LMFDB - Embedded newform 1078.2.e.r.177.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(67,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, 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("1078.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.e (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:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1078.177
Dual form			1078.2.e.r.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.41421 + 2.44949i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.82843 q^{6} -1.00000 q^{8} +(-2.50000 + 4.33013i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.41421 + 2.44949i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.82843 q^{6} -1.00000 q^{8} +(-2.50000 + 4.33013i) q^{9} +(0.500000 + 0.866025i) q^{11} +(1.41421 - 2.44949i) q^{12} +2.82843 q^{13} +(-0.500000 + 0.866025i) q^{16} +(1.41421 + 2.44949i) q^{17} +(2.50000 + 4.33013i) q^{18} +(2.82843 - 4.89898i) q^{19} +1.00000 q^{22} +(-4.00000 + 6.92820i) q^{23} +(-1.41421 - 2.44949i) q^{24} +(2.50000 + 4.33013i) q^{25} +(1.41421 - 2.44949i) q^{26} -5.65685 q^{27} +2.00000 q^{29} +(4.24264 + 7.34847i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.41421 + 2.44949i) q^{33} +2.82843 q^{34} +5.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(-2.82843 - 4.89898i) q^{38} +(4.00000 + 6.92820i) q^{39} -2.82843 q^{41} -4.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(4.00000 + 6.92820i) q^{46} +(1.41421 - 2.44949i) q^{47} -2.82843 q^{48} +5.00000 q^{50} +(-4.00000 + 6.92820i) q^{51} +(-1.41421 - 2.44949i) q^{52} +(-7.00000 - 12.1244i) q^{53} +(-2.82843 + 4.89898i) q^{54} +16.0000 q^{57} +(1.00000 - 1.73205i) q^{58} +(-4.24264 - 7.34847i) q^{59} +(-4.24264 + 7.34847i) q^{61} +8.48528 q^{62} +1.00000 q^{64} +(1.41421 + 2.44949i) q^{66} +(-2.00000 - 3.46410i) q^{67} +(1.41421 - 2.44949i) q^{68} -22.6274 q^{69} +(2.50000 - 4.33013i) q^{72} +(-7.07107 - 12.2474i) q^{73} +(1.00000 + 1.73205i) q^{74} +(-7.07107 + 12.2474i) q^{75} -5.65685 q^{76} +8.00000 q^{78} +(8.00000 - 13.8564i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.41421 + 2.44949i) q^{82} +16.9706 q^{83} +(-2.00000 + 3.46410i) q^{86} +(2.82843 + 4.89898i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-5.65685 + 9.79796i) q^{89} +8.00000 q^{92} +(-12.0000 + 20.7846i) q^{93} +(-1.41421 - 2.44949i) q^{94} +(-1.41421 + 2.44949i) q^{96} +16.9706 q^{97} -5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 10 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 10 * q^9	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 10 q^{9} + 2 q^{11} - 2 q^{16} + 10 q^{18} + 4 q^{22} - 16 q^{23} + 10 q^{25} + 8 q^{29} + 2 q^{32} + 20 q^{36} - 4 q^{37} + 16 q^{39} - 16 q^{43} + 2 q^{44} + 16 q^{46} + 20 q^{50} - 16 q^{51} - 28 q^{53} + 64 q^{57} + 4 q^{58} + 4 q^{64} - 8 q^{67} + 10 q^{72} + 4 q^{74} + 32 q^{78} + 32 q^{79} - 2 q^{81} - 8 q^{86} - 2 q^{88} + 32 q^{92} - 48 q^{93} - 20 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 10 * q^9 + 2 * q^11 - 2 * q^16 + 10 * q^18 + 4 * q^22 - 16 * q^23 + 10 * q^25 + 8 * q^29 + 2 * q^32 + 20 * q^36 - 4 * q^37 + 16 * q^39 - 16 * q^43 + 2 * q^44 + 16 * q^46 + 20 * q^50 - 16 * q^51 - 28 * q^53 + 64 * q^57 + 4 * q^58 + 4 * q^64 - 8 * q^67 + 10 * q^72 + 4 * q^74 + 32 * q^78 + 32 * q^79 - 2 * q^81 - 8 * q^86 - 2 * q^88 + 32 * q^92 - 48 * q^93 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	1.41421	+	2.44949i	0.816497	+	1.41421i	0.908248	+	0.418432i	$0.137420\pi$
$3$	1.41421	+	2.44949i	0.816497	+	1.41421i	−0.0917517	+	0.995782i	$0.529247\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$5$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$6$	2.82843			1.15470
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−2.50000	+	4.33013i	−0.833333	+	1.44338i
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	1.41421	−	2.44949i	0.408248	−	0.707107i
$13$	2.82843			0.784465			0.392232	−	0.919866i	$-0.371703\pi$
$13$	2.82843			0.784465			0.392232	+	0.919866i	$0.371703\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.41421	+	2.44949i	0.342997	+	0.594089i	0.984988	−	0.172624i	$-0.0552245\pi$
$17$	1.41421	+	2.44949i	0.342997	+	0.594089i	−0.641991	+	0.766712i	$0.721891\pi$
$18$	2.50000	+	4.33013i	0.589256	+	1.02062i
$19$	2.82843	−	4.89898i	0.648886	−	1.12390i	−0.334504	−	0.942394i	$-0.608569\pi$
$19$	2.82843	−	4.89898i	0.648886	−	1.12390i	0.983389	−	0.181509i	$-0.0580980\pi$
$20$		0			0
$21$		0			0
$22$	1.00000			0.213201
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	0.0607377	+	0.998154i	$0.480655\pi$
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	−0.894795	+	0.446476i	$0.852679\pi$
$24$	−1.41421	−	2.44949i	−0.288675	−	0.500000i
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$	1.41421	−	2.44949i	0.277350	−	0.480384i
$27$	−5.65685			−1.08866
$28$		0			0
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$		0			0
$31$	4.24264	+	7.34847i	0.762001	+	1.31982i	0.941818	+	0.336124i	$0.109116\pi$
$31$	4.24264	+	7.34847i	0.762001	+	1.31982i	−0.179817	+	0.983700i	$0.557551\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.41421	+	2.44949i	−0.246183	+	0.426401i
$34$	2.82843			0.485071
$35$		0			0
$36$	5.00000			0.833333
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$	−2.82843	−	4.89898i	−0.458831	−	0.794719i
$39$	4.00000	+	6.92820i	0.640513	+	1.10940i
$40$		0			0
$41$	−2.82843			−0.441726			−0.220863	−	0.975305i	$-0.570887\pi$
$41$	−2.82843			−0.441726			−0.220863	+	0.975305i	$0.570887\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$		0			0
$46$	4.00000	+	6.92820i	0.589768	+	1.02151i
$47$	1.41421	−	2.44949i	0.206284	−	0.357295i	−0.744257	−	0.667893i	$-0.767196\pi$
$47$	1.41421	−	2.44949i	0.206284	−	0.357295i	0.950541	+	0.310599i	$0.100530\pi$
$48$	−2.82843			−0.408248
$49$		0			0
$50$	5.00000			0.707107
$51$	−4.00000	+	6.92820i	−0.560112	+	0.970143i
$52$	−1.41421	−	2.44949i	−0.196116	−	0.339683i
$53$	−7.00000	−	12.1244i	−0.961524	−	1.66541i	−0.718677	−	0.695344i	$-0.755252\pi$
$53$	−7.00000	−	12.1244i	−0.961524	−	1.66541i	−0.242846	−	0.970065i	$-0.578081\pi$
$54$	−2.82843	+	4.89898i	−0.384900	+	0.666667i
$55$		0			0
$56$		0			0
$57$	16.0000			2.11925
$58$	1.00000	−	1.73205i	0.131306	−	0.227429i
$59$	−4.24264	−	7.34847i	−0.552345	−	0.956689i	−0.998105	−	0.0615367i	$-0.980400\pi$
$59$	−4.24264	−	7.34847i	−0.552345	−	0.956689i	0.445760	−	0.895152i	$-0.352933\pi$
$60$		0			0
$61$	−4.24264	+	7.34847i	−0.543214	+	0.940875i	0.455502	+	0.890235i	$0.349460\pi$
$61$	−4.24264	+	7.34847i	−0.543214	+	0.940875i	−0.998717	+	0.0506406i	$0.983874\pi$
$62$	8.48528			1.07763
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$	1.41421	+	2.44949i	0.174078	+	0.301511i
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	0.717607	−	0.696449i	$-0.245238\pi$
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	−0.961946	+	0.273241i	$0.911904\pi$
$68$	1.41421	−	2.44949i	0.171499	−	0.297044i
$69$	−22.6274			−2.72402
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	2.50000	−	4.33013i	0.294628	−	0.510310i
