LMFDB - Embedded newform 2646.2.f.c.883.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(883,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("2646.883");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$21.1284163748$
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 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			883.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2646.883
Dual form			2646.2.f.c.1765.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +1.00000 q^{8} -3.00000 q^{10} +(-3.00000 + 5.19615i) q^{11} +(1.00000 + 1.73205i) q^{13} +(-0.500000 + 0.866025i) q^{16} +6.00000 q^{17} +7.00000 q^{19} +(1.50000 - 2.59808i) q^{20} +(-3.00000 - 5.19615i) q^{22} +(1.50000 + 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} -2.00000 q^{26} +(3.00000 - 5.19615i) q^{29} +(1.00000 + 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{34} +2.00000 q^{37} +(-3.50000 + 6.06218i) q^{38} +(1.50000 + 2.59808i) q^{40} +(-1.00000 + 1.73205i) q^{43} +6.00000 q^{44} -3.00000 q^{46} +(-2.00000 - 3.46410i) q^{50} +(1.00000 - 1.73205i) q^{52} -6.00000 q^{53} -18.0000 q^{55} +(3.00000 + 5.19615i) q^{58} +(2.50000 - 4.33013i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} +(-4.00000 - 6.92820i) q^{67} +(-3.00000 - 5.19615i) q^{68} -3.00000 q^{71} -2.00000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(-3.50000 - 6.06218i) q^{76} +(-2.50000 + 4.33013i) q^{79} -3.00000 q^{80} +(-6.00000 + 10.3923i) q^{83} +(9.00000 + 15.5885i) q^{85} +(-1.00000 - 1.73205i) q^{86} +(-3.00000 + 5.19615i) q^{88} +(1.50000 - 2.59808i) q^{92} +(10.5000 + 18.1865i) q^{95} +(1.00000 - 1.73205i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + 3 q^{5} + 2 q^{8} - 6 q^{10} - 6 q^{11} + 2 q^{13} - q^{16} + 12 q^{17} + 14 q^{19} + 3 q^{20} - 6 q^{22} + 3 q^{23} - 4 q^{25} - 4 q^{26} + 6 q^{29} + 2 q^{31} - q^{32} - 6 q^{34}+ \cdots + 2 q^{97}+O(q^{100}) $ 2 * q - q^2 - q^4 + 3 * q^5 + 2 * q^8 - 6 * q^10 - 6 * q^11 + 2 * q^13 - q^16 + 12 * q^17 + 14 * q^19 + 3 * q^20 - 6 * q^22 + 3 * q^23 - 4 * q^25 - 4 * q^26 + 6 * q^29 + 2 * q^31 - q^32 - 6 * q^34 + 4 * q^37 - 7 * q^38 + 3 * q^40 - 2 * q^43 + 12 * q^44 - 6 * q^46 - 4 * q^50 + 2 * q^52 - 12 * q^53 - 36 * q^55 + 6 * q^58 + 5 * q^61 - 4 * q^62 + 2 * q^64 - 6 * q^65 - 8 * q^67 - 6 * q^68 - 6 * q^71 - 4 * q^73 - 2 * q^74 - 7 * q^76 - 5 * q^79 - 6 * q^80 - 12 * q^83 + 18 * q^85 - 2 * q^86 - 6 * q^88 + 3 * q^92 + 21 * q^95 + 2 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	−3.00000			−0.948683
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.0829925	+	0.996550i	$0.526448\pi$
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.821541	+	0.570149i	$0.806886\pi$
$12$		0			0
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.00000			1.45521			0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000			1.45521			0.727607	+	0.685994i	$0.240633\pi$
$18$		0			0
$19$	7.00000			1.60591			0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000			1.60591			0.802955	+	0.596040i	$0.203260\pi$
$20$	1.50000	−	2.59808i	0.335410	−	0.580948i
$21$		0			0
$22$	−3.00000	−	5.19615i	−0.639602	−	1.10782i
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$		0			0
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	−2.00000			−0.392232
$27$		0			0
$28$		0			0
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$		0			0
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−3.00000	+	5.19615i	−0.514496	+	0.891133i
$35$		0			0
$36$		0			0
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	−3.50000	+	6.06218i	−0.567775	+	0.983415i
$39$		0			0
$40$	1.50000	+	2.59808i	0.237171	+	0.410792i
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$		0			0
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	−0.932145	−	0.362084i	$-0.882065\pi$
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	0.779647	+	0.626219i	$0.215399\pi$
$44$	6.00000			0.904534
$45$		0			0
$46$	−3.00000			−0.442326
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$		0			0
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$		0			0
$52$	1.00000	−	1.73205i	0.138675	−	0.240192i
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$	−18.0000			−2.42712
$56$		0			0
$57$		0			0
$58$	3.00000	+	5.19615i	0.393919	+	0.682288i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	−0.660415	−	0.750901i	$-0.729619\pi$
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	0.980507	+	0.196485i	$0.0629528\pi$
$62$	−2.00000			−0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.00000	+	5.19615i	−0.372104	+	0.644503i
$66$		0			0
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$		0			0
$70$		0			0
$71$	−3.00000			−0.356034			−0.178017	−	0.984027i	$-0.556968\pi$
$71$	−3.00000			−0.356034			−0.178017	+	0.984027i	$0.556968\pi$
$72$		0			0
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$	−1.00000	+	1.73205i	−0.116248	+	0.201347i
$75$		0			0
$76$	−3.50000	−	6.06218i	−0.401478	−	0.695379i
$77$		0			0
$78$		0			0
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	−0.971698	−	0.236225i	$-0.924090\pi$
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	0.690426	+	0.723403i	$0.257423\pi$
$80$	−3.00000			−0.335410
$81$		0			0
$82$		0			0
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	0.322396	+	0.946605i	$0.395512\pi$
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	−0.980982	+	0.194099i	$0.937822\pi$
$84$		0			0
$85$	9.00000	+	15.5885i	0.976187	+	1.69081i
$86$	−1.00000	−	1.73205i	−0.107833	−	0.186772i
$87$		0			0
$88$	−3.00000	+	5.19615i	−0.319801	+	0.553912i
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$		0			0
$91$		0			0
$92$	1.50000	−	2.59808i	0.156386	−	0.270868i
$93$		0			0
$94$		0			0
$95$	10.5000	+	18.1865i	1.07728	+	1.86590i
$96$		0			0
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	−0.810782	−	0.585348i	$-0.800958\pi$
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	0.912317	+	0.409484i	$0.134291\pi$
$98$		0			0
$99$		0			0
$100$	4.00000			0.400000
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	−0.998240	−	0.0592978i	$-0.981114\pi$
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	0.550474	+	0.834853i	$0.314447\pi$
$102$		0			0
