LMFDB - Embedded newform 72.3.h.a.53.2

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			53.2
Root			$-0.651388 + 2.66948i$ of defining polynomial
Character	$\chi$	$=$	72.53
Dual form			72.3.h.a.53.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.77521 + 0.921201i) q^{2} +(2.30278 - 3.27066i) q^{4} +1.07498 q^{5} +7.21110 q^{7} +(-1.07498 + 7.92745i) q^{8} +O(q^{10})$	\(q+(-1.77521 + 0.921201i) q^{2} +(2.30278 - 3.27066i) q^{4} +1.07498 q^{5} +7.21110 q^{7} +(-1.07498 + 7.92745i) q^{8} +(-1.90833 + 0.990277i) q^{10} +16.3517 q^{11} +21.6045i q^{13} +(-12.8013 + 6.64288i) q^{14} +(-5.39445 - 15.0632i) q^{16} -18.9819i q^{17} -17.0438i q^{19} +(2.47545 - 3.51591i) q^{20} +(-29.0278 + 15.0632i) q^{22} -1.11567i q^{23} -23.8444 q^{25} +(-19.9021 - 38.3527i) q^{26} +(16.6056 - 23.5851i) q^{28} -29.4784 q^{29} +5.63331 q^{31} +(23.4525 + 21.7710i) q^{32} +(17.4861 + 33.6969i) q^{34} +7.75182 q^{35} +17.0438i q^{37} +(15.7007 + 30.2563i) q^{38} +(-1.15559 + 8.52188i) q^{40} +27.4671i q^{41} -52.3306i q^{43} +(37.6543 - 53.4808i) q^{44} +(1.02776 + 1.98055i) q^{46} +64.5352i q^{47} +3.00000 q^{49} +(42.3290 - 21.9655i) q^{50} +(70.6611 + 49.7504i) q^{52} -35.9283 q^{53} +17.5778 q^{55} +(-7.75182 + 57.1656i) q^{56} +(52.3305 - 27.1556i) q^{58} -56.8069 q^{59} -69.3743i q^{61} +(-10.0003 + 5.18941i) q^{62} +(-61.6888 - 17.0438i) q^{64} +23.2245i q^{65} +69.3743i q^{67} +(-62.0832 - 43.7110i) q^{68} +(-13.7611 + 7.14099i) q^{70} -98.4764i q^{71} +37.6888 q^{73} +(-15.7007 - 30.2563i) q^{74} +(-55.7443 - 39.2479i) q^{76} +117.914 q^{77} -127.322 q^{79} +(-5.79894 - 16.1927i) q^{80} +(-25.3028 - 48.7601i) q^{82} -7.75182 q^{83} -20.4052i q^{85} +(48.2070 + 92.8980i) q^{86} +(-17.5778 + 129.627i) q^{88} -76.1475i q^{89} +155.792i q^{91} +(-3.64898 - 2.56914i) q^{92} +(-59.4500 - 114.564i) q^{94} -18.3218i q^{95} +4.84441 q^{97} +(-5.32564 + 2.76360i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.77521	+	0.921201i	−0.887607	+	0.460601i
$2$	−1.77521	+	0.921201i	−0.887607	+	0.460601i
$3$		0			0
$3$		0			0
$4$	2.30278	−	3.27066i	0.575694	−	0.817665i
$5$	1.07498			0.214997			0.107498	−	0.994205i	$-0.465716\pi$
$5$	1.07498			0.214997			0.107498	+	0.994205i	$0.465716\pi$
$6$		0			0
$7$	7.21110			1.03016			0.515079	−	0.857143i	$-0.327763\pi$
$7$	7.21110			1.03016			0.515079	+	0.857143i	$0.327763\pi$
$8$	−1.07498	+	7.92745i	−0.134373	+	0.990931i
$9$		0			0
$10$	−1.90833	+	0.990277i	−0.190833	+	0.0990277i
$11$	16.3517			1.48652			0.743258	−	0.669004i	$-0.233279\pi$
$11$	16.3517			1.48652			0.743258	+	0.669004i	$0.233279\pi$
$12$		0			0
$13$			21.6045i			1.66189i	0.556357	+	0.830943i	$0.312199\pi$
$13$			21.6045i			1.66189i	−0.556357	+	0.830943i	$0.687801\pi$
$14$	−12.8013	+	6.64288i	−0.914375	+	0.474491i
$15$		0			0
$16$	−5.39445	−	15.0632i	−0.337153	−	0.941450i
$17$		−	18.9819i		−	1.11658i	−0.829646	−	0.558290i	$-0.811458\pi$
$17$		−	18.9819i		−	1.11658i	0.829646	−	0.558290i	$-0.188542\pi$
$18$		0			0
$19$		−	17.0438i		−	0.897040i	−0.893773	−	0.448520i	$-0.851951\pi$
$19$		−	17.0438i		−	0.897040i	0.893773	−	0.448520i	$-0.148049\pi$
$20$	2.47545	−	3.51591i	0.123772	−	0.175795i
$21$		0			0
$22$	−29.0278	+	15.0632i	−1.31944	+	0.684691i
$23$		−	1.11567i		−	0.0485074i	−0.999706	−	0.0242537i	$-0.992279\pi$
$23$		−	1.11567i		−	0.0485074i	0.999706	−	0.0242537i	$-0.00772094\pi$
$24$		0			0
$25$	−23.8444			−0.953776
$26$	−19.9021	−	38.3527i	−0.765466	−	1.47510i
$27$		0			0
$28$	16.6056	−	23.5851i	0.593055	−	0.842324i
$29$	−29.4784			−1.01650			−0.508249	−	0.861210i	$-0.669707\pi$
$29$	−29.4784			−1.01650			−0.508249	+	0.861210i	$0.669707\pi$
$30$		0			0
$31$	5.63331			0.181720			0.0908598	−	0.995864i	$-0.471038\pi$
$31$	5.63331			0.181720			0.0908598	+	0.995864i	$0.471038\pi$
$32$	23.4525	+	21.7710i	0.732892	+	0.680345i
$33$		0			0
$34$	17.4861	+	33.6969i	0.514298	+	0.991085i
$35$	7.75182			0.221480
$36$		0			0
$37$			17.0438i			0.460642i	0.973115	+	0.230321i	$0.0739776\pi$
$37$			17.0438i			0.460642i	−0.973115	+	0.230321i	$0.926022\pi$
$38$	15.7007	+	30.2563i	0.413177	+	0.796219i
$39$		0			0
$40$	−1.15559	+	8.52188i	−0.0288897	+	0.213047i
$41$			27.4671i			0.669930i	0.942231	+	0.334965i	$0.108725\pi$
$41$			27.4671i			0.669930i	−0.942231	+	0.334965i	$0.891275\pi$
$42$		0			0
$43$		−	52.3306i		−	1.21699i	−0.793558	−	0.608495i	$-0.791774\pi$
$43$		−	52.3306i		−	1.21699i	0.793558	−	0.608495i	$-0.208226\pi$
$44$	37.6543	−	53.4808i	0.855779	−	1.21547i
$45$		0			0
$46$	1.02776	+	1.98055i	0.0223425	+	0.0430555i
$47$			64.5352i			1.37309i	0.727087	+	0.686545i	$0.240874\pi$
$47$			64.5352i			1.37309i	−0.727087	+	0.686545i	$0.759126\pi$
$48$		0			0
$49$	3.00000			0.0612245
$50$	42.3290	−	21.9655i	0.846579	−	0.439310i
$51$		0			0
$52$	70.6611	+	49.7504i	1.35887	+	0.956738i
$53$	−35.9283			−0.677893			−0.338946	−	0.940806i	$-0.610071\pi$
$53$	−35.9283			−0.677893			−0.338946	+	0.940806i	$0.610071\pi$
$54$		0			0
$55$	17.5778			0.319596
$56$	−7.75182	+	57.1656i	−0.138425	+	1.02081i
$57$		0			0
$58$	52.3305	−	27.1556i	0.902251	−	0.468199i
$59$	−56.8069			−0.962828			−0.481414	−	0.876493i	$-0.659877\pi$
$59$	−56.8069			−0.962828			−0.481414	+	0.876493i	$0.659877\pi$
$60$		0			0
$61$		−	69.3743i		−	1.13728i	−0.822585	−	0.568642i	$-0.807469\pi$
$61$		−	69.3743i		−	1.13728i	0.822585	−	0.568642i	$-0.192531\pi$
$62$	−10.0003	+	5.18941i	−0.161296	+	0.0837002i
$63$		0			0
$64$	−61.6888	−	17.0438i	−0.963888	−	0.266309i
$65$			23.2245i			0.357300i
$66$		0			0
$67$			69.3743i			1.03544i	0.855551	+	0.517719i	$0.173219\pi$
$67$			69.3743i			1.03544i	−0.855551	+	0.517719i	$0.826781\pi$
$68$	−62.0832	−	43.7110i	−0.912989	−	0.642808i
$69$		0			0
$70$	−13.7611	+	7.14099i	−0.196588	+	0.102014i
$71$		−	98.4764i		−	1.38699i	−0.720461	−	0.693496i	$-0.756070\pi$
$71$		−	98.4764i		−	1.38699i	0.720461	−	0.693496i	$-0.243930\pi$
$72$		0			0
$73$	37.6888			0.516285			0.258143	−	0.966107i	$-0.416890\pi$
$73$	37.6888			0.516285			0.258143	+	0.966107i	$0.416890\pi$
$74$	−15.7007	−	30.2563i	−0.212172	−	0.408869i
$75$		0			0
$76$	−55.7443	−	39.2479i	−0.733478	−	0.516420i
$77$	117.914			1.53135
$78$		0			0
$79$	−127.322			−1.61167			−0.805836	−	0.592138i	$-0.798284\pi$
$79$	−127.322			−1.61167			−0.805836	+	0.592138i	$0.798284\pi$
$80$	−5.79894	−	16.1927i	−0.0724868	−	0.202409i
$81$		0			0
$82$	−25.3028	−	48.7601i	−0.308570	−	0.594635i
$83$	−7.75182			−0.0933954			−0.0466977	−	0.998909i	$-0.514870\pi$
