$	71.7532			0.0867632			0.0433816	+	0.999059i	$0.486187\pi$
$828$		0			0
$829$			952.413i			1.14887i	0.818550	+	0.574435i	$0.194778\pi$
$829$			952.413i			1.14887i	−0.818550	+	0.574435i	$0.805222\pi$
$830$	567.082	+	250.563i	0.683231	+	0.301884i
$831$		0			0
$832$	217.684	+	289.175i	0.261639	+	0.347566i
$833$	731.752			0.878454
$834$		0			0
$835$	770.573			0.922842
$836$	−1601.42	−	1758.47i	−1.91557	−	2.10343i
$837$		0			0
$838$	51.9886	−	117.662i	0.0620389	−	0.140408i
$839$			595.797i			0.710127i	0.934842	+	0.355064i	$0.115541\pi$
$839$			595.797i			0.710127i	−0.934842	+	0.355064i	$0.884459\pi$
$840$		0			0
$841$	−48.2546			−0.0573776
$842$	1053.14	+	465.329i	1.25077	+	0.552647i
$843$		0			0
$844$	134.197	+	147.357i	0.159001	+	0.174594i
$845$		−	755.729i		−	0.894354i
$846$		0			0
$847$			2247.40i			2.65336i
$848$	179.983	+	16.8623i	0.212244	+	0.0198848i
$849$		0			0
$850$	−41.8033	+	94.6104i	−0.0491803	+	0.111306i
$851$	−657.754			−0.772919
$852$		0			0
$853$		−	1077.22i		−	1.26286i	−0.775433	−	0.631429i	$-0.782469\pi$
$853$		−	1077.22i		−	1.26286i	0.775433	−	0.631429i	$-0.217531\pi$
$854$	28.8872	−	65.3783i	0.0338258	−	0.0765554i
$855$		0			0
$856$	−74.8847	+	25.0354i	−0.0874822	+	0.0292469i
$857$	−1262.22			−1.47284			−0.736419	−	0.676526i	$-0.763485\pi$
$857$	−1262.22			−1.47284			−0.736419	+	0.676526i	$0.763485\pi$
$858$		0			0
$859$	−1636.50			−1.90512			−0.952560	−	0.304351i	$-0.901560\pi$
$859$	−1636.50			−1.90512			−0.952560	+	0.304351i	$0.901560\pi$
$860$	−311.949	+	284.089i	−0.362731	+	0.330336i
$861$		0			0
$862$	−59.7742	−	26.4110i	−0.0693436	−	0.0306392i
$863$			1434.00i			1.66165i	0.556536	+	0.830824i	$0.312130\pi$
$863$			1434.00i			1.66165i	−0.556536	+	0.830824i	$0.687870\pi$
$864$		0			0
$865$	561.668			0.649328
$866$	−66.7028	+	150.964i	−0.0770240	+	0.174323i
$867$		0			0
$868$	−196.967	−	216.283i	−0.226920	−	0.249174i
$869$			2416.72i			2.78104i
$870$		0			0
$871$			74.6306i			0.0856838i
$872$	−87.8297	−	262.713i	−0.100722	−	0.301276i
$873$		0			0
$874$	1176.96	+	520.036i	1.34664	+	0.595007i
$875$	1210.77			1.38374
$876$		0			0
$877$			171.723i			0.195807i	0.995196	+	0.0979036i	$0.0312137\pi$
$877$			171.723i			0.195807i	−0.995196	+	0.0979036i	$0.968786\pi$
$878$	−516.480	−	228.205i	−0.588246	−	0.259915i
$879$		0			0
$880$	−1575.31	−	147.589i	−1.79012	−	0.167714i
$881$	403.956			0.458520			0.229260	−	0.973365i	$-0.426369\pi$
$881$	403.956			0.458520			0.229260	+	0.973365i	$0.426369\pi$
$882$		0			0
$883$	−922.826			−1.04510			−0.522552	−	0.852608i	$-0.675020\pi$
$883$	−922.826			−1.04510			−0.522552	+	0.852608i	$0.675020\pi$
$884$	−159.524	+	145.277i	−0.180457	+	0.164340i
$885$		0			0