$73$	−7.07107	−	12.2474i	−0.827606	−	1.43346i	−0.899911	−	0.436073i	$-0.856369\pi$
$73$	−7.07107	−	12.2474i	−0.827606	−	1.43346i	0.0723054	−	0.997383i	$-0.476964\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$	−7.07107	+	12.2474i	−0.816497	+	1.41421i
$76$	−5.65685			−0.648886
$77$		0			0
$78$	8.00000			0.905822
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.0726692	−	0.997356i	$-0.476848\pi$
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.827401	−	0.561611i	$-0.189818\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.41421	+	2.44949i	−0.156174	+	0.270501i
$83$	16.9706			1.86276			0.931381	−	0.364047i	$-0.118605\pi$
$83$	16.9706			1.86276			0.931381	+	0.364047i	$0.118605\pi$
$84$		0			0
$85$		0			0
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$	2.82843	+	4.89898i	0.303239	+	0.525226i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	−5.65685	+	9.79796i	−0.599625	+	1.03858i	0.393251	+	0.919431i	$0.371350\pi$
$89$	−5.65685	+	9.79796i	−0.599625	+	1.03858i	−0.992876	+	0.119150i	$0.961983\pi$
$90$		0			0
$91$		0			0
$92$	8.00000			0.834058
$93$	−12.0000	+	20.7846i	−1.24434	+	2.15526i
$94$	−1.41421	−	2.44949i	−0.145865	−	0.252646i
$95$		0			0
$96$	−1.41421	+	2.44949i	−0.144338	+	0.250000i
$97$	16.9706			1.72310			0.861550	−	0.507673i	$-0.169494\pi$
$97$	16.9706			1.72310			0.861550	+	0.507673i	$0.169494\pi$
$98$		0			0
$99$	−5.00000			−0.502519
$100$	2.50000	−	4.33013i	0.250000	−	0.433013i
$101$	−1.41421	−	2.44949i	−0.140720	−	0.243733i	0.787048	−	0.616891i	$-0.211608\pi$
$101$	−1.41421	−	2.44949i	−0.140720	−	0.243733i	−0.927768	+	0.373158i	$0.878275\pi$
$102$	4.00000	+	6.92820i	0.396059	+	0.685994i
$103$	7.07107	−	12.2474i	0.696733	−	1.20678i	−0.272860	−	0.962054i	$-0.587970\pi$
$103$	7.07107	−	12.2474i	0.696733	−	1.20678i	0.969593	−	0.244723i	$-0.0786971\pi$
$104$	−2.82843			−0.277350
$105$		0			0
$106$	−14.0000			−1.35980
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$	2.82843	+	4.89898i	0.272166	+	0.471405i
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	0.814152	−	0.580651i	$-0.197202\pi$
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	−0.909935	+	0.414751i	$0.863869\pi$
$110$		0			0
$111$	−5.65685			−0.536925
$112$		0			0
$113$	2.00000			0.188144			0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000			0.188144			0.0940721	+	0.995565i	$0.470012\pi$
$114$	8.00000	−	13.8564i	0.749269	−	1.29777i
$115$		0			0
$116$	−1.00000	−	1.73205i	−0.0928477	−	0.160817i
$117$	−7.07107	+	12.2474i	−0.653720	+	1.13228i
$118$	−8.48528			−0.781133
$119$		0			0
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	4.24264	+	7.34847i	0.384111	+	0.665299i
$123$	−4.00000	−	6.92820i	−0.360668	−	0.624695i
$124$	4.24264	−	7.34847i	0.381000	−	0.659912i
$125$		0			0
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−5.65685	−	9.79796i	−0.498058	−	0.862662i
$130$		0			0
$131$	5.65685	−	9.79796i	0.494242	−	0.856052i	−0.505736	−	0.862688i	$-0.668779\pi$
$131$	5.65685	−	9.79796i	0.494242	−	0.856052i	0.999978	+	0.00663646i	$0.00211246\pi$
$132$	2.82843			0.246183
$133$		0			0
$134$	−4.00000			−0.345547
$135$		0			0
$136$	−1.41421	−	2.44949i	−0.121268	−	0.210042i
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	0.905577	−	0.424182i	$-0.139438\pi$
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	−0.820141	+	0.572161i	$0.806105\pi$
$138$	−11.3137	+	19.5959i	−0.963087	+	1.66812i
$139$	16.9706			1.43942			0.719712	−	0.694273i	$-0.244274\pi$
$139$	16.9706			1.43942			0.719712	+	0.694273i	$0.244274\pi$
$140$		0			0
$141$	8.00000			0.673722
$142$		0			0
$143$	1.41421	+	2.44949i	0.118262	+	0.204837i
$144$	−2.50000	−	4.33013i	−0.208333	−	0.360844i
$145$		0			0
$146$	−14.1421			−1.17041
$147$		0			0
$148$	2.00000			0.164399
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$	7.07107	+	12.2474i	0.577350	+	1.00000i
$151$	−8.00000	−	13.8564i	−0.651031	−	1.12762i	−0.982873	−	0.184284i	$-0.941004\pi$
$151$	−8.00000	−	13.8564i	−0.651031	−	1.12762i	0.331842	−	0.943335i	$-0.392330\pi$
$152$	−2.82843	+	4.89898i	−0.229416	+	0.397360i
$153$	−14.1421			−1.14332
$154$		0			0
$155$		0			0
$156$	4.00000	−	6.92820i	0.320256	−	0.554700i
$157$	−5.65685	−	9.79796i	−0.451466	−	0.781962i	0.547011	−	0.837125i	$-0.315765\pi$
$157$	−5.65685	−	9.79796i	−0.451466	−	0.781962i	−0.998477	+	0.0551630i	$0.982432\pi$
$158$	−8.00000	−	13.8564i	−0.636446	−	1.10236i
$159$	19.7990	−	34.2929i	1.57016	−	2.71960i
$160$		0			0
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	−0.777007	−	0.629492i	$-0.783263\pi$
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	0.933659	+	0.358162i	$0.116597\pi$
$164$	1.41421	+	2.44949i	0.110432	+	0.191273i
$165$		0			0
$166$	8.48528	−	14.6969i	0.658586	−	1.14070i
$167$	11.3137			0.875481			0.437741	−	0.899101i	$-0.355779\pi$
$167$	11.3137			0.875481			0.437741	+	0.899101i	$0.355779\pi$
$168$		0			0
$169$	−5.00000			−0.384615
$170$		0			0
$171$	14.1421	+	24.4949i	1.08148	+	1.87317i
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	9.89949	−	17.1464i	0.752645	−	1.30362i	−0.193892	−	0.981023i	$-0.562111\pi$
$173$	9.89949	−	17.1464i	0.752645	−	1.30362i	0.946537	−	0.322596i	$-0.104555\pi$
$174$	5.65685			0.428845
$175$		0			0
$176$	−1.00000			−0.0753778
$177$	12.0000	−	20.7846i	0.901975	−	1.56227i
$178$	5.65685	+	9.79796i	0.423999	+	0.734388i
$179$	−10.0000	−	17.3205i	−0.747435	−	1.29460i	−0.949048	−	0.315130i	$-0.897952\pi$
$179$	−10.0000	−	17.3205i	−0.747435	−	1.29460i	0.201613	−	0.979465i	$-0.435382\pi$
$180$		0			0
$181$	−5.65685			−0.420471			−0.210235	−	0.977651i	$-0.567423\pi$
$181$	−5.65685			−0.420471			−0.210235	+	0.977651i	$0.567423\pi$
$182$		0			0
$183$	−24.0000			−1.77413
$184$	4.00000	−	6.92820i	0.294884	−	0.510754i
$185$		0			0
$186$	12.0000	+	20.7846i	0.879883	+	1.52400i
$187$	−1.41421	+	2.44949i	−0.103418	+	0.179124i
$188$	−2.82843			−0.206284
$189$		0			0
$190$		0			0
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	−0.684244	−	0.729253i	$-0.739868\pi$
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	0.973674	+	0.227946i	$0.0732010\pi$
$192$	1.41421	+	2.44949i	0.102062	+	0.176777i
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	0.999990	+	0.00447566i	$0.00142465\pi$
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	−0.496119	+	0.868255i	$0.665242\pi$
$194$	8.48528	−	14.6969i	0.609208	−	1.05518i
$195$		0			0
$196$		0			0
$197$	−10.0000			−0.712470			−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000			−0.712470			−0.356235	+	0.934396i	$0.615940\pi$
$198$	−2.50000	+	4.33013i	−0.177667	+	0.307729i
$199$	−9.89949	−	17.1464i	−0.701757	−	1.21548i	−0.967849	−	0.251531i	$-0.919066\pi$
$199$	−9.89949	−	17.1464i	−0.701757	−	1.21548i	0.266093	−	0.963947i	$-0.414267\pi$
$200$	−2.50000	−	4.33013i	−0.176777	−	0.306186i
$201$	5.65685	−	9.79796i	0.399004	−	0.691095i
$202$	−2.82843			−0.199007
$203$		0			0
$204$	8.00000			0.560112
$205$		0			0
$206$	−7.07107	−	12.2474i	−0.492665	−	0.853320i
$207$	−20.0000	−	34.6410i	−1.39010	−	2.40772i
$208$	−1.41421	+	2.44949i	−0.0980581	+	0.169842i