$83$	−7.75182			−0.0933954			−0.0466977	+	0.998909i	$0.514870\pi$
$84$		0			0
$85$		−	20.4052i		−	0.240061i
$86$	48.2070	+	92.8980i	0.560547	+	1.08021i
$87$		0			0
$88$	−17.5778	+	129.627i	−0.199748	+	1.47304i
$89$		−	76.1475i		−	0.855590i	−0.903876	−	0.427795i	$-0.859291\pi$
$89$		−	76.1475i		−	0.855590i	0.903876	−	0.427795i	$-0.140709\pi$
$90$		0			0
$91$			155.792i			1.71200i
$92$	−3.64898	−	2.56914i	−0.0396628	−	0.0279254i
$93$		0			0
$94$	−59.4500	−	114.564i	−0.632446	−	1.21877i
$95$		−	18.3218i		−	0.192861i
$96$		0			0
$97$	4.84441			0.0499424			0.0249712	−	0.999688i	$-0.492051\pi$
$97$	4.84441			0.0499424			0.0249712	+	0.999688i	$0.492051\pi$
$98$	−5.32564	+	2.76360i	−0.0543433	+	0.0282000i
$99$		0			0
$100$	−54.9083	+	77.9870i	−0.549083	+	0.779870i
$101$	105.635			1.04589			0.522946	−	0.852366i	$-0.324833\pi$
$101$	105.635			1.04589			0.522946	+	0.852366i	$0.324833\pi$
$102$		0			0
$103$	104.789			1.01737			0.508684	−	0.860953i	$-0.330132\pi$
$103$	104.789			1.01737			0.508684	+	0.860953i	$0.330132\pi$
$104$	−171.269	−	23.2245i	−1.64681	−	0.223313i
$105$		0			0
$106$	63.7805	−	33.0972i	0.601703	−	0.312238i
$107$	65.4067			0.611278			0.305639	−	0.952147i	$-0.401130\pi$
$107$	65.4067			0.611278			0.305639	+	0.952147i	$0.401130\pi$
$108$		0			0
$109$		−	3.36144i		−	0.0308389i	−0.999881	−	0.0154195i	$-0.995092\pi$
$109$		−	3.36144i		−	0.0308389i	0.999881	−	0.0154195i	$-0.00490836\pi$
$110$	−31.2044	+	16.1927i	−0.283676	+	0.147206i
$111$		0			0
$112$	−38.8999	−	108.622i	−0.347321	−	0.969842i
$113$			84.1927i			0.745068i	0.928019	+	0.372534i	$0.121511\pi$
$113$			84.1927i			0.745068i	−0.928019	+	0.372534i	$0.878489\pi$
$114$		0			0
$115$		−	1.19933i		−	0.0104289i
$116$	−67.8822	+	96.4139i	−0.585191	+	0.831155i
$117$		0			0
$118$	100.844	−	52.3306i	0.854614	−	0.443479i
$119$		−	136.880i		−	1.15025i
$120$		0			0
$121$	146.378			1.20973
$122$	63.9077	+	123.154i	0.523834	+	1.00946i
$123$		0			0
$124$	12.9722	−	18.4246i	0.104615	−	0.148586i
$125$	−52.5069			−0.420056
$126$		0			0
$127$	−45.5223			−0.358443			−0.179222	−	0.983809i	$-0.557358\pi$
$127$	−45.5223			−0.358443			−0.179222	+	0.983809i	$0.557358\pi$
$128$	125.212	−	26.5715i	0.978216	−	0.207590i
$129$		0			0
$130$	−21.3944	−	41.2285i	−0.164573	−	0.317142i
$131$	−129.117			−0.985629			−0.492814	−	0.870134i	$-0.664032\pi$
$131$	−129.117			−0.985629			−0.492814	+	0.870134i	$0.664032\pi$
$132$		0			0
$133$		−	122.904i		−	0.924092i
$134$	−63.9077	−	123.154i	−0.476923	−	0.919062i
$135$		0			0
$136$	150.478	+	20.4052i	1.10645	+	0.150038i
$137$			10.9367i			0.0798296i	0.999203	+	0.0399148i	$0.0127087\pi$
$137$			10.9367i			0.0798296i	−0.999203	+	0.0399148i	$0.987291\pi$
$138$		0			0
$139$			1.19933i			0.00862825i	0.999991	+	0.00431412i	$0.00137323\pi$
$139$			1.19933i			0.00862825i	−0.999991	+	0.00431412i	$0.998627\pi$
$140$	17.8507	−	25.3536i	0.127505	−	0.181097i
$141$		0			0
$142$	90.7166	+	174.817i	0.638849	+	1.23110i
$143$			353.270i			2.47042i
$144$		0			0
$145$	−31.6888			−0.218544
$146$	−66.9058	+	34.7190i	−0.458259	+	0.237801i
$147$		0			0
$148$	55.7443	+	39.2479i	0.376651	+	0.265189i
$149$	29.9323			0.200888			0.100444	−	0.994943i	$-0.467974\pi$
$149$	29.9323			0.200888			0.100444	+	0.994943i	$0.467974\pi$
$150$		0			0
$151$	61.5223			0.407432			0.203716	−	0.979030i	$-0.434698\pi$
$151$	61.5223			0.407432			0.203716	+	0.979030i	$0.434698\pi$
$152$	135.113	+	18.3218i	0.888904	+	0.120538i
$153$		0			0
$154$	−209.322	+	108.622i	−1.35923	+	0.705339i
$155$	6.05571			0.0390691
$156$		0			0
$157$			137.549i			0.876110i	0.898948	+	0.438055i	$0.144333\pi$
$157$			137.549i			0.876110i	−0.898948	+	0.438055i	$0.855667\pi$
$158$	226.024	−	117.289i	1.43053	−	0.742338i
$159$		0			0
$160$	25.2111	+	23.4035i	0.157569	+	0.146272i
$161$		−	8.04521i		−	0.0499702i
$162$		0			0
$163$		−	191.079i		−	1.17227i	−0.810215	−	0.586133i	$-0.800650\pi$
$163$		−	191.079i		−	1.17227i	0.810215	−	0.586133i	$-0.199350\pi$
$164$	89.8357	+	63.2507i	0.547779	+	0.385675i
$165$		0			0
$166$	13.7611	−	7.14099i	0.0828984	−	0.0430180i
$167$		−	233.125i		−	1.39596i	−0.716118	−	0.697980i	$-0.754083\pi$
$167$		−	233.125i		−	1.39596i	0.716118	−	0.697980i	$-0.245917\pi$
$168$		0			0
$169$	−297.755			−1.76187
$170$	18.7973	+	36.2236i	0.110572	+	0.213080i
$171$		0			0
$172$	−171.156	−	120.506i	−0.995091	−	0.700614i
$173$	−323.809			−1.87173			−0.935864	−	0.352363i	$-0.885378\pi$
$173$	−323.809			−1.87173			−0.935864	+	0.352363i	$0.885378\pi$
$174$		0			0
$175$	−171.944			−0.982540
$176$	−88.2083	−	246.309i	−0.501184	−	1.39948i
$177$		0			0
$178$	70.1472	+	135.178i	0.394085	+	0.759428i
$179$	185.924			1.03868			0.519342	−	0.854567i	$-0.326177\pi$
$179$	185.924			1.03868			0.519342	+	0.854567i	$0.326177\pi$
$180$		0			0
$181$			126.266i			0.697600i	0.937197	+	0.348800i	$0.113411\pi$
$181$			126.266i			0.697600i	−0.937197	+	0.348800i	$0.886589\pi$
$182$	−143.516	−	276.565i	−0.788551	−	1.51959i
$183$		0			0
$184$	8.84441	+	1.19933i	0.0480674	+	0.00651808i
$185$			18.3218i			0.0990365i
$186$		0			0
$187$		−	310.385i		−	1.65982i
$188$	211.073	+	148.610i	1.12273	+	0.790480i
$189$		0			0
$190$	16.8780	+	32.5250i	0.0888317	+	0.171184i
$191$			233.125i			1.22055i	0.792189	+	0.610275i	$0.208941\pi$
$191$			233.125i			1.22055i	−0.792189	+	0.610275i	$0.791059\pi$
$192$		0			0
$193$	−117.378			−0.608174			−0.304087	−	0.952644i	$-0.598351\pi$
$193$	−117.378			−0.608174			−0.304087	+	0.952644i	$0.598351\pi$
$194$	−8.59987	+	4.46268i	−0.0443292	+	0.0230035i
$195$		0			0
$196$	6.90833	−	9.81198i	0.0352466	−	0.0500611i
$197$	−296.313			−1.50413			−0.752064	−	0.659091i	$-0.770941\pi$
$197$	−296.313			−1.50413			−0.752064	+	0.659091i	$0.770941\pi$
$198$		0			0
$199$	233.011			1.17091			0.585455	−	0.810705i	$-0.300916\pi$
$199$	233.011			1.17091			0.585455	+	0.810705i	$0.300916\pi$
$200$	25.6324	−	189.025i	0.128162	−	0.945126i
$201$		0			0
$202$	−187.525	+	97.3111i	−0.928341	+	0.481738i
$203$	−212.572			−1.04715
$204$		0			0
$205$			29.5267i			0.144033i
$206$	−186.023	+	96.5317i	−0.903023	+	0.468600i
$207$		0			0
$208$	325.433	−	116.544i	1.56458	−	0.560310i
$209$		−	278.694i		−	1.33346i
$210$		0			0
$211$			35.2868i			0.167236i	0.996498	+	0.0836181i	$0.0266476\pi$
$211$			35.2868i			0.167236i	−0.996498	+	0.0836181i	$0.973352\pi$
$212$	−82.7349	+	117.509i	−0.390259	+	0.554289i
$213$		0			0
$214$	−116.111	+	60.2528i	−0.542575	+	0.281555i
