LMFDB - Embedded newform 216.3.u.a.41.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(41,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 17]))

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

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

chi := DirichletCharacter("216.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.u (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.2
Character	$\chi$	$=$	216.41
Dual form			216.3.u.a.137.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.88041 - 0.838587i) q^{3} +(-0.363134 + 0.432766i) q^{5} +(-2.59307 - 0.943802i) q^{7} +(7.59354 + 4.83095i) q^{9} +O(q^{10})$	\(q+(-2.88041 - 0.838587i) q^{3} +(-0.363134 + 0.432766i) q^{5} +(-2.59307 - 0.943802i) q^{7} +(7.59354 + 4.83095i) q^{9} +(0.352516 + 0.420113i) q^{11} +(-1.71148 + 9.70630i) q^{13} +(1.40889 - 0.942025i) q^{15} +(23.5920 + 13.6208i) q^{17} +(5.18471 + 8.98017i) q^{19} +(6.67766 + 4.89306i) q^{21} +(6.28156 + 17.2585i) q^{23} +(4.28578 + 24.3059i) q^{25} +(-17.8214 - 20.2830i) q^{27} +(24.7205 - 4.35888i) q^{29} +(0.905402 - 0.329539i) q^{31} +(-0.663092 - 1.50571i) q^{33} +(1.35008 - 0.779468i) q^{35} +(-15.5358 + 26.9088i) q^{37} +(13.0693 - 26.5229i) q^{39} +(22.2676 + 3.92638i) q^{41} +(-30.0006 + 25.1735i) q^{43} +(-4.84815 + 1.53195i) q^{45} +(9.26638 - 25.4592i) q^{47} +(-31.7029 - 26.6019i) q^{49} +(-56.5323 - 59.0175i) q^{51} -20.3830i q^{53} -0.309821 q^{55} +(-7.40343 - 30.2144i) q^{57} +(-12.1953 + 14.5337i) q^{59} +(-83.5899 - 30.4243i) q^{61} +(-15.1312 - 19.6938i) q^{63} +(-3.57906 - 4.26536i) q^{65} +(1.89686 - 10.7576i) q^{67} +(-3.62078 - 54.9791i) q^{69} +(58.8886 + 33.9994i) q^{71} +(38.8887 + 67.3572i) q^{73} +(8.03778 - 73.6050i) q^{75} +(-0.517598 - 1.42209i) q^{77} +(-0.663068 - 3.76045i) q^{79} +(34.3238 + 73.3681i) q^{81} +(-55.8775 + 9.85270i) q^{83} +(-14.4617 + 5.26362i) q^{85} +(-74.8604 - 8.17487i) q^{87} +(148.661 - 85.8295i) q^{89} +(13.5988 - 23.5538i) q^{91} +(-2.88428 + 0.189951i) q^{93} +(-5.76906 - 1.01724i) q^{95} +(-64.2009 + 53.8710i) q^{97} +(0.647305 + 4.89314i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q+O(q^{10}) $ 108 * q	$ 108 q - 18 q^{11} - 24 q^{15} + 48 q^{21} + 72 q^{23} + 174 q^{27} + 108 q^{29} + 18 q^{33} - 144 q^{39} + 90 q^{41} - 90 q^{43} + 108 q^{45} - 72 q^{49} + 84 q^{51} - 18 q^{57} - 252 q^{59} + 144 q^{61} - 360 q^{63} - 216 q^{65} + 126 q^{67} - 120 q^{69} - 252 q^{75} - 504 q^{77} - 552 q^{81} - 180 q^{83} - 60 q^{87} - 486 q^{89} - 360 q^{93} - 1116 q^{95} + 270 q^{97} - 564 q^{99}+O(q^{100}) $ 108 * q - 18 * q^11 - 24 * q^15 + 48 * q^21 + 72 * q^23 + 174 * q^27 + 108 * q^29 + 18 * q^33 - 144 * q^39 + 90 * q^41 - 90 * q^43 + 108 * q^45 - 72 * q^49 + 84 * q^51 - 18 * q^57 - 252 * q^59 + 144 * q^61 - 360 * q^63 - 216 * q^65 + 126 * q^67 - 120 * q^69 - 252 * q^75 - 504 * q^77 - 552 * q^81 - 180 * q^83 - 60 * q^87 - 486 * q^89 - 360 * q^93 - 1116 * q^95 + 270 * q^97 - 564 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{17}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−2.88041	−	0.838587i	−0.960137	−	0.279529i
$3$	−2.88041	−	0.838587i	−0.960137	−	0.279529i
$4$		0			0
$5$	−0.363134	+	0.432766i	−0.0726268	+	0.0865532i	−0.801134	−	0.598484i	$-0.795770\pi$
$5$	−0.363134	+	0.432766i	−0.0726268	+	0.0865532i	0.728508	+	0.685038i	$0.240214\pi$
$6$		0			0
$7$	−2.59307	−	0.943802i	−0.370439	−	0.134829i	0.150091	−	0.988672i	$-0.452043\pi$
$7$	−2.59307	−	0.943802i	−0.370439	−	0.134829i	−0.520530	+	0.853843i	$0.674266\pi$
$8$		0			0
$9$	7.59354	+	4.83095i	0.843727	+	0.536772i
$10$		0			0
$11$	0.352516	+	0.420113i	0.0320470	+	0.0381921i	0.781830	−	0.623492i	$-0.214287\pi$
$11$	0.352516	+	0.420113i	0.0320470	+	0.0381921i	−0.749783	+	0.661684i	$0.769842\pi$
$12$		0			0
$13$	−1.71148	+	9.70630i	−0.131652	+	0.746638i	0.845480	+	0.534007i	$0.179314\pi$
$13$	−1.71148	+	9.70630i	−0.131652	+	0.746638i	−0.977133	+	0.212631i	$0.931797\pi$
$14$		0			0
$15$	1.40889	−	0.942025i	0.0939258	−	0.0628017i
$16$		0			0
$17$	23.5920	+	13.6208i	1.38776	+	0.801225i	0.993063	−	0.117584i	$-0.0375151\pi$
$17$	23.5920	+	13.6208i	1.38776	+	0.801225i	0.394700	+	0.918810i	$0.370848\pi$
$18$		0			0
$19$	5.18471	+	8.98017i	0.272879	+	0.472641i	0.969598	−	0.244704i	$-0.0786907\pi$
$19$	5.18471	+	8.98017i	0.272879	+	0.472641i	−0.696719	+	0.717345i	$0.745357\pi$
$20$		0			0
$21$	6.67766	+	4.89306i	0.317984	+	0.233003i
$22$		0			0
$23$	6.28156	+	17.2585i	0.273111	+	0.750368i	0.998100	+	0.0616072i	$0.0196226\pi$
$23$	6.28156	+	17.2585i	0.273111	+	0.750368i	−0.724989	+	0.688760i	$0.758155\pi$
$24$		0			0
$25$	4.28578	+	24.3059i	0.171431	+	0.972236i
$26$		0			0
$27$	−17.8214	−	20.2830i	−0.660050	−	0.751221i
$28$		0			0
$29$	24.7205	−	4.35888i	0.852430	−	0.150306i	0.269672	−	0.962952i	$-0.413085\pi$
$29$	24.7205	−	4.35888i	0.852430	−	0.150306i	0.582758	+	0.812646i	$0.301974\pi$
$30$		0			0
$31$	0.905402	−	0.329539i	0.0292065	−	0.0106303i	−0.327376	−	0.944894i	$-0.606164\pi$
$31$	0.905402	−	0.329539i	0.0292065	−	0.0106303i	0.356582	+	0.934264i	$0.383942\pi$
$32$		0			0
$33$	−0.663092	−	1.50571i	−0.0200937	−	0.0456277i
$34$		0			0
$35$	1.35008	−	0.779468i	0.0385737	−	0.0222705i
$36$		0			0
$37$	−15.5358	+	26.9088i	−0.419886	+	0.727264i	−0.995928	−	0.0901567i	$-0.971263\pi$
$37$	−15.5358	+	26.9088i	−0.419886	+	0.727264i	0.576042	+	0.817420i	$0.304597\pi$
$38$		0			0
$39$	13.0693	−	26.5229i	0.335111	−	0.680075i
$40$		0			0
$41$	22.2676	+	3.92638i	0.543113	+	0.0957654i	0.438472	−	0.898745i	$-0.355520\pi$
$41$	22.2676	+	3.92638i	0.543113	+	0.0957654i	0.104640	+	0.994510i	$0.466631\pi$
$42$		0			0
$43$	−30.0006	+	25.1735i	−0.697689	+	0.585431i	−0.921115	−	0.389290i	$-0.872720\pi$
$43$	−30.0006	+	25.1735i	−0.697689	+	0.585431i	0.223426	+	0.974721i	$0.428276\pi$
$44$		0			0
$45$	−4.84815	+	1.53195i	−0.107737	+	0.0340433i
$46$		0			0
$47$	9.26638	−	25.4592i	0.197157	−	0.541684i	−0.801236	−	0.598348i	$-0.795824\pi$
$47$	9.26638	−	25.4592i	0.197157	−	0.541684i	0.998393	+	0.0566637i	$0.0180463\pi$
$48$		0			0
$49$	−31.7029	−	26.6019i	−0.646998	−	0.542896i
$50$		0			0
$51$	−56.5323	−	59.0175i	−1.10848	−	1.15721i
$52$		0			0
$53$		−	20.3830i		−	0.384586i	−0.981338	−	0.192293i	$-0.938408\pi$
$53$		−	20.3830i		−	0.384586i	0.981338	−	0.192293i	$-0.0615924\pi$
$54$		0			0
$55$	−0.309821			−0.00563311
$56$		0			0
$57$	−7.40343	−	30.2144i	−0.129885	−	0.530078i
$58$		0			0
$59$	−12.1953	+	14.5337i	−0.206699	+	0.246334i	−0.859428	−	0.511258i	$-0.829180\pi$
$59$	−12.1953	+	14.5337i	−0.206699	+	0.246334i	0.652728	+	0.757592i	$0.273624\pi$
$60$		0			0
$61$	−83.5899	−	30.4243i	−1.37033	−	0.498758i	−0.451095	−	0.892476i	$-0.648967\pi$
$61$	−83.5899	−	30.4243i	−1.37033	−	0.498758i	−0.919231	+	0.393718i	$0.871189\pi$
$62$		0			0
$63$	−15.1312	−	19.6938i	−0.240177	−	0.312600i
$64$		0			0
$65$	−3.57906	−	4.26536i	−0.0550625	−	0.0656209i
$66$		0			0
$67$	1.89686	−	10.7576i	0.0283114	−	0.160562i	−0.967374	−	0.253351i	$-0.918467\pi$
