LMFDB - Embedded newform 1710.2.l.n.1261.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1261,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("1710.1261");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.l (of order $3$, 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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1261.1
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1710.1261
Dual form			1710.2.l.n.1531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.44949 q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.44949 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +3.00000 q^{11} +(-2.44949 + 4.24264i) q^{13} +(-0.724745 - 1.25529i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.775255 - 1.34278i) q^{17} +(-4.17423 + 1.25529i) q^{19} -1.00000 q^{20} +(1.50000 + 2.59808i) q^{22} +(-2.94949 + 5.10867i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.89898 q^{26} +(0.724745 - 1.25529i) q^{28} +(4.67423 - 8.09601i) q^{29} -0.898979 q^{31} +(0.500000 - 0.866025i) q^{32} +(0.775255 - 1.34278i) q^{34} +(-0.724745 - 1.25529i) q^{35} -9.89898 q^{37} +(-3.17423 - 2.98735i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(2.17423 + 3.76588i) q^{41} +(5.89898 + 10.2173i) q^{43} +(-1.50000 + 2.59808i) q^{44} -5.89898 q^{46} +(-0.550510 + 0.953512i) q^{47} -4.89898 q^{49} -1.00000 q^{50} +(-2.44949 - 4.24264i) q^{52} +(-3.72474 + 6.45145i) q^{53} +(1.50000 + 2.59808i) q^{55} +1.44949 q^{56} +9.34847 q^{58} +(-3.00000 - 5.19615i) q^{59} +(-6.22474 + 10.7816i) q^{61} +(-0.449490 - 0.778539i) q^{62} +1.00000 q^{64} -4.89898 q^{65} +(3.67423 - 6.36396i) q^{67} +1.55051 q^{68} +(0.724745 - 1.25529i) q^{70} +(-1.67423 - 2.89986i) q^{71} +(-5.22474 - 9.04952i) q^{73} +(-4.94949 - 8.57277i) q^{74} +(1.00000 - 4.24264i) q^{76} -4.34847 q^{77} +(-3.44949 - 5.97469i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-2.17423 + 3.76588i) q^{82} -11.7980 q^{83} +(0.775255 - 1.34278i) q^{85} +(-5.89898 + 10.2173i) q^{86} -3.00000 q^{88} +(-2.72474 + 4.71940i) q^{89} +(3.55051 - 6.14966i) q^{91} +(-2.94949 - 5.10867i) q^{92} -1.10102 q^{94} +(-3.17423 - 2.98735i) q^{95} +(9.22474 + 15.9777i) q^{97} +(-2.44949 - 4.24264i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^7 - 4 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{7} - 4 q^{8} - 2 q^{10} + 12 q^{11} + 2 q^{14} - 2 q^{16} - 8 q^{17} - 2 q^{19} - 4 q^{20} + 6 q^{22} - 2 q^{23} - 2 q^{25} - 2 q^{28} + 4 q^{29} + 16 q^{31} + 2 q^{32} + 8 q^{34} + 2 q^{35} - 20 q^{37} + 2 q^{38} - 2 q^{40} - 6 q^{41} + 4 q^{43} - 6 q^{44} - 4 q^{46} - 12 q^{47} - 4 q^{50} - 10 q^{53} + 6 q^{55} - 4 q^{56} + 8 q^{58} - 12 q^{59} - 20 q^{61} + 8 q^{62} + 4 q^{64} + 16 q^{68} - 2 q^{70} + 8 q^{71} - 16 q^{73} - 10 q^{74} + 4 q^{76} + 12 q^{77} - 4 q^{79} + 2 q^{80} + 6 q^{82} - 8 q^{83} + 8 q^{85} - 4 q^{86} - 12 q^{88} - 6 q^{89} + 24 q^{91} - 2 q^{92} - 24 q^{94} + 2 q^{95} + 32 q^{97}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^7 - 4 * q^8 - 2 * q^10 + 12 * q^11 + 2 * q^14 - 2 * q^16 - 8 * q^17 - 2 * q^19 - 4 * q^20 + 6 * q^22 - 2 * q^23 - 2 * q^25 - 2 * q^28 + 4 * q^29 + 16 * q^31 + 2 * q^32 + 8 * q^34 + 2 * q^35 - 20 * q^37 + 2 * q^38 - 2 * q^40 - 6 * q^41 + 4 * q^43 - 6 * q^44 - 4 * q^46 - 12 * q^47 - 4 * q^50 - 10 * q^53 + 6 * q^55 - 4 * q^56 + 8 * q^58 - 12 * q^59 - 20 * q^61 + 8 * q^62 + 4 * q^64 + 16 * q^68 - 2 * q^70 + 8 * q^71 - 16 * q^73 - 10 * q^74 + 4 * q^76 + 12 * q^77 - 4 * q^79 + 2 * q^80 + 6 * q^82 - 8 * q^83 + 8 * q^85 - 4 * q^86 - 12 * q^88 - 6 * q^89 + 24 * q^91 - 2 * q^92 - 24 * q^94 + 2 * q^95 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−1.44949			−0.547856			−0.273928	−	0.961750i	$-0.588323\pi$
$7$	−1.44949			−0.547856			−0.273928	+	0.961750i	$0.588323\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$		0			0
$13$	−2.44949	+	4.24264i	−0.679366	+	1.17670i	0.295806	+	0.955248i	$0.404412\pi$
$13$	−2.44949	+	4.24264i	−0.679366	+	1.17670i	−0.975172	+	0.221449i	$0.928921\pi$
$14$	−0.724745	−	1.25529i	−0.193696	−	0.335492i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.775255	−	1.34278i	−0.188027	−	0.325672i	0.756565	−	0.653918i	$-0.226876\pi$
$17$	−0.775255	−	1.34278i	−0.188027	−	0.325672i	−0.944592	+	0.328246i	$0.893543\pi$
$18$		0			0
$19$	−4.17423	+	1.25529i	−0.957635	+	0.287984i
$19$	−4.17423	+	1.25529i	−0.957635	+	0.287984i
$20$	−1.00000			−0.223607
$21$		0			0
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	−2.94949	+	5.10867i	−0.615011	+	1.06523i	0.375371	+	0.926874i	$0.377515\pi$
$23$	−2.94949	+	5.10867i	−0.615011	+	1.06523i	−0.990383	+	0.138356i	$0.955818\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−4.89898			−0.960769
$27$		0			0
$28$	0.724745	−	1.25529i	0.136964	−	0.237228i
$29$	4.67423	−	8.09601i	0.867984	−	1.50339i	0.00392972	−	0.999992i	$-0.498749\pi$
$29$	4.67423	−	8.09601i	0.867984	−	1.50339i	0.864054	−	0.503399i	$-0.167918\pi$
$30$		0			0
$31$	−0.898979			−0.161461			−0.0807307	−	0.996736i	$-0.525725\pi$
$31$	−0.898979			−0.161461			−0.0807307	+	0.996736i	$0.525725\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	0.775255	−	1.34278i	0.132955	−	0.230285i
$35$	−0.724745	−	1.25529i	−0.122504	−	0.212184i
$36$		0			0
$37$	−9.89898			−1.62738			−0.813691	−	0.581298i	$-0.802545\pi$
$37$	−9.89898			−1.62738			−0.813691	+	0.581298i	$0.802545\pi$
$38$	−3.17423	−	2.98735i	−0.514929	−	0.484611i
$39$		0			0
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	2.17423	+	3.76588i	0.339558	+	0.588132i	0.984350	−	0.176226i	$-0.0563890\pi$
$41$	2.17423	+	3.76588i	0.339558	+	0.588132i	−0.644791	+	0.764359i	$0.723056\pi$
$42$		0			0
$43$	5.89898	+	10.2173i	0.899586	+	1.55813i	0.828024	+	0.560692i	$0.189465\pi$
$43$	5.89898	+	10.2173i	0.899586	+	1.55813i	0.0715617	+	0.997436i	$0.477202\pi$
$44$	−1.50000	+	2.59808i	−0.226134	+	0.391675i
$45$		0			0
$46$	−5.89898			−0.869757
$47$	−0.550510	+	0.953512i	−0.0803002	+	0.139084i	−0.903379	−	0.428843i	$-0.858921\pi$
$47$	−0.550510	+	0.953512i	−0.0803002	+	0.139084i	0.823079	+	0.567927i	$0.192255\pi$
$48$		0			0
$49$	−4.89898			−0.699854
$50$	−1.00000			−0.141421
$51$		0			0
$52$	−2.44949	−	4.24264i	−0.339683	−	0.588348i
$53$	−3.72474	+	6.45145i	−0.511633	+	0.886174i	0.488276	+	0.872689i	$0.337626\pi$
$53$	−3.72474	+	6.45145i	−0.511633	+	0.886174i	−0.999909	+	0.0134852i	$0.995707\pi$
$54$		0			0
$55$	1.50000	+	2.59808i	0.202260	+	0.350325i
$56$	1.44949			0.193696
$57$		0			0
$58$	9.34847			1.22751
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$		0			0
$61$	−6.22474	+	10.7816i	−0.796997	+	1.38044i	0.124566	+	0.992211i	$0.460246\pi$
$61$	−6.22474	+	10.7816i	−0.796997	+	1.38044i	−0.921563	+	0.388228i	$0.873087\pi$
$62$	−0.449490	−	0.778539i	−0.0570853	−	0.0988746i
$63$		0			0
$64$	1.00000			0.125000
$65$	−4.89898			−0.607644
$66$		0			0
$67$	3.67423	−	6.36396i	0.448879	−	0.777482i	−0.549434	−	0.835537i	$-0.685157\pi$
$67$	3.67423	−	6.36396i	0.448879	−	0.777482i	0.998313	+	0.0580554i	$0.0184900\pi$
$68$	1.55051			0.188027
$69$		0			0
$70$	0.724745	−	1.25529i	0.0866236	−	0.150036i
$71$	−1.67423	−	2.89986i	−0.198695	−	0.344150i	0.749410	−	0.662106i	$-0.230337\pi$