$103$	−5.00000	−	8.66025i	−0.492665	−	0.853320i	0.507300	−	0.861770i	$-0.330644\pi$
$103$	−5.00000	−	8.66025i	−0.492665	−	0.853320i	−0.999964	+	0.00844953i	$0.997310\pi$
$104$	1.00000	+	1.73205i	0.0980581	+	0.169842i
$105$		0			0
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$		0			0
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$	9.00000	−	15.5885i	0.858116	−	1.48630i
$111$		0			0
$112$		0			0
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	0.966496	+	0.256681i	$0.0826291\pi$
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	−0.260955	+	0.965351i	$0.584038\pi$
$114$		0			0
$115$	−4.50000	+	7.79423i	−0.419627	+	0.726816i
$116$	−6.00000			−0.557086
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$	2.50000	+	4.33013i	0.226339	+	0.392031i
$123$		0			0
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$	3.00000			0.268328
$126$		0			0
$127$	17.0000			1.50851			0.754253	−	0.656584i	$-0.227999\pi$
$127$	17.0000			1.50851			0.754253	+	0.656584i	$0.227999\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−3.00000	−	5.19615i	−0.263117	−	0.455733i
$131$	4.50000	+	7.79423i	0.393167	+	0.680985i	0.992865	−	0.119241i	$-0.0380462\pi$
$131$	4.50000	+	7.79423i	0.393167	+	0.680985i	−0.599699	+	0.800226i	$0.704713\pi$
$132$		0			0
$133$		0			0
$134$	8.00000			0.691095
$135$		0			0
$136$	6.00000			0.514496
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	−0.708942	−	0.705266i	$-0.750827\pi$
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	0.965250	+	0.261329i	$0.0841608\pi$
$138$		0			0
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	0.952355	−	0.304991i	$-0.0986536\pi$
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	−0.740308	+	0.672268i	$0.765320\pi$
$140$		0			0
$141$		0			0
$142$	1.50000	−	2.59808i	0.125877	−	0.218026i
$143$	−12.0000			−1.00349
$144$		0			0
$145$	18.0000			1.49482
$146$	1.00000	−	1.73205i	0.0827606	−	0.143346i
$147$		0			0
$148$	−1.00000	−	1.73205i	−0.0821995	−	0.142374i
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$		0			0
$151$	−11.5000	+	19.9186i	−0.935857	+	1.62095i	−0.162758	+	0.986666i	$0.552039\pi$
$151$	−11.5000	+	19.9186i	−0.935857	+	1.62095i	−0.773099	+	0.634285i	$0.781294\pi$
$152$	7.00000			0.567775
$153$		0			0
$154$		0			0
$155$	−3.00000	+	5.19615i	−0.240966	+	0.417365i
$156$		0			0
$157$	−6.50000	−	11.2583i	−0.518756	−	0.898513i	−0.999762	−	0.0217953i	$-0.993062\pi$
$157$	−6.50000	−	11.2583i	−0.518756	−	0.898513i	0.481006	−	0.876717i	$-0.340272\pi$
$158$	−2.50000	−	4.33013i	−0.198889	−	0.344486i
$159$		0			0
$160$	1.50000	−	2.59808i	0.118585	−	0.205396i
$161$		0			0
$162$		0			0
$163$	2.00000			0.156652			0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000			0.156652			0.0783260	+	0.996928i	$0.475042\pi$
$164$		0			0
$165$		0			0
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$167$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	−18.0000			−1.38054
$171$		0			0
$172$	2.00000			0.152499
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		0			0
$175$		0			0
$176$	−3.00000	−	5.19615i	−0.226134	−	0.391675i
$177$		0			0
$178$		0			0
$179$	−18.0000			−1.34538			−0.672692	−	0.739923i	$-0.734862\pi$
$179$	−18.0000			−1.34538			−0.672692	+	0.739923i	$0.734862\pi$
$180$		0			0
$181$	25.0000			1.85824			0.929118	−	0.369784i	$-0.120568\pi$
$181$	25.0000			1.85824			0.929118	+	0.369784i	$0.120568\pi$
$182$		0			0
$183$		0			0
$184$	1.50000	+	2.59808i	0.110581	+	0.191533i
$185$	3.00000	+	5.19615i	0.220564	+	0.382029i
$186$		0			0
$187$	−18.0000	+	31.1769i	−1.31629	+	2.27988i
$188$		0			0
$189$		0			0
$190$	−21.0000			−1.52350
$191$	−4.50000	+	7.79423i	−0.325609	+	0.563971i	−0.981635	−	0.190767i	$-0.938902\pi$
$191$	−4.50000	+	7.79423i	−0.325609	+	0.563971i	0.656027	+	0.754738i	$0.272236\pi$
$192$		0			0
$193$	−8.50000	−	14.7224i	−0.611843	−	1.05974i	−0.990930	−	0.134382i	$-0.957095\pi$
$193$	−8.50000	−	14.7224i	−0.611843	−	1.05974i	0.379086	−	0.925361i	$-0.376238\pi$
$194$	1.00000	+	1.73205i	0.0717958	+	0.124354i
$195$		0			0
$196$		0			0
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	−14.0000			−0.992434			−0.496217	−	0.868199i	$-0.665278\pi$
$199$	−14.0000			−0.992434			−0.496217	+	0.868199i	$0.665278\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$		0			0
$202$	−4.50000	−	7.79423i	−0.316619	−	0.548400i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	10.0000			0.696733
$207$		0			0
$208$	−2.00000			−0.138675
$209$	−21.0000	+	36.3731i	−1.45260	+	2.51598i
$210$		0			0
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	0.694857	−	0.719148i	$-0.255467\pi$
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	−0.970229	+	0.242190i	$0.922134\pi$
$212$	3.00000	+	5.19615i	0.206041	+	0.356873i
$213$		0			0
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$	−6.00000			−0.409197
$216$		0			0
$217$		0			0
$218$	5.00000	−	8.66025i	0.338643	−	0.586546i
$219$		0			0
$220$	9.00000	+	15.5885i	0.606780	+	1.05097i
$221$	6.00000	+	10.3923i	0.403604	+	0.699062i
$222$		0			0
$223$	−14.0000	+	24.2487i	−0.937509	+	1.62381i	−0.167412	+	0.985887i	$0.553541\pi$
$223$	−14.0000	+	24.2487i	−0.937509	+	1.62381i	−0.770097	+	0.637927i	$0.779792\pi$
$224$		0			0
$225$		0			0
$226$	−15.0000			−0.997785
$227$	7.50000	−	12.9904i	0.497792	−	0.862202i	−0.502204	−	0.864749i	$-0.667477\pi$
$227$	7.50000	−	12.9904i	0.497792	−	0.862202i	0.999997	+	0.00254715i	$0.000810783\pi$
$228$		0			0
$229$	−0.500000	−	0.866025i	−0.0330409	−	0.0572286i	0.849032	−	0.528341i	$-0.177186\pi$
$229$	−0.500000	−	0.866025i	−0.0330409	−	0.0572286i	−0.882073	+	0.471113i	$0.843853\pi$
$230$	−4.50000	−	7.79423i	−0.296721	−	0.513936i
$231$		0			0
$232$	3.00000	−	5.19615i	0.196960	−	0.341144i
$233$	−9.00000			−0.589610			−0.294805	−	0.955557i	$-0.595255\pi$
$233$	−9.00000			−0.589610			−0.294805	+	0.955557i	$0.595255\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.50000	−	12.9904i	−0.485135	−	0.840278i	0.514719	−	0.857359i	$-0.327896\pi$
$239$	−7.50000	−	12.9904i	−0.485135	−	0.840278i	−0.999854	+	0.0170808i	$0.994563\pi$
$240$		0			0
$241$	4.00000	−	6.92820i	0.257663	−	0.446285i	−0.707953	−	0.706260i	$-0.750381\pi$
$241$	4.00000	−	6.92820i	0.257663	−	0.446285i	0.965615	+	0.259975i	$0.0837143\pi$
