LMFDB - Embedded newform 1764.2.bm.a.1685.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1685,1764)]

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, 1, 5]))

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

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

chi := DirichletCharacter("1764.1685");

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.bm (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			1685.3
Root			$-0.544978 + 1.64408i$ of defining polynomial
Character	$\chi$	$=$	1764.1685
Dual form			1764.2.bm.a.1697.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.615921 + 1.61884i) q^{3} +3.91482 q^{5} +(-2.24128 - 1.99416i) q^{9} +O(q^{10})$	\(q+(-0.615921 + 1.61884i) q^{3} +3.91482 q^{5} +(-2.24128 - 1.99416i) q^{9} -3.69456i q^{11} +(0.480242 - 0.277268i) q^{13} +(-2.41122 + 6.33747i) q^{15} +(2.91916 + 5.05613i) q^{17} +(-4.62434 - 2.66986i) q^{19} +2.27435i q^{23} +10.3258 q^{25} +(4.60867 - 2.40003i) q^{27} +(3.53638 + 2.04173i) q^{29} +(7.00132 + 4.04222i) q^{31} +(5.98090 + 2.27556i) q^{33} +(3.89849 - 6.75239i) q^{37} +(0.153061 + 0.948209i) q^{39} +(3.59234 + 6.22212i) q^{41} +(-0.754009 + 1.30598i) q^{43} +(-8.77422 - 7.80676i) q^{45} +(1.41416 + 2.44940i) q^{47} +(-9.98304 + 1.61147i) q^{51} +(0.0415658 - 0.0239980i) q^{53} -14.4635i q^{55} +(7.17031 - 5.84164i) q^{57} +(4.45656 - 7.71900i) q^{59} +(-6.03343 + 3.48340i) q^{61} +(1.88006 - 1.08545i) q^{65} +(-0.587402 + 1.01741i) q^{67} +(-3.68181 - 1.40082i) q^{69} -6.71061i q^{71} +(3.52692 - 2.03627i) q^{73} +(-6.35989 + 16.7158i) q^{75} +(1.97374 + 3.41861i) q^{79} +(1.04669 + 8.93893i) q^{81} +(3.84674 - 6.66275i) q^{83} +(11.4280 + 19.7938i) q^{85} +(-5.48337 + 4.46729i) q^{87} +(-2.71300 + 4.69905i) q^{89} +(-10.8560 + 8.84433i) q^{93} +(-18.1035 - 10.4520i) q^{95} +(13.9874 + 8.07563i) q^{97} +(-7.36753 + 8.28055i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 3 q^{13} - 3 q^{15} + 9 q^{17} + 16 q^{25} + 9 q^{27} + 6 q^{29} - 6 q^{31} + 27 q^{33} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{51} + 15 q^{57} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} + 21 q^{69} + 15 q^{75} - q^{79} + 6 q^{85} + 3 q^{87} + 21 q^{89} - 69 q^{93} + 6 q^{95} - 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q - 3 * q^13 - 3 * q^15 + 9 * q^17 + 16 * q^25 + 9 * q^27 + 6 * q^29 - 6 * q^31 + 27 * q^33 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^51 + 15 * q^57 + 15 * q^59 - 3 * q^61 - 39 * q^65 - 7 * q^67 + 21 * q^69 + 15 * q^75 - q^79 + 6 * q^85 + 3 * q^87 + 21 * q^89 - 69 * 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 $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

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

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
$3$	−0.615921	+	1.61884i	−0.355602	+	0.934637i
$3$	−0.615921	+	1.61884i	−0.355602	+	0.934637i
$4$		0			0
$5$	3.91482			1.75076			0.875381	−	0.483434i	$-0.160611\pi$
$5$	3.91482			1.75076			0.875381	+	0.483434i	$0.160611\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2.24128	−	1.99416i	−0.747094	−	0.664718i
$10$		0			0
$11$		−	3.69456i		−	1.11395i	−0.830529	−	0.556976i	$-0.811962\pi$
$11$		−	3.69456i		−	1.11395i	0.830529	−	0.556976i	$-0.188038\pi$
$12$		0			0
$13$	0.480242	−	0.277268i	0.133195	−	0.0769002i	−0.431922	−	0.901911i	$-0.642164\pi$
$13$	0.480242	−	0.277268i	0.133195	−	0.0769002i	0.565117	+	0.825011i	$0.308831\pi$
$14$		0			0
$15$	−2.41122	+	6.33747i	−0.622575	+	1.63633i
$16$		0			0
$17$	2.91916	+	5.05613i	0.708000	+	1.22629i	0.965598	+	0.260040i	$0.0837356\pi$
$17$	2.91916	+	5.05613i	0.708000	+	1.22629i	−0.257598	+	0.966252i	$0.582931\pi$
$18$		0			0
$19$	−4.62434	−	2.66986i	−1.06090	−	0.612509i	−0.135216	−	0.990816i	$-0.543173\pi$
$19$	−4.62434	−	2.66986i	−1.06090	−	0.612509i	−0.925680	+	0.378307i	$0.876506\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			2.27435i			0.474236i	0.971481	+	0.237118i	$0.0762027\pi$
$23$			2.27435i			0.474236i	−0.971481	+	0.237118i	$0.923797\pi$
$24$		0			0
$25$	10.3258			2.06516
$26$		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
$31$	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
$33$	5.98090	+	2.27556i	1.04114	+	0.396124i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.89849	−	6.75239i	0.640909	−	1.11009i	−0.344322	−	0.938852i	$-0.611891\pi$
$37$	3.89849	−	6.75239i	0.640909	−	1.11009i	0.985230	−	0.171235i	$-0.0547756\pi$
$38$		0			0
$39$	0.153061	+	0.948209i	0.0245093	+	0.151835i
$40$		0			0
$41$	3.59234	+	6.22212i	0.561030	+	0.971732i	0.997407	+	0.0719684i	$0.0229281\pi$
$41$	3.59234	+	6.22212i	0.561030	+	0.971732i	−0.436377	+	0.899764i	$0.643739\pi$
$42$		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
$45$	−8.77422	−	7.80676i	−1.30798	−	1.16376i
$46$		0			0
$47$	1.41416	+	2.44940i	0.206277	+	0.357282i	0.950539	−	0.310606i	$-0.100532\pi$
