LMFDB - Embedded newform 72.3.h.a.53.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,3,Mod(53,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, 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("72.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	72.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:	$1.96185790339$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.33808912384.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 11x^{6} - 18x^{5} + 47x^{4} - 28x^{3} - 44x^{2} + 48x + 36 $ x^8 - 2x^7 + 11x^6 - 18x^5 + 47x^4 - 28x^3 - 44x^2 + 48*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			53.5
Root			$1.15139 + 0.593052i$ of defining polynomial
Character	$\chi$	$=$	72.53
Dual form			72.3.h.a.53.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16130 - 1.62831i) q^{2} +(-1.30278 - 3.78190i) q^{4} +7.67101 q^{5} -7.21110 q^{7} +(-7.67101 - 2.27059i) q^{8} +O(q^{10})$	\(q+(1.16130 - 1.62831i) q^{2} +(-1.30278 - 3.78190i) q^{4} +7.67101 q^{5} -7.21110 q^{7} +(-7.67101 - 2.27059i) q^{8} +(8.90833 - 12.4908i) q^{10} +6.05164 q^{11} -2.29014i q^{13} +(-8.37424 + 11.7419i) q^{14} +(-12.6056 + 9.85394i) q^{16} +21.8103i q^{17} +34.8355i q^{19} +(-9.99361 - 29.0110i) q^{20} +(7.02776 - 9.85394i) q^{22} -21.5117i q^{23} +33.8444 q^{25} +(-3.72905 - 2.65953i) q^{26} +(9.39445 + 27.2717i) q^{28} +10.9098 q^{29} -37.6333 q^{31} +(1.40645 + 31.9691i) q^{32} +(35.5139 + 25.3282i) q^{34} -55.3164 q^{35} -34.8355i q^{37} +(56.7229 + 40.4544i) q^{38} +(-58.8444 - 17.4177i) q^{40} -13.3250i q^{41} -60.5104i q^{43} +(-7.88393 - 22.8867i) q^{44} +(-35.0278 - 24.9815i) q^{46} +3.34701i q^{47} +3.00000 q^{49} +(39.3034 - 55.1091i) q^{50} +(-8.66106 + 2.98353i) q^{52} -35.1163 q^{53} +46.4222 q^{55} +(55.3164 + 16.3735i) q^{56} +(12.6695 - 17.7644i) q^{58} +37.1615 q^{59} -25.6749i q^{61} +(-43.7035 + 61.2786i) q^{62} +(53.6888 + 34.8355i) q^{64} -17.5677i q^{65} +25.6749i q^{67} +(82.4844 - 28.4139i) q^{68} +(-64.2389 + 90.0722i) q^{70} -37.2881i q^{71} -77.6888 q^{73} +(-56.7229 - 40.4544i) q^{74} +(131.744 - 45.3828i) q^{76} -43.6390 q^{77} +31.3221 q^{79} +(-96.6973 + 75.5897i) q^{80} +(-21.6972 - 15.4743i) q^{82} +55.3164 q^{83} +167.307i q^{85} +(-98.5296 - 70.2706i) q^{86} +(-46.4222 - 13.7408i) q^{88} +5.43682i q^{89} +16.5144i q^{91} +(-81.3553 + 28.0250i) q^{92} +(5.44996 + 3.88687i) q^{94} +267.223i q^{95} -52.8444 q^{97} +(3.48389 - 4.88492i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} + 28 q^{10} - 72 q^{16} - 88 q^{22} + 40 q^{25} + 104 q^{28} - 128 q^{31} + 212 q^{34} - 240 q^{40} - 136 q^{46} + 24 q^{49} + 248 q^{52} + 256 q^{55} + 260 q^{58} - 32 q^{64} - 312 q^{70} - 160 q^{73} + 304 q^{76} - 384 q^{79} - 188 q^{82} - 256 q^{88} - 216 q^{94} - 192 q^{97}+O(q^{100}) $ 8 * q + 4 * q^4 + 28 * q^10 - 72 * q^16 - 88 * q^22 + 40 * q^25 + 104 * q^28 - 128 * q^31 + 212 * q^34 - 240 * q^40 - 136 * q^46 + 24 * q^49 + 248 * q^52 + 256 * q^55 + 260 * q^58 - 32 * q^64 - 312 * q^70 - 160 * q^73 + 304 * q^76 - 384 * q^79 - 188 * q^82 - 256 * q^88 - 216 * q^94 - 192 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	1.16130	−	1.62831i	0.580649	−	0.814154i
$2$	1.16130	−	1.62831i	0.580649	−	0.814154i
$3$		0			0
$3$		0			0
$4$	−1.30278	−	3.78190i	−0.325694	−	0.945475i
$5$	7.67101			1.53420			0.767101	−	0.641526i	$-0.221698\pi$
$5$	7.67101			1.53420			0.767101	+	0.641526i	$0.221698\pi$
$6$		0			0
$7$	−7.21110			−1.03016			−0.515079	−	0.857143i	$-0.672237\pi$
$7$	−7.21110			−1.03016			−0.515079	+	0.857143i	$0.672237\pi$
$8$	−7.67101	−	2.27059i	−0.958876	−	0.283824i
$9$		0			0
$10$	8.90833	−	12.4908i	0.890833	−	1.24908i
$11$	6.05164			0.550149			0.275075	−	0.961423i	$-0.411297\pi$
$11$	6.05164			0.550149			0.275075	+	0.961423i	$0.411297\pi$
$12$		0			0
$13$		−	2.29014i		−	0.176164i	−0.996113	−	0.0880821i	$-0.971926\pi$
$13$		−	2.29014i		−	0.176164i	0.996113	−	0.0880821i	$-0.0280738\pi$
$14$	−8.37424	+	11.7419i	−0.598160	+	0.838707i
$15$		0			0
$16$	−12.6056	+	9.85394i	−0.787847	+	0.615871i
$17$			21.8103i			1.28296i	0.767140	+	0.641479i	$0.221679\pi$
$17$			21.8103i			1.28296i	−0.767140	+	0.641479i	$0.778321\pi$
$18$		0			0
$19$			34.8355i			1.83345i	0.399523	+	0.916723i	$0.369176\pi$
$19$			34.8355i			1.83345i	−0.399523	+	0.916723i	$0.630824\pi$
$20$	−9.99361	−	29.0110i	−0.499680	−	1.45055i
$21$		0			0
$22$	7.02776	−	9.85394i	0.319443	−	0.447906i
$23$		−	21.5117i		−	0.935293i	−0.883915	−	0.467647i	$-0.845102\pi$
$23$		−	21.5117i		−	0.935293i	0.883915	−	0.467647i	$-0.154898\pi$
$24$		0			0
$25$	33.8444			1.35378
$26$	−3.72905	−	2.65953i	−0.143425	−	0.102290i
$27$		0			0
$28$	9.39445	+	27.2717i	0.335516	+	0.973988i
$29$	10.9098			0.376198			0.188099	−	0.982150i	$-0.439767\pi$
$29$	10.9098			0.376198			0.188099	+	0.982150i	$0.439767\pi$
$30$		0			0
$31$	−37.6333			−1.21398			−0.606989	−	0.794710i	$-0.707623\pi$
$31$	−37.6333			−1.21398			−0.606989	+	0.794710i	$0.707623\pi$
$32$	1.40645	+	31.9691i	0.0439516	+	0.999034i
$33$		0			0
$34$	35.5139	+	25.3282i	1.04453	+	0.744948i
$35$	−55.3164			−1.58047
$36$		0			0
$37$		−	34.8355i		−	0.941499i	−0.882267	−	0.470750i	$-0.843983\pi$
$37$		−	34.8355i		−	0.941499i	0.882267	−	0.470750i	$-0.156017\pi$
$38$	56.7229	+	40.4544i	1.49271	+	1.06459i
$39$		0			0
$40$	−58.8444	−	17.4177i	−1.47111	−	0.435443i
$41$		−	13.3250i		−	0.325000i	−0.986709	−	0.162500i	$-0.948044\pi$
$41$		−	13.3250i		−	0.325000i	0.986709	−	0.162500i	$-0.0519558\pi$
$42$		0			0
$43$		−	60.5104i		−	1.40722i	−0.710587	−	0.703609i	$-0.751570\pi$
$43$		−	60.5104i		−	1.40722i	0.710587	−	0.703609i	$-0.248430\pi$
$44$	−7.88393	−	22.8867i	−0.179180	−	0.520152i
$45$		0			0
$46$	−35.0278	−	24.9815i	−0.761473	−	0.543077i
$47$			3.34701i			0.0712129i	0.999366	+	0.0356065i	$0.0113363\pi$
$47$			3.34701i			0.0712129i	−0.999366	+	0.0356065i	$0.988664\pi$
$48$		0			0
$49$	3.00000			0.0612245
$50$	39.3034	−	55.1091i	0.786069	−	1.10218i
$51$		0			0
$52$	−8.66106	+	2.98353i	−0.166559	+	0.0573756i
$53$	−35.1163			−0.662572			−0.331286	−	0.943530i	$-0.607482\pi$
$53$	−35.1163			−0.662572			−0.331286	+	0.943530i	$0.607482\pi$
$54$		0			0
$55$	46.4222			0.844040
$56$	55.3164	+	16.3735i	0.987794	+	0.292383i
$57$		0			0
$58$	12.6695	−	17.7644i	0.218439	−	0.306283i
$59$	37.1615			0.629856			0.314928	−	0.949116i	$-0.398020\pi$
$59$	37.1615			0.629856			0.314928	+	0.949116i	$0.398020\pi$
$60$		0			0
$61$		−	25.6749i		−	0.420901i	−0.977605	−	0.210450i	$-0.932507\pi$
$61$		−	25.6749i		−	0.420901i	0.977605	−	0.210450i	$-0.0674930\pi$
$62$	−43.7035	+	61.2786i	−0.704895	+	0.988365i
$63$		0			0
$64$	53.6888	+	34.8355i	0.838888	+	0.544304i
$65$		−	17.5677i		−	0.270272i
