LMFDB - Embedded newform 320.2.j.b.143.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,2,Mod(47,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("320.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	320.j (of order $4$, 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:	$2.55521286468$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			143.1
Root			$-0.480367 - 1.33013i$ of defining polynomial
Character	$\chi$	$=$	320.143
Dual form			320.2.j.b.47.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.85601i q^{3} +(1.43498 - 1.71489i) q^{5} +(0.458895 - 0.458895i) q^{7} -5.15678 q^{9} +O(q^{10})$	\(q-2.85601i q^{3} +(1.43498 - 1.71489i) q^{5} +(0.458895 - 0.458895i) q^{7} -5.15678 q^{9} +(0.492763 - 0.492763i) q^{11} +4.52109 q^{13} +(-4.89773 - 4.09831i) q^{15} +(-3.12823 + 3.12823i) q^{17} +(-4.04508 + 4.04508i) q^{19} +(-1.31061 - 1.31061i) q^{21} +(1.80660 + 1.80660i) q^{23} +(-0.881683 - 4.92165i) q^{25} +6.15978i q^{27} +(-3.83926 - 3.83926i) q^{29} +0.139949i q^{31} +(-1.40733 - 1.40733i) q^{33} +(-0.128450 - 1.44546i) q^{35} +5.84330 q^{37} -12.9123i q^{39} -4.55648i q^{41} +7.49928 q^{43} +(-7.39986 + 8.84330i) q^{45} +(4.14073 + 4.14073i) q^{47} +6.57883i q^{49} +(8.93426 + 8.93426i) q^{51} +2.75773i q^{53} +(-0.137930 - 1.55214i) q^{55} +(11.5528 + 11.5528i) q^{57} +(3.62521 + 3.62521i) q^{59} +(3.72781 - 3.72781i) q^{61} +(-2.36642 + 2.36642i) q^{63} +(6.48766 - 7.75317i) q^{65} -3.32677 q^{67} +(5.15965 - 5.15965i) q^{69} -1.37056 q^{71} +(-2.55028 + 2.55028i) q^{73} +(-14.0563 + 2.51809i) q^{75} -0.452252i q^{77} +3.86426 q^{79} +2.12204 q^{81} -14.4698i q^{83} +(0.875628 + 9.85351i) q^{85} +(-10.9650 + 10.9650i) q^{87} -3.35011 q^{89} +(2.07470 - 2.07470i) q^{91} +0.399696 q^{93} +(1.13226 + 12.7415i) q^{95} +(-4.95582 + 4.95582i) q^{97} +(-2.54107 + 2.54107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{5} - 2 q^{7} - 10 q^{9}+O(q^{10}) $ 18 * q - 4 * q^5 - 2 * q^7 - 10 * q^9	$ 18 q - 4 q^{5} - 2 q^{7} - 10 q^{9} + 2 q^{11} - 20 q^{15} - 6 q^{17} - 2 q^{19} - 16 q^{21} + 2 q^{23} + 6 q^{25} - 14 q^{29} - 8 q^{33} + 6 q^{35} + 8 q^{37} + 44 q^{43} - 4 q^{45} + 38 q^{47} - 8 q^{51} + 6 q^{55} + 24 q^{57} + 10 q^{59} + 14 q^{61} - 6 q^{63} - 12 q^{67} + 32 q^{69} - 24 q^{71} + 14 q^{73} - 64 q^{75} - 16 q^{79} + 2 q^{81} - 10 q^{85} - 24 q^{87} - 12 q^{89} + 16 q^{93} + 34 q^{95} + 18 q^{97} + 22 q^{99}+O(q^{100}) $ 18 * q - 4 * q^5 - 2 * q^7 - 10 * q^9 + 2 * q^11 - 20 * q^15 - 6 * q^17 - 2 * q^19 - 16 * q^21 + 2 * q^23 + 6 * q^25 - 14 * q^29 - 8 * q^33 + 6 * q^35 + 8 * q^37 + 44 * q^43 - 4 * q^45 + 38 * q^47 - 8 * q^51 + 6 * q^55 + 24 * q^57 + 10 * q^59 + 14 * q^61 - 6 * q^63 - 12 * q^67 + 32 * q^69 - 24 * q^71 + 14 * q^73 - 64 * q^75 - 16 * q^79 + 2 * q^81 - 10 * q^85 - 24 * q^87 - 12 * q^89 + 16 * q^93 + 34 * q^95 + 18 * q^97 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

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
$3$		−	2.85601i		−	1.64892i	−0.565923	−	0.824458i	$-0.691480\pi$
$3$		−	2.85601i		−	1.64892i	0.565923	−	0.824458i	$-0.308520\pi$
$4$		0			0
$5$	1.43498	−	1.71489i	0.641741	−	0.766921i
$5$	1.43498	−	1.71489i	0.641741	−	0.766921i
$6$		0			0
$7$	0.458895	−	0.458895i	0.173446	−	0.173446i	−0.615046	−	0.788491i	$-0.710862\pi$
$7$	0.458895	−	0.458895i	0.173446	−	0.173446i	0.788491	+	0.615046i	$0.210862\pi$
$8$		0			0
$9$	−5.15678			−1.71893
$10$		0			0
$11$	0.492763	−	0.492763i	0.148574	−	0.148574i	−0.628907	−	0.777481i	$-0.716497\pi$
$11$	0.492763	−	0.492763i	0.148574	−	0.148574i	0.777481	+	0.628907i	$0.216497\pi$
$12$		0			0
$13$	4.52109			1.25393			0.626963	−	0.779049i	$-0.284298\pi$
$13$	4.52109			1.25393			0.626963	+	0.779049i	$0.284298\pi$
$14$		0			0
$15$	−4.89773	−	4.09831i	−1.26459	−	1.05818i
$16$		0			0
$17$	−3.12823	+	3.12823i	−0.758708	+	0.758708i	−0.976087	−	0.217379i	$-0.930249\pi$
$17$	−3.12823	+	3.12823i	−0.758708	+	0.758708i	0.217379	+	0.976087i	$0.430249\pi$
$18$		0			0
$19$	−4.04508	+	4.04508i	−0.928005	+	0.928005i	−0.997577	−	0.0695721i	$-0.977837\pi$
$19$	−4.04508	+	4.04508i	−0.928005	+	0.928005i	0.0695721	+	0.997577i	$0.477837\pi$
$20$		0			0
$21$	−1.31061	−	1.31061i	−0.285998	−	0.285998i
$22$		0			0
$23$	1.80660	+	1.80660i	0.376701	+	0.376701i	0.869911	−	0.493209i	$-0.164176\pi$
$23$	1.80660	+	1.80660i	0.376701	+	0.376701i	−0.493209	+	0.869911i	$0.664176\pi$
$24$		0			0
$25$	−0.881683	−	4.92165i	−0.176337	−	0.984330i
$26$		0			0
$27$			6.15978i			1.18545i
$28$		0			0
$29$	−3.83926	−	3.83926i	−0.712932	−	0.712932i	0.254215	−	0.967148i	$-0.418183\pi$
$29$	−3.83926	−	3.83926i	−0.712932	−	0.712932i	−0.967148	+	0.254215i	$0.918183\pi$
$30$		0			0
$31$			0.139949i			0.0251356i	0.999921	+	0.0125678i	$0.00400057\pi$
$31$			0.139949i			0.0251356i	−0.999921	+	0.0125678i	$0.995999\pi$
$32$		0			0
$33$	−1.40733	−	1.40733i	−0.244985	−	0.244985i
$34$		0			0
$35$	−0.128450	−	1.44546i	−0.0217120	−	0.244327i
$36$		0			0
$37$	5.84330			0.960633			0.480317	−	0.877095i	$-0.340522\pi$
$37$	5.84330			0.960633			0.480317	+	0.877095i	$0.340522\pi$
$38$		0			0
$39$		−	12.9123i		−	2.06762i
$40$		0			0
$41$		−	4.55648i		−	0.711602i	−0.934562	−	0.355801i	$-0.884208\pi$
$41$		−	4.55648i		−	0.711602i	0.934562	−	0.355801i	$-0.115792\pi$
$42$		0			0
$43$	7.49928			1.14363			0.571815	−	0.820383i	$-0.306240\pi$
$43$	7.49928			1.14363			0.571815	+	0.820383i	$0.306240\pi$
$44$		0			0
$45$	−7.39986	+	8.84330i	−1.10311	+	1.31828i
$46$		0			0
$47$	4.14073	+	4.14073i	0.603987	+	0.603987i	0.941368	−	0.337381i	$-0.109541\pi$
$47$	4.14073	+	4.14073i	0.603987	+	0.603987i	−0.337381	+	0.941368i	$0.609541\pi$
$48$		0			0
$49$			6.57883i			0.939833i
$50$		0			0
$51$	8.93426	+	8.93426i	1.25105	+	1.25105i
$52$		0			0
$53$			2.75773i			0.378803i	0.981900	+	0.189402i	$0.0606548\pi$
$53$			2.75773i			0.378803i	−0.981900	+	0.189402i	$0.939345\pi$
$54$		0			0
$55$	−0.137930	−	1.55214i	−0.0185985	−	0.209290i
$56$		0			0
$57$	11.5528	+	11.5528i	1.53020	+	1.53020i
$58$		0			0
$59$	3.62521	+	3.62521i	0.471962	+	0.471962i	0.902549	−	0.430587i	$-0.141694\pi$
$59$	3.62521	+	3.62521i	0.471962	+	0.471962i	−0.430587	+	0.902549i	$0.641694\pi$
$60$		0			0
$61$	3.72781	−	3.72781i	0.477298	−	0.477298i	−0.426969	−	0.904266i	$-0.640419\pi$
$61$	3.72781	−	3.72781i	0.477298	−	0.477298i	0.904266	+	0.426969i	$0.140419\pi$
$62$		0			0
$63$	−2.36642	+	2.36642i	−0.298141	+	0.298141i
$64$		0			0
$65$	6.48766	−	7.75317i	0.804696	−	0.961662i
$66$		0			0
$67$	−3.32677			−0.406430			−0.203215	−	0.979134i	$-0.565139\pi$
$67$	−3.32677			−0.406430			−0.203215	+	0.979134i	$0.565139\pi$