$215$		−	56.2545i		−	0.261649i
$216$		0			0
$217$	40.6224			0.187200
$218$	3.09657	+	5.96728i	0.0142044	+	0.0273729i
$219$		0			0
$220$	40.4777	−	57.4910i	0.183990	−	0.261323i
$221$	410.094			1.85563
$222$		0			0
$223$	−51.8335			−0.232437			−0.116219	−	0.993224i	$-0.537077\pi$
$223$	−51.8335			−0.232437			−0.116219	+	0.993224i	$0.537077\pi$
$224$	169.119	+	156.993i	0.754994	+	0.700862i
$225$		0			0
$226$	−77.5584	−	149.460i	−0.343179	−	0.661328i
$227$	334.786			1.47483			0.737413	−	0.675442i	$-0.236047\pi$
$227$	334.786			1.47483			0.737413	+	0.675442i	$0.236047\pi$
$228$		0			0
$229$			219.407i			0.958108i	0.877786	+	0.479054i	$0.159020\pi$
$229$			219.407i			0.958108i	−0.877786	+	0.479054i	$0.840980\pi$
$230$	1.10482	+	2.12906i	0.00480357	+	0.00925679i
$231$		0			0
$232$	31.6888	−	233.689i	0.136590	−	1.00728i
$233$			203.867i			0.874965i	0.899227	+	0.437482i	$0.144130\pi$
$233$			203.867i			0.874965i	−0.899227	+	0.437482i	$0.855870\pi$
$234$		0			0
$235$			69.3743i			0.295210i
$236$	−130.813	+	185.796i	−0.554294	+	0.787271i
$237$		0			0
$238$	126.094	+	242.992i	0.529808	+	1.02097i
$239$			54.0232i			0.226038i	0.993593	+	0.113019i	$0.0360522\pi$
$239$			54.0232i			0.226038i	−0.993593	+	0.113019i	$0.963948\pi$
$240$		0			0
$241$	327.600			1.35933			0.679667	−	0.733520i	$-0.262124\pi$
$241$	327.600			1.35933			0.679667	+	0.733520i	$0.262124\pi$
$242$	−259.852	+	134.843i	−1.07377	+	0.557204i
$243$		0			0
$244$	−226.900	−	159.754i	−0.929918	−	0.654728i
$245$	3.22495			0.0131631
$246$		0			0
$247$	368.222			1.49078
$248$	−6.05571	+	44.6577i	−0.0244182	+	0.180072i
$249$		0			0
$250$	93.2111	−	48.3695i	0.372844	−	0.193478i
$251$	362.281			1.44335			0.721676	−	0.692231i	$-0.243372\pi$
$251$	362.281			1.44335			0.721676	+	0.692231i	$0.243372\pi$
$252$		0			0
$253$		−	18.2431i		−	0.0721070i
$254$	80.8118	−	41.9352i	0.318157	−	0.165099i
$255$		0			0
$256$	−197.800	+	162.515i	−0.772656	+	0.634825i
$257$			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
$259$			122.904i			0.474534i
$260$	75.9595	+	53.4808i	0.292152	+	0.205695i
$261$		0			0
$262$	229.211	−	118.943i	0.874852	−	0.453981i
$263$		−	205.878i		−	0.782806i	−0.920219	−	0.391403i	$-0.871990\pi$
$263$		−	205.878i		−	0.782806i	0.920219	−	0.391403i	$-0.128010\pi$
$264$		0			0
$265$	−38.6224			−0.145745
$266$	113.220	+	218.181i	0.425637	+	0.820231i
$267$		0			0
$268$	226.900	+	159.754i	0.846642	+	0.596095i
$269$	2.77109			0.0103014			0.00515072	−	0.999987i	$-0.498360\pi$
$269$	2.77109			0.0103014			0.00515072	+	0.999987i	$0.498360\pi$
$270$		0			0
$271$	−125.744			−0.464001			−0.232001	−	0.972716i	$-0.574527\pi$
$271$	−125.744			−0.464001			−0.232001	+	0.972716i	$0.574527\pi$
$272$	−285.928	+	102.397i	−1.05120	+	0.376458i
$273$		0			0
$274$	−10.0749	−	19.4149i	−0.0367696	−	0.0708574i
$275$	−389.896			−1.41780
$276$		0			0
$277$			162.752i			0.587552i	0.955874	+	0.293776i	$0.0949119\pi$
$277$			162.752i			0.587552i	−0.955874	+	0.293776i	$0.905088\pi$
$278$	−1.10482	−	2.12906i	−0.00397418	−	0.00765850i
$279$		0			0
$280$	−8.33308	+	61.4521i	−0.0297610	+	0.219472i
$281$		−	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
$283$			31.6888i			0.111975i	0.998431	+	0.0559874i	$0.0178307\pi$
$283$			31.6888i			0.111975i	−0.998431	+	0.0559874i	$0.982169\pi$
$284$	−322.083	−	226.769i	−1.13409	−	0.798482i
$285$		0			0
$286$	−325.433	−	627.131i	−1.13788	−	2.19276i
$287$			198.068i			0.690134i
$288$		0			0
$289$	−71.3112			−0.246751
$290$	56.2545	−	29.1918i	0.193981	−	0.100661i
$291$		0			0
$292$	86.7889	−	123.267i	0.297222	−	0.422148i
$293$	304.913			1.04066			0.520329	−	0.853966i	$-0.325809\pi$
$293$	304.913			1.04066			0.520329	+	0.853966i	$0.325809\pi$
$294$		0			0
$295$	−61.0665			−0.207005
$296$	−135.113	−	18.3218i	−0.456464	−	0.0618978i
$297$		0			0
$298$	−53.1362	+	27.5737i	−0.178310	+	0.0925291i
$299$	24.1035			0.0806137
$300$		0			0
$301$		−	377.361i		−	1.25369i
$302$	−109.215	+	56.6744i	−0.361640	+	0.187664i
$303$		0			0
$304$	−256.733	+	91.9416i	−0.844518	+	0.302440i
$305$		−	74.5763i		−	0.244512i
$306$		0			0
$307$			105.860i			0.344822i	0.985025	+	0.172411i	$0.0551558\pi$
$307$			105.860i			0.344822i	−0.985025	+	0.172411i	$0.944844\pi$
$308$	271.529	−	385.656i	0.881587	−	1.25213i
$309$		0			0
$310$	−10.7502	+	5.57853i	−0.0346780	+	0.0179953i
$311$		−	555.157i		−	1.78507i	−0.450978	−	0.892535i	$-0.648925\pi$
$311$		−	555.157i		−	1.78507i	0.450978	−	0.892535i	$-0.351075\pi$
$312$		0			0
$313$	158.000			0.504792			0.252396	−	0.967624i	$-0.418781\pi$
$313$	158.000			0.504792			0.252396	+	0.967624i	$0.418781\pi$
$314$	−126.711	−	244.180i	−0.403537	−	0.777642i
$315$		0			0
$316$	−293.194	+	416.428i	−0.927830	+	1.31781i
$317$	−97.0351			−0.306105			−0.153052	−	0.988218i	$-0.548910\pi$
$317$	−97.0351			−0.306105			−0.153052	+	0.988218i	$0.548910\pi$
$318$		0			0
$319$	−482.022			−1.51104
$320$	−66.3145	−	18.3218i	−0.207233	−	0.0572555i
$321$		0			0
$322$	7.41126	+	14.2820i	0.0230163	+	0.0443539i
$323$	−323.522			−1.00162
$324$		0			0
$325$		−	515.147i		−	1.58507i
$326$	176.022	+	339.207i	0.539946	+	1.04051i
$327$		0			0
$328$	−217.744	−	29.5267i	−0.663855	−	0.0900205i
$329$			465.370i			1.41450i
$330$		0			0
$331$			619.572i			1.87182i	0.352242	+	0.935909i	$0.385419\pi$
$331$			619.572i			1.87182i	−0.352242	+	0.935909i	$0.614581\pi$
$332$	−17.8507	+	25.3536i	−0.0537672	+	0.0763662i
$333$		0			0
$334$	214.755	+	413.847i	0.642980	+	1.23906i
$335$			74.5763i			0.222616i
$336$		0			0
$337$	−170.755			−0.506692			−0.253346	−	0.967376i	$-0.581531\pi$
$337$	−170.755			−0.506692			−0.253346	+	0.967376i	$0.581531\pi$
$338$	528.580	−	274.293i	1.56384	−	0.811517i
$339$		0			0
$340$	−66.7385	−	46.9886i	−0.196290	−	0.138202i
$341$	92.1141			0.270129
$342$		0			0
$343$	−331.711			−0.967087
$344$	414.848	+	56.2545i	1.20595	+	0.163531i
$345$		0			0
$346$	574.830	−	298.293i	1.66136	−	0.862119i
$347$	−300.386			−0.865666			−0.432833	−	0.901474i	$-0.642486\pi$
$347$	−300.386			−0.865666			−0.432833	+	0.901474i	$0.642486\pi$
$348$		0			0
$349$			53.5299i			0.153381i	0.997055	+	0.0766904i	$0.0244353\pi$
$349$			53.5299i			0.153381i	−0.997055	+	0.0766904i	$0.975565\pi$
$350$	305.238	−	158.396i	0.872110	−	0.452559i
$351$		0			0
$352$	383.489	+	355.993i	1.08946	+	1.01134i
$353$			600.475i			1.70106i	0.525925	+	0.850531i	$0.323719\pi$
$353$			600.475i			1.70106i	−0.525925	+	0.850531i	$0.676281\pi$
$354$		0			0
$355$		−	105.860i		−	0.298199i