$66$		0			0
$67$			25.6749i			0.383208i	0.981472	+	0.191604i	$0.0613689\pi$
$67$			25.6749i			0.383208i	−0.981472	+	0.191604i	$0.938631\pi$
$68$	82.4844	−	28.4139i	1.21301	−	0.417852i
$69$		0			0
$70$	−64.2389	+	90.0722i	−0.917698	+	1.28675i
$71$		−	37.2881i		−	0.525185i	−0.964907	−	0.262592i	$-0.915423\pi$
$71$		−	37.2881i		−	0.525185i	0.964907	−	0.262592i	$-0.0845775\pi$
$72$		0			0
$73$	−77.6888			−1.06423			−0.532115	−	0.846672i	$-0.678603\pi$
$73$	−77.6888			−1.06423			−0.532115	+	0.846672i	$0.678603\pi$
$74$	−56.7229	−	40.4544i	−0.766526	−	0.546681i
$75$		0			0
$76$	131.744	−	45.3828i	1.73348	−	0.597142i
$77$	−43.6390			−0.566740
$78$		0			0
$79$	31.3221			0.396483			0.198241	−	0.980153i	$-0.436477\pi$
$79$	31.3221			0.396483			0.198241	+	0.980153i	$0.436477\pi$
$80$	−96.6973	+	75.5897i	−1.20872	+	0.944871i
$81$		0			0
$82$	−21.6972	−	15.4743i	−0.264600	−	0.188711i
$83$	55.3164			0.666463			0.333232	−	0.942845i	$-0.391861\pi$
$83$	55.3164			0.666463			0.333232	+	0.942845i	$0.391861\pi$
$84$		0			0
$85$			167.307i			1.96832i
$86$	−98.5296	−	70.2706i	−1.14569	−	0.817100i
$87$		0			0
$88$	−46.4222	−	13.7408i	−0.527525	−	0.156146i
$89$			5.43682i			0.0610878i	0.999533	+	0.0305439i	$0.00972394\pi$
$89$			5.43682i			0.0610878i	−0.999533	+	0.0305439i	$0.990276\pi$
$90$		0			0
$91$			16.5144i			0.181477i
$92$	−81.3553	+	28.0250i	−0.884297	+	0.304619i
$93$		0			0
$94$	5.44996	+	3.88687i	0.0579783	+	0.0413497i
$95$			267.223i			2.81288i
$96$		0			0
$97$	−52.8444			−0.544788			−0.272394	−	0.962186i	$-0.587815\pi$
$97$	−52.8444			−0.544788			−0.272394	+	0.962186i	$0.587815\pi$
$98$	3.48389	−	4.88492i	0.0355499	−	0.0498462i
$99$		0			0
$100$	−44.0917	−	127.996i	−0.440917	−	1.27996i
$101$	90.0069			0.891158			0.445579	−	0.895243i	$-0.352998\pi$
$101$	90.0069			0.891158			0.445579	+	0.895243i	$0.352998\pi$
$102$		0			0
$103$	119.211			1.15739			0.578695	−	0.815544i	$-0.303562\pi$
$103$	119.211			1.15739			0.578695	+	0.815544i	$0.303562\pi$
$104$	−5.19996	+	17.5677i	−0.0499996	+	0.168920i
$105$		0			0
$106$	−40.7805	+	57.1802i	−0.384722	+	0.539436i
$107$	24.2066			0.226230			0.113115	−	0.993582i	$-0.463917\pi$
$107$	24.2066			0.226230			0.113115	+	0.993582i	$0.463917\pi$
$108$		0			0
$109$			132.472i			1.21533i	0.794192	+	0.607667i	$0.207895\pi$
$109$			132.472i			1.21533i	−0.794192	+	0.607667i	$0.792105\pi$
$110$	53.9100	−	75.5897i	0.490091	−	0.687179i
$111$		0			0
$112$	90.8999	−	71.0578i	0.811606	−	0.634444i
$113$		−	160.560i		−	1.42089i	−0.703754	−	0.710444i	$-0.748494\pi$
$113$		−	160.560i		−	1.42089i	0.703754	−	0.710444i	$-0.251506\pi$
$114$		0			0
$115$		−	165.017i		−	1.43493i
$116$	−14.2130	−	41.2596i	−0.122525	−	0.355686i
$117$		0			0
$118$	43.1556	−	60.5104i	0.365725	−	0.512800i
$119$		−	157.276i		−	1.32165i
$120$		0			0
$121$	−84.3776			−0.697336
$122$	−41.8067	−	29.8162i	−0.342678	−	0.244395i
$123$		0			0
$124$	49.0278	+	142.325i	0.395385	+	1.14779i
$125$	67.8456			0.542765
$126$		0			0
$127$	−146.478			−1.15337			−0.576684	−	0.816967i	$-0.695654\pi$
$127$	−146.478			−1.15337			−0.576684	+	0.816967i	$0.695654\pi$
$128$	119.072	−	46.9676i	0.930247	−	0.366934i
$129$		0			0
$130$	−28.6056	−	20.4013i	−0.220043	−	0.156933i
$131$	184.956			1.41188			0.705939	−	0.708273i	$-0.250525\pi$
$131$	184.956			1.41188			0.705939	+	0.708273i	$0.250525\pi$
$132$		0			0
$133$		−	251.202i		−	1.88874i
$134$	41.8067	+	29.8162i	0.311990	+	0.222509i
$135$		0			0
$136$	49.5223	−	167.307i	0.364134	−	1.23020i
$137$			133.313i			0.973089i	0.873656	+	0.486544i	$0.161743\pi$
$137$			133.313i			0.973089i	−0.873656	+	0.486544i	$0.838257\pi$
$138$		0			0
$139$			165.017i			1.18717i	0.804771	+	0.593586i	$0.202288\pi$
$139$			165.017i			1.18717i	−0.804771	+	0.593586i	$0.797712\pi$
$140$	72.0649	+	209.201i	0.514749	+	1.49430i
$141$		0			0
$142$	−60.7166	−	43.3026i	−0.427582	−	0.304948i
$143$		−	13.8591i		−	0.0969166i
$144$		0			0
$145$	83.6888			0.577164
$146$	−90.2198	+	126.501i	−0.617944	+	0.866448i
$147$		0			0
$148$	−131.744	+	45.3828i	−0.890164	+	0.306641i
$149$	−228.937			−1.53649			−0.768244	−	0.640157i	$-0.778869\pi$
$149$	−228.937			−1.53649			−0.768244	+	0.640157i	$0.778869\pi$
$150$		0			0
$151$	162.478			1.07601			0.538006	−	0.842941i	$-0.319178\pi$
$151$	162.478			1.07601			0.538006	+	0.842941i	$0.319178\pi$
$152$	79.0972	−	267.223i	0.520376	−	1.75805i
$153$		0			0
$154$	−50.6779	+	71.0578i	−0.329077	+	0.461414i
$155$	−288.686			−1.86249
$156$		0			0
$157$		−	113.667i		−	0.723993i	−0.932179	−	0.361997i	$-0.882095\pi$
$157$		−	113.667i		−	0.723993i	0.932179	−	0.361997i	$-0.117905\pi$
$158$	36.3743	−	51.0021i	0.230217	−	0.322798i
$159$		0			0
$160$	10.7889	+	245.235i	0.0674306	+	1.53272i
$161$			155.123i			0.963499i
$162$		0			0
$163$		−	111.860i		−	0.686259i	−0.939288	−	0.343130i	$-0.888513\pi$
$163$		−	111.860i		−	0.686259i	0.939288	−	0.343130i	$-0.111487\pi$
$164$	−50.3939	+	17.3595i	−0.307280	+	0.105851i
$165$		0			0
$166$	64.2389	−	90.0722i	0.386981	−	0.542604i
$167$		−	151.541i		−	0.907430i	−0.891147	−	0.453715i	$-0.850098\pi$
$167$		−	151.541i		−	0.907430i	0.891147	−	0.453715i	$-0.149902\pi$
$168$		0			0
$169$	163.755			0.968966
$170$	272.427	+	194.293i	1.60251	+	1.14290i
$171$		0			0
$172$	−228.844	+	78.8315i	−1.33049	+	0.458323i
$173$	−98.0198			−0.566588			−0.283294	−	0.959033i	$-0.591427\pi$
$173$	−98.0198			−0.566588			−0.283294	+	0.959033i	$0.591427\pi$
$174$		0			0
$175$	−244.056			−1.39460
$176$	−76.2843	+	59.6325i	−0.433433	+	0.338821i
$177$		0			0
$178$	8.85281	+	6.31376i	0.0497349	+	0.0354706i
$179$	−222.117			−1.24088			−0.620440	−	0.784254i	$-0.713046\pi$
$179$	−222.117			−1.24088			−0.620440	+	0.784254i	$0.713046\pi$
$180$		0			0
$181$			118.731i			0.655971i	0.944683	+	0.327985i	$0.106370\pi$
$181$			118.731i			0.655971i	−0.944683	+	0.327985i	$0.893630\pi$
$182$	26.8905	+	19.1781i	0.147750	+	0.105374i
$183$		0			0
$184$	−48.8444	+	165.017i	−0.265459	+	0.896831i
$185$		−	267.223i		−	1.44445i
$186$		0			0
$187$			131.988i			0.705818i
$188$	12.6581	−	4.36040i	0.0673301	−	0.0231936i
$189$		0			0
$190$	435.122	+	310.326i	2.29012	+	1.63329i
$191$			151.541i			0.793408i	0.917947	+	0.396704i	$0.129846\pi$
$191$			151.541i			0.793408i	−0.917947	+	0.396704i	$0.870154\pi$
$192$		0			0
$193$	113.378			0.587449			0.293724	−	0.955890i	$-0.405105\pi$
$193$	113.378			0.587449			0.293724	+	0.955890i	$0.405105\pi$
$194$	−61.3681	+	86.0470i	−0.316330	+	0.443541i
$195$		0			0
$196$	−3.90833	−	11.3457i	−0.0199404	−	0.0578862i
$197$	319.454			1.62159			0.810796	−	0.585329i	$-0.199035\pi$
$197$	319.454			1.62159			0.810796	+	0.585329i	$0.199035\pi$
$198$		0			0
