LMFDB - Embedded newform 1078.2.e.t.177.1

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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1078.177
Dual form			1078.2.e.t.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.41421 + 2.44949i) q^{5} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.41421 + 2.44949i) q^{5} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(1.41421 + 2.44949i) q^{10} +(-0.500000 - 0.866025i) q^{11} +4.24264 q^{13} +(-0.500000 + 0.866025i) q^{16} +(1.41421 + 2.44949i) q^{17} +(-1.50000 - 2.59808i) q^{18} +(-0.707107 + 1.22474i) q^{19} +2.82843 q^{20} -1.00000 q^{22} +(-3.00000 + 5.19615i) q^{23} +(-1.50000 - 2.59808i) q^{25} +(2.12132 - 3.67423i) q^{26} +8.00000 q^{29} +(0.707107 + 1.22474i) q^{31} +(0.500000 + 0.866025i) q^{32} +2.82843 q^{34} -3.00000 q^{36} +(3.00000 - 5.19615i) q^{37} +(0.707107 + 1.22474i) q^{38} +(1.41421 - 2.44949i) q^{40} +8.48528 q^{41} +10.0000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(4.24264 + 7.34847i) q^{45} +(3.00000 + 5.19615i) q^{46} +(3.53553 - 6.12372i) q^{47} -3.00000 q^{50} +(-2.12132 - 3.67423i) q^{52} +(-3.00000 - 5.19615i) q^{53} +2.82843 q^{55} +(4.00000 - 6.92820i) q^{58} +(7.07107 + 12.2474i) q^{59} +(2.12132 - 3.67423i) q^{61} +1.41421 q^{62} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{65} +(2.00000 + 3.46410i) q^{67} +(1.41421 - 2.44949i) q^{68} +(-1.50000 + 2.59808i) q^{72} +(-4.24264 - 7.34847i) q^{73} +(-3.00000 - 5.19615i) q^{74} +1.41421 q^{76} +(-1.41421 - 2.44949i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(4.24264 - 7.34847i) q^{82} -7.07107 q^{83} -8.00000 q^{85} +(5.00000 - 8.66025i) q^{86} +(0.500000 + 0.866025i) q^{88} +(-9.19239 + 15.9217i) q^{89} +8.48528 q^{90} +6.00000 q^{92} +(-3.53553 - 6.12372i) q^{94} +(-2.00000 - 3.46410i) q^{95} -1.41421 q^{97} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 + 6 * q^9	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 6 q^{9} - 2 q^{11} - 2 q^{16} - 6 q^{18} - 4 q^{22} - 12 q^{23} - 6 q^{25} + 32 q^{29} + 2 q^{32} - 12 q^{36} + 12 q^{37} + 40 q^{43} - 2 q^{44} + 12 q^{46} - 12 q^{50} - 12 q^{53} + 16 q^{58} + 4 q^{64} - 24 q^{65} + 8 q^{67} - 6 q^{72} - 12 q^{74} - 18 q^{81} - 32 q^{85} + 20 q^{86} + 2 q^{88} + 24 q^{92} - 8 q^{95} - 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 + 6 * q^9 - 2 * q^11 - 2 * q^16 - 6 * q^18 - 4 * q^22 - 12 * q^23 - 6 * q^25 + 32 * q^29 + 2 * q^32 - 12 * q^36 + 12 * q^37 + 40 * q^43 - 2 * q^44 + 12 * q^46 - 12 * q^50 - 12 * q^53 + 16 * q^58 + 4 * q^64 - 24 * q^65 + 8 * q^67 - 6 * q^72 - 12 * q^74 - 18 * q^81 - 32 * q^85 + 20 * q^86 + 2 * q^88 + 24 * q^92 - 8 * q^95 - 12 * 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
$3$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$3$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.41421	+	2.44949i	−0.632456	+	1.09545i	0.354593	+	0.935021i	$0.384620\pi$
$5$	−1.41421	+	2.44949i	−0.632456	+	1.09545i	−0.987048	+	0.160424i	$0.948714\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	1.41421	+	2.44949i	0.447214	+	0.774597i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	4.24264			1.17670			0.588348	−	0.808608i	$-0.299778\pi$
$13$	4.24264			1.17670			0.588348	+	0.808608i	$0.299778\pi$
$14$		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	$0.721891\pi$
$18$	−1.50000	−	2.59808i	−0.353553	−	0.612372i
$19$	−0.707107	+	1.22474i	−0.162221	+	0.280976i	−0.935665	−	0.352889i	$-0.885199\pi$
$19$	−0.707107	+	1.22474i	−0.162221	+	0.280976i	0.773444	+	0.633865i	$0.218533\pi$
$20$	2.82843			0.632456
$21$		0			0
$22$	−1.00000			−0.213201
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$		0			0
$25$	−1.50000	−	2.59808i	−0.300000	−	0.519615i
$26$	2.12132	−	3.67423i	0.416025	−	0.720577i
$27$		0			0
$28$		0			0
$29$	8.00000			1.48556			0.742781	−	0.669534i	$-0.233506\pi$
$29$	8.00000			1.48556			0.742781	+	0.669534i	$0.233506\pi$
$30$		0			0
$31$	0.707107	+	1.22474i	0.127000	+	0.219971i	0.922513	−	0.385966i	$-0.126132\pi$
$31$	0.707107	+	1.22474i	0.127000	+	0.219971i	−0.795513	+	0.605937i	$0.792798\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	2.82843			0.485071
$35$		0			0
$36$	−3.00000			−0.500000
$37$	3.00000	−	5.19615i	0.493197	−	0.854242i	−0.506772	−	0.862080i	$-0.669162\pi$
$37$	3.00000	−	5.19615i	0.493197	−	0.854242i	0.999969	+	0.00783774i	$0.00249486\pi$
$38$	0.707107	+	1.22474i	0.114708	+	0.198680i
$39$		0			0
$40$	1.41421	−	2.44949i	0.223607	−	0.387298i
$41$	8.48528			1.32518			0.662589	−	0.748983i	$-0.269458\pi$
$41$	8.48528			1.32518			0.662589	+	0.748983i	$0.269458\pi$
$42$		0			0
$43$	10.0000			1.52499			0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000			1.52499			0.762493	+	0.646997i	$0.223975\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$	4.24264	+	7.34847i	0.632456	+	1.09545i
$46$	3.00000	+	5.19615i	0.442326	+	0.766131i
$47$	3.53553	−	6.12372i	0.515711	−	0.893237i	−0.484123	−	0.875000i	$-0.660861\pi$
$47$	3.53553	−	6.12372i	0.515711	−	0.893237i	0.999834	−	0.0182371i	$-0.00580537\pi$
$48$		0			0
$49$		0			0
$50$	−3.00000			−0.424264
$51$		0			0
$52$	−2.12132	−	3.67423i	−0.294174	−	0.509525i
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$		0			0
$55$	2.82843			0.381385
$56$		0			0
$57$		0			0
$58$	4.00000	−	6.92820i	0.525226	−	0.909718i
$59$	7.07107	+	12.2474i	0.920575	+	1.59448i	0.798528	+	0.601958i	$0.205612\pi$
$59$	7.07107	+	12.2474i	0.920575	+	1.59448i	0.122047	+	0.992524i	$0.461054\pi$
$60$		0			0
$61$	2.12132	−	3.67423i	0.271607	−	0.470438i	−0.697666	−	0.716423i	$-0.745778\pi$
$61$	2.12132	−	3.67423i	0.271607	−	0.470438i	0.969274	+	0.245985i	$0.0791115\pi$
$62$	1.41421			0.179605
$63$		0			0
$64$	1.00000			0.125000
$65$	−6.00000	+	10.3923i	−0.744208	+	1.28901i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	1.41421	−	2.44949i	0.171499	−	0.297044i
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	−1.50000	+	2.59808i	−0.176777	+	0.306186i
$73$	−4.24264	−	7.34847i	−0.496564	−	0.860073i	0.503429	−	0.864037i	$-0.332072\pi$
$73$	−4.24264	−	7.34847i	−0.496564	−	0.860073i	−0.999992	+	0.00396356i	$0.998738\pi$
$74$	−3.00000	−	5.19615i	−0.348743	−	0.604040i
$75$		0			0
$76$	1.41421			0.162221
$77$		0			0
$78$		0			0
$79$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$79$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$80$	−1.41421	−	2.44949i	−0.158114	−	0.273861i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	4.24264	−	7.34847i	0.468521	−	0.811503i
$83$	−7.07107			−0.776151			−0.388075	−	0.921628i	$-0.626860\pi$
$83$	−7.07107			−0.776151			−0.388075	+	0.921628i	$0.626860\pi$