$67$	1.89686	−	10.7576i	0.0283114	−	0.160562i	0.995686	+	0.0927894i	$0.0295783\pi$
$68$		0			0
$69$	−3.62078	−	54.9791i	−0.0524750	−	0.796799i
$70$		0			0
$71$	58.8886	+	33.9994i	0.829417	+	0.478864i	0.853653	−	0.520842i	$-0.174382\pi$
$71$	58.8886	+	33.9994i	0.829417	+	0.478864i	−0.0242359	+	0.999706i	$0.507715\pi$
$72$		0			0
$73$	38.8887	+	67.3572i	0.532722	+	0.922701i	0.999270	+	0.0382052i	$0.0121640\pi$
$73$	38.8887	+	67.3572i	0.532722	+	0.922701i	−0.466548	+	0.884496i	$0.654503\pi$
$74$		0			0
$75$	8.03778	−	73.6050i	0.107170	−	0.981400i
$76$		0			0
$77$	−0.517598	−	1.42209i	−0.00672205	−	0.0184687i
$78$		0			0
$79$	−0.663068	−	3.76045i	−0.00839327	−	0.0476006i	0.980323	−	0.197398i	$-0.0632490\pi$
$79$	−0.663068	−	3.76045i	−0.00839327	−	0.0476006i	−0.988717	+	0.149797i	$0.952138\pi$
$80$		0			0
$81$	34.3238	+	73.3681i	0.423751	+	0.905779i
$82$		0			0
$83$	−55.8775	+	9.85270i	−0.673222	+	0.118707i	−0.499801	−	0.866140i	$-0.666593\pi$
$83$	−55.8775	+	9.85270i	−0.673222	+	0.118707i	−0.173422	+	0.984848i	$0.555482\pi$
$84$		0			0
$85$	−14.4617	+	5.26362i	−0.170137	+	0.0619250i
$86$		0			0
$87$	−74.8604	−	8.17487i	−0.860465	−	0.0939640i
$88$		0			0
$89$	148.661	−	85.8295i	1.67035	−	0.964376i	0.702908	−	0.711281i	$-0.251885\pi$
$89$	148.661	−	85.8295i	1.67035	−	0.964376i	0.967441	−	0.253095i	$-0.0814486\pi$
$90$		0			0
$91$	13.5988	−	23.5538i	0.149438	−	0.258834i
$92$		0			0
$93$	−2.88428	+	0.189951i	−0.0310137	+	0.00204248i
$94$		0			0
$95$	−5.76906	−	1.01724i	−0.0607269	−	0.0107078i
$96$		0			0
$97$	−64.2009	+	53.8710i	−0.661865	+	0.555371i	−0.910645	−	0.413189i	$-0.864415\pi$
$97$	−64.2009	+	53.8710i	−0.661865	+	0.555371i	0.248780	+	0.968560i	$0.419970\pi$
$98$		0			0
$99$	0.647305	+	4.89314i	0.00653844	+	0.0494256i
$100$		0			0
$101$	35.0633	−	96.3357i	0.347162	−	0.953819i	−0.636098	−	0.771608i	$-0.719453\pi$
$101$	35.0633	−	96.3357i	0.347162	−	0.953819i	0.983260	−	0.182210i	$-0.0583252\pi$
$102$		0			0
$103$	34.1499	+	28.6552i	0.331553	+	0.278206i	0.793332	−	0.608789i	$-0.208344\pi$
$103$	34.1499	+	28.6552i	0.331553	+	0.278206i	−0.461779	+	0.886995i	$0.652789\pi$
$104$		0			0
$105$	−4.54243	+	1.11303i	−0.0432613	+	0.0106003i
$106$		0			0
$107$			121.887i			1.13913i	0.821945	+	0.569567i	$0.192889\pi$
$107$			121.887i			1.13913i	−0.821945	+	0.569567i	$0.807111\pi$
$108$		0			0
$109$	−105.140			−0.964590			−0.482295	−	0.876009i	$-0.660197\pi$
$109$	−105.140			−0.964590			−0.482295	+	0.876009i	$0.660197\pi$
$110$		0			0
$111$	67.3148	−	64.4802i	0.606439	−	0.580903i
$112$		0			0
$113$	−62.7812	+	74.8197i	−0.555586	+	0.662122i	−0.968606	−	0.248600i	$-0.920029\pi$
$113$	−62.7812	+	74.8197i	−0.555586	+	0.662122i	0.413020	+	0.910722i	$0.364474\pi$
$114$		0			0
$115$	−9.74992	−	3.54868i	−0.0847820	−	0.0308581i
$116$		0			0
$117$	−59.8869	+	65.4371i	−0.511853	+	0.559292i
$118$		0			0
$119$	−48.3204	−	57.5860i	−0.406054	−	0.483916i
$120$		0			0
$121$	20.9592	−	118.866i	0.173217	−	0.982360i
$122$		0			0
$123$	−60.8473	−	29.9829i	−0.494693	−	0.243764i
$124$		0			0
$125$	−24.3063	−	14.0333i	−0.194450	−	0.112266i
$126$		0			0
$127$	102.296	+	177.182i	0.805480	+	1.39513i	0.915966	+	0.401255i	$0.131426\pi$
$127$	102.296	+	177.182i	0.805480	+	1.39513i	−0.110486	+	0.993878i	$0.535241\pi$
$128$		0			0
$129$	107.524	−	47.3520i	0.833522	−	0.367070i
$130$		0			0
$131$	56.6200	+	155.562i	0.432214	+	1.18750i	0.944451	+	0.328653i	$0.106595\pi$
$131$	56.6200	+	155.562i	0.432214	+	1.18750i	−0.512237	+	0.858844i	$0.671183\pi$
$132$		0			0
$133$	−4.96882	−	28.1796i	−0.0373596	−	0.211877i
$134$		0			0
$135$	15.2493	−	0.347047i	0.112958	−	0.00257072i
$136$		0			0
$137$	64.2272	−	11.3250i	0.468812	−	0.0826641i	0.0657483	−	0.997836i	$-0.479057\pi$
$137$	64.2272	−	11.3250i	0.468812	−	0.0826641i	0.403063	+	0.915172i	$0.367945\pi$
$138$		0			0
$139$	223.020	−	81.1725i	1.60446	−	0.583975i	0.624124	−	0.781325i	$-0.285456\pi$
$139$	223.020	−	81.1725i	1.60446	−	0.583975i	0.980333	+	0.197351i	$0.0632337\pi$
$140$		0			0
$141$	−48.0407	+	65.5622i	−0.340714	+	0.464980i
$142$		0			0
$143$	−4.68107	+	2.70261i	−0.0327347	+	0.0188994i
$144$		0			0
$145$	−7.09046	+	12.2810i	−0.0488997	+	0.0846968i
$146$		0			0
$147$	69.0094	+	103.210i	0.469452	+	0.702109i
$148$		0			0
$149$	−162.337	−	28.6243i	−1.08951	−	0.192110i	−0.400092	−	0.916475i	$-0.631022\pi$
$149$	−162.337	−	28.6243i	−1.08951	−	0.192110i	−0.689416	+	0.724365i	$0.742133\pi$
$150$		0			0
$151$	−98.7562	+	82.8663i	−0.654014	+	0.548783i	−0.908286	−	0.418350i	$-0.862609\pi$
$151$	−98.7562	+	82.8663i	−0.654014	+	0.548783i	0.254272	+	0.967133i	$0.418164\pi$
$152$		0			0
$153$	113.345	+	217.402i	0.740818	+	1.42093i
$154$		0			0
$155$	−0.186169	+	0.511494i	−0.00120109	+	0.00329996i
$156$		0			0
$157$	−176.214	−	147.861i	−1.12238	−	0.941793i	−0.123662	−	0.992324i	$-0.539464\pi$
$157$	−176.214	−	147.861i	−1.12238	−	0.941793i	−0.998722	+	0.0505318i	$0.983908\pi$
$158$		0			0
$159$	−17.0930	+	58.7116i	−0.107503	+	0.369255i
$160$		0			0
$161$		−	50.6810i		−	0.314789i
$162$		0			0
$163$	258.169			1.58386			0.791929	−	0.610614i	$-0.209077\pi$
$163$	258.169			1.58386			0.791929	+	0.610614i	$0.209077\pi$
$164$		0			0
$165$	0.892413	+	0.259812i	0.00540856	+	0.00157462i
$166$		0			0
$167$	−78.2293	+	93.2300i	−0.468439	+	0.558263i	−0.947598	−	0.319464i	$-0.896497\pi$
$167$	−78.2293	+	93.2300i	−0.468439	+	0.558263i	0.479160	+	0.877728i	$0.340941\pi$
$168$		0			0
$169$	67.5250	+	24.5771i	0.399556	+	0.145427i
$170$		0			0
$171$	−4.01249	+	93.2384i	−0.0234648	+	0.545254i
$172$		0			0
$173$	−121.074	−	144.290i	−0.699849	−	0.834047i	0.292661	−	0.956216i	$-0.405459\pi$
$173$	−121.074	−	144.290i	−0.699849	−	0.834047i	−0.992509	+	0.122169i	$0.961015\pi$
$174$		0			0
$175$	11.8266	−	67.0719i	0.0675805	−	0.383268i
$176$		0			0
$177$	47.3151	−	31.6364i	0.267317	−	0.178737i
$178$		0			0
$179$	184.718	+	106.647i	1.03194	+	0.595794i	0.917541	−	0.397641i	$-0.130171\pi$
$179$	184.718	+	106.647i	1.03194	+	0.595794i	0.114404	+	0.993434i	$0.463504\pi$
$180$		0			0
$181$	98.1710	+	170.037i	0.542381	+	0.939432i	0.998767	+	0.0496498i	$0.0158105\pi$
$181$	98.1710	+	170.037i	0.542381	+	0.939432i	−0.456385	+	0.889782i	$0.650856\pi$
$182$		0			0
$183$	215.260	+	157.732i	1.17628	+	0.861922i
$184$		0			0
$185$	−6.00363	−	16.4948i	−0.0324521	−	0.0891613i
$186$		0			0
$187$	2.59427	+	14.7129i	0.0138731	+	0.0786784i
$188$		0			0
$189$	27.0690	+	69.4151i	0.143222	+	0.367276i
$190$		0			0
$191$	−239.536	+	42.2367i	−1.25412	+	0.221135i	−0.760956	−	0.648803i	$-0.775270\pi$
$191$	−239.536	+	42.2367i	−1.25412	+	0.221135i	−0.493161	+	0.869938i	$0.664159\pi$
$192$		0			0
$193$	67.6781	−	24.6328i	0.350664	−	0.127631i	−0.160682	−	0.987006i	$-0.551369\pi$
$193$	67.6781	−	24.6328i	0.350664	−	0.127631i	0.511346	+	0.859375i	$0.329147\pi$
$194$		0			0
$195$	6.73229	+	15.2873i	0.0345246	+	0.0783966i
$196$		0			0
$197$	67.7042	−	39.0891i	0.343676	−	0.198422i	−0.318220	−	0.948017i	$-0.603085\pi$
