LMFDB - Embedded newform 1638.2.r.r.1387.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(757,1638)]

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, 2]))

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

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

chi := DirichletCharacter("1638.757");

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.r (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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1387.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1638.1387
Dual form			1638.2.r.r.757.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{11} +(-3.50000 + 0.866025i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-2.50000 - 4.33013i) q^{19} +(-1.50000 - 2.59808i) q^{22} +(3.00000 - 5.19615i) q^{23} -5.00000 q^{25} +(-1.00000 + 3.46410i) q^{26} +(-0.500000 + 0.866025i) q^{28} +(-1.50000 + 2.59808i) q^{29} -4.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +3.00000 q^{34} +(2.00000 - 3.46410i) q^{37} -5.00000 q^{38} +(-1.50000 + 2.59808i) q^{41} +(-4.00000 - 6.92820i) q^{43} -3.00000 q^{44} +(-3.00000 - 5.19615i) q^{46} -9.00000 q^{47} +(-0.500000 + 0.866025i) q^{49} +(-2.50000 + 4.33013i) q^{50} +(2.50000 + 2.59808i) q^{52} +9.00000 q^{53} +(0.500000 + 0.866025i) q^{56} +(1.50000 + 2.59808i) q^{58} +(-3.00000 - 5.19615i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(-2.00000 + 3.46410i) q^{62} +1.00000 q^{64} +(-7.00000 + 12.1244i) q^{67} +(1.50000 - 2.59808i) q^{68} +(-3.00000 - 5.19615i) q^{71} -4.00000 q^{73} +(-2.00000 - 3.46410i) q^{74} +(-2.50000 + 4.33013i) q^{76} -3.00000 q^{77} -1.00000 q^{79} +(1.50000 + 2.59808i) q^{82} +6.00000 q^{83} -8.00000 q^{86} +(-1.50000 + 2.59808i) q^{88} +(-4.50000 + 7.79423i) q^{89} +(2.50000 + 2.59808i) q^{91} -6.00000 q^{92} +(-4.50000 + 7.79423i) q^{94} +(-4.00000 - 6.92820i) q^{97} +(0.500000 + 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 - q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} - q^{7} - 2 q^{8} + 3 q^{11} - 7 q^{13} - 2 q^{14} - q^{16} + 3 q^{17} - 5 q^{19} - 3 q^{22} + 6 q^{23} - 10 q^{25} - 2 q^{26} - q^{28} - 3 q^{29} - 8 q^{31} + q^{32} + 6 q^{34} + 4 q^{37} - 10 q^{38} - 3 q^{41} - 8 q^{43} - 6 q^{44} - 6 q^{46} - 18 q^{47} - q^{49} - 5 q^{50} + 5 q^{52} + 18 q^{53} + q^{56} + 3 q^{58} - 6 q^{59} - 5 q^{61} - 4 q^{62} + 2 q^{64} - 14 q^{67} + 3 q^{68} - 6 q^{71} - 8 q^{73} - 4 q^{74} - 5 q^{76} - 6 q^{77} - 2 q^{79} + 3 q^{82} + 12 q^{83} - 16 q^{86} - 3 q^{88} - 9 q^{89} + 5 q^{91} - 12 q^{92} - 9 q^{94} - 8 q^{97} + q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 - q^7 - 2 * q^8 + 3 * q^11 - 7 * q^13 - 2 * q^14 - q^16 + 3 * q^17 - 5 * q^19 - 3 * q^22 + 6 * q^23 - 10 * q^25 - 2 * q^26 - q^28 - 3 * q^29 - 8 * q^31 + q^32 + 6 * q^34 + 4 * q^37 - 10 * q^38 - 3 * q^41 - 8 * q^43 - 6 * q^44 - 6 * q^46 - 18 * q^47 - q^49 - 5 * q^50 + 5 * q^52 + 18 * q^53 + q^56 + 3 * q^58 - 6 * q^59 - 5 * q^61 - 4 * q^62 + 2 * q^64 - 14 * q^67 + 3 * q^68 - 6 * q^71 - 8 * q^73 - 4 * q^74 - 5 * q^76 - 6 * q^77 - 2 * q^79 + 3 * q^82 + 12 * q^83 - 16 * q^86 - 3 * q^88 - 9 * q^89 + 5 * q^91 - 12 * q^92 - 9 * q^94 - 8 * q^97 + q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	0.500000	−	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			0			−	1.00000i	$-0.5\pi$
$5$		0			0				1.00000i	$0.5\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	−1.00000			−0.353553
$9$		0			0
$10$		0			0
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		0			0
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	−0.996199	−	0.0871106i	$-0.972237\pi$
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	0.422659	−	0.906289i	$-0.361097\pi$
$20$		0			0
$21$		0			0
$22$	−1.50000	−	2.59808i	−0.319801	−	0.553912i
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$		0			0
$25$	−5.00000			−1.00000
$26$	−1.00000	+	3.46410i	−0.196116	+	0.679366i
$27$		0			0
$28$	−0.500000	+	0.866025i	−0.0944911	+	0.163663i
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	3.00000			0.514496
$35$		0			0
$36$		0			0
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	−0.653476	−	0.756948i	$-0.726690\pi$
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	0.982274	+	0.187453i	$0.0600231\pi$
$38$	−5.00000			−0.811107
$39$		0			0
$40$		0			0
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	0.381246	−	0.924473i	$-0.375495\pi$
$44$	−3.00000			−0.452267
$45$		0			0
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	−9.00000			−1.31278			−0.656392	−	0.754420i	$-0.727918\pi$
$47$	−9.00000			−1.31278			−0.656392	+	0.754420i	$0.727918\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−2.50000	+	4.33013i	−0.353553	+	0.612372i
$51$		0			0
$52$	2.50000	+	2.59808i	0.346688	+	0.360288i
$53$	9.00000			1.23625			0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000			1.23625			0.618123	+	0.786082i	$0.287894\pi$
$54$		0			0
$55$		0			0
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$		0			0
$58$	1.50000	+	2.59808i	0.196960	+	0.341144i
$59$	−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
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	0.660415	−	0.750901i	$-0.270381\pi$
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	−0.980507	+	0.196485i	$0.937047\pi$
$62$	−2.00000	+	3.46410i	−0.254000	+	0.439941i
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−7.00000	+	12.1244i	−0.855186	+	1.48123i	0.0212861	+	0.999773i	$0.493224\pi$
$67$	−7.00000	+	12.1244i	−0.855186	+	1.48123i	−0.876472	+	0.481452i	$0.840109\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$		0			0
$70$		0			0
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	0.631260	−	0.775571i	$-0.282538\pi$
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	−0.987294	+	0.158901i	$0.949205\pi$
$72$		0			0
$73$	−4.00000			−0.468165			−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000			−0.468165			−0.234082	+	0.972217i	$0.575209\pi$
$74$	−2.00000	−	3.46410i	−0.232495	−	0.402694i
$75$		0			0
$76$	−2.50000	+	4.33013i	−0.286770	+	0.496700i
$77$	−3.00000			−0.341882
$78$		0			0
$79$	−1.00000			−0.112509			−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000			−0.112509			−0.0562544	+	0.998416i	$0.517916\pi$
$80$		0			0
$81$		0			0
$82$	1.50000	+	2.59808i	0.165647	+	0.286910i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$		0			0
