LMFDB - Embedded newform 1638.2.bj.h.1135.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(127,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1638.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.bj (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:	$13.0794958511$
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} + 2 x^{14} + 18 x^{13} + 143 x^{12} - 148 x^{11} + 172 x^{10} + 1612 x^{9} + \cdots + 97344 $ x^16 - 2x^15 + 2x^14 + 18x^13 + 143x^12 - 148x^11 + 172x^10 + 1612x^9 + 6655x^8 + 478x^7 + 1106x^6 + 11266x^5 + 55249x^4 + 8856x^3 + 288x^2 + 7488*x + 97344
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1135.1
Root			$-2.02798 - 2.02798i$ of defining polynomial
Character	$\chi$	$=$	1638.1135
Dual form			1638.2.bj.h.127.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -2.19147i q^{5} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-1.09573 + 1.89787i) q^{10} +(-3.54195 - 2.04495i) q^{11} +(3.53557 + 0.706919i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.85204 + 4.93987i) q^{17} +(6.69612 - 3.86601i) q^{19} +(1.89787 - 1.09573i) q^{20} +(2.04495 + 3.54195i) q^{22} +(-1.23791 + 2.14412i) q^{23} +0.197462 q^{25} +(-2.70844 - 2.38000i) q^{26} +(0.866025 + 0.500000i) q^{28} +(4.90888 - 8.50243i) q^{29} +7.19507i q^{31} +(0.866025 - 0.500000i) q^{32} -5.70407i q^{34} +(-1.09573 - 1.89787i) q^{35} +(-8.79425 - 5.07736i) q^{37} -7.73201 q^{38} -2.19147 q^{40} +(-3.14093 - 1.81341i) q^{41} +(-1.37769 - 2.38624i) q^{43} -4.08989i q^{44} +(2.14412 - 1.23791i) q^{46} -7.70008i q^{47} +(0.500000 - 0.866025i) q^{49} +(-0.171007 - 0.0987308i) q^{50} +(1.15558 + 3.41535i) q^{52} +6.31111 q^{53} +(-4.48144 + 7.76207i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-8.50243 + 4.90888i) q^{58} +(4.20781 - 2.42938i) q^{59} +(5.63434 + 9.75896i) q^{61} +(3.59754 - 6.23112i) q^{62} -1.00000 q^{64} +(1.54919 - 7.74810i) q^{65} +(-5.49094 - 3.17020i) q^{67} +(-2.85204 + 4.93987i) q^{68} +2.19147i q^{70} +(-7.21341 + 4.16466i) q^{71} -7.37805i q^{73} +(5.07736 + 8.79425i) q^{74} +(6.69612 + 3.86601i) q^{76} -4.08989 q^{77} +3.45834 q^{79} +(1.89787 + 1.09573i) q^{80} +(1.81341 + 3.14093i) q^{82} +0.332783i q^{83} +(10.8256 - 6.25015i) q^{85} +2.75539i q^{86} +(-2.04495 + 3.54195i) q^{88} +(-11.7151 - 6.76374i) q^{89} +(3.41535 - 1.15558i) q^{91} -2.47582 q^{92} +(-3.85004 + 6.66847i) q^{94} +(-8.47223 - 14.6743i) q^{95} +(10.0600 - 5.80816i) q^{97} +(-0.866025 + 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 2 q^{10} - 12 q^{11} + 10 q^{13} - 16 q^{14} - 8 q^{16} - 6 q^{17} - 4 q^{22} - 12 q^{23} - 20 q^{25} - 2 q^{26} + 16 q^{29} + 2 q^{35} - 6 q^{37} + 4 q^{40} + 12 q^{41} - 6 q^{43} + 6 q^{46}+ \cdots - 24 q^{97}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^10 - 12 * q^11 + 10 * q^13 - 16 * q^14 - 8 * q^16 - 6 * q^17 - 4 * q^22 - 12 * q^23 - 20 * q^25 - 2 * q^26 + 16 * q^29 + 2 * q^35 - 6 * q^37 + 4 * q^40 + 12 * q^41 - 6 * q^43 + 6 * q^46 + 8 * q^49 - 24 * q^50 - 4 * q^52 - 40 * q^53 + 20 * q^55 - 8 * q^56 + 6 * q^58 + 6 * q^59 - 2 * q^61 - 14 * q^62 - 16 * q^64 - 52 * q^65 - 30 * q^67 + 6 * q^68 + 12 * q^71 + 24 * q^74 + 8 * q^77 - 16 * q^79 + 2 * q^82 + 6 * q^85 + 4 * q^88 + 30 * q^89 + 4 * q^91 - 24 * q^92 - 8 * q^94 - 40 * q^95 - 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		−	2.19147i		−	0.980055i	−0.871707	−	0.490027i	$-0.836987\pi$
$5$		−	2.19147i		−	0.980055i	0.871707	−	0.490027i	$-0.163013\pi$
$6$		0			0
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−1.09573	+	1.89787i	−0.346502	+	0.600159i
$11$	−3.54195	−	2.04495i	−1.06794	−	0.616574i	−0.140321	−	0.990106i	$-0.544813\pi$
$11$	−3.54195	−	2.04495i	−1.06794	−	0.616574i	−0.927617	+	0.373532i	$0.878147\pi$
$12$		0			0
$13$	3.53557	+	0.706919i	0.980591	+	0.196064i
$13$	3.53557	+	0.706919i	0.980591	+	0.196064i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.85204	+	4.93987i	0.691720	+	1.19809i	0.971274	+	0.237965i	$0.0764803\pi$
$17$	2.85204	+	4.93987i	0.691720	+	1.19809i	−0.279553	+	0.960130i	$0.590186\pi$
$18$		0			0
$19$	6.69612	−	3.86601i	1.53620	−	0.886923i	0.537139	−	0.843494i	$-0.319505\pi$
$19$	6.69612	−	3.86601i	1.53620	−	0.886923i	0.999057	−	0.0434286i	$-0.0138281\pi$
$20$	1.89787	−	1.09573i	0.424376	−	0.245014i
$21$		0			0
$22$	2.04495	+	3.54195i	0.435984	+	0.755146i
$23$	−1.23791	+	2.14412i	−0.258122	+	0.447080i	−0.965739	−	0.259516i	$-0.916437\pi$
$23$	−1.23791	+	2.14412i	−0.258122	+	0.447080i	0.707617	+	0.706596i	$0.249770\pi$
$24$		0			0
$25$	0.197462			0.0394923
$26$	−2.70844	−	2.38000i	−0.531168	−	0.466755i
$27$		0			0
$28$	0.866025	+	0.500000i	0.163663	+	0.0944911i
$29$	4.90888	−	8.50243i	0.911556	−	1.57886i	0.0996903	−	0.995019i	$-0.468215\pi$
$29$	4.90888	−	8.50243i	0.911556	−	1.57886i	0.811866	−	0.583844i	$-0.198452\pi$
$30$		0			0
$31$			7.19507i			1.29227i	0.763222	+	0.646137i	$0.223616\pi$
$31$			7.19507i			1.29227i	−0.763222	+	0.646137i	$0.776384\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$		−	5.70407i		−	0.978240i
$35$	−1.09573	−	1.89787i	−0.185213	−	0.320798i
$36$		0			0
$37$	−8.79425	−	5.07736i	−1.44577	−	0.834713i	−0.447540	−	0.894264i	$-0.647700\pi$
$37$	−8.79425	−	5.07736i	−1.44577	−	0.834713i	−0.998225	+	0.0595505i	$0.981033\pi$
$38$	−7.73201			−1.25430
$39$		0			0
$40$	−2.19147			−0.346502
$41$	−3.14093	−	1.81341i	−0.490530	−	0.283208i	0.234264	−	0.972173i	$-0.424732\pi$
$41$	−3.14093	−	1.81341i	−0.490530	−	0.283208i	−0.724794	+	0.688965i	$0.758065\pi$
$42$		0			0
$43$	−1.37769	−	2.38624i	−0.210096	−	0.363897i	0.741648	−	0.670789i	$-0.234044\pi$
$43$	−1.37769	−	2.38624i	−0.210096	−	0.363897i	−0.951744	+	0.306892i	$0.900711\pi$
$44$		−	4.08989i		−	0.616574i
$45$		0			0
$46$	2.14412	−	1.23791i	0.316133	−	0.182520i
$47$		−	7.70008i		−	1.12317i	−0.827418	−	0.561586i	$-0.810191\pi$
$47$		−	7.70008i		−	1.12317i	0.827418	−	0.561586i	$-0.189809\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	−0.171007	−	0.0987308i	−0.0241840	−	0.0139626i
$51$		0			0
$52$	1.15558	+	3.41535i	0.160250	+	0.473624i
$53$	6.31111			0.866898			0.433449	−	0.901178i	$-0.357296\pi$
$53$	6.31111			0.866898			0.433449	+	0.901178i	$0.357296\pi$
$54$		0			0
$55$	−4.48144	+	7.76207i	−0.604277	+	1.04664i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$		0			0
$58$	−8.50243	+	4.90888i	−1.11642	+	0.644568i
$59$	4.20781	−	2.42938i	0.547810	−	0.316278i	−0.200428	−	0.979708i	$-0.564233\pi$
$59$	4.20781	−	2.42938i	0.547810	−	0.316278i	0.748238	+	0.663430i	$0.230900\pi$
$60$		0			0
$61$	5.63434	+	9.75896i	0.721403	+	1.24951i	0.960438	+	0.278496i	$0.0898357\pi$
$61$	5.63434	+	9.75896i	0.721403	+	1.24951i	−0.239035	+	0.971011i	$0.576831\pi$
$62$	3.59754	−	6.23112i	0.456888	−	0.791353i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.54919	−	7.74810i	0.192153	−	0.961033i
$66$		0			0
$67$	−5.49094	−	3.17020i	−0.670825	−	0.387301i	0.125564	−	0.992086i	$-0.459926\pi$
$67$	−5.49094	−	3.17020i	−0.670825	−	0.387301i	−0.796389	+	0.604784i	$0.793259\pi$
$68$	−2.85204	+	4.93987i	−0.345860	+	0.599047i
$69$		0			0
$70$			2.19147i			0.261931i
$71$	−7.21341	+	4.16466i	−0.856074	+	0.494255i	−0.862696	−	0.505723i	$-0.831226\pi$
