LMFDB - Embedded newform 1078.2.e.t.67.2

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

Embedding invariants

Embedding label			67.2
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1078.67
Dual form			1078.2.e.t.177.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.41421 + 2.44949i) q^{5} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.41421 + 2.44949i) q^{5} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.41421 + 2.44949i) q^{10} +(-0.500000 + 0.866025i) q^{11} -4.24264 q^{13} +(-0.500000 - 0.866025i) q^{16} +(-1.41421 + 2.44949i) q^{17} +(-1.50000 + 2.59808i) q^{18} +(0.707107 + 1.22474i) q^{19} -2.82843 q^{20} -1.00000 q^{22} +(-3.00000 - 5.19615i) q^{23} +(-1.50000 + 2.59808i) q^{25} +(-2.12132 - 3.67423i) q^{26} +8.00000 q^{29} +(-0.707107 + 1.22474i) q^{31} +(0.500000 - 0.866025i) q^{32} -2.82843 q^{34} -3.00000 q^{36} +(3.00000 + 5.19615i) q^{37} +(-0.707107 + 1.22474i) q^{38} +(-1.41421 - 2.44949i) q^{40} -8.48528 q^{41} +10.0000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-4.24264 + 7.34847i) q^{45} +(3.00000 - 5.19615i) q^{46} +(-3.53553 - 6.12372i) q^{47} -3.00000 q^{50} +(2.12132 - 3.67423i) q^{52} +(-3.00000 + 5.19615i) q^{53} -2.82843 q^{55} +(4.00000 + 6.92820i) q^{58} +(-7.07107 + 12.2474i) q^{59} +(-2.12132 - 3.67423i) q^{61} -1.41421 q^{62} +1.00000 q^{64} +(-6.00000 - 10.3923i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-1.41421 - 2.44949i) q^{68} +(-1.50000 - 2.59808i) q^{72} +(4.24264 - 7.34847i) q^{73} +(-3.00000 + 5.19615i) q^{74} -1.41421 q^{76} +(1.41421 - 2.44949i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-4.24264 - 7.34847i) q^{82} +7.07107 q^{83} -8.00000 q^{85} +(5.00000 + 8.66025i) q^{86} +(0.500000 - 0.866025i) q^{88} +(9.19239 + 15.9217i) q^{89} -8.48528 q^{90} +6.00000 q^{92} +(3.53553 - 6.12372i) q^{94} +(-2.00000 + 3.46410i) q^{95} +1.41421 q^{97} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$3$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.41421	+	2.44949i	0.632456	+	1.09545i	0.987048	+	0.160424i	$0.0512862\pi$
$5$	1.41421	+	2.44949i	0.632456	+	1.09545i	−0.354593	+	0.935021i	$0.615380\pi$
$6$		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	$-0.700222\pi$
$13$	−4.24264			−1.17670			−0.588348	+	0.808608i	$0.700222\pi$
$14$		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	$-0.944775\pi$
$17$	−1.41421	+	2.44949i	−0.342997	+	0.594089i	0.641991	+	0.766712i	$0.278109\pi$
$18$	−1.50000	+	2.59808i	−0.353553	+	0.612372i
$19$	0.707107	+	1.22474i	0.162221	+	0.280976i	0.935665	−	0.352889i	$-0.114801\pi$
$19$	0.707107	+	1.22474i	0.162221	+	0.280976i	−0.773444	+	0.633865i	$0.781467\pi$
$20$	−2.82843			−0.632456
$21$		0			0
$22$	−1.00000			−0.213201
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$		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	$-0.873868\pi$
$31$	−0.707107	+	1.22474i	−0.127000	+	0.219971i	0.795513	+	0.605937i	$0.207202\pi$
$32$	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	0.999969	−	0.00783774i	$-0.00249486\pi$
$37$	3.00000	+	5.19615i	0.493197	+	0.854242i	−0.506772	+	0.862080i	$0.669162\pi$
$38$	−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	$-0.730542\pi$
$41$	−8.48528			−1.32518			−0.662589	+	0.748983i	$0.730542\pi$
