LMFDB - Embedded newform 378.2.f.a.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(127,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, 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("378.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.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:	$3.01834519640$
Analytic rank:	$1$
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			127.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	378.127
Dual form			378.2.f.a.253.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +3.00000 q^{10} +(-3.00000 + 5.19615i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} -6.00000 q^{17} -7.00000 q^{19} +(-1.50000 + 2.59808i) q^{20} +(-3.00000 - 5.19615i) q^{22} +(1.50000 + 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} +2.00000 q^{26} +1.00000 q^{28} +(3.00000 - 5.19615i) q^{29} +(-1.00000 - 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.00000 - 5.19615i) q^{34} +3.00000 q^{35} +2.00000 q^{37} +(3.50000 - 6.06218i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(-1.00000 + 1.73205i) q^{43} +6.00000 q^{44} -3.00000 q^{46} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(-1.00000 + 1.73205i) q^{52} -6.00000 q^{53} +18.0000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(3.00000 + 5.19615i) q^{58} +(-2.50000 + 4.33013i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} +(-4.00000 - 6.92820i) q^{67} +(3.00000 + 5.19615i) q^{68} +(-1.50000 + 2.59808i) q^{70} -3.00000 q^{71} +2.00000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(3.50000 + 6.06218i) q^{76} +(-3.00000 - 5.19615i) q^{77} +(-2.50000 + 4.33013i) q^{79} +3.00000 q^{80} +(6.00000 - 10.3923i) q^{83} +(9.00000 + 15.5885i) q^{85} +(-1.00000 - 1.73205i) q^{86} +(-3.00000 + 5.19615i) q^{88} +2.00000 q^{91} +(1.50000 - 2.59808i) q^{92} +(10.5000 + 18.1865i) q^{95} +(-1.00000 + 1.73205i) q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - 3 q^{5} - q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 - 3 * q^5 - q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} - 3 q^{5} - q^{7} + 2 q^{8} + 6 q^{10} - 6 q^{11} - 2 q^{13} - q^{14} - q^{16} - 12 q^{17} - 14 q^{19} - 3 q^{20} - 6 q^{22} + 3 q^{23} - 4 q^{25} + 4 q^{26} + 2 q^{28} + 6 q^{29} - 2 q^{31} - q^{32} + 6 q^{34} + 6 q^{35} + 4 q^{37} + 7 q^{38} - 3 q^{40} - 2 q^{43} + 12 q^{44} - 6 q^{46} - q^{49} - 4 q^{50} - 2 q^{52} - 12 q^{53} + 36 q^{55} - q^{56} + 6 q^{58} - 5 q^{61} + 4 q^{62} + 2 q^{64} - 6 q^{65} - 8 q^{67} + 6 q^{68} - 3 q^{70} - 6 q^{71} + 4 q^{73} - 2 q^{74} + 7 q^{76} - 6 q^{77} - 5 q^{79} + 6 q^{80} + 12 q^{83} + 18 q^{85} - 2 q^{86} - 6 q^{88} + 4 q^{91} + 3 q^{92} + 21 q^{95} - 2 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 - 3 * q^5 - q^7 + 2 * q^8 + 6 * q^10 - 6 * q^11 - 2 * q^13 - q^14 - q^16 - 12 * q^17 - 14 * q^19 - 3 * q^20 - 6 * q^22 + 3 * q^23 - 4 * q^25 + 4 * q^26 + 2 * q^28 + 6 * q^29 - 2 * q^31 - q^32 + 6 * q^34 + 6 * q^35 + 4 * q^37 + 7 * q^38 - 3 * q^40 - 2 * q^43 + 12 * q^44 - 6 * q^46 - q^49 - 4 * q^50 - 2 * q^52 - 12 * q^53 + 36 * q^55 - q^56 + 6 * q^58 - 5 * q^61 + 4 * q^62 + 2 * q^64 - 6 * q^65 - 8 * q^67 + 6 * q^68 - 3 * q^70 - 6 * q^71 + 4 * q^73 - 2 * q^74 + 7 * q^76 - 6 * q^77 - 5 * q^79 + 6 * q^80 + 12 * q^83 + 18 * q^85 - 2 * q^86 - 6 * q^88 + 4 * q^91 + 3 * q^92 + 21 * q^95 - 2 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	$-0.932609\pi$
