LMFDB - Embedded newform 640.2.j.c.607.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(543,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("640.543");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.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:	$5.11042572936$
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			607.1
Root			$-0.480367 - 1.33013i$ of defining polynomial
Character	$\chi$	$=$	640.607
Dual form			640.2.j.c.543.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			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	0.788491	−	0.615046i	$-0.210862\pi$
$7$	0.458895	+	0.458895i	0.173446	+	0.173446i	−0.615046	+	0.788491i	$0.710862\pi$
$8$		0			0
$9$	−5.15678			−1.71893
$10$		0			0
$11$	−0.492763	−	0.492763i	−0.148574	−	0.148574i	0.628907	−	0.777481i	$-0.283503\pi$
$11$	−0.492763	−	0.492763i	−0.148574	−	0.148574i	−0.777481	+	0.628907i	$0.783503\pi$
$12$		0			0
$13$	−4.52109			−1.25393			−0.626963	−	0.779049i	$-0.715702\pi$
$13$	−4.52109			−1.25393			−0.626963	+	0.779049i	$0.715702\pi$
$14$		0			0
$15$	−4.89773	+	4.09831i	−1.26459	+	1.05818i
$16$		0			0
$17$	−3.12823	−	3.12823i	−0.758708	−	0.758708i	0.217379	−	0.976087i	$-0.430249\pi$
$17$	−3.12823	−	3.12823i	−0.758708	−	0.758708i	−0.976087	+	0.217379i	$0.930249\pi$
$18$		0			0
$19$	4.04508	+	4.04508i	0.928005	+	0.928005i	0.997577	−	0.0695721i	$-0.0221634\pi$
$19$	4.04508	+	4.04508i	0.928005	+	0.928005i	−0.0695721	+	0.997577i	$0.522163\pi$
$20$		0			0
$21$	1.31061	−	1.31061i	0.285998	−	0.285998i
$22$		0			0
$23$	1.80660	−	1.80660i	0.376701	−	0.376701i	−0.493209	−	0.869911i	$-0.664176\pi$
$23$	1.80660	−	1.80660i	0.376701	−	0.376701i	0.869911	+	0.493209i	$0.164176\pi$
$24$		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	$-0.581817\pi$
$29$	3.83926	−	3.83926i	0.712932	−	0.712932i	0.967148	+	0.254215i	$0.0818172\pi$
$30$		0			0
$31$		−	0.139949i		−	0.0251356i	−0.999921	−	0.0125678i	$-0.995999\pi$
$31$		−	0.139949i		−	0.0251356i	0.999921	−	0.0125678i	$-0.00400057\pi$
$32$		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	$-0.659478\pi$
$37$	−5.84330			−0.960633			−0.480317	+	0.877095i	$0.659478\pi$
$38$		0			0
$39$			12.9123i			2.06762i
$40$		0			0
$41$			4.55648i			0.711602i	0.934562	+	0.355801i	$0.115792\pi$
$41$			4.55648i			0.711602i	−0.934562	+	0.355801i	$0.884208\pi$
$42$		0			0
$43$	−7.49928			−1.14363			−0.571815	−	0.820383i	$-0.693760\pi$
$43$	−7.49928			−1.14363			−0.571815	+	0.820383i	$0.693760\pi$
$44$		0			0
$45$	7.39986	+	8.84330i	1.10311	+	1.31828i
$46$		0			0
$47$	4.14073	−	4.14073i	0.603987	−	0.603987i	−0.337381	−	0.941368i	$-0.609541\pi$
$47$	4.14073	−	4.14073i	0.603987	−	0.603987i	0.941368	+	0.337381i	$0.109541\pi$
$48$		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	$-0.858306\pi$
$59$	−3.62521	+	3.62521i	−0.471962	+	0.471962i	0.430587	+	0.902549i	$0.358306\pi$
$60$		0			0
$61$	−3.72781	−	3.72781i	−0.477298	−	0.477298i	0.426969	−	0.904266i	$-0.359581\pi$