$886$	27.6944	−	62.6788i	0.0312578	−	0.0707435i
$887$		−	298.016i		−	0.335982i	−0.985789	−	0.167991i	$-0.946272\pi$
$887$		−	298.016i		−	0.335982i	0.985789	−	0.167991i	$-0.0537279\pi$
$888$		0			0
$889$	1130.98			1.27220
$890$	1158.52	+	511.887i	1.30170	+	0.575154i
$891$		0			0
$892$	564.450	−	514.039i	0.632791	−	0.576277i
$893$		−	1027.46i		−	1.15058i
$894$		0			0
$895$			1692.24i			1.89078i
$896$	−1397.67	+	326.107i	−1.55990	+	0.363959i
$897$		0			0
$898$	−548.237	+	1240.78i	−0.610509	+	1.38172i
$899$	−194.500			−0.216351
$900$		0			0
$901$			107.759i			0.119599i
$902$	−823.844	+	1864.55i	−0.913353	+	2.06713i
$903$		0			0
$904$	−896.189	+	299.613i	−0.991360	+	0.331430i
$905$	1932.09			2.13491
$906$		0			0
$907$	1390.81			1.53342			0.766711	−	0.641992i	$-0.221892\pi$
$907$	1390.81			1.53342			0.766711	+	0.641992i	$0.221892\pi$
$908$	978.002	+	1073.91i	1.07710	+	1.18272i
$909$		0			0
$910$	−639.847	−	282.714i	−0.703128	−	0.310675i
$911$		−	1183.48i		−	1.29910i	−0.760318	−	0.649551i	$-0.774957\pi$
$911$		−	1183.48i		−	1.29910i	0.760318	−	0.649551i	$-0.225043\pi$
$912$		0			0
$913$	−1007.61			−1.10362
$914$	−229.934	+	520.393i	−0.251569	+	0.569358i
$915$		0			0
$916$	−395.616	+	360.283i	−0.431895	+	0.393322i
$917$			532.657i			0.580869i
$918$		0			0
$919$			1112.75i			1.21083i	0.795911	+	0.605414i	$0.206992\pi$
$919$			1112.75i			1.21083i	−0.795911	+	0.605414i	$0.793008\pi$
$920$	811.820	−	271.406i	0.882413	−	0.295007i
$921$		0			0
$922$	−315.274	−	139.303i	−0.341946	−	0.151088i
$923$	−586.846			−0.635803
$924$		0			0
$925$		−	183.854i		−	0.198761i
$926$	1184.00	+	523.147i	1.27862	+	0.564954i
$927$		0			0
$928$	−465.402	+	833.065i	−0.501511	+	0.897700i
$929$	−1045.10			−1.12497			−0.562487	−	0.826806i	$-0.690155\pi$
$929$	−1045.10			−1.12497			−0.562487	+	0.826806i	$0.690155\pi$
$930$		0			0
$931$	2544.46			2.73304
$932$	−69.2534	−	76.0450i	−0.0743063	−	0.0815933i
$933$		0			0
$934$	−152.652	+	345.487i	−0.163439	+	0.369900i
$935$		−	943.166i		−	1.00873i
$936$		0			0
$937$	1096.08			1.16977			0.584887	−	0.811115i	$-0.301139\pi$
$937$	1096.08			1.16977			0.584887	+	0.811115i	$0.301139\pi$
$938$	−270.681	−	119.599i	−0.288572	−	0.127505i
$939$		0			0
$940$	−460.222	−	505.356i	−0.489598	−	0.537612i
$941$			770.502i			0.818812i	0.912352	+	0.409406i	$0.134264\pi$
$941$			770.502i			0.818812i	−0.912352	+	0.409406i	$0.865736\pi$
$942$		0			0
$943$		−	1102.81i		−	1.16947i
$944$	−15.2694	+	162.981i	−0.0161753	+	0.172649i
$945$		0			0
$946$	277.140	−	627.230i	0.292960	−	0.663034i
$947$	253.986			0.268201			0.134100	−	0.990968i	$-0.457186\pi$
$947$	253.986			0.268201			0.134100	+	0.990968i	$0.457186\pi$
$948$		0			0
$949$		−	120.506i		−	0.126982i