$47$	1.41416	+	2.44940i	0.206277	+	0.357282i	−0.744262	+	0.667888i	$0.767199\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−9.98304	+	1.61147i	−1.39790	+	0.225651i
$52$		0			0
$53$	0.0415658	−	0.0239980i	0.00570950	−	0.00329638i	−0.497143	−	0.867669i	$-0.665617\pi$
$53$	0.0415658	−	0.0239980i	0.00570950	−	0.00329638i	0.502852	+	0.864373i	$0.332284\pi$
$54$		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	$-0.636310\pi$
$59$	4.45656	−	7.71900i	0.580195	−	1.00493i	0.995456	−	0.0952251i	$-0.0303571\pi$
$60$		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	$-0.869634\pi$
$71$		−	6.71061i		−	0.796403i	0.917298	−	0.398202i	$-0.130366\pi$
$72$		0			0
$73$	3.52692	−	2.03627i	0.412795	−	0.238327i	−0.279195	−	0.960234i	$-0.590068\pi$
$73$	3.52692	−	2.03627i	0.412795	−	0.238327i	0.691990	+	0.721907i	$0.256734\pi$
$74$		0			0
$75$	−6.35989	+	16.7158i	−0.734377	+	1.93018i
$76$		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
$81$	1.04669	+	8.93893i	0.116299	+	0.993214i
$82$		0			0
$83$	3.84674	−	6.66275i	0.422235	−	0.731332i	−0.573923	−	0.818909i	$-0.694579\pi$
$83$	3.84674	−	6.66275i	0.422235	−	0.731332i	0.996158	+	0.0875774i	$0.0279125\pi$
$84$		0			0
$85$	11.4280	+	19.7938i	1.23954	+	2.14694i
$86$		0			0
$87$	−5.48337	+	4.46729i	−0.587879	+	0.478944i
$88$		0			0
$89$	−2.71300	+	4.69905i	−0.287577	+	0.498099i	−0.973231	−	0.229829i	$-0.926183\pi$
$89$	−2.71300	+	4.69905i	−0.287577	+	0.498099i	0.685654	+	0.727928i	$0.259517\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−10.8560	+	8.84433i	−1.12571	+	0.917115i
$94$		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	$-0.0273309\pi$
$97$	13.9874	+	8.07563i	1.42021	+	0.819956i	0.423890	+	0.905714i	$0.360664\pi$
$98$		0			0
$99$	−7.36753	+	8.28055i	−0.740464	+	0.832227i
$100$		0			0
$101$	−1.62350			−0.161544			−0.0807722	−	0.996733i	$-0.525739\pi$
$101$	−1.62350			−0.161544			−0.0807722	+	0.996733i	$0.525739\pi$
$102$		0			0
$103$			0.395662i			0.0389857i	0.999810	+	0.0194929i	$0.00620517\pi$
$103$			0.395662i			0.0389857i	−0.999810	+	0.0194929i	$0.993795\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.90777	+	2.83350i	0.474452	+	0.273925i	0.718101	−	0.695938i	$-0.245011\pi$
$107$	4.90777	+	2.83350i	0.474452	+	0.273925i	−0.243650	+	0.969863i	$0.578345\pi$
$108$		0			0
$109$	−6.75667	−	11.7029i	−0.647171	−	1.12093i	−0.983795	−	0.179294i	$-0.942619\pi$
$109$	−6.75667	−	11.7029i	−0.647171	−	1.12093i	0.336624	−	0.941639i	$-0.390715\pi$
$110$		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
$115$			8.90369i			0.830273i
$116$		0			0
$117$	−1.62927	−	0.336241i	−0.150626	−	0.0310855i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−2.64977			−0.240888
$122$		0			0
$123$	−12.2852	+	1.98309i	−1.10772	+	0.178809i
$124$		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
$129$	−1.64976	−	2.02500i	−0.145254	−	0.178291i
$130$		0			0
$131$	−10.9072			−0.952968			−0.476484	−	0.879183i	$-0.658089\pi$
$131$	−10.9072			−0.952968			−0.476484	+	0.879183i	$0.658089\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	18.0421	−	9.39570i	1.55282	−	0.808653i
$136$		0			0
$137$			8.80514i			0.752274i	0.926564	+	0.376137i	$0.122748\pi$
$137$			8.80514i			0.752274i	−0.926564	+	0.376137i	$0.877252\pi$
$138$		0			0
$139$	−14.2352	+	8.21869i	−1.20741	+	0.697100i	−0.962193	−	0.272367i	$-0.912193\pi$
$139$	−14.2352	+	8.21869i	−1.20741	+	0.697100i	−0.245220	+	0.969468i	$0.578860\pi$
$140$		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
$149$		−	14.5278i		−	1.19016i	−0.803665	−	0.595082i	$-0.797120\pi$
$149$		−	14.5278i		−	1.19016i	0.803665	−	0.595082i	$-0.202880\pi$
$150$		0			0
$151$	5.60613			0.456221			0.228110	−	0.973635i	$-0.426745\pi$
$151$	5.60613			0.456221			0.228110	+	0.973635i	$0.426745\pi$
$152$		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
$159$	0.0132477	+	0.0820692i	0.00105061	+	0.00650851i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−0.576994	+	0.999383i	−0.0451937	+	0.0782777i	−0.887737	−	0.460350i	$-0.847724\pi$
$163$	−0.576994	+	0.999383i	−0.0451937	+	0.0782777i	0.842544	+	0.538628i	$0.181057\pi$
$164$		0			0
$165$	23.4141	+	8.90840i	1.82279	+	0.693518i
$166$		0			0
$167$	−8.95550	−	15.5114i	−0.692997	−	1.20031i	−0.970851	−	0.239683i	$-0.922957\pi$
$167$	−8.95550	−	15.5114i	−0.692997	−	1.20031i	0.277854	−	0.960623i	$-0.410377\pi$
$168$		0			0
$169$	−6.34625	+	10.9920i	−0.488173	+	0.845540i
$170$		0			0
$171$	5.04033	+	15.2056i	0.385443	+	1.16280i
$172$		0			0
$173$	−3.74814	−	6.49197i	−0.284966	−	0.493576i	0.687635	−	0.726057i	$-0.258649\pi$
$173$	−3.74814	−	6.49197i	−0.284966	−	0.493576i	−0.972601	+	0.232481i	$0.925316\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	9.75092	+	11.9688i	0.732924	+	0.899627i
$178$		0			0
$179$	−0.624382	+	0.360487i	−0.0466685	+	0.0269441i	−0.523153	−	0.852239i	$-0.675244\pi$
$179$	−0.624382	+	0.360487i	−0.0466685	+	0.0269441i	0.476484	+	0.879183i	$0.341911\pi$
