LMFDB - Embedded newform 1764.2.w.b.1109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(509,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1764.509");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.w (of order $6$, degree $2$, not 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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1109.1
Root			$-0.544978 - 1.64408i$ of defining polynomial
Character	$\chi$	$=$	1764.1109
Dual form			1764.2.w.b.509.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70992 + 0.276016i) q^{3} +(1.95741 - 3.39033i) q^{5} +(2.84763 - 0.943929i) q^{9} +O(q^{10})$	\(q+(-1.70992 + 0.276016i) q^{3} +(1.95741 - 3.39033i) q^{5} +(2.84763 - 0.943929i) q^{9} +(-3.19958 + 1.84728i) q^{11} +(-0.480242 + 0.277268i) q^{13} +(-2.41122 + 6.33747i) q^{15} +(-2.91916 + 5.05613i) q^{17} +(-4.62434 + 2.66986i) q^{19} +(-1.96965 - 1.13718i) q^{23} +(-5.16291 - 8.94242i) q^{25} +(-4.60867 + 2.40003i) q^{27} +(3.53638 + 2.04173i) q^{29} +8.08443i q^{31} +(4.96114 - 4.04183i) q^{33} +(3.89849 + 6.75239i) q^{37} +(0.744643 - 0.606659i) q^{39} +(-3.59234 - 6.22212i) q^{41} +(-0.754009 + 1.30598i) q^{43} +(2.37374 - 11.5021i) q^{45} +2.82833 q^{47} +(3.59594 - 9.45130i) q^{51} +(-0.0415658 - 0.0239980i) q^{53} +14.4635i q^{55} +(7.17031 - 5.84164i) q^{57} +8.91313 q^{59} +6.96680i q^{61} +2.17091i q^{65} +1.17480 q^{67} +(3.68181 + 1.40082i) q^{69} -6.71061i q^{71} +(3.52692 + 2.03627i) q^{73} +(11.2964 + 13.8658i) q^{75} -3.94747 q^{79} +(7.21799 - 5.37592i) q^{81} +(-3.84674 + 6.66275i) q^{83} +(11.4280 + 19.7938i) q^{85} +(-6.61047 - 2.51509i) q^{87} +(2.71300 + 4.69905i) q^{89} +(-2.23143 - 13.8237i) q^{93} +20.9041i q^{95} +(-13.9874 - 8.07563i) q^{97} +(-7.36753 + 8.28055i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{9}+O(q^{10}) $ 16 * q + 6 * q^9	$ 16 q + 6 q^{9} - 6 q^{11} + 3 q^{13} - 3 q^{15} - 9 q^{17} + 21 q^{23} - 8 q^{25} - 9 q^{27} + 6 q^{29} + q^{37} - 3 q^{39} + 6 q^{41} - 2 q^{43} + 30 q^{45} + 36 q^{47} - 33 q^{51} + 15 q^{57} + 30 q^{59} + 14 q^{67} - 21 q^{69} + 57 q^{75} + 2 q^{79} + 18 q^{81} + 6 q^{85} - 48 q^{87} - 21 q^{89} + 21 q^{93} + 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q + 6 * q^9 - 6 * q^11 + 3 * q^13 - 3 * q^15 - 9 * q^17 + 21 * q^23 - 8 * q^25 - 9 * q^27 + 6 * q^29 + q^37 - 3 * q^39 + 6 * q^41 - 2 * q^43 + 30 * q^45 + 36 * q^47 - 33 * q^51 + 15 * q^57 + 30 * q^59 + 14 * q^67 - 21 * q^69 + 57 * q^75 + 2 * q^79 + 18 * q^81 + 6 * q^85 - 48 * q^87 - 21 * q^89 + 21 * q^93 + 3 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−1.70992	+	0.276016i	−0.987221	+	0.159358i
$3$	−1.70992	+	0.276016i	−0.987221	+	0.159358i
$4$		0			0
$5$	1.95741	−	3.39033i	0.875381	−	1.51620i	0.0190238	−	0.999819i	$-0.493944\pi$
$5$	1.95741	−	3.39033i	0.875381	−	1.51620i	0.856357	−	0.516385i	$-0.172722\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	2.84763	−	0.943929i	0.949210	−	0.314643i
$10$		0			0
$11$	−3.19958	+	1.84728i	−0.964710	+	0.556976i	−0.897620	−	0.440771i	$-0.854705\pi$
$11$	−3.19958	+	1.84728i	−0.964710	+	0.556976i	−0.0670908	+	0.997747i	$0.521372\pi$
$12$		0			0
$13$	−0.480242	+	0.277268i	−0.133195	+	0.0769002i	−0.565117	−	0.825011i	$-0.691169\pi$
$13$	−0.480242	+	0.277268i	−0.133195	+	0.0769002i	0.431922	+	0.901911i	$0.357836\pi$
$14$		0			0
$15$	−2.41122	+	6.33747i	−0.622575	+	1.63633i
$16$		0			0
$17$	−2.91916	+	5.05613i	−0.708000	+	1.22629i	0.257598	+	0.966252i	$0.417069\pi$
$17$	−2.91916	+	5.05613i	−0.708000	+	1.22629i	−0.965598	+	0.260040i	$0.916264\pi$
$18$		0			0
$19$	−4.62434	+	2.66986i	−1.06090	+	0.612509i	−0.925680	−	0.378307i	$-0.876506\pi$
$19$	−4.62434	+	2.66986i	−1.06090	+	0.612509i	−0.135216	+	0.990816i	$0.543173\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.96965	−	1.13718i	−0.410700	−	0.237118i	0.280390	−	0.959886i	$-0.409536\pi$
$23$	−1.96965	−	1.13718i	−0.410700	−	0.237118i	−0.691090	+	0.722768i	$0.742869\pi$
$24$		0			0
$25$	−5.16291	−	8.94242i	−1.03258	−	1.78848i
$26$		0			0
$27$	−4.60867	+	2.40003i	−0.886939	+	0.461887i
$28$		0			0
$29$	3.53638	+	2.04173i	0.656690	+	0.379140i	0.791014	−	0.611797i	$-0.209553\pi$
$29$	3.53638	+	2.04173i	0.656690	+	0.379140i	−0.134325	+	0.990937i	$0.542887\pi$
$30$		0			0
$31$			8.08443i			1.45201i	0.687691	+	0.726004i	$0.258624\pi$
$31$			8.08443i			1.45201i	−0.687691	+	0.726004i	$0.741376\pi$
$32$		0			0
$33$	4.96114	−	4.04183i	0.863624	−	0.703592i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.89849	+	6.75239i	0.640909	+	1.11009i	0.985230	+	0.171235i	$0.0547756\pi$
$37$	3.89849	+	6.75239i	0.640909	+	1.11009i	−0.344322	+	0.938852i	$0.611891\pi$
$38$		0			0
$39$	0.744643	−	0.606659i	0.119238	−	0.0971432i
$40$		0			0
$41$	−3.59234	−	6.22212i	−0.561030	−	0.971732i	−0.997407	−	0.0719684i	$-0.977072\pi$
$41$	−3.59234	−	6.22212i	−0.561030	−	0.971732i	0.436377	−	0.899764i	$-0.356261\pi$
$42$		0			0
$43$	−0.754009	+	1.30598i	−0.114985	+	0.199160i	−0.917774	−	0.397103i	$-0.870015\pi$
$43$	−0.754009	+	1.30598i	−0.114985	+	0.199160i	0.802789	+	0.596264i	$0.203349\pi$
$44$		0			0
$45$	2.37374	−	11.5021i	0.353857	−	1.71463i
$46$		0			0
$47$	2.82833			0.412554			0.206277	−	0.978494i	$-0.433865\pi$
$47$	2.82833			0.412554			0.206277	+	0.978494i	$0.433865\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	3.59594	−	9.45130i	0.503533	−	1.32345i
$52$		0			0
$53$	−0.0415658	−	0.0239980i	−0.00570950	−	0.00329638i	0.497143	−	0.867669i	$-0.334383\pi$
$53$	−0.0415658	−	0.0239980i	−0.00570950	−	0.00329638i	−0.502852	+	0.864373i	$0.667716\pi$
$54$		0			0
$55$			14.4635i			1.95026i
$56$		0			0
$57$	7.17031	−	5.84164i	0.949731	−	0.773744i
$58$		0			0
$59$	8.91313			1.16039			0.580195	−	0.814477i	$-0.302976\pi$
$59$	8.91313			1.16039			0.580195	+	0.814477i	$0.302976\pi$
$60$		0			0
$61$			6.96680i			0.892008i	0.895031	+	0.446004i	$0.147153\pi$
$61$			6.96680i			0.892008i	−0.895031	+	0.446004i	$0.852847\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			2.17091i			0.269268i
$66$		0			0
$67$	1.17480			0.143525			0.0717626	−	0.997422i	$-0.477138\pi$
$67$	1.17480			0.143525			0.0717626	+	0.997422i	$0.477138\pi$
$68$		0			0
$69$	3.68181	+	1.40082i	0.443238	+	0.168639i
$70$		0			0
$71$		−	6.71061i		−	0.796403i	−0.917298	−	0.398202i	$-0.869634\pi$
$71$		−	6.71061i		−	0.796403i	0.917298	−	0.398202i	$-0.130366\pi$
$72$		0			0
$73$	3.52692	+	2.03627i	0.412795	+	0.238327i	0.691990	−	0.721907i	$-0.256734\pi$
$73$	3.52692	+	2.03627i	0.412795	+	0.238327i	−0.279195	+	0.960234i	$0.590068\pi$
$74$		0			0
$75$	11.2964	+	13.8658i	1.30440	+	1.60108i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−3.94747			−0.444125			−0.222063	−	0.975032i	$-0.571279\pi$