$197$	67.7042	−	39.0891i	0.343676	−	0.198422i	0.661897	+	0.749595i	$0.269752\pi$
$198$		0			0
$199$	187.126	−	324.111i	0.940331	−	1.62870i	0.175490	−	0.984481i	$-0.443849\pi$
$199$	187.126	−	324.111i	0.940331	−	1.62870i	0.764840	−	0.644220i	$-0.222818\pi$
$200$		0			0
$201$	−14.4850	+	29.3957i	−0.0720644	+	0.146247i
$202$		0			0
$203$	−68.2159	−	12.0283i	−0.336039	−	0.0592527i
$204$		0			0
$205$	−9.78533	+	8.21087i	−0.0477333	+	0.0400530i
$206$		0			0
$207$	−35.6754	+	161.399i	−0.172345	+	0.779704i
$208$		0			0
$209$	−1.94499	+	5.34382i	−0.00930618	+	0.0255685i
$210$		0			0
$211$	106.592	+	89.4412i	0.505175	+	0.423892i	0.859427	−	0.511258i	$-0.170820\pi$
$211$	106.592	+	89.4412i	0.505175	+	0.423892i	−0.354253	+	0.935150i	$0.615265\pi$
$212$		0			0
$213$	−141.112	−	147.315i	−0.662498	−	0.691621i
$214$		0			0
$215$		−	22.1246i		−	0.102905i
$216$		0			0
$217$	−2.65879			−0.0122525
$218$		0			0
$219$	−55.5306	−	226.628i	−0.253564	−	1.03483i
$220$		0			0
$221$	−172.585	+	205.679i	−0.780928	+	0.930674i
$222$		0			0
$223$	−387.072	−	140.883i	−1.73575	−	0.631761i	−0.736735	−	0.676182i	$-0.763634\pi$
$223$	−387.072	−	140.883i	−1.73575	−	0.631761i	−0.999013	+	0.0444209i	$0.985856\pi$
$224$		0			0
$225$	−84.8763	+	205.272i	−0.377228	+	0.912321i
$226$		0			0
$227$	−209.781	−	250.007i	−0.924146	−	1.10135i	−0.994594	−	0.103838i	$-0.966888\pi$
$227$	−209.781	−	250.007i	−0.924146	−	1.10135i	0.0704486	−	0.997515i	$-0.477557\pi$
$228$		0			0
$229$	76.7584	−	435.319i	0.335190	−	1.90095i	−0.0901632	−	0.995927i	$-0.528739\pi$
$229$	76.7584	−	435.319i	0.335190	−	1.90095i	0.425353	−	0.905028i	$-0.360150\pi$
$230$		0			0
$231$	0.298351	+	4.53025i	0.00129156	+	0.0196115i
$232$		0			0
$233$	44.2713	+	25.5601i	0.190006	+	0.109700i	0.591985	−	0.805949i	$-0.298344\pi$
$233$	44.2713	+	25.5601i	0.190006	+	0.109700i	−0.401980	+	0.915649i	$0.631678\pi$
$234$		0			0
$235$	7.65293	+	13.2553i	0.0325656	+	0.0564053i
$236$		0			0
$237$	−1.24355	+	11.3877i	−0.00524705	+	0.0480493i
$238$		0			0
$239$	−90.6620	−	249.092i	−0.379339	−	1.04223i	−0.971631	−	0.236502i	$-0.923999\pi$
$239$	−90.6620	−	249.092i	−0.379339	−	1.04223i	0.592292	−	0.805723i	$-0.298223\pi$
$240$		0			0
$241$	−29.5467	−	167.567i	−0.122600	−	0.695301i	−0.982704	−	0.185182i	$-0.940713\pi$
$241$	−29.5467	−	167.567i	−0.122600	−	0.695301i	0.860104	−	0.510119i	$-0.170399\pi$
$242$		0			0
$243$	−37.3413	−	240.114i	−0.153668	−	0.988123i
$244$		0			0
$245$	23.0248	−	4.05989i	0.0939788	−	0.0165710i
$246$		0			0
$247$	−96.0378	+	34.9549i	−0.388817	+	0.141518i
$248$		0			0
$249$	169.212	+	18.4783i	0.679568	+	0.0742099i
$250$		0			0
$251$	−226.468	+	130.751i	−0.902263	+	0.520922i	−0.877934	−	0.478782i	$-0.841078\pi$
$251$	−226.468	+	130.751i	−0.902263	+	0.520922i	−0.0243293	+	0.999704i	$0.507745\pi$
$252$		0			0
$253$	−5.03614	+	8.72286i	−0.0199057	+	0.0344777i
$254$		0			0
$255$	46.0696	−	3.03402i	0.180665	−	0.0118981i
$256$		0			0
$257$	−250.148	−	44.1078i	−0.973338	−	0.171626i	−0.335706	−	0.941967i	$-0.608975\pi$
$257$	−250.148	−	44.1078i	−0.973338	−	0.171626i	−0.637632	+	0.770341i	$0.720086\pi$
$258$		0			0
$259$	65.6819	−	55.1137i	0.253598	−	0.212794i
$260$		0			0
$261$	208.773	+	86.3240i	0.799898	+	0.330743i
$262$		0			0
$263$	155.430	−	427.039i	0.590987	−	1.62372i	−0.177691	−	0.984086i	$-0.556863\pi$
$263$	155.430	−	427.039i	0.590987	−	1.62372i	0.768678	−	0.639637i	$-0.220915\pi$
$264$		0			0
$265$	8.82109	+	7.40177i	0.0332871	+	0.0279312i
$266$		0			0
$267$	−500.181	+	122.559i	−1.87334	+	0.459023i
$268$		0			0
$269$		−	319.258i		−	1.18683i	−0.804896	−	0.593416i	$-0.797779\pi$
$269$		−	319.258i		−	1.18683i	0.804896	−	0.593416i	$-0.202221\pi$
$270$		0			0
$271$	−360.532			−1.33038			−0.665189	−	0.746675i	$-0.731649\pi$
$271$	−360.532			−1.33038			−0.665189	+	0.746675i	$0.731649\pi$
$272$		0			0
$273$	−58.9222	+	56.4410i	−0.215832	+	0.206744i
$274$		0			0
$275$	−8.70041	+	10.3687i	−0.0316378	+	0.0377045i
$276$		0			0
$277$	200.170	+	72.8558i	0.722634	+	0.263017i	0.677044	−	0.735943i	$-0.263261\pi$
$277$	200.170	+	72.8558i	0.722634	+	0.263017i	0.0455906	+	0.998960i	$0.485483\pi$
$278$		0			0
$279$	8.46720	+	1.87158i	0.0303484	+	0.00670817i
$280$		0			0
$281$	55.1073	+	65.6744i	0.196112	+	0.233717i	0.855135	−	0.518406i	$-0.173474\pi$
$281$	55.1073	+	65.6744i	0.196112	+	0.233717i	−0.659023	+	0.752123i	$0.729030\pi$
$282$		0			0
$283$	31.7861	−	180.268i	0.112318	−	0.636988i	−0.875725	−	0.482810i	$-0.839616\pi$
$283$	31.7861	−	180.268i	0.112318	−	0.636988i	0.988043	−	0.154178i	$-0.0492729\pi$
$284$		0			0
$285$	15.7642	+	7.76793i	0.0553130	+	0.0272559i
$286$		0			0
$287$	−54.0359	−	31.1976i	−0.188278	−	0.108703i
$288$		0			0
$289$	226.554	+	392.403i	0.783924	+	1.35780i
$290$		0			0
$291$	230.101	−	101.333i	0.790724	−	0.348222i
$292$		0			0
$293$	124.259	+	341.399i	0.424092	+	1.16518i	0.949344	+	0.314238i	$0.101749\pi$
$293$	124.259	+	341.399i	0.424092	+	1.16518i	−0.525252	+	0.850947i	$0.676029\pi$
$294$		0			0
$295$	−1.86120	−	10.5554i	−0.00630915	−	0.0357810i
$296$		0			0
$297$	2.23881	−	14.6371i	0.00753809	−	0.0492830i
$298$		0			0
$299$	−178.266	+	31.4332i	−0.596209	+	0.105128i
$300$		0			0
$301$	101.553	−	36.9622i	0.337384	−	0.122798i
$302$		0			0
$303$	−181.783	+	248.083i	−0.599943	+	0.818755i
$304$		0			0
$305$	43.5209	−	25.1268i	0.142692	−	0.0823830i
$306$		0			0
$307$	154.891	−	268.279i	0.504532	−	0.873875i	−0.495455	−	0.868634i	$-0.664998\pi$
$307$	154.891	−	268.279i	0.504532	−	0.873875i	0.999986	−	0.00524071i	$-0.00166818\pi$
$308$		0			0
$309$	−74.3360	−	111.176i	−0.240570	−	0.359794i
$310$		0			0
$311$	235.907	+	41.5967i	0.758543	+	0.133752i	0.539525	−	0.841969i	$-0.318604\pi$
$311$	235.907	+	41.5967i	0.758543	+	0.133752i	0.219017	+	0.975721i	$0.429715\pi$
$312$		0			0
$313$	166.438	−	139.658i	0.531751	−	0.446192i	−0.336954	−	0.941521i	$-0.609397\pi$
$313$	166.438	−	139.658i	0.531751	−	0.446192i	0.868706	+	0.495329i	$0.164952\pi$
$314$		0			0
$315$	14.0175	+	0.603237i	0.0444999	+	0.00191504i
$316$		0			0
$317$	−95.9667	+	263.666i	−0.302734	+	0.831755i	0.691288	+	0.722579i	$0.257043\pi$
$317$	−95.9667	+	263.666i	−0.302734	+	0.831755i	−0.994022	+	0.109176i	$0.965179\pi$
$318$		0			0
$319$	10.5456	+	8.84880i	0.0330583	+	0.0277392i
$320$		0			0
$321$	102.213	−	351.086i	0.318421	−	1.09373i
$322$		0			0
$323$			282.480i			0.874551i
$324$		0			0
$325$	−243.255			−0.748478
$326$		0			0
$327$	302.847	+	88.1693i	0.926139	+	0.269631i
$328$		0			0
$329$	−48.0568	+	57.2719i	−0.146069	+	0.174079i
$330$		0			0
$331$	−216.887	−	78.9403i	−0.655246	−	0.238490i	−0.00706375	−	0.999975i	$-0.502248\pi$
$331$	−216.887	−	78.9403i	−0.655246	−	0.238490i	−0.648183	+	0.761485i	$0.724471\pi$
$332$		0			0
$333$	−247.966	+	129.280i	−0.744644	+	0.388229i
$334$		0			0
$335$	3.96672	+	4.72736i	0.0118410	+	0.0141115i
$336$		0			0
$337$	−45.2614	+	256.690i	−0.134307	+	0.761692i	0.841033	+	0.540984i	$0.181948\pi$
$337$	−45.2614	+	256.690i	−0.134307	+	0.761692i	−0.975340	+	0.220708i	$0.929163\pi$