$199$	−41.0109			−0.206085			−0.103043	−	0.994677i	$-0.532858\pi$
$199$	−41.0109			−0.206085			−0.103043	+	0.994677i	$0.532858\pi$
$200$	−259.621	−	76.8469i	−1.29810	−	0.384234i
$201$		0			0
$202$	104.525	−	146.559i	0.517450	−	0.725540i
$203$	−78.6713			−0.387544
$204$		0			0
$205$		−	102.216i		−	0.498616i
$206$	138.440	−	194.112i	0.672037	−	0.942293i
$207$		0			0
$208$	22.5668	+	28.8684i	0.108494	+	0.138790i
$209$			210.812i			1.00867i
$210$		0			0
$211$			95.3459i			0.451876i	0.974142	+	0.225938i	$0.0725447\pi$
$211$			95.3459i			0.451876i	−0.974142	+	0.225938i	$0.927455\pi$
$212$	45.7487	+	132.806i	0.215796	+	0.626445i
$213$		0			0
$214$	28.1110	−	39.4157i	0.131360	−	0.184186i
$215$		−	464.176i		−	2.15896i
$216$		0			0
$217$	271.378			1.25059
$218$	215.704	+	153.839i	0.989470	+	0.705683i
$219$		0			0
$220$	−60.4777	−	175.564i	−0.274899	−	0.798019i
$221$	49.9485			0.226011
$222$		0			0
$223$	−268.167			−1.20254			−0.601270	−	0.799046i	$-0.705338\pi$
$223$	−268.167			−1.20254			−0.601270	+	0.799046i	$0.705338\pi$
$224$	−10.1421	−	230.532i	−0.0452770	−	1.02916i
$225$		0			0
$226$	−261.442	−	186.458i	−1.15682	−	0.825036i
$227$	65.7164			0.289499			0.144750	−	0.989468i	$-0.453762\pi$
$227$	65.7164			0.289499			0.144750	+	0.989468i	$0.453762\pi$
$228$		0			0
$229$		−	155.373i		−	0.678484i	−0.940699	−	0.339242i	$-0.889829\pi$
$229$		−	155.373i		−	0.678484i	0.940699	−	0.339242i	$-0.110171\pi$
$230$	−268.698	−	191.634i	−1.16825	−	0.833190i
$231$		0			0
$232$	−83.6888	−	24.7716i	−0.360728	−	0.106774i
$233$			285.451i			1.22511i	0.790427	+	0.612556i	$0.209859\pi$
$233$			285.451i			1.22511i	−0.790427	+	0.612556i	$0.790141\pi$
$234$		0			0
$235$			25.6749i			0.109255i
$236$	−48.4131	−	140.541i	−0.205140	−	0.595514i
$237$		0			0
$238$	−256.094	−	182.645i	−1.07603	−	0.767414i
$239$			421.153i			1.76214i	0.472982	+	0.881072i	$0.343178\pi$
$239$			421.153i			1.76214i	−0.472982	+	0.881072i	$0.656822\pi$
$240$		0			0
$241$	−191.600			−0.795019			−0.397510	−	0.917598i	$-0.630126\pi$
$241$	−191.600			−0.795019			−0.397510	+	0.917598i	$0.630126\pi$
$242$	−97.9876	+	137.393i	−0.404907	+	0.567739i
$243$		0			0
$244$	−97.1001	+	33.4487i	−0.397951	+	0.137085i
$245$	23.0130			0.0939307
$246$		0			0
$247$	79.7779			0.322988
$248$	288.686	+	85.4499i	1.16405	+	0.344556i
$249$		0			0
$250$	78.7889	−	110.473i	0.315156	−	0.441894i
$251$	483.190			1.92506			0.962529	−	0.271178i	$-0.0874131\pi$
$251$	483.190			1.92506			0.962529	+	0.271178i	$0.0874131\pi$
$252$		0			0
$253$		−	130.181i		−	0.514551i
$254$	−170.104	+	238.511i	−0.669702	+	0.939019i
$255$		0			0
$256$	61.7998	−	248.429i	0.241406	−	0.970424i
$257$			21.2132i			0.0825416i	0.999148	+	0.0412708i	$0.0131406\pi$
$257$			21.2132i			0.0825416i	−0.999148	+	0.0412708i	$0.986859\pi$
$258$		0			0
$259$			251.202i			0.969893i
$260$	−66.4391	+	22.8867i	−0.255535	+	0.0880258i
$261$		0			0
$262$	214.789	−	301.165i	0.819805	−	1.14949i
$263$		−	246.670i		−	0.937910i	−0.883222	−	0.468955i	$-0.844631\pi$
$263$		−	246.670i		−	0.937910i	0.883222	−	0.468955i	$-0.155369\pi$
$264$		0			0
$265$	−269.378			−1.01652
$266$	−409.035	−	291.721i	−1.53772	−	1.09669i
$267$		0			0
$268$	97.1001	−	33.4487i	0.362314	−	0.124809i
$269$	241.040			0.896060			0.448030	−	0.894019i	$-0.352126\pi$
$269$	241.040			0.896060			0.448030	+	0.894019i	$0.352126\pi$
$270$		0			0
$271$	61.7443			0.227839			0.113919	−	0.993490i	$-0.463659\pi$
$271$	61.7443			0.227839			0.113919	+	0.993490i	$0.463659\pi$
$272$	−214.917	−	274.931i	−0.790137	−	1.01077i
$273$		0			0
$274$	217.075	+	154.816i	0.792244	+	0.565023i
$275$	204.814			0.744779
$276$		0			0
$277$			379.093i			1.36857i	0.729215	+	0.684284i	$0.239885\pi$
$277$			379.093i			1.36857i	−0.729215	+	0.684284i	$0.760115\pi$
$278$	268.698	+	191.634i	0.966541	+	0.689330i
$279$		0			0
$280$	424.333	+	125.601i	1.51548	+	0.448575i
$281$		−	301.227i		−	1.07198i	−0.844223	−	0.535992i	$-0.819938\pi$
$281$		−	301.227i		−	1.07198i	0.844223	−	0.535992i	$-0.180062\pi$
$282$		0			0
$283$		−	399.705i		−	1.41238i	−0.708020	−	0.706192i	$-0.750412\pi$
$283$		−	399.705i		−	1.41238i	0.708020	−	0.706192i	$-0.249588\pi$
$284$	−141.020	+	48.5781i	−0.496549	+	0.171050i
$285$		0			0
$286$	−22.5668	−	16.0945i	−0.0789051	−	0.0562745i
$287$			96.0880i			0.334801i
$288$		0			0
$289$	−186.689			−0.645982
$290$	97.1876	−	136.271i	0.335130	−	0.469901i
$291$		0			0
$292$	101.211	+	293.811i	0.346613	+	1.00620i
$293$	−258.085			−0.880838			−0.440419	−	0.897792i	$-0.645170\pi$
$293$	−258.085			−0.880838			−0.440419	+	0.897792i	$0.645170\pi$
$294$		0			0
$295$	285.066			0.966327
$296$	−79.0972	+	267.223i	−0.267220	+	0.902782i
$297$		0			0
$298$	−265.864	+	372.780i	−0.892160	+	1.25094i
$299$	−49.2648			−0.164765
$300$		0			0
$301$			436.347i			1.44966i
$302$	188.685	−	264.564i	0.624785	−	0.876039i
$303$		0			0
$304$	−343.267	−	439.120i	−1.12917	−	1.44448i
$305$		−	196.953i		−	0.645747i
$306$		0			0
$307$			286.038i			0.931719i	0.884859	+	0.465859i	$0.154255\pi$
$307$			286.038i			0.931719i	−0.884859	+	0.465859i	$0.845745\pi$
$308$	56.8518	+	165.038i	0.184584	+	0.535839i
$309$		0			0
$310$	−335.250	+	470.069i	−1.08145	+	1.51635i
$311$			464.647i			1.49404i	0.664800	+	0.747021i	$0.268517\pi$
$311$			464.647i			1.49404i	−0.664800	+	0.747021i	$0.731483\pi$
$312$		0			0
$313$	158.000			0.504792			0.252396	−	0.967624i	$-0.418781\pi$
$313$	158.000			0.504792			0.252396	+	0.967624i	$0.418781\pi$
$314$	−185.085	−	132.001i	−0.589442	−	0.420386i
$315$		0			0
$316$	−40.8057	−	118.457i	−0.129132	−	0.374865i
$317$	−28.6388			−0.0903433			−0.0451717	−	0.998979i	$-0.514383\pi$
$317$	−28.6388			−0.0903433			−0.0451717	+	0.998979i	$0.514383\pi$
$318$		0			0
$319$	66.0219			0.206965
$320$	411.848	+	267.223i	1.28702	+	0.835073i
$321$		0			0
$322$	252.589	+	180.144i	0.784437	+	0.559455i
$323$	−759.772			−2.35224
$324$		0			0
$325$		−	77.5083i		−	0.238487i
$326$	−182.143	−	129.903i	−0.558721	−	0.398476i
$327$		0			0
$328$	−30.2557	+	102.216i	−0.0922429	+	0.311635i
$329$		−	24.1356i		−	0.0733605i
$330$		0			0
$331$		−	428.993i		−	1.29605i	−0.761619	−	0.648026i	$-0.775595\pi$
$331$		−	428.993i		−	1.29605i	0.761619	−	0.648026i	$-0.224405\pi$
$332$	−72.0649	−	209.201i	−0.217063	−	0.630124i
$333$		0			0
$334$	−246.755	−	175.984i	−0.738788	−	0.526898i
$335$			196.953i			0.587919i
$336$		0			0
$337$	290.755			0.862775			0.431388	−	0.902167i	$-0.358024\pi$
$337$	290.755			0.862775			0.431388	+	0.902167i	$0.358024\pi$
$338$	190.169	−	266.644i	0.562629	−	0.788888i
$339$		0			0
$340$	632.738	−	217.963i	1.86100	−	0.641069i
$341$	−227.743			−0.667869
$342$		0			0
$343$	331.711			0.967087
$344$	−137.394	+	464.176i	−0.399403	+	1.34935i