$79$	−3.94747			−0.444125			−0.222063	+	0.975032i	$0.571279\pi$
$80$		0			0
$81$	7.21799	−	5.37592i	0.801999	−	0.597325i
$82$		0			0
$83$	−3.84674	+	6.66275i	−0.422235	+	0.731332i	−0.996158	−	0.0875774i	$-0.972087\pi$
$83$	−3.84674	+	6.66275i	−0.422235	+	0.731332i	0.573923	+	0.818909i	$0.305421\pi$
$84$		0			0
$85$	11.4280	+	19.7938i	1.23954	+	2.14694i
$86$		0			0
$87$	−6.61047	−	2.51509i	−0.708717	−	0.269646i
$88$		0			0
$89$	2.71300	+	4.69905i	0.287577	+	0.498099i	0.973231	−	0.229829i	$-0.0738168\pi$
$89$	2.71300	+	4.69905i	0.287577	+	0.498099i	−0.685654	+	0.727928i	$0.740483\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−2.23143	−	13.8237i	−0.231389	−	1.43345i
$94$		0			0
$95$			20.9041i			2.14471i
$96$		0			0
$97$	−13.9874	−	8.07563i	−1.42021	−	0.819956i	−0.423890	−	0.905714i	$-0.639336\pi$
$97$	−13.9874	−	8.07563i	−1.42021	−	0.819956i	−0.996316	+	0.0857571i	$0.972669\pi$
$98$		0			0
$99$	−7.36753	+	8.28055i	−0.740464	+	0.832227i
$100$		0			0
$101$	−0.811750	−	1.40599i	−0.0807722	−	0.139901i	0.822810	−	0.568317i	$-0.192405\pi$
$101$	−0.811750	−	1.40599i	−0.0807722	−	0.139901i	−0.903582	+	0.428416i	$0.859072\pi$
$102$		0			0
$103$	0.342653	+	0.197831i	0.0337626	+	0.0194929i	0.516786	−	0.856114i	$-0.327128\pi$
$103$	0.342653	+	0.197831i	0.0337626	+	0.0194929i	−0.483024	+	0.875607i	$0.660461\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.90777	+	2.83350i	−0.474452	+	0.273925i	−0.718101	−	0.695938i	$-0.754989\pi$
$107$	−4.90777	+	2.83350i	−0.474452	+	0.273925i	0.243650	+	0.969863i	$0.421655\pi$
$108$		0			0
$109$	−6.75667	+	11.7029i	−0.647171	+	1.12093i	0.336624	+	0.941639i	$0.390715\pi$
$109$	−6.75667	+	11.7029i	−0.647171	+	1.12093i	−0.983795	+	0.179294i	$0.942619\pi$
$110$		0			0
$111$	−8.52987	−	10.4700i	−0.809619	−	0.993766i
$112$		0			0
$113$	1.13651	−	0.656162i	0.106913	−	0.0617265i	−0.445590	−	0.895237i	$-0.647006\pi$
$113$	1.13651	−	0.656162i	0.106913	−	0.0617265i	0.552503	+	0.833511i	$0.313673\pi$
$114$		0			0
$115$	−7.71082	+	4.45184i	−0.719038	+	0.415137i
$116$		0			0
$117$	−1.10583	+	1.24287i	−0.102234	+	0.114903i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.32489	−	2.29477i	0.120444	−	0.208615i
$122$		0			0
$123$	7.86002	+	9.64777i	0.708714	+	0.869910i
$124$		0			0
$125$	−20.8496			−1.86485
$126$		0			0
$127$	−17.3935			−1.54342			−0.771710	−	0.635975i	$-0.780598\pi$
$127$	−17.3935			−1.54342			−0.771710	+	0.635975i	$0.780598\pi$
$128$		0			0
$129$	0.928820	−	2.44124i	0.0817780	−	0.214939i
$130$		0			0
$131$	−5.45361	+	9.44593i	−0.476484	+	0.825295i	−0.999637	−	0.0269442i	$-0.991422\pi$
$131$	−5.45361	+	9.44593i	−0.476484	+	0.825295i	0.523153	+	0.852239i	$0.324756\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.884146	+	20.3228i	−0.0760952	+	1.74911i
$136$		0			0
$137$	7.62547	−	4.40257i	0.651488	−	0.376137i	−0.137538	−	0.990496i	$-0.543919\pi$
$137$	7.62547	−	4.40257i	0.651488	−	0.376137i	0.789026	+	0.614360i	$0.210586\pi$
$138$		0			0
$139$	14.2352	−	8.21869i	1.20741	−	0.697100i	0.245220	−	0.969468i	$-0.421140\pi$
$139$	14.2352	−	8.21869i	1.20741	−	0.697100i	0.962193	+	0.272367i	$0.0878066\pi$
$140$		0			0
$141$	−4.83621	+	0.780664i	−0.407282	+	0.0657438i
$142$		0			0
$143$	1.02438	−	1.77428i	0.0856631	−	0.148373i
$144$		0			0
$145$	13.8443	−	7.99301i	1.14971	−	0.663783i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	12.5814	+	7.26390i	1.03071	+	0.595082i	0.917188	−	0.398454i	$-0.130453\pi$
$149$	12.5814	+	7.26390i	1.03071	+	0.595082i	0.113523	+	0.993535i	$0.463786\pi$
$150$		0			0
$151$	−2.80307	−	4.85505i	−0.228110	−	0.395099i	0.729138	−	0.684367i	$-0.239921\pi$
$151$	−2.80307	−	4.85505i	−0.228110	−	0.395099i	−0.957248	+	0.289268i	$0.906588\pi$
$152$		0			0
$153$	−3.54005	+	17.1535i	−0.286196	+	1.38678i
$154$		0			0
$155$	27.4089	+	15.8246i	2.20154	+	1.27106i
$156$		0			0
$157$			17.8299i			1.42298i	0.702697	+	0.711489i	$0.251979\pi$
$157$			17.8299i			1.42298i	−0.702697	+	0.711489i	$0.748021\pi$
$158$		0			0
$159$	0.0776978	+	0.0295618i	0.00616184	+	0.00234440i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−0.576994	−	0.999383i	−0.0451937	−	0.0782777i	0.842544	−	0.538628i	$-0.181057\pi$
$163$	−0.576994	−	0.999383i	−0.0451937	−	0.0782777i	−0.887737	+	0.460350i	$0.847724\pi$
$164$		0			0
$165$	−3.99217	−	24.7314i	−0.310790	−	1.92534i
$166$		0			0
$167$	8.95550	+	15.5114i	0.692997	+	1.20031i	0.970851	+	0.239683i	$0.0770435\pi$
$167$	8.95550	+	15.5114i	0.692997	+	1.20031i	−0.277854	+	0.960623i	$0.589623\pi$
$168$		0			0
$169$	−6.34625	+	10.9920i	−0.488173	+	0.845540i
$170$		0			0
$171$	−10.6482	+	11.9678i	−0.814292	+	0.915203i
$172$		0			0
$173$	−7.49629			−0.569932			−0.284966	−	0.958538i	$-0.591982\pi$
$173$	−7.49629			−0.569932			−0.284966	+	0.958538i	$0.591982\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−15.2407	+	2.46017i	−1.14556	+	0.184918i
$178$		0			0
$179$	0.624382	+	0.360487i	0.0466685	+	0.0269441i	0.523153	−	0.852239i	$-0.324756\pi$
$179$	0.624382	+	0.360487i	0.0466685	+	0.0269441i	−0.476484	+	0.879183i	$0.658089\pi$
$180$		0			0
$181$		−	5.07121i		−	0.376940i	−0.982079	−	0.188470i	$-0.939647\pi$
$181$		−	5.07121i		−	0.376940i	0.982079	−	0.188470i	$-0.0603529\pi$
$182$		0			0
$183$	−1.92295	−	11.9127i	−0.142149	−	0.880609i
$184$		0			0
$185$	30.5238			2.24416
$186$		0			0
$187$		−	21.5700i		−	1.57736i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	12.7022i		−	0.919101i	−0.888152	−	0.459551i	$-0.848011\pi$
$191$		−	12.7022i		−	0.919101i	0.888152	−	0.459551i	$-0.151989\pi$
$192$		0			0
$193$	−22.8153			−1.64228			−0.821140	−	0.570726i	$-0.806662\pi$
$193$	−22.8153			−1.64228			−0.821140	+	0.570726i	$0.806662\pi$
$194$		0			0
$195$	−0.599205	−	3.71207i	−0.0429100	−	0.265827i
$196$		0			0
$197$		−	0.0311360i		−	0.00221835i	−0.999999	−	0.00110918i	$-0.999647\pi$
$197$		−	0.0311360i		−	0.00221835i	0.999999	−	0.00110918i	$-0.000353062\pi$
$198$		0			0
$199$	−19.9144	−	11.4976i	−1.41169	−	0.815042i	−0.416146	−	0.909298i	$-0.636620\pi$
$199$	−19.9144	−	11.4976i	−1.41169	−	0.815042i	−0.995548	+	0.0942556i	$0.969953\pi$
$200$		0			0
$201$	−2.00882	+	0.324265i	−0.141691	+	0.0228719i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−28.1268			−1.96446
$206$		0			0
$207$	−6.68225	−	1.37905i	−0.464448	−	0.0958506i
$208$		0			0
$209$	9.86397	−	17.0849i	0.682305	−	1.18179i
$210$		0			0
$211$	8.55841	+	14.8236i	0.589185	+	1.02050i	0.994339	+	0.106250i	$0.0338845\pi$
$211$	8.55841	+	14.8236i	0.589185	+	1.02050i	−0.405154	+	0.914248i	$0.632782\pi$
$212$		0			0
