LMFDB - Embedded newform 1764.2.x.b.293.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(293,1764)]

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, 3]))

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

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

chi := DirichletCharacter("1764.293");

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.x (of order $6$, degree $2$, 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			293.6
Root			$-0.544978 - 1.64408i$ of defining polynomial
Character	$\chi$	$=$	1764.293
Dual form			1764.2.x.b.1469.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09400 - 1.34282i) q^{3} +(1.95741 - 3.39033i) q^{5} +(-0.606348 - 2.93808i) q^{9} +O(q^{10})$	\(q+(1.09400 - 1.34282i) q^{3} +(1.95741 - 3.39033i) q^{5} +(-0.606348 - 2.93808i) q^{9} +(3.19958 - 1.84728i) q^{11} +(-0.480242 - 0.277268i) q^{13} +(-2.41122 - 6.33747i) q^{15} +5.83832 q^{17} +5.33973i q^{19} +(1.96965 + 1.13718i) q^{23} +(-5.16291 - 8.94242i) q^{25} +(-4.60867 - 2.40003i) q^{27} +(3.53638 - 2.04173i) q^{29} +(7.00132 + 4.04222i) q^{31} +(1.01976 - 6.31739i) q^{33} -7.79699 q^{37} +(-0.897704 + 0.341550i) q^{39} +(-3.59234 + 6.22212i) q^{41} +(-0.754009 - 1.30598i) q^{43} +(-11.1480 - 3.69531i) q^{45} +(-1.41416 - 2.44940i) q^{47} +(6.38709 - 7.83983i) q^{51} -0.0479960i q^{53} -14.4635i q^{55} +(7.17031 + 5.84164i) q^{57} +(-4.45656 + 7.71900i) q^{59} +(-6.03343 + 3.48340i) q^{61} +(-1.88006 + 1.08545i) q^{65} +(-0.587402 + 1.01741i) q^{67} +(3.68181 - 1.40082i) q^{69} +6.71061i q^{71} +4.07253i q^{73} +(-17.6563 - 2.85009i) q^{75} +(1.97374 + 3.41861i) q^{79} +(-8.26468 + 3.56300i) q^{81} +(-3.84674 - 6.66275i) q^{83} +(11.4280 - 19.7938i) q^{85} +(1.12710 - 6.98238i) q^{87} -5.42600 q^{89} +(13.0874 - 4.97937i) q^{93} +(18.1035 + 10.4520i) q^{95} +(-13.9874 + 8.07563i) q^{97} +(-7.36753 - 8.28055i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 18 q^{17} - 21 q^{23} - 8 q^{25} - 9 q^{27} + 6 q^{29} - 6 q^{31} + 27 q^{33} - 2 q^{37} + 6 q^{39} + 6 q^{41} - 2 q^{43} - 15 q^{45} - 18 q^{47} + 18 q^{51} + 15 q^{57} - 15 q^{59} - 3 q^{61} + 39 q^{65} - 7 q^{67} - 21 q^{69} - 42 q^{75} - q^{79} - 18 q^{81} + 6 q^{85} + 51 q^{87} + 42 q^{89} + 48 q^{93} - 6 q^{95} + 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q - 6 * q^9 + 6 * q^11 + 3 * q^13 - 3 * q^15 + 18 * q^17 - 21 * q^23 - 8 * q^25 - 9 * q^27 + 6 * q^29 - 6 * q^31 + 27 * q^33 - 2 * q^37 + 6 * q^39 + 6 * q^41 - 2 * q^43 - 15 * q^45 - 18 * q^47 + 18 * q^51 + 15 * q^57 - 15 * q^59 - 3 * q^61 + 39 * q^65 - 7 * q^67 - 21 * q^69 - 42 * q^75 - q^79 - 18 * q^81 + 6 * q^85 + 51 * q^87 + 42 * q^89 + 48 * q^93 - 6 * q^95 + 3 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.09400	−	1.34282i	0.631619	−	0.775279i
$3$	1.09400	−	1.34282i	0.631619	−	0.775279i
$4$		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
$9$	−0.606348	−	2.93808i	−0.202116	−	0.979362i
$10$		0			0
$11$	3.19958	−	1.84728i	0.964710	−	0.556976i	0.0670908	−	0.997747i	$-0.478628\pi$
$11$	3.19958	−	1.84728i	0.964710	−	0.556976i	0.897620	+	0.440771i	$0.145295\pi$
$12$		0			0
$13$	−0.480242	−	0.277268i	−0.133195	−	0.0769002i	0.431922	−	0.901911i	$-0.357836\pi$
$13$	−0.480242	−	0.277268i	−0.133195	−	0.0769002i	−0.565117	+	0.825011i	$0.691169\pi$
$14$		0			0
$15$	−2.41122	−	6.33747i	−0.622575	−	1.63633i
$16$		0			0
$17$	5.83832			1.41600			0.708000	−	0.706213i	$-0.249598\pi$
$17$	5.83832			1.41600			0.708000	+	0.706213i	$0.249598\pi$
$18$		0			0
$19$			5.33973i			1.22502i	0.790464	+	0.612509i	$0.209840\pi$
$19$			5.33973i			1.22502i	−0.790464	+	0.612509i	$0.790160\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.96965	+	1.13718i	0.410700	+	0.237118i	0.691090	−	0.722768i	$-0.257131\pi$
$23$	1.96965	+	1.13718i	0.410700	+	0.237118i	−0.280390	+	0.959886i	$0.590464\pi$
$24$		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	−0.134325	−	0.990937i	$-0.542887\pi$
$29$	3.53638	−	2.04173i	0.656690	−	0.379140i	0.791014	+	0.611797i	$0.209553\pi$
$30$		0			0
$31$	7.00132	+	4.04222i	1.25748	+	0.726004i	0.972583	−	0.232556i	$-0.0747089\pi$
$31$	7.00132	+	4.04222i	1.25748	+	0.726004i	0.284892	+	0.958560i	$0.408042\pi$
$32$		0			0
$33$	1.01976	−	6.31739i	0.177517	−	1.09972i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−7.79699			−1.28182			−0.640909	−	0.767617i	$-0.721442\pi$
$37$	−7.79699			−1.28182			−0.640909	+	0.767617i	$0.721442\pi$
$38$		0			0
$39$	−0.897704	+	0.341550i	−0.143748	+	0.0546918i
$40$		0			0
$41$	−3.59234	+	6.22212i	−0.561030	+	0.971732i	0.436377	+	0.899764i	$0.356261\pi$
$41$	−3.59234	+	6.22212i	−0.561030	+	0.971732i	−0.997407	+	0.0719684i	$0.977072\pi$
$42$		0			0
$43$	−0.754009	−	1.30598i	−0.114985	−	0.199160i	0.802789	−	0.596264i	$-0.203349\pi$
$43$	−0.754009	−	1.30598i	−0.114985	−	0.199160i	−0.917774	+	0.397103i	$0.870015\pi$
$44$		0			0
$45$	−11.1480	−	3.69531i	−1.66184	−	0.550865i
$46$		0			0
$47$	−1.41416	−	2.44940i	−0.206277	−	0.357282i	0.744262	−	0.667888i	$-0.232801\pi$
$47$	−1.41416	−	2.44940i	−0.206277	−	0.357282i	−0.950539	+	0.310606i	$0.899468\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	6.38709	−	7.83983i	0.894372	−	1.09780i
$52$		0			0
$53$		−	0.0479960i		−	0.00659276i	−0.999995	−	0.00329638i	$-0.998951\pi$
$53$		−	0.0479960i		−	0.00659276i	0.999995	−	0.00329638i	$-0.00104927\pi$
$54$		0			0
$55$		−	14.4635i		−	1.95026i
$56$		0			0
$57$	7.17031	+	5.84164i	0.949731	+	0.773744i
$58$		0			0
$59$	−4.45656	+	7.71900i	−0.580195	+	1.00493i	0.415261	+	0.909703i	$0.363690\pi$
$59$	−4.45656	+	7.71900i	−0.580195	+	1.00493i	−0.995456	+	0.0952251i	$0.969643\pi$
$60$		0			0
$61$	−6.03343	+	3.48340i	−0.772501	+	0.446004i	−0.833766	−	0.552118i	$-0.813820\pi$