$42$		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	−0.999834	−	0.0182371i	$-0.994195\pi$
$47$	−3.53553	−	6.12372i	−0.515711	−	0.893237i	0.484123	−	0.875000i	$-0.339139\pi$
$48$		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	−0.995117	−	0.0987002i	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$		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	−0.122047	+	0.992524i	$0.538946\pi$
$59$	−7.07107	+	12.2474i	−0.920575	+	1.59448i	−0.798528	+	0.601958i	$0.794388\pi$
$60$		0			0
$61$	−2.12132	−	3.67423i	−0.271607	−	0.470438i	0.697666	−	0.716423i	$-0.254222\pi$
$61$	−2.12132	−	3.67423i	−0.271607	−	0.470438i	−0.969274	+	0.245985i	$0.920888\pi$
$62$	−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	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	−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	$-0.667928\pi$
$73$	4.24264	−	7.34847i	0.496564	−	0.860073i	0.999992	+	0.00396356i	$0.00126164\pi$
$74$	−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	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	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	$-0.373140\pi$
$83$	7.07107			0.776151			0.388075	+	0.921628i	$0.373140\pi$
$84$		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	0.681930	+	0.731418i	$0.261141\pi$
$89$	9.19239	+	15.9217i	0.974391	+	1.68770i	0.292462	+	0.956277i	$0.405526\pi$
$90$	−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	$-0.477127\pi$
$97$	1.41421			0.143592			0.0717958	+	0.997419i	$0.477127\pi$
$98$		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	$-0.855748\pi$
$101$	−0.707107	+	1.22474i	−0.0703598	+	0.121867i	0.828699	+	0.559694i	$0.189081\pi$
$102$		0			0
$103$	2.12132	+	3.67423i	0.209020	+	0.362033i	0.951406	−	0.307939i	$-0.0996393\pi$
$103$	2.12132	+	3.67423i	0.209020	+	0.362033i	−0.742386	+	0.669972i	$0.766306\pi$
$104$	4.24264			0.416025
$105$		0			0
$106$	−6.00000			−0.582772
$107$	−9.00000	−	15.5885i	−0.870063	−	1.50699i	−0.861931	−	0.507026i	$-0.830745\pi$
$107$	−9.00000	−	15.5885i	−0.870063	−	1.50699i	−0.00813215	−	0.999967i	$-0.502589\pi$
$108$		0			0
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	0.307290	+	0.951616i	$0.400578\pi$
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	−0.977769	+	0.209687i	$0.932756\pi$
$110$	−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	$-0.0667055\pi$
$131$	3.53553	+	6.12372i	0.308901	+	0.535032i	−0.669221	+	0.743063i	$0.733372\pi$
$132$		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	−0.996621	−	0.0821359i	$-0.973826\pi$
$137$	−5.00000	+	8.66025i	−0.427179	+	0.739895i	0.569442	+	0.822031i	$0.307159\pi$
$138$		0			0
$139$	21.2132			1.79928			0.899640	−	0.436632i	$-0.143829\pi$
$139$	21.2132			1.79928			0.899640	+	0.436632i	$0.143829\pi$
$140$		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	0.772399	−	0.635138i	$-0.219057\pi$
$149$	−2.00000	−	3.46410i	−0.163846	−	0.283790i	−0.936245	+	0.351348i	$0.885723\pi$
$150$		0			0
$151$	10.0000	−	17.3205i	0.813788	−	1.40952i	−0.0964061	−	0.995342i	$-0.530735\pi$
$151$	10.0000	−	17.3205i	0.813788	−	1.40952i	0.910195	−	0.414181i	$-0.135932\pi$
$152$	−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	$-0.833333\pi$