$68$		0			0
$69$	5.15965	−	5.15965i	0.621149	−	0.621149i
$70$		0			0
$71$	−1.37056			−0.162655			−0.0813275	−	0.996687i	$-0.525916\pi$
$71$	−1.37056			−0.162655			−0.0813275	+	0.996687i	$0.525916\pi$
$72$		0			0
$73$	−2.55028	+	2.55028i	−0.298488	+	0.298488i	−0.840422	−	0.541933i	$-0.817693\pi$
$73$	−2.55028	+	2.55028i	−0.298488	+	0.298488i	0.541933	+	0.840422i	$0.317693\pi$
$74$		0			0
$75$	−14.0563	+	2.51809i	−1.62308	+	0.290764i
$76$		0			0
$77$		−	0.452252i		−	0.0515389i
$78$		0			0
$79$	3.86426			0.434763			0.217382	−	0.976087i	$-0.430248\pi$
$79$	3.86426			0.434763			0.217382	+	0.976087i	$0.430248\pi$
$80$		0			0
$81$	2.12204			0.235782
$82$		0			0
$83$		−	14.4698i		−	1.58827i	−0.607744	−	0.794133i	$-0.707925\pi$
$83$		−	14.4698i		−	1.58827i	0.607744	−	0.794133i	$-0.292075\pi$
$84$		0			0
$85$	0.875628	+	9.85351i	0.0949752	+	1.06876i
$86$		0			0
$87$	−10.9650	+	10.9650i	−1.17557	+	1.17557i
$88$		0			0
$89$	−3.35011			−0.355111			−0.177556	−	0.984111i	$-0.556819\pi$
$89$	−3.35011			−0.355111			−0.177556	+	0.984111i	$0.556819\pi$
$90$		0			0
$91$	2.07470	−	2.07470i	0.217488	−	0.217488i
$92$		0			0
$93$	0.399696			0.0414466
$94$		0			0
$95$	1.13226	+	12.7415i	0.116168	+	1.30725i
$96$		0			0
$97$	−4.95582	+	4.95582i	−0.503187	+	0.503187i	−0.912427	−	0.409240i	$-0.865794\pi$
$97$	−4.95582	+	4.95582i	−0.503187	+	0.503187i	0.409240	+	0.912427i	$0.365794\pi$
$98$		0			0
$99$	−2.54107	+	2.54107i	−0.255387	+	0.255387i
$100$		0			0
$101$	−1.84536	−	1.84536i	−0.183621	−	0.183621i	0.609311	−	0.792931i	$-0.291446\pi$
$101$	−1.84536	−	1.84536i	−0.183621	−	0.183621i	−0.792931	+	0.609311i	$0.791446\pi$
$102$		0			0
$103$	11.6655	+	11.6655i	1.14944	+	1.14944i	0.986664	+	0.162773i	$0.0520437\pi$
$103$	11.6655	+	11.6655i	1.14944	+	1.14944i	0.162773	+	0.986664i	$0.447956\pi$
$104$		0			0
$105$	−4.12823	+	0.366853i	−0.402874	+	0.0358012i
$106$		0			0
$107$		−	15.3106i		−	1.48013i	−0.672534	−	0.740067i	$-0.734794\pi$
$107$		−	15.3106i		−	1.48013i	0.672534	−	0.740067i	$-0.265206\pi$
$108$		0			0
$109$	12.4798	+	12.4798i	1.19535	+	1.19535i	0.975544	+	0.219803i	$0.0705416\pi$
$109$	12.4798	+	12.4798i	1.19535	+	1.19535i	0.219803	+	0.975544i	$0.429458\pi$
$110$		0			0
$111$		−	16.6885i		−	1.58400i
$112$		0			0
$113$	2.53557	+	2.53557i	0.238526	+	0.238526i	0.816240	−	0.577713i	$-0.196055\pi$
$113$	2.53557	+	2.53557i	0.238526	+	0.238526i	−0.577713	+	0.816240i	$0.696055\pi$
$114$		0			0
$115$	5.69053	−	0.505686i	0.530645	−	0.0471555i
$116$		0			0
$117$	−23.3143			−2.15541
$118$		0			0
$119$			2.87106i			0.263189i
$120$		0			0
$121$			10.5144i			0.955852i
$122$		0			0
$123$	−13.0133			−1.17337
$124$		0			0
$125$	−9.70527	−	5.55047i	−0.868066	−	0.496449i
$126$		0			0
$127$	0.615790	+	0.615790i	0.0546426	+	0.0546426i	0.733900	−	0.679257i	$-0.237698\pi$
$127$	0.615790	+	0.615790i	0.0546426	+	0.0546426i	−0.679257	+	0.733900i	$0.737698\pi$
$128$		0			0
$129$		−	21.4180i		−	1.88575i
$130$		0			0
$131$	−9.55413	−	9.55413i	−0.834748	−	0.834748i	0.153414	−	0.988162i	$-0.450973\pi$
$131$	−9.55413	−	9.55413i	−0.834748	−	0.834748i	−0.988162	+	0.153414i	$0.950973\pi$
$132$		0			0
$133$			3.71253i			0.321917i
$134$		0			0
$135$	10.5633	+	8.83914i	0.909147	+	0.760752i
$136$		0			0
$137$	−3.70277	−	3.70277i	−0.316349	−	0.316349i	0.531014	−	0.847363i	$-0.321811\pi$
$137$	−3.70277	−	3.70277i	−0.316349	−	0.316349i	−0.847363	+	0.531014i	$0.821811\pi$
$138$		0			0
$139$	−5.46761	−	5.46761i	−0.463756	−	0.463756i	0.436128	−	0.899885i	$-0.356349\pi$
$139$	−5.46761	−	5.46761i	−0.463756	−	0.463756i	−0.899885	+	0.436128i	$0.856349\pi$
$140$		0			0
$141$	11.8260	−	11.8260i	0.995925	−	0.995925i
$142$		0			0
$143$	2.22783	−	2.22783i	0.186300	−	0.186300i
$144$		0			0
$145$	−12.0931	+	1.07465i	−1.00428	+	0.0892450i
$146$		0			0
$147$	18.7892			1.54971
$148$		0			0
$149$	4.21561	−	4.21561i	0.345356	−	0.345356i	−0.513021	−	0.858376i	$-0.671474\pi$
$149$	4.21561	−	4.21561i	0.345356	−	0.345356i	0.858376	+	0.513021i	$0.171474\pi$
$150$		0			0
$151$	−12.4417			−1.01249			−0.506244	−	0.862390i	$-0.668966\pi$
$151$	−12.4417			−1.01249			−0.506244	+	0.862390i	$0.668966\pi$
$152$		0			0
$153$	16.1316	−	16.1316i	1.30416	−	1.30416i
$154$		0			0
$155$	0.239997	+	0.200824i	0.0192771	+	0.0161306i
$156$		0			0
$157$		−	7.50500i		−	0.598964i	−0.954102	−	0.299482i	$-0.903186\pi$
$157$		−	7.50500i		−	0.598964i	0.954102	−	0.299482i	$-0.0968138\pi$
$158$		0			0
$159$	7.87609			0.624615
$160$		0			0
$161$	1.65807			0.130675
$162$		0			0
$163$			23.7284i			1.85855i	0.369383	+	0.929277i	$0.379569\pi$
$163$			23.7284i			1.85855i	−0.369383	+	0.929277i	$0.620431\pi$
$164$		0			0
$165$	−4.43291	+	0.393929i	−0.345102	+	0.0306673i
$166$		0			0
$167$	0.402976	−	0.402976i	0.0311832	−	0.0311832i	−0.691343	−	0.722526i	$-0.742981\pi$
$167$	0.402976	−	0.402976i	0.0311832	−	0.0311832i	0.722526	+	0.691343i	$0.242981\pi$
$168$		0			0
$169$	7.44028			0.572330
$170$		0			0
$171$	20.8596	−	20.8596i	1.59517	−	1.59517i
$172$		0			0
$173$	−15.4500			−1.17464			−0.587320	−	0.809355i	$-0.699817\pi$
$173$	−15.4500			−1.17464			−0.587320	+	0.809355i	$0.699817\pi$
$174$		0			0
$175$	−2.66312	−	1.85392i	−0.201313	−	0.140143i
$176$		0			0
$177$	10.3536	−	10.3536i	0.778225	−	0.778225i
$178$		0			0
$179$	−5.20444	+	5.20444i	−0.388998	+	0.388998i	−0.874330	−	0.485332i	$-0.838699\pi$
$179$	−5.20444	+	5.20444i	−0.388998	+	0.388998i	0.485332	+	0.874330i	$0.338699\pi$
$180$		0			0
$181$	−9.08925	−	9.08925i	−0.675599	−	0.675599i	0.283402	−	0.959001i	$-0.408537\pi$
$181$	−9.08925	−	9.08925i	−0.675599	−	0.675599i	−0.959001	+	0.283402i	$0.908537\pi$
$182$		0			0
$183$	−10.6467	−	10.6467i	−0.787024	−	0.787024i
$184$		0			0
$185$	8.38500	−	10.0206i	0.616478	−	0.736730i
$186$		0			0
$187$			3.08295i			0.225448i
$188$		0			0
$189$	2.82669	+	2.82669i	0.205611	+	0.205611i
$190$		0			0
$191$			15.1075i			1.09314i	0.837413	+	0.546571i	$0.184067\pi$
$191$			15.1075i			1.09314i	−0.837413	+	0.546571i	$0.815933\pi$
$192$		0			0
$193$	4.19166	+	4.19166i	0.301722	+	0.301722i	0.841687	−	0.539965i	$-0.181563\pi$
$193$	4.19166	+	4.19166i	0.301722	+	0.301722i	−0.539965	+	0.841687i	$0.681563\pi$
$194$		0			0
$195$	−22.1431	−	18.5288i	−1.58570	−	1.32688i
$196$		0			0
$197$	−4.03184			−0.287256			−0.143628	−	0.989632i	$-0.545877\pi$
$197$	−4.03184			−0.287256			−0.143628	+	0.989632i	$0.545877\pi$
$198$		0			0
$199$		−	5.43055i		−	0.384961i	−0.981301	−	0.192481i	$-0.938347\pi$
$199$		−	5.43055i		−	0.384961i	0.981301	−	0.192481i	$-0.0616533\pi$
$200$		0			0
$201$			9.50129i			0.670169i