$61$	−6.03343	+	3.48340i	−0.772501	+	0.446004i	0.0612648	+	0.998122i	$0.480487\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.88006	+	1.08545i	−0.233193	+	0.134634i
$66$		0			0
$67$	−0.587402	+	1.01741i	−0.0717626	+	0.124296i	−0.899674	−	0.436563i	$-0.856196\pi$
$67$	−0.587402	+	1.01741i	−0.0717626	+	0.124296i	0.827911	+	0.560859i	$0.189529\pi$
$68$		0			0
$69$	3.68181	−	1.40082i	0.443238	−	0.168639i
$70$		0			0
$71$			6.71061i			0.796403i	0.917298	+	0.398202i	$0.130366\pi$
$71$			6.71061i			0.796403i	−0.917298	+	0.398202i	$0.869634\pi$
$72$		0			0
$73$			4.07253i			0.476654i	0.971185	+	0.238327i	$0.0765990\pi$
$73$			4.07253i			0.476654i	−0.971185	+	0.238327i	$0.923401\pi$
$74$		0			0
$75$	−17.6563	−	2.85009i	−2.03877	−	0.329101i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	1.97374	+	3.41861i	0.222063	+	0.384624i	0.955434	−	0.295204i	$-0.0953877\pi$
$79$	1.97374	+	3.41861i	0.222063	+	0.384624i	−0.733371	+	0.679828i	$0.762054\pi$
$80$		0			0
$81$	−8.26468	+	3.56300i	−0.918298	+	0.395889i
$82$		0			0
$83$	−3.84674	−	6.66275i	−0.422235	−	0.731332i	0.573923	−	0.818909i	$-0.305421\pi$
$83$	−3.84674	−	6.66275i	−0.422235	−	0.731332i	−0.996158	+	0.0875774i	$0.972087\pi$
$84$		0			0
$85$	11.4280	−	19.7938i	1.23954	−	2.14694i
$86$		0			0
$87$	1.12710	−	6.98238i	0.120838	−	0.748590i
$88$		0			0
$89$	−5.42600			−0.575155			−0.287577	−	0.957757i	$-0.592850\pi$
$89$	−5.42600			−0.575155			−0.287577	+	0.957757i	$0.592850\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	13.0874	−	4.97937i	1.35710	−	0.516337i
$94$		0			0
$95$	18.1035	+	10.4520i	1.85738	+	1.07236i
$96$		0			0
$97$	−13.9874	+	8.07563i	−1.42021	+	0.819956i	−0.996316	−	0.0857571i	$-0.972669\pi$
$97$	−13.9874	+	8.07563i	−1.42021	+	0.819956i	−0.423890	+	0.905714i	$0.639336\pi$
$98$		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	0.483024	−	0.875607i	$-0.339539\pi$
$103$	−0.342653	−	0.197831i	−0.0337626	−	0.0194929i	−0.516786	+	0.856114i	$0.672872\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			5.66700i			0.547850i	0.961751	+	0.273925i	$0.0883219\pi$
$107$			5.66700i			0.547850i	−0.961751	+	0.273925i	$0.911678\pi$
$108$		0			0
$109$	13.5133			1.29434			0.647171	−	0.762345i	$-0.275952\pi$
$109$	13.5133			1.29434			0.647171	+	0.762345i	$0.275952\pi$
$110$		0			0
$111$	−8.52987	+	10.4700i	−0.809619	+	0.993766i
$112$		0			0
$113$	1.13651	+	0.656162i	0.106913	+	0.0617265i	0.552503	−	0.833511i	$-0.313673\pi$
$113$	1.13651	+	0.656162i	0.106913	+	0.0617265i	−0.445590	+	0.895237i	$0.647006\pi$
$114$		0			0
$115$	7.71082	−	4.45184i	0.719038	−	0.415137i
$116$		0			0
$117$	−0.523442	+	1.57911i	−0.0483922	+	0.145989i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.32489	−	2.29477i	0.120444	−	0.208615i
$122$		0			0
$123$	4.42520	+	11.6309i	0.399007	+	1.04872i
$124$		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
$129$	−2.57858	−	0.416237i	−0.227032	−	0.0366476i
$130$		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
$135$	−17.1580	+	10.9271i	−1.47672	+	0.940454i
$136$		0			0
$137$	−7.62547	+	4.40257i	−0.651488	+	0.376137i	−0.789026	−	0.614360i	$-0.789414\pi$
$137$	−7.62547	+	4.40257i	−0.651488	+	0.376137i	0.137538	+	0.990496i	$0.456081\pi$
$138$		0			0
$139$	14.2352	+	8.21869i	1.20741	+	0.697100i	0.962193	−	0.272367i	$-0.0878066\pi$
$139$	14.2352	+	8.21869i	1.20741	+	0.697100i	0.245220	+	0.969468i	$0.421140\pi$
$140$		0			0
$141$	−4.83621	−	0.780664i	−0.407282	−	0.0657438i
$142$		0			0
$143$	−2.04876			−0.171326
$144$		0			0
$145$		−	15.9860i		−	1.32757i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−12.5814	−	7.26390i	−1.03071	−	0.595082i	−0.113523	−	0.993535i	$-0.536214\pi$
$149$	−12.5814	−	7.26390i	−1.03071	−	0.595082i	−0.917188	+	0.398454i	$0.869547\pi$
$150$		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
$157$	15.4411	+	8.91493i	1.23233	+	0.711489i	0.967516	−	0.252809i	$-0.0813545\pi$
$157$	15.4411	+	8.91493i	1.23233	+	0.711489i	0.264819	+	0.964298i	$0.414688\pi$
$158$		0			0
$159$	−0.0644502	−	0.0525074i	−0.00511123	−	0.00416411i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	1.15399			0.0903874			0.0451937	−	0.998978i	$-0.485610\pi$
$163$	1.15399			0.0903874			0.0451937	+	0.998978i	$0.485610\pi$
$164$		0			0
$165$	−19.4220	−	15.8230i	−1.51200	−	1.23182i
$166$		0			0
$167$	8.95550	−	15.5114i	0.692997	−	1.20031i	−0.277854	−	0.960623i	$-0.589623\pi$
$167$	8.95550	−	15.5114i	0.692997	−	1.20031i	0.970851	−	0.239683i	$-0.0770435\pi$
$168$		0			0
$169$	−6.34625	−	10.9920i	−0.488173	−	0.845540i
$170$		0			0
$171$	15.6886	−	3.23773i	1.19974	−	0.247596i
$172$		0			0
$173$	3.74814	+	6.49197i	0.284966	+	0.493576i	0.972601	−	0.232481i	$-0.0746843\pi$
$173$	3.74814	+	6.49197i	0.284966	+	0.493576i	−0.687635	+	0.726057i	$0.741351\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.48979	+	14.4289i	0.412638	+	1.08454i
$178$		0			0
$179$			0.720974i			0.0538881i	0.999637	+	0.0269441i	$0.00857760\pi$
$179$			0.720974i			0.0538881i	−0.999637	+	0.0269441i	$0.991422\pi$
$180$		0			0
$181$			5.07121i			0.376940i	0.982079	+	0.188470i	$0.0603529\pi$
$181$			5.07121i			0.376940i	−0.982079	+	0.188470i	$0.939647\pi$
$182$		0			0
$183$	−1.92295	+	11.9127i	−0.142149	+	0.880609i
$184$		0			0
$185$	−15.2619	+	26.4344i	−1.12208	+	1.94350i
$186$		0			0
$187$	18.6802	−	10.7850i	1.36603	−	0.788678i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.0005	−	6.35111i	0.795965	−	0.459551i	−0.0460934	−	0.998937i	$-0.514677\pi$
$191$	11.0005	−	6.35111i	0.795965	−	0.459551i	0.842058	+	0.539387i	$0.181344\pi$
$192$		0			0
$193$	11.4076	−	19.7586i	0.821140	−	1.42226i	−0.0836931	−	0.996492i	$-0.526672\pi$
$193$	11.4076	−	19.7586i	0.821140	−	1.42226i	0.904834	−	0.425765i	$-0.139995\pi$