$71$	−7.21341	+	4.16466i	−0.856074	+	0.494255i	0.00662155	+	0.999978i	$0.497892\pi$
$72$		0			0
$73$		−	7.37805i		−	0.863536i	−0.901985	−	0.431768i	$-0.857890\pi$
$73$		−	7.37805i		−	0.863536i	0.901985	−	0.431768i	$-0.142110\pi$
$74$	5.07736	+	8.79425i	0.590231	+	1.02231i
$75$		0			0
$76$	6.69612	+	3.86601i	0.768098	+	0.443461i
$77$	−4.08989			−0.466086
$78$		0			0
$79$	3.45834			0.389094			0.194547	−	0.980893i	$-0.437676\pi$
$79$	3.45834			0.389094			0.194547	+	0.980893i	$0.437676\pi$
$80$	1.89787	+	1.09573i	0.212188	+	0.122507i
$81$		0			0
$82$	1.81341	+	3.14093i	0.200258	+	0.346857i
$83$			0.332783i			0.0365277i	0.999833	+	0.0182638i	$0.00581389\pi$
$83$			0.332783i			0.0365277i	−0.999833	+	0.0182638i	$0.994186\pi$
$84$		0			0
$85$	10.8256	−	6.25015i	1.17420	−	0.677924i
$86$			2.75539i			0.297121i
$87$		0			0
$88$	−2.04495	+	3.54195i	−0.217992	+	0.377573i
$89$	−11.7151	−	6.76374i	−1.24180	−	0.716956i	−0.272342	−	0.962200i	$-0.587798\pi$
$89$	−11.7151	−	6.76374i	−1.24180	−	0.716956i	−0.969461	+	0.245245i	$0.921132\pi$
$90$		0			0
$91$	3.41535	−	1.15558i	0.358026	−	0.121137i
$92$	−2.47582			−0.258122
$93$		0			0
$94$	−3.85004	+	6.66847i	−0.397101	+	0.687800i
$95$	−8.47223	−	14.6743i	−0.869233	−	1.50556i
$96$		0			0
$97$	10.0600	−	5.80816i	1.02144	−	0.589729i	0.106920	−	0.994268i	$-0.465901\pi$
$97$	10.0600	−	5.80816i	1.02144	−	0.589729i	0.914521	+	0.404539i	$0.132568\pi$
$98$	−0.866025	+	0.500000i	−0.0874818	+	0.0505076i
$99$		0			0
$100$	0.0987308	+	0.171007i	0.00987308	+	0.0171007i
$101$	1.12692	−	1.95189i	0.112133	−	0.194220i	−0.804497	−	0.593957i	$-0.797565\pi$
$101$	1.12692	−	1.95189i	0.112133	−	0.194220i	0.916630	+	0.399737i	$0.130898\pi$
$102$		0			0
$103$	−16.0325			−1.57973			−0.789867	−	0.613278i	$-0.789850\pi$
$103$	−16.0325			−1.57973			−0.789867	+	0.613278i	$0.789850\pi$
$104$	0.706919	−	3.53557i	0.0693191	−	0.346691i
$105$		0			0
$106$	−5.46559	−	3.15556i	−0.530865	−	0.306495i
$107$	4.30793	−	7.46156i	0.416464	−	0.721336i	−0.579117	−	0.815244i	$-0.696603\pi$
$107$	4.30793	−	7.46156i	0.416464	−	0.721336i	0.995581	+	0.0939082i	$0.0299360\pi$
$108$		0			0
$109$		−	10.0318i		−	0.960870i	−0.877030	−	0.480435i	$-0.840479\pi$
$109$		−	10.0318i		−	0.960870i	0.877030	−	0.480435i	$-0.159521\pi$
$110$	7.76207	−	4.48144i	0.740085	−	0.427288i
$111$		0			0
$112$			1.00000i			0.0944911i
$113$	9.27760	+	16.0693i	0.872763	+	1.51167i	0.859127	+	0.511763i	$0.171007\pi$
$113$	9.27760	+	16.0693i	0.872763	+	1.51167i	0.0136363	+	0.999907i	$0.495659\pi$
$114$		0			0
$115$	4.69878	+	2.71284i	0.438163	+	0.252974i
$116$	9.81776			0.911556
$117$		0			0
$118$	−4.85876			−0.447285
$119$	4.93987	+	2.85204i	0.452837	+	0.261446i
$120$		0			0
$121$	2.86360	+	4.95991i	0.260328	+	0.450901i
$122$		−	11.2687i		−	1.02022i
$123$		0			0
$124$	−6.23112	+	3.59754i	−0.559571	+	0.323068i
$125$		−	11.3901i		−	1.01876i
$126$		0			0
$127$	−0.132439	+	0.229390i	−0.0117520	+	0.0203551i	−0.871842	−	0.489788i	$-0.837074\pi$
$127$	−0.132439	+	0.229390i	−0.0117520	+	0.0203551i	0.860090	+	0.510143i	$0.170408\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−5.21569	+	5.93545i	−0.457446	+	0.520574i
$131$	5.10237			0.445796			0.222898	−	0.974842i	$-0.428448\pi$
$131$	5.10237			0.445796			0.222898	+	0.974842i	$0.428448\pi$
$132$		0			0
$133$	3.86601	−	6.69612i	0.335225	−	0.580627i
$134$	3.17020	+	5.49094i	0.273863	+	0.474345i
$135$		0			0
$136$	4.93987	−	2.85204i	0.423591	−	0.244560i
$137$	−18.8812	+	10.9011i	−1.61313	+	0.931342i	−0.624493	+	0.781030i	$0.714694\pi$
$137$	−18.8812	+	10.9011i	−1.61313	+	0.931342i	−0.988639	+	0.150312i	$0.951972\pi$
$138$		0			0
$139$	−8.22455	−	14.2453i	−0.697597	−	1.20827i	−0.969297	−	0.245892i	$-0.920919\pi$
$139$	−8.22455	−	14.2453i	−0.697597	−	1.20827i	0.271700	−	0.962382i	$-0.412414\pi$
$140$	1.09573	−	1.89787i	0.0926065	−	0.160399i
$141$		0			0
$142$	8.32933			0.698982
$143$	−11.0772	−	9.73392i	−0.926322	−	0.813991i
$144$		0			0
$145$	−18.6328	−	10.7577i	−1.54737	−	0.893375i
$146$	−3.68903	+	6.38958i	−0.305306	+	0.528806i
$147$		0			0
$148$		−	10.1547i		−	0.834713i
$149$	12.8023	−	7.39139i	1.04880	−	0.605526i	0.126489	−	0.991968i	$-0.459629\pi$
$149$	12.8023	−	7.39139i	1.04880	−	0.605526i	0.922314	+	0.386442i	$0.126296\pi$
$150$		0			0
$151$		−	18.9896i		−	1.54535i	−0.634803	−	0.772674i	$-0.718919\pi$
$151$		−	18.9896i		−	1.54535i	0.634803	−	0.772674i	$-0.281081\pi$
$152$	−3.86601	−	6.69612i	−0.313575	−	0.543127i
$153$		0			0
$154$	3.54195	+	2.04495i	0.285418	+	0.164786i
$155$	15.7678			1.26650
$156$		0			0
$157$	−13.5474			−1.08120			−0.540601	−	0.841279i	$-0.681803\pi$
$157$	−13.5474			−1.08120			−0.540601	+	0.841279i	$0.681803\pi$
$158$	−2.99501	−	1.72917i	−0.238270	−	0.137565i
$159$		0			0
$160$	−1.09573	−	1.89787i	−0.0866254	−	0.150040i
$161$			2.47582i			0.195122i
$162$		0			0
$163$	−3.86502	+	2.23147i	−0.302732	+	0.174782i	−0.643670	−	0.765304i	$-0.722589\pi$
$163$	−3.86502	+	2.23147i	−0.302732	+	0.174782i	0.340938	+	0.940086i	$0.389256\pi$
$164$		−	3.62683i		−	0.283208i
$165$		0			0
$166$	0.166392	−	0.288199i	0.0129145	−	0.0223685i
$167$	2.86448	+	1.65381i	0.221660	+	0.127976i	0.606719	−	0.794917i	$-0.292485\pi$
$167$	2.86448	+	1.65381i	0.221660	+	0.127976i	−0.385059	+	0.922892i	$0.625819\pi$
$168$		0			0
$169$	12.0005	+	4.99872i	0.923118	+	0.384517i
$170$	−12.5003			−0.958729
$171$		0			0
$172$	1.37769	−	2.38624i	0.105048	−	0.181949i
$173$	−5.06107	−	8.76603i	−0.384786	−	0.666469i	0.606953	−	0.794737i	$-0.292391\pi$
$173$	−5.06107	−	8.76603i	−0.384786	−	0.666469i	−0.991740	+	0.128268i	$0.959058\pi$
$174$		0			0
$175$	0.171007	−	0.0987308i	0.0129269	−	0.00746335i
$176$	3.54195	−	2.04495i	0.266984	−	0.154144i
$177$		0			0
$178$	6.76374	+	11.7151i	0.506964	+	0.878088i
$179$	−4.62579	+	8.01210i	−0.345748	+	0.598853i	−0.985489	−	0.169737i	$-0.945708\pi$
$179$	−4.62579	+	8.01210i	−0.345748	+	0.598853i	0.639742	+	0.768590i	$0.279041\pi$
$180$		0			0
$181$	23.2645			1.72923			0.864617	−	0.502431i	$-0.167561\pi$
$181$	23.2645			1.72923			0.864617	+	0.502431i	$0.167561\pi$
$182$	−3.53557	−	0.706919i	−0.262074	−	0.0524003i
$183$		0			0
$184$	2.14412	+	1.23791i	0.158067	+	0.0912598i
$185$	−11.1269	+	19.2723i	−0.818065	+	1.41693i
$186$		0			0
$187$		−	23.3290i		−	1.70599i
$188$	6.66847	−	3.85004i	0.486348	−	0.280793i
$189$		0			0
$190$			16.9445i			1.22928i
$191$	−4.45096	−	7.70929i	−0.322060	−	0.557825i	0.658853	−	0.752272i	$-0.271042\pi$
$191$	−4.45096	−	7.70929i	−0.322060	−	0.557825i	−0.980913	+	0.194447i	$0.937709\pi$
$192$		0			0
$193$	7.69754	+	4.44417i	0.554081	+	0.319899i	0.750766	−	0.660568i	$-0.229684\pi$
$193$	7.69754	+	4.44417i	0.554081	+	0.319899i	−0.196685	+	0.980467i	$0.563018\pi$
$194$	−11.6163			−0.834003
$195$		0			0
$196$	1.00000			0.0714286
$197$	20.2586	+	11.6963i	1.44336	+	0.833326i	0.998072	−	0.0620596i	$-0.0197669\pi$
$197$	20.2586	+	11.6963i	1.44336	+	0.833326i	0.445291	+	0.895386i	$0.353100\pi$
$198$		0			0
$199$	−1.96804	−	3.40875i	−0.139511	−	0.241640i	0.787801	−	0.615930i	$-0.211220\pi$
$199$	−1.96804	−	3.40875i	−0.139511	−	0.241640i	−0.927312	+	0.374290i	$0.877886\pi$
$200$		−	0.197462i		−	0.0139626i