$84$		0			0
$85$	−8.00000			−0.867722
$86$	5.00000	−	8.66025i	0.539164	−	0.933859i
$87$		0			0
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	−9.19239	+	15.9217i	−0.974391	+	1.68770i	−0.292462	+	0.956277i	$0.594474\pi$
$89$	−9.19239	+	15.9217i	−0.974391	+	1.68770i	−0.681930	+	0.731418i	$0.738859\pi$
$90$	8.48528			0.894427
$91$		0			0
$92$	6.00000			0.625543
$93$		0			0
$94$	−3.53553	−	6.12372i	−0.364662	−	0.631614i
$95$	−2.00000	−	3.46410i	−0.205196	−	0.355409i
$96$		0			0
$97$	−1.41421			−0.143592			−0.0717958	−	0.997419i	$-0.522873\pi$
$97$	−1.41421			−0.143592			−0.0717958	+	0.997419i	$0.522873\pi$
$98$		0			0
$99$	−3.00000			−0.301511
$100$	−1.50000	+	2.59808i	−0.150000	+	0.259808i
$101$	0.707107	+	1.22474i	0.0703598	+	0.121867i	0.899059	−	0.437828i	$-0.144252\pi$
$101$	0.707107	+	1.22474i	0.0703598	+	0.121867i	−0.828699	+	0.559694i	$0.810919\pi$
$102$		0			0
$103$	−2.12132	+	3.67423i	−0.209020	+	0.362033i	−0.951406	−	0.307939i	$-0.900361\pi$
$103$	−2.12132	+	3.67423i	−0.209020	+	0.362033i	0.742386	+	0.669972i	$0.233694\pi$
$104$	−4.24264			−0.416025
$105$		0			0
$106$	−6.00000			−0.582772
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.00813215	+	0.999967i	$0.502589\pi$
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.861931	+	0.507026i	$0.830745\pi$
$108$		0			0
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	−0.977769	−	0.209687i	$-0.932756\pi$
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	0.307290	−	0.951616i	$-0.400578\pi$
$110$	1.41421	−	2.44949i	0.134840	−	0.233550i
$111$		0			0
$112$		0			0
$113$	8.00000			0.752577			0.376288	−	0.926503i	$-0.377200\pi$
$113$	8.00000			0.752577			0.376288	+	0.926503i	$0.377200\pi$
$114$		0			0
$115$	−8.48528	−	14.6969i	−0.791257	−	1.37050i
$116$	−4.00000	−	6.92820i	−0.371391	−	0.643268i
$117$	6.36396	−	11.0227i	0.588348	−	1.01905i
$118$	14.1421			1.30189
$119$		0			0
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−2.12132	−	3.67423i	−0.192055	−	0.332650i
$123$		0			0
$124$	0.707107	−	1.22474i	0.0635001	−	0.109985i
$125$	−5.65685			−0.505964
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	6.00000	+	10.3923i	0.526235	+	0.911465i
$131$	−3.53553	+	6.12372i	−0.308901	+	0.535032i	−0.978122	−	0.208031i	$-0.933295\pi$
$131$	−3.53553	+	6.12372i	−0.308901	+	0.535032i	0.669221	+	0.743063i	$0.266628\pi$
$132$		0			0
$133$		0			0
$134$	4.00000			0.345547
$135$		0			0
$136$	−1.41421	−	2.44949i	−0.121268	−	0.210042i
$137$	−5.00000	−	8.66025i	−0.427179	−	0.739895i	0.569442	−	0.822031i	$-0.307159\pi$
$137$	−5.00000	−	8.66025i	−0.427179	−	0.739895i	−0.996621	+	0.0821359i	$0.973826\pi$
$138$		0			0
$139$	−21.2132			−1.79928			−0.899640	−	0.436632i	$-0.856171\pi$
$139$	−21.2132			−1.79928			−0.899640	+	0.436632i	$0.856171\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.12132	−	3.67423i	−0.177394	−	0.307255i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	−11.3137	+	19.5959i	−0.939552	+	1.62735i
$146$	−8.48528			−0.702247
$147$		0			0
$148$	−6.00000			−0.493197
$149$	−2.00000	+	3.46410i	−0.163846	+	0.283790i	−0.936245	−	0.351348i	$-0.885723\pi$
$149$	−2.00000	+	3.46410i	−0.163846	+	0.283790i	0.772399	+	0.635138i	$0.219057\pi$
$150$		0			0
$151$	10.0000	+	17.3205i	0.813788	+	1.40952i	0.910195	+	0.414181i	$0.135932\pi$
$151$	10.0000	+	17.3205i	0.813788	+	1.40952i	−0.0964061	+	0.995342i	$0.530735\pi$
$152$	0.707107	−	1.22474i	0.0573539	−	0.0993399i
$153$	8.48528			0.685994
$154$		0			0
$155$	−4.00000			−0.321288
$156$		0			0
$157$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$157$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$158$		0			0
$159$		0			0
$160$	−2.82843			−0.223607
$161$		0			0
$162$	−9.00000			−0.707107
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	−0.361619	−	0.932326i	$-0.617776\pi$
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	0.988227	−	0.152992i	$-0.0488907\pi$
$164$	−4.24264	−	7.34847i	−0.331295	−	0.573819i
$165$		0			0
$166$	−3.53553	+	6.12372i	−0.274411	+	0.475293i
$167$	−14.1421			−1.09435			−0.547176	−	0.837018i	$-0.684297\pi$
$167$	−14.1421			−1.09435			−0.547176	+	0.837018i	$0.684297\pi$
$168$		0			0
$169$	5.00000			0.384615
$170$	−4.00000	+	6.92820i	−0.306786	+	0.531369i
$171$	2.12132	+	3.67423i	0.162221	+	0.280976i
$172$	−5.00000	−	8.66025i	−0.381246	−	0.660338i
$173$	7.77817	−	13.4722i	0.591364	−	1.02427i	−0.402685	−	0.915338i	$-0.631923\pi$
$173$	7.77817	−	13.4722i	0.591364	−	1.02427i	0.994049	−	0.108933i	$-0.0347435\pi$
$174$		0			0
$175$		0			0
$176$	1.00000			0.0753778
$177$		0			0
$178$	9.19239	+	15.9217i	0.688999	+	1.19338i
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	0.998286	−	0.0585225i	$-0.0186389\pi$
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	−0.549825	+	0.835280i	$0.685306\pi$
$180$	4.24264	−	7.34847i	0.316228	−	0.547723i
$181$	−8.48528			−0.630706			−0.315353	−	0.948974i	$-0.602123\pi$
$181$	−8.48528			−0.630706			−0.315353	+	0.948974i	$0.602123\pi$
$182$		0			0
$183$		0			0
$184$	3.00000	−	5.19615i	0.221163	−	0.383065i
$185$	8.48528	+	14.6969i	0.623850	+	1.08054i
$186$		0			0
$187$	1.41421	−	2.44949i	0.103418	−	0.179124i
$188$	−7.07107			−0.515711
$189$		0			0
$190$	−4.00000			−0.290191
$191$	11.0000	−	19.0526i	0.795932	−	1.37859i	−0.126314	−	0.991990i	$-0.540315\pi$
$191$	11.0000	−	19.0526i	0.795932	−	1.37859i	0.922246	−	0.386604i	$-0.126352\pi$
$192$		0			0
$193$	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	$0.665242\pi$
$194$	−0.707107	+	1.22474i	−0.0507673	+	0.0879316i
$195$		0			0
$196$		0			0
$197$	10.0000			0.712470			0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000			0.712470			0.356235	+	0.934396i	$0.384060\pi$
$198$	−1.50000	+	2.59808i	−0.106600	+	0.184637i
$199$	−2.12132	−	3.67423i	−0.150376	−	0.260460i	0.780989	−	0.624544i	$-0.214715\pi$
$199$	−2.12132	−	3.67423i	−0.150376	−	0.260460i	−0.931366	+	0.364085i	$0.881382\pi$
$200$	1.50000	+	2.59808i	0.106066	+	0.183712i
$201$		0			0
$202$	1.41421			0.0995037
$203$		0			0
$204$		0			0
$205$	−12.0000	+	20.7846i	−0.838116	+	1.45166i
$206$	2.12132	+	3.67423i	0.147799	+	0.255996i
$207$	9.00000	+	15.5885i	0.625543	+	1.08347i
$208$	−2.12132	+	3.67423i	−0.147087	+	0.254762i
$209$	1.41421			0.0978232
$210$		0			0
$211$	−14.0000			−0.963800			−0.481900	−	0.876226i	$-0.660053\pi$
$211$	−14.0000			−0.963800			−0.481900	+	0.876226i	$0.660053\pi$
$212$	−3.00000	+	5.19615i	−0.206041	+	0.356873i
$213$		0			0
$214$	9.00000	+	15.5885i	0.615227	+	1.06561i
$215$	−14.1421	+	24.4949i	−0.964486	+	1.67054i
$216$		0			0
$217$		0			0
$218$	−14.0000			−0.948200