$61$	−3.72781	−	3.72781i	−0.477298	−	0.477298i	−0.904266	+	0.426969i	$0.859581\pi$
$62$		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	$-0.434861\pi$
$67$	3.32677			0.406430			0.203215	+	0.979134i	$0.434861\pi$
$68$		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	0.541933	−	0.840422i	$-0.317693\pi$
$73$	−2.55028	−	2.55028i	−0.298488	−	0.298488i	−0.840422	+	0.541933i	$0.817693\pi$
$74$		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	0.409240	−	0.912427i	$-0.365794\pi$
$97$	−4.95582	−	4.95582i	−0.503187	−	0.503187i	−0.912427	+	0.409240i	$0.865794\pi$
$98$		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	$-0.708554\pi$
$101$	1.84536	−	1.84536i	0.183621	−	0.183621i	0.792931	+	0.609311i	$0.208554\pi$
$102$		0			0
$103$	11.6655	−	11.6655i	1.14944	−	1.14944i	0.162773	−	0.986664i	$-0.447956\pi$
$103$	11.6655	−	11.6655i	1.14944	−	1.14944i	0.986664	−	0.162773i	$-0.0520437\pi$
$104$		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	−0.219803	+	0.975544i	$0.570542\pi$
$109$	−12.4798	+	12.4798i	−1.19535	+	1.19535i	−0.975544	+	0.219803i	$0.929458\pi$
$110$		0			0
$111$			16.6885i			1.58400i
$112$		0			0
$113$	2.53557	−	2.53557i	0.238526	−	0.238526i	−0.577713	−	0.816240i	$-0.696055\pi$
$113$	2.53557	−	2.53557i	0.238526	−	0.238526i	0.816240	+	0.577713i	$0.196055\pi$
$114$		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	−0.679257	−	0.733900i	$-0.737698\pi$
$127$	0.615790	−	0.615790i	0.0546426	−	0.0546426i	0.733900	+	0.679257i	$0.237698\pi$
$128$		0			0
$129$			21.4180i			1.88575i
$130$		0			0
$131$	9.55413	−	9.55413i	0.834748	−	0.834748i	−0.153414	−	0.988162i	$-0.549027\pi$
$131$	9.55413	−	9.55413i	0.834748	−	0.834748i	0.988162	+	0.153414i	$0.0490268\pi$
$132$		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	−0.847363	−	0.531014i	$-0.821811\pi$
$137$	−3.70277	+	3.70277i	−0.316349	+	0.316349i	0.531014	+	0.847363i	$0.321811\pi$
$138$		0			0
$139$	5.46761	−	5.46761i	0.463756	−	0.463756i	−0.436128	−	0.899885i	$-0.643651\pi$
$139$	5.46761	−	5.46761i	0.463756	−	0.463756i	0.899885	+	0.436128i	$0.143651\pi$
$140$		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	$-0.328526\pi$
$149$	−4.21561	−	4.21561i	−0.345356	−	0.345356i	−0.858376	+	0.513021i	$0.828526\pi$
$150$		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	0.722526	−	0.691343i	$-0.242981\pi$
$167$	0.402976	+	0.402976i	0.0311832	+	0.0311832i	−0.691343	+	0.722526i	$0.742981\pi$
$168$		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	$-0.300183\pi$
$173$	15.4500			1.17464			0.587320	+	0.809355i	$0.300183\pi$
$174$		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	$-0.161301\pi$
$179$	5.20444	+	5.20444i	0.388998	+	0.388998i	−0.485332	+	0.874330i	$0.661301\pi$
$180$		0			0
$181$	9.08925	−	9.08925i	0.675599	−	0.675599i	−0.283402	−	0.959001i	$-0.591463\pi$
$181$	9.08925	−	9.08925i	0.675599	−	0.675599i	0.959001	+	0.283402i	$0.0914632\pi$
$182$		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	$-0.815933\pi$