$950$	−145.359	+	328.981i	−0.153010	+	0.346296i
$951$		0			0
$952$	−271.265	−	811.397i	−0.284942	−	0.852307i
$953$	1698.69			1.78246			0.891230	−	0.453551i	$-0.149843\pi$
$953$	1698.69			1.78246			0.891230	+	0.453551i	$0.149843\pi$
$954$		0			0
$955$	−1762.00			−1.84503
$956$	1041.82	−	948.772i	1.08977	−	0.992440i
$957$		0			0
$958$	−248.740	−	109.905i	−0.259646	−	0.114724i
$959$		−	2500.49i		−	2.60740i
$960$		0			0
$961$	918.459			0.955732
$962$	154.999	−	350.798i	0.161122	−	0.364655i
$963$		0			0
$964$	854.155	+	937.920i	0.886053	+	0.972946i
$965$			587.089i			0.608382i
$966$		0			0
$967$		−	822.004i		−	0.850056i	−0.905180	−	0.425028i	$-0.860264\pi$
$967$		−	822.004i		−	0.850056i	0.905180	−	0.425028i	$-0.139736\pi$
$968$	1520.75	−	508.414i	1.57102	−	0.525221i
$969$		0			0
$970$	1279.04	+	565.138i	1.31859	+	0.582617i
$971$	−1719.01			−1.77035			−0.885175	−	0.465257i	$-0.845962\pi$
$971$	−1719.01			−1.77035			−0.885175	+	0.465257i	$0.845962\pi$
$972$		0			0
$973$		−	514.968i		−	0.529258i
$974$	1026.39	+	453.505i	1.05378	+	0.465611i
$975$		0			0
$976$	−50.7746	−	4.75700i	−0.0520231	−	0.00487398i
$977$	977.149			1.00015			0.500076	−	0.865981i	$-0.333305\pi$
$977$	977.149			1.00015			0.500076	+	0.865981i	$0.333305\pi$
$978$		0			0
$979$	−2058.49			−2.10264
$980$	1251.49	−	1139.72i	1.27703	−	1.16298i
$981$		0			0
$982$	−18.3217	+	41.4662i	−0.0186576	+	0.0422263i
$983$			675.494i			0.687176i	0.939121	+	0.343588i	$0.111642\pi$
$983$			675.494i			0.687176i	−0.939121	+	0.343588i	$0.888358\pi$
$984$		0			0
$985$	1153.05			1.17061
$986$	−520.311	−	229.898i	−0.527698	−	0.233162i
$987$		0			0
$988$	−554.699	+	505.159i	−0.561436	+	0.511294i
$989$			370.985i			0.375111i
$990$		0			0
$991$		−	1764.75i		−	1.78077i	−0.455206	−	0.890386i	$-0.650434\pi$
$991$		−	1764.75i		−	1.78077i	0.455206	−	0.890386i	$-0.349566\pi$
$992$	−101.794	+	182.210i	−0.102615	+	0.183679i
$993$		0			0
$994$	940.451	−	2128.46i	0.946128	−	2.14130i
$995$	4.59323			0.00461632
$996$		0			0
$997$			1532.31i			1.53692i	0.639896	+	0.768461i	$0.278977\pi$
$997$			1532.31i			1.53692i	−0.639896	+	0.768461i	$0.721023\pi$
$998$	−41.4364	+	93.7800i	−0.0415194	+	0.0939679i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.b.b.163.8	yes	16
3.2	odd	2	inner	216.3.b.b.163.9	yes	16
4.3	odd	2		864.3.b.b.271.3		16
8.3	odd	2	inner	216.3.b.b.163.7	✓	16
8.5	even	2		864.3.b.b.271.14		16
12.11	even	2		864.3.b.b.271.13		16
24.5	odd	2		864.3.b.b.271.4		16
24.11	even	2	inner	216.3.b.b.163.10	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.b.b.163.7	✓	16	8.3	odd	2	inner
216.3.b.b.163.8	yes	16	1.1	even	1	trivial
216.3.b.b.163.9	yes	16	3.2	odd	2	inner
216.3.b.b.163.10	yes	16	24.11	even	2	inner