$213$	1.85224	+	11.4746i	0.126913	+	0.786226i
$214$		0			0
$215$	2.95181	+	5.11268i	0.201312	+	0.348682i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−6.59278	−	2.50836i	−0.445499	−	0.169499i
$220$		0			0
$221$		−	3.23755i		−	0.217781i
$222$		0			0
$223$	−1.25230	−	0.723016i	−0.0838602	−	0.0484167i	0.457484	−	0.889218i	$-0.348751\pi$
$223$	−1.25230	−	0.723016i	−0.0838602	−	0.0484167i	−0.541344	+	0.840801i	$0.682084\pi$
$224$		0			0
$225$	−23.1431	−	20.5913i	−1.54287	−	1.37275i
$226$		0			0
$227$	2.23596	+	3.87280i	0.148406	+	0.257047i	0.930639	−	0.365940i	$-0.119252\pi$
$227$	2.23596	+	3.87280i	0.148406	+	0.257047i	−0.782232	+	0.622987i	$0.785919\pi$
$228$		0			0
$229$	−2.24072	−	1.29368i	−0.148071	−	0.0854888i	0.424134	−	0.905599i	$-0.360579\pi$
$229$	−2.24072	−	1.29368i	−0.148071	−	0.0854888i	−0.572205	+	0.820111i	$0.693912\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	15.0756	−	8.70389i	0.987634	−	0.570211i	0.0830679	−	0.996544i	$-0.473528\pi$
$233$	15.0756	−	8.70389i	0.987634	−	0.570211i	0.904566	+	0.426333i	$0.140195\pi$
$234$		0			0
$235$	5.53620	−	9.58898i	0.361142	−	0.625516i
$236$		0			0
$237$	6.74985	−	1.08957i	0.438450	−	0.0707750i
$238$		0			0
$239$	4.23642	−	2.44590i	0.274031	−	0.158212i	−0.356687	−	0.934224i	$-0.616094\pi$
$239$	4.23642	−	2.44590i	0.274031	−	0.158212i	0.630718	+	0.776012i	$0.282760\pi$
$240$		0			0
$241$	−7.04282	+	4.06618i	−0.453668	+	0.261925i	−0.709378	−	0.704828i	$-0.751024\pi$
$241$	−7.04282	+	4.06618i	−0.453668	+	0.261925i	0.255710	+	0.966754i	$0.417691\pi$
$242$		0			0
$243$	−10.8583	+	11.1847i	−0.696562	+	0.717497i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.48053	−	2.56436i	0.0942041	−	0.163166i
$248$		0			0
$249$	4.73858	−	12.4545i	0.300295	−	0.789272i
$250$		0			0
$251$	25.9341			1.63694			0.818472	−	0.574546i	$-0.194821\pi$
$251$	25.9341			1.63694			0.818472	+	0.574546i	$0.194821\pi$
$252$		0			0
$253$	8.40274			0.528276
$254$		0			0
$255$	−25.0043	−	30.6915i	−1.56583	−	1.92198i
$256$		0			0
$257$	−15.4115	+	26.6935i	−0.961344	+	1.66510i	−0.242213	+	0.970223i	$0.577873\pi$
$257$	−15.4115	+	26.6935i	−0.961344	+	1.66510i	−0.719131	+	0.694874i	$0.755460\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	11.9976	+	2.47600i	0.742630	+	0.153261i
$262$		0			0
$263$	−15.6625	+	9.04276i	−0.965792	+	0.557600i	−0.897951	−	0.440096i	$-0.854944\pi$
$263$	−15.6625	+	9.04276i	−0.965792	+	0.557600i	−0.0678413	+	0.997696i	$0.521611\pi$
$264$		0			0
$265$	−0.162723	+	0.0939479i	−0.00999597	+	0.00577117i
$266$		0			0
$267$	−5.93602	−	7.28616i	−0.363278	−	0.445906i
$268$		0			0
$269$	10.8203	−	18.7413i	0.659725	−	1.14268i	−0.320961	−	0.947092i	$-0.604006\pi$
$269$	10.8203	−	18.7413i	0.659725	−	1.14268i	0.980687	−	0.195585i	$-0.0626607\pi$
$270$		0			0
$271$	12.3453	−	7.12756i	0.749923	−	0.432968i	−0.0757430	−	0.997127i	$-0.524133\pi$
$271$	12.3453	−	7.12756i	0.749923	−	0.432968i	0.825666	+	0.564159i	$0.190800\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	33.0383	+	19.0747i	1.99229	+	1.15025i
$276$		0			0
$277$	−4.40164	−	7.62386i	−0.264469	−	0.458073i	0.702956	−	0.711234i	$-0.251863\pi$
$277$	−4.40164	−	7.62386i	−0.264469	−	0.458073i	−0.967424	+	0.253160i	$0.918530\pi$
$278$		0			0
$279$	7.63113	+	23.0215i	0.456864	+	1.37826i
$280$		0			0
$281$	−16.6889	−	9.63537i	−0.995579	−	0.574798i	−0.0886417	−	0.996064i	$-0.528253\pi$
$281$	−16.6889	−	9.63537i	−0.995579	−	0.574798i	−0.906937	+	0.421266i	$0.861586\pi$
$282$		0			0
$283$			9.61660i			0.571647i	0.958282	+	0.285824i	$0.0922672\pi$
$283$			9.61660i			0.571647i	−0.958282	+	0.285824i	$0.907733\pi$
$284$		0			0
$285$	−5.76987	−	35.7442i	−0.341777	−	2.11731i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−8.54297	−	14.7969i	−0.502528	−	0.870404i
$290$		0			0
$291$	26.1463	+	9.94791i	1.53272	+	0.583157i
$292$		0			0
$293$	−1.22598	−	2.12346i	−0.0716225	−	0.124054i	0.827990	−	0.560743i	$-0.189484\pi$
$293$	−1.22598	−	2.12346i	−0.0716225	−	0.124054i	−0.899613	+	0.436689i	$0.856151\pi$
$294$		0			0
$295$	17.4467	−	30.2185i	1.01578	−	1.75939i
$296$		0			0
$297$	10.3123	−	16.1926i	0.598380	−	0.939590i
$298$		0			0
$299$	1.26121			0.0729376
$300$		0			0
$301$		0			0
$302$		0			0
$303$	1.77610	+	2.18007i	0.102034	+	0.125242i
$304$		0			0
$305$	23.6198	+	13.6369i	1.35247	+	0.780846i
$306$		0			0
$307$		−	10.6839i		−	0.609760i	−0.952391	−	0.304880i	$-0.901384\pi$
$307$		−	10.6839i		−	0.609760i	0.952391	−	0.304880i	$-0.0986163\pi$
$308$		0			0
$309$	−0.640513	−	0.243697i	−0.0364375	−	0.0138634i
$310$		0			0
$311$	20.7665			1.17756			0.588780	−	0.808293i	$-0.299608\pi$
$311$	20.7665			1.17756			0.588780	+	0.808293i	$0.299608\pi$
$312$		0			0
$313$			3.93117i			0.222203i	0.993809	+	0.111101i	$0.0354378\pi$
$313$			3.93117i			0.222203i	−0.993809	+	0.111101i	$0.964562\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			2.29057i			0.128651i	0.997929	+	0.0643256i	$0.0204896\pi$
$317$			2.29057i			0.128651i	−0.997929	+	0.0643256i	$0.979510\pi$
$318$		0			0
$319$	−15.0866			−0.844687
$320$		0			0
$321$	7.60978	−	6.19967i	0.424736	−	0.346032i
$322$		0			0
$323$		−	31.1750i		−	1.73462i
$324$		0			0
$325$	4.95889	+	2.86302i	0.275070	+	0.158812i
$326$		0			0
$327$	8.32315	−	21.8759i	0.460271	−	1.20974i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	6.93577			0.381224			0.190612	−	0.981665i	$-0.438953\pi$
$331$	6.93577			0.381224			0.190612	+	0.981665i	$0.438953\pi$
$332$		0			0
$333$	17.4753	+	15.5484i	0.957638	+	0.852047i
$334$		0			0
$335$	2.29957	−	3.98298i	0.125639	−	0.217613i
$336$		0			0
$337$	−9.59771	−	16.6237i	−0.522821	−	0.905552i	−0.999647	−	0.0265545i	$-0.991546\pi$
$337$	−9.59771	−	16.6237i	−0.522821	−	0.905552i	0.476827	−	0.878997i	$-0.341787\pi$
$338$		0			0
$339$	−1.76222	+	1.43568i	−0.0957106	+	0.0779752i
$340$		0			0
$341$	−14.9342	−	25.8668i	−0.808733	−	1.40077i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	11.9561	−	9.74059i	0.643694	−	0.524416i
$346$		0			0
$347$			8.49036i			0.455786i	0.973686	+	0.227893i	$0.0731837\pi$
$347$			8.49036i			0.455786i	−0.973686	+	0.227893i	$0.926816\pi$
$348$		0			0
$349$	16.5478	+	9.55386i	0.885782	+	0.511407i	0.872560	−	0.488506i	$-0.162458\pi$
$349$	16.5478	+	9.55386i	0.885782	+	0.511407i	0.0132216	+	0.999913i	$0.495791\pi$
$350$		0			0
$351$	1.54782	−	2.43043i	0.0826167	−	0.129727i
$352$		0			0
$353$	−6.82951	−	11.8291i	−0.363498	−	0.629597i	0.625036	−	0.780596i	$-0.285084\pi$
$353$	−6.82951	−	11.8291i	−0.363498	−	0.629597i	−0.988534	+	0.150999i	$0.951751\pi$
$354$		0			0