$209$	5.65685			0.391293
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	−7.00000	+	12.1244i	−0.480762	+	0.832704i
$213$		0			0
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$		0			0
$216$	5.65685			0.384900
$217$		0			0
$218$	−2.00000			−0.135457
$219$	20.0000	−	34.6410i	1.35147	−	2.34082i
$220$		0			0
$221$	4.00000	+	6.92820i	0.269069	+	0.466041i
$222$	−2.82843	+	4.89898i	−0.189832	+	0.328798i
$223$	−14.1421			−0.947027			−0.473514	−	0.880786i	$-0.657015\pi$
$223$	−14.1421			−0.947027			−0.473514	+	0.880786i	$0.657015\pi$
$224$		0			0
$225$	−25.0000			−1.66667
$226$	1.00000	−	1.73205i	0.0665190	−	0.115214i
$227$	5.65685	+	9.79796i	0.375459	+	0.650313i	0.990396	−	0.138263i	$-0.0441519\pi$
$227$	5.65685	+	9.79796i	0.375459	+	0.650313i	−0.614937	+	0.788576i	$0.710819\pi$
$228$	−8.00000	−	13.8564i	−0.529813	−	0.917663i
$229$	−2.82843	+	4.89898i	−0.186908	+	0.323734i	−0.944218	−	0.329322i	$-0.893180\pi$
$229$	−2.82843	+	4.89898i	−0.186908	+	0.323734i	0.757310	+	0.653056i	$0.226513\pi$
$230$		0			0
$231$		0			0
$232$	−2.00000			−0.131306
$233$	−11.0000	+	19.0526i	−0.720634	+	1.24817i	0.240112	+	0.970745i	$0.422816\pi$
$233$	−11.0000	+	19.0526i	−0.720634	+	1.24817i	−0.960746	+	0.277429i	$0.910518\pi$
$234$	7.07107	+	12.2474i	0.462250	+	0.800641i
$235$		0			0
$236$	−4.24264	+	7.34847i	−0.276172	+	0.478345i
$237$	45.2548			2.93962
$238$		0			0
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$		0			0
$241$	7.07107	+	12.2474i	0.455488	+	0.788928i	0.998716	−	0.0506573i	$-0.0161316\pi$
$241$	7.07107	+	12.2474i	0.455488	+	0.788928i	−0.543229	+	0.839585i	$0.682798\pi$
$242$	0.500000	+	0.866025i	0.0321412	+	0.0556702i
$243$	−7.07107	+	12.2474i	−0.453609	+	0.785674i
$244$	8.48528			0.543214
$245$		0			0
$246$	−8.00000			−0.510061
$247$	8.00000	−	13.8564i	0.509028	−	0.881662i
$248$	−4.24264	−	7.34847i	−0.269408	−	0.466628i
$249$	24.0000	+	41.5692i	1.52094	+	2.63434i
$250$		0			0
$251$	14.1421			0.892644			0.446322	−	0.894873i	$-0.352734\pi$
$251$	14.1421			0.892644			0.446322	+	0.894873i	$0.352734\pi$
$252$		0			0
$253$	−8.00000			−0.502956
$254$		0			0
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.65685	+	9.79796i	−0.352865	+	0.611180i	−0.986750	−	0.162247i	$-0.948126\pi$
$257$	−5.65685	+	9.79796i	−0.352865	+	0.611180i	0.633885	+	0.773427i	$0.281459\pi$
$258$	−11.3137			−0.704361
$259$		0			0
$260$		0			0
$261$	−5.00000	+	8.66025i	−0.309492	+	0.536056i
$262$	−5.65685	−	9.79796i	−0.349482	−	0.605320i
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	0.999970	−	0.00771799i	$-0.00245674\pi$
$263$	8.00000	+	13.8564i	0.493301	+	0.854423i	−0.506669	+	0.862141i	$0.669123\pi$
$264$	1.41421	−	2.44949i	0.0870388	−	0.150756i
$265$		0			0
$266$		0			0
$267$	−32.0000			−1.95837
$268$	−2.00000	+	3.46410i	−0.122169	+	0.211604i
$269$	−2.82843	−	4.89898i	−0.172452	−	0.298696i	0.766824	−	0.641857i	$-0.221836\pi$
$269$	−2.82843	−	4.89898i	−0.172452	−	0.298696i	−0.939277	+	0.343161i	$0.888502\pi$
$270$		0			0
$271$	−8.48528	+	14.6969i	−0.515444	+	0.892775i	0.484395	+	0.874849i	$0.339040\pi$
$271$	−8.48528	+	14.6969i	−0.515444	+	0.892775i	−0.999839	+	0.0179261i	$0.994294\pi$
$272$	−2.82843			−0.171499
$273$		0			0
$274$	2.00000			0.120824
$275$	−2.50000	+	4.33013i	−0.150756	+	0.261116i
$276$	11.3137	+	19.5959i	0.681005	+	1.17954i
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	−0.980373	−	0.197153i	$-0.936830\pi$
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	0.319447	−	0.947604i	$-0.396503\pi$
$278$	8.48528	−	14.6969i	0.508913	−	0.881464i
$279$	−42.4264			−2.54000
$280$		0			0
$281$	−10.0000			−0.596550			−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000			−0.596550			−0.298275	+	0.954480i	$0.596411\pi$
$282$	4.00000	−	6.92820i	0.238197	−	0.412568i
$283$	5.65685	+	9.79796i	0.336265	+	0.582428i	0.983727	−	0.179670i	$-0.0575029\pi$
$283$	5.65685	+	9.79796i	0.336265	+	0.582428i	−0.647462	+	0.762098i	$0.724170\pi$
$284$		0			0
$285$		0			0
$286$	2.82843			0.167248
$287$		0			0
$288$	−5.00000			−0.294628
$289$	4.50000	−	7.79423i	0.264706	−	0.458484i
$290$		0			0
$291$	24.0000	+	41.5692i	1.40690	+	2.43683i
$292$	−7.07107	+	12.2474i	−0.413803	+	0.716728i
$293$	−14.1421			−0.826192			−0.413096	−	0.910687i	$-0.635553\pi$
$293$	−14.1421			−0.826192			−0.413096	+	0.910687i	$0.635553\pi$
$294$		0			0
$295$		0			0
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$	−2.82843	−	4.89898i	−0.164122	−	0.284268i
$298$	3.00000	+	5.19615i	0.173785	+	0.301005i
$299$	−11.3137	+	19.5959i	−0.654289	+	1.13326i
$300$	14.1421			0.816497
$301$		0			0
$302$	−16.0000			−0.920697
$303$	4.00000	−	6.92820i	0.229794	−	0.398015i
$304$	2.82843	+	4.89898i	0.162221	+	0.280976i
$305$		0			0
$306$	−7.07107	+	12.2474i	−0.404226	+	0.700140i
$307$	22.6274			1.29141			0.645707	−	0.763585i	$-0.276563\pi$
$307$	22.6274			1.29141			0.645707	+	0.763585i	$0.276563\pi$
$308$		0			0
$309$	40.0000			2.27552
$310$		0			0
$311$	−15.5563	−	26.9444i	−0.882120	−	1.52788i	−0.848980	−	0.528425i	$-0.822783\pi$
$311$	−15.5563	−	26.9444i	−0.882120	−	1.52788i	−0.0331398	−	0.999451i	$-0.510551\pi$
$312$	−4.00000	−	6.92820i	−0.226455	−	0.392232i
$313$	−5.65685	+	9.79796i	−0.319744	+	0.553813i	−0.980435	−	0.196845i	$-0.936930\pi$
$313$	−5.65685	+	9.79796i	−0.319744	+	0.553813i	0.660690	+	0.750659i	$0.270264\pi$
$314$	−11.3137			−0.638470
$315$		0			0
$316$	−16.0000			−0.900070
$317$	1.00000	−	1.73205i	0.0561656	−	0.0972817i	−0.836576	−	0.547852i	$-0.815446\pi$
$317$	1.00000	−	1.73205i	0.0561656	−	0.0972817i	0.892741	+	0.450570i	$0.148779\pi$
$318$	−19.7990	−	34.2929i	−1.11027	−	1.92305i
$319$	1.00000	+	1.73205i	0.0559893	+	0.0969762i
$320$		0			0
$321$	−33.9411			−1.89441
$322$		0			0
$323$	16.0000			0.890264
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	7.07107	+	12.2474i	0.392232	+	0.679366i
$326$	−2.00000	−	3.46410i	−0.110770	−	0.191859i
$327$	2.82843	−	4.89898i	0.156412	−	0.270914i
$328$	2.82843			0.156174
$329$		0			0
$330$		0			0
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	−0.168320	−	0.985732i	$-0.553834\pi$
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	0.937829	−	0.347097i	$-0.112833\pi$
$332$	−8.48528	−	14.6969i	−0.465690	−	0.806599i
$333$	−5.00000	−	8.66025i	−0.273998	−	0.474579i
$334$	5.65685	−	9.79796i	0.309529	−	0.536120i
$335$		0			0
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$	−2.50000	+	4.33013i	−0.135982	+	0.235528i
$339$	2.82843	+	4.89898i	0.153619	+	0.266076i
$340$		0			0
$341$	−4.24264	+	7.34847i	−0.229752	+	0.397942i
$342$	28.2843			1.52944
$343$		0			0
$344$	4.00000			0.215666
$345$		0			0
$346$	−9.89949	−	17.1464i	−0.532200	−	0.921798i
$347$	−14.0000	−	24.2487i	−0.751559	−	1.30174i	−0.947067	−	0.321037i	$-0.895969\pi$
$347$	−14.0000	−	24.2487i	−0.751559	−	1.30174i	0.195507	−	0.980702i	$-0.437365\pi$
$348$	2.82843	−	4.89898i	0.151620	−	0.262613i
$349$	−25.4558			−1.36262			−0.681310	−	0.731995i	$-0.738589\pi$
$349$	−25.4558			−1.36262			−0.681310	+	0.731995i	$0.738589\pi$
$350$		0			0
$351$	−16.0000			−0.854017