$242$	25.0000			1.60706
$243$		0			0
$244$	−5.00000			−0.320092
$245$		0			0
$246$		0			0
$247$	7.00000	+	12.1244i	0.445399	+	0.771454i
$248$	1.00000	+	1.73205i	0.0635001	+	0.109985i
$249$		0			0
$250$	−1.50000	+	2.59808i	−0.0948683	+	0.164317i
$251$	3.00000			0.189358			0.0946792	−	0.995508i	$-0.469817\pi$
$251$	3.00000			0.189358			0.0946792	+	0.995508i	$0.469817\pi$
$252$		0			0
$253$	−18.0000			−1.13165
$254$	−8.50000	+	14.7224i	−0.533337	+	0.923768i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	−0.997374	−	0.0724199i	$-0.976928\pi$
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	0.435970	−	0.899961i	$-0.356405\pi$
$258$		0			0
$259$		0			0
$260$	6.00000			0.372104
$261$		0			0
$262$	−9.00000			−0.556022
$263$	−10.5000	+	18.1865i	−0.647458	+	1.12143i	0.336270	+	0.941766i	$0.390834\pi$
$263$	−10.5000	+	18.1865i	−0.647458	+	1.12143i	−0.983728	+	0.179664i	$0.942499\pi$
$264$		0			0
$265$	−9.00000	−	15.5885i	−0.552866	−	0.957591i
$266$		0			0
$267$		0			0
$268$	−4.00000	+	6.92820i	−0.244339	+	0.423207i
$269$	−9.00000			−0.548740			−0.274370	−	0.961624i	$-0.588469\pi$
$269$	−9.00000			−0.548740			−0.274370	+	0.961624i	$0.588469\pi$
$270$		0			0
$271$	28.0000			1.70088			0.850439	−	0.526073i	$-0.176336\pi$
$271$	28.0000			1.70088			0.850439	+	0.526073i	$0.176336\pi$
$272$	−3.00000	+	5.19615i	−0.181902	+	0.315063i
$273$		0			0
$274$	3.00000	+	5.19615i	0.181237	+	0.313911i
$275$	−12.0000	−	20.7846i	−0.723627	−	1.25336i
$276$		0			0
$277$	8.00000	−	13.8564i	0.480673	−	0.832551i	−0.519081	−	0.854725i	$-0.673726\pi$
$277$	8.00000	−	13.8564i	0.480673	−	0.832551i	0.999754	+	0.0221745i	$0.00705893\pi$
$278$	−5.00000			−0.299880
$279$		0			0
$280$		0			0
$281$	−13.5000	+	23.3827i	−0.805342	+	1.39489i	0.110717	+	0.993852i	$0.464685\pi$
$281$	−13.5000	+	23.3827i	−0.805342	+	1.39489i	−0.916060	+	0.401042i	$0.868648\pi$
$282$		0			0
$283$	−9.50000	−	16.4545i	−0.564716	−	0.978117i	−0.997076	−	0.0764162i	$-0.975652\pi$
$283$	−9.50000	−	16.4545i	−0.564716	−	0.978117i	0.432360	−	0.901701i	$-0.357681\pi$
$284$	1.50000	+	2.59808i	0.0890086	+	0.154167i
$285$		0			0
$286$	6.00000	−	10.3923i	0.354787	−	0.614510i
$287$		0			0
$288$		0			0
$289$	19.0000			1.11765
$290$	−9.00000	+	15.5885i	−0.528498	+	0.915386i
$291$		0			0
$292$	1.00000	+	1.73205i	0.0585206	+	0.101361i
$293$	1.50000	+	2.59808i	0.0876309	+	0.151781i	0.906509	−	0.422186i	$-0.138737\pi$
$293$	1.50000	+	2.59808i	0.0876309	+	0.151781i	−0.818878	+	0.573967i	$0.805404\pi$
$294$		0			0
$295$		0			0
$296$	2.00000			0.116248
$297$		0			0
$298$	6.00000			0.347571
$299$	−3.00000	+	5.19615i	−0.173494	+	0.300501i
$300$		0			0
$301$		0			0
$302$	−11.5000	−	19.9186i	−0.661751	−	1.14619i
$303$		0			0
$304$	−3.50000	+	6.06218i	−0.200739	+	0.347690i
$305$	15.0000			0.858898
$306$		0			0
$307$	25.0000			1.42683			0.713413	−	0.700744i	$-0.247149\pi$
$307$	25.0000			1.42683			0.713413	+	0.700744i	$0.247149\pi$
$308$		0			0
$309$		0			0
$310$	−3.00000	−	5.19615i	−0.170389	−	0.295122i
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	0.644246	−	0.764818i	$-0.277171\pi$
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	−0.984475	+	0.175525i	$0.943838\pi$
$312$		0			0
$313$	−5.00000	+	8.66025i	−0.282617	+	0.489506i	−0.972028	−	0.234863i	$-0.924536\pi$
$313$	−5.00000	+	8.66025i	−0.282617	+	0.489506i	0.689412	+	0.724370i	$0.257869\pi$
$314$	13.0000			0.733632
$315$		0			0
$316$	5.00000			0.281272
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$		0			0
$319$	18.0000	+	31.1769i	1.00781	+	1.74557i
$320$	1.50000	+	2.59808i	0.0838525	+	0.145237i
$321$		0			0
$322$		0			0
$323$	42.0000			2.33694
$324$		0			0
$325$	−8.00000			−0.443760
$326$	−1.00000	+	1.73205i	−0.0553849	+	0.0959294i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−13.0000	+	22.5167i	−0.714545	+	1.23763i	0.248590	+	0.968609i	$0.420033\pi$
$331$	−13.0000	+	22.5167i	−0.714545	+	1.23763i	−0.963135	+	0.269019i	$0.913301\pi$
$332$	12.0000			0.658586
$333$		0			0
$334$		0			0
$335$	12.0000	−	20.7846i	0.655630	−	1.13558i
$336$		0			0
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	0.992938	+	0.118633i	$0.0378512\pi$
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	−0.393730	+	0.919226i	$0.628816\pi$
$338$	4.50000	+	7.79423i	0.244768	+	0.423950i
$339$		0			0
$340$	9.00000	−	15.5885i	0.488094	−	0.845403i
$341$	−12.0000			−0.649836
$342$		0			0
$343$		0			0
$344$	−1.00000	+	1.73205i	−0.0539164	+	0.0933859i
$345$		0			0
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	−12.0000	−	20.7846i	−0.644194	−	1.11578i	−0.984487	−	0.175457i	$-0.943860\pi$
$347$	−12.0000	−	20.7846i	−0.644194	−	1.11578i	0.340293	−	0.940319i	$-0.389474\pi$
$348$		0			0
$349$	13.0000	−	22.5167i	0.695874	−	1.20529i	−0.274011	−	0.961727i	$-0.588351\pi$
$349$	13.0000	−	22.5167i	0.695874	−	1.20529i	0.969885	−	0.243563i	$-0.0783162\pi$
$350$		0			0
$351$		0			0
$352$	6.00000			0.319801
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	−0.520689	−	0.853746i	$-0.674325\pi$
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	0.999711	+	0.0240566i	$0.00765819\pi$
$354$		0			0
$355$	−4.50000	−	7.79423i	−0.238835	−	0.413675i
$356$		0			0
$357$		0			0
$358$	9.00000	−	15.5885i	0.475665	−	0.823876i
$359$	3.00000			0.158334			0.0791670	−	0.996861i	$-0.474774\pi$
$359$	3.00000			0.158334			0.0791670	+	0.996861i	$0.474774\pi$
$360$		0			0
$361$	30.0000			1.57895
$362$	−12.5000	+	21.6506i	−0.656985	+	1.13793i
$363$		0			0
$364$		0			0
$365$	−3.00000	−	5.19615i	−0.157027	−	0.271979i
$366$		0			0
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	−0.742538	−	0.669804i	$-0.766378\pi$
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	0.951336	+	0.308155i	$0.0997115\pi$
$368$	−3.00000			−0.156386
$369$		0			0
$370$	−6.00000			−0.311925
$371$		0			0
$372$		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	$0.951392\pi$
$374$	−18.0000	−	31.1769i	−0.930758	−	1.61212i
$375$		0			0
$376$		0			0
$377$	12.0000			0.618031
$378$		0			0
$379$	2.00000			0.102733			0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000			0.102733			0.0513665	+	0.998680i	$0.483642\pi$
$380$	10.5000	−	18.1865i	0.538639	−	0.932949i
$381$		0			0