$355$	−22.7512	−	13.1354i	−1.20751	−	0.697156i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−14.8909	+	8.59724i	−0.785909	+	0.453745i	−0.838520	−	0.544870i	$-0.816579\pi$
$359$	−14.8909	+	8.59724i	−0.785909	+	0.453745i	0.0526113	+	0.998615i	$0.483246\pi$
$360$		0			0
$361$	4.75635	−	8.23824i	0.250334	−	0.433592i
$362$		0			0
$363$	−1.63205	+	4.28955i	−0.0856604	+	0.225143i
$364$		0			0
$365$	13.8073	−	7.97162i	0.722705	−	0.417254i
$366$		0			0
$367$	−14.6001	+	8.42936i	−0.762118	+	0.440009i	−0.830056	−	0.557680i	$-0.811691\pi$
$367$	−14.6001	+	8.42936i	−0.762118	+	0.440009i	0.0679376	+	0.997690i	$0.478358\pi$
$368$		0			0
$369$	−16.1029	−	14.3274i	−0.838284	−	0.745854i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	0.704288	−	1.21986i	0.0364667	−	0.0631621i	−0.847216	−	0.531248i	$-0.821723\pi$
$373$	0.704288	−	1.21986i	0.0364667	−	0.0631621i	0.883683	+	0.468086i	$0.155056\pi$
$374$		0			0
$375$	35.6511	−	5.75484i	1.84102	−	0.297179i
$376$		0			0
$377$	−2.26442			−0.116624
$378$		0			0
$379$	−0.598572			−0.0307466			−0.0153733	−	0.999882i	$-0.504894\pi$
$379$	−0.598572			−0.0307466			−0.0153733	+	0.999882i	$0.504894\pi$
$380$		0			0
$381$	29.7414	−	4.80088i	1.52370	−	0.245956i
$382$		0			0
$383$	4.26039	−	7.37921i	0.217696	−	0.377060i	−0.736407	−	0.676538i	$-0.763479\pi$
$383$	4.26039	−	7.37921i	0.217696	−	0.377060i	0.954103	+	0.299478i	$0.0968127\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.914384	+	4.43068i	−0.0464807	+	0.225224i
$388$		0			0
$389$	−29.9624	+	17.2988i	−1.51915	+	0.877084i	−0.519409	+	0.854526i	$0.673848\pi$
$389$	−29.9624	+	17.2988i	−1.51915	+	0.877084i	−0.999746	+	0.0225587i	$0.992819\pi$
$390$		0			0
$391$	11.4994	−	6.63920i	0.581551	−	0.335759i
$392$		0			0
$393$	6.71799	−	17.6570i	0.338878	−	0.890680i
$394$		0			0
$395$	−7.72683	+	13.3833i	−0.388779	+	0.673385i
$396$		0			0
$397$	−27.9571	+	16.1411i	−1.40313	+	0.810097i	−0.994712	−	0.102699i	$-0.967252\pi$
$397$	−27.9571	+	16.1411i	−1.40313	+	0.810097i	−0.408416	+	0.912796i	$0.633919\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	11.3473	+	6.55139i	0.566659	+	0.327161i	0.755814	−	0.654787i	$-0.227242\pi$
$401$	11.3473	+	6.55139i	0.566659	+	0.327161i	−0.189155	+	0.981947i	$0.560575\pi$
$402$		0			0
$403$	−2.24155	−	3.88248i	−0.111660	−	0.193400i
$404$		0			0
$405$	−4.09760	−	34.9943i	−0.203611	−	1.73888i
$406$		0			0
$407$	−24.9471	−	14.4032i	−1.23658	−	0.713941i
$408$		0			0
$409$		−	37.3538i		−	1.84703i	−0.383568	−	0.923513i	$-0.625305\pi$
$409$		−	37.3538i		−	1.84703i	0.383568	−	0.923513i	$-0.374695\pi$
$410$		0			0
$411$	−11.8237	+	9.63278i	−0.583222	+	0.475150i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	15.0593	+	26.0835i	0.739232	+	1.28039i
$416$		0			0
$417$	−22.0725	+	17.9824i	−1.08089	+	0.880603i
$418$		0			0
$419$	−14.1954	−	24.5871i	−0.693490	−	1.20116i	−0.970687	−	0.240346i	$-0.922739\pi$
$419$	−14.1954	−	24.5871i	−0.693490	−	1.20116i	0.277198	−	0.960813i	$-0.410594\pi$
$420$		0			0
$421$	−17.3359	+	30.0267i	−0.844901	+	1.46341i	0.0408054	+	0.999167i	$0.487008\pi$
$421$	−17.3359	+	30.0267i	−0.844901	+	1.46341i	−0.885707	+	0.464245i	$0.846326\pi$
$422$		0			0
$423$	8.05403	−	2.66974i	0.391600	−	0.129807i
$424$		0			0
$425$	60.2854			2.92427
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−1.26188	+	3.31662i	−0.0609240	+	0.160128i
$430$		0			0
$431$	13.1844	+	7.61200i	0.635069	+	0.366657i	0.782713	−	0.622383i	$-0.213835\pi$
$431$	13.1844	+	7.61200i	0.635069	+	0.366657i	−0.147643	+	0.989041i	$0.547169\pi$
$432$		0			0
$433$			3.97041i			0.190806i	0.995439	+	0.0954028i	$0.0304139\pi$
$433$			3.97041i			0.190806i	−0.995439	+	0.0954028i	$0.969586\pi$
$434$		0			0
$435$	−21.4664	+	17.4886i	−1.02924	+	0.838516i
$436$		0			0
$437$	12.1444			0.580947
$438$		0			0
$439$			9.49060i			0.452962i	0.974016	+	0.226481i	$0.0727221\pi$
$439$			9.49060i			0.452962i	−0.974016	+	0.226481i	$0.927278\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	32.7883i		−	1.55782i	−0.627135	−	0.778910i	$-0.715773\pi$
$443$		−	32.7883i		−	1.55782i	0.627135	−	0.778910i	$-0.284227\pi$
$444$		0			0
$445$	21.2418			1.00696
$446$		0			0
$447$	−23.5182	−	8.94798i	−1.11237	−	0.423225i
$448$		0			0
$449$			0.658896i			0.0310952i	0.999879	+	0.0155476i	$0.00494916\pi$
$449$			0.658896i			0.0310952i	−0.999879	+	0.0155476i	$0.995051\pi$
$450$		0			0
$451$	22.9880	+	13.2721i	1.08246	+	0.624960i
$452$		0			0
$453$	6.13308	+	7.52804i	0.288157	+	0.353698i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	15.8903			0.743316			0.371658	−	0.928370i	$-0.378789\pi$
$457$	15.8903			0.743316			0.371658	+	0.928370i	$0.378789\pi$
$458$		0			0
$459$	1.31856	−	30.3081i	0.0615451	−	1.41466i
$460$		0			0
$461$	9.81626	−	17.0023i	0.457189	−	0.791874i	−0.541622	−	0.840622i	$-0.682190\pi$
$461$	9.81626	−	17.0023i	0.457189	−	0.791874i	0.998811	+	0.0487477i	$0.0155230\pi$
$462$		0			0
$463$	0.600159	+	1.03951i	0.0278918	+	0.0483099i	0.879634	−	0.475651i	$-0.157787\pi$
$463$	0.600159	+	1.03951i	0.0278918	+	0.0483099i	−0.851743	+	0.523960i	$0.824454\pi$
$464$		0			0
$465$	−51.2348	−	19.4934i	−2.37596	−	0.903983i
$466$		0			0
$467$	−19.2809	−	33.3955i	−0.892213	−	1.54536i	−0.837216	−	0.546872i	$-0.815818\pi$
$467$	−19.2809	−	33.3955i	−0.892213	−	1.54536i	−0.0549972	−	0.998487i	$-0.517515\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−4.92133	−	30.4876i	−0.226763	−	1.40479i
$472$		0			0
$473$		−	5.57146i		−	0.256176i
$474$		0			0
$475$	47.7501	+	27.5685i	2.19093	+	1.26493i
$476$		0			0
$477$	−0.141016	−	0.0291023i	−0.00645670	−	0.00133250i
$478$		0			0
$479$	3.61289	+	6.25771i	0.165077	+	0.285922i	0.936683	−	0.350179i	$-0.113879\pi$
$479$	3.61289	+	6.25771i	0.165077	+	0.285922i	−0.771606	+	0.636101i	$0.780546\pi$
$480$		0			0
$481$	−3.74444	−	2.16185i	−0.170732	−	0.0985720i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−54.7582	+	31.6147i	−2.48644	+	1.43555i
$486$		0			0
$487$	4.85770	−	8.41378i	0.220123	−	0.381265i	−0.734722	−	0.678368i	$-0.762687\pi$
$487$	4.85770	−	8.41378i	0.220123	−	0.381265i	0.954845	+	0.297104i	$0.0960207\pi$
$488$		0			0
$489$	1.26246	+	1.54960i	0.0570903	+	0.0700754i
$490$		0			0
$491$	17.2480	−	9.95814i	0.778392	−	0.449405i	−0.0574682	−	0.998347i	$-0.518303\pi$
$491$	17.2480	−	9.95814i	0.778392	−	0.449405i	0.835860	+	0.548943i	$0.184969\pi$
$492$		0			0
$493$	−20.6465	+	11.9203i	−0.929872	+	0.536862i
$494$		0			0
$495$	13.6526	+	41.1868i	0.613637	+	1.85121i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−17.1920	+	29.7774i	−0.769619	+	1.33302i	0.168150	+	0.985761i	$0.446221\pi$
$499$	−17.1920	+	29.7774i	−0.769619	+	1.33302i	−0.937770	+	0.347258i	$0.887113\pi$
$500$		0			0
