LMFDB - Embedded newform 1456.2.r.j.625.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(417,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 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("1456.417");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.r (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:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			625.1
Root			$0.809017 + 1.40126i$ of defining polynomial
Character	$\chi$	$=$	1456.625
Dual form			1456.2.r.j.417.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11803 - 1.93649i) q^{3} +(-1.11803 + 1.93649i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(-1.11803 - 1.93649i) q^{3} +(-1.11803 + 1.93649i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-1.00000 + 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{11} -1.00000 q^{13} +5.00000 q^{15} +(-0.736068 - 1.27491i) q^{17} +(1.50000 - 2.59808i) q^{19} +(1.11803 - 5.80948i) q^{21} +(-4.11803 + 7.13264i) q^{23} -2.23607 q^{27} +4.47214 q^{29} +(2.50000 + 4.33013i) q^{31} +(-3.35410 + 5.80948i) q^{33} +(-5.59017 + 1.93649i) q^{35} +(-2.35410 + 4.07742i) q^{37} +(1.11803 + 1.93649i) q^{39} -4.47214 q^{41} +8.00000 q^{43} +(-2.23607 - 3.87298i) q^{45} +(-3.73607 + 6.47106i) q^{47} +(1.00000 + 6.92820i) q^{49} +(-1.64590 + 2.85078i) q^{51} +(3.73607 + 6.47106i) q^{53} +6.70820 q^{55} -6.70820 q^{57} +(-0.736068 - 1.27491i) q^{59} +(-1.50000 + 2.59808i) q^{61} +(-5.00000 + 1.73205i) q^{63} +(1.11803 - 1.93649i) q^{65} +(-1.50000 - 2.59808i) q^{67} +18.4164 q^{69} +8.94427 q^{71} +(1.35410 + 2.34537i) q^{73} +(1.50000 - 7.79423i) q^{77} +(-1.35410 + 2.34537i) q^{79} +(5.50000 + 9.52628i) q^{81} +3.29180 q^{85} +(-5.00000 - 8.66025i) q^{87} +(-1.11803 + 1.93649i) q^{89} +(-2.00000 - 1.73205i) q^{91} +(5.59017 - 9.68246i) q^{93} +(3.35410 + 5.80948i) q^{95} +9.41641 q^{97} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{7} - 4 q^{9}+O(q^{10}) $ 4 * q + 8 * q^7 - 4 * q^9	$ 4 q + 8 q^{7} - 4 q^{9} - 6 q^{11} - 4 q^{13} + 20 q^{15} + 6 q^{17} + 6 q^{19} - 12 q^{23} + 10 q^{31} + 4 q^{37} + 32 q^{43} - 6 q^{47} + 4 q^{49} - 20 q^{51} + 6 q^{53} + 6 q^{59} - 6 q^{61} - 20 q^{63} - 6 q^{67} + 20 q^{69} - 8 q^{73} + 6 q^{77} + 8 q^{79} + 22 q^{81} + 40 q^{85} - 20 q^{87} - 8 q^{91} - 16 q^{97} + 24 q^{99}+O(q^{100}) $ 4 * q + 8 * q^7 - 4 * q^9 - 6 * q^11 - 4 * q^13 + 20 * q^15 + 6 * q^17 + 6 * q^19 - 12 * q^23 + 10 * q^31 + 4 * q^37 + 32 * q^43 - 6 * q^47 + 4 * q^49 - 20 * q^51 + 6 * q^53 + 6 * q^59 - 6 * q^61 - 20 * q^63 - 6 * q^67 + 20 * q^69 - 8 * q^73 + 6 * q^77 + 8 * q^79 + 22 * q^81 + 40 * q^85 - 20 * q^87 - 8 * q^91 - 16 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	−1.11803	−	1.93649i	−0.645497	−	1.11803i	−0.984186	−	0.177136i	$-0.943317\pi$
$3$	−1.11803	−	1.93649i	−0.645497	−	1.11803i	0.338689	−	0.940898i	$-0.390016\pi$
$4$		0			0
$5$	−1.11803	+	1.93649i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$5$	−1.11803	+	1.93649i	−0.500000	+	0.866025i	−1.00000			$\pi$
$6$		0			0
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$8$		0			0
$9$	−1.00000	+	1.73205i	−0.333333	+	0.577350i
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		0			0
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	5.00000			1.29099
$16$		0			0
$17$	−0.736068	−	1.27491i	−0.178523	−	0.309210i	0.762852	−	0.646573i	$-0.223798\pi$
$17$	−0.736068	−	1.27491i	−0.178523	−	0.309210i	−0.941375	+	0.337363i	$0.890465\pi$
$18$		0			0
$19$	1.50000	−	2.59808i	0.344124	−	0.596040i	−0.641071	−	0.767482i	$-0.721509\pi$
$19$	1.50000	−	2.59808i	0.344124	−	0.596040i	0.985194	+	0.171442i	$0.0548427\pi$
$20$		0			0
$21$	1.11803	−	5.80948i	0.243975	−	1.26773i
$22$		0			0
$23$	−4.11803	+	7.13264i	−0.858669	+	1.48726i	0.0145291	+	0.999894i	$0.495375\pi$
$23$	−4.11803	+	7.13264i	−0.858669	+	1.48726i	−0.873199	+	0.487365i	$0.837958\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−2.23607			−0.430331
$28$		0			0
$29$	4.47214			0.830455			0.415227	−	0.909718i	$-0.363702\pi$
$29$	4.47214			0.830455			0.415227	+	0.909718i	$0.363702\pi$
$30$		0			0
$31$	2.50000	+	4.33013i	0.449013	+	0.777714i	0.998322	−	0.0579057i	$-0.0184423\pi$
$31$	2.50000	+	4.33013i	0.449013	+	0.777714i	−0.549309	+	0.835619i	$0.685109\pi$
$32$		0			0
$33$	−3.35410	+	5.80948i	−0.583874	+	1.01130i
$34$		0			0
$35$	−5.59017	+	1.93649i	−0.944911	+	0.327327i
$36$		0			0
$37$	−2.35410	+	4.07742i	−0.387012	+	0.670324i	−0.992046	−	0.125875i	$-0.959826\pi$
$37$	−2.35410	+	4.07742i	−0.387012	+	0.670324i	0.605034	+	0.796200i	$0.293159\pi$
$38$		0			0
$39$	1.11803	+	1.93649i	0.179029	+	0.310087i
$40$		0			0
$41$	−4.47214			−0.698430			−0.349215	−	0.937043i	$-0.613552\pi$
$41$	−4.47214			−0.698430			−0.349215	+	0.937043i	$0.613552\pi$
$42$		0			0
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$		0			0
$45$	−2.23607	−	3.87298i	−0.333333	−	0.577350i
$46$		0			0
$47$	−3.73607	+	6.47106i	−0.544962	+	0.943901i	0.453648	+	0.891181i	$0.350122\pi$
$47$	−3.73607	+	6.47106i	−0.544962	+	0.943901i	−0.998609	+	0.0527200i	$0.983211\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$		0			0
$51$	−1.64590	+	2.85078i	−0.230472	+	0.399189i
$52$		0			0
$53$	3.73607	+	6.47106i	0.513188	+	0.888868i	0.999883	+	0.0152962i	$0.00486912\pi$
$53$	3.73607	+	6.47106i	0.513188	+	0.888868i	−0.486695	+	0.873572i	$0.661798\pi$
$54$		0			0
$55$	6.70820			0.904534
$56$		0			0
$57$	−6.70820			−0.888523
$58$		0			0
$59$	−0.736068	−	1.27491i	−0.0958279	−	0.165979i	0.814126	−	0.580688i	$-0.197217\pi$
$59$	−0.736068	−	1.27491i	−0.0958279	−	0.165979i	−0.909954	+	0.414710i	$0.863883\pi$
$60$		0			0
$61$	−1.50000	+	2.59808i	−0.192055	+	0.332650i	−0.945931	−	0.324367i	$-0.894849\pi$
$61$	−1.50000	+	2.59808i	−0.192055	+	0.332650i	0.753876	+	0.657017i	$0.228182\pi$
$62$		0			0
$63$	−5.00000	+	1.73205i	−0.629941	+	0.218218i
$64$		0			0
$65$	1.11803	−	1.93649i	0.138675	−	0.240192i
$66$		0			0
$67$	−1.50000	−	2.59808i	−0.183254	−	0.317406i	0.759733	−	0.650236i	$-0.225330\pi$
$67$	−1.50000	−	2.59808i	−0.183254	−	0.317406i	−0.942987	+	0.332830i	$0.891996\pi$
$68$		0			0
$69$	18.4164			2.21707
$70$		0			0
$71$	8.94427			1.06149			0.530745	−	0.847532i	$-0.321912\pi$
$71$	8.94427			1.06149			0.530745	+	0.847532i	$0.321912\pi$
$72$		0			0
$73$	1.35410	+	2.34537i	0.158486	+	0.274505i	0.934323	−	0.356428i	$-0.116006\pi$