$191$		−	15.1075i		−	1.09314i	0.837413	−	0.546571i	$-0.184067\pi$
$192$		0			0
$193$	4.19166	−	4.19166i	0.301722	−	0.301722i	−0.539965	−	0.841687i	$-0.681563\pi$
$193$	4.19166	−	4.19166i	0.301722	−	0.301722i	0.841687	+	0.539965i	$0.181563\pi$
$194$		0			0
$195$	22.1431	−	18.5288i	1.58570	−	1.32688i
$196$		0			0
$197$	4.03184			0.287256			0.143628	−	0.989632i	$-0.454123\pi$
$197$	4.03184			0.287256			0.143628	+	0.989632i	$0.454123\pi$
$198$		0			0
$199$			5.43055i			0.384961i	0.981301	+	0.192481i	$0.0616533\pi$
$199$			5.43055i			0.384961i	−0.981301	+	0.192481i	$0.938347\pi$
$200$		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	$-0.699739\pi$
$211$	3.23020	−	3.23020i	0.222376	−	0.222376i	0.809498	+	0.587122i	$0.199739\pi$
$212$		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	0.925664	−	0.378347i	$-0.123507\pi$
$223$	8.17319	+	8.17319i	0.547317	+	0.547317i	−0.378347	+	0.925664i	$0.623507\pi$
$224$		0			0
$225$	4.54664	−	25.3799i	0.303110	−	1.69199i
$226$		0			0
$227$	−1.54068			−0.102258			−0.0511292	−	0.998692i	$-0.516282\pi$
$227$	−1.54068			−0.102258			−0.0511292	+	0.998692i	$0.516282\pi$
$228$		0			0
$229$	17.5646	+	17.5646i	1.16070	+	1.16070i	0.984322	+	0.176378i	$0.0564382\pi$
$229$	17.5646	+	17.5646i	1.16070	+	1.16070i	0.176378	+	0.984322i	$0.443562\pi$
$230$		0			0
$231$	−1.29164			−0.0849834
$232$		0			0
$233$	9.99018	+	9.99018i	0.654479	+	0.654479i	0.954068	−	0.299590i	$-0.0968498\pi$
$233$	9.99018	+	9.99018i	0.654479	+	0.654479i	−0.299590	+	0.954068i	$0.596850\pi$
$234$		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	0.969941	+	0.243339i	$0.0782427\pi$
$251$	19.2220	+	19.2220i	1.21328	+	1.21328i	0.243339	+	0.969941i	$0.421757\pi$
$252$		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	0.683077	−	0.730347i	$-0.260642\pi$
$257$	−0.757800	−	0.757800i	−0.0472703	−	0.0472703i	−0.730347	+	0.683077i	$0.760642\pi$
$258$		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	−0.861350	−	0.508012i	$-0.830380\pi$
$263$	−5.73017	+	5.73017i	−0.353338	+	0.353338i	0.508012	+	0.861350i	$0.330380\pi$
$264$		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	$-0.888680\pi$
$269$	−9.78879	+	9.78879i	−0.596833	+	0.596833i	0.342635	+	0.939468i	$0.388680\pi$
$270$		0			0
$271$		−	4.10159i		−	0.249154i	−0.992210	−	0.124577i	$-0.960243\pi$
$271$		−	4.10159i		−	0.249154i	0.992210	−	0.124577i	$-0.0397574\pi$
$272$		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	$-0.765793\pi$
$277$	−24.6755			−1.48261			−0.741305	+	0.671169i	$0.765793\pi$
$278$		0			0
$279$			0.721688i			0.0432063i
$280$		0			0
$281$		−	23.6688i		−	1.41196i	−0.708230	−	0.705981i	$-0.750506\pi$
$281$		−	23.6688i		−	1.41196i	0.708230	−	0.705981i	$-0.249494\pi$
$282$		0			0
$283$	13.0492			0.775694			0.387847	−	0.921724i	$-0.373219\pi$
$283$	13.0492			0.775694			0.387847	+	0.921724i	$0.373219\pi$
$284$		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	$-0.785163\pi$