$501$	−19.5945	−	24.0513i	−0.875420	−	1.07453i
$502$		0			0
$503$	−1.22542			−0.0546388			−0.0273194	−	0.999627i	$-0.508697\pi$
$503$	−1.22542			−0.0546388			−0.0273194	+	0.999627i	$0.508697\pi$
$504$		0			0
$505$	−6.35571			−0.282826
$506$		0			0
$507$	7.81758	−	20.5471i	0.347191	−	0.912529i
$508$		0			0
$509$	−5.05078	+	8.74820i	−0.223872	+	0.387757i	−0.955980	−	0.293431i	$-0.905203\pi$
$509$	−5.05078	+	8.74820i	−0.223872	+	0.387757i	0.732109	+	0.681188i	$0.238536\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	14.9043	−	23.4031i	0.658041	−	1.03327i
$514$		0			0
$515$	1.34143	−	0.774473i	0.0591103	−	0.0341274i
$516$		0			0
$517$	−9.04947	+	5.22471i	−0.397995	+	0.229783i
$518$		0			0
$519$	12.8180	−	2.06910i	0.562649	−	0.0908233i
$520$		0			0
$521$	−10.5390	+	18.2541i	−0.461723	+	0.799728i	−0.999047	−	0.0436480i	$-0.986102\pi$
$521$	−10.5390	+	18.2541i	−0.461723	+	0.799728i	0.537324	+	0.843376i	$0.319435\pi$
$522$		0			0
$523$	−17.0733	+	9.85727i	−0.746563	+	0.431028i	−0.824451	−	0.565934i	$-0.808516\pi$
$523$	−17.0733	+	9.85727i	−0.746563	+	0.431028i	0.0778877	+	0.996962i	$0.475182\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−40.8760	−	23.5997i	−1.78058	−	1.02802i
$528$		0			0
$529$	−8.91366	−	15.4389i	−0.387550	−	0.671257i
$530$		0			0
$531$	25.3813	−	8.41336i	1.10145	−	0.365109i
$532$		0			0
$533$	3.45039	+	1.99208i	0.149453	+	0.0862866i
$534$		0			0
$535$			22.1853i			0.959154i
$536$		0			0
$537$	−1.16714	−	0.444063i	−0.0503658	−	0.0191627i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−4.22475	−	7.31748i	−0.181636	−	0.314603i	0.760802	−	0.648984i	$-0.224806\pi$
$541$	−4.22475	−	7.31748i	−0.181636	−	0.314603i	−0.942438	+	0.334381i	$0.891473\pi$
$542$		0			0
$543$	1.39974	+	8.67135i	0.0600685	+	0.372123i
$544$		0			0
$545$	26.4511	+	45.8147i	1.13304	+	1.96249i
$546$		0			0
$547$	−4.02889	+	6.97824i	−0.172263	+	0.298368i	−0.939211	−	0.343342i	$-0.888441\pi$
$547$	−4.02889	+	6.97824i	−0.172263	+	0.298368i	0.766948	+	0.641709i	$0.221774\pi$
$548$		0			0
$549$	6.57617	+	19.8389i	0.280664	+	0.846703i
$550$		0			0
$551$	−21.8046			−0.928906
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−52.1932	+	8.42507i	−2.21548	+	0.357624i
$556$		0			0
$557$	−18.2294	−	10.5247i	−0.772403	−	0.445947i	0.0613279	−	0.998118i	$-0.480466\pi$
$557$	−18.2294	−	10.5247i	−0.772403	−	0.445947i	−0.833731	+	0.552170i	$0.813800\pi$
$558$		0			0
$559$		−	0.836249i		−	0.0353696i
$560$		0			0
$561$	5.95367	+	36.8829i	0.251364	+	1.55720i
$562$		0			0
$563$	−41.2821			−1.73983			−0.869916	−	0.493200i	$-0.835827\pi$
$563$	−41.2821			−1.73983			−0.869916	+	0.493200i	$0.835827\pi$
$564$		0			0
$565$		−	5.13751i		−	0.216137i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			36.1064i			1.51366i	0.653612	+	0.756829i	$0.273253\pi$
$569$			36.1064i			1.51366i	−0.653612	+	0.756829i	$0.726747\pi$
$570$		0			0
$571$	−19.2422			−0.805262			−0.402631	−	0.915362i	$-0.631904\pi$
$571$	−19.2422			−0.805262			−0.402631	+	0.915362i	$0.631904\pi$
$572$		0			0
$573$	3.50602	+	21.7198i	0.146466	+	0.907356i
$574$		0			0
$575$			23.4846i			0.979375i
$576$		0			0
$577$	25.8102	+	14.9015i	1.07449	+	0.620359i	0.929406	−	0.369060i	$-0.120320\pi$
$577$	25.8102	+	14.9015i	1.07449	+	0.620359i	0.145088	+	0.989419i	$0.453654\pi$
$578$		0			0
$579$	39.0123	−	6.29739i	1.62129	−	0.261711i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.177324			0.00734402
$584$		0			0
$585$	2.04918	+	6.18194i	0.0847233	+	0.255592i
$586$		0			0
$587$	−4.72218	+	8.17905i	−0.194905	+	0.337586i	−0.946869	−	0.321618i	$-0.895773\pi$
$587$	−4.72218	+	8.17905i	−0.194905	+	0.337586i	0.751964	+	0.659204i	$0.229107\pi$
$588$		0			0
$589$	−21.5843	−	37.3852i	−0.889367	−	1.54043i
$590$		0			0
$591$	0.00859405	+	0.0532400i	0.000353512	+	0.00219000i
$592$		0			0
$593$	−12.4176	−	21.5079i	−0.509929	−	0.883223i	−0.999934	−	0.0115033i	$-0.996338\pi$
$593$	−12.4176	−	21.5079i	−0.509929	−	0.883223i	0.490005	−	0.871720i	$-0.336995\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	37.2255	+	14.1632i	1.52354	+	0.579662i
$598$		0			0
$599$			11.8995i			0.486199i	0.970001	+	0.243100i	$0.0781642\pi$
$599$			11.8995i			0.486199i	−0.970001	+	0.243100i	$0.921836\pi$
$600$		0			0
$601$	−22.1276	−	12.7754i	−0.902604	−	0.521118i	−0.0245596	−	0.999698i	$-0.507818\pi$
$601$	−22.1276	−	12.7754i	−0.902604	−	0.521118i	−0.878044	+	0.478580i	$0.841152\pi$
$602$		0			0
$603$	3.34541	−	1.10893i	0.136236	−	0.0451592i
$604$		0			0
$605$	−5.18669	−	8.98361i	−0.210869	−	0.365236i
$606$		0			0
$607$	19.5544	+	11.2897i	0.793687	+	0.458235i	0.841259	−	0.540632i	$-0.181815\pi$
$607$	19.5544	+	11.2897i	0.793687	+	0.458235i	−0.0475718	+	0.998868i	$0.515148\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.35828	+	0.784204i	−0.0549502	+	0.0317255i
$612$		0			0
$613$	−11.4294	+	19.7963i	−0.461628	+	0.799564i	−0.999042	−	0.0437549i	$-0.986068\pi$
$613$	−11.4294	+	19.7963i	−0.461628	+	0.799564i	0.537414	+	0.843319i	$0.319401\pi$
$614$		0			0
$615$	48.0944	−	7.76344i	1.93935	−	0.313052i
$616$		0			0
$617$	1.78792	−	1.03226i	0.0719791	−	0.0415572i	−0.463578	−	0.886056i	$-0.653435\pi$
$617$	1.78792	−	1.03226i	0.0719791	−	0.0415572i	0.535558	+	0.844499i	$0.320101\pi$
$618$		0			0
$619$	28.2233	−	16.2947i	1.13439	−	0.654940i	0.189354	−	0.981909i	$-0.439361\pi$
$619$	28.2233	−	16.2947i	1.13439	−	0.654940i	0.945035	+	0.326969i	$0.106027\pi$
$620$		0			0
$621$	11.8067	+	0.513653i	0.473787	+	0.0206122i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−14.9967	+	25.9751i	−0.599870	+	1.03901i
$626$		0			0
$627$	−12.1509	+	31.9364i	−0.485259	+	1.27542i
$628$		0			0
$629$	−45.5213			−1.81505
$630$		0			0
$631$	38.4706			1.53149			0.765744	−	0.643145i	$-0.222371\pi$
$631$	38.4706			1.53149			0.765744	+	0.643145i	$0.222371\pi$
$632$		0			0
$633$	−18.7257	−	22.9849i	−0.744281	−	0.913566i
$634$		0			0
$635$	−34.0461	+	58.9696i	−1.35108	+	2.34014i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−6.33434	−	19.1093i	−0.250583	−	0.755954i
$640$		0			0
$641$	41.3645	−	23.8818i	1.63380	−	0.943274i	0.650892	−	0.759170i	$-0.274395\pi$
$641$	41.3645	−	23.8818i	1.63380	−	0.943274i	0.982907	−	0.184104i	$-0.0589384\pi$
$642$		0			0
$643$	−29.2346	+	16.8786i	−1.15290	+	0.665626i	−0.949592	−	0.313489i	$-0.898502\pi$
$643$	−29.2346	+	16.8786i	−1.15290	+	0.665626i	−0.203306	+	0.979115i	$0.565169\pi$
$644$		0			0
$645$	−6.45853	−	7.92752i	−0.254304	−	0.312146i
$646$		0			0
$647$	−0.536008	+	0.928393i	−0.0210727	+	0.0364989i	−0.876369	−	0.481640i	$-0.840041\pi$
$647$	−0.536008	+	0.928393i	−0.0210727	+	0.0364989i	0.855297	+	0.518138i	$0.173375\pi$