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	−5.65685	−	9.79796i	−0.301084	−	0.521493i	0.675298	−	0.737545i	$-0.264015\pi$
$353$	−5.65685	−	9.79796i	−0.301084	−	0.521493i	−0.976382	+	0.216052i	$0.930682\pi$
$354$	−12.0000	−	20.7846i	−0.637793	−	1.10469i
$355$		0			0
$356$	11.3137			0.599625
$357$		0			0
$358$	−20.0000			−1.05703
$359$	−16.0000	+	27.7128i	−0.844448	+	1.46263i	0.0416523	+	0.999132i	$0.486738\pi$
$359$	−16.0000	+	27.7128i	−0.844448	+	1.46263i	−0.886100	+	0.463494i	$0.846596\pi$
$360$		0			0
$361$	−6.50000	−	11.2583i	−0.342105	−	0.592544i
$362$	−2.82843	+	4.89898i	−0.148659	+	0.257485i
$363$	−2.82843			−0.148454
$364$		0			0
$365$		0			0
$366$	−12.0000	+	20.7846i	−0.627250	+	1.08643i
$367$	−4.24264	−	7.34847i	−0.221464	−	0.383587i	0.733789	−	0.679378i	$-0.237750\pi$
$367$	−4.24264	−	7.34847i	−0.221464	−	0.383587i	−0.955253	+	0.295791i	$0.904417\pi$
$368$	−4.00000	−	6.92820i	−0.208514	−	0.361158i
$369$	7.07107	−	12.2474i	0.368105	−	0.637577i
$370$		0			0
$371$		0			0
$372$	24.0000			1.24434
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$	1.41421	+	2.44949i	0.0731272	+	0.126660i
$375$		0			0
$376$	−1.41421	+	2.44949i	−0.0729325	+	0.126323i
$377$	5.65685			0.291343
$378$		0			0
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$		0			0
$381$		0			0
$382$	−4.00000	−	6.92820i	−0.204658	−	0.354478i
$383$	−1.41421	+	2.44949i	−0.0722629	+	0.125163i	−0.899893	−	0.436111i	$-0.856355\pi$
$383$	−1.41421	+	2.44949i	−0.0722629	+	0.125163i	0.827630	+	0.561274i	$0.189689\pi$
$384$	2.82843			0.144338
$385$		0			0
$386$	14.0000			0.712581
$387$	10.0000	−	17.3205i	0.508329	−	0.880451i
$388$	−8.48528	−	14.6969i	−0.430775	−	0.746124i
$389$	−13.0000	−	22.5167i	−0.659126	−	1.14164i	−0.980842	−	0.194804i	$-0.937593\pi$
$389$	−13.0000	−	22.5167i	−0.659126	−	1.14164i	0.321716	−	0.946836i	$-0.395740\pi$
$390$		0			0
$391$	−22.6274			−1.14432
$392$		0			0
$393$	32.0000			1.61419
$394$	−5.00000	+	8.66025i	−0.251896	+	0.436297i
$395$		0			0
$396$	2.50000	+	4.33013i	0.125630	+	0.217597i
$397$	−11.3137	+	19.5959i	−0.567819	+	0.983491i	0.428963	+	0.903322i	$0.358879\pi$
$397$	−11.3137	+	19.5959i	−0.567819	+	0.983491i	−0.996781	+	0.0801687i	$0.974454\pi$
$398$	−19.7990			−0.992434
$399$		0			0
$400$	−5.00000			−0.250000
$401$	−15.0000	+	25.9808i	−0.749064	+	1.29742i	0.199207	+	0.979957i	$0.436163\pi$
$401$	−15.0000	+	25.9808i	−0.749064	+	1.29742i	−0.948272	+	0.317460i	$0.897170\pi$
$402$	−5.65685	−	9.79796i	−0.282138	−	0.488678i
$403$	12.0000	+	20.7846i	0.597763	+	1.03536i
$404$	−1.41421	+	2.44949i	−0.0703598	+	0.121867i
$405$		0			0
$406$		0			0
$407$	−2.00000			−0.0991363
$408$	4.00000	−	6.92820i	0.198030	−	0.342997i
$409$	4.24264	+	7.34847i	0.209785	+	0.363358i	0.951647	−	0.307195i	$-0.0993902\pi$
$409$	4.24264	+	7.34847i	0.209785	+	0.363358i	−0.741862	+	0.670553i	$0.766057\pi$
$410$		0			0
$411$	−2.82843	+	4.89898i	−0.139516	+	0.241649i
$412$	−14.1421			−0.696733
$413$		0			0
$414$	−40.0000			−1.96589
$415$		0			0
$416$	1.41421	+	2.44949i	0.0693375	+	0.120096i
$417$	24.0000	+	41.5692i	1.17529	+	2.03565i
$418$	2.82843	−	4.89898i	0.138343	−	0.239617i
$419$	−25.4558			−1.24360			−0.621800	−	0.783176i	$-0.713598\pi$
$419$	−25.4558			−1.24360			−0.621800	+	0.783176i	$0.713598\pi$
$420$		0			0
$421$	14.0000			0.682318			0.341159	−	0.940006i	$-0.389181\pi$
$421$	14.0000			0.682318			0.341159	+	0.940006i	$0.389181\pi$
$422$	2.00000	−	3.46410i	0.0973585	−	0.168630i
$423$	7.07107	+	12.2474i	0.343807	+	0.595491i
$424$	7.00000	+	12.1244i	0.339950	+	0.588811i
$425$	−7.07107	+	12.2474i	−0.342997	+	0.594089i
$426$		0			0
$427$		0			0
$428$	12.0000			0.580042
$429$	−4.00000	+	6.92820i	−0.193122	+	0.334497i
$430$		0			0
$431$	12.0000	+	20.7846i	0.578020	+	1.00116i	0.995706	+	0.0925683i	$0.0295076\pi$
$431$	12.0000	+	20.7846i	0.578020	+	1.00116i	−0.417687	+	0.908591i	$0.637159\pi$
$432$	2.82843	−	4.89898i	0.136083	−	0.235702i
$433$	16.9706			0.815553			0.407777	−	0.913082i	$-0.366304\pi$
$433$	16.9706			0.815553			0.407777	+	0.913082i	$0.366304\pi$
$434$		0			0
$435$		0			0
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$	22.6274	+	39.1918i	1.08242	+	1.87480i
$438$	−20.0000	−	34.6410i	−0.955637	−	1.65521i
$439$	8.48528	−	14.6969i	0.404980	−	0.701447i	−0.589339	−	0.807886i	$-0.700612\pi$
$439$	8.48528	−	14.6969i	0.404980	−	0.701447i	0.994319	+	0.106439i	$0.0339450\pi$
$440$		0			0
$441$		0			0
$442$	8.00000			0.380521
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	−0.972626	−	0.232377i	$-0.925350\pi$
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	0.687557	+	0.726130i	$0.258683\pi$
$444$	2.82843	+	4.89898i	0.134231	+	0.232495i
$445$		0			0
$446$	−7.07107	+	12.2474i	−0.334825	+	0.579934i
$447$	−16.9706			−0.802680
$448$		0			0
$449$	10.0000			0.471929			0.235965	−	0.971762i	$-0.424175\pi$
$449$	10.0000			0.471929			0.235965	+	0.971762i	$0.424175\pi$
$450$	−12.5000	+	21.6506i	−0.589256	+	1.02062i
$451$	−1.41421	−	2.44949i	−0.0665927	−	0.115342i
$452$	−1.00000	−	1.73205i	−0.0470360	−	0.0814688i
$453$	22.6274	−	39.1918i	1.06313	−	1.84139i
$454$	11.3137			0.530979
$455$		0			0
$456$	−16.0000			−0.749269
$457$	11.0000	−	19.0526i	0.514558	−	0.891241i	−0.485299	−	0.874348i	$-0.661289\pi$
$457$	11.0000	−	19.0526i	0.514558	−	0.891241i	0.999857	−	0.0168929i	$-0.00537742\pi$
$458$	2.82843	+	4.89898i	0.132164	+	0.228914i
$459$	−8.00000	−	13.8564i	−0.373408	−	0.646762i
$460$		0			0
$461$	19.7990			0.922131			0.461065	−	0.887366i	$-0.347467\pi$
$461$	19.7990			0.922131			0.461065	+	0.887366i	$0.347467\pi$
$462$		0			0
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$	−1.00000	+	1.73205i	−0.0464238	+	0.0804084i
$465$		0			0
$466$	11.0000	+	19.0526i	0.509565	+	0.882593i
$467$	−12.7279	+	22.0454i	−0.588978	+	1.02014i	0.405389	+	0.914144i	$0.367136\pi$
$467$	−12.7279	+	22.0454i	−0.588978	+	1.02014i	−0.994367	+	0.105995i	$0.966197\pi$
$468$	14.1421			0.653720
$469$		0			0
$470$		0			0
$471$	16.0000	−	27.7128i	0.737241	−	1.27694i
$472$	4.24264	+	7.34847i	0.195283	+	0.338241i
$473$	−2.00000	−	3.46410i	−0.0919601	−	0.159280i
$474$	22.6274	−	39.1918i	1.03931	−	1.80014i
$475$	28.2843			1.29777
$476$		0			0
$477$	70.0000			3.20508
$478$	−8.00000	+	13.8564i	−0.365911	+	0.633777i
$479$	−8.48528	−	14.6969i	−0.387702	−	0.671520i	0.604438	−	0.796652i	$-0.293398\pi$
$479$	−8.48528	−	14.6969i	−0.387702	−	0.671520i	−0.992140	+	0.125132i	$0.960065\pi$
$480$		0			0
$481$	−2.82843	+	4.89898i	−0.128965	+	0.223374i
$482$	14.1421			0.644157
$483$		0			0
$484$	1.00000			0.0454545
$485$		0			0
$486$	7.07107	+	12.2474i	0.320750	+	0.555556i
$487$	4.00000	+	6.92820i	0.181257	+	0.313947i	0.942309	−	0.334744i	$-0.108650\pi$
$487$	4.00000	+	6.92820i	0.181257	+	0.313947i	−0.761052	+	0.648691i	$0.775317\pi$
$488$	4.24264	−	7.34847i	0.192055	−	0.332650i
$489$	11.3137			0.511624
$490$		0			0
$491$	−28.0000			−1.26362			−0.631811	−	0.775122i	$-0.717688\pi$
$491$	−28.0000			−1.26362			−0.631811	+	0.775122i	$0.717688\pi$
$492$	−4.00000	+	6.92820i	−0.180334	+	0.312348i
$493$	2.82843	+	4.89898i	0.127386	+	0.220639i