$382$	−4.50000	−	7.79423i	−0.230240	−	0.398787i
$383$	9.00000	+	15.5885i	0.459879	+	0.796533i	0.998954	−	0.0457244i	$-0.0145596\pi$
$383$	9.00000	+	15.5885i	0.459879	+	0.796533i	−0.539076	+	0.842257i	$0.681226\pi$
$384$		0			0
$385$		0			0
$386$	17.0000			0.865277
$387$		0			0
$388$	−2.00000			−0.101535
$389$	12.0000	−	20.7846i	0.608424	−	1.05382i	−0.383076	−	0.923717i	$-0.625135\pi$
$389$	12.0000	−	20.7846i	0.608424	−	1.05382i	0.991500	−	0.130105i	$-0.0415314\pi$
$390$		0			0
$391$	9.00000	+	15.5885i	0.455150	+	0.788342i
$392$		0			0
$393$		0			0
$394$	9.00000	−	15.5885i	0.453413	−	0.785335i
$395$	−15.0000			−0.754732
$396$		0			0
$397$	−26.0000			−1.30490			−0.652451	−	0.757831i	$-0.726259\pi$
$397$	−26.0000			−1.30490			−0.652451	+	0.757831i	$0.726259\pi$
$398$	7.00000	−	12.1244i	0.350878	−	0.607739i
$399$		0			0
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	0.901046	−	0.433724i	$-0.142801\pi$
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	−0.826139	+	0.563466i	$0.809468\pi$
$402$		0			0
$403$	−2.00000	+	3.46410i	−0.0996271	+	0.172559i
$404$	9.00000			0.447767
$405$		0			0
$406$		0			0
$407$	−6.00000	+	10.3923i	−0.297409	+	0.515127i
$408$		0			0
$409$	16.0000	+	27.7128i	0.791149	+	1.37031i	0.925256	+	0.379344i	$0.123850\pi$
$409$	16.0000	+	27.7128i	0.791149	+	1.37031i	−0.134107	+	0.990967i	$0.542817\pi$
$410$		0			0
$411$		0			0
$412$	−5.00000	+	8.66025i	−0.246332	+	0.426660i
$413$		0			0
$414$		0			0
$415$	−36.0000			−1.76717
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$		0			0
$418$	−21.0000	−	36.3731i	−1.02714	−	1.77906i
$419$	−7.50000	−	12.9904i	−0.366399	−	0.634622i	0.622601	−	0.782540i	$-0.286076\pi$
$419$	−7.50000	−	12.9904i	−0.366399	−	0.634622i	−0.989000	+	0.147918i	$0.952743\pi$
$420$		0			0
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	−0.718076	−	0.695965i	$-0.754977\pi$
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	0.961761	+	0.273890i	$0.0883103\pi$
$422$	8.00000			0.389434
$423$		0			0
$424$	−6.00000			−0.291386
$425$	−12.0000	+	20.7846i	−0.582086	+	1.00820i
$426$		0			0
$427$		0			0
$428$	−6.00000	−	10.3923i	−0.290021	−	0.502331i
$429$		0			0
$430$	3.00000	−	5.19615i	0.144673	−	0.250581i
$431$	−12.0000			−0.578020			−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000			−0.578020			−0.289010	+	0.957326i	$0.593326\pi$
$432$		0			0
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$		0			0
$436$	5.00000	+	8.66025i	0.239457	+	0.414751i
$437$	10.5000	+	18.1865i	0.502283	+	0.869980i
$438$		0			0
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	−0.754642	−	0.656136i	$-0.772190\pi$
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	0.945552	+	0.325471i	$0.105523\pi$
$440$	−18.0000			−0.858116
$441$		0			0
$442$	−12.0000			−0.570782
$443$	9.00000	−	15.5885i	0.427603	−	0.740630i	−0.569057	−	0.822298i	$-0.692691\pi$
$443$	9.00000	−	15.5885i	0.427603	−	0.740630i	0.996660	+	0.0816684i	$0.0260248\pi$
$444$		0			0
$445$		0			0
$446$	−14.0000	−	24.2487i	−0.662919	−	1.14821i
$447$		0			0
$448$		0			0
$449$	−33.0000			−1.55737			−0.778683	−	0.627417i	$-0.784112\pi$
$449$	−33.0000			−1.55737			−0.778683	+	0.627417i	$0.784112\pi$
$450$		0			0
$451$		0			0
$452$	7.50000	−	12.9904i	0.352770	−	0.611016i
$453$		0			0
$454$	7.50000	+	12.9904i	0.351992	+	0.609669i
$455$		0			0
$456$		0			0
$457$	−14.5000	+	25.1147i	−0.678281	+	1.17482i	0.297217	+	0.954810i	$0.403942\pi$
$457$	−14.5000	+	25.1147i	−0.678281	+	1.17482i	−0.975498	+	0.220008i	$0.929392\pi$
$458$	1.00000			0.0467269
$459$		0			0
$460$	9.00000			0.419627
$461$	16.5000	−	28.5788i	0.768482	−	1.33105i	−0.169904	−	0.985461i	$-0.554346\pi$
$461$	16.5000	−	28.5788i	0.768482	−	1.33105i	0.938386	−	0.345589i	$-0.112321\pi$
$462$		0			0
$463$	6.50000	+	11.2583i	0.302081	+	0.523219i	0.976607	−	0.215032i	$-0.0689855\pi$
$463$	6.50000	+	11.2583i	0.302081	+	0.523219i	−0.674526	+	0.738251i	$0.735652\pi$
$464$	3.00000	+	5.19615i	0.139272	+	0.241225i
$465$		0			0
$466$	4.50000	−	7.79423i	0.208458	−	0.361061i
$467$	12.0000			0.555294			0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000			0.555294			0.277647	+	0.960683i	$0.410445\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−6.00000	−	10.3923i	−0.275880	−	0.477839i
$474$		0			0
$475$	−14.0000	+	24.2487i	−0.642364	+	1.11261i
$476$		0			0
$477$		0			0
$478$	15.0000			0.686084
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	−0.789314	−	0.613990i	$-0.789564\pi$
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	0.926388	+	0.376571i	$0.122897\pi$
$480$		0			0
$481$	2.00000	+	3.46410i	0.0911922	+	0.157949i
$482$	4.00000	+	6.92820i	0.182195	+	0.315571i
$483$		0			0
$484$	−12.5000	+	21.6506i	−0.568182	+	0.984120i
$485$	6.00000			0.272446
$486$		0			0
$487$	29.0000			1.31412			0.657058	−	0.753840i	$-0.271801\pi$
$487$	29.0000			1.31412			0.657058	+	0.753840i	$0.271801\pi$
$488$	2.50000	−	4.33013i	0.113170	−	0.196016i
$489$		0			0
$490$		0			0
$491$	9.00000	+	15.5885i	0.406164	+	0.703497i	0.994456	−	0.105151i	$-0.0335327\pi$
$491$	9.00000	+	15.5885i	0.406164	+	0.703497i	−0.588292	+	0.808649i	$0.700199\pi$
$492$		0			0
$493$	18.0000	−	31.1769i	0.810679	−	1.40414i
$494$	−14.0000			−0.629890
$495$		0			0
$496$	−2.00000			−0.0898027
$497$		0			0
$498$		0			0
$499$	−16.0000	−	27.7128i	−0.716258	−	1.24060i	−0.962472	−	0.271380i	$-0.912520\pi$
$499$	−16.0000	−	27.7128i	−0.716258	−	1.24060i	0.246214	−	0.969216i	$-0.420813\pi$
$500$	−1.50000	−	2.59808i	−0.0670820	−	0.116190i
$501$		0			0
$502$	−1.50000	+	2.59808i	−0.0669483	+	0.115958i
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$	−27.0000			−1.20148
$506$	9.00000	−	15.5885i	0.400099	−	0.692991i
$507$		0			0
$508$	−8.50000	−	14.7224i	−0.377127	−	0.653202i
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	−0.979322	−	0.202306i	$-0.935156\pi$
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	0.314459	−	0.949271i	$-0.398177\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	18.0000			0.793946
$515$	15.0000	−	25.9808i	0.660979	−	1.14485i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−3.00000	+	5.19615i	−0.131559	+	0.227866i
$521$	24.0000			1.05146			0.525730	−	0.850652i	$-0.323792\pi$
$521$	24.0000			1.05146			0.525730	+	0.850652i	$0.323792\pi$