$648$		0			0
$649$	−28.5183	+	16.4650i	−1.11944	+	0.646309i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	28.8503	+	16.6567i	1.12900	+	0.651828i	0.943683	−	0.330851i	$-0.107336\pi$
$653$	28.8503	+	16.6567i	1.12900	+	0.651828i	0.185317	+	0.982679i	$0.440669\pi$
$654$		0			0
$655$	21.3499	+	36.9791i	0.834210	+	1.44489i
$656$		0			0
$657$	11.9654	+	2.46937i	0.466817	+	0.0963394i
$658$		0			0
$659$	−8.41890	−	4.86065i	−0.327954	−	0.189344i	0.326979	−	0.945032i	$-0.393969\pi$
$659$	−8.41890	−	4.86065i	−0.327954	−	0.189344i	−0.654932	+	0.755688i	$0.727303\pi$
$660$		0			0
$661$			17.0729i			0.664060i	0.943269	+	0.332030i	$0.107734\pi$
$661$			17.0729i			0.664060i	−0.943269	+	0.332030i	$0.892266\pi$
$662$		0			0
$663$	0.893617	+	5.53595i	0.0347052	+	0.214998i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−4.64362	−	8.04298i	−0.179802	−	0.311426i
$668$		0			0
$669$	2.34089	+	0.890642i	0.0905041	+	0.0344342i
$670$		0			0
$671$	−12.8696	−	22.2909i	−0.496827	−	0.860529i
$672$		0			0
$673$	−18.3359	+	31.7588i	−0.706798	+	1.22421i	0.259240	+	0.965813i	$0.416528\pi$
$673$	−18.3359	+	31.7588i	−0.706798	+	1.22421i	−0.966039	+	0.258398i	$0.916805\pi$
$674$		0			0
$675$	45.2563	+	28.8215i	1.74191	+	1.10934i
$676$		0			0
$677$	40.3538			1.55092			0.775461	−	0.631395i	$-0.217517\pi$
$677$	40.3538			1.55092			0.775461	+	0.631395i	$0.217517\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−4.89227	−	6.00501i	−0.187472	−	0.230112i
$682$		0			0
$683$	8.23662	+	4.75541i	0.315165	+	0.181961i	0.649236	−	0.760587i	$-0.275089\pi$
$683$	8.23662	+	4.75541i	0.315165	+	0.181961i	−0.334070	+	0.942548i	$0.608422\pi$
$684$		0			0
$685$		−	34.4705i		−	1.31705i
$686$		0			0
$687$	4.18852	+	1.59361i	0.159802	+	0.0608000i
$688$		0			0
$689$	0.0266155			0.00101397
$690$		0			0
$691$		−	7.70784i		−	0.293220i	−0.989194	−	0.146610i	$-0.953164\pi$
$691$		−	7.70784i		−	0.293220i	0.989194	−	0.146610i	$-0.0468363\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	64.3494i		−	2.44091i
$696$		0			0
$697$	41.9465			1.58884
$698$		0			0
$699$	−23.3756	+	19.0440i	−0.884145	+	0.720311i
$700$		0			0
$701$			15.6388i			0.590671i	0.955394	+	0.295336i	$0.0954314\pi$
$701$			15.6388i			0.590671i	−0.955394	+	0.295336i	$0.904569\pi$
$702$		0			0
$703$	−36.0559	−	20.8169i	−1.35988	−	0.785124i
$704$		0			0
$705$	−6.81973	+	17.9244i	−0.256846	+	0.675073i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	13.4405			0.504769			0.252384	−	0.967627i	$-0.418785\pi$
$709$	13.4405			0.504769			0.252384	+	0.967627i	$0.418785\pi$
$710$		0			0
$711$	−11.2409	+	3.72614i	−0.421568	+	0.139741i
$712$		0			0
$713$	9.19343	−	15.9235i	0.344297	−	0.596339i
$714$		0			0
$715$	−4.01027	−	6.94599i	−0.149976	−	0.259765i
$716$		0			0
$717$	−6.56881	+	5.35160i	−0.245317	+	0.199859i
$718$		0			0
$719$	−20.0309	−	34.6946i	−0.747027	−	1.29389i	−0.949242	−	0.314548i	$-0.898147\pi$
$719$	−20.0309	−	34.6946i	−0.747027	−	1.29389i	0.202214	−	0.979341i	$-0.435186\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	10.9203	−	8.89675i	0.406131	−	0.330874i
$724$		0			0
$725$		−	42.1651i		−	1.56597i
$726$		0			0
$727$	−43.2091	−	24.9468i	−1.60254	−	0.925225i	−0.990978	−	0.134027i	$-0.957209\pi$
$727$	−43.2091	−	24.9468i	−1.60254	−	0.925225i	−0.611560	−	0.791198i	$-0.709458\pi$
$728$		0			0
$729$	15.4797	−	22.1219i	0.573322	−	0.819330i
$730$		0			0
$731$	−4.40214	−	7.62473i	−0.162819	−	0.282011i
$732$		0			0
$733$	9.91430	+	5.72402i	0.366193	+	0.211422i	0.671794	−	0.740738i	$-0.265524\pi$
$733$	9.91430	+	5.72402i	0.366193	+	0.211422i	−0.305601	+	0.952160i	$0.598857\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.75888	+	2.17019i	−0.138460	+	0.0799400i
$738$		0			0
$739$	4.46303	−	7.73020i	0.164175	−	0.284360i	−0.772187	−	0.635396i	$-0.780837\pi$
$739$	4.46303	−	7.73020i	0.164175	−	0.284360i	0.936362	+	0.351036i	$0.114170\pi$
$740$		0			0
$741$	−1.82378	+	4.79349i	−0.0669984	+	0.176093i
$742$		0			0
$743$	−45.8621	+	26.4785i	−1.68252	+	0.971403i	−0.722540	+	0.691329i	$0.757026\pi$
$743$	−45.8621	+	26.4785i	−1.68252	+	0.971403i	−0.959979	+	0.280074i	$0.909641\pi$
$744$		0			0
$745$	49.2541	−	28.4369i	1.80453	−	1.04185i
$746$		0			0
$747$	−4.66493	+	22.6041i	−0.170681	+	0.827041i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	13.2326	−	22.9195i	0.482865	−	0.836346i	−0.516942	−	0.856021i	$-0.672930\pi$
$751$	13.2326	−	22.9195i	0.482865	−	0.836346i	0.999806	+	0.0196744i	$0.00626295\pi$
$752$		0			0
$753$	−44.3451	+	7.15823i	−1.61603	+	0.260860i
$754$		0			0
$755$	−21.9470			−0.798733
$756$		0			0
$757$	8.46749			0.307756			0.153878	−	0.988090i	$-0.450824\pi$
$757$	8.46749			0.307756			0.153878	+	0.988090i	$0.450824\pi$
$758$		0			0
$759$	−14.3680	+	2.31929i	−0.521525	+	0.0841849i
$760$		0			0
$761$	26.9968	−	46.7599i	0.978635	−	1.69505i	0.311258	−	0.950325i	$-0.399250\pi$
$761$	26.9968	−	46.7599i	0.978635	−	1.69505i	0.667377	−	0.744720i	$-0.267417\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	51.2267	+	45.5783i	1.85210	+	1.64789i
$766$		0			0
$767$	−4.28046	+	2.47132i	−0.154558	+	0.0892343i
$768$		0			0
$769$	−30.1912	+	17.4309i	−1.08872	+	0.628575i	−0.933236	−	0.359263i	$-0.883028\pi$
$769$	−30.1912	+	17.4309i	−1.08872	+	0.628575i	−0.155487	+	0.987838i	$0.549695\pi$
$770$		0			0
$771$	18.9846	−	49.8976i	0.683713	−	1.79702i
$772$		0			0
$773$	1.06375	−	1.84246i	0.0382603	−	0.0662688i	−0.846261	−	0.532768i	$-0.821152\pi$
$773$	1.06375	−	1.84246i	0.0382603	−	0.0662688i	0.884521	+	0.466499i	$0.154485\pi$
$774$		0			0
$775$	72.2944	−	41.7392i	2.59689	−	1.49932i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	33.2244	+	19.1821i	1.19039	+	0.687272i
$780$		0			0
$781$	12.3964	+	21.4712i	0.443577	+	0.768298i
$782$		0			0
$783$	−21.1982	−	0.922233i	−0.757563	−	0.0329579i
$784$		0			0
$785$	60.4492	+	34.9004i	2.15752	+	1.24565i
$786$		0			0
$787$		−	28.3429i		−	1.01032i	−0.863027	−	0.505158i	$-0.831434\pi$
$787$		−	28.3429i		−	1.01032i	0.863027	−	0.505158i	$-0.168566\pi$
$788$		0			0
$789$	24.2856	−	19.7855i	0.864592	−	0.704381i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−1.93167	−	3.34575i	−0.0685956	−	0.118811i
$794$		0			0
$795$	0.252311	−	0.205557i	0.00894854	−	0.00729036i
$796$		0			0
$797$	18.9123	+	32.7570i	0.669907	+	1.16031i	0.977930	+	0.208935i	$0.0669996\pi$
$797$	18.9123	+	32.7570i	0.669907	+	1.16031i	−0.308022	+	0.951379i	$0.599667\pi$
$798$		0			0
$799$	−8.25634	+	14.3004i	−0.292088	+	0.505912i
$800$		0			0
$801$	12.1612	+	10.8203i	0.429695	+	0.382316i
$802$		0			0
$803$	−15.0462			−0.530970