$494$	−8.00000	−	13.8564i	−0.359937	−	0.623429i
$495$		0			0
$496$	−8.48528			−0.381000
$497$		0			0
$498$	48.0000			2.15093
$499$	6.00000	−	10.3923i	0.268597	−	0.465223i	−0.699903	−	0.714238i	$-0.746773\pi$
$499$	6.00000	−	10.3923i	0.268597	−	0.465223i	0.968500	+	0.249015i	$0.0801067\pi$
$500$		0			0
$501$	16.0000	+	27.7128i	0.714827	+	1.23812i
$502$	7.07107	−	12.2474i	0.315597	−	0.546630i
$503$	−5.65685			−0.252227			−0.126113	−	0.992016i	$-0.540250\pi$
$503$	−5.65685			−0.252227			−0.126113	+	0.992016i	$0.540250\pi$
$504$		0			0
$505$		0			0
$506$	−4.00000	+	6.92820i	−0.177822	+	0.307996i
$507$	−7.07107	−	12.2474i	−0.314037	−	0.543928i
$508$		0			0
$509$	−8.48528	+	14.6969i	−0.376103	+	0.651430i	−0.990492	−	0.137574i	$-0.956070\pi$
$509$	−8.48528	+	14.6969i	−0.376103	+	0.651430i	0.614388	+	0.789004i	$0.289403\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−16.0000	+	27.7128i	−0.706417	+	1.22355i
$514$	5.65685	+	9.79796i	0.249513	+	0.432169i
$515$		0			0
$516$	−5.65685	+	9.79796i	−0.249029	+	0.431331i
$517$	2.82843			0.124394
$518$		0			0
$519$	56.0000			2.45813
$520$		0			0
$521$	19.7990	+	34.2929i	0.867409	+	1.50240i	0.864635	+	0.502401i	$0.167550\pi$
$521$	19.7990	+	34.2929i	0.867409	+	1.50240i	0.00277485	+	0.999996i	$0.499117\pi$
$522$	5.00000	+	8.66025i	0.218844	+	0.379049i
$523$	16.9706	−	29.3939i	0.742071	−	1.28530i	−0.209480	−	0.977813i	$-0.567177\pi$
$523$	16.9706	−	29.3939i	0.742071	−	1.28530i	0.951551	−	0.307492i	$-0.0994896\pi$
$524$	−11.3137			−0.494242
$525$		0			0
$526$	16.0000			0.697633
$527$	−12.0000	+	20.7846i	−0.522728	+	0.905392i
$528$	−1.41421	−	2.44949i	−0.0615457	−	0.106600i
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$		0			0
$531$	42.4264			1.84115
$532$		0			0
$533$	−8.00000			−0.346518
$534$	−16.0000	+	27.7128i	−0.692388	+	1.19925i
$535$		0			0
$536$	2.00000	+	3.46410i	0.0863868	+	0.149626i
$537$	28.2843	−	48.9898i	1.22056	−	2.11407i
$538$	−5.65685			−0.243884
$539$		0			0
$540$		0			0
$541$	9.00000	−	15.5885i	0.386940	−	0.670200i	−0.605096	−	0.796152i	$-0.706865\pi$
$541$	9.00000	−	15.5885i	0.386940	−	0.670200i	0.992036	+	0.125952i	$0.0401986\pi$
$542$	8.48528	+	14.6969i	0.364474	+	0.631288i
$543$	−8.00000	−	13.8564i	−0.343313	−	0.594635i
$544$	−1.41421	+	2.44949i	−0.0606339	+	0.105021i
$545$		0			0
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$	1.00000	−	1.73205i	0.0427179	−	0.0739895i
$549$	−21.2132	−	36.7423i	−0.905357	−	1.56813i
$550$	2.50000	+	4.33013i	0.106600	+	0.184637i
$551$	5.65685	−	9.79796i	0.240990	−	0.417407i
$552$	22.6274			0.963087
$553$		0			0
$554$	−22.0000			−0.934690
$555$		0			0
$556$	−8.48528	−	14.6969i	−0.359856	−	0.623289i
$557$	9.00000	+	15.5885i	0.381342	+	0.660504i	0.991254	−	0.131965i	$-0.0421286\pi$
$557$	9.00000	+	15.5885i	0.381342	+	0.660504i	−0.609912	+	0.792469i	$0.708795\pi$
$558$	−21.2132	+	36.7423i	−0.898027	+	1.55543i
$559$	−11.3137			−0.478519
$560$		0			0
$561$	−8.00000			−0.337760
$562$	−5.00000	+	8.66025i	−0.210912	+	0.365311i
$563$	14.1421	+	24.4949i	0.596020	+	1.03234i	0.993402	+	0.114684i	$0.0365854\pi$
$563$	14.1421	+	24.4949i	0.596020	+	1.03234i	−0.397382	+	0.917653i	$0.630081\pi$
$564$	−4.00000	−	6.92820i	−0.168430	−	0.291730i
$565$		0			0
$566$	11.3137			0.475551
$567$		0			0
$568$		0			0
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	−0.922032	−	0.387113i	$-0.873472\pi$
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	0.796266	+	0.604947i	$0.206806\pi$
$570$		0			0
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	0.821138	−	0.570730i	$-0.193340\pi$
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	−0.904835	+	0.425762i	$0.860006\pi$
$572$	1.41421	−	2.44949i	0.0591312	−	0.102418i
$573$	22.6274			0.945274
$574$		0			0
$575$	−40.0000			−1.66812
$576$	−2.50000	+	4.33013i	−0.104167	+	0.180422i
$577$	19.7990	+	34.2929i	0.824243	+	1.42763i	0.902497	+	0.430697i	$0.141732\pi$
$577$	19.7990	+	34.2929i	0.824243	+	1.42763i	−0.0782539	+	0.996933i	$0.524934\pi$
$578$	−4.50000	−	7.79423i	−0.187175	−	0.324197i
$579$	−19.7990	+	34.2929i	−0.822818	+	1.42516i
$580$		0			0
$581$		0			0
$582$	48.0000			1.98966
$583$	7.00000	−	12.1244i	0.289910	−	0.502140i
$584$	7.07107	+	12.2474i	0.292603	+	0.506803i
$585$		0			0
$586$	−7.07107	+	12.2474i	−0.292103	+	0.505937i
$587$	14.1421			0.583708			0.291854	−	0.956463i	$-0.405728\pi$
$587$	14.1421			0.583708			0.291854	+	0.956463i	$0.405728\pi$
$588$		0			0
$589$	48.0000			1.97781
$590$		0			0
$591$	−14.1421	−	24.4949i	−0.581730	−	1.00759i
$592$	−1.00000	−	1.73205i	−0.0410997	−	0.0711868i
$593$	21.2132	−	36.7423i	0.871122	−	1.50883i	0.0102845	−	0.999947i	$-0.496726\pi$
$593$	21.2132	−	36.7423i	0.871122	−	1.50883i	0.860837	−	0.508880i	$-0.169940\pi$
$594$	−5.65685			−0.232104
$595$		0			0
$596$	6.00000			0.245770
$597$	28.0000	−	48.4974i	1.14596	−	1.98487i
$598$	11.3137	+	19.5959i	0.462652	+	0.801337i
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$	7.07107	−	12.2474i	0.288675	−	0.500000i
$601$	−25.4558			−1.03837			−0.519183	−	0.854663i	$-0.673764\pi$
$601$	−25.4558			−1.03837			−0.519183	+	0.854663i	$0.673764\pi$
$602$		0			0
$603$	20.0000			0.814463
$604$	−8.00000	+	13.8564i	−0.325515	+	0.563809i
$605$		0			0
$606$	−4.00000	−	6.92820i	−0.162489	−	0.281439i
$607$	−16.9706	+	29.3939i	−0.688814	+	1.19306i	0.283408	+	0.958999i	$0.408535\pi$
$607$	−16.9706	+	29.3939i	−0.688814	+	1.19306i	−0.972222	+	0.234061i	$0.924798\pi$
$608$	5.65685			0.229416
$609$		0			0
$610$		0			0
$611$	4.00000	−	6.92820i	0.161823	−	0.280285i
$612$	7.07107	+	12.2474i	0.285831	+	0.495074i
$613$	19.0000	+	32.9090i	0.767403	+	1.32918i	0.938967	+	0.344008i	$0.111785\pi$
$613$	19.0000	+	32.9090i	0.767403	+	1.32918i	−0.171564	+	0.985173i	$0.554882\pi$
$614$	11.3137	−	19.5959i	0.456584	−	0.790827i
$615$		0			0
$616$		0			0
$617$	14.0000			0.563619			0.281809	−	0.959470i	$-0.409065\pi$
$617$	14.0000			0.563619			0.281809	+	0.959470i	$0.409065\pi$
$618$	20.0000	−	34.6410i	0.804518	−	1.39347i
$619$	−1.41421	−	2.44949i	−0.0568420	−	0.0984533i	0.836204	−	0.548418i	$-0.184770\pi$
$619$	−1.41421	−	2.44949i	−0.0568420	−	0.0984533i	−0.893046	+	0.449965i	$0.851436\pi$
$620$		0			0
$621$	22.6274	−	39.1918i	0.908007	−	1.57271i
$622$	−31.1127			−1.24751
$623$		0			0
$624$	−8.00000			−0.320256
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$	5.65685	+	9.79796i	0.226093	+	0.391605i
$627$	8.00000	+	13.8564i	0.319489	+	0.553372i
$628$	−5.65685	+	9.79796i	−0.225733	+	0.390981i
$629$	−5.65685			−0.225554
$630$		0			0
$631$	48.0000			1.91085			0.955425	−	0.295234i	$-0.0953977\pi$
$631$	48.0000			1.91085			0.955425	+	0.295234i	$0.0953977\pi$
$632$	−8.00000	+	13.8564i	−0.318223	+	0.551178i
$633$	5.65685	+	9.79796i	0.224840	+	0.389434i
$634$	−1.00000	−	1.73205i	−0.0397151	−	0.0687885i
$635$		0			0
$636$	−39.5980			−1.57016
$637$		0			0
$638$	2.00000			0.0791808
$639$		0			0
$640$		0			0
$641$	13.0000	+	22.5167i	0.513469	+	0.889355i	0.999878	+	0.0156233i	$0.00497325\pi$
$641$	13.0000	+	22.5167i	0.513469	+	0.889355i	−0.486409	+	0.873731i	$0.661693\pi$
$642$	−16.9706	+	29.3939i	−0.669775	+	1.16008i