$338$		0			0
$339$	243.579	−	162.864i	0.718521	−	0.480425i
$340$		0			0
$341$	0.457613	+	0.264203i	0.00134197	+	0.000774788i
$342$		0			0
$343$	124.709	+	216.002i	0.363582	+	0.629742i
$344$		0			0
$345$	25.1079	+	18.3978i	0.0727766	+	0.0533270i
$346$		0			0
$347$	29.0572	+	79.8340i	0.0837383	+	0.230069i	0.974494	−	0.224413i	$-0.0720465\pi$
$347$	29.0572	+	79.8340i	0.0837383	+	0.230069i	−0.890756	+	0.454482i	$0.849824\pi$
$348$		0			0
$349$	69.5531	+	394.455i	0.199293	+	1.13024i	0.906172	+	0.422910i	$0.138991\pi$
$349$	69.5531	+	394.455i	0.199293	+	1.13024i	−0.706879	+	0.707334i	$0.749898\pi$
$350$		0			0
$351$	227.374	−	138.265i	0.647788	−	0.393919i
$352$		0			0
$353$	280.302	−	49.4249i	0.794058	−	0.140014i	0.238118	−	0.971236i	$-0.423470\pi$
$353$	280.302	−	49.4249i	0.794058	−	0.140014i	0.555940	+	0.831222i	$0.312358\pi$
$354$		0			0
$355$	−36.0982	+	13.1387i	−0.101685	+	0.0370104i
$356$		0			0
$357$	90.8917	+	206.392i	0.254599	+	0.578129i
$358$		0			0
$359$	395.652	−	228.430i	1.10210	−	0.636295i	0.165325	−	0.986239i	$-0.447133\pi$
$359$	395.652	−	228.430i	1.10210	−	0.636295i	0.936771	+	0.349944i	$0.113799\pi$
$360$		0			0
$361$	126.738	−	219.516i	0.351074	−	0.608078i
$362$		0			0
$363$	−160.050	+	324.806i	−0.440910	+	0.894781i
$364$		0			0
$365$	−43.2717	−	7.62997i	−0.118553	−	0.0209040i
$366$		0			0
$367$	−433.283	+	363.568i	−1.18061	+	0.990648i	−0.180633	+	0.983551i	$0.557815\pi$
$367$	−433.283	+	363.568i	−1.18061	+	0.990648i	−0.999975	+	0.00709700i	$0.997741\pi$
$368$		0			0
$369$	150.122	+	137.389i	0.406835	+	0.372328i
$370$		0			0
$371$	−19.2376	+	52.8547i	−0.0518532	+	0.142466i
$372$		0			0
$373$	−0.937405	−	0.786577i	−0.00251315	−	0.00210878i	0.641530	−	0.767098i	$-0.278300\pi$
$373$	−0.937405	−	0.786577i	−0.00251315	−	0.00210878i	−0.644043	+	0.764989i	$0.722744\pi$
$374$		0			0
$375$	58.2441	+	60.8045i	0.155318	+	0.162145i
$376$		0			0
$377$			247.404i			0.656245i
$378$		0			0
$379$	−250.285			−0.660382			−0.330191	−	0.943914i	$-0.607113\pi$
$379$	−250.285			−0.660382			−0.330191	+	0.943914i	$0.607113\pi$
$380$		0			0
$381$	−146.072	−	596.141i	−0.383392	−	1.56467i
$382$		0			0
$383$	438.105	−	522.113i	1.14388	−	1.36322i	0.222322	−	0.974973i	$-0.428637\pi$
$383$	438.105	−	522.113i	1.14388	−	1.36322i	0.921556	−	0.388246i	$-0.126919\pi$
$384$		0			0
$385$	0.803390	+	0.292410i	0.00208673	+	0.000759506i
$386$		0			0
$387$	−349.423	+	46.2247i	−0.902902	+	0.119444i
$388$		0			0
$389$	216.060	+	257.490i	0.555424	+	0.661929i	0.968572	−	0.248735i	$-0.0800149\pi$
$389$	216.060	+	257.490i	0.555424	+	0.661929i	−0.413147	+	0.910664i	$0.635570\pi$
$390$		0			0
$391$	−86.8800	+	492.721i	−0.222200	+	1.26016i
$392$		0			0
$393$	−32.6365	−	495.564i	−0.0830446	−	1.26098i
$394$		0			0
$395$	1.86818	+	1.07859i	0.00472956	+	0.00273061i
$396$		0			0
$397$	210.548	+	364.680i	0.530348	+	0.918590i	0.999373	+	0.0354050i	$0.0112721\pi$
$397$	210.548	+	364.680i	0.530348	+	0.918590i	−0.469025	+	0.883185i	$0.655395\pi$
$398$		0			0
$399$	−9.31878	+	85.3356i	−0.0233553	+	0.213874i
$400$		0			0
$401$	−62.7416	−	172.381i	−0.156463	−	0.429878i	0.836549	−	0.547892i	$-0.184569\pi$
$401$	−62.7416	−	172.381i	−0.156463	−	0.429878i	−0.993012	+	0.118014i	$0.962347\pi$
$402$		0			0
$403$	1.64903	+	9.35210i	0.00409188	+	0.0232062i
$404$		0			0
$405$	−44.2154	−	11.7882i	−0.109174	−	0.0291068i
$406$		0			0
$407$	−16.7813	+	2.95900i	−0.0412318	+	0.00727027i
$408$		0			0
$409$	−181.255	+	65.9715i	−0.443167	+	0.161299i	−0.553959	−	0.832544i	$-0.686883\pi$
$409$	−181.255	+	65.9715i	−0.443167	+	0.161299i	0.110792	+	0.993844i	$0.464661\pi$
$410$		0			0
$411$	−194.498	−	21.2395i	−0.473231	−	0.0516775i
$412$		0			0
$413$	45.3402	−	26.1772i	0.109782	−	0.0633829i
$414$		0			0
$415$	16.0271	−	27.7597i	0.0386195	−	0.0668909i
$416$		0			0
$417$	−710.458	+	46.7889i	−1.70374	+	0.112204i
$418$		0			0
$419$	594.464	+	104.820i	1.41877	+	0.250167i	0.829833	−	0.558012i	$-0.188436\pi$
$419$	594.464	+	104.820i	1.41877	+	0.250167i	0.588937	+	0.808179i	$0.299547\pi$
$420$		0			0
$421$	295.228	−	247.725i	0.701253	−	0.588421i	−0.220877	−	0.975302i	$-0.570892\pi$
$421$	295.228	−	247.725i	0.701253	−	0.588421i	0.922130	+	0.386880i	$0.126447\pi$
$422$		0			0
$423$	193.357	−	148.560i	0.457108	−	0.351205i
$424$		0			0
$425$	−229.956	+	631.800i	−0.541074	+	1.48659i
$426$		0			0
$427$	188.040	+	157.785i	0.440376	+	0.369519i
$428$		0			0
$429$	15.7498	−	3.85916i	0.0367128	−	0.00899572i
$430$		0			0
$431$			107.204i			0.248733i	0.992236	+	0.124366i	$0.0396898\pi$
$431$			107.204i			0.248733i	−0.992236	+	0.124366i	$0.960310\pi$
$432$		0			0
$433$	−393.361			−0.908455			−0.454227	−	0.890886i	$-0.650085\pi$
$433$	−393.361			−0.908455			−0.454227	+	0.890886i	$0.650085\pi$
$434$		0			0
$435$	30.7222	−	29.4285i	0.0706257	−	0.0676517i
$436$		0			0
$437$	−122.416	+	145.890i	−0.280128	+	0.333843i
$438$		0			0
$439$	71.1937	+	25.9124i	0.162173	+	0.0590260i	0.421831	−	0.906675i	$-0.361388\pi$
$439$	71.1937	+	25.9124i	0.162173	+	0.0590260i	−0.259658	+	0.965701i	$0.583610\pi$
$440$		0			0
$441$	−112.225	−	355.158i	−0.254478	−	0.805347i
$442$		0			0
$443$	280.910	+	334.776i	0.634109	+	0.755701i	0.983427	−	0.181303i	$-0.0580314\pi$
$443$	280.910	+	334.776i	0.634109	+	0.755701i	−0.349319	+	0.937004i	$0.613587\pi$
$444$		0			0
$445$	−16.8398	+	95.5031i	−0.0378422	+	0.214614i
$446$		0			0
$447$	443.593	+	218.583i	0.992377	+	0.489001i
$448$		0			0
$449$	−31.3960	−	18.1265i	−0.0699244	−	0.0403709i	0.464630	−	0.885505i	$-0.346187\pi$
$449$	−31.3960	−	18.1265i	−0.0699244	−	0.0403709i	−0.534555	+	0.845134i	$0.679521\pi$
$450$		0			0
$451$	6.20018	+	10.7390i	0.0137476	+	0.0238116i
$452$		0			0
$453$	353.949	−	155.873i	0.781344	−	0.344091i
$454$		0			0
$455$	5.25512	+	14.4383i	0.0115497	+	0.0317326i
$456$		0			0
$457$	8.65183	+	49.0670i	0.0189318	+	0.107368i	0.992809	−	0.119706i	$-0.0381953\pi$
$457$	8.65183	+	49.0670i	0.0189318	+	0.107368i	−0.973878	+	0.227074i	$0.927084\pi$
$458$		0			0
$459$	−144.170	−	721.257i	−0.314096	−	1.57137i
$460$		0			0
$461$	817.463	−	144.141i	1.77324	−	0.312670i	0.811035	−	0.584998i	$-0.198905\pi$
$461$	817.463	−	144.141i	1.77324	−	0.312670i	0.962205	+	0.272328i	$0.0877935\pi$
$462$		0			0
$463$	−382.929	+	139.375i	−0.827059	+	0.301025i	−0.720651	−	0.693298i	$-0.756157\pi$
$463$	−382.929	+	139.375i	−0.827059	+	0.301025i	−0.106408	+	0.994323i	$0.533935\pi$
$464$		0			0
$465$	0.965175	−	1.31720i	0.00207564	−	0.00283268i
$466$		0			0
$467$	−91.3883	+	52.7631i	−0.195692	+	0.112983i	−0.594645	−	0.803989i	$-0.702707\pi$
$467$	−91.3883	+	52.7631i	−0.195692	+	0.112983i	0.398952	+	0.916972i	$0.369374\pi$
$468$		0			0
$469$	−15.0718	+	26.1051i	−0.0321360	+	0.0556612i
$470$		0			0
$471$	383.575	+	573.673i	0.814385	+	1.21799i
$472$		0			0
$473$	−21.1514	−	3.72957i	−0.0447176	−	0.00788492i
$474$		0			0
$475$	−196.051	+	164.506i	−0.412738	+	0.346328i
$476$		0			0
$477$	98.4695	−	154.780i	0.206435	−	0.324485i