$219$		0			0
$220$	−1.41421	−	2.44949i	−0.0953463	−	0.165145i
$221$	6.00000	+	10.3923i	0.403604	+	0.699062i
$222$		0			0
$223$	−12.7279			−0.852325			−0.426162	−	0.904647i	$-0.640135\pi$
$223$	−12.7279			−0.852325			−0.426162	+	0.904647i	$0.640135\pi$
$224$		0			0
$225$	−9.00000			−0.600000
$226$	4.00000	−	6.92820i	0.266076	−	0.460857i
$227$	−13.4350	−	23.2702i	−0.891714	−	1.54449i	−0.837819	−	0.545948i	$-0.816170\pi$
$227$	−13.4350	−	23.2702i	−0.891714	−	1.54449i	−0.0538949	−	0.998547i	$-0.517164\pi$
$228$		0			0
$229$	12.7279	−	22.0454i	0.841085	−	1.45680i	−0.0478936	−	0.998852i	$-0.515251\pi$
$229$	12.7279	−	22.0454i	0.841085	−	1.45680i	0.888978	−	0.457949i	$-0.151416\pi$
$230$	−16.9706			−1.11901
$231$		0			0
$232$	−8.00000			−0.525226
$233$	−1.00000	+	1.73205i	−0.0655122	+	0.113470i	−0.896921	−	0.442191i	$-0.854201\pi$
$233$	−1.00000	+	1.73205i	−0.0655122	+	0.113470i	0.831409	+	0.555661i	$0.187535\pi$
$234$	−6.36396	−	11.0227i	−0.416025	−	0.720577i
$235$	10.0000	+	17.3205i	0.652328	+	1.12987i
$236$	7.07107	−	12.2474i	0.460287	−	0.797241i
$237$		0			0
$238$		0			0
$239$	−4.00000			−0.258738			−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000			−0.258738			−0.129369	+	0.991596i	$0.541295\pi$
$240$		0			0
$241$	1.41421	+	2.44949i	0.0910975	+	0.157786i	0.907973	−	0.419028i	$-0.137629\pi$
$241$	1.41421	+	2.44949i	0.0910975	+	0.157786i	−0.816876	+	0.576814i	$0.804296\pi$
$242$	0.500000	+	0.866025i	0.0321412	+	0.0556702i
$243$		0			0
$244$	−4.24264			−0.271607
$245$		0			0
$246$		0			0
$247$	−3.00000	+	5.19615i	−0.190885	+	0.330623i
$248$	−0.707107	−	1.22474i	−0.0449013	−	0.0777714i
$249$		0			0
$250$	−2.82843	+	4.89898i	−0.178885	+	0.309839i
$251$	25.4558			1.60676			0.803379	−	0.595468i	$-0.203033\pi$
$251$	25.4558			1.60676			0.803379	+	0.595468i	$0.203033\pi$
$252$		0			0
$253$	6.00000			0.377217
$254$	4.00000	−	6.92820i	0.250982	−	0.434714i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.19239	+	15.9217i	−0.573405	+	0.993167i	0.422807	+	0.906220i	$0.361045\pi$
$257$	−9.19239	+	15.9217i	−0.573405	+	0.993167i	−0.996213	+	0.0869478i	$0.972289\pi$
$258$		0			0
$259$		0			0
$260$	12.0000			0.744208
$261$	12.0000	−	20.7846i	0.742781	−	1.28654i
$262$	3.53553	+	6.12372i	0.218426	+	0.378325i
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	0.619586	−	0.784929i	$-0.287301\pi$
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$264$		0			0
$265$	16.9706			1.04249
$266$		0			0
$267$		0			0
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	−12.7279	−	22.0454i	−0.776035	−	1.34413i	−0.934211	−	0.356721i	$-0.883895\pi$
$269$	−12.7279	−	22.0454i	−0.776035	−	1.34413i	0.158176	−	0.987411i	$-0.449439\pi$
$270$		0			0
$271$	4.24264	−	7.34847i	0.257722	−	0.446388i	−0.707909	−	0.706303i	$-0.750361\pi$
$271$	4.24264	−	7.34847i	0.257722	−	0.446388i	0.965631	+	0.259916i	$0.0836948\pi$
$272$	−2.82843			−0.171499
$273$		0			0
$274$	−10.0000			−0.604122
$275$	−1.50000	+	2.59808i	−0.0904534	+	0.156670i
$276$		0			0
$277$	−2.00000	−	3.46410i	−0.120168	−	0.208138i	0.799666	−	0.600446i	$-0.205010\pi$
$277$	−2.00000	−	3.46410i	−0.120168	−	0.208138i	−0.919834	+	0.392308i	$0.871677\pi$
$278$	−10.6066	+	18.3712i	−0.636142	+	1.10183i
$279$	4.24264			0.254000
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	2.12132	+	3.67423i	0.126099	+	0.218411i	0.922162	−	0.386804i	$-0.126421\pi$
$283$	2.12132	+	3.67423i	0.126099	+	0.218411i	−0.796063	+	0.605214i	$0.793088\pi$
$284$		0			0
$285$		0			0
$286$	−4.24264			−0.250873
$287$		0			0
$288$	3.00000			0.176777
$289$	4.50000	−	7.79423i	0.264706	−	0.458484i
$290$	11.3137	+	19.5959i	0.664364	+	1.15071i
$291$		0			0
$292$	−4.24264	+	7.34847i	−0.248282	+	0.430037i
$293$	−15.5563			−0.908812			−0.454406	−	0.890795i	$-0.650148\pi$
$293$	−15.5563			−0.908812			−0.454406	+	0.890795i	$0.650148\pi$
$294$		0			0
$295$	−40.0000			−2.32889
$296$	−3.00000	+	5.19615i	−0.174371	+	0.302020i
$297$		0			0
$298$	2.00000	+	3.46410i	0.115857	+	0.200670i
$299$	−12.7279	+	22.0454i	−0.736075	+	1.27492i
$300$		0			0
$301$		0			0
$302$	20.0000			1.15087
$303$		0			0
$304$	−0.707107	−	1.22474i	−0.0405554	−	0.0702439i
$305$	6.00000	+	10.3923i	0.343559	+	0.595062i
$306$	4.24264	−	7.34847i	0.242536	−	0.420084i
$307$	−24.0416			−1.37213			−0.686064	−	0.727541i	$-0.740663\pi$
$307$	−24.0416			−1.37213			−0.686064	+	0.727541i	$0.740663\pi$
$308$		0			0
$309$		0			0
$310$	−2.00000	+	3.46410i	−0.113592	+	0.196748i
$311$	12.0208	+	20.8207i	0.681638	+	1.18063i	0.974481	+	0.224471i	$0.0720654\pi$
$311$	12.0208	+	20.8207i	0.681638	+	1.18063i	−0.292843	+	0.956161i	$0.594601\pi$
$312$		0			0
$313$	6.36396	−	11.0227i	0.359712	−	0.623040i	−0.628200	−	0.778052i	$-0.716208\pi$
$313$	6.36396	−	11.0227i	0.359712	−	0.623040i	0.987913	+	0.155012i	$0.0495415\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	15.0000	−	25.9808i	0.842484	−	1.45922i	−0.0453045	−	0.998973i	$-0.514426\pi$
$317$	15.0000	−	25.9808i	0.842484	−	1.45922i	0.887788	−	0.460252i	$-0.152241\pi$
$318$		0			0
$319$	−4.00000	−	6.92820i	−0.223957	−	0.387905i
$320$	−1.41421	+	2.44949i	−0.0790569	+	0.136931i
$321$		0			0
$322$		0			0
$323$	−4.00000			−0.222566
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−6.36396	−	11.0227i	−0.353009	−	0.611430i
$326$	−8.00000	−	13.8564i	−0.443079	−	0.767435i
$327$		0			0
$328$	−8.48528			−0.468521
$329$		0			0
$330$		0			0
$331$	16.0000	−	27.7128i	0.879440	−	1.52323i	0.0274825	−	0.999622i	$-0.491251\pi$
$331$	16.0000	−	27.7128i	0.879440	−	1.52323i	0.851957	−	0.523612i	$-0.175416\pi$
$332$	3.53553	+	6.12372i	0.194038	+	0.336083i
$333$	−9.00000	−	15.5885i	−0.493197	−	0.854242i
$334$	−7.07107	+	12.2474i	−0.386912	+	0.670151i
$335$	−11.3137			−0.618134
$336$		0			0
$337$	−18.0000			−0.980522			−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000			−0.980522			−0.490261	+	0.871576i	$0.663099\pi$
$338$	2.50000	−	4.33013i	0.135982	−	0.235528i
$339$		0			0
$340$	4.00000	+	6.92820i	0.216930	+	0.375735i
$341$	0.707107	−	1.22474i	0.0382920	−	0.0663237i
$342$	4.24264			0.229416
$343$		0			0
$344$	−10.0000			−0.539164
$345$		0			0
$346$	−7.77817	−	13.4722i	−0.418157	−	0.724270i
$347$	−5.00000	−	8.66025i	−0.268414	−	0.464907i	0.700038	−	0.714105i	$-0.253166\pi$
$347$	−5.00000	−	8.66025i	−0.268414	−	0.464907i	−0.968452	+	0.249198i	$0.919833\pi$
$348$		0			0
$349$	−9.89949			−0.529908			−0.264954	−	0.964261i	$-0.585357\pi$
$349$	−9.89949			−0.529908			−0.264954	+	0.964261i	$0.585357\pi$
$350$		0			0
$351$		0			0
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	14.8492	+	25.7196i	0.790345	+	1.36892i	0.925753	+	0.378128i	$0.123432\pi$