$522$		0			0
$523$	13.0000			0.568450			0.284225	−	0.958758i	$-0.408264\pi$
$523$	13.0000			0.568450			0.284225	+	0.958758i	$0.408264\pi$
$524$	4.50000	−	7.79423i	0.196583	−	0.340492i
$525$		0			0
$526$	−10.5000	−	18.1865i	−0.457822	−	0.792971i
$527$	6.00000	+	10.3923i	0.261364	+	0.452696i
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	18.0000			0.781870
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	18.0000	+	31.1769i	0.778208	+	1.34790i
$536$	−4.00000	−	6.92820i	−0.172774	−	0.299253i
$537$		0			0
$538$	4.50000	−	7.79423i	0.194009	−	0.336033i
$539$		0			0
$540$		0			0
$541$	38.0000			1.63375			0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000			1.63375			0.816874	+	0.576816i	$0.195705\pi$
$542$	−14.0000	+	24.2487i	−0.601351	+	1.04157i
$543$		0			0
$544$	−3.00000	−	5.19615i	−0.128624	−	0.222783i
$545$	−15.0000	−	25.9808i	−0.642529	−	1.11289i
$546$		0			0
$547$	−16.0000	+	27.7128i	−0.684111	+	1.18491i	0.289605	+	0.957146i	$0.406476\pi$
$547$	−16.0000	+	27.7128i	−0.684111	+	1.18491i	−0.973715	+	0.227768i	$0.926857\pi$
$548$	−6.00000			−0.256307
$549$		0			0
$550$	24.0000			1.02336
$551$	21.0000	−	36.3731i	0.894630	−	1.54954i
$552$		0			0
$553$		0			0
$554$	8.00000	+	13.8564i	0.339887	+	0.588702i
$555$		0			0
$556$	2.50000	−	4.33013i	0.106024	−	0.183638i
$557$	24.0000			1.01691			0.508456	−	0.861088i	$-0.330216\pi$
$557$	24.0000			1.01691			0.508456	+	0.861088i	$0.330216\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$		0			0
$561$		0			0
$562$	−13.5000	−	23.3827i	−0.569463	−	0.986339i
$563$	16.5000	+	28.5788i	0.695392	+	1.20445i	0.970048	+	0.242912i	$0.0781026\pi$
$563$	16.5000	+	28.5788i	0.695392	+	1.20445i	−0.274656	+	0.961542i	$0.588564\pi$
$564$		0			0
$565$	−22.5000	+	38.9711i	−0.946582	+	1.63953i
$566$	19.0000			0.798630
$567$		0			0
$568$	−3.00000			−0.125877
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	−0.990668	−	0.136295i	$-0.956481\pi$
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	0.613369	+	0.789797i	$0.289814\pi$
$570$		0			0
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	0.308443	−	0.951243i	$-0.400192\pi$
$572$	6.00000	+	10.3923i	0.250873	+	0.434524i
$573$		0			0
$574$		0			0
$575$	−12.0000			−0.500435
$576$		0			0
$577$	4.00000			0.166522			0.0832611	−	0.996528i	$-0.473466\pi$
$577$	4.00000			0.166522			0.0832611	+	0.996528i	$0.473466\pi$
$578$	−9.50000	+	16.4545i	−0.395148	+	0.684416i
$579$		0			0
$580$	−9.00000	−	15.5885i	−0.373705	−	0.647275i
$581$		0			0
$582$		0			0
$583$	18.0000	−	31.1769i	0.745484	−	1.29122i
$584$	−2.00000			−0.0827606
$585$		0			0
$586$	−3.00000			−0.123929
$587$	1.50000	−	2.59808i	0.0619116	−	0.107234i	−0.833408	−	0.552658i	$-0.813614\pi$
$587$	1.50000	−	2.59808i	0.0619116	−	0.107234i	0.895320	+	0.445424i	$0.146947\pi$
$588$		0			0
$589$	7.00000	+	12.1244i	0.288430	+	0.499575i
$590$		0			0
$591$		0			0
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$	−3.00000	+	5.19615i	−0.122885	+	0.212843i
$597$		0			0
$598$	−3.00000	−	5.19615i	−0.122679	−	0.212486i
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	0.509631	−	0.860393i	$-0.329782\pi$
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	−0.999938	+	0.0111569i	$0.996449\pi$
$600$		0			0
$601$	7.00000	−	12.1244i	0.285536	−	0.494563i	−0.687203	−	0.726465i	$-0.741162\pi$
$601$	7.00000	−	12.1244i	0.285536	−	0.494563i	0.972739	+	0.231903i	$0.0744951\pi$
$602$		0			0
$603$		0			0
$604$	23.0000			0.935857
$605$	37.5000	−	64.9519i	1.52459	−	2.64067i
$606$		0			0
$607$	−11.0000	−	19.0526i	−0.446476	−	0.773320i	0.551678	−	0.834058i	$-0.313988\pi$
$607$	−11.0000	−	19.0526i	−0.446476	−	0.773320i	−0.998154	+	0.0607380i	$0.980655\pi$
$608$	−3.50000	−	6.06218i	−0.141944	−	0.245854i
$609$		0			0
$610$	−7.50000	+	12.9904i	−0.303666	+	0.525965i
$611$		0			0
$612$		0			0
$613$	8.00000			0.323117			0.161558	−	0.986863i	$-0.448348\pi$
$613$	8.00000			0.323117			0.161558	+	0.986863i	$0.448348\pi$
$614$	−12.5000	+	21.6506i	−0.504459	+	0.873749i
$615$		0			0
$616$		0			0
$617$	21.0000	+	36.3731i	0.845428	+	1.46432i	0.885249	+	0.465118i	$0.153988\pi$
$617$	21.0000	+	36.3731i	0.845428	+	1.46432i	−0.0398207	+	0.999207i	$0.512679\pi$
$618$		0			0
$619$	−3.50000	+	6.06218i	−0.140677	+	0.243659i	−0.927752	−	0.373198i	$-0.878261\pi$
$619$	−3.50000	+	6.06218i	−0.140677	+	0.243659i	0.787075	+	0.616858i	$0.211595\pi$
$620$	6.00000			0.240966
$621$		0			0
$622$	12.0000			0.481156
$623$		0			0
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−5.00000	−	8.66025i	−0.199840	−	0.346133i
$627$		0			0
$628$	−6.50000	+	11.2583i	−0.259378	+	0.449256i
$629$	12.0000			0.478471
$630$		0			0
$631$	−7.00000			−0.278666			−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000			−0.278666			−0.139333	+	0.990246i	$0.544496\pi$
$632$	−2.50000	+	4.33013i	−0.0994447	+	0.172243i
$633$		0			0
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	25.5000	+	44.1673i	1.01194	+	1.75273i
$636$		0			0
$637$		0			0
$638$	−36.0000			−1.42525
$639$		0			0
$640$	−3.00000			−0.118585
$641$	13.5000	−	23.3827i	0.533218	−	0.923561i	−0.466029	−	0.884769i	$-0.654316\pi$
$641$	13.5000	−	23.3827i	0.533218	−	0.923561i	0.999247	−	0.0387913i	$-0.0123508\pi$
$642$		0			0
$643$	−2.00000	−	3.46410i	−0.0788723	−	0.136611i	0.823891	−	0.566748i	$-0.191799\pi$
$643$	−2.00000	−	3.46410i	−0.0788723	−	0.136611i	−0.902764	+	0.430137i	$0.858465\pi$
$644$		0			0
$645$		0			0
$646$	−21.0000	+	36.3731i	−0.826234	+	1.43108i
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$		0			0
$649$		0			0
$650$	4.00000	−	6.92820i	0.156893	−	0.271746i
$651$		0			0
$652$	−1.00000	−	1.73205i	−0.0391630	−	0.0678323i
$653$	−18.0000	−	31.1769i	−0.704394	−	1.22005i	−0.966910	−	0.255119i	$-0.917885\pi$
$653$	−18.0000	−	31.1769i	−0.704394	−	1.22005i	0.262515	−	0.964928i	$-0.415448\pi$
$654$		0			0
$655$	−13.5000	+	23.3827i	−0.527489	+	0.913637i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	21.0000	−	36.3731i	0.818044	−	1.41689i	−0.0890776	−	0.996025i	$-0.528392\pi$
$659$	21.0000	−	36.3731i	0.818044	−	1.41689i	0.907122	−	0.420869i	$-0.138275\pi$
$660$		0			0
$661$	2.50000	+	4.33013i	0.0972387	+	0.168422i	0.910541	−	0.413419i	$-0.135666\pi$