$85$		0			0
$86$	−8.00000			−0.862662
$87$		0			0
$88$	−1.50000	+	2.59808i	−0.159901	+	0.276956i
$89$	−4.50000	+	7.79423i	−0.476999	+	0.826187i	−0.999653	−	0.0263586i	$-0.991609\pi$
$89$	−4.50000	+	7.79423i	−0.476999	+	0.826187i	0.522654	+	0.852545i	$0.324942\pi$
$90$		0			0
$91$	2.50000	+	2.59808i	0.262071	+	0.272352i
$92$	−6.00000			−0.625543
$93$		0			0
$94$	−4.50000	+	7.79423i	−0.464140	+	0.803913i
$95$		0			0
$96$		0			0
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	0.588315	−	0.808632i	$-0.299792\pi$
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	−0.994453	+	0.105180i	$0.966458\pi$
$98$	0.500000	+	0.866025i	0.0505076	+	0.0874818i
$99$		0			0
$100$	2.50000	+	4.33013i	0.250000	+	0.433013i
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$		0			0
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$	3.50000	−	0.866025i	0.343203	−	0.0849208i
$105$		0			0
$106$	4.50000	−	7.79423i	0.437079	−	0.757042i
$107$	7.50000	−	12.9904i	0.725052	−	1.25583i	−0.233900	−	0.972261i	$-0.575149\pi$
$107$	7.50000	−	12.9904i	0.725052	−	1.25583i	0.958952	−	0.283567i	$-0.0915178\pi$
$108$		0			0
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$		0			0
$111$		0			0
$112$	1.00000			0.0944911
$113$	−6.00000	−	10.3923i	−0.564433	−	0.977626i	−0.997102	−	0.0760733i	$-0.975762\pi$
$113$	−6.00000	−	10.3923i	−0.564433	−	0.977626i	0.432670	−	0.901553i	$-0.357572\pi$
$114$		0			0
$115$		0			0
$116$	3.00000			0.278543
$117$		0			0
$118$	−6.00000			−0.552345
$119$	1.50000	−	2.59808i	0.137505	−	0.238165i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−5.00000			−0.452679
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$		0			0
$126$		0			0
$127$	−4.00000	+	6.92820i	−0.354943	+	0.614779i	−0.987108	−	0.160055i	$-0.948833\pi$
$127$	−4.00000	+	6.92820i	−0.354943	+	0.614779i	0.632166	+	0.774833i	$0.282166\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	−2.50000	+	4.33013i	−0.216777	+	0.375470i
$134$	7.00000	+	12.1244i	0.604708	+	1.04738i
$135$		0			0
$136$	−1.50000	−	2.59808i	−0.128624	−	0.222783i
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	−0.938148	−	0.346235i	$-0.887460\pi$
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	0.169226	−	0.985577i	$-0.445873\pi$
$138$		0			0
$139$	6.50000	+	11.2583i	0.551323	+	0.954919i	0.998179	+	0.0603135i	$0.0192101\pi$
$139$	6.50000	+	11.2583i	0.551323	+	0.954919i	−0.446857	+	0.894606i	$0.647457\pi$
$140$		0			0
$141$		0			0
$142$	−6.00000			−0.503509
$143$	−3.00000	+	10.3923i	−0.250873	+	0.869048i
$144$		0			0
$145$		0			0
$146$	−2.00000	+	3.46410i	−0.165521	+	0.286691i
$147$		0			0
$148$	−4.00000			−0.328798
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	17.0000			1.38344			0.691720	−	0.722166i	$-0.256853\pi$
$151$	17.0000			1.38344			0.691720	+	0.722166i	$0.256853\pi$
$152$	2.50000	+	4.33013i	0.202777	+	0.351220i
$153$		0			0
$154$	−1.50000	+	2.59808i	−0.120873	+	0.209359i
$155$		0			0
$156$		0			0
$157$	−22.0000			−1.75579			−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000			−1.75579			−0.877896	+	0.478852i	$0.841053\pi$
$158$	−0.500000	+	0.866025i	−0.0397779	+	0.0688973i
$159$		0			0
$160$		0			0
$161$	−6.00000			−0.472866
$162$		0			0
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	0.988227	+	0.152992i	$0.0488907\pi$
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	−0.361619	+	0.932326i	$0.617776\pi$
$164$	3.00000			0.234261
$165$		0			0
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$167$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$168$		0			0
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$		0			0
$171$		0			0
$172$	−4.00000	+	6.92820i	−0.304997	+	0.528271i
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	0.973670	+	0.227964i	$0.0732068\pi$
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	−0.289412	+	0.957205i	$0.593460\pi$
$174$		0			0
$175$	2.50000	+	4.33013i	0.188982	+	0.327327i
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$		0			0
$178$	4.50000	+	7.79423i	0.337289	+	0.584202i
$179$	12.0000	−	20.7846i	0.896922	−	1.55351i	0.0655145	−	0.997852i	$-0.479131\pi$
$179$	12.0000	−	20.7846i	0.896922	−	1.55351i	0.831408	−	0.555663i	$-0.187536\pi$
$180$		0			0
$181$	17.0000			1.26360			0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000			1.26360			0.631800	+	0.775131i	$0.282316\pi$
$182$	3.50000	−	0.866025i	0.259437	−	0.0641941i
$183$		0			0
$184$	−3.00000	+	5.19615i	−0.221163	+	0.383065i
$185$		0			0
$186$		0			0
$187$	9.00000			0.658145
$188$	4.50000	+	7.79423i	0.328196	+	0.568453i
$189$		0			0
$190$		0			0
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	0.982828	+	0.184525i	$0.0590746\pi$
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	−0.331611	+	0.943416i	$0.607592\pi$
$192$		0			0
$193$	9.50000	−	16.4545i	0.683825	−	1.18442i	−0.289980	−	0.957033i	$-0.593649\pi$
$193$	9.50000	−	16.4545i	0.683825	−	1.18442i	0.973805	−	0.227387i	$-0.0730182\pi$
$194$	−8.00000			−0.574367
$195$		0			0
$196$	1.00000			0.0714286
$197$	−4.50000	+	7.79423i	−0.320612	+	0.555316i	−0.980614	−	0.195947i	$-0.937222\pi$
$197$	−4.50000	+	7.79423i	−0.320612	+	0.555316i	0.660003	+	0.751263i	$0.270555\pi$
$198$		0			0
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	−0.965272	−	0.261245i	$-0.915867\pi$
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	0.256391	−	0.966573i	$-0.417466\pi$
$200$	5.00000			0.353553
$201$		0			0
$202$	−3.00000	−	5.19615i	−0.211079	−	0.365600i
$203$	3.00000			0.210559
$204$		0			0
$205$		0			0
$206$	4.00000	−	6.92820i	0.278693	−	0.482711i
$207$		0			0
$208$	1.00000	−	3.46410i	0.0693375	−	0.240192i
$209$	−15.0000			−1.03757
$210$		0			0
$211$	5.00000	−	8.66025i	0.344214	−	0.596196i	−0.640996	−	0.767544i	$-0.721479\pi$
$211$	5.00000	−	8.66025i	0.344214	−	0.596196i	0.985211	+	0.171347i	$0.0548120\pi$
$212$	−4.50000	−	7.79423i	−0.309061	−	0.535310i
$213$		0			0
$214$	−7.50000	−	12.9904i	−0.512689	−	0.888004i
$215$		0			0
$216$		0			0
$217$	2.00000	+	3.46410i	0.135769	+	0.235159i
$218$	−5.00000	+	8.66025i	−0.338643	+	0.586546i
$219$		0			0
$220$		0			0
$221$	−7.50000	−	7.79423i	−0.504505	−	0.524297i
$222$		0			0
$223$	−4.00000	+	6.92820i	−0.267860	+	0.463947i	−0.968309	−	0.249756i	$-0.919650\pi$