$353$	14.8492	+	25.7196i	0.790345	+	1.36892i	−0.135408	+	0.990790i	$0.543234\pi$
$354$		0			0
$355$		0			0
$356$	18.3848			0.974391
$357$		0			0
$358$	12.0000			0.634220
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	0.353529	+	0.935423i	$0.384981\pi$
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	−0.986865	+	0.161546i	$0.948352\pi$
$360$	−4.24264	−	7.34847i	−0.223607	−	0.387298i
$361$	8.50000	+	14.7224i	0.447368	+	0.774865i
$362$	−4.24264	+	7.34847i	−0.222988	+	0.386227i
$363$		0			0
$364$		0			0
$365$	24.0000			1.25622
$366$		0			0
$367$	−12.0208	−	20.8207i	−0.627481	−	1.08683i	−0.988055	−	0.154099i	$-0.950752\pi$
$367$	−12.0208	−	20.8207i	−0.627481	−	1.08683i	0.360574	−	0.932731i	$-0.382581\pi$
$368$	−3.00000	−	5.19615i	−0.156386	−	0.270868i
$369$	12.7279	−	22.0454i	0.662589	−	1.14764i
$370$	16.9706			0.882258
$371$		0			0
$372$		0			0
$373$	−13.0000	+	22.5167i	−0.673114	+	1.16587i	0.303902	+	0.952703i	$0.401711\pi$
$373$	−13.0000	+	22.5167i	−0.673114	+	1.16587i	−0.977016	+	0.213165i	$0.931623\pi$
$374$	−1.41421	−	2.44949i	−0.0731272	−	0.126660i
$375$		0			0
$376$	−3.53553	+	6.12372i	−0.182331	+	0.315807i
$377$	33.9411			1.74806
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$	−2.00000	+	3.46410i	−0.102598	+	0.177705i
$381$		0			0
$382$	−11.0000	−	19.0526i	−0.562809	−	0.974814i
$383$	−17.6777	+	30.6186i	−0.903287	+	1.56454i	−0.0800861	+	0.996788i	$0.525520\pi$
$383$	−17.6777	+	30.6186i	−0.903287	+	1.56454i	−0.823201	+	0.567751i	$0.807814\pi$
$384$		0			0
$385$		0			0
$386$	14.0000			0.712581
$387$	15.0000	−	25.9808i	0.762493	−	1.32068i
$388$	0.707107	+	1.22474i	0.0358979	+	0.0621770i
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	0.998763	−	0.0497253i	$-0.0158346\pi$
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	−0.542445	+	0.840091i	$0.682501\pi$
$390$		0			0
$391$	−16.9706			−0.858238
$392$		0			0
$393$		0			0
$394$	5.00000	−	8.66025i	0.251896	−	0.436297i
$395$		0			0
$396$	1.50000	+	2.59808i	0.0753778	+	0.130558i
$397$	5.65685	−	9.79796i	0.283909	−	0.491745i	−0.688435	−	0.725298i	$-0.741702\pi$
$397$	5.65685	−	9.79796i	0.283909	−	0.491745i	0.972344	+	0.233553i	$0.0750352\pi$
$398$	−4.24264			−0.212664
$399$		0			0
$400$	3.00000			0.150000
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	−0.998350	−	0.0574304i	$-0.981709\pi$
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	0.548911	+	0.835881i	$0.315043\pi$
$402$		0			0
$403$	3.00000	+	5.19615i	0.149441	+	0.258839i
$404$	0.707107	−	1.22474i	0.0351799	−	0.0609333i
$405$	25.4558			1.26491
$406$		0			0
$407$	−6.00000			−0.297409
$408$		0			0
$409$	14.1421	+	24.4949i	0.699284	+	1.21119i	0.968715	+	0.248175i	$0.0798309\pi$
$409$	14.1421	+	24.4949i	0.699284	+	1.21119i	−0.269432	+	0.963020i	$0.586836\pi$
$410$	12.0000	+	20.7846i	0.592638	+	1.02648i
$411$		0			0
$412$	4.24264			0.209020
$413$		0			0
$414$	18.0000			0.884652
$415$	10.0000	−	17.3205i	0.490881	−	0.850230i
$416$	2.12132	+	3.67423i	0.104006	+	0.180144i
$417$		0			0
$418$	0.707107	−	1.22474i	0.0345857	−	0.0599042i
$419$	−22.6274			−1.10542			−0.552711	−	0.833373i	$-0.686407\pi$
$419$	−22.6274			−1.10542			−0.552711	+	0.833373i	$0.686407\pi$
$420$		0			0
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$	−7.00000	+	12.1244i	−0.340755	+	0.590204i
$423$	−10.6066	−	18.3712i	−0.515711	−	0.893237i
$424$	3.00000	+	5.19615i	0.145693	+	0.252347i
$425$	4.24264	−	7.34847i	0.205798	−	0.356453i
$426$		0			0
$427$		0			0
$428$	18.0000			0.870063
$429$		0			0
$430$	14.1421	+	24.4949i	0.681994	+	1.18125i
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	0.973574	−	0.228373i	$-0.0733406\pi$
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	−0.684564	+	0.728953i	$0.740007\pi$
$432$		0			0
$433$	24.0416			1.15537			0.577684	−	0.816261i	$-0.303957\pi$
$433$	24.0416			1.15537			0.577684	+	0.816261i	$0.303957\pi$
$434$		0			0
$435$		0			0
$436$	−7.00000	+	12.1244i	−0.335239	+	0.580651i
$437$	−4.24264	−	7.34847i	−0.202953	−	0.351525i
$438$		0			0
$439$	15.5563	−	26.9444i	0.742464	−	1.28599i	−0.208906	−	0.977936i	$-0.566990\pi$
$439$	15.5563	−	26.9444i	0.742464	−	1.28599i	0.951370	−	0.308050i	$-0.0996763\pi$
$440$	−2.82843			−0.134840
$441$		0			0
$442$	12.0000			0.570782
$443$	−18.0000	+	31.1769i	−0.855206	+	1.48126i	0.0212481	+	0.999774i	$0.493236\pi$
$443$	−18.0000	+	31.1769i	−0.855206	+	1.48126i	−0.876454	+	0.481486i	$0.840097\pi$
$444$		0			0
$445$	−26.0000	−	45.0333i	−1.23252	−	2.13478i
$446$	−6.36396	+	11.0227i	−0.301342	+	0.521940i
$447$		0			0
$448$		0			0
$449$	8.00000			0.377543			0.188772	−	0.982021i	$-0.439549\pi$
$449$	8.00000			0.377543			0.188772	+	0.982021i	$0.439549\pi$
$450$	−4.50000	+	7.79423i	−0.212132	+	0.367423i
$451$	−4.24264	−	7.34847i	−0.199778	−	0.346026i
$452$	−4.00000	−	6.92820i	−0.188144	−	0.325875i
$453$		0			0
$454$	−26.8701			−1.26107
$455$		0			0
$456$		0			0
$457$	−19.0000	+	32.9090i	−0.888783	+	1.53942i	−0.0474665	+	0.998873i	$0.515115\pi$
$457$	−19.0000	+	32.9090i	−0.888783	+	1.53942i	−0.841316	+	0.540544i	$0.818219\pi$
$458$	−12.7279	−	22.0454i	−0.594737	−	1.03011i
$459$		0			0
$460$	−8.48528	+	14.6969i	−0.395628	+	0.685248i
$461$	18.3848			0.856264			0.428132	−	0.903716i	$-0.359172\pi$
$461$	18.3848			0.856264			0.428132	+	0.903716i	$0.359172\pi$
$462$		0			0
$463$	32.0000			1.48717			0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000			1.48717			0.743583	+	0.668644i	$0.233125\pi$
$464$	−4.00000	+	6.92820i	−0.185695	+	0.321634i
$465$		0			0
$466$	1.00000	+	1.73205i	0.0463241	+	0.0802357i
$467$	16.9706	−	29.3939i	0.785304	−	1.36019i	−0.143513	−	0.989648i	$-0.545840\pi$
$467$	16.9706	−	29.3939i	0.785304	−	1.36019i	0.928817	−	0.370538i	$-0.120827\pi$
$468$	−12.7279			−0.588348
$469$		0			0
$470$	20.0000			0.922531
$471$		0			0
$472$	−7.07107	−	12.2474i	−0.325472	−	0.563735i
$473$	−5.00000	−	8.66025i	−0.229900	−	0.398199i
$474$		0			0
$475$	4.24264			0.194666
$476$		0			0
$477$	−18.0000			−0.824163
$478$	−2.00000	+	3.46410i	−0.0914779	+	0.158444i
$479$	5.65685	+	9.79796i	0.258468	+	0.447680i	0.965832	−	0.259170i	$-0.0834489\pi$
$479$	5.65685	+	9.79796i	0.258468	+	0.447680i	−0.707364	+	0.706850i	$0.750116\pi$
$480$		0			0
$481$	12.7279	−	22.0454i	0.580343	−	1.00518i
$482$	2.82843			0.128831
$483$		0			0
$484$	1.00000			0.0454545
$485$	2.00000	−	3.46410i	0.0908153	−	0.157297i
$486$		0			0
$487$	−11.0000	−	19.0526i	−0.498458	−	0.863354i	0.501541	−	0.865134i	$-0.332767\pi$
$487$	−11.0000	−	19.0526i	−0.498458	−	0.863354i	−0.999998	+	0.00178012i	$0.999433\pi$