$71$	−1.67423	−	2.89986i	−0.198695	−	0.344150i	−0.948106	+	0.317956i	$0.897004\pi$
$72$		0			0
$73$	−5.22474	−	9.04952i	−0.611510	−	1.05917i	−0.990986	−	0.133965i	$-0.957229\pi$
$73$	−5.22474	−	9.04952i	−0.611510	−	1.05917i	0.379476	−	0.925202i	$-0.376104\pi$
$74$	−4.94949	−	8.57277i	−0.575366	−	0.996564i
$75$		0			0
$76$	1.00000	−	4.24264i	0.114708	−	0.486664i
$77$	−4.34847			−0.495554
$78$		0			0
$79$	−3.44949	−	5.97469i	−0.388098	−	0.672205i	0.604096	−	0.796912i	$-0.293534\pi$
$79$	−3.44949	−	5.97469i	−0.388098	−	0.672205i	−0.992194	+	0.124706i	$0.960201\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$		0			0
$82$	−2.17423	+	3.76588i	−0.240104	+	0.415872i
$83$	−11.7980			−1.29499			−0.647497	−	0.762068i	$-0.724184\pi$
$83$	−11.7980			−1.29499			−0.647497	+	0.762068i	$0.724184\pi$
$84$		0			0
$85$	0.775255	−	1.34278i	0.0840882	−	0.145645i
$86$	−5.89898	+	10.2173i	−0.636103	+	1.10176i
$87$		0			0
$88$	−3.00000			−0.319801
$89$	−2.72474	+	4.71940i	−0.288822	+	0.500255i	−0.973529	−	0.228564i	$-0.926597\pi$
$89$	−2.72474	+	4.71940i	−0.288822	+	0.500255i	0.684707	+	0.728819i	$0.259930\pi$
$90$		0			0
$91$	3.55051	−	6.14966i	0.372195	−	0.644660i
$92$	−2.94949	−	5.10867i	−0.307506	−	0.532615i
$93$		0			0
$94$	−1.10102			−0.113562
$95$	−3.17423	−	2.98735i	−0.325670	−	0.306495i
$96$		0			0
$97$	9.22474	+	15.9777i	0.936631	+	1.62229i	0.771699	+	0.635987i	$0.219407\pi$
$97$	9.22474	+	15.9777i	0.936631	+	1.62229i	0.164931	+	0.986305i	$0.447260\pi$
$98$	−2.44949	−	4.24264i	−0.247436	−	0.428571i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−0.550510	+	0.953512i	−0.0547778	+	0.0948780i	−0.892114	−	0.451810i	$-0.850778\pi$
$101$	−0.550510	+	0.953512i	−0.0547778	+	0.0948780i	0.837336	+	0.546688i	$0.184112\pi$
$102$		0			0
$103$	11.2474			1.10824			0.554122	−	0.832435i	$-0.313054\pi$
$103$	11.2474			1.10824			0.554122	+	0.832435i	$0.313054\pi$
$104$	2.44949	−	4.24264i	0.240192	−	0.416025i
$105$		0			0
$106$	−7.44949			−0.723558
$107$	2.65153			0.256333			0.128167	−	0.991753i	$-0.459091\pi$
$107$	2.65153			0.256333			0.128167	+	0.991753i	$0.459091\pi$
$108$		0			0
$109$	−0.674235	−	1.16781i	−0.0645800	−	0.111856i	0.831928	−	0.554884i	$-0.187237\pi$
$109$	−0.674235	−	1.16781i	−0.0645800	−	0.111856i	−0.896508	+	0.443028i	$0.853904\pi$
$110$	−1.50000	+	2.59808i	−0.143019	+	0.247717i
$111$		0			0
$112$	0.724745	+	1.25529i	0.0684820	+	0.118614i
$113$	9.55051			0.898436			0.449218	−	0.893422i	$-0.351703\pi$
$113$	9.55051			0.898436			0.449218	+	0.893422i	$0.351703\pi$
$114$		0			0
$115$	−5.89898			−0.550083
$116$	4.67423	+	8.09601i	0.433992	+	0.751696i
$117$		0			0
$118$	3.00000	−	5.19615i	0.276172	−	0.478345i
$119$	1.12372	+	1.94635i	0.103012	+	0.178421i
$120$		0			0
$121$	−2.00000			−0.181818
$122$	−12.4495			−1.12712
$123$		0			0
$124$	0.449490	−	0.778539i	0.0403654	−	0.0699149i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	0.174235	−	0.301783i	0.0154608	−	0.0267789i	−0.858191	−	0.513330i	$-0.828412\pi$
$127$	0.174235	−	0.301783i	0.0154608	−	0.0267789i	0.873652	+	0.486551i	$0.161745\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−2.44949	−	4.24264i	−0.214834	−	0.372104i
$131$	−1.50000	−	2.59808i	−0.131056	−	0.226995i	0.793028	−	0.609185i	$-0.208503\pi$
$131$	−1.50000	−	2.59808i	−0.131056	−	0.226995i	−0.924084	+	0.382190i	$0.875170\pi$
$132$		0			0
$133$	6.05051	−	1.81954i	0.524646	−	0.157774i
$134$	7.34847			0.634811
$135$		0			0
$136$	0.775255	+	1.34278i	0.0664776	+	0.115143i
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$		0			0
$139$	7.34847	−	12.7279i	0.623289	−	1.07957i	−0.365580	−	0.930780i	$-0.619129\pi$
$139$	7.34847	−	12.7279i	0.623289	−	1.07957i	0.988869	−	0.148788i	$-0.0475373\pi$
$140$	1.44949			0.122504
$141$		0			0
$142$	1.67423	−	2.89986i	0.140499	−	0.243351i
$143$	−7.34847	+	12.7279i	−0.614510	+	1.06436i
$144$		0			0
$145$	9.34847			0.776348
$146$	5.22474	−	9.04952i	0.432403	−	0.748944i
$147$		0			0
$148$	4.94949	−	8.57277i	0.406846	−	0.704677i
$149$	6.77526	+	11.7351i	0.555051	+	0.961376i	0.997900	+	0.0647795i	$0.0206344\pi$
$149$	6.77526	+	11.7351i	0.555051	+	0.961376i	−0.442849	+	0.896596i	$0.646032\pi$
$150$		0			0
$151$	−4.65153			−0.378536			−0.189268	−	0.981925i	$-0.560612\pi$
$151$	−4.65153			−0.378536			−0.189268	+	0.981925i	$0.560612\pi$
$152$	4.17423	−	1.25529i	0.338575	−	0.101818i
$153$		0			0
$154$	−2.17423	−	3.76588i	−0.175205	−	0.303464i
$155$	−0.449490	−	0.778539i	−0.0361039	−	0.0625338i
$156$		0			0
$157$	−10.3990	−	18.0116i	−0.829929	−	1.43748i	−0.898093	−	0.439805i	$-0.855048\pi$
$157$	−10.3990	−	18.0116i	−0.829929	−	1.43748i	0.0681644	−	0.997674i	$-0.478286\pi$
$158$	3.44949	−	5.97469i	0.274427	−	0.475321i
$159$		0			0
$160$	1.00000			0.0790569
$161$	4.27526	−	7.40496i	0.336937	−	0.583593i
$162$		0			0
$163$	16.6969			1.30781			0.653903	−	0.756579i	$-0.273131\pi$
$163$	16.6969			1.30781			0.653903	+	0.756579i	$0.273131\pi$
$164$	−4.34847			−0.339558
$165$		0			0
$166$	−5.89898	−	10.2173i	−0.457850	−	0.793019i
$167$	−4.84847	+	8.39780i	−0.375186	+	0.649841i	−0.990355	−	0.138554i	$-0.955754\pi$
$167$	−4.84847	+	8.39780i	−0.375186	+	0.649841i	0.615169	+	0.788395i	$0.289088\pi$
$168$		0			0
$169$	−5.50000	−	9.52628i	−0.423077	−	0.732791i
$170$	1.55051			0.118919
$171$		0			0
$172$	−11.7980			−0.899586
$173$	−2.27526	−	3.94086i	−0.172984	−	0.299618i	0.766477	−	0.642271i	$-0.222008\pi$
$173$	−2.27526	−	3.94086i	−0.172984	−	0.299618i	−0.939462	+	0.342653i	$0.888674\pi$
$174$		0			0
$175$	0.724745	−	1.25529i	0.0547856	−	0.0948914i
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$		0			0
$178$	−5.44949			−0.408457
$179$	20.7980			1.55451			0.777256	−	0.629184i	$-0.216611\pi$
$179$	20.7980			1.55451			0.777256	+	0.629184i	$0.216611\pi$
$180$		0			0
$181$	−8.57321	+	14.8492i	−0.637242	+	1.10374i	0.348793	+	0.937200i	$0.386591\pi$
$181$	−8.57321	+	14.8492i	−0.637242	+	1.10374i	−0.986035	+	0.166536i	$0.946742\pi$
$182$	7.10102			0.526363
$183$		0			0
$184$	2.94949	−	5.10867i	0.217439	−	0.376616i
$185$	−4.94949	−	8.57277i	−0.363894	−	0.630282i
$186$		0			0
$187$	−2.32577	−	4.02834i	−0.170077	−	0.294582i
$188$	−0.550510	−	0.953512i	−0.0401501	−	0.0695420i
$189$		0			0
$190$	1.00000	−	4.24264i	0.0725476	−	0.307794i
$191$	3.79796			0.274811			0.137405	−	0.990515i	$-0.456124\pi$
$191$	3.79796			0.274811			0.137405	+	0.990515i	$0.456124\pi$
$192$		0			0
$193$	10.6742	+	18.4883i	0.768348	+	1.33082i	0.938458	+	0.345393i	$0.112254\pi$
$193$	10.6742	+	18.4883i	0.768348	+	1.33082i	−0.170110	+	0.985425i	$0.554412\pi$
$194$	−9.22474	+	15.9777i	−0.662298	+	1.14713i
$195$		0			0
$196$	2.44949	−	4.24264i	0.174964	−	0.303046i
$197$	−6.55051			−0.466705			−0.233352	−	0.972392i	$-0.574970\pi$
$197$	−6.55051			−0.466705			−0.233352	+	0.972392i	$0.574970\pi$
$198$		0			0
$199$	−3.22474	+	5.58542i	−0.228596	+	0.395940i	−0.957392	−	0.288791i	$-0.906747\pi$
$199$	−3.22474	+	5.58542i	−0.228596	+	0.395940i	0.728796	+	0.684731i	$0.240080\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$		0			0
$202$	−1.10102			−0.0774675
$203$	−6.77526	+	11.7351i	−0.475530	+	0.823642i
$204$		0			0