$223$	−4.00000	+	6.92820i	−0.267860	+	0.463947i	0.700449	+	0.713702i	$0.252983\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$		0			0
$226$	−12.0000			−0.798228
$227$	−9.00000	−	15.5885i	−0.597351	−	1.03464i	−0.993210	−	0.116331i	$-0.962887\pi$
$227$	−9.00000	−	15.5885i	−0.597351	−	1.03464i	0.395860	−	0.918311i	$-0.370447\pi$
$228$		0			0
$229$	17.0000			1.12339			0.561696	−	0.827344i	$-0.310149\pi$
$229$	17.0000			1.12339			0.561696	+	0.827344i	$0.310149\pi$
$230$		0			0
$231$		0			0
$232$	1.50000	−	2.59808i	0.0984798	−	0.170572i
$233$	12.0000			0.786146			0.393073	−	0.919507i	$-0.371412\pi$
$233$	12.0000			0.786146			0.393073	+	0.919507i	$0.371412\pi$
$234$		0			0
$235$		0			0
$236$	−3.00000	+	5.19615i	−0.195283	+	0.338241i
$237$		0			0
$238$	−1.50000	−	2.59808i	−0.0972306	−	0.168408i
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	0.707953	−	0.706260i	$-0.249619\pi$
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	−0.965615	+	0.259975i	$0.916286\pi$
$242$	2.00000			0.128565
$243$		0			0
$244$	−2.50000	+	4.33013i	−0.160046	+	0.277208i
$245$		0			0
$246$		0			0
$247$	12.5000	+	12.9904i	0.795356	+	0.826558i
$248$	4.00000			0.254000
$249$		0			0
$250$		0			0
$251$	15.0000	+	25.9808i	0.946792	+	1.63989i	0.752124	+	0.659022i	$0.229030\pi$
$251$	15.0000	+	25.9808i	0.946792	+	1.63989i	0.194668	+	0.980869i	$0.437637\pi$
$252$		0			0
$253$	−9.00000	−	15.5885i	−0.565825	−	0.980038i
$254$	4.00000	+	6.92820i	0.250982	+	0.434714i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	−0.531487	−	0.847066i	$-0.678367\pi$
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	0.999325	+	0.0367485i	$0.0117000\pi$
$258$		0			0
$259$	−4.00000			−0.248548
$260$		0			0
$261$		0			0
$262$		0			0
$263$	9.00000	−	15.5885i	0.554964	−	0.961225i	−0.442943	−	0.896550i	$-0.646065\pi$
$263$	9.00000	−	15.5885i	0.554964	−	0.961225i	0.997906	−	0.0646755i	$-0.0206012\pi$
$264$		0			0
$265$		0			0
$266$	2.50000	+	4.33013i	0.153285	+	0.265497i
$267$		0			0
$268$	14.0000			0.855186
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	0.956176	+	0.292791i	$0.0945841\pi$
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	−0.224523	+	0.974469i	$0.572083\pi$
$270$		0			0
$271$	14.0000	−	24.2487i	0.850439	−	1.47300i	−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	14.0000	−	24.2487i	0.850439	−	1.47300i	0.880812	−	0.473466i	$-0.156997\pi$
$272$	−3.00000			−0.181902
$273$		0			0
$274$	−18.0000			−1.08742
$275$	−7.50000	+	12.9904i	−0.452267	+	0.783349i
$276$		0			0
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	0.834419	−	0.551131i	$-0.185804\pi$
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	−0.894503	+	0.447062i	$0.852470\pi$
$278$	13.0000			0.779688
$279$		0			0
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$	7.50000	+	7.79423i	0.443484	+	0.460882i
$287$	3.00000			0.177084
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$		0			0
$292$	2.00000	+	3.46410i	0.117041	+	0.202721i
$293$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$293$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$294$		0			0
$295$		0			0
$296$	−2.00000	+	3.46410i	−0.116248	+	0.201347i
$297$		0			0
$298$	6.00000			0.347571
$299$	−6.00000	+	20.7846i	−0.346989	+	1.20201i
$300$		0			0
$301$	−4.00000	+	6.92820i	−0.230556	+	0.399335i
$302$	8.50000	−	14.7224i	0.489120	−	0.847181i
$303$		0			0
$304$	5.00000			0.286770
$305$		0			0
$306$		0			0
$307$	11.0000			0.627803			0.313902	−	0.949456i	$-0.398364\pi$
$307$	11.0000			0.627803			0.313902	+	0.949456i	$0.398364\pi$
$308$	1.50000	+	2.59808i	0.0854704	+	0.148039i
$309$		0			0
$310$		0			0
$311$	15.0000			0.850572			0.425286	−	0.905059i	$-0.360174\pi$
$311$	15.0000			0.850572			0.425286	+	0.905059i	$0.360174\pi$
$312$		0			0
$313$	−22.0000			−1.24351			−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000			−1.24351			−0.621757	+	0.783210i	$0.713581\pi$
$314$	−11.0000	+	19.0526i	−0.620766	+	1.07520i
$315$		0			0
$316$	0.500000	+	0.866025i	0.0281272	+	0.0487177i
$317$	6.00000			0.336994			0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000			0.336994			0.168497	+	0.985702i	$0.446109\pi$
$318$		0			0
$319$	4.50000	+	7.79423i	0.251952	+	0.436393i
$320$		0			0
$321$		0			0
$322$	−3.00000	+	5.19615i	−0.167183	+	0.289570i
$323$	7.50000	−	12.9904i	0.417311	−	0.722804i
$324$		0			0
$325$	17.5000	−	4.33013i	0.970725	−	0.240192i
$326$	16.0000			0.886158
$327$		0			0
$328$	1.50000	−	2.59808i	0.0828236	−	0.143455i
$329$	4.50000	+	7.79423i	0.248093	+	0.429710i
$330$		0			0
$331$	5.00000	+	8.66025i	0.274825	+	0.476011i	0.970091	−	0.242742i	$-0.0780468\pi$
$331$	5.00000	+	8.66025i	0.274825	+	0.476011i	−0.695266	+	0.718752i	$0.744713\pi$
$332$	−3.00000	−	5.19615i	−0.164646	−	0.285176i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−25.0000			−1.36184			−0.680918	−	0.732359i	$-0.738419\pi$
$337$	−25.0000			−1.36184			−0.680918	+	0.732359i	$0.738419\pi$
$338$	0.500000	−	12.9904i	0.0271964	−	0.706584i
$339$		0			0
$340$		0			0
$341$	−6.00000	+	10.3923i	−0.324918	+	0.562775i
$342$		0			0
$343$	1.00000			0.0539949
$344$	4.00000	+	6.92820i	0.215666	+	0.373544i
$345$		0			0
$346$	18.0000			0.967686
$347$	−13.5000	−	23.3827i	−0.724718	−	1.25525i	−0.959090	−	0.283101i	$-0.908637\pi$
$347$	−13.5000	−	23.3827i	−0.724718	−	1.25525i	0.234372	−	0.972147i	$-0.424697\pi$
$348$		0			0
$349$	−1.00000	+	1.73205i	−0.0535288	+	0.0927146i	−0.891548	−	0.452926i	$-0.850380\pi$
$349$	−1.00000	+	1.73205i	−0.0535288	+	0.0927146i	0.838019	+	0.545640i	$0.183714\pi$
$350$	5.00000			0.267261
$351$		0			0
$352$	3.00000			0.159901
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	−0.999711	−	0.0240566i	$-0.992342\pi$
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	0.520689	+	0.853746i	$0.325675\pi$
$354$		0			0
$355$		0			0
$356$	9.00000			0.476999
$357$		0			0
$358$	−12.0000	−	20.7846i	−0.634220	−	1.09850i
$359$	12.0000			0.633336			0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000			0.633336			0.316668	+	0.948536i	$0.397436\pi$
$360$		0			0
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	8.50000	−	14.7224i	0.446750	−	0.773794i
$363$		0			0
$364$	1.00000	−	3.46410i	0.0524142	−	0.181568i
$365$		0			0
$366$		0			0
$367$	−1.00000	+	1.73205i	−0.0521996	+	0.0904123i	−0.890945	−	0.454112i	$-0.849957\pi$