$488$	−2.12132	+	3.67423i	−0.0960277	+	0.166325i
$489$		0			0
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$		0			0
$493$	11.3137	+	19.5959i	0.509544	+	0.882556i
$494$	3.00000	+	5.19615i	0.134976	+	0.233786i
$495$	4.24264	−	7.34847i	0.190693	−	0.330289i
$496$	−1.41421			−0.0635001
$497$		0			0
$498$		0			0
$499$	−8.00000	+	13.8564i	−0.358129	+	0.620298i	−0.987648	−	0.156687i	$-0.949919\pi$
$499$	−8.00000	+	13.8564i	−0.358129	+	0.620298i	0.629519	+	0.776985i	$0.283252\pi$
$500$	2.82843	+	4.89898i	0.126491	+	0.219089i
$501$		0			0
$502$	12.7279	−	22.0454i	0.568075	−	0.983935i
$503$	−14.1421			−0.630567			−0.315283	−	0.948998i	$-0.602100\pi$
$503$	−14.1421			−0.630567			−0.315283	+	0.948998i	$0.602100\pi$
$504$		0			0
$505$	−4.00000			−0.177998
$506$	3.00000	−	5.19615i	0.133366	−	0.230997i
$507$		0			0
$508$	−4.00000	−	6.92820i	−0.177471	−	0.307389i
$509$	15.5563	−	26.9444i	0.689523	−	1.19429i	−0.282469	−	0.959276i	$-0.591154\pi$
$509$	15.5563	−	26.9444i	0.689523	−	1.19429i	0.971992	−	0.235013i	$-0.0755131\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	9.19239	+	15.9217i	0.405459	+	0.702275i
$515$	−6.00000	−	10.3923i	−0.264392	−	0.457940i
$516$		0			0
$517$	−7.07107			−0.310985
$518$		0			0
$519$		0			0
$520$	6.00000	−	10.3923i	0.263117	−	0.455733i
$521$	20.5061	+	35.5176i	0.898388	+	1.55605i	0.829554	+	0.558426i	$0.188595\pi$
$521$	20.5061	+	35.5176i	0.898388	+	1.55605i	0.0688342	+	0.997628i	$0.478072\pi$
$522$	−12.0000	−	20.7846i	−0.525226	−	0.909718i
$523$	9.19239	−	15.9217i	0.401955	−	0.696207i	−0.592007	−	0.805933i	$-0.701664\pi$
$523$	9.19239	−	15.9217i	0.401955	−	0.696207i	0.993962	+	0.109726i	$0.0349975\pi$
$524$	7.07107			0.308901
$525$		0			0
$526$	−12.0000			−0.523225
$527$	−2.00000	+	3.46410i	−0.0871214	+	0.150899i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	8.48528	−	14.6969i	0.368577	−	0.638394i
$531$	42.4264			1.84115
$532$		0			0
$533$	36.0000			1.55933
$534$		0			0
$535$	−25.4558	−	44.0908i	−1.10055	−	1.90621i
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$		0			0
$538$	−25.4558			−1.09748
$539$		0			0
$540$		0			0
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	−0.738296	−	0.674477i	$-0.764369\pi$
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	0.953262	+	0.302144i	$0.0977023\pi$
$542$	−4.24264	−	7.34847i	−0.182237	−	0.315644i
$543$		0			0
$544$	−1.41421	+	2.44949i	−0.0606339	+	0.105021i
$545$	39.5980			1.69619
$546$		0			0
$547$	−12.0000			−0.513083			−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000			−0.513083			−0.256541	+	0.966533i	$0.582583\pi$
$548$	−5.00000	+	8.66025i	−0.213589	+	0.369948i
$549$	−6.36396	−	11.0227i	−0.271607	−	0.470438i
$550$	1.50000	+	2.59808i	0.0639602	+	0.110782i
$551$	−5.65685	+	9.79796i	−0.240990	+	0.417407i
$552$		0			0
$553$		0			0
$554$	−4.00000			−0.169944
$555$		0			0
$556$	10.6066	+	18.3712i	0.449820	+	0.779111i
$557$	−7.00000	−	12.1244i	−0.296600	−	0.513725i	0.678756	−	0.734364i	$-0.262519\pi$
$557$	−7.00000	−	12.1244i	−0.296600	−	0.513725i	−0.975356	+	0.220638i	$0.929186\pi$
$558$	2.12132	−	3.67423i	0.0898027	−	0.155543i
$559$	42.4264			1.79445
$560$		0			0
$561$		0			0
$562$	3.00000	−	5.19615i	0.126547	−	0.219186i
$563$	4.94975	+	8.57321i	0.208607	+	0.361318i	0.951276	−	0.308341i	$-0.0997737\pi$
$563$	4.94975	+	8.57321i	0.208607	+	0.361318i	−0.742669	+	0.669659i	$0.766440\pi$
$564$		0			0
$565$	−11.3137	+	19.5959i	−0.475971	+	0.824406i
$566$	4.24264			0.178331
$567$		0			0
$568$		0			0
$569$	17.0000	−	29.4449i	0.712677	−	1.23439i	−0.251172	−	0.967943i	$-0.580816\pi$
$569$	17.0000	−	29.4449i	0.712677	−	1.23439i	0.963849	−	0.266450i	$-0.0858508\pi$
$570$		0			0
$571$	−6.00000	−	10.3923i	−0.251092	−	0.434904i	0.712735	−	0.701434i	$-0.247456\pi$
$571$	−6.00000	−	10.3923i	−0.251092	−	0.434904i	−0.963827	+	0.266529i	$0.914123\pi$
$572$	−2.12132	+	3.67423i	−0.0886969	+	0.153627i
$573$		0			0
$574$		0			0
$575$	18.0000			0.750652
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	−6.36396	−	11.0227i	−0.264935	−	0.458881i	0.702611	−	0.711574i	$-0.252017\pi$
$577$	−6.36396	−	11.0227i	−0.264935	−	0.458881i	−0.967547	+	0.252693i	$0.918684\pi$
$578$	−4.50000	−	7.79423i	−0.187175	−	0.324197i
$579$		0			0
$580$	22.6274			0.939552
$581$		0			0
$582$		0			0
$583$	−3.00000	+	5.19615i	−0.124247	+	0.215203i
$584$	4.24264	+	7.34847i	0.175562	+	0.304082i
$585$	18.0000	+	31.1769i	0.744208	+	1.28901i
$586$	−7.77817	+	13.4722i	−0.321313	+	0.556531i
$587$	−19.7990			−0.817192			−0.408596	−	0.912715i	$-0.633981\pi$
$587$	−19.7990			−0.817192			−0.408596	+	0.912715i	$0.633981\pi$
$588$		0			0
$589$	−2.00000			−0.0824086
$590$	−20.0000	+	34.6410i	−0.823387	+	1.42615i
$591$		0			0
$592$	3.00000	+	5.19615i	0.123299	+	0.213561i
$593$	−1.41421	+	2.44949i	−0.0580748	+	0.100588i	−0.893601	−	0.448862i	$-0.851830\pi$
$593$	−1.41421	+	2.44949i	−0.0580748	+	0.100588i	0.835526	+	0.549450i	$0.185163\pi$
$594$		0			0
$595$		0			0
$596$	4.00000			0.163846
$597$		0			0
$598$	12.7279	+	22.0454i	0.520483	+	0.901504i
$599$	8.00000	+	13.8564i	0.326871	+	0.566157i	0.981889	−	0.189456i	$-0.0606724\pi$
$599$	8.00000	+	13.8564i	0.326871	+	0.566157i	−0.655018	+	0.755613i	$0.727339\pi$
$600$		0			0
$601$		0			0			−	1.00000i	$-0.5\pi$
$601$		0			0				1.00000i	$0.5\pi$
$602$		0			0
$603$	12.0000			0.488678
$604$	10.0000	−	17.3205i	0.406894	−	0.704761i
$605$	−1.41421	−	2.44949i	−0.0574960	−	0.0995859i
$606$		0			0
$607$	16.9706	−	29.3939i	0.688814	−	1.19306i	−0.283408	−	0.958999i	$-0.591465\pi$
$607$	16.9706	−	29.3939i	0.688814	−	1.19306i	0.972222	−	0.234061i	$-0.0752016\pi$
$608$	−1.41421			−0.0573539
$609$		0			0
$610$	12.0000			0.485866
$611$	15.0000	−	25.9808i	0.606835	−	1.05107i
$612$	−4.24264	−	7.34847i	−0.171499	−	0.297044i
$613$	−22.0000	−	38.1051i	−0.888572	−	1.53905i	−0.841564	−	0.540157i	$-0.818365\pi$
$613$	−22.0000	−	38.1051i	−0.888572	−	1.53905i	−0.0470071	−	0.998895i	$-0.514968\pi$
$614$	−12.0208	+	20.8207i	−0.485121	+	0.840254i
$615$		0			0
$616$		0			0
$617$	−4.00000			−0.161034			−0.0805170	−	0.996753i	$-0.525657\pi$
$617$	−4.00000			−0.161034			−0.0805170	+	0.996753i	$0.525657\pi$
$618$		0			0
$619$	−14.1421	−	24.4949i	−0.568420	−	0.984533i	−0.996722	−	0.0808974i	$-0.974221\pi$
$619$	−14.1421	−	24.4949i	−0.568420	−	0.984533i	0.428302	−	0.903636i	$-0.359112\pi$
$620$	2.00000	+	3.46410i	0.0803219	+	0.139122i
$621$		0			0
$622$	24.0416			0.963982
$623$		0			0
$624$		0			0
$625$	15.5000	−	26.8468i	0.620000	−	1.07387i
$626$	−6.36396	−	11.0227i	−0.254355	−	0.440556i
$627$		0			0
$628$		0			0
$629$	16.9706			0.676661
$630$		0			0