$345$		0			0
$346$	−113.830	+	159.606i	−0.328989	+	0.461290i
$347$	179.756			0.518029			0.259014	−	0.965873i	$-0.416602\pi$
$347$	179.756			0.518029			0.259014	+	0.965873i	$0.416602\pi$
$348$		0			0
$349$			225.527i			0.646210i	0.946363	+	0.323105i	$0.104727\pi$
$349$			225.527i			0.646210i	−0.946363	+	0.323105i	$0.895273\pi$
$350$	−283.421	+	397.398i	−0.809775	+	1.13542i
$351$		0			0
$352$	8.51133	+	193.465i	0.0241799	+	0.549618i
$353$		−	133.784i		−	0.378992i	−0.981881	−	0.189496i	$-0.939315\pi$
$353$		−	133.784i		−	0.378992i	0.981881	−	0.189496i	$-0.0606854\pi$
$354$		0			0
$355$		−	286.038i		−	0.805740i
$356$	20.5615	−	7.08295i	0.0577570	−	0.0198959i
$357$		0			0
$358$	−257.944	+	361.676i	−0.720515	+	1.01027i
$359$		−	239.018i		−	0.665787i	−0.942964	−	0.332894i	$-0.891975\pi$
$359$		−	239.018i		−	0.665787i	0.942964	−	0.332894i	$-0.108025\pi$
$360$		0			0
$361$	−852.511			−2.36153
$362$	193.330	+	137.882i	0.534061	+	0.380889i
$363$		0			0
$364$	62.4558	−	21.5146i	0.171582	−	0.0591059i
$365$	−595.952			−1.63274
$366$		0			0
$367$	−188.389			−0.513320			−0.256660	−	0.966502i	$-0.582622\pi$
$367$	−188.389			−0.513320			−0.256660	+	0.966502i	$0.582622\pi$
$368$	211.975	+	271.167i	0.576020	+	0.736868i
$369$		0			0
$370$	−435.122	−	310.326i	−1.17601	−	0.838718i
$371$	253.227			0.682554
$372$		0			0
$373$		−	561.108i		−	1.50431i	−0.658985	−	0.752156i	$-0.729014\pi$
$373$		−	561.108i		−	1.50431i	0.658985	−	0.752156i	$-0.270986\pi$
$374$	214.917	+	153.277i	0.574645	+	0.409833i
$375$		0			0
$376$	7.59969	−	25.6749i	0.0202119	−	0.0682844i
$377$		−	24.9848i		−	0.0662727i
$378$		0			0
$379$		−	328.227i		−	0.866034i	−0.901386	−	0.433017i	$-0.857449\pi$
$379$		−	328.227i		−	0.866034i	0.901386	−	0.433017i	$-0.142551\pi$
$380$	1010.61	−	348.132i	2.65951	−	0.916137i
$381$		0			0
$382$	246.755	+	175.984i	0.645956	+	0.460691i
$383$		−	204.118i		−	0.532945i	−0.963843	−	0.266472i	$-0.914142\pi$
$383$		−	204.118i		−	0.532945i	0.963843	−	0.266472i	$-0.0858581\pi$
$384$		0			0
$385$	−334.755			−0.869494
$386$	131.665	−	184.614i	0.341102	−	0.478274i
$387$		0			0
$388$	68.8444	+	199.852i	0.177434	+	0.515083i
$389$	60.1746			0.154690			0.0773452	−	0.997004i	$-0.475356\pi$
$389$	60.1746			0.154690			0.0773452	+	0.997004i	$0.475356\pi$
$390$		0			0
$391$	469.177			1.19994
$392$	−23.0130	−	6.81178i	−0.0587067	−	0.0173770i
$393$		0			0
$394$	370.981	−	520.169i	0.941575	−	1.32023i
$395$	240.272			0.608285
$396$		0			0
$397$		−	592.203i		−	1.49170i	−0.666116	−	0.745848i	$-0.732045\pi$
$397$		−	592.203i		−	1.49170i	0.666116	−	0.745848i	$-0.267955\pi$
$398$	−47.6259	+	66.7785i	−0.119663	+	0.167785i
$399$		0			0
$400$	−426.627	+	333.501i	−1.06657	+	0.833752i
$401$		−	653.178i		−	1.62887i	−0.580254	−	0.814436i	$-0.697047\pi$
$401$		−	653.178i		−	1.62887i	0.580254	−	0.814436i	$-0.302953\pi$
$402$		0			0
$403$			86.1854i			0.213859i
$404$	−117.259	−	340.397i	−0.290245	−	0.842568i
$405$		0			0
$406$	−91.3608	+	128.101i	−0.225027	+	0.315520i
$407$		−	210.812i		−	0.517965i
$408$		0			0
$409$	355.156			0.868351			0.434176	−	0.900828i	$-0.357040\pi$
$409$	355.156			0.868351			0.434176	+	0.900828i	$0.357040\pi$
$410$	−166.440	−	118.704i	−0.405950	−	0.289521i
$411$		0			0
$412$	−155.305	−	450.845i	−0.376955	−	1.09428i
$413$	−267.976			−0.648851
$414$		0			0
$415$	424.333			1.02249
$416$	73.2135	−	3.22096i	0.175994	−	0.00774270i
$417$		0			0
$418$	343.267	+	244.815i	0.821212	+	0.585682i
$419$	299.085			0.713808			0.356904	−	0.934141i	$-0.383832\pi$
$419$	299.085			0.713808			0.356904	+	0.934141i	$0.383832\pi$
$420$		0			0
$421$			769.638i			1.82812i	0.405582	+	0.914059i	$0.367069\pi$
$421$			769.638i			1.82812i	−0.405582	+	0.914059i	$0.632931\pi$
$422$	155.253	+	110.725i	0.367897	+	0.262381i
$423$		0			0
$424$	269.378	+	79.7348i	0.635325	+	0.188054i
$425$			738.156i			1.73684i
$426$		0			0
$427$			185.145i			0.433594i
$428$	−31.5357	−	91.5468i	−0.0736816	−	0.213894i
$429$		0			0
$430$	−755.822	−	539.047i	−1.75772	−	1.25360i
$431$			411.583i			0.954948i	0.878646	+	0.477474i	$0.158448\pi$
$431$			411.583i			0.954948i	−0.878646	+	0.477474i	$0.841552\pi$
$432$		0			0
$433$	516.133			1.19199			0.595996	−	0.802987i	$-0.296757\pi$
$433$	516.133			1.19199			0.595996	+	0.802987i	$0.296757\pi$
$434$	315.150	−	441.886i	0.726153	−	1.01817i
$435$		0			0
$436$	500.994	−	172.581i	1.14907	−	0.395827i
$437$	749.372			1.71481
$438$		0			0
$439$	−865.788			−1.97218			−0.986091	−	0.166205i	$-0.946849\pi$
$439$	−865.788			−1.97218			−0.986091	+	0.166205i	$0.946849\pi$
$440$	−356.105	−	105.406i	−0.809330	−	0.239559i
$441$		0			0
$442$	58.0051	−	81.3316i	0.131233	−	0.184008i
$443$	−546.261			−1.23310			−0.616548	−	0.787318i	$-0.711469\pi$
$443$	−546.261			−1.23310			−0.616548	+	0.787318i	$0.711469\pi$
$444$		0			0
$445$			41.7059i			0.0937211i
$446$	−311.421	+	436.658i	−0.698254	+	0.979053i
$447$		0			0
$448$	−387.156	−	251.202i	−0.864187	−	0.560719i
$449$			428.978i			0.955407i	0.878521	+	0.477704i	$0.158531\pi$
$449$			428.978i			0.955407i	−0.878521	+	0.477704i	$0.841469\pi$
$450$		0			0
$451$		−	80.6382i		−	0.178799i
$452$	−607.223	+	209.174i	−1.34341	+	0.462774i
$453$		0			0
$454$	76.3163	−	107.007i	0.168098	−	0.235697i
$455$			126.682i			0.278422i
$456$		0			0
$457$	75.5997			0.165426			0.0827130	−	0.996573i	$-0.473642\pi$
$457$	75.5997			0.165426			0.0827130	+	0.996573i	$0.473642\pi$
$458$	−252.995	−	180.434i	−0.552391	−	0.393961i
$459$		0			0
$460$	−624.077	+	214.980i	−1.35669	+	0.467348i
$461$	771.365			1.67324			0.836622	−	0.547781i	$-0.184527\pi$
$461$	771.365			1.67324			0.836622	+	0.547781i	$0.184527\pi$
$462$		0			0
$463$	−468.278			−1.01140			−0.505699	−	0.862710i	$-0.668765\pi$
$463$	−468.278			−1.01140			−0.505699	+	0.862710i	$0.668765\pi$
$464$	−137.523	+	107.504i	−0.296387	+	0.231690i
$465$		0			0
$466$	464.802	+	331.494i	0.997430	+	0.711360i
$467$	−452.842			−0.969682			−0.484841	−	0.874602i	$-0.661123\pi$
$467$	−452.842			−0.969682			−0.484841	+	0.874602i	$0.661123\pi$
$468$		0			0
$469$		−	185.145i		−	0.394765i
$470$	41.8067	+	29.8162i	0.0889505	+	0.0634388i
$471$		0			0
$472$	−285.066	−	84.3787i	−0.603954	−	0.178768i
$473$		−	366.187i		−	0.774180i
$474$		0			0
$475$			1178.99i			2.48208i
$476$	−594.803	+	204.896i	−1.24959	+	0.430453i
$477$		0			0
$478$	685.766	+	489.083i	1.43466	+	1.02319i
$479$		−	467.523i		−	0.976040i	−0.872832	−	0.488020i	$-0.837719\pi$
$479$		−	467.523i		−	0.976040i	0.872832	−	0.488020i	$-0.162281\pi$
$480$		0			0
$481$	−79.7779			−0.165859
$482$	−222.504	+	311.983i	−0.461627	+	0.647268i
$483$		0			0
$484$	109.925	+	319.108i	0.227118	+	0.659314i
$485$	−405.370			−0.835815
$486$		0			0