$478$		0			0
$479$	228.899	−	628.896i	0.477869	−	1.31293i	−0.433429	−	0.901188i	$-0.642696\pi$
$479$	228.899	−	628.896i	0.477869	−	1.31293i	0.911298	−	0.411747i	$-0.135081\pi$
$480$		0			0
$481$	−234.595	−	196.849i	−0.487724	−	0.409249i
$482$		0			0
$483$	−42.5004	+	145.982i	−0.0879926	+	0.302241i
$484$		0			0
$485$		−	47.3464i		−	0.0976214i
$486$		0			0
$487$	−839.528			−1.72388			−0.861938	−	0.507013i	$-0.830750\pi$
$487$	−839.528			−1.72388			−0.861938	+	0.507013i	$0.830750\pi$
$488$		0			0
$489$	−743.632	−	216.497i	−1.52072	−	0.442734i
$490$		0			0
$491$	92.8716	−	110.680i	0.189148	−	0.225418i	−0.663134	−	0.748501i	$-0.730774\pi$
$491$	92.8716	−	110.680i	0.189148	−	0.225418i	0.852282	+	0.523083i	$0.175218\pi$
$492$		0			0
$493$	642.576	+	233.879i	1.30340	+	0.474399i
$494$		0			0
$495$	−2.35264	−	1.49673i	−0.00475281	−	0.00302370i
$496$		0			0
$497$	−120.614	−	143.742i	−0.242684	−	0.289219i
$498$		0			0
$499$	−81.4687	+	462.032i	−0.163264	+	0.925916i	0.787572	+	0.616222i	$0.211338\pi$
$499$	−81.4687	+	462.032i	−0.163264	+	0.925916i	−0.950836	+	0.309694i	$0.899773\pi$
$500$		0			0
$501$	303.514	−	202.939i	0.605816	−	0.405067i
$502$		0			0
$503$	−71.4714	−	41.2640i	−0.142090	−	0.0820358i	0.427270	−	0.904124i	$-0.359476\pi$
$503$	−71.4714	−	41.2640i	−0.142090	−	0.0820358i	−0.569360	+	0.822088i	$0.692809\pi$
$504$		0			0
$505$	28.9581	+	50.1570i	0.0573429	+	0.0993207i
$506$		0			0
$507$	−173.890	−	127.418i	−0.342978	−	0.251317i
$508$		0			0
$509$	−0.468267	−	1.28655i	−0.000919974	−	0.00252761i	0.939232	−	0.343284i	$-0.111539\pi$
$509$	−0.468267	−	1.28655i	−0.000919974	−	0.00252761i	−0.940152	+	0.340756i	$0.889317\pi$
$510$		0			0
$511$	−37.2694	−	211.365i	−0.0729343	−	0.413631i
$512$		0			0
$513$	89.7461	−	265.200i	0.174944	−	0.516959i
$514$		0			0
$515$	−24.8020	+	4.37326i	−0.0481592	+	0.00849177i
$516$		0			0
$517$	13.9623	−	5.08185i	0.0270063	−	0.00982950i
$518$		0			0
$519$	227.743	+	517.146i	0.438810	+	0.996428i
$520$		0			0
$521$	−98.5961	+	56.9245i	−0.189244	+	0.109260i	−0.591629	−	0.806211i	$-0.701515\pi$
$521$	−98.5961	+	56.9245i	−0.189244	+	0.109260i	0.402385	+	0.915471i	$0.368181\pi$
$522$		0			0
$523$	348.625	−	603.837i	0.666588	−	1.15456i	−0.312265	−	0.949995i	$-0.601088\pi$
$523$	348.625	−	603.837i	0.666588	−	1.15456i	0.978852	−	0.204569i	$-0.0655791\pi$
$524$		0			0
$525$	−90.3111	+	183.277i	−0.172021	+	0.349099i
$526$		0			0
$527$	25.8488	+	4.55784i	0.0490490	+	0.00864866i
$528$		0			0
$529$	146.841	−	123.214i	0.277583	−	0.232920i
$530$		0			0
$531$	−162.817	+	51.4479i	−0.306623	+	0.0968887i
$532$		0			0
$533$	−76.2213	+	209.416i	−0.143004	+	0.392901i
$534$		0			0
$535$	−52.7487	−	44.2615i	−0.0985958	−	0.0827317i
$536$		0			0
$537$	−442.631	−	462.090i	−0.824267	−	0.860502i
$538$		0			0
$539$		−	22.6964i		−	0.0421084i
$540$		0			0
$541$	−926.021			−1.71168			−0.855842	−	0.517237i	$-0.826961\pi$
$541$	−926.021			−1.71168			−0.855842	+	0.517237i	$0.826961\pi$
$542$		0			0
$543$	−140.182	−	572.102i	−0.258162	−	1.05359i
$544$		0			0
$545$	38.1800	−	45.5012i	0.0700551	−	0.0834884i
$546$		0			0
$547$	408.343	+	148.625i	0.746514	+	0.271709i	0.687138	−	0.726527i	$-0.258867\pi$
$547$	408.343	+	148.625i	0.746514	+	0.271709i	0.0593756	+	0.998236i	$0.481089\pi$
$548$		0			0
$549$	−487.766	−	634.847i	−0.888462	−	1.15637i
$550$		0			0
$551$	167.312	+	199.395i	0.303651	+	0.361878i
$552$		0			0
$553$	−1.82973	+	10.3769i	−0.00330874	+	0.0187648i
$554$		0			0
$555$	3.46057	+	52.5465i	0.00623527	+	0.0946784i
$556$		0			0
$557$	−456.621	−	263.630i	−0.819786	−	0.473304i	0.0305568	−	0.999533i	$-0.490272\pi$
$557$	−456.621	−	263.630i	−0.819786	−	0.473304i	−0.850343	+	0.526229i	$0.823605\pi$
$558$		0			0
$559$	−192.996	−	334.279i	−0.345252	−	0.597995i
$560$		0			0
$561$	4.86543	−	44.5546i	0.00867278	−	0.0794200i
$562$		0			0
$563$	−103.873	−	285.388i	−0.184499	−	0.506906i	0.812617	−	0.582798i	$-0.198042\pi$
$563$	−103.873	−	285.388i	−0.184499	−	0.506906i	−0.997116	+	0.0758914i	$0.975820\pi$
$564$		0			0
$565$	−9.58146	−	54.3392i	−0.0169583	−	0.0961755i
$566$		0			0
$567$	−19.7593	−	222.644i	−0.0348489	−	0.392670i
$568$		0			0
$569$	−427.759	+	75.4255i	−0.751774	+	0.132558i	−0.536389	−	0.843971i	$-0.680212\pi$
$569$	−427.759	+	75.4255i	−0.751774	+	0.132558i	−0.215385	+	0.976529i	$0.569101\pi$
$570$		0			0
$571$	−19.1997	+	6.98813i	−0.0336247	+	0.0122384i	−0.358778	−	0.933423i	$-0.616806\pi$
$571$	−19.1997	+	6.98813i	−0.0336247	+	0.0122384i	0.325153	+	0.945661i	$0.394584\pi$
$572$		0			0
$573$	725.383	+	79.2129i	1.26594	+	0.138242i
$574$		0			0
$575$	−392.561	+	226.645i	−0.682714	+	0.394165i
$576$		0			0
$577$	320.535	−	555.183i	0.555520	−	0.962189i	−0.442343	−	0.896846i	$-0.645853\pi$
$577$	320.535	−	555.183i	0.555520	−	0.962189i	0.997863	−	0.0653429i	$-0.0208141\pi$
$578$		0			0
$579$	−215.597	+	14.1987i	−0.372362	+	0.0245228i
$580$		0			0
$581$	154.193	+	27.1885i	0.265393	+	0.0467960i
$582$		0			0
$583$	8.56318	−	7.18536i	0.0146881	−	0.0123248i
$584$		0			0
$585$	−6.57202	−	49.6794i	−0.0112342	−	0.0849221i
$586$		0			0
$587$	−53.4518	+	146.858i	−0.0910593	+	0.250183i	−0.976859	−	0.213884i	$-0.931388\pi$
$587$	−53.4518	+	146.858i	−0.0910593	+	0.250183i	0.885800	+	0.464068i	$0.153611\pi$
$588$		0			0
$589$	7.65356	+	6.42210i	0.0129942	+	0.0109034i
$590$		0			0
$591$	−227.796	+	55.8167i	−0.385441	+	0.0944445i
$592$		0			0
$593$		−	859.004i		−	1.44857i	−0.689499	−	0.724287i	$-0.742169\pi$
$593$		−	859.004i		−	1.44857i	0.689499	−	0.724287i	$-0.257831\pi$
$594$		0			0
$595$	42.4680			0.0713748
$596$		0			0
$597$	−810.795	+	776.653i	−1.35812	+	1.30093i
$598$		0			0
$599$	553.410	−	659.528i	0.923889	−	1.10105i	−0.0707348	−	0.997495i	$-0.522534\pi$
$599$	553.410	−	659.528i	0.923889	−	1.10105i	0.994624	−	0.103553i	$-0.0330212\pi$
$600$		0			0
$601$	−364.077	−	132.513i	−0.605786	−	0.220488i	0.0208727	−	0.999782i	$-0.493356\pi$
$601$	−364.077	−	132.513i	−0.605786	−	0.220488i	−0.626658	+	0.779294i	$0.715578\pi$
$602$		0			0
$603$	66.3735	−	72.5249i	0.110072	−	0.120274i
$604$		0			0
$605$	43.8300	+	52.2345i	0.0724463	+	0.0863381i
$606$		0			0
$607$	−116.195	+	658.975i	−0.191425	+	1.08563i	0.725993	+	0.687702i	$0.241380\pi$
$607$	−116.195	+	658.975i	−0.191425	+	1.08563i	−0.917418	+	0.397924i	$0.869731\pi$
$608$		0			0
$609$	186.403	+	91.8514i	0.306081	+	0.150823i
$610$		0			0
$611$	231.255	+	133.515i	0.378486	+	0.218519i
$612$		0			0
$613$	25.8723	+	44.8121i	0.0422060	+	0.0731029i	0.886357	−	0.463003i	$-0.153228\pi$
$613$	25.8723	+	44.8121i	0.0422060	+	0.0731029i	−0.844151	+	0.536106i	$0.819895\pi$
$614$		0			0
$615$	35.0713	−	15.4448i	0.0570265	−	0.0251135i
$616$		0			0
$617$	−236.282	−	649.179i	−0.382953	−	1.05215i	−0.970107	−	0.242678i	$-0.921974\pi$
$617$	−236.282	−	649.179i	−0.382953	−	1.05215i	0.587154	−	0.809475i	$-0.300248\pi$
$618$		0			0
$619$	−40.7459	−	231.082i	−0.0658254	−	0.373314i	−0.999869	−	0.0161566i	$-0.994857\pi$