$643$	25.4558			1.00388			0.501940	−	0.864902i	$-0.332620\pi$
$643$	25.4558			1.00388			0.501940	+	0.864902i	$0.332620\pi$
$644$		0			0
$645$		0			0
$646$	8.00000	−	13.8564i	0.314756	−	0.545173i
$647$	−7.07107	−	12.2474i	−0.277992	−	0.481497i	0.692893	−	0.721040i	$-0.256336\pi$
$647$	−7.07107	−	12.2474i	−0.277992	−	0.481497i	−0.970886	+	0.239543i	$0.923002\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	4.24264	−	7.34847i	0.166538	−	0.288453i
$650$	14.1421			0.554700
$651$		0			0
$652$	−4.00000			−0.156652
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	−0.986634	−	0.162951i	$-0.947899\pi$
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	0.634437	+	0.772975i	$0.281232\pi$
$654$	−2.82843	−	4.89898i	−0.110600	−	0.191565i
$655$		0			0
$656$	1.41421	−	2.44949i	0.0552158	−	0.0956365i
$657$	70.7107			2.75869
$658$		0			0
$659$	−28.0000			−1.09073			−0.545363	−	0.838200i	$-0.683608\pi$
$659$	−28.0000			−1.09073			−0.545363	+	0.838200i	$0.683608\pi$
$660$		0			0
$661$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$661$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$662$	−14.0000	−	24.2487i	−0.544125	−	0.942453i
$663$	−11.3137	+	19.5959i	−0.439388	+	0.761042i
$664$	−16.9706			−0.658586
$665$		0			0
$666$	−10.0000			−0.387492
$667$	−8.00000	+	13.8564i	−0.309761	+	0.536522i
$668$	−5.65685	−	9.79796i	−0.218870	−	0.379094i
$669$	−20.0000	−	34.6410i	−0.773245	−	1.33930i
$670$		0			0
$671$	−8.48528			−0.327571
$672$		0			0
$673$	14.0000			0.539660			0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000			0.539660			0.269830	+	0.962908i	$0.413032\pi$
$674$	7.00000	−	12.1244i	0.269630	−	0.467013i
$675$	−14.1421	−	24.4949i	−0.544331	−	0.942809i
$676$	2.50000	+	4.33013i	0.0961538	+	0.166543i
$677$	−1.41421	+	2.44949i	−0.0543526	+	0.0941415i	−0.891922	−	0.452190i	$-0.850643\pi$
$677$	−1.41421	+	2.44949i	−0.0543526	+	0.0941415i	0.837569	+	0.546332i	$0.183976\pi$
$678$	5.65685			0.217250
$679$		0			0
$680$		0			0
$681$	−16.0000	+	27.7128i	−0.613121	+	1.06196i
$682$	4.24264	+	7.34847i	0.162459	+	0.281387i
$683$	−14.0000	−	24.2487i	−0.535695	−	0.927851i	−0.999129	−	0.0417198i	$-0.986716\pi$
$683$	−14.0000	−	24.2487i	−0.535695	−	0.927851i	0.463434	−	0.886131i	$-0.346617\pi$
$684$	14.1421	−	24.4949i	0.540738	−	0.936586i
$685$		0			0
$686$		0			0
$687$	−16.0000			−0.610438
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	−19.7990	−	34.2929i	−0.754281	−	1.30645i
$690$		0			0
$691$	−4.24264	+	7.34847i	−0.161398	+	0.279549i	−0.935370	−	0.353670i	$-0.884934\pi$
$691$	−4.24264	+	7.34847i	−0.161398	+	0.279549i	0.773973	+	0.633219i	$0.218267\pi$
$692$	−19.7990			−0.752645
$693$		0			0
$694$	−28.0000			−1.06287
$695$		0			0
$696$	−2.82843	−	4.89898i	−0.107211	−	0.185695i
$697$	−4.00000	−	6.92820i	−0.151511	−	0.262424i
$698$	−12.7279	+	22.0454i	−0.481759	+	0.834431i
$699$	−62.2254			−2.35358
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$	−8.00000	+	13.8564i	−0.301941	+	0.522976i
$703$	5.65685	+	9.79796i	0.213352	+	0.369537i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$		0			0
$706$	−11.3137			−0.425797
$707$		0			0
$708$	−24.0000			−0.901975
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	−0.999908	−	0.0135434i	$-0.995689\pi$
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	0.511683	+	0.859174i	$0.329022\pi$
$710$		0			0
$711$	40.0000	+	69.2820i	1.50012	+	2.59828i
$712$	5.65685	−	9.79796i	0.212000	−	0.367194i
$713$	−67.8823			−2.54221
$714$		0			0
$715$		0			0
$716$	−10.0000	+	17.3205i	−0.373718	+	0.647298i
$717$	−22.6274	−	39.1918i	−0.845036	−	1.46365i
$718$	16.0000	+	27.7128i	0.597115	+	1.03423i
$719$	9.89949	−	17.1464i	0.369189	−	0.639454i	−0.620250	−	0.784404i	$-0.712969\pi$
$719$	9.89949	−	17.1464i	0.369189	−	0.639454i	0.989439	+	0.144950i	$0.0463022\pi$
$720$		0			0
$721$		0			0
$722$	−13.0000			−0.483810
$723$	−20.0000	+	34.6410i	−0.743808	+	1.28831i
$724$	2.82843	+	4.89898i	0.105118	+	0.182069i
$725$	5.00000	+	8.66025i	0.185695	+	0.321634i
$726$	−1.41421	+	2.44949i	−0.0524864	+	0.0909091i
$727$	−19.7990			−0.734304			−0.367152	−	0.930161i	$-0.619667\pi$
$727$	−19.7990			−0.734304			−0.367152	+	0.930161i	$0.619667\pi$
$728$		0			0
$729$	−43.0000			−1.59259
$730$		0			0
$731$	−5.65685	−	9.79796i	−0.209226	−	0.362391i
$732$	12.0000	+	20.7846i	0.443533	+	0.768221i
$733$	24.0416	−	41.6413i	0.887998	−	1.53806i	0.0457593	−	0.998952i	$-0.485429\pi$
$733$	24.0416	−	41.6413i	0.887998	−	1.53806i	0.842239	−	0.539105i	$-0.181237\pi$
$734$	−8.48528			−0.313197
$735$		0			0
$736$	−8.00000			−0.294884
$737$	2.00000	−	3.46410i	0.0736709	−	0.127602i
$738$	−7.07107	−	12.2474i	−0.260290	−	0.450835i
$739$	10.0000	+	17.3205i	0.367856	+	0.637145i	0.989230	−	0.146369i	$-0.0467586\pi$
$739$	10.0000	+	17.3205i	0.367856	+	0.637145i	−0.621374	+	0.783514i	$0.713425\pi$
$740$		0			0
$741$	45.2548			1.66248
$742$		0			0
$743$	−8.00000			−0.293492			−0.146746	−	0.989174i	$-0.546880\pi$
$743$	−8.00000			−0.293492			−0.146746	+	0.989174i	$0.546880\pi$
$744$	12.0000	−	20.7846i	0.439941	−	0.762001i
$745$		0			0
$746$	−5.00000	−	8.66025i	−0.183063	−	0.317074i
$747$	−42.4264	+	73.4847i	−1.55230	+	2.68866i
$748$	2.82843			0.103418
$749$		0			0
$750$		0			0
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	−0.411170	−	0.911559i	$-0.634880\pi$
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	0.995018	−	0.0996961i	$-0.0317870\pi$
$752$	1.41421	+	2.44949i	0.0515711	+	0.0893237i
$753$	20.0000	+	34.6410i	0.728841	+	1.26239i
$754$	2.82843	−	4.89898i	0.103005	−	0.178410i
$755$		0			0
$756$		0			0
$757$	10.0000			0.363456			0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000			0.363456			0.181728	+	0.983349i	$0.441831\pi$
$758$	−6.00000	+	10.3923i	−0.217930	+	0.377466i
$759$	−11.3137	−	19.5959i	−0.410662	−	0.711287i
$760$		0			0
$761$	4.24264	−	7.34847i	0.153796	−	0.266382i	−0.778824	−	0.627242i	$-0.784184\pi$
$761$	4.24264	−	7.34847i	0.153796	−	0.266382i	0.932620	+	0.360860i	$0.117517\pi$
$762$		0			0
$763$		0			0
$764$	−8.00000			−0.289430
$765$		0			0
$766$	1.41421	+	2.44949i	0.0510976	+	0.0885037i
$767$	−12.0000	−	20.7846i	−0.433295	−	0.750489i
$768$	1.41421	−	2.44949i	0.0510310	−	0.0883883i
$769$	2.82843			0.101996			0.0509978	−	0.998699i	$-0.483760\pi$
$769$	2.82843			0.101996			0.0509978	+	0.998699i	$0.483760\pi$
$770$		0			0
$771$	−32.0000			−1.15245
$772$	7.00000	−	12.1244i	0.251936	−	0.436365i
$773$	14.1421	+	24.4949i	0.508657	+	0.881020i	0.999950	+	0.0100256i	$0.00319129\pi$
$773$	14.1421	+	24.4949i	0.508657	+	0.881020i	−0.491292	+	0.870995i	$0.663475\pi$
$774$	−10.0000	−	17.3205i	−0.359443	−	0.622573i
$775$	−21.2132	+	36.7423i	−0.762001	+	1.31982i
$776$	−16.9706			−0.609208
$777$		0			0
$778$	−26.0000			−0.932145
$779$	−8.00000	+	13.8564i	−0.286630	+	0.496457i
$780$		0			0
$781$		0			0
$782$	−11.3137	+	19.5959i	−0.404577	+	0.700749i
$783$	−11.3137			−0.404319
$784$		0			0
$785$		0			0
$786$	16.0000	−	27.7128i	0.570701	−	0.988483i
$787$	−19.7990	−	34.2929i	−0.705758	−	1.22241i	−0.966417	−	0.256978i	$-0.917273\pi$