$202$		0			0
$203$	−3.52363			−0.247310
$204$		0			0
$205$	−7.81385	−	6.53844i	−0.545743	−	0.456664i
$206$		0			0
$207$	−9.31622	−	9.31622i	−0.647522	−	0.647522i
$208$		0			0
$209$			3.98653i			0.275754i
$210$		0			0
$211$	−3.23020	−	3.23020i	−0.222376	−	0.222376i	0.587122	−	0.809498i	$-0.300261\pi$
$211$	−3.23020	−	3.23020i	−0.222376	−	0.222376i	−0.809498	+	0.587122i	$0.800261\pi$
$212$		0			0
$213$			3.91432i			0.268205i
$214$		0			0
$215$	10.7613	−	12.8604i	0.733914	−	0.877074i
$216$		0			0
$217$	0.0642220	+	0.0642220i	0.00435967	+	0.00435967i
$218$		0			0
$219$	7.28363	+	7.28363i	0.492182	+	0.492182i
$220$		0			0
$221$	−14.1430	+	14.1430i	−0.951363	+	0.951363i
$222$		0			0
$223$	8.17319	−	8.17319i	0.547317	−	0.547317i	−0.378347	−	0.925664i	$-0.623507\pi$
$223$	8.17319	−	8.17319i	0.547317	−	0.547317i	0.925664	+	0.378347i	$0.123507\pi$
$224$		0			0
$225$	4.54664	+	25.3799i	0.303110	+	1.69199i
$226$		0			0
$227$	1.54068			0.102258			0.0511292	−	0.998692i	$-0.483718\pi$
$227$	1.54068			0.102258			0.0511292	+	0.998692i	$0.483718\pi$
$228$		0			0
$229$	−17.5646	+	17.5646i	−1.16070	+	1.16070i	−0.176378	+	0.984322i	$0.556438\pi$
$229$	−17.5646	+	17.5646i	−1.16070	+	1.16070i	−0.984322	+	0.176378i	$0.943562\pi$
$230$		0			0
$231$	−1.29164			−0.0849834
$232$		0			0
$233$	9.99018	−	9.99018i	0.654479	−	0.654479i	−0.299590	−	0.954068i	$-0.596850\pi$
$233$	9.99018	−	9.99018i	0.654479	−	0.654479i	0.954068	+	0.299590i	$0.0968498\pi$
$234$		0			0
$235$	13.0427	−	1.15904i	0.850814	−	0.0756072i
$236$		0			0
$237$		−	11.0364i		−	0.716889i
$238$		0			0
$239$	−26.2762			−1.69967			−0.849833	−	0.527052i	$-0.823297\pi$
$239$	−26.2762			−1.69967			−0.849833	+	0.527052i	$0.823297\pi$
$240$		0			0
$241$	−0.113242			−0.00729456			−0.00364728	−	0.999993i	$-0.501161\pi$
$241$	−0.113242			−0.00729456			−0.00364728	+	0.999993i	$0.501161\pi$
$242$		0			0
$243$			12.4188i			0.796665i
$244$		0			0
$245$	11.2820	+	9.44047i	0.720778	+	0.603130i
$246$		0			0
$247$	−18.2882	+	18.2882i	−1.16365	+	1.16365i
$248$		0			0
$249$	−41.3258			−2.61892
$250$		0			0
$251$	−19.2220	+	19.2220i	−1.21328	+	1.21328i	−0.243339	+	0.969941i	$0.578243\pi$
$251$	−19.2220	+	19.2220i	−1.21328	+	1.21328i	−0.969941	+	0.243339i	$0.921757\pi$
$252$		0			0
$253$	1.78045			0.111936
$254$		0			0
$255$	28.1417	−	2.50080i	1.76230	−	0.156606i
$256$		0			0
$257$	−0.757800	+	0.757800i	−0.0472703	+	0.0472703i	−0.730347	−	0.683077i	$-0.760642\pi$
$257$	−0.757800	+	0.757800i	−0.0472703	+	0.0472703i	0.683077	+	0.730347i	$0.260642\pi$
$258$		0			0
$259$	2.68146	−	2.68146i	0.166618	−	0.166618i
$260$		0			0
$261$	19.7982	+	19.7982i	1.22548	+	1.22548i
$262$		0			0
$263$	−5.73017	−	5.73017i	−0.353338	−	0.353338i	0.508012	−	0.861350i	$-0.330380\pi$
$263$	−5.73017	−	5.73017i	−0.353338	−	0.353338i	−0.861350	+	0.508012i	$0.830380\pi$
$264$		0			0
$265$	4.72919	+	3.95728i	0.290512	+	0.243094i
$266$		0			0
$267$			9.56795i			0.585549i
$268$		0			0
$269$	9.78879	+	9.78879i	0.596833	+	0.596833i	0.939468	−	0.342635i	$-0.111320\pi$
$269$	9.78879	+	9.78879i	0.596833	+	0.596833i	−0.342635	+	0.939468i	$0.611320\pi$
$270$		0			0
$271$			4.10159i			0.249154i	0.992210	+	0.124577i	$0.0397574\pi$
$271$			4.10159i			0.249154i	−0.992210	+	0.124577i	$0.960243\pi$
$272$		0			0
$273$	−5.92537	−	5.92537i	−0.358620	−	0.358620i
$274$		0			0
$275$	−2.85967	−	1.99075i	−0.172444	−	0.120046i
$276$		0			0
$277$	24.6755			1.48261			0.741305	−	0.671169i	$-0.234207\pi$
$277$	24.6755			1.48261			0.741305	+	0.671169i	$0.234207\pi$
$278$		0			0
$279$		−	0.721688i		−	0.0432063i
$280$		0			0
$281$			23.6688i			1.41196i	0.708230	+	0.705981i	$0.249494\pi$
$281$			23.6688i			1.41196i	−0.708230	+	0.705981i	$0.750506\pi$
$282$		0			0
$283$	−13.0492			−0.775694			−0.387847	−	0.921724i	$-0.626781\pi$
$283$	−13.0492			−0.775694			−0.387847	+	0.921724i	$0.626781\pi$
$284$		0			0
$285$	36.3897	−	3.23375i	2.15554	−	0.191551i
$286$		0			0
$287$	−2.09094	−	2.09094i	−0.123424	−	0.123424i
$288$		0			0
$289$		−	2.57168i		−	0.151275i
$290$		0			0
$291$	14.1539	+	14.1539i	0.829714	+	0.829714i
$292$		0			0
$293$		−	31.6731i		−	1.85036i	−0.379526	−	0.925181i	$-0.623913\pi$
$293$		−	31.6731i		−	1.85036i	0.379526	−	0.925181i	$-0.376087\pi$
$294$		0			0
$295$	11.4189	−	1.01474i	0.664835	−	0.0590802i
$296$		0			0
$297$	3.03531	+	3.03531i	0.176127	+	0.176127i
$298$		0			0
$299$	8.16779	+	8.16779i	0.472355	+	0.472355i
$300$		0			0
$301$	3.44138	−	3.44138i	0.198358	−	0.198358i
$302$		0			0
$303$	−5.27037	+	5.27037i	−0.302775	+	0.302775i
$304$		0			0
$305$	−1.04346	−	11.7421i	−0.0597482	−	0.672351i
$306$		0			0
$307$	27.3597			1.56150			0.780751	−	0.624843i	$-0.214837\pi$
$307$	27.3597			1.56150			0.780751	+	0.624843i	$0.214837\pi$
$308$		0			0
$309$	33.3168	−	33.3168i	1.89532	−	1.89532i
$310$		0			0
$311$	15.8076			0.896368			0.448184	−	0.893941i	$-0.352071\pi$
$311$	15.8076			0.896368			0.448184	+	0.893941i	$0.352071\pi$
$312$		0			0
$313$	−13.8388	+	13.8388i	−0.782217	+	0.782217i	−0.980205	−	0.197988i	$-0.936559\pi$
$313$	−13.8388	+	13.8388i	−0.782217	+	0.782217i	0.197988	+	0.980205i	$0.436559\pi$
$314$		0			0
$315$	0.662387	+	7.45390i	0.0373213	+	0.419980i
$316$		0			0
$317$			35.0092i			1.96631i	0.182766	+	0.983156i	$0.441495\pi$
$317$			35.0092i			1.96631i	−0.182766	+	0.983156i	$0.558505\pi$
$318$		0			0
$319$	−3.78369			−0.211846
$320$		0			0
$321$	−43.7272			−2.44062
$322$		0			0
$323$		−	25.3079i		−	1.40817i
$324$		0			0
$325$	−3.98617	−	22.2512i	−0.221113	−	1.23428i
$326$		0			0
$327$	35.6424	−	35.6424i	1.97103	−	1.97103i
$328$		0			0
$329$	3.80032			0.209518
$330$		0			0
$331$	−16.8212	+	16.8212i	−0.924578	+	0.924578i	−0.997349	−	0.0727709i	$-0.976816\pi$
$331$	−16.8212	+	16.8212i	−0.924578	+	0.924578i	0.0727709	+	0.997349i	$0.476816\pi$
$332$		0			0
$333$	−30.1326			−1.65126
$334$		0			0
$335$	−4.77384	+	5.70504i	−0.260823	+	0.311700i
$336$		0			0
$337$	14.4984	−	14.4984i	0.789777	−	0.789777i	−0.191680	−	0.981457i	$-0.561394\pi$
$337$	14.4984	−	14.4984i	0.789777	−	0.789777i	0.981457	+	0.191680i	$0.0613937\pi$
$338$		0			0
$339$	7.24160	−	7.24160i	0.393310	−	0.393310i
$340$		0			0
$341$	0.0689618	+	0.0689618i	0.00373449	+	0.00373449i
$342$		0			0
$343$	6.23125	+	6.23125i	0.336456	+	0.336456i
$344$		0			0
$345$	−1.44424	−	16.2522i	−0.0777555	−	0.874989i
$346$		0			0
$347$		−	16.7705i		−	0.900286i	−0.892956	−	0.450143i	$-0.851373\pi$
$347$		−	16.7705i		−	0.900286i	0.892956	−	0.450143i	$-0.148627\pi$
$348$		0			0
$349$	1.86337	+	1.86337i	0.0997439	+	0.0997439i	0.755218	−	0.655474i	$-0.227531\pi$