$356$	−249.053	−	175.351i	−0.699586	−	0.492558i
$357$		0			0
$358$	−330.056	+	171.274i	−0.921943	+	0.478418i
$359$			148.508i			0.413671i	0.978376	+	0.206836i	$0.0663165\pi$
$359$			148.508i			0.413671i	−0.978376	+	0.206836i	$0.933683\pi$
$360$		0			0
$361$	70.5106			0.195320
$362$	−116.316	−	224.149i	−0.321315	−	0.619195i
$363$		0			0
$364$	509.544	+	358.755i	1.39985	+	0.985591i
$365$	40.5149			0.111000
$366$		0			0
$367$	316.389			0.862094			0.431047	−	0.902329i	$-0.358144\pi$
$367$	316.389			0.862094			0.431047	+	0.902329i	$0.358144\pi$
$368$	−16.8055	+	6.01842i	−0.0456673	+	0.0163544i
$369$		0			0
$370$	−16.8780	−	32.5250i	−0.0456163	−	0.0879055i
$371$	−259.083			−0.698336
$372$		0			0
$373$		−	626.768i		−	1.68034i	−0.542321	−	0.840171i	$-0.682455\pi$
$373$		−	626.768i		−	1.68034i	0.542321	−	0.840171i	$-0.317545\pi$
$374$	285.928	+	551.001i	0.764512	+	1.47326i
$375$		0			0
$376$	−511.600	−	69.3743i	−1.36064	−	0.184506i
$377$		−	636.867i		−	1.68930i
$378$		0			0
$379$		−	331.027i		−	0.873423i	−0.899602	−	0.436711i	$-0.856143\pi$
$379$		−	331.027i		−	0.873423i	0.899602	−	0.436711i	$-0.143857\pi$
$380$	−59.9242	−	42.1909i	−0.157695	−	0.111029i
$381$		0			0
$382$	−214.755	−	413.847i	−0.562187	−	1.08337i
$383$			407.765i			1.06466i	0.846537	+	0.532330i	$0.178683\pi$
$383$			407.765i			1.06466i	−0.846537	+	0.532330i	$0.821317\pi$
$384$		0			0
$385$	126.755			0.329234
$386$	208.371	−	108.128i	0.539820	−	0.280126i
$387$		0			0
$388$	11.1556	−	15.8444i	0.0287515	−	0.0408361i
$389$	−53.5819			−0.137743			−0.0688714	−	0.997626i	$-0.521940\pi$
$389$	−53.5819			−0.137743			−0.0688714	+	0.997626i	$0.521940\pi$
$390$		0			0
$391$	−21.1775			−0.0541624
$392$	−3.22495	+	23.7823i	−0.00822692	+	0.0606692i
$393$		0			0
$394$	526.019	−	272.964i	1.33507	−	0.692802i
$395$	−136.869			−0.346504
$396$		0			0
$397$			289.744i			0.729833i	0.931040	+	0.364917i	$0.118902\pi$
$397$			289.744i			0.729833i	−0.931040	+	0.364917i	$0.881098\pi$
$398$	−413.644	+	214.650i	−1.03931	+	0.539322i
$399$		0			0
$400$	128.627	+	359.173i	0.321569	+	0.897933i
$401$			203.458i			0.507376i	0.967286	+	0.253688i	$0.0816436\pi$
$401$			203.458i			0.507376i	−0.967286	+	0.253688i	$0.918356\pi$
$402$		0			0
$403$			121.705i			0.301997i
$404$	243.254	−	345.496i	0.602113	−	0.855189i
$405$		0			0
$406$	377.361	−	195.822i	0.929460	−	0.482319i
$407$			278.694i			0.684752i
$408$		0			0
$409$	412.844			1.00940			0.504700	−	0.863295i	$-0.331603\pi$
$409$	412.844			1.00940			0.504700	+	0.863295i	$0.331603\pi$
$410$	−27.2001	−	52.4163i	−0.0663416	−	0.127845i
$411$		0			0
$412$	241.305	−	342.729i	0.585693	−	0.831866i
$413$	−409.640			−0.991865
$414$		0			0
$415$	−8.33308			−0.0200797
$416$	−470.353	+	506.681i	−1.13066	+	1.21798i
$417$		0			0
$418$	256.733	+	494.742i	0.614195	+	1.18359i
$419$	336.482			0.803059			0.401529	−	0.915846i	$-0.368479\pi$
$419$	336.482			0.803059			0.401529	+	0.915846i	$0.368479\pi$
$420$		0			0
$421$			217.481i			0.516582i	0.966067	+	0.258291i	$0.0831594\pi$
$421$			217.481i			0.516582i	−0.966067	+	0.258291i	$0.916841\pi$
$422$	−32.5063	−	62.6417i	−0.0770291	−	0.148440i
$423$		0			0
$424$	38.6224	−	284.820i	0.0910905	−	0.671745i
$425$			452.611i			1.06497i
$426$		0			0
$427$		−	500.265i		−	1.17158i
$428$	150.617	−	213.923i	0.351909	−	0.499821i
$429$		0			0
$430$	51.8217	+	99.8639i	0.120516	+	0.232242i
$431$		−	750.994i		−	1.74245i	−0.490888	−	0.871223i	$-0.663328\pi$
$431$		−	750.994i		−	1.74245i	0.490888	−	0.871223i	$-0.336672\pi$
$432$		0			0
$433$	−176.133			−0.406773			−0.203387	−	0.979098i	$-0.565195\pi$
$433$	−176.133			−0.406773			−0.203387	+	0.979098i	$0.565195\pi$
$434$	−72.1134	+	37.4214i	−0.166160	+	0.0862244i
$435$		0			0
$436$	−10.9941	−	7.74065i	−0.0252159	−	0.0177538i
$437$	−19.0152			−0.0435130
$438$		0			0
$439$	417.788			0.951681			0.475841	−	0.879531i	$-0.342144\pi$
$439$	417.788			0.951681			0.475841	+	0.879531i	$0.342144\pi$
$440$	−18.8958	+	139.347i	−0.0429451	+	0.316698i
$441$		0			0
$442$	−728.005	+	377.779i	−1.64707	+	0.854704i
$443$	−61.0471			−0.137804			−0.0689020	−	0.997623i	$-0.521950\pi$
$443$	−61.0471			−0.137804			−0.0689020	+	0.997623i	$0.521950\pi$
$444$		0			0
$445$		−	81.8573i		−	0.183949i
$446$	92.0155	−	47.7491i	0.206313	−	0.107061i
$447$		0			0
$448$	−444.844	−	122.904i	−0.992956	−	0.274340i
$449$		−	182.905i		−	0.407360i	−0.979038	−	0.203680i	$-0.934710\pi$
$449$		−	182.905i		−	0.407360i	0.979038	−	0.203680i	$-0.0652902\pi$
$450$		0			0
$451$			449.134i			0.995863i
$452$	275.366	+	193.877i	0.609216	+	0.428931i
$453$		0			0
$454$	−594.316	+	308.405i	−1.30907	+	0.679306i
$455$			167.474i			0.368075i
$456$		0			0
$457$	−443.600			−0.970678			−0.485339	−	0.874326i	$-0.661304\pi$
$457$	−443.600			−0.970678			−0.485339	+	0.874326i	$0.661304\pi$
$458$	−202.118	−	389.494i	−0.441305	−	0.850423i
$459$		0			0
$460$	−3.92259	−	2.76178i	−0.00852737	−	0.00600387i
$461$	728.241			1.57970			0.789850	−	0.613301i	$-0.210159\pi$
$461$	728.241			1.57970			0.789850	+	0.613301i	$0.210159\pi$
$462$		0			0
$463$	−107.722			−0.232662			−0.116331	−	0.993211i	$-0.537113\pi$
$463$	−107.722			−0.232662			−0.116331	+	0.993211i	$0.537113\pi$
$464$	159.020	+	444.039i	0.342715	+	0.956981i
$465$		0			0
$466$	−187.802	−	361.907i	−0.403009	−	0.776625i
$467$	820.248			1.75642			0.878210	−	0.478276i	$-0.158738\pi$
$467$	820.248			1.75642			0.878210	+	0.478276i	$0.158738\pi$
$468$		0			0
$469$			500.265i			1.06666i
$470$	−63.9077	−	123.154i	−0.135974	−	0.262031i
$471$		0			0
$472$	61.0665	−	450.333i	0.129378	−	0.954096i
$473$		−	855.693i		−	1.80908i
$474$		0			0
$475$			406.398i			0.855575i
$476$	−447.689	−	315.204i	−0.940522	−	0.662194i
$477$		0			0
$478$	−49.7662	−	95.9027i	−0.104113	−	0.200633i
$479$		−	120.790i		−	0.252171i	−0.992019	−	0.126085i	$-0.959759\pi$
$479$		−	120.790i		−	0.252171i	0.992019	−	0.126085i	$-0.0402413\pi$
$480$		0			0
$481$	−368.222			−0.765534
$482$	−581.560	+	301.785i	−1.20656	+	0.626111i
$483$		0			0
$484$	337.075	−	478.752i	0.696436	−	0.989156i
$485$	5.20766			0.0107374
$486$		0			0
$487$	−128.234			−0.263314			−0.131657	−	0.991295i	$-0.542030\pi$
$487$	−128.234			−0.263314			−0.131657	+	0.991295i	$0.542030\pi$
$488$	549.961	+	74.5763i	1.12697	+	0.152820i
$489$		0			0
$490$	−5.72498	+	2.97083i	−0.0116836	+	0.00606292i
$491$	382.144			0.778298			0.389149	−	0.921175i	$-0.372769\pi$
$491$	382.144			0.778298			0.389149	+	0.921175i	$0.372769\pi$