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	0.306851	−	0.951757i	$-0.400725\pi$
$6$		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
$10$	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	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$		0			0
$19$	−7.00000			−1.60591			−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−7.00000			−1.60591			−0.802955	+	0.596040i	$0.796740\pi$
$20$	−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
$28$	1.00000			0.188982
$29$	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	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	3.00000	−	5.19615i	0.514496	−	0.891133i
$35$	3.00000			0.507093
$36$		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
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−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
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		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	−0.980507	−	0.196485i	$-0.937047\pi$
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	0.660415	+	0.750901i	$0.270381\pi$
$62$	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
$70$	−1.50000	+	2.59808i	−0.179284	+	0.310530i
$71$	−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	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$	−1.00000	+	1.73205i	−0.116248	+	0.201347i
$75$		0			0
$76$	3.50000	+	6.06218i	0.401478	+	0.695379i
$77$	−3.00000	−	5.19615i	−0.341882	−	0.592157i
$78$		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	$-0.604488\pi$
$83$	6.00000	−	10.3923i	0.658586	−	1.14070i	0.980982	−	0.194099i	$-0.0621783\pi$
$84$		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
$91$	2.00000			0.209657
$92$	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	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$	1.00000			0.101015
$99$		0			0
$100$	4.00000			0.400000
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	−0.550474	−	0.834853i	$-0.685553\pi$
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	0.998240	+	0.0592978i	$0.0188862\pi$
$102$		0			0
$103$	5.00000	+	8.66025i	0.492665	+	0.853320i	0.999964	−	0.00844953i	$-0.00268960\pi$
$103$	5.00000	+	8.66025i	0.492665	+	0.853320i	−0.507300	+	0.861770i	$0.669356\pi$
$104$	−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
$112$	−0.500000	−	0.866025i	−0.0472456	−	0.0818317i
$113$	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
$119$	3.00000	−	5.19615i	0.275010	−	0.476331i
$120$		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	0.599699	−	0.800226i	$-0.295287\pi$
$131$	−4.50000	−	7.79423i	−0.393167	−	0.680985i	−0.992865	+	0.119241i	$0.961954\pi$
$132$		0			0
$133$	3.50000	−	6.06218i	0.303488	−	0.525657i
$134$	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	0.740308	−	0.672268i	$-0.234680\pi$
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	−0.952355	+	0.304991i	$0.901346\pi$
$140$	−1.50000	−	2.59808i	−0.126773	−	0.219578i
$141$		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
$154$	6.00000			0.483494
$155$	−3.00000	+	5.19615i	−0.240966	+	0.417365i
$156$		0			0
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	0.999762	+	0.0217953i	$0.00693820\pi$
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	−0.481006	+	0.876717i	$0.659728\pi$
$158$	−2.50000	−	4.33013i	−0.198889	−	0.344486i
$159$		0			0
$160$	−1.50000	+	2.59808i	−0.118585	+	0.205396i
$161$	−3.00000			−0.236433
$162$		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	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$		0			0