$349$	1.86337	+	1.86337i	0.0997439	+	0.0997439i	−0.655474	+	0.755218i	$0.727531\pi$
$350$		0			0
$351$			27.8489i			1.48647i
$352$		0			0
$353$	24.1362	+	24.1362i	1.28464	+	1.28464i	0.937998	+	0.346642i	$0.112678\pi$
$353$	24.1362	+	24.1362i	1.28464	+	1.28464i	0.346642	+	0.937998i	$0.387322\pi$
$354$		0			0
$355$	−1.96672	+	2.35035i	−0.104382	+	0.124744i
$356$		0			0
$357$	8.19976			0.433978
$358$		0			0
$359$			12.2500i			0.646532i	0.946308	+	0.323266i	$0.104781\pi$
$359$			12.2500i			0.646532i	−0.946308	+	0.323266i	$0.895219\pi$
$360$		0			0
$361$		−	13.7253i		−	0.722386i
$362$		0			0
$363$	30.0291			1.57612
$364$		0			0
$365$	0.713853	+	8.03305i	0.0373648	+	0.420469i
$366$		0			0
$367$	−2.71307	−	2.71307i	−0.141621	−	0.141621i	0.632742	−	0.774363i	$-0.281929\pi$
$367$	−2.71307	−	2.71307i	−0.141621	−	0.141621i	−0.774363	+	0.632742i	$0.781929\pi$
$368$		0			0
$369$			23.4967i			1.22319i
$370$		0			0
$371$	1.26551	+	1.26551i	0.0657018	+	0.0657018i
$372$		0			0
$373$			16.4846i			0.853541i	0.904360	+	0.426771i	$0.140349\pi$
$373$			16.4846i			0.853541i	−0.904360	+	0.426771i	$0.859651\pi$
$374$		0			0
$375$	−15.8522	+	27.7183i	−0.818603	+	1.43137i
$376$		0			0
$377$	−17.3576	−	17.3576i	−0.893964	−	0.893964i
$378$		0			0
$379$	13.7716	+	13.7716i	0.707401	+	0.707401i	0.965988	−	0.258587i	$-0.0832568\pi$
$379$	13.7716	+	13.7716i	0.707401	+	0.707401i	−0.258587	+	0.965988i	$0.583257\pi$
$380$		0			0
$381$	1.75870	−	1.75870i	0.0901011	−	0.0901011i
$382$		0			0
$383$	−11.5530	+	11.5530i	−0.590332	+	0.590332i	−0.937721	−	0.347389i	$-0.887068\pi$
$383$	−11.5530	+	11.5530i	−0.590332	+	0.590332i	0.347389	+	0.937721i	$0.387068\pi$
$384$		0			0
$385$	−0.775562	−	0.648972i	−0.0395263	−	0.0330747i
$386$		0			0
$387$	−38.6722			−1.96582
$388$		0			0
$389$	−15.7728	+	15.7728i	−0.799712	+	0.799712i	−0.983050	−	0.183338i	$-0.941310\pi$
$389$	−15.7728	+	15.7728i	−0.799712	+	0.799712i	0.183338	+	0.983050i	$0.441310\pi$
$390$		0			0
$391$	−11.3029			−0.571612
$392$		0			0
$393$	−27.2867	+	27.2867i	−1.37643	+	1.37643i
$394$		0			0
$395$	5.54512	−	6.62677i	0.279006	−	0.333429i
$396$		0			0
$397$		−	29.9558i		−	1.50344i	−0.659483	−	0.751720i	$-0.729225\pi$
$397$		−	29.9558i		−	1.50344i	0.659483	−	0.751720i	$-0.270775\pi$
$398$		0			0
$399$	10.6030			0.530815
$400$		0			0
$401$	19.9241			0.994963			0.497481	−	0.867475i	$-0.334258\pi$
$401$	19.9241			0.994963			0.497481	+	0.867475i	$0.334258\pi$
$402$		0			0
$403$			0.632724i			0.0315182i
$404$		0			0
$405$	3.04508	−	3.63906i	0.151311	−	0.180826i
$406$		0			0
$407$	2.87936	−	2.87936i	0.142725	−	0.142725i
$408$		0			0
$409$	5.89856			0.291665			0.145832	−	0.989309i	$-0.453414\pi$
$409$	5.89856			0.291665			0.145832	+	0.989309i	$0.453414\pi$
$410$		0			0
$411$	−10.5751	+	10.5751i	−0.521634	+	0.521634i
$412$		0			0
$413$	3.32717			0.163720
$414$		0			0
$415$	−24.8141	−	20.7638i	−1.21808	−	1.01926i
$416$		0			0
$417$	−15.6155	+	15.6155i	−0.764696	+	0.764696i
$418$		0			0
$419$	−8.24430	+	8.24430i	−0.402760	+	0.402760i	−0.879205	−	0.476444i	$-0.841925\pi$
$419$	−8.24430	+	8.24430i	−0.402760	+	0.402760i	0.476444	+	0.879205i	$0.341925\pi$
$420$		0			0
$421$	−17.1776	−	17.1776i	−0.837184	−	0.837184i	0.151304	−	0.988487i	$-0.451653\pi$
$421$	−17.1776	−	17.1776i	−0.837184	−	0.837184i	−0.988487	+	0.151304i	$0.951653\pi$
$422$		0			0
$423$	−21.3528	−	21.3528i	−1.03821	−	1.03821i
$424$		0			0
$425$	18.1542	+	12.6380i	0.880607	+	0.613031i
$426$		0			0
$427$		−	3.42135i		−	0.165571i
$428$		0			0
$429$	−6.36269	−	6.36269i	−0.307194	−	0.307194i
$430$		0			0
$431$		−	32.1769i		−	1.54990i	−0.632020	−	0.774952i	$-0.717774\pi$
$431$		−	32.1769i		−	1.54990i	0.632020	−	0.774952i	$-0.282226\pi$
$432$		0			0
$433$	−20.3383	−	20.3383i	−0.977396	−	0.977396i	0.0223540	−	0.999750i	$-0.492884\pi$
$433$	−20.3383	−	20.3383i	−0.977396	−	0.977396i	−0.999750	+	0.0223540i	$0.992884\pi$
$434$		0			0
$435$	3.06921	+	34.5381i	0.147158	+	1.65598i
$436$		0			0
$437$	−14.6156			−0.699161
$438$		0			0
$439$		−	35.4180i		−	1.69041i	−0.534444	−	0.845204i	$-0.679479\pi$
$439$		−	35.4180i		−	1.69041i	0.534444	−	0.845204i	$-0.320521\pi$
$440$		0			0
$441$		−	33.9256i		−	1.61550i
$442$		0			0
$443$	3.03787			0.144333			0.0721667	−	0.997393i	$-0.477009\pi$
$443$	3.03787			0.144333			0.0721667	+	0.997393i	$0.477009\pi$
$444$		0			0
$445$	−4.80733	+	5.74507i	−0.227890	+	0.272342i
$446$		0			0
$447$	−12.0398	−	12.0398i	−0.569463	−	0.569463i
$448$		0			0
$449$			8.65559i			0.408483i	0.978921	+	0.204241i	$0.0654727\pi$
$449$			8.65559i			0.408483i	−0.978921	+	0.204241i	$0.934527\pi$
$450$		0			0
$451$	−2.24526	−	2.24526i	−0.105725	−	0.105725i
$452$		0			0
$453$			35.5335i			1.66951i
$454$		0			0
$455$	−0.580733	−	6.53504i	−0.0272252	−	0.306367i
$456$		0			0
$457$	−13.5575	−	13.5575i	−0.634193	−	0.634193i	0.314924	−	0.949117i	$-0.398021\pi$
$457$	−13.5575	−	13.5575i	−0.634193	−	0.634193i	−0.949117	+	0.314924i	$0.898021\pi$
$458$		0			0
$459$	−19.2692	−	19.2692i	−0.899411	−	0.899411i
$460$		0			0
$461$	−1.19682	+	1.19682i	−0.0557416	+	0.0557416i	−0.734428	−	0.678687i	$-0.762550\pi$
$461$	−1.19682	+	1.19682i	−0.0557416	+	0.0557416i	0.678687	+	0.734428i	$0.262550\pi$
$462$		0			0
$463$	21.1815	−	21.1815i	0.984390	−	0.984390i	−0.0154904	−	0.999880i	$-0.504931\pi$
$463$	21.1815	−	21.1815i	0.984390	−	0.984390i	0.999880	+	0.0154904i	$0.00493096\pi$
$464$		0			0
$465$	0.573555	−	0.685435i	0.0265980	−	0.0317863i
$466$		0			0
$467$	−24.8448			−1.14968			−0.574840	−	0.818266i	$-0.694936\pi$
$467$	−24.8448			−1.14968			−0.574840	+	0.818266i	$0.694936\pi$
$468$		0			0
$469$	−1.52664	+	1.52664i	−0.0704936	+	0.0704936i
$470$		0			0
$471$	−21.4343			−0.987642
$472$		0			0
$473$	3.69537	−	3.69537i	0.169913	−	0.169913i
$474$		0			0
$475$	23.4749	+	16.3420i	1.07710	+	0.749822i
$476$		0			0
$477$		−	14.2210i		−	0.651135i
$478$		0			0
$479$	23.5766			1.07724			0.538621	−	0.842548i	$-0.318946\pi$
$479$	23.5766			1.07724			0.538621	+	0.842548i	$0.318946\pi$
$480$		0			0
$481$	26.4181			1.20456
$482$		0			0
$483$		−	4.73547i		−	0.215471i
$484$		0			0
$485$	1.38719	+	15.6102i	0.0629891	+	0.708821i
$486$		0			0
$487$	2.63011	−	2.63011i	0.119182	−	0.119182i	−0.645001	−	0.764182i	$-0.723143\pi$
$487$	2.63011	−	2.63011i	0.119182	−	0.119182i	0.764182	+	0.645001i	$0.223143\pi$
$488$		0			0
$489$	67.7686			3.06460
$490$		0			0
$491$	18.6899	−	18.6899i	0.843465	−	0.843465i	−0.145843	−	0.989308i	$-0.546589\pi$
$491$	18.6899	−	18.6899i	0.843465	−	0.843465i	0.989308	+	0.145843i	$0.0465894\pi$
$492$		0			0
$493$	24.0202			1.08182