$194$		0			0
$195$	−0.599205	+	3.71207i	−0.0429100	+	0.265827i
$196$		0			0
$197$			0.0311360i			0.00221835i	0.999999	+	0.00110918i	$0.000353062\pi$
$197$			0.0311360i			0.00221835i	−0.999999	+	0.00110918i	$0.999647\pi$
$198$		0			0
$199$		−	22.9952i		−	1.63008i	−0.579402	−	0.815042i	$-0.696714\pi$
$199$		−	22.9952i		−	1.63008i	0.579402	−	0.815042i	$-0.303286\pi$
$200$		0			0
$201$	0.723587	+	1.90182i	0.0510379	+	0.134144i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	14.0634	+	24.3585i	0.982229	+	1.70127i
$206$		0			0
$207$	2.14683	−	6.47652i	0.149215	−	0.450149i
$208$		0			0
$209$	9.86397	+	17.0849i	0.682305	+	1.18179i
$210$		0			0
$211$	8.55841	−	14.8236i	0.589185	−	1.02050i	−0.405154	−	0.914248i	$-0.632782\pi$
$211$	8.55841	−	14.8236i	0.589185	−	1.02050i	0.994339	−	0.106250i	$-0.0338845\pi$
$212$		0			0
$213$	9.01117	+	7.34138i	0.617435	+	0.503023i
$214$		0			0
$215$	−5.90362			−0.402623
$216$		0			0
$217$		0			0
$218$		0			0
$219$	5.46869	+	4.45533i	0.369540	+	0.301064i
$220$		0			0
$221$	−2.80380	−	1.61878i	−0.188604	−	0.108891i
$222$		0			0
$223$	−1.25230	+	0.723016i	−0.0838602	+	0.0484167i	−0.541344	−	0.840801i	$-0.682084\pi$
$223$	−1.25230	+	0.723016i	−0.0838602	+	0.0484167i	0.457484	+	0.889218i	$0.348751\pi$
$224$		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	0.572205	−	0.820111i	$-0.306088\pi$
$229$	2.24072	+	1.29368i	0.148071	+	0.0854888i	−0.424134	+	0.905599i	$0.639421\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	17.4078i		−	1.14042i	−0.821498	−	0.570211i	$-0.806862\pi$
$233$		−	17.4078i		−	1.14042i	0.821498	−	0.570211i	$-0.193138\pi$
$234$		0			0
$235$	−11.0724			−0.722284
$236$		0			0
$237$	6.74985	+	1.08957i	0.438450	+	0.0707750i
$238$		0			0
$239$	4.23642	+	2.44590i	0.274031	+	0.158212i	0.630718	−	0.776012i	$-0.282760\pi$
$239$	4.23642	+	2.44590i	0.274031	+	0.158212i	−0.356687	+	0.934224i	$0.616094\pi$
$240$		0			0
$241$	7.04282	−	4.06618i	0.453668	−	0.261925i	−0.255710	−	0.966754i	$-0.582309\pi$
$241$	7.04282	−	4.06618i	0.453668	−	0.261925i	0.709378	+	0.704828i	$0.248976\pi$
$242$		0			0
$243$	−4.25704	+	14.9959i	−0.273089	+	0.961989i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.48053	−	2.56436i	0.0942041	−	0.163166i
$248$		0			0
$249$	−13.1552	−	2.12353i	−0.833678	−	0.134573i
$250$		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
$255$	−14.0775	−	37.0001i	−0.881566	−	2.31704i
$256$		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
$261$	−8.14306	−	9.15219i	−0.504043	−	0.566506i
$262$		0			0
$263$	15.6625	−	9.04276i	0.965792	−	0.557600i	0.0678413	−	0.997696i	$-0.478389\pi$
$263$	15.6625	−	9.04276i	0.965792	−	0.557600i	0.897951	+	0.440096i	$0.145056\pi$
$264$		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
$269$	−21.6406			−1.31945			−0.659725	−	0.751507i	$-0.729327\pi$
$269$	−21.6406			−1.31945			−0.659725	+	0.751507i	$0.729327\pi$
$270$		0			0
$271$		−	14.2551i		−	0.865937i	−0.901409	−	0.432968i	$-0.857466\pi$
$271$		−	14.2551i		−	0.865937i	0.901409	−	0.432968i	$-0.142534\pi$
$272$		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	−0.906937	−	0.421266i	$-0.861586\pi$
$281$	−16.6889	+	9.63537i	−0.995579	+	0.574798i	−0.0886417	+	0.996064i	$0.528253\pi$
$282$		0			0
$283$	8.32822	+	4.80830i	0.495061	+	0.285824i	0.726672	−	0.686985i	$-0.241066\pi$
$283$	8.32822	+	4.80830i	0.495061	+	0.285824i	−0.231611	+	0.972809i	$0.574399\pi$
$284$		0			0
$285$	33.8403	−	12.8753i	2.00453	−	0.762665i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	17.0859			1.00506
$290$		0			0
$291$	−4.45801	+	27.6173i	−0.261333	+	1.61896i
$292$		0			0
$293$	−1.22598	+	2.12346i	−0.0716225	+	0.124054i	−0.899613	−	0.436689i	$-0.856151\pi$
$293$	−1.22598	+	2.12346i	−0.0716225	+	0.124054i	0.827990	+	0.560743i	$0.189484\pi$
$294$		0			0
$295$	17.4467	+	30.2185i	1.01578	+	1.75939i
$296$		0			0
$297$	−19.1794	+	0.834401i	−1.11290	+	0.0484168i
$298$		0			0
$299$	−0.630605	−	1.09224i	−0.0364688	−	0.0631658i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−2.77605	−	0.448112i	−0.159480	−	0.0257434i
$304$		0			0
$305$			27.2738i			1.56169i
$306$		0			0
$307$			10.6839i			0.609760i	0.952391	+	0.304880i	$0.0986163\pi$
$307$			10.6839i			0.609760i	−0.952391	+	0.304880i	$0.901384\pi$
$308$		0			0
$309$	−0.640513	+	0.243697i	−0.0364375	+	0.0138634i
$310$		0			0
$311$	−10.3833	+	17.9843i	−0.588780	+	1.01980i	0.405612	+	0.914045i	$0.367058\pi$
$311$	−10.3833	+	17.9843i	−0.588780	+	1.01980i	−0.994393	+	0.105752i	$0.966275\pi$
$312$		0			0
$313$	−3.40449	+	1.96558i	−0.192433	+	0.111101i	−0.593121	−	0.805113i	$-0.702104\pi$
$313$	−3.40449	+	1.96558i	−0.192433	+	0.111101i	0.400688	+	0.916215i	$0.368771\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.98369	+	1.14528i	−0.111415	+	0.0643256i	−0.554672	−	0.832069i	$-0.687156\pi$
$317$	−1.98369	+	1.14528i	−0.111415	+	0.0643256i	0.443257	+	0.896395i	$0.353823\pi$
$318$		0			0
$319$	7.54330	−	13.0654i	0.422344	−	0.731521i
$320$		0			0
$321$	7.60978	+	6.19967i	0.424736	+	0.346032i
$322$		0			0
$323$			31.1750i			1.73462i
$324$		0			0
$325$			5.72603i			0.317623i
$326$		0			0
$327$	14.7835	−	18.1460i	0.817531	−	1.00348i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−3.46788	−	6.00655i	−0.190612	−	0.330150i	0.754841	−	0.655908i	$-0.227714\pi$
$331$	−3.46788	−	6.00655i	−0.190612	−	0.330150i	−0.945453	+	0.325758i	$0.894381\pi$
$332$		0			0
$333$	4.72769	+	22.9082i	0.259076	+	1.25536i
$334$		0			0
$335$	2.29957	+	3.98298i	0.125639	+	0.217613i
$336$		0			0
$337$	−9.59771	+	16.6237i	−0.522821	+	0.905552i	0.476827	+	0.878997i	$0.341787\pi$
$337$	−9.59771	+	16.6237i	−0.522821	+	0.905552i	−0.999647	+	0.0265545i	$0.991546\pi$