$201$		0			0
$202$	−1.95189	+	1.12692i	−0.137334	+	0.0792900i
$203$		−	9.81776i		−	0.689072i
$204$		0			0
$205$	−3.97404	+	6.88324i	−0.277559	+	0.480747i
$206$	13.8846	+	8.01627i	0.967385	+	0.558520i
$207$		0			0
$208$	−2.38000	+	2.70844i	−0.165023	+	0.187796i
$209$	−31.6231			−2.18741
$210$		0			0
$211$	−6.40104	+	11.0869i	−0.440666	+	0.763256i	−0.997739	−	0.0672076i	$-0.978591\pi$
$211$	−6.40104	+	11.0869i	−0.440666	+	0.763256i	0.557073	+	0.830464i	$0.311924\pi$
$212$	3.15556	+	5.46559i	0.216725	+	0.375378i
$213$		0			0
$214$	−7.46156	+	4.30793i	−0.510062	+	0.294484i
$215$	−5.22936	+	3.01917i	−0.356639	+	0.205906i
$216$		0			0
$217$	3.59754	+	6.23112i	0.244217	+	0.422996i
$218$	−5.01589	+	8.68777i	−0.339719	+	0.588410i
$219$		0			0
$220$	−8.96287			−0.604277
$221$	6.59149	+	19.4814i	0.443392	+	1.31046i
$222$		0			0
$223$	16.3236	+	9.42444i	1.09311	+	0.631107i	0.934403	−	0.356218i	$-0.115934\pi$
$223$	16.3236	+	9.42444i	1.09311	+	0.631107i	0.158707	+	0.987326i	$0.449267\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$		0			0
$226$		−	18.5552i		−	1.23427i
$227$	1.14246	−	0.659599i	0.0758276	−	0.0437791i	−0.461607	−	0.887085i	$-0.652727\pi$
$227$	1.14246	−	0.659599i	0.0758276	−	0.0437791i	0.537434	+	0.843306i	$0.319394\pi$
$228$		0			0
$229$			4.34109i			0.286867i	0.989660	+	0.143434i	$0.0458143\pi$
$229$			4.34109i			0.286867i	−0.989660	+	0.143434i	$0.954186\pi$
$230$	−2.71284	−	4.69878i	−0.178879	−	0.309828i
$231$		0			0
$232$	−8.50243	−	4.90888i	−0.558212	−	0.322284i
$233$	5.76422			0.377627			0.188813	−	0.982013i	$-0.439536\pi$
$233$	5.76422			0.377627			0.188813	+	0.982013i	$0.439536\pi$
$234$		0			0
$235$	−16.8745			−1.10077
$236$	4.20781	+	2.42938i	0.273905	+	0.158139i
$237$		0			0
$238$	−2.85204	−	4.93987i	−0.184870	−	0.320204i
$239$			13.0951i			0.847049i	0.905885	+	0.423525i	$0.139207\pi$
$239$			13.0951i			0.847049i	−0.905885	+	0.423525i	$0.860793\pi$
$240$		0			0
$241$	−0.389769	+	0.225033i	−0.0251072	+	0.0144957i	−0.512501	−	0.858687i	$-0.671281\pi$
$241$	−0.389769	+	0.225033i	−0.0251072	+	0.0144957i	0.487394	+	0.873182i	$0.337948\pi$
$242$		−	5.72721i		−	0.368159i
$243$		0			0
$244$	−5.63434	+	9.75896i	−0.360701	+	0.624753i
$245$	−1.89787	−	1.09573i	−0.121250	−	0.0700039i
$246$		0			0
$247$	26.4076	−	8.93493i	1.68027	−	0.568516i
$248$	7.19507			0.456888
$249$		0			0
$250$	−5.69504	+	9.86410i	−0.360186	+	0.623860i
$251$	−9.35111	−	16.1966i	−0.590237	−	1.02232i	−0.994200	−	0.107545i	$-0.965701\pi$
$251$	−9.35111	−	16.1966i	−0.590237	−	1.02232i	0.403963	−	0.914775i	$-0.367632\pi$
$252$		0			0
$253$	8.76922	−	5.06291i	0.551316	−	0.318303i
$254$	0.229390	−	0.132439i	0.0143932	−	0.00830994i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.88929	+	17.1287i	−0.616877	+	1.06846i	0.373175	+	0.927761i	$0.378269\pi$
$257$	−9.88929	+	17.1287i	−0.616877	+	1.06846i	−0.990052	+	0.140701i	$0.955064\pi$
$258$		0			0
$259$	−10.1547			−0.630984
$260$	7.48464	−	2.53241i	0.464178	−	0.157053i
$261$		0			0
$262$	−4.41878	−	2.55119i	−0.272993	−	0.157613i
$263$	11.7723	−	20.3903i	0.725914	−	1.25732i	−0.232683	−	0.972553i	$-0.574750\pi$
$263$	11.7723	−	20.3903i	0.725914	−	1.25732i	0.958597	−	0.284767i	$-0.0919162\pi$
$264$		0			0
$265$		−	13.8306i		−	0.849608i
$266$	−6.69612	+	3.86601i	−0.410565	+	0.237040i
$267$		0			0
$268$		−	6.34039i		−	0.387301i
$269$	11.4216	+	19.7827i	0.696384	+	1.20617i	0.969712	+	0.244252i	$0.0785424\pi$
$269$	11.4216	+	19.7827i	0.696384	+	1.20617i	−0.273327	+	0.961921i	$0.588124\pi$
$270$		0			0
$271$	−11.2562	−	6.49877i	−0.683766	−	0.394772i	0.117507	−	0.993072i	$-0.462510\pi$
$271$	−11.2562	−	6.49877i	−0.683766	−	0.394772i	−0.801272	+	0.598300i	$0.795843\pi$
$272$	−5.70407			−0.345860
$273$		0			0
$274$	21.8022			1.31712
$275$	−0.699399	−	0.403798i	−0.0421753	−	0.0243499i
$276$		0			0
$277$	−13.4753	−	23.3399i	−0.809652	−	1.40236i	−0.913105	−	0.407724i	$-0.866323\pi$
$277$	−13.4753	−	23.3399i	−0.809652	−	1.40236i	0.103453	−	0.994634i	$-0.467011\pi$
$278$			16.4491i			0.986551i
$279$		0			0
$280$	−1.89787	+	1.09573i	−0.113419	+	0.0654827i
$281$			0.0773961i			0.00461706i	0.999997	+	0.00230853i	$0.000734829\pi$
$281$			0.0773961i			0.00461706i	−0.999997	+	0.00230853i	$0.999265\pi$
$282$		0			0
$283$	11.1534	−	19.3183i	0.663002	−	1.14835i	−0.316821	−	0.948485i	$-0.602616\pi$
$283$	11.1534	−	19.3183i	0.663002	−	1.14835i	0.979823	−	0.199867i	$-0.0640511\pi$
$284$	−7.21341	−	4.16466i	−0.428037	−	0.247127i
$285$		0			0
$286$	4.72618	+	13.9684i	0.279465	+	0.825970i
$287$	−3.62683			−0.214085
$288$		0			0
$289$	−7.76822	+	13.4550i	−0.456954	+	0.791468i
$290$	10.7577	+	18.6328i	0.631712	+	1.09416i
$291$		0			0
$292$	6.38958	−	3.68903i	0.373922	−	0.215884i
$293$	−5.16126	+	2.97986i	−0.301524	+	0.174085i	−0.643127	−	0.765759i	$-0.722363\pi$
$293$	−5.16126	+	2.97986i	−0.301524	+	0.174085i	0.341603	+	0.939844i	$0.389030\pi$
$294$		0			0
$295$	−5.32391	−	9.22128i	−0.309970	−	0.536884i
$296$	−5.07736	+	8.79425i	−0.295116	+	0.511155i
$297$		0			0
$298$	−14.7828			−0.856344
$299$	−5.89243	+	6.70559i	−0.340768	+	0.387794i
$300$		0			0
$301$	−2.38624	−	1.37769i	−0.137540	−	0.0794089i
$302$	−9.49478	+	16.4454i	−0.546363	+	0.946329i
$303$		0			0
$304$			7.73201i			0.443461i
$305$	21.3865	−	12.3475i	1.22459	−	0.707015i
$306$		0			0
$307$			31.1089i			1.77548i	0.460349	+	0.887738i	$0.347724\pi$
$307$			31.1089i			1.77548i	−0.460349	+	0.887738i	$0.652276\pi$
$308$	−2.04495	−	3.54195i	−0.116522	−	0.201821i
$309$		0			0
$310$	−13.6553	−	7.88389i	−0.775569	−	0.447775i
$311$	−3.48435			−0.197579			−0.0987896	−	0.995108i	$-0.531497\pi$
$311$	−3.48435			−0.197579			−0.0987896	+	0.995108i	$0.531497\pi$
$312$		0			0
$313$	10.2750			0.580779			0.290389	−	0.956909i	$-0.406215\pi$
$313$	10.2750			0.580779			0.290389	+	0.956909i	$0.406215\pi$
$314$	11.7324	+	6.77371i	0.662098	+	0.382262i
$315$		0			0
$316$	1.72917	+	2.99501i	0.0972734	+	0.168483i
$317$			26.5282i			1.48997i	0.667080	+	0.744986i	$0.267544\pi$
$317$			26.5282i			1.48997i	−0.667080	+	0.744986i	$0.732456\pi$
$318$		0			0
$319$	−34.7740	+	20.0768i	−1.94697	+	1.12408i
$320$			2.19147i			0.122507i
$321$		0			0
$322$	1.23791	−	2.14412i	0.0689860	−	0.119487i
$323$	38.1951	+	22.0520i	2.12523	+	1.22700i
$324$		0			0
$325$	0.698140	+	0.139589i	0.0387258	+	0.00774302i
$326$	4.46294			0.247180
$327$		0			0
$328$	−1.81341	+	3.14093i	−0.100129	+	0.173429i
$329$	−3.85004	−	6.66847i	−0.212260	−	0.367645i
$330$		0			0
$331$	−24.8329	+	14.3373i	−1.36494	+	0.788048i	−0.990277	−	0.139113i	$-0.955575\pi$
$331$	−24.8329	+	14.3373i	−1.36494	+	0.788048i	−0.374663	+	0.927161i	$0.622242\pi$
$332$	−0.288199	+	0.166392i	−0.0158170	+	0.00913192i
$333$		0			0
$334$	−1.65381	−	2.86448i	−0.0904924	−	0.156737i
$335$	−6.94739	+	12.0332i	−0.379576	+	0.657445i
$336$		0			0
$337$	4.82923			0.263065			0.131532	−	0.991312i	$-0.458010\pi$
$337$	4.82923			0.263065			0.131532	+	0.991312i	$0.458010\pi$
$338$	−7.89340	−	10.3293i	−0.429345	−	0.561839i
$339$		0			0
$340$	10.8256	+	6.25015i	0.587099	+	0.338962i
$341$	14.7135	−	25.4846i	0.796783	−	1.38007i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−2.38624	+	1.37769i	−0.128657	+	0.0742803i