$205$	−2.17423	+	3.76588i	−0.151855	+	0.263021i
$206$	5.62372	+	9.74058i	0.391823	+	0.678658i
$207$		0			0
$208$	4.89898			0.339683
$209$	−12.5227	+	3.76588i	−0.866214	+	0.260492i
$210$		0			0
$211$	13.1742	+	22.8184i	0.906952	+	1.57089i	0.818276	+	0.574826i	$0.194930\pi$
$211$	13.1742	+	22.8184i	0.906952	+	1.57089i	0.0886760	+	0.996061i	$0.471736\pi$
$212$	−3.72474	−	6.45145i	−0.255817	−	0.443087i
$213$		0			0
$214$	1.32577	+	2.29629i	0.0906275	+	0.156971i
$215$	−5.89898	+	10.2173i	−0.402307	+	0.696816i
$216$		0			0
$217$	1.30306			0.0884576
$218$	0.674235	−	1.16781i	0.0456649	−	0.0790940i
$219$		0			0
$220$	−3.00000			−0.202260
$221$	7.59592			0.510957
$222$		0			0
$223$	1.72474	+	2.98735i	0.115497	+	0.200047i	0.917978	−	0.396630i	$-0.129820\pi$
$223$	1.72474	+	2.98735i	0.115497	+	0.200047i	−0.802481	+	0.596678i	$0.796487\pi$
$224$	−0.724745	+	1.25529i	−0.0484241	+	0.0838729i
$225$		0			0
$226$	4.77526	+	8.27098i	0.317645	+	0.550178i
$227$	11.3485			0.753224			0.376612	−	0.926371i	$-0.377089\pi$
$227$	11.3485			0.753224			0.376612	+	0.926371i	$0.377089\pi$
$228$		0			0
$229$	8.69694			0.574710			0.287355	−	0.957824i	$-0.407224\pi$
$229$	8.69694			0.574710			0.287355	+	0.957824i	$0.407224\pi$
$230$	−2.94949	−	5.10867i	−0.194484	−	0.336855i
$231$		0			0
$232$	−4.67423	+	8.09601i	−0.306879	+	0.531529i
$233$	−13.8990	−	24.0737i	−0.910552	−	1.57712i	−0.813286	−	0.581865i	$-0.802323\pi$
$233$	−13.8990	−	24.0737i	−0.910552	−	1.57712i	−0.0972668	−	0.995258i	$-0.531010\pi$
$234$		0			0
$235$	−1.10102			−0.0718227
$236$	6.00000			0.390567
$237$		0			0
$238$	−1.12372	+	1.94635i	−0.0728402	+	0.126163i
$239$	29.7980			1.92747			0.963735	−	0.266862i	$-0.0859867\pi$
$239$	29.7980			1.92747			0.963735	+	0.266862i	$0.0859867\pi$
$240$		0			0
$241$	−3.34847	+	5.79972i	−0.215694	+	0.373593i	−0.953487	−	0.301434i	$-0.902535\pi$
$241$	−3.34847	+	5.79972i	−0.215694	+	0.373593i	0.737793	+	0.675027i	$0.235868\pi$
$242$	−1.00000	−	1.73205i	−0.0642824	−	0.111340i
$243$		0			0
$244$	−6.22474	−	10.7816i	−0.398498	−	0.690220i
$245$	−2.44949	−	4.24264i	−0.156492	−	0.271052i
$246$		0			0
$247$	4.89898	−	20.7846i	0.311715	−	1.32249i
$248$	0.898979			0.0570853
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−1.10102	+	1.90702i	−0.0694958	+	0.120370i	−0.898679	−	0.438606i	$-0.855472\pi$
$251$	−1.10102	+	1.90702i	−0.0694958	+	0.120370i	0.829184	+	0.558976i	$0.188806\pi$
$252$		0			0
$253$	−8.84847	+	15.3260i	−0.556298	+	0.963537i
$254$	0.348469			0.0218649
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.89898	−	13.6814i	0.492725	−	0.853424i	−0.507240	−	0.861805i	$-0.669334\pi$
$257$	7.89898	−	13.6814i	0.492725	−	0.853424i	0.999965	+	0.00838040i	$0.00266760\pi$
$258$		0			0
$259$	14.3485			0.891570
$260$	2.44949	−	4.24264i	0.151911	−	0.263117i
$261$		0			0
$262$	1.50000	−	2.59808i	0.0926703	−	0.160510i
$263$	5.05051	+	8.74774i	0.311428	+	0.539409i	0.978672	−	0.205431i	$-0.0658595\pi$
$263$	5.05051	+	8.74774i	0.311428	+	0.539409i	−0.667244	+	0.744839i	$0.732526\pi$
$264$		0			0
$265$	−7.44949			−0.457619
$266$	4.60102	+	4.33013i	0.282107	+	0.265497i
$267$		0			0
$268$	3.67423	+	6.36396i	0.224440	+	0.388741i
$269$	−12.1237	−	20.9989i	−0.739197	−	1.28033i	−0.952858	−	0.303418i	$-0.901872\pi$
$269$	−12.1237	−	20.9989i	−0.739197	−	1.28033i	0.213661	−	0.976908i	$-0.431461\pi$
$270$		0			0
$271$	7.44949	+	12.9029i	0.452524	+	0.783795i	0.998542	−	0.0539785i	$-0.0171903\pi$
$271$	7.44949	+	12.9029i	0.452524	+	0.783795i	−0.546018	+	0.837774i	$0.683857\pi$
$272$	−0.775255	+	1.34278i	−0.0470067	+	0.0814181i
$273$		0			0
$274$	−12.0000			−0.724947
$275$	−1.50000	+	2.59808i	−0.0904534	+	0.156670i
$276$		0			0
$277$	−12.8990			−0.775025			−0.387512	−	0.921865i	$-0.626666\pi$
$277$	−12.8990			−0.775025			−0.387512	+	0.921865i	$0.626666\pi$
$278$	14.6969			0.881464
$279$		0			0
$280$	0.724745	+	1.25529i	0.0433118	+	0.0750182i
$281$	7.17423	−	12.4261i	0.427979	−	0.741281i	−0.568714	−	0.822535i	$-0.692559\pi$
$281$	7.17423	−	12.4261i	0.427979	−	0.741281i	0.996693	+	0.0812537i	$0.0258924\pi$
$282$		0			0
$283$	6.34847	+	10.9959i	0.377377	+	0.653637i	0.990680	−	0.136211i	$-0.0434927\pi$
$283$	6.34847	+	10.9959i	0.377377	+	0.653637i	−0.613302	+	0.789848i	$0.710159\pi$
$284$	3.34847			0.198695
$285$		0			0
$286$	−14.6969			−0.869048
$287$	−3.15153	−	5.45861i	−0.186029	−	0.322212i
$288$		0			0
$289$	7.29796	−	12.6404i	0.429292	−	0.743555i
$290$	4.67423	+	8.09601i	0.274481	+	0.475414i
$291$		0			0
$292$	10.4495			0.611510
$293$	11.4495			0.668886			0.334443	−	0.942416i	$-0.391452\pi$
$293$	11.4495			0.668886			0.334443	+	0.942416i	$0.391452\pi$
$294$		0			0
$295$	3.00000	−	5.19615i	0.174667	−	0.302532i
$296$	9.89898			0.575366
$297$		0			0
$298$	−6.77526	+	11.7351i	−0.392480	+	0.679795i
$299$	−14.4495	−	25.0273i	−0.835636	−	1.44736i
$300$		0			0
$301$	−8.55051	−	14.8099i	−0.492843	−	0.853629i
$302$	−2.32577	−	4.02834i	−0.133833	−	0.231805i
$303$		0			0
$304$	3.17423	+	2.98735i	0.182055	+	0.171336i
$305$	−12.4495			−0.712856
$306$		0			0
$307$	5.12372	+	8.87455i	0.292426	+	0.506497i	0.974383	−	0.224895i	$-0.0722040\pi$
$307$	5.12372	+	8.87455i	0.292426	+	0.506497i	−0.681957	+	0.731393i	$0.738871\pi$
$308$	2.17423	−	3.76588i	0.123889	−	0.214581i
$309$		0			0
$310$	0.449490	−	0.778539i	0.0255293	−	0.0442180i
$311$	9.79796			0.555591			0.277796	−	0.960640i	$-0.410396\pi$
$311$	9.79796			0.555591			0.277796	+	0.960640i	$0.410396\pi$
$312$		0			0
$313$	−15.7980	+	27.3629i	−0.892953	+	1.54664i	−0.0566362	+	0.998395i	$0.518038\pi$
$313$	−15.7980	+	27.3629i	−0.892953	+	1.54664i	−0.836317	+	0.548246i	$0.815296\pi$
$314$	10.3990	−	18.0116i	0.586848	−	1.01645i
$315$		0			0
$316$	6.89898			0.388098
$317$	4.72474	−	8.18350i	0.265368	−	0.459631i	−0.702292	−	0.711889i	$-0.747840\pi$
$317$	4.72474	−	8.18350i	0.265368	−	0.459631i	0.967660	+	0.252258i	$0.0811732\pi$
$318$		0			0
$319$	14.0227	−	24.2880i	0.785121	−	1.35987i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$		0			0
$322$	8.55051			0.476501
$323$	4.92168	+	4.63191i	0.273850	+	0.257726i
$324$		0			0
$325$	−2.44949	−	4.24264i	−0.135873	−	0.235339i
$326$	8.34847	+	14.4600i	0.462379	+	0.800864i
$327$		0			0
$328$	−2.17423	−	3.76588i	−0.120052	−	0.207936i
$329$	0.797959	−	1.38211i	0.0439929	−	0.0761979i
$330$		0			0
$331$	18.3485			1.00852			0.504262	−	0.863551i	$-0.331765\pi$
$331$	18.3485			1.00852			0.504262	+	0.863551i	$0.331765\pi$
$332$	5.89898	−	10.2173i	0.323749	−	0.560749i
$333$		0			0
$334$	−9.69694			−0.530593
$335$	7.34847			0.401490
$336$		0			0
$337$	13.2474	+	22.9453i	0.721635	+	1.24991i	0.960344	+	0.278817i	$0.0899422\pi$
$337$	13.2474	+	22.9453i	0.721635	+	1.24991i	−0.238710	+	0.971091i	$0.576724\pi$
$338$	5.50000	−	9.52628i	0.299161	−	0.518161i
$339$		0			0
$340$	0.775255	+	1.34278i	0.0420441	+	0.0728225i
$341$	−2.69694			−0.146047
$342$		0			0
$343$	17.2474			0.931275
$344$	−5.89898	−	10.2173i	−0.318052	−	0.550882i
$345$		0			0
$346$	2.27526	−	3.94086i	0.122318	−	0.211862i
$347$	5.89898	+	10.2173i	0.316674	+	0.548495i	0.979792	−	0.200020i	$-0.0641006\pi$
$347$	5.89898	+	10.2173i	0.316674	+	0.548495i	−0.663118	+	0.748515i	$0.730767\pi$