$787$	−19.7990	−	34.2929i	−0.705758	−	1.22241i	0.260660	−	0.965431i	$-0.416060\pi$
$788$	5.00000	+	8.66025i	0.178118	+	0.308509i
$789$	−22.6274	+	39.1918i	−0.805557	+	1.39527i
$790$		0			0
$791$		0			0
$792$	5.00000			0.177667
$793$	−12.0000	+	20.7846i	−0.426132	+	0.738083i
$794$	11.3137	+	19.5959i	0.401508	+	0.695433i
$795$		0			0
$796$	−9.89949	+	17.1464i	−0.350878	+	0.607739i
$797$	11.3137			0.400752			0.200376	−	0.979719i	$-0.435784\pi$
$797$	11.3137			0.400752			0.200376	+	0.979719i	$0.435784\pi$
$798$		0			0
$799$	8.00000			0.283020
$800$	−2.50000	+	4.33013i	−0.0883883	+	0.153093i
$801$	−28.2843	−	48.9898i	−0.999376	−	1.73097i
$802$	15.0000	+	25.9808i	0.529668	+	0.917413i
$803$	7.07107	−	12.2474i	0.249533	−	0.432203i
$804$	−11.3137			−0.399004
$805$		0			0
$806$	24.0000			0.845364
$807$	8.00000	−	13.8564i	0.281613	−	0.487769i
$808$	1.41421	+	2.44949i	0.0497519	+	0.0861727i
$809$	3.00000	+	5.19615i	0.105474	+	0.182687i	0.913932	−	0.405868i	$-0.133031\pi$
$809$	3.00000	+	5.19615i	0.105474	+	0.182687i	−0.808458	+	0.588555i	$0.799697\pi$
$810$		0			0
$811$	22.6274			0.794556			0.397278	−	0.917698i	$-0.369955\pi$
$811$	22.6274			0.794556			0.397278	+	0.917698i	$0.369955\pi$
$812$		0			0
$813$	−48.0000			−1.68343
$814$	−1.00000	+	1.73205i	−0.0350500	+	0.0607083i
$815$		0			0
$816$	−4.00000	−	6.92820i	−0.140028	−	0.242536i
$817$	−11.3137	+	19.5959i	−0.395817	+	0.685574i
$818$	8.48528			0.296681
$819$		0			0
$820$		0			0
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	−0.913616	−	0.406578i	$-0.866722\pi$
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	0.808915	+	0.587925i	$0.200055\pi$
$822$	2.82843	+	4.89898i	0.0986527	+	0.170872i
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	−0.997686	−	0.0679910i	$-0.978341\pi$
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	0.439961	−	0.898017i	$-0.354992\pi$
$824$	−7.07107	+	12.2474i	−0.246332	+	0.426660i
$825$	−14.1421			−0.492366
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$	−20.0000	+	34.6410i	−0.695048	+	1.20386i
$829$	5.65685	+	9.79796i	0.196471	+	0.340297i	0.947382	−	0.320106i	$-0.103719\pi$
$829$	5.65685	+	9.79796i	0.196471	+	0.340297i	−0.750911	+	0.660403i	$0.770385\pi$
$830$		0			0
$831$	31.1127	−	53.8888i	1.07929	−	1.86938i
$832$	2.82843			0.0980581
$833$		0			0
$834$	48.0000			1.66210
$835$		0			0
$836$	−2.82843	−	4.89898i	−0.0978232	−	0.169435i
$837$	−24.0000	−	41.5692i	−0.829561	−	1.43684i
$838$	−12.7279	+	22.0454i	−0.439679	+	0.761546i
$839$	2.82843			0.0976481			0.0488241	−	0.998807i	$-0.484453\pi$
$839$	2.82843			0.0976481			0.0488241	+	0.998807i	$0.484453\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	7.00000	−	12.1244i	0.241236	−	0.417833i
$843$	−14.1421	−	24.4949i	−0.487081	−	0.843649i
$844$	−2.00000	−	3.46410i	−0.0688428	−	0.119239i
$845$		0			0
$846$	14.1421			0.486217
$847$		0			0
$848$	14.0000			0.480762
$849$	−16.0000	+	27.7128i	−0.549119	+	0.951101i
$850$	7.07107	+	12.2474i	0.242536	+	0.420084i
$851$	−8.00000	−	13.8564i	−0.274236	−	0.474991i
$852$		0			0
$853$	−8.48528			−0.290531			−0.145265	−	0.989393i	$-0.546404\pi$
$853$	−8.48528			−0.290531			−0.145265	+	0.989393i	$0.546404\pi$
$854$		0			0
$855$		0			0
$856$	6.00000	−	10.3923i	0.205076	−	0.355202i
$857$	21.2132	+	36.7423i	0.724629	+	1.25509i	0.959126	+	0.282978i	$0.0913223\pi$
$857$	21.2132	+	36.7423i	0.724629	+	1.25509i	−0.234497	+	0.972117i	$0.575344\pi$
$858$	4.00000	+	6.92820i	0.136558	+	0.236525i
$859$	−12.7279	+	22.0454i	−0.434271	+	0.752180i	−0.997236	−	0.0743013i	$-0.976327\pi$
$859$	−12.7279	+	22.0454i	−0.434271	+	0.752180i	0.562965	+	0.826481i	$0.309661\pi$
$860$		0			0
$861$		0			0
$862$	24.0000			0.817443
$863$	20.0000	−	34.6410i	0.680808	−	1.17919i	−0.293927	−	0.955828i	$-0.594962\pi$
$863$	20.0000	−	34.6410i	0.680808	−	1.17919i	0.974735	−	0.223366i	$-0.0717045\pi$
$864$	−2.82843	−	4.89898i	−0.0962250	−	0.166667i
$865$		0			0
$866$	8.48528	−	14.6969i	0.288342	−	0.499422i
$867$	25.4558			0.864526
$868$		0			0
$869$	16.0000			0.542763
$870$		0			0
$871$	−5.65685	−	9.79796i	−0.191675	−	0.331991i
$872$	1.00000	+	1.73205i	0.0338643	+	0.0586546i
$873$	−42.4264	+	73.4847i	−1.43592	+	2.48708i
$874$	45.2548			1.53077
$875$		0			0
$876$	−40.0000			−1.35147
$877$	23.0000	−	39.8372i	0.776655	−	1.34521i	−0.157205	−	0.987566i	$-0.550248\pi$
$877$	23.0000	−	39.8372i	0.776655	−	1.34521i	0.933860	−	0.357640i	$-0.116418\pi$
$878$	−8.48528	−	14.6969i	−0.286364	−	0.495998i
$879$	−20.0000	−	34.6410i	−0.674583	−	1.16841i
$880$		0			0
$881$	5.65685			0.190584			0.0952921	−	0.995449i	$-0.469621\pi$
$881$	5.65685			0.190584			0.0952921	+	0.995449i	$0.469621\pi$
$882$		0			0
$883$	36.0000			1.21150			0.605748	−	0.795656i	$-0.292874\pi$
$883$	36.0000			1.21150			0.605748	+	0.795656i	$0.292874\pi$
$884$	4.00000	−	6.92820i	0.134535	−	0.233021i
$885$		0			0
$886$	6.00000	+	10.3923i	0.201574	+	0.349136i
$887$	14.1421	−	24.4949i	0.474846	−	0.822458i	−0.524739	−	0.851263i	$-0.675837\pi$
$887$	14.1421	−	24.4949i	0.474846	−	0.822458i	0.999585	+	0.0288053i	$0.00917026\pi$
$888$	5.65685			0.189832
$889$		0			0
$890$		0			0
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	7.07107	+	12.2474i	0.236757	+	0.410075i
$893$	−8.00000	−	13.8564i	−0.267710	−	0.463687i
$894$	−8.48528	+	14.6969i	−0.283790	+	0.491539i
$895$		0			0
$896$		0			0
$897$	−64.0000			−2.13690
$898$	5.00000	−	8.66025i	0.166852	−	0.288996i
$899$	8.48528	+	14.6969i	0.283000	+	0.490170i
$900$	12.5000	+	21.6506i	0.416667	+	0.721688i
$901$	19.7990	−	34.2929i	0.659600	−	1.14246i
$902$	−2.82843			−0.0941763
$903$		0			0
$904$	−2.00000			−0.0665190
$905$		0			0
$906$	−22.6274	−	39.1918i	−0.751746	−	1.30206i
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	0.534333	−	0.845274i	$-0.320563\pi$
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	−0.999195	+	0.0401089i	$0.987230\pi$
$908$	5.65685	−	9.79796i	0.187729	−	0.325157i
$909$	14.1421			0.469065
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$	−8.00000	+	13.8564i	−0.264906	+	0.458831i
$913$	8.48528	+	14.6969i	0.280822	+	0.486398i
$914$	−11.0000	−	19.0526i	−0.363848	−	0.630203i
$915$		0			0
$916$	5.65685			0.186908
$917$		0			0
$918$	−16.0000			−0.528079
$919$	−16.0000	+	27.7128i	−0.527791	+	0.914161i	0.471684	+	0.881768i	$0.343646\pi$
$919$	−16.0000	+	27.7128i	−0.527791	+	0.914161i	−0.999475	+	0.0323936i	$0.989687\pi$
$920$		0			0
$921$	32.0000	+	55.4256i	1.05444	+	1.82634i
$922$	9.89949	−	17.1464i	0.326023	−	0.564688i
$923$		0			0
$924$		0			0
$925$	−10.0000			−0.328798
$926$	−4.00000	+	6.92820i	−0.131448	+	0.227675i
$927$	35.3553	+	61.2372i	1.16122	+	2.01129i
$928$	1.00000	+	1.73205i	0.0328266	+	0.0568574i
$929$	−14.1421	+	24.4949i	−0.463988	+	0.803652i	−0.999155	−	0.0410949i	$-0.986915\pi$
$929$	−14.1421	+	24.4949i	−0.463988	+	0.803652i	0.535167	+	0.844746i	$0.320249\pi$
$930$		0			0
$931$		0			0
$932$	22.0000			0.720634
$933$	44.0000	−	76.2102i	1.44050	−	2.49501i
$934$	12.7279	+	22.0454i	0.416470	+	0.721348i
$935$		0			0
$936$	7.07107	−	12.2474i	0.231125	−	0.400320i