$494$		0			0
$495$	0.711274	+	8.00403i	0.0319694	+	0.359754i
$496$		0			0
$497$	−0.628940	+	0.628940i	−0.0282118	+	0.0282118i
$498$		0			0
$499$	9.69342	−	9.69342i	0.433937	−	0.433937i	−0.456028	−	0.889965i	$-0.650728\pi$
$499$	9.69342	−	9.69342i	0.433937	−	0.433937i	0.889965	+	0.456028i	$0.150728\pi$
$500$		0			0
$501$	−1.15090	−	1.15090i	−0.0514185	−	0.0514185i
$502$		0			0
$503$	13.0434	+	13.0434i	0.581577	+	0.581577i	0.935336	−	0.353759i	$-0.115097\pi$
$503$	13.0434	+	13.0434i	0.581577	+	0.581577i	−0.353759	+	0.935336i	$0.615097\pi$
$504$		0			0
$505$	−5.81265	+	0.516538i	−0.258659	+	0.0229856i
$506$		0			0
$507$		−	21.2495i		−	0.943724i
$508$		0			0
$509$	−25.8539	−	25.8539i	−1.14595	−	1.14595i	−0.987341	−	0.158611i	$-0.949298\pi$
$509$	−25.8539	−	25.8539i	−1.14595	−	1.14595i	−0.158611	−	0.987341i	$-0.550702\pi$
$510$		0			0
$511$			2.34062i			0.103543i
$512$		0			0
$513$	−24.9168	−	24.9168i	−1.10010	−	1.10010i
$514$		0			0
$515$	36.7448	−	3.26531i	1.61917	−	0.143887i
$516$		0			0
$517$	4.08080			0.179473
$518$		0			0
$519$			44.1252i			1.93688i
$520$		0			0
$521$		−	25.0528i		−	1.09758i	−0.835959	−	0.548792i	$-0.815088\pi$
$521$		−	25.0528i		−	1.09758i	0.835959	−	0.548792i	$-0.184912\pi$
$522$		0			0
$523$	−40.3434			−1.76410			−0.882048	−	0.471160i	$-0.843835\pi$
$523$	−40.3434			−1.76410			−0.882048	+	0.471160i	$0.843835\pi$
$524$		0			0
$525$	−5.29481	+	7.60588i	−0.231084	+	0.331948i
$526$		0			0
$527$	−0.437794	−	0.437794i	−0.0190706	−	0.0190706i
$528$		0			0
$529$		−	16.4724i		−	0.716192i
$530$		0			0
$531$	−18.6944	−	18.6944i	−0.811267	−	0.811267i
$532$		0			0
$533$		−	20.6003i		−	0.892296i
$534$		0			0
$535$	−26.2560	−	21.9704i	−1.13515	−	0.949862i
$536$		0			0
$537$	14.8639	+	14.8639i	0.641425	+	0.641425i
$538$		0			0
$539$	3.24180	+	3.24180i	0.139634	+	0.139634i
$540$		0			0
$541$	−24.7446	+	24.7446i	−1.06385	+	1.06385i	−0.0660360	+	0.997817i	$0.521035\pi$
$541$	−24.7446	+	24.7446i	−1.06385	+	1.06385i	−0.997817	+	0.0660360i	$0.978965\pi$
$542$		0			0
$543$	−25.9590	+	25.9590i	−1.11401	+	1.11401i
$544$		0			0
$545$	39.3097	−	3.49324i	1.68384	−	0.149634i
$546$		0			0
$547$	−19.0254			−0.813465			−0.406733	−	0.913547i	$-0.633332\pi$
$547$	−19.0254			−0.813465			−0.406733	+	0.913547i	$0.633332\pi$
$548$		0			0
$549$	−19.2235	+	19.2235i	−0.820440	+	0.820440i
$550$		0			0
$551$	31.0602			1.32321
$552$		0			0
$553$	1.77329	−	1.77329i	0.0754079	−	0.0754079i
$554$		0			0
$555$	−28.6189	−	23.9476i	−1.21481	−	1.01652i
$556$		0			0
$557$		−	30.9517i		−	1.31146i	−0.754993	−	0.655732i	$-0.772360\pi$
$557$		−	30.9517i		−	1.31146i	0.754993	−	0.655732i	$-0.227640\pi$
$558$		0			0
$559$	33.9050			1.43403
$560$		0			0
$561$	8.80494			0.371745
$562$		0			0
$563$		−	3.50238i		−	0.147608i	−0.997273	−	0.0738039i	$-0.976486\pi$
$563$		−	3.50238i		−	0.147608i	0.997273	−	0.0738039i	$-0.0235139\pi$
$564$		0			0
$565$	7.98670	−	0.709734i	0.336003	−	0.0298587i
$566$		0			0
$567$	0.973793	−	0.973793i	0.0408955	−	0.0408955i
$568$		0			0
$569$	−0.525780			−0.0220418			−0.0110209	−	0.999939i	$-0.503508\pi$
$569$	−0.525780			−0.0220418			−0.0110209	+	0.999939i	$0.503508\pi$
$570$		0			0
$571$	11.2487	−	11.2487i	0.470743	−	0.470743i	−0.431412	−	0.902155i	$-0.641984\pi$
$571$	11.2487	−	11.2487i	0.470743	−	0.470743i	0.902155	+	0.431412i	$0.141984\pi$
$572$		0			0
$573$	43.1472			1.80250
$574$		0			0
$575$	7.29859	−	10.4843i	0.304372	−	0.437224i
$576$		0			0
$577$	−2.92884	+	2.92884i	−0.121929	+	0.121929i	−0.765438	−	0.643509i	$-0.777478\pi$
$577$	−2.92884	+	2.92884i	−0.121929	+	0.121929i	0.643509	+	0.765438i	$0.277478\pi$
$578$		0			0
$579$	11.9714	−	11.9714i	0.497515	−	0.497515i
$580$		0			0
$581$	−6.64011	−	6.64011i	−0.275478	−	0.275478i
$582$		0			0
$583$	1.35891	+	1.35891i	0.0562801	+	0.0562801i
$584$		0			0
$585$	−33.4555	+	39.9814i	−1.38321	+	1.65303i
$586$		0			0
$587$			23.1574i			0.955809i	0.878412	+	0.477905i	$0.158604\pi$
$587$			23.1574i			0.955809i	−0.878412	+	0.477905i	$0.841396\pi$
$588$		0			0
$589$	−0.566106	−	0.566106i	−0.0233260	−	0.0233260i
$590$		0			0
$591$			11.5150i			0.473662i
$592$		0			0
$593$	−13.9325	−	13.9325i	−0.572141	−	0.572141i	0.360585	−	0.932726i	$-0.382577\pi$
$593$	−13.9325	−	13.9325i	−0.572141	−	0.572141i	−0.932726	+	0.360585i	$0.882577\pi$
$594$		0			0
$595$	4.92354	+	4.11990i	0.201846	+	0.168900i
$596$		0			0
$597$	−15.5097			−0.634769
$598$		0			0
$599$			33.5311i			1.37004i	0.728523	+	0.685021i	$0.240207\pi$
$599$			33.5311i			1.37004i	−0.728523	+	0.685021i	$0.759793\pi$
$600$		0			0
$601$			19.4164i			0.792011i	0.918248	+	0.396005i	$0.129604\pi$
$601$			19.4164i			0.792011i	−0.918248	+	0.396005i	$0.870396\pi$
$602$		0			0
$603$	17.1554			0.698623
$604$		0			0
$605$	18.0310	+	15.0879i	0.733063	+	0.613409i
$606$		0			0
$607$	9.51495	+	9.51495i	0.386200	+	0.386200i	0.873330	−	0.487130i	$-0.161956\pi$
$607$	9.51495	+	9.51495i	0.386200	+	0.386200i	−0.487130	+	0.873330i	$0.661956\pi$
$608$		0			0
$609$			10.0635i			0.407794i
$610$		0			0
$611$	18.7206	+	18.7206i	0.757355	+	0.757355i
$612$		0			0
$613$		−	9.37947i		−	0.378833i	−0.981897	−	0.189417i	$-0.939340\pi$
$613$		−	9.37947i		−	0.378833i	0.981897	−	0.189417i	$-0.0606597\pi$
$614$		0			0
$615$	−18.6738	+	22.3164i	−0.753002	+	0.899884i
$616$		0			0
$617$	−3.54768	−	3.54768i	−0.142824	−	0.142824i	0.632079	−	0.774904i	$-0.282202\pi$
$617$	−3.54768	−	3.54768i	−0.142824	−	0.142824i	−0.774904	+	0.632079i	$0.782202\pi$
$618$		0			0
$619$	−24.6158	−	24.6158i	−0.989392	−	0.989392i	0.0105527	−	0.999944i	$-0.496641\pi$
$619$	−24.6158	−	24.6158i	−0.989392	−	0.989392i	−0.999944	+	0.0105527i	$0.996641\pi$
$620$		0			0
$621$	−11.1282	+	11.1282i	−0.446561	+	0.446561i
$622$		0			0
$623$	−1.53735	+	1.53735i	−0.0615926	+	0.0615926i
$624$		0			0
$625$	−23.4453	+	8.67867i	−0.937811	+	0.347147i
$626$		0			0
$627$	11.3856			0.454695
$628$		0			0
$629$	−18.2792	+	18.2792i	−0.728840	+	0.728840i
$630$		0			0
$631$	28.8921			1.15018			0.575088	−	0.818092i	$-0.304968\pi$
$631$	28.8921			1.15018			0.575088	+	0.818092i	$0.304968\pi$
$632$		0			0
$633$	−9.22547	+	9.22547i	−0.366679	+	0.366679i
$634$		0			0
$635$	1.93966	−	0.172367i	0.0769729	−	0.00684016i
$636$		0			0
$637$			29.7435i			1.17848i
$638$		0			0
$639$	7.06765			0.279592
$640$		0			0
$641$	−16.6914			−0.659271			−0.329636	−	0.944108i	$-0.606926\pi$
$641$	−16.6914			−0.659271			−0.329636	+	0.944108i	$0.606926\pi$
$642$		0			0
$643$			5.22468i			0.206041i	0.994679	+	0.103021i	$0.0328507\pi$
$643$			5.22468i			0.206041i	−0.994679	+	0.103021i	$0.967149\pi$