$307$	−27.3597			−1.56150			−0.780751	+	0.624843i	$0.785163\pi$
$308$		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	0.197988	−	0.980205i	$-0.436559\pi$
$313$	−13.8388	−	13.8388i	−0.782217	−	0.782217i	−0.980205	+	0.197988i	$0.936559\pi$
$314$		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	$-0.0231842\pi$
$331$	16.8212	+	16.8212i	0.924578	+	0.924578i	−0.0727709	+	0.997349i	$0.523184\pi$
$332$		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	0.981457	−	0.191680i	$-0.0613937\pi$
$337$	14.4984	+	14.4984i	0.789777	+	0.789777i	−0.191680	+	0.981457i	$0.561394\pi$
$338$		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	$-0.772469\pi$
$349$	−1.86337	+	1.86337i	−0.0997439	+	0.0997439i	0.655474	+	0.755218i	$0.272469\pi$
$350$		0			0
$351$		−	27.8489i		−	1.48647i
$352$		0			0
$353$	24.1362	−	24.1362i	1.28464	−	1.28464i	0.346642	−	0.937998i	$-0.387322\pi$
$353$	24.1362	−	24.1362i	1.28464	−	1.28464i	0.937998	−	0.346642i	$-0.112678\pi$
$354$		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	$-0.895219\pi$
$359$		−	12.2500i		−	0.646532i	0.946308	−	0.323266i	$-0.104781\pi$
$360$		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	−0.774363	−	0.632742i	$-0.781929\pi$
$367$	−2.71307	+	2.71307i	−0.141621	+	0.141621i	0.632742	+	0.774363i	$0.281929\pi$
$368$		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	$-0.916743\pi$
$379$	−13.7716	+	13.7716i	−0.707401	+	0.707401i	0.258587	+	0.965988i	$0.416743\pi$
$380$		0			0
$381$	−1.75870	−	1.75870i	−0.0901011	−	0.0901011i
$382$		0			0
$383$	−11.5530	−	11.5530i	−0.590332	−	0.590332i	0.347389	−	0.937721i	$-0.387068\pi$
$383$	−11.5530	−	11.5530i	−0.590332	−	0.590332i	−0.937721	+	0.347389i	$0.887068\pi$
$384$		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	$-0.0586903\pi$
$389$	15.7728	+	15.7728i	0.799712	+	0.799712i	−0.183338	+	0.983050i	$0.558690\pi$
$390$		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	$-0.158075\pi$
$419$	8.24430	+	8.24430i	0.402760	+	0.402760i	−0.476444	+	0.879205i	$0.658075\pi$
$420$		0			0
$421$	17.1776	−	17.1776i	0.837184	−	0.837184i	−0.151304	−	0.988487i	$-0.548347\pi$
$421$	17.1776	−	17.1776i	0.837184	−	0.837184i	0.988487	+	0.151304i	$0.0483471\pi$
$422$		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	$0.282226\pi$
$431$			32.1769i			1.54990i	−0.632020	+	0.774952i	$0.717774\pi$
$432$		0			0
$433$	−20.3383	+	20.3383i	−0.977396	+	0.977396i	−0.999750	−	0.0223540i	$-0.992884\pi$
$433$	−20.3383	+	20.3383i	−0.977396	+	0.977396i	0.0223540	+	0.999750i	$0.492884\pi$
$434$		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	$0.320521\pi$
$439$			35.4180i			1.69041i	−0.534444	+	0.845204i	$0.679479\pi$
$440$		0			0
$441$			33.9256i			1.61550i
$442$		0			0
$443$	−3.03787			−0.144333			−0.0721667	−	0.997393i	$-0.522991\pi$
$443$	−3.03787			−0.144333			−0.0721667	+	0.997393i	$0.522991\pi$
$444$		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	$-0.934527\pi$