$157$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$158$		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	0.988227	+	0.152992i	$0.0488907\pi$
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	−0.361619	+	0.932326i	$0.617776\pi$
$164$	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	$-0.315703\pi$
$167$	14.1421			1.09435			0.547176	+	0.837018i	$0.315703\pi$
$168$		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	−0.994049	−	0.108933i	$-0.965256\pi$
$173$	−7.77817	−	13.4722i	−0.591364	−	1.02427i	0.402685	−	0.915338i	$-0.368077\pi$
$174$		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	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$	−4.24264	−	7.34847i	−0.316228	−	0.547723i
$181$	8.48528			0.630706			0.315353	−	0.948974i	$-0.397877\pi$
$181$	8.48528			0.630706			0.315353	+	0.948974i	$0.397877\pi$
$182$		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	0.922246	+	0.386604i	$0.126352\pi$
$191$	11.0000	+	19.0526i	0.795932	+	1.37859i	−0.126314	+	0.991990i	$0.540315\pi$
$192$		0			0
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	−0.496119	−	0.868255i	$-0.665242\pi$
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	0.999990	−	0.00447566i	$-0.00142465\pi$
$194$	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	$-0.785285\pi$
$199$	2.12132	−	3.67423i	0.150376	−	0.260460i	0.931366	+	0.364085i	$0.118618\pi$
$200$	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	$-0.359865\pi$
$223$	12.7279			0.852325			0.426162	+	0.904647i	$0.359865\pi$
$224$		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	0.0538949	−	0.998547i	$-0.482836\pi$
$227$	13.4350	−	23.2702i	0.891714	−	1.54449i	0.837819	−	0.545948i	$-0.183830\pi$
$228$		0			0
$229$	−12.7279	−	22.0454i	−0.841085	−	1.45680i	−0.888978	−	0.457949i	$-0.848584\pi$
$229$	−12.7279	−	22.0454i	−0.841085	−	1.45680i	0.0478936	−	0.998852i	$-0.484749\pi$
$230$	16.9706			1.11901
$231$		0			0
$232$	−8.00000			−0.525226
$233$	−1.00000	−	1.73205i	−0.0655122	−	0.113470i	0.831409	−	0.555661i	$-0.187535\pi$
$233$	−1.00000	−	1.73205i	−0.0655122	−	0.113470i	−0.896921	+	0.442191i	$0.854201\pi$
$234$	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	$-0.862371\pi$
$241$	−1.41421	+	2.44949i	−0.0910975	+	0.157786i	0.816876	+	0.576814i	$0.195704\pi$
$242$	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	$-0.796967\pi$
$251$	−25.4558			−1.60676			−0.803379	+	0.595468i	$0.796967\pi$
$252$		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	0.996213	+	0.0869478i	$0.0277113\pi$
$257$	9.19239	+	15.9217i	0.573405	+	0.993167i	−0.422807	+	0.906220i	$0.638955\pi$
$258$		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	−0.989561	−	0.144112i	$-0.953967\pi$
$263$	−6.00000	+	10.3923i	−0.369976	+	0.640817i	0.619586	+	0.784929i	$0.287301\pi$
$264$		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	−0.158176	−	0.987411i	$-0.550561\pi$
$269$	12.7279	−	22.0454i	0.776035	−	1.34413i	0.934211	−	0.356721i	$-0.116105\pi$
$270$		0			0
$271$	−4.24264	−	7.34847i	−0.257722	−	0.446388i	0.707909	−	0.706303i	$-0.249639\pi$
$271$	−4.24264	−	7.34847i	−0.257722	−	0.446388i	−0.965631	+	0.259916i	$0.916305\pi$
$272$	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	−0.919834	−	0.392308i	$-0.871677\pi$