$644$		0			0
$645$	−36.7295	−	30.7343i	−1.44622	−	1.21016i
$646$		0			0
$647$	−21.6797	+	21.6797i	−0.852318	+	0.852318i	−0.990418	−	0.138100i	$-0.955900\pi$
$647$	−21.6797	+	21.6797i	−0.852318	+	0.852318i	0.138100	+	0.990418i	$0.455900\pi$
$648$		0			0
$649$	3.57273			0.140242
$650$		0			0
$651$	0.183418	−	0.183418i	0.00718874	−	0.00718874i
$652$		0			0
$653$	22.7642			0.890833			0.445417	−	0.895323i	$-0.353056\pi$
$653$	22.7642			0.890833			0.445417	+	0.895323i	$0.353056\pi$
$654$		0			0
$655$	−30.0942	+	2.67431i	−1.17588	+	0.104494i
$656$		0			0
$657$	13.1513	−	13.1513i	0.513079	−	0.513079i
$658$		0			0
$659$	1.66201	−	1.66201i	0.0647427	−	0.0647427i	−0.673994	−	0.738737i	$-0.735423\pi$
$659$	1.66201	−	1.66201i	0.0647427	−	0.0647427i	0.738737	+	0.673994i	$0.235423\pi$
$660$		0			0
$661$	−5.62818	−	5.62818i	−0.218911	−	0.218911i	0.589129	−	0.808039i	$-0.299471\pi$
$661$	−5.62818	−	5.62818i	−0.218911	−	0.218911i	−0.808039	+	0.589129i	$0.799471\pi$
$662$		0			0
$663$	40.3926	+	40.3926i	1.56872	+	1.56872i
$664$		0			0
$665$	6.36657	+	5.32739i	0.246885	+	0.206587i
$666$		0			0
$667$		−	13.8720i		−	0.537125i
$668$		0			0
$669$	−23.3427	−	23.3427i	−0.902481	−	0.902481i
$670$		0			0
$671$		−	3.67386i		−	0.141828i
$672$		0			0
$673$	0.278251	+	0.278251i	0.0107258	+	0.0107258i	0.712449	−	0.701724i	$-0.247586\pi$
$673$	0.278251	+	0.278251i	0.0107258	+	0.0107258i	−0.701724	+	0.712449i	$0.747586\pi$
$674$		0			0
$675$	30.3163	−	5.43097i	1.16687	−	0.209038i
$676$		0			0
$677$	26.3591			1.01306			0.506531	−	0.862222i	$-0.330928\pi$
$677$	26.3591			1.01306			0.506531	+	0.862222i	$0.330928\pi$
$678$		0			0
$679$			4.54840i			0.174551i
$680$		0			0
$681$		−	4.40019i		−	0.168616i
$682$		0			0
$683$	2.83023			0.108296			0.0541479	−	0.998533i	$-0.482756\pi$
$683$	2.83023			0.108296			0.0541479	+	0.998533i	$0.482756\pi$
$684$		0			0
$685$	−11.6632	+	1.03645i	−0.445629	+	0.0396006i
$686$		0			0
$687$	50.1646	+	50.1646i	1.91390	+	1.91390i
$688$		0			0
$689$			12.4679i			0.474991i
$690$		0			0
$691$	−22.1815	−	22.1815i	−0.843825	−	0.843825i	0.145529	−	0.989354i	$-0.453512\pi$
$691$	−22.1815	−	22.1815i	−0.843825	−	0.843825i	−0.989354	+	0.145529i	$0.953512\pi$
$692$		0			0
$693$			2.33217i			0.0885917i
$694$		0			0
$695$	−17.2222	+	1.53044i	−0.653276	+	0.0580531i
$696$		0			0
$697$	14.2537	+	14.2537i	0.539898	+	0.539898i
$698$		0			0
$699$	−28.5320	−	28.5320i	−1.07918	−	1.07918i
$700$		0			0
$701$	16.2264	−	16.2264i	0.612864	−	0.612864i	−0.330828	−	0.943691i	$-0.607328\pi$
$701$	16.2264	−	16.2264i	0.612864	−	0.612864i	0.943691	+	0.330828i	$0.107328\pi$
$702$		0			0
$703$	−23.6366	+	23.6366i	−0.891472	+	0.891472i
$704$		0			0
$705$	−3.31022	−	37.2502i	−0.124670	−	1.40292i
$706$		0			0
$707$	−1.69365			−0.0636965
$708$		0			0
$709$	25.3577	−	25.3577i	0.952329	−	0.952329i	−0.0465856	−	0.998914i	$-0.514834\pi$
$709$	25.3577	−	25.3577i	0.952329	−	0.952329i	0.998914	+	0.0465856i	$0.0148340\pi$
$710$		0			0
$711$	−19.9271			−0.747326
$712$		0			0
$713$	−0.252832	+	0.252832i	−0.00946863	+	0.00946863i
$714$		0			0
$715$	−0.623594	−	7.01735i	−0.0233211	−	0.262434i
$716$		0			0
$717$			75.0450i			2.80261i
$718$		0			0
$719$	−41.3374			−1.54163			−0.770813	−	0.637061i	$-0.780150\pi$
$719$	−41.3374			−1.54163			−0.770813	+	0.637061i	$0.780150\pi$
$720$		0			0
$721$	10.7065			0.398730
$722$		0			0
$723$			0.323420i			0.0120281i
$724$		0			0
$725$	−15.5105	+	22.2805i	−0.576045	+	0.827477i
$726$		0			0
$727$	23.4630	−	23.4630i	0.870193	−	0.870193i	−0.122300	−	0.992493i	$-0.539027\pi$
$727$	23.4630	−	23.4630i	0.870193	−	0.870193i	0.992493	+	0.122300i	$0.0390271\pi$
$728$		0			0
$729$	41.8342			1.54942
$730$		0			0
$731$	−23.4595	+	23.4595i	−0.867681	+	0.867681i
$732$		0			0
$733$	−15.1628			−0.560051			−0.280025	−	0.959993i	$-0.590343\pi$
$733$	−15.1628			−0.560051			−0.280025	+	0.959993i	$0.590343\pi$
$734$		0			0
$735$	26.9621	−	32.2214i	0.994511	−	1.18850i
$736$		0			0
$737$	−1.63931	+	1.63931i	−0.0603848	+	0.0603848i
$738$		0			0
$739$	0.974343	−	0.974343i	0.0358418	−	0.0358418i	−0.688959	−	0.724801i	$-0.741932\pi$
$739$	0.974343	−	0.974343i	0.0358418	−	0.0358418i	0.724801	+	0.688959i	$0.241932\pi$
$740$		0			0
$741$	52.2312	+	52.2312i	1.91876	+	1.91876i
$742$		0			0
$743$	−29.0897	−	29.0897i	−1.06720	−	1.06720i	−0.997573	−	0.0696259i	$-0.977819\pi$
$743$	−29.0897	−	29.0897i	−1.06720	−	1.06720i	−0.0696259	−	0.997573i	$-0.522181\pi$
$744$		0			0
$745$	−1.18000	−	13.2786i	−0.0432317	−	0.486490i
$746$		0			0
$747$			74.6176i			2.73011i
$748$		0			0
$749$	−7.02596	−	7.02596i	−0.256723	−	0.256723i
$750$		0			0
$751$		−	7.77705i		−	0.283789i	−0.989882	−	0.141894i	$-0.954681\pi$
$751$		−	7.77705i		−	0.283789i	0.989882	−	0.141894i	$-0.0453193\pi$
$752$		0			0
$753$	54.8981	+	54.8981i	2.00060	+	2.00060i
$754$		0			0
$755$	−17.8535	+	21.3361i	−0.649755	+	0.776498i
$756$		0			0
$757$	1.42073			0.0516372			0.0258186	−	0.999667i	$-0.491781\pi$
$757$	1.42073			0.0516372			0.0258186	+	0.999667i	$0.491781\pi$
$758$		0			0
$759$		−	5.08497i		−	0.184573i
$760$		0			0
$761$			26.6737i			0.966921i	0.875366	+	0.483460i	$0.160620\pi$
$761$			26.6737i			0.966921i	−0.875366	+	0.483460i	$0.839380\pi$
$762$		0			0
$763$	11.4538			0.414656
$764$		0			0
$765$	−4.51542	−	50.8124i	−0.163255	−	1.83713i
$766$		0			0
$767$	16.3899	+	16.3899i	0.591805	+	0.591805i
$768$		0			0
$769$		−	45.8210i		−	1.65235i	−0.563415	−	0.826174i	$-0.690513\pi$
$769$		−	45.8210i		−	1.65235i	0.563415	−	0.826174i	$-0.309487\pi$
$770$		0			0
$771$	2.16428	+	2.16428i	0.0779447	+	0.0779447i
$772$		0			0
$773$		−	18.5473i		−	0.667101i	−0.942732	−	0.333550i	$-0.891753\pi$
$773$		−	18.5473i		−	0.667101i	0.942732	−	0.333550i	$-0.108247\pi$
$774$		0			0
$775$	0.688782	−	0.123391i	0.0247418	−	0.00443233i
$776$		0			0
$777$	−7.65827	−	7.65827i	−0.274739	−	0.274739i
$778$		0			0
$779$	18.4313	+	18.4313i	0.660370	+	0.660370i
$780$		0			0
$781$	−0.675359	+	0.675359i	−0.0241662	+	0.0241662i
$782$		0			0
$783$	23.6490	−	23.6490i	0.845146	−	0.845146i
$784$		0			0
$785$	−12.8702	−	10.7695i	−0.459358	−	0.384380i
$786$		0			0
$787$	21.3016			0.759319			0.379659	−	0.925126i	$-0.376041\pi$
$787$	21.3016			0.759319			0.379659	+	0.925126i	$0.376041\pi$
$788$		0			0
$789$	−16.3654	+	16.3654i	−0.582624	+	0.582624i
$790$		0			0
$791$	2.32712			0.0827427
$792$		0			0
$793$	16.8538	−	16.8538i	0.598496	−	0.598496i
$794$		0			0
$795$	11.3020	−	13.5066i	0.400841	−	0.479030i
$796$		0			0
$797$			2.35457i			0.0834033i	0.999130	+	0.0417016i	$0.0132779\pi$
$797$			2.35457i			0.0834033i	−0.999130	+	0.0417016i	$0.986722\pi$