$345$		0			0
$346$			10.1221i			0.544170i
$347$	15.2594	+	26.4300i	0.819167	+	1.41884i	0.906297	+	0.422642i	$0.138897\pi$
$347$	15.2594	+	26.4300i	0.819167	+	1.41884i	−0.0871296	+	0.996197i	$0.527769\pi$
$348$		0			0
$349$	−4.60570	−	2.65910i	−0.246537	−	0.142338i	0.371640	−	0.928377i	$-0.378795\pi$
$349$	−4.60570	−	2.65910i	−0.246537	−	0.142338i	−0.618178	+	0.786038i	$0.712129\pi$
$350$	−0.197462			−0.0105548
$351$		0			0
$352$	−4.08989			−0.217992
$353$	24.4457	+	14.1137i	1.30111	+	0.751199i	0.980595	−	0.196043i	$-0.0628094\pi$
$353$	24.4457	+	14.1137i	1.30111	+	0.751199i	0.320519	+	0.947242i	$0.396143\pi$
$354$		0			0
$355$	9.12673	+	15.8080i	0.484397	+	0.839000i
$356$		−	13.5275i		−	0.716956i
$357$		0			0
$358$	8.01210	−	4.62579i	0.423453	−	0.244481i
$359$			7.58573i			0.400359i	0.979759	+	0.200180i	$0.0641526\pi$
$359$			7.58573i			0.400359i	−0.979759	+	0.200180i	$0.935847\pi$
$360$		0			0
$361$	20.3920	−	35.3200i	1.07326	−	1.85895i
$362$	−20.1476	−	11.6322i	−1.05894	−	0.611377i
$363$		0			0
$364$	2.70844	+	2.38000i	0.141961	+	0.124746i
$365$	−16.1688			−0.846313
$366$		0			0
$367$	5.92558	−	10.2634i	0.309313	−	0.535746i	−0.668899	−	0.743353i	$-0.733234\pi$
$367$	5.92558	−	10.2634i	0.309313	−	0.535746i	0.978212	+	0.207607i	$0.0665676\pi$
$368$	−1.23791	−	2.14412i	−0.0645305	−	0.111770i
$369$		0			0
$370$	19.2723	−	11.1269i	1.00192	−	0.578459i
$371$	5.46559	−	3.15556i	0.283759	−	0.163828i
$372$		0			0
$373$	14.9133	+	25.8306i	0.772182	+	1.33746i	0.936365	+	0.351028i	$0.114168\pi$
$373$	14.9133	+	25.8306i	0.772182	+	1.33746i	−0.164183	+	0.986430i	$0.552499\pi$
$374$	−11.6645	+	20.2035i	−0.603158	+	1.04470i
$375$		0			0
$376$	−7.70008			−0.397101
$377$	23.3662	−	26.5908i	1.20342	−	1.36949i
$378$		0			0
$379$	−1.55298	−	0.896611i	−0.0797711	−	0.0460558i	0.459584	−	0.888134i	$-0.347999\pi$
$379$	−1.55298	−	0.896611i	−0.0797711	−	0.0460558i	−0.539355	+	0.842079i	$0.681332\pi$
$380$	8.47223	−	14.6743i	0.434616	−	0.752778i
$381$		0			0
$382$			8.90192i			0.455462i
$383$	−14.4611	+	8.34912i	−0.738927	+	0.426620i	−0.821679	−	0.569950i	$-0.806962\pi$
$383$	−14.4611	+	8.34912i	−0.738927	+	0.426620i	0.0827518	+	0.996570i	$0.473629\pi$
$384$		0			0
$385$			8.96287i			0.456790i
$386$	−4.44417	−	7.69754i	−0.226203	−	0.391794i
$387$		0			0
$388$	10.0600	+	5.80816i	0.510720	+	0.294864i
$389$	−15.6288			−0.792413			−0.396207	−	0.918161i	$-0.629674\pi$
$389$	−15.6288			−0.792413			−0.396207	+	0.918161i	$0.629674\pi$
$390$		0			0
$391$	−14.1222			−0.714192
$392$	−0.866025	−	0.500000i	−0.0437409	−	0.0252538i
$393$		0			0
$394$	−11.6963	−	20.2586i	−0.589251	−	1.02061i
$395$		−	7.57885i		−	0.381333i
$396$		0			0
$397$	4.86182	−	2.80697i	0.244008	−	0.140878i	−0.373010	−	0.927827i	$-0.621674\pi$
$397$	4.86182	−	2.80697i	0.244008	−	0.140878i	0.617017	+	0.786950i	$0.288341\pi$
$398$			3.93608i			0.197298i
$399$		0			0
$400$	−0.0987308	+	0.171007i	−0.00493654	+	0.00855034i
$401$	−21.8559	−	12.6185i	−1.09143	−	0.630139i	−0.157475	−	0.987523i	$-0.550335\pi$
$401$	−21.8559	−	12.6185i	−1.09143	−	0.630139i	−0.933957	+	0.357384i	$0.883669\pi$
$402$		0			0
$403$	−5.08633	+	25.4387i	−0.253368	+	1.26719i
$404$	2.25385			0.112133
$405$		0			0
$406$	−4.90888	+	8.50243i	−0.243624	+	0.421969i
$407$	20.7659	+	35.9675i	1.02933	+	1.78284i
$408$		0			0
$409$	25.0467	−	14.4607i	1.23848	−	0.715037i	0.269697	−	0.962945i	$-0.413076\pi$
$409$	25.0467	−	14.4607i	1.23848	−	0.715037i	0.968784	+	0.247908i	$0.0797430\pi$
$410$	6.88324	−	3.97404i	0.339939	−	0.196264i
$411$		0			0
$412$	−8.01627	−	13.8846i	−0.394933	−	0.684045i
$413$	2.42938	−	4.20781i	0.119542	−	0.207053i
$414$		0			0
$415$	0.729284			0.0357991
$416$	3.41535	−	1.15558i	0.167452	−	0.0566568i
$417$		0			0
$418$	27.3864	+	15.8115i	1.33951	+	0.773368i
$419$	−16.0468	+	27.7939i	−0.783938	+	1.35782i	0.145693	+	0.989330i	$0.453459\pi$
$419$	−16.0468	+	27.7939i	−0.783938	+	1.35782i	−0.929631	+	0.368491i	$0.879875\pi$
$420$		0			0
$421$			1.02963i			0.0501810i	0.999685	+	0.0250905i	$0.00798740\pi$
$421$			1.02963i			0.0501810i	−0.999685	+	0.0250905i	$0.992013\pi$
$422$	11.0869	−	6.40104i	0.539703	−	0.311598i
$423$		0			0
$424$		−	6.31111i		−	0.306495i
$425$	0.563168	+	0.975435i	0.0273176	+	0.0473155i
$426$		0			0
$427$	9.75896	+	5.63434i	0.472269	+	0.272665i
$428$	8.61586			0.416464
$429$		0			0
$430$	6.03835			0.291195
$431$	30.5908	+	17.6616i	1.47350	+	0.850728i	0.999555	−	0.0298236i	$-0.00949455\pi$
$431$	30.5908	+	17.6616i	1.47350	+	0.850728i	0.473950	+	0.880552i	$0.342828\pi$
$432$		0			0
$433$	10.0469	+	17.4018i	0.482824	+	0.836276i	0.999806	−	0.0197204i	$-0.00627760\pi$
$433$	10.0469	+	17.4018i	0.482824	+	0.836276i	−0.516981	+	0.855997i	$0.672944\pi$
$434$		−	7.19507i		−	0.345375i
$435$		0			0
$436$	8.68777	−	5.01589i	0.416069	−	0.240217i
$437$			19.1431i			0.915736i
$438$		0			0
$439$	6.52940	−	11.3093i	0.311631	−	0.539761i	−0.667084	−	0.744982i	$-0.732458\pi$
$439$	6.52940	−	11.3093i	0.311631	−	0.539761i	0.978716	+	0.205221i	$0.0657913\pi$
$440$	7.76207	+	4.48144i	0.370042	+	0.213644i
$441$		0			0
$442$	4.03232	−	20.1672i	0.191798	−	0.959254i
$443$	−7.46148			−0.354506			−0.177253	−	0.984165i	$-0.556721\pi$
$443$	−7.46148			−0.354506			−0.177253	+	0.984165i	$0.556721\pi$
$444$		0			0
$445$	−14.8225	+	25.6734i	−0.702656	+	1.21704i
$446$	−9.42444	−	16.3236i	−0.446260	−	0.772945i
$447$		0			0
$448$	−0.866025	+	0.500000i	−0.0409159	+	0.0236228i
$449$	8.28796	−	4.78506i	0.391133	−	0.225821i	−0.291518	−	0.956565i	$-0.594160\pi$
$449$	8.28796	−	4.78506i	0.391133	−	0.225821i	0.682651	+	0.730745i	$0.260827\pi$
$450$		0			0
$451$	7.41667	+	12.8460i	0.349237	+	0.604897i
$452$	−9.27760	+	16.0693i	−0.436382	+	0.755835i
$453$		0			0
$454$	−1.31920			−0.0619130
$455$	−2.53241	−	7.48464i	−0.118721	−	0.350886i
$456$		0			0
$457$	22.3679	+	12.9141i	1.04633	+	0.604097i	0.921619	−	0.388097i	$-0.126867\pi$
$457$	22.3679	+	12.9141i	1.04633	+	0.604097i	0.124708	+	0.992194i	$0.460201\pi$
$458$	2.17054	−	3.75949i	0.101423	−	0.175670i
$459$		0			0
$460$			5.42568i			0.252974i
$461$	1.35535	−	0.782512i	0.0631250	−	0.0364452i	−0.468105	−	0.883673i	$-0.655063\pi$
$461$	1.35535	−	0.782512i	0.0631250	−	0.0364452i	0.531230	+	0.847227i	$0.321730\pi$
$462$		0			0
$463$			20.4863i			0.952080i	0.879424	+	0.476040i	$0.157928\pi$
$463$			20.4863i			0.952080i	−0.879424	+	0.476040i	$0.842072\pi$
$464$	4.90888	+	8.50243i	0.227889	+	0.394716i
$465$		0			0
$466$	−4.99196	−	2.88211i	−0.231248	−	0.133511i
$467$	3.80822			0.176224			0.0881118	−	0.996111i	$-0.471917\pi$
$467$	3.80822			0.176224			0.0881118	+	0.996111i	$0.471917\pi$
$468$		0			0
$469$	−6.34039			−0.292772
$470$	14.6137	+	8.43725i	0.674082	+	0.389181i
$471$		0			0
$472$	−2.42938	−	4.20781i	−0.111821	−	0.193680i
$473$			11.2692i			0.518160i
$474$		0			0
$475$	1.32223	−	0.763388i	0.0606679	−	0.0350266i
$476$			5.70407i			0.261446i
$477$		0			0
$478$	6.54753	−	11.3407i	0.299477	−	0.518710i
$479$	20.8886	+	12.0600i	0.954425	+	0.551037i	0.894453	−	0.447163i	$-0.147566\pi$
$479$	20.8886	+	12.0600i	0.954425	+	0.551037i	0.0599720	+	0.998200i	$0.480899\pi$
$480$		0			0