$348$		0			0
$349$	−20.0454			−1.07301			−0.536503	−	0.843898i	$-0.680255\pi$
$349$	−20.0454			−1.07301			−0.536503	+	0.843898i	$0.680255\pi$
$350$	1.44949			0.0774785
$351$		0			0
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	35.3485			1.88141			0.940705	−	0.339227i	$-0.110165\pi$
$353$	35.3485			1.88141			0.940705	+	0.339227i	$0.110165\pi$
$354$		0			0
$355$	1.67423	−	2.89986i	0.0888591	−	0.153909i
$356$	−2.72474	−	4.71940i	−0.144411	−	0.250128i
$357$		0			0
$358$	10.3990	+	18.0116i	0.549603	+	0.951941i
$359$	13.2247	+	22.9059i	0.697975	+	1.20893i	0.969167	+	0.246403i	$0.0792488\pi$
$359$	13.2247	+	22.9059i	0.697975	+	1.20893i	−0.271192	+	0.962525i	$0.587418\pi$
$360$		0			0
$361$	15.8485	−	10.4798i	0.834130	−	0.551568i
$362$	−17.1464			−0.901196
$363$		0			0
$364$	3.55051	+	6.14966i	0.186097	+	0.322330i
$365$	5.22474	−	9.04952i	0.273476	−	0.473674i
$366$		0			0
$367$	−10.4495	+	18.0990i	−0.545459	+	0.944763i	0.453119	+	0.891450i	$0.350311\pi$
$367$	−10.4495	+	18.0990i	−0.545459	+	0.944763i	−0.998578	+	0.0533125i	$0.983022\pi$
$368$	5.89898			0.307506
$369$		0			0
$370$	4.94949	−	8.57277i	0.257312	−	0.445677i
$371$	5.39898	−	9.35131i	0.280301	−	0.485496i
$372$		0			0
$373$	−3.89898			−0.201882			−0.100941	−	0.994892i	$-0.532185\pi$
$373$	−3.89898			−0.201882			−0.100941	+	0.994892i	$0.532185\pi$
$374$	2.32577	−	4.02834i	0.120262	−	0.208301i
$375$		0			0
$376$	0.550510	−	0.953512i	0.0283904	−	0.0491736i
$377$	22.8990	+	39.6622i	1.17936	+	2.04271i
$378$		0			0
$379$	−6.69694			−0.343999			−0.171999	−	0.985097i	$-0.555023\pi$
$379$	−6.69694			−0.343999			−0.171999	+	0.985097i	$0.555023\pi$
$380$	4.17423	−	1.25529i	0.214134	−	0.0643953i
$381$		0			0
$382$	1.89898	+	3.28913i	0.0971602	+	0.168286i
$383$	15.2474	+	26.4094i	0.779108	+	1.34946i	0.932456	+	0.361283i	$0.117661\pi$
$383$	15.2474	+	26.4094i	0.779108	+	1.34946i	−0.153348	+	0.988172i	$0.549006\pi$
$384$		0			0
$385$	−2.17423	−	3.76588i	−0.110809	−	0.191927i
$386$	−10.6742	+	18.4883i	−0.543304	+	0.941031i
$387$		0			0
$388$	−18.4495			−0.936631
$389$	−11.5732	+	20.0454i	−0.586785	+	1.01634i	0.407865	+	0.913042i	$0.366273\pi$
$389$	−11.5732	+	20.0454i	−0.586785	+	1.01634i	−0.994650	+	0.103300i	$0.967060\pi$
$390$		0			0
$391$	9.14643			0.462555
$392$	4.89898			0.247436
$393$		0			0
$394$	−3.27526	−	5.67291i	−0.165005	−	0.285797i
$395$	3.44949	−	5.97469i	0.173563	−	0.300619i
$396$		0			0
$397$	−5.74745	−	9.95487i	−0.288456	−	0.499621i	0.684985	−	0.728557i	$-0.259809\pi$
$397$	−5.74745	−	9.95487i	−0.288456	−	0.499621i	−0.973441	+	0.228936i	$0.926475\pi$
$398$	−6.44949			−0.323284
$399$		0			0
$400$	1.00000			0.0500000
$401$	−1.89898	−	3.28913i	−0.0948305	−	0.164251i	0.814707	−	0.579872i	$-0.196898\pi$
$401$	−1.89898	−	3.28913i	−0.0948305	−	0.164251i	−0.909538	+	0.415621i	$0.863564\pi$
$402$		0			0
$403$	2.20204	−	3.81405i	0.109691	−	0.189991i
$404$	−0.550510	−	0.953512i	−0.0273889	−	0.0474390i
$405$		0			0
$406$	−13.5505			−0.672501
$407$	−29.6969			−1.47202
$408$		0			0
$409$	4.74745	−	8.22282i	0.234746	−	0.406592i	−0.724453	−	0.689325i	$-0.757907\pi$
$409$	4.74745	−	8.22282i	0.234746	−	0.406592i	0.959199	+	0.282732i	$0.0912408\pi$
$410$	−4.34847			−0.214756
$411$		0			0
$412$	−5.62372	+	9.74058i	−0.277061	+	0.479884i
$413$	4.34847	+	7.53177i	0.213974	+	0.370614i
$414$		0			0
$415$	−5.89898	−	10.2173i	−0.289570	−	0.501549i
$416$	2.44949	+	4.24264i	0.120096	+	0.208013i
$417$		0			0
$418$	−9.52270	−	8.96204i	−0.465771	−	0.438348i
$419$	−21.8990			−1.06984			−0.534918	−	0.844904i	$-0.679657\pi$
$419$	−21.8990			−1.06984			−0.534918	+	0.844904i	$0.679657\pi$
$420$		0			0
$421$	9.32577	+	16.1527i	0.454510	+	0.787234i	0.998660	−	0.0517536i	$-0.0164811\pi$
$421$	9.32577	+	16.1527i	0.454510	+	0.787234i	−0.544150	+	0.838988i	$0.683148\pi$
$422$	−13.1742	+	22.8184i	−0.641312	+	1.11078i
$423$		0			0
$424$	3.72474	−	6.45145i	0.180890	−	0.313310i
$425$	1.55051			0.0752108
$426$		0			0
$427$	9.02270	−	15.6278i	0.436639	−	0.756281i
$428$	−1.32577	+	2.29629i	−0.0640833	+	0.110996i
$429$		0			0
$430$	−11.7980			−0.568948
$431$	5.32577	−	9.22450i	0.256533	−	0.444328i	−0.708778	−	0.705432i	$-0.750753\pi$
$431$	5.32577	−	9.22450i	0.256533	−	0.444328i	0.965311	+	0.261104i	$0.0840864\pi$
$432$		0			0
$433$	−1.67423	+	2.89986i	−0.0804586	+	0.139358i	−0.903447	−	0.428700i	$-0.858972\pi$
$433$	−1.67423	+	2.89986i	−0.0804586	+	0.139358i	0.822988	+	0.568058i	$0.192305\pi$
$434$	0.651531	+	1.12848i	0.0312745	+	0.0541690i
$435$		0			0
$436$	1.34847			0.0645800
$437$	5.89898	−	25.0273i	0.282186	−	1.19722i
$438$		0			0
$439$	−1.67423	−	2.89986i	−0.0799069	−	0.138403i	0.823303	−	0.567603i	$-0.192129\pi$
$439$	−1.67423	−	2.89986i	−0.0799069	−	0.138403i	−0.903210	+	0.429200i	$0.858796\pi$
$440$	−1.50000	−	2.59808i	−0.0715097	−	0.123858i
$441$		0			0
$442$	3.79796	+	6.57826i	0.180650	+	0.312896i
$443$	0.876276	−	1.51775i	0.0416331	−	0.0721107i	−0.844458	−	0.535622i	$-0.820077\pi$
$443$	0.876276	−	1.51775i	0.0416331	−	0.0721107i	0.886091	+	0.463511i	$0.153411\pi$
$444$		0			0
$445$	−5.44949			−0.258331
$446$	−1.72474	+	2.98735i	−0.0816690	+	0.141455i
$447$		0			0
$448$	−1.44949			−0.0684820
$449$	−8.75255			−0.413058			−0.206529	−	0.978440i	$-0.566217\pi$
$449$	−8.75255			−0.413058			−0.206529	+	0.978440i	$0.566217\pi$
$450$		0			0
$451$	6.52270	+	11.2977i	0.307142	+	0.531986i
$452$	−4.77526	+	8.27098i	−0.224609	+	0.389034i
$453$		0			0
$454$	5.67423	+	9.82806i	0.266305	+	0.461254i
$455$	7.10102			0.332901
$456$		0			0
$457$	−12.0454			−0.563460			−0.281730	−	0.959494i	$-0.590908\pi$
$457$	−12.0454			−0.563460			−0.281730	+	0.959494i	$0.590908\pi$
$458$	4.34847	+	7.53177i	0.203191	+	0.351936i
$459$		0			0
$460$	2.94949	−	5.10867i	0.137521	−	0.238193i
$461$	−13.8990	−	24.0737i	−0.647340	−	1.12123i	−0.983756	−	0.179512i	$-0.942548\pi$
$461$	−13.8990	−	24.0737i	−0.647340	−	1.12123i	0.336416	−	0.941714i	$-0.390785\pi$
$462$		0			0
$463$	−15.6515			−0.727388			−0.363694	−	0.931518i	$-0.618485\pi$
$463$	−15.6515			−0.727388			−0.363694	+	0.931518i	$0.618485\pi$
$464$	−9.34847			−0.433992
$465$		0			0
$466$	13.8990	−	24.0737i	0.643858	−	1.11519i
$467$	40.2474			1.86243			0.931215	−	0.364471i	$-0.118750\pi$
$467$	40.2474			1.86243			0.931215	+	0.364471i	$0.118750\pi$
$468$		0			0
$469$	−5.32577	+	9.22450i	−0.245921	+	0.425948i
$470$	−0.550510	−	0.953512i	−0.0253931	−	0.0439822i
$471$		0			0
$472$	3.00000	+	5.19615i	0.138086	+	0.239172i
$473$	17.6969	+	30.6520i	0.813706	+	1.40938i
$474$		0			0
$475$	1.00000	−	4.24264i	0.0458831	−	0.194666i
$476$	−2.24745			−0.103012
$477$		0			0
$478$	14.8990	+	25.8058i	0.681463	+	1.18033i
$479$	5.02270	−	8.69958i	0.229493	−	0.397494i	−0.728165	−	0.685402i	$-0.759626\pi$
$479$	5.02270	−	8.69958i	0.229493	−	0.397494i	0.957658	+	0.287908i	$0.0929598\pi$
$480$		0			0
$481$	24.2474	−	41.9978i	1.10559	−	1.91494i
$482$	−6.69694			−0.305037
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	−9.22474	+	15.9777i	−0.418874	+	0.725511i
$486$		0			0
$487$	−28.1464			−1.27544			−0.637718	−	0.770270i	$-0.720122\pi$
$487$	−28.1464			−1.27544			−0.637718	+	0.770270i	$0.720122\pi$