$73$	1.35410	+	2.34537i	0.158486	+	0.274505i	−0.775837	+	0.630933i	$0.782672\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.50000	−	7.79423i	0.170941	−	0.888235i
$78$		0			0
$79$	−1.35410	+	2.34537i	−0.152348	+	0.263875i	−0.932090	−	0.362226i	$-0.882017\pi$
$79$	−1.35410	+	2.34537i	−0.152348	+	0.263875i	0.779742	+	0.626101i	$0.215350\pi$
$80$		0			0
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$		0			0
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	3.29180			0.357045
$86$		0			0
$87$	−5.00000	−	8.66025i	−0.536056	−	0.928477i
$88$		0			0
$89$	−1.11803	+	1.93649i	−0.118511	+	0.205268i	−0.919178	−	0.393842i	$-0.871146\pi$
$89$	−1.11803	+	1.93649i	−0.118511	+	0.205268i	0.800667	+	0.599110i	$0.204479\pi$
$90$		0			0
$91$	−2.00000	−	1.73205i	−0.209657	−	0.181568i
$92$		0			0
$93$	5.59017	−	9.68246i	0.579674	−	1.00402i
$94$		0			0
$95$	3.35410	+	5.80948i	0.344124	+	0.596040i
$96$		0			0
$97$	9.41641			0.956091			0.478046	−	0.878335i	$-0.341345\pi$
$97$	9.41641			0.956091			0.478046	+	0.878335i	$0.341345\pi$
$98$		0			0
$99$	6.00000			0.603023
$100$		0			0
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	0.998240	−	0.0592978i	$-0.0188862\pi$
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	−0.550474	+	0.834853i	$0.685553\pi$
$102$		0			0
$103$	−1.35410	+	2.34537i	−0.133424	+	0.231097i	−0.924994	−	0.379981i	$-0.875930\pi$
$103$	−1.35410	+	2.34537i	−0.133424	+	0.231097i	0.791571	+	0.611078i	$0.209264\pi$
$104$		0			0
$105$	10.0000	+	8.66025i	0.975900	+	0.845154i
$106$		0			0
$107$	−4.88197	+	8.45581i	−0.471957	+	0.817454i	−0.999485	−	0.0320835i	$-0.989786\pi$
$107$	−4.88197	+	8.45581i	−0.471957	+	0.817454i	0.527528	+	0.849538i	$0.323119\pi$
$108$		0			0
$109$	1.35410	+	2.34537i	0.129699	+	0.224646i	0.923560	−	0.383454i	$-0.125265\pi$
$109$	1.35410	+	2.34537i	0.129699	+	0.224646i	−0.793861	+	0.608100i	$0.791932\pi$
$110$		0			0
$111$	10.5279			0.999261
$112$		0			0
$113$	2.94427			0.276974			0.138487	−	0.990364i	$-0.455776\pi$
$113$	2.94427			0.276974			0.138487	+	0.990364i	$0.455776\pi$
$114$		0			0
$115$	−9.20820	−	15.9491i	−0.858669	−	1.48726i
$116$		0			0
$117$	1.00000	−	1.73205i	0.0924500	−	0.160128i
$118$		0			0
$119$	0.736068	−	3.82472i	0.0674752	−	0.350612i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$	5.00000	+	8.66025i	0.450835	+	0.780869i
$124$		0			0
$125$	−11.1803			−1.00000
$126$		0			0
$127$	11.4164			1.01304			0.506521	−	0.862228i	$-0.330931\pi$
$127$	11.4164			1.01304			0.506521	+	0.862228i	$0.330931\pi$
$128$		0			0
$129$	−8.94427	−	15.4919i	−0.787499	−	1.36399i
$130$		0			0
$131$	−4.11803	+	7.13264i	−0.359794	+	0.623182i	−0.987926	−	0.154925i	$-0.950486\pi$
$131$	−4.11803	+	7.13264i	−0.359794	+	0.623182i	0.628132	+	0.778107i	$0.283820\pi$
$132$		0			0
$133$	7.50000	−	2.59808i	0.650332	−	0.225282i
$134$		0			0
$135$	2.50000	−	4.33013i	0.215166	−	0.372678i
$136$		0			0
$137$	4.11803	+	7.13264i	0.351827	+	0.609383i	0.986570	−	0.163341i	$-0.0522271\pi$
$137$	4.11803	+	7.13264i	0.351827	+	0.609383i	−0.634742	+	0.772724i	$0.718894\pi$
$138$		0			0
$139$	23.4164			1.98615			0.993077	−	0.117466i	$-0.0374771\pi$
$139$	23.4164			1.98615			0.993077	+	0.117466i	$0.0374771\pi$
$140$		0			0
$141$	16.7082			1.40708
$142$		0			0
$143$	1.50000	+	2.59808i	0.125436	+	0.217262i
$144$		0			0
$145$	−5.00000	+	8.66025i	−0.415227	+	0.719195i
$146$		0			0
$147$	12.2984	−	9.68246i	1.01435	−	0.798596i
$148$		0			0
$149$	−0.354102	+	0.613323i	−0.0290092	+	0.0502453i	−0.880166	−	0.474667i	$-0.842569\pi$
$149$	−0.354102	+	0.613323i	−0.0290092	+	0.0502453i	0.851156	+	0.524912i	$0.175902\pi$
$150$		0			0
$151$	10.2082	+	17.6811i	0.830732	+	1.43887i	0.897459	+	0.441098i	$0.145411\pi$
$151$	10.2082	+	17.6811i	0.830732	+	1.43887i	−0.0667268	+	0.997771i	$0.521256\pi$
$152$		0			0
$153$	2.94427			0.238030
$154$		0			0
$155$	−11.1803			−0.898027
$156$		0			0
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	0.691888	−	0.722005i	$-0.256779\pi$
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	−0.971219	+	0.238190i	$0.923446\pi$
$158$		0			0
$159$	8.35410	−	14.4697i	0.662523	−	1.14752i
$160$		0			0
$161$	−20.5902	+	7.13264i	−1.62273	+	0.562131i
$162$		0			0
$163$	−8.20820	+	14.2170i	−0.642916	+	1.11356i	0.341862	+	0.939750i	$0.388942\pi$
$163$	−8.20820	+	14.2170i	−0.642916	+	1.11356i	−0.984779	+	0.173813i	$0.944391\pi$
$164$		0			0
$165$	−7.50000	−	12.9904i	−0.583874	−	1.01130i
$166$		0			0
$167$	−22.4721			−1.73895			−0.869473	−	0.493980i	$-0.835541\pi$
$167$	−22.4721			−1.73895			−0.869473	+	0.493980i	$0.835541\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$	3.00000	+	5.19615i	0.229416	+	0.397360i
$172$		0			0
$173$	8.20820	−	14.2170i	0.624058	−	1.08090i	−0.364664	−	0.931139i	$-0.618816\pi$
$173$	8.20820	−	14.2170i	0.624058	−	1.08090i	0.988722	−	0.149761i	$-0.0478505\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.64590	+	2.85078i	−0.123713	+	0.214278i
$178$		0			0
$179$	−10.0623	−	17.4284i	−0.752092	−	1.30266i	−0.946807	−	0.321802i	$-0.895712\pi$
$179$	−10.0623	−	17.4284i	−0.752092	−	1.30266i	0.194715	−	0.980860i	$-0.437622\pi$
$180$		0			0
$181$	−25.4164			−1.88919			−0.944593	−	0.328243i	$-0.893544\pi$
$181$	−25.4164			−1.88919			−0.944593	+	0.328243i	$0.893544\pi$
$182$		0			0
$183$	6.70820			0.495885
$184$		0			0
$185$	−5.26393	−	9.11740i	−0.387012	−	0.670324i
$186$		0			0
$187$	−2.20820	+	3.82472i	−0.161480	+	0.279691i
$188$		0			0
$189$	−4.47214	−	3.87298i	−0.325300	−	0.281718i
$190$		0			0
$191$	5.59017	−	9.68246i	0.404491	−	0.700598i	−0.589772	−	0.807570i	$-0.700782\pi$
$191$	5.59017	−	9.68246i	0.404491	−	0.700598i	0.994262	+	0.106972i	$0.0341155\pi$
$192$		0			0
$193$	−0.354102	−	0.613323i	−0.0254888	−	0.0441479i	0.853000	−	0.521912i	$-0.174781\pi$
$193$	−0.354102	−	0.613323i	−0.0254888	−	0.0441479i	−0.878488	+	0.477764i	$0.841448\pi$
$194$		0			0
$195$	−5.00000			−0.358057
$196$		0			0
$197$	−9.05573			−0.645194			−0.322597	−	0.946536i	$-0.604556\pi$
$197$	−9.05573			−0.645194			−0.322597	+	0.946536i	$0.604556\pi$
$198$		0			0
$199$	−10.3541	−	17.9338i	−0.733983	−	1.27130i	−0.955168	−	0.296064i	$-0.904326\pi$
$199$	−10.3541	−	17.9338i	−0.733983	−	1.27130i	0.221185	−	0.975232i	$-0.429007\pi$
$200$		0			0
$201$	−3.35410	+	5.80948i	−0.236580	+	0.409769i
$202$		0			0
$203$	8.94427	+	7.74597i	0.627765	+	0.543660i
$204$		0			0
$205$	5.00000	−	8.66025i	0.349215	−	0.604858i
$206$		0			0