$661$	2.50000	+	4.33013i	0.0972387	+	0.168422i	−0.813302	+	0.581842i	$0.802332\pi$
$662$	−13.0000	−	22.5167i	−0.505259	−	0.875135i
$663$		0			0
$664$	−6.00000	+	10.3923i	−0.232845	+	0.403300i
$665$		0			0
$666$		0			0
$667$	18.0000			0.696963
$668$		0			0
$669$		0			0
$670$	12.0000	+	20.7846i	0.463600	+	0.802980i
$671$	15.0000	+	25.9808i	0.579069	+	1.00298i
$672$		0			0
$673$	18.5000	−	32.0429i	0.713123	−	1.23516i	−0.250557	−	0.968102i	$-0.580614\pi$
$673$	18.5000	−	32.0429i	0.713123	−	1.23516i	0.963679	−	0.267063i	$-0.0860531\pi$
$674$	−22.0000			−0.847408
$675$		0			0
$676$	−9.00000			−0.346154
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	0.107772	+	0.994176i	$0.465628\pi$
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	−0.914867	+	0.403755i	$0.867705\pi$
$678$		0			0
$679$		0			0
$680$	9.00000	+	15.5885i	0.345134	+	0.597790i
$681$		0			0
$682$	6.00000	−	10.3923i	0.229752	−	0.397942i
$683$	6.00000			0.229584			0.114792	−	0.993390i	$-0.463380\pi$
$683$	6.00000			0.229584			0.114792	+	0.993390i	$0.463380\pi$
$684$		0			0
$685$	18.0000			0.687745
$686$		0			0
$687$		0			0
$688$	−1.00000	−	1.73205i	−0.0381246	−	0.0660338i
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$		0			0
$691$	23.5000	−	40.7032i	0.893982	−	1.54842i	0.0589228	−	0.998263i	$-0.481233\pi$
$691$	23.5000	−	40.7032i	0.893982	−	1.54842i	0.835059	−	0.550160i	$-0.185433\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	24.0000			0.911028
$695$	−7.50000	+	12.9904i	−0.284491	+	0.492753i
$696$		0			0
$697$		0			0
$698$	13.0000	+	22.5167i	0.492057	+	0.852268i
$699$		0			0
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$		0			0
$703$	14.0000			0.528020
$704$	−3.00000	+	5.19615i	−0.113067	+	0.195837i
$705$		0			0
$706$	9.00000	+	15.5885i	0.338719	+	0.586679i
$707$		0			0
$708$		0			0
$709$	26.0000	−	45.0333i	0.976450	−	1.69126i	0.301388	−	0.953502i	$-0.402550\pi$
$709$	26.0000	−	45.0333i	0.976450	−	1.69126i	0.675063	−	0.737760i	$-0.264116\pi$
$710$	9.00000			0.337764
$711$		0			0
$712$		0			0
$713$	−3.00000	+	5.19615i	−0.112351	+	0.194597i
$714$		0			0
$715$	−18.0000	−	31.1769i	−0.673162	−	1.16595i
$716$	9.00000	+	15.5885i	0.336346	+	0.582568i
$717$		0			0
$718$	−1.50000	+	2.59808i	−0.0559795	+	0.0969593i
$719$	−36.0000			−1.34257			−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000			−1.34257			−0.671287	+	0.741198i	$0.734258\pi$
$720$		0			0
$721$		0			0
$722$	−15.0000	+	25.9808i	−0.558242	+	0.966904i
$723$		0			0
$724$	−12.5000	−	21.6506i	−0.464559	−	0.804640i
$725$	12.0000	+	20.7846i	0.445669	+	0.771921i
$726$		0			0
$727$	4.00000	−	6.92820i	0.148352	−	0.256953i	−0.782267	−	0.622944i	$-0.785937\pi$
$727$	4.00000	−	6.92820i	0.148352	−	0.256953i	0.930618	+	0.365991i	$0.119270\pi$
$728$		0			0
$729$		0			0
$730$	6.00000			0.222070
$731$	−6.00000	+	10.3923i	−0.221918	+	0.384373i
$732$		0			0
$733$	14.5000	+	25.1147i	0.535570	+	0.927634i	0.999136	+	0.0415715i	$0.0132364\pi$
$733$	14.5000	+	25.1147i	0.535570	+	0.927634i	−0.463566	+	0.886062i	$0.653430\pi$
$734$	4.00000	+	6.92820i	0.147643	+	0.255725i
$735$		0			0
$736$	1.50000	−	2.59808i	0.0552907	−	0.0957664i
$737$	48.0000			1.76810
$738$		0			0
$739$	26.0000			0.956425			0.478213	−	0.878244i	$-0.341285\pi$
$739$	26.0000			0.956425			0.478213	+	0.878244i	$0.341285\pi$
$740$	3.00000	−	5.19615i	0.110282	−	0.191014i
$741$		0			0
$742$		0			0
$743$	18.0000	+	31.1769i	0.660356	+	1.14377i	0.980522	+	0.196409i	$0.0629279\pi$
$743$	18.0000	+	31.1769i	0.660356	+	1.14377i	−0.320166	+	0.947361i	$0.603739\pi$
$744$		0			0
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$	14.0000			0.512576
$747$		0			0
$748$	36.0000			1.31629
$749$		0			0
$750$		0			0
$751$	15.5000	+	26.8468i	0.565603	+	0.979653i	0.996993	+	0.0774878i	$0.0246899\pi$
$751$	15.5000	+	26.8468i	0.565603	+	0.979653i	−0.431390	+	0.902165i	$0.641977\pi$
$752$		0			0
$753$		0			0
$754$	−6.00000	+	10.3923i	−0.218507	+	0.378465i
$755$	−69.0000			−2.51117
$756$		0			0
$757$	26.0000			0.944986			0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000			0.944986			0.472493	+	0.881334i	$0.343354\pi$
$758$	−1.00000	+	1.73205i	−0.0363216	+	0.0629109i
$759$		0			0
$760$	10.5000	+	18.1865i	0.380875	+	0.659695i
$761$	21.0000	+	36.3731i	0.761249	+	1.31852i	0.942207	+	0.335032i	$0.108747\pi$
$761$	21.0000	+	36.3731i	0.761249	+	1.31852i	−0.180957	+	0.983491i	$0.557920\pi$
$762$		0			0
$763$		0			0
$764$	9.00000			0.325609
$765$		0			0
$766$	−18.0000			−0.650366
$767$		0			0
$768$		0			0
$769$	7.00000	+	12.1244i	0.252426	+	0.437215i	0.964193	−	0.265200i	$-0.0854381\pi$
$769$	7.00000	+	12.1244i	0.252426	+	0.437215i	−0.711767	+	0.702416i	$0.752105\pi$
$770$		0			0
$771$		0			0
$772$	−8.50000	+	14.7224i	−0.305922	+	0.529872i
$773$	−51.0000			−1.83434			−0.917171	−	0.398493i	$-0.869533\pi$
$773$	−51.0000			−1.83434			−0.917171	+	0.398493i	$0.869533\pi$
$774$		0			0
$775$	−8.00000			−0.287368
$776$	1.00000	−	1.73205i	0.0358979	−	0.0621770i
$777$		0			0
$778$	12.0000	+	20.7846i	0.430221	+	0.745164i
$779$		0			0
$780$		0			0
$781$	9.00000	−	15.5885i	0.322045	−	0.557799i
$782$	−18.0000			−0.643679
$783$		0			0
$784$		0			0
$785$	19.5000	−	33.7750i	0.695985	−	1.20548i
$786$		0			0
$787$	10.0000	+	17.3205i	0.356462	+	0.617409i	0.987367	−	0.158450i	$-0.0506498\pi$
$787$	10.0000	+	17.3205i	0.356462	+	0.617409i	−0.630905	+	0.775860i	$0.717316\pi$
$788$	9.00000	+	15.5885i	0.320612	+	0.555316i
$789$		0			0
$790$	7.50000	−	12.9904i	0.266838	−	0.462177i
$791$		0			0
$792$		0			0
$793$	10.0000			0.355110
$794$	13.0000	−	22.5167i	0.461353	−	0.799086i
$795$		0			0
$796$	7.00000	+	12.1244i	0.248108	+	0.429736i
$797$	−1.50000	−	2.59808i	−0.0531327	−	0.0920286i	0.838236	−	0.545308i	$-0.183587\pi$
$797$	−1.50000	−	2.59808i	−0.0531327	−	0.0920286i	−0.891368	+	0.453279i	$0.850254\pi$
$798$		0			0
$799$		0			0
$800$	4.00000			0.141421
$801$		0			0
$802$	−3.00000			−0.105934
$803$	6.00000	−	10.3923i	0.211735	−	0.366736i
$804$		0			0
$805$		0			0
$806$	−2.00000	−	3.46410i	−0.0704470	−	0.122018i
$807$		0			0
$808$	−4.50000	+	7.79423i	−0.158309	+	0.274200i
$809$	30.0000			1.05474			0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000			1.05474			0.527372	+	0.849635i	$0.323177\pi$