$488$	6.22474	−	10.7816i	0.281781	−	0.488059i
$489$		0			0
$490$	2.44949	−	4.24264i	0.110657	−	0.191663i
$491$	−7.60102	−	13.1654i	−0.343029	−	0.594144i	0.641964	−	0.766734i	$-0.278120\pi$
$491$	−7.60102	−	13.1654i	−0.343029	−	0.594144i	−0.984994	+	0.172590i	$0.944786\pi$
$492$		0			0
$493$	−14.4949			−0.652817
$494$	20.4495	−	6.14966i	0.920066	−	0.276686i
$495$		0			0
$496$	0.449490	+	0.778539i	0.0201827	+	0.0349574i
$497$	2.42679	+	4.20332i	0.108856	+	0.188545i
$498$		0			0
$499$	−5.27526	−	9.13701i	−0.236153	−	0.409029i	0.723454	−	0.690372i	$-0.242553\pi$
$499$	−5.27526	−	9.13701i	−0.236153	−	0.409029i	−0.959607	+	0.281344i	$0.909220\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		0			0
$502$	−2.20204			−0.0982819
$503$	1.15153	−	1.99451i	0.0513442	−	0.0889308i	−0.839211	−	0.543806i	$-0.816983\pi$
$503$	1.15153	−	1.99451i	0.0513442	−	0.0889308i	0.890555	+	0.454875i	$0.150316\pi$
$504$		0			0
$505$	−1.10102			−0.0489948
$506$	−17.6969			−0.786725
$507$		0			0
$508$	0.174235	+	0.301783i	0.00773041	+	0.0133895i
$509$	−1.44949	+	2.51059i	−0.0642475	+	0.111280i	−0.896360	−	0.443327i	$-0.853798\pi$
$509$	−1.44949	+	2.51059i	−0.0642475	+	0.111280i	0.832112	+	0.554607i	$0.187131\pi$
$510$		0			0
$511$	7.57321	+	13.1172i	0.335019	+	0.580270i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	15.7980			0.696818
$515$	5.62372	+	9.74058i	0.247811	+	0.429221i
$516$		0			0
$517$	−1.65153	+	2.86054i	−0.0726342	+	0.125806i
$518$	7.17423	+	12.4261i	0.315218	+	0.545973i
$519$		0			0
$520$	4.89898			0.214834
$521$	−1.10102			−0.0482366			−0.0241183	−	0.999709i	$-0.507678\pi$
$521$	−1.10102			−0.0482366			−0.0241183	+	0.999709i	$0.507678\pi$
$522$		0			0
$523$	−1.57321	+	2.72489i	−0.0687918	+	0.119151i	−0.898370	−	0.439240i	$-0.855248\pi$
$523$	−1.57321	+	2.72489i	−0.0687918	+	0.119151i	0.829578	+	0.558391i	$0.188581\pi$
$524$	3.00000			0.131056
$525$		0			0
$526$	−5.05051	+	8.74774i	−0.220213	+	0.381420i
$527$	0.696938	+	1.20713i	0.0303591	+	0.0525835i
$528$		0			0
$529$	−5.89898	−	10.2173i	−0.256477	−	0.444232i
$530$	−3.72474	−	6.45145i	−0.161793	−	0.280233i
$531$		0			0
$532$	−1.44949	+	6.14966i	−0.0628434	+	0.266622i
$533$	−21.3031			−0.922738
$534$		0			0
$535$	1.32577	+	2.29629i	0.0573178	+	0.0992774i
$536$	−3.67423	+	6.36396i	−0.158703	+	0.274881i
$537$		0			0
$538$	12.1237	−	20.9989i	0.522691	−	0.905327i
$539$	−14.6969			−0.633042
$540$		0			0
$541$	−9.55051	+	16.5420i	−0.410609	+	0.711195i	−0.994956	−	0.100308i	$-0.968017\pi$
$541$	−9.55051	+	16.5420i	−0.410609	+	0.711195i	0.584348	+	0.811503i	$0.301350\pi$
$542$	−7.44949	+	12.9029i	−0.319983	+	0.554227i
$543$		0			0
$544$	−1.55051			−0.0664776
$545$	0.674235	−	1.16781i	0.0288810	−	0.0500234i
$546$		0			0
$547$	1.65153	−	2.86054i	0.0706144	−	0.122308i	−0.828556	−	0.559906i	$-0.810837\pi$
$547$	1.65153	−	2.86054i	0.0706144	−	0.122308i	0.899171	+	0.437598i	$0.144171\pi$
$548$	−6.00000	−	10.3923i	−0.256307	−	0.443937i
$549$		0			0
$550$	−3.00000			−0.127920
$551$	−9.34847	+	39.6622i	−0.398258	+	1.68967i
$552$		0			0
$553$	5.00000	+	8.66025i	0.212622	+	0.368271i
$554$	−6.44949	−	11.1708i	−0.274013	−	0.474604i
$555$		0			0
$556$	7.34847	+	12.7279i	0.311645	+	0.539784i
$557$	−9.17423	+	15.8902i	−0.388725	+	0.673291i	−0.992278	−	0.124031i	$-0.960418\pi$
$557$	−9.17423	+	15.8902i	−0.388725	+	0.673291i	0.603553	+	0.797323i	$0.293751\pi$
$558$		0			0
$559$	−57.7980			−2.44459
$560$	−0.724745	+	1.25529i	−0.0306261	+	0.0530459i
$561$		0			0
$562$	14.3485			0.605254
$563$	−29.3939			−1.23880			−0.619402	−	0.785074i	$-0.712625\pi$
$563$	−29.3939			−1.23880			−0.619402	+	0.785074i	$0.712625\pi$
$564$		0			0
$565$	4.77526	+	8.27098i	0.200896	+	0.347963i
$566$	−6.34847	+	10.9959i	−0.266846	+	0.462191i
$567$		0			0
$568$	1.67423	+	2.89986i	0.0702493	+	0.121675i
$569$	7.44949			0.312299			0.156149	−	0.987733i	$-0.450092\pi$
$569$	7.44949			0.312299			0.156149	+	0.987733i	$0.450092\pi$
$570$		0			0
$571$	−8.20204			−0.343245			−0.171622	−	0.985163i	$-0.554901\pi$
$571$	−8.20204			−0.343245			−0.171622	+	0.985163i	$0.554901\pi$
$572$	−7.34847	−	12.7279i	−0.307255	−	0.532181i
$573$		0			0
$574$	3.15153	−	5.45861i	0.131542	−	0.227838i
$575$	−2.94949	−	5.10867i	−0.123002	−	0.213046i
$576$		0			0
$577$	11.1464			0.464032			0.232016	−	0.972712i	$-0.425468\pi$
$577$	11.1464			0.464032			0.232016	+	0.972712i	$0.425468\pi$
$578$	14.5959			0.607110
$579$		0			0
$580$	−4.67423	+	8.09601i	−0.194087	+	0.336169i
$581$	17.1010			0.709470
$582$		0			0
$583$	−11.1742	+	19.3543i	−0.462790	+	0.801575i
$584$	5.22474	+	9.04952i	0.216201	+	0.374472i
$585$		0			0
$586$	5.72474	+	9.91555i	0.236487	+	0.409608i
$587$	−16.2474	−	28.1414i	−0.670604	−	1.16152i	−0.977733	−	0.209852i	$-0.932702\pi$
$587$	−16.2474	−	28.1414i	−0.670604	−	1.16152i	0.307129	−	0.951668i	$-0.400632\pi$
$588$		0			0
$589$	3.75255	−	1.12848i	0.154621	−	0.0464984i
$590$	6.00000			0.247016
$591$		0			0
$592$	4.94949	+	8.57277i	0.203423	+	0.352339i
$593$	−17.5732	+	30.4377i	−0.721645	+	1.24993i	0.238695	+	0.971095i	$0.423281\pi$
$593$	−17.5732	+	30.4377i	−0.721645	+	1.24993i	−0.960340	+	0.278832i	$0.910053\pi$
$594$		0			0
$595$	−1.12372	+	1.94635i	−0.0460682	+	0.0797925i
$596$	−13.5505			−0.555051
$597$		0			0
$598$	14.4495	−	25.0273i	0.590884	−	1.02344i
$599$	12.6742	−	21.9524i	0.517855	−	0.896951i	−0.481930	−	0.876210i	$-0.660064\pi$
$599$	12.6742	−	21.9524i	0.517855	−	0.896951i	0.999785	−	0.0207416i	$-0.00660273\pi$
$600$		0			0
$601$	19.0000			0.775026			0.387513	−	0.921864i	$-0.373334\pi$
$601$	19.0000			0.775026			0.387513	+	0.921864i	$0.373334\pi$
$602$	8.55051	−	14.8099i	0.348493	−	0.603607i
$603$		0			0
$604$	2.32577	−	4.02834i	0.0946341	−	0.163911i
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$		0			0
$607$	29.4495			1.19532			0.597659	−	0.801750i	$-0.296098\pi$
$607$	29.4495			1.19532			0.597659	+	0.801750i	$0.296098\pi$
$608$	−1.00000	+	4.24264i	−0.0405554	+	0.172062i
$609$		0			0
$610$	−6.22474	−	10.7816i	−0.252033	−	0.436533i
$611$	−2.69694	−	4.67123i	−0.109106	−	0.188978i
$612$		0			0
$613$	−5.74745	−	9.95487i	−0.232137	−	0.402074i	0.726300	−	0.687378i	$-0.241239\pi$
$613$	−5.74745	−	9.95487i	−0.232137	−	0.402074i	−0.958437	+	0.285305i	$0.907905\pi$
$614$	−5.12372	+	8.87455i	−0.206777	+	0.358148i
$615$		0			0
$616$	4.34847			0.175205
$617$	7.79796	−	13.5065i	0.313934	−	0.543750i	−0.665276	−	0.746597i	$-0.731686\pi$
$617$	7.79796	−	13.5065i	0.313934	−	0.543750i	0.979210	+	0.202848i	$0.0650196\pi$
$618$		0			0
$619$	23.0454			0.926273			0.463137	−	0.886287i	$-0.346724\pi$
$619$	23.0454			0.926273			0.463137	+	0.886287i	$0.346724\pi$
$620$	0.898979			0.0361039
$621$		0			0
$622$	4.89898	+	8.48528i	0.196431	+	0.340229i
$623$	3.94949	−	6.84072i	0.158233	−	0.274068i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−31.5959			−1.26283
$627$		0			0
$628$	20.7980			0.829929
$629$	7.67423	+	13.2922i	0.305992	+	0.529993i
$630$		0			0
$631$	13.1237	−	22.7310i	0.522447	−	0.904905i	−0.477212	−	0.878788i	$-0.658353\pi$
$631$	13.1237	−	22.7310i	0.522447	−	0.904905i	0.999659	−	0.0261167i	$-0.00831416\pi$