$175$	−2.00000	−	3.46410i	−0.151186	−	0.261861i
$176$	−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	$-0.879432\pi$
$181$	−25.0000			−1.85824			−0.929118	+	0.369784i	$0.879432\pi$
$182$	−1.00000	+	1.73205i	−0.0741249	+	0.128388i
$183$		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
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	−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	$-0.334722\pi$
$199$	14.0000			0.992434			0.496217	+	0.868199i	$0.334722\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$		0			0
$202$	4.50000	+	7.79423i	0.316619	+	0.548400i
$203$	3.00000	+	5.19615i	0.210559	+	0.364698i
$204$		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
$217$	2.00000			0.135769
$218$	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	$-0.446459\pi$
$223$	14.0000	−	24.2487i	0.937509	−	1.62381i	0.770097	−	0.637927i	$-0.220208\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	−15.0000			−0.997785
$227$	−7.50000	+	12.9904i	−0.497792	+	0.862202i	−0.999997	−	0.00254715i	$-0.999189\pi$
$227$	−7.50000	+	12.9904i	−0.497792	+	0.862202i	0.502204	+	0.864749i	$0.332523\pi$
$228$		0			0
$229$	0.500000	+	0.866025i	0.0330409	+	0.0572286i	0.882073	−	0.471113i	$-0.156147\pi$
$229$	0.500000	+	0.866025i	0.0330409	+	0.0572286i	−0.849032	+	0.528341i	$0.822814\pi$
$230$	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
$238$	3.00000	+	5.19615i	0.194461	+	0.336817i
$239$	−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	−0.965615	−	0.259975i	$-0.916286\pi$
$241$	−4.00000	+	6.92820i	−0.257663	+	0.446285i	0.707953	+	0.706260i	$0.249619\pi$
$242$	25.0000			1.60706
$243$		0			0
$244$	5.00000			0.320092
$245$	−1.50000	+	2.59808i	−0.0958315	+	0.165985i
$246$		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	$-0.530183\pi$
$251$	−3.00000			−0.189358			−0.0946792	+	0.995508i	$0.530183\pi$
$252$		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	$0.0230722\pi$
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	−0.435970	+	0.899961i	$0.643595\pi$
$258$		0			0
$259$	−1.00000	+	1.73205i	−0.0621370	+	0.107624i
$260$	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
$266$	3.50000	+	6.06218i	0.214599	+	0.371696i
$267$		0			0
$268$	−4.00000	+	6.92820i	−0.244339	+	0.423207i
$269$	9.00000			0.548740			0.274370	−	0.961624i	$-0.411531\pi$
$269$	9.00000			0.548740			0.274370	+	0.961624i	$0.411531\pi$
$270$		0			0
$271$	−28.0000			−1.70088			−0.850439	−	0.526073i	$-0.823664\pi$
$271$	−28.0000			−1.70088			−0.850439	+	0.526073i	$0.823664\pi$
$272$	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
$280$	3.00000			0.179284
$281$	−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	$0.0243478\pi$
$283$	9.50000	+	16.4545i	0.564716	+	0.978117i	−0.432360	+	0.901701i	$0.642319\pi$
$284$	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	0.818878	−	0.573967i	$-0.194596\pi$
$293$	−1.50000	−	2.59808i	−0.0876309	−	0.151781i	−0.906509	+	0.422186i	$0.861263\pi$
$294$		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
$301$	−1.00000	−	1.73205i	−0.0576390	−	0.0998337i
$302$	−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	$-0.752851\pi$
$307$	−25.0000			−1.42683			−0.713413	+	0.700744i	$0.752851\pi$
$308$	−3.00000	+	5.19615i	−0.170941	+	0.296078i
$309$		0			0
$310$	−3.00000	−	5.19615i	−0.170389	−	0.295122i
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	0.984475	−	0.175525i	$-0.0561621\pi$