864.3.b.b.271.3		16	4.3	odd	2
864.3.b.b.271.4		16	24.5	odd	2
864.3.b.b.271.13		16	12.11	even	2
864.3.b.b.271.14		16	8.5	even	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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.808307 + 1.82938i) q^{2} +(-2.69328 - 2.95740i) q^{4} -5.51565i q^{5} +11.2126i q^{7} +(7.58722 - 2.53655i) q^{8} +O(q^{10})\)	\(q+(-0.808307 + 1.82938i) q^{2} +(-2.69328 - 2.95740i) q^{4} -5.51565i q^{5} +11.2126i q^{7} +(7.58722 - 2.53655i) q^{8} +(10.0902 + 4.45834i) q^{10} -17.9286 q^{11} +5.65548i q^{13} +(-20.5121 - 9.06320i) q^{14} +(-1.49248 + 15.9302i) q^{16} -9.53773 q^{17} -33.1648 q^{19} +(-16.3120 + 14.8552i) q^{20} +(14.4918 - 32.7983i) q^{22} +19.3990i q^{23} -5.42237 q^{25} +(-10.3460 - 4.57136i) q^{26} +(33.1601 - 30.1986i) q^{28} -29.8204i q^{29} -6.52238i q^{31} +(-27.9361 - 15.6068i) q^{32} +(7.70941 - 17.4482i) q^{34} +61.8446 q^{35} +33.9065i q^{37} +(26.8073 - 60.6710i) q^{38} +(-13.9907 - 41.8484i) q^{40} -56.8489 q^{41} +19.1239 q^{43} +(48.2868 + 53.0222i) q^{44} +(-35.4883 - 15.6804i) q^{46} +30.9806i q^{47} -76.7218 q^{49} +(4.38294 - 9.91959i) q^{50} +(16.7255 - 15.2318i) q^{52} -11.2982i q^{53} +98.8879i q^{55} +(28.4412 + 85.0723i) q^{56} +(54.5529 + 24.1040i) q^{58} +10.2309 q^{59} +3.18731i q^{61} +(11.9319 + 5.27208i) q^{62} +(51.1318 - 38.4907i) q^{64} +31.1936 q^{65} +13.1962 q^{67} +(25.6878 + 28.2069i) q^{68} +(-49.9894 + 113.137i) q^{70} +103.766i q^{71} -21.3079 q^{73} +(-62.0280 - 27.4069i) q^{74} +(89.3220 + 98.0816i) q^{76} -201.026i q^{77} -134.797i q^{79} +(87.8656 + 8.23201i) q^{80} +(45.9514 - 103.998i) q^{82} +56.2011 q^{83} +52.6068i q^{85} +(-15.4580 + 34.9849i) q^{86} +(-136.028 + 45.4768i) q^{88} +114.816 q^{89} -63.4125 q^{91} +(57.3708 - 52.2471i) q^{92} +(-56.6754 - 25.0418i) q^{94} +182.925i q^{95} +126.760 q^{97} +(62.0148 - 140.354i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4}+O(q^{10}) \) 16 * q + 4 * q^4	\( 16 q + 4 q^{4} + 24 q^{10} + 16 q^{16} - 64 q^{19} + 80 q^{22} - 80 q^{25} - 12 q^{28} + 8 q^{34} - 72 q^{40} - 64 q^{43} - 192 q^{46} - 128 q^{49} + 84 q^{52} - 96 q^{58} + 376 q^{64} + 128 q^{67} + 192 q^{70} + 80 q^{73} + 308 q^{76} + 272 q^{82} - 136 q^{88} + 192 q^{91} + 336 q^{94} + 80 q^{97}+O(q^{100}) \) 16 * q + 4 * q^4 + 24 * q^10 + 16 * q^16 - 64 * q^19 + 80 * q^22 - 80 * q^25 - 12 * q^28 + 8 * q^34 - 72 * q^40 - 64 * q^43 - 192 * q^46 - 128 * q^49 + 84 * q^52 - 96 * q^58 + 376 * q^64 + 128 * q^67 + 192 * q^70 + 80 * q^73 + 308 * q^76 + 272 * q^82 - 136 * q^88 + 192 * q^91 + 336 * q^94 + 80 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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