$631$	−38.0000			−1.51276			−0.756378	−	0.654135i	$-0.773033\pi$
$631$	−38.0000			−1.51276			−0.756378	+	0.654135i	$0.773033\pi$
$632$		0			0
$633$		0			0
$634$	−15.0000	−	25.9808i	−0.595726	−	1.03183i
$635$	−11.3137	+	19.5959i	−0.448971	+	0.777640i
$636$		0			0
$637$		0			0
$638$	−8.00000			−0.316723
$639$		0			0
$640$	1.41421	+	2.44949i	0.0559017	+	0.0968246i
$641$	−2.00000	−	3.46410i	−0.0789953	−	0.136824i	0.823821	−	0.566849i	$-0.191838\pi$
$641$	−2.00000	−	3.46410i	−0.0789953	−	0.136824i	−0.902817	+	0.430026i	$0.858505\pi$
$642$		0			0
$643$	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
$646$	−2.00000	+	3.46410i	−0.0786889	+	0.136293i
$647$	3.53553	+	6.12372i	0.138996	+	0.240748i	0.927117	−	0.374772i	$-0.122279\pi$
$647$	3.53553	+	6.12372i	0.138996	+	0.240748i	−0.788121	+	0.615521i	$0.788946\pi$
$648$	4.50000	+	7.79423i	0.176777	+	0.306186i
$649$	7.07107	−	12.2474i	0.277564	−	0.480754i
$650$	−12.7279			−0.499230
$651$		0			0
$652$	−16.0000			−0.626608
$653$	1.00000	−	1.73205i	0.0391330	−	0.0677804i	−0.845796	−	0.533507i	$-0.820874\pi$
$653$	1.00000	−	1.73205i	0.0391330	−	0.0677804i	0.884929	+	0.465727i	$0.154207\pi$
$654$		0			0
$655$	−10.0000	−	17.3205i	−0.390732	−	0.676768i
$656$	−4.24264	+	7.34847i	−0.165647	+	0.286910i
$657$	−25.4558			−0.993127
$658$		0			0
$659$	46.0000			1.79191			0.895953	−	0.444149i	$-0.146494\pi$
$659$	46.0000			1.79191			0.895953	+	0.444149i	$0.146494\pi$
$660$		0			0
$661$	4.24264	+	7.34847i	0.165020	+	0.285822i	0.936662	−	0.350234i	$-0.113898\pi$
$661$	4.24264	+	7.34847i	0.165020	+	0.285822i	−0.771643	+	0.636056i	$0.780565\pi$
$662$	−16.0000	−	27.7128i	−0.621858	−	1.07709i
$663$		0			0
$664$	7.07107			0.274411
$665$		0			0
$666$	−18.0000			−0.697486
$667$	−24.0000	+	41.5692i	−0.929284	+	1.60957i
$668$	7.07107	+	12.2474i	0.273588	+	0.473868i
$669$		0			0
$670$	−5.65685	+	9.79796i	−0.218543	+	0.378528i
$671$	−4.24264			−0.163785
$672$		0			0
$673$	−14.0000			−0.539660			−0.269830	−	0.962908i	$-0.586968\pi$
$673$	−14.0000			−0.539660			−0.269830	+	0.962908i	$0.586968\pi$
$674$	−9.00000	+	15.5885i	−0.346667	+	0.600445i
$675$		0			0
$676$	−2.50000	−	4.33013i	−0.0961538	−	0.166543i
$677$	0.707107	−	1.22474i	0.0271763	−	0.0470708i	−0.852117	−	0.523351i	$-0.824682\pi$
$677$	0.707107	−	1.22474i	0.0271763	−	0.0470708i	0.879294	+	0.476280i	$0.158015\pi$
$678$		0			0
$679$		0			0
$680$	8.00000			0.306786
$681$		0			0
$682$	−0.707107	−	1.22474i	−0.0270765	−	0.0468979i
$683$	−4.00000	−	6.92820i	−0.153056	−	0.265100i	0.779294	−	0.626659i	$-0.215578\pi$
$683$	−4.00000	−	6.92820i	−0.153056	−	0.265100i	−0.932349	+	0.361559i	$0.882245\pi$
$684$	2.12132	−	3.67423i	0.0811107	−	0.140488i
$685$	28.2843			1.08069
$686$		0			0
$687$		0			0
$688$	−5.00000	+	8.66025i	−0.190623	+	0.330169i
$689$	−12.7279	−	22.0454i	−0.484895	−	0.839863i
$690$		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	$0.218267\pi$
$692$	−15.5563			−0.591364
$693$		0			0
$694$	−10.0000			−0.379595
$695$	30.0000	−	51.9615i	1.13796	−	1.97101i
$696$		0			0
$697$	12.0000	+	20.7846i	0.454532	+	0.787273i
$698$	−4.94975	+	8.57321i	−0.187351	+	0.324501i
$699$		0			0
$700$		0			0
$701$	2.00000			0.0755390			0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000			0.0755390			0.0377695	+	0.999286i	$0.487975\pi$
$702$		0			0
$703$	4.24264	+	7.34847i	0.160014	+	0.277153i
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$		0			0
$706$	29.6985			1.11772
$707$		0			0
$708$		0			0
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	0.249952	+	0.968258i	$0.419585\pi$
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	−0.963512	+	0.267664i	$0.913748\pi$
$710$		0			0
$711$		0			0
$712$	9.19239	−	15.9217i	0.344499	−	0.596690i
$713$	−8.48528			−0.317776
$714$		0			0
$715$	12.0000			0.448775
$716$	6.00000	−	10.3923i	0.224231	−	0.388379i
$717$		0			0
$718$	12.0000	+	20.7846i	0.447836	+	0.775675i
$719$	−2.12132	+	3.67423i	−0.0791119	+	0.137026i	−0.902867	−	0.429920i	$-0.858542\pi$
$719$	−2.12132	+	3.67423i	−0.0791119	+	0.137026i	0.823755	+	0.566946i	$0.191875\pi$
$720$	−8.48528			−0.316228
$721$		0			0
$722$	17.0000			0.632674
$723$		0			0
$724$	4.24264	+	7.34847i	0.157676	+	0.273104i
$725$	−12.0000	−	20.7846i	−0.445669	−	0.771921i
$726$		0			0
$727$	15.5563			0.576953			0.288477	−	0.957487i	$-0.406851\pi$
$727$	15.5563			0.576953			0.288477	+	0.957487i	$0.406851\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	12.0000	−	20.7846i	0.444140	−	0.769273i
$731$	14.1421	+	24.4949i	0.523066	+	0.905977i
$732$		0			0
$733$	−6.36396	+	11.0227i	−0.235058	+	0.407133i	−0.959290	−	0.282424i	$-0.908861\pi$
$733$	−6.36396	+	11.0227i	−0.235058	+	0.407133i	0.724231	+	0.689557i	$0.242195\pi$
$734$	−24.0416			−0.887393
$735$		0			0
$736$	−6.00000			−0.221163
$737$	2.00000	−	3.46410i	0.0736709	−	0.127602i
$738$	−12.7279	−	22.0454i	−0.468521	−	0.811503i
$739$	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	$0.713425\pi$
$740$	8.48528	−	14.6969i	0.311925	−	0.540270i
$741$		0			0
$742$		0			0
$743$	−12.0000			−0.440237			−0.220119	−	0.975473i	$-0.570644\pi$
$743$	−12.0000			−0.440237			−0.220119	+	0.975473i	$0.570644\pi$
$744$		0			0
$745$	−5.65685	−	9.79796i	−0.207251	−	0.358969i
$746$	13.0000	+	22.5167i	0.475964	+	0.824394i
$747$	−10.6066	+	18.3712i	−0.388075	+	0.672166i
$748$	−2.82843			−0.103418
$749$		0			0
$750$		0			0
$751$	1.00000	−	1.73205i	0.0364905	−	0.0632034i	−0.847203	−	0.531269i	$-0.821715\pi$
$751$	1.00000	−	1.73205i	0.0364905	−	0.0632034i	0.883694	+	0.468065i	$0.155049\pi$
$752$	3.53553	+	6.12372i	0.128928	+	0.223309i
$753$		0			0
$754$	16.9706	−	29.3939i	0.618031	−	1.07046i
$755$	−56.5685			−2.05874
$756$		0			0
$757$	26.0000			0.944986			0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000			0.944986			0.472493	+	0.881334i	$0.343354\pi$
$758$	−14.0000	+	24.2487i	−0.508503	+	0.880753i
$759$		0			0
$760$	2.00000	+	3.46410i	0.0725476	+	0.125656i
$761$	−11.3137	+	19.5959i	−0.410122	+	0.710351i	−0.994903	−	0.100840i	$-0.967847\pi$
$761$	−11.3137	+	19.5959i	−0.410122	+	0.710351i	0.584781	+	0.811191i	$0.301180\pi$
$762$		0			0
$763$		0			0
$764$	−22.0000			−0.795932
$765$	−12.0000	+	20.7846i	−0.433861	+	0.751469i
$766$	17.6777	+	30.6186i	0.638720	+	1.10630i
$767$	30.0000	+	51.9615i	1.08324	+	1.87622i
$768$		0			0
$769$	16.9706			0.611974			0.305987	−	0.952036i	$-0.401014\pi$
$769$	16.9706			0.611974			0.305987	+	0.952036i	$0.401014\pi$
$770$		0			0
$771$		0			0
$772$	7.00000	−	12.1244i	0.251936	−	0.436365i
$773$	11.3137	+	19.5959i	0.406926	+	0.704816i	0.994544	−	0.104323i	$-0.0332674\pi$