$487$	−863.766			−1.77365			−0.886824	−	0.462108i	$-0.847093\pi$
$487$	−863.766			−1.77365			−0.886824	+	0.462108i	$0.847093\pi$
$488$	−58.2973	+	196.953i	−0.119462	+	0.403592i
$489$		0			0
$490$	26.7250	−	37.4723i	0.0545408	−	0.0764741i
$491$	−149.498			−0.304476			−0.152238	−	0.988344i	$-0.548648\pi$
$491$	−149.498			−0.304476			−0.152238	+	0.988344i	$0.548648\pi$
$492$		0			0
$493$			237.945i			0.482647i
$494$	92.6459	−	129.903i	0.187542	−	0.262962i
$495$		0			0
$496$	474.389	−	370.836i	0.956429	−	0.747654i
$497$			268.889i			0.541023i
$498$		0			0
$499$		−	205.400i		−	0.411622i	−0.978592	−	0.205811i	$-0.934017\pi$
$499$		−	205.400i		−	0.411622i	0.978592	−	0.205811i	$-0.0659833\pi$
$500$	−88.3876	−	256.585i	−0.176775	−	0.513170i
$501$		0			0
$502$	561.127	−	786.782i	1.11778	−	1.56729i
$503$			349.923i			0.695673i	0.937555	+	0.347836i	$0.113084\pi$
$503$			349.923i			0.695673i	−0.937555	+	0.347836i	$0.886916\pi$
$504$		0			0
$505$	690.444			1.36722
$506$	−211.975	−	151.179i	−0.418924	−	0.298773i
$507$		0			0
$508$	190.828	+	553.964i	0.375645	+	1.09048i
$509$	529.468			1.04021			0.520106	−	0.854102i	$-0.325892\pi$
$509$	529.468			1.04021			0.520106	+	0.854102i	$0.325892\pi$
$510$		0			0
$511$	560.222			1.09632
$512$	−332.750	−	389.129i	−0.649903	−	0.760017i
$513$		0			0
$514$	34.5416	+	24.6348i	0.0672016	+	0.0479277i
$515$	914.470			1.77567
$516$		0			0
$517$			20.2549i			0.0391777i
$518$	409.035	+	291.721i	0.789642	+	0.563167i
$519$		0			0
$520$	−39.8890	+	134.762i	−0.0767096	+	0.259157i
$521$			367.318i			0.705026i	0.935807	+	0.352513i	$0.114673\pi$
$521$			367.318i			0.705026i	−0.935807	+	0.352513i	$0.885327\pi$
$522$		0			0
$523$			577.495i			1.10420i	0.833779	+	0.552099i	$0.186173\pi$
$523$			577.495i			1.10420i	−0.833779	+	0.552099i	$0.813827\pi$
$524$	−240.956	−	699.485i	−0.459840	−	1.33490i
$525$		0			0
$526$	−401.655	−	286.458i	−0.763603	−	0.544596i
$527$		−	820.793i		−	1.55748i
$528$		0			0
$529$	66.2447			0.125226
$530$	−312.828	+	438.630i	−0.590241	+	0.827603i
$531$		0			0
$532$	−950.022	+	327.260i	−1.78576	+	0.615151i
$533$	−30.5161			−0.0572534
$534$		0			0
$535$	185.689			0.347082
$536$	58.2973	−	196.953i	0.108764	−	0.367449i
$537$		0			0
$538$	279.919	−	392.488i	0.520296	−	0.729531i
$539$	18.1549			0.0336826
$540$		0			0
$541$			326.777i			0.604023i	0.953304	+	0.302012i	$0.0976582\pi$
$541$			326.777i			0.604023i	−0.953304	+	0.302012i	$0.902342\pi$
$542$	71.7035	−	100.539i	0.132294	−	0.185496i
$543$		0			0
$544$	−697.255	+	30.6751i	−1.28172	+	0.0563880i
$545$			1016.19i			1.86457i
$546$		0			0
$547$			273.137i			0.499336i	0.968332	+	0.249668i	$0.0803214\pi$
$547$			273.137i			0.499336i	−0.968332	+	0.249668i	$0.919679\pi$
$548$	504.177	−	173.677i	0.920031	−	0.316929i
$549$		0			0
$550$	237.850	−	333.501i	0.432455	−	0.606365i
$551$			380.046i			0.689739i
$552$		0			0
$553$	−225.867			−0.408440
$554$	617.281	+	440.240i	1.11423	+	0.794658i
$555$		0			0
$556$	624.077	−	214.980i	1.12244	−	0.386655i
$557$	93.2457			0.167407			0.0837035	−	0.996491i	$-0.473325\pi$
$557$	93.2457			0.167407			0.0837035	+	0.996491i	$0.473325\pi$
$558$		0			0
$559$	−138.577			−0.247902
$560$	697.294	−	545.085i	1.24517	−	0.973366i
$561$		0			0
$562$	−490.491	−	349.815i	−0.872760	−	0.622446i
$563$	42.3615			0.0752424			0.0376212	−	0.999292i	$-0.488022\pi$
$563$	42.3615			0.0752424			0.0376212	+	0.999292i	$0.488022\pi$
$564$		0			0
$565$		−	1231.66i		−	2.17993i
$566$	−650.842	−	464.176i	−1.14990	−	0.820099i
$567$		0			0
$568$	−84.6662	+	286.038i	−0.149060	+	0.503587i
$569$		−	1055.57i		−	1.85513i	−0.373663	−	0.927564i	$-0.621898\pi$
$569$		−	1055.57i		−	1.85513i	0.373663	−	0.927564i	$-0.378102\pi$
$570$		0			0
$571$		−	21.9344i		−	0.0384141i	−0.999816	−	0.0192070i	$-0.993886\pi$
$571$		−	21.9344i		−	0.0384141i	0.999816	−	0.0192070i	$-0.00611417\pi$
$572$	−52.4137	+	18.0553i	−0.0916323	+	0.0315651i
$573$		0			0
$574$	156.461	+	111.587i	0.272580	+	0.194402i
$575$		−	728.052i		−	1.26618i
$576$		0			0
$577$	161.378			0.279684			0.139842	−	0.990174i	$-0.455341\pi$
$577$	161.378			0.279684			0.139842	+	0.990174i	$0.455341\pi$
$578$	−216.801	+	303.987i	−0.375089	+	0.525929i
$579$		0			0
$580$	−109.028	−	316.503i	−0.187979	−	0.545695i
$581$	−398.893			−0.686562
$582$		0			0
$583$	−212.511			−0.364513
$584$	595.952	+	176.400i	1.02047	+	0.302054i
$585$		0			0
$586$	−299.714	+	420.243i	−0.511457	+	0.717138i
$587$	−481.396			−0.820096			−0.410048	−	0.912064i	$-0.634488\pi$
$587$	−481.396			−0.820096			−0.410048	+	0.912064i	$0.634488\pi$
$588$		0			0
$589$		−	1310.97i		−	2.22576i
$590$	331.047	−	464.176i	0.561097	−	0.786739i
$591$		0			0
$592$	343.267	+	439.120i	0.579842	+	0.741757i
$593$		−	321.781i		−	0.542632i	−0.962490	−	0.271316i	$-0.912541\pi$
$593$		−	321.781i		−	0.542632i	0.962490	−	0.271316i	$-0.0874588\pi$
$594$		0			0
$595$		−	1206.47i		−	2.02768i
$596$	298.253	+	865.816i	0.500425	+	1.45271i
$597$		0			0
$598$	−57.2111	+	80.2183i	−0.0956707	+	0.134144i
$599$		−	35.8419i		−	0.0598362i	−0.999552	−	0.0299181i	$-0.990475\pi$
$599$		−	35.8419i		−	0.0598362i	0.999552	−	0.0299181i	$-0.00952464\pi$
$600$		0			0
$601$	147.867			0.246035			0.123018	−	0.992404i	$-0.460743\pi$
$601$	147.867			0.246035			0.123018	+	0.992404i	$0.460743\pi$
$602$	710.507	+	506.729i	1.18024	+	0.841742i
$603$		0			0
$604$	−211.672	−	614.475i	−0.350450	−	1.01734i
$605$	−647.262			−1.06985
$606$		0			0
$607$	−636.611			−1.04878			−0.524391	−	0.851478i	$-0.675707\pi$
$607$	−636.611			−1.04878			−0.524391	+	0.851478i	$0.675707\pi$
$608$	−1113.66	+	48.9944i	−1.83167	+	0.0805829i
$609$		0			0
$610$	−320.700	−	228.721i	−0.525737	−	0.374952i
$611$	7.66510			0.0125452
$612$		0			0
$613$			870.887i			1.42070i	0.703850	+	0.710348i	$0.251463\pi$
$613$			870.887i			1.42070i	−0.703850	+	0.710348i	$0.748537\pi$
$614$	465.758	+	332.175i	0.758563	+	0.541001i
$615$		0			0
$616$	334.755	+	99.0864i	0.543434	+	0.160855i
$617$			1126.69i			1.82607i	0.407876	+	0.913037i	$0.366270\pi$
$617$			1126.69i			1.82607i	−0.407876	+	0.913037i	$0.633730\pi$
$618$		0			0
$619$		−	311.713i		−	0.503575i	−0.967783	−	0.251787i	$-0.918982\pi$
$619$		−	311.713i		−	0.503575i	0.967783	−	0.251787i	$-0.0810183\pi$
$620$	376.092	+	1091.78i	0.606601	+	1.76094i
$621$		0			0
$622$	756.589	+	539.594i	1.21638	+	0.867514i
$623$		−	39.2054i		−	0.0629301i
$624$		0			0
$625$	−325.666			−0.521066
$626$	183.485	−	257.273i	0.293107	−	0.410979i
$627$		0			0
$628$	−429.877	+	148.083i	−0.684518	+	0.235800i
$629$	759.772			1.20790
$630$		0			0
$631$	−203.278			−0.322153			−0.161076	−	0.986942i	$-0.551497\pi$
$631$	−203.278			−0.322153			−0.161076	+	0.986942i	$0.551497\pi$