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	−0.644246	+	0.764818i	$0.722829\pi$
$312$		0			0
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	−0.689412	−	0.724370i	$-0.742131\pi$
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	0.972028	+	0.234863i	$0.0754642\pi$
$314$	−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
$322$	1.50000	−	2.59808i	0.0835917	−	0.144785i
$323$	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
$343$	1.00000			0.0539949
$344$	−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	$0.411649\pi$
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	−0.969885	+	0.243563i	$0.921684\pi$
$350$	4.00000			0.213809
$351$		0			0
$352$	6.00000			0.319801
$353$	−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
$355$	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
$364$	−1.00000	−	1.73205i	−0.0524142	−	0.0907841i
$365$	−3.00000	−	5.19615i	−0.157027	−	0.271979i
$366$		0			0
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	−0.951336	−	0.308155i	$-0.900289\pi$
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	0.742538	+	0.669804i	$0.233622\pi$
$368$	−3.00000			−0.156386
$369$		0			0
$370$	6.00000			0.311925
$371$	3.00000	−	5.19615i	0.155752	−	0.269771i
$372$		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	0.539076	−	0.842257i	$-0.318774\pi$
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	−0.998954	+	0.0457244i	$0.985440\pi$
$384$		0			0
$385$	−9.00000	+	15.5885i	−0.458682	+	0.794461i
$386$	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
$392$	−0.500000	−	0.866025i	−0.0252538	−	0.0437409i
$393$		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	$-0.273741\pi$
$397$	26.0000			1.30490			0.652451	+	0.757831i	$0.273741\pi$
$398$	−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
$406$	−6.00000			−0.297775
$407$	−6.00000	+	10.3923i	−0.297409	+	0.515127i
$408$		0			0
$409$	−16.0000	−	27.7128i	−0.791149	−	1.37031i	−0.925256	−	0.379344i	$-0.876150\pi$
$409$	−16.0000	−	27.7128i	−0.791149	−	1.37031i	0.134107	−	0.990967i	$-0.457183\pi$
$410$		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	0.989000	−	0.147918i	$-0.0472572\pi$
$419$	7.50000	+	12.9904i	0.366399	+	0.634622i	−0.622601	+	0.782540i	$0.713924\pi$
$420$		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
$427$	−2.50000	−	4.33013i	−0.120983	−	0.209550i
$428$	−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	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$	−1.00000	+	1.73205i	−0.0480015	+	0.0831411i
$435$		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	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$	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
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	−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
$455$	−3.00000	−	5.19615i	−0.140642	−	0.243599i
$456$		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	$0.445654\pi$
$461$	−16.5000	+	28.5788i	−0.768482	+	1.33105i	−0.938386	+	0.345589i	$0.887679\pi$
$462$		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	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$		0			0
$469$	8.00000			0.369406
$470$		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
$476$	−6.00000			−0.275010
$477$		0			0
$478$	15.0000			0.686084
$479$	−3.00000	+	5.19615i	−0.137073	+	0.237418i	−0.926388	−	0.376571i	$-0.877103\pi$
$479$	−3.00000	+	5.19615i	−0.137073	+	0.237418i	0.789314	+	0.613990i	$0.210436\pi$