$207$	−8.23607	−	14.2653i	−0.572446	−	0.991506i
$208$		0			0
$209$	−9.00000			−0.622543
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$	−10.0000	−	17.3205i	−0.685189	−	1.18678i
$214$		0			0
$215$	−8.94427	+	15.4919i	−0.609994	+	1.05654i
$216$		0			0
$217$	−2.50000	+	12.9904i	−0.169711	+	0.881845i
$218$		0			0
$219$	3.02786	−	5.24441i	0.204604	−	0.354385i
$220$		0			0
$221$	0.736068	+	1.27491i	0.0495133	+	0.0857595i
$222$		0			0
$223$	4.00000			0.267860			0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000			0.267860			0.133930	+	0.990991i	$0.457240\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.97214	+	5.14789i	0.197268	+	0.341677i	0.947642	−	0.319336i	$-0.103460\pi$
$227$	2.97214	+	5.14789i	0.197268	+	0.341677i	−0.750374	+	0.661014i	$0.770127\pi$
$228$		0			0
$229$	−12.0623	+	20.8925i	−0.797100	+	1.38062i	0.124398	+	0.992232i	$0.460300\pi$
$229$	−12.0623	+	20.8925i	−0.797100	+	1.38062i	−0.921497	+	0.388385i	$0.873033\pi$
$230$		0			0
$231$	−16.7705	+	5.80948i	−1.10342	+	0.382235i
$232$		0			0
$233$	−5.97214	+	10.3440i	−0.391248	+	0.677661i	−0.992614	−	0.121312i	$-0.961290\pi$
$233$	−5.97214	+	10.3440i	−0.391248	+	0.677661i	0.601367	+	0.798973i	$0.294623\pi$
$234$		0			0
$235$	−8.35410	−	14.4697i	−0.544962	−	0.943901i
$236$		0			0
$237$	6.05573			0.393362
$238$		0			0
$239$	−19.4164			−1.25594			−0.627972	−	0.778236i	$-0.716115\pi$
$239$	−19.4164			−1.25594			−0.627972	+	0.778236i	$0.716115\pi$
$240$		0			0
$241$	−2.35410	−	4.07742i	−0.151641	−	0.262650i	0.780190	−	0.625543i	$-0.215122\pi$
$241$	−2.35410	−	4.07742i	−0.151641	−	0.262650i	−0.931831	+	0.362893i	$0.881789\pi$
$242$		0			0
$243$	8.94427	−	15.4919i	0.573775	−	0.993808i
$244$		0			0
$245$	−14.5344	−	5.80948i	−0.928571	−	0.371154i
$246$		0			0
$247$	−1.50000	+	2.59808i	−0.0954427	+	0.165312i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.52786			−0.0964379			−0.0482190	−	0.998837i	$-0.515355\pi$
$251$	−1.52786			−0.0964379			−0.0482190	+	0.998837i	$0.515355\pi$
$252$		0			0
$253$	24.7082			1.55339
$254$		0			0
$255$	−3.68034	−	6.37454i	−0.230472	−	0.399189i
$256$		0			0
$257$	0.0278640	−	0.0482619i	0.00173811	−	0.00301050i	−0.865155	−	0.501504i	$-0.832780\pi$
$257$	0.0278640	−	0.0482619i	0.00173811	−	0.00301050i	0.866893	+	0.498494i	$0.166113\pi$
$258$		0			0
$259$	−11.7705	+	4.07742i	−0.731384	+	0.253359i
$260$		0			0
$261$	−4.47214	+	7.74597i	−0.276818	+	0.479463i
$262$		0			0
$263$	13.0623	+	22.6246i	0.805456	+	1.39509i	0.915983	+	0.401218i	$0.131413\pi$
$263$	13.0623	+	22.6246i	0.805456	+	1.39509i	−0.110526	+	0.993873i	$0.535254\pi$
$264$		0			0
$265$	−16.7082			−1.02638
$266$		0			0
$267$	5.00000			0.305995
$268$		0			0
$269$	−6.73607	−	11.6672i	−0.410705	−	0.711362i	0.584262	−	0.811565i	$-0.301384\pi$
$269$	−6.73607	−	11.6672i	−0.410705	−	0.711362i	−0.994967	+	0.100203i	$0.968051\pi$
$270$		0			0
$271$	−10.2082	+	17.6811i	−0.620104	+	1.07405i	0.369362	+	0.929286i	$0.379576\pi$
$271$	−10.2082	+	17.6811i	−0.620104	+	1.07405i	−0.989466	+	0.144766i	$0.953757\pi$
$272$		0			0
$273$	−1.11803	+	5.80948i	−0.0676665	+	0.351605i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	0.208204	+	0.360620i	0.0125098	+	0.0216675i	0.872213	−	0.489127i	$-0.162685\pi$
$277$	0.208204	+	0.360620i	0.0125098	+	0.0216675i	−0.859703	+	0.510795i	$0.829351\pi$
$278$		0			0
$279$	−10.0000			−0.598684
$280$		0			0
$281$	26.9443			1.60736			0.803680	−	0.595061i	$-0.202872\pi$
$281$	26.9443			1.60736			0.803680	+	0.595061i	$0.202872\pi$
$282$		0			0
$283$	13.0623	+	22.6246i	0.776473	+	1.34489i	0.933963	+	0.357371i	$0.116327\pi$
$283$	13.0623	+	22.6246i	0.776473	+	1.34489i	−0.157489	+	0.987521i	$0.550340\pi$
$284$		0			0
$285$	7.50000	−	12.9904i	0.444262	−	0.769484i
$286$		0			0
$287$	−8.94427	−	7.74597i	−0.527964	−	0.457230i
$288$		0			0
$289$	7.41641	−	12.8456i	0.436259	−	0.755623i
$290$		0			0
$291$	−10.5279	−	18.2348i	−0.617154	−	1.06894i
$292$		0			0
$293$	−14.9443			−0.873054			−0.436527	−	0.899691i	$-0.643792\pi$
$293$	−14.9443			−0.873054			−0.436527	+	0.899691i	$0.643792\pi$
$294$		0			0
$295$	3.29180			0.191656
$296$		0			0
$297$	3.35410	+	5.80948i	0.194625	+	0.337100i
$298$		0			0
$299$	4.11803	−	7.13264i	0.238152	−	0.412491i
$300$		0			0
$301$	16.0000	+	13.8564i	0.922225	+	0.798670i
$302$		0			0
$303$	10.0623	−	17.4284i	0.578064	−	1.00124i
$304$		0			0
$305$	−3.35410	−	5.80948i	−0.192055	−	0.332650i
$306$		0			0
$307$	−19.4164			−1.10815			−0.554076	−	0.832466i	$-0.686928\pi$
$307$	−19.4164			−1.10815			−0.554076	+	0.832466i	$0.686928\pi$
$308$		0			0
$309$	6.05573			0.344498
$310$		0			0
$311$	−13.8820	−	24.0443i	−0.787174	−	1.36343i	−0.927692	−	0.373347i	$-0.878210\pi$
$311$	−13.8820	−	24.0443i	−0.787174	−	1.36343i	0.140518	−	0.990078i	$-0.455123\pi$
$312$		0			0
$313$	2.79180	−	4.83553i	0.157802	−	0.273320i	−0.776274	−	0.630396i	$-0.782893\pi$
$313$	2.79180	−	4.83553i	0.157802	−	0.273320i	0.934076	+	0.357075i	$0.116226\pi$
$314$		0			0
$315$	2.23607	−	11.6190i	0.125988	−	0.654654i
$316$		0			0
$317$	4.11803	−	7.13264i	0.231292	−	0.400609i	−0.726897	−	0.686747i	$-0.759038\pi$
$317$	4.11803	−	7.13264i	0.231292	−	0.400609i	0.958189	+	0.286138i	$0.0923714\pi$
$318$		0			0
$319$	−6.70820	−	11.6190i	−0.375587	−	0.650536i
$320$		0			0
$321$	21.8328			1.21859
$322$		0			0
$323$	−4.41641			−0.245736
$324$		0			0
$325$		0			0
$326$		0			0
$327$	3.02786	−	5.24441i	0.167441	−	0.290017i
$328$		0			0
$329$	−18.6803	+	6.47106i	−1.02988	+	0.356761i
$330$		0			0
$331$	−0.791796	+	1.37143i	−0.0435210	+	0.0753807i	−0.886965	−	0.461836i	$-0.847191\pi$
$331$	−0.791796	+	1.37143i	−0.0435210	+	0.0753807i	0.843444	+	0.537217i	$0.180524\pi$
$332$		0			0
$333$	−4.70820	−	8.15485i	−0.258008	−	0.446883i
$334$		0			0
$335$	6.70820			0.366508
$336$		0			0
$337$	18.0000			0.980522			0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000			0.980522			0.490261	+	0.871576i	$0.336901\pi$
$338$		0			0
$339$	−3.29180	−	5.70156i	−0.178786	−	0.309666i
$340$		0			0
$341$	7.50000	−	12.9904i	0.406148	−	0.703469i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$	−20.5902	+	35.6632i	−1.10854	+	1.92004i
$346$		0			0
$347$	11.5344	+	19.9782i	0.619201	+	1.07249i	0.989632	+	0.143628i	$0.0458768\pi$
$347$	11.5344	+	19.9782i	0.619201	+	1.07249i	−0.370430	+	0.928860i	$0.620790\pi$
$348$		0			0
$349$	−29.4164			−1.57462			−0.787312	−	0.616555i	$-0.788528\pi$