$367$	−1.00000	+	1.73205i	−0.0521996	+	0.0904123i	0.838745	+	0.544524i	$0.183290\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$		0			0
$370$		0			0
$371$	−4.50000	−	7.79423i	−0.233628	−	0.404656i
$372$		0			0
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	0.625917	−	0.779890i	$-0.284725\pi$
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	−0.988363	+	0.152115i	$0.951392\pi$
$374$	4.50000	−	7.79423i	0.232689	−	0.403030i
$375$		0			0
$376$	9.00000			0.464140
$377$	3.00000	−	10.3923i	0.154508	−	0.535231i
$378$		0			0
$379$	17.0000	−	29.4449i	0.873231	−	1.51248i	0.0145964	−	0.999893i	$-0.495354\pi$
$379$	17.0000	−	29.4449i	0.873231	−	1.51248i	0.858635	−	0.512588i	$-0.171313\pi$
$380$		0			0
$381$		0			0
$382$	18.0000			0.920960
$383$	4.50000	+	7.79423i	0.229939	+	0.398266i	0.957790	−	0.287469i	$-0.0928139\pi$
$383$	4.50000	+	7.79423i	0.229939	+	0.398266i	−0.727851	+	0.685736i	$0.759481\pi$
$384$		0			0
$385$		0			0
$386$	−9.50000	−	16.4545i	−0.483537	−	0.837511i
$387$		0			0
$388$	−4.00000	+	6.92820i	−0.203069	+	0.351726i
$389$	6.00000			0.304212			0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000			0.304212			0.152106	+	0.988364i	$0.451394\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$	0.500000	−	0.866025i	0.0252538	−	0.0437409i
$393$		0			0
$394$	4.50000	+	7.79423i	0.226707	+	0.392668i
$395$		0			0
$396$		0			0
$397$	18.5000	+	32.0429i	0.928488	+	1.60819i	0.785853	+	0.618414i	$0.212224\pi$
$397$	18.5000	+	32.0429i	0.928488	+	1.60819i	0.142636	+	0.989775i	$0.454442\pi$
$398$	−20.0000			−1.00251
$399$		0			0
$400$	2.50000	−	4.33013i	0.125000	−	0.216506i
$401$	15.0000	−	25.9808i	0.749064	−	1.29742i	−0.199207	−	0.979957i	$-0.563837\pi$
$401$	15.0000	−	25.9808i	0.749064	−	1.29742i	0.948272	−	0.317460i	$-0.102830\pi$
$402$		0			0
$403$	14.0000	−	3.46410i	0.697390	−	0.172559i
$404$	−6.00000			−0.298511
$405$		0			0
$406$	1.50000	−	2.59808i	0.0744438	−	0.128940i
$407$	−6.00000	−	10.3923i	−0.297409	−	0.515127i
$408$		0			0
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	0.639430	−	0.768849i	$-0.279170\pi$
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	−0.985558	+	0.169338i	$0.945837\pi$
$410$		0			0
$411$		0			0
$412$	−4.00000	−	6.92820i	−0.197066	−	0.341328i
$413$	−3.00000	+	5.19615i	−0.147620	+	0.255686i
$414$		0			0
$415$		0			0
$416$	−2.50000	−	2.59808i	−0.122573	−	0.127381i
$417$		0			0
$418$	−7.50000	+	12.9904i	−0.366837	+	0.635380i
$419$	3.00000	−	5.19615i	0.146560	−	0.253849i	−0.783394	−	0.621525i	$-0.786513\pi$
$419$	3.00000	−	5.19615i	0.146560	−	0.253849i	0.929954	+	0.367677i	$0.119847\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	−5.00000	−	8.66025i	−0.243396	−	0.421575i
$423$		0			0
$424$	−9.00000			−0.437079
$425$	−7.50000	−	12.9904i	−0.363803	−	0.630126i
$426$		0			0
$427$	−2.50000	+	4.33013i	−0.120983	+	0.209550i
$428$	−15.0000			−0.725052
$429$		0			0
$430$		0			0
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	0.237460	+	0.971397i	$0.423685\pi$
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	−0.959985	+	0.280052i	$0.909648\pi$
$432$		0			0
$433$	17.0000	+	29.4449i	0.816968	+	1.41503i	0.907906	+	0.419173i	$0.137680\pi$
$433$	17.0000	+	29.4449i	0.816968	+	1.41503i	−0.0909384	+	0.995857i	$0.528987\pi$
$434$	4.00000			0.192006
$435$		0			0
$436$	5.00000	+	8.66025i	0.239457	+	0.414751i
$437$	−30.0000			−1.43509
$438$		0			0
$439$	2.00000	−	3.46410i	0.0954548	−	0.165333i	−0.814344	−	0.580383i	$-0.802903\pi$
$439$	2.00000	−	3.46410i	0.0954548	−	0.165333i	0.909798	+	0.415051i	$0.136236\pi$
$440$		0			0
$441$		0			0
$442$	−10.5000	+	2.59808i	−0.499434	+	0.123578i
$443$	9.00000			0.427603			0.213801	−	0.976877i	$-0.431415\pi$
$443$	9.00000			0.427603			0.213801	+	0.976877i	$0.431415\pi$
$444$		0			0
$445$		0			0
$446$	4.00000	+	6.92820i	0.189405	+	0.328060i
$447$		0			0
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	6.00000	+	10.3923i	0.283158	+	0.490443i	0.972161	−	0.234315i	$-0.0752847\pi$
$449$	6.00000	+	10.3923i	0.283158	+	0.490443i	−0.689003	+	0.724758i	$0.741951\pi$
$450$		0			0
$451$	4.50000	+	7.79423i	0.211897	+	0.367016i
$452$	−6.00000	+	10.3923i	−0.282216	+	0.488813i
$453$		0			0
$454$	−18.0000			−0.844782
$455$		0			0
$456$		0			0
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	0.958950	+	0.283577i	$0.0915211\pi$
$458$	8.50000	−	14.7224i	0.397179	−	0.687934i
$459$		0			0
$460$		0			0
$461$	−6.00000	−	10.3923i	−0.279448	−	0.484018i	0.691800	−	0.722089i	$-0.256818\pi$
$461$	−6.00000	−	10.3923i	−0.279448	−	0.484018i	−0.971248	+	0.238071i	$0.923485\pi$
$462$		0			0
$463$	5.00000			0.232370			0.116185	−	0.993228i	$-0.462933\pi$
$463$	5.00000			0.232370			0.116185	+	0.993228i	$0.462933\pi$
$464$	−1.50000	−	2.59808i	−0.0696358	−	0.120613i
$465$		0			0
$466$	6.00000	−	10.3923i	0.277945	−	0.481414i
$467$		0			0			−	1.00000i	$-0.5\pi$
$467$		0			0				1.00000i	$0.5\pi$
$468$		0			0
$469$	14.0000			0.646460
$470$		0			0
$471$		0			0
$472$	3.00000	+	5.19615i	0.138086	+	0.239172i
$473$	−24.0000			−1.10352
$474$		0			0
$475$	12.5000	+	21.6506i	0.573539	+	0.993399i
$476$	−3.00000			−0.137505
$477$		0			0
$478$	−3.00000	+	5.19615i	−0.137217	+	0.237666i
$479$	13.5000	−	23.3827i	0.616831	−	1.06838i	−0.373230	−	0.927739i	$-0.621750\pi$
$479$	13.5000	−	23.3827i	0.616831	−	1.06838i	0.990060	−	0.140643i	$-0.0449170\pi$
$480$		0			0
$481$	−4.00000	+	13.8564i	−0.182384	+	0.631798i
$482$	−8.00000			−0.364390
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$		0			0
$486$		0			0
$487$	−11.5000	−	19.9186i	−0.521115	−	0.902597i	−0.999698	−	0.0245553i	$-0.992183\pi$
$487$	−11.5000	−	19.9186i	−0.521115	−	0.902597i	0.478584	−	0.878042i	$-0.341150\pi$
$488$	2.50000	+	4.33013i	0.113170	+	0.196016i
$489$		0			0
$490$		0			0
$491$	18.0000	−	31.1769i	0.812329	−	1.40699i	−0.0989017	−	0.995097i	$-0.531533\pi$
$491$	18.0000	−	31.1769i	0.812329	−	1.40699i	0.911230	−	0.411897i	$-0.135134\pi$
$492$		0			0
$493$	−9.00000			−0.405340
$494$	17.5000	−	4.33013i	0.787362	−	0.194822i
$495$		0			0
$496$	2.00000	−	3.46410i	0.0898027	−	0.155543i
$497$	−3.00000	+	5.19615i	−0.134568	+	0.233079i
$498$		0			0
$499$	−40.0000			−1.79065			−0.895323	−	0.445418i	$-0.853055\pi$
$499$	−40.0000			−1.79065			−0.895323	+	0.445418i	$0.853055\pi$
$500$		0			0
$501$		0			0
$502$	30.0000			1.33897
$503$	12.0000	+	20.7846i	0.535054	+	0.926740i	0.999161	+	0.0409609i	$0.0130419\pi$