$480$		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
$490$	−1.50000	−	2.59808i	−0.0677631	−	0.117369i
$491$	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
$497$	1.50000	−	2.59808i	0.0672842	−	0.116540i
$498$		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	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		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	$0.0648436\pi$
$509$	15.0000	+	25.9808i	0.664863	+	1.15158i	−0.314459	+	0.949271i	$0.601823\pi$
$510$		0			0
$511$	−1.00000	+	1.73205i	−0.0442374	+	0.0766214i
$512$	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
$518$	−1.00000	−	1.73205i	−0.0439375	−	0.0761019i
$519$		0			0
$520$	−3.00000	+	5.19615i	−0.131559	+	0.227866i
$521$	−24.0000			−1.05146			−0.525730	−	0.850652i	$-0.676208\pi$
$521$	−24.0000			−1.05146			−0.525730	+	0.850652i	$0.676208\pi$
$522$		0			0
$523$	−13.0000			−0.568450			−0.284225	−	0.958758i	$-0.591736\pi$
$523$	−13.0000			−0.568450			−0.284225	+	0.958758i	$0.591736\pi$
$524$	−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
$532$	−7.00000			−0.303488
$533$		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
$539$	6.00000			0.258438
$540$		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
$553$	−2.50000	−	4.33013i	−0.106311	−	0.184136i
$554$	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
$560$	−1.50000	+	2.59808i	−0.0633866	+	0.109789i
$561$		0			0
$562$	−13.5000	−	23.3827i	−0.569463	−	0.986339i
$563$	−16.5000	−	28.5788i	−0.695392	−	1.20445i	−0.970048	−	0.242912i	$-0.921897\pi$
$563$	−16.5000	−	28.5788i	−0.695392	−	1.20445i	0.274656	−	0.961542i	$-0.411436\pi$
$564$		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	$-0.526534\pi$
$577$	−4.00000			−0.166522			−0.0832611	+	0.996528i	$0.526534\pi$
$578$	−9.50000	+	16.4545i	−0.395148	+	0.684416i
$579$		0			0
$580$	9.00000	+	15.5885i	0.373705	+	0.647275i
$581$	6.00000	+	10.3923i	0.248922	+	0.431145i
$582$		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	−0.895320	−	0.445424i	$-0.853053\pi$
$587$	−1.50000	+	2.59808i	−0.0619116	+	0.107234i	0.833408	+	0.552658i	$0.186386\pi$
$588$		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
$595$	−18.0000			−0.737928
$596$	−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	−0.972739	−	0.231903i	$-0.925505\pi$
$601$	−7.00000	+	12.1244i	−0.285536	+	0.494563i	0.687203	+	0.726465i	$0.258838\pi$
$602$	2.00000			0.0815139
$603$		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	0.998154	−	0.0607380i	$-0.0193454\pi$
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	−0.551678	+	0.834058i	$0.686012\pi$
$608$	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
$616$	−3.00000	−	5.19615i	−0.120873	−	0.209359i
$617$	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	−0.787075	−	0.616858i	$-0.788405\pi$
$619$	3.50000	−	6.06218i	0.140677	−	0.243659i	0.927752	+	0.373198i	$0.121739\pi$
$620$	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
$637$	−1.00000	+	1.73205i	−0.0396214	+	0.0686264i
$638$	−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	0.902764	−	0.430137i	$-0.141535\pi$
$643$	2.00000	+	3.46410i	0.0788723	+	0.136611i	−0.823891	+	0.566748i	$0.808201\pi$
$644$	1.50000	+	2.59808i	0.0591083	+	0.102379i
$645$		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	0.813302	−	0.581842i	$-0.197668\pi$
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	−0.910541	+	0.413419i	$0.864334\pi$