$277$	−2.00000	+	3.46410i	−0.120168	+	0.208138i	0.799666	+	0.600446i	$0.205010\pi$
$278$	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	$-0.873579\pi$
$283$	−2.12132	+	3.67423i	−0.126099	+	0.218411i	0.796063	+	0.605214i	$0.206912\pi$
$284$		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	$-0.349852\pi$
$293$	15.5563			0.908812			0.454406	+	0.890795i	$0.349852\pi$
$294$		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	$-0.259337\pi$
$307$	24.0416			1.37213			0.686064	+	0.727541i	$0.259337\pi$
$308$		0			0
$309$		0			0
$310$	−2.00000	−	3.46410i	−0.113592	−	0.196748i
$311$	−12.0208	+	20.8207i	−0.681638	+	1.18063i	0.292843	+	0.956161i	$0.405399\pi$
$311$	−12.0208	+	20.8207i	−0.681638	+	1.18063i	−0.974481	+	0.224471i	$0.927935\pi$
$312$		0			0
$313$	−6.36396	−	11.0227i	−0.359712	−	0.623040i	0.628200	−	0.778052i	$-0.283792\pi$
$313$	−6.36396	−	11.0227i	−0.359712	−	0.623040i	−0.987913	+	0.155012i	$0.950459\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	15.0000	+	25.9808i	0.842484	+	1.45922i	0.887788	+	0.460252i	$0.152241\pi$
$317$	15.0000	+	25.9808i	0.842484	+	1.45922i	−0.0453045	+	0.998973i	$0.514426\pi$
$318$		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	0.851957	+	0.523612i	$0.175416\pi$
$331$	16.0000	+	27.7128i	0.879440	+	1.52323i	0.0274825	+	0.999622i	$0.491251\pi$
$332$	−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	−0.968452	−	0.249198i	$-0.919833\pi$
$347$	−5.00000	+	8.66025i	−0.268414	+	0.464907i	0.700038	+	0.714105i	$0.253166\pi$
$348$		0			0
$349$	9.89949			0.529908			0.264954	−	0.964261i	$-0.414643\pi$
$349$	9.89949			0.529908			0.264954	+	0.964261i	$0.414643\pi$
$350$		0			0
$351$		0			0
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	−14.8492	+	25.7196i	−0.790345	+	1.36892i	0.135408	+	0.990790i	$0.456766\pi$
$353$	−14.8492	+	25.7196i	−0.790345	+	1.36892i	−0.925753	+	0.378128i	$0.876568\pi$
$354$		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	−0.986865	−	0.161546i	$-0.948352\pi$
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	0.353529	−	0.935423i	$-0.384981\pi$
$360$	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	−0.360574	−	0.932731i	$-0.617419\pi$
$367$	12.0208	−	20.8207i	0.627481	−	1.08683i	0.988055	−	0.154099i	$-0.0492475\pi$
$368$	−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	−0.977016	−	0.213165i	$-0.931623\pi$
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	0.303902	−	0.952703i	$-0.401711\pi$
$374$	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	0.823201	+	0.567751i	$0.192186\pi$
$383$	17.6777	+	30.6186i	0.903287	+	1.56454i	0.0800861	+	0.996788i	$0.474480\pi$
$384$		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	−0.542445	−	0.840091i	$-0.682501\pi$
$389$	9.00000	−	15.5885i	0.456318	−	0.790366i	0.998763	+	0.0497253i	$0.0158346\pi$
$390$		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	$-0.258298\pi$
$397$	−5.65685	−	9.79796i	−0.283909	−	0.491745i	−0.972344	+	0.233553i	$0.924965\pi$
$398$	4.24264			0.212664
$399$		0			0
$400$	3.00000			0.150000
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$		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	0.269432	+	0.963020i	$0.413164\pi$