$619$	−40.7459	−	231.082i	−0.0658254	−	0.373314i	0.934044	−	0.357158i	$-0.116254\pi$
$620$		0			0
$621$	238.107	−	434.978i	0.383425	−	0.700448i
$622$		0			0
$623$	−466.495	+	82.2557i	−0.748788	+	0.132032i
$624$		0			0
$625$	−564.911	+	205.611i	−0.903857	+	0.328977i
$626$		0			0
$627$	10.0836	−	13.7614i	0.0160824	−	0.0219479i
$628$		0			0
$629$	−733.039	+	423.220i	−1.16540	+	0.672846i
$630$		0			0
$631$	183.421	−	317.694i	0.290683	−	0.503477i	−0.683289	−	0.730148i	$-0.739451\pi$
$631$	183.421	−	317.694i	0.290683	−	0.503477i	0.973971	+	0.226671i	$0.0727843\pi$
$632$		0			0
$633$	−232.024	−	347.014i	−0.366547	−	0.548205i
$634$		0			0
$635$	−113.825	−	20.0705i	−0.179253	−	0.0316071i
$636$		0			0
$637$	312.465	−	262.189i	0.490526	−	0.411600i
$638$		0			0
$639$	282.924	+	542.664i	0.442761	+	0.849239i
$640$		0			0
$641$	−294.110	+	808.059i	−0.458829	+	1.26062i	0.467528	+	0.883978i	$0.345145\pi$
$641$	−294.110	+	808.059i	−0.458829	+	1.26062i	−0.926358	+	0.376645i	$0.877078\pi$
$642$		0			0
$643$	330.358	+	277.203i	0.513776	+	0.431109i	0.862455	−	0.506133i	$-0.168925\pi$
$643$	330.358	+	277.203i	0.513776	+	0.431109i	−0.348680	+	0.937242i	$0.613370\pi$
$644$		0			0
$645$	−18.5534	+	63.7280i	−0.0287650	+	0.0988031i
$646$		0			0
$647$		−	147.889i		−	0.228577i	−0.993448	−	0.114288i	$-0.963541\pi$
$647$		−	147.889i		−	0.228577i	0.993448	−	0.114288i	$-0.0364588\pi$
$648$		0			0
$649$	−10.4048			−0.0160321
$650$		0			0
$651$	7.65842	+	2.22963i	0.0117641	+	0.00342493i
$652$		0			0
$653$	384.976	−	458.796i	0.589550	−	0.702598i	−0.385970	−	0.922511i	$-0.626133\pi$
$653$	384.976	−	458.796i	0.589550	−	0.702598i	0.975519	+	0.219914i	$0.0705776\pi$
$654$		0			0
$655$	−87.8826	−	31.9867i	−0.134172	−	0.0488346i
$656$		0			0
$657$	−30.0963	+	699.349i	−0.0458086	+	1.06446i
$658$		0			0
$659$	703.887	+	838.859i	1.06811	+	1.27293i	0.960364	+	0.278750i	$0.0899200\pi$
$659$	703.887	+	838.859i	1.06811	+	1.27293i	0.107749	+	0.994178i	$0.465636\pi$
$660$		0			0
$661$	30.0923	−	170.662i	0.0455254	−	0.258188i	−0.953547	−	0.301244i	$-0.902598\pi$
$661$	30.0923	−	170.662i	0.0455254	−	0.258188i	0.999073	+	0.0430560i	$0.0137094\pi$
$662$		0			0
$663$	669.596	−	447.712i	1.00995	−	0.675283i
$664$		0			0
$665$	13.9995	+	8.08263i	0.0210519	+	0.0121543i
$666$		0			0
$667$	230.511	+	399.256i	0.345593	+	0.598585i
$668$		0			0
$669$	996.784	+	730.393i	1.48996	+	1.09177i
$670$		0			0
$671$	−16.6852	−	45.8423i	−0.0248662	−	0.0683193i
$672$		0			0
$673$	−41.2876	−	234.154i	−0.0613486	−	0.347925i	−0.999995	−	0.00304518i	$-0.999031\pi$
$673$	−41.2876	−	234.154i	−0.0613486	−	0.347925i	0.938647	−	0.344880i	$-0.112080\pi$
$674$		0			0
$675$	416.617	−	520.093i	0.617211	−	0.770507i
$676$		0			0
$677$	921.231	−	162.438i	1.36076	−	0.239938i	0.554834	−	0.831961i	$-0.312782\pi$
$677$	921.231	−	162.438i	1.36076	−	0.239938i	0.805921	+	0.592023i	$0.201671\pi$
$678$		0			0
$679$	217.321	−	79.0985i	0.320061	−	0.116493i
$680$		0			0
$681$	394.603	+	896.044i	0.579446	+	1.31578i
$682$		0			0
$683$	−636.019	+	367.206i	−0.931214	+	0.537636i	−0.887195	−	0.461394i	$-0.847349\pi$
$683$	−636.019	+	367.206i	−0.931214	+	0.537636i	−0.0440184	+	0.999031i	$0.514016\pi$
$684$		0			0
$685$	−18.4220	+	31.9078i	−0.0268934	+	0.0465808i
$686$		0			0
$687$	−586.148	+	1189.53i	−0.853200	+	1.73148i
$688$		0			0
$689$	197.844	+	34.8852i	0.287146	+	0.0506317i
$690$		0			0
$691$	983.527	−	825.277i	1.42334	−	1.19432i	0.473816	−	0.880624i	$-0.342876\pi$
$691$	983.527	−	825.277i	1.42334	−	1.19432i	0.949523	−	0.313699i	$-0.101568\pi$
$692$		0			0
$693$	2.93964	−	13.2992i	0.00424190	−	0.0191908i
$694$		0			0
$695$	−45.8573	+	125.992i	−0.0659817	+	0.181283i
$696$		0			0
$697$	471.856	+	395.935i	0.676982	+	0.568055i
$698$		0			0
$699$	−106.085	−	110.749i	−0.151767	−	0.158439i
$700$		0			0
$701$			361.350i			0.515478i	0.966215	+	0.257739i	$0.0829775\pi$
$701$			361.350i			0.515478i	−0.966215	+	0.257739i	$0.917023\pi$
$702$		0			0
$703$	−322.194			−0.458313
$704$		0			0
$705$	−10.9279	−	44.5982i	−0.0155006	−	0.0632599i
$706$		0			0
$707$	−181.844	+	216.713i	−0.257205	+	0.306524i
$708$		0			0
$709$	1132.45	+	412.177i	1.59724	+	0.581349i	0.978861	−	0.204527i	$-0.0655656\pi$
$709$	1132.45	+	412.177i	1.59724	+	0.581349i	0.618384	+	0.785876i	$0.287788\pi$
$710$		0			0
$711$	13.1315	−	31.7584i	0.0184691	−	0.0446672i
$712$		0			0
$713$	11.3747	+	13.5558i	0.0159533	+	0.0190124i
$714$		0			0
$715$	0.530254	−	3.00722i	0.000741613	−	0.00420590i
$716$		0			0
$717$	52.2588	+	793.515i	0.0728853	+	1.10672i
$718$		0			0
$719$	−1047.62	−	604.844i	−1.45705	−	0.841230i	−0.458188	−	0.888856i	$-0.651501\pi$
$719$	−1047.62	−	604.844i	−1.45705	−	0.841230i	−0.998865	+	0.0476257i	$0.984835\pi$
$720$		0			0
$721$	−61.5085	−	106.536i	−0.0853100	−	0.147761i
$722$		0			0
$723$	−55.4133	+	507.441i	−0.0766436	+	0.701854i
$724$		0			0
$725$	211.893	+	582.172i	0.292266	+	0.802995i
$726$		0			0
$727$	72.2341	+	409.660i	0.0993591	+	0.563494i	0.993324	+	0.115357i	$0.0368011\pi$
$727$	72.2341	+	409.660i	0.0993591	+	0.563494i	−0.893965	+	0.448137i	$0.852088\pi$
$728$		0			0
$729$	−93.7981	+	722.940i	−0.128667	+	0.991688i
$730$		0			0
$731$	−1050.66	+	185.259i	−1.43729	+	0.253433i
$732$		0			0
$733$	503.883	−	183.398i	0.687425	−	0.250202i	0.0253927	−	0.999678i	$-0.491916\pi$
$733$	503.883	−	183.398i	0.687425	−	0.250202i	0.662032	+	0.749475i	$0.269694\pi$
$734$		0			0
$735$	−69.7255	−	7.61413i	−0.0948646	−	0.0103594i
$736$		0			0
$737$	5.18809	−	2.99535i	0.00703948	−	0.00406424i
$738$		0			0
$739$	527.106	−	912.975i	0.713270	−	1.23542i	−0.250354	−	0.968154i	$-0.580547\pi$
$739$	527.106	−	912.975i	0.713270	−	1.23542i	0.963623	−	0.267265i	$-0.0861198\pi$
$740$		0			0
$741$	305.941	−	20.1485i	0.412876	−	0.0271909i
$742$		0			0
$743$	−194.700	−	34.3308i	−0.262046	−	0.0462057i	0.0410817	−	0.999156i	$-0.486920\pi$
$743$	−194.700	−	34.3308i	−0.262046	−	0.0462057i	−0.303127	+	0.952950i	$0.598031\pi$
$744$		0			0
$745$	71.3376	−	59.8594i	0.0957552	−	0.0803482i
$746$		0			0
$747$	−471.906	−	195.124i	−0.631735	−	0.261211i
$748$		0			0
$749$	115.038	−	316.063i	0.153588	−	0.421980i
$750$		0			0
$751$	−316.268	−	265.381i	−0.421129	−	0.353370i	0.407463	−	0.913222i	$-0.366413\pi$
$751$	−316.268	−	265.381i	−0.421129	−	0.353370i	−0.828593	+	0.559852i	$0.810858\pi$
$752$		0			0
$753$	761.968	−	186.705i	1.01191	−	0.247948i
$754$		0			0
$755$		−	72.8299i		−	0.0964634i
$756$		0			0
$757$	−496.308			−0.655625			−0.327812	−	0.944743i	$-0.606311\pi$
$757$	−496.308			−0.655625			−0.327812	+	0.944743i	$0.606311\pi$
$758$		0			0
$759$	21.8210	−	20.9022i	0.0287497	−	0.0275391i
$760$		0			0
$761$	−33.2715	+	39.6515i	−0.0437208	+	0.0521044i	−0.787462	−	0.616364i	$-0.788605\pi$
$761$	−33.2715	+	39.6515i	−0.0437208	+	0.0521044i	0.743741	+	0.668468i	$0.233050\pi$
$762$		0			0
$763$	272.637	+	99.2316i	0.357322	+	0.130055i
$764$		0			0
$765$	−135.244	−	29.8941i	−0.176789	−	0.0390773i
$766$		0			0
$767$	−120.197	−	143.245i	−0.156710	−	0.186760i
$768$		0			0