$492$		0			0
$493$			559.555i			1.13500i
$494$	−653.673	+	339.207i	−1.32323	+	0.686653i
$495$		0			0
$496$	−30.3886	−	84.8556i	−0.0612673	−	0.171080i
$497$		−	710.123i		−	1.42882i
$498$		0			0
$499$		−	554.995i		−	1.11221i	−0.831111	−	0.556107i	$-0.812295\pi$
$499$		−	554.995i		−	1.11221i	0.831111	−	0.556107i	$-0.187705\pi$
$500$	−120.912	+	171.732i	−0.241823	+	0.343465i
$501$		0			0
$502$	−643.127	+	333.734i	−1.28113	+	0.664809i
$503$		−	78.3943i		−	0.155854i	−0.996959	−	0.0779268i	$-0.975170\pi$
$503$		−	78.3943i		−	0.155854i	0.996959	−	0.0779268i	$-0.0248300\pi$
$504$		0			0
$505$	113.556			0.224863
$506$	16.8055	+	32.3854i	0.0332125	+	0.0640027i
$507$		0			0
$508$	−104.828	+	148.888i	−0.206354	+	0.293087i
$509$	−514.941			−1.01167			−0.505836	−	0.862630i	$-0.668816\pi$
$509$	−514.941			−1.01167			−0.505836	+	0.862630i	$0.668816\pi$
$510$		0			0
$511$	271.778			0.531855
$512$	201.428	−	470.713i	0.393414	−	0.919361i
$513$		0			0
$514$	−19.5416	−	37.6580i	−0.0380187	−	0.0732646i
$515$	112.646			0.218731
$516$		0			0
$517$			1055.26i			2.04112i
$518$	−113.220	−	218.181i	−0.218571	−	0.421200i
$519$		0			0
$520$	−184.111	−	24.9660i	−0.354060	−	0.0480115i
$521$			489.695i			0.939914i	0.882689	+	0.469957i	$0.155730\pi$
$521$			489.695i			0.939914i	−0.882689	+	0.469957i	$0.844270\pi$
$522$		0			0
$523$		−	774.165i		−	1.48024i	−0.672476	−	0.740119i	$-0.734769\pi$
$523$		−	774.165i		−	1.48024i	0.672476	−	0.740119i	$-0.265231\pi$
$524$	−297.328	+	422.299i	−0.567421	+	0.805915i
$525$		0			0
$526$	189.655	+	365.478i	0.360561	+	0.694825i
$527$		−	106.931i		−	0.202905i
$528$		0			0
$529$	527.755			0.997647
$530$	68.5630	−	35.5790i	0.129364	−	0.0671301i
$531$		0			0
$532$	−401.978	−	283.021i	−0.755598	−	0.531994i
$533$	−593.415			−1.11335
$534$		0			0
$535$	70.3112			0.131423
$536$	−549.961	−	74.5763i	−1.02605	−	0.139135i
$537$		0			0
$538$	−4.91928	+	2.55273i	−0.00914363	+	0.00474485i
$539$	49.0551			0.0910112
$540$		0			0
$541$		−	590.045i		−	1.09066i	−0.838223	−	0.545328i	$-0.816405\pi$
$541$		−	590.045i		−	1.09066i	0.838223	−	0.545328i	$-0.183595\pi$
$542$	223.223	−	115.836i	0.411851	−	0.213719i
$543$		0			0
$544$	413.255	−	445.173i	0.759660	−	0.818333i
$545$		−	3.61350i		−	0.00663027i
$546$		0			0
$547$		−	707.189i		−	1.29285i	−0.762977	−	0.646425i	$-0.776263\pi$
$547$		−	707.189i		−	1.29285i	0.762977	−	0.646425i	$-0.223737\pi$
$548$	35.7701	+	25.1847i	0.0652739	+	0.0459574i
$549$		0			0
$550$	692.150	−	359.173i	1.25845	−	0.653042i
$551$			502.423i			0.911838i
$552$		0			0
$553$	−918.133			−1.66028
$554$	−149.927	−	288.919i	−0.270627	−	0.521515i
$555$		0			0
$556$	3.92259	+	2.76178i	0.00705502	+	0.00496723i
$557$	75.0816			0.134796			0.0673982	−	0.997726i	$-0.478530\pi$
$557$	75.0816			0.134796			0.0673982	+	0.997726i	$0.478530\pi$
$558$		0			0
$559$	1130.58			2.02250
$560$	−41.8168	−	116.767i	−0.0746728	−	0.208513i
$561$		0			0
$562$	277.491	+	534.744i	0.493757	+	0.951501i
$563$	114.462			0.203307			0.101653	−	0.994820i	$-0.467587\pi$
$563$	114.462			0.203307			0.101653	+	0.994820i	$0.467587\pi$
$564$		0			0
$565$			90.5058i			0.160187i
$566$	−29.1918	−	56.2545i	−0.0515756	−	0.0993896i
$567$		0			0
$568$	780.666	+	105.860i	1.37441	+	0.186374i
$569$			45.8199i			0.0805270i	0.999189	+	0.0402635i	$0.0128197\pi$
$569$			45.8199i			0.0805270i	−0.999189	+	0.0402635i	$0.987180\pi$
$570$		0			0
$571$			830.093i			1.45375i	0.686768	+	0.726877i	$0.259029\pi$
$571$			830.093i			1.45375i	−0.686768	+	0.726877i	$0.740971\pi$
$572$	1155.43	+	813.502i	2.01998	+	1.42221i
$573$		0			0
$574$	−182.461	−	351.614i	−0.317876	−	0.612568i
$575$			26.6025i			0.0462652i
$576$		0			0
$577$	−69.3776			−0.120239			−0.0601193	−	0.998191i	$-0.519148\pi$
$577$	−69.3776			−0.120239			−0.0601193	+	0.998191i	$0.519148\pi$
$578$	126.593	−	65.6920i	0.219018	−	0.113654i
$579$		0			0
$580$	−72.9722	+	103.643i	−0.125814	+	0.178696i
$581$	−55.8991			−0.0962120
$582$		0			0
$583$	−587.489			−1.00770
$584$	−40.5149	+	298.776i	−0.0693748	+	0.511603i
$585$		0			0
$586$	−541.286	+	280.886i	−0.923696	+	0.479328i
$587$	428.655			0.730248			0.365124	−	0.930959i	$-0.381027\pi$
$587$	428.655			0.730248			0.365124	+	0.930959i	$0.381027\pi$
$588$		0			0
$589$		−	96.0127i		−	0.163010i
$590$	108.406	−	56.2545i	0.183739	−	0.0953466i
$591$		0			0
$592$	256.733	−	91.9416i	0.433671	−	0.155307i
$593$		−	77.0276i		−	0.129895i	−0.997889	−	0.0649474i	$-0.979312\pi$
$593$		−	77.0276i		−	0.129895i	0.997889	−	0.0649474i	$-0.0206880\pi$
$594$		0			0
$595$		−	147.144i		−	0.247301i
$596$	68.9273	−	97.8984i	0.115650	−	0.164259i
$597$		0			0
$598$	−42.7889	+	22.2042i	−0.0715533	+	0.0371307i
$599$			963.566i			1.60862i	0.594207	+	0.804312i	$0.297466\pi$
$599$			963.566i			1.60862i	−0.594207	+	0.804312i	$0.702534\pi$
$600$		0			0
$601$	840.133			1.39789			0.698946	−	0.715175i	$-0.253653\pi$
$601$	840.133			1.39789			0.698946	+	0.715175i	$0.253653\pi$
$602$	347.626	+	669.897i	0.577451	+	1.11279i
$603$		0			0
$604$	141.672	−	201.219i	0.234556	−	0.333143i
$605$	157.354			0.260089
$606$		0			0
$607$	156.611			0.258008			0.129004	−	0.991644i	$-0.458822\pi$
$607$	156.611			0.258008			0.129004	+	0.991644i	$0.458822\pi$
$608$	371.060	−	399.719i	0.610296	−	0.657433i
$609$		0			0
$610$	68.6998	+	132.389i	0.112623	+	0.217031i
$611$	−1394.25			−2.28192
$612$		0			0
$613$		−	426.094i		−	0.695096i	−0.937662	−	0.347548i	$-0.887014\pi$
$613$		−	426.094i		−	0.695096i	0.937662	−	0.347548i	$-0.112986\pi$
$614$	−97.5188	−	187.925i	−0.158825	−	0.306067i
$615$		0			0
$616$	−126.755	+	934.754i	−0.205772	+	1.51746i
$617$			963.520i			1.56162i	0.624769	+	0.780810i	$0.285193\pi$
$617$			963.520i			1.56162i	−0.624769	+	0.780810i	$0.714807\pi$
$618$		0			0
$619$		−	175.235i		−	0.283093i	−0.989932	−	0.141547i	$-0.954792\pi$
$619$		−	175.235i		−	0.283093i	0.989932	−	0.141547i	$-0.0452075\pi$
$620$	13.9449	−	19.8062i	0.0224919	−	0.0319455i
$621$		0			0
$622$	511.411	+	985.523i	0.822205	+	1.58444i
$623$		−	549.107i		−	0.881392i
$624$		0			0
$625$	539.666			0.863466
$626$	−280.484	+	145.550i	−0.448057	+	0.232508i
$627$		0			0
$628$	449.877	+	316.745i	0.716365	+	0.504371i
$629$	323.522			0.514344
$630$		0			0
$631$	−1140.72			−1.80780			−0.903900	−	0.427744i	$-0.859308\pi$
$631$	−1140.72			−1.80780			−0.903900	+	0.427744i	$0.859308\pi$
$632$	136.869	−	1009.34i	0.216565	−	1.59706i
$633$		0			0
$634$	172.258	−	89.3889i	0.271701	−	0.140992i