$481$	−27.5034	−	24.1682i	−1.25405	−	1.10197i
$482$	0.450067			0.0205000
$483$		0			0
$484$	−2.86360	+	4.95991i	−0.130164	+	0.225450i
$485$	−12.7284	−	22.0462i	−0.577967	−	1.00107i
$486$		0			0
$487$	−6.65422	+	3.84182i	−0.301532	+	0.174089i	−0.643131	−	0.765756i	$-0.722365\pi$
$487$	−6.65422	+	3.84182i	−0.301532	+	0.174089i	0.341599	+	0.939846i	$0.389031\pi$
$488$	9.75896	−	5.63434i	0.441767	−	0.255054i
$489$		0			0
$490$	1.09573	+	1.89787i	0.0495002	+	0.0857369i
$491$	−16.2767	+	28.1921i	−0.734557	+	1.27229i	0.220360	+	0.975419i	$0.429277\pi$
$491$	−16.2767	+	28.1921i	−0.734557	+	1.27229i	−0.954917	+	0.296872i	$0.904056\pi$
$492$		0			0
$493$	56.0012			2.52217
$494$	−27.3371	−	5.46590i	−1.22995	−	0.245923i
$495$		0			0
$496$	−6.23112	−	3.59754i	−0.279785	−	0.161534i
$497$	−4.16466	+	7.21341i	−0.186811	+	0.323566i
$498$		0			0
$499$			5.87524i			0.263012i	0.991315	+	0.131506i	$0.0419813\pi$
$499$			5.87524i			0.263012i	−0.991315	+	0.131506i	$0.958019\pi$
$500$	9.86410	−	5.69504i	0.441136	−	0.254690i
$501$		0			0
$502$			18.7022i			0.834721i
$503$	11.0238	+	19.0939i	0.491529	+	0.851353i	0.999952	−	0.00975426i	$-0.00310493\pi$
$503$	11.0238	+	19.0939i	0.491529	+	0.851353i	−0.508424	+	0.861107i	$0.669772\pi$
$504$		0			0
$505$	−4.27750	−	2.46962i	−0.190346	−	0.109897i
$506$	−10.1258			−0.450148
$507$		0			0
$508$	−0.264877			−0.0117520
$509$	5.86940	+	3.38870i	0.260156	+	0.150201i	0.624406	−	0.781100i	$-0.285341\pi$
$509$	5.86940	+	3.38870i	0.260156	+	0.150201i	−0.364249	+	0.931301i	$0.618674\pi$
$510$		0			0
$511$	−3.68903	−	6.38958i	−0.163193	−	0.282658i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	17.1287	−	9.88929i	0.755517	−	0.436198i
$515$			35.1348i			1.54823i
$516$		0			0
$517$	−15.7463	+	27.2733i	−0.692519	+	1.19948i
$518$	8.79425	+	5.07736i	0.386397	+	0.223086i
$519$		0			0
$520$	−7.74810	−	1.54919i	−0.339777	−	0.0679365i
$521$	2.61232			0.114448			0.0572240	−	0.998361i	$-0.481775\pi$
$521$	2.61232			0.114448			0.0572240	+	0.998361i	$0.481775\pi$
$522$		0			0
$523$	−4.02060	+	6.96388i	−0.175809	+	0.304509i	−0.940441	−	0.339957i	$-0.889587\pi$
$523$	−4.02060	+	6.96388i	−0.175809	+	0.304509i	0.764632	+	0.644467i	$0.222921\pi$
$524$	2.55119	+	4.41878i	0.111449	+	0.193035i
$525$		0			0
$526$	−20.3903	+	11.7723i	−0.889059	+	0.513299i
$527$	−35.5427	+	20.5206i	−1.54827	+	0.893892i
$528$		0			0
$529$	8.43516	+	14.6101i	0.366746	+	0.635223i
$530$	−6.91531	+	11.9777i	−0.300382	+	0.520276i
$531$		0			0
$532$	7.73201			0.335225
$533$	−9.82303	−	8.63184i	−0.425483	−	0.373886i
$534$		0			0
$535$	−16.3518	−	9.44070i	−0.706949	−	0.408157i
$536$	−3.17020	+	5.49094i	−0.136932	+	0.237172i
$537$		0			0
$538$		−	22.8431i		−	0.984836i
$539$	−3.54195	+	2.04495i	−0.152563	+	0.0880820i
$540$		0			0
$541$		−	21.6552i		−	0.931029i	−0.885040	−	0.465514i	$-0.845869\pi$
$541$		−	21.6552i		−	0.931029i	0.885040	−	0.465514i	$-0.154131\pi$
$542$	6.49877	+	11.2562i	0.279146	+	0.483495i
$543$		0			0
$544$	4.93987	+	2.85204i	0.211795	+	0.122280i
$545$	−21.9843			−0.941705
$546$		0			0
$547$	−32.9495			−1.40882			−0.704409	−	0.709795i	$-0.748788\pi$
$547$	−32.9495			−1.40882			−0.704409	+	0.709795i	$0.748788\pi$
$548$	−18.8812	−	10.9011i	−0.806566	−	0.465671i
$549$		0			0
$550$	0.403798	+	0.699399i	0.0172180	+	0.0298225i
$551$		−	75.9111i		−	3.23392i
$552$		0			0
$553$	2.99501	−	1.72917i	0.127361	−	0.0735318i
$554$			26.9506i			1.14502i
$555$		0			0
$556$	8.22455	−	14.2453i	0.348799	−	0.604137i
$557$	0.280535	+	0.161967i	0.0118866	+	0.00686276i	0.505932	−	0.862574i	$-0.331149\pi$
$557$	0.280535	+	0.161967i	0.0118866	+	0.00686276i	−0.494045	+	0.869436i	$0.664482\pi$
$558$		0			0
$559$	−3.18406	−	9.41062i	−0.134671	−	0.398027i
$560$	2.19147			0.0926065
$561$		0			0
$562$	0.0386980	−	0.0670270i	0.00163238	−	0.00282736i
$563$	−18.3668	−	31.8123i	−0.774070	−	1.34073i	−0.935316	−	0.353815i	$-0.884884\pi$
$563$	−18.3668	−	31.8123i	−0.774070	−	1.34073i	0.161245	−	0.986914i	$-0.448449\pi$
$564$		0			0
$565$	35.2153	−	20.3316i	1.48152	−	0.855356i
$566$	−19.3183	+	11.1534i	−0.812008	+	0.468813i
$567$		0			0
$568$	4.16466	+	7.21341i	0.174745	+	0.302668i
$569$	1.32995	−	2.30354i	0.0557544	−	0.0965695i	−0.836801	−	0.547507i	$-0.815577\pi$
$569$	1.32995	−	2.30354i	0.0557544	−	0.0965695i	0.892556	+	0.450937i	$0.148910\pi$
$570$		0			0
$571$	4.29994			0.179947			0.0899735	−	0.995944i	$-0.471322\pi$
$571$	4.29994			0.179947			0.0899735	+	0.995944i	$0.471322\pi$
$572$	2.89122	−	14.4601i	0.120888	−	0.604607i
$573$		0			0
$574$	3.14093	+	1.81341i	0.131100	+	0.0756905i
$575$	−0.244439	+	0.423381i	−0.0101938	+	0.0176562i
$576$		0			0
$577$		−	2.08429i		−	0.0867702i	−0.999058	−	0.0433851i	$-0.986186\pi$
$577$		−	2.08429i		−	0.0867702i	0.999058	−	0.0433851i	$-0.0138142\pi$
$578$	13.4550	−	7.76822i	0.559652	−	0.323115i
$579$		0			0
$580$		−	21.5153i		−	0.893375i
$581$	0.166392	+	0.288199i	0.00690308	+	0.0119565i
$582$		0			0
$583$	−22.3536	−	12.9059i	−0.925793	−	0.534507i
$584$	−7.37805			−0.305306
$585$		0			0
$586$	5.95971			0.246193
$587$	−12.9028	−	7.44945i	−0.532556	−	0.307472i	0.209500	−	0.977809i	$-0.432816\pi$
$587$	−12.9028	−	7.44945i	−0.532556	−	0.307472i	−0.742057	+	0.670337i	$0.766150\pi$
$588$		0			0
$589$	27.8162	+	48.1791i	1.14615	+	1.98518i
$590$			10.6478i			0.438364i
$591$		0			0
$592$	8.79425	−	5.07736i	0.361441	−	0.208678i
$593$		−	1.36361i		−	0.0559968i	−0.999608	−	0.0279984i	$-0.991087\pi$
$593$		−	1.36361i		−	0.0559968i	0.999608	−	0.0279984i	$-0.00891334\pi$
$594$		0			0
$595$	6.25015	−	10.8256i	0.256231	−	0.443805i
$596$	12.8023	+	7.39139i	0.524401	+	0.302763i
$597$		0			0
$598$	8.45579	−	2.86100i	0.345783	−	0.116995i
$599$	−18.0030			−0.735581			−0.367790	−	0.929909i	$-0.619886\pi$
$599$	−18.0030			−0.735581			−0.367790	+	0.929909i	$0.619886\pi$
$600$		0			0
$601$	6.76892	−	11.7241i	0.276110	−	0.478237i	−0.694305	−	0.719681i	$-0.744288\pi$
$601$	6.76892	−	11.7241i	0.276110	−	0.478237i	0.970415	+	0.241445i	$0.0776213\pi$
$602$	1.37769	+	2.38624i	0.0561506	+	0.0972557i
$603$		0			0
$604$	16.4454	−	9.49478i	0.669155	−	0.386337i
$605$	10.8695	−	6.27550i	0.441907	−	0.255135i
$606$		0			0
$607$	1.10556	+	1.91489i	0.0448733	+	0.0777228i	0.887590	−	0.460635i	$-0.152378\pi$
$607$	1.10556	+	1.91489i	0.0448733	+	0.0777228i	−0.842716	+	0.538358i	$0.819045\pi$
$608$	3.86601	−	6.69612i	0.156787	−	0.271563i
$609$		0			0
$610$	−24.6950			−0.999870
$611$	5.44333	−	27.2242i	0.220214	−	1.10137i
$612$		0			0
$613$	22.5849	+	13.0394i	0.912195	+	0.526656i	0.881137	−	0.472862i	$-0.156779\pi$
$613$	22.5849	+	13.0394i	0.912195	+	0.526656i	0.0310579	+	0.999518i	$0.490112\pi$
$614$	15.5544	−	26.9411i	0.627726	−	1.08725i
$615$		0			0
$616$			4.08989i			0.164786i
$617$	24.5921	−	14.1983i	0.990042	−	0.571601i	0.0847549	−	0.996402i	$-0.472989\pi$
$617$	24.5921	−	14.1983i	0.990042	−	0.571601i	0.905287	+	0.424801i	$0.139656\pi$
$618$		0			0
$619$			14.7197i			0.591633i	0.955245	+	0.295817i	$0.0955918\pi$
$619$			14.7197i			0.591633i	−0.955245	+	0.295817i	$0.904408\pi$
$620$	7.88389	+	13.6553i	0.316625	+	0.548410i
$621$		0			0
$622$	3.01753	+	1.74217i	0.120992	+	0.0698548i