$632$	−240.272	−	71.1198i	−0.380178	−	0.112531i
$633$		0			0
$634$	−33.2582	+	46.6329i	−0.0524577	+	0.0735534i
$635$	−1123.63			−1.76950
$636$		0			0
$637$		−	6.87041i		−	0.0107856i
$638$	76.6711	−	107.504i	0.120174	−	0.168502i
$639$		0			0
$640$	913.400	−	360.289i	1.42719	−	0.562951i
$641$		−	586.490i		−	0.914960i	−0.889220	−	0.457480i	$-0.848752\pi$
$641$		−	586.490i		−	0.914960i	0.889220	−	0.457480i	$-0.151248\pi$
$642$		0			0
$643$		−	9.16054i		−	0.0142466i	−0.999975	−	0.00712328i	$-0.997733\pi$
$643$		−	9.16054i		−	0.0142466i	0.999975	−	0.00712328i	$-0.00226743\pi$
$644$	586.661	−	202.091i	0.910965	−	0.313806i
$645$		0			0
$646$	−882.321	+	1237.14i	−1.36582	+	1.91508i
$647$			859.040i			1.32773i	0.747853	+	0.663864i	$0.231085\pi$
$647$			859.040i			1.32773i	−0.747853	+	0.663864i	$0.768915\pi$
$648$		0			0
$649$	224.888			0.346515
$650$	−126.207	−	90.0102i	−0.194165	−	0.138477i
$651$		0			0
$652$	−423.045	+	145.729i	−0.648841	+	0.223511i
$653$	−131.775			−0.201799			−0.100899	−	0.994897i	$-0.532172\pi$
$653$	−131.775			−0.201799			−0.100899	+	0.994897i	$0.532172\pi$
$654$		0			0
$655$	1418.80			2.16611
$656$	131.304	+	167.969i	0.200158	+	0.256050i
$657$		0			0
$658$	−39.3002	−	28.0286i	−0.0597268	−	0.0425967i
$659$	−305.137			−0.463030			−0.231515	−	0.972831i	$-0.574368\pi$
$659$	−305.137			−0.463030			−0.231515	+	0.972831i	$0.574368\pi$
$660$		0			0
$661$			623.298i			0.942962i	0.881876	+	0.471481i	$0.156280\pi$
$661$			623.298i			0.942962i	−0.881876	+	0.471481i	$0.843720\pi$
$662$	−698.533	−	498.189i	−1.05519	−	0.752551i
$663$		0			0
$664$	−424.333	−	125.601i	−0.639056	−	0.189158i
$665$		−	1926.97i		−	2.89771i
$666$		0			0
$667$		−	234.688i		−	0.351856i
$668$	−573.113	+	197.424i	−0.857953	+	0.295545i
$669$		0			0
$670$	320.700	+	228.721i	0.478656	+	0.341374i
$671$		−	155.376i		−	0.231558i
$672$		0			0
$673$	−263.867			−0.392076			−0.196038	−	0.980596i	$-0.562808\pi$
$673$	−263.867			−0.392076			−0.196038	+	0.980596i	$0.562808\pi$
$674$	337.653	−	473.439i	0.500969	−	0.702432i
$675$		0			0
$676$	−213.336	−	619.306i	−0.315586	−	0.916134i
$677$	−788.411			−1.16457			−0.582283	−	0.812986i	$-0.697840\pi$
$677$	−788.411			−1.16457			−0.582283	+	0.812986i	$0.697840\pi$
$678$		0			0
$679$	381.066			0.561217
$680$	379.886	−	1283.41i	0.558656	−	1.88737i
$681$		0			0
$682$	−264.478	+	370.836i	−0.387797	+	0.543748i
$683$	905.773			1.32617			0.663084	−	0.748545i	$-0.269247\pi$
$683$	905.773			1.32617			0.663084	+	0.748545i	$0.269247\pi$
$684$		0			0
$685$			1022.65i			1.49291i
$686$	385.215	−	540.127i	0.561538	−	0.787358i
$687$		0			0
$688$	596.266	+	762.767i	0.866665	+	1.10867i
$689$			80.4211i			0.116721i
$690$		0			0
$691$		−	45.8027i		−	0.0662847i	−0.999451	−	0.0331423i	$-0.989449\pi$
$691$		−	45.8027i		−	0.0662847i	0.999451	−	0.0331423i	$-0.0105515\pi$
$692$	127.698	+	370.701i	0.184534	+	0.535695i
$693$		0			0
$694$	208.750	−	292.698i	0.300793	−	0.421755i
$695$			1265.85i			1.82136i
$696$		0			0
$697$	290.622			0.416962
$698$	367.228	+	261.904i	0.526114	+	0.375221i
$699$		0			0
$700$	317.950	+	922.994i	0.454214	+	1.31856i
$701$	−1019.73			−1.45468			−0.727339	−	0.686279i	$-0.759243\pi$
$701$	−1019.73			−1.45468			−0.727339	+	0.686279i	$0.759243\pi$
$702$		0			0
$703$	1213.51			1.72619
$704$	324.905	+	210.812i	0.461513	+	0.299449i
$705$		0			0
$706$	−217.842	−	155.363i	−0.308558	−	0.220061i
$707$	−649.049			−0.918033
$708$		0			0
$709$			84.7350i			0.119513i	0.998213	+	0.0597567i	$0.0190325\pi$
$709$			84.7350i			0.119513i	−0.998213	+	0.0597567i	$0.980968\pi$
$710$	−465.758	−	332.175i	−0.655997	−	0.467852i
$711$		0			0
$712$	12.3448	−	41.7059i	0.0173382	−	0.0585757i
$713$			809.558i			1.13543i
$714$		0			0
$715$		−	106.313i		−	0.148690i
$716$	289.369	+	840.026i	0.404147	+	1.17322i
$717$		0			0
$718$	−389.194	−	277.571i	−0.542053	−	0.386589i
$719$		−	646.311i		−	0.898903i	−0.893305	−	0.449451i	$-0.851619\pi$
$719$		−	646.311i		−	0.898903i	0.893305	−	0.449451i	$-0.148381\pi$
$720$		0			0
$721$	−859.643			−1.19229
$722$	−990.018	+	1388.15i	−1.37122	+	1.92265i
$723$		0			0
$724$	449.028	−	154.679i	0.620204	−	0.213646i
$725$	369.234			0.509288
$726$		0			0
$727$	−648.789			−0.892419			−0.446210	−	0.894928i	$-0.647226\pi$
$727$	−648.789			−0.892419			−0.446210	+	0.894928i	$0.647226\pi$
$728$	37.4975	−	126.682i	0.0515075	−	0.174014i
$729$		0			0
$730$	−692.077	+	970.393i	−0.948051	+	1.32931i
$731$	1319.75			1.80540
$732$		0			0
$733$			696.353i			0.950004i	0.879985	+	0.475002i	$0.157553\pi$
$733$			696.353i			0.950004i	−0.879985	+	0.475002i	$0.842447\pi$
$734$	−218.775	+	306.755i	−0.298059	+	0.417922i
$735$		0			0
$736$	687.711	−	30.2552i	0.934390	−	0.0411076i
$737$			155.376i			0.210822i
$738$		0			0
$739$			740.833i			1.00248i	0.865308	+	0.501240i	$0.167123\pi$
$739$			740.833i			1.00248i	−0.865308	+	0.501240i	$0.832877\pi$
$740$	−1010.61	+	348.132i	−1.36569	+	0.470449i
$741$		0			0
$742$	294.072	−	412.332i	0.396324	−	0.555704i
$743$		−	111.377i		−	0.149901i	−0.997187	−	0.0749507i	$-0.976120\pi$
$743$		−	111.377i		−	0.149901i	0.997187	−	0.0749507i	$-0.0238800\pi$
$744$		0			0
$745$	−1756.18			−2.35728
$746$	−913.657	−	651.614i	−1.22474	−	0.873477i
$747$		0			0
$748$	499.166	−	171.951i	0.667334	−	0.229881i
$749$	−174.556			−0.233052
$750$		0			0
$751$	923.699			1.22996			0.614979	−	0.788543i	$-0.289164\pi$
$751$	923.699			1.22996			0.614979	+	0.788543i	$0.289164\pi$
$752$	−32.9812	−	42.1909i	−0.0438580	−	0.0561049i
$753$		0			0
$754$	−40.6830	−	29.0148i	−0.0539562	−	0.0384812i
$755$	1246.37			1.65082
$756$		0			0
$757$		−	1233.47i		−	1.62941i	−0.579873	−	0.814707i	$-0.696898\pi$
$757$		−	1233.47i		−	1.62941i	0.579873	−	0.814707i	$-0.303102\pi$
$758$	−534.455	−	381.169i	−0.705085	−	0.502862i
$759$		0			0
$760$	606.755	−	2049.87i	0.798362	−	2.69720i
$761$			179.070i			0.235309i	0.993055	+	0.117654i	$0.0375375\pi$
$761$			179.070i			0.235309i	−0.993055	+	0.117654i	$0.962463\pi$
$762$		0			0
$763$		−	955.266i		−	1.25199i
$764$	573.113	−	197.424i	0.750147	−	0.258408i
$765$		0			0
$766$	−332.367	−	237.042i	−0.433899	−	0.309454i
$767$		−	85.1049i		−	0.110958i
$768$		0			0
$769$	−251.511			−0.327062			−0.163531	−	0.986538i	$-0.552288\pi$
$769$	−251.511			−0.327062			−0.163531	+	0.986538i	$0.552288\pi$
$770$	−388.751	+	545.085i	−0.504871	+	0.707902i
$771$		0			0
$772$	−147.706	−	428.783i	−0.191329	−	0.555418i
$773$	184.110			0.238176			0.119088	−	0.992884i	$-0.462003\pi$
$773$	184.110			0.238176			0.119088	+	0.992884i	$0.462003\pi$
$774$		0			0
$775$	−1273.68			−1.64345
$776$	405.370	+	119.988i	0.522384	+	0.154624i
$777$		0			0
$778$	69.8806	−	97.9827i	0.0898208	−	0.125942i