$180$		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	−0.842058	−	0.539387i	$-0.818656\pi$
$191$	−11.0005	+	6.35111i	−0.795965	+	0.459551i	0.0460934	+	0.998937i	$0.485323\pi$
$192$		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	$-0.999647\pi$
$197$		−	0.0311360i		−	0.00221835i	0.999999	−	0.00110918i	$-0.000353062\pi$
$198$		0			0
$199$	−19.9144	+	11.4976i	−1.41169	+	0.815042i	−0.995548	−	0.0942556i	$-0.969953\pi$
$199$	−19.9144	+	11.4976i	−1.41169	+	0.815042i	−0.416146	+	0.909298i	$0.636620\pi$
$200$		0			0
$201$	−1.28523	−	1.57755i	−0.0906532	−	0.111272i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	14.0634	+	24.3585i	0.982229	+	1.70127i
$206$		0			0
$207$	4.53542	−	5.09747i	0.315233	−	0.354299i
$208$		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
$213$	10.8634	+	4.13321i	0.744348	+	0.283203i
$214$		0			0
$215$	−2.95181	+	5.11268i	−0.201312	+	0.348682i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	1.12409	+	6.96369i	0.0759587	+	0.470563i
$220$		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	$-0.317916\pi$
$223$	1.25230	+	0.723016i	0.0838602	+	0.0484167i	−0.457484	+	0.889218i	$0.651249\pi$
$224$		0			0
$225$	−23.1431	−	20.5913i	−1.54287	−	1.37275i
$226$		0			0
$227$	4.47193			0.296812			0.148406	−	0.988926i	$-0.452586\pi$
$227$	4.47193			0.296812			0.148406	+	0.988926i	$0.452586\pi$
$228$		0			0
$229$		−	2.58736i		−	0.170978i	−0.996339	−	0.0854888i	$-0.972755\pi$
$229$		−	2.58736i		−	0.170978i	0.996339	−	0.0854888i	$-0.0272452\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−15.0756	−	8.70389i	−0.987634	−	0.570211i	−0.0830679	−	0.996544i	$-0.526472\pi$
$233$	−15.0756	−	8.70389i	−0.987634	−	0.570211i	−0.904566	+	0.426333i	$0.859805\pi$
$234$		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
$241$			8.13235i			0.523851i	0.965088	+	0.261925i	$0.0843574\pi$
$241$			8.13235i			0.523851i	−0.965088	+	0.261925i	$0.915643\pi$
$242$		0			0
$243$	−15.1154	−	3.81125i	−0.969651	−	0.244492i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−2.96107			−0.188408
$248$		0			0
$249$	8.41663	+	10.3310i	0.533382	+	0.654699i
$250$		0			0
$251$	−25.9341			−1.63694			−0.818472	−	0.574546i	$-0.805179\pi$
$251$	−25.9341			−1.63694			−0.818472	+	0.574546i	$0.805179\pi$
$252$		0			0
$253$	8.40274			0.528276
$254$		0			0
$255$	−39.0818	+	6.30862i	−2.44740	+	0.395061i
$256$		0			0
$257$	−30.8230			−1.92269			−0.961344	−	0.275349i	$-0.911207\pi$
$257$	−30.8230			−1.92269			−0.961344	+	0.275349i	$0.911207\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3.85450	−	11.6282i	−0.238588	−	0.719767i
$262$		0			0
$263$		−	18.0855i		−	1.11520i	−0.830110	−	0.557600i	$-0.811722\pi$
$263$		−	18.0855i		−	1.11520i	0.830110	−	0.557600i	$-0.188278\pi$
$264$		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	−0.980687	−	0.195585i	$-0.937339\pi$
$269$	−10.8203	−	18.7413i	−0.659725	−	1.14268i	0.320961	−	0.947092i	$-0.395994\pi$
$270$		0			0
$271$	12.3453	+	7.12756i	0.749923	+	0.432968i	0.825666	−	0.564159i	$-0.190800\pi$
$271$	12.3453	+	7.12756i	0.749923	+	0.432968i	−0.0757430	+	0.997127i	$0.524133\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	38.1494i		−	2.30049i
$276$		0			0
$277$	8.80327			0.528937			0.264469	−	0.964394i	$-0.414803\pi$
$277$	8.80327			0.528937			0.264469	+	0.964394i	$0.414803\pi$
$278$		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
$283$	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
$285$	28.0705	−	22.8690i	1.66275	−	1.35464i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−8.54297	+	14.7969i	−0.502528	+	0.870404i
$290$		0			0
$291$	−21.6883	+	17.6694i	−1.27139	+	1.03580i
$292$		0			0
$293$	1.22598	+	2.12346i	0.0716225	+	0.124054i	0.899613	−	0.436689i	$-0.143849\pi$
$293$	1.22598	+	2.12346i	0.0716225	+	0.124054i	−0.827990	+	0.560743i	$0.810516\pi$
$294$		0			0
$295$	17.4467	−	30.2185i	1.01578	−	1.75939i
$296$		0			0
$297$	−8.86706	−	17.0270i	−0.514519	−	0.988007i
$298$		0			0
$299$	0.630605	+	1.09224i	0.0364688	+	0.0631658i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	0.999949	−	2.62819i	0.0574455	−	0.150985i
$304$		0			0
$305$	−23.6198	+	13.6369i	−1.35247	+	0.780846i
$306$		0			0
$307$			10.6839i			0.609760i	0.952391	+	0.304880i	$0.0986163\pi$
$307$			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	$-0.632942\pi$
$311$	10.3833	−	17.9843i	0.588780	−	1.01980i	0.994393	−	0.105752i	$-0.0337250\pi$
$312$		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	−0.443257	−	0.896395i	$-0.646177\pi$
$317$	1.98369	−	1.14528i	0.111415	−	0.0643256i	0.554672	+	0.832069i	$0.312844\pi$
$318$		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
$325$	4.95889	−	2.86302i	0.275070	−	0.158812i
$326$		0			0
$327$	23.1067	−	3.72990i	1.27780	−	0.206264i
$328$		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
$333$	−22.2029	+	7.35981i	−1.21671	+	0.403315i