$503$	12.0000	+	20.7846i	0.535054	+	0.926740i	−0.464107	+	0.885779i	$0.653625\pi$
$504$		0			0
$505$		0			0
$506$	−18.0000			−0.800198
$507$		0			0
$508$	8.00000			0.354943
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648436\pi$
$510$		0			0
$511$	2.00000	+	3.46410i	0.0884748	+	0.153243i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−7.50000	−	12.9904i	−0.330811	−	0.572981i
$515$		0			0
$516$		0			0
$517$	−13.5000	+	23.3827i	−0.593729	+	1.02837i
$518$	−2.00000	+	3.46410i	−0.0878750	+	0.152204i
$519$		0			0
$520$		0			0
$521$	−27.0000			−1.18289			−0.591446	−	0.806345i	$-0.701443\pi$
$521$	−27.0000			−1.18289			−0.591446	+	0.806345i	$0.701443\pi$
$522$		0			0
$523$	−14.5000	+	25.1147i	−0.634041	+	1.09819i	0.352677	+	0.935745i	$0.385272\pi$
$523$	−14.5000	+	25.1147i	−0.634041	+	1.09819i	−0.986718	+	0.162446i	$0.948062\pi$
$524$		0			0
$525$		0			0
$526$	−9.00000	−	15.5885i	−0.392419	−	0.679689i
$527$	−6.00000	−	10.3923i	−0.261364	−	0.452696i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$		0			0
$532$	5.00000			0.216777
$533$	3.00000	−	10.3923i	0.129944	−	0.450141i
$534$		0			0
$535$		0			0
$536$	7.00000	−	12.1244i	0.302354	−	0.523692i
$537$		0			0
$538$	24.0000			1.03471
$539$	1.50000	+	2.59808i	0.0646096	+	0.111907i
$540$		0			0
$541$	−10.0000			−0.429934			−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000			−0.429934			−0.214967	+	0.976621i	$0.568964\pi$
$542$	−14.0000	−	24.2487i	−0.601351	−	1.04157i
$543$		0			0
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$		0			0
$546$		0			0
$547$	−22.0000			−0.940652			−0.470326	−	0.882493i	$-0.655864\pi$
$547$	−22.0000			−0.940652			−0.470326	+	0.882493i	$0.655864\pi$
$548$	−9.00000	+	15.5885i	−0.384461	+	0.665906i
$549$		0			0
$550$	7.50000	+	12.9904i	0.319801	+	0.553912i
$551$	15.0000			0.639021
$552$		0			0
$553$	0.500000	+	0.866025i	0.0212622	+	0.0368271i
$554$	−2.00000			−0.0849719
$555$		0			0
$556$	6.50000	−	11.2583i	0.275661	−	0.477460i
$557$	−7.50000	+	12.9904i	−0.317785	+	0.550420i	−0.980026	−	0.198871i	$-0.936272\pi$
$557$	−7.50000	+	12.9904i	−0.317785	+	0.550420i	0.662240	+	0.749291i	$0.269606\pi$
$558$		0			0
$559$	20.0000	+	20.7846i	0.845910	+	0.879095i
$560$		0			0
$561$		0			0
$562$	−3.00000	+	5.19615i	−0.126547	+	0.219186i
$563$	12.0000	+	20.7846i	0.505740	+	0.875967i	0.999978	+	0.00664037i	$0.00211371\pi$
$563$	12.0000	+	20.7846i	0.505740	+	0.875967i	−0.494238	+	0.869326i	$0.664553\pi$
$564$		0			0
$565$		0			0
$566$	−2.00000	−	3.46410i	−0.0840663	−	0.145607i
$567$		0			0
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	−0.922032	−	0.387113i	$-0.873472\pi$
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	0.796266	+	0.604947i	$0.206806\pi$
$570$		0			0
$571$	2.00000			0.0836974			0.0418487	−	0.999124i	$-0.486675\pi$
$571$	2.00000			0.0836974			0.0418487	+	0.999124i	$0.486675\pi$
$572$	10.5000	−	2.59808i	0.439027	−	0.108631i
$573$		0			0
$574$	1.50000	−	2.59808i	0.0626088	−	0.108442i
$575$	−15.0000	+	25.9808i	−0.625543	+	1.08347i
$576$		0			0
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$		0			0
$580$		0			0
$581$	−3.00000	−	5.19615i	−0.124461	−	0.215573i
$582$		0			0
$583$	13.5000	−	23.3827i	0.559113	−	0.968412i
$584$	4.00000			0.165521
$585$		0			0
$586$		0			0
$587$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$587$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$588$		0			0
$589$	10.0000	+	17.3205i	0.412043	+	0.713679i
$590$		0			0
$591$		0			0
$592$	2.00000	+	3.46410i	0.0821995	+	0.142374i
$593$	15.0000			0.615976			0.307988	−	0.951390i	$-0.400344\pi$
$593$	15.0000			0.615976			0.307988	+	0.951390i	$0.400344\pi$
$594$		0			0
$595$		0			0
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$		0			0
$598$	15.0000	+	15.5885i	0.613396	+	0.637459i
$599$	−6.00000			−0.245153			−0.122577	−	0.992459i	$-0.539116\pi$
$599$	−6.00000			−0.245153			−0.122577	+	0.992459i	$0.539116\pi$
$600$		0			0
$601$	20.0000	−	34.6410i	0.815817	−	1.41304i	−0.0929227	−	0.995673i	$-0.529621\pi$
$601$	20.0000	−	34.6410i	0.815817	−	1.41304i	0.908740	−	0.417363i	$-0.137046\pi$
$602$	4.00000	+	6.92820i	0.163028	+	0.282372i
$603$		0			0
$604$	−8.50000	−	14.7224i	−0.345860	−	0.599047i
$605$		0			0
$606$		0			0
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	0.981454	−	0.191700i	$-0.0614000\pi$
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	−0.656744	+	0.754114i	$0.728067\pi$
$608$	2.50000	−	4.33013i	0.101388	−	0.175610i
$609$		0			0
$610$		0			0
$611$	31.5000	−	7.79423i	1.27435	−	0.315321i
$612$		0			0
$613$	−4.00000	+	6.92820i	−0.161558	+	0.279827i	−0.935428	−	0.353518i	$-0.884985\pi$
$613$	−4.00000	+	6.92820i	−0.161558	+	0.279827i	0.773869	+	0.633345i	$0.218319\pi$
$614$	5.50000	−	9.52628i	0.221962	−	0.384449i
$615$		0			0
$616$	3.00000			0.120873
$617$	−9.00000	−	15.5885i	−0.362326	−	0.627568i	0.626017	−	0.779809i	$-0.284684\pi$
$617$	−9.00000	−	15.5885i	−0.362326	−	0.627568i	−0.988343	+	0.152242i	$0.951351\pi$
$618$		0			0
$619$	−25.0000			−1.00483			−0.502417	−	0.864625i	$-0.667556\pi$
$619$	−25.0000			−1.00483			−0.502417	+	0.864625i	$0.667556\pi$
$620$		0			0
$621$		0			0
$622$	7.50000	−	12.9904i	0.300723	−	0.520867i
$623$	9.00000			0.360577
$624$		0			0
$625$	25.0000			1.00000
$626$	−11.0000	+	19.0526i	−0.439648	+	0.761493i
$627$		0			0
$628$	11.0000	+	19.0526i	0.438948	+	0.760280i
$629$	12.0000			0.478471
$630$		0			0
$631$	−11.5000	−	19.9186i	−0.457808	−	0.792946i	0.541037	−	0.840999i	$-0.318032\pi$
$631$	−11.5000	−	19.9186i	−0.457808	−	0.792946i	−0.998845	+	0.0480524i	$0.984699\pi$
$632$	1.00000			0.0397779
$633$		0			0
$634$	3.00000	−	5.19615i	0.119145	−	0.206366i
$635$		0			0
$636$		0			0
$637$	1.00000	−	3.46410i	0.0396214	−	0.137253i
$638$	9.00000			0.356313
$639$		0			0
$640$		0			0
$641$	3.00000	+	5.19615i	0.118493	+	0.205236i	0.919171	−	0.393860i	$-0.128860\pi$
$641$	3.00000	+	5.19615i	0.118493	+	0.205236i	−0.800678	+	0.599095i	$0.795527\pi$
$642$		0			0
$643$	−8.50000	−	14.7224i	−0.335207	−	0.580596i	0.648317	−	0.761370i	$-0.275473\pi$
$643$	−8.50000	−	14.7224i	−0.335207	−	0.580596i	−0.983525	+	0.180774i	$0.942140\pi$
$644$	3.00000	+	5.19615i	0.118217	+	0.204757i
$645$		0			0
$646$	−7.50000	−	12.9904i	−0.295084	−	0.511100i
$647$	−22.5000	+	38.9711i	−0.884566	+	1.53211i	−0.0383563	+	0.999264i	$0.512212\pi$