$779$	464.183			0.595870
$780$		0			0
$781$		−	225.654i		−	0.288930i
$782$	544.855	−	763.966i	0.696745	−	0.976938i
$783$		0			0
$784$	−37.8167	+	29.5618i	−0.0482355	+	0.0377064i
$785$		−	871.941i		−	1.11075i
$786$		0			0
$787$			1351.36i			1.71710i	0.512731	+	0.858550i	$0.328634\pi$
$787$			1351.36i			1.71710i	−0.512731	+	0.858550i	$0.671366\pi$
$788$	−416.176	−	1208.14i	−0.528143	−	1.53317i
$789$		0			0
$790$	279.028	−	391.238i	0.353200	−	0.495237i
$791$			1157.82i			1.46374i
$792$		0			0
$793$	−58.7991			−0.0741476
$794$	−964.289	−	687.724i	−1.21447	−	0.866151i
$795$		0			0
$796$	53.4281	+	155.099i	0.0671207	+	0.194848i
$797$	1407.20			1.76562			0.882812	−	0.469727i	$-0.155648\pi$
$797$	1407.20			1.76562			0.882812	+	0.469727i	$0.155648\pi$
$798$		0			0
$799$	−72.9992			−0.0913632
$800$	47.6005	+	1081.97i	0.0595006	+	1.35247i
$801$		0			0
$802$	−1063.57	−	758.534i	−1.32615	−	0.945802i
$803$	−470.145			−0.585485
$804$		0			0
$805$			1189.95i			1.47820i
$806$	140.336	+	100.087i	0.174115	+	0.124177i
$807$		0			0
$808$	−690.444	−	204.369i	−0.854510	−	0.252932i
$809$			741.991i			0.917171i	0.888650	+	0.458585i	$0.151644\pi$
$809$			741.991i			0.917171i	−0.888650	+	0.458585i	$0.848356\pi$
$810$		0			0
$811$		−	716.837i		−	0.883893i	−0.897041	−	0.441947i	$-0.854288\pi$
$811$		−	716.837i		−	0.883893i	0.897041	−	0.441947i	$-0.145712\pi$
$812$	102.491	+	297.527i	0.126221	+	0.366413i
$813$		0			0
$814$	−343.267	−	244.815i	−0.421703	−	0.300756i
$815$		−	858.082i		−	1.05286i
$816$		0			0
$817$	2107.91			2.58006
$818$	412.441	−	578.303i	0.504207	−	0.706972i
$819$		0			0
$820$	−386.572	+	133.165i	−0.471429	+	0.162396i
$821$	−244.447			−0.297743			−0.148871	−	0.988857i	$-0.547564\pi$
$821$	−244.447			−0.297743			−0.148871	+	0.988857i	$0.547564\pi$
$822$		0			0
$823$	331.500			0.402795			0.201398	−	0.979510i	$-0.435452\pi$
$823$	331.500			0.402795			0.201398	+	0.979510i	$0.435452\pi$
$824$	−914.470	−	270.680i	−1.10979	−	0.328495i
$825$		0			0
$826$	−311.199	+	436.347i	−0.376755	+	0.528265i
$827$	724.314			0.875833			0.437916	−	0.899016i	$-0.355717\pi$
$827$	724.314			0.875833			0.437916	+	0.899016i	$0.355717\pi$
$828$		0			0
$829$			77.5083i			0.0934961i	0.998907	+	0.0467481i	$0.0148858\pi$
$829$			77.5083i			0.0934961i	−0.998907	+	0.0467481i	$0.985114\pi$
$830$	492.777	−	690.945i	0.593707	−	0.832464i
$831$		0			0
$832$	79.7779	−	122.955i	0.0958870	−	0.147782i
$833$			65.4309i			0.0785485i
$834$		0			0
$835$		−	1162.47i		−	1.39218i
$836$	797.269	−	274.640i	0.953672	−	0.328517i
$837$		0			0
$838$	347.327	−	487.003i	0.414472	−	0.581150i
$839$			952.252i			1.13498i	0.823379	+	0.567492i	$0.192086\pi$
$839$			952.252i			1.13498i	−0.823379	+	0.567492i	$0.807914\pi$
$840$		0			0
$841$	−721.977			−0.858475
$842$	1253.21	+	893.778i	1.48837	+	1.06149i
$843$		0			0
$844$	360.589	−	124.214i	0.427238	−	0.147173i
$845$	1256.17			1.48659
$846$		0			0
$847$	608.456			0.718366
$848$	442.661	−	346.034i	0.522005	−	0.408059i
$849$		0			0
$850$	1201.95	+	857.219i	1.41405	+	1.00849i
$851$	−749.372			−0.880578
$852$		0			0
$853$			282.424i			0.331095i	0.986202	+	0.165548i	$0.0529392\pi$
$853$			282.424i			0.331095i	−0.986202	+	0.165548i	$0.947061\pi$
$854$	301.473	+	215.008i	0.353012	+	0.251766i
$855$		0			0
$856$	−185.689	−	54.9632i	−0.216926	−	0.0642094i
$857$		−	539.665i		−	0.629714i	−0.949139	−	0.314857i	$-0.898044\pi$
$857$		−	539.665i		−	0.629714i	0.949139	−	0.314857i	$-0.101956\pi$
$858$		0			0
$859$		−	53.2837i		−	0.0620299i	−0.999519	−	0.0310150i	$-0.990126\pi$
$859$		−	53.2837i		−	0.0620299i	0.999519	−	0.0310150i	$-0.00987395\pi$
$860$	−1755.47	+	604.717i	−2.04124	+	0.703160i
$861$		0			0
$862$	670.183	+	477.970i	0.777475	+	0.554489i
$863$			632.435i			0.732834i	0.930451	+	0.366417i	$0.119416\pi$
$863$			632.435i			0.732834i	−0.930451	+	0.366417i	$0.880584\pi$
$864$		0			0
$865$	−751.911			−0.869261
$866$	599.384	−	840.424i	0.692129	−	0.970466i
$867$		0			0
$868$	−353.544	−	1026.32i	−0.407309	−	1.18240i
$869$	189.550			0.218125
$870$		0			0
$871$	58.7991			0.0675075
$872$	300.789	−	1016.19i	0.344941	−	1.16536i
$873$		0			0
$874$	870.244	−	1220.21i	0.995702	−	1.39612i
$875$	−489.241			−0.559133
$876$		0			0
$877$			346.548i			0.395152i	0.980288	+	0.197576i	$0.0633069\pi$
$877$			346.548i			0.395152i	−0.980288	+	0.197576i	$0.936693\pi$
$878$	−1005.44	+	1409.77i	−1.14515	+	1.60566i
$879$		0			0
$880$	−585.177	+	457.441i	−0.664974	+	0.519820i
$881$		−	1394.26i		−	1.58258i	−0.611438	−	0.791292i	$-0.709409\pi$
$881$		−	1394.26i		−	1.58258i	0.611438	−	0.791292i	$-0.290591\pi$
$882$		0			0
$883$			1714.29i			1.94144i	0.240212	+	0.970720i	$0.422783\pi$
$883$			1714.29i			1.94144i	−0.240212	+	0.970720i	$0.577217\pi$
$884$	−65.0717	−	188.900i	−0.0736105	−	0.213688i
$885$		0			0
$886$	−634.372	+	889.482i	−0.715995	+	1.00393i
$887$		−	1149.19i		−	1.29559i	−0.761815	−	0.647795i	$-0.775691\pi$
$887$		−	1149.19i		−	1.29559i	0.761815	−	0.647795i	$-0.224309\pi$
$888$		0			0
$889$	1056.27			1.18815
$890$	67.9100	+	48.4329i	0.0763034	+	0.0544190i
$891$		0			0
$892$	349.361	+	1014.18i	0.391660	+	1.13697i
$893$	−116.595			−0.130565
$894$		0			0
$895$	−1703.87			−1.90376
$896$	−858.638	+	338.688i	−0.958301	+	0.378000i
$897$		0			0
$898$	698.508	+	498.171i	0.777849	+	0.554756i
$899$	−410.570			−0.456696
$900$		0			0
$901$		−	765.897i		−	0.850052i
$902$	−131.304	−	93.6449i	−0.145570	−	0.103819i
$903$		0			0
$904$	−364.567	+	1231.66i	−0.403282	+	1.36246i
$905$			910.785i			1.00639i
$906$		0			0
$907$		−	507.952i		−	0.560035i	−0.959995	−	0.280017i	$-0.909660\pi$
$907$		−	507.952i		−	0.560035i	0.959995	−	0.280017i	$-0.0903402\pi$
$908$	−85.6137	−	248.533i	−0.0942882	−	0.273715i
$909$		0			0
$910$	206.278	+	147.116i	0.226679	+	0.161666i
$911$		−	1488.13i		−	1.63351i	−0.576984	−	0.816756i	$-0.695770\pi$
$911$		−	1488.13i		−	1.63351i	0.576984	−	0.816756i	$-0.304230\pi$
$912$		0			0
$913$	334.755			0.366654
$914$	87.7937	−	123.100i	0.0960544	−	0.134682i
$915$		0			0
$916$	−587.605	+	202.416i	−0.641490	+	0.220978i
$917$	−1333.74			−1.45446
$918$		0			0
$919$	−335.790			−0.365386			−0.182693	−	0.983170i	$-0.558481\pi$
$919$	−335.790			−0.365386			−0.182693	+	0.983170i	$0.558481\pi$
$920$	−374.686	+	1265.85i	−0.407267	+	1.37592i
$921$		0			0
$922$	895.785	−	1256.02i	0.971567	−	1.36228i
$923$	−85.3949			−0.0925188
$924$		0			0
$925$		−	1178.99i		−	1.27458i
$926$	−543.810	+	762.500i	−0.587267	+	0.823434i
$927$		0			0
$928$	15.3440	+	348.775i	0.0165345	+	0.375835i
$929$			1685.87i			1.81471i	0.420363	+	0.907356i	$0.361903\pi$
$929$			1685.87i			1.81471i	−0.420363	+	0.907356i	$0.638097\pi$
$930$		0			0
$931$			104.506i			0.112252i