$334$		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
$339$	0.362223	+	2.24396i	0.0196732	+	0.121875i
$340$		0			0
$341$	14.9342	−	25.8668i	0.808733	−	1.40077i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−14.4136	−	5.48397i	−0.776004	−	0.295247i
$346$		0			0
$347$	−7.35287	−	4.24518i	−0.394723	−	0.227893i	0.289482	−	0.957184i	$-0.406517\pi$
$347$	−7.35287	−	4.24518i	−0.394723	−	0.227893i	−0.684204	+	0.729290i	$0.739850\pi$
$348$		0			0
$349$	−16.5478	−	9.55386i	−0.885782	−	0.511407i	−0.0132216	−	0.999913i	$-0.504209\pi$
$349$	−16.5478	−	9.55386i	−0.885782	−	0.511407i	−0.872560	+	0.488506i	$0.837542\pi$
$350$		0			0
$351$	1.54782	−	2.43043i	0.0826167	−	0.129727i
$352$		0			0
$353$	−13.6590			−0.726996			−0.363498	−	0.931595i	$-0.618418\pi$
$353$	−13.6590			−0.726996			−0.363498	+	0.931595i	$0.618418\pi$
$354$		0			0
$355$		−	26.2708i		−	1.39431i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	14.8909	+	8.59724i	0.785909	+	0.453745i	0.838520	−	0.544870i	$-0.183421\pi$
$359$	14.8909	+	8.59724i	0.785909	+	0.453745i	−0.0526113	+	0.998615i	$0.516754\pi$
$360$		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
$367$			16.8587i			0.880018i	0.897993	+	0.440009i	$0.145025\pi$
$367$			16.8587i			0.880018i	−0.897993	+	0.440009i	$0.854975\pi$
$368$		0			0
$369$	4.35642	−	21.1092i	0.226786	−	1.09890i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.40858			−0.0729333			−0.0364667	−	0.999335i	$-0.511610\pi$
$373$	−1.40858			−0.0729333			−0.0364667	+	0.999335i	$0.511610\pi$
$374$		0			0
$375$	−12.8417	+	33.7522i	−0.663144	+	1.74296i
$376$		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
$381$	10.7130	−	28.1572i	0.548844	−	1.44254i
$382$		0			0
$383$	8.52077			0.435391			0.217696	−	0.976017i	$-0.430146\pi$
$383$	8.52077			0.435391			0.217696	+	0.976017i	$0.430146\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	4.29428	−	1.42346i	0.218290	−	0.0723586i
$388$		0			0
$389$		−	34.5976i		−	1.75417i	−0.480336	−	0.877084i	$-0.659485\pi$
$389$		−	34.5976i		−	1.75417i	0.480336	−	0.877084i	$-0.340515\pi$
$390$		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	−0.408416	−	0.912796i	$-0.633919\pi$
$397$	−27.9571	−	16.1411i	−1.40313	−	0.810097i	−0.994712	+	0.102699i	$0.967252\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	13.1028i		−	0.654321i	−0.944969	−	0.327161i	$-0.893908\pi$
$401$		−	13.1028i		−	0.654321i	0.944969	−	0.327161i	$-0.106092\pi$
$402$		0			0
$403$	4.48310			0.223319
$404$		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
$411$	−14.2541	−	5.42327i	−0.703103	−	0.267510i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	15.0593	−	26.0835i	0.739232	−	1.28039i
$416$		0			0
$417$	−4.53698	−	28.1066i	−0.222177	−	1.37638i
$418$		0			0
$419$	14.1954	+	24.5871i	0.693490	+	1.20116i	0.970687	+	0.240346i	$0.0772610\pi$
$419$	14.1954	+	24.5871i	0.693490	+	1.20116i	−0.277198	+	0.960813i	$0.589406\pi$
$420$		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
$423$	1.71495	−	8.30987i	0.0833838	−	0.404040i
$424$		0			0
$425$	30.1427	+	52.2087i	1.46214	+	2.53249i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	3.50322	−	0.565492i	0.169137	−	0.0273022i
$430$		0			0
$431$	−13.1844	+	7.61200i	−0.635069	+	0.366657i	−0.782713	−	0.622383i	$-0.786165\pi$
$431$	−13.1844	+	7.61200i	−0.635069	+	0.366657i	0.147643	+	0.989041i	$0.452831\pi$
$432$		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	−0.988124	−	0.153660i	$-0.950894\pi$
$443$	−28.3955	+	16.3942i	−1.34911	+	0.778910i	−0.360989	+	0.932570i	$0.617561\pi$
$444$		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	$0.00494916\pi$
$449$			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
$453$	−3.45294	+	9.07543i	−0.162233	+	0.426401i
$454$		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
$459$	25.5883	+	16.2960i	1.19436	+	0.760630i
$460$		0			0
$461$	−9.81626	+	17.0023i	−0.457189	+	0.791874i	−0.998811	−	0.0487477i	$-0.984477\pi$
$461$	−9.81626	+	17.0023i	−0.457189	+	0.791874i	0.541622	+	0.840622i	$0.317810\pi$
$462$		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
$465$	−42.4992	+	34.6240i	−1.97085	+	1.60565i
$466$		0			0
$467$	19.2809	−	33.3955i	0.892213	−	1.54536i	0.0549972	−	0.998487i	$-0.482485\pi$
$467$	19.2809	−	33.3955i	0.892213	−	1.54536i	0.837216	−	0.546872i	$-0.184182\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−23.9424	+	19.5058i	−1.10321	+	0.898779i
$472$		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
$479$	7.22578			0.330154			0.165077	−	0.986281i	$-0.447213\pi$
$479$	7.22578			0.330154			0.165077	+	0.986281i	$0.447213\pi$
$480$		0			0
$481$		−	4.32371i		−	0.197144i
$482$		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	0.954845	−	0.297104i	$-0.0960207\pi$
$487$	4.85770	+	8.41378i	0.220123	+	0.381265i	−0.734722	+	0.678368i	$0.762687\pi$
$488$		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