$349$	−29.4164			−1.57462			−0.787312	+	0.616555i	$0.788528\pi$
$350$		0			0
$351$	2.23607			0.119352
$352$		0			0
$353$	−8.64590	−	14.9751i	−0.460175	−	0.797046i	0.538795	−	0.842437i	$-0.318880\pi$
$353$	−8.64590	−	14.9751i	−0.460175	−	0.797046i	−0.998969	+	0.0453912i	$0.985547\pi$
$354$		0			0
$355$	−10.0000	+	17.3205i	−0.530745	+	0.919277i
$356$		0			0
$357$	−8.22949	+	2.85078i	−0.435551	+	0.150879i
$358$		0			0
$359$	5.97214	−	10.3440i	0.315197	−	0.545938i	−0.664282	−	0.747482i	$-0.731263\pi$
$359$	5.97214	−	10.3440i	0.315197	−	0.545938i	0.979479	+	0.201544i	$0.0645960\pi$
$360$		0			0
$361$	5.00000	+	8.66025i	0.263158	+	0.455803i
$362$		0			0
$363$	−4.47214			−0.234726
$364$		0			0
$365$	−6.05573			−0.316971
$366$		0			0
$367$	−6.35410	−	11.0056i	−0.331681	−	0.574489i	0.651160	−	0.758940i	$-0.274283\pi$
$367$	−6.35410	−	11.0056i	−0.331681	−	0.574489i	−0.982842	+	0.184451i	$0.940949\pi$
$368$		0			0
$369$	4.47214	−	7.74597i	0.232810	−	0.403239i
$370$		0			0
$371$	−3.73607	+	19.4132i	−0.193967	+	1.00788i
$372$		0			0
$373$	0.791796	−	1.37143i	0.0409976	−	0.0710100i	−0.844798	−	0.535085i	$-0.820280\pi$
$373$	0.791796	−	1.37143i	0.0409976	−	0.0710100i	0.885796	+	0.464075i	$0.153613\pi$
$374$		0			0
$375$	12.5000	+	21.6506i	0.645497	+	1.11803i
$376$		0			0
$377$	−4.47214			−0.230327
$378$		0			0
$379$	15.4164			0.791888			0.395944	−	0.918275i	$-0.370417\pi$
$379$	15.4164			0.791888			0.395944	+	0.918275i	$0.370417\pi$
$380$		0			0
$381$	−12.7639	−	22.1078i	−0.653916	−	1.13262i
$382$		0			0
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	−0.608290	−	0.793715i	$-0.708144\pi$
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	0.991522	+	0.129937i	$0.0414776\pi$
$384$		0			0
$385$	13.4164	+	11.6190i	0.683763	+	0.592157i
$386$		0			0
$387$	−8.00000	+	13.8564i	−0.406663	+	0.704361i
$388$		0			0
$389$	−0.736068	−	1.27491i	−0.0373201	−	0.0646404i	0.846762	−	0.531972i	$-0.178549\pi$
$389$	−0.736068	−	1.27491i	−0.0373201	−	0.0646404i	−0.884082	+	0.467332i	$0.845215\pi$
$390$		0			0
$391$	12.1246			0.613168
$392$		0			0
$393$	18.4164			0.928985
$394$		0			0
$395$	−3.02786	−	5.24441i	−0.152348	−	0.263875i
$396$		0			0
$397$	13.0623	−	22.6246i	0.655578	−	1.13549i	−0.326170	−	0.945311i	$-0.605758\pi$
$397$	13.0623	−	22.6246i	0.655578	−	1.13549i	0.981748	−	0.190184i	$-0.0609084\pi$
$398$		0			0
$399$	−13.4164	−	11.6190i	−0.671660	−	0.581675i
$400$		0			0
$401$	−7.11803	+	12.3288i	−0.355458	+	0.615671i	−0.987196	−	0.159511i	$-0.949008\pi$
$401$	−7.11803	+	12.3288i	−0.355458	+	0.615671i	0.631739	+	0.775182i	$0.282342\pi$
$402$		0			0
$403$	−2.50000	−	4.33013i	−0.124534	−	0.215699i
$404$		0			0
$405$	−24.5967			−1.22222
$406$		0			0
$407$	14.1246			0.700131
$408$		0			0
$409$	−4.35410	−	7.54153i	−0.215296	−	0.372904i	0.738068	−	0.674727i	$-0.235738\pi$
$409$	−4.35410	−	7.54153i	−0.215296	−	0.372904i	−0.953364	+	0.301822i	$0.902405\pi$
$410$		0			0
$411$	9.20820	−	15.9491i	0.454207	−	0.786710i
$412$		0			0
$413$	0.736068	−	3.82472i	0.0362195	−	0.188202i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−26.1803	−	45.3457i	−1.28206	−	2.22059i
$418$		0			0
$419$	−32.9443			−1.60943			−0.804717	−	0.593659i	$-0.797683\pi$
$419$	−32.9443			−1.60943			−0.804717	+	0.593659i	$0.797683\pi$
$420$		0			0
$421$	13.4164			0.653876			0.326938	−	0.945046i	$-0.393983\pi$
$421$	13.4164			0.653876			0.326938	+	0.945046i	$0.393983\pi$
$422$		0			0
$423$	−7.47214	−	12.9421i	−0.363308	−	0.629267i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−7.50000	+	2.59808i	−0.362950	+	0.125730i
$428$		0			0
$429$	3.35410	−	5.80948i	0.161938	−	0.280484i
$430$		0			0
$431$	−15.6803	−	27.1591i	−0.755295	−	1.30821i	−0.945227	−	0.326413i	$-0.894160\pi$
$431$	−15.6803	−	27.1591i	−0.755295	−	1.30821i	0.189932	−	0.981797i	$-0.439173\pi$
$432$		0			0
$433$	29.4164			1.41366			0.706831	−	0.707382i	$-0.250124\pi$
$433$	29.4164			1.41366			0.706831	+	0.707382i	$0.250124\pi$
$434$		0			0
$435$	22.3607			1.07211
$436$		0			0
$437$	12.3541	+	21.3979i	0.590977	+	1.02360i
$438$		0			0
$439$	12.0623	−	20.8925i	0.575702	−	0.997146i	−0.420262	−	0.907403i	$-0.638062\pi$
$439$	12.0623	−	20.8925i	0.575702	−	0.997146i	0.995965	−	0.0897433i	$-0.0286047\pi$
$440$		0			0
$441$	−13.0000	−	5.19615i	−0.619048	−	0.247436i
$442$		0			0
$443$	1.11803	−	1.93649i	0.0531194	−	0.0920055i	−0.838243	−	0.545297i	$-0.816417\pi$
$443$	1.11803	−	1.93649i	0.0531194	−	0.0920055i	0.891362	+	0.453291i	$0.149750\pi$
$444$		0			0
$445$	−2.50000	−	4.33013i	−0.118511	−	0.205268i
$446$		0			0
$447$	1.58359			0.0749013
$448$		0			0
$449$	−34.3607			−1.62158			−0.810790	−	0.585337i	$-0.800962\pi$
$449$	−34.3607			−1.62158			−0.810790	+	0.585337i	$0.800962\pi$
$450$		0			0
$451$	6.70820	+	11.6190i	0.315877	+	0.547115i
$452$		0			0
$453$	22.8262	−	39.5362i	1.07247	−	1.85757i
$454$		0			0
$455$	5.59017	−	1.93649i	0.262071	−	0.0907841i
$456$		0			0
$457$	3.06231	−	5.30407i	0.143249	−	0.248114i	−0.785470	−	0.618900i	$-0.787578\pi$
$457$	3.06231	−	5.30407i	0.143249	−	0.248114i	0.928718	+	0.370786i	$0.120912\pi$
$458$		0			0
$459$	1.64590	+	2.85078i	0.0768239	+	0.133063i
$460$		0			0
$461$	34.3607			1.60034			0.800168	−	0.599776i	$-0.204744\pi$
$461$	34.3607			1.60034			0.800168	+	0.599776i	$0.204744\pi$
$462$		0			0
$463$	24.0000			1.11537			0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000			1.11537			0.557687	+	0.830051i	$0.311689\pi$
$464$		0			0
$465$	12.5000	+	21.6506i	0.579674	+	1.00402i
$466$		0			0
$467$	4.82624	−	8.35929i	0.223332	−	0.386822i	−0.732486	−	0.680782i	$-0.761640\pi$
$467$	4.82624	−	8.35929i	0.223332	−	0.386822i	0.955818	+	0.293960i	$0.0949734\pi$
$468$		0			0
$469$	1.50000	−	7.79423i	0.0692636	−	0.359904i
$470$		0			0
$471$	−7.82624	+	13.5554i	−0.360614	+	0.624602i
$472$		0			0
$473$	−12.0000	−	20.7846i	−0.551761	−	0.955677i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−14.9443			−0.684251
$478$		0			0
$479$	11.9164	+	20.6398i	0.544475	+	0.943058i	0.998640	+	0.0521401i	$0.0166043\pi$
$479$	11.9164	+	20.6398i	0.544475	+	0.943058i	−0.454165	+	0.890917i	$0.650062\pi$
$480$		0			0
$481$	2.35410	−	4.07742i	0.107338	−	0.185915i
$482$		0			0
$483$	36.8328	+	31.8982i	1.67595	+	1.45142i
$484$		0			0
$485$	−10.5279	+	18.2348i	−0.478046	+	0.827999i
$486$		0			0
$487$	−10.9164	−	18.9078i	−0.494670	−	0.856793i	0.505311	−	0.862937i	$-0.331378\pi$