$409$	−14.1421	+	24.4949i	−0.699284	+	1.21119i	−0.968715	+	0.248175i	$0.920169\pi$
$410$	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	$-0.313593\pi$
$419$	22.6274			1.10542			0.552711	+	0.833373i	$0.313593\pi$
$420$		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	−0.684564	−	0.728953i	$-0.740007\pi$
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	0.973574	+	0.228373i	$0.0733406\pi$
$432$		0			0
$433$	−24.0416			−1.15537			−0.577684	−	0.816261i	$-0.696043\pi$
$433$	−24.0416			−1.15537			−0.577684	+	0.816261i	$0.696043\pi$
$434$		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	−0.951370	−	0.308050i	$-0.900324\pi$
$439$	−15.5563	−	26.9444i	−0.742464	−	1.28599i	0.208906	−	0.977936i	$-0.433010\pi$
$440$	2.82843			0.134840
$441$		0			0
$442$	12.0000			0.570782
$443$	−18.0000	−	31.1769i	−0.855206	−	1.48126i	−0.876454	−	0.481486i	$-0.840097\pi$
$443$	−18.0000	−	31.1769i	−0.855206	−	1.48126i	0.0212481	−	0.999774i	$-0.493236\pi$
$444$		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	−0.841316	−	0.540544i	$-0.818219\pi$
$457$	−19.0000	−	32.9090i	−0.888783	−	1.53942i	−0.0474665	−	0.998873i	$-0.515115\pi$
$458$	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	$-0.640828\pi$
$461$	−18.3848			−0.856264			−0.428132	+	0.903716i	$0.640828\pi$
$462$		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	−0.928817	−	0.370538i	$-0.879173\pi$
$467$	−16.9706	−	29.3939i	−0.785304	−	1.36019i	0.143513	−	0.989648i	$-0.454160\pi$
$468$	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	$-0.916551\pi$
$479$	−5.65685	+	9.79796i	−0.258468	+	0.447680i	0.707364	+	0.706850i	$0.249884\pi$
$480$		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	−0.999998	−	0.00178012i	$-0.999433\pi$
$487$	−11.0000	+	19.0526i	−0.498458	+	0.863354i	0.501541	+	0.865134i	$0.332767\pi$
$488$	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	0.629519	−	0.776985i	$-0.283252\pi$
$499$	−8.00000	−	13.8564i	−0.358129	−	0.620298i	−0.987648	+	0.156687i	$0.949919\pi$
$500$	−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	$-0.397900\pi$
$503$	14.1421			0.630567			0.315283	+	0.948998i	$0.397900\pi$
$504$		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	−0.971992	−	0.235013i	$-0.924487\pi$
$509$	−15.5563	−	26.9444i	−0.689523	−	1.19429i	0.282469	−	0.959276i	$-0.408846\pi$
$510$		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	−0.0688342	+	0.997628i	$0.521928\pi$
$521$	−20.5061	+	35.5176i	−0.898388	+	1.55605i	−0.829554	+	0.558426i	$0.811405\pi$
$522$	−12.0000	+	20.7846i	−0.525226	+	0.909718i
$523$	−9.19239	−	15.9217i	−0.401955	−	0.696207i	0.592007	−	0.805933i	$-0.298336\pi$
$523$	−9.19239	−	15.9217i	−0.401955	−	0.696207i	−0.993962	+	0.109726i	$0.965003\pi$
$524$	−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	0.953262	−	0.302144i	$-0.0977023\pi$
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	−0.738296	+	0.674477i	$0.764369\pi$
$542$	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	−0.975356	−	0.220638i	$-0.929186\pi$
$557$	−7.00000	+	12.1244i	−0.296600	+	0.513725i	0.678756	+	0.734364i	$0.262519\pi$
$558$	−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	$-0.900226\pi$
$563$	−4.94975	+	8.57321i	−0.208607	+	0.361318i	0.742669	+	0.669659i	$0.233560\pi$