$623$	−13.5275			−0.541967
$624$		0			0
$625$	−23.9737			−0.958948
$626$	−8.89843	−	5.13751i	−0.355653	−	0.205336i
$627$		0			0
$628$	−6.77371	−	11.7324i	−0.270300	−	0.468174i
$629$		−	57.9233i		−	2.30955i
$630$		0			0
$631$	−24.3684	+	14.0691i	−0.970090	+	0.560082i	−0.899264	−	0.437407i	$-0.855897\pi$
$631$	−24.3684	+	14.0691i	−0.970090	+	0.560082i	−0.0708262	+	0.997489i	$0.522564\pi$
$632$		−	3.45834i		−	0.137565i
$633$		0			0
$634$	13.2641	−	22.9741i	0.526785	−	0.912418i
$635$	0.502702	+	0.290235i	0.0199491	+	0.0115176i
$636$		0			0
$637$	2.38000	−	2.70844i	0.0942988	−	0.107312i
$638$	40.1536			1.58970
$639$		0			0
$640$	1.09573	−	1.89787i	0.0433127	−	0.0750198i
$641$	−3.89572	−	6.74758i	−0.153872	−	0.266513i	0.778776	−	0.627302i	$-0.215841\pi$
$641$	−3.89572	−	6.74758i	−0.153872	−	0.266513i	−0.932648	+	0.360789i	$0.882508\pi$
$642$		0			0
$643$	−29.3656	+	16.9542i	−1.15807	+	0.668610i	−0.950840	−	0.309683i	$-0.899777\pi$
$643$	−29.3656	+	16.9542i	−1.15807	+	0.668610i	−0.207227	+	0.978293i	$0.566444\pi$
$644$	−2.14412	+	1.23791i	−0.0844902	+	0.0487804i
$645$		0			0
$646$	−22.0520	−	38.1951i	−0.867624	−	1.50277i
$647$	−2.20290	+	3.81554i	−0.0866050	+	0.150004i	−0.906074	−	0.423119i	$-0.860935\pi$
$647$	−2.20290	+	3.81554i	−0.0866050	+	0.150004i	0.819469	+	0.573123i	$0.194268\pi$
$648$		0			0
$649$	−19.8718			−0.780036
$650$	−0.534812	−	0.469958i	−0.0209771	−	0.0184333i
$651$		0			0
$652$	−3.86502	−	2.23147i	−0.151366	−	0.0873912i
$653$	13.8081	−	23.9163i	0.540352	−	0.935916i	−0.458532	−	0.888678i	$-0.651625\pi$
$653$	13.8081	−	23.9163i	0.540352	−	0.935916i	0.998884	−	0.0472385i	$-0.0150421\pi$
$654$		0			0
$655$		−	11.1817i		−	0.436905i
$656$	3.14093	−	1.81341i	0.122633	−	0.0708019i
$657$		0			0
$658$			7.70008i			0.300181i
$659$	3.72022	+	6.44362i	0.144919	+	0.251008i	0.929343	−	0.369218i	$-0.120374\pi$
$659$	3.72022	+	6.44362i	0.144919	+	0.251008i	−0.784423	+	0.620226i	$0.787041\pi$
$660$		0			0
$661$	1.02781	+	0.593407i	0.0399772	+	0.0230809i	0.519855	−	0.854254i	$-0.325986\pi$
$661$	1.02781	+	0.593407i	0.0399772	+	0.0230809i	−0.479878	+	0.877335i	$0.659319\pi$
$662$	28.6746			1.11447
$663$		0			0
$664$	0.332783			0.0129145
$665$	−14.6743	−	8.47223i	−0.569047	−	0.328539i
$666$		0			0
$667$	12.1535	+	21.0505i	0.470585	+	0.815077i
$668$			3.30762i			0.127976i
$669$		0			0
$670$	12.0332	−	6.94739i	0.464884	−	0.268401i
$671$		−	46.0876i		−	1.77919i
$672$		0			0
$673$	−1.14981	+	1.99153i	−0.0443219	+	0.0767678i	−0.887335	−	0.461125i	$-0.847446\pi$
$673$	−1.14981	+	1.99153i	−0.0443219	+	0.0767678i	0.843013	+	0.537893i	$0.180779\pi$
$674$	−4.18223	−	2.41461i	−0.161094	−	0.0930074i
$675$		0			0
$676$	1.67124	+	12.8921i	0.0642786	+	0.495851i
$677$	−6.12752			−0.235500			−0.117750	−	0.993043i	$-0.537568\pi$
$677$	−6.12752			−0.235500			−0.117750	+	0.993043i	$0.537568\pi$
$678$		0			0
$679$	5.80816	−	10.0600i	0.222897	−	0.386068i
$680$	−6.25015	−	10.8256i	−0.239682	−	0.415142i
$681$		0			0
$682$	−25.4846	+	14.7135i	−0.975855	+	0.563410i
$683$	8.69462	−	5.01984i	0.332691	−	0.192079i	−0.324344	−	0.945939i	$-0.605144\pi$
$683$	8.69462	−	5.01984i	0.332691	−	0.192079i	0.657035	+	0.753860i	$0.271810\pi$
$684$		0			0
$685$	23.8894	+	41.3776i	0.912766	+	1.58096i
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$		0			0
$688$	2.75539			0.105048
$689$	22.3134	+	4.46144i	0.850073	+	0.169967i
$690$		0			0
$691$	−19.2007	−	11.0855i	−0.730428	−	0.421713i	0.0881509	−	0.996107i	$-0.471904\pi$
$691$	−19.2007	−	11.0855i	−0.730428	−	0.421713i	−0.818579	+	0.574394i	$0.805238\pi$
$692$	5.06107	−	8.76603i	0.192393	−	0.333235i
$693$		0			0
$694$		−	30.5188i		−	1.15848i
$695$	−31.2182	+	18.0238i	−1.18417	+	0.683684i
$696$		0			0
$697$		−	20.6877i		−	0.783602i
$698$	2.65910	+	4.60570i	0.100648	+	0.174328i
$699$		0			0
$700$	0.171007	+	0.0987308i	0.00646345	+	0.00373167i
$701$	−21.3510			−0.806416			−0.403208	−	0.915108i	$-0.632105\pi$
$701$	−21.3510			−0.806416			−0.403208	+	0.915108i	$0.632105\pi$
$702$		0			0
$703$	−78.5165			−2.96130
$704$	3.54195	+	2.04495i	0.133492	+	0.0770718i
$705$		0			0
$706$	−14.1137	−	24.4457i	−0.531178	−	0.920027i
$707$		−	2.25385i		−	0.0847646i
$708$		0			0
$709$	21.5442	−	12.4385i	0.809109	−	0.467139i	−0.0375376	−	0.999295i	$-0.511951\pi$
$709$	21.5442	−	12.4385i	0.809109	−	0.467139i	0.846646	+	0.532156i	$0.178618\pi$
$710$		−	18.2535i		−	0.685040i
$711$		0			0
$712$	−6.76374	+	11.7151i	−0.253482	+	0.439044i
$713$	−15.4271	−	8.90685i	−0.577750	−	0.333564i
$714$		0			0
$715$	−21.3316	+	24.2754i	−0.797756	+	0.907847i
$716$	−9.25158			−0.345748
$717$		0			0
$718$	3.79286	−	6.56943i	0.141548	−	0.245169i
$719$	−11.5010	−	19.9203i	−0.428914	−	0.742901i	0.567863	−	0.823123i	$-0.307770\pi$
$719$	−11.5010	−	19.9203i	−0.428914	−	0.742901i	−0.996777	+	0.0802222i	$0.974437\pi$
$720$		0			0
$721$	−13.8846	+	8.01627i	−0.517089	+	0.298542i
$722$	−35.3200	+	20.3920i	−1.31447	+	0.758912i
$723$		0			0
$724$	11.6322	+	20.1476i	0.432309	+	0.748781i
$725$	0.969316	−	1.67890i	0.0359995	−	0.0623529i
$726$		0			0
$727$	−3.42508			−0.127029			−0.0635146	−	0.997981i	$-0.520231\pi$
$727$	−3.42508			−0.127029			−0.0635146	+	0.997981i	$0.520231\pi$
$728$	−1.15558	−	3.41535i	−0.0428285	−	0.126581i
$729$		0			0
$730$	14.0026	+	8.08439i	0.518258	+	0.299217i
$731$	7.85846	−	13.6113i	0.290656	−	0.503431i
$732$		0			0
$733$			21.6929i			0.801247i	0.916243	+	0.400624i	$0.131206\pi$
$733$			21.6929i			0.801247i	−0.916243	+	0.400624i	$0.868794\pi$
$734$	−10.2634	+	5.92558i	−0.378829	+	0.218717i
$735$		0			0
$736$			2.47582i			0.0912598i
$737$	12.9658	+	22.4573i	0.477600	+	0.827227i
$738$		0			0
$739$	−44.6284	−	25.7662i	−1.64168	−	0.947826i	−0.980236	−	0.197833i	$-0.936610\pi$
$739$	−44.6284	−	25.7662i	−1.64168	−	0.947826i	−0.661447	−	0.749992i	$-0.730057\pi$
$740$	−22.2538			−0.818065
$741$		0			0
$742$	−6.31111			−0.231688
$743$	41.6540	+	24.0489i	1.52814	+	0.882270i	0.999440	+	0.0334593i	$0.0106524\pi$
$743$	41.6540	+	24.0489i	1.52814	+	0.882270i	0.528697	+	0.848811i	$0.322681\pi$
$744$		0			0
$745$	−16.1980	−	28.0558i	−0.593449	−	1.02788i
$746$		−	29.8266i		−	1.09203i
$747$		0			0
$748$	20.2035	−	11.6645i	0.738714	−	0.426497i
$749$		−	8.61586i		−	0.314817i
$750$		0			0
$751$	−14.7133	+	25.4842i	−0.536896	+	0.929931i	0.462173	+	0.886790i	$0.347070\pi$
$751$	−14.7133	+	25.4842i	−0.536896	+	0.929931i	−0.999069	+	0.0431415i	$0.986263\pi$
$752$	6.66847	+	3.85004i	0.243174	+	0.140397i
$753$		0			0
$754$	−33.5311	+	11.3452i	−1.22113	+	0.413167i
$755$	−41.6150			−1.51453
$756$		0			0
$757$	10.0541	−	17.4142i	0.365423	−	0.632931i	−0.623421	−	0.781886i	$-0.714258\pi$
$757$	10.0541	−	17.4142i	0.365423	−	0.632931i	0.988844	+	0.148955i	$0.0475911\pi$
$758$	0.896611	+	1.55298i	0.0325664	+	0.0564067i
$759$		0			0
$760$	−14.6743	+	8.47223i	−0.532294	+	0.307320i
$761$	−28.0939	+	16.2200i	−1.01840	+	0.587976i	−0.913642	−	0.406521i	$-0.866742\pi$
$761$	−28.0939	+	16.2200i	−1.01840	+	0.587976i	−0.104763	+	0.994497i	$0.533409\pi$
$762$		0			0
$763$	−5.01589	−	8.68777i	−0.181587	−	0.314518i
$764$	4.45096	−	7.70929i	0.161030	−	0.278912i
$765$		0			0
$766$	16.6982			0.603332