$647$	−22.5000	+	38.9711i	−0.884566	+	1.53211i	−0.846210	+	0.532850i	$0.821121\pi$
$648$		0			0
$649$	−18.0000			−0.706562
$650$	5.00000	−	17.3205i	0.196116	−	0.679366i
$651$		0			0
$652$	8.00000	−	13.8564i	0.313304	−	0.542659i
$653$	−16.5000	+	28.5788i	−0.645695	+	1.11838i	0.338446	+	0.940986i	$0.390099\pi$
$653$	−16.5000	+	28.5788i	−0.645695	+	1.11838i	−0.984141	+	0.177390i	$0.943234\pi$
$654$		0			0
$655$		0			0
$656$	−1.50000	−	2.59808i	−0.0585652	−	0.101438i
$657$		0			0
$658$	9.00000			0.350857
$659$	−7.50000	−	12.9904i	−0.292159	−	0.506033i	0.682161	−	0.731202i	$-0.261040\pi$
$659$	−7.50000	−	12.9904i	−0.292159	−	0.506033i	−0.974320	+	0.225168i	$0.927707\pi$
$660$		0			0
$661$	11.0000	−	19.0526i	0.427850	−	0.741059i	−0.568831	−	0.822454i	$-0.692604\pi$
$661$	11.0000	−	19.0526i	0.427850	−	0.741059i	0.996682	+	0.0813955i	$0.0259377\pi$
$662$	10.0000			0.388661
$663$		0			0
$664$	−6.00000			−0.232845
$665$		0			0
$666$		0			0
$667$	9.00000	+	15.5885i	0.348481	+	0.603587i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−15.0000			−0.579069
$672$		0			0
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	−0.856228	−	0.516599i	$-0.827198\pi$
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	0.875501	+	0.483216i	$0.160531\pi$
$674$	−12.5000	+	21.6506i	−0.481482	+	0.833951i
$675$		0			0
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	−6.00000			−0.230599			−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000			−0.230599			−0.115299	+	0.993331i	$0.536783\pi$
$678$		0			0
$679$	−4.00000	+	6.92820i	−0.153506	+	0.265880i
$680$		0			0
$681$		0			0
$682$	6.00000	+	10.3923i	0.229752	+	0.397942i
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	0.957685	−	0.287819i	$-0.0929302\pi$
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	−0.728101	+	0.685470i	$0.759597\pi$
$684$		0			0
$685$		0			0
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$		0			0
$688$	8.00000			0.304997
$689$	−31.5000	+	7.79423i	−1.20005	+	0.296936i
$690$		0			0
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	−0.932024	−	0.362397i	$-0.881959\pi$
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	0.779857	+	0.625958i	$0.215292\pi$
$692$	9.00000	−	15.5885i	0.342129	−	0.592584i
$693$		0			0
$694$	−27.0000			−1.02491
$695$		0			0
$696$		0			0
$697$	−9.00000			−0.340899
$698$	1.00000	+	1.73205i	0.0378506	+	0.0655591i
$699$		0			0
$700$	2.50000	−	4.33013i	0.0944911	−	0.163663i
$701$	15.0000			0.566542			0.283271	−	0.959040i	$-0.408580\pi$
$701$	15.0000			0.566542			0.283271	+	0.959040i	$0.408580\pi$
$702$		0			0
$703$	−20.0000			−0.754314
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$		0			0
$706$	9.00000	+	15.5885i	0.338719	+	0.586679i
$707$	−6.00000			−0.225653
$708$		0			0
$709$	−1.00000	−	1.73205i	−0.0375558	−	0.0650485i	0.846637	−	0.532172i	$-0.178624\pi$
$709$	−1.00000	−	1.73205i	−0.0375558	−	0.0650485i	−0.884192	+	0.467123i	$0.845291\pi$
$710$		0			0
$711$		0			0
$712$	4.50000	−	7.79423i	0.168645	−	0.292101i
$713$	−12.0000	+	20.7846i	−0.449404	+	0.778390i
$714$		0			0
$715$		0			0
$716$	−24.0000			−0.896922
$717$		0			0
$718$	6.00000	−	10.3923i	0.223918	−	0.387837i
$719$	13.5000	+	23.3827i	0.503465	+	0.872027i	0.999992	+	0.00400572i	$0.00127506\pi$
$719$	13.5000	+	23.3827i	0.503465	+	0.872027i	−0.496527	+	0.868021i	$0.665392\pi$
$720$		0			0
$721$	−4.00000	−	6.92820i	−0.148968	−	0.258020i
$722$	3.00000	+	5.19615i	0.111648	+	0.193381i
$723$		0			0
$724$	−8.50000	−	14.7224i	−0.315900	−	0.547155i
$725$	7.50000	−	12.9904i	0.278543	−	0.482451i
$726$		0			0
$727$	−28.0000			−1.03846			−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000			−1.03846			−0.519231	+	0.854634i	$0.673782\pi$
$728$	−2.50000	−	2.59808i	−0.0926562	−	0.0962911i
$729$		0			0
$730$		0			0
$731$	12.0000	−	20.7846i	0.443836	−	0.768747i
$732$		0			0
$733$	−49.0000			−1.80986			−0.904928	−	0.425564i	$-0.860076\pi$
$733$	−49.0000			−1.80986			−0.904928	+	0.425564i	$0.860076\pi$
$734$	1.00000	+	1.73205i	0.0369107	+	0.0639312i
$735$		0			0
$736$	6.00000			0.221163
$737$	21.0000	+	36.3731i	0.773545	+	1.33982i
$738$		0			0
$739$	5.00000	−	8.66025i	0.183928	−	0.318573i	−0.759287	−	0.650756i	$-0.774452\pi$
$739$	5.00000	−	8.66025i	0.183928	−	0.318573i	0.943215	+	0.332184i	$0.107785\pi$
$740$		0			0
$741$		0			0
$742$	−9.00000			−0.330400
$743$	−12.0000	+	20.7846i	−0.440237	+	0.762513i	−0.997707	−	0.0676840i	$-0.978439\pi$
$743$	−12.0000	+	20.7846i	−0.440237	+	0.762513i	0.557470	+	0.830197i	$0.311772\pi$
$744$		0			0
$745$		0			0
$746$	−14.0000			−0.512576
$747$		0			0
$748$	−4.50000	−	7.79423i	−0.164536	−	0.284985i
$749$	−15.0000			−0.548088
$750$		0			0
$751$	−5.50000	+	9.52628i	−0.200698	+	0.347619i	−0.948753	−	0.316017i	$-0.897654\pi$
$751$	−5.50000	+	9.52628i	−0.200698	+	0.347619i	0.748056	+	0.663636i	$0.230988\pi$
$752$	4.50000	−	7.79423i	0.164098	−	0.284226i
$753$		0			0
$754$	−7.50000	−	7.79423i	−0.273134	−	0.283849i
$755$		0			0
$756$		0			0
$757$	−1.00000	+	1.73205i	−0.0363456	+	0.0629525i	−0.883626	−	0.468193i	$-0.844905\pi$
$757$	−1.00000	+	1.73205i	−0.0363456	+	0.0629525i	0.847280	+	0.531146i	$0.178238\pi$
$758$	−17.0000	−	29.4449i	−0.617468	−	1.06949i
$759$		0			0
$760$		0			0
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	−0.942207	−	0.335032i	$-0.891253\pi$
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	0.180957	−	0.983491i	$-0.442080\pi$
$762$		0			0
$763$	5.00000	+	8.66025i	0.181012	+	0.313522i
$764$	9.00000	−	15.5885i	0.325609	−	0.563971i
$765$		0			0
$766$	9.00000			0.325183
$767$	15.0000	+	15.5885i	0.541619	+	0.562867i
$768$		0			0
$769$	−22.0000	+	38.1051i	−0.793340	+	1.37411i	0.130547	+	0.991442i	$0.458327\pi$
$769$	−22.0000	+	38.1051i	−0.793340	+	1.37411i	−0.923888	+	0.382664i	$0.875007\pi$
$770$		0			0
$771$		0			0
$772$	−19.0000			−0.683825
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	0.981250	−	0.192740i	$-0.0617373\pi$
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	−0.657542	+	0.753418i	$0.728404\pi$
$774$		0			0
$775$	20.0000			0.718421
$776$	4.00000	+	6.92820i	0.143592	+	0.248708i
$777$		0			0
$778$	3.00000	−	5.19615i	0.107555	−	0.186291i
$779$	15.0000			0.537431
$780$		0			0
$781$	−18.0000			−0.644091
$782$	9.00000	−	15.5885i	0.321839	−	0.557442i
$783$		0			0