$773$	11.3137	+	19.5959i	0.406926	+	0.704816i	−0.587618	+	0.809139i	$0.699934\pi$
$774$	−15.0000	−	25.9808i	−0.539164	−	0.933859i
$775$	2.12132	−	3.67423i	0.0762001	−	0.131982i
$776$	1.41421			0.0507673
$777$		0			0
$778$	18.0000			0.645331
$779$	−6.00000	+	10.3923i	−0.214972	+	0.372343i
$780$		0			0
$781$		0			0
$782$	−8.48528	+	14.6969i	−0.303433	+	0.525561i
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−7.77817	−	13.4722i	−0.277262	−	0.480232i	0.693441	−	0.720513i	$-0.256094\pi$
$787$	−7.77817	−	13.4722i	−0.277262	−	0.480232i	−0.970703	+	0.240281i	$0.922760\pi$
$788$	−5.00000	−	8.66025i	−0.178118	−	0.308509i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	3.00000			0.106600
$793$	9.00000	−	15.5885i	0.319599	−	0.553562i
$794$	−5.65685	−	9.79796i	−0.200754	−	0.347717i
$795$		0			0
$796$	−2.12132	+	3.67423i	−0.0751882	+	0.130230i
$797$	−39.5980			−1.40263			−0.701316	−	0.712850i	$-0.747404\pi$
$797$	−39.5980			−1.40263			−0.701316	+	0.712850i	$0.747404\pi$
$798$		0			0
$799$	20.0000			0.707549
$800$	1.50000	−	2.59808i	0.0530330	−	0.0918559i
$801$	27.5772	+	47.7650i	0.974391	+	1.68770i
$802$	9.00000	+	15.5885i	0.317801	+	0.550448i
$803$	−4.24264	+	7.34847i	−0.149720	+	0.259322i
$804$		0			0
$805$		0			0
$806$	6.00000			0.211341
$807$		0			0
$808$	−0.707107	−	1.22474i	−0.0248759	−	0.0430864i
$809$	−27.0000	−	46.7654i	−0.949269	−	1.64418i	−0.746968	−	0.664860i	$-0.768491\pi$
$809$	−27.0000	−	46.7654i	−0.949269	−	1.64418i	−0.202301	−	0.979323i	$-0.564842\pi$
$810$	12.7279	−	22.0454i	0.447214	−	0.774597i
$811$	18.3848			0.645577			0.322788	−	0.946471i	$-0.395380\pi$
$811$	18.3848			0.645577			0.322788	+	0.946471i	$0.395380\pi$
$812$		0			0
$813$		0			0
$814$	−3.00000	+	5.19615i	−0.105150	+	0.182125i
$815$	22.6274	+	39.1918i	0.792604	+	1.37283i
$816$		0			0
$817$	−7.07107	+	12.2474i	−0.247385	+	0.428484i
$818$	28.2843			0.988936
$819$		0			0
$820$	24.0000			0.838116
$821$	10.0000	−	17.3205i	0.349002	−	0.604490i	−0.637070	−	0.770806i	$-0.719854\pi$
$821$	10.0000	−	17.3205i	0.349002	−	0.604490i	0.986073	+	0.166316i	$0.0531872\pi$
$822$		0			0
$823$	21.0000	+	36.3731i	0.732014	+	1.26789i	0.956021	+	0.293298i	$0.0947528\pi$
$823$	21.0000	+	36.3731i	0.732014	+	1.26789i	−0.224007	+	0.974588i	$0.571914\pi$
$824$	2.12132	−	3.67423i	0.0738997	−	0.127998i
$825$		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	$0.715277\pi$
$828$	9.00000	−	15.5885i	0.312772	−	0.541736i
$829$	−12.7279	−	22.0454i	−0.442059	−	0.765669i	0.555783	−	0.831327i	$-0.312418\pi$
$829$	−12.7279	−	22.0454i	−0.442059	−	0.765669i	−0.997842	+	0.0656587i	$0.979085\pi$
$830$	−10.0000	−	17.3205i	−0.347105	−	0.601204i
$831$		0			0
$832$	4.24264			0.147087
$833$		0			0
$834$		0			0
$835$	20.0000	−	34.6410i	0.692129	−	1.19880i
$836$	−0.707107	−	1.22474i	−0.0244558	−	0.0423587i
$837$		0			0
$838$	−11.3137	+	19.5959i	−0.390826	+	0.676930i
$839$	−15.5563			−0.537065			−0.268532	−	0.963271i	$-0.586539\pi$
$839$	−15.5563			−0.537065			−0.268532	+	0.963271i	$0.586539\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$	1.00000	−	1.73205i	0.0344623	−	0.0596904i
$843$		0			0
$844$	7.00000	+	12.1244i	0.240950	+	0.417338i
$845$	−7.07107	+	12.2474i	−0.243252	+	0.421325i
$846$	−21.2132			−0.729325
$847$		0			0
$848$	6.00000			0.206041
$849$		0			0
$850$	−4.24264	−	7.34847i	−0.145521	−	0.252050i
$851$	18.0000	+	31.1769i	0.617032	+	1.06873i
$852$		0			0
$853$	−38.1838			−1.30739			−0.653694	−	0.756759i	$-0.726781\pi$
$853$	−38.1838			−1.30739			−0.653694	+	0.756759i	$0.726781\pi$
$854$		0			0
$855$	−12.0000			−0.410391
$856$	9.00000	−	15.5885i	0.307614	−	0.532803i
$857$	−11.3137	−	19.5959i	−0.386469	−	0.669384i	0.605503	−	0.795843i	$-0.292972\pi$
$857$	−11.3137	−	19.5959i	−0.386469	−	0.669384i	−0.991972	+	0.126459i	$0.959639\pi$
$858$		0			0
$859$	9.89949	−	17.1464i	0.337766	−	0.585029i	−0.646246	−	0.763129i	$-0.723662\pi$
$859$	9.89949	−	17.1464i	0.337766	−	0.585029i	0.984012	+	0.178101i	$0.0569953\pi$
$860$	28.2843			0.964486
$861$		0			0
$862$	12.0000			0.408722
$863$	−23.0000	+	39.8372i	−0.782929	+	1.35607i	0.147299	+	0.989092i	$0.452942\pi$
$863$	−23.0000	+	39.8372i	−0.782929	+	1.35607i	−0.930228	+	0.366981i	$0.880391\pi$
$864$		0			0
$865$	22.0000	+	38.1051i	0.748022	+	1.29561i
$866$	12.0208	−	20.8207i	0.408484	−	0.707515i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	8.48528	+	14.6969i	0.287513	+	0.497987i
$872$	7.00000	+	12.1244i	0.237050	+	0.410582i
$873$	−2.12132	+	3.67423i	−0.0717958	+	0.124354i
$874$	−8.48528			−0.287019
$875$		0			0
$876$		0			0
$877$	−21.0000	+	36.3731i	−0.709120	+	1.22823i	0.256064	+	0.966660i	$0.417574\pi$
$877$	−21.0000	+	36.3731i	−0.709120	+	1.22823i	−0.965184	+	0.261571i	$0.915759\pi$
$878$	−15.5563	−	26.9444i	−0.525001	−	0.909329i
$879$		0			0
$880$	−1.41421	+	2.44949i	−0.0476731	+	0.0825723i
$881$	43.8406			1.47703			0.738514	−	0.674238i	$-0.235528\pi$
$881$	43.8406			1.47703			0.738514	+	0.674238i	$0.235528\pi$
$882$		0			0
$883$	28.0000			0.942275			0.471138	−	0.882060i	$-0.343844\pi$
$883$	28.0000			0.942275			0.471138	+	0.882060i	$0.343844\pi$
$884$	6.00000	−	10.3923i	0.201802	−	0.349531i
$885$		0			0
$886$	18.0000	+	31.1769i	0.604722	+	1.04741i
$887$	−2.82843	+	4.89898i	−0.0949693	+	0.164492i	−0.909596	−	0.415494i	$-0.863609\pi$
$887$	−2.82843	+	4.89898i	−0.0949693	+	0.164492i	0.814627	+	0.579986i	$0.196942\pi$
$888$		0			0
$889$		0			0
$890$	−52.0000			−1.74304
$891$	−4.50000	+	7.79423i	−0.150756	+	0.261116i
$892$	6.36396	+	11.0227i	0.213081	+	0.369067i
$893$	5.00000	+	8.66025i	0.167319	+	0.289804i
$894$		0			0
$895$	−33.9411			−1.13453
$896$		0			0
$897$		0			0
$898$	4.00000	−	6.92820i	0.133482	−	0.231197i
$899$	5.65685	+	9.79796i	0.188667	+	0.326780i
$900$	4.50000	+	7.79423i	0.150000	+	0.259808i
$901$	8.48528	−	14.6969i	0.282686	−	0.489626i
$902$	−8.48528			−0.282529
$903$		0			0
$904$	−8.00000			−0.266076
$905$	12.0000	−	20.7846i	0.398893	−	0.690904i
$906$		0			0
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	0.948278	−	0.317441i	$-0.102824\pi$
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	−0.749051	+	0.662512i	$0.769490\pi$
$908$	−13.4350	+	23.2702i	−0.445857	+	0.772247i
$909$	4.24264			0.140720
$910$		0			0
$911$	−10.0000			−0.331315			−0.165657	−	0.986183i	$-0.552975\pi$
$911$	−10.0000			−0.331315			−0.165657	+	0.986183i	$0.552975\pi$
$912$		0			0
$913$	3.53553	+	6.12372i	0.117009	+	0.202666i
$914$	19.0000	+	32.9090i	0.628464	+	1.08853i
$915$		0			0
$916$	−25.4558			−0.841085
$917$		0			0
$918$		0			0
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$	8.48528	+	14.6969i	0.279751	+	0.484544i