$564$		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	0.963849	+	0.266450i	$0.0858508\pi$
$569$	17.0000	+	29.4449i	0.712677	+	1.23439i	−0.251172	+	0.967943i	$0.580816\pi$
$570$		0			0
$571$	−6.00000	+	10.3923i	−0.251092	+	0.434904i	−0.963827	−	0.266529i	$-0.914123\pi$
$571$	−6.00000	+	10.3923i	−0.251092	+	0.434904i	0.712735	+	0.701434i	$0.247456\pi$
$572$	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	$-0.747983\pi$
$577$	6.36396	−	11.0227i	0.264935	−	0.458881i	0.967547	+	0.252693i	$0.0813161\pi$
$578$	−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	$-0.366019\pi$
$587$	19.7990			0.817192			0.408596	+	0.912715i	$0.366019\pi$
$588$		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	$-0.148170\pi$
$593$	1.41421	+	2.44949i	0.0580748	+	0.100588i	−0.835526	+	0.549450i	$0.814837\pi$
$594$		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	−0.655018	−	0.755613i	$-0.727339\pi$
$599$	8.00000	−	13.8564i	0.326871	−	0.566157i	0.981889	+	0.189456i	$0.0606724\pi$
$600$		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	−0.972222	−	0.234061i	$-0.924798\pi$
$607$	−16.9706	−	29.3939i	−0.688814	−	1.19306i	0.283408	−	0.958999i	$-0.408535\pi$
$608$	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	−0.0470071	+	0.998895i	$0.514968\pi$
$613$	−22.0000	+	38.1051i	−0.888572	+	1.53905i	−0.841564	+	0.540157i	$0.818365\pi$
$614$	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	−0.428302	−	0.903636i	$-0.640888\pi$
$619$	14.1421	−	24.4949i	0.568420	−	0.984533i	0.996722	−	0.0808974i	$-0.0257786\pi$
$620$	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	−0.902817	−	0.430026i	$-0.858505\pi$
$641$	−2.00000	+	3.46410i	−0.0789953	+	0.136824i	0.823821	+	0.566849i	$0.191838\pi$
$642$		0			0
$643$	−25.4558			−1.00388			−0.501940	−	0.864902i	$-0.667380\pi$
$643$	−25.4558			−1.00388			−0.501940	+	0.864902i	$0.667380\pi$
$644$		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	$-0.877721\pi$
$647$	−3.53553	+	6.12372i	−0.138996	+	0.240748i	0.788121	+	0.615521i	$0.211054\pi$
$648$	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	0.884929	−	0.465727i	$-0.154207\pi$
$653$	1.00000	+	1.73205i	0.0391330	+	0.0677804i	−0.845796	+	0.533507i	$0.820874\pi$
$654$		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	$-0.886102\pi$
$661$	−4.24264	+	7.34847i	−0.165020	+	0.285822i	0.771643	+	0.636056i	$0.219435\pi$
$662$	−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	$-0.175318\pi$
$677$	−0.707107	−	1.22474i	−0.0271763	−	0.0470708i	−0.879294	+	0.476280i	$0.841985\pi$
$678$		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	−0.932349	−	0.361559i	$-0.882245\pi$
$683$	−4.00000	+	6.92820i	−0.153056	+	0.265100i	0.779294	+	0.626659i	$0.215578\pi$
$684$	−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	$-0.115066\pi$
$691$	4.24264	+	7.34847i	0.161398	+	0.279549i	−0.773973	+	0.633219i	$0.781733\pi$
$692$	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	−0.963512	−	0.267664i	$-0.913748\pi$
$709$	−19.0000	−	32.9090i	−0.713560	−	1.23592i	0.249952	−	0.968258i	$-0.419585\pi$
$710$		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	$-0.141458\pi$
$719$	2.12132	+	3.67423i	0.0791119	+	0.137026i	−0.823755	+	0.566946i	$0.808125\pi$