$338$		0			0
$339$	2.12444	−	0.808288i	0.115384	−	0.0439002i
$340$		0			0
$341$	29.8684			1.61747
$342$		0			0
$343$		0			0
$344$		0			0
$345$	2.45756	−	15.2246i	0.132311	−	0.819663i
$346$		0			0
$347$	7.35287	+	4.24518i	0.394723	+	0.227893i	0.684204	−	0.729290i	$-0.260150\pi$
$347$	7.35287	+	4.24518i	0.394723	+	0.227893i	−0.289482	+	0.957184i	$0.593483\pi$
$348$		0			0
$349$	16.5478	−	9.55386i	0.885782	−	0.511407i	0.0132216	−	0.999913i	$-0.495791\pi$
$349$	16.5478	−	9.55386i	0.885782	−	0.511407i	0.872560	+	0.488506i	$0.162458\pi$
$350$		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
$359$			17.1945i			0.907490i	0.891132	+	0.453745i	$0.149912\pi$
$359$			17.1945i			0.907490i	−0.891132	+	0.453745i	$0.850088\pi$
$360$		0			0
$361$	−9.51270			−0.500668
$362$		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	−0.0679376	−	0.997690i	$-0.521642\pi$
$367$	14.6001	−	8.42936i	0.762118	−	0.440009i	0.830056	+	0.557680i	$0.188309\pi$
$368$		0			0
$369$	20.4593	+	6.78184i	1.06507	+	0.353048i
$370$		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
$375$	−22.8094	+	27.9974i	−1.17787	+	1.44578i
$376$		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
$381$	−19.0284	+	23.3563i	−0.974853	+	1.19658i
$382$		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
$387$	−3.37989	+	3.00722i	−0.171810	+	0.152866i
$388$		0			0
$389$	29.9624	−	17.2988i	1.51915	−	0.877084i	0.519409	−	0.854526i	$-0.326152\pi$
$389$	29.9624	−	17.2988i	1.51915	−	0.877084i	0.999746	−	0.0225587i	$-0.00718126\pi$
$390$		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
$395$	15.4537			0.777558
$396$		0			0
$397$			32.2821i			1.62019i	0.586296	+	0.810097i	$0.300586\pi$
$397$			32.2821i			1.62019i	−0.586296	+	0.810097i	$0.699414\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−11.3473	−	6.55139i	−0.566659	−	0.327161i	0.189155	−	0.981947i	$-0.439425\pi$
$401$	−11.3473	−	6.55139i	−0.566659	−	0.327161i	−0.755814	+	0.654787i	$0.772758\pi$
$402$		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
$409$	−32.3493	−	18.6769i	−1.59957	−	0.923513i	−0.991569	−	0.129577i	$-0.958638\pi$
$409$	−32.3493	−	18.6769i	−1.59957	−	0.923513i	−0.608002	−	0.793936i	$-0.708029\pi$
$410$		0			0
$411$	−2.43036	+	15.0561i	−0.119881	+	0.742660i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−30.1186			−1.47846
$416$		0			0
$417$	26.6095	−	10.1241i	1.30307	−	0.495781i
$418$		0			0
$419$	−14.1954	+	24.5871i	−0.693490	+	1.20116i	0.277198	+	0.960813i	$0.410594\pi$
$419$	−14.1954	+	24.5871i	−0.693490	+	1.20116i	−0.970687	+	0.240346i	$0.922739\pi$
$420$		0			0
$421$	−17.3359	−	30.0267i	−0.844901	−	1.46341i	−0.885707	−	0.464245i	$-0.846326\pi$
$421$	−17.3359	−	30.0267i	−0.844901	−	1.46341i	0.0408054	−	0.999167i	$-0.487008\pi$
$422$		0			0
$423$	−6.33908	+	5.64013i	−0.308217	+	0.274232i
$424$		0			0
$425$	−30.1427	−	52.2087i	−1.46214	−	2.53249i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−2.24134	+	2.75113i	−0.108213	+	0.132826i
$430$		0			0
$431$			15.2240i			0.733315i	0.930356	+	0.366657i	$0.119498\pi$
$431$			15.2240i			0.733315i	−0.930356	+	0.366657i	$0.880502\pi$
$432$		0			0
$433$		−	3.97041i		−	0.190806i	−0.995439	−	0.0954028i	$-0.969586\pi$
$433$		−	3.97041i		−	0.190806i	0.995439	−	0.0954028i	$-0.0304139\pi$
$434$		0			0
$435$	−21.4664	−	17.4886i	−1.02924	−	0.838516i
$436$		0			0
$437$	−6.07222	+	10.5174i	−0.290474	+	0.503115i
$438$		0			0
$439$	−8.21910	+	4.74530i	−0.392276	+	0.226481i	−0.683146	−	0.730282i	$-0.739389\pi$
$439$	−8.21910	+	4.74530i	−0.392276	+	0.226481i	0.290870	+	0.956763i	$0.406055\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	28.3955	−	16.3942i	1.34911	−	0.778910i	0.360989	−	0.932570i	$-0.382439\pi$
$443$	28.3955	−	16.3942i	1.34911	−	0.778910i	0.988124	+	0.153660i	$0.0491060\pi$
$444$		0			0
$445$	−10.6209	+	18.3960i	−0.503479	+	0.872052i
$446$		0			0
$447$	−23.5182	+	8.94798i	−1.11237	+	0.423225i
$448$		0			0
$449$		−	0.658896i		−	0.0310952i	−0.999879	−	0.0155476i	$-0.995051\pi$
$449$		−	0.658896i		−	0.0310952i	0.999879	−	0.0155476i	$-0.00494916\pi$
$450$		0			0
$451$			26.5443i			1.24992i
$452$		0			0
$453$	−9.58602	−	1.54738i	−0.450390	−	0.0727024i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−7.94514	−	13.7614i	−0.371658	−	0.643730i	0.618163	−	0.786050i	$-0.287877\pi$
$457$	−7.94514	−	13.7614i	−0.371658	−	0.643730i	−0.989821	+	0.142320i	$0.954544\pi$
$458$		0			0
$459$	−26.9069	−	14.0122i	−1.25591	−	0.654031i
$460$		0			0
$461$	9.81626	+	17.0023i	0.457189	+	0.791874i	0.998811	−	0.0487477i	$-0.0155230\pi$
$461$	9.81626	+	17.0023i	0.457189	+	0.791874i	−0.541622	+	0.840622i	$0.682190\pi$
$462$		0			0
$463$	0.600159	−	1.03951i	0.0278918	−	0.0483099i	−0.851743	−	0.523960i	$-0.824454\pi$
$463$	0.600159	−	1.03951i	0.0278918	−	0.0483099i	0.879634	+	0.475651i	$0.157787\pi$
$464$		0			0
$465$	8.73567	−	54.1173i	0.405107	−	2.50963i
$466$		0			0
$467$	38.5618			1.78443			0.892213	−	0.451614i	$-0.149152\pi$
$467$	38.5618			1.78443			0.892213	+	0.451614i	$0.149152\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	28.8637	−	10.9818i	1.32997	−	0.506014i
$472$		0			0
$473$	−4.82503	−	2.78573i	−0.221855	−	0.128088i
$474$		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
$485$			63.2293i			2.87110i
$486$		0			0
$487$	−9.71539			−0.440247			−0.220123	−	0.975472i	$-0.570646\pi$
$487$	−9.71539			−0.440247			−0.220123	+	0.975472i	$0.570646\pi$
$488$		0			0
$489$	1.26246	−	1.54960i	0.0570903	−	0.0700754i
$490$		0			0
$491$	17.2480	+	9.95814i	0.778392	+	0.449405i	0.835860	−	0.548943i	$-0.184969\pi$
$491$	17.2480	+	9.95814i	0.778392	+	0.449405i	−0.0574682	+	0.998347i	$0.518303\pi$
$492$		0			0
$493$	20.6465	−	11.9203i	0.929872	−	0.536862i