$632$	3.44949	+	5.97469i	0.137213	+	0.237660i
$633$		0			0
$634$	9.44949			0.375287
$635$	0.348469			0.0138286
$636$		0			0
$637$	12.0000	−	20.7846i	0.475457	−	0.823516i
$638$	28.0454			1.11033
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−5.65153	−	9.78874i	−0.223222	−	0.386632i	0.732563	−	0.680700i	$-0.238324\pi$
$641$	−5.65153	−	9.78874i	−0.223222	−	0.386632i	−0.955785	+	0.294068i	$0.904991\pi$
$642$		0			0
$643$	−10.1237	−	17.5348i	−0.399241	−	0.691505i	0.594392	−	0.804176i	$-0.297393\pi$
$643$	−10.1237	−	17.5348i	−0.399241	−	0.691505i	−0.993632	+	0.112670i	$0.964060\pi$
$644$	4.27526	+	7.40496i	0.168469	+	0.291796i
$645$		0			0
$646$	−1.55051	+	6.57826i	−0.0610040	+	0.258818i
$647$	−0.101021			−0.00397153			−0.00198576	−	0.999998i	$-0.500632\pi$
$647$	−0.101021			−0.00397153			−0.00198576	+	0.999998i	$0.500632\pi$
$648$		0			0
$649$	−9.00000	−	15.5885i	−0.353281	−	0.611900i
$650$	2.44949	−	4.24264i	0.0960769	−	0.166410i
$651$		0			0
$652$	−8.34847	+	14.4600i	−0.326951	+	0.566296i
$653$	40.3485			1.57896			0.789479	−	0.613778i	$-0.210351\pi$
$653$	40.3485			1.57896			0.789479	+	0.613778i	$0.210351\pi$
$654$		0			0
$655$	1.50000	−	2.59808i	0.0586098	−	0.101515i
$656$	2.17423	−	3.76588i	0.0848896	−	0.147033i
$657$		0			0
$658$	1.59592			0.0622154
$659$	11.2980	−	19.5686i	0.440106	−	0.762286i	−0.557591	−	0.830116i	$-0.688274\pi$
$659$	11.2980	−	19.5686i	0.440106	−	0.762286i	0.997697	+	0.0678299i	$0.0216075\pi$
$660$		0			0
$661$	6.89898	−	11.9494i	0.268339	−	0.464777i	−0.700094	−	0.714051i	$-0.746859\pi$
$661$	6.89898	−	11.9494i	0.268339	−	0.464777i	0.968433	+	0.249274i	$0.0801919\pi$
$662$	9.17423	+	15.8902i	0.356567	+	0.617592i
$663$		0			0
$664$	11.7980			0.457850
$665$	4.60102	+	4.33013i	0.178420	+	0.167915i
$666$		0			0
$667$	27.5732	+	47.7582i	1.06764	+	1.84921i
$668$	−4.84847	−	8.39780i	−0.187593	−	0.324920i
$669$		0			0
$670$	3.67423	+	6.36396i	0.141948	+	0.245861i
$671$	−18.6742	+	32.3447i	−0.720911	+	1.24865i
$672$		0			0
$673$	−40.4949			−1.56096			−0.780482	−	0.625179i	$-0.785026\pi$
$673$	−40.4949			−1.56096			−0.780482	+	0.625179i	$0.785026\pi$
$674$	−13.2474	+	22.9453i	−0.510273	+	0.883818i
$675$		0			0
$676$	11.0000			0.423077
$677$	−29.9444			−1.15086			−0.575428	−	0.817852i	$-0.695165\pi$
$677$	−29.9444			−1.15086			−0.575428	+	0.817852i	$0.695165\pi$
$678$		0			0
$679$	−13.3712	−	23.1596i	−0.513139	−	0.888782i
$680$	−0.775255	+	1.34278i	−0.0297297	+	0.0514933i
$681$		0			0
$682$	−1.34847	−	2.33562i	−0.0516356	−	0.0894354i
$683$	17.7526			0.679282			0.339641	−	0.940555i	$-0.389694\pi$
$683$	17.7526			0.679282			0.339641	+	0.940555i	$0.389694\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$	8.62372	+	14.9367i	0.329255	+	0.570287i
$687$		0			0
$688$	5.89898	−	10.2173i	0.224896	−	0.389532i
$689$	−18.2474	−	31.6055i	−0.695172	−	1.20407i
$690$		0			0
$691$	−31.4495			−1.19639			−0.598197	−	0.801349i	$-0.704116\pi$
$691$	−31.4495			−1.19639			−0.598197	+	0.801349i	$0.704116\pi$
$692$	4.55051			0.172984
$693$		0			0
$694$	−5.89898	+	10.2173i	−0.223922	+	0.387845i
$695$	14.6969			0.557487
$696$		0			0
$697$	3.37117	−	5.83904i	0.127692	−	0.221170i
$698$	−10.0227	−	17.3598i	−0.379365	−	0.657079i
$699$		0			0
$700$	0.724745	+	1.25529i	0.0273928	+	0.0474457i
$701$	2.10102	+	3.63907i	0.0793544	+	0.137446i	0.902972	−	0.429700i	$-0.141381\pi$
$701$	2.10102	+	3.63907i	0.0793544	+	0.137446i	−0.823617	+	0.567146i	$0.808047\pi$
$702$		0			0
$703$	41.3207	−	12.4261i	1.55844	−	0.468661i
$704$	3.00000			0.113067
$705$		0			0
$706$	17.6742	+	30.6127i	0.665179	+	1.15212i
$707$	0.797959	−	1.38211i	0.0300103	−	0.0519794i
$708$		0			0
$709$	−22.4722	+	38.9230i	−0.843961	+	1.46178i	0.0425596	+	0.999094i	$0.486449\pi$
$709$	−22.4722	+	38.9230i	−0.843961	+	1.46178i	−0.886521	+	0.462689i	$0.846885\pi$
$710$	3.34847			0.125666
$711$		0			0
$712$	2.72474	−	4.71940i	0.102114	−	0.176867i
$713$	2.65153	−	4.59259i	0.0993006	−	0.171994i
$714$		0			0
$715$	−14.6969			−0.549634
$716$	−10.3990	+	18.0116i	−0.388628	+	0.673124i
$717$		0			0
$718$	−13.2247	+	22.9059i	−0.493543	+	0.854842i
$719$	−17.3485	−	30.0484i	−0.646989	−	1.12062i	−0.983838	−	0.179059i	$-0.942695\pi$
$719$	−17.3485	−	30.0484i	−0.646989	−	1.12062i	0.336850	−	0.941558i	$-0.390639\pi$
$720$		0			0
$721$	−16.3031			−0.607158
$722$	17.0000	+	8.48528i	0.632674	+	0.315789i
$723$		0			0
$724$	−8.57321	−	14.8492i	−0.318621	−	0.551868i
$725$	4.67423	+	8.09601i	0.173597	+	0.300678i
$726$		0			0
$727$	−4.10102	−	7.10318i	−0.152098	−	0.263442i	0.779900	−	0.625904i	$-0.215270\pi$
$727$	−4.10102	−	7.10318i	−0.152098	−	0.263442i	−0.931999	+	0.362462i	$0.881936\pi$
$728$	−3.55051	+	6.14966i	−0.131591	+	0.227922i
$729$		0			0
$730$	10.4495			0.386753
$731$	9.14643	−	15.8421i	0.338293	−	0.585940i
$732$		0			0
$733$	−2.59592			−0.0958824			−0.0479412	−	0.998850i	$-0.515266\pi$
$733$	−2.59592			−0.0958824			−0.0479412	+	0.998850i	$0.515266\pi$
$734$	−20.8990			−0.771395
$735$		0			0
$736$	2.94949	+	5.10867i	0.108720	+	0.188308i
$737$	11.0227	−	19.0919i	0.406027	−	0.703259i
$738$		0			0
$739$	−18.9722	−	32.8608i	−0.697903	−	1.20880i	−0.969192	−	0.246306i	$-0.920783\pi$
$739$	−18.9722	−	32.8608i	−0.697903	−	1.20880i	0.271289	−	0.962498i	$-0.412550\pi$
$740$	9.89898			0.363894
$741$		0			0
$742$	10.7980			0.396406
$743$	−9.84847	−	17.0580i	−0.361305	−	0.625799i	0.626871	−	0.779123i	$-0.284335\pi$
$743$	−9.84847	−	17.0580i	−0.361305	−	0.625799i	−0.988176	+	0.153324i	$0.951002\pi$
$744$		0			0
$745$	−6.77526	+	11.7351i	−0.248226	+	0.429940i
$746$	−1.94949	−	3.37662i	−0.0713759	−	0.123627i
$747$		0			0
$748$	4.65153			0.170077
$749$	−3.84337			−0.140434
$750$		0			0
$751$	22.4949	−	38.9623i	0.820850	−	1.42175i	−0.0841993	−	0.996449i	$-0.526833\pi$
$751$	22.4949	−	38.9623i	0.820850	−	1.42175i	0.905050	−	0.425306i	$-0.139833\pi$
$752$	1.10102			0.0401501
$753$		0			0
$754$	−22.8990	+	39.6622i	−0.833932	+	1.44441i
$755$	−2.32577	−	4.02834i	−0.0846433	−	0.146606i
$756$		0			0
$757$	2.19694	+	3.80521i	0.0798491	+	0.138303i	0.903185	−	0.429252i	$-0.141223\pi$
$757$	2.19694	+	3.80521i	0.0798491	+	0.138303i	−0.823336	+	0.567555i	$0.807889\pi$
$758$	−3.34847	−	5.79972i	−0.121622	−	0.210655i
$759$		0			0
$760$	3.17423	+	2.98735i	0.115142	+	0.108362i
$761$	−21.4495			−0.777543			−0.388772	−	0.921334i	$-0.627101\pi$
$761$	−21.4495			−0.777543			−0.388772	+	0.921334i	$0.627101\pi$
$762$		0			0
$763$	0.977296	+	1.69273i	0.0353805	+	0.0612808i
$764$	−1.89898	+	3.28913i	−0.0687027	+	0.118997i
$765$		0			0
$766$	−15.2474	+	26.4094i	−0.550913	+	0.954209i
$767$	29.3939			1.06135
$768$		0			0
$769$	16.8990	−	29.2699i	0.609393	−	1.05550i	−0.381948	−	0.924184i	$-0.624747\pi$
$769$	16.8990	−	29.2699i	0.609393	−	1.05550i	0.991341	−	0.131315i	$-0.0419201\pi$
$770$	2.17423	−	3.76588i	0.0783540	−	0.135713i
$771$		0			0
$772$	−21.3485			−0.768348
$773$	−22.5227	+	39.0105i	−0.810085	+	1.40311i	0.102718	+	0.994710i	$0.467246\pi$
$773$	−22.5227	+	39.0105i	−0.810085	+	1.40311i	−0.912804	+	0.408399i	$0.866087\pi$
$774$		0			0
$775$	0.449490	−	0.778539i	0.0161461	−	0.0279659i
$776$	−9.22474	−	15.9777i	−0.331149	−	0.573567i
$777$		0			0