$720$	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	$-0.593149\pi$
$727$	−15.5563			−0.576953			−0.288477	+	0.957487i	$0.593149\pi$
$728$		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	$-0.0911386\pi$
$733$	6.36396	+	11.0227i	0.235058	+	0.407133i	−0.724231	+	0.689557i	$0.757805\pi$
$734$	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	−0.621374	−	0.783514i	$-0.713425\pi$
$739$	10.0000	−	17.3205i	0.367856	−	0.637145i	0.989230	+	0.146369i	$0.0467586\pi$
$740$	−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	0.883694	−	0.468065i	$-0.155049\pi$
$751$	1.00000	+	1.73205i	0.0364905	+	0.0632034i	−0.847203	+	0.531269i	$0.821715\pi$
$752$	−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	$-0.0321529\pi$
$761$	11.3137	+	19.5959i	0.410122	+	0.710351i	−0.584781	+	0.811191i	$0.698820\pi$
$762$		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	$-0.598986\pi$
$769$	−16.9706			−0.611974			−0.305987	+	0.952036i	$0.598986\pi$
$770$		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	$-0.966733\pi$
$773$	−11.3137	+	19.5959i	−0.406926	+	0.704816i	0.587618	+	0.809139i	$0.300066\pi$
$774$	−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	$-0.743906\pi$
$787$	7.77817	−	13.4722i	0.277262	−	0.480232i	0.970703	+	0.240281i	$0.0772397\pi$
$788$	−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	$-0.252596\pi$
$797$	39.5980			1.40263			0.701316	+	0.712850i	$0.252596\pi$
$798$		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	−0.202301	+	0.979323i	$0.564842\pi$
$809$	−27.0000	+	46.7654i	−0.949269	+	1.64418i	−0.746968	+	0.664860i	$0.768491\pi$
$810$	−12.7279	−	22.0454i	−0.447214	−	0.774597i
$811$	−18.3848			−0.645577			−0.322788	−	0.946471i	$-0.604620\pi$
$811$	−18.3848			−0.645577			−0.322788	+	0.946471i	$0.604620\pi$
$812$		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	0.986073	−	0.166316i	$-0.0531872\pi$
$821$	10.0000	+	17.3205i	0.349002	+	0.604490i	−0.637070	+	0.770806i	$0.719854\pi$
$822$		0			0
$823$	21.0000	−	36.3731i	0.732014	−	1.26789i	−0.224007	−	0.974588i	$-0.571914\pi$
$823$	21.0000	−	36.3731i	0.732014	−	1.26789i	0.956021	−	0.293298i	$-0.0947528\pi$
$824$	−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	$-0.687582\pi$
$829$	12.7279	−	22.0454i	0.442059	−	0.765669i	0.997842	+	0.0656587i	$0.0209148\pi$
$830$	−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	$-0.413461\pi$
$839$	15.5563			0.537065			0.268532	+	0.963271i	$0.413461\pi$
$840$		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	$-0.273219\pi$
$853$	38.1838			1.30739			0.653694	+	0.756759i	$0.273219\pi$
$854$		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	$-0.707028\pi$
$857$	11.3137	−	19.5959i	0.386469	−	0.669384i	0.991972	+	0.126459i	$0.0403613\pi$
$858$		0			0
$859$	−9.89949	−	17.1464i	−0.337766	−	0.585029i	0.646246	−	0.763129i	$-0.276338\pi$
$859$	−9.89949	−	17.1464i	−0.337766	−	0.585029i	−0.984012	+	0.178101i	$0.943005\pi$
$860$	−28.2843			−0.964486
$861$		0			0
$862$	12.0000			0.408722
$863$	−23.0000	−	39.8372i	−0.782929	−	1.35607i	−0.930228	−	0.366981i	$-0.880391\pi$
$863$	−23.0000	−	39.8372i	−0.782929	−	1.35607i	0.147299	−	0.989092i	$-0.452942\pi$
$864$		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	−0.965184	−	0.261571i	$-0.915759\pi$