$662$	−13.0000	−	22.5167i	−0.505259	−	0.875135i
$663$		0			0
$664$	6.00000	−	10.3923i	0.232845	−	0.403300i
$665$	−21.0000			−0.814345
$666$		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	$-0.534372\pi$
$677$	21.0000	−	36.3731i	0.807096	−	1.39793i	0.914867	−	0.403755i	$-0.132295\pi$
$678$		0			0
$679$	−1.00000	−	1.73205i	−0.0383765	−	0.0664700i
$680$	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
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$		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	$0.518767\pi$
$691$	−23.5000	+	40.7032i	−0.893982	+	1.54842i	−0.835059	+	0.550160i	$0.814567\pi$
$692$	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
$700$	−2.00000	+	3.46410i	−0.0755929	+	0.130931i
$701$	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
$707$	4.50000	+	7.79423i	0.169240	+	0.293132i
$708$		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	$-0.265742\pi$
$719$	36.0000			1.34257			0.671287	+	0.741198i	$0.265742\pi$
$720$		0			0
$721$	−10.0000			−0.372419
$722$	−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	−0.930618	−	0.365991i	$-0.880730\pi$
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	0.782267	+	0.622944i	$0.214063\pi$
$728$	2.00000			0.0741249
$729$		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	$-0.986764\pi$
$733$	−14.5000	−	25.1147i	−0.535570	−	0.927634i	0.463566	−	0.886062i	$-0.346570\pi$
$734$	−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
$742$	3.00000	+	5.19615i	0.110133	+	0.190757i
$743$	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
$749$	−6.00000	+	10.3923i	−0.219235	+	0.379727i
$750$		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	$-0.891253\pi$
$761$	−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			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	0.711767	−	0.702416i	$-0.247895\pi$
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	−0.964193	+	0.265200i	$0.914562\pi$
$770$	−9.00000	−	15.5885i	−0.324337	−	0.561769i
$771$		0			0
$772$	−8.50000	+	14.7224i	−0.305922	+	0.529872i
$773$	51.0000			1.83434			0.917171	−	0.398493i	$-0.130467\pi$
$773$	51.0000			1.83434			0.917171	+	0.398493i	$0.130467\pi$
$774$		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
$784$	1.00000			0.0357143
$785$	19.5000	−	33.7750i	0.695985	−	1.20548i
$786$		0			0
$787$	−10.0000	−	17.3205i	−0.356462	−	0.617409i	0.630905	−	0.775860i	$-0.282684\pi$
$787$	−10.0000	−	17.3205i	−0.356462	−	0.617409i	−0.987367	+	0.158450i	$0.949350\pi$
$788$	9.00000	+	15.5885i	0.320612	+	0.555316i
$789$		0			0
$790$	−7.50000	+	12.9904i	−0.266838	+	0.462177i
$791$	−15.0000			−0.533339
$792$		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	0.891368	−	0.453279i	$-0.149746\pi$
$797$	1.50000	+	2.59808i	0.0531327	+	0.0920286i	−0.838236	+	0.545308i	$0.816413\pi$
$798$		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
$805$	4.50000	+	7.79423i	0.158604	+	0.274710i
$806$	−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	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$	3.00000	−	5.19615i	0.105279	−	0.182349i
$813$		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	$-0.701044\pi$
$829$	−34.0000			−1.18087			−0.590434	+	0.807086i	$0.701044\pi$
$830$	18.0000	−	31.1769i	0.624789	−	1.08217i
$831$		0			0
$832$	−1.00000	−	1.73205i	−0.0346688	−	0.0600481i
$833$	3.00000	+	5.19615i	0.103944	+	0.180036i
$834$		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
$847$	25.0000			0.859010