$493$			23.8405i			1.07372i
$494$		0			0
$495$	−28.8425	+	32.4169i	−1.29638	+	1.45703i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	34.3840			1.53924			0.769619	−	0.638503i	$-0.220446\pi$
$499$	34.3840			1.53924			0.769619	+	0.638503i	$0.220446\pi$
$500$		0			0
$501$	30.6263	−	4.94372i	1.36828	−	0.220869i
$502$		0			0
$503$	1.22542			0.0546388			0.0273194	−	0.999627i	$-0.491303\pi$
$503$	1.22542			0.0546388			0.0273194	+	0.999627i	$0.491303\pi$
$504$		0			0
$505$	−6.35571			−0.282826
$506$		0			0
$507$	−13.8855	−	17.0438i	−0.616678	−	0.756940i
$508$		0			0
$509$	−10.1016			−0.447744			−0.223872	−	0.974619i	$-0.571870\pi$
$509$	−10.1016			−0.447744			−0.223872	+	0.974619i	$0.571870\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−27.7198	−	1.20596i	−1.22386	−	0.0532442i
$514$		0			0
$515$			1.54895i			0.0682547i
$516$		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	$-0.0138980\pi$
$521$	10.5390	+	18.2541i	0.461723	+	0.799728i	−0.537324	+	0.843376i	$0.680565\pi$
$522$		0			0
$523$	−17.0733	−	9.85727i	−0.746563	−	0.431028i	0.0778877	−	0.996962i	$-0.475182\pi$
$523$	−17.0733	−	9.85727i	−0.746563	−	0.431028i	−0.824451	+	0.565934i	$0.808516\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			47.1995i			2.05604i
$528$		0			0
$529$	17.8273			0.775101
$530$		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
$537$	−0.199000	−	1.23281i	−0.00858750	−	0.0531995i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−4.22475	+	7.31748i	−0.181636	+	0.314603i	−0.942438	−	0.334381i	$-0.891473\pi$
$541$	−4.22475	+	7.31748i	−0.181636	+	0.314603i	0.760802	+	0.648984i	$0.224806\pi$
$542$		0			0
$543$	−8.20948	−	3.12347i	−0.352302	−	0.134041i
$544$		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
$549$	20.4691	+	4.22431i	0.873598	+	0.180289i
$550$		0			0
$551$	−10.9023	−	18.8833i	−0.464453	−	0.804456i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	33.3929	+	40.9881i	1.41745	+	1.73985i
$556$		0			0
$557$	18.2294	−	10.5247i	0.772403	−	0.445947i	−0.0613279	−	0.998118i	$-0.519534\pi$
$557$	18.2294	−	10.5247i	0.772403	−	0.445947i	0.833731	+	0.552170i	$0.186200\pi$
$558$		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	$0.502494\pi$
$563$	−20.6410	+	35.7513i	−0.869916	+	1.50674i	−0.862082	+	0.506769i	$0.830840\pi$
$564$		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	0.328627	−	0.944460i	$-0.393414\pi$
$569$	31.2691	−	18.0532i	1.31087	−	0.756829i	0.982240	+	0.187630i	$0.0600807\pi$
$570$		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
$577$	25.8102	−	14.9015i	1.07449	−	0.620359i	0.145088	−	0.989419i	$-0.453654\pi$
$577$	25.8102	−	14.9015i	1.07449	−	0.620359i	0.929406	+	0.369060i	$0.120320\pi$
$578$		0			0
$579$	24.9598	+	30.6369i	1.03730	+	1.27323i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.0886621	−	0.153567i	−0.00367201	−	0.00636010i
$584$		0			0
$585$	−6.37831	−	1.31633i	−0.263711	−	0.0544233i
$586$		0			0
$587$	4.72218	−	8.17905i	0.194905	−	0.337586i	−0.751964	−	0.659204i	$-0.770893\pi$
$587$	4.72218	−	8.17905i	0.194905	−	0.337586i	0.946869	+	0.321618i	$0.104227\pi$
$588$		0			0
$589$	−21.5843	−	37.3852i	−0.889367	−	1.54043i
$590$		0			0
$591$	0.0504043	+	0.0191774i	0.00207335	+	0.000788851i
$592$		0			0
$593$	12.4176	−	21.5079i	0.509929	−	0.883223i	−0.490005	−	0.871720i	$-0.663005\pi$
$593$	12.4176	−	21.5079i	0.509929	−	0.883223i	0.999934	−	0.0115033i	$-0.00366171\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−6.34704	−	39.3198i	−0.259767	−	1.60925i
$598$		0			0
$599$	−10.3052	−	5.94974i	−0.421061	−	0.243100i	0.274470	−	0.961596i	$-0.411498\pi$
$599$	−10.3052	−	5.94974i	−0.421061	−	0.243100i	−0.695531	+	0.718496i	$0.744831\pi$
$600$		0			0
$601$	22.1276	+	12.7754i	0.902604	+	0.521118i	0.878044	−	0.478580i	$-0.158848\pi$
$601$	22.1276	+	12.7754i	0.902604	+	0.521118i	0.0245596	+	0.999698i	$0.492182\pi$
$602$		0			0
$603$	3.34541	−	1.10893i	0.136236	−	0.0451592i
$604$		0			0
$605$	−10.3734			−0.421738
$606$		0			0
$607$			22.5794i			0.916471i	0.888831	+	0.458235i	$0.151518\pi$
$607$			22.5794i			0.916471i	−0.888831	+	0.458235i	$0.848482\pi$
$608$		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	0.537414	−	0.843319i	$-0.319401\pi$
$613$	−11.4294	−	19.7963i	−0.461628	−	0.799564i	−0.999042	+	0.0437549i	$0.986068\pi$
$614$		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
$619$		−	32.5894i		−	1.30988i	−0.755681	−	0.654940i	$-0.772694\pi$
$619$		−	32.5894i		−	1.30988i	0.755681	−	0.654940i	$-0.227306\pi$
$620$		0			0
$621$	5.45852	+	10.4817i	0.219043	+	0.420618i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	29.9935			1.19974
$626$		0			0
$627$	−21.5823	−	26.4911i	−0.861913	−	1.05795i
$628$		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
$633$	−29.2683	+	4.72452i	−1.16331	+	0.187783i
$634$		0			0
$635$	−68.0923			−2.70216
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−13.3820	+	15.0404i	−0.529384	+	0.594988i