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−13.3289	+	35.0327i	−0.469200	+	1.23321i
$808$		0			0
$809$	39.2475	+	22.6595i	1.37987	+	0.796667i	0.992143	−	0.125109i	$-0.0399280\pi$
$809$	39.2475	+	22.6595i	1.37987	+	0.796667i	0.387724	+	0.921776i	$0.373261\pi$
$810$		0			0
$811$		−	5.45145i		−	0.191426i	−0.995409	−	0.0957132i	$-0.969487\pi$
$811$		−	5.45145i		−	0.191426i	0.995409	−	0.0957132i	$-0.0305132\pi$
$812$		0			0
$813$	−19.1421	+	15.5950i	−0.671343	+	0.546942i
$814$		0			0
$815$	−4.51766			−0.158247
$816$		0			0
$817$		−	8.05240i		−	0.281718i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	49.3196i		−	1.72127i	−0.509225	−	0.860634i	$-0.670068\pi$
$821$		−	49.3196i		−	1.72127i	0.509225	−	0.860634i	$-0.329932\pi$
$822$		0			0
$823$	−23.6992			−0.826101			−0.413050	−	0.910708i	$-0.635537\pi$
$823$	−23.6992			−0.826101			−0.413050	+	0.910708i	$0.635537\pi$
$824$		0			0
$825$	−61.7577	−	23.4970i	−2.15013	−	0.818061i
$826$		0			0
$827$		−	19.9706i		−	0.694445i	−0.937783	−	0.347222i	$-0.887125\pi$
$827$		−	19.9706i		−	0.694445i	0.937783	−	0.347222i	$-0.112875\pi$
$828$		0			0
$829$	13.3741	+	7.72155i	0.464503	+	0.268181i	0.713936	−	0.700211i	$-0.246911\pi$
$829$	13.3741	+	7.72155i	0.464503	+	0.268181i	−0.249433	+	0.968392i	$0.580244\pi$
$830$		0			0
$831$	9.63074	+	11.8212i	0.334087	+	0.410074i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	70.1183			2.42654
$836$		0			0
$837$	−19.4029	−	37.2585i	−0.670663	−	1.28784i
$838$		0			0
$839$	5.53910	−	9.59401i	0.191231	−	0.331222i	−0.754427	−	0.656383i	$-0.772085\pi$
$839$	5.53910	−	9.59401i	0.191231	−	0.331222i	0.945658	+	0.325162i	$0.105419\pi$
$840$		0			0
$841$	−6.16267	−	10.6741i	−0.212506	−	0.368071i
$842$		0			0
$843$	31.1962	+	11.8693i	1.07445	+	0.408799i
$844$		0			0
$845$	24.8444	+	43.0318i	0.854674	+	1.48034i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−2.65434	−	16.4436i	−0.0910966	−	0.564342i
$850$		0			0
$851$		−	17.7331i		−	0.607883i
$852$		0			0
$853$	42.1706	+	24.3472i	1.44389	+	0.833633i	0.998107	−	0.0615058i	$-0.0195903\pi$
$853$	42.1706	+	24.3472i	1.44389	+	0.833633i	0.445788	+	0.895139i	$0.352924\pi$
$854$		0			0
$855$	19.7320	+	59.5271i	0.674819	+	2.03578i
$856$		0			0
$857$	−8.39130	−	14.5342i	−0.286641	−	0.496477i	0.686365	−	0.727258i	$-0.259205\pi$
$857$	−8.39130	−	14.5342i	−0.286641	−	0.496477i	−0.973006	+	0.230780i	$0.925872\pi$
$858$		0			0
$859$	21.7682	+	12.5679i	0.742722	+	0.428811i	0.823058	−	0.567957i	$-0.192266\pi$
$859$	21.7682	+	12.5679i	0.742722	+	0.428811i	−0.0803361	+	0.996768i	$0.525599\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	5.87377	−	3.39122i	0.199945	−	0.115438i	−0.396685	−	0.917955i	$-0.629839\pi$
$863$	5.87377	−	3.39122i	0.199945	−	0.115438i	0.596630	+	0.802516i	$0.296506\pi$
$864$		0			0
$865$	−14.6733	+	25.4149i	−0.498907	+	0.864133i
$866$		0			0
$867$	18.6919	+	22.9434i	0.634812	+	0.779199i
$868$		0			0
$869$	12.6303	−	7.29209i	0.428452	−	0.247367i
$870$		0			0
$871$	−0.564190	+	0.325735i	−0.0191168	+	0.0110371i
$872$		0			0
$873$	−47.4538	−	9.79329i	−1.60607	−	0.331453i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	21.8630	−	37.8678i	0.738260	−	1.27870i	−0.215019	−	0.976610i	$-0.568981\pi$
$877$	21.8630	−	37.8678i	0.738260	−	1.27870i	0.953278	−	0.302093i	$-0.0976854\pi$
$878$		0			0
$879$	2.68243	+	3.29255i	0.0904761	+	0.111055i
$880$		0			0
$881$	27.5307			0.927531			0.463766	−	0.885958i	$-0.346498\pi$
$881$	27.5307			0.927531			0.463766	+	0.885958i	$0.346498\pi$
$882$		0			0
$883$	5.56040			0.187122			0.0935612	−	0.995614i	$-0.470175\pi$
$883$	5.56040			0.187122			0.0935612	+	0.995614i	$0.470175\pi$
$884$		0			0
$885$	−21.4915	+	56.4867i	−0.722430	+	1.89878i
$886$		0			0
$887$	−12.3092	+	21.3202i	−0.413303	+	0.715862i	−0.995249	−	0.0973655i	$-0.968958\pi$
$887$	−12.3092	+	21.3202i	−0.413303	+	0.715862i	0.581945	+	0.813228i	$0.302292\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−13.1637	+	30.5344i	−0.441002	+	1.02294i
$892$		0			0
$893$	−13.0792	+	7.55125i	−0.437677	+	0.252693i
$894$		0			0
$895$	2.44434	−	1.41124i	0.0817054	−	0.0471726i
$896$		0			0
$897$	−2.15656	+	0.348114i	−0.0720056	+	0.0116232i
$898$		0			0
$899$	−16.5062	+	28.5896i	−0.550514	+	0.953518i
$900$		0			0
$901$	0.242674	−	0.140108i	0.00808465	−	0.00466767i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−17.1931	−	9.92644i	−0.571518	−	0.329966i
$906$		0			0
$907$	5.04337	+	8.73537i	0.167462	+	0.290053i	0.937527	−	0.347913i	$-0.113109\pi$
$907$	5.04337	+	8.73537i	0.167462	+	0.290053i	−0.770065	+	0.637966i	$0.779776\pi$
$908$		0			0
$909$	−3.63872	−	3.23751i	−0.120689	−	0.107381i
$910$		0			0
$911$	23.5808	+	13.6144i	0.781267	+	0.451065i	0.836879	−	0.547388i	$-0.184378\pi$
$911$	23.5808	+	13.6144i	0.781267	+	0.451065i	−0.0556121	+	0.998452i	$0.517711\pi$
$912$		0			0
$913$		−	28.4240i		−	0.940698i
$914$		0			0
$915$	−44.1519	−	16.7985i	−1.45962	−	0.555341i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−19.8493	−	34.3800i	−0.654769	−	1.13409i	−0.981952	−	0.189132i	$-0.939433\pi$
$919$	−19.8493	−	34.3800i	−0.654769	−	1.13409i	0.327183	−	0.944961i	$-0.393901\pi$
$920$		0			0
$921$	2.94892	+	18.2685i	0.0971701	+	0.601968i
$922$		0			0
$923$	1.86064	+	3.22272i	0.0612436	+	0.106077i
$924$		0			0
$925$	40.2552	−	69.7240i	1.32358	−	2.29251i
$926$		0			0
$927$	1.16249	+	0.239909i	0.0381811	+	0.00787965i
$928$		0			0
$929$	0.284567			0.00933633			0.00466816	−	0.999989i	$-0.498514\pi$
$929$	0.284567			0.00933633			0.00466816	+	0.999989i	$0.498514\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−35.5090	+	5.73189i	−1.16251	+	0.187654i
$934$		0			0
$935$	−73.1295	−	42.2214i	−2.39159	−	1.38079i
$936$		0			0
$937$			21.7298i			0.709881i	0.934889	+	0.354940i	$0.115499\pi$
$937$			21.7298i			0.709881i	−0.934889	+	0.354940i	$0.884501\pi$
$938$		0			0
$939$	−1.08507	−	6.72197i	−0.0354098	−	0.219363i
$940$		0			0
$941$	11.2848			0.367875			0.183938	−	0.982938i	$-0.441116\pi$
$941$	11.2848			0.367875			0.183938	+	0.982938i	$0.441116\pi$
$942$		0			0
$943$			16.3405i			0.532121i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			22.7131i			0.738077i	0.929414	+	0.369039i	$0.120313\pi$
$947$			22.7131i			0.738077i	−0.929414	+	0.369039i	$0.879687\pi$
$948$		0			0
$949$	−2.25836			−0.0733096
$950$		0			0
$951$	−0.632234	−	3.91668i	−0.0205016	−	0.127007i
$952$		0			0
$953$			16.5638i			0.536554i	0.963342	+	0.268277i	$0.0864543\pi$
$953$			16.5638i			0.536554i	−0.963342	+	0.268277i	$0.913546\pi$
$954$		0			0
$955$	−43.0648	−	24.8635i	−1.39354	−	0.804563i
$956$		0			0
$957$	25.7968	−	4.16414i	0.833893	−	0.134608i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−34.3581			−1.10832