$494$		0			0
$495$	−42.4951	+	8.76994i	−1.91001	+	0.394179i
$496$		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
$501$	−11.0318	−	28.9950i	−0.492863	−	1.29540i
$502$		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
$507$	−21.7031	−	3.50333i	−0.963869	−	0.155588i
$508$		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
$513$	12.8155	−	24.6090i	0.565819	−	1.08652i
$514$		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
$521$	21.0781			0.923446			0.461723	−	0.887024i	$-0.347231\pi$
$521$	21.0781			0.923446			0.461723	+	0.887024i	$0.347231\pi$
$522$		0			0
$523$			19.7145i			0.862057i	0.902338	+	0.431028i	$0.141849\pi$
$523$			19.7145i			0.862057i	−0.902338	+	0.431028i	$0.858151\pi$
$524$		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
$535$	19.2130	+	11.0926i	0.830652	+	0.479577i
$536$		0			0
$537$	0.968140	+	0.788742i	0.0417783	+	0.0340367i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	8.44950			0.363272			0.181636	−	0.983366i	$-0.441861\pi$
$541$	8.44950			0.363272			0.181636	+	0.983366i	$0.441861\pi$
$542$		0			0
$543$	6.80974	+	5.54788i	0.292234	+	0.238082i
$544$		0			0
$545$	26.4511	−	45.8147i	1.13304	−	1.96249i
$546$		0			0
$547$	−4.02889	−	6.97824i	−0.172263	−	0.298368i	0.766948	−	0.641709i	$-0.221774\pi$
$547$	−4.02889	−	6.97824i	−0.172263	−	0.298368i	−0.939211	+	0.343342i	$0.888441\pi$
$548$		0			0
$549$	13.8929	+	15.6146i	0.592934	+	0.666414i
$550$		0			0
$551$	10.9023	+	18.8833i	0.464453	+	0.804456i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	18.8003	+	49.4132i	0.798027	+	2.09747i
$556$		0			0
$557$		−	21.0495i		−	0.891895i	−0.895059	−	0.445947i	$-0.852867\pi$
$557$		−	21.0495i		−	0.891895i	0.895059	−	0.445947i	$-0.147133\pi$
$558$		0			0
$559$			0.836249i			0.0353696i
$560$		0			0
$561$	5.95367	−	36.8829i	0.251364	−	1.55720i
$562$		0			0
$563$	20.6410	−	35.7513i	0.869916	−	1.50674i	0.00783378	−	0.999969i	$-0.497506\pi$
$563$	20.6410	−	35.7513i	0.869916	−	1.50674i	0.862082	−	0.506769i	$-0.169160\pi$
$564$		0			0
$565$	4.44922	−	2.56876i	0.187180	−	0.108068i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−31.2691	+	18.0532i	−1.31087	+	0.756829i	−0.982240	−	0.187630i	$-0.939919\pi$
$569$	−31.2691	+	18.0532i	−1.31087	+	0.756829i	−0.328627	+	0.944460i	$0.606586\pi$
$570$		0			0
$571$	9.62111	−	16.6642i	0.402631	−	0.697377i	−0.591412	−	0.806370i	$-0.701429\pi$
$571$	9.62111	−	16.6642i	0.402631	−	0.697377i	0.994043	+	0.108993i	$0.0347625\pi$
$572$		0			0
$573$	3.50602	−	21.7198i	0.146466	−	0.907356i
$574$		0			0
$575$		−	23.4846i		−	0.979375i
$576$		0			0
$577$			29.8031i			1.24072i	0.784318	+	0.620359i	$0.213013\pi$
$577$			29.8031i			1.24072i	−0.784318	+	0.620359i	$0.786987\pi$
$578$		0			0
$579$	−14.0524	−	36.9343i	−0.583999	−	1.53494i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.0886621	−	0.153567i	−0.00367201	−	0.00636010i
$584$		0			0
$585$	4.32912	+	4.86561i	0.178987	+	0.201168i
$586$		0			0
$587$	−4.72218	−	8.17905i	−0.194905	−	0.337586i	0.751964	−	0.659204i	$-0.229107\pi$
$587$	−4.72218	−	8.17905i	−0.194905	−	0.337586i	−0.946869	+	0.321618i	$0.895773\pi$
$588$		0			0
$589$	−21.5843	+	37.3852i	−0.889367	+	1.54043i
$590$		0			0
$591$	0.0418102	+	0.0340627i	0.00171984	+	0.00140115i
$592$		0			0
$593$	24.8352			1.01986			0.509929	−	0.860216i	$-0.329672\pi$
$593$	24.8352			1.01986			0.509929	+	0.860216i	$0.329672\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−30.8784	−	25.1566i	−1.26377	−	1.02959i
$598$		0			0
$599$	10.3052	+	5.94974i	0.421061	+	0.243100i	0.695531	−	0.718496i	$-0.255169\pi$
$599$	10.3052	+	5.94974i	0.421061	+	0.243100i	−0.274470	+	0.961596i	$0.588502\pi$
$600$		0			0
$601$	−22.1276	+	12.7754i	−0.902604	+	0.521118i	−0.878044	−	0.478580i	$-0.841152\pi$
$601$	−22.1276	+	12.7754i	−0.902604	+	0.521118i	−0.0245596	+	0.999698i	$0.507818\pi$
$602$		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	0.0475718	−	0.998868i	$-0.484852\pi$
$607$	−19.5544	−	11.2897i	−0.793687	−	0.458235i	−0.841259	+	0.540632i	$0.818185\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			1.56841i			0.0634510i
$612$		0			0
$613$	22.8588			0.923257			0.461628	−	0.887073i	$-0.347265\pi$
$613$	22.8588			0.923257			0.461628	+	0.887073i	$0.347265\pi$
$614$		0			0
$615$	48.0944	+	7.76344i	1.93935	+	0.313052i
$616$		0			0
$617$	1.78792	+	1.03226i	0.0719791	+	0.0415572i	0.535558	−	0.844499i	$-0.320101\pi$
$617$	1.78792	+	1.03226i	0.0719791	+	0.0415572i	−0.463578	+	0.886056i	$0.653435\pi$
$618$		0			0
$619$	−28.2233	+	16.2947i	−1.13439	+	0.654940i	−0.945035	−	0.326969i	$-0.893973\pi$
$619$	−28.2233	+	16.2947i	−1.13439	+	0.654940i	−0.189354	+	0.981909i	$0.560639\pi$
$620$		0			0
$621$	−6.34820	−	9.96809i	−0.254744	−	0.400006i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−14.9967	+	25.9751i	−0.599870	+	1.03901i
$626$		0			0
$627$	33.7331	+	5.44523i	1.34717	+	0.217462i
$628$		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
$633$	−10.5426	−	27.7094i	−0.419031	−	1.10135i
$634$		0			0
$635$	−34.0461	+	58.9696i	−1.35108	+	2.34014i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	19.7163	−	4.06897i	0.779967	−	0.160966i
$640$		0			0
$641$	−41.3645	+	23.8818i	−1.63380	+	0.943274i	−0.650892	+	0.759170i	$0.725605\pi$
$641$	−41.3645	+	23.8818i	−1.63380	+	0.943274i	−0.982907	+	0.184104i	$0.941062\pi$
$642$		0			0
$643$	−29.2346	−	16.8786i	−1.15290	−	0.665626i	−0.203306	−	0.979115i	$-0.565169\pi$
$643$	−29.2346	−	16.8786i	−1.15290	−	0.665626i	−0.949592	+	0.313489i	$0.898502\pi$
$644$		0			0
$645$	−6.45853	+	7.92752i	−0.254304	+	0.312146i
$646$		0			0
$647$	1.07202			0.0421453			0.0210727	−	0.999778i	$-0.493292\pi$
$647$	1.07202			0.0421453			0.0210727	+	0.999778i	$0.493292\pi$