$640$		0			0
$641$			47.7636i			1.88655i	0.332014	+	0.943274i	$0.392272\pi$
$641$			47.7636i			1.88655i	−0.332014	+	0.943274i	$0.607728\pi$
$642$		0			0
$643$	29.2346	−	16.8786i	1.15290	−	0.665626i	0.203306	−	0.979115i	$-0.434831\pi$
$643$	29.2346	−	16.8786i	1.15290	−	0.665626i	0.949592	+	0.313489i	$0.101498\pi$
$644$		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	$-0.159959\pi$
$647$	0.536008	+	0.928393i	0.0210727	+	0.0364989i	−0.855297	+	0.518138i	$0.826625\pi$
$648$		0			0
$649$	−28.5183	−	16.4650i	−1.11944	−	0.646309i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	33.3135i		−	1.30366i	−0.758367	−	0.651828i	$-0.774002\pi$
$653$		−	33.3135i		−	1.30366i	0.758367	−	0.651828i	$-0.225998\pi$
$654$		0			0
$655$	−42.6998			−1.66842
$656$		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
$661$	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
$663$	−4.34746	+	3.54187i	−0.168841	+	0.137555i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−4.64362	+	8.04298i	−0.179802	+	0.311426i
$668$		0			0
$669$	−1.94176	+	1.58195i	−0.0750730	+	0.0611618i
$670$		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
$675$	47.5883	−	24.7823i	1.83167	−	0.953872i
$676$		0			0
$677$	20.1769	+	34.9474i	0.775461	+	1.34314i	0.934535	+	0.355872i	$0.115816\pi$
$677$	20.1769	+	34.9474i	0.775461	+	1.34314i	−0.159073	+	0.987267i	$0.550851\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−2.75436	+	7.23933i	−0.105547	+	0.277412i
$682$		0			0
$683$	−8.23662	+	4.75541i	−0.315165	+	0.181961i	−0.649236	−	0.760587i	$-0.724911\pi$
$683$	−8.23662	+	4.75541i	−0.315165	+	0.181961i	0.334070	+	0.942548i	$0.391578\pi$
$684$		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	$0.0954314\pi$
$701$			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
$705$	−18.9329	+	3.05616i	−0.713053	+	0.115102i
$706$		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
$711$	2.39354	−	11.5980i	0.0897649	−	0.434959i
$712$		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
$717$	1.35021	+	8.36456i	0.0504247	+	0.312380i
$718$		0			0
$719$	20.0309	−	34.6946i	0.747027	−	1.29389i	−0.202214	−	0.979341i	$-0.564814\pi$
$719$	20.0309	−	34.6946i	0.747027	−	1.29389i	0.949242	−	0.314548i	$-0.101853\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−13.1650	−	5.00889i	−0.489610	−	0.186283i
$724$		0			0
$725$	36.5161	+	21.0826i	1.35617	+	0.782986i
$726$		0			0
$727$	43.2091	+	24.9468i	1.60254	+	0.925225i	0.990978	+	0.134027i	$0.0427910\pi$
$727$	43.2091	+	24.9468i	1.60254	+	0.925225i	0.611560	+	0.791198i	$0.290542\pi$
$728$		0			0
$729$	15.4797	−	22.1219i	0.573322	−	0.819330i
$730$		0			0
$731$	−8.80428			−0.325638
$732$		0			0
$733$			11.4480i			0.422843i	0.977395	+	0.211422i	$0.0678093\pi$
$733$			11.4480i			0.422843i	−0.977395	+	0.211422i	$0.932191\pi$
$734$		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	0.936362	−	0.351036i	$-0.114170\pi$
$739$	4.46303	+	7.73020i	0.164175	+	0.284360i	−0.772187	+	0.635396i	$0.780837\pi$
$740$		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
$745$		−	56.8737i		−	2.08369i
$746$		0			0
$747$	−21.9082	+	7.26210i	−0.801579	+	0.265706i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−26.4652			−0.965729			−0.482865	−	0.875695i	$-0.660404\pi$
$751$	−26.4652			−0.965729			−0.482865	+	0.875695i	$0.660404\pi$
$752$		0			0
$753$	15.9734	−	41.9831i	0.582101	−	1.52995i
$754$		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
$759$	−5.17542	+	13.6027i	−0.187856	+	0.493746i
$760$		0			0
$761$	53.9937			1.95727			0.978635	−	0.205605i	$-0.0659162\pi$
$761$	53.9937			1.95727			0.978635	+	0.205605i	$0.0659162\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	13.8587	−	67.1528i	0.501061	−	2.42791i
$766$		0			0
$767$		−	4.94264i		−	0.178469i
$768$		0			0
$769$	30.1912	−	17.4309i	1.08872	−	0.628575i	0.155487	−	0.987838i	$-0.450305\pi$
$769$	30.1912	−	17.4309i	1.08872	−	0.628575i	0.933236	+	0.359263i	$0.116972\pi$
$770$		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	$-0.178848\pi$
$773$	−1.06375	−	1.84246i	−0.0382603	−	0.0662688i	−0.884521	+	0.466499i	$0.845515\pi$
$774$		0			0
$775$	72.2944	+	41.7392i	2.59689	+	1.49932i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	38.3643i		−	1.37454i
$780$		0			0
$781$	−24.7928			−0.887155
$782$		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
$789$	29.2775	+	11.1393i	1.04231	+	0.396568i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−1.93167	+	3.34575i	−0.0685956	+	0.118811i
$794$		0			0
$795$	0.0518623	+	0.321286i	0.00183937	+	0.0113948i
$796$		0			0
$797$	−18.9123	−	32.7570i	−0.669907	−	1.16031i	−0.977930	−	0.208935i	$-0.933000\pi$
$797$	−18.9123	−	32.7570i	−0.669907	−	1.16031i	0.308022	−	0.951379i	$-0.400333\pi$
$798$		0			0
$799$	−8.25634	+	14.3004i	−0.292088	+	0.505912i
$800$		0			0
$801$	15.4512	−	5.12176i	0.545943	−	0.180969i