$848$	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	$0.371177\pi$
$853$	−17.5000	+	30.3109i	−0.599189	+	1.03783i	−0.992941	+	0.118609i	$0.962157\pi$
$854$	5.00000			0.171096
$855$		0			0
$856$	12.0000			0.410152
$857$	27.0000	−	46.7654i	0.922302	−	1.59747i	0.126459	−	0.991972i	$-0.459639\pi$
$857$	27.0000	−	46.7654i	0.922302	−	1.59747i	0.795843	−	0.605503i	$-0.207028\pi$
$858$		0			0
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	0.898126	−	0.439738i	$-0.144929\pi$
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	−0.829887	+	0.557931i	$0.811595\pi$
$860$	−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
$868$	−1.00000	−	1.73205i	−0.0339422	−	0.0587896i
$869$	−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
$875$	1.50000	−	2.59808i	0.0507093	−	0.0878310i
$876$		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	0.994077	−	0.108678i	$-0.0346618\pi$
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	−0.591156	+	0.806557i	$0.701328\pi$
$888$		0			0
$889$	−8.50000	+	14.7224i	−0.285081	+	0.493775i
$890$		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
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$		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
$910$	6.00000			0.198898
$911$	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
$917$	9.00000			0.297206
$918$		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
$931$	3.50000	+	6.06218i	0.114708	+	0.198680i
$932$	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	$-0.286847\pi$
$937$	38.0000			1.24141			0.620703	+	0.784046i	$0.286847\pi$
$938$	−4.00000	+	6.92820i	−0.130605	+	0.226214i
$939$		0			0
$940$		0			0
$941$	10.5000	+	18.1865i	0.342290	+	0.592864i	0.984858	−	0.173365i	$-0.0554641\pi$
$941$	10.5000	+	18.1865i	0.342290	+	0.592864i	−0.642567	+	0.766229i	$0.722131\pi$
$942$		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
$952$	3.00000	−	5.19615i	0.0972306	−	0.168408i
$953$	−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
$959$	3.00000	+	5.19615i	0.0968751	+	0.167793i
$960$		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	$-0.422627\pi$
$971$	15.0000			0.481373			0.240686	+	0.970603i	$0.422627\pi$
$972$		0			0
$973$	5.00000			0.160293
$974$	−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
$980$	3.00000			0.0958315
$981$		0			0
$982$	−18.0000			−0.574403
$983$	9.00000	−	15.5885i	0.287055	−	0.497195i	−0.686050	−	0.727554i	$-0.740657\pi$
$983$	9.00000	−	15.5885i	0.287055	−	0.497195i	0.973106	+	0.230360i	$0.0739903\pi$
$984$		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
$994$	1.50000	+	2.59808i	0.0475771	+	0.0824060i
$995$	−21.0000	−	36.3731i	−0.665745	−	1.15310i
$996$		0			0
$997$	27.5000	−	47.6314i	0.870934	−	1.50850i	0.00990158	−	0.999951i	$-0.496848\pi$
$997$	27.5000	−	47.6314i	0.870934	−	1.50850i	0.861032	−	0.508551i	$-0.169818\pi$
$998$	32.0000			1.01294
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.a.43.1	✓	2	3.2	odd	2
126.2.f.a.85.1	yes	2	9.5	odd	6
378.2.f.a.127.1		2	1.1	even	1	trivial
378.2.f.a.253.1		2	9.4	even	3	inner
882.2.e.b.373.1		2	63.32	odd	6
882.2.e.b.655.1		2	21.2	odd	6
882.2.e.d.373.1		2	63.59	even	6
882.2.e.d.655.1		2	21.5	even	6
882.2.f.h.295.1		2	21.20	even	2
882.2.f.h.589.1		2	63.41	even	6
882.2.h.f.67.1		2	63.5	even	6
882.2.h.f.79.1		2	21.17	even	6
882.2.h.j.67.1		2	63.23	odd	6
882.2.h.j.79.1		2	21.11	odd	6
1008.2.r.d.337.1		2	36.23	even	6
1008.2.r.d.673.1		2	12.11	even	2
1134.2.a.a.1.1		1	9.2	odd	6