$648$		0			0
$649$			32.9301i			1.29262i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−28.8503	−	16.6567i	−1.12900	−	0.651828i	−0.185317	−	0.982679i	$-0.559331\pi$
$653$	−28.8503	−	16.6567i	−1.12900	−	0.651828i	−0.943683	+	0.330851i	$0.892664\pi$
$654$		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	−0.654932	−	0.755688i	$-0.727303\pi$
$659$	−8.41890	+	4.86065i	−0.327954	+	0.189344i	0.326979	+	0.945032i	$0.393969\pi$
$660$		0			0
$661$	14.7856	+	8.53647i	0.575093	+	0.332030i	0.759181	−	0.650880i	$-0.225600\pi$
$661$	14.7856	+	8.53647i	0.575093	+	0.332030i	−0.184088	+	0.982910i	$0.558933\pi$
$662$		0			0
$663$	−5.24108	+	1.99408i	−0.203547	+	0.0774436i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	9.28724			0.359603
$668$		0			0
$669$	−0.399128	+	2.47259i	−0.0154312	+	0.0955960i
$670$		0			0
$671$	−12.8696	+	22.2909i	−0.496827	+	0.860529i
$672$		0			0
$673$	−18.3359	−	31.7588i	−0.706798	−	1.22421i	−0.966039	−	0.258398i	$-0.916805\pi$
$673$	−18.3359	−	31.7588i	−0.706798	−	1.22421i	0.259240	−	0.965813i	$-0.416528\pi$
$674$		0			0
$675$	2.33204	+	53.6038i	0.0897604	+	2.06321i
$676$		0			0
$677$	−20.1769	−	34.9474i	−0.775461	−	1.34314i	−0.934535	−	0.355872i	$-0.884184\pi$
$677$	−20.1769	−	34.9474i	−0.775461	−	1.34314i	0.159073	−	0.987267i	$-0.449149\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	7.64663	+	1.23432i	0.293019	+	0.0472994i
$682$		0			0
$683$			9.51083i			0.363922i	0.983306	+	0.181961i	$0.0582444\pi$
$683$			9.51083i			0.363922i	−0.983306	+	0.181961i	$0.941756\pi$
$684$		0			0
$685$			34.4705i			1.31705i
$686$		0			0
$687$	4.18852	−	1.59361i	0.159802	−	0.0608000i
$688$		0			0
$689$	−0.0133077	+	0.0230497i	−0.000506985	+	0.000878123i
$690$		0			0
$691$	6.67519	−	3.85392i	0.253936	−	0.146610i	−0.367629	−	0.929972i	$-0.619830\pi$
$691$	6.67519	−	3.85392i	0.253936	−	0.146610i	0.621565	+	0.783362i	$0.286497\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	55.7282	−	32.1747i	2.11389	−	1.22046i
$696$		0			0
$697$	−20.9732	+	36.3267i	−0.794418	+	1.37597i
$698$		0			0
$699$	−23.3756	−	19.0440i	−0.884145	−	0.720311i
$700$		0			0
$701$		−	15.6388i		−	0.590671i	−0.955394	−	0.295336i	$-0.904569\pi$
$701$		−	15.6388i		−	0.590671i	0.955394	−	0.295336i	$-0.0954314\pi$
$702$		0			0
$703$		−	41.6338i		−	1.57025i
$704$		0			0
$705$	−12.1132	+	14.8683i	−0.456208	+	0.559972i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−6.72025	−	11.6398i	−0.252384	−	0.437142i	0.711797	−	0.702385i	$-0.247881\pi$
$709$	−6.72025	−	11.6398i	−0.252384	−	0.437142i	−0.964182	+	0.265242i	$0.914548\pi$
$710$		0			0
$711$	8.84740	−	7.87187i	0.331803	−	0.295218i
$712$		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
$717$	7.91903	−	3.01296i	0.295742	−	0.112521i
$718$		0			0
$719$	40.0619			1.49405			0.747027	−	0.664793i	$-0.231480\pi$
$719$	40.0619			1.49405			0.747027	+	0.664793i	$0.231480\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	2.24466	−	13.9056i	0.0834798	−	0.517156i
$724$		0			0
$725$	−36.5161	−	21.0826i	−1.35617	−	0.782986i
$726$		0			0
$727$	−43.2091	+	24.9468i	−1.60254	+	0.925225i	−0.611560	+	0.791198i	$0.709458\pi$
$727$	−43.2091	+	24.9468i	−1.60254	+	0.925225i	−0.990978	+	0.134027i	$0.957209\pi$
$728$		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	0.305601	−	0.952160i	$-0.401143\pi$
$733$	−9.91430	−	5.72402i	−0.366193	−	0.211422i	−0.671794	+	0.740738i	$0.734476\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			4.34038i			0.159880i
$738$		0			0
$739$	−8.92607			−0.328351			−0.164175	−	0.986431i	$-0.552496\pi$
$739$	−8.92607			−0.328351			−0.164175	+	0.986431i	$0.552496\pi$
$740$		0			0
$741$	−1.82378	−	4.79349i	−0.0669984	−	0.176093i
$742$		0			0
$743$	−45.8621	−	26.4785i	−1.68252	−	0.971403i	−0.959979	−	0.280074i	$-0.909641\pi$
$743$	−45.8621	−	26.4785i	−1.68252	−	0.971403i	−0.722540	−	0.691329i	$-0.757026\pi$
$744$		0			0
$745$	−49.2541	+	28.4369i	−1.80453	+	1.04185i
$746$		0			0
$747$	−17.2433	+	15.3420i	−0.630898	+	0.561334i
$748$		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
$753$	28.3718	−	34.8249i	1.03392	−	1.26909i
$754$		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
$759$	9.19256	−	11.2834i	0.333669	−	0.409561i
$760$		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
$765$	−65.0853	−	21.5744i	−2.35317	−	0.780025i
$766$		0			0
$767$	4.28046	−	2.47132i	0.154558	−	0.0892343i
$768$		0			0
$769$	−30.1912	−	17.4309i	−1.08872	−	0.628575i	−0.155487	−	0.987838i	$-0.549695\pi$
$769$	−30.1912	−	17.4309i	−1.08872	−	0.628575i	−0.933236	+	0.359263i	$0.883028\pi$
$770$		0			0
$771$	18.9846	+	49.8976i	0.683713	+	1.79702i
$772$		0			0
$773$	−2.12749			−0.0765207			−0.0382603	−	0.999268i	$-0.512182\pi$
$773$	−2.12749			−0.0765207			−0.0382603	+	0.999268i	$0.512182\pi$
$774$		0			0
$775$		−	83.4784i		−	2.99863i
$776$		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
$787$	−24.5457	−	14.1715i	−0.874959	−	0.505158i	−0.00596615	−	0.999982i	$-0.501899\pi$
$787$	−24.5457	−	14.1715i	−0.874959	−	0.505158i	−0.868993	+	0.494824i	$0.835232\pi$
$788$		0			0
$789$	4.99190	−	30.9247i	0.177716	−	1.10095i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	3.86334			0.137191
$794$		0			0
$795$	−0.304173	+	0.115729i	−0.0107879	+	0.00410449i
$796$		0			0
$797$	18.9123	−	32.7570i	0.669907	−	1.16031i	−0.308022	−	0.951379i	$-0.599667\pi$
$797$	18.9123	−	32.7570i	0.669907	−	1.16031i	0.977930	−	0.208935i	$-0.0669996\pi$
$798$		0			0
$799$	−8.25634	−	14.3004i	−0.292088	−	0.505912i
$800$		0			0
$801$	3.29005	+	15.9420i	0.116248	+	0.563285i
$802$		0			0
$803$	7.52311	+	13.0304i	0.265485	+	0.459833i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−23.6747	+	29.0595i	−0.833389	+	1.02294i