$487$	−10.9164	−	18.9078i	−0.494670	−	0.856793i	−0.999981	+	0.00614405i	$0.998044\pi$
$488$		0			0
$489$	36.7082			1.66000
$490$		0			0
$491$	25.5279			1.15206			0.576028	−	0.817430i	$-0.304602\pi$
$491$	25.5279			1.15206			0.576028	+	0.817430i	$0.304602\pi$
$492$		0			0
$493$	−3.29180	−	5.70156i	−0.148255	−	0.256785i
$494$		0			0
$495$	−6.70820	+	11.6190i	−0.301511	+	0.522233i
$496$		0			0
$497$	17.8885	+	15.4919i	0.802411	+	0.694908i
$498$		0			0
$499$	13.2082	−	22.8773i	0.591280	−	1.02413i	−0.402780	−	0.915297i	$-0.631956\pi$
$499$	13.2082	−	22.8773i	0.591280	−	1.02413i	0.994060	−	0.108831i	$-0.0347107\pi$
$500$		0			0
$501$	25.1246	+	43.5171i	1.12248	+	1.94420i
$502$		0			0
$503$	−20.9443			−0.933859			−0.466929	−	0.884295i	$-0.654640\pi$
$503$	−20.9443			−0.933859			−0.466929	+	0.884295i	$0.654640\pi$
$504$		0			0
$505$	−20.1246			−0.895533
$506$		0			0
$507$	−1.11803	−	1.93649i	−0.0496536	−	0.0860026i
$508$		0			0
$509$	10.1180	−	17.5249i	0.448474	−	0.776780i	−0.549813	−	0.835288i	$-0.685301\pi$
$509$	10.1180	−	17.5249i	0.448474	−	0.776780i	0.998287	+	0.0585081i	$0.0186343\pi$
$510$		0			0
$511$	−1.35410	+	7.03612i	−0.0599019	+	0.311260i
$512$		0			0
$513$	−3.35410	+	5.80948i	−0.148087	+	0.256495i
$514$		0			0
$515$	−3.02786	−	5.24441i	−0.133424	−	0.231097i
$516$		0			0
$517$	22.4164			0.985872
$518$		0			0
$519$	−36.7082			−1.61131
$520$		0			0
$521$	8.97214	+	15.5402i	0.393076	+	0.680828i	0.992854	−	0.119339i	$-0.0380775\pi$
$521$	8.97214	+	15.5402i	0.393076	+	0.680828i	−0.599777	+	0.800167i	$0.704744\pi$
$522$		0			0
$523$	16.3541	−	28.3261i	0.715115	−	1.23862i	−0.247800	−	0.968811i	$-0.579708\pi$
$523$	16.3541	−	28.3261i	0.715115	−	1.23862i	0.962915	−	0.269804i	$-0.0869590\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.68034	−	6.37454i	0.160318	−	0.277679i
$528$		0			0
$529$	−22.4164	−	38.8264i	−0.974626	−	1.68810i
$530$		0			0
$531$	2.94427			0.127771
$532$		0			0
$533$	4.47214			0.193710
$534$		0			0
$535$	−10.9164	−	18.9078i	−0.471957	−	0.817454i
$536$		0			0
$537$	−22.5000	+	38.9711i	−0.970947	+	1.68173i
$538$		0			0
$539$	16.5000	−	12.9904i	0.710705	−	0.559535i
$540$		0			0
$541$	−0.645898	+	1.11873i	−0.0277693	+	0.0480979i	−0.879576	−	0.475758i	$-0.842174\pi$
$541$	−0.645898	+	1.11873i	−0.0277693	+	0.0480979i	0.851807	+	0.523856i	$0.175507\pi$
$542$		0			0
$543$	28.4164	+	49.2187i	1.21946	+	2.11217i
$544$		0			0
$545$	−6.05573			−0.259399
$546$		0			0
$547$	4.58359			0.195980			0.0979901	−	0.995187i	$-0.468759\pi$
$547$	4.58359			0.195980			0.0979901	+	0.995187i	$0.468759\pi$
$548$		0			0
$549$	−3.00000	−	5.19615i	−0.128037	−	0.221766i
$550$		0			0
$551$	6.70820	−	11.6190i	0.285779	−	0.494984i
$552$		0			0
$553$	−6.77051	+	2.34537i	−0.287911	+	0.0997354i
$554$		0			0
$555$	−11.7705	+	20.3871i	−0.499630	+	0.865385i
$556$		0			0
$557$	9.35410	+	16.2018i	0.396346	+	0.686491i	0.993272	−	0.115805i	$-0.0369447\pi$
$557$	9.35410	+	16.2018i	0.396346	+	0.686491i	−0.596926	+	0.802296i	$0.703611\pi$
$558$		0			0
$559$	−8.00000			−0.338364
$560$		0			0
$561$	9.87539			0.416939
$562$		0			0
$563$	6.29837	+	10.9091i	0.265445	+	0.459764i	0.967680	−	0.252181i	$-0.0811479\pi$
$563$	6.29837	+	10.9091i	0.265445	+	0.459764i	−0.702235	+	0.711945i	$0.747815\pi$
$564$		0			0
$565$	−3.29180	+	5.70156i	−0.138487	+	0.239866i
$566$		0			0
$567$	−5.50000	+	28.5788i	−0.230978	+	1.20020i
$568$		0			0
$569$	−12.7361	+	22.0595i	−0.533924	+	0.924783i	0.465291	+	0.885158i	$0.345950\pi$
$569$	−12.7361	+	22.0595i	−0.533924	+	0.924783i	−0.999215	+	0.0396252i	$0.987384\pi$
$570$		0			0
$571$	−18.0623	−	31.2848i	−0.755884	−	1.30923i	−0.944934	−	0.327262i	$-0.893874\pi$
$571$	−18.0623	−	31.2848i	−0.755884	−	1.30923i	0.189050	−	0.981968i	$-0.439459\pi$
$572$		0			0
$573$	−25.0000			−1.04439
$574$		0			0
$575$		0			0
$576$		0			0
$577$	9.64590	+	16.7072i	0.401564	+	0.695529i	0.993915	−	0.110151i	$-0.0351334\pi$
$577$	9.64590	+	16.7072i	0.401564	+	0.695529i	−0.592351	+	0.805680i	$0.701800\pi$
$578$		0			0
$579$	−0.791796	+	1.37143i	−0.0329059	+	0.0569947i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	11.2082	−	19.4132i	0.464196	−	0.804012i
$584$		0			0
$585$	2.23607	+	3.87298i	0.0924500	+	0.160128i
$586$		0			0
$587$	6.11146			0.252247			0.126123	−	0.992015i	$-0.459746\pi$
$587$	6.11146			0.252247			0.126123	+	0.992015i	$0.459746\pi$
$588$		0			0
$589$	15.0000			0.618064
$590$		0			0
$591$	10.1246	+	17.5363i	0.416471	+	0.721349i
$592$		0			0
$593$	−13.8820	+	24.0443i	−0.570064	+	0.987380i	0.426495	+	0.904490i	$0.359748\pi$
$593$	−13.8820	+	24.0443i	−0.570064	+	0.987380i	−0.996559	+	0.0828898i	$0.973585\pi$
$594$		0			0
$595$	6.58359	+	5.70156i	0.269901	+	0.233741i
$596$		0			0
$597$	−23.1525	+	40.1013i	−0.947568	+	1.64124i
$598$		0			0
$599$	−8.53444	−	14.7821i	−0.348708	−	0.603980i	0.637312	−	0.770606i	$-0.280046\pi$
$599$	−8.53444	−	14.7821i	−0.348708	−	0.603980i	−0.986020	+	0.166626i	$0.946713\pi$
$600$		0			0
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$		0			0
$603$	6.00000			0.244339
$604$		0			0
$605$	2.23607	+	3.87298i	0.0909091	+	0.157459i
$606$		0			0
$607$	12.0623	−	20.8925i	0.489594	−	0.848001i	−0.510334	−	0.859976i	$-0.670478\pi$
$607$	12.0623	−	20.8925i	0.489594	−	0.848001i	0.999928	+	0.0119745i	$0.00381171\pi$
$608$		0			0
$609$	5.00000	−	25.9808i	0.202610	−	1.05279i
$610$		0			0
$611$	3.73607	−	6.47106i	0.151145	−	0.261791i
$612$		0			0
$613$	9.06231	+	15.6964i	0.366023	+	0.633971i	0.988940	−	0.148318i	$-0.0473858\pi$
$613$	9.06231	+	15.6964i	0.366023	+	0.633971i	−0.622917	+	0.782288i	$0.714052\pi$
$614$		0			0
$615$	−22.3607			−0.901670
$616$		0			0
$617$	−4.47214			−0.180041			−0.0900207	−	0.995940i	$-0.528693\pi$
$617$	−4.47214			−0.180041			−0.0900207	+	0.995940i	$0.528693\pi$
$618$		0			0
$619$	8.50000	+	14.7224i	0.341644	+	0.591744i	0.984738	−	0.174042i	$-0.0556830\pi$
$619$	8.50000	+	14.7224i	0.341644	+	0.591744i	−0.643094	+	0.765787i	$0.722350\pi$
$620$		0			0
$621$	9.20820	−	15.9491i	0.369512	−	0.640014i
$622$		0			0
$623$	−5.59017	+	1.93649i	−0.223965	+	0.0775839i
$624$		0			0
$625$	12.5000	−	21.6506i	0.500000	−	0.866025i
$626$		0			0
$627$	10.0623	+	17.4284i	0.401850	+	0.696024i
$628$		0			0
$629$	6.93112			0.276362
$630$		0			0
$631$	−22.8328			−0.908960			−0.454480	−	0.890757i	$-0.650175\pi$
$631$	−22.8328			−0.908960			−0.454480	+	0.890757i	$0.650175\pi$
$632$		0			0
$633$	4.47214	+	7.74597i	0.177751	+	0.307875i