$921$		0			0
$922$	9.19239	−	15.9217i	0.302735	−	0.524353i
$923$		0			0
$924$		0			0
$925$	−18.0000			−0.591836
$926$	16.0000	−	27.7128i	0.525793	−	0.910700i
$927$	6.36396	+	11.0227i	0.209020	+	0.362033i
$928$	4.00000	+	6.92820i	0.131306	+	0.227429i
$929$	−0.707107	+	1.22474i	−0.0231994	+	0.0401826i	−0.877392	−	0.479774i	$-0.840719\pi$
$929$	−0.707107	+	1.22474i	−0.0231994	+	0.0401826i	0.854193	+	0.519957i	$0.174052\pi$
$930$		0			0
$931$		0			0
$932$	2.00000			0.0655122
$933$		0			0
$934$	−16.9706	−	29.3939i	−0.555294	−	0.961797i
$935$	4.00000	+	6.92820i	0.130814	+	0.226576i
$936$	−6.36396	+	11.0227i	−0.208013	+	0.360288i
$937$	−19.7990			−0.646805			−0.323402	−	0.946262i	$-0.604827\pi$
$937$	−19.7990			−0.646805			−0.323402	+	0.946262i	$0.604827\pi$
$938$		0			0
$939$		0			0
$940$	10.0000	−	17.3205i	0.326164	−	0.564933i
$941$	−19.0919	−	33.0681i	−0.622378	−	1.07799i	−0.989042	−	0.147636i	$-0.952834\pi$
$941$	−19.0919	−	33.0681i	−0.622378	−	1.07799i	0.366664	−	0.930353i	$-0.380500\pi$
$942$		0			0
$943$	−25.4558	+	44.0908i	−0.828956	+	1.43579i
$944$	−14.1421			−0.460287
$945$		0			0
$946$	−10.0000			−0.325128
$947$	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	$0.145965\pi$
$948$		0			0
$949$	−18.0000	−	31.1769i	−0.584305	−	1.01205i
$950$	2.12132	−	3.67423i	0.0688247	−	0.119208i
$951$		0			0
$952$		0			0
$953$	−14.0000			−0.453504			−0.226752	−	0.973952i	$-0.572811\pi$
$953$	−14.0000			−0.453504			−0.226752	+	0.973952i	$0.572811\pi$
$954$	−9.00000	+	15.5885i	−0.291386	+	0.504695i
$955$	31.1127	+	53.8888i	1.00678	+	1.74380i
$956$	2.00000	+	3.46410i	0.0646846	+	0.112037i
$957$		0			0
$958$	11.3137			0.365529
$959$		0			0
$960$		0			0
$961$	14.5000	−	25.1147i	0.467742	−	0.810153i
$962$	−12.7279	−	22.0454i	−0.410365	−	0.710772i
$963$	27.0000	+	46.7654i	0.870063	+	1.50699i
$964$	1.41421	−	2.44949i	0.0455488	−	0.0788928i
$965$	−39.5980			−1.27470
$966$		0			0
$967$	−40.0000			−1.28631			−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000			−1.28631			−0.643157	+	0.765735i	$0.722376\pi$
$968$	0.500000	−	0.866025i	0.0160706	−	0.0278351i
$969$		0			0
$970$	−2.00000	−	3.46410i	−0.0642161	−	0.111226i
$971$	5.65685	−	9.79796i	0.181537	−	0.314431i	−0.760867	−	0.648908i	$-0.775226\pi$
$971$	5.65685	−	9.79796i	0.181537	−	0.314431i	0.942404	+	0.334476i	$0.108559\pi$
$972$		0			0
$973$		0			0
$974$	−22.0000			−0.704925
$975$		0			0
$976$	2.12132	+	3.67423i	0.0679018	+	0.117609i
$977$	−12.0000	−	20.7846i	−0.383914	−	0.664959i	0.607704	−	0.794164i	$-0.292091\pi$
$977$	−12.0000	−	20.7846i	−0.383914	−	0.664959i	−0.991618	+	0.129205i	$0.958757\pi$
$978$		0			0
$979$	18.3848			0.587580
$980$		0			0
$981$	−42.0000			−1.34096
$982$	−6.00000	+	10.3923i	−0.191468	+	0.331632i
$983$	10.6066	+	18.3712i	0.338298	+	0.585949i	0.984113	−	0.177545i	$-0.0568155\pi$
$983$	10.6066	+	18.3712i	0.338298	+	0.585949i	−0.645815	+	0.763494i	$0.723482\pi$
$984$		0			0
$985$	−14.1421	+	24.4949i	−0.450606	+	0.780472i
$986$	22.6274			0.720604
$987$		0			0
$988$	6.00000			0.190885
$989$	−30.0000	+	51.9615i	−0.953945	+	1.65228i
$990$	−4.24264	−	7.34847i	−0.134840	−	0.233550i
$991$	−12.0000	−	20.7846i	−0.381193	−	0.660245i	0.610040	−	0.792370i	$-0.291153\pi$
$991$	−12.0000	−	20.7846i	−0.381193	−	0.660245i	−0.991233	+	0.132125i	$0.957820\pi$
$992$	−0.707107	+	1.22474i	−0.0224507	+	0.0388857i
$993$		0			0
$994$		0			0
$995$	12.0000			0.380426
$996$		0			0
$997$	−28.9914	−	50.2145i	−0.918166	−	1.59031i	−0.802198	−	0.597057i	$-0.796336\pi$
$997$	−28.9914	−	50.2145i	−0.918166	−	1.59031i	−0.115968	−	0.993253i	$-0.536997\pi$
$998$	8.00000	+	13.8564i	0.253236	+	0.438617i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1078.2.a.p.1.1	✓	2	7.5	odd	6
1078.2.a.p.1.2	yes	2	7.2	even	3
1078.2.e.t.67.1		4	7.4	even	3	inner
1078.2.e.t.67.2		4	7.3	odd	6	inner
1078.2.e.t.177.1		4	1.1	even	1	trivial
1078.2.e.t.177.2		4	7.6	odd	2	inner
8624.2.a.bl.1.1		2	28.19	even	6
8624.2.a.bl.1.2		2	28.23	odd	6
9702.2.a.df.1.1		2	21.2	odd	6
9702.2.a.df.1.2		2	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.41421 + 2.44949i) q^{5} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.41421 + 2.44949i) q^{5} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(1.41421 + 2.44949i) q^{10} +(-0.500000 - 0.866025i) q^{11} +4.24264 q^{13} +(-0.500000 + 0.866025i) q^{16} +(1.41421 + 2.44949i) q^{17} +(-1.50000 - 2.59808i) q^{18} +(-0.707107 + 1.22474i) q^{19} +2.82843 q^{20} -1.00000 q^{22} +(-3.00000 + 5.19615i) q^{23} +(-1.50000 - 2.59808i) q^{25} +(2.12132 - 3.67423i) q^{26} +8.00000 q^{29} +(0.707107 + 1.22474i) q^{31} +(0.500000 + 0.866025i) q^{32} +2.82843 q^{34} -3.00000 q^{36} +(3.00000 - 5.19615i) q^{37} +(0.707107 + 1.22474i) q^{38} +(1.41421 - 2.44949i) q^{40} +8.48528 q^{41} +10.0000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(4.24264 + 7.34847i) q^{45} +(3.00000 + 5.19615i) q^{46} +(3.53553 - 6.12372i) q^{47} -3.00000 q^{50} +(-2.12132 - 3.67423i) q^{52} +(-3.00000 - 5.19615i) q^{53} +2.82843 q^{55} +(4.00000 - 6.92820i) q^{58} +(7.07107 + 12.2474i) q^{59} +(2.12132 - 3.67423i) q^{61} +1.41421 q^{62} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{65} +(2.00000 + 3.46410i) q^{67} +(1.41421 - 2.44949i) q^{68} +(-1.50000 + 2.59808i) q^{72} +(-4.24264 - 7.34847i) q^{73} +(-3.00000 - 5.19615i) q^{74} +1.41421 q^{76} +(-1.41421 - 2.44949i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(4.24264 - 7.34847i) q^{82} -7.07107 q^{83} -8.00000 q^{85} +(5.00000 - 8.66025i) q^{86} +(0.500000 + 0.866025i) q^{88} +(-9.19239 + 15.9217i) q^{89} +8.48528 q^{90} +6.00000 q^{92} +(-3.53553 - 6.12372i) q^{94} +(-2.00000 - 3.46410i) q^{95} -1.41421 q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 + 6 * q^9	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 6 q^{9} - 2 q^{11} - 2 q^{16} - 6 q^{18} - 4 q^{22} - 12 q^{23} - 6 q^{25} + 32 q^{29} + 2 q^{32} - 12 q^{36} + 12 q^{37} + 40 q^{43} - 2 q^{44} + 12 q^{46} - 12 q^{50} - 12 q^{53} + 16 q^{58} + 4 q^{64} - 24 q^{65} + 8 q^{67} - 6 q^{72} - 12 q^{74} - 18 q^{81} - 32 q^{85} + 20 q^{86} + 2 q^{88} + 24 q^{92} - 8 q^{95} - 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 + 6 * q^9 - 2 * q^11 - 2 * q^16 - 6 * q^18 - 4 * q^22 - 12 * q^23 - 6 * q^25 + 32 * q^29 + 2 * q^32 - 12 * q^36 + 12 * q^37 + 40 * q^43 - 2 * q^44 + 12 * q^46 - 12 * q^50 - 12 * q^53 + 16 * q^58 + 4 * q^64 - 24 * q^65 + 8 * q^67 - 6 * q^72 - 12 * q^74 - 18 * q^81 - 32 * q^85 + 20 * q^86 + 2 * q^88 + 24 * q^92 - 8 * q^95 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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