$810$		0			0
$811$	16.0000			0.561836			0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000			0.561836			0.280918	+	0.959732i	$0.409361\pi$
$812$		0			0
$813$		0			0
$814$	−6.00000	−	10.3923i	−0.210300	−	0.364250i
$815$	3.00000	+	5.19615i	0.105085	+	0.182013i
$816$		0			0
$817$	−7.00000	+	12.1244i	−0.244899	+	0.424178i
$818$	−32.0000			−1.11885
$819$		0			0
$820$		0			0
$821$	−12.0000	+	20.7846i	−0.418803	+	0.725388i	−0.995819	−	0.0913446i	$-0.970884\pi$
$821$	−12.0000	+	20.7846i	−0.418803	+	0.725388i	0.577016	+	0.816733i	$0.304217\pi$
$822$		0			0
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	0.787850	−	0.615867i	$-0.211194\pi$
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	−0.927281	+	0.374365i	$0.877861\pi$
$824$	−5.00000	−	8.66025i	−0.174183	−	0.301694i
$825$		0			0
$826$		0			0
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$		0			0
$829$	34.0000			1.18087			0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000			1.18087			0.590434	+	0.807086i	$0.298956\pi$
$830$	18.0000	−	31.1769i	0.624789	−	1.08217i
$831$		0			0
$832$	1.00000	+	1.73205i	0.0346688	+	0.0600481i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	42.0000			1.45260
$837$		0			0
$838$	15.0000			0.518166
$839$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$839$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	5.00000	+	8.66025i	0.172311	+	0.298452i
$843$		0			0
$844$	−4.00000	+	6.92820i	−0.137686	+	0.238479i
$845$	27.0000			0.928828
$846$		0			0
$847$		0			0
$848$	3.00000	−	5.19615i	0.103020	−	0.178437i
$849$		0			0
$850$	−12.0000	−	20.7846i	−0.411597	−	0.712906i
$851$	3.00000	+	5.19615i	0.102839	+	0.178122i
$852$		0			0
$853$	17.5000	−	30.3109i	0.599189	−	1.03783i	−0.393753	−	0.919216i	$-0.628823\pi$
$853$	17.5000	−	30.3109i	0.599189	−	1.03783i	0.992941	−	0.118609i	$-0.0378434\pi$
$854$		0			0
$855$		0			0
$856$	12.0000			0.410152
$857$	−27.0000	+	46.7654i	−0.922302	+	1.59747i	−0.126459	+	0.991972i	$0.540361\pi$
$857$	−27.0000	+	46.7654i	−0.922302	+	1.59747i	−0.795843	+	0.605503i	$0.792972\pi$
$858$		0			0
$859$	−2.00000	−	3.46410i	−0.0682391	−	0.118194i	0.829887	−	0.557931i	$-0.188405\pi$
$859$	−2.00000	−	3.46410i	−0.0682391	−	0.118194i	−0.898126	+	0.439738i	$0.855071\pi$
$860$	3.00000	+	5.19615i	0.102299	+	0.177187i
$861$		0			0
$862$	6.00000	−	10.3923i	0.204361	−	0.353963i
$863$	−9.00000			−0.306364			−0.153182	−	0.988198i	$-0.548952\pi$
$863$	−9.00000			−0.306364			−0.153182	+	0.988198i	$0.548952\pi$
$864$		0			0
$865$	18.0000			0.612018
$866$	7.00000	−	12.1244i	0.237870	−	0.412002i
$867$		0			0
$868$		0			0
$869$	−15.0000	−	25.9808i	−0.508840	−	0.881337i
$870$		0			0
$871$	8.00000	−	13.8564i	0.271070	−	0.469506i
$872$	−10.0000			−0.338643
$873$		0			0
$874$	−21.0000			−0.710336
$875$		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	$0.712196\pi$
$878$	4.00000	+	6.92820i	0.134993	+	0.233816i
$879$		0			0
$880$	9.00000	−	15.5885i	0.303390	−	0.525487i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	−34.0000			−1.14419			−0.572096	−	0.820187i	$-0.693869\pi$
$883$	−34.0000			−1.14419			−0.572096	+	0.820187i	$0.693869\pi$
$884$	6.00000	−	10.3923i	0.201802	−	0.349531i
$885$		0			0
$886$	9.00000	+	15.5885i	0.302361	+	0.523704i
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	0.591156	−	0.806557i	$-0.298672\pi$
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	−0.994077	+	0.108678i	$0.965338\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	28.0000			0.937509
$893$		0			0
$894$		0			0
$895$	−27.0000	−	46.7654i	−0.902510	−	1.56319i
$896$		0			0
$897$		0			0
$898$	16.5000	−	28.5788i	0.550612	−	0.953688i
$899$	12.0000			0.400222
$900$		0			0
$901$	−36.0000			−1.19933
$902$		0			0
$903$		0			0
$904$	7.50000	+	12.9904i	0.249446	+	0.432054i
$905$	37.5000	+	64.9519i	1.24654	+	2.15907i
$906$		0			0
$907$	−16.0000	+	27.7128i	−0.531271	+	0.920189i	0.468063	+	0.883695i	$0.344952\pi$
$907$	−16.0000	+	27.7128i	−0.531271	+	0.920189i	−0.999334	+	0.0364935i	$0.988381\pi$
$908$	−15.0000			−0.497792
$909$		0			0
$910$		0			0
$911$	7.50000	−	12.9904i	0.248486	−	0.430391i	−0.714620	−	0.699513i	$-0.753400\pi$
$911$	7.50000	−	12.9904i	0.248486	−	0.430391i	0.963106	+	0.269122i	$0.0867336\pi$
$912$		0			0
$913$	−36.0000	−	62.3538i	−1.19143	−	2.06361i
$914$	−14.5000	−	25.1147i	−0.479617	−	0.830722i
$915$		0			0
$916$	−0.500000	+	0.866025i	−0.0165205	+	0.0286143i
$917$		0			0
$918$		0			0
$919$	11.0000			0.362857			0.181428	−	0.983404i	$-0.441928\pi$
$919$	11.0000			0.362857			0.181428	+	0.983404i	$0.441928\pi$
$920$	−4.50000	+	7.79423i	−0.148361	+	0.256968i
$921$		0			0
$922$	16.5000	+	28.5788i	0.543399	+	0.941194i
$923$	−3.00000	−	5.19615i	−0.0987462	−	0.171033i
$924$		0			0
$925$	−4.00000	+	6.92820i	−0.131519	+	0.227798i
$926$	−13.0000			−0.427207
$927$		0			0
$928$	−6.00000			−0.196960
$929$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$929$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$930$		0			0
$931$		0			0
$932$	4.50000	+	7.79423i	0.147402	+	0.255308i
$933$		0			0
$934$	−6.00000	+	10.3923i	−0.196326	+	0.340047i
$935$	−108.000			−3.53198
$936$		0			0
$937$	−38.0000			−1.24141			−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000			−1.24141			−0.620703	+	0.784046i	$0.713153\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−10.5000	−	18.1865i	−0.342290	−	0.592864i	0.642567	−	0.766229i	$-0.277869\pi$
$941$	−10.5000	−	18.1865i	−0.342290	−	0.592864i	−0.984858	+	0.173365i	$0.944536\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	12.0000			0.390154
$947$	−12.0000	+	20.7846i	−0.389948	+	0.675409i	−0.992442	−	0.122714i	$-0.960840\pi$
$947$	−12.0000	+	20.7846i	−0.389948	+	0.675409i	0.602494	+	0.798123i	$0.294174\pi$
$948$		0			0
$949$	−2.00000	−	3.46410i	−0.0649227	−	0.112449i
$950$	−14.0000	−	24.2487i	−0.454220	−	0.786732i
$951$		0			0
$952$		0			0
$953$	−42.0000			−1.36051			−0.680257	−	0.732974i	$-0.738132\pi$
$953$	−42.0000			−1.36051			−0.680257	+	0.732974i	$0.738132\pi$
$954$		0			0
$955$	−27.0000			−0.873699
$956$	−7.50000	+	12.9904i	−0.242567	+	0.420139i
$957$		0			0
$958$	3.00000	+	5.19615i	0.0969256	+	0.167880i
$959$		0			0