$767$	16.5944	−	5.61466i	0.599188	−	0.202734i
$768$		0			0
$769$	−37.1542	−	21.4510i	−1.33982	−	0.773543i	−0.353036	−	0.935610i	$-0.614851\pi$
$769$	−37.1542	−	21.4510i	−1.33982	−	0.773543i	−0.986780	+	0.162067i	$0.948184\pi$
$770$	4.48144	−	7.76207i	0.161500	−	0.279726i
$771$		0			0
$772$			8.88835i			0.319899i
$773$	−12.8157	+	7.39912i	−0.460947	+	0.266128i	−0.712442	−	0.701731i	$-0.752411\pi$
$773$	−12.8157	+	7.39912i	−0.460947	+	0.266128i	0.251495	+	0.967858i	$0.419078\pi$
$774$		0			0
$775$			1.42075i			0.0510349i
$776$	−5.80816	−	10.0600i	−0.208501	−	0.361134i
$777$		0			0
$778$	13.5350	+	7.81441i	0.485252	+	0.280160i
$779$	−28.0427			−1.00473
$780$		0			0
$781$	34.0660			1.21898
$782$	12.2302	+	7.06112i	0.437352	+	0.252505i
$783$		0			0
$784$	0.500000	+	0.866025i	0.0178571	+	0.0309295i
$785$			29.6887i			1.05964i
$786$		0			0
$787$	24.2123	−	13.9790i	0.863076	−	0.498297i	−0.00196533	−	0.999998i	$-0.500626\pi$
$787$	24.2123	−	13.9790i	0.863076	−	0.498297i	0.865041	+	0.501701i	$0.167292\pi$
$788$			23.3926i			0.833326i
$789$		0			0
$790$	−3.78942	+	6.56347i	−0.134822	+	0.233518i
$791$	16.0693	+	9.27760i	0.571358	+	0.329873i
$792$		0			0
$793$	13.0218	+	38.4865i	0.462418	+	1.36670i
$794$	−5.61394			−0.199231
$795$		0			0
$796$	1.96804	−	3.40875i	0.0697554	−	0.120820i
$797$	8.78182	+	15.2106i	0.311068	+	0.538786i	0.978594	−	0.205801i	$-0.0659800\pi$
$797$	8.78182	+	15.2106i	0.311068	+	0.538786i	−0.667526	+	0.744587i	$0.732647\pi$
$798$		0			0
$799$	38.0374	−	21.9609i	1.34567	−	0.776921i
$800$	0.171007	−	0.0987308i	0.00604600	−	0.00349066i
$801$		0			0
$802$	12.6185	+	21.8559i	0.445575	+	0.771759i
$803$	−15.0877	+	26.1327i	−0.532434	+	0.922203i
$804$		0			0
$805$	5.42568			0.191230
$806$	17.1242	−	19.4874i	0.603176	−	0.686414i
$807$		0			0
$808$	−1.95189	−	1.12692i	−0.0686672	−	0.0396450i
$809$	5.97749	−	10.3533i	0.210157	−	0.364003i	−0.741606	−	0.670835i	$-0.765936\pi$
$809$	5.97749	−	10.3533i	0.210157	−	0.364003i	0.951764	+	0.306832i	$0.0992690\pi$
$810$		0			0
$811$		−	5.88549i		−	0.206667i	−0.994647	−	0.103334i	$-0.967049\pi$
$811$		−	5.88549i		−	0.206667i	0.994647	−	0.103334i	$-0.0329510\pi$
$812$	8.50243	−	4.90888i	0.298377	−	0.172268i
$813$		0			0
$814$		−	41.5317i		−	1.45569i
$815$	4.89020	+	8.47008i	0.171296	+	0.296694i
$816$		0			0
$817$	−18.4504	−	10.6523i	−0.645498	−	0.372678i
$818$	−28.9215			−1.01122
$819$		0			0
$820$	−7.94809			−0.277559
$821$	26.2172	+	15.1365i	0.914987	+	0.528268i	0.882032	−	0.471189i	$-0.156175\pi$
$821$	26.2172	+	15.1365i	0.914987	+	0.528268i	0.0329546	+	0.999457i	$0.489508\pi$
$822$		0			0
$823$	18.2981	+	31.6932i	0.637831	+	1.10476i	0.985908	+	0.167290i	$0.0535016\pi$
$823$	18.2981	+	31.6932i	0.637831	+	1.10476i	−0.348076	+	0.937466i	$0.613165\pi$
$824$			16.0325i			0.558520i
$825$		0			0
$826$	−4.20781	+	2.42938i	−0.146408	+	0.0845289i
$827$		−	43.4520i		−	1.51098i	−0.655163	−	0.755488i	$-0.727400\pi$
$827$		−	43.4520i		−	1.51098i	0.655163	−	0.755488i	$-0.272600\pi$
$828$		0			0
$829$	−0.418633	+	0.725093i	−0.0145397	+	0.0251835i	−0.873204	−	0.487355i	$-0.837962\pi$
$829$	−0.418633	+	0.725093i	−0.0145397	+	0.0251835i	0.858664	+	0.512539i	$0.171295\pi$
$830$	−0.631578	−	0.364642i	−0.0219224	−	0.0126569i
$831$		0			0
$832$	−3.53557	−	0.706919i	−0.122574	−	0.0245080i
$833$	5.70407			0.197634
$834$		0			0
$835$	3.62427	−	6.27742i	0.125423	−	0.217239i
$836$	−15.8115	−	27.3864i	−0.546854	−	0.947178i
$837$		0			0
$838$	27.7939	−	16.0468i	0.960124	−	0.554328i
$839$	33.2964	−	19.2237i	1.14952	−	0.663675i	0.200749	−	0.979643i	$-0.435663\pi$
$839$	33.2964	−	19.2237i	1.14952	−	0.663675i	0.948770	+	0.315968i	$0.102329\pi$
$840$		0			0
$841$	−33.6942	−	58.3601i	−1.16187	−	2.01242i
$842$	0.514814	−	0.891684i	0.0177417	−	0.0307295i
$843$		0			0
$844$	−12.8021			−0.440666
$845$	10.9545	−	26.2988i	0.376848	−	0.904706i
$846$		0			0
$847$	4.95991	+	2.86360i	0.170424	+	0.0983946i
$848$	−3.15556	+	5.46559i	−0.108362	+	0.187689i
$849$		0			0
$850$		−	1.12634i		−	0.0386330i
$851$	21.7730	−	12.5706i	0.746367	−	0.430915i
$852$		0			0
$853$			32.9422i			1.12792i	0.825803	+	0.563959i	$0.190722\pi$
$853$			32.9422i			1.12792i	−0.825803	+	0.563959i	$0.809278\pi$
$854$	−5.63434	−	9.75896i	−0.192803	−	0.333945i
$855$		0			0
$856$	−7.46156	−	4.30793i	−0.255031	−	0.147242i
$857$	22.1242			0.755750			0.377875	−	0.925857i	$-0.376655\pi$
$857$	22.1242			0.755750			0.377875	+	0.925857i	$0.376655\pi$
$858$		0			0
$859$	18.4476			0.629425			0.314712	−	0.949187i	$-0.398092\pi$
$859$	18.4476			0.629425			0.314712	+	0.949187i	$0.398092\pi$
$860$	−5.22936	−	3.01917i	−0.178320	−	0.102953i
$861$		0			0
$862$	−17.6616	−	30.5908i	−0.601556	−	1.04193i
$863$		−	45.1859i		−	1.53814i	−0.639162	−	0.769072i	$-0.720719\pi$
$863$		−	45.1859i		−	1.53814i	0.639162	−	0.769072i	$-0.279281\pi$
$864$		0			0
$865$	−19.2105	+	11.0912i	−0.653176	+	0.377112i
$866$		−	20.0939i		−	0.682817i
$867$		0			0
$868$	−3.59754	+	6.23112i	−0.122108	+	0.211498i
$869$	−12.2493	−	7.07212i	−0.415528	−	0.239905i
$870$		0			0
$871$	−17.1725	−	15.0901i	−0.581869	−	0.511309i
$872$	−10.0318			−0.339719
$873$		0			0
$874$	9.57153	−	16.5784i	0.323762	−	0.560772i
$875$	−5.69504	−	9.86410i	−0.192527	−	0.333467i
$876$		0			0
$877$	15.2612	−	8.81106i	0.515334	−	0.297528i	−0.219689	−	0.975570i	$-0.570504\pi$
$877$	15.2612	−	8.81106i	0.515334	−	0.297528i	0.735024	+	0.678041i	$0.237171\pi$
$878$	−11.3093	+	6.52940i	−0.381669	+	0.220357i
$879$		0			0
$880$	−4.48144	−	7.76207i	−0.151069	−	0.261659i
$881$	−1.23560	+	2.14012i	−0.0416283	+	0.0721023i	−0.886089	−	0.463515i	$-0.846588\pi$
$881$	−1.23560	+	2.14012i	−0.0416283	+	0.0721023i	0.844461	+	0.535618i	$0.179921\pi$
$882$		0			0
$883$	−3.93880			−0.132551			−0.0662756	−	0.997801i	$-0.521112\pi$
$883$	−3.93880			−0.132551			−0.0662756	+	0.997801i	$0.521112\pi$
$884$	−13.5757	+	15.4491i	−0.456599	+	0.519610i
$885$		0			0
$886$	6.46183	+	3.73074i	0.217089	+	0.125337i
$887$	−3.57140	+	6.18584i	−0.119916	+	0.207700i	−0.919734	−	0.392542i	$-0.871596\pi$
$887$	−3.57140	+	6.18584i	−0.119916	+	0.207700i	0.799818	+	0.600242i	$0.204929\pi$
$888$		0			0
$889$			0.264877i			0.00888370i
$890$	25.6734	−	14.8225i	0.860574	−	0.496853i
$891$		0			0
$892$			18.8489i			0.631107i
$893$	−29.7686	−	51.5607i	−0.996167	−	1.72541i
$894$		0			0
$895$	17.5583	+	10.1373i	0.586908	+	0.338852i
$896$	1.00000			0.0334077
$897$		0			0
$898$	−9.57011			−0.319359
$899$	61.1756	+	35.3198i	2.04032	+	1.17798i
$900$		0			0
$901$	17.9995	+	31.1761i	0.599651	+	1.03863i
$902$		−	14.8333i		−	0.493896i
$903$		0			0
$904$	16.0693	−	9.27760i	0.534456	−	0.308568i
$905$		−	50.9834i		−	1.69474i
$906$		0			0
$907$	3.67909	−	6.37237i	0.122162	−	0.211591i	−0.798458	−	0.602051i	$-0.794351\pi$
$907$	3.67909	−	6.37237i	0.122162	−	0.211591i	0.920620	+	0.390459i	$0.127684\pi$
$908$	1.14246	+	0.659599i	0.0379138	+	0.0218895i
$909$		0			0
$910$	−1.54919	+	7.74810i	−0.0513552	+	0.256847i
$911$	23.9499			0.793497			0.396748	−	0.917927i	$-0.370139\pi$
$911$	23.9499			0.793497			0.396748	+	0.917927i	$0.370139\pi$
$912$		0			0
$913$	0.680523	−	1.17870i	0.0225220	−	0.0390093i
$914$	−12.9141	−	22.3679i	−0.427161	−	0.739864i