$937$	−42.4264			−1.38601			−0.693005	−	0.720933i	$-0.743714\pi$
$937$	−42.4264			−1.38601			−0.693005	+	0.720933i	$0.743714\pi$
$938$		0			0
$939$	−32.0000			−1.04428
$940$		0			0
$941$	1.41421	+	2.44949i	0.0461020	+	0.0798511i	0.888156	−	0.459543i	$-0.151987\pi$
$941$	1.41421	+	2.44949i	0.0461020	+	0.0798511i	−0.842054	+	0.539394i	$0.818653\pi$
$942$	−16.0000	−	27.7128i	−0.521308	−	0.902932i
$943$	11.3137	−	19.5959i	0.368425	−	0.638131i
$944$	8.48528			0.276172
$945$		0			0
$946$	−4.00000			−0.130051
$947$	2.00000	−	3.46410i	0.0649913	−	0.112568i	−0.831699	−	0.555227i	$-0.812631\pi$
$947$	2.00000	−	3.46410i	0.0649913	−	0.112568i	0.896690	+	0.442659i	$0.145965\pi$
$948$	−22.6274	−	39.1918i	−0.734904	−	1.27289i
$949$	−20.0000	−	34.6410i	−0.649227	−	1.12449i
$950$	14.1421	−	24.4949i	0.458831	−	0.794719i
$951$	5.65685			0.183436
$952$		0			0
$953$	−22.0000			−0.712650			−0.356325	−	0.934362i	$-0.615970\pi$
$953$	−22.0000			−0.712650			−0.356325	+	0.934362i	$0.615970\pi$
$954$	35.0000	−	60.6218i	1.13317	−	1.96270i
$955$		0			0
$956$	8.00000	+	13.8564i	0.258738	+	0.448148i
$957$	−2.82843	+	4.89898i	−0.0914301	+	0.158362i
$958$	−16.9706			−0.548294
$959$		0			0
$960$		0			0
$961$	−20.5000	+	35.5070i	−0.661290	+	1.14539i
$962$	2.82843	+	4.89898i	0.0911922	+	0.157949i
$963$	−30.0000	−	51.9615i	−0.966736	−	1.67444i
$964$	7.07107	−	12.2474i	0.227744	−	0.394464i
$965$		0			0
$966$		0			0
$967$	16.0000			0.514525			0.257263	−	0.966342i	$-0.417179\pi$
$967$	16.0000			0.514525			0.257263	+	0.966342i	$0.417179\pi$
$968$	0.500000	−	0.866025i	0.0160706	−	0.0278351i
$969$	22.6274	+	39.1918i	0.726897	+	1.25902i
$970$		0			0
$971$	−18.3848	+	31.8434i	−0.589996	+	1.02190i	0.404237	+	0.914654i	$0.367537\pi$
$971$	−18.3848	+	31.8434i	−0.589996	+	1.02190i	−0.994232	+	0.107248i	$0.965796\pi$
$972$	14.1421			0.453609
$973$		0			0
$974$	8.00000			0.256337
$975$	−20.0000	+	34.6410i	−0.640513	+	1.10940i
$976$	−4.24264	−	7.34847i	−0.135804	−	0.235219i
$977$	9.00000	+	15.5885i	0.287936	+	0.498719i	0.973317	−	0.229465i	$-0.0736978\pi$
$977$	9.00000	+	15.5885i	0.287936	+	0.498719i	−0.685381	+	0.728184i	$0.740364\pi$
$978$	5.65685	−	9.79796i	0.180886	−	0.313304i
$979$	−11.3137			−0.361588
$980$		0			0
$981$	10.0000			0.319275
$982$	−14.0000	+	24.2487i	−0.446758	+	0.773807i
$983$	1.41421	+	2.44949i	0.0451064	+	0.0781266i	0.887697	−	0.460428i	$-0.152304\pi$
$983$	1.41421	+	2.44949i	0.0451064	+	0.0781266i	−0.842591	+	0.538554i	$0.818971\pi$
$984$	4.00000	+	6.92820i	0.127515	+	0.220863i
$985$		0			0
$986$	5.65685			0.180151
$987$		0			0
$988$	−16.0000			−0.509028
$989$	16.0000	−	27.7128i	0.508770	−	0.881216i
$990$		0			0
$991$	20.0000	+	34.6410i	0.635321	+	1.10041i	0.986447	+	0.164080i	$0.0524655\pi$
$991$	20.0000	+	34.6410i	0.635321	+	1.10041i	−0.351126	+	0.936328i	$0.614201\pi$
$992$	−4.24264	+	7.34847i	−0.134704	+	0.233314i
$993$	79.1960			2.51321
$994$		0			0
$995$		0			0
$996$	24.0000	−	41.5692i	0.760469	−	1.31717i
$997$	21.2132	+	36.7423i	0.671829	+	1.16364i	0.977385	+	0.211468i	$0.0678243\pi$
$997$	21.2132	+	36.7423i	0.671829	+	1.16364i	−0.305556	+	0.952174i	$0.598842\pi$
$998$	−6.00000	−	10.3923i	−0.189927	−	0.328963i
$999$	5.65685	−	9.79796i	0.178975	−	0.309994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.e.r.177.2		4
7.2	even	3		1078.2.a.r.1.1	✓	2
7.3	odd	6	inner	1078.2.e.r.67.1		4
7.4	even	3	inner	1078.2.e.r.67.2		4
7.5	odd	6		1078.2.a.r.1.2	yes	2
7.6	odd	2	inner	1078.2.e.r.177.1		4
21.2	odd	6		9702.2.a.dn.1.2		2
21.5	even	6		9702.2.a.dn.1.1		2
28.19	even	6		8624.2.a.by.1.1		2
28.23	odd	6		8624.2.a.by.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1078.2.a.r.1.1	✓	2	7.2	even	3
1078.2.a.r.1.2	yes	2	7.5	odd	6
1078.2.e.r.67.1		4	7.3	odd	6	inner
1078.2.e.r.67.2		4	7.4	even	3	inner
1078.2.e.r.177.1		4	7.6	odd	2	inner
1078.2.e.r.177.2		4	1.1	even	1	trivial
8624.2.a.by.1.1		2	28.19	even	6
8624.2.a.by.1.2		2	28.23	odd	6
9702.2.a.dn.1.1		2	21.5	even	6
9702.2.a.dn.1.2		2	21.2	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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.41421 + 2.44949i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.82843 q^{6} -1.00000 q^{8} +(-2.50000 + 4.33013i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.41421 + 2.44949i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.82843 q^{6} -1.00000 q^{8} +(-2.50000 + 4.33013i) q^{9} +(0.500000 + 0.866025i) q^{11} +(1.41421 - 2.44949i) q^{12} +2.82843 q^{13} +(-0.500000 + 0.866025i) q^{16} +(1.41421 + 2.44949i) q^{17} +(2.50000 + 4.33013i) q^{18} +(2.82843 - 4.89898i) q^{19} +1.00000 q^{22} +(-4.00000 + 6.92820i) q^{23} +(-1.41421 - 2.44949i) q^{24} +(2.50000 + 4.33013i) q^{25} +(1.41421 - 2.44949i) q^{26} -5.65685 q^{27} +2.00000 q^{29} +(4.24264 + 7.34847i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.41421 + 2.44949i) q^{33} +2.82843 q^{34} +5.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(-2.82843 - 4.89898i) q^{38} +(4.00000 + 6.92820i) q^{39} -2.82843 q^{41} -4.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(4.00000 + 6.92820i) q^{46} +(1.41421 - 2.44949i) q^{47} -2.82843 q^{48} +5.00000 q^{50} +(-4.00000 + 6.92820i) q^{51} +(-1.41421 - 2.44949i) q^{52} +(-7.00000 - 12.1244i) q^{53} +(-2.82843 + 4.89898i) q^{54} +16.0000 q^{57} +(1.00000 - 1.73205i) q^{58} +(-4.24264 - 7.34847i) q^{59} +(-4.24264 + 7.34847i) q^{61} +8.48528 q^{62} +1.00000 q^{64} +(1.41421 + 2.44949i) q^{66} +(-2.00000 - 3.46410i) q^{67} +(1.41421 - 2.44949i) q^{68} -22.6274 q^{69} +(2.50000 - 4.33013i) q^{72} +(-7.07107 - 12.2474i) q^{73} +(1.00000 + 1.73205i) q^{74} +(-7.07107 + 12.2474i) q^{75} -5.65685 q^{76} +8.00000 q^{78} +(8.00000 - 13.8564i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.41421 + 2.44949i) q^{82} +16.9706 q^{83} +(-2.00000 + 3.46410i) q^{86} +(2.82843 + 4.89898i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-5.65685 + 9.79796i) q^{89} +8.00000 q^{92} +(-12.0000 + 20.7846i) q^{93} +(-1.41421 - 2.44949i) q^{94} +(-1.41421 + 2.44949i) q^{96} +16.9706 q^{97} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 10 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 10 * q^9	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 10 q^{9} + 2 q^{11} - 2 q^{16} + 10 q^{18} + 4 q^{22} - 16 q^{23} + 10 q^{25} + 8 q^{29} + 2 q^{32} + 20 q^{36} - 4 q^{37} + 16 q^{39} - 16 q^{43} + 2 q^{44} + 16 q^{46} + 20 q^{50} - 16 q^{51} - 28 q^{53} + 64 q^{57} + 4 q^{58} + 4 q^{64} - 8 q^{67} + 10 q^{72} + 4 q^{74} + 32 q^{78} + 32 q^{79} - 2 q^{81} - 8 q^{86} - 2 q^{88} + 32 q^{92} - 48 q^{93} - 20 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 10 * q^9 + 2 * q^11 - 2 * q^16 + 10 * q^18 + 4 * q^22 - 16 * q^23 + 10 * q^25 + 8 * q^29 + 2 * q^32 + 20 * q^36 - 4 * q^37 + 16 * q^39 - 16 * q^43 + 2 * q^44 + 16 * q^46 + 20 * q^50 - 16 * q^51 - 28 * q^53 + 64 * q^57 + 4 * q^58 + 4 * q^64 - 8 * q^67 + 10 * q^72 + 4 * q^74 + 32 * q^78 + 32 * q^79 - 2 * q^81 - 8 * q^86 - 2 * q^88 + 32 * q^92 - 48 * q^93 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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