$962$		0			0
$963$	−11.3009	+	12.7013i	−0.364166	+	0.409295i
$964$		0			0
$965$	−44.6589	+	77.3515i	−1.43762	+	2.49003i
$966$		0			0
$967$	8.38867	+	14.5296i	0.269762	+	0.467241i	0.968800	−	0.247843i	$-0.0797218\pi$
$967$	8.38867	+	14.5296i	0.269762	+	0.467241i	−0.699039	+	0.715084i	$0.746388\pi$
$968$		0			0
$969$	8.60481	+	53.3067i	0.276426	+	1.71246i
$970$		0			0
$971$	15.6820	+	27.1620i	0.503259	+	0.871670i	0.999993	+	0.00376705i	$0.00119909\pi$
$971$	15.6820	+	27.1620i	0.503259	+	0.871670i	−0.496734	+	0.867903i	$0.665468\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−9.26953	−	3.52679i	−0.296862	−	0.112948i
$976$		0			0
$977$		−	56.6904i		−	1.81369i	−0.421469	−	0.906843i	$-0.638485\pi$
$977$		−	56.6904i		−	1.81369i	0.421469	−	0.906843i	$-0.361515\pi$
$978$		0			0
$979$	−17.3609	−	10.0233i	−0.554858	−	0.320347i
$980$		0			0
$981$	−8.19378	+	39.7033i	−0.261607	+	1.26763i
$982$		0			0
$983$	−19.9204	−	34.5032i	−0.635362	−	1.10048i	−0.986438	−	0.164133i	$-0.947517\pi$
$983$	−19.9204	−	34.5032i	−0.635362	−	1.10048i	0.351076	−	0.936347i	$-0.385816\pi$
$984$		0			0
$985$	−0.105562	−	0.0609460i	−0.00336347	−	0.00194190i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.97026	−	1.71488i	0.0944489	−	0.0545301i
$990$		0			0
$991$	31.2975	−	54.2089i	0.994199	−	1.72200i	0.403952	−	0.914780i	$-0.367636\pi$
$991$	31.2975	−	54.2089i	0.994199	−	1.72200i	0.590247	−	0.807223i	$-0.299030\pi$
$992$		0			0
$993$	−11.8596	+	1.91438i	−0.376352	+	0.0607511i
$994$		0			0
$995$	−77.9613	+	45.0110i	−2.47154	+	1.42694i
$996$		0			0
$997$	−39.0613	+	22.5520i	−1.23708	+	0.714230i	−0.968497	−	0.249025i	$-0.919890\pi$
$997$	−39.0613	+	22.5520i	−1.23708	+	0.714230i	−0.268586	+	0.963256i	$0.586556\pi$
$998$		0			0
$999$	−34.1728	−	21.7630i	−1.08118	−	0.688552i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.w.b.1109.1		16
3.2	odd	2		5292.2.w.b.521.1		16
7.2	even	3		252.2.bm.a.173.6	yes	16
7.3	odd	6		1764.2.x.a.1469.3		16
7.4	even	3		1764.2.x.b.1469.6		16
7.5	odd	6		1764.2.bm.a.1685.3		16
7.6	odd	2		252.2.w.a.101.8	yes	16
9.4	even	3		5292.2.bm.a.2285.1		16
9.5	odd	6		1764.2.bm.a.1697.3		16
21.2	odd	6		756.2.bm.a.89.8		16
21.5	even	6		5292.2.bm.a.4625.1		16
21.11	odd	6		5292.2.x.b.4409.1		16
21.17	even	6		5292.2.x.a.4409.8		16
21.20	even	2		756.2.w.a.521.8		16
28.23	odd	6		1008.2.df.d.929.3		16
28.27	even	2		1008.2.ca.d.353.1		16
63.2	odd	6		2268.2.t.b.2105.1		16
63.4	even	3		5292.2.x.a.881.8		16
63.5	even	6	inner	1764.2.w.b.509.1		16
63.13	odd	6		756.2.bm.a.17.8		16
63.16	even	3		2268.2.t.a.2105.8		16
63.20	even	6		2268.2.t.a.1781.8		16
63.23	odd	6		252.2.w.a.5.8	✓	16
63.31	odd	6		5292.2.x.b.881.1		16
63.32	odd	6		1764.2.x.a.293.3		16
63.34	odd	6		2268.2.t.b.1781.1		16
63.40	odd	6		5292.2.w.b.1097.1		16
63.41	even	6		252.2.bm.a.185.6	yes	16
63.58	even	3		756.2.w.a.341.8		16
63.59	even	6		1764.2.x.b.293.6		16
84.23	even	6		3024.2.df.d.1601.8		16
84.83	odd	2		3024.2.ca.d.2033.8		16
252.23	even	6		1008.2.ca.d.257.1		16
252.139	even	6		3024.2.df.d.17.8		16
252.167	odd	6		1008.2.df.d.689.3		16
252.247	odd	6		3024.2.ca.d.2609.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.8	✓	16	63.23	odd	6
252.2.w.a.101.8	yes	16	7.6	odd	2
252.2.bm.a.173.6	yes	16	7.2	even	3
252.2.bm.a.185.6	yes	16	63.41	even	6
756.2.w.a.341.8		16	63.58	even	3
756.2.w.a.521.8		16	21.20	even	2
756.2.bm.a.17.8		16	63.13	odd	6
756.2.bm.a.89.8		16	21.2	odd	6
1008.2.ca.d.257.1		16	252.23	even	6
1008.2.ca.d.353.1		16	28.27	even	2
1008.2.df.d.689.3		16	252.167	odd	6
1008.2.df.d.929.3		16	28.23	odd	6
1764.2.w.b.509.1		16	63.5	even	6	inner
1764.2.w.b.1109.1		16	1.1	even	1	trivial
1764.2.x.a.293.3		16	63.32	odd	6
1764.2.x.a.1469.3		16	7.3	odd	6
1764.2.x.b.293.6		16	63.59	even	6
1764.2.x.b.1469.6		16	7.4	even	3
1764.2.bm.a.1685.3		16	7.5	odd	6
1764.2.bm.a.1697.3		16	9.5	odd	6
2268.2.t.a.1781.8		16	63.20	even	6
2268.2.t.a.2105.8		16	63.16	even	3
2268.2.t.b.1781.1		16	63.34	odd	6
2268.2.t.b.2105.1		16	63.2	odd	6
3024.2.ca.d.2033.8		16	84.83	odd	2
3024.2.ca.d.2609.8		16	252.247	odd	6
3024.2.df.d.17.8		16	252.139	even	6
3024.2.df.d.1601.8		16	84.23	even	6
5292.2.w.b.521.1		16	3.2	odd	2
5292.2.w.b.1097.1		16	63.40	odd	6
5292.2.x.a.881.8		16	63.4	even	3
5292.2.x.a.4409.8		16	21.17	even	6
5292.2.x.b.881.1		16	63.31	odd	6
5292.2.x.b.4409.1		16	21.11	odd	6
5292.2.bm.a.2285.1		16	9.4	even	3
5292.2.bm.a.4625.1		16	21.5	even	6

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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.70992 + 0.276016i) q^{3} +(1.95741 - 3.39033i) q^{5} +(2.84763 - 0.943929i) q^{9} +O(q^{10})\)	\(q+(-1.70992 + 0.276016i) q^{3} +(1.95741 - 3.39033i) q^{5} +(2.84763 - 0.943929i) q^{9} +(-3.19958 + 1.84728i) q^{11} +(-0.480242 + 0.277268i) q^{13} +(-2.41122 + 6.33747i) q^{15} +(-2.91916 + 5.05613i) q^{17} +(-4.62434 + 2.66986i) q^{19} +(-1.96965 - 1.13718i) q^{23} +(-5.16291 - 8.94242i) q^{25} +(-4.60867 + 2.40003i) q^{27} +(3.53638 + 2.04173i) q^{29} +8.08443i q^{31} +(4.96114 - 4.04183i) q^{33} +(3.89849 + 6.75239i) q^{37} +(0.744643 - 0.606659i) q^{39} +(-3.59234 - 6.22212i) q^{41} +(-0.754009 + 1.30598i) q^{43} +(2.37374 - 11.5021i) q^{45} +2.82833 q^{47} +(3.59594 - 9.45130i) q^{51} +(-0.0415658 - 0.0239980i) q^{53} +14.4635i q^{55} +(7.17031 - 5.84164i) q^{57} +8.91313 q^{59} +6.96680i q^{61} +2.17091i q^{65} +1.17480 q^{67} +(3.68181 + 1.40082i) q^{69} -6.71061i q^{71} +(3.52692 + 2.03627i) q^{73} +(11.2964 + 13.8658i) q^{75} -3.94747 q^{79} +(7.21799 - 5.37592i) q^{81} +(-3.84674 + 6.66275i) q^{83} +(11.4280 + 19.7938i) q^{85} +(-6.61047 - 2.51509i) q^{87} +(2.71300 + 4.69905i) q^{89} +(-2.23143 - 13.8237i) q^{93} +20.9041i q^{95} +(-13.9874 - 8.07563i) q^{97} +(-7.36753 + 8.28055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{9}+O(q^{10}) \) 16 * q + 6 * q^9	\( 16 q + 6 q^{9} - 6 q^{11} + 3 q^{13} - 3 q^{15} - 9 q^{17} + 21 q^{23} - 8 q^{25} - 9 q^{27} + 6 q^{29} + q^{37} - 3 q^{39} + 6 q^{41} - 2 q^{43} + 30 q^{45} + 36 q^{47} - 33 q^{51} + 15 q^{57} + 30 q^{59} + 14 q^{67} - 21 q^{69} + 57 q^{75} + 2 q^{79} + 18 q^{81} + 6 q^{85} - 48 q^{87} - 21 q^{89} + 21 q^{93} + 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q + 6 * q^9 - 6 * q^11 + 3 * q^13 - 3 * q^15 - 9 * q^17 + 21 * q^23 - 8 * q^25 - 9 * q^27 + 6 * q^29 + q^37 - 3 * q^39 + 6 * q^41 - 2 * q^43 + 30 * q^45 + 36 * q^47 - 33 * q^51 + 15 * q^57 + 30 * q^59 + 14 * q^67 - 21 * q^69 + 57 * q^75 + 2 * q^79 + 18 * q^81 + 6 * q^85 - 48 * q^87 - 21 * q^89 + 21 * q^93 + 3 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more