$798$		0			0
$799$	−25.9063			−0.916500
$800$		0			0
$801$	17.2758			0.610410
$802$		0			0
$803$			2.51337i			0.0886949i
$804$		0			0
$805$	2.37930	−	2.84341i	0.0838592	−	0.100217i
$806$		0			0
$807$	27.9569	−	27.9569i	0.984128	−	0.984128i
$808$		0			0
$809$	−23.9476			−0.841952			−0.420976	−	0.907072i	$-0.638312\pi$
$809$	−23.9476			−0.841952			−0.420976	+	0.907072i	$0.638312\pi$
$810$		0			0
$811$	1.33006	−	1.33006i	0.0467048	−	0.0467048i	−0.683369	−	0.730073i	$-0.739486\pi$
$811$	1.33006	−	1.33006i	0.0467048	−	0.0467048i	0.730073	+	0.683369i	$0.239486\pi$
$812$		0			0
$813$	11.7142			0.410834
$814$		0			0
$815$	40.6916	+	34.0498i	1.42537	+	1.19271i
$816$		0			0
$817$	−30.3352	+	30.3352i	−1.06129	+	1.06129i
$818$		0			0
$819$	−10.6988	+	10.6988i	−0.373846	+	0.373846i
$820$		0			0
$821$	36.4676	+	36.4676i	1.27273	+	1.27273i	0.944651	+	0.328076i	$0.106400\pi$
$821$	36.4676	+	36.4676i	1.27273	+	1.27273i	0.328076	+	0.944651i	$0.393600\pi$
$822$		0			0
$823$	−26.3978	−	26.3978i	−0.920170	−	0.920170i	0.0768712	−	0.997041i	$-0.475507\pi$
$823$	−26.3978	−	26.3978i	−0.920170	−	0.920170i	−0.997041	+	0.0768712i	$0.975507\pi$
$824$		0			0
$825$	−5.68559	+	8.16723i	−0.197947	+	0.284346i
$826$		0			0
$827$		−	1.99830i		−	0.0694878i	−0.999396	−	0.0347439i	$-0.988938\pi$
$827$		−	1.99830i		−	0.0694878i	0.999396	−	0.0347439i	$-0.0110616\pi$
$828$		0			0
$829$	−13.0376	−	13.0376i	−0.452813	−	0.452813i	0.443474	−	0.896287i	$-0.353746\pi$
$829$	−13.0376	−	13.0376i	−0.452813	−	0.452813i	−0.896287	+	0.443474i	$0.853746\pi$
$830$		0			0
$831$		−	70.4735i		−	2.44470i
$832$		0			0
$833$	−20.5801	−	20.5801i	−0.713059	−	0.713059i
$834$		0			0
$835$	−0.112797	−	1.26932i	−0.00390352	−	0.0439266i
$836$		0			0
$837$	−0.862057			−0.0297971
$838$		0			0
$839$		−	15.4102i		−	0.532018i	−0.963971	−	0.266009i	$-0.914295\pi$
$839$		−	15.4102i		−	0.532018i	0.963971	−	0.266009i	$-0.0857050\pi$
$840$		0			0
$841$			0.479815i			0.0165453i
$842$		0			0
$843$	67.5983			2.32821
$844$		0			0
$845$	10.6766	−	12.7593i	0.367287	−	0.438932i
$846$		0			0
$847$	4.82499	+	4.82499i	0.165789	+	0.165789i
$848$		0			0
$849$			37.2686i			1.27906i
$850$		0			0
$851$	10.5565	+	10.5565i	0.361872	+	0.361872i
$852$		0			0
$853$			7.96419i			0.272689i	0.990662	+	0.136344i	$0.0435353\pi$
$853$			7.96419i			0.272689i	−0.990662	+	0.136344i	$0.956465\pi$
$854$		0			0
$855$	−5.83883	−	65.7049i	−0.199684	−	2.24706i
$856$		0			0
$857$	5.35407	+	5.35407i	0.182891	+	0.182891i	0.792615	−	0.609723i	$-0.208719\pi$
$857$	5.35407	+	5.35407i	0.182891	+	0.182891i	−0.609723	+	0.792615i	$0.708719\pi$
$858$		0			0
$859$	−35.0058	−	35.0058i	−1.19438	−	1.19438i	−0.975824	−	0.218559i	$-0.929864\pi$
$859$	−35.0058	−	35.0058i	−1.19438	−	1.19438i	−0.218559	−	0.975824i	$-0.570136\pi$
$860$		0			0
$861$	−5.97175	+	5.97175i	−0.203517	+	0.203517i
$862$		0			0
$863$	36.7138	−	36.7138i	1.24975	−	1.24975i	0.293923	−	0.955829i	$-0.405039\pi$
$863$	36.7138	−	36.7138i	1.24975	−	1.24975i	0.955829	−	0.293923i	$-0.0949610\pi$
$864$		0			0
$865$	−22.1703	+	26.4950i	−0.753814	+	0.900856i
$866$		0			0
$867$	−7.34475			−0.249441
$868$		0			0
$869$	1.90416	−	1.90416i	0.0645943	−	0.0645943i
$870$		0			0
$871$	−15.0406			−0.509633
$872$		0			0
$873$	25.5561	−	25.5561i	0.864942	−	0.864942i
$874$		0			0
$875$	−7.00078	+	1.90662i	−0.236669	+	0.0644555i
$876$		0			0
$877$			14.3410i			0.484262i	0.970244	+	0.242131i	$0.0778463\pi$
$877$			14.3410i			0.484262i	−0.970244	+	0.242131i	$0.922154\pi$
$878$		0			0
$879$	−90.4586			−3.05109
$880$		0			0
$881$	−13.6397			−0.459533			−0.229767	−	0.973246i	$-0.573796\pi$
$881$	−13.6397			−0.459533			−0.229767	+	0.973246i	$0.573796\pi$
$882$		0			0
$883$		−	6.12563i		−	0.206144i	−0.994674	−	0.103072i	$-0.967133\pi$
$883$		−	6.12563i		−	0.206144i	0.994674	−	0.103072i	$-0.0328672\pi$
$884$		0			0
$885$	−2.89809	−	32.6125i	−0.0974184	−	1.09626i
$886$		0			0
$887$	−25.5187	+	25.5187i	−0.856834	+	0.856834i	−0.990964	−	0.134130i	$-0.957176\pi$
$887$	−25.5187	+	25.5187i	−0.856834	+	0.856834i	0.134130	+	0.990964i	$0.457176\pi$
$888$		0			0
$889$	0.565166			0.0189551
$890$		0			0
$891$	1.04566	−	1.04566i	0.0350310	−	0.0350310i
$892$		0			0
$893$	−33.4992			−1.12101
$894$		0			0
$895$	1.45678	+	16.3933i	0.0486948	+	0.547967i
$896$		0			0
$897$	23.3273	−	23.3273i	0.778875	−	0.778875i
$898$		0			0
$899$	0.537302	−	0.537302i	0.0179200	−	0.0179200i
$900$		0			0
$901$	−8.62682	−	8.62682i	−0.287401	−	0.287401i
$902$		0			0
$903$	−9.82861	−	9.82861i	−0.327076	−	0.327076i
$904$		0			0
$905$	−28.6299	+	2.54418i	−0.951691	+	0.0845715i
$906$		0			0
$907$			32.1815i			1.06857i	0.845305	+	0.534284i	$0.179419\pi$
$907$			32.1815i			1.06857i	−0.845305	+	0.534284i	$0.820581\pi$
$908$		0			0
$909$	9.51614	+	9.51614i	0.315630	+	0.315630i
$910$		0			0
$911$			38.6282i			1.27981i	0.768455	+	0.639904i	$0.221026\pi$
$911$			38.6282i			1.27981i	−0.768455	+	0.639904i	$0.778974\pi$
$912$		0			0
$913$	−7.13018	−	7.13018i	−0.235974	−	0.235974i
$914$		0			0
$915$	−33.5356	+	2.98012i	−1.10865	+	0.0985198i
$916$		0			0
$917$	−8.76867			−0.289567
$918$		0			0
$919$			19.1924i			0.633099i	0.948576	+	0.316550i	$0.102524\pi$
$919$			19.1924i			0.633099i	−0.948576	+	0.316550i	$0.897476\pi$
$920$		0			0
$921$		−	78.1395i		−	2.57479i
$922$		0			0
$923$	−6.19641			−0.203957
$924$		0			0
$925$	−5.15194	−	28.7587i	−0.169395	−	0.945580i
$926$		0			0
$927$	−60.1564	−	60.1564i	−1.97580	−	1.97580i
$928$		0			0
$929$			16.8576i			0.553081i	0.961002	+	0.276541i	$0.0891880\pi$
$929$			16.8576i			0.553081i	−0.961002	+	0.276541i	$0.910812\pi$
$930$		0			0
$931$	−26.6119	−	26.6119i	−0.872170	−	0.872170i
$932$		0			0
$933$		−	45.1467i		−	1.47804i
$934$		0			0
$935$	5.28692	+	4.42397i	0.172901	+	0.144679i
$936$		0			0
$937$	−23.9511	−	23.9511i	−0.782449	−	0.782449i	0.197795	−	0.980243i	$-0.436622\pi$
$937$	−23.9511	−	23.9511i	−0.782449	−	0.782449i	−0.980243	+	0.197795i	$0.936622\pi$
$938$		0			0
$939$	39.5238	+	39.5238i	1.28981	+	1.28981i
$940$		0			0
$941$	14.2496	−	14.2496i	0.464525	−	0.464525i	−0.435610	−	0.900135i	$-0.643467\pi$
$941$	14.2496	−	14.2496i	0.464525	−	0.464525i	0.900135	+	0.435610i	$0.143467\pi$
$942$		0			0
$943$	8.23171	−	8.23171i	0.268061	−	0.268061i
$944$		0			0
$945$	8.90369	−	0.791222i	0.289637	−	0.0257385i
$946$		0			0
$947$	−20.2943			−0.659477			−0.329738	−	0.944072i	$-0.606961\pi$
$947$	−20.2943			−0.659477			−0.329738	+	0.944072i	$0.606961\pi$
$948$		0			0
$949$	−11.5301	+	11.5301i	−0.374282	+	0.374282i
$950$		0			0
$951$	99.9866			3.24229