$634$		0			0
$635$	−12.7639	+	22.1078i	−0.506521	+	0.877320i
$636$		0			0
$637$	−1.00000	−	6.92820i	−0.0396214	−	0.274505i
$638$		0			0
$639$	−8.94427	+	15.4919i	−0.353830	+	0.612851i
$640$		0			0
$641$	−5.97214	−	10.3440i	−0.235885	−	0.408565i	0.723644	−	0.690173i	$-0.242466\pi$
$641$	−5.97214	−	10.3440i	−0.235885	−	0.408565i	−0.959530	+	0.281608i	$0.909132\pi$
$642$		0			0
$643$	−34.8328			−1.37367			−0.686836	−	0.726812i	$-0.741001\pi$
$643$	−34.8328			−1.37367			−0.686836	+	0.726812i	$0.741001\pi$
$644$		0			0
$645$	40.0000			1.57500
$646$		0			0
$647$	10.1180	+	17.5249i	0.397781	+	0.688977i	0.993452	−	0.114252i	$-0.0364471\pi$
$647$	10.1180	+	17.5249i	0.397781	+	0.688977i	−0.595671	+	0.803229i	$0.703114\pi$
$648$		0			0
$649$	−2.20820	+	3.82472i	−0.0866796	+	0.150133i
$650$		0			0
$651$	27.9508	−	9.68246i	1.09548	−	0.379485i
$652$		0			0
$653$	−2.26393	+	3.92125i	−0.0885945	+	0.153450i	−0.906917	−	0.421309i	$-0.861571\pi$
$653$	−2.26393	+	3.92125i	−0.0885945	+	0.153450i	0.818323	+	0.574759i	$0.194904\pi$
$654$		0			0
$655$	−9.20820	−	15.9491i	−0.359794	−	0.623182i
$656$		0			0
$657$	−5.41641			−0.211314
$658$		0			0
$659$	8.94427			0.348419			0.174210	−	0.984709i	$-0.444263\pi$
$659$	8.94427			0.348419			0.174210	+	0.984709i	$0.444263\pi$
$660$		0			0
$661$	3.35410	+	5.80948i	0.130459	+	0.225962i	0.923854	−	0.382746i	$-0.125021\pi$
$661$	3.35410	+	5.80948i	0.130459	+	0.225962i	−0.793394	+	0.608708i	$0.791688\pi$
$662$		0			0
$663$	1.64590	−	2.85078i	0.0639214	−	0.110715i
$664$		0			0
$665$	−3.35410	+	17.4284i	−0.130066	+	0.675845i
$666$		0			0
$667$	−18.4164	+	31.8982i	−0.713086	+	1.23510i
$668$		0			0
$669$	−4.47214	−	7.74597i	−0.172903	−	0.299476i
$670$		0			0
$671$	9.00000			0.347441
$672$		0			0
$673$	−9.41641			−0.362976			−0.181488	−	0.983393i	$-0.558091\pi$
$673$	−9.41641			−0.362976			−0.181488	+	0.983393i	$0.558091\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1.44427	−	2.50155i	0.0555079	−	0.0961425i	−0.836936	−	0.547300i	$-0.815656\pi$
$677$	1.44427	−	2.50155i	0.0555079	−	0.0961425i	0.892444	+	0.451158i	$0.148989\pi$
$678$		0			0
$679$	18.8328	+	16.3097i	0.722737	+	0.625909i
$680$		0			0
$681$	6.64590	−	11.5110i	0.254671	−	0.441104i
$682$		0			0
$683$	−6.73607	−	11.6672i	−0.257748	−	0.446433i	0.707890	−	0.706323i	$-0.249647\pi$
$683$	−6.73607	−	11.6672i	−0.257748	−	0.446433i	−0.965638	+	0.259889i	$0.916314\pi$
$684$		0			0
$685$	−18.4164			−0.703655
$686$		0			0
$687$	53.9443			2.05810
$688$		0			0
$689$	−3.73607	−	6.47106i	−0.142333	−	0.246528i
$690$		0			0
$691$	−25.9164	+	44.8885i	−0.985907	+	1.70764i	−0.348070	+	0.937468i	$0.613163\pi$
$691$	−25.9164	+	44.8885i	−0.985907	+	1.70764i	−0.637836	+	0.770172i	$0.720170\pi$
$692$		0			0
$693$	12.0000	+	10.3923i	0.455842	+	0.394771i
$694$		0			0
$695$	−26.1803	+	45.3457i	−0.993077	+	1.72006i
$696$		0			0
$697$	3.29180	+	5.70156i	0.124686	+	0.215962i
$698$		0			0
$699$	26.7082			1.01020
$700$		0			0
$701$	−22.3607			−0.844551			−0.422276	−	0.906467i	$-0.638769\pi$
$701$	−22.3607			−0.844551			−0.422276	+	0.906467i	$0.638769\pi$
$702$		0			0
$703$	7.06231	+	12.2323i	0.266360	+	0.461349i
$704$		0			0
$705$	−18.6803	+	32.3553i	−0.703542	+	1.21857i
$706$		0			0
$707$	−4.50000	+	23.3827i	−0.169240	+	0.879396i
$708$		0			0
$709$	25.0623	−	43.4092i	0.941235	−	1.63027i	0.178114	−	0.984010i	$-0.443000\pi$
$709$	25.0623	−	43.4092i	0.941235	−	1.63027i	0.763120	−	0.646256i	$-0.223666\pi$
$710$		0			0
$711$	−2.70820	−	4.69075i	−0.101566	−	0.175917i
$712$		0			0
$713$	−41.1803			−1.54222
$714$		0			0
$715$	−6.70820			−0.250873
$716$		0			0
$717$	21.7082	+	37.5997i	0.810708	+	1.40419i
$718$		0			0
$719$	12.3541	−	21.3979i	0.460730	−	0.798008i	−0.538267	−	0.842774i	$-0.680921\pi$
$719$	12.3541	−	21.3979i	0.460730	−	0.798008i	0.998998	+	0.0447660i	$0.0142542\pi$
$720$		0			0
$721$	−6.77051	+	2.34537i	−0.252147	+	0.0873463i
$722$		0			0
$723$	−5.26393	+	9.11740i	−0.195768	+	0.339080i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	38.8328			1.44023			0.720115	−	0.693855i	$-0.244089\pi$
$727$	38.8328			1.44023			0.720115	+	0.693855i	$0.244089\pi$
$728$		0			0
$729$	−7.00000			−0.259259
$730$		0			0
$731$	−5.88854	−	10.1993i	−0.217796	−	0.377233i
$732$		0			0
$733$	−14.3541	+	24.8620i	−0.530181	+	0.918300i	0.469199	+	0.883092i	$0.344543\pi$
$733$	−14.3541	+	24.8620i	−0.530181	+	0.918300i	−0.999380	+	0.0352078i	$0.988791\pi$
$734$		0			0
$735$	5.00000	+	34.6410i	0.184428	+	1.27775i
$736$		0			0
$737$	−4.50000	+	7.79423i	−0.165760	+	0.287104i
$738$		0			0
$739$	−8.91641	−	15.4437i	−0.327995	−	0.568105i	0.654119	−	0.756392i	$-0.273040\pi$
$739$	−8.91641	−	15.4437i	−0.327995	−	0.568105i	−0.982114	+	0.188287i	$0.939706\pi$
$740$		0			0
$741$	6.70820			0.246432
$742$		0			0
$743$	−32.9443			−1.20861			−0.604304	−	0.796754i	$-0.706549\pi$
$743$	−32.9443			−1.20861			−0.604304	+	0.796754i	$0.706549\pi$
$744$		0			0
$745$	−0.791796	−	1.37143i	−0.0290092	−	0.0502453i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−24.4098	+	8.45581i	−0.891916	+	0.308969i
$750$		0			0
$751$	−5.06231	+	8.76817i	−0.184726	+	0.319955i	−0.943484	−	0.331417i	$-0.892473\pi$
$751$	−5.06231	+	8.76817i	−0.184726	+	0.319955i	0.758758	+	0.651373i	$0.225806\pi$
$752$		0			0
$753$	1.70820	+	2.95870i	0.0622504	+	0.107821i
$754$		0			0
$755$	−45.6525			−1.66146
$756$		0			0
$757$	−52.8328			−1.92024			−0.960121	−	0.279586i	$-0.909803\pi$
$757$	−52.8328			−1.92024			−0.960121	+	0.279586i	$0.909803\pi$
$758$		0			0
$759$	−27.6246	−	47.8472i	−1.00271	−	1.73674i
$760$		0			0
$761$	16.7705	−	29.0474i	0.607931	−	1.05297i	−0.383650	−	0.923478i	$-0.625333\pi$
$761$	16.7705	−	29.0474i	0.607931	−	1.05297i	0.991581	−	0.129488i	$-0.0413334\pi$
$762$		0			0
$763$	−1.35410	+	7.03612i	−0.0490218	+	0.254725i
$764$		0			0
$765$	−3.29180	+	5.70156i	−0.119015	+	0.206140i
$766$		0			0
$767$	0.736068	+	1.27491i	0.0265779	+	0.0460342i
$768$		0			0
$769$	46.0000			1.65880			0.829401	−	0.558653i	$-0.188682\pi$
$769$	46.0000			1.65880			0.829401	+	0.558653i	$0.188682\pi$
$770$		0			0
$771$	−0.124612			−0.00448778
$772$		0			0
$773$	23.5344	+	40.7628i	0.846475	+	1.46614i	0.884334	+	0.466855i	$0.154613\pi$
$773$	23.5344	+	40.7628i	0.846475	+	1.46614i	−0.0378590	+	0.999283i	$0.512054\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	21.0557	+	18.2348i	0.755370	+	0.654170i
$778$		0			0