$449$		−	8.65559i		−	0.408483i	0.978921	−	0.204241i	$-0.0654727\pi$
$450$		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	−0.949117	−	0.314924i	$-0.898021\pi$
$457$	−13.5575	+	13.5575i	−0.634193	+	0.634193i	0.314924	+	0.949117i	$0.398021\pi$
$458$		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	$-0.237450\pi$
$461$	1.19682	+	1.19682i	0.0557416	+	0.0557416i	−0.678687	+	0.734428i	$0.737450\pi$
$462$		0			0
$463$	21.1815	+	21.1815i	0.984390	+	0.984390i	0.999880	−	0.0154904i	$-0.00493096\pi$
$463$	21.1815	+	21.1815i	0.984390	+	0.984390i	−0.0154904	+	0.999880i	$0.504931\pi$
$464$		0			0
$465$	0.573555	+	0.685435i	0.0265980	+	0.0317863i
$466$		0			0
$467$	24.8448			1.14968			0.574840	−	0.818266i	$-0.305064\pi$
$467$	24.8448			1.14968			0.574840	+	0.818266i	$0.305064\pi$
$468$		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	0.764182	−	0.645001i	$-0.223143\pi$
$487$	2.63011	+	2.63011i	0.119182	+	0.119182i	−0.645001	+	0.764182i	$0.723143\pi$
$488$		0			0
$489$	67.7686			3.06460
$490$		0			0
$491$	−18.6899	−	18.6899i	−0.843465	−	0.843465i	0.145843	−	0.989308i	$-0.453411\pi$
$491$	−18.6899	−	18.6899i	−0.843465	−	0.843465i	−0.989308	+	0.145843i	$0.953411\pi$
$492$		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	$-0.349272\pi$
$499$	−9.69342	−	9.69342i	−0.433937	−	0.433937i	−0.889965	+	0.456028i	$0.849272\pi$
$500$		0			0
$501$	1.15090	−	1.15090i	0.0514185	−	0.0514185i
$502$		0			0
$503$	13.0434	−	13.0434i	0.581577	−	0.581577i	−0.353759	−	0.935336i	$-0.615097\pi$
$503$	13.0434	−	13.0434i	0.581577	−	0.581577i	0.935336	+	0.353759i	$0.115097\pi$
$504$		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	0.158611	−	0.987341i	$-0.449298\pi$
$509$	25.8539	−	25.8539i	1.14595	−	1.14595i	0.987341	−	0.158611i	$-0.0507016\pi$
$510$		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	$0.184912\pi$
$521$			25.0528i			1.09758i	−0.835959	+	0.548792i	$0.815088\pi$
$522$		0			0
$523$	40.3434			1.76410			0.882048	−	0.471160i	$-0.156165\pi$
$523$	40.3434			1.76410			0.882048	+	0.471160i	$0.156165\pi$
$524$		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	0.997817	+	0.0660360i	$0.0210352\pi$
$541$	24.7446	+	24.7446i	1.06385	+	1.06385i	0.0660360	+	0.997817i	$0.478965\pi$
$542$		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	$-0.366668\pi$
$547$	19.0254			0.813465			0.406733	+	0.913547i	$0.366668\pi$
$548$		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	$-0.358016\pi$
$571$	−11.2487	−	11.2487i	−0.470743	−	0.470743i	−0.902155	+	0.431412i	$0.858016\pi$
$572$		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	0.643509	−	0.765438i	$-0.277478\pi$
$577$	−2.92884	−	2.92884i	−0.121929	−	0.121929i	−0.765438	+	0.643509i	$0.777478\pi$
$578$		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	−0.932726	−	0.360585i	$-0.882577\pi$
$593$	−13.9325	+	13.9325i	−0.572141	+	0.572141i	0.360585	+	0.932726i	$0.382577\pi$
$594$		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	$-0.759793\pi$