$952$		0			0
$953$	−10.9257	+	10.9257i	−0.353919	+	0.353919i	−0.861565	−	0.507647i	$-0.830516\pi$
$953$	−10.9257	+	10.9257i	−0.353919	+	0.353919i	0.507647	+	0.861565i	$0.330516\pi$
$954$		0			0
$955$	25.9077	+	21.6789i	0.838353	+	0.701514i
$956$		0			0
$957$			10.8062i			0.349316i
$958$		0			0
$959$	−3.39836			−0.109739
$960$		0			0
$961$	30.9804			0.999368
$962$		0			0
$963$			78.9535i			2.54424i
$964$		0			0
$965$	13.2032	−	1.17329i	0.425025	−	0.0377696i
$966$		0			0
$967$	−10.7569	+	10.7569i	−0.345918	+	0.345918i	−0.858586	−	0.512669i	$-0.828657\pi$
$967$	−10.7569	+	10.7569i	−0.345918	+	0.345918i	0.512669	+	0.858586i	$0.328657\pi$
$968$		0			0
$969$	−72.2796			−2.32195
$970$		0			0
$971$	18.7456	−	18.7456i	0.601574	−	0.601574i	−0.339156	−	0.940730i	$-0.610142\pi$
$971$	18.7456	−	18.7456i	0.601574	−	0.601574i	0.940730	+	0.339156i	$0.110142\pi$
$972$		0			0
$973$	−5.01811			−0.160873
$974$		0			0
$975$	−63.5497	+	11.3845i	−2.03522	+	0.364597i
$976$		0			0
$977$	−26.3906	+	26.3906i	−0.844309	+	0.844309i	−0.989416	−	0.145107i	$-0.953647\pi$
$977$	−26.3906	+	26.3906i	−0.844309	+	0.844309i	0.145107	+	0.989416i	$0.453647\pi$
$978$		0			0
$979$	−1.65081	+	1.65081i	−0.0527602	+	0.0527602i
$980$		0			0
$981$	−64.3556	−	64.3556i	−2.05472	−	2.05472i
$982$		0			0
$983$	4.87875	+	4.87875i	0.155608	+	0.155608i	0.780617	−	0.625009i	$-0.214905\pi$
$983$	4.87875	+	4.87875i	0.155608	+	0.155608i	−0.625009	+	0.780617i	$0.714905\pi$
$984$		0			0
$985$	−5.78559	+	6.91415i	−0.184344	+	0.220303i
$986$		0			0
$987$		−	10.8537i		−	0.345478i
$988$		0			0
$989$	13.5482	+	13.5482i	0.430807	+	0.430807i
$990$		0			0
$991$			61.2103i			1.94441i	0.234130	+	0.972205i	$0.424776\pi$
$991$			61.2103i			1.94441i	−0.234130	+	0.972205i	$0.575224\pi$
$992$		0			0
$993$	48.0415	+	48.0415i	1.52455	+	1.52455i
$994$		0			0
$995$	−9.31279	−	7.79271i	−0.295235	−	0.247046i
$996$		0			0
$997$	39.1082			1.23857			0.619284	−	0.785167i	$-0.287423\pi$
$997$	39.1082			1.23857			0.619284	+	0.785167i	$0.287423\pi$
$998$		0			0
$999$			35.9935i			1.13878i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.2.j.b.143.1		18
4.3	odd	2		80.2.j.b.43.5	✓	18
5.2	odd	4		320.2.s.b.207.1		18
5.3	odd	4		1600.2.s.d.207.9		18
5.4	even	2		1600.2.j.d.143.9		18
8.3	odd	2		640.2.j.d.543.1		18
8.5	even	2		640.2.j.c.543.9		18
12.11	even	2		720.2.bd.g.523.5		18
16.3	odd	4		320.2.s.b.303.1		18
16.5	even	4		640.2.s.d.223.1		18
16.11	odd	4		640.2.s.c.223.9		18
16.13	even	4		80.2.s.b.3.1	yes	18
20.3	even	4		400.2.s.d.107.9		18
20.7	even	4		80.2.s.b.27.1	yes	18
20.19	odd	2		400.2.j.d.43.5		18
40.27	even	4		640.2.s.d.287.1		18
40.37	odd	4		640.2.s.c.287.9		18
48.29	odd	4		720.2.z.g.163.9		18
60.47	odd	4		720.2.z.g.667.9		18
80.3	even	4		1600.2.j.d.1007.1		18
80.13	odd	4		400.2.j.d.307.5		18
80.19	odd	4		1600.2.s.d.943.9		18
80.27	even	4		640.2.j.c.607.1		18
80.29	even	4		400.2.s.d.243.9		18
80.37	odd	4		640.2.j.d.607.9		18
80.67	even	4	inner	320.2.j.b.47.9		18
80.77	odd	4		80.2.j.b.67.5	yes	18
240.77	even	4		720.2.bd.g.307.5		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.5	✓	18	4.3	odd	2
80.2.j.b.67.5	yes	18	80.77	odd	4
80.2.s.b.3.1	yes	18	16.13	even	4
80.2.s.b.27.1	yes	18	20.7	even	4
320.2.j.b.47.9		18	80.67	even	4	inner
320.2.j.b.143.1		18	1.1	even	1	trivial
320.2.s.b.207.1		18	5.2	odd	4
320.2.s.b.303.1		18	16.3	odd	4
400.2.j.d.43.5		18	20.19	odd	2
400.2.j.d.307.5		18	80.13	odd	4
400.2.s.d.107.9		18	20.3	even	4
400.2.s.d.243.9		18	80.29	even	4
640.2.j.c.543.9		18	8.5	even	2
640.2.j.c.607.1		18	80.27	even	4
640.2.j.d.543.1		18	8.3	odd	2
640.2.j.d.607.9		18	80.37	odd	4
640.2.s.c.223.9		18	16.11	odd	4
640.2.s.c.287.9		18	40.37	odd	4
640.2.s.d.223.1		18	16.5	even	4
640.2.s.d.287.1		18	40.27	even	4
720.2.z.g.163.9		18	48.29	odd	4
720.2.z.g.667.9		18	60.47	odd	4
720.2.bd.g.307.5		18	240.77	even	4
720.2.bd.g.523.5		18	12.11	even	2
1600.2.j.d.143.9		18	5.4	even	2
1600.2.j.d.1007.1		18	80.3	even	4
1600.2.s.d.207.9		18	5.3	odd	4
1600.2.s.d.943.9		18	80.19	odd	4

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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	320.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.85601i q^{3} +(1.43498 - 1.71489i) q^{5} +(0.458895 - 0.458895i) q^{7} -5.15678 q^{9} +O(q^{10})\)	\(q-2.85601i q^{3} +(1.43498 - 1.71489i) q^{5} +(0.458895 - 0.458895i) q^{7} -5.15678 q^{9} +(0.492763 - 0.492763i) q^{11} +4.52109 q^{13} +(-4.89773 - 4.09831i) q^{15} +(-3.12823 + 3.12823i) q^{17} +(-4.04508 + 4.04508i) q^{19} +(-1.31061 - 1.31061i) q^{21} +(1.80660 + 1.80660i) q^{23} +(-0.881683 - 4.92165i) q^{25} +6.15978i q^{27} +(-3.83926 - 3.83926i) q^{29} +0.139949i q^{31} +(-1.40733 - 1.40733i) q^{33} +(-0.128450 - 1.44546i) q^{35} +5.84330 q^{37} -12.9123i q^{39} -4.55648i q^{41} +7.49928 q^{43} +(-7.39986 + 8.84330i) q^{45} +(4.14073 + 4.14073i) q^{47} +6.57883i q^{49} +(8.93426 + 8.93426i) q^{51} +2.75773i q^{53} +(-0.137930 - 1.55214i) q^{55} +(11.5528 + 11.5528i) q^{57} +(3.62521 + 3.62521i) q^{59} +(3.72781 - 3.72781i) q^{61} +(-2.36642 + 2.36642i) q^{63} +(6.48766 - 7.75317i) q^{65} -3.32677 q^{67} +(5.15965 - 5.15965i) q^{69} -1.37056 q^{71} +(-2.55028 + 2.55028i) q^{73} +(-14.0563 + 2.51809i) q^{75} -0.452252i q^{77} +3.86426 q^{79} +2.12204 q^{81} -14.4698i q^{83} +(0.875628 + 9.85351i) q^{85} +(-10.9650 + 10.9650i) q^{87} -3.35011 q^{89} +(2.07470 - 2.07470i) q^{91} +0.399696 q^{93} +(1.13226 + 12.7415i) q^{95} +(-4.95582 + 4.95582i) q^{97} +(-2.54107 + 2.54107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{5} - 2 q^{7} - 10 q^{9}+O(q^{10}) \) 18 * q - 4 * q^5 - 2 * q^7 - 10 * q^9	\( 18 q - 4 q^{5} - 2 q^{7} - 10 q^{9} + 2 q^{11} - 20 q^{15} - 6 q^{17} - 2 q^{19} - 16 q^{21} + 2 q^{23} + 6 q^{25} - 14 q^{29} - 8 q^{33} + 6 q^{35} + 8 q^{37} + 44 q^{43} - 4 q^{45} + 38 q^{47} - 8 q^{51} + 6 q^{55} + 24 q^{57} + 10 q^{59} + 14 q^{61} - 6 q^{63} - 12 q^{67} + 32 q^{69} - 24 q^{71} + 14 q^{73} - 64 q^{75} - 16 q^{79} + 2 q^{81} - 10 q^{85} - 24 q^{87} - 12 q^{89} + 16 q^{93} + 34 q^{95} + 18 q^{97} + 22 q^{99}+O(q^{100}) \) 18 * q - 4 * q^5 - 2 * q^7 - 10 * q^9 + 2 * q^11 - 20 * q^15 - 6 * q^17 - 2 * q^19 - 16 * q^21 + 2 * q^23 + 6 * q^25 - 14 * q^29 - 8 * q^33 + 6 * q^35 + 8 * q^37 + 44 * q^43 - 4 * q^45 + 38 * q^47 - 8 * q^51 + 6 * q^55 + 24 * q^57 + 10 * q^59 + 14 * q^61 - 6 * q^63 - 12 * q^67 + 32 * q^69 - 24 * q^71 + 14 * q^73 - 64 * q^75 - 16 * q^79 + 2 * q^81 - 10 * q^85 - 24 * q^87 - 12 * q^89 + 16 * q^93 + 34 * q^95 + 18 * q^97 + 22 * q^99

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