$635$	−48.9357			−0.0770641
$636$		0			0
$637$			64.8136i			0.101748i
$638$	855.692	−	444.039i	1.34121	−	0.695986i
$639$		0			0
$640$	134.600	−	28.5639i	0.210313	−	0.0446312i
$641$			351.730i			0.548721i	0.961627	+	0.274360i	$0.0884661\pi$
$641$			351.730i			0.548721i	−0.961627	+	0.274360i	$0.911534\pi$
$642$		0			0
$643$			86.4181i			0.134398i	0.997740	+	0.0671991i	$0.0214063\pi$
$643$			86.4181i			0.134398i	−0.997740	+	0.0671991i	$0.978594\pi$
$644$	−26.3131	−	18.5263i	−0.0408589	−	0.0287676i
$645$		0			0
$646$	574.321	−	298.029i	0.889042	−	0.461345i
$647$			430.723i			0.665723i	0.942976	+	0.332861i	$0.108014\pi$
$647$			430.723i			0.665723i	−0.942976	+	0.332861i	$0.891986\pi$
$648$		0			0
$649$	−928.888			−1.43126
$650$	474.554	+	914.497i	0.730083	+	1.40692i
$651$		0			0
$652$	−624.955	−	440.013i	−0.958521	−	0.674866i
$653$	−886.670			−1.35784			−0.678920	−	0.734212i	$-0.737552\pi$
$653$	−886.670			−1.35784			−0.678920	+	0.734212i	$0.737552\pi$
$654$		0			0
$655$	−138.799			−0.211907
$656$	413.743	−	148.170i	0.630706	−	0.225869i
$657$		0			0
$658$	−428.700	−	826.132i	−0.651519	−	1.25552i
$659$	−352.833			−0.535407			−0.267704	−	0.963501i	$-0.586265\pi$
$659$	−352.833			−0.535407			−0.267704	+	0.963501i	$0.586265\pi$
$660$		0			0
$661$		−	1206.26i		−	1.82489i	−0.409195	−	0.912447i	$-0.634190\pi$
$661$		−	1206.26i		−	1.82489i	0.409195	−	0.912447i	$-0.365810\pi$
$662$	−570.750	−	1099.87i	−0.862161	−	1.66144i
$663$		0			0
$664$	8.33308	−	61.4521i	0.0125498	−	0.0925484i
$665$		−	132.120i		−	0.198677i
$666$		0			0
$667$			32.8882i			0.0493076i
$668$	−762.474	−	536.835i	−1.14143	−	0.803645i
$669$		0			0
$670$	−68.6998	−	132.389i	−0.102537	−	0.197595i
$671$		−	1134.39i		−	1.69059i
$672$		0			0
$673$	−956.133			−1.42070			−0.710351	−	0.703847i	$-0.751464\pi$
$673$	−956.133			−1.42070			−0.710351	+	0.703847i	$0.751464\pi$
$674$	303.127	−	157.300i	0.449744	−	0.233383i
$675$		0			0
$676$	−685.664	+	973.857i	−1.01430	+	1.44062i
$677$	−420.557			−0.621207			−0.310604	−	0.950540i	$-0.600531\pi$
$677$	−420.557			−0.621207			−0.310604	+	0.950540i	$0.600531\pi$
$678$		0			0
$679$	34.9335			0.0514485
$680$	161.761	+	21.9352i	0.237884	+	0.0322577i
$681$		0			0
$682$	−163.522	+	84.8556i	−0.239769	+	0.124422i
$683$	−539.725			−0.790227			−0.395113	−	0.918632i	$-0.629295\pi$
$683$	−539.725			−0.790227			−0.395113	+	0.918632i	$0.629295\pi$
$684$		0			0
$685$			11.7567i			0.0171631i
$686$	588.858	−	305.572i	0.858393	−	0.445441i
$687$		0			0
$688$	−788.266	+	282.295i	−1.14574	+	0.410312i
$689$		−	776.214i		−	1.12658i
$690$		0			0
$691$			432.090i			0.625312i	0.949866	+	0.312656i	$0.101219\pi$
$691$			432.090i			0.625312i	−0.949866	+	0.312656i	$0.898781\pi$
$692$	−745.659	+	1059.07i	−1.07754	+	1.53045i
$693$		0			0
$694$	533.250	−	276.716i	0.768371	−	0.398726i
$695$			1.28926i			0.00185504i
$696$		0			0
$697$	521.378			0.748031
$698$	−49.3118	−	95.0271i	−0.0706473	−	0.136142i
$699$		0			0
$700$	−395.950	+	562.372i	−0.565642	+	0.803389i
$701$	880.339			1.25583			0.627917	−	0.778280i	$-0.283908\pi$
$701$	880.339			1.25583			0.627917	+	0.778280i	$0.283908\pi$
$702$		0			0
$703$	290.489			0.413214
$704$	−1008.72	−	278.694i	−1.43284	−	0.395872i
$705$		0			0
$706$	−553.158	−	1065.97i	−0.783510	−	1.50987i
$707$	761.745			1.07743
$708$		0			0
$709$		−	799.367i		−	1.12746i	−0.825960	−	0.563729i	$-0.809366\pi$
$709$		−	799.367i		−	1.12746i	0.825960	−	0.563729i	$-0.190634\pi$
$710$	97.5188	+	187.925i	0.137350	+	0.264683i
$711$		0			0
$712$	603.655	+	81.8573i	0.847830	+	0.114968i
$713$		−	6.28491i		−	0.00881474i
$714$		0			0
$715$			379.760i			0.531133i
$716$	428.142	−	608.095i	0.597963	−	0.849295i
$717$		0			0
$718$	−136.806	−	263.633i	−0.190537	−	0.367178i
$719$		−	258.786i		−	0.359924i	−0.983674	−	0.179962i	$-0.942402\pi$
$719$		−	258.786i		−	0.359924i	0.983674	−	0.179962i	$-0.0575975\pi$
$720$		0			0
$721$	755.643			1.04805
$722$	−125.171	+	64.9544i	−0.173368	+	0.0899646i
$723$		0			0
$724$	412.972	+	290.762i	0.570404	+	0.401604i
$725$	702.896			0.969511
$726$		0			0
$727$	−663.211			−0.912257			−0.456129	−	0.889914i	$-0.650764\pi$
$727$	−663.211			−0.912257			−0.456129	+	0.889914i	$0.650764\pi$
$728$	−1235.04	−	167.474i	−1.69648	−	0.230047i
$729$		0			0
$730$	−71.9226	+	37.3224i	−0.0985241	+	0.0511265i
$731$	−993.332			−1.35887
$732$		0			0
$733$			908.826i			1.23987i	0.784653	+	0.619936i	$0.212841\pi$
$733$			908.826i			1.23987i	−0.784653	+	0.619936i	$0.787159\pi$
$734$	−561.658	+	291.458i	−0.765201	+	0.397081i
$735$		0			0
$736$	24.2893	−	26.1653i	0.0330017	−	0.0355507i
$737$			1134.39i			1.53920i
$738$		0			0
$739$			1112.39i			1.50526i	0.658443	+	0.752631i	$0.271215\pi$
$739$			1112.39i			1.50526i	−0.658443	+	0.752631i	$0.728785\pi$
$740$	59.9242	+	42.1909i	0.0809787	+	0.0570147i
$741$		0			0
$742$	459.928	−	238.667i	0.619849	−	0.321654i
$743$			541.298i			0.728530i	0.931295	+	0.364265i	$0.118680\pi$
$743$			541.298i			0.728530i	−0.931295	+	0.364265i	$0.881320\pi$
$744$		0			0
$745$	32.1767			0.0431902
$746$	577.379	+	1112.65i	0.773967	+	1.49148i
$747$		0			0
$748$	−1015.17	−	714.748i	−1.35717	−	0.955546i
$749$	471.655			0.629713
$750$		0			0
$751$	−763.699			−1.01691			−0.508455	−	0.861089i	$-0.669783\pi$
$751$	−763.699			−1.01691			−0.508455	+	0.861089i	$0.669783\pi$
$752$	972.107	−	348.132i	1.29270	−	0.462942i
$753$		0			0
$754$	586.683	+	1130.58i	0.778094	+	1.49944i
$755$	66.1354			0.0875966
$756$		0			0
$757$			419.134i			0.553678i	0.960916	+	0.276839i	$0.0892869\pi$
$757$			419.134i			0.553678i	−0.960916	+	0.276839i	$0.910713\pi$
$758$	304.943	+	587.644i	0.402299	+	0.775257i
$759$		0			0
$760$	145.245	+	19.6956i	0.191111	+	0.0259152i
$761$		−	1330.24i		−	1.74802i	−0.485912	−	0.874008i	$-0.661512\pi$
$761$		−	1330.24i		−	1.74802i	0.485912	−	0.874008i	$-0.338488\pi$
$762$		0			0
$763$		−	24.2397i		−	0.0317690i
$764$	762.474	+	536.835i	0.998002	+	0.702664i
$765$		0			0
$766$	−375.633	−	723.870i	−0.490383	−	0.945000i
$767$		−	1227.29i		−	1.60011i
$768$		0			0
$769$	671.511			0.873226			0.436613	−	0.899649i	$-0.356178\pi$
$769$	671.511			0.873226			0.436613	+	0.899649i	$0.356178\pi$
$770$	−225.018	+	116.767i	−0.292231	+	0.151646i
$771$		0			0
$772$	−270.294	+	383.902i	−0.350122	+	0.497283i
$773$	1421.13			1.83846			0.919229	−	0.393724i	$-0.128813\pi$
$773$	1421.13			1.83846			0.919229	+	0.393724i	$0.128813\pi$
$774$		0			0
$775$	−134.323			−0.173320