$778$	−23.1464			−0.829840
$779$	−13.8031	−	12.9904i	−0.494546	−	0.465429i
$780$		0			0
$781$	−5.02270	−	8.69958i	−0.179726	−	0.311295i
$782$	4.57321	+	7.92104i	0.163538	+	0.283256i
$783$		0			0
$784$	2.44949	+	4.24264i	0.0874818	+	0.151523i
$785$	10.3990	−	18.0116i	0.371155	−	0.642860i
$786$		0			0
$787$	20.0454			0.714542			0.357271	−	0.934001i	$-0.383707\pi$
$787$	20.0454			0.714542			0.357271	+	0.934001i	$0.383707\pi$
$788$	3.27526	−	5.67291i	0.116676	−	0.202089i
$789$		0			0
$790$	6.89898			0.245455
$791$	−13.8434			−0.492213
$792$		0			0
$793$	−30.4949	−	52.8187i	−1.08291	−	1.87565i
$794$	5.74745	−	9.95487i	0.203969	−	0.353285i
$795$		0			0
$796$	−3.22474	−	5.58542i	−0.114298	−	0.197970i
$797$	−16.3485			−0.579092			−0.289546	−	0.957164i	$-0.593504\pi$
$797$	−16.3485			−0.579092			−0.289546	+	0.957164i	$0.593504\pi$
$798$		0			0
$799$	1.70714			0.0603944
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$		0			0
$802$	1.89898	−	3.28913i	0.0670553	−	0.116143i
$803$	−15.6742	−	27.1486i	−0.553132	−	0.958052i
$804$		0			0
$805$	8.55051			0.301366
$806$	4.40408			0.155127
$807$		0			0
$808$	0.550510	−	0.953512i	0.0193669	−	0.0335444i
$809$	−20.4949			−0.720562			−0.360281	−	0.932844i	$-0.617319\pi$
$809$	−20.4949			−0.720562			−0.360281	+	0.932844i	$0.617319\pi$
$810$		0			0
$811$	−10.4217	+	18.0509i	−0.365955	+	0.633852i	−0.988929	−	0.148390i	$-0.952591\pi$
$811$	−10.4217	+	18.0509i	−0.365955	+	0.633852i	0.622974	+	0.782242i	$0.285924\pi$
$812$	−6.77526	−	11.7351i	−0.237765	−	0.411821i
$813$		0			0
$814$	−14.8485	−	25.7183i	−0.520439	−	0.901426i
$815$	8.34847	+	14.4600i	0.292434	+	0.506511i
$816$		0			0
$817$	−37.4495	−	35.2446i	−1.31019	−	1.23305i
$818$	9.49490			0.331981
$819$		0			0
$820$	−2.17423	−	3.76588i	−0.0759276	−	0.131510i
$821$	11.0000	−	19.0526i	0.383903	−	0.664939i	−0.607714	−	0.794156i	$-0.707913\pi$
$821$	11.0000	−	19.0526i	0.383903	−	0.664939i	0.991616	+	0.129217i	$0.0412465\pi$
$822$		0			0
$823$	0.926786	−	1.60524i	0.0323057	−	0.0559552i	−0.849421	−	0.527717i	$-0.823048\pi$
$823$	0.926786	−	1.60524i	0.0323057	−	0.0559552i	0.881726	+	0.471761i	$0.156382\pi$
$824$	−11.2474			−0.391823
$825$		0			0
$826$	−4.34847	+	7.53177i	−0.151303	+	0.262064i
$827$	−10.5732	+	18.3133i	−0.367667	+	0.636817i	−0.989200	−	0.146570i	$-0.953177\pi$
$827$	−10.5732	+	18.3133i	−0.367667	+	0.636817i	0.621534	+	0.783388i	$0.286510\pi$
$828$		0			0
$829$	23.1010			0.802332			0.401166	−	0.916005i	$-0.368605\pi$
$829$	23.1010			0.802332			0.401166	+	0.916005i	$0.368605\pi$
$830$	5.89898	−	10.2173i	0.204757	−	0.354649i
$831$		0			0
$832$	−2.44949	+	4.24264i	−0.0849208	+	0.147087i
$833$	3.79796	+	6.57826i	0.131591	+	0.227923i
$834$		0			0
$835$	−9.69694			−0.335576
$836$	3.00000	−	12.7279i	0.103757	−	0.440204i
$837$		0			0
$838$	−10.9495	−	18.9651i	−0.378244	−	0.655138i
$839$	27.2474	+	47.1940i	0.940686	+	1.62932i	0.764166	+	0.645020i	$0.223151\pi$
$839$	27.2474	+	47.1940i	0.940686	+	1.62932i	0.176520	+	0.984297i	$0.443516\pi$
$840$		0			0
$841$	−29.1969	−	50.5706i	−1.00679	−	1.74381i
$842$	−9.32577	+	16.1527i	−0.321387	+	0.556659i
$843$		0			0
$844$	−26.3485			−0.906952
$845$	5.50000	−	9.52628i	0.189206	−	0.327714i
$846$		0			0
$847$	2.89898			0.0996101
$848$	7.44949			0.255817
$849$		0			0
$850$	0.775255	+	1.34278i	0.0265910	+	0.0460570i
$851$	29.1969	−	50.5706i	1.00086	−	1.73354i
$852$		0			0
$853$	7.69694	+	13.3315i	0.263538	+	0.456461i	0.967180	−	0.254094i	$-0.0817772\pi$
$853$	7.69694	+	13.3315i	0.263538	+	0.456461i	−0.703641	+	0.710555i	$0.748444\pi$
$854$	18.0454			0.617501
$855$		0			0
$856$	−2.65153			−0.0906275
$857$	−21.7980	−	37.7552i	−0.744604	−	1.28969i	−0.950380	−	0.311093i	$-0.899305\pi$
$857$	−21.7980	−	37.7552i	−0.744604	−	1.28969i	0.205775	−	0.978599i	$-0.434028\pi$
$858$		0			0
$859$	−16.5227	+	28.6182i	−0.563747	+	0.976439i	0.433418	+	0.901193i	$0.357308\pi$
$859$	−16.5227	+	28.6182i	−0.563747	+	0.976439i	−0.997165	+	0.0752459i	$0.976026\pi$
$860$	−5.89898	−	10.2173i	−0.201154	−	0.348408i
$861$		0			0
$862$	10.6515			0.362793
$863$	−29.0000			−0.987171			−0.493586	−	0.869697i	$-0.664314\pi$
$863$	−29.0000			−0.987171			−0.493586	+	0.869697i	$0.664314\pi$
$864$		0			0
$865$	2.27526	−	3.94086i	0.0773610	−	0.133993i
$866$	−3.34847			−0.113786
$867$		0			0
$868$	−0.651531	+	1.12848i	−0.0221144	+	0.0383033i
$869$	−10.3485	−	17.9241i	−0.351048	−	0.608033i
$870$		0			0
$871$	18.0000	+	31.1769i	0.609907	+	1.05639i
$872$	0.674235	+	1.16781i	0.0228325	+	0.0395470i
$873$		0			0
$874$	24.6237	−	7.40496i	0.832910	−	0.250476i
$875$	1.44949			0.0490017
$876$		0			0
$877$	−16.7474	−	29.0074i	−0.565521	−	0.979511i	−0.997001	−	0.0773888i	$-0.975342\pi$
$877$	−16.7474	−	29.0074i	−0.565521	−	0.979511i	0.431480	−	0.902123i	$-0.357992\pi$
$878$	1.67423	−	2.89986i	0.0565027	−	0.0978655i
$879$		0			0
$880$	1.50000	−	2.59808i	0.0505650	−	0.0875811i
$881$	−37.0454			−1.24809			−0.624046	−	0.781388i	$-0.714512\pi$
$881$	−37.0454			−1.24809			−0.624046	+	0.781388i	$0.714512\pi$
$882$		0			0
$883$	−23.4722	+	40.6550i	−0.789902	+	1.36815i	0.136124	+	0.990692i	$0.456535\pi$
$883$	−23.4722	+	40.6550i	−0.789902	+	1.36815i	−0.926026	+	0.377459i	$0.876798\pi$
$884$	−3.79796	+	6.57826i	−0.127739	+	0.221251i
$885$		0			0
$886$	1.75255			0.0588781
$887$	−21.8990	+	37.9301i	−0.735296	+	1.27357i	0.219298	+	0.975658i	$0.429623\pi$
$887$	−21.8990	+	37.9301i	−0.735296	+	1.27357i	−0.954593	+	0.297912i	$0.903710\pi$
$888$		0			0
$889$	−0.252551	+	0.437432i	−0.00847030	+	0.0146710i
$890$	−2.72474	−	4.71940i	−0.0913337	−	0.158195i
$891$		0			0
$892$	−3.44949			−0.115497
$893$	1.10102	−	4.67123i	0.0368442	−	0.156317i
$894$		0			0
$895$	10.3990	+	18.0116i	0.347600	+	0.602060i
$896$	−0.724745	−	1.25529i	−0.0242120	−	0.0419365i
$897$		0			0
$898$	−4.37628	−	7.57993i	−0.146038	−	0.252946i
$899$	−4.20204	+	7.27815i	−0.140146	+	0.242740i
$900$		0			0
$901$	11.5505			0.384803
$902$	−6.52270	+	11.2977i	−0.217182	+	0.376171i
$903$		0			0
$904$	−9.55051			−0.317645
$905$	−17.1464			−0.569967
$906$		0			0
$907$	18.7980	+	32.5590i	0.624176	+	1.08110i	0.988700	+	0.149910i	$0.0478985\pi$
$907$	18.7980	+	32.5590i	0.624176	+	1.08110i	−0.364524	+	0.931194i	$0.618768\pi$
$908$	−5.67423	+	9.82806i	−0.188306	+	0.326156i
$909$		0			0
$910$	3.55051	+	6.14966i	0.117698	+	0.203859i
$911$	54.0908			1.79211			0.896054	−	0.443944i	$-0.146421\pi$
$911$	54.0908			1.79211			0.896054	+	0.443944i	$0.146421\pi$
$912$		0			0
$913$	−35.3939			−1.17137
$914$	−6.02270	−	10.4316i	−0.199213	−	0.345048i
$915$		0			0
$916$	−4.34847	+	7.53177i	−0.143677	+	0.248857i
$917$	2.17423	+	3.76588i	0.0717996	+	0.124360i
$918$		0			0
$919$	−15.5505			−0.512964			−0.256482	−	0.966549i	$-0.582563\pi$
$919$	−15.5505			−0.512964			−0.256482	+	0.966549i	$0.582563\pi$
$920$	5.89898			0.194484
$921$		0			0
$922$	13.8990	−	24.0737i	0.457739	−	0.792826i
$923$	16.4041			0.539947
$924$		0			0
$925$	4.94949	−	8.57277i	0.162738	−	0.281871i
$926$	−7.82577	−	13.5546i	−0.257171	−	0.445433i
$927$		0			0
$928$	−4.67423	−	8.09601i	−0.153439	−	0.265765i
$929$	17.2753	+	29.9216i	0.566783	+	0.981696i	0.996881	+	0.0789146i	$0.0251454\pi$