$802$		0			0
$803$	−7.52311	−	13.0304i	−0.265485	−	0.459833i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	37.0036	−	5.97316i	1.30259	−	0.210265i
$808$		0			0
$809$	−39.2475	+	22.6595i	−1.37987	+	0.796667i	−0.992143	−	0.125109i	$-0.960072\pi$
$809$	−39.2475	+	22.6595i	−1.37987	+	0.796667i	−0.387724	+	0.921776i	$0.626739\pi$
$810$		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	−0.999943	−	0.0106847i	$-0.996599\pi$
$821$	−42.7121	+	24.6598i	−1.49066	+	0.860634i	−0.490718	+	0.871318i	$0.663266\pi$
$822$		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	$-0.887125\pi$
$827$		−	19.9706i		−	0.694445i	0.937783	−	0.347222i	$-0.112875\pi$
$828$		0			0
$829$	13.3741	−	7.72155i	0.464503	−	0.268181i	−0.249433	−	0.968392i	$-0.580244\pi$
$829$	13.3741	−	7.72155i	0.464503	−	0.268181i	0.713936	+	0.700211i	$0.246911\pi$
$830$		0			0
$831$	−5.42212	+	14.2511i	−0.188091	+	0.494365i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−35.0592	−	60.7242i	−1.21327	−	2.10145i
$836$		0			0
$837$	41.9682	+	1.82584i	1.45063	+	0.0631101i
$838$		0			0
$839$	−5.53910	+	9.59401i	−0.191231	+	0.331222i	−0.945658	−	0.325162i	$-0.894581\pi$
$839$	−5.53910	+	9.59401i	−0.191231	+	0.331222i	0.754427	+	0.656383i	$0.227915\pi$
$840$		0			0
$841$	−6.16267	−	10.6741i	−0.212506	−	0.368071i
$842$		0			0
$843$	25.8772	−	21.0821i	0.891258	−	0.726106i
$844$		0			0
$845$	−24.8444	+	43.0318i	−0.854674	+	1.48034i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−12.9134	+	10.5205i	−0.443186	+	0.361063i
$850$		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	$-0.647076\pi$
$853$	−42.1706	−	24.3472i	−1.44389	−	0.833633i	−0.998107	+	0.0615058i	$0.980410\pi$
$854$		0			0
$855$	19.7320	+	59.5271i	0.674819	+	2.03578i
$856$		0			0
$857$	−16.7826			−0.573283			−0.286641	−	0.958038i	$-0.592539\pi$
$857$	−16.7826			−0.573283			−0.286641	+	0.958038i	$0.592539\pi$
$858$		0			0
$859$			25.1358i			0.857622i	0.903394	+	0.428811i	$0.141067\pi$
$859$			25.1358i			0.857622i	−0.903394	+	0.428811i	$0.858933\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−5.87377	−	3.39122i	−0.199945	−	0.115438i	0.396685	−	0.917955i	$-0.370161\pi$
$863$	−5.87377	−	3.39122i	−0.199945	−	0.115438i	−0.596630	+	0.802516i	$0.703494\pi$
$864$		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
$871$			0.651470i			0.0220742i
$872$		0			0
$873$	−15.2457	−	45.9928i	−0.515987	−	1.55662i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−43.7259			−1.47652			−0.738260	−	0.674517i	$-0.764352\pi$
$877$	−43.7259			−1.47652			−0.738260	+	0.674517i	$0.764352\pi$
$878$		0			0
$879$	−4.19264	+	0.676780i	−0.141414	+	0.0228272i
$880$		0			0
$881$	−27.5307			−0.927531			−0.463766	−	0.885958i	$-0.653502\pi$
$881$	−27.5307			−0.927531			−0.463766	+	0.885958i	$0.653502\pi$
$882$		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
$885$	38.1731	+	46.8555i	1.28318	+	1.57503i
$886$		0			0
$887$	−24.6185			−0.826607			−0.413303	−	0.910593i	$-0.635625\pi$
$887$	−24.6185			−0.826607			−0.413303	+	0.910593i	$0.635625\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	33.0254	−	3.86706i	1.10639	−	0.129551i
$892$		0			0
$893$		−	15.1025i		−	0.505386i
$894$		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
$905$			19.8529i			0.659932i
$906$		0			0
$907$	−10.0867			−0.334925			−0.167462	−	0.985878i	$-0.553557\pi$
$907$	−10.0867			−0.334925			−0.167462	+	0.985878i	$0.553557\pi$
$908$		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
$913$	−24.6159	−	14.2120i	−0.814668	−	0.470349i
$914$		0			0
$915$	−7.52801	−	46.6359i	−0.248868	−	1.54174i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−19.8493	+	34.3800i	−0.654769	+	1.13409i	0.327183	+	0.944961i	$0.393901\pi$
$919$	−19.8493	+	34.3800i	−0.654769	+	1.13409i	−0.981952	+	0.189132i	$0.939433\pi$
$920$		0			0
$921$	−17.2954	−	6.58041i	−0.569904	−	0.216832i
$922$		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
$927$	0.789012	−	0.886790i	0.0259145	−	0.0291260i
$928$		0			0
$929$	0.142283	+	0.246442i	0.00466816	+	0.00808550i	0.868350	−	0.495952i	$-0.165181\pi$
$929$	0.142283	+	0.246442i	0.00466816	+	0.00808550i	−0.863682	+	0.504037i	$0.831847\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	22.7185	+	27.8857i	0.743769	+	0.912938i
$934$		0			0
$935$	73.1295	−	42.2214i	2.39159	−	1.38079i
$936$		0			0
$937$		−	21.7298i		−	0.709881i	−0.934889	−	0.354940i	$-0.884501\pi$
$937$		−	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	−0.759280	−	0.650764i	$-0.774449\pi$
$941$	5.64242	−	9.77295i	0.183938	−	0.318589i	0.943218	+	0.332174i	$0.107782\pi$
$942$		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	−0.145110	−	0.989416i	$-0.546354\pi$
$947$	19.6701	−	11.3566i	0.639194	−	0.369039i	0.784304	+	0.620377i	$0.213020\pi$
$948$		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	$0.0864543\pi$
$953$			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