$599$		−	33.5311i		−	1.37004i	0.728523	−	0.685021i	$-0.240207\pi$
$600$		0			0
$601$		−	19.4164i		−	0.792011i	−0.918248	−	0.396005i	$-0.870396\pi$
$601$		−	19.4164i		−	0.792011i	0.918248	−	0.396005i	$-0.129604\pi$
$602$		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	−0.487130	−	0.873330i	$-0.661956\pi$
$607$	9.51495	−	9.51495i	0.386200	−	0.386200i	0.873330	+	0.487130i	$0.161956\pi$
$608$		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	−0.774904	−	0.632079i	$-0.782202\pi$
$617$	−3.54768	+	3.54768i	−0.142824	+	0.142824i	0.632079	+	0.774904i	$0.282202\pi$
$618$		0			0
$619$	24.6158	−	24.6158i	0.989392	−	0.989392i	−0.0105527	−	0.999944i	$-0.503359\pi$
$619$	24.6158	−	24.6158i	0.989392	−	0.989392i	0.999944	+	0.0105527i	$0.00335910\pi$
$620$		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	0.138100	−	0.990418i	$-0.455900\pi$
$647$	−21.6797	−	21.6797i	−0.852318	−	0.852318i	−0.990418	+	0.138100i	$0.955900\pi$
$648$		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	$-0.646944\pi$
$653$	−22.7642			−0.890833			−0.445417	+	0.895323i	$0.646944\pi$
$654$		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	$-0.264577\pi$
$659$	−1.66201	−	1.66201i	−0.0647427	−	0.0647427i	−0.738737	+	0.673994i	$0.764577\pi$
$660$		0			0
$661$	5.62818	−	5.62818i	0.218911	−	0.218911i	−0.589129	−	0.808039i	$-0.700529\pi$
$661$	5.62818	−	5.62818i	0.218911	−	0.218911i	0.808039	+	0.589129i	$0.200529\pi$
$662$		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	−0.701724	−	0.712449i	$-0.747586\pi$
$673$	0.278251	−	0.278251i	0.0107258	−	0.0107258i	0.712449	+	0.701724i	$0.247586\pi$
$674$		0			0
$675$	−30.3163	−	5.43097i	−1.16687	−	0.209038i
$676$		0			0
$677$	−26.3591			−1.01306			−0.506531	−	0.862222i	$-0.669072\pi$
$677$	−26.3591			−1.01306			−0.506531	+	0.862222i	$0.669072\pi$
$678$		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	$-0.517244\pi$
$683$	−2.83023			−0.108296			−0.0541479	+	0.998533i	$0.517244\pi$
$684$		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	$-0.546488\pi$
$691$	22.1815	−	22.1815i	0.843825	−	0.843825i	0.989354	+	0.145529i	$0.0464884\pi$
$692$		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	$-0.392672\pi$
$701$	−16.2264	−	16.2264i	−0.612864	−	0.612864i	−0.943691	+	0.330828i	$0.892672\pi$
$702$		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	$-0.485166\pi$
$709$	−25.3577	−	25.3577i	−0.952329	−	0.952329i	−0.998914	+	0.0465856i	$0.985166\pi$
$710$		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	0.992493	−	0.122300i	$-0.0390271\pi$
$727$	23.4630	+	23.4630i	0.870193	+	0.870193i	−0.122300	+	0.992493i	$0.539027\pi$
$728$		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	$-0.409657\pi$
$733$	15.1628			0.560051			0.280025	+	0.959993i	$0.409657\pi$
$734$		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	$-0.258068\pi$
$739$	−0.974343	−	0.974343i	−0.0358418	−	0.0358418i	−0.724801	+	0.688959i	$0.758068\pi$