$877$	−21.0000	−	36.3731i	−0.709120	−	1.22823i	0.256064	−	0.966660i	$-0.417574\pi$
$878$	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	$-0.764472\pi$
$881$	−43.8406			−1.47703			−0.738514	+	0.674238i	$0.764472\pi$
$882$		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	$-0.136391\pi$
$887$	2.82843	+	4.89898i	0.0949693	+	0.164492i	−0.814627	+	0.579986i	$0.803058\pi$
$888$		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	−0.749051	−	0.662512i	$-0.769490\pi$
$907$	6.00000	−	10.3923i	0.199227	−	0.345071i	0.948278	+	0.317441i	$0.102824\pi$
$908$	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	0.967274	−	0.253735i	$-0.0816592\pi$
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	−0.703378	+	0.710816i	$0.748326\pi$
$920$	−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	$-0.159281\pi$
$929$	0.707107	+	1.22474i	0.0231994	+	0.0401826i	−0.854193	+	0.519957i	$0.825948\pi$
$930$		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	$-0.395173\pi$
$937$	19.7990			0.646805			0.323402	+	0.946262i	$0.395173\pi$
$938$		0			0
$939$		0			0
$940$	10.0000	+	17.3205i	0.326164	+	0.564933i
$941$	19.0919	−	33.0681i	0.622378	−	1.07799i	−0.366664	−	0.930353i	$-0.619500\pi$
$941$	19.0919	−	33.0681i	0.622378	−	1.07799i	0.989042	−	0.147636i	$-0.0471665\pi$
$942$		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	0.896690	−	0.442659i	$-0.145965\pi$
$947$	2.00000	+	3.46410i	0.0649913	+	0.112568i	−0.831699	+	0.555227i	$0.812631\pi$
$948$		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	$-0.224774\pi$
$971$	−5.65685	−	9.79796i	−0.181537	−	0.314431i	−0.942404	+	0.334476i	$0.891441\pi$
$972$		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	−0.991618	−	0.129205i	$-0.958757\pi$
$977$	−12.0000	+	20.7846i	−0.383914	+	0.664959i	0.607704	+	0.794164i	$0.292091\pi$
$978$		0			0
$979$	−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	$-0.943185\pi$
$983$	−10.6066	+	18.3712i	−0.338298	+	0.585949i	0.645815	+	0.763494i	$0.276518\pi$
$984$		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	−0.991233	−	0.132125i	$-0.957820\pi$
$991$	−12.0000	+	20.7846i	−0.381193	+	0.660245i	0.610040	+	0.792370i	$0.291153\pi$
$992$	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	0.115968	−	0.993253i	$-0.463003\pi$
$997$	28.9914	−	50.2145i	0.918166	−	1.59031i	0.802198	−	0.597057i	$-0.203664\pi$
$998$	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.67.2		4
7.2	even	3	inner	1078.2.e.t.177.2		4
7.3	odd	6		1078.2.a.p.1.2	yes	2
7.4	even	3		1078.2.a.p.1.1	✓	2
7.5	odd	6	inner	1078.2.e.t.177.1		4
7.6	odd	2	inner	1078.2.e.t.67.1		4
21.11	odd	6		9702.2.a.df.1.2		2
21.17	even	6		9702.2.a.df.1.1		2
28.3	even	6		8624.2.a.bl.1.2		2
28.11	odd	6		8624.2.a.bl.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1078.2.a.p.1.1	✓	2	7.4	even	3
1078.2.a.p.1.2	yes	2	7.3	odd	6
1078.2.e.t.67.1		4	7.6	odd	2	inner
1078.2.e.t.67.2		4	1.1	even	1	trivial
1078.2.e.t.177.1		4	7.5	odd	6	inner
1078.2.e.t.177.2		4	7.2	even	3	inner
8624.2.a.bl.1.1		2	28.11	odd	6
8624.2.a.bl.1.2		2	28.3	even	6
9702.2.a.df.1.1		2	21.17	even	6
9702.2.a.df.1.2		2	21.11	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)

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