$915$		0			0
$916$	−3.75949	+	2.17054i	−0.124217	+	0.0717168i
$917$	4.41878	−	2.55119i	0.145921	−	0.0842476i
$918$		0			0
$919$	18.9710	+	32.8588i	0.625797	+	1.08391i	0.988386	+	0.151963i	$0.0485595\pi$
$919$	18.9710	+	32.8588i	0.625797	+	1.08391i	−0.362589	+	0.931949i	$0.618107\pi$
$920$	2.71284	−	4.69878i	0.0894397	−	0.154914i
$921$		0			0
$922$	−1.56502			−0.0515413
$923$	−28.4476	+	9.62517i	−0.936364	+	0.316816i
$924$		0			0
$925$	−1.73653	−	1.00258i	−0.0570966	−	0.0329648i
$926$	10.2432	−	17.7417i	0.336611	−	0.583027i
$927$		0			0
$928$		−	9.81776i		−	0.322284i
$929$	−5.58551	+	3.22479i	−0.183254	+	0.105802i	−0.588821	−	0.808264i	$-0.700408\pi$
$929$	−5.58551	+	3.22479i	−0.183254	+	0.105802i	0.405566	+	0.914066i	$0.367074\pi$
$930$		0			0
$931$		−	7.73201i		−	0.253406i
$932$	2.88211	+	4.99196i	0.0944067	+	0.163517i
$933$		0			0
$934$	−3.29802	−	1.90411i	−0.107914	−	0.0623044i
$935$	−51.1249			−1.67196
$936$		0			0
$937$	−29.8183			−0.974120			−0.487060	−	0.873368i	$-0.661931\pi$
$937$	−29.8183			−0.974120			−0.487060	+	0.873368i	$0.661931\pi$
$938$	5.49094	+	3.17020i	0.179286	+	0.103511i
$939$		0			0
$940$	−8.43725	−	14.6137i	−0.275193	−	0.476648i
$941$			21.5581i			0.702774i	0.936230	+	0.351387i	$0.114290\pi$
$941$			21.5581i			0.702774i	−0.936230	+	0.351387i	$0.885710\pi$
$942$		0			0
$943$	7.77636	−	4.48968i	0.253233	−	0.146204i
$944$			4.85876i			0.158139i
$945$		0			0
$946$	5.63462	−	9.75944i	0.183197	−	0.317307i
$947$	26.4885	+	15.2932i	0.860762	+	0.496961i	0.864267	−	0.503033i	$-0.167783\pi$
$947$	26.4885	+	15.2932i	0.860762	+	0.496961i	−0.00350556	+	0.999994i	$0.501116\pi$
$948$		0			0
$949$	5.21568	−	26.0856i	0.169308	−	0.846776i
$950$	−1.52678			−0.0495351
$951$		0			0
$952$	2.85204	−	4.93987i	0.0924350	−	0.160102i
$953$	2.64767	+	4.58590i	0.0857664	+	0.148552i	0.905718	−	0.423882i	$-0.139333\pi$
$953$	2.64767	+	4.58590i	0.0857664	+	0.148552i	−0.819951	+	0.572434i	$0.805999\pi$
$954$		0			0
$955$	−16.8947	+	9.75414i	−0.546699	+	0.315637i
$956$	−11.3407	+	6.54753i	−0.366783	+	0.211762i
$957$		0			0
$958$	−12.0600	−	20.8886i	−0.389642	−	0.674880i
$959$	−10.9011	+	18.8812i	−0.352014	+	0.609706i
$960$		0			0
$961$	−20.7691			−0.669971
$962$	11.7346	+	34.6820i	0.378337	+	1.11819i
$963$		0			0
$964$	−0.389769	−	0.225033i	−0.0125536	−	0.00724784i
$965$	9.73927	−	16.8689i	0.313518	−	0.543030i
$966$		0			0
$967$			46.8612i			1.50695i	0.657474	+	0.753477i	$0.271625\pi$
$967$			46.8612i			1.50695i	−0.657474	+	0.753477i	$0.728375\pi$
$968$	4.95991	−	2.86360i	0.159417	−	0.0920397i
$969$		0			0
$970$			25.4568i			0.817368i
$971$	−23.5583	−	40.8042i	−0.756023	−	1.30947i	−0.944864	−	0.327463i	$-0.893806\pi$
$971$	−23.5583	−	40.8042i	−0.756023	−	1.30947i	0.188841	−	0.982008i	$-0.439527\pi$
$972$		0			0
$973$	−14.2453	−	8.22455i	−0.456685	−	0.263667i
$974$	7.68364			0.246200
$975$		0			0
$976$	−11.2687			−0.360701
$977$	4.49153	+	2.59319i	0.143697	+	0.0829635i	0.570125	−	0.821558i	$-0.306895\pi$
$977$	4.49153	+	2.59319i	0.143697	+	0.0829635i	−0.426428	+	0.904522i	$0.640228\pi$
$978$		0			0
$979$	27.6630	+	47.9137i	0.884113	+	1.53133i
$980$		−	2.19147i		−	0.0700039i
$981$		0			0
$982$	28.1921	−	16.2767i	0.899645	−	0.519411i
$983$			12.1664i			0.388046i	0.980997	+	0.194023i	$0.0621537\pi$
$983$			12.1664i			0.388046i	−0.980997	+	0.194023i	$0.937846\pi$
$984$		0			0
$985$	25.6321	−	44.3960i	0.816706	−	1.41458i
$986$	−48.4985	−	28.0006i	−1.54451	−	0.891721i
$987$		0			0
$988$	20.9417	+	18.4022i	0.666243	+	0.585450i
$989$	6.82184			0.216922
$990$		0			0
$991$	22.1272	−	38.3254i	0.702894	−	1.21745i	−0.264553	−	0.964371i	$-0.585224\pi$
$991$	22.1272	−	38.3254i	0.702894	−	1.21745i	0.967446	−	0.253076i	$-0.0814424\pi$
$992$	3.59754	+	6.23112i	0.114222	+	0.197838i
$993$		0			0
$994$	7.21341	−	4.16466i	0.228795	−	0.132095i
$995$	−7.47016	+	4.31290i	−0.236820	+	0.136728i
$996$		0			0
$997$	−18.4175	−	31.9001i	−0.583289	−	1.01029i	−0.995086	−	0.0990113i	$-0.968432\pi$
$997$	−18.4175	−	31.9001i	−0.583289	−	1.01029i	0.411797	−	0.911276i	$-0.364901\pi$
$998$	2.93762	−	5.08811i	0.0929888	−	0.161061i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.bj.h.1135.1	yes	16
3.2	odd	2		1638.2.bj.i.1135.8	yes	16
13.10	even	6	inner	1638.2.bj.h.127.4	✓	16
39.23	odd	6		1638.2.bj.i.127.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.bj.h.127.4	✓	16	13.10	even	6	inner
1638.2.bj.h.1135.1	yes	16	1.1	even	1	trivial
1638.2.bj.i.127.5	yes	16	39.23	odd	6
1638.2.bj.i.1135.8	yes	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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -2.19147i q^{5} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-1.09573 + 1.89787i) q^{10} +(-3.54195 - 2.04495i) q^{11} +(3.53557 + 0.706919i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.85204 + 4.93987i) q^{17} +(6.69612 - 3.86601i) q^{19} +(1.89787 - 1.09573i) q^{20} +(2.04495 + 3.54195i) q^{22} +(-1.23791 + 2.14412i) q^{23} +0.197462 q^{25} +(-2.70844 - 2.38000i) q^{26} +(0.866025 + 0.500000i) q^{28} +(4.90888 - 8.50243i) q^{29} +7.19507i q^{31} +(0.866025 - 0.500000i) q^{32} -5.70407i q^{34} +(-1.09573 - 1.89787i) q^{35} +(-8.79425 - 5.07736i) q^{37} -7.73201 q^{38} -2.19147 q^{40} +(-3.14093 - 1.81341i) q^{41} +(-1.37769 - 2.38624i) q^{43} -4.08989i q^{44} +(2.14412 - 1.23791i) q^{46} -7.70008i q^{47} +(0.500000 - 0.866025i) q^{49} +(-0.171007 - 0.0987308i) q^{50} +(1.15558 + 3.41535i) q^{52} +6.31111 q^{53} +(-4.48144 + 7.76207i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-8.50243 + 4.90888i) q^{58} +(4.20781 - 2.42938i) q^{59} +(5.63434 + 9.75896i) q^{61} +(3.59754 - 6.23112i) q^{62} -1.00000 q^{64} +(1.54919 - 7.74810i) q^{65} +(-5.49094 - 3.17020i) q^{67} +(-2.85204 + 4.93987i) q^{68} +2.19147i q^{70} +(-7.21341 + 4.16466i) q^{71} -7.37805i q^{73} +(5.07736 + 8.79425i) q^{74} +(6.69612 + 3.86601i) q^{76} -4.08989 q^{77} +3.45834 q^{79} +(1.89787 + 1.09573i) q^{80} +(1.81341 + 3.14093i) q^{82} +0.332783i q^{83} +(10.8256 - 6.25015i) q^{85} +2.75539i q^{86} +(-2.04495 + 3.54195i) q^{88} +(-11.7151 - 6.76374i) q^{89} +(3.41535 - 1.15558i) q^{91} -2.47582 q^{92} +(-3.85004 + 6.66847i) q^{94} +(-8.47223 - 14.6743i) q^{95} +(10.0600 - 5.80816i) q^{97} +(-0.866025 + 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{10} - 12 q^{11} + 10 q^{13} - 16 q^{14} - 8 q^{16} - 6 q^{17} - 4 q^{22} - 12 q^{23} - 20 q^{25} - 2 q^{26} + 16 q^{29} + 2 q^{35} - 6 q^{37} + 4 q^{40} + 12 q^{41} - 6 q^{43} + 6 q^{46}+ \cdots - 24 q^{97}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^10 - 12 * q^11 + 10 * q^13 - 16 * q^14 - 8 * q^16 - 6 * q^17 - 4 * q^22 - 12 * q^23 - 20 * q^25 - 2 * q^26 + 16 * q^29 + 2 * q^35 - 6 * q^37 + 4 * q^40 + 12 * q^41 - 6 * q^43 + 6 * q^46 + 8 * q^49 - 24 * q^50 - 4 * q^52 - 40 * q^53 + 20 * q^55 - 8 * q^56 + 6 * q^58 + 6 * q^59 - 2 * q^61 - 14 * q^62 - 16 * q^64 - 52 * q^65 - 30 * q^67 + 6 * q^68 + 12 * q^71 + 24 * q^74 + 8 * q^77 - 16 * q^79 + 2 * q^82 + 6 * q^85 + 4 * q^88 + 30 * q^89 + 4 * q^91 - 24 * q^92 - 8 * q^94 - 40 * q^95 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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