$929$	17.2753	+	29.9216i	0.566783	+	0.981696i	−0.430099	+	0.902782i	$0.641521\pi$
$930$		0			0
$931$	20.4495	−	6.14966i	0.670205	−	0.201547i
$932$	27.7980			0.910552
$933$		0			0
$934$	20.1237	+	34.8553i	0.658468	+	1.14050i
$935$	2.32577	−	4.02834i	0.0760607	−	0.131741i
$936$		0			0
$937$	13.0227	−	22.5560i	0.425433	−	0.736872i	−0.571028	−	0.820931i	$-0.693455\pi$
$937$	13.0227	−	22.5560i	0.425433	−	0.736872i	0.996461	+	0.0840590i	$0.0267884\pi$
$938$	−10.6515			−0.347785
$939$		0			0
$940$	0.550510	−	0.953512i	0.0179557	−	0.0311001i
$941$	−7.77526	+	13.4671i	−0.253466	+	0.439016i	−0.964478	−	0.264164i	$-0.914904\pi$
$941$	−7.77526	+	13.4671i	−0.253466	+	0.439016i	0.711012	+	0.703180i	$0.248237\pi$
$942$		0			0
$943$	−25.6515			−0.835329
$944$	−3.00000	+	5.19615i	−0.0976417	+	0.169120i
$945$		0			0
$946$	−17.6969	+	30.6520i	−0.575377	+	0.996582i
$947$	−12.2247	−	21.1739i	−0.397251	−	0.688059i	0.596135	−	0.802884i	$-0.296702\pi$
$947$	−12.2247	−	21.1739i	−0.397251	−	0.688059i	−0.993386	+	0.114826i	$0.963369\pi$
$948$		0			0
$949$	51.1918			1.66176
$950$	4.17423	−	1.25529i	0.135430	−	0.0407271i
$951$		0			0
$952$	−1.12372	−	1.94635i	−0.0364201	−	0.0630815i
$953$	−20.6969	−	35.8481i	−0.670440	−	1.16124i	−0.977780	−	0.209636i	$-0.932772\pi$
$953$	−20.6969	−	35.8481i	−0.670440	−	1.16124i	0.307340	−	0.951600i	$-0.400561\pi$
$954$		0			0
$955$	1.89898	+	3.28913i	0.0614495	+	0.106434i
$956$	−14.8990	+	25.8058i	−0.481867	+	0.834619i
$957$		0			0
$958$	10.0454			0.324552
$959$	8.69694	−	15.0635i	0.280839	−	0.486427i
$960$		0			0
$961$	−30.1918			−0.973930
$962$	48.4949			1.56354
$963$		0			0
$964$	−3.34847	−	5.79972i	−0.107847	−	0.186796i
$965$	−10.6742	+	18.4883i	−0.343616	+	0.595160i
$966$		0			0
$967$	−6.44949	−	11.1708i	−0.207402	−	0.359230i	0.743494	−	0.668743i	$-0.233167\pi$
$967$	−6.44949	−	11.1708i	−0.207402	−	0.359230i	−0.950895	+	0.309513i	$0.899834\pi$
$968$	2.00000			0.0642824
$969$		0			0
$970$	−18.4495			−0.592377
$971$	1.65153	+	2.86054i	0.0530001	+	0.0917989i	0.891308	−	0.453398i	$-0.149788\pi$
$971$	1.65153	+	2.86054i	0.0530001	+	0.0917989i	−0.838308	+	0.545197i	$0.816455\pi$
$972$		0			0
$973$	−10.6515	+	18.4490i	−0.341472	+	0.591448i
$974$	−14.0732	−	24.3755i	−0.450935	−	0.781042i
$975$		0			0
$976$	12.4495			0.398498
$977$	8.94439			0.286156			0.143078	−	0.989711i	$-0.454300\pi$
$977$	8.94439			0.286156			0.143078	+	0.989711i	$0.454300\pi$
$978$		0			0
$979$	−8.17423	+	14.1582i	−0.261250	+	0.452498i
$980$	4.89898			0.156492
$981$		0			0
$982$	7.60102	−	13.1654i	0.242558	−	0.420123i
$983$	−12.0959	−	20.9507i	−0.385800	−	0.668225i	0.606080	−	0.795404i	$-0.292741\pi$
$983$	−12.0959	−	20.9507i	−0.385800	−	0.668225i	−0.991880	+	0.127179i	$0.959408\pi$
$984$		0			0
$985$	−3.27526	−	5.67291i	−0.104358	−	0.180754i
$986$	−7.24745	−	12.5529i	−0.230806	−	0.399767i
$987$		0			0
$988$	15.5505	+	14.6349i	0.494728	+	0.465600i
$989$	−69.5959			−2.21302
$990$		0			0
$991$	−10.6742	−	18.4883i	−0.339078	−	0.587301i	0.645181	−	0.764029i	$-0.276782\pi$
$991$	−10.6742	−	18.4883i	−0.339078	−	0.587301i	−0.984260	+	0.176729i	$0.943448\pi$
$992$	−0.449490	+	0.778539i	−0.0142713	+	0.0247186i
$993$		0			0
$994$	−2.42679	+	4.20332i	−0.0769730	+	0.133321i
$995$	−6.44949			−0.204463
$996$		0			0
$997$	−12.2980	+	21.3007i	−0.389480	+	0.674600i	−0.992380	−	0.123218i	$-0.960679\pi$
$997$	−12.2980	+	21.3007i	−0.389480	+	0.674600i	0.602899	+	0.797817i	$0.294012\pi$
$998$	5.27526	−	9.13701i	0.166985	−	0.289227i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.l.n.1261.1		4
3.2	odd	2		570.2.i.f.121.1	✓	4
19.11	even	3	inner	1710.2.l.n.1531.1		4
57.11	odd	6		570.2.i.f.391.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.f.121.1	✓	4	3.2	odd	2
570.2.i.f.391.1	yes	4	57.11	odd	6
1710.2.l.n.1261.1		4	1.1	even	1	trivial
1710.2.l.n.1531.1		4	19.11	even	3	inner

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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.44949 q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.44949 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +3.00000 q^{11} +(-2.44949 + 4.24264i) q^{13} +(-0.724745 - 1.25529i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.775255 - 1.34278i) q^{17} +(-4.17423 + 1.25529i) q^{19} -1.00000 q^{20} +(1.50000 + 2.59808i) q^{22} +(-2.94949 + 5.10867i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.89898 q^{26} +(0.724745 - 1.25529i) q^{28} +(4.67423 - 8.09601i) q^{29} -0.898979 q^{31} +(0.500000 - 0.866025i) q^{32} +(0.775255 - 1.34278i) q^{34} +(-0.724745 - 1.25529i) q^{35} -9.89898 q^{37} +(-3.17423 - 2.98735i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(2.17423 + 3.76588i) q^{41} +(5.89898 + 10.2173i) q^{43} +(-1.50000 + 2.59808i) q^{44} -5.89898 q^{46} +(-0.550510 + 0.953512i) q^{47} -4.89898 q^{49} -1.00000 q^{50} +(-2.44949 - 4.24264i) q^{52} +(-3.72474 + 6.45145i) q^{53} +(1.50000 + 2.59808i) q^{55} +1.44949 q^{56} +9.34847 q^{58} +(-3.00000 - 5.19615i) q^{59} +(-6.22474 + 10.7816i) q^{61} +(-0.449490 - 0.778539i) q^{62} +1.00000 q^{64} -4.89898 q^{65} +(3.67423 - 6.36396i) q^{67} +1.55051 q^{68} +(0.724745 - 1.25529i) q^{70} +(-1.67423 - 2.89986i) q^{71} +(-5.22474 - 9.04952i) q^{73} +(-4.94949 - 8.57277i) q^{74} +(1.00000 - 4.24264i) q^{76} -4.34847 q^{77} +(-3.44949 - 5.97469i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-2.17423 + 3.76588i) q^{82} -11.7980 q^{83} +(0.775255 - 1.34278i) q^{85} +(-5.89898 + 10.2173i) q^{86} -3.00000 q^{88} +(-2.72474 + 4.71940i) q^{89} +(3.55051 - 6.14966i) q^{91} +(-2.94949 - 5.10867i) q^{92} -1.10102 q^{94} +(-3.17423 - 2.98735i) q^{95} +(9.22474 + 15.9777i) q^{97} +(-2.44949 - 4.24264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^7 - 4 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{7} - 4 q^{8} - 2 q^{10} + 12 q^{11} + 2 q^{14} - 2 q^{16} - 8 q^{17} - 2 q^{19} - 4 q^{20} + 6 q^{22} - 2 q^{23} - 2 q^{25} - 2 q^{28} + 4 q^{29} + 16 q^{31} + 2 q^{32} + 8 q^{34} + 2 q^{35} - 20 q^{37} + 2 q^{38} - 2 q^{40} - 6 q^{41} + 4 q^{43} - 6 q^{44} - 4 q^{46} - 12 q^{47} - 4 q^{50} - 10 q^{53} + 6 q^{55} - 4 q^{56} + 8 q^{58} - 12 q^{59} - 20 q^{61} + 8 q^{62} + 4 q^{64} + 16 q^{68} - 2 q^{70} + 8 q^{71} - 16 q^{73} - 10 q^{74} + 4 q^{76} + 12 q^{77} - 4 q^{79} + 2 q^{80} + 6 q^{82} - 8 q^{83} + 8 q^{85} - 4 q^{86} - 12 q^{88} - 6 q^{89} + 24 q^{91} - 2 q^{92} - 24 q^{94} + 2 q^{95} + 32 q^{97}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^7 - 4 * q^8 - 2 * q^10 + 12 * q^11 + 2 * q^14 - 2 * q^16 - 8 * q^17 - 2 * q^19 - 4 * q^20 + 6 * q^22 - 2 * q^23 - 2 * q^25 - 2 * q^28 + 4 * q^29 + 16 * q^31 + 2 * q^32 + 8 * q^34 + 2 * q^35 - 20 * q^37 + 2 * q^38 - 2 * q^40 - 6 * q^41 + 4 * q^43 - 6 * q^44 - 4 * q^46 - 12 * q^47 - 4 * q^50 - 10 * q^53 + 6 * q^55 - 4 * q^56 + 8 * q^58 - 12 * q^59 - 20 * q^61 + 8 * q^62 + 4 * q^64 + 16 * q^68 - 2 * q^70 + 8 * q^71 - 16 * q^73 - 10 * q^74 + 4 * q^76 + 12 * q^77 - 4 * q^79 + 2 * q^80 + 6 * q^82 - 8 * q^83 + 8 * q^85 - 4 * q^86 - 12 * q^88 - 6 * q^89 + 24 * q^91 - 2 * q^92 - 24 * q^94 + 2 * q^95 + 32 * q^97

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