$784$	−0.500000	−	0.866025i	−0.0178571	−	0.0309295i
$785$		0			0
$786$		0			0
$787$	−5.50000	−	9.52628i	−0.196054	−	0.339575i	0.751192	−	0.660084i	$-0.229479\pi$
$787$	−5.50000	−	9.52628i	−0.196054	−	0.339575i	−0.947245	+	0.320509i	$0.896146\pi$
$788$	9.00000			0.320612
$789$		0			0
$790$		0			0
$791$	−6.00000	+	10.3923i	−0.213335	+	0.369508i
$792$		0			0
$793$	12.5000	+	12.9904i	0.443888	+	0.461302i
$794$	37.0000			1.31308
$795$		0			0
$796$	−10.0000	+	17.3205i	−0.354441	+	0.613909i
$797$	−3.00000	−	5.19615i	−0.106265	−	0.184057i	0.807989	−	0.589197i	$-0.200556\pi$
$797$	−3.00000	−	5.19615i	−0.106265	−	0.184057i	−0.914255	+	0.405140i	$0.867223\pi$
$798$		0			0
$799$	−13.5000	−	23.3827i	−0.477596	−	0.827220i
$800$	−2.50000	−	4.33013i	−0.0883883	−	0.153093i
$801$		0			0
$802$	−15.0000	−	25.9808i	−0.529668	−	0.917413i
$803$	−6.00000	+	10.3923i	−0.211735	+	0.366736i
$804$		0			0
$805$		0			0
$806$	4.00000	−	13.8564i	0.140894	−	0.488071i
$807$		0			0
$808$	−3.00000	+	5.19615i	−0.105540	+	0.182800i
$809$	−21.0000	+	36.3731i	−0.738321	+	1.27881i	0.214930	+	0.976629i	$0.431048\pi$
$809$	−21.0000	+	36.3731i	−0.738321	+	1.27881i	−0.953251	+	0.302180i	$0.902286\pi$
$810$		0			0
$811$	−40.0000			−1.40459			−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000			−1.40459			−0.702295	+	0.711886i	$0.747841\pi$
$812$	−1.50000	−	2.59808i	−0.0526397	−	0.0911746i
$813$		0			0
$814$	−12.0000			−0.420600
$815$		0			0
$816$		0			0
$817$	−20.0000	+	34.6410i	−0.699711	+	1.21194i
$818$	−14.0000			−0.489499
$819$		0			0
$820$		0			0
$821$	−22.5000	+	38.9711i	−0.785255	+	1.36010i	0.143591	+	0.989637i	$0.454135\pi$
$821$	−22.5000	+	38.9711i	−0.785255	+	1.36010i	−0.928846	+	0.370465i	$0.879198\pi$
$822$		0			0
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	−0.997686	−	0.0679910i	$-0.978341\pi$
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	0.439961	−	0.898017i	$-0.354992\pi$
$824$	−8.00000			−0.278693
$825$		0			0
$826$	3.00000	+	5.19615i	0.104383	+	0.180797i
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	12.5000	−	21.6506i	0.434143	−	0.751958i	−0.563082	−	0.826401i	$-0.690385\pi$
$829$	12.5000	−	21.6506i	0.434143	−	0.751958i	0.997225	+	0.0744432i	$0.0237179\pi$
$830$		0			0
$831$		0			0
$832$	−3.50000	+	0.866025i	−0.121341	+	0.0300240i
$833$	−3.00000			−0.103944
$834$		0			0
$835$		0			0
$836$	7.50000	+	12.9904i	0.259393	+	0.449282i
$837$		0			0
$838$	−3.00000	−	5.19615i	−0.103633	−	0.179498i
$839$	18.0000	+	31.1769i	0.621429	+	1.07635i	0.989220	+	0.146438i	$0.0467809\pi$
$839$	18.0000	+	31.1769i	0.621429	+	1.07635i	−0.367791	+	0.929909i	$0.619886\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	−5.00000	+	8.66025i	−0.172311	+	0.298452i
$843$		0			0
$844$	−10.0000			−0.344214
$845$		0			0
$846$		0			0
$847$	1.00000	−	1.73205i	0.0343604	−	0.0595140i
$848$	−4.50000	+	7.79423i	−0.154531	+	0.267655i
$849$		0			0
$850$	−15.0000			−0.514496
$851$	−12.0000	−	20.7846i	−0.411355	−	0.712487i
$852$		0			0
$853$	−37.0000			−1.26686			−0.633428	−	0.773802i	$-0.718353\pi$
$853$	−37.0000			−1.26686			−0.633428	+	0.773802i	$0.718353\pi$
$854$	2.50000	+	4.33013i	0.0855482	+	0.148174i
$855$		0			0
$856$	−7.50000	+	12.9904i	−0.256345	+	0.444002i
$857$	−18.0000			−0.614868			−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000			−0.614868			−0.307434	+	0.951569i	$0.599470\pi$
$858$		0			0
$859$	5.00000			0.170598			0.0852989	−	0.996355i	$-0.472815\pi$
$859$	5.00000			0.170598			0.0852989	+	0.996355i	$0.472815\pi$
$860$		0			0
$861$		0			0
$862$	15.0000	+	25.9808i	0.510902	+	0.884908i
$863$	30.0000			1.02121			0.510606	−	0.859815i	$-0.329421\pi$
$863$	30.0000			1.02121			0.510606	+	0.859815i	$0.329421\pi$
$864$		0			0
$865$		0			0
$866$	34.0000			1.15537
$867$		0			0
$868$	2.00000	−	3.46410i	0.0678844	−	0.117579i
$869$	−1.50000	+	2.59808i	−0.0508840	+	0.0881337i
$870$		0			0
$871$	14.0000	−	48.4974i	0.474372	−	1.64327i
$872$	10.0000			0.338643
$873$		0			0
$874$	−15.0000	+	25.9808i	−0.507383	+	0.878812i
$875$		0			0
$876$		0			0
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	0.989788	−	0.142548i	$-0.0455296\pi$
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	−0.618344	+	0.785907i	$0.712196\pi$
$878$	−2.00000	−	3.46410i	−0.0674967	−	0.116908i
$879$		0			0
$880$		0			0
$881$	21.0000	−	36.3731i	0.707508	−	1.22544i	−0.258271	−	0.966073i	$-0.583153\pi$
$881$	21.0000	−	36.3731i	0.707508	−	1.22544i	0.965779	−	0.259367i	$-0.0835140\pi$
$882$		0			0
$883$	−52.0000			−1.74994			−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000			−1.74994			−0.874970	+	0.484178i	$0.839119\pi$
$884$	−3.00000	+	10.3923i	−0.100901	+	0.349531i
$885$		0			0
$886$	4.50000	−	7.79423i	0.151180	−	0.261852i
$887$	1.50000	−	2.59808i	0.0503651	−	0.0872349i	−0.839744	−	0.542983i	$-0.817295\pi$
$887$	1.50000	−	2.59808i	0.0503651	−	0.0872349i	0.890109	+	0.455748i	$0.150628\pi$
$888$		0			0
$889$	8.00000			0.268311
$890$		0			0
$891$		0			0
$892$	8.00000			0.267860
$893$	22.5000	+	38.9711i	0.752934	+	1.30412i
$894$		0			0
$895$		0			0
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	12.0000			0.400445
$899$	6.00000	−	10.3923i	0.200111	−	0.346603i
$900$		0			0
$901$	13.5000	+	23.3827i	0.449750	+	0.778990i
$902$	9.00000			0.299667
$903$		0			0
$904$	6.00000	+	10.3923i	0.199557	+	0.345643i
$905$		0			0
$906$		0			0
$907$	−25.0000	+	43.3013i	−0.830111	+	1.43780i	0.0678380	+	0.997696i	$0.478390\pi$
$907$	−25.0000	+	43.3013i	−0.830111	+	1.43780i	−0.897949	+	0.440099i	$0.854943\pi$
$908$	−9.00000	+	15.5885i	−0.298675	+	0.517321i
$909$		0			0
$910$		0			0
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$		0			0
$913$	9.00000	−	15.5885i	0.297857	−	0.515903i
$914$	−5.00000	−	8.66025i	−0.165385	−	0.286456i
$915$		0			0
$916$	−8.50000	−	14.7224i	−0.280848	−	0.486443i
$917$		0			0
$918$		0			0
$919$	3.50000	+	6.06218i	0.115454	+	0.199973i	0.917961	−	0.396670i	$-0.129834\pi$
$919$	3.50000	+	6.06218i	0.115454	+	0.199973i	−0.802507	+	0.596643i	$0.796501\pi$
$920$		0			0
$921$		0			0
$922$	−12.0000			−0.395199
$923$	15.0000	+	15.5885i	0.493731	+	0.513100i
$924$		0			0
$925$	−10.0000	+	17.3205i	−0.328798	+	0.569495i
$926$	2.50000	−	4.33013i	0.0821551	−	0.142297i
$927$		0			0
$928$	−3.00000			−0.0984798
$929$	−19.5000	−	33.7750i	−0.639774	−	1.10812i	−0.985482	−	0.169779i	$-0.945695\pi$