$932$	1079.55	−	371.879i	1.15831	−	0.399012i
$933$		0			0
$934$	−525.884	+	737.366i	−0.563045	+	0.789471i
$935$			1012.48i			1.08287i
$936$		0			0
$937$	−49.7342			−0.0530781			−0.0265390	−	0.999648i	$-0.508449\pi$
$937$	−49.7342			−0.0530781			−0.0265390	+	0.999648i	$0.508449\pi$
$938$	−301.473	−	215.008i	−0.321399	−	0.229220i
$939$		0			0
$940$	97.1001	−	33.4487i	0.103298	−	0.0355837i
$941$	−1689.50			−1.79543			−0.897715	−	0.440577i	$-0.854774\pi$
$941$	−1689.50			−1.79543			−0.897715	+	0.440577i	$0.854774\pi$
$942$		0			0
$943$	−286.644			−0.303971
$944$	−468.441	+	366.187i	−0.496230	+	0.387910i
$945$		0			0
$946$	−596.266	−	425.252i	−0.630302	−	0.449527i
$947$	−1036.44			−1.09445			−0.547225	−	0.836986i	$-0.684316\pi$
$947$	−1036.44			−1.09445			−0.547225	+	0.836986i	$0.684316\pi$
$948$		0			0
$949$			177.918i			0.187479i
$950$	1919.75	+	1369.15i	2.02079	+	1.44121i
$951$		0			0
$952$	−357.110	+	1206.47i	−0.375116	+	1.26730i
$953$			388.814i			0.407989i	0.978972	+	0.203995i	$0.0653925\pi$
$953$			388.814i			0.407989i	−0.978972	+	0.203995i	$0.934608\pi$
$954$		0			0
$955$			1162.47i			1.21725i
$956$	1592.76	−	548.667i	1.66606	−	0.573920i
$957$		0			0
$958$	−761.272	−	542.933i	−0.794647	−	0.566736i
$959$		−	961.335i		−	1.00243i
$960$		0			0
$961$	455.266			0.473742
$962$	−92.6459	+	129.903i	−0.0963056	+	0.135034i
$963$		0			0
$964$	249.611	+	724.611i	0.258933	+	0.751671i
$965$	869.721			0.901265
$966$		0			0
$967$	−201.899			−0.208789			−0.104395	−	0.994536i	$-0.533290\pi$
$967$	−201.899			−0.208789			−0.104395	+	0.994536i	$0.533290\pi$
$968$	647.262	+	191.587i	0.668659	+	0.197921i
$969$		0			0
$970$	−470.755	+	660.067i	−0.485315	+	0.680482i
$971$	−1500.54			−1.54535			−0.772676	−	0.634800i	$-0.781082\pi$
$971$	−1500.54			−1.54535			−0.772676	+	0.634800i	$0.781082\pi$
$972$		0			0
$973$		−	1189.95i		−	1.22297i
$974$	−1003.09	+	1406.48i	−1.02987	+	1.44402i
$975$		0			0
$976$	252.999	+	323.647i	0.259221	+	0.331605i
$977$			866.378i			0.886774i	0.896330	+	0.443387i	$0.146223\pi$
$977$			866.378i			0.886774i	−0.896330	+	0.443387i	$0.853777\pi$
$978$		0			0
$979$			32.9017i			0.0336074i
$980$	−29.9808	−	87.0330i	−0.0305927	−	0.0888092i
$981$		0			0
$982$	−173.611	+	243.428i	−0.176794	+	0.247890i
$983$		−	613.800i		−	0.624415i	−0.950014	−	0.312207i	$-0.898932\pi$
$983$		−	613.800i		−	0.624415i	0.950014	−	0.312207i	$-0.101068\pi$
$984$		0			0
$985$	2450.53			2.48785
$986$	387.448	+	276.325i	0.392949	+	0.280248i
$987$		0			0
$988$	−103.933	−	301.712i	−0.105195	−	0.305377i
$989$	−1301.68			−1.31616
$990$		0			0
$991$	1460.50			1.47376			0.736882	−	0.676022i	$-0.236297\pi$
$991$	1460.50			1.47376			0.736882	+	0.676022i	$0.236297\pi$
$992$	−52.9294	−	1203.10i	−0.0533562	−	1.21280i
$993$		0			0
$994$	437.833	+	312.260i	0.440476	+	0.314145i
$995$	−314.595			−0.316176
$996$		0			0
$997$		−	1378.84i		−	1.38299i	−0.722382	−	0.691494i	$-0.756953\pi$
$997$		−	1378.84i		−	1.38299i	0.722382	−	0.691494i	$-0.243047\pi$
$998$	−334.454	−	238.530i	−0.335124	−	0.239008i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.3.h.a.53.5	yes	8
3.2	odd	2	inner	72.3.h.a.53.4	yes	8
4.3	odd	2		288.3.h.a.17.7		8
8.3	odd	2		288.3.h.a.17.2		8
8.5	even	2	inner	72.3.h.a.53.3	✓	8
12.11	even	2		288.3.h.a.17.1		8
16.3	odd	4		2304.3.e.o.1025.2		8
16.5	even	4		2304.3.e.n.1025.7		8
16.11	odd	4		2304.3.e.o.1025.7		8
16.13	even	4		2304.3.e.n.1025.2		8
24.5	odd	2	inner	72.3.h.a.53.6	yes	8
24.11	even	2		288.3.h.a.17.8		8
48.5	odd	4		2304.3.e.n.1025.1		8
48.11	even	4		2304.3.e.o.1025.1		8
48.29	odd	4		2304.3.e.n.1025.8		8
48.35	even	4		2304.3.e.o.1025.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.h.a.53.3	✓	8	8.5	even	2	inner
72.3.h.a.53.4	yes	8	3.2	odd	2	inner
72.3.h.a.53.5	yes	8	1.1	even	1	trivial
72.3.h.a.53.6	yes	8	24.5	odd	2	inner
288.3.h.a.17.1		8	12.11	even	2
288.3.h.a.17.2		8	8.3	odd	2
288.3.h.a.17.7		8	4.3	odd	2
288.3.h.a.17.8		8	24.11	even	2
2304.3.e.n.1025.1		8	48.5	odd	4
2304.3.e.n.1025.2		8	16.13	even	4
2304.3.e.n.1025.7		8	16.5	even	4
2304.3.e.n.1025.8		8	48.29	odd	4
2304.3.e.o.1025.1		8	48.11	even	4
2304.3.e.o.1025.2		8	16.3	odd	4
2304.3.e.o.1025.7		8	16.11	odd	4
2304.3.e.o.1025.8		8	48.35	even	4

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	72.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16130 - 1.62831i) q^{2} +(-1.30278 - 3.78190i) q^{4} +7.67101 q^{5} -7.21110 q^{7} +(-7.67101 - 2.27059i) q^{8} +O(q^{10})\)	\(q+(1.16130 - 1.62831i) q^{2} +(-1.30278 - 3.78190i) q^{4} +7.67101 q^{5} -7.21110 q^{7} +(-7.67101 - 2.27059i) q^{8} +(8.90833 - 12.4908i) q^{10} +6.05164 q^{11} -2.29014i q^{13} +(-8.37424 + 11.7419i) q^{14} +(-12.6056 + 9.85394i) q^{16} +21.8103i q^{17} +34.8355i q^{19} +(-9.99361 - 29.0110i) q^{20} +(7.02776 - 9.85394i) q^{22} -21.5117i q^{23} +33.8444 q^{25} +(-3.72905 - 2.65953i) q^{26} +(9.39445 + 27.2717i) q^{28} +10.9098 q^{29} -37.6333 q^{31} +(1.40645 + 31.9691i) q^{32} +(35.5139 + 25.3282i) q^{34} -55.3164 q^{35} -34.8355i q^{37} +(56.7229 + 40.4544i) q^{38} +(-58.8444 - 17.4177i) q^{40} -13.3250i q^{41} -60.5104i q^{43} +(-7.88393 - 22.8867i) q^{44} +(-35.0278 - 24.9815i) q^{46} +3.34701i q^{47} +3.00000 q^{49} +(39.3034 - 55.1091i) q^{50} +(-8.66106 + 2.98353i) q^{52} -35.1163 q^{53} +46.4222 q^{55} +(55.3164 + 16.3735i) q^{56} +(12.6695 - 17.7644i) q^{58} +37.1615 q^{59} -25.6749i q^{61} +(-43.7035 + 61.2786i) q^{62} +(53.6888 + 34.8355i) q^{64} -17.5677i q^{65} +25.6749i q^{67} +(82.4844 - 28.4139i) q^{68} +(-64.2389 + 90.0722i) q^{70} -37.2881i q^{71} -77.6888 q^{73} +(-56.7229 - 40.4544i) q^{74} +(131.744 - 45.3828i) q^{76} -43.6390 q^{77} +31.3221 q^{79} +(-96.6973 + 75.5897i) q^{80} +(-21.6972 - 15.4743i) q^{82} +55.3164 q^{83} +167.307i q^{85} +(-98.5296 - 70.2706i) q^{86} +(-46.4222 - 13.7408i) q^{88} +5.43682i q^{89} +16.5144i q^{91} +(-81.3553 + 28.0250i) q^{92} +(5.44996 + 3.88687i) q^{94} +267.223i q^{95} -52.8444 q^{97} +(3.48389 - 4.88492i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} + 28 q^{10} - 72 q^{16} - 88 q^{22} + 40 q^{25} + 104 q^{28} - 128 q^{31} + 212 q^{34} - 240 q^{40} - 136 q^{46} + 24 q^{49} + 248 q^{52} + 256 q^{55} + 260 q^{58} - 32 q^{64} - 312 q^{70} - 160 q^{73} + 304 q^{76} - 384 q^{79} - 188 q^{82} - 256 q^{88} - 216 q^{94} - 192 q^{97}+O(q^{100}) \) 8 * q + 4 * q^4 + 28 * q^10 - 72 * q^16 - 88 * q^22 + 40 * q^25 + 104 * q^28 - 128 * q^31 + 212 * q^34 - 240 * q^40 - 136 * q^46 + 24 * q^49 + 248 * q^52 + 256 * q^55 + 260 * q^58 - 32 * q^64 - 312 * q^70 - 160 * q^73 + 304 * q^76 - 384 * q^79 - 188 * q^82 - 256 * q^88 - 216 * q^94 - 192 * q^97

Introduction

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