$740$		0			0
$741$	−52.2312	+	52.2312i	−1.91876	+	1.91876i
$742$		0			0
$743$	−29.0897	+	29.0897i	−1.06720	+	1.06720i	−0.0696259	+	0.997573i	$0.522181\pi$
$743$	−29.0897	+	29.0897i	−1.06720	+	1.06720i	−0.997573	+	0.0696259i	$0.977819\pi$
$744$		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	$0.0453193\pi$
$751$			7.77705i			0.283789i	−0.989882	+	0.141894i	$0.954681\pi$
$752$		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	$-0.508219\pi$
$757$	−1.42073			−0.0516372			−0.0258186	+	0.999667i	$0.508219\pi$
$758$		0			0
$759$			5.08497i			0.184573i
$760$		0			0
$761$		−	26.6737i		−	0.966921i	−0.875366	−	0.483460i	$-0.839380\pi$
$761$		−	26.6737i		−	0.966921i	0.875366	−	0.483460i	$-0.160620\pi$
$762$		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	$0.309487\pi$
$769$			45.8210i			1.65235i	−0.563415	+	0.826174i	$0.690513\pi$
$770$		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	$-0.623959\pi$
$787$	−21.3016			−0.759319			−0.379659	+	0.925126i	$0.623959\pi$
$788$		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	$-0.260514\pi$
$811$	−1.33006	−	1.33006i	−0.0467048	−	0.0467048i	−0.730073	+	0.683369i	$0.760514\pi$
$812$		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	−0.328076	+	0.944651i	$0.606400\pi$
$821$	−36.4676	+	36.4676i	−1.27273	+	1.27273i	−0.944651	+	0.328076i	$0.893600\pi$
$822$		0			0
$823$	−26.3978	+	26.3978i	−0.920170	+	0.920170i	−0.997041	−	0.0768712i	$-0.975507\pi$
$823$	−26.3978	+	26.3978i	−0.920170	+	0.920170i	0.0768712	+	0.997041i	$0.475507\pi$
$824$		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	$-0.646254\pi$
$829$	13.0376	−	13.0376i	0.452813	−	0.452813i	0.896287	+	0.443474i	$0.146254\pi$
$830$		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	$0.0857050\pi$
$839$			15.4102i			0.532018i	−0.963971	+	0.266009i	$0.914295\pi$
$840$		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	−0.609723	−	0.792615i	$-0.708719\pi$
$857$	5.35407	−	5.35407i	0.182891	−	0.182891i	0.792615	+	0.609723i	$0.208719\pi$
$858$		0			0
$859$	35.0058	−	35.0058i	1.19438	−	1.19438i	0.218559	−	0.975824i	$-0.429864\pi$
$859$	35.0058	−	35.0058i	1.19438	−	1.19438i	0.975824	−	0.218559i	$-0.0701355\pi$
$860$		0			0
$861$	5.97175	+	5.97175i	0.203517	+	0.203517i
$862$		0			0
$863$	36.7138	+	36.7138i	1.24975	+	1.24975i	0.955829	+	0.293923i	$0.0949610\pi$
$863$	36.7138	+	36.7138i	1.24975	+	1.24975i	0.293923	+	0.955829i	$0.405039\pi$
$864$		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	0.134130	−	0.990964i	$-0.457176\pi$
$887$	−25.5187	−	25.5187i	−0.856834	−	0.856834i	−0.990964	+	0.134130i	$0.957176\pi$
$888$		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	$-0.778974\pi$
$911$		−	38.6282i		−	1.27981i	0.768455	−	0.639904i	$-0.221026\pi$
$912$		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	$-0.897476\pi$
$919$		−	19.1924i		−	0.633099i	0.948576	−	0.316550i	$-0.102524\pi$
$920$		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	$-0.910812\pi$