$769$	−167.549	+	950.219i	−0.217879	+	1.23566i	0.657960	+	0.753053i	$0.271420\pi$
$769$	−167.549	+	950.219i	−0.217879	+	1.23566i	−0.875839	+	0.482603i	$0.839691\pi$
$770$		0			0
$771$	683.540	+	336.819i	0.886563	+	0.436860i
$772$		0			0
$773$	−634.350	−	366.242i	−0.820634	−	0.473793i	0.0300011	−	0.999550i	$-0.490449\pi$
$773$	−634.350	−	366.242i	−0.820634	−	0.473793i	−0.850635	+	0.525757i	$0.823782\pi$
$774$		0			0
$775$	11.8901	+	20.5943i	0.0153421	+	0.0265732i
$776$		0			0
$777$	−235.409	+	103.670i	−0.302971	+	0.133424i
$778$		0			0
$779$	80.1915	+	220.324i	0.102942	+	0.282830i
$780$		0			0
$781$	6.47564	+	36.7252i	0.00829148	+	0.0470233i
$782$		0			0
$783$	−528.963	−	423.723i	−0.675560	−	0.541154i
$784$		0			0
$785$	127.979	−	22.5661i	0.163030	−	0.0287467i
$786$		0			0
$787$	401.147	−	146.006i	0.509717	−	0.185522i	−0.0743423	−	0.997233i	$-0.523686\pi$
$787$	401.147	−	146.006i	0.509717	−	0.185522i	0.584059	+	0.811711i	$0.301464\pi$
$788$		0			0
$789$	−805.810	+	1099.71i	−1.02131	+	1.39380i
$790$		0			0
$791$	233.411	−	134.760i	0.295084	−	0.170367i
$792$		0			0
$793$	438.369	−	759.278i	0.552799	−	0.957476i
$794$		0			0
$795$	−19.2013	−	28.7174i	−0.0241526	−	0.0361225i
$796$		0			0
$797$	173.023	+	30.5086i	0.217093	+	0.0382793i	0.281136	−	0.959668i	$-0.409289\pi$
$797$	173.023	+	30.5086i	0.217093	+	0.0382793i	−0.0640438	+	0.997947i	$0.520400\pi$
$798$		0			0
$799$	565.387	−	474.416i	0.707618	−	0.593762i
$800$		0			0
$801$	1543.50	+	66.4241i	1.92697	+	0.0829265i
$802$		0			0
$803$	−14.5887	+	40.0821i	−0.0181678	+	0.0499155i
$804$		0			0
$805$	21.9330	+	18.4040i	0.0272460	+	0.0228621i
$806$		0			0
$807$	−267.725	+	919.594i	−0.331754	+	1.13952i
$808$		0			0
$809$			330.232i			0.408198i	0.978950	+	0.204099i	$0.0654265\pi$
$809$			330.232i			0.408198i	−0.978950	+	0.204099i	$0.934574\pi$
$810$		0			0
$811$	−1041.63			−1.28438			−0.642191	−	0.766545i	$-0.721974\pi$
$811$	−1041.63			−1.28438			−0.642191	+	0.766545i	$0.721974\pi$
$812$		0			0
$813$	1038.48	+	302.338i	1.27734	+	0.371879i
$814$		0			0
$815$	−93.7498	+	111.727i	−0.115030	+	0.137088i
$816$		0			0
$817$	−381.607	−	138.894i	−0.467083	−	0.170004i
$818$		0			0
$819$	217.051	−	113.162i	0.265019	−	0.138171i
$820$		0			0
$821$	−214.318	−	255.415i	−0.261045	−	0.311102i	0.619563	−	0.784947i	$-0.287310\pi$
$821$	−214.318	−	255.415i	−0.261045	−	0.311102i	−0.880608	+	0.473845i	$0.842866\pi$
$822$		0			0
$823$	148.989	−	844.956i	0.181031	−	1.02668i	−0.749918	−	0.661530i	$-0.769907\pi$
$823$	148.989	−	844.956i	0.181031	−	1.02668i	0.930949	−	0.365148i	$-0.118982\pi$
$824$		0			0
$825$	33.7558	−	22.5702i	0.0409162	−	0.0273578i
$826$		0			0
$827$	−466.776	−	269.493i	−0.564421	−	0.325869i	0.190497	−	0.981688i	$-0.438990\pi$
$827$	−466.776	−	269.493i	−0.564421	−	0.325869i	−0.754918	+	0.655819i	$0.772323\pi$
$828$		0			0
$829$	−133.281	−	230.849i	−0.160773	−	0.278467i	0.774373	−	0.632729i	$-0.218065\pi$
$829$	−133.281	−	230.849i	−0.160773	−	0.278467i	−0.935146	+	0.354262i	$0.884732\pi$
$830$		0			0
$831$	−515.475	−	377.714i	−0.620307	−	0.454530i
$832$		0			0
$833$	−385.594	−	1059.41i	−0.462898	−	1.27180i
$834$		0			0
$835$	−11.9391	−	67.7099i	−0.0142983	−	0.0810898i
$836$		0			0
$837$	−22.8195	−	12.4914i	−0.0272635	−	0.0149240i
$838$		0			0
$839$	−190.649	+	33.6165i	−0.227233	+	0.0400673i	−0.286105	−	0.958198i	$-0.592361\pi$
$839$	−190.649	+	33.6165i	−0.227233	+	0.0400673i	0.0588721	+	0.998266i	$0.481250\pi$
$840$		0			0
$841$	−198.180	+	72.1317i	−0.235648	+	0.0857689i
$842$		0			0
$843$	−103.658	−	235.382i	−0.122963	−	0.279219i
$844$		0			0
$845$	−35.1568	+	20.2978i	−0.0416056	+	0.0240210i
$846$		0			0
$847$	−166.534	+	288.446i	−0.196617	+	0.340550i
$848$		0			0
$849$	−242.727	+	492.590i	−0.285898	+	0.580200i
$850$		0			0
$851$	−561.992	−	99.0944i	−0.660391	−	0.116445i
$852$		0			0
$853$	−95.2154	+	79.8952i	−0.111624	+	0.0936638i	−0.696891	−	0.717177i	$-0.745434\pi$
$853$	−95.2154	+	79.8952i	−0.111624	+	0.0936638i	0.585267	+	0.810840i	$0.300990\pi$
$854$		0			0
$855$	−38.8934	−	35.5945i	−0.0454893	−	0.0416310i
$856$		0			0
$857$	−159.411	+	437.979i	−0.186011	+	0.511060i	−0.997288	−	0.0736016i	$-0.976551\pi$
$857$	−159.411	+	437.979i	−0.186011	+	0.511060i	0.811277	+	0.584662i	$0.198773\pi$
$858$		0			0
$859$	−76.1676	−	63.9122i	−0.0886701	−	0.0744031i	0.597375	−	0.801962i	$-0.296210\pi$
$859$	−76.1676	−	63.9122i	−0.0886701	−	0.0744031i	−0.686045	+	0.727559i	$0.740655\pi$
$860$		0			0
$861$	129.484	+	135.176i	0.150387	+	0.156999i
$862$		0			0
$863$			593.823i			0.688092i	0.938953	+	0.344046i	$0.111798\pi$
$863$			593.823i			0.688092i	−0.938953	+	0.344046i	$0.888202\pi$
$864$		0			0
$865$	106.410			0.123017
$866$		0			0
$867$	−323.505	−	1320.27i	−0.373131	−	1.52280i
$868$		0			0
$869$	1.34607	−	1.60418i	0.00154899	−	0.00184601i
$870$		0			0
$871$	101.170	+	36.8230i	0.116154	+	0.0422767i
$872$		0			0
$873$	−747.761	+	98.9201i	−0.856541	+	0.113311i
$874$		0			0
$875$	49.7834	+	59.3296i	0.0568954	+	0.0678053i
$876$		0			0
$877$	−11.2841	+	63.9955i	−0.0128667	+	0.0729709i	−0.990565	−	0.137044i	$-0.956240\pi$
$877$	−11.2841	+	63.9955i	−0.0128667	+	0.0729709i	0.977698	+	0.210014i	$0.0673511\pi$
$878$		0			0
$879$	−71.6246	−	1087.57i	−0.0814842	−	1.23728i
$880$		0			0
$881$	616.732	+	356.071i	0.700037	+	0.404166i	0.807361	−	0.590058i	$-0.200895\pi$
$881$	616.732	+	356.071i	0.700037	+	0.404166i	−0.107324	+	0.994224i	$0.534228\pi$
$882$		0			0
$883$	444.700	+	770.243i	0.503624	+	0.872303i	0.999991	+	0.00418993i	$0.00133370\pi$
$883$	444.700	+	770.243i	0.503624	+	0.872303i	−0.496367	+	0.868113i	$0.665333\pi$
$884$		0			0
$885$	−3.49059	+	31.9646i	−0.00394417	+	0.0361182i
$886$		0			0
$887$	−232.091	−	637.665i	−0.261658	−	0.718900i	−0.999056	−	0.0434415i	$-0.986168\pi$
$887$	−232.091	−	637.665i	−0.261658	−	0.718900i	0.737398	−	0.675459i	$-0.236054\pi$
$888$		0			0
$889$	−98.0365	−	555.993i	−0.110277	−	0.625414i
$890$		0			0
$891$	−18.7232	+	40.2833i	−0.0210136	+	0.0452114i
$892$		0			0
$893$	276.671	−	48.7846i	0.309822	−	0.0546300i
$894$		0			0
$895$	−113.231	+	41.2126i	−0.126515	+	0.0460476i
$896$		0			0
$897$	539.840	+	58.9514i	0.601829	+	0.0657206i
$898$		0			0
$899$	20.9455	−	12.0929i	0.0232987	−	0.0134515i
$900$		0			0
$901$	277.634	−	480.876i	0.308140	−	0.533714i
$902$		0			0
$903$	−323.510	+	21.3055i	−0.358261	+	0.0235941i
$904$		0			0
$905$	−109.236	−	19.2612i	−0.120702	−	0.0212831i
$906$		0			0
$907$	312.227	−	261.989i	0.344241	−	0.288853i	−0.454232	−	0.890884i	$-0.650086\pi$
$907$	312.227	−	261.989i	0.344241	−	0.288853i	0.798473	+	0.602031i	$0.205642\pi$
$908$		0			0
$909$	731.648	−	562.140i	0.804893	−	0.618416i
$910$		0			0
$911$	−44.7790	+	123.029i	−0.0491537	+	0.135049i	−0.961840	−	0.273612i	$-0.911782\pi$
$911$	−44.7790	+	123.029i	−0.0491537	+	0.135049i	0.912687	+	0.408660i	$0.134004\pi$
$912$		0			0
$913$	−23.8370	−	20.0016i	−0.0261084	−	0.0219076i
$914$		0			0
$915$	−146.429	+	35.8795i	−0.160032	+	0.0392126i