$776$	−5.20766	+	38.4038i	−0.00671090	+	0.0494894i
$777$		0			0
$778$	95.1194	−	49.3597i	0.122261	−	0.0634444i
$779$	468.143			0.600954
$780$		0			0
$781$		−	1610.25i		−	2.06179i
$782$	37.5946	−	19.5087i	0.0480749	−	0.0249472i
$783$		0			0
$784$	−16.1833	−	45.1896i	−0.0206420	−	0.0576398i
$785$			147.863i			0.188361i
$786$		0			0
$787$			649.808i			0.825677i	0.910804	+	0.412839i	$0.135463\pi$
$787$			649.808i			0.825677i	−0.910804	+	0.412839i	$0.864537\pi$
$788$	−682.343	+	969.140i	−0.865917	+	1.22987i
$789$		0			0
$790$	242.972	−	126.084i	0.307560	−	0.159600i
$791$			607.122i			0.767538i
$792$		0			0
$793$	1498.80			1.89004
$794$	−266.912	−	514.357i	−0.336162	−	0.647805i
$795$		0			0
$796$	536.572	−	762.100i	0.674085	−	0.957412i
$797$	−422.946			−0.530672			−0.265336	−	0.964156i	$-0.585483\pi$
$797$	−422.946			−0.530672			−0.265336	+	0.964156i	$0.585483\pi$
$798$		0			0
$799$	1225.00			1.53317
$800$	−559.212	−	519.118i	−0.699015	−	0.648897i
$801$		0			0
$802$	−187.426	−	361.181i	−0.233698	−	0.450351i
$803$	616.276			0.767467
$804$		0			0
$805$		−	8.64847i		−	0.0107434i
$806$	−112.115	−	216.052i	−0.139100	−	0.268055i
$807$		0			0
$808$	−113.556	+	837.416i	−0.140539	+	1.03641i
$809$			1353.87i			1.67351i	0.547574	+	0.836757i	$0.315552\pi$
$809$			1353.87i			1.67351i	−0.547574	+	0.836757i	$0.684448\pi$
$810$		0			0
$811$			842.340i			1.03864i	0.854579	+	0.519322i	$0.173815\pi$
$811$			842.340i			1.03864i	−0.854579	+	0.519322i	$0.826185\pi$
$812$	−489.505	+	695.251i	−0.602839	+	0.856220i
$813$		0			0
$814$	−256.733	−	494.742i	−0.315397	−	0.607791i
$815$		−	205.407i		−	0.252033i
$816$		0			0
$817$	−891.909			−1.09169
$818$	−732.888	+	380.313i	−0.895951	+	0.464930i
$819$		0			0
$820$	96.5719	+	67.9934i	0.117771	+	0.0829188i
$821$	616.897			0.751397			0.375698	−	0.926742i	$-0.377403\pi$
$821$	616.897			0.751397			0.375698	+	0.926742i	$0.377403\pi$
$822$		0			0
$823$	980.500			1.19137			0.595686	−	0.803217i	$-0.296880\pi$
$823$	980.500			1.19137			0.595686	+	0.803217i	$0.296880\pi$
$824$	−112.646	+	830.708i	−0.136707	+	1.00814i
$825$		0			0
$826$	727.199	−	377.361i	0.880387	−	0.456854i
$827$	70.4951			0.0852419			0.0426210	−	0.999091i	$-0.486429\pi$
$827$	70.4951			0.0852419			0.0426210	+	0.999091i	$0.486429\pi$
$828$		0			0
$829$			515.147i			0.621408i	0.950507	+	0.310704i	$0.100565\pi$
$829$			515.147i			0.621408i	−0.950507	+	0.310704i	$0.899435\pi$
$830$	14.7930	−	7.67644i	0.0178229	−	0.00924873i
$831$		0			0
$832$	368.222	−	1332.76i	0.442575	−	1.60187i
$833$		−	56.9456i		−	0.0683621i
$834$		0			0
$835$		−	250.606i		−	0.300127i
$836$	−911.514	−	641.770i	−1.09033	−	0.767667i
$837$		0			0
$838$	−597.327	+	309.967i	−0.712801	+	0.369889i
$839$		−	47.1556i		−	0.0562045i	−0.999605	−	0.0281022i	$-0.991054\pi$
$839$		−	47.1556i		−	0.0562045i	0.999605	−	0.0281022i	$-0.00894640\pi$
$840$		0			0
$841$	27.9773			0.0332667
$842$	−200.344	−	386.076i	−0.237938	−	0.458522i
$843$		0			0
$844$	115.411	+	81.2576i	0.136743	+	0.0962768i
$845$	−320.082			−0.378795
$846$		0			0
$847$	1055.54			1.24622
$848$	193.813	+	541.195i	0.228554	+	0.638202i
$849$		0			0
$850$	−416.946	−	803.482i	−0.490525	−	0.945273i
$851$	19.0152			0.0223445
$852$		0			0
$853$			763.118i			0.894628i	0.894377	+	0.447314i	$0.147619\pi$
$853$			763.118i			0.894628i	−0.894377	+	0.447314i	$0.852381\pi$
$854$	460.845	+	888.079i	0.539631	+	1.03990i
$855$		0			0
$856$	−70.3112	+	518.508i	−0.0821392	+	0.605734i
$857$		−	1641.05i		−	1.91488i	−0.288631	−	0.957440i	$-0.593200\pi$
$857$		−	1641.05i		−	1.91488i	0.288631	−	0.957440i	$-0.406800\pi$
$858$		0			0
$859$		−	1366.84i		−	1.59120i	−0.605819	−	0.795602i	$-0.707155\pi$
$859$		−	1366.84i		−	1.59120i	0.605819	−	0.795602i	$-0.292845\pi$
$860$	−183.989	−	129.542i	−0.213941	−	0.150630i
$861$		0			0
$862$	691.817	+	1333.18i	0.802572	+	1.54661i
$863$		−	836.082i		−	0.968809i	−0.874844	−	0.484405i	$-0.839036\pi$
$863$		−	836.082i		−	0.968809i	0.874844	−	0.484405i	$-0.160964\pi$
$864$		0			0
$865$	−348.089			−0.402415
$866$	312.674	−	162.254i	0.361055	−	0.187360i
$867$		0			0
$868$	93.5442	−	132.862i	0.107770	−	0.153067i
$869$	−2081.93			−2.39578
$870$		0			0
$871$	−1498.80			−1.72078
$872$	26.6477	+	3.61350i	0.0305592	+	0.00414392i
$873$		0			0
$874$	33.7561	−	17.5168i	0.0386225	−	0.0200421i
$875$	−378.633			−0.432723
$876$		0			0
$877$			158.191i			0.180377i	0.995925	+	0.0901887i	$0.0287470\pi$
$877$			158.191i			0.180377i	−0.995925	+	0.0901887i	$0.971253\pi$
$878$	−741.664	+	384.867i	−0.844719	+	0.438345i
$879$		0			0
$880$	−94.8225	−	264.778i	−0.107753	−	0.300884i
$881$			237.430i			0.269500i	0.990880	+	0.134750i	$0.0430232\pi$
$881$			237.430i			0.269500i	−0.990880	+	0.134750i	$0.956977\pi$
$882$		0			0
$883$		−	592.933i		−	0.671499i	−0.941951	−	0.335749i	$-0.891011\pi$
$883$		−	592.933i		−	0.671499i	0.941951	−	0.335749i	$-0.108989\pi$
$884$	944.355	−	1341.28i	1.06827	−	1.51728i
$885$		0			0
$886$	108.372	−	56.2367i	0.122316	−	0.0634726i
$887$			1420.72i			1.60171i	0.598858	+	0.800855i	$0.295621\pi$
$887$			1420.72i			1.60171i	−0.598858	+	0.800855i	$0.704379\pi$
$888$		0			0
$889$	−328.266			−0.369253
$890$	75.4071	+	145.314i	0.0847271	+	0.163275i
$891$		0			0
$892$	−119.361	+	169.530i	−0.133813	+	0.190056i
$893$	1099.92			1.23172
$894$		0			0
$895$	199.866			0.223313
$896$	902.914	−	191.610i	1.00772	−	0.213850i
$897$		0			0
$898$	168.492	+	324.695i	0.187630	+	0.361576i
$899$	−166.061			−0.184717
$900$		0			0
$901$			681.987i			0.756922i
$902$	−413.743	−	797.310i	−0.458695	−	0.883935i
$903$		0			0
$904$	−667.433	−	90.5058i	−0.738311	−	0.100117i
$905$			135.734i			0.149982i
$906$		0			0
$907$		−	816.648i		−	0.900383i	−0.892932	−	0.450192i	$-0.851356\pi$
$907$		−	816.648i		−	0.900383i	0.892932	−	0.450192i	$-0.148644\pi$
$908$	770.936	−	1094.97i	0.849048	−	1.20591i
$909$		0			0
$910$	−154.278	−	297.303i	−0.169536	−	0.326706i
$911$			469.895i			0.515801i	0.966171	+	0.257901i	$0.0830307\pi$
$911$			469.895i			0.515801i	−0.966171	+	0.257901i	$0.916969\pi$
$912$		0			0
$913$	−126.755			−0.138834
$914$	787.485	−	408.645i	0.861581	−	0.447095i
$915$		0			0
$916$	717.605	+	505.244i	0.783411	+	0.551577i
$917$	−931.079			−1.01535
$918$		0			0
$919$	−1648.21			−1.79348			−0.896741	−	0.442555i	$-0.854072\pi$
$919$	−1648.21			−1.79348			−0.896741	+	0.442555i	$0.854072\pi$
$920$	9.50760	+	1.28926i	0.0103343	+	0.00140137i
$921$		0			0
$922$	−1292.78	+	670.857i	−1.40215	+	0.727611i
$923$	2127.53			2.30502