$929$		−	16.8576i		−	0.553081i	0.961002	−	0.276541i	$-0.0891880\pi$
$930$		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	−0.980243	−	0.197795i	$-0.936622\pi$
$937$	−23.9511	+	23.9511i	−0.782449	+	0.782449i	0.197795	+	0.980243i	$0.436622\pi$
$938$		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	$-0.356533\pi$
$941$	−14.2496	−	14.2496i	−0.464525	−	0.464525i	−0.900135	+	0.435610i	$0.856533\pi$
$942$		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	$-0.393039\pi$
$947$	20.2943			0.659477			0.329738	+	0.944072i	$0.393039\pi$
$948$		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	0.507647	−	0.861565i	$-0.330516\pi$
$953$	−10.9257	−	10.9257i	−0.353919	−	0.353919i	−0.861565	+	0.507647i	$0.830516\pi$
$954$		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	0.512669	−	0.858586i	$-0.328657\pi$
$967$	−10.7569	−	10.7569i	−0.345918	−	0.345918i	−0.858586	+	0.512669i	$0.828657\pi$
$968$		0			0
$969$	−72.2796			−2.32195
$970$		0			0
$971$	−18.7456	−	18.7456i	−0.601574	−	0.601574i	0.339156	−	0.940730i	$-0.389858\pi$
$971$	−18.7456	−	18.7456i	−0.601574	−	0.601574i	−0.940730	+	0.339156i	$0.889858\pi$
$972$		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	0.145107	−	0.989416i	$-0.453647\pi$
$977$	−26.3906	−	26.3906i	−0.844309	−	0.844309i	−0.989416	+	0.145107i	$0.953647\pi$
$978$		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	−0.625009	−	0.780617i	$-0.714905\pi$
$983$	4.87875	−	4.87875i	0.155608	−	0.155608i	0.780617	+	0.625009i	$0.214905\pi$
$984$		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	$-0.575224\pi$
$991$		−	61.2103i		−	1.94441i	0.234130	−	0.972205i	$-0.424776\pi$
$992$		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	$-0.712577\pi$
$997$	−39.1082			−1.23857			−0.619284	+	0.785167i	$0.712577\pi$
$998$		0			0
$999$		−	35.9935i		−	1.13878i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.5	✓	18	80.13	odd	4
80.2.j.b.67.5	yes	18	8.3	odd	2
80.2.s.b.3.1	yes	18	40.3	even	4
80.2.s.b.27.1	yes	18	16.13	even	4
320.2.j.b.47.9		18	8.5	even	2
320.2.j.b.143.1		18	80.3	even	4
320.2.s.b.207.1		18	16.3	odd	4
320.2.s.b.303.1		18	40.13	odd	4
400.2.j.d.43.5		18	80.77	odd	4
400.2.j.d.307.5		18	40.19	odd	2
400.2.s.d.107.9		18	80.29	even	4
400.2.s.d.243.9		18	40.27	even	4
640.2.j.c.543.9		18	80.43	even	4	inner
640.2.j.c.607.1		18	1.1	even	1	trivial
640.2.j.d.543.1		18	80.53	odd	4
640.2.j.d.607.9		18	4.3	odd	2
640.2.s.c.223.9		18	5.3	odd	4
640.2.s.c.287.9		18	16.11	odd	4
640.2.s.d.223.1		18	20.3	even	4
640.2.s.d.287.1		18	16.5	even	4
720.2.z.g.163.9		18	120.83	odd	4
720.2.z.g.667.9		18	48.29	odd	4
720.2.bd.g.307.5		18	24.11	even	2
720.2.bd.g.523.5		18	240.173	even	4
1600.2.j.d.143.9		18	80.67	even	4
1600.2.j.d.1007.1		18	40.29	even	2
1600.2.s.d.207.9		18	80.19	odd	4
1600.2.s.d.943.9		18	40.37	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.j (of order \(4\), degree \(2\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more