$779$	−6.70820	+	11.6190i	−0.240346	+	0.416292i
$780$		0			0
$781$	−13.4164	−	23.2379i	−0.480077	−	0.831517i
$782$		0			0
$783$	−10.0000			−0.357371
$784$		0			0
$785$	15.6525			0.558661
$786$		0			0
$787$	10.2082	+	17.6811i	0.363883	+	0.630264i	0.988596	−	0.150590i	$-0.0481174\pi$
$787$	10.2082	+	17.6811i	0.363883	+	0.630264i	−0.624713	+	0.780854i	$0.714784\pi$
$788$		0			0
$789$	29.2082	−	50.5901i	1.03984	−	1.80106i
$790$		0			0
$791$	5.88854	+	5.09963i	0.209373	+	0.181322i
$792$		0			0
$793$	1.50000	−	2.59808i	0.0532666	−	0.0922604i
$794$		0			0
$795$	18.6803	+	32.3553i	0.662523	+	1.14752i
$796$		0			0
$797$	9.05573			0.320770			0.160385	−	0.987055i	$-0.448726\pi$
$797$	9.05573			0.320770			0.160385	+	0.987055i	$0.448726\pi$
$798$		0			0
$799$	11.0000			0.389152
$800$		0			0
$801$	−2.23607	−	3.87298i	−0.0790076	−	0.136845i
$802$		0			0
$803$	4.06231	−	7.03612i	0.143356	−	0.248299i
$804$		0			0
$805$	9.20820	−	47.8472i	0.324547	−	1.68639i
$806$		0			0
$807$	−15.0623	+	26.0887i	−0.530218	+	0.918365i
$808$		0			0
$809$	−11.2082	−	19.4132i	−0.394059	−	0.682531i	0.598921	−	0.800808i	$-0.295596\pi$
$809$	−11.2082	−	19.4132i	−0.394059	−	0.682531i	−0.992981	+	0.118277i	$0.962263\pi$
$810$		0			0
$811$	14.8328			0.520851			0.260425	−	0.965494i	$-0.416137\pi$
$811$	14.8328			0.520851			0.260425	+	0.965494i	$0.416137\pi$
$812$		0			0
$813$	45.6525			1.60110
$814$		0			0
$815$	−18.3541	−	31.7902i	−0.642916	−	1.11356i
$816$		0			0
$817$	12.0000	−	20.7846i	0.419827	−	0.727161i
$818$		0			0
$819$	5.00000	−	1.73205i	0.174714	−	0.0605228i
$820$		0			0
$821$	−19.1180	+	33.1134i	−0.667224	+	1.15567i	0.311453	+	0.950261i	$0.399184\pi$
$821$	−19.1180	+	33.1134i	−0.667224	+	1.15567i	−0.978677	+	0.205404i	$0.934149\pi$
$822$		0			0
$823$	17.0623	+	29.5528i	0.594755	+	1.03015i	0.993581	+	0.113119i	$0.0360841\pi$
$823$	17.0623	+	29.5528i	0.594755	+	1.03015i	−0.398827	+	0.917026i	$0.630583\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−26.8328			−0.933068			−0.466534	−	0.884503i	$-0.654498\pi$
$827$	−26.8328			−0.933068			−0.466534	+	0.884503i	$0.654498\pi$
$828$		0			0
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	0.997225	−	0.0744432i	$-0.0237179\pi$
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	−0.563082	+	0.826401i	$0.690385\pi$
$830$		0			0
$831$	0.465558	−	0.806370i	0.0161500	−	0.0279727i
$832$		0			0
$833$	8.09675	−	6.37454i	0.280536	−	0.220865i
$834$		0			0
$835$	25.1246	−	43.5171i	0.869473	−	1.50597i
$836$		0			0
$837$	−5.59017	−	9.68246i	−0.193225	−	0.334675i
$838$		0			0
$839$	5.88854			0.203295			0.101648	−	0.994820i	$-0.467589\pi$
$839$	5.88854			0.203295			0.101648	+	0.994820i	$0.467589\pi$
$840$		0			0
$841$	−9.00000			−0.310345
$842$		0			0
$843$	−30.1246	−	52.1774i	−1.03755	−	1.79708i
$844$		0			0
$845$	−1.11803	+	1.93649i	−0.0384615	+	0.0666173i
$846$		0			0
$847$	5.00000	−	1.73205i	0.171802	−	0.0595140i
$848$		0			0
$849$	29.2082	−	50.5901i	1.00242	−	1.73625i
$850$		0			0
$851$	−19.3885	−	33.5819i	−0.664631	−	1.15117i
$852$		0			0
$853$	−52.2492			−1.78898			−0.894490	−	0.447089i	$-0.852461\pi$
$853$	−52.2492			−1.78898			−0.894490	+	0.447089i	$0.852461\pi$
$854$		0			0
$855$	−13.4164			−0.458831
$856$		0			0
$857$	0.680340	+	1.17838i	0.0232400	+	0.0402528i	0.877411	−	0.479739i	$-0.159268\pi$
$857$	0.680340	+	1.17838i	0.0232400	+	0.0402528i	−0.854172	+	0.519991i	$0.825935\pi$
$858$		0			0
$859$	10.3541	−	17.9338i	0.353277	−	0.611894i	−0.633544	−	0.773707i	$-0.718401\pi$
$859$	10.3541	−	17.9338i	0.353277	−	0.611894i	0.986822	+	0.161812i	$0.0517338\pi$
$860$		0			0
$861$	−5.00000	+	25.9808i	−0.170400	+	0.885422i
$862$		0			0
$863$	11.9721	−	20.7363i	0.407536	−	0.705873i	−0.587077	−	0.809531i	$-0.699721\pi$
$863$	11.9721	−	20.7363i	0.407536	−	0.705873i	0.994613	+	0.103658i	$0.0330547\pi$
$864$		0			0
$865$	18.3541	+	31.7902i	0.624058	+	1.08090i
$866$		0			0
$867$	−33.1672			−1.12642
$868$		0			0
$869$	8.12461			0.275609
$870$		0			0
$871$	1.50000	+	2.59808i	0.0508256	+	0.0880325i
$872$		0			0
$873$	−9.41641	+	16.3097i	−0.318697	+	0.552000i
$874$		0			0
$875$	−22.3607	−	19.3649i	−0.755929	−	0.654654i
$876$		0			0
$877$	−16.0623	+	27.8207i	−0.542386	+	0.939439i	0.456381	+	0.889785i	$0.349145\pi$
$877$	−16.0623	+	27.8207i	−0.542386	+	0.939439i	−0.998766	+	0.0496548i	$0.984188\pi$
$878$		0			0
$879$	16.7082	+	28.9395i	0.563554	+	0.976104i
$880$		0			0
$881$	43.3050			1.45898			0.729490	−	0.683991i	$-0.239757\pi$
$881$	43.3050			1.45898			0.729490	+	0.683991i	$0.239757\pi$
$882$		0			0
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$		0			0
$885$	−3.68034	−	6.37454i	−0.123713	−	0.214278i
$886$		0			0
$887$	−10.1180	+	17.5249i	−0.339730	+	0.588430i	−0.984382	−	0.176046i	$-0.943669\pi$
$887$	−10.1180	+	17.5249i	−0.339730	+	0.588430i	0.644652	+	0.764477i	$0.277002\pi$
$888$		0			0
$889$	22.8328	+	19.7738i	0.765788	+	0.663192i
$890$		0			0
$891$	16.5000	−	28.5788i	0.552771	−	0.957427i
$892$		0			0
$893$	11.2082	+	19.4132i	0.375068	+	0.649637i
$894$		0			0
$895$	45.0000			1.50418
$896$		0			0
$897$	−18.4164			−0.614906
$898$		0			0
$899$	11.1803	+	19.3649i	0.372885	+	0.645856i
$900$		0			0
$901$	5.50000	−	9.52628i	0.183232	−	0.317366i
$902$		0			0
$903$	8.94427	−	46.4758i	0.297647	−	1.54662i
$904$		0			0
$905$	28.4164	−	49.2187i	0.944593	−	1.63608i
$906$		0			0
$907$	9.35410	+	16.2018i	0.310598	+	0.537971i	0.978492	−	0.206285i	$-0.0661374\pi$
$907$	9.35410	+	16.2018i	0.310598	+	0.537971i	−0.667894	+	0.744256i	$0.732804\pi$
$908$		0			0
$909$	−18.0000			−0.597022
$910$		0			0
$911$	34.2492			1.13473			0.567364	−	0.823467i	$-0.307963\pi$
$911$	34.2492			1.13473			0.567364	+	0.823467i	$0.307963\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−7.50000	+	12.9904i	−0.247942	+	0.429449i
$916$		0			0
$917$	−20.5902	+	7.13264i	−0.679947	+	0.235541i
$918$		0			0
$919$	10.0623	−	17.4284i	0.331925	−	0.574911i	−0.650964	−	0.759108i	$-0.725635\pi$
$919$	10.0623	−	17.4284i	0.331925	−	0.574911i	0.982889	+	0.184198i	$0.0589686\pi$
$920$		0			0
$921$	21.7082	+	37.5997i	0.715310	+	1.23895i
$922$		0			0
$923$	−8.94427			−0.294404
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−2.70820	−	4.69075i	−0.0889491	−	0.154064i
$928$		0			0
$929$	12.4098	−	21.4945i	0.407153	−	0.705210i	−0.587416	−	0.809285i	$-0.699855\pi$
$929$	12.4098	−	21.4945i	0.407153	−	0.705210i	0.994569	+	0.104075i	$0.0331881\pi$