1134.2.a.h.1.1		1	9.7	even	3
2646.2.e.f.1549.1		2	63.4	even	3
2646.2.e.f.2125.1		2	7.2	even	3
2646.2.e.j.1549.1		2	63.31	odd	6
2646.2.e.j.2125.1		2	7.5	odd	6
2646.2.f.c.883.1		2	7.6	odd	2
2646.2.f.c.1765.1		2	63.13	odd	6
2646.2.h.a.361.1		2	63.40	odd	6
2646.2.h.a.667.1		2	7.3	odd	6
2646.2.h.e.361.1		2	63.58	even	3
2646.2.h.e.667.1		2	7.4	even	3
3024.2.r.a.1009.1		2	36.31	odd	6
3024.2.r.a.2017.1		2	4.3	odd	2
7938.2.a.l.1.1		1	63.20	even	6
7938.2.a.u.1.1		1	63.34	odd	6
9072.2.a.c.1.1		1	36.11	even	6
9072.2.a.w.1.1		1	36.7	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +3.00000 q^{10} +(-3.00000 + 5.19615i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} -6.00000 q^{17} -7.00000 q^{19} +(-1.50000 + 2.59808i) q^{20} +(-3.00000 - 5.19615i) q^{22} +(1.50000 + 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} +2.00000 q^{26} +1.00000 q^{28} +(3.00000 - 5.19615i) q^{29} +(-1.00000 - 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.00000 - 5.19615i) q^{34} +3.00000 q^{35} +2.00000 q^{37} +(3.50000 - 6.06218i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(-1.00000 + 1.73205i) q^{43} +6.00000 q^{44} -3.00000 q^{46} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(-1.00000 + 1.73205i) q^{52} -6.00000 q^{53} +18.0000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(3.00000 + 5.19615i) q^{58} +(-2.50000 + 4.33013i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} +(-4.00000 - 6.92820i) q^{67} +(3.00000 + 5.19615i) q^{68} +(-1.50000 + 2.59808i) q^{70} -3.00000 q^{71} +2.00000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(3.50000 + 6.06218i) q^{76} +(-3.00000 - 5.19615i) q^{77} +(-2.50000 + 4.33013i) q^{79} +3.00000 q^{80} +(6.00000 - 10.3923i) q^{83} +(9.00000 + 15.5885i) q^{85} +(-1.00000 - 1.73205i) q^{86} +(-3.00000 + 5.19615i) q^{88} +2.00000 q^{91} +(1.50000 - 2.59808i) q^{92} +(10.5000 + 18.1865i) q^{95} +(-1.00000 + 1.73205i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - 3 q^{5} - q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 - 3 * q^5 - q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} - 3 q^{5} - q^{7} + 2 q^{8} + 6 q^{10} - 6 q^{11} - 2 q^{13} - q^{14} - q^{16} - 12 q^{17} - 14 q^{19} - 3 q^{20} - 6 q^{22} + 3 q^{23} - 4 q^{25} + 4 q^{26} + 2 q^{28} + 6 q^{29} - 2 q^{31} - q^{32} + 6 q^{34} + 6 q^{35} + 4 q^{37} + 7 q^{38} - 3 q^{40} - 2 q^{43} + 12 q^{44} - 6 q^{46} - q^{49} - 4 q^{50} - 2 q^{52} - 12 q^{53} + 36 q^{55} - q^{56} + 6 q^{58} - 5 q^{61} + 4 q^{62} + 2 q^{64} - 6 q^{65} - 8 q^{67} + 6 q^{68} - 3 q^{70} - 6 q^{71} + 4 q^{73} - 2 q^{74} + 7 q^{76} - 6 q^{77} - 5 q^{79} + 6 q^{80} + 12 q^{83} + 18 q^{85} - 2 q^{86} - 6 q^{88} + 4 q^{91} + 3 q^{92} + 21 q^{95} - 2 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 - 3 * q^5 - q^7 + 2 * q^8 + 6 * q^10 - 6 * q^11 - 2 * q^13 - q^14 - q^16 - 12 * q^17 - 14 * q^19 - 3 * q^20 - 6 * q^22 + 3 * q^23 - 4 * q^25 + 4 * q^26 + 2 * q^28 + 6 * q^29 - 2 * q^31 - q^32 + 6 * q^34 + 6 * q^35 + 4 * q^37 + 7 * q^38 - 3 * q^40 - 2 * q^43 + 12 * q^44 - 6 * q^46 - q^49 - 4 * q^50 - 2 * q^52 - 12 * q^53 + 36 * q^55 - q^56 + 6 * q^58 - 5 * q^61 + 4 * q^62 + 2 * q^64 - 6 * q^65 - 8 * q^67 + 6 * q^68 - 3 * q^70 - 6 * q^71 + 4 * q^73 - 2 * q^74 + 7 * q^76 - 6 * q^77 - 5 * q^79 + 6 * q^80 + 12 * q^83 + 18 * q^85 - 2 * q^86 - 6 * q^88 + 4 * q^91 + 3 * q^92 + 21 * q^95 - 2 * q^97 + 2 * q^98

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