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	−4.00000			−0.128965
$963$		0			0
$964$	−8.00000			−0.257663
$965$	25.5000	−	44.1673i	0.820874	−	1.42180i
$966$		0			0
$967$	−8.50000	−	14.7224i	−0.273342	−	0.473441i	0.696374	−	0.717679i	$-0.254796\pi$
$967$	−8.50000	−	14.7224i	−0.273342	−	0.473441i	−0.969715	+	0.244238i	$0.921462\pi$
$968$	−12.5000	−	21.6506i	−0.401765	−	0.695878i
$969$		0			0
$970$	−3.00000	+	5.19615i	−0.0963242	+	0.166838i
$971$	−15.0000			−0.481373			−0.240686	−	0.970603i	$-0.577373\pi$
$971$	−15.0000			−0.481373			−0.240686	+	0.970603i	$0.577373\pi$
$972$		0			0
$973$		0			0
$974$	−14.5000	+	25.1147i	−0.464610	+	0.804728i
$975$		0			0
$976$	2.50000	+	4.33013i	0.0800230	+	0.138604i
$977$	3.00000	+	5.19615i	0.0959785	+	0.166240i	0.910017	−	0.414572i	$-0.136069\pi$
$977$	3.00000	+	5.19615i	0.0959785	+	0.166240i	−0.814038	+	0.580812i	$0.802735\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	−18.0000			−0.574403
$983$	−9.00000	+	15.5885i	−0.287055	+	0.497195i	−0.973106	−	0.230360i	$-0.926010\pi$
$983$	−9.00000	+	15.5885i	−0.287055	+	0.497195i	0.686050	+	0.727554i	$0.259343\pi$
$984$		0			0
$985$	−27.0000	−	46.7654i	−0.860292	−	1.49007i
$986$	18.0000	+	31.1769i	0.573237	+	0.992875i
$987$		0			0
$988$	7.00000	−	12.1244i	0.222700	−	0.385727i
$989$	−6.00000			−0.190789
$990$		0			0
$991$	−40.0000			−1.27064			−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000			−1.27064			−0.635321	+	0.772248i	$0.719132\pi$
$992$	1.00000	−	1.73205i	0.0317500	−	0.0549927i
$993$		0			0
$994$		0			0
$995$	−21.0000	−	36.3731i	−0.665745	−	1.15310i
$996$		0			0
$997$	−27.5000	+	47.6314i	−0.870934	+	1.50850i	−0.00990158	+	0.999951i	$0.503152\pi$
$997$	−27.5000	+	47.6314i	−0.870934	+	1.50850i	−0.861032	+	0.508551i	$0.830182\pi$
$998$	32.0000			1.01294
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.f.c.883.1		2
3.2	odd	2		882.2.f.h.295.1		2
7.2	even	3		2646.2.e.j.2125.1		2
7.3	odd	6		2646.2.h.e.667.1		2
7.4	even	3		2646.2.h.a.667.1		2
7.5	odd	6		2646.2.e.f.2125.1		2
7.6	odd	2		378.2.f.a.127.1		2
9.2	odd	6		7938.2.a.l.1.1		1
9.4	even	3	inner	2646.2.f.c.1765.1		2
9.5	odd	6		882.2.f.h.589.1		2
9.7	even	3		7938.2.a.u.1.1		1
21.2	odd	6		882.2.e.d.655.1		2
21.5	even	6		882.2.e.b.655.1		2
21.11	odd	6		882.2.h.f.79.1		2
21.17	even	6		882.2.h.j.79.1		2
21.20	even	2		126.2.f.a.43.1	✓	2
28.27	even	2		3024.2.r.a.2017.1		2
63.4	even	3		2646.2.e.j.1549.1		2
63.5	even	6		882.2.h.j.67.1		2
63.13	odd	6		378.2.f.a.253.1		2
63.20	even	6		1134.2.a.a.1.1		1
63.23	odd	6		882.2.h.f.67.1		2
63.31	odd	6		2646.2.e.f.1549.1		2
63.32	odd	6		882.2.e.d.373.1		2
63.34	odd	6		1134.2.a.h.1.1		1
63.40	odd	6		2646.2.h.e.361.1		2
63.41	even	6		126.2.f.a.85.1	yes	2
63.58	even	3		2646.2.h.a.361.1		2
63.59	even	6		882.2.e.b.373.1		2
84.83	odd	2		1008.2.r.d.673.1		2
252.83	odd	6		9072.2.a.c.1.1		1
252.139	even	6		3024.2.r.a.1009.1		2
252.167	odd	6		1008.2.r.d.337.1		2
252.223	even	6		9072.2.a.w.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.a.43.1	✓	2	21.20	even	2
126.2.f.a.85.1	yes	2	63.41	even	6
378.2.f.a.127.1		2	7.6	odd	2
378.2.f.a.253.1		2	63.13	odd	6
882.2.e.b.373.1		2	63.59	even	6
882.2.e.b.655.1		2	21.5	even	6
882.2.e.d.373.1		2	63.32	odd	6
882.2.e.d.655.1		2	21.2	odd	6
882.2.f.h.295.1		2	3.2	odd	2
882.2.f.h.589.1		2	9.5	odd	6
882.2.h.f.67.1		2	63.23	odd	6
882.2.h.f.79.1		2	21.11	odd	6
882.2.h.j.67.1		2	63.5	even	6
882.2.h.j.79.1		2	21.17	even	6
1008.2.r.d.337.1		2	252.167	odd	6
1008.2.r.d.673.1		2	84.83	odd	2
1134.2.a.a.1.1		1	63.20	even	6
1134.2.a.h.1.1		1	63.34	odd	6
2646.2.e.f.1549.1		2	63.31	odd	6
2646.2.e.f.2125.1		2	7.5	odd	6
2646.2.e.j.1549.1		2	63.4	even	3
2646.2.e.j.2125.1		2	7.2	even	3
2646.2.f.c.883.1		2	1.1	even	1	trivial
2646.2.f.c.1765.1		2	9.4	even	3	inner
2646.2.h.a.361.1		2	63.58	even	3
2646.2.h.a.667.1		2	7.4	even	3
2646.2.h.e.361.1		2	63.40	odd	6
2646.2.h.e.667.1		2	7.3	odd	6
3024.2.r.a.1009.1		2	252.139	even	6
3024.2.r.a.2017.1		2	28.27	even	2
7938.2.a.l.1.1		1	9.2	odd	6
7938.2.a.u.1.1		1	9.7	even	3
9072.2.a.c.1.1		1	252.83	odd	6
9072.2.a.w.1.1		1	252.223	even	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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +1.00000 q^{8} -3.00000 q^{10} +(-3.00000 + 5.19615i) q^{11} +(1.00000 + 1.73205i) q^{13} +(-0.500000 + 0.866025i) q^{16} +6.00000 q^{17} +7.00000 q^{19} +(1.50000 - 2.59808i) q^{20} +(-3.00000 - 5.19615i) q^{22} +(1.50000 + 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} -2.00000 q^{26} +(3.00000 - 5.19615i) q^{29} +(1.00000 + 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{34} +2.00000 q^{37} +(-3.50000 + 6.06218i) q^{38} +(1.50000 + 2.59808i) q^{40} +(-1.00000 + 1.73205i) q^{43} +6.00000 q^{44} -3.00000 q^{46} +(-2.00000 - 3.46410i) q^{50} +(1.00000 - 1.73205i) q^{52} -6.00000 q^{53} -18.0000 q^{55} +(3.00000 + 5.19615i) q^{58} +(2.50000 - 4.33013i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} +(-4.00000 - 6.92820i) q^{67} +(-3.00000 - 5.19615i) q^{68} -3.00000 q^{71} -2.00000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(-3.50000 - 6.06218i) q^{76} +(-2.50000 + 4.33013i) q^{79} -3.00000 q^{80} +(-6.00000 + 10.3923i) q^{83} +(9.00000 + 15.5885i) q^{85} +(-1.00000 - 1.73205i) q^{86} +(-3.00000 + 5.19615i) q^{88} +(1.50000 - 2.59808i) q^{92} +(10.5000 + 18.1865i) q^{95} +(1.00000 - 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + 3 q^{5} + 2 q^{8} - 6 q^{10} - 6 q^{11} + 2 q^{13} - q^{16} + 12 q^{17} + 14 q^{19} + 3 q^{20} - 6 q^{22} + 3 q^{23} - 4 q^{25} - 4 q^{26} + 6 q^{29} + 2 q^{31} - q^{32} - 6 q^{34}+ \cdots + 2 q^{97}+O(q^{100}) \) 2 * q - q^2 - q^4 + 3 * q^5 + 2 * q^8 - 6 * q^10 - 6 * q^11 + 2 * q^13 - q^16 + 12 * q^17 + 14 * q^19 + 3 * q^20 - 6 * q^22 + 3 * q^23 - 4 * q^25 - 4 * q^26 + 6 * q^29 + 2 * q^31 - q^32 - 6 * q^34 + 4 * q^37 - 7 * q^38 + 3 * q^40 - 2 * q^43 + 12 * q^44 - 6 * q^46 - 4 * q^50 + 2 * q^52 - 12 * q^53 - 36 * q^55 + 6 * q^58 + 5 * q^61 - 4 * q^62 + 2 * q^64 - 6 * q^65 - 8 * q^67 - 6 * q^68 - 6 * q^71 - 4 * q^73 - 2 * q^74 - 7 * q^76 - 5 * q^79 - 6 * q^80 - 12 * q^83 + 18 * q^85 - 2 * q^86 - 6 * q^88 + 3 * q^92 + 21 * q^95 + 2 * q^97

Introduction

L-functions

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