$916$		0			0
$917$		−	456.822i		−	0.498170i
$918$		0			0
$919$	1254.90			1.36550			0.682752	−	0.730650i	$-0.260783\pi$
$919$	1254.90			1.36550			0.682752	+	0.730650i	$0.260783\pi$
$920$		0			0
$921$	−671.126	+	642.866i	−0.728693	+	0.698008i
$922$		0			0
$923$	−430.795	+	513.401i	−0.466733	+	0.556231i
$924$		0			0
$925$	−720.624	−	262.286i	−0.779053	−	0.283552i
$926$		0			0
$927$	120.887	+	382.571i	0.130407	+	0.412698i
$928$		0			0
$929$	−822.051	−	979.682i	−0.884877	−	1.05456i	−0.998138	−	0.0609903i	$-0.980574\pi$
$929$	−822.051	−	979.682i	−0.884877	−	1.05456i	0.113261	−	0.993565i	$-0.463870\pi$
$930$		0			0
$931$	74.5194	−	422.621i	0.0800423	−	0.453943i
$932$		0			0
$933$	−644.626	−	317.644i	−0.690918	−	0.340455i
$934$		0			0
$935$	−7.30930	−	4.22002i	−0.00781743	−	0.00451339i
$936$		0			0
$937$	−46.8477	−	81.1425i	−0.0499975	−	0.0865982i	0.839944	−	0.542674i	$-0.182588\pi$
$937$	−46.8477	−	81.1425i	−0.0499975	−	0.0865982i	−0.889941	+	0.456076i	$0.849255\pi$
$938$		0			0
$939$	−596.526	+	262.700i	−0.635278	+	0.279766i
$940$		0			0
$941$	136.614	+	375.343i	0.145179	+	0.398877i	0.990874	−	0.134790i	$-0.0430360\pi$
$941$	136.614	+	375.343i	0.145179	+	0.398877i	−0.845695	+	0.533667i	$0.820814\pi$
$942$		0			0
$943$	72.1122	+	408.969i	0.0764710	+	0.433689i
$944$		0			0
$945$	−39.8702	−	13.4924i	−0.0421907	−	0.0142777i
$946$		0			0
$947$	−3.66471	+	0.646187i	−0.00386981	+	0.000682351i	−0.175583	−	0.984465i	$-0.556181\pi$
$947$	−3.66471	+	0.646187i	−0.00386981	+	0.000682351i	0.171713	+	0.985147i	$0.445070\pi$
$948$		0			0
$949$	−720.346	+	262.184i	−0.759058	+	0.276274i
$950$		0			0
$951$	497.531	−	678.991i	0.523166	−	0.713976i
$952$		0			0
$953$	898.938	−	519.002i	0.943272	−	0.544598i	0.0522873	−	0.998632i	$-0.483349\pi$
$953$	898.938	−	519.002i	0.943272	−	0.544598i	0.890984	+	0.454034i	$0.150016\pi$
$954$		0			0
$955$	68.7052	−	119.001i	0.0719426	−	0.124608i
$956$		0			0
$957$	−22.9552	−	34.3316i	−0.0239866	−	0.0358742i
$958$		0			0
$959$	−177.234	−	31.2512i	−0.184812	−	0.0325873i
$960$		0			0
$961$	−735.458	+	617.122i	−0.765304	+	0.642167i
$962$		0			0
$963$	−588.832	+	925.557i	−0.611456	+	0.961119i
$964$		0			0
$965$	−13.9160	+	38.2338i	−0.0144207	+	0.0396205i
$966$		0			0
$967$	681.631	+	571.956i	0.704892	+	0.591475i	0.923161	−	0.384414i	$-0.125596\pi$
$967$	681.631	+	571.956i	0.704892	+	0.591475i	−0.218269	+	0.975889i	$0.570041\pi$
$968$		0			0
$969$	236.884	−	813.659i	0.244462	−	0.839689i
$970$		0			0
$971$		−	44.8968i		−	0.0462377i	−0.999733	−	0.0231188i	$-0.992640\pi$
$971$		−	44.8968i		−	0.0462377i	0.999733	−	0.0231188i	$-0.00735961\pi$
$972$		0			0
$973$	−654.917			−0.673090
$974$		0			0
$975$	700.675	+	203.991i	0.718641	+	0.209221i
$976$		0			0
$977$	1079.36	−	1286.33i	1.10477	−	1.31661i	0.160648	−	0.987012i	$-0.448642\pi$
$977$	1079.36	−	1286.33i	1.10477	−	1.31661i	0.944121	−	0.329600i	$-0.106914\pi$
$978$		0			0
$979$	88.4635	+	32.1981i	0.0903611	+	0.0328888i
$980$		0			0
$981$	−798.387	−	507.928i	−0.813851	−	0.517765i
$982$		0			0
$983$	1169.73	+	1394.03i	1.18996	+	1.41814i	0.884885	+	0.465810i	$0.154237\pi$
$983$	1169.73	+	1394.03i	1.18996	+	1.41814i	0.305075	+	0.952328i	$0.401319\pi$
$984$		0			0
$985$	−7.66928	+	43.4947i	−0.00778607	+	0.0441570i
$986$		0			0
$987$	186.451	−	124.667i	0.188907	−	0.126309i
$988$		0			0
$989$	−622.907	−	359.636i	−0.629835	−	0.363636i
$990$		0			0
$991$	−341.977	−	592.322i	−0.345083	−	0.597701i	0.640286	−	0.768137i	$-0.278816\pi$
$991$	−341.977	−	592.322i	−0.345083	−	0.597701i	−0.985369	+	0.170435i	$0.945483\pi$
$992$		0			0
$993$	558.524	+	409.259i	0.562462	+	0.412144i
$994$		0			0
$995$	72.3127	+	198.678i	0.0726761	+	0.199676i
$996$		0			0
$997$	−3.47071	−	19.6834i	−0.00348116	−	0.0197426i	0.983018	−	0.183511i	$-0.0587462\pi$
$997$	−3.47071	−	19.6834i	−0.00348116	−	0.0197426i	−0.986499	+	0.163768i	$0.947635\pi$
$998$		0			0
$999$	822.658	−	164.439i	0.823482	−	0.164604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.u.a.41.2	✓	108
4.3	odd	2		432.3.bc.d.257.17		108
27.2	odd	18	inner	216.3.u.a.137.2	yes	108
108.83	even	18		432.3.bc.d.353.17		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.u.a.41.2	✓	108	1.1	even	1	trivial
216.3.u.a.137.2	yes	108	27.2	odd	18	inner
432.3.bc.d.257.17		108	4.3	odd	2
432.3.bc.d.353.17		108	108.83	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.u (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.88041 - 0.838587i) q^{3} +(-0.363134 + 0.432766i) q^{5} +(-2.59307 - 0.943802i) q^{7} +(7.59354 + 4.83095i) q^{9} +O(q^{10})\)	\(q+(-2.88041 - 0.838587i) q^{3} +(-0.363134 + 0.432766i) q^{5} +(-2.59307 - 0.943802i) q^{7} +(7.59354 + 4.83095i) q^{9} +(0.352516 + 0.420113i) q^{11} +(-1.71148 + 9.70630i) q^{13} +(1.40889 - 0.942025i) q^{15} +(23.5920 + 13.6208i) q^{17} +(5.18471 + 8.98017i) q^{19} +(6.67766 + 4.89306i) q^{21} +(6.28156 + 17.2585i) q^{23} +(4.28578 + 24.3059i) q^{25} +(-17.8214 - 20.2830i) q^{27} +(24.7205 - 4.35888i) q^{29} +(0.905402 - 0.329539i) q^{31} +(-0.663092 - 1.50571i) q^{33} +(1.35008 - 0.779468i) q^{35} +(-15.5358 + 26.9088i) q^{37} +(13.0693 - 26.5229i) q^{39} +(22.2676 + 3.92638i) q^{41} +(-30.0006 + 25.1735i) q^{43} +(-4.84815 + 1.53195i) q^{45} +(9.26638 - 25.4592i) q^{47} +(-31.7029 - 26.6019i) q^{49} +(-56.5323 - 59.0175i) q^{51} -20.3830i q^{53} -0.309821 q^{55} +(-7.40343 - 30.2144i) q^{57} +(-12.1953 + 14.5337i) q^{59} +(-83.5899 - 30.4243i) q^{61} +(-15.1312 - 19.6938i) q^{63} +(-3.57906 - 4.26536i) q^{65} +(1.89686 - 10.7576i) q^{67} +(-3.62078 - 54.9791i) q^{69} +(58.8886 + 33.9994i) q^{71} +(38.8887 + 67.3572i) q^{73} +(8.03778 - 73.6050i) q^{75} +(-0.517598 - 1.42209i) q^{77} +(-0.663068 - 3.76045i) q^{79} +(34.3238 + 73.3681i) q^{81} +(-55.8775 + 9.85270i) q^{83} +(-14.4617 + 5.26362i) q^{85} +(-74.8604 - 8.17487i) q^{87} +(148.661 - 85.8295i) q^{89} +(13.5988 - 23.5538i) q^{91} +(-2.88428 + 0.189951i) q^{93} +(-5.76906 - 1.01724i) q^{95} +(-64.2009 + 53.8710i) q^{97} +(0.647305 + 4.89314i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q+O(q^{10}) \) 108 * q	\( 108 q - 18 q^{11} - 24 q^{15} + 48 q^{21} + 72 q^{23} + 174 q^{27} + 108 q^{29} + 18 q^{33} - 144 q^{39} + 90 q^{41} - 90 q^{43} + 108 q^{45} - 72 q^{49} + 84 q^{51} - 18 q^{57} - 252 q^{59} + 144 q^{61} - 360 q^{63} - 216 q^{65} + 126 q^{67} - 120 q^{69} - 252 q^{75} - 504 q^{77} - 552 q^{81} - 180 q^{83} - 60 q^{87} - 486 q^{89} - 360 q^{93} - 1116 q^{95} + 270 q^{97} - 564 q^{99}+O(q^{100}) \) 108 * q - 18 * q^11 - 24 * q^15 + 48 * q^21 + 72 * q^23 + 174 * q^27 + 108 * q^29 + 18 * q^33 - 144 * q^39 + 90 * q^41 - 90 * q^43 + 108 * q^45 - 72 * q^49 + 84 * q^51 - 18 * q^57 - 252 * q^59 + 144 * q^61 - 360 * q^63 - 216 * q^65 + 126 * q^67 - 120 * q^69 - 252 * q^75 - 504 * q^77 - 552 * q^81 - 180 * q^83 - 60 * q^87 - 486 * q^89 - 360 * q^93 - 1116 * q^95 + 270 * q^97 - 564 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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