$957$	16.5047	+	20.2586i	0.533520	+	0.654868i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	17.1790	+	29.7550i	0.554162	+	0.959837i
$962$		0			0
$963$	−5.34925	−	16.1375i	−0.172377	−	0.520024i
$964$		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
$969$	50.4674	+	19.2014i	1.62125	+	0.616837i
$970$		0			0
$971$	−15.6820	+	27.1620i	−0.503259	+	0.871670i	0.496734	+	0.867903i	$0.334532\pi$
$971$	−15.6820	+	27.1620i	−0.503259	+	0.871670i	−0.999993	+	0.00376705i	$0.998801\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	1.58048	+	9.79104i	0.0506158	+	0.313564i
$976$		0			0
$977$	49.0953	+	28.3452i	1.57070	+	0.906843i	0.996083	+	0.0884183i	$0.0281812\pi$
$977$	49.0953	+	28.3452i	1.57070	+	0.906843i	0.574614	+	0.818424i	$0.305152\pi$
$978$		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
$983$	−39.8408			−1.27072			−0.635362	−	0.772214i	$-0.719149\pi$
$983$	−39.8408			−1.27072			−0.635362	+	0.772214i	$0.719149\pi$
$984$		0			0
$985$		−	0.121892i		−	0.00388380i
$986$		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	0.590247	+	0.807223i	$0.299030\pi$
$991$	31.2975	+	54.2089i	0.994199	+	1.72200i	0.403952	+	0.914780i	$0.367636\pi$
$992$		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
$997$			45.1041i			1.42846i	0.699911	+	0.714230i	$0.253223\pi$
$997$			45.1041i			1.42846i	−0.699911	+	0.714230i	$0.746777\pi$
$998$		0			0
$999$	1.76092	−	40.4761i	0.0557130	−	1.28061i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.8	✓	16	63.41	even	6
252.2.w.a.101.8	yes	16	7.4	even	3
252.2.bm.a.173.6	yes	16	7.6	odd	2
252.2.bm.a.185.6	yes	16	63.32	odd	6
756.2.w.a.341.8		16	63.13	odd	6
756.2.w.a.521.8		16	21.11	odd	6
756.2.bm.a.17.8		16	63.4	even	3
756.2.bm.a.89.8		16	21.20	even	2
1008.2.ca.d.257.1		16	252.167	odd	6
1008.2.ca.d.353.1		16	28.11	odd	6
1008.2.df.d.689.3		16	252.95	even	6
1008.2.df.d.929.3		16	28.27	even	2
1764.2.w.b.509.1		16	9.5	odd	6
1764.2.w.b.1109.1		16	7.3	odd	6
1764.2.x.a.293.3		16	63.5	even	6
1764.2.x.a.1469.3		16	7.2	even	3
1764.2.x.b.293.6		16	63.23	odd	6
1764.2.x.b.1469.6		16	7.5	odd	6
1764.2.bm.a.1685.3		16	1.1	even	1	trivial
1764.2.bm.a.1697.3		16	63.59	even	6	inner
2268.2.t.a.1781.8		16	63.11	odd	6
2268.2.t.a.2105.8		16	63.34	odd	6
2268.2.t.b.1781.1		16	63.25	even	3
2268.2.t.b.2105.1		16	63.20	even	6
3024.2.ca.d.2033.8		16	84.11	even	6
3024.2.ca.d.2609.8		16	252.139	even	6
3024.2.df.d.17.8		16	252.67	odd	6
3024.2.df.d.1601.8		16	84.83	odd	2
5292.2.w.b.521.1		16	21.17	even	6
5292.2.w.b.1097.1		16	9.4	even	3
5292.2.x.a.881.8		16	63.40	odd	6
5292.2.x.a.4409.8		16	21.2	odd	6
5292.2.x.b.881.1		16	63.58	even	3
5292.2.x.b.4409.1		16	21.5	even	6
5292.2.bm.a.2285.1		16	63.31	odd	6
5292.2.bm.a.4625.1		16	3.2	odd	2

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.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.615921 + 1.61884i) q^{3} +3.91482 q^{5} +(-2.24128 - 1.99416i) q^{9} +O(q^{10})\)	\(q+(-0.615921 + 1.61884i) q^{3} +3.91482 q^{5} +(-2.24128 - 1.99416i) q^{9} -3.69456i q^{11} +(0.480242 - 0.277268i) q^{13} +(-2.41122 + 6.33747i) q^{15} +(2.91916 + 5.05613i) q^{17} +(-4.62434 - 2.66986i) q^{19} +2.27435i q^{23} +10.3258 q^{25} +(4.60867 - 2.40003i) q^{27} +(3.53638 + 2.04173i) q^{29} +(7.00132 + 4.04222i) q^{31} +(5.98090 + 2.27556i) q^{33} +(3.89849 - 6.75239i) q^{37} +(0.153061 + 0.948209i) q^{39} +(3.59234 + 6.22212i) q^{41} +(-0.754009 + 1.30598i) q^{43} +(-8.77422 - 7.80676i) q^{45} +(1.41416 + 2.44940i) q^{47} +(-9.98304 + 1.61147i) q^{51} +(0.0415658 - 0.0239980i) q^{53} -14.4635i q^{55} +(7.17031 - 5.84164i) q^{57} +(4.45656 - 7.71900i) q^{59} +(-6.03343 + 3.48340i) q^{61} +(1.88006 - 1.08545i) q^{65} +(-0.587402 + 1.01741i) q^{67} +(-3.68181 - 1.40082i) q^{69} -6.71061i q^{71} +(3.52692 - 2.03627i) q^{73} +(-6.35989 + 16.7158i) q^{75} +(1.97374 + 3.41861i) q^{79} +(1.04669 + 8.93893i) q^{81} +(3.84674 - 6.66275i) q^{83} +(11.4280 + 19.7938i) q^{85} +(-5.48337 + 4.46729i) q^{87} +(-2.71300 + 4.69905i) q^{89} +(-10.8560 + 8.84433i) q^{93} +(-18.1035 - 10.4520i) q^{95} +(13.9874 + 8.07563i) q^{97} +(-7.36753 + 8.28055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 3 q^{13} - 3 q^{15} + 9 q^{17} + 16 q^{25} + 9 q^{27} + 6 q^{29} - 6 q^{31} + 27 q^{33} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{51} + 15 q^{57} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} + 21 q^{69} + 15 q^{75} - q^{79} + 6 q^{85} + 3 q^{87} + 21 q^{89} - 69 q^{93} + 6 q^{95} - 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q - 3 * q^13 - 3 * q^15 + 9 * q^17 + 16 * q^25 + 9 * q^27 + 6 * q^29 - 6 * q^31 + 27 * q^33 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^51 + 15 * q^57 + 15 * q^59 - 3 * q^61 - 39 * q^65 - 7 * q^67 + 21 * q^69 + 15 * q^75 - q^79 + 6 * q^85 + 3 * q^87 + 21 * q^89 - 69 * q^93 + 6 * q^95 - 3 * q^97 - 9 * q^99

Introduction

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