$924$		0			0
$925$		−	406.398i		−	0.439349i
$926$	191.230	−	99.2341i	0.206512	−	0.107164i
$927$		0			0
$928$	−691.344	−	641.776i	−0.744983	−	0.691569i
$929$			421.311i			0.453510i	0.973952	+	0.226755i	$0.0728116\pi$
$929$			421.311i			0.453510i	−0.973952	+	0.226755i	$0.927188\pi$
$930$		0			0
$931$		−	51.1313i		−	0.0549208i
$932$	666.779	+	469.459i	0.715428	+	0.503712i
$933$		0			0
$934$	−1456.12	+	755.614i	−1.55901	+	0.809008i
$935$		−	333.659i		−	0.356855i
$936$		0			0
$937$	−1434.27			−1.53070			−0.765350	−	0.643614i	$-0.777434\pi$
$937$	−1434.27			−1.53070			−0.765350	+	0.643614i	$0.777434\pi$
$938$	−460.845	−	888.079i	−0.491306	−	0.946779i
$939$		0			0
$940$	226.900	+	159.754i	0.241383	+	0.169951i
$941$	−732.876			−0.778827			−0.389413	−	0.921063i	$-0.627322\pi$
$941$	−732.876			−0.778827			−0.389413	+	0.921063i	$0.627322\pi$
$942$		0			0
$943$	30.6443			0.0324966
$944$	306.442	+	855.693i	0.324621	+	0.906455i
$945$		0			0
$946$	788.266	+	1519.04i	0.833262	+	1.60575i
$947$	−1385.53			−1.46308			−0.731538	−	0.681800i	$-0.761197\pi$
$947$	−1385.53			−1.46308			−0.731538	+	0.681800i	$0.761197\pi$
$948$		0			0
$949$			814.249i			0.858007i
$950$	−374.375	−	721.444i	−0.394079	−	0.759415i
$951$		0			0
$952$	1085.11	+	147.144i	1.13982	+	0.154563i
$953$		−	957.328i		−	1.00454i	−0.864711	−	0.502270i	$-0.832498\pi$
$953$		−	957.328i		−	1.00454i	0.864711	−	0.502270i	$-0.167502\pi$
$954$		0			0
$955$			250.606i			0.262414i
$956$	176.692	+	124.403i	0.184824	+	0.130129i
$957$		0			0
$958$	111.272	+	214.428i	0.116150	+	0.223829i
$959$			78.8654i			0.0822371i
$960$		0			0
$961$	−929.266			−0.966978
$962$	653.673	−	339.207i	0.679494	−	0.352606i
$963$		0			0
$964$	754.389	−	1071.47i	0.782561	−	1.11148i
$965$	−126.179			−0.130755
$966$		0			0
$967$	1225.90			1.26773			0.633867	−	0.773442i	$-0.281467\pi$
$967$	1225.90			1.26773			0.633867	+	0.773442i	$0.281467\pi$
$968$	−157.354	+	1160.40i	−0.162555	+	1.19876i
$969$		0			0
$970$	−9.24472	+	4.79731i	−0.00953064	+	0.00494568i
$971$	−752.906			−0.775393			−0.387696	−	0.921787i	$-0.626729\pi$
$971$	−752.906			−0.775393			−0.387696	+	0.921787i	$0.626729\pi$
$972$		0			0
$973$			8.64847i			0.00888845i
$974$	227.642	−	118.129i	0.233719	−	0.121282i
$975$		0			0
$976$	−1045.00	+	374.236i	−1.07070	+	0.383439i
$977$		−	642.932i		−	0.658068i	−0.944318	−	0.329034i	$-0.893277\pi$
$977$		−	642.932i		−	0.658068i	0.944318	−	0.329034i	$-0.106723\pi$
$978$		0			0
$979$		−	1245.14i		−	1.27185i
$980$	7.42634	−	10.5477i	0.00757790	−	0.0107630i
$981$		0			0
$982$	−678.389	+	352.032i	−0.690823	+	0.358485i
$983$			161.251i			0.164040i	0.996631	+	0.0820200i	$0.0261371\pi$
$983$			161.251i			0.164040i	−0.996631	+	0.0820200i	$0.973863\pi$
$984$		0			0
$985$	−318.532			−0.323382
$986$	−515.463	−	993.331i	−0.522782	−	1.00744i
$987$		0			0
$988$	847.933	−	1204.33i	0.858232	−	1.21896i
$989$	−58.3836			−0.0590330
$990$		0			0
$991$	811.500			0.818870			0.409435	−	0.912339i	$-0.365726\pi$
$991$	811.500			0.818870			0.409435	+	0.912339i	$0.365726\pi$
$992$	132.115	+	122.643i	0.133181	+	0.123632i
$993$		0			0
$994$	654.167	+	1260.62i	0.658115	+	1.26823i
$995$	250.483			0.251742
$996$		0			0
$997$		−	390.554i		−	0.391729i	−0.980631	−	0.195864i	$-0.937249\pi$
$997$		−	390.554i		−	0.391729i	0.980631	−	0.195864i	$-0.0627513\pi$
$998$	511.262	+	985.235i	0.512286	+	0.987209i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.3.h.a.53.2	yes	8
3.2	odd	2	inner	72.3.h.a.53.7	yes	8
4.3	odd	2		288.3.h.a.17.6		8
8.3	odd	2		288.3.h.a.17.3		8
8.5	even	2	inner	72.3.h.a.53.8	yes	8
12.11	even	2		288.3.h.a.17.4		8
16.3	odd	4		2304.3.e.o.1025.3		8
16.5	even	4		2304.3.e.n.1025.6		8
16.11	odd	4		2304.3.e.o.1025.6		8
16.13	even	4		2304.3.e.n.1025.3		8
24.5	odd	2	inner	72.3.h.a.53.1	✓	8
24.11	even	2		288.3.h.a.17.5		8
48.5	odd	4		2304.3.e.n.1025.4		8
48.11	even	4		2304.3.e.o.1025.4		8
48.29	odd	4		2304.3.e.n.1025.5		8
48.35	even	4		2304.3.e.o.1025.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.h.a.53.1	✓	8	24.5	odd	2	inner
72.3.h.a.53.2	yes	8	1.1	even	1	trivial
72.3.h.a.53.7	yes	8	3.2	odd	2	inner
72.3.h.a.53.8	yes	8	8.5	even	2	inner
288.3.h.a.17.3		8	8.3	odd	2
288.3.h.a.17.4		8	12.11	even	2
288.3.h.a.17.5		8	24.11	even	2
288.3.h.a.17.6		8	4.3	odd	2
2304.3.e.n.1025.3		8	16.13	even	4
2304.3.e.n.1025.4		8	48.5	odd	4
2304.3.e.n.1025.5		8	48.29	odd	4
2304.3.e.n.1025.6		8	16.5	even	4
2304.3.e.o.1025.3		8	16.3	odd	4
2304.3.e.o.1025.4		8	48.11	even	4
2304.3.e.o.1025.5		8	48.35	even	4
2304.3.e.o.1025.6		8	16.11	odd	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)

\(f(q)\)	\(=\)	\(q+(-1.77521 + 0.921201i) q^{2} +(2.30278 - 3.27066i) q^{4} +1.07498 q^{5} +7.21110 q^{7} +(-1.07498 + 7.92745i) q^{8} +O(q^{10})\)	\(q+(-1.77521 + 0.921201i) q^{2} +(2.30278 - 3.27066i) q^{4} +1.07498 q^{5} +7.21110 q^{7} +(-1.07498 + 7.92745i) q^{8} +(-1.90833 + 0.990277i) q^{10} +16.3517 q^{11} +21.6045i q^{13} +(-12.8013 + 6.64288i) q^{14} +(-5.39445 - 15.0632i) q^{16} -18.9819i q^{17} -17.0438i q^{19} +(2.47545 - 3.51591i) q^{20} +(-29.0278 + 15.0632i) q^{22} -1.11567i q^{23} -23.8444 q^{25} +(-19.9021 - 38.3527i) q^{26} +(16.6056 - 23.5851i) q^{28} -29.4784 q^{29} +5.63331 q^{31} +(23.4525 + 21.7710i) q^{32} +(17.4861 + 33.6969i) q^{34} +7.75182 q^{35} +17.0438i q^{37} +(15.7007 + 30.2563i) q^{38} +(-1.15559 + 8.52188i) q^{40} +27.4671i q^{41} -52.3306i q^{43} +(37.6543 - 53.4808i) q^{44} +(1.02776 + 1.98055i) q^{46} +64.5352i q^{47} +3.00000 q^{49} +(42.3290 - 21.9655i) q^{50} +(70.6611 + 49.7504i) q^{52} -35.9283 q^{53} +17.5778 q^{55} +(-7.75182 + 57.1656i) q^{56} +(52.3305 - 27.1556i) q^{58} -56.8069 q^{59} -69.3743i q^{61} +(-10.0003 + 5.18941i) q^{62} +(-61.6888 - 17.0438i) q^{64} +23.2245i q^{65} +69.3743i q^{67} +(-62.0832 - 43.7110i) q^{68} +(-13.7611 + 7.14099i) q^{70} -98.4764i q^{71} +37.6888 q^{73} +(-15.7007 - 30.2563i) q^{74} +(-55.7443 - 39.2479i) q^{76} +117.914 q^{77} -127.322 q^{79} +(-5.79894 - 16.1927i) q^{80} +(-25.3028 - 48.7601i) q^{82} -7.75182 q^{83} -20.4052i q^{85} +(48.2070 + 92.8980i) q^{86} +(-17.5778 + 129.627i) q^{88} -76.1475i q^{89} +155.792i q^{91} +(-3.64898 - 2.56914i) q^{92} +(-59.4500 - 114.564i) q^{94} -18.3218i q^{95} +4.84441 q^{97} +(-5.32564 + 2.76360i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 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

L-functions

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