$929$	−19.5000	−	33.7750i	−0.639774	−	1.10812i	0.345708	−	0.938342i	$-0.387639\pi$
$930$		0			0
$931$	5.00000			0.163868
$932$	−6.00000	−	10.3923i	−0.196537	−	0.340411i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	32.0000			1.04539			0.522697	−	0.852518i	$-0.324926\pi$
$937$	32.0000			1.04539			0.522697	+	0.852518i	$0.324926\pi$
$938$	7.00000	−	12.1244i	0.228558	−	0.395874i
$939$		0			0
$940$		0			0
$941$	−12.0000			−0.391189			−0.195594	−	0.980685i	$-0.562664\pi$
$941$	−12.0000			−0.391189			−0.195594	+	0.980685i	$0.562664\pi$
$942$		0			0
$943$	9.00000	+	15.5885i	0.293080	+	0.507630i
$944$	6.00000			0.195283
$945$		0			0
$946$	−12.0000	+	20.7846i	−0.390154	+	0.675766i
$947$	−13.5000	+	23.3827i	−0.438691	+	0.759835i	−0.997589	−	0.0694014i	$-0.977891\pi$
$947$	−13.5000	+	23.3827i	−0.438691	+	0.759835i	0.558898	+	0.829237i	$0.311224\pi$
$948$		0			0
$949$	14.0000	−	3.46410i	0.454459	−	0.112449i
$950$	25.0000			0.811107
$951$		0			0
$952$	−1.50000	+	2.59808i	−0.0486153	+	0.0842041i
$953$	−18.0000	−	31.1769i	−0.583077	−	1.00992i	−0.995112	−	0.0987513i	$-0.968515\pi$
$953$	−18.0000	−	31.1769i	−0.583077	−	1.00992i	0.412035	−	0.911168i	$-0.364818\pi$
$954$		0			0
$955$		0			0
$956$	3.00000	+	5.19615i	0.0970269	+	0.168056i
$957$		0			0
$958$	−13.5000	−	23.3827i	−0.436165	−	0.755460i
$959$	−9.00000	+	15.5885i	−0.290625	+	0.503378i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	10.0000	+	10.3923i	0.322413	+	0.335061i
$963$		0			0
$964$	−4.00000	+	6.92820i	−0.128831	+	0.223142i
$965$		0			0
$966$		0			0
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$	−1.00000	−	1.73205i	−0.0321412	−	0.0556702i
$969$		0			0
$970$		0			0
$971$	21.0000	+	36.3731i	0.673922	+	1.16727i	0.976783	+	0.214232i	$0.0687250\pi$
$971$	21.0000	+	36.3731i	0.673922	+	1.16727i	−0.302861	+	0.953035i	$0.597942\pi$
$972$		0			0
$973$	6.50000	−	11.2583i	0.208380	−	0.360925i
$974$	−23.0000			−0.736968
$975$		0			0
$976$	5.00000			0.160046
$977$	−12.0000	+	20.7846i	−0.383914	+	0.664959i	−0.991618	−	0.129205i	$-0.958757\pi$
$977$	−12.0000	+	20.7846i	−0.383914	+	0.664959i	0.607704	+	0.794164i	$0.292091\pi$
$978$		0			0
$979$	13.5000	+	23.3827i	0.431462	+	0.747314i
$980$		0			0
$981$		0			0
$982$	−18.0000	−	31.1769i	−0.574403	−	0.994895i
$983$	48.0000			1.53096			0.765481	−	0.643458i	$-0.222501\pi$
$983$	48.0000			1.53096			0.765481	+	0.643458i	$0.222501\pi$
$984$		0			0
$985$		0			0
$986$	−4.50000	+	7.79423i	−0.143309	+	0.248219i
$987$		0			0
$988$	5.00000	−	17.3205i	0.159071	−	0.551039i
$989$	−48.0000			−1.52631
$990$		0			0
$991$	21.5000	−	37.2391i	0.682970	−	1.18294i	−0.291100	−	0.956693i	$-0.594021\pi$
$991$	21.5000	−	37.2391i	0.682970	−	1.18294i	0.974070	−	0.226246i	$-0.0726454\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$		0			0
$994$	3.00000	+	5.19615i	0.0951542	+	0.164812i
$995$		0			0
$996$		0			0
$997$	3.50000	+	6.06218i	0.110846	+	0.191991i	0.916112	−	0.400923i	$-0.131311\pi$
$997$	3.50000	+	6.06218i	0.110846	+	0.191991i	−0.805266	+	0.592914i	$0.797977\pi$
$998$	−20.0000	+	34.6410i	−0.633089	+	1.09654i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.r.r.1387.1		2
3.2	odd	2		546.2.l.a.295.1	yes	2
13.3	even	3	inner	1638.2.r.r.757.1		2
39.17	odd	6		7098.2.a.l.1.1		1
39.29	odd	6		546.2.l.a.211.1	✓	2
39.35	odd	6		7098.2.a.bb.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.a.211.1	✓	2	39.29	odd	6
546.2.l.a.295.1	yes	2	3.2	odd	2
1638.2.r.r.757.1		2	13.3	even	3	inner
1638.2.r.r.1387.1		2	1.1	even	1	trivial
7098.2.a.l.1.1		1	39.17	odd	6
7098.2.a.bb.1.1		1	39.35	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.r (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{11} +(-3.50000 + 0.866025i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-2.50000 - 4.33013i) q^{19} +(-1.50000 - 2.59808i) q^{22} +(3.00000 - 5.19615i) q^{23} -5.00000 q^{25} +(-1.00000 + 3.46410i) q^{26} +(-0.500000 + 0.866025i) q^{28} +(-1.50000 + 2.59808i) q^{29} -4.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +3.00000 q^{34} +(2.00000 - 3.46410i) q^{37} -5.00000 q^{38} +(-1.50000 + 2.59808i) q^{41} +(-4.00000 - 6.92820i) q^{43} -3.00000 q^{44} +(-3.00000 - 5.19615i) q^{46} -9.00000 q^{47} +(-0.500000 + 0.866025i) q^{49} +(-2.50000 + 4.33013i) q^{50} +(2.50000 + 2.59808i) q^{52} +9.00000 q^{53} +(0.500000 + 0.866025i) q^{56} +(1.50000 + 2.59808i) q^{58} +(-3.00000 - 5.19615i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(-2.00000 + 3.46410i) q^{62} +1.00000 q^{64} +(-7.00000 + 12.1244i) q^{67} +(1.50000 - 2.59808i) q^{68} +(-3.00000 - 5.19615i) q^{71} -4.00000 q^{73} +(-2.00000 - 3.46410i) q^{74} +(-2.50000 + 4.33013i) q^{76} -3.00000 q^{77} -1.00000 q^{79} +(1.50000 + 2.59808i) q^{82} +6.00000 q^{83} -8.00000 q^{86} +(-1.50000 + 2.59808i) q^{88} +(-4.50000 + 7.79423i) q^{89} +(2.50000 + 2.59808i) q^{91} -6.00000 q^{92} +(-4.50000 + 7.79423i) q^{94} +(-4.00000 - 6.92820i) q^{97} +(0.500000 + 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 - q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} - q^{7} - 2 q^{8} + 3 q^{11} - 7 q^{13} - 2 q^{14} - q^{16} + 3 q^{17} - 5 q^{19} - 3 q^{22} + 6 q^{23} - 10 q^{25} - 2 q^{26} - q^{28} - 3 q^{29} - 8 q^{31} + q^{32} + 6 q^{34} + 4 q^{37} - 10 q^{38} - 3 q^{41} - 8 q^{43} - 6 q^{44} - 6 q^{46} - 18 q^{47} - q^{49} - 5 q^{50} + 5 q^{52} + 18 q^{53} + q^{56} + 3 q^{58} - 6 q^{59} - 5 q^{61} - 4 q^{62} + 2 q^{64} - 14 q^{67} + 3 q^{68} - 6 q^{71} - 8 q^{73} - 4 q^{74} - 5 q^{76} - 6 q^{77} - 2 q^{79} + 3 q^{82} + 12 q^{83} - 16 q^{86} - 3 q^{88} - 9 q^{89} + 5 q^{91} - 12 q^{92} - 9 q^{94} - 8 q^{97} + q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 - q^7 - 2 * q^8 + 3 * q^11 - 7 * q^13 - 2 * q^14 - q^16 + 3 * q^17 - 5 * q^19 - 3 * q^22 + 6 * q^23 - 10 * q^25 - 2 * q^26 - q^28 - 3 * q^29 - 8 * q^31 + q^32 + 6 * q^34 + 4 * q^37 - 10 * q^38 - 3 * q^41 - 8 * q^43 - 6 * q^44 - 6 * q^46 - 18 * q^47 - q^49 - 5 * q^50 + 5 * q^52 + 18 * q^53 + q^56 + 3 * q^58 - 6 * q^59 - 5 * q^61 - 4 * q^62 + 2 * q^64 - 14 * q^67 + 3 * q^68 - 6 * q^71 - 8 * q^73 - 4 * q^74 - 5 * q^76 - 6 * q^77 - 2 * q^79 + 3 * q^82 + 12 * q^83 - 16 * q^86 - 3 * q^88 - 9 * q^89 + 5 * q^91 - 12 * q^92 - 9 * q^94 - 8 * q^97 + q^98

Introduction

L-functions

Modular forms

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