$808$		0			0
$809$			45.3191i			1.59333i	0.604419	+	0.796667i	$0.293405\pi$
$809$			45.3191i			1.59333i	−0.604419	+	0.796667i	$0.706595\pi$
$810$		0			0
$811$			5.45145i			0.191426i	0.995409	+	0.0957132i	$0.0305132\pi$
$811$			5.45145i			0.191426i	−0.995409	+	0.0957132i	$0.969487\pi$
$812$		0			0
$813$	−19.1421	−	15.5950i	−0.671343	−	0.546942i
$814$		0			0
$815$	2.25883	−	3.91241i	0.0791233	−	0.137046i
$816$		0			0
$817$	6.97359	−	4.02620i	0.243975	−	0.140859i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	42.7121	−	24.6598i	1.49066	−	0.860634i	0.490718	−	0.871318i	$-0.336734\pi$
$821$	42.7121	−	24.6598i	1.49066	−	0.860634i	0.999943	+	0.0106847i	$0.00340111\pi$
$822$		0			0
$823$	11.8496	−	20.5241i	0.413050	−	0.715424i	−0.582171	−	0.813066i	$-0.697797\pi$
$823$	11.8496	−	20.5241i	0.413050	−	0.715424i	0.995222	+	0.0976419i	$0.0311300\pi$
$824$		0			0
$825$	−61.7577	+	23.4970i	−2.15013	+	0.818061i
$826$		0			0
$827$			19.9706i			0.694445i	0.937783	+	0.347222i	$0.112875\pi$
$827$			19.9706i			0.694445i	−0.937783	+	0.347222i	$0.887125\pi$
$828$		0			0
$829$			15.4431i			0.536361i	0.963369	+	0.268181i	$0.0864224\pi$
$829$			15.4431i			0.536361i	−0.963369	+	0.268181i	$0.913578\pi$
$830$		0			0
$831$	−15.0529	−	2.42985i	−0.522178	−	0.0842904i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−35.0592	−	60.7242i	−1.21327	−	2.10145i
$836$		0			0
$837$	−22.5653	−	35.4327i	−0.779972	−	1.22473i
$838$		0			0
$839$	5.53910	+	9.59401i	0.191231	+	0.331222i	0.945658	−	0.325162i	$-0.105419\pi$
$839$	5.53910	+	9.59401i	0.191231	+	0.331222i	−0.754427	+	0.656383i	$0.772085\pi$
$840$		0			0
$841$	−6.16267	+	10.6741i	−0.212506	+	0.368071i
$842$		0			0
$843$	−5.31903	+	32.9513i	−0.183197	+	1.13490i
$844$		0			0
$845$	−49.6888			−1.70935
$846$		0			0
$847$		0			0
$848$		0			0
$849$	15.5677	−	5.92307i	0.534283	−	0.203279i
$850$		0			0
$851$	−15.3573	−	8.86656i	−0.526442	−	0.303942i
$852$		0			0
$853$	42.1706	−	24.3472i	1.44389	−	0.833633i	0.445788	−	0.895139i	$-0.352924\pi$
$853$	42.1706	−	24.3472i	1.44389	−	0.833633i	0.998107	+	0.0615058i	$0.0195903\pi$
$854$		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	0.0803361	−	0.996768i	$-0.474401\pi$
$859$	−21.7682	−	12.5679i	−0.742722	−	0.428811i	−0.823058	+	0.567957i	$0.807734\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	6.78244i		−	0.230877i	−0.993315	−	0.115438i	$-0.963173\pi$
$863$		−	6.78244i		−	0.230877i	0.993315	−	0.115438i	$-0.0368273\pi$
$864$		0			0
$865$	29.3466			0.997815
$866$		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
$873$	32.2081	+	36.1995i	1.09008	+	1.22517i
$874$		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
$879$	1.51021	+	3.96933i	0.0509382	+	0.133882i
$880$		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
$885$	59.6646	+	9.63112i	2.00560	+	0.323746i
$886$		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
$891$	−19.8617	+	26.6673i	−0.665391	+	0.893388i
$892$		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
$899$	33.0125			1.10103
$900$		0			0
$901$		−	0.280216i		−	0.00933535i
$902$		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	−0.0556121	−	0.998452i	$-0.517711\pi$
$911$	23.5808	−	13.6144i	0.781267	−	0.451065i	0.836879	+	0.547388i	$0.184378\pi$
$912$		0			0
$913$	−24.6159	−	14.2120i	−0.814668	−	0.470349i
$914$		0			0
$915$	36.6239	+	29.8374i	1.21075	+	0.986394i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	39.6986			1.30954			0.654769	−	0.755829i	$-0.272766\pi$
$919$	39.6986			1.30954			0.654769	+	0.755829i	$0.272766\pi$
$920$		0			0
$921$	14.3465	+	11.6881i	0.472734	+	0.385136i
$922$		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
$927$	−0.373477	+	1.12670i	−0.0122666	+	0.0370057i
$928$		0			0
$929$	−0.142283	−	0.246442i	−0.00466816	−	0.00808550i	0.863682	−	0.504037i	$-0.168153\pi$
$929$	−0.142283	−	0.246442i	−0.00466816	−	0.00808550i	−0.868350	+	0.495952i	$0.834819\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	12.7905	+	33.6176i	0.418743	+	1.10059i
$934$		0			0
$935$		−	84.4427i		−	2.76157i
$936$		0			0
$937$		−	21.7298i		−	0.709881i	−0.934889	−	0.354940i	$-0.884501\pi$
$937$		−	21.7298i		−	0.709881i	0.934889	−	0.354940i	$-0.115499\pi$
$938$		0			0
$939$	−1.08507	+	6.72197i	−0.0354098	+	0.219363i
$940$		0			0
$941$	−5.64242	+	9.77295i	−0.183938	+	0.318589i	−0.943218	−	0.332174i	$-0.892218\pi$
$941$	−5.64242	+	9.77295i	−0.183938	+	0.318589i	0.759280	+	0.650764i	$0.225551\pi$
$942$		0			0
$943$	−14.1513	+	8.17026i	−0.460830	+	0.266060i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−19.6701	+	11.3566i	−0.639194	+	0.369039i	−0.784304	−	0.620377i	$-0.786980\pi$
$947$	−19.6701	+	11.3566i	−0.639194	+	0.369039i	0.145110	+	0.989416i	$0.453646\pi$
$948$		0			0
$949$	1.12918	−	1.95580i	0.0366548	−	0.0634880i
$950$		0			0
$951$	−0.632234	+	3.91668i	−0.0205016	+	0.127007i
$952$		0			0
$953$		−	16.5638i		−	0.536554i	−0.963342	−	0.268277i	$-0.913546\pi$
$953$		−	16.5638i		−	0.536554i	0.963342	−	0.268277i	$-0.0864543\pi$
$954$		0			0
$955$		−	49.7270i		−	1.60913i
$956$		0			0
$957$	−9.29215	−	24.4228i	−0.300373	−	0.789476i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	17.1790	+	29.7550i	0.554162	+	0.959837i
$962$		0			0
$963$	16.6501	−	3.43618i	0.536543	−	0.110729i
$964$		0			0
$965$	−44.6589	−	77.3515i	−1.43762	−	2.49003i
$966$		0			0
$967$	8.38867	−	14.5296i	0.269762	−	0.467241i	−0.699039	−	0.715084i	$-0.746388\pi$
$967$	8.38867	−	14.5296i	0.269762	−	0.467241i	0.968800	+	0.247843i	$0.0797218\pi$
$968$		0			0
$969$	41.8625	+	34.1053i	1.34482	+	1.09562i
$970$		0			0
$971$	−31.3640			−1.00652			−0.503259	−	0.864136i	$-0.667866\pi$