$930$		0			0
$931$	19.5000	+	7.79423i	0.639087	+	0.255446i
$932$		0			0
$933$	−31.0410	+	53.7646i	−1.01624	+	1.76017i
$934$		0			0
$935$	−4.93769	−	8.55234i	−0.161480	−	0.279691i
$936$		0			0
$937$	25.4164			0.830318			0.415159	−	0.909749i	$-0.363726\pi$
$937$	25.4164			0.830318			0.415159	+	0.909749i	$0.363726\pi$
$938$		0			0
$939$	−12.4853			−0.407442
$940$		0			0
$941$	−25.1180	−	43.5057i	−0.818825	−	1.41825i	−0.906549	−	0.422101i	$-0.861293\pi$
$941$	−25.1180	−	43.5057i	−0.818825	−	1.41825i	0.0877244	−	0.996145i	$-0.472041\pi$
$942$		0			0
$943$	18.4164	−	31.8982i	0.599721	−	1.03875i
$944$		0			0
$945$	12.5000	−	4.33013i	0.406625	−	0.140859i
$946$		0			0
$947$	−11.2639	+	19.5097i	−0.366029	+	0.633980i	−0.988941	−	0.148312i	$-0.952616\pi$
$947$	−11.2639	+	19.5097i	−0.366029	+	0.633980i	0.622912	+	0.782292i	$0.285949\pi$
$948$		0			0
$949$	−1.35410	−	2.34537i	−0.0439560	−	0.0761340i
$950$		0			0
$951$	−18.4164			−0.597193
$952$		0			0
$953$	−41.7771			−1.35329			−0.676646	−	0.736308i	$-0.736567\pi$
$953$	−41.7771			−1.35329			−0.676646	+	0.736308i	$0.736567\pi$
$954$		0			0
$955$	12.5000	+	21.6506i	0.404491	+	0.700598i
$956$		0			0
$957$	−15.0000	+	25.9808i	−0.484881	+	0.839839i
$958$		0			0
$959$	−4.11803	+	21.3979i	−0.132978	+	0.690975i
$960$		0			0
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$		0			0
$963$	−9.76393	−	16.9116i	−0.314638	−	0.544970i
$964$		0			0
$965$	1.58359			0.0509776
$966$		0			0
$967$	−16.5836			−0.533292			−0.266646	−	0.963794i	$-0.585916\pi$
$967$	−16.5836			−0.533292			−0.266646	+	0.963794i	$0.585916\pi$
$968$		0			0
$969$	4.93769	+	8.55234i	0.158622	+	0.274741i
$970$		0			0
$971$	−5.64590	+	9.77898i	−0.181185	+	0.313822i	−0.942285	−	0.334813i	$-0.891327\pi$
$971$	−5.64590	+	9.77898i	−0.181185	+	0.313822i	0.761099	+	0.648636i	$0.224660\pi$
$972$		0			0
$973$	46.8328	+	40.5584i	1.50139	+	1.30024i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.17376	+	2.03302i	0.0375520	+	0.0650419i	0.884191	−	0.467126i	$-0.154711\pi$
$977$	1.17376	+	2.03302i	0.0375520	+	0.0650419i	−0.846639	+	0.532168i	$0.821377\pi$
$978$		0			0
$979$	6.70820			0.214395
$980$		0			0
$981$	−5.41641			−0.172933
$982$		0			0
$983$	3.73607	+	6.47106i	0.119162	+	0.206395i	0.919436	−	0.393240i	$-0.128646\pi$
$983$	3.73607	+	6.47106i	0.119162	+	0.206395i	−0.800274	+	0.599635i	$0.795313\pi$
$984$		0			0
$985$	10.1246	−	17.5363i	0.322597	−	0.558754i
$986$		0			0
$987$	33.4164	+	28.9395i	1.06366	+	0.921153i
$988$		0			0
$989$	−32.9443	+	57.0612i	−1.04757	+	1.81444i
$990$		0			0
$991$	15.3541	+	26.5941i	0.487739	+	0.844789i	0.999901	−	0.0141002i	$-0.00448840\pi$
$991$	15.3541	+	26.5941i	0.487739	+	0.844789i	−0.512161	+	0.858889i	$0.671155\pi$
$992$		0			0
$993$	3.54102			0.112371
$994$		0			0
$995$	46.3050			1.46797
$996$		0			0
$997$	−13.2082	−	22.8773i	−0.418308	−	0.724531i	0.577461	−	0.816418i	$-0.304043\pi$
$997$	−13.2082	−	22.8773i	−0.418308	−	0.724531i	−0.995769	+	0.0918873i	$0.970710\pi$
$998$		0			0
$999$	5.26393	−	9.11740i	0.166543	−	0.288462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.r.j.625.1		4
4.3	odd	2		91.2.e.b.79.2	yes	4
7.4	even	3	inner	1456.2.r.j.417.1		4
12.11	even	2		819.2.j.c.352.1		4
28.3	even	6		637.2.e.h.508.2		4
28.11	odd	6		91.2.e.b.53.2	✓	4
28.19	even	6		637.2.a.e.1.1		2
28.23	odd	6		637.2.a.f.1.1		2
28.27	even	2		637.2.e.h.79.2		4
52.51	odd	2		1183.2.e.d.170.1		4
84.11	even	6		819.2.j.c.235.1		4
84.23	even	6		5733.2.a.v.1.2		2
84.47	odd	6		5733.2.a.w.1.2		2
364.51	odd	6		8281.2.a.z.1.2		2
364.103	even	6		8281.2.a.ba.1.2		2
364.207	odd	6		1183.2.e.d.508.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.b.53.2	✓	4	28.11	odd	6
91.2.e.b.79.2	yes	4	4.3	odd	2
637.2.a.e.1.1		2	28.19	even	6
637.2.a.f.1.1		2	28.23	odd	6
637.2.e.h.79.2		4	28.27	even	2
637.2.e.h.508.2		4	28.3	even	6
819.2.j.c.235.1		4	84.11	even	6
819.2.j.c.352.1		4	12.11	even	2
1183.2.e.d.170.1		4	52.51	odd	2
1183.2.e.d.508.1		4	364.207	odd	6
1456.2.r.j.417.1		4	7.4	even	3	inner
1456.2.r.j.625.1		4	1.1	even	1	trivial
5733.2.a.v.1.2		2	84.23	even	6
5733.2.a.w.1.2		2	84.47	odd	6
8281.2.a.z.1.2		2	364.51	odd	6
8281.2.a.ba.1.2		2	364.103	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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.11803 - 1.93649i) q^{3} +(-1.11803 + 1.93649i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(-1.11803 - 1.93649i) q^{3} +(-1.11803 + 1.93649i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-1.00000 + 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{11} -1.00000 q^{13} +5.00000 q^{15} +(-0.736068 - 1.27491i) q^{17} +(1.50000 - 2.59808i) q^{19} +(1.11803 - 5.80948i) q^{21} +(-4.11803 + 7.13264i) q^{23} -2.23607 q^{27} +4.47214 q^{29} +(2.50000 + 4.33013i) q^{31} +(-3.35410 + 5.80948i) q^{33} +(-5.59017 + 1.93649i) q^{35} +(-2.35410 + 4.07742i) q^{37} +(1.11803 + 1.93649i) q^{39} -4.47214 q^{41} +8.00000 q^{43} +(-2.23607 - 3.87298i) q^{45} +(-3.73607 + 6.47106i) q^{47} +(1.00000 + 6.92820i) q^{49} +(-1.64590 + 2.85078i) q^{51} +(3.73607 + 6.47106i) q^{53} +6.70820 q^{55} -6.70820 q^{57} +(-0.736068 - 1.27491i) q^{59} +(-1.50000 + 2.59808i) q^{61} +(-5.00000 + 1.73205i) q^{63} +(1.11803 - 1.93649i) q^{65} +(-1.50000 - 2.59808i) q^{67} +18.4164 q^{69} +8.94427 q^{71} +(1.35410 + 2.34537i) q^{73} +(1.50000 - 7.79423i) q^{77} +(-1.35410 + 2.34537i) q^{79} +(5.50000 + 9.52628i) q^{81} +3.29180 q^{85} +(-5.00000 - 8.66025i) q^{87} +(-1.11803 + 1.93649i) q^{89} +(-2.00000 - 1.73205i) q^{91} +(5.59017 - 9.68246i) q^{93} +(3.35410 + 5.80948i) q^{95} +9.41641 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 4 * q + 8 * q^7 - 4 * q^9	\( 4 q + 8 q^{7} - 4 q^{9} - 6 q^{11} - 4 q^{13} + 20 q^{15} + 6 q^{17} + 6 q^{19} - 12 q^{23} + 10 q^{31} + 4 q^{37} + 32 q^{43} - 6 q^{47} + 4 q^{49} - 20 q^{51} + 6 q^{53} + 6 q^{59} - 6 q^{61} - 20 q^{63} - 6 q^{67} + 20 q^{69} - 8 q^{73} + 6 q^{77} + 8 q^{79} + 22 q^{81} + 40 q^{85} - 20 q^{87} - 8 q^{91} - 16 q^{97} + 24 q^{99}+O(q^{100}) \) 4 * q + 8 * q^7 - 4 * q^9 - 6 * q^11 - 4 * q^13 + 20 * q^15 + 6 * q^17 + 6 * q^19 - 12 * q^23 + 10 * q^31 + 4 * q^37 + 32 * q^43 - 6 * q^47 + 4 * q^49 - 20 * q^51 + 6 * q^53 + 6 * q^59 - 6 * q^61 - 20 * q^63 - 6 * q^67 + 20 * q^69 - 8 * q^73 + 6 * q^77 + 8 * q^79 + 22 * q^81 + 40 * q^85 - 20 * q^87 - 8 * q^91 - 16 * q^97 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more