$971$	−31.3640			−1.00652			−0.503259	+	0.864136i	$0.667866\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	7.68905	+	6.26425i	0.246247	+	0.200617i
$976$		0			0
$977$	−49.0953	−	28.3452i	−1.57070	−	0.906843i	−0.996083	−	0.0884183i	$-0.971819\pi$
$977$	−49.0953	−	28.3452i	−1.57070	−	0.906843i	−0.574614	−	0.818424i	$-0.694848\pi$
$978$		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
$989$		−	3.42977i		−	0.109060i
$990$		0			0
$991$	−62.5951			−1.98840			−0.994199	−	0.107558i	$-0.965697\pi$
$991$	−62.5951			−1.98840			−0.994199	+	0.107558i	$0.965697\pi$
$992$		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	0.268586	−	0.963256i	$-0.413444\pi$
$997$	39.0613	−	22.5520i	1.23708	−	0.714230i	0.968497	+	0.249025i	$0.0801102\pi$
$998$		0			0
$999$	35.9338	+	18.7130i	1.13689	+	0.592054i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.x.b.293.6		16
3.2	odd	2		5292.2.x.b.881.1		16
7.2	even	3		252.2.bm.a.185.6	yes	16
7.3	odd	6		252.2.w.a.5.8	✓	16
7.4	even	3		1764.2.w.b.509.1		16
7.5	odd	6		1764.2.bm.a.1697.3		16
7.6	odd	2		1764.2.x.a.293.3		16
9.2	odd	6		1764.2.x.a.1469.3		16
9.7	even	3		5292.2.x.a.4409.8		16
21.2	odd	6		756.2.bm.a.17.8		16
21.5	even	6		5292.2.bm.a.2285.1		16
21.11	odd	6		5292.2.w.b.1097.1		16
21.17	even	6		756.2.w.a.341.8		16
21.20	even	2		5292.2.x.a.881.8		16
28.3	even	6		1008.2.ca.d.257.1		16
28.23	odd	6		1008.2.df.d.689.3		16
63.2	odd	6		252.2.w.a.101.8	yes	16
63.11	odd	6		1764.2.bm.a.1685.3		16
63.16	even	3		756.2.w.a.521.8		16
63.20	even	6	inner	1764.2.x.b.1469.6		16
63.23	odd	6		2268.2.t.b.1781.1		16
63.25	even	3		5292.2.bm.a.4625.1		16
63.31	odd	6		2268.2.t.b.2105.1		16
63.34	odd	6		5292.2.x.b.4409.1		16
63.38	even	6		252.2.bm.a.173.6	yes	16
63.47	even	6		1764.2.w.b.1109.1		16
63.52	odd	6		756.2.bm.a.89.8		16
63.58	even	3		2268.2.t.a.1781.8		16
63.59	even	6		2268.2.t.a.2105.8		16
63.61	odd	6		5292.2.w.b.521.1		16
84.23	even	6		3024.2.df.d.17.8		16
84.59	odd	6		3024.2.ca.d.2609.8		16
252.79	odd	6		3024.2.ca.d.2033.8		16
252.115	even	6		3024.2.df.d.1601.8		16
252.191	even	6		1008.2.ca.d.353.1		16
252.227	odd	6		1008.2.df.d.929.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.8	✓	16	7.3	odd	6
252.2.w.a.101.8	yes	16	63.2	odd	6
252.2.bm.a.173.6	yes	16	63.38	even	6
252.2.bm.a.185.6	yes	16	7.2	even	3
756.2.w.a.341.8		16	21.17	even	6
756.2.w.a.521.8		16	63.16	even	3
756.2.bm.a.17.8		16	21.2	odd	6
756.2.bm.a.89.8		16	63.52	odd	6
1008.2.ca.d.257.1		16	28.3	even	6
1008.2.ca.d.353.1		16	252.191	even	6
1008.2.df.d.689.3		16	28.23	odd	6
1008.2.df.d.929.3		16	252.227	odd	6
1764.2.w.b.509.1		16	7.4	even	3
1764.2.w.b.1109.1		16	63.47	even	6
1764.2.x.a.293.3		16	7.6	odd	2
1764.2.x.a.1469.3		16	9.2	odd	6
1764.2.x.b.293.6		16	1.1	even	1	trivial
1764.2.x.b.1469.6		16	63.20	even	6	inner
1764.2.bm.a.1685.3		16	63.11	odd	6
1764.2.bm.a.1697.3		16	7.5	odd	6
2268.2.t.a.1781.8		16	63.58	even	3
2268.2.t.a.2105.8		16	63.59	even	6
2268.2.t.b.1781.1		16	63.23	odd	6
2268.2.t.b.2105.1		16	63.31	odd	6
3024.2.ca.d.2033.8		16	252.79	odd	6
3024.2.ca.d.2609.8		16	84.59	odd	6
3024.2.df.d.17.8		16	84.23	even	6
3024.2.df.d.1601.8		16	252.115	even	6
5292.2.w.b.521.1		16	63.61	odd	6
5292.2.w.b.1097.1		16	21.11	odd	6
5292.2.x.a.881.8		16	21.20	even	2
5292.2.x.a.4409.8		16	9.7	even	3
5292.2.x.b.881.1		16	3.2	odd	2
5292.2.x.b.4409.1		16	63.34	odd	6
5292.2.bm.a.2285.1		16	21.5	even	6
5292.2.bm.a.4625.1		16	63.25	even	3

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.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09400 - 1.34282i) q^{3} +(1.95741 - 3.39033i) q^{5} +(-0.606348 - 2.93808i) q^{9} +O(q^{10})\)	\(q+(1.09400 - 1.34282i) q^{3} +(1.95741 - 3.39033i) q^{5} +(-0.606348 - 2.93808i) q^{9} +(3.19958 - 1.84728i) q^{11} +(-0.480242 - 0.277268i) q^{13} +(-2.41122 - 6.33747i) q^{15} +5.83832 q^{17} +5.33973i q^{19} +(1.96965 + 1.13718i) q^{23} +(-5.16291 - 8.94242i) q^{25} +(-4.60867 - 2.40003i) q^{27} +(3.53638 - 2.04173i) q^{29} +(7.00132 + 4.04222i) q^{31} +(1.01976 - 6.31739i) q^{33} -7.79699 q^{37} +(-0.897704 + 0.341550i) q^{39} +(-3.59234 + 6.22212i) q^{41} +(-0.754009 - 1.30598i) q^{43} +(-11.1480 - 3.69531i) q^{45} +(-1.41416 - 2.44940i) q^{47} +(6.38709 - 7.83983i) q^{51} -0.0479960i q^{53} -14.4635i q^{55} +(7.17031 + 5.84164i) q^{57} +(-4.45656 + 7.71900i) q^{59} +(-6.03343 + 3.48340i) q^{61} +(-1.88006 + 1.08545i) q^{65} +(-0.587402 + 1.01741i) q^{67} +(3.68181 - 1.40082i) q^{69} +6.71061i q^{71} +4.07253i q^{73} +(-17.6563 - 2.85009i) q^{75} +(1.97374 + 3.41861i) q^{79} +(-8.26468 + 3.56300i) q^{81} +(-3.84674 - 6.66275i) q^{83} +(11.4280 - 19.7938i) q^{85} +(1.12710 - 6.98238i) q^{87} -5.42600 q^{89} +(13.0874 - 4.97937i) q^{93} +(18.1035 + 10.4520i) q^{95} +(-13.9874 + 8.07563i) q^{97} +(-7.36753 - 8.28055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{9}+O(q^{10}) \) 16 * q - 6 * q^9	\( 16 q - 6 q^{9} + 6 q^{11} + 3 q^{13} - 3 q^{15} + 18 q^{17} - 21 q^{23} - 8 q^{25} - 9 q^{27} + 6 q^{29} - 6 q^{31} + 27 q^{33} - 2 q^{37} + 6 q^{39} + 6 q^{41} - 2 q^{43} - 15 q^{45} - 18 q^{47} + 18 q^{51} + 15 q^{57} - 15 q^{59} - 3 q^{61} + 39 q^{65} - 7 q^{67} - 21 q^{69} - 42 q^{75} - q^{79} - 18 q^{81} + 6 q^{85} + 51 q^{87} + 42 q^{89} + 48 q^{93} - 6 q^{95} + 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q - 6 * q^9 + 6 * q^11 + 3 * q^13 - 3 * q^15 + 18 * q^17 - 21 * q^23 - 8 * q^25 - 9 * q^27 + 6 * q^29 - 6 * q^31 + 27 * q^33 - 2 * q^37 + 6 * q^39 + 6 * q^41 - 2 * q^43 - 15 * q^45 - 18 * q^47 + 18 * q^51 + 15 * q^57 - 15 * q^59 - 3 * q^61 + 39 * q^65 - 7 * q^67 - 21 * q^69 - 42 * q^75 - q^79 - 18 * q^81 + 6 * q^85 + 51 * q^87 + 42 * q^89 + 48 * q^93 - 6 * q^95 + 3 * q^97 - 9 * q^99

Introduction

L-functions

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